LMFDB - Embedded newform 128.3.l.a.43.9

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			43.9
Character	$\chi$	$=$	128.43
Dual form			128.3.l.a.3.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39308 - 1.43504i) q^{2} +(0.447688 + 0.367408i) q^{3} +(-0.118660 + 3.99824i) q^{4} +(-2.47385 + 0.750435i) q^{5} +(-0.0964209 - 1.15428i) q^{6} +(0.987061 - 4.96229i) q^{7} +(5.90292 - 5.39958i) q^{8} +(-1.69038 - 8.49810i) q^{9} +O(q^{10})$	\(q+(-1.39308 - 1.43504i) q^{2} +(0.447688 + 0.367408i) q^{3} +(-0.118660 + 3.99824i) q^{4} +(-2.47385 + 0.750435i) q^{5} +(-0.0964209 - 1.15428i) q^{6} +(0.987061 - 4.96229i) q^{7} +(5.90292 - 5.39958i) q^{8} +(-1.69038 - 8.49810i) q^{9} +(4.52318 + 2.50465i) q^{10} +(0.355541 - 3.60986i) q^{11} +(-1.52211 + 1.74637i) q^{12} +(6.50922 - 21.4580i) q^{13} +(-8.49613 + 5.49640i) q^{14} +(-1.38323 - 0.572953i) q^{15} +(-15.9718 - 0.948863i) q^{16} +(9.43380 + 22.7752i) q^{17} +(-9.84025 + 14.2643i) q^{18} +(-13.6843 - 25.6016i) q^{19} +(-2.70687 - 9.98011i) q^{20} +(2.26508 - 1.85891i) q^{21} +(-5.67558 + 4.51861i) q^{22} +(-6.73776 - 4.50203i) q^{23} +(4.62652 - 0.248547i) q^{24} +(-15.2299 + 10.1763i) q^{25} +(-39.8609 + 20.5517i) q^{26} +(4.82259 - 9.02243i) q^{27} +(19.7233 + 4.53533i) q^{28} +(0.212124 + 2.15373i) q^{29} +(1.10474 + 2.78316i) q^{30} +(36.6146 - 36.6146i) q^{31} +(20.8884 + 24.2420i) q^{32} +(1.48547 - 1.48547i) q^{33} +(19.5412 - 45.2655i) q^{34} +(1.28203 + 13.0167i) q^{35} +(34.1780 - 5.75015i) q^{36} +(-10.2620 + 19.1989i) q^{37} +(-17.6759 + 55.3026i) q^{38} +(10.7979 - 7.21496i) q^{39} +(-10.5509 + 17.7875i) q^{40} +(63.1162 + 42.1729i) q^{41} +(-5.82304 - 0.660874i) q^{42} +(-35.7546 + 29.3430i) q^{43} +(14.3909 + 1.84988i) q^{44} +(10.5590 + 19.7545i) q^{45} +(2.92566 + 15.9406i) q^{46} +(-15.2774 - 36.8829i) q^{47} +(-6.80178 - 6.29298i) q^{48} +(21.6200 + 8.95532i) q^{49} +(35.8199 + 7.67910i) q^{50} +(-4.14440 + 13.6622i) q^{51} +(85.0219 + 28.5716i) q^{52} +(1.07836 - 10.9488i) q^{53} +(-19.6658 + 5.64837i) q^{54} +(1.82941 + 9.19709i) q^{55} +(-20.9678 - 34.6217i) q^{56} +(3.27992 - 16.4893i) q^{57} +(2.79517 - 3.30472i) q^{58} +(-55.6877 + 16.8927i) q^{59} +(2.45494 - 5.46250i) q^{60} +(12.5610 + 10.3085i) q^{61} +(-103.550 - 1.53625i) q^{62} -43.8386 q^{63} +(5.68900 - 63.7466i) q^{64} +57.9687i q^{65} +(-4.20107 - 0.0623261i) q^{66} +(58.9442 - 71.8237i) q^{67} +(-92.1801 + 35.0161i) q^{68} +(-1.36233 - 4.49101i) q^{69} +(16.8935 - 19.9731i) q^{70} +(50.6193 + 10.0688i) q^{71} +(-55.8644 - 41.0363i) q^{72} +(-60.4009 + 12.0145i) q^{73} +(41.8469 - 12.0192i) q^{74} +(-10.5571 - 1.03979i) q^{75} +(103.985 - 51.6754i) q^{76} +(-17.5623 - 5.32745i) q^{77} +(-25.3961 - 5.44444i) q^{78} +(6.16159 - 14.8754i) q^{79} +(40.2241 - 9.63848i) q^{80} +(-66.5714 + 27.5748i) q^{81} +(-27.4062 - 149.324i) q^{82} +(-90.7299 + 48.4961i) q^{83} +(7.16357 + 9.27692i) q^{84} +(-40.4292 - 49.2631i) q^{85} +(91.9172 + 10.4320i) q^{86} +(-0.696332 + 1.04213i) q^{87} +(-17.3930 - 23.2285i) q^{88} +(-4.77326 - 7.14369i) q^{89} +(13.6389 - 42.6722i) q^{90} +(-100.056 - 53.4810i) q^{91} +(18.7997 - 26.4050i) q^{92} +(29.8445 - 2.93942i) q^{93} +(-31.6457 + 73.3045i) q^{94} +(53.0654 + 53.0654i) q^{95} +(0.444768 + 18.5274i) q^{96} +(107.677 + 107.677i) q^{97} +(-17.2672 - 43.5010i) q^{98} +(-31.2780 + 3.08061i) 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 $

$2$	−1.39308	−	1.43504i	−0.696540	−	0.717518i
$2$	−1.39308	−	1.43504i	−0.696540	−	0.717518i
$3$	0.447688	+	0.367408i	0.149229	+	0.122469i	0.706046	−	0.708166i	$-0.250477\pi$
$3$	0.447688	+	0.367408i	0.149229	+	0.122469i	−0.556816	+	0.830636i	$0.687977\pi$
$4$	−0.118660	+	3.99824i	−0.0296650	+	0.999560i
$5$	−2.47385	+	0.750435i	−0.494771	+	0.150087i	−0.527802	−	0.849367i	$-0.676984\pi$
$5$	−2.47385	+	0.750435i	−0.494771	+	0.150087i	0.0330316	+	0.999454i	$0.489484\pi$
$6$	−0.0964209	−	1.15428i	−0.0160702	−	0.192380i
$7$	0.987061	−	4.96229i	0.141009	−	0.708899i	−0.843993	−	0.536354i	$-0.819801\pi$
$7$	0.987061	−	4.96229i	0.141009	−	0.708899i	0.985002	−	0.172545i	$-0.0551989\pi$
$8$	5.90292	−	5.39958i	0.737865	−	0.674948i
$9$	−1.69038	−	8.49810i	−0.187820	−	0.944233i
$10$	4.52318	+	2.50465i	0.452318	+	0.250465i
$11$	0.355541	−	3.60986i	0.0323219	−	0.328169i	−0.965404	−	0.260760i	$-0.916027\pi$
$11$	0.355541	−	3.60986i	0.0323219	−	0.328169i	0.997725	−	0.0674091i	$-0.0214733\pi$
$12$	−1.52211	+	1.74637i	−0.126842	+	0.145531i
$13$	6.50922	−	21.4580i	0.500709	−	1.65062i	−0.234002	−	0.972236i	$-0.575182\pi$
$13$	6.50922	−	21.4580i	0.500709	−	1.65062i	0.734711	−	0.678380i	$-0.237318\pi$
$14$	−8.49613	+	5.49640i	−0.606866	+	0.392600i
$15$	−1.38323	−	0.572953i	−0.0922154	−	0.0381969i
$16$	−15.9718	−	0.948863i	−0.998240	−	0.0593039i
$17$	9.43380	+	22.7752i	0.554929	+	1.33972i	0.913737	+	0.406306i	$0.133183\pi$
$17$	9.43380	+	22.7752i	0.554929	+	1.33972i	−0.358808	+	0.933412i	$0.616817\pi$
$18$	−9.84025	+	14.2643i	−0.546681	+	0.792460i
$19$	−13.6843	−	25.6016i	−0.720229	−	1.34745i	−0.929217	−	0.369535i	$-0.879517\pi$
$19$	−13.6843	−	25.6016i	−0.720229	−	1.34745i	0.208988	−	0.977918i	$-0.432983\pi$
$20$	−2.70687	−	9.98011i	−0.135344	−	0.499005i
$21$	2.26508	−	1.85891i	0.107861	−	0.0885193i
$22$	−5.67558	+	4.51861i	−0.257981	+	0.205392i
$23$	−6.73776	−	4.50203i	−0.292946	−	0.195740i	0.400409	−	0.916337i	$-0.368868\pi$
$23$	−6.73776	−	4.50203i	−0.292946	−	0.195740i	−0.693355	+	0.720596i	$0.743868\pi$
$24$	4.62652	−	0.248547i	0.192772	−	0.0103561i
$25$	−15.2299	+	10.1763i	−0.609198	+	0.407053i
$26$	−39.8609	+	20.5517i	−1.53311	+	0.790452i
$27$	4.82259	−	9.02243i	0.178614	−	0.334164i
$28$	19.7233	+	4.53533i	0.704404	+	0.161976i
$29$	0.212124	+	2.15373i	0.00731461	+	0.0742665i	0.998149	−	0.0608157i	$-0.0193702\pi$
$29$	0.212124	+	2.15373i	0.00731461	+	0.0742665i	−0.990834	+	0.135082i	$0.956870\pi$
$30$	1.10474	+	2.78316i	0.0368247	+	0.0927719i
$31$	36.6146	−	36.6146i	1.18112	−	1.18112i	0.201663	−	0.979455i	$-0.435366\pi$
$31$	36.6146	−	36.6146i	1.18112	−	1.18112i	0.979455	−	0.201663i	$-0.0646345\pi$
$32$	20.8884	+	24.2420i	0.652762	+	0.757563i
$33$	1.48547	−	1.48547i	0.0450141	−	0.0450141i
$34$	19.5412	−	45.2655i	0.574742	−	1.33134i
$35$	1.28203	+	13.0167i	0.0366295	+	0.371906i
$36$	34.1780	−	5.75015i	0.949389	−	0.159726i
$37$	−10.2620	+	19.1989i	−0.277352	+	0.518889i	−0.981572	−	0.191093i	$-0.938797\pi$
$37$	−10.2620	+	19.1989i	−0.277352	+	0.518889i	0.704220	+	0.709982i	$0.251297\pi$
$38$	−17.6759	+	55.3026i	−0.465154	+	1.45533i
$39$	10.7979	−	7.21496i	0.276870	−	0.184999i
$40$	−10.5509	+	17.7875i	−0.263773	+	0.444689i
$41$	63.1162	+	42.1729i	1.53942	+	1.02861i	0.979829	+	0.199839i	$0.0640421\pi$
$41$	63.1162	+	42.1729i	1.53942	+	1.02861i	0.559592	+	0.828768i	$0.310958\pi$
$42$	−5.82304	−	0.660874i	−0.138644	−	0.0157351i
$43$	−35.7546	+	29.3430i	−0.831501	+	0.682395i	−0.950577	−	0.310490i	$-0.899507\pi$
$43$	−35.7546	+	29.3430i	−0.831501	+	0.682395i	0.119076	+	0.992885i	$0.462007\pi$
$44$	14.3909	+	1.84988i	0.327066	+	0.0420428i
$45$	10.5590	+	19.7545i	0.234645	+	0.438990i
$46$	2.92566	+	15.9406i	0.0636013	+	0.346535i
$47$	−15.2774	−	36.8829i	−0.325051	−	0.784743i	−0.998945	−	0.0459151i	$-0.985380\pi$
$47$	−15.2774	−	36.8829i	−0.325051	−	0.784743i	0.673894	−	0.738828i	$-0.264620\pi$
$48$	−6.80178	−	6.29298i	−0.141704	−	0.131104i
$49$	21.6200	+	8.95532i	0.441225	+	0.182762i
$50$	35.8199	+	7.67910i	0.716398	+	0.153582i
$51$	−4.14440	+	13.6622i	−0.0812627	+	0.267887i
$52$	85.0219	+	28.5716i	1.63504	+	0.549454i
$53$	1.07836	−	10.9488i	0.0203464	−	0.206581i	−0.979637	−	0.200778i	$-0.935653\pi$
$53$	1.07836	−	10.9488i	0.0203464	−	0.206581i	0.999983	−	0.00580265i	$-0.00184705\pi$
$54$	−19.6658	+	5.64837i	−0.364181	+	0.104599i
$55$	1.82941	+	9.19709i	0.0332621	+	0.167220i
$56$	−20.9678	−	34.6217i	−0.374424	−	0.618245i
$57$	3.27992	−	16.4893i	0.0575425	−	0.289286i
$58$	2.79517	−	3.30472i	0.0481926	−	0.0569779i
$59$	−55.6877	+	16.8927i	−0.943859	+	0.286316i	−0.724458	−	0.689318i	$-0.757910\pi$
$59$	−55.6877	+	16.8927i	−0.943859	+	0.286316i	−0.219400	+	0.975635i	$0.570410\pi$
$60$	2.45494	−	5.46250i	0.0409156	−	0.0910417i
$61$	12.5610	+	10.3085i	0.205917	+	0.168992i	0.731700	−	0.681627i	$-0.238727\pi$
$61$	12.5610	+	10.3085i	0.205917	+	0.168992i	−0.525782	+	0.850619i	$0.676227\pi$
$62$	−103.550	−	1.53625i	−1.67017	−	0.0247783i
$63$	−43.8386			−0.695850
$64$	5.68900	−	63.7466i	0.0888906	−	0.996041i
$65$			57.9687i			0.891826i
$66$	−4.20107	−	0.0623261i	−0.0636525	−	0.000944335i
$67$	58.9442	−	71.8237i	0.879764	−	1.07200i	−0.117121	−	0.993118i	$-0.537366\pi$
$67$	58.9442	−	71.8237i	0.879764	−	1.07200i	0.996884	−	0.0788776i	$-0.0251336\pi$
$68$	−92.1801	+	35.0161i	−1.35559	+	0.514942i
$69$	−1.36233	−	4.49101i	−0.0197440	−	0.0650871i
$70$	16.8935	−	19.9731i	0.241335	−	0.285330i
$71$	50.6193	+	10.0688i	0.712948	+	0.141814i	0.538222	−	0.842803i	$-0.319096\pi$
$71$	50.6193	+	10.0688i	0.712948	+	0.141814i	0.174726	+	0.984617i	$0.444096\pi$
$72$	−55.8644	−	41.0363i	−0.775894	−	0.569949i
$73$	−60.4009	+	12.0145i	−0.827409	+	0.164582i	−0.590590	−	0.806972i	$-0.701105\pi$
$73$	−60.4009	+	12.0145i	−0.827409	+	0.164582i	−0.236819	+	0.971554i	$0.576105\pi$
$74$	41.8469	−	12.0192i	0.565498	−	0.162422i
$75$	−10.5571	−	1.03979i	−0.140762	−	0.0138638i
$76$	103.985	−	51.6754i	1.36823	−	0.679940i
$77$	−17.5623	−	5.32745i	−0.228081	−	0.0691877i
$78$	−25.3961	−	5.44444i	−0.325591	−	0.0698005i
$79$	6.16159	−	14.8754i	0.0779948	−	0.188296i	−0.880073	−	0.474839i	$-0.842506\pi$
$79$	6.16159	−	14.8754i	0.0779948	−	0.188296i	0.958067	+	0.286543i	$0.0925062\pi$
$80$	40.2241	−	9.63848i	0.502801	−	0.120481i
$81$	−66.5714	+	27.5748i	−0.821869	+	0.340429i
$82$	−27.4062	−	149.324i	−0.334222	−	1.82103i
$83$	−90.7299	+	48.4961i	−1.09313	+	0.584291i	−0.916520	−	0.399990i	$-0.869014\pi$
$83$	−90.7299	+	48.4961i	−1.09313	+	0.584291i	−0.176612	+	0.984281i	$0.556514\pi$
$84$	7.16357	+	9.27692i	0.0852806	+	0.110440i
$85$	−40.4292	−	49.2631i	−0.475637	−	0.579565i
$86$	91.9172	+	10.4320i	1.06880	+	0.121302i
$87$	−0.696332	+	1.04213i	−0.00800381	+	0.0119786i
$88$	−17.3930	−	23.2285i	−0.197648	−	0.263960i
$89$	−4.77326	−	7.14369i	−0.0536321	−	0.0802662i	0.803684	−	0.595056i	$-0.202870\pi$
$89$	−4.77326	−	7.14369i	−0.0536321	−	0.0802662i	−0.857317	+	0.514790i	$0.827870\pi$
$90$	13.6389	−	42.6722i	0.151544	−	0.474136i
$91$	−100.056	−	53.4810i	−1.09952	−	0.587703i
$92$	18.7997	−	26.4050i	0.204344	−	0.287011i
$93$	29.8445	−	2.93942i	0.320908	−	0.0316067i
$94$	−31.6457	+	73.3045i	−0.336656	+	0.779835i
$95$	53.0654	+	53.0654i	0.558583	+	0.558583i
$96$	0.444768	+	18.5274i	0.00463300	+	0.192994i
$97$	107.677	+	107.677i	1.11007	+	1.11007i	0.993140	+	0.116931i	$0.0373057\pi$
$97$	107.677	+	107.677i	1.11007	+	1.11007i	0.116931	+	0.993140i	$0.462694\pi$
$98$	−17.2672	−	43.5010i	−0.176196	−	0.443888i
$99$	−31.2780	+	3.08061i	−0.315939	+	0.0311173i
$100$	−38.8802	−	62.1005i	−0.388802	−	0.621005i
$101$	−63.6422	−	34.0175i	−0.630121	−	0.336807i	0.125229	−	0.992128i	$-0.460033\pi$
$101$	−63.6422	−	34.0175i	−0.630121	−	0.336807i	−0.755350	+	0.655321i	$0.772533\pi$
$102$	25.3793	−	13.0852i	0.248817	−	0.128287i
$103$	35.3634	+	52.9250i	0.343334	+	0.513835i	0.962448	−	0.271466i	$-0.0875084\pi$
$103$	35.3634	+	52.9250i	0.343334	+	0.513835i	−0.619115	+	0.785301i	$0.712508\pi$
$104$	−77.4409	−	161.812i	−0.744624	−	1.55588i
$105$	−4.20849	+	6.29846i	−0.0400809	+	0.0599853i
$106$	−17.2141	+	13.7050i	−0.162398	+	0.129293i
$107$	61.5178	+	74.9597i	0.574933	+	0.700558i	0.976560	−	0.215245i	$-0.0690551\pi$
$107$	61.5178	+	74.9597i	0.574933	+	0.700558i	−0.401627	+	0.915803i	$0.631555\pi$
$108$	35.5016	+	20.3525i	0.328718	+	0.188449i
$109$	62.2472	−	33.2718i	0.571075	−	0.305246i	−0.160468	−	0.987041i	$-0.551300\pi$
$109$	62.2472	−	33.2718i	0.571075	−	0.305246i	0.731543	+	0.681795i	$0.238800\pi$
$110$	10.6496	−	15.4375i	0.0968149	−	0.140341i
$111$	−11.6480	+	4.82476i	−0.104937	+	0.0434663i
$112$	−20.4737	+	78.3203i	−0.182801	+	0.699289i
$113$	−2.31953	+	5.59984i	−0.0205268	+	0.0495561i	−0.933811	−	0.357768i	$-0.883538\pi$
$113$	−2.31953	+	5.59984i	−0.0205268	+	0.0495561i	0.913284	+	0.407324i	$0.133538\pi$
$114$	−28.2319	+	18.2641i	−0.247648	+	0.160211i
$115$	20.0467	+	6.08110i	0.174319	+	0.0528792i
$116$	−8.63629	+	0.592560i	−0.0744508	+	0.00510827i
$117$	−193.355	−	19.0438i	−1.65261	−	0.162768i
$118$	101.819	+	56.3810i	0.862872	+	0.477805i
$119$	122.329	−	24.3327i	1.02797	−	0.204477i
$120$	−11.2588	+	4.08677i	−0.0938235	+	0.0340564i
$121$	105.770	+	21.0390i	0.874135	+	0.173876i
$122$	−2.70532	−	32.3860i	−0.0221747	−	0.265459i
$123$	12.7617	+	42.0697i	0.103754	+	0.342030i
$124$	142.049	+	150.739i	1.14556	+	1.21564i
$125$	71.0403	−	86.5629i	0.568323	−	0.692503i
$126$	61.0706	+	62.9099i	0.484687	+	0.499285i
$127$		−	146.631i		−	1.15457i	−0.816541	−	0.577287i	$-0.804111\pi$
$127$		−	146.631i		−	1.15457i	0.816541	−	0.577287i	$-0.195889\pi$
$128$	−99.4040	+	80.6402i	−0.776594	+	0.630002i
$129$	−26.7877			−0.207657
$130$	83.1872	−	80.7550i	0.639902	−	0.621192i
$131$	47.5561	+	39.0283i	0.363024	+	0.297926i	0.798168	−	0.602435i	$-0.205803\pi$
$131$	47.5561	+	39.0283i	0.363024	+	0.297926i	−0.435144	+	0.900361i	$0.643303\pi$
$132$	5.76298	+	6.11551i	0.0436589	+	0.0463296i
$133$	−140.550	+	42.6354i	−1.05677	+	0.320567i
$134$	−185.184	+	15.4690i	−1.38197	+	0.115441i
$135$	−5.15963	+	25.9392i	−0.0382195	+	0.192142i
$136$	178.664	+	83.5017i	1.31370	+	0.613983i
$137$	−2.64904	−	13.3176i	−0.0193361	−	0.0972090i	0.969912	−	0.243455i	$-0.0782809\pi$
$137$	−2.64904	−	13.3176i	−0.0193361	−	0.0972090i	−0.989248	+	0.146246i	$0.953281\pi$
$138$	−4.54693	+	8.21134i	−0.0329488	+	0.0595024i
$139$	−7.86889	+	79.8941i	−0.0566107	+	0.574778i	0.924480	+	0.381230i	$0.124499\pi$
$139$	−7.86889	+	79.8941i	−0.0566107	+	0.574778i	−0.981091	+	0.193548i	$0.938001\pi$
$140$	−52.1961	+	3.58132i	−0.372829	+	0.0255808i
$141$	6.71157	−	22.1251i	0.0475998	−	0.156916i
$142$	−56.0676	−	86.6672i	−0.394842	−	0.610332i
$143$	−75.1462	−	31.1266i	−0.525498	−	0.217668i
$144$	18.9349	+	137.334i	0.131492	+	0.953710i
$145$	−2.14100	−	5.16882i	−0.0147655	−	0.0356470i
$146$	101.384	+	69.9403i	0.694414	+	0.479043i
$147$	6.38878	+	11.9526i	0.0434611	+	0.0813100i
$148$	−75.5440	−	43.3081i	−0.510433	−	0.292622i
$149$	192.392	−	157.892i	1.29122	−	1.05968i	0.296719	−	0.954965i	$-0.404107\pi$
$149$	192.392	−	157.892i	1.29122	−	1.05968i	0.994502	−	0.104714i	$-0.0333926\pi$
$150$	13.2148	+	16.5984i	0.0880986	+	0.110656i
$151$	135.805	+	90.7420i	0.899370	+	0.600940i	0.916992	−	0.398905i	$-0.130610\pi$
$151$	135.805	+	90.7420i	0.899370	+	0.600940i	−0.0176220	+	0.999845i	$0.505610\pi$
$152$	−219.016	−	77.2346i	−1.44089	−	0.508122i
$153$	177.599	−	118.668i	1.16078	−	0.775608i
$154$	16.8205	+	32.6241i	0.109224	+	0.211844i
$155$	−63.1024	+	118.056i	−0.407112	+	0.761653i
$156$	27.5658	+	44.0289i	0.176704	+	0.282237i
$157$	8.73463	+	88.6842i	0.0556346	+	0.564868i	0.982083	+	0.188447i	$0.0603453\pi$
$157$	8.73463	+	88.6842i	0.0556346	+	0.564868i	−0.926449	+	0.376421i	$0.877155\pi$
$158$	−29.9303	+	11.8805i	−0.189432	+	0.0751930i
$159$	4.50544	−	4.50544i	0.0283361	−	0.0283361i
$160$	−69.8669	−	44.2958i	−0.436668	−	0.276849i
$161$	−28.9910	+	28.9910i	−0.180068	+	0.180068i
$162$	132.310	+	57.1185i	0.816728	+	0.352583i
$163$	−7.24734	−	73.5835i	−0.0444622	−	0.451433i	−0.991481	−	0.130254i	$-0.958421\pi$
$163$	−7.24734	−	73.5835i	−0.0444622	−	0.451433i	0.947018	−	0.321179i	$-0.104079\pi$
$164$	−176.107	+	247.350i	−1.07382	+	1.50823i
$165$	−2.56008	+	4.78957i	−0.0155156	+	0.0290277i
$166$	195.988	+	62.6418i	1.18065	+	0.377360i
$167$	−21.3102	+	14.2390i	−0.127606	+	0.0852636i	−0.617735	−	0.786386i	$-0.711950\pi$
$167$	−21.3102	+	14.2390i	−0.127606	+	0.0852636i	0.490129	+	0.871650i	$0.336950\pi$
$168$	3.33329	−	23.2035i	0.0198410	−	0.138116i
$169$	−277.558	−	185.458i	−1.64235	−	1.09739i
$170$	−14.3733	+	126.645i	−0.0845487	+	0.744969i
$171$	−194.433	+	159.567i	−1.13704	+	0.933142i
$172$	−113.078	−	146.437i	−0.657429	−	0.851379i
$173$	−72.6347	−	135.890i	−0.419854	−	0.785491i	0.579716	−	0.814819i	$-0.303163\pi$
$173$	−72.6347	−	135.890i	−0.419854	−	0.785491i	−0.999570	+	0.0293273i	$0.990663\pi$
$174$	2.46555	−	0.452514i	0.0141698	−	0.00260065i
$175$	35.4650	+	85.6201i	0.202657	+	0.489258i
$176$	−9.10390	+	57.3188i	−0.0517267	+	0.325675i
$177$	−31.1372	−	12.8975i	−0.175916	−	0.0728670i
$178$	−3.60193	+	16.8015i	−0.0202355	+	0.0943906i
$179$	71.1854	−	234.667i	0.397684	−	1.31099i	−0.498341	−	0.866981i	$-0.666057\pi$
$179$	71.1854	−	234.667i	0.397684	−	1.31099i	0.896024	−	0.444006i	$-0.146443\pi$
$180$	−80.2363	+	39.8734i	−0.445757	+	0.221519i
$181$	10.2660	−	104.233i	0.0567184	−	0.575872i	−0.924261	−	0.381761i	$-0.875318\pi$
$181$	10.2660	−	104.233i	0.0567184	−	0.575872i	0.980980	−	0.194111i	$-0.0621822\pi$
$182$	62.6386	+	218.087i	0.344168	+	1.19828i
$183$	1.83596	+	9.22999i	0.0100326	+	0.0504371i
$184$	−64.0816	+	9.80598i	−0.348269	+	0.0532934i
$185$	10.9792	−	55.1962i	0.0593470	−	0.298358i
$186$	−45.7939	−	38.7331i	−0.246204	−	0.208242i
$187$	85.5695	−	25.9572i	0.457591	−	0.138809i
$188$	149.280	−	56.7062i	0.794040	−	0.301629i
$189$	−40.0117	−	32.8368i	−0.211702	−	0.173740i
$190$	2.22648	−	150.075i	0.0117183	−	0.789869i
$191$	42.8643			0.224420			0.112210	−	0.993684i	$-0.464207\pi$
$191$	42.8643			0.224420			0.112210	+	0.993684i	$0.464207\pi$
$192$	25.9679	−	26.4484i	0.135250	−	0.137752i
$193$			18.5719i			0.0962276i	0.998842	+	0.0481138i	$0.0153210\pi$
$193$			18.5719i			0.0962276i	−0.998842	+	0.0481138i	$0.984679\pi$
$194$	4.51783	−	304.523i	0.0232878	−	1.56971i
$195$	−21.2982	+	25.9519i	−0.109221	+	0.133087i
$196$	−38.3709	+	85.3795i	−0.195770	+	0.435610i
$197$	44.4938	+	146.676i	0.225857	+	0.744550i	0.994487	+	0.104857i	$0.0334384\pi$
$197$	44.4938	+	146.676i	0.225857	+	0.744550i	−0.768631	+	0.639693i	$0.779062\pi$
$198$	47.9935	+	40.5935i	0.242391	+	0.205018i
$199$	369.865	+	73.5707i	1.85862	+	0.369702i	0.991682	−	0.128715i	$-0.0410853\pi$
$199$	369.865	+	73.5707i	1.85862	+	0.369702i	0.866937	+	0.498418i	$0.166085\pi$
$200$	−34.9533	+	142.305i	−0.174766	+	0.711527i
$201$	52.7772	−	10.4980i	0.262573	−	0.0522291i
$202$	39.8423	+	138.718i	0.197239	+	0.686722i
$203$	10.8968	+	1.07324i	0.0536788	+	0.00528690i
$204$	−54.1332	−	18.1915i	−0.265359	−	0.0891738i
$205$	−187.788	−	56.9650i	−0.916041	−	0.277878i
$206$	26.6854	−	124.476i	0.129541	−	0.604254i
$207$	−26.8693	+	64.8683i	−0.129803	+	0.313373i
$208$	−124.325	+	336.547i	−0.597716	+	1.61802i
$209$	−97.2837	+	40.2962i	−0.465472	+	0.192805i
$210$	14.9013	−	2.73491i	0.0709585	−	0.0130234i
$211$	170.813	−	91.3017i	0.809543	−	0.432710i	−0.0140431	−	0.999901i	$-0.504470\pi$
$211$	170.813	−	91.3017i	0.809543	−	0.432710i	0.823586	+	0.567192i	$0.191970\pi$
$212$	43.6479	+	5.61073i	0.205886	+	0.0264657i
$213$	18.9623	+	23.1056i	0.0890249	+	0.108477i
$214$	21.8707	−	192.705i	0.102199	−	0.900492i
$215$	66.4315	−	99.4218i	0.308984	−	0.462427i
$216$	−20.2500	−	79.2987i	−0.0937500	−	0.367124i
$217$	−145.552	−	217.833i	−0.670745	−	1.00384i
$218$	−134.462	−	42.9767i	−0.616796	−	0.197141i
$219$	−31.4550	−	16.8130i	−0.143630	−	0.0767718i
$220$	−36.9892	+	6.22311i	−0.168133	+	0.0282869i
$221$	550.117	−	54.1818i	2.48922	−	0.245167i
$222$	23.1503	+	9.99404i	0.104281	+	0.0450182i
$223$	−258.061	−	258.061i	−1.15722	−	1.15722i	−0.985070	−	0.172152i	$-0.944928\pi$
$223$	−258.061	−	258.061i	−1.15722	−	1.15722i	−0.172152	−	0.985070i	$-0.555072\pi$
$224$	140.914	−	79.7259i	0.629081	−	0.355919i
$225$	112.224	+	112.224i	0.498772	+	0.498772i
$226$	11.2673	−	4.47241i	0.0498551	−	0.0197894i
$227$	302.974	−	29.8403i	1.33469	−	0.131455i	0.594630	−	0.803999i	$-0.297298\pi$
$227$	302.974	−	29.8403i	1.33469	−	0.131455i	0.740057	+	0.672544i	$0.234798\pi$
$228$	65.5389	+	15.0705i	0.287451	+	0.0660988i
$229$	−111.163	−	59.4177i	−0.485427	−	0.259466i	0.210480	−	0.977598i	$-0.432497\pi$
$229$	−111.163	−	59.4177i	−0.485427	−	0.259466i	−0.695907	+	0.718132i	$0.744997\pi$
$230$	−19.2001	−	37.2392i	−0.0834785	−	0.161910i
$231$	−5.90507	−	8.83756i	−0.0255631	−	0.0382578i
$232$	12.8814	+	11.5679i	0.0555232	+	0.0498617i
$233$	38.1107	−	57.0367i	0.163565	−	0.244793i	−0.740629	−	0.671914i	$-0.765472\pi$
$233$	38.1107	−	57.0367i	0.163565	−	0.244793i	0.904194	+	0.427121i	$0.140472\pi$
$234$	242.031	+	304.001i	1.03432	+	1.29915i
$235$	65.4723	+	79.7783i	0.278606	+	0.339482i
$236$	−60.9330	−	224.657i	−0.258191	−	0.951937i
$237$	8.22381	−	4.39572i	0.0346996	−	0.0185473i
$238$	−205.332	−	141.649i	−0.862741	−	0.595164i
$239$	−295.451	+	122.380i	−1.23620	+	0.512049i	−0.902524	−	0.430640i	$-0.858288\pi$
$239$	−295.451	+	122.380i	−1.23620	+	0.512049i	−0.333672	+	0.942689i	$0.608288\pi$
$240$	21.5491	+	10.4636i	0.0897879	+	0.0435984i
$241$	3.97263	−	9.59079i	0.0164840	−	0.0397958i	−0.915423	−	0.402493i	$-0.868144\pi$
$241$	3.97263	−	9.59079i	0.0164840	−	0.0397958i	0.931907	+	0.362697i	$0.118144\pi$
$242$	−117.155	−	181.093i	−0.484110	−	0.748319i
$243$	−128.044	−	38.8416i	−0.526928	−	0.159842i
$244$	−42.7064	+	48.9985i	−0.175026	+	0.200813i
$245$	−60.2052	−	5.92970i	−0.245736	−	0.0242028i
$246$	42.5935	−	76.9200i	0.173144	−	0.312683i
$247$	−638.434	+	126.992i	−2.58475	+	0.514139i
$248$	18.4296	−	413.837i	0.0743129	−	1.66870i
$249$	−58.4366	−	11.6238i	−0.234685	−	0.0466818i
$250$	−223.186	+	18.6435i	−0.892743	+	0.0745740i
$251$	−40.6738	−	134.084i	−0.162047	−	0.534197i	0.837885	−	0.545847i	$-0.183792\pi$
$251$	−40.6738	−	134.084i	−0.162047	−	0.534197i	−0.999932	+	0.0116492i	$0.996292\pi$
$252$	5.20189	−	175.277i	0.0206424	−	0.695544i
$253$	−18.6473	+	22.7217i	−0.0737046	+	0.0898093i
$254$	−210.421	+	204.269i	−0.828428	+	0.804207i
$255$		−	36.9085i		−	0.144739i
$256$	254.199	+	30.3102i	0.992966	+	0.118399i
$257$	88.4286			0.344080			0.172040	−	0.985090i	$-0.444964\pi$
$257$	88.4286			0.344080			0.172040	+	0.985090i	$0.444964\pi$
$258$	37.3175	+	38.4414i	0.144641	+	0.148998i
$259$	85.1412	+	69.8736i	0.328730	+	0.269782i
$260$	−231.773	−	6.87857i	−0.891434	−	0.0264560i
$261$	17.9440	−	5.44326i	0.0687510	−	0.0208554i
$262$	−10.2424	−	122.614i	−0.0390931	−	0.467993i
$263$	−82.3684	+	414.094i	−0.313188	+	1.57450i	0.428364	+	0.903606i	$0.359090\pi$
$263$	−82.3684	+	414.094i	−0.313188	+	1.57450i	−0.741552	+	0.670896i	$0.765910\pi$
$264$	0.747694	−	16.7895i	0.00283217	−	0.0635965i
$265$	5.54865	+	27.8949i	0.0209383	+	0.105264i
$266$	256.981	+	142.300i	0.966092	+	0.534962i
$267$	0.487718	−	4.95188i	0.00182666	−	0.0185464i
$268$	280.174	+	244.196i	1.04543	+	0.911177i
$269$	−98.8382	+	325.826i	−0.367428	+	1.21125i	0.557200	+	0.830378i	$0.311876\pi$
$269$	−98.8382	+	325.826i	−0.367428	+	1.21125i	−0.924628	+	0.380871i	$0.875624\pi$
$270$	44.4115	−	28.7311i	0.164487	−	0.106412i
$271$	113.266	+	46.9162i	0.417955	+	0.173123i	0.581743	−	0.813373i	$-0.302371\pi$
$271$	113.266	+	46.9162i	0.417955	+	0.173123i	−0.163787	+	0.986496i	$0.552371\pi$
$272$	−129.065	−	372.713i	−0.474502	−	1.37027i
$273$	−25.1445	−	60.7042i	−0.0921044	−	0.222360i
$274$	−15.4210	+	22.3540i	−0.0562809	+	0.0815839i
$275$	31.3203	+	58.5961i	0.113892	+	0.213077i
$276$	18.1178	−	4.91403i	0.0656442	−	0.0178045i
$277$	−245.409	+	201.402i	−0.885952	+	0.727082i	−0.962873	−	0.269955i	$-0.912991\pi$
$277$	−245.409	+	201.402i	−0.885952	+	0.727082i	0.0769208	+	0.997037i	$0.475491\pi$
$278$	125.613	−	100.007i	0.451845	−	0.359736i
$279$	−373.047	−	249.262i	−1.33709	−	0.893413i
$280$	77.8526	+	69.9142i	0.278045	+	0.249694i
$281$	274.686	−	183.540i	0.977532	−	0.653166i	0.0393198	−	0.999227i	$-0.487481\pi$
$281$	274.686	−	183.540i	0.977532	−	0.653166i	0.938212	+	0.346061i	$0.112481\pi$
$282$	−41.1001	+	21.1907i	−0.145745	+	0.0751442i
$283$	153.776	−	287.695i	0.543378	−	1.01659i	−0.449020	−	0.893522i	$-0.648227\pi$
$283$	153.776	−	287.695i	0.543378	−	1.01659i	0.992398	−	0.123067i	$-0.0392731\pi$
$284$	−46.2640	+	201.193i	−0.162901	+	0.708427i
$285$	4.26009	+	43.2534i	0.0149477	+	0.151766i
$286$	60.0168	+	151.199i	0.209849	+	0.528669i
$287$	271.574	−	271.574i	0.946251	−	0.946251i
$288$	170.702	−	218.490i	0.592715	−	0.758645i
$289$	−225.359	+	225.359i	−0.779791	+	0.779791i
$290$	−4.43487	+	10.2730i	−0.0152927	+	0.0354241i
$291$	8.64430	+	87.7671i	0.0297055	+	0.301605i
$292$	−40.8696	−	242.923i	−0.139964	−	0.831927i
$293$	−120.464	+	225.373i	−0.411141	+	0.769190i	−0.999215	−	0.0396170i	$-0.987386\pi$
$293$	−120.464	+	225.373i	−0.411141	+	0.769190i	0.588074	+	0.808807i	$0.299886\pi$
$294$	8.25230	−	25.8190i	0.0280690	−	0.0878198i
$295$	125.086	−	83.5800i	0.424021	−	0.283322i
$296$	43.0901	+	168.740i	0.145575	+	0.570068i
$297$	−30.8551	−	20.6167i	−0.103889	−	0.0694166i
$298$	−494.598	−	56.1334i	−1.65973	−	0.188367i
$299$	−140.462	+	115.274i	−0.469773	+	0.385533i
$300$	5.41003	−	42.0865i	0.0180334	−	0.140288i
$301$	110.317	+	206.388i	0.366500	+	0.685674i
$302$	−58.9690	−	321.296i	−0.195262	−	1.06389i
$303$	−15.9936	−	38.6119i	−0.0527840	−	0.127432i
$304$	194.272	+	421.889i	0.639052	+	1.38779i
$305$	−38.8098	−	16.0756i	−0.127245	−	0.0527067i
$306$	−417.703	−	89.5475i	−1.36504	−	0.292639i
$307$	−168.425	+	555.224i	−0.548617	+	1.80855i	0.0387797	+	0.999248i	$0.487653\pi$
$307$	−168.425	+	555.224i	−0.548617	+	1.80855i	−0.587396	+	0.809299i	$0.699847\pi$
$308$	23.3844	−	69.5860i	0.0759233	−	0.225928i
$309$	−3.61332	+	36.6867i	−0.0116936	+	0.118727i
$310$	257.322	−	73.9075i	0.830070	−	0.238411i
$311$	66.2638	+	333.131i	0.213067	+	1.07116i	0.928175	+	0.372145i	$0.121378\pi$
$311$	66.2638	+	333.131i	0.213067	+	1.07116i	−0.715108	+	0.699014i	$0.753622\pi$
$312$	24.7817	−	100.894i	0.0794285	−	0.323377i
$313$	−12.4116	+	62.3971i	−0.0396535	+	0.199352i	−0.995534	−	0.0944043i	$-0.969905\pi$
$313$	−12.4116	+	62.3971i	−0.0396535	+	0.199352i	0.955880	+	0.293756i	$0.0949054\pi$
$314$	115.097	−	136.079i	0.366551	−	0.433371i
$315$	108.450	−	32.8980i	0.344286	−	0.104438i
$316$	58.7443	+	26.4006i	0.185900	+	0.0835463i
$317$	272.135	+	223.335i	0.858470	+	0.704528i	0.956838	−	0.290622i	$-0.0938623\pi$
$317$	272.135	+	223.335i	0.858470	+	0.704528i	−0.0983683	+	0.995150i	$0.531362\pi$
$318$	−12.7419	−	0.189036i	−0.0400689	−	0.000594453i
$319$	7.85008			0.0246084
$320$	33.7640	+	161.969i	0.105512	+	0.506153i
$321$			56.1607i			0.174956i
$322$	81.9898	+	1.21638i	0.254627	+	0.00377758i
$323$	453.987	−	553.184i	1.40553	−	1.71264i
$324$	−102.351	−	269.440i	−0.315899	−	0.831606i
$325$	119.229	+	393.044i	0.366857	+	1.20937i
$326$	−95.4989	+	112.908i	−0.292941	+	0.346343i
$327$	40.0917	+	7.97473i	0.122605	+	0.0243876i
$328$	600.286	−	91.8579i	1.83014	−	0.280054i
$329$	−198.104	+	39.4053i	−0.602139	+	0.119773i
$330$	10.4396	−	2.99844i	0.0316351	−	0.00908619i
$331$	287.852	+	28.3510i	0.869645	+	0.0856526i	0.522989	−	0.852340i	$-0.324817\pi$
$331$	287.852	+	28.3510i	0.869645	+	0.0856526i	0.346656	+	0.937992i	$0.387317\pi$
$332$	−183.133	−	368.514i	−0.551606	−	1.10998i
$333$	180.501	+	54.7543i	0.542044	+	0.164427i
$334$	50.1203	+	10.7448i	0.150061	+	0.0321701i
$335$	−91.9202	+	221.915i	−0.274389	+	0.662433i
$336$	−37.9414	+	27.5409i	−0.112921	+	0.0819669i
$337$	−127.311	+	52.7341i	−0.377779	+	0.156481i	−0.563489	−	0.826123i	$-0.690541\pi$
$337$	−127.311	+	52.7341i	−0.377779	+	0.156481i	0.185711	+	0.982604i	$0.440541\pi$
$338$	120.521	+	656.664i	0.356570	+	1.94279i
$339$	−3.09585	+	1.65477i	−0.00913231	+	0.00488132i
$340$	201.763	−	155.800i	0.593420	−	0.458235i
$341$	−119.156	−	145.192i	−0.349431	−	0.425783i
$342$	499.846	+	56.7290i	1.46154	+	0.165874i
$343$	203.514	−	304.580i	0.593335	−	0.887989i
$344$	−52.6164	+	366.269i	−0.152955	+	1.06474i
$345$	6.74043	+	10.0878i	0.0195375	+	0.0292399i
$346$	−93.8212	+	293.539i	−0.271160	+	0.848379i
$347$	−526.273	−	281.299i	−1.51664	−	0.810659i	−0.517646	−	0.855595i	$-0.673192\pi$
$347$	−526.273	−	281.299i	−1.51664	−	0.810659i	−0.998990	+	0.0449359i	$0.985692\pi$
$348$	−4.08408	−	2.90776i	−0.0117358	−	0.00835563i
$349$	−261.166	+	25.7226i	−0.748326	+	0.0737037i	−0.464989	−	0.885317i	$-0.653942\pi$
$349$	−261.166	+	25.7226i	−0.748326	+	0.0737037i	−0.283337	+	0.959020i	$0.591442\pi$
$350$	73.4624	−	170.169i	0.209893	−	0.486197i
$351$	−162.212	−	162.212i	−0.462143	−	0.462143i
$352$	94.9371	−	66.7852i	0.269708	−	0.189731i
$353$	244.178	+	244.178i	0.691723	+	0.691723i	0.962611	−	0.270888i	$-0.0873172\pi$
$353$	244.178	+	244.178i	0.691723	+	0.691723i	−0.270888	+	0.962611i	$0.587317\pi$
$354$	24.8683	+	62.6502i	0.0702494	+	0.176978i
$355$	−132.781	+	13.0778i	−0.374030	+	0.0368388i
$356$	29.1286	−	18.2370i	0.0818219	−	0.0512274i
$357$	63.7053	+	34.0512i	0.178446	+	0.0953814i
$358$	−435.922	+	224.756i	−1.21766	+	0.627809i
$359$	84.8886	+	127.045i	0.236459	+	0.353885i	0.930653	−	0.365902i	$-0.119239\pi$
$359$	84.8886	+	127.045i	0.236459	+	0.353885i	−0.694195	+	0.719787i	$0.744239\pi$
$360$	168.995	+	59.5952i	0.469431	+	0.165542i
$361$	−267.620	+	400.522i	−0.741330	+	1.10948i
$362$	−163.879	+	130.472i	−0.452705	+	0.360421i
$363$	39.6222	+	48.2798i	0.109152	+	0.133002i
$364$	225.702	−	393.701i	0.620062	−	1.08160i
$365$	140.407	−	75.0490i	0.384676	−	0.205614i
$366$	10.6877	−	15.4928i	0.0292015	−	0.0423300i
$367$	−621.861	+	257.583i	−1.69444	+	0.701861i	−0.999846	−	0.0175375i	$-0.994417\pi$
$367$	−621.861	+	257.583i	−1.69444	+	0.701861i	−0.694597	+	0.719399i	$0.744417\pi$
$368$	103.343	+	78.2989i	0.280822	+	0.212769i
$369$	251.699	−	607.656i	0.682112	−	1.64676i
$370$	−94.5034	+	61.1371i	−0.255415	+	0.165235i
$371$	−53.2667	−	16.1583i	−0.143576	−	0.0435533i
$372$	8.21117	+	119.674i	0.0220730	+	0.321705i
$373$	358.531	+	35.3122i	0.961208	+	0.0946708i	0.566434	−	0.824107i	$-0.308323\pi$
$373$	358.531	+	35.3122i	0.961208	+	0.0946708i	0.394775	+	0.918778i	$0.370823\pi$
$374$	−156.455	−	86.6349i	−0.418328	−	0.231644i
$375$	63.6078	−	12.6524i	0.169621	−	0.0337397i
$376$	−289.334	−	135.225i	−0.769505	−	0.359642i
$377$	47.5954	+	9.46732i	0.126248	+	0.0251123i
$378$	8.61754	+	103.163i	0.0227977	+	0.272917i
$379$	8.48306	+	27.9649i	0.0223827	+	0.0737860i	0.967420	−	0.253176i	$-0.0814751\pi$
$379$	8.48306	+	27.9649i	0.0223827	+	0.0737860i	−0.945038	+	0.326962i	$0.893975\pi$
$380$	−218.465	+	205.872i	−0.574908	+	0.541767i
$381$	53.8734	−	65.6449i	0.141400	−	0.172296i
$382$	−59.7134	−	61.5119i	−0.156318	−	0.161026i
$383$			404.481i			1.05609i	0.849217	+	0.528043i	$0.177074\pi$
$383$			404.481i			1.05609i	−0.849217	+	0.528043i	$0.822926\pi$
$384$	−74.1299	−	0.420176i	−0.193047	−	0.00109421i
$385$	47.4444			0.123232
$386$	26.6514	−	25.8722i	0.0690450	−	0.0670263i
$387$	309.798	+	254.245i	0.800513	+	0.656964i
$388$	−443.295	+	417.741i	−1.14251	+	1.07665i
$389$	461.728	−	140.064i	1.18696	−	0.360061i	0.365765	−	0.930707i	$-0.380807\pi$
$389$	461.728	−	140.064i	1.18696	−	0.360061i	0.821196	+	0.570647i	$0.193307\pi$
$390$	66.9120	−	5.58940i	0.171569	−	0.0143318i
$391$	38.9719	−	195.925i	0.0996724	−	0.501087i
$392$	175.976	−	63.8767i	0.448920	−	0.162951i
$393$	6.95099	+	34.9450i	0.0176870	+	0.0889185i
$394$	148.502	−	268.182i	0.376910	−	0.680665i
$395$	−4.07985	+	41.4234i	−0.0103287	+	0.104869i
$396$	−8.60558	−	125.422i	−0.0217313	−	0.316723i
$397$	9.57929	−	31.5787i	0.0241292	−	0.0795433i	−0.944049	−	0.329805i	$-0.893017\pi$
$397$	9.57929	−	31.5787i	0.0241292	−	0.0795433i	0.968178	+	0.250262i	$0.0805168\pi$
$398$	−409.675	−	633.260i	−1.02933	−	1.59111i
$399$	−78.5871	−	32.5519i	−0.196960	−	0.0815836i
$400$	252.906	−	148.083i	0.632265	−	0.370209i
$401$	−84.1105	−	203.061i	−0.209752	−	0.506386i	0.783632	−	0.621225i	$-0.213365\pi$
$401$	−84.1105	−	203.061i	−0.209752	−	0.506386i	−0.993384	+	0.114839i	$0.963365\pi$
$402$	−88.5879	−	61.1126i	−0.220368	−	0.152021i
$403$	−547.345	−	1024.01i	−1.35818	−	2.54097i
$404$	143.562	−	250.420i	0.355351	−	0.619852i
$405$	143.995	−	118.173i	0.355543	−	0.291786i
$406$	−13.6400	−	17.1324i	−0.0335960	−	0.0421981i
$407$	65.6568	+	43.8705i	0.161319	+	0.107790i
$408$	49.3064	+	103.025i	0.120849	+	0.252513i
$409$	114.064	−	76.2151i	0.278885	−	0.186345i	−0.408259	−	0.912866i	$-0.633864\pi$
$409$	114.064	−	76.2151i	0.278885	−	0.186345i	0.687144	+	0.726521i	$0.258864\pi$
$410$	179.857	+	348.840i	0.438676	+	0.850829i
$411$	3.70706	−	6.93543i	0.00901962	−	0.0168745i
$412$	−215.803	+	135.111i	−0.523794	+	0.327939i
$413$	28.8592	+	293.013i	0.0698770	+	0.709474i
$414$	130.519	−	51.8082i	0.315264	−	0.125141i
$415$	188.059	−	188.059i	0.453155	−	0.453155i
$416$	656.152	−	290.427i	1.57729	−	0.698141i
$417$	−32.8766	+	32.8766i	−0.0788407	+	0.0788407i
$418$	193.350	+	83.4698i	0.462561	+	0.199689i
$419$	−18.5811	−	188.657i	−0.0443464	−	0.450256i	−0.991560	−	0.129652i	$-0.958614\pi$
$419$	−18.5811	−	188.657i	−0.0443464	−	0.450256i	0.947213	−	0.320604i	$-0.103886\pi$
$420$	−24.6834	−	17.5739i	−0.0587699	−	0.0418427i
$421$	−225.633	+	422.130i	−0.535946	+	1.00268i	0.457590	+	0.889163i	$0.348713\pi$
$421$	−225.633	+	422.130i	−0.535946	+	1.00268i	−0.993536	+	0.113520i	$0.963787\pi$
$422$	−368.978	−	117.933i	−0.874356	−	0.279462i
$423$	−287.610	+	192.175i	−0.679929	+	0.454314i
$424$	−52.7534	−	70.4525i	−0.124418	−	0.166162i
$425$	−375.444	−	250.864i	−0.883398	−	0.590267i
$426$	6.74144	−	59.3996i	0.0158250	−	0.139436i
$427$	63.5523	−	52.1560i	0.148834	−	0.122145i
$428$	−307.007	+	237.068i	−0.717305	+	0.553898i
$429$	−22.2059	−	41.5443i	−0.0517620	−	0.0968399i
$430$	−235.218	+	43.1708i	−0.547019	+	0.100397i
$431$	−239.448	−	578.079i	−0.555564	−	1.34125i	−0.913246	−	0.407407i	$-0.866433\pi$
$431$	−239.448	−	578.079i	−0.555564	−	1.34125i	0.357682	−	0.933843i	$-0.383567\pi$
$432$	−85.5867	+	139.529i	−0.198117	+	0.322983i
$433$	−148.936	−	61.6913i	−0.343963	−	0.142474i	0.204013	−	0.978968i	$-0.434602\pi$
$433$	−148.936	−	61.6913i	−0.343963	−	0.142474i	−0.547976	+	0.836494i	$0.684602\pi$
$434$	−109.834	+	512.331i	−0.253074	+	1.18049i
$435$	0.940569	−	3.10064i	0.00216223	−	0.00712791i
$436$	125.642	+	252.827i	0.288171	+	0.579879i
$437$	−23.0573	+	234.105i	−0.0527627	+	0.535709i
$438$	19.6920	+	68.5609i	0.0449588	+	0.156532i
$439$	−141.329	−	710.511i	−0.321935	−	1.61848i	−0.715110	−	0.699012i	$-0.753623\pi$
$439$	−141.329	−	710.511i	−0.321935	−	1.61848i	0.393175	−	0.919464i	$-0.371377\pi$
$440$	60.4593	+	44.4116i	0.137408	+	0.100935i
$441$	39.5571	−	198.867i	0.0896987	−	0.450946i
$442$	−844.110	−	713.959i	−1.90975	−	1.61529i
$443$	299.076	−	90.7236i	0.675115	−	0.204794i	0.0659324	−	0.997824i	$-0.478998\pi$
$443$	299.076	−	90.7236i	0.675115	−	0.204794i	0.609182	+	0.793030i	$0.291498\pi$
$444$	−17.9084	−	47.1440i	−0.0403342	−	0.106180i
$445$	17.1692	+	14.0904i	0.0385825	+	0.0316639i
$446$	−10.8275	+	729.826i	−0.0242770	+	1.63638i
$447$	144.142			0.322466
$448$	−310.714	−	91.1523i	−0.693558	−	0.203465i
$449$		−	521.323i		−	1.16107i	−0.814234	−	0.580537i	$-0.802842\pi$
$449$		−	521.323i		−	1.16107i	0.814234	−	0.580537i	$-0.197158\pi$
$450$	4.70860	−	317.382i	0.0104636	−	0.705293i
$451$	174.679	−	212.847i	0.387315	−	0.471944i
$452$	−22.1143	−	9.93851i	−0.0489253	−	0.0219879i
$453$	27.4589	+	90.5199i	0.0606157	+	0.199823i
$454$	−464.889	−	393.209i	−1.02398	−	0.866099i
$455$	287.658	+	57.2187i	0.632215	+	0.125755i
$456$	−69.6741	−	115.045i	−0.152794	−	0.252292i
$457$	378.907	−	75.3692i	0.829117	−	0.164922i	0.237753	−	0.971326i	$-0.423589\pi$
$457$	378.907	−	75.3692i	0.829117	−	0.164922i	0.591365	+	0.806404i	$0.298589\pi$
$458$	69.5919	+	242.296i	0.151947	+	0.529031i
$459$	250.983	+	24.7197i	0.546804	+	0.0538555i
$460$	−26.6925	+	79.4300i	−0.0580271	+	0.172674i
$461$	−751.094	−	227.842i	−1.62927	−	0.494234i	−0.662325	−	0.749217i	$-0.730430\pi$
$461$	−751.094	−	227.842i	−1.62927	−	0.494234i	−0.966946	+	0.254983i	$0.917930\pi$
$462$	−4.45599	+	20.7854i	−0.00964500	+	0.0449900i
$463$	61.8783	−	149.387i	0.133646	−	0.322651i	−0.842862	−	0.538130i	$-0.819131\pi$
$463$	61.8783	−	149.387i	0.133646	−	0.322651i	0.976509	+	0.215478i	$0.0691311\pi$
$464$	−1.34441	−	34.6003i	−0.00289744	−	0.0745695i
$465$	−71.6250	+	29.6680i	−0.154032	+	0.0638022i
$466$	−134.941	+	24.7664i	−0.289573	+	0.0531468i
$467$	−439.520	+	234.928i	−0.941157	+	0.503059i	−0.869261	−	0.494353i	$-0.835405\pi$
$467$	−439.520	+	234.928i	−0.941157	+	0.503059i	−0.0718956	+	0.997412i	$0.522905\pi$
$468$	99.0854	−	770.821i	0.211721	−	1.64705i
$469$	−298.229	−	363.393i	−0.635882	−	0.774824i
$470$	23.2766	−	205.093i	0.0495246	−	0.436367i
$471$	−28.6729	+	42.9120i	−0.0608767	+	0.0911084i
$472$	−237.507	+	400.406i	−0.503192	+	0.848319i
$473$	93.2121	+	139.502i	0.197066	+	0.294930i
$474$	−17.7644	−	5.67789i	−0.0374777	−	0.0119787i
$475$	468.942	+	250.655i	0.987246	+	0.527694i
$476$	82.7726	+	491.988i	0.173892	+	1.03359i
$477$	−94.8667	+	9.34355i	−0.198882	+	0.0195882i
$478$	587.206	+	253.498i	1.22846	+	0.530330i
$479$	−1.72812	−	1.72812i	−0.00360777	−	0.00360777i	0.705301	−	0.708908i	$-0.250812\pi$
$479$	−1.72812	−	1.72812i	−0.00360777	−	0.00360777i	−0.708908	+	0.705301i	$0.750812\pi$
$480$	−15.0039	−	45.5004i	−0.0312582	−	0.0947925i
$481$	345.172	+	345.172i	0.717613	+	0.717613i
$482$	−19.2973	+	7.65985i	−0.0400359	+	0.0158918i
$483$	−23.6304	+	2.32739i	−0.0489243	+	0.00481862i
$484$	−96.6698	+	420.399i	−0.199731	+	0.868592i
$485$	−347.182	−	185.572i	−0.715838	−	0.382623i
$486$	122.636	+	237.857i	0.252337	+	0.489417i
$487$	−95.6396	−	143.135i	−0.196385	−	0.293911i	0.720187	−	0.693780i	$-0.244056\pi$
$487$	−95.6396	−	143.135i	−0.196385	−	0.293911i	−0.916573	+	0.399868i	$0.869056\pi$
$488$	129.808	−	6.97358i	0.266000	−	0.0142901i
$489$	23.7906	−	35.6052i	0.0486516	−	0.0728123i
$490$	75.3613	+	94.6572i	0.153799	+	0.193178i
$491$	−91.5524	−	111.557i	−0.186461	−	0.227204i	0.671387	−	0.741107i	$-0.265699\pi$
$491$	−91.5524	−	111.557i	−0.186461	−	0.227204i	−0.857848	+	0.513903i	$0.828199\pi$
$492$	−169.719	+	46.0324i	−0.344958	+	0.0935618i
$493$	−47.0504	+	25.1490i	−0.0954370	+	0.0510121i
$494$	1071.63	+	739.265i	2.16929	+	1.49649i
$495$	75.0654	−	31.0931i	0.151647	−	0.0628143i
$496$	−619.546	+	550.061i	−1.24908	+	1.10899i
$497$	99.9287	−	241.249i	0.201064	−	0.485411i
$498$	64.7263	+	100.051i	0.129972	+	0.200907i
$499$	343.717	+	104.265i	0.688812	+	0.208949i	0.615239	−	0.788341i	$-0.289060\pi$
$499$	343.717	+	104.265i	0.688812	+	0.208949i	0.0735734	+	0.997290i	$0.476560\pi$
$500$	337.670	+	294.308i	0.675339	+	0.588616i
$501$	−14.7719	−	1.45490i	−0.0294847	−	0.00290399i
$502$	−135.753	+	245.157i	−0.270424	+	0.488361i
$503$	−778.377	+	154.829i	−1.54747	+	0.307811i	−0.893624	−	0.448817i	$-0.851846\pi$
$503$	−778.377	+	154.829i	−1.54747	+	0.307811i	−0.653846	+	0.756628i	$0.726846\pi$
$504$	−258.776	+	236.710i	−0.513444	+	0.469663i
$505$	182.969	+	36.3949i	0.362316	+	0.0720691i
$506$	58.5837	−	4.89370i	0.115778	−	0.00967135i
$507$	−56.1205	−	185.004i	−0.110691	−	0.364900i
$508$	586.266	+	17.3992i	1.15407	+	0.0342505i
$509$	503.062	−	612.983i	0.988334	−	1.20429i	0.00943216	−	0.999956i	$-0.496998\pi$
$509$	503.062	−	612.983i	0.988334	−	1.20429i	0.978902	−	0.204333i	$-0.0655024\pi$
$510$	−52.9650	+	51.4165i	−0.103853	+	0.100817i
$511$			311.586i			0.609757i
$512$	−310.624	−	407.010i	−0.606687	−	0.794941i
$513$	−296.983			−0.578914
$514$	−123.188	−	126.898i	−0.239666	−	0.246884i
$515$	−127.201	−	104.391i	−0.246991	−	0.202701i
$516$	3.17864	−	107.104i	0.00616015	−	0.207566i
$517$	−138.574	+	42.0360i	−0.268035	+	0.0813075i
$518$	−18.3373	−	219.520i	−0.0354002	−	0.423784i
$519$	17.4094	−	87.5229i	0.0335441	−	0.168638i
$520$	313.007	+	342.185i	0.601936	+	0.658048i
$521$	138.749	+	697.540i	0.266313	+	1.33885i	0.849963	+	0.526842i	$0.176624\pi$
$521$	138.749	+	697.540i	0.266313	+	1.33885i	−0.583650	+	0.812006i	$0.698376\pi$
$522$	−32.8087	−	18.1674i	−0.0628519	−	0.0348035i
$523$	−2.73358	+	27.7545i	−0.00522674	+	0.0530679i	−0.997444	−	0.0714483i	$-0.977238\pi$
$523$	−2.73358	+	27.7545i	−0.00522674	+	0.0530679i	0.992218	+	0.124516i	$0.0397379\pi$
$524$	−161.687	+	185.510i	−0.308564	+	0.354026i
$525$	−15.5803	+	51.3612i	−0.0296767	+	0.0978309i
$526$	708.986	−	458.664i	1.34788	−	0.871985i
$527$	1179.32	+	488.491i	2.23780	+	0.926928i
$528$	−25.1351	+	22.3161i	−0.0476044	+	0.0422654i
$529$	−177.310	−	428.065i	−0.335180	−	0.809197i
$530$	32.3005	−	46.8224i	0.0609444	−	0.0883441i
$531$	237.689	+	444.684i	0.447625	+	0.837447i
$532$	−153.789	−	567.011i	−0.289077	−	1.06581i
$533$	1315.78	−	1079.84i	2.46864	−	2.02596i
$534$	−7.78556	+	6.19847i	−0.0145797	+	0.0116076i
$535$	−208.439	−	139.274i	−0.389605	−	0.260326i
$536$	−39.8750	−	742.244i	−0.0743937	−	1.38478i
$537$	118.087	−	78.9034i	0.219902	−	0.146934i
$538$	605.262	−	312.065i	1.12502	−	0.580046i
$539$	40.0143	−	74.8615i	0.0742380	−	0.138890i
$540$	−103.099	−	23.7074i	−0.190924	−	0.0439026i
$541$	85.2521	+	865.579i	0.157582	+	1.59996i	0.670757	+	0.741677i	$0.265969\pi$
$541$	85.2521	+	865.579i	0.157582	+	1.59996i	−0.513175	+	0.858284i	$0.671531\pi$
$542$	−90.4618	−	227.899i	−0.166904	−	0.420477i
$543$	42.8920	−	42.8920i	0.0789908	−	0.0789908i
$544$	−355.060	+	704.432i	−0.652684	+	1.29491i
$545$	−129.022	+	129.022i	−0.236738	+	0.236738i
$546$	−52.0844	+	120.649i	−0.0953927	+	0.220969i
$547$	49.5084	+	502.668i	0.0905090	+	0.918954i	0.928019	+	0.372532i	$0.121510\pi$
$547$	49.5084	+	502.668i	0.0905090	+	0.918954i	−0.837510	+	0.546422i	$0.815990\pi$
$548$	53.5614	−	9.01124i	0.0977399	−	0.0164439i
$549$	66.3700	−	124.169i	0.120892	−	0.226174i
$550$	40.4559	−	126.575i	0.0735563	−	0.230136i
$551$	52.2361	−	34.9031i	0.0948024	−	0.0633449i
$552$	−32.2914	−	19.1541i	−0.0584988	−	0.0346994i
$553$	−67.7342	−	45.2585i	−0.122485	−	0.0818418i
$554$	630.893	+	71.6019i	1.13880	+	0.129245i
$555$	25.1948	−	20.6768i	0.0453960	−	0.0372556i
$556$	−318.502	−	40.9419i	−0.572846	−	0.0736366i
$557$	−137.698	−	257.615i	−0.247214	−	0.462505i	0.727456	−	0.686155i	$-0.240703\pi$
$557$	−137.698	−	257.615i	−0.247214	−	0.462505i	−0.974670	+	0.223650i	$0.928203\pi$
$558$	161.984	+	882.579i	0.290294	+	1.58168i
$559$	396.908	+	958.221i	0.710033	+	1.71417i
$560$	−8.12537	−	209.117i	−0.0145096	−	0.373424i
$561$	47.8453	+	19.8182i	0.0852858	+	0.0353265i
$562$	−646.046	−	138.500i	−1.14955	−	0.246441i
$563$	−280.214	+	923.742i	−0.497716	+	1.64075i	0.243809	+	0.969823i	$0.421603\pi$
$563$	−280.214	+	923.742i	−0.497716	+	1.64075i	−0.741525	+	0.670925i	$0.765897\pi$
$564$	87.6650	+	29.4598i	0.155434	+	0.0522338i
$565$	1.53586	−	15.5938i	0.00271833	−	0.0275997i
$566$	−627.075	+	180.107i	−1.10791	+	0.318211i
$567$	71.1240	+	357.565i	0.125439	+	0.630625i
$568$	353.169	−	213.888i	0.621777	−	0.376563i
$569$	−86.6887	+	435.814i	−0.152353	+	0.765929i	0.826751	+	0.562568i	$0.190187\pi$
$569$	−86.6887	+	435.814i	−0.152353	+	0.765929i	−0.979104	+	0.203361i	$0.934813\pi$
$570$	56.1356	−	66.3688i	0.0984835	−	0.116437i
$571$	501.678	−	152.182i	0.878596	−	0.266519i	0.181408	−	0.983408i	$-0.441934\pi$
$571$	501.678	−	152.182i	0.878596	−	0.266519i	0.697188	+	0.716889i	$0.254434\pi$
$572$	133.368	−	296.759i	0.233161	−	0.518810i
$573$	19.1898	+	15.7487i	0.0334901	+	0.0274846i
$574$	−768.043	−	11.3945i	−1.33805	−	0.0198511i
$575$	148.430			0.258139
$576$	−551.342	+	59.4102i	−0.957191	+	0.103143i
$577$		−	128.777i		−	0.223184i	−0.993754	−	0.111592i	$-0.964405\pi$
$577$		−	128.777i		−	0.223184i	0.993754	−	0.111592i	$-0.0355950\pi$
$578$	637.343	+	9.45547i	1.10267	+	0.0163590i
$579$	−6.82348	+	8.31443i	−0.0117849	+	0.0143600i
$580$	20.9202	−	7.94688i	0.0360694	−	0.0137015i
$581$	151.096	+	498.097i	0.260062	+	0.857310i
$582$	113.907	−	134.671i	0.195716	−	0.231394i
$583$	−39.1402	−	7.78548i	−0.0671359	−	0.0133542i
$584$	−291.668	+	397.060i	−0.499432	+	0.679897i
$585$	492.624	−	97.9890i	0.842092	−	0.167503i
$586$	491.234	−	141.091i	0.838283	−	0.240770i
$587$	−408.260	−	40.2101i	−0.695502	−	0.0685010i	−0.255913	−	0.966700i	$-0.582376\pi$
$587$	−408.260	−	40.2101i	−0.695502	−	0.0685010i	−0.439589	+	0.898199i	$0.644876\pi$
$588$	−48.5473	+	24.1256i	−0.0825635	+	0.0410299i
$589$	−1438.44	−	436.346i	−2.44218	−	0.740826i
$590$	−294.195	−	63.0699i	−0.498636	−	0.106898i
$591$	−33.9707	+	82.0126i	−0.0574801	+	0.138769i
$592$	182.120	−	296.904i	0.307636	−	0.501527i
$593$	−656.068	+	271.752i	−1.10635	+	0.458267i	−0.859681	−	0.510832i	$-0.829338\pi$
$593$	−656.068	+	271.752i	−1.10635	+	0.458267i	−0.246674	+	0.969099i	$0.579338\pi$
$594$	13.3979	+	72.9990i	0.0225553	+	0.122894i
$595$	−284.364	+	151.996i	−0.477922	+	0.255455i
$596$	608.461	+	787.965i	1.02091	+	1.32209i
$597$	138.554	+	168.828i	0.232083	+	0.282794i
$598$	361.098	+	40.9821i	0.603842	+	0.0685319i
$599$	−53.5510	+	80.1448i	−0.0894007	+	0.133798i	−0.873474	−	0.486870i	$-0.838138\pi$
$599$	−53.5510	+	80.1448i	−0.0894007	+	0.133798i	0.784074	+	0.620668i	$0.213138\pi$
$600$	−67.9323	+	50.8663i	−0.113221	+	0.0847772i
$601$	−575.559	−	861.384i	−0.957668	−	1.43325i	−0.900485	−	0.434888i	$-0.856788\pi$
$601$	−575.559	−	861.384i	−0.957668	−	1.43325i	−0.0571834	−	0.998364i	$-0.518212\pi$
$602$	142.494	−	445.823i	0.236702	−	0.740570i
$603$	−710.003	−	379.504i	−1.17745	−	0.629360i
$604$	−378.923	+	532.213i	−0.627355	+	0.881148i
$605$	−277.449	+	27.3263i	−0.458593	+	0.0451675i
$606$	−33.1292	+	76.7408i	−0.0546686	+	0.126635i
$607$	165.249	+	165.249i	0.272239	+	0.272239i	0.830001	−	0.557762i	$-0.188340\pi$
$607$	165.249	+	165.249i	0.272239	+	0.272239i	−0.557762	+	0.830001i	$0.688340\pi$
$608$	334.791	−	866.512i	0.550643	−	1.42518i
$609$	4.48405	+	4.48405i	0.00736297	+	0.00736297i
$610$	30.9962	+	78.0881i	0.0508134	+	0.128013i
$611$	−890.878	+	87.7438i	−1.45807	+	0.143607i
$612$	453.389	+	724.166i	0.740832	+	1.18328i
$613$	−221.440	−	118.362i	−0.361239	−	0.193086i	0.280785	−	0.959771i	$-0.409405\pi$
$613$	−221.440	−	118.362i	−0.361239	−	0.193086i	−0.642024	+	0.766684i	$0.721905\pi$
$614$	1031.40	−	531.774i	1.67980	−	0.866082i
$615$	−63.1412	−	94.4975i	−0.102669	−	0.153655i
$616$	−132.435	+	63.3813i	−0.214991	+	0.102892i
$617$	−539.133	+	806.870i	−0.873798	+	1.30773i	0.0767173	+	0.997053i	$0.475556\pi$
$617$	−539.133	+	806.870i	−0.873798	+	1.30773i	−0.950515	+	0.310678i	$0.899444\pi$
$618$	57.6804	−	45.9222i	0.0933339	−	0.0743078i
$619$	643.343	+	783.915i	1.03933	+	1.26642i	0.963046	+	0.269336i	$0.0868042\pi$
$619$	643.343	+	783.915i	1.03933	+	1.26642i	0.0762797	+	0.997086i	$0.475696\pi$
$620$	−464.529	−	266.307i	−0.749241	−	0.429527i
$621$	−73.1127	+	39.0795i	−0.117734	+	0.0629300i
$622$	385.744	−	559.168i	0.620167	−	0.898984i
$623$	−40.1606	+	16.6351i	−0.0644632	+	0.0267015i
$624$	−179.309	+	104.990i	−0.287354	+	0.168254i
$625$	64.4558	−	155.610i	0.103129	−	0.248976i
$626$	106.832	−	69.1131i	0.170659	−	0.110404i
$627$	−58.3579	−	17.7027i	−0.0930748	−	0.0282339i
$628$	−355.617	+	24.3999i	−0.566269	+	0.0388533i
$629$	−534.068	−	52.6011i	−0.849075	−	0.0836266i
$630$	−198.290	−	109.800i	−0.314745	−	0.174286i
$631$	315.190	−	62.6951i	0.499508	−	0.0993584i	0.0610951	−	0.998132i	$-0.480541\pi$
$631$	315.190	−	62.6951i	0.499508	−	0.0993584i	0.438413	+	0.898774i	$0.355541\pi$
$632$	−43.9495	−	121.078i	−0.0695404	−	0.191580i
$633$	110.016	+	21.8836i	0.173801	+	0.0345712i
$634$	−58.6111	−	701.647i	−0.0924465	−	1.10670i
$635$	110.037	+	362.744i	0.173287	+	0.571250i
$636$	17.4792	+	18.5485i	0.0274831	+	0.0291642i
$637$	332.893	−	405.631i	0.522595	−	0.636783i
$638$	−10.9358	−	11.2652i	−0.0171407	−	0.0176570i
$639$		−	447.188i		−	0.699825i
$640$	185.396	−	274.088i	0.289681	−	0.428263i
$641$	8.68542			0.0135498			0.00677490	−	0.999977i	$-0.497843\pi$
$641$	8.68542			0.0135498			0.00677490	+	0.999977i	$0.497843\pi$
$642$	80.5927	−	78.2364i	0.125534	−	0.121863i
$643$	444.433	+	364.736i	0.691186	+	0.567242i	0.913056	−	0.407835i	$-0.133716\pi$
$643$	444.433	+	364.736i	0.691186	+	0.567242i	−0.221870	+	0.975076i	$0.571216\pi$
$644$	−112.473	−	119.353i	−0.174647	−	0.185331i
$645$	66.2690	−	20.1025i	0.102743	−	0.0311666i
$646$	−1426.28	+	119.142i	−2.20786	+	0.184431i
$647$	−75.3503	+	378.812i	−0.116461	+	0.585489i	0.877847	+	0.478942i	$0.158980\pi$
$647$	−75.3503	+	378.812i	−0.116461	+	0.585489i	−0.994308	+	0.106547i	$0.966020\pi$
$648$	−244.073	+	522.229i	−0.376657	+	0.805910i
$649$	41.1810	+	207.031i	0.0634530	+	0.319000i
$650$	397.938	−	718.639i	0.612212	−	1.10560i
$651$	14.8720	−	150.998i	0.0228449	−	0.231948i
$652$	295.064	−	20.2452i	0.452553	−	0.0310509i
$653$	6.58437	−	21.7058i	0.0100833	−	0.0332400i	−0.951754	−	0.306861i	$-0.900721\pi$
$653$	6.58437	−	21.7058i	0.0100833	−	0.0332400i	0.961838	+	0.273621i	$0.0882214\pi$
$654$	−44.4069	−	68.6425i	−0.0679004	−	0.104958i
$655$	−146.935	−	60.8625i	−0.224328	−	0.0929198i
$656$	−968.066	−	733.468i	−1.47571	−	1.11809i
$657$	204.200	+	492.983i	0.310807	+	0.750355i
$658$	332.522	+	229.391i	0.505353	+	0.348619i
$659$	−214.656	−	401.593i	−0.325730	−	0.609397i	0.664749	−	0.747067i	$-0.268539\pi$
$659$	−214.656	−	401.593i	−0.325730	−	0.609397i	−0.990478	+	0.137670i	$0.956039\pi$
$660$	−18.8461	−	10.8041i	−0.0285546	−	0.0163699i
$661$	51.1206	−	41.9536i	0.0773383	−	0.0634699i	−0.594930	−	0.803778i	$-0.702820\pi$
$661$	51.1206	−	41.9536i	0.0773383	−	0.0634699i	0.672268	+	0.740308i	$0.265320\pi$
$662$	−360.317	−	452.574i	−0.544285	−	0.683647i
$663$	266.188	+	177.861i	0.401490	+	0.268267i
$664$	−273.713	+	776.173i	−0.412218	+	1.16893i
$665$	315.705	−	210.947i	0.474744	−	0.317214i
$666$	−172.877	−	335.302i	−0.259576	−	0.503456i
$667$	8.26690	−	15.4663i	0.0123942	−	0.0231878i
$668$	−54.4023	−	86.8929i	−0.0814406	−	0.130079i
$669$	−20.7171	−	210.344i	−0.0309673	−	0.314416i
$670$	446.508	−	177.236i	0.666430	−	0.264532i
$671$	41.6782	−	41.6782i	0.0621136	−	0.0621136i
$672$	92.3775	+	16.0806i	0.137467	+	0.0239295i
$673$	862.576	−	862.576i	1.28169	−	1.28169i	0.341982	−	0.939707i	$-0.388902\pi$
$673$	862.576	−	862.576i	1.28169	−	1.28169i	0.939707	−	0.341982i	$-0.111098\pi$
$674$	253.030	+	109.234i	0.375416	+	0.162068i
$675$	18.3674	+	186.487i	0.0272110	+	0.276277i
$676$	774.441	−	1087.74i	1.14562	−	1.60908i
$677$	466.158	−	872.120i	0.688564	−	1.28821i	−0.258140	−	0.966107i	$-0.583110\pi$
$677$	466.158	−	872.120i	0.688564	−	1.28821i	0.946704	−	0.322105i	$-0.104390\pi$
$678$	6.68742	+	2.13744i	0.00986345	+	0.00315256i
$679$	640.608	−	428.041i	0.943458	−	0.630399i
$680$	−504.650	−	72.4955i	−0.742133	−	0.106611i
$681$	146.601	+	97.9560i	0.215274	+	0.143841i
$682$	−42.3621	+	373.257i	−0.0621145	+	0.547298i
$683$	−517.738	+	424.896i	−0.758034	+	0.622103i	−0.931920	−	0.362663i	$-0.881868\pi$
$683$	−517.738	+	424.896i	−0.758034	+	0.622103i	0.173886	+	0.984766i	$0.444368\pi$
$684$	−614.917	−	796.325i	−0.899001	−	1.16422i
$685$	16.5474	+	30.9580i	0.0241567	+	0.0451941i
$686$	−720.595	+	132.254i	−1.05043	+	0.192791i
$687$	−27.9357	−	67.4427i	−0.0406633	−	0.0981699i
$688$	598.908	−	434.736i	0.870506	−	0.631883i
$689$	−227.920	−	94.4075i	−0.330798	−	0.137021i
$690$	5.08636	−	23.7258i	0.00737154	−	0.0343852i
$691$	−71.2300	+	234.814i	−0.103083	+	0.339818i	−0.993277	−	0.115764i	$-0.963069\pi$
$691$	−71.2300	+	234.814i	−0.103083	+	0.339818i	0.890194	+	0.455581i	$0.150569\pi$
$692$	551.940	−	274.286i	0.797601	−	0.396367i
$693$	−15.5864	+	158.251i	−0.0224912	+	0.228357i
$694$	329.466	+	1147.09i	0.474735	+	1.65287i
$695$	−40.4889	−	203.552i	−0.0582574	−	0.292880i
$696$	1.51670	+	9.91154i	0.00217916	+	0.0142407i
$697$	−365.071	+	1835.34i	−0.523775	+	2.63319i
$698$	400.738	+	338.949i	0.574123	+	0.485600i
$699$	38.0175	−	11.5325i	0.0543884	−	0.0164985i
$700$	−346.538	+	131.638i	−0.495054	+	0.188054i
$701$	−931.372	−	764.358i	−1.32863	−	1.09038i	−0.988696	−	0.149934i	$-0.952094\pi$
$701$	−931.372	−	764.358i	−1.32863	−	1.09038i	−0.339938	−	0.940448i	$-0.610406\pi$
$702$	−6.80598	+	458.755i	−0.00969513	+	0.653497i
$703$	631.951			0.898935
$704$	−228.094	−	43.2010i	−0.323997	−	0.0613651i
$705$			59.7708i			0.0847813i
$706$	10.2451	−	690.565i	0.0145114	−	0.978137i
$707$	−231.623	+	282.234i	−0.327614	+	0.399199i
$708$	55.2619	−	122.964i	0.0780535	−	0.173677i
$709$	102.418	+	337.627i	0.144454	+	0.476202i	0.999073	−	0.0430548i	$-0.0137090\pi$
$709$	102.418	+	337.627i	0.144454	+	0.476202i	−0.854619	+	0.519256i	$0.826209\pi$
$710$	203.741	+	172.327i	0.286959	+	0.242714i
$711$	−136.828	−	27.2168i	−0.192444	−	0.0382796i
$712$	−66.7491	−	16.3950i	−0.0937488	−	0.0230267i
$713$	−411.541	+	81.8606i	−0.577196	+	0.114811i
$714$	−39.8818	−	138.855i	−0.0558569	−	0.194475i
$715$	209.259	+	20.6102i	0.292670	+	0.0288255i
$716$	929.807	+	312.462i	1.29861	+	0.436399i
$717$	−177.233	−	53.7631i	−0.247187	−	0.0749834i
$718$	64.0574	−	298.802i	0.0892164	−	0.416159i
$719$	51.9986	−	125.536i	0.0723207	−	0.174598i	−0.883585	−	0.468270i	$-0.844877\pi$
$719$	51.9986	−	125.536i	0.0723207	−	0.174598i	0.955906	+	0.293672i	$0.0948775\pi$
$720$	−149.903	−	325.535i	−0.208198	−	0.452132i
$721$	297.535	−	123.243i	0.412670	−	0.170934i
$722$	947.580	−	173.914i	1.31244	−	0.240878i
$723$	5.30223	−	2.83410i	0.00733366	−	0.00391992i
$724$	415.530	+	53.4144i	0.573936	+	0.0737767i
$725$	−25.1476	−	30.6425i	−0.0346864	−	0.0422655i
$726$	14.0864	−	124.117i	0.0194028	−	0.170960i
$727$	617.945	−	924.820i	0.849993	−	1.27211i	−0.110521	−	0.993874i	$-0.535252\pi$
$727$	617.945	−	924.820i	0.849993	−	1.27211i	0.960514	−	0.278231i	$-0.0897482\pi$
$728$	−879.397	+	224.566i	−1.20796	+	0.308470i
$729$	317.238	+	474.781i	0.435169	+	0.651277i
$730$	−303.296	−	96.9397i	−0.415474	−	0.132794i
$731$	−1005.59	−	537.501i	−1.37564	−	0.735296i
$732$	−37.1216	+	6.24538i	−0.0507125	+	0.00853193i
$733$	192.932	−	19.0021i	0.263208	−	0.0259238i	0.0344478	−	0.999406i	$-0.489033\pi$
$733$	192.932	−	19.0021i	0.263208	−	0.0259238i	0.228760	+	0.973483i	$0.426533\pi$
$734$	1235.94	+	533.559i	1.68385	+	0.726920i
$735$	−24.7745	−	24.7745i	−0.0337069	−	0.0337069i
$736$	−31.6027	−	257.377i	−0.0429385	−	0.349697i
$737$	−238.317	−	238.317i	−0.323361	−	0.323361i
$738$	−1222.65	+	485.315i	−1.65670	+	0.657609i
$739$	−653.645	+	64.3784i	−0.884499	+	0.0871155i	−0.530056	−	0.847962i	$-0.677829\pi$
$739$	−653.645	+	64.3784i	−0.884499	+	0.0871155i	−0.354442	+	0.935078i	$0.615329\pi$
$740$	219.385	+	50.4471i	0.296466	+	0.0681717i
$741$	−332.477	−	177.713i	−0.448687	−	0.239828i
$742$	51.0170	+	98.9493i	0.0687560	+	0.133355i
$743$	−436.978	−	653.984i	−0.588127	−	0.880194i	0.411384	−	0.911462i	$-0.365045\pi$
$743$	−436.978	−	653.984i	−0.588127	−	0.880194i	−0.999511	+	0.0312681i	$0.990045\pi$
$744$	160.298	−	178.499i	0.215454	−	0.239918i
$745$	−357.462	+	534.980i	−0.479815	+	0.718093i
$746$	−448.787	−	563.697i	−0.601592	−	0.755627i
$747$	565.493	+	689.055i	0.757018	+	0.922430i
$748$	93.6295	+	345.207i	0.125173	+	0.461507i
$749$	432.694	−	231.280i	0.577695	−	0.308785i
$750$	−106.767	−	73.6538i	−0.142357	−	0.0982051i
$751$	−58.2559	+	24.1304i	−0.0775711	+	0.0321310i	−0.421132	−	0.907000i	$-0.638367\pi$
$751$	−58.2559	+	24.1304i	−0.0775711	+	0.0321310i	0.343560	+	0.939131i	$0.388367\pi$
$752$	209.011	+	603.584i	0.277941	+	0.802639i
$753$	31.0542	−	74.9715i	0.0412407	−	0.0995638i
$754$	−52.7183	−	81.4899i	−0.0699181	−	0.108077i
$755$	−404.058	−	122.570i	−0.535176	−	0.162344i
$756$	136.037	−	156.080i	0.179943	−	0.206455i
$757$	−58.1065	−	5.72299i	−0.0767589	−	0.00756009i	0.0595648	−	0.998224i	$-0.481029\pi$
$757$	−58.1065	−	5.72299i	−0.0767589	−	0.00756009i	−0.136324	+	0.990664i	$0.543529\pi$
$758$	28.3131	−	51.1308i	0.0373523	−	0.0674549i
$759$	−16.6963	+	3.32110i	−0.0219978	+	0.00437563i
$760$	599.772	+	26.7099i	0.789174	+	0.0351447i
$761$	454.626	+	90.4308i	0.597406	+	0.118831i	0.484526	−	0.874777i	$-0.338992\pi$
$761$	454.626	+	90.4308i	0.597406	+	0.118831i	0.112881	+	0.993609i	$0.463992\pi$
$762$	−169.253	+	14.1383i	−0.222117	+	0.0185542i
$763$	−103.663	−	341.730i	−0.135862	−	0.447877i
$764$	−5.08628	+	171.382i	−0.00665744	+	0.224322i
$765$	−350.302	+	426.844i	−0.457911	+	0.557966i
$766$	580.445	−	563.474i	0.757762	−	0.735606i
$767$			1304.90i			1.70131i
$768$	102.666	+	106.964i	0.133679	+	0.139277i
$769$	75.6175			0.0983322			0.0491661	−	0.998791i	$-0.484344\pi$
$769$	75.6175			0.0983322			0.0491661	+	0.998791i	$0.484344\pi$
$770$	−66.0938	−	68.0844i	−0.0858361	−	0.0884213i
$771$	39.5885	+	32.4894i	0.0513469	+	0.0421393i
$772$	−74.2550	−	2.20375i	−0.0961852	−	0.00285459i
$773$	708.164	−	214.819i	0.916124	−	0.277903i	0.203194	−	0.979138i	$-0.434868\pi$
$773$	708.164	−	214.819i	0.916124	−	0.277903i	0.712930	+	0.701235i	$0.247368\pi$
$774$	−66.7229	−	798.755i	−0.0862053	−	1.03198i
$775$	−185.037	+	930.241i	−0.238757	+	1.20031i
$776$	1217.02	+	54.1981i	1.56832	+	0.0698429i
$777$	12.4446	+	62.5631i	0.0160162	+	0.0805188i
$778$	−844.220	−	467.477i	−1.08512	−	0.600870i
$779$	215.990	−	2192.99i	0.277266	−	2.81513i
$780$	−101.235	−	88.2347i	−0.129788	−	0.113121i
$781$	54.3442	−	179.149i	0.0695829	−	0.229384i
$782$	−335.451	+	217.013i	−0.428965	+	0.277510i
$783$	20.4548	+	8.47267i	0.0261237	+	0.0108208i
$784$	−336.815	−	163.547i	−0.429610	−	0.208606i
$785$	−88.1600	−	212.837i	−0.112306	−	0.271130i
$786$	40.4641	−	58.6561i	0.0514810	−	0.0746260i
$787$	−157.343	−	294.369i	−0.199928	−	0.374039i	0.761899	−	0.647695i	$-0.224267\pi$
$787$	−157.343	−	294.369i	−0.199928	−	0.374039i	−0.961828	+	0.273656i	$0.911767\pi$
$788$	−591.727	+	160.492i	−0.750922	+	0.203670i
$789$	−189.017	+	155.122i	−0.239565	+	0.196606i
$790$	65.1277	−	51.8514i	0.0824401	−	0.0656347i
$791$	25.4985	+	17.0376i	0.0322358	+	0.0215393i
$792$	−167.997	+	187.073i	−0.212118	+	0.236203i
$793$	302.962	−	202.433i	0.382045	−	0.255275i
$794$	−58.6613	+	30.2450i	−0.0738807	+	0.0380919i
$795$	−7.76476	+	14.5268i	−0.00976700	+	0.0182728i
$796$	−338.042	+	1470.08i	−0.424676	+	1.84683i
$797$	24.1737	+	245.440i	0.0303309	+	0.307955i	0.998366	+	0.0571406i	$0.0181983\pi$
$797$	24.1737	+	245.440i	0.0303309	+	0.307955i	−0.968035	+	0.250814i	$0.919302\pi$
$798$	62.7650	+	158.123i	0.0786529	+	0.198149i
$799$	695.892	−	695.892i	0.870954	−	0.870954i
$800$	−564.823	−	156.638i	−0.706029	−	0.195797i
$801$	−52.6392	+	52.6392i	−0.0657168	+	0.0657168i
$802$	−174.227	+	403.581i	−0.217241	+	0.503218i
$803$	21.8957	+	222.311i	0.0272673	+	0.276850i
$804$	35.7111	+	212.262i	0.0444168	+	0.264007i
$805$	49.9636	−	93.4752i	0.0620665	−	0.116118i
$806$	−706.997	+	2211.99i	−0.877168	+	2.74440i
$807$	−163.960	+	109.554i	−0.203172	+	0.135755i
$808$	−559.355	+	142.839i	−0.692271	+	0.176781i
$809$	−992.657	−	663.272i	−1.22702	−	0.819867i	−0.238525	−	0.971136i	$-0.576664\pi$
$809$	−992.657	−	663.272i	−1.22702	−	0.819867i	−0.988493	+	0.151270i	$0.951664\pi$
$810$	−370.179	−	42.0128i	−0.457012	−	0.0518676i
$811$	−539.447	+	442.713i	−0.665163	+	0.545885i	−0.905257	−	0.424865i	$-0.860322\pi$
$811$	−539.447	+	442.713i	−0.665163	+	0.545885i	0.240094	+	0.970750i	$0.422822\pi$
$812$	−5.58409	+	43.4407i	−0.00687696	+	0.0534984i
$813$	33.4704	+	62.6186i	0.0411690	+	0.0770217i
$814$	−28.5094	−	155.335i	−0.0350238	−	0.190829i
$815$	73.1485	+	176.596i	0.0897528	+	0.216682i
$816$	79.1572	−	214.279i	0.0970064	−	0.262596i
$817$	1240.51	+	513.834i	1.51837	+	0.628928i
$818$	−268.272	−	57.5123i	−0.327960	−	0.0703084i
$819$	−285.355	+	940.688i	−0.348418	+	1.14858i
$820$	250.043	−	744.063i	0.304930	−	0.907395i
$821$	−14.3689	+	145.890i	−0.0175017	+	0.177698i	−0.999961	−	0.00877664i	$-0.997206\pi$
$821$	−14.3689	+	145.890i	−0.0175017	+	0.177698i	0.982460	+	0.186475i	$0.0597063\pi$
$822$	−15.1168	+	4.34183i	−0.0183903	+	0.00528203i
$823$	−75.2056	−	378.084i	−0.0913798	−	0.459397i	−0.999198	−	0.0400341i	$-0.987253\pi$
$823$	−75.2056	−	378.084i	−0.0913798	−	0.459397i	0.907818	−	0.419363i	$-0.137747\pi$
$824$	494.520	+	121.465i	0.600146	+	0.147409i
$825$	−7.50698	+	37.7401i	−0.00909936	+	0.0457456i
$826$	380.281	−	449.604i	0.460388	−	0.544315i
$827$	469.278	−	142.354i	0.567446	−	0.172133i	0.00649094	−	0.999979i	$-0.497934\pi$
$827$	469.278	−	142.354i	0.567446	−	0.172133i	0.560956	+	0.827846i	$0.310434\pi$
$828$	−256.171	−	115.127i	−0.309385	−	0.139043i
$829$	−1173.42	−	962.999i	−1.41546	−	1.16164i	−0.962884	−	0.269915i	$-0.913004\pi$
$829$	−1173.42	−	962.999i	−1.41546	−	1.16164i	−0.452578	−	0.891725i	$-0.649496\pi$
$830$	−531.853	−	7.89046i	−0.640787	−	0.00950658i
$831$	−183.863			−0.221255
$832$	−1330.85	−	537.015i	−1.59957	−	0.645451i
$833$			576.884i			0.692537i
$834$	92.9788	+	1.37941i	0.111485	+	0.00165397i
$835$	42.0328	−	51.2172i	0.0503387	−	0.0613379i
$836$	−149.570	−	393.745i	−0.178912	−	0.470987i
$837$	−153.776	−	506.931i	−0.183722	−	0.605652i
$838$	−244.845	+	289.479i	−0.292178	+	0.345441i
$839$	505.641	+	100.578i	0.602671	+	0.119879i	0.486990	−	0.873408i	$-0.338095\pi$
$839$	505.641	+	100.578i	0.602671	+	0.119879i	0.115681	+	0.993286i	$0.463095\pi$
$840$	9.16662	+	59.9034i	0.0109126	+	0.0713136i
$841$	820.247	−	163.157i	0.975323	−	0.194004i
$842$	920.097	−	264.269i	1.09275	−	0.313858i
$843$	190.408	+	18.7535i	0.225869	+	0.0222462i
$844$	344.777	+	693.787i	0.408504	+	0.822023i
$845$	825.812	+	250.507i	0.977292	+	0.296458i
$846$	676.442	+	145.016i	0.799577	+	0.171414i
$847$	208.804	−	504.096i	0.246521	−	0.595155i
$848$	−27.6123	+	173.849i	−0.0325617	+	0.205011i
$849$	174.545	−	72.2989i	0.205589	−	0.0851578i
$850$	163.025	+	888.249i	0.191794	+	1.04500i
$851$	155.577	−	83.1576i	0.182817	−	0.0977175i
$852$	−94.6319	+	73.0741i	−0.111070	+	0.0857677i
$853$	508.683	+	619.832i	0.596346	+	0.726649i	0.980478	−	0.196629i	$-0.0629994\pi$
$853$	508.683	+	619.832i	0.596346	+	0.726649i	−0.384132	+	0.923278i	$0.625499\pi$
$854$	−163.379	−	18.5424i	−0.191310	−	0.0217124i
$855$	361.255	−	540.656i	0.422520	−	0.632346i
$856$	767.886	+	110.311i	0.897063	+	0.128868i
$857$	185.329	+	277.365i	0.216254	+	0.323647i	0.923697	−	0.383123i	$-0.125152\pi$
$857$	185.329	+	277.365i	0.216254	+	0.323647i	−0.707443	+	0.706770i	$0.750152\pi$
$858$	−28.6830	+	89.7408i	−0.0334301	+	0.104593i
$859$	347.928	+	185.972i	0.405039	+	0.216498i	0.661319	−	0.750105i	$-0.269997\pi$
$859$	347.928	+	185.972i	0.405039	+	0.216498i	−0.256280	+	0.966603i	$0.582497\pi$
$860$	389.629	+	277.406i	0.453057	+	0.322566i
$861$	221.359	−	21.8020i	0.257095	−	0.0253217i
$862$	−495.994	+	1148.93i	−0.575399	+	1.33286i
$863$	−181.904	−	181.904i	−0.210781	−	0.210781i	0.593818	−	0.804599i	$-0.297620\pi$
$863$	−181.904	−	181.904i	−0.210781	−	0.210781i	−0.804599	+	0.593818i	$0.797620\pi$
$864$	319.458	−	71.5547i	0.369743	−	0.0828180i
$865$	281.664	+	281.664i	0.325623	+	0.325623i
$866$	118.950	+	299.670i	0.137356	+	0.346039i
$867$	−183.690	+	18.0919i	−0.211868	+	0.0208672i
$868$	888.222	−	556.102i	1.02330	−	0.640671i
$869$	−51.5075	−	27.5313i	−0.0592721	−	0.0316816i
$870$	−5.75982	+	2.96969i	−0.00662048	+	0.00341343i
$871$	−1157.51	−	1732.34i	−1.32895	−	1.98891i
$872$	187.787	−	532.510i	0.215352	−	0.610677i
$873$	733.035	−	1097.06i	0.839673	−	1.25666i
$874$	368.070	−	293.039i	0.421132	−	0.335284i
$875$	−359.429	−	437.966i	−0.410776	−	0.500532i
$876$	70.9550	−	123.769i	0.0809988	−	0.141289i
$877$	267.546	−	143.006i	0.305070	−	0.163063i	−0.311758	−	0.950162i	$-0.600918\pi$
$877$	267.546	−	143.006i	0.305070	−	0.163063i	0.616827	+	0.787099i	$0.288418\pi$
$878$	−822.726	+	1192.61i	−0.937046	+	1.35833i
$879$	−136.734	+	56.6371i	−0.155556	+	0.0644336i
$880$	−20.4923	−	148.630i	−0.0232867	−	0.168898i
$881$	45.0818	−	108.837i	0.0511712	−	0.123538i	−0.896227	−	0.443596i	$-0.853702\pi$
$881$	45.0818	−	108.837i	0.0511712	−	0.123538i	0.947398	+	0.320058i	$0.103702\pi$
$882$	−340.488	+	220.272i	−0.386041	+	0.249741i
$883$	719.279	+	218.191i	0.814586	+	0.247102i	0.669972	−	0.742386i	$-0.266306\pi$
$883$	719.279	+	218.191i	0.814586	+	0.247102i	0.144614	+	0.989488i	$0.453806\pi$
$884$	151.355	+	2205.93i	0.171216	+	2.49539i
$885$	86.7076	+	8.53996i	0.0979747	+	0.00964967i
$886$	−546.828	−	302.799i	−0.617187	−	0.341760i
$887$	−649.173	+	129.129i	−0.731875	+	0.145579i	−0.546940	−	0.837172i	$-0.684207\pi$
$887$	−649.173	+	129.129i	−0.731875	+	0.145579i	−0.184935	+	0.982751i	$0.559207\pi$
$888$	−42.7056	+	91.3746i	−0.0480919	+	0.102899i
$889$	−727.626	−	144.734i	−0.818476	−	0.162805i
$890$	−3.69783	−	44.2675i	−0.00415486	−	0.0497388i
$891$	75.8723	+	250.118i	0.0851541	+	0.280716i
$892$	1062.41	−	1001.17i	1.19104	−	1.12238i
$893$	−735.201	+	895.845i	−0.823293	+	1.00319i
$894$	−200.802	−	206.850i	−0.224611	−	0.231376i
$895$			633.951i			0.708325i
$896$	302.042	+	572.869i	0.337101	+	0.639362i
$897$	−105.236			−0.117320
$898$	−748.117	+	726.244i	−0.833093	+	0.808735i
$899$	86.6248	+	71.0911i	0.0963568	+	0.0790780i
$900$	−462.014	+	435.381i	−0.513349	+	0.483757i
$901$	259.534	−	78.7287i	0.288051	−	0.0873793i
$902$	−548.785	+	45.8419i	−0.608409	+	0.0508225i
$903$	−26.4411	+	132.929i	−0.0292814	+	0.147208i
$904$	16.5448	+	45.5799i	0.0183018	+	0.0504202i
$905$	52.8233	+	265.561i	0.0583683	+	0.293437i
$906$	91.6470	−	165.506i	0.101156	−	0.182678i
$907$	4.25154	−	43.1666i	0.00468748	−	0.0475927i	−0.992556	−	0.121785i	$-0.961138\pi$
$907$	4.25154	−	43.1666i	0.00468748	−	0.0475927i	0.997244	+	0.0741927i	$0.0236380\pi$
$908$	83.3579	+	1214.90i	0.0918038	+	1.33800i
$909$	−181.504	+	598.340i	−0.199675	+	0.658240i
$910$	−318.619	−	492.509i	−0.350131	−	0.541219i
$911$	363.796	+	150.689i	0.399337	+	0.165411i	0.573308	−	0.819340i	$-0.305660\pi$
$911$	363.796	+	150.689i	0.399337	+	0.165411i	−0.173971	+	0.984751i	$0.555660\pi$
$912$	−68.0324	+	260.252i	−0.0745970	+	0.285364i
$913$	142.806	+	344.765i	0.156414	+	0.377618i
$914$	−636.005	−	438.750i	−0.695848	−	0.480032i
$915$	−11.4684	−	21.4559i	−0.0125338	−	0.0234491i
$916$	250.757	−	437.405i	0.273752	−	0.477516i
$917$	240.610	−	197.464i	0.262389	−	0.215337i
$918$	−314.166	−	394.606i	−0.342228	−	0.429854i
$919$	−183.373	−	122.526i	−0.199535	−	0.133325i	0.451789	−	0.892125i	$-0.350786\pi$
$919$	−183.373	−	122.526i	−0.199535	−	0.133325i	−0.651324	+	0.758800i	$0.725786\pi$
$920$	151.170	−	72.3476i	0.164315	−	0.0786387i
$921$	−279.396	+	186.686i	−0.303361	+	0.202700i
$922$	719.372	+	1395.25i	0.780230	+	1.51328i
$923$	545.548	−	1020.65i	0.591060	−	1.10580i
$924$	36.0354	−	22.5612i	0.0389993	−	0.0244169i
$925$	−39.0841	−	396.827i	−0.0422531	−	0.429002i
$926$	−300.578	+	119.311i	−0.324598	+	0.128845i
$927$	389.984	−	389.984i	0.420695	−	0.420695i
$928$	−47.7798	+	50.1302i	−0.0514868	+	0.0540196i
$929$	−878.158	+	878.158i	−0.945273	+	0.945273i	−0.998578	−	0.0533057i	$-0.983024\pi$
$929$	−878.158	+	878.158i	−0.945273	+	0.945273i	0.0533057	+	0.998578i	$0.483024\pi$
$930$	142.354	+	61.4546i	0.153069	+	0.0660802i
$931$	−66.5857	−	676.056i	−0.0715206	−	0.726161i
$932$	223.524	+	159.144i	0.239833	+	0.170755i
$933$	−92.7294	+	173.484i	−0.0993884	+	0.185943i
$934$	949.417	+	303.454i	1.01651	+	0.324897i
$935$	−192.207	+	128.429i	−0.205569	+	0.137357i
$936$	−1244.19	+	931.624i	−1.32926	+	0.995324i
$937$	763.050	+	509.853i	0.814354	+	0.544134i	0.891571	−	0.452880i	$-0.149604\pi$
$937$	763.050	+	509.853i	0.814354	+	0.544134i	−0.0772174	+	0.997014i	$0.524604\pi$
$938$	−106.026	+	934.204i	−0.113034	+	0.995953i
$939$	−28.4817	+	23.3743i	−0.0303320	+	0.0248928i
$940$	−326.742	+	252.308i	−0.347597	+	0.268412i
$941$	437.478	+	818.463i	0.464907	+	0.869780i	0.999693	+	0.0247924i	$0.00789247\pi$
$941$	437.478	+	818.463i	0.464907	+	0.869780i	−0.534785	+	0.844988i	$0.679608\pi$
$942$	101.524	−	18.6332i	0.107775	−	0.0197805i
$943$	−235.398	−	568.302i	−0.249627	−	0.602653i
$944$	905.463	−	216.967i	0.959177	−	0.229838i
$945$	123.625	+	51.2072i	0.130820	+	0.0541875i
$946$	70.3383	−	328.100i	0.0743533	−	0.346828i
$947$	307.184	−	1012.65i	0.324376	−	1.06932i	−0.631456	−	0.775411i	$-0.717543\pi$
$947$	307.184	−	1012.65i	0.324376	−	1.06932i	0.955832	−	0.293913i	$-0.0949574\pi$
$948$	16.5993	+	33.4024i	0.0175098	+	0.0352346i
$949$	−135.355	+	1374.29i	−0.142630	+	1.44814i
$950$	−293.575	−	1022.13i	−0.309026	−	1.07593i
$951$	39.7763	+	199.969i	0.0418258	+	0.210273i
$952$	590.712	−	804.160i	0.620495	−	0.844705i
$953$	29.0197	−	145.892i	0.0304509	−	0.153087i	−0.962568	−	0.271039i	$-0.912633\pi$
$953$	29.0197	−	145.892i	0.0304509	−	0.153087i	0.993019	+	0.117952i	$0.0376328\pi$
$954$	145.565	+	123.121i	0.152584	+	0.129058i
$955$	−106.040	+	32.1669i	−0.111037	+	0.0336826i
$956$	−454.245	−	1195.80i	−0.475152	−	1.25084i
$957$	3.51439	+	2.88418i	0.00367230	+	0.00301378i
$958$	−0.0725073	+	4.88733i	−7.56861e−5	+	0.00510159i
$959$	−68.7008			−0.0716379
$960$	−44.3930	+	84.9168i	−0.0462428	+	0.0884550i
$961$		−	1720.27i		−	1.79008i
$962$	14.4825	−	976.186i	0.0150546	−	1.01475i
$963$	533.027	−	649.495i	0.553506	−	0.674450i
$964$	37.8749	+	17.0216i	0.0392893	+	0.0176572i
$965$	−13.9370	−	45.9442i	−0.0144425	−	0.0476106i
$966$	36.2590	+	30.6683i	0.0375351	+	0.0317477i
$967$	1239.75	+	246.602i	1.28206	+	0.255017i	0.788683	−	0.614800i	$-0.210763\pi$
$967$	1239.75	+	246.602i	1.28206	+	0.255017i	0.493375	+	0.869817i	$0.335763\pi$
$968$	737.956	−	446.924i	0.762351	−	0.461698i
$969$	406.489	−	80.8556i	0.419493	−	0.0834424i
$970$	217.348	+	756.735i	0.224070	+	0.780139i
$971$	−40.5796	−	3.99674i	−0.0417915	−	0.00411611i	0.0770998	−	0.997023i	$-0.475434\pi$
$971$	−40.5796	−	3.99674i	−0.0417915	−	0.00411611i	−0.118891	+	0.992907i	$0.537934\pi$
$972$	170.492	−	507.340i	0.175403	−	0.521955i
$973$	388.691	+	117.908i	0.399477	+	0.121180i
$974$	−72.1701	+	336.645i	−0.0740966	+	0.345631i
$975$	−91.0304	+	219.767i	−0.0933645	+	0.225402i
$976$	−190.840	−	176.564i	−0.195533	−	0.180906i
$977$	−1003.78	+	415.781i	−1.02741	+	0.425569i	−0.831779	−	0.555107i	$-0.812677\pi$
$977$	−1003.78	+	415.781i	−1.02741	+	0.425569i	−0.195636	+	0.980677i	$0.562677\pi$
$978$	−84.2370	+	15.4604i	−0.0861319	+	0.0158082i
$979$	−27.4848	+	14.6910i	−0.0280744	+	0.0150061i
$980$	30.8523	−	240.011i	0.0314819	−	0.244909i
$981$	−387.969	−	472.741i	−0.395483	−	0.481897i
$982$	−32.5485	+	286.789i	−0.0331451	+	0.292046i
$983$	−292.702	+	438.059i	−0.297764	+	0.445635i	−0.949940	−	0.312433i	$-0.898856\pi$
$983$	−292.702	+	438.059i	−0.297764	+	0.445635i	0.652176	+	0.758067i	$0.273856\pi$
$984$	302.491	+	179.426i	0.307409	+	0.182344i
$985$	−220.142	−	329.466i	−0.223495	−	0.334483i
$986$	101.635	+	32.4846i	0.103078	+	0.0329458i
$987$	−103.166	−	55.1436i	−0.104525	−	0.0558699i
$988$	−431.989	−	2567.68i	−0.437236	−	2.59887i
$989$	373.009	−	36.7381i	0.377157	−	0.0371468i
$990$	−149.192	−	64.4064i	−0.150699	−	0.0650570i
$991$	−632.357	−	632.357i	−0.638100	−	0.638100i	0.311986	−	0.950087i	$-0.399006\pi$
$991$	−632.357	−	632.357i	−0.638100	−	0.638100i	−0.950087	+	0.311986i	$0.899006\pi$
$992$	1652.43	+	122.792i	1.66576	+	0.123782i
$993$	118.452	+	118.452i	0.119287	+	0.119287i
$994$	−485.410	+	192.678i	−0.488340	+	0.193841i
$995$	−970.202	+	95.5566i	−0.975078	+	0.0960368i
$996$	53.4087	−	232.264i	0.0536232	−	0.233197i
$997$	887.928	+	474.607i	0.890599	+	0.476035i	0.852193	−	0.523227i	$-0.175272\pi$
$997$	887.928	+	474.607i	0.890599	+	0.476035i	0.0384060	+	0.999262i	$0.487772\pi$
$998$	−329.201	−	638.497i	−0.329860	−	0.639776i
$999$	123.731	+	185.177i	0.123855	+	0.185362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.l.a.43.9	yes	496
128.3	odd	32	inner	128.3.l.a.3.9	✓	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.3.l.a.3.9	✓	496	128.3	odd	32	inner
128.3.l.a.43.9	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)

\(f(q)\)	\(=\)	\(q+(-1.39308 - 1.43504i) q^{2} +(0.447688 + 0.367408i) q^{3} +(-0.118660 + 3.99824i) q^{4} +(-2.47385 + 0.750435i) q^{5} +(-0.0964209 - 1.15428i) q^{6} +(0.987061 - 4.96229i) q^{7} +(5.90292 - 5.39958i) q^{8} +(-1.69038 - 8.49810i) q^{9} +O(q^{10})\)	\(q+(-1.39308 - 1.43504i) q^{2} +(0.447688 + 0.367408i) q^{3} +(-0.118660 + 3.99824i) q^{4} +(-2.47385 + 0.750435i) q^{5} +(-0.0964209 - 1.15428i) q^{6} +(0.987061 - 4.96229i) q^{7} +(5.90292 - 5.39958i) q^{8} +(-1.69038 - 8.49810i) q^{9} +(4.52318 + 2.50465i) q^{10} +(0.355541 - 3.60986i) q^{11} +(-1.52211 + 1.74637i) q^{12} +(6.50922 - 21.4580i) q^{13} +(-8.49613 + 5.49640i) q^{14} +(-1.38323 - 0.572953i) q^{15} +(-15.9718 - 0.948863i) q^{16} +(9.43380 + 22.7752i) q^{17} +(-9.84025 + 14.2643i) q^{18} +(-13.6843 - 25.6016i) q^{19} +(-2.70687 - 9.98011i) q^{20} +(2.26508 - 1.85891i) q^{21} +(-5.67558 + 4.51861i) q^{22} +(-6.73776 - 4.50203i) q^{23} +(4.62652 - 0.248547i) q^{24} +(-15.2299 + 10.1763i) q^{25} +(-39.8609 + 20.5517i) q^{26} +(4.82259 - 9.02243i) q^{27} +(19.7233 + 4.53533i) q^{28} +(0.212124 + 2.15373i) q^{29} +(1.10474 + 2.78316i) q^{30} +(36.6146 - 36.6146i) q^{31} +(20.8884 + 24.2420i) q^{32} +(1.48547 - 1.48547i) q^{33} +(19.5412 - 45.2655i) q^{34} +(1.28203 + 13.0167i) q^{35} +(34.1780 - 5.75015i) q^{36} +(-10.2620 + 19.1989i) q^{37} +(-17.6759 + 55.3026i) q^{38} +(10.7979 - 7.21496i) q^{39} +(-10.5509 + 17.7875i) q^{40} +(63.1162 + 42.1729i) q^{41} +(-5.82304 - 0.660874i) q^{42} +(-35.7546 + 29.3430i) q^{43} +(14.3909 + 1.84988i) q^{44} +(10.5590 + 19.7545i) q^{45} +(2.92566 + 15.9406i) q^{46} +(-15.2774 - 36.8829i) q^{47} +(-6.80178 - 6.29298i) q^{48} +(21.6200 + 8.95532i) q^{49} +(35.8199 + 7.67910i) q^{50} +(-4.14440 + 13.6622i) q^{51} +(85.0219 + 28.5716i) q^{52} +(1.07836 - 10.9488i) q^{53} +(-19.6658 + 5.64837i) q^{54} +(1.82941 + 9.19709i) q^{55} +(-20.9678 - 34.6217i) q^{56} +(3.27992 - 16.4893i) q^{57} +(2.79517 - 3.30472i) q^{58} +(-55.6877 + 16.8927i) q^{59} +(2.45494 - 5.46250i) q^{60} +(12.5610 + 10.3085i) q^{61} +(-103.550 - 1.53625i) q^{62} -43.8386 q^{63} +(5.68900 - 63.7466i) q^{64} +57.9687i q^{65} +(-4.20107 - 0.0623261i) q^{66} +(58.9442 - 71.8237i) q^{67} +(-92.1801 + 35.0161i) q^{68} +(-1.36233 - 4.49101i) q^{69} +(16.8935 - 19.9731i) q^{70} +(50.6193 + 10.0688i) q^{71} +(-55.8644 - 41.0363i) q^{72} +(-60.4009 + 12.0145i) q^{73} +(41.8469 - 12.0192i) q^{74} +(-10.5571 - 1.03979i) q^{75} +(103.985 - 51.6754i) q^{76} +(-17.5623 - 5.32745i) q^{77} +(-25.3961 - 5.44444i) q^{78} +(6.16159 - 14.8754i) q^{79} +(40.2241 - 9.63848i) q^{80} +(-66.5714 + 27.5748i) q^{81} +(-27.4062 - 149.324i) q^{82} +(-90.7299 + 48.4961i) q^{83} +(7.16357 + 9.27692i) q^{84} +(-40.4292 - 49.2631i) q^{85} +(91.9172 + 10.4320i) q^{86} +(-0.696332 + 1.04213i) q^{87} +(-17.3930 - 23.2285i) q^{88} +(-4.77326 - 7.14369i) q^{89} +(13.6389 - 42.6722i) q^{90} +(-100.056 - 53.4810i) q^{91} +(18.7997 - 26.4050i) q^{92} +(29.8445 - 2.93942i) q^{93} +(-31.6457 + 73.3045i) q^{94} +(53.0654 + 53.0654i) q^{95} +(0.444768 + 18.5274i) q^{96} +(107.677 + 107.677i) q^{97} +(-17.2672 - 43.5010i) q^{98} +(-31.2780 + 3.08061i) 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

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