LMFDB - Embedded newform 128.3.l.a.43.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(3,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.l (of order $32$, degree $16$, 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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$31$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			43.12
Character	$\chi$	$=$	128.43
Dual form			128.3.l.a.3.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687532 - 1.87811i) q^{2} +(3.91403 + 3.21216i) q^{3} +(-3.05460 + 2.58252i) q^{4} +(-8.46864 + 2.56894i) q^{5} +(3.34178 - 9.55944i) q^{6} +(-0.593205 + 2.98225i) q^{7} +(6.95040 + 3.96131i) q^{8} +(3.24584 + 16.3179i) q^{9} +O(q^{10})$	\(q+(-0.687532 - 1.87811i) q^{2} +(3.91403 + 3.21216i) q^{3} +(-3.05460 + 2.58252i) q^{4} +(-8.46864 + 2.56894i) q^{5} +(3.34178 - 9.55944i) q^{6} +(-0.593205 + 2.98225i) q^{7} +(6.95040 + 3.96131i) q^{8} +(3.24584 + 16.3179i) q^{9} +(10.6472 + 14.1388i) q^{10} +(0.723029 - 7.34104i) q^{11} +(-20.2513 + 0.296198i) q^{12} +(-5.58169 + 18.4004i) q^{13} +(6.00883 - 0.936283i) q^{14} +(-41.3984 - 17.1478i) q^{15} +(2.66116 - 15.7771i) q^{16} +(0.326137 + 0.787364i) q^{17} +(28.4153 - 17.3151i) q^{18} +(3.73151 + 6.98117i) q^{19} +(19.2340 - 29.7175i) q^{20} +(-11.9013 + 9.76713i) q^{21} +(-14.2844 + 3.68927i) q^{22} +(28.7178 + 19.1886i) q^{23} +(14.4797 + 37.8305i) q^{24} +(44.3318 - 29.6215i) q^{25} +(38.3955 - 2.16780i) q^{26} +(-18.2298 + 34.1056i) q^{27} +(-5.88971 - 10.6415i) q^{28} +(-5.16616 - 52.4529i) q^{29} +(-3.74271 + 89.5403i) q^{30} +(13.3385 - 13.3385i) q^{31} +(-31.4609 + 5.84932i) q^{32} +(26.4106 - 26.4106i) q^{33} +(1.25453 - 1.15386i) q^{34} +(-2.63755 - 26.7795i) q^{35} +(-52.0561 - 41.4623i) q^{36} +(-19.3999 + 36.2946i) q^{37} +(10.5459 - 11.8080i) q^{38} +(-80.9519 + 54.0903i) q^{39} +(-69.0368 - 15.6918i) q^{40} +(16.0435 + 10.7200i) q^{41} +(26.5263 + 15.6367i) q^{42} +(-3.22073 + 2.64318i) q^{43} +(16.7498 + 24.2912i) q^{44} +(-69.4075 - 129.852i) q^{45} +(16.2940 - 67.1280i) q^{46} +(1.11778 + 2.69856i) q^{47} +(61.0946 - 53.2041i) q^{48} +(36.7282 + 15.2133i) q^{49} +(-86.1120 - 62.8942i) q^{50} +(-1.25263 + 4.12937i) q^{51} +(-30.4695 - 70.6206i) q^{52} +(4.28928 - 43.5498i) q^{53} +(76.5878 + 10.7890i) q^{54} +(12.7356 + 64.0261i) q^{55} +(-15.9366 + 18.3779i) q^{56} +(-7.81939 + 39.3107i) q^{57} +(-94.9605 + 45.7657i) q^{58} +(-21.3979 + 6.49099i) q^{59} +(170.740 - 54.5326i) q^{60} +(50.4076 + 41.3684i) q^{61} +(-34.2218 - 15.8805i) q^{62} -50.5895 q^{63} +(32.6160 + 55.0654i) q^{64} -170.165i q^{65} +(-67.7601 - 31.4439i) q^{66} +(-72.5273 + 88.3748i) q^{67} +(-3.02960 - 1.56283i) q^{68} +(50.7654 + 167.351i) q^{69} +(-48.4814 + 23.3654i) q^{70} +(34.6028 + 6.88293i) q^{71} +(-42.0805 + 126.274i) q^{72} +(-41.7484 + 8.30428i) q^{73} +(81.5033 + 11.4814i) q^{74} +(268.665 + 26.4612i) q^{75} +(-29.4273 - 11.6880i) q^{76} +(21.4639 + 6.51099i) q^{77} +(157.245 + 114.848i) q^{78} +(14.4300 - 34.8371i) q^{79} +(17.9940 + 140.447i) q^{80} +(-42.5646 + 17.6308i) q^{81} +(9.10281 - 37.5019i) q^{82} +(-29.0696 + 15.5380i) q^{83} +(11.1298 - 60.5700i) q^{84} +(-4.78463 - 5.83008i) q^{85} +(7.17855 + 4.23161i) q^{86} +(148.267 - 221.897i) q^{87} +(34.1055 - 48.1590i) q^{88} +(-42.1422 - 63.0703i) q^{89} +(-196.157 + 219.633i) q^{90} +(-51.5633 - 27.5612i) q^{91} +(-137.276 + 15.5508i) q^{92} +(95.0527 - 9.36188i) q^{93} +(4.29969 - 3.95466i) q^{94} +(-49.5350 - 49.5350i) q^{95} +(-141.928 - 78.1629i) q^{96} +(55.5595 + 55.5595i) q^{97} +(3.32049 - 79.4393i) q^{98} +(122.137 - 12.0295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{29}{32}\right)$	$-1$

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 $

$2$	−0.687532	−	1.87811i	−0.343766	−	0.939055i
$2$	−0.687532	−	1.87811i	−0.343766	−	0.939055i
$3$	3.91403	+	3.21216i	1.30468	+	1.07072i	0.992697	+	0.120632i	$0.0384920\pi$
$3$	3.91403	+	3.21216i	1.30468	+	1.07072i	0.311979	+	0.950089i	$0.399008\pi$
$4$	−3.05460	+	2.58252i	−0.763650	+	0.645630i
$5$	−8.46864	+	2.56894i	−1.69373	+	0.513787i	−0.982034	−	0.188702i	$-0.939572\pi$
$5$	−8.46864	+	2.56894i	−1.69373	+	0.513787i	−0.711695	+	0.702489i	$0.752072\pi$
$6$	3.34178	−	9.55944i	0.556963	−	1.59324i
$7$	−0.593205	+	2.98225i	−0.0847436	+	0.426035i	0.915001	+	0.403451i	$0.132189\pi$
$7$	−0.593205	+	2.98225i	−0.0847436	+	0.426035i	−0.999745	+	0.0225842i	$0.992811\pi$
$8$	6.95040	+	3.96131i	0.868800	+	0.495164i
$9$	3.24584	+	16.3179i	0.360649	+	1.81310i
$10$	10.6472	+	14.1388i	1.06472	+	1.41388i
$11$	0.723029	−	7.34104i	0.0657299	−	0.667367i	−0.904711	−	0.426027i	$-0.859913\pi$
$11$	0.723029	−	7.34104i	0.0657299	−	0.667367i	0.970441	−	0.241340i	$-0.0775870\pi$
$12$	−20.2513	+	0.296198i	−1.68761	+	0.0246832i
$13$	−5.58169	+	18.4004i	−0.429361	+	1.41541i	0.429436	+	0.903097i	$0.358712\pi$
$13$	−5.58169	+	18.4004i	−0.429361	+	1.41541i	−0.858797	+	0.512316i	$0.828788\pi$
$14$	6.00883	−	0.936283i	0.429202	−	0.0668773i
$15$	−41.3984	−	17.1478i	−2.75989	−	1.14318i
$16$	2.66116	−	15.7771i	0.166323	−	0.986071i
$17$	0.326137	+	0.787364i	0.0191845	+	0.0463155i	0.933182	−	0.359405i	$-0.117020\pi$
$17$	0.326137	+	0.787364i	0.0191845	+	0.0463155i	−0.913997	+	0.405721i	$0.867020\pi$
$18$	28.4153	−	17.3151i	1.57863	−	0.961952i
$19$	3.73151	+	6.98117i	0.196395	+	0.367430i	0.960772	−	0.277340i	$-0.0894530\pi$
$19$	3.73151	+	6.98117i	0.196395	+	0.367430i	−0.764376	+	0.644770i	$0.776953\pi$
$20$	19.2340	−	29.7175i	0.961700	−	1.48588i
$21$	−11.9013	+	9.76713i	−0.566727	+	0.465101i
$22$	−14.2844	+	3.68927i	−0.649290	+	0.167694i
$23$	28.7178	+	19.1886i	1.24860	+	0.834288i	0.991246	−	0.132029i	$-0.0421492\pi$
$23$	28.7178	+	19.1886i	1.24860	+	0.834288i	0.257354	+	0.966317i	$0.417149\pi$
$24$	14.4797	+	37.8305i	0.603320	+	1.57627i
$25$	44.3318	−	29.6215i	1.77327	−	1.18486i
$26$	38.3955	−	2.16780i	1.47675	−	0.0833771i
$27$	−18.2298	+	34.1056i	−0.675179	+	1.26317i
$28$	−5.88971	−	10.6415i	−0.210347	−	0.380055i
$29$	−5.16616	−	52.4529i	−0.178144	−	1.80872i	−0.504432	−	0.863451i	$-0.668298\pi$
$29$	−5.16616	−	52.4529i	−0.178144	−	1.80872i	0.326289	−	0.945270i	$-0.394202\pi$
$30$	−3.74271	+	89.5403i	−0.124757	+	2.98468i
$31$	13.3385	−	13.3385i	0.430274	−	0.430274i	−0.458447	−	0.888722i	$-0.651594\pi$
$31$	13.3385	−	13.3385i	0.430274	−	0.430274i	0.888722	+	0.458447i	$0.151594\pi$
$32$	−31.4609	+	5.84932i	−0.983152	+	0.182791i
$33$	26.4106	−	26.4106i	0.800320	−	0.800320i
$34$	1.25453	−	1.15386i	0.0368979	−	0.0339370i
$35$	−2.63755	−	26.7795i	−0.0753585	−	0.765128i
$36$	−52.0561	−	41.4623i	−1.44600	−	1.15173i
$37$	−19.3999	+	36.2946i	−0.524321	+	0.980935i	0.470797	+	0.882242i	$0.343966\pi$
$37$	−19.3999	+	36.2946i	−0.524321	+	0.980935i	−0.995118	+	0.0986937i	$0.968534\pi$
$38$	10.5459	−	11.8080i	0.277523	−	0.310736i
$39$	−80.9519	+	54.0903i	−2.07569	+	1.38693i
$40$	−69.0368	−	15.6918i	−1.72592	−	0.392296i
$41$	16.0435	+	10.7200i	0.391306	+	0.261462i	0.735623	−	0.677391i	$-0.236890\pi$
$41$	16.0435	+	10.7200i	0.391306	+	0.261462i	−0.344317	+	0.938853i	$0.611890\pi$
$42$	26.5263	+	15.6367i	0.631577	+	0.372303i
$43$	−3.22073	+	2.64318i	−0.0749007	+	0.0614694i	−0.671099	−	0.741368i	$-0.734177\pi$
$43$	−3.22073	+	2.64318i	−0.0749007	+	0.0614694i	0.596198	+	0.802837i	$0.296677\pi$
$44$	16.7498	+	24.2912i	0.380678	+	0.552072i
$45$	−69.4075	−	129.852i	−1.54239	−	2.88561i
$46$	16.2940	−	67.1280i	0.354216	−	1.45930i
$47$	1.11778	+	2.69856i	0.0237826	+	0.0574162i	0.935325	−	0.353791i	$-0.115107\pi$
$47$	1.11778	+	2.69856i	0.0237826	+	0.0574162i	−0.911542	+	0.411207i	$0.865107\pi$
$48$	61.0946	−	53.2041i	1.27280	−	1.10842i
$49$	36.7282	+	15.2133i	0.749555	+	0.310476i
$50$	−86.1120	−	62.8942i	−1.72224	−	1.25788i
$51$	−1.25263	+	4.12937i	−0.0245614	+	0.0809681i
$52$	−30.4695	−	70.6206i	−0.585952	−	1.35809i
$53$	4.28928	−	43.5498i	0.0809298	−	0.821694i	−0.865955	−	0.500122i	$-0.833289\pi$
$53$	4.28928	−	43.5498i	0.0809298	−	0.821694i	0.946885	−	0.321573i	$-0.104211\pi$
$54$	76.5878	+	10.7890i	1.41829	+	0.199795i
$55$	12.7356	+	64.0261i	0.231556	+	1.16411i
$56$	−15.9366	+	18.3779i	−0.284582	+	0.328177i
$57$	−7.81939	+	39.3107i	−0.137182	+	0.689662i
$58$	−94.9605	+	45.7657i	−1.63725	+	0.789063i
$59$	−21.3979	+	6.49099i	−0.362677	+	0.110017i	−0.466363	−	0.884593i	$-0.654436\pi$
$59$	−21.3979	+	6.49099i	−0.362677	+	0.110017i	0.103687	+	0.994610i	$0.466936\pi$
$60$	170.740	−	54.5326i	2.84567	−	0.908877i
$61$	50.4076	+	41.3684i	0.826354	+	0.678171i	0.949345	−	0.314237i	$-0.101749\pi$
$61$	50.4076	+	41.3684i	0.826354	+	0.678171i	−0.122991	+	0.992408i	$0.539249\pi$
$62$	−34.2218	−	15.8805i	−0.551965	−	0.256138i
$63$	−50.5895			−0.803008
$64$	32.6160	+	55.0654i	0.509625	+	0.860396i
$65$		−	170.165i		−	2.61793i
$66$	−67.7601	−	31.4439i	−1.02667	−	0.476422i
$67$	−72.5273	+	88.3748i	−1.08250	+	1.31903i	−0.138027	+	0.990428i	$0.544076\pi$
$67$	−72.5273	+	88.3748i	−1.08250	+	1.31903i	−0.944470	+	0.328598i	$0.893424\pi$
$68$	−3.02960	−	1.56283i	−0.0445530	−	0.0229828i
$69$	50.7654	+	167.351i	0.735730	+	2.42538i
$70$	−48.4814	+	23.3654i	−0.692592	+	0.333791i
$71$	34.6028	+	6.88293i	0.487364	+	0.0969427i	0.432655	−	0.901560i	$-0.357577\pi$
$71$	34.6028	+	6.88293i	0.487364	+	0.0969427i	0.0547090	+	0.998502i	$0.482577\pi$
$72$	−42.0805	+	126.274i	−0.584452	+	1.75380i
$73$	−41.7484	+	8.30428i	−0.571896	+	0.113757i	−0.472563	−	0.881297i	$-0.656671\pi$
$73$	−41.7484	+	8.30428i	−0.571896	+	0.113757i	−0.0993335	+	0.995054i	$0.531671\pi$
$74$	81.5033	+	11.4814i	1.10140	+	0.155154i
$75$	268.665	+	26.4612i	3.58220	+	0.352816i
$76$	−29.4273	−	11.6880i	−0.387201	−	0.153789i
$77$	21.4639	+	6.51099i	0.278752	+	0.0845584i
$78$	157.245	+	114.848i	2.01596	+	1.47241i
$79$	14.4300	−	34.8371i	0.182658	−	0.440977i	−0.805854	−	0.592114i	$-0.798294\pi$
$79$	14.4300	−	34.8371i	0.182658	−	0.440977i	0.988513	+	0.151137i	$0.0482936\pi$
$80$	17.9940	+	140.447i	0.224925	+	1.75559i
$81$	−42.5646	+	17.6308i	−0.525489	+	0.217665i
$82$	9.10281	−	37.5019i	0.111010	−	0.457340i
$83$	−29.0696	+	15.5380i	−0.350236	+	0.187205i	−0.637128	−	0.770758i	$-0.719878\pi$
$83$	−29.0696	+	15.5380i	−0.350236	+	0.187205i	0.286892	+	0.957963i	$0.407378\pi$
$84$	11.1298	−	60.5700i	0.132498	−	0.721071i
$85$	−4.78463	−	5.83008i	−0.0562897	−	0.0685892i
$86$	7.17855	+	4.23161i	0.0834715	+	0.0492048i
$87$	148.267	−	221.897i	1.70422	−	2.55054i
$88$	34.1055	−	48.1590i	0.387562	−	0.547261i
$89$	−42.1422	−	63.0703i	−0.473508	−	0.708655i	0.515439	−	0.856926i	$-0.327629\pi$
$89$	−42.1422	−	63.0703i	−0.473508	−	0.708655i	−0.988947	+	0.148272i	$0.952629\pi$
$90$	−196.157	+	219.633i	−2.17952	+	2.44036i
$91$	−51.5633	−	27.5612i	−0.566630	−	0.302870i
$92$	−137.276	+	15.5508i	−1.49214	+	0.169030i
$93$	95.0527	−	9.36188i	1.02207	−	0.100665i
$94$	4.29969	−	3.95466i	0.0457414	−	0.0420709i
$95$	−49.5350	−	49.5350i	−0.521421	−	0.521421i
$96$	−141.928	−	78.1629i	−1.47841	−	0.814197i
$97$	55.5595	+	55.5595i	0.572778	+	0.572778i	0.932904	−	0.360126i	$-0.117266\pi$
$97$	55.5595	+	55.5595i	0.572778	+	0.572778i	−0.360126	+	0.932904i	$0.617266\pi$
$98$	3.32049	−	79.4393i	0.0338826	−	0.810605i
$99$	122.137	−	12.0295i	1.23371	−	0.121510i
$100$	−58.9176	+	204.970i	−0.589176	+	2.04970i
$101$	75.6414	+	40.4311i	0.748924	+	0.400308i	0.801256	−	0.598321i	$-0.204165\pi$
$101$	75.6414	+	40.4311i	0.748924	+	0.400308i	−0.0523319	+	0.998630i	$0.516665\pi$
$102$	8.61664	−	0.486494i	0.0844769	−	0.00476955i
$103$	−3.14444	−	4.70599i	−0.0305286	−	0.0456893i	0.815891	−	0.578205i	$-0.196247\pi$
$103$	−3.14444	−	4.70599i	−0.0305286	−	0.0456893i	−0.846420	+	0.532516i	$0.821247\pi$
$104$	−111.685	+	105.779i	−1.07389	+	1.01711i
$105$	75.6966	−	113.288i	0.720920	−	1.07893i
$106$	−84.7404	+	21.8861i	−0.799437	+	0.206473i
$107$	85.5853	+	104.286i	0.799863	+	0.974636i	0.999987	−	0.00513504i	$-0.00163454\pi$
$107$	85.5853	+	104.286i	0.799863	+	0.974636i	−0.200124	+	0.979771i	$0.564135\pi$
$108$	−32.3937	−	151.258i	−0.299941	−	1.40054i
$109$	100.435	−	53.6836i	0.921421	−	0.492510i	0.0587484	−	0.998273i	$-0.481289\pi$
$109$	100.435	−	53.6836i	0.921421	−	0.492510i	0.862672	+	0.505763i	$0.168789\pi$
$110$	111.492	−	67.9388i	1.01356	−	0.617625i
$111$	−192.516	+	79.7427i	−1.73438	+	0.718402i
$112$	45.4727	+	17.2953i	0.406006	+	0.154423i
$113$	1.07515	−	2.59565i	0.00951462	−	0.0229703i	−0.919051	−	0.394139i	$-0.871043\pi$
$113$	1.07515	−	2.59565i	0.00951462	−	0.0229703i	0.928565	+	0.371169i	$0.121043\pi$
$114$	79.2060	−	12.3417i	0.694789	−	0.108260i
$115$	−292.495	−	88.7275i	−2.54344	−	0.771543i
$116$	151.241	+	146.881i	1.30380	+	1.26622i
$117$	−318.373	−	31.3570i	−2.72114	−	0.268009i
$118$	26.9025	+	35.7249i	0.227988	+	0.302753i
$119$	−2.54158	+	0.505552i	−0.0213578	+	0.00424833i
$120$	−219.807	−	283.176i	−1.83173	−	2.35980i
$121$	65.3069	+	12.9904i	0.539727	+	0.107358i
$122$	43.0377	−	123.113i	0.352768	−	1.00912i
$123$	28.3607	+	93.4927i	0.230575	+	0.760103i
$124$	−6.29682	+	75.1908i	−0.0507808	+	0.606377i
$125$	−158.979	+	193.717i	−1.27183	+	1.54973i
$126$	34.7819	+	95.0127i	0.276047	+	0.754069i
$127$		−	188.646i		−	1.48540i	−0.669622	−	0.742702i	$-0.733544\pi$
$127$		−	188.646i		−	1.48540i	0.669622	−	0.742702i	$-0.266456\pi$
$128$	80.9943	−	99.1157i	0.632768	−	0.774341i
$129$	−21.0964			−0.163538
$130$	−319.589	+	116.994i	−2.45838	+	0.899954i
$131$	−48.0104	−	39.4012i	−0.366492	−	0.300772i	0.433065	−	0.901363i	$-0.357432\pi$
$131$	−48.0104	−	39.4012i	−0.366492	−	0.300772i	−0.799557	+	0.600591i	$0.794932\pi$
$132$	−12.4679	+	148.880i	−0.0944535	+	1.12788i
$133$	−23.0331	+	6.98702i	−0.173181	+	0.0525340i
$134$	215.842	+	75.4539i	1.61076	+	0.563088i
$135$	66.7669	−	335.660i	0.494570	−	2.48637i
$136$	−0.852214	+	6.76442i	−0.00626628	+	0.0497384i
$137$	4.42130	+	22.2274i	0.0322723	+	0.162244i	0.993561	−	0.113300i	$-0.0361421\pi$
$137$	4.42130	+	22.2274i	0.0322723	+	0.162244i	−0.961289	+	0.275544i	$0.911142\pi$
$138$	279.401	−	210.402i	2.02465	−	1.52465i
$139$	−0.275060	+	2.79273i	−0.00197885	+	0.0200916i	−0.996123	−	0.0879663i	$-0.971963\pi$
$139$	−0.275060	+	2.79273i	−0.00197885	+	0.0200916i	0.994145	+	0.108058i	$0.0344632\pi$
$140$	77.2152	+	74.9891i	0.551537	+	0.535636i
$141$	−4.29319	+	14.1527i	−0.0304481	+	0.100374i
$142$	−10.8636	−	69.7202i	−0.0765045	−	0.490987i
$143$	131.042	+	54.2794i	0.916378	+	0.379576i
$144$	266.088	−	7.78535i	1.84783	−	0.0540649i
$145$	178.499	+	430.934i	1.23102	+	2.97196i
$146$	44.2997	+	72.6987i	0.303423	+	0.497937i
$147$	94.8876	+	177.522i	0.645494	+	1.20763i
$148$	−34.4728	−	160.966i	−0.232924	−	1.08761i
$149$	35.8424	−	29.4151i	0.240553	−	0.197417i	−0.506391	−	0.862304i	$-0.669021\pi$
$149$	35.8424	−	29.4151i	0.240553	−	0.197417i	0.746943	+	0.664888i	$0.231521\pi$
$150$	−135.019	−	522.776i	−0.900125	−	3.48517i
$151$	−191.552	−	127.991i	−1.26855	−	0.847620i	−0.275051	−	0.961430i	$-0.588695\pi$
$151$	−191.552	−	127.991i	−1.26855	−	0.847620i	−0.993503	+	0.113809i	$0.963695\pi$
$152$	−1.71910	+	63.3036i	−0.0113098	+	0.416471i
$153$	−11.7896	+	7.87753i	−0.0770560	+	0.0514871i
$154$	−2.52872	−	44.7880i	−0.0164203	−	0.290831i
$155$	−78.6933	+	147.225i	−0.507699	+	0.949837i
$156$	107.586	−	374.284i	0.689655	−	2.39926i
$157$	−6.61962	−	67.2101i	−0.0421632	−	0.428090i	−0.992975	−	0.118322i	$-0.962249\pi$
$157$	−6.61962	−	67.2101i	−0.0421632	−	0.428090i	0.950812	−	0.309768i	$-0.100251\pi$
$158$	−75.3491	−	3.14953i	−0.476893	−	0.0199337i
$159$	156.677	−	156.677i	0.985392	−	0.985392i
$160$	251.404	−	130.357i	1.57128	−	0.814730i
$161$	−74.2607	+	74.2607i	−0.461247	+	0.461247i
$162$	62.3772	+	67.8193i	0.385045	+	0.418638i
$163$	12.0663	+	122.511i	0.0740264	+	0.751603i	0.958515	+	0.285041i	$0.0920074\pi$
$163$	12.0663	+	122.511i	0.0740264	+	0.751603i	−0.884489	+	0.466561i	$0.845493\pi$
$164$	−76.6911	+	8.68763i	−0.467629	+	0.0529733i
$165$	−155.815	+	291.509i	−0.944331	+	1.76672i
$166$	49.1683	+	43.9130i	0.296195	+	0.264536i
$167$	123.763	−	82.6956i	0.741094	−	0.495183i	−0.126803	−	0.991928i	$-0.540472\pi$
$167$	123.763	−	82.6956i	0.741094	−	0.495183i	0.867897	+	0.496745i	$0.165472\pi$
$168$	−121.409	+	20.7407i	−0.722674	+	0.123457i
$169$	−166.900	−	111.519i	−0.987574	−	0.659876i
$170$	−7.65996	+	12.9944i	−0.0450586	+	0.0764378i
$171$	−101.806	+	83.5503i	−0.595358	+	0.488598i
$172$	3.01196	−	16.3915i	0.0175114	−	0.0952993i
$173$	47.7094	+	89.2580i	0.275777	+	0.515942i	0.981237	−	0.192808i	$-0.0617594\pi$
$173$	47.7094	+	89.2580i	0.275777	+	0.515942i	−0.705460	+	0.708750i	$0.749259\pi$
$174$	−518.685	−	125.900i	−2.98095	−	0.723565i
$175$	62.0409	+	149.780i	0.354519	+	0.855885i
$176$	−113.897	−	30.9430i	−0.647139	−	0.175813i
$177$	−104.602	−	43.3276i	−0.590973	−	0.244789i
$178$	−89.4788	+	122.511i	−0.502690	+	0.688261i
$179$	52.3241	−	172.489i	0.292313	−	0.963628i	−0.680638	−	0.732620i	$-0.738297\pi$
$179$	52.3241	−	172.489i	0.292313	−	0.963628i	0.972952	−	0.231009i	$-0.0742025\pi$
$180$	547.359	+	217.401i	3.04088	+	1.20778i
$181$	−5.82109	+	59.1026i	−0.0321607	+	0.326534i	0.965621	+	0.259956i	$0.0837080\pi$
$181$	−5.82109	+	59.1026i	−0.0321607	+	0.326534i	−0.997781	+	0.0665777i	$0.978792\pi$
$182$	−16.3115	+	115.791i	−0.0896237	+	0.636213i
$183$	64.4147	+	323.835i	0.351993	+	1.76959i
$184$	123.588	+	247.129i	0.671674	+	1.34309i
$185$	71.0521	−	357.203i	0.384066	−	1.93083i
$186$	−82.9344	−	172.083i	−0.445884	−	0.925177i
$187$	6.01588	−	1.82490i	0.0321705	−	0.00975880i
$188$	−10.3835	−	5.35634i	−0.0552312	−	0.0284911i
$189$	−90.8973	−	74.5975i	−0.480938	−	0.394696i
$190$	−58.9753	+	127.089i	−0.310397	+	0.668890i
$191$	−329.085			−1.72296			−0.861478	−	0.507795i	$-0.830461\pi$
$191$	−329.085			−1.72296			−0.861478	+	0.507795i	$0.830461\pi$
$192$	−49.2188	+	320.295i	−0.256348	+	1.66821i
$193$		−	328.598i		−	1.70258i	−0.524697	−	0.851289i	$-0.675821\pi$
$193$		−	328.598i		−	1.70258i	0.524697	−	0.851289i	$-0.324179\pi$
$194$	66.1479	−	142.546i	0.340969	−	0.734772i
$195$	546.598	−	666.032i	2.80307	−	3.41555i
$196$	−151.479	+	48.3808i	−0.772851	+	0.246841i
$197$	−70.8743	−	233.641i	−0.359768	−	1.18600i	−0.930942	−	0.365167i	$-0.881012\pi$
$197$	−70.8743	−	233.641i	−0.359768	−	1.18600i	0.571174	−	0.820829i	$-0.306488\pi$
$198$	−106.566	−	221.117i	−0.538212	−	1.11675i
$199$	−14.5171	−	2.88762i	−0.0729500	−	0.0145107i	0.158480	−	0.987362i	$-0.449341\pi$
$199$	−14.5171	−	2.88762i	−0.0729500	−	0.0145107i	−0.231430	+	0.972851i	$0.574341\pi$
$200$	425.464	−	30.2695i	2.12732	−	0.151347i
$201$	−567.748	+	112.932i	−2.82462	+	0.561851i
$202$	23.9283	−	169.861i	0.118457	−	0.840894i
$203$	159.492	+	15.7086i	0.785675	+	0.0773823i
$204$	−6.83790	−	15.8485i	−0.0335191	−	0.0776889i
$205$	−163.406	−	49.5686i	−0.797102	−	0.241798i
$206$	−6.67647	+	9.14114i	−0.0324101	+	0.0443744i
$207$	−219.905	+	530.898i	−1.06234	+	2.56473i
$208$	275.451	+	137.030i	1.32429	+	0.658796i
$209$	53.9470	−	22.3456i	0.258120	−	0.106917i
$210$	−264.811	−	64.2775i	−1.26101	−	0.306083i
$211$	−38.2306	+	20.4347i	−0.181188	+	0.0968468i	−0.559497	−	0.828832i	$-0.689006\pi$
$211$	−38.2306	+	20.4347i	−0.181188	+	0.0968468i	0.378309	+	0.925679i	$0.376506\pi$
$212$	99.3662	+	144.104i	0.468709	+	0.679738i
$213$	113.327	+	138.090i	0.532054	+	0.648309i
$214$	137.018	−	232.439i	0.640271	−	1.08616i
$215$	20.4850	−	30.6580i	0.0952793	−	0.142596i
$216$	−261.808	+	164.834i	−1.21207	+	0.763119i
$217$	31.8662	+	47.6912i	0.146849	+	0.219775i
$218$	−169.876	−	151.719i	−0.779247	−	0.695957i
$219$	−190.079	−	101.600i	−0.867942	−	0.463925i
$220$	−204.251	−	162.684i	−0.928413	−	0.739473i
$221$	−16.3082	+	1.60622i	−0.0737927	+	0.00726795i
$222$	282.126	+	306.740i	1.27084	+	1.38171i
$223$	273.825	+	273.825i	1.22792	+	1.22792i	0.964751	+	0.263164i	$0.0847662\pi$
$223$	273.825	+	273.825i	1.22792	+	1.22792i	0.263164	+	0.964751i	$0.415234\pi$
$224$	1.21863	−	97.2938i	0.00544032	−	0.434347i
$225$	627.256	+	627.256i	2.78780	+	2.78780i
$226$	−5.61411	−	0.234665i	−0.0248412	−	0.00103834i
$227$	−240.105	+	23.6483i	−1.05773	+	0.104178i	−0.611897	−	0.790937i	$-0.709593\pi$
$227$	−240.105	+	23.6483i	−1.05773	+	0.104178i	−0.445836	+	0.895115i	$0.647093\pi$
$228$	−77.6357	−	140.272i	−0.340507	−	0.615229i
$229$	−78.5078	−	41.9633i	−0.342829	−	0.183246i	0.290993	−	0.956725i	$-0.406015\pi$
$229$	−78.5078	−	41.9633i	−0.342829	−	0.183246i	−0.633821	+	0.773480i	$0.718515\pi$
$230$	34.4598	+	610.341i	0.149825	+	2.65366i
$231$	63.0959	+	94.4296i	0.273142	+	0.408786i
$232$	171.876	−	385.033i	0.740843	−	1.65963i
$233$	−212.685	+	318.305i	−0.912809	+	1.36612i	0.0176981	+	0.999843i	$0.494366\pi$
$233$	−212.685	+	318.305i	−0.912809	+	1.36612i	−0.930508	+	0.366273i	$0.880634\pi$
$234$	160.000	+	619.499i	0.683759	+	2.64743i
$235$	−16.3985	−	19.9817i	−0.0697810	−	0.0850283i
$236$	48.5990	−	75.0880i	0.205928	−	0.318169i
$237$	168.382	−	90.0021i	0.710473	−	0.379756i
$238$	2.69690	+	4.42578i	0.0113315	+	0.0185957i
$239$	−225.722	+	93.4970i	−0.944442	+	0.391201i	−0.801139	−	0.598478i	$-0.795772\pi$
$239$	−225.722	+	93.4970i	−0.944442	+	0.391201i	−0.143303	+	0.989679i	$0.545772\pi$
$240$	−380.711	+	607.515i	−1.58629	+	2.53131i
$241$	116.766	−	281.898i	0.484507	−	1.16970i	−0.472941	−	0.881094i	$-0.656807\pi$
$241$	116.766	−	281.898i	0.484507	−	1.16970i	0.957447	−	0.288608i	$-0.0931925\pi$
$242$	−20.5033	−	131.585i	−0.0847242	−	0.543740i
$243$	109.829	+	33.3161i	0.451970	+	0.137103i
$244$	−260.810	+	3.81464i	−1.06889	+	0.0156338i
$245$	−350.120	−	34.4838i	−1.42906	−	0.140750i
$246$	156.091	−	117.544i	0.634515	−	0.477820i
$247$	−149.284	+	29.6945i	−0.604390	+	0.120221i
$248$	145.546	−	39.8699i	0.586878	−	0.160766i
$249$	−163.690	−	32.5599i	−0.657388	−	0.130763i
$250$	473.125	+	165.394i	1.89250	+	0.661577i
$251$	−57.2400	−	188.695i	−0.228048	−	0.751773i	−0.994049	−	0.108934i	$-0.965256\pi$
$251$	−57.2400	−	188.695i	−0.228048	−	0.751773i	0.766001	−	0.642839i	$-0.222244\pi$
$252$	154.531	−	130.648i	0.613217	−	0.518446i
$253$	161.628	−	196.945i	0.638847	−	0.778437i
$254$	−354.299	+	129.700i	−1.39488	+	0.510631i
$255$		−	38.1881i		−	0.149757i
$256$	−241.836	−	83.9711i	−0.944673	−	0.328012i
$257$	275.737			1.07291			0.536453	−	0.843930i	$-0.319764\pi$
$257$	275.737			1.07291			0.536453	+	0.843930i	$0.319764\pi$
$258$	14.5044	+	39.6213i	0.0562187	+	0.153571i
$259$	−96.7313	−	79.3853i	−0.373480	−	0.306507i
$260$	439.455	+	519.787i	1.69021	+	1.99918i
$261$	839.154	−	254.555i	3.21515	−	0.975305i
$262$	−40.9910	+	117.258i	−0.156454	+	0.447551i
$263$	15.3363	−	77.1009i	0.0583130	−	0.293159i	−0.940614	−	0.339479i	$-0.889749\pi$
$263$	15.3363	−	77.1009i	0.0583130	−	0.293159i	0.998927	+	0.0463195i	$0.0147492\pi$
$264$	288.184	−	78.9434i	1.09161	−	0.299028i
$265$	75.5522	+	379.827i	0.285103	+	1.43331i
$266$	28.9584	+	38.4549i	0.108866	+	0.144567i
$267$	37.6460	−	382.226i	0.140996	−	1.43156i
$268$	−6.68785	−	457.253i	−0.0249547	−	1.70617i
$269$	−106.363	+	350.633i	−0.395403	+	1.30347i	0.502996	+	0.864289i	$0.332231\pi$
$269$	−106.363	+	350.633i	−0.395403	+	1.30347i	−0.898399	+	0.439180i	$0.855269\pi$
$270$	−676.311	+	105.381i	−2.50485	+	0.390301i
$271$	236.422	+	97.9294i	0.872407	+	0.361363i	0.773547	−	0.633738i	$-0.218480\pi$
$271$	236.422	+	97.9294i	0.872407	+	0.361363i	0.0988600	+	0.995101i	$0.468480\pi$
$272$	13.2903	−	3.05020i	0.0488613	−	0.0112140i
$273$	−113.289	−	273.505i	−0.414980	−	1.00185i
$274$	38.7057	−	23.5857i	0.141262	−	0.0860793i
$275$	−185.400	−	346.859i	−0.674181	−	1.26130i
$276$	−587.256	−	380.088i	−2.12774	−	1.37713i
$277$	238.072	−	195.380i	0.859464	−	0.705344i	−0.0975983	−	0.995226i	$-0.531116\pi$
$277$	238.072	−	195.380i	0.859464	−	0.705344i	0.957062	+	0.289882i	$0.0936160\pi$
$278$	5.43417	−	1.40350i	0.0195474	−	0.00504856i
$279$	260.951	+	174.362i	0.935309	+	0.624954i
$280$	87.7499	−	196.576i	0.313392	−	0.702058i
$281$	−74.3682	+	49.6913i	−0.264656	+	0.176837i	−0.680817	−	0.732453i	$-0.738375\pi$
$281$	−74.3682	+	49.6913i	−0.264656	+	0.176837i	0.416161	+	0.909291i	$0.363375\pi$
$282$	29.5321	−	1.66738i	0.104724	−	0.00591269i
$283$	−136.617	+	255.593i	−0.482747	+	0.903156i	0.516164	+	0.856490i	$0.327360\pi$
$283$	−136.617	+	255.593i	−0.482747	+	0.903156i	−0.998911	+	0.0466660i	$0.985140\pi$
$284$	−123.473	+	68.3379i	−0.434764	+	0.240627i
$285$	−34.7671	−	352.996i	−0.121990	−	1.23858i
$286$	11.8472	−	283.430i	0.0414236	−	0.991016i
$287$	−41.4866	+	41.4866i	−0.144553	+	0.144553i
$288$	−197.566	−	494.390i	−0.685992	−	1.71663i
$289$	203.840	−	203.840i	0.705330	−	0.705330i
$290$	686.618	−	631.521i	2.36765	−	2.17766i
$291$	38.9954	+	395.927i	0.134005	+	1.36058i
$292$	106.079	−	133.183i	0.363284	−	0.456105i
$293$	140.862	−	263.534i	0.480756	−	0.899432i	−0.518266	−	0.855220i	$-0.673422\pi$
$293$	140.862	−	263.534i	0.480756	−	0.899432i	0.999022	−	0.0442123i	$-0.0140778\pi$
$294$	268.168	−	300.262i	0.912137	−	1.02130i
$295$	164.536	−	109.940i	0.557751	−	0.372677i
$296$	−278.611	+	175.413i	−0.941254	+	0.592611i
$297$	237.190	+	158.485i	0.798620	+	0.533621i
$298$	−79.8875	−	47.0922i	−0.268079	−	0.158027i
$299$	−513.372	+	421.313i	−1.71696	+	1.40907i
$300$	−889.001	+	613.005i	−2.96334	+	2.04335i
$301$	−5.97207	−	11.1730i	−0.0198408	−	0.0371195i
$302$	−108.683	+	447.753i	−0.359877	+	1.48262i
$303$	166.191	+	401.221i	0.548486	+	1.32416i
$304$	120.073	−	40.2946i	0.394977	−	0.132548i
$305$	−533.157	−	220.841i	−1.74805	−	0.724068i
$306$	22.9006	+	16.7260i	0.0748385	+	0.0546603i
$307$	159.335	−	525.258i	0.519008	−	1.71094i	−0.169340	−	0.985558i	$-0.554164\pi$
$307$	159.335	−	525.258i	0.519008	−	1.71094i	0.688348	−	0.725381i	$-0.258336\pi$
$308$	−82.3783	+	35.5424i	−0.267462	+	0.115397i
$309$	2.80896	−	28.5199i	0.00909049	−	0.0922973i
$310$	330.609	+	46.5730i	1.06648	+	0.150235i
$311$	−81.5648	−	410.054i	−0.262266	−	1.31850i	−0.857307	−	0.514806i	$-0.827864\pi$
$311$	−81.5648	−	410.054i	−0.262266	−	1.31850i	0.595040	−	0.803696i	$-0.297136\pi$
$312$	−776.916	+	55.2735i	−2.49012	+	0.177159i
$313$	−69.1865	+	347.824i	−0.221043	+	1.11126i	0.697696	+	0.716394i	$0.254209\pi$
$313$	−69.1865	+	347.824i	−0.221043	+	1.11126i	−0.918739	+	0.394865i	$0.870791\pi$
$314$	−121.677	+	58.6415i	−0.387506	+	0.186756i
$315$	428.425	−	129.961i	1.36008	−	0.412575i
$316$	45.8897	+	143.679i	0.145221	+	0.454682i
$317$	−22.7315	−	18.6553i	−0.0717082	−	0.0588494i	0.597856	−	0.801603i	$-0.296019\pi$
$317$	−22.7315	−	18.6553i	−0.0717082	−	0.0588494i	−0.669565	+	0.742754i	$0.733519\pi$
$318$	−401.978	−	186.537i	−1.26408	−	0.586594i
$319$	−388.794			−1.21879
$320$	−417.673	−	382.541i	−1.30523	−	1.19544i
$321$			683.092i			2.12801i
$322$	190.527	+	88.4133i	0.591697	+	0.274575i
$323$	−4.27974	+	5.21488i	−0.0132500	+	0.0161451i
$324$	84.4859	−	163.779i	0.260759	−	0.505492i
$325$	297.601	+	981.060i	0.915696	+	3.01864i
$326$	221.794	−	106.892i	0.680349	−	0.327890i
$327$	565.545	+	112.494i	1.72950	+	0.344018i
$328$	69.0439	+	138.061i	0.210500	+	0.420919i
$329$	−8.71085	+	1.73270i	−0.0264767	+	0.00526655i
$330$	654.613	+	92.2157i	1.98368	+	0.279441i
$331$	−56.8989	−	5.60405i	−0.171900	−	0.0169307i	0.0117010	−	0.999932i	$-0.496275\pi$
$331$	−56.8989	−	5.60405i	−0.171900	−	0.0169307i	−0.183601	+	0.983001i	$0.558775\pi$
$332$	48.6687	−	122.535i	0.146592	−	0.369082i
$333$	−655.221	−	198.759i	−1.96763	−	0.596875i
$334$	−240.402	−	175.584i	−0.719767	−	0.525701i
$335$	387.179	−	934.733i	1.15576	−	2.79025i
$336$	122.426	+	213.760i	0.364363	+	0.636191i
$337$	131.314	−	54.3921i	0.389656	−	0.161401i	−0.179249	−	0.983804i	$-0.557367\pi$
$337$	131.314	−	54.3921i	0.389656	−	0.161401i	0.568906	+	0.822403i	$0.307367\pi$
$338$	−94.6961	+	390.130i	−0.280166	+	1.15423i
$339$	12.5458	−	6.70588i	0.0370083	−	0.0197814i
$340$	29.6714	+	5.45217i	0.0872689	+	0.0160358i
$341$	−88.2743	−	107.563i	−0.258869	−	0.315433i
$342$	226.912	+	133.760i	0.663484	+	0.391111i
$343$	−149.933	+	224.391i	−0.437123	+	0.654201i
$344$	−32.8558	+	5.61287i	−0.0955111	+	0.0163165i
$345$	−859.828	−	1286.82i	−2.49226	−	3.72992i
$346$	134.835	−	150.971i	0.389696	−	0.436333i
$347$	13.7094	+	7.32782i	0.0395083	+	0.0211176i	0.491033	−	0.871141i	$-0.336620\pi$
$347$	13.7094	+	7.32782i	0.0395083	+	0.0211176i	−0.451524	+	0.892259i	$0.649120\pi$
$348$	120.158	+	1060.71i	0.345281	+	3.04801i
$349$	335.871	−	33.0805i	0.962383	−	0.0947864i	0.395394	−	0.918512i	$-0.370608\pi$
$349$	335.871	−	33.0805i	0.962383	−	0.0947864i	0.566989	+	0.823725i	$0.308108\pi$
$350$	238.648	−	219.498i	0.681852	−	0.627137i
$351$	−525.803	−	525.803i	−1.49801	−	1.49801i
$352$	20.1930	+	235.185i	0.0573665	+	0.668138i
$353$	−27.5849	−	27.5849i	−0.0781442	−	0.0781442i	0.666954	−	0.745099i	$-0.267598\pi$
$353$	−27.5849	−	27.5849i	−0.0781442	−	0.0781442i	−0.745099	+	0.666954i	$0.767598\pi$
$354$	−9.45679	+	226.244i	−0.0267141	+	0.639106i
$355$	−310.721	+	30.6033i	−0.875270	+	0.0862066i
$356$	291.608	+	83.8213i	0.819123	+	0.235453i
$357$	−11.5717	−	6.18522i	−0.0324138	−	0.0173255i
$358$	−359.929	+	20.3215i	−1.00539	+	0.0567640i
$359$	232.033	+	347.262i	0.646331	+	0.967302i	0.999496	+	0.0317415i	$0.0101053\pi$
$359$	232.033	+	347.262i	0.646331	+	0.967302i	−0.353165	+	0.935561i	$0.614895\pi$
$360$	31.9758	−	1177.47i	0.0888218	−	3.27075i
$361$	165.748	−	248.060i	0.459137	−	0.687147i
$362$	115.003	−	29.7022i	0.317689	−	0.0820504i
$363$	213.886	+	260.621i	0.589218	+	0.717964i
$364$	228.683	−	48.9751i	0.628249	−	0.134547i
$365$	332.220	−	177.575i	0.910191	−	0.486507i
$366$	563.910	−	343.624i	1.54074	−	0.938865i
$367$	356.531	−	147.680i	0.971473	−	0.402397i	0.160213	−	0.987083i	$-0.448782\pi$
$367$	356.531	−	147.680i	0.971473	−	0.402397i	0.811260	+	0.584685i	$0.198782\pi$
$368$	379.164	−	402.021i	1.03034	−	1.09245i
$369$	−122.853	+	296.593i	−0.332934	+	0.803774i
$370$	−719.718	+	112.145i	−1.94518	+	0.303094i
$371$	127.332	+	38.6257i	0.343212	+	0.104112i
$372$	−266.171	+	274.073i	−0.715513	+	0.736754i
$373$	67.1344	+	6.61216i	0.179985	+	0.0177270i	0.187608	−	0.982244i	$-0.439927\pi$
$373$	67.1344	+	6.61216i	0.179985	+	0.0177270i	−0.00762310	+	0.999971i	$0.502427\pi$
$374$	−7.56346	−	10.0438i	−0.0202232	−	0.0268551i
$375$	−1244.50	+	247.546i	−3.31867	+	0.660124i
$376$	−2.92083	+	23.1840i	−0.00776815	+	0.0616595i
$377$	993.989	+	197.717i	2.63658	+	0.524448i
$378$	−77.6076	+	222.003i	−0.205311	+	0.587311i
$379$	−159.365	−	525.357i	−0.420489	−	1.38617i	−0.870070	−	0.492928i	$-0.835927\pi$
$379$	−159.365	−	525.357i	−0.420489	−	1.38617i	0.449581	−	0.893240i	$-0.351573\pi$
$380$	279.235	+	23.3844i	0.734829	+	0.0615379i
$381$	605.963	−	738.368i	1.59045	−	1.93797i
$382$	226.256	+	618.057i	0.592293	+	1.61795i
$383$			541.721i			1.41442i	0.707005	+	0.707208i	$0.250046\pi$
$383$			541.721i			1.41442i	−0.707005	+	0.707208i	$0.749954\pi$
$384$	635.390	−	127.775i	1.65466	−	0.332747i
$385$	−198.496			−0.515575
$386$	−617.143	+	225.921i	−1.59882	+	0.585288i
$387$	−53.5853	−	43.9763i	−0.138463	−	0.113634i
$388$	−313.195	−	26.2284i	−0.807205	−	0.0675991i
$389$	−375.905	+	114.030i	−0.966337	+	0.293135i	−0.733734	−	0.679437i	$-0.762224\pi$
$389$	−375.905	+	114.030i	−0.966337	+	0.293135i	−0.232603	+	0.972572i	$0.574724\pi$
$390$	−1626.69	−	568.654i	−4.17099	−	1.45809i
$391$	−5.74250	+	28.8695i	−0.0146867	+	0.0738350i
$392$	195.011	+	251.230i	0.497477	+	0.640894i
$393$	−61.3515	−	308.435i	−0.156111	−	0.784821i
$394$	−390.076	+	293.746i	−0.990040	+	0.745547i
$395$	−32.7083	+	332.093i	−0.0828059	+	0.840742i
$396$	−342.014	+	352.168i	−0.863673	+	0.889312i
$397$	−94.5163	+	311.578i	−0.238076	+	0.784832i	0.753742	+	0.657171i	$0.228247\pi$
$397$	−94.5163	+	311.578i	−0.238076	+	0.784832i	−0.991818	+	0.127661i	$0.959253\pi$
$398$	4.55766	+	29.2500i	0.0114514	+	0.0734924i
$399$	−112.596	−	46.6387i	−0.282195	−	0.116889i
$400$	−349.369	−	778.257i	−0.873423	−	1.94564i
$401$	−236.333	−	570.558i	−0.589358	−	1.42284i	−0.884117	−	0.467265i	$-0.845239\pi$
$401$	−236.333	−	570.558i	−0.589358	−	1.42284i	0.294759	−	0.955572i	$-0.404761\pi$
$402$	602.444	+	988.649i	1.49862	+	2.45933i
$403$	170.982	+	319.885i	0.424273	+	0.793759i
$404$	−335.468	+	71.8444i	−0.830367	+	0.177833i
$405$	315.172	−	258.655i	0.778203	−	0.638655i
$406$	−80.1534	−	310.344i	−0.197422	−	0.764394i
$407$	252.413	+	168.657i	0.620180	+	0.414391i
$408$	−25.0640	+	23.7387i	−0.0614314	+	0.0581831i
$409$	66.3422	−	44.3284i	0.162206	−	0.108382i	−0.471818	−	0.881696i	$-0.656402\pi$
$409$	66.3422	−	44.3284i	0.162206	−	0.108382i	0.634024	+	0.773313i	$0.281402\pi$
$410$	19.2514	+	340.974i	0.0469545	+	0.831645i
$411$	−54.0928	+	101.201i	−0.131613	+	0.246230i
$412$	21.7584	+	6.25433i	0.0528115	+	0.0151804i
$413$	−6.66436	−	67.6643i	−0.0161365	−	0.163836i
$414$	1148.28	+	47.9970i	2.77362	+	0.115935i
$415$	206.264	−	206.264i	0.497021	−	0.497021i
$416$	67.9751	−	611.541i	0.163402	−	1.47005i
$417$	−10.0473	+	10.0473i	−0.0240942	+	0.0240942i
$418$	−79.0578	−	85.9552i	−0.189133	−	0.205634i
$419$	−66.2099	−	672.240i	−0.158019	−	1.60439i	−0.667970	−	0.744188i	$-0.732836\pi$
$419$	−66.2099	−	672.240i	−0.158019	−	1.60439i	0.509951	−	0.860203i	$-0.329664\pi$
$420$	61.3458	+	541.537i	0.146061	+	1.28937i
$421$	−174.080	+	325.682i	−0.413493	+	0.773591i	−0.999321	−	0.0368446i	$-0.988269\pi$
$421$	−174.080	+	325.682i	−0.413493	+	0.773591i	0.585828	+	0.810435i	$0.300769\pi$
$422$	64.6634	+	57.7518i	0.153231	+	0.136853i
$423$	−40.4068	+	26.9990i	−0.0955244	+	0.0638273i
$424$	202.327	−	285.697i	0.477185	−	0.673814i
$425$	37.7812	+	25.2446i	0.0888969	+	0.0593990i
$426$	181.432	−	307.783i	0.425896	−	0.722494i
$427$	−153.273	+	125.788i	−0.358953	+	0.294585i
$428$	−530.750	−	97.5261i	−1.24007	−	0.227865i
$429$	338.549	+	633.380i	0.789157	+	1.47641i
$430$	−71.6633	−	17.3948i	−0.166659	−	0.0404531i
$431$	93.5523	+	225.855i	0.217059	+	0.524026i	0.994477	−	0.104958i	$-0.0334709\pi$
$431$	93.5523	+	225.855i	0.217059	+	0.524026i	−0.777418	+	0.628984i	$0.783471\pi$
$432$	489.577	+	378.376i	1.13328	+	0.875869i
$433$	−204.431	−	84.6782i	−0.472127	−	0.195562i	0.133917	−	0.990993i	$-0.457245\pi$
$433$	−204.431	−	84.6782i	−0.472127	−	0.195562i	−0.606044	+	0.795431i	$0.707245\pi$
$434$	67.6602	−	92.6375i	0.155899	−	0.213450i
$435$	−685.580	+	2260.05i	−1.57605	+	5.19552i
$436$	−168.149	+	423.357i	−0.385664	+	0.971002i
$437$	−26.7982	+	272.086i	−0.0613230	+	0.622623i
$438$	−60.1296	+	426.843i	−0.137282	+	0.974527i
$439$	88.4638	+	444.737i	0.201512	+	1.01307i	0.940615	+	0.339476i	$0.110250\pi$
$439$	88.4638	+	444.737i	0.201512	+	1.01307i	−0.739103	+	0.673593i	$0.764750\pi$
$440$	−165.110	+	495.456i	−0.375250	+	1.12604i
$441$	−129.036	+	648.708i	−0.292599	+	1.47099i
$442$	14.2291	+	29.5243i	0.0321924	+	0.0667970i
$443$	−12.5543	+	3.80829i	−0.0283392	+	0.00859660i	−0.304422	−	0.952537i	$-0.598463\pi$
$443$	−12.5543	+	3.80829i	−0.0283392	+	0.00859660i	0.276083	+	0.961134i	$0.410963\pi$
$444$	382.122	−	740.758i	0.860634	−	1.66837i
$445$	518.911	+	425.859i	1.16609	+	0.956986i
$446$	326.010	−	702.537i	0.730965	−	1.57520i
$447$	234.774			0.525222
$448$	−183.566	+	64.6039i	−0.409747	+	0.144205i
$449$		−	102.650i		−	0.228620i	−0.993445	−	0.114310i	$-0.963534\pi$
$449$		−	102.650i		−	0.228620i	0.993445	−	0.114310i	$-0.0364657\pi$
$450$	746.798	−	1609.31i	1.65955	−	3.57625i
$451$	90.2955	−	110.025i	0.200212	−	0.243959i
$452$	3.41916	+	10.7053i	0.00756450	+	0.0236842i
$453$	−338.612	−	1116.25i	−0.747488	−	2.46414i
$454$	209.494	+	434.685i	0.461441	+	0.957457i
$455$	507.474	+	100.943i	1.11533	+	0.221853i
$456$	−210.070	+	242.250i	−0.460679	+	0.531250i
$457$	540.684	−	107.549i	1.18312	−	0.235336i	0.435948	−	0.899972i	$-0.356413\pi$
$457$	540.684	−	107.549i	1.18312	−	0.235336i	0.747168	+	0.664636i	$0.231413\pi$
$458$	−24.8351	+	176.297i	−0.0542251	+	0.384929i
$459$	−32.7990	−	3.23042i	−0.0714575	−	0.00703795i
$460$	1122.60	−	484.348i	2.44043	−	1.05293i
$461$	−250.564	−	76.0078i	−0.543523	−	0.164876i	0.00657122	−	0.999978i	$-0.497908\pi$
$461$	−250.564	−	76.0078i	−0.543523	−	0.164876i	−0.550094	+	0.835102i	$0.685408\pi$
$462$	133.969	−	183.424i	0.289976	−	0.397023i
$463$	−5.25187	+	12.6791i	−0.0113431	+	0.0273848i	−0.929450	−	0.368949i	$-0.879718\pi$
$463$	−5.25187	+	12.6791i	−0.0113431	+	0.0273848i	0.918106	+	0.396334i	$0.129718\pi$
$464$	−841.305	−	58.0786i	−1.81316	−	0.125169i
$465$	−780.918	+	323.467i	−1.67939	+	0.695627i
$466$	744.040	+	180.600i	1.59665	+	0.387555i
$467$	−709.162	+	379.055i	−1.51855	+	0.811681i	−0.999083	−	0.0428104i	$-0.986369\pi$
$467$	−709.162	+	379.055i	−1.51855	+	0.811681i	−0.519465	+	0.854492i	$0.673869\pi$
$468$	1053.48	−	726.422i	2.25103	−	1.55218i
$469$	−220.532	−	268.719i	−0.470217	−	0.572961i
$470$	−26.2533	+	44.5363i	−0.0558580	+	0.0947580i
$471$	189.980	−	284.326i	0.403355	−	0.603664i
$472$	−174.437	−	39.6489i	−0.369570	−	0.0840019i
$473$	17.0750	+	25.5546i	0.0360995	+	0.0540266i
$474$	−284.802	−	254.361i	−0.600848	−	0.536626i
$475$	372.218	+	198.954i	0.783616	+	0.418851i
$476$	6.45791	−	8.10794i	0.0135670	−	0.0170335i
$477$	724.565	−	71.3634i	1.51900	−	0.149609i
$478$	330.789	+	359.648i	0.692026	+	0.752402i
$479$	83.3076	+	83.3076i	0.173920	+	0.173920i	0.788699	−	0.614779i	$-0.210755\pi$
$479$	83.3076	+	83.3076i	0.173920	+	0.173920i	−0.614779	+	0.788699i	$0.710755\pi$
$480$	1402.73	+	297.331i	2.92236	+	0.619439i
$481$	−559.550	−	559.550i	−1.16331	−	1.16331i
$482$	−609.717	−	25.4856i	−1.26497	−	0.0528748i
$483$	−529.196	+	52.1213i	−1.09564	+	0.107912i
$484$	−233.034	+	128.976i	−0.481476	+	0.266480i
$485$	−613.242	−	327.785i	−1.26442	−	0.675845i
$486$	−12.9392	−	229.176i	−0.0266240	−	0.471556i
$487$	−40.1604	−	60.1042i	−0.0824648	−	0.123417i	0.787944	−	0.615747i	$-0.211146\pi$
$487$	−40.1604	−	60.1042i	−0.0824648	−	0.123417i	−0.870409	+	0.492329i	$0.836146\pi$
$488$	186.479	+	487.207i	0.382130	+	0.998375i
$489$	−346.298	+	518.272i	−0.708176	+	1.05986i
$490$	175.954	+	681.273i	0.359090	+	1.39035i
$491$	172.577	+	210.285i	0.351480	+	0.428280i	0.918498	−	0.395426i	$-0.129403\pi$
$491$	172.577	+	210.285i	0.351480	+	0.428280i	−0.567018	+	0.823705i	$0.691903\pi$
$492$	−328.077	−	212.341i	−0.666824	−	0.431587i
$493$	39.6147	−	21.1745i	0.0803543	−	0.0429503i
$494$	158.407	+	259.956i	0.320662	+	0.526228i
$495$	−1003.43	+	415.636i	−2.02714	+	0.839669i
$496$	−174.948	−	245.939i	−0.352717	−	0.495846i
$497$	−41.0532	+	99.1111i	−0.0826020	+	0.199419i
$498$	51.3908	+	329.813i	0.103194	+	0.662276i
$499$	281.953	+	85.5296i	0.565037	+	0.171402i	0.559864	−	0.828585i	$-0.310853\pi$
$499$	281.953	+	85.5296i	0.565037	+	0.171402i	0.00517299	+	0.999987i	$0.498353\pi$
$500$	−14.6597	−	1002.30i	−0.0293194	−	2.00459i
$501$	750.042	+	73.8727i	1.49709	+	0.147451i
$502$	−315.036	+	237.237i	−0.627561	+	0.472583i
$503$	214.260	−	42.6189i	0.425964	−	0.0847295i	0.0225469	−	0.999746i	$-0.492822\pi$
$503$	214.260	−	42.6189i	0.425964	−	0.0847295i	0.403417	+	0.915016i	$0.367822\pi$
$504$	−351.617	−	200.401i	−0.697653	−	0.397621i
$505$	−744.445	−	148.079i	−1.47415	−	0.293226i
$506$	−481.008	−	168.150i	−0.950609	−	0.332312i
$507$	−295.035	−	972.599i	−0.581922	−	1.91834i
$508$	487.183	+	576.239i	0.959022	+	1.13433i
$509$	190.890	−	232.600i	0.375030	−	0.456975i	−0.550956	−	0.834535i	$-0.685737\pi$
$509$	190.890	−	232.600i	0.375030	−	0.456975i	0.925985	+	0.377560i	$0.123237\pi$
$510$	−71.7215	+	26.2555i	−0.140630	+	0.0514814i
$511$		−	129.430i		−	0.253288i
$512$	8.56311	+	511.928i	0.0167248	+	0.999860i
$513$	−306.122			−0.596729
$514$	−189.578	−	517.864i	−0.368829	−	1.00752i
$515$	38.7186	+	31.7755i	0.0751817	+	0.0617000i
$516$	64.4410	−	54.4818i	0.124886	−	0.105585i
$517$	20.6184	−	6.25453i	0.0398809	−	0.0120977i
$518$	−82.5886	+	236.252i	−0.159437	+	0.456085i
$519$	−99.9751	+	502.609i	−0.192630	+	0.968418i
$520$	674.078	−	1182.72i	1.29630	−	2.27445i
$521$	148.851	+	748.324i	0.285702	+	1.43632i	0.810821	+	0.585294i	$0.199021\pi$
$521$	148.851	+	748.324i	0.285702	+	1.43632i	−0.525119	+	0.851029i	$0.675979\pi$
$522$	−1055.03	−	1401.01i	−2.02112	−	2.68393i
$523$	41.7793	−	424.192i	0.0798839	−	0.811075i	−0.868866	−	0.495047i	$-0.835151\pi$
$523$	41.7793	−	424.192i	0.0798839	−	0.811075i	0.948750	−	0.316028i	$-0.102349\pi$
$524$	248.407	−	3.63324i	0.474059	−	0.00693366i
$525$	−238.287	+	785.528i	−0.453881	+	1.49624i
$526$	−155.348	+	24.2060i	−0.295339	+	0.0460190i
$527$	14.8524	+	6.15208i	0.0281830	+	0.0116738i
$528$	−346.400	−	486.966i	−0.656061	−	0.922284i
$529$	254.070	+	613.378i	0.480283	+	1.15950i
$530$	661.412	−	403.038i	1.24795	−	0.760450i
$531$	−175.374	−	328.101i	−0.330270	−	0.617893i
$532$	52.3128	−	80.8260i	0.0983323	−	0.151929i
$533$	−286.801	+	235.372i	−0.538089	+	0.441598i
$534$	−743.746	+	192.089i	−1.39278	+	0.359718i
$535$	−992.696	−	663.298i	−1.85551	−	1.23981i
$536$	−854.174	+	326.936i	−1.59361	+	0.609956i
$537$	758.862	−	507.055i	1.41315	−	0.944237i
$538$	731.656	−	41.3092i	1.35996	−	0.0767829i
$539$	138.237	−	258.623i	0.256470	−	0.479821i
$540$	662.903	+	1197.73i	1.22760	+	2.21803i
$541$	39.8328	+	404.430i	0.0736282	+	0.747559i	0.959138	+	0.282939i	$0.0913093\pi$
$541$	39.8328	+	404.430i	0.0736282	+	0.747559i	−0.885510	+	0.464621i	$0.846191\pi$
$542$	21.3743	−	511.357i	0.0394360	−	0.943463i
$543$	−212.631	+	212.631i	−0.391585	+	0.391585i
$544$	−14.8661	−	22.8635i	−0.0273274	−	0.0420284i
$545$	−712.638	+	712.638i	−1.30759	+	1.30759i
$546$	−435.783	+	400.814i	−0.798137	+	0.734091i
$547$	−103.390	−	1049.73i	−0.189012	−	1.91907i	−0.358485	−	0.933535i	$-0.616707\pi$
$547$	−103.390	−	1049.73i	−0.189012	−	1.91907i	0.169473	−	0.985535i	$-0.445793\pi$
$548$	−70.9080	−	56.4776i	−0.129394	−	0.103061i
$549$	−511.432	+	956.822i	−0.931570	+	1.74285i
$550$	−523.971	+	586.677i	−0.952674	+	1.06669i
$551$	346.905	−	231.795i	0.629592	−	0.420680i
$552$	−310.090	+	1364.25i	−0.561758	+	2.47147i
$553$	95.3329	+	63.6994i	0.172392	+	0.115189i
$554$	−530.628	−	312.795i	−0.957812	−	0.564611i
$555$	1425.49	−	1169.87i	2.56846	−	2.10788i
$556$	−6.37209	−	9.24103i	−0.0114606	−	0.0166206i
$557$	−273.928	−	512.483i	−0.491792	−	0.920078i	−0.998325	−	0.0578572i	$-0.981573\pi$
$557$	−273.928	−	512.483i	−0.491792	−	0.920078i	0.506533	−	0.862221i	$-0.330927\pi$
$558$	148.059	−	609.975i	0.265339	−	1.09315i
$559$	−30.6585	−	74.0161i	−0.0548452	−	0.132408i
$560$	−429.523	−	29.6516i	−0.767005	−	0.0529493i
$561$	29.4082	+	12.1813i	0.0524210	+	0.0217135i
$562$	144.456	+	105.507i	0.257040	+	0.187736i
$563$	56.5899	−	186.552i	0.100515	−	0.331353i	−0.892232	−	0.451578i	$-0.850861\pi$
$563$	56.5899	−	186.552i	0.100515	−	0.331353i	0.992747	+	0.120224i	$0.0383614\pi$
$564$	−23.4358	−	54.3182i	−0.0415528	−	0.0963089i
$565$	−2.43703	+	24.7436i	−0.00431333	+	0.0437940i
$566$	573.961	+	80.8542i	1.01407	+	0.142852i
$567$	−27.3299	−	137.397i	−0.0482009	−	0.242323i
$568$	213.238	+	184.912i	0.375419	+	0.325549i
$569$	−140.162	+	704.643i	−0.246331	+	1.23839i	0.637452	+	0.770490i	$0.279988\pi$
$569$	−140.162	+	704.643i	−0.246331	+	1.23839i	−0.883783	+	0.467898i	$0.845012\pi$
$570$	−639.062	+	307.992i	−1.12116	+	0.540337i
$571$	602.720	−	182.833i	1.05555	−	0.320198i	0.285632	−	0.958339i	$-0.407796\pi$
$571$	602.720	−	182.833i	1.05555	−	0.320198i	0.769919	+	0.638141i	$0.220296\pi$
$572$	−540.459	+	172.617i	−0.944859	+	0.301778i
$573$	−1288.05	−	1057.07i	−2.24790	−	1.84480i
$574$	106.440	+	49.3931i	0.185435	+	0.0860507i
$575$	1841.51			3.20262
$576$	−792.686	+	710.959i	−1.37619	+	1.23430i
$577$		−	844.999i		−	1.46447i	−0.681053	−	0.732234i	$-0.738478\pi$
$577$		−	844.999i		−	1.46447i	0.681053	−	0.732234i	$-0.261522\pi$
$578$	−522.981	−	242.688i	−0.904812	−	0.419875i
$579$	1055.51	−	1286.14i	1.82299	−	2.22131i
$580$	−1658.14	−	855.354i	−2.85886	−	1.47475i
$581$	−29.0939	−	95.9098i	−0.0500756	−	0.165077i
$582$	716.785	−	345.450i	1.23159	−	0.593557i
$583$	−316.599	−	62.9755i	−0.543052	−	0.108020i
$584$	−323.064	−	107.661i	−0.553192	−	0.184350i
$585$	2776.74	−	552.329i	4.74657	−	0.944151i
$586$	−591.792	−	83.3660i	−1.00988	−	0.142263i
$587$	389.942	+	38.4059i	0.664296	+	0.0654275i	0.424545	−	0.905407i	$-0.360434\pi$
$587$	389.942	+	38.4059i	0.664296	+	0.0654275i	0.239751	+	0.970834i	$0.422934\pi$
$588$	−748.299	−	297.210i	−1.27262	−	0.505460i
$589$	142.891	+	43.3455i	0.242599	+	0.0735918i
$590$	−319.603	−	233.431i	−0.541700	−	0.395645i
$591$	473.089	−	1142.14i	0.800489	−	1.93255i
$592$	520.999	+	402.660i	0.880066	+	0.680170i
$593$	−292.298	+	121.074i	−0.492913	+	0.204171i	−0.615272	−	0.788315i	$-0.710954\pi$
$593$	−292.298	+	121.074i	−0.492913	+	0.204171i	0.122359	+	0.992486i	$0.460954\pi$
$594$	134.577	−	554.433i	0.226561	−	0.933389i
$595$	20.2250	−	10.8105i	0.0339916	−	0.0181689i
$596$	−33.5191	+	182.415i	−0.0562400	+	0.306065i
$597$	−47.5447	−	57.9333i	−0.0796393	−	0.0970408i
$598$	1144.23	+	674.503i	1.91343	+	1.12793i
$599$	189.146	−	283.077i	0.315769	−	0.472582i	−0.639303	−	0.768955i	$-0.720777\pi$
$599$	189.146	−	283.077i	0.315769	−	0.472582i	0.955072	+	0.296373i	$0.0957771\pi$
$600$	1762.51	+	1248.18i	2.93751	+	2.08030i
$601$	−19.5120	−	29.2018i	−0.0324659	−	0.0485887i	0.814882	−	0.579627i	$-0.196802\pi$
$601$	−19.5120	−	29.2018i	−0.0324659	−	0.0485887i	−0.847348	+	0.531039i	$0.821802\pi$
$602$	−16.8781	+	18.8980i	−0.0280367	+	0.0313920i
$603$	−1677.50	−	896.645i	−2.78193	−	1.48697i
$604$	915.652	−	103.726i	1.51598	−	0.171731i
$605$	−586.433	+	57.7586i	−0.969310	+	0.0954687i
$606$	639.276	−	587.978i	1.05491	−	0.970260i
$607$	−559.239	−	559.239i	−0.921316	−	0.921316i	0.0758068	−	0.997123i	$-0.475847\pi$
$607$	−559.239	−	559.239i	−0.921316	−	0.921316i	−0.997123	+	0.0758068i	$0.975847\pi$
$608$	−158.232	−	197.807i	−0.260249	−	0.325340i
$609$	573.798	+	573.798i	0.942197	+	0.942197i
$610$	−48.2012	+	1153.16i	−0.0790184	+	1.89043i
$611$	−55.8937	+	5.50505i	−0.0914790	+	0.00900989i
$612$	15.6685	−	54.5095i	0.0256021	−	0.0890678i
$613$	804.204	+	429.856i	1.31191	+	0.701233i	0.971049	−	0.238879i	$-0.0767799\pi$
$613$	804.204	+	429.856i	1.31191	+	0.701233i	0.340866	+	0.940112i	$0.389280\pi$
$614$	−1096.04	+	61.8823i	−1.78508	+	0.100785i
$615$	−480.353	−	718.899i	−0.781062	−	1.16894i
$616$	123.390	+	130.279i	0.200309	+	0.211492i
$617$	−196.326	+	293.822i	−0.318194	+	0.476211i	−0.955745	−	0.294197i	$-0.904948\pi$
$617$	−196.326	+	293.822i	−0.318194	+	0.476211i	0.637550	+	0.770409i	$0.279948\pi$
$618$	−55.4947	+	14.3328i	−0.0897973	+	0.0231922i
$619$	451.133	+	549.707i	0.728810	+	0.888057i	0.997164	−	0.0752631i	$-0.0239797\pi$
$619$	451.133	+	549.707i	0.728810	+	0.888057i	−0.268354	+	0.963320i	$0.586480\pi$
$620$	−139.835	−	652.940i	−0.225540	−	1.05313i
$621$	−1177.96	+	629.633i	−1.89688	+	1.01390i
$622$	−714.049	+	435.113i	−1.14799	+	0.699539i
$623$	213.090	−	88.2647i	0.342038	−	0.141677i
$624$	637.964	+	1421.13i	1.02238	+	2.27746i
$625$	338.601	−	817.456i	0.541762	−	1.30793i
$626$	700.820	−	109.200i	1.11952	−	0.174441i
$627$	282.928	+	85.8252i	0.451241	+	0.136882i
$628$	193.792	+	188.205i	0.308586	+	0.299689i
$629$	−34.9041	−	3.43775i	−0.0554914	−	0.00546543i
$630$	−538.637	−	715.276i	−0.854979	−	1.13536i
$631$	−744.299	+	148.050i	−1.17956	+	0.234628i	−0.745655	−	0.666333i	$-0.767863\pi$
$631$	−744.299	+	148.050i	−1.17956	+	0.234628i	−0.433901	+	0.900961i	$0.642863\pi$
$632$	238.295	−	184.970i	0.377049	−	0.292674i
$633$	−215.275	−	42.8209i	−0.340087	−	0.0676476i
$634$	−19.4080	+	55.5184i	−0.0306120	+	0.0875684i
$635$	484.620	+	1597.58i	0.763182	+	2.51587i
$636$	−73.9640	+	883.209i	−0.116296	+	1.38869i
$637$	−484.936	+	590.897i	−0.761281	+	0.927624i
$638$	267.308	+	730.199i	0.418979	+	1.14451i
$639$			586.987i			0.918603i
$640$	−431.290	+	1047.44i	−0.673891	+	1.63663i
$641$	705.138			1.10006			0.550029	−	0.835145i	$-0.314617\pi$
$641$	705.138			1.10006			0.550029	+	0.835145i	$0.314617\pi$
$642$	1282.92	−	469.648i	1.99832	−	0.731538i
$643$	382.032	+	313.526i	0.594140	+	0.487598i	0.882746	−	0.469850i	$-0.155692\pi$
$643$	382.032	+	313.526i	0.594140	+	0.487598i	−0.288606	+	0.957448i	$0.593192\pi$
$644$	35.0569	−	418.617i	0.0544362	−	0.650026i
$645$	178.658	−	54.1952i	0.276989	−	0.0840236i
$646$	12.7366	+	4.45243i	0.0197161	+	0.00689230i
$647$	−214.804	+	1079.89i	−0.332000	+	1.66908i	0.349252	+	0.937029i	$0.386436\pi$
$647$	−214.804	+	1079.89i	−0.332000	+	1.66908i	−0.681252	+	0.732049i	$0.738564\pi$
$648$	−365.682	−	46.0704i	−0.564325	−	0.0710963i
$649$	32.1793	+	161.776i	0.0495829	+	0.249270i
$650$	1637.93	−	1233.44i	2.51989	−	1.89760i
$651$	−28.4664	+	289.024i	−0.0437272	+	0.443969i
$652$	−353.246	−	343.061i	−0.541788	−	0.526168i
$653$	166.882	−	550.138i	0.255563	−	0.842478i	−0.731458	−	0.681886i	$-0.761160\pi$
$653$	166.882	−	550.138i	0.255563	−	0.842478i	0.987021	−	0.160591i	$-0.0513401\pi$
$654$	−177.554	−	1139.50i	−0.271490	−	1.74235i
$655$	507.802	+	210.339i	0.775271	+	0.321128i
$656$	211.825	−	224.594i	0.322904	−	0.342368i
$657$	−271.017	−	654.294i	−0.412507	−	0.995881i
$658$	9.24318	+	15.1687i	0.0140474	+	0.0230527i
$659$	327.529	+	612.763i	0.497009	+	0.929838i	0.997928	+	0.0643435i	$0.0204953\pi$
$659$	327.529	+	612.763i	0.497009	+	0.929838i	−0.500919	+	0.865494i	$0.667005\pi$
$660$	−276.876	−	1292.84i	−0.419509	−	1.95884i
$661$	114.511	−	93.9769i	0.173239	−	0.142174i	−0.543778	−	0.839229i	$-0.683007\pi$
$661$	114.511	−	93.9769i	0.173239	−	0.142174i	0.717018	+	0.697055i	$0.245507\pi$
$662$	28.5947	+	110.715i	0.0431945	+	0.167244i
$663$	−68.9902	−	46.0978i	−0.104058	−	0.0695291i
$664$	−263.596	−	7.15831i	−0.396982	−	0.0107806i
$665$	177.110	−	118.341i	0.266331	−	0.177957i
$666$	77.1937	+	1367.23i	0.115906	+	2.05290i
$667$	858.139	−	1605.46i	1.28656	−	2.40699i
$668$	−164.482	+	572.222i	−0.246231	+	0.856619i
$669$	192.189	+	1951.33i	0.287278	+	2.91679i
$670$	−2021.73	−	84.5066i	−3.01751	−	0.126129i
$671$	340.133	−	340.133i	0.506905	−	0.506905i
$672$	317.293	−	376.897i	0.472163	−	0.560858i
$673$	329.441	−	329.441i	0.489511	−	0.489511i	−0.418641	−	0.908152i	$-0.637493\pi$
$673$	329.441	−	329.441i	0.489511	−	0.489511i	0.908152	+	0.418641i	$0.137493\pi$
$674$	−192.437	−	209.226i	−0.285515	−	0.310425i
$675$	202.100	+	2051.96i	0.299408	+	3.03994i
$676$	797.813	−	90.3769i	1.18020	−	0.133694i
$677$	25.0872	−	46.9349i	0.0370564	−	0.0693277i	−0.862712	−	0.505696i	$-0.831236\pi$
$677$	25.0872	−	46.9349i	0.0370564	−	0.0693277i	0.899768	+	0.436369i	$0.143736\pi$
$678$	−21.2200	−	18.9519i	−0.0312980	−	0.0279527i
$679$	−198.650	+	132.734i	−0.292563	+	0.195484i
$680$	−10.1603	−	59.4748i	−0.0149416	−	0.0874629i
$681$	−1015.74	−	678.697i	−1.49154	−	0.996618i
$682$	−141.323	+	239.742i	−0.207219	+	0.351527i
$683$	−299.402	+	245.713i	−0.438363	+	0.359755i	−0.827539	−	0.561408i	$-0.810260\pi$
$683$	−299.402	+	245.713i	−0.438363	+	0.359755i	0.389176	+	0.921163i	$0.372760\pi$
$684$	95.2071	−	518.130i	0.139192	−	0.757499i
$685$	−94.5431	−	176.878i	−0.138019	−	0.258216i
$686$	524.515	+	127.315i	0.764599	+	0.185591i
$687$	−172.489	−	416.425i	−0.251076	−	0.606150i
$688$	33.1310	+	57.8479i	0.0481555	+	0.0840812i
$689$	777.391	+	322.006i	1.12829	+	0.467353i
$690$	−1825.64	+	2499.58i	−2.64585	+	3.62259i
$691$	−242.668	+	799.969i	−0.351184	+	1.15770i	0.586425	+	0.810004i	$0.300535\pi$
$691$	−242.668	+	799.969i	−0.351184	+	1.15770i	−0.937608	+	0.347694i	$0.886965\pi$
$692$	−376.244	−	149.437i	−0.543705	−	0.215949i
$693$	−36.5777	+	371.379i	−0.0527817	+	0.535901i
$694$	4.33682	−	30.7859i	0.00624902	−	0.0443600i
$695$	−4.84496	−	24.3573i	−0.00697117	−	0.0350464i
$696$	1909.52	−	954.940i	2.74356	−	1.37204i
$697$	−3.20812	+	16.1283i	−0.00460275	+	0.0231396i
$698$	−293.051	−	608.060i	−0.419844	−	0.871146i
$699$	−1854.90	+	562.678i	−2.65365	+	0.804976i
$700$	−576.320	−	297.296i	−0.823314	−	0.424708i
$701$	570.073	+	467.847i	0.813228	+	0.667399i	0.946150	−	0.323727i	$-0.104936\pi$
$701$	570.073	+	467.847i	0.813228	+	0.667399i	−0.132922	+	0.991126i	$0.542436\pi$
$702$	−626.010	+	1349.02i	−0.891752	+	1.92168i
$703$	−325.770			−0.463399
$704$	427.819	−	199.622i	0.607698	−	0.283553i
$705$		−	130.884i		−	0.185650i
$706$	−32.8420	+	70.7730i	−0.0465184	+	0.100245i
$707$	−165.446	+	201.597i	−0.234012	+	0.285144i
$708$	431.412	−	137.789i	0.609340	−	0.194617i
$709$	50.1466	+	165.311i	0.0707287	+	0.233161i	0.985177	−	0.171542i	$-0.0548749\pi$
$709$	50.1466	+	165.311i	0.0707287	+	0.233161i	−0.914448	+	0.404703i	$0.867375\pi$
$710$	271.107	+	562.527i	0.381841	+	0.792292i
$711$	615.307	+	122.392i	0.865411	+	0.172141i
$712$	−43.0640	−	605.302i	−0.0604832	−	0.850143i
$713$	639.000	−	127.105i	0.896213	−	0.178268i
$714$	−3.66059	+	25.9855i	−0.00512688	+	0.0363943i
$715$	−1249.19	−	123.034i	−1.74712	−	0.172076i
$716$	285.628	+	662.014i	0.398922	+	0.924601i
$717$	−1183.81	−	359.105i	−1.65106	−	0.500843i
$718$	492.666	−	674.537i	0.686164	−	0.939466i
$719$	117.919	−	284.682i	0.164004	−	0.395941i	−0.820417	−	0.571765i	$-0.806259\pi$
$719$	117.919	−	284.682i	0.164004	−	0.395941i	0.984422	+	0.175824i	$0.0562589\pi$
$720$	−2233.40	+	749.494i	−3.10195	+	1.04096i
$721$	15.8997	−	6.58588i	0.0220523	−	0.00913437i
$722$	−579.841	−	140.745i	−0.803104	−	0.194937i
$723$	1362.53	−	728.287i	1.88455	−	1.00731i
$724$	−134.853	−	195.568i	−0.186260	−	0.270121i
$725$	−1782.76	−	2172.30i	−2.45898	−	2.99628i
$726$	342.422	−	580.887i	0.471655	−	0.800120i
$727$	−454.480	+	680.177i	−0.625144	+	0.935594i	0.374820	+	0.927098i	$0.377705\pi$
$727$	−454.480	+	680.177i	−0.625144	+	0.935594i	−0.999964	+	0.00849671i	$0.997295\pi$
$728$	−249.207	−	395.820i	−0.342318	−	0.543708i
$729$	553.220	+	827.952i	0.758875	+	1.13574i
$730$	−561.917	−	501.857i	−0.769750	−	0.687475i
$731$	−3.13155	−	1.67385i	−0.00428392	−	0.00228980i
$732$	−1033.07	−	822.833i	−1.41130	−	1.12409i
$733$	−17.4487	+	1.71855i	−0.0238045	+	0.00234454i	−0.109912	−	0.993941i	$-0.535057\pi$
$733$	−17.4487	+	1.71855i	−0.0238045	+	0.00234454i	0.0861079	+	0.996286i	$0.472557\pi$
$734$	−522.485	−	568.069i	−0.711833	−	0.773936i
$735$	−1259.61	−	1259.61i	−1.71376	−	1.71376i
$736$	−1015.73	−	435.711i	−1.38006	−	0.591998i
$737$	596.323	+	596.323i	0.809123	+	0.809123i
$738$	641.499	+	26.8141i	0.869240	+	0.0363335i
$739$	242.724	−	23.9062i	0.328449	−	0.0323495i	0.0675514	−	0.997716i	$-0.478481\pi$
$739$	242.724	−	23.9062i	0.328449	−	0.0323495i	0.260898	+	0.965366i	$0.415981\pi$
$740$	705.449	+	1274.61i	0.953309	+	1.72244i
$741$	−679.686	−	363.300i	−0.917256	−	0.490283i
$742$	−15.0013	−	265.699i	−0.0202174	−	0.358086i
$743$	−241.093	−	360.821i	−0.324486	−	0.485627i	0.632983	−	0.774166i	$-0.281830\pi$
$743$	−241.093	−	360.821i	−0.324486	−	0.485627i	−0.957468	+	0.288539i	$0.906830\pi$
$744$	697.739	+	311.465i	0.937822	+	0.418635i
$745$	−227.971	+	341.183i	−0.306001	+	0.457963i
$746$	−33.7387	−	130.632i	−0.0452261	−	0.175110i
$747$	−347.903	−	423.921i	−0.465734	−	0.567498i
$748$	−13.6633	+	21.1105i	−0.0182664	+	0.0282225i
$749$	−361.776	+	193.373i	−0.483012	+	0.258175i
$750$	1320.55	+	2167.11i	1.76074	+	2.88948i
$751$	−1306.63	+	541.224i	−1.73985	+	0.720671i	−0.741067	+	0.671431i	$0.765680\pi$
$751$	−1306.63	+	541.224i	−1.73985	+	0.720671i	−0.998787	+	0.0492399i	$0.984320\pi$
$752$	45.5502	−	10.4541i	0.0605721	−	0.0139017i
$753$	382.080	−	922.422i	0.507410	−	1.22500i
$754$	−312.065	−	2002.76i	−0.413880	−	2.65618i
$755$	1950.98	+	591.824i	2.58408	+	0.783873i
$756$	470.305	−	6.87875i	0.622096	−	0.00909887i
$757$	320.953	+	31.6111i	0.423980	+	0.0417584i	0.307757	−	0.951465i	$-0.400421\pi$
$757$	320.953	+	31.6111i	0.423980	+	0.0417584i	0.116222	+	0.993223i	$0.462921\pi$
$758$	−877.111	+	660.506i	−1.15714	+	0.871380i
$759$	1265.24	−	251.671i	1.66698	−	0.331582i
$760$	−148.064	−	540.512i	−0.194821	−	0.711199i
$761$	419.404	+	83.4246i	0.551122	+	0.109625i	0.462793	−	0.886466i	$-0.346847\pi$
$761$	419.404	+	83.4246i	0.551122	+	0.109625i	0.0883289	+	0.996091i	$0.471847\pi$
$762$	−1803.35	−	630.414i	−2.36661	−	0.827315i
$763$	100.519	+	331.367i	0.131742	+	0.434295i
$764$	1005.22	−	849.868i	1.31574	−	1.11239i
$765$	79.6047	−	96.9987i	0.104058	−	0.126796i
$766$	1017.41	−	372.451i	1.32822	−	0.486228i
$767$		−	429.960i		−	0.560574i
$768$	−676.826	−	1105.48i	−0.881284	−	1.43943i
$769$	26.6551			0.0346620			0.0173310	−	0.999850i	$-0.494483\pi$
$769$	26.6551			0.0346620			0.0173310	+	0.999850i	$0.494483\pi$
$770$	136.472	+	372.798i	0.177237	+	0.484153i
$771$	1079.24	+	885.712i	1.39980	+	1.14878i
$772$	848.610	+	1003.73i	1.09924	+	1.30017i
$773$	1252.84	−	380.044i	1.62074	−	0.491648i	0.655984	−	0.754775i	$-0.272254\pi$
$773$	1252.84	−	380.044i	1.62074	−	0.491648i	0.964761	+	0.263128i	$0.0847540\pi$
$774$	−45.7508	+	130.874i	−0.0591095	+	0.169088i
$775$	196.212	−	986.427i	0.253177	−	1.27281i
$776$	166.072	+	606.249i	0.214010	+	0.781248i
$777$	−123.611	−	621.433i	−0.159087	−	0.799785i
$778$	472.607	+	627.592i	0.607464	+	0.806674i
$779$	−14.9711	+	152.004i	−0.0192184	+	0.195127i
$780$	50.4026	+	3446.06i	0.0646188	+	4.41803i
$781$	75.5467	−	249.044i	0.0967307	−	0.318879i
$782$	58.1683	−	9.06364i	0.0743840	−	0.0115903i
$783$	1883.12	+	780.013i	2.40500	+	0.996186i
$784$	337.762	−	538.981i	0.430820	−	0.687476i
$785$	228.718	+	552.173i	0.291360	+	0.703405i
$786$	−537.093	+	327.283i	−0.683325	+	0.416391i
$787$	−595.091	−	1113.34i	−0.756151	−	1.41466i	−0.904830	−	0.425773i	$-0.860002\pi$
$787$	−595.091	−	1113.34i	−0.756151	−	1.41466i	0.148679	−	0.988885i	$-0.452498\pi$
$788$	819.876	+	530.646i	1.04045	+	0.673409i
$789$	307.688	−	252.513i	0.389972	−	0.320041i
$790$	646.196	−	166.895i	0.817969	−	0.211259i
$791$	7.10307	+	4.74612i	0.00897986	+	0.00600015i
$792$	896.555	+	400.214i	1.13201	+	0.505321i
$793$	−1042.55	+	696.612i	−1.31470	+	0.878452i
$794$	650.162	−	36.7080i	0.818843	−	0.0462318i
$795$	−924.351	+	1729.34i	−1.16271	+	2.17527i
$796$	51.8011	−	28.6701i	0.0650768	−	0.0360177i
$797$	−5.07123	−	51.4890i	−0.00636289	−	0.0646035i	0.991479	−	0.130267i	$-0.0415835\pi$
$797$	−5.07123	−	51.4890i	−0.00636289	−	0.0646035i	−0.997842	+	0.0656637i	$0.979084\pi$
$798$	−10.1795	+	243.533i	−0.0127562	+	0.305179i
$799$	−1.76020	+	1.76020i	−0.00220301	+	0.00220301i
$800$	−1221.45	+	1191.23i	−1.52681	+	1.48904i
$801$	892.389	−	892.389i	1.11409	−	1.11409i
$802$	−909.084	+	836.136i	−1.13352	+	1.04256i
$803$	30.7767	+	312.481i	0.0383272	+	0.389142i
$804$	1442.59	−	1811.18i	1.79427	−	2.25272i
$805$	438.117	−	819.659i	0.544244	−	1.01821i
$806$	483.224	−	541.054i	0.599533	−	0.671283i
$807$	−1542.60	+	1030.73i	−1.91152	+	1.27724i
$808$	365.577	+	580.652i	0.452447	+	0.718628i
$809$	−348.409	−	232.800i	−0.430667	−	0.287762i	0.321283	−	0.946983i	$-0.395886\pi$
$809$	−348.409	−	232.800i	−0.430667	−	0.287762i	−0.751949	+	0.659221i	$0.770886\pi$
$810$	−702.474	−	414.095i	−0.867252	−	0.511228i
$811$	−267.775	+	219.757i	−0.330179	+	0.270971i	−0.784846	−	0.619691i	$-0.787258\pi$
$811$	−267.775	+	219.757i	−0.330179	+	0.270971i	0.454668	+	0.890661i	$0.349758\pi$
$812$	−527.752	+	363.908i	−0.649941	+	0.448163i
$813$	610.799	+	1142.73i	0.751291	+	1.40557i
$814$	143.215	−	590.018i	0.175940	−	0.724837i
$815$	−416.909	−	1006.51i	−0.511545	−	1.23498i
$816$	61.8162	+	30.7519i	0.0757552	+	0.0376861i
$817$	−30.4707	−	12.6214i	−0.0372958	−	0.0154484i
$818$	−128.866	−	94.1208i	−0.157538	−	0.115062i
$819$	282.375	−	930.866i	0.344780	−	1.13659i
$820$	627.152	−	270.587i	0.764819	−	0.329984i
$821$	−9.34587	+	94.8902i	−0.0113835	+	0.115579i	−0.999197	−	0.0400624i	$-0.987244\pi$
$821$	−9.34587	+	94.8902i	−0.0113835	+	0.115579i	0.987814	+	0.155641i	$0.0497443\pi$
$822$	227.256	+	32.0137i	0.276468	+	0.0389461i
$823$	263.773	+	1326.08i	0.320502	+	1.61127i	0.719618	+	0.694371i	$0.244317\pi$
$823$	263.773	+	1326.08i	0.320502	+	1.61127i	−0.399116	+	0.916901i	$0.630683\pi$
$824$	−3.21323	−	45.1646i	−0.00389955	−	0.0548115i
$825$	388.505	−	1953.15i	0.470916	−	2.36745i
$826$	−122.499	+	59.0378i	−0.148304	+	0.0714743i
$827$	9.10385	−	2.76162i	0.0110083	−	0.00333933i	−0.284776	−	0.958594i	$-0.591919\pi$
$827$	9.10385	−	2.76162i	0.0110083	−	0.00333933i	0.295784	+	0.955255i	$0.404419\pi$
$828$	−699.333	−	2189.59i	−0.844606	−	2.64443i
$829$	−504.567	−	414.087i	−0.608645	−	0.499502i	0.278840	−	0.960337i	$-0.410050\pi$
$829$	−504.567	−	414.087i	−0.608645	−	0.499502i	−0.887486	+	0.460835i	$0.847550\pi$
$830$	−529.199	−	245.573i	−0.637589	−	0.295871i
$831$	1559.41			1.87655
$832$	−1195.28	+	292.789i	−1.43663	+	0.351910i
$833$			33.8801i			0.0406724i
$834$	25.7778	+	11.9621i	0.0309086	+	0.0143431i
$835$	−835.663	+	1018.26i	−1.00079	+	1.21947i
$836$	−107.079	+	207.576i	−0.128084	+	0.248297i
$837$	211.759	+	698.077i	0.252998	+	0.834023i
$838$	−1217.02	+	586.536i	−1.45229	+	0.699924i
$839$	−1110.38	−	220.868i	−1.32345	−	0.263252i	−0.517731	−	0.855543i	$-0.673223\pi$
$839$	−1110.38	−	220.868i	−1.32345	−	0.263252i	−0.805724	+	0.592292i	$0.798223\pi$
$840$	974.890	−	487.538i	1.16058	−	0.580403i
$841$	−1899.78	+	377.890i	−2.25895	+	0.449334i
$842$	731.352	+	103.026i	0.868589	+	0.122359i
$843$	−450.696	−	44.3897i	−0.534633	−	0.0526568i
$844$	64.0062	−	161.151i	0.0758367	−	0.190937i
$845$	1699.90	+	515.660i	2.01172	+	0.610248i
$846$	78.4880	+	57.3258i	0.0927754	+	0.0677610i
$847$	−77.4809	+	187.055i	−0.0914768	+	0.220845i
$848$	−675.677	−	183.566i	−0.796789	−	0.216469i
$849$	−1355.73	+	561.562i	−1.59686	+	0.661440i
$850$	21.4363	−	88.3137i	0.0252192	−	0.103898i
$851$	−1253.57	+	670.045i	−1.47305	+	0.787361i
$852$	−702.790	−	129.139i	−0.824871	−	0.151571i
$853$	−158.154	−	192.711i	−0.185409	−	0.225921i	0.672008	−	0.740544i	$-0.265432\pi$
$853$	−158.154	−	192.711i	−0.185409	−	0.225921i	−0.857417	+	0.514622i	$0.827932\pi$
$854$	341.623	+	201.380i	0.400027	+	0.235808i
$855$	647.526	−	969.091i	0.757340	−	1.13344i
$856$	181.742	+	1063.86i	0.212316	+	1.24283i
$857$	−616.721	−	922.988i	−0.719628	−	1.07700i	−0.993344	−	0.115189i	$-0.963253\pi$
$857$	−616.721	−	922.988i	−0.719628	−	1.07700i	0.273716	−	0.961811i	$-0.411747\pi$
$858$	956.794	−	1071.30i	1.11515	−	1.24860i
$859$	375.791	+	200.865i	0.437475	+	0.233835i	0.675405	−	0.737447i	$-0.263969\pi$
$859$	375.791	+	200.865i	0.437475	+	0.233835i	−0.237930	+	0.971282i	$0.576469\pi$
$860$	16.6014	+	146.551i	0.0193040	+	0.170408i
$861$	−295.642	+	29.1182i	−0.343370	+	0.0338190i
$862$	359.861	−	330.984i	0.417472	−	0.383972i
$863$	−35.4487	−	35.4487i	−0.0410761	−	0.0410761i	0.686270	−	0.727347i	$-0.259247\pi$
$863$	−35.4487	−	35.4487i	−0.0410761	−	0.0410761i	−0.727347	+	0.686270i	$0.759247\pi$
$864$	374.032	−	1179.62i	0.432907	−	1.36531i
$865$	−633.332	−	633.332i	−0.732176	−	0.732176i
$866$	−18.4821	+	442.163i	−0.0213419	+	0.510581i
$867$	1452.60	−	143.069i	1.67544	−	0.165016i
$868$	−220.502	−	63.3822i	−0.254035	−	0.0730210i
$869$	−245.307	−	131.120i	−0.282287	−	0.150886i
$870$	4715.99	−	266.264i	5.42068	−	0.306050i
$871$	−1221.30	−	1827.81i	−1.40219	−	2.09852i
$872$	910.719	+	24.7319i	1.04440	+	0.0283622i
$873$	−726.278	+	1086.95i	−0.831934	+	1.24508i
$874$	529.433	−	136.738i	0.605759	−	0.156451i
$875$	−483.404	−	589.029i	−0.552461	−	0.673176i
$876$	842.999	−	180.538i	0.962328	−	0.206094i
$877$	−252.095	+	134.747i	−0.287451	+	0.153646i	−0.608820	−	0.793308i	$-0.708357\pi$
$877$	−252.095	+	134.747i	−0.287451	+	0.153646i	0.321369	+	0.946954i	$0.395857\pi$
$878$	774.444	−	471.916i	0.882055	−	0.537490i
$879$	1397.85	−	579.008i	1.59027	−	0.658712i
$880$	1044.04	−	30.5471i	1.18641	−	0.0347126i
$881$	−263.623	+	636.443i	−0.299232	+	0.722410i	0.700728	+	0.713429i	$0.252859\pi$
$881$	−263.623	+	636.443i	−0.299232	+	0.722410i	−0.999960	+	0.00898093i	$0.997141\pi$
$882$	1307.06	−	203.663i	1.48193	−	0.230911i
$883$	−325.816	−	98.8352i	−0.368987	−	0.111931i	0.100345	−	0.994953i	$-0.468005\pi$
$883$	−325.816	−	98.8352i	−0.368987	−	0.111931i	−0.469332	+	0.883022i	$0.655505\pi$
$884$	45.6669	−	47.0226i	0.0516594	−	0.0531930i
$885$	997.145	+	98.2102i	1.12672	+	0.110972i
$886$	15.7838	+	20.9600i	0.0178147	+	0.0236568i
$887$	654.056	−	130.100i	0.737380	−	0.146674i	0.187909	−	0.982186i	$-0.439829\pi$
$887$	654.056	−	130.100i	0.737380	−	0.146674i	0.549472	+	0.835512i	$0.314829\pi$
$888$	−1653.95	−	208.372i	−1.86255	−	0.234653i
$889$	562.590	+	111.906i	0.632834	+	0.125879i
$890$	443.043	−	1267.36i	0.497801	−	1.42400i
$891$	98.6533	+	325.216i	0.110722	+	0.365001i
$892$	−1543.59	−	129.267i	−1.73048	−	0.144918i
$893$	−14.6681	+	17.8731i	−0.0164256	+	0.0200147i
$894$	−161.415	−	440.932i	−0.180553	−	0.493212i
$895$			1595.17i			1.78231i
$896$	247.541	+	300.341i	0.276273	+	0.335202i
$897$	−3362.68			−3.74881
$898$	−192.789	+	70.5753i	−0.214687	+	0.0785917i
$899$	−768.552	−	630.735i	−0.854897	−	0.701596i
$900$	−3535.92	−	296.114i	−3.92880	−	0.329016i
$901$	35.6884	−	10.8260i	0.0396098	−	0.0120155i
$902$	−268.721	−	93.9390i	−0.297917	−	0.104145i
$903$	12.5145	−	62.9146i	0.0138588	−	0.0696728i
$904$	17.7549	−	13.7818i	0.0196404	−	0.0152453i
$905$	−102.534	−	515.473i	−0.113297	−	0.569583i
$906$	−1863.64	+	1403.41i	−2.05700	+	1.54902i
$907$	1.48851	−	15.1131i	0.00164114	−	0.0166628i	−0.994329	−	0.106345i	$-0.966085\pi$
$907$	1.48851	−	15.1131i	0.00164114	−	0.0166628i	0.995970	+	0.0896823i	$0.0285852\pi$
$908$	672.354	−	692.313i	0.740477	−	0.762460i
$909$	−414.233	+	1365.54i	−0.455702	+	1.50225i
$910$	−159.323	−	1022.49i	−0.175080	−	1.12362i
$911$	−1439.81	−	596.391i	−1.58048	−	0.654655i	−0.591988	−	0.805947i	$-0.701657\pi$
$911$	−1439.81	−	596.391i	−1.58048	−	0.654655i	−0.988489	+	0.151292i	$0.951657\pi$
$912$	599.402	+	227.980i	0.657239	+	0.249978i
$913$	93.0470	+	224.635i	0.101913	+	0.246041i
$914$	−573.726	−	941.521i	−0.627709	−	1.03011i
$915$	−1377.42	−	2576.96i	−1.50537	−	2.81635i
$916$	348.181	−	74.5670i	0.380110	−	0.0814050i
$917$	145.984	−	119.806i	0.159197	−	0.130650i
$918$	16.4833	+	63.8211i	0.0179556	+	0.0695219i
$919$	−755.717	−	504.954i	−0.822325	−	0.549460i	0.0717265	−	0.997424i	$-0.477149\pi$
$919$	−755.717	−	504.954i	−0.822325	−	0.549460i	−0.894051	+	0.447964i	$0.852149\pi$
$920$	−1681.48	−	1775.36i	−1.82770	−	1.92973i
$921$	2310.86	−	1544.07i	2.50907	−	1.67651i
$922$	29.5197	+	522.845i	0.0320171	+	0.567077i
$923$	−319.791	+	598.287i	−0.346469	+	0.648198i
$924$	−436.599	−	125.498i	−0.472510	−	0.135821i
$925$	215.072	+	2183.66i	0.232510	+	2.36071i
$926$	27.4237	+	1.14629i	0.0296152	+	0.00123789i
$927$	66.5857	−	66.5857i	0.0718292	−	0.0718292i
$928$	469.346	+	1620.00i	0.505761	+	1.74568i
$929$	934.677	−	934.677i	1.00611	−	1.00611i	0.00613016	−	0.999981i	$-0.498049\pi$
$929$	934.677	−	934.677i	1.00611	−	1.00611i	0.999981	−	0.00613016i	$-0.00195130\pi$
$930$	1144.41	+	1244.26i	1.23055	+	1.33791i
$931$	30.8450	+	313.174i	0.0331310	+	0.336385i
$932$	−172.363	−	1521.56i	−0.184939	−	1.63257i
$933$	997.913	−	1866.96i	1.06957	−	2.00103i
$934$	1199.48	+	1071.27i	1.28424	+	1.14697i
$935$	−46.2583	+	30.9088i	−0.0494741	+	0.0330575i
$936$	−2088.60	−	1479.12i	−2.23142	−	1.58026i
$937$	204.942	+	136.938i	0.218721	+	0.146145i	0.660104	−	0.751174i	$-0.270512\pi$
$937$	204.942	+	136.938i	0.218721	+	0.146145i	−0.441383	+	0.897319i	$0.645512\pi$
$938$	−353.061	+	598.936i	−0.376397	+	0.638524i
$939$	−1388.07	+	1139.16i	−1.47824	+	1.21316i
$940$	101.694	+	18.6864i	0.108185	+	0.0198792i
$941$	−276.684	−	517.640i	−0.294032	−	0.550096i	0.690918	−	0.722933i	$-0.257207\pi$
$941$	−276.684	−	517.640i	−0.294032	−	0.550096i	−0.984950	+	0.172837i	$0.944707\pi$
$942$	−664.613	−	161.321i	−0.705534	−	0.171254i
$943$	255.034	+	615.707i	0.270450	+	0.652924i
$944$	45.4659	+	354.872i	0.0481630	+	0.375923i
$945$	961.413	+	398.230i	1.01737	+	0.421408i
$946$	36.2547	−	49.6384i	0.0383243	−	0.0524719i
$947$	4.79783	−	15.8163i	0.00506635	−	0.0167015i	−0.954371	−	0.298624i	$-0.903472\pi$
$947$	4.79783	−	15.8163i	0.00506635	−	0.0167015i	0.959437	+	0.281923i	$0.0909722\pi$
$948$	−281.908	+	709.771i	−0.297371	+	0.748703i
$949$	80.2251	−	814.539i	0.0845364	−	0.858313i
$950$	117.747	−	835.853i	0.123944	−	0.879845i
$951$	−29.0481	−	146.035i	−0.0305448	−	0.153559i
$952$	−19.6676	−	6.55420i	−0.0206593	−	0.00688467i
$953$	−103.087	+	518.254i	−0.108171	+	0.543813i	0.888255	+	0.459350i	$0.151918\pi$
$953$	−103.087	+	518.254i	−0.108171	+	0.543813i	−0.996427	+	0.0844634i	$0.973082\pi$
$954$	−632.189	−	1311.75i	−0.662672	−	1.37500i
$955$	2786.90	−	845.397i	2.91822	−	0.885232i
$956$	448.032	−	868.527i	0.468652	−	0.908501i
$957$	−1521.75	−	1248.87i	−1.59013	−	1.30498i
$958$	99.1843	−	213.737i	0.103533	−	0.223108i
$959$	−68.9102			−0.0718563
$960$	−406.002	−	2838.91i	−0.422918	−	2.95720i
$961$			605.169i			0.629728i
$962$	−666.189	+	1435.61i	−0.692504	+	1.49231i
$963$	−1423.94	+	1735.07i	−1.47864	+	1.80173i
$964$	371.335	+	1162.64i	0.385202	+	1.20606i
$965$	844.146	+	2782.78i	0.874763	+	2.88371i
$966$	461.729	+	958.054i	0.477980	+	0.991775i
$967$	1248.57	+	248.357i	1.29118	+	0.256832i	0.792457	−	0.609928i	$-0.208802\pi$
$967$	1248.57	+	248.357i	1.29118	+	0.256832i	0.498725	+	0.866760i	$0.333802\pi$
$968$	402.450	+	348.989i	0.415754	+	0.360526i
$969$	−33.5020	+	6.66397i	−0.0345738	+	0.00687716i
$970$	−193.993	+	1377.10i	−0.199992	+	1.41969i
$971$	−26.4311	−	2.60324i	−0.0272205	−	0.00268099i	0.0843977	−	0.996432i	$-0.473103\pi$
$971$	−26.4311	−	2.60324i	−0.0272205	−	0.00268099i	−0.111618	+	0.993751i	$0.535603\pi$
$972$	−421.522	+	181.867i	−0.433665	+	0.187106i
$973$	−8.16545	−	2.47696i	−0.00839203	−	0.00254569i
$974$	−85.2709	+	116.749i	−0.0875471	+	0.119866i
$975$	−1986.50	+	4795.84i	−2.03744	+	4.91881i
$976$	786.818	−	685.199i	0.806166	−	0.702048i
$977$	−548.498	+	227.195i	−0.561410	+	0.232544i	−0.645297	−	0.763932i	$-0.723266\pi$
$977$	−548.498	+	227.195i	−0.561410	+	0.232544i	0.0838872	+	0.996475i	$0.473266\pi$
$978$	1211.46	+	294.058i	1.23871	+	0.300673i
$979$	−493.471	+	263.766i	−0.504056	+	0.269424i
$980$	1158.53	−	798.859i	1.18218	−	0.815162i
$981$	1202.00	+	1464.64i	1.22528	+	1.49301i
$982$	276.287	−	468.696i	0.281351	−	0.477287i
$983$	−591.890	+	885.826i	−0.602126	+	0.901145i	−0.999866	−	0.0163527i	$-0.994795\pi$
$983$	−591.890	+	885.826i	−0.602126	+	0.901145i	0.397740	+	0.917498i	$0.369795\pi$
$984$	−173.236	+	762.157i	−0.176052	+	0.774549i
$985$	1200.42	+	1796.55i	1.21870	+	1.82391i
$986$	−67.0044	−	59.8426i	−0.0679558	−	0.0606923i
$987$	−39.6602	−	21.1988i	−0.0401826	−	0.0214780i
$988$	379.317	−	476.235i	0.383924	−	0.482019i
$989$	−143.211	+	14.1051i	−0.144804	+	0.0142620i
$990$	1470.50	+	1598.80i	1.48536	+	1.61495i
$991$	148.459	+	148.459i	0.149807	+	0.149807i	0.778032	−	0.628225i	$-0.216218\pi$
$991$	148.459	+	148.459i	0.149807	+	0.149807i	−0.628225	+	0.778032i	$0.716218\pi$
$992$	−341.619	+	497.662i	−0.344374	+	0.501675i
$993$	−204.703	−	204.703i	−0.206146	−	0.206146i
$994$	214.367	+	8.96036i	0.215661	+	0.00901445i
$995$	130.358	−	12.8391i	0.131013	−	0.0129036i
$996$	584.093	−	323.275i	0.586439	−	0.324573i
$997$	144.318	+	77.1398i	0.144753	+	0.0773719i	0.542183	−	0.840260i	$-0.317598\pi$
$997$	144.318	+	77.1398i	0.144753	+	0.0773719i	−0.397430	+	0.917632i	$0.630098\pi$
$998$	−33.2178	−	588.344i	−0.0332844	−	0.589523i
$999$	−884.194	−	1323.29i	−0.885079	−	1.32461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.l.a.43.12	yes	496
128.3	odd	32	inner	128.3.l.a.3.12	✓	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.3.l.a.3.12	✓	496	128.3	odd	32	inner
128.3.l.a.43.12	yes	496	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687532 - 1.87811i) q^{2} +(3.91403 + 3.21216i) q^{3} +(-3.05460 + 2.58252i) q^{4} +(-8.46864 + 2.56894i) q^{5} +(3.34178 - 9.55944i) q^{6} +(-0.593205 + 2.98225i) q^{7} +(6.95040 + 3.96131i) q^{8} +(3.24584 + 16.3179i) q^{9} +O(q^{10})\)	\(q+(-0.687532 - 1.87811i) q^{2} +(3.91403 + 3.21216i) q^{3} +(-3.05460 + 2.58252i) q^{4} +(-8.46864 + 2.56894i) q^{5} +(3.34178 - 9.55944i) q^{6} +(-0.593205 + 2.98225i) q^{7} +(6.95040 + 3.96131i) q^{8} +(3.24584 + 16.3179i) q^{9} +(10.6472 + 14.1388i) q^{10} +(0.723029 - 7.34104i) q^{11} +(-20.2513 + 0.296198i) q^{12} +(-5.58169 + 18.4004i) q^{13} +(6.00883 - 0.936283i) q^{14} +(-41.3984 - 17.1478i) q^{15} +(2.66116 - 15.7771i) q^{16} +(0.326137 + 0.787364i) q^{17} +(28.4153 - 17.3151i) q^{18} +(3.73151 + 6.98117i) q^{19} +(19.2340 - 29.7175i) q^{20} +(-11.9013 + 9.76713i) q^{21} +(-14.2844 + 3.68927i) q^{22} +(28.7178 + 19.1886i) q^{23} +(14.4797 + 37.8305i) q^{24} +(44.3318 - 29.6215i) q^{25} +(38.3955 - 2.16780i) q^{26} +(-18.2298 + 34.1056i) q^{27} +(-5.88971 - 10.6415i) q^{28} +(-5.16616 - 52.4529i) q^{29} +(-3.74271 + 89.5403i) q^{30} +(13.3385 - 13.3385i) q^{31} +(-31.4609 + 5.84932i) q^{32} +(26.4106 - 26.4106i) q^{33} +(1.25453 - 1.15386i) q^{34} +(-2.63755 - 26.7795i) q^{35} +(-52.0561 - 41.4623i) q^{36} +(-19.3999 + 36.2946i) q^{37} +(10.5459 - 11.8080i) q^{38} +(-80.9519 + 54.0903i) q^{39} +(-69.0368 - 15.6918i) q^{40} +(16.0435 + 10.7200i) q^{41} +(26.5263 + 15.6367i) q^{42} +(-3.22073 + 2.64318i) q^{43} +(16.7498 + 24.2912i) q^{44} +(-69.4075 - 129.852i) q^{45} +(16.2940 - 67.1280i) q^{46} +(1.11778 + 2.69856i) q^{47} +(61.0946 - 53.2041i) q^{48} +(36.7282 + 15.2133i) q^{49} +(-86.1120 - 62.8942i) q^{50} +(-1.25263 + 4.12937i) q^{51} +(-30.4695 - 70.6206i) q^{52} +(4.28928 - 43.5498i) q^{53} +(76.5878 + 10.7890i) q^{54} +(12.7356 + 64.0261i) q^{55} +(-15.9366 + 18.3779i) q^{56} +(-7.81939 + 39.3107i) q^{57} +(-94.9605 + 45.7657i) q^{58} +(-21.3979 + 6.49099i) q^{59} +(170.740 - 54.5326i) q^{60} +(50.4076 + 41.3684i) q^{61} +(-34.2218 - 15.8805i) q^{62} -50.5895 q^{63} +(32.6160 + 55.0654i) q^{64} -170.165i q^{65} +(-67.7601 - 31.4439i) q^{66} +(-72.5273 + 88.3748i) q^{67} +(-3.02960 - 1.56283i) q^{68} +(50.7654 + 167.351i) q^{69} +(-48.4814 + 23.3654i) q^{70} +(34.6028 + 6.88293i) q^{71} +(-42.0805 + 126.274i) q^{72} +(-41.7484 + 8.30428i) q^{73} +(81.5033 + 11.4814i) q^{74} +(268.665 + 26.4612i) q^{75} +(-29.4273 - 11.6880i) q^{76} +(21.4639 + 6.51099i) q^{77} +(157.245 + 114.848i) q^{78} +(14.4300 - 34.8371i) q^{79} +(17.9940 + 140.447i) q^{80} +(-42.5646 + 17.6308i) q^{81} +(9.10281 - 37.5019i) q^{82} +(-29.0696 + 15.5380i) q^{83} +(11.1298 - 60.5700i) q^{84} +(-4.78463 - 5.83008i) q^{85} +(7.17855 + 4.23161i) q^{86} +(148.267 - 221.897i) q^{87} +(34.1055 - 48.1590i) q^{88} +(-42.1422 - 63.0703i) q^{89} +(-196.157 + 219.633i) q^{90} +(-51.5633 - 27.5612i) q^{91} +(-137.276 + 15.5508i) q^{92} +(95.0527 - 9.36188i) q^{93} +(4.29969 - 3.95466i) q^{94} +(-49.5350 - 49.5350i) q^{95} +(-141.928 - 78.1629i) q^{96} +(55.5595 + 55.5595i) q^{97} +(3.32049 - 79.4393i) q^{98} +(122.137 - 12.0295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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