LMFDB - Embedded newform 731.2.m.b.87.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.4
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65901 - 1.65901i) q^{2} +(1.85997 - 0.770425i) q^{3} +3.50461i q^{4} +(-1.10929 - 2.67805i) q^{5} +(-4.36385 - 1.80756i) q^{6} +(1.56474 - 3.77763i) q^{7} +(2.49616 - 2.49616i) q^{8} +(0.744616 - 0.744616i) q^{9} +O(q^{10})$	\(q+(-1.65901 - 1.65901i) q^{2} +(1.85997 - 0.770425i) q^{3} +3.50461i q^{4} +(-1.10929 - 2.67805i) q^{5} +(-4.36385 - 1.80756i) q^{6} +(1.56474 - 3.77763i) q^{7} +(2.49616 - 2.49616i) q^{8} +(0.744616 - 0.744616i) q^{9} +(-2.60260 + 6.28322i) q^{10} +(0.630143 + 0.261014i) q^{11} +(2.70004 + 6.51847i) q^{12} -1.93711i q^{13} +(-8.86304 + 3.67119i) q^{14} +(-4.12648 - 4.12648i) q^{15} -1.27307 q^{16} +(-3.56276 - 2.07526i) q^{17} -2.47065 q^{18} +(0.0217925 + 0.0217925i) q^{19} +(9.38553 - 3.88761i) q^{20} -8.23180i q^{21} +(-0.612388 - 1.47844i) q^{22} +(-0.0312517 - 0.0129449i) q^{23} +(2.71968 - 6.56588i) q^{24} +(-2.40592 + 2.40592i) q^{25} +(-3.21367 + 3.21367i) q^{26} +(-1.49998 + 3.62128i) q^{27} +(13.2391 + 5.48382i) q^{28} +(2.42117 + 5.84523i) q^{29} +13.6917i q^{30} +(8.27427 - 3.42731i) q^{31} +(-2.88029 - 2.88029i) q^{32} +1.37314 q^{33} +(2.46778 + 9.35353i) q^{34} -11.8524 q^{35} +(2.60959 + 2.60959i) q^{36} +(0.752944 - 0.311880i) q^{37} -0.0723079i q^{38} +(-1.49239 - 3.60296i) q^{39} +(-9.45379 - 3.91589i) q^{40} +(-1.86411 + 4.50036i) q^{41} +(-13.6566 + 13.6566i) q^{42} +(0.707107 - 0.707107i) q^{43} +(-0.914752 + 2.20841i) q^{44} +(-2.82011 - 1.16813i) q^{45} +(0.0303711 + 0.0733223i) q^{46} -8.89473i q^{47} +(-2.36787 + 0.980803i) q^{48} +(-6.87230 - 6.87230i) q^{49} +7.98287 q^{50} +(-8.22547 - 1.11508i) q^{51} +6.78880 q^{52} +(-7.74831 - 7.74831i) q^{53} +(8.49621 - 3.51924i) q^{54} -1.97710i q^{55} +(-5.52371 - 13.3354i) q^{56} +(0.0573230 + 0.0237439i) q^{57} +(5.68054 - 13.7140i) q^{58} +(-7.50816 + 7.50816i) q^{59} +(14.4617 - 14.4617i) q^{60} +(-4.73678 + 11.4356i) q^{61} +(-19.4130 - 8.04113i) q^{62} +(-1.64775 - 3.97802i) q^{63} +12.1030i q^{64} +(-5.18767 + 2.14880i) q^{65} +(-2.27805 - 2.27805i) q^{66} +6.91188 q^{67} +(7.27298 - 12.4861i) q^{68} -0.0681002 q^{69} +(19.6633 + 19.6633i) q^{70} +(7.71337 - 3.19498i) q^{71} -3.71736i q^{72} +(2.73862 + 6.61160i) q^{73} +(-1.76655 - 0.731729i) q^{74} +(-2.62136 + 6.32851i) q^{75} +(-0.0763743 + 0.0763743i) q^{76} +(1.97203 - 1.97203i) q^{77} +(-3.50144 + 8.45323i) q^{78} +(-5.09309 - 2.10963i) q^{79} +(1.41220 + 3.40934i) q^{80} +11.0502i q^{81} +(10.5587 - 4.37356i) q^{82} +(9.19920 + 9.19920i) q^{83} +28.8492 q^{84} +(-1.60554 + 11.8433i) q^{85} -2.34619 q^{86} +(9.00663 + 9.00663i) q^{87} +(2.22447 - 0.921405i) q^{88} -1.53381i q^{89} +(2.74065 + 6.61652i) q^{90} +(-7.31766 - 3.03108i) q^{91} +(0.0453667 - 0.109525i) q^{92} +(12.7494 - 12.7494i) q^{93} +(-14.7564 + 14.7564i) q^{94} +(0.0341874 - 0.0825357i) q^{95} +(-7.57630 - 3.13820i) q^{96} +(-5.32659 - 12.8595i) q^{97} +22.8024i q^{98} +(0.663570 - 0.274860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.65901	−	1.65901i	−1.17310	−	1.17310i	−0.981468	−	0.191627i	$-0.938623\pi$
$2$	−1.65901	−	1.65901i	−1.17310	−	1.17310i	−0.191627	−	0.981468i	$-0.561377\pi$
$3$	1.85997	−	0.770425i	1.07385	−	0.444805i	0.225505	−	0.974242i	$-0.427597\pi$
$3$	1.85997	−	0.770425i	1.07385	−	0.444805i	0.848349	+	0.529437i	$0.177597\pi$
$4$			3.50461i			1.75230i
$5$	−1.10929	−	2.67805i	−0.496088	−	1.19766i	−0.951574	−	0.307419i	$-0.900535\pi$
$5$	−1.10929	−	2.67805i	−0.496088	−	1.19766i	0.455487	−	0.890243i	$-0.349465\pi$
$6$	−4.36385	−	1.80756i	−1.78153	−	0.737935i
$7$	1.56474	−	3.77763i	0.591418	−	1.42781i	−0.290715	−	0.956810i	$-0.593893\pi$
$7$	1.56474	−	3.77763i	0.591418	−	1.42781i	0.882133	−	0.471000i	$-0.156107\pi$
$8$	2.49616	−	2.49616i	0.882525	−	0.882525i
$9$	0.744616	−	0.744616i	0.248205	−	0.248205i
$10$	−2.60260	+	6.28322i	−0.823013	+	1.98693i
$11$	0.630143	+	0.261014i	0.189995	+	0.0786986i	0.475653	−	0.879633i	$-0.342212\pi$
$11$	0.630143	+	0.261014i	0.189995	+	0.0786986i	−0.285657	+	0.958332i	$0.592212\pi$
$12$	2.70004	+	6.51847i	0.779434	+	1.88172i
$13$		−	1.93711i		−	0.537256i	−0.963244	−	0.268628i	$-0.913430\pi$
$13$		−	1.93711i		−	0.537256i	0.963244	−	0.268628i	$-0.0865703\pi$
$14$	−8.86304	+	3.67119i	−2.36875	+	0.981167i
$15$	−4.12648	−	4.12648i	−1.06545	−	1.06545i
$16$	−1.27307			−0.318267
$17$	−3.56276	−	2.07526i	−0.864097	−	0.503325i
$17$	−3.56276	−	2.07526i	−0.864097	−	0.503325i
$18$	−2.47065			−0.582337
$19$	0.0217925	+	0.0217925i	0.00499955	+	0.00499955i	0.709602	−	0.704603i	$-0.248875\pi$
$19$	0.0217925	+	0.0217925i	0.00499955	+	0.00499955i	−0.704603	+	0.709602i	$0.748875\pi$
$20$	9.38553	−	3.88761i	2.09867	−	0.869297i
$21$		−	8.23180i		−	1.79633i
$22$	−0.612388	−	1.47844i	−0.130562	−	0.315204i
$23$	−0.0312517	−	0.0129449i	−0.00651642	−	0.00269919i	0.379423	−	0.925223i	$-0.376123\pi$
$23$	−0.0312517	−	0.0129449i	−0.00651642	−	0.00269919i	−0.385939	+	0.922524i	$0.626123\pi$
$24$	2.71968	−	6.56588i	0.555152	−	1.34026i
$25$	−2.40592	+	2.40592i	−0.481183	+	0.481183i
$26$	−3.21367	+	3.21367i	−0.630253	+	0.630253i
$27$	−1.49998	+	3.62128i	−0.288672	+	0.696915i
$28$	13.2391	+	5.48382i	2.50196	+	1.03634i
$29$	2.42117	+	5.84523i	0.449601	+	1.08543i	0.972472	+	0.233021i	$0.0748609\pi$
$29$	2.42117	+	5.84523i	0.449601	+	1.08543i	−0.522871	+	0.852412i	$0.675139\pi$
$30$			13.6917i			2.49975i
$31$	8.27427	−	3.42731i	1.48610	−	0.615564i	0.515638	−	0.856807i	$-0.327555\pi$
$31$	8.27427	−	3.42731i	1.48610	−	0.615564i	0.970465	+	0.241243i	$0.0775551\pi$
$32$	−2.88029	−	2.88029i	−0.509168	−	0.509168i
$33$	1.37314			0.239033
$34$	2.46778	+	9.35353i	0.423220	+	1.60412i
$35$	−11.8524			−2.00343
$36$	2.60959	+	2.60959i	0.434931	+	0.434931i
$37$	0.752944	−	0.311880i	0.123783	−	0.0512727i	−0.319932	−	0.947440i	$-0.603660\pi$
$37$	0.752944	−	0.311880i	0.123783	−	0.0512727i	0.443715	+	0.896168i	$0.353660\pi$
$38$		−	0.0723079i		−	0.0117299i
$39$	−1.49239	−	3.60296i	−0.238974	−	0.576935i
$40$	−9.45379	−	3.91589i	−1.49478	−	0.619156i
$41$	−1.86411	+	4.50036i	−0.291125	+	0.702838i	−0.999997	−	0.00249918i	$-0.999204\pi$
$41$	−1.86411	+	4.50036i	−0.291125	+	0.702838i	0.708872	+	0.705337i	$0.249204\pi$
$42$	−13.6566	+	13.6566i	−2.10726	+	2.10726i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	−0.914752	+	2.20841i	−0.137904	+	0.332930i
$45$	−2.82011	−	1.16813i	−0.420398	−	0.174134i
$46$	0.0303711	+	0.0733223i	0.00447797	+	0.0108108i
$47$		−	8.89473i		−	1.29743i	−0.761032	−	0.648715i	$-0.775307\pi$
$47$		−	8.89473i		−	1.29743i	0.761032	−	0.648715i	$-0.224693\pi$
$48$	−2.36787	+	0.980803i	−0.341772	+	0.141567i
$49$	−6.87230	−	6.87230i	−0.981758	−	0.981758i
$50$	7.98287			1.12895
$51$	−8.22547	−	1.11508i	−1.15180	−	0.156143i
$52$	6.78880			0.941437
$53$	−7.74831	−	7.74831i	−1.06431	−	1.06431i	−0.997785	−	0.0665276i	$-0.978808\pi$
$53$	−7.74831	−	7.74831i	−1.06431	−	1.06431i	−0.0665276	−	0.997785i	$-0.521192\pi$
$54$	8.49621	−	3.51924i	1.15619	−	0.478908i
$55$		−	1.97710i		−	0.266592i
$56$	−5.52371	−	13.3354i	−0.738136	−	1.78202i
$57$	0.0573230	+	0.0237439i	0.00759261	+	0.00314496i
$58$	5.68054	−	13.7140i	0.745891	−	1.80074i
$59$	−7.50816	+	7.50816i	−0.977479	+	0.977479i	−0.999752	−	0.0222732i	$-0.992910\pi$
$59$	−7.50816	+	7.50816i	−0.977479	+	0.977479i	0.0222732	+	0.999752i	$0.492910\pi$
$60$	14.4617	−	14.4617i	1.86700	−	1.86700i
$61$	−4.73678	+	11.4356i	−0.606483	+	1.46418i	0.260317	+	0.965523i	$0.416173\pi$
$61$	−4.73678	+	11.4356i	−0.606483	+	1.46418i	−0.866800	+	0.498656i	$0.833827\pi$
$62$	−19.4130	−	8.04113i	−2.46545	−	1.02122i
$63$	−1.64775	−	3.97802i	−0.207597	−	0.501183i
$64$			12.1030i			1.51287i
$65$	−5.18767	+	2.14880i	−0.643451	+	0.266526i
$66$	−2.27805	−	2.27805i	−0.280408	−	0.280408i
$67$	6.91188			0.844420			0.422210	−	0.906498i	$-0.361254\pi$
$67$	6.91188			0.844420			0.422210	+	0.906498i	$0.361254\pi$
$68$	7.27298	−	12.4861i	0.881978	−	1.51416i
$69$	−0.0681002			−0.00819830
$70$	19.6633	+	19.6633i	2.35021	+	2.35021i
$71$	7.71337	−	3.19498i	0.915408	−	0.379175i	0.125284	−	0.992121i	$-0.460016\pi$
$71$	7.71337	−	3.19498i	0.915408	−	0.379175i	0.790125	+	0.612946i	$0.210016\pi$
$72$		−	3.71736i		−	0.438095i
$73$	2.73862	+	6.61160i	0.320531	+	0.773829i	0.999223	+	0.0394070i	$0.0125469\pi$
$73$	2.73862	+	6.61160i	0.320531	+	0.773829i	−0.678693	+	0.734422i	$0.737453\pi$
$74$	−1.76655	−	0.731729i	−0.205357	−	0.0850618i
$75$	−2.62136	+	6.32851i	−0.302688	+	0.730754i
$76$	−0.0763743	+	0.0763743i	−0.00876073	+	0.00876073i
$77$	1.97203	−	1.97203i	0.224733	−	0.224733i
$78$	−3.50144	+	8.45323i	−0.396460	+	0.957140i
$79$	−5.09309	−	2.10963i	−0.573017	−	0.237352i	0.0773081	−	0.997007i	$-0.475367\pi$
$79$	−5.09309	−	2.10963i	−0.573017	−	0.237352i	−0.650326	+	0.759656i	$0.725367\pi$
$80$	1.41220	+	3.40934i	0.157888	+	0.381176i
$81$			11.0502i			1.22780i
$82$	10.5587	−	4.37356i	1.16601	−	0.482979i
$83$	9.19920	+	9.19920i	1.00974	+	1.00974i	0.999952	+	0.00979120i	$0.00311669\pi$
$83$	9.19920	+	9.19920i	1.00974	+	1.00974i	0.00979120	+	0.999952i	$0.496883\pi$
$84$	28.8492			3.14771
$85$	−1.60554	+	11.8433i	−0.174145	+	1.28459i
$86$	−2.34619			−0.252996
$87$	9.00663	+	9.00663i	0.965612	+	0.965612i
$88$	2.22447	−	0.921405i	0.237129	−	0.0982221i
$89$		−	1.53381i		−	0.162584i	−0.996690	−	0.0812919i	$-0.974095\pi$
$89$		−	1.53381i		−	0.162584i	0.996690	−	0.0812919i	$-0.0259046\pi$
$90$	2.74065	+	6.61652i	0.288890	+	0.697442i
$91$	−7.31766	−	3.03108i	−0.767100	−	0.317743i
$92$	0.0453667	−	0.109525i	0.00472980	−	0.0114188i
$93$	12.7494	−	12.7494i	1.32205	−	1.32205i
$94$	−14.7564	+	14.7564i	−1.52201	+	1.52201i
$95$	0.0341874	−	0.0825357i	0.00350755	−	0.00846798i
$96$	−7.57630	−	3.13820i	−0.773252	−	0.320292i
$97$	−5.32659	−	12.8595i	−0.540834	−	1.30569i	−0.924136	−	0.382065i	$-0.875213\pi$
$97$	−5.32659	−	12.8595i	−0.540834	−	1.30569i	0.383302	−	0.923623i	$-0.374787\pi$
$98$			22.8024i			2.30339i
$99$	0.663570	−	0.274860i	0.0666913	−	0.0276244i
$100$	−8.43180	−	8.43180i	−0.843180	−	0.843180i
$101$	7.68098			0.764286			0.382143	−	0.924103i	$-0.375186\pi$
$101$	7.68098			0.764286			0.382143	+	0.924103i	$0.375186\pi$
$102$	11.7962	+	15.4960i	1.16800	+	1.53434i
$103$	4.06894			0.400925			0.200462	−	0.979701i	$-0.435756\pi$
$103$	4.06894			0.400925			0.200462	+	0.979701i	$0.435756\pi$
$104$	−4.83532	−	4.83532i	−0.474142	−	0.474142i
$105$	−22.0452	+	9.13142i	−2.15139	+	0.891135i
$106$			25.7090i			2.49708i
$107$	−2.03931	−	4.92333i	−0.197148	−	0.475957i	0.794130	−	0.607748i	$-0.207927\pi$
$107$	−2.03931	−	4.92333i	−0.197148	−	0.475957i	−0.991277	+	0.131792i	$0.957927\pi$
$108$	−12.6912	−	5.25685i	−1.22121	−	0.505841i
$109$	−3.79500	+	9.16194i	−0.363495	+	0.877555i	0.631289	+	0.775548i	$0.282526\pi$
$109$	−3.79500	+	9.16194i	−0.363495	+	0.877555i	−0.994784	+	0.102007i	$0.967474\pi$
$110$	−3.28002	+	3.28002i	−0.312737	+	0.312737i
$111$	1.16017	−	1.16017i	0.110119	−	0.110119i
$112$	−1.99203	+	4.80917i	−0.188229	+	0.454424i
$113$	5.93225	+	2.45722i	0.558059	+	0.231156i	0.643842	−	0.765158i	$-0.277339\pi$
$113$	5.93225	+	2.45722i	0.558059	+	0.231156i	−0.0857831	+	0.996314i	$0.527339\pi$
$114$	−0.0557078	−	0.134491i	−0.00521752	−	0.0125962i
$115$			0.0980531i			0.00914350i
$116$	−20.4853	+	8.48527i	−1.90201	+	0.787838i
$117$	−1.44240	−	1.44240i	−0.133350	−	0.133350i
$118$	24.9122			2.29335
$119$	−13.4144	+	10.2115i	−1.22969	+	0.936091i
$120$	−20.6007			−1.88058
$121$	−7.44922	−	7.44922i	−0.677202	−	0.677202i
$122$	26.8301	−	11.1134i	2.42908	−	1.00616i
$123$			9.80670i			0.884240i
$124$	12.0114	+	28.9981i	1.07866	+	2.60410i
$125$	−4.27824	−	1.77211i	−0.382657	−	0.158502i
$126$	−3.86593	+	9.33318i	−0.344405	+	0.831466i
$127$	7.55113	−	7.55113i	0.670055	−	0.670055i	−0.287674	−	0.957728i	$-0.592882\pi$
$127$	7.55113	−	7.55113i	0.670055	−	0.670055i	0.957728	+	0.287674i	$0.0928819\pi$
$128$	14.3183	−	14.3183i	1.26557	−	1.26557i
$129$	0.770425	−	1.85997i	0.0678321	−	0.163761i
$130$	12.1713	+	5.04150i	1.06749	+	0.442169i
$131$	−1.38002	−	3.33167i	−0.120573	−	0.291089i	0.852057	−	0.523449i	$-0.175355\pi$
$131$	−1.38002	−	3.33167i	−0.120573	−	0.291089i	−0.972630	+	0.232360i	$0.925355\pi$
$132$			4.81232i			0.418858i
$133$	0.116424	−	0.0482243i	0.0100952	−	0.00418158i
$134$	−11.4669	−	11.4669i	−0.990585	−	0.990585i
$135$	11.3619			0.977875
$136$	−14.0734	+	3.71304i	−1.20678	+	0.318391i
$137$	−10.0926			−0.862267			−0.431134	−	0.902288i	$-0.641886\pi$
$137$	−10.0926			−0.862267			−0.431134	+	0.902288i	$0.641886\pi$
$138$	0.112979	+	0.112979i	0.00961739	+	0.00961739i
$139$	14.1274	−	5.85176i	1.19827	−	0.496340i	0.307831	−	0.951441i	$-0.400397\pi$
$139$	14.1274	−	5.85176i	1.19827	−	0.496340i	0.890440	+	0.455101i	$0.150397\pi$
$140$		−	41.5382i		−	3.51062i
$141$	−6.85272	−	16.5439i	−0.577103	−	1.39325i
$142$	−18.0970	−	7.49604i	−1.51867	−	0.629053i
$143$	0.505611	−	1.22065i	0.0422813	−	0.102076i
$144$	−0.947946	+	0.947946i	−0.0789955	+	0.0789955i
$145$	12.9681	−	12.9681i	1.07694	−	1.07694i
$146$	6.42531	−	15.5121i	0.531763	−	1.28379i
$147$	−18.0769	−	7.48769i	−1.49096	−	0.617574i
$148$	1.09302	+	2.63878i	0.0898454	+	0.216906i
$149$		−	12.0290i		−	0.985451i	−0.870185	−	0.492725i	$-0.836001\pi$
$149$		−	12.0290i		−	0.985451i	0.870185	−	0.492725i	$-0.163999\pi$
$150$	14.8479	−	6.15020i	1.21233	−	0.502162i
$151$	12.4592	+	12.4592i	1.01391	+	1.01391i	0.999902	+	0.0140123i	$0.00446041\pi$
$151$	12.4592	+	12.4592i	1.01391	+	1.01391i	0.0140123	+	0.999902i	$0.495540\pi$
$152$	0.108795			0.00882445
$153$	−4.19816	+	1.10762i	−0.339401	+	0.0895456i
$154$	−6.54321			−0.527267
$155$	−18.3571	−	18.3571i	−1.47447	−	1.47447i
$156$	12.6270	−	5.23026i	1.01097	−	0.418756i
$157$			11.8763i			0.947828i	0.880571	+	0.473914i	$0.157159\pi$
$157$			11.8763i			0.947828i	−0.880571	+	0.473914i	$0.842841\pi$
$158$	4.94959	+	11.9494i	0.393768	+	0.950640i
$159$	−20.3811	−	8.44214i	−1.61633	−	0.669505i
$160$	−4.51850	+	10.9086i	−0.357219	+	0.862402i
$161$	−0.0978017	+	0.0978017i	−0.00770786	+	0.00770786i
$162$	18.3324	−	18.3324i	1.44033	−	1.44033i
$163$	6.41164	−	15.4791i	0.502198	−	1.21241i	−0.446086	−	0.894990i	$-0.647182\pi$
$163$	6.41164	−	15.4791i	0.502198	−	1.21241i	0.948284	−	0.317424i	$-0.102818\pi$
$164$	−15.7720	−	6.53298i	−1.23159	−	0.510140i
$165$	−1.52320	−	3.67734i	−0.118581	−	0.286281i
$166$		−	30.5231i		−	2.36905i
$167$	0.469647	−	0.194534i	0.0363424	−	0.0150535i	−0.364438	−	0.931228i	$-0.618739\pi$
$167$	0.469647	−	0.194534i	0.0363424	−	0.0150535i	0.400781	+	0.916174i	$0.368739\pi$
$168$	−20.5479	−	20.5479i	−1.58530	−	1.58530i
$169$	9.24762			0.711356
$170$	22.3118	−	16.9846i	1.71123	−	1.30266i
$171$	0.0324541			0.00248183
$172$	2.47813	+	2.47813i	0.188956	+	0.188956i
$173$	4.32712	−	1.79235i	0.328985	−	0.136270i	−0.212077	−	0.977253i	$-0.568023\pi$
$173$	4.32712	−	1.79235i	0.328985	−	0.136270i	0.541061	+	0.840983i	$0.318023\pi$
$174$		−	29.8841i		−	2.26551i
$175$	5.32401	+	12.8533i	0.402458	+	0.971619i
$176$	−0.802215	−	0.332288i	−0.0604692	−	0.0250472i
$177$	−8.18048	+	19.7494i	−0.614882	+	1.48446i
$178$	−2.54460	+	2.54460i	−0.190726	+	0.190726i
$179$	3.90917	−	3.90917i	0.292185	−	0.292185i	−0.545758	−	0.837943i	$-0.683758\pi$
$179$	3.90917	−	3.90917i	0.292185	−	0.292185i	0.837943	+	0.545758i	$0.183758\pi$
$180$	4.09383	−	9.88339i	0.305136	−	0.736664i
$181$	−6.34698	−	2.62901i	−0.471768	−	0.195413i	0.134116	−	0.990966i	$-0.457180\pi$
$181$	−6.34698	−	2.62901i	−0.471768	−	0.195413i	−0.605884	+	0.795553i	$0.707180\pi$
$182$	7.11148	+	17.1686i	0.527138	+	1.27262i
$183$			24.9192i			1.84208i
$184$	−0.110321	+	0.0456966i	−0.00813300	+	0.00336880i
$185$	−1.67046	−	1.67046i	−0.122815	−	0.122815i
$186$	−42.3027			−3.10179
$187$	−1.70338	−	2.23764i	−0.124563	−	0.163633i
$188$	31.1725			2.27349
$189$	11.3328	+	11.3328i	0.824336	+	0.824336i
$190$	−0.193644	+	0.0802101i	−0.0140484	+	0.00581905i
$191$		−	15.0054i		−	1.08575i	−0.839813	−	0.542875i	$-0.817336\pi$
$191$		−	15.0054i		−	1.08575i	0.839813	−	0.542875i	$-0.182664\pi$
$192$	9.32443	+	22.5112i	0.672933	+	1.62460i
$193$	−15.8550	−	6.56735i	−1.14127	−	0.472729i	−0.269671	−	0.962952i	$-0.586915\pi$
$193$	−15.8550	−	6.56735i	−1.14127	−	0.472729i	−0.871597	+	0.490224i	$0.836915\pi$
$194$	−12.4972	+	30.1709i	−0.897247	+	2.16615i
$195$	−7.99342	+	7.99342i	−0.572421	+	0.572421i
$196$	24.0847	−	24.0847i	1.72034	−	1.72034i
$197$	7.48845	−	18.0787i	0.533530	−	1.28806i	−0.395641	−	0.918405i	$-0.629477\pi$
$197$	7.48845	−	18.0787i	0.533530	−	1.28806i	0.929171	−	0.369650i	$-0.120523\pi$
$198$	−1.55686	−	0.644873i	−0.110641	−	0.0458291i
$199$	0.930285	+	2.24591i	0.0659462	+	0.159208i	0.953417	−	0.301656i	$-0.0975395\pi$
$199$	0.930285	+	2.24591i	0.0659462	+	0.159208i	−0.887471	+	0.460864i	$0.847539\pi$
$200$			12.0111i			0.849313i
$201$	12.8559	−	5.32508i	0.906784	−	0.375602i
$202$	−12.7428	−	12.7428i	−0.896581	−	0.896581i
$203$	25.8696			1.81569
$204$	3.90793	−	28.8271i	0.273610	−	2.01830i
$205$	14.1200			0.986186
$206$	−6.75040	−	6.75040i	−0.470323	−	0.470323i
$207$	−0.0329094	+	0.0136315i	−0.00228736	+	0.000947457i
$208$			2.46607i			0.170991i
$209$	0.00804426	+	0.0194206i	0.000556433	+	0.00134335i
$210$	51.7222	+	21.4240i	3.56917	+	1.47840i
$211$	2.07252	−	5.00351i	0.142678	−	0.344456i	−0.836345	−	0.548203i	$-0.815312\pi$
$211$	2.07252	−	5.00351i	0.142678	−	0.344456i	0.979024	+	0.203747i	$0.0653121\pi$
$212$	27.1548	−	27.1548i	1.86500	−	1.86500i
$213$	11.8851	−	11.8851i	0.814357	−	0.814357i
$214$	−4.78461	+	11.5511i	−0.327069	+	0.789616i
$215$	−2.67805	−	1.10929i	−0.182642	−	0.0756527i
$216$	5.29509	+	12.7835i	0.360285	+	0.869805i
$217$		−	36.6200i		−	2.48593i
$218$	21.4957	−	8.90379i	1.45587	−	0.603041i
$219$	10.1875	+	10.1875i	0.688407	+	0.688407i
$220$	6.92895			0.467150
$221$	−4.02000	+	6.90145i	−0.270414	+	0.464242i
$222$	−3.84947			−0.258360
$223$	−18.7454	−	18.7454i	−1.25528	−	1.25528i	−0.953319	−	0.301964i	$-0.902358\pi$
$223$	−18.7454	−	18.7454i	−1.25528	−	1.25528i	−0.301964	−	0.953319i	$-0.597642\pi$
$224$	−15.3876	+	6.37374i	−1.02813	+	0.425863i
$225$			3.58297i			0.238865i
$226$	−5.76510	−	13.9182i	−0.383489	−	0.925824i
$227$	7.27764	+	3.01450i	0.483034	+	0.200079i	0.610893	−	0.791713i	$-0.290811\pi$
$227$	7.27764	+	3.01450i	0.483034	+	0.200079i	−0.127859	+	0.991792i	$0.540811\pi$
$228$	−0.0832133	+	0.200895i	−0.00551093	+	0.0133046i
$229$	6.07825	−	6.07825i	0.401662	−	0.401662i	−0.477156	−	0.878818i	$-0.658332\pi$
$229$	6.07825	−	6.07825i	0.401662	−	0.401662i	0.878818	+	0.477156i	$0.158332\pi$
$230$	0.162671	−	0.162671i	0.0107262	−	0.0107262i
$231$	2.14861	−	5.18721i	0.141368	−	0.341293i
$232$	20.6343	+	8.54699i	1.35470	+	0.561137i
$233$	0.810268	+	1.95616i	0.0530824	+	0.128152i	0.948196	−	0.317686i	$-0.102906\pi$
$233$	0.810268	+	1.95616i	0.0530824	+	0.128152i	−0.895114	+	0.445838i	$0.852906\pi$
$234$			4.78590i			0.312864i
$235$	−23.8206	+	9.86680i	−1.55388	+	0.643639i
$236$	−26.3132	−	26.3132i	−1.71284	−	1.71284i
$237$	−11.0983			−0.720913
$238$	39.1956	+	5.31353i	2.54067	+	0.344425i
$239$	24.0619			1.55644			0.778219	−	0.627993i	$-0.216123\pi$
$239$	24.0619			1.55644			0.778219	+	0.627993i	$0.216123\pi$
$240$	5.25328	+	5.25328i	0.339098	+	0.339098i
$241$	−11.2934	+	4.67786i	−0.727469	+	0.301327i	−0.715511	−	0.698601i	$-0.753806\pi$
$241$	−11.2934	+	4.67786i	−0.727469	+	0.301327i	−0.0119574	+	0.999929i	$0.503806\pi$
$242$			24.7166i			1.58884i
$243$	4.01343	+	9.68927i	0.257462	+	0.621567i
$244$	−40.0773	−	16.6006i	−2.56569	−	1.06274i
$245$	−10.7810	+	26.0277i	−0.688775	+	1.66285i
$246$	16.2694	−	16.2694i	1.03730	−	1.03730i
$247$	0.0422144	−	0.0422144i	0.00268604	−	0.00268604i
$248$	12.0988	−	29.2090i	0.768272	−	1.85477i
$249$	24.1975	+	10.0229i	1.53346	+	0.635178i
$250$	4.15770	+	10.0376i	0.262956	+	0.634832i
$251$		−	20.4076i		−	1.28812i	−0.764976	−	0.644059i	$-0.777249\pi$
$251$		−	20.4076i		−	1.28812i	0.764976	−	0.644059i	$-0.222751\pi$
$252$	13.9414	−	5.77471i	0.878225	−	0.363773i
$253$	−0.0163142	−	0.0163142i	−0.00102567	−	0.00102567i
$254$	−25.0548			−1.57208
$255$	6.13815	+	23.2652i	0.384386	+	1.45692i
$256$	−23.3025			−1.45641
$257$	7.67065	+	7.67065i	0.478482	+	0.478482i	0.904646	−	0.426164i	$-0.140135\pi$
$257$	7.67065	+	7.67065i	0.478482	+	0.478482i	−0.426164	+	0.904646i	$0.640135\pi$
$258$	−4.36385	+	1.80756i	−0.271681	+	0.112534i
$259$		−	3.33236i		−	0.207063i
$260$	−7.53072	−	18.1808i	−0.467035	−	1.12752i
$261$	6.15530	+	2.54961i	0.381003	+	0.157817i
$262$	−3.23779	+	7.81672i	−0.200031	+	0.482919i
$263$	−11.2711	+	11.2711i	−0.695006	+	0.695006i	−0.963329	−	0.268323i	$-0.913531\pi$
$263$	−11.2711	+	11.2711i	−0.695006	+	0.695006i	0.268323	+	0.963329i	$0.413531\pi$
$264$	3.42757	−	3.42757i	0.210952	−	0.210952i
$265$	−12.1553	+	29.3455i	−0.746694	+	1.80268i
$266$	−0.273152	−	0.113143i	−0.0167480	−	0.00693727i
$267$	−1.18169	−	2.85285i	−0.0723181	−	0.174591i
$268$			24.2234i			1.47968i
$269$	11.3430	−	4.69841i	0.691593	−	0.286467i	−0.00907077	−	0.999959i	$-0.502887\pi$
$269$	11.3430	−	4.69841i	0.691593	−	0.286467i	0.700664	+	0.713492i	$0.252887\pi$
$270$	−18.8494	−	18.8494i	−1.14714	−	1.14714i
$271$	0.280813			0.0170582			0.00852909	−	0.999964i	$-0.497285\pi$
$271$	0.280813			0.0170582			0.00852909	+	0.999964i	$0.497285\pi$
$272$	4.53564	+	2.64195i	0.275013	+	0.160192i
$273$	−15.9459			−0.965087
$274$	16.7437	+	16.7437i	1.01152	+	1.01152i
$275$	−2.14405	+	0.888095i	−0.129291	+	0.0535541i
$276$		−	0.238665i		−	0.0143659i
$277$	8.11939	+	19.6019i	0.487847	+	1.17777i	0.955801	+	0.294014i	$0.0949913\pi$
$277$	8.11939	+	19.6019i	0.487847	+	1.17777i	−0.467954	+	0.883753i	$0.655009\pi$
$278$	−33.1456	−	13.7293i	−1.98794	−	0.823431i
$279$	3.60912	−	8.71318i	0.216072	−	0.521645i
$280$	−29.5855	+	29.5855i	−1.76807	+	1.76807i
$281$	−9.83817	+	9.83817i	−0.586896	+	0.586896i	−0.936789	−	0.349894i	$-0.886218\pi$
$281$	−9.83817	+	9.83817i	−0.586896	+	0.586896i	0.349894	+	0.936789i	$0.386218\pi$
$282$	−16.0778	+	38.8152i	−0.957419	+	2.31141i
$283$	−17.4431	−	7.22515i	−1.03688	−	0.429491i	−0.201690	−	0.979449i	$-0.564643\pi$
$283$	−17.4431	−	7.22515i	−1.03688	−	0.429491i	−0.835192	+	0.549959i	$0.814643\pi$
$284$	11.1972	+	27.0323i	0.664429	+	1.60407i
$285$		−	0.179853i		−	0.0106536i
$286$	−2.86389	+	1.18626i	−0.169345	+	0.0701451i
$287$	14.0838	+	14.0838i	0.831342	+	0.831342i
$288$	−4.28942			−0.252756
$289$	8.38658	+	14.7873i	0.493328	+	0.869843i
$290$	−43.0282			−2.52670
$291$	−19.8146	−	19.8146i	−1.16155	−	1.16155i
$292$	−23.1711	+	9.59778i	−1.35598	+	0.561667i
$293$		−	10.3951i		−	0.607286i	−0.952786	−	0.303643i	$-0.901797\pi$
$293$		−	10.3951i		−	0.607286i	0.952786	−	0.303643i	$-0.0982030\pi$
$294$	17.5675	+	42.4118i	1.02456	+	2.47351i
$295$	28.4359	+	11.7785i	1.65560	+	0.685774i
$296$	1.10097	−	2.65797i	0.0639924	−	0.154491i
$297$	−1.89041	+	1.89041i	−0.109693	+	0.109693i
$298$	−19.9561	+	19.9561i	−1.15603	+	1.15603i
$299$	−0.0250756	+	0.0605377i	−0.00145016	+	0.00350099i
$300$	−22.1790	−	9.18683i	−1.28050	−	0.530402i
$301$	−1.56474	−	3.77763i	−0.0901904	−	0.217739i
$302$		−	41.3398i		−	2.37884i
$303$	14.2864	−	5.91762i	0.820732	−	0.339958i
$304$	−0.0277433	−	0.0277433i	−0.00159119	−	0.00159119i
$305$	35.8796			2.05446
$306$	8.80233	+	5.12724i	0.503196	+	0.293105i
$307$	−17.0705			−0.974264			−0.487132	−	0.873328i	$-0.661957\pi$
$307$	−17.0705			−0.974264			−0.487132	+	0.873328i	$0.661957\pi$
$308$	6.91118	+	6.91118i	0.393801	+	0.393801i
$309$	7.56811	−	3.13482i	0.430535	−	0.178333i
$310$			60.9090i			3.45940i
$311$	−1.25923	−	3.04006i	−0.0714045	−	0.172386i	0.884148	−	0.467207i	$-0.154740\pi$
$311$	−1.25923	−	3.04006i	−0.0714045	−	0.172386i	−0.955552	+	0.294822i	$0.904740\pi$
$312$	−12.7188	−	5.26830i	−0.720061	−	0.298259i
$313$	13.4838	−	32.5528i	0.762151	−	1.83999i	0.296468	−	0.955043i	$-0.404191\pi$
$313$	13.4838	−	32.5528i	0.762151	−	1.83999i	0.465682	−	0.884952i	$-0.345809\pi$
$314$	19.7028	−	19.7028i	1.11189	−	1.11189i
$315$	−8.82551	+	8.82551i	−0.497261	+	0.497261i
$316$	7.39342	−	17.8493i	0.415912	−	1.00410i
$317$	26.1577	+	10.8349i	1.46916	+	0.608546i	0.966667	−	0.256035i	$-0.0824163\pi$
$317$	26.1577	+	10.8349i	1.46916	+	0.608546i	0.502493	+	0.864581i	$0.332416\pi$
$318$	19.8069	+	47.8180i	1.11071	+	2.68150i
$319$			4.31529i			0.241610i
$320$	32.4124	−	13.4256i	1.81191	−	0.750517i
$321$	−7.58612	−	7.58612i	−0.423416	−	0.423416i
$322$	0.324508			0.0180841
$323$	−0.0324164	−	0.122867i	−0.00180370	−	0.00683649i
$324$	−38.7267			−2.15149
$325$	4.66052	+	4.66052i	0.258519	+	0.258519i
$326$	−36.3168	+	15.0429i	−2.01140	+	0.833151i
$327$			19.9647i			1.10405i
$328$	6.58049	+	15.8867i	0.363347	+	0.877197i
$329$	−33.6010	−	13.9180i	−1.85248	−	0.767323i
$330$	−3.57373	+	8.62774i	−0.196727	+	0.474941i
$331$	17.9091	−	17.9091i	0.984375	−	0.984375i	−0.0155049	−	0.999880i	$-0.504936\pi$
$331$	17.9091	−	17.9091i	0.984375	−	0.984375i	0.999880	+	0.0155049i	$0.00493556\pi$
$332$	−32.2396	+	32.2396i	−1.76938	+	1.76938i
$333$	0.328424	−	0.792885i	0.0179975	−	0.0434498i
$334$	−1.10188	−	0.456414i	−0.0602922	−	0.0249739i
$335$	−7.66724	−	18.5104i	−0.418906	−	1.01133i
$336$			10.4796i			0.571711i
$337$	2.42287	−	1.00359i	0.131982	−	0.0546689i	−0.315715	−	0.948854i	$-0.602244\pi$
$337$	2.42287	−	1.00359i	0.131982	−	0.0546689i	0.447697	+	0.894185i	$0.352244\pi$
$338$	−15.3419	−	15.3419i	−0.834488	−	0.834488i
$339$	12.9269			0.702094
$340$	−41.5062	−	5.62678i	−2.25099	−	0.305155i
$341$	6.10855			0.330797
$342$	−0.0538416	−	0.0538416i	−0.00291142	−	0.00291142i
$343$	−10.2710	+	4.25439i	−0.554582	+	0.229716i
$344$		−	3.53010i		−	0.190330i
$345$	0.0755426	+	0.182376i	0.00406708	+	0.00981879i
$346$	−10.1522	−	4.20520i	−0.545788	−	0.226073i
$347$	−0.700675	+	1.69158i	−0.0376142	+	0.0908087i	−0.941570	−	0.336817i	$-0.890650\pi$
$347$	−0.700675	+	1.69158i	−0.0376142	+	0.0908087i	0.903956	+	0.427625i	$0.140650\pi$
$348$	−31.5647	+	31.5647i	−1.69205	+	1.69205i
$349$	−16.3804	+	16.3804i	−0.876823	+	0.876823i	−0.993205	−	0.116381i	$-0.962870\pi$
$349$	−16.3804	+	16.3804i	−0.876823	+	0.876823i	0.116381	+	0.993205i	$0.462870\pi$
$350$	12.4912	−	30.1563i	0.667680	−	1.61192i
$351$	7.01480	+	2.90562i	0.374422	+	0.155091i
$352$	−1.06320	−	2.56679i	−0.0566687	−	0.136810i
$353$			22.8295i			1.21509i	0.794284	+	0.607546i	$0.207846\pi$
$353$			22.8295i			1.21509i	−0.794284	+	0.607546i	$0.792154\pi$
$354$	46.3359	−	19.1930i	2.46273	−	1.02009i
$355$	−17.1127	−	17.1127i	−0.908246	−	0.908246i
$356$	5.37541			0.284896
$357$	−17.0831	+	29.3280i	−0.904135	+	1.55220i
$358$	−12.9707			−0.685521
$359$	20.9198	+	20.9198i	1.10410	+	1.10410i	0.993910	+	0.110193i	$0.0351470\pi$
$359$	20.9198	+	20.9198i	1.10410	+	1.10410i	0.110193	+	0.993910i	$0.464853\pi$
$360$	−9.95528	+	4.12361i	−0.524689	+	0.217333i
$361$		−	18.9991i		−	0.999950i
$362$	6.16815	+	14.8912i	0.324191	+	0.782666i
$363$	−19.5944	−	8.11627i	−1.02844	−	0.425994i
$364$	10.6227	−	25.6456i	0.556783	−	1.34419i
$365$	14.6683	−	14.6683i	0.767774	−	0.767774i
$366$	41.3412	−	41.3412i	2.16094	−	2.16094i
$367$	−2.05262	+	4.95545i	−0.107146	+	0.258672i	−0.968355	−	0.249579i	$-0.919708\pi$
$367$	−2.05262	+	4.95545i	−0.107146	+	0.258672i	0.861209	+	0.508251i	$0.169708\pi$
$368$	0.0397855	+	0.0164797i	0.00207396	+	0.000859062i
$369$	1.96299	+	4.73909i	0.102189	+	0.246707i
$370$			5.54261i			0.288147i
$371$	−41.3944	+	17.1461i	−2.14909	+	0.890182i
$372$	44.6817	+	44.6817i	2.31664	+	2.31664i
$373$	8.60408			0.445502			0.222751	−	0.974875i	$-0.428496\pi$
$373$	8.60408			0.445502			0.222751	+	0.974875i	$0.428496\pi$
$374$	−0.886346	+	6.53818i	−0.0458319	+	0.338081i
$375$	−9.32268			−0.481421
$376$	−22.2026	−	22.2026i	−1.14501	−	1.14501i
$377$	11.3228	−	4.69007i	0.583155	−	0.241551i
$378$		−	37.6022i		−	1.93405i
$379$	10.7893	+	26.0477i	0.554209	+	1.33798i	0.914291	+	0.405059i	$0.132749\pi$
$379$	10.7893	+	26.0477i	0.554209	+	1.33798i	−0.360081	+	0.932921i	$0.617251\pi$
$380$	0.289255	+	0.119813i	0.0148385	+	0.00614630i
$381$	8.22730	−	19.8625i	0.421498	−	1.01759i
$382$	−24.8940	+	24.8940i	−1.27369	+	1.27369i
$383$	−2.94810	+	2.94810i	−0.150641	+	0.150641i	−0.778404	−	0.627763i	$-0.783971\pi$
$383$	−2.94810	+	2.94810i	−0.150641	+	0.150641i	0.627763	+	0.778404i	$0.283971\pi$
$384$	15.6005	−	37.6629i	0.796109	−	1.92198i
$385$	−7.46873	−	3.09365i	−0.380642	−	0.157667i
$386$	15.4083	+	37.1988i	0.784260	+	1.89337i
$387$		−	1.05305i		−	0.0535293i
$388$	45.0676	−	18.6676i	2.28796	−	0.947705i
$389$	14.2202	+	14.2202i	0.720995	+	0.720995i	0.968808	−	0.247813i	$-0.0797118\pi$
$389$	14.2202	+	14.2202i	0.720995	+	0.720995i	−0.247813	+	0.968808i	$0.579712\pi$
$390$	26.5223			1.34301
$391$	0.0844783	+	0.110975i	0.00427225	+	0.00561224i
$392$	−34.3087			−1.73285
$393$	−5.13360	−	5.13360i	−0.258956	−	0.258956i
$394$	−42.4161	+	17.5693i	−2.13689	+	0.885130i
$395$			15.9797i			0.804028i
$396$	0.963275	+	2.32555i	0.0484064	+	0.116863i
$397$	5.77524	+	2.39218i	0.289851	+	0.120060i	0.522871	−	0.852412i	$-0.324861\pi$
$397$	5.77524	+	2.39218i	0.289851	+	0.120060i	−0.233020	+	0.972472i	$0.574861\pi$
$398$	2.18263	−	5.26932i	0.109405	−	0.264127i
$399$	0.179392	−	0.179392i	0.00898081	−	0.00898081i
$400$	3.06289	−	3.06289i	0.153145	−	0.153145i
$401$	6.01706	−	14.5265i	0.300478	−	0.725417i	−0.699465	−	0.714667i	$-0.746578\pi$
$401$	6.01706	−	14.5265i	0.300478	−	0.725417i	0.999942	−	0.0107500i	$-0.00342189\pi$
$402$	−30.1624	−	12.4937i	−1.50436	−	0.623127i
$403$	−6.63907	−	16.0281i	−0.330716	−	0.798418i
$404$			26.9188i			1.33926i
$405$	29.5931	−	12.2579i	1.47049	−	0.609098i
$406$	−42.9179	−	42.9179i	−2.12998	−	2.12998i
$407$	0.555868			0.0275533
$408$	−23.3155	+	17.7486i	−1.15429	+	0.878689i
$409$	21.9060			1.08318			0.541591	−	0.840642i	$-0.317822\pi$
$409$	21.9060			1.08318			0.541591	+	0.840642i	$0.317822\pi$
$410$	−23.4252	−	23.4252i	−1.15689	−	1.15689i
$411$	−18.7719	+	7.77558i	−0.925950	+	0.383541i
$412$			14.2601i			0.702542i
$413$	16.6147	+	40.1114i	0.817555	+	1.97375i
$414$	0.0772118	+	0.0319822i	0.00379475	+	0.00157184i
$415$	14.4314	−	34.8405i	0.708410	−	1.71025i
$416$	−5.57942	+	5.57942i	−0.273554	+	0.273554i
$417$	21.7682	−	21.7682i	1.06599	−	1.06599i
$418$	0.0188734	−	0.0455643i	0.000923126	−	0.00222862i
$419$	17.0503	+	7.06247i	0.832962	+	0.345024i	0.758075	−	0.652168i	$-0.226140\pi$
$419$	17.0503	+	7.06247i	0.832962	+	0.345024i	0.0748877	+	0.997192i	$0.476140\pi$
$420$	−32.0020	−	77.2598i	−1.56154	−	3.76989i
$421$		−	7.49933i		−	0.365495i	−0.983160	−	0.182747i	$-0.941501\pi$
$421$		−	7.49933i		−	0.365495i	0.983160	−	0.182747i	$-0.0584991\pi$
$422$	−11.7392	+	4.86253i	−0.571455	+	0.236704i
$423$	−6.62316	−	6.62316i	−0.322029	−	0.322029i
$424$	−38.6820			−1.87856
$425$	13.5646	−	3.57881i	0.657981	−	0.173598i
$426$	−39.4351			−1.91064
$427$	35.7876	+	35.7876i	1.73188	+	1.73188i
$428$	17.2544	−	7.14699i	0.834021	−	0.345463i
$429$		−	2.65992i		−	0.128422i
$430$	2.60260	+	6.28322i	0.125508	+	0.303004i
$431$	−13.6760	−	5.66479i	−0.658750	−	0.272863i	0.0281623	−	0.999603i	$-0.491034\pi$
$431$	−13.6760	−	5.66479i	−0.658750	−	0.272863i	−0.686913	+	0.726740i	$0.741034\pi$
$432$	1.90958	−	4.61013i	0.0918746	−	0.221805i
$433$	−24.0425	+	24.0425i	−1.15541	+	1.15541i	−0.169959	+	0.985451i	$0.554364\pi$
$433$	−24.0425	+	24.0425i	−1.15541	+	1.15541i	−0.985451	+	0.169959i	$0.945636\pi$
$434$	−60.7528	+	60.7528i	−2.91623	+	2.91623i
$435$	14.1293	−	34.1111i	0.677448	−	1.63550i
$436$	−32.1090	−	13.3000i	−1.53774	−	0.636954i
$437$	−0.000398951	0	0.000963153i	−1.90844e−5	0	4.60739e-5i
$438$		−	33.8022i		−	1.61513i
$439$	−30.4748	+	12.6231i	−1.45448	+	0.602466i	−0.963261	−	0.268568i	$-0.913450\pi$
$439$	−30.4748	+	12.6231i	−1.45448	+	0.602466i	−0.491222	+	0.871034i	$0.663450\pi$
$440$	−4.93514	−	4.93514i	−0.235274	−	0.235274i
$441$	−10.2345			−0.487355
$442$	18.1188	−	4.78035i	0.861822	−	0.227378i
$443$	2.58523			0.122828			0.0614141	−	0.998112i	$-0.480439\pi$
$443$	2.58523			0.122828			0.0614141	+	0.998112i	$0.480439\pi$
$444$	4.06596	+	4.06596i	0.192962	+	0.192962i
$445$	−4.10763	+	1.70144i	−0.194720	+	0.0806558i
$446$			62.1974i			2.94513i
$447$	−9.26741	−	22.3735i	−0.438334	−	1.05823i
$448$	45.7205	+	18.9381i	2.16009	+	0.894739i
$449$	4.57918	−	11.0551i	0.216105	−	0.521723i	−0.778235	−	0.627974i	$-0.783885\pi$
$449$	4.57918	−	11.0551i	0.216105	−	0.521723i	0.994339	+	0.106251i	$0.0338846\pi$
$450$	5.94417	−	5.94417i	0.280211	−	0.280211i
$451$	−2.34931	+	2.34931i	−0.110625	+	0.110625i
$452$	−8.61159	+	20.7902i	−0.405055	+	0.977890i
$453$	32.7726	+	13.5749i	1.53979	+	0.637802i
$454$	−7.07258	−	17.0747i	−0.331933	−	0.801357i
$455$			22.9594i			1.07635i
$456$	0.202356	−	0.0838185i	0.00947618	−	0.00392516i
$457$	−2.73739	−	2.73739i	−0.128050	−	0.128050i	0.640177	−	0.768227i	$-0.278861\pi$
$457$	−2.73739	−	2.73739i	−0.128050	−	0.128050i	−0.768227	+	0.640177i	$0.778861\pi$
$458$	−20.1677			−0.942376
$459$	12.8592	−	9.78890i	0.600215	−	0.456907i
$460$	−0.343638			−0.0160222
$461$	−5.15755	−	5.15755i	−0.240211	−	0.240211i	0.576726	−	0.816937i	$-0.304330\pi$
$461$	−5.15755	−	5.15755i	−0.240211	−	0.240211i	−0.816937	+	0.576726i	$0.804330\pi$
$462$	−12.1702	+	5.04106i	−0.566208	+	0.234531i
$463$			39.1180i			1.81797i	0.416831	+	0.908984i	$0.363141\pi$
$463$			39.1180i			1.81797i	−0.416831	+	0.908984i	$0.636859\pi$
$464$	−3.08232	−	7.44137i	−0.143093	−	0.345457i
$465$	−48.2863	−	20.0008i	−2.23922	−	0.927517i
$466$	1.90104	−	4.58952i	0.0880641	−	0.212605i
$467$	−14.6055	+	14.6055i	−0.675860	+	0.675860i	−0.959061	−	0.283201i	$-0.908604\pi$
$467$	−14.6055	+	14.6055i	−0.675860	+	0.675860i	0.283201	+	0.959061i	$0.408604\pi$
$468$	5.05505	−	5.05505i	0.233670	−	0.233670i
$469$	10.8153	−	26.1105i	0.499405	−	1.20567i
$470$	55.8876	+	23.1494i	2.57790	+	1.06780i
$471$	9.14977	+	22.0895i	0.421599	+	1.01783i
$472$			37.4831i			1.72530i
$473$	0.630143	−	0.261014i	0.0289740	−	0.0120014i
$474$	18.4122	+	18.4122i	0.845699	+	0.845699i
$475$	−0.104862			−0.00481140
$476$	−35.7875	−	47.0122i	−1.64032	−	2.15480i
$477$	−11.5390			−0.528336
$478$	−39.9189	−	39.9189i	−1.82585	−	1.82585i
$479$	−33.5928	+	13.9146i	−1.53489	+	0.635774i	−0.980507	−	0.196485i	$-0.937047\pi$
$479$	−33.5928	+	13.9146i	−1.53489	+	0.635774i	−0.554387	+	0.832259i	$0.687047\pi$
$480$			23.7709i			1.08499i
$481$	−0.604144	−	1.45853i	−0.0275466	−	0.0665033i
$482$	26.4964	+	10.9751i	1.20688	+	0.499904i
$483$	−0.106559	+	0.257257i	−0.00484862	+	0.0117056i
$484$	26.1066	−	26.1066i	1.18666	−	1.18666i
$485$	−28.5298	+	28.5298i	−1.29547	+	1.29547i
$486$	9.41627	−	22.7329i	0.427131	−	1.03118i
$487$	−2.17583	−	0.901258i	−0.0985962	−	0.0408399i	0.332840	−	0.942983i	$-0.391993\pi$
$487$	−2.17583	−	0.901258i	−0.0985962	−	0.0408399i	−0.431436	+	0.902143i	$0.641993\pi$
$488$	16.7213	+	40.3688i	0.756939	+	1.82741i
$489$		−	33.7303i		−	1.52534i
$490$	61.0660	−	25.2944i	2.75868	−	1.14268i
$491$	20.8897	+	20.8897i	0.942737	+	0.942737i	0.998447	−	0.0557099i	$-0.0177422\pi$
$491$	20.8897	+	20.8897i	0.942737	+	0.942737i	−0.0557099	+	0.998447i	$0.517742\pi$
$492$	−34.3686			−1.54946
$493$	3.50431	−	25.8498i	0.157826	−	1.16421i
$494$	−0.140068			−0.00630196
$495$	−1.47218	−	1.47218i	−0.0661694	−	0.0661694i
$496$	−10.5337	+	4.36320i	−0.472977	+	0.195914i
$497$		−	34.1376i		−	1.53128i
$498$	−23.5157	−	56.7720i	−1.05377	−	2.54402i
$499$	−7.73853	−	3.20540i	−0.346424	−	0.143494i	0.202686	−	0.979244i	$-0.435033\pi$
$499$	−7.73853	−	3.20540i	−0.346424	−	0.143494i	−0.549110	+	0.835750i	$0.685033\pi$
$500$	6.21054	−	14.9936i	0.277744	−	0.670532i
$501$	0.723655	−	0.723655i	0.0323305	−	0.0323305i
$502$	−33.8564	+	33.8564i	−1.51108	+	1.51108i
$503$	−7.52014	+	18.1552i	−0.335306	+	0.809501i	0.662847	+	0.748755i	$0.269348\pi$
$503$	−7.52014	+	18.1552i	−0.335306	+	0.809501i	−0.998153	+	0.0607464i	$0.980652\pi$
$504$	−14.0428	−	5.81672i	−0.625516	−	0.259097i
$505$	−8.52040	−	20.5701i	−0.379153	−	0.915356i
$506$			0.0541308i			0.00240641i
$507$	17.2003	−	7.12460i	0.763892	−	0.316415i
$508$	26.4638	+	26.4638i	1.17414	+	1.17414i
$509$	7.62322			0.337893			0.168947	−	0.985625i	$-0.445963\pi$
$509$	7.62322			0.337893			0.168947	+	0.985625i	$0.445963\pi$
$510$	28.4139	−	48.7803i	1.25819	−	2.16003i
$511$	29.2614			1.29445
$512$	10.0224	+	10.0224i	0.442930	+	0.442930i
$513$	−0.111605	+	0.0462284i	−0.00492749	+	0.00204103i
$514$		−	25.4513i		−	1.12261i
$515$	−4.51362	−	10.8968i	−0.198894	−	0.480172i
$516$	6.51847	+	2.70004i	0.286960	+	0.118863i
$517$	2.32165	−	5.60495i	0.102106	−	0.246506i
$518$	−5.52840	+	5.52840i	−0.242904	+	0.242904i
$519$	6.66744	−	6.66744i	0.292668	−	0.292668i
$520$	−7.58549	+	18.3130i	−0.332646	+	0.803078i
$521$	21.1493	+	8.76034i	0.926569	+	0.383798i	0.794376	−	0.607426i	$-0.207798\pi$
$521$	21.1493	+	8.76034i	0.926569	+	0.383798i	0.132193	+	0.991224i	$0.457798\pi$
$522$	−5.98186	−	14.4415i	−0.261819	−	0.632087i
$523$			25.7722i			1.12694i	0.826136	+	0.563470i	$0.190534\pi$
$523$			25.7722i			1.12694i	−0.826136	+	0.563470i	$0.809466\pi$
$524$	11.6762	−	4.83644i	0.510077	−	0.211281i
$525$	19.8050	+	19.8050i	0.864362	+	0.864362i
$526$	37.3977			1.63062
$527$	−36.5918	−	4.96056i	−1.59397	−	0.216085i
$528$	−1.74810			−0.0760762
$529$	−16.2626	−	16.2626i	−0.707072	−	0.707072i
$530$	68.8501	−	28.5186i	2.99066	−	1.23877i
$531$			11.1814i			0.485231i
$532$	0.169007	+	0.408020i	0.00732740	+	0.0176899i
$533$	8.71767	+	3.61098i	0.377604	+	0.156409i
$534$	−2.77246	+	6.69332i	−0.119976	+	0.289648i
$535$	−10.9228	+	10.9228i	−0.472233	+	0.472233i
$536$	17.2531	−	17.2531i	0.745222	−	0.745222i
$537$	4.25922	−	10.2827i	0.183799	−	0.443729i
$538$	−26.6128	−	11.0234i	−1.14736	−	0.475251i
$539$	−2.53677	−	6.12430i	−0.109266	−	0.263792i
$540$			39.8190i			1.71353i
$541$	30.7004	−	12.7165i	1.31991	−	0.546726i	0.392152	−	0.919901i	$-0.371731\pi$
$541$	30.7004	−	12.7165i	1.31991	−	0.546726i	0.927761	+	0.373175i	$0.121731\pi$
$542$	−0.465871	−	0.465871i	−0.0200109	−	0.0200109i
$543$	−13.8307			−0.593530
$544$	4.28444	+	16.2391i	0.183694	+	0.696247i
$545$	28.7459			1.23134
$546$	26.4543	+	26.4543i	1.13214	+	1.13214i
$547$	−14.3086	+	5.92682i	−0.611792	+	0.253412i	−0.666994	−	0.745063i	$-0.732420\pi$
$547$	−14.3086	+	5.92682i	−0.611792	+	0.253412i	0.0552026	+	0.998475i	$0.482420\pi$
$548$		−	35.3706i		−	1.51096i
$549$	4.98805	+	12.0422i	0.212885	+	0.513949i
$550$	5.03035	+	2.08364i	0.214495	+	0.0888467i
$551$	−0.0746189	+	0.180146i	−0.00317887	+	0.00767447i
$552$	−0.169989	+	0.169989i	−0.00723520	+	0.00723520i
$553$	−15.9388	+	15.9388i	−0.677786	+	0.677786i
$554$	19.0496	−	45.9899i	0.809342	−	1.95392i
$555$	−4.39397	−	1.82004i	−0.186514	−	0.0772565i
$556$	20.5081	+	49.5110i	0.869739	+	2.09973i
$557$			23.1606i			0.981344i	0.871344	+	0.490672i	$0.163249\pi$
$557$			23.1606i			0.981344i	−0.871344	+	0.490672i	$0.836751\pi$
$558$	−20.4428	+	8.46768i	−0.865412	+	0.358465i
$559$	−1.36974	−	1.36974i	−0.0579338	−	0.0579338i
$560$	15.0889			0.637624
$561$	−4.89217	−	2.84962i	−0.206548	−	0.120311i
$562$	32.6432			1.37697
$563$	28.0528	+	28.0528i	1.18229	+	1.18229i	0.979151	+	0.203136i	$0.0651133\pi$
$563$	28.0528	+	28.0528i	1.18229	+	1.18229i	0.203136	+	0.979151i	$0.434887\pi$
$564$	57.9800	−	24.0161i	2.44140	−	1.01126i
$565$		−	18.6126i		−	0.783040i
$566$	16.9516	+	40.9247i	0.712528	+	1.72019i
$567$	41.7437	+	17.2908i	1.75307	+	0.726145i
$568$	11.2786	−	27.2290i	0.473240	−	1.14250i
$569$	0.130069	−	0.130069i	0.00545276	−	0.00545276i	−0.704375	−	0.709828i	$-0.748773\pi$
$569$	0.130069	−	0.130069i	0.00545276	−	0.00545276i	0.709828	+	0.704375i	$0.248773\pi$
$570$	−0.298377	+	0.298377i	−0.0124976	+	0.0124976i
$571$	−7.54580	+	18.2172i	−0.315782	+	0.762365i	0.683687	+	0.729775i	$0.260375\pi$
$571$	−7.54580	+	18.2172i	−0.315782	+	0.762365i	−0.999469	+	0.0325894i	$0.989625\pi$
$572$	4.27791	+	1.77197i	0.178869	+	0.0740898i
$573$	−11.5605	−	27.9096i	−0.482948	−	1.16594i
$574$		−	46.7304i		−	1.95049i
$575$	0.106333	−	0.0440446i	0.00443440	−	0.00183679i
$576$	9.01206	+	9.01206i	0.375503	+	0.375503i
$577$	41.4941			1.72742			0.863712	−	0.503986i	$-0.168134\pi$
$577$	41.4941			1.72742			0.863712	+	0.503986i	$0.168134\pi$
$578$	10.6189	−	38.4457i	0.441688	−	1.59913i
$579$	−34.5495			−1.43583
$580$	45.4480	+	45.4480i	1.88713	+	1.88713i
$581$	49.1456	−	20.3568i	2.03890	−	0.844541i
$582$			65.7452i			2.72522i
$583$	−2.86013	−	6.90496i	−0.118454	−	0.285974i
$584$	23.3396	+	9.66758i	0.965800	+	0.400047i
$585$	−2.26279	+	5.46285i	−0.0935548	+	0.225861i
$586$	−17.2455	+	17.2455i	−0.712404	+	0.712404i
$587$	−18.2388	+	18.2388i	−0.752796	+	0.752796i	−0.975000	−	0.222204i	$-0.928675\pi$
$587$	−18.2388	+	18.2388i	−0.752796	+	0.752796i	0.222204	+	0.975000i	$0.428675\pi$
$588$	26.2414	−	63.3524i	1.08218	−	2.61261i
$589$	0.255007	+	0.105627i	0.0105074	+	0.00435230i
$590$	−27.6347	−	66.7161i	−1.13770	−	2.74666i
$591$		−	39.3952i		−	1.62050i
$592$	−0.958549	+	0.397044i	−0.0393961	+	0.0163184i
$593$	−23.4238	−	23.4238i	−0.961901	−	0.961901i	0.0373997	−	0.999300i	$-0.488093\pi$
$593$	−23.4238	−	23.4238i	−0.961901	−	0.961901i	−0.999300	+	0.0373997i	$0.988093\pi$
$594$	6.27240			0.257360
$595$	42.2274	+	24.5969i	1.73116	+	1.00837i
$596$	42.1568			1.72681
$597$	3.46061	+	3.46061i	0.141633	+	0.141633i
$598$	0.142033	−	0.0588320i	0.00580816	−	0.00240582i
$599$		−	40.7415i		−	1.66465i	−0.554287	−	0.832326i	$-0.687009\pi$
$599$		−	40.7415i		−	1.66465i	0.554287	−	0.832326i	$-0.312991\pi$
$600$	9.25365	+	22.3403i	0.377779	+	0.912038i
$601$	−37.2309	−	15.4216i	−1.51868	−	0.629058i	−0.541354	−	0.840794i	$-0.682088\pi$
$601$	−37.2309	−	15.4216i	−1.51868	−	0.629058i	−0.977327	+	0.211736i	$0.932088\pi$
$602$	−3.67119	+	8.86304i	−0.149627	+	0.361230i
$603$	5.14669	−	5.14669i	0.209590	−	0.209590i
$604$	−43.6646	+	43.6646i	−1.77669	+	1.77669i
$605$	−11.6861	+	28.2127i	−0.475107	+	1.14701i
$606$	−33.5186	−	13.8839i	−1.36160	−	0.563994i
$607$	8.79778	+	21.2397i	0.357091	+	0.862094i	0.995706	+	0.0925677i	$0.0295075\pi$
$607$	8.79778	+	21.2397i	0.357091	+	0.862094i	−0.638616	+	0.769526i	$0.720493\pi$
$608$		−	0.125537i		−	0.00509122i
$609$	48.1168	−	19.9306i	1.94979	−	0.807629i
$610$	−59.5245	−	59.5245i	−2.41008	−	2.41008i
$611$	−17.2300			−0.697052
$612$	−3.88177	−	14.7129i	−0.156911	−	0.594735i
$613$	−15.2271			−0.615017			−0.307509	−	0.951545i	$-0.599495\pi$
$613$	−15.2271			−0.615017			−0.307509	+	0.951545i	$0.599495\pi$
$614$	28.3200	+	28.3200i	1.14290	+	1.14290i
$615$	26.2628	−	10.8784i	1.05902	−	0.438661i
$616$		−	9.84498i		−	0.396665i
$617$	2.42520	+	5.85495i	0.0976348	+	0.235711i	0.965149	−	0.261701i	$-0.0842835\pi$
$617$	2.42520	+	5.85495i	0.0976348	+	0.235711i	−0.867514	+	0.497413i	$0.834284\pi$
$618$	−17.7562	−	7.35487i	−0.714261	−	0.295856i
$619$	−12.5453	+	30.2871i	−0.504239	+	1.21734i	0.442915	+	0.896564i	$0.353944\pi$
$619$	−12.5453	+	30.2871i	−0.504239	+	1.21734i	−0.947154	+	0.320778i	$0.896056\pi$
$620$	64.3343	−	64.3343i	2.58373	−	2.58373i
$621$	0.0937538	−	0.0937538i	0.00376221	−	0.00376221i
$622$	−2.95440	+	7.13255i	−0.118461	+	0.285989i
$623$	−5.79417	−	2.40002i	−0.232139	−	0.0961550i
$624$	1.89992	+	4.58681i	0.0760576	+	0.183619i
$625$			30.4355i			1.21742i
$626$	−76.3751	+	31.6356i	−3.05256	+	1.26441i
$627$	0.0299242	+	0.0299242i	0.00119506	+	0.00119506i
$628$	−41.6216			−1.66088
$629$	−3.32979	−	0.451402i	−0.132768	−	0.0179986i
$630$	29.2832			1.16667
$631$	17.5437	+	17.5437i	0.698403	+	0.698403i	0.964066	−	0.265663i	$-0.0855907\pi$
$631$	17.5437	+	17.5437i	0.698403	+	0.698403i	−0.265663	+	0.964066i	$0.585591\pi$
$632$	−17.9791	+	7.44719i	−0.715171	+	0.296233i
$633$		−	10.9031i		−	0.433359i
$634$	−25.4206	−	61.3708i	−1.00958	−	2.43735i
$635$	−28.5987	−	11.8460i	−1.13490	−	0.470093i
$636$	29.5864	−	71.4279i	1.17318	−	2.83230i
$637$	−13.3124	+	13.3124i	−0.527456	+	0.527456i
$638$	7.15910	−	7.15910i	0.283432	−	0.283432i
$639$	3.36446	−	8.12253i	0.133096	−	0.321322i
$640$	−54.2284	−	22.4621i	−2.14357	−	0.887894i
$641$	8.46960	+	20.4474i	0.334529	+	0.807624i	0.998221	+	0.0596186i	$0.0189884\pi$
$641$	8.46960	+	20.4474i	0.334529	+	0.807624i	−0.663692	+	0.748006i	$0.731012\pi$
$642$			25.1709i			0.993415i
$643$	−21.0777	+	8.73066i	−0.831223	+	0.344304i	−0.757387	−	0.652967i	$-0.773524\pi$
$643$	−21.0777	+	8.73066i	−0.831223	+	0.344304i	−0.0738361	+	0.997270i	$0.523524\pi$
$644$	−0.342757	−	0.342757i	−0.0135065	−	0.0135065i
$645$	−5.83572			−0.229781
$646$	−0.150058	+	0.257616i	−0.00590395	+	0.0101358i
$647$	−39.0761			−1.53624			−0.768119	−	0.640307i	$-0.778807\pi$
$647$	−39.0761			−1.53624			−0.768119	+	0.640307i	$0.778807\pi$
$648$	27.5831	+	27.5831i	1.08357	+	1.08357i
$649$	−6.69095	+	2.77148i	−0.262643	+	0.108790i
$650$		−	15.4637i		−	0.606534i
$651$	−28.2130	−	68.1121i	−1.10575	−	2.66952i
$652$	54.2481	+	22.4703i	2.12452	+	0.880004i
$653$	−15.3146	+	36.9728i	−0.599308	+	1.44686i	0.274981	+	0.961450i	$0.411329\pi$
$653$	−15.3146	+	36.9728i	−0.599308	+	1.44686i	−0.874288	+	0.485407i	$0.838671\pi$
$654$	33.1216	−	33.1216i	1.29516	−	1.29516i
$655$	−7.39154	+	7.39154i	−0.288811	+	0.288811i
$656$	2.37314	−	5.72926i	0.0926555	−	0.223690i
$657$	6.96232	+	2.88389i	0.271626	+	0.112511i
$658$	32.6542	+	78.8343i	1.27299	+	3.07328i
$659$		−	39.0352i		−	1.52060i	−0.649574	−	0.760298i	$-0.725053\pi$
$659$		−	39.0352i		−	1.52060i	0.649574	−	0.760298i	$-0.274947\pi$
$660$	12.8876	−	5.33823i	0.501651	−	0.207791i
$661$	−18.2480	−	18.2480i	−0.709767	−	0.709767i	0.256719	−	0.966486i	$-0.417358\pi$
$661$	−18.2480	−	18.2480i	−0.709767	−	0.709767i	−0.966486	+	0.256719i	$0.917358\pi$
$662$	−59.4228			−2.30953
$663$	−2.16003	+	15.9336i	−0.0838887	+	0.618810i
$664$	45.9253			1.78225
$665$	−0.258294	−	0.258294i	−0.0100162	−	0.0100162i
$666$	−1.86026	+	0.770544i	−0.0720836	+	0.0298580i
$667$		−	0.214015i		−	0.00828669i
$668$	0.681766	+	1.64593i	0.0263783	+	0.0636829i
$669$	−49.3078	−	20.4239i	−1.90635	−	0.789635i
$670$	−17.9888	+	43.4288i	−0.694969	+	1.67780i
$671$	−5.96971	+	5.96971i	−0.230458	+	0.230458i
$672$	−23.7099	+	23.7099i	−0.914631	+	0.914631i
$673$	16.4553	−	39.7266i	0.634304	−	1.53135i	−0.199857	−	0.979825i	$-0.564048\pi$
$673$	16.4553	−	39.7266i	0.634304	−	1.53135i	0.834161	−	0.551521i	$-0.185952\pi$
$674$	−5.68452	−	2.35461i	−0.218960	−	0.0906961i
$675$	−5.10366	−	12.3213i	−0.196440	−	0.474248i
$676$			32.4093i			1.24651i
$677$	20.5767	−	8.52316i	0.790828	−	0.327571i	0.0495513	−	0.998772i	$-0.484221\pi$
$677$	20.5767	−	8.52316i	0.790828	−	0.327571i	0.741276	+	0.671200i	$0.234221\pi$
$678$	−21.4459	−	21.4459i	−0.823623	−	0.823623i
$679$	−56.9133			−2.18413
$680$	25.5551	+	33.5705i	0.979995	+	1.28737i
$681$	15.8586			0.607705
$682$	−10.1341	−	10.1341i	−0.388056	−	0.388056i
$683$	17.2964	−	7.16442i	0.661829	−	0.274139i	−0.0263787	−	0.999652i	$-0.508398\pi$
$683$	17.2964	−	7.16442i	0.661829	−	0.274139i	0.688208	+	0.725513i	$0.258398\pi$
$684$			0.113739i			0.00434892i
$685$	11.1956	+	27.0285i	0.427760	+	1.03270i
$686$	24.0977	+	9.98161i	0.920056	+	0.381100i
$687$	6.62253	−	15.9882i	0.252665	−	0.609988i
$688$	−0.900194	+	0.900194i	−0.0343196	+	0.0343196i
$689$	−15.0093	+	15.0093i	−0.571809	+	0.571809i
$690$	0.177237	−	0.427889i	0.00674731	−	0.0162894i
$691$	20.3006	+	8.40877i	0.772270	+	0.319885i	0.733791	−	0.679375i	$-0.237749\pi$
$691$	20.3006	+	8.40877i	0.772270	+	0.319885i	0.0384783	+	0.999259i	$0.487749\pi$
$692$	6.28149	+	15.1649i	0.238787	+	0.576482i
$693$		−	2.93680i		−	0.111560i
$694$	3.96876	−	1.64392i	0.150652	−	0.0624022i
$695$	−31.3426	−	31.3426i	−1.18889	−	1.18889i
$696$	44.9639			1.70435
$697$	15.9808	−	12.1652i	0.605316	−	0.460790i
$698$	54.3504			2.05719
$699$	3.01415	+	3.01415i	0.114006	+	0.114006i
$700$	−45.0458	+	18.6586i	−1.70257	+	0.705228i
$701$		−	15.9216i		−	0.601350i	−0.953727	−	0.300675i	$-0.902788\pi$
$701$		−	15.9216i		−	0.601350i	0.953727	−	0.300675i	$-0.0972119\pi$
$702$	−6.81715	−	16.4580i	−0.257297	−	0.621169i
$703$	0.0232052	+	0.00961191i	0.000875201	+	0.000362520i
$704$	−3.15904	+	7.62660i	−0.119061	+	0.287438i
$705$	−36.7039	+	36.7039i	−1.38235	+	1.38235i
$706$	37.8743	−	37.8743i	1.42542	−	1.42542i
$707$	12.0188	−	29.0159i	0.452013	−	1.09126i
$708$	−69.2140	−	28.6694i	−2.60122	−	1.07746i
$709$	−15.7223	−	37.9570i	−0.590464	−	1.42551i	−0.883055	−	0.469269i	$-0.844517\pi$
$709$	−15.7223	−	37.9570i	−0.590464	−	1.42551i	0.292591	−	0.956238i	$-0.405483\pi$
$710$			56.7800i			2.13092i
$711$	−5.36326	+	2.22153i	−0.201138	+	0.0833140i
$712$	−3.82864	−	3.82864i	−0.143484	−	0.143484i
$713$	−0.302951			−0.0113456
$714$	76.9963	−	20.3142i	2.88151	−	0.760241i
$715$	−3.82984			−0.143228
$716$	13.7001	+	13.7001i	0.511997	+	0.511997i
$717$	44.7545	−	18.5379i	1.67139	−	0.692312i
$718$		−	69.4121i		−	2.59044i
$719$	−11.4309	−	27.5967i	−0.426302	−	1.02918i	−0.980450	−	0.196767i	$-0.936956\pi$
$719$	−11.4309	−	27.5967i	−0.426302	−	1.02918i	0.554148	−	0.832418i	$-0.313044\pi$
$720$	3.59019	+	1.48711i	0.133799	+	0.0554212i
$721$	6.36686	−	15.3710i	0.237114	−	0.572444i
$722$	−31.5196	+	31.5196i	−1.17304	+	1.17304i
$723$	−17.4014	+	17.4014i	−0.647164	+	0.647164i
$724$	9.21364	−	22.2437i	0.342422	−	0.826681i
$725$	−19.8883	−	8.23800i	−0.738633	−	0.305952i
$726$	19.0423	+	45.9722i	0.706726	+	1.70619i
$727$			18.1844i			0.674422i	0.941429	+	0.337211i	$0.109484\pi$
$727$			18.1844i			0.674422i	−0.941429	+	0.337211i	$0.890516\pi$
$728$	−25.8321	+	10.7000i	−0.957401	+	0.396568i
$729$	−8.51136	−	8.51136i	−0.315236	−	0.315236i
$730$	−48.6697			−1.80135
$731$	−3.98669	+	1.05182i	−0.147453	+	0.0389031i
$732$	−87.3322			−3.22789
$733$	−5.29415	−	5.29415i	−0.195544	−	0.195544i	0.602543	−	0.798087i	$-0.294154\pi$
$733$	−5.29415	−	5.29415i	−0.195544	−	0.195544i	−0.798087	+	0.602543i	$0.794154\pi$
$734$	11.6264	−	4.81583i	0.429139	−	0.177755i
$735$			56.7168i			2.09203i
$736$	0.0527288	+	0.127299i	0.00194361	+	0.00469229i
$737$	4.35547	+	1.80410i	0.160436	+	0.0664547i
$738$	4.60556	−	11.1188i	0.169533	−	0.409289i
$739$	−10.2932	+	10.2932i	−0.378641	+	0.378641i	−0.870612	−	0.491971i	$-0.836277\pi$
$739$	−10.2932	+	10.2932i	−0.378641	+	0.378641i	0.491971	+	0.870612i	$0.336277\pi$
$740$	5.85431	−	5.85431i	0.215209	−	0.215209i
$741$	0.0459945	−	0.111041i	0.00168965	−	0.00407918i
$742$	97.1191	+	40.2280i	3.56535	+	1.47682i
$743$	3.99003	+	9.63278i	0.146380	+	0.353393i	0.980015	−	0.198923i	$-0.0637444\pi$
$743$	3.99003	+	9.63278i	0.146380	+	0.353393i	−0.833635	+	0.552316i	$0.813744\pi$
$744$		−	63.6491i		−	2.33349i
$745$	−32.2142	+	13.3436i	−1.18024	+	0.488870i
$746$	−14.2742	−	14.2742i	−0.522616	−	0.522616i
$747$	13.6997			0.501247
$748$	7.84206	−	5.96968i	0.286734	−	0.218273i
$749$	−21.7895			−0.796172
$750$	15.4664	+	15.4664i	0.564753	+	0.564753i
$751$	−18.7873	+	7.78196i	−0.685559	+	0.283968i	−0.698149	−	0.715953i	$-0.745992\pi$
$751$	−18.7873	+	7.78196i	−0.685559	+	0.283968i	0.0125896	+	0.999921i	$0.495992\pi$
$752$			11.3236i			0.412929i
$753$	−15.7225	−	37.9576i	−0.572961	−	1.38325i
$754$	−26.5655	−	11.0038i	−0.967459	−	0.400735i
$755$	19.5456	−	47.1872i	0.711336	−	1.71732i
$756$	−39.7169	+	39.7169i	−1.44449	+	1.44449i
$757$	−21.1340	+	21.1340i	−0.768128	+	0.768128i	−0.977777	−	0.209649i	$-0.932768\pi$
$757$	−21.1340	+	21.1340i	−0.768128	+	0.768128i	0.209649	+	0.977777i	$0.432768\pi$
$758$	25.3138	−	61.1128i	0.919437	−	2.21972i
$759$	−0.0429129	−	0.0177751i	−0.00155764	−	0.000645195i
$760$	−0.120685	−	0.291359i	−0.00437770	−	0.0105687i
$761$		−	0.536041i		−	0.0194315i	−0.999953	−	0.00971574i	$-0.996907\pi$
$761$		−	0.536041i		−	0.0194315i	0.999953	−	0.00971574i	$-0.00309267\pi$
$762$	−46.6011	+	19.3028i	−1.68818	+	0.699267i
$763$	28.6722	+	28.6722i	1.03800	+	1.03800i
$764$	52.5880			1.90257
$765$	7.62322	+	10.0142i	0.275618	+	0.362066i
$766$	9.78183			0.353432
$767$	14.5441	+	14.5441i	0.525157	+	0.525157i
$768$	−43.3420	+	17.9528i	−1.56397	+	0.647817i
$769$			50.7332i			1.82949i	0.404037	+	0.914743i	$0.367607\pi$
$769$			50.7332i			1.82949i	−0.404037	+	0.914743i	$0.632393\pi$
$770$	7.25829	+	17.5231i	0.261571	+	0.631488i
$771$	20.1768	+	8.35752i	0.726651	+	0.300989i
$772$	23.0160	−	55.5656i	0.828364	−	1.99985i
$773$	31.2741	−	31.2741i	1.12485	−	1.12485i	0.133848	−	0.991002i	$-0.457267\pi$
$773$	31.2741	−	31.2741i	1.12485	−	1.12485i	0.991002	−	0.133848i	$-0.0427335\pi$
$774$	−1.74701	+	1.74701i	−0.0627950	+	0.0627950i
$775$	−11.6614	+	28.1530i	−0.418889	+	1.01129i
$776$	−45.3954	−	18.8034i	−1.62960	−	0.675003i
$777$	−2.56733	−	6.19808i	−0.0921025	−	0.222355i
$778$		−	47.1830i		−	1.69159i
$779$	−0.138698	+	0.0574505i	−0.00496937	+	0.00205838i
$780$	−28.0138	−	28.0138i	−1.00306	−	1.00306i
$781$	5.69446			0.203764
$782$	0.0439579	−	0.324258i	0.00157193	−	0.0115954i
$783$	−24.7989			−0.886241
$784$	8.74890	+	8.74890i	0.312461	+	0.312461i
$785$	31.8052	−	13.1742i	1.13518	−	0.470206i
$786$			17.0334i			0.607560i
$787$	−12.3160	−	29.7334i	−0.439017	−	1.05988i	−0.976289	−	0.216472i	$-0.930545\pi$
$787$	−12.3160	−	29.7334i	−0.439017	−	1.05988i	0.537271	−	0.843409i	$-0.319455\pi$
$788$	63.3589	+	26.2441i	2.25707	+	0.934907i
$789$	−12.2804	+	29.6475i	−0.437193	+	1.05548i
$790$	26.5105	−	26.5105i	0.943202	−	0.943202i
$791$	18.5649	−	18.5649i	0.660093	−	0.660093i
$792$	0.970282	−	2.34247i	0.0344775	−	0.0832359i
$793$	22.1520	+	9.17565i	0.786640	+	0.325837i
$794$	−5.61252	−	13.5498i	−0.199181	−	0.480865i
$795$			63.9465i			2.26795i
$796$	−7.87102	+	3.26029i	−0.278981	+	0.115558i
$797$	19.3257	+	19.3257i	0.684552	+	0.684552i	0.961022	−	0.276471i	$-0.0891649\pi$
$797$	19.3257	+	19.3257i	0.684552	+	0.684552i	−0.276471	+	0.961022i	$0.589165\pi$
$798$	−0.595224			−0.0210707
$799$	−18.4589	+	31.6898i	−0.653029	+	1.12111i
$800$	13.8595			0.490006
$801$	−1.14210	−	1.14210i	−0.0403541	−	0.0403541i
$802$	−34.0819	+	14.1172i	−1.20347	+	0.498495i
$803$			4.88107i			0.172249i
$804$	18.6623	+	45.0549i	0.658170	+	1.58896i
$805$	0.370408	+	0.153428i	0.0130552	+	0.00540763i
$806$	−15.5765	+	37.6050i	−0.548660	+	1.32458i
$807$	17.4778	−	17.4778i	0.615248	−	0.615248i
$808$	19.1729	−	19.1729i	0.674502	−	0.674502i
$809$	−10.5724	+	25.5239i	−0.371704	+	0.897373i	0.621758	+	0.783210i	$0.286419\pi$
$809$	−10.5724	+	25.5239i	−0.371704	+	0.897373i	−0.993462	+	0.114164i	$0.963581\pi$
$810$	−69.4311	−	28.7593i	−2.43956	−	1.01050i
$811$	13.3175	+	32.1513i	0.467641	+	1.12899i	0.965190	+	0.261550i	$0.0842336\pi$
$811$	13.3175	+	32.1513i	0.467641	+	1.12899i	−0.497549	+	0.867436i	$0.665766\pi$
$812$			90.6630i			3.18165i
$813$	0.522304	−	0.216346i	0.0183180	−	0.00758757i
$814$	−0.922188	−	0.922188i	−0.0323227	−	0.0323227i
$815$	−48.5661			−1.70120
$816$	10.4716	+	1.41958i	0.366579	+	0.0496951i
$817$	0.0308193			0.00107823
$818$	−36.3422	−	36.3422i	−1.27068	−	1.27068i
$819$	−7.70584	+	3.19186i	−0.269264	+	0.111533i
$820$			49.4852i			1.72810i
$821$	8.42697	+	20.3445i	0.294103	+	0.710028i	0.999999	+	0.00171200i	$0.000544946\pi$
$821$	8.42697	+	20.3445i	0.294103	+	0.710028i	−0.705895	+	0.708316i	$0.749455\pi$
$822$	44.0425	+	18.2430i	1.53616	+	0.636297i
$823$	14.2419	−	34.3829i	0.496441	−	1.19851i	−0.454947	−	0.890519i	$-0.650342\pi$
$823$	14.2419	−	34.3829i	0.496441	−	1.19851i	0.951388	−	0.307996i	$-0.0996582\pi$
$824$	10.1567	−	10.1567i	0.353826	−	0.353826i
$825$	−3.30366	+	3.30366i	−0.115019	+	0.115019i
$826$	38.9812	−	94.1089i	1.35633	−	3.27447i
$827$	−33.5043	−	13.8779i	−1.16506	−	0.482582i	−0.285501	−	0.958378i	$-0.592160\pi$
$827$	−33.5043	−	13.8779i	−1.16506	−	0.482582i	−0.879556	+	0.475796i	$0.842160\pi$
$828$	−0.0477732	−	0.115335i	−0.00166023	−	0.00400816i
$829$		−	28.7563i		−	0.998748i	−0.866387	−	0.499374i	$-0.833563\pi$
$829$		−	28.7563i		−	0.998748i	0.866387	−	0.499374i	$-0.166437\pi$
$830$	−81.7424	+	33.8588i	−2.83732	+	1.17526i
$831$	30.2037	+	30.2037i	1.04775	+	1.04775i
$832$	23.4447			0.812800
$833$	10.2226	+	38.7462i	0.354191	+	1.34248i
$834$	−72.2272			−2.50102
$835$	−1.04194	−	1.04194i	−0.0360580	−	0.0360580i
$836$	−0.0680615	+	0.0281920i	−0.00235396	+	0.000975040i
$837$			35.1043i			1.21338i
$838$	−16.5699	−	40.0033i	−0.572398	−	1.38189i
$839$	−11.8953	−	4.92720i	−0.410672	−	0.170106i	0.167776	−	0.985825i	$-0.446341\pi$
$839$	−11.8953	−	4.92720i	−0.410672	−	0.170106i	−0.578448	+	0.815719i	$0.696341\pi$
$840$	−32.2348	+	77.8217i	−1.11221	+	2.68510i
$841$	−7.79855	+	7.79855i	−0.268916	+	0.268916i
$842$	−12.4414	+	12.4414i	−0.428760	+	0.428760i
$843$	−10.7191	+	25.8783i	−0.369187	+	0.891295i
$844$	17.5353	+	7.26338i	0.603591	+	0.250016i
$845$	−10.2583	−	24.7656i	−0.352895	−	0.851963i
$846$			21.9757i			0.755541i
$847$	−39.7965	+	16.4843i	−1.36742	+	0.566406i
$848$	9.86412	+	9.86412i	0.338735	+	0.338735i
$849$	−38.0100			−1.30450
$850$	−28.4411	−	16.5665i	−0.975521	−	0.568228i
$851$	−0.0275680			−0.000945018
$852$	41.6528	+	41.6528i	1.42700	+	1.42700i
$853$	5.35646	−	2.21872i	0.183402	−	0.0759674i	−0.289093	−	0.957301i	$-0.593354\pi$
$853$	5.35646	−	2.21872i	0.183402	−	0.0759674i	0.472494	+	0.881334i	$0.343354\pi$
$854$		−	118.744i		−	4.06333i
$855$	−0.0360009	−	0.0869138i	−0.00123120	−	0.00297239i
$856$	−17.3799	−	7.19897i	−0.594031	−	0.246056i
$857$	−11.8882	+	28.7007i	−0.406093	+	0.980396i	0.580062	+	0.814572i	$0.303028\pi$
$857$	−11.8882	+	28.7007i	−0.406093	+	0.980396i	−0.986155	+	0.165824i	$0.946972\pi$
$858$	−4.41282	+	4.41282i	−0.150651	+	0.150651i
$859$	20.7586	−	20.7586i	0.708275	−	0.708275i	−0.257897	−	0.966172i	$-0.583030\pi$
$859$	20.7586	−	20.7586i	0.708275	−	0.708275i	0.966172	+	0.257897i	$0.0830297\pi$
$860$	3.88761	−	9.38553i	0.132567	−	0.320044i
$861$	37.0461	+	15.3450i	1.26253	+	0.522955i
$862$	13.2907	+	32.0865i	0.452682	+	1.09287i
$863$			24.0383i			0.818272i	0.912473	+	0.409136i	$0.134170\pi$
$863$			24.0383i			0.818272i	−0.912473	+	0.409136i	$0.865830\pi$
$864$	14.7507	−	6.10994i	0.501829	−	0.207864i
$865$	−9.60003	−	9.60003i	−0.326411	−	0.326411i
$866$	79.7735			2.71081
$867$	26.9913	+	21.0428i	0.916673	+	0.714650i
$868$	128.339			4.35610
$869$	−2.65873	−	2.65873i	−0.0901914	−	0.0901914i
$870$	−80.0312	+	33.1500i	−2.71331	+	1.12389i
$871$		−	13.3890i		−	0.453670i
$872$	13.3967	+	32.3426i	0.453670	+	1.09526i
$873$	−13.5417	−	5.60915i	−0.458316	−	0.189841i
$874$	−0.000936015		0.00225974i	−3.16612e−5		7.64369e-5i
$875$	−13.3887	+	13.3887i	−0.452621	+	0.452621i
$876$	−35.7032	+	35.7032i	−1.20630	+	1.20630i
$877$	0.426600	−	1.02990i	0.0144053	−	0.0347774i	−0.916513	−	0.400004i	$-0.869009\pi$
$877$	0.426600	−	1.02990i	0.0144053	−	0.0347774i	0.930919	+	0.365227i	$0.119009\pi$
$878$	71.4997	+	29.6161i	2.41300	+	0.999496i
$879$	−8.00861	−	19.3345i	−0.270124	−	0.652137i
$880$			2.51698i			0.0848472i
$881$	−1.68700	+	0.698778i	−0.0568364	+	0.0235424i	−0.410921	−	0.911671i	$-0.634793\pi$
$881$	−1.68700	+	0.698778i	−0.0568364	+	0.0235424i	0.354084	+	0.935214i	$0.384793\pi$
$882$	16.9790	+	16.9790i	0.571714	+	0.571714i
$883$	36.4079			1.22522			0.612612	−	0.790384i	$-0.290119\pi$
$883$	36.4079			1.22522			0.612612	+	0.790384i	$0.290119\pi$
$884$	−24.1869	−	14.0885i	−0.813493	−	0.473849i
$885$	61.9645			2.08291
$886$	−4.28892	−	4.28892i	−0.144089	−	0.144089i
$887$	−13.3007	+	5.50933i	−0.446594	+	0.184985i	−0.594635	−	0.803996i	$-0.702703\pi$
$887$	−13.3007	+	5.50933i	−0.446594	+	0.184985i	0.148041	+	0.988981i	$0.452703\pi$
$888$		−	5.79195i		−	0.194365i
$889$	−16.7098	−	40.3410i	−0.560428	−	1.35299i
$890$	9.63728	+	3.99189i	0.323042	+	0.133809i
$891$	−2.88426	+	6.96323i	−0.0966265	+	0.233277i
$892$	65.6952	−	65.6952i	2.19964	−	2.19964i
$893$	0.193839	−	0.193839i	0.00648656	−	0.00648656i
$894$	−21.7431	+	52.4925i	−0.727199	+	1.75561i
$895$	−14.8053	−	6.13257i	−0.494888	−	0.204989i
$896$	−31.6848	−	76.4939i	−1.05852	−	2.55548i
$897$			0.131917i			0.00440459i
$898$	−25.9374	+	10.7436i	−0.865542	+	0.358519i
$899$	40.0669	+	40.0669i	1.33631	+	1.33631i
$900$	−12.5569			−0.418563
$901$	11.5256	+	43.6852i	0.383974	+	1.45536i
$902$	7.79505			0.259547
$903$	−5.82076	−	5.82076i	−0.193703	−	0.193703i
$904$	20.9414	−	8.67423i	0.696502	−	0.288501i
$905$			19.9139i			0.661960i
$906$	−31.8492	−	76.8907i	−1.05812	−	2.55452i
$907$	−10.5751	−	4.38037i	−0.351142	−	0.145448i	0.200139	−	0.979768i	$-0.435861\pi$
$907$	−10.5751	−	4.38037i	−0.351142	−	0.145448i	−0.551281	+	0.834320i	$0.685861\pi$
$908$	−10.5646	+	25.5053i	−0.350600	+	0.846423i
$909$	5.71938	−	5.71938i	0.189700	−	0.189700i
$910$	38.0898	−	38.0898i	1.26267	−	1.26267i
$911$	−5.95321	+	14.3723i	−0.197239	+	0.476176i	−0.991294	−	0.131670i	$-0.957966\pi$
$911$	−5.95321	+	14.3723i	−0.197239	+	0.476176i	0.794055	+	0.607846i	$0.207966\pi$
$912$	−0.0729760	−	0.0302276i	−0.00241648	−	0.00100094i
$913$	3.39569	+	8.19793i	0.112381	+	0.271312i
$914$			9.08269i			0.300429i
$915$	66.7350	−	27.6426i	2.20619	−	0.913835i
$916$	21.3019	+	21.3019i	0.703834	+	0.703834i
$917$	−14.7452			−0.486929
$918$	−37.5733	−	5.09361i	−1.24010	−	0.168114i
$919$	46.7340			1.54161			0.770806	−	0.637070i	$-0.219854\pi$
$919$	46.7340			1.54161			0.770806	+	0.637070i	$0.219854\pi$
$920$	0.244756	+	0.244756i	0.00806937	+	0.00806937i
$921$	−31.7506	+	13.1515i	−1.04622	+	0.433358i
$922$			17.1128i			0.563581i
$923$	−6.18902	−	14.9416i	−0.203714	−	0.491809i
$924$	18.1791	+	7.53005i	0.598050	+	0.247720i
$925$	−1.06116	+	2.56188i	−0.0348909	+	0.0842340i
$926$	64.8971	−	64.8971i	2.13265	−	2.13265i
$927$	3.02980	−	3.02980i	0.0995117	−	0.0995117i
$928$	9.86227	−	23.8096i	0.323745	−	0.781589i
$929$	24.1241	+	9.99252i	0.791486	+	0.327844i	0.741541	−	0.670908i	$-0.234095\pi$
$929$	24.1241	+	9.99252i	0.791486	+	0.327844i	0.0499449	+	0.998752i	$0.484095\pi$
$930$	46.9258	+	113.289i	1.53876	+	3.71489i
$931$		−	0.299530i		−	0.00981669i
$932$	−6.85557	+	2.83967i	−0.224562	+	0.0930165i
$933$	−4.68427	−	4.68427i	−0.153356	−	0.153356i
$934$	48.4611			1.58570
$935$	−4.10299	+	7.04393i	−0.134182	+	0.230361i
$936$	−7.20091			−0.235369
$937$	20.7130	+	20.7130i	0.676663	+	0.676663i	0.959244	−	0.282581i	$-0.0911905\pi$
$937$	20.7130	+	20.7130i	0.676663	+	0.676663i	−0.282581	+	0.959244i	$0.591190\pi$
$938$	−61.2602	+	25.3748i	−2.00022	+	0.828517i
$939$		−	70.9356i		−	2.31490i
$940$	−34.5793	−	83.4817i	−1.12785	−	2.72287i
$941$	25.7754	+	10.6765i	0.840256	+	0.348045i	0.760954	−	0.648805i	$-0.224731\pi$
$941$	25.7754	+	10.6765i	0.840256	+	0.348045i	0.0793013	+	0.996851i	$0.474731\pi$
$942$	21.4671	−	51.8261i	0.699436	−	1.68859i
$943$	0.116513	−	0.116513i	0.00379419	−	0.00379419i
$944$	9.55839	−	9.55839i	0.311099	−	0.311099i
$945$	17.7784	−	42.9210i	0.578333	−	1.39622i
$946$	−1.47844	−	0.612388i	−0.0480681	−	0.0199105i
$947$	2.85646	+	6.89610i	0.0928225	+	0.224093i	0.963471	−	0.267812i	$-0.0863006\pi$
$947$	2.85646	+	6.89610i	0.0928225	+	0.224093i	−0.870649	+	0.491905i	$0.836301\pi$
$948$		−	38.8952i		−	1.26326i
$949$	12.8074	−	5.30499i	0.415745	−	0.172207i
$950$	0.173967	+	0.173967i	0.00564423	+	0.00564423i
$951$	56.9999			1.84835
$952$	−7.99479	+	58.9740i	−0.259113	+	1.91136i
$953$	−6.81253			−0.220680			−0.110340	−	0.993894i	$-0.535194\pi$
$953$	−6.81253			−0.220680			−0.110340	+	0.993894i	$0.535194\pi$
$954$	19.1433	+	19.1433i	0.619788	+	0.619788i
$955$	−40.1852	+	16.6452i	−1.30036	+	0.538628i
$956$			84.3277i			2.72735i
$957$	3.32461	+	8.02632i	0.107469	+	0.259454i
$958$	78.8151	+	32.6463i	2.54640	+	1.05475i
$959$	−15.7923	+	38.1260i	−0.509960	+	1.23115i
$960$	49.9426	−	49.9426i	1.61189	−	1.61189i
$961$	34.7967	−	34.7967i	1.12248	−	1.12248i
$962$	−1.41744	+	3.42199i	−0.0457000	+	0.110330i
$963$	−5.18450	−	2.14749i	−0.167068	−	0.0692019i
$964$	−16.3941	−	39.5788i	−0.528017	−	1.27475i
$965$			49.7456i			1.60137i
$966$	0.603574	−	0.250009i	0.0194197	−	0.00804390i
$967$	1.70645	+	1.70645i	0.0548759	+	0.0548759i	0.734012	−	0.679136i	$-0.237645\pi$
$967$	1.70645	+	1.70645i	0.0548759	+	0.0548759i	−0.679136	+	0.734012i	$0.737645\pi$
$968$	−37.1889			−1.19530
$969$	−0.154953	−	0.203554i	−0.00497782	−	0.00653910i
$970$	94.6622			3.03942
$971$	−20.8694	−	20.8694i	−0.669730	−	0.669730i	0.287923	−	0.957653i	$-0.407035\pi$
$971$	−20.8694	−	20.8694i	−0.669730	−	0.669730i	−0.957653	+	0.287923i	$0.907035\pi$
$972$	−33.9571	+	14.0655i	−1.08918	+	0.451151i
$973$		−	62.5246i		−	2.00445i
$974$	2.11452	+	5.10491i	0.0677537	+	0.163572i
$975$	12.2590	+	5.07784i	0.392602	+	0.162621i
$976$	6.03025	−	14.5583i	0.193023	−	0.466000i
$977$	40.6556	−	40.6556i	1.30069	−	1.30069i	0.372762	−	0.927927i	$-0.378411\pi$
$977$	40.6556	−	40.6556i	1.30069	−	1.30069i	0.927927	−	0.372762i	$-0.121589\pi$
$978$	−55.9588	+	55.9588i	−1.78937	+	1.78937i
$979$	0.400346	−	0.966521i	0.0127951	−	0.0308902i
$980$	−91.2170	−	37.7833i	−2.91382	−	1.20694i
$981$	3.99631	+	9.64794i	0.127592	+	0.308035i
$982$		−	69.3122i		−	2.21184i
$983$	−57.0209	+	23.6188i	−1.81868	+	0.753323i	−0.841720	+	0.539914i	$0.818457\pi$
$983$	−57.0209	+	23.6188i	−1.81868	+	0.753323i	−0.976963	+	0.213409i	$0.931543\pi$
$984$	24.4791	+	24.4791i	0.780364	+	0.780364i
$985$	−56.7226			−1.80733
$986$	−48.6986	+	37.0712i	−1.55088	+	1.18059i
$987$	−73.2196			−2.33061
$988$	0.147945	+	0.147945i	0.00470676	+	0.00470676i
$989$	−0.0312517	+	0.0129449i	−0.000993745	+	0.000411623i
$990$			4.88470i			0.155246i
$991$	−9.83522	−	23.7443i	−0.312426	−	0.754263i	−0.999614	−	0.0277837i	$-0.991155\pi$
$991$	−9.83522	−	23.7443i	−0.312426	−	0.754263i	0.687188	−	0.726480i	$-0.258845\pi$
$992$	−33.7039	−	13.9606i	−1.07010	−	0.443250i
$993$	19.5128	−	47.1081i	0.619220	−	1.49493i
$994$	−56.6345	+	56.6345i	−1.79634	+	1.79634i
$995$	4.98270	−	4.98270i	0.157962	−	0.157962i
$996$	−35.1265	+	84.8029i	−1.11303	+	2.68708i
$997$	53.0415	+	21.9705i	1.67984	+	0.695813i	0.999318	−	0.0369131i	$-0.0117525\pi$
$997$	53.0415	+	21.9705i	1.67984	+	0.695813i	0.680523	+	0.732726i	$0.261752\pi$
$998$	7.52049	+	18.1561i	0.238057	+	0.574720i
$999$			3.19443i			0.101067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.4	✓	116
17.9	even	8	inner	731.2.m.b.689.4	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.4	✓	116	1.1	even	1	trivial
731.2.m.b.689.4	yes	116	17.9	even	8	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65901 - 1.65901i) q^{2} +(1.85997 - 0.770425i) q^{3} +3.50461i q^{4} +(-1.10929 - 2.67805i) q^{5} +(-4.36385 - 1.80756i) q^{6} +(1.56474 - 3.77763i) q^{7} +(2.49616 - 2.49616i) q^{8} +(0.744616 - 0.744616i) q^{9} +O(q^{10})\)	\(q+(-1.65901 - 1.65901i) q^{2} +(1.85997 - 0.770425i) q^{3} +3.50461i q^{4} +(-1.10929 - 2.67805i) q^{5} +(-4.36385 - 1.80756i) q^{6} +(1.56474 - 3.77763i) q^{7} +(2.49616 - 2.49616i) q^{8} +(0.744616 - 0.744616i) q^{9} +(-2.60260 + 6.28322i) q^{10} +(0.630143 + 0.261014i) q^{11} +(2.70004 + 6.51847i) q^{12} -1.93711i q^{13} +(-8.86304 + 3.67119i) q^{14} +(-4.12648 - 4.12648i) q^{15} -1.27307 q^{16} +(-3.56276 - 2.07526i) q^{17} -2.47065 q^{18} +(0.0217925 + 0.0217925i) q^{19} +(9.38553 - 3.88761i) q^{20} -8.23180i q^{21} +(-0.612388 - 1.47844i) q^{22} +(-0.0312517 - 0.0129449i) q^{23} +(2.71968 - 6.56588i) q^{24} +(-2.40592 + 2.40592i) q^{25} +(-3.21367 + 3.21367i) q^{26} +(-1.49998 + 3.62128i) q^{27} +(13.2391 + 5.48382i) q^{28} +(2.42117 + 5.84523i) q^{29} +13.6917i q^{30} +(8.27427 - 3.42731i) q^{31} +(-2.88029 - 2.88029i) q^{32} +1.37314 q^{33} +(2.46778 + 9.35353i) q^{34} -11.8524 q^{35} +(2.60959 + 2.60959i) q^{36} +(0.752944 - 0.311880i) q^{37} -0.0723079i q^{38} +(-1.49239 - 3.60296i) q^{39} +(-9.45379 - 3.91589i) q^{40} +(-1.86411 + 4.50036i) q^{41} +(-13.6566 + 13.6566i) q^{42} +(0.707107 - 0.707107i) q^{43} +(-0.914752 + 2.20841i) q^{44} +(-2.82011 - 1.16813i) q^{45} +(0.0303711 + 0.0733223i) q^{46} -8.89473i q^{47} +(-2.36787 + 0.980803i) q^{48} +(-6.87230 - 6.87230i) q^{49} +7.98287 q^{50} +(-8.22547 - 1.11508i) q^{51} +6.78880 q^{52} +(-7.74831 - 7.74831i) q^{53} +(8.49621 - 3.51924i) q^{54} -1.97710i q^{55} +(-5.52371 - 13.3354i) q^{56} +(0.0573230 + 0.0237439i) q^{57} +(5.68054 - 13.7140i) q^{58} +(-7.50816 + 7.50816i) q^{59} +(14.4617 - 14.4617i) q^{60} +(-4.73678 + 11.4356i) q^{61} +(-19.4130 - 8.04113i) q^{62} +(-1.64775 - 3.97802i) q^{63} +12.1030i q^{64} +(-5.18767 + 2.14880i) q^{65} +(-2.27805 - 2.27805i) q^{66} +6.91188 q^{67} +(7.27298 - 12.4861i) q^{68} -0.0681002 q^{69} +(19.6633 + 19.6633i) q^{70} +(7.71337 - 3.19498i) q^{71} -3.71736i q^{72} +(2.73862 + 6.61160i) q^{73} +(-1.76655 - 0.731729i) q^{74} +(-2.62136 + 6.32851i) q^{75} +(-0.0763743 + 0.0763743i) q^{76} +(1.97203 - 1.97203i) q^{77} +(-3.50144 + 8.45323i) q^{78} +(-5.09309 - 2.10963i) q^{79} +(1.41220 + 3.40934i) q^{80} +11.0502i q^{81} +(10.5587 - 4.37356i) q^{82} +(9.19920 + 9.19920i) q^{83} +28.8492 q^{84} +(-1.60554 + 11.8433i) q^{85} -2.34619 q^{86} +(9.00663 + 9.00663i) q^{87} +(2.22447 - 0.921405i) q^{88} -1.53381i q^{89} +(2.74065 + 6.61652i) q^{90} +(-7.31766 - 3.03108i) q^{91} +(0.0453667 - 0.109525i) q^{92} +(12.7494 - 12.7494i) q^{93} +(-14.7564 + 14.7564i) q^{94} +(0.0341874 - 0.0825357i) q^{95} +(-7.57630 - 3.13820i) q^{96} +(-5.32659 - 12.8595i) q^{97} +22.8024i q^{98} +(0.663570 - 0.274860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Introduction

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