LMFDB - Embedded newform 140.2.o.a.31.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(31,140)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("140.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	140.31
Dual form			140.2.o.a.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.288532 + 1.38447i) q^{2} +(-0.450639 + 0.780530i) q^{3} +(-1.83350 + 0.798926i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.21064 - 0.398687i) q^{6} +(-2.29962 + 1.30833i) q^{7} +(-1.63511 - 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +O(q^{10})$	\(q+(0.288532 + 1.38447i) q^{2} +(-0.450639 + 0.780530i) q^{3} +(-1.83350 + 0.798926i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.21064 - 0.398687i) q^{6} +(-2.29962 + 1.30833i) q^{7} +(-1.63511 - 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +(-0.942109 - 1.05472i) q^{10} +(3.24107 + 1.87123i) q^{11} +(0.202661 - 1.79113i) q^{12} -2.41990i q^{13} +(-2.47486 - 2.80626i) q^{14} -0.901278i q^{15} +(2.72344 - 2.92966i) q^{16} +(-0.505515 - 0.291859i) q^{17} +(-2.30740 + 2.06105i) q^{18} +(3.07977 + 5.33433i) q^{19} +(1.18839 - 1.60864i) q^{20} +(0.0151060 - 2.38451i) q^{21} +(-1.65551 + 5.02706i) q^{22} +(3.73439 - 2.15605i) q^{23} +(2.53823 - 0.236220i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.35028 - 0.698219i) q^{26} -4.67556 q^{27} +(3.17109 - 4.23606i) q^{28} -0.435463 q^{29} +(1.24779 - 0.260047i) q^{30} +(1.26933 - 2.19854i) q^{31} +(4.84181 + 2.92521i) q^{32} +(-2.92110 + 1.68650i) q^{33} +(0.258212 - 0.784080i) q^{34} +(1.33736 - 2.28286i) q^{35} +(-3.51922 - 2.59985i) q^{36} +(5.65039 + 9.78676i) q^{37} +(-6.49659 + 5.80297i) q^{38} +(1.88881 + 1.09050i) q^{39} +(2.57000 + 1.18115i) q^{40} -7.35068i q^{41} +(3.30563 - 0.667093i) q^{42} +5.80096i q^{43} +(-7.43747 - 0.841528i) q^{44} +(-1.89460 - 1.09385i) q^{45} +(4.06247 + 4.54805i) q^{46} +(-5.78826 - 10.0256i) q^{47} +(1.05940 + 3.44594i) q^{48} +(3.57652 - 6.01735i) q^{49} +(1.34325 + 0.442358i) q^{50} +(0.455610 - 0.263046i) q^{51} +(1.93332 + 4.43689i) q^{52} +(1.55746 - 2.69759i) q^{53} +(-1.34905 - 6.47316i) q^{54} -3.74246 q^{55} +(6.77964 + 3.16804i) q^{56} -5.55147 q^{57} +(-0.125645 - 0.602884i) q^{58} +(1.73534 - 3.00569i) q^{59} +(0.720054 + 1.65249i) q^{60} +(-8.99597 + 5.19383i) q^{61} +(3.41004 + 1.12299i) q^{62} +(-4.99421 - 2.92575i) q^{63} +(-2.65284 + 7.54735i) q^{64} +(1.20995 + 2.09570i) q^{65} +(-3.17773 - 3.55756i) q^{66} +(-8.52602 - 4.92250i) q^{67} +(1.16004 + 0.131255i) q^{68} +3.88640i q^{69} +(3.54642 + 1.19286i) q^{70} -9.96771i q^{71} +(2.58400 - 5.62238i) q^{72} +(8.48612 + 4.89946i) q^{73} +(-11.9191 + 10.6466i) q^{74} +(0.450639 + 0.780530i) q^{75} +(-9.90849 - 7.31997i) q^{76} +(-9.90142 - 0.0627260i) q^{77} +(-0.964785 + 2.92964i) q^{78} +(0.397549 - 0.229525i) q^{79} +(-0.893735 + 3.89888i) q^{80} +(-1.17456 + 2.03439i) q^{81} +(10.1768 - 2.12091i) q^{82} +2.59747 q^{83} +(1.87735 + 4.38406i) q^{84} +0.583719 q^{85} +(-8.03123 + 1.67376i) q^{86} +(0.196236 - 0.339892i) q^{87} +(-0.980878 - 10.5397i) q^{88} +(-8.55647 + 4.94008i) q^{89} +(0.967745 - 2.93862i) q^{90} +(3.16604 + 5.56486i) q^{91} +(-5.12447 + 6.93662i) q^{92} +(1.14402 + 1.98149i) q^{93} +(12.2100 - 10.9064i) q^{94} +(-5.33433 - 3.07977i) q^{95} +(-4.46512 + 2.46097i) q^{96} -4.54044i q^{97} +(9.36276 + 3.21538i) q^{98} +8.18738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	$ 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.288532	+	1.38447i	0.204023	+	0.978966i
$2$	0.288532	+	1.38447i	0.204023	+	0.978966i
$3$	−0.450639	+	0.780530i	−0.260177	+	0.450639i	−0.966289	−	0.257461i	$-0.917114\pi$
$3$	−0.450639	+	0.780530i	−0.260177	+	0.450639i	0.706112	+	0.708100i	$0.250447\pi$
$4$	−1.83350	+	0.798926i	−0.916749	+	0.399463i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−1.21064	−	0.398687i	−0.494242	−	0.162763i
$7$	−2.29962	+	1.30833i	−0.869175	+	0.494504i
$7$	−2.29962	+	1.30833i	−0.869175	+	0.494504i
$8$	−1.63511	−	2.30790i	−0.578098	−	0.815967i
$9$	1.09385	+	1.89460i	0.364616	+	0.631534i
$10$	−0.942109	−	1.05472i	−0.297921	−	0.333531i
$11$	3.24107	+	1.87123i	0.977218	+	0.564197i	0.901429	−	0.432927i	$-0.142519\pi$
$11$	3.24107	+	1.87123i	0.977218	+	0.564197i	0.0757892	+	0.997124i	$0.475852\pi$
$12$	0.202661	−	1.79113i	0.0585032	−	0.517054i
$13$		−	2.41990i		−	0.671161i	−0.942012	−	0.335580i	$-0.891068\pi$
$13$		−	2.41990i		−	0.671161i	0.942012	−	0.335580i	$-0.108932\pi$
$14$	−2.47486	−	2.80626i	−0.661434	−	0.750003i
$15$		−	0.901278i		−	0.232709i
$16$	2.72344	−	2.92966i	0.680859	−	0.732415i
$17$	−0.505515	−	0.291859i	−0.122605	−	0.0707863i	0.437443	−	0.899246i	$-0.355884\pi$
$17$	−0.505515	−	0.291859i	−0.122605	−	0.0707863i	−0.560048	+	0.828460i	$0.689218\pi$
$18$	−2.30740	+	2.06105i	−0.543860	+	0.485794i
$19$	3.07977	+	5.33433i	0.706549	+	1.22378i	0.966130	+	0.258057i	$0.0830822\pi$
$19$	3.07977	+	5.33433i	0.706549	+	1.22378i	−0.259581	+	0.965721i	$0.583584\pi$
$20$	1.18839	−	1.60864i	0.265733	−	0.359703i
$21$	0.0151060	−	2.38451i	0.00329639	−	0.520343i
$22$	−1.65551	+	5.02706i	−0.352955	+	1.07177i
$23$	3.73439	−	2.15605i	0.778674	−	0.449568i	−0.0572861	−	0.998358i	$-0.518245\pi$
$23$	3.73439	−	2.15605i	0.778674	−	0.449568i	0.835960	+	0.548790i	$0.184911\pi$
$24$	2.53823	−	0.236220i	0.518114	−	0.0482182i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	3.35028	−	0.698219i	0.657043	−	0.136932i
$27$	−4.67556			−0.899812
$28$	3.17109	−	4.23606i	0.599280	−	0.800539i
$29$	−0.435463			−0.0808634			−0.0404317	−	0.999182i	$-0.512873\pi$
$29$	−0.435463			−0.0808634			−0.0404317	+	0.999182i	$0.512873\pi$
$30$	1.24779	−	0.260047i	0.227814	−	0.0474779i
$31$	1.26933	−	2.19854i	0.227978	−	0.394869i	−0.729231	−	0.684268i	$-0.760122\pi$
$31$	1.26933	−	2.19854i	0.227978	−	0.394869i	0.957209	+	0.289399i	$0.0934554\pi$
$32$	4.84181	+	2.92521i	0.855920	+	0.517109i
$33$	−2.92110	+	1.68650i	−0.508499	+	0.293582i
$34$	0.258212	−	0.784080i	0.0442831	−	0.134469i
$35$	1.33736	−	2.28286i	0.226056	−	0.385874i
$36$	−3.51922	−	2.59985i	−0.586536	−	0.433308i
$37$	5.65039	+	9.78676i	0.928918	+	1.60893i	0.785136	+	0.619324i	$0.212593\pi$
$37$	5.65039	+	9.78676i	0.928918	+	1.60893i	0.143782	+	0.989609i	$0.454073\pi$
$38$	−6.49659	+	5.80297i	−1.05389	+	0.941366i
$39$	1.88881	+	1.09050i	0.302451	+	0.174620i
$40$	2.57000	+	1.18115i	0.406352	+	0.186756i
$41$		−	7.35068i		−	1.14798i	−0.818861	−	0.573992i	$-0.805394\pi$
$41$		−	7.35068i		−	1.14798i	0.818861	−	0.573992i	$-0.194606\pi$
$42$	3.30563	−	0.667093i	0.510070	−	0.102935i
$43$			5.80096i			0.884637i	0.896858	+	0.442319i	$0.145844\pi$
$43$			5.80096i			0.884637i	−0.896858	+	0.442319i	$0.854156\pi$
$44$	−7.43747	−	0.841528i	−1.12124	−	0.126865i
$45$	−1.89460	−	1.09385i	−0.282431	−	0.163061i
$46$	4.06247	+	4.54805i	0.598979	+	0.670573i
$47$	−5.78826	−	10.0256i	−0.844305	−	1.46238i	−0.886223	−	0.463258i	$-0.846680\pi$
$47$	−5.78826	−	10.0256i	−0.844305	−	1.46238i	0.0419181	−	0.999121i	$-0.486653\pi$
$48$	1.05940	+	3.44594i	0.152911	+	0.497379i
$49$	3.57652	−	6.01735i	0.510932	−	0.859621i
$50$	1.34325	+	0.442358i	0.189964	+	0.0625588i
$51$	0.455610	−	0.263046i	0.0637981	−	0.0368339i
$52$	1.93332	+	4.43689i	0.268104	+	0.615286i
$53$	1.55746	−	2.69759i	0.213933	−	0.370543i	−0.739009	−	0.673696i	$-0.764706\pi$
$53$	1.55746	−	2.69759i	0.213933	−	0.370543i	0.952942	+	0.303153i	$0.0980393\pi$
$54$	−1.34905	−	6.47316i	−0.183582	−	0.880885i
$55$	−3.74246			−0.504633
$56$	6.77964	+	3.16804i	0.905968	+	0.423347i
$57$	−5.55147			−0.735310
$58$	−0.125645	−	0.602884i	−0.0164980	−	0.0791625i
$59$	1.73534	−	3.00569i	0.225922	−	0.391308i	−0.730674	−	0.682727i	$-0.760794\pi$
$59$	1.73534	−	3.00569i	0.225922	−	0.391308i	0.956596	+	0.291419i	$0.0941273\pi$
$60$	0.720054	+	1.65249i	0.0929586	+	0.213336i
$61$	−8.99597	+	5.19383i	−1.15182	+	0.665001i	−0.949329	−	0.314284i	$-0.898236\pi$
$61$	−8.99597	+	5.19383i	−1.15182	+	0.665001i	−0.202487	+	0.979285i	$0.564902\pi$
$62$	3.41004	+	1.12299i	0.433076	+	0.142620i
$63$	−4.99421	−	2.92575i	−0.629211	−	0.368610i
$64$	−2.65284	+	7.54735i	−0.331605	+	0.943418i
$65$	1.20995	+	2.09570i	0.150076	+	0.259939i
$66$	−3.17773	−	3.55756i	−0.391152	−	0.437906i
$67$	−8.52602	−	4.92250i	−1.04162	−	0.601379i	−0.121327	−	0.992613i	$-0.538715\pi$
$67$	−8.52602	−	4.92250i	−1.04162	−	0.601379i	−0.920291	+	0.391234i	$0.872048\pi$
$68$	1.16004	+	0.131255i	0.140675	+	0.0159170i
$69$			3.88640i			0.467868i
$70$	3.54642	+	1.19286i	0.423878	+	0.142574i
$71$		−	9.96771i		−	1.18295i	−0.806324	−	0.591475i	$-0.798546\pi$
$71$		−	9.96771i		−	1.18295i	0.806324	−	0.591475i	$-0.201454\pi$
$72$	2.58400	−	5.62238i	0.304527	−	0.662604i
$73$	8.48612	+	4.89946i	0.993225	+	0.573439i	0.906237	−	0.422771i	$-0.138942\pi$
$73$	8.48612	+	4.89946i	0.993225	+	0.573439i	0.0869881	+	0.996209i	$0.472276\pi$
$74$	−11.9191	+	10.6466i	−1.38557	+	1.23764i
$75$	0.450639	+	0.780530i	0.0520353	+	0.0901278i
$76$	−9.90849	−	7.31997i	−1.13658	−	0.839658i
$77$	−9.90142	−	0.0627260i	−1.12837	−	0.00714829i
$78$	−0.964785	+	2.92964i	−0.109240	+	0.331716i
$79$	0.397549	−	0.229525i	0.0447278	−	0.0258236i	−0.477469	−	0.878648i	$-0.658446\pi$
$79$	0.397549	−	0.229525i	0.0447278	−	0.0258236i	0.522197	+	0.852825i	$0.325113\pi$
$80$	−0.893735	+	3.89888i	−0.0999226	+	0.435908i
$81$	−1.17456	+	2.03439i	−0.130506	+	0.226044i
$82$	10.1768	−	2.12091i	1.12384	−	0.234215i
$83$	2.59747			0.285109			0.142554	−	0.989787i	$-0.454468\pi$
$83$	2.59747			0.285109			0.142554	+	0.989787i	$0.454468\pi$
$84$	1.87735	+	4.38406i	0.204836	+	0.478341i
$85$	0.583719			0.0633132
$86$	−8.03123	+	1.67376i	−0.866030	+	0.180486i
$87$	0.196236	−	0.339892i	0.0210388	−	0.0364402i
$88$	−0.980878	−	10.5397i	−0.104562	−	1.12354i
$89$	−8.55647	+	4.94008i	−0.906984	+	0.523648i	−0.879460	−	0.475973i	$-0.842096\pi$
$89$	−8.55647	+	4.94008i	−0.906984	+	0.523648i	−0.0275247	+	0.999621i	$0.508763\pi$
$90$	0.967745	−	2.93862i	0.102009	−	0.309758i
$91$	3.16604	+	5.56486i	0.331891	+	0.583356i
$92$	−5.12447	+	6.93662i	−0.534263	+	0.723192i
$93$	1.14402	+	1.98149i	0.118629	+	0.205471i
$94$	12.2100	−	10.9064i	1.25936	−	1.12490i
$95$	−5.33433	−	3.07977i	−0.547290	−	0.315978i
$96$	−4.46512	+	2.46097i	−0.455720	+	0.251171i
$97$		−	4.54044i		−	0.461011i	−0.973071	−	0.230506i	$-0.925962\pi$
$97$		−	4.54044i		−	0.461011i	0.973071	−	0.230506i	$-0.0740380\pi$
$98$	9.36276	+	3.21538i	0.945782	+	0.324803i
$99$			8.18738i			0.822862i
$100$	−0.224860	+	1.98732i	−0.0224860	+	0.198732i
$101$	7.91930	+	4.57221i	0.787999	+	0.454952i	0.839258	−	0.543734i	$-0.182990\pi$
$101$	7.91930	+	4.57221i	0.787999	+	0.454952i	−0.0512584	+	0.998685i	$0.516323\pi$
$102$	0.495637	+	0.554880i	0.0490754	+	0.0549413i
$103$	5.11597	+	8.86113i	0.504092	+	0.873113i	0.999989	+	0.00473128i	$0.00150602\pi$
$103$	5.11597	+	8.86113i	0.504092	+	0.873113i	−0.495897	+	0.868381i	$0.665161\pi$
$104$	−5.58490	+	3.95681i	−0.547645	+	0.387997i
$105$	1.17917	+	2.07260i	0.115075	+	0.202265i
$106$	4.18410	+	1.37790i	0.406396	+	0.133834i
$107$	5.48368	−	3.16601i	0.530128	−	0.306069i	−0.210941	−	0.977499i	$-0.567653\pi$
$107$	5.48368	−	3.16601i	0.530128	−	0.306069i	0.741068	+	0.671430i	$0.234319\pi$
$108$	8.57263	−	3.73542i	0.824902	−	0.359441i
$109$	9.38027	−	16.2471i	0.898467	−	1.55619i	0.0690134	−	0.997616i	$-0.478015\pi$
$109$	9.38027	−	16.2471i	0.898467	−	1.55619i	0.829454	−	0.558575i	$-0.188652\pi$
$110$	−1.07982	−	5.18132i	−0.102957	−	0.494019i
$111$	−10.1851			−0.966731
$112$	−2.42990	+	10.3003i	−0.229604	+	0.973284i
$113$	4.17847			0.393077			0.196539	−	0.980496i	$-0.437030\pi$
$113$	4.17847			0.393077			0.196539	+	0.980496i	$0.437030\pi$
$114$	−1.60177	−	7.68582i	−0.150020	−	0.719843i
$115$	−2.15605	+	3.73439i	−0.201053	+	0.348234i
$116$	0.798420	−	0.347902i	0.0741315	−	0.0323019i
$117$	4.58475	−	2.64701i	0.423861	−	0.244716i
$118$	4.66198	+	1.53528i	0.429170	+	0.141334i
$119$	1.54434	+	0.00978348i	0.141570	+	0.000896851i
$120$	−2.08006	+	1.47369i	−0.189883	+	0.134529i
$121$	1.50301	+	2.60329i	0.136637	+	0.236663i
$122$	−9.78631	−	10.9560i	−0.886010	−	0.991913i
$123$	5.73743	+	3.31250i	0.517326	+	0.298678i
$124$	−0.570840	+	5.04511i	−0.0512629	+	0.453064i
$125$			1.00000i			0.0894427i
$126$	2.60961	−	7.75849i	0.232483	−	0.691182i
$127$			4.91036i			0.435724i	0.975980	+	0.217862i	$0.0699083\pi$
$127$			4.91036i			0.435724i	−0.975980	+	0.217862i	$0.930092\pi$
$128$	−11.2145	−	1.49512i	−0.991230	−	0.132151i
$129$	−4.52782	−	2.61414i	−0.398652	−	0.230162i
$130$	−2.55232	+	2.27981i	−0.223853	+	0.199953i
$131$	7.93723	+	13.7477i	0.693479	+	1.20114i	0.970691	+	0.240332i	$0.0772564\pi$
$131$	7.93723	+	13.7477i	0.693479	+	1.20114i	−0.277212	+	0.960809i	$0.589410\pi$
$132$	4.00845	−	5.42594i	0.348891	−	0.472267i
$133$	−14.0614	−	8.23756i	−1.21928	−	0.714287i
$134$	4.35501	−	13.2243i	0.376216	−	1.14240i
$135$	4.04915	−	2.33778i	0.348496	−	0.201204i
$136$	0.152989	+	1.64390i	0.0131187	+	0.140963i
$137$	3.92110	−	6.79155i	0.335002	−	0.580241i	−0.648483	−	0.761229i	$-0.724596\pi$
$137$	3.92110	−	6.79155i	0.335002	−	0.580241i	0.983485	+	0.180988i	$0.0579295\pi$
$138$	−5.38060	+	1.12135i	−0.458027	+	0.0954557i
$139$	17.4044			1.47623			0.738113	−	0.674677i	$-0.235717\pi$
$139$	17.4044			1.47623			0.738113	+	0.674677i	$0.235717\pi$
$140$	−0.628219	+	5.25408i	−0.0530942	+	0.444051i
$141$	10.4337			0.878674
$142$	13.8000	−	2.87600i	1.15807	−	0.241349i
$143$	4.52820	−	7.84307i	0.378667	−	0.655871i
$144$	8.52956	+	1.95522i	0.710797	+	0.162935i
$145$	0.377122	−	0.217731i	0.0313183	−	0.0180816i
$146$	−4.33463	+	13.1624i	−0.358736	+	1.08933i
$147$	3.08500	+	5.50324i	0.254446	+	0.453899i
$148$	−18.1789	−	13.4298i	−1.49429	−	1.10392i
$149$	−0.825776	−	1.43029i	−0.0676502	−	0.117174i	0.830216	−	0.557441i	$-0.188217\pi$
$149$	−0.825776	−	1.43029i	−0.0676502	−	0.117174i	−0.897867	+	0.440268i	$0.854884\pi$
$150$	−0.950594	+	0.849103i	−0.0776157	+	0.0693289i
$151$	−6.37060	−	3.67807i	−0.518432	−	0.299317i	0.217861	−	0.975980i	$-0.430092\pi$
$151$	−6.37060	−	3.67807i	−0.518432	−	0.299317i	−0.736293	+	0.676663i	$0.763425\pi$
$152$	7.27534	−	15.8300i	0.590108	−	1.28398i
$153$		−	1.27700i		−	0.103239i
$154$	−2.77003	−	13.7263i	−0.223216	−	1.10610i
$155$			2.53865i			0.203909i
$156$	−4.33436	−	0.490420i	−0.347026	−	0.0392650i
$157$	−2.66953	−	1.54125i	−0.213052	−	0.123005i	0.389677	−	0.920952i	$-0.372587\pi$
$157$	−2.66953	−	1.54125i	−0.213052	−	0.123005i	−0.602729	+	0.797946i	$0.705920\pi$
$158$	0.432476	+	0.484169i	0.0344059	+	0.0385184i
$159$	1.40370	+	2.43128i	0.111321	+	0.192813i
$160$	−5.65574	−	0.112397i	−0.447125	−	0.00888579i
$161$	−5.76685	+	9.84393i	−0.454491	+	0.775810i
$162$	−3.15545	−	1.03915i	−0.247915	−	0.0816433i
$163$	−3.91284	+	2.25908i	−0.306477	+	0.176945i	−0.645349	−	0.763888i	$-0.723288\pi$
$163$	−3.91284	+	2.25908i	−0.306477	+	0.176945i	0.338872	+	0.940833i	$0.389955\pi$
$164$	5.87265	+	13.4775i	0.458577	+	1.05241i
$165$	1.68650	−	2.92110i	0.131294	−	0.227408i
$166$	0.749452	+	3.59611i	0.0581687	+	0.279112i
$167$	16.9358			1.31053			0.655266	−	0.755398i	$-0.272556\pi$
$167$	16.9358			1.31053			0.655266	+	0.755398i	$0.272556\pi$
$168$	−5.52792	+	3.86407i	−0.426488	+	0.298119i
$169$	7.14406			0.549543
$170$	0.168421	+	0.808139i	0.0129173	+	0.0619815i
$171$	−6.73762	+	11.6699i	−0.515238	+	0.892419i
$172$	−4.63453	−	10.6360i	−0.353380	−	0.810991i
$173$	0.114919	−	0.0663486i	0.00873715	−	0.00504439i	−0.495625	−	0.868537i	$-0.665061\pi$
$173$	0.114919	−	0.0663486i	0.00873715	−	0.00504439i	0.504362	+	0.863492i	$0.331728\pi$
$174$	0.527189	+	0.173613i	0.0399661	+	0.0131616i
$175$	−0.0167606	+	2.64570i	−0.00126698	+	0.199996i
$176$	14.3089	−	4.39904i	1.07857	−	0.331590i
$177$	1.56402	+	2.70897i	0.117559	+	0.203618i
$178$	−9.30820	−	10.4208i	−0.697679	−	0.781071i
$179$	−13.9422	−	8.04953i	−1.04209	−	0.601650i	−0.121664	−	0.992571i	$-0.538823\pi$
$179$	−13.9422	−	8.04953i	−1.04209	−	0.601650i	−0.920424	+	0.390921i	$0.872157\pi$
$180$	4.34765	+	0.491925i	0.324055	+	0.0366659i
$181$		−	3.99317i		−	0.296810i	−0.988927	−	0.148405i	$-0.952586\pi$
$181$		−	3.99317i		−	0.296810i	0.988927	−	0.148405i	$-0.0474139\pi$
$182$	−6.79087	+	5.98892i	−0.503373	+	0.443928i
$183$		−	9.36216i		−	0.692071i
$184$	−11.0821	−	5.09323i	−0.816983	−	0.375478i
$185$	−9.78676	−	5.65039i	−0.719537	−	0.415425i
$186$	−2.41323	+	2.15558i	−0.176946	+	0.158054i
$187$	−1.09227	−	1.89187i	−0.0798749	−	0.138347i
$188$	18.6225	+	13.7575i	1.35818	+	1.00337i
$189$	10.7520	−	6.11719i	0.782094	−	0.444960i
$190$	2.72472	−	8.27381i	0.197672	−	0.600245i
$191$	−17.3638	+	10.0250i	−1.25640	+	0.725385i	−0.972373	−	0.233431i	$-0.925005\pi$
$191$	−17.3638	+	10.0250i	−1.25640	+	0.725385i	−0.284030	+	0.958815i	$0.591671\pi$
$192$	−4.69546	−	5.47175i	−0.338865	−	0.394889i
$193$	−9.66959	+	16.7482i	−0.696032	+	1.20556i	0.273799	+	0.961787i	$0.411720\pi$
$193$	−9.66959	+	16.7482i	−0.696032	+	1.20556i	−0.969832	+	0.243776i	$0.921614\pi$
$194$	6.28608	−	1.31006i	0.451315	−	0.0940568i
$195$	−2.18101			−0.156185
$196$	−1.75014	+	13.8902i	−0.125010	+	0.992155i
$197$	−1.63738			−0.116659			−0.0583293	−	0.998297i	$-0.518577\pi$
$197$	−1.63738			−0.116659			−0.0583293	+	0.998297i	$0.518577\pi$
$198$	−11.3352	+	2.36232i	−0.805554	+	0.167883i
$199$	−0.391632	+	0.678326i	−0.0277621	+	0.0480853i	−0.879573	−	0.475765i	$-0.842171\pi$
$199$	−0.391632	+	0.678326i	−0.0277621	+	0.0480853i	0.851811	+	0.523850i	$0.175505\pi$
$200$	−2.81626	+	0.262094i	−0.199139	+	0.0185329i
$201$	7.68431	−	4.43654i	0.542009	−	0.312929i
$202$	−4.04510	+	12.2832i	−0.284612	+	0.864245i
$203$	1.00140	−	0.569731i	0.0702845	−	0.0399873i
$204$	−0.625205	+	0.846294i	−0.0437731	+	0.0592524i
$205$	3.67534	+	6.36588i	0.256697	+	0.444612i
$206$	−10.7918	+	9.63961i	−0.751901	+	0.671624i
$207$	8.16972	+	4.71679i	0.567835	+	0.327839i
$208$	−7.08949	−	6.59045i	−0.491568	−	0.456966i
$209$			23.0519i			1.59453i
$210$	−2.52922	+	2.23054i	−0.174533	+	0.153922i
$211$		−	9.22534i		−	0.635099i	−0.948242	−	0.317549i	$-0.897140\pi$
$211$		−	9.22534i		−	0.635099i	0.948242	−	0.317549i	$-0.102860\pi$
$212$	−0.700417	+	6.19032i	−0.0481048	+	0.425153i
$213$	7.78009	+	4.49184i	0.533083	+	0.307776i
$214$	5.96545	+	6.67849i	0.407790	+	0.456532i
$215$	−2.90048	−	5.02378i	−0.197811	−	0.342619i
$216$	7.64505	+	10.7907i	0.520180	+	0.734217i
$217$	−0.0425494	+	6.71651i	−0.00288844	+	0.455946i
$218$	25.2001	+	8.29887i	1.70677	+	0.562071i
$219$	−7.64835	+	4.41578i	−0.516828	+	0.298391i
$220$	6.86180	−	2.98995i	0.462622	−	0.201582i
$221$	−0.706272	+	1.22330i	−0.0475090	+	0.0822880i
$222$	−2.93874	−	14.1010i	−0.197235	−	0.946397i
$223$	−24.2380			−1.62310			−0.811550	−	0.584284i	$-0.801376\pi$
$223$	−24.2380			−1.62310			−0.811550	+	0.584284i	$0.801376\pi$
$224$	−14.9615	−	0.392163i	−0.999657	−	0.0262025i
$225$	2.18770			0.145847
$226$	1.20562	+	5.78495i	0.0801967	+	0.384809i
$227$	−5.31623	+	9.20798i	−0.352851	+	0.611155i	−0.986748	−	0.162262i	$-0.948121\pi$
$227$	−5.31623	+	9.20798i	−0.352851	+	0.611155i	0.633897	+	0.773417i	$0.281454\pi$
$228$	10.1786	−	4.43521i	0.674095	−	0.293729i
$229$	−25.5589	+	14.7564i	−1.68898	+	0.975132i	−0.733676	+	0.679499i	$0.762197\pi$
$229$	−25.5589	+	14.7564i	−1.68898	+	0.975132i	−0.955302	+	0.295633i	$0.904470\pi$
$230$	−5.79223	−	1.90749i	−0.381928	−	0.125776i
$231$	4.51093	−	7.70009i	0.296797	−	0.506629i
$232$	0.712029	+	1.00501i	0.0467470	+	0.0659819i
$233$	−14.0351	−	24.3096i	−0.919472	−	1.59257i	−0.800218	−	0.599709i	$-0.795283\pi$
$233$	−14.0351	−	24.3096i	−0.919472	−	1.59257i	−0.119254	−	0.992864i	$-0.538050\pi$
$234$	4.98755	+	5.58370i	0.326046	+	0.365018i
$235$	10.0256	+	5.78826i	0.653996	+	0.377585i
$236$	−0.780415	+	6.89734i	−0.0508007	+	0.448979i
$237$			0.413732i			0.0268748i
$238$	0.432047	+	2.14092i	0.0280055	+	0.138775i
$239$		−	13.6279i		−	0.881512i	−0.897627	−	0.440756i	$-0.854710\pi$
$239$		−	13.6279i		−	0.881512i	0.897627	−	0.440756i	$-0.145290\pi$
$240$	−2.64044	−	2.45457i	−0.170439	−	0.158442i
$241$	−3.64372	−	2.10370i	−0.234713	−	0.135512i	0.378031	−	0.925793i	$-0.376601\pi$
$241$	−3.64372	−	2.10370i	−0.234713	−	0.135512i	−0.612744	+	0.790281i	$0.709934\pi$
$242$	−3.17050	+	2.83200i	−0.203808	+	0.182048i
$243$	−8.07194	−	13.9810i	−0.517815	−	0.896882i
$244$	12.3446	−	16.7100i	0.790283	−	1.06975i
$245$	−0.0886870	+	6.99944i	−0.00566601	+	0.447178i
$246$	−2.93062	+	8.89904i	−0.186850	+	0.567382i
$247$	12.9086	−	7.45276i	0.821352	−	0.474208i
$248$	−7.14950	+	0.665366i	−0.453993	+	0.0422508i
$249$	−1.17052	+	2.02740i	−0.0741787	+	0.128481i
$250$	−1.38447	+	0.288532i	−0.0875614	+	0.0182484i
$251$	18.8826			1.19186			0.595928	−	0.803038i	$-0.296784\pi$
$251$	18.8826			1.19186			0.595928	+	0.803038i	$0.296784\pi$
$252$	11.4943	+	1.37435i	0.724075	+	0.0865761i
$253$	16.1379			1.01458
$254$	−6.79824	+	1.41680i	−0.426559	+	0.0888977i
$255$	−0.263046	+	0.455610i	−0.0164726	+	0.0285314i
$256$	−1.16580	−	15.9575i	−0.0728623	−	0.997342i
$257$	22.3734	−	12.9173i	1.39561	−	0.805757i	0.401682	−	0.915779i	$-0.368426\pi$
$257$	22.3734	−	12.9173i	1.39561	−	0.805757i	0.993929	+	0.110022i	$0.0350923\pi$
$258$	2.31277	−	7.02288i	0.143987	−	0.437225i
$259$	−25.7981	−	15.1133i	−1.60302	−	0.939092i
$260$	−3.89275	−	2.87580i	−0.241418	−	0.178349i
$261$	−0.476330	−	0.825028i	−0.0294841	−	0.0510680i
$262$	−16.7431	+	14.9555i	−1.03439	+	0.923953i
$263$	9.26400	+	5.34857i	0.571243	+	0.329807i	0.757645	−	0.652666i	$-0.226350\pi$
$263$	9.26400	+	5.34857i	0.571243	+	0.329807i	−0.186403	+	0.982473i	$0.559683\pi$
$264$	8.66860	+	3.98401i	0.533515	+	0.245199i
$265$			3.11491i			0.191347i
$266$	7.34747	−	21.8443i	0.450502	−	1.33936i
$267$		−	8.90478i		−	0.544963i
$268$	19.5651	+	2.21374i	1.19513	+	0.135226i
$269$	−7.24441	−	4.18256i	−0.441699	−	0.255015i	0.262619	−	0.964900i	$-0.415414\pi$
$269$	−7.24441	−	4.18256i	−0.441699	−	0.255015i	−0.704318	+	0.709884i	$0.748747\pi$
$270$	4.40489	+	4.93139i	0.268073	+	0.300115i
$271$	−13.5557	−	23.4791i	−0.823448	−	1.42625i	−0.903100	−	0.429430i	$-0.858714\pi$
$271$	−13.5557	−	23.4791i	−0.823448	−	1.42625i	0.0796525	−	0.996823i	$-0.474619\pi$
$272$	−2.23179	+	0.686127i	−0.135322	+	0.0416025i
$273$	−5.77028	−	0.0365550i	−0.349234	−	0.00221241i
$274$	10.5340	+	3.46906i	0.636385	+	0.209574i
$275$	3.24107	−	1.87123i	0.195444	−	0.112839i
$276$	−3.10495	−	7.12571i	−0.186896	−	0.428918i
$277$	−1.67991	+	2.90970i	−0.100936	+	0.174827i	−0.912071	−	0.410033i	$-0.865517\pi$
$277$	−1.67991	+	2.90970i	−0.100936	+	0.174827i	0.811134	+	0.584860i	$0.198850\pi$
$278$	5.02173	+	24.0959i	0.301184	+	1.44517i
$279$	5.55380			0.332497
$280$	−7.45536	+	0.646220i	−0.445543	+	0.0386190i
$281$	−7.33947			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$281$	−7.33947			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$282$	3.01045	+	14.4451i	0.179269	+	0.860192i
$283$	3.60282	−	6.24027i	0.214165	−	0.370945i	−0.738849	−	0.673871i	$-0.764630\pi$
$283$	3.60282	−	6.24027i	0.214165	−	0.370945i	0.953014	+	0.302926i	$0.0979635\pi$
$284$	7.96346	+	18.2758i	0.472544	+	1.08447i
$285$	4.80771	−	2.77573i	0.284784	−	0.164420i
$286$	12.1650	+	4.00617i	0.719332	+	0.236890i
$287$	9.61715	+	16.9038i	0.567682	+	0.997799i
$288$	−0.245892	+	12.3730i	−0.0144893	+	0.729089i
$289$	−8.32964	−	14.4274i	−0.489979	−	0.848668i
$290$	0.410254	+	0.459290i	0.0240909	+	0.0269705i
$291$	3.54395	+	2.04610i	0.207750	+	0.119944i
$292$	−19.4736	−	2.20338i	−1.13961	−	0.128943i
$293$		−	8.47879i		−	0.495336i	−0.968845	−	0.247668i	$-0.920336\pi$
$293$		−	8.47879i		−	0.495336i	0.968845	−	0.247668i	$-0.0796642\pi$
$294$	−6.72893	+	5.85894i	−0.392439	+	0.341700i
$295$			3.47068i			0.202071i
$296$	13.3479	−	29.0430i	0.775831	−	1.68809i
$297$	−15.1538	−	8.74905i	−0.879312	−	0.507671i
$298$	1.74192	−	1.55594i	0.100907	−	0.0901333i
$299$	−5.21744	−	9.03686i	−0.301732	−	0.522615i
$300$	−1.44983	−	1.07107i	−0.0837060	−	0.0618384i
$301$	−7.58959	−	13.3400i	−0.437457	−	0.768905i
$302$	3.25404	−	9.88112i	0.187249	−	0.568595i
$303$	−7.13749	+	4.12083i	−0.410038	+	0.236736i
$304$	24.0153	+	5.50501i	1.37737	+	0.315734i
$305$	5.19383	−	8.99597i	0.297398	−	0.515108i
$306$	1.76796	−	0.368455i	0.101068	−	0.0210632i
$307$	−10.4271			−0.595104			−0.297552	−	0.954706i	$-0.596170\pi$
$307$	−10.4271			−0.595104			−0.297552	+	0.954706i	$0.596170\pi$
$308$	18.2044	−	7.79549i	1.03729	−	0.444189i
$309$	−9.22183			−0.524612
$310$	−3.51468	+	0.732482i	−0.199620	+	0.0416022i
$311$	3.96296	−	6.86404i	0.224719	−	0.389224i	−0.731516	−	0.681824i	$-0.761187\pi$
$311$	3.96296	−	6.86404i	0.224719	−	0.389224i	0.956235	+	0.292600i	$0.0945203\pi$
$312$	−0.571629	−	6.14228i	−0.0323621	−	0.347738i
$313$	12.5285	−	7.23333i	0.708152	−	0.408852i	−0.102224	−	0.994761i	$-0.532596\pi$
$313$	12.5285	−	7.23333i	0.708152	−	0.408852i	0.810376	+	0.585910i	$0.199263\pi$
$314$	1.36357	−	4.14058i	0.0769507	−	0.233666i
$315$	5.78799	+	0.0366672i	0.326116	+	0.00206596i
$316$	−0.545533	+	0.738447i	−0.0306886	+	0.0415409i
$317$	−1.76853	−	3.06318i	−0.0993305	−	0.172046i	0.812077	−	0.583550i	$-0.198337\pi$
$317$	−1.76853	−	3.06318i	−0.0993305	−	0.172046i	−0.911408	+	0.411504i	$0.865003\pi$
$318$	−2.96101	+	2.64488i	−0.166045	+	0.148317i
$319$	−1.41136	−	0.814851i	−0.0790212	−	0.0456229i
$320$	−1.47625	−	7.86261i	−0.0825249	−	0.439533i
$321$			5.70690i			0.318528i
$322$	−15.2925	−	5.14373i	−0.852219	−	0.286649i
$323$		−	3.59544i		−	0.200056i
$324$	0.528221	−	4.66844i	0.0293456	−	0.259358i
$325$	−2.09570	−	1.20995i	−0.116248	−	0.0671161i
$326$	−4.25660	−	4.76538i	−0.235751	−	0.263930i
$327$	8.45423	+	14.6432i	0.467520	+	0.809769i
$328$	−16.9647	+	12.0192i	−0.936717	+	0.663648i
$329$	26.4276	+	15.4820i	1.45700	+	0.853552i
$330$	4.53078	+	1.49207i	0.249411	+	0.0821359i
$331$	20.3773	−	11.7649i	1.12004	−	0.646655i	0.178629	−	0.983917i	$-0.442834\pi$
$331$	20.3773	−	11.7649i	1.12004	−	0.646655i	0.941411	+	0.337261i	$0.109501\pi$
$332$	−4.76245	+	2.07518i	−0.261373	+	0.113890i
$333$	−12.3613	+	21.4105i	−0.677397	+	1.17329i
$334$	4.88652	+	23.4471i	0.267378	+	1.28297i
$335$	9.84499			0.537890
$336$	−6.94466	−	6.53831i	−0.378862	−	0.356694i
$337$	5.10057			0.277846			0.138923	−	0.990303i	$-0.455636\pi$
$337$	5.10057			0.277846			0.138923	+	0.990303i	$0.455636\pi$
$338$	2.06129	+	9.89072i	0.112119	+	0.537984i
$339$	−1.88298	+	3.26142i	−0.102269	+	0.177136i
$340$	−1.07025	+	0.466348i	−0.0580423	+	0.0252913i
$341$	8.22794	−	4.75040i	0.445568	−	0.257249i
$342$	−18.1006	−	5.96087i	−0.978768	−	0.322327i
$343$	−0.351954	+	18.5169i	−0.0190037	+	0.999819i
$344$	13.3880	−	9.48520i	0.721835	−	0.511407i
$345$	−1.94320	−	3.36572i	−0.104618	−	0.181204i
$346$	0.125015	+	0.139958i	0.00672087	+	0.00752420i
$347$	1.44316	+	0.833209i	0.0774729	+	0.0447290i	0.538236	−	0.842794i	$-0.319091\pi$
$347$	1.44316	+	0.833209i	0.0774729	+	0.0447290i	−0.460763	+	0.887523i	$0.652424\pi$
$348$	−0.0882513	+	0.779969i	−0.00473077	+	0.0418107i
$349$			27.6081i			1.47783i	0.673801	+	0.738913i	$0.264661\pi$
$349$			27.6081i			1.47783i	−0.673801	+	0.738913i	$0.735339\pi$
$350$	−3.66772	+	0.740164i	−0.196048	+	0.0395634i
$351$			11.3144i			0.603918i
$352$	10.2189	+	18.5409i	0.544669	+	0.988236i
$353$	23.5193	+	13.5789i	1.25180	+	0.722730i	0.971468	−	0.237172i	$-0.0762205\pi$
$353$	23.5193	+	13.5789i	1.25180	+	0.722730i	0.280337	+	0.959902i	$0.409554\pi$
$354$	−3.29920	+	2.94696i	−0.175351	+	0.156629i
$355$	4.98385	+	8.63229i	0.264516	+	0.458154i
$356$	11.7415	−	15.8936i	0.622300	−	0.842360i
$357$	−0.703578	+	1.20100i	−0.0372373	+	0.0635635i
$358$	7.12154	−	21.6251i	0.376385	−	1.14292i
$359$	−14.5102	+	8.37747i	−0.765819	+	0.442146i	−0.831381	−	0.555703i	$-0.812449\pi$
$359$	−14.5102	+	8.37747i	−0.765819	+	0.442146i	0.0655619	+	0.997849i	$0.479116\pi$
$360$	0.573383	+	6.16112i	0.0302199	+	0.324720i
$361$	−9.47002	+	16.4026i	−0.498422	+	0.863293i
$362$	5.52841	−	1.15216i	0.290567	−	0.0605560i
$363$	−2.70926			−0.142199
$364$	−10.2508	−	7.67374i	−0.537290	−	0.402213i
$365$	−9.79892			−0.512899
$366$	12.9616	−	2.70128i	0.677514	−	0.141198i
$367$	−4.22213	+	7.31294i	−0.220393	+	0.381732i	−0.954927	−	0.296839i	$-0.904067\pi$
$367$	−4.22213	+	7.31294i	−0.220393	+	0.381732i	0.734534	+	0.678572i	$0.237401\pi$
$368$	3.85388	−	16.8124i	0.200897	−	0.876404i
$369$	13.9266	−	8.04054i	0.724991	−	0.418574i
$370$	4.99899	−	15.1798i	0.259885	−	0.789158i
$371$	−0.0522078	+	8.24111i	−0.00271049	+	0.427857i
$372$	−3.68062	−	2.71908i	−0.190831	−	0.140978i
$373$	5.18861	+	8.98694i	0.268656	+	0.465326i	0.968515	−	0.248955i	$-0.0800871\pi$
$373$	5.18861	+	8.98694i	0.268656	+	0.465326i	−0.699859	+	0.714281i	$0.746754\pi$
$374$	2.30408	−	2.05808i	0.119141	−	0.106421i
$375$	−0.780530	−	0.450639i	−0.0403064	−	0.0232709i
$376$	−13.6736	+	29.7517i	−0.705162	+	1.53432i
$377$			1.05378i			0.0542723i
$378$	11.5714	+	13.1208i	0.595166	+	0.674862i
$379$		−	11.7976i		−	0.606002i	−0.952990	−	0.303001i	$-0.902011\pi$
$379$		−	11.7976i		−	0.606002i	0.952990	−	0.303001i	$-0.0979886\pi$
$380$	12.2410	+	1.38503i	0.627950	+	0.0710507i
$381$	−3.83268	−	2.21280i	−0.196354	−	0.113365i
$382$	−18.8893	−	21.1471i	−0.966462	−	1.08198i
$383$	0.478522	+	0.828825i	0.0244514	+	0.0423510i	0.877992	−	0.478675i	$-0.158883\pi$
$383$	0.478522	+	0.828825i	0.0244514	+	0.0423510i	−0.853541	+	0.521026i	$0.825549\pi$
$384$	6.22067	−	8.07948i	0.317447	−	0.412304i
$385$	8.60625	−	4.89639i	0.438615	−	0.249543i
$386$	−25.9773	−	8.55483i	−1.32221	−	0.435430i
$387$	−10.9905	+	6.34537i	−0.558679	+	0.322553i
$388$	3.62747	+	8.32488i	0.184157	+	0.422632i
$389$	15.0820	−	26.1228i	0.764689	−	1.32448i	−0.175722	−	0.984440i	$-0.556226\pi$
$389$	15.0820	−	26.1228i	0.764689	−	1.32448i	0.940411	−	0.340041i	$-0.110441\pi$
$390$	−0.629290	−	3.01953i	−0.0318653	−	0.152900i
$391$	−2.51705			−0.127293
$392$	−19.7355	+	1.58475i	−0.996792	+	0.0800418i
$393$	−14.3073			−0.721708
$394$	−0.472436	−	2.26690i	−0.0238010	−	0.114205i
$395$	−0.229525	+	0.397549i	−0.0115487	+	0.0200029i
$396$	−6.54110	−	15.0115i	−0.328703	−	0.754358i
$397$	−5.37540	+	3.10349i	−0.269783	+	0.155760i	−0.628789	−	0.777576i	$-0.716449\pi$
$397$	−5.37540	+	3.10349i	−0.269783	+	0.155760i	0.359006	+	0.933335i	$0.383116\pi$
$398$	−1.05212	−	0.346483i	−0.0527380	−	0.0173676i
$399$	12.7663	−	7.26317i	0.639113	−	0.363613i
$400$	−1.17544	−	3.82339i	−0.0587720	−	0.191170i
$401$	−13.1565	−	22.7877i	−0.657004	−	1.13796i	−0.981387	−	0.192038i	$-0.938490\pi$
$401$	−13.1565	−	22.7877i	−0.657004	−	1.13796i	0.324384	−	0.945926i	$-0.394843\pi$
$402$	8.35941	+	9.35859i	0.416930	+	0.466764i
$403$	−5.32025	−	3.07165i	−0.265020	−	0.153010i
$404$	−18.1729	−	2.05621i	−0.904134	−	0.102300i
$405$		−	2.34912i		−	0.116728i
$406$	1.07771	+	1.22202i	0.0534858	+	0.0606478i
$407$			42.2927i			2.09637i
$408$	−1.35206	−	0.621394i	−0.0669368	−	0.0307636i
$409$	−15.9374	−	9.20148i	−0.788055	−	0.454984i	0.0512223	−	0.998687i	$-0.483688\pi$
$409$	−15.9374	−	9.20148i	−0.788055	−	0.454984i	−0.839277	+	0.543703i	$0.817022\pi$
$410$	−7.75290	+	6.92515i	−0.382888	+	0.342009i
$411$	3.53400	+	6.12107i	0.174320	+	0.301930i
$412$	−16.4595	−	12.1596i	−0.810902	−	0.599060i
$413$	−0.0581707	+	9.18236i	−0.00286239	+	0.451834i
$414$	−4.17302	+	12.6716i	−0.205093	+	0.622777i
$415$	−2.24947	+	1.29873i	−0.110422	+	0.0637523i
$416$	7.07872	−	11.7167i	0.347063	−	0.574460i
$417$	−7.84312	+	13.5847i	−0.384079	+	0.665245i
$418$	−31.9146	+	6.65120i	−1.56099	+	0.325321i
$419$	−35.2426			−1.72171			−0.860856	−	0.508848i	$-0.830072\pi$
$419$	−35.2426			−1.72171			−0.860856	+	0.508848i	$0.830072\pi$
$420$	−3.81786	−	2.85804i	−0.186293	−	0.139458i
$421$	−15.6669			−0.763558			−0.381779	−	0.924254i	$-0.624688\pi$
$421$	−15.6669			−0.763558			−0.381779	+	0.924254i	$0.624688\pi$
$422$	12.7722	−	2.66181i	0.621740	−	0.129575i
$423$	12.6630	−	21.9329i	0.615695	−	1.06641i
$424$	−8.77239	+	0.816400i	−0.426025	+	0.0396479i
$425$	−0.505515	+	0.291859i	−0.0245211	+	0.0141573i
$426$	−3.97400	+	12.0673i	−0.192541	+	0.584664i
$427$	13.8921	−	23.7136i	0.672285	−	1.14758i
$428$	−7.52492	+	10.1859i	−0.363731	+	0.492355i
$429$	4.08117	+	7.06879i	0.197041	+	0.341284i
$430$	6.11837	−	5.46514i	0.295054	−	0.263552i
$431$	1.73673	+	1.00270i	0.0836555	+	0.0482985i	0.541244	−	0.840865i	$-0.317953\pi$
$431$	1.73673	+	1.00270i	0.0836555	+	0.0482985i	−0.457589	+	0.889164i	$0.651287\pi$
$432$	−12.7336	+	13.6978i	−0.612645	+	0.659035i
$433$		−	13.5978i		−	0.653469i	−0.945116	−	0.326734i	$-0.894052\pi$
$433$		−	13.5978i		−	0.653469i	0.945116	−	0.326734i	$-0.105948\pi$
$434$	−9.31106	+	1.87902i	−0.446945	+	0.0901957i
$435$			0.392473i			0.0188176i
$436$	−4.21849	+	37.2832i	−0.202029	+	1.78554i
$437$	23.0022	+	13.2803i	1.10034	+	0.635283i
$438$	−8.32029	−	9.31480i	−0.397559	−	0.445078i
$439$	14.5247	+	25.1574i	0.693224	+	1.20070i	0.970776	+	0.239989i	$0.0771437\pi$
$439$	14.5247	+	25.1574i	0.693224	+	1.20070i	−0.277552	+	0.960711i	$0.589523\pi$
$440$	6.11933	+	8.63724i	0.291728	+	0.411764i
$441$	15.3127	+	0.194020i	0.729174	+	0.00923907i
$442$	−1.89740	−	0.624849i	−0.0902500	−	0.0297211i
$443$	−12.6757	+	7.31831i	−0.602240	+	0.347703i	−0.769922	−	0.638138i	$-0.779705\pi$
$443$	−12.6757	+	7.31831i	−0.602240	+	0.347703i	0.167683	+	0.985841i	$0.446372\pi$
$444$	18.6744	−	8.13717i	0.886250	−	0.386173i
$445$	4.94008	−	8.55647i	0.234182	−	0.405616i
$446$	−6.99345	−	33.5568i	−0.331149	−	1.58896i
$447$	1.48851			0.0704040
$448$	−3.77393	−	20.8268i	−0.178301	−	0.983976i
$449$	−27.0699			−1.27751			−0.638754	−	0.769411i	$-0.720550\pi$
$449$	−27.0699			−1.27751			−0.638754	+	0.769411i	$0.720550\pi$
$450$	0.631220	+	3.02880i	0.0297560	+	0.142779i
$451$	13.7548	−	23.8241i	0.647689	−	1.12183i
$452$	−7.66122	+	3.33829i	−0.360353	+	0.157020i
$453$	5.74168	−	3.31496i	0.269768	−	0.155750i
$454$	−14.2820	−	4.70335i	−0.670290	−	0.220739i
$455$	−5.52431	−	3.23629i	−0.258983	−	0.151720i
$456$	9.07725	+	12.8122i	0.425081	+	0.599989i
$457$	3.80306	+	6.58709i	0.177900	+	0.308131i	0.941161	−	0.337959i	$-0.109736\pi$
$457$	3.80306	+	6.58709i	0.177900	+	0.308131i	−0.763261	+	0.646090i	$0.776403\pi$
$458$	−27.8043	−	31.1277i	−1.29921	−	1.45450i
$459$	2.36357	+	1.36461i	0.110322	+	0.0636943i
$460$	0.969617	−	8.56952i	0.0452086	−	0.399556i
$461$		−	12.7953i		−	0.595936i	−0.954576	−	0.297968i	$-0.903691\pi$
$461$		−	12.7953i		−	0.595936i	0.954576	−	0.297968i	$-0.0963089\pi$
$462$	11.9621	+	4.02351i	0.556526	+	0.187191i
$463$			27.9178i			1.29745i	0.761024	+	0.648724i	$0.224697\pi$
$463$			27.9178i			1.29745i	−0.761024	+	0.648724i	$0.775303\pi$
$464$	−1.18595	+	1.27576i	−0.0550566	+	0.0592255i
$465$	−1.98149	−	1.14402i	−0.0918895	−	0.0530524i
$466$	29.6062	−	26.4453i	1.37148	−	1.22505i
$467$	−11.3054	−	19.5815i	−0.523152	−	0.906126i	−0.999637	−	0.0269432i	$-0.991423\pi$
$467$	−11.3054	−	19.5815i	−0.523152	−	0.906126i	0.476485	−	0.879183i	$-0.341911\pi$
$468$	−6.29138	+	8.51617i	−0.290819	+	0.393660i
$469$	26.0469	+	0.165008i	1.20273	+	0.00761937i
$470$	−5.12097	+	15.5502i	−0.236213	+	0.717276i
$471$	2.40599	−	1.38910i	0.110862	−	0.0640062i
$472$	−9.77432	+	0.909644i	−0.449899	+	0.0418698i
$473$	−10.8549	+	18.8013i	−0.499110	+	0.864484i
$474$	−0.572798	+	0.119375i	−0.0263095	+	0.00548307i
$475$	6.15955			0.282620
$476$	−2.83937	+	1.21588i	−0.130142	+	0.0557297i
$477$	6.81448			0.312014
$478$	18.8673	−	3.93207i	0.862971	−	0.179849i
$479$	−10.9907	+	19.0365i	−0.502180	+	0.869801i	0.497817	+	0.867282i	$0.334135\pi$
$479$	−10.9907	+	19.0365i	−0.502180	+	0.869801i	−0.999997	+	0.00251901i	$0.999198\pi$
$480$	2.63643	−	4.36382i	0.120336	−	0.199180i
$481$	23.6830	−	13.6734i	1.07985	−	0.623453i
$482$	1.86118	−	5.65160i	0.0847744	−	0.257423i
$483$	−5.08471	−	8.93726i	−0.231362	−	0.406659i
$484$	−4.83560	−	3.57234i	−0.219800	−	0.162379i
$485$	2.27022	+	3.93213i	0.103085	+	0.178549i
$486$	17.0272	−	15.2093i	0.772371	−	0.689908i
$487$	21.9822	+	12.6914i	0.996108	+	0.575103i	0.907095	−	0.420927i	$-0.138295\pi$
$487$	21.9822	+	12.6914i	0.996108	+	0.575103i	0.0890138	+	0.996030i	$0.471628\pi$
$488$	26.6962	+	12.2694i	1.20848	+	0.555408i
$489$		−	4.07212i		−	0.184147i
$490$	−9.71608	+	1.89678i	−0.438928	+	0.0856876i
$491$			36.4635i			1.64557i	0.568350	+	0.822787i	$0.307582\pi$
$491$			36.4635i			1.64557i	−0.568350	+	0.822787i	$0.692418\pi$
$492$	−13.1660	−	1.48970i	−0.593570	−	0.0671607i
$493$	0.220133	+	0.127094i	0.00991429	+	0.00572402i
$494$	14.0426	+	15.7211i	0.631808	+	0.707326i
$495$	−4.09369	−	7.09048i	−0.183998	−	0.318693i
$496$	−2.98403	−	9.70626i	−0.133987	−	0.435824i
$497$	13.0411	+	22.9220i	0.584973	+	1.02819i
$498$	−3.14460	−	1.03558i	−0.140913	−	0.0464053i
$499$	10.2874	−	5.93945i	0.460528	−	0.265886i	−0.251738	−	0.967795i	$-0.581002\pi$
$499$	10.2874	−	5.93945i	0.460528	−	0.265886i	0.712266	+	0.701909i	$0.247669\pi$
$500$	−0.798926	−	1.83350i	−0.0357290	−	0.0819966i
$501$	−7.63194	+	13.2189i	−0.340970	+	0.590577i
$502$	5.44822	+	26.1423i	0.243166	+	1.16679i
$503$	17.3055			0.771614			0.385807	−	0.922580i	$-0.373923\pi$
$503$	17.3055			0.771614			0.385807	+	0.922580i	$0.373923\pi$
$504$	1.41373	+	16.3101i	0.0629727	+	0.726509i
$505$	−9.14442			−0.406921
$506$	4.65629	+	22.3424i	0.206997	+	0.993239i
$507$	−3.21939	+	5.57615i	−0.142978	+	0.247646i
$508$	−3.92301	−	9.00314i	−0.174056	−	0.399450i
$509$	−11.8717	+	6.85414i	−0.526205	+	0.303805i	−0.739470	−	0.673190i	$-0.764924\pi$
$509$	−11.8717	+	6.85414i	−0.526205	+	0.303805i	0.213265	+	0.976994i	$0.431590\pi$
$510$	−0.706674	−	0.232721i	−0.0312921	−	0.0103051i
$511$	−25.9250	−	0.164236i	−1.14685	−	0.00726537i
$512$	21.7562	−	6.21824i	0.961498	−	0.274810i
$513$	−14.3997	−	24.9410i	−0.635761	−	1.10117i
$514$	24.3389	+	27.2481i	1.07355	+	1.20186i
$515$	−8.86113	−	5.11597i	−0.390468	−	0.225437i
$516$	10.3903	+	1.17563i	0.457405	+	0.0517541i
$517$		−	43.3247i		−	1.90542i
$518$	13.4802	−	40.0773i	0.592287	−	1.76089i
$519$			0.119597i			0.00524973i
$520$	2.85827	−	6.21915i	0.125343	−	0.272728i
$521$	31.4817	+	18.1760i	1.37924	+	0.796304i	0.992068	−	0.125704i	$-0.0401190\pi$
$521$	31.4817	+	18.1760i	1.37924	+	0.796304i	0.387171	+	0.922008i	$0.373452\pi$
$522$	1.00479	−	0.897511i	0.0439784	−	0.0392830i
$523$	−2.13211	−	3.69292i	−0.0932306	−	0.161480i	0.815638	−	0.578562i	$-0.196386\pi$
$523$	−2.13211	−	3.69292i	−0.0932306	−	0.161480i	−0.908869	+	0.417082i	$0.863053\pi$
$524$	−25.5363	−	18.8651i	−1.11556	−	0.824126i
$525$	−2.05749	−	1.20534i	−0.0897964	−	0.0526052i
$526$	−4.73196	+	14.3689i	−0.206323	+	0.626515i
$527$	−1.28333	+	0.740929i	−0.0559026	+	0.0322754i
$528$	−3.01457	+	13.1509i	−0.131192	+	0.572320i
$529$	−2.20289	+	3.81552i	−0.0957778	+	0.165892i
$530$	−4.31249	+	0.898751i	−0.187323	+	0.0390392i
$531$	7.59279			0.329499
$532$	32.3628	+	3.86955i	1.40310	+	0.167766i
$533$	−17.7879			−0.770482
$534$	12.3284	−	2.56931i	0.533501	−	0.111185i
$535$	−3.16601	+	5.48368i	−0.136878	+	0.237080i
$536$	2.58032	+	27.7260i	0.111453	+	1.19758i
$537$	12.5658	−	7.25487i	0.542254	−	0.313071i
$538$	3.70038	−	11.2364i	0.159535	−	0.484438i
$539$	22.8516	−	12.8101i	0.984288	−	0.551771i
$540$	−5.55640	+	7.52129i	−0.239110	+	0.323665i
$541$	3.34133	+	5.78736i	0.143655	+	0.248818i	0.928870	−	0.370405i	$-0.120781\pi$
$541$	3.34133	+	5.78736i	0.143655	+	0.248818i	−0.785215	+	0.619223i	$0.787448\pi$
$542$	28.5948	−	25.5418i	1.22825	−	1.09712i
$543$	3.11679	+	1.79948i	0.133754	+	0.0772229i
$544$	−1.59386	−	2.89187i	−0.0683362	−	0.123988i
$545$			18.7605i			0.803614i
$546$	−1.61430	−	7.99932i	−0.0690857	−	0.342339i
$547$		−	45.6888i		−	1.95351i	−0.214353	−	0.976756i	$-0.568764\pi$
$547$		−	45.6888i		−	1.95351i	0.214353	−	0.976756i	$-0.431236\pi$
$548$	−1.76339	+	15.5850i	−0.0753285	+	0.665757i
$549$	−19.6805	−	11.3625i	−0.839942	−	0.484941i
$550$	3.52581	+	3.94724i	0.150341	+	0.168311i
$551$	−1.34113	−	2.32290i	−0.0571339	−	0.0989589i
$552$	8.96944	−	6.35469i	0.381765	−	0.270474i
$553$	−0.613918	+	1.04795i	−0.0261064	+	0.0445633i
$554$	−4.51309	−	1.48625i	−0.191743	−	0.0631445i
$555$	8.82059	−	5.09257i	0.374413	−	0.216168i
$556$	−31.9110	+	13.9049i	−1.35333	+	0.589697i
$557$	−2.44203	+	4.22972i	−0.103472	+	0.179219i	−0.913113	−	0.407707i	$-0.866329\pi$
$557$	−2.44203	+	4.22972i	−0.103472	+	0.179219i	0.809641	+	0.586926i	$0.199662\pi$
$558$	1.60245	+	7.68906i	0.0678371	+	0.325504i
$559$	14.0378			0.593734
$560$	−3.04578	−	10.1352i	−0.128708	−	0.428292i
$561$	1.96888			0.0831263
$562$	−2.11767	−	10.1613i	−0.0893286	−	0.428627i
$563$	−1.36792	+	2.36931i	−0.0576509	+	0.0998543i	−0.893410	−	0.449241i	$-0.851694\pi$
$563$	−1.36792	+	2.36931i	−0.0576509	+	0.0998543i	0.835760	+	0.549096i	$0.185028\pi$
$564$	−19.1301	+	8.33573i	−0.805524	+	0.350997i
$565$	−3.61866	+	2.08923i	−0.152238	+	0.0878947i
$566$	9.67897	+	3.18747i	0.406838	+	0.133979i
$567$	0.0393726	−	6.21505i	0.00165349	−	0.261008i
$568$	−23.0045	+	16.2983i	−0.965248	+	0.683861i
$569$	−2.29674	−	3.97807i	−0.0962843	−	0.166769i	0.813860	−	0.581062i	$-0.197362\pi$
$569$	−2.29674	−	3.97807i	−0.0962843	−	0.166769i	−0.910144	+	0.414292i	$0.864029\pi$
$570$	5.23009	+	5.85523i	0.219064	+	0.245249i
$571$	4.86573	+	2.80923i	0.203625	+	0.117563i	0.598345	−	0.801239i	$-0.295825\pi$
$571$	4.86573	+	2.80923i	0.203625	+	0.117563i	−0.394720	+	0.918801i	$0.629159\pi$
$572$	−2.03642	+	17.9980i	−0.0851469	+	0.752532i
$573$		−	18.0707i		−	0.754912i
$574$	−20.6279	+	18.1919i	−0.860992	+	0.759316i
$575$		−	4.31210i		−	0.179827i
$576$	−17.2010	+	3.22959i	−0.716709	+	0.134566i
$577$	−29.7446	−	17.1731i	−1.23828	−	0.714924i	−0.269541	−	0.962989i	$-0.586872\pi$
$577$	−29.7446	−	17.1731i	−1.23828	−	0.714924i	−0.968743	+	0.248065i	$0.920205\pi$
$578$	17.5708	−	15.6949i	0.730850	−	0.652820i
$579$	−8.71499	−	15.0948i	−0.362182	−	0.627318i
$580$	−0.517501	+	0.700502i	−0.0214881	+	0.0290868i
$581$	−5.97319	+	3.39835i	−0.247810	+	0.140987i
$582$	−1.81021	+	5.49684i	−0.0750358	+	0.227851i
$583$	10.0956	−	5.82872i	0.418118	−	0.241401i
$584$	−2.56824	−	27.5963i	−0.106275	−	1.14194i
$585$	−2.64701	+	4.58475i	−0.109440	+	0.189556i
$586$	11.7386	−	2.44640i	0.484917	−	0.101060i
$587$	−40.1422			−1.65685			−0.828423	−	0.560103i	$-0.810762\pi$
$587$	−40.1422			−1.65685			−0.828423	+	0.560103i	$0.810762\pi$
$588$	−10.0530	−	7.62549i	−0.414579	−	0.314470i
$589$	15.6369			0.644309
$590$	−4.80504	+	1.00140i	−0.197820	+	0.0412270i
$591$	0.737868	−	1.27802i	0.0303518	−	0.0525709i
$592$	44.0603	+	10.0999i	1.81087	+	0.415103i
$593$	9.46884	−	5.46684i	0.388839	−	0.224496i	−0.292818	−	0.956168i	$-0.594593\pi$
$593$	9.46884	−	5.46684i	0.388839	−	0.224496i	0.681657	+	0.731672i	$0.261260\pi$
$594$	7.74042	−	23.5043i	0.317593	−	0.964394i
$595$	−1.34233	+	0.763699i	−0.0550303	+	0.0313086i
$596$	2.65675	+	1.96269i	0.108825	+	0.0803951i
$597$	−0.352969	−	0.611361i	−0.0144461	−	0.0250213i
$598$	11.0058	−	9.83079i	0.450063	−	0.402011i
$599$	4.51466	+	2.60654i	0.184464	+	0.106500i	0.589388	−	0.807850i	$-0.299369\pi$
$599$	4.51466	+	2.60654i	0.184464	+	0.106500i	−0.404924	+	0.914350i	$0.632702\pi$
$600$	1.06454	−	2.31628i	0.0434598	−	0.0945618i
$601$			16.1103i			0.657154i	0.944477	+	0.328577i	$0.106569\pi$
$601$			16.1103i			0.657154i	−0.944477	+	0.328577i	$0.893431\pi$
$602$	16.2790	−	14.3566i	0.663481	−	0.585129i
$603$		−	21.5379i		−	0.877090i
$604$	14.6190	+	1.65410i	0.594838	+	0.0673042i
$605$	−2.60329	−	1.50301i	−0.105839	−	0.0611060i
$606$	−7.76455	−	8.69263i	−0.315413	−	0.353114i
$607$	4.82810	+	8.36252i	0.195967	+	0.339424i	0.947217	−	0.320593i	$-0.103882\pi$
$607$	4.82810	+	8.36252i	0.195967	+	0.339424i	−0.751250	+	0.660017i	$0.770549\pi$
$608$	−0.692317	+	34.8368i	−0.0280772	+	1.41282i
$609$	−0.00657809	+	1.03837i	−0.000266558	+	0.0420767i
$610$	13.9532	+	4.59506i	0.564949	+	0.186048i
$611$	−24.2609	+	14.0070i	−0.981491	+	0.566664i
$612$	1.02023	+	2.34138i	0.0412403	+	0.0946446i
$613$	−3.92388	+	6.79635i	−0.158484	+	0.274502i	−0.934322	−	0.356430i	$-0.883994\pi$
$613$	−3.92388	+	6.79635i	−0.158484	+	0.274502i	0.775838	+	0.630932i	$0.217327\pi$
$614$	−3.00854	−	14.4359i	−0.121415	−	0.582586i
$615$	−6.62501			−0.267146
$616$	16.0451	+	22.9541i	0.646477	+	0.924847i
$617$	−28.8434			−1.16119			−0.580597	−	0.814191i	$-0.697181\pi$
$617$	−28.8434			−1.16119			−0.580597	+	0.814191i	$0.697181\pi$
$618$	−2.66079	−	12.7673i	−0.107033	−	0.513577i
$619$	1.24278	−	2.15256i	0.0499517	−	0.0865189i	−0.839968	−	0.542635i	$-0.817427\pi$
$619$	1.24278	−	2.15256i	0.0499517	−	0.0865189i	0.889920	+	0.456116i	$0.150760\pi$
$620$	−2.02819	−	4.65461i	−0.0814542	−	0.186934i
$621$	−17.4604	+	10.0807i	−0.700660	+	0.404526i
$622$	10.6465	+	3.50609i	0.426885	+	0.140581i
$623$	13.2134	−	22.5550i	0.529383	−	0.903649i
$624$	8.33885	−	2.56364i	0.333821	−	0.102628i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.6292	+	15.2582i	0.544731	+	0.609842i
$627$	−17.9927	−	10.3881i	−0.718558	−	0.414860i
$628$	6.12592	+	0.693131i	0.244451	+	0.0276589i
$629$		−	6.59647i		−	0.263019i
$630$	1.61925	+	8.02386i	0.0645126	+	0.319678i
$631$		−	8.90728i		−	0.354593i	−0.984157	−	0.177297i	$-0.943265\pi$
$631$		−	8.90728i		−	0.354593i	0.984157	−	0.177297i	$-0.0567352\pi$
$632$	−1.17976	−	0.542207i	−0.0469283	−	0.0215678i
$633$	7.20066	+	4.15730i	0.286200	+	0.165238i
$634$	3.73060	−	3.33230i	0.148161	−	0.132342i
$635$	−2.45518	−	4.25250i	−0.0974309	−	0.168755i
$636$	−4.51609	−	3.33630i	−0.179075	−	0.132293i
$637$	−14.5614	−	8.65485i	−0.576944	−	0.342917i
$638$	0.720911	−	2.18910i	0.0285412	−	0.0866672i
$639$	18.8848	−	10.9032i	0.747073	−	0.431323i
$640$	10.4596	−	4.31243i	0.413451	−	0.170464i
$641$	−7.31652	+	12.6726i	−0.288985	+	0.500537i	−0.973568	−	0.228398i	$-0.926651\pi$
$641$	−7.31652	+	12.6726i	−0.288985	+	0.500537i	0.684583	+	0.728935i	$0.259984\pi$
$642$	−7.90102	+	1.64662i	−0.311828	+	0.0649870i
$643$	24.2513			0.956380			0.478190	−	0.878256i	$-0.341293\pi$
$643$	24.2513			0.956380			0.478190	+	0.878256i	$0.341293\pi$
$644$	2.70894	−	22.6561i	0.106747	−	0.892776i
$645$	5.22827			0.205863
$646$	4.97777	−	1.03740i	0.195848	−	0.0408160i
$647$	14.9578	−	25.9077i	0.588053	−	1.01854i	−0.406435	−	0.913680i	$-0.633228\pi$
$647$	14.9578	−	25.9077i	0.588053	−	1.01854i	0.994487	−	0.104857i	$-0.0334386\pi$
$648$	6.61571	−	0.615690i	0.259890	−	0.0241866i
$649$	11.2487	−	6.49444i	0.441550	−	0.254929i
$650$	1.07046	−	3.25054i	0.0419870	−	0.127496i
$651$	−5.22326	−	3.05993i	−0.204716	−	0.119928i
$652$	5.36935	−	7.26808i	0.210280	−	0.284640i
$653$	7.78155	+	13.4780i	0.304516	+	0.527436i	0.977153	−	0.212535i	$-0.0681721\pi$
$653$	7.78155	+	13.4780i	0.304516	+	0.527436i	−0.672638	+	0.739972i	$0.734839\pi$
$654$	−17.8337	+	15.9296i	−0.697351	+	0.622898i
$655$	−13.7477	−	7.93723i	−0.537167	−	0.310133i
$656$	−21.5350	−	20.0191i	−0.840800	−	0.781615i
$657$			21.4371i			0.836340i
$658$	−13.8092	+	41.0552i	−0.538337	+	1.60050i
$659$			30.2702i			1.17916i	0.807710	+	0.589580i	$0.200707\pi$
$659$			30.2702i			1.17916i	−0.807710	+	0.589580i	$0.799293\pi$
$660$	−0.758451	+	6.70323i	−0.0295227	+	0.260923i
$661$	15.5209	+	8.96099i	0.603693	+	0.348542i	0.770493	−	0.637449i	$-0.220010\pi$
$661$	15.5209	+	8.96099i	0.603693	+	0.348542i	−0.166800	+	0.985991i	$0.553344\pi$
$662$	22.1676	+	24.8172i	0.861567	+	0.964549i
$663$	−0.636547	−	1.10253i	−0.0247214	−	0.0428188i
$664$	−4.24714	−	5.99470i	−0.164821	−	0.232640i
$665$	16.2963	+	0.103238i	0.631944	+	0.00400339i
$666$	−33.2087	−	10.9363i	−1.28681	−	0.423772i
$667$	−1.62619	+	0.938880i	−0.0629662	+	0.0363536i
$668$	−31.0518	+	13.5305i	−1.20143	+	0.523509i
$669$	10.9226	−	18.9185i	0.422292	−	0.731432i
$670$	2.84059	+	13.6301i	0.109742	+	0.526576i
$671$	−38.8754			−1.50077
$672$	7.04833	−	11.5012i	0.271895	−	0.443667i
$673$	21.1876			0.816723			0.408362	−	0.912820i	$-0.366100\pi$
$673$	21.1876			0.816723			0.408362	+	0.912820i	$0.366100\pi$
$674$	1.47168	+	7.06157i	0.0566868	+	0.272001i
$675$	−2.33778	+	4.04915i	−0.0899812	+	0.155852i
$676$	−13.0986	+	5.70758i	−0.503794	+	0.219522i
$677$	−21.8732	+	12.6285i	−0.840657	+	0.485353i	−0.857487	−	0.514505i	$-0.827976\pi$
$677$	−21.8732	+	12.6285i	−0.840657	+	0.485353i	0.0168308	+	0.999858i	$0.494642\pi$
$678$	−5.05863	−	1.66590i	−0.194275	−	0.0639786i
$679$	5.94041	+	10.4413i	0.227972	+	0.400700i
$680$	−0.954444	−	1.34717i	−0.0366012	−	0.0516615i
$681$	−4.79140	−	8.29895i	−0.183607	−	0.318016i
$682$	8.95080	+	10.0207i	0.342744	+	0.383711i
$683$	−19.1391	−	11.0499i	−0.732336	−	0.422814i	0.0869404	−	0.996214i	$-0.472291\pi$
$683$	−19.1391	−	11.0499i	−0.732336	−	0.422814i	−0.819276	+	0.573399i	$0.805624\pi$
$684$	3.03003	−	26.7796i	0.115856	−	1.02394i
$685$			7.84221i			0.299635i
$686$	−25.7376	+	4.85545i	−0.982667	+	0.185382i
$687$		−	26.5993i		−	1.01483i
$688$	16.9948	+	15.7985i	0.647921	+	0.602313i
$689$	−6.52791	−	3.76889i	−0.248694	−	0.143583i
$690$	4.09906	−	3.66142i	0.156048	−	0.139388i
$691$	−9.05508	−	15.6839i	−0.344471	−	0.596642i	0.640786	−	0.767719i	$-0.278609\pi$
$691$	−9.05508	−	15.6839i	−0.344471	−	0.596642i	−0.985258	+	0.171077i	$0.945275\pi$
$692$	−0.157697	+	0.213462i	−0.00599473	+	0.00811461i
$693$	−10.7118	−	18.8279i	−0.406908	−	0.715212i
$694$	−0.737153	+	2.23841i	−0.0279819	+	0.0849691i
$695$	−15.0727	+	8.70222i	−0.571740	+	0.330094i
$696$	−1.10530	+	0.102865i	−0.0418965	+	0.00389908i
$697$	−2.14537	+	3.71588i	−0.0812615	+	0.140749i
$698$	−38.2225	+	7.96581i	−1.44674	+	0.301510i
$699$	25.2991			0.956901
$700$	−2.08299	−	4.86427i	−0.0787295	−	0.183852i
$701$	14.4315			0.545070			0.272535	−	0.962146i	$-0.412138\pi$
$701$	14.4315			0.545070			0.272535	+	0.962146i	$0.412138\pi$
$702$	−15.6644	+	3.26456i	−0.591215	+	0.123213i
$703$	−34.8038	+	60.2820i	−1.31265	+	2.27358i
$704$	−22.7209	+	19.4974i	−0.856324	+	0.734835i
$705$	−9.03582	+	5.21684i	−0.340309	+	0.196477i
$706$	−12.0134	+	36.4796i	−0.452131	+	1.37293i
$707$	−24.1934	−	0.153266i	−0.909885	−	0.00576416i
$708$	−5.03189	−	3.71735i	−0.189110	−	0.139706i
$709$	18.5131	+	32.0657i	0.695275	+	1.20425i	0.970088	+	0.242753i	$0.0780505\pi$
$709$	18.5131	+	32.0657i	0.695275	+	1.20425i	−0.274814	+	0.961498i	$0.588616\pi$
$710$	−10.5131	+	9.39067i	−0.394550	+	0.352426i
$711$	0.869718	+	0.502132i	0.0326170	+	0.0188314i
$712$	25.3920	+	11.6699i	0.951605	+	0.437350i
$713$		−	10.9469i		−	0.409965i
$714$	−1.86575	−	0.627554i	−0.0698238	−	0.0234856i
$715$			9.05640i			0.338690i
$716$	31.9940	+	3.62003i	1.19567	+	0.135287i
$717$	10.6369	+	6.14124i	0.397244	+	0.229349i
$718$	−15.7850	−	17.6717i	−0.589091	−	0.659503i
$719$	10.0975	+	17.4894i	0.376573	+	0.652243i	0.990561	−	0.137072i	$-0.0437692\pi$
$719$	10.0975	+	17.4894i	0.376573	+	0.652243i	−0.613988	+	0.789315i	$0.710436\pi$
$720$	−8.36443	+	2.57151i	−0.311724	+	0.0958345i
$721$	−23.3581	−	13.6838i	−0.869902	−	0.509613i
$722$	−25.4412	−	8.37828i	−0.946824	−	0.311807i
$723$	3.28401	−	1.89602i	0.122134	−	0.0705138i
$724$	3.19024	+	7.32147i	0.118564	+	0.272100i
$725$	−0.217731	+	0.377122i	−0.00808634	+	0.0140060i
$726$	−0.781708	−	3.75088i	−0.0290119	−	0.139208i
$727$	−10.7925			−0.400272			−0.200136	−	0.979768i	$-0.564138\pi$
$727$	−10.7925			−0.400272			−0.200136	+	0.979768i	$0.564138\pi$
$728$	7.66635	−	16.4061i	0.284134	−	0.608050i
$729$	7.50278			0.277881
$730$	−2.82730	−	13.5663i	−0.104643	−	0.502111i
$731$	1.69306	−	2.93247i	0.0626202	−	0.108461i
$732$	7.47967	+	17.1655i	0.276457	+	0.634456i
$733$	6.26329	−	3.61611i	0.231340	−	0.133564i	−0.379850	−	0.925048i	$-0.624024\pi$
$733$	6.26329	−	3.61611i	0.231340	−	0.133564i	0.611190	+	0.791484i	$0.290691\pi$
$734$	−11.3427	−	3.73538i	−0.418668	−	0.137875i
$735$	−5.42330	−	3.22344i	−0.200042	−	0.118898i
$736$	24.3881	+	0.484669i	0.898958	+	0.0178651i
$737$	−18.4223	−	31.9083i	−0.678593	−	1.17536i
$738$	15.1501	+	16.9610i	0.557684	+	0.624343i
$739$	−1.71927	−	0.992622i	−0.0632444	−	0.0365142i	0.468044	−	0.883705i	$-0.344959\pi$
$739$	−1.71927	−	0.992622i	−0.0632444	−	0.0365142i	−0.531289	+	0.847191i	$0.678292\pi$
$740$	22.4582	+	2.54109i	0.825582	+	0.0934122i
$741$			13.4340i			0.493511i
$742$	−11.4246	+	2.30554i	−0.419411	+	0.0846391i
$743$		−	19.8225i		−	0.727216i	−0.931552	−	0.363608i	$-0.881545\pi$
$743$		−	19.8225i		−	0.727216i	0.931552	−	0.363608i	$-0.118455\pi$
$744$	2.70250	−	5.88023i	0.0990786	−	0.215580i
$745$	1.43029	+	0.825776i	0.0524016	+	0.0302541i
$746$	−10.9450	+	9.77648i	−0.400727	+	0.357942i
$747$	2.84124	+	4.92116i	0.103955	+	0.180056i
$748$	3.51414	+	2.59610i	0.128490	+	0.0949228i
$749$	−8.46821	+	14.4551i	−0.309421	+	0.528178i
$750$	0.398687	−	1.21064i	0.0145580	−	0.0442064i
$751$	20.8718	−	12.0504i	0.761624	−	0.439724i	−0.0682545	−	0.997668i	$-0.521743\pi$
$751$	20.8718	−	12.0504i	0.761624	−	0.439724i	0.829879	+	0.557944i	$0.188410\pi$
$752$	−45.1355	−	10.3464i	−1.64592	−	0.377293i
$753$	−8.50921	+	14.7384i	−0.310093	+	0.537097i
$754$	−1.45892	+	0.304048i	−0.0531308	+	0.0110728i
$755$	7.35613			0.267717
$756$	−14.8266	+	19.8059i	−0.539239	+	0.720335i
$757$	34.8711			1.26741			0.633706	−	0.773574i	$-0.281533\pi$
$757$	34.8711			1.26741			0.633706	+	0.773574i	$0.281533\pi$
$758$	16.3334	−	3.40398i	0.593256	−	0.123638i
$759$	−7.27236	+	12.5961i	−0.263970	+	0.457209i
$760$	1.61438	+	17.3469i	0.0585598	+	0.629237i
$761$	7.76620	−	4.48382i	0.281524	−	0.162538i	−0.352589	−	0.935778i	$-0.614699\pi$
$761$	7.76620	−	4.48382i	0.281524	−	0.162538i	0.634113	+	0.773240i	$0.281365\pi$
$762$	1.95770	−	5.94469i	0.0709200	−	0.215353i
$763$	−0.314438	+	49.6347i	−0.0113834	+	1.79690i
$764$	23.8273	−	32.2533i	0.862043	−	1.16688i
$765$	0.638500	+	1.10591i	0.0230850	+	0.0399844i
$766$	−1.00941	+	0.901641i	−0.0364715	+	0.0325776i
$767$	−7.27349	−	4.19935i	−0.262631	−	0.151630i
$768$	12.9806	+	6.28112i	0.468398	+	0.226650i
$769$			0.573577i			0.0206837i	0.999947	+	0.0103419i	$0.00329197\pi$
$769$			0.573577i			0.0206837i	−0.999947	+	0.0103419i	$0.996708\pi$
$770$	9.26207	+	10.5023i	0.333782	+	0.378477i
$771$			23.2841i			0.838556i
$772$	4.34860	−	38.4331i	0.156509	−	1.38324i
$773$	−3.76591	−	2.17425i	−0.135450	−	0.0782023i	0.430744	−	0.902474i	$-0.358251\pi$
$773$	−3.76591	−	2.17425i	−0.135450	−	0.0782023i	−0.566194	+	0.824272i	$0.691585\pi$
$774$	−11.9561	−	13.3851i	−0.429752	−	0.481119i
$775$	−1.26933	−	2.19854i	−0.0455955	−	0.0789738i
$776$	−10.4789	+	7.42411i	−0.376170	+	0.266510i
$777$	23.4220	−	13.3256i	0.840259	−	0.478052i
$778$	40.5179	+	13.3433i	1.45264	+	0.478381i
$779$	39.2109	−	22.6384i	1.40488	−	0.811107i
$780$	3.99887	−	1.74246i	0.143183	−	0.0623901i
$781$	18.6519	−	32.3060i	0.667417	−	1.15600i
$782$	−0.726250	−	3.48478i	−0.0259707	−	0.124615i
$783$	2.03603			0.0727618
$784$	−7.88834	−	26.8659i	−0.281726	−	0.959495i
$785$	3.08251			0.110019
$786$	−4.12811	−	19.8080i	−0.147245	−	0.706528i
$787$	10.5248	−	18.2295i	0.375168	−	0.649811i	−0.615184	−	0.788384i	$-0.710918\pi$
$787$	10.5248	−	18.2295i	0.375168	−	0.649811i	0.990352	+	0.138573i	$0.0442516\pi$
$788$	3.00214	−	1.30815i	0.106947	−	0.0466008i
$789$	−8.34944	+	4.82055i	−0.297248	+	0.171616i
$790$	−0.616619	−	0.203065i	−0.0219383	−	0.00722471i
$791$	−9.60890	+	5.46683i	−0.341653	+	0.194378i
$792$	18.8957	−	13.3873i	0.671428	−	0.475695i
$793$	12.5686	+	21.7694i	0.446323	+	0.773054i
$794$	−5.84765	−	6.54661i	−0.207525	−	0.232330i
$795$	−2.43128	−	1.40370i	−0.0862286	−	0.0497841i
$796$	0.176124	−	1.55660i	0.00624256	−	0.0551721i
$797$			14.7349i			0.521938i	0.965347	+	0.260969i	$0.0840420\pi$
$797$			14.7349i			0.521938i	−0.965347	+	0.260969i	$0.915958\pi$
$798$	13.7391	+	15.5788i	0.486359	+	0.551485i
$799$			6.75744i			0.239061i
$800$	4.95421	−	2.73053i	0.175158	−	0.0965388i
$801$	−18.7190	−	10.8074i	−0.661403	−	0.381861i
$802$	27.7528	−	24.7897i	0.979984	−	0.875355i
$803$	18.3360	+	31.7590i	0.647065	+	1.12075i
$804$	−10.5447	+	14.2736i	−0.371883	+	0.503390i
$805$	0.0722735	−	11.4085i	0.00254731	−	0.402097i
$806$	2.71753	−	8.25198i	0.0957210	−	0.290663i
$807$	6.52923	−	3.76965i	0.229840	−	0.132698i
$808$	−2.39670	−	25.7530i	−0.0843156	−	0.905988i
$809$	7.23808	−	12.5367i	0.254477	−	0.440768i	−0.710276	−	0.703923i	$-0.751430\pi$
$809$	7.23808	−	12.5367i	0.254477	−	0.440768i	0.964753	+	0.263156i	$0.0847632\pi$
$810$	3.25227	−	0.677795i	0.114273	−	0.0238153i
$811$	18.5825			0.652521			0.326260	−	0.945280i	$-0.394211\pi$
$811$	18.5825			0.652521			0.326260	+	0.945280i	$0.394211\pi$
$812$	−1.38089	+	1.84464i	−0.0484598	+	0.0647343i
$813$	24.4348			0.856967
$814$	−58.5529	+	12.2028i	−2.05228	+	0.427708i
$815$	2.25908	−	3.91284i	0.0791321	−	0.137061i
$816$	0.470188	−	2.05117i	0.0164599	−	0.0718054i
$817$	−30.9442	+	17.8656i	−1.08260	+	0.625040i
$818$	8.14069	−	24.7198i	0.284633	−	0.864306i
$819$	−7.08003	+	12.0855i	−0.247396	+	0.422302i
$820$	−11.8246	−	8.73551i	−0.412933	−	0.305057i
$821$	8.20275	+	14.2076i	0.286278	+	0.495848i	0.972918	−	0.231149i	$-0.0742486\pi$
$821$	8.20275	+	14.2076i	0.286278	+	0.495848i	−0.686640	+	0.726997i	$0.740915\pi$
$822$	−7.45475	+	6.65884i	−0.260014	+	0.232254i
$823$	38.0161	+	21.9486i	1.32516	+	0.765081i	0.984547	−	0.175123i	$-0.0560323\pi$
$823$	38.0161	+	21.9486i	1.32516	+	0.765081i	0.340612	+	0.940204i	$0.389366\pi$
$824$	12.0854	−	26.2961i	0.421017	−	0.916067i
$825$			3.37300i			0.117433i
$826$	−12.7295	+	2.56887i	−0.442915	+	0.0893823i
$827$			8.10796i			0.281941i	0.990014	+	0.140971i	$0.0450224\pi$
$827$			8.10796i			0.281941i	−0.990014	+	0.140971i	$0.954978\pi$
$828$	−18.7475	−	2.12123i	−0.651522	−	0.0737178i
$829$	−36.5657	−	21.1112i	−1.26998	−	0.733223i	−0.294995	−	0.955499i	$-0.595318\pi$
$829$	−36.5657	−	21.1112i	−1.26998	−	0.733223i	−0.974984	+	0.222276i	$0.928651\pi$
$830$	−2.44710	−	2.73959i	−0.0849400	−	0.0950927i
$831$	−1.51407	−	2.62245i	−0.0525225	−	0.0909716i
$832$	18.2639	+	6.41961i	0.633185	+	0.222560i
$833$	−3.56421	+	1.99802i	−0.123492	+	0.0692273i
$834$	−21.0705	−	6.93893i	−0.729613	−	0.240275i
$835$	−14.6668	+	8.46791i	−0.507567	+	0.293044i
$836$	−18.4167	−	42.2656i	−0.636956	−	1.46179i
$837$	−5.93481	+	10.2794i	−0.205137	+	0.355308i
$838$	−10.1686	−	48.7922i	−0.351269	−	1.68550i
$839$	31.8404			1.09925			0.549627	−	0.835410i	$-0.314770\pi$
$839$	31.8404			1.09925			0.549627	+	0.835410i	$0.314770\pi$
$840$	2.85528	−	6.11034i	0.0985166	−	0.210827i
$841$	−28.8104			−0.993461
$842$	−4.52040	−	21.6903i	−0.155783	−	0.747497i
$843$	3.30745	−	5.72868i	0.113915	−	0.197306i
$844$	7.37036	+	16.9147i	0.253698	+	0.582227i
$845$	−6.18694	+	3.57203i	−0.212837	+	0.122882i
$846$	34.0191	+	11.2031i	1.16960	+	0.385171i
$847$	−6.86233	−	4.02014i	−0.235792	−	0.138134i
$848$	−3.66139	−	11.9095i	−0.125733	−	0.408975i
$849$	3.24714	+	5.62422i	0.111442	+	0.193023i
$850$	−0.549927	−	0.615659i	−0.0188623	−	0.0211169i
$851$	42.2015	+	24.3650i	1.44665	+	0.835223i
$852$	−17.8534	−	2.02007i	−0.611649	−	0.0692063i
$853$		−	16.2023i		−	0.554755i	−0.960761	−	0.277378i	$-0.910535\pi$
$853$		−	16.2023i		−	0.554755i	0.960761	−	0.277378i	$-0.0894653\pi$
$854$	36.8390	+	12.3910i	1.26060	+	0.424011i
$855$		−	13.4752i		−	0.460843i
$856$	−16.2733	−	7.47905i	−0.556208	−	0.255629i
$857$	35.4659	+	20.4762i	1.21149	+	0.699455i	0.963084	−	0.269201i	$-0.0867596\pi$
$857$	35.4659	+	20.4762i	1.21149	+	0.699455i	0.248407	+	0.968656i	$0.420093\pi$
$858$	−8.60896	+	7.68981i	−0.293905	+	0.262526i
$859$	6.02640	+	10.4380i	0.205618	+	0.356141i	0.950329	−	0.311246i	$-0.100746\pi$
$859$	6.02640	+	10.4380i	0.205618	+	0.356141i	−0.744711	+	0.667387i	$0.767413\pi$
$860$	9.33165	+	6.89382i	0.318206	+	0.235077i
$861$	−17.5278	−	0.111039i	−0.597345	−	0.00378421i
$862$	−0.887107	+	2.69376i	−0.0302150	+	0.0917499i
$863$	0.494372	−	0.285426i	0.0168286	−	0.00971602i	−0.491562	−	0.870843i	$-0.663574\pi$
$863$	0.494372	−	0.285426i	0.0168286	−	0.00971602i	0.508391	+	0.861127i	$0.330241\pi$
$864$	−22.6382	−	13.6770i	−0.770167	−	0.465300i
$865$	−0.0663486	+	0.114919i	−0.00225592	+	0.00390737i
$866$	18.8257	−	3.92340i	0.639724	−	0.133323i
$867$	15.0146			0.509924
$868$	−5.28797	−	12.3487i	−0.179486	−	0.419142i
$869$	1.71798			0.0582784
$870$	−0.543366	+	0.113241i	−0.0184218	+	0.00383923i
$871$	−11.9120	+	20.6321i	−0.403622	+	0.699093i
$872$	−52.8345	+	4.91703i	−1.78920	+	0.166512i
$873$	8.60232	−	4.96655i	0.291144	−	0.168092i
$874$	−11.7493	+	35.6775i	−0.397426	+	1.20681i
$875$	−1.30833	−	2.29962i	−0.0442298	−	0.0777414i
$876$	10.4954	−	14.2068i	0.354605	−	0.480003i
$877$	−9.47193	−	16.4059i	−0.319844	−	0.553987i	0.660611	−	0.750728i	$-0.270297\pi$
$877$	−9.47193	−	16.4059i	−0.319844	−	0.553987i	−0.980455	+	0.196742i	$0.936964\pi$
$878$	−30.6388	+	27.3676i	−1.03401	+	0.923613i
$879$	6.61794	+	3.82087i	0.223218	+	0.128875i
$880$	−10.1924	+	10.9641i	−0.343584	+	0.369601i
$881$		−	35.7695i		−	1.20511i	−0.798079	−	0.602553i	$-0.794150\pi$
$881$		−	35.7695i		−	1.20511i	0.798079	−	0.602553i	$-0.205850\pi$
$882$	4.14957	+	21.2559i	0.139723	+	0.715722i
$883$		−	25.4594i		−	0.856776i	−0.903595	−	0.428388i	$-0.859082\pi$
$883$		−	25.4594i		−	0.856776i	0.903595	−	0.428388i	$-0.140918\pi$
$884$	0.317624	−	2.80717i	0.0106828	−	0.0944155i
$885$	−2.70897	−	1.56402i	−0.0910609	−	0.0525740i
$886$	−13.7893	−	15.4375i	−0.463260	−	0.518633i
$887$	5.30243	+	9.18408i	0.178038	+	0.308371i	0.941209	−	0.337826i	$-0.109692\pi$
$887$	5.30243	+	9.18408i	0.178038	+	0.308371i	−0.763170	+	0.646197i	$0.776358\pi$
$888$	16.6538	+	23.5063i	0.558865	+	0.788821i
$889$	−6.42439	−	11.2920i	−0.215467	−	0.378721i
$890$	13.2715	+	4.37057i	0.444863	+	0.146502i
$891$	−7.61364	+	4.39574i	−0.255067	+	0.147263i
$892$	44.4404	−	19.3644i	1.48798	−	0.648368i
$893$	35.6531	−	61.7530i	1.19309	−	2.06648i
$894$	0.429482	+	2.06079i	0.0143640	+	0.0689231i
$895$	16.0991			0.538132
$896$	27.7452	−	11.2341i	0.926902	−	0.375305i
$897$	9.40472			0.314014
$898$	−7.81053	−	37.4774i	−0.260641	−	1.25064i
$899$	−0.552744	+	0.957381i	−0.0184350	+	0.0319304i
$900$	−4.01114	+	1.74781i	−0.133705	+	0.0582603i
$901$	−1.57463	+	0.909116i	−0.0524587	+	0.0302870i
$902$	36.9523	+	12.1691i	1.23038	+	0.405187i
$903$	13.8324	+	0.0876291i	0.460315	+	0.00291611i
$904$	−6.83225	−	9.64350i	−0.227237	−	0.320738i
$905$	1.99658	+	3.45818i	0.0663687	+	0.114954i
$906$	6.24611	+	6.99269i	0.207513	+	0.232317i
$907$	−13.3054	−	7.68190i	−0.441800	−	0.255073i	0.262561	−	0.964915i	$-0.415433\pi$
$907$	−13.3054	−	7.68190i	−0.441800	−	0.255073i	−0.704361	+	0.709842i	$0.748766\pi$
$908$	2.39081	−	21.1301i	0.0793418	−	0.701227i
$909$			20.0052i			0.663531i
$910$	2.88660	−	8.58199i	0.0956900	−	0.284490i
$911$		−	22.0734i		−	0.731324i	−0.930748	−	0.365662i	$-0.880843\pi$
$911$		−	22.0734i		−	0.731324i	0.930748	−	0.365662i	$-0.119157\pi$
$912$	−15.1191	+	16.2639i	−0.500642	+	0.538552i
$913$	8.41856	+	4.86046i	0.278614	+	0.160858i
$914$	−8.02231	+	7.16579i	−0.265354	+	0.237023i
$915$	4.68108	+	8.10787i	0.154752	+	0.268038i
$916$	35.0729	−	47.4755i	1.15884	−	1.56864i
$917$	−36.2392	−	21.2299i	−1.19672	−	0.701074i
$918$	−1.20729	+	3.66601i	−0.0398464	+	0.120996i
$919$	−45.1598	+	26.0730i	−1.48968	+	0.860069i	−0.999930	−	0.0117923i	$-0.996246\pi$
$919$	−45.1598	+	26.0730i	−1.48968	+	0.860069i	−0.489753	+	0.871861i	$0.662913\pi$
$920$	12.1440	−	1.13018i	0.400375	−	0.0372608i
$921$	4.69884	−	8.13863i	0.154832	−	0.268177i
$922$	17.7147	−	3.69185i	0.583401	−	0.121585i
$923$	−24.1209			−0.793949
$924$	−2.11898	+	17.7220i	−0.0697094	+	0.583011i
$925$	11.3008			0.371567
$926$	−38.6512	+	8.05516i	−1.27016	+	0.264709i
$927$	−11.1922	+	19.3855i	−0.367600	+	0.636702i
$928$	−2.10843	−	1.27382i	−0.0692126	−	0.0418152i
$929$	24.8707	−	14.3591i	0.815982	−	0.471107i	−0.0330469	−	0.999454i	$-0.510521\pi$
$929$	24.8707	−	14.3591i	0.815982	−	0.471107i	0.849029	+	0.528346i	$0.177188\pi$
$930$	1.01213	−	3.07340i	0.0331890	−	0.100781i
$931$	43.1134	+	0.546272i	1.41298	+	0.0179033i
$932$	45.1549	+	33.3585i	1.47910	+	1.09270i
$933$	3.57173	+	6.18641i	0.116933	+	0.202534i
$934$	23.8480	−	21.3019i	0.780332	−	0.697018i
$935$	1.89187	+	1.09227i	0.0618708	+	0.0357211i
$936$	−13.6056	−	6.25302i	−0.444713	−	0.204386i
$937$			44.9045i			1.46697i	0.679707	+	0.733484i	$0.262107\pi$
$937$			44.9045i			1.46697i	−0.679707	+	0.733484i	$0.737893\pi$
$938$	7.28691	+	36.1087i	0.237926	+	1.17899i
$939$			13.0385i			0.425495i
$940$	−23.0063	−	2.60309i	−0.750381	−	0.0849035i
$941$	15.3727	+	8.87541i	0.501134	+	0.289330i	0.729182	−	0.684320i	$-0.239901\pi$
$941$	15.3727	+	8.87541i	0.501134	+	0.289330i	−0.228048	+	0.973650i	$0.573234\pi$
$942$	2.61736	+	2.93021i	0.0852783	+	0.0954715i
$943$	−15.8484	−	27.4503i	−0.516096	−	0.893905i
$944$	−4.07957	−	13.2698i	−0.132779	−	0.431894i
$945$	−6.25292	+	10.6737i	−0.203408	+	0.347214i
$946$	−29.1618	−	9.60352i	−0.948130	−	0.312237i
$947$	−32.1100	+	18.5387i	−1.04344	+	0.602428i	−0.920804	−	0.390025i	$-0.872467\pi$
$947$	−32.1100	+	18.5387i	−1.04344	+	0.602428i	−0.122631	+	0.992452i	$0.539133\pi$
$948$	−0.330541	−	0.758577i	−0.0107355	−	0.0246374i
$949$	11.8562	−	20.5356i	0.384869	−	0.666613i
$950$	1.77723	+	8.52769i	0.0576608	+	0.276675i
$951$	3.18787			0.103374
$952$	−2.50259	−	3.58019i	−0.0811094	−	0.116035i
$953$	−28.5420			−0.924567			−0.462283	−	0.886732i	$-0.652970\pi$
$953$	−28.5420			−0.924567			−0.462283	+	0.886732i	$0.652970\pi$
$954$	1.96619	+	9.43443i	0.0636579	+	0.305451i
$955$	10.0250	−	17.3638i	0.324402	−	0.561881i
$956$	10.8876	+	24.9866i	0.352131	+	0.808126i
$957$	1.27203	−	0.734408i	0.0411189	−	0.0237400i
$958$	−29.5266	−	9.72368i	−0.953962	−	0.314158i
$959$	−0.131440	+	20.7481i	−0.00424442	+	0.669991i
$960$	6.80226	+	2.39094i	0.219542	+	0.0771674i
$961$	12.2776	+	21.2655i	0.396052	+	0.685983i
$962$	25.7637	+	28.8431i	0.830654	+	0.929940i
$963$	11.9966	+	6.92626i	0.386586	+	0.223196i
$964$	8.36146	+	0.946076i	0.269305	+	0.0304711i
$965$		−	19.3392i		−	0.622550i
$966$	10.9062	−	9.61830i	0.350902	−	0.309464i
$967$		−	5.33936i		−	0.171702i	−0.996308	−	0.0858510i	$-0.972639\pi$
$967$		−	5.33936i		−	0.171702i	0.996308	−	0.0858510i	$-0.0273609\pi$
$968$	3.55056	−	7.72546i	0.114119	−	0.248306i
$969$	2.80635	+	1.62025i	0.0901530	+	0.0520498i
$970$	−4.78888	+	4.27759i	−0.153762	+	0.137345i
$971$	5.49906	+	9.52465i	0.176473	+	0.305660i	0.940670	−	0.339323i	$-0.110198\pi$
$971$	5.49906	+	9.52465i	0.176473	+	0.305660i	−0.764197	+	0.644983i	$0.776864\pi$
$972$	25.9697	+	19.1853i	0.832978	+	0.615368i
$973$	−40.0236	+	22.7708i	−1.28310	+	0.729999i
$974$	−11.2283	+	34.0955i	−0.359778	+	1.09249i
$975$	1.88881	−	1.09050i	0.0604902	−	0.0349241i
$976$	−9.28381	+	40.5002i	−0.297168	+	1.29638i
$977$	15.7434	−	27.2684i	0.503676	−	0.872392i	−0.496315	−	0.868142i	$-0.665314\pi$
$977$	15.7434	−	27.2684i	0.503676	−	0.872392i	0.999991	−	0.00424979i	$-0.00135275\pi$
$978$	5.63771	−	1.17493i	0.180274	−	0.0375703i
$979$	−36.9761			−1.18176
$980$	−5.42942	−	12.9043i	−0.173437	−	0.412213i
$981$	41.0424			1.31038
$982$	−50.4825	+	10.5209i	−1.61096	+	0.335735i
$983$	17.2762	−	29.9232i	0.551025	−	0.954402i	−0.447176	−	0.894446i	$-0.647570\pi$
$983$	17.2762	−	29.9232i	0.551025	−	0.954402i	0.998201	−	0.0599567i	$-0.0190963\pi$
$984$	−1.73638	−	18.6577i	−0.0553537	−	0.594787i
$985$	1.41801	−	0.818690i	0.0451817	−	0.0260856i
$986$	−0.112442	+	0.341438i	−0.00358088	+	0.0108736i
$987$	−23.9935	+	13.6507i	−0.763722	+	0.434507i
$988$	−17.7136	+	23.9776i	−0.563545	+	0.762829i
$989$	12.5072	+	21.6630i	0.397704	+	0.688844i
$990$	8.63537	−	7.71340i	0.274450	−	0.245148i
$991$	−47.8668	−	27.6359i	−1.52054	−	0.877884i	−0.999707	−	0.0242247i	$-0.992288\pi$
$991$	−47.8668	−	27.6359i	−1.52054	−	0.877884i	−0.520833	−	0.853659i	$-0.674378\pi$
$992$	12.5770	−	6.93186i	0.399321	−	0.220087i
$993$			21.2068i			0.672978i
$994$	−27.9719	+	24.6687i	−0.887216	+	0.782443i
$995$		−	0.783264i		−	0.0248311i
$996$	0.526405	−	4.65239i	0.0166798	−	0.147417i
$997$	13.2344	+	7.64087i	0.419137	+	0.241989i	0.694708	−	0.719292i	$-0.255534\pi$
$997$	13.2344	+	7.64087i	0.419137	+	0.241989i	−0.275571	+	0.961281i	$0.588867\pi$
$998$	11.1912	+	12.5289i	0.354252	+	0.396595i
$999$	−26.4187	−	45.7586i	−0.835851	−	1.44774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.o.a.31.9	✓	32
4.3	odd	2	inner	140.2.o.a.31.13	yes	32
5.2	odd	4		700.2.t.c.199.1		32
5.3	odd	4		700.2.t.d.199.16		32
5.4	even	2		700.2.p.c.451.8		32
7.2	even	3		980.2.o.f.411.13		32
7.3	odd	6		980.2.g.a.391.5		32
7.4	even	3		980.2.g.a.391.6		32
7.5	odd	6	inner	140.2.o.a.131.13	yes	32
7.6	odd	2		980.2.o.f.31.9		32
20.3	even	4		700.2.t.d.199.11		32
20.7	even	4		700.2.t.c.199.6		32
20.19	odd	2		700.2.p.c.451.4		32
28.3	even	6		980.2.g.a.391.8		32
28.11	odd	6		980.2.g.a.391.7		32
28.19	even	6	inner	140.2.o.a.131.9	yes	32
28.23	odd	6		980.2.o.f.411.9		32
28.27	even	2		980.2.o.f.31.13		32
35.12	even	12		700.2.t.d.299.11		32
35.19	odd	6		700.2.p.c.551.4		32
35.33	even	12		700.2.t.c.299.6		32
140.19	even	6		700.2.p.c.551.8		32
140.47	odd	12		700.2.t.d.299.16		32
140.103	odd	12		700.2.t.c.299.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.9	✓	32	1.1	even	1	trivial
140.2.o.a.31.13	yes	32	4.3	odd	2	inner
140.2.o.a.131.9	yes	32	28.19	even	6	inner
140.2.o.a.131.13	yes	32	7.5	odd	6	inner
700.2.p.c.451.4		32	20.19	odd	2
700.2.p.c.451.8		32	5.4	even	2
700.2.p.c.551.4		32	35.19	odd	6
700.2.p.c.551.8		32	140.19	even	6
700.2.t.c.199.1		32	5.2	odd	4
700.2.t.c.199.6		32	20.7	even	4
700.2.t.c.299.1		32	140.103	odd	12
700.2.t.c.299.6		32	35.33	even	12
700.2.t.d.199.11		32	20.3	even	4
700.2.t.d.199.16		32	5.3	odd	4
700.2.t.d.299.11		32	35.12	even	12
700.2.t.d.299.16		32	140.47	odd	12
980.2.g.a.391.5		32	7.3	odd	6
980.2.g.a.391.6		32	7.4	even	3
980.2.g.a.391.7		32	28.11	odd	6
980.2.g.a.391.8		32	28.3	even	6
980.2.o.f.31.9		32	7.6	odd	2
980.2.o.f.31.13		32	28.27	even	2
980.2.o.f.411.9		32	28.23	odd	6
980.2.o.f.411.13		32	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.288532 + 1.38447i) q^{2} +(-0.450639 + 0.780530i) q^{3} +(-1.83350 + 0.798926i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.21064 - 0.398687i) q^{6} +(-2.29962 + 1.30833i) q^{7} +(-1.63511 - 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +O(q^{10})\)	\(q+(0.288532 + 1.38447i) q^{2} +(-0.450639 + 0.780530i) q^{3} +(-1.83350 + 0.798926i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-1.21064 - 0.398687i) q^{6} +(-2.29962 + 1.30833i) q^{7} +(-1.63511 - 2.30790i) q^{8} +(1.09385 + 1.89460i) q^{9} +(-0.942109 - 1.05472i) q^{10} +(3.24107 + 1.87123i) q^{11} +(0.202661 - 1.79113i) q^{12} -2.41990i q^{13} +(-2.47486 - 2.80626i) q^{14} -0.901278i q^{15} +(2.72344 - 2.92966i) q^{16} +(-0.505515 - 0.291859i) q^{17} +(-2.30740 + 2.06105i) q^{18} +(3.07977 + 5.33433i) q^{19} +(1.18839 - 1.60864i) q^{20} +(0.0151060 - 2.38451i) q^{21} +(-1.65551 + 5.02706i) q^{22} +(3.73439 - 2.15605i) q^{23} +(2.53823 - 0.236220i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.35028 - 0.698219i) q^{26} -4.67556 q^{27} +(3.17109 - 4.23606i) q^{28} -0.435463 q^{29} +(1.24779 - 0.260047i) q^{30} +(1.26933 - 2.19854i) q^{31} +(4.84181 + 2.92521i) q^{32} +(-2.92110 + 1.68650i) q^{33} +(0.258212 - 0.784080i) q^{34} +(1.33736 - 2.28286i) q^{35} +(-3.51922 - 2.59985i) q^{36} +(5.65039 + 9.78676i) q^{37} +(-6.49659 + 5.80297i) q^{38} +(1.88881 + 1.09050i) q^{39} +(2.57000 + 1.18115i) q^{40} -7.35068i q^{41} +(3.30563 - 0.667093i) q^{42} +5.80096i q^{43} +(-7.43747 - 0.841528i) q^{44} +(-1.89460 - 1.09385i) q^{45} +(4.06247 + 4.54805i) q^{46} +(-5.78826 - 10.0256i) q^{47} +(1.05940 + 3.44594i) q^{48} +(3.57652 - 6.01735i) q^{49} +(1.34325 + 0.442358i) q^{50} +(0.455610 - 0.263046i) q^{51} +(1.93332 + 4.43689i) q^{52} +(1.55746 - 2.69759i) q^{53} +(-1.34905 - 6.47316i) q^{54} -3.74246 q^{55} +(6.77964 + 3.16804i) q^{56} -5.55147 q^{57} +(-0.125645 - 0.602884i) q^{58} +(1.73534 - 3.00569i) q^{59} +(0.720054 + 1.65249i) q^{60} +(-8.99597 + 5.19383i) q^{61} +(3.41004 + 1.12299i) q^{62} +(-4.99421 - 2.92575i) q^{63} +(-2.65284 + 7.54735i) q^{64} +(1.20995 + 2.09570i) q^{65} +(-3.17773 - 3.55756i) q^{66} +(-8.52602 - 4.92250i) q^{67} +(1.16004 + 0.131255i) q^{68} +3.88640i q^{69} +(3.54642 + 1.19286i) q^{70} -9.96771i q^{71} +(2.58400 - 5.62238i) q^{72} +(8.48612 + 4.89946i) q^{73} +(-11.9191 + 10.6466i) q^{74} +(0.450639 + 0.780530i) q^{75} +(-9.90849 - 7.31997i) q^{76} +(-9.90142 - 0.0627260i) q^{77} +(-0.964785 + 2.92964i) q^{78} +(0.397549 - 0.229525i) q^{79} +(-0.893735 + 3.89888i) q^{80} +(-1.17456 + 2.03439i) q^{81} +(10.1768 - 2.12091i) q^{82} +2.59747 q^{83} +(1.87735 + 4.38406i) q^{84} +0.583719 q^{85} +(-8.03123 + 1.67376i) q^{86} +(0.196236 - 0.339892i) q^{87} +(-0.980878 - 10.5397i) q^{88} +(-8.55647 + 4.94008i) q^{89} +(0.967745 - 2.93862i) q^{90} +(3.16604 + 5.56486i) q^{91} +(-5.12447 + 6.93662i) q^{92} +(1.14402 + 1.98149i) q^{93} +(12.2100 - 10.9064i) q^{94} +(-5.33433 - 3.07977i) q^{95} +(-4.46512 + 2.46097i) q^{96} -4.54044i q^{97} +(9.36276 + 3.21538i) q^{98} +8.18738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9	\( 32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} - 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} - 8 q^{22} + 36 q^{24} + 16 q^{25} + 30 q^{26} + 2 q^{28} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} - 60 q^{38} - 62 q^{42} - 18 q^{44} + 12 q^{45} + 2 q^{46} - 16 q^{49} + 4 q^{50} - 36 q^{52} - 8 q^{53} + 12 q^{54} - 4 q^{56} + 48 q^{57} + 2 q^{58} + 14 q^{60} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 24 q^{66} + 60 q^{68} - 4 q^{70} + 4 q^{72} - 72 q^{73} + 38 q^{74} - 40 q^{77} + 120 q^{78} - 36 q^{81} + 42 q^{82} - 20 q^{84} + 28 q^{86} + 4 q^{88} - 60 q^{89} - 4 q^{92} - 8 q^{93} + 18 q^{94} - 60 q^{96} + 78 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 - 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 - 8 * q^22 + 36 * q^24 + 16 * q^25 + 30 * q^26 + 2 * q^28 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 - 60 * q^38 - 62 * q^42 - 18 * q^44 + 12 * q^45 + 2 * q^46 - 16 * q^49 + 4 * q^50 - 36 * q^52 - 8 * q^53 + 12 * q^54 - 4 * q^56 + 48 * q^57 + 2 * q^58 + 14 * q^60 + 24 * q^61 + 4 * q^64 + 4 * q^65 + 24 * q^66 + 60 * q^68 - 4 * q^70 + 4 * q^72 - 72 * q^73 + 38 * q^74 - 40 * q^77 + 120 * q^78 - 36 * q^81 + 42 * q^82 - 20 * q^84 + 28 * q^86 + 4 * q^88 - 60 * q^89 - 4 * q^92 - 8 * q^93 + 18 * q^94 - 60 * q^96 + 78 * q^98

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