LMFDB - Embedded newform 1155.2.l.e.1121.17

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.542651 q^{2} +(-1.58724 + 0.693309i) q^{3} -1.70553 q^{4} -1.00000i q^{5} +(0.861316 - 0.376225i) q^{6} +1.00000i q^{7} +2.01081 q^{8} +(2.03865 - 2.20089i) q^{9} +O(q^{10})$	\(q-0.542651 q^{2} +(-1.58724 + 0.693309i) q^{3} -1.70553 q^{4} -1.00000i q^{5} +(0.861316 - 0.376225i) q^{6} +1.00000i q^{7} +2.01081 q^{8} +(2.03865 - 2.20089i) q^{9} +0.542651i q^{10} +(-2.53297 + 2.14104i) q^{11} +(2.70708 - 1.18246i) q^{12} -0.789935i q^{13} -0.542651i q^{14} +(0.693309 + 1.58724i) q^{15} +2.31989 q^{16} -0.309636 q^{17} +(-1.10627 + 1.19432i) q^{18} +4.40077i q^{19} +1.70553i q^{20} +(-0.693309 - 1.58724i) q^{21} +(1.37452 - 1.16184i) q^{22} +2.63832i q^{23} +(-3.19163 + 1.39411i) q^{24} -1.00000 q^{25} +0.428659i q^{26} +(-1.70992 + 4.90675i) q^{27} -1.70553i q^{28} +8.52492 q^{29} +(-0.376225 - 0.861316i) q^{30} -7.18749 q^{31} -5.28051 q^{32} +(2.53602 - 5.15447i) q^{33} +0.168024 q^{34} +1.00000 q^{35} +(-3.47697 + 3.75369i) q^{36} -4.98548 q^{37} -2.38808i q^{38} +(0.547669 + 1.25381i) q^{39} -2.01081i q^{40} +4.02277 q^{41} +(0.376225 + 0.861316i) q^{42} -9.93941i q^{43} +(4.32006 - 3.65161i) q^{44} +(-2.20089 - 2.03865i) q^{45} -1.43169i q^{46} +2.67389i q^{47} +(-3.68222 + 1.60840i) q^{48} -1.00000 q^{49} +0.542651 q^{50} +(0.491465 - 0.214673i) q^{51} +1.34726i q^{52} -4.44117i q^{53} +(0.927889 - 2.66265i) q^{54} +(2.14104 + 2.53297i) q^{55} +2.01081i q^{56} +(-3.05109 - 6.98506i) q^{57} -4.62606 q^{58} -9.09504i q^{59} +(-1.18246 - 2.70708i) q^{60} -7.24601i q^{61} +3.90030 q^{62} +(2.20089 + 2.03865i) q^{63} -1.77431 q^{64} -0.789935 q^{65} +(-1.37618 + 2.79708i) q^{66} -13.6366 q^{67} +0.528093 q^{68} +(-1.82917 - 4.18765i) q^{69} -0.542651 q^{70} +3.04059i q^{71} +(4.09933 - 4.42557i) q^{72} -5.23719i q^{73} +2.70538 q^{74} +(1.58724 - 0.693309i) q^{75} -7.50564i q^{76} +(-2.14104 - 2.53297i) q^{77} +(-0.297193 - 0.680384i) q^{78} -7.41575i q^{79} -2.31989i q^{80} +(-0.687846 - 8.97368i) q^{81} -2.18296 q^{82} -3.28544 q^{83} +(1.18246 + 2.70708i) q^{84} +0.309636i q^{85} +5.39363i q^{86} +(-13.5311 + 5.91040i) q^{87} +(-5.09332 + 4.30523i) q^{88} -10.4559i q^{89} +(1.19432 + 1.10627i) q^{90} +0.789935 q^{91} -4.49974i q^{92} +(11.4083 - 4.98315i) q^{93} -1.45099i q^{94} +4.40077 q^{95} +(8.38143 - 3.66103i) q^{96} -15.3773 q^{97} +0.542651 q^{98} +(-0.451631 + 9.93962i) 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 $

$2$	−0.542651			−0.383712			−0.191856	−	0.981423i	$-0.561451\pi$
$2$	−0.542651			−0.383712			−0.191856	+	0.981423i	$0.561451\pi$
$3$	−1.58724	+	0.693309i	−0.916392	+	0.400282i
$3$	−1.58724	+	0.693309i	−0.916392	+	0.400282i
$4$	−1.70553			−0.852765
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.861316	−	0.376225i	0.351631	−	0.153593i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.01081			0.710929
$9$	2.03865	−	2.20089i	0.679549	−	0.733630i
$10$			0.542651i			0.171601i
$11$	−2.53297	+	2.14104i	−0.763719	+	0.645548i
$11$	−2.53297	+	2.14104i	−0.763719	+	0.645548i
$12$	2.70708	−	1.18246i	0.781467	−	0.341346i
$13$		−	0.789935i		−	0.219088i	−0.993982	−	0.109544i	$-0.965061\pi$
$13$		−	0.789935i		−	0.219088i	0.993982	−	0.109544i	$-0.0349391\pi$
$14$		−	0.542651i		−	0.145030i
$15$	0.693309	+	1.58724i	0.179012	+	0.409823i
$16$	2.31989			0.579973
$17$	−0.309636			−0.0750977			−0.0375488	−	0.999295i	$-0.511955\pi$
$17$	−0.309636			−0.0750977			−0.0375488	+	0.999295i	$0.511955\pi$
$18$	−1.10627	+	1.19432i	−0.260751	+	0.281503i
$19$			4.40077i			1.00961i	0.863235	+	0.504803i	$0.168435\pi$
$19$			4.40077i			1.00961i	−0.863235	+	0.504803i	$0.831565\pi$
$20$			1.70553i			0.381368i
$21$	−0.693309	−	1.58724i	−0.151292	−	0.346364i
$22$	1.37452	−	1.16184i	0.293049	−	0.247705i
$23$			2.63832i			0.550128i	0.961426	+	0.275064i	$0.0886991\pi$
$23$			2.63832i			0.550128i	−0.961426	+	0.275064i	$0.911301\pi$
$24$	−3.19163	+	1.39411i	−0.651489	+	0.284572i
$25$	−1.00000			−0.200000
$26$			0.428659i			0.0840669i
$27$	−1.70992	+	4.90675i	−0.329074	+	0.944304i
$28$		−	1.70553i		−	0.322315i
$29$	8.52492			1.58304			0.791519	−	0.611145i	$-0.209291\pi$
$29$	8.52492			1.58304			0.791519	+	0.611145i	$0.209291\pi$
$30$	−0.376225	−	0.861316i	−0.0686889	−	0.157254i
$31$	−7.18749			−1.29091			−0.645456	−	0.763798i	$-0.723333\pi$
$31$	−7.18749			−1.29091			−0.645456	+	0.763798i	$0.723333\pi$
$32$	−5.28051			−0.933471
$33$	2.53602	−	5.15447i	0.441465	−	0.897278i
$34$	0.168024			0.0288159
$35$	1.00000			0.169031
$36$	−3.47697	+	3.75369i	−0.579495	+	0.625614i
$37$	−4.98548			−0.819608			−0.409804	−	0.912174i	$-0.634403\pi$
$37$	−4.98548			−0.819608			−0.409804	+	0.912174i	$0.634403\pi$
$38$		−	2.38808i		−	0.387398i
$39$	0.547669	+	1.25381i	0.0876972	+	0.200771i
$40$		−	2.01081i		−	0.317937i
$41$	4.02277			0.628252			0.314126	−	0.949381i	$-0.398289\pi$
$41$	4.02277			0.628252			0.314126	+	0.949381i	$0.398289\pi$
$42$	0.376225	+	0.861316i	0.0580528	+	0.132904i
$43$		−	9.93941i		−	1.51575i	−0.652403	−	0.757873i	$-0.726239\pi$
$43$		−	9.93941i		−	1.51575i	0.652403	−	0.757873i	$-0.273761\pi$
$44$	4.32006	−	3.65161i	0.651273	−	0.550501i
$45$	−2.20089	−	2.03865i	−0.328090	−	0.303903i
$46$		−	1.43169i		−	0.211091i
$47$			2.67389i			0.390026i	0.980801	+	0.195013i	$0.0624749\pi$
$47$			2.67389i			0.390026i	−0.980801	+	0.195013i	$0.937525\pi$
$48$	−3.68222	+	1.60840i	−0.531482	+	0.232153i
$49$	−1.00000			−0.142857
$50$	0.542651			0.0767425
$51$	0.491465	−	0.214673i	0.0688189	−	0.0300602i
$52$			1.34726i			0.186831i
$53$		−	4.44117i		−	0.610042i	−0.952346	−	0.305021i	$-0.901337\pi$
$53$		−	4.44117i		−	0.610042i	0.952346	−	0.305021i	$-0.0986635\pi$
$54$	0.927889	−	2.66265i	0.126270	−	0.362341i
$55$	2.14104	+	2.53297i	0.288698	+	0.341546i
$56$			2.01081i			0.268706i
$57$	−3.05109	−	6.98506i	−0.404127	−	0.925194i
$58$	−4.62606			−0.607431
$59$		−	9.09504i		−	1.18407i	−0.805911	−	0.592037i	$-0.798324\pi$
$59$		−	9.09504i		−	1.18407i	0.805911	−	0.592037i	$-0.201676\pi$
$60$	−1.18246	−	2.70708i	−0.152655	−	0.349483i
$61$		−	7.24601i		−	0.927756i	−0.885899	−	0.463878i	$-0.846458\pi$
$61$		−	7.24601i		−	0.927756i	0.885899	−	0.463878i	$-0.153542\pi$
$62$	3.90030			0.495339
$63$	2.20089	+	2.03865i	0.277286	+	0.256845i
$64$	−1.77431			−0.221788
$65$	−0.789935			−0.0979793
$66$	−1.37618	+	2.79708i	−0.169396	+	0.344297i
$67$	−13.6366			−1.66598			−0.832991	−	0.553287i	$-0.813373\pi$
$67$	−13.6366			−1.66598			−0.832991	+	0.553287i	$0.813373\pi$
$68$	0.528093			0.0640406
$69$	−1.82917	−	4.18765i	−0.220207	−	0.504133i
$70$	−0.542651			−0.0648592
$71$			3.04059i			0.360852i	0.983589	+	0.180426i	$0.0577476\pi$
$71$			3.04059i			0.360852i	−0.983589	+	0.180426i	$0.942252\pi$
$72$	4.09933	−	4.42557i	0.483111	−	0.521559i
$73$		−	5.23719i		−	0.612967i	−0.951876	−	0.306483i	$-0.900848\pi$
$73$		−	5.23719i		−	0.612967i	0.951876	−	0.306483i	$-0.0991524\pi$
$74$	2.70538			0.314494
$75$	1.58724	−	0.693309i	0.183278	−	0.0800564i
$76$		−	7.50564i		−	0.860956i
$77$	−2.14104	−	2.53297i	−0.243994	−	0.288659i
$78$	−0.297193	−	0.680384i	−0.0336505	−	0.0770383i
$79$		−	7.41575i		−	0.834337i	−0.908829	−	0.417168i	$-0.863023\pi$
$79$		−	7.41575i		−	0.834337i	0.908829	−	0.417168i	$-0.136977\pi$
$80$		−	2.31989i		−	0.259372i
$81$	−0.687846	−	8.97368i	−0.0764273	−	0.997075i
$82$	−2.18296			−0.241068
$83$	−3.28544			−0.360623			−0.180312	−	0.983610i	$-0.557711\pi$
$83$	−3.28544			−0.360623			−0.180312	+	0.983610i	$0.557711\pi$
$84$	1.18246	+	2.70708i	0.129017	+	0.295367i
$85$			0.309636i			0.0335847i
$86$			5.39363i			0.581610i
$87$	−13.5311	+	5.91040i	−1.45068	+	0.633661i
$88$	−5.09332	+	4.30523i	−0.542950	+	0.458939i
$89$		−	10.4559i		−	1.10832i	−0.832409	−	0.554162i	$-0.813039\pi$
$89$		−	10.4559i		−	1.10832i	0.832409	−	0.554162i	$-0.186961\pi$
$90$	1.19432	+	1.10627i	0.125892	+	0.116611i
$91$	0.789935			0.0828076
$92$		−	4.49974i		−	0.469130i
$93$	11.4083	−	4.98315i	1.18298	−	0.516729i
$94$		−	1.45099i		−	0.149658i
$95$	4.40077			0.451509
$96$	8.38143	−	3.66103i	0.855426	−	0.373652i
$97$	−15.3773			−1.56133			−0.780664	−	0.624951i	$-0.785119\pi$
$97$	−15.3773			−1.56133			−0.780664	+	0.624951i	$0.785119\pi$
$98$	0.542651			0.0548160
$99$	−0.451631	+	9.93962i	−0.0453906	+	0.998969i
$100$	1.70553			0.170553
$101$	7.15140			0.711591			0.355795	−	0.934564i	$-0.384210\pi$
$101$	7.15140			0.711591			0.355795	+	0.934564i	$0.384210\pi$
$102$	−0.266694	+	0.116493i	−0.0264067	+	0.0115345i
$103$	−4.53024			−0.446378			−0.223189	−	0.974775i	$-0.571647\pi$
$103$	−4.53024			−0.446378			−0.223189	+	0.974775i	$0.571647\pi$
$104$		−	1.58841i		−	0.155756i
$105$	−1.58724	+	0.693309i	−0.154899	+	0.0676600i
$106$			2.41001i			0.234081i
$107$	0.0565066			0.00546270			0.00273135	−	0.999996i	$-0.499131\pi$
$107$	0.0565066			0.00546270			0.00273135	+	0.999996i	$0.499131\pi$
$108$	2.91632	−	8.36861i	0.280623	−	0.805269i
$109$		−	7.94508i		−	0.761000i	−0.924781	−	0.380500i	$-0.875752\pi$
$109$		−	7.94508i		−	0.761000i	0.924781	−	0.380500i	$-0.124248\pi$
$110$	−1.16184	−	1.37452i	−0.110777	−	0.131055i
$111$	7.91314	−	3.45648i	0.751082	−	0.328074i
$112$			2.31989i			0.219209i
$113$			4.18977i			0.394140i	0.980389	+	0.197070i	$0.0631426\pi$
$113$			4.18977i			0.394140i	−0.980389	+	0.197070i	$0.936857\pi$
$114$	1.65568	+	3.79045i	0.155068	+	0.355008i
$115$	2.63832			0.246025
$116$	−14.5395			−1.34996
$117$	−1.73856	−	1.61040i	−0.160730	−	0.148881i
$118$			4.93543i			0.454344i
$119$		−	0.309636i		−	0.0283842i
$120$	1.39411	+	3.19163i	0.127264	+	0.291355i
$121$	1.83188	−	10.8464i	0.166535	−	0.986036i
$122$			3.93205i			0.355992i
$123$	−6.38510	+	2.78902i	−0.575725	+	0.251478i
$124$	12.2585			1.10084
$125$			1.00000i			0.0894427i
$126$	−1.19432	−	1.10627i	−0.106398	−	0.0985547i
$127$		−	21.5047i		−	1.90824i	−0.299429	−	0.954118i	$-0.596796\pi$
$127$		−	21.5047i		−	1.90824i	0.299429	−	0.954118i	$-0.403204\pi$
$128$	11.5239			1.01857
$129$	6.89108	+	15.7762i	0.606726	+	1.38902i
$130$	0.428659			0.0375959
$131$	−16.0288			−1.40044			−0.700222	−	0.713925i	$-0.746916\pi$
$131$	−16.0288			−1.40044			−0.700222	+	0.713925i	$0.746916\pi$
$132$	−4.32526	+	8.79111i	−0.376466	+	0.765168i
$133$	−4.40077			−0.381595
$134$	7.39994			0.639258
$135$	4.90675	+	1.70992i	0.422306	+	0.147166i
$136$	−0.622618			−0.0533891
$137$			11.6227i			0.992990i	0.868039	+	0.496495i	$0.165380\pi$
$137$			11.6227i			0.992990i	−0.868039	+	0.496495i	$0.834620\pi$
$138$	0.992603	+	2.27243i	0.0844960	+	0.193442i
$139$			9.10895i			0.772611i	0.922371	+	0.386305i	$0.126249\pi$
$139$			9.10895i			0.772611i	−0.922371	+	0.386305i	$0.873751\pi$
$140$	−1.70553			−0.144144
$141$	−1.85383	−	4.24409i	−0.156120	−	0.357417i
$142$		−	1.64998i		−	0.138463i
$143$	1.69128	+	2.00088i	0.141432	+	0.167322i
$144$	4.72944	−	5.10583i	0.394120	−	0.425486i
$145$		−	8.52492i		−	0.707956i
$146$			2.84197i			0.235203i
$147$	1.58724	−	0.693309i	0.130913	−	0.0571831i
$148$	8.50289			0.698933
$149$	24.0115			1.96709			0.983547	−	0.180651i	$-0.0578203\pi$
$149$	24.0115			1.96709			0.983547	+	0.180651i	$0.0578203\pi$
$150$	−0.861316	+	0.376225i	−0.0703262	+	0.0307186i
$151$			11.6986i			0.952016i	0.879441	+	0.476008i	$0.157917\pi$
$151$			11.6986i			0.952016i	−0.879441	+	0.476008i	$0.842083\pi$
$152$			8.84911i			0.717757i
$153$	−0.631237	+	0.681474i	−0.0510325	+	0.0550939i
$154$	1.16184	+	1.37452i	0.0936236	+	0.110762i
$155$			7.18749i			0.577313i
$156$	−0.934065	−	2.13842i	−0.0747850	−	0.171210i
$157$	−14.6402			−1.16841			−0.584207	−	0.811604i	$-0.698595\pi$
$157$	−14.6402			−1.16841			−0.584207	+	0.811604i	$0.698595\pi$
$158$			4.02416i			0.320145i
$159$	3.07910	+	7.04920i	0.244189	+	0.559038i
$160$			5.28051i			0.417461i
$161$	−2.63832			−0.207929
$162$	0.373260	+	4.86958i	0.0293261	+	0.382590i
$163$	10.9322			0.856278			0.428139	−	0.903713i	$-0.359169\pi$
$163$	10.9322			0.856278			0.428139	+	0.903713i	$0.359169\pi$
$164$	−6.86096			−0.535751
$165$	−5.15447	−	2.53602i	−0.401275	−	0.197429i
$166$	1.78285			0.138376
$167$	−16.6877			−1.29133			−0.645666	−	0.763620i	$-0.723420\pi$
$167$	−16.6877			−1.29133			−0.645666	+	0.763620i	$0.723420\pi$
$168$	−1.39411	−	3.19163i	−0.107558	−	0.246240i
$169$	12.3760			0.952000
$170$		−	0.168024i		−	0.0128869i
$171$	9.68561	+	8.97161i	0.740677	+	0.686076i
$172$			16.9520i			1.29257i
$173$	−2.87637			−0.218686			−0.109343	−	0.994004i	$-0.534875\pi$
$173$	−2.87637			−0.218686			−0.109343	+	0.994004i	$0.534875\pi$
$174$	7.34265	−	3.20729i	0.556645	−	0.243144i
$175$		−	1.00000i		−	0.0755929i
$176$	−5.87622	+	4.96698i	−0.442936	+	0.374400i
$177$	6.30567	+	14.4360i	0.473963	+	1.08508i
$178$			5.67391i			0.425278i
$179$		−	14.0046i		−	1.04675i	−0.852101	−	0.523377i	$-0.824672\pi$
$179$		−	14.0046i		−	1.04675i	0.852101	−	0.523377i	$-0.175328\pi$
$180$	3.75369	+	3.47697i	0.279783	+	0.259158i
$181$	−13.6922			−1.01773			−0.508867	−	0.860845i	$-0.669936\pi$
$181$	−13.6922			−1.01773			−0.508867	+	0.860845i	$0.669936\pi$
$182$	−0.428659			−0.0317743
$183$	5.02372	+	11.5011i	0.371364	+	0.850188i
$184$			5.30517i			0.391102i
$185$			4.98548i			0.366540i
$186$	−6.19070	+	2.70411i	−0.453924	+	0.198275i
$187$	0.784298	−	0.662943i	0.0573535	−	0.0484792i
$188$		−	4.56039i		−	0.332601i
$189$	−4.90675	−	1.70992i	−0.356913	−	0.124378i
$190$	−2.38808			−0.173250
$191$			3.55828i			0.257468i	0.991679	+	0.128734i	$0.0410913\pi$
$191$			3.55828i			0.257468i	−0.991679	+	0.128734i	$0.958909\pi$
$192$	2.81625	−	1.23014i	0.203245	−	0.0887778i
$193$			8.81975i			0.634859i	0.948282	+	0.317430i	$0.102820\pi$
$193$			8.81975i			0.634859i	−0.948282	+	0.317430i	$0.897180\pi$
$194$	8.34451			0.599101
$195$	1.25381	−	0.547669i	0.0897875	−	0.0392194i
$196$	1.70553			0.121824
$197$	−17.5014			−1.24692			−0.623461	−	0.781855i	$-0.714274\pi$
$197$	−17.5014			−1.24692			−0.623461	+	0.781855i	$0.714274\pi$
$198$	0.245078	−	5.39375i	0.0174169	−	0.383317i
$199$	14.6165			1.03614			0.518068	−	0.855339i	$-0.326651\pi$
$199$	14.6165			1.03614			0.518068	+	0.855339i	$0.326651\pi$
$200$	−2.01081			−0.142186
$201$	21.6446	−	9.45441i	1.52669	−	0.666862i
$202$	−3.88072			−0.273046
$203$			8.52492i			0.598332i
$204$	−0.838208	+	0.366131i	−0.0586863	+	0.0256343i
$205$		−	4.02277i		−	0.280963i
$206$	2.45834			0.171281
$207$	5.80666	+	5.37861i	0.403591	+	0.373839i
$208$		−	1.83256i		−	0.127065i
$209$	−9.42223	−	11.1470i	−0.651749	−	0.771055i
$210$	0.861316	−	0.376225i	0.0594365	−	0.0259620i
$211$		−	22.1927i		−	1.52781i	−0.645329	−	0.763905i	$-0.723280\pi$
$211$		−	22.1927i		−	1.52781i	0.645329	−	0.763905i	$-0.276720\pi$
$212$			7.57455i			0.520222i
$213$	−2.10807	−	4.82614i	−0.144442	−	0.330682i
$214$	−0.0306634			−0.00209610
$215$	−9.93941			−0.677862
$216$	−3.43832	+	9.86654i	−0.233948	+	0.671333i
$217$		−	7.18749i		−	0.487919i
$218$			4.31140i			0.292005i
$219$	3.63099	+	8.31266i	0.245360	+	0.561718i
$220$	−3.65161	−	4.32006i	−0.246191	−	0.291258i
$221$			0.244592i			0.0164530i
$222$	−4.29408	+	1.87566i	−0.288200	+	0.125886i
$223$	−4.04488			−0.270865			−0.135433	−	0.990787i	$-0.543242\pi$
$223$	−4.04488			−0.270865			−0.135433	+	0.990787i	$0.543242\pi$
$224$		−	5.28051i		−	0.352819i
$225$	−2.03865	+	2.20089i	−0.135910	+	0.146726i
$226$		−	2.27358i		−	0.151236i
$227$	11.0913			0.736155			0.368078	−	0.929795i	$-0.380016\pi$
$227$	11.0913			0.736155			0.368078	+	0.929795i	$0.380016\pi$
$228$	5.20373	+	11.9132i	0.344625	+	0.788973i
$229$	−24.7988			−1.63875			−0.819374	−	0.573259i	$-0.805679\pi$
$229$	−24.7988			−1.63875			−0.819374	+	0.573259i	$0.805679\pi$
$230$	−1.43169			−0.0944028
$231$	5.15447	+	2.53602i	0.339139	+	0.166858i
$232$	17.1420			1.12543
$233$	−17.3571			−1.13710			−0.568552	−	0.822647i	$-0.692496\pi$
$233$	−17.3571			−1.13710			−0.568552	+	0.822647i	$0.692496\pi$
$234$	0.943432	+	0.873884i	0.0616741	+	0.0571276i
$235$	2.67389			0.174425
$236$			15.5119i			1.00974i
$237$	5.14140	+	11.7705i	0.333970	+	0.764579i
$238$			0.168024i			0.0108914i
$239$	−10.7839			−0.697552			−0.348776	−	0.937206i	$-0.613403\pi$
$239$	−10.7839			−0.697552			−0.348776	+	0.937206i	$0.613403\pi$
$240$	1.60840	+	3.68222i	0.103822	+	0.237686i
$241$			24.8089i			1.59808i	0.601277	+	0.799040i	$0.294659\pi$
$241$			24.8089i			1.59808i	−0.601277	+	0.799040i	$0.705341\pi$
$242$	−0.994073	+	5.88581i	−0.0639014	+	0.378354i
$243$	7.31330	+	13.7665i	0.469149	+	0.883119i
$244$			12.3583i			0.791158i
$245$			1.00000i			0.0638877i
$246$	3.46488	−	1.51347i	0.220913	−	0.0964952i
$247$	3.47632			0.221193
$248$	−14.4527			−0.917746
$249$	5.21477	−	2.27782i	0.330472	−	0.144351i
$250$		−	0.542651i		−	0.0343203i
$251$		−	21.2859i		−	1.34355i	−0.740754	−	0.671776i	$-0.765532\pi$
$251$		−	21.2859i		−	1.34355i	0.740754	−	0.671776i	$-0.234468\pi$
$252$	−3.75369	−	3.47697i	−0.236460	−	0.219029i
$253$	−5.64876	−	6.68280i	−0.355134	−	0.420144i
$254$			11.6696i			0.732214i
$255$	−0.214673	−	0.491465i	−0.0134433	−	0.0307767i
$256$	−2.70482			−0.169051
$257$			6.68376i			0.416921i	0.978031	+	0.208461i	$0.0668453\pi$
$257$			6.68376i			0.416921i	−0.978031	+	0.208461i	$0.933155\pi$
$258$	−3.73945	−	8.56097i	−0.232808	−	0.532983i
$259$		−	4.98548i		−	0.309783i
$260$	1.34726			0.0835533
$261$	17.3793	−	18.7624i	1.07575	−	1.16136i
$262$	8.69805			0.537368
$263$	12.8589			0.792917			0.396458	−	0.918053i	$-0.370239\pi$
$263$	12.8589			0.792917			0.396458	+	0.918053i	$0.370239\pi$
$264$	5.09946	−	10.3647i	0.313850	−	0.637901i
$265$	−4.44117			−0.272819
$266$	2.38808			0.146423
$267$	7.24917	+	16.5960i	0.443642	+	1.01566i
$268$	23.2577			1.42069
$269$		−	20.5204i		−	1.25115i	−0.780163	−	0.625577i	$-0.784864\pi$
$269$		−	20.5204i		−	1.25115i	0.780163	−	0.625577i	$-0.215136\pi$
$270$	−2.66265	−	0.927889i	−0.162044	−	0.0564695i
$271$			14.8743i			0.903550i	0.892132	+	0.451775i	$0.149209\pi$
$271$			14.8743i			0.903550i	−0.892132	+	0.451775i	$0.850791\pi$
$272$	−0.718321			−0.0435546
$273$	−1.25381	+	0.547669i	−0.0758843	+	0.0331464i
$274$		−	6.30705i		−	0.381023i
$275$	2.53297	−	2.14104i	0.152744	−	0.129110i
$276$	3.11971	+	7.14215i	0.187784	+	0.429907i
$277$		−	0.419323i		−	0.0251947i	−0.999921	−	0.0125973i	$-0.995990\pi$
$277$		−	0.419323i		−	0.0251947i	0.999921	−	0.0125973i	$-0.00400996\pi$
$278$		−	4.94298i		−	0.296460i
$279$	−14.6527	+	15.8189i	−0.877237	+	0.947052i
$280$	2.01081			0.120169
$281$	22.9725			1.37042			0.685212	−	0.728344i	$-0.259710\pi$
$281$	22.9725			1.37042			0.685212	+	0.728344i	$0.259710\pi$
$282$	1.00598	+	2.30306i	0.0599054	+	0.137145i
$283$		−	22.7343i		−	1.35141i	−0.737170	−	0.675707i	$-0.763838\pi$
$283$		−	22.7343i		−	1.35141i	0.737170	−	0.675707i	$-0.236162\pi$
$284$		−	5.18582i		−	0.307722i
$285$	−6.98506	+	3.05109i	−0.413759	+	0.180731i
$286$	−0.917777	−	1.08578i	−0.0542693	−	0.0642035i
$287$			4.02277i			0.237457i
$288$	−10.7651	+	11.6218i	−0.634339	+	0.684823i
$289$	−16.9041			−0.994360
$290$			4.62606i			0.271651i
$291$	24.4074	−	10.6612i	1.43079	−	0.624971i
$292$			8.93218i			0.522716i
$293$	10.2110			0.596535			0.298268	−	0.954482i	$-0.403591\pi$
$293$	10.2110			0.596535			0.298268	+	0.954482i	$0.403591\pi$
$294$	−0.861316	+	0.376225i	−0.0502330	+	0.0219419i
$295$	−9.09504			−0.529534
$296$	−10.0249			−0.582683
$297$	−6.17438	−	16.0897i	−0.358274	−	0.933617i
$298$	−13.0298			−0.754798
$299$	2.08410			0.120527
$300$	−2.70708	+	1.18246i	−0.156293	+	0.0682693i
$301$	9.93941			0.572898
$302$		−	6.34824i		−	0.365300i
$303$	−11.3510	+	4.95813i	−0.652096	+	0.284837i
$304$			10.2093i			0.585544i
$305$	−7.24601			−0.414905
$306$	0.342542	−	0.369803i	0.0195818	−	0.0211402i
$307$			11.9304i			0.680903i	0.940262	+	0.340451i	$0.110580\pi$
$307$			11.9304i			0.680903i	−0.940262	+	0.340451i	$0.889420\pi$
$308$	3.65161	+	4.32006i	0.208070	+	0.246158i
$309$	7.19056	−	3.14085i	0.409057	−	0.178677i
$310$		−	3.90030i		−	0.221522i
$311$			14.6868i			0.832811i	0.909179	+	0.416406i	$0.136710\pi$
$311$			14.6868i			0.832811i	−0.909179	+	0.416406i	$0.863290\pi$
$312$	1.10126	+	2.52118i	0.0623464	+	0.142734i
$313$	−14.0289			−0.792962			−0.396481	−	0.918043i	$-0.629769\pi$
$313$	−14.0289			−0.792962			−0.396481	+	0.918043i	$0.629769\pi$
$314$	7.94452			0.448335
$315$	2.03865	−	2.20089i	0.114865	−	0.124006i
$316$			12.6478i			0.711493i
$317$		−	7.34312i		−	0.412431i	−0.978507	−	0.206215i	$-0.933885\pi$
$317$		−	7.34312i		−	0.412431i	0.978507	−	0.206215i	$-0.0661148\pi$
$318$	−1.67088	−	3.82525i	−0.0936983	−	0.214510i
$319$	−21.5934	+	18.2522i	−1.20900	+	1.02193i
$320$			1.77431i			0.0991867i
$321$	−0.0896894	+	0.0391765i	−0.00500597	+	0.00218662i
$322$	1.43169			0.0797849
$323$		−	1.36263i		−	0.0758190i
$324$	1.17314	+	15.3049i	0.0651745	+	0.850271i
$325$			0.789935i			0.0438177i
$326$	−5.93239			−0.328565
$327$	5.50839	+	12.6107i	0.304615	+	0.697375i
$328$	8.08903			0.446642
$329$	−2.67389			−0.147416
$330$	2.79708	+	1.37618i	0.153974	+	0.0757560i
$331$	−5.39735			−0.296665			−0.148333	−	0.988938i	$-0.547391\pi$
$331$	−5.39735			−0.296665			−0.148333	+	0.988938i	$0.547391\pi$
$332$	5.60341			0.307527
$333$	−10.1636	+	10.9725i	−0.556964	+	0.601290i
$334$	9.05559			0.495500
$335$			13.6366i			0.745050i
$336$	−1.60840	−	3.68222i	−0.0877455	−	0.200881i
$337$		−	20.2511i		−	1.10315i	−0.834127	−	0.551573i	$-0.814028\pi$
$337$		−	20.2511i		−	1.10315i	0.834127	−	0.551573i	$-0.185972\pi$
$338$	−6.71585			−0.365294
$339$	−2.90480	−	6.65015i	−0.157767	−	0.361187i
$340$		−	0.528093i		−	0.0286398i
$341$	18.2057	−	15.3887i	0.985894	−	0.833346i
$342$	−5.25591	−	4.86845i	−0.284207	−	0.263256i
$343$		−	1.00000i		−	0.0539949i
$344$		−	19.9863i		−	1.07759i
$345$	−4.18765	+	1.82917i	−0.225455	+	0.0984794i
$346$	1.56086			0.0839125
$347$	4.69198			0.251879			0.125939	−	0.992038i	$-0.459805\pi$
$347$	4.69198			0.251879			0.125939	+	0.992038i	$0.459805\pi$
$348$	23.0776	−	10.0804i	1.23709	−	0.540364i
$349$			9.59887i			0.513816i	0.966436	+	0.256908i	$0.0827037\pi$
$349$			9.59887i			0.513816i	−0.966436	+	0.256908i	$0.917296\pi$
$350$			0.542651i			0.0290059i
$351$	3.87601	+	1.35072i	0.206886	+	0.0720963i
$352$	13.3754	−	11.3058i	0.712910	−	0.602601i
$353$		−	21.6457i		−	1.15209i	−0.817420	−	0.576043i	$-0.804596\pi$
$353$		−	21.6457i		−	1.15209i	0.817420	−	0.576043i	$-0.195404\pi$
$354$	−3.42178	−	7.83371i	−0.181866	−	0.416357i
$355$	3.04059			0.161378
$356$			17.8329i			0.945140i
$357$	0.214673	+	0.491465i	0.0113617	+	0.0260111i
$358$			7.59962i			0.401652i
$359$	28.5526			1.50695			0.753475	−	0.657477i	$-0.228376\pi$
$359$	28.5526			1.50695			0.753475	+	0.657477i	$0.228376\pi$
$360$	−4.42557	−	4.09933i	−0.233248	−	0.216054i
$361$	−0.366753			−0.0193028
$362$	7.43010			0.390517
$363$	4.61227	+	18.4859i	0.242081	+	0.970256i
$364$	−1.34726			−0.0706154
$365$	−5.23719			−0.274127
$366$	−2.72613	−	6.24110i	−0.142497	−	0.326228i
$367$	7.83869			0.409176			0.204588	−	0.978848i	$-0.434415\pi$
$367$	7.83869			0.409176			0.204588	+	0.978848i	$0.434415\pi$
$368$			6.12062i			0.319060i
$369$	8.20101	−	8.85369i	0.426928	−	0.460905i
$370$		−	2.70538i		−	0.140646i
$371$	4.44117			0.230574
$372$	−19.4571	+	8.49891i	−1.00880	+	0.440648i
$373$		−	23.4221i		−	1.21275i	−0.795178	−	0.606376i	$-0.792623\pi$
$373$		−	23.4221i		−	1.21275i	0.795178	−	0.606376i	$-0.207377\pi$
$374$	−0.425600	+	0.359747i	−0.0220073	+	0.0186021i
$375$	−0.693309	−	1.58724i	−0.0358023	−	0.0819646i
$376$			5.37668i			0.277281i
$377$		−	6.73413i		−	0.346825i
$378$	2.66265	+	0.927889i	0.136952	+	0.0477255i
$379$	20.4544			1.05067			0.525336	−	0.850895i	$-0.323940\pi$
$379$	20.4544			1.05067			0.525336	+	0.850895i	$0.323940\pi$
$380$	−7.50564			−0.385031
$381$	14.9094	+	34.1331i	0.763833	+	1.74869i
$382$		−	1.93090i		−	0.0987936i
$383$		−	8.98387i		−	0.459054i	−0.973302	−	0.229527i	$-0.926282\pi$
$383$		−	8.98387i		−	0.459054i	0.973302	−	0.229527i	$-0.0737180\pi$
$384$	−18.2911	+	7.98959i	−0.933413	+	0.407717i
$385$	−2.53297	+	2.14104i	−0.129092	+	0.109118i
$386$		−	4.78605i		−	0.243603i
$387$	−21.8756	−	20.2629i	−1.11200	−	1.03002i
$388$	26.2264			1.33145
$389$			9.80514i			0.497140i	0.968614	+	0.248570i	$0.0799607\pi$
$389$			9.80514i			0.497140i	−0.968614	+	0.248570i	$0.920039\pi$
$390$	−0.680384	+	0.297193i	−0.0344526	+	0.0150490i
$391$		−	0.816919i		−	0.0413134i
$392$	−2.01081			−0.101561
$393$	25.4415	−	11.1129i	1.28336	−	0.560572i
$394$	9.49714			0.478459
$395$	−7.41575			−0.373127
$396$	0.770269	−	16.9523i	0.0387075	−	0.851886i
$397$	−20.0282			−1.00518			−0.502592	−	0.864523i	$-0.667620\pi$
$397$	−20.0282			−1.00518			−0.502592	+	0.864523i	$0.667620\pi$
$398$	−7.93166			−0.397578
$399$	6.98506	−	3.05109i	0.349691	−	0.152746i
$400$	−2.31989			−0.115995
$401$		−	36.0449i		−	1.79999i	−0.435895	−	0.899997i	$-0.643568\pi$
$401$		−	36.0449i		−	1.79999i	0.435895	−	0.899997i	$-0.356432\pi$
$402$	−11.7455	+	5.13044i	−0.585811	+	0.255883i
$403$			5.67765i			0.282824i
$404$	−12.1969			−0.606820
$405$	−8.97368	+	0.687846i	−0.445906	+	0.0341793i
$406$		−	4.62606i		−	0.229587i
$407$	12.6281	−	10.6741i	0.625951	−	0.529097i
$408$	0.988243	−	0.431667i	0.0489253	−	0.0213707i
$409$		−	26.2275i		−	1.29687i	−0.761272	−	0.648433i	$-0.775425\pi$
$409$		−	26.2275i		−	1.29687i	0.761272	−	0.648433i	$-0.224575\pi$
$410$			2.18296i			0.107809i
$411$	−8.05809	−	18.4479i	−0.397476	−	0.909968i
$412$	7.72646			0.380655
$413$	9.09504			0.447538
$414$	−3.15099	−	2.91871i	−0.154863	−	0.143447i
$415$			3.28544i			0.161276i
$416$			4.17126i			0.204513i
$417$	−6.31531	−	14.4581i	−0.309262	−	0.708015i
$418$	5.11298	+	6.04894i	0.250084	+	0.295863i
$419$		−	21.4266i		−	1.04676i	−0.852100	−	0.523379i	$-0.824671\pi$
$419$		−	21.4266i		−	1.04676i	0.852100	−	0.523379i	$-0.175329\pi$
$420$	2.70708	−	1.18246i	0.132092	−	0.0576981i
$421$	20.9936			1.02316			0.511582	−	0.859234i	$-0.329060\pi$
$421$	20.9936			1.02316			0.511582	+	0.859234i	$0.329060\pi$
$422$			12.0429i			0.586240i
$423$	5.88493	+	5.45110i	0.286135	+	0.265042i
$424$		−	8.93036i		−	0.433696i
$425$	0.309636			0.0150195
$426$	1.14395	+	2.61891i	0.0554244	+	0.126887i
$427$	7.24601			0.350659
$428$	−0.0963737			−0.00465840
$429$	−4.07170	−	2.00329i	−0.196583	−	0.0967199i
$430$	5.39363			0.260104
$431$	−23.5231			−1.13307			−0.566533	−	0.824039i	$-0.691716\pi$
$431$	−23.5231			−1.13307			−0.566533	+	0.824039i	$0.691716\pi$
$432$	−3.96682	+	11.3831i	−0.190854	+	0.547671i
$433$	−8.37974			−0.402705			−0.201352	−	0.979519i	$-0.564534\pi$
$433$	−8.37974			−0.402705			−0.201352	+	0.979519i	$0.564534\pi$
$434$			3.90030i			0.187220i
$435$	5.91040	+	13.5311i	0.283382	+	0.648765i
$436$			13.5506i			0.648954i
$437$	−11.6106			−0.555413
$438$	−1.97036	−	4.51088i	−0.0941475	−	0.215538i
$439$			4.62690i			0.220830i	0.993886	+	0.110415i	$0.0352180\pi$
$439$			4.62690i			0.220830i	−0.993886	+	0.110415i	$0.964782\pi$
$440$	4.30523	+	5.09332i	0.205244	+	0.242815i
$441$	−2.03865	+	2.20089i	−0.0970784	+	0.104804i
$442$		−	0.132728i		−	0.00631323i
$443$		−	4.53289i		−	0.215364i	−0.994185	−	0.107682i	$-0.965657\pi$
$443$		−	4.53289i		−	0.215364i	0.994185	−	0.107682i	$-0.0343429\pi$
$444$	−13.4961	+	5.89513i	−0.640497	+	0.279770i
$445$	−10.4559			−0.495658
$446$	2.19496			0.103934
$447$	−38.1119	+	16.6473i	−1.80263	+	0.787393i
$448$		−	1.77431i		−	0.0838281i
$449$			38.3667i			1.81064i	0.424735	+	0.905318i	$0.360367\pi$
$449$			38.3667i			1.81064i	−0.424735	+	0.905318i	$0.639633\pi$
$450$	1.10627	−	1.19432i	0.0521502	−	0.0563006i
$451$	−10.1896	+	8.61293i	−0.479808	+	0.405567i
$452$		−	7.14577i		−	0.336109i
$453$	−8.11072	−	18.5684i	−0.381075	−	0.872420i
$454$	−6.01870			−0.282472
$455$		−	0.789935i		−	0.0370327i
$456$	−6.13516	−	14.0456i	−0.287305	−	0.657747i
$457$			31.5423i			1.47549i	0.675081	+	0.737744i	$0.264109\pi$
$457$			31.5423i			1.47549i	−0.675081	+	0.737744i	$0.735891\pi$
$458$	13.4571			0.628808
$459$	0.529451	−	1.51930i	0.0247127	−	0.0709150i
$460$	−4.49974			−0.209801
$461$	−24.8628			−1.15798			−0.578989	−	0.815336i	$-0.696552\pi$
$461$	−24.8628			−1.15798			−0.578989	+	0.815336i	$0.696552\pi$
$462$	−2.79708	−	1.37618i	−0.130132	−	0.0640255i
$463$	20.9538			0.973805			0.486902	−	0.873456i	$-0.338127\pi$
$463$	20.9538			0.973805			0.486902	+	0.873456i	$0.338127\pi$
$464$	19.7769			0.918118
$465$	−4.98315	−	11.4083i	−0.231088	−	0.529045i
$466$	9.41887			0.436321
$467$			4.75057i			0.219830i	0.993941	+	0.109915i	$0.0350579\pi$
$467$			4.75057i			0.219830i	−0.993941	+	0.109915i	$0.964942\pi$
$468$	2.96517	+	2.74658i	0.137065	+	0.126961i
$469$		−	13.6366i		−	0.629682i
$470$	−1.45099			−0.0669290
$471$	23.2375	−	10.1502i	1.07073	−	0.467695i
$472$		−	18.2884i		−	0.841792i
$473$	21.2807	+	25.1762i	0.978487	+	1.15760i
$474$	−2.78999	−	6.38730i	−0.128148	−	0.293379i
$475$		−	4.40077i		−	0.201921i
$476$			0.528093i			0.0242051i
$477$	−9.77454	−	9.05398i	−0.447545	−	0.414553i
$478$	5.85189			0.267659
$479$	−12.6329			−0.577210			−0.288605	−	0.957448i	$-0.593191\pi$
$479$	−12.6329			−0.577210			−0.288605	+	0.957448i	$0.593191\pi$
$480$	−3.66103	−	8.38143i	−0.167102	−	0.382558i
$481$			3.93820i			0.179567i
$482$		−	13.4626i		−	0.613203i
$483$	4.18765	−	1.82917i	0.190544	−	0.0832302i
$484$	−3.12433	+	18.4988i	−0.142015	+	0.840856i
$485$			15.3773i			0.698247i
$486$	−3.96857	−	7.47039i	−0.180018	−	0.338864i
$487$	−2.89838			−0.131338			−0.0656691	−	0.997841i	$-0.520918\pi$
$487$	−2.89838			−0.131338			−0.0656691	+	0.997841i	$0.520918\pi$
$488$		−	14.5703i		−	0.659569i
$489$	−17.3520	+	7.57941i	−0.784687	+	0.342753i
$490$		−	0.542651i		−	0.0245145i
$491$	26.6935			1.20466			0.602331	−	0.798247i	$-0.294239\pi$
$491$	26.6935			1.20466			0.602331	+	0.798247i	$0.294239\pi$
$492$	10.8900	−	4.75676i	0.490958	−	0.214451i
$493$	−2.63962			−0.118882
$494$	−1.88643			−0.0848744
$495$	9.93962	+	0.451631i	0.446753	+	0.0202993i
$496$	−16.6742			−0.748694
$497$	−3.04059			−0.136389
$498$	−2.82980	+	1.23606i	−0.126806	+	0.0553893i
$499$	−14.9834			−0.670750			−0.335375	−	0.942085i	$-0.608863\pi$
$499$	−14.9834			−0.670750			−0.335375	+	0.942085i	$0.608863\pi$
$500$		−	1.70553i		−	0.0762736i
$501$	26.4873	−	11.5697i	1.18337	−	0.516897i
$502$			11.5508i			0.515538i
$503$	−36.8058			−1.64109			−0.820545	−	0.571582i	$-0.806330\pi$
$503$	−36.8058			−1.64109			−0.820545	+	0.571582i	$0.806330\pi$
$504$	4.42557	+	4.09933i	0.197131	+	0.182599i
$505$		−	7.15140i		−	0.318233i
$506$	3.06531	+	3.62643i	0.136269	+	0.161214i
$507$	−19.6437	+	8.58039i	−0.872405	+	0.381069i
$508$			36.6770i			1.62728i
$509$			8.60517i			0.381417i	0.981647	+	0.190709i	$0.0610786\pi$
$509$			8.60517i			0.381417i	−0.981647	+	0.190709i	$0.938921\pi$
$510$	0.116493	+	0.266694i	0.00515838	+	0.0118094i
$511$	5.23719			0.231680
$512$	−21.5799			−0.953707
$513$	−21.5935	−	7.52495i	−0.953374	−	0.332235i
$514$		−	3.62695i		−	0.159978i
$515$			4.53024i			0.199626i
$516$	−11.7529	−	26.9068i	−0.517394	−	1.18450i
$517$	−5.72490	−	6.77287i	−0.251781	−	0.297871i
$518$			2.70538i			0.118867i
$519$	4.56547	−	1.99421i	0.200402	−	0.0875361i
$520$	−1.58841			−0.0696563
$521$			39.5467i			1.73257i	0.499548	+	0.866286i	$0.333500\pi$
$521$			39.5467i			1.73257i	−0.499548	+	0.866286i	$0.666500\pi$
$522$	−9.43089	+	10.1814i	−0.412779	+	0.445630i
$523$			11.3071i			0.494424i	0.968961	+	0.247212i	$0.0795144\pi$
$523$			11.3071i			0.494424i	−0.968961	+	0.247212i	$0.920486\pi$
$524$	27.3376			1.19425
$525$	0.693309	+	1.58724i	0.0302585	+	0.0692727i
$526$	−6.97792			−0.304252
$527$	2.22550			0.0969444
$528$	5.88330	−	11.9578i	0.256038	−	0.520397i
$529$	16.0392			0.697359
$530$	2.41001			0.104684
$531$	−20.0172	−	18.5416i	−0.868672	−	0.804635i
$532$	7.50564			0.325411
$533$		−	3.17773i		−	0.137643i
$534$	−3.93377	−	9.00585i	−0.170231	−	0.389721i
$535$		−	0.0565066i		−	0.00244299i
$536$	−27.4207			−1.18439
$537$	9.70952	+	22.2287i	0.418997	+	0.959237i
$538$			11.1354i			0.480083i
$539$	2.53297	−	2.14104i	0.109103	−	0.0922212i
$540$	−8.36861	−	2.91632i	−0.360127	−	0.125498i
$541$			11.2009i			0.481565i	0.970579	+	0.240783i	$0.0774041\pi$
$541$			11.2009i			0.481565i	−0.970579	+	0.240783i	$0.922596\pi$
$542$		−	8.07156i		−	0.346703i
$543$	21.7328	−	9.49294i	0.932644	−	0.407381i
$544$	1.63503			0.0701015
$545$	−7.94508			−0.340330
$546$	0.680384	−	0.297193i	0.0291177	−	0.0127187i
$547$		−	27.8582i		−	1.19113i	−0.803307	−	0.595565i	$-0.796928\pi$
$547$		−	27.8582i		−	1.19113i	0.803307	−	0.595565i	$-0.203072\pi$
$548$		−	19.8228i		−	0.846787i
$549$	−15.9477	−	14.7720i	−0.680630	−	0.630455i
$550$	−1.37452	+	1.16184i	−0.0586097	+	0.0495410i
$551$			37.5162i			1.59824i
$552$	−3.67812	−	8.42056i	−0.156551	−	0.358403i
$553$	7.41575			0.315350
$554$			0.227546i			0.00966750i
$555$	−3.45648	−	7.91314i	−0.146719	−	0.335894i
$556$		−	15.5356i		−	0.658855i
$557$	34.3566			1.45574			0.727868	−	0.685717i	$-0.240511\pi$
$557$	34.3566			1.45574			0.727868	+	0.685717i	$0.240511\pi$
$558$	7.95133	−	8.58414i	0.336607	−	0.363396i
$559$	−7.85148			−0.332082
$560$	2.31989			0.0980333
$561$	−0.785243	+	1.59601i	−0.0331530	+	0.0673835i
$562$	−12.4660			−0.525848
$563$	−32.8760			−1.38556			−0.692780	−	0.721149i	$-0.743614\pi$
$563$	−32.8760			−1.38556			−0.692780	+	0.721149i	$0.743614\pi$
$564$	3.16176	+	7.23842i	0.133134	+	0.304793i
$565$	4.18977			0.176265
$566$			12.3368i			0.518554i
$567$	8.97368	−	0.687846i	0.376859	−	0.0288868i
$568$			6.11405i			0.256540i
$569$	−23.2173			−0.973322			−0.486661	−	0.873591i	$-0.661785\pi$
$569$	−23.2173			−0.973322			−0.486661	+	0.873591i	$0.661785\pi$
$570$	3.79045	−	1.65568i	0.158765	−	0.0693487i
$571$		−	11.5002i		−	0.481269i	−0.970616	−	0.240635i	$-0.922644\pi$
$571$		−	11.5002i		−	0.481269i	0.970616	−	0.240635i	$-0.0773555\pi$
$572$	−2.88453	−	3.41256i	−0.120608	−	0.142686i
$573$	−2.46698	−	5.64783i	−0.103060	−	0.235941i
$574$		−	2.18296i		−	0.0911151i
$575$		−	2.63832i		−	0.110026i
$576$	−3.61718	+	3.90505i	−0.150716	+	0.162711i
$577$	9.84839			0.409994			0.204997	−	0.978763i	$-0.434282\pi$
$577$	9.84839			0.409994			0.204997	+	0.978763i	$0.434282\pi$
$578$	9.17304			0.381548
$579$	−6.11481	−	13.9990i	−0.254123	−	0.581780i
$580$			14.5395i			0.603720i
$581$		−	3.28544i		−	0.136303i
$582$	−13.2447	+	5.78532i	−0.549011	+	0.239809i
$583$	9.50874	+	11.2494i	0.393812	+	0.465901i
$584$		−	10.5310i		−	0.435776i
$585$	−1.61040	+	1.73856i	−0.0665817	+	0.0718806i
$586$	−5.54103			−0.228898
$587$		−	30.8489i		−	1.27327i	−0.771165	−	0.636636i	$-0.780325\pi$
$587$		−	30.8489i		−	1.27327i	0.771165	−	0.636636i	$-0.219675\pi$
$588$	−2.70708	+	1.18246i	−0.111638	+	0.0487638i
$589$		−	31.6305i		−	1.30331i
$590$	4.93543			0.203189
$591$	27.7788	−	12.1339i	1.14267	−	0.499120i
$592$	−11.5658			−0.475350
$593$	18.5481			0.761681			0.380840	−	0.924641i	$-0.375635\pi$
$593$	18.5481			0.761681			0.380840	+	0.924641i	$0.375635\pi$
$594$	3.35053	+	8.73107i	0.137474	+	0.358240i
$595$	−0.309636			−0.0126938
$596$	−40.9522			−1.67747
$597$	−23.1999	+	10.1338i	−0.949507	+	0.414747i
$598$	−1.13094			−0.0462476
$599$		−	4.48648i		−	0.183313i	−0.995791	−	0.0916563i	$-0.970784\pi$
$599$		−	4.48648i		−	0.183313i	0.995791	−	0.0916563i	$-0.0292161\pi$
$600$	3.19163	−	1.39411i	0.130298	−	0.0569144i
$601$			18.3319i			0.747775i	0.927474	+	0.373887i	$0.121975\pi$
$601$			18.3319i			0.747775i	−0.927474	+	0.373887i	$0.878025\pi$
$602$	−5.39363			−0.219828
$603$	−27.8003	+	30.0128i	−1.13212	+	1.22221i
$604$		−	19.9523i		−	0.811846i
$605$	−10.8464	−	1.83188i	−0.440969	−	0.0744766i
$606$	6.15962	−	2.69053i	0.250217	−	0.109295i
$607$		−	22.5287i		−	0.914411i	−0.889361	−	0.457205i	$-0.848850\pi$
$607$		−	22.5287i		−	0.914411i	0.889361	−	0.457205i	$-0.151150\pi$
$608$		−	23.2383i		−	0.942438i
$609$	−5.91040	−	13.5311i	−0.239501	−	0.548307i
$610$	3.93205			0.159204
$611$	2.11219			0.0854502
$612$	1.07659	−	1.16227i	0.0435187	−	0.0469822i
$613$		−	23.3552i		−	0.943309i	−0.881784	−	0.471654i	$-0.843657\pi$
$613$		−	23.3552i		−	0.943309i	0.881784	−	0.471654i	$-0.156343\pi$
$614$		−	6.47404i		−	0.261271i
$615$	2.78902	+	6.38510i	0.112464	+	0.257472i
$616$	−4.30523	−	5.09332i	−0.173463	−	0.205216i
$617$		−	6.84531i		−	0.275582i	−0.990461	−	0.137791i	$-0.956000\pi$
$617$		−	6.84531i		−	0.275582i	0.990461	−	0.137791i	$-0.0440002\pi$
$618$	−3.90197	+	1.70439i	−0.156960	+	0.0685605i
$619$	12.6437			0.508194			0.254097	−	0.967179i	$-0.418222\pi$
$619$	12.6437			0.508194			0.254097	+	0.967179i	$0.418222\pi$
$620$		−	12.2585i		−	0.492312i
$621$	−12.9456	−	4.51132i	−0.519489	−	0.181033i
$622$		−	7.96980i		−	0.319560i
$623$	10.4559			0.418907
$624$	1.27053	+	2.90871i	0.0508620	+	0.116442i
$625$	1.00000			0.0400000
$626$	7.61282			0.304269
$627$	22.6836	+	11.1604i	0.905897	+	0.445705i
$628$	24.9693			0.996383
$629$	1.54368			0.0615507
$630$	−1.10627	+	1.19432i	−0.0440750	+	0.0475827i
$631$	11.7331			0.467087			0.233544	−	0.972346i	$-0.424968\pi$
$631$	11.7331			0.467087			0.233544	+	0.972346i	$0.424968\pi$
$632$		−	14.9117i		−	0.593154i
$633$	15.3864	+	35.2251i	0.611555	+	1.40007i
$634$			3.98475i			0.158255i
$635$	−21.5047			−0.853389
$636$	−5.25150	−	12.0226i	−0.208236	−	0.476728i
$637$			0.789935i			0.0312983i
$638$	11.7177	−	9.90458i	0.463907	−	0.392126i
$639$	6.69201	+	6.19869i	0.264732	+	0.245216i
$640$		−	11.5239i		−	0.455520i
$641$		−	32.6283i		−	1.28874i	−0.764714	−	0.644370i	$-0.777120\pi$
$641$		−	32.6283i		−	1.28874i	0.764714	−	0.644370i	$-0.222880\pi$
$642$	0.0486700	−	0.0212592i	0.00192085	−	0.000839033i
$643$	−35.0676			−1.38293			−0.691466	−	0.722409i	$-0.743035\pi$
$643$	−35.0676			−1.38293			−0.691466	+	0.722409i	$0.743035\pi$
$644$	4.49974			0.177315
$645$	15.7762	−	6.89108i	0.621187	−	0.271336i
$646$			0.739435i			0.0290927i
$647$			13.9595i			0.548803i	0.961615	+	0.274401i	$0.0884797\pi$
$647$			13.9595i			0.548803i	−0.961615	+	0.274401i	$0.911520\pi$
$648$	−1.38313	−	18.0444i	−0.0543344	−	0.708849i
$649$	19.4729	+	23.0375i	0.764377	+	0.904300i
$650$		−	0.428659i		−	0.0168134i
$651$	4.98315	+	11.4083i	0.195305	+	0.447125i
$652$	−18.6452			−0.730204
$653$		−	38.6175i		−	1.51122i	−0.655023	−	0.755609i	$-0.727341\pi$
$653$		−	38.6175i		−	1.51122i	0.655023	−	0.755609i	$-0.272659\pi$
$654$	−2.98913	−	6.84322i	−0.116884	−	0.267591i
$655$			16.0288i			0.626298i
$656$	9.33240			0.364369
$657$	−11.5265	−	10.6768i	−0.449691	−	0.416541i
$658$	1.45099			0.0565654
$659$	−1.08943			−0.0424381			−0.0212191	−	0.999775i	$-0.506755\pi$
$659$	−1.08943			−0.0424381			−0.0212191	+	0.999775i	$0.506755\pi$
$660$	8.79111	+	4.32526i	0.342193	+	0.168361i
$661$	−21.8553			−0.850074			−0.425037	−	0.905176i	$-0.639739\pi$
$661$	−21.8553			−0.850074			−0.425037	+	0.905176i	$0.639739\pi$
$662$	2.92888			0.113834
$663$	−0.169578	−	0.388225i	−0.00658585	−	0.0150774i
$664$	−6.60639			−0.256378
$665$			4.40077i			0.170654i
$666$	5.51531	−	5.95424i	0.213714	−	0.230722i
$667$			22.4915i			0.870874i
$668$	28.4613			1.10120
$669$	6.42019	−	2.80435i	0.248219	−	0.108422i
$670$		−	7.39994i		−	0.285885i
$671$	15.5140	+	18.3539i	0.598911	+	0.708545i
$672$	3.66103	+	8.38143i	0.141227	+	0.323321i
$673$			38.5367i			1.48548i	0.669580	+	0.742740i	$0.266474\pi$
$673$			38.5367i			1.48548i	−0.669580	+	0.742740i	$0.733526\pi$
$674$			10.9893i			0.423291i
$675$	1.70992	−	4.90675i	0.0658148	−	0.188861i
$676$	−21.1076			−0.811832
$677$	19.4145			0.746162			0.373081	−	0.927799i	$-0.378301\pi$
$677$	19.4145			0.746162			0.373081	+	0.927799i	$0.378301\pi$
$678$	1.57629	+	3.60871i	0.0605372	+	0.138592i
$679$		−	15.3773i		−	0.590126i
$680$			0.622618i			0.0238763i
$681$	−17.6045	+	7.68969i	−0.674607	+	0.294670i
$682$	−9.87935	+	8.35071i	−0.378300	+	0.319765i
$683$		−	7.94563i		−	0.304031i	−0.988378	−	0.152015i	$-0.951424\pi$
$683$		−	7.94563i		−	0.304031i	0.988378	−	0.152015i	$-0.0485764\pi$
$684$	−16.5191	−	15.3013i	−0.631623	−	0.585061i
$685$	11.6227			0.444079
$686$			0.542651i			0.0207185i
$687$	39.3615	−	17.1932i	1.50174	−	0.655962i
$688$		−	23.0583i		−	0.879091i
$689$	−3.50824			−0.133653
$690$	2.27243	−	0.992603i	0.0865100	−	0.0377877i
$691$	2.20102			0.0837309			0.0418654	−	0.999123i	$-0.486670\pi$
$691$	2.20102			0.0837309			0.0418654	+	0.999123i	$0.486670\pi$
$692$	4.90573			0.186488
$693$	−9.93962	−	0.451631i	−0.377575	−	0.0171560i
$694$	−2.54611			−0.0966491
$695$	9.10895			0.345522
$696$	−27.2084	+	11.8847i	−1.03133	+	0.450488i
$697$	−1.24559			−0.0471802
$698$		−	5.20884i		−	0.197157i
$699$	27.5499	−	12.0339i	1.04203	−	0.455162i
$700$			1.70553i			0.0644630i
$701$	−50.3357			−1.90115			−0.950577	−	0.310490i	$-0.899507\pi$
$701$	−50.3357			−1.90115			−0.950577	+	0.310490i	$0.899507\pi$
$702$	−2.10332	−	0.732972i	−0.0793848	−	0.0276642i
$703$		−	21.9399i		−	0.827481i
$704$	4.49427	−	3.79886i	0.169384	−	0.143175i
$705$	−4.24409	+	1.85383i	−0.159842	+	0.0698192i
$706$			11.7461i			0.442069i
$707$			7.15140i			0.268956i
$708$	−10.7545	−	24.6210i	−0.404179	−	0.925314i
$709$	−19.5800			−0.735343			−0.367672	−	0.929956i	$-0.619845\pi$
$709$	−19.5800			−0.735343			−0.367672	+	0.929956i	$0.619845\pi$
$710$	−1.64998			−0.0619227
$711$	−16.3213	−	15.1181i	−0.612095	−	0.566972i
$712$		−	21.0248i		−	0.787940i
$713$		−	18.9629i		−	0.710167i
$714$	−0.116493	−	0.266694i	−0.00435963	−	0.00998078i
$715$	2.00088	−	1.69128i	0.0748287	−	0.0632504i
$716$			23.8853i			0.892635i
$717$	17.1166	−	7.47656i	0.639231	−	0.279217i
$718$	−15.4941			−0.578235
$719$		−	5.09923i		−	0.190169i	−0.995469	−	0.0950847i	$-0.969688\pi$
$719$		−	5.09923i		−	0.190169i	0.995469	−	0.0950847i	$-0.0303122\pi$
$720$	−5.10583	−	4.72944i	−0.190283	−	0.176256i
$721$		−	4.53024i		−	0.168715i
$722$	0.199019			0.00740672
$723$	−17.2002	−	39.3776i	−0.639683	−	1.46447i
$724$	23.3525			0.867888
$725$	−8.52492			−0.316607
$726$	−2.50285	−	10.0314i	−0.0928895	−	0.372299i
$727$	46.8319			1.73690			0.868449	−	0.495778i	$-0.165117\pi$
$727$	46.8319			1.73690			0.868449	+	0.495778i	$0.165117\pi$
$728$	1.58841			0.0588703
$729$	−21.1524	−	16.7803i	−0.783421	−	0.621492i
$730$	2.84197			0.105186
$731$			3.07759i			0.113829i
$732$	−8.56811	−	19.6155i	−0.316686	−	0.725011i
$733$		−	20.2922i		−	0.749510i	−0.927124	−	0.374755i	$-0.877727\pi$
$733$		−	20.2922i		−	0.749510i	0.927124	−	0.374755i	$-0.122273\pi$
$734$	−4.25367			−0.157006
$735$	−0.693309	−	1.58724i	−0.0255731	−	0.0585461i
$736$		−	13.9317i		−	0.513529i
$737$	34.5412	−	29.1966i	1.27234	−	1.07547i
$738$	−4.45029	+	4.80446i	−0.163817	+	0.176855i
$739$			26.8937i			0.989301i	0.869092	+	0.494651i	$0.164704\pi$
$739$			26.8937i			0.989301i	−0.869092	+	0.494651i	$0.835296\pi$
$740$		−	8.50289i		−	0.312572i
$741$	−5.51774	+	2.41016i	−0.202699	+	0.0885395i
$742$	−2.41001			−0.0884742
$743$	17.4219			0.639147			0.319574	−	0.947561i	$-0.396460\pi$
$743$	17.4219			0.639147			0.319574	+	0.947561i	$0.396460\pi$
$744$	22.9398	−	10.0202i	0.841015	−	0.367357i
$745$		−	24.0115i		−	0.879711i
$746$			12.7100i			0.465348i
$747$	−6.69784	+	7.23089i	−0.245061	+	0.264564i
$748$	−1.33764	+	1.13067i	−0.0489091	+	0.0413413i
$749$			0.0565066i			0.00206471i
$750$	0.376225	+	0.861316i	0.0137378	+	0.0314508i
$751$	−13.3035			−0.485450			−0.242725	−	0.970095i	$-0.578041\pi$
$751$	−13.3035			−0.485450			−0.242725	+	0.970095i	$0.578041\pi$
$752$			6.20312i			0.226205i
$753$	14.7577	+	33.7857i	0.537800	+	1.23122i
$754$			3.65428i			0.133081i
$755$	11.6986			0.425754
$756$	8.36861	+	2.91632i	0.304363	+	0.106065i
$757$	−30.1903			−1.09729			−0.548643	−	0.836057i	$-0.684855\pi$
$757$	−30.1903			−1.09729			−0.548643	+	0.836057i	$0.684855\pi$
$758$	−11.0996			−0.403155
$759$	13.5992	+	6.69085i	0.493618	+	0.242862i
$760$	8.84911			0.320991
$761$	3.60539			0.130695			0.0653477	−	0.997863i	$-0.479184\pi$
$761$	3.60539			0.130695			0.0653477	+	0.997863i	$0.479184\pi$
$762$	−8.09062	−	18.5224i	−0.293092	−	0.670995i
$763$	7.94508			0.287631
$764$		−	6.06875i		−	0.219560i
$765$	0.681474	+	0.631237i	0.0246388	+	0.0228224i
$766$			4.87511i			0.176145i
$767$	−7.18449			−0.259417
$768$	4.29319	−	1.87528i	0.154917	−	0.0676682i
$769$		−	13.7794i		−	0.496899i	−0.968645	−	0.248449i	$-0.920079\pi$
$769$		−	13.7794i		−	0.496899i	0.968645	−	0.248449i	$-0.0799209\pi$
$770$	1.37452	−	1.16184i	0.0495342	−	0.0418698i
$771$	−4.63391	−	10.6087i	−0.166886	−	0.382063i
$772$		−	15.0423i		−	0.541386i
$773$			50.0158i			1.79894i	0.436979	+	0.899472i	$0.356048\pi$
$773$			50.0158i			1.79894i	−0.436979	+	0.899472i	$0.643952\pi$
$774$	11.8708	+	10.9957i	0.426687	+	0.395232i
$775$	7.18749			0.258182
$776$	−30.9208			−1.10999
$777$	3.45648	+	7.91314i	0.124000	+	0.283882i
$778$		−	5.32077i		−	0.190759i
$779$			17.7033i			0.634286i
$780$	−2.13842	+	0.934065i	−0.0765676	+	0.0334449i
$781$	−6.51003	−	7.70173i	−0.232947	−	0.275589i
$782$			0.443302i			0.0158524i
$783$	−14.5769	+	41.8296i	−0.520936	+	1.49487i
$784$	−2.31989			−0.0828532
$785$			14.6402i			0.522531i
$786$	−13.8059	+	6.03044i	−0.492439	+	0.215099i
$787$			41.1946i			1.46843i	0.678917	+	0.734215i	$0.262450\pi$
$787$			41.1946i			1.46843i	−0.678917	+	0.734215i	$0.737550\pi$
$788$	29.8491			1.06333
$789$	−20.4102	+	8.91522i	−0.726622	+	0.317390i
$790$	4.02416			0.143173
$791$	−4.18977			−0.148971
$792$	−0.908143	+	19.9867i	−0.0322695	+	0.710196i
$793$	−5.72387			−0.203261
$794$	10.8683			0.385702
$795$	7.04920	−	3.07910i	0.250009	−	0.109205i
$796$	−24.9289			−0.883581
$797$			43.0217i			1.52391i	0.647632	+	0.761953i	$0.275759\pi$
$797$			43.0217i			1.52391i	−0.647632	+	0.761953i	$0.724241\pi$
$798$	−3.79045	+	1.65568i	−0.134181	+	0.0586104i
$799$		−	0.827930i		−	0.0292901i
$800$	5.28051			0.186694
$801$	−23.0123	−	21.3159i	−0.813100	−	0.753160i
$802$			19.5598i			0.690680i
$803$	11.2130	+	13.2656i	0.395700	+	0.468135i
$804$	−36.9155	+	16.1248i	−1.30191	+	0.568677i
$805$			2.63832i			0.0929887i
$806$		−	3.08098i		−	0.108523i
$807$	14.2270	+	32.5708i	0.500814	+	1.14655i
$808$	14.3801			0.505890
$809$	−4.48542			−0.157699			−0.0788496	−	0.996887i	$-0.525125\pi$
$809$	−4.48542			−0.157699			−0.0788496	+	0.996887i	$0.525125\pi$
$810$	4.86958	−	0.373260i	0.171099	−	0.0131150i
$811$			8.48856i			0.298074i	0.988832	+	0.149037i	$0.0476173\pi$
$811$			8.48856i			0.298074i	−0.988832	+	0.149037i	$0.952383\pi$
$812$		−	14.5395i		−	0.510236i
$813$	−10.3125	−	23.6091i	−0.361675	−	0.828006i
$814$	−6.85264	+	5.79233i	−0.240185	+	0.203021i
$815$		−	10.9322i		−	0.382939i
$816$	1.14015	−	0.498018i	0.0399131	−	0.0174341i
$817$	43.7410			1.53030
$818$			14.2324i			0.497623i
$819$	1.61040	−	1.73856i	0.0562718	−	0.0607502i
$820$			6.86096i			0.239595i
$821$	−35.1625			−1.22718			−0.613591	−	0.789624i	$-0.710275\pi$
$821$	−35.1625			−1.22718			−0.613591	+	0.789624i	$0.710275\pi$
$822$	4.37273	+	10.0108i	0.152517	+	0.349166i
$823$	−10.5446			−0.367563			−0.183781	−	0.982967i	$-0.558834\pi$
$823$	−10.5446			−0.367563			−0.183781	+	0.982967i	$0.558834\pi$
$824$	−9.10945			−0.317343
$825$	−2.53602	+	5.15447i	−0.0882930	+	0.179456i
$826$	−4.93543			−0.171726
$827$	35.7876			1.24446			0.622228	−	0.782836i	$-0.286228\pi$
$827$	35.7876			1.24446			0.622228	+	0.782836i	$0.286228\pi$
$828$	−9.90344	−	9.17337i	−0.344168	−	0.318797i
$829$	−26.1229			−0.907287			−0.453644	−	0.891183i	$-0.649876\pi$
$829$	−26.1229			−0.907287			−0.453644	+	0.891183i	$0.649876\pi$
$830$		−	1.78285i		−	0.0618835i
$831$	0.290720	+	0.665565i	0.0100850	+	0.0230882i
$832$			1.40159i			0.0485912i
$833$	0.309636			0.0107282
$834$	3.42701	+	7.84569i	0.118668	+	0.271674i
$835$			16.6877i			0.577501i
$836$	16.0699	+	19.0116i	0.555789	+	0.657529i
$837$	12.2900	−	35.2672i	0.424805	−	1.21901i
$838$			11.6272i			0.401654i
$839$			21.4315i			0.739896i	0.929052	+	0.369948i	$0.120625\pi$
$839$			21.4315i			0.739896i	−0.929052	+	0.369948i	$0.879375\pi$
$840$	−3.19163	+	1.39411i	−0.110122	+	0.0481014i
$841$	43.6742			1.50601
$842$	−11.3922			−0.392601
$843$	−36.4628	+	15.9270i	−1.25585	+	0.548556i
$844$			37.8503i			1.30286i
$845$		−	12.3760i		−	0.425747i
$846$	−3.19346	−	2.95805i	−0.109794	−	0.101700i
$847$	10.8464	+	1.83188i	0.372686	+	0.0629442i
$848$		−	10.3030i		−	0.353808i
$849$	15.7619	+	36.0847i	0.540947	+	1.23843i
$850$	−0.168024			−0.00576318
$851$		−	13.1533i		−	0.450890i
$852$	3.59537	+	8.23112i	0.123175	+	0.281994i
$853$		−	2.56250i		−	0.0877384i	−0.999037	−	0.0438692i	$-0.986032\pi$
$853$		−	2.56250i		−	0.0877384i	0.999037	−	0.0438692i	$-0.0139685\pi$
$854$	−3.93205			−0.134552
$855$	8.97161	−	9.68561i	0.306822	−	0.331241i
$856$	0.113624			0.00388359
$857$	0.346965			0.0118521			0.00592604	−	0.999982i	$-0.498114\pi$
$857$	0.346965			0.0118521			0.00592604	+	0.999982i	$0.498114\pi$
$858$	2.20951	+	1.08709i	0.0754314	+	0.0371126i
$859$	−32.2002			−1.09866			−0.549329	−	0.835606i	$-0.685116\pi$
$859$	−32.2002			−1.09866			−0.549329	+	0.835606i	$0.685116\pi$
$860$	16.9520			0.578057
$861$	−2.78902	−	6.38510i	−0.0950497	−	0.217604i
$862$	12.7648			0.434771
$863$		−	3.44112i		−	0.117137i	−0.998283	−	0.0585686i	$-0.981346\pi$
$863$		−	3.44112i		−	0.117137i	0.998283	−	0.0585686i	$-0.0186536\pi$
$864$	9.02924	−	25.9101i	0.307181	−	0.881481i
$865$			2.87637i			0.0977993i
$866$	4.54728			0.154523
$867$	26.8309	−	11.7198i	0.911224	−	0.398025i
$868$			12.2585i			0.416080i
$869$	15.8774	+	18.7839i	0.538605	+	0.637199i
$870$	−3.20729	−	7.34265i	−0.108737	−	0.248939i
$871$			10.7721i			0.364997i
$872$		−	15.9760i		−	0.541017i
$873$	−31.3489	+	33.8437i	−1.06100	+	1.14544i
$874$	6.30053			0.213119
$875$	−1.00000			−0.0338062
$876$	−6.19276	−	14.1775i	−0.209234	−	0.479013i
$877$			16.5976i			0.560462i	0.959933	+	0.280231i	$0.0904110\pi$
$877$			16.5976i			0.560462i	−0.959933	+	0.280231i	$0.909589\pi$
$878$		−	2.51079i		−	0.0847352i
$879$	−16.2073	+	7.07940i	−0.546660	+	0.238782i
$880$	4.96698	+	5.87622i	0.167437	+	0.198087i
$881$		−	23.6598i		−	0.797120i	−0.917142	−	0.398560i	$-0.869510\pi$
$881$		−	23.6598i		−	0.797120i	0.917142	−	0.398560i	$-0.130490\pi$
$882$	1.10627	−	1.19432i	0.0372502	−	0.0402147i
$883$	18.0809			0.608469			0.304235	−	0.952597i	$-0.401599\pi$
$883$	18.0809			0.608469			0.304235	+	0.952597i	$0.401599\pi$
$884$		−	0.417159i		−	0.0140306i
$885$	14.4360	−	6.30567i	0.485260	−	0.211963i
$886$			2.45978i			0.0826379i
$887$	15.5291			0.521415			0.260708	−	0.965418i	$-0.416044\pi$
$887$	15.5291			0.521415			0.260708	+	0.965418i	$0.416044\pi$
$888$	15.9118	−	6.95032i	0.533966	−	0.233238i
$889$	21.5047			0.721246
$890$	5.67391			0.190190
$891$	20.9553	+	21.2574i	0.702029	+	0.712148i
$892$	6.89867			0.230984
$893$	−11.7671			−0.393773
$894$	20.6815	−	9.03370i	0.691691	−	0.302132i
$895$	−14.0046			−0.468123
$896$			11.5239i			0.384985i
$897$	−3.30797	+	1.44493i	−0.110450	+	0.0482447i
$898$		−	20.8197i		−	0.694763i
$899$	−61.2728			−2.04356
$900$	3.47697	−	3.75369i	0.115899	−	0.125123i
$901$			1.37515i			0.0458127i
$902$	5.52938	−	4.67381i	0.184108	−	0.155621i
$903$	−15.7762	+	6.89108i	−0.524999	+	0.229321i
$904$			8.42482i			0.280205i
$905$			13.6922i			0.455145i
$906$	4.40129	+	10.0762i	0.146223	+	0.334758i
$907$	−21.2004			−0.703949			−0.351975	−	0.936010i	$-0.614490\pi$
$907$	−21.2004			−0.703949			−0.351975	+	0.936010i	$0.614490\pi$
$908$	−18.9165			−0.627767
$909$	14.5792	−	15.7395i	0.483561	−	0.522045i
$910$			0.428659i			0.0142099i
$911$			52.3817i			1.73548i	0.497016	+	0.867741i	$0.334429\pi$
$911$			52.3817i			1.73548i	−0.497016	+	0.867741i	$0.665571\pi$
$912$	−7.07820	−	16.2046i	−0.234383	−	0.536587i
$913$	8.32191	−	7.03426i	0.275415	−	0.232800i
$914$		−	17.1165i		−	0.566163i
$915$	11.5011	−	5.02372i	0.380216	−	0.166079i
$916$	42.2950			1.39747
$917$		−	16.0288i		−	0.529318i
$918$	−0.287307	+	0.824452i	−0.00948256	+	0.0272110i
$919$			27.8239i			0.917827i	0.888481	+	0.458913i	$0.151761\pi$
$919$			27.8239i			0.917827i	−0.888481	+	0.458913i	$0.848239\pi$
$920$	5.30517			0.174906
$921$	−8.27144	−	18.9364i	−0.272553	−	0.623974i
$922$	13.4918			0.444330
$923$	2.40187			0.0790584
$924$	−8.79111	−	4.32526i	−0.289206	−	0.142291i
$925$	4.98548			0.163922
$926$	−11.3706			−0.373661
$927$	−9.23555	+	9.97056i	−0.303335	+	0.327476i
$928$	−45.0159			−1.47772
$929$			5.85715i			0.192167i	0.995373	+	0.0960835i	$0.0306316\pi$
$929$			5.85715i			0.192167i	−0.995373	+	0.0960835i	$0.969368\pi$
$930$	2.70411	+	6.19070i	0.0886713	+	0.203001i
$931$		−	4.40077i		−	0.144229i
$932$	29.6031			0.969682
$933$	−10.1825	−	23.3114i	−0.333359	−	0.763181i
$934$		−	2.57790i		−	0.0843516i
$935$	−0.662943	−	0.784298i	−0.0216805	−	0.0256493i
$936$	−3.49591	−	3.23820i	−0.114268	−	0.105844i
$937$		−	24.9140i		−	0.813906i	−0.913449	−	0.406953i	$-0.866591\pi$
$937$		−	24.9140i		−	0.813906i	0.913449	−	0.406953i	$-0.133409\pi$
$938$			7.39994i			0.241617i
$939$	22.2672	−	9.72638i	0.726664	−	0.317408i
$940$	−4.56039			−0.148744
$941$	47.1865			1.53824			0.769119	−	0.639106i	$-0.220696\pi$
$941$	47.1865			1.53824			0.769119	+	0.639106i	$0.220696\pi$
$942$	−12.6098	+	5.50801i	−0.410851	+	0.179461i
$943$			10.6134i			0.345619i
$944$		−	21.0995i		−	0.686730i
$945$	−1.70992	+	4.90675i	−0.0556236	+	0.159617i
$946$	−11.5480	−	13.6619i	−0.375457	−	0.444187i
$947$			5.39589i			0.175343i	0.996149	+	0.0876715i	$0.0279426\pi$
$947$			5.39589i			0.175343i	−0.996149	+	0.0876715i	$0.972057\pi$
$948$	−8.76881	−	20.0750i	−0.284798	−	0.652006i
$949$	−4.13704			−0.134294
$950$			2.38808i			0.0774796i
$951$	5.09105	+	11.6553i	0.165089	+	0.377948i
$952$		−	0.622618i		−	0.0201792i
$953$	−23.7368			−0.768911			−0.384456	−	0.923143i	$-0.625611\pi$
$953$	−23.7368			−0.768911			−0.384456	+	0.923143i	$0.625611\pi$
$954$	5.30417	+	4.91315i	0.171729	+	0.159069i
$955$	3.55828			0.115143
$956$	18.3922			0.594847
$957$	21.6194	−	43.9414i	0.698856	−	1.42043i
$958$	6.85524			0.221483
$959$	−11.6227			−0.375315
$960$	−1.23014	−	2.81625i	−0.0397027	−	0.0908939i
$961$	20.6600			0.666453
$962$		−	2.13707i		−	0.0689019i
$963$	0.115197	−	0.124365i	0.00371217	−	0.00400760i
$964$		−	42.3123i		−	1.36279i
$965$	8.81975			0.283918
$966$	−2.27243	+	0.992603i	−0.0731143	+	0.0319365i
$967$			23.6190i			0.759534i	0.925082	+	0.379767i	$0.123996\pi$
$967$			23.6190i			0.759534i	−0.925082	+	0.379767i	$0.876004\pi$
$968$	3.68357	−	21.8100i	0.118394	−	0.701001i
$969$	0.944726	+	2.16282i	0.0303490	+	0.0694799i
$970$		−	8.34451i		−	0.267926i
$971$			13.7400i			0.440936i	0.975394	+	0.220468i	$0.0707585\pi$
$971$			13.7400i			0.440936i	−0.975394	+	0.220468i	$0.929242\pi$
$972$	−12.4731	−	23.4791i	−0.400073	−	0.753093i
$973$	−9.10895			−0.292020
$974$	1.57281			0.0503961
$975$	−0.547669	−	1.25381i	−0.0175394	−	0.0401542i
$976$		−	16.8099i		−	0.538073i
$977$		−	28.8246i		−	0.922181i	−0.887353	−	0.461090i	$-0.847458\pi$
$977$		−	28.8246i		−	0.922181i	0.887353	−	0.461090i	$-0.152542\pi$
$978$	9.41611	−	4.11298i	0.301094	−	0.131519i
$979$	22.3865	+	26.4845i	0.715477	+	0.846449i
$980$		−	1.70553i		−	0.0544811i
$981$	−17.4862	−	16.1972i	−0.558293	−	0.517137i
$982$	−14.4853			−0.462243
$983$			45.2956i			1.44470i	0.691525	+	0.722352i	$0.256939\pi$
$983$			45.2956i			1.44470i	−0.691525	+	0.722352i	$0.743061\pi$
$984$	−12.8392	+	5.60820i	−0.409299	+	0.178783i
$985$			17.5014i			0.557640i
$986$	1.43239			0.0456166
$987$	4.24409	−	1.85383i	0.135091	−	0.0590080i
$988$	−5.92896			−0.188625
$989$	26.2234			0.833855
$990$	−5.39375	−	0.245078i	−0.171425	−	0.00778909i
$991$	30.0845			0.955665			0.477832	−	0.878451i	$-0.341423\pi$
$991$	30.0845			0.955665			0.477832	+	0.878451i	$0.341423\pi$
$992$	37.9536			1.20503
$993$	8.56688	−	3.74203i	0.271862	−	0.118750i
$994$	1.64998			0.0523342
$995$		−	14.6165i		−	0.463374i
$996$	−8.89394	+	3.88489i	−0.281815	+	0.123098i
$997$			6.79947i			0.215341i	0.994187	+	0.107671i	$0.0343392\pi$
$997$			6.79947i			0.215341i	−0.994187	+	0.107671i	$0.965661\pi$
$998$	8.13077			0.257375
$999$	8.52477	−	24.4625i	0.269712	−	0.773959i

Twists

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

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

\(f(q)\)	\(=\)	\(q-0.542651 q^{2} +(-1.58724 + 0.693309i) q^{3} -1.70553 q^{4} -1.00000i q^{5} +(0.861316 - 0.376225i) q^{6} +1.00000i q^{7} +2.01081 q^{8} +(2.03865 - 2.20089i) q^{9} +O(q^{10})\)	\(q-0.542651 q^{2} +(-1.58724 + 0.693309i) q^{3} -1.70553 q^{4} -1.00000i q^{5} +(0.861316 - 0.376225i) q^{6} +1.00000i q^{7} +2.01081 q^{8} +(2.03865 - 2.20089i) q^{9} +0.542651i q^{10} +(-2.53297 + 2.14104i) q^{11} +(2.70708 - 1.18246i) q^{12} -0.789935i q^{13} -0.542651i q^{14} +(0.693309 + 1.58724i) q^{15} +2.31989 q^{16} -0.309636 q^{17} +(-1.10627 + 1.19432i) q^{18} +4.40077i q^{19} +1.70553i q^{20} +(-0.693309 - 1.58724i) q^{21} +(1.37452 - 1.16184i) q^{22} +2.63832i q^{23} +(-3.19163 + 1.39411i) q^{24} -1.00000 q^{25} +0.428659i q^{26} +(-1.70992 + 4.90675i) q^{27} -1.70553i q^{28} +8.52492 q^{29} +(-0.376225 - 0.861316i) q^{30} -7.18749 q^{31} -5.28051 q^{32} +(2.53602 - 5.15447i) q^{33} +0.168024 q^{34} +1.00000 q^{35} +(-3.47697 + 3.75369i) q^{36} -4.98548 q^{37} -2.38808i q^{38} +(0.547669 + 1.25381i) q^{39} -2.01081i q^{40} +4.02277 q^{41} +(0.376225 + 0.861316i) q^{42} -9.93941i q^{43} +(4.32006 - 3.65161i) q^{44} +(-2.20089 - 2.03865i) q^{45} -1.43169i q^{46} +2.67389i q^{47} +(-3.68222 + 1.60840i) q^{48} -1.00000 q^{49} +0.542651 q^{50} +(0.491465 - 0.214673i) q^{51} +1.34726i q^{52} -4.44117i q^{53} +(0.927889 - 2.66265i) q^{54} +(2.14104 + 2.53297i) q^{55} +2.01081i q^{56} +(-3.05109 - 6.98506i) q^{57} -4.62606 q^{58} -9.09504i q^{59} +(-1.18246 - 2.70708i) q^{60} -7.24601i q^{61} +3.90030 q^{62} +(2.20089 + 2.03865i) q^{63} -1.77431 q^{64} -0.789935 q^{65} +(-1.37618 + 2.79708i) q^{66} -13.6366 q^{67} +0.528093 q^{68} +(-1.82917 - 4.18765i) q^{69} -0.542651 q^{70} +3.04059i q^{71} +(4.09933 - 4.42557i) q^{72} -5.23719i q^{73} +2.70538 q^{74} +(1.58724 - 0.693309i) q^{75} -7.50564i q^{76} +(-2.14104 - 2.53297i) q^{77} +(-0.297193 - 0.680384i) q^{78} -7.41575i q^{79} -2.31989i q^{80} +(-0.687846 - 8.97368i) q^{81} -2.18296 q^{82} -3.28544 q^{83} +(1.18246 + 2.70708i) q^{84} +0.309636i q^{85} +5.39363i q^{86} +(-13.5311 + 5.91040i) q^{87} +(-5.09332 + 4.30523i) q^{88} -10.4559i q^{89} +(1.19432 + 1.10627i) q^{90} +0.789935 q^{91} -4.49974i q^{92} +(11.4083 - 4.98315i) q^{93} -1.45099i q^{94} +4.40077 q^{95} +(8.38143 - 3.66103i) q^{96} -15.3773 q^{97} +0.542651 q^{98} +(-0.451631 + 9.93962i) 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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