LMFDB - Embedded newform 187.2.h.a.111.1

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			111.1
Character	$\chi$	$=$	187.111
Dual form			187.2.h.a.155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71399 + 1.71399i) q^{2} +(2.67857 + 1.10950i) q^{3} -3.87553i q^{4} +(0.851663 - 2.05610i) q^{5} +(-6.49271 + 2.68937i) q^{6} +(0.471206 + 1.13759i) q^{7} +(3.21463 + 3.21463i) q^{8} +(3.82242 + 3.82242i) q^{9} +O(q^{10})$	\(q+(-1.71399 + 1.71399i) q^{2} +(2.67857 + 1.10950i) q^{3} -3.87553i q^{4} +(0.851663 - 2.05610i) q^{5} +(-6.49271 + 2.68937i) q^{6} +(0.471206 + 1.13759i) q^{7} +(3.21463 + 3.21463i) q^{8} +(3.82242 + 3.82242i) q^{9} +(2.06439 + 4.98387i) q^{10} +(0.923880 - 0.382683i) q^{11} +(4.29990 - 10.3809i) q^{12} +3.75385i q^{13} +(-2.75747 - 1.14218i) q^{14} +(4.56248 - 4.56248i) q^{15} -3.26865 q^{16} +(-3.77509 - 1.65793i) q^{17} -13.1032 q^{18} +(2.75737 - 2.75737i) q^{19} +(-7.96845 - 3.30064i) q^{20} +3.56992i q^{21} +(-0.927605 + 2.23944i) q^{22} +(-8.29905 + 3.43758i) q^{23} +(5.04398 + 12.1773i) q^{24} +(0.0333320 + 0.0333320i) q^{25} +(-6.43406 - 6.43406i) q^{26} +(2.66915 + 6.44390i) q^{27} +(4.40877 - 1.82617i) q^{28} +(2.48680 - 6.00367i) q^{29} +15.6401i q^{30} +(-6.47526 - 2.68214i) q^{31} +(-0.826831 + 0.826831i) q^{32} +2.89926 q^{33} +(9.31213 - 3.62879i) q^{34} +2.74031 q^{35} +(14.8139 - 14.8139i) q^{36} +(4.97036 + 2.05879i) q^{37} +9.45222i q^{38} +(-4.16490 + 10.0549i) q^{39} +(9.34738 - 3.87181i) q^{40} +(-2.66858 - 6.44252i) q^{41} +(-6.11882 - 6.11882i) q^{42} +(-4.82075 - 4.82075i) q^{43} +(-1.48310 - 3.58052i) q^{44} +(11.1147 - 4.60386i) q^{45} +(8.33252 - 20.1165i) q^{46} -1.98367i q^{47} +(-8.75531 - 3.62657i) q^{48} +(3.87767 - 3.87767i) q^{49} -0.114261 q^{50} +(-8.27236 - 8.62933i) q^{51} +14.5481 q^{52} +(-4.68426 + 4.68426i) q^{53} +(-15.6197 - 6.46989i) q^{54} -2.22550i q^{55} +(-2.14219 + 5.17170i) q^{56} +(10.4451 - 4.32651i) q^{57} +(6.02788 + 14.5526i) q^{58} +(1.51994 + 1.51994i) q^{59} +(-17.6820 - 17.6820i) q^{60} +(5.67744 + 13.7066i) q^{61} +(15.6957 - 6.50137i) q^{62} +(-2.54721 + 6.14951i) q^{63} -9.37166i q^{64} +(7.71828 + 3.19702i) q^{65} +(-4.96931 + 4.96931i) q^{66} -0.314059 q^{67} +(-6.42534 + 14.6304i) q^{68} -26.0436 q^{69} +(-4.69686 + 4.69686i) q^{70} +(6.39319 + 2.64815i) q^{71} +24.5754i q^{72} +(0.545343 - 1.31657i) q^{73} +(-12.0479 + 4.99040i) q^{74} +(0.0523002 + 0.126264i) q^{75} +(-10.6863 - 10.6863i) q^{76} +(0.870676 + 0.870676i) q^{77} +(-10.0955 - 24.3727i) q^{78} +(-10.8330 + 4.48717i) q^{79} +(-2.78379 + 6.72066i) q^{80} +4.00469i q^{81} +(15.6163 + 6.46850i) q^{82} +(2.66015 - 2.66015i) q^{83} +13.8353 q^{84} +(-6.62396 + 6.34995i) q^{85} +16.5254 q^{86} +(13.3221 - 13.3221i) q^{87} +(4.20012 + 1.73975i) q^{88} -6.87587i q^{89} +(-11.1595 + 26.9414i) q^{90} +(-4.27035 + 1.76884i) q^{91} +(13.3224 + 32.1632i) q^{92} +(-14.3686 - 14.3686i) q^{93} +(3.39999 + 3.39999i) q^{94} +(-3.32107 - 8.01777i) q^{95} +(-3.13209 + 1.29736i) q^{96} +(0.458542 - 1.10702i) q^{97} +13.2926i q^{98} +(4.99424 + 2.06868i) 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 $

$2$	−1.71399	+	1.71399i	−1.21197	+	1.21197i	−0.241598	+	0.970376i	$0.577671\pi$
$2$	−1.71399	+	1.71399i	−1.21197	+	1.21197i	−0.970376	+	0.241598i	$0.922329\pi$
$3$	2.67857	+	1.10950i	1.54647	+	0.640570i	0.982674	−	0.185342i	$-0.0593393\pi$
$3$	2.67857	+	1.10950i	1.54647	+	0.640570i	0.563799	+	0.825912i	$0.309339\pi$
$4$		−	3.87553i		−	1.93776i
$5$	0.851663	−	2.05610i	0.380875	−	0.919514i	−0.610922	−	0.791691i	$-0.709201\pi$
$5$	0.851663	−	2.05610i	0.380875	−	0.919514i	0.991797	−	0.127823i	$-0.0407990\pi$
$6$	−6.49271	+	2.68937i	−2.65064	+	1.09793i
$7$	0.471206	+	1.13759i	0.178099	+	0.429970i	0.987568	−	0.157194i	$-0.0502447\pi$
$7$	0.471206	+	1.13759i	0.178099	+	0.429970i	−0.809469	+	0.587163i	$0.800245\pi$
$8$	3.21463	+	3.21463i	1.13654	+	1.13654i
$9$	3.82242	+	3.82242i	1.27414	+	1.27414i
$10$	2.06439	+	4.98387i	0.652817	+	1.57604i
$11$	0.923880	−	0.382683i	0.278560	−	0.115383i
$11$	0.923880	−	0.382683i	0.278560	−	0.115383i
$12$	4.29990	−	10.3809i	1.24127	−	2.99670i
$13$			3.75385i			1.04113i	0.853822	+	0.520565i	$0.174279\pi$
$13$			3.75385i			1.04113i	−0.853822	+	0.520565i	$0.825721\pi$
$14$	−2.75747	−	1.14218i	−0.736964	−	0.305260i
$15$	4.56248	−	4.56248i	1.17803	−	1.17803i
$16$	−3.26865			−0.817163
$17$	−3.77509	−	1.65793i	−0.915593	−	0.402106i
$17$	−3.77509	−	1.65793i	−0.915593	−	0.402106i
$18$	−13.1032			−3.08845
$19$	2.75737	−	2.75737i	0.632585	−	0.632585i	−0.316131	−	0.948716i	$-0.602384\pi$
$19$	2.75737	−	2.75737i	0.632585	−	0.632585i	0.948716	+	0.316131i	$0.102384\pi$
$20$	−7.96845	−	3.30064i	−1.78180	−	0.738046i
$21$			3.56992i			0.779021i
$22$	−0.927605	+	2.23944i	−0.197766	+	0.477449i
$23$	−8.29905	+	3.43758i	−1.73047	+	0.716785i	−0.731067	+	0.682306i	$0.760977\pi$
$23$	−8.29905	+	3.43758i	−1.73047	+	0.716785i	−0.999405	+	0.0344792i	$0.989023\pi$
$24$	5.04398	+	12.1773i	1.02960	+	2.48567i
$25$	0.0333320	+	0.0333320i	0.00666640	+	0.00666640i
$26$	−6.43406	−	6.43406i	−1.26182	−	1.26182i
$27$	2.66915	+	6.44390i	0.513679	+	1.24013i
$28$	4.40877	−	1.82617i	0.833179	−	0.345114i
$29$	2.48680	−	6.00367i	0.461788	−	1.11485i	−0.505875	−	0.862607i	$-0.668830\pi$
$29$	2.48680	−	6.00367i	0.461788	−	1.11485i	0.967663	−	0.252247i	$-0.0811696\pi$
$30$			15.6401i			2.85548i
$31$	−6.47526	−	2.68214i	−1.16299	−	0.481727i	−0.284121	−	0.958788i	$-0.591702\pi$
$31$	−6.47526	−	2.68214i	−1.16299	−	0.481727i	−0.878870	+	0.477062i	$0.841702\pi$
$32$	−0.826831	+	0.826831i	−0.146165	+	0.146165i
$33$	2.89926			0.504697
$34$	9.31213	−	3.62879i	1.59702	−	0.622333i
$35$	2.74031			0.463197
$36$	14.8139	−	14.8139i	2.46898	−	2.46898i
$37$	4.97036	+	2.05879i	0.817122	+	0.338463i	0.751792	−	0.659401i	$-0.229190\pi$
$37$	4.97036	+	2.05879i	0.817122	+	0.338463i	0.0653303	+	0.997864i	$0.479190\pi$
$38$			9.45222i			1.53335i
$39$	−4.16490	+	10.0549i	−0.666917	+	1.61008i
$40$	9.34738	−	3.87181i	1.47795	−	0.612187i
$41$	−2.66858	−	6.44252i	−0.416762	−	1.00615i	−0.983279	−	0.182103i	$-0.941710\pi$
$41$	−2.66858	−	6.44252i	−0.416762	−	1.00615i	0.566517	−	0.824050i	$-0.308290\pi$
$42$	−6.11882	−	6.11882i	−0.944154	−	0.944154i
$43$	−4.82075	−	4.82075i	−0.735157	−	0.735157i	0.236479	−	0.971637i	$-0.424006\pi$
$43$	−4.82075	−	4.82075i	−0.735157	−	0.735157i	−0.971637	+	0.236479i	$0.924006\pi$
$44$	−1.48310	−	3.58052i	−0.223586	−	0.539784i
$45$	11.1147	−	4.60386i	1.65688	−	0.686302i
$46$	8.33252	−	20.1165i	1.22856	−	2.96601i
$47$		−	1.98367i		−	0.289348i	−0.989479	−	0.144674i	$-0.953787\pi$
$47$		−	1.98367i		−	0.289348i	0.989479	−	0.144674i	$-0.0462133\pi$
$48$	−8.75531	−	3.62657i	−1.26372	−	0.523450i
$49$	3.87767	−	3.87767i	0.553952	−	0.553952i
$50$	−0.114261			−0.0161590
$51$	−8.27236	−	8.62933i	−1.15836	−	1.20835i
$52$	14.5481			2.01746
$53$	−4.68426	+	4.68426i	−0.643433	+	0.643433i	−0.951398	−	0.307965i	$-0.900352\pi$
$53$	−4.68426	+	4.68426i	−0.643433	+	0.643433i	0.307965	+	0.951398i	$0.400352\pi$
$54$	−15.6197	−	6.46989i	−2.12557	−	0.880440i
$55$		−	2.22550i		−	0.300087i
$56$	−2.14219	+	5.17170i	−0.286262	+	0.691098i
$57$	10.4451	−	4.32651i	1.38349	−	0.573060i
$58$	6.02788	+	14.5526i	0.791499	+	1.91085i
$59$	1.51994	+	1.51994i	0.197880	+	0.197880i	0.799091	−	0.601211i	$-0.205315\pi$
$59$	1.51994	+	1.51994i	0.197880	+	0.197880i	−0.601211	+	0.799091i	$0.705315\pi$
$60$	−17.6820	−	17.6820i	−2.28274	−	2.28274i
$61$	5.67744	+	13.7066i	0.726922	+	1.75494i	0.652591	+	0.757711i	$0.273682\pi$
$61$	5.67744	+	13.7066i	0.726922	+	1.75494i	0.0743312	+	0.997234i	$0.476318\pi$
$62$	15.6957	−	6.50137i	1.99336	−	0.825675i
$63$	−2.54721	+	6.14951i	−0.320919	+	0.774766i
$64$		−	9.37166i		−	1.17146i
$65$	7.71828	+	3.19702i	0.957334	+	0.396541i
$66$	−4.96931	+	4.96931i	−0.611680	+	0.611680i
$67$	−0.314059			−0.0383684			−0.0191842	−	0.999816i	$-0.506107\pi$
$67$	−0.314059			−0.0383684			−0.0191842	+	0.999816i	$0.506107\pi$
$68$	−6.42534	+	14.6304i	−0.779186	+	1.77420i
$69$	−26.0436			−3.13528
$70$	−4.69686	+	4.69686i	−0.561383	+	0.561383i
$71$	6.39319	+	2.64815i	0.758732	+	0.314277i	0.728299	−	0.685260i	$-0.240311\pi$
$71$	6.39319	+	2.64815i	0.758732	+	0.314277i	0.0304332	+	0.999537i	$0.490311\pi$
$72$			24.5754i			2.89624i
$73$	0.545343	−	1.31657i	0.0638275	−	0.154093i	−0.888748	−	0.458397i	$-0.848424\pi$
$73$	0.545343	−	1.31657i	0.0638275	−	0.154093i	0.952575	+	0.304304i	$0.0984238\pi$
$74$	−12.0479	+	4.99040i	−1.40054	+	0.580122i
$75$	0.0523002	+	0.126264i	0.00603911	+	0.0145797i
$76$	−10.6863	−	10.6863i	−1.22580	−	1.22580i
$77$	0.870676	+	0.870676i	0.0992227	+	0.0992227i
$78$	−10.0955	−	24.3727i	−1.14309	−	2.75966i
$79$	−10.8330	+	4.48717i	−1.21881	+	0.504846i	−0.897030	−	0.441970i	$-0.854280\pi$
$79$	−10.8330	+	4.48717i	−1.21881	+	0.504846i	−0.321776	+	0.946816i	$0.604280\pi$
$80$	−2.78379	+	6.72066i	−0.311237	+	0.751393i
$81$			4.00469i			0.444965i
$82$	15.6163	+	6.46850i	1.72454	+	0.714327i
$83$	2.66015	−	2.66015i	0.291989	−	0.291989i	−0.545876	−	0.837866i	$-0.683803\pi$
$83$	2.66015	−	2.66015i	0.291989	−	0.291989i	0.837866	+	0.545876i	$0.183803\pi$
$84$	13.8353			1.50956
$85$	−6.62396	+	6.34995i	−0.718469	+	0.688749i
$86$	16.5254			1.78198
$87$	13.3221	−	13.3221i	1.42828	−	1.42828i
$88$	4.20012	+	1.73975i	0.447734	+	0.185458i
$89$		−	6.87587i		−	0.728840i	−0.931235	−	0.364420i	$-0.881267\pi$
$89$		−	6.87587i		−	0.728840i	0.931235	−	0.364420i	$-0.118733\pi$
$90$	−11.1595	+	26.9414i	−1.17632	+	2.83988i
$91$	−4.27035	+	1.76884i	−0.447655	+	0.185425i
$92$	13.3224	+	32.1632i	1.38896	+	3.35325i
$93$	−14.3686	−	14.3686i	−1.48995	−	1.48995i
$94$	3.39999	+	3.39999i	0.350682	+	0.350682i
$95$	−3.32107	−	8.01777i	−0.340735	−	0.822606i
$96$	−3.13209	+	1.29736i	−0.319668	+	0.132411i
$97$	0.458542	−	1.10702i	0.0465579	−	0.112401i	−0.898890	−	0.438175i	$-0.855625\pi$
$97$	0.458542	−	1.10702i	0.0465579	−	0.112401i	0.945448	+	0.325774i	$0.105625\pi$
$98$			13.2926i			1.34275i
$99$	4.99424	+	2.06868i	0.501940	+	0.207910i
$100$	0.129179	−	0.129179i	0.0129179	−	0.0129179i
$101$	−0.427658			−0.0425536			−0.0212768	−	0.999774i	$-0.506773\pi$
$101$	−0.427658			−0.0425536			−0.0212768	+	0.999774i	$0.506773\pi$
$102$	28.9693	+	0.611833i	2.86839	+	0.0605805i
$103$	−7.73900			−0.762547			−0.381273	−	0.924462i	$-0.624514\pi$
$103$	−7.73900			−0.762547			−0.381273	+	0.924462i	$0.624514\pi$
$104$	−12.0673	+	12.0673i	−1.18329	+	1.18329i
$105$	7.34011	+	3.04037i	0.716321	+	0.296710i
$106$		−	16.0576i		−	1.55965i
$107$	2.54781	−	6.15096i	0.246306	−	0.594636i	−0.751579	−	0.659644i	$-0.770707\pi$
$107$	2.54781	−	6.15096i	0.246306	−	0.594636i	0.997885	+	0.0650079i	$0.0207073\pi$
$108$	24.9735	−	10.3444i	2.40308	−	0.995387i
$109$	−2.84475	−	6.86783i	−0.272478	−	0.657819i	0.727110	−	0.686520i	$-0.240863\pi$
$109$	−2.84475	−	6.86783i	−0.272478	−	0.657819i	−0.999588	+	0.0287015i	$0.990863\pi$
$110$	3.81449	+	3.81449i	0.363697	+	0.363697i
$111$	11.0292	+	11.0292i	1.04685	+	1.04685i
$112$	−1.54021	−	3.71839i	−0.145536	−	0.351355i
$113$	−16.2896	+	6.74738i	−1.53240	+	0.634740i	−0.980028	−	0.198860i	$-0.936276\pi$
$113$	−16.2896	+	6.74738i	−1.53240	+	0.634740i	−0.552369	+	0.833600i	$0.686276\pi$
$114$	−10.4872	+	25.3184i	−0.982220	+	2.37129i
$115$			19.9913i			1.86420i
$116$	−23.2674	−	9.63767i	−2.16032	−	0.894835i
$117$	−14.3488	+	14.3488i	−1.32655	+	1.32655i
$118$	−5.21034			−0.479651
$119$	0.107200	−	5.07574i	0.00982698	−	0.465292i
$120$	29.3334			2.67776
$121$	0.707107	−	0.707107i	0.0642824	−	0.0642824i
$122$	−33.2240	−	13.7618i	−3.00796	−	1.24594i
$123$		−	20.2175i		−	1.82295i
$124$	−10.3947	+	25.0950i	−0.933472	+	2.25360i
$125$	10.3774	−	4.29846i	0.928183	−	0.384466i
$126$	−6.17431	−	14.9061i	−0.550051	−	1.32794i
$127$	−6.08390	−	6.08390i	−0.539859	−	0.539859i	0.383629	−	0.923487i	$-0.374674\pi$
$127$	−6.08390	−	6.08390i	−0.539859	−	0.539859i	−0.923487	+	0.383629i	$0.874674\pi$
$128$	14.4093	+	14.4093i	1.27361	+	1.27361i
$129$	−7.56409	−	18.2613i	−0.665981	−	1.60782i
$130$	−18.7087	+	7.74940i	−1.64086	+	0.679667i
$131$	−5.32845	+	12.8640i	−0.465549	+	1.12393i	0.500537	+	0.865715i	$0.333136\pi$
$131$	−5.32845	+	12.8640i	−0.465549	+	1.12393i	−0.966086	+	0.258220i	$0.916864\pi$
$132$		−	11.2362i		−	0.977983i
$133$	4.43606	+	1.83748i	0.384655	+	0.159329i
$134$	0.538293	−	0.538293i	0.0465015	−	0.0465015i
$135$	15.5225			1.33596
$136$	−6.80590	−	17.4651i	−0.583601	−	1.49762i
$137$	13.1080			1.11989			0.559947	−	0.828528i	$-0.310821\pi$
$137$	13.1080			1.11989			0.559947	+	0.828528i	$0.310821\pi$
$138$	44.6385	−	44.6385i	3.79988	−	3.79988i
$139$	8.24648	+	3.41580i	0.699457	+	0.289725i	0.703934	−	0.710265i	$-0.251425\pi$
$139$	8.24648	+	3.41580i	0.699457	+	0.289725i	−0.00447682	+	0.999990i	$0.501425\pi$
$140$		−	10.6201i		−	0.897566i
$141$	2.20088	−	5.31340i	0.185348	−	0.447469i
$142$	−15.4968	+	6.41897i	−1.30046	+	0.538668i
$143$	1.43654	+	3.46811i	0.120129	+	0.290018i
$144$	−12.4942	−	12.4942i	−1.04118	−	1.04118i
$145$	−10.2262	−	10.2262i	−0.849240	−	0.849240i
$146$	1.32188	+	3.19131i	0.109400	+	0.264114i
$147$	14.6889	−	6.08433i	1.21152	−	0.501827i
$148$	7.97890	−	19.2628i	0.655861	−	1.58339i
$149$		−	3.60131i		−	0.295031i	−0.989060	−	0.147515i	$-0.952872\pi$
$149$		−	3.60131i		−	0.295031i	0.989060	−	0.147515i	$-0.0471276\pi$
$150$	−0.306057	−	0.126773i	−0.0249895	−	0.0103510i
$151$	−2.30877	+	2.30877i	−0.187885	+	0.187885i	−0.794781	−	0.606896i	$-0.792414\pi$
$151$	−2.30877	+	2.30877i	−0.187885	+	0.187885i	0.606896	+	0.794781i	$0.292414\pi$
$152$	17.7279			1.43792
$153$	−8.09269	−	20.7673i	−0.654255	−	1.67894i
$154$	−2.98466			−0.240511
$155$	−11.0295	+	11.0295i	−0.885909	+	0.885909i
$156$	38.9682	+	16.1412i	3.11995	+	1.29233i
$157$		−	14.5256i		−	1.15927i	−0.814878	−	0.579633i	$-0.803196\pi$
$157$		−	14.5256i		−	1.15927i	0.814878	−	0.579633i	$-0.196804\pi$
$158$	10.8767	−	26.2586i	0.865301	−	2.08902i
$159$	−17.7443	+	7.34993i	−1.40721	+	0.582887i
$160$	0.995863	+	2.40423i	0.0787299	+	0.190071i
$161$	−7.82113	−	7.82113i	−0.616392	−	0.616392i
$162$	−6.86400	−	6.86400i	−0.539287	−	0.539287i
$163$	3.64580	+	8.80175i	0.285561	+	0.689406i	0.999946	−	0.0103466i	$-0.00329349\pi$
$163$	3.64580	+	8.80175i	0.285561	+	0.689406i	−0.714385	+	0.699753i	$0.753293\pi$
$164$	−24.9682	+	10.3422i	−1.94969	+	0.807587i
$165$	2.46919	−	5.96116i	0.192227	−	0.464076i
$166$			9.11895i			0.707768i
$167$	−0.465617	−	0.192865i	−0.0360306	−	0.0149243i	0.364595	−	0.931166i	$-0.381207\pi$
$167$	−0.465617	−	0.192865i	−0.0360306	−	0.0149243i	−0.400626	+	0.916242i	$0.631207\pi$
$168$	−11.4760	+	11.4760i	−0.885393	+	0.885393i
$169$	−1.09139			−0.0839532
$170$	0.469649	−	22.2371i	0.0360205	−	1.70551i
$171$	21.0797			1.61200
$172$	−18.6829	+	18.6829i	−1.42456	+	1.42456i
$173$	13.6627	+	5.65928i	1.03876	+	0.430267i	0.835865	−	0.548935i	$-0.184966\pi$
$173$	13.6627	+	5.65928i	1.03876	+	0.430267i	0.202891	+	0.979201i	$0.434966\pi$
$174$			45.6681i			3.46209i
$175$	−0.0222120	+	0.0536245i	−0.00167907	+	0.00405363i
$176$	−3.01984	+	1.25086i	−0.227629	+	0.0942870i
$177$	2.38490	+	5.75766i	0.179260	+	0.432772i
$178$	11.7852	+	11.7852i	0.883336	+	0.883336i
$179$	9.52635	+	9.52635i	0.712033	+	0.712033i	0.966960	−	0.254928i	$-0.0820516\pi$
$179$	9.52635	+	9.52635i	0.712033	+	0.712033i	−0.254928	+	0.966960i	$0.582052\pi$
$180$	−17.8424	−	43.0753i	−1.32989	−	3.21064i
$181$	−14.2745	+	5.91269i	−1.06102	+	0.439487i	−0.843812	−	0.536639i	$-0.819694\pi$
$181$	−14.2745	+	5.91269i	−1.06102	+	0.439487i	−0.217204	+	0.976126i	$0.569694\pi$
$182$	4.28757	−	10.3511i	0.317816	−	0.767276i
$183$			43.0131i			3.17962i
$184$	−37.7290	−	15.6279i	−2.78142	−	1.15210i
$185$	8.46614	−	8.46614i	0.622443	−	0.622443i
$186$	49.2553			3.61157
$187$	−4.12219	−	0.0870607i	−0.301444	−	0.00636651i
$188$	−7.68776			−0.560688
$189$	−6.07282	+	6.07282i	−0.441732	+	0.441732i
$190$	19.4347	+	8.05010i	1.40994	+	0.584016i
$191$			21.8145i			1.57844i	0.614108	+	0.789222i	$0.289516\pi$
$191$			21.8145i			1.57844i	−0.614108	+	0.789222i	$0.710484\pi$
$192$	10.3979	−	25.1027i	0.750401	−	1.81163i
$193$	19.8276	−	8.21287i	1.42722	−	0.591175i	0.470559	−	0.882369i	$-0.344052\pi$
$193$	19.8276	−	8.21287i	1.42722	−	0.591175i	0.956664	+	0.291194i	$0.0940524\pi$
$194$	1.11148	+	2.68336i	0.0797998	+	0.192654i
$195$	17.1269	+	17.1269i	1.22648	+	1.22648i
$196$	−15.0280	−	15.0280i	−1.07343	−	1.07343i
$197$	2.23101	+	5.38614i	0.158953	+	0.383747i	0.983212	−	0.182466i	$-0.0584080\pi$
$197$	2.23101	+	5.38614i	0.158953	+	0.383747i	−0.824259	+	0.566213i	$0.808408\pi$
$198$	−12.1058	+	5.01438i	−0.860320	+	0.356356i
$199$	0.308044	−	0.743685i	0.0218367	−	0.0527184i	−0.912585	−	0.408887i	$-0.865917\pi$
$199$	0.308044	−	0.743685i	0.0218367	−	0.0527184i	0.934422	+	0.356168i	$0.115917\pi$
$200$			0.214300i			0.0151533i
$201$	−0.841228	−	0.348448i	−0.0593356	−	0.0245776i
$202$	0.733002	−	0.733002i	0.0515738	−	0.0515738i
$203$	8.00153			0.561597
$204$	−33.4432	+	32.0598i	−2.34149	+	2.24463i
$205$	−15.5192			−1.08391
$206$	13.2646	−	13.2646i	0.924187	−	0.924187i
$207$	−44.8624	−	18.5826i	−3.11815	−	1.29158i
$208$		−	12.2700i		−	0.850773i
$209$	1.49228	−	3.60268i	0.103223	−	0.249203i
$210$	−17.7920	+	7.36971i	−1.22777	+	0.508558i
$211$	2.62871	+	6.34626i	0.180968	+	0.436895i	0.988166	−	0.153385i	$-0.0490175\pi$
$211$	2.62871	+	6.34626i	0.180968	+	0.436895i	−0.807199	+	0.590280i	$0.799017\pi$
$212$	18.1540	+	18.1540i	1.24682	+	1.24682i
$213$	14.1865	+	14.1865i	0.972042	+	0.972042i
$214$	6.17576	+	14.9096i	0.422166	+	1.01920i
$215$	−14.0176	+	5.80627i	−0.955991	+	0.395984i
$216$	−12.1344	+	29.2951i	−0.825644	+	1.99328i
$217$		−	8.63005i		−	0.585846i
$218$	16.6473	+	6.89553i	1.12750	+	0.467024i
$219$	2.92148	−	2.92148i	0.197415	−	0.197415i
$220$	−8.62499			−0.581497
$221$	6.22361	−	14.1711i	0.418645	−	0.953252i
$222$	−37.8080			−2.53751
$223$	−11.3286	+	11.3286i	−0.758616	+	0.758616i	−0.976070	−	0.217454i	$-0.930225\pi$
$223$	−11.3286	+	11.3286i	−0.758616	+	0.758616i	0.217454	+	0.976070i	$0.430225\pi$
$224$	−1.33021	−	0.550989i	−0.0888781	−	0.0368145i
$225$			0.254818i			0.0169879i
$226$	16.3553	−	39.4852i	1.08794	−	2.62651i
$227$	−2.52815	+	1.04719i	−0.167799	+	0.0695047i	−0.465002	−	0.885310i	$-0.653946\pi$
$227$	−2.52815	+	1.04719i	−0.167799	+	0.0695047i	0.297203	+	0.954814i	$0.403946\pi$
$228$	−16.7675	−	40.4803i	−1.11045	−	2.68088i
$229$	9.90382	+	9.90382i	0.654463	+	0.654463i	0.954064	−	0.299602i	$-0.0968538\pi$
$229$	9.90382	+	9.90382i	0.654463	+	0.654463i	−0.299602	+	0.954064i	$0.596854\pi$
$230$	−34.2649	−	34.2649i	−2.25936	−	2.25936i
$231$	1.36615	+	3.29818i	0.0898861	+	0.217004i
$232$	27.2938	−	11.3054i	1.79192	−	0.742239i
$233$	−6.69838	+	16.1713i	−0.438826	+	1.05942i	0.537529	+	0.843245i	$0.319358\pi$
$233$	−6.69838	+	16.1713i	−0.438826	+	1.05942i	−0.976355	+	0.216174i	$0.930642\pi$
$234$		−	49.1874i		−	3.21548i
$235$	−4.07861	−	1.68942i	−0.266059	−	0.110205i
$236$	5.89059	−	5.89059i	0.383444	−	0.383444i
$237$	−33.9954			−2.20824
$238$	8.51602	+	8.88350i	0.552012	+	0.575832i
$239$	13.7083			0.886719			0.443360	−	0.896344i	$-0.353787\pi$
$239$	13.7083			0.886719			0.443360	+	0.896344i	$0.353787\pi$
$240$	−14.9131	+	14.9131i	−0.962639	+	0.962639i
$241$	−17.0610	−	7.06689i	−1.09899	−	0.455219i	−0.241860	−	0.970311i	$-0.577758\pi$
$241$	−17.0610	−	7.06689i	−1.09899	−	0.455219i	−0.857135	+	0.515093i	$0.827758\pi$
$242$			2.42395i			0.155817i
$243$	3.56425	−	8.60487i	0.228647	−	0.552003i
$244$	53.1201	−	22.0031i	3.40067	−	1.40860i
$245$	−4.67039	−	11.2753i	−0.298380	−	0.720354i
$246$	34.6527	+	34.6527i	2.20937	+	2.20937i
$247$	10.3508	+	10.3508i	0.658603	+	0.658603i
$248$	−12.1935	−	29.4377i	−0.774287	−	1.86929i
$249$	10.0768	−	4.17396i	0.638594	−	0.264514i
$250$	−10.4192	+	25.1543i	−0.658971	+	1.59090i
$251$			0.470751i			0.0297136i	0.999890	+	0.0148568i	$0.00472923\pi$
$251$			0.470751i			0.0297136i	−0.999890	+	0.0148568i	$0.995271\pi$
$252$	23.8326	+	9.87179i	1.50131	+	0.621864i
$253$	−6.35182	+	6.35182i	−0.399336	+	0.399336i
$254$	20.8555			1.30859
$255$	−24.7880	+	9.65950i	−1.55228	+	0.604901i
$256$	−30.6514			−1.91571
$257$	−2.75611	+	2.75611i	−0.171921	+	0.171921i	−0.787823	−	0.615902i	$-0.788792\pi$
$257$	−2.75611	+	2.75611i	−0.171921	+	0.171921i	0.615902	+	0.787823i	$0.288792\pi$
$258$	44.2645	+	18.3350i	2.75579	+	1.14148i
$259$			6.62436i			0.411618i
$260$	12.3901	−	29.9124i	0.768402	−	1.85509i
$261$	32.4542	−	13.4430i	2.00886	−	0.832099i
$262$	−12.9159	−	31.1817i	−0.797946	−	1.92641i
$263$	4.08511	+	4.08511i	0.251898	+	0.251898i	0.821749	−	0.569850i	$-0.192999\pi$
$263$	4.08511	+	4.08511i	0.251898	+	0.251898i	−0.569850	+	0.821749i	$0.692999\pi$
$264$	9.32007	+	9.32007i	0.573611	+	0.573611i
$265$	5.64188	+	13.6207i	0.346578	+	0.836713i
$266$	−10.7528	+	4.45395i	−0.659295	+	0.273089i
$267$	7.62877	−	18.4175i	0.466873	−	1.12713i
$268$			1.21714i			0.0743488i
$269$	−27.8948	−	11.5544i	−1.70077	−	0.704484i	−0.700814	−	0.713344i	$-0.747180\pi$
$269$	−27.8948	−	11.5544i	−1.70077	−	0.704484i	−0.999961	+	0.00886005i	$0.997180\pi$
$270$	−26.6054	+	26.6054i	−1.61915	+	1.61915i
$271$	−4.84766			−0.294474			−0.147237	−	0.989101i	$-0.547038\pi$
$271$	−4.84766			−0.294474			−0.147237	+	0.989101i	$0.547038\pi$
$272$	12.3394	+	5.41918i	0.748189	+	0.328586i
$273$	−13.4010			−0.811063
$274$	−22.4670	+	22.4670i	−1.35728	+	1.35728i
$275$	0.0435503	+	0.0180391i	0.00262618	+	0.00108780i
$276$			100.933i			6.07543i
$277$	−4.41364	+	10.6555i	−0.265190	+	0.640225i	−0.999244	−	0.0388657i	$-0.987626\pi$
$277$	−4.41364	+	10.6555i	−0.265190	+	0.640225i	0.734055	+	0.679090i	$0.237626\pi$
$278$	−19.9890	+	8.27973i	−1.19886	+	0.496585i
$279$	−14.4989	−	35.0035i	−0.868027	−	2.09560i
$280$	8.80909	+	8.80909i	0.526444	+	0.526444i
$281$	14.3046	+	14.3046i	0.853339	+	0.853339i	0.990543	−	0.137204i	$-0.0438116\pi$
$281$	14.3046	+	14.3046i	0.853339	+	0.853339i	−0.137204	+	0.990543i	$0.543812\pi$
$282$	5.33482	+	12.8794i	0.317684	+	0.766957i
$283$	19.6159	−	8.12516i	1.16604	−	0.482991i	0.286160	−	0.958182i	$-0.407621\pi$
$283$	19.6159	−	8.12516i	1.16604	−	0.482991i	0.879883	+	0.475191i	$0.157621\pi$
$284$	10.2630	−	24.7770i	0.608995	−	1.47024i
$285$		−	25.1609i		−	1.49040i
$286$	−8.40651	−	3.48209i	−0.497087	−	0.205900i
$287$	6.07152	−	6.07152i	0.358390	−	0.358390i
$288$	−6.32100			−0.372469
$289$	11.5026	+	12.5176i	0.676621	+	0.736331i
$290$	35.0552			2.05851
$291$	2.45647	−	2.45647i	0.144001	−	0.144001i
$292$	−5.10241	−	2.11349i	−0.298596	−	0.123683i
$293$		−	17.8502i		−	1.04282i	−0.853306	−	0.521410i	$-0.825406\pi$
$293$		−	17.8502i		−	1.04282i	0.853306	−	0.521410i	$-0.174594\pi$
$294$	−14.7481	+	35.6051i	−0.860126	+	2.07653i
$295$	4.41963	−	1.83067i	0.257321	−	0.106586i
$296$	9.35963	+	22.5961i	0.544017	+	1.31337i
$297$	4.93195	+	4.93195i	0.286181	+	0.286181i
$298$	6.17261	+	6.17261i	0.357570	+	0.357570i
$299$	−12.9042	−	31.1534i	−0.746267	−	1.80165i
$300$	0.489339	−	0.202691i	0.0282520	−	0.0117024i
$301$	3.21248	−	7.75561i	0.185164	−	0.447026i
$302$		−	7.91441i		−	0.455423i
$303$	−1.14551	−	0.474486i	−0.0658079	−	0.0272585i
$304$	−9.01289	+	9.01289i	−0.516925	+	0.516925i
$305$	33.0173			1.89056
$306$	49.4657	+	21.7241i	2.82777	+	1.24189i
$307$	5.14227			0.293485			0.146742	−	0.989175i	$-0.453121\pi$
$307$	5.14227			0.293485			0.146742	+	0.989175i	$0.453121\pi$
$308$	3.37433	−	3.37433i	0.192270	−	0.192270i
$309$	−20.7295	−	8.58642i	−1.17926	−	0.488465i
$310$		−	37.8088i		−	2.14740i
$311$	−5.59717	+	13.5128i	−0.317387	+	0.766239i	0.682005	+	0.731348i	$0.261108\pi$
$311$	−5.59717	+	13.5128i	−0.317387	+	0.766239i	−0.999391	+	0.0348911i	$0.988892\pi$
$312$	−45.7116	+	18.9344i	−2.58791	+	1.07195i
$313$	−3.97571	−	9.59821i	−0.224720	−	0.542523i	0.770799	−	0.637078i	$-0.219857\pi$
$313$	−3.97571	−	9.59821i	−0.224720	−	0.542523i	−0.995520	+	0.0945553i	$0.969857\pi$
$314$	24.8967	+	24.8967i	1.40500	+	1.40500i
$315$	10.4746	+	10.4746i	0.590178	+	0.590178i
$316$	17.3901	+	41.9835i	0.978271	+	2.36176i
$317$	12.3720	−	5.12465i	0.694881	−	0.287829i	−0.00715090	−	0.999974i	$-0.502276\pi$
$317$	12.3720	−	5.12465i	0.694881	−	0.287829i	0.702032	+	0.712145i	$0.252276\pi$
$318$	17.8159	−	43.0113i	0.999063	−	2.41195i
$319$		−	6.49833i		−	0.363836i
$320$	−19.2690	−	7.98150i	−1.07717	−	0.446179i
$321$	13.6490	−	13.6490i	0.761811	−	0.761811i
$322$	26.8107			1.49410
$323$	−14.9808	+	5.83780i	−0.833556	+	0.324824i
$324$	15.5203			0.862238
$325$	−0.125123	+	0.125123i	−0.00694059	+	0.00694059i
$326$	−21.3350	−	8.83724i	−1.18164	−	0.489449i
$327$		−	21.5522i		−	1.19184i
$328$	12.1318	−	29.2889i	0.669869	−	1.61721i
$329$	2.25661	−	0.934717i	0.124411	−	0.0515326i
$330$	5.98520	+	14.4496i	0.329474	+	0.795422i
$331$	0.439746	+	0.439746i	0.0241706	+	0.0241706i	0.719089	−	0.694918i	$-0.244559\pi$
$331$	0.439746	+	0.439746i	0.0241706	+	0.0241706i	−0.694918	+	0.719089i	$0.744559\pi$
$332$	−10.3095	−	10.3095i	−0.565806	−	0.565806i
$333$	11.1293	+	26.8684i	0.609879	+	1.47238i
$334$	1.12863	−	0.467495i	0.0617560	−	0.0255802i
$335$	−0.267472	+	0.645735i	−0.0146136	+	0.0352802i
$336$		−	11.6688i		−	0.636587i
$337$	−14.0782	−	5.83139i	−0.766889	−	0.317656i	−0.0352775	−	0.999378i	$-0.511232\pi$
$337$	−14.0782	−	5.83139i	−0.766889	−	0.317656i	−0.731612	+	0.681722i	$0.761232\pi$
$338$	1.87064	−	1.87064i	0.101749	−	0.101749i
$339$	−51.1191			−2.77641
$340$	24.6094	+	25.6713i	1.33463	+	1.39222i
$341$	−7.00877			−0.379546
$342$	−36.1304	+	36.1304i	−1.95371	+	1.95371i
$343$	14.2015	+	5.88247i	0.766811	+	0.317623i
$344$		−	30.9939i		−	1.67108i
$345$	−22.1804	+	53.5481i	−1.19415	+	2.88293i
$346$	−33.1177	+	13.7178i	−1.78042	+	0.737473i
$347$	6.34724	+	15.3236i	0.340738	+	0.822613i	0.997642	+	0.0686390i	$0.0218657\pi$
$347$	6.34724	+	15.3236i	0.340738	+	0.822613i	−0.656904	+	0.753974i	$0.728134\pi$
$348$	−51.6303	−	51.6303i	−2.76768	−	2.76768i
$349$	8.02573	+	8.02573i	0.429607	+	0.429607i	0.888495	−	0.458887i	$-0.151752\pi$
$349$	8.02573	+	8.02573i	0.429607	+	0.429607i	−0.458887	+	0.888495i	$0.651752\pi$
$350$	−0.0538407	−	0.129983i	−0.00287791	−	0.00694788i
$351$	−24.1894	+	10.0196i	−1.29114	+	0.534806i
$352$	−0.447478	+	1.08031i	−0.0238507	+	0.0575806i
$353$			20.2610i			1.07839i	0.842182	+	0.539193i	$0.181271\pi$
$353$			20.2610i			1.07839i	−0.842182	+	0.539193i	$0.818729\pi$
$354$	−13.9563	−	5.78087i	−0.741767	−	0.307250i
$355$	10.8897	−	10.8897i	0.577964	−	0.577964i
$356$	−26.6476			−1.41232
$357$	5.91867	−	13.4768i	0.313249	−	0.713267i
$358$	−32.6561			−1.72593
$359$	−6.29071	+	6.29071i	−0.332011	+	0.332011i	−0.853350	−	0.521339i	$-0.825433\pi$
$359$	−6.29071	+	6.29071i	−0.332011	+	0.332011i	0.521339	+	0.853350i	$0.325433\pi$
$360$	50.5294	+	20.9300i	2.66313	+	1.10311i
$361$			3.79380i			0.199674i
$362$	14.3321	−	34.6007i	0.753276	−	1.81857i
$363$	2.67857	−	1.10950i	0.140588	−	0.0582336i
$364$	6.85518	+	16.5499i	0.359309	+	0.867449i
$365$	−2.24255	−	2.24255i	−0.117381	−	0.117381i
$366$	−73.7240	−	73.7240i	−3.85362	−	3.85362i
$367$	−5.78203	−	13.9590i	−0.301819	−	0.728656i	−0.999920	−	0.0126567i	$-0.995971\pi$
$367$	−5.78203	−	13.9590i	−0.301819	−	0.728656i	0.698101	−	0.716000i	$-0.254029\pi$
$368$	27.1267	−	11.2363i	1.41408	−	0.585730i
$369$	14.4256	−	34.8265i	0.750967	−	1.81300i
$370$			29.0218i			1.50877i
$371$	−7.53603	−	3.12153i	−0.391251	−	0.162062i
$372$	−55.6859	+	55.6859i	−2.88718	+	2.88718i
$373$	17.3128			0.896421			0.448211	−	0.893928i	$-0.352061\pi$
$373$	17.3128			0.896421			0.448211	+	0.893928i	$0.352061\pi$
$374$	7.21461	−	6.91617i	0.373059	−	0.357626i
$375$	32.5657			1.68169
$376$	6.37677	−	6.37677i	0.328857	−	0.328857i
$377$	22.5369	+	9.33508i	1.16071	+	0.480781i
$378$		−	20.8175i		−	1.07074i
$379$	−5.95011	+	14.3648i	−0.305636	+	0.737871i	0.694200	+	0.719782i	$0.255758\pi$
$379$	−5.95011	+	14.3648i	−0.305636	+	0.737871i	−0.999836	+	0.0180893i	$0.994242\pi$
$380$	−31.0731	+	12.8709i	−1.59402	+	0.660263i
$381$	−9.54606	−	23.0462i	−0.489059	−	1.18069i
$382$	−37.3899	−	37.3899i	−1.91303	−	1.91303i
$383$	9.12858	+	9.12858i	0.466449	+	0.466449i	0.900762	−	0.434313i	$-0.143009\pi$
$383$	9.12858	+	9.12858i	0.466449	+	0.466449i	−0.434313	+	0.900762i	$0.643009\pi$
$384$	22.6092	+	54.5834i	1.15377	+	2.78545i
$385$	2.53172	−	1.04867i	0.129028	−	0.0534452i
$386$	−19.9076	+	48.0611i	−1.01327	+	2.44625i
$387$		−	36.8539i		−	1.87339i
$388$	−4.29028	−	1.77709i	−0.217806	−	0.0902182i
$389$	15.6113	−	15.6113i	0.791525	−	0.791525i	−0.190217	−	0.981742i	$-0.560919\pi$
$389$	15.6113	−	15.6113i	0.791525	−	0.791525i	0.981742	+	0.190217i	$0.0609192\pi$
$390$	−58.7105			−2.97292
$391$	37.0289	+	0.782052i	1.87263	+	0.0395500i
$392$	24.9306			1.25918
$393$	−28.5453	+	28.5453i	−1.43992	+	1.43992i
$394$	−13.0557	−	5.40786i	−0.657738	−	0.272444i
$395$			26.0952i			1.31299i
$396$	8.01723	−	19.3553i	0.402881	−	0.972641i
$397$	19.5967	−	8.11723i	0.983531	−	0.407392i	0.167799	−	0.985821i	$-0.446334\pi$
$397$	19.5967	−	8.11723i	0.983531	−	0.407392i	0.815733	+	0.578429i	$0.196334\pi$
$398$	0.746683	+	1.80265i	0.0374279	+	0.0903588i
$399$	9.84361	+	9.84361i	0.492797	+	0.492797i
$400$	−0.108951	−	0.108951i	−0.00544753	−	0.00544753i
$401$	−6.14432	−	14.8337i	−0.306833	−	0.740760i	−0.999804	−	0.0197946i	$-0.993699\pi$
$401$	−6.14432	−	14.8337i	−0.306833	−	0.740760i	0.692971	−	0.720965i	$-0.256301\pi$
$402$	2.03909	−	0.844620i	0.101701	−	0.0421258i
$403$	10.0684	−	24.3072i	0.501540	−	1.21083i
$404$			1.65740i			0.0824587i
$405$	8.23403	+	3.41065i	0.409152	+	0.169476i
$406$	−13.7145	+	13.7145i	−0.680641	+	0.680641i
$407$	5.37988			0.266671
$408$	1.14751	−	54.3328i	0.0568102	−	2.68987i
$409$	7.72738			0.382095			0.191047	−	0.981581i	$-0.438812\pi$
$409$	7.72738			0.382095			0.191047	+	0.981581i	$0.438812\pi$
$410$	26.5997	−	26.5997i	1.31367	−	1.31367i
$411$	35.1108	+	14.5434i	1.73189	+	0.717371i
$412$			29.9927i			1.47763i
$413$	−1.01287	+	2.44529i	−0.0498401	+	0.120325i
$414$	108.744	−	45.0433i	5.34448	−	2.21376i
$415$	−3.20397	−	7.73508i	−0.157277	−	0.379700i
$416$	−3.10380	−	3.10380i	−0.152176	−	0.152176i
$417$	18.2989	+	18.2989i	0.896103	+	0.896103i
$418$	3.61721	+	8.73271i	0.176923	+	0.427131i
$419$	−10.8159	+	4.48010i	−0.528392	+	0.218867i	−0.630899	−	0.775865i	$-0.717314\pi$
$419$	−10.8159	+	4.48010i	−0.528392	+	0.218867i	0.102506	+	0.994732i	$0.467314\pi$
$420$	11.7830	−	28.4468i	0.574954	−	1.38806i
$421$		−	31.9585i		−	1.55756i	−0.627296	−	0.778781i	$-0.715838\pi$
$421$		−	31.9585i		−	1.55756i	0.627296	−	0.778781i	$-0.284162\pi$
$422$	−15.3830	−	6.37185i	−0.748833	−	0.310177i
$423$	7.58243	−	7.58243i	0.368670	−	0.368670i
$424$	−30.1164			−1.46258
$425$	−0.0705692	−	0.181093i	−0.00342311	−	0.00878431i
$426$	−48.6310			−2.35618
$427$	−12.9172	+	12.9172i	−0.625109	+	0.625109i
$428$	−23.8382	−	9.87411i	−1.15226	−	0.477283i
$429$			10.8834i			0.525455i
$430$	14.0741	−	33.9779i	0.678713	−	1.63856i
$431$	−0.554549	+	0.229702i	−0.0267117	+	0.0110643i	−0.395999	−	0.918251i	$-0.629602\pi$
$431$	−0.554549	+	0.229702i	−0.0267117	+	0.0110643i	0.369288	+	0.929315i	$0.379602\pi$
$432$	−8.72453	−	21.0629i	−0.419759	−	1.01339i
$433$	−10.0936	−	10.0936i	−0.485067	−	0.485067i	0.421679	−	0.906745i	$-0.361441\pi$
$433$	−10.0936	−	10.0936i	−0.485067	−	0.485067i	−0.906745	+	0.421679i	$0.861441\pi$
$434$	14.7918	+	14.7918i	0.710030	+	0.710030i
$435$	−16.0456	−	38.7376i	−0.769329	−	1.85733i
$436$	−26.6165	+	11.0249i	−1.27470	+	0.527997i
$437$	−13.4049	+	32.3623i	−0.641243	+	1.54810i
$438$			10.0148i			0.478524i
$439$	11.6904	+	4.84233i	0.557954	+	0.231112i	0.643797	−	0.765197i	$-0.277358\pi$
$439$	11.6904	+	4.84233i	0.557954	+	0.231112i	−0.0858429	+	0.996309i	$0.527358\pi$
$440$	7.15418	−	7.15418i	0.341062	−	0.341062i
$441$	29.6442			1.41163
$442$	13.6219	+	34.9563i	0.647930	+	1.66270i
$443$	10.6345			0.505260			0.252630	−	0.967563i	$-0.418705\pi$
$443$	10.6345			0.505260			0.252630	+	0.967563i	$0.418705\pi$
$444$	42.7441	−	42.7441i	2.02854	−	2.02854i
$445$	−14.1374	−	5.85592i	−0.670179	−	0.277597i
$446$		−	38.8341i		−	1.83885i
$447$	3.99565	−	9.64636i	0.188988	−	0.456257i
$448$	10.6611	−	4.41599i	0.503691	−	0.208636i
$449$	6.45647	+	15.5873i	0.304700	+	0.735611i	0.999860	+	0.0167552i	$0.00533361\pi$
$449$	6.45647	+	15.5873i	0.304700	+	0.735611i	−0.695160	+	0.718855i	$0.744666\pi$
$450$	−0.436756	−	0.436756i	−0.0205889	−	0.0205889i
$451$	−4.93089	−	4.93089i	−0.232187	−	0.232187i
$452$	26.1496	+	63.1308i	1.22998	+	2.96942i
$453$	−8.74577	+	3.62262i	−0.410912	+	0.170205i
$454$	2.53834	−	6.12810i	0.119130	−	0.287606i
$455$			10.2867i			0.482248i
$456$	47.4854	+	19.6691i	2.22371	+	0.921089i
$457$	3.86444	−	3.86444i	0.180771	−	0.180771i	−0.610921	−	0.791692i	$-0.709201\pi$
$457$	3.86444	−	3.86444i	0.180771	−	0.180771i	0.791692	+	0.610921i	$0.209201\pi$
$458$	−33.9501			−1.58638
$459$	0.607234	−	28.7515i	0.0283432	−	1.34201i
$460$	77.4769			3.61238
$461$	3.26885	−	3.26885i	0.152246	−	0.152246i	−0.626875	−	0.779120i	$-0.715666\pi$
$461$	3.26885	−	3.26885i	0.152246	−	0.152246i	0.779120	+	0.626875i	$0.215666\pi$
$462$	−7.99462	−	3.31148i	−0.371943	−	0.154064i
$463$		−	27.5566i		−	1.28066i	−0.768098	−	0.640332i	$-0.778797\pi$
$463$		−	27.5566i		−	1.28066i	0.768098	−	0.640332i	$-0.221203\pi$
$464$	−8.12849	+	19.6239i	−0.377356	+	0.911017i
$465$	−41.7804	+	17.3060i	−1.93752	+	0.802547i
$466$	−16.2365	−	39.1985i	−0.752143	−	1.81583i
$467$	21.1421	+	21.1421i	0.978339	+	0.978339i	0.999770	−	0.0214310i	$-0.00682222\pi$
$467$	21.1421	+	21.1421i	0.978339	+	0.978339i	−0.0214310	+	0.999770i	$0.506822\pi$
$468$	55.6092	+	55.6092i	2.57054	+	2.57054i
$469$	−0.147986	−	0.357271i	−0.00683338	−	0.0164972i
$470$	9.88635	−	4.09506i	0.456023	−	0.188891i
$471$	16.1161	−	38.9077i	0.742591	−	1.79277i
$472$			9.77213i			0.449799i
$473$	−6.29861	−	2.60897i	−0.289610	−	0.119961i
$474$	58.2678	−	58.2678i	2.67633	−	2.67633i
$475$	0.183817			0.00843412
$476$	−19.6712	−	0.415455i	−0.901626	−	0.0190424i
$477$	−35.8105			−1.63965
$478$	−23.4960	+	23.4960i	−1.07468	+	1.07468i
$479$	−3.66324	−	1.51736i	−0.167378	−	0.0693301i	0.297421	−	0.954746i	$-0.403873\pi$
$479$	−3.66324	−	1.51736i	−0.167378	−	0.0693301i	−0.464799	+	0.885416i	$0.653873\pi$
$480$			7.54480i			0.344371i
$481$	−7.72839	+	18.6580i	−0.352384	+	0.850731i
$482$	41.3550	−	17.1298i	1.88367	−	0.780240i
$483$	−12.2719	−	29.6270i	−0.558391	−	1.34807i
$484$	−2.74041	−	2.74041i	−0.124564	−	0.124564i
$485$	−1.88561	−	1.88561i	−0.0856213	−	0.0856213i
$486$	8.63957	+	20.8578i	0.391899	+	0.946127i
$487$	−34.0791	+	14.1160i	−1.54427	+	0.639659i	−0.982269	−	0.187476i	$-0.939969\pi$
$487$	−34.0791	+	14.1160i	−1.54427	+	0.639659i	−0.562003	+	0.827135i	$0.689969\pi$
$488$	−25.8107	+	62.3124i	−1.16839	+	2.82075i
$489$			27.6211i			1.24907i
$490$	27.3308	+	11.3208i	1.23468	+	0.511421i
$491$	−20.7918	+	20.7918i	−0.938323	+	0.938323i	−0.998205	−	0.0598827i	$-0.980927\pi$
$491$	−20.7918	+	20.7918i	−0.938323	+	0.938323i	0.0598827	+	0.998205i	$0.480927\pi$
$492$	−78.3536			−3.53245
$493$	−19.3415	+	18.5414i	−0.871099	+	0.835065i
$494$	−35.4822			−1.59642
$495$	8.50682	−	8.50682i	0.382353	−	0.382353i
$496$	21.1654	+	8.76698i	0.950353	+	0.393649i
$497$			8.52067i			0.382204i
$498$	−10.1175	+	24.4257i	−0.453375	+	1.09454i
$499$	−34.2183	+	14.1737i	−1.53182	+	0.634502i	−0.979917	−	0.199405i	$-0.936099\pi$
$499$	−34.2183	+	14.1737i	−1.53182	+	0.634502i	−0.551906	+	0.833907i	$0.686099\pi$
$500$	−16.6588	−	40.2179i	−0.745004	−	1.79860i
$501$	−1.03320	−	1.03320i	−0.0461602	−	0.0461602i
$502$	−0.806863	−	0.806863i	−0.0360121	−	0.0360121i
$503$	−3.07113	−	7.41437i	−0.136935	−	0.330591i	0.840505	−	0.541804i	$-0.182259\pi$
$503$	−3.07113	−	7.41437i	−0.136935	−	0.330591i	−0.977440	+	0.211213i	$0.932259\pi$
$504$	−27.9568	+	11.5801i	−1.24529	+	0.515818i
$505$	−0.364220	+	0.879306i	−0.0162076	+	0.0391286i
$506$		−	21.7739i		−	0.967969i
$507$	−2.92337	−	1.21090i	−0.129831	−	0.0537779i
$508$	−23.5783	+	23.5783i	−1.04612	+	1.04612i
$509$	−15.1263			−0.670463			−0.335231	−	0.942136i	$-0.608815\pi$
$509$	−15.1263			−0.670463			−0.335231	+	0.942136i	$0.608815\pi$
$510$	25.9301	−	59.0427i	1.14820	−	2.61445i
$511$	1.75469			0.0776231
$512$	23.7177	−	23.7177i	1.04818	−	1.04818i
$513$	25.1281	+	10.4084i	1.10943	+	0.459542i
$514$		−	9.44790i		−	0.416729i
$515$	−6.59102	+	15.9121i	−0.290435	+	0.701173i
$516$	−70.7723	+	29.3148i	−3.11557	+	1.29051i
$517$	−0.759117	−	1.83267i	−0.0333859	−	0.0806008i
$518$	−11.3541	−	11.3541i	−0.498870	−	0.498870i
$519$	30.3175	+	30.3175i	1.33079	+	1.33079i
$520$	14.5342	+	35.0887i	0.637367	+	1.53874i
$521$	22.0421	−	9.13013i	0.965682	−	0.399998i	0.156579	−	0.987665i	$-0.449954\pi$
$521$	22.0421	−	9.13013i	0.965682	−	0.399998i	0.809103	+	0.587667i	$0.199954\pi$
$522$	−32.5851	+	78.6673i	−1.42621	+	3.44317i
$523$			2.84189i			0.124267i	0.998068	+	0.0621336i	$0.0197905\pi$
$523$			2.84189i			0.124267i	−0.998068	+	0.0621336i	$0.980210\pi$
$524$	49.8548	+	20.6506i	2.17792	+	0.902124i
$525$	−0.118993	+	0.118993i	−0.00519327	+	0.00519327i
$526$	−14.0037			−0.610589
$527$	19.9979	+	20.8608i	0.871121	+	0.908711i
$528$	−9.47668			−0.412420
$529$	40.7939	−	40.7939i	1.77365	−	1.77365i
$530$	−33.0159	−	13.6756i	−1.43412	−	0.594031i
$531$			11.6197i			0.504254i
$532$	7.12118	−	17.1921i	0.308742	−	0.745370i
$533$	24.1843	−	10.0175i	1.04754	−	0.433904i
$534$	18.4917	+	44.6430i	0.800216	+	1.93189i
$535$	−10.4771	−	10.4771i	−0.452964	−	0.452964i
$536$	−1.00958	−	1.00958i	−0.0436074	−	0.0436074i
$537$	14.9475	+	36.0865i	0.645032	+	1.55725i
$538$	67.6155	−	28.0073i	2.91511	−	1.20748i
$539$	2.09858	−	5.06641i	0.0903921	−	0.218226i
$540$		−	60.1579i		−	2.58878i
$541$	1.66740	+	0.690658i	0.0716870	+	0.0296937i	0.418239	−	0.908337i	$-0.362648\pi$
$541$	1.66740	+	0.690658i	0.0716870	+	0.0296937i	−0.346552	+	0.938031i	$0.612648\pi$
$542$	8.30884	−	8.30884i	0.356895	−	0.356895i
$543$	−44.7954			−1.92235
$544$	4.49219	−	1.75053i	0.192601	−	0.0750536i
$545$	−16.5437			−0.708654
$546$	22.9691	−	22.9691i	0.982988	−	0.982988i
$547$	−30.5479	−	12.6534i	−1.30613	−	0.541019i	−0.382381	−	0.924005i	$-0.624896\pi$
$547$	−30.5479	−	12.6534i	−1.30613	−	0.541019i	−0.923754	+	0.382986i	$0.874896\pi$
$548$		−	50.8005i		−	2.17009i
$549$	−30.6907	+	74.0939i	−1.30985	+	3.16225i
$550$	−0.105564	+	0.0437259i	−0.00450125	+	0.00186448i
$551$	−9.69732	−	23.4114i	−0.413120	−	0.997359i
$552$	−83.7206	−	83.7206i	−3.56339	−	3.56339i
$553$	−10.2091	−	10.2091i	−0.434137	−	0.434137i
$554$	−10.6984	−	25.8283i	−0.454533	−	1.09734i
$555$	32.0703	−	13.2840i	1.36131	−	0.563873i
$556$	13.2380	−	31.9594i	0.561418	−	1.35538i
$557$		−	19.3131i		−	0.818323i	−0.912462	−	0.409162i	$-0.865821\pi$
$557$		−	19.3131i		−	0.818323i	0.912462	−	0.409162i	$-0.134179\pi$
$558$	84.8466	+	35.1446i	3.59184	+	1.48779i
$559$	18.0964	−	18.0964i	0.765395	−	0.765395i
$560$	−8.95711			−0.378507
$561$	−10.9450	−	4.80676i	−0.462097	−	0.202942i
$562$	−49.0358			−2.06845
$563$	16.8401	−	16.8401i	0.709726	−	0.709726i	−0.256752	−	0.966477i	$-0.582652\pi$
$563$	16.8401	−	16.8401i	0.709726	−	0.709726i	0.966477	+	0.256752i	$0.0826523\pi$
$564$	−20.5922	−	8.52957i	−0.867088	−	0.359160i
$565$			39.2395i			1.65082i
$566$	−19.6950	+	47.5479i	−0.827841	+	1.99859i
$567$	−4.55571	+	1.88704i	−0.191322	+	0.0792480i
$568$	12.0389	+	29.0646i	0.505143	+	1.21952i
$569$	26.3498	+	26.3498i	1.10464	+	1.10464i	0.993843	+	0.110798i	$0.0353408\pi$
$569$	26.3498	+	26.3498i	1.10464	+	1.10464i	0.110798	+	0.993843i	$0.464659\pi$
$570$	43.1255	+	43.1255i	1.80633	+	1.80633i
$571$	−9.46560	−	22.8520i	−0.396123	−	0.956326i	−0.988576	−	0.150721i	$-0.951840\pi$
$571$	−9.46560	−	22.8520i	−0.396123	−	0.956326i	0.592453	−	0.805605i	$-0.298160\pi$
$572$	13.4407	−	5.56733i	0.561985	−	0.232782i
$573$	−24.2032	+	58.4317i	−1.01110	+	2.44102i
$574$			20.8130i			0.868720i
$575$	−0.391205	−	0.162043i	−0.0163144	−	0.00675764i
$576$	35.8225	−	35.8225i	1.49260	−	1.49260i
$577$	32.3285			1.34585			0.672926	−	0.739710i	$-0.265037\pi$
$577$	32.3285			1.34585			0.672926	+	0.739710i	$0.265037\pi$
$578$	−41.1704	−	1.73982i	−1.71246	−	0.0723668i
$579$	62.2218			2.58585
$580$	−39.6319	+	39.6319i	−1.64563	+	1.64563i
$581$	4.27965	+	1.77269i	0.177550	+	0.0735435i
$582$			8.42075i			0.349051i
$583$	−2.53510	+	6.12028i	−0.104993	+	0.253476i
$584$	5.98538	−	2.47922i	0.247677	−	0.102591i
$585$	17.2822	+	41.7229i	0.714530	+	1.72503i
$586$	30.5951	+	30.5951i	1.26387	+	1.26387i
$587$	−33.0349	−	33.0349i	−1.36350	−	1.36350i	−0.869416	−	0.494081i	$-0.835505\pi$
$587$	−33.0349	−	33.0349i	−1.36350	−	1.36350i	−0.494081	−	0.869416i	$-0.664495\pi$
$588$	−23.5800	−	56.9271i	−0.972422	−	2.34763i
$589$	−25.2504	+	10.4590i	−1.04042	+	0.430957i
$590$	−4.43745	+	10.7130i	−0.182687	+	0.441046i
$591$			16.9025i			0.695275i
$592$	−16.2464	−	6.72947i	−0.667722	−	0.276579i
$593$	−25.6963	+	25.6963i	−1.05522	+	1.05522i	−0.0568350	+	0.998384i	$0.518101\pi$
$593$	−25.6963	+	25.6963i	−1.05522	+	1.05522i	−0.998384	+	0.0568350i	$0.981899\pi$
$594$	−16.9066			−0.693687
$595$	−10.3449	−	4.54323i	−0.424100	−	0.186254i
$596$	−13.9570			−0.571700
$597$	1.65024	−	1.65024i	0.0675397	−	0.0675397i
$598$	75.5142	+	31.2790i	3.08801	+	1.27909i
$599$		−	34.2393i		−	1.39898i	−0.714643	−	0.699490i	$-0.753411\pi$
$599$		−	34.2393i		−	1.39898i	0.714643	−	0.699490i	$-0.246589\pi$
$600$	−0.237766	+	0.574018i	−0.00970676	+	0.0234342i
$601$	23.6248	−	9.78573i	0.963678	−	0.399168i	0.155323	−	0.987864i	$-0.450358\pi$
$601$	23.6248	−	9.78573i	0.963678	−	0.399168i	0.808355	+	0.588695i	$0.200358\pi$
$602$	7.78689	+	18.7992i	0.317370	+	0.766199i
$603$	−1.20047	−	1.20047i	−0.0488867	−	0.0488867i
$604$	8.94769	+	8.94769i	0.364076	+	0.364076i
$605$	−0.851663	−	2.05610i	−0.0346250	−	0.0835922i
$606$	2.77666	−	1.15013i	0.112794	−	0.0467209i
$607$	−5.67753	+	13.7068i	−0.230444	+	0.556341i	−0.996230	−	0.0867550i	$-0.972350\pi$
$607$	−5.67753	+	13.7068i	−0.230444	+	0.556341i	0.765786	+	0.643096i	$0.222350\pi$
$608$			4.55976i			0.184923i
$609$	21.4327	+	8.87770i	0.868495	+	0.359742i
$610$	−56.5913	+	56.5913i	−2.29131	+	2.29131i
$611$	7.44640			0.301249
$612$	−80.4842	+	31.3634i	−3.25338	+	1.26779i
$613$	9.65494			0.389959			0.194980	−	0.980807i	$-0.437536\pi$
$613$	9.65494			0.389959			0.194980	+	0.980807i	$0.437536\pi$
$614$	−8.81380	+	8.81380i	−0.355696	+	0.355696i
$615$	−41.5692	−	17.2185i	−1.67623	−	0.694318i
$616$			5.59781i			0.225542i
$617$	11.9087	−	28.7503i	0.479428	−	1.15744i	−0.480449	−	0.877022i	$-0.659526\pi$
$617$	11.9087	−	28.7503i	0.479428	−	1.15744i	0.959878	−	0.280419i	$-0.0904735\pi$
$618$	50.2471	−	20.8130i	2.02124	−	0.837224i
$619$	−12.7935	−	30.8863i	−0.514216	−	1.24143i	−0.941409	−	0.337267i	$-0.890498\pi$
$619$	−12.7935	−	30.8863i	−0.514216	−	1.24143i	0.427193	−	0.904160i	$-0.359502\pi$
$620$	42.7450	+	42.7450i	1.71668	+	1.71668i
$621$	−44.3029	−	44.3029i	−1.77781	−	1.77781i
$622$	−13.5673	−	32.7543i	−0.543998	−	1.31333i
$623$	7.82193	−	3.23995i	0.313379	−	0.129806i
$624$	13.6136	−	32.8661i	0.544980	−	1.31570i
$625$		−	24.7621i		−	0.990483i
$626$	23.2656	+	9.63691i	0.929879	+	0.385168i
$627$	7.99435	−	7.99435i	0.319263	−	0.319263i
$628$	−56.2942			−2.24638
$629$	−15.3502	−	16.0126i	−0.612053	−	0.638464i
$630$	−35.9068			−1.43056
$631$	8.57062	−	8.57062i	0.341191	−	0.341191i	−0.515624	−	0.856815i	$-0.672440\pi$
$631$	8.57062	−	8.57062i	0.341191	−	0.341191i	0.856815	+	0.515624i	$0.172440\pi$
$632$	−49.2487	−	20.3995i	−1.95901	−	0.811447i
$633$			19.9154i			0.791568i
$634$	−12.4219	+	29.9891i	−0.493337	+	1.19102i
$635$	−17.6905	+	7.32765i	−0.702026	+	0.290789i
$636$	28.4848	+	68.7685i	1.12950	+	2.72685i
$637$	14.5562	+	14.5562i	0.576737	+	0.576737i
$638$	11.1381	+	11.1381i	0.440960	+	0.440960i
$639$	14.3151	+	34.5598i	0.566298	+	1.36717i
$640$	41.8987	−	17.3550i	1.65619	−	0.686017i
$641$	4.57115	−	11.0357i	0.180549	−	0.435885i	−0.807531	−	0.589826i	$-0.799196\pi$
$641$	4.57115	−	11.0357i	0.180549	−	0.435885i	0.988080	+	0.153941i	$0.0491965\pi$
$642$			46.7884i			1.84659i
$643$	23.7833	+	9.85136i	0.937921	+	0.388500i	0.798678	−	0.601759i	$-0.205533\pi$
$643$	23.7833	+	9.85136i	0.937921	+	0.388500i	0.139243	+	0.990258i	$0.455533\pi$
$644$	−30.3110	+	30.3110i	−1.19442	+	1.19442i
$645$	−43.9891			−1.73207
$646$	15.6711	−	35.6829i	0.616570	−	1.40393i
$647$	18.9212			0.743868			0.371934	−	0.928259i	$-0.378695\pi$
$647$	18.9212			0.743868			0.371934	+	0.928259i	$0.378695\pi$
$648$	−12.8736	+	12.8736i	−0.505723	+	0.505723i
$649$	1.98590	+	0.822588i	0.0779535	+	0.0322894i
$650$		−	0.428920i		−	0.0168236i
$651$	9.57504	−	23.1162i	0.375275	−	0.905995i
$652$	34.1114	−	14.1294i	1.33591	−	0.553350i
$653$	8.50682	+	20.5373i	0.332898	+	0.803686i	0.998360	+	0.0572544i	$0.0182346\pi$
$653$	8.50682	+	20.5373i	0.332898	+	0.803686i	−0.665462	+	0.746432i	$0.731765\pi$
$654$	36.9403	+	36.9403i	1.44448	+	1.44448i
$655$	21.9116	+	21.9116i	0.856158	+	0.856158i
$656$	8.72266	+	21.0584i	0.340563	+	0.822191i
$657$	7.11703	−	2.94797i	0.277662	−	0.115011i
$658$	−2.26571	+	5.46990i	−0.0883264	+	0.213239i
$659$		−	2.77302i		−	0.108021i	−0.998540	−	0.0540107i	$-0.982800\pi$
$659$		−	2.77302i		−	0.108021i	0.998540	−	0.0540107i	$-0.0172005\pi$
$660$	−23.1026	−	9.56943i	−0.899269	−	0.372490i
$661$	−7.92234	+	7.92234i	−0.308143	+	0.308143i	−0.844189	−	0.536046i	$-0.819918\pi$
$661$	−7.92234	+	7.92234i	−0.308143	+	0.308143i	0.536046	+	0.844189i	$0.319918\pi$
$662$	−1.50744			−0.0585884
$663$	32.3932	−	31.0532i	1.25805	−	1.20601i
$664$	17.1028			0.663718
$665$	7.55605	−	7.55605i	0.293011	−	0.293011i
$666$	−65.1276	−	26.9767i	−2.52364	−	1.04533i
$667$			58.3734i			2.26023i
$668$	−0.747454	+	1.80451i	−0.0289198	+	0.0698187i
$669$	−42.9133	+	17.7753i	−1.65913	+	0.687232i
$670$	−0.648338	−	1.56523i	−0.0250475	−	0.0604700i
$671$	10.4905	+	10.4905i	0.404983	+	0.404983i
$672$	−2.95173	−	2.95173i	−0.113865	−	0.113865i
$673$	−0.897621	−	2.16705i	−0.0346007	−	0.0835336i	0.905635	−	0.424059i	$-0.139395\pi$
$673$	−0.897621	−	2.16705i	−0.0346007	−	0.0835336i	−0.940235	+	0.340525i	$0.889395\pi$
$674$	34.1249	−	14.1350i	1.31444	−	0.544459i
$675$	−0.125820	+	0.303756i	−0.00484281	+	0.0116916i
$676$			4.22972i			0.162681i
$677$	−12.3195	−	5.10290i	−0.473477	−	0.196120i	0.133168	−	0.991093i	$-0.457485\pi$
$677$	−12.3195	−	5.10290i	−0.473477	−	0.196120i	−0.606645	+	0.794973i	$0.707485\pi$
$678$	87.6176	−	87.6176i	3.36493	−	3.36493i
$679$	1.47540			0.0566208
$680$	−41.7064	−	0.880839i	−1.59937	−	0.0337787i
$681$	−7.93368			−0.304019
$682$	12.0130	−	12.0130i	0.460000	−	0.460000i
$683$	−18.5922	−	7.70114i	−0.711411	−	0.294676i	−0.00252262	−	0.999997i	$-0.500803\pi$
$683$	−18.5922	−	7.70114i	−0.711411	−	0.294676i	−0.708888	+	0.705321i	$0.750803\pi$
$684$		−	81.6949i		−	3.12368i
$685$	11.1636	−	26.9514i	0.426540	−	1.02976i
$686$	−34.4238	+	14.2588i	−1.31431	+	0.544403i
$687$	15.5398	+	37.5163i	0.592879	+	1.43134i
$688$	15.7573	+	15.7573i	0.600743	+	0.600743i
$689$	−17.5840	−	17.5840i	−0.669897	−	0.669897i
$690$	−53.7640	−	129.798i	−2.04676	−	4.94132i
$691$	−6.49661	+	2.69098i	−0.247143	+	0.102370i	−0.502816	−	0.864393i	$-0.667703\pi$
$691$	−6.49661	+	2.69098i	−0.247143	+	0.102370i	0.255674	+	0.966763i	$0.417703\pi$
$692$	21.9327	−	52.9502i	0.833755	−	2.01286i
$693$			6.65619i			0.252848i
$694$	−37.1436	−	15.3854i	−1.40995	−	0.584021i
$695$	14.0464	−	14.0464i	0.532812	−	0.532812i
$696$	85.6516			3.24662
$697$	−0.607104	+	28.7454i	−0.0229957	+	1.08881i
$698$	−27.5120			−1.04135
$699$	−35.8842	+	35.8842i	−1.35726	+	1.35726i
$700$	0.207823	+	0.0860831i	0.00785497	+	0.00325364i
$701$		−	40.4381i		−	1.52733i	−0.645615	−	0.763663i	$-0.723399\pi$
$701$		−	40.4381i		−	1.52733i	0.645615	−	0.763663i	$-0.276601\pi$
$702$	24.2870	−	58.6340i	0.916653	−	2.21300i
$703$	19.3820	−	8.02828i	0.731005	−	0.302792i
$704$	−3.58638	−	8.65829i	−0.135167	−	0.326322i
$705$	−9.05044	−	9.05044i	−0.340859	−	0.340859i
$706$	−34.7272	−	34.7272i	−1.30698	−	1.30698i
$707$	−0.201515	−	0.486501i	−0.00757876	−	0.0182967i
$708$	22.3139	−	9.24274i	0.838609	−	0.347363i
$709$	3.11253	−	7.51431i	0.116894	−	0.282206i	−0.854594	−	0.519297i	$-0.826194\pi$
$709$	3.11253	−	7.51431i	0.116894	−	0.282206i	0.971487	+	0.237091i	$0.0761939\pi$
$710$			37.3296i			1.40096i
$711$	−58.5601	−	24.2564i	−2.19618	−	0.909686i
$712$	22.1034	−	22.1034i	0.828360	−	0.828360i
$713$	62.9586			2.35782
$714$	12.9545	+	33.2436i	0.484811	+	1.24411i
$715$	8.35420			0.312429
$716$	36.9196	−	36.9196i	1.37975	−	1.37975i
$717$	36.7188	+	15.2094i	1.37129	+	0.568006i
$718$		−	21.5644i		−	0.804777i
$719$	3.90076	−	9.41726i	0.145474	−	0.351205i	−0.834301	−	0.551310i	$-0.814128\pi$
$719$	3.90076	−	9.41726i	0.145474	−	0.351205i	0.979774	+	0.200105i	$0.0641283\pi$
$720$	−36.3300	+	15.0484i	−1.35394	+	0.560821i
$721$	−3.64667	−	8.80384i	−0.135809	−	0.327872i
$722$	−6.50253	−	6.50253i	−0.241999	−	0.241999i
$723$	−37.8583	−	37.8583i	−1.40797	−	1.40797i
$724$	22.9148	+	55.3212i	0.851622	+	2.05600i
$725$	0.283004	−	0.117224i	0.0105105	−	0.00435360i
$726$	−2.68937	+	6.49271i	−0.0998119	+	0.240967i
$727$		−	36.0707i		−	1.33779i	−0.743358	−	0.668894i	$-0.766768\pi$
$727$		−	36.0707i		−	1.33779i	0.743358	−	0.668894i	$-0.233232\pi$
$728$	−19.4138	−	8.04145i	−0.719523	−	0.298036i
$729$	27.5894	−	27.5894i	1.02183	−	1.02183i
$730$	7.68743			0.284525
$731$	10.2063	+	26.1912i	0.377494	+	0.968716i
$732$	166.698			6.16135
$733$	−25.1929	+	25.1929i	−0.930523	+	0.930523i	−0.997738	−	0.0672159i	$-0.978588\pi$
$733$	−25.1929	+	25.1929i	−0.930523	+	0.930523i	0.0672159	+	0.997738i	$0.478588\pi$
$734$	33.8360	+	14.0153i	1.24891	+	0.517315i
$735$		−	35.3835i		−	1.30514i
$736$	4.01962	−	9.70422i	0.148165	−	0.357702i
$737$	−0.290152	+	0.120185i	−0.0106879	+	0.00442707i
$738$	34.9669	+	84.4177i	1.28715	+	3.10746i
$739$	−17.7490	−	17.7490i	−0.652909	−	0.652909i	0.300783	−	0.953693i	$-0.402752\pi$
$739$	−17.7490	−	17.7490i	−0.652909	−	0.652909i	−0.953693	+	0.300783i	$0.902752\pi$
$740$	−32.8108	−	32.8108i	−1.20615	−	1.20615i
$741$	16.2411	+	39.2094i	0.596631	+	1.44039i
$742$	18.2670	−	7.56642i	0.670601	−	0.277772i
$743$	1.86034	−	4.49125i	0.0682491	−	0.164768i	−0.886074	−	0.463543i	$-0.846578\pi$
$743$	1.86034	−	4.49125i	0.0682491	−	0.164768i	0.954324	+	0.298775i	$0.0965780\pi$
$744$		−	92.3796i		−	3.38680i
$745$	−7.40464	−	3.06710i	−0.271285	−	0.112370i
$746$	−29.6739	+	29.6739i	−1.08644	+	1.08644i
$747$	20.3365			0.744072
$748$	−0.337406	+	15.9756i	−0.0123368	+	0.584127i
$749$	8.19783			0.299542
$750$	−55.8174	+	55.8174i	−2.03816	+	2.03816i
$751$	−17.2763	−	7.15607i	−0.630420	−	0.261129i	0.0445115	−	0.999009i	$-0.485827\pi$
$751$	−17.2763	−	7.15607i	−0.630420	−	0.261129i	−0.674932	+	0.737880i	$0.735827\pi$
$752$			6.48392i			0.236444i
$753$	−0.522299	+	1.26094i	−0.0190336	+	0.0459512i
$754$	−54.6282	+	22.6278i	−1.98944	+	0.824054i
$755$	2.78076	+	6.71334i	0.101202	+	0.244323i
$756$	23.5354	+	23.5354i	0.855973	+	0.855973i
$757$	11.1972	+	11.1972i	0.406968	+	0.406968i	0.880680	−	0.473712i	$-0.157086\pi$
$757$	11.1972	+	11.1972i	0.406968	+	0.406968i	−0.473712	+	0.880680i	$0.657086\pi$
$758$	−14.4227	−	34.8196i	−0.523858	−	1.26470i
$759$	−24.0611	+	9.96645i	−0.873364	+	0.361759i
$760$	15.0982	−	36.4502i	0.547669	−	1.32219i
$761$			16.7710i			0.607947i	0.952681	+	0.303973i	$0.0983134\pi$
$761$			16.7710i			0.607947i	−0.952681	+	0.303973i	$0.901687\pi$
$762$	55.8629	+	23.1392i	2.02370	+	0.838243i
$763$	6.47233	−	6.47233i	0.234314	−	0.234314i
$764$	84.5428			3.05865
$765$	−49.5918	−	1.04738i	−1.79299	−	0.0378681i
$766$	−31.2926			−1.13065
$767$	−5.70564	+	5.70564i	−0.206019	+	0.206019i
$768$	−82.1019	−	34.0077i	−2.96260	−	1.22715i
$769$		−	23.8668i		−	0.860657i	−0.902672	−	0.430329i	$-0.858398\pi$
$769$		−	23.8668i		−	0.860657i	0.902672	−	0.430329i	$-0.141602\pi$
$770$	−2.54192	+	6.13675i	−0.0916046	+	0.221153i
$771$	−10.4403	+	4.32453i	−0.376000	+	0.155744i
$772$	−31.8292	−	76.8424i	−1.14556	−	2.76562i
$773$	24.4388	+	24.4388i	0.879001	+	0.879001i	0.993431	−	0.114430i	$-0.0365043\pi$
$773$	24.4388	+	24.4388i	0.879001	+	0.879001i	−0.114430	+	0.993431i	$0.536504\pi$
$774$	63.1672	+	63.1672i	2.27050	+	2.27050i
$775$	−0.126432	−	0.305234i	−0.00454158	−	0.0109643i
$776$	5.03271	−	2.08462i	0.180664	−	0.0748333i
$777$	−7.34973	+	17.7438i	−0.263670	+	0.636556i
$778$			53.5153i			1.91862i
$779$	−25.1227	−	10.4062i	−0.900114	−	0.372840i
$780$	66.3756	−	66.3756i	2.37663	−	2.37663i
$781$	6.91994			0.247615
$782$	−64.8076	+	62.1268i	−2.31752	+	2.22165i
$783$	45.3247			1.61977
$784$	−12.6747	+	12.6747i	−0.452669	+	0.452669i
$785$	−29.8660	−	12.3709i	−1.06596	−	0.441536i
$786$		−	97.8526i		−	3.49029i
$787$	6.92347	−	16.7147i	0.246795	−	0.595816i	−0.751133	−	0.660151i	$-0.770492\pi$
$787$	6.92347	−	16.7147i	0.246795	−	0.595816i	0.997928	+	0.0643345i	$0.0204925\pi$
$788$	20.8741	−	8.64635i	0.743610	−	0.308013i
$789$	6.40982	+	15.4747i	0.228196	+	0.550913i
$790$	−44.7269	−	44.7269i	−1.59131	−	1.59131i
$791$	−15.3515	−	15.3515i	−0.545838	−	0.545838i
$792$	9.40460	+	22.7047i	0.334178	+	0.806777i
$793$	−51.4523	+	21.3123i	−1.82713	+	0.756821i
$794$	−19.6757	+	47.5014i	−0.698266	+	1.68576i
$795$			42.7437i			1.51596i
$796$	−2.88217	−	1.19383i	−0.102156	−	0.0423143i
$797$	20.4469	−	20.4469i	0.724268	−	0.724268i	−0.245204	−	0.969472i	$-0.578855\pi$
$797$	20.4469	−	20.4469i	0.724268	−	0.724268i	0.969472	+	0.245204i	$0.0788548\pi$
$798$	−33.7437			−1.19451
$799$	−3.28878	+	7.48852i	−0.116349	+	0.264925i
$800$	−0.0551199			−0.00194878
$801$	26.2825	−	26.2825i	0.928646	−	0.928646i
$802$	35.9561	+	14.8935i	1.26966	+	0.525908i
$803$		−	1.42505i		−	0.0502889i
$804$	−1.35042	+	3.26020i	−0.0476256	+	0.114978i
$805$	−22.7420	+	9.42003i	−0.801549	+	0.332013i
$806$	24.4052	+	58.9193i	0.859635	+	2.07534i
$807$	−61.8985	−	61.8985i	−2.17893	−	2.17893i
$808$	−1.37476	−	1.37476i	−0.0483640	−	0.0483640i
$809$	−9.27154	−	22.3835i	−0.325970	−	0.786962i	−0.998884	−	0.0472403i	$-0.984957\pi$
$809$	−9.27154	−	22.3835i	−0.325970	−	0.786962i	0.672913	−	0.739721i	$-0.265043\pi$
$810$	−19.9589	+	8.26723i	−0.701283	+	0.290481i
$811$	0.417217	−	1.00725i	0.0146505	−	0.0353693i	−0.916385	−	0.400298i	$-0.868907\pi$
$811$	0.417217	−	1.00725i	0.0146505	−	0.0353693i	0.931035	+	0.364929i	$0.118907\pi$
$812$		−	31.0101i		−	1.08824i
$813$	−12.9848	−	5.37848i	−0.455396	−	0.188631i
$814$	−9.22106	+	9.22106i	−0.323198	+	0.323198i
$815$	21.2022			0.742682
$816$	27.0395	+	28.2063i	0.946571	+	0.987417i
$817$	−26.5852			−0.930098
$818$	−13.2447	+	13.2447i	−0.463089	+	0.463089i
$819$	−23.0844	−	9.56185i	−0.806633	−	0.334118i
$820$			60.1450i			2.10035i
$821$	−11.5567	+	27.9004i	−0.403333	+	0.973732i	0.583518	+	0.812100i	$0.301676\pi$
$821$	−11.5567	+	27.9004i	−0.403333	+	0.973732i	−0.986851	+	0.161632i	$0.948324\pi$
$822$	−85.1067	+	35.2524i	−2.96844	+	1.22957i
$823$	−17.3290	−	41.8359i	−0.604051	−	1.45831i	−0.869377	−	0.494149i	$-0.835480\pi$
$823$	−17.3290	−	41.8359i	−0.604051	−	1.45831i	0.265326	−	0.964159i	$-0.414520\pi$
$824$	−24.8781	−	24.8781i	−0.866668	−	0.866668i
$825$	0.0966382	+	0.0966382i	0.00336451	+	0.00336451i
$826$	−2.45515	−	5.92725i	−0.0854254	−	0.206235i
$827$	−27.1751	+	11.2563i	−0.944971	+	0.391420i	−0.801338	−	0.598211i	$-0.795878\pi$
$827$	−27.1751	+	11.2563i	−0.944971	+	0.391420i	−0.143632	+	0.989631i	$0.545878\pi$
$828$	−72.0174	+	173.865i	−2.50278	+	6.04224i
$829$		−	17.4722i		−	0.606835i	−0.952858	−	0.303418i	$-0.901872\pi$
$829$		−	17.4722i		−	0.606835i	0.952858	−	0.303418i	$-0.0981277\pi$
$830$	18.7494	+	7.76627i	0.650802	+	0.269571i
$831$	−23.6445	+	23.6445i	−0.820217	+	0.820217i
$832$	35.1798			1.21964
$833$	−21.0674	+	8.20964i	−0.729942	+	0.284447i
$834$	−62.7284			−2.17211
$835$	−0.793098	+	0.793098i	−0.0274463	+	0.0274463i
$836$	−13.9623	−	5.78337i	−0.482896	−	0.200022i
$837$		−	48.8850i		−	1.68971i
$838$	10.8595	−	26.2172i	0.375137	−	0.905660i
$839$	−21.7986	+	9.02929i	−0.752573	+	0.311726i	−0.725791	−	0.687915i	$-0.758526\pi$
$839$	−21.7986	+	9.02929i	−0.752573	+	0.311726i	−0.0267819	+	0.999641i	$0.508526\pi$
$840$	13.8221	+	33.3694i	0.476907	+	1.15136i
$841$	−9.35379	−	9.35379i	−0.322544	−	0.322544i
$842$	54.7765	+	54.7765i	1.88772	+	1.88772i
$843$	22.4449	+	54.1867i	0.773042	+	1.86629i
$844$	24.5951	−	10.1876i	0.846598	−	0.350672i
$845$	−0.929498	+	2.24401i	−0.0319757	+	0.0771962i
$846$			25.9924i			0.893637i
$847$	1.13759	+	0.471206i	0.0390881	+	0.0161908i
$848$	15.3112	−	15.3112i	0.525789	−	0.525789i
$849$	61.5573			2.11264
$850$	0.431347	+	0.189437i	0.0147951	+	0.00649763i
$851$	−48.3265			−1.65661
$852$	54.9801	−	54.9801i	1.88359	−	1.88359i
$853$	−49.3796	−	20.4537i	−1.69072	−	0.700321i	−0.690978	−	0.722876i	$-0.742820\pi$
$853$	−49.3796	−	20.4537i	−1.69072	−	0.700321i	−0.999746	+	0.0225550i	$0.992820\pi$
$854$		−	44.2800i		−	1.51523i
$855$	17.9528	−	43.3419i	0.613973	−	1.48226i
$856$	27.9634	−	11.5828i	0.955768	−	0.395892i
$857$	10.7050	+	25.8442i	0.365676	+	0.882820i	0.994448	+	0.105230i	$0.0335579\pi$
$857$	10.7050	+	25.8442i	0.365676	+	0.882820i	−0.628772	+	0.777590i	$0.716442\pi$
$858$	−18.6540	−	18.6540i	−0.636838	−	0.636838i
$859$	−4.74712	−	4.74712i	−0.161970	−	0.161970i	0.621469	−	0.783439i	$-0.286536\pi$
$859$	−4.74712	−	4.74712i	−0.161970	−	0.161970i	−0.783439	+	0.621469i	$0.786536\pi$
$860$	22.5023	+	54.3255i	0.767324	+	1.85248i
$861$	22.9993	−	9.52663i	0.783815	−	0.324667i
$862$	0.556785	−	1.34420i	0.0189642	−	0.0457836i
$863$			7.90197i			0.268986i	0.990915	+	0.134493i	$0.0429406\pi$
$863$			7.90197i			0.268986i	−0.990915	+	0.134493i	$0.957059\pi$
$864$	−7.53496	−	3.12108i	−0.256345	−	0.106181i
$865$	23.2720	−	23.2720i	0.791273	−	0.791273i
$866$	34.6006			1.17578
$867$	16.9221	+	46.2914i	0.574705	+	1.57214i
$868$	−33.4460			−1.13523
$869$	−8.29120	+	8.29120i	−0.281260	+	0.281260i
$870$	93.8979	+	38.8938i	3.18344	+	1.31862i
$871$		−	1.17893i		−	0.0399465i
$872$	12.9327	−	31.2224i	0.437958	−	1.05732i
$873$	5.98424	−	2.47875i	0.202536	−	0.0838931i
$874$	−32.4928	−	78.4445i	−1.09908	−	2.65342i
$875$	9.77980	+	9.77980i	0.330617	+	0.330617i
$876$	−11.3223	−	11.3223i	−0.382544	−	0.382544i
$877$	1.91287	+	4.61807i	0.0645929	+	0.155941i	0.952880	−	0.303348i	$-0.0981043\pi$
$877$	1.91287	+	4.61807i	0.0645929	+	0.155941i	−0.888287	+	0.459289i	$0.848104\pi$
$878$	−28.3370	+	11.7376i	−0.956327	+	0.396124i
$879$	19.8048	−	47.8130i	0.667999	−	1.61269i
$880$			7.27439i			0.245220i
$881$	48.2852	+	20.0004i	1.62677	+	0.673831i	0.994865	−	0.101214i	$-0.0322726\pi$
$881$	48.2852	+	20.0004i	1.62677	+	0.673831i	0.631907	+	0.775045i	$0.282273\pi$
$882$	−50.8098	+	50.8098i	−1.71086	+	1.71086i
$883$	−19.9361			−0.670903			−0.335451	−	0.942058i	$-0.608889\pi$
$883$	−19.9361			−0.670903			−0.335451	+	0.942058i	$0.608889\pi$
$884$	−54.9205	−	24.1197i	−1.84718	−	0.811235i
$885$	13.8694			0.466216
$886$	−18.2274	+	18.2274i	−0.612362	+	0.612362i
$887$	33.8119	+	14.0054i	1.13529	+	0.470254i	0.869577	−	0.493797i	$-0.164391\pi$
$887$	33.8119	+	14.0054i	1.13529	+	0.470254i	0.265717	+	0.964051i	$0.414391\pi$
$888$			70.9098i			2.37958i
$889$	4.05423	−	9.78777i	0.135974	−	0.328271i
$890$	34.2684	−	14.1944i	1.14868	−	0.475799i
$891$	1.53253	+	3.69985i	0.0513416	+	0.123950i
$892$	43.9041	+	43.9041i	1.47002	+	1.47002i
$893$	−5.46971	−	5.46971i	−0.183037	−	0.183037i
$894$	9.68526	+	23.3823i	0.323923	+	0.782020i
$895$	27.7003	−	11.4738i	0.925920	−	0.383528i
$896$	−9.60215	+	23.1816i	−0.320785	+	0.774444i
$897$		−	97.7637i		−	3.26424i
$898$	−37.7828	−	15.6502i	−1.26083	−	0.522253i
$899$	−32.2054	+	32.2054i	−1.07411	+	1.07411i
$900$	0.987554			0.0329185
$901$	25.4496	−	9.91733i	0.847851	−	0.330394i
$902$	16.9030			0.562809
$903$	17.2097	−	17.2097i	0.572703	−	0.572703i
$904$	−74.0555	−	30.6748i	−2.46305	−	1.02023i
$905$			34.3854i			1.14301i
$906$	8.78104	−	21.1993i	0.291730	−	0.704300i
$907$	−42.8115	+	17.7331i	−1.42153	+	0.588818i	−0.955245	−	0.295814i	$-0.904409\pi$
$907$	−42.8115	+	17.7331i	−1.42153	+	0.588818i	−0.466288	+	0.884633i	$0.654409\pi$
$908$	4.05843	+	9.79791i	0.134684	+	0.325155i
$909$	−1.63469	−	1.63469i	−0.0542193	−	0.0542193i
$910$	−17.6313	−	17.6313i	−0.584473	−	0.584473i
$911$	13.0840	+	31.5877i	0.433494	+	1.04655i	0.978153	+	0.207889i	$0.0666591\pi$
$911$	13.0840	+	31.5877i	0.433494	+	1.04655i	−0.544659	+	0.838658i	$0.683341\pi$
$912$	−34.1414	+	14.1418i	−1.13054	+	0.468283i
$913$	1.43966	−	3.47565i	0.0476459	−	0.115027i
$914$			13.2472i			0.438179i
$915$	88.4390	+	36.6326i	2.92370	+	1.21104i
$916$	38.3825	−	38.3825i	1.26819	−	1.26819i
$917$	−17.1448			−0.566172
$918$	48.2391	+	50.3207i	1.59213	+	1.66083i
$919$	15.0627			0.496874			0.248437	−	0.968648i	$-0.420083\pi$
$919$	15.0627			0.496874			0.248437	+	0.968648i	$0.420083\pi$
$920$	−64.2648	+	64.2648i	−2.11875	+	2.11875i
$921$	13.7739	+	5.70535i	0.453866	+	0.187998i
$922$			11.2056i			0.369036i
$923$	−9.94074	+	23.9991i	−0.327204	+	0.789939i
$924$	12.7822	−	5.29455i	0.420503	−	0.174178i
$925$	0.0970484	+	0.234296i	0.00319093	+	0.00770359i
$926$	47.2318	+	47.2318i	1.55213	+	1.55213i
$927$	−29.5818	−	29.5818i	−0.971593	−	0.971593i
$928$	2.90786	+	7.02019i	0.0954551	+	0.230449i
$929$	14.9128	−	6.17709i	0.489273	−	0.202664i	−0.124387	−	0.992234i	$-0.539696\pi$
$929$	14.9128	−	6.17709i	0.489273	−	0.202664i	0.613660	+	0.789570i	$0.289696\pi$
$930$	41.9489	−	101.274i	1.37556	−	3.32089i
$931$		−	21.3843i		−	0.700843i
$932$	62.6724	+	25.9598i	2.05290	+	0.850340i
$933$	−29.9848	+	29.9848i	−0.981660	+	0.981660i
$934$	−72.4747			−2.37144
$935$	−3.68972	+	8.40147i	−0.120667	+	0.274757i
$936$	−92.2523			−3.01536
$937$	−11.4566	+	11.4566i	−0.374270	+	0.374270i	−0.869030	−	0.494759i	$-0.835256\pi$
$937$	−11.4566	+	11.4566i	−0.374270	+	0.374270i	0.494759	+	0.869030i	$0.335256\pi$
$938$	0.866006	+	0.358711i	0.0282761	+	0.0117123i
$939$		−	30.1205i		−	0.982946i
$940$	−6.54738	+	15.8068i	−0.213552	+	0.515560i
$941$	7.30398	−	3.02541i	0.238103	−	0.0986254i	−0.260441	−	0.965490i	$-0.583868\pi$
$941$	7.30398	−	3.02541i	0.238103	−	0.0986254i	0.498544	+	0.866864i	$0.333868\pi$
$942$	39.0646	+	94.3103i	1.27279	+	3.07280i
$943$	44.2934	+	44.2934i	1.44239	+	1.44239i
$944$	−4.96817	−	4.96817i	−0.161700	−	0.161700i
$945$	7.31430	+	17.6583i	0.237934	+	0.574424i
$946$	15.2675	−	6.32401i	0.496389	−	0.205611i
$947$	−9.68179	+	23.3739i	−0.314616	+	0.759550i	0.684906	+	0.728631i	$0.259843\pi$
$947$	−9.68179	+	23.3739i	−0.314616	+	0.759550i	−0.999522	+	0.0309186i	$0.990157\pi$
$948$			131.750i			4.27904i
$949$	4.94222	+	2.04713i	0.160431	+	0.0664528i
$950$	−0.315061	+	0.315061i	−0.0102219	+	0.0102219i
$951$	38.8251			1.25899
$952$	16.6612	−	15.9720i	0.539994	−	0.517656i
$953$	−43.6979			−1.41552			−0.707758	−	0.706455i	$-0.750293\pi$
$953$	−43.6979			−1.41552			−0.707758	+	0.706455i	$0.750293\pi$
$954$	61.3788	−	61.3788i	1.98721	−	1.98721i
$955$	44.8528	+	18.5786i	1.45140	+	0.601190i
$956$		−	53.1270i		−	1.71825i
$957$	7.20989	−	17.4062i	0.233063	−	0.562663i
$958$	8.87951	−	3.67801i	0.286884	−	0.118831i
$959$	6.17659	+	14.9116i	0.199452	+	0.481521i
$960$	−42.7580	−	42.7580i	−1.38001	−	1.38001i
$961$	12.8148	+	12.8148i	0.413380	+	0.413380i
$962$	−18.7332	−	45.2260i	−0.603983	−	1.45814i
$963$	33.2504	−	13.7728i	1.07148	−	0.443821i
$964$	−27.3879	+	66.1203i	−0.882106	+	2.12959i
$965$		−	47.7621i		−	1.53752i
$966$	71.8143	+	29.7465i	2.31059	+	0.957077i
$967$	10.0635	−	10.0635i	0.323619	−	0.323619i	−0.526534	−	0.850154i	$-0.676509\pi$
$967$	10.0635	−	10.0635i	0.323619	−	0.323619i	0.850154	+	0.526534i	$0.176509\pi$
$968$	4.54618			0.146120
$969$	−46.6043	−	0.984283i	−1.49714	−	0.0316197i
$970$	6.46385			0.207542
$971$	−13.8843	+	13.8843i	−0.445568	+	0.445568i	−0.893878	−	0.448310i	$-0.852026\pi$
$971$	−13.8843	+	13.8843i	−0.445568	+	0.445568i	0.448310	+	0.893878i	$0.352026\pi$
$972$	−33.3484	−	13.8134i	−1.06965	−	0.443064i
$973$			10.9907i			0.352345i
$974$	34.2165	−	82.6060i	1.09637	−	2.64687i
$975$	−0.473976	+	0.196327i	−0.0151794	+	0.00628750i
$976$	−18.5576	−	44.8019i	−0.594013	−	1.43408i
$977$	−39.6475	−	39.6475i	−1.26844	−	1.26844i	−0.946895	−	0.321542i	$-0.895799\pi$
$977$	−39.6475	−	39.6475i	−1.26844	−	1.26844i	−0.321542	−	0.946895i	$-0.604201\pi$
$978$	−47.3423	−	47.3423i	−1.51384	−	1.51384i
$979$	−2.63128	−	6.35247i	−0.0840961	−	0.203026i
$980$	−43.6978	+	18.1002i	−1.39587	+	0.578190i
$981$	15.3779	−	37.1256i	0.490980	−	1.18533i
$982$		−	71.2740i		−	2.27445i
$983$	4.19575	+	1.73793i	0.133823	+	0.0554315i	0.448590	−	0.893738i	$-0.351926\pi$
$983$	4.19575	+	1.73793i	0.133823	+	0.0554315i	−0.314767	+	0.949169i	$0.601926\pi$
$984$	64.9920	−	64.9920i	2.07187	−	2.07187i
$985$	12.9745			0.413402
$986$	1.37135	−	64.9311i	0.0436726	−	2.06783i
$987$	7.08155			0.225408
$988$	40.1147	−	40.1147i	1.27622	−	1.27622i
$989$	56.5794	+	23.4359i	1.79912	+	0.745219i
$990$			29.1612i			0.926804i
$991$	−23.0523	+	55.6531i	−0.732279	+	1.76788i	−0.0974310	+	0.995242i	$0.531063\pi$
$991$	−23.0523	+	55.6531i	−0.732279	+	1.76788i	−0.634848	+	0.772637i	$0.718937\pi$
$992$	7.57162	−	3.13627i	0.240399	−	0.0995767i
$993$	0.689992	+	1.66579i	0.0218962	+	0.0528622i
$994$	−14.6043	−	14.6043i	−0.463222	−	0.463222i
$995$	−1.26674	−	1.26674i	−0.0401583	−	0.0401583i
$996$	−16.1763	−	39.0530i	−0.512566	−	1.23744i
$997$	−0.460854	+	0.190892i	−0.0145954	+	0.00604561i	−0.389969	−	0.920828i	$-0.627514\pi$
$997$	−0.460854	+	0.190892i	−0.0145954	+	0.00604561i	0.375374	+	0.926874i	$0.377514\pi$
$998$	34.3563	−	82.9435i	1.08753	−	2.62553i
$999$			37.5237i			1.18720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.111.1	✓	56
17.2	even	8	inner	187.2.h.a.155.1	yes	56
17.6	odd	16		3179.2.a.bi.1.2		28
17.11	odd	16		3179.2.a.bh.1.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.111.1	✓	56	1.1	even	1	trivial
187.2.h.a.155.1	yes	56	17.2	even	8	inner
3179.2.a.bh.1.2		28	17.11	odd	16
3179.2.a.bi.1.2		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)

\(f(q)\)	\(=\)	\(q+(-1.71399 + 1.71399i) q^{2} +(2.67857 + 1.10950i) q^{3} -3.87553i q^{4} +(0.851663 - 2.05610i) q^{5} +(-6.49271 + 2.68937i) q^{6} +(0.471206 + 1.13759i) q^{7} +(3.21463 + 3.21463i) q^{8} +(3.82242 + 3.82242i) q^{9} +O(q^{10})\)	\(q+(-1.71399 + 1.71399i) q^{2} +(2.67857 + 1.10950i) q^{3} -3.87553i q^{4} +(0.851663 - 2.05610i) q^{5} +(-6.49271 + 2.68937i) q^{6} +(0.471206 + 1.13759i) q^{7} +(3.21463 + 3.21463i) q^{8} +(3.82242 + 3.82242i) q^{9} +(2.06439 + 4.98387i) q^{10} +(0.923880 - 0.382683i) q^{11} +(4.29990 - 10.3809i) q^{12} +3.75385i q^{13} +(-2.75747 - 1.14218i) q^{14} +(4.56248 - 4.56248i) q^{15} -3.26865 q^{16} +(-3.77509 - 1.65793i) q^{17} -13.1032 q^{18} +(2.75737 - 2.75737i) q^{19} +(-7.96845 - 3.30064i) q^{20} +3.56992i q^{21} +(-0.927605 + 2.23944i) q^{22} +(-8.29905 + 3.43758i) q^{23} +(5.04398 + 12.1773i) q^{24} +(0.0333320 + 0.0333320i) q^{25} +(-6.43406 - 6.43406i) q^{26} +(2.66915 + 6.44390i) q^{27} +(4.40877 - 1.82617i) q^{28} +(2.48680 - 6.00367i) q^{29} +15.6401i q^{30} +(-6.47526 - 2.68214i) q^{31} +(-0.826831 + 0.826831i) q^{32} +2.89926 q^{33} +(9.31213 - 3.62879i) q^{34} +2.74031 q^{35} +(14.8139 - 14.8139i) q^{36} +(4.97036 + 2.05879i) q^{37} +9.45222i q^{38} +(-4.16490 + 10.0549i) q^{39} +(9.34738 - 3.87181i) q^{40} +(-2.66858 - 6.44252i) q^{41} +(-6.11882 - 6.11882i) q^{42} +(-4.82075 - 4.82075i) q^{43} +(-1.48310 - 3.58052i) q^{44} +(11.1147 - 4.60386i) q^{45} +(8.33252 - 20.1165i) q^{46} -1.98367i q^{47} +(-8.75531 - 3.62657i) q^{48} +(3.87767 - 3.87767i) q^{49} -0.114261 q^{50} +(-8.27236 - 8.62933i) q^{51} +14.5481 q^{52} +(-4.68426 + 4.68426i) q^{53} +(-15.6197 - 6.46989i) q^{54} -2.22550i q^{55} +(-2.14219 + 5.17170i) q^{56} +(10.4451 - 4.32651i) q^{57} +(6.02788 + 14.5526i) q^{58} +(1.51994 + 1.51994i) q^{59} +(-17.6820 - 17.6820i) q^{60} +(5.67744 + 13.7066i) q^{61} +(15.6957 - 6.50137i) q^{62} +(-2.54721 + 6.14951i) q^{63} -9.37166i q^{64} +(7.71828 + 3.19702i) q^{65} +(-4.96931 + 4.96931i) q^{66} -0.314059 q^{67} +(-6.42534 + 14.6304i) q^{68} -26.0436 q^{69} +(-4.69686 + 4.69686i) q^{70} +(6.39319 + 2.64815i) q^{71} +24.5754i q^{72} +(0.545343 - 1.31657i) q^{73} +(-12.0479 + 4.99040i) q^{74} +(0.0523002 + 0.126264i) q^{75} +(-10.6863 - 10.6863i) q^{76} +(0.870676 + 0.870676i) q^{77} +(-10.0955 - 24.3727i) q^{78} +(-10.8330 + 4.48717i) q^{79} +(-2.78379 + 6.72066i) q^{80} +4.00469i q^{81} +(15.6163 + 6.46850i) q^{82} +(2.66015 - 2.66015i) q^{83} +13.8353 q^{84} +(-6.62396 + 6.34995i) q^{85} +16.5254 q^{86} +(13.3221 - 13.3221i) q^{87} +(4.20012 + 1.73975i) q^{88} -6.87587i q^{89} +(-11.1595 + 26.9414i) q^{90} +(-4.27035 + 1.76884i) q^{91} +(13.3224 + 32.1632i) q^{92} +(-14.3686 - 14.3686i) q^{93} +(3.39999 + 3.39999i) q^{94} +(-3.32107 - 8.01777i) q^{95} +(-3.13209 + 1.29736i) q^{96} +(0.458542 - 1.10702i) q^{97} +13.2926i q^{98} +(4.99424 + 2.06868i) 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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