LMFDB - Embedded newform 1110.2.x.d.751.8

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} + 60x^{14} + 1362x^{12} + 15028x^{10} + 86441x^{8} + 260376x^{6} + 382684x^{4} + 224224x^{2} + 38416 $ x^16 + 60x^14 + 1362x^12 + 15028x^10 + 86441x^8 + 260376x^6 + 382684x^4 + 224224*x^2 + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.8
Root			$-3.78749i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.d.841.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.89374 - 3.28006i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(1.89374 - 3.28006i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -3.84038 q^{11} +(0.500000 + 0.866025i) q^{12} +(5.82335 + 3.36212i) q^{13} -3.78749i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.14609 - 2.39374i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-4.79142 - 2.76633i) q^{19} +(0.866025 - 0.500000i) q^{20} +(1.89374 + 3.28006i) q^{21} +(-3.32587 + 1.92019i) q^{22} -8.45628i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +6.72423 q^{26} +1.00000 q^{27} +(-1.89374 - 3.28006i) q^{28} -1.86387i q^{29} +(-0.500000 + 0.866025i) q^{30} +8.49606i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.92019 - 3.32587i) q^{33} +(2.39374 - 4.14609i) q^{34} +(3.28006 - 1.89374i) q^{35} -1.00000 q^{36} +(2.29396 + 5.63363i) q^{37} -5.53266 q^{38} +(-5.82335 + 3.36212i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.99616 - 8.65360i) q^{41} +(3.28006 + 1.89374i) q^{42} -0.0397760i q^{43} +(-1.92019 + 3.32587i) q^{44} -1.00000i q^{45} +(-4.22814 - 7.32335i) q^{46} +1.04092 q^{47} +1.00000 q^{48} +(-3.67253 - 6.36102i) q^{49} +(0.866025 + 0.500000i) q^{50} +4.78749i q^{51} +(5.82335 - 3.36212i) q^{52} +(-1.60374 - 2.77776i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-3.32587 - 1.92019i) q^{55} +(-3.28006 - 1.89374i) q^{56} +(4.79142 - 2.76633i) q^{57} +(-0.931933 - 1.61416i) q^{58} +(1.56278 - 0.902271i) q^{59} +1.00000i q^{60} +(11.4759 + 6.62563i) q^{61} +(4.24803 + 7.35780i) q^{62} -3.78749 q^{63} -1.00000 q^{64} +(3.36212 + 5.82335i) q^{65} -3.84038i q^{66} +(4.58744 - 7.94568i) q^{67} -4.78749i q^{68} +(7.32335 + 4.22814i) q^{69} +(1.89374 - 3.28006i) q^{70} +(-0.928191 + 1.60767i) q^{71} +(-0.866025 + 0.500000i) q^{72} -11.8343 q^{73} +(4.80344 + 3.73188i) q^{74} -1.00000 q^{75} +(-4.79142 + 2.76633i) q^{76} +(-7.27270 + 12.5967i) q^{77} +(-3.36212 + 5.82335i) q^{78} +(-3.13047 - 1.80738i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -9.99232i q^{82} +(6.79367 + 11.7670i) q^{83} +3.78749 q^{84} +4.78749 q^{85} +(-0.0198880 - 0.0344471i) q^{86} +(1.61416 + 0.931933i) q^{87} +3.84038i q^{88} +(14.8116 - 8.55149i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(22.0559 - 12.7340i) q^{91} +(-7.32335 - 4.22814i) q^{92} +(-7.35780 - 4.24803i) q^{93} +(0.901463 - 0.520460i) q^{94} +(-2.76633 - 4.79142i) q^{95} +(0.866025 - 0.500000i) q^{96} +6.15065i q^{97} +(-6.36102 - 3.67253i) q^{98} +(1.92019 + 3.32587i) 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} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * 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
$7$	1.89374	−	3.28006i	0.715768	−	1.23975i	−0.246895	−	0.969042i	$-0.579410\pi$
$7$	1.89374	−	3.28006i	0.715768	−	1.23975i	0.962663	−	0.270704i	$-0.0872565\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	−3.84038			−1.15792			−0.578960	−	0.815356i	$-0.696541\pi$
$11$	−3.84038			−1.15792			−0.578960	+	0.815356i	$0.696541\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	5.82335	+	3.36212i	1.61511	+	0.932483i	0.988161	+	0.153421i	$0.0490290\pi$
$13$	5.82335	+	3.36212i	1.61511	+	0.932483i	0.626947	+	0.779062i	$0.284304\pi$
$14$		−	3.78749i		−	1.01225i
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.14609	−	2.39374i	1.00557	−	0.580568i	0.0956811	−	0.995412i	$-0.469497\pi$
$17$	4.14609	−	2.39374i	1.00557	−	0.580568i	0.909893	+	0.414844i	$0.136164\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−4.79142	−	2.76633i	−1.09923	−	0.634639i	−0.163210	−	0.986591i	$-0.552185\pi$
$19$	−4.79142	−	2.76633i	−1.09923	−	0.634639i	−0.936018	+	0.351952i	$0.885518\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	1.89374	+	3.28006i	0.413249	+	0.715768i
$22$	−3.32587	+	1.92019i	−0.709078	+	0.409386i
$23$		−	8.45628i		−	1.76326i	−0.471945	−	0.881628i	$-0.656448\pi$
$23$		−	8.45628i		−	1.76326i	0.471945	−	0.881628i	$-0.343552\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	6.72423			1.31873
$27$	1.00000			0.192450
$28$	−1.89374	−	3.28006i	−0.357884	−	0.619873i
$29$		−	1.86387i		−	0.346111i	−0.984912	−	0.173056i	$-0.944636\pi$
$29$		−	1.86387i		−	0.346111i	0.984912	−	0.173056i	$-0.0553640\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$			8.49606i			1.52594i	0.646436	+	0.762968i	$0.276259\pi$
$31$			8.49606i			1.52594i	−0.646436	+	0.762968i	$0.723741\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.92019	−	3.32587i	0.334263	−	0.578960i
$34$	2.39374	−	4.14609i	0.410524	−	0.711048i
$35$	3.28006	−	1.89374i	0.554432	−	0.320101i
$36$	−1.00000			−0.166667
$37$	2.29396	+	5.63363i	0.377125	+	0.926162i
$37$	2.29396	+	5.63363i	0.377125	+	0.926162i
$38$	−5.53266			−0.897516
$39$	−5.82335	+	3.36212i	−0.932483	+	0.538369i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	4.99616	−	8.65360i	0.780269	−	1.35147i	−0.151516	−	0.988455i	$-0.548416\pi$
$41$	4.99616	−	8.65360i	0.780269	−	1.35147i	0.931785	−	0.363011i	$-0.118251\pi$
$42$	3.28006	+	1.89374i	0.506124	+	0.292211i
$43$		−	0.0397760i		−	0.00606579i	−0.999995	−	0.00303289i	$-0.999035\pi$
$43$		−	0.0397760i		−	0.00606579i	0.999995	−	0.00303289i	$-0.000965402\pi$
$44$	−1.92019	+	3.32587i	−0.289480	+	0.501394i
$45$		−	1.00000i		−	0.149071i
$46$	−4.22814	−	7.32335i	−0.623405	−	1.07977i
$47$	1.04092			0.151834			0.0759169	−	0.997114i	$-0.475812\pi$
$47$	1.04092			0.151834			0.0759169	+	0.997114i	$0.475812\pi$
$48$	1.00000			0.144338
$49$	−3.67253	−	6.36102i	−0.524648	−	0.908717i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$			4.78749i			0.670382i
$52$	5.82335	−	3.36212i	0.807554	−	0.466241i
$53$	−1.60374	−	2.77776i	−0.220291	−	0.381555i	0.734606	−	0.678494i	$-0.237367\pi$
$53$	−1.60374	−	2.77776i	−0.220291	−	0.381555i	−0.954896	+	0.296940i	$0.904034\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−3.32587	−	1.92019i	−0.448460	−	0.258919i
$56$	−3.28006	−	1.89374i	−0.438317	−	0.253062i
$57$	4.79142	−	2.76633i	0.634639	−	0.366409i
$58$	−0.931933	−	1.61416i	−0.122369	−	0.211949i
$59$	1.56278	−	0.902271i	0.203456	−	0.117466i	−0.394810	−	0.918763i	$-0.629190\pi$
$59$	1.56278	−	0.902271i	0.203456	−	0.117466i	0.598267	+	0.801297i	$0.295856\pi$
$60$			1.00000i			0.129099i
$61$	11.4759	+	6.62563i	1.46934	+	0.848325i	0.999409	−	0.0343779i	$-0.0109450\pi$
$61$	11.4759	+	6.62563i	1.46934	+	0.848325i	0.469932	+	0.882702i	$0.344278\pi$
$62$	4.24803	+	7.35780i	0.539500	+	0.934442i
$63$	−3.78749			−0.477179
$64$	−1.00000			−0.125000
$65$	3.36212	+	5.82335i	0.417019	+	0.722298i
$66$		−	3.84038i		−	0.472719i
$67$	4.58744	−	7.94568i	0.560445	−	0.970719i	−0.437013	−	0.899455i	$-0.643964\pi$
$67$	4.58744	−	7.94568i	0.560445	−	0.970719i	0.997458	−	0.0712634i	$-0.0227031\pi$
$68$		−	4.78749i		−	0.580568i
$69$	7.32335	+	4.22814i	0.881628	+	0.509008i
$70$	1.89374	−	3.28006i	0.226346	−	0.392042i
$71$	−0.928191	+	1.60767i	−0.110156	+	0.190796i	−0.915833	−	0.401559i	$-0.868468\pi$
$71$	−0.928191	+	1.60767i	−0.110156	+	0.190796i	0.805677	+	0.592355i	$0.201802\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−11.8343			−1.38510			−0.692550	−	0.721370i	$-0.743513\pi$
$73$	−11.8343			−1.38510			−0.692550	+	0.721370i	$0.743513\pi$
$74$	4.80344	+	3.73188i	0.558389	+	0.433822i
$75$	−1.00000			−0.115470
$76$	−4.79142	+	2.76633i	−0.549614	+	0.317320i
$77$	−7.27270	+	12.5967i	−0.828802	+	1.43553i
$78$	−3.36212	+	5.82335i	−0.380685	+	0.659365i
$79$	−3.13047	−	1.80738i	−0.352205	−	0.203346i	0.313451	−	0.949604i	$-0.398515\pi$
$79$	−3.13047	−	1.80738i	−0.352205	−	0.203346i	−0.665656	+	0.746259i	$0.731848\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	9.99232i		−	1.10347i
$83$	6.79367	+	11.7670i	0.745702	+	1.29159i	0.949866	+	0.312657i	$0.101219\pi$
$83$	6.79367	+	11.7670i	0.745702	+	1.29159i	−0.204164	+	0.978937i	$0.565448\pi$
$84$	3.78749			0.413249
$85$	4.78749			0.519276
$86$	−0.0198880	−	0.0344471i	−0.00214458	−	0.00371452i
$87$	1.61416	+	0.931933i	0.173056	+	0.0999137i
$88$			3.84038i			0.409386i
$89$	14.8116	−	8.55149i	1.57003	−	0.906457i	0.573865	−	0.818950i	$-0.305443\pi$
$89$	14.8116	−	8.55149i	1.57003	−	0.906457i	0.996164	−	0.0875067i	$-0.0278899\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	22.0559	−	12.7340i	2.31209	−	1.33488i
$92$	−7.32335	−	4.22814i	−0.763512	−	0.440814i
$93$	−7.35780	−	4.24803i	−0.762968	−	0.440500i
$94$	0.901463	−	0.520460i	0.0929789	−	0.0536814i
$95$	−2.76633	−	4.79142i	−0.283819	−	0.491590i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$			6.15065i			0.624504i	0.949999	+	0.312252i	$0.101083\pi$
$97$			6.15065i			0.624504i	−0.949999	+	0.312252i	$0.898917\pi$
$98$	−6.36102	−	3.67253i	−0.642560	−	0.370982i
$99$	1.92019	+	3.32587i	0.192987	+	0.334263i
$100$	1.00000			0.100000
$101$	−8.96357			−0.891909			−0.445954	−	0.895056i	$-0.647136\pi$
$101$	−8.96357			−0.891909			−0.445954	+	0.895056i	$0.647136\pi$
$102$	2.39374	+	4.14609i	0.237016	+	0.410524i
$103$			14.7060i			1.44903i	0.689260	+	0.724514i	$0.257936\pi$
$103$			14.7060i			1.44903i	−0.689260	+	0.724514i	$0.742064\pi$
$104$	3.36212	−	5.82335i	0.329683	−	0.571027i
$105$			3.78749i			0.369621i
$106$	−2.77776	−	1.60374i	−0.269800	−	0.155769i
$107$	−1.95561	+	3.38721i	−0.189056	+	0.327454i	−0.944936	−	0.327256i	$-0.893876\pi$
$107$	−1.95561	+	3.38721i	−0.189056	+	0.327454i	0.755880	+	0.654710i	$0.227209\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	3.31422	−	1.91346i	0.317444	−	0.183277i	−0.332809	−	0.942994i	$-0.607996\pi$
$109$	3.31422	−	1.91346i	0.317444	−	0.183277i	0.650253	+	0.759718i	$0.274663\pi$
$110$	−3.84038			−0.366166
$111$	−6.02584	−	0.830184i	−0.571948	−	0.0787976i
$112$	−3.78749			−0.357884
$113$	−14.1231	+	8.15399i	−1.32859	+	0.767062i	−0.985082	−	0.172087i	$-0.944949\pi$
$113$	−14.1231	+	8.15399i	−1.32859	+	0.767062i	−0.343509	+	0.939149i	$0.611616\pi$
$114$	2.76633	−	4.79142i	0.259090	−	0.448758i
$115$	4.22814	−	7.32335i	0.394276	−	0.682906i
$116$	−1.61416	−	0.931933i	−0.149871	−	0.0865278i
$117$		−	6.72423i		−	0.621655i
$118$	0.902271	−	1.56278i	0.0830607	−	0.143865i
$119$		−	18.1326i		−	1.66221i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	3.74855			0.340777
$122$	13.2513			1.19971
$123$	4.99616	+	8.65360i	0.450488	+	0.780269i
$124$	7.35780	+	4.24803i	0.660750	+	0.381484i
$125$			1.00000i			0.0894427i
$126$	−3.28006	+	1.89374i	−0.292211	+	0.168708i
$127$	−5.63891	−	9.76689i	−0.500373	−	0.866671i	−1.00000		0.000430450i	$-0.999863\pi$
$127$	−5.63891	−	9.76689i	−0.500373	−	0.866671i	0.499627	−	0.866241i	$-0.333470\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	0.0344471	+	0.0198880i	0.00303289	+	0.00175104i
$130$	5.82335	+	3.36212i	0.510742	+	0.294877i
$131$	7.20809	−	4.16159i	0.629774	−	0.363600i	−0.150891	−	0.988550i	$-0.548214\pi$
$131$	7.20809	−	4.16159i	0.629774	−	0.363600i	0.780664	+	0.624950i	$0.214881\pi$
$132$	−1.92019	−	3.32587i	−0.167131	−	0.289480i
$133$	−18.1475	+	10.4774i	−1.57358	+	0.908509i
$134$		−	9.17488i		−	0.792589i
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$	−2.39374	−	4.14609i	−0.205262	−	0.355524i
$137$	−15.6219			−1.33467			−0.667334	−	0.744759i	$-0.732565\pi$
$137$	−15.6219			−1.33467			−0.667334	+	0.744759i	$0.732565\pi$
$138$	8.45628			0.719846
$139$	−1.46820	−	2.54301i	−0.124531	−	0.215695i	0.797018	−	0.603955i	$-0.206409\pi$
$139$	−1.46820	−	2.54301i	−0.124531	−	0.215695i	−0.921550	+	0.388260i	$0.873076\pi$
$140$		−	3.78749i		−	0.320101i
$141$	−0.520460	+	0.901463i	−0.0438307	+	0.0759169i
$142$			1.85638i			0.155784i
$143$	−22.3639	−	12.9118i	−1.87016	−	1.07974i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.931933	−	1.61416i	0.0773928	−	0.134048i
$146$	−10.2488	+	5.91715i	−0.848197	+	0.489707i
$147$	7.34507			0.605811
$148$	6.02584	+	0.830184i	0.495321	+	0.0682407i
$149$	−16.2875			−1.33433			−0.667163	−	0.744912i	$-0.732492\pi$
$149$	−16.2875			−1.33433			−0.667163	+	0.744912i	$0.732492\pi$
$150$	−0.866025	+	0.500000i	−0.0707107	+	0.0408248i
$151$	−10.1392	+	17.5616i	−0.825117	+	1.42914i	0.0767136	+	0.997053i	$0.475557\pi$
$151$	−10.1392	+	17.5616i	−0.825117	+	1.42914i	−0.901830	+	0.432091i	$0.857776\pi$
$152$	−2.76633	+	4.79142i	−0.224379	+	0.388636i
$153$	−4.14609	−	2.39374i	−0.335191	−	0.193523i
$154$			14.5454i			1.17210i
$155$	−4.24803	+	7.35780i	−0.341210	+	0.590993i
$156$			6.72423i			0.538369i
$157$	3.39853	+	5.88642i	0.271232	+	0.469788i	0.969178	−	0.246363i	$-0.0792356\pi$
$157$	3.39853	+	5.88642i	0.271232	+	0.469788i	−0.697945	+	0.716151i	$0.745902\pi$
$158$	−3.61475			−0.287574
$159$	3.20748			0.254370
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−27.7371	−	16.0140i	−2.18599	−	1.26208i
$162$			1.00000i			0.0785674i
$163$	−7.74406	+	4.47104i	−0.606562	+	0.350199i	−0.771619	−	0.636085i	$-0.780553\pi$
$163$	−7.74406	+	4.47104i	−0.606562	+	0.350199i	0.165057	+	0.986284i	$0.447219\pi$
$164$	−4.99616	−	8.65360i	−0.390134	−	0.675733i
$165$	3.32587	−	1.92019i	0.258919	−	0.149487i
$166$	11.7670	+	6.79367i	0.913295	+	0.527291i
$167$	2.72208	+	1.57160i	0.210641	+	0.121614i	0.601609	−	0.798790i	$-0.294526\pi$
$167$	2.72208	+	1.57160i	0.210641	+	0.121614i	−0.390968	+	0.920404i	$0.627860\pi$
$168$	3.28006	−	1.89374i	0.253062	−	0.146106i
$169$	16.1076	+	27.8992i	1.23905	+	2.14610i
$170$	4.14609	−	2.39374i	0.317990	−	0.183592i
$171$			5.53266i			0.423093i
$172$	−0.0344471	−	0.0198880i	−0.00262656	−	0.00151645i
$173$	−0.362029	−	0.627052i	−0.0275245	−	0.0476739i	0.851935	−	0.523648i	$-0.175429\pi$
$173$	−0.362029	−	0.627052i	−0.0275245	−	0.0476739i	−0.879460	+	0.475974i	$0.842096\pi$
$174$	1.86387			0.141299
$175$	3.78749			0.286307
$176$	1.92019	+	3.32587i	0.144740	+	0.250697i
$177$			1.80454i			0.135638i
$178$	8.55149	−	14.8116i	0.640962	−	1.11018i
$179$			20.9563i			1.56635i	0.621801	+	0.783175i	$0.286401\pi$
$179$			20.9563i			1.56635i	−0.621801	+	0.783175i	$0.713599\pi$
$180$	−0.866025	−	0.500000i	−0.0645497	−	0.0372678i
$181$	−7.72795	+	13.3852i	−0.574414	+	0.994914i	0.421691	+	0.906740i	$0.361437\pi$
$181$	−7.72795	+	13.3852i	−0.574414	+	0.994914i	−0.996105	+	0.0881744i	$0.971897\pi$
$182$	12.7340	−	22.0559i	0.943905	−	1.63489i
$183$	−11.4759	+	6.62563i	−0.848325	+	0.489780i
$184$	−8.45628			−0.623405
$185$	−0.830184	+	6.02584i	−0.0610363	+	0.443029i
$186$	−8.49606			−0.622961
$187$	−15.9226	+	9.19290i	−1.16437	+	0.672251i
$188$	0.520460	−	0.901463i	0.0379585	−	0.0657460i
$189$	1.89374	−	3.28006i	0.137750	−	0.238589i
$190$	−4.79142	−	2.76633i	−0.347606	−	0.200691i
$191$			3.03855i			0.219862i	0.993939	+	0.109931i	$0.0350630\pi$
$191$			3.03855i			0.219862i	−0.993939	+	0.109931i	$0.964937\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$		−	14.3431i		−	1.03244i	−0.856456	−	0.516220i	$-0.827339\pi$
$193$		−	14.3431i		−	1.03244i	0.856456	−	0.516220i	$-0.172661\pi$
$194$	3.07533	+	5.32662i	0.220796	+	0.382429i
$195$	−6.72423			−0.481532
$196$	−7.34507			−0.524648
$197$	−0.401713	−	0.695787i	−0.0286209	−	0.0495728i	0.851360	−	0.524582i	$-0.175778\pi$
$197$	−0.401713	−	0.695787i	−0.0286209	−	0.0495728i	−0.879981	+	0.475009i	$0.842445\pi$
$198$	3.32587	+	1.92019i	0.236359	+	0.136462i
$199$			4.01820i			0.284842i	0.989806	+	0.142421i	$0.0454888\pi$
$199$			4.01820i			0.284842i	−0.989806	+	0.142421i	$0.954511\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	4.58744	+	7.94568i	0.323573	+	0.560445i
$202$	−7.76268	+	4.48179i	−0.546180	+	0.315337i
$203$	−6.11359	−	3.52969i	−0.429090	−	0.247735i
$204$	4.14609	+	2.39374i	0.290284	+	0.167596i
$205$	8.65360	−	4.99616i	0.604394	−	0.348947i
$206$	7.35302	+	12.7358i	0.512309	+	0.887345i
$207$	−7.32335	+	4.22814i	−0.509008	+	0.293876i
$208$		−	6.72423i		−	0.466241i
$209$	18.4009	+	10.6238i	1.27282	+	0.734861i
$210$	1.89374	+	3.28006i	0.130681	+	0.226346i
$211$	−9.46215			−0.651401			−0.325701	−	0.945473i	$-0.605600\pi$
$211$	−9.46215			−0.651401			−0.325701	+	0.945473i	$0.605600\pi$
$212$	−3.20748			−0.220291
$213$	−0.928191	−	1.60767i	−0.0635986	−	0.110156i
$214$			3.91122i			0.267365i
$215$	0.0198880	−	0.0344471i	0.00135635	−	0.00234927i
$216$		−	1.00000i		−	0.0680414i
$217$	27.8676	+	16.0894i	1.89178	+	1.09222i
$218$	1.91346	−	3.31422i	0.129596	−	0.224467i
$219$	5.91715	−	10.2488i	0.399844	−	0.692550i
$220$	−3.32587	+	1.92019i	−0.224230	+	0.129459i
$221$	32.1922			2.16548
$222$	−5.63363	+	2.29396i	−0.378104	+	0.153961i
$223$	11.8558			0.793923			0.396961	−	0.917835i	$-0.370065\pi$
$223$	11.8558			0.793923			0.396961	+	0.917835i	$0.370065\pi$
$224$	−3.28006	+	1.89374i	−0.219158	+	0.126531i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−8.15399	+	14.1231i	−0.542395	+	0.939456i
$227$	10.7982	+	6.23432i	0.716699	+	0.413786i	0.813537	−	0.581514i	$-0.197539\pi$
$227$	10.7982	+	6.23432i	0.716699	+	0.413786i	−0.0968375	+	0.995300i	$0.530873\pi$
$228$		−	5.53266i		−	0.366409i
$229$	−5.00593	+	8.67053i	−0.330801	+	0.572965i	−0.982669	−	0.185368i	$-0.940652\pi$
$229$	−5.00593	+	8.67053i	−0.330801	+	0.572965i	0.651868	+	0.758332i	$0.273986\pi$
$230$		−	8.45628i		−	0.557591i
$231$	−7.27270	−	12.5967i	−0.478509	−	0.828802i
$232$	−1.86387			−0.122369
$233$	9.91106			0.649295			0.324648	−	0.945835i	$-0.394754\pi$
$233$	9.91106			0.649295			0.324648	+	0.945835i	$0.394754\pi$
$234$	−3.36212	−	5.82335i	−0.219788	−	0.380685i
$235$	0.901463	+	0.520460i	0.0588050	+	0.0339511i
$236$		−	1.80454i		−	0.117466i
$237$	3.13047	−	1.80738i	0.203346	−	0.117402i
$238$	−9.06628	−	15.7033i	−0.587680	−	1.01789i
$239$	−13.5328	+	7.81314i	−0.875361	+	0.505390i	−0.869126	−	0.494591i	$-0.835318\pi$
$239$	−13.5328	+	7.81314i	−0.875361	+	0.505390i	−0.00623501	+	0.999981i	$0.501985\pi$
$240$	0.866025	+	0.500000i	0.0559017	+	0.0322749i
$241$	−11.0815	−	6.39792i	−0.713824	−	0.412127i	0.0986513	−	0.995122i	$-0.468547\pi$
$241$	−11.0815	−	6.39792i	−0.713824	−	0.412127i	−0.812475	+	0.582996i	$0.801880\pi$
$242$	3.24634	−	1.87427i	0.208682	−	0.120483i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	11.4759	−	6.62563i	0.734671	−	0.424162i
$245$		−	7.34507i		−	0.469259i
$246$	8.65360	+	4.99616i	0.551733	+	0.318543i
$247$	−18.6014	−	32.2186i	−1.18358	−	2.05002i
$248$	8.49606			0.539500
$249$	−13.5873			−0.861063
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$		−	9.23928i		−	0.583178i	−0.956544	−	0.291589i	$-0.905816\pi$
$251$		−	9.23928i		−	0.583178i	0.956544	−	0.291589i	$-0.0941840\pi$
$252$	−1.89374	+	3.28006i	−0.119295	+	0.206624i
$253$			32.4754i			2.04171i
$254$	−9.76689	−	5.63891i	−0.612829	−	0.353817i
$255$	−2.39374	+	4.14609i	−0.149902	+	0.259638i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.4372	+	6.02592i	−0.651055	+	0.375887i	−0.788860	−	0.614573i	$-0.789328\pi$
$257$	−10.4372	+	6.02592i	−0.651055	+	0.375887i	0.137805	+	0.990459i	$0.455995\pi$
$258$	0.0397760			0.00247635
$259$	22.8228	+	3.14431i	1.41814	+	0.195378i
$260$	6.72423			0.417019
$261$	−1.61416	+	0.931933i	−0.0999137	+	0.0576852i
$262$	4.16159	−	7.20809i	0.257104	−	0.445317i
$263$	−3.65537	+	6.33128i	−0.225400	+	0.390404i	−0.956439	−	0.291931i	$-0.905702\pi$
$263$	−3.65537	+	6.33128i	−0.225400	+	0.390404i	0.731040	+	0.682335i	$0.239035\pi$
$264$	−3.32587	−	1.92019i	−0.204693	−	0.118180i
$265$		−	3.20748i		−	0.197034i
$266$	−10.4774	+	18.1475i	−0.642413	+	1.11269i
$267$			17.1030i			1.04669i
$268$	−4.58744	−	7.94568i	−0.280222	−	0.485359i
$269$	−15.1627			−0.924484			−0.462242	−	0.886754i	$-0.652955\pi$
$269$	−15.1627			−0.924484			−0.462242	+	0.886754i	$0.652955\pi$
$270$	1.00000			0.0608581
$271$	−5.39620	−	9.34650i	−0.327796	−	0.567759i	0.654278	−	0.756254i	$-0.272973\pi$
$271$	−5.39620	−	9.34650i	−0.327796	−	0.567759i	−0.982074	+	0.188495i	$0.939639\pi$
$272$	−4.14609	−	2.39374i	−0.251393	−	0.145142i
$273$			25.4679i			1.54139i
$274$	−13.5290	+	7.81094i	−0.817314	+	0.471876i
$275$	−1.92019	−	3.32587i	−0.115792	−	0.200558i
$276$	7.32335	−	4.22814i	0.440814	−	0.254504i
$277$	6.93540	+	4.00416i	0.416708	+	0.240587i	0.693668	−	0.720295i	$-0.255994\pi$
$277$	6.93540	+	4.00416i	0.416708	+	0.240587i	−0.276960	+	0.960882i	$0.589327\pi$
$278$	−2.54301	−	1.46820i	−0.152519	−	0.0880571i
$279$	7.35780	−	4.24803i	0.440500	−	0.254323i
$280$	−1.89374	−	3.28006i	−0.113173	−	0.196021i
$281$	21.6964	−	12.5264i	1.29430	−	0.747262i	0.314884	−	0.949130i	$-0.398034\pi$
$281$	21.6964	−	12.5264i	1.29430	−	0.747262i	0.979413	+	0.201868i	$0.0647011\pi$
$282$			1.04092i			0.0619859i
$283$	3.42387	+	1.97677i	0.203528	+	0.117507i	0.598300	−	0.801272i	$-0.295843\pi$
$283$	3.42387	+	1.97677i	0.203528	+	0.117507i	−0.394772	+	0.918779i	$0.629176\pi$
$284$	0.928191	+	1.60767i	0.0550780	+	0.0953979i
$285$	5.53266			0.327726
$286$	−25.8236			−1.52698
$287$	−18.9229	−	32.7754i	−1.11698	−	1.93467i
$288$			1.00000i			0.0589256i
$289$	2.96002	−	5.12691i	0.174119	−	0.301583i
$290$		−	1.86387i		−	0.109450i
$291$	−5.32662	−	3.07533i	−0.312252	−	0.180279i
$292$	−5.91715	+	10.2488i	−0.346275	+	0.599766i
$293$	−6.27495	+	10.8685i	−0.366586	+	0.634946i	−0.989029	−	0.147719i	$-0.952807\pi$
$293$	−6.27495	+	10.8685i	−0.366586	+	0.634946i	0.622443	+	0.782665i	$0.286140\pi$
$294$	6.36102	−	3.67253i	0.370982	−	0.214187i
$295$	1.80454			0.105064
$296$	5.63363	−	2.29396i	0.327448	−	0.133334i
$297$	−3.84038			−0.222842
$298$	−14.1054	+	8.14376i	−0.817105	+	0.471756i
$299$	28.4310	−	49.2439i	1.64421	−	2.84785i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−0.130468	−	0.0753256i	−0.00752004	−	0.00434170i
$302$			20.2784i			1.16689i
$303$	4.48179	−	7.76268i	0.257472	−	0.445954i
$304$			5.53266i			0.317320i
$305$	6.62563	+	11.4759i	0.379382	+	0.657109i
$306$	−4.78749			−0.273682
$307$	−2.35294			−0.134289			−0.0671446	−	0.997743i	$-0.521389\pi$
$307$	−2.35294			−0.134289			−0.0671446	+	0.997743i	$0.521389\pi$
$308$	7.27270	+	12.5967i	0.414401	+	0.717763i
$309$	−12.7358	−	7.35302i	−0.724514	−	0.418298i
$310$			8.49606i			0.482544i
$311$	−19.5888	+	11.3096i	−1.11078	+	0.641309i	−0.939031	−	0.343832i	$-0.888275\pi$
$311$	−19.5888	+	11.3096i	−1.11078	+	0.641309i	−0.171748	+	0.985141i	$0.554942\pi$
$312$	3.36212	+	5.82335i	0.190342	+	0.329683i
$313$	13.5051	−	7.79719i	0.763355	−	0.440723i	−0.0671443	−	0.997743i	$-0.521389\pi$
$313$	13.5051	−	7.79719i	0.763355	−	0.440723i	0.830499	+	0.557020i	$0.188055\pi$
$314$	5.88642	+	3.39853i	0.332190	+	0.191790i
$315$	−3.28006	−	1.89374i	−0.184811	−	0.106700i
$316$	−3.13047	+	1.80738i	−0.176103	+	0.101673i
$317$	12.3149	+	21.3299i	0.691671	+	1.19801i	0.971290	+	0.237898i	$0.0764585\pi$
$317$	12.3149	+	21.3299i	0.691671	+	1.19801i	−0.279619	+	0.960111i	$0.590208\pi$
$318$	2.77776	−	1.60374i	0.155769	−	0.0899333i
$319$			7.15796i			0.400769i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−1.95561	−	3.38721i	−0.109151	−	0.189056i
$322$	−32.0281			−1.78485
$323$	−26.4875			−1.47381
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$			6.72423i			0.372993i
$326$	−4.47104	+	7.74406i	−0.247628	+	0.428904i
$327$			3.82693i			0.211630i
$328$	−8.65360	−	4.99616i	−0.477815	−	0.275867i
$329$	1.97124	−	3.41428i	0.108678	−	0.188235i
$330$	1.92019	−	3.32587i	0.105703	−	0.183083i
$331$	7.39622	−	4.27021i	0.406533	−	0.234712i	−0.282766	−	0.959189i	$-0.591252\pi$
$331$	7.39622	−	4.27021i	0.406533	−	0.234712i	0.689299	+	0.724477i	$0.257919\pi$
$332$	13.5873			0.745702
$333$	3.73188	−	4.80344i	0.204506	−	0.263227i
$334$	3.14319			0.171988
$335$	7.94568	−	4.58744i	0.434119	−	0.250638i
$336$	1.89374	−	3.28006i	0.103312	−	0.178942i
$337$	6.00674	−	10.4040i	0.327208	−	0.566741i	−0.654749	−	0.755847i	$-0.727226\pi$
$337$	6.00674	−	10.4040i	0.327208	−	0.566741i	0.981957	+	0.189106i	$0.0605589\pi$
$338$	27.8992	+	16.1076i	1.51752	+	0.876140i
$339$		−	16.3080i		−	0.885727i
$340$	2.39374	−	4.14609i	0.129819	−	0.224853i
$341$		−	32.6281i		−	1.76691i
$342$	2.76633	+	4.79142i	0.149586	+	0.259090i
$343$	−1.30694			−0.0705683
$344$	−0.0397760			−0.00214458
$345$	4.22814	+	7.32335i	0.227635	+	0.394276i
$346$	−0.627052	−	0.362029i	−0.0337105	−	0.0194628i
$347$		−	5.81798i		−	0.312325i	−0.987731	−	0.156163i	$-0.950088\pi$
$347$		−	5.81798i		−	0.312325i	0.987731	−	0.156163i	$-0.0499124\pi$
$348$	1.61416	−	0.931933i	0.0865278	−	0.0499569i
$349$	14.8951	+	25.7991i	0.797318	+	1.38099i	0.921357	+	0.388717i	$0.127082\pi$
$349$	14.8951	+	25.7991i	0.797318	+	1.38099i	−0.124039	+	0.992277i	$0.539585\pi$
$350$	3.28006	−	1.89374i	0.175327	−	0.101225i
$351$	5.82335	+	3.36212i	0.310828	+	0.179456i
$352$	3.32587	+	1.92019i	0.177269	+	0.102347i
$353$	−13.6952	+	7.90695i	−0.728924	+	0.420845i	−0.818029	−	0.575178i	$-0.804933\pi$
$353$	−13.6952	+	7.90695i	−0.728924	+	0.420845i	0.0891041	+	0.996022i	$0.471600\pi$
$354$	0.902271	+	1.56278i	0.0479551	+	0.0830607i
$355$	−1.60767	+	0.928191i	−0.0853265	+	0.0492633i
$356$		−	17.1030i		−	0.906457i
$357$	15.7033	+	9.06628i	0.831104	+	0.479838i
$358$	10.4782	+	18.1487i	0.553788	+	0.959190i
$359$	20.8727			1.10162			0.550809	−	0.834631i	$-0.314319\pi$
$359$	20.8727			1.10162			0.550809	+	0.834631i	$0.314319\pi$
$360$	−1.00000			−0.0527046
$361$	5.80516	+	10.0548i	0.305534	+	0.529201i
$362$			15.4559i			0.812344i
$363$	−1.87427	+	3.24634i	−0.0983739	+	0.170389i
$364$		−	25.4679i		−	1.33488i
$365$	−10.2488	−	5.91715i	−0.536447	−	0.309718i
$366$	−6.62563	+	11.4759i	−0.346327	+	0.599856i
$367$	12.5188	−	21.6833i	0.653478	−	1.13186i	−0.328795	−	0.944401i	$-0.606643\pi$
$367$	12.5188	−	21.6833i	0.653478	−	1.13186i	0.982273	−	0.187456i	$-0.0600242\pi$
$368$	−7.32335	+	4.22814i	−0.381756	+	0.220407i
$369$	−9.99232			−0.520179
$370$	2.29396	+	5.63363i	0.119257	+	0.292878i
$371$	−12.1483			−0.630708
$372$	−7.35780	+	4.24803i	−0.381484	+	0.220250i
$373$	8.34468	−	14.4534i	0.432071	−	0.748369i	−0.564980	−	0.825104i	$-0.691116\pi$
$373$	8.34468	−	14.4534i	0.432071	−	0.748369i	0.997052	+	0.0767350i	$0.0244495\pi$
$374$	−9.19290	+	15.9226i	−0.475353	+	0.823336i
$375$	−0.866025	−	0.500000i	−0.0447214	−	0.0258199i
$376$		−	1.04092i		−	0.0536814i
$377$	6.26653	−	10.8540i	0.322743	−	0.559007i
$378$		−	3.78749i		−	0.194807i
$379$	12.4760	+	21.6091i	0.640849	+	1.10998i	0.985244	+	0.171158i	$0.0547509\pi$
$379$	12.4760	+	21.6091i	0.640849	+	1.10998i	−0.344394	+	0.938825i	$0.611916\pi$
$380$	−5.53266			−0.283819
$381$	11.2778			0.577781
$382$	1.51928	+	2.63146i	0.0777329	+	0.134637i
$383$	−8.07527	−	4.66226i	−0.412627	−	0.238230i	0.279291	−	0.960207i	$-0.409901\pi$
$383$	−8.07527	−	4.66226i	−0.412627	−	0.238230i	−0.691918	+	0.721976i	$0.743234\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−12.5967	+	7.27270i	−0.641987	+	0.370651i
$386$	−7.17156	−	12.4215i	−0.365023	−	0.632238i
$387$	−0.0344471	+	0.0198880i	−0.00175104	+	0.00101096i
$388$	5.32662	+	3.07533i	0.270418	+	0.156126i
$389$	18.8460	+	10.8808i	0.955532	+	0.551677i	0.894795	−	0.446477i	$-0.147322\pi$
$389$	18.8460	+	10.8808i	0.955532	+	0.551677i	0.0607371	+	0.998154i	$0.480655\pi$
$390$	−5.82335	+	3.36212i	−0.294877	+	0.170247i
$391$	−20.2422	−	35.0605i	−1.02369	−	1.77308i
$392$	−6.36102	+	3.67253i	−0.321280	+	0.185491i
$393$			8.32318i			0.419849i
$394$	−0.695787	−	0.401713i	−0.0350533	−	0.0202380i
$395$	−1.80738	−	3.13047i	−0.0909390	−	0.157511i
$396$	3.84038			0.192987
$397$	−4.30813			−0.216219			−0.108109	−	0.994139i	$-0.534480\pi$
$397$	−4.30813			−0.216219			−0.108109	+	0.994139i	$0.534480\pi$
$398$	2.00910	+	3.47986i	0.100707	+	0.174430i
$399$		−	20.9549i		−	1.04906i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$		−	15.7601i		−	0.787021i	−0.919320	−	0.393510i	$-0.871261\pi$
$401$		−	15.7601i		−	0.787021i	0.919320	−	0.393510i	$-0.128739\pi$
$402$	7.94568	+	4.58744i	0.396294	+	0.228801i
$403$	−28.5647	+	49.4755i	−1.42291	+	2.46455i
$404$	−4.48179	+	7.76268i	−0.222977	+	0.386208i
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	−7.05937			−0.350351
$407$	−8.80969	−	21.6353i	−0.436680	−	1.07242i
$408$	4.78749			0.237016
$409$	25.1445	−	14.5172i	1.24331	−	0.717828i	0.273547	−	0.961859i	$-0.411803\pi$
$409$	25.1445	−	14.5172i	1.24331	−	0.717828i	0.969768	+	0.244030i	$0.0784697\pi$
$410$	4.99616	−	8.65360i	0.246743	−	0.427371i
$411$	7.81094	−	13.5290i	0.385285	−	0.667334i
$412$	12.7358	+	7.35302i	0.627448	+	0.362257i
$413$		−	6.83468i		−	0.336313i
$414$	−4.22814	+	7.32335i	−0.207802	+	0.359923i
$415$			13.5873i			0.666976i
$416$	−3.36212	−	5.82335i	−0.164841	−	0.285513i
$417$	2.93641			0.143797
$418$	21.2475			1.03925
$419$	−14.1287	−	24.4716i	−0.690230	−	1.19551i	−0.971762	−	0.235962i	$-0.924176\pi$
$419$	−14.1287	−	24.4716i	−0.690230	−	1.19551i	0.281532	−	0.959552i	$-0.409157\pi$
$420$	3.28006	+	1.89374i	0.160051	+	0.0924053i
$421$			3.46274i			0.168763i	0.996434	+	0.0843817i	$0.0268915\pi$
$421$			3.46274i			0.168763i	−0.996434	+	0.0843817i	$0.973108\pi$
$422$	−8.19446	+	4.73108i	−0.398900	+	0.230305i
$423$	−0.520460	−	0.901463i	−0.0253056	−	0.0438307i
$424$	−2.77776	+	1.60374i	−0.134900	+	0.0778845i
$425$	4.14609	+	2.39374i	0.201115	+	0.116114i
$426$	−1.60767	−	0.928191i	−0.0778921	−	0.0449710i
$427$	43.4649	−	25.0945i	2.10341	−	1.21441i
$428$	1.95561	+	3.38721i	0.0945279	+	0.163727i
$429$	22.3639	−	12.9118i	1.07974	−	0.623388i
$430$		−	0.0397760i		−	0.00191817i
$431$	1.54704	+	0.893186i	0.0745185	+	0.0430233i	0.536796	−	0.843712i	$-0.319634\pi$
$431$	1.54704	+	0.893186i	0.0745185	+	0.0430233i	−0.462278	+	0.886735i	$0.652968\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−33.6257			−1.61595			−0.807974	−	0.589218i	$-0.799436\pi$
$433$	−33.6257			−1.61595			−0.807974	+	0.589218i	$0.799436\pi$
$434$	32.1787			1.54463
$435$	0.931933	+	1.61416i	0.0446828	+	0.0773928i
$436$		−	3.82693i		−	0.183277i
$437$	−23.3929	+	40.5176i	−1.11903	+	1.93822i
$438$		−	11.8343i		−	0.565465i
$439$	10.2005	+	5.88926i	0.486843	+	0.281079i	0.723264	−	0.690572i	$-0.242641\pi$
$439$	10.2005	+	5.88926i	0.486843	+	0.281079i	−0.236421	+	0.971651i	$0.575974\pi$
$440$	−1.92019	+	3.32587i	−0.0915416	+	0.158555i
$441$	−3.67253	+	6.36102i	−0.174883	+	0.302906i
$442$	27.8792	−	16.0961i	1.32608	−	0.765613i
$443$	−26.7397			−1.27044			−0.635220	−	0.772331i	$-0.719091\pi$
$443$	−26.7397			−1.27044			−0.635220	+	0.772331i	$0.719091\pi$
$444$	−3.73188	+	4.80344i	−0.177107	+	0.227961i
$445$	17.1030			0.810759
$446$	10.2674	−	5.92790i	0.486176	−	0.280694i
$447$	8.14376	−	14.1054i	0.385187	−	0.667163i
$448$	−1.89374	+	3.28006i	−0.0894710	+	0.154968i
$449$	12.1655	+	7.02375i	0.574125	+	0.331471i	0.758795	−	0.651329i	$-0.225788\pi$
$449$	12.1655	+	7.02375i	0.574125	+	0.331471i	−0.184670	+	0.982801i	$0.559122\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−19.1872	+	33.2331i	−0.903488	+	1.56489i
$452$			16.3080i			0.767062i
$453$	−10.1392	−	17.5616i	−0.476381	−	0.825117i
$454$	12.4686			0.585182
$455$	25.4679			1.19396
$456$	−2.76633	−	4.79142i	−0.129545	−	0.224379i
$457$	10.5277	+	6.07816i	0.492464	+	0.284324i	0.725596	−	0.688121i	$-0.241564\pi$
$457$	10.5277	+	6.07816i	0.492464	+	0.284324i	−0.233132	+	0.972445i	$0.574897\pi$
$458$			10.0119i			0.467824i
$459$	4.14609	−	2.39374i	0.193523	−	0.111730i
$460$	−4.22814	−	7.32335i	−0.197138	−	0.341453i
$461$	28.6410	−	16.5359i	1.33395	−	0.770154i	0.348044	−	0.937478i	$-0.386846\pi$
$461$	28.6410	−	16.5359i	1.33395	−	0.770154i	0.985902	+	0.167324i	$0.0535127\pi$
$462$	−12.5967	−	7.27270i	−0.586051	−	0.338357i
$463$	32.8685	+	18.9767i	1.52753	+	0.881920i	0.999465	+	0.0327173i	$0.0104161\pi$
$463$	32.8685	+	18.9767i	1.52753	+	0.881920i	0.528066	+	0.849203i	$0.322917\pi$
$464$	−1.61416	+	0.931933i	−0.0749353	+	0.0432639i
$465$	−4.24803	−	7.35780i	−0.196998	−	0.341210i
$466$	8.58323	−	4.95553i	0.397610	−	0.229561i
$467$			13.0633i			0.604500i	0.953229	+	0.302250i	$0.0977377\pi$
$467$			13.0633i			0.604500i	−0.953229	+	0.302250i	$0.902262\pi$
$468$	−5.82335	−	3.36212i	−0.269185	−	0.155414i
$469$	−17.3749	−	30.0942i	−0.802297	−	1.38962i
$470$	1.04092			0.0480141
$471$	−6.79706			−0.313192
$472$	−0.902271	−	1.56278i	−0.0415304	−	0.0719327i
$473$			0.152755i			0.00702369i
$474$	1.80738	−	3.13047i	0.0830155	−	0.143787i
$475$		−	5.53266i		−	0.253856i
$476$	−15.7033	−	9.06628i	−0.719758	−	0.415552i
$477$	−1.60374	+	2.77776i	−0.0734302	+	0.127185i
$478$	−7.81314	+	13.5328i	−0.357365	+	0.618974i
$479$	−3.55432	+	2.05209i	−0.162401	+	0.0937623i	−0.578998	−	0.815329i	$-0.696556\pi$
$479$	−3.55432	+	2.05209i	−0.162401	+	0.0937623i	0.416597	+	0.909091i	$0.363223\pi$
$480$	1.00000			0.0456435
$481$	−5.58235	+	40.5192i	−0.254533	+	1.84751i
$482$	−12.7958			−0.582835
$483$	27.7371	−	16.0140i	1.26208	−	0.728664i
$484$	1.87427	−	3.24634i	0.0851943	−	0.147561i
$485$	−3.07533	+	5.32662i	−0.139643	+	0.241869i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$		−	32.1531i		−	1.45699i	−0.685049	−	0.728497i	$-0.740219\pi$
$487$		−	32.1531i		−	1.45699i	0.685049	−	0.728497i	$-0.259781\pi$
$488$	6.62563	−	11.4759i	0.299928	−	0.519491i
$489$		−	8.94207i		−	0.404375i
$490$	−3.67253	−	6.36102i	−0.165908	−	0.287361i
$491$	31.3238			1.41362			0.706812	−	0.707402i	$-0.250133\pi$
$491$	31.3238			1.41362			0.706812	+	0.707402i	$0.250133\pi$
$492$	9.99232			0.450488
$493$	−4.46162	−	7.72775i	−0.200941	−	0.348040i
$494$	−32.2186	−	18.6014i	−1.44958	−	0.836918i
$495$			3.84038i			0.172612i
$496$	7.35780	−	4.24803i	0.330375	−	0.190742i
$497$	3.51551	+	6.08905i	0.157692	+	0.273131i
$498$	−11.7670	+	6.79367i	−0.527291	+	0.304432i
$499$	−24.8514	−	14.3480i	−1.11250	−	0.642303i	−0.173025	−	0.984917i	$-0.555354\pi$
$499$	−24.8514	−	14.3480i	−1.11250	−	0.642303i	−0.939476	+	0.342615i	$0.888687\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−2.72208	+	1.57160i	−0.121614	+	0.0702137i
$502$	−4.61964	−	8.00145i	−0.206185	−	0.357122i
$503$	−17.4569	+	10.0787i	−0.778364	+	0.449389i	−0.835850	−	0.548957i	$-0.815025\pi$
$503$	−17.4569	+	10.0787i	−0.778364	+	0.449389i	0.0574859	+	0.998346i	$0.481692\pi$
$504$			3.78749i			0.168708i
$505$	−7.76268	−	4.48179i	−0.345435	−	0.199437i
$506$	16.2377	+	28.1245i	0.721853	+	1.25029i
$507$	−32.2153			−1.43073
$508$	−11.2778			−0.500373
$509$	−16.5772	−	28.7126i	−0.734772	−	1.27266i	−0.954823	−	0.297174i	$-0.903956\pi$
$509$	−16.5772	−	28.7126i	−0.734772	−	1.27266i	0.220052	−	0.975488i	$-0.429377\pi$
$510$			4.78749i			0.211994i
$511$	−22.4111	+	38.8172i	−0.991410	+	1.71717i
$512$			1.00000i			0.0441942i
$513$	−4.79142	−	2.76633i	−0.211546	−	0.122136i
$514$	−6.02592	+	10.4372i	−0.265792	+	0.460365i
$515$	−7.35302	+	12.7358i	−0.324013	+	0.561206i
$516$	0.0344471	−	0.0198880i	0.00151645	−	0.000875521i
$517$	−3.99753			−0.175811
$518$	21.3373	−	8.68835i	0.937507	−	0.381744i
$519$	0.724057			0.0317826
$520$	5.82335	−	3.36212i	0.255371	−	0.147438i
$521$	−12.7108	+	22.0158i	−0.556870	+	0.964528i	0.440885	+	0.897564i	$0.354665\pi$
$521$	−12.7108	+	22.0158i	−0.556870	+	0.964528i	−0.997755	+	0.0669640i	$0.978669\pi$
$522$	−0.931933	+	1.61416i	−0.0407896	+	0.0706497i
$523$	15.7552	+	9.09627i	0.688927	+	0.397752i	0.803210	−	0.595696i	$-0.203124\pi$
$523$	15.7552	+	9.09627i	0.688927	+	0.397752i	−0.114283	+	0.993448i	$0.536457\pi$
$524$		−	8.32318i		−	0.363600i
$525$	−1.89374	+	3.28006i	−0.0826498	+	0.143154i
$526$			7.31074i			0.318763i
$527$	20.3374	+	35.2254i	0.885910	+	1.53444i
$528$	−3.84038			−0.167131
$529$	−48.5087			−2.10907
$530$	−1.60374	−	2.77776i	−0.0696620	−	0.120658i
$531$	−1.56278	−	0.902271i	−0.0678188	−	0.0391552i
$532$			20.9549i			0.908509i
$533$	58.1888	−	33.5953i	2.52044	−	1.45517i
$534$	8.55149	+	14.8116i	0.370059	+	0.640962i
$535$	−3.38721	+	1.95561i	−0.146442	+	0.0845483i
$536$	−7.94568	−	4.58744i	−0.343201	−	0.198147i
$537$	−18.1487	−	10.4782i	−0.783175	−	0.452166i
$538$	−13.1312	+	7.58133i	−0.566128	+	0.326854i
$539$	14.1039	+	24.4287i	0.607500	+	1.05222i
$540$	0.866025	−	0.500000i	0.0372678	−	0.0215166i
$541$		−	32.6823i		−	1.40512i	−0.711624	−	0.702560i	$-0.752040\pi$
$541$		−	32.6823i		−	1.40512i	0.711624	−	0.702560i	$-0.247960\pi$
$542$	−9.34650	−	5.39620i	−0.401466	−	0.231787i
$543$	−7.72795	−	13.3852i	−0.331638	−	0.574414i
$544$	−4.78749			−0.205262
$545$	3.82693			0.163928
$546$	12.7340	+	22.0559i	0.544964	+	0.943905i
$547$		−	21.1126i		−	0.902711i	−0.892344	−	0.451355i	$-0.850941\pi$
$547$		−	21.1126i		−	0.902711i	0.892344	−	0.451355i	$-0.149059\pi$
$548$	−7.81094	+	13.5290i	−0.333667	+	0.577928i
$549$		−	13.2513i		−	0.565550i
$550$	−3.32587	−	1.92019i	−0.141816	−	0.0818773i
$551$	−5.15607	+	8.93057i	−0.219656	+	0.380455i
$552$	4.22814	−	7.32335i	0.179962	−	0.311703i
$553$	−11.8566	+	6.84542i	−0.504194	+	0.291097i
$554$	8.00832			0.340241
$555$	−4.80344	−	3.73188i	−0.203895	−	0.158410i
$556$	−2.93641			−0.124531
$557$	−14.5555	+	8.40363i	−0.616737	+	0.356073i	−0.775598	−	0.631228i	$-0.782551\pi$
$557$	−14.5555	+	8.40363i	−0.616737	+	0.356073i	0.158860	+	0.987301i	$0.449218\pi$
$558$	4.24803	−	7.35780i	0.179833	−	0.311481i
$559$	0.133732	−	0.231630i	0.00565624	−	0.00979690i
$560$	−3.28006	−	1.89374i	−0.138608	−	0.0800253i
$561$		−	18.3858i		−	0.776249i
$562$	12.5264	−	21.6964i	0.528394	−	0.915206i
$563$			5.35688i			0.225766i	0.993608	+	0.112883i	$0.0360085\pi$
$563$			5.35688i			0.225766i	−0.993608	+	0.112883i	$0.963992\pi$
$564$	0.520460	+	0.901463i	0.0219153	+	0.0379585i
$565$	−16.3080			−0.686082
$566$	3.95355			0.166180
$567$	1.89374	+	3.28006i	0.0795298	+	0.137750i
$568$	1.60767	+	0.928191i	0.0674565	+	0.0389460i
$569$			8.95342i			0.375347i	0.982231	+	0.187673i	$0.0600947\pi$
$569$			8.95342i			0.375347i	−0.982231	+	0.187673i	$0.939905\pi$
$570$	4.79142	−	2.76633i	0.200691	−	0.115869i
$571$	−18.6922	−	32.3758i	−0.782242	−	1.35488i	−0.930633	−	0.365955i	$-0.880743\pi$
$571$	−18.6922	−	32.3758i	−0.782242	−	1.35488i	0.148390	−	0.988929i	$-0.452591\pi$
$572$	−22.3639	+	12.9118i	−0.935082	+	0.539870i
$573$	−2.63146	−	1.51928i	−0.109931	−	0.0634686i
$574$	−32.7754	−	18.9229i	−1.36802	−	0.789826i
$575$	7.32335	−	4.22814i	0.305405	−	0.176326i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	3.18442	−	1.83852i	0.132569	−	0.0765387i	−0.432249	−	0.901754i	$-0.642280\pi$
$577$	3.18442	−	1.83852i	0.132569	−	0.0765387i	0.564818	+	0.825216i	$0.308946\pi$
$578$		−	5.92005i		−	0.246241i
$579$	12.4215	+	7.17156i	0.516220	+	0.298040i
$580$	−0.931933	−	1.61416i	−0.0386964	−	0.0670242i
$581$	51.4619			2.13500
$582$	−6.15065			−0.254953
$583$	6.15898	+	10.6677i	0.255079	+	0.441809i
$584$			11.8343i			0.489707i
$585$	3.36212	−	5.82335i	0.139006	−	0.240766i
$586$			12.5499i			0.518431i
$587$	−33.6978	−	19.4555i	−1.39086	−	0.803013i	−0.397448	−	0.917625i	$-0.630104\pi$
$587$	−33.6978	−	19.4555i	−1.39086	−	0.803013i	−0.993410	+	0.114612i	$0.963438\pi$
$588$	3.67253	−	6.36102i	0.151453	−	0.262324i
$589$	23.5029	−	40.7082i	0.968420	−	1.67735i
$590$	1.56278	−	0.902271i	0.0643386	−	0.0371459i
$591$	0.803426			0.0330485
$592$	3.73188	−	4.80344i	0.153379	−	0.197420i
$593$	2.91438			0.119679			0.0598397	−	0.998208i	$-0.480941\pi$
$593$	2.91438			0.119679			0.0598397	+	0.998208i	$0.480941\pi$
$594$	−3.32587	+	1.92019i	−0.136462	+	0.0787864i
$595$	9.06628	−	15.7033i	0.371681	−	0.643771i
$596$	−8.14376	+	14.1054i	−0.333582	+	0.577780i
$597$	−3.47986	−	2.00910i	−0.142421	−	0.0822269i
$598$		−	56.8620i		−	2.32526i
$599$	−1.93950	+	3.35931i	−0.0792458	+	0.137258i	−0.902925	−	0.429799i	$-0.858585\pi$
$599$	−1.93950	+	3.35931i	−0.0792458	+	0.137258i	0.823679	+	0.567056i	$0.191918\pi$
$600$			1.00000i			0.0408248i
$601$	−20.7686	−	35.9723i	−0.847170	−	1.46734i	−0.883723	−	0.468010i	$-0.844971\pi$
$601$	−20.7686	−	35.9723i	−0.847170	−	1.46734i	0.0365530	−	0.999332i	$-0.488362\pi$
$602$	−0.150651			−0.00614009
$603$	−9.17488			−0.373630
$604$	10.1392	+	17.5616i	0.412558	+	0.714572i
$605$	3.24634	+	1.87427i	0.131982	+	0.0762001i
$606$		−	8.96357i		−	0.364120i
$607$	−10.3055	+	5.94986i	−0.418286	+	0.241497i	−0.694344	−	0.719644i	$-0.744305\pi$
$607$	−10.3055	+	5.94986i	−0.418286	+	0.241497i	0.276058	+	0.961141i	$0.410972\pi$
$608$	2.76633	+	4.79142i	0.112189	+	0.194318i
$609$	6.11359	−	3.52969i	0.247735	−	0.143030i
$610$	11.4759	+	6.62563i	0.464646	+	0.268264i
$611$	6.06165	+	3.49969i	0.245228	+	0.141582i
$612$	−4.14609	+	2.39374i	−0.167596	+	0.0967614i
$613$	−4.99067	−	8.64409i	−0.201571	−	0.349132i	0.747464	−	0.664303i	$-0.231271\pi$
$613$	−4.99067	−	8.64409i	−0.201571	−	0.349132i	−0.949035	+	0.315171i	$0.897938\pi$
$614$	−2.03770	+	1.17647i	−0.0822350	+	0.0474784i
$615$			9.99232i			0.402929i
$616$	12.5967	+	7.27270i	0.507535	+	0.293026i
$617$	−9.78398	−	16.9464i	−0.393888	−	0.682234i	0.599070	−	0.800696i	$-0.295537\pi$
$617$	−9.78398	−	16.9464i	−0.393888	−	0.682234i	−0.992959	+	0.118462i	$0.962204\pi$
$618$	−14.7060			−0.591563
$619$	27.2882			1.09680			0.548402	−	0.836215i	$-0.315236\pi$
$619$	27.2882			1.09680			0.548402	+	0.836215i	$0.315236\pi$
$620$	4.24803	+	7.35780i	0.170605	+	0.295496i
$621$		−	8.45628i		−	0.339339i
$622$	−11.3096	+	19.5888i	−0.453474	+	0.785439i
$623$		−	64.7774i		−	2.59525i
$624$	5.82335	+	3.36212i	0.233121	+	0.134592i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	7.79719	−	13.5051i	0.311638	−	0.539773i
$627$	−18.4009	+	10.6238i	−0.734861	+	0.424272i
$628$	6.79706			0.271232
$629$	22.9964	+	17.8663i	0.916927	+	0.712378i
$630$	−3.78749			−0.150897
$631$	17.1937	−	9.92680i	0.684471	−	0.395180i	−0.117066	−	0.993124i	$-0.537349\pi$
$631$	17.1937	−	9.92680i	0.684471	−	0.395180i	0.801538	+	0.597945i	$0.204016\pi$
$632$	−1.80738	+	3.13047i	−0.0718936	+	0.124523i
$633$	4.73108	−	8.19446i	0.188043	−	0.325701i
$634$	21.3299	+	12.3149i	0.847120	+	0.489085i
$635$		−	11.2778i		−	0.447547i
$636$	1.60374	−	2.77776i	0.0635924	−	0.110145i
$637$		−	49.3899i		−	1.95690i
$638$	3.57898	+	6.19898i	0.141693	+	0.245420i
$639$	1.85638			0.0734374
$640$	−1.00000			−0.0395285
$641$	4.37909	+	7.58480i	0.172964	+	0.299582i	0.939455	−	0.342673i	$-0.111332\pi$
$641$	4.37909	+	7.58480i	0.172964	+	0.299582i	−0.766491	+	0.642255i	$0.777999\pi$
$642$	−3.38721	−	1.95561i	−0.133683	−	0.0771817i
$643$			23.7722i			0.937485i	0.883335	+	0.468742i	$0.155293\pi$
$643$			23.7722i			0.937485i	−0.883335	+	0.468742i	$0.844707\pi$
$644$	−27.7371	+	16.0140i	−1.09300	+	0.631041i
$645$	0.0198880	+	0.0344471i	0.000783090	+	0.00135635i
$646$	−22.9389	+	13.2438i	−0.902518	+	0.521069i
$647$	14.1817	+	8.18780i	0.557539	+	0.321896i	0.752157	−	0.658984i	$-0.229013\pi$
$647$	14.1817	+	8.18780i	0.557539	+	0.321896i	−0.194618	+	0.980879i	$0.562347\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−6.00167	+	3.46507i	−0.235586	+	0.136016i
$650$	3.36212	+	5.82335i	0.131873	+	0.228411i
$651$	−27.8676	+	16.0894i	−1.09222	+	0.630592i
$652$			8.94207i			0.350199i
$653$	19.1663	+	11.0657i	0.750034	+	0.433032i	0.825706	−	0.564100i	$-0.190777\pi$
$653$	19.1663	+	11.0657i	0.750034	+	0.433032i	−0.0756720	+	0.997133i	$0.524110\pi$
$654$	1.91346	+	3.31422i	0.0748223	+	0.129596i
$655$	8.32318			0.325214
$656$	−9.99232			−0.390134
$657$	5.91715	+	10.2488i	0.230850	+	0.399844i
$658$		−	3.94247i		−	0.153694i
$659$	−1.48559	+	2.57312i	−0.0578705	+	0.100235i	−0.893509	−	0.449045i	$-0.851764\pi$
$659$	−1.48559	+	2.57312i	−0.0578705	+	0.100235i	0.835639	+	0.549279i	$0.185098\pi$
$660$		−	3.84038i		−	0.149487i
$661$	−7.65152	−	4.41761i	−0.297609	−	0.171825i	0.343759	−	0.939058i	$-0.388300\pi$
$661$	−7.65152	−	4.41761i	−0.297609	−	0.171825i	−0.641368	+	0.767233i	$0.721633\pi$
$662$	4.27021	−	7.39622i	0.165966	−	0.287462i
$663$	−16.0961	+	27.8792i	−0.625120	+	1.08274i
$664$	11.7670	−	6.79367i	0.456647	−	0.263645i
$665$	−20.9549			−0.812595
$666$	0.830184	−	6.02584i	0.0321690	−	0.233497i
$667$	−15.7614			−0.610283
$668$	2.72208	−	1.57160i	0.105321	−	0.0608069i
$669$	−5.92790	+	10.2674i	−0.229186	+	0.396961i
$670$	4.58744	−	7.94568i	0.177228	−	0.306968i
$671$	−44.0719	−	25.4449i	−1.70138	−	0.982291i
$672$		−	3.78749i		−	0.146106i
$673$	13.7552	−	23.8248i	0.530226	−	0.918378i	−0.469152	−	0.883117i	$-0.655440\pi$
$673$	13.7552	−	23.8248i	0.530226	−	0.918378i	0.999378	−	0.0352608i	$-0.0112262\pi$
$674$		−	12.0135i		−	0.462742i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	32.2153			1.23905
$677$	−6.30629			−0.242370			−0.121185	−	0.992630i	$-0.538669\pi$
$677$	−6.30629			−0.242370			−0.121185	+	0.992630i	$0.538669\pi$
$678$	−8.15399	−	14.1231i	−0.313152	−	0.542395i
$679$	20.1745	+	11.6478i	0.774227	+	0.447000i
$680$		−	4.78749i		−	0.183592i
$681$	−10.7982	+	6.23432i	−0.413786	+	0.238900i
$682$	−16.3141	−	28.2568i	−0.624698	−	1.08201i
$683$	−32.6161	+	18.8309i	−1.24802	+	0.720544i	−0.970714	−	0.240238i	$-0.922774\pi$
$683$	−32.6161	+	18.8309i	−1.24802	+	0.720544i	−0.277305	+	0.960782i	$0.589441\pi$
$684$	4.79142	+	2.76633i	0.183205	+	0.105773i
$685$	−13.5290	−	7.81094i	−0.516915	−	0.298441i
$686$	−1.13185	+	0.653472i	−0.0432141	+	0.0249497i
$687$	−5.00593	−	8.67053i	−0.190988	−	0.330801i
$688$	−0.0344471	+	0.0198880i	−0.00131328	+	0.000758223i
$689$		−	21.5678i		−	0.821669i
$690$	7.32335	+	4.22814i	0.278795	+	0.160963i
$691$	10.7311	+	18.5868i	0.408230	+	0.707075i	0.994692	−	0.102902i	$-0.0328128\pi$
$691$	10.7311	+	18.5868i	0.408230	+	0.707075i	−0.586461	+	0.809977i	$0.699479\pi$
$692$	−0.724057			−0.0275245
$693$	14.5454			0.552534
$694$	−2.90899	−	5.03851i	−0.110424	−	0.191259i
$695$		−	2.93641i		−	0.111384i
$696$	0.931933	−	1.61416i	0.0353248	−	0.0611844i
$697$		−	47.8381i		−	1.81200i
$698$	25.7991	+	14.8951i	0.976511	+	0.563789i
$699$	−4.95553	+	8.58323i	−0.187435	+	0.324648i
$700$	1.89374	−	3.28006i	0.0715768	−	0.123975i
$701$	36.0348	−	20.8047i	1.36102	−	0.785783i	0.371257	−	0.928530i	$-0.378927\pi$
$701$	36.0348	−	20.8047i	1.36102	−	0.785783i	0.989759	+	0.142747i	$0.0455934\pi$
$702$	6.72423			0.253790
$703$	4.59312	−	33.3389i	0.173233	−	1.25740i
$704$	3.84038			0.144740
$705$	−0.901463	+	0.520460i	−0.0339511	+	0.0196017i
$706$	−7.90695	+	13.6952i	−0.297582	+	0.515427i
$707$	−16.9747	+	29.4011i	−0.638400	+	1.10574i
$708$	1.56278	+	0.902271i	0.0587328	+	0.0339094i
$709$			40.2595i			1.51198i	0.654584	+	0.755989i	$0.272844\pi$
$709$			40.2595i			1.51198i	−0.654584	+	0.755989i	$0.727156\pi$
$710$	−0.928191	+	1.60767i	−0.0348344	+	0.0603349i
$711$			3.61475i			0.135564i
$712$	−8.55149	−	14.8116i	−0.320481	−	0.555089i
$713$	71.8450			2.69062
$714$	18.1326			0.678594
$715$	−12.9118	−	22.3639i	−0.482874	−	0.836363i
$716$	18.1487	+	10.4782i	0.678249	+	0.391587i
$717$		−	15.6263i		−	0.583574i
$718$	18.0763	−	10.4363i	0.674601	−	0.389481i
$719$	16.2180	+	28.0903i	0.604828	+	1.04759i	0.992079	+	0.125618i	$0.0400914\pi$
$719$	16.2180	+	28.0903i	0.604828	+	1.04759i	−0.387251	+	0.921974i	$0.626575\pi$
$720$	−0.866025	+	0.500000i	−0.0322749	+	0.0186339i
$721$	48.2367	+	27.8495i	1.79643	+	1.03717i
$722$	10.0548	+	5.80516i	0.374202	+	0.216046i
$723$	11.0815	−	6.39792i	0.412127	−	0.237941i
$724$	7.72795	+	13.3852i	0.287207	+	0.497457i
$725$	1.61416	−	0.931933i	0.0599482	−	0.0346111i
$726$			3.74855i			0.139122i
$727$	−5.34178	−	3.08408i	−0.198116	−	0.114382i	0.397661	−	0.917533i	$-0.369822\pi$
$727$	−5.34178	−	3.08408i	−0.198116	−	0.114382i	−0.595776	+	0.803150i	$0.703155\pi$
$728$	−12.7340	−	22.0559i	−0.471952	−	0.817446i
$729$	1.00000			0.0370370
$730$	−11.8343			−0.438007
$731$	−0.0952136	−	0.164915i	−0.00352160	−	0.00609960i
$732$			13.2513i			0.489780i
$733$	−5.59909	+	9.69791i	−0.206807	+	0.358201i	−0.950707	−	0.310091i	$-0.899641\pi$
$733$	−5.59909	+	9.69791i	−0.206807	+	0.358201i	0.743900	+	0.668291i	$0.232974\pi$
$734$		−	25.0377i		−	0.924158i
$735$	6.36102	+	3.67253i	0.234630	+	0.135463i
$736$	−4.22814	+	7.32335i	−0.155851	+	0.269942i
$737$	−17.6175	+	30.5144i	−0.648950	+	1.12401i
$738$	−8.65360	+	4.99616i	−0.318543	+	0.183911i
$739$	47.1766			1.73542			0.867709	−	0.497073i	$-0.165592\pi$
$739$	47.1766			1.73542			0.867709	+	0.497073i	$0.165592\pi$
$740$	4.80344	+	3.73188i	0.176578	+	0.137187i
$741$	37.2029			1.36668
$742$	−10.5207	+	6.07415i	−0.386228	+	0.222989i
$743$	7.62157	−	13.2009i	0.279608	−	0.484296i	−0.691679	−	0.722205i	$-0.743129\pi$
$743$	7.62157	−	13.2009i	0.279608	−	0.484296i	0.971287	+	0.237909i	$0.0764621\pi$
$744$	−4.24803	+	7.35780i	−0.155740	+	0.269750i
$745$	−14.1054	−	8.14376i	−0.516782	−	0.298364i
$746$		−	16.6894i		−	0.611041i
$747$	6.79367	−	11.7670i	0.248567	−	0.430531i
$748$			18.3858i			0.672251i
$749$	7.40684	+	12.8290i	0.270640	+	0.468762i
$750$	−1.00000			−0.0365148
$751$	43.2557			1.57842			0.789212	−	0.614120i	$-0.210489\pi$
$751$	43.2557			1.57842			0.789212	+	0.614120i	$0.210489\pi$
$752$	−0.520460	−	0.901463i	−0.0189792	−	0.0328730i
$753$	8.00145	+	4.61964i	0.291589	+	0.168349i
$754$		−	12.5331i		−	0.456427i
$755$	−17.5616	+	10.1392i	−0.639133	+	0.369003i
$756$	−1.89374	−	3.28006i	−0.0688748	−	0.119295i
$757$	−9.03971	+	5.21908i	−0.328554	+	0.189691i	−0.655199	−	0.755456i	$-0.727415\pi$
$757$	−9.03971	+	5.21908i	−0.328554	+	0.189691i	0.326645	+	0.945147i	$0.394082\pi$
$758$	21.6091	+	12.4760i	0.784877	+	0.453149i
$759$	−28.1245	−	16.2377i	−1.02085	−	0.589391i
$760$	−4.79142	+	2.76633i	−0.173803	+	0.100345i
$761$	−25.3188	−	43.8534i	−0.917805	−	1.58969i	−0.802742	−	0.596327i	$-0.796626\pi$
$761$	−25.3188	−	43.8534i	−0.917805	−	1.58969i	−0.115064	−	0.993358i	$-0.536707\pi$
$762$	9.76689	−	5.63891i	0.353817	−	0.204276i
$763$		−	14.4944i		−	0.524734i
$764$	2.63146	+	1.51928i	0.0952030	+	0.0549655i
$765$	−2.39374	−	4.14609i	−0.0865460	−	0.149902i
$766$	−9.32452			−0.336909
$767$	12.1341			0.438139
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$			49.0740i			1.76965i	0.465920	+	0.884827i	$0.345724\pi$
$769$			49.0740i			1.76965i	−0.465920	+	0.884827i	$0.654276\pi$
$770$	−7.27270	+	12.5967i	−0.262090	+	0.453953i
$771$		−	12.0518i		−	0.434036i
$772$	−12.4215	−	7.17156i	−0.447060	−	0.258110i
$773$	−16.7780	+	29.0604i	−0.603464	+	1.04523i	0.388828	+	0.921310i	$0.372880\pi$
$773$	−16.7780	+	29.0604i	−0.603464	+	1.04523i	−0.992292	+	0.123920i	$0.960453\pi$
$774$	−0.0198880	+	0.0344471i	−0.000714860	+	0.00123817i
$775$	−7.35780	+	4.24803i	−0.264300	+	0.152594i
$776$	6.15065			0.220796
$777$	−14.1345	+	18.1930i	−0.507071	+	0.652670i
$778$	21.7615			0.780189
$779$	−47.8774	+	27.6420i	−1.71539	+	0.990379i
$780$	−3.36212	+	5.82335i	−0.120383	+	0.208510i
$781$	3.56461	−	6.17409i	0.127552	−	0.220926i
$782$	−35.0605	−	20.2422i	−1.25376	−	0.723859i
$783$		−	1.86387i		−	0.0666091i
$784$	−3.67253	+	6.36102i	−0.131162	+	0.227179i
$785$			6.79706i			0.242597i
$786$	4.16159	+	7.20809i	0.148439	+	0.257104i
$787$	33.2665			1.18582			0.592912	−	0.805267i	$-0.297978\pi$
$787$	33.2665			1.18582			0.592912	+	0.805267i	$0.297978\pi$
$788$	−0.803426			−0.0286209
$789$	−3.65537	−	6.33128i	−0.130135	−	0.225400i
$790$	−3.13047	−	1.80738i	−0.111377	−	0.0643036i
$791$			61.7663i			2.19616i
$792$	3.32587	−	1.92019i	0.118180	−	0.0682310i
$793$	44.5522	+	77.1667i	1.58210	+	2.74027i
$794$	−3.73095	+	2.15406i	−0.132406	+	0.0764448i
$795$	2.77776	+	1.60374i	0.0985170	+	0.0568788i
$796$	3.47986	+	2.00910i	0.123340	+	0.0712106i
$797$	25.4158	−	14.6738i	0.900275	−	0.519774i	0.0229858	−	0.999736i	$-0.492683\pi$
$797$	25.4158	−	14.6738i	0.900275	−	0.519774i	0.877289	+	0.479962i	$0.159349\pi$
$798$	−10.4774	−	18.1475i	−0.370897	−	0.642413i
$799$	4.31575	−	2.49170i	0.152680	−	0.0881499i
$800$		−	1.00000i		−	0.0353553i
$801$	−14.8116	−	8.55149i	−0.523343	−	0.302152i
$802$	−7.88004	−	13.6486i	−0.278254	−	0.481950i
$803$	45.4482			1.60383
$804$	9.17488			0.323573
$805$	−16.0140	−	27.7371i	−0.564421	−	0.977605i
$806$			57.1294i			2.01230i
$807$	7.58133	−	13.1312i	0.266875	−	0.462242i
$808$			8.96357i			0.315337i
$809$	−17.2300	−	9.94776i	−0.605775	−	0.349745i	0.165535	−	0.986204i	$-0.447065\pi$
$809$	−17.2300	−	9.94776i	−0.605775	−	0.349745i	−0.771310	+	0.636459i	$0.780398\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	12.9034	−	22.3493i	0.453098	−	0.784789i	−0.545478	−	0.838125i	$-0.683652\pi$
$811$	12.9034	−	22.3493i	0.453098	−	0.784789i	0.998577	+	0.0533355i	$0.0169853\pi$
$812$	−6.11359	+	3.52969i	−0.214545	+	0.123868i
$813$	10.7924			0.378506
$814$	−18.4471	−	14.3319i	−0.646569	−	0.502331i
$815$	−8.94207			−0.313227
$816$	4.14609	−	2.39374i	0.145142	−	0.0837978i
$817$	−0.110034	+	0.190584i	−0.00384959	+	0.00666768i
$818$	14.5172	−	25.1445i	0.507581	−	0.879156i
$819$	−22.0559	−	12.7340i	−0.770695	−	0.444961i
$820$		−	9.99232i		−	0.348947i
$821$	1.17515	−	2.03542i	0.0410129	−	0.0710365i	−0.844790	−	0.535098i	$-0.820275\pi$
$821$	1.17515	−	2.03542i	0.0410129	−	0.0710365i	0.885803	+	0.464061i	$0.153608\pi$
$822$		−	15.6219i		−	0.544876i
$823$	5.13012	+	8.88563i	0.178825	+	0.309734i	0.941478	−	0.337074i	$-0.109437\pi$
$823$	5.13012	+	8.88563i	0.178825	+	0.309734i	−0.762653	+	0.646807i	$0.776104\pi$
$824$	14.7060			0.512309
$825$	3.84038			0.133705
$826$	−3.41734	−	5.91901i	−0.118904	−	0.205949i
$827$	19.6335	+	11.3354i	0.682724	+	0.394171i	0.800881	−	0.598824i	$-0.204365\pi$
$827$	19.6335	+	11.3354i	0.682724	+	0.394171i	−0.118157	+	0.992995i	$0.537699\pi$
$828$			8.45628i			0.293876i
$829$	−13.9690	+	8.06501i	−0.485164	+	0.280109i	−0.722566	−	0.691302i	$-0.757037\pi$
$829$	−13.9690	+	8.06501i	−0.485164	+	0.280109i	0.237402	+	0.971411i	$0.423704\pi$
$830$	6.79367	+	11.7670i	0.235812	+	0.408438i
$831$	−6.93540	+	4.00416i	−0.240587	+	0.138903i
$832$	−5.82335	−	3.36212i	−0.201888	−	0.116560i
$833$	−30.4533	−	17.5822i	−1.05514	−	0.609188i
$834$	2.54301	−	1.46820i	0.0880571	−	0.0508398i
$835$	1.57160	+	2.72208i	0.0543873	+	0.0942016i
$836$	18.4009	−	10.6238i	0.636409	−	0.367431i
$837$			8.49606i			0.293667i
$838$	−24.4716	−	14.1287i	−0.845356	−	0.488066i
$839$	6.02505	+	10.4357i	0.208008	+	0.360280i	0.951087	−	0.308923i	$-0.0999687\pi$
$839$	6.02505	+	10.4357i	0.208008	+	0.360280i	−0.743079	+	0.669204i	$0.766635\pi$
$840$	3.78749			0.130681
$841$	25.5260			0.880207
$842$	1.73137	+	2.99882i	0.0596669	+	0.103346i
$843$			25.0528i			0.862864i
$844$	−4.73108	+	8.19446i	−0.162850	+	0.282065i
$845$			32.2153i			1.10824i
$846$	−0.901463	−	0.520460i	−0.0309930	−	0.0178938i
$847$	7.09879	−	12.2955i	0.243917	−	0.422477i
$848$	−1.60374	+	2.77776i	−0.0550727	+	0.0953886i
$849$	−3.42387	+	1.97677i	−0.117507	+	0.0678427i
$850$	4.78749			0.164209
$851$	47.6395	−	19.3984i	1.63306	−	0.664968i
$852$	−1.85638			−0.0635986
$853$	−23.5276	+	13.5837i	−0.805571	+	0.465097i	−0.845415	−	0.534109i	$-0.820647\pi$
$853$	−23.5276	+	13.5837i	−0.805571	+	0.465097i	0.0398445	+	0.999206i	$0.487314\pi$
$854$	25.0945	−	43.4649i	0.858716	−	1.48734i
$855$	−2.76633	+	4.79142i	−0.0946065	+	0.163863i
$856$	3.38721	+	1.95561i	0.115773	+	0.0668413i
$857$			26.7290i			0.913046i	0.889712	+	0.456523i	$0.150905\pi$
$857$			26.7290i			0.913046i	−0.889712	+	0.456523i	$0.849095\pi$
$858$	12.9118	−	22.3639i	0.440802	−	0.763491i
$859$		−	35.7523i		−	1.21985i	−0.792458	−	0.609926i	$-0.791199\pi$
$859$		−	35.7523i		−	1.21985i	0.792458	−	0.609926i	$-0.208801\pi$
$860$	−0.0198880	−	0.0344471i	−0.000678176	−	0.00117463i
$861$	37.8458			1.28978
$862$	1.78637			0.0608441
$863$	14.4391	+	25.0092i	0.491512	+	0.851324i	0.999952	−	0.00977353i	$-0.00311106\pi$
$863$	14.4391	+	25.0092i	0.491512	+	0.851324i	−0.508440	+	0.861097i	$0.669778\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		−	0.724057i		−	0.0246187i
$866$	−29.1207	+	16.8128i	−0.989562	+	0.571324i
$867$	2.96002	+	5.12691i	0.100528	+	0.174119i
$868$	27.8676	−	16.0894i	0.945888	−	0.546108i
$869$	12.0222	+	6.94102i	0.407825	+	0.235458i
$870$	1.61416	+	0.931933i	0.0547250	+	0.0315955i
$871$	53.4285	−	30.8470i	1.81036	−	1.04521i
$872$	−1.91346	−	3.31422i	−0.0647981	−	0.112234i
$873$	5.32662	−	3.07533i	0.180279	−	0.104084i
$874$			46.7857i			1.58255i
$875$	3.28006	+	1.89374i	0.110886	+	0.0640202i
$876$	−5.91715	−	10.2488i	−0.199922	−	0.346275i
$877$	23.8280			0.804613			0.402307	−	0.915505i	$-0.368209\pi$
$877$	23.8280			0.804613			0.402307	+	0.915505i	$0.368209\pi$
$878$	11.7785			0.397506
$879$	−6.27495	−	10.8685i	−0.211649	−	0.366586i
$880$			3.84038i			0.129459i
$881$	−21.2103	+	36.7374i	−0.714594	+	1.23771i	0.248522	+	0.968626i	$0.420055\pi$
$881$	−21.2103	+	36.7374i	−0.714594	+	1.23771i	−0.963116	+	0.269087i	$0.913278\pi$
$882$			7.34507i			0.247321i
$883$	5.82032	+	3.36036i	0.195869	+	0.113085i	0.594727	−	0.803927i	$-0.297260\pi$
$883$	5.82032	+	3.36036i	0.195869	+	0.113085i	−0.398858	+	0.917013i	$0.630593\pi$
$884$	16.0961	−	27.8792i	0.541370	−	0.937680i
$885$	−0.902271	+	1.56278i	−0.0303295	+	0.0525322i
$886$	−23.1572	+	13.3698i	−0.777983	+	0.449168i
$887$	3.85496			0.129437			0.0647184	−	0.997904i	$-0.479385\pi$
$887$	3.85496			0.129437			0.0647184	+	0.997904i	$0.479385\pi$
$888$	−0.830184	+	6.02584i	−0.0278591	+	0.202214i
$889$	−42.7146			−1.43260
$890$	14.8116	−	8.55149i	0.496487	−	0.286647i
$891$	1.92019	−	3.32587i	0.0643288	−	0.111421i
$892$	5.92790	−	10.2674i	0.198481	−	0.343779i
$893$	−4.98749	−	2.87953i	−0.166900	−	0.0963597i
$894$		−	16.2875i		−	0.544736i
$895$	−10.4782	+	18.1487i	−0.350247	+	0.606645i
$896$			3.78749i			0.126531i
$897$	28.4310	+	49.2439i	0.949283	+	1.64421i
$898$	14.0475			0.468771
$899$	15.8355			0.528144
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−13.2985	−	7.67789i	−0.443037	−	0.255787i
$902$			38.3743i			1.27773i
$903$	0.130468	−	0.0753256i	0.00434170	−	0.00250668i
$904$	8.15399	+	14.1231i	0.271198	+	0.469728i
$905$	−13.3852	+	7.72795i	−0.444939	+	0.256886i
$906$	−17.5616	−	10.1392i	−0.583446	−	0.336852i
$907$	−16.1579	−	9.32878i	−0.536515	−	0.309757i	0.207150	−	0.978309i	$-0.433581\pi$
$907$	−16.1579	−	9.32878i	−0.536515	−	0.309757i	−0.743665	+	0.668552i	$0.766914\pi$
$908$	10.7982	−	6.23432i	0.358350	−	0.206893i
$909$	4.48179	+	7.76268i	0.148651	+	0.257472i
$910$	22.0559	−	12.7340i	0.731146	−	0.422127i
$911$		−	6.79087i		−	0.224992i	−0.993652	−	0.112496i	$-0.964116\pi$
$911$		−	6.79087i		−	0.224992i	0.993652	−	0.112496i	$-0.0358845\pi$
$912$	−4.79142	−	2.76633i	−0.158660	−	0.0916023i
$913$	−26.0903	−	45.1897i	−0.863463	−	1.49556i
$914$	12.1563			0.402095
$915$	−13.2513			−0.438073
$916$	5.00593	+	8.67053i	0.165401	+	0.286482i
$917$		−	31.5240i		−	1.04101i
$918$	2.39374	−	4.14609i	0.0790053	−	0.136841i
$919$			15.0052i			0.494976i	0.968891	+	0.247488i	$0.0796051\pi$
$919$			15.0052i			0.494976i	−0.968891	+	0.247488i	$0.920395\pi$
$920$	−7.32335	−	4.22814i	−0.241444	−	0.139398i
$921$	1.17647	−	2.03770i	0.0387660	−	0.0671446i
$922$	16.5359	−	28.6410i	0.544581	−	0.943242i
$923$	−10.8104	+	6.24137i	−0.355828	+	0.205437i
$924$	−14.5454			−0.478509
$925$	−3.73188	+	4.80344i	−0.122704	+	0.157936i
$926$	37.9533			1.24722
$927$	12.7358	−	7.35302i	0.418298	−	0.241505i
$928$	−0.931933	+	1.61416i	−0.0305922	+	0.0529872i
$929$	−4.02128	+	6.96506i	−0.131934	+	0.228516i	−0.924422	−	0.381371i	$-0.875452\pi$
$929$	−4.02128	+	6.96506i	−0.131934	+	0.228516i	0.792488	+	0.609887i	$0.208785\pi$
$930$	−7.35780	−	4.24803i	−0.241272	−	0.139298i
$931$			40.6378i			1.33185i
$932$	4.95553	−	8.58323i	0.162324	−	0.281153i
$933$		−	22.6192i		−	0.740519i
$934$	6.53167	+	11.3132i	0.213723	+	0.370179i
$935$	−18.3858			−0.601280
$936$	−6.72423			−0.219788
$937$	−11.6870	−	20.2425i	−0.381799	−	0.661295i	0.609521	−	0.792770i	$-0.291362\pi$
$937$	−11.6870	−	20.2425i	−0.381799	−	0.661295i	−0.991319	+	0.131475i	$0.958029\pi$
$938$	−30.0942	−	17.3749i	−0.982609	−	0.567310i
$939$			15.5944i			0.508903i
$940$	0.901463	−	0.520460i	0.0294025	−	0.0169755i
$941$	−8.10702	−	14.0418i	−0.264281	−	0.457749i	0.703094	−	0.711097i	$-0.251801\pi$
$941$	−8.10702	−	14.0418i	−0.264281	−	0.457749i	−0.967375	+	0.253348i	$0.918468\pi$
$942$	−5.88642	+	3.39853i	−0.191790	+	0.110730i
$943$	−73.1773	−	42.2489i	−2.38298	−	1.37581i
$944$	−1.56278	−	0.902271i	−0.0508641	−	0.0293664i
$945$	3.28006	−	1.89374i	0.106700	−	0.0616035i
$946$	0.0763776	+	0.132290i	0.00248325	+	0.00430112i
$947$	13.9750	−	8.06844i	0.454125	−	0.262189i	−0.255446	−	0.966823i	$-0.582222\pi$
$947$	13.9750	−	8.06844i	0.454125	−	0.262189i	0.709571	+	0.704634i	$0.248889\pi$
$948$		−	3.61475i		−	0.117402i
$949$	−68.9153	−	39.7883i	−2.23709	−	1.29158i
$950$	−2.76633	−	4.79142i	−0.0897516	−	0.155454i
$951$	−24.6297			−0.798673
$952$	−18.1326			−0.587680
$953$	5.18120	+	8.97411i	0.167836	+	0.290700i	0.937659	−	0.347558i	$-0.112989\pi$
$953$	5.18120	+	8.97411i	0.167836	+	0.290700i	−0.769823	+	0.638257i	$0.779656\pi$
$954$			3.20748i			0.103846i
$955$	−1.51928	+	2.63146i	−0.0491626	+	0.0851521i
$956$			15.6263i			0.505390i
$957$	−6.19898	−	3.57898i	−0.200384	−	0.115692i
$958$	−2.05209	+	3.55432i	−0.0663000	+	0.114835i
$959$	−29.5839	+	51.2408i	−0.955313	+	1.65465i
$960$	0.866025	−	0.500000i	0.0279508	−	0.0161374i
$961$	−41.1830			−1.32848
$962$	15.4251	+	37.8818i	0.497326	+	1.22136i
$963$	3.91122			0.126037
$964$	−11.0815	+	6.39792i	−0.356912	+	0.206063i
$965$	7.17156	−	12.4215i	0.230861	−	0.399862i
$966$	16.0140	−	27.7371i	0.515243	−	0.892427i
$967$	−16.2667	−	9.39158i	−0.523102	−	0.302013i	0.215101	−	0.976592i	$-0.430992\pi$
$967$	−16.2667	−	9.39158i	−0.523102	−	0.302013i	−0.738203	+	0.674579i	$0.764325\pi$
$968$		−	3.74855i		−	0.120483i
$969$	13.2438	−	22.9389i	0.425451	−	0.736903i
$970$			6.15065i			0.197486i
$971$	1.43963	+	2.49352i	0.0462000	+	0.0800207i	0.888201	−	0.459456i	$-0.151956\pi$
$971$	1.43963	+	2.49352i	0.0462000	+	0.0800207i	−0.842001	+	0.539476i	$0.818622\pi$
$972$	−1.00000			−0.0320750
$973$	−11.1216			−0.356543
$974$	−16.0765	−	27.8454i	−0.515125	−	0.892223i
$975$	−5.82335	−	3.36212i	−0.186497	−	0.107674i
$976$		−	13.2513i		−	0.424162i
$977$	14.3874	−	8.30659i	0.460295	−	0.265751i	−0.251873	−	0.967760i	$-0.581047\pi$
$977$	14.3874	−	8.30659i	0.460295	−	0.265751i	0.712168	+	0.702009i	$0.247713\pi$
$978$	−4.47104	−	7.74406i	−0.142968	−	0.247628i
$979$	−56.8823	+	32.8410i	−1.81797	+	1.04960i
$980$	−6.36102	−	3.67253i	−0.203195	−	0.117315i
$981$	−3.31422	−	1.91346i	−0.105815	−	0.0610922i
$982$	27.1272	−	15.6619i	0.865664	−	0.499791i
$983$	−15.1275	−	26.2015i	−0.482491	−	0.835699i	0.517307	−	0.855800i	$-0.326934\pi$
$983$	−15.1275	−	26.2015i	−0.482491	−	0.835699i	−0.999798	+	0.0201012i	$0.993601\pi$
$984$	8.65360	−	4.99616i	0.275867	−	0.159272i
$985$		−	0.803426i		−	0.0255993i
$986$	−7.72775	−	4.46162i	−0.246102	−	0.142087i
$987$	1.97124	+	3.41428i	0.0627452	+	0.108678i
$988$	−37.2029			−1.18358
$989$	−0.336357			−0.0106955
$990$	1.92019	+	3.32587i	0.0610277	+	0.105703i
$991$		−	61.6071i		−	1.95701i	−0.206214	−	0.978507i	$-0.566114\pi$
$991$		−	61.6071i		−	1.95701i	0.206214	−	0.978507i	$-0.433886\pi$
$992$	4.24803	−	7.35780i	0.134875	−	0.233610i
$993$			8.54041i			0.271022i
$994$	6.08905	+	3.51551i	0.193133	+	0.111505i
$995$	−2.00910	+	3.47986i	−0.0636927	+	0.110319i
$996$	−6.79367	+	11.7670i	−0.215266	+	0.372851i
$997$	−28.7258	+	16.5848i	−0.909755	+	0.525247i	−0.880352	−	0.474321i	$-0.842694\pi$
$997$	−28.7258	+	16.5848i	−0.909755	+	0.525247i	−0.0294024	+	0.999568i	$0.509360\pi$
$998$	−28.6959			−0.908353
$999$	2.29396	+	5.63363i	0.0725777	+	0.178240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.d.751.8	✓	16
37.27	even	6	inner	1110.2.x.d.841.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.d.751.8	✓	16	1.1	even	1	trivial
1110.2.x.d.841.8	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(1.89374 - 3.28006i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(1.89374 - 3.28006i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -3.84038 q^{11} +(0.500000 + 0.866025i) q^{12} +(5.82335 + 3.36212i) q^{13} -3.78749i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.14609 - 2.39374i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-4.79142 - 2.76633i) q^{19} +(0.866025 - 0.500000i) q^{20} +(1.89374 + 3.28006i) q^{21} +(-3.32587 + 1.92019i) q^{22} -8.45628i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +6.72423 q^{26} +1.00000 q^{27} +(-1.89374 - 3.28006i) q^{28} -1.86387i q^{29} +(-0.500000 + 0.866025i) q^{30} +8.49606i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.92019 - 3.32587i) q^{33} +(2.39374 - 4.14609i) q^{34} +(3.28006 - 1.89374i) q^{35} -1.00000 q^{36} +(2.29396 + 5.63363i) q^{37} -5.53266 q^{38} +(-5.82335 + 3.36212i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.99616 - 8.65360i) q^{41} +(3.28006 + 1.89374i) q^{42} -0.0397760i q^{43} +(-1.92019 + 3.32587i) q^{44} -1.00000i q^{45} +(-4.22814 - 7.32335i) q^{46} +1.04092 q^{47} +1.00000 q^{48} +(-3.67253 - 6.36102i) q^{49} +(0.866025 + 0.500000i) q^{50} +4.78749i q^{51} +(5.82335 - 3.36212i) q^{52} +(-1.60374 - 2.77776i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-3.32587 - 1.92019i) q^{55} +(-3.28006 - 1.89374i) q^{56} +(4.79142 - 2.76633i) q^{57} +(-0.931933 - 1.61416i) q^{58} +(1.56278 - 0.902271i) q^{59} +1.00000i q^{60} +(11.4759 + 6.62563i) q^{61} +(4.24803 + 7.35780i) q^{62} -3.78749 q^{63} -1.00000 q^{64} +(3.36212 + 5.82335i) q^{65} -3.84038i q^{66} +(4.58744 - 7.94568i) q^{67} -4.78749i q^{68} +(7.32335 + 4.22814i) q^{69} +(1.89374 - 3.28006i) q^{70} +(-0.928191 + 1.60767i) q^{71} +(-0.866025 + 0.500000i) q^{72} -11.8343 q^{73} +(4.80344 + 3.73188i) q^{74} -1.00000 q^{75} +(-4.79142 + 2.76633i) q^{76} +(-7.27270 + 12.5967i) q^{77} +(-3.36212 + 5.82335i) q^{78} +(-3.13047 - 1.80738i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -9.99232i q^{82} +(6.79367 + 11.7670i) q^{83} +3.78749 q^{84} +4.78749 q^{85} +(-0.0198880 - 0.0344471i) q^{86} +(1.61416 + 0.931933i) q^{87} +3.84038i q^{88} +(14.8116 - 8.55149i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(22.0559 - 12.7340i) q^{91} +(-7.32335 - 4.22814i) q^{92} +(-7.35780 - 4.24803i) q^{93} +(0.901463 - 0.520460i) q^{94} +(-2.76633 - 4.79142i) q^{95} +(0.866025 - 0.500000i) q^{96} +6.15065i q^{97} +(-6.36102 - 3.67253i) q^{98} +(1.92019 + 3.32587i) 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	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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