LMFDB - Embedded newform 1155.2.l.f.1121.15

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			1121.15
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.490604 q^{2} +(1.73069 + 0.0687106i) q^{3} -1.75931 q^{4} -1.00000i q^{5} +(-0.849081 - 0.0337096i) q^{6} -1.00000i q^{7} +1.84433 q^{8} +(2.99056 + 0.237833i) q^{9} +O(q^{10})$	\(q-0.490604 q^{2} +(1.73069 + 0.0687106i) q^{3} -1.75931 q^{4} -1.00000i q^{5} +(-0.849081 - 0.0337096i) q^{6} -1.00000i q^{7} +1.84433 q^{8} +(2.99056 + 0.237833i) q^{9} +0.490604i q^{10} +(1.95686 + 2.67782i) q^{11} +(-3.04481 - 0.120883i) q^{12} -2.97821i q^{13} +0.490604i q^{14} +(0.0687106 - 1.73069i) q^{15} +2.61378 q^{16} -3.37240 q^{17} +(-1.46718 - 0.116682i) q^{18} -5.83105i q^{19} +1.75931i q^{20} +(0.0687106 - 1.73069i) q^{21} +(-0.960040 - 1.31375i) q^{22} +0.534992i q^{23} +(3.19196 + 0.126725i) q^{24} -1.00000 q^{25} +1.46112i q^{26} +(5.15938 + 0.617098i) q^{27} +1.75931i q^{28} -4.74626 q^{29} +(-0.0337096 + 0.849081i) q^{30} +7.76804 q^{31} -4.97099 q^{32} +(3.20271 + 4.76892i) q^{33} +1.65451 q^{34} -1.00000 q^{35} +(-5.26131 - 0.418422i) q^{36} +1.78005 q^{37} +2.86074i q^{38} +(0.204634 - 5.15434i) q^{39} -1.84433i q^{40} +8.07126 q^{41} +(-0.0337096 + 0.849081i) q^{42} -2.55936i q^{43} +(-3.44271 - 4.71111i) q^{44} +(0.237833 - 2.99056i) q^{45} -0.262469i q^{46} -7.04571i q^{47} +(4.52364 + 0.179594i) q^{48} -1.00000 q^{49} +0.490604 q^{50} +(-5.83656 - 0.231719i) q^{51} +5.23958i q^{52} +3.11078i q^{53} +(-2.53121 - 0.302750i) q^{54} +(2.67782 - 1.95686i) q^{55} -1.84433i q^{56} +(0.400655 - 10.0917i) q^{57} +2.32853 q^{58} -5.20131i q^{59} +(-0.120883 + 3.04481i) q^{60} -9.92271i q^{61} -3.81103 q^{62} +(0.237833 - 2.99056i) q^{63} -2.78878 q^{64} -2.97821 q^{65} +(-1.57126 - 2.33965i) q^{66} +2.50383 q^{67} +5.93308 q^{68} +(-0.0367596 + 0.925904i) q^{69} +0.490604 q^{70} -11.7766i q^{71} +(5.51557 + 0.438643i) q^{72} -5.53389i q^{73} -0.873298 q^{74} +(-1.73069 - 0.0687106i) q^{75} +10.2586i q^{76} +(2.67782 - 1.95686i) q^{77} +(-0.100394 + 2.52874i) q^{78} -1.72774i q^{79} -2.61378i q^{80} +(8.88687 + 1.42251i) q^{81} -3.95979 q^{82} +16.9550 q^{83} +(-0.120883 + 3.04481i) q^{84} +3.37240i q^{85} +1.25563i q^{86} +(-8.21429 - 0.326118i) q^{87} +(3.60909 + 4.93878i) q^{88} +6.67557i q^{89} +(-0.116682 + 1.46718i) q^{90} -2.97821 q^{91} -0.941216i q^{92} +(13.4441 + 0.533747i) q^{93} +3.45665i q^{94} -5.83105 q^{95} +(-8.60323 - 0.341560i) q^{96} +3.15746 q^{97} +0.490604 q^{98} +(5.21522 + 8.47358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.490604			−0.346909			−0.173455	−	0.984842i	$-0.555493\pi$
$2$	−0.490604			−0.346909			−0.173455	+	0.984842i	$0.555493\pi$
$3$	1.73069	+	0.0687106i	0.999213	+	0.0396701i
$3$	1.73069	+	0.0687106i	0.999213	+	0.0396701i
$4$	−1.75931			−0.879654
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.849081	−	0.0337096i	−0.346636	−	0.0137619i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.84433			0.652069
$9$	2.99056	+	0.237833i	0.996853	+	0.0792777i
$10$			0.490604i			0.155142i
$11$	1.95686	+	2.67782i	0.590014	+	0.807393i
$11$	1.95686	+	2.67782i	0.590014	+	0.807393i
$12$	−3.04481	−	0.120883i	−0.878962	−	0.0348959i
$13$		−	2.97821i		−	0.826006i	−0.910730	−	0.413003i	$-0.864480\pi$
$13$		−	2.97821i		−	0.826006i	0.910730	−	0.413003i	$-0.135520\pi$
$14$			0.490604i			0.131119i
$15$	0.0687106	−	1.73069i	0.0177410	−	0.446862i
$16$	2.61378			0.653445
$17$	−3.37240			−0.817926			−0.408963	−	0.912551i	$-0.634109\pi$
$17$	−3.37240			−0.817926			−0.408963	+	0.912551i	$0.634109\pi$
$18$	−1.46718	−	0.116682i	−0.345817	−	0.0275021i
$19$		−	5.83105i		−	1.33774i	−0.743381	−	0.668868i	$-0.766779\pi$
$19$		−	5.83105i		−	1.33774i	0.743381	−	0.668868i	$-0.233221\pi$
$20$			1.75931i			0.393393i
$21$	0.0687106	−	1.73069i	0.0149939	−	0.377667i
$22$	−0.960040	−	1.31375i	−0.204681	−	0.280092i
$23$			0.534992i			0.111554i	0.998443	+	0.0557768i	$0.0177635\pi$
$23$			0.534992i			0.111554i	−0.998443	+	0.0557768i	$0.982236\pi$
$24$	3.19196	+	0.126725i	0.651556	+	0.0258676i
$25$	−1.00000			−0.200000
$26$			1.46112i			0.286549i
$27$	5.15938	+	0.617098i	0.992923	+	0.118760i
$28$			1.75931i			0.332478i
$29$	−4.74626			−0.881358			−0.440679	−	0.897665i	$-0.645262\pi$
$29$	−4.74626			−0.881358			−0.440679	+	0.897665i	$0.645262\pi$
$30$	−0.0337096	+	0.849081i	−0.00615451	+	0.155020i
$31$	7.76804			1.39518			0.697591	−	0.716496i	$-0.254255\pi$
$31$	7.76804			1.39518			0.697591	+	0.716496i	$0.254255\pi$
$32$	−4.97099			−0.878755
$33$	3.20271	+	4.76892i	0.557521	+	0.830163i
$34$	1.65451			0.283746
$35$	−1.00000			−0.169031
$36$	−5.26131	−	0.418422i	−0.876885	−	0.0697369i
$37$	1.78005			0.292638			0.146319	−	0.989237i	$-0.453257\pi$
$37$	1.78005			0.292638			0.146319	+	0.989237i	$0.453257\pi$
$38$			2.86074i			0.464073i
$39$	0.204634	−	5.15434i	0.0327677	−	0.825356i
$40$		−	1.84433i		−	0.291614i
$41$	8.07126			1.26052			0.630260	−	0.776384i	$-0.282948\pi$
$41$	8.07126			1.26052			0.630260	+	0.776384i	$0.282948\pi$
$42$	−0.0337096	+	0.849081i	−0.00520151	+	0.131016i
$43$		−	2.55936i		−	0.390299i	−0.980774	−	0.195150i	$-0.937481\pi$
$43$		−	2.55936i		−	0.390299i	0.980774	−	0.195150i	$-0.0625192\pi$
$44$	−3.44271	−	4.71111i	−0.519008	−	0.710226i
$45$	0.237833	−	2.99056i	0.0354541	−	0.445806i
$46$		−	0.262469i		−	0.0386989i
$47$		−	7.04571i		−	1.02772i	−0.857873	−	0.513862i	$-0.828215\pi$
$47$		−	7.04571i		−	1.02772i	0.857873	−	0.513862i	$-0.171785\pi$
$48$	4.52364	+	0.179594i	0.652931	+	0.0259222i
$49$	−1.00000			−0.142857
$50$	0.490604			0.0693818
$51$	−5.83656	−	0.231719i	−0.817282	−	0.0324472i
$52$			5.23958i			0.726599i
$53$			3.11078i			0.427299i	0.976910	+	0.213649i	$0.0685350\pi$
$53$			3.11078i			0.427299i	−0.976910	+	0.213649i	$0.931465\pi$
$54$	−2.53121	−	0.302750i	−0.344454	−	0.0411991i
$55$	2.67782	−	1.95686i	0.361077	−	0.263862i
$56$		−	1.84433i		−	0.246459i
$57$	0.400655	−	10.0917i	0.0530681	−	1.33668i
$58$	2.32853			0.305751
$59$		−	5.20131i		−	0.677153i	−0.940939	−	0.338577i	$-0.890055\pi$
$59$		−	5.20131i		−	0.677153i	0.940939	−	0.338577i	$-0.109945\pi$
$60$	−0.120883	+	3.04481i	−0.0156059	+	0.393084i
$61$		−	9.92271i		−	1.27047i	−0.772318	−	0.635237i	$-0.780903\pi$
$61$		−	9.92271i		−	1.27047i	0.772318	−	0.635237i	$-0.219097\pi$
$62$	−3.81103			−0.484001
$63$	0.237833	−	2.99056i	0.0299641	−	0.376775i
$64$	−2.78878			−0.348597
$65$	−2.97821			−0.369401
$66$	−1.57126	−	2.33965i	−0.193409	−	0.287991i
$67$	2.50383			0.305891			0.152946	−	0.988235i	$-0.451124\pi$
$67$	2.50383			0.305891			0.152946	+	0.988235i	$0.451124\pi$
$68$	5.93308			0.719492
$69$	−0.0367596	+	0.925904i	−0.00442534	+	0.111466i
$70$	0.490604			0.0586383
$71$		−	11.7766i		−	1.39762i	−0.715305	−	0.698812i	$-0.753712\pi$
$71$		−	11.7766i		−	1.39762i	0.715305	−	0.698812i	$-0.246288\pi$
$72$	5.51557	+	0.438643i	0.650017	+	0.0516945i
$73$		−	5.53389i		−	0.647693i	−0.946110	−	0.323846i	$-0.895024\pi$
$73$		−	5.53389i		−	0.647693i	0.946110	−	0.323846i	$-0.104976\pi$
$74$	−0.873298			−0.101519
$75$	−1.73069	−	0.0687106i	−0.199843	−	0.00793401i
$76$			10.2586i			1.17674i
$77$	2.67782	−	1.95686i	0.305166	−	0.223004i
$78$	−0.100394	+	2.52874i	−0.0113674	+	0.286323i
$79$		−	1.72774i		−	0.194386i	−0.995266	−	0.0971928i	$-0.969014\pi$
$79$		−	1.72774i		−	0.194386i	0.995266	−	0.0971928i	$-0.0309864\pi$
$80$		−	2.61378i		−	0.292230i
$81$	8.88687	+	1.42251i	0.987430	+	0.158056i
$82$	−3.95979			−0.437286
$83$	16.9550			1.86105			0.930524	−	0.366230i	$-0.119352\pi$
$83$	16.9550			1.86105			0.930524	+	0.366230i	$0.119352\pi$
$84$	−0.120883	+	3.04481i	−0.0131894	+	0.332216i
$85$			3.37240i			0.365788i
$86$			1.25563i			0.135398i
$87$	−8.21429	−	0.326118i	−0.880664	−	0.0349635i
$88$	3.60909	+	4.93878i	0.384730	+	0.526476i
$89$			6.67557i			0.707609i	0.935319	+	0.353805i	$0.115112\pi$
$89$			6.67557i			0.707609i	−0.935319	+	0.353805i	$0.884888\pi$
$90$	−0.116682	+	1.46718i	−0.0122993	+	0.154654i
$91$	−2.97821			−0.312201
$92$		−	0.941216i		−	0.0981285i
$93$	13.4441	+	0.533747i	1.39408	+	0.0553470i
$94$			3.45665i			0.356526i
$95$	−5.83105			−0.598254
$96$	−8.60323	−	0.341560i	−0.878063	−	0.0348603i
$97$	3.15746			0.320592			0.160296	−	0.987069i	$-0.448755\pi$
$97$	3.15746			0.320592			0.160296	+	0.987069i	$0.448755\pi$
$98$	0.490604			0.0495584
$99$	5.21522	+	8.47358i	0.524149	+	0.851627i
$100$	1.75931			0.175931
$101$	−0.271916			−0.0270566			−0.0135283	−	0.999908i	$-0.504306\pi$
$101$	−0.271916			−0.0270566			−0.0135283	+	0.999908i	$0.504306\pi$
$102$	2.86344	+	0.113682i	0.283523	+	0.0112562i
$103$	−13.2038			−1.30101			−0.650503	−	0.759504i	$-0.725442\pi$
$103$	−13.2038			−1.30101			−0.650503	+	0.759504i	$0.725442\pi$
$104$		−	5.49280i		−	0.538613i
$105$	−1.73069	−	0.0687106i	−0.168898	−	0.00670546i
$106$		−	1.52616i		−	0.148234i
$107$	−4.99401			−0.482789			−0.241395	−	0.970427i	$-0.577605\pi$
$107$	−4.99401			−0.482789			−0.241395	+	0.970427i	$0.577605\pi$
$108$	−9.07694	−	1.08566i	−0.873429	−	0.104468i
$109$		−	3.80235i		−	0.364199i	−0.983280	−	0.182100i	$-0.941711\pi$
$109$		−	3.80235i		−	0.364199i	0.983280	−	0.182100i	$-0.0582893\pi$
$110$	−1.31375	+	0.960040i	−0.125261	+	0.0915363i
$111$	3.08071	+	0.122308i	0.292408	+	0.0116090i
$112$		−	2.61378i		−	0.246979i
$113$			19.5958i			1.84342i	0.387881	+	0.921710i	$0.373207\pi$
$113$			19.5958i			1.84342i	−0.387881	+	0.921710i	$0.626793\pi$
$114$	−0.196563	+	4.95104i	−0.0184098	+	0.463707i
$115$	0.534992			0.0498882
$116$	8.35013			0.775290
$117$	0.708316	−	8.90650i	0.0654838	−	0.823406i
$118$			2.55178i			0.234911i
$119$			3.37240i			0.309147i
$120$	0.126725	−	3.19196i	0.0115684	−	0.291385i
$121$	−3.34143	+	10.4802i	−0.303766	+	0.952747i
$122$			4.86812i			0.440739i
$123$	13.9688	+	0.554581i	1.25953	+	0.0500049i
$124$	−13.6664			−1.22728
$125$			1.00000i			0.0894427i
$126$	−0.116682	+	1.46718i	−0.0103948	+	0.130707i
$127$			9.90806i			0.879198i	0.898194	+	0.439599i	$0.144879\pi$
$127$			9.90806i			0.879198i	−0.898194	+	0.439599i	$0.855121\pi$
$128$	11.3102			0.999687
$129$	0.175855	−	4.42946i	0.0154832	−	0.389992i
$130$	1.46112			0.128149
$131$	−13.1997			−1.15326			−0.576630	−	0.817005i	$-0.695633\pi$
$131$	−13.1997			−1.15326			−0.576630	+	0.817005i	$0.695633\pi$
$132$	−5.63456	−	8.39001i	−0.490425	−	0.730256i
$133$	−5.83105			−0.505617
$134$	−1.22839			−0.106116
$135$	0.617098	−	5.15938i	0.0531113	−	0.444049i
$136$	−6.21981			−0.533344
$137$		−	9.29296i		−	0.793951i	−0.917829	−	0.396975i	$-0.870060\pi$
$137$		−	9.29296i		−	0.793951i	0.917829	−	0.396975i	$-0.129940\pi$
$138$	0.0180344	−	0.454252i	0.00153519	−	0.0386685i
$139$			20.8023i			1.76443i	0.470851	+	0.882213i	$0.343947\pi$
$139$			20.8023i			1.76443i	−0.470851	+	0.882213i	$0.656053\pi$
$140$	1.75931			0.148689
$141$	0.484115	−	12.1939i	0.0407698	−	1.02691i
$142$			5.77764i			0.484848i
$143$	7.97510	−	5.82792i	0.666911	−	0.487355i
$144$	7.81666	+	0.621644i	0.651389	+	0.0518036i
$145$			4.74626i			0.394155i
$146$			2.71495i			0.224691i
$147$	−1.73069	−	0.0687106i	−0.142745	−	0.00566715i
$148$	−3.13165			−0.257420
$149$	18.3474			1.50308			0.751538	−	0.659690i	$-0.229312\pi$
$149$	18.3474			1.50308			0.751538	+	0.659690i	$0.229312\pi$
$150$	0.849081	+	0.0337096i	0.0693272	+	0.00275238i
$151$			10.8008i			0.878954i	0.898254	+	0.439477i	$0.144836\pi$
$151$			10.8008i			0.878954i	−0.898254	+	0.439477i	$0.855164\pi$
$152$		−	10.7544i		−	0.872296i
$153$	−10.0853	−	0.802067i	−0.815352	−	0.0648433i
$154$	−1.31375	+	0.960040i	−0.105865	+	0.0773623i
$155$		−	7.76804i		−	0.623944i
$156$	−0.360015	+	9.06808i	−0.0288242	+	0.726028i
$157$	−10.5748			−0.843964			−0.421982	−	0.906604i	$-0.638666\pi$
$157$	−10.5748			−0.843964			−0.421982	+	0.906604i	$0.638666\pi$
$158$			0.847634i			0.0674342i
$159$	−0.213744	+	5.38379i	−0.0169510	+	0.426962i
$160$			4.97099i			0.392991i
$161$	0.534992			0.0421633
$162$	−4.35993	−	0.697887i	−0.342548	−	0.0548312i
$163$	−12.6883			−0.993824			−0.496912	−	0.867801i	$-0.665533\pi$
$163$	−12.6883			−0.993824			−0.496912	+	0.867801i	$0.665533\pi$
$164$	−14.1998			−1.10882
$165$	4.76892	−	3.20271i	0.371260	−	0.249331i
$166$	−8.31816			−0.645615
$167$	−11.8822			−0.919472			−0.459736	−	0.888056i	$-0.652056\pi$
$167$	−11.8822			−0.919472			−0.459736	+	0.888056i	$0.652056\pi$
$168$	0.126725	−	3.19196i	0.00977704	−	0.246265i
$169$	4.13029			0.317714
$170$		−	1.65451i		−	0.126895i
$171$	1.38682	−	17.4381i	0.106053	−	1.33353i
$172$			4.50271i			0.343328i
$173$	7.71148			0.586293			0.293147	−	0.956068i	$-0.405298\pi$
$173$	7.71148			0.586293			0.293147	+	0.956068i	$0.405298\pi$
$174$	4.02996	+	0.159995i	0.305510	+	0.0121292i
$175$			1.00000i			0.0755929i
$176$	5.11479	+	6.99923i	0.385542	+	0.527587i
$177$	0.357385	−	9.00185i	0.0268627	−	0.676620i
$178$		−	3.27506i		−	0.245476i
$179$		−	10.6876i		−	0.798830i	−0.916770	−	0.399415i	$-0.869213\pi$
$179$		−	10.6876i		−	0.798830i	0.916770	−	0.399415i	$-0.130787\pi$
$180$	−0.418422	+	5.26131i	−0.0311873	+	0.392155i
$181$	16.1089			1.19737			0.598683	−	0.800986i	$-0.295691\pi$
$181$	16.1089			1.19737			0.598683	+	0.800986i	$0.295691\pi$
$182$	1.46112			0.108305
$183$	0.681795	−	17.1731i	0.0503998	−	1.26947i
$184$			0.986701i			0.0727406i
$185$		−	1.78005i		−	0.130872i
$186$	−6.59570	−	0.261858i	−0.483620	−	0.0192004i
$187$	−6.59929	−	9.03066i	−0.482588	−	0.660388i
$188$			12.3956i			0.904041i
$189$	0.617098	−	5.15938i	0.0448872	−	0.375290i
$190$	2.86074			0.207540
$191$			21.3291i			1.54332i	0.636034	+	0.771661i	$0.280574\pi$
$191$			21.3291i			1.54332i	−0.636034	+	0.771661i	$0.719426\pi$
$192$	−4.82650	−	0.191619i	−0.348323	−	0.0138289i
$193$			19.7764i			1.42353i	0.702416	+	0.711767i	$0.252105\pi$
$193$			19.7764i			1.42353i	−0.702416	+	0.711767i	$0.747895\pi$
$194$	−1.54906			−0.111216
$195$	−5.15434	−	0.204634i	−0.369110	−	0.0146542i
$196$	1.75931			0.125665
$197$	−14.5481			−1.03651			−0.518255	−	0.855226i	$-0.673418\pi$
$197$	−14.5481			−1.03651			−0.518255	+	0.855226i	$0.673418\pi$
$198$	−2.55860	−	4.15717i	−0.181832	−	0.295437i
$199$	14.8317			1.05139			0.525695	−	0.850673i	$-0.323805\pi$
$199$	14.8317			1.05139			0.525695	+	0.850673i	$0.323805\pi$
$200$	−1.84433			−0.130414
$201$	4.33334	+	0.172039i	0.305651	+	0.0121347i
$202$	0.133403			0.00938619
$203$			4.74626i			0.333122i
$204$	10.2683	+	0.407665i	0.718926	+	0.0285423i
$205$		−	8.07126i		−	0.563721i
$206$	6.47782			0.451331
$207$	−0.127239	+	1.59992i	−0.00884370	+	0.111202i
$208$		−	7.78438i		−	0.539750i
$209$	15.6145	−	11.4105i	1.08008	−	0.789283i
$210$	0.849081	+	0.0337096i	0.0585922	+	0.00232619i
$211$		−	1.71199i		−	0.117858i	−0.998262	−	0.0589290i	$-0.981231\pi$
$211$		−	1.71199i		−	0.117858i	0.998262	−	0.0589290i	$-0.0187686\pi$
$212$		−	5.47282i		−	0.375875i
$213$	0.809176	−	20.3816i	0.0554438	−	1.39652i
$214$	2.45008			0.167484
$215$	−2.55936			−0.174547
$216$	9.51560	+	1.13813i	0.647454	+	0.0774400i
$217$		−	7.76804i		−	0.527329i
$218$			1.86545i			0.126344i
$219$	0.380237	−	9.57743i	0.0256940	−	0.647183i
$220$	−4.71111	+	3.44271i	−0.317623	+	0.232108i
$221$			10.0437i			0.675612i
$222$	−1.51141	−	0.0600048i	−0.101439	−	0.00402726i
$223$	19.0733			1.27724			0.638621	−	0.769521i	$-0.279505\pi$
$223$	19.0733			1.27724			0.638621	+	0.769521i	$0.279505\pi$
$224$			4.97099i			0.332138i
$225$	−2.99056	−	0.237833i	−0.199371	−	0.0158555i
$226$		−	9.61377i		−	0.639499i
$227$	−17.8641			−1.18568			−0.592839	−	0.805321i	$-0.701993\pi$
$227$	−17.8641			−1.18568			−0.592839	+	0.805321i	$0.701993\pi$
$228$	−0.704876	+	17.7545i	−0.0466815	+	1.17582i
$229$	−19.0429			−1.25839			−0.629196	−	0.777247i	$-0.716616\pi$
$229$	−19.0429			−1.25839			−0.629196	+	0.777247i	$0.716616\pi$
$230$	−0.262469			−0.0173067
$231$	4.76892	−	3.20271i	0.313772	−	0.210723i
$232$	−8.75367			−0.574706
$233$	−23.6456			−1.54907			−0.774536	−	0.632530i	$-0.782016\pi$
$233$	−23.6456			−1.54907			−0.774536	+	0.632530i	$0.782016\pi$
$234$	−0.347502	+	4.36956i	−0.0227169	+	0.285647i
$235$	−7.04571			−0.459612
$236$			9.15071i			0.595661i
$237$	0.118714	−	2.99017i	0.00771129	−	0.194233i
$238$		−	1.65451i		−	0.107246i
$239$	7.11125			0.459988			0.229994	−	0.973192i	$-0.426129\pi$
$239$	7.11125			0.459988			0.229994	+	0.973192i	$0.426129\pi$
$240$	0.179594	−	4.52364i	0.0115928	−	0.292000i
$241$			13.3092i			0.857322i	0.903465	+	0.428661i	$0.141015\pi$
$241$			13.3092i			0.857322i	−0.903465	+	0.428661i	$0.858985\pi$
$242$	1.63932	−	5.14163i	0.105379	−	0.330516i
$243$	15.2827	+	3.07254i	0.980383	+	0.197103i
$244$			17.4571i			1.11758i
$245$			1.00000i			0.0638877i
$246$	−6.85316	−	0.272079i	−0.436941	−	0.0173471i
$247$	−17.3661			−1.10498
$248$	14.3268			0.909755
$249$	29.3437	+	1.16498i	1.85958	+	0.0738279i
$250$		−	0.490604i		−	0.0310285i
$251$		−	3.28171i		−	0.207140i	−0.994622	−	0.103570i	$-0.966973\pi$
$251$		−	3.28171i		−	0.207140i	0.994622	−	0.103570i	$-0.0330266\pi$
$252$	−0.418422	+	5.26131i	−0.0263581	+	0.331432i
$253$	−1.43261	+	1.04690i	−0.0900675	+	0.0658182i
$254$		−	4.86093i		−	0.305002i
$255$	−0.231719	+	5.83656i	−0.0145108	+	0.365500i
$256$	0.0287489			0.00179681
$257$		−	13.2070i		−	0.823832i	−0.911222	−	0.411916i	$-0.864860\pi$
$257$		−	13.2070i		−	0.823832i	0.911222	−	0.411916i	$-0.135140\pi$
$258$	−0.0862752	+	2.17311i	−0.00537126	+	0.135292i
$259$		−	1.78005i		−	0.110607i
$260$	5.23958			0.324945
$261$	−14.1940	−	1.12882i	−0.878584	−	0.0698720i
$262$	6.47580			0.400077
$263$	−24.2692			−1.49650			−0.748251	−	0.663416i	$-0.769106\pi$
$263$	−24.2692			−1.49650			−0.748251	+	0.663416i	$0.769106\pi$
$264$	5.90686	+	8.79547i	0.363542	+	0.541324i
$265$	3.11078			0.191094
$266$	2.86074			0.175403
$267$	−0.458682	+	11.5533i	−0.0280709	+	0.707052i
$268$	−4.40501			−0.269079
$269$			25.6227i			1.56225i	0.624377	+	0.781123i	$0.285353\pi$
$269$			25.6227i			1.56225i	−0.624377	+	0.781123i	$0.714647\pi$
$270$	−0.302750	+	2.53121i	−0.0184248	+	0.154045i
$271$			16.7313i			1.01635i	0.861253	+	0.508177i	$0.169681\pi$
$271$			16.7313i			1.01635i	−0.861253	+	0.508177i	$0.830319\pi$
$272$	−8.81470			−0.534470
$273$	−5.15434	−	0.204634i	−0.311955	−	0.0123850i
$274$			4.55916i			0.275429i
$275$	−1.95686	−	2.67782i	−0.118003	−	0.161479i
$276$	0.0646715	−	1.62895i	0.00389276	−	0.0980513i
$277$		−	9.99712i		−	0.600668i	−0.953834	−	0.300334i	$-0.902902\pi$
$277$		−	9.99712i		−	0.600668i	0.953834	−	0.300334i	$-0.0970982\pi$
$278$		−	10.2057i		−	0.612095i
$279$	23.2308	+	1.84750i	1.39079	+	0.110607i
$280$	−1.84433			−0.110220
$281$	32.1240			1.91636			0.958179	−	0.286170i	$-0.0923821\pi$
$281$	32.1240			1.91636			0.958179	+	0.286170i	$0.0923821\pi$
$282$	−0.237509	+	5.98238i	−0.0141434	+	0.356246i
$283$			23.4182i			1.39207i	0.718009	+	0.696034i	$0.245054\pi$
$283$			23.4182i			1.39207i	−0.718009	+	0.696034i	$0.754946\pi$
$284$			20.7187i			1.22943i
$285$	−10.0917	−	0.400655i	−0.597783	−	0.0237328i
$286$	−3.91261	+	2.85920i	−0.231358	+	0.169068i
$287$		−	8.07126i		−	0.476431i
$288$	−14.8660	−	1.18227i	−0.875989	−	0.0696657i
$289$	−5.62695			−0.330997
$290$		−	2.32853i		−	0.136736i
$291$	5.46458	+	0.216951i	0.320340	+	0.0127179i
$292$			9.73582i			0.569746i
$293$	−23.2710			−1.35951			−0.679753	−	0.733441i	$-0.737913\pi$
$293$	−23.2710			−1.35951			−0.679753	+	0.733441i	$0.737913\pi$
$294$	0.849081	+	0.0337096i	0.0495194	+	0.00196599i
$295$	−5.20131			−0.302832
$296$	3.28300			0.190820
$297$	8.44369	+	15.0235i	0.489952	+	0.871749i
$298$	−9.00129			−0.521431
$299$	1.59332			0.0921439
$300$	3.04481	+	0.120883i	0.175792	+	0.00697919i
$301$	−2.55936			−0.147519
$302$		−	5.29890i		−	0.304917i
$303$	−0.470601	−	0.0186835i	−0.0270353	−	0.00107334i
$304$		−	15.2411i		−	0.874137i
$305$	−9.92271			−0.568173
$306$	4.94790	+	0.393497i	0.282853	+	0.0224947i
$307$			32.6253i			1.86203i	0.364985	+	0.931013i	$0.381074\pi$
$307$			32.6253i			1.86203i	−0.364985	+	0.931013i	$0.618926\pi$
$308$	−4.71111	+	3.44271i	−0.268440	+	0.196167i
$309$	−22.8516	−	0.907239i	−1.29998	−	0.0516110i
$310$			3.81103i			0.216452i
$311$		−	8.19185i		−	0.464517i	−0.972654	−	0.232259i	$-0.925388\pi$
$311$		−	8.19185i		−	0.464517i	0.972654	−	0.232259i	$-0.0746116\pi$
$312$	0.377413	−	9.50631i	0.0213668	−	0.538189i
$313$	−8.64904			−0.488873			−0.244436	−	0.969665i	$-0.578603\pi$
$313$	−8.64904			−0.488873			−0.244436	+	0.969665i	$0.578603\pi$
$314$	5.18806			0.292779
$315$	−2.99056	−	0.237833i	−0.168499	−	0.0134004i
$316$			3.03962i			0.170992i
$317$		−	10.0960i		−	0.567045i	−0.958966	−	0.283523i	$-0.908497\pi$
$317$		−	10.0960i		−	0.567045i	0.958966	−	0.283523i	$-0.0915031\pi$
$318$	0.104863	−	2.64131i	0.00588044	−	0.148117i
$319$	−9.28775	−	12.7096i	−0.520014	−	0.711602i
$320$			2.78878i			0.155897i
$321$	−8.64307	−	0.343141i	−0.482409	−	0.0191523i
$322$	−0.262469			−0.0146268
$323$			19.6646i			1.09417i
$324$	−15.6347	−	2.50263i	−0.868597	−	0.139035i
$325$			2.97821i			0.165201i
$326$	6.22492			0.344767
$327$	0.261262	−	6.58068i	0.0144478	−	0.363913i
$328$	14.8861			0.821946
$329$	−7.04571			−0.388443
$330$	−2.33965	+	1.57126i	−0.128794	+	0.0864951i
$331$	−14.9283			−0.820536			−0.410268	−	0.911965i	$-0.634565\pi$
$331$	−14.9283			−0.820536			−0.410268	+	0.911965i	$0.634565\pi$
$332$	−29.8290			−1.63708
$333$	5.32334	+	0.423354i	0.291717	+	0.0231997i
$334$	5.82945			0.318973
$335$		−	2.50383i		−	0.136799i
$336$	0.179594	−	4.52364i	0.00979768	−	0.246785i
$337$			26.5132i			1.44427i	0.691753	+	0.722134i	$0.256839\pi$
$337$			26.5132i			1.44427i	−0.691753	+	0.722134i	$0.743161\pi$
$338$	−2.02633			−0.110218
$339$	−1.34644	+	33.9142i	−0.0731286	+	1.84197i
$340$		−	5.93308i		−	0.321767i
$341$	15.2009	+	20.8014i	0.823177	+	1.12646i
$342$	−0.680377	+	8.55520i	−0.0367906	+	0.462612i
$343$			1.00000i			0.0539949i
$344$		−	4.72031i		−	0.254502i
$345$	0.925904	+	0.0367596i	0.0498490	+	0.00197907i
$346$	−3.78328			−0.203390
$347$	20.7590			1.11440			0.557201	−	0.830378i	$-0.311875\pi$
$347$	20.7590			1.11440			0.557201	+	0.830378i	$0.311875\pi$
$348$	14.4515	+	0.573742i	0.774680	+	0.0307558i
$349$		−	10.5536i		−	0.564922i	−0.959279	−	0.282461i	$-0.908849\pi$
$349$		−	10.5536i		−	0.564922i	0.959279	−	0.282461i	$-0.0911508\pi$
$350$		−	0.490604i		−	0.0262239i
$351$	1.83784	−	15.3657i	0.0980969	−	0.820160i
$352$	−9.72751	−	13.3114i	−0.518478	−	0.709501i
$353$		−	30.1161i		−	1.60292i	−0.598049	−	0.801459i	$-0.704057\pi$
$353$		−	30.1161i		−	1.60292i	0.598049	−	0.801459i	$-0.295943\pi$
$354$	−0.175334	+	4.41634i	−0.00931892	+	0.234726i
$355$	−11.7766			−0.625036
$356$		−	11.7444i		−	0.622451i
$357$	−0.231719	+	5.83656i	−0.0122639	+	0.308904i
$358$			5.24338i			0.277121i
$359$	6.60528			0.348613			0.174307	−	0.984691i	$-0.444232\pi$
$359$	6.60528			0.348613			0.174307	+	0.984691i	$0.444232\pi$
$360$	0.438643	−	5.51557i	0.0231185	−	0.290696i
$361$	−15.0012			−0.789536
$362$	−7.90309			−0.415377
$363$	−6.50307	+	17.9084i	−0.341323	+	0.939946i
$364$	5.23958			0.274629
$365$	−5.53389			−0.289657
$366$	−0.334491	+	8.42519i	−0.0174841	+	0.440392i
$367$	19.1067			0.997363			0.498682	−	0.866785i	$-0.333818\pi$
$367$	19.1067			0.997363			0.498682	+	0.866785i	$0.333818\pi$
$368$			1.39835i			0.0728941i
$369$	24.1376	+	1.91961i	1.25655	+	0.0999310i
$370$			0.873298i			0.0454006i
$371$	3.11078			0.161504
$372$	−23.6522	−	0.939025i	−1.22631	−	0.0486862i
$373$		−	9.08731i		−	0.470523i	−0.971932	−	0.235262i	$-0.924405\pi$
$373$		−	9.08731i		−	0.470523i	0.971932	−	0.235262i	$-0.0755947\pi$
$374$	3.23764	+	4.43048i	0.167414	+	0.229094i
$375$	−0.0687106	+	1.73069i	−0.00354820	+	0.0893723i
$376$		−	12.9946i		−	0.670146i
$377$			14.1353i			0.728007i
$378$	−0.302750	+	2.53121i	−0.0155718	+	0.130191i
$379$	11.7940			0.605817			0.302908	−	0.953020i	$-0.402042\pi$
$379$	11.7940			0.605817			0.302908	+	0.953020i	$0.402042\pi$
$380$	10.2586			0.526256
$381$	−0.680788	+	17.1478i	−0.0348779	+	0.878506i
$382$		−	10.4641i		−	0.535392i
$383$		−	34.7413i		−	1.77520i	−0.460616	−	0.887599i	$-0.652372\pi$
$383$		−	34.7413i		−	1.77520i	0.460616	−	0.887599i	$-0.347628\pi$
$384$	19.5744	+	0.777128i	0.998900	+	0.0396576i
$385$	−1.95686	−	2.67782i	−0.0997306	−	0.136474i
$386$		−	9.70236i		−	0.493837i
$387$	0.608701	−	7.65392i	0.0309420	−	0.389071i
$388$	−5.55495			−0.282010
$389$			1.81931i			0.0922426i	0.998936	+	0.0461213i	$0.0146861\pi$
$389$			1.81931i			0.0922426i	−0.998936	+	0.0461213i	$0.985314\pi$
$390$	2.52874	+	0.100394i	0.128048	+	0.00508366i
$391$		−	1.80420i		−	0.0912425i
$392$	−1.84433			−0.0931527
$393$	−22.8445	−	0.906957i	−1.15235	−	0.0457499i
$394$	7.13736			0.359575
$395$	−1.72774			−0.0869319
$396$	−9.17517	−	14.9076i	−0.461070	−	0.749137i
$397$	18.8027			0.943681			0.471841	−	0.881684i	$-0.343590\pi$
$397$	18.8027			0.943681			0.471841	+	0.881684i	$0.343590\pi$
$398$	−7.27648			−0.364737
$399$	−10.0917	−	0.400655i	−0.505219	−	0.0200578i
$400$	−2.61378			−0.130689
$401$			23.5966i			1.17836i	0.808003	+	0.589178i	$0.200548\pi$
$401$			23.5966i			1.17836i	−0.808003	+	0.589178i	$0.799452\pi$
$402$	−2.12595	−	0.0844032i	−0.106033	−	0.00420965i
$403$		−	23.1348i		−	1.15243i
$404$	0.478384			0.0238005
$405$	1.42251	−	8.88687i	0.0706849	−	0.441592i
$406$		−	2.32853i		−	0.115563i
$407$	3.48330	+	4.76665i	0.172661	+	0.236274i
$408$	−10.7645	−	0.427367i	−0.532924	−	0.0211578i
$409$			36.9496i			1.82704i	0.406795	+	0.913519i	$0.366646\pi$
$409$			36.9496i			1.82704i	−0.406795	+	0.913519i	$0.633354\pi$
$410$			3.95979i			0.195560i
$411$	0.638524	−	16.0832i	0.0314961	−	0.793326i
$412$	23.2295			1.14444
$413$	−5.20131			−0.255940
$414$	0.0624238	−	0.784928i	0.00306796	−	0.0385771i
$415$		−	16.9550i		−	0.832286i
$416$			14.8046i			0.725857i
$417$	−1.42934	+	36.0022i	−0.0699949	+	1.76304i
$418$	−7.66053	+	5.59805i	−0.374689	+	0.273809i
$419$			22.1898i			1.08404i	0.840365	+	0.542021i	$0.182341\pi$
$419$			22.1898i			1.08404i	−0.840365	+	0.542021i	$0.817659\pi$
$420$	3.04481	+	0.120883i	0.148572	+	0.00589849i
$421$	−3.68743			−0.179714			−0.0898571	−	0.995955i	$-0.528641\pi$
$421$	−3.68743			−0.179714			−0.0898571	+	0.995955i	$0.528641\pi$
$422$			0.839907i			0.0408860i
$423$	1.67570	−	21.0706i	0.0814755	−	1.02449i
$424$			5.73731i			0.278628i
$425$	3.37240			0.163585
$426$	−0.396985	+	9.99928i	−0.0192340	+	0.484467i
$427$	−9.92271			−0.480194
$428$	8.78601			0.424688
$429$	14.2028	−	9.53834i	0.685720	−	0.460515i
$430$	1.25563			0.0605520
$431$	4.42854			0.213315			0.106658	−	0.994296i	$-0.465985\pi$
$431$	4.42854			0.213315			0.106658	+	0.994296i	$0.465985\pi$
$432$	13.4855	+	1.61296i	0.648821	+	0.0776035i
$433$	−6.77641			−0.325653			−0.162827	−	0.986655i	$-0.552061\pi$
$433$	−6.77641			−0.325653			−0.162827	+	0.986655i	$0.552061\pi$
$434$			3.81103i			0.182935i
$435$	−0.326118	+	8.21429i	−0.0156362	+	0.393845i
$436$			6.68951i			0.320369i
$437$	3.11957			0.149229
$438$	−0.186545	+	4.69872i	−0.00891349	+	0.224514i
$439$		−	11.3056i		−	0.539587i	−0.962918	−	0.269793i	$-0.913045\pi$
$439$		−	11.3056i		−	0.539587i	0.962918	−	0.269793i	$-0.0869554\pi$
$440$	4.93878	−	3.60909i	0.235447	−	0.172057i
$441$	−2.99056	−	0.237833i	−0.142408	−	0.0113254i
$442$		−	4.92747i		−	0.234376i
$443$			4.03192i			0.191562i	0.995402	+	0.0957812i	$0.0305349\pi$
$443$			4.03192i			0.191562i	−0.995402	+	0.0957812i	$0.969465\pi$
$444$	−5.41992	−	0.215178i	−0.257218	−	0.0102119i
$445$	6.67557			0.316452
$446$	−9.35743			−0.443087
$447$	31.7536	+	1.26066i	1.50189	+	0.0596271i
$448$			2.78878i			0.131757i
$449$			18.8092i			0.887660i	0.896111	+	0.443830i	$0.146381\pi$
$449$			18.8092i			0.887660i	−0.896111	+	0.443830i	$0.853619\pi$
$450$	1.46718	+	0.116682i	0.0691634	+	0.00550043i
$451$	15.7943	+	21.6134i	0.743724	+	1.01773i
$452$		−	34.4751i		−	1.62157i
$453$	−0.742127	+	18.6928i	−0.0348682	+	0.878262i
$454$	8.76417			0.411323
$455$			2.97821i			0.139620i
$456$	0.738940	−	18.6125i	0.0346040	−	0.871609i
$457$		−	17.7621i		−	0.830877i	−0.909621	−	0.415439i	$-0.863628\pi$
$457$		−	17.7621i		−	0.830877i	0.909621	−	0.415439i	$-0.136372\pi$
$458$	9.34252			0.436548
$459$	−17.3995	−	2.08110i	−0.812138	−	0.0971373i
$460$	−0.941216			−0.0438844
$461$	−13.0400			−0.607331			−0.303666	−	0.952779i	$-0.598211\pi$
$461$	−13.0400			−0.607331			−0.303666	+	0.952779i	$0.598211\pi$
$462$	−2.33965	+	1.57126i	−0.108850	+	0.0731017i
$463$	17.0271			0.791315			0.395658	−	0.918398i	$-0.370517\pi$
$463$	17.0271			0.791315			0.395658	+	0.918398i	$0.370517\pi$
$464$	−12.4057			−0.575919
$465$	0.533747	−	13.4441i	0.0247519	−	0.623453i
$466$	11.6006			0.537387
$467$			8.69534i			0.402372i	0.979553	+	0.201186i	$0.0644796\pi$
$467$			8.69534i			0.402372i	−0.979553	+	0.201186i	$0.935520\pi$
$468$	−1.24615	+	15.6693i	−0.0576031	+	0.724313i
$469$		−	2.50383i		−	0.115616i
$470$	3.45665			0.159443
$471$	−18.3018	−	0.726604i	−0.843300	−	0.0334801i
$472$		−	9.59294i		−	0.441551i
$473$	6.85351	−	5.00830i	0.315125	−	0.230282i
$474$	−0.0582414	+	1.46699i	−0.00267512	+	0.0673811i
$475$			5.83105i			0.267547i
$476$		−	5.93308i		−	0.271942i
$477$	−0.739847	+	9.30297i	−0.0338752	+	0.425954i
$478$	−3.48880			−0.159574
$479$	−11.2518			−0.514109			−0.257055	−	0.966397i	$-0.582752\pi$
$479$	−11.2518			−0.514109			−0.257055	+	0.966397i	$0.582752\pi$
$480$	−0.341560	+	8.60323i	−0.0155900	+	0.392682i
$481$		−	5.30135i		−	0.241721i
$482$		−	6.52955i		−	0.297413i
$483$	0.925904	+	0.0367596i	0.0421301	+	0.00167262i
$484$	5.87860	−	18.4379i	0.267209	−	0.838087i
$485$		−	3.15746i		−	0.143373i
$486$	−7.49772	−	1.50740i	−0.340104	−	0.0683769i
$487$	−4.04149			−0.183137			−0.0915687	−	0.995799i	$-0.529188\pi$
$487$	−4.04149			−0.183137			−0.0915687	+	0.995799i	$0.529188\pi$
$488$		−	18.3008i		−	0.828436i
$489$	−21.9595	−	0.871820i	−0.993042	−	0.0394251i
$490$		−	0.490604i		−	0.0221632i
$491$	17.3239			0.781817			0.390909	−	0.920429i	$-0.372161\pi$
$491$	17.3239			0.781817			0.390909	+	0.920429i	$0.372161\pi$
$492$	−24.5755	−	0.975679i	−1.10795	−	0.0439870i
$493$	16.0063			0.720886
$494$	8.51986			0.383327
$495$	8.47358	−	5.21522i	0.380859	−	0.234407i
$496$	20.3040			0.911675
$497$	−11.7766			−0.528252
$498$	−14.3961	−	0.571546i	−0.645106	−	0.0256116i
$499$	−40.7534			−1.82437			−0.912187	−	0.409773i	$-0.865608\pi$
$499$	−40.7534			−1.82437			−0.912187	+	0.409773i	$0.865608\pi$
$500$		−	1.75931i		−	0.0786787i
$501$	−20.5644	−	0.816433i	−0.918749	−	0.0364755i
$502$			1.61002i			0.0718587i
$503$	4.84131			0.215863			0.107932	−	0.994158i	$-0.465577\pi$
$503$	4.84131			0.215863			0.107932	+	0.994158i	$0.465577\pi$
$504$	0.438643	−	5.51557i	0.0195387	−	0.245683i
$505$			0.271916i			0.0121001i
$506$	0.702844	−	0.513614i	0.0312452	−	0.0228329i
$507$	7.14823	+	0.283794i	0.317464	+	0.0126037i
$508$		−	17.4313i		−	0.773390i
$509$			15.5735i			0.690285i	0.938550	+	0.345142i	$0.112169\pi$
$509$			15.5735i			0.690285i	−0.938550	+	0.345142i	$0.887831\pi$
$510$	0.113682	−	2.86344i	0.00503394	−	0.126795i
$511$	−5.53389			−0.244805
$512$	−22.6344			−1.00031
$513$	3.59833	−	30.0846i	0.158870	−	1.32827i
$514$			6.47942i			0.285795i
$515$			13.2038i			0.581828i
$516$	−0.309384	+	7.79278i	−0.0136198	+	0.343058i
$517$	18.8671	−	13.7874i	0.829776	−	0.606371i
$518$			0.873298i			0.0383705i
$519$	13.3462	+	0.529860i	0.585832	+	0.0232583i
$520$	−5.49280			−0.240875
$521$		−	12.2802i		−	0.538005i	−0.963140	−	0.269002i	$-0.913306\pi$
$521$		−	12.2802i		−	0.538005i	0.963140	−	0.269002i	$-0.0866939\pi$
$522$	6.96361	+	0.553802i	0.304789	+	0.0242392i
$523$		−	0.545475i		−	0.0238519i	−0.999929	−	0.0119260i	$-0.996204\pi$
$523$		−	0.545475i		−	0.0238519i	0.999929	−	0.0119260i	$-0.00379624\pi$
$524$	23.2223			1.01447
$525$	−0.0687106	+	1.73069i	−0.00299878	+	0.0755334i
$526$	11.9065			0.519150
$527$	−26.1969			−1.14116
$528$	8.37119	+	12.4649i	0.364309	+	0.542466i
$529$	22.7138			0.987556
$530$	−1.52616			−0.0662922
$531$	1.23704	−	15.5548i	0.0536831	−	0.675022i
$532$	10.2586			0.444768
$533$		−	24.0379i		−	1.04120i
$534$	0.225031	−	5.66810i	0.00973805	−	0.245283i
$535$			4.99401i			0.215910i
$536$	4.61789			0.199462
$537$	0.734352	−	18.4969i	0.0316896	−	0.798201i
$538$		−	12.5706i		−	0.541957i
$539$	−1.95686	−	2.67782i	−0.0842878	−	0.115342i
$540$	−1.08566	+	9.07694i	−0.0467196	+	0.390609i
$541$		−	35.1484i		−	1.51115i	−0.655063	−	0.755574i	$-0.727358\pi$
$541$		−	35.1484i		−	1.51115i	0.655063	−	0.755574i	$-0.272642\pi$
$542$		−	8.20844i		−	0.352583i
$543$	27.8795	+	1.10685i	1.19642	+	0.0474996i
$544$	16.7641			0.718757
$545$	−3.80235			−0.162875
$546$	2.52874	+	0.100394i	0.108220	+	0.00429648i
$547$		−	20.3182i		−	0.868745i	−0.900733	−	0.434373i	$-0.856970\pi$
$547$		−	20.3182i		−	0.868745i	0.900733	−	0.434373i	$-0.143030\pi$
$548$			16.3492i			0.698402i
$549$	2.35995	−	29.6744i	0.100720	−	1.26647i
$550$	0.960040	+	1.31375i	0.0409363	+	0.0560184i
$551$			27.6757i			1.17902i
$552$	−0.0677968	+	1.70767i	−0.00288562	+	0.0726833i
$553$	−1.72774			−0.0734709
$554$			4.90462i			0.208377i
$555$	0.122308	−	3.08071i	0.00519169	−	0.130769i
$556$		−	36.5976i		−	1.55208i
$557$	−2.47926			−0.105050			−0.0525249	−	0.998620i	$-0.516727\pi$
$557$	−2.47926			−0.105050			−0.0525249	+	0.998620i	$0.516727\pi$
$558$	−11.3971	−	0.906389i	−0.482478	−	0.0383705i
$559$	−7.62231			−0.322389
$560$	−2.61378			−0.110452
$561$	−10.8008	−	16.0827i	−0.456011	−	0.679012i
$562$	−15.7602			−0.664802
$563$	15.9404			0.671810			0.335905	−	0.941896i	$-0.390958\pi$
$563$	15.9404			0.671810			0.335905	+	0.941896i	$0.390958\pi$
$564$	−0.851708	+	21.4529i	−0.0358634	+	0.903329i
$565$	19.5958			0.824402
$566$		−	11.4891i		−	0.482921i
$567$	1.42251	−	8.88687i	0.0597397	−	0.373213i
$568$		−	21.7199i		−	0.911347i
$569$	45.4243			1.90429			0.952143	−	0.305654i	$-0.0988751\pi$
$569$	45.4243			1.90429			0.952143	+	0.305654i	$0.0988751\pi$
$570$	4.95104	+	0.196563i	0.207376	+	0.00823311i
$571$		−	2.02258i		−	0.0846424i	−0.999104	−	0.0423212i	$-0.986525\pi$
$571$		−	2.02258i		−	0.0846424i	0.999104	−	0.0423212i	$-0.0134753\pi$
$572$	−14.0307	+	10.2531i	−0.586651	+	0.428704i
$573$	−1.46554	+	36.9141i	−0.0612237	+	1.54211i
$574$			3.95979i			0.165278i
$575$		−	0.534992i		−	0.0223107i
$576$	−8.34000	−	0.663263i	−0.347500	−	0.0276360i
$577$	31.3943			1.30696			0.653482	−	0.756942i	$-0.273308\pi$
$577$	31.3943			1.30696			0.653482	+	0.756942i	$0.273308\pi$
$578$	2.76060			0.114826
$579$	−1.35885	+	34.2267i	−0.0564717	+	1.42241i
$580$		−	8.35013i		−	0.346720i
$581$		−	16.9550i		−	0.703410i
$582$	−2.68094	−	0.106437i	−0.111129	−	0.00441196i
$583$	−8.33011	+	6.08735i	−0.344998	+	0.252112i
$584$		−	10.2063i		−	0.422340i
$585$	−8.90650	−	0.708316i	−0.368238	−	0.0292853i
$586$	11.4168			0.471625
$587$		−	1.51800i		−	0.0626548i	−0.999509	−	0.0313274i	$-0.990027\pi$
$587$		−	1.51800i		−	0.0626548i	0.999509	−	0.0313274i	$-0.00997345\pi$
$588$	3.04481	+	0.120883i	0.125566	+	0.00498513i
$589$		−	45.2959i		−	1.86638i
$590$	2.55178			0.105055
$591$	−25.1782	−	0.999609i	−1.03569	−	0.0411184i
$592$	4.65266			0.191223
$593$	−17.8674			−0.733725			−0.366862	−	0.930275i	$-0.619568\pi$
$593$	−17.8674			−0.733725			−0.366862	+	0.930275i	$0.619568\pi$
$594$	−4.14250	−	7.37056i	−0.169969	−	0.302418i
$595$	3.37240			0.138255
$596$	−32.2787			−1.32219
$597$	25.6690	+	1.01909i	1.05056	+	0.0417087i
$598$	−0.781687			−0.0319655
$599$		−	19.6140i		−	0.801406i	−0.916208	−	0.400703i	$-0.868766\pi$
$599$		−	19.6140i		−	0.801406i	0.916208	−	0.400703i	$-0.131234\pi$
$600$	−3.19196	−	0.126725i	−0.130311	−	0.00517352i
$601$		−	17.5947i		−	0.717703i	−0.933395	−	0.358851i	$-0.883168\pi$
$601$		−	17.5947i		−	0.717703i	0.933395	−	0.358851i	$-0.116832\pi$
$602$	1.25563			0.0511757
$603$	7.48784	+	0.595493i	0.304929	+	0.0242504i
$604$		−	19.0019i		−	0.773176i
$605$	10.4802	+	3.34143i	0.426081	+	0.135848i
$606$	0.230879	+	0.00916618i	0.00937880	+	0.000372351i
$607$		−	11.1294i		−	0.451730i	−0.974159	−	0.225865i	$-0.927479\pi$
$607$		−	11.1294i		−	0.451730i	0.974159	−	0.225865i	$-0.0725208\pi$
$608$			28.9861i			1.17554i
$609$	−0.326118	+	8.21429i	−0.0132150	+	0.332860i
$610$	4.86812			0.197104
$611$	−20.9836			−0.848905
$612$	17.7432	+	1.41108i	0.717227	+	0.0570397i
$613$		−	13.9450i		−	0.563232i	−0.959527	−	0.281616i	$-0.909130\pi$
$613$		−	13.9450i		−	0.563232i	0.959527	−	0.281616i	$-0.0908705\pi$
$614$		−	16.0061i		−	0.645954i
$615$	0.554581	−	13.9688i	0.0223629	−	0.563278i
$616$	4.93878	−	3.60909i	0.198989	−	0.145414i
$617$		−	43.8916i		−	1.76701i	−0.468421	−	0.883505i	$-0.655177\pi$
$617$		−	43.8916i		−	1.76701i	0.468421	−	0.883505i	$-0.344823\pi$
$618$	11.2111	+	0.445094i	0.450976	+	0.0179043i
$619$	40.6225			1.63275			0.816377	−	0.577519i	$-0.195979\pi$
$619$	40.6225			1.63275			0.816377	+	0.577519i	$0.195979\pi$
$620$			13.6664i			0.548855i
$621$	−0.330142	+	2.76023i	−0.0132481	+	0.110764i
$622$			4.01895i			0.161145i
$623$	6.67557			0.267451
$624$	0.534869	−	13.4723i	0.0214119	−	0.539325i
$625$	1.00000			0.0400000
$626$	4.24325			0.169594
$627$	27.8079	−	18.6752i	1.11054	−	0.745815i
$628$	18.6044			0.742397
$629$	−6.00303			−0.239356
$630$	1.46718	+	0.116682i	0.0584538	+	0.00464871i
$631$	−11.5367			−0.459268			−0.229634	−	0.973277i	$-0.573753\pi$
$631$	−11.5367			−0.459268			−0.229634	+	0.973277i	$0.573753\pi$
$632$		−	3.18652i		−	0.126753i
$633$	0.117632	−	2.96291i	0.00467544	−	0.117765i
$634$			4.95311i			0.196713i
$635$	9.90806			0.393189
$636$	0.376041	−	9.47175i	0.0149110	−	0.375579i
$637$			2.97821i			0.118001i
$638$	4.55660	+	6.23539i	0.180398	+	0.246861i
$639$	2.80086	−	35.2186i	0.110800	−	1.39323i
$640$		−	11.3102i		−	0.447074i
$641$			0.638739i			0.0252287i	0.999920	+	0.0126143i	$0.00401537\pi$
$641$			0.638739i			0.0252287i	−0.999920	+	0.0126143i	$0.995985\pi$
$642$	4.24032	+	0.168346i	0.167352	+	0.00664410i
$643$	6.10948			0.240934			0.120467	−	0.992717i	$-0.461561\pi$
$643$	6.10948			0.240934			0.120467	+	0.992717i	$0.461561\pi$
$644$	−0.941216			−0.0370891
$645$	−4.42946	−	0.175855i	−0.174410	−	0.00692429i
$646$		−	9.64753i		−	0.379577i
$647$			44.1280i			1.73485i	0.497567	+	0.867425i	$0.334227\pi$
$647$			44.1280i			1.73485i	−0.497567	+	0.867425i	$0.665773\pi$
$648$	16.3903	+	2.62357i	0.643873	+	0.103064i
$649$	13.9282	−	10.1782i	0.546729	−	0.399530i
$650$		−	1.46112i		−	0.0573098i
$651$	0.533747	−	13.4441i	0.0209192	−	0.526914i
$652$	22.3226			0.874221
$653$			9.92004i			0.388201i	0.980982	+	0.194101i	$0.0621788\pi$
$653$			9.92004i			0.388201i	−0.980982	+	0.194101i	$0.937821\pi$
$654$	−0.128176	+	3.22851i	−0.00501208	+	0.126245i
$655$			13.1997i			0.515754i
$656$	21.0965			0.823680
$657$	1.31614	−	16.5494i	0.0513476	−	0.645654i
$658$	3.45665			0.134754
$659$	−35.5133			−1.38340			−0.691701	−	0.722184i	$-0.743138\pi$
$659$	−35.5133			−1.38340			−0.691701	+	0.722184i	$0.743138\pi$
$660$	−8.39001	+	5.63456i	−0.326581	+	0.219325i
$661$	30.1589			1.17305			0.586523	−	0.809932i	$-0.300496\pi$
$661$	30.1589			1.17305			0.586523	+	0.809932i	$0.300496\pi$
$662$	7.32390			0.284651
$663$	−0.690108	+	17.3825i	−0.0268016	+	0.675080i
$664$	31.2705			1.21353
$665$			5.83105i			0.226119i
$666$	−2.61165	−	0.207699i	−0.101199	−	0.00804818i
$667$		−	2.53921i		−	0.0983186i
$668$	20.9045			0.808818
$669$	33.0099	+	1.31054i	1.27624	+	0.0506683i
$670$			1.22839i			0.0474567i
$671$	26.5712	−	19.4173i	1.02577	−	0.749597i
$672$	−0.341560	+	8.60323i	−0.0131759	+	0.331877i
$673$			4.72241i			0.182035i	0.995849	+	0.0910177i	$0.0290120\pi$
$673$			4.72241i			0.182035i	−0.995849	+	0.0910177i	$0.970988\pi$
$674$		−	13.0075i		−	0.501030i
$675$	−5.15938	−	0.617098i	−0.198585	−	0.0237521i
$676$	−7.26644			−0.279479
$677$	−17.6564			−0.678589			−0.339295	−	0.940680i	$-0.610188\pi$
$677$	−17.6564			−0.678589			−0.339295	+	0.940680i	$0.610188\pi$
$678$	0.660568	−	16.6384i	0.0253690	−	0.638995i
$679$		−	3.15746i		−	0.121172i
$680$			6.21981i			0.238519i
$681$	−30.9171	−	1.22745i	−1.18475	−	0.0470360i
$682$	−7.45764	−	10.2052i	−0.285568	−	0.390779i
$683$			18.2750i			0.699275i	0.936885	+	0.349637i	$0.113695\pi$
$683$			18.2750i			0.699275i	−0.936885	+	0.349637i	$0.886305\pi$
$684$	−2.43984	+	30.6790i	−0.0932896	+	1.17304i
$685$	−9.29296			−0.355066
$686$		−	0.490604i		−	0.0187313i
$687$	−32.9573	−	1.30845i	−1.25740	−	0.0499205i
$688$		−	6.68961i		−	0.255039i
$689$	9.26455			0.352951
$690$	−0.454252	−	0.0180344i	−0.0172931	−	0.000686557i
$691$	−1.88342			−0.0716486			−0.0358243	−	0.999358i	$-0.511406\pi$
$691$	−1.88342			−0.0716486			−0.0358243	+	0.999358i	$0.511406\pi$
$692$	−13.5669			−0.515735
$693$	8.47358	−	5.21522i	0.321885	−	0.198110i
$694$	−10.1844			−0.386596
$695$	20.8023			0.789075
$696$	−15.1499	−	0.601469i	−0.574254	−	0.0227986i
$697$	−27.2195			−1.03101
$698$			5.17764i			0.195977i
$699$	−40.9231	−	1.62470i	−1.54785	−	0.0614518i
$700$		−	1.75931i		−	0.0664956i
$701$	16.6849			0.630178			0.315089	−	0.949062i	$-0.397966\pi$
$701$	16.6849			0.630178			0.315089	+	0.949062i	$0.397966\pi$
$702$	−0.901653	+	7.53846i	−0.0340307	+	0.284521i
$703$		−	10.3796i		−	0.391473i
$704$	−5.45724	−	7.46784i	−0.205677	−	0.281455i
$705$	−12.1939	−	0.484115i	−0.459250	−	0.0182328i
$706$			14.7751i			0.556067i
$707$			0.271916i			0.0102264i
$708$	−0.628751	+	15.8370i	−0.0236299	+	0.595192i
$709$	17.6350			0.662295			0.331148	−	0.943579i	$-0.392564\pi$
$709$	17.6350			0.662295			0.331148	+	0.943579i	$0.392564\pi$
$710$	5.77764			0.216831
$711$	0.410913	−	5.16690i	0.0154104	−	0.193774i
$712$			12.3120i			0.461410i
$713$			4.15584i			0.155637i
$714$	0.113682	−	2.86344i	0.00425445	−	0.107161i
$715$	−5.82792	−	7.97510i	−0.217952	−	0.298252i
$716$			18.8028i			0.702694i
$717$	12.3073	+	0.488618i	0.459626	+	0.0182478i
$718$	−3.24057			−0.120937
$719$			8.47143i			0.315931i	0.987445	+	0.157966i	$0.0504935\pi$
$719$			8.47143i			0.315931i	−0.987445	+	0.157966i	$0.949507\pi$
$720$	0.621644	−	7.81666i	0.0231673	−	0.291310i
$721$			13.2038i			0.491734i
$722$	7.35964			0.273897
$723$	−0.914484	+	23.0341i	−0.0340100	+	0.856647i
$724$	−28.3405			−1.05327
$725$	4.74626			0.176272
$726$	3.19043	−	8.78591i	0.118408	−	0.326076i
$727$	2.29068			0.0849567			0.0424784	−	0.999097i	$-0.486475\pi$
$727$	2.29068			0.0849567			0.0424784	+	0.999097i	$0.486475\pi$
$728$	−5.49280			−0.203577
$729$	26.2384	+	6.36768i	0.971792	+	0.235840i
$730$	2.71495			0.100485
$731$			8.63118i			0.319236i
$732$	−1.19949	+	30.2128i	−0.0443343	+	1.11670i
$733$		−	38.7102i		−	1.42979i	−0.699230	−	0.714897i	$-0.746474\pi$
$733$		−	38.7102i		−	1.42979i	0.699230	−	0.714897i	$-0.253526\pi$
$734$	−9.37383			−0.345994
$735$	−0.0687106	+	1.73069i	−0.00253443	+	0.0638374i
$736$		−	2.65944i		−	0.0980282i
$737$	4.89963	+	6.70480i	0.180480	+	0.246974i
$738$	−11.8420	−	0.941769i	−0.435909	−	0.0346670i
$739$			30.3786i			1.11749i	0.829338	+	0.558747i	$0.188718\pi$
$739$			30.3786i			1.11749i	−0.829338	+	0.558747i	$0.811282\pi$
$740$			3.13165i			0.115122i
$741$	−30.0553	−	1.19323i	−1.10411	−	0.0438345i
$742$	−1.52616			−0.0560271
$743$	−35.3186			−1.29571			−0.647856	−	0.761763i	$-0.724334\pi$
$743$	−35.3186			−1.29571			−0.647856	+	0.761763i	$0.724334\pi$
$744$	24.7953	+	0.984405i	0.909039	+	0.0360900i
$745$		−	18.3474i		−	0.672196i
$746$			4.45827i			0.163229i
$747$	50.7048	+	4.03245i	1.85519	+	0.147540i
$748$	11.6102	+	15.8877i	0.424511	+	0.580913i
$749$			4.99401i			0.182477i
$750$	0.0337096	−	0.849081i	0.00123090	−	0.0310041i
$751$	−22.4423			−0.818933			−0.409466	−	0.912325i	$-0.634285\pi$
$751$	−22.4423			−0.818933			−0.409466	+	0.912325i	$0.634285\pi$
$752$		−	18.4160i		−	0.671561i
$753$	0.225488	−	5.67962i	0.00821726	−	0.206977i
$754$		−	6.93485i		−	0.252552i
$755$	10.8008			0.393080
$756$	−1.08566	+	9.07694i	−0.0394852	+	0.330125i
$757$	−6.21568			−0.225913			−0.112956	−	0.993600i	$-0.536032\pi$
$757$	−6.21568			−0.225913			−0.112956	+	0.993600i	$0.536032\pi$
$758$	−5.78617			−0.210163
$759$	−2.55134	+	1.71342i	−0.0926076	+	0.0621934i
$760$	−10.7544			−0.390103
$761$	−17.7631			−0.643912			−0.321956	−	0.946755i	$-0.604340\pi$
$761$	−17.7631			−0.643912			−0.321956	+	0.946755i	$0.604340\pi$
$762$	0.333997	−	8.41275i	0.0120994	−	0.304762i
$763$	−3.80235			−0.137654
$764$		−	37.5245i		−	1.35759i
$765$	−0.802067	+	10.0853i	−0.0289988	+	0.364636i
$766$			17.0442i			0.615833i
$767$	−15.4906			−0.559333
$768$	0.0497554	+	0.00197536i	0.00179539	+	7.12795e-5i
$769$			5.91891i			0.213441i	0.994289	+	0.106721i	$0.0340351\pi$
$769$			5.91891i			0.213441i	−0.994289	+	0.106721i	$0.965965\pi$
$770$	0.960040	+	1.31375i	0.0345975	+	0.0473442i
$771$	0.907463	−	22.8572i	0.0326815	−	0.823184i
$772$		−	34.7927i		−	1.25222i
$773$		−	43.0325i		−	1.54777i	−0.633324	−	0.773886i	$-0.718310\pi$
$773$		−	43.0325i		−	1.54777i	0.633324	−	0.773886i	$-0.281690\pi$
$774$	−0.298631	+	3.75504i	−0.0107341	+	0.134972i
$775$	−7.76804			−0.279036
$776$	5.82341			0.209048
$777$	0.122308	−	3.08071i	0.00438778	−	0.110520i
$778$		−	0.892559i		−	0.0319998i
$779$		−	47.0640i		−	1.68624i
$780$	9.06808	+	0.360015i	0.324689	+	0.0128906i
$781$	31.5356	−	23.0451i	1.12843	−	0.824618i
$782$			0.885149i			0.0316529i
$783$	−24.4877	−	2.92890i	−0.875121	−	0.104671i
$784$	−2.61378			−0.0933493
$785$			10.5748i			0.377432i
$786$	11.2076	+	0.444956i	0.399762	+	0.0158711i
$787$			52.6276i			1.87597i	0.346673	+	0.937986i	$0.387311\pi$
$787$			52.6276i			1.87597i	−0.346673	+	0.937986i	$0.612689\pi$
$788$	25.5946			0.911771
$789$	−42.0024	−	1.66755i	−1.49532	−	0.0593663i
$790$	0.847634			0.0301575
$791$	19.5958			0.696747
$792$	9.61858	+	15.6281i	0.341781	+	0.555319i
$793$	−29.5519			−1.04942
$794$	−9.22468			−0.327372
$795$	5.38379	+	0.213744i	0.190943	+	0.00758070i
$796$	−26.0935			−0.924860
$797$			1.04556i			0.0370355i	0.999829	+	0.0185178i	$0.00589472\pi$
$797$			1.04556i			0.0370355i	−0.999829	+	0.0185178i	$0.994105\pi$
$798$	4.95104	+	0.196563i	0.175265	+	0.00695825i
$799$			23.7609i			0.840601i
$800$	4.97099			0.175751
$801$	−1.58767	+	19.9637i	−0.0560976	+	0.705382i
$802$		−	11.5766i		−	0.408783i
$803$	14.8188	−	10.8290i	0.522942	−	0.382148i
$804$	−7.62369	−	0.302670i	−0.268867	−	0.0106744i
$805$		−	0.534992i		−	0.0188560i
$806$			11.3500i			0.399788i
$807$	−1.76055	+	44.3450i	−0.0619744	+	1.56102i
$808$	−0.501502			−0.0176428
$809$	−4.79424			−0.168557			−0.0842783	−	0.996442i	$-0.526858\pi$
$809$	−4.79424			−0.168557			−0.0842783	+	0.996442i	$0.526858\pi$
$810$	−0.697887	+	4.35993i	−0.0245212	+	0.153192i
$811$			18.2116i			0.639496i	0.947503	+	0.319748i	$0.103598\pi$
$811$			18.2116i			0.639496i	−0.947503	+	0.319748i	$0.896402\pi$
$812$		−	8.35013i		−	0.293032i
$813$	−1.14962	+	28.9567i	−0.0403188	+	1.01555i
$814$	−1.70892	−	2.33853i	−0.0598976	−	0.0819656i
$815$			12.6883i			0.444452i
$816$	−15.2555	−	0.605663i	−0.534049	−	0.0212025i
$817$	−14.9238			−0.522117
$818$		−	18.1276i		−	0.633816i
$819$	−8.90650	−	0.708316i	−0.311218	−	0.0247506i
$820$			14.1998i			0.495880i
$821$	11.7217			0.409089			0.204545	−	0.978857i	$-0.434429\pi$
$821$	11.7217			0.409089			0.204545	+	0.978857i	$0.434429\pi$
$822$	−0.313262	+	7.89048i	−0.0109263	+	0.275212i
$823$	−4.68990			−0.163480			−0.0817399	−	0.996654i	$-0.526048\pi$
$823$	−4.68990			−0.163480			−0.0817399	+	0.996654i	$0.526048\pi$
$824$	−24.3521			−0.848346
$825$	−3.20271	−	4.76892i	−0.111504	−	0.166033i
$826$	2.55178			0.0887879
$827$	13.5357			0.470683			0.235341	−	0.971913i	$-0.424379\pi$
$827$	13.5357			0.470683			0.235341	+	0.971913i	$0.424379\pi$
$828$	0.223852	−	2.81476i	0.00777940	−	0.0978197i
$829$	4.11554			0.142939			0.0714693	−	0.997443i	$-0.477231\pi$
$829$	4.11554			0.142939			0.0714693	+	0.997443i	$0.477231\pi$
$830$			8.31816i			0.288728i
$831$	0.686908	−	17.3019i	0.0238286	−	0.600196i
$832$			8.30556i			0.287943i
$833$	3.37240			0.116847
$834$	0.701237	−	17.6628i	0.0242819	−	0.611613i
$835$			11.8822i			0.411201i
$836$	−27.4707	+	20.0746i	−0.950095	+	0.694296i
$837$	40.0783	+	4.79364i	1.38531	+	0.165692i
$838$		−	10.8864i		−	0.376064i
$839$		−	12.2273i		−	0.422132i	−0.977472	−	0.211066i	$-0.932306\pi$
$839$		−	12.2273i		−	0.422132i	0.977472	−	0.211066i	$-0.0676935\pi$
$840$	−3.19196	−	0.126725i	−0.110133	−	0.00437243i
$841$	−6.47303			−0.223208
$842$	1.80906			0.0623445
$843$	55.5966	+	2.20726i	1.91485	+	0.0760220i
$844$			3.01191i			0.103674i
$845$		−	4.13029i		−	0.142086i
$846$	−0.822106	+	10.3373i	−0.0282646	+	0.355404i
$847$	10.4802	+	3.34143i	0.360104	+	0.114813i
$848$			8.13090i			0.279216i
$849$	−1.60908	+	40.5296i	−0.0552234	+	1.39097i
$850$	−1.65451			−0.0567492
$851$			0.952312i			0.0326448i
$852$	−1.42359	+	35.8575i	−0.0487714	+	1.22846i
$853$			17.7152i			0.606558i	0.952902	+	0.303279i	$0.0980814\pi$
$853$			17.7152i			0.606558i	−0.952902	+	0.303279i	$0.901919\pi$
$854$	4.86812			0.166584
$855$	−17.4381	−	1.38682i	−0.596371	−	0.0474281i
$856$	−9.21061			−0.314812
$857$	−16.8055			−0.574066			−0.287033	−	0.957921i	$-0.592669\pi$
$857$	−16.8055			−0.574066			−0.287033	+	0.957921i	$0.592669\pi$
$858$	−6.96796	+	4.67954i	−0.237882	+	0.159757i
$859$	−36.4103			−1.24230			−0.621152	−	0.783690i	$-0.713335\pi$
$859$	−36.4103			−1.24230			−0.621152	+	0.783690i	$0.713335\pi$
$860$	4.50271			0.153541
$861$	0.554581	−	13.9688i	0.0189001	−	0.476056i
$862$	−2.17266			−0.0740010
$863$			43.2927i			1.47370i	0.676057	+	0.736850i	$0.263687\pi$
$863$			43.2927i			1.47370i	−0.676057	+	0.736850i	$0.736313\pi$
$864$	−25.6472	−	3.06759i	−0.872536	−	0.104361i
$865$		−	7.71148i		−	0.262198i
$866$	3.32453			0.112972
$867$	−9.73849	−	0.386631i	−0.330736	−	0.0131307i
$868$			13.6664i			0.463867i
$869$	4.62657	−	3.38093i	0.156946	−	0.114690i
$870$	0.159995	−	4.02996i	0.00542433	−	0.136628i
$871$		−	7.45692i		−	0.252668i
$872$		−	7.01279i		−	0.237483i
$873$	9.44258	+	0.750949i	0.319583	+	0.0254158i
$874$	−1.53047			−0.0517689
$875$	1.00000			0.0338062
$876$	−0.668954	+	16.8497i	−0.0226018	+	0.569297i
$877$			42.1639i			1.42377i	0.702294	+	0.711887i	$0.252159\pi$
$877$			42.1639i			1.42377i	−0.702294	+	0.711887i	$0.747841\pi$
$878$			5.54656i			0.187187i
$879$	−40.2748	−	1.59896i	−1.35844	−	0.0539317i
$880$	6.99923	−	5.11479i	0.235944	−	0.172420i
$881$			53.8283i			1.81352i	0.421644	+	0.906761i	$0.361453\pi$
$881$			53.8283i			1.81352i	−0.421644	+	0.906761i	$0.638547\pi$
$882$	1.46718	+	0.116682i	0.0494025	+	0.00392888i
$883$	−45.0604			−1.51640			−0.758201	−	0.652021i	$-0.773921\pi$
$883$	−45.0604			−1.51640			−0.758201	+	0.652021i	$0.773921\pi$
$884$		−	17.6699i		−	0.594305i
$885$	−9.00185	−	0.357385i	−0.302594	−	0.0120134i
$886$		−	1.97808i		−	0.0664548i
$887$	30.4640			1.02288			0.511440	−	0.859319i	$-0.329112\pi$
$887$	30.4640			1.02288			0.511440	+	0.859319i	$0.329112\pi$
$888$	5.68184	+	0.225577i	0.190670	+	0.00756986i
$889$	9.90806			0.332306
$890$	−3.27506			−0.109780
$891$	13.5811	+	26.5811i	0.454984	+	0.890499i
$892$	−33.5558			−1.12353
$893$	−41.0839			−1.37482
$894$	−15.5784	−	0.618484i	−0.521020	−	0.0206852i
$895$	−10.6876			−0.357248
$896$		−	11.3102i		−	0.377846i
$897$	2.75753	+	0.109478i	0.0920713	+	0.00365535i
$898$		−	9.22785i		−	0.307937i
$899$	−36.8691			−1.22965
$900$	5.26131	+	0.418422i	0.175377	+	0.0139474i
$901$		−	10.4908i		−	0.349499i
$902$	−7.74874	−	10.6036i	−0.258005	−	0.353061i
$903$	−4.42946	−	0.175855i	−0.147403	−	0.00585210i
$904$			36.1411i			1.20204i
$905$		−	16.1089i		−	0.535478i
$906$	0.364090	−	9.17073i	0.0120961	−	0.304677i
$907$	−25.8497			−0.858325			−0.429162	−	0.903227i	$-0.641191\pi$
$907$	−25.8497			−0.858325			−0.429162	+	0.903227i	$0.641191\pi$
$908$	31.4284			1.04299
$909$	−0.813180	−	0.0646705i	−0.0269715	−	0.00214499i
$910$		−	1.46112i		−	0.0484356i
$911$			24.3387i			0.806376i	0.915117	+	0.403188i	$0.132098\pi$
$911$			24.3387i			0.806376i	−0.915117	+	0.403188i	$0.867902\pi$
$912$	1.04722	−	26.3776i	0.0346771	−	0.873449i
$913$	33.1784	+	45.4023i	1.09805	+	1.50260i
$914$			8.71416i			0.288239i
$915$	−17.1731	−	0.681795i	−0.567726	−	0.0225395i
$916$	33.5024			1.10695
$917$			13.1997i			0.435891i
$918$	8.53624	+	1.02099i	0.281738	+	0.0336978i
$919$		−	15.3207i		−	0.505385i	−0.967547	−	0.252692i	$-0.918684\pi$
$919$		−	15.3207i		−	0.505385i	0.967547	−	0.252692i	$-0.0813161\pi$
$920$	0.986701			0.0325306
$921$	−2.24171	+	56.4643i	−0.0738667	+	1.86056i
$922$	6.39745			0.210689
$923$	−35.0731			−1.15445
$924$	−8.39001	+	5.63456i	−0.276011	+	0.185363i
$925$	−1.78005			−0.0585276
$926$	−8.35354			−0.274514
$927$	−39.4866	−	3.14029i	−1.29691	−	0.103141i
$928$	23.5936			0.774498
$929$			56.0153i			1.83780i	0.394489	+	0.918901i	$0.370922\pi$
$929$			56.0153i			1.83780i	−0.394489	+	0.918901i	$0.629078\pi$
$930$	−0.261858	+	6.59570i	−0.00858666	+	0.216282i
$931$			5.83105i			0.191105i
$932$	41.5998			1.36265
$933$	0.562867	−	14.1775i	0.0184274	−	0.464152i
$934$		−	4.26596i		−	0.139587i
$935$	−9.03066	+	6.59929i	−0.295334	+	0.215820i
$936$	1.30637	−	16.4265i	0.0427000	−	0.536918i
$937$		−	41.5993i		−	1.35899i	−0.733681	−	0.679494i	$-0.762199\pi$
$937$		−	41.5993i		−	1.35899i	0.733681	−	0.679494i	$-0.237801\pi$
$938$			1.22839i			0.0401083i
$939$	−14.9688	−	0.594280i	−0.488488	−	0.0193936i
$940$	12.3956			0.404299
$941$	33.3139			1.08600			0.543000	−	0.839732i	$-0.317288\pi$
$941$	33.3139			1.08600			0.543000	+	0.839732i	$0.317288\pi$
$942$	8.97890	+	0.356474i	0.292548	+	0.0116146i
$943$			4.31806i			0.140615i
$944$		−	13.5951i		−	0.442483i
$945$	−5.15938	−	0.617098i	−0.167835	−	0.0200742i
$946$	−3.36236	+	2.45709i	−0.109320	+	0.0798869i
$947$			7.26096i			0.235950i	0.993017	+	0.117975i	$0.0376402\pi$
$947$			7.26096i			0.235950i	−0.993017	+	0.117975i	$0.962360\pi$
$948$	−0.208854	+	5.26064i	−0.00678327	+	0.170858i
$949$	−16.4811			−0.534998
$950$		−	2.86074i		−	0.0928145i
$951$	0.693699	−	17.4729i	0.0224947	−	0.566599i
$952$			6.21981i			0.201585i
$953$	7.05817			0.228636			0.114318	−	0.993444i	$-0.463532\pi$
$953$	7.05817			0.228636			0.114318	+	0.993444i	$0.463532\pi$
$954$	0.362971	−	4.56407i	0.0117516	−	0.147767i
$955$	21.3291			0.690195
$956$	−12.5109			−0.404631
$957$	−15.2009	−	22.6345i	−0.491375	−	0.731671i
$958$	5.52019			0.178349
$959$	−9.29296			−0.300085
$960$	−0.191619	+	4.82650i	−0.00618446	+	0.155775i
$961$	29.3425			0.946532
$962$			2.60086i			0.0838552i
$963$	−14.9349	−	1.18774i	−0.481270	−	0.0382744i
$964$		−	23.4150i		−	0.754147i
$965$	19.7764			0.636624
$966$	−0.454252	−	0.0180344i	−0.0146153	−	0.000580247i
$967$			39.4733i			1.26938i	0.772768	+	0.634689i	$0.218872\pi$
$967$			39.4733i			1.26938i	−0.772768	+	0.634689i	$0.781128\pi$
$968$	−6.16270	+	19.3290i	−0.198077	+	0.621257i
$969$	−1.35117	+	34.0333i	−0.0434057	+	1.09331i
$970$			1.54906i			0.0497374i
$971$			2.87595i			0.0922937i	0.998935	+	0.0461469i	$0.0146942\pi$
$971$			2.87595i			0.0922937i	−0.998935	+	0.0461469i	$0.985306\pi$
$972$	−26.8869	−	5.40554i	−0.862398	−	0.173383i
$973$	20.8023			0.666890
$974$	1.98277			0.0635320
$975$	−0.204634	+	5.15434i	−0.00655354	+	0.165071i
$976$		−	25.9358i		−	0.830185i
$977$		−	12.4496i		−	0.398297i	−0.979969	−	0.199148i	$-0.936182\pi$
$977$		−	12.4496i		−	0.398297i	0.979969	−	0.199148i	$-0.0638176\pi$
$978$	10.7734	+	0.427718i	0.344495	+	0.0136769i
$979$	−17.8760	+	13.0631i	−0.571319	+	0.417500i
$980$		−	1.75931i		−	0.0561990i
$981$	0.904325	−	11.3712i	0.0288729	−	0.363053i
$982$	−8.49917			−0.271220
$983$		−	49.6476i		−	1.58351i	−0.610837	−	0.791756i	$-0.709167\pi$
$983$		−	49.6476i		−	1.58351i	0.610837	−	0.791756i	$-0.290833\pi$
$984$	25.7631	+	1.02283i	0.821299	+	0.0326066i
$985$			14.5481i			0.463542i
$986$	−7.85273			−0.250082
$987$	−12.1939	−	0.484115i	−0.388137	−	0.0154096i
$988$	30.5523			0.971998
$989$	1.36924			0.0435392
$990$	−4.15717	+	2.55860i	−0.132123	+	0.0813178i
$991$	−56.7903			−1.80400			−0.902001	−	0.431734i	$-0.857902\pi$
$991$	−56.7903			−1.80400			−0.902001	+	0.431734i	$0.857902\pi$
$992$	−38.6149			−1.22602
$993$	−25.8363	−	1.02573i	−0.819890	−	0.0325507i
$994$	5.77764			0.183256
$995$		−	14.8317i		−	0.470196i
$996$	−51.6247	−	2.04957i	−1.63579	−	0.0649430i
$997$		−	2.20986i		−	0.0699870i	−0.999388	−	0.0349935i	$-0.988859\pi$
$997$		−	2.20986i		−	0.0699870i	0.999388	−	0.0349935i	$-0.0111410\pi$
$998$	19.9938			0.632892
$999$	9.18395	+	1.09846i	0.290567	+	0.0347539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.15	yes	40
3.2	odd	2		1155.2.l.e.1121.26	yes	40
11.10	odd	2		1155.2.l.e.1121.25	✓	40
33.32	even	2	inner	1155.2.l.f.1121.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.25	✓	40	11.10	odd	2
1155.2.l.e.1121.26	yes	40	3.2	odd	2
1155.2.l.f.1121.15	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.16	yes	40	33.32	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.490604 q^{2} +(1.73069 + 0.0687106i) q^{3} -1.75931 q^{4} -1.00000i q^{5} +(-0.849081 - 0.0337096i) q^{6} -1.00000i q^{7} +1.84433 q^{8} +(2.99056 + 0.237833i) q^{9} +O(q^{10})\)	\(q-0.490604 q^{2} +(1.73069 + 0.0687106i) q^{3} -1.75931 q^{4} -1.00000i q^{5} +(-0.849081 - 0.0337096i) q^{6} -1.00000i q^{7} +1.84433 q^{8} +(2.99056 + 0.237833i) q^{9} +0.490604i q^{10} +(1.95686 + 2.67782i) q^{11} +(-3.04481 - 0.120883i) q^{12} -2.97821i q^{13} +0.490604i q^{14} +(0.0687106 - 1.73069i) q^{15} +2.61378 q^{16} -3.37240 q^{17} +(-1.46718 - 0.116682i) q^{18} -5.83105i q^{19} +1.75931i q^{20} +(0.0687106 - 1.73069i) q^{21} +(-0.960040 - 1.31375i) q^{22} +0.534992i q^{23} +(3.19196 + 0.126725i) q^{24} -1.00000 q^{25} +1.46112i q^{26} +(5.15938 + 0.617098i) q^{27} +1.75931i q^{28} -4.74626 q^{29} +(-0.0337096 + 0.849081i) q^{30} +7.76804 q^{31} -4.97099 q^{32} +(3.20271 + 4.76892i) q^{33} +1.65451 q^{34} -1.00000 q^{35} +(-5.26131 - 0.418422i) q^{36} +1.78005 q^{37} +2.86074i q^{38} +(0.204634 - 5.15434i) q^{39} -1.84433i q^{40} +8.07126 q^{41} +(-0.0337096 + 0.849081i) q^{42} -2.55936i q^{43} +(-3.44271 - 4.71111i) q^{44} +(0.237833 - 2.99056i) q^{45} -0.262469i q^{46} -7.04571i q^{47} +(4.52364 + 0.179594i) q^{48} -1.00000 q^{49} +0.490604 q^{50} +(-5.83656 - 0.231719i) q^{51} +5.23958i q^{52} +3.11078i q^{53} +(-2.53121 - 0.302750i) q^{54} +(2.67782 - 1.95686i) q^{55} -1.84433i q^{56} +(0.400655 - 10.0917i) q^{57} +2.32853 q^{58} -5.20131i q^{59} +(-0.120883 + 3.04481i) q^{60} -9.92271i q^{61} -3.81103 q^{62} +(0.237833 - 2.99056i) q^{63} -2.78878 q^{64} -2.97821 q^{65} +(-1.57126 - 2.33965i) q^{66} +2.50383 q^{67} +5.93308 q^{68} +(-0.0367596 + 0.925904i) q^{69} +0.490604 q^{70} -11.7766i q^{71} +(5.51557 + 0.438643i) q^{72} -5.53389i q^{73} -0.873298 q^{74} +(-1.73069 - 0.0687106i) q^{75} +10.2586i q^{76} +(2.67782 - 1.95686i) q^{77} +(-0.100394 + 2.52874i) q^{78} -1.72774i q^{79} -2.61378i q^{80} +(8.88687 + 1.42251i) q^{81} -3.95979 q^{82} +16.9550 q^{83} +(-0.120883 + 3.04481i) q^{84} +3.37240i q^{85} +1.25563i q^{86} +(-8.21429 - 0.326118i) q^{87} +(3.60909 + 4.93878i) q^{88} +6.67557i q^{89} +(-0.116682 + 1.46718i) q^{90} -2.97821 q^{91} -0.941216i q^{92} +(13.4441 + 0.533747i) q^{93} +3.45665i q^{94} -5.83105 q^{95} +(-8.60323 - 0.341560i) q^{96} +3.15746 q^{97} +0.490604 q^{98} +(5.21522 + 8.47358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

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