LMFDB - Embedded newform 187.2.h.a.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(100,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("187.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.h (of order $8$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			100.2
Character	$\chi$	$=$	187.100
Dual form			187.2.h.a.144.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45974 - 1.45974i) q^{2} +(-1.02130 - 2.46565i) q^{3} +2.26167i q^{4} +(-1.65483 + 0.685451i) q^{5} +(-2.10836 + 5.09004i) q^{6} +(-0.400229 - 0.165780i) q^{7} +(0.381975 - 0.381975i) q^{8} +(-2.91503 + 2.91503i) q^{9} +O(q^{10})$	\(q+(-1.45974 - 1.45974i) q^{2} +(-1.02130 - 2.46565i) q^{3} +2.26167i q^{4} +(-1.65483 + 0.685451i) q^{5} +(-2.10836 + 5.09004i) q^{6} +(-0.400229 - 0.165780i) q^{7} +(0.381975 - 0.381975i) q^{8} +(-2.91503 + 2.91503i) q^{9} +(3.41619 + 1.41503i) q^{10} +(-0.382683 + 0.923880i) q^{11} +(5.57649 - 2.30986i) q^{12} -4.97018i q^{13} +(0.342234 + 0.826225i) q^{14} +(3.38016 + 3.38016i) q^{15} +3.40818 q^{16} +(-1.96041 + 3.62723i) q^{17} +8.51035 q^{18} +(0.0504966 + 0.0504966i) q^{19} +(-1.55027 - 3.74268i) q^{20} +1.15613i q^{21} +(1.90724 - 0.790005i) q^{22} +(1.15112 - 2.77906i) q^{23} +(-1.33193 - 0.551703i) q^{24} +(-1.26693 + 1.26693i) q^{25} +(-7.25517 + 7.25517i) q^{26} +(2.76761 + 1.14638i) q^{27} +(0.374941 - 0.905187i) q^{28} +(-7.19936 + 2.98207i) q^{29} -9.86830i q^{30} +(2.29702 + 5.54550i) q^{31} +(-5.73900 - 5.73900i) q^{32} +2.66880 q^{33} +(8.15649 - 2.43312i) q^{34} +0.775944 q^{35} +(-6.59284 - 6.59284i) q^{36} +(-2.62706 - 6.34228i) q^{37} -0.147424i q^{38} +(-12.2547 + 5.07607i) q^{39} +(-0.370277 + 0.893928i) q^{40} +(-7.19622 - 2.98077i) q^{41} +(1.68765 - 1.68765i) q^{42} +(-2.52664 + 2.52664i) q^{43} +(-2.08951 - 0.865505i) q^{44} +(2.82575 - 6.82197i) q^{45} +(-5.73703 + 2.37636i) q^{46} +1.33656i q^{47} +(-3.48079 - 8.40336i) q^{48} +(-4.81705 - 4.81705i) q^{49} +3.69877 q^{50} +(10.9456 + 1.12917i) q^{51} +11.2409 q^{52} +(1.43933 + 1.43933i) q^{53} +(-2.36657 - 5.71341i) q^{54} -1.79117i q^{55} +(-0.216201 + 0.0895536i) q^{56} +(0.0729344 - 0.176079i) q^{57} +(14.8622 + 6.15614i) q^{58} +(5.94972 - 5.94972i) q^{59} +(-7.64482 + 7.64482i) q^{60} +(-6.64758 - 2.75352i) q^{61} +(4.74193 - 11.4480i) q^{62} +(1.64993 - 0.683424i) q^{63} +9.93853i q^{64} +(3.40682 + 8.22479i) q^{65} +(-3.89574 - 3.89574i) q^{66} +8.63417 q^{67} +(-8.20361 - 4.43381i) q^{68} -8.02781 q^{69} +(-1.13267 - 1.13267i) q^{70} +(0.171987 + 0.415214i) q^{71} +2.22694i q^{72} +(-6.55147 + 2.71371i) q^{73} +(-5.42325 + 13.0929i) q^{74} +(4.41771 + 1.82988i) q^{75} +(-0.114207 + 0.114207i) q^{76} +(0.306322 - 0.306322i) q^{77} +(25.2984 + 10.4789i) q^{78} +(-3.49368 + 8.43448i) q^{79} +(-5.63995 + 2.33614i) q^{80} +4.37265i q^{81} +(6.15345 + 14.8557i) q^{82} +(-11.5538 - 11.5538i) q^{83} -2.61480 q^{84} +(0.757847 - 7.34620i) q^{85} +7.37646 q^{86} +(14.7055 + 14.7055i) q^{87} +(0.206723 + 0.499075i) q^{88} -17.2300i q^{89} +(-14.0832 + 5.83344i) q^{90} +(-0.823958 + 1.98921i) q^{91} +(6.28532 + 2.60346i) q^{92} +(11.3273 - 11.3273i) q^{93} +(1.95103 - 1.95103i) q^{94} +(-0.118176 - 0.0489502i) q^{95} +(-8.28908 + 20.0116i) q^{96} +(9.20938 - 3.81465i) q^{97} +14.0633i q^{98} +(-1.57760 - 3.80867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 16 q^{6}+O(q^{10}) $ 56 * q - 16 * q^6	$ 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) $ 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−1.45974	−	1.45974i	−1.03219	−	1.03219i	−0.999464	−	0.0327267i	$-0.989581\pi$
$2$	−1.45974	−	1.45974i	−1.03219	−	1.03219i	−0.0327267	−	0.999464i	$-0.510419\pi$
$3$	−1.02130	−	2.46565i	−0.589650	−	1.42354i	−0.883838	−	0.467794i	$-0.845049\pi$
$3$	−1.02130	−	2.46565i	−0.589650	−	1.42354i	0.294188	−	0.955748i	$-0.404951\pi$
$4$			2.26167i			1.13084i
$5$	−1.65483	+	0.685451i	−0.740061	+	0.306543i	−0.720679	−	0.693269i	$-0.756170\pi$
$5$	−1.65483	+	0.685451i	−0.740061	+	0.306543i	−0.0193818	+	0.999812i	$0.506170\pi$
$6$	−2.10836	+	5.09004i	−0.860735	+	2.07800i
$7$	−0.400229	−	0.165780i	−0.151272	−	0.0626590i	0.305763	−	0.952108i	$-0.401089\pi$
$7$	−0.400229	−	0.165780i	−0.151272	−	0.0626590i	−0.457035	+	0.889449i	$0.651089\pi$
$8$	0.381975	−	0.381975i	0.135049	−	0.135049i
$9$	−2.91503	+	2.91503i	−0.971676	+	0.971676i
$10$	3.41619	+	1.41503i	1.08030	+	0.447473i
$11$	−0.382683	+	0.923880i	−0.115383	+	0.278560i
$11$	−0.382683	+	0.923880i	−0.115383	+	0.278560i
$12$	5.57649	−	2.30986i	1.60979	−	0.666798i
$13$		−	4.97018i		−	1.37848i	−0.724533	−	0.689241i	$-0.757944\pi$
$13$		−	4.97018i		−	1.37848i	0.724533	−	0.689241i	$-0.242056\pi$
$14$	0.342234	+	0.826225i	0.0914658	+	0.220818i
$15$	3.38016	+	3.38016i	0.872754	+	0.872754i
$16$	3.40818			0.852045
$17$	−1.96041	+	3.62723i	−0.475469	+	0.879732i
$17$	−1.96041	+	3.62723i	−0.475469	+	0.879732i
$18$	8.51035			2.00591
$19$	0.0504966	+	0.0504966i	0.0115847	+	0.0115847i	0.712875	−	0.701291i	$-0.247392\pi$
$19$	0.0504966	+	0.0504966i	0.0115847	+	0.0115847i	−0.701291	+	0.712875i	$0.747392\pi$
$20$	−1.55027	−	3.74268i	−0.346650	−	0.836888i
$21$			1.15613i			0.252289i
$22$	1.90724	−	0.790005i	0.406625	−	0.168430i
$23$	1.15112	−	2.77906i	0.240026	−	0.579473i	−0.757259	−	0.653115i	$-0.773462\pi$
$23$	1.15112	−	2.77906i	0.240026	−	0.579473i	0.997285	+	0.0736413i	$0.0234620\pi$
$24$	−1.33193	−	0.551703i	−0.271879	−	0.112616i
$25$	−1.26693	+	1.26693i	−0.253386	+	0.253386i
$26$	−7.25517	+	7.25517i	−1.42286	+	1.42286i
$27$	2.76761	+	1.14638i	0.532628	+	0.220622i
$28$	0.374941	−	0.905187i	0.0708571	−	0.171064i
$29$	−7.19936	+	2.98207i	−1.33689	+	0.553757i	−0.932612	−	0.360880i	$-0.882477\pi$
$29$	−7.19936	+	2.98207i	−1.33689	+	0.553757i	−0.404276	+	0.914637i	$0.632477\pi$
$30$		−	9.86830i		−	1.80170i
$31$	2.29702	+	5.54550i	0.412557	+	0.996002i	0.984449	+	0.175672i	$0.0562099\pi$
$31$	2.29702	+	5.54550i	0.412557	+	0.996002i	−0.571891	+	0.820329i	$0.693790\pi$
$32$	−5.73900	−	5.73900i	−1.01452	−	1.01452i
$33$	2.66880			0.464578
$34$	8.15649	−	2.43312i	1.39883	−	0.417277i
$35$	0.775944			0.131158
$36$	−6.59284	−	6.59284i	−1.09881	−	1.09881i
$37$	−2.62706	−	6.34228i	−0.431886	−	1.04266i	−0.978679	−	0.205396i	$-0.934152\pi$
$37$	−2.62706	−	6.34228i	−0.431886	−	1.04266i	0.546793	−	0.837268i	$-0.315848\pi$
$38$		−	0.147424i		−	0.0239153i
$39$	−12.2547	+	5.07607i	−1.96232	+	0.812822i
$40$	−0.370277	+	0.893928i	−0.0585460	+	0.141342i
$41$	−7.19622	−	2.98077i	−1.12386	−	0.465518i	−0.258171	−	0.966099i	$-0.583120\pi$
$41$	−7.19622	−	2.98077i	−1.12386	−	0.465518i	−0.865690	+	0.500581i	$0.833120\pi$
$42$	1.68765	−	1.68765i	0.260411	−	0.260411i
$43$	−2.52664	+	2.52664i	−0.385309	+	0.385309i	−0.873010	−	0.487702i	$-0.837835\pi$
$43$	−2.52664	+	2.52664i	−0.385309	+	0.385309i	0.487702	+	0.873010i	$0.337835\pi$
$44$	−2.08951	−	0.865505i	−0.315006	−	0.130480i
$45$	2.82575	−	6.82197i	0.421238	−	1.01696i
$46$	−5.73703	+	2.37636i	−0.845880	+	0.350375i
$47$			1.33656i			0.194957i	0.995238	+	0.0974786i	$0.0310778\pi$
$47$			1.33656i			0.194957i	−0.995238	+	0.0974786i	$0.968922\pi$
$48$	−3.48079	−	8.40336i	−0.502408	−	1.21292i
$49$	−4.81705	−	4.81705i	−0.688150	−	0.688150i
$50$	3.69877			0.523085
$51$	10.9456	+	1.12917i	1.53270	+	0.158116i
$52$	11.2409			1.55884
$53$	1.43933	+	1.43933i	0.197707	+	0.197707i	0.799016	−	0.601309i	$-0.205354\pi$
$53$	1.43933	+	1.43933i	0.197707	+	0.197707i	−0.601309	+	0.799016i	$0.705354\pi$
$54$	−2.36657	−	5.71341i	−0.322050	−	0.777497i
$55$		−	1.79117i		−	0.241521i
$56$	−0.216201	+	0.0895536i	−0.0288911	+	0.0119671i
$57$	0.0729344	−	0.176079i	0.00966040	−	0.0233223i
$58$	14.8622	+	6.15614i	1.95151	+	0.808341i
$59$	5.94972	−	5.94972i	0.774588	−	0.774588i	−0.204317	−	0.978905i	$-0.565497\pi$
$59$	5.94972	−	5.94972i	0.774588	−	0.774588i	0.978905	+	0.204317i	$0.0654973\pi$
$60$	−7.64482	+	7.64482i	−0.986942	+	0.986942i
$61$	−6.64758	−	2.75352i	−0.851136	−	0.352552i	−0.0859013	−	0.996304i	$-0.527377\pi$
$61$	−6.64758	−	2.75352i	−0.851136	−	0.352552i	−0.765234	+	0.643752i	$0.777377\pi$
$62$	4.74193	−	11.4480i	0.602226	−	1.45390i
$63$	1.64993	−	0.683424i	0.207872	−	0.0861033i
$64$			9.93853i			1.24232i
$65$	3.40682	+	8.22479i	0.422564	+	1.02016i
$66$	−3.89574	−	3.89574i	−0.479533	−	0.479533i
$67$	8.63417			1.05483			0.527416	−	0.849607i	$-0.323161\pi$
$67$	8.63417			1.05483			0.527416	+	0.849607i	$0.323161\pi$
$68$	−8.20361	−	4.43381i	−0.994834	−	0.537678i
$69$	−8.02781			−0.966435
$70$	−1.13267	−	1.13267i	−0.135381	−	0.135381i
$71$	0.171987	+	0.415214i	0.0204111	+	0.0492768i	0.933757	−	0.357909i	$-0.116510\pi$
$71$	0.171987	+	0.415214i	0.0204111	+	0.0492768i	−0.913345	+	0.407186i	$0.866510\pi$
$72$			2.22694i			0.262447i
$73$	−6.55147	+	2.71371i	−0.766792	+	0.317616i	−0.731572	−	0.681764i	$-0.761213\pi$
$73$	−6.55147	+	2.71371i	−0.766792	+	0.317616i	−0.0352196	+	0.999380i	$0.511213\pi$
$74$	−5.42325	+	13.0929i	−0.630440	+	1.52202i
$75$	4.41771	+	1.82988i	0.510114	+	0.211296i
$76$	−0.114207	+	0.114207i	−0.0131004	+	0.0131004i
$77$	0.306322	−	0.306322i	0.0349086	−	0.0349086i
$78$	25.2984	+	10.4789i	2.86448	+	1.18651i
$79$	−3.49368	+	8.43448i	−0.393069	+	0.948953i	0.596198	+	0.802837i	$0.296677\pi$
$79$	−3.49368	+	8.43448i	−0.393069	+	0.948953i	−0.989267	+	0.146116i	$0.953323\pi$
$80$	−5.63995	+	2.33614i	−0.630565	+	0.261189i
$81$			4.37265i			0.485850i
$82$	6.15345	+	14.8557i	0.679535	+	1.64054i
$83$	−11.5538	−	11.5538i	−1.26820	−	1.26820i	−0.947018	−	0.321182i	$-0.895920\pi$
$83$	−11.5538	−	11.5538i	−1.26820	−	1.26820i	−0.321182	−	0.947018i	$-0.604080\pi$
$84$	−2.61480			−0.285298
$85$	0.757847	−	7.34620i	0.0822000	−	0.796807i
$86$	7.37646			0.795424
$87$	14.7055	+	14.7055i	1.57659	+	1.57659i
$88$	0.206723	+	0.499075i	0.0220368	+	0.0532015i
$89$		−	17.2300i		−	1.82638i	−0.407532	−	0.913191i	$-0.633611\pi$
$89$		−	17.2300i		−	1.82638i	0.407532	−	0.913191i	$-0.366389\pi$
$90$	−14.0832	+	5.83344i	−1.48450	+	0.614898i
$91$	−0.823958	+	1.98921i	−0.0863743	+	0.208526i
$92$	6.28532	+	2.60346i	0.655290	+	0.271430i
$93$	11.3273	−	11.3273i	1.17458	−	1.17458i
$94$	1.95103	−	1.95103i	0.201233	−	0.201233i
$95$	−0.118176	−	0.0489502i	−0.0121246	−	0.00502218i
$96$	−8.28908	+	20.0116i	−0.846001	+	2.04243i
$97$	9.20938	−	3.81465i	0.935071	−	0.387319i	0.137471	−	0.990506i	$-0.456103\pi$
$97$	9.20938	−	3.81465i	0.935071	−	0.387319i	0.797600	+	0.603187i	$0.206103\pi$
$98$			14.0633i			1.42060i
$99$	−1.57760	−	3.80867i	−0.158555	−	0.382785i
$100$	−2.86538	−	2.86538i	−0.286538	−	0.286538i
$101$	16.7302			1.66472			0.832360	−	0.554235i	$-0.186989\pi$
$101$	16.7302			1.66472			0.832360	+	0.554235i	$0.186989\pi$
$102$	−14.3295	−	17.6261i	−1.41883	−	1.74524i
$103$	2.27820			0.224478			0.112239	−	0.993681i	$-0.464198\pi$
$103$	2.27820			0.224478			0.112239	+	0.993681i	$0.464198\pi$
$104$	−1.89849	−	1.89849i	−0.186162	−	0.186162i
$105$	−0.792474	−	1.91320i	−0.0773376	−	0.186709i
$106$		−	4.20208i		−	0.408143i
$107$	−10.8020	+	4.47432i	−1.04427	+	0.432549i	−0.837841	−	0.545914i	$-0.816183\pi$
$107$	−10.8020	+	4.47432i	−1.04427	+	0.432549i	−0.206424	+	0.978463i	$0.566183\pi$
$108$	−2.59275	+	6.25944i	−0.249487	+	0.602315i
$109$	−4.82614	−	1.99905i	−0.462260	−	0.191475i	0.139384	−	0.990238i	$-0.455488\pi$
$109$	−4.82614	−	1.99905i	−0.462260	−	0.191475i	−0.601645	+	0.798764i	$0.705488\pi$
$110$	−2.61464	+	2.61464i	−0.249296	+	0.249296i
$111$	−12.9548	+	12.9548i	−1.22961	+	1.22961i
$112$	−1.36405	−	0.565009i	−0.128891	−	0.0533883i
$113$	1.04409	−	2.52067i	0.0982201	−	0.237124i	−0.867130	−	0.498081i	$-0.834038\pi$
$113$	1.04409	−	2.52067i	0.0982201	−	0.237124i	0.965350	+	0.260957i	$0.0840381\pi$
$114$	−0.363495	+	0.150564i	−0.0340444	+	0.0141017i
$115$			5.38789i			0.502424i
$116$	−6.74448	−	16.2826i	−0.626209	−	1.51180i
$117$	14.4882	+	14.4882i	1.33944	+	1.33944i
$118$	−17.3701			−1.59905
$119$	1.38594	−	1.12673i	0.127048	−	0.103287i
$120$	2.58228			0.235728
$121$	−0.707107	−	0.707107i	−0.0642824	−	0.0642824i
$122$	5.68432	+	13.7232i	0.514634	+	1.24244i
$123$			20.7876i			1.87435i
$124$	−12.5421	+	5.19512i	−1.12632	+	0.466535i
$125$	4.65539	−	11.2391i	0.416390	−	1.00526i
$126$	−3.40609	−	1.41085i	−0.303439	−	0.125688i
$127$	10.7867	−	10.7867i	0.957167	−	0.957167i	−0.0419525	−	0.999120i	$-0.513358\pi$
$127$	10.7867	−	10.7867i	0.957167	−	0.957167i	0.999120	+	0.0419525i	$0.0133578\pi$
$128$	3.02965	−	3.02965i	0.267785	−	0.267785i
$129$	8.81026	+	3.64933i	0.775700	+	0.321306i
$130$	7.03298	−	16.9791i	0.616833	−	1.48917i
$131$	17.3396	−	7.18231i	1.51497	−	0.627522i	0.538395	−	0.842693i	$-0.319031\pi$
$131$	17.3396	−	7.18231i	1.51497	−	0.627522i	0.976576	+	0.215171i	$0.0690309\pi$
$132$			6.03595i			0.525362i
$133$	−0.0118389	−	0.0285816i	−0.00102656	−	0.00247833i
$134$	−12.6036	−	12.6036i	−1.08879	−	1.08879i
$135$	−5.36571			−0.461807
$136$	0.636684	+	2.13434i	0.0545952	+	0.183018i
$137$	−13.0800			−1.11750			−0.558748	−	0.829337i	$-0.688718\pi$
$137$	−13.0800			−1.11750			−0.558748	+	0.829337i	$0.688718\pi$
$138$	11.7185	+	11.7185i	0.997546	+	0.997546i
$139$	−7.43974	−	17.9611i	−0.631031	−	1.52344i	−0.838329	−	0.545165i	$-0.816467\pi$
$139$	−7.43974	−	17.9611i	−0.631031	−	1.52344i	0.207298	−	0.978278i	$-0.433533\pi$
$140$			1.75493i			0.148319i
$141$	3.29548	−	1.36503i	0.277530	−	0.114957i
$142$	0.355047	−	0.857160i	0.0297949	−	0.0719313i
$143$	4.59185	+	1.90201i	0.383990	+	0.159054i
$144$	−9.93493	+	9.93493i	−0.827911	+	0.827911i
$145$	9.86963	−	9.86963i	0.819628	−	0.819628i
$146$	13.5247	+	5.60213i	1.11932	+	0.463636i
$147$	−6.95746	+	16.7968i	−0.573842	+	1.38538i
$148$	14.3442	−	5.94155i	1.17908	−	0.488392i
$149$		−	7.74406i		−	0.634418i	−0.948356	−	0.317209i	$-0.897254\pi$
$149$		−	7.74406i		−	0.634418i	0.948356	−	0.317209i	$-0.102746\pi$
$150$	−3.77756	−	9.11985i	−0.308437	−	0.744632i
$151$	3.94357	+	3.94357i	0.320923	+	0.320923i	0.849121	−	0.528198i	$-0.177132\pi$
$151$	3.94357	+	3.94357i	0.320923	+	0.320923i	−0.528198	+	0.849121i	$0.677132\pi$
$152$	0.0385769			0.00312900
$153$	−4.85883	−	16.2881i	−0.392813	−	1.31682i
$154$	−0.894300			−0.0720647
$155$	−7.60235	−	7.60235i	−0.610635	−	0.610635i
$156$	−11.4804	−	27.7162i	−0.919169	−	2.21907i
$157$			13.2252i			1.05549i	0.849404	+	0.527743i	$0.176961\pi$
$157$			13.2252i			1.05549i	−0.849404	+	0.527743i	$0.823039\pi$
$158$	17.4120	−	7.21228i	1.38522	−	0.573778i
$159$	2.07888	−	5.01886i	0.164866	−	0.398022i
$160$	13.4309	+	5.56324i	1.06180	+	0.439813i
$161$	−0.921425	+	0.921425i	−0.0726185	+	0.0726185i
$162$	6.38292	−	6.38292i	0.501490	−	0.501490i
$163$	−20.5516	−	8.51277i	−1.60973	−	0.666772i	−0.616980	−	0.786978i	$-0.711644\pi$
$163$	−20.5516	−	8.51277i	−1.60973	−	0.666772i	−0.992749	+	0.120207i	$0.961644\pi$
$164$	6.74153	−	16.2755i	0.526425	−	1.27090i
$165$	−4.41639	+	1.82933i	−0.343816	+	0.142413i
$166$			33.7312i			2.61805i
$167$	−5.42837	−	13.1052i	−0.420060	−	1.01411i	−0.982329	−	0.187160i	$-0.940072\pi$
$167$	−5.42837	−	13.1052i	−0.420060	−	1.01411i	0.562270	−	0.826954i	$-0.309928\pi$
$168$	0.441615	+	0.441615i	0.0340713	+	0.0340713i
$169$	−11.7027			−0.900211
$170$	−11.8298	+	9.61727i	−0.907304	+	0.737611i
$171$	−0.294398			−0.0225132
$172$	−5.71443	−	5.71443i	−0.435721	−	0.435721i
$173$	5.01564	+	12.1088i	0.381332	+	0.920617i	0.991709	+	0.128506i	$0.0410181\pi$
$173$	5.01564	+	12.1088i	0.381332	+	0.920617i	−0.610377	+	0.792111i	$0.708982\pi$
$174$		−	42.9323i		−	3.25469i
$175$	0.717093	−	0.297029i	0.0542071	−	0.0224533i
$176$	−1.30425	+	3.14875i	−0.0983118	+	0.237346i
$177$	−20.7464	−	8.59343i	−1.55939	−	0.645922i
$178$	−25.1514	+	25.1514i	−1.88517	+	1.88517i
$179$	7.83859	−	7.83859i	0.585884	−	0.585884i	−0.350630	−	0.936514i	$-0.614033\pi$
$179$	7.83859	−	7.83859i	0.585884	−	0.585884i	0.936514	+	0.350630i	$0.114033\pi$
$180$	15.4291	+	6.39093i	1.15002	+	0.476352i
$181$	1.70622	−	4.11918i	0.126822	−	0.306176i	−0.847697	−	0.530481i	$-0.822011\pi$
$181$	1.70622	−	4.11918i	0.126822	−	0.306176i	0.974519	+	0.224305i	$0.0720112\pi$
$182$	4.10649	−	1.70097i	0.304393	−	0.126084i
$183$			19.2028i			1.41951i
$184$	−0.621830	−	1.50123i	−0.0458419	−	0.110672i
$185$	8.69465	+	8.69465i	0.639243	+	0.639243i
$186$	−33.0698			−2.42479
$187$	−2.60091	−	3.19926i	−0.190197	−	0.233953i
$188$	−3.02286			−0.220465
$189$	−0.917632	−	0.917632i	−0.0667479	−	0.0667479i
$190$	0.101052	+	0.243961i	0.00733107	+	0.0176988i
$191$			23.5043i			1.70071i	0.526208	+	0.850356i	$0.323613\pi$
$191$			23.5043i			1.70071i	−0.526208	+	0.850356i	$0.676387\pi$
$192$	24.5049	−	10.1503i	1.76849	−	0.732532i
$193$	−5.11360	+	12.3453i	−0.368085	+	0.888636i	0.625979	+	0.779840i	$0.284700\pi$
$193$	−5.11360	+	12.3453i	−0.368085	+	0.888636i	−0.994064	+	0.108796i	$0.965300\pi$
$194$	−19.0117	−	7.87490i	−1.36496	−	0.565385i
$195$	16.8000	−	16.8000i	1.20307	−	1.20307i
$196$	10.8946	−	10.8946i	0.778185	−	0.778185i
$197$	7.53664	+	3.12178i	0.536963	+	0.222418i	0.634650	−	0.772800i	$-0.281144\pi$
$197$	7.53664	+	3.12178i	0.536963	+	0.222418i	−0.0976866	+	0.995217i	$0.531144\pi$
$198$	−3.25677	+	7.86254i	−0.231449	+	0.558767i
$199$	−19.7071	+	8.16295i	−1.39700	+	0.578656i	−0.948971	−	0.315363i	$-0.897874\pi$
$199$	−19.7071	+	8.16295i	−1.39700	+	0.578656i	−0.448029	+	0.894019i	$0.647874\pi$
$200$			0.967870i			0.0684387i
$201$	−8.81811	−	21.2888i	−0.621982	−	1.50160i
$202$	−24.4218	−	24.4218i	−1.71831	−	1.71831i
$203$	3.37576			0.236932
$204$	−2.55382	+	24.7555i	−0.178803	+	1.73323i
$205$	13.9517			0.974427
$206$	−3.32558	−	3.32558i	−0.231704	−	0.231704i
$207$	4.74547	+	11.4566i	0.329833	+	0.796287i
$208$		−	16.9393i		−	1.17453i
$209$	−0.0659770	+	0.0273286i	−0.00456373	+	0.00189036i
$210$	−1.63597	+	3.94958i	−0.112893	+	0.272547i
$211$	1.55187	+	0.642806i	0.106835	+	0.0442526i	0.435461	−	0.900208i	$-0.356585\pi$
$211$	1.55187	+	0.642806i	0.106835	+	0.0442526i	−0.328626	+	0.944460i	$0.606585\pi$
$212$	−3.25529	+	3.25529i	−0.223574	+	0.223574i
$213$	0.848119	−	0.848119i	0.0581121	−	0.0581121i
$214$	22.2994	+	9.23671i	1.52435	+	0.631408i
$215$	2.44926	−	5.91303i	0.167038	−	0.403266i
$216$	1.49505	−	0.619270i	0.101725	−	0.0421360i
$217$		−	2.60027i		−	0.176518i
$218$	4.12681	+	9.96300i	0.279503	+	0.674779i
$219$	13.3821	+	13.3821i	0.904278	+	0.904278i
$220$	4.05104			0.273121
$221$	18.0280	+	9.74360i	1.21269	+	0.655425i
$222$	37.8212			2.53839
$223$	13.7198	+	13.7198i	0.918749	+	0.918749i	0.996939	−	0.0781896i	$-0.0249139\pi$
$223$	13.7198	+	13.7198i	0.918749	+	0.918749i	−0.0781896	+	0.996939i	$0.524914\pi$
$224$	1.34550	+	3.24833i	0.0899001	+	0.217038i
$225$		−	7.38626i		−	0.492417i
$226$	−5.20362	+	2.15541i	−0.346139	+	0.143376i
$227$	2.05527	−	4.96186i	0.136413	−	0.329330i	−0.840880	−	0.541221i	$-0.817962\pi$
$227$	2.05527	−	4.96186i	0.136413	−	0.329330i	0.977293	+	0.211891i	$0.0679622\pi$
$228$	0.398234	+	0.164954i	0.0263737	+	0.0109243i
$229$	−8.58698	+	8.58698i	−0.567444	+	0.567444i	−0.931412	−	0.363968i	$-0.881422\pi$
$229$	−8.58698	+	8.58698i	−0.567444	+	0.567444i	0.363968	+	0.931412i	$0.381422\pi$
$230$	7.86492	−	7.86492i	0.518597	−	0.518597i
$231$	−1.06813	−	0.442434i	−0.0702777	−	0.0291100i
$232$	−1.61090	+	3.88906i	−0.105761	+	0.255329i
$233$	−9.37899	+	3.88490i	−0.614438	+	0.254508i	−0.668125	−	0.744049i	$-0.732903\pi$
$233$	−9.37899	+	3.88490i	−0.614438	+	0.254508i	0.0536868	+	0.998558i	$0.482903\pi$
$234$		−	42.2980i		−	2.76511i
$235$	−0.916147	−	2.21177i	−0.0597628	−	0.144280i
$236$	13.4563	+	13.4563i	0.875933	+	0.875933i
$237$	24.3645			1.58265
$238$	−3.66783	−	0.378379i	−0.237750	−	0.0245267i
$239$	−5.36807			−0.347232			−0.173616	−	0.984813i	$-0.555545\pi$
$239$	−5.36807			−0.347232			−0.173616	+	0.984813i	$0.555545\pi$
$240$	11.5202	+	11.5202i	0.743625	+	0.743625i
$241$	0.336088	+	0.811387i	0.0216493	+	0.0522660i	0.934335	−	0.356397i	$-0.115995\pi$
$241$	0.336088	+	0.811387i	0.0216493	+	0.0522660i	−0.912685	+	0.408663i	$0.865995\pi$
$242$			2.06438i			0.132704i
$243$	19.0842	−	7.90495i	1.22425	−	0.507103i
$244$	6.22756	−	15.0347i	0.398679	−	0.962496i
$245$	11.2732	+	4.66952i	0.720220	+	0.298325i
$246$	30.3445	−	30.3445i	1.93469	−	1.93469i
$247$	0.250978	−	0.250978i	0.0159693	−	0.0159693i
$248$	2.99565	+	1.24084i	0.190224	+	0.0787934i
$249$	−16.6877	+	40.2877i	−1.05754	+	2.55313i
$250$	−23.2018	+	9.61049i	−1.46741	+	0.607821i
$251$			26.8734i			1.69624i	0.529808	+	0.848118i	$0.322264\pi$
$251$			26.8734i			1.69624i	−0.529808	+	0.848118i	$0.677736\pi$
$252$	1.54568	+	3.73161i	0.0973688	+	0.235069i
$253$	2.12700	+	2.12700i	0.133723	+	0.133723i
$254$	−31.4916			−1.97596
$255$	−18.8871	+	5.63412i	−1.18276	+	0.352822i
$256$	11.0321			0.689504
$257$	−10.7866	−	10.7866i	−0.672852	−	0.672852i	0.285520	−	0.958373i	$-0.407834\pi$
$257$	−10.7866	−	10.7866i	−0.672852	−	0.672852i	−0.958373	+	0.285520i	$0.907834\pi$
$258$	−7.53361	−	18.1877i	−0.469022	−	1.13232i
$259$			2.97388i			0.184788i
$260$	−18.6018	+	7.70512i	−1.15363	+	0.477851i
$261$	12.2935	−	29.6792i	0.760949	−	1.83709i
$262$	−35.7956	−	14.8270i	−2.21146	−	0.916018i
$263$	0.819101	−	0.819101i	0.0505079	−	0.0505079i	−0.681402	−	0.731910i	$-0.738629\pi$
$263$	0.819101	−	0.819101i	0.0505079	−	0.0505079i	0.731910	+	0.681402i	$0.238629\pi$
$264$	1.01941	−	1.01941i	0.0627406	−	0.0627406i
$265$	−3.36843	−	1.39525i	−0.206921	−	0.0857094i
$266$	−0.0244399	+	0.0590032i	−0.00149851	+	0.00361772i
$267$	−42.4832	+	17.5971i	−2.59993	+	1.07693i
$268$			19.5277i			1.19284i
$269$	12.0872	+	29.1810i	0.736967	+	1.77920i	0.617819	+	0.786320i	$0.288016\pi$
$269$	12.0872	+	29.1810i	0.736967	+	1.77920i	0.119148	+	0.992876i	$0.461984\pi$
$270$	7.83254	+	7.83254i	0.476673	+	0.476673i
$271$	20.5379			1.24759			0.623794	−	0.781589i	$-0.285591\pi$
$271$	20.5379			1.24759			0.623794	+	0.781589i	$0.285591\pi$
$272$	−6.68143	+	12.3622i	−0.405121	+	0.749572i
$273$	5.74620			0.347776
$274$	19.0933	+	19.0933i	1.15347	+	1.15347i
$275$	−0.685656	−	1.65532i	−0.0413466	−	0.0998196i
$276$		−	18.1563i		−	1.09288i
$277$	−16.1157	+	6.67535i	−0.968300	+	0.401083i	−0.810079	−	0.586321i	$-0.800576\pi$
$277$	−16.1157	+	6.67535i	−0.968300	+	0.401083i	−0.158221	+	0.987404i	$0.550576\pi$
$278$	−15.3585	+	37.0786i	−0.921140	+	2.22383i
$279$	−22.8612	−	9.46941i	−1.36866	−	0.566919i
$280$	0.296391	−	0.296391i	0.0177128	−	0.0177128i
$281$	−3.66525	+	3.66525i	−0.218650	+	0.218650i	−0.807930	−	0.589279i	$-0.799412\pi$
$281$	−3.66525	+	3.66525i	−0.218650	+	0.218650i	0.589279	+	0.807930i	$0.299412\pi$
$282$	−6.80313	−	2.81795i	−0.405121	−	0.167807i
$283$	8.62565	−	20.8242i	0.512742	−	1.23787i	−0.429540	−	0.903048i	$-0.641324\pi$
$283$	8.62565	−	20.8242i	0.512742	−	1.23787i	0.942282	−	0.334820i	$-0.108676\pi$
$284$	−0.939078	+	0.388979i	−0.0557240	+	0.0230816i
$285$			0.341373i			0.0202212i
$286$	−3.92647	−	9.47934i	−0.232177	−	0.560525i
$287$	2.38598	+	2.38598i	0.140840	+	0.140840i
$288$	33.4587			1.97157
$289$	−9.31359	−	14.2217i	−0.547858	−	0.836571i
$290$	−28.8142			−1.69203
$291$	−18.8112	−	18.8112i	−1.10273	−	1.10273i
$292$	−6.13752	−	14.8173i	−0.359171	−	0.867116i
$293$		−	5.00079i		−	0.292150i	−0.989274	−	0.146075i	$-0.953336\pi$
$293$		−	5.00079i		−	0.292150i	0.989274	−	0.146075i	$-0.0466640\pi$
$294$	34.6750	−	14.3629i	2.02229	−	0.837659i
$295$	−5.76751	+	13.9240i	−0.335797	+	0.810687i
$296$	−3.42606	−	1.41912i	−0.199136	−	0.0824848i
$297$	−2.11824	+	2.11824i	−0.122913	+	0.122913i
$298$	−11.3043	+	11.3043i	−0.654840	+	0.654840i
$299$	−13.8124	−	5.72129i	−0.798793	−	0.330871i
$300$	−4.13858	+	9.99142i	−0.238941	+	0.576855i
$301$	1.43010	−	0.592367i	0.0824296	−	0.0341435i
$302$		−	11.5132i		−	0.662508i
$303$	−17.0867	−	41.2508i	−0.981603	−	2.36980i
$304$	0.172102	+	0.172102i	0.00987070	+	0.00987070i
$305$	12.8880			0.737965
$306$	−16.6838	+	30.8690i	−0.953748	+	1.76466i
$307$	3.65731			0.208734			0.104367	−	0.994539i	$-0.466718\pi$
$307$	3.65731			0.208734			0.104367	+	0.994539i	$0.466718\pi$
$308$	0.692800	+	0.692800i	0.0394760	+	0.0394760i
$309$	−2.32674	−	5.61725i	−0.132364	−	0.319554i
$310$			22.1949i			1.26058i
$311$	17.8568	−	7.39652i	1.01257	−	0.419418i	0.186175	−	0.982517i	$-0.440391\pi$
$311$	17.8568	−	7.39652i	1.01257	−	0.419418i	0.826390	+	0.563098i	$0.190391\pi$
$312$	−2.74206	+	6.61993i	−0.155239	+	0.374780i
$313$	−27.2753	−	11.2978i	−1.54169	−	0.638588i	−0.559899	−	0.828561i	$-0.689160\pi$
$313$	−27.2753	−	11.2978i	−1.54169	−	0.638588i	−0.981789	+	0.189973i	$0.939160\pi$
$314$	19.3053	−	19.3053i	1.08946	−	1.08946i
$315$	−2.26190	+	2.26190i	−0.127443	+	0.127443i
$316$	−19.0760	−	7.90156i	−1.07311	−	0.444497i
$317$	3.12888	−	7.55377i	0.175735	−	0.424262i	−0.811329	−	0.584590i	$-0.801255\pi$
$317$	3.12888	−	7.55377i	0.175735	−	0.424262i	0.987064	+	0.160328i	$0.0512552\pi$
$318$	−10.3609	+	4.29161i	−0.581008	+	0.240661i
$319$		−	7.79254i		−	0.436298i
$320$	−6.81238	−	16.4465i	−0.380823	−	0.919389i
$321$	22.0642	+	22.0642i	1.23150	+	1.23150i
$322$	2.69008			0.149912
$323$	−0.282157	+	0.0841688i	−0.0156996	+	0.00468328i
$324$	−9.88950			−0.549417
$325$	6.29686	+	6.29686i	0.349287	+	0.349287i
$326$	17.5736	+	42.4265i	0.973312	+	2.34978i
$327$			13.9412i			0.770950i
$328$	−3.88736	+	1.61020i	−0.214643	+	0.0889082i
$329$	0.221575	−	0.534930i	0.0122158	−	0.0294916i
$330$	9.11712	+	3.77644i	0.501881	+	0.207886i
$331$	8.65499	−	8.65499i	0.475721	−	0.475721i	−0.428039	−	0.903760i	$-0.640795\pi$
$331$	8.65499	−	8.65499i	0.475721	−	0.475721i	0.903760	+	0.428039i	$0.140795\pi$
$332$	26.1310	−	26.1310i	1.43413	−	1.43413i
$333$	26.1459	+	10.8300i	1.43278	+	0.593479i
$334$	−11.2062	+	27.0542i	−0.613177	+	1.48034i
$335$	−14.2881	+	5.91831i	−0.780640	+	0.323352i
$336$			3.94031i			0.214962i
$337$	5.29877	+	12.7924i	0.288643	+	0.696845i	0.999982	−	0.00600377i	$-0.00191107\pi$
$337$	5.29877	+	12.7924i	0.288643	+	0.696845i	−0.711339	+	0.702849i	$0.751911\pi$
$338$	17.0829	+	17.0829i	0.929189	+	0.929189i
$339$	−7.28141			−0.395472
$340$	16.6147	+	1.71400i	0.901059	+	0.0929548i
$341$	−6.00241			−0.325049
$342$	0.429744	+	0.429744i	0.0232379	+	0.0232379i
$343$	2.28981	+	5.52809i	0.123638	+	0.298489i
$344$			1.93023i			0.104071i
$345$	13.2846	−	5.50268i	0.715221	−	0.296254i
$346$	10.3542	−	24.9973i	0.556645	−	1.34386i
$347$	15.7283	+	6.51489i	0.844341	+	0.349738i	0.762564	−	0.646913i	$-0.223940\pi$
$347$	15.7283	+	6.51489i	0.844341	+	0.349738i	0.0817775	+	0.996651i	$0.473940\pi$
$348$	−33.2590	+	33.2590i	−1.78287	+	1.78287i
$349$	7.87592	−	7.87592i	0.421588	−	0.421588i	−0.464162	−	0.885750i	$-0.653644\pi$
$349$	7.87592	−	7.87592i	0.421588	−	0.421588i	0.885750	+	0.464162i	$0.153644\pi$
$350$	−1.48035	−	0.613182i	−0.0791282	−	0.0327760i
$351$	5.69774	−	13.7556i	0.304123	−	0.734217i
$352$	7.49837	−	3.10593i	0.399664	−	0.165546i
$353$		−	26.9051i		−	1.43201i	−0.698094	−	0.716006i	$-0.745968\pi$
$353$		−	26.9051i		−	1.43201i	0.698094	−	0.716006i	$-0.254032\pi$
$354$	17.7401	+	42.8285i	0.942877	+	2.27631i
$355$	−0.569218	−	0.569218i	−0.0302109	−	0.0302109i
$356$	38.9687			2.06534
$357$	−4.19357	−	2.26650i	−0.221947	−	0.119956i
$358$	−22.8846			−1.20949
$359$	−5.09233	−	5.09233i	−0.268763	−	0.268763i	0.559839	−	0.828602i	$-0.310863\pi$
$359$	−5.09233	−	5.09233i	−0.268763	−	0.268763i	−0.828602	+	0.559839i	$0.810863\pi$
$360$	−1.52646	−	3.68519i	−0.0804513	−	0.194227i
$361$		−	18.9949i		−	0.999732i
$362$	−8.50356	+	3.52229i	−0.446937	+	0.185127i
$363$	−1.02130	+	2.46565i	−0.0536046	+	0.129413i
$364$	−4.49895	−	1.86353i	−0.235809	−	0.0976753i
$365$	8.98143	−	8.98143i	0.470110	−	0.470110i
$366$	28.0310	−	28.0310i	1.46520	−	1.46520i
$367$	−4.81934	−	1.99624i	−0.251567	−	0.104203i	0.253336	−	0.967378i	$-0.418472\pi$
$367$	−4.81934	−	1.99624i	−0.251567	−	0.104203i	−0.504904	+	0.863176i	$0.668472\pi$
$368$	3.92323	−	9.47152i	0.204513	−	0.493737i
$369$	29.6662	−	12.2881i	1.54436	−	0.639695i
$370$		−	25.3838i		−	1.31964i
$371$	−0.337448	−	0.814673i	−0.0175195	−	0.0422957i
$372$	25.6186	+	25.6186i	1.32826	+	1.32826i
$373$	−24.9667			−1.29273			−0.646363	−	0.763030i	$-0.723711\pi$
$373$	−24.9667			−1.29273			−0.646363	+	0.763030i	$0.723711\pi$
$374$	−0.873443	+	8.46673i	−0.0451646	+	0.437804i
$375$	−32.4662			−1.67655
$376$	0.510533	+	0.510533i	0.0263287	+	0.0263287i
$377$	14.8215	+	35.7822i	0.763344	+	1.84288i
$378$			2.67900i			0.137793i
$379$	11.2662	−	4.66663i	0.578708	−	0.239709i	−0.0740763	−	0.997253i	$-0.523601\pi$
$379$	11.2662	−	4.66663i	0.578708	−	0.239709i	0.652784	+	0.757544i	$0.273601\pi$
$380$	0.110709	−	0.267276i	0.00567927	−	0.0137110i
$381$	−37.6128	−	15.5797i	−1.92696	−	0.798173i
$382$	34.3101	−	34.3101i	1.75546	−	1.75546i
$383$	−6.49211	+	6.49211i	−0.331731	+	0.331731i	−0.853244	−	0.521512i	$-0.825368\pi$
$383$	−6.49211	+	6.49211i	−0.331731	+	0.331731i	0.521512	+	0.853244i	$0.325368\pi$
$384$	−10.5642	−	4.37585i	−0.539103	−	0.223304i
$385$	−0.296941	+	0.716878i	−0.0151335	+	0.0365355i
$386$	25.4855	−	10.5564i	1.29718	−	0.537308i
$387$		−	14.7304i		−	0.748790i
$388$	8.62749	+	20.8286i	0.437995	+	1.05741i
$389$	−3.96805	−	3.96805i	−0.201188	−	0.201188i	0.599321	−	0.800509i	$-0.295437\pi$
$389$	−3.96805	−	3.96805i	−0.201188	−	0.201188i	−0.800509	+	0.599321i	$0.795437\pi$
$390$	−49.0473			−2.48361
$391$	7.82360	+	9.62347i	0.395657	+	0.486680i
$392$	−3.67999			−0.185867
$393$	−35.4181	−	35.4181i	−1.78661	−	1.78661i
$394$	−6.44454	−	15.5585i	−0.324671	−	0.783826i
$395$		−	16.3523i		−	0.822776i
$396$	8.61396	−	3.56802i	0.432868	−	0.179300i
$397$	−1.34262	+	3.24137i	−0.0673841	+	0.162680i	−0.953984	−	0.299858i	$-0.903061\pi$
$397$	−1.34262	+	3.24137i	−0.0673841	+	0.162680i	0.886600	+	0.462537i	$0.153061\pi$
$398$	40.6830	+	16.8514i	2.03925	+	0.844687i
$399$	−0.0583809	+	0.0583809i	−0.00292270	+	0.00292270i
$400$	−4.31792	+	4.31792i	−0.215896	+	0.215896i
$401$	−10.9940	−	4.55388i	−0.549016	−	0.227410i	0.0908930	−	0.995861i	$-0.471028\pi$
$401$	−10.9940	−	4.55388i	−0.549016	−	0.227410i	−0.639909	+	0.768451i	$0.721028\pi$
$402$	−18.2040	+	43.9482i	−0.907931	+	2.19194i
$403$	27.5622	−	11.4166i	1.37297	−	0.568703i
$404$			37.8383i			1.88253i
$405$	−2.99724	−	7.23597i	−0.148934	−	0.359558i
$406$	−4.92773	−	4.92773i	−0.244559	−	0.244559i
$407$	6.86483			0.340277
$408$	4.61228	−	3.74965i	0.228342	−	0.185635i
$409$	20.3531			1.00640			0.503198	−	0.864171i	$-0.332157\pi$
$409$	20.3531			1.00640			0.503198	+	0.864171i	$0.332157\pi$
$410$	−20.3658	−	20.3658i	−1.00579	−	1.00579i
$411$	13.3586	+	32.2505i	0.658932	+	1.59080i
$412$			5.15256i			0.253848i
$413$	−3.36760	+	1.39490i	−0.165709	+	0.0686388i
$414$	9.79646	−	23.6508i	0.481470	−	1.16237i
$415$	27.0392	+	11.2000i	1.32730	+	0.549787i
$416$	−28.5239	+	28.5239i	−1.39850	+	1.39850i
$417$	−36.6875	+	36.6875i	−1.79660	+	1.79660i
$418$	0.136202	+	0.0564166i	0.00666185	+	0.00275943i
$419$	12.9586	−	31.2849i	0.633071	−	1.52837i	−0.202671	−	0.979247i	$-0.564962\pi$
$419$	12.9586	−	31.2849i	0.633071	−	1.52837i	0.835742	−	0.549122i	$-0.185038\pi$
$420$	4.32704	−	1.79232i	0.211138	−	0.0874562i
$421$		−	13.1999i		−	0.643325i	−0.946854	−	0.321663i	$-0.895758\pi$
$421$		−	13.1999i		−	0.643325i	0.946854	−	0.321663i	$-0.104242\pi$
$422$	−1.32700	−	3.20366i	−0.0645972	−	0.155952i
$423$	−3.89611	−	3.89611i	−0.189435	−	0.189435i
$424$	1.09958			0.0534001
$425$	−2.11174	−	7.07913i	−0.102434	−	0.343388i
$426$	−2.47606			−0.119966
$427$	2.20408	+	2.20408i	0.106663	+	0.106663i
$428$	−10.1195	−	24.4305i	−0.489142	−	1.18089i
$429$		−	13.2644i		−	0.640412i
$430$	−12.2068	+	5.05621i	−0.588662	+	0.243832i
$431$	3.64331	−	8.79572i	0.175492	−	0.423675i	−0.811519	−	0.584325i	$-0.801359\pi$
$431$	3.64331	−	8.79572i	0.175492	−	0.423675i	0.987011	+	0.160650i	$0.0513592\pi$
$432$	9.43253	+	3.90708i	0.453823	+	0.187980i
$433$	−12.3445	+	12.3445i	−0.593241	+	0.593241i	−0.938505	−	0.345264i	$-0.887789\pi$
$433$	−12.3445	+	12.3445i	−0.593241	+	0.593241i	0.345264	+	0.938505i	$0.387789\pi$
$434$	−3.79572	+	3.79572i	−0.182200	+	0.182200i
$435$	−34.4149	−	14.2551i	−1.65007	−	0.683481i
$436$	4.52120	−	10.9152i	0.216526	−	0.522741i
$437$	0.198461	−	0.0822052i	0.00949367	−	0.00393241i
$438$		−	39.0687i		−	1.86677i
$439$	4.90118	+	11.8325i	0.233920	+	0.564734i	0.996632	−	0.0820051i	$-0.0261324\pi$
$439$	4.90118	+	11.8325i	0.233920	+	0.564734i	−0.762712	+	0.646739i	$0.776132\pi$
$440$	−0.684183	−	0.684183i	−0.0326171	−	0.0326171i
$441$	28.0836			1.33732
$442$	−12.0931	−	40.5393i	−0.575209	−	1.92826i
$443$	−7.14043			−0.339252			−0.169626	−	0.985509i	$-0.554256\pi$
$443$	−7.14043			−0.339252			−0.169626	+	0.985509i	$0.554256\pi$
$444$	−29.2995	−	29.2995i	−1.39049	−	1.39049i
$445$	11.8104	+	28.5127i	0.559865	+	1.35163i
$446$		−	40.0548i		−	1.89665i
$447$	−19.0941	+	7.90903i	−0.903120	+	0.374085i
$448$	1.64761	−	3.97769i	0.0778423	−	0.187928i
$449$	−2.51520	−	1.04183i	−0.118700	−	0.0491671i	0.322543	−	0.946555i	$-0.395462\pi$
$449$	−2.51520	−	1.04183i	−0.118700	−	0.0491671i	−0.441243	+	0.897388i	$0.645462\pi$
$450$	−10.7820	+	10.7820i	−0.508268	+	0.508268i
$451$	5.50775	−	5.50775i	0.259350	−	0.259350i
$452$	5.70092	+	2.36140i	0.268149	+	0.111071i
$453$	5.69586	−	13.7510i	0.267615	−	0.646080i
$454$	−10.2432	+	4.24286i	−0.480736	+	0.199127i
$455$		−	3.85658i		−	0.180799i
$456$	−0.0393988	−	0.0951170i	−0.00184502	−	0.00445426i
$457$	10.2949	+	10.2949i	0.481577	+	0.481577i	0.905635	−	0.424058i	$-0.139395\pi$
$457$	10.2949	+	10.2949i	0.481577	+	0.481577i	−0.424058	+	0.905635i	$0.639395\pi$
$458$	25.0695			1.17142
$459$	−9.58385	+	7.79139i	−0.447336	+	0.363671i
$460$	−12.1857			−0.568159
$461$	−18.4490	−	18.4490i	−0.859255	−	0.859255i	0.131995	−	0.991250i	$-0.457862\pi$
$461$	−18.4490	−	18.4490i	−0.859255	−	0.859255i	−0.991250	+	0.131995i	$0.957862\pi$
$462$	0.913352	+	2.20503i	0.0424930	+	0.102587i
$463$			2.84672i			0.132298i	0.997810	+	0.0661490i	$0.0210713\pi$
$463$			2.84672i			0.132298i	−0.997810	+	0.0661490i	$0.978929\pi$
$464$	−24.5367	+	10.1634i	−1.13909	+	0.471826i
$465$	−10.9804	+	26.5090i	−0.509203	+	1.22933i
$466$	19.3618	+	8.01993i	0.896919	+	0.371516i
$467$	13.2555	−	13.2555i	0.613393	−	0.613393i	−0.330435	−	0.943829i	$-0.607196\pi$
$467$	13.2555	−	13.2555i	0.613393	−	0.613393i	0.943829	+	0.330435i	$0.107196\pi$
$468$	−32.7676	+	32.7676i	−1.51468	+	1.51468i
$469$	−3.45565	−	1.43138i	−0.159567	−	0.0660948i
$470$	−1.89128	+	4.56595i	−0.0872381	+	0.210611i
$471$	32.6086	−	13.5069i	1.50253	−	0.622367i
$472$		−	4.54529i		−	0.209214i
$473$	−1.36741	−	3.30121i	−0.0628734	−	0.151790i
$474$	−35.5659	−	35.5659i	−1.63359	−	1.63359i
$475$	−0.127951			−0.00587080
$476$	2.54828	+	3.13453i	0.116800	+	0.143671i
$477$	−8.39136			−0.384214
$478$	7.83598	+	7.83598i	0.358409	+	0.358409i
$479$	3.10860	+	7.50483i	0.142036	+	0.342904i	0.978849	−	0.204584i	$-0.0655841\pi$
$479$	3.10860	+	7.50483i	0.142036	+	0.342904i	−0.836813	+	0.547488i	$0.815584\pi$
$480$		−	38.7975i		−	1.77086i
$481$	−31.5223	+	13.0570i	−1.43729	+	0.595346i
$482$	0.693813	−	1.67501i	0.0316023	−	0.0762948i
$483$	3.21296	+	1.33085i	0.146195	+	0.0605559i
$484$	1.59924	−	1.59924i	0.0726929	−	0.0726929i
$485$	−12.6252	+	12.6252i	−0.573279	+	0.573279i
$486$	−39.3972	−	16.3188i	−1.78709	−	0.740238i
$487$	−0.272834	+	0.658679i	−0.0123633	+	0.0298476i	−0.929941	−	0.367710i	$-0.880142\pi$
$487$	−0.272834	+	0.658679i	−0.0123633	+	0.0298476i	0.917577	+	0.397557i	$0.130142\pi$
$488$	−3.59099	+	1.48744i	−0.162556	+	0.0673331i
$489$			59.3672i			2.68468i
$490$	−9.63968	−	23.2723i	−0.435476	−	1.05133i
$491$	−11.9282	−	11.9282i	−0.538314	−	0.538314i	0.384719	−	0.923034i	$-0.374298\pi$
$491$	−11.9282	−	11.9282i	−0.538314	−	0.538314i	−0.923034	+	0.384719i	$0.874298\pi$
$492$	−47.0148			−2.11959
$493$	3.29703	−	31.9598i	0.148491	−	1.43940i
$494$	−0.732723			−0.0329668
$495$	5.22131	+	5.22131i	0.234681	+	0.234681i
$496$	7.82866	+	18.9001i	0.351517	+	0.848638i
$497$		−	0.194693i		−	0.00873316i
$498$	83.1692	−	34.4498i	3.72690	−	1.54373i
$499$	−1.64451	+	3.97021i	−0.0736185	+	0.177731i	−0.956405	−	0.292044i	$-0.905665\pi$
$499$	−1.64451	+	3.97021i	−0.0736185	+	0.177731i	0.882786	+	0.469774i	$0.155665\pi$
$500$	25.4192	+	10.5290i	1.13678	+	0.470870i
$501$	−26.7689	+	26.7689i	−1.19594	+	1.19594i
$502$	39.2282	−	39.2282i	1.75084	−	1.75084i
$503$	7.17119	+	2.97040i	0.319748	+	0.132444i	0.536784	−	0.843720i	$-0.319639\pi$
$503$	7.17119	+	2.97040i	0.319748	+	0.132444i	−0.217036	+	0.976164i	$0.569639\pi$
$504$	0.369182	−	0.891284i	0.0164447	−	0.0397010i
$505$	−27.6856	+	11.4678i	−1.23199	+	0.510309i
$506$		−	6.20972i		−	0.276056i
$507$	11.9521	+	28.8548i	0.530809	+	1.28149i
$508$	24.3961	+	24.3961i	1.08240	+	1.08240i
$509$	6.80086			0.301443			0.150721	−	0.988576i	$-0.451840\pi$
$509$	6.80086			0.301443			0.150721	+	0.988576i	$0.451840\pi$
$510$	35.7946	+	19.3459i	1.58501	+	0.856651i
$511$	3.07197			0.135896
$512$	−22.1632	−	22.1632i	−0.979486	−	0.979486i
$513$	0.0818667	+	0.197644i	0.00361450	+	0.00872618i
$514$			31.4914i			1.38902i
$515$	−3.77003	+	1.56160i	−0.166127	+	0.0688123i
$516$	−8.25359	+	19.9259i	−0.363344	+	0.877190i
$517$	−1.23482	−	0.511479i	−0.0543073	−	0.0224948i
$518$	4.34108	−	4.34108i	0.190736	−	0.190736i
$519$	24.7336	−	24.7336i	1.08568	−	1.08568i
$520$	4.44299	+	1.84035i	0.194838	+	0.0807045i
$521$	−8.39270	+	20.2618i	−0.367691	+	0.887684i	0.626437	+	0.779472i	$0.284513\pi$
$521$	−8.39270	+	20.2618i	−0.367691	+	0.887684i	−0.994128	+	0.108212i	$0.965487\pi$
$522$	−61.2691	+	25.3785i	−2.68168	+	1.11079i
$523$			39.9420i			1.74654i	0.487237	+	0.873270i	$0.338005\pi$
$523$			39.9420i			1.74654i	−0.487237	+	0.873270i	$0.661995\pi$
$524$	16.2440	+	39.2166i	0.709625	+	1.71319i
$525$	−1.46474	−	1.46474i	−0.0639264	−	0.0639264i
$526$	−2.39135			−0.104268
$527$	−24.6179	−	2.53963i	−1.07237	−	0.110628i
$528$	9.09573			0.395841
$529$	9.86539	+	9.86539i	0.428930	+	0.428930i
$530$	2.88033	+	6.95372i	0.125113	+	0.302050i
$531$			34.6872i			1.50530i
$532$	0.0646421	−	0.0267757i	0.00280259	−	0.00116087i
$533$	−14.8150	+	35.7665i	−0.641708	+	1.54922i
$534$	87.7015	+	36.3272i	3.79522	+	1.57203i
$535$	14.8084	−	14.8084i	0.640225	−	0.640225i
$536$	3.29804	−	3.29804i	0.142454	−	0.142454i
$537$	−27.3328	−	11.3216i	−1.17950	−	0.488564i
$538$	24.9525	−	60.2407i	1.07578	−	2.59716i
$539$	6.29378	−	2.60697i	0.271092	−	0.112290i
$540$		−	12.1355i		−	0.522228i
$541$	2.62808	+	6.34476i	0.112990	+	0.272782i	0.970252	−	0.242099i	$-0.0778359\pi$
$541$	2.62808	+	6.34476i	0.112990	+	0.272782i	−0.857261	+	0.514882i	$0.827836\pi$
$542$	−29.9799	−	29.9799i	−1.28775	−	1.28775i
$543$	−11.8990			−0.510635
$544$	32.0675	−	9.56589i	1.37488	−	0.410134i
$545$	9.35668			0.400796
$546$	−8.38795	−	8.38795i	−0.358971	−	0.358971i
$547$	−4.12937	−	9.96918i	−0.176559	−	0.426251i	0.810681	−	0.585488i	$-0.199097\pi$
$547$	−4.12937	−	9.96918i	−0.176559	−	0.426251i	−0.987241	+	0.159236i	$0.949097\pi$
$548$		−	29.5826i		−	1.26371i
$549$	27.4045	−	11.3513i	1.16959	−	0.484462i
$550$	−1.41546	+	3.41721i	−0.0603553	+	0.145711i
$551$	−0.514128	−	0.212959i	−0.0219026	−	0.00907236i
$552$	−3.06643	+	3.06643i	−0.130516	+	0.130516i
$553$	2.79654	−	2.79654i	0.118921	−	0.118921i
$554$	33.2690	+	13.7805i	1.41346	+	0.585476i
$555$	12.5580	−	30.3178i	0.533059	−	1.28692i
$556$	40.6222	−	16.8263i	1.72277	−	0.713593i
$557$		−	3.94309i		−	0.167074i	−0.996505	−	0.0835371i	$-0.973378\pi$
$557$		−	3.94309i		−	0.167074i	0.996505	−	0.0835371i	$-0.0266217\pi$
$558$	19.5485	+	47.1942i	0.827553	+	1.99789i
$559$	12.5579	+	12.5579i	0.531141	+	0.531141i
$560$	2.64456			0.111753
$561$	−5.23193	+	9.68034i	−0.220892	+	0.408704i
$562$	10.7006			0.451378
$563$	−3.60886	−	3.60886i	−0.152096	−	0.152096i	0.626958	−	0.779053i	$-0.284300\pi$
$563$	−3.60886	−	3.60886i	−0.152096	−	0.152096i	−0.779053	+	0.626958i	$0.784300\pi$
$564$	3.08726	+	7.45331i	0.129997	+	0.313841i
$565$			4.88694i			0.205595i
$566$	−42.9890	+	17.8066i	−1.80696	+	0.748469i
$567$	0.724899	−	1.75006i	0.0304429	−	0.0734956i
$568$	0.224296	+	0.0929065i	0.00941126	+	0.00389827i
$569$	−7.12268	+	7.12268i	−0.298598	+	0.298598i	−0.840465	−	0.541866i	$-0.817718\pi$
$569$	−7.12268	+	7.12268i	−0.298598	+	0.298598i	0.541866	+	0.840465i	$0.317718\pi$
$570$	0.498316	−	0.498316i	0.0208722	−	0.0208722i
$571$	−0.403574	−	0.167166i	−0.0168891	−	0.00699568i	0.374223	−	0.927339i	$-0.377909\pi$
$571$	−0.403574	−	0.167166i	−0.0168891	−	0.00699568i	−0.391112	+	0.920343i	$0.627909\pi$
$572$	−4.30172	+	10.3853i	−0.179864	+	0.434230i
$573$	57.9533	−	24.0050i	2.42103	−	1.00283i
$574$		−	6.96582i		−	0.290748i
$575$	2.06247	+	4.97925i	0.0860111	+	0.207649i
$576$	−28.9711	−	28.9711i	−1.20713	−	1.20713i
$577$	−0.679953			−0.0283068			−0.0141534	−	0.999900i	$-0.504505\pi$
$577$	−0.679953			−0.0283068			−0.0141534	+	0.999900i	$0.504505\pi$
$578$	−7.16457	+	34.3554i	−0.298007	+	1.42900i
$579$	35.6617			1.48205
$580$	22.3219	+	22.3219i	0.926866	+	0.926866i
$581$	2.70878	+	6.53958i	0.112379	+	0.271308i
$582$			54.9187i			2.27645i
$583$	−1.88057	+	0.778959i	−0.0778853	+	0.0322612i
$584$	−1.46593	+	3.53907i	−0.0606606	+	0.146448i
$585$	−33.9065	−	14.0445i	−1.40186	−	0.580669i
$586$	−7.29985	+	7.29985i	−0.301554	+	0.301554i
$587$	3.21525	−	3.21525i	0.132707	−	0.132707i	−0.637633	−	0.770340i	$-0.720086\pi$
$587$	3.21525	−	3.21525i	0.132707	−	0.132707i	0.770340	+	0.637633i	$0.220086\pi$
$588$	−37.9889	−	15.7355i	−1.56664	−	0.648922i
$589$	−0.164037	+	0.396021i	−0.00675904	+	0.0163178i
$590$	28.7445	−	11.9063i	1.18339	−	0.490177i
$591$		−	21.7710i		−	0.895538i
$592$	−8.95348	−	21.6156i	−0.367986	−	0.888397i
$593$	1.28643	+	1.28643i	0.0528272	+	0.0528272i	0.733027	−	0.680200i	$-0.238107\pi$
$593$	1.28643	+	1.28643i	0.0528272	+	0.0528272i	−0.680200	+	0.733027i	$0.738107\pi$
$594$	6.18416			0.253739
$595$	−1.52117	+	2.81453i	−0.0623618	+	0.115384i
$596$	17.5145			0.717423
$597$	40.2539	+	40.2539i	1.64748	+	1.64748i
$598$	11.8109	+	28.5141i	0.482985	+	1.16603i
$599$			13.0472i			0.533092i	0.963822	+	0.266546i	$0.0858825\pi$
$599$			13.0472i			0.533092i	−0.963822	+	0.266546i	$0.914118\pi$
$600$	2.38642	−	0.988489i	0.0974254	−	0.0403549i
$601$	−4.82503	+	11.6486i	−0.196817	+	0.475158i	−0.991218	−	0.132235i	$-0.957785\pi$
$601$	−4.82503	+	11.6486i	−0.196817	+	0.475158i	0.794401	+	0.607393i	$0.207785\pi$
$602$	−2.95227	−	1.22287i	−0.120326	−	0.0498405i
$603$	−25.1688	+	25.1688i	−1.02495	+	1.02495i
$604$	−8.91907	+	8.91907i	−0.362912	+	0.362912i
$605$	1.65483	+	0.685451i	0.0672783	+	0.0278676i
$606$	−35.2734	+	85.1575i	−1.43288	+	3.45929i
$607$	8.43220	−	3.49273i	0.342252	−	0.141766i	−0.204935	−	0.978776i	$-0.565698\pi$
$607$	8.43220	−	3.49273i	0.342252	−	0.141766i	0.547188	+	0.837010i	$0.315698\pi$
$608$		−	0.579600i		−	0.0235059i
$609$	−3.44768	−	8.32343i	−0.139707	−	0.337283i
$610$	−18.8131	−	18.8131i	−0.761721	−	0.761721i
$611$	6.64295			0.268745
$612$	36.8384	−	10.9891i	1.48910	−	0.444207i
$613$	−36.6191			−1.47903			−0.739516	−	0.673139i	$-0.764946\pi$
$613$	−36.6191			−1.47903			−0.739516	+	0.673139i	$0.764946\pi$
$614$	−5.33872	−	5.33872i	−0.215453	−	0.215453i
$615$	−14.2489	−	34.3999i	−0.574571	−	1.38714i
$616$		−	0.234015i		−	0.00942872i
$617$	3.10717	−	1.28703i	0.125090	−	0.0518140i	−0.319260	−	0.947667i	$-0.603434\pi$
$617$	3.10717	−	1.28703i	0.125090	−	0.0518140i	0.444351	+	0.895853i	$0.353434\pi$
$618$	−4.80328	+	11.5961i	−0.193216	+	0.466465i
$619$	−13.4475	−	5.57016i	−0.540502	−	0.223883i	0.0956936	−	0.995411i	$-0.469493\pi$
$619$	−13.4475	−	5.57016i	−0.540502	−	0.223883i	−0.636196	+	0.771527i	$0.719493\pi$
$620$	17.1940	−	17.1940i	0.690529	−	0.690529i
$621$	6.37173	−	6.37173i	0.255689	−	0.255689i
$622$	−36.8632	−	15.2693i	−1.47808	−	0.612241i
$623$	−2.85640	+	6.89596i	−0.114439	+	0.276281i
$624$	−41.7663	+	17.3002i	−1.67199	+	0.692560i
$625$			12.8313i			0.513250i
$626$	23.3229	+	56.3065i	0.932172	+	2.25046i
$627$	0.134765	+	0.134765i	0.00538200	+	0.00538200i
$628$	−29.9111			−1.19358
$629$	28.1550	+	2.90452i	1.12261	+	0.115811i
$630$	6.60356			0.263092
$631$	3.47009	+	3.47009i	0.138142	+	0.138142i	0.772796	−	0.634654i	$-0.218857\pi$
$631$	3.47009	+	3.47009i	0.138142	+	0.138142i	−0.634654	+	0.772796i	$0.718857\pi$
$632$	1.88726	+	4.55626i	0.0750714	+	0.181238i
$633$		−	4.48287i		−	0.178178i
$634$	−15.5939	+	6.45919i	−0.619312	+	0.256527i
$635$	−10.4564	+	25.2439i	−0.414949	+	1.00178i
$636$	11.3510	+	4.70175i	0.450098	+	0.186437i
$637$	−23.9416	+	23.9416i	−0.948601	+	0.948601i
$638$	−11.3751	+	11.3751i	−0.450343	+	0.450343i
$639$	−1.71171	−	0.709012i	−0.0677141	−	0.0280481i
$640$	−2.93686	+	7.09021i	−0.116090	+	0.280265i
$641$	4.83567	−	2.00300i	0.190997	−	0.0791137i	−0.285135	−	0.958487i	$-0.592038\pi$
$641$	4.83567	−	2.00300i	0.190997	−	0.0791137i	0.476132	+	0.879374i	$0.342038\pi$
$642$		−	64.4159i		−	2.54229i
$643$	−6.19776	−	14.9627i	−0.244416	−	0.590072i	0.753296	−	0.657682i	$-0.228463\pi$
$643$	−6.19776	−	14.9627i	−0.244416	−	0.590072i	−0.997712	+	0.0676096i	$0.978463\pi$
$644$	−2.08396	−	2.08396i	−0.0821197	−	0.0821197i
$645$	−17.0809			−0.672559
$646$	0.534740	+	0.289011i	0.0210391	+	0.0113710i
$647$	−23.3703			−0.918780			−0.459390	−	0.888235i	$-0.651932\pi$
$647$	−23.3703			−0.918780			−0.459390	+	0.888235i	$0.651932\pi$
$648$	1.67024	+	1.67024i	0.0656134	+	0.0656134i
$649$	3.21997	+	7.77369i	0.126395	+	0.305144i
$650$		−	18.3836i		−	0.721062i
$651$	−6.41135	+	2.65567i	−0.251281	+	0.104084i
$652$	19.2531	−	46.4811i	0.754010	−	1.82034i
$653$	6.70988	+	2.77933i	0.262578	+	0.108763i	0.510089	−	0.860122i	$-0.329613\pi$
$653$	6.70988	+	2.77933i	0.262578	+	0.108763i	−0.247511	+	0.968885i	$0.579613\pi$
$654$	20.3505	−	20.3505i	0.795767	−	0.795767i
$655$	−23.7710	+	23.7710i	−0.928808	+	0.928808i
$656$	−24.5260	−	10.1590i	−0.957580	−	0.396642i
$657$	11.1872	−	27.0082i	0.436454	−	1.05369i
$658$	−1.10430	+	0.457416i	−0.0430501	+	0.0178319i
$659$		−	45.6467i		−	1.77814i	−0.457768	−	0.889072i	$-0.651351\pi$
$659$		−	45.6467i		−	1.77814i	0.457768	−	0.889072i	$-0.348649\pi$
$660$	−4.13735	−	9.98844i	−0.161046	−	0.388800i
$661$	−34.9161	−	34.9161i	−1.35808	−	1.35808i	−0.876283	−	0.481797i	$-0.839984\pi$
$661$	−34.9161	−	34.9161i	−1.35808	−	1.35808i	−0.481797	−	0.876283i	$-0.660016\pi$
$662$	−25.2680			−0.982070
$663$	5.61219	−	54.4018i	0.217959	−	2.11279i
$664$	−8.82656			−0.342537
$665$	0.0391825	+	0.0391825i	0.00151943	+	0.00151943i
$666$	−22.3572	−	53.9750i	−0.866324	−	2.09149i
$667$			23.4402i			0.907607i
$668$	29.6398	−	12.2772i	1.14680	−	0.475019i
$669$	19.8161	−	47.8404i	0.766137	−	1.84962i
$670$	29.4960	+	12.2176i	1.13953	+	0.472009i
$671$	5.08784	−	5.08784i	0.196414	−	0.196414i
$672$	6.63506	−	6.63506i	0.255953	−	0.255953i
$673$	30.7723	+	12.7463i	1.18619	+	0.491334i	0.886511	−	0.462708i	$-0.153122\pi$
$673$	30.7723	+	12.7463i	1.18619	+	0.491334i	0.299674	+	0.954042i	$0.403122\pi$
$674$	10.9387	−	26.4083i	0.421343	−	1.01721i
$675$	−4.95875	+	2.05398i	−0.190862	+	0.0790578i
$676$		−	26.4678i		−	1.01799i
$677$	−16.1252	−	38.9297i	−0.619742	−	1.49619i	−0.852004	−	0.523536i	$-0.824613\pi$
$677$	−16.1252	−	38.9297i	−0.619742	−	1.49619i	0.232262	−	0.972653i	$-0.425387\pi$
$678$	10.6289	+	10.6289i	0.408202	+	0.408202i
$679$	−4.31825			−0.165719
$680$	−2.51659	−	3.09555i	−0.0965067	−	0.118709i
$681$	−14.3332			−0.549251
$682$	8.76195	+	8.76195i	0.335512	+	0.335512i
$683$	−2.39371	−	5.77892i	−0.0915927	−	0.221124i	0.871444	−	0.490495i	$-0.163184\pi$
$683$	−2.39371	−	5.77892i	−0.0915927	−	0.221124i	−0.963036	+	0.269371i	$0.913184\pi$
$684$		−	0.665832i		−	0.0254587i
$685$	21.6451	−	8.96568i	0.827015	−	0.342561i
$686$	4.72705	−	11.4121i	0.180479	−	0.435716i
$687$	29.9424	+	12.4025i	1.14237	+	0.473186i
$688$	−8.61124	+	8.61124i	−0.328300	+	0.328300i
$689$	7.15372	−	7.15372i	0.272535	−	0.272535i
$690$	−27.4246	−	11.3596i	−1.04404	−	0.432454i
$691$	−13.8772	+	33.5026i	−0.527914	+	1.27450i	0.404973	+	0.914329i	$0.367281\pi$
$691$	−13.8772	+	33.5026i	−0.527914	+	1.27450i	−0.932887	+	0.360169i	$0.882719\pi$
$692$	−27.3862	+	11.3437i	−1.04107	+	0.431224i
$693$			1.78587i			0.0678397i
$694$	−13.4492	−	32.4693i	−0.510526	−	1.23252i
$695$	24.6230	+	24.6230i	0.934002	+	0.934002i
$696$	11.2343			0.425833
$697$	24.9195	−	20.2588i	0.943892	−	0.767357i
$698$	−22.9936			−0.870319
$699$	19.1576	+	19.1576i	0.724607	+	0.724607i
$700$	0.671784	+	1.62183i	0.0253910	+	0.0612994i
$701$			43.1404i			1.62939i	0.579889	+	0.814695i	$0.303096\pi$
$701$			43.1404i			1.62939i	−0.579889	+	0.814695i	$0.696904\pi$
$702$	−28.3967	+	11.7623i	−1.07177	+	0.443940i
$703$	0.187606	−	0.452921i	0.00707570	−	0.0170822i
$704$	−9.18200	−	3.80331i	−0.346060	−	0.143343i
$705$	−4.51779	+	4.51779i	−0.170150	+	0.170150i
$706$	−39.2743	+	39.2743i	−1.47811	+	1.47811i
$707$	−6.69592	−	2.77354i	−0.251826	−	0.104310i
$708$	19.4355	−	46.9216i	0.730432	−	1.76342i
$709$	16.8634	−	6.98503i	0.633317	−	0.262328i	−0.0428447	−	0.999082i	$-0.513642\pi$
$709$	16.8634	−	6.98503i	0.633317	−	0.262328i	0.676162	+	0.736753i	$0.263642\pi$
$710$			1.66182i			0.0623669i
$711$	−14.4026	−	34.7709i	−0.540139	−	1.30401i
$712$	−6.58145	−	6.58145i	−0.246650	−	0.246650i
$713$	18.0554			0.676181
$714$	2.81302	+	9.43000i	0.105275	+	0.352909i
$715$	−8.90245			−0.332933
$716$	17.7283	+	17.7283i	0.662539	+	0.662539i
$717$	5.48243	+	13.2358i	0.204745	+	0.494298i
$718$			14.8669i			0.554829i
$719$	26.5326	−	10.9902i	0.989500	−	0.409864i	0.171564	−	0.985173i	$-0.445118\pi$
$719$	26.5326	−	10.9902i	0.989500	−	0.409864i	0.817936	+	0.575309i	$0.195118\pi$
$720$	9.63068	−	23.2505i	0.358914	−	0.866495i
$721$	−0.911803	−	0.377681i	−0.0339573	−	0.0140656i
$722$	−27.7276	+	27.7276i	−1.03191	+	1.03191i
$723$	1.65735	−	1.65735i	0.0616373	−	0.0616373i
$724$	9.31624	+	3.85891i	0.346235	+	0.143415i
$725$	5.34300	−	12.8991i	0.198434	−	0.479062i
$726$	5.09004	−	2.10836i	0.188909	−	0.0782486i
$727$		−	21.0642i		−	0.781228i	−0.920554	−	0.390614i	$-0.872263\pi$
$727$		−	21.0642i		−	0.781228i	0.920554	−	0.390614i	$-0.127737\pi$
$728$	0.445098	+	1.07456i	0.0164964	+	0.0398259i
$729$	−29.7058	−	29.7058i	−1.10022	−	1.10022i
$730$	−26.2211			−0.970486
$731$	−4.21145	−	14.1179i	−0.155766	−	0.522171i
$732$	−43.4304			−1.60523
$733$	30.3650	+	30.3650i	1.12156	+	1.12156i	0.991508	+	0.130048i	$0.0415131\pi$
$733$	30.3650	+	30.3650i	1.12156	+	1.12156i	0.130048	+	0.991508i	$0.458487\pi$
$734$	4.12099	+	9.94896i	0.152109	+	0.367223i
$735$		−	32.5648i		−	1.20117i
$736$	−22.5553	+	9.34271i	−0.831400	+	0.344377i
$737$	−3.30415	+	7.97694i	−0.121710	+	0.293834i
$738$	−61.2424	−	25.3674i	−2.25436	−	0.933788i
$739$	−28.9638	+	28.9638i	−1.06545	+	1.06545i	−0.0677491	+	0.997702i	$0.521582\pi$
$739$	−28.9638	+	28.9638i	−1.06545	+	1.06545i	−0.997702	+	0.0677491i	$0.978418\pi$
$740$	−19.6645	+	19.6645i	−0.722880	+	0.722880i
$741$	−0.875146	−	0.362497i	−0.0321493	−	0.0133167i
$742$	−0.696623	+	1.68180i	−0.0255738	+	0.0617407i
$743$	−17.7140	+	7.33738i	−0.649864	+	0.269182i	−0.683166	−	0.730263i	$-0.739398\pi$
$743$	−17.7140	+	7.33738i	−0.649864	+	0.269182i	0.0333025	+	0.999445i	$0.489398\pi$
$744$		−	8.65349i		−	0.317252i
$745$	5.30817	+	12.8151i	0.194476	+	0.469508i
$746$	36.4449	+	36.4449i	1.33434	+	1.33434i
$747$	67.3595			2.46456
$748$	7.23569	−	5.88240i	0.264563	−	0.215082i
$749$	5.06501			0.185072
$750$	47.3921	+	47.3921i	1.73052	+	1.73052i
$751$	−18.8445	−	45.4947i	−0.687647	−	1.66013i	−0.749469	−	0.662040i	$-0.769691\pi$
$751$	−18.8445	−	45.4947i	−0.687647	−	1.66013i	0.0618218	−	0.998087i	$-0.480309\pi$
$752$			4.55523i			0.166112i
$753$	66.2603	−	27.4459i	2.41466	−	1.00019i
$754$	30.5972	−	73.8681i	1.11428	−	2.69012i
$755$	−9.22905	−	3.82280i	−0.335879	−	0.139126i
$756$	2.07538	−	2.07538i	0.0754810	−	0.0754810i
$757$	−22.9498	+	22.9498i	−0.834124	+	0.834124i	−0.988078	−	0.153954i	$-0.950799\pi$
$757$	−22.9498	+	22.9498i	−0.834124	+	0.834124i	0.153954	+	0.988078i	$0.450799\pi$
$758$	−23.2578	−	9.63371i	−0.844762	−	0.349912i
$759$	3.07211	−	7.41673i	0.111511	−	0.269210i
$760$	−0.0638381	+	0.0264426i	−0.00231565	+	0.000959174i
$761$		−	50.2368i		−	1.82108i	−0.413418	−	0.910541i	$-0.635665\pi$
$761$		−	50.2368i		−	1.82108i	0.413418	−	0.910541i	$-0.364335\pi$
$762$	32.1625	+	77.6471i	1.16512	+	2.81286i
$763$	1.60016	+	1.60016i	0.0579296	+	0.0579296i
$764$	−53.1591			−1.92323
$765$	19.2052	+	23.6235i	0.694367	+	0.854110i
$766$	18.9536			0.684820
$767$	−29.5712	−	29.5712i	−1.06775	−	1.06775i
$768$	−11.2671	−	27.2012i	−0.406566	−	0.981538i
$769$		−	9.58409i		−	0.345611i	−0.984956	−	0.172806i	$-0.944717\pi$
$769$		−	9.58409i		−	0.345611i	0.984956	−	0.172806i	$-0.0552832\pi$
$770$	1.47991	−	0.612999i	0.0533323	−	0.0220910i
$771$	−15.5796	+	37.6125i	−0.561086	+	1.35458i
$772$	−27.9211	−	11.5653i	−1.00490	−	0.416244i
$773$	8.63089	−	8.63089i	0.310431	−	0.310431i	−0.534645	−	0.845077i	$-0.679555\pi$
$773$	8.63089	−	8.63089i	0.310431	−	0.310431i	0.845077	+	0.534645i	$0.179555\pi$
$774$	−21.5026	+	21.5026i	−0.772894	+	0.772894i
$775$	−9.93591	−	4.11559i	−0.356908	−	0.147836i
$776$	2.06065	−	4.97486i	0.0739731	−	0.178587i
$777$	7.33253	−	3.03723i	0.263053	−	0.108960i
$778$			11.5846i			0.415329i
$779$	−0.212866	−	0.513904i	−0.00762671	−	0.0184125i
$780$	37.9962	+	37.9962i	1.36048	+	1.36048i
$781$	−0.449424			−0.0160817
$782$	2.62734	−	25.4682i	0.0939535	−	0.910740i
$783$	−23.3437			−0.834235
$784$	−16.4174	−	16.4174i	−0.586334	−	0.586334i
$785$	−9.06523	−	21.8854i	−0.323552	−	0.781123i
$786$			103.402i			3.68824i
$787$	−1.34290	+	0.556247i	−0.0478692	+	0.0198281i	−0.406490	−	0.913655i	$-0.633247\pi$
$787$	−1.34290	+	0.556247i	−0.0478692	+	0.0198281i	0.358620	+	0.933483i	$0.383247\pi$
$788$	−7.06044	+	17.0454i	−0.251518	+	0.607218i
$789$	−2.85616	−	1.18306i	−0.101682	−	0.0421181i
$790$	−23.8702	+	23.8702i	−0.849262	+	0.849262i
$791$	−0.835753	+	0.835753i	−0.0297160	+	0.0297160i
$792$	−2.05742	−	0.852212i	−0.0731073	−	0.0302820i
$793$	−13.6855	+	33.0397i	−0.485986	+	1.17327i
$794$	6.69143	−	2.77168i	0.237470	−	0.0983632i
$795$			9.73032i			0.345099i
$796$	−18.4619	−	44.5710i	−0.654366	−	1.57978i
$797$	31.0017	+	31.0017i	1.09813	+	1.09813i	0.994629	+	0.103506i	$0.0330061\pi$
$797$	31.0017	+	31.0017i	1.09813	+	1.09813i	0.103506	+	0.994629i	$0.466994\pi$
$798$	0.170442			0.00603357
$799$	−4.84801	−	2.62020i	−0.171510	−	0.0926961i
$800$	14.5418			0.514130
$801$	50.2261	+	50.2261i	1.77465	+	1.77465i
$802$	9.40094	+	22.6959i	0.331959	+	0.801419i
$803$		−	7.09126i		−	0.250245i
$804$	48.1483	−	19.9437i	1.69806	−	0.703360i
$805$	0.893206	−	2.15639i	0.0314814	−	0.0760028i
$806$	−56.8989	−	23.5683i	−2.00418	−	0.830157i
$807$	59.6053	−	59.6053i	2.09821	−	2.09821i
$808$	6.39054	−	6.39054i	0.224818	−	0.224818i
$809$	22.4438	+	9.29651i	0.789081	+	0.326848i	0.740574	−	0.671975i	$-0.234554\pi$
$809$	22.4438	+	9.29651i	0.789081	+	0.326848i	0.0485068	+	0.998823i	$0.484554\pi$
$810$	−6.18745	+	14.9378i	−0.217405	+	0.524861i
$811$	21.5830	−	8.93999i	0.757883	−	0.313925i	0.0299296	−	0.999552i	$-0.490472\pi$
$811$	21.5830	−	8.93999i	0.757883	−	0.313925i	0.727953	+	0.685627i	$0.240472\pi$
$812$			7.63487i			0.267932i
$813$	−20.9754	−	50.6391i	−0.735640	−	1.77599i
$814$	−10.0209	−	10.0209i	−0.351231	−	0.351231i
$815$	39.8445			1.39569
$816$	37.3047	+	3.84842i	1.30593	+	0.134722i
$817$	−0.255173			−0.00892739
$818$	−29.7102	−	29.7102i	−1.03879	−	1.03879i
$819$	−3.39674	−	8.20047i	−0.118692	−	0.286547i
$820$			31.5541i			1.10192i
$821$	−24.5267	+	10.1593i	−0.855986	+	0.354561i	−0.767136	−	0.641484i	$-0.778319\pi$
$821$	−24.5267	+	10.1593i	−0.855986	+	0.354561i	−0.0888496	+	0.996045i	$0.528319\pi$
$822$	27.5773	−	66.5775i	0.961868	−	2.32216i
$823$	34.8437	+	14.4327i	1.21457	+	0.503093i	0.895681	−	0.444698i	$-0.146689\pi$
$823$	34.8437	+	14.4327i	1.21457	+	0.503093i	0.318893	+	0.947791i	$0.396689\pi$
$824$	0.870218	−	0.870218i	0.0303155	−	0.0303155i
$825$	−3.38117	+	3.38117i	−0.117717	+	0.117717i
$826$	6.95201	+	2.87962i	0.241891	+	0.100195i
$827$	2.96855	−	7.16671i	0.103227	−	0.249211i	−0.863825	−	0.503792i	$-0.831938\pi$
$827$	2.96855	−	7.16671i	0.103227	−	0.249211i	0.967051	+	0.254581i	$0.0819377\pi$
$828$	−25.9110	+	10.7327i	−0.900471	+	0.372987i
$829$			28.8180i			1.00089i	0.865768	+	0.500446i	$0.166830\pi$
$829$			28.8180i			1.00089i	−0.865768	+	0.500446i	$0.833170\pi$
$830$	−23.1211	−	55.8193i	−0.802545	−	1.93751i
$831$	32.9181	+	32.9181i	1.14192	+	1.14192i
$832$	49.3963			1.71251
$833$	26.9159	−	8.02915i	0.932581	−	0.278194i
$834$	107.108			3.70886
$835$	17.9660	+	17.9660i	0.621739	+	0.621739i
$836$	−0.0618083	−	0.149218i	−0.00213769	−	0.00516083i
$837$			17.9811i			0.621517i
$838$	−64.5841	+	26.7516i	−2.23102	+	0.924118i
$839$	5.35489	−	12.9279i	0.184871	−	0.446319i	−0.804087	−	0.594512i	$-0.797345\pi$
$839$	5.35489	−	12.9279i	0.184871	−	0.446319i	0.988959	+	0.148192i	$0.0473455\pi$
$840$	−1.03350	−	0.428090i	−0.0356592	−	0.0147705i
$841$	22.4320	−	22.4320i	0.773517	−	0.773517i
$842$	−19.2685	+	19.2685i	−0.664035	+	0.664035i
$843$	12.7805	+	5.29387i	0.440185	+	0.182331i
$844$	−1.45382	+	3.50983i	−0.0500425	+	0.120813i
$845$	19.3660	−	8.02166i	0.666211	−	0.275953i
$846$			11.3746i			0.391067i
$847$	0.165780	+	0.400229i	0.00569628	+	0.0137520i
$848$	4.90549	+	4.90549i	0.168455	+	0.168455i
$849$	−60.1544			−2.06449
$850$	−7.25110	+	13.4163i	−0.248711	+	0.460174i
$851$	−20.6496			−0.707860
$852$	1.91817	+	1.91817i	0.0657154	+	0.0657154i
$853$	−16.6133	−	40.1080i	−0.568828	−	1.37327i	−0.902544	−	0.430598i	$-0.858303\pi$
$853$	−16.6133	−	40.1080i	−0.568828	−	1.37327i	0.333716	−	0.942674i	$-0.391697\pi$
$854$		−	6.43475i		−	0.220193i
$855$	0.487178	−	0.201796i	0.0166611	−	0.00690126i
$856$	−2.41700	+	5.83516i	−0.0826115	+	0.199442i
$857$	2.09096	+	0.866103i	0.0714257	+	0.0295855i	0.418110	−	0.908396i	$-0.362693\pi$
$857$	2.09096	+	0.866103i	0.0714257	+	0.0295855i	−0.346685	+	0.937982i	$0.612693\pi$
$858$	−19.3626	+	19.3626i	−0.661027	+	0.661027i
$859$	14.7177	−	14.7177i	0.502161	−	0.502161i	−0.409948	−	0.912109i	$-0.634453\pi$
$859$	14.7177	−	14.7177i	0.502161	−	0.502161i	0.912109	+	0.409948i	$0.134453\pi$
$860$	13.3734	+	5.53943i	0.456028	+	0.188893i
$861$	3.44617	−	8.31980i	0.117445	−	0.283538i
$862$	−18.1577	+	7.52118i	−0.618455	+	0.256172i
$863$		−	31.9101i		−	1.08623i	−0.839658	−	0.543116i	$-0.817244\pi$
$863$		−	31.9101i		−	1.08623i	0.839658	−	0.543116i	$-0.182756\pi$
$864$	−9.30425	−	22.4624i	−0.316537	−	0.764188i
$865$	−16.6000	−	16.6000i	−0.564418	−	0.564418i
$866$	36.0396			1.22468
$867$	−25.5537	+	37.4887i	−0.867849	+	1.27318i
$868$	5.88097			0.199613
$869$	−6.45547	−	6.45547i	−0.218987	−	0.218987i
$870$	29.4280	+	71.0455i	0.997703	+	2.40867i
$871$		−	42.9134i		−	1.45407i
$872$	−2.60705	+	1.07988i	−0.0882860	+	0.0365693i
$873$	−15.7258	+	37.9654i	−0.532237	+	1.28493i
$874$	−0.409699	−	0.169703i	−0.0138583	−	0.00574028i
$875$	−3.72644	+	3.72644i	−0.125977	+	0.125977i
$876$	−30.2659	+	30.2659i	−1.02259	+	1.02259i
$877$	44.6270	+	18.4851i	1.50695	+	0.624198i	0.974925	−	0.222533i	$-0.0714324\pi$
$877$	44.6270	+	18.4851i	1.50695	+	0.624198i	0.532022	+	0.846731i	$0.321432\pi$
$878$	10.1179	−	24.4268i	0.341463	−	0.824364i
$879$	−12.3302	+	5.10733i	−0.415887	+	0.172266i
$880$		−	6.10463i		−	0.205787i
$881$	15.7848	+	38.1078i	0.531803	+	1.28389i	0.930328	+	0.366729i	$0.119522\pi$
$881$	15.7848	+	38.1078i	0.531803	+	1.28389i	−0.398525	+	0.917157i	$0.630478\pi$
$882$	−40.9948	−	40.9948i	−1.38037	−	1.38037i
$883$	−57.0972			−1.92147			−0.960737	−	0.277462i	$-0.910507\pi$
$883$	−57.0972			−1.92147			−0.960737	+	0.277462i	$0.910507\pi$
$884$	−22.0368	+	40.7735i	−0.741179	+	1.37136i
$885$	40.2220			1.35205
$886$	10.4232	+	10.4232i	0.350173	+	0.350173i
$887$	−5.80868	−	14.0234i	−0.195036	−	0.470859i	0.795861	−	0.605479i	$-0.207019\pi$
$887$	−5.80868	−	14.0234i	−0.195036	−	0.470859i	−0.990897	+	0.134620i	$0.957019\pi$
$888$			9.89681i			0.332115i
$889$	−6.10539	+	2.52893i	−0.204768	+	0.0848177i
$890$	24.3811	−	58.8612i	0.817256	−	1.97303i
$891$	−4.03980	−	1.67334i	−0.135338	−	0.0560590i
$892$	−31.0298	+	31.0298i	−1.03896	+	1.03896i
$893$	−0.0674917	+	0.0674917i	−0.00225853	+	0.00225853i
$894$	39.4175	+	16.3273i	1.31832	+	0.546066i
$895$	−7.59854	+	18.3445i	−0.253991	+	0.613189i
$896$	−1.71481	+	0.710297i	−0.0572877	+	0.0237293i
$897$			39.8997i			1.33221i
$898$	2.15074	+	5.19234i	0.0717711	+	0.173271i
$899$	−33.0742	−	33.0742i	−1.10309	−	1.10309i
$900$	16.7053			0.556843
$901$	−8.04244	+	2.39910i	−0.267933	+	0.0799256i
$902$	−16.0797			−0.535397
$903$	−2.92113	−	2.92113i	−0.0972092	−	0.0972092i
$904$	−0.564014	−	1.36165i	−0.0187588	−	0.0452878i
$905$			7.98606i			0.265466i
$906$	−28.3874	+	11.7584i	−0.943107	+	0.390648i
$907$	1.39625	−	3.37083i	0.0463616	−	0.111927i	−0.899002	−	0.437944i	$-0.855707\pi$
$907$	1.39625	−	3.37083i	0.0463616	−	0.111927i	0.945364	+	0.326017i	$0.105707\pi$
$908$	11.2221	+	4.64835i	0.372419	+	0.154261i
$909$	−48.7691	+	48.7691i	−1.61757	+	1.61757i
$910$	−5.62960	+	5.62960i	−0.186620	+	0.186620i
$911$	−49.8359	−	20.6427i	−1.65114	−	0.683923i	−0.653787	−	0.756679i	$-0.726821\pi$
$911$	−49.8359	−	20.6427i	−1.65114	−	0.683923i	−0.997350	+	0.0727558i	$0.976821\pi$
$912$	0.248573	−	0.600109i	0.00823109	−	0.0198716i
$913$	15.0958	−	6.25290i	0.499599	−	0.206941i
$914$		−	30.0558i		−	0.994159i
$915$	−13.1626	−	31.7772i	−0.435141	−	1.05052i
$916$	−19.4210	−	19.4210i	−0.641686	−	0.641686i
$917$	−8.13051			−0.268493
$918$	25.3633	+	2.61652i	0.837114	+	0.0863582i
$919$	27.6984			0.913688			0.456844	−	0.889547i	$-0.348980\pi$
$919$	27.6984			0.913688			0.456844	+	0.889547i	$0.348980\pi$
$920$	2.05804	+	2.05804i	0.0678516	+	0.0678516i
$921$	−3.73523	−	9.01764i	−0.123080	−	0.297141i
$922$			53.8614i			1.77383i
$923$	2.06369	−	0.854808i	0.0679272	−	0.0281363i
$924$	1.00064	−	2.41576i	0.0329187	−	0.0794727i
$925$	11.3635	+	4.70692i	0.373630	+	0.154762i
$926$	4.15546	−	4.15546i	0.136557	−	0.136557i
$927$	−6.64103	+	6.64103i	−0.218120	+	0.218120i
$928$	58.4313	+	24.2030i	1.91810	+	0.794504i
$929$	−19.5644	+	47.2327i	−0.641887	+	1.54965i	0.182243	+	0.983253i	$0.441664\pi$
$929$	−19.5644	+	47.2327i	−0.641887	+	1.54965i	−0.824131	+	0.566400i	$0.808336\pi$
$930$	54.7247	−	22.6677i	1.79449	−	0.743304i
$931$		−	0.486489i		−	0.0159440i
$932$	−8.78638	−	21.2122i	−0.287808	−	0.694829i
$933$	−36.4744	−	36.4744i	−1.19412	−	1.19412i
$934$	−38.6992			−1.26628
$935$	6.49699	+	3.51143i	0.212474	+	0.114836i
$936$	11.0683			0.361778
$937$	−23.8738	−	23.8738i	−0.779921	−	0.779921i	0.199896	−	0.979817i	$-0.435940\pi$
$937$	−23.8738	−	23.8738i	−0.779921	−	0.779921i	−0.979817	+	0.199896i	$0.935940\pi$
$938$	2.95491	+	7.13377i	0.0964811	+	0.232926i
$939$			78.7896i			2.57120i
$940$	5.00231	−	2.07202i	0.163157	−	0.0675820i
$941$	−3.47504	+	8.38949i	−0.113283	+	0.273489i	−0.970345	−	0.241724i	$-0.922287\pi$
$941$	−3.47504	+	8.38949i	−0.113283	+	0.273489i	0.857062	+	0.515213i	$0.172287\pi$
$942$	−67.3167	−	27.8835i	−2.19330	−	0.908493i
$943$	−16.5675	+	16.5675i	−0.539511	+	0.539511i
$944$	20.2777	−	20.2777i	0.659984	−	0.659984i
$945$	2.14751	+	0.889529i	0.0698586	+	0.0289364i
$946$	−2.82285	+	6.81496i	−0.0917788	+	0.221574i
$947$	−54.7988	+	22.6984i	−1.78072	+	0.737599i	−0.788217	+	0.615398i	$0.788995\pi$
$947$	−54.7988	+	22.6984i	−1.78072	+	0.737599i	−0.992505	+	0.122202i	$0.961005\pi$
$948$			55.1047i			1.78972i
$949$	13.4876	+	32.5620i	0.437827	+	1.05701i
$950$	0.186775	+	0.186775i	0.00605979	+	0.00605979i
$951$	−21.8205			−0.707577
$952$	0.0990119	−	0.959774i	0.00320900	−	0.0311065i
$953$	−34.3735			−1.11347			−0.556734	−	0.830691i	$-0.687946\pi$
$953$	−34.3735			−1.11347			−0.556734	+	0.830691i	$0.687946\pi$
$954$	12.2492	+	12.2492i	0.396582	+	0.396582i
$955$	−16.1111	−	38.8955i	−0.521342	−	1.25863i
$956$		−	12.1408i		−	0.392662i
$957$	−19.2136	+	7.95855i	−0.621089	+	0.257263i
$958$	6.41734	−	15.4928i	0.207335	−	0.500551i
$959$	5.23498	+	2.16840i	0.169046	+	0.0700213i
$960$	−33.5938	+	33.5938i	−1.08424	+	1.08424i
$961$	−3.55598	+	3.55598i	−0.114709	+	0.114709i
$962$	65.0741	+	26.9546i	2.09807	+	0.869050i
$963$	18.4453	−	44.5308i	0.594390	−	1.43498i
$964$	−1.83509	+	0.760120i	−0.0591044	+	0.0244818i
$965$		−	23.9345i		−	0.770479i
$966$	−2.74739	−	6.63278i	−0.0883958	−	0.213406i
$967$	−4.98941	−	4.98941i	−0.160449	−	0.160449i	0.622317	−	0.782765i	$-0.286192\pi$
$967$	−4.98941	−	4.98941i	−0.160449	−	0.160449i	−0.782765	+	0.622317i	$0.786192\pi$
$968$	−0.540195			−0.0173625
$969$	0.495698	+	0.609737i	0.0159241	+	0.0195876i
$970$	36.8589			1.18347
$971$	12.9818	+	12.9818i	0.416606	+	0.416606i	0.884032	−	0.467426i	$-0.154819\pi$
$971$	12.9818	+	12.9818i	0.416606	+	0.416606i	−0.467426	+	0.884032i	$0.654819\pi$
$972$	17.8784	+	43.1623i	0.573451	+	1.38443i
$973$			8.42192i			0.269995i
$974$	1.35977	−	0.563233i	0.0435697	−	0.0180472i
$975$	9.09482	−	21.9568i	0.291267	−	0.703182i
$976$	−22.6562	−	9.38449i	−0.725206	−	0.300390i
$977$	2.44744	−	2.44744i	0.0783006	−	0.0783006i	−0.666872	−	0.745172i	$-0.732367\pi$
$977$	2.44744	−	2.44744i	0.0783006	−	0.0783006i	0.745172	+	0.666872i	$0.232367\pi$
$978$	86.6606	−	86.6606i	2.77110	−	2.77110i
$979$	15.9185	+	6.59365i	0.508757	+	0.210734i
$980$	−10.5609	+	25.4964i	−0.337357	+	0.814452i
$981$	19.8956	−	8.24104i	0.635218	−	0.263116i
$982$			34.8242i			1.11129i
$983$	8.02576	+	19.3759i	0.255982	+	0.617995i	0.998665	−	0.0516476i	$-0.0164473\pi$
$983$	8.02576	+	19.3759i	0.255982	+	0.617995i	−0.742683	+	0.669643i	$0.766447\pi$
$984$	7.94035	+	7.94035i	0.253129	+	0.253129i
$985$	−14.6117			−0.465566
$986$	−51.4658	+	41.8402i	−1.63901	+	1.33246i
$987$	−1.54524			−0.0491856
$988$	0.567629	+	0.567629i	0.0180587	+	0.0180587i
$989$	4.11320	+	9.93014i	0.130792	+	0.315760i
$990$		−	15.2435i		−	0.484470i
$991$	−19.1003	+	7.91161i	−0.606742	+	0.251321i	−0.664835	−	0.746991i	$-0.731498\pi$
$991$	−19.1003	+	7.91161i	−0.606742	+	0.251321i	0.0580930	+	0.998311i	$0.481498\pi$
$992$	18.6430	−	45.0083i	0.591917	−	1.42901i
$993$	−30.1795	−	12.5008i	−0.957718	−	0.396700i
$994$	−0.284200	+	0.284200i	−0.00901429	+	0.00901429i
$995$	27.0165	−	27.0165i	0.856482	−	0.856482i
$996$	−91.1176	−	37.7421i	−2.88717	−	1.19591i
$997$	0.785914	−	1.89736i	0.0248901	−	0.0600901i	−0.910946	−	0.412526i	$-0.864647\pi$
$997$	0.785914	−	1.89736i	0.0248901	−	0.0600901i	0.935836	+	0.352436i	$0.114647\pi$
$998$	8.19602	−	3.39490i	0.259441	−	0.107464i
$999$		−	20.5646i		−	0.650635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.100.2	✓	56
17.5	odd	16		3179.2.a.bi.1.24		28
17.8	even	8	inner	187.2.h.a.144.2	yes	56
17.12	odd	16		3179.2.a.bh.1.24		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.2	✓	56	1.1	even	1	trivial
187.2.h.a.144.2	yes	56	17.8	even	8	inner
3179.2.a.bh.1.24		28	17.12	odd	16
3179.2.a.bi.1.24		28	17.5	odd	16

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45974 - 1.45974i) q^{2} +(-1.02130 - 2.46565i) q^{3} +2.26167i q^{4} +(-1.65483 + 0.685451i) q^{5} +(-2.10836 + 5.09004i) q^{6} +(-0.400229 - 0.165780i) q^{7} +(0.381975 - 0.381975i) q^{8} +(-2.91503 + 2.91503i) q^{9} +O(q^{10})\)	\(q+(-1.45974 - 1.45974i) q^{2} +(-1.02130 - 2.46565i) q^{3} +2.26167i q^{4} +(-1.65483 + 0.685451i) q^{5} +(-2.10836 + 5.09004i) q^{6} +(-0.400229 - 0.165780i) q^{7} +(0.381975 - 0.381975i) q^{8} +(-2.91503 + 2.91503i) q^{9} +(3.41619 + 1.41503i) q^{10} +(-0.382683 + 0.923880i) q^{11} +(5.57649 - 2.30986i) q^{12} -4.97018i q^{13} +(0.342234 + 0.826225i) q^{14} +(3.38016 + 3.38016i) q^{15} +3.40818 q^{16} +(-1.96041 + 3.62723i) q^{17} +8.51035 q^{18} +(0.0504966 + 0.0504966i) q^{19} +(-1.55027 - 3.74268i) q^{20} +1.15613i q^{21} +(1.90724 - 0.790005i) q^{22} +(1.15112 - 2.77906i) q^{23} +(-1.33193 - 0.551703i) q^{24} +(-1.26693 + 1.26693i) q^{25} +(-7.25517 + 7.25517i) q^{26} +(2.76761 + 1.14638i) q^{27} +(0.374941 - 0.905187i) q^{28} +(-7.19936 + 2.98207i) q^{29} -9.86830i q^{30} +(2.29702 + 5.54550i) q^{31} +(-5.73900 - 5.73900i) q^{32} +2.66880 q^{33} +(8.15649 - 2.43312i) q^{34} +0.775944 q^{35} +(-6.59284 - 6.59284i) q^{36} +(-2.62706 - 6.34228i) q^{37} -0.147424i q^{38} +(-12.2547 + 5.07607i) q^{39} +(-0.370277 + 0.893928i) q^{40} +(-7.19622 - 2.98077i) q^{41} +(1.68765 - 1.68765i) q^{42} +(-2.52664 + 2.52664i) q^{43} +(-2.08951 - 0.865505i) q^{44} +(2.82575 - 6.82197i) q^{45} +(-5.73703 + 2.37636i) q^{46} +1.33656i q^{47} +(-3.48079 - 8.40336i) q^{48} +(-4.81705 - 4.81705i) q^{49} +3.69877 q^{50} +(10.9456 + 1.12917i) q^{51} +11.2409 q^{52} +(1.43933 + 1.43933i) q^{53} +(-2.36657 - 5.71341i) q^{54} -1.79117i q^{55} +(-0.216201 + 0.0895536i) q^{56} +(0.0729344 - 0.176079i) q^{57} +(14.8622 + 6.15614i) q^{58} +(5.94972 - 5.94972i) q^{59} +(-7.64482 + 7.64482i) q^{60} +(-6.64758 - 2.75352i) q^{61} +(4.74193 - 11.4480i) q^{62} +(1.64993 - 0.683424i) q^{63} +9.93853i q^{64} +(3.40682 + 8.22479i) q^{65} +(-3.89574 - 3.89574i) q^{66} +8.63417 q^{67} +(-8.20361 - 4.43381i) q^{68} -8.02781 q^{69} +(-1.13267 - 1.13267i) q^{70} +(0.171987 + 0.415214i) q^{71} +2.22694i q^{72} +(-6.55147 + 2.71371i) q^{73} +(-5.42325 + 13.0929i) q^{74} +(4.41771 + 1.82988i) q^{75} +(-0.114207 + 0.114207i) q^{76} +(0.306322 - 0.306322i) q^{77} +(25.2984 + 10.4789i) q^{78} +(-3.49368 + 8.43448i) q^{79} +(-5.63995 + 2.33614i) q^{80} +4.37265i q^{81} +(6.15345 + 14.8557i) q^{82} +(-11.5538 - 11.5538i) q^{83} -2.61480 q^{84} +(0.757847 - 7.34620i) q^{85} +7.37646 q^{86} +(14.7055 + 14.7055i) q^{87} +(0.206723 + 0.499075i) q^{88} -17.2300i q^{89} +(-14.0832 + 5.83344i) q^{90} +(-0.823958 + 1.98921i) q^{91} +(6.28532 + 2.60346i) q^{92} +(11.3273 - 11.3273i) q^{93} +(1.95103 - 1.95103i) q^{94} +(-0.118176 - 0.0489502i) q^{95} +(-8.28908 + 20.0116i) q^{96} +(9.20938 - 3.81465i) q^{97} +14.0633i q^{98} +(-1.57760 - 3.80867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 16 q^{6}+O(q^{10}) \) 56 * q - 16 * q^6	\( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more