LMFDB - Embedded newform 1155.2.l.c.1121.2

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:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.c.1121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000i q^{5} +(-1.41421 - 2.00000i) q^{6} -1.00000i q^{7} +2.82843 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000i q^{5} +(-1.41421 - 2.00000i) q^{6} -1.00000i q^{7} +2.82843 q^{8} +(-1.00000 + 2.82843i) q^{9} -1.41421i q^{10} +(3.00000 + 1.41421i) q^{11} +2.24264i q^{13} +1.41421i q^{14} +(-1.41421 + 1.00000i) q^{15} -4.00000 q^{16} +5.82843 q^{17} +(1.41421 - 4.00000i) q^{18} -3.24264i q^{19} +(1.41421 - 1.00000i) q^{21} +(-4.24264 - 2.00000i) q^{22} +1.24264i q^{23} +(2.82843 + 4.00000i) q^{24} -1.00000 q^{25} -3.17157i q^{26} +(-5.00000 + 1.41421i) q^{27} -5.82843 q^{29} +(2.00000 - 1.41421i) q^{30} +8.24264 q^{31} +(1.00000 + 5.65685i) q^{33} -8.24264 q^{34} +1.00000 q^{35} +8.24264 q^{37} +4.58579i q^{38} +(-3.17157 + 2.24264i) q^{39} +2.82843i q^{40} +4.58579 q^{41} +(-2.00000 + 1.41421i) q^{42} -3.24264i q^{43} +(-2.82843 - 1.00000i) q^{45} -1.75736i q^{46} +1.07107i q^{47} +(-4.00000 - 5.65685i) q^{48} -1.00000 q^{49} +1.41421 q^{50} +(5.82843 + 8.24264i) q^{51} +4.41421i q^{53} +(7.07107 - 2.00000i) q^{54} +(-1.41421 + 3.00000i) q^{55} -2.82843i q^{56} +(4.58579 - 3.24264i) q^{57} +8.24264 q^{58} +12.8995i q^{59} +9.24264i q^{61} -11.6569 q^{62} +(2.82843 + 1.00000i) q^{63} +8.00000 q^{64} -2.24264 q^{65} +(-1.41421 - 8.00000i) q^{66} -12.4853 q^{67} +(-1.75736 + 1.24264i) q^{69} -1.41421 q^{70} +1.75736i q^{71} +(-2.82843 + 8.00000i) q^{72} -6.48528i q^{73} -11.6569 q^{74} +(-1.00000 - 1.41421i) q^{75} +(1.41421 - 3.00000i) q^{77} +(4.48528 - 3.17157i) q^{78} -6.24264i q^{79} -4.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} -6.48528 q^{82} -17.1421 q^{83} +5.82843i q^{85} +4.58579i q^{86} +(-5.82843 - 8.24264i) q^{87} +(8.48528 + 4.00000i) q^{88} +16.4142i q^{89} +(4.00000 + 1.41421i) q^{90} +2.24264 q^{91} +(8.24264 + 11.6569i) q^{93} -1.51472i q^{94} +3.24264 q^{95} -7.00000 q^{97} +1.41421 q^{98} +(-7.00000 + 7.07107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^9	$ 4 q + 4 q^{3} - 4 q^{9} + 12 q^{11} - 16 q^{16} + 12 q^{17} - 4 q^{25} - 20 q^{27} - 12 q^{29} + 8 q^{30} + 16 q^{31} + 4 q^{33} - 16 q^{34} + 4 q^{35} + 16 q^{37} - 24 q^{39} + 24 q^{41} - 8 q^{42} - 16 q^{48} - 4 q^{49} + 12 q^{51} + 24 q^{57} + 16 q^{58} - 24 q^{62} + 32 q^{64} + 8 q^{65} - 16 q^{67} - 24 q^{69} - 24 q^{74} - 4 q^{75} - 16 q^{78} - 28 q^{81} + 8 q^{82} - 12 q^{83} - 12 q^{87} + 16 q^{90} - 8 q^{91} + 16 q^{93} - 4 q^{95} - 28 q^{97} - 28 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^9 + 12 * q^11 - 16 * q^16 + 12 * q^17 - 4 * q^25 - 20 * q^27 - 12 * q^29 + 8 * q^30 + 16 * q^31 + 4 * q^33 - 16 * q^34 + 4 * q^35 + 16 * q^37 - 24 * q^39 + 24 * q^41 - 8 * q^42 - 16 * q^48 - 4 * q^49 + 12 * q^51 + 24 * q^57 + 16 * q^58 - 24 * q^62 + 32 * q^64 + 8 * q^65 - 16 * q^67 - 24 * q^69 - 24 * q^74 - 4 * q^75 - 16 * q^78 - 28 * q^81 + 8 * q^82 - 12 * q^83 - 12 * q^87 + 16 * q^90 - 8 * q^91 + 16 * q^93 - 4 * q^95 - 28 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.41421			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−1.41421			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.41421	−	2.00000i	−0.577350	−	0.816497i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.82843			1.00000
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$		−	1.41421i		−	0.447214i
$11$	3.00000	+	1.41421i	0.904534	+	0.426401i
$11$	3.00000	+	1.41421i	0.904534	+	0.426401i
$12$		0			0
$13$			2.24264i			0.621997i	0.950410	+	0.310998i	$0.100663\pi$
$13$			2.24264i			0.621997i	−0.950410	+	0.310998i	$0.899337\pi$
$14$			1.41421i			0.377964i
$15$	−1.41421	+	1.00000i	−0.365148	+	0.258199i
$16$	−4.00000			−1.00000
$17$	5.82843			1.41360			0.706801	−	0.707413i	$-0.250138\pi$
$17$	5.82843			1.41360			0.706801	+	0.707413i	$0.250138\pi$
$18$	1.41421	−	4.00000i	0.333333	−	0.942809i
$19$		−	3.24264i		−	0.743913i	−0.928250	−	0.371956i	$-0.878687\pi$
$19$		−	3.24264i		−	0.743913i	0.928250	−	0.371956i	$-0.121313\pi$
$20$		0			0
$21$	1.41421	−	1.00000i	0.308607	−	0.218218i
$22$	−4.24264	−	2.00000i	−0.904534	−	0.426401i
$23$			1.24264i			0.259108i	0.991572	+	0.129554i	$0.0413546\pi$
$23$			1.24264i			0.259108i	−0.991572	+	0.129554i	$0.958645\pi$
$24$	2.82843	+	4.00000i	0.577350	+	0.816497i
$25$	−1.00000			−0.200000
$26$		−	3.17157i		−	0.621997i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$		0			0
$29$	−5.82843			−1.08231			−0.541156	−	0.840922i	$-0.682013\pi$
$29$	−5.82843			−1.08231			−0.541156	+	0.840922i	$0.682013\pi$
$30$	2.00000	−	1.41421i	0.365148	−	0.258199i
$31$	8.24264			1.48042			0.740211	−	0.672375i	$-0.234726\pi$
$31$	8.24264			1.48042			0.740211	+	0.672375i	$0.234726\pi$
$32$		0			0
$33$	1.00000	+	5.65685i	0.174078	+	0.984732i
$34$	−8.24264			−1.41360
$35$	1.00000			0.169031
$36$		0			0
$37$	8.24264			1.35508			0.677541	−	0.735485i	$-0.263046\pi$
$37$	8.24264			1.35508			0.677541	+	0.735485i	$0.263046\pi$
$38$			4.58579i			0.743913i
$39$	−3.17157	+	2.24264i	−0.507858	+	0.359110i
$40$			2.82843i			0.447214i
$41$	4.58579			0.716180			0.358090	−	0.933687i	$-0.383428\pi$
$41$	4.58579			0.716180			0.358090	+	0.933687i	$0.383428\pi$
$42$	−2.00000	+	1.41421i	−0.308607	+	0.218218i
$43$		−	3.24264i		−	0.494498i	−0.968952	−	0.247249i	$-0.920473\pi$
$43$		−	3.24264i		−	0.494498i	0.968952	−	0.247249i	$-0.0795266\pi$
$44$		0			0
$45$	−2.82843	−	1.00000i	−0.421637	−	0.149071i
$46$		−	1.75736i		−	0.259108i
$47$			1.07107i			0.156231i	0.996944	+	0.0781156i	$0.0248903\pi$
$47$			1.07107i			0.156231i	−0.996944	+	0.0781156i	$0.975110\pi$
$48$	−4.00000	−	5.65685i	−0.577350	−	0.816497i
$49$	−1.00000			−0.142857
$50$	1.41421			0.200000
$51$	5.82843	+	8.24264i	0.816143	+	1.15420i
$52$		0			0
$53$			4.41421i			0.606339i	0.952937	+	0.303169i	$0.0980448\pi$
$53$			4.41421i			0.606339i	−0.952937	+	0.303169i	$0.901955\pi$
$54$	7.07107	−	2.00000i	0.962250	−	0.272166i
$55$	−1.41421	+	3.00000i	−0.190693	+	0.404520i
$56$		−	2.82843i		−	0.377964i
$57$	4.58579	−	3.24264i	0.607402	−	0.429498i
$58$	8.24264			1.08231
$59$			12.8995i			1.67937i	0.543073	+	0.839686i	$0.317261\pi$
$59$			12.8995i			1.67937i	−0.543073	+	0.839686i	$0.682739\pi$
$60$		0			0
$61$			9.24264i			1.18340i	0.806159	+	0.591699i	$0.201543\pi$
$61$			9.24264i			1.18340i	−0.806159	+	0.591699i	$0.798457\pi$
$62$	−11.6569			−1.48042
$63$	2.82843	+	1.00000i	0.356348	+	0.125988i
$64$	8.00000			1.00000
$65$	−2.24264			−0.278165
$66$	−1.41421	−	8.00000i	−0.174078	−	0.984732i
$67$	−12.4853			−1.52532			−0.762660	−	0.646800i	$-0.776107\pi$
$67$	−12.4853			−1.52532			−0.762660	+	0.646800i	$0.776107\pi$
$68$		0			0
$69$	−1.75736	+	1.24264i	−0.211561	+	0.149596i
$70$	−1.41421			−0.169031
$71$			1.75736i			0.208560i	0.994548	+	0.104280i	$0.0332538\pi$
$71$			1.75736i			0.208560i	−0.994548	+	0.104280i	$0.966746\pi$
$72$	−2.82843	+	8.00000i	−0.333333	+	0.942809i
$73$		−	6.48528i		−	0.759045i	−0.925183	−	0.379522i	$-0.876088\pi$
$73$		−	6.48528i		−	0.759045i	0.925183	−	0.379522i	$-0.123912\pi$
$74$	−11.6569			−1.35508
$75$	−1.00000	−	1.41421i	−0.115470	−	0.163299i
$76$		0			0
$77$	1.41421	−	3.00000i	0.161165	−	0.341882i
$78$	4.48528	−	3.17157i	0.507858	−	0.359110i
$79$		−	6.24264i		−	0.702352i	−0.936309	−	0.351176i	$-0.885782\pi$
$79$		−	6.24264i		−	0.702352i	0.936309	−	0.351176i	$-0.114218\pi$
$80$		−	4.00000i		−	0.447214i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	−6.48528			−0.716180
$83$	−17.1421			−1.88159			−0.940797	−	0.338971i	$-0.889921\pi$
$83$	−17.1421			−1.88159			−0.940797	+	0.338971i	$0.889921\pi$
$84$		0			0
$85$			5.82843i			0.632182i
$86$			4.58579i			0.494498i
$87$	−5.82843	−	8.24264i	−0.624873	−	0.883704i
$88$	8.48528	+	4.00000i	0.904534	+	0.426401i
$89$			16.4142i			1.73990i	0.493137	+	0.869952i	$0.335850\pi$
$89$			16.4142i			1.73990i	−0.493137	+	0.869952i	$0.664150\pi$
$90$	4.00000	+	1.41421i	0.421637	+	0.149071i
$91$	2.24264			0.235093
$92$		0			0
$93$	8.24264	+	11.6569i	0.854722	+	1.20876i
$94$		−	1.51472i		−	0.156231i
$95$	3.24264			0.332688
$96$		0			0
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	1.41421			0.142857
$99$	−7.00000	+	7.07107i	−0.703526	+	0.710669i
$100$		0			0
$101$	−2.48528			−0.247295			−0.123647	−	0.992326i	$-0.539459\pi$
$101$	−2.48528			−0.247295			−0.123647	+	0.992326i	$0.539459\pi$
$102$	−8.24264	−	11.6569i	−0.816143	−	1.15420i
$103$	−0.514719			−0.0507167			−0.0253584	−	0.999678i	$-0.508073\pi$
$103$	−0.514719			−0.0507167			−0.0253584	+	0.999678i	$0.508073\pi$
$104$			6.34315i			0.621997i
$105$	1.00000	+	1.41421i	0.0975900	+	0.138013i
$106$		−	6.24264i		−	0.606339i
$107$	−7.41421			−0.716759			−0.358380	−	0.933576i	$-0.616671\pi$
$107$	−7.41421			−0.716759			−0.358380	+	0.933576i	$0.616671\pi$
$108$		0			0
$109$			3.75736i			0.359890i	0.983677	+	0.179945i	$0.0575919\pi$
$109$			3.75736i			0.359890i	−0.983677	+	0.179945i	$0.942408\pi$
$110$	2.00000	−	4.24264i	0.190693	−	0.404520i
$111$	8.24264	+	11.6569i	0.782357	+	1.10642i
$112$			4.00000i			0.377964i
$113$		−	18.8995i		−	1.77791i	−0.457990	−	0.888957i	$-0.651430\pi$
$113$		−	18.8995i		−	1.77791i	0.457990	−	0.888957i	$-0.348570\pi$
$114$	−6.48528	+	4.58579i	−0.607402	+	0.429498i
$115$	−1.24264			−0.115877
$116$		0			0
$117$	−6.34315	−	2.24264i	−0.586424	−	0.207332i
$118$		−	18.2426i		−	1.67937i
$119$		−	5.82843i		−	0.534291i
$120$	−4.00000	+	2.82843i	−0.365148	+	0.258199i
$121$	7.00000	+	8.48528i	0.636364	+	0.771389i
$122$		−	13.0711i		−	1.18340i
$123$	4.58579	+	6.48528i	0.413486	+	0.584758i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$	−4.00000	−	1.41421i	−0.356348	−	0.125988i
$127$			13.2426i			1.17509i	0.809190	+	0.587547i	$0.199906\pi$
$127$			13.2426i			1.17509i	−0.809190	+	0.587547i	$0.800094\pi$
$128$	−11.3137			−1.00000
$129$	4.58579	−	3.24264i	0.403756	−	0.285499i
$130$	3.17157			0.278165
$131$	19.4142			1.69623			0.848114	−	0.529814i	$-0.177738\pi$
$131$	19.4142			1.69623			0.848114	+	0.529814i	$0.177738\pi$
$132$		0			0
$133$	−3.24264			−0.281173
$134$	17.6569			1.52532
$135$	−1.41421	−	5.00000i	−0.121716	−	0.430331i
$136$	16.4853			1.41360
$137$			14.4853i			1.23756i	0.785564	+	0.618781i	$0.212373\pi$
$137$			14.4853i			1.23756i	−0.785564	+	0.618781i	$0.787627\pi$
$138$	2.48528	−	1.75736i	0.211561	−	0.149596i
$139$		−	12.4853i		−	1.05899i	−0.848314	−	0.529494i	$-0.822382\pi$
$139$		−	12.4853i		−	1.05899i	0.848314	−	0.529494i	$-0.177618\pi$
$140$		0			0
$141$	−1.51472	+	1.07107i	−0.127562	+	0.0902002i
$142$		−	2.48528i		−	0.208560i
$143$	−3.17157	+	6.72792i	−0.265220	+	0.562617i
$144$	4.00000	−	11.3137i	0.333333	−	0.942809i
$145$		−	5.82843i		−	0.484025i
$146$			9.17157i			0.759045i
$147$	−1.00000	−	1.41421i	−0.0824786	−	0.116642i
$148$		0			0
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	1.41421	+	2.00000i	0.115470	+	0.163299i
$151$			10.0000i			0.813788i	0.913475	+	0.406894i	$0.133388\pi$
$151$			10.0000i			0.813788i	−0.913475	+	0.406894i	$0.866612\pi$
$152$		−	9.17157i		−	0.743913i
$153$	−5.82843	+	16.4853i	−0.471200	+	1.33276i
$154$	−2.00000	+	4.24264i	−0.161165	+	0.341882i
$155$			8.24264i			0.662065i
$156$		0			0
$157$	11.0000			0.877896			0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000			0.877896			0.438948	+	0.898513i	$0.355351\pi$
$158$			8.82843i			0.702352i
$159$	−6.24264	+	4.41421i	−0.495074	+	0.350070i
$160$		0			0
$161$	1.24264			0.0979338
$162$	9.89949	+	8.00000i	0.777778	+	0.628539i
$163$	2.24264			0.175657			0.0878286	−	0.996136i	$-0.472007\pi$
$163$	2.24264			0.175657			0.0878286	+	0.996136i	$0.472007\pi$
$164$		0			0
$165$	−5.65685	+	1.00000i	−0.440386	+	0.0778499i
$166$	24.2426			1.88159
$167$	−20.1421			−1.55865			−0.779323	−	0.626623i	$-0.784437\pi$
$167$	−20.1421			−1.55865			−0.779323	+	0.626623i	$0.784437\pi$
$168$	4.00000	−	2.82843i	0.308607	−	0.218218i
$169$	7.97056			0.613120
$170$		−	8.24264i		−	0.632182i
$171$	9.17157	+	3.24264i	0.701368	+	0.247971i
$172$		0			0
$173$	2.82843			0.215041			0.107521	−	0.994203i	$-0.465709\pi$
$173$	2.82843			0.215041			0.107521	+	0.994203i	$0.465709\pi$
$174$	8.24264	+	11.6569i	0.624873	+	0.883704i
$175$			1.00000i			0.0755929i
$176$	−12.0000	−	5.65685i	−0.904534	−	0.426401i
$177$	−18.2426	+	12.8995i	−1.37120	+	0.969585i
$178$		−	23.2132i		−	1.73990i
$179$		−	13.4142i		−	1.00263i	−0.865266	−	0.501313i	$-0.832851\pi$
$179$		−	13.4142i		−	1.00263i	0.865266	−	0.501313i	$-0.167149\pi$
$180$		0			0
$181$	−10.9706			−0.815436			−0.407718	−	0.913108i	$-0.633675\pi$
$181$	−10.9706			−0.815436			−0.407718	+	0.913108i	$0.633675\pi$
$182$	−3.17157			−0.235093
$183$	−13.0711	+	9.24264i	−0.966241	+	0.683236i
$184$			3.51472i			0.259108i
$185$			8.24264i			0.606011i
$186$	−11.6569	−	16.4853i	−0.854722	−	1.20876i
$187$	17.4853	+	8.24264i	1.27865	+	0.602762i
$188$		0			0
$189$	1.41421	+	5.00000i	0.102869	+	0.363696i
$190$	−4.58579			−0.332688
$191$			9.17157i			0.663632i	0.943344	+	0.331816i	$0.107661\pi$
$191$			9.17157i			0.663632i	−0.943344	+	0.331816i	$0.892339\pi$
$192$	8.00000	+	11.3137i	0.577350	+	0.816497i
$193$		−	10.0000i		−	0.719816i	−0.932988	−	0.359908i	$-0.882808\pi$
$193$		−	10.0000i		−	0.719816i	0.932988	−	0.359908i	$-0.117192\pi$
$194$	9.89949			0.710742
$195$	−2.24264	−	3.17157i	−0.160599	−	0.227121i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	9.89949	−	10.0000i	0.703526	−	0.710669i
$199$	7.51472			0.532704			0.266352	−	0.963876i	$-0.414182\pi$
$199$	7.51472			0.532704			0.266352	+	0.963876i	$0.414182\pi$
$200$	−2.82843			−0.200000
$201$	−12.4853	−	17.6569i	−0.880644	−	1.24542i
$202$	3.51472			0.247295
$203$			5.82843i			0.409075i
$204$		0			0
$205$			4.58579i			0.320285i
$206$	0.727922			0.0507167
$207$	−3.51472	−	1.24264i	−0.244290	−	0.0863695i
$208$		−	8.97056i		−	0.621997i
$209$	4.58579	−	9.72792i	0.317205	−	0.672894i
$210$	−1.41421	−	2.00000i	−0.0975900	−	0.138013i
$211$			8.00000i			0.550743i	0.961338	+	0.275371i	$0.0888008\pi$
$211$			8.00000i			0.550743i	−0.961338	+	0.275371i	$0.911199\pi$
$212$		0			0
$213$	−2.48528	+	1.75736i	−0.170289	+	0.120412i
$214$	10.4853			0.716759
$215$	3.24264			0.221146
$216$	−14.1421	+	4.00000i	−0.962250	+	0.272166i
$217$		−	8.24264i		−	0.559547i
$218$		−	5.31371i		−	0.359890i
$219$	9.17157	−	6.48528i	0.619757	−	0.438235i
$220$		0			0
$221$			13.0711i			0.879255i
$222$	−11.6569	−	16.4853i	−0.782357	−	1.10642i
$223$	17.0000			1.13840			0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000			1.13840			0.569202	+	0.822198i	$0.307252\pi$
$224$		0			0
$225$	1.00000	−	2.82843i	0.0666667	−	0.188562i
$226$			26.7279i			1.77791i
$227$	6.17157			0.409622			0.204811	−	0.978802i	$-0.434342\pi$
$227$	6.17157			0.409622			0.204811	+	0.978802i	$0.434342\pi$
$228$		0			0
$229$	18.7279			1.23758			0.618788	−	0.785558i	$-0.287624\pi$
$229$	18.7279			1.23758			0.618788	+	0.785558i	$0.287624\pi$
$230$	1.75736			0.115877
$231$	5.65685	−	1.00000i	0.372194	−	0.0657952i
$232$	−16.4853			−1.08231
$233$	9.55635			0.626057			0.313029	−	0.949744i	$-0.398656\pi$
$233$	9.55635			0.626057			0.313029	+	0.949744i	$0.398656\pi$
$234$	8.97056	+	3.17157i	0.586424	+	0.207332i
$235$	−1.07107			−0.0698688
$236$		0			0
$237$	8.82843	−	6.24264i	0.573468	−	0.405503i
$238$			8.24264i			0.534291i
$239$	8.65685			0.559965			0.279983	−	0.960005i	$-0.409671\pi$
$239$	8.65685			0.559965			0.279983	+	0.960005i	$0.409671\pi$
$240$	5.65685	−	4.00000i	0.365148	−	0.258199i
$241$		−	9.51472i		−	0.612897i	−0.951887	−	0.306448i	$-0.900859\pi$
$241$		−	9.51472i		−	0.612897i	0.951887	−	0.306448i	$-0.0991407\pi$
$242$	−9.89949	−	12.0000i	−0.636364	−	0.771389i
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$		0			0
$245$		−	1.00000i		−	0.0638877i
$246$	−6.48528	−	9.17157i	−0.413486	−	0.584758i
$247$	7.27208			0.462711
$248$	23.3137			1.48042
$249$	−17.1421	−	24.2426i	−1.08634	−	1.53631i
$250$			1.41421i			0.0894427i
$251$		−	28.9706i		−	1.82861i	−0.405031	−	0.914303i	$-0.632739\pi$
$251$		−	28.9706i		−	1.82861i	0.405031	−	0.914303i	$-0.367261\pi$
$252$		0			0
$253$	−1.75736	+	3.72792i	−0.110484	+	0.234372i
$254$		−	18.7279i		−	1.17509i
$255$	−8.24264	+	5.82843i	−0.516174	+	0.364990i
$256$		0			0
$257$		−	22.2426i		−	1.38746i	−0.720236	−	0.693729i	$-0.755967\pi$
$257$		−	22.2426i		−	1.38746i	0.720236	−	0.693729i	$-0.244033\pi$
$258$	−6.48528	+	4.58579i	−0.403756	+	0.285499i
$259$		−	8.24264i		−	0.512173i
$260$		0			0
$261$	5.82843	−	16.4853i	0.360771	−	1.02041i
$262$	−27.4558			−1.69623
$263$	20.8284			1.28434			0.642168	−	0.766564i	$-0.278035\pi$
$263$	20.8284			1.28434			0.642168	+	0.766564i	$0.278035\pi$
$264$	2.82843	+	16.0000i	0.174078	+	0.984732i
$265$	−4.41421			−0.271163
$266$	4.58579			0.281173
$267$	−23.2132	+	16.4142i	−1.42062	+	1.00453i
$268$		0			0
$269$			0.556349i			0.0339212i	0.999856	+	0.0169606i	$0.00539899\pi$
$269$			0.556349i			0.0339212i	−0.999856	+	0.0169606i	$0.994601\pi$
$270$	2.00000	+	7.07107i	0.121716	+	0.430331i
$271$		−	14.7574i		−	0.896446i	−0.893922	−	0.448223i	$-0.852057\pi$
$271$		−	14.7574i		−	0.896446i	0.893922	−	0.448223i	$-0.147943\pi$
$272$	−23.3137			−1.41360
$273$	2.24264	+	3.17157i	0.135731	+	0.191952i
$274$		−	20.4853i		−	1.23756i
$275$	−3.00000	−	1.41421i	−0.180907	−	0.0852803i
$276$		0			0
$277$			8.48528i			0.509831i	0.966963	+	0.254916i	$0.0820477\pi$
$277$			8.48528i			0.509831i	−0.966963	+	0.254916i	$0.917952\pi$
$278$			17.6569i			1.05899i
$279$	−8.24264	+	23.3137i	−0.493474	+	1.39576i
$280$	2.82843			0.169031
$281$	5.31371			0.316989			0.158495	−	0.987360i	$-0.449336\pi$
$281$	5.31371			0.316989			0.158495	+	0.987360i	$0.449336\pi$
$282$	2.14214	−	1.51472i	0.127562	−	0.0902002i
$283$		−	29.2132i		−	1.73654i	−0.496088	−	0.868272i	$-0.665231\pi$
$283$		−	29.2132i		−	1.73654i	0.496088	−	0.868272i	$-0.334769\pi$
$284$		0			0
$285$	3.24264	+	4.58579i	0.192077	+	0.271639i
$286$	4.48528	−	9.51472i	0.265220	−	0.562617i
$287$		−	4.58579i		−	0.270690i
$288$		0			0
$289$	16.9706			0.998268
$290$			8.24264i			0.484025i
$291$	−7.00000	−	9.89949i	−0.410347	−	0.580319i
$292$		0			0
$293$	−3.34315			−0.195309			−0.0976543	−	0.995220i	$-0.531134\pi$
$293$	−3.34315			−0.195309			−0.0976543	+	0.995220i	$0.531134\pi$
$294$	1.41421	+	2.00000i	0.0824786	+	0.116642i
$295$	−12.8995			−0.751038
$296$	23.3137			1.35508
$297$	−17.0000	−	2.82843i	−0.986440	−	0.164122i
$298$		0			0
$299$	−2.78680			−0.161165
$300$		0			0
$301$	−3.24264			−0.186903
$302$		−	14.1421i		−	0.813788i
$303$	−2.48528	−	3.51472i	−0.142776	−	0.201915i
$304$			12.9706i			0.743913i
$305$	−9.24264			−0.529232
$306$	8.24264	−	23.3137i	0.471200	−	1.33276i
$307$		−	20.4853i		−	1.16916i	−0.811337	−	0.584578i	$-0.801260\pi$
$307$		−	20.4853i		−	1.16916i	0.811337	−	0.584578i	$-0.198740\pi$
$308$		0			0
$309$	−0.514719	−	0.727922i	−0.0292813	−	0.0414100i
$310$		−	11.6569i		−	0.662065i
$311$			14.8284i			0.840843i	0.907329	+	0.420421i	$0.138118\pi$
$311$			14.8284i			0.840843i	−0.907329	+	0.420421i	$0.861882\pi$
$312$	−8.97056	+	6.34315i	−0.507858	+	0.359110i
$313$	−26.4558			−1.49537			−0.747686	−	0.664052i	$-0.768835\pi$
$313$	−26.4558			−1.49537			−0.747686	+	0.664052i	$0.768835\pi$
$314$	−15.5563			−0.877896
$315$	−1.00000	+	2.82843i	−0.0563436	+	0.159364i
$316$		0			0
$317$		−	32.8284i		−	1.84383i	−0.387394	−	0.921914i	$-0.626625\pi$
$317$		−	32.8284i		−	1.84383i	0.387394	−	0.921914i	$-0.373375\pi$
$318$	8.82843	−	6.24264i	0.495074	−	0.350070i
$319$	−17.4853	−	8.24264i	−0.978988	−	0.461499i
$320$			8.00000i			0.447214i
$321$	−7.41421	−	10.4853i	−0.413821	−	0.585231i
$322$	−1.75736			−0.0979338
$323$		−	18.8995i		−	1.05160i
$324$		0			0
$325$		−	2.24264i		−	0.124399i
$326$	−3.17157			−0.175657
$327$	−5.31371	+	3.75736i	−0.293849	+	0.207782i
$328$	12.9706			0.716180
$329$	1.07107			0.0590499
$330$	8.00000	−	1.41421i	0.440386	−	0.0778499i
$331$	2.51472			0.138221			0.0691107	−	0.997609i	$-0.477984\pi$
$331$	2.51472			0.138221			0.0691107	+	0.997609i	$0.477984\pi$
$332$		0			0
$333$	−8.24264	+	23.3137i	−0.451694	+	1.27758i
$334$	28.4853			1.55865
$335$		−	12.4853i		−	0.682144i
$336$	−5.65685	+	4.00000i	−0.308607	+	0.218218i
$337$			27.2426i			1.48400i	0.670399	+	0.742001i	$0.266123\pi$
$337$			27.2426i			1.48400i	−0.670399	+	0.742001i	$0.733877\pi$
$338$	−11.2721			−0.613120
$339$	26.7279	−	18.8995i	1.45166	−	1.02648i
$340$		0			0
$341$	24.7279	+	11.6569i	1.33909	+	0.631254i
$342$	−12.9706	−	4.58579i	−0.701368	−	0.247971i
$343$			1.00000i			0.0539949i
$344$		−	9.17157i		−	0.494498i
$345$	−1.24264	−	1.75736i	−0.0669015	−	0.0946130i
$346$	−4.00000			−0.215041
$347$	−26.8284			−1.44023			−0.720113	−	0.693857i	$-0.755910\pi$
$347$	−26.8284			−1.44023			−0.720113	+	0.693857i	$0.755910\pi$
$348$		0			0
$349$		−	12.7574i		−	0.682886i	−0.939903	−	0.341443i	$-0.889084\pi$
$349$		−	12.7574i		−	0.682886i	0.939903	−	0.341443i	$-0.110916\pi$
$350$		−	1.41421i		−	0.0755929i
$351$	−3.17157	−	11.2132i	−0.169286	−	0.598517i
$352$		0			0
$353$			18.0000i			0.958043i	0.877803	+	0.479022i	$0.159008\pi$
$353$			18.0000i			0.958043i	−0.877803	+	0.479022i	$0.840992\pi$
$354$	25.7990	−	18.2426i	1.37120	−	0.969585i
$355$	−1.75736			−0.0932709
$356$		0			0
$357$	8.24264	−	5.82843i	0.436247	−	0.308473i
$358$			18.9706i			1.00263i
$359$	13.6274			0.719228			0.359614	−	0.933101i	$-0.382908\pi$
$359$	13.6274			0.719228			0.359614	+	0.933101i	$0.382908\pi$
$360$	−8.00000	−	2.82843i	−0.421637	−	0.149071i
$361$	8.48528			0.446594
$362$	15.5147			0.815436
$363$	−5.00000	+	18.3848i	−0.262432	+	0.964951i
$364$		0			0
$365$	6.48528			0.339455
$366$	18.4853	−	13.0711i	0.966241	−	0.683236i
$367$	3.00000			0.156599			0.0782994	−	0.996930i	$-0.475051\pi$
$367$	3.00000			0.156599			0.0782994	+	0.996930i	$0.475051\pi$
$368$		−	4.97056i		−	0.259108i
$369$	−4.58579	+	12.9706i	−0.238727	+	0.675221i
$370$		−	11.6569i		−	0.606011i
$371$	4.41421			0.229175
$372$		0			0
$373$		−	6.21320i		−	0.321707i	−0.986978	−	0.160854i	$-0.948575\pi$
$373$		−	6.21320i		−	0.321707i	0.986978	−	0.160854i	$-0.0514247\pi$
$374$	−24.7279	−	11.6569i	−1.27865	−	0.602762i
$375$	1.41421	−	1.00000i	0.0730297	−	0.0516398i
$376$			3.02944i			0.156231i
$377$		−	13.0711i		−	0.673194i
$378$	−2.00000	−	7.07107i	−0.102869	−	0.363696i
$379$	18.4558			0.948013			0.474007	−	0.880521i	$-0.342807\pi$
$379$	18.4558			0.948013			0.474007	+	0.880521i	$0.342807\pi$
$380$		0			0
$381$	−18.7279	+	13.2426i	−0.959461	+	0.678441i
$382$		−	12.9706i		−	0.663632i
$383$		−	37.4142i		−	1.91178i	−0.293730	−	0.955889i	$-0.594897\pi$
$383$		−	37.4142i		−	1.91178i	0.293730	−	0.955889i	$-0.405103\pi$
$384$	−11.3137	−	16.0000i	−0.577350	−	0.816497i
$385$	3.00000	+	1.41421i	0.152894	+	0.0720750i
$386$			14.1421i			0.719816i
$387$	9.17157	+	3.24264i	0.466217	+	0.164833i
$388$		0			0
$389$			1.75736i			0.0891017i	0.999007	+	0.0445508i	$0.0141857\pi$
$389$			1.75736i			0.0891017i	−0.999007	+	0.0445508i	$0.985814\pi$
$390$	3.17157	+	4.48528i	0.160599	+	0.227121i
$391$			7.24264i			0.366276i
$392$	−2.82843			−0.142857
$393$	19.4142	+	27.4558i	0.979318	+	1.38496i
$394$	8.48528			0.427482
$395$	6.24264			0.314101
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	−10.6274			−0.532704
$399$	−3.24264	−	4.58579i	−0.162335	−	0.229576i
$400$	4.00000			0.200000
$401$			5.27208i			0.263275i	0.991298	+	0.131638i	$0.0420235\pi$
$401$			5.27208i			0.263275i	−0.991298	+	0.131638i	$0.957977\pi$
$402$	17.6569	+	24.9706i	0.880644	+	1.24542i
$403$			18.4853i			0.920817i
$404$		0			0
$405$	5.65685	−	7.00000i	0.281091	−	0.347833i
$406$		−	8.24264i		−	0.409075i
$407$	24.7279	+	11.6569i	1.22572	+	0.577809i
$408$	16.4853	+	23.3137i	0.816143	+	1.15420i
$409$		−	18.4853i		−	0.914038i	−0.889457	−	0.457019i	$-0.848917\pi$
$409$		−	18.4853i		−	0.914038i	0.889457	−	0.457019i	$-0.151083\pi$
$410$		−	6.48528i		−	0.320285i
$411$	−20.4853	+	14.4853i	−1.01046	+	0.714506i
$412$		0			0
$413$	12.8995			0.634743
$414$	4.97056	+	1.75736i	0.244290	+	0.0863695i
$415$		−	17.1421i		−	0.841474i
$416$		0			0
$417$	17.6569	−	12.4853i	0.864660	−	0.611407i
$418$	−6.48528	+	13.7574i	−0.317205	+	0.672894i
$419$			25.5858i			1.24995i	0.780646	+	0.624974i	$0.214890\pi$
$419$			25.5858i			1.24995i	−0.780646	+	0.624974i	$0.785110\pi$
$420$		0			0
$421$	−21.4853			−1.04713			−0.523564	−	0.851986i	$-0.675398\pi$
$421$	−21.4853			−1.04713			−0.523564	+	0.851986i	$0.675398\pi$
$422$		−	11.3137i		−	0.550743i
$423$	−3.02944	−	1.07107i	−0.147296	−	0.0520771i
$424$			12.4853i			0.606339i
$425$	−5.82843			−0.282720
$426$	3.51472	−	2.48528i	0.170289	−	0.120412i
$427$	9.24264			0.447283
$428$		0			0
$429$	−12.6863	+	2.24264i	−0.612500	+	0.108276i
$430$	−4.58579			−0.221146
$431$	23.6569			1.13951			0.569755	−	0.821814i	$-0.307038\pi$
$431$	23.6569			1.13951			0.569755	+	0.821814i	$0.307038\pi$
$432$	20.0000	−	5.65685i	0.962250	−	0.272166i
$433$	−12.0000			−0.576683			−0.288342	−	0.957528i	$-0.593104\pi$
$433$	−12.0000			−0.576683			−0.288342	+	0.957528i	$0.593104\pi$
$434$			11.6569i			0.559547i
$435$	8.24264	−	5.82843i	0.395204	−	0.279452i
$436$		0			0
$437$	4.02944			0.192754
$438$	−12.9706	+	9.17157i	−0.619757	+	0.438235i
$439$			5.24264i			0.250218i	0.992143	+	0.125109i	$0.0399280\pi$
$439$			5.24264i			0.250218i	−0.992143	+	0.125109i	$0.960072\pi$
$440$	−4.00000	+	8.48528i	−0.190693	+	0.404520i
$441$	1.00000	−	2.82843i	0.0476190	−	0.134687i
$442$		−	18.4853i		−	0.879255i
$443$		−	11.3137i		−	0.537531i	−0.963206	−	0.268765i	$-0.913384\pi$
$443$		−	11.3137i		−	0.537531i	0.963206	−	0.268765i	$-0.0866156\pi$
$444$		0			0
$445$	−16.4142			−0.778108
$446$	−24.0416			−1.13840
$447$		0			0
$448$		−	8.00000i		−	0.377964i
$449$		−	11.2721i		−	0.531962i	−0.963978	−	0.265981i	$-0.914304\pi$
$449$		−	11.2721i		−	0.531962i	0.963978	−	0.265981i	$-0.0856959\pi$
$450$	−1.41421	+	4.00000i	−0.0666667	+	0.188562i
$451$	13.7574	+	6.48528i	0.647809	+	0.305380i
$452$		0			0
$453$	−14.1421	+	10.0000i	−0.664455	+	0.469841i
$454$	−8.72792			−0.409622
$455$			2.24264i			0.105137i
$456$	12.9706	−	9.17157i	0.607402	−	0.429498i
$457$			32.2132i			1.50687i	0.657522	+	0.753435i	$0.271605\pi$
$457$			32.2132i			1.50687i	−0.657522	+	0.753435i	$0.728395\pi$
$458$	−26.4853			−1.23758
$459$	−29.1421	+	8.24264i	−1.36024	+	0.384734i
$460$		0			0
$461$	−18.3431			−0.854325			−0.427163	−	0.904175i	$-0.640487\pi$
$461$	−18.3431			−0.854325			−0.427163	+	0.904175i	$0.640487\pi$
$462$	−8.00000	+	1.41421i	−0.372194	+	0.0657952i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	23.3137			1.08231
$465$	−11.6569	+	8.24264i	−0.540574	+	0.382243i
$466$	−13.5147			−0.626057
$467$		−	11.6569i		−	0.539415i	−0.962942	−	0.269707i	$-0.913073\pi$
$467$		−	11.6569i		−	0.539415i	0.962942	−	0.269707i	$-0.0869270\pi$
$468$		0			0
$469$			12.4853i			0.576517i
$470$	1.51472			0.0698688
$471$	11.0000	+	15.5563i	0.506853	+	0.716799i
$472$			36.4853i			1.67937i
$473$	4.58579	−	9.72792i	0.210855	−	0.447290i
$474$	−12.4853	+	8.82843i	−0.573468	+	0.405503i
$475$			3.24264i			0.148783i
$476$		0			0
$477$	−12.4853	−	4.41421i	−0.571662	−	0.202113i
$478$	−12.2426			−0.559965
$479$	−15.2132			−0.695109			−0.347555	−	0.937660i	$-0.612988\pi$
$479$	−15.2132			−0.695109			−0.347555	+	0.937660i	$0.612988\pi$
$480$		0			0
$481$			18.4853i			0.842856i
$482$			13.4558i			0.612897i
$483$	1.24264	+	1.75736i	0.0565421	+	0.0799626i
$484$		0			0
$485$		−	7.00000i		−	0.317854i
$486$	−1.41421	+	22.0000i	−0.0641500	+	0.997940i
$487$	36.9706			1.67530			0.837648	−	0.546210i	$-0.183930\pi$
$487$	36.9706			1.67530			0.837648	+	0.546210i	$0.183930\pi$
$488$			26.1421i			1.18340i
$489$	2.24264	+	3.17157i	0.101416	+	0.143423i
$490$			1.41421i			0.0638877i
$491$	−26.6569			−1.20301			−0.601503	−	0.798870i	$-0.705431\pi$
$491$	−26.6569			−1.20301			−0.601503	+	0.798870i	$0.705431\pi$
$492$		0			0
$493$	−33.9706			−1.52996
$494$	−10.2843			−0.462711
$495$	−7.07107	−	7.00000i	−0.317821	−	0.314627i
$496$	−32.9706			−1.48042
$497$	1.75736			0.0788283
$498$	24.2426	+	34.2843i	1.08634	+	1.53631i
$499$	5.48528			0.245555			0.122777	−	0.992434i	$-0.460820\pi$
$499$	5.48528			0.245555			0.122777	+	0.992434i	$0.460820\pi$
$500$		0			0
$501$	−20.1421	−	28.4853i	−0.899884	−	1.27263i
$502$			40.9706i			1.82861i
$503$	40.4558			1.80384			0.901918	−	0.431906i	$-0.142159\pi$
$503$	40.4558			1.80384			0.901918	+	0.431906i	$0.142159\pi$
$504$	8.00000	+	2.82843i	0.356348	+	0.125988i
$505$		−	2.48528i		−	0.110594i
$506$	2.48528	−	5.27208i	0.110484	−	0.234372i
$507$	7.97056	+	11.2721i	0.353985	+	0.500611i
$508$		0			0
$509$			37.2426i			1.65075i	0.564584	+	0.825376i	$0.309037\pi$
$509$			37.2426i			1.65075i	−0.564584	+	0.825376i	$0.690963\pi$
$510$	11.6569	−	8.24264i	0.516174	−	0.364990i
$511$	−6.48528			−0.286892
$512$	22.6274			1.00000
$513$	4.58579	+	16.2132i	0.202467	+	0.715830i
$514$			31.4558i			1.38746i
$515$		−	0.514719i		−	0.0226812i
$516$		0			0
$517$	−1.51472	+	3.21320i	−0.0666172	+	0.141317i
$518$			11.6569i			0.512173i
$519$	2.82843	+	4.00000i	0.124154	+	0.175581i
$520$	−6.34315			−0.278165
$521$			10.4142i			0.456255i	0.973631	+	0.228127i	$0.0732603\pi$
$521$			10.4142i			0.456255i	−0.973631	+	0.228127i	$0.926740\pi$
$522$	−8.24264	+	23.3137i	−0.360771	+	1.02041i
$523$		−	6.97056i		−	0.304801i	−0.988319	−	0.152401i	$-0.951300\pi$
$523$		−	6.97056i		−	0.304801i	0.988319	−	0.152401i	$-0.0487004\pi$
$524$		0			0
$525$	−1.41421	+	1.00000i	−0.0617213	+	0.0436436i
$526$	−29.4558			−1.28434
$527$	48.0416			2.09273
$528$	−4.00000	−	22.6274i	−0.174078	−	0.984732i
$529$	21.4558			0.932863
$530$	6.24264			0.271163
$531$	−36.4853	−	12.8995i	−1.58333	−	0.559790i
$532$		0			0
$533$			10.2843i			0.445461i
$534$	32.8284	−	23.2132i	1.42062	−	1.00453i
$535$		−	7.41421i		−	0.320544i
$536$	−35.3137			−1.52532
$537$	18.9706	−	13.4142i	0.818640	−	0.578866i
$538$		−	0.786797i		−	0.0339212i
$539$	−3.00000	−	1.41421i	−0.129219	−	0.0609145i
$540$		0			0
$541$			10.7279i			0.461229i	0.973045	+	0.230615i	$0.0740737\pi$
$541$			10.7279i			0.461229i	−0.973045	+	0.230615i	$0.925926\pi$
$542$			20.8701i			0.896446i
$543$	−10.9706	−	15.5147i	−0.470792	−	0.665800i
$544$		0			0
$545$	−3.75736			−0.160948
$546$	−3.17157	−	4.48528i	−0.135731	−	0.191952i
$547$		−	23.2426i		−	0.993784i	−0.867813	−	0.496892i	$-0.834475\pi$
$547$		−	23.2426i		−	0.993784i	0.867813	−	0.496892i	$-0.165525\pi$
$548$		0			0
$549$	−26.1421	−	9.24264i	−1.11572	−	0.394466i
$550$	4.24264	+	2.00000i	0.180907	+	0.0852803i
$551$			18.8995i			0.805146i
$552$	−4.97056	+	3.51472i	−0.211561	+	0.149596i
$553$	−6.24264			−0.265464
$554$		−	12.0000i		−	0.509831i
$555$	−11.6569	+	8.24264i	−0.494806	+	0.349881i
$556$		0			0
$557$	27.1716			1.15130			0.575648	−	0.817697i	$-0.304750\pi$
$557$	27.1716			1.15130			0.575648	+	0.817697i	$0.304750\pi$
$558$	11.6569	−	32.9706i	0.493474	−	1.39576i
$559$	7.27208			0.307576
$560$	−4.00000			−0.169031
$561$	5.82843	+	32.9706i	0.246076	+	1.39202i
$562$	−7.51472			−0.316989
$563$	−25.1127			−1.05837			−0.529187	−	0.848505i	$-0.677503\pi$
$563$	−25.1127			−1.05837			−0.529187	+	0.848505i	$0.677503\pi$
$564$		0			0
$565$	18.8995			0.795108
$566$			41.3137i			1.73654i
$567$	−5.65685	+	7.00000i	−0.237566	+	0.293972i
$568$			4.97056i			0.208560i
$569$	−17.1421			−0.718636			−0.359318	−	0.933215i	$-0.616991\pi$
$569$	−17.1421			−0.718636			−0.359318	+	0.933215i	$0.616991\pi$
$570$	−4.58579	−	6.48528i	−0.192077	−	0.271639i
$571$		−	40.1838i		−	1.68164i	−0.541316	−	0.840819i	$-0.682074\pi$
$571$		−	40.1838i		−	1.68164i	0.541316	−	0.840819i	$-0.317926\pi$
$572$		0			0
$573$	−12.9706	+	9.17157i	−0.541853	+	0.383148i
$574$			6.48528i			0.270690i
$575$		−	1.24264i		−	0.0518217i
$576$	−8.00000	+	22.6274i	−0.333333	+	0.942809i
$577$	−21.4558			−0.893218			−0.446609	−	0.894729i	$-0.647369\pi$
$577$	−21.4558			−0.893218			−0.446609	+	0.894729i	$0.647369\pi$
$578$	−24.0000			−0.998268
$579$	14.1421	−	10.0000i	0.587727	−	0.415586i
$580$		0			0
$581$			17.1421i			0.711176i
$582$	9.89949	+	14.0000i	0.410347	+	0.580319i
$583$	−6.24264	+	13.2426i	−0.258544	+	0.548454i
$584$		−	18.3431i		−	0.759045i
$585$	2.24264	−	6.34315i	0.0927218	−	0.262257i
$586$	4.72792			0.195309
$587$		−	36.0416i		−	1.48760i	−0.668404	−	0.743799i	$-0.733022\pi$
$587$		−	36.0416i		−	1.48760i	0.668404	−	0.743799i	$-0.266978\pi$
$588$		0			0
$589$		−	26.7279i		−	1.10130i
$590$	18.2426			0.751038
$591$	−6.00000	−	8.48528i	−0.246807	−	0.349038i
$592$	−32.9706			−1.35508
$593$	26.8284			1.10171			0.550856	−	0.834600i	$-0.314301\pi$
$593$	26.8284			1.10171			0.550856	+	0.834600i	$0.314301\pi$
$594$	24.0416	+	4.00000i	0.986440	+	0.164122i
$595$	5.82843			0.238942
$596$		0			0
$597$	7.51472	+	10.6274i	0.307557	+	0.434951i
$598$	3.94113			0.161165
$599$			25.1127i			1.02608i	0.858366	+	0.513039i	$0.171480\pi$
$599$			25.1127i			1.02608i	−0.858366	+	0.513039i	$0.828520\pi$
$600$	−2.82843	−	4.00000i	−0.115470	−	0.163299i
$601$		−	4.27208i		−	0.174262i	−0.996197	−	0.0871308i	$-0.972230\pi$
$601$		−	4.27208i		−	0.174262i	0.996197	−	0.0871308i	$-0.0277698\pi$
$602$	4.58579			0.186903
$603$	12.4853	−	35.3137i	0.508440	−	1.43809i
$604$		0			0
$605$	−8.48528	+	7.00000i	−0.344976	+	0.284590i
$606$	3.51472	+	4.97056i	0.142776	+	0.201915i
$607$		−	26.4853i		−	1.07500i	−0.843262	−	0.537502i	$-0.819368\pi$
$607$		−	26.4853i		−	1.07500i	0.843262	−	0.537502i	$-0.180632\pi$
$608$		0			0
$609$	−8.24264	+	5.82843i	−0.334009	+	0.236180i
$610$	13.0711			0.529232
$611$	−2.40202			−0.0971753
$612$		0			0
$613$			18.4853i			0.746613i	0.927708	+	0.373307i	$0.121776\pi$
$613$			18.4853i			0.746613i	−0.927708	+	0.373307i	$0.878224\pi$
$614$			28.9706i			1.16916i
$615$	−6.48528	+	4.58579i	−0.261512	+	0.184917i
$616$	4.00000	−	8.48528i	0.161165	−	0.341882i
$617$		−	5.31371i		−	0.213922i	−0.994263	−	0.106961i	$-0.965888\pi$
$617$		−	5.31371i		−	0.213922i	0.994263	−	0.106961i	$-0.0341120\pi$
$618$	0.727922	+	1.02944i	0.0292813	+	0.0414100i
$619$	2.48528			0.0998919			0.0499459	−	0.998752i	$-0.484095\pi$
$619$	2.48528			0.0998919			0.0499459	+	0.998752i	$0.484095\pi$
$620$		0			0
$621$	−1.75736	−	6.21320i	−0.0705204	−	0.249327i
$622$		−	20.9706i		−	0.840843i
$623$	16.4142			0.657622
$624$	12.6863	−	8.97056i	0.507858	−	0.359110i
$625$	1.00000			0.0400000
$626$	37.4142			1.49537
$627$	18.3431	−	3.24264i	0.732555	−	0.129499i
$628$		0			0
$629$	48.0416			1.91555
$630$	1.41421	−	4.00000i	0.0563436	−	0.159364i
$631$	15.0000			0.597141			0.298570	−	0.954388i	$-0.403490\pi$
$631$	15.0000			0.597141			0.298570	+	0.954388i	$0.403490\pi$
$632$		−	17.6569i		−	0.702352i
$633$	−11.3137	+	8.00000i	−0.449680	+	0.317971i
$634$			46.4264i			1.84383i
$635$	−13.2426			−0.525518
$636$		0			0
$637$		−	2.24264i		−	0.0888567i
$638$	24.7279	+	11.6569i	0.978988	+	0.461499i
$639$	−4.97056	−	1.75736i	−0.196632	−	0.0695201i
$640$		−	11.3137i		−	0.447214i
$641$			31.4558i			1.24243i	0.783640	+	0.621216i	$0.213361\pi$
$641$			31.4558i			1.24243i	−0.783640	+	0.621216i	$0.786639\pi$
$642$	10.4853	+	14.8284i	0.413821	+	0.585231i
$643$	−15.9706			−0.629818			−0.314909	−	0.949122i	$-0.601974\pi$
$643$	−15.9706			−0.629818			−0.314909	+	0.949122i	$0.601974\pi$
$644$		0			0
$645$	3.24264	+	4.58579i	0.127679	+	0.180565i
$646$			26.7279i			1.05160i
$647$			43.7990i			1.72192i	0.508676	+	0.860958i	$0.330135\pi$
$647$			43.7990i			1.72192i	−0.508676	+	0.860958i	$0.669865\pi$
$648$	−19.7990	−	16.0000i	−0.777778	−	0.628539i
$649$	−18.2426	+	38.6985i	−0.716086	+	1.51905i
$650$			3.17157i			0.124399i
$651$	11.6569	−	8.24264i	0.456868	−	0.323055i
$652$		0			0
$653$			18.2132i			0.712738i	0.934345	+	0.356369i	$0.115985\pi$
$653$			18.2132i			0.712738i	−0.934345	+	0.356369i	$0.884015\pi$
$654$	7.51472	−	5.31371i	0.293849	−	0.207782i
$655$			19.4142i			0.758576i
$656$	−18.3431			−0.716180
$657$	18.3431	+	6.48528i	0.715634	+	0.253015i
$658$	−1.51472			−0.0590499
$659$	−13.2843			−0.517482			−0.258741	−	0.965947i	$-0.583308\pi$
$659$	−13.2843			−0.517482			−0.258741	+	0.965947i	$0.583308\pi$
$660$		0			0
$661$	17.2132			0.669516			0.334758	−	0.942304i	$-0.391345\pi$
$661$	17.2132			0.669516			0.334758	+	0.942304i	$0.391345\pi$
$662$	−3.55635			−0.138221
$663$	−18.4853	+	13.0711i	−0.717909	+	0.507638i
$664$	−48.4853			−1.88159
$665$		−	3.24264i		−	0.125744i
$666$	11.6569	−	32.9706i	0.451694	−	1.27758i
$667$		−	7.24264i		−	0.280436i
$668$		0			0
$669$	17.0000	+	24.0416i	0.657258	+	0.929503i
$670$			17.6569i			0.682144i
$671$	−13.0711	+	27.7279i	−0.504603	+	1.07042i
$672$		0			0
$673$			10.2721i			0.395960i	0.980206	+	0.197980i	$0.0634380\pi$
$673$			10.2721i			0.395960i	−0.980206	+	0.197980i	$0.936562\pi$
$674$		−	38.5269i		−	1.48400i
$675$	5.00000	−	1.41421i	0.192450	−	0.0544331i
$676$		0			0
$677$	−6.17157			−0.237193			−0.118596	−	0.992943i	$-0.537839\pi$
$677$	−6.17157			−0.237193			−0.118596	+	0.992943i	$0.537839\pi$
$678$	−37.7990	+	26.7279i	−1.45166	+	1.02648i
$679$			7.00000i			0.268635i
$680$			16.4853i			0.632182i
$681$	6.17157	+	8.72792i	0.236495	+	0.334455i
$682$	−34.9706	−	16.4853i	−1.33909	−	0.631254i
$683$		−	11.6569i		−	0.446037i	−0.974814	−	0.223019i	$-0.928409\pi$
$683$		−	11.6569i		−	0.446037i	0.974814	−	0.223019i	$-0.0715911\pi$
$684$		0			0
$685$	−14.4853			−0.553454
$686$		−	1.41421i		−	0.0539949i
$687$	18.7279	+	26.4853i	0.714515	+	1.01048i
$688$			12.9706i			0.494498i
$689$	−9.89949			−0.377141
$690$	1.75736	+	2.48528i	0.0669015	+	0.0946130i
$691$	−9.02944			−0.343496			−0.171748	−	0.985141i	$-0.554941\pi$
$691$	−9.02944			−0.343496			−0.171748	+	0.985141i	$0.554941\pi$
$692$		0			0
$693$	7.07107	+	7.00000i	0.268608	+	0.265908i
$694$	37.9411			1.44023
$695$	12.4853			0.473594
$696$	−16.4853	−	23.3137i	−0.624873	−	0.883704i
$697$	26.7279			1.01239
$698$			18.0416i			0.682886i
$699$	9.55635	+	13.5147i	0.361454	+	0.511174i
$700$		0			0
$701$	37.9706			1.43413			0.717064	−	0.697007i	$-0.245485\pi$
$701$	37.9706			1.43413			0.717064	+	0.697007i	$0.245485\pi$
$702$	4.48528	+	15.8579i	0.169286	+	0.598517i
$703$		−	26.7279i		−	1.00806i
$704$	24.0000	+	11.3137i	0.904534	+	0.426401i
$705$	−1.07107	−	1.51472i	−0.0403387	−	0.0570476i
$706$		−	25.4558i		−	0.958043i
$707$			2.48528i			0.0934686i
$708$		0			0
$709$	−50.9411			−1.91313			−0.956567	−	0.291512i	$-0.905842\pi$
$709$	−50.9411			−1.91313			−0.956567	+	0.291512i	$0.905842\pi$
$710$	2.48528			0.0932709
$711$	17.6569	+	6.24264i	0.662184	+	0.234117i
$712$			46.4264i			1.73990i
$713$			10.2426i			0.383590i
$714$	−11.6569	+	8.24264i	−0.436247	+	0.308473i
$715$	−6.72792	−	3.17157i	−0.251610	−	0.118610i
$716$		0			0
$717$	8.65685	+	12.2426i	0.323296	+	0.457210i
$718$	−19.2721			−0.719228
$719$		−	47.5269i		−	1.77245i	−0.463251	−	0.886227i	$-0.653317\pi$
$719$		−	47.5269i		−	1.77245i	0.463251	−	0.886227i	$-0.346683\pi$
$720$	11.3137	+	4.00000i	0.421637	+	0.149071i
$721$			0.514719i			0.0191691i
$722$	−12.0000			−0.446594
$723$	13.4558	−	9.51472i	0.500428	−	0.353856i
$724$		0			0
$725$	5.82843			0.216462
$726$	7.07107	−	26.0000i	0.262432	−	0.964951i
$727$	20.4558			0.758665			0.379333	−	0.925260i	$-0.376154\pi$
$727$	20.4558			0.758665			0.379333	+	0.925260i	$0.376154\pi$
$728$	6.34315			0.235093
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	−9.17157			−0.339455
$731$		−	18.8995i		−	0.699023i
$732$		0			0
$733$		−	21.4558i		−	0.792490i	−0.918145	−	0.396245i	$-0.870313\pi$
$733$		−	21.4558i		−	0.792490i	0.918145	−	0.396245i	$-0.129687\pi$
$734$	−4.24264			−0.156599
$735$	1.41421	−	1.00000i	0.0521641	−	0.0368856i
$736$		0			0
$737$	−37.4558	−	17.6569i	−1.37970	−	0.650399i
$738$	6.48528	−	18.3431i	0.238727	−	0.675221i
$739$			30.4853i			1.12142i	0.828013	+	0.560710i	$0.189472\pi$
$739$			30.4853i			1.12142i	−0.828013	+	0.560710i	$0.810528\pi$
$740$		0			0
$741$	7.27208	+	10.2843i	0.267146	+	0.377802i
$742$	−6.24264			−0.229175
$743$	−46.6274			−1.71059			−0.855297	−	0.518138i	$-0.826625\pi$
$743$	−46.6274			−1.71059			−0.855297	+	0.518138i	$0.826625\pi$
$744$	23.3137	+	32.9706i	0.854722	+	1.20876i
$745$		0			0
$746$			8.78680i			0.321707i
$747$	17.1421	−	48.4853i	0.627198	−	1.77398i
$748$		0			0
$749$			7.41421i			0.270909i
$750$	−2.00000	+	1.41421i	−0.0730297	+	0.0516398i
$751$	7.97056			0.290850			0.145425	−	0.989369i	$-0.453545\pi$
$751$	7.97056			0.290850			0.145425	+	0.989369i	$0.453545\pi$
$752$		−	4.28427i		−	0.156231i
$753$	40.9706	−	28.9706i	1.49305	−	1.05575i
$754$			18.4853i			0.673194i
$755$	−10.0000			−0.363937
$756$		0			0
$757$	−9.45584			−0.343679			−0.171839	−	0.985125i	$-0.554971\pi$
$757$	−9.45584			−0.343679			−0.171839	+	0.985125i	$0.554971\pi$
$758$	−26.1005			−0.948013
$759$	−7.02944	+	1.24264i	−0.255152	+	0.0451050i
$760$	9.17157			0.332688
$761$	−7.02944			−0.254817			−0.127408	−	0.991850i	$-0.540666\pi$
$761$	−7.02944			−0.254817			−0.127408	+	0.991850i	$0.540666\pi$
$762$	26.4853	−	18.7279i	0.959461	−	0.678441i
$763$	3.75736			0.136026
$764$		0			0
$765$	−16.4853	−	5.82843i	−0.596027	−	0.210727i
$766$			52.9117i			1.91178i
$767$	−28.9289			−1.04456
$768$		0			0
$769$		−	51.6690i		−	1.86323i	−0.363442	−	0.931617i	$-0.618399\pi$
$769$		−	51.6690i		−	1.86323i	0.363442	−	0.931617i	$-0.381601\pi$
$770$	−4.24264	−	2.00000i	−0.152894	−	0.0720750i
$771$	31.4558	−	22.2426i	1.13285	−	0.801049i
$772$		0			0
$773$		−	14.8284i		−	0.533341i	−0.963788	−	0.266671i	$-0.914076\pi$
$773$		−	14.8284i		−	0.533341i	0.963788	−	0.266671i	$-0.0859236\pi$
$774$	−12.9706	−	4.58579i	−0.466217	−	0.164833i
$775$	−8.24264			−0.296084
$776$	−19.7990			−0.710742
$777$	11.6569	−	8.24264i	0.418187	−	0.295703i
$778$		−	2.48528i		−	0.0891017i
$779$		−	14.8701i		−	0.532775i
$780$		0			0
$781$	−2.48528	+	5.27208i	−0.0889304	+	0.188650i
$782$		−	10.2426i		−	0.366276i
$783$	29.1421	−	8.24264i	1.04145	−	0.294568i
$784$	4.00000			0.142857
$785$			11.0000i			0.392607i
$786$	−27.4558	−	38.8284i	−0.979318	−	1.38496i
$787$			15.4558i			0.550941i	0.961309	+	0.275471i	$0.0888337\pi$
$787$			15.4558i			0.550941i	−0.961309	+	0.275471i	$0.911166\pi$
$788$		0			0
$789$	20.8284	+	29.4558i	0.741512	+	1.04866i
$790$	−8.82843			−0.314101
$791$	−18.8995			−0.671989
$792$	−19.7990	+	20.0000i	−0.703526	+	0.710669i
$793$	−20.7279			−0.736070
$794$	48.0833			1.70641
$795$	−4.41421	−	6.24264i	−0.156556	−	0.221404i
$796$		0			0
$797$			7.79899i			0.276254i	0.990414	+	0.138127i	$0.0441083\pi$
$797$			7.79899i			0.276254i	−0.990414	+	0.138127i	$0.955892\pi$
$798$	4.58579	+	6.48528i	0.162335	+	0.229576i
$799$			6.24264i			0.220849i
$800$		0			0
$801$	−46.4264	−	16.4142i	−1.64040	−	0.579968i
$802$		−	7.45584i		−	0.263275i
$803$	9.17157	−	19.4558i	0.323658	−	0.686582i
$804$		0			0
$805$			1.24264i			0.0437973i
$806$		−	26.1421i		−	0.920817i
$807$	−0.786797	+	0.556349i	−0.0276966	+	0.0195844i
$808$	−7.02944			−0.247295
$809$	−21.1716			−0.744353			−0.372176	−	0.928162i	$-0.621388\pi$
$809$	−21.1716			−0.744353			−0.372176	+	0.928162i	$0.621388\pi$
$810$	−8.00000	+	9.89949i	−0.281091	+	0.347833i
$811$		−	2.00000i		−	0.0702295i	−0.999383	−	0.0351147i	$-0.988820\pi$
$811$		−	2.00000i		−	0.0702295i	0.999383	−	0.0351147i	$-0.0111797\pi$
$812$		0			0
$813$	20.8701	−	14.7574i	0.731945	−	0.517563i
$814$	−34.9706	−	16.4853i	−1.22572	−	0.577809i
$815$			2.24264i			0.0785563i
$816$	−23.3137	−	32.9706i	−0.816143	−	1.15420i
$817$	−10.5147			−0.367863
$818$			26.1421i			0.914038i
$819$	−2.24264	+	6.34315i	−0.0783642	+	0.221647i
$820$		0			0
$821$	0.857864			0.0299397			0.0149698	−	0.999888i	$-0.495235\pi$
$821$	0.857864			0.0299397			0.0149698	+	0.999888i	$0.495235\pi$
$822$	28.9706	−	20.4853i	1.01046	−	0.714506i
$823$	41.2132			1.43660			0.718301	−	0.695732i	$-0.244920\pi$
$823$	41.2132			1.43660			0.718301	+	0.695732i	$0.244920\pi$
$824$	−1.45584			−0.0507167
$825$	−1.00000	−	5.65685i	−0.0348155	−	0.196946i
$826$	−18.2426			−0.634743
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$		0			0
$829$	−3.02944			−0.105217			−0.0526084	−	0.998615i	$-0.516753\pi$
$829$	−3.02944			−0.105217			−0.0526084	+	0.998615i	$0.516753\pi$
$830$			24.2426i			0.841474i
$831$	−12.0000	+	8.48528i	−0.416275	+	0.294351i
$832$			17.9411i			0.621997i
$833$	−5.82843			−0.201943
$834$	−24.9706	+	17.6569i	−0.864660	+	0.611407i
$835$		−	20.1421i		−	0.697047i
$836$		0			0
$837$	−41.2132	+	11.6569i	−1.42454	+	0.402920i
$838$		−	36.1838i		−	1.24995i
$839$		−	4.41421i		−	0.152396i	−0.997093	−	0.0761978i	$-0.975722\pi$
$839$		−	4.41421i		−	0.152396i	0.997093	−	0.0761978i	$-0.0242780\pi$
$840$	2.82843	+	4.00000i	0.0975900	+	0.138013i
$841$	4.97056			0.171399
$842$	30.3848			1.04713
$843$	5.31371	+	7.51472i	0.183014	+	0.258821i
$844$		0			0
$845$			7.97056i			0.274196i
$846$	4.28427	+	1.51472i	0.147296	+	0.0520771i
$847$	8.48528	−	7.00000i	0.291558	−	0.240523i
$848$		−	17.6569i		−	0.606339i
$849$	41.3137	−	29.2132i	1.41788	−	1.00259i
$850$	8.24264			0.282720
$851$			10.2426i			0.351113i
$852$		0			0
$853$		−	35.7574i		−	1.22431i	−0.790738	−	0.612154i	$-0.790303\pi$
$853$		−	35.7574i		−	1.22431i	0.790738	−	0.612154i	$-0.209697\pi$
$854$	−13.0711			−0.447283
$855$	−3.24264	+	9.17157i	−0.110896	+	0.313661i
$856$	−20.9706			−0.716759
$857$	−1.02944			−0.0351649			−0.0175825	−	0.999845i	$-0.505597\pi$
$857$	−1.02944			−0.0351649			−0.0175825	+	0.999845i	$0.505597\pi$
$858$	17.9411	−	3.17157i	0.612500	−	0.108276i
$859$	−32.1838			−1.09810			−0.549048	−	0.835791i	$-0.685010\pi$
$859$	−32.1838			−1.09810			−0.549048	+	0.835791i	$0.685010\pi$
$860$		0			0
$861$	6.48528	−	4.58579i	0.221018	−	0.156283i
$862$	−33.4558			−1.13951
$863$		−	29.8701i		−	1.01679i	−0.861124	−	0.508394i	$-0.830239\pi$
$863$		−	29.8701i		−	1.01679i	0.861124	−	0.508394i	$-0.169761\pi$
$864$		0			0
$865$			2.82843i			0.0961694i
$866$	16.9706			0.576683
$867$	16.9706	+	24.0000i	0.576351	+	0.815083i
$868$		0			0
$869$	8.82843	−	18.7279i	0.299484	−	0.635301i
$870$	−11.6569	+	8.24264i	−0.395204	+	0.279452i
$871$		−	28.0000i		−	0.948744i
$872$			10.6274i			0.359890i
$873$	7.00000	−	19.7990i	0.236914	−	0.670094i
$874$	−5.69848			−0.192754
$875$	−1.00000			−0.0338062
$876$		0			0
$877$			3.72792i			0.125883i	0.998017	+	0.0629415i	$0.0200482\pi$
$877$			3.72792i			0.125883i	−0.998017	+	0.0629415i	$0.979952\pi$
$878$		−	7.41421i		−	0.250218i
$879$	−3.34315	−	4.72792i	−0.112762	−	0.159469i
$880$	5.65685	−	12.0000i	0.190693	−	0.404520i
$881$			18.2132i			0.613618i	0.951771	+	0.306809i	$0.0992614\pi$
$881$			18.2132i			0.613618i	−0.951771	+	0.306809i	$0.900739\pi$
$882$	−1.41421	+	4.00000i	−0.0476190	+	0.134687i
$883$	−4.97056			−0.167273			−0.0836364	−	0.996496i	$-0.526653\pi$
$883$	−4.97056			−0.167273			−0.0836364	+	0.996496i	$0.526653\pi$
$884$		0			0
$885$	−12.8995	−	18.2426i	−0.433612	−	0.613220i
$886$			16.0000i			0.537531i
$887$	−36.9411			−1.24036			−0.620181	−	0.784459i	$-0.712941\pi$
$887$	−36.9411			−1.24036			−0.620181	+	0.784459i	$0.712941\pi$
$888$	23.3137	+	32.9706i	0.782357	+	1.10642i
$889$	13.2426			0.444144
$890$	23.2132			0.778108
$891$	−13.0000	−	26.8701i	−0.435516	−	0.900181i
$892$		0			0
$893$	3.47309			0.116222
$894$		0			0
$895$	13.4142			0.448388
$896$			11.3137i			0.377964i
$897$	−2.78680	−	3.94113i	−0.0930484	−	0.131590i
$898$			15.9411i			0.531962i
$899$	−48.0416			−1.60228
$900$		0			0
$901$			25.7279i			0.857121i
$902$	−19.4558	−	9.17157i	−0.647809	−	0.305380i
$903$	−3.24264	−	4.58579i	−0.107908	−	0.152605i
$904$		−	53.4558i		−	1.77791i
$905$		−	10.9706i		−	0.364674i
$906$	20.0000	−	14.1421i	0.664455	−	0.469841i
$907$	30.7279			1.02030			0.510152	−	0.860084i	$-0.329589\pi$
$907$	30.7279			1.02030			0.510152	+	0.860084i	$0.329589\pi$
$908$		0			0
$909$	2.48528	−	7.02944i	0.0824316	−	0.233152i
$910$		−	3.17157i		−	0.105137i
$911$			1.71573i			0.0568446i	0.999596	+	0.0284223i	$0.00904832\pi$
$911$			1.71573i			0.0568446i	−0.999596	+	0.0284223i	$0.990952\pi$
$912$	−18.3431	+	12.9706i	−0.607402	+	0.429498i
$913$	−51.4264	−	24.2426i	−1.70197	−	0.802314i
$914$		−	45.5563i		−	1.50687i
$915$	−9.24264	−	13.0711i	−0.305552	−	0.432116i
$916$		0			0
$917$		−	19.4142i		−	0.641114i
$918$	41.2132	−	11.6569i	1.36024	−	0.384734i
$919$		−	48.9706i		−	1.61539i	−0.589601	−	0.807695i	$-0.700715\pi$
$919$		−	48.9706i		−	1.61539i	0.589601	−	0.807695i	$-0.299285\pi$
$920$	−3.51472			−0.115877
$921$	28.9706	−	20.4853i	0.954612	−	0.675013i
$922$	25.9411			0.854325
$923$	−3.94113			−0.129724
$924$		0			0
$925$	−8.24264			−0.271016
$926$	−36.7696			−1.20832
$927$	0.514719	−	1.45584i	0.0169056	−	0.0478162i
$928$		0			0
$929$			19.7990i			0.649584i	0.945786	+	0.324792i	$0.105294\pi$
$929$			19.7990i			0.649584i	−0.945786	+	0.324792i	$0.894706\pi$
$930$	16.4853	−	11.6569i	0.540574	−	0.382243i
$931$			3.24264i			0.106273i
$932$		0			0
$933$	−20.9706	+	14.8284i	−0.686545	+	0.485461i
$934$			16.4853i			0.539415i
$935$	−8.24264	+	17.4853i	−0.269563	+	0.571830i
$936$	−17.9411	−	6.34315i	−0.586424	−	0.207332i
$937$		−	36.7279i		−	1.19985i	−0.800057	−	0.599924i	$-0.795197\pi$
$937$		−	36.7279i		−	1.19985i	0.800057	−	0.599924i	$-0.204803\pi$
$938$		−	17.6569i		−	0.576517i
$939$	−26.4558	−	37.4142i	−0.863354	−	1.22097i
$940$		0			0
$941$	−12.3848			−0.403732			−0.201866	−	0.979413i	$-0.564701\pi$
$941$	−12.3848			−0.403732			−0.201866	+	0.979413i	$0.564701\pi$
$942$	−15.5563	−	22.0000i	−0.506853	−	0.716799i
$943$			5.69848i			0.185568i
$944$		−	51.5980i		−	1.67937i
$945$	−5.00000	+	1.41421i	−0.162650	+	0.0460044i
$946$	−6.48528	+	13.7574i	−0.210855	+	0.447290i
$947$		−	44.3553i		−	1.44135i	−0.693271	−	0.720677i	$-0.743831\pi$
$947$		−	44.3553i		−	1.44135i	0.693271	−	0.720677i	$-0.256169\pi$
$948$		0			0
$949$	14.5442			0.472123
$950$		−	4.58579i		−	0.148783i
$951$	46.4264	−	32.8284i	1.50548	−	1.06453i
$952$		−	16.4853i		−	0.534291i
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$	17.6569	+	6.24264i	0.571662	+	0.202113i
$955$	−9.17157			−0.296785
$956$		0			0
$957$	−5.82843	−	32.9706i	−0.188406	−	1.06579i
$958$	21.5147			0.695109
$959$	14.4853			0.467754
$960$	−11.3137	+	8.00000i	−0.365148	+	0.258199i
$961$	36.9411			1.19165
$962$		−	26.1421i		−	0.842856i
$963$	7.41421	−	20.9706i	0.238920	−	0.675767i
$964$		0			0
$965$	10.0000			0.321911
$966$	−1.75736	−	2.48528i	−0.0565421	−	0.0799626i
$967$			40.2132i			1.29317i	0.762842	+	0.646585i	$0.223803\pi$
$967$			40.2132i			1.29317i	−0.762842	+	0.646585i	$0.776197\pi$
$968$	19.7990	+	24.0000i	0.636364	+	0.771389i
$969$	26.7279	−	18.8995i	0.858625	−	0.607139i
$970$			9.89949i			0.317854i
$971$			0.129942i			0.00417005i	0.999998	+	0.00208502i	$0.000663684\pi$
$971$			0.129942i			0.00417005i	−0.999998	+	0.00208502i	$0.999336\pi$
$972$		0			0
$973$	−12.4853			−0.400260
$974$	−52.2843			−1.67530
$975$	3.17157	−	2.24264i	0.101572	−	0.0718220i
$976$		−	36.9706i		−	1.18340i
$977$			23.1005i			0.739051i	0.929221	+	0.369525i	$0.120480\pi$
$977$			23.1005i			0.739051i	−0.929221	+	0.369525i	$0.879520\pi$
$978$	−3.17157	−	4.48528i	−0.101416	−	0.143423i
$979$	−23.2132	+	49.2426i	−0.741897	+	1.57380i
$980$		0			0
$981$	−10.6274	−	3.75736i	−0.339307	−	0.119963i
$982$	37.6985			1.20301
$983$		−	22.6274i		−	0.721703i	−0.932623	−	0.360851i	$-0.882486\pi$
$983$		−	22.6274i		−	0.721703i	0.932623	−	0.360851i	$-0.117514\pi$
$984$	12.9706	+	18.3431i	0.413486	+	0.584758i
$985$		−	6.00000i		−	0.191176i
$986$	48.0416			1.52996
$987$	1.07107	+	1.51472i	0.0340925	+	0.0482140i
$988$		0			0
$989$	4.02944			0.128129
$990$	10.0000	+	9.89949i	0.317821	+	0.314627i
$991$	44.5147			1.41406			0.707028	−	0.707185i	$-0.250035\pi$
$991$	44.5147			1.41406			0.707028	+	0.707185i	$0.250035\pi$
$992$		0			0
$993$	2.51472	+	3.55635i	0.0798022	+	0.112857i
$994$	−2.48528			−0.0788283
$995$			7.51472i			0.238233i
$996$		0			0
$997$		−	7.02944i		−	0.222625i	−0.993785	−	0.111312i	$-0.964495\pi$
$997$		−	7.02944i		−	0.222625i	0.993785	−	0.111312i	$-0.0355054\pi$
$998$	−7.75736			−0.245555
$999$	−41.2132	+	11.6569i	−1.30393	+	0.368807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.c.1121.2	yes	4
3.2	odd	2		1155.2.l.b.1121.3	✓	4
11.10	odd	2		1155.2.l.b.1121.4	yes	4
33.32	even	2	inner	1155.2.l.c.1121.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.b.1121.3	✓	4	3.2	odd	2
1155.2.l.b.1121.4	yes	4	11.10	odd	2
1155.2.l.c.1121.1	yes	4	33.32	even	2	inner
1155.2.l.c.1121.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000i q^{5} +(-1.41421 - 2.00000i) q^{6} -1.00000i q^{7} +2.82843 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(1.00000 + 1.41421i) q^{3} +1.00000i q^{5} +(-1.41421 - 2.00000i) q^{6} -1.00000i q^{7} +2.82843 q^{8} +(-1.00000 + 2.82843i) q^{9} -1.41421i q^{10} +(3.00000 + 1.41421i) q^{11} +2.24264i q^{13} +1.41421i q^{14} +(-1.41421 + 1.00000i) q^{15} -4.00000 q^{16} +5.82843 q^{17} +(1.41421 - 4.00000i) q^{18} -3.24264i q^{19} +(1.41421 - 1.00000i) q^{21} +(-4.24264 - 2.00000i) q^{22} +1.24264i q^{23} +(2.82843 + 4.00000i) q^{24} -1.00000 q^{25} -3.17157i q^{26} +(-5.00000 + 1.41421i) q^{27} -5.82843 q^{29} +(2.00000 - 1.41421i) q^{30} +8.24264 q^{31} +(1.00000 + 5.65685i) q^{33} -8.24264 q^{34} +1.00000 q^{35} +8.24264 q^{37} +4.58579i q^{38} +(-3.17157 + 2.24264i) q^{39} +2.82843i q^{40} +4.58579 q^{41} +(-2.00000 + 1.41421i) q^{42} -3.24264i q^{43} +(-2.82843 - 1.00000i) q^{45} -1.75736i q^{46} +1.07107i q^{47} +(-4.00000 - 5.65685i) q^{48} -1.00000 q^{49} +1.41421 q^{50} +(5.82843 + 8.24264i) q^{51} +4.41421i q^{53} +(7.07107 - 2.00000i) q^{54} +(-1.41421 + 3.00000i) q^{55} -2.82843i q^{56} +(4.58579 - 3.24264i) q^{57} +8.24264 q^{58} +12.8995i q^{59} +9.24264i q^{61} -11.6569 q^{62} +(2.82843 + 1.00000i) q^{63} +8.00000 q^{64} -2.24264 q^{65} +(-1.41421 - 8.00000i) q^{66} -12.4853 q^{67} +(-1.75736 + 1.24264i) q^{69} -1.41421 q^{70} +1.75736i q^{71} +(-2.82843 + 8.00000i) q^{72} -6.48528i q^{73} -11.6569 q^{74} +(-1.00000 - 1.41421i) q^{75} +(1.41421 - 3.00000i) q^{77} +(4.48528 - 3.17157i) q^{78} -6.24264i q^{79} -4.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} -6.48528 q^{82} -17.1421 q^{83} +5.82843i q^{85} +4.58579i q^{86} +(-5.82843 - 8.24264i) q^{87} +(8.48528 + 4.00000i) q^{88} +16.4142i q^{89} +(4.00000 + 1.41421i) q^{90} +2.24264 q^{91} +(8.24264 + 11.6569i) q^{93} -1.51472i q^{94} +3.24264 q^{95} -7.00000 q^{97} +1.41421 q^{98} +(-7.00000 + 7.07107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^9	\( 4 q + 4 q^{3} - 4 q^{9} + 12 q^{11} - 16 q^{16} + 12 q^{17} - 4 q^{25} - 20 q^{27} - 12 q^{29} + 8 q^{30} + 16 q^{31} + 4 q^{33} - 16 q^{34} + 4 q^{35} + 16 q^{37} - 24 q^{39} + 24 q^{41} - 8 q^{42} - 16 q^{48} - 4 q^{49} + 12 q^{51} + 24 q^{57} + 16 q^{58} - 24 q^{62} + 32 q^{64} + 8 q^{65} - 16 q^{67} - 24 q^{69} - 24 q^{74} - 4 q^{75} - 16 q^{78} - 28 q^{81} + 8 q^{82} - 12 q^{83} - 12 q^{87} + 16 q^{90} - 8 q^{91} + 16 q^{93} - 4 q^{95} - 28 q^{97} - 28 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^9 + 12 * q^11 - 16 * q^16 + 12 * q^17 - 4 * q^25 - 20 * q^27 - 12 * q^29 + 8 * q^30 + 16 * q^31 + 4 * q^33 - 16 * q^34 + 4 * q^35 + 16 * q^37 - 24 * q^39 + 24 * q^41 - 8 * q^42 - 16 * q^48 - 4 * q^49 + 12 * q^51 + 24 * q^57 + 16 * q^58 - 24 * q^62 + 32 * q^64 + 8 * q^65 - 16 * q^67 - 24 * q^69 - 24 * q^74 - 4 * q^75 - 16 * q^78 - 28 * q^81 + 8 * q^82 - 12 * q^83 - 12 * q^87 + 16 * q^90 - 8 * q^91 + 16 * q^93 - 4 * q^95 - 28 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more