LMFDB - Embedded newform 45.4.l.a.2.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, 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:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.11
Character	$\chi$	$=$	45.2
Dual form			45.4.l.a.23.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.385641 + 1.43923i) q^{2} +(4.61491 + 2.38802i) q^{3} +(5.00553 - 2.88994i) q^{4} +(4.60989 - 10.1857i) q^{5} +(-1.65722 + 7.56285i) q^{6} +(-24.7344 + 6.62758i) q^{7} +(14.5184 + 14.5184i) q^{8} +(15.5947 + 22.0410i) q^{9} +O(q^{10})$	\(q+(0.385641 + 1.43923i) q^{2} +(4.61491 + 2.38802i) q^{3} +(5.00553 - 2.88994i) q^{4} +(4.60989 - 10.1857i) q^{5} +(-1.65722 + 7.56285i) q^{6} +(-24.7344 + 6.62758i) q^{7} +(14.5184 + 14.5184i) q^{8} +(15.5947 + 22.0410i) q^{9} +(16.4374 + 2.70668i) q^{10} +(11.8937 + 6.86683i) q^{11} +(30.0013 - 1.38352i) q^{12} +(-80.7799 - 21.6449i) q^{13} +(-19.0773 - 33.0428i) q^{14} +(45.5979 - 35.9976i) q^{15} +(7.82311 - 13.5500i) q^{16} +(-19.6420 + 19.6420i) q^{17} +(-25.7081 + 30.9444i) q^{18} +23.7249i q^{19} +(-6.36120 - 64.3073i) q^{20} +(-129.974 - 28.4807i) q^{21} +(-5.29627 + 19.7659i) q^{22} +(19.8727 - 74.1658i) q^{23} +(32.3308 + 101.671i) q^{24} +(-82.4978 - 93.9102i) q^{25} -124.608i q^{26} +(19.3339 + 138.958i) q^{27} +(-104.656 + 104.656i) q^{28} +(103.697 - 179.609i) q^{29} +(69.3934 + 51.7439i) q^{30} +(-16.4679 - 28.5232i) q^{31} +(181.178 + 48.5466i) q^{32} +(38.4902 + 60.0922i) q^{33} +(-35.8441 - 20.6946i) q^{34} +(-46.5165 + 282.491i) q^{35} +(141.757 + 65.2589i) q^{36} +(156.441 + 156.441i) q^{37} +(-34.1457 + 9.14932i) q^{38} +(-321.103 - 292.793i) q^{39} +(214.808 - 80.9520i) q^{40} +(-247.106 + 142.667i) q^{41} +(-9.13295 - 198.046i) q^{42} +(32.8295 + 122.522i) q^{43} +79.3790 q^{44} +(296.393 - 57.2370i) q^{45} +114.406 q^{46} +(89.1338 + 332.652i) q^{47} +(68.4606 - 43.8503i) q^{48} +(270.821 - 156.359i) q^{49} +(103.344 - 154.949i) q^{50} +(-137.551 + 43.7404i) q^{51} +(-466.899 + 125.105i) q^{52} +(-169.925 - 169.925i) q^{53} +(-192.536 + 81.4138i) q^{54} +(124.772 - 89.4906i) q^{55} +(-455.326 - 262.882i) q^{56} +(-56.6556 + 109.488i) q^{57} +(298.489 + 79.9798i) q^{58} +(219.565 + 380.298i) q^{59} +(124.211 - 311.963i) q^{60} +(138.080 - 239.161i) q^{61} +(34.7009 - 34.7009i) q^{62} +(-531.805 - 441.816i) q^{63} +154.310i q^{64} +(-592.856 + 723.021i) q^{65} +(-71.6433 + 78.5704i) q^{66} +(244.540 - 912.635i) q^{67} +(-41.5543 + 155.083i) q^{68} +(268.820 - 294.812i) q^{69} +(-424.509 + 41.9919i) q^{70} -112.676i q^{71} +(-93.5891 + 546.409i) q^{72} +(-474.023 + 474.023i) q^{73} +(-164.825 + 285.485i) q^{74} +(-156.460 - 630.393i) q^{75} +(68.5637 + 118.756i) q^{76} +(-339.695 - 91.0209i) q^{77} +(297.567 - 575.056i) q^{78} +(286.620 + 165.480i) q^{79} +(-101.953 - 142.148i) q^{80} +(-242.609 + 687.446i) q^{81} +(-300.625 - 300.625i) q^{82} +(1449.19 - 388.308i) q^{83} +(-732.896 + 233.056i) q^{84} +(109.520 + 290.615i) q^{85} +(-163.677 + 94.4988i) q^{86} +(907.461 - 581.246i) q^{87} +(72.9820 + 272.373i) q^{88} +598.425 q^{89} +(196.679 + 404.506i) q^{90} +2141.50 q^{91} +(-114.862 - 428.670i) q^{92} +(-7.88376 - 170.958i) q^{93} +(-444.390 + 256.569i) q^{94} +(241.656 + 109.369i) q^{95} +(720.191 + 656.695i) q^{96} +(-288.897 + 77.4097i) q^{97} +(329.477 + 329.477i) q^{98} +(34.1273 + 369.235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.385641	+	1.43923i	0.136345	+	0.508846i	0.999989	+	0.00474347i	$0.00150990\pi$
$2$	0.385641	+	1.43923i	0.136345	+	0.508846i	−0.863644	+	0.504102i	$0.831823\pi$
$3$	4.61491	+	2.38802i	0.888139	+	0.459575i
$3$	4.61491	+	2.38802i	0.888139	+	0.459575i
$4$	5.00553	−	2.88994i	0.625691	−	0.361243i
$5$	4.60989	−	10.1857i	0.412321	−	0.911038i
$5$	4.60989	−	10.1857i	0.412321	−	0.911038i
$6$	−1.65722	+	7.56285i	−0.112759	+	0.514587i
$7$	−24.7344	+	6.62758i	−1.33553	+	0.357855i	−0.854776	−	0.518997i	$-0.826305\pi$
$7$	−24.7344	+	6.62758i	−1.33553	+	0.357855i	−0.480759	+	0.876853i	$0.659639\pi$
$8$	14.5184	+	14.5184i	0.641628	+	0.641628i
$9$	15.5947	+	22.0410i	0.577582	+	0.816332i
$10$	16.4374	+	2.70668i	0.519796	+	0.0855926i
$11$	11.8937	+	6.86683i	0.326008	+	0.188221i	0.654067	−	0.756436i	$-0.273061\pi$
$11$	11.8937	+	6.86683i	0.326008	+	0.188221i	−0.328059	+	0.944657i	$0.606395\pi$
$12$	30.0013	−	1.38352i	0.721719	−	0.0332823i
$13$	−80.7799	−	21.6449i	−1.72341	−	0.461786i	−0.744761	−	0.667331i	$-0.767437\pi$
$13$	−80.7799	−	21.6449i	−1.72341	−	0.461786i	−0.978648	+	0.205545i	$0.934103\pi$
$14$	−19.0773	−	33.0428i	−0.364186	−	0.630789i
$15$	45.5979	−	35.9976i	0.784889	−	0.619637i
$16$	7.82311	−	13.5500i	0.122236	−	0.211719i
$17$	−19.6420	+	19.6420i	−0.280228	+	0.280228i	−0.833200	−	0.552972i	$-0.813494\pi$
$17$	−19.6420	+	19.6420i	−0.280228	+	0.280228i	0.552972	+	0.833200i	$0.313494\pi$
$18$	−25.7081	+	30.9444i	−0.336637	+	0.405203i
$19$			23.7249i			0.286467i	0.989689	+	0.143233i	$0.0457500\pi$
$19$			23.7249i			0.286467i	−0.989689	+	0.143233i	$0.954250\pi$
$20$	−6.36120	−	64.3073i	−0.0711204	−	0.718977i
$21$	−129.974	−	28.4807i	−1.35060	−	0.295952i
$22$	−5.29627	+	19.7659i	−0.0513258	+	0.191551i
$23$	19.8727	−	74.1658i	0.180162	−	0.672375i	−0.815452	−	0.578825i	$-0.803512\pi$
$23$	19.8727	−	74.1658i	0.180162	−	0.672375i	0.995615	−	0.0935508i	$-0.0298218\pi$
$24$	32.3308	+	101.671i	0.274979	+	0.864731i
$25$	−82.4978	−	93.9102i	−0.659982	−	0.751281i
$26$		−	124.608i		−	0.939911i
$27$	19.3339	+	138.958i	0.137808	+	0.990459i
$28$	−104.656	+	104.656i	−0.706360	+	0.706360i
$29$	103.697	−	179.609i	0.664002	−	1.15009i	−0.315552	−	0.948908i	$-0.602190\pi$
$29$	103.697	−	179.609i	0.664002	−	1.15009i	0.979555	−	0.201178i	$-0.0644768\pi$
$30$	69.3934	+	51.7439i	0.422315	+	0.314903i
$31$	−16.4679	−	28.5232i	−0.0954104	−	0.165256i	0.814369	−	0.580347i	$-0.197083\pi$
$31$	−16.4679	−	28.5232i	−0.0954104	−	0.165256i	−0.909780	+	0.415091i	$0.863750\pi$
$32$	181.178	+	48.5466i	1.00088	+	0.268185i
$33$	38.4902	+	60.0922i	0.203039	+	0.316991i
$34$	−35.8441	−	20.6946i	−0.180800	−	0.104385i
$35$	−46.5165	+	282.491i	−0.224649	+	1.36427i
$36$	141.757	+	65.2589i	0.656283	+	0.302124i
$37$	156.441	+	156.441i	0.695101	+	0.695101i	0.963350	−	0.268249i	$-0.0864449\pi$
$37$	156.441	+	156.441i	0.695101	+	0.695101i	−0.268249	+	0.963350i	$0.586445\pi$
$38$	−34.1457	+	9.14932i	−0.145768	+	0.0390583i
$39$	−321.103	−	292.793i	−1.31840	−	1.20216i
$40$	214.808	−	80.9520i	0.849104	−	0.319991i
$41$	−247.106	+	142.667i	−0.941255	+	0.543434i	−0.890354	−	0.455270i	$-0.849543\pi$
$41$	−247.106	+	142.667i	−0.941255	+	0.543434i	−0.0509015	+	0.998704i	$0.516209\pi$
$42$	−9.13295	−	198.046i	−0.0335535	−	0.727600i
$43$	32.8295	+	122.522i	0.116429	+	0.434520i	0.999390	−	0.0349271i	$-0.0111199\pi$
$43$	32.8295	+	122.522i	0.116429	+	0.434520i	−0.882961	+	0.469447i	$0.844453\pi$
$44$	79.3790			0.271974
$45$	296.393	−	57.2370i	0.981860	−	0.189608i
$46$	114.406			0.366700
$47$	89.1338	+	332.652i	0.276628	+	1.03239i	0.954743	+	0.297433i	$0.0961305\pi$
$47$	89.1338	+	332.652i	0.276628	+	1.03239i	−0.678115	+	0.734956i	$0.737203\pi$
$48$	68.4606	−	43.8503i	0.205863	−	0.131859i
$49$	270.821	−	156.359i	0.789567	−	0.455857i
$50$	103.344	−	154.949i	0.292301	−	0.438262i
$51$	−137.551	+	43.7404i	−0.377667	+	0.120096i
$52$	−466.899	+	125.105i	−1.24514	+	0.333634i
$53$	−169.925	−	169.925i	−0.440397	−	0.440397i	0.451748	−	0.892145i	$-0.350800\pi$
$53$	−169.925	−	169.925i	−0.440397	−	0.440397i	−0.892145	+	0.451748i	$0.850800\pi$
$54$	−192.536	+	81.4138i	−0.485201	+	0.205167i
$55$	124.772	−	89.4906i	0.305896	−	0.219398i
$56$	−455.326	−	262.882i	−1.08653	−	0.627306i
$57$	−56.6556	+	109.488i	−0.131653	+	0.254423i
$58$	298.489	+	79.9798i	0.675750	+	0.181067i
$59$	219.565	+	380.298i	0.484491	+	0.839162i	0.999841	−	0.0178172i	$-0.00567168\pi$
$59$	219.565	+	380.298i	0.484491	+	0.839162i	−0.515351	+	0.856979i	$0.672338\pi$
$60$	124.211	−	311.963i	0.267259	−	0.671237i
$61$	138.080	−	239.161i	0.289824	−	0.501990i	−0.683943	−	0.729535i	$-0.739736\pi$
$61$	138.080	−	239.161i	0.289824	−	0.501990i	0.973768	+	0.227545i	$0.0730698\pi$
$62$	34.7009	−	34.7009i	0.0710810	−	0.0710810i
$63$	−531.805	−	441.816i	−1.06351	−	0.883549i
$64$			154.310i			0.301386i
$65$	−592.856	+	723.021i	−1.13130	+	1.37969i
$66$	−71.6433	+	78.5704i	−0.133616	+	0.146536i
$67$	244.540	−	912.635i	0.445900	−	1.66412i	−0.267649	−	0.963516i	$-0.586247\pi$
$67$	244.540	−	912.635i	0.445900	−	1.66412i	0.713549	−	0.700605i	$-0.247087\pi$
$68$	−41.5543	+	155.083i	−0.0741058	+	0.276567i
$69$	268.820	−	294.812i	0.469016	−	0.514365i
$70$	−424.509	+	41.9919i	−0.724835	+	0.0716999i
$71$		−	112.676i		−	0.188341i	−0.995556	−	0.0941705i	$-0.969980\pi$
$71$		−	112.676i		−	0.188341i	0.995556	−	0.0941705i	$-0.0300199\pi$
$72$	−93.5891	+	546.409i	−0.153189	+	0.894374i
$73$	−474.023	+	474.023i	−0.760002	+	0.760002i	−0.976322	−	0.216320i	$-0.930595\pi$
$73$	−474.023	+	474.023i	−0.760002	+	0.760002i	0.216320	+	0.976322i	$0.430595\pi$
$74$	−164.825	+	285.485i	−0.258926	+	0.448473i
$75$	−156.460	−	630.393i	−0.240886	−	0.970553i
$76$	68.5637	+	118.756i	0.103484	+	0.179240i
$77$	−339.695	−	91.0209i	−0.502751	−	0.134712i
$78$	297.567	−	575.056i	0.431959	−	0.834772i
$79$	286.620	+	165.480i	0.408194	+	0.235671i	0.690013	−	0.723797i	$-0.257605\pi$
$79$	286.620	+	165.480i	0.408194	+	0.235671i	−0.281820	+	0.959467i	$0.590938\pi$
$80$	−101.953	−	142.148i	−0.142484	−	0.198658i
$81$	−242.609	+	687.446i	−0.332797	+	0.942998i
$82$	−300.625	−	300.625i	−0.404859	−	0.404859i
$83$	1449.19	−	388.308i	1.91649	−	0.513523i	0.925674	−	0.378321i	$-0.123498\pi$
$83$	1449.19	−	388.308i	1.91649	−	0.513523i	0.990818	−	0.135202i	$-0.0431682\pi$
$84$	−732.896	+	233.056i	−0.951971	+	0.302721i
$85$	109.520	+	290.615i	0.139754	+	0.370842i
$86$	−163.677	+	94.4988i	−0.205229	+	0.118489i
$87$	907.461	−	581.246i	1.11828	−	0.716278i
$88$	72.9820	+	272.373i	0.0884080	+	0.329943i
$89$	598.425			0.712730			0.356365	−	0.934347i	$-0.384016\pi$
$89$	598.425			0.712730			0.356365	+	0.934347i	$0.384016\pi$
$90$	196.679	+	404.506i	0.230353	+	0.473763i
$91$	2141.50			2.46692
$92$	−114.862	−	428.670i	−0.130165	−	0.485782i
$93$	−7.88376	−	170.958i	−0.00879041	−	0.190618i
$94$	−444.390	+	256.569i	−0.487610	+	0.281522i
$95$	241.656	+	109.369i	0.260982	+	0.118116i
$96$	720.191	+	656.695i	0.765669	+	0.698164i
$97$	−288.897	+	77.4097i	−0.302402	+	0.0810285i	−0.406830	−	0.913504i	$-0.633366\pi$
$97$	−288.897	+	77.4097i	−0.302402	+	0.0810285i	0.104427	+	0.994533i	$0.466699\pi$
$98$	329.477	+	329.477i	0.339614	+	0.339614i
$99$	34.1273	+	369.235i	0.0346457	+	0.374844i
$100$	−684.340	−	231.656i	−0.684340	−	0.231656i
$101$	−72.2861	−	41.7344i	−0.0712152	−	0.0411161i	0.463970	−	0.885851i	$-0.346425\pi$
$101$	−72.2861	−	41.7344i	−0.0712152	−	0.0411161i	−0.535185	+	0.844735i	$0.679758\pi$
$102$	−115.998	−	181.100i	−0.112603	−	0.175800i
$103$	−253.003	−	67.7920i	−0.242031	−	0.0648519i	0.135764	−	0.990741i	$-0.456651\pi$
$103$	−253.003	−	67.7920i	−0.242031	−	0.0648519i	−0.377795	+	0.925889i	$0.623318\pi$
$104$	−858.544	−	1487.04i	−0.809492	−	1.40208i
$105$	−889.262	+	1192.59i	−0.826506	+	1.10842i
$106$	179.032	−	310.092i	0.164048	−	0.284140i
$107$	−278.425	+	278.425i	−0.251555	+	0.251555i	−0.821608	−	0.570053i	$-0.806923\pi$
$107$	−278.425	+	278.425i	−0.251555	+	0.251555i	0.570053	+	0.821608i	$0.306923\pi$
$108$	498.356	+	639.682i	0.444022	+	0.569939i
$109$			1231.78i			1.08242i	0.840889	+	0.541208i	$0.182033\pi$
$109$			1231.78i			1.08242i	−0.840889	+	0.541208i	$0.817967\pi$
$110$	176.915	+	145.065i	0.153347	+	0.125740i
$111$	348.376	+	1095.54i	0.297896	+	0.936797i
$112$	−103.696	+	387.000i	−0.0874857	+	0.326501i
$113$	−24.1251	+	90.0361i	−0.0200841	+	0.0749547i	−0.975241	−	0.221147i	$-0.929020\pi$
$113$	−24.1251	+	90.0361i	−0.0200841	+	0.0749547i	0.955156	+	0.296102i	$0.0956867\pi$
$114$	−179.428	−	39.3174i	−0.147412	−	0.0323019i
$115$	−663.821	−	544.314i	−0.538275	−	0.441370i
$116$		−	1198.72i		−	0.959465i
$117$	−782.665	−	2118.01i	−0.618440	−	1.67359i
$118$	−462.664	+	462.664i	−0.360946	+	0.360946i
$119$	355.654	−	616.012i	0.273973	−	0.474535i
$120$	1184.64	+	139.381i	0.901182	+	0.106030i
$121$	−571.193	−	989.336i	−0.429146	−	0.743303i
$122$	397.457	+	106.498i	0.294952	+	0.0790321i
$123$	−1481.06	+	68.2995i	−1.08571	+	0.0500680i
$124$	−164.861	−	95.1827i	−0.119395	−	0.0689327i
$125$	−1336.85	+	407.384i	−0.956571	+	0.291500i
$126$	430.790	−	935.774i	0.304586	−	0.661630i
$127$	−394.695	−	394.695i	−0.275776	−	0.275776i	0.555644	−	0.831420i	$-0.312472\pi$
$127$	−394.695	−	394.695i	−0.275776	−	0.275776i	−0.831420	+	0.555644i	$0.812472\pi$
$128$	1227.34	−	328.864i	0.847519	−	0.227092i
$129$	−141.079	+	643.823i	−0.0962889	+	0.439422i
$130$	−1269.23	−	574.431i	−0.856295	−	0.387545i
$131$	566.164	−	326.875i	0.377603	−	0.218009i	−0.299172	−	0.954199i	$-0.596710\pi$
$131$	566.164	−	326.875i	0.377603	−	0.218009i	0.676775	+	0.736190i	$0.263377\pi$
$132$	366.327	+	189.559i	0.241550	+	0.124992i
$133$	−157.239	−	586.823i	−0.102514	−	0.382587i
$134$	1407.80			0.907577
$135$	1504.51	+	443.650i	0.959167	+	0.282839i
$136$	−570.339			−0.359604
$137$	−2.65200	−	9.89738i	−0.00165383	−	0.00617219i	0.965094	−	0.261904i	$-0.0843503\pi$
$137$	−2.65200	−	9.89738i	−0.00165383	−	0.00617219i	−0.966748	+	0.255732i	$0.917684\pi$
$138$	527.971	+	273.203i	0.325680	+	0.168526i
$139$	−1435.50	+	828.789i	−0.875956	+	0.505734i	−0.869323	−	0.494244i	$-0.835445\pi$
$139$	−1435.50	+	828.789i	−0.875956	+	0.505734i	−0.00663323	+	0.999978i	$0.502111\pi$
$140$	583.542	+	1548.45i	0.352274	+	0.934768i
$141$	−383.035	+	1748.01i	−0.228776	+	1.04404i
$142$	162.167	−	43.4526i	0.0958366	−	0.0256793i
$143$	−812.140	−	812.140i	−0.474927	−	0.474927i
$144$	420.655	−	38.8799i	0.243435	−	0.0224999i
$145$	−1351.41	−	1884.21i	−0.773990	−	1.07914i
$146$	−865.032	−	499.427i	−0.490346	−	0.283102i
$147$	1623.20	−	74.8545i	0.910745	−	0.0419993i
$148$	1235.18	+	330.964i	0.686019	+	0.183818i
$149$	−763.694	−	1322.76i	−0.419894	−	0.727278i	0.576034	−	0.817426i	$-0.304600\pi$
$149$	−763.694	−	1322.76i	−0.419894	−	0.727278i	−0.995928	+	0.0901473i	$0.971266\pi$
$150$	846.945	−	468.288i	0.461018	−	0.254904i
$151$	−219.184	+	379.637i	−0.118125	+	0.204599i	−0.919025	−	0.394200i	$-0.871022\pi$
$151$	−219.184	+	379.637i	−0.118125	+	0.204599i	0.800900	+	0.598799i	$0.204355\pi$
$152$	−344.448	+	344.448i	−0.183805	+	0.183805i
$153$	−739.239	−	126.617i	−0.390614	−	0.0669044i
$154$		−	524.001i		−	0.274190i
$155$	−366.445	+	36.2484i	−0.189894	+	0.0187841i
$156$	−2453.45	−	537.615i	−1.25919	−	0.275921i
$157$	−394.505	+	1472.31i	−0.200541	+	0.748430i	0.790221	+	0.612821i	$0.209965\pi$
$157$	−394.505	+	1472.31i	−0.200541	+	0.748430i	−0.990763	+	0.135608i	$0.956701\pi$
$158$	−127.632	+	476.330i	−0.0642650	+	0.239840i
$159$	−378.405	−	1189.97i	−0.188739	−	0.593529i
$160$	1329.69	−	1621.64i	0.657010	−	0.801261i
$161$			1966.16i			0.962453i
$162$	−1082.96	−	84.0636i	−0.525216	−	0.0407695i
$163$	1347.15	−	1347.15i	0.647345	−	0.647345i	−0.305006	−	0.952350i	$-0.598658\pi$
$163$	1347.15	−	1347.15i	0.647345	−	0.647345i	0.952350	+	0.305006i	$0.0986584\pi$
$164$	−824.597	+	1428.24i	−0.392623	+	0.680044i
$165$	789.518	−	115.032i	0.372508	−	0.0542740i
$166$	1117.73	+	1935.97i	0.522608	+	0.905183i
$167$	−114.108	−	30.5750i	−0.0528737	−	0.0141675i	0.232285	−	0.972648i	$-0.425380\pi$
$167$	−114.108	−	30.5750i	−0.0528737	−	0.0141675i	−0.285159	+	0.958480i	$0.592046\pi$
$168$	−1473.52	−	2300.50i	−0.676692	−	1.05647i
$169$	4154.23	+	2398.45i	1.89087	+	1.09169i
$170$	−376.027	+	269.698i	−0.169647	+	0.121676i
$171$	−522.921	+	369.984i	−0.233852	+	0.165458i
$172$	518.410	+	518.410i	0.229816	+	0.229816i
$173$	−474.757	+	127.211i	−0.208642	+	0.0559056i	−0.361626	−	0.932323i	$-0.617778\pi$
$173$	−474.757	+	127.211i	−0.208642	+	0.0559056i	0.152984	+	0.988229i	$0.451112\pi$
$174$	1186.50	+	1081.90i	0.516946	+	0.471370i
$175$	2662.93	+	1776.06i	1.15028	+	0.767184i
$176$	186.091	−	107.440i	0.0796998	−	0.0460147i
$177$	105.114	+	2279.37i	0.0446374	+	0.967952i
$178$	230.778	+	861.274i	0.0971770	+	0.362670i
$179$	641.856			0.268015			0.134007	−	0.990980i	$-0.457215\pi$
$179$	641.856			0.268015			0.134007	+	0.990980i	$0.457215\pi$
$180$	1318.19	−	1143.06i	0.545846	−	0.473326i
$181$	−1243.05			−0.510470			−0.255235	−	0.966879i	$-0.582153\pi$
$181$	−1243.05			−0.510470			−0.255235	+	0.966879i	$0.582153\pi$
$182$	825.851	+	3082.12i	0.336352	+	1.25528i
$183$	1208.35	−	773.968i	0.488106	−	0.312641i
$184$	1365.29	−	788.248i	0.547012	−	0.315817i
$185$	2314.64	−	872.288i	0.919869	−	0.346659i
$186$	243.008	−	77.2750i	0.0957968	−	0.0304628i
$187$	−368.494	+	98.7376i	−0.144101	+	0.0386118i
$188$	1407.51	+	1407.51i	0.546027	+	0.546027i
$189$	−1399.17	−	3308.90i	−0.538488	−	1.27348i
$190$	−64.2157	+	389.976i	−0.0245195	+	0.148904i
$191$	−3517.42	−	2030.79i	−1.33252	−	0.769332i	−0.346837	−	0.937925i	$-0.612744\pi$
$191$	−3517.42	−	2030.79i	−1.33252	−	0.769332i	−0.985686	+	0.168593i	$0.946078\pi$
$192$	−368.495	+	712.125i	−0.138509	+	0.267673i
$193$	−2470.21	−	661.892i	−0.921295	−	0.246860i	−0.233156	−	0.972439i	$-0.574905\pi$
$193$	−2470.21	−	661.892i	−0.921295	−	0.246860i	−0.688139	+	0.725579i	$0.741572\pi$
$194$	−222.821	−	385.938i	−0.0824620	−	0.142828i
$195$	−4462.56	+	1920.92i	−1.63882	+	0.705436i
$196$	903.736	−	1565.32i	0.329350	−	0.570451i
$197$	1350.59	−	1350.59i	0.488454	−	0.488454i	−0.419364	−	0.907818i	$-0.637747\pi$
$197$	1350.59	−	1350.59i	0.488454	−	0.488454i	0.907818	+	0.419364i	$0.137747\pi$
$198$	−518.255	+	191.510i	−0.186014	+	0.0687373i
$199$		−	4890.58i		−	1.74213i	−0.491167	−	0.871065i	$-0.663430\pi$
$199$		−	4890.58i		−	1.74213i	0.491167	−	0.871065i	$-0.336570\pi$
$200$	165.689	−	2561.16i	0.0585800	−	0.905506i
$201$	3307.92	−	3627.76i	1.16081	−	1.27305i
$202$	32.1890	−	120.131i	0.0112119	−	0.0418435i
$203$	−1374.52	+	5129.78i	−0.475234	+	1.77360i
$204$	−562.109	+	616.459i	−0.192919	+	0.211572i
$205$	314.031	+	3174.63i	0.106990	+	1.08159i
$206$		−	390.274i		−	0.131999i
$207$	1944.59	−	718.582i	0.652941	−	0.241280i
$208$	−925.239	+	925.239i	−0.308432	+	0.308432i
$209$	−162.915	+	282.177i	−0.0539190	+	0.0933905i
$210$	−2059.34	−	819.946i	−0.676706	−	0.269436i
$211$	−1481.97	−	2566.85i	−0.483522	−	0.837484i	0.516299	−	0.856408i	$-0.327309\pi$
$211$	−1481.97	−	2566.85i	−0.483522	−	0.837484i	−0.999821	+	0.0189240i	$0.993976\pi$
$212$	−1341.64	−	359.492i	−0.434643	−	0.116462i
$213$	269.073	−	519.991i	0.0865568	−	0.167273i
$214$	−508.090	−	293.346i	−0.162301	−	0.0937043i
$215$	1399.31	+	230.419i	0.443871	+	0.0730903i
$216$	−1736.74	+	2298.14i	−0.547085	+	0.723927i
$217$	596.365	+	596.365i	0.186562	+	0.186562i
$218$	−1772.82	+	475.026i	−0.550782	+	0.147582i
$219$	−3319.55	+	1055.60i	−1.02427	+	0.325710i
$220$	365.929	−	808.533i	0.112141	−	0.247778i
$221$	2011.82	−	1161.53i	0.612353	−	0.353542i
$222$	−1442.40	+	923.882i	−0.436069	+	0.279310i
$223$	605.443	+	2259.54i	0.181809	+	0.678521i	0.995291	+	0.0969311i	$0.0309026\pi$
$223$	605.443	+	2259.54i	0.181809	+	0.678521i	−0.813482	+	0.581590i	$0.802431\pi$
$224$	−4803.09			−1.43268
$225$	783.341	−	3282.83i	0.232101	−	0.972692i
$226$	−138.887			−0.0408787
$227$	530.537	+	1979.99i	0.155123	+	0.578928i	0.999095	+	0.0425397i	$0.0135449\pi$
$227$	530.537	+	1979.99i	0.155123	+	0.578928i	−0.843972	+	0.536388i	$0.819788\pi$
$228$	32.8239	+	711.779i	0.00953427	+	0.206749i
$229$	−3464.76	+	2000.38i	−0.999815	+	0.577244i	−0.908194	−	0.418550i	$-0.862538\pi$
$229$	−3464.76	+	2000.38i	−0.999815	+	0.577244i	−0.0916215	+	0.995794i	$0.529205\pi$
$230$	527.397	−	1165.30i	0.151198	−	0.334077i
$231$	−1350.30	−	1231.25i	−0.384602	−	0.350694i
$232$	4113.14	−	1102.11i	1.16397	−	0.311885i
$233$	−4906.70	−	4906.70i	−1.37961	−	1.37961i	−0.845271	−	0.534337i	$-0.820561\pi$
$233$	−4906.70	−	4906.70i	−1.37961	−	1.37961i	−0.534337	−	0.845271i	$-0.679439\pi$
$234$	2746.49	−	1943.23i	0.767280	−	0.542876i
$235$	3799.20	+	625.598i	1.05461	+	0.173657i
$236$	2198.08	+	1269.06i	0.606283	+	0.350038i
$237$	927.556	+	1448.13i	0.254225	+	0.396904i
$238$	1023.74	+	274.310i	0.278820	+	0.0747096i
$239$	2501.24	+	4332.28i	0.676954	+	1.17252i	0.975894	+	0.218247i	$0.0700339\pi$
$239$	2501.24	+	4332.28i	0.676954	+	1.17252i	−0.298939	+	0.954272i	$0.596633\pi$
$240$	−131.051	−	899.466i	−0.0352471	−	0.241918i
$241$	−1825.14	+	3161.24i	−0.487834	+	0.844952i	−0.999902	−	0.0139921i	$-0.995546\pi$
$241$	−1825.14	+	3161.24i	−0.487834	+	0.844952i	0.512069	+	0.858945i	$0.328879\pi$
$242$	1203.61	−	1203.61i	0.319715	−	0.319715i
$243$	−2761.25	+	2593.14i	−0.728948	+	0.684569i
$244$		−	1596.17i		−	0.418788i
$245$	−344.169	−	3479.31i	−0.0897477	−	0.907285i
$246$	−669.458	−	2105.25i	−0.173508	−	0.545634i
$247$	513.524	−	1916.50i	0.132286	−	0.493700i
$248$	175.024	−	653.199i	0.0448147	−	0.167251i
$249$	7615.15	+	1668.68i	1.93811	+	0.424692i
$250$	−1101.86	−	1766.93i	−0.278752	−	0.447003i
$251$			3563.08i			0.896013i	0.894030	+	0.448007i	$0.147866\pi$
$251$			3563.08i			0.896013i	−0.894030	+	0.448007i	$0.852134\pi$
$252$	−3938.79	−	674.637i	−0.984605	−	0.168643i
$253$	745.643	−	745.643i	0.185289	−	0.185289i
$254$	415.847	−	720.268i	0.102727	−	0.177928i
$255$	−188.569	+	1602.70i	−0.0463083	+	0.393587i
$256$	1563.86	+	2708.69i	0.381803	+	0.661302i
$257$	−6663.08	−	1785.37i	−1.61724	−	0.433339i	−0.667053	−	0.745010i	$-0.732444\pi$
$257$	−6663.08	−	1785.37i	−1.61724	−	0.433339i	−0.950190	+	0.311672i	$0.899111\pi$
$258$	−981.017	+	45.2399i	−0.236727	+	0.0109167i
$259$	−4906.30	−	2832.66i	−1.17708	−	0.679586i
$260$	−878.067	+	5332.42i	−0.209444	+	1.27193i
$261$	5575.88	−	515.362i	1.32237	−	0.122223i
$262$	688.785	+	688.785i	0.162417	+	0.162417i
$263$	4933.33	−	1321.88i	1.15666	−	0.309927i	0.371030	−	0.928621i	$-0.379005\pi$
$263$	4933.33	−	1321.88i	1.15666	−	0.309927i	0.785632	+	0.618694i	$0.212338\pi$
$264$	−313.626	+	1431.26i	−0.0731149	+	0.333666i
$265$	−2514.15	+	947.474i	−0.582804	+	0.219634i
$266$	783.937	−	452.607i	0.180700	−	0.104327i
$267$	2761.68	+	1429.05i	0.633003	+	0.327553i
$268$	−1413.41	−	5274.93i	−0.322157	−	1.20230i
$269$	6950.52			1.57539			0.787696	−	0.616064i	$-0.211274\pi$
$269$	6950.52			1.57539			0.787696	+	0.616064i	$0.211274\pi$
$270$	−58.3139	+	2336.43i	−0.0131440	+	0.526632i
$271$	−5694.64			−1.27648			−0.638238	−	0.769839i	$-0.720336\pi$
$271$	−5694.64			−1.27648			−0.638238	+	0.769839i	$0.720336\pi$
$272$	112.488	+	419.810i	0.0250756	+	0.0935836i
$273$	9882.82	+	5113.94i	2.19097	+	1.13374i
$274$	13.2219	−	7.63368i	0.00291520	−	0.00168309i
$275$	−336.339	−	1683.44i	−0.0737527	−	0.369146i
$276$	493.596	−	2252.56i	0.107648	−	0.491262i
$277$	−2770.99	+	742.484i	−0.601056	+	0.161052i	−0.546501	−	0.837458i	$-0.684041\pi$
$277$	−2770.99	+	742.484i	−0.601056	+	0.161052i	−0.0545548	+	0.998511i	$0.517374\pi$
$278$	−1746.41	−	1746.41i	−0.376772	−	0.376772i
$279$	371.868	−	807.781i	0.0797962	−	0.173335i
$280$	−4776.65	+	3425.96i	−1.01950	+	0.731215i
$281$	5092.45	+	2940.13i	1.08110	+	0.624176i	0.931194	−	0.364524i	$-0.118768\pi$
$281$	5092.45	+	2940.13i	1.08110	+	0.624176i	0.149910	+	0.988700i	$0.452102\pi$
$282$	−2663.51	+	122.828i	−0.562446	+	0.0259373i
$283$	1756.05	+	470.532i	0.368856	+	0.0988348i	0.438486	−	0.898738i	$-0.355515\pi$
$283$	1756.05	+	470.532i	0.368856	+	0.0988348i	−0.0696293	+	0.997573i	$0.522182\pi$
$284$	−325.628	−	564.005i	−0.0680369	−	0.117843i
$285$	854.041	+	1081.81i	0.177505	+	0.224845i
$286$	855.664	−	1482.05i	0.176911	−	0.306418i
$287$	5166.49	−	5166.49i	1.06261	−	1.06261i
$288$	1755.41	+	4750.42i	0.359162	+	0.971948i
$289$			4141.39i			0.842945i
$290$	2190.65	−	2671.62i	0.443585	−	0.540976i
$291$	−1518.09	−	332.653i	−0.305814	−	0.0670119i
$292$	−1002.84	+	3742.63i	−0.200981	+	0.750072i
$293$	1783.36	−	6655.60i	0.355581	−	1.32705i	−0.524172	−	0.851613i	$-0.675625\pi$
$293$	1783.36	−	6655.60i	0.355581	−	1.32705i	0.879752	−	0.475432i	$-0.157708\pi$
$294$	733.707	+	2307.30i	0.145547	+	0.457703i
$295$	4885.78	−	483.296i	0.964275	−	0.0953850i
$296$			4542.54i			0.891992i
$297$	−724.246	+	1785.48i	−0.141498	+	0.348836i
$298$	1609.24	−	1609.24i	0.312822	−	0.312822i
$299$	−3210.62	+	5560.96i	−0.620987	+	1.07558i
$300$	−2604.97	−	2703.29i	−0.501326	−	0.520248i
$301$	−1624.04	−	2812.92i	−0.310991	−	0.538652i
$302$	−630.912	−	169.052i	−0.120215	−	0.0322115i
$303$	−233.931	−	365.221i	−0.0443531	−	0.0692455i
$304$	321.473	+	185.603i	0.0606505	+	0.0350166i
$305$	−1799.49	−	2508.95i	−0.337832	−	0.471022i
$306$	−102.850	−	1112.77i	−0.0192141	−	0.207884i
$307$	−1580.63	−	1580.63i	−0.293848	−	0.293848i	0.544750	−	0.838598i	$-0.316624\pi$
$307$	−1580.63	−	1580.63i	−0.293848	−	0.293848i	−0.838598	+	0.544750i	$0.816624\pi$
$308$	−1963.40	+	526.091i	−0.363230	+	0.0973273i
$309$	−1005.70	−	917.031i	−0.185153	−	0.168829i
$310$	−193.486	−	513.421i	−0.0354493	−	0.0940657i
$311$	−1301.03	+	751.148i	−0.237217	+	0.136957i	−0.613897	−	0.789386i	$-0.710399\pi$
$311$	−1301.03	+	751.148i	−0.237217	+	0.136957i	0.376680	+	0.926343i	$0.377066\pi$
$312$	−411.015	−	8912.78i	−0.0745806	−	1.61727i
$313$	−1012.40	−	3778.34i	−0.182825	−	0.682314i	−0.995086	−	0.0990184i	$-0.968430\pi$
$313$	−1012.40	−	3778.34i	−0.182825	−	0.682314i	0.812260	−	0.583295i	$-0.198237\pi$
$314$	−2271.14			−0.408178
$315$	−6951.78	+	3380.09i	−1.24346	+	0.604593i
$316$	1912.92			0.340538
$317$	−998.390	−	3726.04i	−0.176893	−	0.660175i	−0.996221	−	0.0868500i	$-0.972320\pi$
$317$	−998.390	−	3726.04i	−0.176893	−	0.660175i	0.819328	−	0.573325i	$-0.194347\pi$
$318$	1566.72	−	1003.52i	0.276281	−	0.176963i
$319$	2466.68	−	1424.14i	0.432940	−	0.249958i
$320$	1571.76	+	711.351i	0.274574	+	0.124268i
$321$	−1949.79	+	620.020i	−0.339024	+	0.107807i
$322$	−2829.76	+	758.232i	−0.489740	+	0.131225i
$323$	−466.004	−	466.004i	−0.0802761	−	0.0802761i
$324$	772.293	+	4142.16i	0.132423	+	0.710247i
$325$	4631.48	+	9371.71i	0.790488	+	1.59953i
$326$	2458.39	+	1419.35i	0.417661	+	0.241136i
$327$	−2941.52	+	5684.56i	−0.497451	+	0.961335i
$328$	−5658.87	−	1516.29i	−0.952618	−	0.255253i
$329$	−4409.35	−	7637.22i	−0.738892	−	1.27980i
$330$	470.028	+	1091.94i	0.0784067	+	0.182149i
$331$	−3448.09	+	5972.26i	−0.572580	+	0.991738i	0.423720	+	0.905793i	$0.360724\pi$
$331$	−3448.09	+	5972.26i	−0.572580	+	0.991738i	−0.996300	+	0.0859446i	$0.972609\pi$
$332$	6131.76	−	6131.76i	1.01363	−	1.01363i
$333$	−1008.46	+	5887.76i	−0.165955	+	0.968912i
$334$		−	176.018i		−	0.0288362i
$335$	−8168.54	−	6697.97i	−1.33222	−	1.09238i
$336$	−1402.71	+	1538.34i	−0.227751	+	0.249772i
$337$	1772.28	−	6614.22i	0.286475	−	1.06914i	−0.661280	−	0.750139i	$-0.729987\pi$
$337$	1772.28	−	6614.22i	0.286475	−	1.06914i	0.947755	−	0.318999i	$-0.103347\pi$
$338$	−1849.88	+	6903.85i	−0.297693	+	1.11101i
$339$	−326.343	+	357.897i	−0.0522847	+	0.0573401i
$340$	1388.07	+	1138.17i	0.221407	+	0.181548i
$341$		−	452.329i		−	0.0718329i
$342$	−734.153	−	609.924i	−0.116077	−	0.0964354i
$343$	548.319	−	548.319i	0.0863162	−	0.0863162i
$344$	−1302.18	+	2255.45i	−0.204096	+	0.353504i
$345$	−1763.64	−	4097.17i	−0.275221	−	0.639375i
$346$	−366.172	−	634.229i	−0.0568946	−	0.0985444i
$347$	−260.095	−	69.6922i	−0.0402381	−	0.0107818i	0.238644	−	0.971107i	$-0.423297\pi$
$347$	−260.095	−	69.6922i	−0.0402381	−	0.0107818i	−0.278882	+	0.960325i	$0.589964\pi$
$348$	2862.56	−	5531.96i	0.440946	−	0.852138i
$349$	−8184.76	−	4725.48i	−1.25536	−	0.724782i	−0.283190	−	0.959064i	$-0.591393\pi$
$349$	−8184.76	−	4725.48i	−1.25536	−	0.724782i	−0.972169	+	0.234282i	$0.924726\pi$
$350$	−1529.22	+	4517.50i	−0.233544	+	0.689916i
$351$	1445.93	−	11643.5i	0.219881	−	1.77060i
$352$	1821.52	+	1821.52i	0.275816	+	0.275816i
$353$	342.585	−	91.7954i	0.0516543	−	0.0138407i	−0.232899	−	0.972501i	$-0.574821\pi$
$353$	342.585	−	91.7954i	0.0516543	−	0.0138407i	0.284554	+	0.958660i	$0.408155\pi$
$354$	−3240.00	+	1030.30i	−0.486452	+	0.154689i
$355$	−1147.69	−	519.426i	−0.171586	−	0.0776570i
$356$	2995.44	−	1729.42i	0.445949	−	0.257469i
$357$	3112.36	−	1993.53i	0.461411	−	0.295542i
$358$	247.526	+	923.781i	0.0365424	+	0.136378i
$359$	2385.59			0.350715			0.175358	−	0.984505i	$-0.443892\pi$
$359$	2385.59			0.350715			0.175358	+	0.984505i	$0.443892\pi$
$360$	5134.14	+	3472.16i	0.751647	+	0.508330i
$361$	6296.13			0.917937
$362$	−479.371	−	1789.04i	−0.0695999	−	0.259750i
$363$	−273.450	−	5929.71i	−0.0395383	−	0.857381i
$364$	10719.3	−	6188.81i	1.54353	−	0.891159i
$365$	2643.07	+	7013.46i	0.379026	+	1.00576i
$366$	1579.91	+	1440.62i	0.225637	+	0.205744i
$367$	3206.46	−	859.169i	0.456065	−	0.122202i	−0.0234708	−	0.999725i	$-0.507472\pi$
$367$	3206.46	−	859.169i	0.456065	−	0.122202i	0.479536	+	0.877522i	$0.340805\pi$
$368$	−849.482	−	849.482i	−0.120332	−	0.120332i
$369$	−6998.06	−	3221.61i	−0.987275	−	0.454499i
$370$	2148.05	+	2994.92i	0.301815	+	0.420806i
$371$	5329.20	+	3076.82i	0.745764	+	0.430567i
$372$	−533.521	−	832.951i	−0.0743596	−	0.116093i
$373$	10590.5	+	2837.71i	1.47012	+	0.393917i	0.902971	−	0.429701i	$-0.141381\pi$
$373$	10590.5	+	2837.71i	1.47012	+	0.393917i	0.567145	+	0.823618i	$0.308048\pi$
$374$	−284.213	−	492.271i	−0.0392949	−	0.0680608i
$375$	−7142.27	−	1312.38i	−0.983534	−	0.180723i
$376$	−3535.49	+	6123.65i	−0.484917	+	0.839901i
$377$	−12264.3	+	12264.3i	−1.67544	+	1.67544i
$378$	4222.70	−	3289.77i	0.574583	−	0.447640i
$379$			1340.48i			0.181677i	0.995866	+	0.0908385i	$0.0289547\pi$
$379$			1340.48i			0.181677i	−0.995866	+	0.0908385i	$0.971045\pi$
$380$	1525.69	−	150.919i	0.205963	−	0.0203737i
$381$	−878.940	−	2764.02i	−0.118188	−	0.371666i
$382$	1566.31	−	5845.55i	0.209789	−	0.782943i
$383$	−3683.28	+	13746.2i	−0.491401	+	1.83394i	0.0579162	+	0.998321i	$0.481554\pi$
$383$	−3683.28	+	13746.2i	−0.491401	+	1.83394i	−0.549318	+	0.835614i	$0.685112\pi$
$384$	6449.39	+	1413.23i	0.857081	+	0.187809i
$385$	−2493.07	+	3040.44i	−0.330022	+	0.402481i
$386$		−	3810.47i		−	0.502455i
$387$	−2188.53	+	2634.28i	−0.287465	+	0.346016i
$388$	−1222.37	+	1222.37i	−0.159940	+	0.159940i
$389$	−5939.24	+	10287.1i	−0.774116	+	1.34081i	0.161174	+	0.986926i	$0.448472\pi$
$389$	−5939.24	+	10287.1i	−0.774116	+	1.34081i	−0.935290	+	0.353883i	$0.884861\pi$
$390$	−4485.60	−	5681.88i	−0.582403	−	0.737726i
$391$	1066.42	+	1847.10i	0.137932	+	0.238905i
$392$	6201.96	+	1661.81i	0.799098	+	0.214118i
$393$	3393.38	−	156.486i	0.435555	−	0.0200857i
$394$	2464.66	+	1422.97i	0.315146	+	0.181950i
$395$	3006.83	−	2156.59i	0.383012	−	0.274708i
$396$	1237.89	+	1749.59i	0.157087	+	0.222021i
$397$	1019.37	+	1019.37i	0.128869	+	0.128869i	0.768599	−	0.639731i	$-0.220954\pi$
$397$	1019.37	+	1019.37i	0.128869	+	0.128869i	−0.639731	+	0.768599i	$0.720954\pi$
$398$	7038.68	−	1886.01i	0.886476	−	0.237530i
$399$	675.703	−	3083.62i	0.0847806	−	0.386903i
$400$	−1917.87	+	383.177i	−0.239734	+	0.0478972i
$401$	8126.77	−	4691.99i	1.01205	−	0.584306i	0.100257	−	0.994962i	$-0.468033\pi$
$401$	8126.77	−	4691.99i	1.01205	−	0.584306i	0.911791	+	0.410655i	$0.134700\pi$
$402$	6496.86	+	3361.85i	0.806055	+	0.417100i
$403$	712.893	+	2660.55i	0.0881184	+	0.328862i
$404$	−482.440			−0.0594116
$405$	5883.73	+	5640.20i	0.721888	+	0.692009i
$406$	−7913.02			−0.967283
$407$	786.408	+	2934.92i	0.0957760	+	0.357441i
$408$	−2632.06	−	1361.98i	−0.319378	−	0.165265i
$409$	2717.07	−	1568.70i	0.328485	−	0.189651i	−0.326683	−	0.945134i	$-0.605931\pi$
$409$	2717.07	−	1568.70i	0.328485	−	0.189651i	0.655168	+	0.755483i	$0.272598\pi$
$410$	−4447.93	+	1676.23i	−0.535775	+	0.201910i
$411$	11.3964	−	52.0085i	0.00136775	−	0.00624183i
$412$	−1462.33	+	391.830i	−0.174864	+	0.0468546i
$413$	−7951.27	−	7951.27i	−0.947353	−	0.947353i
$414$	1784.12	+	2521.61i	0.211799	+	0.299349i
$415$	2725.39	−	16551.1i	0.322372	−	1.95773i
$416$	−13584.8	−	7843.18i	−1.60108	−	0.924383i
$417$	−8603.88	+	396.770i	−1.01039	+	0.0465946i
$418$	−468.946	−	125.654i	−0.0548729	−	0.0147032i
$419$	1590.40	+	2754.66i	0.185433	+	0.321179i	0.943722	−	0.330739i	$-0.107298\pi$
$419$	1590.40	+	2754.66i	0.185433	+	0.321179i	−0.758290	+	0.651918i	$0.773965\pi$
$420$	−1004.73	+	8539.44i	−0.116728	+	0.992100i
$421$	1402.60	−	2429.37i	0.162372	−	0.281236i	−0.773347	−	0.633983i	$-0.781419\pi$
$421$	1402.60	−	2429.37i	0.162372	−	0.281236i	0.935719	+	0.352747i	$0.114752\pi$
$422$	3122.79	−	3122.79i	0.360225	−	0.360225i
$423$	−5941.96	+	7152.21i	−0.682997	+	0.822110i
$424$		−	4934.08i		−	0.565142i
$425$	3465.00	+	224.161i	0.395475	+	0.0255845i
$426$	852.154	+	186.729i	0.0969178	+	0.0212372i
$427$	−1830.27	+	6830.64i	−0.207430	+	0.774141i
$428$	−589.032	+	2198.30i	−0.0665232	+	0.248268i
$429$	−1808.54	−	5687.36i	−0.203537	−	0.640066i
$430$	208.006	+	2102.79i	0.0233278	+	0.235827i
$431$			14909.0i			1.66623i	0.553103	+	0.833113i	$0.313444\pi$
$431$			14909.0i			1.66623i	−0.553103	+	0.833113i	$0.686556\pi$
$432$	2034.13	+	825.105i	0.226544	+	0.0918932i
$433$	3778.79	−	3778.79i	0.419393	−	0.419393i	−0.465602	−	0.884994i	$-0.654162\pi$
$433$	3778.79	−	3778.79i	0.419393	−	0.419393i	0.884994	+	0.465602i	$0.154162\pi$
$434$	−628.325	+	1088.29i	−0.0694944	+	0.120368i
$435$	−1737.11	−	11922.6i	−0.191467	−	1.31413i
$436$	3559.78	+	6165.72i	0.391015	+	0.677258i
$437$	1759.58	+	471.478i	0.192613	+	0.0516106i
$438$	−2799.40	−	4370.52i	−0.305390	−	0.476784i
$439$	1424.98	+	822.711i	0.154921	+	0.0894438i	0.575457	−	0.817832i	$-0.304824\pi$
$439$	1424.98	+	822.711i	0.154921	+	0.0894438i	−0.420535	+	0.907276i	$0.638158\pi$
$440$	3110.75	+	512.234i	0.337044	+	0.0554995i
$441$	7669.69	+	3530.80i	0.828170	+	0.381254i
$442$	2447.55	+	2447.55i	0.263389	+	0.263389i
$443$	−6607.83	+	1770.56i	−0.708685	+	0.189891i	−0.595117	−	0.803639i	$-0.702894\pi$
$443$	−6607.83	+	1770.56i	−0.708685	+	0.189891i	−0.113567	+	0.993530i	$0.536228\pi$
$444$	4909.87	+	4476.99i	0.524802	+	0.478533i
$445$	2758.68	−	6095.39i	0.293874	−	0.649324i
$446$	−3018.53	+	1742.75i	−0.320474	+	0.185026i
$447$	−365.607	−	7928.12i	−0.0386860	−	0.838897i
$448$	−1022.70	−	3816.77i	−0.107853	−	0.402512i
$449$	7775.18			0.817224			0.408612	−	0.912708i	$-0.366013\pi$
$449$	7775.18			0.817224			0.408612	+	0.912708i	$0.366013\pi$
$450$	5026.85	−	138.586i	0.526596	−	0.0145178i
$451$	−3918.67			−0.409142
$452$	139.440	+	520.399i	0.0145104	+	0.0541537i
$453$	−1918.09	+	1228.57i	−0.198940	+	0.127425i
$454$	−2645.07	+	1527.13i	−0.273435	+	0.157868i
$455$	9872.08	−	21812.7i	1.01717	−	2.24746i
$456$	−2412.14	+	767.046i	−0.247717	+	0.0787724i
$457$	2300.05	−	616.297i	0.235431	−	0.0630834i	−0.139175	−	0.990268i	$-0.544445\pi$
$457$	2300.05	−	616.297i	0.235431	−	0.0630834i	0.374605	+	0.927184i	$0.377778\pi$
$458$	−4215.17	−	4215.17i	−0.430048	−	0.430048i
$459$	−3109.15	−	2349.64i	−0.316172	−	0.238937i
$460$	−4895.81	−	806.173i	−0.496236	−	0.0817130i
$461$	−7507.21	−	4334.29i	−0.758451	−	0.437892i	0.0702886	−	0.997527i	$-0.477608\pi$
$461$	−7507.21	−	4334.29i	−0.758451	−	0.437892i	−0.828739	+	0.559635i	$0.810941\pi$
$462$	1251.33	−	2418.22i	0.126011	−	0.243519i
$463$	−4939.17	−	1323.45i	−0.495772	−	0.132842i	0.00226497	−	0.999997i	$-0.499279\pi$
$463$	−4939.17	−	1323.45i	−0.495772	−	0.132842i	−0.498037	+	0.867156i	$0.665946\pi$
$464$	−1622.47	−	2810.20i	−0.162330	−	0.281164i
$465$	−1777.67	−	707.795i	−0.177285	−	0.0705876i
$466$	5169.66	−	8954.12i	0.513906	−	0.890111i
$467$	−4104.76	+	4104.76i	−0.406736	+	0.406736i	−0.880599	−	0.473863i	$-0.842859\pi$
$467$	−4104.76	+	4104.76i	−0.406736	+	0.406736i	0.473863	+	0.880599i	$0.342859\pi$
$468$	−10038.6	−	8339.92i	−0.991526	−	0.823746i
$469$			24194.2i			2.38206i
$470$	564.747	+	5709.19i	0.0554251	+	0.560309i
$471$	−5336.52	+	5852.50i	−0.522068	+	0.572546i
$472$	−2333.58	+	8709.04i	−0.227567	+	0.849292i
$473$	−450.870	+	1682.67i	−0.0438288	+	0.163571i
$474$	−1726.49	+	1893.43i	−0.167301	+	0.183477i
$475$	2228.01	−	1957.25i	0.215217	−	0.189063i
$476$		−	4111.29i		−	0.395883i
$477$	1095.38	−	6395.26i	0.105145	−	0.613876i
$478$	−5270.58	+	5270.58i	−0.504332	+	0.504332i
$479$	7608.37	−	13178.1i	0.725752	−	1.25704i	−0.232912	−	0.972498i	$-0.574825\pi$
$479$	7608.37	−	13178.1i	0.725752	−	1.25704i	0.958664	−	0.284541i	$-0.0918413\pi$
$480$	10008.9	−	4308.37i	0.951755	−	0.409686i
$481$	−9251.13	−	16023.4i	−0.876955	−	1.51893i
$482$	−5253.62	−	1407.70i	−0.496464	−	0.133027i
$483$	−4695.22	+	9073.63i	−0.442319	+	0.854792i
$484$	−5718.25	−	3301.43i	−0.537026	−	0.310052i
$485$	−543.310	+	3299.47i	−0.0508669	+	0.308910i
$486$	−4796.99	−	2974.06i	−0.447728	−	0.277585i
$487$	1399.75	+	1399.75i	0.130244	+	0.130244i	0.769223	−	0.638980i	$-0.220643\pi$
$487$	1399.75	+	1399.75i	0.130244	+	0.130244i	−0.638980	+	0.769223i	$0.720643\pi$
$488$	5476.92	−	1467.54i	0.508050	−	0.136132i
$489$	9434.01	−	2999.96i	0.872435	−	0.277429i
$490$	4874.81	−	1837.11i	0.449432	−	0.169371i
$491$	−10186.1	+	5880.94i	−0.936235	+	0.540536i	−0.888778	−	0.458338i	$-0.848445\pi$
$491$	−10186.1	+	5880.94i	−0.936235	+	0.540536i	−0.0474571	+	0.998873i	$0.515112\pi$
$492$	−7216.12	+	4622.06i	−0.661235	+	0.423534i
$493$	1491.05	+	5564.68i	0.136214	+	0.508358i
$494$	2956.32			0.269254
$495$	3918.25	+	1354.52i	0.355782	+	0.122992i
$496$	−515.321			−0.0466504
$497$	746.771	+	2786.99i	0.0673989	+	0.251536i
$498$	535.098	+	11603.5i	0.0481492	+	1.04411i
$499$	−13118.8	+	7574.16i	−1.17691	+	0.679491i	−0.955298	−	0.295644i	$-0.904466\pi$
$499$	−13118.8	+	7574.16i	−1.17691	+	0.679491i	−0.221614	+	0.975134i	$0.571133\pi$
$500$	−5514.32	+	5902.59i	−0.493216	+	0.527943i
$501$	−453.582	−	413.592i	−0.0404482	−	0.0368821i
$502$	−5128.10	+	1374.07i	−0.455933	+	0.122167i
$503$	10418.9	+	10418.9i	0.923572	+	0.923572i	0.997280	−	0.0737075i	$-0.0234831\pi$
$503$	10418.9	+	10418.9i	0.923572	+	0.923572i	−0.0737075	+	0.997280i	$0.523483\pi$
$504$	−1306.49	−	14135.4i	−0.115468	−	1.24929i
$505$	−758.326	+	543.895i	−0.0668219	+	0.0479267i
$506$	1360.71	+	785.604i	0.119547	+	0.0690205i
$507$	13443.9	+	20989.0i	1.17764	+	1.83857i
$508$	−3116.30	−	835.011i	−0.272172	−	0.0729284i
$509$	−5758.26	−	9973.60i	−0.501435	−	0.868511i	−0.999999	−	0.00165784i	$-0.999472\pi$
$509$	−5758.26	−	9973.60i	−0.501435	−	0.868511i	0.498564	−	0.866853i	$-0.333861\pi$
$510$	−2379.37	+	346.672i	−0.206589	+	0.0300998i
$511$	8583.07	−	14866.3i	0.743038	−	1.28698i
$512$	3892.45	−	3892.45i	0.335983	−	0.335983i
$513$	−3296.76	+	458.696i	−0.283734	+	0.0394774i
$514$		−	10278.2i		−	0.882011i
$515$	−1856.83	+	2264.51i	−0.158877	+	0.193759i
$516$	1154.44	+	3630.38i	0.0984910	+	0.309726i
$517$	−1224.13	+	4568.53i	−0.104134	+	0.388634i
$518$	2184.78	−	8153.71i	0.185316	−	0.691609i
$519$	−2494.74	−	546.664i	−0.210996	−	0.0462348i
$520$	−19104.4	+	1889.79i	−1.61112	+	0.159370i
$521$		−	17652.9i		−	1.48443i	−0.670162	−	0.742215i	$-0.733775\pi$
$521$		−	17652.9i		−	1.48443i	0.670162	−	0.742215i	$-0.266225\pi$
$522$	2892.02	+	7826.24i	0.242491	+	0.656217i
$523$	3650.39	−	3650.39i	0.305202	−	0.305202i	−0.537843	−	0.843045i	$-0.680761\pi$
$523$	3650.39	−	3650.39i	0.305202	−	0.305202i	0.843045	+	0.537843i	$0.180761\pi$
$524$	1889.30	−	3272.36i	0.157508	−	0.272813i
$525$	8047.93	+	14555.5i	0.669030	+	1.21001i
$526$	3804.99	+	6590.44i	0.315410	+	0.546306i
$527$	883.714	+	236.791i	0.0730459	+	0.0195726i
$528$	1115.36	−	51.4353i	0.0919317	−	0.00423946i
$529$	5431.29	+	3135.76i	0.446395	+	0.257726i
$530$	−2333.20	−	3253.06i	−0.191222	−	0.266611i
$531$	−4958.08	+	10770.1i	−0.405202	+	0.880191i
$532$	−2482.95	−	2482.95i	−0.202349	−	0.202349i
$533$	23049.2	−	6176.01i	1.87312	−	0.501900i
$534$	−991.721	+	4525.80i	−0.0803670	+	0.366761i
$535$	1552.45	+	4119.46i	0.125455	+	0.332897i
$536$	16800.3	−	9699.66i	1.35385	−	0.781645i
$537$	2962.11	+	1532.77i	0.238034	+	0.123173i
$538$	2680.41	+	10003.4i	0.214797	+	0.801632i
$539$	4294.76			0.343207
$540$	8812.99	−	2127.25i	0.702316	−	0.169523i
$541$	572.214			0.0454739			0.0227370	−	0.999741i	$-0.492762\pi$
$541$	572.214			0.0454739			0.0227370	+	0.999741i	$0.492762\pi$
$542$	−2196.09	−	8195.92i	−0.174041	−	0.649529i
$543$	−5736.55	−	2968.42i	−0.453368	−	0.234599i
$544$	−4512.25	+	2605.15i	−0.355627	+	0.205321i
$545$	12546.6	+	5678.38i	0.986122	+	0.446303i
$546$	−3548.93	+	16195.8i	−0.278169	+	1.26945i
$547$	18801.1	−	5037.74i	1.46961	−	0.393781i	0.566812	−	0.823847i	$-0.308177\pi$
$547$	18801.1	−	5037.74i	1.46961	−	0.393781i	0.902797	+	0.430066i	$0.141510\pi$
$548$	−41.8775	−	41.8775i	−0.00326445	−	0.00326445i
$549$	7424.65	−	686.239i	0.577188	−	0.0533478i
$550$	2293.15	−	1133.27i	0.177783	−	0.0878599i
$551$	4261.20	+	2460.21i	0.329462	+	0.190215i
$552$	8183.02	−	377.362i	0.630964	−	0.0290971i
$553$	−8186.13	−	2193.47i	−0.629493	−	0.168672i
$554$	−2137.22	−	3701.77i	−0.163902	−	0.283886i
$555$	12764.9	+	1501.88i	0.976287	+	0.114867i
$556$	−4790.31	+	8297.06i	−0.365385	+	0.632866i
$557$	−7665.26	+	7665.26i	−0.583101	+	0.583101i	−0.935754	−	0.352653i	$-0.885280\pi$
$557$	−7665.26	+	7665.26i	−0.583101	+	0.583101i	0.352653	+	0.935754i	$0.385280\pi$
$558$	1305.99	+	223.691i	0.0990808	+	0.0169706i
$559$		−	10607.9i		−	0.802621i
$560$	3463.85	+	2840.25i	0.261383	+	0.214326i
$561$	−1936.35	−	424.305i	−0.145727	−	0.0319326i
$562$	−2267.67	+	8463.06i	−0.170206	+	0.635218i
$563$	1798.36	−	6711.58i	0.134622	−	0.502415i	−0.865378	−	0.501121i	$-0.832921\pi$
$563$	1798.36	−	6711.58i	0.134622	−	0.502415i	0.999999	−	0.00129433i	$-0.000411998\pi$
$564$	3134.36	+	9856.67i	0.234008	+	0.735888i
$565$	805.868	+	660.788i	0.0600055	+	0.0492028i
$566$			2708.82i			0.201167i
$567$	1444.70	−	18611.5i	0.107005	−	1.37850i
$568$	1635.88	−	1635.88i	0.120845	−	0.120845i
$569$	1142.29	−	1978.50i	0.0841603	−	0.145770i	−0.820873	−	0.571111i	$-0.806513\pi$
$569$	1142.29	−	1978.50i	0.0841603	−	0.145770i	0.905033	+	0.425341i	$0.139846\pi$
$570$	−1227.62	+	1646.35i	−0.0902094	+	0.120979i
$571$	9342.12	+	16181.0i	0.684686	+	1.18591i	0.973535	+	0.228536i	$0.0733939\pi$
$571$	9342.12	+	16181.0i	0.684686	+	1.18591i	−0.288850	+	0.957375i	$0.593273\pi$
$572$	−6412.23	−	1718.15i	−0.468722	−	0.125594i
$573$	−11383.0	−	17771.6i	−0.829900	−	1.29567i
$574$	9428.20	+	5443.38i	0.685585	+	0.395823i
$575$	−8604.37	+	4252.27i	−0.624047	+	0.308403i
$576$	−3401.14	+	2406.42i	−0.246031	+	0.174075i
$577$	−17462.0	−	17462.0i	−1.25989	−	1.25989i	−0.951146	−	0.308740i	$-0.900093\pi$
$577$	−17462.0	−	17462.0i	−1.25989	−	1.25989i	−0.308740	−	0.951146i	$-0.599907\pi$
$578$	−5960.42	+	1597.09i	−0.428929	+	0.114931i
$579$	−9819.20	−	8953.49i	−0.704787	−	0.642650i
$580$	−12209.8	−	5525.95i	−0.874109	−	0.395608i
$581$	−33271.3	+	19209.2i	−2.37578	+	1.37165i
$582$	−106.672	−	2313.17i	−0.00759744	−	0.164749i
$583$	−854.193	−	3187.89i	−0.0606810	−	0.226465i
$584$	−13764.1			−0.975277
$585$	−25181.5	−	1791.81i	−1.77970	−	0.126636i
$586$	10266.7			0.723743
$587$	5997.68	+	22383.6i	0.421722	+	1.57389i	0.770980	+	0.636860i	$0.219767\pi$
$587$	5997.68	+	22383.6i	0.421722	+	1.57389i	−0.349258	+	0.937027i	$0.613566\pi$
$588$	7908.67	−	5065.65i	0.554673	−	0.355279i
$589$	676.712	−	390.700i	0.0473403	−	0.0273319i
$590$	2579.73	+	6845.40i	0.180010	+	0.477662i
$591$	9458.08	−	3007.61i	0.658297	−	0.209334i
$592$	3343.63	−	895.924i	0.232133	−	0.0621997i
$593$	13119.3	+	13119.3i	0.908505	+	0.908505i	0.996152	−	0.0876470i	$-0.0279347\pi$
$593$	13119.3	+	13119.3i	0.908505	+	0.908505i	−0.0876470	+	0.996152i	$0.527935\pi$
$594$	−2849.03	−	353.804i	−0.196796	−	0.0244389i
$595$	−4634.99	−	6462.34i	−0.319355	−	0.445261i
$596$	−7645.39	−	4414.07i	−0.525449	−	0.303368i
$597$	11678.8	−	22569.6i	0.800639	−	1.54725i
$598$	−9241.67	−	2476.30i	−0.631973	−	0.169337i
$599$	3451.75	+	5978.61i	0.235450	+	0.407812i	0.959403	−	0.282037i	$-0.0910102\pi$
$599$	3451.75	+	5978.61i	0.235450	+	0.407812i	−0.723953	+	0.689849i	$0.757677\pi$
$600$	6880.73	−	11423.8i	0.468175	−	0.777293i
$601$	9078.32	−	15724.1i	0.616161	−	1.06722i	−0.374019	−	0.927421i	$-0.622021\pi$
$601$	9078.32	−	15724.1i	0.616161	−	1.06722i	0.990180	−	0.139801i	$-0.0446462\pi$
$602$	3422.15	−	3422.15i	0.231689	−	0.231689i
$603$	23928.9	−	8842.40i	1.61602	−	0.597165i
$604$			2533.71i			0.170688i
$605$	−12710.2	+	1257.28i	−0.854123	+	0.0844889i
$606$	435.425	−	477.526i	0.0291880	−	0.0320102i
$607$	1987.32	−	7416.77i	0.132888	−	0.495943i	−0.867110	−	0.498116i	$-0.834025\pi$
$607$	1987.32	−	7416.77i	0.132888	−	0.495943i	0.999998	+	0.00217355i	$0.000691863\pi$
$608$	−1151.76	+	4298.44i	−0.0768260	+	0.286719i
$609$	−18593.3	+	20391.1i	−1.23717	+	1.35679i
$610$	2917.00	−	3557.44i	0.193616	−	0.236126i
$611$		−	28800.9i		−	1.90697i
$612$	−4066.20	+	1502.57i	−0.268572	+	0.0992450i
$613$	−13352.5	+	13352.5i	−0.879776	+	0.879776i	−0.993511	−	0.113735i	$-0.963718\pi$
$613$	−13352.5	+	13352.5i	−0.879776	+	0.879776i	0.113735	+	0.993511i	$0.463718\pi$
$614$	1665.34	−	2884.45i	0.109459	−	0.189588i
$615$	−6131.85	+	15400.5i	−0.402049	+	1.00977i
$616$	−3610.34	−	6253.29i	−0.236144	−	0.409013i
$617$	11449.3	+	3067.84i	0.747054	+	0.200172i	0.612211	−	0.790695i	$-0.290280\pi$
$617$	11449.3	+	3067.84i	0.747054	+	0.200172i	0.134843	+	0.990867i	$0.456947\pi$
$618$	931.983	−	1801.08i	0.0606632	−	0.117233i
$619$	6467.28	+	3733.89i	0.419939	+	0.242452i	0.695051	−	0.718960i	$-0.255382\pi$
$619$	6467.28	+	3733.89i	0.419939	+	0.242452i	−0.275112	+	0.961412i	$0.588715\pi$
$620$	−1729.50	+	1240.45i	−0.112029	+	0.0803510i
$621$	10690.1	+	1327.54i	0.690788	+	0.0857849i
$622$	−1582.81	−	1582.81i	−0.102033	−	0.102033i
$623$	−14801.7	+	3966.11i	−0.951875	+	0.255054i
$624$	−6479.38	+	2060.40i	−0.415677	+	0.132183i
$625$	−2013.23	+	15494.8i	−0.128847	+	0.991664i
$626$	5047.48	−	2914.17i	0.322265	−	0.186060i
$627$	−1425.68	+	913.177i	−0.0908075	+	0.0581639i
$628$	2280.20	+	8509.81i	0.144888	+	0.540730i
$629$	−6145.61			−0.389573
$630$	−7545.64	−	8701.73i	−0.477183	−	0.550294i
$631$	2875.59			0.181419			0.0907094	−	0.995877i	$-0.471087\pi$
$631$	2875.59			0.181419			0.0907094	+	0.995877i	$0.471087\pi$
$632$	1758.76	+	6563.77i	0.110696	+	0.413121i
$633$	−709.472	−	15384.7i	−0.0445481	−	0.966017i
$634$	4977.63	−	2873.83i	0.311809	−	0.180023i
$635$	−5839.75	+	2200.75i	−0.364950	+	0.137534i
$636$	−5333.08	−	4862.89i	−0.332500	−	0.303185i
$637$	−25261.3	+	6768.74i	−1.57125	+	0.421016i
$638$	3000.93	+	3000.93i	0.186219	+	0.186219i
$639$	2483.50	−	1757.16i	0.153749	−	0.108782i
$640$	2308.18	−	14017.4i	0.142561	−	0.865758i
$641$	3459.55	+	1997.37i	0.213173	+	0.123076i	0.602785	−	0.797903i	$-0.294058\pi$
$641$	3459.55	+	1997.37i	0.213173	+	0.123076i	−0.389612	+	0.920979i	$0.627391\pi$
$642$	−1644.27	−	2567.09i	−0.101081	−	0.157812i
$643$	16791.7	+	4499.32i	1.02986	+	0.275950i	0.733905	−	0.679252i	$-0.237696\pi$
$643$	16791.7	+	4499.32i	1.02986	+	0.275950i	0.295955	+	0.955202i	$0.404362\pi$
$644$	5682.08	+	9841.66i	0.347679	+	0.602198i
$645$	5907.44	+	4404.94i	0.360629	+	0.268906i
$646$	490.978	−	850.399i	0.0299029	−	0.0517934i
$647$	7322.01	−	7322.01i	0.444912	−	0.444912i	−0.448747	−	0.893659i	$-0.648130\pi$
$647$	7322.01	−	7322.01i	0.444912	−	0.444912i	0.893659	+	0.448747i	$0.148130\pi$
$648$	−13502.9	+	6458.31i	−0.818586	+	0.391522i
$649$			6030.87i			0.364765i
$650$	−11702.0	+	10279.9i	−0.706138	+	0.620325i
$651$	1328.04	+	4176.30i	0.0799537	+	0.251432i
$652$	2850.02	−	10636.4i	0.171189	−	0.638887i
$653$	2194.10	−	8188.49i	0.131488	−	0.490720i	−0.868499	−	0.495690i	$-0.834915\pi$
$653$	2194.10	−	8188.49i	0.131488	−	0.490720i	0.999988	+	0.00496957i	$0.00158187\pi$
$654$	−9315.77	−	2041.33i	−0.556996	−	0.122053i
$655$	−719.501	−	7273.64i	−0.0429210	−	0.433900i
$656$			4464.39i			0.265709i
$657$	−17840.2	−	3055.67i	−1.05938	−	0.181451i
$658$	9291.31	−	9291.31i	0.550476	−	0.550476i
$659$	4605.68	−	7977.27i	0.272249	−	0.471548i	−0.697189	−	0.716888i	$-0.745566\pi$
$659$	4605.68	−	7977.27i	0.272249	−	0.471548i	0.969437	+	0.245339i	$0.0788994\pi$
$660$	3619.52	−	2857.46i	0.213469	−	0.168525i
$661$	7007.31	+	12137.0i	0.412334	+	0.714183i	0.995145	−	0.0984247i	$-0.0313804\pi$
$661$	7007.31	+	12137.0i	0.412334	+	0.714183i	−0.582811	+	0.812608i	$0.698047\pi$
$662$	−9925.20	−	2659.45i	−0.582710	−	0.156137i
$663$	12058.1	−	556.064i	0.706333	−	0.0325727i
$664$	26677.4	+	15402.2i	1.55917	+	0.900184i
$665$	−6702.07	−	1103.60i	−0.390820	−	0.0643546i
$666$	−8862.77	+	819.160i	−0.515654	+	0.0476604i
$667$	−11260.1	−	11260.1i	−0.653661	−	0.653661i
$668$	−659.529	+	176.720i	−0.0382005	+	0.0102358i
$669$	−2601.77	+	11873.4i	−0.150359	+	0.686176i
$670$	6489.81	−	14339.5i	0.374214	−	0.826838i
$671$	3284.55	−	1896.34i	0.188970	−	0.109102i
$672$	−22165.8	−	11469.9i	−1.27242	−	0.658423i
$673$	3782.31	+	14115.8i	0.216638	+	0.808503i	0.985584	+	0.169189i	$0.0541148\pi$
$673$	3782.31	+	14115.8i	0.216638	+	0.808503i	−0.768946	+	0.639314i	$0.779218\pi$
$674$	10202.9			0.583086
$675$	11454.5	−	13279.3i	0.653162	−	0.757218i
$676$	27725.5			1.57746
$677$	−4597.75	−	17159.0i	−0.261013	−	0.974113i	−0.964646	−	0.263550i	$-0.915107\pi$
$677$	−4597.75	−	17159.0i	−0.261013	−	0.974113i	0.703633	−	0.710564i	$-0.251560\pi$
$678$	−640.949	−	331.664i	−0.0363060	−	0.0187868i
$679$	6632.67	−	3829.37i	0.374872	−	0.216433i
$680$	−2629.20	+	5809.31i	−0.148272	+	0.327613i
$681$	−2279.88	+	10404.4i	−0.128289	+	0.585459i
$682$	651.007	−	174.437i	0.0365519	−	0.00979404i
$683$	−15195.5	−	15195.5i	−0.851301	−	0.851301i	0.138993	−	0.990293i	$-0.455614\pi$
$683$	−15195.5	−	15195.5i	−0.851301	−	0.851301i	−0.990293	+	0.138993i	$0.955614\pi$
$684$	−1548.26	+	3363.18i	−0.0865487	+	0.188003i
$685$	−113.037	−	18.6134i	−0.00630502	−	0.00103822i
$686$	1000.61	+	577.705i	0.0556904	+	0.0321529i
$687$	−20766.5	+	957.652i	−1.15326	+	0.0531830i
$688$	1917.00	+	513.658i	0.106228	+	0.0284637i
$689$	10048.5	+	17404.6i	0.555615	+	0.962353i
$690$	5216.66	−	4118.33i	0.287818	−	0.227220i
$691$	−10015.8	+	17347.9i	−0.551404	+	0.955060i	0.446770	+	0.894649i	$0.352574\pi$
$691$	−10015.8	+	17347.9i	−0.551404	+	0.955060i	−0.998174	+	0.0604108i	$0.980759\pi$
$692$	−2008.78	+	2008.78i	−0.110350	+	0.110350i
$693$	−3291.25	−	8906.65i	−0.180410	−	0.488219i
$694$		−	401.213i		−	0.0219450i
$695$	1824.29	+	18442.3i	0.0995673	+	1.00655i
$696$	21613.6	+	4736.11i	1.17710	+	0.257934i
$697$	2051.39	−	7655.90i	0.111481	−	0.416051i
$698$	3644.68	−	13602.1i	0.197641	−	0.737605i
$699$	−10926.7	−	34361.3i	−0.591251	−	1.85932i
$700$	18462.1	+	1194.37i	0.996859	+	0.0644899i
$701$			16064.1i			0.865523i	0.901508	+	0.432762i	$0.142461\pi$
$701$			16064.1i			0.865523i	−0.901508	+	0.432762i	$0.857539\pi$
$702$	17315.3	−	2409.17i	0.930944	−	0.129527i
$703$	−3711.55	+	3711.55i	−0.199123	+	0.199123i
$704$	−1059.62	+	1835.31i	−0.0567271	+	0.0982543i
$705$	16039.0	+	11959.6i	0.856828	+	0.638902i
$706$	264.230	+	457.660i	0.0140856	+	0.0243970i
$707$	2064.55	+	553.196i	0.109824	+	0.0294273i
$708$	7113.39	+	11105.7i	0.377595	+	0.589514i
$709$	−15927.0	−	9195.47i	−0.843656	−	0.487085i	0.0148496	−	0.999890i	$-0.495273\pi$
$709$	−15927.0	−	9195.47i	−0.843656	−	0.487085i	−0.858505	+	0.512805i	$0.828606\pi$
$710$	304.978	−	1852.10i	0.0161206	−	0.0978989i
$711$	822.417	+	8898.01i	0.0433798	+	0.469341i
$712$	8688.16	+	8688.16i	0.457307	+	0.457307i
$713$	−2442.71	+	654.522i	−0.128303	+	0.0343788i
$714$	4069.40	+	3710.63i	0.213296	+	0.194491i
$715$	−12016.1	+	4528.35i	−0.628499	+	0.236854i
$716$	3212.83	−	1854.93i	0.167694	−	0.0968184i
$717$	1197.43	+	25966.1i	0.0623696	+	1.35247i
$718$	919.983	+	3433.42i	0.0478182	+	0.178460i
$719$	4922.15			0.255306			0.127653	−	0.991819i	$-0.459256\pi$
$719$	4922.15			0.255306			0.127653	+	0.991819i	$0.459256\pi$
$720$	1543.15	−	4463.90i	0.0798749	−	0.231055i
$721$	6707.20			0.346448
$722$	2428.05	+	9061.60i	0.125156	+	0.467088i
$723$	−15972.0	+	10230.4i	−0.821583	+	0.526239i
$724$	−6222.11	+	3592.34i	−0.319396	+	0.184404i
$725$	−25421.9	+	5079.10i	−1.30227	+	0.260184i
$726$	8428.79	−	2680.30i	0.430884	−	0.137018i
$727$	12915.5	−	3460.69i	0.658884	−	0.176547i	0.0861414	−	0.996283i	$-0.472546\pi$
$727$	12915.5	−	3460.69i	0.658884	−	0.176547i	0.572742	+	0.819736i	$0.305880\pi$
$728$	31091.1	+	31091.1i	1.58285	+	1.58285i
$729$	−18935.4	+	5373.19i	−0.962018	+	0.272986i
$730$	−9074.72	+	6508.67i	−0.460097	+	0.329996i
$731$	−3051.40	−	1761.73i	−0.154391	−	0.0891379i
$732$	3811.68	−	7366.17i	0.192464	−	0.371942i
$733$	19604.8	+	5253.09i	0.987886	+	0.264703i	0.716362	−	0.697729i	$-0.245806\pi$
$733$	19604.8	+	5253.09i	0.987886	+	0.264703i	0.271524	+	0.962432i	$0.412472\pi$
$734$	2473.09	+	4283.51i	0.124364	+	0.215405i
$735$	6720.35	−	16878.6i	0.337257	−	0.847041i
$736$	7200.99	−	12472.5i	0.360641	−	0.624649i
$737$	9175.40	−	9175.40i	0.458589	−	0.458589i
$738$	1937.90	−	11314.2i	0.0966602	−	0.564339i
$739$			21111.0i			1.05085i	0.850839	+	0.525427i	$0.176094\pi$
$739$			21111.0i			1.05085i	−0.850839	+	0.525427i	$0.823906\pi$
$740$	9065.14	−	11055.4i	0.450326	−	0.549198i
$741$	6946.50	−	7618.15i	0.344381	−	0.377679i
$742$	−2373.10	+	8856.51i	−0.117411	+	0.438184i
$743$	4564.40	−	17034.6i	0.225372	−	0.841101i	−0.756883	−	0.653551i	$-0.773279\pi$
$743$	4564.40	−	17034.6i	0.225372	−	0.841101i	0.982255	−	0.187550i	$-0.0600547\pi$
$744$	2367.57	−	2596.49i	0.116666	−	0.127946i
$745$	−16993.8	+	1681.01i	−0.835710	+	0.0826675i
$746$			16336.5i			0.801771i
$747$	31158.4	+	25885.9i	1.52614	+	1.26789i
$748$	−1559.16	+	1559.16i	−0.0762146	+	0.0762146i
$749$	5041.40	−	8731.96i	0.245940	−	0.425980i
$750$	−865.529	−	10785.5i	−0.0421395	−	0.525108i
$751$	−1012.62	−	1753.91i	−0.0492023	−	0.0852210i	0.840375	−	0.542005i	$-0.182335\pi$
$751$	−1012.62	−	1753.91i	−0.0492023	−	0.0852210i	−0.889578	+	0.456784i	$0.849001\pi$
$752$	5204.74	+	1394.61i	0.252390	+	0.0676278i
$753$	−8508.69	+	16443.3i	−0.411785	+	0.795785i
$754$	−22380.7	−	12921.5i	−1.08098	−	0.624103i
$755$	2856.46	+	3982.63i	0.137692	+	0.191977i
$756$	−16566.1	−	12519.3i	−0.796962	−	0.602278i
$757$	314.843	+	314.843i	0.0151164	+	0.0151164i	0.714625	−	0.699508i	$-0.246598\pi$
$757$	314.843	+	314.843i	0.0151164	+	0.0151164i	−0.699508	+	0.714625i	$0.746598\pi$
$758$	−1929.26	+	516.943i	−0.0924456	+	0.0247707i
$759$	5221.69	−	1660.46i	0.249717	−	0.0794085i
$760$	1920.58	+	5096.31i	0.0916668	+	0.243240i
$761$	8783.13	−	5070.94i	0.418381	−	0.241553i	−0.276003	−	0.961157i	$-0.589010\pi$
$761$	8783.13	−	5070.94i	0.418381	−	0.241553i	0.694385	+	0.719604i	$0.255677\pi$
$762$	3639.11	−	2330.92i	0.173007	−	0.110814i
$763$	−8163.72	−	30467.4i	−0.387348	−	1.44560i
$764$	−23475.4			−1.11166
$765$	−4697.50	+	6945.99i	−0.222011	+	0.328278i
$766$	−21204.4			−1.00019
$767$	−9504.93	−	35472.9i	−0.447462	−	1.66995i
$768$	748.677	+	16234.9i	0.0351765	+	0.762795i
$769$	11311.9	−	6530.95i	0.530454	−	0.306258i	−0.210748	−	0.977541i	$-0.567590\pi$
$769$	11311.9	−	6530.95i	0.530454	−	0.306258i	0.741201	+	0.671283i	$0.234256\pi$
$770$	−5337.33	−	2415.59i	−0.249797	−	0.113054i
$771$	−26486.0	−	24150.9i	−1.23719	−	1.12811i
$772$	−14277.6	+	3825.66i	−0.665623	+	0.178353i
$773$	−17678.7	−	17678.7i	−0.822587	−	0.822587i	0.163891	−	0.986478i	$-0.447595\pi$
$773$	−17678.7	−	17678.7i	−0.822587	−	0.822587i	−0.986478	+	0.163891i	$0.947595\pi$
$774$	−4635.34	−	2133.91i	−0.215263	−	0.0990980i
$775$	−1320.06	+	3899.61i	−0.0611843	+	0.180746i
$776$	−5318.18	−	3070.45i	−0.246020	−	0.142040i
$777$	−15877.7	−	24788.8i	−0.733088	−	1.14452i
$778$	−17095.9	−	4580.83i	−0.787812	−	0.211093i
$779$	−3384.76	−	5862.57i	−0.155676	−	0.269638i
$780$	−16786.1	+	22511.8i	−0.770564	+	1.03340i
$781$	773.729	−	1340.14i	0.0354497	−	0.0614007i
$782$	−2247.15	+	2247.15i	−0.102759	+	0.102759i
$783$	26962.8	+	10937.0i	1.23062	+	0.499176i
$784$		−	4892.85i		−	0.222888i
$785$	13177.9	+	10805.5i	0.599161	+	0.491294i
$786$	1533.85	+	4823.51i	0.0696062	+	0.218892i
$787$	−498.448	+	1860.23i	−0.0225766	+	0.0842568i	−0.976295	−	0.216444i	$-0.930554\pi$
$787$	−498.448	+	1860.23i	−0.0225766	+	0.0842568i	0.953718	+	0.300701i	$0.0972207\pi$
$788$	2857.29	−	10663.5i	0.129171	−	0.482072i
$789$	25923.5	+	5680.53i	1.16971	+	0.256314i
$790$	4263.39	+	3495.85i	0.192006	+	0.157439i
$791$		−	2386.88i		−	0.107292i
$792$	−4865.22	+	5856.17i	−0.218280	+	0.262740i
$793$	−16330.7	+	16330.7i	−0.731298	+	0.731298i
$794$	−1074.00	+	1860.23i	−0.0480037	+	0.0831449i
$795$	−13865.2	−	1631.33i	−0.618549	−	0.0727766i
$796$	−14133.5	−	24479.9i	−0.629332	−	1.09004i
$797$	17871.1	+	4788.55i	0.794263	+	0.212822i	0.633064	−	0.774100i	$-0.281797\pi$
$797$	17871.1	+	4788.55i	0.794263	+	0.212822i	0.161199	+	0.986922i	$0.448464\pi$
$798$	4698.63	−	216.679i	0.208433	−	0.00961196i
$799$	−8284.70	−	4783.17i	−0.366823	−	0.211785i
$800$	−10387.8	−	21019.5i	−0.459080	−	0.928938i
$801$	9332.28	+	13189.9i	0.411660	+	0.581824i
$802$	9886.89	+	9886.89i	0.435309	+	0.435309i
$803$	−8892.92	+	2382.85i	−0.390815	+	0.104719i
$804$	6073.87	−	27718.6i	0.266429	−	1.21587i
$805$	20026.7	+	9063.77i	0.876832	+	0.396840i
$806$	−3554.23	+	2052.04i	−0.155326	+	0.0896773i
$807$	32076.0	+	16598.0i	1.39917	+	0.724010i
$808$	−443.561	−	1655.39i	−0.0193124	−	0.0720749i
$809$	3636.86			0.158054			0.0790268	−	0.996872i	$-0.474819\pi$
$809$	3636.86			0.158054			0.0790268	+	0.996872i	$0.474819\pi$
$810$	−5848.55	+	10643.2i	−0.253700	+	0.461682i
$811$	−5975.99			−0.258749			−0.129374	−	0.991596i	$-0.541297\pi$
$811$	−5975.99			−0.258749			−0.129374	+	0.991596i	$0.541297\pi$
$812$	7944.58	+	29649.6i	0.343350	+	1.28140i
$813$	−26280.2	−	13598.9i	−1.13369	−	0.586636i
$814$	−3920.76	+	2263.65i	−0.168824	+	0.0974704i
$815$	−7511.49	−	19932.0i	−0.322842	−	0.856670i
$816$	−483.394	+	2206.01i	−0.0207380	+	0.0946394i
$817$	−2906.82	+	778.879i	−0.124476	+	0.0333531i
$818$	3305.54	+	3305.54i	0.141290	+	0.141290i
$819$	33396.1	+	47200.7i	1.42485	+	2.01383i
$820$	10746.4	+	14983.2i	0.457659	+	0.638092i
$821$	−17908.5	−	10339.5i	−0.761279	−	0.439525i	0.0684756	−	0.997653i	$-0.478186\pi$
$821$	−17908.5	−	10339.5i	−0.761279	−	0.439525i	−0.829755	+	0.558128i	$0.811520\pi$
$822$	79.2473	−	3.65451i	0.00336261	−	0.000155068i
$823$	−22313.2	−	5978.81i	−0.945066	−	0.253230i	−0.246799	−	0.969067i	$-0.579379\pi$
$823$	−22313.2	−	5978.81i	−0.945066	−	0.253230i	−0.698268	+	0.715837i	$0.746045\pi$
$824$	−2688.97	−	4657.43i	−0.113683	−	0.196904i
$825$	2467.91	−	8572.09i	0.104147	−	0.361748i
$826$	8377.40	−	14510.1i	0.352890	−	0.611223i
$827$	−21798.8	+	21798.8i	−0.916590	+	0.916590i	−0.996780	−	0.0801900i	$-0.974447\pi$
$827$	−21798.8	+	21798.8i	−0.916590	+	0.916590i	0.0801900	+	0.996780i	$0.474447\pi$
$828$	7657.07	−	9216.65i	0.321379	−	0.386837i
$829$		−	39148.0i		−	1.64013i	−0.572270	−	0.820065i	$-0.693937\pi$
$829$		−	39148.0i		−	1.64013i	0.572270	−	0.820065i	$-0.306063\pi$
$830$	24871.9	−	2460.30i	1.04014	−	0.102889i
$831$	−14560.9	−	3190.68i	−0.607837	−	0.133193i
$832$	3340.02	−	12465.1i	0.139176	−	0.519412i
$833$	−2248.27	+	8390.66i	−0.0935149	+	0.349002i
$834$	−3889.06	−	12230.0i	−0.161471	−	0.507781i
$835$	−837.453	+	1021.32i	−0.0347081	+	0.0423284i
$836$			1883.26i			0.0779115i
$837$	3645.13	−	2839.81i	0.150531	−	0.117274i
$838$	−3351.27	+	3351.27i	−0.138148	+	0.138148i
$839$	8171.00	−	14152.6i	0.336227	−	0.582362i	−0.647493	−	0.762071i	$-0.724183\pi$
$839$	8171.00	−	14152.6i	0.336227	−	0.582362i	0.983720	+	0.179710i	$0.0575159\pi$
$840$	−30225.1	+	4403.75i	−1.24150	+	0.180886i
$841$	−9311.67	−	16128.3i	−0.381798	−	0.661294i
$842$	4037.34	+	1081.80i	0.165244	+	0.0442771i
$843$	16480.1	+	25729.3i	0.673316	+	1.05120i
$844$	−14836.1	−	8565.63i	−0.605071	−	0.349338i
$845$	43580.5	−	31257.3i	1.77422	−	1.27252i
$846$	−12585.2	−	5793.67i	−0.511450	−	0.235450i
$847$	20685.0	+	20685.0i	0.839134	+	0.839134i
$848$	−3631.84	+	973.148i	−0.147073	+	0.0394080i
$849$	6980.37	+	6364.94i	0.282174	+	0.257296i
$850$	1013.63	+	5073.39i	0.0409024	+	0.204724i
$851$	14711.5	−	8493.67i	0.592600	−	0.342138i
$852$	−155.890	−	3380.44i	−0.00626842	−	0.135929i
$853$	−8216.62	−	30664.8i	−0.329814	−	1.23088i	−0.909383	−	0.415960i	$-0.863445\pi$
$853$	−8216.62	−	30664.8i	−0.329814	−	1.23088i	0.579568	−	0.814924i	$-0.303221\pi$
$854$	−10536.7			−0.422200
$855$	1357.94	+	7031.91i	0.0543166	+	0.281270i
$856$	−8084.55			−0.322809
$857$	−4502.95	−	16805.2i	−0.179484	−	0.669843i	−0.995744	−	0.0921589i	$-0.970623\pi$
$857$	−4502.95	−	16805.2i	−0.179484	−	0.669843i	0.816260	−	0.577684i	$-0.196043\pi$
$858$	7487.98	−	4796.20i	0.297944	−	0.190839i
$859$	−20096.3	+	11602.6i	−0.798226	+	0.460856i	−0.842850	−	0.538148i	$-0.819124\pi$
$859$	−20096.3	+	11602.6i	−0.798226	+	0.460856i	0.0446246	+	0.999004i	$0.485791\pi$
$860$	7670.19	−	2890.56i	0.304129	−	0.114613i
$861$	36180.6	−	11505.2i	1.43209	−	0.455396i
$862$	−21457.6	+	5749.54i	−0.847852	+	0.227181i
$863$	3319.49	+	3319.49i	0.130935	+	0.130935i	0.769537	−	0.638602i	$-0.220487\pi$
$863$	3319.49	+	3319.49i	0.130935	+	0.130935i	−0.638602	+	0.769537i	$0.720487\pi$
$864$	−3243.03	+	26114.7i	−0.127697	+	1.02829i
$865$	−892.846	+	5422.17i	−0.0350956	+	0.213132i
$866$	6895.81	+	3981.30i	0.270588	+	0.156224i
$867$	−9889.71	+	19112.1i	−0.387396	+	0.748652i
$868$	4708.58	+	1261.66i	0.184124	+	0.0493359i
$869$	2272.65	+	3936.35i	0.0887162	+	0.153661i
$870$	16489.5	−	7097.97i	0.642584	−	0.276602i
$871$	−39507.8	+	68429.5i	−1.53694	+	2.66205i
$872$	−17883.5	+	17883.5i	−0.694508	+	0.694508i
$873$	−6211.45	−	5160.39i	−0.240809	−	0.200060i
$874$			2714.26i			0.105047i
$875$	30366.2	−	18936.5i	1.17322	−	0.731622i
$876$	−13565.5	+	14877.1i	−0.523214	+	0.573803i
$877$	3114.52	−	11623.6i	0.119920	−	0.447548i	−0.879688	−	0.475552i	$-0.842248\pi$
$877$	3114.52	−	11623.6i	0.119920	−	0.447548i	0.999608	+	0.0280039i	$0.00891510\pi$
$878$	−634.543	+	2368.15i	−0.0243904	+	0.0910262i
$879$	24123.8	−	26456.3i	0.925681	−	1.01518i
$880$	−236.492	−	2390.76i	−0.00905924	−	0.0915825i
$881$			4720.28i			0.180511i	0.995919	+	0.0902556i	$0.0287684\pi$
$881$			4720.28i			0.180511i	−0.995919	+	0.0902556i	$0.971232\pi$
$882$	−2123.89	+	12400.1i	−0.0810829	+	0.473393i
$883$	−7647.30	+	7647.30i	−0.291452	+	0.291452i	−0.837654	−	0.546202i	$-0.816073\pi$
$883$	−7647.30	+	7647.30i	−0.291452	+	0.291452i	0.546202	+	0.837654i	$0.316073\pi$
$884$	6713.50	−	11628.1i	0.255429	−	0.442416i
$885$	23701.5	+	9436.97i	0.900247	+	0.358441i
$886$	−5096.50	−	8827.40i	−0.193251	−	0.334720i
$887$	9698.64	+	2598.74i	0.367135	+	0.0983735i	0.437670	−	0.899136i	$-0.355804\pi$
$887$	9698.64	+	2598.74i	0.367135	+	0.0983735i	−0.0705349	+	0.997509i	$0.522471\pi$
$888$	−10847.7	+	20963.4i	−0.409937	+	0.792213i
$889$	12378.4	+	7146.69i	0.466996	+	0.269620i
$890$	9836.55	+	1619.74i	0.370474	+	0.0610044i
$891$	−7606.10	+	6510.32i	−0.285986	+	0.244786i
$892$	9560.52	+	9560.52i	0.358868	+	0.358868i
$893$	−7892.14	+	2114.69i	−0.295745	+	0.0792447i
$894$	11269.4	−	3583.60i	0.421595	−	0.134064i
$895$	2958.89	−	6537.77i	0.110508	−	0.244172i
$896$	−28178.0	+	16268.6i	−1.05063	+	0.606579i
$897$	−28096.4	+	17996.3i	−1.04583	+	0.669876i
$898$	2998.43	+	11190.3i	0.111424	+	0.415841i
$899$	−6830.70			−0.253411
$900$	−5566.17	−	18696.1i	−0.206154	−	0.692450i
$901$	6675.33			0.246823
$902$	−1511.20	−	5639.88i	−0.0557844	−	0.208190i
$903$	−777.486	−	16859.6i	−0.0286524	−	0.621321i
$904$	−1657.44	+	956.921i	−0.0609795	+	0.0352065i
$905$	−5730.32	+	12661.3i	−0.210478	+	0.465058i
$906$	−2507.90	−	2286.79i	−0.0919641	−	0.0838561i
$907$	26724.8	−	7160.88i	0.978369	−	0.262153i	0.266012	−	0.963970i	$-0.414294\pi$
$907$	26724.8	−	7160.88i	0.978369	−	0.262153i	0.712358	+	0.701817i	$0.247627\pi$
$908$	8377.68	+	8377.68i	0.306193	+	0.306193i
$909$	−207.415	−	2244.09i	−0.00756823	−	0.0818832i
$910$	35200.7	+	5796.34i	1.28230	+	0.211150i
$911$	40788.9	+	23549.5i	1.48342	+	0.856453i	0.999823	−	0.0188372i	$-0.00599642\pi$
$911$	40788.9	+	23549.5i	1.48342	+	0.856453i	0.483598	+	0.875290i	$0.339330\pi$
$912$	1040.35	+	1624.22i	0.0377734	+	0.0589730i
$913$	19902.6	+	5332.90i	0.721447	+	0.193311i
$914$	1773.99	+	3072.64i	0.0641995	+	0.111197i
$915$	−2313.08	−	15875.8i	−0.0835717	−	0.573592i
$916$	−11562.0	+	20025.9i	−0.417050	+	0.722352i
$917$	−11837.4	+	11837.4i	−0.426286	+	0.426286i
$918$	2182.67	−	5380.92i	0.0784735	−	0.193461i
$919$			2547.69i			0.0914479i	0.998954	+	0.0457239i	$0.0145595\pi$
$919$			2547.69i			0.0914479i	−0.998954	+	0.0457239i	$0.985441\pi$
$920$	−1735.05	−	17540.2i	−0.0621772	−	0.628567i
$921$	−3519.88	−	11069.0i	−0.125933	−	0.396023i
$922$	3342.96	−	12476.1i	0.119409	−	0.445639i
$923$	−2438.87	+	9101.98i	−0.0869733	+	0.324589i
$924$	−10317.2	−	2260.77i	−0.367328	−	0.0804912i
$925$	1785.36	−	27597.4i	0.0634620	−	0.980971i
$926$		−	7618.99i		−	0.270384i
$927$	−2451.31	−	6633.64i	−0.0868519	−	0.235035i
$928$	27507.1	−	27507.1i	0.973021	−	0.973021i
$929$	−25014.8	+	43327.0i	−0.883434	+	1.53015i	−0.0359367	+	0.999354i	$0.511441\pi$
$929$	−25014.8	+	43327.0i	−0.883434	+	1.53015i	−0.847498	+	0.530799i	$0.821892\pi$
$930$	333.139	−	2831.44i	0.0117463	−	0.0998350i
$931$	3709.60	+	6425.22i	0.130588	+	0.226185i
$932$	−38740.7	−	10380.6i	−1.36158	−	0.364835i
$933$	−7797.87	+	359.601i	−0.273623	+	0.0126182i
$934$	−7490.67	−	4324.74i	−0.262422	−	0.151510i
$935$	−693.003	+	4208.54i	−0.0242392	+	0.147202i
$936$	19387.1	−	42113.2i	0.677016	−	1.47063i
$937$	33647.3	+	33647.3i	1.17312	+	1.17312i	0.981462	+	0.191655i	$0.0613855\pi$
$937$	33647.3	+	33647.3i	1.17312	+	1.17312i	0.191655	+	0.981462i	$0.438615\pi$
$938$	−34821.1	+	9330.30i	−1.21210	+	0.324782i
$939$	4350.60	−	19854.3i	0.151200	−	0.690011i
$940$	20824.9	−	7848.02i	0.722590	−	0.272313i
$941$	5692.71	−	3286.68i	0.197212	−	0.113861i	−0.398142	−	0.917324i	$-0.630345\pi$
$941$	5692.71	−	3286.68i	0.197212	−	0.113861i	0.595355	+	0.803463i	$0.297012\pi$
$942$	−10481.1	−	5423.53i	−0.362519	−	0.187588i
$943$	5670.33	+	21162.0i	0.195813	+	0.730783i
$944$	6870.73			0.236889
$945$	−40153.5	−	1002.17i	−1.38222	−	0.0344981i
$946$	−2595.63			−0.0892084
$947$	−9489.79	−	35416.4i	−0.325636	−	1.21529i	−0.913671	−	0.406453i	$-0.866765\pi$
$947$	−9489.79	−	35416.4i	−0.325636	−	1.21529i	0.588036	−	0.808835i	$-0.299901\pi$
$948$	8827.93	+	4568.08i	0.302445	+	0.156502i
$949$	48551.7	−	28031.3i	1.66075	−	0.958836i
$950$	3676.16	+	2451.83i	0.125548	+	0.0837346i
$951$	4290.39	−	19579.5i	0.146294	−	0.667623i
$952$	14107.0	−	3779.96i	0.480264	−	0.128686i
$953$	6706.27	+	6706.27i	0.227951	+	0.227951i	0.811836	−	0.583885i	$-0.198468\pi$
$953$	6706.27	+	6706.27i	0.227951	+	0.227951i	−0.583885	+	0.811836i	$0.698468\pi$
$954$	9626.69	−	889.767i	0.326704	−	0.0301963i
$955$	−36900.0	+	26465.8i	−1.25032	+	0.896767i
$956$	25040.1	+	14456.9i	0.847129	+	0.489090i
$957$	14784.4	−	681.786i	0.499385	−	0.0230293i
$958$	21900.4	+	5868.20i	0.738592	+	0.197905i
$959$	131.191	+	227.230i	0.00441751	+	0.00765134i
$960$	5554.79	+	7036.20i	0.186750	+	0.236555i
$961$	14353.1	−	24860.3i	0.481794	−	0.834491i
$962$	19493.8	−	19493.8i	0.653333	−	0.653333i
$963$	−10478.7	−	1794.80i	−0.350646	−	0.0600587i
$964$			21098.3i			0.704906i
$965$	−18129.3	+	22109.7i	−0.604769	+	0.737549i
$966$	−14869.7	−	3258.35i	−0.495265	−	0.108526i
$967$	−8701.12	+	32473.0i	−0.289358	+	1.07990i	0.656237	+	0.754554i	$0.272147\pi$
$967$	−8701.12	+	32473.0i	−0.289358	+	1.07990i	−0.945596	+	0.325345i	$0.894520\pi$
$968$	6070.75	−	22656.3i	0.201572	−	0.752275i
$969$	−1037.74	−	3263.39i	−0.0344035	−	0.108189i
$970$	−4958.24	+	490.463i	−0.164123	+	0.0162349i
$971$		−	34772.8i		−	1.14924i	−0.818421	−	0.574620i	$-0.805150\pi$
$971$		−	34772.8i		−	1.14924i	0.818421	−	0.574620i	$-0.194850\pi$
$972$	−6327.50	+	20959.9i	−0.208801	+	0.691656i
$973$	30013.6	−	30013.6i	0.988890	−	0.988890i
$974$	−1474.76	+	2554.37i	−0.0485159	+	0.0840320i
$975$	−1005.95	+	54309.6i	−0.0330424	+	1.78390i
$976$	−2160.42	−	3741.96i	−0.0708539	−	0.122723i
$977$	42844.6	+	11480.2i	1.40299	+	0.375930i	0.879417	−	0.476052i	$-0.157933\pi$
$977$	42844.6	+	11480.2i	1.40299	+	0.375930i	0.523571	+	0.851982i	$0.324599\pi$
$978$	7955.78	+	12420.8i	0.260121	+	0.406109i
$979$	7117.49	+	4109.29i	0.232356	+	0.134151i
$980$	−11777.8	−	16421.2i	−0.383905	−	0.535260i
$981$	−27149.7	+	19209.3i	−0.883611	+	0.625184i
$982$	−12392.2	−	12392.2i	−0.402700	−	0.402700i
$983$	−54645.5	+	14642.2i	−1.77306	+	0.475091i	−0.989291	−	0.145956i	$-0.953374\pi$
$983$	−54645.5	+	14642.2i	−1.77306	+	0.475091i	−0.783773	+	0.621048i	$0.786707\pi$
$984$	−22494.2	−	20511.0i	−0.728749	−	0.664499i
$985$	−7530.65	−	19982.8i	−0.243601	−	0.646401i
$986$	−7433.86	+	4291.94i	−0.240104	+	0.138624i
$987$	−2110.91	−	45774.7i	−0.0680760	−	1.47621i
$988$	−2968.11	−	11077.1i	−0.0955751	−	0.356691i
$989$	9739.32			0.313137
$990$	−438.436	+	6161.63i	−0.0140751	+	0.197808i
$991$	−45374.8			−1.45447			−0.727234	−	0.686390i	$-0.759195\pi$
$991$	−45374.8			−1.45447			−0.727234	+	0.686390i	$0.759195\pi$
$992$	−1598.92	−	5967.26i	−0.0511752	−	0.190988i
$993$	−30174.5	+	19327.3i	−0.964308	+	0.617658i
$994$	−3723.14	+	2149.55i	−0.118804	+	0.0685913i
$995$	−49814.1	−	22545.0i	−1.58715	−	0.718318i
$996$	42940.2	−	13654.7i	1.36608	−	0.434404i
$997$	−46082.2	+	12347.7i	−1.46383	+	0.392232i	−0.900811	−	0.434212i	$-0.857027\pi$
$997$	−46082.2	+	12347.7i	−1.46383	+	0.392232i	−0.563019	+	0.826444i	$0.690360\pi$
$998$	−15960.1	−	15960.1i	−0.506222	−	0.506222i
$999$	−18714.0	+	24763.3i	−0.592679	+	0.784259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.2.11	✓	64
3.2	odd	2		135.4.m.a.62.6		64
5.2	odd	4		225.4.p.b.218.6		64
5.3	odd	4	inner	45.4.l.a.38.11	yes	64
5.4	even	2		225.4.p.b.182.6		64
9.4	even	3		135.4.m.a.17.6		64
9.5	odd	6	inner	45.4.l.a.32.11	yes	64
15.8	even	4		135.4.m.a.8.6		64
45.13	odd	12		135.4.m.a.98.6		64
45.14	odd	6		225.4.p.b.32.6		64
45.23	even	12	inner	45.4.l.a.23.11	yes	64
45.32	even	12		225.4.p.b.68.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.11	✓	64	1.1	even	1	trivial
45.4.l.a.23.11	yes	64	45.23	even	12	inner
45.4.l.a.32.11	yes	64	9.5	odd	6	inner
45.4.l.a.38.11	yes	64	5.3	odd	4	inner
135.4.m.a.8.6		64	15.8	even	4
135.4.m.a.17.6		64	9.4	even	3
135.4.m.a.62.6		64	3.2	odd	2
135.4.m.a.98.6		64	45.13	odd	12
225.4.p.b.32.6		64	45.14	odd	6
225.4.p.b.68.6		64	45.32	even	12
225.4.p.b.182.6		64	5.4	even	2
225.4.p.b.218.6		64	5.2	odd	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.385641 + 1.43923i) q^{2} +(4.61491 + 2.38802i) q^{3} +(5.00553 - 2.88994i) q^{4} +(4.60989 - 10.1857i) q^{5} +(-1.65722 + 7.56285i) q^{6} +(-24.7344 + 6.62758i) q^{7} +(14.5184 + 14.5184i) q^{8} +(15.5947 + 22.0410i) q^{9} +O(q^{10})\)	\(q+(0.385641 + 1.43923i) q^{2} +(4.61491 + 2.38802i) q^{3} +(5.00553 - 2.88994i) q^{4} +(4.60989 - 10.1857i) q^{5} +(-1.65722 + 7.56285i) q^{6} +(-24.7344 + 6.62758i) q^{7} +(14.5184 + 14.5184i) q^{8} +(15.5947 + 22.0410i) q^{9} +(16.4374 + 2.70668i) q^{10} +(11.8937 + 6.86683i) q^{11} +(30.0013 - 1.38352i) q^{12} +(-80.7799 - 21.6449i) q^{13} +(-19.0773 - 33.0428i) q^{14} +(45.5979 - 35.9976i) q^{15} +(7.82311 - 13.5500i) q^{16} +(-19.6420 + 19.6420i) q^{17} +(-25.7081 + 30.9444i) q^{18} +23.7249i q^{19} +(-6.36120 - 64.3073i) q^{20} +(-129.974 - 28.4807i) q^{21} +(-5.29627 + 19.7659i) q^{22} +(19.8727 - 74.1658i) q^{23} +(32.3308 + 101.671i) q^{24} +(-82.4978 - 93.9102i) q^{25} -124.608i q^{26} +(19.3339 + 138.958i) q^{27} +(-104.656 + 104.656i) q^{28} +(103.697 - 179.609i) q^{29} +(69.3934 + 51.7439i) q^{30} +(-16.4679 - 28.5232i) q^{31} +(181.178 + 48.5466i) q^{32} +(38.4902 + 60.0922i) q^{33} +(-35.8441 - 20.6946i) q^{34} +(-46.5165 + 282.491i) q^{35} +(141.757 + 65.2589i) q^{36} +(156.441 + 156.441i) q^{37} +(-34.1457 + 9.14932i) q^{38} +(-321.103 - 292.793i) q^{39} +(214.808 - 80.9520i) q^{40} +(-247.106 + 142.667i) q^{41} +(-9.13295 - 198.046i) q^{42} +(32.8295 + 122.522i) q^{43} +79.3790 q^{44} +(296.393 - 57.2370i) q^{45} +114.406 q^{46} +(89.1338 + 332.652i) q^{47} +(68.4606 - 43.8503i) q^{48} +(270.821 - 156.359i) q^{49} +(103.344 - 154.949i) q^{50} +(-137.551 + 43.7404i) q^{51} +(-466.899 + 125.105i) q^{52} +(-169.925 - 169.925i) q^{53} +(-192.536 + 81.4138i) q^{54} +(124.772 - 89.4906i) q^{55} +(-455.326 - 262.882i) q^{56} +(-56.6556 + 109.488i) q^{57} +(298.489 + 79.9798i) q^{58} +(219.565 + 380.298i) q^{59} +(124.211 - 311.963i) q^{60} +(138.080 - 239.161i) q^{61} +(34.7009 - 34.7009i) q^{62} +(-531.805 - 441.816i) q^{63} +154.310i q^{64} +(-592.856 + 723.021i) q^{65} +(-71.6433 + 78.5704i) q^{66} +(244.540 - 912.635i) q^{67} +(-41.5543 + 155.083i) q^{68} +(268.820 - 294.812i) q^{69} +(-424.509 + 41.9919i) q^{70} -112.676i q^{71} +(-93.5891 + 546.409i) q^{72} +(-474.023 + 474.023i) q^{73} +(-164.825 + 285.485i) q^{74} +(-156.460 - 630.393i) q^{75} +(68.5637 + 118.756i) q^{76} +(-339.695 - 91.0209i) q^{77} +(297.567 - 575.056i) q^{78} +(286.620 + 165.480i) q^{79} +(-101.953 - 142.148i) q^{80} +(-242.609 + 687.446i) q^{81} +(-300.625 - 300.625i) q^{82} +(1449.19 - 388.308i) q^{83} +(-732.896 + 233.056i) q^{84} +(109.520 + 290.615i) q^{85} +(-163.677 + 94.4988i) q^{86} +(907.461 - 581.246i) q^{87} +(72.9820 + 272.373i) q^{88} +598.425 q^{89} +(196.679 + 404.506i) q^{90} +2141.50 q^{91} +(-114.862 - 428.670i) q^{92} +(-7.88376 - 170.958i) q^{93} +(-444.390 + 256.569i) q^{94} +(241.656 + 109.369i) q^{95} +(720.191 + 656.695i) q^{96} +(-288.897 + 77.4097i) q^{97} +(329.477 + 329.477i) q^{98} +(34.1273 + 369.235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

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