LMFDB - Embedded newform 1110.2.x.e.841.5

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} + 44x^{14} + 724x^{12} + 5750x^{10} + 23344x^{8} + 47024x^{6} + 43297x^{4} + 13976x^{2} + 676 $ x^16 + 44x^14 + 724x^12 + 5750x^10 + 23344x^8 + 47024x^6 + 43297x^4 + 13976*x^2 + 676
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.5
Root			$-2.47236i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.e.751.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-2.53766 - 4.39536i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-2.53766 - 4.39536i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -5.13920 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.681083 + 0.393223i) q^{13} -5.07532i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.84853 - 2.79930i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(6.64800 - 3.83822i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(2.53766 - 4.39536i) q^{21} +(-4.45068 - 2.56960i) q^{22} -6.29521i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -0.786447 q^{26} -1.00000 q^{27} +(2.53766 - 4.39536i) q^{28} -4.70306i q^{29} +(-0.500000 - 0.866025i) q^{30} +8.40882i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.56960 - 4.45068i) q^{33} +(-2.79930 - 4.84853i) q^{34} +(4.39536 + 2.53766i) q^{35} -1.00000 q^{36} +(0.791278 + 6.03108i) q^{37} +7.67645 q^{38} +(-0.681083 - 0.393223i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.61317 - 4.52615i) q^{41} +(4.39536 - 2.53766i) q^{42} -3.03010i q^{43} +(-2.56960 - 4.45068i) q^{44} -1.00000i q^{45} +(3.14760 - 5.45181i) q^{46} -11.5997 q^{47} -1.00000 q^{48} +(-9.37944 + 16.2457i) q^{49} +(0.866025 - 0.500000i) q^{50} -5.59861i q^{51} +(-0.681083 - 0.393223i) q^{52} +(-3.98543 + 6.90297i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(4.45068 - 2.56960i) q^{55} +(4.39536 - 2.53766i) q^{56} +(6.64800 + 3.83822i) q^{57} +(2.35153 - 4.07297i) q^{58} +(8.75099 + 5.05239i) q^{59} -1.00000i q^{60} +(-5.76440 + 3.32808i) q^{61} +(-4.20441 + 7.28225i) q^{62} +5.07532 q^{63} -1.00000 q^{64} +(0.393223 - 0.681083i) q^{65} -5.13920i q^{66} +(-0.326942 - 0.566281i) q^{67} -5.59861i q^{68} +(5.45181 - 3.14760i) q^{69} +(2.53766 + 4.39536i) q^{70} +(-7.39598 - 12.8102i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.85481 q^{73} +(-2.33027 + 5.61870i) q^{74} +1.00000 q^{75} +(6.64800 + 3.83822i) q^{76} +(13.0415 + 22.5886i) q^{77} +(-0.393223 - 0.681083i) q^{78} +(10.5907 - 6.11454i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -5.22635i q^{82} +(2.45001 - 4.24354i) q^{83} +5.07532 q^{84} +5.59861 q^{85} +(1.51505 - 2.62415i) q^{86} +(4.07297 - 2.35153i) q^{87} -5.13920i q^{88} +(2.16653 + 1.25084i) q^{89} +(0.500000 - 0.866025i) q^{90} +(3.45671 + 1.99573i) q^{91} +(5.45181 - 3.14760i) q^{92} +(-7.28225 + 4.20441i) q^{93} +(-10.0457 - 5.79986i) q^{94} +(-3.83822 + 6.64800i) q^{95} +(-0.866025 - 0.500000i) q^{96} -18.1242i q^{97} +(-16.2457 + 9.37944i) q^{98} +(2.56960 - 4.45068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	−2.53766	−	4.39536i	−0.959145	−	1.66129i	−0.724583	−	0.689188i	$-0.757968\pi$
$7$	−2.53766	−	4.39536i	−0.959145	−	1.66129i	−0.234563	−	0.972101i	$-0.575366\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	−5.13920			−1.54953			−0.774764	−	0.632251i	$-0.782131\pi$
$11$	−5.13920			−1.54953			−0.774764	+	0.632251i	$0.782131\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−0.681083	+	0.393223i	−0.188898	+	0.109061i	−0.591467	−	0.806329i	$-0.701451\pi$
$13$	−0.681083	+	0.393223i	−0.188898	+	0.109061i	0.402568	+	0.915390i	$0.368118\pi$
$14$		−	5.07532i		−	1.35644i
$15$	−0.866025	−	0.500000i	−0.223607	−	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.84853	−	2.79930i	−1.17594	−	0.678931i	−0.220870	−	0.975303i	$-0.570890\pi$
$17$	−4.84853	−	2.79930i	−1.17594	−	0.678931i	−0.955072	+	0.296373i	$0.904223\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	6.64800	−	3.83822i	1.52516	−	0.880549i	0.525600	−	0.850732i	$-0.323841\pi$
$19$	6.64800	−	3.83822i	1.52516	−	0.880549i	0.999555	−	0.0298174i	$-0.00949259\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	2.53766	−	4.39536i	0.553763	−	0.959145i
$22$	−4.45068	−	2.56960i	−0.948888	−	0.547841i
$23$		−	6.29521i		−	1.31264i	−0.754482	−	0.656321i	$-0.772112\pi$
$23$		−	6.29521i		−	1.31264i	0.754482	−	0.656321i	$-0.227888\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.786447			−0.154235
$27$	−1.00000			−0.192450
$28$	2.53766	−	4.39536i	0.479573	−	0.830644i
$29$		−	4.70306i		−	0.873337i	−0.899622	−	0.436669i	$-0.856158\pi$
$29$		−	4.70306i		−	0.873337i	0.899622	−	0.436669i	$-0.143842\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$			8.40882i			1.51027i	0.655570	+	0.755135i	$0.272428\pi$
$31$			8.40882i			1.51027i	−0.655570	+	0.755135i	$0.727572\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−2.56960	−	4.45068i	−0.447310	−	0.774764i
$34$	−2.79930	−	4.84853i	−0.480076	−	0.831517i
$35$	4.39536	+	2.53766i	0.742951	+	0.428943i
$36$	−1.00000			−0.166667
$37$	0.791278	+	6.03108i	0.130085	+	0.991503i
$37$	0.791278	+	6.03108i	0.130085	+	0.991503i
$38$	7.67645			1.24528
$39$	−0.681083	−	0.393223i	−0.109061	−	0.0629661i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−2.61317	−	4.52615i	−0.408109	−	0.706866i	0.586569	−	0.809900i	$-0.300478\pi$
$41$	−2.61317	−	4.52615i	−0.408109	−	0.706866i	−0.994678	+	0.103034i	$0.967145\pi$
$42$	4.39536	−	2.53766i	0.678218	−	0.391570i
$43$		−	3.03010i		−	0.462087i	−0.972943	−	0.231043i	$-0.925786\pi$
$43$		−	3.03010i		−	0.462087i	0.972943	−	0.231043i	$-0.0742139\pi$
$44$	−2.56960	−	4.45068i	−0.387382	−	0.670965i
$45$		−	1.00000i		−	0.149071i
$46$	3.14760	−	5.45181i	0.464089	−	0.803826i
$47$	−11.5997			−1.69199			−0.845997	−	0.533188i	$-0.820994\pi$
$47$	−11.5997			−1.69199			−0.845997	+	0.533188i	$0.820994\pi$
$48$	−1.00000			−0.144338
$49$	−9.37944	+	16.2457i	−1.33992	+	2.32081i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		−	5.59861i		−	0.783962i
$52$	−0.681083	−	0.393223i	−0.0944492	−	0.0545303i
$53$	−3.98543	+	6.90297i	−0.547441	+	0.948196i	0.451008	+	0.892520i	$0.351065\pi$
$53$	−3.98543	+	6.90297i	−0.547441	+	0.948196i	−0.998449	+	0.0556758i	$0.982269\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	4.45068	−	2.56960i	0.600129	−	0.346485i
$56$	4.39536	−	2.53766i	0.587354	−	0.339109i
$57$	6.64800	+	3.83822i	0.880549	+	0.508385i
$58$	2.35153	−	4.07297i	0.308771	−	0.534808i
$59$	8.75099	+	5.05239i	1.13928	+	0.657765i	0.946253	−	0.323428i	$-0.104835\pi$
$59$	8.75099	+	5.05239i	1.13928	+	0.657765i	0.193029	+	0.981193i	$0.438169\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−5.76440	+	3.32808i	−0.738055	+	0.426116i	−0.821362	−	0.570408i	$-0.806785\pi$
$61$	−5.76440	+	3.32808i	−0.738055	+	0.426116i	0.0833066	+	0.996524i	$0.473452\pi$
$62$	−4.20441	+	7.28225i	−0.533961	+	0.924847i
$63$	5.07532			0.639430
$64$	−1.00000			−0.125000
$65$	0.393223	−	0.681083i	0.0487733	−	0.0844779i
$66$		−	5.13920i		−	0.632592i
$67$	−0.326942	−	0.566281i	−0.0399424	−	0.0691822i	0.845363	−	0.534192i	$-0.179384\pi$
$67$	−0.326942	−	0.566281i	−0.0399424	−	0.0691822i	−0.885305	+	0.465010i	$0.846051\pi$
$68$		−	5.59861i		−	0.678931i
$69$	5.45181	−	3.14760i	0.656321	−	0.378927i
$70$	2.53766	+	4.39536i	0.303308	+	0.525346i
$71$	−7.39598	−	12.8102i	−0.877742	−	1.52029i	−0.853813	−	0.520580i	$-0.825716\pi$
$71$	−7.39598	−	12.8102i	−0.877742	−	1.52029i	−0.0239285	−	0.999714i	$-0.507617\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	−2.85481			−0.334130			−0.167065	−	0.985946i	$-0.553429\pi$
$73$	−2.85481			−0.334130			−0.167065	+	0.985946i	$0.553429\pi$
$74$	−2.33027	+	5.61870i	−0.270889	+	0.653161i
$75$	1.00000			0.115470
$76$	6.64800	+	3.83822i	0.762578	+	0.440275i
$77$	13.0415	+	22.5886i	1.48622	+	2.57421i
$78$	−0.393223	−	0.681083i	−0.0445238	−	0.0771174i
$79$	10.5907	−	6.11454i	1.19155	−	0.687940i	0.232889	−	0.972503i	$-0.425182\pi$
$79$	10.5907	−	6.11454i	1.19155	−	0.687940i	0.958657	+	0.284564i	$0.0918487\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	5.22635i		−	0.577154i
$83$	2.45001	−	4.24354i	0.268924	−	0.465789i	−0.699661	−	0.714475i	$-0.746665\pi$
$83$	2.45001	−	4.24354i	0.268924	−	0.465789i	0.968584	+	0.248686i	$0.0799987\pi$
$84$	5.07532			0.553763
$85$	5.59861			0.607254
$86$	1.51505	−	2.62415i	0.163372	−	0.282969i
$87$	4.07297	−	2.35153i	0.436669	−	0.252111i
$88$		−	5.13920i		−	0.547841i
$89$	2.16653	+	1.25084i	0.229651	+	0.132589i	0.610411	−	0.792085i	$-0.291004\pi$
$89$	2.16653	+	1.25084i	0.229651	+	0.132589i	−0.380760	+	0.924674i	$0.624338\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	3.45671	+	1.99573i	0.362362	+	0.209210i
$92$	5.45181	−	3.14760i	0.568391	−	0.328160i
$93$	−7.28225	+	4.20441i	−0.755135	+	0.435977i
$94$	−10.0457	−	5.79986i	−1.03613	−	0.598210i
$95$	−3.83822	+	6.64800i	−0.393794	+	0.682070i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$		−	18.1242i		−	1.84024i	−0.391642	−	0.920118i	$-0.628093\pi$
$97$		−	18.1242i		−	1.84024i	0.391642	−	0.920118i	$-0.371907\pi$
$98$	−16.2457	+	9.37944i	−1.64106	+	0.947467i
$99$	2.56960	−	4.45068i	0.258255	−	0.447310i
$100$	1.00000			0.100000
$101$	−8.35745			−0.831597			−0.415799	−	0.909457i	$-0.636498\pi$
$101$	−8.35745			−0.831597			−0.415799	+	0.909457i	$0.636498\pi$
$102$	2.79930	−	4.84853i	0.277172	−	0.480076i
$103$		−	0.674598i		−	0.0664701i	−0.999448	−	0.0332350i	$-0.989419\pi$
$103$		−	0.674598i		−	0.0664701i	0.999448	−	0.0332350i	$-0.0105810\pi$
$104$	−0.393223	−	0.681083i	−0.0385587	−	0.0667857i
$105$			5.07532i			0.495301i
$106$	−6.90297	+	3.98543i	−0.670476	+	0.387099i
$107$	4.05189	+	7.01809i	0.391711	+	0.678464i	0.992675	−	0.120812i	$-0.0385499\pi$
$107$	4.05189	+	7.01809i	0.391711	+	0.678464i	−0.600964	+	0.799276i	$0.705217\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	2.89690	+	1.67252i	0.277472	+	0.160199i	0.632279	−	0.774741i	$-0.282120\pi$
$109$	2.89690	+	1.67252i	0.277472	+	0.160199i	−0.354806	+	0.934940i	$0.615453\pi$
$110$	5.13920			0.490004
$111$	−4.82743	+	3.70080i	−0.458199	+	0.351265i
$112$	5.07532			0.479573
$113$	−1.92106	−	1.10912i	−0.180718	−	0.104338i	0.406912	−	0.913467i	$-0.366606\pi$
$113$	−1.92106	−	1.10912i	−0.180718	−	0.104338i	−0.587630	+	0.809130i	$0.699939\pi$
$114$	3.83822	+	6.64800i	0.359483	+	0.622642i
$115$	3.14760	+	5.45181i	0.293516	+	0.508384i
$116$	4.07297	−	2.35153i	0.378166	−	0.218334i
$117$		−	0.786447i		−	0.0727070i
$118$	5.05239	+	8.75099i	0.465110	+	0.805594i
$119$			28.4147i			2.60477i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	15.4114			1.40103
$122$	−6.65615			−0.602620
$123$	2.61317	−	4.52615i	0.235622	−	0.408109i
$124$	−7.28225	+	4.20441i	−0.653966	+	0.377567i
$125$			1.00000i			0.0894427i
$126$	4.39536	+	2.53766i	0.391570	+	0.226073i
$127$	−1.74203	+	3.01728i	−0.154580	+	0.267740i	−0.932906	−	0.360120i	$-0.882736\pi$
$127$	−1.74203	+	3.01728i	−0.154580	+	0.267740i	0.778326	+	0.627860i	$0.216069\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	2.62415	−	1.51505i	0.231043	−	0.133393i
$130$	0.681083	−	0.393223i	0.0597349	−	0.0344880i
$131$	3.32238	+	1.91818i	0.290278	+	0.167592i	0.638067	−	0.769981i	$-0.279734\pi$
$131$	3.32238	+	1.91818i	0.290278	+	0.167592i	−0.347789	+	0.937573i	$0.613068\pi$
$132$	2.56960	−	4.45068i	0.223655	−	0.387382i
$133$	−33.7407	−	19.4802i	−2.92569	−	1.68915i
$134$		−	0.653885i		−	0.0564870i
$135$	0.866025	−	0.500000i	0.0745356	−	0.0430331i
$136$	2.79930	−	4.84853i	0.240038	−	0.415758i
$137$	6.26408			0.535176			0.267588	−	0.963533i	$-0.413773\pi$
$137$	6.26408			0.535176			0.267588	+	0.963533i	$0.413773\pi$
$138$	6.29521			0.535884
$139$	0.868795	−	1.50480i	0.0736903	−	0.127635i	−0.826826	−	0.562458i	$-0.809856\pi$
$139$	0.868795	−	1.50480i	0.0736903	−	0.127635i	0.900516	+	0.434823i	$0.143189\pi$
$140$			5.07532i			0.428943i
$141$	−5.79986	−	10.0457i	−0.488436	−	0.845997i
$142$		−	14.7920i		−	1.24131i
$143$	3.50022	−	2.02085i	0.292703	−	0.168992i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.35153	+	4.07297i	0.195284	+	0.338242i
$146$	−2.47233	−	1.42740i	−0.204612	−	0.118133i
$147$	−18.7589			−1.54721
$148$	−4.82743	+	3.70080i	−0.396812	+	0.304204i
$149$	−12.6579			−1.03697			−0.518487	−	0.855086i	$-0.673504\pi$
$149$	−12.6579			−1.03697			−0.518487	+	0.855086i	$0.673504\pi$
$150$	0.866025	+	0.500000i	0.0707107	+	0.0408248i
$151$	6.87125	+	11.9014i	0.559174	+	0.968519i	0.997566	+	0.0697343i	$0.0222151\pi$
$151$	6.87125	+	11.9014i	0.559174	+	0.968519i	−0.438391	+	0.898784i	$0.644452\pi$
$152$	3.83822	+	6.64800i	0.311321	+	0.539224i
$153$	4.84853	−	2.79930i	0.391981	−	0.226310i
$154$			26.0831i			2.10184i
$155$	−4.20441	−	7.28225i	−0.337706	−	0.584925i
$156$		−	0.786447i		−	0.0629661i
$157$	0.961987	−	1.66621i	0.0767749	−	0.132978i	−0.825082	−	0.565013i	$-0.808871\pi$
$157$	0.961987	−	1.66621i	0.0767749	−	0.132978i	0.901857	+	0.432035i	$0.142204\pi$
$158$	12.2291			0.972894
$159$	−7.97086			−0.632131
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−27.6697	+	15.9751i	−2.18068	+	1.25901i
$162$		−	1.00000i		−	0.0785674i
$163$	−8.54182	−	4.93162i	−0.669047	−	0.386274i	0.126669	−	0.991945i	$-0.459572\pi$
$163$	−8.54182	−	4.93162i	−0.669047	−	0.386274i	−0.795715	+	0.605671i	$0.792905\pi$
$164$	2.61317	−	4.52615i	0.204055	−	0.353433i
$165$	4.45068	+	2.56960i	0.346485	+	0.200043i
$166$	4.24354	−	2.45001i	0.329363	−	0.190158i
$167$	−12.1154	+	6.99484i	−0.937520	+	0.541277i	−0.889182	−	0.457554i	$-0.848726\pi$
$167$	−12.1154	+	6.99484i	−0.937520	+	0.541277i	−0.0483377	+	0.998831i	$0.515392\pi$
$168$	4.39536	+	2.53766i	0.339109	+	0.195785i
$169$	−6.19075	+	10.7227i	−0.476212	+	0.824823i
$170$	4.84853	+	2.79930i	0.371866	+	0.214697i
$171$			7.67645i			0.587033i
$172$	2.62415	−	1.51505i	0.200089	−	0.115522i
$173$	7.40791	−	12.8309i	0.563213	−	0.975514i	−0.434000	−	0.900913i	$-0.642898\pi$
$173$	7.40791	−	12.8309i	0.563213	−	0.975514i	0.997213	−	0.0746012i	$-0.0237684\pi$
$174$	4.70306			0.356538
$175$	−5.07532			−0.383658
$176$	2.56960	−	4.45068i	0.193691	−	0.335482i
$177$			10.1048i			0.759521i
$178$	1.25084	+	2.16653i	0.0937548	+	0.162388i
$179$			2.96879i			0.221897i	0.993826	+	0.110949i	$0.0353889\pi$
$179$			2.96879i			0.221897i	−0.993826	+	0.110949i	$0.964611\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	−0.0806879	−	0.139755i	−0.00599748	−	0.0103879i	0.863011	−	0.505185i	$-0.168576\pi$
$181$	−0.0806879	−	0.139755i	−0.00599748	−	0.0103879i	−0.869009	+	0.494797i	$0.835242\pi$
$182$	1.99573	+	3.45671i	0.147934	+	0.256229i
$183$	−5.76440	−	3.32808i	−0.426116	−	0.246018i
$184$	6.29521			0.464089
$185$	−3.70080	−	4.82743i	−0.272089	−	0.354919i
$186$	−8.40882			−0.616565
$187$	24.9176	+	14.3862i	1.82215	+	1.05202i
$188$	−5.79986	−	10.0457i	−0.422998	−	0.732655i
$189$	2.53766	+	4.39536i	0.184588	+	0.319715i
$190$	−6.64800	+	3.83822i	−0.482297	+	0.278454i
$191$		−	3.21946i		−	0.232952i	−0.993194	−	0.116476i	$-0.962840\pi$
$191$		−	3.21946i		−	0.232952i	0.993194	−	0.116476i	$-0.0371598\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$		−	4.75451i		−	0.342237i	−0.985250	−	0.171119i	$-0.945262\pi$
$193$		−	4.75451i		−	0.342237i	0.985250	−	0.171119i	$-0.0547381\pi$
$194$	9.06211	−	15.6960i	0.650621	−	1.12691i
$195$	0.786447			0.0563186
$196$	−18.7589			−1.33992
$197$	9.78151	−	16.9421i	0.696903	−	1.20707i	−0.272631	−	0.962119i	$-0.587894\pi$
$197$	9.78151	−	16.9421i	0.696903	−	1.20707i	0.969535	−	0.244954i	$-0.0787727\pi$
$198$	4.45068	−	2.56960i	0.316296	−	0.182614i
$199$			1.47554i			0.104598i	0.998631	+	0.0522990i	$0.0166549\pi$
$199$			1.47554i			0.104598i	−0.998631	+	0.0522990i	$0.983345\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	0.326942	−	0.566281i	0.0230607	−	0.0399424i
$202$	−7.23776	−	4.17872i	−0.509247	−	0.294014i
$203$	−20.6716	+	11.9348i	−1.45086	+	0.837657i
$204$	4.84853	−	2.79930i	0.339465	−	0.195990i
$205$	4.52615	+	2.61317i	0.316120	+	0.182512i
$206$	0.337299	−	0.584219i	0.0235007	−	0.0407045i
$207$	5.45181	+	3.14760i	0.378927	+	0.218774i
$208$		−	0.786447i		−	0.0545303i
$209$	−34.1654	+	19.7254i	−2.36327	+	1.36443i
$210$	−2.53766	+	4.39536i	−0.175115	+	0.303308i
$211$	9.89862			0.681449			0.340724	−	0.940163i	$-0.389328\pi$
$211$	9.89862			0.681449			0.340724	+	0.940163i	$0.389328\pi$
$212$	−7.97086			−0.547441
$213$	7.39598	−	12.8102i	0.506764	−	0.877742i
$214$			8.10379i			0.553963i
$215$	1.51505	+	2.62415i	0.103326	+	0.178965i
$216$		−	1.00000i		−	0.0680414i
$217$	36.9598	−	21.3387i	2.50899	−	1.44857i
$218$	1.67252	+	2.89690i	0.113278	+	0.196203i
$219$	−1.42740	−	2.47233i	−0.0964549	−	0.167065i
$220$	4.45068	+	2.56960i	0.300065	+	0.173242i
$221$	4.40300			0.296178
$222$	−6.03108	+	0.791278i	−0.404779	+	0.0531071i
$223$	5.84761			0.391585			0.195792	−	0.980645i	$-0.437272\pi$
$223$	5.84761			0.391585			0.195792	+	0.980645i	$0.437272\pi$
$224$	4.39536	+	2.53766i	0.293677	+	0.169555i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	−1.10912	−	1.92106i	−0.0737779	−	0.127787i
$227$	16.0215	−	9.25001i	1.06338	−	0.613945i	0.137017	−	0.990569i	$-0.456248\pi$
$227$	16.0215	−	9.25001i	1.06338	−	0.613945i	0.926366	+	0.376624i	$0.122915\pi$
$228$			7.67645i			0.508385i
$229$	−3.03424	−	5.25546i	−0.200508	−	0.347291i	0.748184	−	0.663491i	$-0.230926\pi$
$229$	−3.03424	−	5.25546i	−0.200508	−	0.347291i	−0.948692	+	0.316201i	$0.897593\pi$
$230$			6.29521i			0.415094i
$231$	−13.0415	+	22.5886i	−0.858071	+	1.48622i
$232$	4.70306			0.308771
$233$	6.54718			0.428920			0.214460	−	0.976733i	$-0.431201\pi$
$233$	6.54718			0.428920			0.214460	+	0.976733i	$0.431201\pi$
$234$	0.393223	−	0.681083i	0.0257058	−	0.0445238i
$235$	10.0457	−	5.79986i	0.655306	−	0.378341i
$236$			10.1048i			0.657765i
$237$	10.5907	+	6.11454i	0.687940	+	0.397182i
$238$	−14.2074	+	24.6079i	−0.920926	+	1.59509i
$239$	−10.2113	−	5.89547i	−0.660511	−	0.381346i	0.131960	−	0.991255i	$-0.457873\pi$
$239$	−10.2113	−	5.89547i	−0.660511	−	0.381346i	−0.792472	+	0.609909i	$0.791206\pi$
$240$	0.866025	−	0.500000i	0.0559017	−	0.0322749i
$241$	−4.21824	+	2.43540i	−0.271721	+	0.156878i	−0.629669	−	0.776863i	$-0.716810\pi$
$241$	−4.21824	+	2.43540i	−0.271721	+	0.156878i	0.357948	+	0.933741i	$0.383476\pi$
$242$	13.3466	+	7.70569i	0.857955	+	0.495340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−5.76440	−	3.32808i	−0.369028	−	0.213058i
$245$		−	18.7589i		−	1.19846i
$246$	4.52615	−	2.61317i	0.288577	−	0.166610i
$247$	−3.01856	+	5.22830i	−0.192066	+	0.332669i
$248$	−8.40882			−0.533961
$249$	4.90002			0.310526
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$		−	5.76790i		−	0.364067i	−0.983292	−	0.182033i	$-0.941732\pi$
$251$		−	5.76790i		−	0.364067i	0.983292	−	0.182033i	$-0.0582679\pi$
$252$	2.53766	+	4.39536i	0.159858	+	0.276881i
$253$			32.3523i			2.03397i
$254$	−3.01728	+	1.74203i	−0.189321	+	0.109304i
$255$	2.79930	+	4.84853i	0.175299	+	0.303627i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.14091	+	2.39075i	0.258303	+	0.149131i	0.623560	−	0.781775i	$-0.285686\pi$
$257$	4.14091	+	2.39075i	0.258303	+	0.149131i	−0.365257	+	0.930907i	$0.619019\pi$
$258$	3.03010			0.188646
$259$	24.5007	−	18.7828i	1.52240	−	1.16710i
$260$	0.786447			0.0487733
$261$	4.07297	+	2.35153i	0.252111	+	0.145556i
$262$	1.91818	+	3.32238i	0.118506	+	0.205258i
$263$	−2.94053	−	5.09315i	−0.181321	−	0.314057i	0.761010	−	0.648741i	$-0.224704\pi$
$263$	−2.94053	−	5.09315i	−0.181321	−	0.314057i	−0.942331	+	0.334683i	$0.891371\pi$
$264$	4.45068	−	2.56960i	0.273920	−	0.158148i
$265$		−	7.97086i		−	0.489646i
$266$	−19.4802	−	33.7407i	−1.19441	−	2.06878i
$267$			2.50169i			0.153101i
$268$	0.326942	−	0.566281i	0.0199712	−	0.0345911i
$269$	13.7281			0.837019			0.418510	−	0.908212i	$-0.362553\pi$
$269$	13.7281			0.837019			0.418510	+	0.908212i	$0.362553\pi$
$270$	1.00000			0.0608581
$271$	−10.1793	+	17.6311i	−0.618348	+	1.07101i	0.371439	+	0.928457i	$0.378865\pi$
$271$	−10.1793	+	17.6311i	−0.618348	+	1.07101i	−0.989787	+	0.142553i	$0.954469\pi$
$272$	4.84853	−	2.79930i	0.293986	−	0.169733i
$273$			3.99147i			0.241575i
$274$	5.42485	+	3.13204i	0.327727	+	0.189213i
$275$	−2.56960	+	4.45068i	−0.154953	+	0.268386i
$276$	5.45181	+	3.14760i	0.328160	+	0.189464i
$277$	−5.09110	+	2.93935i	−0.305895	+	0.176608i	−0.645088	−	0.764108i	$-0.723179\pi$
$277$	−5.09110	+	2.93935i	−0.305895	+	0.176608i	0.339193	+	0.940717i	$0.389846\pi$
$278$	1.50480	−	0.868795i	0.0902518	−	0.0521069i
$279$	−7.28225	−	4.20441i	−0.435977	−	0.251712i
$280$	−2.53766	+	4.39536i	−0.151654	+	0.262673i
$281$	1.97571	+	1.14068i	0.117861	+	0.0680470i	0.557771	−	0.829995i	$-0.311657\pi$
$281$	1.97571	+	1.14068i	0.117861	+	0.0680470i	−0.439911	+	0.898042i	$0.644990\pi$
$282$		−	11.5997i		−	0.690754i
$283$	27.4642	−	15.8565i	1.63258	−	0.942569i	0.649283	−	0.760547i	$-0.275069\pi$
$283$	27.4642	−	15.8565i	1.63258	−	0.942569i	0.983294	−	0.182022i	$-0.0582642\pi$
$284$	7.39598	−	12.8102i	0.438871	−	0.760147i
$285$	−7.67645			−0.454714
$286$	4.04171			0.238991
$287$	−13.2627	+	22.9717i	−0.782872	+	1.35597i
$288$		−	1.00000i		−	0.0589256i
$289$	7.17219	+	12.4226i	0.421894	+	0.730741i
$290$			4.70306i			0.276173i
$291$	15.6960	−	9.06211i	0.920118	−	0.531230i
$292$	−1.42740	−	2.47233i	−0.0835324	−	0.144682i
$293$	−1.93484	−	3.35125i	−0.113035	−	0.195782i	0.803958	−	0.594686i	$-0.202724\pi$
$293$	−1.93484	−	3.35125i	−0.113035	−	0.195782i	−0.916992	+	0.398905i	$0.869390\pi$
$294$	−16.2457	−	9.37944i	−0.947467	−	0.547020i
$295$	−10.1048			−0.588323
$296$	−6.03108	+	0.791278i	−0.350549	+	0.0459921i
$297$	5.13920			0.298207
$298$	−10.9620	−	6.32893i	−0.635014	−	0.366625i
$299$	2.47542	+	4.28756i	0.143157	+	0.247956i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−13.3184	+	7.68938i	−0.767659	+	0.443208i
$302$			13.7425i			0.790792i
$303$	−4.17872	−	7.23776i	−0.240061	−	0.415799i
$304$			7.67645i			0.440275i
$305$	3.32808	−	5.76440i	0.190565	−	0.330068i
$306$	5.59861			0.320051
$307$	8.57659			0.489492			0.244746	−	0.969587i	$-0.421295\pi$
$307$	8.57659			0.489492			0.244746	+	0.969587i	$0.421295\pi$
$308$	−13.0415	+	22.5886i	−0.743111	+	1.28711i
$309$	0.584219	−	0.337299i	0.0332350	−	0.0191883i
$310$		−	8.40882i		−	0.477589i
$311$	9.95407	+	5.74699i	0.564444	+	0.325882i	0.754927	−	0.655809i	$-0.227672\pi$
$311$	9.95407	+	5.74699i	0.564444	+	0.325882i	−0.190483	+	0.981690i	$0.561006\pi$
$312$	0.393223	−	0.681083i	0.0222619	−	0.0385587i
$313$	−29.1579	−	16.8343i	−1.64810	−	0.951534i	−0.977825	−	0.209425i	$-0.932841\pi$
$313$	−29.1579	−	16.8343i	−1.64810	−	0.951534i	−0.670280	−	0.742109i	$-0.733826\pi$
$314$	1.66621	−	0.961987i	0.0940297	−	0.0542881i
$315$	−4.39536	+	2.53766i	−0.247650	+	0.142981i
$316$	10.5907	+	6.11454i	0.595773	+	0.343970i
$317$	−15.7867	+	27.3433i	−0.886668	+	1.53575i	−0.0428783	+	0.999080i	$0.513653\pi$
$317$	−15.7867	+	27.3433i	−0.886668	+	1.53575i	−0.843790	+	0.536674i	$0.819681\pi$
$318$	−6.90297	−	3.98543i	−0.387099	−	0.223492i
$319$			24.1700i			1.35326i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−4.05189	+	7.01809i	−0.226155	+	0.391711i
$322$	−31.9502			−1.78052
$323$	−42.9774			−2.39133
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			0.786447i			0.0436242i
$326$	−4.93162	−	8.54182i	−0.273137	−	0.473088i
$327$			3.34505i			0.184982i
$328$	4.52615	−	2.61317i	0.249915	−	0.144288i
$329$	29.4362	+	50.9849i	1.62287	+	2.81089i
$330$	2.56960	+	4.45068i	0.141452	+	0.245002i
$331$	−17.1734	−	9.91508i	−0.943936	−	0.544982i	−0.0527444	−	0.998608i	$-0.516797\pi$
$331$	−17.1734	−	9.91508i	−0.943936	−	0.544982i	−0.891192	+	0.453626i	$0.850130\pi$
$332$	4.90002			0.268924
$333$	−5.61870	−	2.33027i	−0.307903	−	0.127698i
$334$	−13.9897			−0.765482
$335$	0.566281	+	0.326942i	0.0309392	+	0.0178628i
$336$	2.53766	+	4.39536i	0.138441	+	0.239786i
$337$	−14.3498	−	24.8546i	−0.781683	−	1.35391i	−0.930961	−	0.365119i	$-0.881028\pi$
$337$	−14.3498	−	24.8546i	−0.781683	−	1.35391i	0.149278	−	0.988795i	$-0.452305\pi$
$338$	−10.7227	+	6.19075i	−0.583238	+	0.336732i
$339$		−	2.21825i		−	0.120479i
$340$	2.79930	+	4.84853i	0.151814	+	0.262949i
$341$		−	43.2146i		−	2.34020i
$342$	−3.83822	+	6.64800i	−0.207547	+	0.359483i
$343$	59.6801			3.22242
$344$	3.03010			0.163372
$345$	−3.14760	+	5.45181i	−0.169461	+	0.293516i
$346$	12.8309	−	7.40791i	0.689793	−	0.398252i
$347$			13.1654i			0.706753i	0.935481	+	0.353377i	$0.114967\pi$
$347$			13.1654i			0.706753i	−0.935481	+	0.353377i	$0.885033\pi$
$348$	4.07297	+	2.35153i	0.218334	+	0.126055i
$349$	0.489360	−	0.847597i	0.0261948	−	0.0453708i	−0.852631	−	0.522514i	$-0.824994\pi$
$349$	0.489360	−	0.847597i	0.0261948	−	0.0453708i	0.878826	+	0.477143i	$0.158328\pi$
$350$	−4.39536	−	2.53766i	−0.234942	−	0.135644i
$351$	0.681083	−	0.393223i	0.0363535	−	0.0209887i
$352$	4.45068	−	2.56960i	0.237222	−	0.136960i
$353$	4.62659	+	2.67116i	0.246249	+	0.142172i	0.618045	−	0.786142i	$-0.287925\pi$
$353$	4.62659	+	2.67116i	0.246249	+	0.142172i	−0.371797	+	0.928314i	$0.621258\pi$
$354$	−5.05239	+	8.75099i	−0.268531	+	0.465110i
$355$	12.8102	+	7.39598i	0.679896	+	0.392538i
$356$			2.50169i			0.132589i
$357$	−24.6079	+	14.2074i	−1.30239	+	0.751933i
$358$	−1.48439	+	2.57104i	−0.0784526	+	0.135884i
$359$	8.26049			0.435972			0.217986	−	0.975952i	$-0.430051\pi$
$359$	8.26049			0.435972			0.217986	+	0.975952i	$0.430051\pi$
$360$	1.00000			0.0527046
$361$	19.9639	−	34.5785i	1.05073	−	1.81992i
$362$		−	0.161376i		−	0.00848172i
$363$	7.70569	+	13.3466i	0.404444	+	0.700517i
$364$			3.99147i			0.209210i
$365$	2.47233	−	1.42740i	0.129408	−	0.0747137i
$366$	−3.32808	−	5.76440i	−0.173961	−	0.301310i
$367$	−10.3861	−	17.9893i	−0.542150	−	0.939032i	−0.998780	−	0.0493750i	$-0.984277\pi$
$367$	−10.3861	−	17.9893i	−0.542150	−	0.939032i	0.456630	−	0.889657i	$-0.349056\pi$
$368$	5.45181	+	3.14760i	0.284195	+	0.164080i
$369$	5.22635			0.272073
$370$	−0.791278	−	6.03108i	−0.0411366	−	0.313541i
$371$	40.4547			2.10030
$372$	−7.28225	−	4.20441i	−0.377567	−	0.217989i
$373$	−17.0590	−	29.5471i	−0.883282	−	1.52989i	−0.847670	−	0.530523i	$-0.821995\pi$
$373$	−17.0590	−	29.5471i	−0.883282	−	1.52989i	−0.0356116	−	0.999366i	$-0.511338\pi$
$374$	14.3862	+	24.9176i	0.743892	+	1.28846i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$		−	11.5997i		−	0.598210i
$377$	1.84935	+	3.20318i	0.0952466	+	0.164972i
$378$			5.07532i			0.261046i
$379$	4.09315	−	7.08954i	0.210251	−	0.364165i	−0.741542	−	0.670906i	$-0.765905\pi$
$379$	4.09315	−	7.08954i	0.210251	−	0.364165i	0.951793	+	0.306741i	$0.0992386\pi$
$380$	−7.67645			−0.393794
$381$	−3.48405			−0.178493
$382$	1.60973	−	2.78813i	0.0823609	−	0.142653i
$383$	15.2917	−	8.82866i	0.781368	−	0.451123i	−0.0555466	−	0.998456i	$-0.517690\pi$
$383$	15.2917	−	8.82866i	0.781368	−	0.451123i	0.836915	+	0.547333i	$0.184357\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−22.5886	−	13.0415i	−1.15122	−	0.664659i
$386$	2.37725	−	4.11753i	0.120999	−	0.209577i
$387$	2.62415	+	1.51505i	0.133393	+	0.0770144i
$388$	15.6960	−	9.06211i	0.796845	−	0.460059i
$389$	−24.1074	+	13.9184i	−1.22229	+	0.705691i	−0.965406	−	0.260750i	$-0.916030\pi$
$389$	−24.1074	+	13.9184i	−1.22229	+	0.705691i	−0.256887	+	0.966442i	$0.582697\pi$
$390$	0.681083	+	0.393223i	0.0344880	+	0.0199116i
$391$	−17.6222	+	30.5225i	−0.891193	+	1.54359i
$392$	−16.2457	−	9.37944i	−0.820530	−	0.473733i
$393$			3.83636i			0.193519i
$394$	16.9421	−	9.78151i	0.853529	−	0.492785i
$395$	−6.11454	+	10.5907i	−0.307656	+	0.532876i
$396$	5.13920			0.258255
$397$	−30.7578			−1.54369			−0.771844	−	0.635812i	$-0.780665\pi$
$397$	−30.7578			−1.54369			−0.771844	+	0.635812i	$0.780665\pi$
$398$	−0.737768	+	1.27785i	−0.0369810	+	0.0640530i
$399$		−	38.9604i		−	1.95046i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			38.7121i			1.93319i	0.256312	+	0.966594i	$0.417493\pi$
$401$			38.7121i			1.93319i	−0.256312	+	0.966594i	$0.582507\pi$
$402$	0.566281	−	0.326942i	0.0282435	−	0.0163064i
$403$	−3.30654	−	5.72710i	−0.164711	−	0.285287i
$404$	−4.17872	−	7.23776i	−0.207899	−	0.360092i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−23.8696			−1.18463
$407$	−4.06654	−	30.9949i	−0.201571	−	1.53636i
$408$	5.59861			0.277172
$409$	7.92594	+	4.57604i	0.391913	+	0.226271i	0.682988	−	0.730429i	$-0.260680\pi$
$409$	7.92594	+	4.57604i	0.391913	+	0.226271i	−0.291076	+	0.956700i	$0.594013\pi$
$410$	2.61317	+	4.52615i	0.129055	+	0.223531i
$411$	3.13204	+	5.42485i	0.154492	+	0.267588i
$412$	0.584219	−	0.337299i	0.0287824	−	0.0166175i
$413$		−	51.2850i		−	2.52357i
$414$	3.14760	+	5.45181i	0.154696	+	0.267942i
$415$			4.90002i			0.240533i
$416$	0.393223	−	0.681083i	0.0192794	−	0.0333928i
$417$	1.73759			0.0850902
$418$	−39.4508			−1.92960
$419$	−1.41505	+	2.45094i	−0.0691299	+	0.119736i	−0.898519	−	0.438936i	$-0.855356\pi$
$419$	−1.41505	+	2.45094i	−0.0691299	+	0.119736i	0.829389	+	0.558672i	$0.188689\pi$
$420$	−4.39536	+	2.53766i	−0.214471	+	0.123825i
$421$		−	38.0649i		−	1.85517i	−0.373610	−	0.927586i	$-0.621880\pi$
$421$		−	38.0649i		−	1.85517i	0.373610	−	0.927586i	$-0.378120\pi$
$422$	8.57245	+	4.94931i	0.417301	+	0.240929i
$423$	5.79986	−	10.0457i	0.281999	−	0.488436i
$424$	−6.90297	−	3.98543i	−0.335238	−	0.193550i
$425$	−4.84853	+	2.79930i	−0.235188	+	0.135786i
$426$	12.8102	−	7.39598i	0.620657	−	0.358337i
$427$	29.2562	+	16.8910i	1.41580	+	0.817415i
$428$	−4.05189	+	7.01809i	−0.195856	+	0.339232i
$429$	3.50022	+	2.02085i	0.168992	+	0.0975677i
$430$			3.03010i			0.146125i
$431$	2.51650	−	1.45290i	0.121216	−	0.0699839i	−0.438166	−	0.898894i	$-0.644372\pi$
$431$	2.51650	−	1.45290i	0.121216	−	0.0699839i	0.559382	+	0.828910i	$0.311039\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	36.1643			1.73795			0.868973	−	0.494860i	$-0.164781\pi$
$433$	36.1643			1.73795			0.868973	+	0.494860i	$0.164781\pi$
$434$	42.6775			2.04858
$435$	−2.35153	+	4.07297i	−0.112747	+	0.195284i
$436$			3.34505i			0.160199i
$437$	−24.1624	−	41.8505i	−1.15585	−	2.00198i
$438$		−	2.85481i		−	0.136408i
$439$	19.6714	−	11.3573i	0.938863	−	0.542053i	0.0492595	−	0.998786i	$-0.484314\pi$
$439$	19.6714	−	11.3573i	0.938863	−	0.542053i	0.889604	+	0.456733i	$0.150981\pi$
$440$	2.56960	+	4.45068i	0.122501	+	0.212178i
$441$	−9.37944	−	16.2457i	−0.446640	−	0.773603i
$442$	3.81311	+	2.20150i	0.181371	+	0.104715i
$443$	10.1398			0.481755			0.240878	−	0.970555i	$-0.422565\pi$
$443$	10.1398			0.481755			0.240878	+	0.970555i	$0.422565\pi$
$444$	−5.61870	−	2.33027i	−0.266652	−	0.110590i
$445$	−2.50169			−0.118591
$446$	5.06418	+	2.92380i	0.239796	+	0.138446i
$447$	−6.32893	−	10.9620i	−0.299348	−	0.518487i
$448$	2.53766	+	4.39536i	0.119893	+	0.207661i
$449$	21.5256	−	12.4278i	1.01585	−	0.586504i	0.102954	−	0.994686i	$-0.467171\pi$
$449$	21.5256	−	12.4278i	1.01585	−	0.586504i	0.912900	+	0.408182i	$0.133837\pi$
$450$			1.00000i			0.0471405i
$451$	13.4296	+	23.2608i	0.632376	+	1.09531i
$452$		−	2.21825i		−	0.104338i
$453$	−6.87125	+	11.9014i	−0.322840	+	0.559174i
$454$	18.5000			0.868249
$455$	−3.99147			−0.187123
$456$	−3.83822	+	6.64800i	−0.179741	+	0.311321i
$457$	−14.8170	+	8.55460i	−0.693110	+	0.400167i	−0.804776	−	0.593579i	$-0.797715\pi$
$457$	−14.8170	+	8.55460i	−0.693110	+	0.400167i	0.111666	+	0.993746i	$0.464381\pi$
$458$		−	6.06849i		−	0.283562i
$459$	4.84853	+	2.79930i	0.226310	+	0.130660i
$460$	−3.14760	+	5.45181i	−0.146758	+	0.254192i
$461$	8.92504	+	5.15288i	0.415681	+	0.239993i	0.693228	−	0.720719i	$-0.256188\pi$
$461$	8.92504	+	5.15288i	0.415681	+	0.239993i	−0.277547	+	0.960712i	$0.589521\pi$
$462$	−22.5886	+	13.0415i	−1.05092	+	0.606748i
$463$	−13.3964	+	7.73444i	−0.622585	+	0.359450i	−0.777875	−	0.628419i	$-0.783702\pi$
$463$	−13.3964	+	7.73444i	−0.622585	+	0.359450i	0.155290	+	0.987869i	$0.450369\pi$
$464$	4.07297	+	2.35153i	0.189083	+	0.109167i
$465$	4.20441	−	7.28225i	0.194975	−	0.337706i
$466$	5.67003	+	3.27359i	0.262659	+	0.151646i
$467$		−	15.8106i		−	0.731630i	−0.930688	−	0.365815i	$-0.880790\pi$
$467$		−	15.8106i		−	0.731630i	0.930688	−	0.365815i	$-0.119210\pi$
$468$	0.681083	−	0.393223i	0.0314831	−	0.0181768i
$469$	−1.65934	+	2.87406i	−0.0766211	+	0.132712i
$470$	11.5997			0.535055
$471$	1.92397			0.0886520
$472$	−5.05239	+	8.75099i	−0.232555	+	0.402797i
$473$			15.5723i			0.716016i
$474$	6.11454	+	10.5907i	0.280850	+	0.486447i
$475$		−	7.67645i		−	0.352220i
$476$	−24.6079	+	14.2074i	−1.12790	+	0.651193i
$477$	−3.98543	−	6.90297i	−0.182480	−	0.316065i
$478$	−5.89547	−	10.2113i	−0.269653	−	0.467052i
$479$	22.6684	+	13.0876i	1.03574	+	0.597988i	0.918625	−	0.395130i	$-0.129301\pi$
$479$	22.6684	+	13.0876i	1.03574	+	0.597988i	0.117120	+	0.993118i	$0.462634\pi$
$480$	1.00000			0.0456435
$481$	−2.91049	−	3.79651i	−0.132707	−	0.173106i
$482$	−4.87081			−0.221859
$483$	−27.6697	−	15.9751i	−1.25901	−	0.726892i
$484$	7.70569	+	13.3466i	0.350259	+	0.606666i
$485$	9.06211	+	15.6960i	0.411489	+	0.712720i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$		−	23.4755i		−	1.06378i	−0.846815	−	0.531888i	$-0.821483\pi$
$487$		−	23.4755i		−	1.06378i	0.846815	−	0.531888i	$-0.178517\pi$
$488$	−3.32808	−	5.76440i	−0.150655	−	0.260942i
$489$		−	9.86324i		−	0.446031i
$490$	9.37944	−	16.2457i	0.423720	−	0.733904i
$491$	13.2021			0.595802			0.297901	−	0.954597i	$-0.403713\pi$
$491$	13.2021			0.595802			0.297901	+	0.954597i	$0.403713\pi$
$492$	5.22635			0.235622
$493$	−13.1653	+	22.8030i	−0.592935	+	1.02699i
$494$	−5.22830	+	3.01856i	−0.235232	+	0.135811i
$495$			5.13920i			0.230990i
$496$	−7.28225	−	4.20441i	−0.326983	−	0.188784i
$497$	−37.5370	+	65.0160i	−1.68376	+	2.91636i
$498$	4.24354	+	2.45001i	0.190158	+	0.109788i
$499$	7.08350	−	4.08966i	0.317101	−	0.183078i	−0.332999	−	0.942927i	$-0.608060\pi$
$499$	7.08350	−	4.08966i	0.317101	−	0.183078i	0.650100	+	0.759849i	$0.274727\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−12.1154	−	6.99484i	−0.541277	−	0.312507i
$502$	2.88395	−	4.99515i	0.128717	−	0.222944i
$503$	4.63980	+	2.67879i	0.206878	+	0.119441i	0.599860	−	0.800105i	$-0.295223\pi$
$503$	4.63980	+	2.67879i	0.206878	+	0.119441i	−0.392982	+	0.919546i	$0.628556\pi$
$504$			5.07532i			0.226073i
$505$	7.23776	−	4.17872i	0.322076	−	0.185951i
$506$	−16.1762	+	28.0179i	−0.719118	+	1.24555i
$507$	−12.3815			−0.549882
$508$	−3.48405			−0.154580
$509$	−15.7333	+	27.2509i	−0.697366	+	1.20787i	0.272011	+	0.962294i	$0.412311\pi$
$509$	−15.7333	+	27.2509i	−0.697366	+	1.20787i	−0.969377	+	0.245579i	$0.921022\pi$
$510$			5.59861i			0.247910i
$511$	7.24453	+	12.5479i	0.320479	+	0.555086i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.64800	+	3.83822i	−0.293516	+	0.169462i
$514$	2.39075	+	4.14091i	0.105452	+	0.182647i
$515$	0.337299	+	0.584219i	0.0148632	+	0.0257438i
$516$	2.62415	+	1.51505i	0.115522	+	0.0666965i
$517$	59.6133			2.62179
$518$	30.6096	−	4.01599i	1.34491	−	0.176452i
$519$	14.8158			0.650343
$520$	0.681083	+	0.393223i	0.0298675	+	0.0172440i
$521$	7.10379	+	12.3041i	0.311223	+	0.539054i	0.978627	−	0.205642i	$-0.0659281\pi$
$521$	7.10379	+	12.3041i	0.311223	+	0.539054i	−0.667405	+	0.744695i	$0.732595\pi$
$522$	2.35153	+	4.07297i	0.102924	+	0.178269i
$523$	−11.2873	+	6.51673i	−0.493559	+	0.284957i	−0.726050	−	0.687642i	$-0.758646\pi$
$523$	−11.2873	+	6.51673i	−0.493559	+	0.284957i	0.232491	+	0.972599i	$0.425312\pi$
$524$			3.83636i			0.167592i
$525$	−2.53766	−	4.39536i	−0.110753	−	0.191829i
$526$		−	5.88106i		−	0.256427i
$527$	23.5388	−	40.7705i	1.02537	−	1.77599i
$528$	5.13920			0.223655
$529$	−16.6297			−0.723028
$530$	3.98543	−	6.90297i	0.173116	−	0.299846i
$531$	−8.75099	+	5.05239i	−0.379761	+	0.219255i
$532$		−	38.9604i		−	1.68915i
$533$	3.55958	+	2.05512i	0.154182	+	0.0890172i
$534$	−1.25084	+	2.16653i	−0.0541293	+	0.0937548i
$535$	−7.01809	−	4.05189i	−0.303418	−	0.175179i
$536$	0.566281	−	0.326942i	0.0244596	−	0.0141218i
$537$	−2.57104	+	1.48439i	−0.110949	+	0.0640563i
$538$	11.8889	+	6.86407i	0.512568	+	0.295931i
$539$	48.2028	−	83.4897i	2.07624	−	3.59616i
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$		−	7.25945i		−	0.312108i	−0.987749	−	0.156054i	$-0.950123\pi$
$541$		−	7.25945i		−	0.312108i	0.987749	−	0.156054i	$-0.0498774\pi$
$542$	−17.6311	+	10.1793i	−0.757319	+	0.437238i
$543$	0.0806879	−	0.139755i	0.00346265	−	0.00599748i
$544$	5.59861			0.240038
$545$	−3.34505			−0.143286
$546$	−1.99573	+	3.45671i	−0.0854095	+	0.147934i
$547$			16.3085i			0.697301i	0.937253	+	0.348650i	$0.113360\pi$
$547$			16.3085i			0.697301i	−0.937253	+	0.348650i	$0.886640\pi$
$548$	3.13204	+	5.42485i	0.133794	+	0.231738i
$549$		−	6.65615i		−	0.284078i
$550$	−4.45068	+	2.56960i	−0.189778	+	0.109568i
$551$	−18.0514	−	31.2660i	−0.769016	−	1.33197i
$552$	3.14760	+	5.45181i	0.133971	+	0.232044i
$553$	−53.7512	−	31.0333i	−2.28573	−	1.31967i
$554$	−5.87870			−0.249762
$555$	2.33027	−	5.61870i	0.0989145	−	0.238501i
$556$	1.73759			0.0736903
$557$	−34.4569	−	19.8937i	−1.45998	−	0.842922i	−0.460974	−	0.887414i	$-0.652500\pi$
$557$	−34.4569	−	19.8937i	−1.45998	−	0.842922i	−0.999010	+	0.0444914i	$0.985833\pi$
$558$	−4.20441	−	7.28225i	−0.177987	−	0.308282i
$559$	1.19151	+	2.06375i	0.0503954	+	0.0872874i
$560$	−4.39536	+	2.53766i	−0.185738	+	0.107236i
$561$			28.7724i			1.21477i
$562$	1.14068	+	1.97571i	0.0481165	+	0.0833402i
$563$		−	4.71024i		−	0.198513i	−0.995062	−	0.0992565i	$-0.968354\pi$
$563$		−	4.71024i		−	0.198513i	0.995062	−	0.0992565i	$-0.0316464\pi$
$564$	5.79986	−	10.0457i	0.244218	−	0.422998i
$565$	2.21825			0.0933225
$566$	31.7129			1.33299
$567$	−2.53766	+	4.39536i	−0.106572	+	0.184588i
$568$	12.8102	−	7.39598i	0.537505	−	0.310329i
$569$			0.0439038i			0.00184054i	1.00000		0.000920272i	$0.000292932\pi$
$569$			0.0439038i			0.00184054i	−1.00000		0.000920272i	$0.999707\pi$
$570$	−6.64800	−	3.83822i	−0.278454	−	0.160766i
$571$	12.9136	−	22.3670i	0.540418	−	0.936031i	−0.458462	−	0.888714i	$-0.651600\pi$
$571$	12.9136	−	22.3670i	0.540418	−	0.936031i	0.998880	−	0.0473171i	$-0.0150671\pi$
$572$	3.50022	+	2.02085i	0.146352	+	0.0844961i
$573$	2.78813	−	1.60973i	0.116476	−	0.0672474i
$574$	−22.9717	+	13.2627i	−0.958819	+	0.553574i
$575$	−5.45181	−	3.14760i	−0.227356	−	0.131264i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	12.0167	+	6.93782i	0.500260	+	0.288825i	0.728821	−	0.684704i	$-0.240069\pi$
$577$	12.0167	+	6.93782i	0.500260	+	0.288825i	−0.228561	+	0.973530i	$0.573402\pi$
$578$			14.3444i			0.596648i
$579$	4.11753	−	2.37725i	0.171119	−	0.0987953i
$580$	−2.35153	+	4.07297i	−0.0976421	+	0.169121i
$581$	−24.8692			−1.03175
$582$	18.1242			0.751273
$583$	20.4819	−	35.4757i	0.848275	−	1.46926i
$584$		−	2.85481i		−	0.118133i
$585$	0.393223	+	0.681083i	0.0162578	+	0.0281593i
$586$		−	3.86969i		−	0.159855i
$587$	29.1389	−	16.8234i	1.20269	−	0.694374i	0.241539	−	0.970391i	$-0.422348\pi$
$587$	29.1389	−	16.8234i	1.20269	−	0.694374i	0.961153	+	0.276017i	$0.0890145\pi$
$588$	−9.37944	−	16.2457i	−0.386802	−	0.669960i
$589$	32.2749	+	55.9018i	1.32987	+	2.30340i
$590$	−8.75099	−	5.05239i	−0.360273	−	0.208003i
$591$	19.5630			0.804715
$592$	−5.61870	−	2.33027i	−0.230927	−	0.0957736i
$593$	−12.6277			−0.518558			−0.259279	−	0.965802i	$-0.583485\pi$
$593$	−12.6277			−0.518558			−0.259279	+	0.965802i	$0.583485\pi$
$594$	4.45068	+	2.56960i	0.182614	+	0.105432i
$595$	−14.2074	−	24.6079i	−0.582445	−	1.00882i
$596$	−6.32893	−	10.9620i	−0.259243	−	0.449023i
$597$	−1.27785	+	0.737768i	−0.0522990	+	0.0301949i
$598$			4.95085i			0.202455i
$599$	−23.1405	−	40.0806i	−0.945497	−	1.63765i	−0.754753	−	0.656009i	$-0.772243\pi$
$599$	−23.1405	−	40.0806i	−0.945497	−	1.63765i	−0.190744	−	0.981640i	$-0.561090\pi$
$600$			1.00000i			0.0408248i
$601$	−5.10759	+	8.84661i	−0.208343	+	0.360861i	−0.951193	−	0.308598i	$-0.900140\pi$
$601$	−5.10759	+	8.84661i	−0.208343	+	0.360861i	0.742850	+	0.669458i	$0.233474\pi$
$602$	−15.3788			−0.626791
$603$	0.653885			0.0266282
$604$	−6.87125	+	11.9014i	−0.279587	+	0.484259i
$605$	−13.3466	+	7.70569i	−0.542618	+	0.313281i
$606$		−	8.35745i		−	0.339498i
$607$	−11.3087	−	6.52908i	−0.459006	−	0.265007i	0.252620	−	0.967566i	$-0.418708\pi$
$607$	−11.3087	−	6.52908i	−0.459006	−	0.265007i	−0.711626	+	0.702558i	$0.752041\pi$
$608$	−3.83822	+	6.64800i	−0.155661	+	0.269612i
$609$	−20.6716	−	11.9348i	−0.837657	−	0.483622i
$610$	5.76440	−	3.32808i	0.233394	−	0.134750i
$611$	7.90037	−	4.56128i	0.319615	−	0.184530i
$612$	4.84853	+	2.79930i	0.195990	+	0.113155i
$613$	−5.98714	+	10.3700i	−0.241818	+	0.418842i	−0.961232	−	0.275740i	$-0.911077\pi$
$613$	−5.98714	+	10.3700i	−0.241818	+	0.418842i	0.719414	+	0.694582i	$0.244411\pi$
$614$	7.42754	+	4.28829i	0.299751	+	0.173061i
$615$			5.22635i			0.210747i
$616$	−22.5886	+	13.0415i	−0.910121	+	0.525459i
$617$	−8.60935	+	14.9118i	−0.346599	+	0.600328i	−0.985643	−	0.168843i	$-0.945997\pi$
$617$	−8.60935	+	14.9118i	−0.346599	+	0.600328i	0.639044	+	0.769171i	$0.279330\pi$
$618$	0.674598			0.0271363
$619$	25.2303			1.01409			0.507045	−	0.861919i	$-0.330738\pi$
$619$	25.2303			1.01409			0.507045	+	0.861919i	$0.330738\pi$
$620$	4.20441	−	7.28225i	0.168853	−	0.292462i
$621$			6.29521i			0.252618i
$622$	5.74699	+	9.95407i	0.230433	+	0.399122i
$623$		−	12.6969i		−	0.508690i
$624$	0.681083	−	0.393223i	0.0272651	−	0.0157415i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−16.8343	−	29.1579i	−0.672836	−	1.16539i
$627$	−34.1654	−	19.7254i	−1.36443	−	0.787757i
$628$	1.92397			0.0767749
$629$	13.0463	−	31.4569i	0.520189	−	1.25427i
$630$	−5.07532			−0.202206
$631$	−39.3198	−	22.7013i	−1.56530	−	0.903725i	−0.996706	−	0.0811054i	$-0.974155\pi$
$631$	−39.3198	−	22.7013i	−1.56530	−	0.903725i	−0.568592	−	0.822620i	$-0.692512\pi$
$632$	6.11454	+	10.5907i	0.243223	+	0.421275i
$633$	4.94931	+	8.57245i	0.196717	+	0.340724i
$634$	−27.3433	+	15.7867i	−1.08594	+	0.626969i
$635$		−	3.48405i		−	0.138260i
$636$	−3.98543	−	6.90297i	−0.158033	−	0.273721i
$637$		−	14.7529i		−	0.584530i
$638$	−12.0850	+	20.9318i	−0.478449	+	0.828699i
$639$	14.7920			0.585161
$640$	1.00000			0.0395285
$641$	13.9932	−	24.2370i	0.552699	−	0.957303i	−0.445379	−	0.895342i	$-0.646931\pi$
$641$	13.9932	−	24.2370i	0.552699	−	0.957303i	0.998079	−	0.0619613i	$-0.0197355\pi$
$642$	−7.01809	+	4.05189i	−0.276982	+	0.159915i
$643$			32.4766i			1.28075i	0.768061	+	0.640377i	$0.221222\pi$
$643$			32.4766i			1.28075i	−0.768061	+	0.640377i	$0.778778\pi$
$644$	−27.6697	−	15.9751i	−1.09034	−	0.629507i
$645$	−1.51505	+	2.62415i	−0.0596551	+	0.103326i
$646$	−37.2195	−	21.4887i	−1.46438	−	0.845462i
$647$	−2.02125	+	1.16697i	−0.0794635	+	0.0458783i	−0.539205	−	0.842174i	$-0.681275\pi$
$647$	−2.02125	+	1.16697i	−0.0794635	+	0.0458783i	0.459742	+	0.888053i	$0.347942\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−44.9731	−	25.9652i	−1.76535	−	1.01922i
$650$	−0.393223	+	0.681083i	−0.0154235	+	0.0267143i
$651$	36.9598	+	21.3387i	1.44857	+	0.836331i
$652$		−	9.86324i		−	0.386274i
$653$	34.7721	−	20.0757i	1.36074	−	0.785622i	0.371015	−	0.928627i	$-0.379010\pi$
$653$	34.7721	−	20.0757i	1.36074	−	0.785622i	0.989722	+	0.143005i	$0.0456764\pi$
$654$	−1.67252	+	2.89690i	−0.0654009	+	0.113278i
$655$	−3.83636			−0.149899
$656$	5.22635			0.204055
$657$	1.42740	−	2.47233i	0.0556883	−	0.0964549i
$658$			58.8723i			2.29508i
$659$	−7.70650	−	13.3481i	−0.300203	−	0.519966i	0.675979	−	0.736921i	$-0.263721\pi$
$659$	−7.70650	−	13.3481i	−0.300203	−	0.519966i	−0.976182	+	0.216955i	$0.930388\pi$
$660$			5.13920i			0.200043i
$661$	−9.31655	+	5.37891i	−0.362372	+	0.209215i	−0.670121	−	0.742252i	$-0.733758\pi$
$661$	−9.31655	+	5.37891i	−0.362372	+	0.209215i	0.307749	+	0.951468i	$0.400424\pi$
$662$	−9.91508	−	17.1734i	−0.385360	−	0.667464i
$663$	2.20150	+	3.81311i	0.0854993	+	0.148089i
$664$	4.24354	+	2.45001i	0.164681	+	0.0950789i
$665$	38.9604			1.51082
$666$	−3.70080	−	4.82743i	−0.143403	−	0.187059i
$667$	−29.6068			−1.14638
$668$	−12.1154	−	6.99484i	−0.468760	−	0.270639i
$669$	2.92380	+	5.06418i	0.113041	+	0.195792i
$670$	0.326942	+	0.566281i	0.0126309	+	0.0218773i
$671$	29.6244	−	17.1036i	1.14364	−	0.660279i
$672$			5.07532i			0.195785i
$673$	−0.430243	−	0.745202i	−0.0165846	−	0.0287254i	0.857614	−	0.514294i	$-0.171946\pi$
$673$	−0.430243	−	0.745202i	−0.0165846	−	0.0287254i	−0.874199	+	0.485569i	$0.838613\pi$
$674$		−	28.6996i		−	1.10547i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−12.3815			−0.476212
$677$	40.3203			1.54963			0.774817	−	0.632185i	$-0.217842\pi$
$677$	40.3203			1.54963			0.774817	+	0.632185i	$0.217842\pi$
$678$	1.10912	−	1.92106i	0.0425957	−	0.0737779i
$679$	−79.6624	+	45.9931i	−3.05716	+	1.76505i
$680$			5.59861i			0.214697i
$681$	16.0215	+	9.25001i	0.613945	+	0.354461i
$682$	21.6073	−	37.4250i	0.827387	−	1.43308i
$683$	−20.6494	−	11.9219i	−0.790127	−	0.456180i	0.0498806	−	0.998755i	$-0.484116\pi$
$683$	−20.6494	−	11.9219i	−0.790127	−	0.456180i	−0.840007	+	0.542575i	$0.817449\pi$
$684$	−6.64800	+	3.83822i	−0.254193	+	0.146758i
$685$	−5.42485	+	3.13204i	−0.207273	+	0.119669i
$686$	51.6845	+	29.8400i	1.97332	+	1.13930i
$687$	3.03424	−	5.25546i	0.115764	−	0.200508i
$688$	2.62415	+	1.51505i	0.100045	+	0.0577608i
$689$		−	6.26866i		−	0.238817i
$690$	−5.45181	+	3.14760i	−0.207547	+	0.119827i
$691$	8.14952	−	14.1154i	0.310022	−	0.536974i	−0.668345	−	0.743852i	$-0.732997\pi$
$691$	8.14952	−	14.1154i	0.310022	−	0.536974i	0.978367	+	0.206877i	$0.0663301\pi$
$692$	14.8158			0.563213
$693$	−26.0831			−0.990815
$694$	−6.58268	+	11.4015i	−0.249875	+	0.432796i
$695$			1.73759i			0.0659106i
$696$	2.35153	+	4.07297i	0.0891346	+	0.154386i
$697$			29.2603i			1.10831i
$698$	0.847597	−	0.489360i	0.0320820	−	0.0185226i
$699$	3.27359	+	5.67003i	0.123819	+	0.214460i
$700$	−2.53766	−	4.39536i	−0.0959145	−	0.166129i
$701$	−12.4274	−	7.17498i	−0.469377	−	0.270995i	0.246602	−	0.969117i	$-0.420686\pi$
$701$	−12.4274	−	7.17498i	−0.469377	−	0.270995i	−0.715979	+	0.698122i	$0.754019\pi$
$702$	0.786447			0.0296825
$703$	28.4090	+	37.0575i	1.07147	+	1.39765i
$704$	5.13920			0.193691
$705$	10.0457	+	5.79986i	0.378341	+	0.218435i
$706$	2.67116	+	4.62659i	0.100531	+	0.174124i
$707$	21.2084	+	36.7340i	0.797623	+	1.38152i
$708$	−8.75099	+	5.05239i	−0.328882	+	0.189880i
$709$		−	14.7322i		−	0.553281i	−0.960974	−	0.276640i	$-0.910779\pi$
$709$		−	14.7322i		−	0.553281i	0.960974	−	0.276640i	$-0.0892211\pi$
$710$	7.39598	+	12.8102i	0.277566	+	0.480759i
$711$			12.2291i			0.458626i
$712$	−1.25084	+	2.16653i	−0.0468774	+	0.0811940i
$713$	52.9353			1.98244
$714$	−28.4147			−1.06339
$715$	−2.02085	+	3.50022i	−0.0755756	+	0.130901i
$716$	−2.57104	+	1.48439i	−0.0960844	+	0.0554744i
$717$		−	11.7909i		−	0.440341i
$718$	7.15380	+	4.13025i	0.266977	+	0.154139i
$719$	−5.80711	+	10.0582i	−0.216569	+	0.375108i	−0.953757	−	0.300580i	$-0.902820\pi$
$719$	−5.80711	+	10.0582i	−0.216569	+	0.375108i	0.737188	+	0.675688i	$0.236153\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	−2.96510	+	1.71190i	−0.110426	+	0.0637545i
$722$	34.5785	−	19.9639i	1.28688	−	0.742981i
$723$	−4.21824	−	2.43540i	−0.156878	−	0.0905737i
$724$	0.0806879	−	0.139755i	0.00299874	−	0.00519397i
$725$	−4.07297	−	2.35153i	−0.151266	−	0.0873337i
$726$			15.4114i			0.571970i
$727$	23.3931	−	13.5060i	0.867603	−	0.500911i	0.00105199	−	0.999999i	$-0.499665\pi$
$727$	23.3931	−	13.5060i	0.867603	−	0.500911i	0.866551	+	0.499089i	$0.166332\pi$
$728$	−1.99573	+	3.45671i	−0.0739668	+	0.128114i
$729$	1.00000			0.0370370
$730$	2.85481			0.105661
$731$	−8.48218	+	14.6916i	−0.313725	+	0.543387i
$732$		−	6.65615i		−	0.246018i
$733$	11.4746	+	19.8746i	0.423825	+	0.734086i	0.996310	−	0.0858291i	$-0.0273539\pi$
$733$	11.4746	+	19.8746i	0.423825	+	0.734086i	−0.572485	+	0.819915i	$0.694021\pi$
$734$		−	20.7722i		−	0.766716i
$735$	16.2457	−	9.37944i	0.599230	−	0.345966i
$736$	3.14760	+	5.45181i	0.116022	+	0.200956i
$737$	1.68022	+	2.91023i	0.0618918	+	0.107200i
$738$	4.52615	+	2.61317i	0.166610	+	0.0961923i
$739$	−42.8997			−1.57809			−0.789045	−	0.614336i	$-0.789424\pi$
$739$	−42.8997			−1.57809			−0.789045	+	0.614336i	$0.789424\pi$
$740$	2.33027	−	5.61870i	0.0856625	−	0.206548i
$741$	−6.03712			−0.221779
$742$	35.0348	+	20.2273i	1.28617	+	0.742569i
$743$	−16.3307	−	28.2855i	−0.599114	−	1.03770i	−0.992952	−	0.118516i	$-0.962186\pi$
$743$	−16.3307	−	28.2855i	−0.599114	−	1.03770i	0.393838	−	0.919180i	$-0.371147\pi$
$744$	−4.20441	−	7.28225i	−0.154141	−	0.266980i
$745$	10.9620	−	6.32893i	0.401618	−	0.231874i
$746$		−	34.1180i		−	1.24915i
$747$	2.45001	+	4.24354i	0.0896412	+	0.155263i
$748$			28.7724i			1.05202i
$749$	20.5647	−	35.6190i	0.751416	−	1.30149i
$750$	−1.00000			−0.0365148
$751$	10.4755			0.382257			0.191128	−	0.981565i	$-0.438785\pi$
$751$	10.4755			0.382257			0.191128	+	0.981565i	$0.438785\pi$
$752$	5.79986	−	10.0457i	0.211499	−	0.366327i
$753$	4.99515	−	2.88395i	0.182033	−	0.105097i
$754$			3.69871i			0.134699i
$755$	−11.9014	−	6.87125i	−0.433135	−	0.250070i
$756$	−2.53766	+	4.39536i	−0.0922938	+	0.159858i
$757$	−36.9271	−	21.3199i	−1.34214	−	0.774884i	−0.355018	−	0.934859i	$-0.615525\pi$
$757$	−36.9271	−	21.3199i	−1.34214	−	0.774884i	−0.987121	+	0.159975i	$0.948859\pi$
$758$	7.08954	−	4.09315i	0.257504	−	0.148670i
$759$	−28.0179	+	16.1762i	−1.01699	+	0.587158i
$760$	−6.64800	−	3.83822i	−0.241148	−	0.139227i
$761$	4.36731	−	7.56440i	0.158315	−	0.274209i	−0.775946	−	0.630799i	$-0.782727\pi$
$761$	4.36731	−	7.56440i	0.158315	−	0.274209i	0.934261	+	0.356590i	$0.116061\pi$
$762$	−3.01728	−	1.74203i	−0.109304	−	0.0631070i
$763$		−	16.9772i		−	0.614616i
$764$	2.78813	−	1.60973i	0.100871	−	0.0582380i
$765$	−2.79930	+	4.84853i	−0.101209	+	0.175299i
$766$	17.6573			0.637985
$767$	−7.94687			−0.286945
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$			51.0429i			1.84065i	0.391150	+	0.920327i	$0.372077\pi$
$769$			51.0429i			1.84065i	−0.391150	+	0.920327i	$0.627923\pi$
$770$	−13.0415	−	22.5886i	−0.469985	−	0.814037i
$771$			4.78151i			0.172202i
$772$	4.11753	−	2.37725i	0.148193	−	0.0855593i
$773$	−8.80103	−	15.2438i	−0.316551	−	0.548282i	0.663215	−	0.748429i	$-0.269192\pi$
$773$	−8.80103	−	15.2438i	−0.316551	−	0.548282i	−0.979766	+	0.200147i	$0.935858\pi$
$774$	1.51505	+	2.62415i	0.0544574	+	0.0943230i
$775$	7.28225	+	4.20441i	0.261586	+	0.151027i
$776$	18.1242			0.650621
$777$	28.5167	+	11.8269i	1.02303	+	0.424287i
$778$	−27.8368			−0.997998
$779$	−34.7448	−	20.0599i	−1.24486	−	0.718720i
$780$	0.393223	+	0.681083i	0.0140797	+	0.0243867i
$781$	38.0094	+	65.8343i	1.36008	+	2.35574i
$782$	−30.5225	+	17.6222i	−1.09148	+	0.630168i
$783$			4.70306i			0.168074i
$784$	−9.37944	−	16.2457i	−0.334980	−	0.580202i
$785$			1.92397i			0.0686696i
$786$	−1.91818	+	3.32238i	−0.0684192	+	0.118506i
$787$	11.4068			0.406608			0.203304	−	0.979116i	$-0.434832\pi$
$787$	11.4068			0.406608			0.203304	+	0.979116i	$0.434832\pi$
$788$	19.5630			0.696903
$789$	2.94053	−	5.09315i	0.104686	−	0.181321i
$790$	−10.5907	+	6.11454i	−0.376800	+	0.217546i
$791$			11.2583i			0.400300i
$792$	4.45068	+	2.56960i	0.158148	+	0.0913068i
$793$	2.61735	−	4.53339i	0.0929449	−	0.160985i
$794$	−26.6370	−	15.3789i	−0.945312	−	0.545776i
$795$	6.90297	−	3.98543i	0.244823	−	0.141349i
$796$	−1.27785	+	0.737768i	−0.0452923	+	0.0261495i
$797$	33.1767	+	19.1546i	1.17518	+	0.678490i	0.954895	−	0.296945i	$-0.0959678\pi$
$797$	33.1767	+	19.1546i	1.17518	+	0.678490i	0.220285	+	0.975435i	$0.429301\pi$
$798$	19.4802	−	33.7407i	0.689592	−	1.19441i
$799$	56.2417	+	32.4711i	1.98969	+	1.14875i
$800$			1.00000i			0.0353553i
$801$	−2.16653	+	1.25084i	−0.0765504	+	0.0441964i
$802$	−19.3560	+	33.5256i	−0.683485	+	1.18383i
$803$	14.6714			0.517743
$804$	0.653885			0.0230607
$805$	15.9751	−	27.6697i	0.563048	−	0.975228i
$806$		−	6.61309i		−	0.232936i
$807$	6.86407	+	11.8889i	0.241627	+	0.418510i
$808$		−	8.35745i		−	0.294014i
$809$	−28.5069	+	16.4585i	−1.00225	+	0.578649i	−0.908913	−	0.416985i	$-0.863087\pi$
$809$	−28.5069	+	16.4585i	−1.00225	+	0.578649i	−0.0933366	+	0.995635i	$0.529753\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	−17.1554	−	29.7140i	−0.602407	−	1.04340i	−0.992456	−	0.122605i	$-0.960875\pi$
$811$	−17.1554	−	29.7140i	−0.602407	−	1.04340i	0.390049	−	0.920794i	$-0.372458\pi$
$812$	−20.6716	−	11.9348i	−0.725432	−	0.418829i
$813$	−20.3586			−0.714007
$814$	11.9757	−	28.8756i	0.419749	−	1.01209i
$815$	9.86324			0.345494
$816$	4.84853	+	2.79930i	0.169733	+	0.0979952i
$817$	−11.6302	−	20.1441i	−0.406890	−	0.704754i
$818$	4.57604	+	7.92594i	0.159998	+	0.277124i
$819$	−3.45671	+	1.99573i	−0.120787	+	0.0697366i
$820$			5.22635i			0.182512i
$821$	−6.74301	−	11.6792i	−0.235333	−	0.407608i	0.724037	−	0.689761i	$-0.242285\pi$
$821$	−6.74301	−	11.6792i	−0.235333	−	0.407608i	−0.959369	+	0.282154i	$0.908951\pi$
$822$			6.26408i			0.218485i
$823$	−19.3805	+	33.5679i	−0.675560	+	1.17011i	0.300744	+	0.953705i	$0.402765\pi$
$823$	−19.3805	+	33.5679i	−0.675560	+	1.17011i	−0.976305	+	0.216400i	$0.930568\pi$
$824$	0.674598			0.0235007
$825$	−5.13920			−0.178924
$826$	25.6425	−	44.4141i	0.892216	−	1.54536i
$827$	−39.1664	+	22.6127i	−1.36195	+	0.786321i	−0.989883	−	0.141885i	$-0.954684\pi$
$827$	−39.1664	+	22.6127i	−1.36195	+	0.786321i	−0.372065	+	0.928207i	$0.621350\pi$
$828$			6.29521i			0.218774i
$829$	−7.89212	−	4.55652i	−0.274105	−	0.158254i	0.356647	−	0.934239i	$-0.383920\pi$
$829$	−7.89212	−	4.55652i	−0.274105	−	0.158254i	−0.630751	+	0.775985i	$0.717253\pi$
$830$	−2.45001	+	4.24354i	−0.0850411	+	0.147296i
$831$	−5.09110	−	2.93935i	−0.176608	−	0.101965i
$832$	0.681083	−	0.393223i	0.0236123	−	0.0136326i
$833$	90.9531	−	52.5118i	3.15134	−	1.81943i
$834$	1.50480	+	0.868795i	0.0521069	+	0.0300839i
$835$	6.99484	−	12.1154i	0.242067	−	0.419272i
$836$	−34.1654	−	19.7254i	−1.18164	−	0.682217i
$837$		−	8.40882i		−	0.290651i
$838$	−2.45094	+	1.41505i	−0.0846664	+	0.0488822i
$839$	−2.26885	+	3.92977i	−0.0783295	+	0.135671i	−0.902529	−	0.430628i	$-0.858292\pi$
$839$	−2.26885	+	3.92977i	−0.0783295	+	0.135671i	0.824200	+	0.566299i	$0.191625\pi$
$840$	−5.07532			−0.175115
$841$	6.88119			0.237282
$842$	19.0325	−	32.9652i	0.655902	−	1.13606i
$843$			2.28135i			0.0785739i
$844$	4.94931	+	8.57245i	0.170362	+	0.295076i
$845$		−	12.3815i		−	0.425937i
$846$	10.0457	−	5.79986i	0.345377	−	0.199403i
$847$	−39.1088	−	67.7385i	−1.34380	−	2.32752i
$848$	−3.98543	−	6.90297i	−0.136860	−	0.237049i
$849$	27.4642	+	15.8565i	0.942569	+	0.544192i
$850$	−5.59861			−0.192031
$851$	37.9669	−	4.98126i	1.30149	−	0.170755i
$852$	14.7920			0.506764
$853$	0.210746	+	0.121674i	0.00721580	+	0.00416604i	0.503604	−	0.863935i	$-0.332007\pi$
$853$	0.210746	+	0.121674i	0.00721580	+	0.00416604i	−0.496388	+	0.868101i	$0.665341\pi$
$854$	16.8910	+	29.2562i	0.578000	+	1.00113i
$855$	−3.83822	−	6.64800i	−0.131265	−	0.227357i
$856$	−7.01809	+	4.05189i	−0.239873	+	0.138491i
$857$			48.5788i			1.65942i	0.558194	+	0.829711i	$0.311495\pi$
$857$			48.5788i			1.65942i	−0.558194	+	0.829711i	$0.688505\pi$
$858$	2.02085	+	3.50022i	0.0689908	+	0.119496i
$859$			12.9602i			0.442195i	0.975252	+	0.221097i	$0.0709639\pi$
$859$			12.9602i			0.442195i	−0.975252	+	0.221097i	$0.929036\pi$
$860$	−1.51505	+	2.62415i	−0.0516629	+	0.0894827i
$861$	−26.5254			−0.903983
$862$	2.90581			0.0989721
$863$	19.6483	−	34.0318i	0.668835	−	1.15846i	−0.309395	−	0.950934i	$-0.600127\pi$
$863$	19.6483	−	34.0318i	0.668835	−	1.15846i	0.978230	−	0.207523i	$-0.0665401\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$			14.8158i			0.503753i
$866$	31.3192	+	18.0821i	1.06427	+	0.614456i
$867$	−7.17219	+	12.4226i	−0.243580	+	0.421894i
$868$	36.9598	+	21.3387i	1.25450	+	0.724284i
$869$	−54.4277	+	31.4239i	−1.84633	+	1.06598i
$870$	−4.07297	+	2.35153i	−0.138087	+	0.0797244i
$871$	0.445350	+	0.257123i	0.0150901	+	0.00871227i
$872$	−1.67252	+	2.89690i	−0.0566388	+	0.0981013i
$873$	15.6960	+	9.06211i	0.531230	+	0.306706i
$874$		−	48.3248i		−	1.63461i
$875$	4.39536	−	2.53766i	0.148590	−	0.0857886i
$876$	1.42740	−	2.47233i	0.0482275	−	0.0835324i
$877$	−22.0587			−0.744870			−0.372435	−	0.928058i	$-0.621477\pi$
$877$	−22.0587			−0.744870			−0.372435	+	0.928058i	$0.621477\pi$
$878$	22.7145			0.766579
$879$	1.93484	−	3.35125i	0.0652606	−	0.113035i
$880$			5.13920i			0.173242i
$881$	−8.18528	−	14.1773i	−0.275769	−	0.477646i	0.694560	−	0.719435i	$-0.255599\pi$
$881$	−8.18528	−	14.1773i	−0.275769	−	0.477646i	−0.970329	+	0.241789i	$0.922266\pi$
$882$		−	18.7589i		−	0.631644i
$883$	−14.7440	+	8.51245i	−0.496175	+	0.286467i	−0.727133	−	0.686497i	$-0.759148\pi$
$883$	−14.7440	+	8.51245i	−0.496175	+	0.286467i	0.230957	+	0.972964i	$0.425814\pi$
$884$	2.20150	+	3.81311i	0.0740445	+	0.128249i
$885$	−5.05239	−	8.75099i	−0.169834	−	0.294161i
$886$	8.78131	+	5.06989i	0.295014	+	0.170326i
$887$	−44.2741			−1.48658			−0.743289	−	0.668970i	$-0.766735\pi$
$887$	−44.2741			−1.48658			−0.743289	+	0.668970i	$0.766735\pi$
$888$	−3.70080	−	4.82743i	−0.124191	−	0.161998i
$889$	17.6827			0.593058
$890$	−2.16653	−	1.25084i	−0.0726221	−	0.0419284i
$891$	2.56960	+	4.45068i	0.0860848	+	0.149103i
$892$	2.92380	+	5.06418i	0.0978962	+	0.169561i
$893$	−77.1150	+	44.5223i	−2.58055	+	1.48988i
$894$		−	12.6579i		−	0.423342i
$895$	−1.48439	−	2.57104i	−0.0496178	−	0.0859405i
$896$			5.07532i			0.169555i
$897$	−2.47542	+	4.28756i	−0.0826520	+	0.143157i
$898$	24.8556			0.829441
$899$	39.5472			1.31897
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	38.6470	−	22.3129i	1.28752	−	0.743349i
$902$			26.8593i			0.894315i
$903$	−13.3184	−	7.68938i	−0.443208	−	0.255886i
$904$	1.10912	−	1.92106i	0.0368889	−	0.0638935i
$905$	0.139755	+	0.0806879i	0.00464563	+	0.00268216i
$906$	−11.9014	+	6.87125i	−0.395396	+	0.228282i
$907$	18.7038	−	10.7987i	0.621051	−	0.358564i	−0.156227	−	0.987721i	$-0.549933\pi$
$907$	18.7038	−	10.7987i	0.621051	−	0.358564i	0.777278	+	0.629157i	$0.216600\pi$
$908$	16.0215	+	9.25001i	0.531692	+	0.306972i
$909$	4.17872	−	7.23776i	0.138600	−	0.240061i
$910$	−3.45671	−	1.99573i	−0.114589	−	0.0661580i
$911$			35.6304i			1.18049i	0.807225	+	0.590244i	$0.200968\pi$
$911$			35.6304i			1.18049i	−0.807225	+	0.590244i	$0.799032\pi$
$912$	−6.64800	+	3.83822i	−0.220137	+	0.127096i
$913$	−12.5911	+	21.8084i	−0.416704	+	0.721753i
$914$	−17.1092			−0.565922
$915$	6.65615			0.220046
$916$	3.03424	−	5.25546i	0.100254	−	0.173645i
$917$		−	19.4708i		−	0.642981i
$918$	2.79930	+	4.84853i	0.0923908	+	0.160025i
$919$		−	13.5811i		−	0.448000i	−0.974589	−	0.224000i	$-0.928088\pi$
$919$		−	13.5811i		−	0.448000i	0.974589	−	0.224000i	$-0.0719115\pi$
$920$	−5.45181	+	3.14760i	−0.179741	+	0.103773i
$921$	4.28829	+	7.42754i	0.141304	+	0.244746i
$922$	5.15288	+	8.92504i	0.169701	+	0.293931i
$923$	10.0746	+	5.81655i	0.331608	+	0.191454i
$924$	−26.0831			−0.858071
$925$	5.61870	+	2.33027i	0.184742	+	0.0766189i
$926$	−15.4689			−0.508339
$927$	0.584219	+	0.337299i	0.0191883	+	0.0110783i
$928$	2.35153	+	4.07297i	0.0771928	+	0.133702i
$929$	−10.5205	−	18.2221i	−0.345168	−	0.597848i	0.640217	−	0.768194i	$-0.278845\pi$
$929$	−10.5205	−	18.2221i	−0.345168	−	0.597848i	−0.985384	+	0.170347i	$0.945511\pi$
$930$	7.28225	−	4.20441i	0.238795	−	0.137868i
$931$			144.002i			4.71946i
$932$	3.27359	+	5.67003i	0.107230	+	0.185728i
$933$			11.4940i			0.376296i
$934$	7.90532	−	13.6924i	0.258670	−	0.448030i
$935$	−28.7724			−0.940957
$936$	0.786447			0.0257058
$937$	18.1512	−	31.4388i	0.592974	−	1.02706i	−0.400855	−	0.916142i	$-0.631287\pi$
$937$	18.1512	−	31.4388i	0.592974	−	1.02706i	0.993829	−	0.110920i	$-0.0353798\pi$
$938$	−2.87406	+	1.65934i	−0.0938413	+	0.0541793i
$939$		−	33.6687i		−	1.09874i
$940$	10.0457	+	5.79986i	0.327653	+	0.189171i
$941$	−10.6577	+	18.4597i	−0.347431	+	0.601768i	−0.985792	−	0.167969i	$-0.946279\pi$
$941$	−10.6577	+	18.4597i	−0.347431	+	0.601768i	0.638361	+	0.769737i	$0.279613\pi$
$942$	1.66621	+	0.961987i	0.0542881	+	0.0313432i
$943$	−28.4931	+	16.4505i	−0.927862	+	0.535701i
$944$	−8.75099	+	5.05239i	−0.284821	+	0.164441i
$945$	−4.39536	−	2.53766i	−0.142981	−	0.0825501i
$946$	−7.78616	+	13.4860i	−0.253150	+	0.438468i
$947$	−20.8198	−	12.0203i	−0.676552	−	0.390607i	0.122003	−	0.992530i	$-0.461068\pi$
$947$	−20.8198	−	12.0203i	−0.676552	−	0.390607i	−0.798555	+	0.601922i	$0.794402\pi$
$948$			12.2291i			0.397182i
$949$	1.94436	−	1.12258i	0.0631166	−	0.0364404i
$950$	3.83822	−	6.64800i	0.124528	−	0.215690i
$951$	−31.5734			−1.02384
$952$	−28.4147			−0.920926
$953$	−7.29950	+	12.6431i	−0.236454	+	0.409550i	−0.959694	−	0.281046i	$-0.909319\pi$
$953$	−7.29950	+	12.6431i	−0.236454	+	0.409550i	0.723240	+	0.690597i	$0.242652\pi$
$954$		−	7.97086i		−	0.258066i
$955$	1.60973	+	2.78813i	0.0520896	+	0.0902219i
$956$		−	11.7909i		−	0.381346i
$957$	−20.9318	+	12.0850i	−0.676630	+	0.390652i
$958$	13.0876	+	22.6684i	0.422841	+	0.732382i
$959$	−15.8961	−	27.5329i	−0.513312	−	0.889082i
$960$	0.866025	+	0.500000i	0.0279508	+	0.0161374i
$961$	−39.7083			−1.28091
$962$	−0.622298	−	4.74312i	−0.0200637	−	0.152924i
$963$	−8.10379			−0.261141
$964$	−4.21824	−	2.43540i	−0.135860	−	0.0784391i
$965$	2.37725	+	4.11753i	0.0765265	+	0.132548i
$966$	−15.9751	−	27.6697i	−0.513990	−	0.890258i
$967$	40.3655	−	23.3050i	1.29807	−	0.749440i	0.317998	−	0.948091i	$-0.396990\pi$
$967$	40.3655	−	23.3050i	1.29807	−	0.749440i	0.980070	+	0.198652i	$0.0636563\pi$
$968$			15.4114i			0.495340i
$969$	−21.4887	−	37.2195i	−0.690317	−	1.19566i
$970$			18.1242i			0.581933i
$971$	−10.7138	+	18.5569i	−0.343823	+	0.595519i	−0.985139	−	0.171758i	$-0.945055\pi$
$971$	−10.7138	+	18.5569i	−0.343823	+	0.595519i	0.641316	+	0.767277i	$0.278389\pi$
$972$	1.00000			0.0320750
$973$	−8.81883			−0.282719
$974$	11.7377	−	20.3304i	0.376101	−	0.651427i
$975$	−0.681083	+	0.393223i	−0.0218121	+	0.0125932i
$976$		−	6.65615i		−	0.213058i
$977$	−20.1582	−	11.6383i	−0.644917	−	0.372343i	0.141589	−	0.989926i	$-0.454779\pi$
$977$	−20.1582	−	11.6383i	−0.644917	−	0.372343i	−0.786506	+	0.617582i	$0.788112\pi$
$978$	4.93162	−	8.54182i	0.157696	−	0.273137i
$979$	−11.1342	−	6.42834i	−0.355851	−	0.205451i
$980$	16.2457	−	9.37944i	0.518949	−	0.299615i
$981$	−2.89690	+	1.67252i	−0.0924908	+	0.0533996i
$982$	11.4333	+	6.60104i	0.364853	+	0.210648i
$983$	0.163598	−	0.283359i	0.00521795	−	0.00903776i	−0.863405	−	0.504512i	$-0.831672\pi$
$983$	0.163598	−	0.283359i	0.00521795	−	0.00903776i	0.868623	+	0.495474i	$0.165006\pi$
$984$	4.52615	+	2.61317i	0.144288	+	0.0833050i
$985$			19.5630i			0.623329i
$986$	−22.8030	+	13.1653i	−0.726195	+	0.419269i
$987$	−29.4362	+	50.9849i	−0.936963	+	1.62287i
$988$	−6.03712			−0.192066
$989$	−19.0751			−0.606554
$990$	−2.56960	+	4.45068i	−0.0816673	+	0.141452i
$991$		−	50.3850i		−	1.60053i	−0.599645	−	0.800266i	$-0.704692\pi$
$991$		−	50.3850i		−	1.60053i	0.599645	−	0.800266i	$-0.295308\pi$
$992$	−4.20441	−	7.28225i	−0.133490	−	0.231212i
$993$		−	19.8302i		−	0.629291i
$994$	−65.0160	+	37.5370i	−2.06218	+	1.19060i
$995$	−0.737768	−	1.27785i	−0.0233888	−	0.0405106i
$996$	2.45001	+	4.24354i	0.0776316	+	0.134462i
$997$	−24.4112	−	14.0938i	−0.773112	−	0.446356i	0.0608719	−	0.998146i	$-0.480612\pi$
$997$	−24.4112	−	14.0938i	−0.773112	−	0.446356i	−0.833983	+	0.551789i	$0.813945\pi$
$998$	8.17933			0.258912
$999$	−0.791278	−	6.03108i	−0.0250349	−	0.190815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.e.841.5	yes	16
37.11	even	6	inner	1110.2.x.e.751.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.e.751.5	✓	16	37.11	even	6	inner
1110.2.x.e.841.5	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-2.53766 - 4.39536i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-2.53766 - 4.39536i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -5.13920 q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.681083 + 0.393223i) q^{13} -5.07532i q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-4.84853 - 2.79930i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(6.64800 - 3.83822i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(2.53766 - 4.39536i) q^{21} +(-4.45068 - 2.56960i) q^{22} -6.29521i q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -0.786447 q^{26} -1.00000 q^{27} +(2.53766 - 4.39536i) q^{28} -4.70306i q^{29} +(-0.500000 - 0.866025i) q^{30} +8.40882i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.56960 - 4.45068i) q^{33} +(-2.79930 - 4.84853i) q^{34} +(4.39536 + 2.53766i) q^{35} -1.00000 q^{36} +(0.791278 + 6.03108i) q^{37} +7.67645 q^{38} +(-0.681083 - 0.393223i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.61317 - 4.52615i) q^{41} +(4.39536 - 2.53766i) q^{42} -3.03010i q^{43} +(-2.56960 - 4.45068i) q^{44} -1.00000i q^{45} +(3.14760 - 5.45181i) q^{46} -11.5997 q^{47} -1.00000 q^{48} +(-9.37944 + 16.2457i) q^{49} +(0.866025 - 0.500000i) q^{50} -5.59861i q^{51} +(-0.681083 - 0.393223i) q^{52} +(-3.98543 + 6.90297i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(4.45068 - 2.56960i) q^{55} +(4.39536 - 2.53766i) q^{56} +(6.64800 + 3.83822i) q^{57} +(2.35153 - 4.07297i) q^{58} +(8.75099 + 5.05239i) q^{59} -1.00000i q^{60} +(-5.76440 + 3.32808i) q^{61} +(-4.20441 + 7.28225i) q^{62} +5.07532 q^{63} -1.00000 q^{64} +(0.393223 - 0.681083i) q^{65} -5.13920i q^{66} +(-0.326942 - 0.566281i) q^{67} -5.59861i q^{68} +(5.45181 - 3.14760i) q^{69} +(2.53766 + 4.39536i) q^{70} +(-7.39598 - 12.8102i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.85481 q^{73} +(-2.33027 + 5.61870i) q^{74} +1.00000 q^{75} +(6.64800 + 3.83822i) q^{76} +(13.0415 + 22.5886i) q^{77} +(-0.393223 - 0.681083i) q^{78} +(10.5907 - 6.11454i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -5.22635i q^{82} +(2.45001 - 4.24354i) q^{83} +5.07532 q^{84} +5.59861 q^{85} +(1.51505 - 2.62415i) q^{86} +(4.07297 - 2.35153i) q^{87} -5.13920i q^{88} +(2.16653 + 1.25084i) q^{89} +(0.500000 - 0.866025i) q^{90} +(3.45671 + 1.99573i) q^{91} +(5.45181 - 3.14760i) q^{92} +(-7.28225 + 4.20441i) q^{93} +(-10.0457 - 5.79986i) q^{94} +(-3.83822 + 6.64800i) q^{95} +(-0.866025 - 0.500000i) q^{96} -18.1242i q^{97} +(-16.2457 + 9.37944i) q^{98} +(2.56960 - 4.45068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 8 q^{16} - 6 q^{17} - 6 q^{19} + 4 q^{21} + 12 q^{22} + 8 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} - 8 q^{30} - 2 q^{33} + 2 q^{34} + 18 q^{35} - 16 q^{36} - 12 q^{37} + 12 q^{38} - 8 q^{40} + 4 q^{41} + 18 q^{42} - 2 q^{44} + 12 q^{47} - 16 q^{48} - 42 q^{49} - 16 q^{53} - 12 q^{55} + 18 q^{56} - 6 q^{57} + 2 q^{58} + 48 q^{59} - 12 q^{61} - 4 q^{62} + 8 q^{63} - 16 q^{64} + 4 q^{65} + 6 q^{67} - 18 q^{69} + 4 q^{70} - 6 q^{71} - 52 q^{73} - 16 q^{74} + 16 q^{75} - 6 q^{76} + 10 q^{77} - 4 q^{78} + 78 q^{79} - 8 q^{81} + 36 q^{83} + 8 q^{84} - 4 q^{85} - 6 q^{86} + 12 q^{87} + 18 q^{89} + 8 q^{90} - 66 q^{91} - 18 q^{92} - 36 q^{93} + 12 q^{94} - 6 q^{95} - 12 q^{98} + 2 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 8 * q^16 - 6 * q^17 - 6 * q^19 + 4 * q^21 + 12 * q^22 + 8 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 - 8 * q^30 - 2 * q^33 + 2 * q^34 + 18 * q^35 - 16 * q^36 - 12 * q^37 + 12 * q^38 - 8 * q^40 + 4 * q^41 + 18 * q^42 - 2 * q^44 + 12 * q^47 - 16 * q^48 - 42 * q^49 - 16 * q^53 - 12 * q^55 + 18 * q^56 - 6 * q^57 + 2 * q^58 + 48 * q^59 - 12 * q^61 - 4 * q^62 + 8 * q^63 - 16 * q^64 + 4 * q^65 + 6 * q^67 - 18 * q^69 + 4 * q^70 - 6 * q^71 - 52 * q^73 - 16 * q^74 + 16 * q^75 - 6 * q^76 + 10 * q^77 - 4 * q^78 + 78 * q^79 - 8 * q^81 + 36 * q^83 + 8 * q^84 - 4 * q^85 - 6 * q^86 + 12 * q^87 + 18 * q^89 + 8 * q^90 - 66 * q^91 - 18 * q^92 - 36 * q^93 + 12 * q^94 - 6 * q^95 - 12 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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