LMFDB - Embedded newform 187.2.h.a.111.4

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			111.4
Character	$\chi$	$=$	187.111
Dual form			187.2.h.a.155.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31588 + 1.31588i) q^{2} +(-2.81689 - 1.16679i) q^{3} -1.46310i q^{4} +(-1.53116 + 3.69655i) q^{5} +(5.24206 - 2.17133i) q^{6} +(-1.11207 - 2.68478i) q^{7} +(-0.706501 - 0.706501i) q^{8} +(4.45214 + 4.45214i) q^{9} +O(q^{10})$	\(q+(-1.31588 + 1.31588i) q^{2} +(-2.81689 - 1.16679i) q^{3} -1.46310i q^{4} +(-1.53116 + 3.69655i) q^{5} +(5.24206 - 2.17133i) q^{6} +(-1.11207 - 2.68478i) q^{7} +(-0.706501 - 0.706501i) q^{8} +(4.45214 + 4.45214i) q^{9} +(-2.84940 - 6.87905i) q^{10} +(0.923880 - 0.382683i) q^{11} +(-1.70713 + 4.12138i) q^{12} -0.505453i q^{13} +(4.99622 + 2.06950i) q^{14} +(8.62622 - 8.62622i) q^{15} +4.78554 q^{16} +(3.39114 - 2.34525i) q^{17} -11.7170 q^{18} +(2.95106 - 2.95106i) q^{19} +(5.40841 + 2.24024i) q^{20} +8.86030i q^{21} +(-0.712151 + 1.71928i) q^{22} +(-2.28779 + 0.947633i) q^{23} +(1.16579 + 2.81448i) q^{24} +(-7.78448 - 7.78448i) q^{25} +(0.665117 + 0.665117i) q^{26} +(-3.84607 - 9.28523i) q^{27} +(-3.92810 + 1.62707i) q^{28} +(-0.633917 + 1.53041i) q^{29} +22.7022i q^{30} +(-7.69024 - 3.18540i) q^{31} +(-4.88421 + 4.88421i) q^{32} -3.04898 q^{33} +(-1.37626 + 7.54841i) q^{34} +11.6272 q^{35} +(6.51391 - 6.51391i) q^{36} +(4.07137 + 1.68641i) q^{37} +7.76650i q^{38} +(-0.589759 + 1.42381i) q^{39} +(3.69338 - 1.52985i) q^{40} +(-2.78181 - 6.71588i) q^{41} +(-11.6591 - 11.6591i) q^{42} +(2.14615 + 2.14615i) q^{43} +(-0.559903 - 1.35173i) q^{44} +(-23.2745 + 9.64060i) q^{45} +(1.76349 - 4.25744i) q^{46} -6.44748i q^{47} +(-13.4803 - 5.58374i) q^{48} +(-1.02160 + 1.02160i) q^{49} +20.4869 q^{50} +(-12.2889 + 2.64955i) q^{51} -0.739527 q^{52} +(4.83565 - 4.83565i) q^{53} +(17.2792 + 7.15730i) q^{54} +4.00111i q^{55} +(-1.11112 + 2.68248i) q^{56} +(-11.7561 + 4.86953i) q^{57} +(-1.17968 - 2.84800i) q^{58} +(-0.870401 - 0.870401i) q^{59} +(-12.6210 - 12.6210i) q^{60} +(-1.13407 - 2.73789i) q^{61} +(14.3111 - 5.92784i) q^{62} +(7.00192 - 16.9041i) q^{63} -3.28302i q^{64} +(1.86843 + 0.773930i) q^{65} +(4.01210 - 4.01210i) q^{66} +2.22966 q^{67} +(-3.43133 - 4.96156i) q^{68} +7.55014 q^{69} +(-15.3000 + 15.3000i) q^{70} +(2.10352 + 0.871308i) q^{71} -6.29088i q^{72} +(0.892084 - 2.15368i) q^{73} +(-7.57657 + 3.13832i) q^{74} +(12.8451 + 31.0109i) q^{75} +(-4.31769 - 4.31769i) q^{76} +(-2.05484 - 2.05484i) q^{77} +(-1.09751 - 2.64962i) q^{78} +(8.16888 - 3.38366i) q^{79} +(-7.32743 + 17.6900i) q^{80} +11.7542i q^{81} +(12.4979 + 5.17678i) q^{82} +(-1.38151 + 1.38151i) q^{83} +12.9635 q^{84} +(3.47696 + 16.1264i) q^{85} -5.64818 q^{86} +(3.57135 - 3.57135i) q^{87} +(-0.923088 - 0.382356i) q^{88} -9.25188i q^{89} +(17.9406 - 43.3124i) q^{90} +(-1.35703 + 0.562101i) q^{91} +(1.38648 + 3.34726i) q^{92} +(17.9458 + 17.9458i) q^{93} +(8.48413 + 8.48413i) q^{94} +(6.39019 + 15.4273i) q^{95} +(19.4571 - 8.05941i) q^{96} +(4.69110 - 11.3253i) q^{97} -2.68863i q^{98} +(5.81699 + 2.40948i) 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 $

$2$	−1.31588	+	1.31588i	−0.930470	+	0.930470i	−0.997735	−	0.0672652i	$-0.978573\pi$
$2$	−1.31588	+	1.31588i	−0.930470	+	0.930470i	0.0672652	+	0.997735i	$0.478573\pi$
$3$	−2.81689	−	1.16679i	−1.62633	−	0.673649i	−0.631518	−	0.775361i	$-0.717568\pi$
$3$	−2.81689	−	1.16679i	−1.62633	−	0.673649i	−0.994814	+	0.101713i	$0.967568\pi$
$4$		−	1.46310i		−	0.731549i
$5$	−1.53116	+	3.69655i	−0.684756	+	1.65315i	0.0703328	+	0.997524i	$0.477594\pi$
$5$	−1.53116	+	3.69655i	−0.684756	+	1.65315i	−0.755088	+	0.655623i	$0.772406\pi$
$6$	5.24206	−	2.17133i	2.14006	−	0.886443i
$7$	−1.11207	−	2.68478i	−0.420324	−	1.01475i	−0.982252	−	0.187566i	$-0.939940\pi$
$7$	−1.11207	−	2.68478i	−0.420324	−	1.01475i	0.561928	−	0.827186i	$-0.310060\pi$
$8$	−0.706501	−	0.706501i	−0.249786	−	0.249786i
$9$	4.45214	+	4.45214i	1.48405	+	1.48405i
$10$	−2.84940	−	6.87905i	−0.901059	−	2.17535i
$11$	0.923880	−	0.382683i	0.278560	−	0.115383i
$11$	0.923880	−	0.382683i	0.278560	−	0.115383i
$12$	−1.70713	+	4.12138i	−0.492807	+	1.18974i
$13$		−	0.505453i		−	0.140187i	−0.997540	−	0.0700937i	$-0.977670\pi$
$13$		−	0.505453i		−	0.140187i	0.997540	−	0.0700937i	$-0.0223298\pi$
$14$	4.99622	+	2.06950i	1.33530	+	0.553098i
$15$	8.62622	−	8.62622i	2.22728	−	2.22728i
$16$	4.78554			1.19639
$17$	3.39114	−	2.34525i	0.822471	−	0.568807i
$17$	3.39114	−	2.34525i	0.822471	−	0.568807i
$18$	−11.7170			−2.76172
$19$	2.95106	−	2.95106i	0.677019	−	0.677019i	−0.282305	−	0.959325i	$-0.591099\pi$
$19$	2.95106	−	2.95106i	0.677019	−	0.677019i	0.959325	+	0.282305i	$0.0910991\pi$
$20$	5.40841	+	2.24024i	1.20936	+	0.500932i
$21$			8.86030i			1.93347i
$22$	−0.712151	+	1.71928i	−0.151831	+	0.366553i
$23$	−2.28779	+	0.947633i	−0.477037	+	0.197595i	−0.608229	−	0.793762i	$-0.708120\pi$
$23$	−2.28779	+	0.947633i	−0.477037	+	0.197595i	0.131192	+	0.991357i	$0.458120\pi$
$24$	1.16579	+	2.81448i	0.237967	+	0.574503i
$25$	−7.78448	−	7.78448i	−1.55690	−	1.55690i
$26$	0.665117	+	0.665117i	0.130440	+	0.130440i
$27$	−3.84607	−	9.28523i	−0.740176	−	1.78694i
$28$	−3.92810	+	1.62707i	−0.742341	+	0.307488i
$29$	−0.633917	+	1.53041i	−0.117715	+	0.284190i	−0.971745	−	0.236035i	$-0.924152\pi$
$29$	−0.633917	+	1.53041i	−0.117715	+	0.284190i	0.854029	+	0.520225i	$0.174152\pi$
$30$			22.7022i			4.14483i
$31$	−7.69024	−	3.18540i	−1.38121	−	0.572115i	−0.436404	−	0.899751i	$-0.643748\pi$
$31$	−7.69024	−	3.18540i	−1.38121	−	0.572115i	−0.944804	+	0.327636i	$0.893748\pi$
$32$	−4.88421	+	4.88421i	−0.863415	+	0.863415i
$33$	−3.04898			−0.530759
$34$	−1.37626	+	7.54841i	−0.236027	+	1.29454i
$35$	11.6272			1.96535
$36$	6.51391	−	6.51391i	1.08565	−	1.08565i
$37$	4.07137	+	1.68641i	0.669328	+	0.277245i	0.691358	−	0.722512i	$-0.257013\pi$
$37$	4.07137	+	1.68641i	0.669328	+	0.277245i	−0.0220296	+	0.999757i	$0.507013\pi$
$38$			7.76650i			1.25989i
$39$	−0.589759	+	1.42381i	−0.0944371	+	0.227991i
$40$	3.69338	−	1.52985i	0.583975	−	0.241890i
$41$	−2.78181	−	6.71588i	−0.434446	−	1.04884i	−0.977837	−	0.209366i	$-0.932860\pi$
$41$	−2.78181	−	6.71588i	−0.434446	−	1.04884i	0.543392	−	0.839479i	$-0.317140\pi$
$42$	−11.6591	−	11.6591i	−1.79904	−	1.79904i
$43$	2.14615	+	2.14615i	0.327285	+	0.327285i	0.851553	−	0.524268i	$-0.175661\pi$
$43$	2.14615	+	2.14615i	0.327285	+	0.327285i	−0.524268	+	0.851553i	$0.675661\pi$
$44$	−0.559903	−	1.35173i	−0.0844086	−	0.203780i
$45$	−23.2745	+	9.64060i	−3.46955	+	1.43714i
$46$	1.76349	−	4.25744i	0.260012	−	0.627725i
$47$		−	6.44748i		−	0.940461i	−0.882544	−	0.470231i	$-0.844171\pi$
$47$		−	6.44748i		−	0.940461i	0.882544	−	0.470231i	$-0.155829\pi$
$48$	−13.4803	−	5.58374i	−1.94572	−	0.805943i
$49$	−1.02160	+	1.02160i	−0.145944	+	0.145944i
$50$	20.4869			2.89729
$51$	−12.2889	+	2.64955i	−1.72079	+	0.371012i
$52$	−0.739527			−0.102554
$53$	4.83565	−	4.83565i	0.664228	−	0.664228i	−0.292146	−	0.956374i	$-0.594369\pi$
$53$	4.83565	−	4.83565i	0.664228	−	0.664228i	0.956374	+	0.292146i	$0.0943692\pi$
$54$	17.2792	+	7.15730i	2.35141	+	0.973985i
$55$			4.00111i			0.539510i
$56$	−1.11112	+	2.68248i	−0.148480	+	0.358462i
$57$	−11.7561	+	4.86953i	−1.55713	+	0.644985i
$58$	−1.17968	−	2.84800i	−0.154900	−	0.373961i
$59$	−0.870401	−	0.870401i	−0.113317	−	0.113317i	0.648175	−	0.761491i	$-0.275533\pi$
$59$	−0.870401	−	0.870401i	−0.113317	−	0.113317i	−0.761491	+	0.648175i	$0.775533\pi$
$60$	−12.6210	−	12.6210i	−1.62936	−	1.62936i
$61$	−1.13407	−	2.73789i	−0.145203	−	0.350551i	0.834499	−	0.551009i	$-0.185757\pi$
$61$	−1.13407	−	2.73789i	−0.145203	−	0.350551i	−0.979702	+	0.200458i	$0.935757\pi$
$62$	14.3111	−	5.92784i	1.81751	−	0.752837i
$63$	7.00192	−	16.9041i	0.882158	−	2.12972i
$64$		−	3.28302i		−	0.410377i
$65$	1.86843	+	0.773930i	0.231750	+	0.0959942i
$66$	4.01210	−	4.01210i	0.493855	−	0.493855i
$67$	2.22966			0.272396			0.136198	−	0.990682i	$-0.456512\pi$
$67$	2.22966			0.272396			0.136198	+	0.990682i	$0.456512\pi$
$68$	−3.43133	−	4.96156i	−0.416110	−	0.601678i
$69$	7.55014			0.908930
$70$	−15.3000	+	15.3000i	−1.82870	+	1.82870i
$71$	2.10352	+	0.871308i	0.249642	+	0.103405i	0.503996	−	0.863706i	$-0.331863\pi$
$71$	2.10352	+	0.871308i	0.249642	+	0.103405i	−0.254353	+	0.967111i	$0.581863\pi$
$72$		−	6.29088i		−	0.741387i
$73$	0.892084	−	2.15368i	0.104411	−	0.252069i	−0.863037	−	0.505141i	$-0.831441\pi$
$73$	0.892084	−	2.15368i	0.104411	−	0.252069i	0.967448	+	0.253071i	$0.0814407\pi$
$74$	−7.57657	+	3.13832i	−0.880758	+	0.364822i
$75$	12.8451	+	31.0109i	1.48323	+	3.58083i
$76$	−4.31769	−	4.31769i	−0.495272	−	0.495272i
$77$	−2.05484	−	2.05484i	−0.234171	−	0.234171i
$78$	−1.09751	−	2.64962i	−0.124268	−	0.300010i
$79$	8.16888	−	3.38366i	0.919071	−	0.380692i	0.127549	−	0.991832i	$-0.459289\pi$
$79$	8.16888	−	3.38366i	0.919071	−	0.380692i	0.791522	+	0.611141i	$0.209289\pi$
$80$	−7.32743	+	17.6900i	−0.819232	+	1.97780i
$81$			11.7542i			1.30602i
$82$	12.4979	+	5.17678i	1.38016	+	0.571680i
$83$	−1.38151	+	1.38151i	−0.151641	+	0.151641i	−0.778850	−	0.627210i	$-0.784197\pi$
$83$	−1.38151	+	1.38151i	−0.151641	+	0.151641i	0.627210	+	0.778850i	$0.284197\pi$
$84$	12.9635			1.41443
$85$	3.47696	+	16.1264i	0.377129	+	1.74916i
$86$	−5.64818			−0.609058
$87$	3.57135	−	3.57135i	0.382889	−	0.382889i
$88$	−0.923088	−	0.382356i	−0.0984016	−	0.0407593i
$89$		−	9.25188i		−	0.980697i	−0.871526	−	0.490348i	$-0.836870\pi$
$89$		−	9.25188i		−	0.980697i	0.871526	−	0.490348i	$-0.163130\pi$
$90$	17.9406	−	43.3124i	1.89110	−	4.56553i
$91$	−1.35703	+	0.562101i	−0.142256	+	0.0589242i
$92$	1.38648	+	3.34726i	0.144550	+	0.348976i
$93$	17.9458	+	17.9458i	1.86090	+	1.86090i
$94$	8.48413	+	8.48413i	0.875071	+	0.875071i
$95$	6.39019	+	15.4273i	0.655619	+	1.58280i
$96$	19.4571	−	8.05941i	1.98584	−	0.822560i
$97$	4.69110	−	11.3253i	0.476309	−	1.14991i	−0.485018	−	0.874504i	$-0.661187\pi$
$97$	4.69110	−	11.3253i	0.476309	−	1.14991i	0.961327	−	0.275408i	$-0.0888130\pi$
$98$		−	2.68863i		−	0.271592i
$99$	5.81699	+	2.40948i	0.584630	+	0.242162i
$100$	−11.3895	+	11.3895i	−1.13895	+	1.13895i
$101$	0.925257			0.0920665			0.0460333	−	0.998940i	$-0.485342\pi$
$101$	0.925257			0.0920665			0.0460333	+	0.998940i	$0.485342\pi$
$102$	12.6842	−	19.6572i	1.25593	−	1.94636i
$103$	−17.6838			−1.74243			−0.871217	−	0.490898i	$-0.836669\pi$
$103$	−17.6838			−1.74243			−0.871217	+	0.490898i	$0.836669\pi$
$104$	−0.357103	+	0.357103i	−0.0350169	+	0.0350169i
$105$	−32.7525	−	13.5665i	−3.19632	−	1.32396i
$106$			12.7263i			1.23609i
$107$	−1.67260	+	4.03802i	−0.161697	+	0.390370i	−0.983874	−	0.178861i	$-0.942759\pi$
$107$	−1.67260	+	4.03802i	−0.161697	+	0.390370i	0.822178	+	0.569231i	$0.192759\pi$
$108$	−13.5852	+	5.62717i	−1.30724	+	0.541475i
$109$	−4.83926	−	11.6830i	−0.463517	−	1.11903i	−0.966943	−	0.254991i	$-0.917927\pi$
$109$	−4.83926	−	11.6830i	−0.463517	−	1.11903i	0.503426	−	0.864038i	$-0.332073\pi$
$110$	−5.26500	−	5.26500i	−0.501998	−	0.501998i
$111$	−9.50089	−	9.50089i	−0.901784	−	0.901784i
$112$	−5.32187	−	12.8481i	−0.502870	−	1.21404i
$113$	−10.3794	+	4.29929i	−0.976412	+	0.404443i	−0.813095	−	0.582130i	$-0.802219\pi$
$113$	−10.3794	+	4.29929i	−0.976412	+	0.404443i	−0.163317	+	0.986574i	$0.552219\pi$
$114$	9.06190	−	21.8774i	0.848725	−	2.04900i
$115$		−	9.90790i		−	0.923916i
$116$	2.23914	+	0.927483i	0.207899	+	0.0861146i
$117$	2.25035	−	2.25035i	0.208045	−	0.208045i
$118$	2.29069			0.210875
$119$	−10.0677	−	6.49637i	−0.922903	−	0.595522i
$120$	−12.1889			−1.11269
$121$	0.707107	−	0.707107i	0.0642824	−	0.0642824i
$122$	5.09505	+	2.11044i	0.461284	+	0.191070i
$123$			22.1637i			1.99843i
$124$	−4.66055	+	11.2516i	−0.418530	+	1.01042i
$125$	22.2123	−	9.20062i	1.98672	−	0.822928i
$126$	13.0301	+	31.4575i	1.16082	+	2.80246i
$127$	2.13181	+	2.13181i	0.189168	+	0.189168i	0.795336	−	0.606169i	$-0.207294\pi$
$127$	2.13181	+	2.13181i	0.189168	+	0.189168i	−0.606169	+	0.795336i	$0.707294\pi$
$128$	−5.44835	−	5.44835i	−0.481571	−	0.481571i
$129$	−3.54136	−	8.54960i	−0.311799	−	0.752750i
$130$	−3.47704	+	1.44024i	−0.304956	+	0.126317i
$131$	1.11495	−	2.69173i	0.0974136	−	0.235177i	−0.867659	−	0.497160i	$-0.834376\pi$
$131$	1.11495	−	2.69173i	0.0974136	−	0.235177i	0.965073	+	0.261982i	$0.0843763\pi$
$132$			4.46095i			0.388276i
$133$	−11.2047	−	4.64116i	−0.971575	−	0.402439i
$134$	−2.93397	+	2.93397i	−0.253457	+	0.253457i
$135$	40.2122			3.46092
$136$	−4.05276	−	0.738920i	−0.347522	−	0.0633618i
$137$	−3.13630			−0.267952			−0.133976	−	0.990985i	$-0.542775\pi$
$137$	−3.13630			−0.267952			−0.133976	+	0.990985i	$0.542775\pi$
$138$	−9.93510	+	9.93510i	−0.845732	+	0.845732i
$139$	7.42035	+	3.07361i	0.629386	+	0.260700i	0.674492	−	0.738282i	$-0.264363\pi$
$139$	7.42035	+	3.07361i	0.629386	+	0.260700i	−0.0451060	+	0.998982i	$0.514363\pi$
$140$		−	17.0117i		−	1.43775i
$141$	−7.52287	+	18.1618i	−0.633540	+	1.52950i
$142$	−3.91453	+	1.62145i	−0.328500	+	0.136069i
$143$	−0.193429	−	0.466978i	−0.0161753	−	0.0390506i
$144$	21.3059	+	21.3059i	1.77549	+	1.77549i
$145$	−4.68661	−	4.68661i	−0.389202	−	0.389202i
$146$	1.66012	+	4.00787i	0.137392	+	0.331694i
$147$	4.06975	−	1.68575i	0.335667	−	0.139038i
$148$	2.46739	−	5.95680i	0.202818	−	0.489646i
$149$			5.02880i			0.411975i	0.978555	+	0.205988i	$0.0660407\pi$
$149$			5.02880i			0.411975i	−0.978555	+	0.205988i	$0.933959\pi$
$150$	−57.7094	−	23.9040i	−4.71195	−	1.95176i
$151$	9.04519	−	9.04519i	0.736087	−	0.736087i	−0.235731	−	0.971818i	$-0.575748\pi$
$151$	9.04519	−	9.04519i	0.736087	−	0.736087i	0.971818	+	0.235731i	$0.0757485\pi$
$152$	−4.16985			−0.338220
$153$	25.5392	+	4.65642i	2.06472	+	0.376450i
$154$	5.40787			0.435779
$155$	23.5500	−	23.5500i	1.89158	−	1.89158i
$156$	2.08317	+	0.862875i	0.166787	+	0.0690853i
$157$			15.1696i			1.21067i	0.795973	+	0.605333i	$0.206960\pi$
$157$			15.1696i			1.21067i	−0.795973	+	0.605333i	$0.793040\pi$
$158$	−6.29679	+	15.2018i	−0.500946	+	1.20939i
$159$	−19.2637	+	7.97929i	−1.52771	+	0.632799i
$160$	−10.5762	−	25.5332i	−0.836123	−	2.01858i
$161$	5.08838	+	5.08838i	0.401020	+	0.401020i
$162$	−15.4672	−	15.4672i	−1.21521	−	1.21521i
$163$	−1.05940	−	2.55761i	−0.0829784	−	0.200327i	0.876945	−	0.480591i	$-0.159578\pi$
$163$	−1.05940	−	2.55761i	−0.0829784	−	0.200327i	−0.959923	+	0.280264i	$0.909578\pi$
$164$	−9.82599	+	4.07006i	−0.767281	+	0.317818i
$165$	4.66847	−	11.2707i	0.363440	−	0.877422i
$166$		−	3.63582i		−	0.282195i
$167$	6.03437	+	2.49952i	0.466954	+	0.193419i	0.603739	−	0.797182i	$-0.293677\pi$
$167$	6.03437	+	2.49952i	0.466954	+	0.193419i	−0.136785	+	0.990601i	$0.543677\pi$
$168$	6.25981	−	6.25981i	0.482955	−	0.482955i
$169$	12.7445			0.980347
$170$	−25.7958	−	16.6453i	−1.97845	−	1.27663i
$171$	26.2770			2.00945
$172$	3.14003	−	3.14003i	0.239425	−	0.239425i
$173$	−23.0064	−	9.52956i	−1.74914	−	0.724519i	−0.997919	−	0.0644723i	$-0.979464\pi$
$173$	−23.0064	−	9.52956i	−1.74914	−	0.724519i	−0.751224	−	0.660047i	$-0.770536\pi$
$174$			9.39896i			0.712533i
$175$	−12.2427	+	29.5566i	−0.925463	+	2.23427i
$176$	4.42126	−	1.83135i	0.333265	−	0.138043i
$177$	1.43624	+	3.46740i	0.107955	+	0.260626i
$178$	12.1744	+	12.1744i	0.912509	+	0.912509i
$179$	−5.10748	−	5.10748i	−0.381751	−	0.381751i	0.489982	−	0.871733i	$-0.337003\pi$
$179$	−5.10748	−	5.10748i	−0.381751	−	0.381751i	−0.871733	+	0.489982i	$0.837003\pi$
$180$	14.1051	+	34.0528i	1.05133	+	2.53815i
$181$	−23.7668	+	9.84453i	−1.76657	+	0.731738i	−0.771096	+	0.636719i	$0.780291\pi$
$181$	−23.7668	+	9.84453i	−1.76657	+	0.731738i	−0.995475	+	0.0950189i	$0.969709\pi$
$182$	1.04604	−	2.52535i	0.0775374	−	0.187192i
$183$			9.03556i			0.667928i
$184$	2.28583	+	0.946822i	0.168514	+	0.0698006i
$185$	−12.4678	+	12.4678i	−0.916653	+	0.916653i
$186$	−47.2293			−3.46302
$187$	2.23551	−	3.46446i	0.163477	−	0.253346i
$188$	−9.43329			−0.687993
$189$	−20.6517	+	20.6517i	−1.50219	+	1.50219i
$190$	−28.7092	−	11.8918i	−2.08279	−	0.862718i
$191$			9.33409i			0.675391i	0.941255	+	0.337696i	$0.109647\pi$
$191$			9.33409i			0.675391i	−0.941255	+	0.337696i	$0.890353\pi$
$192$	−3.83061	+	9.24790i	−0.276450	+	0.667410i
$193$	21.5154	−	8.91198i	1.54871	−	0.641498i	0.565631	−	0.824659i	$-0.308633\pi$
$193$	21.5154	−	8.91198i	1.54871	−	0.641498i	0.983083	+	0.183160i	$0.0586327\pi$
$194$	8.72986	+	21.0757i	0.626767	+	1.51315i
$195$	−4.36015	−	4.36015i	−0.312237	−	0.312237i
$196$	1.49471	+	1.49471i	0.106765	+	0.106765i
$197$	−1.39027	−	3.35640i	−0.0990523	−	0.239133i	0.866584	−	0.499032i	$-0.166311\pi$
$197$	−1.39027	−	3.35640i	−0.0990523	−	0.239133i	−0.965636	+	0.259898i	$0.916311\pi$
$198$	−10.8251	+	4.48389i	−0.769305	+	0.318656i
$199$	−0.0649323	+	0.156760i	−0.00460293	+	0.0111124i	−0.926164	−	0.377120i	$-0.876914\pi$
$199$	−0.0649323	+	0.156760i	−0.00460293	+	0.0111124i	0.921561	+	0.388233i	$0.126914\pi$
$200$			10.9995i			0.777781i
$201$	−6.28070	−	2.60155i	−0.443007	−	0.183499i
$202$	−1.21753	+	1.21753i	−0.0856651	+	0.0856651i
$203$	4.81379			0.337862
$204$	3.87655	+	17.9798i	0.271413	+	1.25884i
$205$	29.0850			2.03138
$206$	23.2698	−	23.2698i	1.62128	−	1.62128i
$207$	−14.4045	−	5.96655i	−1.00118	−	0.414704i
$208$		−	2.41887i		−	0.167718i
$209$	1.59710	−	3.85574i	0.110474	−	0.266707i
$210$	60.9504	−	25.2465i	4.20598	−	1.74217i
$211$	−7.70983	−	18.6132i	−0.530767	−	1.28138i	−0.931016	−	0.364978i	$-0.881077\pi$
$211$	−7.70983	−	18.6132i	−0.530767	−	1.28138i	0.400250	−	0.916406i	$-0.368923\pi$
$212$	−7.07503	−	7.07503i	−0.485915	−	0.485915i
$213$	−4.90876	−	4.90876i	−0.336343	−	0.336343i
$214$	−3.11261	−	7.51451i	−0.212774	−	0.513681i
$215$	−11.2195	+	4.64726i	−0.765161	+	0.316940i
$216$	−3.84277	+	9.27727i	−0.261468	+	0.631239i
$217$			24.1890i			1.64206i
$218$	21.7414	+	9.00557i	1.47251	+	0.609934i
$219$	−5.02580	+	5.02580i	−0.339612	+	0.339612i
$220$	5.85402			0.394678
$221$	−1.18541	−	1.71406i	−0.0797396	−	0.115300i
$222$	25.0041			1.67817
$223$	0.809064	−	0.809064i	0.0541789	−	0.0541789i	−0.679498	−	0.733677i	$-0.737802\pi$
$223$	0.809064	−	0.809064i	0.0541789	−	0.0541789i	0.733677	+	0.679498i	$0.237802\pi$
$224$	18.5446	+	7.68144i	1.23907	+	0.513238i
$225$		−	69.3151i		−	4.62101i
$226$	8.00072	−	19.3155i	0.532200	−	1.28484i
$227$	−12.7855	+	5.29594i	−0.848606	+	0.351504i	−0.764241	−	0.644931i	$-0.776886\pi$
$227$	−12.7855	+	5.29594i	−0.848606	+	0.351504i	−0.0843648	+	0.996435i	$0.526886\pi$
$228$	7.12459	+	17.2003i	0.471838	+	1.13912i
$229$	16.5094	+	16.5094i	1.09097	+	1.09097i	0.995425	+	0.0955499i	$0.0304609\pi$
$229$	16.5094	+	16.5094i	1.09097	+	1.09097i	0.0955499	+	0.995425i	$0.469539\pi$
$230$	13.0376	+	13.0376i	0.859676	+	0.859676i
$231$	3.39069	+	8.18585i	0.223091	+	0.538589i
$232$	1.52910	−	0.633374i	0.100390	−	0.0415831i
$233$	−0.778365	+	1.87914i	−0.0509924	+	0.123106i	−0.947323	−	0.320280i	$-0.896223\pi$
$233$	−0.778365	+	1.87914i	−0.0509924	+	0.123106i	0.896331	+	0.443386i	$0.146223\pi$
$234$			5.92238i			0.387158i
$235$	23.8334	+	9.87212i	1.55472	+	0.643986i
$236$	−1.27348	+	1.27348i	−0.0828966	+	0.0828966i
$237$	−26.9589			−1.75117
$238$	21.7964	−	4.69942i	1.41285	−	0.304618i
$239$	−29.9599			−1.93795			−0.968974	−	0.247163i	$-0.920502\pi$
$239$	−29.9599			−1.93795			−0.968974	+	0.247163i	$0.920502\pi$
$240$	41.2811	−	41.2811i	2.66468	−	2.66468i
$241$	23.5163	+	9.74079i	1.51482	+	0.627459i	0.976546	−	0.215310i	$-0.0690763\pi$
$241$	23.5163	+	9.74079i	1.51482	+	0.627459i	0.538275	+	0.842769i	$0.319076\pi$
$242$			1.86094i			0.119626i
$243$	2.17653	−	5.25461i	0.139624	−	0.337083i
$244$	−4.00580	+	1.65926i	−0.256445	+	0.106223i
$245$	−2.21217	−	5.34065i	−0.141330	−	0.341202i
$246$	−29.1648	−	29.1648i	−1.85948	−	1.85948i
$247$	−1.49162	−	1.49162i	−0.0949096	−	0.0949096i
$248$	3.18267	+	7.68365i	0.202100	+	0.487913i
$249$	5.50351	−	2.27963i	0.348771	−	0.144466i
$250$	−17.1218	+	41.3357i	−1.08288	+	2.61430i
$251$		−	14.3640i		−	0.906648i	−0.891346	−	0.453324i	$-0.850238\pi$
$251$		−	14.3640i		−	0.906648i	0.891346	−	0.453324i	$-0.149762\pi$
$252$	−24.7324	−	10.2445i	−1.55799	−	0.645342i
$253$	−1.75100	+	1.75100i	−0.110084	+	0.110084i
$254$	−5.61043			−0.352030
$255$	9.02204	−	49.4833i	0.564982	−	3.09876i
$256$	20.9048			1.30655
$257$	−11.2835	+	11.2835i	−0.703847	+	0.703847i	−0.965234	−	0.261387i	$-0.915820\pi$
$257$	−11.2835	+	11.2835i	−0.703847	+	0.703847i	0.261387	+	0.965234i	$0.415820\pi$
$258$	15.9103	+	6.59026i	0.990531	+	0.410291i
$259$		−	12.8061i		−	0.795735i
$260$	1.13233	−	2.73370i	0.0702244	−	0.169537i
$261$	−9.63588	+	3.99131i	−0.596446	+	0.247056i
$262$	2.07486	+	5.00914i	0.128185	+	0.309466i
$263$	12.8987	+	12.8987i	0.795368	+	0.795368i	0.982361	−	0.186993i	$-0.0598743\pi$
$263$	12.8987	+	12.8987i	0.795368	+	0.795368i	−0.186993	+	0.982361i	$0.559874\pi$
$264$	2.15411	+	2.15411i	0.132576	+	0.132576i
$265$	10.4711	+	25.2794i	0.643232	+	1.55290i
$266$	20.8514	−	8.63692i	1.27848	−	0.529563i
$267$	−10.7950	+	26.0615i	−0.660645	+	1.59494i
$268$		−	3.26221i		−	0.199271i
$269$	−4.53901	−	1.88012i	−0.276748	−	0.114633i	0.239993	−	0.970775i	$-0.422855\pi$
$269$	−4.53901	−	1.88012i	−0.276748	−	0.114633i	−0.516741	+	0.856142i	$0.672855\pi$
$270$	−52.9146	+	52.9146i	−3.22028	+	3.22028i
$271$	−30.2021			−1.83465			−0.917324	−	0.398142i	$-0.869655\pi$
$271$	−30.2021			−1.83465			−0.917324	+	0.398142i	$0.869655\pi$
$272$	16.2284	−	11.2233i	0.983992	−	0.680512i
$273$	4.47846			0.271049
$274$	4.12701	−	4.12701i	0.249322	−	0.249322i
$275$	−10.1709	−	4.21293i	−0.613329	−	0.254049i
$276$		−	11.0466i		−	0.664926i
$277$	−4.67754	+	11.2926i	−0.281046	+	0.678506i	−0.999861	−	0.0166965i	$-0.994685\pi$
$277$	−4.67754	+	11.2926i	−0.281046	+	0.678506i	0.718814	+	0.695202i	$0.244685\pi$
$278$	−13.8088	+	5.71981i	−0.828199	+	0.343051i
$279$	−20.0561	−	48.4198i	−1.20073	−	2.89882i
$280$	−8.21463	−	8.21463i	−0.490918	−	0.490918i
$281$	4.23697	+	4.23697i	0.252757	+	0.252757i	0.822100	−	0.569343i	$-0.192802\pi$
$281$	4.23697	+	4.23697i	0.252757	+	0.252757i	−0.569343	+	0.822100i	$0.692802\pi$
$282$	−13.9996	−	33.7981i	−0.833665	−	2.01265i
$283$	13.0559	−	5.40794i	0.776094	−	0.321469i	0.0407561	−	0.999169i	$-0.487023\pi$
$283$	13.0559	−	5.40794i	0.776094	−	0.321469i	0.735338	+	0.677700i	$0.237023\pi$
$284$	1.27481	−	3.07766i	0.0756460	−	0.182626i
$285$		−	50.9129i		−	3.01582i
$286$	0.869018	+	0.359959i	0.0513861	+	0.0212848i
$287$	−14.9371	+	14.9371i	−0.881710	+	0.881710i
$288$	−43.4903			−2.56269
$289$	5.99960	−	15.9061i	0.352918	−	0.935654i
$290$	12.3341			0.724281
$291$	−26.4286	+	26.4286i	−1.54927	+	1.54927i
$292$	−3.15105	−	1.30521i	−0.184401	−	0.0763814i
$293$		−	30.5759i		−	1.78626i	−0.449794	−	0.893132i	$-0.648503\pi$
$293$		−	30.5759i		−	1.78626i	0.449794	−	0.893132i	$-0.351497\pi$
$294$	−3.13707	+	7.57356i	−0.182958	+	0.441699i
$295$	4.55020	−	1.88476i	0.264923	−	0.109735i
$296$	−1.68497	−	4.06788i	−0.0979369	−	0.236441i
$297$	−7.10660	−	7.10660i	−0.412367	−	0.412367i
$298$	−6.61731	−	6.61731i	−0.383331	−	0.383331i
$299$	0.478984	+	1.15637i	0.0277004	+	0.0668746i
$300$	45.3720	−	18.7937i	2.61955	−	1.08505i
$301$	3.37528	−	8.14864i	0.194548	−	0.469680i
$302$			23.8048i			1.36981i
$303$	−2.60635	−	1.07958i	−0.149731	−	0.0620205i
$304$	14.1224	−	14.1224i	0.809976	−	0.809976i
$305$	11.8572			0.678940
$306$	−39.7339	+	27.4792i	−2.27143	+	1.57088i
$307$	−1.89438			−0.108118			−0.0540589	−	0.998538i	$-0.517216\pi$
$307$	−1.89438			−0.108118			−0.0540589	+	0.998538i	$0.517216\pi$
$308$	−3.00644	+	3.00644i	−0.171308	+	0.171308i
$309$	49.8132	+	20.6333i	2.83377	+	1.17379i
$310$			61.9780i			3.52012i
$311$	6.51683	−	15.7330i	0.369536	−	0.892138i	−0.624291	−	0.781192i	$-0.714612\pi$
$311$	6.51683	−	15.7330i	0.369536	−	0.892138i	0.993826	−	0.110946i	$-0.0353880\pi$
$312$	1.42259	−	0.589254i	0.0805381	−	0.0333600i
$313$	−1.99285	−	4.81116i	−0.112643	−	0.271943i	0.857498	−	0.514488i	$-0.172018\pi$
$313$	−1.99285	−	4.81116i	−0.112643	−	0.271943i	−0.970140	+	0.242545i	$0.922018\pi$
$314$	−19.9614	−	19.9614i	−1.12649	−	1.12649i
$315$	51.7658	+	51.7658i	2.91667	+	2.91667i
$316$	−4.95063	−	11.9519i	−0.278494	−	0.672345i
$317$	9.58193	−	3.96896i	0.538175	−	0.222919i	−0.0970047	−	0.995284i	$-0.530926\pi$
$317$	9.58193	−	3.96896i	0.538175	−	0.222919i	0.635179	+	0.772365i	$0.280926\pi$
$318$	14.8490	−	35.8486i	0.832689	−	2.01029i
$319$			1.65651i			0.0927465i
$320$	12.1358	+	5.02683i	0.678414	+	0.281008i
$321$	9.42307	−	9.42307i	0.525944	−	0.525944i
$322$	−13.3914			−0.746275
$323$	3.08647	−	16.9284i	0.171736	−	0.941922i
$324$	17.1975			0.955419
$325$	−3.93469	+	3.93469i	−0.218257	+	0.218257i
$326$	4.75956	+	1.97147i	0.263608	+	0.109190i
$327$			38.5562i			2.13216i
$328$	−2.77943	+	6.71013i	−0.153468	+	0.370505i
$329$	−17.3101	+	7.17007i	−0.954335	+	0.395299i
$330$	8.68775	+	20.9741i	0.478245	+	1.15459i
$331$	−23.0145	−	23.0145i	−1.26499	−	1.26499i	−0.948643	−	0.316349i	$-0.897543\pi$
$331$	−23.0145	−	23.0145i	−1.26499	−	1.26499i	−0.316349	−	0.948643i	$-0.602457\pi$
$332$	2.02129	+	2.02129i	0.110933	+	0.110933i
$333$	10.6181	+	25.6344i	0.581869	+	1.40476i
$334$	−11.2296	+	4.65146i	−0.614457	+	0.254516i
$335$	−3.41397	+	8.24204i	−0.186525	+	0.450311i
$336$			42.4013i			2.31318i
$337$	32.0441	+	13.2731i	1.74555	+	0.723031i	0.998287	+	0.0585034i	$0.0186328\pi$
$337$	32.0441	+	13.2731i	1.74555	+	0.723031i	0.747264	+	0.664528i	$0.231367\pi$
$338$	−16.7703	+	16.7703i	−0.912184	+	0.912184i
$339$	34.2540			1.86042
$340$	23.5946	−	5.08713i	1.27959	−	0.275888i
$341$	−8.32386			−0.450762
$342$	−34.5775	+	34.5775i	−1.86974	+	1.86974i
$343$	−14.9146	−	6.17783i	−0.805312	−	0.333571i
$344$		−	3.03252i		−	0.163503i
$345$	−11.5605	+	27.9094i	−0.622395	+	1.50259i
$346$	42.8135	−	17.7339i	2.30167	−	0.953383i
$347$	4.95358	+	11.9590i	0.265922	+	0.641993i	0.999284	−	0.0378458i	$-0.0120496\pi$
$347$	4.95358	+	11.9590i	0.265922	+	0.641993i	−0.733361	+	0.679839i	$0.762050\pi$
$348$	−5.22523	−	5.22523i	−0.280102	−	0.280102i
$349$	7.87750	+	7.87750i	0.421673	+	0.421673i	0.885779	−	0.464106i	$-0.153624\pi$
$349$	7.87750	+	7.87750i	0.421673	+	0.421673i	−0.464106	+	0.885779i	$0.653624\pi$
$350$	−22.7830	−	55.0030i	−1.21780	−	2.94003i
$351$	−4.69325	+	1.94401i	−0.250507	+	0.103763i
$352$	−2.64332	+	6.38153i	−0.140889	+	0.340137i
$353$		−	32.3097i		−	1.71967i	−0.510573	−	0.859835i	$-0.670567\pi$
$353$		−	32.3097i		−	1.71967i	0.510573	−	0.859835i	$-0.329433\pi$
$354$	−6.45262	−	2.67276i	−0.342953	−	0.142056i
$355$	−6.44167	+	6.44167i	−0.341888	+	0.341888i
$356$	−13.5364			−0.717427
$357$	20.7796	+	30.0465i	1.09977	+	1.59023i
$358$	13.4417			0.710415
$359$	20.7579	−	20.7579i	1.09556	−	1.09556i	0.100639	−	0.994923i	$-0.467911\pi$
$359$	20.7579	−	20.7579i	1.09556	−	1.09556i	0.994923	−	0.100639i	$-0.0320888\pi$
$360$	23.2545	+	9.63234i	1.22562	+	0.507669i
$361$			1.58251i			0.0832899i
$362$	18.3201	−	44.2286i	0.962882	−	2.32460i
$363$	−2.81689	+	1.16679i	−0.147848	+	0.0612408i
$364$	0.822408	+	1.98547i	0.0431059	+	0.104067i
$365$	6.59526	+	6.59526i	0.345212	+	0.345212i
$366$	−11.8897	−	11.8897i	−0.621487	−	0.621487i
$367$	0.586636	+	1.41626i	0.0306221	+	0.0739284i	0.938451	−	0.345413i	$-0.112261\pi$
$367$	0.586636	+	1.41626i	0.0306221	+	0.0739284i	−0.907829	+	0.419341i	$0.862261\pi$
$368$	−10.9483	+	4.53494i	−0.570720	+	0.236400i
$369$	17.5150	−	42.2850i	0.911796	−	2.20127i
$370$		−	32.8124i		−	1.70584i
$371$	−18.3603	−	7.60508i	−0.953218	−	0.394836i
$372$	26.2565	−	26.2565i	1.36134	−	1.36134i
$373$	−10.3262			−0.534670			−0.267335	−	0.963604i	$-0.586143\pi$
$373$	−10.3262			−0.534670			−0.267335	+	0.963604i	$0.586143\pi$
$374$	1.61715	+	7.50050i	0.0836209	+	0.387842i
$375$	−73.3047			−3.78544
$376$	−4.55515	+	4.55515i	−0.234914	+	0.234914i
$377$	0.773551	+	0.320415i	0.0398399	+	0.0165022i
$378$		−	54.3505i		−	2.79549i
$379$	−3.63333	+	8.77164i	−0.186632	+	0.450569i	−0.989307	−	0.145847i	$-0.953409\pi$
$379$	−3.63333	+	8.77164i	−0.186632	+	0.450569i	0.802675	+	0.596416i	$0.203409\pi$
$380$	22.5716	−	9.34946i	1.15790	−	0.479617i
$381$	−3.51769	−	8.49246i	−0.180217	−	0.435082i
$382$	−12.2826	−	12.2826i	−0.628431	−	0.628431i
$383$	2.67457	+	2.67457i	0.136664	+	0.136664i	0.772130	−	0.635465i	$-0.219192\pi$
$383$	2.67457	+	2.67457i	0.136664	+	0.136664i	−0.635465	+	0.772130i	$0.719192\pi$
$384$	8.99030	+	21.7045i	0.458784	+	1.10760i
$385$	10.7421	−	4.44953i	0.547469	−	0.226769i
$386$	−16.5847	+	40.0389i	−0.844137	+	2.03793i
$387$			19.1099i			0.971413i
$388$	−16.5700	−	6.86354i	−0.841217	−	0.348443i
$389$	−24.2688	+	24.2688i	−1.23048	+	1.23048i	−0.266697	+	0.963780i	$0.585932\pi$
$389$	−24.2688	+	24.2688i	−1.23048	+	1.23048i	−0.963780	+	0.266697i	$0.914068\pi$
$390$	11.4749			0.581054
$391$	−5.53577	+	8.57899i	−0.279956	+	0.433858i
$392$	1.44353			0.0729093
$393$	−6.28138	+	6.28138i	−0.316854	+	0.316854i
$394$	6.24605	+	2.58720i	0.314672	+	0.130341i
$395$			35.3776i			1.78004i
$396$	3.52530	−	8.51083i	0.177153	−	0.427685i
$397$	14.3602	−	5.94819i	0.720718	−	0.298531i	0.00798664	−	0.999968i	$-0.497458\pi$
$397$	14.3602	−	5.94819i	0.720718	−	0.298531i	0.712732	+	0.701437i	$0.247458\pi$
$398$	−0.120835	−	0.291722i	−0.00605691	−	0.0146227i
$399$	26.1472	+	26.1472i	1.30900	+	1.30900i
$400$	−37.2530	−	37.2530i	−1.86265	−	1.86265i
$401$	−9.87743	−	23.8462i	−0.493255	−	1.19082i	−0.953054	−	0.302800i	$-0.902079\pi$
$401$	−9.87743	−	23.8462i	−0.493255	−	1.19082i	0.459799	−	0.888023i	$-0.347921\pi$
$402$	11.6880	−	4.84133i	0.582945	−	0.241464i
$403$	−1.61007	+	3.88706i	−0.0802034	+	0.193628i
$404$		−	1.35374i		−	0.0673511i
$405$	−43.4500	−	17.9976i	−2.15905	−	0.894306i
$406$	−6.33438	+	6.33438i	−0.314370	+	0.314370i
$407$	4.40681			0.218438
$408$	10.5540	+	6.81019i	0.522502	+	0.337155i
$409$	−15.2246			−0.752809			−0.376405	−	0.926455i	$-0.622840\pi$
$409$	−15.2246			−0.752809			−0.376405	+	0.926455i	$0.622840\pi$
$410$	−38.2724	+	38.2724i	−1.89014	+	1.89014i
$411$	8.83461	+	3.65942i	0.435779	+	0.180506i
$412$			25.8731i			1.27467i
$413$	−1.36889	+	3.30479i	−0.0673586	+	0.162618i
$414$	26.8060	−	11.1034i	1.31744	−	0.545702i
$415$	−2.99151	−	7.22215i	−0.146848	−	0.354521i
$416$	2.46874	+	2.46874i	0.121040	+	0.121040i
$417$	−17.3160	−	17.3160i	−0.847970	−	0.847970i
$418$	2.97211	+	7.17531i	0.145371	+	0.350956i
$419$	18.7056	−	7.74812i	0.913829	−	0.378520i	0.124308	−	0.992244i	$-0.460329\pi$
$419$	18.7056	−	7.74812i	0.913829	−	0.378520i	0.789521	+	0.613723i	$0.210329\pi$
$420$	−19.8492	+	47.9201i	−0.968540	+	2.33826i
$421$			19.4317i			0.947041i	0.880783	+	0.473521i	$0.157017\pi$
$421$			19.4317i			0.947041i	−0.880783	+	0.473521i	$0.842983\pi$
$422$	34.6380	+	14.3475i	1.68615	+	0.698427i
$423$	28.7050	−	28.7050i	1.39569	−	1.39569i
$424$	−6.83279			−0.331830
$425$	−44.6548	−	8.14168i	−2.16608	−	0.394929i
$426$	12.9187			0.625913
$427$	−6.08947	+	6.08947i	−0.294690	+	0.294690i
$428$	5.90801	+	2.44718i	0.285575	+	0.118289i
$429$			1.54112i			0.0744058i
$430$	8.64826	−	20.8788i	0.417056	−	1.00686i
$431$	33.3570	−	13.8169i	1.60675	−	0.665538i	0.614400	−	0.788995i	$-0.289398\pi$
$431$	33.3570	−	13.8169i	1.60675	−	0.665538i	0.992350	+	0.123457i	$0.0393981\pi$
$432$	−18.4055	−	44.4348i	−0.885535	−	2.13787i
$433$	6.75007	+	6.75007i	0.324388	+	0.324388i	0.850448	−	0.526060i	$-0.176331\pi$
$433$	6.75007	+	6.75007i	0.324388	+	0.324388i	−0.526060	+	0.850448i	$0.676331\pi$
$434$	−31.8299	−	31.8299i	−1.52789	−	1.52789i
$435$	7.73335	+	18.6700i	0.370786	+	0.895157i
$436$	−17.0934	+	7.08031i	−0.818624	+	0.339085i
$437$	−3.95488	+	9.54792i	−0.189187	+	0.456739i
$438$		−	13.2267i		−	0.631998i
$439$	−16.2676	−	6.73826i	−0.776410	−	0.321599i	−0.0409441	−	0.999161i	$-0.513037\pi$
$439$	−16.2676	−	6.73826i	−0.776410	−	0.321599i	−0.735466	+	0.677562i	$0.763037\pi$
$440$	2.82679	−	2.82679i	0.134762	−	0.134762i
$441$	−9.09665			−0.433174
$442$	3.81537	+	0.695637i	0.181479	+	0.0330881i
$443$	6.24098			0.296518			0.148259	−	0.988949i	$-0.452633\pi$
$443$	6.24098			0.296518			0.148259	+	0.988949i	$0.452633\pi$
$444$	−13.9007	+	13.9007i	−0.659699	+	0.659699i
$445$	34.2000	+	14.1661i	1.62124	+	0.671538i
$446$			2.12927i			0.100824i
$447$	5.86757	−	14.1656i	0.277527	−	0.670008i
$448$	−8.81419	+	3.65096i	−0.416432	+	0.172492i
$449$	5.43085	+	13.1112i	0.256298	+	0.618757i	0.998688	−	0.0512106i	$-0.0163080\pi$
$449$	5.43085	+	13.1112i	0.256298	+	0.618757i	−0.742390	+	0.669968i	$0.766308\pi$
$450$	91.2106	+	91.2106i	4.29971	+	4.29971i
$451$	−5.14011	−	5.14011i	−0.242039	−	0.242039i
$452$	6.29028	+	15.1861i	0.295870	+	0.714293i
$453$	−36.0332	+	14.9254i	−1.69299	+	0.701258i
$454$	9.85543	−	23.7931i	0.462538	−	1.11667i
$455$		−	5.87700i		−	0.275518i
$456$	11.7460	+	4.86536i	0.550057	+	0.227841i
$457$	1.24741	−	1.24741i	0.0583514	−	0.0583514i	−0.677329	−	0.735680i	$-0.736863\pi$
$457$	1.24741	−	1.24741i	0.0583514	−	0.0583514i	0.735680	+	0.677329i	$0.236863\pi$
$458$	−43.4490			−2.03024
$459$	−34.8187	−	22.4675i	−1.62520	−	1.04869i
$460$	−14.4962			−0.675890
$461$	17.9748	−	17.9748i	0.837170	−	0.837170i	−0.151315	−	0.988486i	$-0.548351\pi$
$461$	17.9748	−	17.9748i	0.837170	−	0.837170i	0.988486	+	0.151315i	$0.0483508\pi$
$462$	−15.2334	−	6.30987i	−0.708720	−	0.293562i
$463$		−	39.0926i		−	1.81679i	−0.418117	−	0.908393i	$-0.637310\pi$
$463$		−	39.0926i		−	1.81679i	0.418117	−	0.908393i	$-0.362690\pi$
$464$	−3.03364	+	7.32385i	−0.140833	+	0.340001i
$465$	−93.8156	+	38.8597i	−4.35060	+	1.80208i
$466$	−1.44849	−	3.49696i	−0.0671000	−	0.161994i
$467$	5.22675	+	5.22675i	0.241865	+	0.241865i	0.817621	−	0.575756i	$-0.195292\pi$
$467$	5.22675	+	5.22675i	0.241865	+	0.241865i	−0.575756	+	0.817621i	$0.695292\pi$
$468$	−3.29247	−	3.29247i	−0.152195	−	0.152195i
$469$	−2.47955	−	5.98615i	−0.114495	−	0.276415i
$470$	−44.3525	+	18.3714i	−2.04583	+	0.847411i
$471$	17.6998	−	42.7311i	0.815563	−	1.96894i
$472$			1.22988i			0.0566097i
$473$	2.80409	+	1.16149i	0.128932	+	0.0534054i
$474$	35.4747	−	35.4747i	1.62941	−	1.62941i
$475$	−45.9449			−2.10810
$476$	−9.50483	+	14.7300i	−0.435653	+	0.675148i
$477$	43.0580			1.97149
$478$	39.4238	−	39.4238i	1.80320	−	1.80320i
$479$	7.89522	+	3.27031i	0.360742	+	0.149424i	0.555690	−	0.831389i	$-0.312454\pi$
$479$	7.89522	+	3.27031i	0.360742	+	0.149424i	−0.194949	+	0.980813i	$0.562454\pi$
$480$			84.2645i			3.84613i
$481$	0.852404	−	2.05788i	0.0388663	−	0.0938314i
$482$	−43.7625	+	18.1270i	−1.99333	+	0.825663i
$483$	−8.39631	−	20.2705i	−0.382045	−	0.922339i
$484$	−1.03457	−	1.03457i	−0.0470257	−	0.0470257i
$485$	34.6818	+	34.6818i	1.57482	+	1.57482i
$486$	4.05039	+	9.77851i	0.183730	+	0.443562i
$487$	7.50208	−	3.10746i	0.339952	−	0.140813i	−0.206175	−	0.978515i	$-0.566102\pi$
$487$	7.50208	−	3.10746i	0.339952	−	0.140813i	0.546127	+	0.837702i	$0.316102\pi$
$488$	−1.13310	+	2.73554i	−0.0512930	+	0.123832i
$489$			8.44060i			0.381697i
$490$	9.93863	+	4.11672i	0.448982	+	0.185974i
$491$	−12.6176	+	12.6176i	−0.569426	+	0.569426i	−0.931968	−	0.362542i	$-0.881909\pi$
$491$	−12.6176	+	12.6176i	−0.569426	+	0.569426i	0.362542	+	0.931968i	$0.381909\pi$
$492$	32.4276			1.46195
$493$	1.43950	+	6.67653i	0.0648318	+	0.300696i
$494$	3.92560			0.176621
$495$	−17.8135	+	17.8135i	−0.800657	+	0.800657i
$496$	−36.8020	−	15.2439i	−1.65246	−	0.684470i
$497$		−	6.61647i		−	0.296789i
$498$	−4.24225	+	10.2417i	−0.190100	+	0.458942i
$499$	−2.30494	+	0.954737i	−0.103183	+	0.0427399i	−0.433678	−	0.901068i	$-0.642784\pi$
$499$	−2.30494	+	0.954737i	−0.103183	+	0.0427399i	0.330495	+	0.943808i	$0.392784\pi$
$500$	−13.4614	−	32.4987i	−0.602012	−	1.45339i
$501$	−14.0817	−	14.0817i	−0.629126	−	0.629126i
$502$	18.9014	+	18.9014i	0.843609	+	0.843609i
$503$	5.37510	+	12.9766i	0.239664	+	0.578599i	0.997248	−	0.0741379i	$-0.0236205\pi$
$503$	5.37510	+	12.9766i	0.239664	+	0.578599i	−0.757584	+	0.652737i	$0.773621\pi$
$504$	−16.8896	+	6.99592i	−0.752325	+	0.311623i
$505$	−1.41672	+	3.42026i	−0.0630431	+	0.152199i
$506$		−	4.60822i		−	0.204860i
$507$	−35.8999	−	14.8702i	−1.59437	−	0.660410i
$508$	3.11905	−	3.11905i	0.138385	−	0.138385i
$509$	26.4685			1.17319			0.586597	−	0.809879i	$-0.300467\pi$
$509$	26.4685			1.17319			0.586597	+	0.809879i	$0.300467\pi$
$510$	53.2423	+	76.9862i	2.35761	+	3.40901i
$511$	−6.77423			−0.299674
$512$	−16.6116	+	16.6116i	−0.734136	+	0.734136i
$513$	−38.7512	−	16.0513i	−1.71091	−	0.708681i
$514$		−	29.6956i		−	1.30982i
$515$	27.0767	−	65.3689i	1.19314	−	2.88050i
$516$	−12.5089	+	5.18135i	−0.550673	+	0.228096i
$517$	−2.46734	−	5.95669i	−0.108514	−	0.261975i
$518$	16.8514	+	16.8514i	0.740408	+	0.740408i
$519$	53.6874	+	53.6874i	2.35662	+	2.35662i
$520$	−0.773267	−	1.86683i	−0.0339100	−	0.0818660i
$521$	−13.7449	+	5.69334i	−0.602176	+	0.249430i	−0.662879	−	0.748726i	$-0.730666\pi$
$521$	−13.7449	+	5.69334i	−0.602176	+	0.249430i	0.0607029	+	0.998156i	$0.480666\pi$
$522$	7.42760	−	17.9318i	0.325097	−	0.784854i
$523$		−	43.6952i		−	1.91066i	−0.295541	−	0.955330i	$-0.595500\pi$
$523$		−	43.6952i		−	1.91066i	0.295541	−	0.955330i	$-0.404500\pi$
$524$	−3.93826	−	1.63128i	−0.172044	−	0.0712628i
$525$	68.9728	−	68.9728i	3.01022	−	3.01022i
$526$	−33.9464			−1.48013
$527$	−33.5492	+	7.23341i	−1.46143	+	0.315092i
$528$	−14.5910			−0.634992
$529$	−11.9275	+	11.9275i	−0.518586	+	0.518586i
$530$	−47.0434	−	19.4860i	−2.04344	−	0.846419i
$531$		−	7.75028i		−	0.336334i
$532$	−6.79046	+	16.3936i	−0.294404	+	0.710754i
$533$	−3.39456	+	1.40607i	−0.147035	+	0.0609038i
$534$	−20.0889	−	48.4989i	−0.869332	−	2.09875i
$535$	−12.3657	−	12.3657i	−0.534616	−	0.534616i
$536$	−1.57526	−	1.57526i	−0.0680408	−	0.0680408i
$537$	8.42783	+	20.3466i	0.363688	+	0.878019i
$538$	8.44682	−	3.49879i	0.364168	−	0.150843i
$539$	−0.552889	+	1.33479i	−0.0238146	+	0.0574935i
$540$		−	58.8344i		−	2.53183i
$541$	−16.1537	−	6.69107i	−0.694501	−	0.287672i	0.00737299	−	0.999973i	$-0.497653\pi$
$541$	−16.1537	−	6.69107i	−0.694501	−	0.287672i	−0.701874	+	0.712301i	$0.747653\pi$
$542$	39.7424	−	39.7424i	1.70708	−	1.70708i
$543$	78.4349			3.36596
$544$	−5.10833	+	28.0177i	−0.219018	+	1.20125i
$545$	50.5965			2.16732
$546$	−5.89314	+	5.89314i	−0.252203	+	0.252203i
$547$	32.2259	+	13.3484i	1.37788	+	0.570736i	0.943913	−	0.330194i	$-0.107114\pi$
$547$	32.2259	+	13.3484i	1.37788	+	0.570736i	0.433965	+	0.900930i	$0.357114\pi$
$548$			4.58872i			0.196020i
$549$	7.14042	−	17.2385i	0.304746	−	0.735721i
$550$	18.9275	−	7.84001i	0.807070	−	0.334299i
$551$	2.64561	+	6.38706i	0.112707	+	0.272098i
$552$	−5.33418	−	5.33418i	−0.227038	−	0.227038i
$553$	−18.1688	−	18.1688i	−0.772616	−	0.772616i
$554$	−8.70462	−	21.0148i	−0.369824	−	0.892834i
$555$	49.6679	−	20.5731i	2.10828	−	0.873279i
$556$	4.49699	−	10.8567i	0.190715	−	0.460427i
$557$		−	3.97182i		−	0.168292i	−0.996453	−	0.0841458i	$-0.973184\pi$
$557$		−	3.97182i		−	0.168292i	0.996453	−	0.0841458i	$-0.0268161\pi$
$558$	90.1064	+	37.3233i	3.81451	+	1.58002i
$559$	1.08478	−	1.08478i	0.0458813	−	0.0458813i
$560$	55.6424			2.35132
$561$	−10.3395	+	7.15062i	−0.436534	+	0.301899i
$562$	−11.1507			−0.470365
$563$	−5.25310	+	5.25310i	−0.221392	+	0.221392i	−0.809084	−	0.587693i	$-0.800036\pi$
$563$	−5.25310	+	5.25310i	−0.221392	+	0.221392i	0.587693	+	0.809084i	$0.300036\pi$
$564$	26.5725	+	11.0067i	1.11890	+	0.463466i
$565$		−	44.9509i		−	1.89110i
$566$	−10.0639	+	24.2963i	−0.423015	+	1.02125i
$567$	31.5575	−	13.0715i	1.32529	−	0.548953i
$568$	−0.870562	−	2.10172i	−0.0365280	−	0.0881864i
$569$	−18.3003	−	18.3003i	−0.767188	−	0.767188i	0.210423	−	0.977610i	$-0.432516\pi$
$569$	−18.3003	−	18.3003i	−0.767188	−	0.767188i	−0.977610	+	0.210423i	$0.932516\pi$
$570$	66.9955	+	66.9955i	2.80613	+	2.80613i
$571$	6.84043	+	16.5143i	0.286263	+	0.691100i	0.999956	−	0.00935824i	$-0.00297886\pi$
$571$	6.84043	+	16.5143i	0.286263	+	0.691100i	−0.713693	+	0.700459i	$0.752979\pi$
$572$	−0.683234	+	0.283005i	−0.0285674	+	0.0118330i
$573$	10.8910	−	26.2931i	0.454976	−	1.09841i
$574$		−	39.3110i		−	1.64081i
$575$	25.1861	+	10.4324i	1.05033	+	0.435062i
$576$	14.6164	−	14.6164i	0.609019	−	0.609019i
$577$	−18.1277			−0.754665			−0.377332	−	0.926078i	$-0.623159\pi$
$577$	−18.1277			−0.754665			−0.377332	+	0.926078i	$0.623159\pi$
$578$	13.0358	+	28.8254i	0.542219	+	1.19898i
$579$	−71.0050			−2.95087
$580$	−6.85697	+	6.85697i	−0.284720	+	0.284720i
$581$	5.24541	+	2.17272i	0.217616	+	0.0901396i
$582$		−	69.5540i		−	2.88310i
$583$	2.61704	−	6.31809i	0.108387	−	0.261668i
$584$	−2.15184	+	0.891320i	−0.0890437	+	0.0368831i
$585$	4.87287	+	11.7641i	0.201468	+	0.486388i
$586$	40.2344	+	40.2344i	1.66207	+	1.66207i
$587$	−16.1693	−	16.1693i	−0.667378	−	0.667378i	0.289730	−	0.957108i	$-0.406434\pi$
$587$	−16.1693	−	16.1693i	−0.667378	−	0.667378i	−0.957108	+	0.289730i	$0.906434\pi$
$588$	−2.46641	−	5.95444i	−0.101713	−	0.245557i
$589$	−32.0947	+	13.2940i	−1.32244	+	0.547771i
$590$	−3.50742	+	8.46765i	−0.144398	+	0.348608i
$591$			11.0768i			0.455637i
$592$	19.4837	+	8.07041i	0.800775	+	0.331692i
$593$	−6.97178	+	6.97178i	−0.286297	+	0.286297i	−0.835614	−	0.549317i	$-0.814888\pi$
$593$	−6.97178	+	6.97178i	−0.286297	+	0.286297i	0.549317	+	0.835614i	$0.314888\pi$
$594$	18.7029			0.767390
$595$	39.4294	−	27.2687i	1.61645	−	1.11791i
$596$	7.35762			0.301380
$597$	0.365814	−	0.365814i	0.0149718	−	0.0149718i
$598$	−2.15193	−	0.891361i	−0.0879992	−	0.0364504i
$599$			37.6577i			1.53865i	0.638857	+	0.769325i	$0.279407\pi$
$599$			37.6577i			1.53865i	−0.638857	+	0.769325i	$0.720593\pi$
$600$	12.8341	−	30.9843i	0.523951	−	1.26493i
$601$	14.2799	−	5.91492i	0.582488	−	0.241275i	−0.0719269	−	0.997410i	$-0.522915\pi$
$601$	14.2799	−	5.91492i	0.582488	−	0.241275i	0.654415	+	0.756135i	$0.272915\pi$
$602$	6.28119	+	15.1641i	0.256002	+	0.618044i
$603$	9.92675	+	9.92675i	0.404248	+	0.404248i
$604$	−13.2340	−	13.2340i	−0.538484	−	0.538484i
$605$	1.53116	+	3.69655i	0.0622505	+	0.150286i
$606$	4.85025	−	2.00904i	0.197028	−	0.0816117i
$607$	−5.80776	+	14.0212i	−0.235730	+	0.569101i	−0.996833	−	0.0795297i	$-0.974658\pi$
$607$	−5.80776	+	14.0212i	−0.235730	+	0.569101i	0.761103	+	0.648631i	$0.224658\pi$
$608$			28.8272i			1.16910i
$609$	−13.5599	−	5.61669i	−0.549475	−	0.227600i
$610$	−15.6027	+	15.6027i	−0.631734	+	0.631734i
$611$	−3.25890			−0.131841
$612$	6.81280	−	37.3663i	0.275391	−	1.51044i
$613$	−8.45011			−0.341297			−0.170648	−	0.985332i	$-0.554586\pi$
$613$	−8.45011			−0.341297			−0.170648	+	0.985332i	$0.554586\pi$
$614$	2.49278	−	2.49278i	0.100600	−	0.100600i
$615$	−81.9292	−	33.9362i	−3.30370	−	1.36844i
$616$			2.90350i			0.116985i
$617$	−8.84739	+	21.3595i	−0.356183	+	0.859901i	0.639647	+	0.768669i	$0.279080\pi$
$617$	−8.84739	+	21.3595i	−0.356183	+	0.859901i	−0.995830	+	0.0912320i	$0.970920\pi$
$618$	−92.6994	+	38.3973i	−3.72892	+	1.54457i
$619$	15.8637	+	38.2984i	0.637617	+	1.53934i	0.829846	+	0.557993i	$0.188428\pi$
$619$	15.8637	+	38.2984i	0.637617	+	1.53934i	−0.192229	+	0.981350i	$0.561572\pi$
$620$	−34.4559	−	34.4559i	−1.38378	−	1.38378i
$621$	17.5980	+	17.5980i	0.706182	+	0.706182i
$622$	12.1274	+	29.2782i	0.486266	+	1.17395i
$623$	−24.8393	+	10.2888i	−0.995165	+	0.412211i
$624$	−2.82232	+	6.81368i	−0.112983	+	0.272765i
$625$			41.1517i			1.64607i
$626$	8.95329	+	3.70857i	0.357845	+	0.148224i
$627$	−8.99771	+	8.99771i	−0.359334	+	0.359334i
$628$	22.1946			0.885661
$629$	17.7616	−	3.82951i	0.708202	−	0.152692i
$630$	−136.236			−5.42776
$631$	−33.7872	+	33.7872i	−1.34505	+	1.34505i	−0.454093	+	0.890954i	$0.650036\pi$
$631$	−33.7872	+	33.7872i	−1.34505	+	1.34505i	−0.890954	+	0.454093i	$0.849964\pi$
$632$	−8.16189	−	3.38076i	−0.324662	−	0.134480i
$633$			61.4270i			2.44151i
$634$	−7.38600	+	17.8314i	−0.293336	+	0.708175i
$635$	−11.1445	+	4.61620i	−0.442256	+	0.183188i
$636$	11.6745	+	28.1847i	0.462923	+	1.11760i
$637$	0.516373	+	0.516373i	0.0204595	+	0.0204595i
$638$	−2.17977	−	2.17977i	−0.0862978	−	0.0862978i
$639$	5.48599	+	13.2444i	0.217023	+	0.523939i
$640$	28.4824	−	11.7978i	1.12587	−	0.466349i
$641$	6.05284	−	14.6128i	0.239073	−	0.577173i	−0.758115	−	0.652121i	$-0.773879\pi$
$641$	6.05284	−	14.6128i	0.239073	−	0.577173i	0.997187	+	0.0749487i	$0.0238793\pi$
$642$			24.7993i			0.978751i
$643$	18.8633	+	7.81343i	0.743895	+	0.308132i	0.722248	−	0.691634i	$-0.243109\pi$
$643$	18.8633	+	7.81343i	0.743895	+	0.308132i	0.0216474	+	0.999766i	$0.493109\pi$
$644$	7.44479	−	7.44479i	0.293366	−	0.293366i
$645$	37.0264			1.45791
$646$	18.2144	+	26.3372i	0.716635	+	1.03623i
$647$	4.63482			0.182213			0.0911067	−	0.995841i	$-0.470960\pi$
$647$	4.63482			0.182213			0.0911067	+	0.995841i	$0.470960\pi$
$648$	8.30436	−	8.30436i	0.326226	−	0.326226i
$649$	−1.13723	−	0.471058i	−0.0446403	−	0.0184906i
$650$		−	10.3552i		−	0.406164i
$651$	28.2236	−	68.1378i	1.10617	−	2.67053i
$652$	−3.74203	+	1.55000i	−0.146549	+	0.0607027i
$653$	9.00285	+	21.7348i	0.352309	+	0.850549i	0.996334	+	0.0855447i	$0.0272630\pi$
$653$	9.00285	+	21.7348i	0.352309	+	0.850549i	−0.644026	+	0.765004i	$0.722737\pi$
$654$	−50.7354	−	50.7354i	−1.98391	−	1.98391i
$655$	8.24293	+	8.24293i	0.322078	+	0.322078i
$656$	−13.3125	−	32.1391i	−0.519764	−	1.25482i
$657$	13.5602	−	5.61680i	0.529032	−	0.219132i
$658$	13.3431	−	32.2130i	0.520167	−	1.25579i
$659$		−	7.49057i		−	0.291791i	−0.989300	−	0.145896i	$-0.953394\pi$
$659$		−	7.49057i		−	0.291791i	0.989300	−	0.145896i	$-0.0466064\pi$
$660$	−16.4901	−	6.83043i	−0.641877	−	0.265874i
$661$	−28.6165	+	28.6165i	−1.11305	+	1.11305i	−0.120318	+	0.992735i	$0.538391\pi$
$661$	−28.6165	+	28.6165i	−1.11305	+	1.11305i	−0.992735	+	0.120318i	$0.961609\pi$
$662$	60.5688			2.35407
$663$	1.33922	+	6.21145i	0.0520112	+	0.241233i
$664$	1.95208			0.0757555
$665$	34.3125	−	34.3125i	1.33058	−	1.33058i
$666$	−47.7041	−	19.7597i	−1.84850	−	0.765672i
$667$		−	4.10198i		−	0.158829i
$668$	3.65704	−	8.82888i	0.141495	−	0.341600i
$669$	−3.22305	+	1.33503i	−0.124610	+	0.0516154i
$670$	−6.35319	−	15.3379i	−0.245445	−	0.592557i
$671$	−2.09549	−	2.09549i	−0.0808955	−	0.0808955i
$672$	−43.2755	−	43.2755i	−1.66939	−	1.66939i
$673$	−13.2167	−	31.9080i	−0.509467	−	1.22996i	−0.944191	−	0.329398i	$-0.893154\pi$
$673$	−13.2167	−	31.9080i	−0.509467	−	1.22996i	0.434725	−	0.900563i	$-0.356846\pi$
$674$	−59.6321	+	24.7004i	−2.29694	+	0.951424i
$675$	−42.3410	+	102.220i	−1.62971	+	3.93446i
$676$		−	18.6465i		−	0.717172i
$677$	30.1027	+	12.4689i	1.15694	+	0.479220i	0.876855	−	0.480755i	$-0.159637\pi$
$677$	30.1027	+	12.4689i	1.15694	+	0.479220i	0.280085	+	0.959975i	$0.409637\pi$
$678$	−45.0743	+	45.0743i	−1.73107	+	1.73107i
$679$	−35.6229			−1.36708
$680$	8.93688	−	13.8498i	0.342714	−	0.531117i
$681$	42.1947			1.61690
$682$	10.9532	−	10.9532i	0.419421	−	0.419421i
$683$	13.4784	+	5.58292i	0.515735	+	0.213624i	0.625342	−	0.780351i	$-0.284959\pi$
$683$	13.4784	+	5.58292i	0.515735	+	0.213624i	−0.109607	+	0.993975i	$0.534959\pi$
$684$		−	38.4458i		−	1.47001i
$685$	4.80218	−	11.5935i	0.183482	−	0.442965i
$686$	27.7552	−	11.4966i	1.05970	−	0.438941i
$687$	−27.2421	−	65.7684i	−1.03935	−	2.50922i
$688$	10.2705	+	10.2705i	0.391559	+	0.391559i
$689$	−2.44420	−	2.44420i	−0.0931165	−	0.0931165i
$690$	−21.5133	−	51.9378i	−0.818999	−	1.97724i
$691$	−21.1646	+	8.76665i	−0.805138	+	0.333499i	−0.747012	−	0.664810i	$-0.768512\pi$
$691$	−21.1646	+	8.76665i	−0.805138	+	0.333499i	−0.0581258	+	0.998309i	$0.518512\pi$
$692$	−13.9427	+	33.6606i	−0.530021	+	1.27958i
$693$		−	18.2969i		−	0.695041i
$694$	−22.2550	−	9.21832i	−0.844788	−	0.349923i
$695$	−22.7235	+	22.7235i	−0.861952	+	0.861952i
$696$	−5.04633			−0.191280
$697$	−25.1839	−	16.2504i	−0.953909	−	0.615529i
$698$	−20.7317			−0.784708
$699$	4.38513	−	4.38513i	0.165861	−	0.165861i
$700$	43.2441	+	17.9123i	1.63447	+	0.677021i
$701$		−	29.8956i		−	1.12914i	−0.825385	−	0.564570i	$-0.809042\pi$
$701$		−	29.8956i		−	1.12914i	0.825385	−	0.564570i	$-0.190958\pi$
$702$	3.61768	−	8.73385i	0.136540	−	0.329638i
$703$	16.9915	−	7.03813i	0.640848	−	0.265448i
$704$	−1.25636	−	3.03311i	−0.0473507	−	0.114315i
$705$	−55.6173	−	55.6173i	−2.09467	−	2.09467i
$706$	42.5157	+	42.5157i	1.60010	+	1.60010i
$707$	−1.02895	−	2.48411i	−0.0386978	−	0.0934247i
$708$	5.07314	−	2.10136i	0.190660	−	0.0789741i
$709$	−4.48586	+	10.8298i	−0.168470	+	0.406722i	−0.985455	−	0.169936i	$-0.945644\pi$
$709$	−4.48586	+	10.8298i	−0.168470	+	0.406722i	0.816985	+	0.576659i	$0.195644\pi$
$710$		−	16.9530i		−	0.636233i
$711$	51.4335	+	21.3044i	1.92891	+	0.798979i
$712$	−6.53646	+	6.53646i	−0.244964	+	0.244964i
$713$	20.6122			0.771934
$714$	−66.8812	−	12.1941i	−2.50297	−	0.456353i
$715$	2.02238			0.0756326
$716$	−7.47274	+	7.47274i	−0.279269	+	0.279269i
$717$	84.3938	+	34.9571i	3.15175	+	1.30550i
$718$			54.6301i			2.03878i
$719$	−9.71355	+	23.4506i	−0.362254	+	0.874560i	0.632715	+	0.774384i	$0.281940\pi$
$719$	−9.71355	+	23.4506i	−0.362254	+	0.874560i	−0.994970	+	0.100175i	$0.968060\pi$
$720$	−111.381	+	46.1355i	−4.15092	+	1.71937i
$721$	19.6657	+	47.4771i	0.732387	+	1.76814i
$722$	−2.08240	−	2.08240i	−0.0774988	−	0.0774988i
$723$	−54.8774	−	54.8774i	−2.04091	−	2.04091i
$724$	14.4035	+	34.7731i	0.535302	+	1.29233i
$725$	16.8482	−	6.97874i	0.625726	−	0.259184i
$726$	2.17133	−	5.24206i	0.0805857	−	0.194551i
$727$			43.7703i			1.62335i	0.584110	+	0.811675i	$0.301444\pi$
$727$			43.7703i			1.62335i	−0.584110	+	0.811675i	$0.698556\pi$
$728$	1.35587	+	0.561620i	0.0502519	+	0.0208150i
$729$	12.6723	−	12.6723i	0.469346	−	0.469346i
$730$	−17.3572			−0.642419
$731$	12.3112	+	2.24463i	0.455345	+	0.0830207i
$732$	13.2199			0.488621
$733$	−2.70148	+	2.70148i	−0.0997816	+	0.0997816i	−0.755235	−	0.655454i	$-0.772477\pi$
$733$	−2.70148	+	2.70148i	−0.0997816	+	0.0997816i	0.655454	+	0.755235i	$0.272477\pi$
$734$	−2.63558	−	1.09169i	−0.0972811	−	0.0402952i
$735$			17.6252i			0.650114i
$736$	6.54560	−	15.8025i	0.241274	−	0.582487i
$737$	2.05994	−	0.853254i	0.0758788	−	0.0314300i
$738$	32.5944	+	78.6899i	1.19982	+	2.89661i
$739$	−20.3814	−	20.3814i	−0.749743	−	0.749743i	0.224688	−	0.974431i	$-0.427864\pi$
$739$	−20.3814	−	20.3814i	−0.749743	−	0.749743i	−0.974431	+	0.224688i	$0.927864\pi$
$740$	18.2416	+	18.2416i	0.670576	+	0.670576i
$741$	2.46132	+	5.94215i	0.0904188	+	0.218290i
$742$	34.1674	−	14.1526i	1.25432	−	0.519558i
$743$	1.31750	−	3.18072i	0.0483343	−	0.116689i	−0.897868	−	0.440264i	$-0.854885\pi$
$743$	1.31750	−	3.18072i	0.0483343	−	0.116689i	0.946203	+	0.323575i	$0.104885\pi$
$744$		−	25.3575i		−	0.929652i
$745$	−18.5892	−	7.69990i	−0.681056	−	0.282102i
$746$	13.5881	−	13.5881i	0.497495	−	0.497495i
$747$	−12.3014			−0.450084
$748$	−5.06884	−	3.27077i	−0.185335	−	0.119591i
$749$	12.7013			0.464094
$750$	96.4604	−	96.4604i	3.52224	−	3.52224i
$751$	16.2917	+	6.74823i	0.594492	+	0.246247i	0.659582	−	0.751633i	$-0.270733\pi$
$751$	16.2917	+	6.74823i	0.594492	+	0.246247i	−0.0650899	+	0.997879i	$0.520733\pi$
$752$		−	30.8547i		−	1.12515i
$753$	−16.7598	+	40.4618i	−0.610762	+	1.47451i
$754$	−1.43953	+	0.596274i	−0.0524247	+	0.0217150i
$755$	19.5863	+	47.2856i	0.712820	+	1.72090i
$756$	30.2155	+	30.2155i	1.09893	+	1.09893i
$757$	2.91291	+	2.91291i	0.105872	+	0.105872i	0.758058	−	0.652187i	$-0.226148\pi$
$757$	2.91291	+	2.91291i	0.105872	+	0.105872i	−0.652187	+	0.758058i	$0.726148\pi$
$758$	−6.76141	−	16.3235i	−0.245586	−	0.592896i
$759$	6.97542	−	2.88931i	0.253192	−	0.104875i
$760$	6.38471	−	15.4141i	0.231598	−	0.559127i
$761$		−	4.80735i		−	0.174266i	−0.996197	−	0.0871331i	$-0.972229\pi$
$761$		−	4.80735i		−	0.174266i	0.996197	−	0.0871331i	$-0.0277705\pi$
$762$	15.8040	+	6.54621i	0.572517	+	0.237144i
$763$	−25.9847	+	25.9847i	−0.940710	+	0.940710i
$764$	13.6567			0.494082
$765$	−56.3173	+	87.2770i	−2.03615	+	3.15551i
$766$	−7.03886			−0.254324
$767$	−0.439947	+	0.439947i	−0.0158856	+	0.0158856i
$768$	−58.8866	−	24.3916i	−2.12489	−	0.880157i
$769$		−	32.8832i		−	1.18580i	−0.805277	−	0.592899i	$-0.797983\pi$
$769$		−	32.8832i		−	1.18580i	0.805277	−	0.592899i	$-0.202017\pi$
$770$	−8.28031	+	19.9904i	−0.298402	+	0.720406i
$771$	44.9500	−	18.6189i	1.61883	−	0.670543i
$772$	−13.0391	−	31.4792i	−0.469287	−	1.13296i
$773$	−20.2988	−	20.2988i	−0.730099	−	0.730099i	0.240540	−	0.970639i	$-0.422675\pi$
$773$	−20.2988	−	20.2988i	−0.730099	−	0.730099i	−0.970639	+	0.240540i	$0.922675\pi$
$774$	−25.1464	−	25.1464i	−0.903870	−	0.903870i
$775$	35.0678	+	84.6612i	1.25967	+	3.04112i
$776$	−11.3156	+	4.68708i	−0.406207	+	0.168257i
$777$	−14.9421	+	36.0735i	−0.536046	+	1.29413i
$778$		−	63.8698i		−	2.28985i
$779$	−28.0282	−	11.6097i	−1.00422	−	0.415960i
$780$	−6.37932	+	6.37932i	−0.228416	+	0.228416i
$781$	2.27684			0.0814717
$782$	−4.00453	−	18.5734i	−0.143202	−	0.664182i
$783$	16.6483			0.594962
$784$	−4.88893	+	4.88893i	−0.174605	+	0.174605i
$785$	−56.0751	−	23.2271i	−2.00141	−	0.829010i
$786$		−	16.5311i		−	0.589646i
$787$	−20.7105	+	49.9995i	−0.738249	+	1.78229i	−0.125375	+	0.992109i	$0.540014\pi$
$787$	−20.7105	+	49.9995i	−0.738249	+	1.78229i	−0.612873	+	0.790181i	$0.709986\pi$
$788$	−4.91074	+	2.03409i	−0.174938	+	0.0724616i
$789$	−21.2841	−	51.3843i	−0.757733	−	1.82933i
$790$	−46.5528	−	46.5528i	−1.65627	−	1.65627i
$791$	23.0853	+	23.0853i	0.820820	+	0.820820i
$792$	−2.40741	−	5.81201i	−0.0855438	−	0.206521i
$793$	−1.38387	+	0.573220i	−0.0491428	+	0.0203556i
$794$	−11.0692	+	26.7235i	−0.392832	+	0.948381i
$795$		−	83.4268i		−	2.95884i
$796$	0.229356	+	0.0950022i	0.00812930	+	0.00336726i
$797$	10.1871	−	10.1871i	0.360847	−	0.360847i	−0.503278	−	0.864125i	$-0.667873\pi$
$797$	10.1871	−	10.1871i	0.360847	−	0.360847i	0.864125	+	0.503278i	$0.167873\pi$
$798$	−68.8135			−2.43597
$799$	−15.1209	−	21.8643i	−0.534941	−	0.773502i
$800$	76.0421			2.68849
$801$	41.1906	−	41.1906i	1.45540	−	1.45540i
$802$	44.3764	+	18.3813i	1.56698	+	0.649066i
$803$		−	2.33113i		−	0.0822637i
$804$	−3.80632	+	9.18928i	−0.134239	+	0.324081i
$805$	−26.6006	+	11.0183i	−0.937546	+	0.388344i
$806$	−2.99625	−	7.23358i	−0.105538	−	0.254792i
$807$	10.5922	+	10.5922i	0.372862	+	0.372862i
$808$	−0.653695	−	0.653695i	−0.0229969	−	0.0229969i
$809$	−13.7447	−	33.1827i	−0.483239	−	1.16664i	−0.958062	−	0.286561i	$-0.907488\pi$
$809$	−13.7447	−	33.1827i	−0.483239	−	1.16664i	0.474823	−	0.880082i	$-0.342512\pi$
$810$	80.8578	−	33.4924i	2.84105	−	1.17680i
$811$	8.86187	−	21.3944i	0.311182	−	0.751261i	−0.688479	−	0.725256i	$-0.741721\pi$
$811$	8.86187	−	21.3944i	0.311182	−	0.751261i	0.999662	−	0.0260049i	$-0.00827854\pi$
$812$		−	7.04304i		−	0.247162i
$813$	85.0760	+	35.2396i	2.98374	+	1.23591i
$814$	−5.79885	+	5.79885i	−0.203250	+	0.203250i
$815$	11.0764			0.387991
$816$	−58.8089	+	12.6795i	−2.05872	+	0.443873i
$817$	12.6669			0.443157
$818$	20.0338	−	20.0338i	0.700466	−	0.700466i
$819$	−8.54424	−	3.53914i	−0.298560	−	0.123668i
$820$		−	42.5542i		−	1.48606i
$821$	1.01687	−	2.45493i	0.0354889	−	0.0856778i	−0.905141	−	0.425111i	$-0.860235\pi$
$821$	1.01687	−	2.45493i	0.0354889	−	0.0856778i	0.940630	+	0.339433i	$0.110235\pi$
$822$	−16.4407	+	6.80996i	−0.573435	+	0.237524i
$823$	0.0787077	+	0.190017i	0.00274358	+	0.00662358i	0.925245	−	0.379369i	$-0.123859\pi$
$823$	0.0787077	+	0.190017i	0.00274358	+	0.00662358i	−0.922502	+	0.385993i	$0.873859\pi$
$824$	12.4936	+	12.4936i	0.435235	+	0.435235i
$825$	23.7347	+	23.7347i	0.826337	+	0.826337i
$826$	−2.54742	−	6.15001i	−0.0886360	−	0.213986i
$827$	−16.5054	+	6.83676i	−0.573949	+	0.237737i	−0.650728	−	0.759311i	$-0.725536\pi$
$827$	−16.5054	+	6.83676i	−0.573949	+	0.237737i	0.0767795	+	0.997048i	$0.475536\pi$
$828$	−8.72965	+	21.0752i	−0.303376	+	0.732415i
$829$		−	0.286953i		−	0.00996627i	−0.999988	−	0.00498314i	$-0.998414\pi$
$829$		−	0.286953i		−	0.00996627i	0.999988	−	0.00498314i	$-0.00158619\pi$
$830$	13.4400	+	5.56703i	0.466509	+	0.193234i
$831$	26.3522	−	26.3522i	0.914149	−	0.914149i
$832$	−1.65941			−0.0575298
$833$	−1.06848	+	5.86032i	−0.0370207	+	0.203048i
$834$	45.5718			1.57802
$835$	−18.4792	+	18.4792i	−0.639499	+	0.639499i
$836$	−5.64133	−	2.33671i	−0.195109	−	0.0808170i
$837$			83.6569i			2.89160i
$838$	−14.4188	+	34.8100i	−0.498089	+	1.20249i
$839$	48.1849	−	19.9588i	1.66353	−	0.689055i	0.665188	−	0.746676i	$-0.268351\pi$
$839$	48.1849	−	19.9588i	1.66353	−	0.689055i	0.998339	+	0.0576208i	$0.0183514\pi$
$840$	13.5549	+	32.7245i	0.467689	+	1.12910i
$841$	18.5658	+	18.5658i	0.640200	+	0.640200i
$842$	−25.5698	−	25.5698i	−0.881194	−	0.881194i
$843$	−6.99141	−	16.8787i	−0.240797	−	0.581335i
$844$	−27.2329	+	11.2802i	−0.937395	+	0.388282i
$845$	−19.5139	+	47.1107i	−0.671299	+	1.62066i
$846$			75.5450i			2.59729i
$847$	−2.68478	−	1.11207i	−0.0922502	−	0.0382113i
$848$	23.1412	−	23.1412i	0.794673	−	0.794673i
$849$	−43.0870			−1.47874
$850$	69.4740	−	48.0470i	2.38294	−	1.64800i
$851$	−10.9125			−0.374077
$852$	−7.18199	+	7.18199i	−0.246051	+	0.246051i
$853$	−13.2988	−	5.50856i	−0.455344	−	0.188610i	0.143210	−	0.989692i	$-0.454258\pi$
$853$	−13.2988	−	5.50856i	−0.455344	−	0.188610i	−0.598554	+	0.801083i	$0.704258\pi$
$854$		−	16.0261i		−	0.548400i
$855$	−40.2343	+	97.1343i	−1.37599	+	3.32192i
$856$	4.03456	−	1.67117i	0.137898	−	0.0571194i
$857$	4.38214	+	10.5794i	0.149691	+	0.361387i	0.980883	−	0.194600i	$-0.0623408\pi$
$857$	4.38214	+	10.5794i	0.149691	+	0.361387i	−0.831192	+	0.555986i	$0.812341\pi$
$858$	−2.02793	−	2.02793i	−0.0692323	−	0.0692323i
$859$	21.0243	+	21.0243i	0.717341	+	0.717341i	0.968060	−	0.250719i	$-0.0806671\pi$
$859$	21.0243	+	21.0243i	0.717341	+	0.717341i	−0.250719	+	0.968060i	$0.580667\pi$
$860$	6.79939	+	16.4152i	0.231857	+	0.559753i
$861$	59.5047	−	24.6477i	2.02792	−	0.839990i
$862$	−25.7125	+	62.0754i	−0.875770	+	2.11430i
$863$		−	0.284056i		−	0.00966939i	−0.999988	−	0.00483469i	$-0.998461\pi$
$863$		−	0.284056i		−	0.00966939i	0.999988	−	0.00483469i	$-0.00153894\pi$
$864$	64.1360	+	26.5660i	2.18195	+	0.903794i
$865$	70.4530	−	70.4530i	2.39547	−	2.39547i
$866$	−17.7646			−0.603666
$867$	−35.4594	+	37.8055i	−1.20426	+	1.28394i
$868$	35.3909			1.20125
$869$	6.25219	−	6.25219i	0.212091	−	0.212091i
$870$	−34.7437	−	14.3913i	−1.17792	−	0.487911i
$871$		−	1.12699i		−	0.0381865i
$872$	−4.83512	+	11.6730i	−0.163738	+	0.395298i
$873$	71.3073	−	29.5364i	2.41339	−	0.999657i
$874$	−7.35979	−	17.7681i	−0.248949	−	0.601015i
$875$	−49.4033	−	49.4033i	−1.67014	−	1.67014i
$876$	7.35324	+	7.35324i	0.248443	+	0.248443i
$877$	1.45975	+	3.52415i	0.0492923	+	0.119002i	0.946608	−	0.322388i	$-0.104486\pi$
$877$	1.45975	+	3.52415i	0.0492923	+	0.119002i	−0.897315	+	0.441390i	$0.854486\pi$
$878$	30.2730	−	12.5395i	1.02166	−	0.423187i
$879$	−35.6758	+	86.1290i	−1.20331	+	2.90506i
$880$			19.1475i			0.645462i
$881$	28.4727	+	11.7938i	0.959269	+	0.397342i	0.806707	−	0.590952i	$-0.201248\pi$
$881$	28.4727	+	11.7938i	0.959269	+	0.397342i	0.152562	+	0.988294i	$0.451248\pi$
$882$	11.9701	−	11.9701i	0.403055	−	0.403055i
$883$	−24.7589			−0.833203			−0.416602	−	0.909089i	$-0.636779\pi$
$883$	−24.7589			−0.833203			−0.416602	+	0.909089i	$0.636779\pi$
$884$	−2.50784	+	1.73438i	−0.0843477	+	0.0583334i
$885$	−15.0165			−0.504775
$886$	−8.21240	+	8.21240i	−0.275901	+	0.275901i
$887$	14.2843	+	5.91676i	0.479620	+	0.198665i	0.609377	−	0.792881i	$-0.291420\pi$
$887$	14.2843	+	5.91676i	0.479620	+	0.198665i	−0.129757	+	0.991546i	$0.541420\pi$
$888$			13.4248i			0.450506i
$889$	3.35272	−	8.09418i	0.112447	−	0.271470i
$890$	−63.6441	+	26.3623i	−2.13336	+	0.883665i
$891$	4.49814	+	10.8595i	0.150693	+	0.363806i
$892$	−1.18374	−	1.18374i	−0.0396345	−	0.0396345i
$893$	−19.0269	−	19.0269i	−0.636710	−	0.636710i
$894$	10.9192	+	26.3613i	0.365193	+	0.881653i
$895$	26.7004	−	11.0597i	0.892496	−	0.369684i
$896$	−8.56867	+	20.6866i	−0.286259	+	0.691091i
$897$		−	3.81624i		−	0.127421i
$898$	−24.3992	−	10.1065i	−0.814212	−	0.337258i
$899$	9.74995	−	9.74995i	0.325179	−	0.325179i
$900$	−101.415			−3.38049
$901$	5.05754	−	27.7392i	0.168491	−	0.924126i
$902$	13.5276			0.450419
$903$	−19.0156	+	19.0156i	−0.632798	+	0.632798i
$904$	10.3705	+	4.29561i	0.344918	+	0.142870i
$905$		−	102.929i		−	3.42146i
$906$	27.7753	−	67.0556i	0.922773	−	2.22777i
$907$	−6.05666	+	2.50875i	−0.201108	+	0.0833018i	−0.480964	−	0.876740i	$-0.659713\pi$
$907$	−6.05666	+	2.50875i	−0.201108	+	0.0833018i	0.279856	+	0.960042i	$0.409713\pi$
$908$	7.74848	+	18.7065i	0.257142	+	0.620796i
$909$	4.11937	+	4.11937i	0.136631	+	0.136631i
$910$	7.73345	+	7.73345i	0.256361	+	0.256361i
$911$	−12.9735	−	31.3207i	−0.429830	−	1.03770i	−0.979341	−	0.202215i	$-0.935186\pi$
$911$	−12.9735	−	31.3207i	−0.429830	−	1.03770i	0.549511	−	0.835487i	$-0.314814\pi$
$912$	−56.2592	+	23.3033i	−1.86293	+	0.771650i
$913$	−0.747670	+	1.80504i	−0.0247443	+	0.0597379i
$914$			3.28289i			0.108588i
$915$	−33.4004	−	13.8349i	−1.10418	−	0.457367i
$916$	24.1549	−	24.1549i	0.798101	−	0.798101i
$917$	−8.46661			−0.279592
$918$	75.3819	−	16.2528i	2.48797	−	0.536422i
$919$	19.4750			0.642420			0.321210	−	0.947008i	$-0.395910\pi$
$919$	19.4750			0.642420			0.321210	+	0.947008i	$0.395910\pi$
$920$	−6.99994	+	6.99994i	−0.230781	+	0.230781i
$921$	5.33625	+	2.21035i	0.175835	+	0.0728334i
$922$			47.3055i			1.55792i
$923$	0.440406	−	1.06323i	0.0144961	−	0.0349967i
$924$	11.9767	−	4.96091i	0.394004	−	0.163202i
$925$	−18.5656	−	44.8213i	−0.610433	−	1.47372i
$926$	51.4413	+	51.4413i	1.69047	+	1.69047i
$927$	−78.7305	−	78.7305i	−2.58585	−	2.58585i
$928$	−4.37867	−	10.5710i	−0.143737	−	0.347011i
$929$	11.5543	−	4.78594i	0.379084	−	0.157022i	−0.185001	−	0.982738i	$-0.559229\pi$
$929$	11.5543	−	4.78594i	0.379084	−	0.157022i	0.564085	+	0.825717i	$0.309229\pi$
$930$	72.3156	−	174.585i	2.37132	−	5.72488i
$931$			6.02963i			0.197613i
$932$	2.74936	+	1.13882i	0.0900584	+	0.0373034i
$933$	−36.7144	+	36.7144i	−1.20197	+	1.20197i
$934$	−13.7556			−0.450097
$935$	9.38361	+	13.5683i	0.306877	+	0.443732i
$936$	−3.17974			−0.103933
$937$	28.9034	−	28.9034i	0.944232	−	0.944232i	−0.0542928	−	0.998525i	$-0.517290\pi$
$937$	28.9034	−	28.9034i	0.944232	−	0.944232i	0.998525	+	0.0542928i	$0.0172904\pi$
$938$	11.1399	+	4.61429i	0.363730	+	0.150662i
$939$			15.8778i			0.518151i
$940$	14.4439	−	34.8706i	0.471107	−	1.13735i
$941$	10.8456	−	4.49240i	0.353557	−	0.146448i	−0.198834	−	0.980033i	$-0.563715\pi$
$941$	10.8456	−	4.49240i	0.353557	−	0.146448i	0.552391	+	0.833585i	$0.313715\pi$
$942$	32.9382	+	79.5199i	1.07319	+	2.59090i
$943$	12.7284	+	12.7284i	0.414493	+	0.414493i
$944$	−4.16534	−	4.16534i	−0.135570	−	0.135570i
$945$	−44.7190	−	107.961i	−1.45471	−	3.51197i
$946$	−5.21823	+	2.16146i	−0.169659	+	0.0702752i
$947$	15.4955	−	37.4094i	0.503536	−	1.21564i	−0.444010	−	0.896022i	$-0.646444\pi$
$947$	15.4955	−	37.4094i	0.503536	−	1.21564i	0.947545	−	0.319621i	$-0.103556\pi$
$948$			39.4434i			1.28106i
$949$	−1.08859	−	0.450907i	−0.0353370	−	0.0146371i
$950$	60.4581	−	60.4581i	1.96152	−	1.96152i
$951$	−31.6222			−1.02542
$952$	2.52313	+	11.7025i	0.0817752	+	0.379281i
$953$	19.9059			0.644817			0.322408	−	0.946601i	$-0.395508\pi$
$953$	19.9059			0.644817			0.322408	+	0.946601i	$0.395508\pi$
$954$	−56.6593	+	56.6593i	−1.83441	+	1.83441i
$955$	−34.5039	−	14.2920i	−1.11652	−	0.462478i
$956$			43.8343i			1.41770i
$957$	1.93280	−	4.66619i	0.0624786	−	0.150837i
$958$	−14.6925	+	6.08585i	−0.474694	+	0.196625i
$959$	3.48780	+	8.42029i	0.112627	+	0.271905i
$960$	−28.3200	−	28.3200i	−0.914025	−	0.914025i
$961$	27.0727	+	27.0727i	0.873313	+	0.873313i
$962$	1.58627	+	3.82960i	0.0511435	+	0.123471i
$963$	−25.4245	+	10.5312i	−0.819292	+	0.339362i
$964$	14.2517	−	34.4067i	0.459017	−	1.10816i
$965$			93.1785i			2.99952i
$966$	37.7221	+	15.6250i	1.21369	+	0.502727i
$967$	9.20763	−	9.20763i	0.296097	−	0.296097i	−0.543386	−	0.839483i	$-0.682858\pi$
$967$	9.20763	−	9.20763i	0.296097	−	0.296097i	0.839483	+	0.543386i	$0.182858\pi$
$968$	−0.999144			−0.0321137
$969$	−28.4462	+	44.0842i	−0.913824	+	1.41619i
$970$	−91.2743			−2.93064
$971$	−21.7100	+	21.7100i	−0.696707	+	0.696707i	−0.963699	−	0.266992i	$-0.913970\pi$
$971$	−21.7100	+	21.7100i	−0.696707	+	0.696707i	0.266992	+	0.963699i	$0.413970\pi$
$972$	−7.68800	−	3.18448i	−0.246593	−	0.102142i
$973$		−	23.3401i		−	0.748250i
$974$	−5.78281	+	13.9609i	−0.185293	+	0.447337i
$975$	15.6746	−	6.49261i	0.501988	−	0.207930i
$976$	−5.42714	−	13.1023i	−0.173719	−	0.419394i
$977$	28.0946	+	28.0946i	0.898827	+	0.898827i	0.995332	−	0.0965053i	$-0.0307665\pi$
$977$	28.0946	+	28.0946i	0.898827	+	0.898827i	−0.0965053	+	0.995332i	$0.530766\pi$
$978$	−11.1068	−	11.1068i	−0.355158	−	0.355158i
$979$	−3.54054	−	8.54762i	−0.113156	−	0.273183i
$980$	−7.81389	+	3.23662i	−0.249606	+	0.103390i
$981$	30.4693	−	73.5594i	0.972809	−	2.34857i
$982$		−	33.2067i		−	1.05967i
$983$	12.5363	+	5.19269i	0.399845	+	0.165621i	0.573538	−	0.819179i	$-0.305570\pi$
$983$	12.5363	+	5.19269i	0.399845	+	0.165621i	−0.173694	+	0.984800i	$0.555570\pi$
$984$	15.6587	−	15.6587i	0.499180	−	0.499180i
$985$	14.5358			0.463149
$986$	−10.6797	−	6.89132i	−0.340112	−	0.219464i
$987$	57.1266			1.81836
$988$	−2.18239	+	2.18239i	−0.0694310	+	0.0694310i
$989$	−6.94371	−	2.87618i	−0.220797	−	0.0914572i
$990$		−	46.8810i		−	1.48998i
$991$	−17.5359	+	42.3355i	−0.557048	+	1.34483i	0.355046	+	0.934849i	$0.384465\pi$
$991$	−17.5359	+	42.3355i	−0.557048	+	1.34483i	−0.912093	+	0.409983i	$0.865535\pi$
$992$	53.1189	−	22.0026i	1.68653	−	0.698583i
$993$	37.9761	+	91.6825i	1.20514	+	2.90946i
$994$	8.70650	+	8.70650i	0.276153	+	0.276153i
$995$	−0.480050	−	0.480050i	−0.0152186	−	0.0152186i
$996$	−3.33532	−	8.05217i	−0.105684	−	0.255143i
$997$	−13.1120	+	5.43115i	−0.415260	+	0.172006i	−0.580524	−	0.814243i	$-0.697152\pi$
$997$	−13.1120	+	5.43115i	−0.415260	+	0.172006i	0.165264	+	0.986249i	$0.447152\pi$
$998$	1.77671	−	4.28935i	0.0562407	−	0.135777i
$999$		−	44.2896i		−	1.40126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.111.4	✓	56
17.2	even	8	inner	187.2.h.a.155.4	yes	56
17.6	odd	16		3179.2.a.bi.1.6		28
17.11	odd	16		3179.2.a.bh.1.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.111.4	✓	56	1.1	even	1	trivial
187.2.h.a.155.4	yes	56	17.2	even	8	inner
3179.2.a.bh.1.6		28	17.11	odd	16
3179.2.a.bi.1.6		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)

\(f(q)\)	\(=\)	\(q+(-1.31588 + 1.31588i) q^{2} +(-2.81689 - 1.16679i) q^{3} -1.46310i q^{4} +(-1.53116 + 3.69655i) q^{5} +(5.24206 - 2.17133i) q^{6} +(-1.11207 - 2.68478i) q^{7} +(-0.706501 - 0.706501i) q^{8} +(4.45214 + 4.45214i) q^{9} +O(q^{10})\)	\(q+(-1.31588 + 1.31588i) q^{2} +(-2.81689 - 1.16679i) q^{3} -1.46310i q^{4} +(-1.53116 + 3.69655i) q^{5} +(5.24206 - 2.17133i) q^{6} +(-1.11207 - 2.68478i) q^{7} +(-0.706501 - 0.706501i) q^{8} +(4.45214 + 4.45214i) q^{9} +(-2.84940 - 6.87905i) q^{10} +(0.923880 - 0.382683i) q^{11} +(-1.70713 + 4.12138i) q^{12} -0.505453i q^{13} +(4.99622 + 2.06950i) q^{14} +(8.62622 - 8.62622i) q^{15} +4.78554 q^{16} +(3.39114 - 2.34525i) q^{17} -11.7170 q^{18} +(2.95106 - 2.95106i) q^{19} +(5.40841 + 2.24024i) q^{20} +8.86030i q^{21} +(-0.712151 + 1.71928i) q^{22} +(-2.28779 + 0.947633i) q^{23} +(1.16579 + 2.81448i) q^{24} +(-7.78448 - 7.78448i) q^{25} +(0.665117 + 0.665117i) q^{26} +(-3.84607 - 9.28523i) q^{27} +(-3.92810 + 1.62707i) q^{28} +(-0.633917 + 1.53041i) q^{29} +22.7022i q^{30} +(-7.69024 - 3.18540i) q^{31} +(-4.88421 + 4.88421i) q^{32} -3.04898 q^{33} +(-1.37626 + 7.54841i) q^{34} +11.6272 q^{35} +(6.51391 - 6.51391i) q^{36} +(4.07137 + 1.68641i) q^{37} +7.76650i q^{38} +(-0.589759 + 1.42381i) q^{39} +(3.69338 - 1.52985i) q^{40} +(-2.78181 - 6.71588i) q^{41} +(-11.6591 - 11.6591i) q^{42} +(2.14615 + 2.14615i) q^{43} +(-0.559903 - 1.35173i) q^{44} +(-23.2745 + 9.64060i) q^{45} +(1.76349 - 4.25744i) q^{46} -6.44748i q^{47} +(-13.4803 - 5.58374i) q^{48} +(-1.02160 + 1.02160i) q^{49} +20.4869 q^{50} +(-12.2889 + 2.64955i) q^{51} -0.739527 q^{52} +(4.83565 - 4.83565i) q^{53} +(17.2792 + 7.15730i) q^{54} +4.00111i q^{55} +(-1.11112 + 2.68248i) q^{56} +(-11.7561 + 4.86953i) q^{57} +(-1.17968 - 2.84800i) q^{58} +(-0.870401 - 0.870401i) q^{59} +(-12.6210 - 12.6210i) q^{60} +(-1.13407 - 2.73789i) q^{61} +(14.3111 - 5.92784i) q^{62} +(7.00192 - 16.9041i) q^{63} -3.28302i q^{64} +(1.86843 + 0.773930i) q^{65} +(4.01210 - 4.01210i) q^{66} +2.22966 q^{67} +(-3.43133 - 4.96156i) q^{68} +7.55014 q^{69} +(-15.3000 + 15.3000i) q^{70} +(2.10352 + 0.871308i) q^{71} -6.29088i q^{72} +(0.892084 - 2.15368i) q^{73} +(-7.57657 + 3.13832i) q^{74} +(12.8451 + 31.0109i) q^{75} +(-4.31769 - 4.31769i) q^{76} +(-2.05484 - 2.05484i) q^{77} +(-1.09751 - 2.64962i) q^{78} +(8.16888 - 3.38366i) q^{79} +(-7.32743 + 17.6900i) q^{80} +11.7542i q^{81} +(12.4979 + 5.17678i) q^{82} +(-1.38151 + 1.38151i) q^{83} +12.9635 q^{84} +(3.47696 + 16.1264i) q^{85} -5.64818 q^{86} +(3.57135 - 3.57135i) q^{87} +(-0.923088 - 0.382356i) q^{88} -9.25188i q^{89} +(17.9406 - 43.3124i) q^{90} +(-1.35703 + 0.562101i) q^{91} +(1.38648 + 3.34726i) q^{92} +(17.9458 + 17.9458i) q^{93} +(8.48413 + 8.48413i) q^{94} +(6.39019 + 15.4273i) q^{95} +(19.4571 - 8.05941i) q^{96} +(4.69110 - 11.3253i) q^{97} -2.68863i q^{98} +(5.81699 + 2.40948i) 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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