LMFDB - Embedded newform 152.2.o.c.107.9

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			107.9
Character	$\chi$	$=$	152.107
Dual form			152.2.o.c.27.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.397742 - 1.35713i) q^{2} +(1.27630 - 0.736872i) q^{3} +(-1.68360 - 1.07957i) q^{4} +(2.34524 - 1.35403i) q^{5} +(-0.492393 - 2.02519i) q^{6} +3.01597i q^{7} +(-2.13476 + 1.85548i) q^{8} +(-0.414040 + 0.717138i) q^{9} +(-0.904789 - 3.72135i) q^{10} -3.11370 q^{11} +(-2.94429 - 0.137261i) q^{12} +(-0.218909 + 0.379162i) q^{13} +(4.09307 + 1.19958i) q^{14} +(1.99549 - 3.45629i) q^{15} +(1.66904 + 3.63515i) 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} +(-1.23845 + 4.22570i) q^{22} +(1.81421 + 1.04744i) q^{23} +(-1.35735 + 3.94119i) q^{24} +(1.16678 - 2.02092i) q^{25} +(0.427502 + 0.447896i) q^{26} +5.64161i q^{27} +(3.25597 - 5.07770i) q^{28} +(1.58443 - 2.74431i) q^{29} +(-3.89694 - 4.08285i) q^{30} -9.77556 q^{31} +(5.59722 - 0.819250i) q^{32} +(-3.97402 + 2.29440i) q^{33} +(-8.85724 + 2.15350i) q^{34} +(4.08371 + 7.07319i) q^{35} +(1.47128 - 0.760389i) q^{36} +8.36258 q^{37} +(4.78726 - 3.88358i) q^{38} +0.645232i q^{39} +(-2.49417 + 7.24207i) q^{40} +(4.66208 - 2.69165i) q^{41} +(6.10791 - 1.48504i) q^{42} +(-2.43347 - 4.21489i) q^{43} +(5.24224 + 3.36148i) q^{44} +2.24248i q^{45} +(2.14310 - 2.04551i) q^{46} +(1.22865 + 0.709359i) q^{47} +(4.80883 + 3.40967i) q^{48} -2.09609 q^{49} +(-2.27857 - 2.38727i) q^{50} +(-8.22635 - 4.74949i) q^{51} +(0.777889 - 0.402029i) q^{52} +(-1.63792 + 2.83695i) q^{53} +(7.65639 + 2.24390i) 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} +(-7.09093 + 3.66474i) q^{60} +(-9.56035 - 5.51967i) q^{61} +(-3.88815 + 13.2667i) q^{62} +(-2.16287 - 1.24873i) q^{63} +(1.11442 - 7.92200i) q^{64} +1.18563i q^{65} +(1.53317 + 6.30584i) q^{66} +(4.49875 + 2.59735i) q^{67} +(-0.600315 + 12.8770i) q^{68} +3.08731 q^{69} +(11.2235 - 2.72882i) q^{70} +(-4.40927 - 7.63707i) q^{71} +(-0.446756 - 2.29916i) q^{72} +(-6.90160 - 11.9539i) q^{73} +(3.32615 - 11.3491i) q^{74} -3.43906i q^{75} +(-3.36643 - 8.04159i) q^{76} -9.39085i q^{77} +(0.875663 + 0.256636i) q^{78} +(0.939415 + 1.62711i) q^{79} +(8.83639 + 6.26539i) q^{80} +(2.91502 + 5.04897i) q^{81} +(-1.79862 - 7.39762i) q^{82} +3.79468 q^{83} +(0.413974 - 8.87989i) q^{84} +(-15.1162 - 8.72734i) q^{85} +(-6.68804 + 1.62609i) q^{86} -4.67009i q^{87} +(6.64702 - 5.77740i) q^{88} +(10.7709 + 6.21857i) q^{89} +(3.04334 + 0.891930i) q^{90} +(-1.14354 - 0.660224i) q^{91} +(-1.92363 - 3.72205i) 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} +(-0.833701 + 2.84466i) 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 $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.397742	−	1.35713i	0.281246	−	0.959636i
$2$	0.397742	−	1.35713i	0.281246	−	0.959636i
$3$	1.27630	−	0.736872i	0.736872	−	0.425433i	−0.0840591	−	0.996461i	$-0.526788\pi$
$3$	1.27630	−	0.736872i	0.736872	−	0.425433i	0.820931	+	0.571028i	$0.193455\pi$
$4$	−1.68360	−	1.07957i	−0.841801	−	0.539787i
$5$	2.34524	−	1.35403i	1.04882	−	0.605539i	0.126504	−	0.991966i	$-0.459624\pi$
$5$	2.34524	−	1.35403i	1.04882	−	0.605539i	0.922320	+	0.386427i	$0.126291\pi$
$6$	−0.492393	−	2.02519i	−0.201019	−	0.826780i
$7$			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
$10$	−0.904789	−	3.72135i	−0.286119	−	1.17679i
$11$	−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	$-0.852671\pi$
$13$	−0.218909	+	0.379162i	−0.0607144	+	0.105160i	0.834071	+	0.551658i	$0.186005\pi$
$14$	4.09307	+	1.19958i	1.09392	+	0.320601i
$15$	1.99549	−	3.45629i	0.515233	−	0.892409i
$16$	1.66904	+	3.63515i	0.417259	+	0.908787i
$17$	−3.22274	−	5.58194i	−0.781629	−	1.35382i	−0.930993	−	0.365038i	$-0.881056\pi$
$17$	−3.22274	−	5.58194i	−0.781629	−	1.35382i	0.149364	−	0.988782i	$-0.452277\pi$
$18$	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
$22$	−1.23845	+	4.22570i	−0.264039	+	0.900923i
$23$	1.81421	+	1.04744i	0.378290	+	0.218406i	0.677074	−	0.735915i	$-0.263248\pi$
$23$	1.81421	+	1.04744i	0.378290	+	0.218406i	−0.298784	+	0.954321i	$0.596581\pi$
$24$	−1.35735	+	3.94119i	−0.277067	+	0.804492i
$25$	1.16678	−	2.02092i	0.233355	−	0.404183i
$26$	0.427502	+	0.447896i	0.0838401	+	0.0878397i
$27$			5.64161i			1.08573i
$28$	3.25597	−	5.07770i	0.615320	−	0.959595i
$29$	1.58443	−	2.74431i	0.294221	−	0.509606i	−0.680582	−	0.732672i	$-0.738273\pi$
$29$	1.58443	−	2.74431i	0.294221	−	0.509606i	0.974803	+	0.223066i	$0.0716064\pi$
$30$	−3.89694	−	4.08285i	−0.711481	−	0.745422i
$31$	−9.77556			−1.75574			−0.877871	−	0.478897i	$-0.841037\pi$
$31$	−9.77556			−1.75574			−0.877871	+	0.478897i	$0.841037\pi$
$32$	5.59722	−	0.819250i	0.989457	−	0.144824i
$33$	−3.97402	+	2.29440i	−0.691788	+	0.399404i
$34$	−8.85724	+	2.15350i	−1.51900	+	0.369322i
$35$	4.08371	+	7.07319i	0.690272	+	1.19559i
$36$	1.47128	−	0.760389i	0.245214	−	0.126732i
$37$	8.36258			1.37480			0.687400	−	0.726279i	$-0.258752\pi$
$37$	8.36258			1.37480			0.687400	+	0.726279i	$0.258752\pi$
$38$	4.78726	−	3.88358i	0.776596	−	0.630000i
$39$			0.645232i			0.103320i
$40$	−2.49417	+	7.24207i	−0.394363	+	1.14507i
$41$	4.66208	−	2.69165i	0.728094	−	0.420365i	−0.0896306	−	0.995975i	$-0.528569\pi$
$41$	4.66208	−	2.69165i	0.728094	−	0.420365i	0.817724	+	0.575610i	$0.195235\pi$
$42$	6.10791	−	1.48504i	0.942471	−	0.229147i
$43$	−2.43347	−	4.21489i	−0.371100	−	0.642764i	0.618635	−	0.785679i	$-0.287686\pi$
$43$	−2.43347	−	4.21489i	−0.371100	−	0.642764i	−0.989735	+	0.142914i	$0.954353\pi$
$44$	5.24224	+	3.36148i	0.790298	+	0.506762i
$45$			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	$-0.300339\pi$
$47$	1.22865	+	0.709359i	0.179216	+	0.103471i	−0.407708	+	0.913112i	$0.633672\pi$
$48$	4.80883	+	3.40967i	0.694095	+	0.492144i
$49$	−2.09609			−0.299441
$50$	−2.27857	−	2.38727i	−0.322238	−	0.337611i
$51$	−8.22635	−	4.74949i	−1.15192	−	0.665061i
$52$	0.777889	−	0.402029i	0.107874	−	0.0557514i
$53$	−1.63792	+	2.83695i	−0.224985	+	0.389686i	−0.956315	−	0.292338i	$-0.905567\pi$
$53$	−1.63792	+	2.83695i	−0.224985	+	0.389686i	0.731330	+	0.682024i	$0.238900\pi$
$54$	7.65639	+	2.24390i	1.04190	+	0.305357i
$55$	−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	−0.606923	−	0.794761i	$-0.707596\pi$
$59$	−1.70599	+	0.984956i	−0.222102	+	0.128230i	0.384821	+	0.922991i	$0.374263\pi$
$60$	−7.09093	+	3.66474i	−0.915435	+	0.473115i
$61$	−9.56035	−	5.51967i	−1.22408	−	0.706722i	−0.258293	−	0.966067i	$-0.583160\pi$
$61$	−9.56035	−	5.51967i	−1.22408	−	0.706722i	−0.965785	+	0.259345i	$0.916493\pi$
$62$	−3.88815	+	13.2667i	−0.493795	+	1.68487i
$63$	−2.16287	−	1.24873i	−0.272496	−	0.157326i
$64$	1.11442	−	7.92200i	0.139302	−	0.990250i
$65$			1.18563i			0.147060i
$66$	1.53317	+	6.30584i	0.188720	+	0.776195i
$67$	4.49875	+	2.59735i	0.549609	+	0.317317i	0.748964	−	0.662610i	$-0.230551\pi$
$67$	4.49875	+	2.59735i	0.549609	+	0.317317i	−0.199355	+	0.979927i	$0.563885\pi$
$68$	−0.600315	+	12.8770i	−0.0727989	+	1.56156i
$69$	3.08731			0.371668
$70$	11.2235	−	2.72882i	1.34146	−	0.326156i
$71$	−4.40927	−	7.63707i	−0.523284	−	0.906354i	−0.999633	−	0.0270976i	$-0.991374\pi$
$71$	−4.40927	−	7.63707i	−0.523284	−	0.906354i	0.476349	−	0.879256i	$-0.341960\pi$
$72$	−0.446756	−	2.29916i	−0.0526507	−	0.270959i
$73$	−6.90160	−	11.9539i	−0.807772	−	1.39910i	−0.914404	−	0.404803i	$-0.867340\pi$
$73$	−6.90160	−	11.9539i	−0.807772	−	1.39910i	0.106632	−	0.994299i	$-0.465993\pi$
$74$	3.32615	−	11.3491i	0.386657	−	1.31931i
$75$		−	3.43906i		−	0.397108i
$76$	−3.36643	−	8.04159i	−0.386156	−	0.922434i
$77$		−	9.39085i		−	1.07019i
$78$	0.875663	+	0.256636i	0.0991493	+	0.0290583i
$79$	0.939415	+	1.62711i	0.105692	+	0.183065i	0.914021	−	0.405667i	$-0.132961\pi$
$79$	0.939415	+	1.62711i	0.105692	+	0.183065i	−0.808328	+	0.588732i	$0.799627\pi$
$80$	8.83639	+	6.26539i	0.987938	+	0.700492i
$81$	2.91502	+	5.04897i	0.323891	+	0.560996i
$82$	−1.79862	−	7.39762i	−0.198624	−	0.816931i
$83$	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
$86$	−6.68804	+	1.62609i	−0.721190	+	0.175346i
$87$		−	4.67009i		−	0.500686i
$88$	6.64702	−	5.77740i	0.708575	−	0.615873i
$89$	10.7709	+	6.21857i	1.14171	+	0.659167i	0.946854	−	0.321664i	$-0.104242\pi$
$89$	10.7709	+	6.21857i	1.14171	+	0.659167i	0.194857	+	0.980832i	$0.437576\pi$
$90$	3.04334	+	0.891930i	0.320797	+	0.0940177i
$91$	−1.14354	−	0.660224i	−0.119876	−	0.0692102i
$92$	−1.92363	−	3.72205i	−0.200552	−	0.388050i
$93$	−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	−0.652197	+	0.758050i	$0.726152\pi$
$97$	−16.1008	+	9.29578i	−1.63479	+	0.943844i	−0.982589	+	0.185794i	$0.940514\pi$
$98$	−0.833701	+	2.84466i	−0.0842165	+	0.287354i
$99$	1.28920	−	2.23296i	0.129569	−	0.224421i
$100$	−4.14612	+	2.14280i	−0.414612	+	0.214280i
$101$	−1.29368	−	0.746904i	−0.128726	−	0.0743198i	0.434254	−	0.900790i	$-0.357012\pi$
$101$	−1.29368	−	0.746904i	−0.128726	−	0.0743198i	−0.562980	+	0.826470i	$0.690345\pi$
$102$	−9.71764	+	9.27516i	−0.962189	+	0.918378i
$103$	−5.61948			−0.553704			−0.276852	−	0.960913i	$-0.589291\pi$
$103$	−5.61948			−0.553704			−0.276852	+	0.960913i	$0.589291\pi$
$104$	−0.236207	−	1.21560i	−0.0231620	−	0.119199i
$105$	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	$-0.856551\pi$
$107$		−	9.01090i		−	0.871117i	0.900160	−	0.435558i	$-0.143449\pi$
$108$	6.09054	−	9.49823i	0.586062	−	0.913967i
$109$	5.62286	+	9.73908i	0.538573	+	0.932835i	0.998981	+	0.0451280i	$0.0143696\pi$
$109$	5.62286	+	9.73908i	0.538573	+	0.932835i	−0.460409	+	0.887707i	$0.652297\pi$
$110$	2.81725	+	11.5872i	0.268614	+	1.10480i
$111$	10.6732	−	6.16215i	1.01305	−	0.584885i
$112$	−10.9635	+	5.03377i	−1.03595	+	0.475647i
$113$			4.22083i			0.397063i	0.980095	+	0.198531i	$0.0636171\pi$
$113$			4.22083i			0.397063i	−0.980095	+	0.198531i	$0.936383\pi$
$114$	3.24827	−	8.48420i	0.304229	−	0.794618i
$115$	5.67303			0.529013
$116$	−5.63024	+	2.90982i	−0.522755	+	0.270170i
$117$	−0.181274	−	0.313976i	−0.0167588	−	0.0290271i
$118$	0.658168	+	2.70701i	0.0605893	+	0.249201i
$119$	16.8350	−	9.71969i	1.54326	−	0.891002i
$120$	2.15316	+	11.0809i	0.196556	+	1.01155i
$121$	−1.30484			−0.118622
$122$	−11.2935	+	10.7792i	−1.02246	+	0.975906i
$123$	3.96680	−	6.87070i	0.357675	−	0.619510i
$124$	16.4582	+	10.5534i	1.47799	+	0.947727i
$125$			7.22088i			0.645855i
$126$	−2.55496	+	2.43862i	−0.227614	+	0.217250i
$127$	−7.86010	+	13.6141i	−0.697471	+	1.20806i	0.271869	+	0.962334i	$0.412358\pi$
$127$	−7.86010	+	13.6141i	−0.697471	+	1.20806i	−0.969340	+	0.245721i	$0.920975\pi$
$128$	−10.3079	−	4.66332i	−0.911101	−	0.412183i
$129$	−6.21166	−	3.58631i	−0.546906	−	0.315757i
$130$	1.60906	+	0.471576i	0.141124	+	0.0413600i
$131$	−5.08127	−	8.80102i	−0.443953	−	0.768948i	0.554026	−	0.832499i	$-0.313091\pi$
$131$	−5.08127	−	8.80102i	−0.443953	−	0.768948i	−0.997979	+	0.0635510i	$0.979757\pi$
$132$	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
$136$	17.2369	+	5.93641i	1.47806	+	0.509043i
$137$	−7.17527	+	12.4279i	−0.613024	+	1.06179i	0.377703	+	0.925927i	$0.376714\pi$
$137$	−7.17527	+	12.4279i	−0.613024	+	1.06179i	−0.990728	+	0.135863i	$0.956619\pi$
$138$	1.22795	−	4.18988i	0.104530	−	0.356666i
$139$	5.30773	−	9.19326i	0.450196	−	0.779763i	−0.548202	−	0.836346i	$-0.684687\pi$
$139$	5.30773	−	9.19326i	0.450196	−	0.779763i	0.998398	+	0.0565836i	$0.0180207\pi$
$140$	0.760692	−	16.3171i	0.0642902	−	1.37905i
$141$	2.09083			0.176079
$142$	−12.1182	+	2.94636i	−1.01694	+	0.247253i
$143$	0.681618	−	1.18060i	0.0569998	−	0.0987265i
$144$	−3.29795	−	0.308166i	−0.274829	−	0.0256805i
$145$		−	8.58144i		−	0.712650i
$146$	−18.9681	+	4.61180i	−1.56981	+	0.381675i
$147$	−2.67523	+	1.54455i	−0.220650	+	0.127392i
$148$	−14.0793	−	9.02803i	−1.15731	−	0.742099i
$149$	16.0045	−	9.24023i	1.31114	−	0.756989i	0.328858	−	0.944379i	$-0.393336\pi$
$149$	16.0045	−	9.24023i	1.31114	−	0.756989i	0.982286	+	0.187390i	$0.0600029\pi$
$150$	−4.66725	−	1.36786i	−0.381079	−	0.111685i
$151$	18.5105			1.50637			0.753183	−	0.657811i	$-0.228517\pi$
$151$	18.5105			1.50637			0.753183	+	0.657811i	$0.228517\pi$
$152$	−12.2525	+	1.37020i	−0.993805	+	0.111138i
$153$	5.33737			0.431501
$154$	−12.7446	−	3.73513i	−1.02699	−	0.300986i
$155$	−22.9261	+	13.2364i	−1.84147	+	1.06317i
$156$	0.696575	−	1.08631i	0.0557707	−	0.0869747i
$157$	21.2242	−	12.2538i	1.69388	−	0.977961i	0.742545	−	0.669796i	$-0.233618\pi$
$157$	21.2242	−	12.2538i	1.69388	−	0.977961i	0.951333	−	0.308165i	$-0.0997149\pi$
$158$	2.58185	−	0.627737i	0.205401	−	0.0499400i
$159$			4.82774i			0.382864i
$160$	12.0175	−	9.50012i	0.950070	−	0.751050i
$161$	−3.15904	+	5.47162i	−0.248967	+	0.431224i
$162$	8.01153	−	1.94788i	0.629445	−	0.153040i
$163$	−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
$166$	1.50930	−	5.14988i	0.117145	−	0.399708i
$167$	3.39245	−	5.87589i	0.262515	−	0.454690i	−0.704394	−	0.709809i	$-0.748781\pi$
$167$	3.39245	−	5.87589i	0.262515	−	0.454690i	0.966910	+	0.255119i	$0.0821146\pi$
$168$	−11.8865	−	4.09372i	−0.917064	−	0.315837i
$169$	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	0.980327	+	0.197382i	$0.0632440\pi$
$173$	8.69543	+	15.0609i	0.661101	+	1.14506i	−0.319225	+	0.947679i	$0.603423\pi$
$174$	−6.33792	−	1.85749i	−0.480476	−	0.140816i
$175$	6.09502	+	3.51896i	0.460741	+	0.266009i
$176$	−5.19689	−	11.3188i	−0.391730	−	0.853185i
$177$	−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	$-0.960827\pi$
$179$		−	3.28473i		−	0.245513i	0.992437	−	0.122756i	$-0.0391733\pi$
$180$	2.42093	−	3.77545i	0.180445	−	0.281406i
$181$	−4.17326	+	7.22829i	−0.310196	+	0.537275i	−0.978405	−	0.206699i	$-0.933728\pi$
$181$	−4.17326	+	7.22829i	−0.310196	+	0.537275i	0.668209	+	0.743974i	$0.267061\pi$
$182$	−1.35084	+	1.28933i	−0.100131	+	0.0955718i
$183$	−16.2692			−1.20265
$184$	−5.81641	+	1.13020i	−0.428791	+	0.0833196i
$185$	19.6123	−	11.3232i	1.44192	−	0.832495i
$186$	4.81342	+	19.7973i	0.352937	+	1.45161i
$187$	10.0347	+	17.3805i	0.733806	+	1.27099i
$188$	−1.30275	−	2.52069i	−0.0950125	−	0.183841i
$189$	−17.0149			−1.23765
$190$	5.96881	−	15.5900i	0.433023	−	1.13102i
$191$			4.43183i			0.320676i	0.987062	+	0.160338i	$0.0512584\pi$
$191$			4.43183i			0.320676i	−0.987062	+	0.160338i	$0.948742\pi$
$192$	−4.41517	−	10.9320i	−0.318637	−	0.788951i
$193$	−6.12690	+	3.53737i	−0.441024	+	0.254625i	−0.704032	−	0.710168i	$-0.748619\pi$
$193$	−6.12690	+	3.53737i	−0.441024	+	0.254625i	0.263008	+	0.964794i	$0.415286\pi$
$194$	6.21164	+	25.5482i	0.445970	+	1.83425i
$195$	0.873661	+	1.51322i	0.0625641	+	0.108364i
$196$	3.52898	+	2.26288i	0.252070	+	0.161634i
$197$		−	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	$-0.252622\pi$
$199$	6.12926	+	3.53873i	0.434492	+	0.250854i	−0.266766	+	0.963761i	$0.585955\pi$
$200$	1.25897	+	6.47910i	0.0890227	+	0.458141i
$201$	7.65566			0.539989
$202$	−1.52820	+	1.45861i	−0.107523	+	0.102628i
$203$	8.27677	+	4.77860i	0.580916	+	0.335392i
$204$	8.72249	+	16.8772i	0.610696	+	1.18164i
$205$	7.28913	−	12.6251i	0.509095	−	0.881779i
$206$	−2.23510	+	7.62636i	−0.155727	+	0.531354i
$207$	−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	0.152806	−	0.988256i	$-0.451169\pi$
$211$	15.7615	−	9.09989i	1.08506	−	0.626462i	0.932258	+	0.361794i	$0.117836\pi$
$212$	5.82030	−	3.00805i	0.399740	−	0.206594i
$213$	−11.2551	−	6.49813i	−0.771186	−	0.445244i
$214$	−12.2290	−	3.58401i	−0.835955	−	0.244998i
$215$	−11.4141	−	6.58996i	−0.778438	−	0.449431i
$216$	−10.4679	−	12.0435i	−0.712248	−	0.819456i
$217$		−	29.4828i		−	2.00142i
$218$	15.4536	−	3.75731i	1.04665	−	0.254477i
$219$	−17.6170	−	10.1712i	−1.19045	−	0.687306i
$220$	16.8459	+	0.785342i	1.13575	+	0.0529477i
$221$	2.82195			0.189825
$222$	−4.11768	−	16.9358i	−0.276360	−	1.13666i
$223$	−0.772936	−	1.33877i	−0.0517596	−	0.0896503i	0.838985	−	0.544155i	$-0.183150\pi$
$223$	−0.772936	−	1.33877i	−0.0517596	−	0.0896503i	−0.890744	+	0.454505i	$0.849816\pi$
$224$	2.47084	+	16.8810i	0.165090	+	1.12791i
$225$	0.966184	+	1.67348i	0.0644123	+	0.111565i
$226$	5.72822	+	1.67880i	0.381035	+	0.111672i
$227$		−	3.30271i		−	0.219209i	−0.993975	−	0.109604i	$-0.965042\pi$
$227$		−	3.30271i		−	0.219209i	0.993975	−	0.109604i	$-0.0349584\pi$
$228$	−10.2222	−	7.78285i	−0.676981	−	0.515432i
$229$		−	8.81252i		−	0.582348i	−0.956670	−	0.291174i	$-0.905954\pi$
$229$		−	8.81252i		−	0.582348i	0.956670	−	0.291174i	$-0.0940458\pi$
$230$	2.25640	−	7.69904i	0.148783	−	0.507659i
$231$	−6.91985	−	11.9855i	−0.455293	−	0.788590i
$232$	1.70963	+	8.79833i	0.112243	+	0.577639i
$233$	3.15790	+	5.46965i	0.206881	+	0.358329i	0.950730	−	0.310019i	$-0.100335\pi$
$233$	3.15790	+	5.46965i	0.206881	+	0.358329i	−0.743849	+	0.668347i	$0.767002\pi$
$234$	−0.498207	+	0.121131i	−0.0325688	+	0.00791860i
$235$	3.84197			0.250622
$236$	3.93555	+	0.183473i	0.256183	+	0.0119430i
$237$	2.39795	+	1.38446i	0.155764	+	0.0899301i
$238$	−6.49490	−	26.7132i	−0.421002	−	1.73156i
$239$		−	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	0.551160	−	0.834400i	$-0.314185\pi$
$241$	1.61651	+	0.933290i	0.104128	+	0.0601185i	−0.447031	+	0.894518i	$0.647519\pi$
$242$	−0.518990	+	1.77084i	−0.0333620	+	0.113834i
$243$	−7.21645	−	4.16642i	−0.462935	−	0.267276i
$244$	10.1369	+	19.6140i	0.648951	+	1.25566i
$245$	−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
$250$	9.79968	+	2.87205i	0.619786	+	0.181644i
$251$	10.1173	−	17.5236i	0.638596	−	1.10608i	−0.347145	−	0.937811i	$-0.612849\pi$
$251$	10.1173	−	17.5236i	0.638596	−	1.10608i	0.985741	−	0.168269i	$-0.0538177\pi$
$252$	2.29331	+	4.43735i	0.144465	+	0.279527i
$253$	−5.64893	−	3.26141i	−0.355145	−	0.205043i
$254$	15.3498	+	16.0821i	0.963132	+	1.00908i
$255$	−25.7237			−1.61088
$256$	−10.4286	+	12.1344i	−0.651789	+	0.758400i
$257$	−10.3865	−	5.99663i	−0.647890	−	0.374060i	0.139757	−	0.990186i	$-0.455368\pi$
$257$	−10.3865	−	5.99663i	−0.647890	−	0.374060i	−0.787647	+	0.616126i	$0.788701\pi$
$258$	−7.33772	+	7.00361i	−0.456827	+	0.436026i
$259$			25.2213i			1.56718i
$260$	1.27998	−	1.99614i	0.0793810	−	0.123795i
$261$	1.31204	+	2.27251i	0.0812129	+	0.140665i
$262$	−13.9652	+	3.39541i	−0.862770	+	0.209769i
$263$	−24.8302	+	14.3357i	−1.53109	+	0.883978i	−0.531783	+	0.846881i	$0.678478\pi$
$263$	−24.8302	+	14.3357i	−1.53109	+	0.883978i	−0.999312	+	0.0370975i	$0.988189\pi$
$264$	4.22638	−	12.2717i	0.260116	−	0.755271i
$265$			8.87113i			0.544949i
$266$	11.7128	+	14.4382i	0.718156	+	0.885265i
$267$	18.3292			1.12173
$268$	−4.77007	−	9.22964i	−0.291378	−	0.563790i
$269$	7.77990	+	13.4752i	0.474349	+	0.821596i	0.999569	−	0.0293704i	$-0.00935023\pi$
$269$	7.77990	+	13.4752i	0.474349	+	0.821596i	−0.525220	+	0.850967i	$0.676017\pi$
$270$	20.9944	−	5.10446i	1.27768	−	0.310648i
$271$	2.99285	−	1.72792i	0.181803	−	0.104964i	−0.406337	−	0.913723i	$-0.633194\pi$
$271$	2.99285	−	1.72792i	0.181803	−	0.104964i	0.588139	+	0.808760i	$0.299861\pi$
$272$	14.9123	−	21.0316i	0.904193	−	1.27523i
$273$	−1.94600			−0.117777
$274$	14.0124	+	14.6809i	0.846520	+	0.886904i
$275$	−3.63300	+	6.29253i	−0.219078	+	0.379454i
$276$	−5.19780	−	3.33298i	−0.312871	−	0.200622i
$277$		−	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
$280$	−21.8419	−	7.52235i	−1.30530	−	0.449546i
$281$	4.69854	+	2.71270i	0.280291	+	0.161826i	0.633555	−	0.773697i	$-0.281595\pi$
$281$	4.69854	+	2.71270i	0.280291	+	0.161826i	−0.353264	+	0.935524i	$0.614928\pi$
$282$	0.831609	−	2.83752i	0.0495216	−	0.168972i
$283$	8.05693	+	13.9550i	0.478935	+	0.829540i	0.999708	−	0.0241553i	$-0.00768962\pi$
$283$	8.05693	+	13.9550i	0.478935	+	0.829540i	−0.520773	+	0.853695i	$0.674356\pi$
$284$	−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
$288$	−1.72996	+	4.35318i	−0.101939	+	0.256514i
$289$	−12.2721	+	21.2559i	−0.721887	+	1.25034i
$290$	−11.6461	−	3.41320i	−0.683884	−	0.200430i
$291$	−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	$-0.744659\pi$
$293$	−23.7978			−1.39028			−0.695142	+	0.718872i	$0.744659\pi$
$294$	1.03210	+	4.24497i	0.0601932	+	0.247572i
$295$	−2.66731	+	4.61992i	−0.155297	+	0.268982i
$296$	−17.8521	+	15.5166i	−1.03763	+	0.901882i
$297$		−	17.5663i		−	1.01930i
$298$	−6.17452	−	25.3955i	−0.357680	−	1.47112i
$299$	−0.794296	+	0.458587i	−0.0459353	+	0.0265208i
$300$	−3.71272	+	5.79001i	−0.214354	+	0.334286i
$301$	12.7120	−	7.33927i	0.732707	−	0.423028i
$302$	7.36241	−	25.1212i	0.423659	−	1.44556i
$303$	−2.20149			−0.126472
$304$	−3.01377	+	17.1732i	−0.172851	+	0.984948i
$305$	−29.8951			−1.71179
$306$	2.12289	−	7.24350i	0.121358	−	0.414084i
$307$	−1.43431	+	0.828099i	−0.0818604	+	0.0472621i	−0.540371	−	0.841427i	$-0.681716\pi$
$307$	−1.43431	+	0.828099i	−0.0818604	+	0.0472621i	0.458511	+	0.888689i	$0.348383\pi$
$308$	−10.1381	+	15.8105i	−0.577673	+	0.900884i
$309$	−7.17214	+	4.14084i	−0.408009	+	0.235564i
$310$	8.84482	+	36.3783i	0.502352	+	2.06615i
$311$		−	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	−0.452450	−	0.891790i	$-0.649450\pi$
$313$	9.66128	−	16.7338i	0.546088	−	0.945852i	0.998538	−	0.0540617i	$-0.0172168\pi$
$314$	−8.18826	−	33.6779i	−0.462090	−	1.90055i
$315$	−6.76327			−0.381067
$316$	0.174989	−	3.75358i	0.00984392	−	0.211156i
$317$	−10.4707	+	18.1358i	−0.588093	+	1.01861i	0.406389	+	0.913700i	$0.366788\pi$
$317$	−10.4707	+	18.1358i	−0.588093	+	1.01861i	−0.994482	+	0.104907i	$0.966545\pi$
$318$	6.55187	+	1.92019i	0.367410	+	0.107679i
$319$	−4.93345	+	8.54498i	−0.276220	+	0.478427i
$320$	−8.11302	−	20.0880i	−0.453532	−	1.12295i
$321$	−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
$326$	−2.38752	+	8.14643i	−0.132233	+	0.451189i
$327$	14.3529	+	8.28666i	0.793718	+	0.458253i
$328$	−4.95813	+	14.3964i	−0.273767	+	0.794908i
$329$	−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	$0.0649284\pi$
$331$			7.37076i			0.405134i	−0.979268	+	0.202567i	$0.935072\pi$
$332$	−6.38874	−	4.09664i	−0.350628	−	0.224832i
$333$	−3.46244	+	5.99713i	−0.189741	+	0.328641i
$334$	−6.62503	−	6.94108i	−0.362505	−	0.379799i
$335$	14.0675			0.768592
$336$	−10.2835	+	14.5033i	−0.561010	+	0.791220i
$337$	−9.00098	+	5.19672i	−0.490315	+	0.283083i	−0.724705	−	0.689059i	$-0.758024\pi$
$337$	−9.00098	+	5.19672i	−0.490315	+	0.283083i	0.234390	+	0.972143i	$0.424691\pi$
$338$	17.6009	−	4.27939i	0.957364	−	0.232768i
$339$	3.11021	+	5.38705i	0.168924	+	0.292584i
$340$	16.0279	+	31.0125i	0.869233	+	1.68189i
$341$	30.4382			1.64832
$342$	0.802947	+	5.04108i	0.0434184	+	0.272591i
$343$			14.7901i			0.798588i
$344$	13.0155	+	4.48254i	0.701748	+	0.241683i
$345$	7.24048	−	4.18029i	0.389814	−	0.225060i
$346$	23.8982	−	5.81047i	1.28477	−	0.312373i
$347$	9.25966	+	16.0382i	0.497085	+	0.860976i	0.999994	−	0.00336302i	$-0.00107049\pi$
$347$	9.25966	+	16.0382i	0.497085	+	0.860976i	−0.502910	+	0.864339i	$0.667737\pi$
$348$	−5.04171	+	7.86257i	−0.270264	+	0.421478i
$349$		−	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
$352$	−17.4281	+	2.55090i	−0.928920	+	0.135964i
$353$	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
$356$	−11.4205	−	22.0976i	−0.605284	−	1.17117i
$357$	14.3243	−	24.8105i	0.758124	−	1.31311i
$358$	−4.45781	−	1.30648i	−0.235603	−	0.0690494i
$359$	−3.07083	+	1.77294i	−0.162072	+	0.0935724i	−0.578842	−	0.815440i	$-0.696495\pi$
$359$	−3.07083	+	1.77294i	−0.162072	+	0.0935724i	0.416770	+	0.909012i	$0.363162\pi$
$360$	−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
$364$	1.21251	+	2.34609i	0.0635527	+	0.122969i
$365$	−32.3719	−	18.6899i	−1.69442	−	0.978275i
$366$	−6.47093	+	22.0794i	−0.338241	+	1.15411i
$367$	−30.3020	−	17.4948i	−1.58175	−	0.913224i	−0.994604	−	0.103742i	$-0.966918\pi$
$367$	−30.3020	−	17.4948i	−1.58175	−	0.913224i	−0.587145	−	0.809481i	$-0.699748\pi$
$368$	−0.779598	+	8.34315i	−0.0406393	+	0.434917i
$369$			4.45780i			0.232064i
$370$	−7.56637	−	31.1201i	−0.393357	−	1.61786i
$371$	−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	$-0.449148\pi$
$373$	6.14462			0.318157			0.159078	+	0.987266i	$0.449148\pi$
$374$	27.5788	−	6.70537i	1.42607	−	0.346726i
$375$	5.32086	+	9.21601i	0.274768	+	0.475913i
$376$	−3.93907	+	0.765411i	−0.203142	+	0.0394730i
$377$	0.693692	+	1.20151i	0.0357270	+	0.0618809i
$378$	−6.76755	+	23.0915i	−0.348085	+	1.18770i
$379$			16.1488i			0.829507i	0.909934	+	0.414753i	$0.136132\pi$
$379$			16.1488i			0.829507i	−0.909934	+	0.414753i	$0.863868\pi$
$380$	−18.7836	−	14.3012i	−0.963579	−	0.733639i
$381$			23.1675i			1.18691i
$382$	6.01457	+	1.76272i	0.307732	+	0.0901888i
$383$	−5.82205	−	10.0841i	−0.297493	−	0.515272i	0.678069	−	0.734998i	$-0.262817\pi$
$383$	−5.82205	−	10.0841i	−0.297493	−	0.515272i	−0.975562	+	0.219726i	$0.929484\pi$
$384$	−16.5923	+	1.64383i	−0.846721	+	0.0838865i
$385$	−12.7155	−	22.0238i	−0.648040	−	1.12244i
$386$	2.36374	+	9.72197i	0.120311	+	0.494835i
$387$	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	$-0.219022\pi$
$389$	12.0060	+	6.93167i	0.608729	+	0.351450i	−0.163739	+	0.986504i	$0.552355\pi$
$390$	2.40113	−	0.583798i	0.121586	−	0.0295618i
$391$		−	13.5025i		−	0.682848i
$392$	4.47465	−	3.88924i	0.226004	−	0.196436i
$393$	−12.9704	−	7.48849i	−0.654272	−	0.377744i
$394$	−15.3219	−	4.49047i	−0.771905	−	0.226226i
$395$	4.40631	+	2.54399i	0.221706	+	0.128002i
$396$	−4.58114	+	2.36763i	−0.230211	+	0.118978i
$397$	10.1183	−	5.84182i	0.507825	−	0.293193i	−0.224114	−	0.974563i	$-0.571949\pi$
$397$	10.1183	−	5.84182i	0.507825	−	0.293193i	0.731939	+	0.681370i	$0.238616\pi$
$398$	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	0.140988	−	0.990011i	$-0.454972\pi$
$401$	21.4038	−	12.3575i	1.06886	−	0.617105i	0.927869	+	0.372907i	$0.121639\pi$
$402$	3.04498	−	10.3897i	0.151870	−	0.518193i
$403$	2.13996	−	3.70652i	0.106599	−	0.184635i
$404$	1.37170	+	2.65411i	0.0682445	+	0.132047i
$405$	13.6729	+	7.89403i	0.679410	+	0.392258i
$406$	9.77720	−	9.33201i	0.485234	−	0.463140i
$407$	−26.0386			−1.29069
$408$	26.3739	−	5.12478i	1.30570	−	0.253714i
$409$	16.4212	+	9.48080i	0.811978	+	0.468796i	0.847642	−	0.530568i	$-0.178021\pi$
$409$	16.4212	+	9.48080i	0.811978	+	0.468796i	−0.0356645	+	0.999364i	$0.511355\pi$
$410$	−14.2348	−	14.9138i	−0.703005	−	0.736542i
$411$			21.1490i			1.04320i
$412$	9.46097	+	6.06665i	0.466109	+	0.298882i
$413$	−2.97060	−	5.14523i	−0.146174	−	0.253180i
$414$	0.579589	+	2.38382i	0.0284853	+	0.117158i
$415$	8.89945	−	5.13810i	0.436857	−	0.252219i
$416$	−0.914653	+	2.30159i	−0.0448445	+	0.112845i
$417$		−	15.6445i		−	0.766113i
$418$	−14.9061	+	12.0923i	−0.729081	+	0.591454i
$419$	8.83253			0.431497			0.215749	−	0.976449i	$-0.430781\pi$
$419$	8.83253			0.431497			0.215749	+	0.976449i	$0.430781\pi$
$420$	−11.0527	−	21.3860i	−0.539319	−	1.04353i
$421$	−0.915408	−	1.58553i	−0.0446143	−	0.0772742i	0.842856	−	0.538139i	$-0.180873\pi$
$421$	−0.915408	−	1.58553i	−0.0446143	−	0.0772742i	−0.887470	+	0.460865i	$0.847539\pi$
$422$	−6.08074	−	25.0098i	−0.296006	−	1.21746i
$423$	−1.01742	+	0.587406i	−0.0494685	+	0.0285607i
$424$	−1.76734	−	9.09534i	−0.0858296	−	0.441709i
$425$	−15.0409			−0.729588
$426$	−13.2954	+	12.6900i	−0.644165	+	0.614834i
$427$	16.6472	−	28.8338i	0.805613	−	1.39536i
$428$	−9.72794	+	15.1708i	−0.470218	+	0.733307i
$429$		−	2.00906i		−	0.0969984i
$430$	−13.4833	+	12.8694i	−0.650223	+	0.620616i
$431$	11.5493	−	20.0040i	0.556310	−	0.963557i	−0.441490	−	0.897266i	$-0.645550\pi$
$431$	11.5493	−	20.0040i	0.556310	−	0.963557i	0.997800	−	0.0662911i	$-0.0211166\pi$
$432$	−20.5081	+	9.41606i	−0.986696	+	0.453030i
$433$	1.33452	+	0.770486i	0.0641330	+	0.0370272i	0.531724	−	0.846918i	$-0.321545\pi$
$433$	1.33452	+	0.770486i	0.0641330	+	0.0370272i	−0.467591	+	0.883945i	$0.654878\pi$
$434$	−40.0120	−	11.7265i	−1.92064	−	0.562892i
$435$	−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	0.852169	+	0.523266i	$0.175287\pi$
$439$	18.4223	+	31.9083i	0.879246	+	1.52290i	0.0270772	+	0.999633i	$0.491380\pi$
$440$	7.76611	−	22.5497i	0.370235	−	1.07501i
$441$	0.867864	−	1.50318i	0.0413269	−	0.0715802i
$442$	1.12241	−	3.82975i	0.0533874	−	0.182162i
$443$	−12.8595	+	22.2732i	−0.610971	+	1.05823i	0.380106	+	0.924943i	$0.375887\pi$
$443$	−12.8595	+	22.2732i	−0.610971	+	1.05823i	−0.991077	+	0.133290i	$0.957446\pi$
$444$	−24.6219	−	1.14785i	−1.16850	−	0.0544747i
$445$	33.6804			1.59661
$446$	−2.12431	+	0.516492i	−0.100589	+	0.0244566i
$447$	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	$-0.903729\pi$
$449$		−	12.6228i		−	0.595707i	0.954612	−	0.297853i	$-0.0962706\pi$
$450$	2.65542	−	0.645624i	0.125178	−	0.0304350i
$451$	−14.5163	+	8.38100i	−0.683547	+	0.394646i
$452$	4.55670	−	7.10621i	0.214329	−	0.334248i
$453$	23.6250	−	13.6399i	1.11000	−	0.640858i
$454$	−4.48221	−	1.31363i	−0.210360	−	0.0616515i
$455$	−3.57584			−0.167638
$456$	−14.6281	+	10.7773i	−0.685025	+	0.504692i
$457$	3.27588			0.153239			0.0766197	−	0.997060i	$-0.475587\pi$
$457$	3.27588			0.153239			0.0766197	+	0.997060i	$0.475587\pi$
$458$	−11.9597	−	3.50511i	−0.558842	−	0.163783i
$459$	31.4911	−	18.1814i	1.46988	−	0.848636i
$460$	−9.55113	−	6.12446i	−0.445324	−	0.285554i
$461$	−14.3820	+	8.30348i	−0.669839	+	0.386732i	−0.796015	−	0.605276i	$-0.793063\pi$
$461$	−14.3820	+	8.30348i	−0.669839	+	0.386732i	0.126177	+	0.992008i	$0.459729\pi$
$462$	−19.0182	+	4.62399i	−0.884808	+	0.215127i
$463$			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
$466$	8.67905	−	2.11018i	0.402049	−	0.0977521i
$467$	−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
$470$	1.52811	−	5.21405i	0.0704865	−	0.240506i
$471$	18.0590	−	31.2791i	0.832114	−	1.44126i
$472$	1.81433	−	5.26808i	0.0835113	−	0.242483i
$473$	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
$478$	−35.6399	−	10.4452i	−1.63013	−	0.477751i
$479$	−30.9763	−	17.8841i	−1.41534	−	0.817148i	−0.419456	−	0.907776i	$-0.637779\pi$
$479$	−30.9763	−	17.8841i	−1.41534	−	0.817148i	−0.995885	+	0.0906279i	$0.971113\pi$
$480$	8.33761	−	20.9804i	0.380558	−	0.957619i
$481$	−1.83064	+	3.17077i	−0.0834702	+	0.144575i
$482$	1.90955	−	1.82260i	0.0869775	−	0.0830171i
$483$			9.31123i			0.423676i
$484$	2.19684	+	1.40867i	0.0998562	+	0.0640307i
$485$	−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	$-0.478438\pi$
$487$	2.98739			0.135372			0.0676858	+	0.997707i	$0.478438\pi$
$488$	30.6507	−	5.95582i	1.38749	−	0.269607i
$489$	−7.66123	+	4.42321i	−0.346453	+	0.200025i
$490$	1.89652	+	7.80028i	0.0856759	+	0.352381i
$491$	−16.2391	−	28.1269i	−0.732858	−	1.26935i	−0.955657	−	0.294483i	$-0.904853\pi$
$491$	−16.2391	−	28.1269i	−0.732858	−	1.26935i	0.222798	−	0.974865i	$-0.428481\pi$
$492$	−14.0960	+	7.28508i	−0.635495	+	0.328437i
$493$	−20.4248			−0.919887
$494$	0.424530	+	2.66529i	0.0191005	+	0.119917i
$495$		−	6.98244i		−	0.313837i
$496$	−16.3158	−	35.5356i	−0.732600	−	1.59560i
$497$	23.0332	−	13.2982i	1.03318	−	0.596507i
$498$	−1.86848	−	7.68495i	−0.0837284	−	0.344371i
$499$	−4.86494	−	8.42632i	−0.217785	−	0.377214i	0.736346	−	0.676605i	$-0.236550\pi$
$499$	−4.86494	−	8.42632i	−0.217785	−	0.377214i	−0.954130	+	0.299391i	$0.903216\pi$
$500$	7.79548	−	12.1571i	0.348624	−	0.543682i
$501$		−	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	$-0.199730\pi$
$503$	15.8302	+	9.13954i	0.705832	+	0.407512i	−0.103684	+	0.994610i	$0.533063\pi$
$504$	6.93421	−	1.34740i	0.308874	−	0.0600181i
$505$	−4.04531			−0.180014
$506$	−6.67297	+	6.36913i	−0.296650	+	0.283142i
$507$	16.3472	+	9.43809i	0.726007	+	0.419160i
$508$	27.9307	−	14.4352i	1.23923	−	0.640457i
$509$	−2.39384	+	4.14625i	−0.106105	+	0.183779i	−0.914189	−	0.405288i	$-0.867171\pi$
$509$	−2.39384	+	4.14625i	−0.106105	+	0.183779i	0.808084	+	0.589067i	$0.200505\pi$
$510$	−10.2314	+	34.9104i	−0.453054	+	1.54586i
$511$	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
$516$	6.58629	+	12.7439i	0.289945	+	0.561018i
$517$	−3.82564	−	2.20874i	−0.168252	−	0.0971401i
$518$	34.2286	+	10.0316i	1.50392	+	0.440762i
$519$	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	$-0.897730\pi$
$521$		−	14.4161i		−	0.631582i	0.948829	−	0.315791i	$-0.102270\pi$
$522$	3.60594	−	0.876729i	0.157828	−	0.0383734i
$523$	−13.5585	−	7.82801i	−0.592873	−	0.342295i	0.173360	−	0.984859i	$-0.444538\pi$
$523$	−13.5585	−	7.82801i	−0.592873	−	0.342295i	−0.766233	+	0.642563i	$0.777871\pi$
$524$	−0.946513	+	20.3030i	−0.0413486	+	0.886942i
$525$	10.3721			0.452676
$526$	9.57942	+	39.3997i	0.417683	+	1.71791i
$527$	31.5041	+	54.5666i	1.37234	+	2.37696i
$528$	−14.9733	−	10.6167i	−0.651628	−	0.462033i
$529$	−9.30575	−	16.1180i	−0.404598	−	0.700784i
$530$	12.0393	+	3.52842i	0.522953	+	0.153265i
$531$		−	1.63125i		−	0.0707900i
$532$	24.2532	−	10.1531i	1.05151	−	0.440191i
$533$			2.35691i			0.102089i
$534$	7.29027	−	24.8750i	0.315481	−	1.07645i
$535$	−12.2010	−	21.1328i	−0.527495	−	0.913649i
$536$	−14.4231	+	2.80259i	−0.622982	+	0.121053i
$537$	−2.42043	−	4.19230i	−0.104449	−	0.180911i
$538$	21.3820	−	5.19869i	0.921842	−	0.224131i
$539$	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	$-0.389772\pi$
$541$	−7.10566	−	4.10246i	−0.305496	−	0.176378i	−0.644909	+	0.764259i	$0.723105\pi$
$542$	−1.15463	−	4.74895i	−0.0495958	−	0.203985i
$543$			12.3006i			0.527870i
$544$	−22.6114	−	28.6031i	−0.969454	−	1.22635i
$545$	26.3740	+	15.2270i	1.12974	+	0.652254i
$546$	−0.774006	+	2.64097i	−0.0331244	+	0.113023i
$547$	25.9507	+	14.9826i	1.10957	+	0.640611i	0.938718	−	0.344685i	$-0.112014\pi$
$547$	25.9507	+	14.9826i	1.10957	+	0.640611i	0.170853	+	0.985297i	$0.445348\pi$
$548$	25.4972	−	13.1775i	1.08919	−	0.562913i
$549$	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
$554$	−1.92011	−	0.562738i	−0.0815777	−	0.0239084i
$555$	16.6874	−	28.9035i	0.708342	−	1.22688i
$556$	−18.8609	+	9.74771i	−0.799882	+	0.413395i
$557$	−33.2847	−	19.2169i	−1.41032	−	0.814247i	−0.414900	−	0.909867i	$-0.636183\pi$
$557$	−33.2847	−	19.2169i	−1.41032	−	0.814247i	−0.995418	+	0.0956198i	$0.969517\pi$
$558$	−7.90421	−	8.28129i	−0.334612	−	0.350575i
$559$	2.13083			0.0901246
$560$	−18.8962	+	26.6503i	−0.798511	+	1.12618i
$561$	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	$-0.999775\pi$
$563$		−	0.0334791i		−	0.00141098i	1.00000		0.000705488i	$-0.000224564\pi$
$564$	−3.52012	−	2.25720i	−0.148224	−	0.0950454i
$565$	5.71512	+	9.89888i	0.240437	+	0.416449i
$566$	22.1434	−	5.38381i	0.930755	−	0.226298i
$567$	−15.2275	+	8.79162i	−0.639496	+	0.369213i
$568$	23.5831	+	8.12204i	0.989526	+	0.340793i
$569$			0.534632i			0.0224129i	0.999937	+	0.0112065i	$0.00356720\pi$
$569$			0.534632i			0.0224129i	−0.999937	+	0.0112065i	$0.996433\pi$
$570$	−3.86985	−	24.2958i	−0.162090	−	1.01764i
$571$	−37.1365			−1.55411			−0.777057	−	0.629430i	$-0.783288\pi$
$571$	−37.1365			−1.55411			−0.777057	+	0.629430i	$0.783288\pi$
$572$	−2.42212	+	1.25180i	−0.101274	+	0.0523404i
$573$	3.26569	+	5.65634i	0.136426	+	0.236297i
$574$	22.3110	−	5.42458i	0.931244	−	0.226418i
$575$	4.23356	−	2.44425i	0.176552	−	0.101932i
$576$	5.21976	+	4.07922i	0.217490	+	0.169967i
$577$	−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
$580$	−9.26431	+	14.4477i	−0.384679	+	0.599910i
$581$			11.4447i			0.474804i
$582$	26.7536	+	28.0299i	1.10897	+	1.16188i
$583$	5.09999	−	8.83344i	0.211220	−	0.365844i
$584$	36.9135	+	12.7130i	1.52749	+	0.526069i
$585$	−0.850264	−	0.490900i	−0.0351541	−	0.0202962i
$586$	−9.46539	+	32.2967i	−0.391012	+	1.33417i
$587$	−9.70642	−	16.8120i	−0.400627	−	0.693906i	0.593175	−	0.805074i	$-0.297874\pi$
$587$	−9.70642	−	16.8120i	−0.400627	−	0.693906i	−0.993802	+	0.111168i	$0.964541\pi$
$588$	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
$592$	13.9575	+	30.3992i	0.573648	+	1.24940i
$593$	−14.9132	+	25.8304i	−0.612411	+	1.06073i	0.378422	+	0.925633i	$0.376467\pi$
$593$	−14.9132	+	25.8304i	−0.612411	+	1.06073i	−0.990833	+	0.135093i	$0.956867\pi$
$594$	−23.8398	−	6.98685i	−0.978157	−	0.286674i
$595$	26.3214	−	45.5900i	1.07907	−	1.86901i
$596$	−36.9208	−	1.72122i	−1.51234	−	0.0705040i
$597$	10.4304			0.426886
$598$	0.306437	+	1.26036i	0.0125312	+	0.0515400i
$599$	−3.62259	+	6.27451i	−0.148015	+	0.256369i	−0.930494	−	0.366308i	$-0.880622\pi$
$599$	−3.62259	+	6.27451i	−0.148015	+	0.256369i	0.782479	+	0.622677i	$0.213955\pi$
$600$	6.38109	+	7.34157i	0.260507	+	0.299718i
$601$			23.7575i			0.969088i	0.874767	+	0.484544i	$0.161015\pi$
$601$			23.7575i			0.969088i	−0.874767	+	0.484544i	$0.838985\pi$
$602$	−4.90425	−	20.1709i	−0.199882	−	0.822106i
$603$	−3.72532	+	2.15082i	−0.151707	+	0.0875880i
$604$	−31.1644	−	19.9835i	−1.26806	−	0.813117i
$605$	−3.06017	+	1.76679i	−0.124414	+	0.0718303i
$606$	−0.875625	+	2.98771i	−0.0355698	+	0.121367i
$607$	−15.5235			−0.630081			−0.315041	−	0.949078i	$-0.602018\pi$
$607$	−15.5235			−0.630081			−0.315041	+	0.949078i	$0.602018\pi$
$608$	22.1075	+	10.9206i	0.896577	+	0.442887i
$609$	14.0849			0.570747
$610$	−11.8905	+	40.5716i	−0.481434	+	1.64270i
$611$	−0.537924	+	0.310570i	−0.0217621	+	0.0125643i
$612$	−8.98601	−	5.76209i	−0.363238	−	0.232919i
$613$	−6.02011	+	3.47571i	−0.243150	+	0.140383i	−0.616624	−	0.787258i	$-0.711500\pi$
$613$	−6.02011	+	3.47571i	−0.243150	+	0.140383i	0.373474	+	0.927641i	$0.378167\pi$
$614$	0.553353	+	2.27591i	0.0223315	+	0.0918484i
$615$		−	21.4846i		−	0.866344i
$616$	17.4245	+	20.0472i	0.702053	+	0.807726i
$617$	−13.4941	+	23.3725i	−0.543253	+	0.940943i	0.455461	+	0.890256i	$0.349474\pi$
$617$	−13.4941	+	23.3725i	−0.543253	+	0.940943i	−0.998715	+	0.0506869i	$0.983859\pi$
$618$	2.76699	+	11.3805i	0.111305	+	0.457791i
$619$	−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
$622$	−0.883480	−	0.258926i	−0.0354243	−	0.0103820i
$623$	−18.7550	+	32.4847i	−0.751405	+	1.30147i
$624$	−2.34551	+	1.07692i	−0.0938957	+	0.0431111i
$625$	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
$630$	−2.69004	+	9.17864i	−0.107174	+	0.365686i
$631$	7.72930	+	4.46251i	0.307699	+	0.177650i	0.645896	−	0.763425i	$-0.276484\pi$
$631$	7.72930	+	4.46251i	0.307699	+	0.177650i	−0.338198	+	0.941075i	$0.609817\pi$
$632$	−5.02450	−	1.73044i	−0.199864	−	0.0688332i
$633$	13.4109	−	23.2284i	0.533036	−	0.923245i
$634$	20.4480	+	21.4235i	0.812093	+	0.850834i
$635$			42.5711i			1.68938i
$636$	5.21190	−	8.12799i	0.206665	−	0.322296i
$637$	0.458852	−	0.794756i	0.0181804	−	0.0314894i
$638$	9.63441	+	10.0940i	0.381430	+	0.399626i
$639$	7.30245			0.288880
$640$	−30.4889	+	3.02060i	−1.20518	+	0.119400i
$641$	1.70881	−	0.986580i	0.0674938	−	0.0389675i	−0.465873	−	0.884851i	$-0.654260\pi$
$641$	1.70881	−	0.986580i	0.0674938	−	0.0389675i	0.533367	+	0.845884i	$0.320926\pi$
$642$	−18.2488	+	4.43691i	−0.720222	+	0.175111i
$643$	−6.70192	−	11.6081i	−0.264298	−	0.457777i	0.703082	−	0.711109i	$-0.251807\pi$
$643$	−6.70192	−	11.6081i	−0.264298	−	0.457777i	−0.967379	+	0.253332i	$0.918474\pi$
$644$	11.2256	−	5.80161i	0.442350	−	0.228616i
$645$	−19.4238			−0.764812
$646$	−37.1060	−	14.2064i	−1.45992	−	0.558945i
$647$			25.2982i			0.994575i	0.867586	+	0.497288i	$0.165671\pi$
$647$			25.2982i			0.994575i	−0.867586	+	0.497288i	$0.834329\pi$
$648$	−15.5911	−	5.36959i	−0.612477	−	0.210937i
$649$	5.31196	−	3.06686i	0.208513	−	0.120385i
$650$	1.40396	−	0.341351i	0.0550678	−	0.0133889i
$651$	−21.7250	−	37.6289i	−0.851472	−	1.47479i
$652$	10.1061	+	6.48035i	0.395787	+	0.253790i
$653$		−	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
$656$	17.5657	+	12.4549i	0.685827	+	0.486281i
$657$	11.4302			0.445933
$658$	4.17800	+	4.37731i	0.162875	+	0.170645i
$659$	−6.55373	−	3.78380i	−0.255297	−	0.147396i	0.366890	−	0.930264i	$-0.380422\pi$
$659$	−6.55373	−	3.78380i	−0.255297	−	0.147396i	−0.622187	+	0.782868i	$0.713756\pi$
$660$	22.0791	−	11.4109i	0.859426	−	0.444169i
$661$	7.23786	−	12.5363i	0.281520	−	0.487607i	−0.690239	−	0.723581i	$-0.742495\pi$
$661$	7.23786	−	12.5363i	0.281520	−	0.487607i	0.971759	+	0.235974i	$0.0758280\pi$
$662$	10.0031	+	2.93166i	0.388781	+	0.113942i
$663$	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
$668$	−12.0550	+	6.23027i	−0.466422	+	0.241056i
$669$	−1.97300	−	1.13911i	−0.0762804	−	0.0440405i
$670$	5.59525	−	19.0915i	0.216163	−	0.737568i
$671$	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	$0.170794\pi$
$673$			26.5226i			1.02237i	−0.859470	+	0.511186i	$0.829206\pi$
$674$	3.47256	+	14.2825i	0.133758	+	0.550140i
$675$	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	$-0.462287\pi$
$677$	6.15109			0.236405			0.118203	+	0.992989i	$0.462287\pi$
$678$	8.54798	−	2.07831i	0.328283	−	0.0798170i
$679$	−28.0358	−	48.5595i	−1.07592	−	1.86354i
$680$	48.4629	−	9.41695i	1.85847	−	0.361124i
$681$	−2.43367	−	4.21525i	−0.0932586	−	0.161529i
$682$	12.1065	−	41.3086i	0.463584	−	1.58179i
$683$			2.04240i			0.0781501i	0.999236	+	0.0390750i	$0.0124411\pi$
$683$			2.04240i			0.0781501i	−0.999236	+	0.0390750i	$0.987559\pi$
$684$	7.16077	+	0.915346i	0.273799	+	0.0349991i
$685$			38.8620i			1.48484i
$686$	20.0720	+	5.88263i	0.766354	+	0.224600i
$687$	−6.49370	−	11.2474i	−0.247750	−	0.429115i
$688$	11.2602	−	15.8808i	0.429291	−	0.605451i
$689$	−0.717109	−	1.24207i	−0.0273197	−	0.0473191i
$690$	−2.79336	−	11.4890i	−0.106341	−	0.437377i
$691$	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
$694$	25.4489	−	6.18750i	0.966026	−	0.234874i
$695$		−	28.7473i		−	1.09045i
$696$	8.66524	+	9.96953i	0.328455	+	0.377894i
$697$	−30.0493	−	17.3490i	−1.13820	−	0.657139i
$698$	−21.8713	−	6.40994i	−0.827840	−	0.242620i
$699$	8.06086	+	4.65394i	0.304890	+	0.176028i
$700$	−6.46262	−	12.5046i	−0.244264	−	0.472628i
$701$	−24.5743	+	14.1880i	−0.928159	+	0.535873i	−0.886229	−	0.463248i	$-0.846684\pi$
$701$	−24.5743	+	14.1880i	−0.928159	+	0.535873i	−0.0419298	+	0.999121i	$0.513351\pi$
$702$	−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
$706$	12.7562	−	43.5253i	0.480087	−	1.63810i
$707$	2.25264	−	3.90169i	0.0847193	−	0.146738i
$708$	5.15814	−	2.66583i	0.193855	−	0.100188i
$709$	4.47396	+	2.58304i	0.168023	+	0.0970082i	0.581653	−	0.813437i	$-0.302406\pi$
$709$	4.47396	+	2.58304i	0.168023	+	0.0970082i	−0.413630	+	0.910445i	$0.635739\pi$
$710$	−24.4308	+	23.3184i	−0.916871	+	0.875123i
$711$	−1.55582			−0.0583479
$712$	−34.5317	+	6.70994i	−1.29413	+	0.251466i
$713$	−17.7350	−	10.2393i	−0.664179	−	0.383464i
$714$	−27.9736	−	29.3081i	−1.04689	−	1.09683i
$715$		−	3.69172i		−	0.138062i
$716$	−3.54612	+	5.53019i	−0.132525	+	0.206673i
$717$	−19.3511	−	33.5171i	−0.722681	−	1.25172i
$718$	1.18472	+	4.87269i	0.0442133	+	0.181847i
$719$	−30.3540	+	17.5249i	−1.13201	+	0.653568i	−0.944441	−	0.328682i	$-0.893395\pi$
$719$	−30.3540	+	17.5249i	−1.13201	+	0.653568i	−0.187573	+	0.982251i	$0.560062\pi$
$720$	−8.15177	+	3.74279i	−0.303798	+	0.139486i
$721$		−	16.9482i		−	0.631184i
$722$	26.7896	−	2.07769i	0.997006	−	0.0773238i
$723$	2.75086			0.102306
$724$	14.8296	−	7.66423i	0.551137	−	0.284839i
$725$	−3.69735	−	6.40400i	−0.137316	−	0.237839i
$726$	0.642495	+	2.64255i	0.0238452	+	0.0980743i
$727$	−7.95388	+	4.59217i	−0.294993	+	0.170314i	−0.640191	−	0.768215i	$-0.721145\pi$
$727$	−7.95388	+	4.59217i	−0.294993	+	0.170314i	0.345198	+	0.938530i	$0.387812\pi$
$728$	3.66622	−	0.712392i	0.135879	−	0.0264030i
$729$	−29.7706			−1.10261
$730$	−38.2403	+	36.4991i	−1.41534	+	1.35089i
$731$	−15.6848	+	27.1670i	−0.580125	+	1.00481i
$732$	27.3908	+	17.5638i	1.01239	+	0.649176i
$733$		−	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
$736$	11.0127	+	4.37643i	0.405932	+	0.161318i
$737$	−14.0078	−	8.08739i	−0.515983	−	0.297903i
$738$	6.04982	+	1.77305i	0.222697	+	0.0652671i
$739$	3.24715	+	5.62423i	0.119448	+	0.206891i	0.919549	−	0.392975i	$-0.128554\pi$
$739$	3.24715	+	5.62423i	0.119448	+	0.206891i	−0.800101	+	0.599865i	$0.795221\pi$
$740$	−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	−0.927662	−	0.373422i	$-0.878184\pi$
$743$	−21.4582	−	37.1666i	−0.787224	−	1.36351i	0.140438	−	0.990089i	$-0.455149\pi$
$744$	13.2688	−	38.5273i	0.486459	−	1.41248i
$745$	25.0230	−	43.3412i	0.916773	−	1.58790i
$746$	2.44397	−	8.33905i	0.0894802	−	0.305314i
$747$	−1.57115	+	2.72131i	−0.0574854	+	0.0995676i
$748$	1.86920	−	40.0951i	0.0683448	−	1.46602i
$749$	27.1766			0.993012
$750$	14.6236	−	3.55551i	0.533980	−	0.129829i
$751$	21.3186	−	36.9250i	0.777928	−	1.34741i	−0.155205	−	0.987882i	$-0.549604\pi$
$751$	21.3186	−	36.9250i	0.777928	−	1.34741i	0.933134	−	0.359529i	$-0.117063\pi$
$752$	−0.527970	+	5.65026i	−0.0192531	+	0.206044i
$753$		−	29.8205i		−	1.08672i
$754$	1.90652	−	0.463540i	0.0694312	−	0.0168811i
$755$	43.4117	−	25.0638i	1.57991	−	0.912164i
$756$	28.6464	+	18.3689i	1.04186	+	0.668070i
$757$	−33.2731	+	19.2102i	−1.20933	+	0.698208i	−0.962613	−	0.270879i	$-0.912686\pi$
$757$	−33.2731	+	19.2102i	−1.20933	+	0.698208i	−0.246718	+	0.969087i	$0.579352\pi$
$758$	21.9160	+	6.42304i	0.796024	+	0.233295i
$759$	−9.61296			−0.348928
$760$	−26.8797	+	19.8036i	−0.975028	+	0.718352i
$761$	−5.18110			−0.187815			−0.0939074	−	0.995581i	$-0.529936\pi$
$761$	−5.18110			−0.187815			−0.0939074	+	0.995581i	$0.529936\pi$
$762$	31.4414	+	9.21470i	1.13900	+	0.333813i
$763$	−29.3728	+	16.9584i	−1.06337	+	0.613935i
$764$	4.78449	−	7.46144i	0.173097	−	0.269946i
$765$	12.5174	−	7.22694i	0.452569	−	0.261291i
$766$	−16.0011	+	3.89041i	−0.578142	+	0.140566i
$767$		−	0.862463i		−	0.0311417i
$768$	−4.36855	+	23.1717i	−0.157636	+	0.836136i
$769$	23.3360	−	40.4192i	0.841519	−	1.45755i	−0.0470919	−	0.998891i	$-0.514995\pi$
$769$	23.3360	−	40.4192i	0.841519	−	1.45755i	0.888611	−	0.458663i	$-0.151671\pi$
$770$	−34.9466	+	8.49673i	−1.25939	+	0.306201i
$771$	−17.6750			−0.636549
$772$	14.1341	+	0.658923i	0.508698	+	0.0237152i
$773$	16.0227	−	27.7521i	0.576296	−	0.998175i	−0.419603	−	0.907708i	$-0.637831\pi$
$773$	16.0227	−	27.7521i	0.576296	−	0.998175i	0.995899	−	0.0904668i	$-0.0288359\pi$
$774$	1.60298	−	5.46952i	0.0576180	−	0.196598i
$775$	−11.4059	+	19.7556i	−0.409712	+	0.709641i
$776$	17.1232	−	49.7189i	0.614687	−	1.78480i
$777$	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
$782$	−18.3246	−	5.37049i	−0.655286	−	0.192048i
$783$	15.4823	+	8.93874i	0.553294	+	0.319444i
$784$	−3.49845	−	7.61959i	−0.124945	−	0.272128i
$785$	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	$0.194597\pi$
$787$			32.2037i			1.14794i	−0.818878	+	0.573968i	$0.805403\pi$
$788$	−12.1883	+	19.0077i	−0.434190	+	0.677122i
$789$	−21.1272	+	36.5933i	−0.752147	+	1.30276i
$790$	5.20509	−	4.96809i	0.185189	−	0.176757i
$791$	−12.7299			−0.452624
$792$	1.39107	+	7.15891i	0.0494294	+	0.254381i
$793$	4.18570	−	2.41661i	0.148638	−	0.0858164i
$794$	−3.90363	−	16.0554i	−0.138535	−	0.569786i
$795$	6.53688	+	11.3222i	0.231839	+	0.401558i
$796$	−6.49892	−	12.5748i	−0.230348	−	0.445703i
$797$	52.1341			1.84668			0.923342	−	0.383979i	$-0.125446\pi$
$797$	52.1341			1.84668			0.923342	+	0.383979i	$0.125446\pi$
$798$	25.5881	+	9.79670i	0.905809	+	0.346799i
$799$		−	9.14431i		−	0.323503i
$800$	4.87506	−	12.2674i	0.172359	−	0.433717i
$801$	−8.91915	+	5.14947i	−0.315143	+	0.181948i
$802$	−8.25755	−	33.9629i	−0.291584	−	1.19927i
$803$	21.4896	+	37.2210i	0.758350	+	1.31350i
$804$	−12.8891	−	8.26486i	−0.454563	−	0.291479i
$805$			17.1097i			0.603038i
$806$	−4.17907	−	4.37844i	−0.147202	−	0.154224i
$807$	19.8590	+	11.4656i	0.699068	+	0.403607i
$808$	4.14755	−	0.805922i	0.145910	−	0.0283522i
$809$	−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	0.339990	−	0.940429i	$-0.389576\pi$
$811$	−8.67018	−	5.00573i	−0.304451	−	0.175775i	−0.644441	+	0.764654i	$0.722910\pi$
$812$	−8.77595	−	16.9807i	−0.307975	−	0.595904i
$813$	2.54651	−	4.41069i	0.0893101	−	0.154690i
$814$	−10.3566	+	35.3378i	−0.363000	+	1.23859i
$815$	−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
$820$	−25.9018	+	13.3866i	−0.904530	+	0.467479i
$821$	8.96021	+	5.17318i	0.312714	+	0.180545i	0.648140	−	0.761521i	$-0.275547\pi$
$821$	8.96021	+	5.17318i	0.312714	+	0.180545i	−0.335427	+	0.942066i	$0.608880\pi$
$822$	28.7019	+	8.41184i	1.00110	+	0.293397i
$823$	−19.1933	−	11.0812i	−0.669036	−	0.386268i	0.126676	−	0.991944i	$-0.459569\pi$
$823$	−19.1933	−	11.0812i	−0.669036	−	0.386268i	−0.795711	+	0.605676i	$0.792903\pi$
$824$	11.9962	−	10.4268i	0.417909	−	0.363235i
$825$			10.7082i			0.372812i
$826$	−8.16428	+	1.98502i	−0.284072	+	0.0690676i
$827$	−15.5457	−	8.97531i	−0.540577	−	0.312102i	0.204736	−	0.978817i	$-0.434366\pi$
$827$	−15.5457	−	8.97531i	−0.540577	−	0.312102i	−0.745313	+	0.666715i	$0.767700\pi$
$828$	3.46568	+	0.161568i	0.120441	+	0.00561486i
$829$	30.6699			1.06521			0.532605	−	0.846364i	$-0.321213\pi$
$829$	30.6699			1.06521			0.532605	+	0.846364i	$0.321213\pi$
$830$	−3.43339	−	14.1213i	−0.119175	−	0.490159i
$831$	−1.04255	−	1.80575i	−0.0361656	−	0.0626407i
$832$	2.75976	+	2.15674i	0.0956775	+	0.0747716i
$833$	6.75514	+	11.7002i	0.234052	+	0.405389i
$834$	−21.2316	−	6.22246i	−0.735190	−	0.215466i
$835$		−	18.3739i		−	0.635853i
$836$	10.4821	+	25.0391i	0.362530	+	0.865997i
$837$		−	55.1499i		−	1.90626i
$838$	3.51307	−	11.9869i	0.121357	−	0.414080i
$839$	18.8792	+	32.6997i	0.651782	+	1.12892i	0.982690	+	0.185256i	$0.0593115\pi$
$839$	18.8792	+	32.6997i	0.651782	+	1.12892i	−0.330908	+	0.943663i	$0.607355\pi$
$840$	−33.4198	+	6.49389i	−1.15309	+	0.224060i
$841$	9.47916	+	16.4184i	0.326868	+	0.566151i
$842$	−2.51587	+	0.611695i	−0.0867027	+	0.0210804i
$843$	7.99566			0.275385
$844$	−36.3601	−	1.69508i	−1.25157	−	0.0583471i
$845$	30.0386	+	17.3428i	1.03336	+	0.596610i
$846$	0.392517	+	1.61440i	0.0134950	+	0.0555043i
$847$		−	3.93537i		−	0.135221i
$848$	−13.0465	−	1.21909i	−0.448019	−	0.0418636i
$849$	20.5661	+	11.8739i	0.705827	+	0.407510i
$850$	−5.98237	+	20.4124i	−0.205194	+	0.700139i
$851$	15.1715	+	8.75927i	0.520073	+	0.300264i
$852$	11.9339	+	23.0910i	0.408848	+	0.791084i
$853$	3.05229	−	1.76224i	0.104508	−	0.0603379i	−0.446835	−	0.894616i	$-0.647449\pi$
$853$	3.05229	−	1.76224i	0.104508	−	0.0603379i	0.551343	+	0.834279i	$0.314116\pi$
$854$	−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	−0.931796	−	0.362982i	$-0.881759\pi$
$857$	−31.7144	+	18.3103i	−1.08334	+	0.625468i	−0.151547	+	0.988450i	$0.548425\pi$
$858$	−2.72656	−	0.799087i	−0.0930831	−	0.0272804i
$859$	−2.99574	+	5.18877i	−0.102213	+	0.177038i	−0.912596	−	0.408862i	$-0.865926\pi$
$859$	−2.99574	+	5.18877i	−0.102213	+	0.177038i	0.810383	+	0.585900i	$0.199259\pi$
$860$	12.1025	+	23.4173i	0.412693	+	0.798523i
$861$	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	$-0.432359\pi$
$863$	12.3914			0.421808			0.210904	+	0.977507i	$0.432359\pi$
$864$	4.62189	+	31.5773i	0.157240	+	1.07428i
$865$	40.7858	+	23.5477i	1.38676	+	0.800645i
$866$	1.57644	−	1.50466i	0.0535697	−	0.0511305i
$867$			36.1718i			1.22846i
$868$	−31.8289	+	49.6373i	−1.08034	+	1.68480i
$869$	−2.92506	−	5.06635i	−0.0992259	−	0.171864i
$870$	−17.3790	+	4.22544i	−0.589205	+	0.143256i
$871$	−1.96963	+	1.13717i	−0.0667385	+	0.0385315i
$872$	−30.0741	−	10.3575i	−1.01844	−	0.350751i
$873$		−	15.3953i		−	0.521052i
$874$	12.7529	−	2.03129i	0.431374	−	0.0687095i
$875$	−21.7780			−0.736230
$876$	18.6795	+	36.1431i	0.631122	+	1.22116i
$877$	−10.4760	−	18.1449i	−0.353749	−	0.612711i	0.633154	−	0.774026i	$-0.281760\pi$
$877$	−10.4760	−	18.1449i	−0.353749	−	0.612711i	−0.986903	+	0.161315i	$0.948427\pi$
$878$	50.6310	−	12.3101i	1.70871	−	0.415447i
$879$	−30.3732	+	17.5359i	−1.02446	+	0.591473i
$880$	−27.5139	−	19.5086i	−0.927494	−	0.657634i
$881$	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	−0.808950	−	0.587877i	$-0.799964\pi$
$883$	3.10945	−	5.38572i	0.104641	−	0.181244i	0.913592	+	0.406633i	$0.133297\pi$
$884$	−4.75104	−	3.04650i	−0.159795	−	0.102465i
$885$			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	$-0.840510\pi$
$887$	−0.671412	+	1.16292i	−0.0225438	+	0.0390470i	0.854533	+	0.519396i	$0.173843\pi$
$888$	−11.3509	+	32.9585i	−0.380912	+	1.10601i
$889$	−41.0597	−	23.7058i	−1.37710	−	0.795069i
$890$	13.3961	−	45.7087i	0.449039	−	1.53216i
$891$	−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
$896$	14.0644	−	31.0884i	0.469860	−	1.03859i
$897$	−0.675839	+	1.17059i	−0.0225656	+	0.0390848i
$898$	−17.1308	−	5.02061i	−0.571661	−	0.167540i
$899$	−15.4887	+	26.8272i	−0.516577	+	0.894737i
$900$	0.179976	−	3.86054i	0.00599919	−	0.128685i
$901$	21.1143			0.703419
$902$	5.60036	+	23.0340i	0.186472	+	0.766949i
$903$	10.8162	−	18.7342i	0.359941	−	0.623435i
$904$	−7.83166	−	9.01047i	−0.260477	−	0.299684i
$905$			22.6028i			0.751342i
$906$	−9.11446	−	37.4873i	−0.302808	−	1.24543i
$907$	5.49954	−	3.17516i	0.182609	−	0.105429i	−0.405909	−	0.913914i	$-0.633045\pi$
$907$	5.49954	−	3.17516i	0.182609	−	0.105429i	0.588518	+	0.808484i	$0.299712\pi$
$908$	−3.56552	+	5.56045i	−0.118326	+	0.184530i
$909$	1.07127	−	0.618497i	0.0355317	−	0.0205142i
$910$	−1.42226	+	4.85288i	−0.0471475	+	0.160871i
$911$	−32.3135			−1.07059			−0.535296	−	0.844664i	$-0.679800\pi$
$911$	−32.3135			−1.07059			−0.535296	+	0.844664i	$0.679800\pi$
$912$	8.80794	+	24.1388i	0.291660	+	0.799317i
$913$	−11.8155			−0.391037
$914$	1.30296	−	4.44580i	0.0430979	−	0.147054i
$915$	−38.1551	+	22.0289i	−1.26137	+	0.728252i
$916$	−9.51377	+	14.8368i	−0.314344	+	0.490221i
$917$	26.5436	−	15.3250i	0.876547	−	0.506075i
$918$	−12.1492	−	49.9691i	−0.400984	−	1.64923i
$919$			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
$922$	5.54856	+	22.8209i	0.182732	+	0.751568i
$923$	3.86091			0.127083
$924$	−1.28899	+	27.6494i	−0.0424048	+	0.909597i
$925$	9.75726	−	16.9001i	0.320817	−	0.555671i
$926$	39.7063	+	11.6370i	1.30483	+	0.382414i
$927$	2.32669	−	4.02994i	0.0764185	−	0.132361i
$928$	6.62012	−	16.6586i	0.217316	−	0.546844i
$929$	−25.4113	−	44.0137i	−0.833719	−	1.44404i	−0.895069	−	0.445927i	$-0.852874\pi$
$929$	−25.4113	−	44.0137i	−0.833719	−	1.44404i	0.0613502	−	0.998116i	$-0.480459\pi$
$930$	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
$934$	−3.06026	+	10.4419i	−0.100135	+	0.341669i
$935$	47.0674	+	27.1744i	1.53927	+	0.888697i
$936$	0.969553	+	0.333914i	0.0316908	+	0.0109143i
$937$	−16.1691	+	28.0057i	−0.528221	+	0.914906i	0.471238	+	0.882006i	$0.343807\pi$
$937$	−16.1691	+	28.0057i	−0.528221	+	0.914906i	−0.999459	+	0.0328994i	$0.989526\pi$
$938$	15.2979	+	16.0277i	0.499495	+	0.523324i
$939$		−	28.4765i		−	0.929295i
$940$	−6.46834	−	4.14769i	−0.210974	−	0.135283i
$941$	14.0148	−	24.2743i	0.456868	−	0.791319i	−0.541925	−	0.840427i	$-0.682304\pi$
$941$	14.0148	−	24.2743i	0.456868	−	0.791319i	0.998793	+	0.0491078i	$0.0156378\pi$
$942$	−35.2670	−	36.9494i	−1.14906	−	1.20388i
$943$	11.2773			0.367241
$944$	−6.42783	−	4.55762i	−0.209208	−	0.148338i
$945$	−39.9041	+	23.0387i	−1.29808	+	0.749448i
$946$	20.8246	−	5.06317i	0.677066	−	0.164618i
$947$	−7.39400	−	12.8068i	−0.240273	−	0.416164i	0.720519	−	0.693435i	$-0.243903\pi$
$947$	−7.39400	−	12.8068i	−0.240273	−	0.416164i	−0.960792	+	0.277271i	$0.910570\pi$
$948$	−2.54257	−	4.91964i	−0.0825788	−	0.159782i
$949$	6.04329			0.196174
$950$	−2.26273	−	14.2059i	−0.0734125	−	0.460900i
$951$			30.8623i			1.00078i
$952$	−17.9041	+	51.9861i	−0.580274	+	1.68488i
$953$	−6.69642	+	3.86618i	−0.216918	+	0.125238i	−0.604523	−	0.796588i	$-0.706636\pi$
$953$	−6.69642	+	3.86618i	−0.216918	+	0.125238i	0.387604	+	0.921826i	$0.373303\pi$
$954$	−3.72767	+	0.906325i	−0.120688	+	0.0293434i
$955$	6.00082	+	10.3937i	0.194182	+	0.336333i
$956$	−28.3509	+	44.2134i	−0.916934	+	1.42996i
$957$			14.5413i			0.470053i
$958$	−36.5917	+	34.9255i	−1.18222	+	1.12839i
$959$	−37.4823	−	21.6404i	−1.21037	−	0.698805i
$960$	−25.1569	−	19.6600i	−0.811935	−	0.634524i
$961$	64.5615			2.08263
$962$	3.57502	+	3.74557i	0.115263	+	0.120762i
$963$	6.46206	+	3.73087i	0.208237	+	0.120226i
$964$	−1.71400	−	3.31643i	−0.0552041	−	0.106815i
$965$	−9.57939	+	16.5920i	−0.308371	+	0.534115i
$966$	12.6365	+	3.70346i	0.406574	+	0.119157i
$967$	29.1031	−	16.8027i	0.935892	−	0.540338i	0.0472221	−	0.998884i	$-0.484963\pi$
$967$	29.1031	−	16.8027i	0.935892	−	0.540338i	0.888670	+	0.458547i	$0.151630\pi$
$968$	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	−0.264265	−	0.964450i	$-0.585130\pi$
$971$	13.6746	−	7.89505i	0.438840	−	0.253364i	0.703105	+	0.711086i	$0.251796\pi$
$972$	7.65167	+	14.8053i	0.245428	+	0.474880i
$973$	27.7266	+	16.0080i	0.888875	+	0.513192i
$974$	1.18821	−	4.05428i	0.0380727	−	0.129907i
$975$	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	$-0.825478\pi$
$977$		−	32.5834i		−	1.04243i	0.853424	−	0.521217i	$-0.174522\pi$
$978$	2.95568	+	12.1566i	0.0945124	+	0.388725i
$979$	−33.5373	−	19.3628i	−1.07186	−	0.618838i
$980$	11.3403	+	0.528677i	0.362253	+	0.0168880i
$981$	−9.31236			−0.297321
$982$	−44.6308	+	10.8513i	−1.42422	+	0.346278i
$983$	−3.64307	−	6.30998i	−0.116196	−	0.201257i	0.802061	−	0.597242i	$-0.203737\pi$
$983$	−3.64307	−	6.30998i	−0.116196	−	0.201257i	−0.918257	+	0.395985i	$0.870403\pi$
$984$	4.28025	+	22.0276i	0.136449	+	0.702215i
$985$	−15.2868	−	26.4776i	−0.487079	−	0.843646i
$986$	−8.12380	+	27.7191i	−0.258715	+	0.882757i
$987$			6.30588i			0.200718i
$988$	3.78600	+	0.483957i	0.120449	+	0.0153967i
$989$		−	10.1956i		−	0.324202i
$990$	−9.47607	−	2.77721i	−0.301169	−	0.0882654i
$991$	1.76345	+	3.05438i	0.0560177	+	0.0970256i	0.892674	−	0.450702i	$-0.148826\pi$
$991$	1.76345	+	3.05438i	0.0560177	+	0.0970256i	−0.836657	+	0.547728i	$0.815493\pi$
$992$	−54.7159	+	8.00863i	−1.73723	+	0.254274i
$993$	5.43131	+	9.40730i	0.172357	+	0.298532i
$994$	−8.88615	−	36.5483i	−0.281852	−	1.15924i
$995$	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	$-0.414515\pi$
$997$	−13.7973	−	7.96589i	−0.436966	−	0.252282i	−0.702310	+	0.711871i	$0.747848\pi$
$998$	−13.3706	+	3.25085i	−0.423239	+	0.102904i
$999$			47.1784i			1.49266i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.9	✓	28	152.27	even	6	inner
152.2.o.c.27.13	yes	28	19.8	odd	6	inner
152.2.o.c.107.9	yes	28	1.1	even	1	trivial
152.2.o.c.107.13	yes	28	8.3	odd	2	inner
608.2.s.c.335.3		28	8.5	even	2
608.2.s.c.335.4		28	4.3	odd	2
608.2.s.c.559.3		28	76.27	even	6
608.2.s.c.559.4		28	152.141	odd	6

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+(0.397742 - 1.35713i) q^{2} +(1.27630 - 0.736872i) q^{3} +(-1.68360 - 1.07957i) q^{4} +(2.34524 - 1.35403i) q^{5} +(-0.492393 - 2.02519i) q^{6} +3.01597i q^{7} +(-2.13476 + 1.85548i) q^{8} +(-0.414040 + 0.717138i) q^{9} +(-0.904789 - 3.72135i) q^{10} -3.11370 q^{11} +(-2.94429 - 0.137261i) q^{12} +(-0.218909 + 0.379162i) q^{13} +(4.09307 + 1.19958i) q^{14} +(1.99549 - 3.45629i) q^{15} +(1.66904 + 3.63515i) 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} +(-1.23845 + 4.22570i) q^{22} +(1.81421 + 1.04744i) q^{23} +(-1.35735 + 3.94119i) q^{24} +(1.16678 - 2.02092i) q^{25} +(0.427502 + 0.447896i) q^{26} +5.64161i q^{27} +(3.25597 - 5.07770i) q^{28} +(1.58443 - 2.74431i) q^{29} +(-3.89694 - 4.08285i) q^{30} -9.77556 q^{31} +(5.59722 - 0.819250i) q^{32} +(-3.97402 + 2.29440i) q^{33} +(-8.85724 + 2.15350i) q^{34} +(4.08371 + 7.07319i) q^{35} +(1.47128 - 0.760389i) q^{36} +8.36258 q^{37} +(4.78726 - 3.88358i) q^{38} +0.645232i q^{39} +(-2.49417 + 7.24207i) q^{40} +(4.66208 - 2.69165i) q^{41} +(6.10791 - 1.48504i) q^{42} +(-2.43347 - 4.21489i) q^{43} +(5.24224 + 3.36148i) q^{44} +2.24248i q^{45} +(2.14310 - 2.04551i) q^{46} +(1.22865 + 0.709359i) q^{47} +(4.80883 + 3.40967i) q^{48} -2.09609 q^{49} +(-2.27857 - 2.38727i) q^{50} +(-8.22635 - 4.74949i) q^{51} +(0.777889 - 0.402029i) q^{52} +(-1.63792 + 2.83695i) q^{53} +(7.65639 + 2.24390i) 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} +(-7.09093 + 3.66474i) q^{60} +(-9.56035 - 5.51967i) q^{61} +(-3.88815 + 13.2667i) q^{62} +(-2.16287 - 1.24873i) q^{63} +(1.11442 - 7.92200i) q^{64} +1.18563i q^{65} +(1.53317 + 6.30584i) q^{66} +(4.49875 + 2.59735i) q^{67} +(-0.600315 + 12.8770i) q^{68} +3.08731 q^{69} +(11.2235 - 2.72882i) q^{70} +(-4.40927 - 7.63707i) q^{71} +(-0.446756 - 2.29916i) q^{72} +(-6.90160 - 11.9539i) q^{73} +(3.32615 - 11.3491i) q^{74} -3.43906i q^{75} +(-3.36643 - 8.04159i) q^{76} -9.39085i q^{77} +(0.875663 + 0.256636i) q^{78} +(0.939415 + 1.62711i) q^{79} +(8.83639 + 6.26539i) q^{80} +(2.91502 + 5.04897i) q^{81} +(-1.79862 - 7.39762i) q^{82} +3.79468 q^{83} +(0.413974 - 8.87989i) q^{84} +(-15.1162 - 8.72734i) q^{85} +(-6.68804 + 1.62609i) q^{86} -4.67009i q^{87} +(6.64702 - 5.77740i) q^{88} +(10.7709 + 6.21857i) q^{89} +(3.04334 + 0.891930i) q^{90} +(-1.14354 - 0.660224i) q^{91} +(-1.92363 - 3.72205i) 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} +(-0.833701 + 2.84466i) 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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