LMFDB - Embedded newform 187.2.h.a.111.5

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			111.5
Character	$\chi$	$=$	187.111
Dual form			187.2.h.a.155.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900361 + 0.900361i) q^{2} +(0.234589 + 0.0971699i) q^{3} +0.378700i q^{4} +(-0.780524 + 1.88435i) q^{5} +(-0.298703 + 0.123727i) q^{6} +(0.838489 + 2.02429i) q^{7} +(-2.14169 - 2.14169i) q^{8} +(-2.07573 - 2.07573i) q^{9} +O(q^{10})$	\(q+(-0.900361 + 0.900361i) q^{2} +(0.234589 + 0.0971699i) q^{3} +0.378700i q^{4} +(-0.780524 + 1.88435i) q^{5} +(-0.298703 + 0.123727i) q^{6} +(0.838489 + 2.02429i) q^{7} +(-2.14169 - 2.14169i) q^{8} +(-2.07573 - 2.07573i) q^{9} +(-0.993844 - 2.39935i) q^{10} +(0.923880 - 0.382683i) q^{11} +(-0.0367982 + 0.0888387i) q^{12} +3.83860i q^{13} +(-2.57754 - 1.06765i) q^{14} +(-0.366205 + 0.366205i) q^{15} +3.09919 q^{16} +(-3.43240 + 2.28443i) q^{17} +3.73781 q^{18} +(-2.45993 + 2.45993i) q^{19} +(-0.713603 - 0.295584i) q^{20} +0.556352i q^{21} +(-0.487272 + 1.17638i) q^{22} +(2.58739 - 1.07173i) q^{23} +(-0.294309 - 0.710524i) q^{24} +(0.593971 + 0.593971i) q^{25} +(-3.45612 - 3.45612i) q^{26} +(-0.576755 - 1.39241i) q^{27} +(-0.766598 + 0.317535i) q^{28} +(2.12074 - 5.11992i) q^{29} -0.659433i q^{30} +(2.73874 + 1.13442i) q^{31} +(1.49299 - 1.49299i) q^{32} +0.253917 q^{33} +(1.03358 - 5.14721i) q^{34} -4.46894 q^{35} +(0.786078 - 0.786078i) q^{36} +(5.36581 + 2.22259i) q^{37} -4.42965i q^{38} +(-0.372996 + 0.900492i) q^{39} +(5.70733 - 2.36406i) q^{40} +(3.38382 + 8.16927i) q^{41} +(-0.500918 - 0.500918i) q^{42} +(2.45357 + 2.45357i) q^{43} +(0.144922 + 0.349873i) q^{44} +(5.53156 - 2.29125i) q^{45} +(-1.36464 + 3.29453i) q^{46} +6.12096i q^{47} +(0.727035 + 0.301148i) q^{48} +(1.55505 - 1.55505i) q^{49} -1.06958 q^{50} +(-1.02718 + 0.202377i) q^{51} -1.45368 q^{52} +(9.18770 - 9.18770i) q^{53} +(1.77296 + 0.734383i) q^{54} +2.03961i q^{55} +(2.53962 - 6.13119i) q^{56} +(-0.816103 + 0.338041i) q^{57} +(2.70034 + 6.51920i) q^{58} +(-3.09297 - 3.09297i) q^{59} +(-0.138682 - 0.138682i) q^{60} +(-2.55329 - 6.16418i) q^{61} +(-3.48724 + 1.44446i) q^{62} +(2.46141 - 5.94236i) q^{63} +8.88683i q^{64} +(-7.23327 - 2.99612i) q^{65} +(-0.228617 + 0.228617i) q^{66} +14.1891 q^{67} +(-0.865114 - 1.29985i) q^{68} +0.711114 q^{69} +(4.02366 - 4.02366i) q^{70} +(-8.28235 - 3.43066i) q^{71} +8.89114i q^{72} +(-0.375757 + 0.907158i) q^{73} +(-6.83230 + 2.83003i) q^{74} +(0.0816228 + 0.197055i) q^{75} +(-0.931574 - 0.931574i) q^{76} +(1.54933 + 1.54933i) q^{77} +(-0.474937 - 1.14660i) q^{78} +(-7.82616 + 3.24170i) q^{79} +(-2.41899 + 5.83996i) q^{80} +8.42389i q^{81} +(-10.4020 - 4.30863i) q^{82} +(-10.3463 + 10.3463i) q^{83} -0.210690 q^{84} +(-1.62561 - 8.25090i) q^{85} -4.41819 q^{86} +(0.995004 - 0.995004i) q^{87} +(-2.79825 - 1.15907i) q^{88} -0.726133i q^{89} +(-2.91745 + 7.04336i) q^{90} +(-7.77044 + 3.21862i) q^{91} +(0.405865 + 0.979844i) q^{92} +(0.532246 + 0.532246i) q^{93} +(-5.51108 - 5.51108i) q^{94} +(-2.71534 - 6.55540i) q^{95} +(0.495312 - 0.205165i) q^{96} +(4.53925 - 10.9587i) q^{97} +2.80022i q^{98} +(-2.71207 - 1.12338i) 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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.900361	+	0.900361i	−0.636651	+	0.636651i	−0.949728	−	0.313076i	$-0.898640\pi$
$2$	−0.900361	+	0.900361i	−0.636651	+	0.636651i	0.313076	+	0.949728i	$0.398640\pi$
$3$	0.234589	+	0.0971699i	0.135440	+	0.0561011i	0.449374	−	0.893344i	$-0.351647\pi$
$3$	0.234589	+	0.0971699i	0.135440	+	0.0561011i	−0.313934	+	0.949445i	$0.601647\pi$
$4$			0.378700i			0.189350i
$5$	−0.780524	+	1.88435i	−0.349061	+	0.842708i	0.647670	+	0.761921i	$0.275743\pi$
$5$	−0.780524	+	1.88435i	−0.349061	+	0.842708i	−0.996731	+	0.0807871i	$0.974257\pi$
$6$	−0.298703	+	0.123727i	−0.121945	+	0.0505112i
$7$	0.838489	+	2.02429i	0.316919	+	0.765110i	0.999414	+	0.0342203i	$0.0108948\pi$
$7$	0.838489	+	2.02429i	0.316919	+	0.765110i	−0.682495	+	0.730890i	$0.739105\pi$
$8$	−2.14169	−	2.14169i	−0.757201	−	0.757201i
$9$	−2.07573	−	2.07573i	−0.691910	−	0.691910i
$10$	−0.993844	−	2.39935i	−0.314281	−	0.758741i
$11$	0.923880	−	0.382683i	0.278560	−	0.115383i
$11$	0.923880	−	0.382683i	0.278560	−	0.115383i
$12$	−0.0367982	+	0.0888387i	−0.0106227	+	0.0256455i
$13$			3.83860i			1.06464i	0.846545	+	0.532318i	$0.178679\pi$
$13$			3.83860i			1.06464i	−0.846545	+	0.532318i	$0.821321\pi$
$14$	−2.57754	−	1.06765i	−0.688876	−	0.285342i
$15$	−0.366205	+	0.366205i	−0.0945536	+	0.0945536i
$16$	3.09919			0.774797
$17$	−3.43240	+	2.28443i	−0.832479	+	0.554057i
$17$	−3.43240	+	2.28443i	−0.832479	+	0.554057i
$18$	3.73781			0.881011
$19$	−2.45993	+	2.45993i	−0.564346	+	0.564346i	−0.930539	−	0.366193i	$-0.880661\pi$
$19$	−2.45993	+	2.45993i	−0.564346	+	0.564346i	0.366193	+	0.930539i	$0.380661\pi$
$20$	−0.713603	−	0.295584i	−0.159567	−	0.0660946i
$21$			0.556352i			0.121406i
$22$	−0.487272	+	1.17638i	−0.103887	+	0.250805i
$23$	2.58739	−	1.07173i	0.539509	−	0.223472i	−0.0962535	−	0.995357i	$-0.530686\pi$
$23$	2.58739	−	1.07173i	0.539509	−	0.223472i	0.635762	+	0.771885i	$0.280686\pi$
$24$	−0.294309	−	0.710524i	−0.0600755	−	0.145035i
$25$	0.593971	+	0.593971i	0.118794	+	0.118794i
$26$	−3.45612	−	3.45612i	−0.677802	−	0.677802i
$27$	−0.576755	−	1.39241i	−0.110996	−	0.267969i
$28$	−0.766598	+	0.317535i	−0.144873	+	0.0600086i
$29$	2.12074	−	5.11992i	0.393811	−	0.950745i	−0.595290	−	0.803511i	$-0.702963\pi$
$29$	2.12074	−	5.11992i	0.393811	−	0.950745i	0.989102	−	0.147234i	$-0.0470370\pi$
$30$		−	0.659433i		−	0.120395i
$31$	2.73874	+	1.13442i	0.491892	+	0.203748i	0.614820	−	0.788667i	$-0.289229\pi$
$31$	2.73874	+	1.13442i	0.491892	+	0.203748i	−0.122928	+	0.992416i	$0.539229\pi$
$32$	1.49299	−	1.49299i	0.263926	−	0.263926i
$33$	0.253917			0.0442013
$34$	1.03358	−	5.14721i	0.177258	−	0.882740i
$35$	−4.46894			−0.755389
$36$	0.786078	−	0.786078i	0.131013	−	0.131013i
$37$	5.36581	+	2.22259i	0.882134	+	0.365392i	0.777324	−	0.629100i	$-0.216577\pi$
$37$	5.36581	+	2.22259i	0.882134	+	0.365392i	0.104810	+	0.994492i	$0.466577\pi$
$38$		−	4.42965i		−	0.718584i
$39$	−0.372996	+	0.900492i	−0.0597272	+	0.144194i
$40$	5.70733	−	2.36406i	0.902409	−	0.373790i
$41$	3.38382	+	8.16927i	0.528464	+	1.27583i	0.932529	+	0.361095i	$0.117597\pi$
$41$	3.38382	+	8.16927i	0.528464	+	1.27583i	−0.404065	+	0.914730i	$0.632403\pi$
$42$	−0.500918	−	0.500918i	−0.0772933	−	0.0772933i
$43$	2.45357	+	2.45357i	0.374166	+	0.374166i	0.868992	−	0.494826i	$-0.164768\pi$
$43$	2.45357	+	2.45357i	0.374166	+	0.374166i	−0.494826	+	0.868992i	$0.664768\pi$
$44$	0.144922	+	0.349873i	0.0218478	+	0.0527453i
$45$	5.53156	−	2.29125i	0.824597	−	0.341559i
$46$	−1.36464	+	3.29453i	−0.201205	+	0.485753i
$47$			6.12096i			0.892834i	0.894825	+	0.446417i	$0.147300\pi$
$47$			6.12096i			0.892834i	−0.894825	+	0.446417i	$0.852700\pi$
$48$	0.727035	+	0.301148i	0.104938	+	0.0434669i
$49$	1.55505	−	1.55505i	0.222151	−	0.222151i
$50$	−1.06958			−0.151261
$51$	−1.02718	+	0.202377i	−0.143834	+	0.0283384i
$52$	−1.45368			−0.201588
$53$	9.18770	−	9.18770i	1.26203	−	1.26203i	0.311920	−	0.950108i	$-0.399028\pi$
$53$	9.18770	−	9.18770i	1.26203	−	1.26203i	0.950108	−	0.311920i	$-0.100972\pi$
$54$	1.77296	+	0.734383i	0.241269	+	0.0999369i
$55$			2.03961i			0.275021i
$56$	2.53962	−	6.13119i	0.339371	−	0.819314i
$57$	−0.816103	+	0.338041i	−0.108095	+	0.0447746i
$58$	2.70034	+	6.51920i	0.354572	+	0.856014i
$59$	−3.09297	−	3.09297i	−0.402670	−	0.402670i	0.476503	−	0.879173i	$-0.341904\pi$
$59$	−3.09297	−	3.09297i	−0.402670	−	0.402670i	−0.879173	+	0.476503i	$0.841904\pi$
$60$	−0.138682	−	0.138682i	−0.0179037	−	0.0179037i
$61$	−2.55329	−	6.16418i	−0.326915	−	0.789243i	−0.998818	−	0.0486035i	$-0.984523\pi$
$61$	−2.55329	−	6.16418i	−0.326915	−	0.789243i	0.671903	−	0.740639i	$-0.265477\pi$
$62$	−3.48724	+	1.44446i	−0.442880	+	0.183447i
$63$	2.46141	−	5.94236i	0.310108	−	0.748667i
$64$			8.88683i			1.11085i
$65$	−7.23327	−	2.99612i	−0.897176	−	0.371623i
$66$	−0.228617	+	0.228617i	−0.0281408	+	0.0281408i
$67$	14.1891			1.73347			0.866737	−	0.498765i	$-0.166213\pi$
$67$	14.1891			1.73347			0.866737	+	0.498765i	$0.166213\pi$
$68$	−0.865114	−	1.29985i	−0.104910	−	0.157630i
$69$	0.711114			0.0856080
$70$	4.02366	−	4.02366i	0.480919	−	0.480919i
$71$	−8.28235	−	3.43066i	−0.982934	−	0.407144i	−0.167422	−	0.985885i	$-0.553544\pi$
$71$	−8.28235	−	3.43066i	−0.982934	−	0.407144i	−0.815512	+	0.578741i	$0.803544\pi$
$72$			8.89114i			1.04783i
$73$	−0.375757	+	0.907158i	−0.0439790	+	0.106175i	−0.944343	−	0.328964i	$-0.893301\pi$
$73$	−0.375757	+	0.907158i	−0.0439790	+	0.106175i	0.900364	+	0.435139i	$0.143301\pi$
$74$	−6.83230	+	2.83003i	−0.794239	+	0.328985i
$75$	0.0816228	+	0.197055i	0.00942499	+	0.0227540i
$76$	−0.931574	−	0.931574i	−0.106859	−	0.106859i
$77$	1.54933	+	1.54933i	0.176562	+	0.176562i
$78$	−0.474937	−	1.14660i	−0.0537760	−	0.129827i
$79$	−7.82616	+	3.24170i	−0.880512	+	0.364720i	−0.776695	−	0.629876i	$-0.783106\pi$
$79$	−7.82616	+	3.24170i	−0.880512	+	0.364720i	−0.103817	+	0.994596i	$0.533106\pi$
$80$	−2.41899	+	5.83996i	−0.270451	+	0.652927i
$81$			8.42389i			0.935988i
$82$	−10.4020	−	4.30863i	−1.14870	−	0.475809i
$83$	−10.3463	+	10.3463i	−1.13566	+	1.13566i	−0.146439	+	0.989220i	$0.546781\pi$
$83$	−10.3463	+	10.3463i	−1.13566	+	1.13566i	−0.989220	+	0.146439i	$0.953219\pi$
$84$	−0.210690			−0.0229882
$85$	−1.62561	−	8.25090i	−0.176322	−	0.894936i
$86$	−4.41819			−0.476426
$87$	0.995004	−	0.995004i	0.106676	−	0.106676i
$88$	−2.79825	−	1.15907i	−0.298295	−	0.123558i
$89$		−	0.726133i		−	0.0769700i	−0.999259	−	0.0384850i	$-0.987747\pi$
$89$		−	0.726133i		−	0.0769700i	0.999259	−	0.0384850i	$-0.0122532\pi$
$90$	−2.91745	+	7.04336i	−0.307527	+	0.742435i
$91$	−7.77044	+	3.21862i	−0.814564	+	0.337403i
$92$	0.405865	+	0.979844i	0.0423143	+	0.102156i
$93$	0.532246	+	0.532246i	0.0551913	+	0.0551913i
$94$	−5.51108	−	5.51108i	−0.568424	−	0.568424i
$95$	−2.71534	−	6.55540i	−0.278588	−	0.672570i
$96$	0.495312	−	0.205165i	0.0505526	−	0.0209396i
$97$	4.53925	−	10.9587i	0.460891	−	1.11269i	−0.507141	−	0.861863i	$-0.669298\pi$
$97$	4.53925	−	10.9587i	0.460891	−	1.11269i	0.968032	−	0.250827i	$-0.0807024\pi$
$98$			2.80022i			0.282865i
$99$	−2.71207	−	1.12338i	−0.272574	−	0.112904i
$100$	−0.224936	+	0.224936i	−0.0224936	+	0.0224936i
$101$	9.08387			0.903879			0.451939	−	0.892049i	$-0.350732\pi$
$101$	9.08387			0.903879			0.451939	+	0.892049i	$0.350732\pi$
$102$	0.742622	−	1.10705i	0.0735305	−	0.109614i
$103$	−1.91921			−0.189105			−0.0945525	−	0.995520i	$-0.530142\pi$
$103$	−1.91921			−0.189105			−0.0945525	+	0.995520i	$0.530142\pi$
$104$	8.22108	−	8.22108i	0.806143	−	0.806143i
$105$	−1.04836	−	0.434246i	−0.102310	−	0.0423781i
$106$			16.5445i			1.60694i
$107$	−5.67835	+	13.7088i	−0.548947	+	1.32528i	0.369316	+	0.929304i	$0.379592\pi$
$107$	−5.67835	+	13.7088i	−0.548947	+	1.32528i	−0.918263	+	0.395971i	$0.870408\pi$
$108$	0.527305	−	0.218417i	0.0507399	−	0.0210172i
$109$	−4.28165	−	10.3368i	−0.410108	−	0.990088i	−0.985108	−	0.171935i	$-0.944998\pi$
$109$	−4.28165	−	10.3368i	−0.410108	−	0.990088i	0.575001	−	0.818153i	$-0.305002\pi$
$110$	−1.83638	−	1.83638i	−0.175092	−	0.175092i
$111$	1.04279	+	1.04279i	0.0989773	+	0.0989773i
$112$	2.59864	+	6.27366i	0.245548	+	0.592805i
$113$	−8.95648	+	3.70989i	−0.842554	+	0.348997i	−0.761860	−	0.647741i	$-0.775714\pi$
$113$	−8.95648	+	3.70989i	−0.842554	+	0.348997i	−0.0806942	+	0.996739i	$0.525714\pi$
$114$	0.430429	−	1.03915i	0.0403133	−	0.0973250i
$115$			5.71207i			0.532653i
$116$	1.93891	+	0.803123i	0.180023	+	0.0745681i
$117$	7.96789	−	7.96789i	0.736632	−	0.736632i
$118$	5.56958			0.512721
$119$	−7.50239	−	5.03270i	−0.687743	−	0.461347i
$120$	1.56859			0.143192
$121$	0.707107	−	0.707107i	0.0642824	−	0.0642824i
$122$	7.84887	+	3.25111i	0.710603	+	0.294342i
$123$			2.24523i			0.202445i
$124$	−0.429605	+	1.03716i	−0.0385797	+	0.0931396i
$125$	−11.0046	+	4.55826i	−0.984283	+	0.407703i
$126$	3.13412	+	7.56643i	0.279209	+	0.674071i
$127$	6.28233	+	6.28233i	0.557467	+	0.557467i	0.928585	−	0.371119i	$-0.121026\pi$
$127$	6.28233	+	6.28233i	0.557467	+	0.557467i	−0.371119	+	0.928585i	$0.621026\pi$
$128$	−5.01538	−	5.01538i	−0.443301	−	0.443301i
$129$	0.337167	+	0.813993i	0.0296859	+	0.0716681i
$130$	9.21014	−	3.81496i	0.807783	−	0.334595i
$131$	5.20790	−	12.5730i	0.455017	−	1.09851i	−0.515374	−	0.856966i	$-0.672347\pi$
$131$	5.20790	−	12.5730i	0.455017	−	1.09851i	0.970390	−	0.241542i	$-0.0776531\pi$
$132$			0.0961583i			0.00836951i
$133$	−7.04224	−	2.91699i	−0.610639	−	0.252935i
$134$	−12.7753	+	12.7753i	−1.10362	+	1.10362i
$135$	3.07396			0.264564
$136$	12.2437	+	2.45858i	1.04989	+	0.210822i
$137$	14.5092			1.23960			0.619801	−	0.784759i	$-0.287213\pi$
$137$	14.5092			1.23960			0.619801	+	0.784759i	$0.287213\pi$
$138$	−0.640259	+	0.640259i	−0.0545025	+	0.0545025i
$139$	−13.5194	−	5.59991i	−1.14670	−	0.474978i	−0.273273	−	0.961936i	$-0.588106\pi$
$139$	−13.5194	−	5.59991i	−1.14670	−	0.474978i	−0.873425	+	0.486958i	$0.838106\pi$
$140$		−	1.69239i		−	0.143033i
$141$	−0.594773	+	1.43591i	−0.0500890	+	0.120925i
$142$	10.5459	−	4.36827i	0.884995	−	0.366577i
$143$	1.46897	+	3.54640i	0.122841	+	0.296565i
$144$	−6.43308	−	6.43308i	−0.536090	−	0.536090i
$145$	7.99244	+	7.99244i	0.663736	+	0.663736i
$146$	−0.478453	−	1.15509i	−0.0395970	−	0.0955957i
$147$	0.515903	−	0.213694i	0.0425509	−	0.0176252i
$148$	−0.841695	+	2.03203i	−0.0691869	+	0.167032i
$149$		−	4.83452i		−	0.396060i	−0.980196	−	0.198030i	$-0.936546\pi$
$149$		−	4.83452i		−	0.396060i	0.980196	−	0.198030i	$-0.0634543\pi$
$150$	−0.250911	−	0.103931i	−0.0204868	−	0.00848590i
$151$	7.26706	−	7.26706i	0.591385	−	0.591385i	−0.346620	−	0.938005i	$-0.612671\pi$
$151$	7.26706	−	7.26706i	0.591385	−	0.591385i	0.938005	+	0.346620i	$0.112671\pi$
$152$	10.5368			0.854648
$153$	11.8666	+	2.38287i	0.959358	+	0.192643i
$154$	−2.78991			−0.224817
$155$	−4.27530	+	4.27530i	−0.343400	+	0.343400i
$156$	−0.341016	−	0.141253i	−0.0273031	−	0.0113093i
$157$		−	4.38407i		−	0.349886i	−0.984579	−	0.174943i	$-0.944026\pi$
$157$		−	4.38407i		−	0.349886i	0.984579	−	0.174943i	$-0.0559742\pi$
$158$	4.12767	−	9.96508i	0.328380	−	0.792779i
$159$	3.04810	−	1.26257i	0.241730	−	0.100128i
$160$	1.64800	+	3.97863i	0.130286	+	0.314538i
$161$	4.33900	+	4.33900i	0.341961	+	0.341961i
$162$	−7.58454	−	7.58454i	−0.595898	−	0.595898i
$163$	−0.392060	−	0.946517i	−0.0307085	−	0.0741369i	0.907781	−	0.419444i	$-0.137775\pi$
$163$	−0.392060	−	0.946517i	−0.0307085	−	0.0741369i	−0.938490	+	0.345307i	$0.887775\pi$
$164$	−3.09370	+	1.28145i	−0.241577	+	0.100065i
$165$	−0.198188	+	0.478469i	−0.0154290	+	0.0372488i
$166$		−	18.6309i		−	1.44604i
$167$	−12.4191	−	5.14417i	−0.961021	−	0.398068i	−0.153659	−	0.988124i	$-0.549106\pi$
$167$	−12.4191	−	5.14417i	−0.961021	−	0.398068i	−0.807362	+	0.590056i	$0.799106\pi$
$168$	1.19153	−	1.19153i	0.0919288	−	0.0919288i
$169$	−1.73483			−0.133448
$170$	8.89242	+	5.96516i	0.682018	+	0.457507i
$171$	10.2123			0.780954
$172$	−0.929165	+	0.929165i	−0.0708482	+	0.0708482i
$173$	18.0746	+	7.48676i	1.37419	+	0.569208i	0.942921	−	0.333016i	$-0.108066\pi$
$173$	18.0746	+	7.48676i	1.37419	+	0.569208i	0.431268	+	0.902224i	$0.358066\pi$
$174$			1.79173i			0.135830i
$175$	−0.704332	+	1.70041i	−0.0532425	+	0.128539i
$176$	2.86328	−	1.18601i	0.215828	−	0.0893987i
$177$	−0.425033	−	1.02612i	−0.0319474	−	0.0771279i
$178$	0.653782	+	0.653782i	0.0490031	+	0.0490031i
$179$	−15.4991	−	15.4991i	−1.15846	−	1.15846i	−0.984807	−	0.173652i	$-0.944443\pi$
$179$	−15.4991	−	15.4991i	−1.15846	−	1.15846i	−0.173652	−	0.984807i	$-0.555557\pi$
$180$	0.867695	+	2.09480i	0.0646742	+	0.156137i
$181$	1.26956	−	0.525870i	0.0943659	−	0.0390876i	−0.335001	−	0.942218i	$-0.608737\pi$
$181$	1.26956	−	0.525870i	0.0943659	−	0.0390876i	0.429367	+	0.903130i	$0.358737\pi$
$182$	4.09828	−	9.89413i	0.303785	−	0.733401i
$183$		−	1.69415i		−	0.125235i
$184$	−7.83671	−	3.24607i	−0.577730	−	0.239303i
$185$	−8.37629	+	8.37629i	−0.615837	+	0.615837i
$186$	−0.958427			−0.0702753
$187$	−2.29691	+	3.42406i	−0.167967	+	0.250392i
$188$	−2.31801			−0.169058
$189$	2.33504	−	2.33504i	0.169849	−	0.169849i
$190$	8.34701	+	3.45745i	0.605556	+	0.250830i
$191$			1.64666i			0.119148i	0.998224	+	0.0595741i	$0.0189743\pi$
$191$			1.64666i			0.119148i	−0.998224	+	0.0595741i	$0.981026\pi$
$192$	−0.863533	+	2.08475i	−0.0623201	+	0.150454i
$193$	13.7145	−	5.68075i	0.987194	−	0.408909i	0.170108	−	0.985425i	$-0.445588\pi$
$193$	13.7145	−	5.68075i	0.987194	−	0.408909i	0.817086	+	0.576516i	$0.195588\pi$
$194$	5.77984	+	13.9538i	0.414969	+	1.00182i
$195$	−1.40571	−	1.40571i	−0.100665	−	0.100665i
$196$	0.588898	+	0.588898i	0.0420642	+	0.0420642i
$197$	0.203314	+	0.490842i	0.0144855	+	0.0349711i	0.930957	−	0.365129i	$-0.118975\pi$
$197$	0.203314	+	0.490842i	0.0144855	+	0.0349711i	−0.916471	+	0.400100i	$0.868975\pi$
$198$	3.45329	−	1.43040i	0.245415	−	0.101654i
$199$	−1.69804	+	4.09943i	−0.120371	+	0.290601i	−0.972568	−	0.232621i	$-0.925270\pi$
$199$	−1.69804	+	4.09943i	−0.120371	+	0.290601i	0.852197	+	0.523221i	$0.175270\pi$
$200$		−	2.54420i		−	0.179902i
$201$	3.32861	+	1.37875i	0.234782	+	0.0972498i
$202$	−8.17876	+	8.17876i	−0.575456	+	0.575456i
$203$	12.1424			0.852231
$204$	−0.0766400	−	0.388993i	−0.00536588	−	0.0272350i
$205$	−18.0349			−1.25961
$206$	1.72798	−	1.72798i	0.120394	−	0.120394i
$207$	−7.59536	−	3.14610i	−0.527914	−	0.218669i
$208$			11.8965i			0.824876i
$209$	−1.33130	+	3.21405i	−0.0920882	+	0.222321i
$210$	1.33488	−	0.552927i	0.0921158	−	0.0381556i
$211$	−6.98064	−	16.8528i	−0.480567	−	1.16019i	−0.959340	−	0.282253i	$-0.908918\pi$
$211$	−6.98064	−	16.8528i	−0.480567	−	1.16019i	0.478773	−	0.877939i	$-0.341082\pi$
$212$	3.47938	+	3.47938i	0.238965	+	0.238965i
$213$	−1.60959	−	1.60959i	−0.110287	−	0.110287i
$214$	−7.23026	−	17.4554i	−0.494251	−	1.19323i
$215$	−6.53845	+	2.70832i	−0.445919	+	0.184706i
$216$	−1.74688	+	4.21733i	−0.118860	+	0.286953i
$217$			6.49520i			0.440923i
$218$	13.1619	+	5.45184i	0.891437	+	0.369245i
$219$	−0.176297	+	0.176297i	−0.0119130	+	0.0119130i
$220$	−0.772398			−0.0520751
$221$	−8.76902	−	13.1756i	−0.589868	−	0.886287i
$222$	−1.87778			−0.126028
$223$	−15.3516	+	15.3516i	−1.02802	+	1.02802i	−0.0284261	+	0.999596i	$0.509050\pi$
$223$	−15.3516	+	15.3516i	−1.02802	+	1.02802i	−0.999596	+	0.0284261i	$0.990950\pi$
$224$	4.27410	+	1.77039i	0.285575	+	0.118289i
$225$		−	2.46585i		−	0.164390i
$226$	4.72382	−	11.4043i	0.314224	−	0.758603i
$227$	15.7757	−	6.53451i	1.04707	−	0.433711i	0.208225	−	0.978081i	$-0.433231\pi$
$227$	15.7757	−	6.53451i	1.04707	−	0.433711i	0.838845	+	0.544370i	$0.183231\pi$
$228$	−0.128016	−	0.309058i	−0.00847806	−	0.0204679i
$229$	−17.5325	−	17.5325i	−1.15858	−	1.15858i	−0.984782	−	0.173795i	$-0.944397\pi$
$229$	−17.5325	−	17.5325i	−1.15858	−	1.15858i	−0.173795	−	0.984782i	$-0.555603\pi$
$230$	−5.14293	−	5.14293i	−0.339115	−	0.339115i
$231$	0.212907	+	0.514003i	0.0140082	+	0.0338189i
$232$	−15.5072	+	6.42331i	−1.01810	+	0.421711i
$233$	1.21069	−	2.92286i	0.0793149	−	0.191483i	−0.879248	−	0.476365i	$-0.841954\pi$
$233$	1.21069	−	2.92286i	0.0793149	−	0.191483i	0.958563	+	0.284882i	$0.0919543\pi$
$234$			14.3480i			0.937956i
$235$	−11.5340	−	4.77756i	−0.752398	−	0.311654i
$236$	1.17131	−	1.17131i	0.0762455	−	0.0762455i
$237$	−2.15093			−0.139718
$238$	11.2861	−	2.22361i	0.731570	−	0.144135i
$239$	20.0557			1.29730			0.648648	−	0.761088i	$-0.275335\pi$
$239$	20.0557			1.29730			0.648648	+	0.761088i	$0.275335\pi$
$240$	−1.13494	+	1.13494i	−0.0732598	+	0.0732598i
$241$	11.5105	+	4.76782i	0.741459	+	0.307123i	0.721252	−	0.692673i	$-0.243567\pi$
$241$	11.5105	+	4.76782i	0.741459	+	0.307123i	0.0202079	+	0.999796i	$0.493567\pi$
$242$			1.27330i			0.0818510i
$243$	−2.54881	+	6.15338i	−0.163506	+	0.394739i
$244$	2.33437	−	0.966929i	0.149443	−	0.0619013i
$245$	1.71651	+	4.14403i	0.109664	+	0.264752i
$246$	−2.02151	−	2.02151i	−0.128887	−	0.128887i
$247$	−9.44267	−	9.44267i	−0.600823	−	0.600823i
$248$	−3.43594	−	8.29510i	−0.218183	−	0.526739i
$249$	−3.43249	+	1.42178i	−0.217525	+	0.0901019i
$250$	5.80405	−	14.0122i	0.367080	−	0.886210i
$251$			11.5107i			0.726548i	0.931682	+	0.363274i	$0.118341\pi$
$251$			11.5107i			0.726548i	−0.931682	+	0.363274i	$0.881659\pi$
$252$	2.25037	+	0.932134i	0.141760	+	0.0587189i
$253$	1.98030	−	1.98030i	0.124501	−	0.124501i
$254$	−11.3127			−0.709824
$255$	0.420390	−	2.09353i	0.0263259	−	0.131102i
$256$	−8.74236			−0.546397
$257$	3.17010	−	3.17010i	0.197745	−	0.197745i	−0.601287	−	0.799033i	$-0.705345\pi$
$257$	3.17010	−	3.17010i	0.197745	−	0.197745i	0.799033	+	0.601287i	$0.205345\pi$
$258$	−1.03646	−	0.429316i	−0.0645272	−	0.0267280i
$259$			12.7256i			0.790730i
$260$	1.13463	−	2.73923i	0.0703667	−	0.169880i
$261$	−15.0296	+	6.22548i	−0.930312	+	0.385348i
$262$	6.63124	+	16.0092i	0.409679	+	0.989053i
$263$	11.7977	+	11.7977i	0.727480	+	0.727480i	0.970117	−	0.242637i	$-0.0780124\pi$
$263$	11.7977	+	11.7977i	0.727480	+	0.727480i	−0.242637	+	0.970117i	$0.578012\pi$
$264$	−0.543812	−	0.543812i	−0.0334693	−	0.0334693i
$265$	10.1416	+	24.4841i	0.622996	+	1.50405i
$266$	8.96690	−	3.71421i	0.549796	−	0.227733i
$267$	0.0705583	−	0.170343i	0.00431810	−	0.0104248i
$268$			5.37341i			0.328233i
$269$	5.72113	+	2.36977i	0.348823	+	0.144487i	0.550214	−	0.835024i	$-0.314546\pi$
$269$	5.72113	+	2.36977i	0.348823	+	0.144487i	−0.201391	+	0.979511i	$0.564546\pi$
$270$	−2.76767	+	2.76767i	−0.168435	+	0.168435i
$271$	−12.8736			−0.782016			−0.391008	−	0.920387i	$-0.627874\pi$
$271$	−12.8736			−0.782016			−0.391008	+	0.920387i	$0.627874\pi$
$272$	−10.6376	+	7.07989i	−0.645002	+	0.429281i
$273$	−2.13561			−0.129253
$274$	−13.0635	+	13.0635i	−0.789194	+	0.789194i
$275$	0.776060	+	0.321455i	0.0467982	+	0.0193844i
$276$			0.269298i			0.0162099i
$277$	4.23856	−	10.2328i	0.254670	−	0.614829i	−0.743899	−	0.668292i	$-0.767026\pi$
$277$	4.23856	−	10.2328i	0.254670	−	0.614829i	0.998570	+	0.0534628i	$0.0170259\pi$
$278$	17.2143	−	7.13038i	1.03244	−	0.427652i
$279$	−3.33013	−	8.03963i	−0.199369	−	0.481320i
$280$	9.57108	+	9.57108i	0.571981	+	0.571981i
$281$	18.4401	+	18.4401i	1.10004	+	1.10004i	0.994405	+	0.105637i	$0.0336882\pi$
$281$	18.4401	+	18.4401i	1.10004	+	1.10004i	0.105637	+	0.994405i	$0.466312\pi$
$282$	−0.757327	−	1.82835i	−0.0450981	−	0.108877i
$283$	−8.10220	+	3.35604i	−0.481626	+	0.199496i	−0.610268	−	0.792195i	$-0.708938\pi$
$283$	−8.10220	+	3.35604i	−0.481626	+	0.199496i	0.128642	+	0.991691i	$0.458938\pi$
$284$	1.29919	−	3.13652i	0.0770927	−	0.186118i
$285$		−	1.80167i		−	0.106722i
$286$	−4.51564	−	1.87044i	−0.267016	−	0.110601i
$287$	−13.6997	+	13.6997i	−0.808667	+	0.808667i
$288$	−6.19809			−0.365226
$289$	6.56273	−	15.6822i	0.386043	−	0.922481i
$290$	−14.3922			−0.845137
$291$	2.12972	−	2.12972i	0.124846	−	0.124846i
$292$	−0.343540	−	0.142299i	−0.0201042	−	0.00832742i
$293$		−	4.24644i		−	0.248080i	−0.992277	−	0.124040i	$-0.960415\pi$
$293$		−	4.24644i		−	0.248080i	0.992277	−	0.124040i	$-0.0395851\pi$
$294$	−0.272097	+	0.656901i	−0.0158690	+	0.0383112i
$295$	8.24238	−	3.41410i	0.479890	−	0.198777i
$296$	−6.73180	−	16.2520i	−0.391278	−	0.944628i
$297$	−1.06570	−	1.06570i	−0.0618384	−	0.0618384i
$298$	4.35282	+	4.35282i	0.252152	+	0.252152i
$299$	4.11395	+	9.93196i	0.237916	+	0.574380i
$300$	−0.0746246	+	0.0309105i	−0.00430846	+	0.00178462i
$301$	−2.90945	+	7.02403i	−0.167698	+	0.404858i
$302$			13.0860i			0.753012i
$303$	2.13098	+	0.882679i	0.122421	+	0.0507086i
$304$	−7.62378	+	7.62378i	−0.437254	+	0.437254i
$305$	13.6084			0.779214
$306$	−12.8297	+	8.53879i	−0.733423	+	0.488130i
$307$	15.5251			0.886067			0.443034	−	0.896505i	$-0.353902\pi$
$307$	15.5251			0.886067			0.443034	+	0.896505i	$0.353902\pi$
$308$	−0.586729	+	0.586729i	−0.0334320	+	0.0334320i
$309$	−0.450224	−	0.186489i	−0.0256124	−	0.0106090i
$310$		−	7.69863i		−	0.437253i
$311$	0.470682	−	1.13633i	0.0266899	−	0.0644352i	−0.909973	−	0.414668i	$-0.863898\pi$
$311$	0.470682	−	1.13633i	0.0266899	−	0.0644352i	0.936663	+	0.350233i	$0.113898\pi$
$312$	2.72742	−	1.12973i	0.154410	−	0.0639585i
$313$	−10.6258	−	25.6530i	−0.600607	−	1.44999i	−0.872958	−	0.487796i	$-0.837801\pi$
$313$	−10.6258	−	25.6530i	−0.600607	−	1.44999i	0.272350	−	0.962198i	$-0.412199\pi$
$314$	3.94724	+	3.94724i	0.222756	+	0.222756i
$315$	9.27631	+	9.27631i	0.522661	+	0.522661i
$316$	−1.22763	−	2.96377i	−0.0690597	−	0.166725i
$317$	−14.9283	+	6.18350i	−0.838456	+	0.347300i	−0.760244	−	0.649637i	$-0.774921\pi$
$317$	−14.9283	+	6.18350i	−0.838456	+	0.347300i	−0.0782112	+	0.996937i	$0.524921\pi$
$318$	−1.60763	+	3.88116i	−0.0901513	+	0.217644i
$319$		−	5.54176i		−	0.310279i
$320$	−16.7459	−	6.93639i	−0.936125	−	0.387756i
$321$	−2.66416	+	2.66416i	−0.148699	+	0.148699i
$322$	−7.81334			−0.435420
$323$	2.82391	−	14.0630i	0.157127	−	0.782486i
$324$	−3.19012			−0.177229
$325$	−2.28001	+	2.28001i	−0.126472	+	0.126472i
$326$	1.20520	+	0.499211i	0.0667500	+	0.0276488i
$327$		−	2.84095i		−	0.157105i
$328$	10.2489	−	24.7431i	0.565903	−	1.36621i
$329$	−12.3906	+	5.13236i	−0.683117	+	0.282956i
$330$	−0.252354	−	0.609236i	−0.0138916	−	0.0335374i
$331$	11.1868	+	11.1868i	0.614880	+	0.614880i	0.944214	−	0.329333i	$-0.106824\pi$
$331$	11.1868	+	11.1868i	0.614880	+	0.614880i	−0.329333	+	0.944214i	$0.606824\pi$
$332$	−3.91816	−	3.91816i	−0.215037	−	0.215037i
$333$	−6.52448	−	15.7515i	−0.357539	−	0.863176i
$334$	15.8133	−	6.55009i	0.865266	−	0.358405i
$335$	−11.0749	+	26.7373i	−0.605088	+	1.46081i
$336$			1.72424i			0.0940650i
$337$	−24.6586	−	10.2139i	−1.34324	−	0.556387i	−0.408835	−	0.912608i	$-0.634065\pi$
$337$	−24.6586	−	10.2139i	−1.34324	−	0.556387i	−0.934402	+	0.356221i	$0.884065\pi$
$338$	1.56197	−	1.56197i	0.0849600	−	0.0849600i
$339$	−2.46158			−0.133695
$340$	3.12461	−	0.615616i	0.169456	−	0.0333865i
$341$	2.96439			0.160531
$342$	−9.19476	+	9.19476i	−0.497195	+	0.497195i
$343$	18.6218	+	7.71341i	1.00548	+	0.416485i
$344$		−	10.5096i		−	0.566637i
$345$	−0.555041	+	1.33999i	−0.0298824	+	0.0721425i
$346$	−23.0145	+	9.53291i	−1.23727	+	0.512493i
$347$	−7.17138	−	17.3133i	−0.384980	−	0.929424i	−0.990986	−	0.133964i	$-0.957229\pi$
$347$	−7.17138	−	17.3133i	−0.384980	−	0.929424i	0.606006	−	0.795460i	$-0.292771\pi$
$348$	0.376807	+	0.376807i	0.0201990	+	0.0201990i
$349$	7.26513	+	7.26513i	0.388893	+	0.388893i	0.874293	−	0.485399i	$-0.161326\pi$
$349$	7.26513	+	7.26513i	0.388893	+	0.388893i	−0.485399	+	0.874293i	$0.661326\pi$
$350$	−0.896828	−	2.16513i	−0.0479375	−	0.115731i
$351$	5.34490	−	2.21393i	0.285289	−	0.118171i
$352$	0.808000	−	1.95068i	0.0430665	−	0.103972i
$353$			2.84463i			0.151405i	0.997130	+	0.0757023i	$0.0241199\pi$
$353$			2.84463i			0.151405i	−0.997130	+	0.0757023i	$0.975880\pi$
$354$	1.30656	+	0.541195i	0.0694429	+	0.0287642i
$355$	12.9291	−	12.9291i	0.686208	−	0.686208i
$356$	0.274986			0.0145743
$357$	−1.27095	−	1.90962i	−0.0672658	−	0.101068i
$358$	27.9096			1.47507
$359$	−8.48274	+	8.48274i	−0.447702	+	0.447702i	−0.894590	−	0.446888i	$-0.852532\pi$
$359$	−8.48274	+	8.48274i	−0.447702	+	0.447702i	0.446888	+	0.894590i	$0.352532\pi$
$360$	−16.7540	−	6.93975i	−0.883015	−	0.365757i
$361$			6.89750i			0.363026i
$362$	−0.669592	+	1.61654i	−0.0351930	+	0.0849634i
$363$	0.234589	−	0.0971699i	0.0123127	−	0.00510010i
$364$	−1.21889	−	2.94266i	−0.0638872	−	0.154237i
$365$	−1.41612	−	1.41612i	−0.0741230	−	0.0741230i
$366$	1.52535	+	1.52535i	0.0797312	+	0.0797312i
$367$	0.260825	+	0.629686i	0.0136149	+	0.0328694i	0.930541	−	0.366188i	$-0.119337\pi$
$367$	0.260825	+	0.629686i	0.0136149	+	0.0328694i	−0.916926	+	0.399058i	$0.869337\pi$
$368$	8.01881	−	3.32150i	0.418010	−	0.173145i
$369$	9.93330	−	23.9811i	0.517107	−	1.24841i
$370$		−	15.0834i		−	0.784147i
$371$	26.3024	+	10.8948i	1.36555	+	0.565630i
$372$	−0.201561	+	0.201561i	−0.0104505	+	0.0104505i
$373$	−32.6440			−1.69024			−0.845121	−	0.534576i	$-0.820471\pi$
$373$	−32.6440			−1.69024			−0.845121	+	0.534576i	$0.820471\pi$
$374$	−1.01485	−	5.15094i	−0.0524765	−	0.266349i
$375$	−3.02449			−0.156184
$376$	13.1092	−	13.1092i	0.676055	−	0.676055i
$377$	19.6533	+	8.14066i	1.01220	+	0.419265i
$378$			4.20476i			0.216269i
$379$	−13.3970	+	32.3431i	−0.688155	+	1.66135i	0.0603103	+	0.998180i	$0.480791\pi$
$379$	−13.3970	+	32.3431i	−0.688155	+	1.66135i	−0.748465	+	0.663174i	$0.769209\pi$
$380$	2.48253	−	1.02830i	0.127351	−	0.0527505i
$381$	0.863312	+	2.08422i	0.0442288	+	0.106778i
$382$	−1.48259	−	1.48259i	−0.0758559	−	0.0758559i
$383$	19.5014	+	19.5014i	0.996475	+	0.996475i	0.999994	−	0.00351832i	$-0.00111992\pi$
$383$	19.5014	+	19.5014i	0.996475	+	0.996475i	−0.00351832	+	0.999994i	$0.501120\pi$
$384$	−0.689209	−	1.66390i	−0.0351710	−	0.0849104i
$385$	−4.12876	+	1.71019i	−0.210421	+	0.0871593i
$386$	−7.23331	+	17.4628i	−0.368166	+	0.888831i
$387$		−	10.1859i		−	0.517778i
$388$	4.15006	+	1.71901i	0.210688	+	0.0872696i
$389$	5.17075	−	5.17075i	0.262167	−	0.262167i	−0.563767	−	0.825934i	$-0.690648\pi$
$389$	5.17075	−	5.17075i	0.262167	−	0.262167i	0.825934	+	0.563767i	$0.190648\pi$
$390$	2.53130			0.128177
$391$	−6.43266	+	9.58934i	−0.325314	+	0.484954i
$392$	−6.66088			−0.336425
$393$	2.44343	−	2.44343i	0.123255	−	0.123255i
$394$	−0.624991	−	0.258880i	−0.0314866	−	0.0130422i
$395$		−	17.2775i		−	0.869324i
$396$	0.425422	−	1.02706i	0.0213783	−	0.0516117i
$397$	19.2249	−	7.96321i	0.964869	−	0.399662i	0.156069	−	0.987746i	$-0.450118\pi$
$397$	19.2249	−	7.96321i	0.964869	−	0.399662i	0.808800	+	0.588084i	$0.200118\pi$
$398$	−2.16212	−	5.21982i	−0.108377	−	0.261646i
$399$	−1.36859	−	1.36859i	−0.0685150	−	0.0685150i
$400$	1.84083	+	1.84083i	0.0920413	+	0.0920413i
$401$	2.67238	+	6.45170i	0.133452	+	0.322183i	0.976453	−	0.215730i	$-0.0692131\pi$
$401$	2.67238	+	6.45170i	0.133452	+	0.322183i	−0.843001	+	0.537913i	$0.819213\pi$
$402$	−4.23832	+	1.75557i	−0.211388	+	0.0875599i
$403$	−4.35459	+	10.5129i	−0.216918	+	0.523685i
$404$			3.44006i			0.171149i
$405$	−15.8736	−	6.57505i	−0.788764	−	0.326717i
$406$	−10.9326	+	10.9326i	−0.542574	+	0.542574i
$407$	5.80791			0.287888
$408$	2.63333	+	1.76647i	0.130369	+	0.0874535i
$409$	24.2847			1.20080			0.600402	−	0.799699i	$-0.295007\pi$
$409$	24.2847			1.20080			0.600402	+	0.799699i	$0.295007\pi$
$410$	16.2379	−	16.2379i	0.801935	−	0.801935i
$411$	3.40369	+	1.40985i	0.167892	+	0.0695430i
$412$		−	0.726802i		−	0.0358070i
$413$	3.66765	−	8.85449i	0.180473	−	0.435701i
$414$	9.67119	−	4.00594i	0.475313	−	0.196881i
$415$	−11.4206	−	27.5717i	−0.560614	−	1.35344i
$416$	5.73098	+	5.73098i	0.280985	+	0.280985i
$417$	−2.62735	−	2.62735i	−0.128662	−	0.128662i
$418$	−1.69515	−	4.09246i	−0.0829126	−	0.200169i
$419$	16.4964	−	6.83303i	0.805902	−	0.333815i	0.0585842	−	0.998282i	$-0.481341\pi$
$419$	16.4964	−	6.83303i	0.805902	−	0.333815i	0.747318	+	0.664467i	$0.231341\pi$
$420$	0.164449	−	0.397015i	0.00802429	−	0.0193723i
$421$		−	38.2665i		−	1.86500i	−0.361174	−	0.932498i	$-0.617624\pi$
$421$		−	38.2665i		−	1.86500i	0.361174	−	0.932498i	$-0.382376\pi$
$422$	21.4587	+	8.88847i	1.04459	+	0.432684i
$423$	12.7055	−	12.7055i	0.617761	−	0.617761i
$424$	−39.3544			−1.91122
$425$	−3.39563	−	0.681858i	−0.164712	−	0.0330750i
$426$	2.89842			0.140429
$427$	10.3372	−	10.3372i	0.500252	−	0.500252i
$428$	−5.19150	−	2.15039i	−0.250941	−	0.103943i
$429$			0.974686i			0.0470583i
$430$	3.44851	−	8.32543i	0.166302	−	0.401488i
$431$	17.9044	−	7.41624i	0.862424	−	0.357228i	0.0927690	−	0.995688i	$-0.470428\pi$
$431$	17.9044	−	7.41624i	0.862424	−	0.357228i	0.769655	+	0.638460i	$0.220428\pi$
$432$	−1.78747	−	4.31534i	−0.0859997	−	0.207622i
$433$	20.6400	+	20.6400i	0.991896	+	0.991896i	0.999967	−	0.00807104i	$-0.00256912\pi$
$433$	20.6400	+	20.6400i	0.991896	+	0.991896i	−0.00807104	+	0.999967i	$0.502569\pi$
$434$	−5.84803	−	5.84803i	−0.280714	−	0.280714i
$435$	1.09831	+	2.65156i	0.0526601	+	0.127133i
$436$	3.91455	−	1.62146i	0.187473	−	0.0776538i
$437$	−3.72841	+	9.00119i	−0.178354	+	0.430585i
$438$		−	0.317462i		−	0.0151689i
$439$	−3.49409	−	1.44730i	−0.166764	−	0.0690759i	0.297740	−	0.954647i	$-0.403767\pi$
$439$	−3.49409	−	1.44730i	−0.166764	−	0.0690759i	−0.464504	+	0.885571i	$0.653767\pi$
$440$	4.36820	−	4.36820i	0.208246	−	0.208246i
$441$	−6.45574			−0.307416
$442$	19.7581	+	3.96751i	0.939796	+	0.188715i
$443$	−23.6690			−1.12455			−0.562274	−	0.826951i	$-0.690074\pi$
$443$	−23.6690			−1.12455			−0.562274	+	0.826951i	$0.690074\pi$
$444$	−0.394904	+	0.394904i	−0.0187413	+	0.0187413i
$445$	1.36829	+	0.566765i	0.0648632	+	0.0268672i
$446$		−	27.6440i		−	1.30898i
$447$	0.469770	−	1.13413i	0.0222194	−	0.0536423i
$448$	−17.9895	+	7.45151i	−0.849926	+	0.352051i
$449$	10.0563	+	24.2780i	0.474586	+	1.14575i	0.962115	+	0.272645i	$0.0878983\pi$
$449$	10.0563	+	24.2780i	0.474586	+	1.14575i	−0.487529	+	0.873107i	$0.662102\pi$
$450$	2.22015	+	2.22015i	0.104659	+	0.104659i
$451$	6.25249	+	6.25249i	0.294418	+	0.294418i
$452$	−1.40494	−	3.39181i	−0.0660826	−	0.159537i
$453$	2.41091	−	0.998632i	0.113275	−	0.0469198i
$454$	−8.32041	+	20.0873i	−0.390496	+	0.942742i
$455$		−	17.1545i		−	0.804213i
$456$	2.47182	+	1.02386i	0.115753	+	0.0479466i
$457$	−12.6131	+	12.6131i	−0.590018	+	0.590018i	−0.937636	−	0.347618i	$-0.886991\pi$
$457$	−12.6131	+	12.6131i	−0.590018	+	0.590018i	0.347618	+	0.937636i	$0.386991\pi$
$458$	31.5711			1.47522
$459$	5.16052	+	3.46174i	0.240872	+	0.161580i
$460$	−2.16316			−0.100858
$461$	−9.90165	+	9.90165i	−0.461166	+	0.461166i	−0.899038	−	0.437872i	$-0.855732\pi$
$461$	−9.90165	+	9.90165i	−0.461166	+	0.461166i	0.437872	+	0.899038i	$0.355732\pi$
$462$	−0.654481	−	0.271095i	−0.0304492	−	0.0126125i
$463$			15.5197i			0.721261i	0.932709	+	0.360630i	$0.117438\pi$
$463$			15.5197i			0.721261i	−0.932709	+	0.360630i	$0.882562\pi$
$464$	6.57257	−	15.8676i	0.305124	−	0.736634i
$465$	−1.41837	+	0.587507i	−0.0657753	+	0.0272450i
$466$	1.54157	+	3.72169i	0.0714120	+	0.172404i
$467$	−0.206731	−	0.206731i	−0.00956639	−	0.00956639i	0.702307	−	0.711874i	$-0.252153\pi$
$467$	−0.206731	−	0.206731i	−0.00956639	−	0.00956639i	−0.711874	+	0.702307i	$0.752153\pi$
$468$	3.01744	+	3.01744i	0.139481	+	0.139481i
$469$	11.8974	+	28.7229i	0.549371	+	1.32630i
$470$	14.6863	−	6.08328i	0.677430	−	0.280601i
$471$	0.425999	−	1.02845i	0.0196290	−	0.0473886i
$472$			13.2484i			0.609805i
$473$	3.20574	+	1.32786i	0.147400	+	0.0610551i
$474$	1.93661	−	1.93661i	0.0889515	−	0.0889515i
$475$	−2.92225			−0.134082
$476$	1.90588	−	2.84115i	0.0873560	−	0.130224i
$477$	−38.1424			−1.74642
$478$	−18.0574	+	18.0574i	−0.825926	+	0.825926i
$479$	−33.5323	−	13.8895i	−1.53213	−	0.634629i	−0.552153	−	0.833743i	$-0.686194\pi$
$479$	−33.5323	−	13.8895i	−1.53213	−	0.634629i	−0.979976	+	0.199114i	$0.936194\pi$
$480$			1.09348i			0.0499103i
$481$	−8.53164	+	20.5972i	−0.389009	+	0.939151i
$482$	−14.6564	+	6.07089i	−0.667581	+	0.276521i
$483$	0.596261	+	1.43950i	0.0271308	+	0.0654996i
$484$	0.267781	+	0.267781i	0.0121719	+	0.0121719i
$485$	17.1071	+	17.1071i	0.776793	+	0.776793i
$486$	−3.24541	−	7.83511i	−0.147215	−	0.355408i
$487$	32.8564	−	13.6096i	1.48887	−	0.616709i	0.517796	−	0.855504i	$-0.326753\pi$
$487$	32.8564	−	13.6096i	1.48887	−	0.616709i	0.971070	+	0.238795i	$0.0767525\pi$
$488$	−7.73341	+	18.6701i	−0.350075	+	0.845156i
$489$		−	0.260139i		−	0.0117639i
$490$	−5.27660	−	2.18564i	−0.238372	−	0.0987371i
$491$	14.3926	−	14.3926i	0.649528	−	0.649528i	−0.303351	−	0.952879i	$-0.598105\pi$
$491$	14.3926	−	14.3926i	0.649528	−	0.649528i	0.952879	+	0.303351i	$0.0981053\pi$
$492$	−0.850266			−0.0383329
$493$	4.41689	+	22.4183i	0.198927	+	1.00967i
$494$	17.0036			0.765030
$495$	4.23368	−	4.23368i	0.190290	−	0.190290i
$496$	8.48786	+	3.51579i	0.381116	+	0.157863i
$497$		−	19.6425i		−	0.881085i
$498$	1.81036	−	4.37060i	0.0811243	−	0.195851i
$499$	23.8392	−	9.87452i	1.06719	−	0.442044i	0.221191	−	0.975230i	$-0.429005\pi$
$499$	23.8392	−	9.87452i	1.06719	−	0.442044i	0.845998	+	0.533186i	$0.179005\pi$
$500$	−1.72621	−	4.16744i	−0.0771985	−	0.186374i
$501$	−2.41353	−	2.41353i	−0.107829	−	0.107829i
$502$	−10.3638	−	10.3638i	−0.462558	−	0.462558i
$503$	−7.16698	−	17.3026i	−0.319560	−	0.771486i	−0.999277	−	0.0380118i	$-0.987898\pi$
$503$	−7.16698	−	17.3026i	−0.319560	−	0.771486i	0.679717	−	0.733474i	$-0.262102\pi$
$504$	−17.9983	+	7.45512i	−0.801706	+	0.332078i
$505$	−7.09018	+	17.1172i	−0.315509	+	0.761706i
$506$			3.56598i			0.158527i
$507$	−0.406971	−	0.168573i	−0.0180742	−	0.00748659i
$508$	−2.37912	+	2.37912i	−0.105556	+	0.105556i
$509$	36.7987			1.63107			0.815536	−	0.578706i	$-0.196442\pi$
$509$	36.7987			1.63107			0.815536	+	0.578706i	$0.196442\pi$
$510$	1.50643	+	2.26344i	0.0667059	+	0.100227i
$511$	−2.15142			−0.0951732
$512$	17.9020	−	17.9020i	0.791166	−	0.791166i
$513$	4.84400	+	2.00645i	0.213868	+	0.0885870i
$514$			5.70847i			0.251790i
$515$	1.49799	−	3.61646i	0.0660092	−	0.159360i
$516$	−0.308259	+	0.127685i	−0.0135703	+	0.00562102i
$517$	2.34239	+	5.65503i	0.103018	+	0.248708i
$518$	−11.4576	−	11.4576i	−0.503419	−	0.503419i
$519$	3.51262	+	3.51262i	0.154187	+	0.154187i
$520$	9.07466	+	21.9082i	0.397950	+	0.960736i
$521$	−30.3932	+	12.5893i	−1.33155	+	0.551546i	−0.931097	−	0.364772i	$-0.881147\pi$
$521$	−30.3932	+	12.5893i	−1.33155	+	0.551546i	−0.400453	+	0.916317i	$0.631147\pi$
$522$	7.92693	−	19.1373i	0.346952	−	0.837617i
$523$			5.19610i			0.227210i	0.993526	+	0.113605i	$0.0362398\pi$
$523$			5.19610i			0.227210i	−0.993526	+	0.113605i	$0.963760\pi$
$524$	4.76139	+	1.97223i	0.208002	+	0.0861573i
$525$	−0.330457	+	0.330457i	−0.0144223	+	0.0144223i
$526$	−21.2445			−0.926303
$527$	−11.9919	+	2.36267i	−0.522378	+	0.102920i
$528$	0.786937			0.0342470
$529$	−10.7175	+	10.7175i	−0.465977	+	0.465977i
$530$	−31.1757	−	12.9134i	−1.35418	−	0.560921i
$531$			12.8403i			0.557223i
$532$	1.10466	−	2.66689i	0.0478932	−	0.115624i
$533$	−31.3585	+	12.9891i	−1.35829	+	0.562622i
$534$	0.0898421	+	0.216898i	0.00388785	+	0.00938610i
$535$	−21.4000	−	21.4000i	−0.925204	−	0.925204i
$536$	−30.3886	−	30.3886i	−1.31259	−	1.31259i
$537$	−2.12987	−	5.14197i	−0.0919109	−	0.221892i
$538$	−7.28473	+	3.01743i	−0.314067	+	0.130091i
$539$	0.841589	−	2.03178i	0.0362498	−	0.0875148i
$540$			1.16411i			0.0500952i
$541$	8.38033	+	3.47125i	0.360299	+	0.149241i	0.555487	−	0.831525i	$-0.312532\pi$
$541$	8.38033	+	3.47125i	0.360299	+	0.149241i	−0.195188	+	0.980766i	$0.562532\pi$
$542$	11.5909	−	11.5909i	0.497872	−	0.497872i
$543$	0.348924			0.0149738
$544$	−1.71390	+	8.53517i	−0.0734829	+	0.365942i
$545$	22.8201			0.977507
$546$	1.92282	−	1.92282i	0.0822892	−	0.0822892i
$547$	4.04739	+	1.67648i	0.173054	+	0.0716812i	0.467528	−	0.883978i	$-0.345145\pi$
$547$	4.04739	+	1.67648i	0.173054	+	0.0716812i	−0.294475	+	0.955659i	$0.595145\pi$
$548$			5.49462i			0.234718i
$549$	−7.49524	+	18.0951i	−0.319889	+	0.772281i
$550$	−0.988159	+	0.409309i	−0.0421353	+	0.0174530i
$551$	7.37776	+	17.8115i	0.314303	+	0.758795i
$552$	−1.52298	−	1.52298i	−0.0648225	−	0.0648225i
$553$	−13.1243	−	13.1243i	−0.558102	−	0.558102i
$554$	5.39697	+	13.0294i	0.229295	+	0.553568i
$555$	−2.77891	+	1.15106i	−0.117958	+	0.0488598i
$556$	2.12068	−	5.11978i	0.0899370	−	0.217127i
$557$		−	25.5376i		−	1.08206i	−0.841003	−	0.541031i	$-0.818034\pi$
$557$		−	25.5376i		−	1.08206i	0.841003	−	0.541031i	$-0.181966\pi$
$558$	10.2369	+	4.24026i	0.433362	+	0.179504i
$559$	−9.41826	+	9.41826i	−0.398350	+	0.398350i
$560$	−13.8501			−0.585273
$561$	−0.871545	+	0.580057i	−0.0367967	+	0.0244900i
$562$	−33.2054			−1.40069
$563$	−26.3431	+	26.3431i	−1.11023	+	1.11023i	−0.117112	+	0.993119i	$0.537364\pi$
$563$	−26.3431	+	26.3431i	−1.11023	+	1.11023i	−0.993119	+	0.117112i	$0.962636\pi$
$564$	−0.543778	−	0.225240i	−0.0228972	−	0.00948433i
$565$		−	19.7728i		−	0.831848i
$566$	4.27325	−	10.3165i	0.179618	−	0.433637i
$567$	−17.0524	+	7.06334i	−0.716134	+	0.296632i
$568$	10.3908	+	25.0856i	0.435988	+	1.05257i
$569$	12.8283	+	12.8283i	0.537792	+	0.537792i	0.922880	−	0.385088i	$-0.125829\pi$
$569$	12.8283	+	12.8283i	0.537792	+	0.537792i	−0.385088	+	0.922880i	$0.625829\pi$
$570$	1.62216	+	1.62216i	0.0679447	+	0.0679447i
$571$	4.84631	+	11.7000i	0.202812	+	0.489631i	0.992259	−	0.124188i	$-0.0396325\pi$
$571$	4.84631	+	11.7000i	0.202812	+	0.489631i	−0.789447	+	0.613819i	$0.789633\pi$
$572$	−1.34302	+	0.556297i	−0.0561545	+	0.0232600i
$573$	−0.160006	+	0.386289i	−0.00668435	+	0.0161374i
$574$		−	24.6693i		−	1.02968i
$575$	2.17341	+	0.900257i	0.0906376	+	0.0375433i
$576$	18.4467	−	18.4467i	0.768611	−	0.768611i
$577$	−25.3084			−1.05360			−0.526802	−	0.849988i	$-0.676609\pi$
$577$	−25.3084			−1.05360			−0.526802	+	0.849988i	$0.676609\pi$
$578$	8.21080	+	20.0284i	0.341524	+	0.833074i
$579$	3.76928			0.156646
$580$	−3.02673	+	3.02673i	−0.125678	+	0.125678i
$581$	−29.6193	−	12.2687i	−1.22882	−	0.508993i
$582$			3.83503i			0.158967i
$583$	4.97235	−	12.0043i	0.205934	−	0.497168i
$584$	2.74760	−	1.13810i	0.113697	−	0.0470947i
$585$	8.79518	+	21.2334i	0.363636	+	0.877895i
$586$	3.82333	+	3.82333i	0.157940	+	0.157940i
$587$	−14.5146	−	14.5146i	−0.599083	−	0.599083i	0.340985	−	0.940069i	$-0.389239\pi$
$587$	−14.5146	−	14.5146i	−0.599083	−	0.599083i	−0.940069	+	0.340985i	$0.889239\pi$
$588$	0.0809258	+	0.195372i	0.00333732	+	0.00805701i
$589$	−9.52769	+	3.94650i	−0.392582	+	0.162613i
$590$	−4.34719	+	10.4950i	−0.178971	+	0.432074i
$591$			0.134902i			0.00554913i
$592$	16.6297	+	6.88823i	0.683475	+	0.283104i
$593$	−19.2198	+	19.2198i	−0.789264	+	0.789264i	−0.981373	−	0.192110i	$-0.938467\pi$
$593$	−19.2198	+	19.2198i	−0.789264	+	0.789264i	0.192110	+	0.981373i	$0.438467\pi$
$594$	1.91904			0.0787390
$595$	15.3392	−	10.2090i	0.628845	−	0.418528i
$596$	1.83083			0.0749938
$597$	−0.796682	+	0.796682i	−0.0326060	+	0.0326060i
$598$	−12.6464	−	5.23831i	−0.517149	−	0.214210i
$599$			8.53787i			0.348848i	0.984671	+	0.174424i	$0.0558063\pi$
$599$			8.53787i			0.348848i	−0.984671	+	0.174424i	$0.944194\pi$
$600$	0.247220	−	0.596841i	0.0100927	−	0.0243659i
$601$	4.08875	−	1.69362i	0.166784	−	0.0690840i	−0.297730	−	0.954650i	$-0.596229\pi$
$601$	4.08875	−	1.69362i	0.166784	−	0.0690840i	0.464513	+	0.885566i	$0.346229\pi$
$602$	−3.70461	−	8.94372i	−0.150989	−	0.364519i
$603$	−29.4528	−	29.4528i	−1.19941	−	1.19941i
$604$	2.75203	+	2.75203i	0.111979	+	0.111979i
$605$	0.780524	+	1.88435i	0.0317328	+	0.0766098i
$606$	−2.71338	+	1.12392i	−0.110223	+	0.0456560i
$607$	15.0213	−	36.2647i	0.609696	−	1.47194i	−0.253635	−	0.967300i	$-0.581626\pi$
$607$	15.0213	−	36.2647i	0.609696	−	1.47194i	0.863332	−	0.504637i	$-0.168374\pi$
$608$			7.34529i			0.297891i
$609$	2.84848	+	1.17988i	0.115426	+	0.0478111i
$610$	−12.2525	+	12.2525i	−0.496088	+	0.496088i
$611$	−23.4959			−0.950543
$612$	−0.902391	+	4.49388i	−0.0364770	+	0.181654i
$613$	−17.7537			−0.717067			−0.358533	−	0.933517i	$-0.616723\pi$
$613$	−17.7537			−0.717067			−0.358533	+	0.933517i	$0.616723\pi$
$614$	−13.9782	+	13.9782i	−0.564116	+	0.564116i
$615$	−4.23079	−	1.75245i	−0.170602	−	0.0706657i
$616$		−	6.63635i		−	0.267386i
$617$	−0.947138	+	2.28659i	−0.0381303	+	0.0920548i	−0.941797	−	0.336181i	$-0.890865\pi$
$617$	−0.947138	+	2.28659i	−0.0381303	+	0.0920548i	0.903667	+	0.428236i	$0.140865\pi$
$618$	0.573272	−	0.237457i	0.0230604	−	0.00955192i
$619$	−10.6189	−	25.6362i	−0.426809	−	1.03041i	−0.980293	−	0.197548i	$-0.936702\pi$
$619$	−10.6189	−	25.6362i	−0.426809	−	1.03041i	0.553485	−	0.832859i	$-0.313298\pi$
$620$	−1.61905	−	1.61905i	−0.0650228	−	0.0650228i
$621$	−2.98458	−	2.98458i	−0.119767	−	0.119767i
$622$	0.599321	+	1.44689i	0.0240306	+	0.0580150i
$623$	1.46991	−	0.608855i	0.0588905	−	0.0243933i
$624$	−1.15598	+	2.79079i	−0.0462764	+	0.111721i
$625$		−	20.0944i		−	0.803776i
$626$	32.6641	+	13.5299i	1.30552	+	0.540764i
$627$	−0.624618	+	0.624618i	−0.0249448	+	0.0249448i
$628$	1.66024			0.0662509
$629$	−23.4950	+	4.62902i	−0.936806	+	0.184571i
$630$	−16.7041			−0.665506
$631$	−0.681644	+	0.681644i	−0.0271358	+	0.0271358i	−0.720545	−	0.693409i	$-0.756108\pi$
$631$	−0.681644	+	0.681644i	−0.0271358	+	0.0271358i	0.693409	+	0.720545i	$0.256108\pi$
$632$	23.7039	+	9.81849i	0.942892	+	0.390559i
$633$		−	4.63178i		−	0.184097i
$634$	7.87346	−	19.0082i	0.312695	−	0.754913i
$635$	−16.7416	+	6.93461i	−0.664371	+	0.275192i
$636$	0.478133	+	1.15431i	0.0189592	+	0.0457716i
$637$	5.96923	+	5.96923i	0.236509	+	0.236509i
$638$	4.98958	+	4.98958i	0.197540	+	0.197540i
$639$	10.0708	+	24.3130i	0.398394	+	0.961809i
$640$	13.3654	−	5.53612i	0.528313	−	0.218834i
$641$	−15.4134	+	37.2112i	−0.608793	+	1.46976i	0.255521	+	0.966803i	$0.417753\pi$
$641$	−15.4134	+	37.2112i	−0.608793	+	1.46976i	−0.864314	+	0.502952i	$0.832247\pi$
$642$		−	4.79741i		−	0.189339i
$643$	35.5811	+	14.7382i	1.40318	+	0.581217i	0.950576	−	0.310493i	$-0.100494\pi$
$643$	35.5811	+	14.7382i	1.40318	+	0.581217i	0.452607	+	0.891710i	$0.350494\pi$
$644$	−1.64318	+	1.64318i	−0.0647503	+	0.0647503i
$645$	−1.79702			−0.0707574
$646$	10.1192	+	15.2043i	0.398136	+	0.598206i
$647$	31.1572			1.22492			0.612458	−	0.790503i	$-0.290181\pi$
$647$	31.1572			1.22492			0.612458	+	0.790503i	$0.290181\pi$
$648$	18.0414	−	18.0414i	0.708731	−	0.708731i
$649$	−4.04116	−	1.67390i	−0.158629	−	0.0657064i
$650$		−	4.10567i		−	0.161038i
$651$	−0.631138	+	1.52370i	−0.0247363	+	0.0597186i
$652$	0.358446	−	0.148473i	0.0140378	−	0.00581465i
$653$	−1.83862	−	4.43883i	−0.0719508	−	0.173705i	0.883813	−	0.467841i	$-0.154968\pi$
$653$	−1.83862	−	4.43883i	−0.0719508	−	0.173705i	−0.955763	+	0.294136i	$0.904968\pi$
$654$	2.55788	+	2.55788i	0.100021	+	0.100021i
$655$	19.6270	+	19.6270i	0.766892	+	0.766892i
$656$	10.4871	+	25.3181i	0.409452	+	0.988505i
$657$	2.66299	−	1.10304i	0.103893	−	0.0430339i
$658$	6.53505	−	15.7770i	0.254763	−	0.615052i
$659$		−	16.8391i		−	0.655960i	−0.944685	−	0.327980i	$-0.893632\pi$
$659$		−	16.8391i		−	0.655960i	0.944685	−	0.327980i	$-0.106368\pi$
$660$	−0.181196	−	0.0750539i	−0.00705305	−	0.00292147i
$661$	25.9329	−	25.9329i	1.00867	−	1.00867i	0.00871182	−	0.999962i	$-0.497227\pi$
$661$	25.9329	−	25.9329i	1.00867	−	1.00867i	0.999962	−	0.00871182i	$-0.00277309\pi$
$662$	−20.1443			−0.782929
$663$	−0.776843	−	3.94293i	−0.0301701	−	0.153131i
$664$	44.3173			1.71985
$665$	10.9933	−	10.9933i	0.426301	−	0.426301i
$666$	20.0564	+	8.30764i	0.777170	+	0.321914i
$667$		−	15.5201i		−	0.600941i
$668$	1.94810	−	4.70312i	0.0753741	−	0.181969i
$669$	−5.09304	+	2.10961i	−0.196908	+	0.0815621i
$670$	−14.1017	−	34.0446i	−0.544798	−	1.31526i
$671$	−4.71786	−	4.71786i	−0.182131	−	0.182131i
$672$	0.830628	+	0.830628i	0.0320422	+	0.0320422i
$673$	−1.45288	−	3.50757i	−0.0560046	−	0.135207i	0.893401	−	0.449261i	$-0.148313\pi$
$673$	−1.45288	−	3.50757i	−0.0560046	−	0.135207i	−0.949405	+	0.314054i	$0.898313\pi$
$674$	31.3978	−	13.0054i	1.20940	−	0.500949i
$675$	0.484475	−	1.16963i	0.0186474	−	0.0450189i
$676$		−	0.656978i		−	0.0252684i
$677$	9.21865	+	3.81849i	0.354302	+	0.146757i	0.552733	−	0.833358i	$-0.313585\pi$
$677$	9.21865	+	3.81849i	0.354302	+	0.146757i	−0.198432	+	0.980115i	$0.563585\pi$
$678$	2.21631	−	2.21631i	0.0851169	−	0.0851169i
$679$	25.9898			0.997396
$680$	−14.1893	+	21.1524i	−0.544136	+	0.811158i
$681$	4.33576			0.166147
$682$	−2.66902	+	2.66902i	−0.102202	+	0.102202i
$683$	−31.6471	−	13.1087i	−1.21094	−	0.501590i	−0.316424	−	0.948618i	$-0.602482\pi$
$683$	−31.6471	−	13.1087i	−1.21094	−	0.501590i	−0.894520	+	0.447028i	$0.852482\pi$
$684$			3.86739i			0.147873i
$685$	−11.3248	+	27.3404i	−0.432697	+	1.04462i
$686$	−23.7112	+	9.82151i	−0.905299	+	0.374987i
$687$	−2.40929	−	5.81655i	−0.0919202	−	0.221915i
$688$	7.60407	+	7.60407i	0.289902	+	0.289902i
$689$	35.2679	+	35.2679i	1.34360	+	1.34360i
$690$	−0.706736	−	1.70621i	−0.0269050	−	0.0649543i
$691$	13.4258	−	5.56115i	0.510741	−	0.211556i	−0.112403	−	0.993663i	$-0.535855\pi$
$691$	13.4258	−	5.56115i	0.510741	−	0.211556i	0.623145	+	0.782107i	$0.285855\pi$
$692$	−2.83523	+	6.84486i	−0.107779	+	0.260202i
$693$		−	6.43197i		−	0.244330i
$694$	22.0450	+	9.13134i	0.836817	+	0.346621i
$695$	21.1044	−	21.1044i	0.800535	−	0.800535i
$696$	−4.26198			−0.161550
$697$	−30.2768	−	20.3101i	−1.14681	−	0.769299i
$698$	−13.0825			−0.495179
$699$	0.568028	−	0.568028i	0.0214848	−	0.0214848i
$700$	−0.643944	−	0.266730i	−0.0243388	−	0.0100815i
$701$		−	33.4365i		−	1.26288i	−0.775426	−	0.631439i	$-0.782465\pi$
$701$		−	33.4365i		−	1.26288i	0.775426	−	0.631439i	$-0.217535\pi$
$702$	−2.81900	+	6.80567i	−0.106396	+	0.256864i
$703$	−18.6669	+	7.73210i	−0.704037	+	0.291622i
$704$	3.40084	+	8.21036i	0.128174	+	0.309440i
$705$	−2.24152	−	2.24152i	−0.0844207	−	0.0844207i
$706$	−2.56120	−	2.56120i	−0.0963919	−	0.0963919i
$707$	7.61673	+	18.3884i	0.286456	+	0.691567i
$708$	0.388591	−	0.160960i	0.0146041	−	0.00604924i
$709$	14.9352	−	36.0567i	0.560902	−	1.35414i	−0.348143	−	0.937441i	$-0.613188\pi$
$709$	14.9352	−	36.0567i	0.560902	−	1.35414i	0.909046	−	0.416697i	$-0.136812\pi$
$710$			23.2818i			0.873750i
$711$	22.9739	+	9.51611i	0.861589	+	0.356882i
$712$	−1.55515	+	1.55515i	−0.0582818	+	0.0582818i
$713$	8.30198			0.310912
$714$	2.86366	+	0.575037i	0.107170	+	0.0215202i
$715$	−7.82923			−0.292797
$716$	5.86951	−	5.86951i	0.219354	−	0.219354i
$717$	4.70485	+	1.94881i	0.175706	+	0.0727797i
$718$		−	15.2751i		−	0.570060i
$719$	−11.4295	+	27.5932i	−0.426248	+	1.02905i	0.554219	+	0.832371i	$0.313017\pi$
$719$	−11.4295	+	27.5932i	−0.426248	+	1.02905i	−0.980467	+	0.196683i	$0.936983\pi$
$720$	17.1434	−	7.10101i	0.638895	−	0.264639i
$721$	−1.60923	−	3.88503i	−0.0599310	−	0.144686i
$722$	−6.21024	−	6.21024i	−0.231121	−	0.231121i
$723$	2.23696	+	2.23696i	0.0831933	+	0.0831933i
$724$	0.199147	+	0.480783i	0.00740124	+	0.0178682i
$725$	4.30074	−	1.78142i	0.159725	−	0.0661604i
$726$	−0.123727	+	0.298703i	−0.00459193	+	0.0110859i
$727$		−	34.1722i		−	1.26738i	−0.773588	−	0.633689i	$-0.781540\pi$
$727$		−	34.1722i		−	1.26738i	0.773588	−	0.633689i	$-0.218460\pi$
$728$	23.5352	+	9.74858i	0.872271	+	0.361306i
$729$	16.6739	−	16.6739i	0.617553	−	0.617553i
$730$	2.55003			0.0943810
$731$	−14.0266	−	2.81661i	−0.518794	−	0.104176i
$732$	0.641574			0.0237133
$733$	−7.19345	+	7.19345i	−0.265696	+	0.265696i	−0.827363	−	0.561667i	$-0.810160\pi$
$733$	−7.19345	+	7.19345i	−0.265696	+	0.265696i	0.561667	+	0.827363i	$0.310160\pi$
$734$	−0.801781	−	0.332109i	−0.0295943	−	0.0122584i
$735$			1.13894i			0.0420103i
$736$	2.26286	−	5.46304i	0.0834102	−	0.201370i
$737$	13.1090	−	5.42993i	0.482877	−	0.200014i
$738$	12.6481	+	30.5352i	0.465583	+	1.12402i
$739$	11.2984	+	11.2984i	0.415617	+	0.415617i	0.883690	−	0.468073i	$-0.155052\pi$
$739$	11.2984	+	11.2984i	0.415617	+	0.415617i	−0.468073	+	0.883690i	$0.655052\pi$
$740$	−3.17210	−	3.17210i	−0.116609	−	0.116609i
$741$	−1.29760	−	3.13269i	−0.0476686	−	0.115082i
$742$	−33.4909	+	13.8724i	−1.22949	+	0.509271i
$743$	19.6079	−	47.3377i	0.719344	−	1.73665i	0.0441337	−	0.999026i	$-0.485947\pi$
$743$	19.6079	−	47.3377i	0.719344	−	1.73665i	0.675211	−	0.737625i	$-0.264053\pi$
$744$		−	2.27981i		−	0.0835819i
$745$	9.10994	+	3.77346i	0.333763	+	0.138249i
$746$	29.3914	−	29.3914i	1.07609	−	1.07609i
$747$	42.9525			1.57155
$748$	−1.29669	−	0.869838i	−0.0474117	−	0.0318044i
$749$	−32.5118			−1.18795
$750$	2.72313	−	2.72313i	0.0994347	−	0.0994347i
$751$	12.8002	+	5.30203i	0.467087	+	0.193474i	0.603798	−	0.797137i	$-0.293653\pi$
$751$	12.8002	+	5.30203i	0.467087	+	0.193474i	−0.136711	+	0.990611i	$0.543653\pi$
$752$			18.9700i			0.691765i
$753$	−1.11849	+	2.70028i	−0.0407601	+	0.0984036i
$754$	−25.0246	+	10.3655i	−0.911342	+	0.377490i
$755$	8.02158	+	19.3658i	0.291935	+	0.704794i
$756$	0.884278	+	0.884278i	0.0321609	+	0.0321609i
$757$	21.1127	+	21.1127i	0.767355	+	0.767355i	0.977640	−	0.210285i	$-0.0674392\pi$
$757$	21.1127	+	21.1127i	0.767355	+	0.767355i	−0.210285	+	0.977640i	$0.567439\pi$
$758$	−17.0584	−	41.1826i	−0.619588	−	1.49582i
$759$	0.656983	−	0.272131i	0.0238470	−	0.00987775i
$760$	−8.22423	+	19.8550i	−0.298324	+	0.720218i
$761$			0.110322i			0.00399919i	0.999998	+	0.00199959i	$0.000636491\pi$
$761$			0.110322i			0.00399919i	−0.999998	+	0.00199959i	$0.999364\pi$
$762$	−2.65384	−	1.09926i	−0.0961386	−	0.0398219i
$763$	17.3346	−	17.3346i	0.627555	−	0.627555i
$764$	−0.623590			−0.0225607
$765$	−13.7523	+	20.5010i	−0.497216	+	0.741214i
$766$	−35.1166			−1.26882
$767$	11.8727	−	11.8727i	0.428697	−	0.428697i
$768$	−2.05086	−	0.849494i	−0.0740041	−	0.0306535i
$769$		−	45.8440i		−	1.65318i	−0.562808	−	0.826588i	$-0.690279\pi$
$769$		−	45.8440i		−	1.65318i	0.562808	−	0.826588i	$-0.309721\pi$
$770$	2.17759	−	5.25716i	0.0784748	−	0.189455i
$771$	1.05171	−	0.435632i	0.0378763	−	0.0156889i
$772$	2.15130	+	5.19369i	0.0774268	+	0.186925i
$773$	−20.6355	−	20.6355i	−0.742208	−	0.742208i	0.230794	−	0.973003i	$-0.425868\pi$
$773$	−20.6355	−	20.6355i	−0.742208	−	0.742208i	−0.973003	+	0.230794i	$0.925868\pi$
$774$	9.17098	+	9.17098i	0.329644	+	0.329644i
$775$	0.952916	+	2.30054i	0.0342298	+	0.0826379i
$776$	−33.1918	+	13.7485i	−1.19152	+	0.493543i
$777$	−1.23654	+	2.98528i	−0.0443608	+	0.107096i
$778$			9.31108i			0.333818i
$779$	−28.4198	−	11.7719i	−1.01824	−	0.421771i
$780$	0.532342	−	0.532342i	0.0190609	−	0.0190609i
$781$	−8.96475			−0.320784
$782$	−2.84215	−	14.4256i	−0.101635	−	0.515858i
$783$	−8.35216			−0.298482
$784$	4.81940	−	4.81940i	0.172122	−	0.172122i
$785$	8.26112	+	3.42187i	0.294852	+	0.122132i
$786$			4.39994i			0.156941i
$787$	13.7048	−	33.0863i	0.488523	−	1.17940i	−0.466940	−	0.884289i	$-0.654643\pi$
$787$	13.7048	−	33.0863i	0.488523	−	1.17940i	0.955463	−	0.295111i	$-0.0953566\pi$
$788$	−0.185882	+	0.0769948i	−0.00662177	+	0.00274283i
$789$	1.62123	+	3.91401i	0.0577175	+	0.139342i
$790$	15.5560	+	15.5560i	0.553456	+	0.553456i
$791$	−15.0198	−	15.0198i	−0.534043	−	0.534043i
$792$	3.40249	+	8.21434i	0.120902	+	0.291884i
$793$	23.6618	−	9.80104i	0.840255	−	0.348045i
$794$	−10.1396	+	24.4791i	−0.359840	+	0.868731i
$795$			6.72916i			0.238659i
$796$	−1.55245	−	0.643047i	−0.0550252	−	0.0227922i
$797$	13.3579	−	13.3579i	0.473160	−	0.473160i	−0.429776	−	0.902936i	$-0.641407\pi$
$797$	13.3579	−	13.3579i	0.473160	−	0.473160i	0.902936	+	0.429776i	$0.141407\pi$
$798$	2.46445			0.0872404
$799$	−13.9829	−	21.0096i	−0.494681	−	0.743266i
$800$	1.77358			0.0627056
$801$	−1.50726	+	1.50726i	−0.0532563	+	0.0532563i
$802$	−8.21497	−	3.40275i	−0.290081	−	0.120155i
$803$			0.981901i			0.0346505i
$804$	−0.522134	+	1.26054i	−0.0184142	+	0.0444559i
$805$	−11.5629	+	4.78951i	−0.407539	+	0.168808i
$806$	−5.54471	−	13.3861i	−0.195304	−	0.471506i
$807$	1.11184	+	1.11184i	0.0391387	+	0.0391387i
$808$	−19.4548	−	19.4548i	−0.684418	−	0.684418i
$809$	−9.96534	−	24.0585i	−0.350363	−	0.845851i	−0.996575	−	0.0826929i	$-0.973648\pi$
$809$	−9.96534	−	24.0585i	−0.350363	−	0.845851i	0.646212	−	0.763158i	$-0.276352\pi$
$810$	20.2119	−	8.37203i	0.710173	−	0.294163i
$811$	−7.78836	+	18.8028i	−0.273486	+	0.660254i	−0.999628	−	0.0272914i	$-0.991312\pi$
$811$	−7.78836	+	18.8028i	−0.273486	+	0.660254i	0.726141	+	0.687545i	$0.241312\pi$
$812$			4.59833i			0.161370i
$813$	−3.02001	−	1.25093i	−0.105916	−	0.0438719i
$814$	−5.22922	+	5.22922i	−0.183284	+	0.183284i
$815$	2.08958			0.0731949
$816$	−3.18343	+	0.627204i	−0.111442	+	0.0219565i
$817$	−12.0712			−0.422318
$818$	−21.8650	+	21.8650i	−0.764493	+	0.764493i
$819$	22.8103	+	9.44835i	0.797057	+	0.330152i
$820$		−	6.82982i		−	0.238508i
$821$	15.1805	−	36.6491i	0.529804	−	1.27906i	−0.401847	−	0.915707i	$-0.631632\pi$
$821$	15.1805	−	36.6491i	0.529804	−	1.27906i	0.931651	−	0.363354i	$-0.118368\pi$
$822$	−4.33393	+	1.79517i	−0.151163	+	0.0626138i
$823$	−0.117863	−	0.284547i	−0.00410846	−	0.00991869i	0.921812	−	0.387637i	$-0.126709\pi$
$823$	−0.117863	−	0.284547i	−0.00410846	−	0.00991869i	−0.925920	+	0.377719i	$0.876709\pi$
$824$	4.11034	+	4.11034i	0.143191	+	0.143191i
$825$	0.150819	+	0.150819i	0.00525086	+	0.00525086i
$826$	4.67003	+	11.2745i	0.162491	+	0.392288i
$827$	−26.9781	+	11.1747i	−0.938121	+	0.388582i	−0.798754	−	0.601658i	$-0.794507\pi$
$827$	−26.9781	+	11.1747i	−0.938121	+	0.388582i	−0.139367	+	0.990241i	$0.544507\pi$
$828$	1.19143	−	2.87636i	0.0414049	−	0.0999604i
$829$		−	3.09484i		−	0.107488i	−0.998555	−	0.0537441i	$-0.982884\pi$
$829$		−	3.09484i		−	0.107488i	0.998555	−	0.0537441i	$-0.0171155\pi$
$830$	35.1072	+	14.5419i	1.21859	+	0.504755i
$831$	1.98864	−	1.98864i	0.0689851	−	0.0689851i
$832$	−34.1130			−1.18265
$833$	−1.78515	+	8.88998i	−0.0618517	+	0.308020i
$834$	4.73113			0.163826
$835$	19.3869	−	19.3869i	0.670910	−	0.670910i
$836$	−1.21716	−	0.504164i	−0.0420964	−	0.0174369i
$837$		−	4.46772i		−	0.154427i
$838$	−8.70052	+	21.0049i	−0.300554	+	0.725603i
$839$	−31.9129	+	13.2188i	−1.10176	+	0.456362i	−0.858091	−	0.513497i	$-0.828350\pi$
$839$	−31.9129	+	13.2188i	−1.10176	+	0.456362i	−0.243665	+	0.969859i	$0.578350\pi$
$840$	1.31525	+	3.17529i	0.0453804	+	0.109558i
$841$	−1.20992	−	1.20992i	−0.0417212	−	0.0417212i
$842$	34.4537	+	34.4537i	1.18735	+	1.18735i
$843$	2.53402	+	6.11765i	0.0872761	+	0.210703i
$844$	6.38213	−	2.64357i	0.219682	−	0.0909953i
$845$	1.35407	−	3.26902i	0.0465816	−	0.112458i
$846$			22.8790i			0.786597i
$847$	2.02429	+	0.838489i	0.0695555	+	0.0288108i
$848$	28.4744	−	28.4744i	0.977815	−	0.977815i
$849$	−2.22679			−0.0764233
$850$	3.67121	−	2.44338i	0.125922	−	0.0838071i
$851$	16.2655			0.557574
$852$	0.609551	−	0.609551i	0.0208829	−	0.0208829i
$853$	−26.7306	−	11.0722i	−0.915239	−	0.379104i	−0.125179	−	0.992134i	$-0.539951\pi$
$853$	−26.7306	−	11.0722i	−0.915239	−	0.379104i	−0.790060	+	0.613030i	$0.789951\pi$
$854$			18.6144i			0.636972i
$855$	−7.97094	+	19.2436i	−0.272600	+	0.658116i
$856$	41.5211	−	17.1986i	1.41916	−	0.587837i
$857$	14.8394	+	35.8256i	0.506905	+	1.22378i	0.945656	+	0.325169i	$0.105421\pi$
$857$	14.8394	+	35.8256i	0.506905	+	1.22378i	−0.438751	+	0.898609i	$0.644579\pi$
$858$	−0.877569	−	0.877569i	−0.0299597	−	0.0299597i
$859$	2.81159	+	2.81159i	0.0959302	+	0.0959302i	0.753443	−	0.657513i	$-0.228392\pi$
$859$	2.81159	+	2.81159i	0.0959302	+	0.0959302i	−0.657513	+	0.753443i	$0.728392\pi$
$860$	−1.02564	−	2.47611i	−0.0349740	−	0.0844346i
$861$	−4.54499	+	1.88260i	−0.154893	+	0.0641587i
$862$	−9.44312	+	22.7977i	−0.321634	+	0.776493i
$863$			22.0432i			0.750361i	0.926952	+	0.375180i	$0.122419\pi$
$863$			22.0432i			0.750361i	−0.926952	+	0.375180i	$0.877581\pi$
$864$	−2.93994	−	1.21776i	−0.100019	−	0.0414291i
$865$	−28.2154	+	28.2154i	−0.959352	+	0.959352i
$866$	−37.1670			−1.26298
$867$	3.06338	−	3.04116i	0.104038	−	0.103283i
$868$	−2.45973			−0.0834887
$869$	−5.98989	+	5.98989i	−0.203193	+	0.203193i
$870$	−3.37624	−	1.39848i	−0.114465	−	0.0474131i
$871$			54.4663i			1.84552i
$872$	−12.9683	+	31.3082i	−0.439162	+	1.06023i
$873$	−32.1696	+	13.3251i	−1.08878	+	0.450986i
$874$	−4.74740	−	11.4612i	−0.160583	−	0.387682i
$875$	−18.4545	−	18.4545i	−0.623876	−	0.623876i
$876$	−0.0667636	−	0.0667636i	−0.00225573	−	0.00225573i
$877$	−10.6661	−	25.7502i	−0.360168	−	0.869523i	−0.995275	−	0.0970984i	$-0.969044\pi$
$877$	−10.6661	−	25.7502i	−0.360168	−	0.869523i	0.635107	−	0.772424i	$-0.280956\pi$
$878$	4.44904	−	1.84285i	0.150148	−	0.0621933i
$879$	0.412627	−	0.996169i	0.0139175	−	0.0335999i
$880$			6.32113i			0.213085i
$881$	−54.3637	−	22.5182i	−1.83156	−	0.758657i	−0.966341	−	0.257264i	$-0.917179\pi$
$881$	−54.3637	−	22.5182i	−1.83156	−	0.758657i	−0.865219	−	0.501394i	$-0.832821\pi$
$882$	5.81250	−	5.81250i	0.195717	−	0.195717i
$883$	−17.3251			−0.583034			−0.291517	−	0.956566i	$-0.594160\pi$
$883$	−17.3251			−0.583034			−0.291517	+	0.956566i	$0.594160\pi$
$884$	4.98959	−	3.32082i	0.167818	−	0.111691i
$885$	2.26532			0.0761478
$886$	21.3107	−	21.3107i	0.715946	−	0.715946i
$887$	−38.5544	−	15.9697i	−1.29453	−	0.536211i	−0.374197	−	0.927349i	$-0.622082\pi$
$887$	−38.5544	−	15.9697i	−1.29453	−	0.536211i	−0.920332	+	0.391138i	$0.872082\pi$
$888$		−	4.46667i		−	0.149892i
$889$	−7.44961	+	17.9849i	−0.249852	+	0.603196i
$890$	−1.74225	+	0.721663i	−0.0584003	+	0.0241902i
$891$	3.22368	+	7.78266i	0.107997	+	0.260729i
$892$	−5.81366	−	5.81366i	−0.194656	−	0.194656i
$893$	−15.0571	−	15.0571i	−0.503868	−	0.503868i
$894$	0.598160	+	1.44409i	0.0200055	+	0.0482975i
$895$	41.3032	−	17.1084i	1.38061	−	0.571869i
$896$	5.94725	−	14.3579i	0.198684	−	0.479665i
$897$			2.72968i			0.0911413i
$898$	−30.9133	−	12.8047i	−1.03159	−	0.427299i
$899$	11.6163	−	11.6163i	0.387425	−	0.387425i
$900$	0.933815			0.0311272
$901$	−10.5472	+	52.5246i	−0.351377	+	1.74985i
$902$	−11.2590			−0.374883
$903$	−1.36505	+	1.36505i	−0.0454260	+	0.0454260i
$904$	27.1274	+	11.2365i	0.902245	+	0.373722i
$905$			2.80276i			0.0931669i
$906$	−1.27156	+	3.06982i	−0.0422448	+	0.101988i
$907$	−47.2489	+	19.5711i	−1.56887	+	0.649849i	−0.986602	−	0.163144i	$-0.947836\pi$
$907$	−47.2489	+	19.5711i	−1.56887	+	0.649849i	−0.582273	+	0.812994i	$0.697836\pi$
$908$	2.47462	+	5.97425i	0.0821231	+	0.198263i
$909$	−18.8557	−	18.8557i	−0.625403	−	0.625403i
$910$	15.4452	+	15.4452i	0.512004	+	0.512004i
$911$	−1.61404	−	3.89664i	−0.0534756	−	0.129101i	0.894884	−	0.446299i	$-0.147258\pi$
$911$	−1.61404	−	3.89664i	−0.0534756	−	0.129101i	−0.948360	+	0.317197i	$0.897258\pi$
$912$	−2.52926	+	1.04765i	−0.0837520	+	0.0346912i
$913$	−5.59940	+	13.5182i	−0.185313	+	0.447386i
$914$		−	22.7128i		−	0.751272i
$915$	3.19238	+	1.32233i	0.105537	+	0.0437147i
$916$	6.63953	−	6.63953i	0.219376	−	0.219376i
$917$	29.8182			0.984683
$918$	−7.76315	+	1.52951i	−0.256222	+	0.0504813i
$919$	34.3768			1.13398			0.566992	−	0.823723i	$-0.308107\pi$
$919$	34.3768			1.13398			0.566992	+	0.823723i	$0.308107\pi$
$920$	12.2335	−	12.2335i	0.403326	−	0.403326i
$921$	3.64203	+	1.50858i	0.120009	+	0.0497093i
$922$		−	17.8301i		−	0.587204i
$923$	13.1689	−	31.7926i	0.433460	−	1.04647i
$924$	−0.194653	+	0.0806277i	−0.00640360	+	0.00265246i
$925$	1.86698	+	4.50729i	0.0613859	+	0.148199i
$926$	−13.9733	−	13.9733i	−0.459192	−	0.459192i
$927$	3.98375	+	3.98375i	0.130844	+	0.130844i
$928$	−4.47774	−	10.8102i	−0.146989	−	0.354863i
$929$	52.4020	−	21.7056i	1.71926	−	0.712139i	0.719409	−	0.694586i	$-0.244413\pi$
$929$	52.4020	−	21.7056i	1.71926	−	0.712139i	0.999846	−	0.0175525i	$-0.00558742\pi$
$930$	0.748075	−	1.80601i	0.0245303	−	0.0592215i
$931$			7.65064i			0.250740i
$932$	1.10689	+	0.458487i	0.0362573	+	0.0150183i
$933$	0.220834	−	0.220834i	0.00722977	−	0.00722977i
$934$	0.372266			0.0121809
$935$	−4.65935	−	7.00075i	−0.152377	−	0.228949i
$936$	−34.1295			−1.11556
$937$	−17.8869	+	17.8869i	−0.584339	+	0.584339i	−0.936093	−	0.351754i	$-0.885585\pi$
$937$	−17.8869	+	17.8869i	−0.584339	+	0.584339i	0.351754	+	0.936093i	$0.385585\pi$
$938$	−36.5729	−	15.1490i	−1.19415	−	0.494633i
$939$		−	7.05043i		−	0.230082i
$940$	1.80926	−	4.36794i	0.0590115	−	0.142466i
$941$	9.23461	−	3.82510i	0.301040	−	0.124695i	−0.227051	−	0.973883i	$-0.572908\pi$
$941$	9.23461	−	3.82510i	0.301040	−	0.124695i	0.528090	+	0.849188i	$0.322908\pi$
$942$	0.542426	+	1.30953i	0.0176732	+	0.0426669i
$943$	17.5105	+	17.5105i	0.570222	+	0.570222i
$944$	−9.58569	−	9.58569i	−0.311988	−	0.311988i
$945$	2.57748	+	6.22259i	0.0838455	+	0.202421i
$946$	−4.08188	+	1.69077i	−0.132713	+	0.0549717i
$947$	−19.8891	+	48.0166i	−0.646310	+	1.56033i	0.171714	+	0.985147i	$0.445070\pi$
$947$	−19.8891	+	48.0166i	−0.646310	+	1.56033i	−0.818024	+	0.575184i	$0.804930\pi$
$948$		−	0.814555i		−	0.0264555i
$949$	−3.48221	−	1.44238i	−0.113037	−	0.0468216i
$950$	2.63108	−	2.63108i	0.0853635	−	0.0853635i
$951$	−4.10286			−0.133044
$952$	5.28930	+	26.8463i	0.171427	+	0.870093i
$953$	−25.7051			−0.832670			−0.416335	−	0.909211i	$-0.636686\pi$
$953$	−25.7051			−0.832670			−0.416335	+	0.909211i	$0.636686\pi$
$954$	34.3419	−	34.3419i	1.11186	−	1.11186i
$955$	−3.10289	−	1.28526i	−0.100407	−	0.0415900i
$956$			7.59509i			0.245643i
$957$	0.538492	−	1.30003i	0.0174070	−	0.0420242i
$958$	42.6968	−	17.6856i	1.37947	−	0.571395i
$959$	12.1658	+	29.3708i	0.392853	+	0.948432i
$960$	−3.25440	−	3.25440i	−0.105035	−	0.105035i
$961$	−15.7065	−	15.7065i	−0.506663	−	0.506663i
$962$	−10.8634	−	26.2265i	−0.350249	−	0.845575i
$963$	40.2424	−	16.6689i	1.29679	−	0.537149i
$964$	−1.80557	+	4.35904i	−0.0581536	+	0.140395i
$965$			30.2770i			0.974650i
$966$	−1.83292	−	0.759221i	−0.0589733	−	0.0244275i
$967$	8.68605	−	8.68605i	0.279325	−	0.279325i	−0.553515	−	0.832839i	$-0.686714\pi$
$967$	8.68605	−	8.68605i	0.279325	−	0.279325i	0.832839	+	0.553515i	$0.186714\pi$
$968$	−3.02881			−0.0973495
$969$	2.02896	−	3.02462i	0.0651796	−	0.0971649i
$970$	−30.8051			−0.989093
$971$	−35.5339	+	35.5339i	−1.14034	+	1.14034i	−0.151950	+	0.988388i	$0.548555\pi$
$971$	−35.5339	+	35.5339i	−1.14034	+	1.14034i	−0.988388	+	0.151950i	$0.951445\pi$
$972$	−2.33028	−	0.965234i	−0.0747438	−	0.0309599i
$973$		−	32.0626i		−	1.02788i
$974$	−17.3291	+	41.8362i	−0.555260	+	1.34052i
$975$	−0.756415	+	0.313317i	−0.0242247	+	0.0100342i
$976$	−7.91312	−	19.1040i	−0.253293	−	0.611503i
$977$	19.9558	+	19.9558i	0.638444	+	0.638444i	0.950172	−	0.311728i	$-0.100908\pi$
$977$	19.9558	+	19.9558i	0.638444	+	0.638444i	−0.311728	+	0.950172i	$0.600908\pi$
$978$	0.234219	+	0.234219i	0.00748949	+	0.00748949i
$979$	−0.277879	−	0.670860i	−0.00888106	−	0.0214408i
$980$	−1.56934	+	0.650042i	−0.0501307	+	0.0207648i
$981$	−12.5689	+	30.3440i	−0.401294	+	0.968810i
$982$			25.9171i			0.827046i
$983$	9.55576	+	3.95813i	0.304781	+	0.126245i	0.529832	−	0.848102i	$-0.322255\pi$
$983$	9.55576	+	3.95813i	0.304781	+	0.126245i	−0.225051	+	0.974347i	$0.572255\pi$
$984$	4.80857	−	4.80857i	0.153292	−	0.153292i
$985$	−1.08361			−0.0345267
$986$	−24.1613	−	16.2078i	−0.769454	−	0.516160i
$987$	−3.40541			−0.108395
$988$	3.57594	−	3.57594i	0.113766	−	0.113766i
$989$	8.97791	+	3.71877i	0.285481	+	0.118250i
$990$			7.62367i			0.242296i
$991$	15.3955	−	37.1681i	0.489055	−	1.18068i	−0.466142	−	0.884710i	$-0.654356\pi$
$991$	15.3955	−	37.1681i	0.489055	−	1.18068i	0.955197	−	0.295972i	$-0.0956436\pi$
$992$	5.78259	−	2.39523i	0.183597	−	0.0760485i
$993$	1.53727	+	3.71131i	0.0487839	+	0.117775i
$994$	17.6853	+	17.6853i	0.560944	+	0.560944i
$995$	−6.39941	−	6.39941i	−0.202875	−	0.202875i
$996$	−0.538429	−	1.29988i	−0.0170608	−	0.0411884i
$997$	−19.2197	+	7.96105i	−0.608693	+	0.252129i	−0.665670	−	0.746247i	$-0.731854\pi$
$997$	−19.2197	+	7.96105i	−0.608693	+	0.252129i	0.0569765	+	0.998376i	$0.481854\pi$
$998$	−12.5733	+	30.3545i	−0.398000	+	0.960856i
$999$		−	8.75329i		−	0.276942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.111.5	✓	56
17.2	even	8	inner	187.2.h.a.155.5	yes	56
17.6	odd	16		3179.2.a.bi.1.9		28
17.11	odd	16		3179.2.a.bh.1.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.111.5	✓	56	1.1	even	1	trivial
187.2.h.a.155.5	yes	56	17.2	even	8	inner
3179.2.a.bh.1.9		28	17.11	odd	16
3179.2.a.bi.1.9		28	17.6	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)

\(f(q)\)	\(=\)	\(q+(-0.900361 + 0.900361i) q^{2} +(0.234589 + 0.0971699i) q^{3} +0.378700i q^{4} +(-0.780524 + 1.88435i) q^{5} +(-0.298703 + 0.123727i) q^{6} +(0.838489 + 2.02429i) q^{7} +(-2.14169 - 2.14169i) q^{8} +(-2.07573 - 2.07573i) q^{9} +O(q^{10})\)	\(q+(-0.900361 + 0.900361i) q^{2} +(0.234589 + 0.0971699i) q^{3} +0.378700i q^{4} +(-0.780524 + 1.88435i) q^{5} +(-0.298703 + 0.123727i) q^{6} +(0.838489 + 2.02429i) q^{7} +(-2.14169 - 2.14169i) q^{8} +(-2.07573 - 2.07573i) q^{9} +(-0.993844 - 2.39935i) q^{10} +(0.923880 - 0.382683i) q^{11} +(-0.0367982 + 0.0888387i) q^{12} +3.83860i q^{13} +(-2.57754 - 1.06765i) q^{14} +(-0.366205 + 0.366205i) q^{15} +3.09919 q^{16} +(-3.43240 + 2.28443i) q^{17} +3.73781 q^{18} +(-2.45993 + 2.45993i) q^{19} +(-0.713603 - 0.295584i) q^{20} +0.556352i q^{21} +(-0.487272 + 1.17638i) q^{22} +(2.58739 - 1.07173i) q^{23} +(-0.294309 - 0.710524i) q^{24} +(0.593971 + 0.593971i) q^{25} +(-3.45612 - 3.45612i) q^{26} +(-0.576755 - 1.39241i) q^{27} +(-0.766598 + 0.317535i) q^{28} +(2.12074 - 5.11992i) q^{29} -0.659433i q^{30} +(2.73874 + 1.13442i) q^{31} +(1.49299 - 1.49299i) q^{32} +0.253917 q^{33} +(1.03358 - 5.14721i) q^{34} -4.46894 q^{35} +(0.786078 - 0.786078i) q^{36} +(5.36581 + 2.22259i) q^{37} -4.42965i q^{38} +(-0.372996 + 0.900492i) q^{39} +(5.70733 - 2.36406i) q^{40} +(3.38382 + 8.16927i) q^{41} +(-0.500918 - 0.500918i) q^{42} +(2.45357 + 2.45357i) q^{43} +(0.144922 + 0.349873i) q^{44} +(5.53156 - 2.29125i) q^{45} +(-1.36464 + 3.29453i) q^{46} +6.12096i q^{47} +(0.727035 + 0.301148i) q^{48} +(1.55505 - 1.55505i) q^{49} -1.06958 q^{50} +(-1.02718 + 0.202377i) q^{51} -1.45368 q^{52} +(9.18770 - 9.18770i) q^{53} +(1.77296 + 0.734383i) q^{54} +2.03961i q^{55} +(2.53962 - 6.13119i) q^{56} +(-0.816103 + 0.338041i) q^{57} +(2.70034 + 6.51920i) q^{58} +(-3.09297 - 3.09297i) q^{59} +(-0.138682 - 0.138682i) q^{60} +(-2.55329 - 6.16418i) q^{61} +(-3.48724 + 1.44446i) q^{62} +(2.46141 - 5.94236i) q^{63} +8.88683i q^{64} +(-7.23327 - 2.99612i) q^{65} +(-0.228617 + 0.228617i) q^{66} +14.1891 q^{67} +(-0.865114 - 1.29985i) q^{68} +0.711114 q^{69} +(4.02366 - 4.02366i) q^{70} +(-8.28235 - 3.43066i) q^{71} +8.89114i q^{72} +(-0.375757 + 0.907158i) q^{73} +(-6.83230 + 2.83003i) q^{74} +(0.0816228 + 0.197055i) q^{75} +(-0.931574 - 0.931574i) q^{76} +(1.54933 + 1.54933i) q^{77} +(-0.474937 - 1.14660i) q^{78} +(-7.82616 + 3.24170i) q^{79} +(-2.41899 + 5.83996i) q^{80} +8.42389i q^{81} +(-10.4020 - 4.30863i) q^{82} +(-10.3463 + 10.3463i) q^{83} -0.210690 q^{84} +(-1.62561 - 8.25090i) q^{85} -4.41819 q^{86} +(0.995004 - 0.995004i) q^{87} +(-2.79825 - 1.15907i) q^{88} -0.726133i q^{89} +(-2.91745 + 7.04336i) q^{90} +(-7.77044 + 3.21862i) q^{91} +(0.405865 + 0.979844i) q^{92} +(0.532246 + 0.532246i) q^{93} +(-5.51108 - 5.51108i) q^{94} +(-2.71534 - 6.55540i) q^{95} +(0.495312 - 0.205165i) q^{96} +(4.53925 - 10.9587i) q^{97} +2.80022i q^{98} +(-2.71207 - 1.12338i) 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

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