LMFDB - Embedded newform 1110.2.x.c.751.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{13} + 398 x^{12} - 136 x^{11} + 32 x^{10} - 824 x^{9} + 17825 x^{8} - 11480 x^{7} + \cdots + 20736 $ x^16 - 8x^13 + 398x^12 - 136x^11 + 32x^10 - 824x^9 + 17825x^8 - 11480x^7 + 3104x^6 + 11296x^5 + 68320x^4 - 21120x^3 + 4608x^2 + 13824*x + 20736
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.3
Root			$1.71606 + 1.71606i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.c.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(0.166951 - 0.289168i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(0.166951 - 0.289168i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -1.33390 q^{11} +(0.500000 + 0.866025i) q^{12} +(-4.47231 - 2.58209i) q^{13} +0.333902i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.57117 - 3.79387i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.08794 + 0.628123i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.166951 + 0.289168i) q^{21} +(1.15519 - 0.666951i) q^{22} -5.10784i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +5.16418 q^{26} +1.00000 q^{27} +(-0.166951 - 0.289168i) q^{28} -3.35447i q^{29} +(0.500000 - 0.866025i) q^{30} +6.07862i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.666951 - 1.15519i) q^{33} +(-3.79387 + 6.57117i) q^{34} +(0.289168 - 0.166951i) q^{35} -1.00000 q^{36} +(-4.37005 - 4.23115i) q^{37} -1.25625 q^{38} +(4.47231 - 2.58209i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.53821 - 6.12836i) q^{41} +(-0.289168 - 0.166951i) q^{42} -5.39573i q^{43} +(-0.666951 + 1.15519i) q^{44} -1.00000i q^{45} +(2.55392 + 4.42352i) q^{46} -10.6107 q^{47} +1.00000 q^{48} +(3.44425 + 5.96562i) q^{49} +(-0.866025 - 0.500000i) q^{50} +7.58773i q^{51} +(-4.47231 + 2.58209i) q^{52} +(-1.15017 - 1.99214i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-1.15519 - 0.666951i) q^{55} +(0.289168 + 0.166951i) q^{56} +(-1.08794 + 0.628123i) q^{57} +(1.67724 + 2.90506i) q^{58} +(11.1138 - 6.41656i) q^{59} +1.00000i q^{60} +(-6.12836 - 3.53821i) q^{61} +(-3.03931 - 5.26424i) q^{62} -0.333902 q^{63} -1.00000 q^{64} +(-2.58209 - 4.47231i) q^{65} +1.33390i q^{66} +(3.61637 - 6.26373i) q^{67} -7.58773i q^{68} +(4.42352 + 2.55392i) q^{69} +(-0.166951 + 0.289168i) q^{70} +(0.103651 - 0.179529i) q^{71} +(0.866025 - 0.500000i) q^{72} +8.99086 q^{73} +(5.90015 + 1.47926i) q^{74} -1.00000 q^{75} +(1.08794 - 0.628123i) q^{76} +(-0.222697 + 0.385722i) q^{77} +(-2.58209 + 4.47231i) q^{78} +(14.9895 + 8.65419i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +7.07642i q^{82} +(2.98704 + 5.17370i) q^{83} +0.333902 q^{84} +7.58773 q^{85} +(2.69787 + 4.67284i) q^{86} +(2.90506 + 1.67724i) q^{87} -1.33390i q^{88} +(12.4396 - 7.18201i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-1.49331 + 0.862165i) q^{91} +(-4.42352 - 2.55392i) q^{92} +(-5.26424 - 3.03931i) q^{93} +(9.18915 - 5.30536i) q^{94} +(0.628123 + 1.08794i) q^{95} +(-0.866025 + 0.500000i) q^{96} -4.55681i q^{97} +(-5.96562 - 3.44425i) q^{98} +(0.666951 + 1.15519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$		−	1.00000i		−	0.408248i
$7$	0.166951	−	0.289168i	0.0631016	−	0.109295i	−0.832749	−	0.553651i	$-0.813234\pi$
$7$	0.166951	−	0.289168i	0.0631016	−	0.109295i	0.895850	+	0.444356i	$0.146567\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	−1.33390			−0.402187			−0.201093	−	0.979572i	$-0.564449\pi$
$11$	−1.33390			−0.402187			−0.201093	+	0.979572i	$0.564449\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−4.47231	−	2.58209i	−1.24040	−	0.716143i	−0.271221	−	0.962517i	$-0.587427\pi$
$13$	−4.47231	−	2.58209i	−1.24040	−	0.716143i	−0.969175	+	0.246374i	$0.920761\pi$
$14$			0.333902i			0.0892391i
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.57117	−	3.79387i	1.59374	−	0.920148i	0.601086	−	0.799184i	$-0.294735\pi$
$17$	6.57117	−	3.79387i	1.59374	−	0.920148i	0.992657	−	0.120964i	$-0.0385984\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	1.08794	+	0.628123i	0.249591	+	0.144101i	0.619577	−	0.784936i	$-0.287304\pi$
$19$	1.08794	+	0.628123i	0.249591	+	0.144101i	−0.369986	+	0.929037i	$0.620638\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	0.166951	+	0.289168i	0.0364317	+	0.0631016i
$22$	1.15519	−	0.666951i	0.246288	−	0.142194i
$23$		−	5.10784i		−	1.06506i	−0.846412	−	0.532529i	$-0.821242\pi$
$23$		−	5.10784i		−	1.06506i	0.846412	−	0.532529i	$-0.178758\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	5.16418			1.01278
$27$	1.00000			0.192450
$28$	−0.166951	−	0.289168i	−0.0315508	−	0.0546476i
$29$		−	3.35447i		−	0.622910i	−0.950261	−	0.311455i	$-0.899184\pi$
$29$		−	3.35447i		−	0.622910i	0.950261	−	0.311455i	$-0.100816\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$			6.07862i			1.09175i	0.837866	+	0.545876i	$0.183803\pi$
$31$			6.07862i			1.09175i	−0.837866	+	0.545876i	$0.816197\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.666951	−	1.15519i	0.116101	−	0.201093i
$34$	−3.79387	+	6.57117i	−0.650643	+	1.12695i
$35$	0.289168	−	0.166951i	0.0488783	−	0.0282199i
$36$	−1.00000			−0.166667
$37$	−4.37005	−	4.23115i	−0.718432	−	0.695597i
$37$	−4.37005	−	4.23115i	−0.718432	−	0.695597i
$38$	−1.25625			−0.203790
$39$	4.47231	−	2.58209i	0.716143	−	0.413465i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	3.53821	−	6.12836i	0.552575	−	0.957088i	−0.445512	−	0.895276i	$-0.646979\pi$
$41$	3.53821	−	6.12836i	0.552575	−	0.957088i	0.998088	−	0.0618127i	$-0.0196882\pi$
$42$	−0.289168	−	0.166951i	−0.0446196	−	0.0257611i
$43$		−	5.39573i		−	0.822842i	−0.911445	−	0.411421i	$-0.865033\pi$
$43$		−	5.39573i		−	0.822842i	0.911445	−	0.411421i	$-0.134967\pi$
$44$	−0.666951	+	1.15519i	−0.100547	+	0.174152i
$45$		−	1.00000i		−	0.149071i
$46$	2.55392	+	4.42352i	0.376555	+	0.652212i
$47$	−10.6107			−1.54773			−0.773866	−	0.633349i	$-0.781680\pi$
$47$	−10.6107			−1.54773			−0.773866	+	0.633349i	$0.781680\pi$
$48$	1.00000			0.144338
$49$	3.44425	+	5.96562i	0.492036	+	0.852232i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$			7.58773i			1.06250i
$52$	−4.47231	+	2.58209i	−0.620198	+	0.358071i
$53$	−1.15017	−	1.99214i	−0.157987	−	0.273642i	0.776155	−	0.630542i	$-0.217167\pi$
$53$	−1.15017	−	1.99214i	−0.157987	−	0.273642i	−0.934143	+	0.356900i	$0.883834\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−1.15519	−	0.666951i	−0.155766	−	0.0899317i
$56$	0.289168	+	0.166951i	0.0386417	+	0.0223098i
$57$	−1.08794	+	0.628123i	−0.144101	+	0.0831969i
$58$	1.67724	+	2.90506i	0.220232	+	0.381453i
$59$	11.1138	−	6.41656i	1.44690	−	0.835366i	0.448600	−	0.893732i	$-0.351923\pi$
$59$	11.1138	−	6.41656i	1.44690	−	0.835366i	0.998295	+	0.0583670i	$0.0185894\pi$
$60$			1.00000i			0.129099i
$61$	−6.12836	−	3.53821i	−0.784656	−	0.453021i	0.0534221	−	0.998572i	$-0.482987\pi$
$61$	−6.12836	−	3.53821i	−0.784656	−	0.453021i	−0.838078	+	0.545551i	$0.816320\pi$
$62$	−3.03931	−	5.26424i	−0.385993	−	0.668559i
$63$	−0.333902			−0.0420677
$64$	−1.00000			−0.125000
$65$	−2.58209	−	4.47231i	−0.320269	−	0.554722i
$66$			1.33390i			0.164192i
$67$	3.61637	−	6.26373i	0.441809	−	0.765236i	−0.556015	−	0.831173i	$-0.687670\pi$
$67$	3.61637	−	6.26373i	0.441809	−	0.765236i	0.997824	+	0.0659364i	$0.0210034\pi$
$68$		−	7.58773i		−	0.920148i
$69$	4.42352	+	2.55392i	0.532529	+	0.307456i
$70$	−0.166951	+	0.289168i	−0.0199545	+	0.0345622i
$71$	0.103651	−	0.179529i	0.0123011	−	0.0213061i	−0.859809	−	0.510615i	$-0.829418\pi$
$71$	0.103651	−	0.179529i	0.0123011	−	0.0213061i	0.872110	+	0.489309i	$0.162751\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	8.99086			1.05230			0.526150	−	0.850392i	$-0.323635\pi$
$73$	8.99086			1.05230			0.526150	+	0.850392i	$0.323635\pi$
$74$	5.90015	+	1.47926i	0.685879	+	0.171961i
$75$	−1.00000			−0.115470
$76$	1.08794	−	0.628123i	0.124795	−	0.0720506i
$77$	−0.222697	+	0.385722i	−0.0253786	+	0.0439571i
$78$	−2.58209	+	4.47231i	−0.292364	+	0.506389i
$79$	14.9895	+	8.65419i	1.68645	+	0.973672i	0.957201	+	0.289424i	$0.0934638\pi$
$79$	14.9895	+	8.65419i	1.68645	+	0.973672i	0.729249	+	0.684248i	$0.239870\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$			7.07642i			0.781459i
$83$	2.98704	+	5.17370i	0.327870	+	0.567887i	0.982089	−	0.188418i	$-0.0603360\pi$
$83$	2.98704	+	5.17370i	0.327870	+	0.567887i	−0.654219	+	0.756305i	$0.727003\pi$
$84$	0.333902			0.0364317
$85$	7.58773			0.823005
$86$	2.69787	+	4.67284i	0.290919	+	0.503886i
$87$	2.90506	+	1.67724i	0.311455	+	0.179819i
$88$		−	1.33390i		−	0.142194i
$89$	12.4396	−	7.18201i	1.31860	−	0.761291i	0.335092	−	0.942185i	$-0.391232\pi$
$89$	12.4396	−	7.18201i	1.31860	−	0.761291i	0.983503	+	0.180894i	$0.0578991\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−1.49331	+	0.862165i	−0.156542	+	0.0903795i
$92$	−4.42352	−	2.55392i	−0.461183	−	0.266264i
$93$	−5.26424	−	3.03931i	−0.545876	−	0.315162i
$94$	9.18915	−	5.30536i	0.947788	−	0.547206i
$95$	0.628123	+	1.08794i	0.0644441	+	0.111620i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$		−	4.55681i		−	0.462674i	−0.972874	−	0.231337i	$-0.925690\pi$
$97$		−	4.55681i		−	0.462674i	0.972874	−	0.231337i	$-0.0743100\pi$
$98$	−5.96562	−	3.44425i	−0.602619	−	0.347922i
$99$	0.666951	+	1.15519i	0.0670311	+	0.116101i
$100$	1.00000			0.100000
$101$	6.65390			0.662088			0.331044	−	0.943615i	$-0.392599\pi$
$101$	6.65390			0.662088			0.331044	+	0.943615i	$0.392599\pi$
$102$	−3.79387	−	6.57117i	−0.375649	−	0.650643i
$103$		−	3.75454i		−	0.369946i	−0.982744	−	0.184973i	$-0.940780\pi$
$103$		−	3.75454i		−	0.369946i	0.982744	−	0.184973i	$-0.0592197\pi$
$104$	2.58209	−	4.47231i	0.253195	−	0.438546i
$105$			0.333902i			0.0325855i
$106$	1.99214	+	1.15017i	0.193494	+	0.111714i
$107$	2.32092	−	4.01995i	0.224372	−	0.388624i	−0.731759	−	0.681564i	$-0.761300\pi$
$107$	2.32092	−	4.01995i	0.224372	−	0.388624i	0.956131	+	0.292940i	$0.0946336\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−14.5390	+	8.39410i	−1.39258	+	0.804009i	−0.993601	−	0.112950i	$-0.963970\pi$
$109$	−14.5390	+	8.39410i	−1.39258	+	0.804009i	−0.398983	+	0.916958i	$0.630637\pi$
$110$	1.33390			0.127183
$111$	5.84931	−	1.66900i	0.555192	−	0.158414i
$112$	−0.333902			−0.0315508
$113$	8.62576	−	4.98008i	0.811443	−	0.468487i	−0.0360138	−	0.999351i	$-0.511466\pi$
$113$	8.62576	−	4.98008i	0.811443	−	0.468487i	0.847457	+	0.530864i	$0.178133\pi$
$114$	0.628123	−	1.08794i	0.0588291	−	0.101895i
$115$	2.55392	−	4.42352i	0.238154	−	0.412495i
$116$	−2.90506	−	1.67724i	−0.269728	−	0.155727i
$117$			5.16418i			0.477428i
$118$	−6.41656	+	11.1138i	−0.590693	+	1.02311i
$119$		−	2.53356i		−	0.232251i
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−9.22070			−0.838246
$122$	7.07642			0.640669
$123$	3.53821	+	6.12836i	0.319029	+	0.552575i
$124$	5.26424	+	3.03931i	0.472742	+	0.272938i
$125$			1.00000i			0.0894427i
$126$	0.289168	−	0.166951i	0.0257611	−	0.0148732i
$127$	8.24903	+	14.2877i	0.731983	+	1.26783i	0.956035	+	0.293254i	$0.0947382\pi$
$127$	8.24903	+	14.2877i	0.731983	+	1.26783i	−0.224052	+	0.974577i	$0.571929\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	4.67284	+	2.69787i	0.411421	+	0.237534i
$130$	4.47231	+	2.58209i	0.392247	+	0.226464i
$131$	−10.2546	+	5.92052i	−0.895952	+	0.517278i	−0.875885	−	0.482521i	$-0.839721\pi$
$131$	−10.2546	+	5.92052i	−0.895952	+	0.517278i	−0.0200671	+	0.999799i	$0.506388\pi$
$132$	−0.666951	−	1.15519i	−0.0580506	−	0.100547i
$133$	0.363266	−	0.209732i	0.0314992	−	0.0181860i
$134$			7.23273i			0.624813i
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$	3.79387	+	6.57117i	0.325321	+	0.563473i
$137$	−6.95611			−0.594301			−0.297150	−	0.954831i	$-0.596036\pi$
$137$	−6.95611			−0.594301			−0.297150	+	0.954831i	$0.596036\pi$
$138$	−5.10784			−0.434808
$139$	−3.91284	−	6.77723i	−0.331882	−	0.574837i	0.650999	−	0.759079i	$-0.274350\pi$
$139$	−3.91284	−	6.77723i	−0.331882	−	0.574837i	−0.982881	+	0.184242i	$0.941017\pi$
$140$		−	0.333902i		−	0.0282199i
$141$	5.30536	−	9.18915i	0.446792	−	0.773866i
$142$			0.207302i			0.0173964i
$143$	5.96562	+	3.44425i	0.498871	+	0.288023i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.67724	−	2.90506i	0.139287	−	0.241252i
$146$	−7.78631	+	4.49543i	−0.644400	+	0.372044i
$147$	−6.88851			−0.568155
$148$	−5.84931	+	1.66900i	−0.480810	+	0.137191i
$149$	11.6088			0.951033			0.475516	−	0.879707i	$-0.342261\pi$
$149$	11.6088			0.951033			0.475516	+	0.879707i	$0.342261\pi$
$150$	0.866025	−	0.500000i	0.0707107	−	0.0408248i
$151$	−2.27814	+	3.94586i	−0.185392	+	0.321109i	−0.943709	−	0.330778i	$-0.892689\pi$
$151$	−2.27814	+	3.94586i	−0.185392	+	0.321109i	0.758316	+	0.651887i	$0.226022\pi$
$152$	−0.628123	+	1.08794i	−0.0509475	+	0.0882437i
$153$	−6.57117	−	3.79387i	−0.531248	−	0.306716i
$154$		−	0.445393i		−	0.0358908i
$155$	−3.03931	+	5.26424i	−0.244123	+	0.422834i
$156$		−	5.16418i		−	0.413465i
$157$	−10.1360	−	17.5561i	−0.808940	−	1.40113i	−0.913598	−	0.406618i	$-0.866708\pi$
$157$	−10.1360	−	17.5561i	−0.808940	−	1.40113i	0.104658	−	0.994508i	$-0.466625\pi$
$158$	−17.3084			−1.37698
$159$	2.30033			0.182428
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−1.47702	−	0.852759i	−0.116406	−	0.0672068i
$162$		−	1.00000i		−	0.0785674i
$163$	−3.85249	+	2.22424i	−0.301751	+	0.174216i	−0.643229	−	0.765674i	$-0.722406\pi$
$163$	−3.85249	+	2.22424i	−0.301751	+	0.174216i	0.341478	+	0.939890i	$0.389072\pi$
$164$	−3.53821	−	6.12836i	−0.276288	−	0.478544i
$165$	1.15519	−	0.666951i	0.0899317	−	0.0519221i
$166$	−5.17370	−	2.98704i	−0.401557	−	0.231839i
$167$	11.4926	+	6.63523i	0.889321	+	0.513450i	0.873720	−	0.486429i	$-0.161701\pi$
$167$	11.4926	+	6.63523i	0.889321	+	0.513450i	0.0156006	+	0.999878i	$0.495034\pi$
$168$	−0.289168	+	0.166951i	−0.0223098	+	0.0128806i
$169$	6.83437	+	11.8375i	0.525721	+	0.910575i
$170$	−6.57117	+	3.79387i	−0.503986	+	0.290976i
$171$		−	1.25625i		−	0.0960675i
$172$	−4.67284	−	2.69787i	−0.356301	−	0.205710i
$173$	−7.53921	−	13.0583i	−0.573195	−	0.992804i	−0.996235	−	0.0866924i	$-0.972370\pi$
$173$	−7.53921	−	13.0583i	−0.573195	−	0.992804i	0.423040	−	0.906111i	$-0.360963\pi$
$174$	−3.35447			−0.254302
$175$	0.333902			0.0252406
$176$	0.666951	+	1.15519i	0.0502733	+	0.0870760i
$177$			12.8331i			0.964597i
$178$	−7.18201	+	12.4396i	−0.538314	+	0.932388i
$179$		−	18.8813i		−	1.41126i	−0.708582	−	0.705629i	$-0.750665\pi$
$179$		−	18.8813i		−	1.41126i	0.708582	−	0.705629i	$-0.249335\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	6.64591	−	11.5111i	0.493987	−	0.855610i	−0.505989	−	0.862540i	$-0.668873\pi$
$181$	6.64591	−	11.5111i	0.493987	−	0.855610i	0.999976	+	0.00692987i	$0.00220586\pi$
$182$	0.862165	−	1.49331i	0.0639080	−	0.110692i
$183$	6.12836	−	3.53821i	0.453021	−	0.261552i
$184$	5.10784			0.376555
$185$	−1.66900	−	5.84931i	−0.122707	−	0.430050i
$186$	6.07862			0.445706
$187$	−8.76530	+	5.06065i	−0.640982	+	0.370071i
$188$	−5.30536	+	9.18915i	−0.386933	+	0.670188i
$189$	0.166951	−	0.289168i	0.0121439	−	0.0210339i
$190$	−1.08794	−	0.628123i	−0.0789275	−	0.0455688i
$191$		−	10.0260i		−	0.725453i	−0.931896	−	0.362727i	$-0.881846\pi$
$191$		−	10.0260i		−	0.725453i	0.931896	−	0.362727i	$-0.118154\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$			7.17567i			0.516516i	0.966076	+	0.258258i	$0.0831485\pi$
$193$			7.17567i			0.516516i	−0.966076	+	0.258258i	$0.916852\pi$
$194$	2.27840	+	3.94631i	0.163580	+	0.283329i
$195$	5.16418			0.369814
$196$	6.88851			0.492036
$197$	−8.78077	−	15.2087i	−0.625604	−	1.08358i	−0.988424	−	0.151718i	$-0.951519\pi$
$197$	−8.78077	−	15.2087i	−0.625604	−	1.08358i	0.362820	−	0.931859i	$-0.381814\pi$
$198$	−1.15519	−	0.666951i	−0.0820960	−	0.0473982i
$199$			11.9431i			0.846621i	0.905985	+	0.423310i	$0.139132\pi$
$199$			11.9431i			0.846621i	−0.905985	+	0.423310i	$0.860868\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	3.61637	+	6.26373i	0.255079	+	0.441809i
$202$	−5.76245	+	3.32695i	−0.405444	+	0.234083i
$203$	−0.970005	−	0.560033i	−0.0680810	−	0.0393066i
$204$	6.57117	+	3.79387i	0.460074	+	0.265624i
$205$	6.12836	−	3.53821i	0.428023	−	0.247119i
$206$	1.87727	+	3.25153i	0.130796	+	0.226545i
$207$	−4.42352	+	2.55392i	−0.307456	+	0.177510i
$208$			5.16418i			0.358071i
$209$	−1.45121	−	0.837855i	−0.100382	−	0.0579556i
$210$	−0.166951	−	0.289168i	−0.0115207	−	0.0199545i
$211$	6.70752			0.461765			0.230882	−	0.972982i	$-0.425839\pi$
$211$	6.70752			0.461765			0.230882	+	0.972982i	$0.425839\pi$
$212$	−2.30033			−0.157987
$213$	0.103651	+	0.179529i	0.00710205	+	0.0123011i
$214$			4.64184i			0.317310i
$215$	2.69787	−	4.67284i	0.183993	−	0.318685i
$216$			1.00000i			0.0680414i
$217$	1.75774	+	1.01483i	0.119323	+	0.0688913i
$218$	8.39410	−	14.5390i	0.568520	−	0.984705i
$219$	−4.49543	+	7.78631i	−0.303773	+	0.526150i
$220$	−1.15519	+	0.666951i	−0.0778831	+	0.0449658i
$221$	−39.1844			−2.63583
$222$	−4.23115	+	4.37005i	−0.283976	+	0.293299i
$223$	−23.8571			−1.59759			−0.798795	−	0.601603i	$-0.794529\pi$
$223$	−23.8571			−1.59759			−0.798795	+	0.601603i	$0.794529\pi$
$224$	0.289168	−	0.166951i	0.0193208	−	0.0111549i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−4.98008	+	8.62576i	−0.331270	+	0.573777i
$227$	17.9658	+	10.3726i	1.19243	+	0.688451i	0.958858	−	0.283888i	$-0.0916243\pi$
$227$	17.9658	+	10.3726i	1.19243	+	0.688451i	0.233575	+	0.972339i	$0.424958\pi$
$228$			1.25625i			0.0831969i
$229$	−3.26245	+	5.65073i	−0.215589	+	0.373411i	−0.953455	−	0.301537i	$-0.902500\pi$
$229$	−3.26245	+	5.65073i	−0.215589	+	0.373411i	0.737866	+	0.674947i	$0.235834\pi$
$230$			5.10784i			0.336801i
$231$	−0.222697	−	0.385722i	−0.0146524	−	0.0253786i
$232$	3.35447			0.220232
$233$	−16.2778			−1.06640			−0.533198	−	0.845991i	$-0.679010\pi$
$233$	−16.2778			−1.06640			−0.533198	+	0.845991i	$0.679010\pi$
$234$	−2.58209	−	4.47231i	−0.168796	−	0.292364i
$235$	−9.18915	−	5.30536i	−0.599434	−	0.346083i
$236$		−	12.8331i		−	0.835366i
$237$	−14.9895	+	8.65419i	−0.973672	+	0.562150i
$238$	1.26678	+	2.19413i	0.0821132	+	0.142224i
$239$	−7.11623	+	4.10856i	−0.460311	+	0.265761i	−0.712175	−	0.702002i	$-0.752290\pi$
$239$	−7.11623	+	4.10856i	−0.460311	+	0.265761i	0.251864	+	0.967763i	$0.418956\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	−18.6050	−	10.7416i	−1.19845	−	0.691926i	−0.238242	−	0.971206i	$-0.576571\pi$
$241$	−18.6050	−	10.7416i	−1.19845	−	0.691926i	−0.960210	+	0.279279i	$0.909904\pi$
$242$	7.98536	−	4.61035i	0.513319	−	0.296365i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−6.12836	+	3.53821i	−0.392328	+	0.226511i
$245$			6.88851i			0.440091i
$246$	−6.12836	−	3.53821i	−0.390730	−	0.225588i
$247$	−3.24374	−	5.61832i	−0.206394	−	0.357485i
$248$	−6.07862			−0.385993
$249$	−5.97407			−0.378591
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$			0.0183961i			0.00116115i	1.00000		0.000580574i	$0.000184803\pi$
$251$			0.0183961i			0.00116115i	−1.00000		0.000580574i	$0.999815\pi$
$252$	−0.166951	+	0.289168i	−0.0105169	+	0.0182159i
$253$			6.81336i			0.428352i
$254$	−14.2877	−	8.24903i	−0.896492	−	0.517590i
$255$	−3.79387	+	6.57117i	−0.237581	+	0.411503i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.87293	+	2.23604i	−0.241587	+	0.139480i	−0.615906	−	0.787820i	$-0.711210\pi$
$257$	−3.87293	+	2.23604i	−0.241587	+	0.139480i	0.374319	+	0.927300i	$0.377876\pi$
$258$	−5.39573			−0.335924
$259$	−1.95310	+	0.557282i	−0.121360	+	0.0346278i
$260$	−5.16418			−0.320269
$261$	−2.90506	+	1.67724i	−0.179819	+	0.103818i
$262$	5.92052	−	10.2546i	0.365771	−	0.633533i
$263$	−12.3395	+	21.3726i	−0.760884	+	1.31789i	0.181512	+	0.983389i	$0.441901\pi$
$263$	−12.3395	+	21.3726i	−0.760884	+	1.31789i	−0.942396	+	0.334501i	$0.891432\pi$
$264$	1.15519	+	0.666951i	0.0710972	+	0.0410480i
$265$		−	2.30033i		−	0.141308i
$266$	−0.209732	+	0.363266i	−0.0128595	+	0.0222733i
$267$			14.3640i			0.879063i
$268$	−3.61637	−	6.26373i	−0.220905	−	0.382618i
$269$	29.8136			1.81777			0.908885	−	0.417048i	$-0.136935\pi$
$269$	29.8136			1.81777			0.908885	+	0.417048i	$0.136935\pi$
$270$	−1.00000			−0.0608581
$271$	10.1222	+	17.5321i	0.614878	+	1.06500i	0.990406	+	0.138189i	$0.0441280\pi$
$271$	10.1222	+	17.5321i	0.614878	+	1.06500i	−0.375528	+	0.926811i	$0.622539\pi$
$272$	−6.57117	−	3.79387i	−0.398436	−	0.230037i
$273$		−	1.72433i		−	0.104361i
$274$	6.02417	−	3.47805i	0.363933	−	0.210117i
$275$	−0.666951	−	1.15519i	−0.0402187	−	0.0696608i
$276$	4.42352	−	2.55392i	0.266264	−	0.153728i
$277$	−14.3284	−	8.27251i	−0.860910	−	0.497047i	0.00340662	−	0.999994i	$-0.498916\pi$
$277$	−14.3284	−	8.27251i	−0.860910	−	0.497047i	−0.864317	+	0.502947i	$0.832249\pi$
$278$	6.77723	+	3.91284i	0.406471	+	0.234676i
$279$	5.26424	−	3.03931i	0.315162	−	0.181959i
$280$	0.166951	+	0.289168i	0.00997724	+	0.0172811i
$281$	−16.9767	+	9.80150i	−1.01275	+	0.584709i	−0.911994	−	0.410203i	$-0.865458\pi$
$281$	−16.9767	+	9.80150i	−1.01275	+	0.584709i	−0.100751	+	0.994912i	$0.532125\pi$
$282$			10.6107i			0.631859i
$283$	0.889398	+	0.513494i	0.0528692	+	0.0305241i	0.526202	−	0.850360i	$-0.323616\pi$
$283$	0.889398	+	0.513494i	0.0528692	+	0.0305241i	−0.473332	+	0.880884i	$0.656949\pi$
$284$	−0.103651	−	0.179529i	−0.00615055	−	0.0106531i
$285$	−1.25625			−0.0744136
$286$	−6.88851			−0.407326
$287$	−1.18142	−	2.04627i	−0.0697368	−	0.120788i
$288$		−	1.00000i		−	0.0589256i
$289$	20.2869	−	35.1379i	1.19334	−	2.06693i
$290$			3.35447i			0.196981i
$291$	3.94631	+	2.27840i	0.231337	+	0.133562i
$292$	4.49543	−	7.78631i	0.263075	−	0.455659i
$293$	−0.264857	+	0.458746i	−0.0154731	+	0.0268002i	−0.873658	−	0.486540i	$-0.838259\pi$
$293$	−0.264857	+	0.458746i	−0.0154731	+	0.0268002i	0.858185	+	0.513340i	$0.171592\pi$
$294$	5.96562	−	3.44425i	0.347922	−	0.200873i
$295$	12.8331			0.747174
$296$	4.23115	−	4.37005i	0.245931	−	0.254004i
$297$	−1.33390			−0.0774009
$298$	−10.0535	+	5.80442i	−0.582386	+	0.336241i
$299$	−13.1889	+	22.8438i	−0.762733	+	1.32109i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−1.56027	−	0.900824i	−0.0899326	−	0.0519226i
$302$		−	4.55628i		−	0.262185i
$303$	−3.32695	+	5.76245i	−0.191128	+	0.331044i
$304$		−	1.25625i		−	0.0720506i
$305$	−3.53821	−	6.12836i	−0.202597	−	0.350909i
$306$	7.58773			0.433762
$307$	−17.3584			−0.990698			−0.495349	−	0.868694i	$-0.664960\pi$
$307$	−17.3584			−0.990698			−0.495349	+	0.868694i	$0.664960\pi$
$308$	0.222697	+	0.385722i	0.0126893	+	0.0219785i
$309$	3.25153	+	1.87727i	0.184973	+	0.106794i
$310$		−	6.07862i		−	0.345242i
$311$	−26.2256	+	15.1414i	−1.48712	+	0.858589i	−0.999892	−	0.0146856i	$-0.995325\pi$
$311$	−26.2256	+	15.1414i	−1.48712	+	0.858589i	−0.487228	+	0.873275i	$0.661992\pi$
$312$	2.58209	+	4.47231i	0.146182	+	0.253195i
$313$	−0.794616	+	0.458772i	−0.0449144	+	0.0259313i	−0.522289	−	0.852769i	$-0.674922\pi$
$313$	−0.794616	+	0.458772i	−0.0449144	+	0.0259313i	0.477375	+	0.878700i	$0.341588\pi$
$314$	17.5561	+	10.1360i	0.990746	+	0.572007i
$315$	−0.289168	−	0.166951i	−0.0162928	−	0.00940663i
$316$	14.9895	−	8.65419i	0.843225	−	0.486836i
$317$	−6.34618	−	10.9919i	−0.356437	−	0.617367i	0.630926	−	0.775843i	$-0.282675\pi$
$317$	−6.34618	−	10.9919i	−0.356437	−	0.617367i	−0.987363	+	0.158476i	$0.949342\pi$
$318$	−1.99214	+	1.15017i	−0.111714	+	0.0644981i
$319$			4.47454i			0.250526i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	2.32092	+	4.01995i	0.129541	+	0.224372i
$322$	1.70552			0.0950448
$323$	9.53206			0.530378
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		−	5.16418i		−	0.286457i
$326$	2.22424	−	3.85249i	0.123189	−	0.213370i
$327$		−	16.7882i		−	0.928389i
$328$	6.12836	+	3.53821i	0.338382	+	0.195365i
$329$	−1.77147	+	3.06828i	−0.0976644	+	0.169160i
$330$	−0.666951	+	1.15519i	−0.0367145	+	0.0635913i
$331$	−23.0748	+	13.3222i	−1.26830	+	0.732256i	−0.974667	−	0.223661i	$-0.928199\pi$
$331$	−23.0748	+	13.3222i	−1.26830	+	0.732256i	−0.293637	+	0.955917i	$0.594866\pi$
$332$	5.97407			0.327870
$333$	−1.47926	+	5.90015i	−0.0810630	+	0.323326i
$334$	−13.2705			−0.726127
$335$	6.26373	−	3.61637i	0.342224	−	0.197583i
$336$	0.166951	−	0.289168i	0.00910793	−	0.0157754i
$337$	13.3678	−	23.1538i	0.728192	−	1.26127i	−0.229454	−	0.973319i	$-0.573694\pi$
$337$	13.3678	−	23.1538i	0.728192	−	1.26127i	0.957647	−	0.287946i	$-0.0929725\pi$
$338$	−11.8375	−	6.83437i	−0.643874	−	0.371741i
$339$			9.96017i			0.540962i
$340$	3.79387	−	6.57117i	0.205751	−	0.356372i
$341$		−	8.10828i		−	0.439088i
$342$	0.628123	+	1.08794i	0.0339650	+	0.0588291i
$343$	4.63741			0.250396
$344$	5.39573			0.290919
$345$	2.55392	+	4.42352i	0.137498	+	0.238154i
$346$	13.0583	+	7.53921i	0.702018	+	0.405310i
$347$		−	0.289026i		−	0.0155158i	−0.999970	−	0.00775788i	$-0.997531\pi$
$347$		−	0.289026i		−	0.0155158i	0.999970	−	0.00775788i	$-0.00246943\pi$
$348$	2.90506	−	1.67724i	0.155727	−	0.0899093i
$349$	10.2006	+	17.6679i	0.546024	+	0.945741i	0.998542	+	0.0539860i	$0.0171926\pi$
$349$	10.2006	+	17.6679i	0.546024	+	0.945741i	−0.452518	+	0.891755i	$0.649474\pi$
$350$	−0.289168	+	0.166951i	−0.0154567	+	0.00892391i
$351$	−4.47231	−	2.58209i	−0.238714	−	0.137822i
$352$	−1.15519	−	0.666951i	−0.0615720	−	0.0355486i
$353$	1.42321	−	0.821689i	0.0757496	−	0.0437341i	−0.461647	−	0.887064i	$-0.652741\pi$
$353$	1.42321	−	0.821689i	0.0757496	−	0.0437341i	0.537396	+	0.843330i	$0.319408\pi$
$354$	−6.41656	−	11.1138i	−0.341037	−	0.590693i
$355$	0.179529	−	0.103651i	0.00952840	−	0.00550122i
$356$		−	14.3640i		−	0.761291i
$357$	2.19413	+	1.26678i	0.116126	+	0.0670452i
$358$	9.44067	+	16.3517i	0.498955	+	0.864215i
$359$	25.4992			1.34580			0.672899	−	0.739734i	$-0.265049\pi$
$359$	25.4992			1.34580			0.672899	+	0.739734i	$0.265049\pi$
$360$	1.00000			0.0527046
$361$	−8.71092	−	15.0878i	−0.458470	−	0.794093i
$362$			13.2918i			0.698602i
$363$	4.61035	−	7.98536i	0.241981	−	0.419123i
$364$			1.72433i			0.0903795i
$365$	7.78631	+	4.49543i	0.407554	+	0.235301i
$366$	−3.53821	+	6.12836i	−0.184945	+	0.320334i
$367$	−13.8219	+	23.9403i	−0.721500	+	1.24967i	0.238899	+	0.971044i	$0.423214\pi$
$367$	−13.8219	+	23.9403i	−0.721500	+	1.24967i	−0.960399	+	0.278630i	$0.910120\pi$
$368$	−4.42352	+	2.55392i	−0.230592	+	0.133132i
$369$	−7.07642			−0.368384
$370$	4.37005	+	4.23115i	0.227188	+	0.219967i
$371$	−0.768086			−0.0398770
$372$	−5.26424	+	3.03931i	−0.272938	+	0.157581i
$373$	−7.75347	+	13.4294i	−0.401459	+	0.695348i	−0.993902	−	0.110264i	$-0.964830\pi$
$373$	−7.75347	+	13.4294i	−0.401459	+	0.695348i	0.592443	+	0.805612i	$0.298164\pi$
$374$	5.06065	−	8.76530i	0.261680	−	0.453243i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$		−	10.6107i		−	0.547206i
$377$	−8.66154	+	15.0022i	−0.446092	+	0.772654i
$378$			0.333902i			0.0171741i
$379$	−13.3626	−	23.1448i	−0.686393	−	1.18887i	−0.972997	−	0.230818i	$-0.925860\pi$
$379$	−13.3626	−	23.1448i	−0.686393	−	1.18887i	0.286604	−	0.958049i	$-0.407474\pi$
$380$	1.25625			0.0644441
$381$	−16.4981			−0.845221
$382$	5.01298	+	8.68274i	0.256486	+	0.444247i
$383$	1.12643	+	0.650343i	0.0575578	+	0.0332310i	0.528503	−	0.848932i	$-0.322754\pi$
$383$	1.12643	+	0.650343i	0.0575578	+	0.0332310i	−0.470945	+	0.882163i	$0.656087\pi$
$384$			1.00000i			0.0510310i
$385$	−0.385722	+	0.222697i	−0.0196582	+	0.0113497i
$386$	−3.58784	−	6.21431i	−0.182616	−	0.316300i
$387$	−4.67284	+	2.69787i	−0.237534	+	0.137140i
$388$	−3.94631	−	2.27840i	−0.200344	−	0.115668i
$389$	31.3485	+	18.0991i	1.58943	+	0.917660i	0.993400	+	0.114701i	$0.0365909\pi$
$389$	31.3485	+	18.0991i	1.58943	+	0.917660i	0.596034	+	0.802959i	$0.296742\pi$
$390$	−4.47231	+	2.58209i	−0.226464	+	0.130749i
$391$	−19.3785	−	33.5645i	−0.980011	−	1.69743i
$392$	−5.96562	+	3.44425i	−0.301310	+	0.173961i
$393$		−	11.8410i		−	0.597301i
$394$	15.2087	+	8.78077i	0.766205	+	0.442369i
$395$	8.65419	+	14.9895i	0.435440	+	0.754203i
$396$	1.33390			0.0670311
$397$	27.1538			1.36281			0.681406	−	0.731906i	$-0.261369\pi$
$397$	27.1538			1.36281			0.681406	+	0.731906i	$0.261369\pi$
$398$	−5.97153	−	10.3430i	−0.299326	−	0.518447i
$399$			0.419463i			0.0209994i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			36.9356i			1.84448i	0.386621	+	0.922239i	$0.373642\pi$
$401$			36.9356i			1.84448i	−0.386621	+	0.922239i	$0.626358\pi$
$402$	−6.26373	−	3.61637i	−0.312406	−	0.180368i
$403$	15.6955	−	27.1855i	0.781850	−	1.35420i
$404$	3.32695	−	5.76245i	0.165522	−	0.286692i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	1.12007			0.0555879
$407$	5.82922	+	5.64395i	0.288944	+	0.279760i
$408$	−7.58773			−0.375649
$409$	−12.9660	+	7.48592i	−0.641127	+	0.370155i	−0.785049	−	0.619434i	$-0.787362\pi$
$409$	−12.9660	+	7.48592i	−0.641127	+	0.370155i	0.143922	+	0.989589i	$0.454029\pi$
$410$	−3.53821	+	6.12836i	−0.174740	+	0.302658i
$411$	3.47805	−	6.02417i	0.171560	−	0.297150i
$412$	−3.25153	−	1.87727i	−0.160191	−	0.0924864i
$413$		−	4.28501i		−	0.210852i
$414$	2.55392	−	4.42352i	0.125518	−	0.217404i
$415$			5.97407i			0.293256i
$416$	−2.58209	−	4.47231i	−0.126597	−	0.219273i
$417$	7.82567			0.383225
$418$	1.67571			0.0819616
$419$	0.902123	+	1.56252i	0.0440716	+	0.0763342i	0.887220	−	0.461347i	$-0.152634\pi$
$419$	0.902123	+	1.56252i	0.0440716	+	0.0763342i	−0.843148	+	0.537681i	$0.819300\pi$
$420$	0.289168	+	0.166951i	0.0141099	+	0.00814638i
$421$		−	17.8338i		−	0.869166i	−0.900632	−	0.434583i	$-0.856896\pi$
$421$		−	17.8338i		−	0.869166i	0.900632	−	0.434583i	$-0.143104\pi$
$422$	−5.80888	+	3.35376i	−0.282772	+	0.163258i
$423$	5.30536	+	9.18915i	0.257955	+	0.446792i
$424$	1.99214	−	1.15017i	0.0967471	−	0.0558570i
$425$	6.57117	+	3.79387i	0.318749	+	0.184030i
$426$	−0.179529	−	0.103651i	−0.00869820	−	0.00502191i
$427$	−2.04627	+	1.18142i	−0.0990261	+	0.0571727i
$428$	−2.32092	−	4.01995i	−0.112186	−	0.194312i
$429$	−5.96562	+	3.44425i	−0.288023	+	0.166290i
$430$			5.39573i			0.260205i
$431$	5.51611	+	3.18473i	0.265702	+	0.153403i	0.626933	−	0.779073i	$-0.284310\pi$
$431$	5.51611	+	3.18473i	0.265702	+	0.153403i	−0.361231	+	0.932476i	$0.617643\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	6.88354			0.330802			0.165401	−	0.986226i	$-0.447108\pi$
$433$	6.88354			0.330802			0.165401	+	0.986226i	$0.447108\pi$
$434$	−2.02966			−0.0974270
$435$	1.67724	+	2.90506i	0.0804173	+	0.139287i
$436$			16.7882i			0.804009i
$437$	3.20835	−	5.55702i	0.153476	−	0.265829i
$438$		−	8.99086i		−	0.429600i
$439$	−30.3895	−	17.5454i	−1.45041	−	0.837394i	−0.451905	−	0.892066i	$-0.649255\pi$
$439$	−30.3895	−	17.5454i	−1.45041	−	0.837394i	−0.998504	+	0.0546718i	$0.982589\pi$
$440$	0.666951	−	1.15519i	0.0317956	−	0.0550717i
$441$	3.44425	−	5.96562i	0.164012	−	0.284077i
$442$	33.9347	−	19.5922i	1.61411	−	0.931906i
$443$	12.9115			0.613443			0.306721	−	0.951799i	$-0.400768\pi$
$443$	12.9115			0.613443			0.306721	+	0.951799i	$0.400768\pi$
$444$	1.47926	−	5.90015i	0.0702027	−	0.280009i
$445$	14.3640			0.680920
$446$	20.6609	−	11.9286i	0.978320	−	0.564833i
$447$	−5.80442	+	10.0535i	−0.274540	+	0.475516i
$448$	−0.166951	+	0.289168i	−0.00788770	+	0.0136619i
$449$	−10.5199	−	6.07367i	−0.496465	−	0.286634i	0.230787	−	0.973004i	$-0.425870\pi$
$449$	−10.5199	−	6.07367i	−0.496465	−	0.286634i	−0.727253	+	0.686370i	$0.759203\pi$
$450$			1.00000i			0.0471405i
$451$	−4.71962	+	8.17463i	−0.222238	+	0.384928i
$452$		−	9.96017i		−	0.468487i
$453$	−2.27814	−	3.94586i	−0.107036	−	0.185392i
$454$	−20.7451			−0.973617
$455$	−1.72433			−0.0808379
$456$	−0.628123	−	1.08794i	−0.0294146	−	0.0509475i
$457$	16.2920	+	9.40620i	0.762108	+	0.440003i	0.830052	−	0.557686i	$-0.188311\pi$
$457$	16.2920	+	9.40620i	0.762108	+	0.440003i	−0.0679440	+	0.997689i	$0.521644\pi$
$458$		−	6.52490i		−	0.304888i
$459$	6.57117	−	3.79387i	0.306716	−	0.177083i
$460$	−2.55392	−	4.42352i	−0.119077	−	0.206248i
$461$	1.84164	−	1.06327i	0.0857739	−	0.0495216i	−0.456500	−	0.889724i	$-0.650897\pi$
$461$	1.84164	−	1.06327i	0.0857739	−	0.0495216i	0.542273	+	0.840202i	$0.317564\pi$
$462$	0.385722	+	0.222697i	0.0179454	+	0.0103608i
$463$	−0.608694	−	0.351430i	−0.0282884	−	0.0163323i	0.485789	−	0.874076i	$-0.338532\pi$
$463$	−0.608694	−	0.351430i	−0.0282884	−	0.0163323i	−0.514078	+	0.857744i	$0.671866\pi$
$464$	−2.90506	+	1.67724i	−0.134864	+	0.0778637i
$465$	−3.03931	−	5.26424i	−0.140945	−	0.244123i
$466$	14.0970	−	8.13891i	0.653031	−	0.377028i
$467$			15.9873i			0.739804i	0.929071	+	0.369902i	$0.120609\pi$
$467$			15.9873i			0.739804i	−0.929071	+	0.369902i	$0.879391\pi$
$468$	4.47231	+	2.58209i	0.206733	+	0.119357i
$469$	−1.20751	−	2.09147i	−0.0557578	−	0.0965753i
$470$	10.6107			0.489436
$471$	20.2720			0.934084
$472$	6.41656	+	11.1138i	0.295346	+	0.511555i
$473$			7.19738i			0.330936i
$474$	8.65419	−	14.9895i	0.397500	−	0.688490i
$475$			1.25625i			0.0576405i
$476$	−2.19413	−	1.26678i	−0.100568	−	0.0580628i
$477$	−1.15017	+	1.99214i	−0.0526624	+	0.0912140i
$478$	4.10856	−	7.11623i	0.187921	−	0.325489i
$479$	−16.0220	+	9.25029i	−0.732063	+	0.422657i	−0.819176	−	0.573542i	$-0.805569\pi$
$479$	−16.0220	+	9.25029i	−0.732063	+	0.422657i	0.0871135	+	0.996198i	$0.472236\pi$
$480$	−1.00000			−0.0456435
$481$	8.61900	+	30.2069i	0.392993	+	1.37732i
$482$	21.4832			0.978532
$483$	1.47702	−	0.852759i	0.0672068	−	0.0388019i
$484$	−4.61035	+	7.98536i	−0.209561	+	0.362971i
$485$	2.27840	−	3.94631i	0.103457	−	0.179193i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$			3.34182i			0.151432i	0.997129	+	0.0757161i	$0.0241243\pi$
$487$			3.34182i			0.151432i	−0.997129	+	0.0757161i	$0.975876\pi$
$488$	3.53821	−	6.12836i	0.160167	−	0.277418i
$489$		−	4.44848i		−	0.201167i
$490$	−3.44425	−	5.96562i	−0.155596	−	0.269499i
$491$	−10.4195			−0.470224			−0.235112	−	0.971968i	$-0.575546\pi$
$491$	−10.4195			−0.470224			−0.235112	+	0.971968i	$0.575546\pi$
$492$	7.07642			0.319029
$493$	−12.7264	−	22.0428i	−0.573169	−	0.992758i
$494$	5.61832	+	3.24374i	0.252780	+	0.145943i
$495$			1.33390i			0.0599544i
$496$	5.26424	−	3.03931i	0.236371	−	0.136469i
$497$	−0.0346093	−	0.0599451i	−0.00155244	−	0.00268890i
$498$	5.17370	−	2.98704i	0.231839	−	0.133852i
$499$	35.1779	+	20.3100i	1.57478	+	0.909200i	0.995570	+	0.0940211i	$0.0299721\pi$
$499$	35.1779	+	20.3100i	1.57478	+	0.909200i	0.579210	+	0.815179i	$0.303361\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−11.4926	+	6.63523i	−0.513450	+	0.296440i
$502$	−0.00919803	−	0.0159315i	−0.000410528	−	0.000711056i
$503$	30.1989	−	17.4354i	1.34650	−	0.777404i	0.358751	−	0.933433i	$-0.383203\pi$
$503$	30.1989	−	17.4354i	1.34650	−	0.777404i	0.987752	+	0.156029i	$0.0498695\pi$
$504$		−	0.333902i		−	0.0148732i
$505$	5.76245	+	3.32695i	0.256426	+	0.148047i
$506$	−3.40668	−	5.90054i	−0.151445	−	0.262311i
$507$	−13.6687			−0.607050
$508$	16.4981			0.731983
$509$	−13.0755	−	22.6475i	−0.579562	−	1.00383i	−0.995529	−	0.0944517i	$-0.969890\pi$
$509$	−13.0755	−	22.6475i	−0.579562	−	1.00383i	0.415967	−	0.909380i	$-0.363443\pi$
$510$		−	7.58773i		−	0.335991i
$511$	1.50103	−	2.59987i	0.0664018	−	0.115011i
$512$		−	1.00000i		−	0.0441942i
$513$	1.08794	+	0.628123i	0.0480338	+	0.0277323i
$514$	2.23604	−	3.87293i	0.0986273	−	0.170827i
$515$	1.87727	−	3.25153i	0.0827224	−	0.143279i
$516$	4.67284	−	2.69787i	0.205710	−	0.118767i
$517$	14.1537			0.622477
$518$	1.41279	−	1.45917i	0.0620745	−	0.0641122i
$519$	15.0784			0.661869
$520$	4.47231	−	2.58209i	0.196124	−	0.113232i
$521$	0.640653	−	1.10964i	0.0280675	−	0.0486144i	−0.851650	−	0.524110i	$-0.824398\pi$
$521$	0.640653	−	1.10964i	0.0280675	−	0.0486144i	0.879718	+	0.475496i	$0.157731\pi$
$522$	1.67724	−	2.90506i	0.0734106	−	0.127151i
$523$	6.97423	+	4.02657i	0.304962	+	0.176070i	0.644670	−	0.764461i	$-0.276995\pi$
$523$	6.97423	+	4.02657i	0.304962	+	0.176070i	−0.339708	+	0.940531i	$0.610328\pi$
$524$			11.8410i			0.517278i
$525$	−0.166951	+	0.289168i	−0.00728635	+	0.0126203i
$526$		−	24.6789i		−	1.07605i
$527$	23.0615	+	39.9436i	1.00457	+	1.73997i
$528$	−1.33390			−0.0580506
$529$	−3.09000			−0.134348
$530$	1.15017	+	1.99214i	0.0499600	+	0.0865332i
$531$	−11.1138	−	6.41656i	−0.482298	−	0.278455i
$532$		−	0.419463i		−	0.0181860i
$533$	−31.6479	+	18.2719i	−1.37082	+	0.791445i
$534$	−7.18201	−	12.4396i	−0.310796	−	0.538314i
$535$	4.01995	−	2.32092i	0.173798	−	0.100342i
$536$	6.26373	+	3.61637i	0.270552	+	0.156203i
$537$	16.3517	+	9.44067i	0.705629	+	0.407395i
$538$	−25.8194	+	14.9068i	−1.11315	+	0.642679i
$539$	−4.59430	−	7.95756i	−0.197890	−	0.342756i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$			28.7276i			1.23510i	0.786533	+	0.617549i	$0.211874\pi$
$541$			28.7276i			1.23510i	−0.786533	+	0.617549i	$0.788126\pi$
$542$	−17.5321	−	10.1222i	−0.753068	−	0.434784i
$543$	6.64591	+	11.5111i	0.285203	+	0.493987i
$544$	7.58773			0.325321
$545$	−16.7882			−0.719127
$546$	0.862165	+	1.49331i	0.0368973	+	0.0639080i
$547$		−	27.6106i		−	1.18054i	−0.807204	−	0.590272i	$-0.799020\pi$
$547$		−	27.6106i		−	1.18054i	0.807204	−	0.590272i	$-0.200980\pi$
$548$	−3.47805	+	6.02417i	−0.148575	+	0.257340i
$549$			7.07642i			0.302014i
$550$	1.15519	+	0.666951i	0.0492576	+	0.0284389i
$551$	2.10702	−	3.64947i	0.0897621	−	0.155472i
$552$	−2.55392	+	4.42352i	−0.108702	+	0.188277i
$553$	5.00503	−	2.88965i	0.212835	−	0.122881i
$554$	16.5450			0.702930
$555$	5.90015	+	1.47926i	0.250447	+	0.0627912i
$556$	−7.82567			−0.331882
$557$	−17.5057	+	10.1069i	−0.741742	+	0.428245i	−0.822702	−	0.568473i	$-0.807535\pi$
$557$	−17.5057	+	10.1069i	−0.741742	+	0.428245i	0.0809606	+	0.996717i	$0.474201\pi$
$558$	−3.03931	+	5.26424i	−0.128664	+	0.222853i
$559$	−13.9323	+	24.1314i	−0.589272	+	1.02065i
$560$	−0.289168	−	0.166951i	−0.0122196	−	0.00705497i
$561$		−	10.1213i		−	0.427321i
$562$	9.80150	−	16.9767i	0.413451	−	0.716119i
$563$		−	16.1127i		−	0.679071i	−0.940593	−	0.339536i	$-0.889730\pi$
$563$		−	16.1127i		−	0.679071i	0.940593	−	0.339536i	$-0.110270\pi$
$564$	−5.30536	−	9.18915i	−0.223396	−	0.386933i
$565$	9.96017			0.419027
$566$	−1.02699			−0.0431675
$567$	0.166951	+	0.289168i	0.00701129	+	0.0121439i
$568$	0.179529	+	0.103651i	0.00753286	+	0.00434910i
$569$		−	41.3336i		−	1.73279i	−0.499355	−	0.866397i	$-0.666430\pi$
$569$		−	41.3336i		−	1.73279i	0.499355	−	0.866397i	$-0.333570\pi$
$570$	1.08794	−	0.628123i	0.0455688	−	0.0263092i
$571$	−14.2403	−	24.6649i	−0.595938	−	1.03219i	−0.993414	−	0.114582i	$-0.963447\pi$
$571$	−14.2403	−	24.6649i	−0.595938	−	1.03219i	0.397476	−	0.917612i	$-0.369886\pi$
$572$	5.96562	−	3.44425i	0.249435	−	0.144012i
$573$	8.68274	+	5.01298i	0.362727	+	0.209420i
$574$	2.04627	+	1.18142i	0.0854098	+	0.0493113i
$575$	4.42352	−	2.55392i	0.184473	−	0.106506i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	15.8663	−	9.16042i	0.660523	−	0.381353i	−0.131953	−	0.991256i	$-0.542125\pi$
$577$	15.8663	−	9.16042i	0.660523	−	0.381353i	0.792476	+	0.609903i	$0.208792\pi$
$578$			40.5737i			1.68764i
$579$	−6.21431	−	3.58784i	−0.258258	−	0.149105i
$580$	−1.67724	−	2.90506i	−0.0696434	−	0.120626i
$581$	1.99476			0.0827564
$582$	−4.55681			−0.188886
$583$	1.53421	+	2.65733i	0.0635404	+	0.110055i
$584$			8.99086i			0.372044i
$585$	−2.58209	+	4.47231i	−0.106756	+	0.184907i
$586$		−	0.529714i		−	0.0218823i
$587$	9.57790	+	5.52981i	0.395322	+	0.228240i	0.684464	−	0.729047i	$-0.260036\pi$
$587$	9.57790	+	5.52981i	0.395322	+	0.228240i	−0.289141	+	0.957286i	$0.593370\pi$
$588$	−3.44425	+	5.96562i	−0.142039	+	0.246018i
$589$	−3.81812	+	6.61318i	−0.157323	+	0.272491i
$590$	−11.1138	+	6.41656i	−0.457549	+	0.264166i
$591$	17.5615			0.722385
$592$	−1.47926	+	5.90015i	−0.0607973	+	0.242495i
$593$	−19.5569			−0.803107			−0.401554	−	0.915835i	$-0.631530\pi$
$593$	−19.5569			−0.803107			−0.401554	+	0.915835i	$0.631530\pi$
$594$	1.15519	−	0.666951i	0.0473982	−	0.0273653i
$595$	1.26678	−	2.19413i	0.0519330	−	0.0899505i
$596$	5.80442	−	10.0535i	0.237758	−	0.411809i
$597$	−10.3430	−	5.97153i	−0.423310	−	0.244398i
$598$		−	26.3778i		−	1.07867i
$599$	20.4550	−	35.4291i	0.835769	−	1.44759i	−0.0576344	−	0.998338i	$-0.518356\pi$
$599$	20.4550	−	35.4291i	0.835769	−	1.44759i	0.893403	−	0.449256i	$-0.148311\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−19.5345	−	33.8347i	−0.796827	−	1.38015i	−0.921672	−	0.387969i	$-0.873177\pi$
$601$	−19.5345	−	33.8347i	−0.796827	−	1.38015i	0.124845	−	0.992176i	$-0.460157\pi$
$602$	1.80165			0.0734297
$603$	−7.23273			−0.294540
$604$	2.27814	+	3.94586i	0.0926962	+	0.160555i
$605$	−7.98536	−	4.61035i	−0.324651	−	0.187437i
$606$		−	6.65390i		−	0.270296i
$607$	14.8818	−	8.59201i	0.604034	−	0.348739i	−0.166593	−	0.986026i	$-0.553277\pi$
$607$	14.8818	−	8.59201i	0.604034	−	0.348739i	0.770627	+	0.637287i	$0.219943\pi$
$608$	0.628123	+	1.08794i	0.0254737	+	0.0441218i
$609$	0.970005	−	0.560033i	0.0393066	−	0.0226937i
$610$	6.12836	+	3.53821i	0.248130	+	0.143258i
$611$	47.4544	+	27.3978i	1.91980	+	1.10840i
$612$	−6.57117	+	3.79387i	−0.265624	+	0.153358i
$613$	−6.37758	−	11.0463i	−0.257588	−	0.446156i	0.708007	−	0.706205i	$-0.249594\pi$
$613$	−6.37758	−	11.0463i	−0.257588	−	0.446156i	−0.965595	+	0.260049i	$0.916261\pi$
$614$	15.0328	−	8.67921i	0.606676	−	0.350265i
$615$			7.07642i			0.285349i
$616$	−0.385722	−	0.222697i	−0.0155412	−	0.00897270i
$617$	−3.11606	−	5.39718i	−0.125448	−	0.217282i	0.796460	−	0.604691i	$-0.206703\pi$
$617$	−3.11606	−	5.39718i	−0.125448	−	0.217282i	−0.921908	+	0.387409i	$0.873370\pi$
$618$	−3.75454			−0.151030
$619$	6.66413			0.267854			0.133927	−	0.990991i	$-0.457241\pi$
$619$	6.66413			0.267854			0.133927	+	0.990991i	$0.457241\pi$
$620$	3.03931	+	5.26424i	0.122062	+	0.211417i
$621$		−	5.10784i		−	0.204970i
$622$	15.1414	−	26.2256i	0.607114	−	1.05155i
$623$		−	4.79618i		−	0.192155i
$624$	−4.47231	−	2.58209i	−0.179036	−	0.103366i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.458772	−	0.794616i	0.0183362	−	0.0317593i
$627$	1.45121	−	0.837855i	0.0579556	−	0.0334607i
$628$	−20.2720			−0.808940
$629$	−44.7688	−	11.2242i	−1.78505	−	0.447540i
$630$	0.333902			0.0133030
$631$	22.3289	−	12.8916i	0.888899	−	0.513206i	0.0153171	−	0.999883i	$-0.495124\pi$
$631$	22.3289	−	12.8916i	0.888899	−	0.513206i	0.873582	+	0.486676i	$0.161791\pi$
$632$	−8.65419	+	14.9895i	−0.344245	+	0.596250i
$633$	−3.35376	+	5.80888i	−0.133300	+	0.230882i
$634$	10.9919	+	6.34618i	0.436544	+	0.252039i
$635$			16.4981i			0.654705i
$636$	1.15017	−	1.99214i	0.0456070	−	0.0789937i
$637$		−	35.5735i		−	1.40947i
$638$	−2.23727	−	3.87506i	−0.0885743	−	0.153415i
$639$	−0.207302			−0.00820074
$640$	1.00000			0.0395285
$641$	11.0631	+	19.1618i	0.436966	+	0.756847i	0.997454	−	0.0713157i	$-0.0227198\pi$
$641$	11.0631	+	19.1618i	0.436966	+	0.756847i	−0.560488	+	0.828162i	$0.689386\pi$
$642$	−4.01995	−	2.32092i	−0.158655	−	0.0915995i
$643$		−	12.1621i		−	0.479628i	−0.970819	−	0.239814i	$-0.922914\pi$
$643$		−	12.1621i		−	0.479628i	0.970819	−	0.239814i	$-0.0770865\pi$
$644$	−1.47702	+	0.852759i	−0.0582028	+	0.0336034i
$645$	2.69787	+	4.67284i	0.106228	+	0.183993i
$646$	−8.25501	+	4.76603i	−0.324789	+	0.187517i
$647$	29.0543	+	16.7745i	1.14224	+	0.659474i	0.946985	−	0.321278i	$-0.104112\pi$
$647$	29.0543	+	16.7745i	1.14224	+	0.659474i	0.195257	+	0.980752i	$0.437446\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−14.8247	+	8.55907i	−0.581922	+	0.335973i
$650$	2.58209	+	4.47231i	0.101278	+	0.175418i
$651$	−1.75774	+	1.01483i	−0.0688913	+	0.0397744i
$652$			4.44848i			0.174216i
$653$	38.4394	+	22.1930i	1.50425	+	0.868479i	0.999988	+	0.00492733i	$0.00156842\pi$
$653$	38.4394	+	22.1930i	1.50425	+	0.868479i	0.504261	+	0.863551i	$0.331765\pi$
$654$	8.39410	+	14.5390i	0.328235	+	0.568520i
$655$	−11.8410			−0.462667
$656$	−7.07642			−0.276288
$657$	−4.49543	−	7.78631i	−0.175383	−	0.303773i
$658$		−	3.54294i		−	0.138118i
$659$	−1.16656	+	2.02054i	−0.0454427	+	0.0787090i	−0.887852	−	0.460129i	$-0.847803\pi$
$659$	−1.16656	+	2.02054i	−0.0454427	+	0.0787090i	0.842409	+	0.538838i	$0.181136\pi$
$660$		−	1.33390i		−	0.0519221i
$661$	36.5398	+	21.0963i	1.42123	+	0.820550i	0.996404	−	0.0847236i	$-0.0270007\pi$
$661$	36.5398	+	21.0963i	1.42123	+	0.820550i	0.424829	+	0.905273i	$0.360334\pi$
$662$	13.3222	−	23.0748i	0.517783	−	0.896827i
$663$	19.5922	−	33.9347i	0.760898	−	1.31791i
$664$	−5.17370	+	2.98704i	−0.200778	+	0.115919i
$665$	0.419463			0.0162661
$666$	−1.66900	−	5.84931i	−0.0646723	−	0.226656i
$667$	−17.1341			−0.663435
$668$	11.4926	−	6.63523i	0.444660	−	0.256725i
$669$	11.9286	−	20.6609i	0.461185	−	0.798795i
$670$	−3.61637	+	6.26373i	−0.139712	+	0.241989i
$671$	8.17463	+	4.71962i	0.315578	+	0.182199i
$672$			0.333902i			0.0128806i
$673$	−15.8975	+	27.5352i	−0.612803	+	1.06141i	0.377963	+	0.925821i	$0.376625\pi$
$673$	−15.8975	+	27.5352i	−0.612803	+	1.06141i	−0.990766	+	0.135585i	$0.956709\pi$
$674$			26.7357i			1.02982i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	13.6687			0.525721
$677$	−12.9169			−0.496435			−0.248218	−	0.968704i	$-0.579845\pi$
$677$	−12.9169			−0.496435			−0.248218	+	0.968704i	$0.579845\pi$
$678$	−4.98008	−	8.62576i	−0.191259	−	0.331270i
$679$	−1.31768	−	0.760764i	−0.0505680	−	0.0291955i
$680$			7.58773i			0.290976i
$681$	−17.9658	+	10.3726i	−0.688451	+	0.397477i
$682$	4.05414	+	7.02198i	0.155241	+	0.268885i
$683$	−23.2853	+	13.4438i	−0.890988	+	0.514412i	−0.874266	−	0.485448i	$-0.838657\pi$
$683$	−23.2853	+	13.4438i	−0.890988	+	0.514412i	−0.0167225	+	0.999860i	$0.505323\pi$
$684$	−1.08794	−	0.628123i	−0.0415985	−	0.0240169i
$685$	−6.02417	−	3.47805i	−0.230172	−	0.132890i
$686$	−4.01611	+	2.31870i	−0.153336	+	0.0885285i
$687$	−3.26245	−	5.65073i	−0.124470	−	0.215589i
$688$	−4.67284	+	2.69787i	−0.178150	+	0.102855i
$689$			11.8793i			0.452566i
$690$	−4.42352	−	2.55392i	−0.168400	−	0.0972260i
$691$	13.3388	+	23.1035i	0.507431	+	0.878897i	0.999963	+	0.00860245i	$0.00273828\pi$
$691$	13.3388	+	23.1035i	0.507431	+	0.878897i	−0.492532	+	0.870295i	$0.663928\pi$
$692$	−15.0784			−0.573195
$693$	0.445393			0.0169191
$694$	0.144513	+	0.250304i	0.00548565	+	0.00950142i
$695$		−	7.82567i		−	0.296845i
$696$	−1.67724	+	2.90506i	−0.0635754	+	0.110116i
$697$		−	53.6940i		−	2.03380i
$698$	−17.6679	−	10.2006i	−0.668740	−	0.386097i
$699$	8.13891	−	14.0970i	0.307842	−	0.533198i
$700$	0.166951	−	0.289168i	0.00631016	−	0.0109295i
$701$	12.0485	−	6.95619i	0.455064	−	0.262731i	−0.254902	−	0.966967i	$-0.582043\pi$
$701$	12.0485	−	6.95619i	0.455064	−	0.262731i	0.709967	+	0.704235i	$0.248710\pi$
$702$	5.16418			0.194909
$703$	−2.09667	−	7.34817i	−0.0790774	−	0.277142i
$704$	1.33390			0.0502733
$705$	9.18915	−	5.30536i	0.346083	−	0.199811i
$706$	−0.821689	+	1.42321i	−0.0309247	+	0.0535631i
$707$	1.11088	−	1.92409i	0.0417788	−	0.0723630i
$708$	11.1138	+	6.41656i	0.417683	+	0.241149i
$709$			36.6945i			1.37809i	0.724718	+	0.689046i	$0.241970\pi$
$709$			36.6945i			1.37809i	−0.724718	+	0.689046i	$0.758030\pi$
$710$	−0.103651	+	0.179529i	−0.00388995	+	0.00673759i
$711$		−	17.3084i		−	0.649115i
$712$	7.18201	+	12.4396i	0.269157	+	0.466194i
$713$	31.0486			1.16278
$714$	−2.53356			−0.0948162
$715$	3.44425	+	5.96562i	0.128808	+	0.223102i
$716$	−16.3517	−	9.44067i	−0.611092	−	0.352814i
$717$		−	8.21712i		−	0.306874i
$718$	−22.0830	+	12.7496i	−0.824130	+	0.475812i
$719$	11.0925	+	19.2128i	0.413680	+	0.716516i	0.995289	−	0.0969532i	$-0.0309097\pi$
$719$	11.0925	+	19.2128i	0.413680	+	0.716516i	−0.581608	+	0.813469i	$0.697576\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	−1.08569	−	0.626825i	−0.0404333	−	0.0233442i
$722$	15.0878	+	8.71092i	0.561508	+	0.324187i
$723$	18.6050	−	10.7416i	0.691926	−	0.399484i
$724$	−6.64591	−	11.5111i	−0.246993	−	0.427805i
$725$	2.90506	−	1.67724i	0.107891	−	0.0622910i
$726$			9.22070i			0.342212i
$727$	18.6298	+	10.7559i	0.690941	+	0.398915i	0.803965	−	0.594677i	$-0.202720\pi$
$727$	18.6298	+	10.7559i	0.690941	+	0.398915i	−0.113023	+	0.993592i	$0.536053\pi$
$728$	−0.862165	−	1.49331i	−0.0319540	−	0.0553459i
$729$	1.00000			0.0370370
$730$	−8.99086			−0.332766
$731$	−20.4707	−	35.4563i	−0.757136	−	1.31140i
$732$		−	7.07642i		−	0.261552i
$733$	18.2252	−	31.5669i	0.673162	−	1.16595i	−0.303840	−	0.952723i	$-0.598269\pi$
$733$	18.2252	−	31.5669i	0.673162	−	1.16595i	0.977002	−	0.213228i	$-0.0683977\pi$
$734$		−	27.6439i		−	1.02035i
$735$	−5.96562	−	3.44425i	−0.220045	−	0.127043i
$736$	2.55392	−	4.42352i	0.0941387	−	0.163053i
$737$	−4.82388	+	8.35520i	−0.177690	+	0.307768i
$738$	6.12836	−	3.53821i	0.225588	−	0.130243i
$739$	−20.7789			−0.764364			−0.382182	−	0.924087i	$-0.624827\pi$
$739$	−20.7789			−0.764364			−0.382182	+	0.924087i	$0.624827\pi$
$740$	−5.90015	−	1.47926i	−0.216894	−	0.0543787i
$741$	6.48748			0.238323
$742$	0.665182	−	0.384043i	0.0244196	−	0.0140987i
$743$	−7.47140	+	12.9408i	−0.274099	+	0.474754i	−0.969907	−	0.243474i	$-0.921713\pi$
$743$	−7.47140	+	12.9408i	−0.274099	+	0.474754i	0.695808	+	0.718228i	$0.255046\pi$
$744$	3.03931	−	5.26424i	0.111426	−	0.192996i
$745$	10.0535	+	5.80442i	0.368333	+	0.212657i
$746$		−	15.5069i		−	0.567749i
$747$	2.98704	−	5.17370i	0.109290	−	0.189296i
$748$			10.1213i			0.370071i
$749$	−0.774961	−	1.34227i	−0.0283165	−	0.0490456i
$750$	1.00000			0.0365148
$751$	30.6311			1.11774			0.558872	−	0.829254i	$-0.311234\pi$
$751$	30.6311			1.11774			0.558872	+	0.829254i	$0.311234\pi$
$752$	5.30536	+	9.18915i	0.193467	+	0.335094i
$753$	−0.0159315	−	0.00919803i	−0.000580574	−	0.000335195i
$754$		−	17.3231i		−	0.630870i
$755$	−3.94586	+	2.27814i	−0.143604	+	0.0829100i
$756$	−0.166951	−	0.289168i	−0.00607195	−	0.0105169i
$757$	−8.25290	+	4.76482i	−0.299957	+	0.173180i	−0.642423	−	0.766350i	$-0.722071\pi$
$757$	−8.25290	+	4.76482i	−0.299957	+	0.173180i	0.342467	+	0.939530i	$0.388738\pi$
$758$	23.1448	+	13.3626i	0.840656	+	0.485353i
$759$	−5.90054	−	3.40668i	−0.214176	−	0.123655i
$760$	−1.08794	+	0.628123i	−0.0394638	+	0.0227844i
$761$	4.65781	+	8.06757i	0.168846	+	0.292449i	0.938014	−	0.346597i	$-0.112663\pi$
$761$	4.65781	+	8.06757i	0.168846	+	0.292449i	−0.769169	+	0.639046i	$0.779329\pi$
$762$	14.2877	−	8.24903i	0.517590	−	0.298831i
$763$			5.60562i			0.202937i
$764$	−8.68274	−	5.01298i	−0.314130	−	0.181363i
$765$	−3.79387	−	6.57117i	−0.137168	−	0.237581i
$766$	−1.30069			−0.0469957
$767$	−66.2726			−2.39296
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$		−	3.83208i		−	0.138188i	−0.997610	−	0.0690942i	$-0.977989\pi$
$769$		−	3.83208i		−	0.138188i	0.997610	−	0.0690942i	$-0.0220109\pi$
$770$	0.222697	−	0.385722i	0.00802543	−	0.0139004i
$771$		−	4.47207i		−	0.161058i
$772$	6.21431	+	3.58784i	0.223658	+	0.129129i
$773$	20.4894	−	35.4887i	0.736954	−	1.27644i	−0.216907	−	0.976192i	$-0.569597\pi$
$773$	20.4894	−	35.4887i	0.736954	−	1.27644i	0.953861	−	0.300249i	$-0.0970698\pi$
$774$	2.69787	−	4.67284i	0.0969728	−	0.167962i
$775$	−5.26424	+	3.03931i	−0.189097	+	0.109175i
$776$	4.55681			0.163580
$777$	0.493929	−	1.97007i	0.0177196	−	0.0706760i
$778$	−36.1982			−1.29777
$779$	7.69872	−	4.44486i	0.275835	−	0.159254i
$780$	2.58209	−	4.47231i	0.0924536	−	0.160134i
$781$	−0.138260	+	0.239474i	−0.00494734	+	0.00856905i
$782$	33.5645	+	19.3785i	1.20026	+	0.692972i
$783$		−	3.35447i		−	0.119879i
$784$	3.44425	−	5.96562i	0.123009	−	0.213058i
$785$		−	20.2720i		−	0.723538i
$786$	5.92052	+	10.2546i	0.211178	+	0.365771i
$787$	−16.5453			−0.589776			−0.294888	−	0.955532i	$-0.595282\pi$
$787$	−16.5453			−0.589776			−0.294888	+	0.955532i	$0.595282\pi$
$788$	−17.5615			−0.625604
$789$	−12.3395	−	21.3726i	−0.439296	−	0.760884i
$790$	−14.9895	−	8.65419i	−0.533302	−	0.307902i
$791$		−	3.32572i		−	0.118249i
$792$	−1.15519	+	0.666951i	−0.0410480	+	0.0236991i
$793$	18.2719	+	31.6479i	0.648856	+	1.12385i
$794$	−23.5159	+	13.5769i	−0.834548	+	0.481827i
$795$	1.99214	+	1.15017i	0.0706541	+	0.0407922i
$796$	10.3430	+	5.97153i	0.366598	+	0.211655i
$797$	−26.3962	+	15.2399i	−0.935003	+	0.539824i	−0.888390	−	0.459089i	$-0.848176\pi$
$797$	−26.3962	+	15.2399i	−0.935003	+	0.539824i	−0.0466125	+	0.998913i	$0.514843\pi$
$798$	−0.209732	−	0.363266i	−0.00742442	−	0.0128595i
$799$	−69.7248	+	40.2556i	−2.46669	+	1.42414i
$800$			1.00000i			0.0353553i
$801$	−12.4396	−	7.18201i	−0.439532	−	0.253764i
$802$	−18.4678	−	31.9872i	−0.652121	−	1.12951i
$803$	−11.9929			−0.423221
$804$	7.23273			0.255079
$805$	−0.852759	−	1.47702i	−0.0300558	−	0.0520582i
$806$			31.3911i			1.10570i
$807$	−14.9068	+	25.8194i	−0.524745	+	0.908885i
$808$			6.65390i			0.234083i
$809$	−2.21452	−	1.27855i	−0.0778583	−	0.0449515i	0.460565	−	0.887626i	$-0.347647\pi$
$809$	−2.21452	−	1.27855i	−0.0778583	−	0.0449515i	−0.538424	+	0.842674i	$0.680980\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	4.50959	−	7.81083i	0.158353	−	0.274275i	−0.775922	−	0.630829i	$-0.782715\pi$
$811$	4.50959	−	7.81083i	0.158353	−	0.274275i	0.934275	+	0.356554i	$0.116048\pi$
$812$	−0.970005	+	0.560033i	−0.0340405	+	0.0196533i
$813$	−20.2443			−0.710000
$814$	−7.87023	−	1.97319i	−0.275851	−	0.0691603i
$815$	−4.44848			−0.155823
$816$	6.57117	−	3.79387i	0.230037	−	0.132812i
$817$	3.38918	−	5.87024i	0.118573	−	0.205374i
$818$	7.48592	−	12.9660i	0.261739	−	0.453345i
$819$	1.49331	+	0.862165i	0.0521806	+	0.0301265i
$820$		−	7.07642i		−	0.247119i
$821$	−26.9618	+	46.6992i	−0.940974	+	1.62981i	−0.177355	+	0.984147i	$0.556754\pi$
$821$	−26.9618	+	46.6992i	−0.940974	+	1.62981i	−0.763619	+	0.645667i	$0.776579\pi$
$822$			6.95611i			0.242622i
$823$	21.2258	+	36.7642i	0.739885	+	1.28152i	0.952547	+	0.304393i	$0.0984535\pi$
$823$	21.2258	+	36.7642i	0.739885	+	1.28152i	−0.212661	+	0.977126i	$0.568213\pi$
$824$	3.75454			0.130796
$825$	1.33390			0.0464405
$826$	2.14251	+	3.71093i	0.0745473	+	0.129120i
$827$	33.5677	+	19.3803i	1.16726	+	0.673920i	0.953034	−	0.302864i	$-0.0979427\pi$
$827$	33.5677	+	19.3803i	1.16726	+	0.673920i	0.214229	+	0.976783i	$0.431276\pi$
$828$			5.10784i			0.177510i
$829$	0.473881	−	0.273595i	0.0164586	−	0.00950236i	−0.491748	−	0.870737i	$-0.663642\pi$
$829$	0.473881	−	0.273595i	0.0164586	−	0.00950236i	0.508207	+	0.861235i	$0.330309\pi$
$830$	−2.98704	−	5.17370i	−0.103682	−	0.179582i
$831$	14.3284	−	8.27251i	0.497047	−	0.286970i
$832$	4.47231	+	2.58209i	0.155049	+	0.0895178i
$833$	45.2656	+	26.1341i	1.56836	+	0.905493i
$834$	−6.77723	+	3.91284i	−0.234676	+	0.135490i
$835$	6.63523	+	11.4926i	0.229622	+	0.397716i
$836$	−1.45121	+	0.837855i	−0.0501910	+	0.0289778i
$837$			6.07862i			0.210108i
$838$	−1.56252	−	0.902123i	−0.0539764	−	0.0311633i
$839$	−14.8778	−	25.7692i	−0.513640	−	0.889650i	−0.999875	−	0.0158220i	$-0.994964\pi$
$839$	−14.8778	−	25.7692i	−0.513640	−	0.889650i	0.486235	−	0.873828i	$-0.338370\pi$
$840$	−0.333902			−0.0115207
$841$	17.7475			0.611984
$842$	8.91690	+	15.4445i	0.307297	+	0.532254i
$843$		−	19.6030i		−	0.675163i
$844$	3.35376	−	5.80888i	0.115441	−	0.199950i
$845$			13.6687i			0.470219i
$846$	−9.18915	−	5.30536i	−0.315929	−	0.182402i
$847$	−1.53941	+	2.66633i	−0.0528947	+	0.0916162i
$848$	−1.15017	+	1.99214i	−0.0394968	+	0.0684105i
$849$	−0.889398	+	0.513494i	−0.0305241	+	0.0176231i
$850$	−7.58773			−0.260257
$851$	−21.6120	+	22.3215i	−0.740851	+	0.765171i
$852$	0.207302			0.00710205
$853$	−9.32240	+	5.38229i	−0.319193	+	0.184286i	−0.651033	−	0.759050i	$-0.725664\pi$
$853$	−9.32240	+	5.38229i	−0.319193	+	0.184286i	0.331840	+	0.943336i	$0.392331\pi$
$854$	1.18142	−	2.04627i	0.0404272	−	0.0700220i
$855$	0.628123	−	1.08794i	0.0214814	−	0.0372068i
$856$	4.01995	+	2.32092i	0.137399	+	0.0793275i
$857$		−	0.343352i		−	0.0117287i	−0.999983	−	0.00586433i	$-0.998133\pi$
$857$		−	0.343352i		−	0.0117287i	0.999983	−	0.00586433i	$-0.00186669\pi$
$858$	3.44425	−	5.96562i	0.117585	−	0.203663i
$859$		−	10.1872i		−	0.347582i	−0.984783	−	0.173791i	$-0.944398\pi$
$859$		−	10.1872i		−	0.347582i	0.984783	−	0.173791i	$-0.0556016\pi$
$860$	−2.69787	−	4.67284i	−0.0919965	−	0.159343i
$861$	2.36283			0.0805251
$862$	−6.36945			−0.216944
$863$	16.6764	+	28.8844i	0.567673	+	0.983238i	0.996796	+	0.0799919i	$0.0254894\pi$
$863$	16.6764	+	28.8844i	0.567673	+	0.983238i	−0.429123	+	0.903246i	$0.641177\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		−	15.0784i		−	0.512682i
$866$	−5.96132	+	3.44177i	−0.202574	+	0.116956i
$867$	20.2869	+	35.1379i	0.688978	+	1.19334i
$868$	1.75774	−	1.01483i	0.0596616	−	0.0344456i
$869$	−19.9945	−	11.5438i	−0.678268	−	0.391598i
$870$	−2.90506	−	1.67724i	−0.0984907	−	0.0568636i
$871$	−32.3470	+	18.6756i	−1.09604	+	0.632797i
$872$	−8.39410	−	14.5390i	−0.284260	−	0.492353i
$873$	−3.94631	+	2.27840i	−0.133562	+	0.0771123i
$874$			6.41670i			0.217048i
$875$	0.289168	+	0.166951i	0.00977566	+	0.00564398i
$876$	4.49543	+	7.78631i	0.151886	+	0.263075i
$877$	13.7317			0.463686			0.231843	−	0.972753i	$-0.425524\pi$
$877$	13.7317			0.463686			0.231843	+	0.972753i	$0.425524\pi$
$878$	35.0907			1.18425
$879$	−0.264857	−	0.458746i	−0.00893340	−	0.0154731i
$880$			1.33390i			0.0449658i
$881$	−26.4233	+	45.7665i	−0.890225	+	1.54191i	−0.0506188	+	0.998718i	$0.516119\pi$
$881$	−26.4233	+	45.7665i	−0.890225	+	1.54191i	−0.839606	+	0.543196i	$0.817214\pi$
$882$			6.88851i			0.231948i
$883$	4.66907	+	2.69569i	0.157127	+	0.0907172i	0.576502	−	0.817096i	$-0.304417\pi$
$883$	4.66907	+	2.69569i	0.157127	+	0.0907172i	−0.419375	+	0.907813i	$0.637751\pi$
$884$	−19.5922	+	33.9347i	−0.658957	+	1.14135i
$885$	−6.41656	+	11.1138i	−0.215690	+	0.373587i
$886$	−11.1817	+	6.45574i	−0.375656	+	0.216885i
$887$	3.88986			0.130609			0.0653043	−	0.997865i	$-0.479198\pi$
$887$	3.88986			0.130609			0.0653043	+	0.997865i	$0.479198\pi$
$888$	1.66900	+	5.84931i	0.0560079	+	0.196290i
$889$	5.50874			0.184757
$890$	−12.4396	+	7.18201i	−0.416976	+	0.240741i
$891$	0.666951	−	1.15519i	0.0223437	−	0.0387004i
$892$	−11.9286	+	20.6609i	−0.399398	+	0.691777i
$893$	−11.5438	−	6.66483i	−0.386300	−	0.223030i
$894$		−	11.6088i		−	0.388258i
$895$	9.44067	−	16.3517i	0.315567	−	0.546578i
$896$		−	0.333902i		−	0.0111549i
$897$	−13.1889	−	22.8438i	−0.440364	−	0.762733i
$898$	12.1473			0.405362
$899$	20.3905			0.680063
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−15.1159	−	8.72715i	−0.503582	−	0.290743i
$902$		−	9.43925i		−	0.314293i
$903$	1.56027	−	0.900824i	0.0519226	−	0.0299775i
$904$	4.98008	+	8.62576i	0.165635	+	0.286888i
$905$	11.5111	−	6.64591i	0.382640	−	0.220918i
$906$	3.94586	+	2.27814i	0.131092	+	0.0756862i
$907$	27.6453	+	15.9610i	0.917946	+	0.529976i	0.882979	−	0.469412i	$-0.155534\pi$
$907$	27.6453	+	15.9610i	0.917946	+	0.529976i	0.0349669	+	0.999388i	$0.488867\pi$
$908$	17.9658	−	10.3726i	0.596216	−	0.344226i
$909$	−3.32695	−	5.76245i	−0.110348	−	0.191128i
$910$	1.49331	−	0.862165i	0.0495029	−	0.0285805i
$911$			18.3778i			0.608884i	0.952531	+	0.304442i	$0.0984700\pi$
$911$			18.3778i			0.608884i	−0.952531	+	0.304442i	$0.901530\pi$
$912$	1.08794	+	0.628123i	0.0360253	+	0.0207992i
$913$	−3.98441	−	6.90121i	−0.131865	−	0.228397i
$914$	−18.8124			−0.622259
$915$	7.07642			0.233939
$916$	3.26245	+	5.65073i	0.107794	+	0.186705i
$917$			3.95375i			0.130564i
$918$	−3.79387	+	6.57117i	−0.125216	+	0.216881i
$919$			29.0564i			0.958481i	0.877684	+	0.479240i	$0.159088\pi$
$919$			29.0564i			0.958481i	−0.877684	+	0.479240i	$0.840912\pi$
$920$	4.42352	+	2.55392i	0.145839	+	0.0842002i
$921$	8.67921	−	15.0328i	0.285990	−	0.495349i
$922$	−1.06327	+	1.84164i	−0.0350171	+	0.0606513i
$923$	−0.927119	+	0.535272i	−0.0305165	+	0.0176187i
$924$	−0.445393			−0.0146524
$925$	1.47926	−	5.90015i	0.0486378	−	0.193996i
$926$	0.702860			0.0230974
$927$	−3.25153	+	1.87727i	−0.106794	+	0.0616576i
$928$	1.67724	−	2.90506i	0.0550580	−	0.0953632i
$929$	10.4708	−	18.1359i	0.343535	−	0.595020i	−0.641552	−	0.767080i	$-0.721709\pi$
$929$	10.4708	−	18.1359i	0.343535	−	0.595020i	0.985086	+	0.172060i	$0.0550423\pi$
$930$	5.26424	+	3.03931i	0.172621	+	0.0996629i
$931$			8.65366i			0.283612i
$932$	−8.13891	+	14.0970i	−0.266599	+	0.461763i
$933$		−	30.2828i		−	0.991413i
$934$	−7.99365	−	13.8454i	−0.261560	−	0.453036i
$935$	−10.1213			−0.331002
$936$	−5.16418			−0.168796
$937$	14.2696	+	24.7157i	0.466168	+	0.807426i	0.999253	−	0.0386351i	$-0.0123010\pi$
$937$	14.2696	+	24.7157i	0.466168	+	0.807426i	−0.533086	+	0.846061i	$0.678968\pi$
$938$	2.09147	+	1.20751i	0.0682890	+	0.0394267i
$939$		−	0.917544i		−	0.0299429i
$940$	−9.18915	+	5.30536i	−0.299717	+	0.173042i
$941$	3.97694	+	6.88825i	0.129644	+	0.224551i	0.923539	−	0.383505i	$-0.125283\pi$
$941$	3.97694	+	6.88825i	0.129644	+	0.224551i	−0.793894	+	0.608056i	$0.791950\pi$
$942$	−17.5561	+	10.1360i	−0.572007	+	0.330249i
$943$	−31.3026	−	18.0726i	−1.01935	−	0.588524i
$944$	−11.1138	−	6.41656i	−0.361724	−	0.208841i
$945$	0.289168	−	0.166951i	0.00940663	−	0.00543092i
$946$	−3.59869	−	6.23312i	−0.117004	−	0.202656i
$947$	−19.2913	+	11.1378i	−0.626883	+	0.361931i	−0.779544	−	0.626348i	$-0.784549\pi$
$947$	−19.2913	+	11.1378i	−0.626883	+	0.361931i	0.152661	+	0.988279i	$0.451216\pi$
$948$			17.3084i			0.562150i
$949$	−40.2099	−	23.2152i	−1.30527	−	0.753597i
$950$	−0.628123	−	1.08794i	−0.0203790	−	0.0352975i
$951$	12.6924			0.411578
$952$	2.53356			0.0821132
$953$	1.82948	+	3.16875i	0.0592627	+	0.102646i	0.894135	−	0.447798i	$-0.147792\pi$
$953$	1.82948	+	3.16875i	0.0592627	+	0.102646i	−0.834872	+	0.550444i	$0.814458\pi$
$954$		−	2.30033i		−	0.0744759i
$955$	5.01298	−	8.68274i	0.162216	−	0.280967i
$956$			8.21712i			0.265761i
$957$	−3.87506	−	2.23727i	−0.125263	−	0.0723206i
$958$	9.25029	−	16.0220i	0.298863	−	0.517647i
$959$	−1.16133	+	2.01148i	−0.0375013	+	0.0649542i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	−5.94959			−0.191922
$962$	−22.5677	−	21.8504i	−0.727612	−	0.704486i
$963$	−4.64184			−0.149581
$964$	−18.6050	+	10.7416i	−0.599226	+	0.345963i
$965$	−3.58784	+	6.21431i	−0.115497	+	0.200046i
$966$	−0.852759	+	1.47702i	−0.0274371	+	0.0475224i
$967$	18.2171	+	10.5176i	0.585822	+	0.338224i	0.763444	−	0.645874i	$-0.223507\pi$
$967$	18.2171	+	10.5176i	0.585822	+	0.338224i	−0.177622	+	0.984099i	$0.556840\pi$
$968$		−	9.22070i		−	0.296365i
$969$	−4.76603	+	8.25501i	−0.153107	+	0.265189i
$970$			4.55681i			0.146310i
$971$	−5.01403	−	8.68455i	−0.160908	−	0.278700i	0.774287	−	0.632835i	$-0.218109\pi$
$971$	−5.01403	−	8.68455i	−0.160908	−	0.278700i	−0.935195	+	0.354134i	$0.884776\pi$
$972$	−1.00000			−0.0320750
$973$	−2.61301			−0.0837693
$974$	−1.67091	−	2.89410i	−0.0535394	−	0.0927329i
$975$	4.47231	+	2.58209i	0.143229	+	0.0826930i
$976$			7.07642i			0.226511i
$977$	45.1221	−	26.0512i	1.44358	−	0.833453i	0.445496	−	0.895284i	$-0.353027\pi$
$977$	45.1221	−	26.0512i	1.44358	−	0.833453i	0.998087	+	0.0618311i	$0.0196940\pi$
$978$	2.22424	+	3.85249i	0.0711233	+	0.123189i
$979$	−16.5932	+	9.58010i	−0.530321	+	0.306181i
$980$	5.96562	+	3.44425i	0.190565	+	0.110023i
$981$	14.5390	+	8.39410i	0.464195	+	0.268003i
$982$	9.02352	−	5.20973i	0.287952	−	0.166249i
$983$	−29.8632	−	51.7246i	−0.952489	−	1.64976i	−0.740013	−	0.672593i	$-0.765181\pi$
$983$	−29.8632	−	51.7246i	−0.952489	−	1.64976i	−0.212476	−	0.977166i	$-0.568153\pi$
$984$	−6.12836	+	3.53821i	−0.195365	+	0.112794i
$985$		−	17.5615i		−	0.559557i
$986$	22.0428	+	12.7264i	0.701986	+	0.405292i
$987$	−1.77147	−	3.06828i	−0.0563866	−	0.0976644i
$988$	−6.48748			−0.206394
$989$	−27.5605			−0.876374
$990$	−0.666951	−	1.15519i	−0.0211971	−	0.0367145i
$991$			13.6954i			0.435048i	0.976055	+	0.217524i	$0.0697980\pi$
$991$			13.6954i			0.435048i	−0.976055	+	0.217524i	$0.930202\pi$
$992$	−3.03931	+	5.26424i	−0.0964981	+	0.167140i
$993$		−	26.6445i		−	0.845536i
$994$	0.0599451	+	0.0346093i	0.00190134	+	0.00109774i
$995$	−5.97153	+	10.3430i	−0.189310	+	0.327895i
$996$	−2.98704	+	5.17370i	−0.0946478	+	0.163935i
$997$	−14.0692	+	8.12287i	−0.445577	+	0.257254i	−0.705960	−	0.708251i	$-0.749484\pi$
$997$	−14.0692	+	8.12287i	−0.445577	+	0.257254i	0.260383	+	0.965505i	$0.416151\pi$
$998$	−40.6200			−1.28580
$999$	−4.37005	−	4.23115i	−0.138262	−	0.133868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.c.751.3	✓	16
37.27	even	6	inner	1110.2.x.c.841.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.c.751.3	✓	16	1.1	even	1	trivial
1110.2.x.c.841.3	yes	16	37.27	even	6	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(0.166951 - 0.289168i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(0.166951 - 0.289168i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -1.33390 q^{11} +(0.500000 + 0.866025i) q^{12} +(-4.47231 - 2.58209i) q^{13} +0.333902i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.57117 - 3.79387i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.08794 + 0.628123i) q^{19} +(0.866025 - 0.500000i) q^{20} +(0.166951 + 0.289168i) q^{21} +(1.15519 - 0.666951i) q^{22} -5.10784i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +5.16418 q^{26} +1.00000 q^{27} +(-0.166951 - 0.289168i) q^{28} -3.35447i q^{29} +(0.500000 - 0.866025i) q^{30} +6.07862i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.666951 - 1.15519i) q^{33} +(-3.79387 + 6.57117i) q^{34} +(0.289168 - 0.166951i) q^{35} -1.00000 q^{36} +(-4.37005 - 4.23115i) q^{37} -1.25625 q^{38} +(4.47231 - 2.58209i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(3.53821 - 6.12836i) q^{41} +(-0.289168 - 0.166951i) q^{42} -5.39573i q^{43} +(-0.666951 + 1.15519i) q^{44} -1.00000i q^{45} +(2.55392 + 4.42352i) q^{46} -10.6107 q^{47} +1.00000 q^{48} +(3.44425 + 5.96562i) q^{49} +(-0.866025 - 0.500000i) q^{50} +7.58773i q^{51} +(-4.47231 + 2.58209i) q^{52} +(-1.15017 - 1.99214i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-1.15519 - 0.666951i) q^{55} +(0.289168 + 0.166951i) q^{56} +(-1.08794 + 0.628123i) q^{57} +(1.67724 + 2.90506i) q^{58} +(11.1138 - 6.41656i) q^{59} +1.00000i q^{60} +(-6.12836 - 3.53821i) q^{61} +(-3.03931 - 5.26424i) q^{62} -0.333902 q^{63} -1.00000 q^{64} +(-2.58209 - 4.47231i) q^{65} +1.33390i q^{66} +(3.61637 - 6.26373i) q^{67} -7.58773i q^{68} +(4.42352 + 2.55392i) q^{69} +(-0.166951 + 0.289168i) q^{70} +(0.103651 - 0.179529i) q^{71} +(0.866025 - 0.500000i) q^{72} +8.99086 q^{73} +(5.90015 + 1.47926i) q^{74} -1.00000 q^{75} +(1.08794 - 0.628123i) q^{76} +(-0.222697 + 0.385722i) q^{77} +(-2.58209 + 4.47231i) q^{78} +(14.9895 + 8.65419i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +7.07642i q^{82} +(2.98704 + 5.17370i) q^{83} +0.333902 q^{84} +7.58773 q^{85} +(2.69787 + 4.67284i) q^{86} +(2.90506 + 1.67724i) q^{87} -1.33390i q^{88} +(12.4396 - 7.18201i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-1.49331 + 0.862165i) q^{91} +(-4.42352 - 2.55392i) q^{92} +(-5.26424 - 3.03931i) q^{93} +(9.18915 - 5.30536i) q^{94} +(0.628123 + 1.08794i) q^{95} +(-0.866025 + 0.500000i) q^{96} -4.55681i q^{97} +(-5.96562 - 3.44425i) q^{98} +(0.666951 + 1.15519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more