LMFDB - Embedded newform 152.2.o.c.27.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(27,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.13
Character	$\chi$	$=$	152.27
Dual form			152.2.o.c.107.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37418 - 0.334110i) q^{2} +(1.27630 + 0.736872i) q^{3} +(1.77674 - 0.918256i) q^{4} +(-2.34524 - 1.35403i) q^{5} +(2.00006 + 0.586169i) q^{6} +3.01597i q^{7} +(2.13476 - 1.85548i) q^{8} +(-0.414040 - 0.717138i) q^{9} +(-3.67518 - 1.07711i) q^{10} -3.11370 q^{11} +(2.94429 + 0.137261i) q^{12} +(0.218909 + 0.379162i) q^{13} +(1.00767 + 4.14449i) q^{14} +(-1.99549 - 3.45629i) q^{15} +(2.31361 - 3.26300i) q^{16} +(-3.22274 + 5.58194i) q^{17} +(-0.808569 - 0.847142i) q^{18} +(3.58731 - 2.47613i) q^{19} +(-5.41023 - 0.252221i) q^{20} +(-2.22238 + 3.84928i) q^{21} +(-4.27879 + 1.04032i) q^{22} +(-1.81421 + 1.04744i) q^{23} +(4.09184 - 0.795097i) q^{24} +(1.16678 + 2.02092i) q^{25} +(0.427502 + 0.447896i) q^{26} -5.64161i q^{27} +(2.76943 + 5.35860i) q^{28} +(-1.58443 - 2.74431i) q^{29} +(-3.89694 - 4.08285i) q^{30} +9.77556 q^{31} +(2.08912 - 5.25696i) q^{32} +(-3.97402 - 2.29440i) q^{33} +(-2.56363 + 8.74735i) q^{34} +(4.08371 - 7.07319i) q^{35} +(-1.39416 - 0.893974i) q^{36} -8.36258 q^{37} +(4.10230 - 4.60121i) q^{38} +0.645232i q^{39} +(-7.51890 + 1.46102i) q^{40} +(4.66208 + 2.69165i) q^{41} +(-1.76787 + 6.03213i) q^{42} +(-2.43347 + 4.21489i) q^{43} +(-5.53225 + 2.85918i) q^{44} +2.24248i q^{45} +(-2.14310 + 2.04551i) q^{46} +(-1.22865 + 0.709359i) q^{47} +(5.35728 - 2.45973i) q^{48} -2.09609 q^{49} +(2.27857 + 2.38727i) q^{50} +(-8.22635 + 4.74949i) q^{51} +(0.737112 + 0.472657i) q^{52} +(1.63792 + 2.83695i) q^{53} +(-1.88492 - 7.75258i) q^{54} +(7.30239 + 4.21604i) q^{55} +(5.59606 + 6.43838i) q^{56} +(6.40307 - 0.516904i) q^{57} +(-3.09420 - 3.24181i) q^{58} +(-1.70599 - 0.984956i) q^{59} +(-6.71922 - 4.30856i) q^{60} +(9.56035 - 5.51967i) q^{61} +(13.4334 - 3.26612i) q^{62} +(2.16287 - 1.24873i) q^{63} +(1.11442 - 7.92200i) q^{64} -1.18563i q^{65} +(-6.22760 - 1.82516i) q^{66} +(4.49875 - 2.59735i) q^{67} +(-0.600315 + 12.8770i) q^{68} -3.08731 q^{69} +(3.24852 - 11.0842i) q^{70} +(4.40927 - 7.63707i) q^{71} +(-2.21451 - 0.762678i) q^{72} +(-6.90160 + 11.9539i) q^{73} +(-11.4917 + 2.79403i) q^{74} +3.43906i q^{75} +(4.09999 - 7.69351i) q^{76} -9.39085i q^{77} +(0.215579 + 0.886664i) q^{78} +(-0.939415 + 1.62711i) q^{79} +(-9.84418 + 4.51984i) q^{80} +(2.91502 - 5.04897i) q^{81} +(7.30584 + 2.14116i) q^{82} +3.79468 q^{83} +(-0.413974 + 8.87989i) q^{84} +(15.1162 - 8.72734i) q^{85} +(-1.93578 + 6.60506i) q^{86} -4.67009i q^{87} +(-6.64702 + 5.77740i) q^{88} +(10.7709 - 6.21857i) q^{89} +(0.749238 + 3.08158i) q^{90} +(-1.14354 + 0.660224i) q^{91} +(-2.26157 + 3.52694i) q^{92} +(12.4765 + 7.20333i) q^{93} +(-1.45138 + 1.38529i) q^{94} +(-11.7659 + 0.949828i) q^{95} +(6.54004 - 5.17004i) q^{96} +(-16.1008 - 9.29578i) q^{97} +(-2.88040 + 0.700325i) q^{98} +(1.28920 + 2.23296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.37418	−	0.334110i	0.971692	−	0.236252i
$2$	1.37418	−	0.334110i	0.971692	−	0.236252i
$3$	1.27630	+	0.736872i	0.736872	+	0.425433i	0.820931	−	0.571028i	$-0.193455\pi$
$3$	1.27630	+	0.736872i	0.736872	+	0.425433i	−0.0840591	+	0.996461i	$0.526788\pi$
$4$	1.77674	−	0.918256i	0.888370	−	0.459128i
$5$	−2.34524	−	1.35403i	−1.04882	−	0.605539i	−0.126504	−	0.991966i	$-0.540376\pi$
$5$	−2.34524	−	1.35403i	−1.04882	−	0.605539i	−0.922320	+	0.386427i	$0.873709\pi$
$6$	2.00006	+	0.586169i	0.816522	+	0.239303i
$7$			3.01597i			1.13993i	0.821669	+	0.569965i	$0.193043\pi$
$7$			3.01597i			1.13993i	−0.821669	+	0.569965i	$0.806957\pi$
$8$	2.13476	−	1.85548i	0.754752	−	0.656010i
$9$	−0.414040	−	0.717138i	−0.138013	−	0.239046i
$10$	−3.67518	−	1.07711i	−1.16219	−	0.340611i
$11$	−3.11370			−0.938817			−0.469409	−	0.882981i	$-0.655533\pi$
$11$	−3.11370			−0.938817			−0.469409	+	0.882981i	$0.655533\pi$
$12$	2.94429	+	0.137261i	0.849943	+	0.0396237i
$13$	0.218909	+	0.379162i	0.0607144	+	0.105160i	0.894785	−	0.446497i	$-0.147329\pi$
$13$	0.218909	+	0.379162i	0.0607144	+	0.105160i	−0.834071	+	0.551658i	$0.813995\pi$
$14$	1.00767	+	4.14449i	0.269311	+	1.10766i
$15$	−1.99549	−	3.45629i	−0.515233	−	0.892409i
$16$	2.31361	−	3.26300i	0.578403	−	0.815751i
$17$	−3.22274	+	5.58194i	−0.781629	+	1.35382i	0.149364	+	0.988782i	$0.452277\pi$
$17$	−3.22274	+	5.58194i	−0.781629	+	1.35382i	−0.930993	+	0.365038i	$0.881056\pi$
$18$	−0.808569	−	0.847142i	−0.190582	−	0.199673i
$19$	3.58731	−	2.47613i	0.822984	−	0.568064i
$19$	3.58731	−	2.47613i	0.822984	−	0.568064i
$20$	−5.41023	−	0.252221i	−1.20976	−	0.0563984i
$21$	−2.22238	+	3.84928i	−0.484964	+	0.839982i
$22$	−4.27879	+	1.04032i	−0.912241	+	0.221797i
$23$	−1.81421	+	1.04744i	−0.378290	+	0.218406i	−0.677074	−	0.735915i	$-0.736752\pi$
$23$	−1.81421	+	1.04744i	−0.378290	+	0.218406i	0.298784	+	0.954321i	$0.403419\pi$
$24$	4.09184	−	0.795097i	0.835244	−	0.162298i
$25$	1.16678	+	2.02092i	0.233355	+	0.404183i
$26$	0.427502	+	0.447896i	0.0838401	+	0.0878397i
$27$		−	5.64161i		−	1.08573i
$28$	2.76943	+	5.35860i	0.523374	+	1.01268i
$29$	−1.58443	−	2.74431i	−0.294221	−	0.509606i	0.680582	−	0.732672i	$-0.261727\pi$
$29$	−1.58443	−	2.74431i	−0.294221	−	0.509606i	−0.974803	+	0.223066i	$0.928394\pi$
$30$	−3.89694	−	4.08285i	−0.711481	−	0.745422i
$31$	9.77556			1.75574			0.877871	−	0.478897i	$-0.158963\pi$
$31$	9.77556			1.75574			0.877871	+	0.478897i	$0.158963\pi$
$32$	2.08912	−	5.25696i	0.369307	−	0.929307i
$33$	−3.97402	−	2.29440i	−0.691788	−	0.399404i
$34$	−2.56363	+	8.74735i	−0.439660	+	1.50016i
$35$	4.08371	−	7.07319i	0.690272	−	1.19559i
$36$	−1.39416	−	0.893974i	−0.232360	−	0.148996i
$37$	−8.36258			−1.37480			−0.687400	−	0.726279i	$-0.741248\pi$
$37$	−8.36258			−1.37480			−0.687400	+	0.726279i	$0.741248\pi$
$38$	4.10230	−	4.60121i	0.665481	−	0.746415i
$39$			0.645232i			0.103320i
$40$	−7.51890	+	1.46102i	−1.18884	+	0.231007i
$41$	4.66208	+	2.69165i	0.728094	+	0.420365i	0.817724	−	0.575610i	$-0.195235\pi$
$41$	4.66208	+	2.69165i	0.728094	+	0.420365i	−0.0896306	+	0.995975i	$0.528569\pi$
$42$	−1.76787	+	6.03213i	−0.272788	+	0.930778i
$43$	−2.43347	+	4.21489i	−0.371100	+	0.642764i	−0.989735	−	0.142914i	$-0.954353\pi$
$43$	−2.43347	+	4.21489i	−0.371100	+	0.642764i	0.618635	+	0.785679i	$0.287686\pi$
$44$	−5.53225	+	2.85918i	−0.834017	+	0.431037i
$45$			2.24248i			0.334290i
$46$	−2.14310	+	2.04551i	−0.315982	+	0.301595i
$47$	−1.22865	+	0.709359i	−0.179216	+	0.103471i	−0.586924	−	0.809642i	$-0.699661\pi$
$47$	−1.22865	+	0.709359i	−0.179216	+	0.103471i	0.407708	+	0.913112i	$0.366328\pi$
$48$	5.35728	−	2.45973i	0.773256	−	0.355032i
$49$	−2.09609			−0.299441
$50$	2.27857	+	2.38727i	0.322238	+	0.337611i
$51$	−8.22635	+	4.74949i	−1.15192	+	0.665061i
$52$	0.737112	+	0.472657i	0.102219	+	0.0655458i
$53$	1.63792	+	2.83695i	0.224985	+	0.389686i	0.956315	−	0.292338i	$-0.0944333\pi$
$53$	1.63792	+	2.83695i	0.224985	+	0.389686i	−0.731330	+	0.682024i	$0.761100\pi$
$54$	−1.88492	−	7.75258i	−0.256505	−	1.05499i
$55$	7.30239	+	4.21604i	0.984655	+	0.568491i
$56$	5.59606	+	6.43838i	0.747805	+	0.860365i
$57$	6.40307	−	0.516904i	0.848107	−	0.0684655i
$58$	−3.09420	−	3.24181i	−0.406288	−	0.425670i
$59$	−1.70599	−	0.984956i	−0.222102	−	0.128230i	0.384821	−	0.922991i	$-0.374263\pi$
$59$	−1.70599	−	0.984956i	−0.222102	−	0.128230i	−0.606923	+	0.794761i	$0.707596\pi$
$60$	−6.71922	−	4.30856i	−0.867447	−	0.556232i
$61$	9.56035	−	5.51967i	1.22408	−	0.706722i	0.258293	−	0.966067i	$-0.416840\pi$
$61$	9.56035	−	5.51967i	1.22408	−	0.706722i	0.965785	+	0.259345i	$0.0835067\pi$
$62$	13.4334	−	3.26612i	1.70604	−	0.414797i
$63$	2.16287	−	1.24873i	0.272496	−	0.157326i
$64$	1.11442	−	7.92200i	0.139302	−	0.990250i
$65$		−	1.18563i		−	0.147060i
$66$	−6.22760	−	1.82516i	−0.766565	−	0.224661i
$67$	4.49875	−	2.59735i	0.549609	−	0.317317i	−0.199355	−	0.979927i	$-0.563885\pi$
$67$	4.49875	−	2.59735i	0.549609	−	0.317317i	0.748964	+	0.662610i	$0.230551\pi$
$68$	−0.600315	+	12.8770i	−0.0727989	+	1.56156i
$69$	−3.08731			−0.371668
$70$	3.24852	−	11.0842i	0.388273	−	1.32482i
$71$	4.40927	−	7.63707i	0.523284	−	0.906354i	−0.476349	−	0.879256i	$-0.658040\pi$
$71$	4.40927	−	7.63707i	0.523284	−	0.906354i	0.999633	−	0.0270976i	$-0.00862647\pi$
$72$	−2.21451	−	0.762678i	−0.260983	−	0.0898825i
$73$	−6.90160	+	11.9539i	−0.807772	+	1.39910i	0.106632	+	0.994299i	$0.465993\pi$
$73$	−6.90160	+	11.9539i	−0.807772	+	1.39910i	−0.914404	+	0.404803i	$0.867340\pi$
$74$	−11.4917	+	2.79403i	−1.33588	+	0.324799i
$75$			3.43906i			0.397108i
$76$	4.09999	−	7.69351i	0.470301	−	0.882506i
$77$		−	9.39085i		−	1.07019i
$78$	0.215579	+	0.886664i	0.0244095	+	0.100395i
$79$	−0.939415	+	1.62711i	−0.105692	+	0.183065i	−0.914021	−	0.405667i	$-0.867039\pi$
$79$	−0.939415	+	1.62711i	−0.105692	+	0.183065i	0.808328	+	0.588732i	$0.200373\pi$
$80$	−9.84418	+	4.51984i	−1.10061	+	0.505334i
$81$	2.91502	−	5.04897i	0.323891	−	0.560996i
$82$	7.30584	+	2.14116i	0.806795	+	0.236452i
$83$	3.79468			0.416520			0.208260	−	0.978073i	$-0.433220\pi$
$83$	3.79468			0.416520			0.208260	+	0.978073i	$0.433220\pi$
$84$	−0.413974	+	8.87989i	−0.0451683	+	0.968876i
$85$	15.1162	−	8.72734i	1.63958	−	0.946613i
$86$	−1.93578	+	6.60506i	−0.208741	+	0.712242i
$87$		−	4.67009i		−	0.500686i
$88$	−6.64702	+	5.77740i	−0.708575	+	0.615873i
$89$	10.7709	−	6.21857i	1.14171	−	0.659167i	0.194857	−	0.980832i	$-0.437576\pi$
$89$	10.7709	−	6.21857i	1.14171	−	0.659167i	0.946854	+	0.321664i	$0.104242\pi$
$90$	0.749238	+	3.08158i	0.0789766	+	0.324827i
$91$	−1.14354	+	0.660224i	−0.119876	+	0.0692102i
$92$	−2.26157	+	3.52694i	−0.235785	+	0.367708i
$93$	12.4765	+	7.20333i	1.29376	+	0.746951i
$94$	−1.45138	+	1.38529i	−0.149698	+	0.142882i
$95$	−11.7659	+	0.949828i	−1.20715	+	0.0974503i
$96$	6.54004	−	5.17004i	0.667490	−	0.527665i
$97$	−16.1008	−	9.29578i	−1.63479	−	0.943844i	−0.982589	−	0.185794i	$-0.940514\pi$
$97$	−16.1008	−	9.29578i	−1.63479	−	0.943844i	−0.652197	−	0.758050i	$-0.726152\pi$
$98$	−2.88040	+	0.700325i	−0.290964	+	0.0707435i
$99$	1.28920	+	2.23296i	0.129569	+	0.224421i
$100$	3.92878	+	2.51924i	0.392878	+	0.251924i
$101$	1.29368	−	0.746904i	0.128726	−	0.0743198i	−0.434254	−	0.900790i	$-0.642988\pi$
$101$	1.29368	−	0.746904i	0.128726	−	0.0743198i	0.562980	+	0.826470i	$0.309655\pi$
$102$	−9.71764	+	9.27516i	−0.962189	+	0.918378i
$103$	5.61948			0.553704			0.276852	−	0.960913i	$-0.410709\pi$
$103$	5.61948			0.553704			0.276852	+	0.960913i	$0.410709\pi$
$104$	1.17084	+	0.403239i	0.114811	+	0.0395409i
$105$	10.4241	−	6.01834i	1.01728	−	0.587329i
$106$	3.19865	+	3.35124i	0.310680	+	0.325501i
$107$			9.01090i			0.871117i	0.900160	+	0.435558i	$0.143449\pi$
$107$			9.01090i			0.871117i	−0.900160	+	0.435558i	$0.856551\pi$
$108$	−5.18044	−	10.0237i	−0.498488	−	0.964528i
$109$	−5.62286	+	9.73908i	−0.538573	+	0.932835i	0.460409	+	0.887707i	$0.347703\pi$
$109$	−5.62286	+	9.73908i	−0.538573	+	0.932835i	−0.998981	+	0.0451280i	$0.985630\pi$
$110$	11.4434	+	3.35379i	1.09109	+	0.319771i
$111$	−10.6732	−	6.16215i	−1.01305	−	0.584885i
$112$	9.84113	+	6.97779i	0.929899	+	0.659339i
$113$		−	4.22083i		−	0.397063i	−0.980095	−	0.198531i	$-0.936383\pi$
$113$		−	4.22083i		−	0.397063i	0.980095	−	0.198531i	$-0.0636171\pi$
$114$	8.62626	−	2.84965i	0.807924	−	0.266894i
$115$	5.67303			0.529013
$116$	−5.33510	−	3.42102i	−0.495352	−	0.317634i
$117$	0.181274	−	0.313976i	0.0167588	−	0.0290271i
$118$	−2.67343	−	0.783517i	−0.246109	−	0.0721286i
$119$	−16.8350	−	9.71969i	−1.54326	−	0.891002i
$120$	−10.6729	−	3.67577i	−0.974302	−	0.335550i
$121$	−1.30484			−0.118622
$122$	11.2935	−	10.7792i	1.02246	−	0.975906i
$123$	3.96680	+	6.87070i	0.357675	+	0.619510i
$124$	17.3686	−	8.97646i	1.55975	−	0.806110i
$125$			7.22088i			0.645855i
$126$	2.55496	−	2.43862i	0.227614	−	0.217250i
$127$	7.86010	+	13.6141i	0.697471	+	1.20806i	0.969340	+	0.245721i	$0.0790248\pi$
$127$	7.86010	+	13.6141i	0.697471	+	1.20806i	−0.271869	+	0.962334i	$0.587642\pi$
$128$	−1.11541	−	11.2586i	−0.0985895	−	0.995128i
$129$	−6.21166	+	3.58631i	−0.546906	+	0.315757i
$130$	−0.396133	−	1.62928i	−0.0347432	−	0.142897i
$131$	−5.08127	+	8.80102i	−0.443953	+	0.768948i	−0.997979	−	0.0635510i	$-0.979757\pi$
$131$	−5.08127	+	8.80102i	−0.443953	+	0.768948i	0.554026	+	0.832499i	$0.313091\pi$
$132$	−9.16765	−	0.427389i	−0.797941	−	0.0371995i
$133$	7.46795	+	10.8192i	0.647553	+	0.938145i
$134$	5.31429	−	5.07231i	0.459084	−	0.438181i
$135$	−7.63889	+	13.2309i	−0.657451	+	1.13874i
$136$	3.47739	+	17.8958i	0.298184	+	1.53456i
$137$	−7.17527	−	12.4279i	−0.613024	−	1.06179i	−0.990728	−	0.135863i	$-0.956619\pi$
$137$	−7.17527	−	12.4279i	−0.613024	−	1.06179i	0.377703	−	0.925927i	$-0.376714\pi$
$138$	−4.24251	+	1.03150i	−0.361147	+	0.0878072i
$139$	5.30773	+	9.19326i	0.450196	+	0.779763i	0.998398	−	0.0565836i	$-0.0180207\pi$
$139$	5.30773	+	9.19326i	0.450196	+	0.779763i	−0.548202	+	0.836346i	$0.684687\pi$
$140$	0.760692	−	16.3171i	0.0642902	−	1.37905i
$141$	−2.09083			−0.176079
$142$	3.50750	−	11.9679i	0.294343	−	1.00432i
$143$	−0.681618	−	1.18060i	−0.0569998	−	0.0987265i
$144$	−3.29795	−	0.308166i	−0.274829	−	0.0256805i
$145$			8.58144i			0.712650i
$146$	−5.49011	+	18.7327i	−0.454365	+	1.55033i
$147$	−2.67523	−	1.54455i	−0.220650	−	0.127392i
$148$	−14.8581	+	7.67899i	−1.22133	+	0.631209i
$149$	−16.0045	−	9.24023i	−1.31114	−	0.756989i	−0.328858	−	0.944379i	$-0.606664\pi$
$149$	−16.0045	−	9.24023i	−1.31114	−	0.756989i	−0.982286	+	0.187390i	$0.939997\pi$
$150$	1.14902	+	4.72588i	0.0938175	+	0.385867i
$151$	−18.5105			−1.50637			−0.753183	−	0.657811i	$-0.771483\pi$
$151$	−18.5105			−1.50637			−0.753183	+	0.657811i	$0.771483\pi$
$152$	3.06364	−	11.9421i	0.248494	−	0.968633i
$153$	5.33737			0.431501
$154$	−3.13758	−	12.9047i	−0.252833	−	1.03989i
$155$	−22.9261	−	13.2364i	−1.84147	−	1.06317i
$156$	0.592488	+	1.14641i	0.0474370	+	0.0917862i
$157$	−21.2242	−	12.2538i	−1.69388	−	0.977961i	−0.951333	−	0.308165i	$-0.900285\pi$
$157$	−21.2242	−	12.2538i	−1.69388	−	0.977961i	−0.742545	−	0.669796i	$-0.766382\pi$
$158$	−0.747289	+	2.54982i	−0.0594511	+	0.202852i
$159$			4.82774i			0.382864i
$160$	−12.0175	+	9.50012i	−0.950070	+	0.751050i
$161$	−3.15904	−	5.47162i	−0.248967	−	0.431224i
$162$	2.31885	−	7.91213i	0.182186	−	0.621635i
$163$	−6.00269			−0.470167			−0.235084	−	0.971975i	$-0.575536\pi$
$163$	−6.00269			−0.470167			−0.235084	+	0.971975i	$0.575536\pi$
$164$	10.7549	+	0.501387i	0.839818	+	0.0391517i
$165$	6.21336	+	10.7619i	0.483709	+	0.837809i
$166$	5.21458	−	1.26784i	0.404730	−	0.0984037i
$167$	−3.39245	−	5.87589i	−0.262515	−	0.454690i	0.704394	−	0.709809i	$-0.251219\pi$
$167$	−3.39245	−	5.87589i	−0.262515	−	0.454690i	−0.966910	+	0.255119i	$0.917885\pi$
$168$	2.39799	+	12.3409i	0.185009	+	0.952120i
$169$	6.40416	−	11.0923i	0.492628	−	0.853256i
$170$	17.8565	−	17.0434i	1.36953	−	1.30717i
$171$	−3.26102	−	1.54738i	−0.249376	−	0.118331i
$172$	−0.453294	+	9.72331i	−0.0345633	+	0.741395i
$173$	−8.69543	+	15.0609i	−0.661101	+	1.14506i	0.319225	+	0.947679i	$0.396577\pi$
$173$	−8.69543	+	15.0609i	−0.661101	+	1.14506i	−0.980327	+	0.197382i	$0.936756\pi$
$174$	−1.56033	−	6.41754i	−0.118288	−	0.486512i
$175$	−6.09502	+	3.51896i	−0.460741	+	0.266009i
$176$	−7.20391	+	10.1600i	−0.543015	+	0.765841i
$177$	−1.45157	−	2.51420i	−0.109107	−	0.188979i
$178$	12.7234	−	12.1441i	0.953662	−	0.910239i
$179$			3.28473i			0.245513i	0.992437	+	0.122756i	$0.0391733\pi$
$179$			3.28473i			0.245513i	−0.992437	+	0.122756i	$0.960827\pi$
$180$	2.05917	+	3.98431i	0.153482	+	0.296973i
$181$	4.17326	+	7.22829i	0.310196	+	0.537275i	0.978405	−	0.206699i	$-0.0662721\pi$
$181$	4.17326	+	7.22829i	0.310196	+	0.537275i	−0.668209	+	0.743974i	$0.732939\pi$
$182$	−1.35084	+	1.28933i	−0.100131	+	0.0955718i
$183$	16.2692			1.20265
$184$	−1.92942	+	5.60226i	−0.142239	+	0.413004i
$185$	19.6123	+	11.3232i	1.44192	+	0.832495i
$186$	19.5517	+	5.73013i	1.43360	+	0.420154i
$187$	10.0347	−	17.3805i	0.733806	−	1.27099i
$188$	−1.53161	+	2.38856i	−0.111704	+	0.174204i
$189$	17.0149			1.23765
$190$	−15.8511	+	5.23633i	−1.14996	+	0.379883i
$191$			4.43183i			0.320676i	0.987062	+	0.160338i	$0.0512584\pi$
$191$			4.43183i			0.320676i	−0.987062	+	0.160338i	$0.948742\pi$
$192$	7.25983	−	9.28966i	0.523933	−	0.670423i
$193$	−6.12690	−	3.53737i	−0.441024	−	0.254625i	0.263008	−	0.964794i	$-0.415286\pi$
$193$	−6.12690	−	3.53737i	−0.441024	−	0.254625i	−0.704032	+	0.710168i	$0.748619\pi$
$194$	−25.2312	−	7.39464i	−1.81149	−	0.530904i
$195$	0.873661	−	1.51322i	0.0625641	−	0.108364i
$196$	−3.72420	+	1.92474i	−0.266014	+	0.137482i
$197$		−	11.2899i		−	0.804372i	−0.915558	−	0.402186i	$-0.868250\pi$
$197$		−	11.2899i		−	0.804372i	0.915558	−	0.402186i	$-0.131750\pi$
$198$	2.51765	+	2.63775i	0.178921	+	0.187457i
$199$	−6.12926	+	3.53873i	−0.434492	+	0.250854i	−0.701258	−	0.712907i	$-0.747378\pi$
$199$	−6.12926	+	3.53873i	−0.434492	+	0.250854i	0.266766	+	0.963761i	$0.414045\pi$
$200$	6.24055	+	2.14925i	0.441273	+	0.151975i
$201$	7.65566			0.539989
$202$	1.52820	−	1.45861i	0.107523	−	0.102628i
$203$	8.27677	−	4.77860i	0.580916	−	0.335392i
$204$	−10.2549	+	15.9925i	−0.717983	+	1.11970i
$205$	−7.28913	−	12.6251i	−0.509095	−	0.881779i
$206$	7.72217	−	1.87753i	0.538029	−	0.130813i
$207$	1.50231	+	0.867362i	0.104418	+	0.0602858i
$208$	1.74368	+	0.162932i	0.120902	+	0.0112973i
$209$	−11.1698	+	7.70995i	−0.772632	+	0.533308i
$210$	12.3137	−	11.7531i	0.849729	−	0.811038i
$211$	15.7615	+	9.09989i	1.08506	+	0.626462i	0.932258	−	0.361794i	$-0.117836\pi$
$211$	15.7615	+	9.09989i	1.08506	+	0.626462i	0.152806	+	0.988256i	$0.451169\pi$
$212$	5.51520	+	3.53651i	0.378786	+	0.242888i
$213$	11.2551	−	6.49813i	0.771186	−	0.445244i
$214$	3.01064	+	12.3826i	0.205803	+	0.846457i
$215$	11.4141	−	6.58996i	0.778438	−	0.449431i
$216$	−10.4679	−	12.0435i	−0.712248	−	0.819456i
$217$			29.4828i			2.00142i
$218$	−4.47289	+	15.2619i	−0.302943	+	1.03367i
$219$	−17.6170	+	10.1712i	−1.19045	+	0.687306i
$220$	16.8459	+	0.785342i	1.13575	+	0.0529477i
$221$	−2.82195			−0.189825
$222$	−16.7257	−	4.90189i	−1.12255	−	0.328993i
$223$	0.772936	−	1.33877i	0.0517596	−	0.0896503i	−0.838985	−	0.544155i	$-0.816850\pi$
$223$	0.772936	−	1.33877i	0.0517596	−	0.0896503i	0.890744	+	0.454505i	$0.150184\pi$
$224$	15.8548	+	6.30072i	1.05935	+	0.420984i
$225$	0.966184	−	1.67348i	0.0644123	−	0.111565i
$226$	−1.41022	−	5.80018i	−0.0938067	−	0.385823i
$227$			3.30271i			0.219209i	0.993975	+	0.109604i	$0.0349584\pi$
$227$			3.30271i			0.219209i	−0.993975	+	0.109604i	$0.965042\pi$
$228$	10.9019	−	6.79806i	0.721999	−	0.450212i
$229$		−	8.81252i		−	0.582348i	−0.956670	−	0.291174i	$-0.905954\pi$
$229$		−	8.81252i		−	0.582348i	0.956670	−	0.291174i	$-0.0940458\pi$
$230$	7.79576	−	1.89542i	0.514037	−	0.124980i
$231$	6.91985	−	11.9855i	0.455293	−	0.788590i
$232$	−8.47439	−	2.91858i	−0.556371	−	0.191614i
$233$	3.15790	−	5.46965i	0.206881	−	0.358329i	−0.743849	−	0.668347i	$-0.767002\pi$
$233$	3.15790	−	5.46965i	0.206881	−	0.358329i	0.950730	+	0.310019i	$0.100335\pi$
$234$	0.144201	−	0.492025i	0.00942669	−	0.0321647i
$235$	3.84197			0.250622
$236$	−3.93555	−	0.183473i	−0.256183	−	0.0119430i
$237$	−2.39795	+	1.38446i	−0.155764	+	0.0899301i
$238$	−26.3818	−	7.73185i	−1.71007	−	0.501181i
$239$		−	26.2612i		−	1.69870i	−0.527834	−	0.849348i	$-0.676996\pi$
$239$		−	26.2612i		−	1.69870i	0.527834	−	0.849348i	$-0.323004\pi$
$240$	−15.8947	−	1.48522i	−1.02600	−	0.0958708i
$241$	1.61651	−	0.933290i	0.104128	−	0.0601185i	−0.447031	−	0.894518i	$-0.647519\pi$
$241$	1.61651	−	0.933290i	0.104128	−	0.0601185i	0.551160	+	0.834400i	$0.314185\pi$
$242$	−1.79309	+	0.435961i	−0.115264	+	0.0280247i
$243$	−7.21645	+	4.16642i	−0.462935	+	0.267276i
$244$	11.9178	−	18.5859i	0.762959	−	1.18984i
$245$	4.91583	+	2.83816i	0.314061	+	0.181323i
$246$	7.74667	+	8.11623i	0.493910	+	0.517472i
$247$	1.72415	+	0.818120i	0.109705	+	0.0520558i
$248$	20.8685	−	18.1383i	1.32515	−	1.15178i
$249$	4.84315	+	2.79619i	0.306922	+	0.177202i
$250$	2.41257	+	9.92279i	0.152584	+	0.627572i
$251$	10.1173	+	17.5236i	0.638596	+	1.10608i	0.985741	+	0.168269i	$0.0538177\pi$
$251$	10.1173	+	17.5236i	0.638596	+	1.10608i	−0.347145	+	0.937811i	$0.612849\pi$
$252$	2.69620	−	4.20474i	0.169845	−	0.264874i
$253$	5.64893	−	3.26141i	0.355145	−	0.205043i
$254$	15.3498	+	16.0821i	0.963132	+	1.00908i
$255$	25.7237			1.61088
$256$	−5.29439	−	15.0987i	−0.330899	−	0.943666i
$257$	−10.3865	+	5.99663i	−0.647890	+	0.374060i	−0.787647	−	0.616126i	$-0.788701\pi$
$257$	−10.3865	+	5.99663i	−0.647890	+	0.374060i	0.139757	+	0.990186i	$0.455368\pi$
$258$	−7.33772	+	7.00361i	−0.456827	+	0.436026i
$259$		−	25.2213i		−	1.56718i
$260$	−1.08872	−	2.10656i	−0.0675193	−	0.130644i
$261$	−1.31204	+	2.27251i	−0.0812129	+	0.140665i
$262$	−4.04207	+	13.7919i	−0.249720	+	0.852065i
$263$	24.8302	+	14.3357i	1.53109	+	0.883978i	0.999312	+	0.0370975i	$0.0118112\pi$
$263$	24.8302	+	14.3357i	1.53109	+	0.883978i	0.531783	+	0.846881i	$0.321522\pi$
$264$	−12.7408	+	2.47570i	−0.784142	+	0.152369i
$265$		−	8.87113i		−	0.544949i
$266$	13.8771	+	12.3724i	0.850861	+	0.758602i
$267$	18.3292			1.12173
$268$	5.60807	−	8.74582i	0.342568	−	0.534236i
$269$	−7.77990	+	13.4752i	−0.474349	+	0.821596i	−0.999569	−	0.0293704i	$-0.990650\pi$
$269$	−7.77990	+	13.4752i	−0.474349	+	0.821596i	0.525220	+	0.850967i	$0.323983\pi$
$270$	−6.07661	+	20.7339i	−0.369811	+	1.26183i
$271$	−2.99285	−	1.72792i	−0.181803	−	0.104964i	0.406337	−	0.913723i	$-0.366806\pi$
$271$	−2.99285	−	1.72792i	−0.181803	−	0.104964i	−0.588139	+	0.808760i	$0.700139\pi$
$272$	10.7577	+	23.4303i	0.652284	+	1.42067i
$273$	−1.94600			−0.117777
$274$	−14.0124	−	14.6809i	−0.846520	−	0.886904i
$275$	−3.63300	−	6.29253i	−0.219078	−	0.379454i
$276$	−5.48534	+	2.83494i	−0.330179	+	0.170643i
$277$		−	1.41483i		−	0.0850090i	−0.999096	−	0.0425045i	$-0.986466\pi$
$277$		−	1.41483i		−	0.0850090i	0.999096	−	0.0425045i	$-0.0135337\pi$
$278$	10.3653	+	10.8598i	0.621672	+	0.651329i
$279$	−4.04747	−	7.01043i	−0.242316	−	0.419703i
$280$	−4.40639	−	22.6768i	−0.263332	−	1.35520i
$281$	4.69854	−	2.71270i	0.280291	−	0.161826i	−0.353264	−	0.935524i	$-0.614928\pi$
$281$	4.69854	−	2.71270i	0.280291	−	0.161826i	0.633555	+	0.773697i	$0.281595\pi$
$282$	−2.87317	+	0.698567i	−0.171095	+	0.0415991i
$283$	8.05693	−	13.9550i	0.478935	−	0.829540i	−0.520773	−	0.853695i	$-0.674356\pi$
$283$	8.05693	−	13.9550i	0.478935	−	0.829540i	0.999708	+	0.0241553i	$0.00768962\pi$
$284$	0.821335	−	17.6179i	0.0487373	−	1.04543i
$285$	−15.7167	−	7.45766i	−0.930974	−	0.441754i
$286$	−1.33112	−	1.39462i	−0.0787105	−	0.0824654i
$287$	−8.11794	+	14.0607i	−0.479187	+	0.829976i
$288$	−4.63494	+	0.678405i	−0.273117	+	0.0399754i
$289$	−12.2721	−	21.2559i	−0.721887	−	1.25034i
$290$	2.86715	+	11.7924i	0.168365	+	0.692476i
$291$	−13.6996	−	23.7284i	−0.803085	−	1.39098i
$292$	−1.28560	+	27.5765i	−0.0752338	+	1.61379i
$293$	23.7978			1.39028			0.695142	−	0.718872i	$-0.255341\pi$
$293$	23.7978			1.39028			0.695142	+	0.718872i	$0.255341\pi$
$294$	−4.19230	−	1.22866i	−0.244500	−	0.0716570i
$295$	2.66731	+	4.61992i	0.155297	+	0.268982i
$296$	−17.8521	+	15.5166i	−1.03763	+	0.901882i
$297$			17.5663i			1.01930i
$298$	−25.0804	−	7.35045i	−1.45287	−	0.425800i
$299$	−0.794296	−	0.458587i	−0.0459353	−	0.0265208i
$300$	3.15793	+	6.11031i	0.182323	+	0.352779i
$301$	−12.7120	−	7.33927i	−0.732707	−	0.423028i
$302$	−25.4368	+	6.18457i	−1.46372	+	0.355882i
$303$	2.20149			0.126472
$304$	0.220002	−	17.4342i	0.0126180	−	0.999920i
$305$	−29.8951			−1.71179
$306$	7.33451	−	1.78327i	0.419286	−	0.101943i
$307$	−1.43431	−	0.828099i	−0.0818604	−	0.0472621i	0.458511	−	0.888689i	$-0.348383\pi$
$307$	−1.43431	−	0.828099i	−0.0818604	−	0.0472621i	−0.540371	+	0.841427i	$0.681716\pi$
$308$	−8.62320	−	16.6851i	−0.491352	−	0.950722i
$309$	7.17214	+	4.14084i	0.408009	+	0.235564i
$310$	−35.9269	−	10.5293i	−2.04051	−	0.598025i
$311$		−	0.650991i		−	0.0369143i	−0.999830	−	0.0184572i	$-0.994125\pi$
$311$		−	0.650991i		−	0.0369143i	0.999830	−	0.0184572i	$-0.00587543\pi$
$312$	1.19721	+	1.37742i	0.0677788	+	0.0779808i
$313$	9.66128	+	16.7338i	0.546088	+	0.945852i	0.998538	+	0.0540617i	$0.0172168\pi$
$313$	9.66128	+	16.7338i	0.546088	+	0.945852i	−0.452450	+	0.891790i	$0.649450\pi$
$314$	−33.2600	−	9.74771i	−1.87697	−	0.550095i
$315$	−6.76327			−0.381067
$316$	−0.174989	+	3.75358i	−0.00984392	+	0.211156i
$317$	10.4707	+	18.1358i	0.588093	+	1.01861i	0.994482	+	0.104907i	$0.0334545\pi$
$317$	10.4707	+	18.1358i	0.588093	+	1.01861i	−0.406389	+	0.913700i	$0.633212\pi$
$318$	1.61300	+	6.63418i	0.0904524	+	0.372026i
$319$	4.93345	+	8.54498i	0.276220	+	0.478427i
$320$	−13.3402	+	17.0701i	−0.745739	+	0.954245i
$321$	−6.63988	+	11.5006i	−0.370602	+	0.641901i
$322$	−6.16921	−	6.46352i	−0.343797	−	0.360198i
$323$	2.26070	+	28.0041i	0.125789	+	1.55819i
$324$	0.542995	−	11.6474i	0.0301664	−	0.647080i
$325$	−0.510836	+	0.884793i	−0.0283361	+	0.0490795i
$326$	−8.24878	+	2.00556i	−0.456858	+	0.111078i
$327$	−14.3529	+	8.28666i	−0.793718	+	0.458253i
$328$	14.9467	−	2.90434i	0.825294	−	0.160365i
$329$	−2.13941	−	3.70556i	−0.117949	−	0.204294i
$330$	12.1339	+	12.7128i	0.667950	+	0.699815i
$331$		−	7.37076i		−	0.405134i	−0.979268	−	0.202567i	$-0.935072\pi$
$331$		−	7.37076i		−	0.405134i	0.979268	−	0.202567i	$-0.0649284\pi$
$332$	6.74216	−	3.48449i	0.370024	−	0.191236i
$333$	3.46244	+	5.99713i	0.189741	+	0.328641i
$334$	−6.62503	−	6.94108i	−0.362505	−	0.379799i
$335$	−14.0675			−0.768592
$336$	7.41849	+	16.1574i	0.404712	+	0.881458i
$337$	−9.00098	−	5.19672i	−0.490315	−	0.283083i	0.234390	−	0.972143i	$-0.424691\pi$
$337$	−9.00098	−	5.19672i	−0.490315	−	0.283083i	−0.724705	+	0.689059i	$0.758024\pi$
$338$	5.09440	−	17.3825i	0.277099	−	0.945486i
$339$	3.11021	−	5.38705i	0.168924	−	0.292584i
$340$	18.8436	−	29.3868i	1.02194	−	1.59372i
$341$	−30.4382			−1.64832
$342$	−4.99822	−	1.03683i	−0.270273	−	0.0560655i
$343$			14.7901i			0.798588i
$344$	2.62575	+	13.5130i	0.141571	+	0.728573i
$345$	7.24048	+	4.18029i	0.389814	+	0.225060i
$346$	−6.91707	+	23.6017i	−0.371864	+	1.26883i
$347$	9.25966	−	16.0382i	0.497085	−	0.860976i	−0.502910	−	0.864339i	$-0.667737\pi$
$347$	9.25966	−	16.0382i	0.497085	−	0.860976i	0.999994	+	0.00336302i	$0.00107049\pi$
$348$	−4.28833	−	8.29753i	−0.229879	−	0.444794i
$349$		−	16.1158i		−	0.862661i	−0.902194	−	0.431330i	$-0.858044\pi$
$349$		−	16.1158i		−	0.862661i	0.902194	−	0.431330i	$-0.141956\pi$
$350$	−7.19994	+	6.87210i	−0.384853	+	0.367329i
$351$	2.13908	−	1.23500i	0.114176	−	0.0659194i
$352$	−6.50489	+	16.3686i	−0.346712	+	0.872450i
$353$	32.0716			1.70700			0.853500	−	0.521093i	$-0.174476\pi$
$353$	32.0716			1.70700			0.853500	+	0.521093i	$0.174476\pi$
$354$	−2.83474	−	2.96997i	−0.150665	−	0.157852i
$355$	−20.6816	+	11.9405i	−1.09767	+	0.633737i
$356$	13.4268	−	20.9392i	0.711620	−	1.10978i
$357$	−14.3243	−	24.8105i	−0.758124	−	1.31311i
$358$	1.09746	+	4.51382i	0.0580028	+	0.238563i
$359$	3.07083	+	1.77294i	0.162072	+	0.0935724i	0.578842	−	0.815440i	$-0.303505\pi$
$359$	3.07083	+	1.77294i	0.162072	+	0.0935724i	−0.416770	+	0.909012i	$0.636838\pi$
$360$	4.16088	+	4.78717i	0.219297	+	0.252306i
$361$	6.73752	−	17.7653i	0.354607	−	0.935016i
$362$	8.14985	+	8.53864i	0.428347	+	0.448781i
$363$	−1.66537	−	0.961501i	−0.0874092	−	0.0504657i
$364$	−1.42552	+	2.22311i	−0.0747176	+	0.116523i
$365$	32.3719	−	18.6899i	1.69442	−	0.978275i
$366$	22.3568	−	5.43570i	1.16861	−	0.284128i
$367$	30.3020	−	17.4948i	1.58175	−	0.913224i	0.587145	−	0.809481i	$-0.300252\pi$
$367$	30.3020	−	17.4948i	1.58175	−	0.913224i	0.994604	−	0.103742i	$-0.0330817\pi$
$368$	−0.779598	+	8.34315i	−0.0406393	+	0.434917i
$369$		−	4.45780i		−	0.232064i
$370$	30.7340	+	9.00738i	1.59778	+	0.468272i
$371$	−8.55617	+	4.93991i	−0.444214	+	0.256467i
$372$	28.7821	+	1.34180i	1.49228	+	0.0695691i
$373$	−6.14462			−0.318157			−0.159078	−	0.987266i	$-0.550852\pi$
$373$	−6.14462			−0.318157			−0.159078	+	0.987266i	$0.550852\pi$
$374$	7.98240	−	27.2367i	0.412760	−	1.40837i
$375$	−5.32086	+	9.21601i	−0.274768	+	0.475913i
$376$	−1.30667	+	3.79404i	−0.0673863	+	0.195663i
$377$	0.693692	−	1.20151i	0.0357270	−	0.0618809i
$378$	23.3816	−	5.68487i	1.20262	−	0.292398i
$379$		−	16.1488i		−	0.829507i	−0.909934	−	0.414753i	$-0.863868\pi$
$379$		−	16.1488i		−	0.829507i	0.909934	−	0.414753i	$-0.136132\pi$
$380$	−20.0327	+	12.4917i	−1.02765	+	0.640809i
$381$			23.1675i			1.18691i
$382$	1.48072	+	6.09013i	0.0757603	+	0.311598i
$383$	5.82205	−	10.0841i	0.297493	−	0.515272i	−0.678069	−	0.734998i	$-0.737183\pi$
$383$	5.82205	−	10.0841i	0.297493	−	0.515272i	0.975562	+	0.219726i	$0.0705163\pi$
$384$	6.87254	−	15.1912i	0.350713	−	0.775225i
$385$	−12.7155	+	22.0238i	−0.648040	+	1.12244i
$386$	−9.60134	−	2.81392i	−0.488695	−	0.143225i
$387$	4.03021			0.204867
$388$	−37.1428	−	1.73157i	−1.88564	−	0.0879072i
$389$	−12.0060	+	6.93167i	−0.608729	+	0.351450i	−0.772468	−	0.635054i	$-0.780978\pi$
$389$	−12.0060	+	6.93167i	−0.608729	+	0.351450i	0.163739	+	0.986504i	$0.447645\pi$
$390$	0.694983	−	2.37134i	0.0351918	−	0.120078i
$391$		−	13.5025i		−	0.682848i
$392$	−4.47465	+	3.88924i	−0.226004	+	0.196436i
$393$	−12.9704	+	7.48849i	−0.654272	+	0.377744i
$394$	−3.77208	−	15.5144i	−0.190034	−	0.781602i
$395$	4.40631	−	2.54399i	0.221706	−	0.128002i
$396$	4.34100	+	2.78357i	0.218143	+	0.139880i
$397$	−10.1183	−	5.84182i	−0.507825	−	0.293193i	0.224114	−	0.974563i	$-0.428051\pi$
$397$	−10.1183	−	5.84182i	−0.507825	−	0.293193i	−0.731939	+	0.681370i	$0.761384\pi$
$398$	−7.24038	+	6.91070i	−0.362928	+	0.346402i
$399$	1.55897	+	19.3115i	0.0780459	+	0.966783i
$400$	9.29372	+	0.868421i	0.464686	+	0.0434210i
$401$	21.4038	+	12.3575i	1.06886	+	0.617105i	0.927869	−	0.372907i	$-0.121639\pi$
$401$	21.4038	+	12.3575i	1.06886	+	0.617105i	0.140988	+	0.990011i	$0.454972\pi$
$402$	10.5203	−	2.55784i	0.524703	−	0.127573i
$403$	2.13996	+	3.70652i	0.106599	+	0.184635i
$404$	1.61268	−	2.51498i	0.0802337	−	0.125125i
$405$	−13.6729	+	7.89403i	−0.679410	+	0.392258i
$406$	9.77720	−	9.33201i	0.485234	−	0.463140i
$407$	26.0386			1.29069
$408$	−8.74875	+	25.4028i	−0.433128	+	1.25763i
$409$	16.4212	−	9.48080i	0.811978	−	0.468796i	−0.0356645	−	0.999364i	$-0.511355\pi$
$409$	16.4212	−	9.48080i	0.811978	−	0.468796i	0.847642	+	0.530568i	$0.178021\pi$
$410$	−14.2348	−	14.9138i	−0.703005	−	0.736542i
$411$		−	21.1490i		−	1.04320i
$412$	9.98435	−	5.16012i	0.491894	−	0.254221i
$413$	2.97060	−	5.14523i	0.146174	−	0.253180i
$414$	2.35424	+	0.689972i	0.115705	+	0.0339103i
$415$	−8.89945	−	5.13810i	−0.436857	−	0.252219i
$416$	2.45056	−	0.358683i	0.120149	−	0.0175859i
$417$			15.6445i			0.766113i
$418$	−12.7734	+	14.3268i	−0.624765	+	0.700747i
$419$	8.83253			0.431497			0.215749	−	0.976449i	$-0.430781\pi$
$419$	8.83253			0.431497			0.215749	+	0.976449i	$0.430781\pi$
$420$	12.9945	−	20.2650i	0.634066	−	0.988830i
$421$	0.915408	−	1.58553i	0.0446143	−	0.0772742i	−0.842856	−	0.538139i	$-0.819127\pi$
$421$	0.915408	−	1.58553i	0.0446143	−	0.0772742i	0.887470	+	0.460865i	$0.152461\pi$
$422$	24.6995	+	7.23881i	1.20235	+	0.352380i
$423$	1.01742	+	0.587406i	0.0494685	+	0.0285607i
$424$	8.76046	+	3.01711i	0.425446	+	0.146524i
$425$	−15.0409			−0.729588
$426$	13.2954	−	12.6900i	0.644165	−	0.614834i
$427$	16.6472	+	28.8338i	0.805613	+	1.39536i
$428$	8.27431	+	16.0100i	0.399954	+	0.773874i
$429$		−	2.00906i		−	0.0969984i
$430$	13.4833	−	12.8694i	0.650223	−	0.620616i
$431$	−11.5493	−	20.0040i	−0.556310	−	0.963557i	−0.997800	−	0.0662911i	$-0.978883\pi$
$431$	−11.5493	−	20.0040i	−0.556310	−	0.963557i	0.441490	−	0.897266i	$-0.354450\pi$
$432$	−18.4086	−	13.0525i	−0.885684	−	0.627989i
$433$	1.33452	−	0.770486i	0.0641330	−	0.0370272i	−0.467591	−	0.883945i	$-0.654878\pi$
$433$	1.33452	−	0.770486i	0.0641330	−	0.0370272i	0.531724	+	0.846918i	$0.321545\pi$
$434$	9.85051	+	40.5147i	0.472840	+	1.94477i
$435$	−6.32342	+	10.9525i	−0.303185	+	0.525132i
$436$	−1.04740	+	22.4671i	−0.0501613	+	1.07598i
$437$	−3.91455	+	8.24971i	−0.187258	+	0.394637i
$438$	−20.8107	+	19.8631i	−0.994372	+	0.949095i
$439$	−18.4223	+	31.9083i	−0.879246	+	1.52290i	−0.0270772	+	0.999633i	$0.508620\pi$
$439$	−18.4223	+	31.9083i	−0.879246	+	1.52290i	−0.852169	+	0.523266i	$0.824713\pi$
$440$	23.4116	−	4.54918i	1.11611	−	0.216874i
$441$	0.867864	+	1.50318i	0.0413269	+	0.0715802i
$442$	−3.87786	+	0.942841i	−0.184451	+	0.0448464i
$443$	−12.8595	−	22.2732i	−0.610971	−	1.05823i	−0.991077	−	0.133290i	$-0.957446\pi$
$443$	−12.8595	−	22.2732i	−0.610971	−	1.05823i	0.380106	−	0.924943i	$-0.375887\pi$
$444$	−24.6219	−	1.14785i	−1.16850	−	0.0544747i
$445$	−33.6804			−1.59661
$446$	0.614858	−	2.09795i	0.0291144	−	0.0993408i
$447$	−13.6177	−	23.5866i	−0.644097	−	1.11561i
$448$	23.8925	+	3.36105i	1.12882	+	0.158795i
$449$			12.6228i			0.595707i	0.954612	+	0.297853i	$0.0962706\pi$
$449$			12.6228i			0.595707i	−0.954612	+	0.297853i	$0.903729\pi$
$450$	0.768583	−	2.62247i	0.0362314	−	0.123625i
$451$	−14.5163	−	8.38100i	−0.683547	−	0.394646i
$452$	−3.87580	−	7.49933i	−0.182303	−	0.352739i
$453$	−23.6250	−	13.6399i	−1.11000	−	0.640858i
$454$	1.10347	+	4.53852i	0.0517884	+	0.213003i
$455$	3.57584			0.167638
$456$	12.7099	−	12.9842i	0.595197	−	0.608041i
$457$	3.27588			0.153239			0.0766197	−	0.997060i	$-0.475587\pi$
$457$	3.27588			0.153239			0.0766197	+	0.997060i	$0.475587\pi$
$458$	−2.94435	−	12.1100i	−0.137581	−	0.565862i
$459$	31.4911	+	18.1814i	1.46988	+	0.848636i
$460$	10.0795	−	5.20929i	0.469959	−	0.242884i
$461$	14.3820	+	8.30348i	0.669839	+	0.386732i	0.796015	−	0.605276i	$-0.206937\pi$
$461$	14.3820	+	8.30348i	0.669839	+	0.386732i	−0.126177	+	0.992008i	$0.540271\pi$
$462$	5.50463	−	18.7823i	0.256098	−	0.873830i
$463$			29.2576i			1.35972i	0.733344	+	0.679858i	$0.237958\pi$
$463$			29.2576i			1.35972i	−0.733344	+	0.679858i	$0.762042\pi$
$464$	−12.6205	−	1.17928i	−0.585890	−	0.0547466i
$465$	−19.5070	−	33.7871i	−0.904616	−	1.56684i
$466$	2.51206	−	8.57137i	0.116369	−	0.397061i
$467$	−7.69409			−0.356040			−0.178020	−	0.984027i	$-0.556969\pi$
$467$	−7.69409			−0.356040			−0.178020	+	0.984027i	$0.556969\pi$
$468$	0.0337668	−	0.724310i	0.00156087	−	0.0334813i
$469$	7.83354	+	13.5681i	0.361719	+	0.626516i
$470$	5.27955	−	1.28364i	0.243528	−	0.0592099i
$471$	−18.0590	−	31.2791i	−0.832114	−	1.44126i
$472$	−5.46946	+	1.06278i	−0.251752	+	0.0489186i
$473$	7.57710	−	13.1239i	0.348395	−	0.603438i
$474$	−2.83265	+	2.70367i	−0.130108	+	0.124184i
$475$	9.18964	+	4.36055i	0.421650	+	0.200076i
$476$	−38.8366	−	1.81053i	−1.78007	−	0.0829856i
$477$	1.35633	−	2.34923i	0.0621019	−	0.107564i
$478$	−8.77414	−	36.0876i	−0.401320	−	1.65061i
$479$	30.9763	−	17.8841i	1.41534	−	0.817148i	0.419456	−	0.907776i	$-0.362221\pi$
$479$	30.9763	−	17.8841i	1.41534	−	0.817148i	0.995885	+	0.0906279i	$0.0288874\pi$
$480$	−22.3384	+	3.26961i	−1.01960	+	0.149237i
$481$	−1.83064	−	3.17077i	−0.0834702	−	0.144575i
$482$	1.90955	−	1.82260i	0.0869775	−	0.0830171i
$483$		−	9.31123i		−	0.423676i
$484$	−2.31837	+	1.19818i	−0.105380	+	0.0544627i
$485$	25.1735	+	43.6017i	1.14307	+	1.97985i
$486$	−8.52465	+	8.13650i	−0.386686	+	0.369079i
$487$	−2.98739			−0.135372			−0.0676858	−	0.997707i	$-0.521562\pi$
$487$	−2.98739			−0.135372			−0.0676858	+	0.997707i	$0.521562\pi$
$488$	10.1675	−	29.5222i	0.460259	−	1.33641i
$489$	−7.66123	−	4.42321i	−0.346453	−	0.200025i
$490$	7.70350	+	2.25771i	0.348008	+	0.101993i
$491$	−16.2391	+	28.1269i	−0.732858	+	1.26935i	0.222798	+	0.974865i	$0.428481\pi$
$491$	−16.2391	+	28.1269i	−0.732858	+	1.26935i	−0.955657	+	0.294483i	$0.904853\pi$
$492$	13.3570	+	8.56492i	0.602182	+	0.386136i
$493$	20.4248			0.919887
$494$	2.64263	+	0.548189i	0.118898	+	0.0246642i
$495$		−	6.98244i		−	0.313837i
$496$	22.6169	−	31.8977i	1.01553	−	1.43225i
$497$	23.0332	+	13.2982i	1.03318	+	0.596507i
$498$	7.58960	+	2.22433i	0.340098	+	0.0996744i
$499$	−4.86494	+	8.42632i	−0.217785	+	0.377214i	−0.954130	−	0.299391i	$-0.903216\pi$
$499$	−4.86494	+	8.42632i	−0.217785	+	0.377214i	0.736346	+	0.676605i	$0.236550\pi$
$500$	6.63062	+	12.8296i	0.296530	+	0.573759i
$501$		−	9.99919i		−	0.446731i
$502$	19.7578	+	20.7003i	0.881832	+	0.923900i
$503$	−15.8302	+	9.13954i	−0.705832	+	0.407512i	−0.809516	−	0.587098i	$-0.800270\pi$
$503$	−15.8302	+	9.13954i	−0.705832	+	0.407512i	0.103684	+	0.994610i	$0.466937\pi$
$504$	2.30022	−	6.67890i	0.102460	−	0.297502i
$505$	−4.04531			−0.180014
$506$	6.67297	−	6.36913i	0.296650	−	0.283142i
$507$	16.3472	−	9.43809i	0.726007	−	0.419160i
$508$	26.4666	+	16.9711i	1.17426	+	0.752972i
$509$	2.39384	+	4.14625i	0.106105	+	0.183779i	0.914189	−	0.405288i	$-0.132829\pi$
$509$	2.39384	+	4.14625i	0.106105	+	0.183779i	−0.808084	+	0.589067i	$0.799495\pi$
$510$	35.3490	−	8.59457i	1.56528	−	0.380574i
$511$	−36.0527	−	20.8150i	−1.59488	−	0.920803i
$512$	−12.3201	−	18.9794i	−0.544475	−	0.838777i
$513$	−13.9694	−	20.2382i	−0.616763	−	0.893537i
$514$	−12.2693	+	11.7107i	−0.541177	+	0.516536i
$515$	−13.1790	−	7.60892i	−0.580738	−	0.335289i
$516$	−7.74337	+	12.0758i	−0.340883	+	0.531609i
$517$	3.82564	−	2.20874i	0.168252	−	0.0971401i
$518$	−8.42670	−	34.6586i	−0.370248	−	1.52281i
$519$	−22.1959	+	12.8148i	−0.974294	+	0.562509i
$520$	−2.19992	−	2.53105i	−0.0964727	−	0.110994i
$521$			14.4161i			0.631582i	0.948829	+	0.315791i	$0.102270\pi$
$521$			14.4161i			0.631582i	−0.948829	+	0.315791i	$0.897730\pi$
$522$	−1.04370	+	3.56120i	−0.0456816	+	0.155870i
$523$	−13.5585	+	7.82801i	−0.592873	+	0.342295i	−0.766233	−	0.642563i	$-0.777871\pi$
$523$	−13.5585	+	7.82801i	−0.592873	+	0.342295i	0.173360	+	0.984859i	$0.444538\pi$
$524$	−0.946513	+	20.3030i	−0.0413486	+	0.886942i
$525$	−10.3721			−0.452676
$526$	38.9109	+	11.4038i	1.69659	+	0.497230i
$527$	−31.5041	+	54.5666i	−1.37234	+	2.37696i
$528$	−16.6810	+	7.65889i	−0.725947	+	0.333310i
$529$	−9.30575	+	16.1180i	−0.404598	+	0.700784i
$530$	−2.96394	−	12.1905i	−0.128745	−	0.529523i
$531$			1.63125i			0.0707900i
$532$	23.2034	+	12.3654i	1.00600	+	0.536110i
$533$			2.35691i			0.102089i
$534$	25.1876	−	6.12396i	1.08997	−	0.265010i
$535$	12.2010	−	21.1328i	0.527495	−	0.913649i
$536$	4.78443	−	13.8920i	0.206656	−	0.600045i
$537$	−2.42043	+	4.19230i	−0.104449	+	0.180911i
$538$	−6.18878	+	21.1167i	−0.266817	+	0.910404i
$539$	6.52660			0.281120
$540$	−1.42293	+	30.5224i	−0.0612333	+	1.31347i
$541$	7.10566	−	4.10246i	0.305496	−	0.176378i	−0.339413	−	0.940637i	$-0.610228\pi$
$541$	7.10566	−	4.10246i	0.305496	−	0.176378i	0.644909	+	0.764259i	$0.276895\pi$
$542$	−4.69003	−	1.37453i	−0.201454	−	0.0590413i
$543$			12.3006i			0.527870i
$544$	22.6114	+	28.6031i	0.969454	+	1.22635i
$545$	26.3740	−	15.2270i	1.12974	−	0.652254i
$546$	−2.67415	+	0.650179i	−0.114443	+	0.0278251i
$547$	25.9507	−	14.9826i	1.10957	−	0.640611i	0.170853	−	0.985297i	$-0.445348\pi$
$547$	25.9507	−	14.9826i	1.10957	−	0.640611i	0.938718	+	0.344685i	$0.112014\pi$
$548$	−24.1606	−	15.4925i	−1.03209	−	0.661805i
$549$	−7.91674	−	4.57073i	−0.337878	−	0.195074i
$550$	−7.09479	−	7.43325i	−0.302523	−	0.316955i
$551$	−12.4791	−	5.92143i	−0.531629	−	0.252261i
$552$	−6.59066	+	5.72842i	−0.280517	+	0.243818i
$553$	−4.90733	−	2.83325i	−0.208681	−	0.120482i
$554$	−0.472710	−	1.94423i	−0.0200835	−	0.0826025i
$555$	16.6874	+	28.9035i	0.708342	+	1.22688i
$556$	17.8722	+	11.4602i	0.757952	+	0.486020i
$557$	33.2847	−	19.2169i	1.41032	−	0.814247i	0.414900	−	0.909867i	$-0.363817\pi$
$557$	33.2847	−	19.2169i	1.41032	−	0.814247i	0.995418	+	0.0956198i	$0.0304833\pi$
$558$	−7.90421	−	8.28129i	−0.334612	−	0.350575i
$559$	−2.13083			−0.0901246
$560$	−13.6317	−	29.6898i	−0.576045	−	1.25462i
$561$	25.6144	−	14.7885i	1.08144	−	0.624371i
$562$	5.55030	−	5.29757i	0.234125	−	0.223465i
$563$			0.0334791i			0.00141098i	1.00000		0.000705488i	$0.000224564\pi$
$563$			0.0334791i			0.00141098i	−1.00000		0.000705488i	$0.999775\pi$
$564$	−3.71486	+	1.91991i	−0.156424	+	0.0808430i
$565$	−5.71512	+	9.89888i	−0.240437	+	0.416449i
$566$	6.40916	−	21.8686i	0.269397	−	0.919206i
$567$	15.2275	+	8.79162i	0.639496	+	0.369213i
$568$	−4.75767	−	24.4846i	−0.199627	−	1.02735i
$569$		−	0.534632i		−	0.0224129i	−0.999937	−	0.0112065i	$-0.996433\pi$
$569$		−	0.534632i		−	0.0224129i	0.999937	−	0.0112065i	$-0.00356720\pi$
$570$	−24.0892	−	4.99707i	−1.00899	−	0.209304i
$571$	−37.1365			−1.55411			−0.777057	−	0.629430i	$-0.783288\pi$
$571$	−37.1365			−1.55411			−0.777057	+	0.629430i	$0.783288\pi$
$572$	−2.29515	−	1.47172i	−0.0959650	−	0.0615355i
$573$	−3.26569	+	5.65634i	−0.136426	+	0.236297i
$574$	−6.45769	+	22.0342i	−0.269539	+	0.919690i
$575$	−4.23356	−	2.44425i	−0.176552	−	0.101932i
$576$	−6.14258	+	2.48083i	−0.255941	+	0.103368i
$577$	−25.7080			−1.07024			−0.535118	−	0.844777i	$-0.679733\pi$
$577$	−25.7080			−1.07024			−0.535118	+	0.844777i	$0.679733\pi$
$578$	−23.9658	−	25.1091i	−0.996847	−	1.04440i
$579$	−5.21318	−	9.02949i	−0.216652	−	0.375253i
$580$	7.87996	+	15.2470i	0.327198	+	0.633097i
$581$			11.4447i			0.474804i
$582$	−26.7536	−	28.0299i	−1.10897	−	1.16188i
$583$	−5.09999	−	8.83344i	−0.211220	−	0.365844i
$584$	7.44695	+	38.3245i	0.308157	+	1.58588i
$585$	−0.850264	+	0.490900i	−0.0351541	+	0.0202962i
$586$	32.7025	−	7.95110i	1.35093	−	0.328457i
$587$	−9.70642	+	16.8120i	−0.400627	+	0.693906i	−0.993802	−	0.111168i	$-0.964541\pi$
$587$	−9.70642	+	16.8120i	−0.400627	+	0.693906i	0.593175	+	0.805074i	$0.297874\pi$
$588$	−6.17149	−	0.287710i	−0.254508	−	0.0118650i
$589$	35.0679	−	24.2056i	1.44495	−	0.997374i
$590$	5.20893	+	5.45743i	0.214448	+	0.224679i
$591$	8.31921	−	14.4093i	0.342207	−	0.592719i
$592$	−19.3478	+	27.2871i	−0.795189	+	1.12149i
$593$	−14.9132	−	25.8304i	−0.612411	−	1.06073i	−0.990833	−	0.135093i	$-0.956867\pi$
$593$	−14.9132	−	25.8304i	−0.612411	−	1.06073i	0.378422	−	0.925633i	$-0.376467\pi$
$594$	5.86909	+	24.1393i	0.240811	+	0.990446i
$595$	26.3214	+	45.5900i	1.07907	+	1.86901i
$596$	−36.9208	−	1.72122i	−1.51234	−	0.0705040i
$597$	−10.4304			−0.426886
$598$	−1.24472	−	0.364798i	−0.0509005	−	0.0149177i
$599$	3.62259	+	6.27451i	0.148015	+	0.256369i	0.930494	−	0.366308i	$-0.119378\pi$
$599$	3.62259	+	6.27451i	0.148015	+	0.256369i	−0.782479	+	0.622677i	$0.786045\pi$
$600$	6.38109	+	7.34157i	0.260507	+	0.299718i
$601$		−	23.7575i		−	0.969088i	−0.874767	−	0.484544i	$-0.838985\pi$
$601$		−	23.7575i		−	0.969088i	0.874767	−	0.484544i	$-0.161015\pi$
$602$	−19.9207	−	5.83827i	−0.811906	−	0.237950i
$603$	−3.72532	−	2.15082i	−0.151707	−	0.0875880i
$604$	−32.8884	+	16.9974i	−1.33821	+	0.691615i
$605$	3.06017	+	1.76679i	0.124414	+	0.0718303i
$606$	3.02524	−	0.735541i	0.122892	−	0.0298793i
$607$	15.5235			0.630081			0.315041	−	0.949078i	$-0.397982\pi$
$607$	15.5235			0.630081			0.315041	+	0.949078i	$0.397982\pi$
$608$	−5.52263	−	24.0312i	−0.223972	−	0.974596i
$609$	14.0849			0.570747
$610$	−41.0813	+	9.98828i	−1.66333	+	0.404413i
$611$	−0.537924	−	0.310570i	−0.0217621	−	0.0125643i
$612$	9.48312	−	4.90107i	0.383332	−	0.198114i
$613$	6.02011	+	3.47571i	0.243150	+	0.140383i	0.616624	−	0.787258i	$-0.288500\pi$
$613$	6.02011	+	3.47571i	0.243150	+	0.140383i	−0.373474	+	0.927641i	$0.621833\pi$
$614$	−2.24768	−	0.658739i	−0.0907088	−	0.0265845i
$615$		−	21.4846i		−	0.866344i
$616$	−17.4245	−	20.0472i	−0.702053	−	0.807726i
$617$	−13.4941	−	23.3725i	−0.543253	−	0.940943i	−0.998715	−	0.0506869i	$-0.983859\pi$
$617$	−13.4941	−	23.3725i	−0.543253	−	0.940943i	0.455461	−	0.890256i	$-0.349474\pi$
$618$	11.2393	+	3.29397i	0.452111	+	0.132503i
$619$	−21.2410			−0.853747			−0.426874	−	0.904311i	$-0.640385\pi$
$619$	−21.2410			−0.853747			−0.426874	+	0.904311i	$0.640385\pi$
$620$	−52.8880	−	2.46560i	−2.12403	−	0.0990210i
$621$	5.90923	+	10.2351i	0.237129	+	0.410720i
$622$	−0.217503	−	0.894579i	−0.00872108	−	0.0358694i
$623$	18.7550	+	32.4847i	0.751405	+	1.30147i
$624$	2.10539	+	1.49282i	0.0842832	+	0.0597605i
$625$	15.6111	−	27.0393i	0.624446	−	1.08157i
$626$	18.8673	+	19.7673i	0.754088	+	0.790062i
$627$	−19.9373	+	1.60948i	−0.796218	+	0.0642766i
$628$	−48.9621	−	2.28258i	−1.95380	−	0.0910848i
$629$	26.9504	−	46.6795i	1.07458	−	1.86123i
$630$	−9.29395	+	2.25968i	−0.370280	+	0.0900278i
$631$	−7.72930	+	4.46251i	−0.307699	+	0.177650i	−0.645896	−	0.763425i	$-0.723516\pi$
$631$	−7.72930	+	4.46251i	−0.307699	+	0.177650i	0.338198	+	0.941075i	$0.390183\pi$
$632$	1.01364	+	5.21656i	0.0403206	+	0.207504i
$633$	13.4109	+	23.2284i	0.533036	+	0.923245i
$634$	20.4480	+	21.4235i	0.812093	+	0.850834i
$635$		−	42.5711i		−	1.68938i
$636$	4.43310	+	8.57764i	0.175784	+	0.340125i
$637$	−0.458852	−	0.794756i	−0.0181804	−	0.0314894i
$638$	9.63441	+	10.0940i	0.381430	+	0.399626i
$639$	−7.30245			−0.288880
$640$	−12.6285	+	27.9144i	−0.499186	+	1.10341i
$641$	1.70881	+	0.986580i	0.0674938	+	0.0389675i	0.533367	−	0.845884i	$-0.320926\pi$
$641$	1.70881	+	0.986580i	0.0674938	+	0.0389675i	−0.465873	+	0.884851i	$0.654260\pi$
$642$	−5.28191	+	18.0224i	−0.208461	+	0.711286i
$643$	−6.70192	+	11.6081i	−0.264298	+	0.457777i	−0.967379	−	0.253332i	$-0.918474\pi$
$643$	−6.70192	+	11.6081i	−0.264298	+	0.457777i	0.703082	+	0.711109i	$0.251807\pi$
$644$	−10.6371	−	6.82084i	−0.419162	−	0.268779i
$645$	19.4238			0.764812
$646$	12.4631	+	37.7273i	0.490352	+	1.48436i
$647$			25.2982i			0.994575i	0.867586	+	0.497288i	$0.165671\pi$
$647$			25.2982i			0.994575i	−0.867586	+	0.497288i	$0.834329\pi$
$648$	−3.14536	−	16.1871i	−0.123561	−	0.635889i
$649$	5.31196	+	3.06686i	0.208513	+	0.120385i
$650$	−0.406361	+	1.38654i	−0.0159388	+	0.0543846i
$651$	−21.7250	+	37.6289i	−0.851472	+	1.47479i
$652$	−10.6652	+	5.51201i	−0.417682	+	0.215867i
$653$		−	2.28865i		−	0.0895618i	−0.998997	−	0.0447809i	$-0.985741\pi$
$653$		−	2.28865i		−	0.0895618i	0.998997	−	0.0447809i	$-0.0142590\pi$
$654$	−16.9548	+	16.1828i	−0.662986	+	0.632798i
$655$	23.8336	−	13.7603i	0.931257	−	0.537661i
$656$	19.5691	−	8.98493i	0.764045	−	0.350803i
$657$	11.4302			0.445933
$658$	−4.17800	−	4.37731i	−0.162875	−	0.170645i
$659$	−6.55373	+	3.78380i	−0.255297	+	0.147396i	−0.622187	−	0.782868i	$-0.713756\pi$
$659$	−6.55373	+	3.78380i	−0.255297	+	0.147396i	0.366890	+	0.930264i	$0.380422\pi$
$660$	20.9217	+	13.4156i	0.814375	+	0.522200i
$661$	−7.23786	−	12.5363i	−0.281520	−	0.487607i	0.690239	−	0.723581i	$-0.257505\pi$
$661$	−7.23786	−	12.5363i	−0.281520	−	0.487607i	−0.971759	+	0.235974i	$0.924172\pi$
$662$	−2.46265	−	10.1288i	−0.0957136	−	0.393665i
$663$	−3.60165	−	2.07941i	−0.139876	−	0.0807577i
$664$	8.10074	−	7.04094i	0.314370	−	0.273242i
$665$	−2.86465	−	35.4855i	−0.111086	−	1.37607i
$666$	6.76172	+	7.08429i	0.262011	+	0.274511i
$667$	5.74899	+	3.31918i	0.222602	+	0.128519i
$668$	−11.4231	−	7.32480i	−0.441972	−	0.283405i
$669$	1.97300	−	1.13911i	0.0762804	−	0.0440405i
$670$	−19.3313	+	4.70011i	−0.746834	+	0.181581i
$671$	−29.7681	+	17.1866i	−1.14919	+	0.663482i
$672$	15.5927	+	19.7246i	0.601501	+	0.760892i
$673$		−	26.5226i		−	1.02237i	−0.859470	−	0.511186i	$-0.829206\pi$
$673$		−	26.5226i		−	1.02237i	0.859470	−	0.511186i	$-0.170794\pi$
$674$	−14.1052	−	4.13390i	−0.543314	−	0.159232i
$675$	11.4012	−	6.58249i	0.438833	−	0.253360i
$676$	1.19293	−	25.5888i	0.0458821	−	0.984186i
$677$	−6.15109			−0.236405			−0.118203	−	0.992989i	$-0.537713\pi$
$677$	−6.15109			−0.236405			−0.118203	+	0.992989i	$0.537713\pi$
$678$	2.47412	−	8.44193i	0.0950181	−	0.324210i
$679$	28.0358	−	48.5595i	1.07592	−	1.86354i
$680$	16.0761	−	46.6786i	0.616491	−	1.79004i
$681$	−2.43367	+	4.21525i	−0.0932586	+	0.161529i
$682$	−41.8276	+	10.1697i	−1.60166	+	0.389419i
$683$		−	2.04240i		−	0.0781501i	−0.999236	−	0.0390750i	$-0.987559\pi$
$683$		−	2.04240i		−	0.0781501i	0.999236	−	0.0390750i	$-0.0124411\pi$
$684$	−7.21487	+	0.245163i	−0.275867	+	0.00937406i
$685$			38.8620i			1.48484i
$686$	4.94152	+	20.3242i	0.188668	+	0.775982i
$687$	6.49370	−	11.2474i	0.247750	−	0.429115i
$688$	8.12310	+	17.6920i	0.309690	+	0.674502i
$689$	−0.717109	+	1.24207i	−0.0273197	+	0.0473191i
$690$	11.3464	+	3.32536i	0.431950	+	0.126594i
$691$	45.7370			1.73992			0.869960	−	0.493123i	$-0.164145\pi$
$691$	45.7370			1.73992			0.869960	+	0.493123i	$0.164145\pi$
$692$	−1.61974	+	34.7440i	−0.0615733	+	1.32077i
$693$	−6.73454	+	3.88819i	−0.255824	+	0.147700i
$694$	7.36591	−	25.1331i	0.279606	−	0.954041i
$695$		−	28.7473i		−	1.09045i
$696$	−8.66524	−	9.96953i	−0.328455	−	0.377894i
$697$	−30.0493	+	17.3490i	−1.13820	+	0.657139i
$698$	−5.38447	−	22.1461i	−0.203805	−	0.838240i
$699$	8.06086	−	4.65394i	0.304890	−	0.176028i
$700$	−7.59797	+	11.8491i	−0.287176	+	0.447853i
$701$	24.5743	+	14.1880i	0.928159	+	0.535873i	0.886229	−	0.463248i	$-0.153316\pi$
$701$	24.5743	+	14.1880i	0.928159	+	0.535873i	0.0419298	+	0.999121i	$0.486649\pi$
$702$	2.52686	−	2.41180i	0.0953700	−	0.0910275i
$703$	−29.9991	+	20.7069i	−1.13144	+	0.780974i
$704$	−3.46997	+	24.6668i	−0.130779	+	0.929664i
$705$	4.90350	+	2.83104i	0.184676	+	0.106623i
$706$	44.0722	−	10.7155i	1.65868	−	0.403282i
$707$	2.25264	+	3.90169i	0.0847193	+	0.146738i
$708$	−4.88775	−	3.13416i	−0.183693	−	0.117789i
$709$	−4.47396	+	2.58304i	−0.168023	+	0.0970082i	−0.581653	−	0.813437i	$-0.697594\pi$
$709$	−4.47396	+	2.58304i	−0.168023	+	0.0970082i	0.413630	+	0.910445i	$0.364261\pi$
$710$	−24.4308	+	23.3184i	−0.916871	+	0.875123i
$711$	1.55582			0.0583479
$712$	11.4549	−	33.2603i	0.429289	−	1.24648i
$713$	−17.7350	+	10.2393i	−0.664179	+	0.383464i
$714$	−27.9736	−	29.3081i	−1.04689	−	1.09683i
$715$			3.69172i			0.138062i
$716$	3.01623	+	5.83612i	0.112722	+	0.218106i
$717$	19.3511	−	33.5171i	0.722681	−	1.25172i
$718$	4.81223	+	1.41035i	0.179591	+	0.0526337i
$719$	30.3540	+	17.5249i	1.13201	+	0.653568i	0.944441	−	0.328682i	$-0.106605\pi$
$719$	30.3540	+	17.5249i	1.13201	+	0.653568i	0.187573	+	0.982251i	$0.439938\pi$
$720$	7.31724	+	5.18824i	0.272697	+	0.193354i
$721$			16.9482i			0.631184i
$722$	3.32300	−	26.6638i	0.123669	−	0.992324i
$723$	2.75086			0.102306
$724$	14.0522	+	9.01068i	0.522246	+	0.334879i
$725$	3.69735	−	6.40400i	0.137316	−	0.237839i
$726$	−2.60976	−	0.764858i	−0.0968574	−	0.0283866i
$727$	7.95388	+	4.59217i	0.294993	+	0.170314i	0.640191	−	0.768215i	$-0.278855\pi$
$727$	7.95388	+	4.59217i	0.294993	+	0.170314i	−0.345198	+	0.938530i	$0.612188\pi$
$728$	−1.21616	+	3.53123i	−0.0450738	+	0.130876i
$729$	−29.7706			−1.10261
$730$	38.2403	−	36.4991i	1.41534	−	1.35089i
$731$	−15.6848	−	27.1670i	−0.580125	−	1.00481i
$732$	28.9061	−	14.9393i	1.06840	−	0.552171i
$733$		−	1.04212i		−	0.0384918i	−0.999815	−	0.0192459i	$-0.993873\pi$
$733$		−	1.04212i		−	0.0384918i	0.999815	−	0.0192459i	$-0.00612653\pi$
$734$	35.7951	−	34.1653i	1.32122	−	1.26106i
$735$	4.18272	+	7.24468i	0.154282	+	0.267224i
$736$	1.71623	+	11.7255i	0.0632609	+	0.432206i
$737$	−14.0078	+	8.08739i	−0.515983	+	0.297903i
$738$	−1.48940	−	6.12582i	−0.0548255	−	0.225495i
$739$	3.24715	−	5.62423i	0.119448	−	0.206891i	−0.800101	−	0.599865i	$-0.795221\pi$
$739$	3.24715	−	5.62423i	0.119448	−	0.206891i	0.919549	+	0.392975i	$0.128554\pi$
$740$	45.2435	+	2.10922i	1.66318	+	0.0775364i
$741$	1.59768	+	2.31464i	0.0586922	+	0.0850305i
$742$	−10.1072	+	9.64703i	−0.371049	+	0.354154i
$743$	21.4582	−	37.1666i	0.787224	−	1.36351i	−0.140438	−	0.990089i	$-0.544851\pi$
$743$	21.4582	−	37.1666i	0.787224	−	1.36351i	0.927662	−	0.373422i	$-0.121816\pi$
$744$	40.0000	−	7.77252i	1.46647	−	0.284954i
$745$	25.0230	+	43.3412i	0.916773	+	1.58790i
$746$	−8.44382	+	2.05298i	−0.309150	+	0.0751651i
$747$	−1.57115	−	2.72131i	−0.0574854	−	0.0995676i
$748$	1.86920	−	40.0951i	0.0683448	−	1.46602i
$749$	−27.1766			−0.993012
$750$	−4.23266	+	14.4422i	−0.154555	+	0.527355i
$751$	−21.3186	−	36.9250i	−0.777928	−	1.34741i	−0.933134	−	0.359529i	$-0.882937\pi$
$751$	−21.3186	−	36.9250i	−0.777928	−	1.34741i	0.155205	−	0.987882i	$-0.450396\pi$
$752$	−0.527970	+	5.65026i	−0.0192531	+	0.206044i
$753$			29.8205i			1.08672i
$754$	0.551821	−	1.88286i	0.0200961	−	0.0685697i
$755$	43.4117	+	25.0638i	1.57991	+	0.912164i
$756$	30.2311	−	15.6241i	1.09950	−	0.568242i
$757$	33.2731	+	19.2102i	1.20933	+	0.698208i	0.962613	−	0.270879i	$-0.0873144\pi$
$757$	33.2731	+	19.2102i	1.20933	+	0.698208i	0.246718	+	0.969087i	$0.420648\pi$
$758$	−5.39547	−	22.1913i	−0.195972	−	0.806025i
$759$	9.61296			0.348928
$760$	−23.3549	+	23.8589i	−0.847172	+	0.865454i
$761$	−5.18110			−0.187815			−0.0939074	−	0.995581i	$-0.529936\pi$
$761$	−5.18110			−0.187815			−0.0939074	+	0.995581i	$0.529936\pi$
$762$	7.74052	+	31.8364i	0.280409	+	1.15331i
$763$	−29.3728	−	16.9584i	−1.06337	−	0.613935i
$764$	4.06955	+	7.87421i	0.147231	+	0.284879i
$765$	−12.5174	−	7.22694i	−0.452569	−	0.261291i
$766$	4.63134	−	15.8025i	0.167337	−	0.570969i
$767$		−	0.862463i		−	0.0311417i
$768$	4.36855	−	23.1717i	0.157636	−	0.836136i
$769$	23.3360	+	40.4192i	0.841519	+	1.45755i	0.888611	+	0.458663i	$0.151671\pi$
$769$	23.3360	+	40.4192i	0.841519	+	1.45755i	−0.0470919	+	0.998891i	$0.514995\pi$
$770$	−10.1149	+	34.5130i	−0.364517	+	1.24376i
$771$	−17.6750			−0.636549
$772$	−14.1341	−	0.658923i	−0.508698	−	0.0237152i
$773$	−16.0227	−	27.7521i	−0.576296	−	0.998175i	−0.995899	−	0.0904668i	$-0.971164\pi$
$773$	−16.0227	−	27.7521i	−0.576296	−	0.998175i	0.419603	−	0.907708i	$-0.362169\pi$
$774$	5.53823	−	1.34654i	0.199068	−	0.0484002i
$775$	11.4059	+	19.7556i	0.409712	+	0.709641i
$776$	−51.6194	+	10.0303i	−1.85303	+	0.360067i
$777$	18.5849	−	32.1899i	0.666728	−	1.15481i
$778$	−14.1825	+	13.5367i	−0.508466	+	0.485314i
$779$	23.3892	−	1.88815i	0.838004	−	0.0676500i
$780$	0.162741	−	3.49085i	0.00582706	−	0.124993i
$781$	−13.7292	+	23.7796i	−0.491268	+	0.850901i
$782$	−4.51131	−	18.5548i	−0.161324	−	0.663518i
$783$	−15.4823	+	8.93874i	−0.553294	+	0.319444i
$784$	−4.84953	+	6.83954i	−0.173198	+	0.244269i
$785$	33.1840	+	57.4763i	1.18439	+	2.05142i
$786$	−15.3217	+	14.6241i	−0.546508	+	0.521624i
$787$		−	32.2037i		−	1.14794i	−0.818878	−	0.573968i	$-0.805403\pi$
$787$		−	32.2037i		−	1.14794i	0.818878	−	0.573968i	$-0.194597\pi$
$788$	−10.3670	−	20.0592i	−0.369310	−	0.714581i
$789$	21.1272	+	36.5933i	0.752147	+	1.30276i
$790$	5.20509	−	4.96809i	0.185189	−	0.176757i
$791$	12.7299			0.452624
$792$	6.89533	+	2.37476i	0.245015	+	0.0843833i
$793$	4.18570	+	2.41661i	0.148638	+	0.0858164i
$794$	−15.8562	−	4.64708i	−0.562717	−	0.164919i
$795$	6.53688	−	11.3222i	0.231839	−	0.401558i
$796$	−7.64065	+	11.9156i	−0.270816	+	0.422339i
$797$	−52.1341			−1.84668			−0.923342	−	0.383979i	$-0.874554\pi$
$797$	−52.1341			−1.84668			−0.923342	+	0.383979i	$0.874554\pi$
$798$	8.59447	+	26.0166i	0.304241	+	0.920977i
$799$		−	9.14431i		−	0.323503i
$800$	13.0614	−	1.91176i	0.461790	−	0.0675911i
$801$	−8.91915	−	5.14947i	−0.315143	−	0.181948i
$802$	33.5415	+	9.83019i	1.18439	+	0.347116i
$803$	21.4896	−	37.2210i	0.758350	−	1.31350i
$804$	13.6021	−	7.02986i	0.479710	−	0.247924i
$805$			17.1097i			0.603038i
$806$	4.17907	+	4.37844i	0.147202	+	0.154224i
$807$	−19.8590	+	11.4656i	−0.699068	+	0.403607i
$808$	1.37583	−	3.99485i	0.0484015	−	0.140538i
$809$	−28.3362			−0.996249			−0.498124	−	0.867106i	$-0.665978\pi$
$809$	−28.3362			−0.996249			−0.498124	+	0.867106i	$0.665978\pi$
$810$	−16.1515	+	15.4161i	−0.567506	+	0.541665i
$811$	−8.67018	+	5.00573i	−0.304451	+	0.175775i	−0.644441	−	0.764654i	$-0.722910\pi$
$811$	−8.67018	+	5.00573i	−0.304451	+	0.175775i	0.339990	+	0.940429i	$0.389576\pi$
$812$	10.3177	−	16.0905i	0.362080	−	0.564667i
$813$	−2.54651	−	4.41069i	−0.0893101	−	0.154690i
$814$	35.7817	−	8.69977i	1.25415	−	0.304927i
$815$	14.0778	+	8.12780i	0.493123	+	0.284705i
$816$	−3.53500	+	37.8311i	−0.123750	+	1.32435i
$817$	1.70704	+	21.1457i	0.0597217	+	0.739794i
$818$	19.3981	−	18.5148i	0.678238	−	0.647356i
$819$	0.946943	+	0.546718i	0.0330889	+	0.0191039i
$820$	−24.5440	−	15.7383i	−0.857114	−	0.549606i
$821$	−8.96021	+	5.17318i	−0.312714	+	0.180545i	−0.648140	−	0.761521i	$-0.724453\pi$
$821$	−8.96021	+	5.17318i	−0.312714	+	0.180545i	0.335427	+	0.942066i	$0.391120\pi$
$822$	−7.06610	−	29.0625i	−0.246459	−	1.01367i
$823$	19.1933	−	11.0812i	0.669036	−	0.386268i	−0.126676	−	0.991944i	$-0.540431\pi$
$823$	19.1933	−	11.0812i	0.669036	−	0.386268i	0.795711	+	0.605676i	$0.207097\pi$
$824$	11.9962	−	10.4268i	0.417909	−	0.363235i
$825$		−	10.7082i		−	0.372812i
$826$	2.36306	−	8.06298i	0.0822215	−	0.280547i
$827$	−15.5457	+	8.97531i	−0.540577	+	0.312102i	−0.745313	−	0.666715i	$-0.767700\pi$
$827$	−15.5457	+	8.97531i	−0.540577	+	0.312102i	0.204736	+	0.978817i	$0.434366\pi$
$828$	3.46568	+	0.161568i	0.120441	+	0.00561486i
$829$	−30.6699			−1.06521			−0.532605	−	0.846364i	$-0.678787\pi$
$829$	−30.6699			−1.06521			−0.532605	+	0.846364i	$0.678787\pi$
$830$	−13.9461	−	4.08727i	−0.484078	−	0.141871i
$831$	1.04255	−	1.80575i	0.0361656	−	0.0626407i
$832$	3.24767	−	1.31165i	0.112593	−	0.0454734i
$833$	6.75514	−	11.7002i	0.234052	−	0.405389i
$834$	5.22698	+	21.4983i	0.180996	+	0.744426i
$835$			18.3739i			0.635853i
$836$	−12.7661	+	23.9553i	−0.441527	+	0.828512i
$837$		−	55.1499i		−	1.90626i
$838$	12.1375	−	2.95104i	0.419282	−	0.101942i
$839$	−18.8792	+	32.6997i	−0.651782	+	1.12892i	0.330908	+	0.943663i	$0.392645\pi$
$839$	−18.8792	+	32.6997i	−0.651782	+	1.12892i	−0.982690	+	0.185256i	$0.940688\pi$
$840$	11.0860	−	32.1893i	0.382504	−	1.11064i
$841$	9.47916	−	16.4184i	0.326868	−	0.566151i
$842$	0.728192	−	2.48466i	0.0250952	−	0.0856269i
$843$	7.99566			0.275385
$844$	36.3601	+	1.69508i	1.25157	+	0.0583471i
$845$	−30.0386	+	17.3428i	−1.03336	+	0.596610i
$846$	1.59437	+	0.467272i	0.0548157	+	0.0160651i
$847$		−	3.93537i		−	0.135221i
$848$	13.0465	+	1.21909i	0.448019	+	0.0418636i
$849$	20.5661	−	11.8739i	0.705827	−	0.407510i
$850$	−20.6688	+	5.02531i	−0.708935	+	0.172367i
$851$	15.1715	−	8.75927i	0.520073	−	0.300264i
$852$	14.0304	−	21.8805i	0.480674	−	0.749615i
$853$	−3.05229	−	1.76224i	−0.104508	−	0.0603379i	0.446835	−	0.894616i	$-0.352551\pi$
$853$	−3.05229	−	1.76224i	−0.104508	−	0.0603379i	−0.551343	+	0.834279i	$0.685884\pi$
$854$	32.5099	+	34.0608i	1.11246	+	1.16554i
$855$	5.55269	+	8.04448i	0.189898	+	0.275115i
$856$	16.7195	+	19.2361i	0.571461	+	0.657477i
$857$	−31.7144	−	18.3103i	−1.08334	−	0.625468i	−0.151547	−	0.988450i	$-0.548425\pi$
$857$	−31.7144	−	18.3103i	−1.08334	−	0.625468i	−0.931796	+	0.362982i	$0.881759\pi$
$858$	−0.671248	−	2.76081i	−0.0229160	−	0.0942525i
$859$	−2.99574	−	5.18877i	−0.102213	−	0.177038i	0.810383	−	0.585900i	$-0.199259\pi$
$859$	−2.99574	−	5.18877i	−0.102213	−	0.177038i	−0.912596	+	0.408862i	$0.865926\pi$
$860$	14.2287	−	22.1897i	0.485195	−	0.756664i
$861$	−20.7218	+	11.9638i	−0.706199	+	0.407724i
$862$	−22.5543	−	23.6303i	−0.768204	−	0.804851i
$863$	−12.3914			−0.421808			−0.210904	−	0.977507i	$-0.567641\pi$
$863$	−12.3914			−0.421808			−0.210904	+	0.977507i	$0.567641\pi$
$864$	−29.6577	−	11.7860i	−1.00898	−	0.400967i
$865$	40.7858	−	23.5477i	1.38676	−	0.800645i
$866$	1.57644	−	1.50466i	0.0535697	−	0.0511305i
$867$		−	36.1718i		−	1.22846i
$868$	27.0728	+	52.3833i	0.918909	+	1.77800i
$869$	2.92506	−	5.06635i	0.0992259	−	0.171864i
$870$	−5.03018	+	17.1634i	−0.170539	+	0.581894i
$871$	1.96963	+	1.13717i	0.0667385	+	0.0385315i
$872$	6.06716	+	31.2237i	0.205460	+	1.05737i
$873$			15.3953i			0.521052i
$874$	−2.62297	+	12.6445i	−0.0887234	+	0.427706i
$875$	−21.7780			−0.736230
$876$	−21.9611	+	34.2485i	−0.741997	+	1.15715i
$877$	10.4760	−	18.1449i	0.353749	−	0.612711i	−0.633154	−	0.774026i	$-0.718240\pi$
$877$	10.4760	−	18.1449i	0.353749	−	0.612711i	0.986903	+	0.161315i	$0.0515735\pi$
$878$	−14.6546	+	50.0028i	−0.494569	+	1.68751i
$879$	30.3732	+	17.5359i	1.02446	+	0.591473i
$880$	30.6519	−	14.0735i	1.03327	−	0.474416i
$881$	16.3102			0.549504			0.274752	−	0.961515i	$-0.411404\pi$
$881$	16.3102			0.549504			0.274752	+	0.961515i	$0.411404\pi$
$882$	1.69483	+	1.77568i	0.0570679	+	0.0597904i
$883$	3.10945	+	5.38572i	0.104641	+	0.181244i	0.913592	−	0.406633i	$-0.133297\pi$
$883$	3.10945	+	5.38572i	0.104641	+	0.181244i	−0.808950	+	0.587877i	$0.799964\pi$
$884$	−5.01386	+	2.59127i	−0.168635	+	0.0871538i
$885$			7.86187i			0.264274i
$886$	−25.1129	−	26.3109i	−0.843685	−	0.883933i
$887$	0.671412	+	1.16292i	0.0225438	+	0.0390470i	0.877077	−	0.480349i	$-0.159490\pi$
$887$	0.671412	+	1.16292i	0.0225438	+	0.0390470i	−0.854533	+	0.519396i	$0.826157\pi$
$888$	−34.2184	+	6.64906i	−1.14829	+	0.223128i
$889$	−41.0597	+	23.7058i	−1.37710	+	0.795069i
$890$	−46.2830	+	11.2530i	−1.55141	+	0.377201i
$891$	−9.07652	+	15.7210i	−0.304075	+	0.526673i
$892$	0.143979	−	3.08839i	0.00482076	−	0.103407i
$893$	−2.65106	+	5.58698i	−0.0887144	+	0.186961i
$894$	−26.5937	−	27.8624i	−0.889428	−	0.931858i
$895$	4.44762	−	7.70350i	0.148667	−	0.257500i
$896$	33.9556	−	3.36405i	1.13438	−	0.112385i
$897$	−0.675839	−	1.17059i	−0.0225656	−	0.0390848i
$898$	4.21741	+	17.3460i	0.140737	+	0.578843i
$899$	−15.4887	−	26.8272i	−0.516577	−	0.894737i
$900$	0.179976	−	3.86054i	0.00599919	−	0.128685i
$901$	−21.1143			−0.703419
$902$	−22.7482	−	6.66695i	−0.757433	−	0.221985i
$903$	−10.8162	−	18.7342i	−0.359941	−	0.623435i
$904$	−7.83166	−	9.01047i	−0.260477	−	0.299684i
$905$		−	22.6028i		−	0.751342i
$906$	−37.0222	−	10.8503i	−1.22998	−	0.360477i
$907$	5.49954	+	3.17516i	0.182609	+	0.105429i	0.588518	−	0.808484i	$-0.299712\pi$
$907$	5.49954	+	3.17516i	0.182609	+	0.105429i	−0.405909	+	0.913914i	$0.633045\pi$
$908$	3.03273	+	5.86806i	0.100645	+	0.194738i
$909$	−1.07127	−	0.618497i	−0.0355317	−	0.0205142i
$910$	4.91385	−	1.19473i	0.162892	−	0.0396048i
$911$	32.3135			1.07059			0.535296	−	0.844664i	$-0.320200\pi$
$911$	32.3135			1.07059			0.535296	+	0.844664i	$0.320200\pi$
$912$	13.1276	−	22.0892i	0.434697	−	0.731445i
$913$	−11.8155			−0.391037
$914$	4.50165	−	1.09451i	0.148901	−	0.0362031i
$915$	−38.1551	−	22.0289i	−1.26137	−	0.728252i
$916$	−8.09215	−	15.6576i	−0.267372	−	0.517340i
$917$	−26.5436	−	15.3250i	−0.876547	−	0.506075i
$918$	49.3491	+	14.4630i	1.62876	+	0.477351i
$919$			38.7254i			1.27743i	0.769443	+	0.638716i	$0.220534\pi$
$919$			38.7254i			1.27743i	−0.769443	+	0.638716i	$0.779466\pi$
$920$	12.1106	−	10.5262i	0.399274	−	0.347038i
$921$	−1.22041	−	2.11380i	−0.0402137	−	0.0696522i
$922$	22.5378	+	6.60528i	0.742243	+	0.217533i
$923$	3.86091			0.127083
$924$	1.28899	−	27.6494i	0.0424048	−	0.909597i
$925$	−9.75726	−	16.9001i	−0.320817	−	0.555671i
$926$	9.77526	+	40.2052i	0.321235	+	1.32122i
$927$	−2.32669	−	4.02994i	−0.0764185	−	0.132361i
$928$	−17.7368	+	2.59609i	−0.582239	+	0.0852208i
$929$	−25.4113	+	44.0137i	−0.833719	+	1.44404i	0.0613502	+	0.998116i	$0.480459\pi$
$929$	−25.4113	+	44.0137i	−0.833719	+	1.44404i	−0.895069	+	0.445927i	$0.852874\pi$
$930$	−38.0948	−	39.9121i	−1.24918	−	1.30877i
$931$	−7.51930	+	5.19019i	−0.246435	+	0.170102i
$932$	0.588238	−	12.6179i	0.0192684	−	0.413313i
$933$	0.479697	−	0.830860i	0.0157046	−	0.0272011i
$934$	−10.5731	+	2.57068i	−0.345961	+	0.0841151i
$935$	−47.0674	+	27.1744i	−1.53927	+	0.888697i
$936$	−0.195598	−	1.00661i	−0.00639332	−	0.0329022i
$937$	−16.1691	−	28.0057i	−0.528221	−	0.914906i	−0.999459	−	0.0328994i	$-0.989526\pi$
$937$	−16.1691	−	28.0057i	−0.528221	−	0.914906i	0.471238	−	0.882006i	$-0.343807\pi$
$938$	15.2979	+	16.0277i	0.499495	+	0.523324i
$939$			28.4765i			0.929295i
$940$	6.82617	−	3.52791i	0.222645	−	0.115068i
$941$	−14.0148	−	24.2743i	−0.456868	−	0.791319i	0.541925	−	0.840427i	$-0.317696\pi$
$941$	−14.0148	−	24.2743i	−0.456868	−	0.791319i	−0.998793	+	0.0491078i	$0.984362\pi$
$942$	−35.2670	−	36.9494i	−1.14906	−	1.20388i
$943$	−11.2773			−0.367241
$944$	−7.16093	+	3.28786i	−0.233068	+	0.107011i
$945$	−39.9041	−	23.0387i	−1.29808	−	0.749448i
$946$	6.02746	−	20.5662i	0.195969	−	0.668665i
$947$	−7.39400	+	12.8068i	−0.240273	+	0.416164i	−0.960792	−	0.277271i	$-0.910570\pi$
$947$	−7.39400	+	12.8068i	−0.240273	+	0.416164i	0.720519	+	0.693435i	$0.243903\pi$
$948$	−2.98925	+	4.66175i	−0.0970863	+	0.151407i
$949$	−6.04329			−0.196174
$950$	14.0851	+	2.92182i	0.456982	+	0.0947964i
$951$			30.8623i			1.00078i
$952$	−53.9733	+	10.4877i	−1.74929	+	0.339908i
$953$	−6.69642	−	3.86618i	−0.216918	−	0.125238i	0.387604	−	0.921826i	$-0.373303\pi$
$953$	−6.69642	−	3.86618i	−0.216918	−	0.125238i	−0.604523	+	0.796588i	$0.706636\pi$
$954$	1.07893	−	3.68142i	0.0349318	−	0.119190i
$955$	6.00082	−	10.3937i	0.194182	−	0.336333i
$956$	−24.1145	−	46.6593i	−0.779918	−	1.50907i
$957$			14.5413i			0.470053i
$958$	36.5917	−	34.9255i	1.18222	−	1.12839i
$959$	37.4823	−	21.6404i	1.21037	−	0.698805i
$960$	−29.6045	+	11.9565i	−0.955481	+	0.385895i
$961$	64.5615			2.08263
$962$	−3.57502	−	3.74557i	−0.115263	−	0.120762i
$963$	6.46206	−	3.73087i	0.208237	−	0.120226i
$964$	2.01511	−	3.14258i	0.0649024	−	0.101216i
$965$	9.57939	+	16.5920i	0.308371	+	0.534115i
$966$	−3.11098	−	12.7953i	−0.100094	−	0.411682i
$967$	−29.1031	−	16.8027i	−0.935892	−	0.540338i	−0.0472221	−	0.998884i	$-0.515037\pi$
$967$	−29.1031	−	16.8027i	−0.935892	−	0.540338i	−0.888670	+	0.458547i	$0.848370\pi$
$968$	−2.78553	+	2.42110i	−0.0895302	+	0.0778172i
$969$	−17.7501	+	37.4074i	−0.570215	+	1.20170i
$970$	49.1607	+	51.5059i	1.57845	+	1.65376i
$971$	13.6746	+	7.89505i	0.438840	+	0.253364i	0.703105	−	0.711086i	$-0.251796\pi$
$971$	13.6746	+	7.89505i	0.438840	+	0.253364i	−0.264265	+	0.964450i	$0.585130\pi$
$972$	−8.99592	+	14.0292i	−0.288544	+	0.449986i
$973$	−27.7266	+	16.0080i	−0.888875	+	0.513192i
$974$	−4.10521	+	0.998119i	−0.131539	+	0.0319818i
$975$	−1.30396	+	0.752841i	−0.0417601	+	0.0241102i
$976$	4.10824	−	43.9659i	0.131502	−	1.40731i
$977$			32.5834i			1.04243i	0.853424	+	0.521217i	$0.174522\pi$
$977$			32.5834i			1.04243i	−0.853424	+	0.521217i	$0.825478\pi$
$978$	−12.0058	−	3.51859i	−0.383902	−	0.112512i
$979$	−33.5373	+	19.3628i	−1.07186	+	0.618838i
$980$	11.3403	+	0.528677i	0.362253	+	0.0168880i
$981$	9.31236			0.297321
$982$	−12.9179	+	44.0770i	−0.412227	+	1.40655i
$983$	3.64307	−	6.30998i	0.116196	−	0.201257i	−0.802061	−	0.597242i	$-0.796263\pi$
$983$	3.64307	−	6.30998i	0.116196	−	0.201257i	0.918257	+	0.395985i	$0.129597\pi$
$984$	21.2166	+	7.30701i	0.676361	+	0.232939i
$985$	−15.2868	+	26.4776i	−0.487079	+	0.843646i
$986$	28.0674	−	6.82414i	0.893847	−	0.217325i
$987$		−	6.30588i		−	0.200718i
$988$	3.81461	−	0.129621i	0.121359	−	0.00412381i
$989$		−	10.1956i		−	0.324202i
$990$	−2.33291	−	9.59512i	−0.0741446	−	0.304953i
$991$	−1.76345	+	3.05438i	−0.0560177	+	0.0970256i	−0.892674	−	0.450702i	$-0.851174\pi$
$991$	−1.76345	+	3.05438i	−0.0560177	+	0.0970256i	0.836657	+	0.547728i	$0.184507\pi$
$992$	20.4223	−	51.3897i	0.648408	−	1.63162i
$993$	5.43131	−	9.40730i	0.172357	−	0.298532i
$994$	36.0948	+	10.5785i	1.14486	+	0.335530i
$995$	19.1661			0.607608
$996$	11.1726	+	0.520861i	0.354019	+	0.0165041i
$997$	13.7973	−	7.96589i	0.436966	−	0.252282i	−0.265344	−	0.964154i	$-0.585485\pi$
$997$	13.7973	−	7.96589i	0.436966	−	0.252282i	0.702310	+	0.711871i	$0.252152\pi$
$998$	−3.86998	+	13.2047i	−0.122502	+	0.417988i
$999$			47.1784i			1.49266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.27.13	yes	28
4.3	odd	2		608.2.s.c.559.3		28
8.3	odd	2	inner	152.2.o.c.27.9	✓	28
8.5	even	2		608.2.s.c.559.4		28
19.12	odd	6	inner	152.2.o.c.107.9	yes	28
76.31	even	6		608.2.s.c.335.4		28
152.69	odd	6		608.2.s.c.335.3		28
152.107	even	6	inner	152.2.o.c.107.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.9	✓	28	8.3	odd	2	inner
152.2.o.c.27.13	yes	28	1.1	even	1	trivial
152.2.o.c.107.9	yes	28	19.12	odd	6	inner
152.2.o.c.107.13	yes	28	152.107	even	6	inner
608.2.s.c.335.3		28	152.69	odd	6
608.2.s.c.335.4		28	76.31	even	6
608.2.s.c.559.3		28	4.3	odd	2
608.2.s.c.559.4		28	8.5	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37418 - 0.334110i) q^{2} +(1.27630 + 0.736872i) q^{3} +(1.77674 - 0.918256i) q^{4} +(-2.34524 - 1.35403i) q^{5} +(2.00006 + 0.586169i) q^{6} +3.01597i q^{7} +(2.13476 - 1.85548i) q^{8} +(-0.414040 - 0.717138i) q^{9} +(-3.67518 - 1.07711i) q^{10} -3.11370 q^{11} +(2.94429 + 0.137261i) q^{12} +(0.218909 + 0.379162i) q^{13} +(1.00767 + 4.14449i) q^{14} +(-1.99549 - 3.45629i) q^{15} +(2.31361 - 3.26300i) q^{16} +(-3.22274 + 5.58194i) q^{17} +(-0.808569 - 0.847142i) q^{18} +(3.58731 - 2.47613i) q^{19} +(-5.41023 - 0.252221i) q^{20} +(-2.22238 + 3.84928i) q^{21} +(-4.27879 + 1.04032i) q^{22} +(-1.81421 + 1.04744i) q^{23} +(4.09184 - 0.795097i) q^{24} +(1.16678 + 2.02092i) q^{25} +(0.427502 + 0.447896i) q^{26} -5.64161i q^{27} +(2.76943 + 5.35860i) q^{28} +(-1.58443 - 2.74431i) q^{29} +(-3.89694 - 4.08285i) q^{30} +9.77556 q^{31} +(2.08912 - 5.25696i) q^{32} +(-3.97402 - 2.29440i) q^{33} +(-2.56363 + 8.74735i) q^{34} +(4.08371 - 7.07319i) q^{35} +(-1.39416 - 0.893974i) q^{36} -8.36258 q^{37} +(4.10230 - 4.60121i) q^{38} +0.645232i q^{39} +(-7.51890 + 1.46102i) q^{40} +(4.66208 + 2.69165i) q^{41} +(-1.76787 + 6.03213i) q^{42} +(-2.43347 + 4.21489i) q^{43} +(-5.53225 + 2.85918i) q^{44} +2.24248i q^{45} +(-2.14310 + 2.04551i) q^{46} +(-1.22865 + 0.709359i) q^{47} +(5.35728 - 2.45973i) q^{48} -2.09609 q^{49} +(2.27857 + 2.38727i) q^{50} +(-8.22635 + 4.74949i) q^{51} +(0.737112 + 0.472657i) q^{52} +(1.63792 + 2.83695i) q^{53} +(-1.88492 - 7.75258i) q^{54} +(7.30239 + 4.21604i) q^{55} +(5.59606 + 6.43838i) q^{56} +(6.40307 - 0.516904i) q^{57} +(-3.09420 - 3.24181i) q^{58} +(-1.70599 - 0.984956i) q^{59} +(-6.71922 - 4.30856i) q^{60} +(9.56035 - 5.51967i) q^{61} +(13.4334 - 3.26612i) q^{62} +(2.16287 - 1.24873i) q^{63} +(1.11442 - 7.92200i) q^{64} -1.18563i q^{65} +(-6.22760 - 1.82516i) q^{66} +(4.49875 - 2.59735i) q^{67} +(-0.600315 + 12.8770i) q^{68} -3.08731 q^{69} +(3.24852 - 11.0842i) q^{70} +(4.40927 - 7.63707i) q^{71} +(-2.21451 - 0.762678i) q^{72} +(-6.90160 + 11.9539i) q^{73} +(-11.4917 + 2.79403i) q^{74} +3.43906i q^{75} +(4.09999 - 7.69351i) q^{76} -9.39085i q^{77} +(0.215579 + 0.886664i) q^{78} +(-0.939415 + 1.62711i) q^{79} +(-9.84418 + 4.51984i) q^{80} +(2.91502 - 5.04897i) q^{81} +(7.30584 + 2.14116i) q^{82} +3.79468 q^{83} +(-0.413974 + 8.87989i) q^{84} +(15.1162 - 8.72734i) q^{85} +(-1.93578 + 6.60506i) q^{86} -4.67009i q^{87} +(-6.64702 + 5.77740i) q^{88} +(10.7709 - 6.21857i) q^{89} +(0.749238 + 3.08158i) q^{90} +(-1.14354 + 0.660224i) q^{91} +(-2.26157 + 3.52694i) q^{92} +(12.4765 + 7.20333i) q^{93} +(-1.45138 + 1.38529i) q^{94} +(-11.7659 + 0.949828i) q^{95} +(6.54004 - 5.17004i) q^{96} +(-16.1008 - 9.29578i) q^{97} +(-2.88040 + 0.700325i) q^{98} +(1.28920 + 2.23296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

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