LMFDB - Embedded newform 128.3.l.a.43.7

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			43.7
Character	$\chi$	$=$	128.43
Dual form			128.3.l.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57051 + 1.23834i) q^{2} +(-3.06977 - 2.51930i) q^{3} +(0.933028 - 3.88966i) q^{4} +(-2.31969 + 0.703669i) q^{5} +(7.94087 + 0.155169i) q^{6} +(0.668264 - 3.35959i) q^{7} +(3.35139 + 7.26417i) q^{8} +(1.32084 + 6.64029i) q^{9} +O(q^{10})$	\(q+(-1.57051 + 1.23834i) q^{2} +(-3.06977 - 2.51930i) q^{3} +(0.933028 - 3.88966i) q^{4} +(-2.31969 + 0.703669i) q^{5} +(7.94087 + 0.155169i) q^{6} +(0.668264 - 3.35959i) q^{7} +(3.35139 + 7.26417i) q^{8} +(1.32084 + 6.64029i) q^{9} +(2.77172 - 3.97768i) q^{10} +(-0.756988 + 7.68583i) q^{11} +(-12.6634 + 9.58981i) q^{12} +(-5.37205 + 17.7093i) q^{13} +(3.11080 + 6.10382i) q^{14} +(8.89366 + 3.68388i) q^{15} +(-14.2589 - 7.25832i) q^{16} +(7.14813 + 17.2571i) q^{17} +(-10.2973 - 8.79303i) q^{18} +(-5.16252 - 9.65839i) q^{19} +(0.572702 + 9.67933i) q^{20} +(-10.5152 + 8.62963i) q^{21} +(-8.32881 - 13.0081i) q^{22} +(9.35088 + 6.24806i) q^{23} +(8.01261 - 30.7425i) q^{24} +(-15.9010 + 10.6247i) q^{25} +(-13.4932 - 34.4651i) q^{26} +(-4.17386 + 7.80874i) q^{27} +(-12.4442 - 5.73391i) q^{28} +(3.05110 + 30.9783i) q^{29} +(-18.5295 + 5.22780i) q^{30} +(31.4307 - 31.4307i) q^{31} +(31.3821 - 6.25809i) q^{32} +(21.6867 - 21.6867i) q^{33} +(-32.5964 - 18.2507i) q^{34} +(0.813877 + 8.26343i) q^{35} +(27.0609 + 1.05797i) q^{36} +(-1.11698 + 2.08972i) q^{37} +(20.0682 + 8.77569i) q^{38} +(61.1060 - 40.8297i) q^{39} +(-12.8857 - 14.4923i) q^{40} +(-21.7739 - 14.5488i) q^{41} +(5.82790 - 26.5744i) q^{42} +(-24.7111 + 20.2799i) q^{43} +(29.1890 + 10.1155i) q^{44} +(-7.73649 - 14.4740i) q^{45} +(-22.4229 + 1.76691i) q^{46} +(10.7217 + 25.8845i) q^{47} +(25.4858 + 58.2039i) q^{48} +(34.4298 + 14.2613i) q^{49} +(11.8157 - 36.3770i) q^{50} +(21.5327 - 70.9838i) q^{51} +(63.8708 + 37.4187i) q^{52} +(0.467870 - 4.75036i) q^{53} +(-3.11477 - 17.4324i) q^{54} +(-3.65230 - 18.3614i) q^{55} +(26.6442 - 6.40491i) q^{56} +(-8.48461 + 42.6550i) q^{57} +(-43.1535 - 44.8736i) q^{58} +(-63.8118 + 19.3571i) q^{59} +(22.6271 - 31.1562i) q^{60} +(-75.2167 - 61.7287i) q^{61} +(-10.4405 + 88.2842i) q^{62} +23.1913 q^{63} +(-41.5364 + 48.6901i) q^{64} -44.8601i q^{65} +(-7.20375 + 60.9147i) q^{66} +(-39.2184 + 47.7878i) q^{67} +(73.7938 - 11.7024i) q^{68} +(-12.9644 - 42.7378i) q^{69} +(-11.5111 - 11.9700i) q^{70} +(-111.715 - 22.2214i) q^{71} +(-43.8096 + 31.8490i) q^{72} +(-105.633 + 21.0117i) q^{73} +(-0.833552 - 4.66512i) q^{74} +(75.5791 + 7.44389i) q^{75} +(-42.3847 + 11.0689i) q^{76} +(25.3154 + 7.67933i) q^{77} +(-45.4067 + 139.794i) q^{78} +(-8.95686 + 21.6238i) q^{79} +(38.1837 + 6.80347i) q^{80} +(88.7805 - 36.7741i) q^{81} +(52.2126 - 4.11431i) q^{82} +(22.6453 - 12.1042i) q^{83} +(23.7553 + 48.9524i) q^{84} +(-28.7247 - 35.0012i) q^{85} +(13.6958 - 62.4506i) q^{86} +(68.6775 - 102.783i) q^{87} +(-58.3681 + 20.2593i) q^{88} +(58.8575 + 88.0865i) q^{89} +(30.0740 + 13.1511i) q^{90} +(55.9060 + 29.8824i) q^{91} +(33.0275 - 30.5421i) q^{92} +(-175.668 + 17.3018i) q^{93} +(-48.8924 - 27.3749i) q^{94} +(18.7717 + 18.7717i) q^{95} +(-112.102 - 59.8500i) q^{96} +(67.0884 + 67.0884i) q^{97} +(-71.7329 + 20.2383i) q^{98} +(-52.0360 + 5.12510i) 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 $

$2$	−1.57051	+	1.23834i	−0.785257	+	0.619170i
$2$	−1.57051	+	1.23834i	−0.785257	+	0.619170i
$3$	−3.06977	−	2.51930i	−1.02326	−	0.839766i	−0.0360737	−	0.999349i	$-0.511485\pi$
$3$	−3.06977	−	2.51930i	−1.02326	−	0.839766i	−0.987185	+	0.159583i	$0.948985\pi$
$4$	0.933028	−	3.88966i	0.233257	−	0.972415i
$5$	−2.31969	+	0.703669i	−0.463937	+	0.140734i	−0.513595	−	0.858032i	$-0.671687\pi$
$5$	−2.31969	+	0.703669i	−0.463937	+	0.140734i	0.0496583	+	0.998766i	$0.484187\pi$
$6$	7.94087	+	0.155169i	1.32348	+	0.0258615i
$7$	0.668264	−	3.35959i	0.0954663	−	0.479941i	−0.903242	−	0.429131i	$-0.858820\pi$
$7$	0.668264	−	3.35959i	0.0954663	−	0.479941i	0.998708	−	0.0508100i	$-0.0161803\pi$
$8$	3.35139	+	7.26417i	0.418924	+	0.908021i
$9$	1.32084	+	6.64029i	0.146760	+	0.737810i
$10$	2.77172	−	3.97768i	0.277172	−	0.397768i
$11$	−0.756988	+	7.68583i	−0.0688171	+	0.698712i	0.897441	+	0.441135i	$0.145424\pi$
$11$	−0.756988	+	7.68583i	−0.0688171	+	0.698712i	−0.966258	+	0.257577i	$0.917076\pi$
$12$	−12.6634	+	9.58981i	−1.05528	+	0.799150i
$13$	−5.37205	+	17.7093i	−0.413235	+	1.36225i	0.465545	+	0.885024i	$0.345858\pi$
$13$	−5.37205	+	17.7093i	−0.413235	+	1.36225i	−0.878779	+	0.477228i	$0.841642\pi$
$14$	3.11080	+	6.10382i	0.222200	+	0.435987i
$15$	8.89366	+	3.68388i	0.592911	+	0.245592i
$16$	−14.2589	−	7.25832i	−0.891182	−	0.453645i
$17$	7.14813	+	17.2571i	0.420479	+	1.01512i	0.982207	+	0.187803i	$0.0601367\pi$
$17$	7.14813	+	17.2571i	0.420479	+	1.01512i	−0.561728	+	0.827322i	$0.689863\pi$
$18$	−10.2973	−	8.79303i	−0.572074	−	0.488502i
$19$	−5.16252	−	9.65839i	−0.271712	−	0.508337i	0.708646	−	0.705564i	$-0.249306\pi$
$19$	−5.16252	−	9.65839i	−0.271712	−	0.508337i	−0.980358	+	0.197227i	$0.936806\pi$
$20$	0.572702	+	9.67933i	0.0286351	+	0.483967i
$21$	−10.5152	+	8.62963i	−0.500725	+	0.410935i
$22$	−8.32881	−	13.0081i	−0.378582	−	0.591278i
$23$	9.35088	+	6.24806i	0.406560	+	0.271655i	0.741991	−	0.670410i	$-0.233882\pi$
$23$	9.35088	+	6.24806i	0.406560	+	0.271655i	−0.335431	+	0.942065i	$0.608882\pi$
$24$	8.01261	−	30.7425i	0.333859	−	1.28094i
$25$	−15.9010	+	10.6247i	−0.636038	+	0.424987i
$26$	−13.4932	−	34.4651i	−0.518970	−	1.32558i
$27$	−4.17386	+	7.80874i	−0.154587	+	0.289212i
$28$	−12.4442	−	5.73391i	−0.444434	−	0.204783i
$29$	3.05110	+	30.9783i	0.105210	+	1.06822i	0.892320	+	0.451404i	$0.149077\pi$
$29$	3.05110	+	30.9783i	0.105210	+	1.06822i	−0.787109	+	0.616814i	$0.788423\pi$
$30$	−18.5295	+	5.22780i	−0.617650	+	0.174260i
$31$	31.4307	−	31.4307i	1.01389	−	1.01389i	0.0139910	−	0.999902i	$-0.495546\pi$
$31$	31.4307	−	31.4307i	1.01389	−	1.01389i	0.999902	−	0.0139910i	$-0.00445361\pi$
$32$	31.3821	−	6.25809i	0.980691	−	0.195565i
$33$	21.6867	−	21.6867i	0.657172	−	0.657172i
$34$	−32.5964	−	18.2507i	−0.958719	−	0.536786i
$35$	0.813877	+	8.26343i	0.0232536	+	0.236098i
$36$	27.0609	+	1.05797i	0.751691	+	0.0293882i
$37$	−1.11698	+	2.08972i	−0.0301886	+	0.0564788i	−0.896563	−	0.442916i	$-0.853944\pi$
$37$	−1.11698	+	2.08972i	−0.0301886	+	0.0564788i	0.866375	+	0.499394i	$0.166444\pi$
$38$	20.0682	+	8.77569i	0.528110	+	0.230939i
$39$	61.1060	−	40.8297i	1.56682	−	1.04692i
$40$	−12.8857	−	14.4923i	−0.322143	−	0.362308i
$41$	−21.7739	−	14.5488i	−0.531070	−	0.354849i	0.260943	−	0.965354i	$-0.415967\pi$
$41$	−21.7739	−	14.5488i	−0.531070	−	0.354849i	−0.792013	+	0.610505i	$0.790967\pi$
$42$	5.82790	−	26.5744i	0.138760	−	0.632723i
$43$	−24.7111	+	20.2799i	−0.574677	+	0.471625i	−0.876276	−	0.481810i	$-0.839980\pi$
$43$	−24.7111	+	20.2799i	−0.574677	+	0.471625i	0.301599	+	0.953435i	$0.402480\pi$
$44$	29.1890	+	10.1155i	0.663386	+	0.229898i
$45$	−7.73649	−	14.4740i	−0.171922	−	0.321644i
$46$	−22.4229	+	1.76691i	−0.487455	+	0.0384110i
$47$	10.7217	+	25.8845i	0.228122	+	0.550734i	0.995949	−	0.0899228i	$-0.0286620\pi$
$47$	10.7217	+	25.8845i	0.228122	+	0.550734i	−0.767827	+	0.640657i	$0.778662\pi$
$48$	25.4858	+	58.2039i	0.530954	+	1.21258i
$49$	34.4298	+	14.2613i	0.702650	+	0.291047i
$50$	11.8157	−	36.3770i	0.236314	−	0.727540i
$51$	21.5327	−	70.9838i	0.422210	−	1.39184i
$52$	63.8708	+	37.4187i	1.22829	+	0.719591i
$53$	0.467870	−	4.75036i	0.00882773	−	0.0896295i	−0.989761	−	0.142732i	$-0.954411\pi$
$53$	0.467870	−	4.75036i	0.00882773	−	0.0896295i	0.998589	+	0.0531030i	$0.0169112\pi$
$54$	−3.11477	−	17.4324i	−0.0576810	−	0.322822i
$55$	−3.65230	−	18.3614i	−0.0664055	−	0.333843i
$56$	26.6442	−	6.40491i	0.475790	−	0.114373i
$57$	−8.48461	+	42.6550i	−0.148853	+	0.748334i
$58$	−43.1535	−	44.8736i	−0.744026	−	0.773682i
$59$	−63.8118	+	19.3571i	−1.08156	+	0.328086i	−0.780267	−	0.625447i	$-0.784917\pi$
$59$	−63.8118	+	19.3571i	−1.08156	+	0.328086i	−0.301289	+	0.953533i	$0.597417\pi$
$60$	22.6271	−	31.1562i	0.377118	−	0.519270i
$61$	−75.2167	−	61.7287i	−1.23306	−	1.01195i	−0.999213	−	0.0396728i	$-0.987368\pi$
$61$	−75.2167	−	61.7287i	−1.23306	−	1.01195i	−0.233847	−	0.972273i	$-0.575132\pi$
$62$	−10.4405	+	88.2842i	−0.168394	+	1.42394i
$63$	23.1913			0.368116
$64$	−41.5364	+	48.6901i	−0.649006	+	0.760783i
$65$		−	44.8601i		−	0.690156i
$66$	−7.20375	+	60.9147i	−0.109148	+	0.922950i
$67$	−39.2184	+	47.7878i	−0.585349	+	0.713250i	−0.978505	−	0.206221i	$-0.933883\pi$
$67$	−39.2184	+	47.7878i	−0.585349	+	0.713250i	0.393156	+	0.919472i	$0.371383\pi$
$68$	73.7938	−	11.7024i	1.08520	−	0.172095i
$69$	−12.9644	−	42.7378i	−0.187889	−	0.619388i
$70$	−11.5111	−	11.9700i	−0.164445	−	0.171000i
$71$	−111.715	−	22.2214i	−1.57345	−	0.312978i	−0.670227	−	0.742156i	$-0.733803\pi$
$71$	−111.715	−	22.2214i	−1.57345	−	0.312978i	−0.903220	+	0.429178i	$0.858803\pi$
$72$	−43.8096	+	31.8490i	−0.608467	+	0.442347i
$73$	−105.633	+	21.0117i	−1.44702	+	0.287831i	−0.855226	−	0.518255i	$-0.826582\pi$
$73$	−105.633	+	21.0117i	−1.44702	+	0.287831i	−0.591798	+	0.806086i	$0.701582\pi$
$74$	−0.833552	−	4.66512i	−0.0112642	−	0.0630422i
$75$	75.5791	+	7.44389i	1.00772	+	0.0992519i
$76$	−42.3847	+	11.0689i	−0.557693	+	0.145643i
$77$	25.3154	+	7.67933i	0.328771	+	0.0997315i
$78$	−45.4067	+	139.794i	−0.582137	+	1.79223i
$79$	−8.95686	+	21.6238i	−0.113378	+	0.273718i	−0.970375	−	0.241602i	$-0.922327\pi$
$79$	−8.95686	+	21.6238i	−0.113378	+	0.273718i	0.856997	+	0.515321i	$0.172327\pi$
$80$	38.1837	+	6.80347i	0.477296	+	0.0850434i
$81$	88.7805	−	36.7741i	1.09606	−	0.454001i
$82$	52.2126	−	4.11431i	0.636738	−	0.0501745i
$83$	22.6453	−	12.1042i	0.272835	−	0.145833i	−0.329306	−	0.944223i	$-0.606815\pi$
$83$	22.6453	−	12.1042i	0.272835	−	0.145833i	0.602141	+	0.798390i	$0.294315\pi$
$84$	23.7553	+	48.9524i	0.282801	+	0.582766i
$85$	−28.7247	−	35.0012i	−0.337938	−	0.411779i
$86$	13.6958	−	62.4506i	0.159253	−	0.726170i
$87$	68.6775	−	102.783i	0.789396	−	1.18141i
$88$	−58.3681	+	20.2593i	−0.663274	+	0.230219i
$89$	58.8575	+	88.0865i	0.661321	+	0.989736i	0.998827	+	0.0484133i	$0.0154164\pi$
$89$	58.8575	+	88.0865i	0.661321	+	0.989736i	−0.337507	+	0.941323i	$0.609584\pi$
$90$	30.0740	+	13.1511i	0.334155	+	0.146124i
$91$	55.9060	+	29.8824i	0.614351	+	0.328378i
$92$	33.0275	−	30.5421i	0.358994	−	0.331980i
$93$	−175.668	+	17.3018i	−1.88891	+	0.186041i
$94$	−48.8924	−	27.3749i	−0.520132	−	0.291222i
$95$	18.7717	+	18.7717i	0.197597	+	0.197597i
$96$	−112.102	−	59.8500i	−1.16773	−	0.623437i
$97$	67.0884	+	67.0884i	0.691633	+	0.691633i	0.962591	−	0.270958i	$-0.0873406\pi$
$97$	67.0884	+	67.0884i	0.691633	+	0.691633i	−0.270958	+	0.962591i	$0.587341\pi$
$98$	−71.7329	+	20.2383i	−0.731968	+	0.206513i
$99$	−52.0360	+	5.12510i	−0.525616	+	0.0517687i
$100$	26.4904	+	71.7624i	0.264904	+	0.717624i
$101$	59.8780	+	32.0054i	0.592851	+	0.316886i	0.740397	−	0.672170i	$-0.234637\pi$
$101$	59.8780	+	32.0054i	0.592851	+	0.316886i	−0.147546	+	0.989055i	$0.547137\pi$
$102$	54.0847	+	138.146i	0.530242	+	1.35437i
$103$	−89.8658	−	134.494i	−0.872484	−	1.30576i	−0.951108	−	0.308860i	$-0.900053\pi$
$103$	−89.8658	−	134.494i	−0.872484	−	1.30576i	0.0786241	−	0.996904i	$-0.474947\pi$
$104$	−146.647	+	20.3272i	−1.41007	+	0.195454i
$105$	18.3196	−	27.4173i	0.174473	−	0.261117i
$106$	5.14777	+	8.03989i	0.0485638	+	0.0758480i
$107$	31.8430	+	38.8008i	0.297598	+	0.362624i	0.900245	−	0.435384i	$-0.143387\pi$
$107$	31.8430	+	38.8008i	0.297598	+	0.362624i	−0.602647	+	0.798008i	$0.705887\pi$
$108$	26.4790	+	23.5207i	0.245176	+	0.217784i
$109$	152.305	−	81.4088i	1.39729	−	0.746869i	0.410964	−	0.911652i	$-0.365192\pi$
$109$	152.305	−	81.4088i	1.39729	−	0.746869i	0.986330	+	0.164782i	$0.0526921\pi$
$110$	28.4736	+	24.3140i	0.258851	+	0.221036i
$111$	8.69349	−	3.60096i	0.0783197	−	0.0324411i
$112$	−33.9137	+	43.0536i	−0.302801	+	0.384407i
$113$	−79.7993	+	192.653i	−0.706189	+	1.70489i	0.00312314	+	0.999995i	$0.499006\pi$
$113$	−79.7993	+	192.653i	−0.706189	+	1.70489i	−0.709312	+	0.704895i	$0.750994\pi$
$114$	−39.4962	−	77.4972i	−0.346458	−	0.679800i
$115$	−26.0877	−	7.91361i	−0.226849	−	0.0688140i
$116$	123.342	+	17.0359i	1.06329	+	0.146861i
$117$	−124.690	−	12.2809i	−1.06573	−	0.104965i
$118$	76.2466	−	109.421i	0.646158	−	0.927299i
$119$	62.7537	−	12.4825i	0.527342	−	0.104895i
$120$	3.04582	+	76.9512i	0.0253818	+	0.641260i
$121$	60.1761	+	11.9698i	0.497323	+	0.0989238i
$122$	194.570	+	3.80201i	1.59484	+	0.0311640i
$123$	30.1880	+	99.5165i	0.245431	+	0.809077i
$124$	−92.9290	−	151.580i	−0.749427	−	1.22242i
$125$	67.8542	−	82.6806i	0.542834	−	0.661445i
$126$	−36.4223	+	28.7188i	−0.289066	+	0.227927i
$127$			106.511i			0.838668i	0.907832	+	0.419334i	$0.137736\pi$
$127$			106.511i			0.838668i	−0.907832	+	0.419334i	$0.862264\pi$
$128$	4.93853	−	127.905i	0.0385822	−	0.999255i
$129$	126.949			0.984098
$130$	55.5521	+	70.4534i	0.427324	+	0.541949i
$131$	−128.669	−	105.596i	−0.982209	−	0.806078i	−0.00119221	−	0.999999i	$-0.500379\pi$
$131$	−128.669	−	105.596i	−0.982209	−	0.806078i	−0.981017	+	0.193921i	$0.937879\pi$
$132$	−64.1195	−	104.588i	−0.485754	−	0.792334i
$133$	−35.8982	+	10.8896i	−0.269911	+	0.0818766i
$134$	2.41555	−	123.617i	0.0180265	−	0.922516i
$135$	4.18727	−	21.0508i	0.0310168	−	0.155932i
$136$	−101.403	+	109.761i	−0.745607	+	0.807063i
$137$	6.97564	+	35.0689i	0.0509171	+	0.255977i	0.997857	−	0.0654334i	$-0.0208430\pi$
$137$	6.97564	+	35.0689i	0.0509171	+	0.255977i	−0.946940	+	0.321411i	$0.895843\pi$
$138$	73.2847	+	51.0660i	0.531048	+	0.370044i
$139$	6.14086	−	62.3492i	0.0441788	−	0.448555i	−0.947494	−	0.319773i	$-0.896393\pi$
$139$	6.14086	−	62.3492i	0.0441788	−	0.448555i	0.991673	−	0.128782i	$-0.0411067\pi$
$140$	32.9013	+	4.54430i	0.235009	+	0.0324593i
$141$	32.2976	−	106.471i	0.229061	−	0.755112i
$142$	202.967	−	103.442i	1.42935	−	0.728463i
$143$	−132.044	−	54.6944i	−0.923384	−	0.382478i
$144$	29.3637	−	104.270i	0.203915	−	0.724100i
$145$	−28.8761	−	69.7130i	−0.199145	−	0.480779i
$146$	139.878	−	163.808i	0.958070	−	1.12198i
$147$	−69.7633	−	130.518i	−0.474581	−	0.887878i
$148$	7.08612	+	6.29442i	0.0478792	+	0.0425299i
$149$	97.6998	−	80.1802i	0.655703	−	0.538122i	−0.246658	−	0.969103i	$-0.579332\pi$
$149$	97.6998	−	80.1802i	0.655703	−	0.538122i	0.902361	+	0.430981i	$0.141832\pi$
$150$	−127.916	+	81.9019i	−0.852774	+	0.546012i
$151$	72.4085	+	48.3818i	0.479526	+	0.320409i	0.771734	−	0.635946i	$-0.219390\pi$
$151$	72.4085	+	48.3818i	0.479526	+	0.320409i	−0.292207	+	0.956355i	$0.594390\pi$
$152$	52.8586	−	69.8705i	0.347754	−	0.459674i
$153$	−105.151	+	70.2596i	−0.687261	+	0.459213i
$154$	−49.2677	+	19.2885i	−0.319920	+	0.125250i
$155$	−50.7925	+	95.0261i	−0.327694	+	0.613072i
$156$	−101.800	−	275.777i	−0.652565	−	1.76780i
$157$	−15.1577	−	153.899i	−0.0965459	−	0.980247i	−0.914397	−	0.404818i	$-0.867335\pi$
$157$	−15.1577	−	153.899i	−0.0965459	−	0.980247i	0.817851	−	0.575429i	$-0.195165\pi$
$158$	−12.7107	−	45.0521i	−0.0804475	−	0.285140i
$159$	−13.4038	+	13.4038i	−0.0843009	+	0.0843009i
$160$	−68.3930	+	36.5994i	−0.427456	+	0.228746i
$161$	27.2398	−	27.2398i	0.169191	−	0.169191i
$162$	−93.8922	+	167.695i	−0.579582	+	1.03515i
$163$	27.0348	+	274.489i	0.165857	+	1.68398i	0.613444	+	0.789738i	$0.289784\pi$
$163$	27.0348	+	274.489i	0.165857	+	1.68398i	−0.447587	+	0.894241i	$0.647716\pi$
$164$	−76.9056	+	71.1185i	−0.468937	+	0.433649i
$165$	−35.0460	+	65.5665i	−0.212400	+	0.397373i
$166$	−20.5757	+	47.0523i	−0.123950	+	0.283448i
$167$	120.067	−	80.2260i	0.718962	−	0.480395i	−0.141481	−	0.989941i	$-0.545187\pi$
$167$	120.067	−	80.2260i	0.718962	−	0.480395i	0.860444	+	0.509546i	$0.170187\pi$
$168$	−97.9277	−	47.4632i	−0.582903	−	0.282519i
$169$	−144.241	−	96.3791i	−0.853500	−	0.570290i
$170$	88.4559	+	19.3989i	0.520329	+	0.114111i
$171$	57.3157	−	47.0378i	0.335180	−	0.275075i
$172$	55.8257	+	115.040i	0.324568	+	0.668835i
$173$	−68.8001	−	128.716i	−0.397688	−	0.744022i	0.600776	−	0.799417i	$-0.294858\pi$
$173$	−68.8001	−	128.716i	−0.397688	−	0.744022i	−0.998465	+	0.0553948i	$0.982358\pi$
$174$	19.4215	+	246.468i	0.111618	+	1.41648i
$175$	25.0685	+	60.5208i	0.143249	+	0.345833i
$176$	66.5800	−	104.097i	0.378296	−	0.591461i
$177$	244.654	+	101.339i	1.38223	+	0.572537i
$178$	−201.518	−	65.4555i	−1.13212	−	0.367727i
$179$	−76.6054	+	252.534i	−0.427963	+	1.41081i	0.432657	+	0.901559i	$0.357576\pi$
$179$	−76.6054	+	252.534i	−0.427963	+	1.41081i	−0.860620	+	0.509247i	$0.829924\pi$
$180$	−63.5172	+	16.5877i	−0.352873	+	0.0921540i
$181$	−11.4658	+	116.415i	−0.0633472	+	0.643175i	0.910120	+	0.414346i	$0.135990\pi$
$181$	−11.4658	+	116.415i	−0.0633472	+	0.643175i	−0.973467	+	0.228829i	$0.926510\pi$
$182$	−124.806	+	22.2999i	−0.685745	+	0.122527i
$183$	75.3851	+	378.987i	0.411940	+	2.07096i
$184$	−14.0485	+	88.8661i	−0.0763507	+	0.482968i
$185$	1.12057	−	5.63346i	0.00605711	−	0.0304512i
$186$	254.464	−	244.710i	1.36809	−	1.31565i
$187$	−138.046	+	41.8759i	−0.738216	+	0.223935i
$188$	110.686	−	17.5529i	0.588753	−	0.0933663i
$189$	23.4449	+	19.2407i	0.124047	+	0.101803i
$190$	−52.7271	−	6.23548i	−0.277511	−	0.0328183i
$191$	−305.021			−1.59697			−0.798485	−	0.602014i	$-0.794365\pi$
$191$	−305.021			−1.59697			−0.798485	+	0.602014i	$0.794365\pi$
$192$	250.172	−	44.8252i	1.30298	−	0.233464i
$193$		−	355.972i		−	1.84441i	−0.386697	−	0.922207i	$-0.626384\pi$
$193$		−	355.972i		−	1.84441i	0.386697	−	0.922207i	$-0.373616\pi$
$194$	−188.441	−	22.2850i	−0.971347	−	0.114871i
$195$	−113.016	+	137.710i	−0.579569	+	0.706207i
$196$	87.5956	−	120.614i	0.446916	−	0.615378i
$197$	37.9802	+	125.204i	0.192793	+	0.635554i	0.999033	+	0.0439651i	$0.0139990\pi$
$197$	37.9802	+	125.204i	0.192793	+	0.635554i	−0.806240	+	0.591589i	$0.798501\pi$
$198$	75.3767	−	72.4873i	0.380690	−	0.366098i
$199$	−22.0823	−	4.39244i	−0.110966	−	0.0220726i	0.139295	−	0.990251i	$-0.455516\pi$
$199$	−22.0823	−	4.39244i	−0.110966	−	0.0220726i	−0.250261	+	0.968178i	$0.580516\pi$
$200$	−130.470	−	79.8998i	−0.652349	−	0.399499i
$201$	240.783	−	47.8948i	1.19793	−	0.238283i
$202$	−133.673	+	23.8843i	−0.661747	+	0.118239i
$203$	106.113	+	10.4513i	0.522726	+	0.0514840i
$204$	−256.012	−	149.985i	−1.25496	−	0.735219i
$205$	60.7461	+	18.4271i	0.296322	+	0.0898884i
$206$	307.684	+	99.9398i	1.49361	+	0.485145i
$207$	−29.1380	+	70.3453i	−0.140763	+	0.339832i
$208$	205.139	−	213.523i	0.986247	−	1.02655i
$209$	78.1407	−	32.3669i	0.373879	−	0.154866i
$210$	5.18066	+	65.7451i	0.0246698	+	0.313072i
$211$	246.968	−	132.007i	1.17046	−	0.625626i	0.232580	−	0.972577i	$-0.425283\pi$
$211$	246.968	−	132.007i	1.17046	−	0.625626i	0.937883	+	0.346951i	$0.112783\pi$
$212$	−18.0408	−	6.25207i	−0.0850979	−	0.0294909i
$213$	286.957	+	349.658i	1.34721	+	1.64158i
$214$	−98.0584	−	21.5047i	−0.458217	−	0.100489i
$215$	43.0517	−	64.4314i	0.200240	−	0.299681i
$216$	−70.7122	−	4.14950i	−0.327371	−	0.0192106i
$217$	−84.5902	−	126.598i	−0.389817	−	0.583402i
$218$	−138.385	+	316.459i	−0.634796	+	1.45165i
$219$	377.204	+	201.620i	1.72239	+	0.920637i
$220$	−74.8272	−	2.92545i	−0.340124	−	0.0132975i
$221$	−344.011	+	33.8822i	−1.55661	+	0.153313i
$222$	−9.19403	+	16.4208i	−0.0414145	+	0.0739678i
$223$	179.457	+	179.457i	0.804739	+	0.804739i	0.983832	−	0.179093i	$-0.0573162\pi$
$223$	179.457	+	179.457i	0.804739	+	0.804739i	−0.179093	+	0.983832i	$0.557316\pi$
$224$	−0.0530913	−	109.613i	−0.000237015	−	0.489344i
$225$	−91.5535	−	91.5535i	−0.406905	−	0.406905i
$226$	−113.243	−	401.382i	−0.501077	−	1.77603i
$227$	−343.513	+	33.8331i	−1.51328	+	0.149045i	−0.820307	−	0.571923i	$-0.806197\pi$
$227$	−343.513	+	33.8331i	−1.51328	+	0.149045i	−0.692968	+	0.720968i	$0.743697\pi$
$228$	157.997	+	72.8006i	0.692970	+	0.319301i
$229$	320.788	+	171.464i	1.40082	+	0.748753i	0.986865	−	0.161545i	$-0.0516476\pi$
$229$	320.788	+	171.464i	1.40082	+	0.748753i	0.413953	+	0.910298i	$0.364148\pi$
$230$	50.7708	−	19.8770i	0.220743	−	0.0864216i
$231$	−58.3659	−	87.3508i	−0.252666	−	0.378142i
$232$	−214.806	+	125.984i	−0.925890	+	0.543035i
$233$	121.267	−	181.488i	0.520458	−	0.778920i	−0.474388	−	0.880316i	$-0.657331\pi$
$233$	121.267	−	181.488i	0.520458	−	0.778920i	0.994846	+	0.101395i	$0.0323307\pi$
$234$	211.036	−	135.122i	0.901864	−	0.577444i
$235$	−43.0851	−	52.4994i	−0.183341	−	0.223402i
$236$	15.7543	+	266.267i	0.0667557	+	1.12825i
$237$	81.9723	−	43.8151i	0.345874	−	0.184874i
$238$	−83.0980	+	97.3143i	−0.349151	+	0.408884i
$239$	2.16576	−	0.897087i	0.00906176	−	0.00375350i	−0.378148	−	0.925745i	$-0.623439\pi$
$239$	2.16576	−	0.897087i	0.00906176	−	0.00375350i	0.387210	+	0.921992i	$0.373439\pi$
$240$	−100.075	−	117.081i	−0.416980	−	0.487838i
$241$	−56.5810	+	136.599i	−0.234776	+	0.566800i	−0.996728	−	0.0808346i	$-0.974241\pi$
$241$	−56.5810	+	136.599i	−0.234776	+	0.566800i	0.761951	+	0.647634i	$0.224241\pi$
$242$	−109.330	+	55.7198i	−0.451777	+	0.230247i
$243$	−288.924	−	87.6443i	−1.18899	−	0.360676i
$244$	−310.283	+	234.973i	−1.27165	+	0.963003i
$245$	−89.9016	−	8.85454i	−0.366945	−	0.0361410i
$246$	−170.646	−	118.909i	−0.693683	−	0.483370i
$247$	198.777	−	39.5391i	0.804764	−	0.160077i
$248$	333.654	+	122.981i	1.34538	+	0.495893i
$249$	−100.010	−	19.8932i	−0.401646	−	0.0798925i
$250$	−4.17929	+	213.878i	−0.0167172	+	0.855510i
$251$	−17.7830	−	58.6225i	−0.0708484	−	0.233556i	0.914364	−	0.404893i	$-0.132691\pi$
$251$	−17.7830	−	58.6225i	−0.0708484	−	0.233556i	−0.985212	+	0.171337i	$0.945191\pi$
$252$	21.6382	−	90.2064i	0.0858657	−	0.357962i
$253$	−55.1000	+	67.1395i	−0.217787	+	0.265374i
$254$	−131.897	−	167.277i	−0.519278	−	0.658570i
$255$			179.812i			0.705145i
$256$	150.633	+	206.992i	0.588412	+	0.808561i
$257$	−398.946			−1.55232			−0.776159	−	0.630537i	$-0.782835\pi$
$257$	−398.946			−1.55232			−0.776159	+	0.630537i	$0.782835\pi$
$258$	−199.375	+	157.206i	−0.772770	+	0.609324i
$259$	6.27415	+	5.14906i	0.0242245	+	0.0198806i
$260$	−174.491	−	41.8557i	−0.671118	−	0.160984i
$261$	−201.675	+	61.1775i	−0.772702	+	0.234397i
$262$	332.841	+	6.50391i	1.27039	+	0.0248241i
$263$	−16.1277	+	81.0794i	−0.0613220	+	0.308287i	−0.999258	−	0.0385225i	$-0.987735\pi$
$263$	−16.1277	+	81.0794i	−0.0613220	+	0.308287i	0.937936	+	0.346809i	$0.112735\pi$
$264$	230.216	+	84.8553i	0.872031	+	0.321421i
$265$	2.25737	+	11.3486i	0.00851838	+	0.0428248i
$266$	42.8936	−	61.5564i	0.161254	−	0.231415i
$267$	41.2369	−	418.686i	0.154445	−	1.56811i
$268$	149.286	+	197.134i	0.557039	+	0.735573i
$269$	32.9512	−	108.626i	0.122495	−	0.403813i	−0.874150	−	0.485656i	$-0.838581\pi$
$269$	32.9512	−	108.626i	0.122495	−	0.403813i	0.996645	+	0.0818432i	$0.0260807\pi$
$270$	19.4919	+	38.2459i	0.0721923	+	0.141651i
$271$	−216.654	−	89.7409i	−0.799460	−	0.331147i	−0.0547198	−	0.998502i	$-0.517427\pi$
$271$	−216.654	−	89.7409i	−0.799460	−	0.331147i	−0.744740	+	0.667355i	$0.767427\pi$
$272$	23.3331	−	297.951i	0.0857835	−	1.09541i
$273$	−96.3361	−	232.576i	−0.352880	−	0.851927i
$274$	−54.3826	−	46.4380i	−0.198476	−	0.169482i
$275$	−69.6226	−	130.255i	−0.253173	−	0.473653i
$276$	−178.332	+	10.5514i	−0.646129	+	0.0382299i
$277$	3.30908	−	2.71569i	0.0119461	−	0.00980395i	−0.628401	−	0.777889i	$-0.716290\pi$
$277$	3.30908	−	2.71569i	0.0119461	−	0.00980395i	0.640347	+	0.768085i	$0.278790\pi$
$278$	67.5652	+	105.525i	0.243040	+	0.379585i
$279$	250.224	+	167.194i	0.896860	+	0.599262i
$280$	−57.2993	+	33.6061i	−0.204640	+	0.120022i
$281$	−366.297	+	244.752i	−1.30355	+	0.871002i	−0.996733	−	0.0807671i	$-0.974263\pi$
$281$	−366.297	+	244.752i	−1.30355	+	0.871002i	−0.306814	+	0.951769i	$0.599263\pi$
$282$	81.1233	+	207.209i	0.287671	+	0.734785i
$283$	252.976	−	473.285i	0.893909	−	1.67239i	0.166659	−	0.986015i	$-0.446702\pi$
$283$	252.976	−	473.285i	0.893909	−	1.67239i	0.727251	−	0.686372i	$-0.240798\pi$
$284$	−190.667	+	413.799i	−0.671362	+	1.45704i
$285$	−10.3334	−	104.917i	−0.0362575	−	0.368128i
$286$	275.107	−	77.6170i	0.961913	−	0.271388i
$287$	−63.4288	+	63.4288i	−0.221006	+	0.221006i
$288$	83.0062	+	200.120i	0.288216	+	0.694863i
$289$	−42.3586	+	42.3586i	−0.146570	+	0.146570i
$290$	131.679	+	73.7268i	0.454064	+	0.254230i
$291$	−36.9305	−	374.962i	−0.126909	−	1.28853i
$292$	−16.8301	+	430.480i	−0.0576373	+	1.47425i
$293$	128.333	−	240.095i	0.437998	−	0.819436i	−0.561972	−	0.827156i	$-0.689957\pi$
$293$	128.333	−	240.095i	0.437998	−	0.819436i	0.999970	+	0.00771965i	$0.00245727\pi$
$294$	271.190	+	118.590i	0.922415	+	0.403366i
$295$	134.402	−	89.8047i	0.455601	−	0.304423i
$296$	−18.9235	−	1.11046i	−0.0639307	−	0.00375155i
$297$	−56.8570	−	37.9907i	−0.191438	−	0.127915i
$298$	−54.1486	+	246.910i	−0.181707	+	0.828556i
$299$	−160.882	+	132.033i	−0.538067	+	0.441580i
$300$	99.4716	−	287.032i	0.331572	−	0.956772i
$301$	51.6186	+	96.5715i	0.171490	+	0.320836i
$302$	−173.632	+	13.6820i	−0.574939	+	0.0453047i
$303$	−103.181	−	249.100i	−0.340530	−	0.822112i
$304$	3.50819	+	175.189i	0.0115401	+	0.576281i
$305$	217.916	+	90.2636i	0.714477	+	0.295946i
$306$	78.1357	−	240.556i	0.255345	−	0.786131i
$307$	13.8283	−	45.5858i	0.0450433	−	0.148488i	−0.931534	−	0.363654i	$-0.881529\pi$
$307$	13.8283	−	45.5858i	0.0450433	−	0.148488i	0.976578	+	0.215166i	$0.0690292\pi$
$308$	53.4899	−	91.3031i	0.173669	−	0.296439i
$309$	−62.9620	+	639.264i	−0.203761	+	2.06882i
$310$	−37.9043	−	212.138i	−0.122272	−	0.684317i
$311$	−87.2021	−	438.395i	−0.280393	−	1.40963i	−0.822234	−	0.569149i	$-0.807273\pi$
$311$	−87.2021	−	438.395i	−0.280393	−	1.40963i	0.541842	−	0.840481i	$-0.317727\pi$
$312$	501.384	+	307.048i	1.60700	+	0.984128i
$313$	−9.01696	+	45.3313i	−0.0288082	+	0.144829i	−0.992512	−	0.122144i	$-0.961023\pi$
$313$	−9.01696	+	45.3313i	−0.0288082	+	0.144829i	0.963704	+	0.266972i	$0.0860232\pi$
$314$	214.384	+	222.930i	0.682753	+	0.709968i
$315$	−53.7966	+	16.3190i	−0.170783	+	0.0518064i
$316$	75.7521	+	55.0147i	0.239722	+	0.174097i
$317$	278.506	+	228.564i	0.878567	+	0.721021i	0.961286	−	0.275552i	$-0.0888605\pi$
$317$	278.506	+	228.564i	0.878567	+	0.721021i	−0.0827194	+	0.996573i	$0.526361\pi$
$318$	4.45240	−	37.6494i	0.0140013	−	0.118394i
$319$	−240.404			−0.753616
$320$	62.0896	−	142.174i	0.194030	−	0.444293i
$321$		−	199.332i		−	0.620971i
$322$	−9.04834	+	76.5125i	−0.0281004	+	0.237617i
$323$	129.774	−	158.130i	0.401776	−	0.489566i
$324$	−60.2041	−	379.637i	−0.185815	−	1.17172i
$325$	−102.735	−	338.671i	−0.316107	−	1.04206i
$326$	−382.369	−	397.610i	−1.17291	−	1.21966i
$327$	−672.635	−	133.795i	−2.05699	−	0.409160i
$328$	32.7125	−	206.928i	0.0997333	−	0.630878i
$329$	94.1263	−	18.7229i	0.286098	−	0.0569084i
$330$	−26.1534	−	146.372i	−0.0792526	−	0.443552i
$331$	326.270	+	32.1348i	0.985709	+	0.0970839i	0.578008	−	0.816031i	$-0.303830\pi$
$331$	326.270	+	32.1348i	0.985709	+	0.0970839i	0.407702	+	0.913115i	$0.366330\pi$
$332$	−25.9524	−	99.3760i	−0.0781699	−	0.299325i
$333$	−15.3517	−	4.65688i	−0.0461011	−	0.0139846i
$334$	−89.2193	+	274.679i	−0.267124	+	0.822394i
$335$	57.3476	−	138.449i	0.171187	−	0.413282i
$336$	212.572	−	46.7262i	0.632656	−	0.139066i
$337$	−93.0972	+	38.5621i	−0.276253	+	0.114428i	−0.516509	−	0.856282i	$-0.672769\pi$
$337$	−93.0972	+	38.5621i	−0.276253	+	0.114428i	0.240256	+	0.970710i	$0.422769\pi$
$338$	345.883	−	27.2553i	1.02332	−	0.0806370i
$339$	730.315	−	390.362i	2.15432	−	1.15151i
$340$	−162.944	+	79.0723i	−0.479246	+	0.232566i
$341$	217.778	+	265.363i	0.638646	+	0.778192i
$342$	−31.7664	+	144.850i	−0.0928841	+	0.423538i
$343$	164.170	−	245.698i	0.478630	−	0.716320i
$344$	−230.133	−	111.540i	−0.668992	−	0.324244i
$345$	60.1465	+	90.0156i	0.174338	+	0.260915i
$346$	267.446	+	116.952i	0.772964	+	0.338012i
$347$	−7.28257	−	3.89262i	−0.0209872	−	0.0112179i	0.460870	−	0.887468i	$-0.347538\pi$
$347$	−7.28257	−	3.89262i	−0.0209872	−	0.0112179i	−0.481857	+	0.876250i	$0.660038\pi$
$348$	−335.713	−	363.032i	−0.964694	−	1.04319i
$349$	−392.543	+	38.6621i	−1.12476	+	0.110780i	−0.643248	−	0.765658i	$-0.722414\pi$
$349$	−392.543	+	38.6621i	−1.12476	+	0.110780i	−0.481516	+	0.876437i	$0.659914\pi$
$350$	−114.316	−	64.0053i	−0.326616	−	0.182872i
$351$	−115.865	−	115.865i	−0.330100	−	0.330100i
$352$	24.3427	+	245.935i	0.0691555	+	0.698678i
$353$	−57.9731	−	57.9731i	−0.164230	−	0.164230i	0.620208	−	0.784438i	$-0.287048\pi$
$353$	−57.9731	−	57.9731i	−0.164230	−	0.164230i	−0.784438	+	0.620208i	$0.787048\pi$
$354$	−509.725	+	143.811i	−1.43990	+	0.406245i
$355$	274.779	−	27.0634i	0.774027	−	0.0762350i
$356$	397.542	−	146.749i	1.11669	−	0.412215i
$357$	−224.087	−	119.777i	−0.627694	−	0.335510i
$358$	−192.413	−	491.472i	−0.537468	−	1.37283i
$359$	219.285	+	328.183i	0.610821	+	0.914159i	0.999975	−	0.00701386i	$-0.00223260\pi$
$359$	219.285	+	328.183i	0.610821	+	0.914159i	−0.389154	+	0.921173i	$0.627233\pi$
$360$	79.2133	−	104.707i	0.220037	−	0.290853i
$361$	133.928	−	200.437i	0.370991	−	0.555228i
$362$	−126.154	−	197.029i	−0.348491	−	0.544280i
$363$	−154.572	−	188.346i	−0.425817	−	0.518860i
$364$	168.394	−	189.574i	0.462621	−	0.520808i
$365$	230.250	−	123.071i	0.630821	−	0.337181i
$366$	−587.708	−	501.851i	−1.60576	−	1.37118i
$367$	634.100	−	262.653i	1.72779	−	0.715676i	0.728255	−	0.685306i	$-0.240332\pi$
$367$	634.100	−	262.653i	1.72779	−	0.715676i	0.999539	−	0.0303695i	$-0.00966839\pi$
$368$	−87.9830	−	156.962i	−0.239084	−	0.426528i
$369$	67.8488	−	163.801i	0.183872	−	0.443906i
$370$	5.21628	+	10.2351i	0.0140981	+	0.0276624i
$371$	−15.6466	−	4.74635i	−0.0421741	−	0.0127934i
$372$	−96.6053	+	699.434i	−0.259692	+	1.88020i
$373$	85.7557	+	8.44620i	0.229908	+	0.0226440i	0.212315	−	0.977201i	$-0.431900\pi$
$373$	85.7557	+	8.44620i	0.229908	+	0.0226440i	0.0175930	+	0.999845i	$0.494400\pi$
$374$	164.947	−	236.715i	0.441035	−	0.632928i
$375$	−416.594	+	82.8658i	−1.11092	+	0.220975i
$376$	−152.097	+	164.633i	−0.404513	+	0.437855i
$377$	−564.995	−	112.384i	−1.49866	−	0.298102i
$378$	−60.6471	−	1.18508i	−0.160442	−	0.00313513i
$379$	197.876	+	652.310i	0.522101	+	1.72114i	0.679569	+	0.733612i	$0.262167\pi$
$379$	197.876	+	652.310i	0.522101	+	1.72114i	−0.157468	+	0.987524i	$0.550333\pi$
$380$	90.5302	−	55.5011i	0.238237	−	0.146056i
$381$	268.333	−	326.964i	0.704285	−	0.858174i
$382$	479.040	−	377.720i	1.25403	−	0.988796i
$383$			699.647i			1.82676i	0.407114	+	0.913378i	$0.366535\pi$
$383$			699.647i			1.82676i	−0.407114	+	0.913378i	$0.633465\pi$
$384$	−337.390	+	380.197i	−0.878621	+	0.990096i
$385$	−64.1274			−0.166565
$386$	440.814	+	559.059i	1.14201	+	1.44834i
$387$	−167.304	−	137.303i	−0.432310	−	0.354787i
$388$	323.546	−	198.356i	0.833882	−	0.511226i
$389$	7.00107	−	2.12375i	0.0179976	−	0.00545951i	−0.281273	−	0.959628i	$-0.590757\pi$
$389$	7.00107	−	2.12375i	0.0179976	−	0.00545951i	0.299271	+	0.954168i	$0.403257\pi$
$390$	6.96091	−	356.228i	0.0178485	−	0.913406i
$391$	−40.9822	+	206.031i	−0.104814	+	0.526934i
$392$	11.7912	+	297.899i	0.0300796	+	0.759947i
$393$	128.958	+	648.314i	0.328136	+	1.64965i
$394$	−214.694	−	149.602i	−0.544908	−	0.379701i
$395$	5.56112	−	56.4630i	0.0140788	−	0.142944i
$396$	−28.6161	+	207.184i	−0.0722630	+	0.523193i
$397$	−109.499	+	360.969i	−0.275816	+	0.909242i	0.704146	+	0.710055i	$0.251330\pi$
$397$	−109.499	+	360.969i	−0.275816	+	0.909242i	−0.979962	+	0.199187i	$0.936170\pi$
$398$	40.1199	−	20.4470i	0.100804	−	0.0513743i
$399$	137.633	+	57.0096i	0.344946	+	0.142881i
$400$	303.848	−	36.0821i	0.759619	−	0.0902053i
$401$	151.425	+	365.572i	0.377618	+	0.911650i	0.992411	+	0.122962i	$0.0392393\pi$
$401$	151.425	+	365.572i	0.377618	+	0.911650i	−0.614794	+	0.788688i	$0.710761\pi$
$402$	−318.844	+	373.391i	−0.793143	+	0.928834i
$403$	387.768	+	725.462i	0.962203	+	1.80015i
$404$	180.358	−	203.043i	0.446431	−	0.502582i
$405$	−180.066	+	147.776i	−0.444608	+	0.364880i
$406$	−179.595	+	114.991i	−0.442352	+	0.283228i
$407$	−15.2157	−	10.1668i	−0.0373849	−	0.0249798i
$408$	587.803	−	81.4771i	1.44069	−	0.199699i
$409$	−179.528	+	119.957i	−0.438945	+	0.293293i	−0.755339	−	0.655334i	$-0.772528\pi$
$409$	−179.528	+	119.957i	−0.438945	+	0.293293i	0.316394	+	0.948628i	$0.397528\pi$
$410$	−118.222	+	46.2842i	−0.288345	+	0.112888i
$411$	66.9354	−	125.227i	0.162860	−	0.304689i
$412$	−606.982	+	224.061i	−1.47326	+	0.543838i
$413$	22.3888	+	227.317i	0.0542101	+	0.550404i
$414$	−41.3498	−	146.561i	−0.0998787	−	0.354012i
$415$	−44.0126	+	44.0126i	−0.106055	+	0.106055i
$416$	−57.7600	+	589.373i	−0.138846	+	1.41676i
$417$	−175.927	+	175.927i	−0.421888	+	0.421888i
$418$	−82.6398	+	147.598i	−0.197703	+	0.353104i
$419$	−31.2958	−	317.752i	−0.0746917	−	0.758358i	−0.957463	−	0.288555i	$-0.906825\pi$
$419$	−31.2958	−	317.752i	−0.0746917	−	0.758358i	0.882772	−	0.469802i	$-0.155675\pi$
$420$	−89.5511	−	96.8382i	−0.213217	−	0.230567i
$421$	293.970	−	549.980i	0.698267	−	1.30636i	−0.243435	−	0.969917i	$-0.578274\pi$
$421$	293.970	−	549.980i	0.698267	−	1.30636i	0.941702	−	0.336448i	$-0.109226\pi$
$422$	−224.397	+	513.149i	−0.531746	+	1.21599i
$423$	−157.719	+	105.385i	−0.372858	+	0.249136i
$424$	36.0755	−	12.5216i	0.0850836	−	0.0295321i
$425$	−297.013	−	198.458i	−0.698855	−	0.466960i
$426$	−883.664	−	193.792i	−2.07433	−	0.454911i
$427$	−257.648	+	211.446i	−0.603390	+	0.495190i
$428$	180.632	−	87.6562i	0.422038	−	0.204804i
$429$	267.554	+	500.558i	0.623668	+	1.16680i
$430$	12.1747	+	154.503i	0.0283133	+	0.359309i
$431$	−9.61411	−	23.2105i	−0.0223065	−	0.0538527i	0.912334	−	0.409447i	$-0.134278\pi$
$431$	−9.61411	−	23.2105i	−0.0223065	−	0.0538527i	−0.934640	+	0.355595i	$0.884278\pi$
$432$	116.193	−	81.0489i	0.268965	−	0.187613i
$433$	−42.3849	−	17.5564i	−0.0978866	−	0.0405460i	0.333203	−	0.942855i	$-0.391871\pi$
$433$	−42.3849	−	17.5564i	−0.0978866	−	0.0405460i	−0.431089	+	0.902309i	$0.641871\pi$
$434$	289.622	+	94.0728i	0.667331	+	0.216758i
$435$	−86.9848	+	286.751i	−0.199965	+	0.659197i
$436$	−174.548	−	668.372i	−0.400338	−	1.53296i
$437$	12.0721	−	122.570i	0.0276250	−	0.280481i
$438$	−842.077	+	150.460i	−1.92255	+	0.343516i
$439$	3.39537	+	17.0697i	0.00773434	+	0.0388831i	0.984460	−	0.175610i	$-0.0561899\pi$
$439$	3.39537	+	17.0697i	0.00773434	+	0.0388831i	−0.976725	+	0.214494i	$0.931190\pi$
$440$	121.140	−	88.0670i	0.275318	−	0.200152i
$441$	−49.2231	+	247.461i	−0.111617	+	0.561136i
$442$	498.317	−	479.216i	1.12741	−	1.08420i
$443$	102.863	−	31.2032i	0.232197	−	0.0704361i	−0.172042	−	0.985090i	$-0.555037\pi$
$443$	102.863	−	31.2032i	0.232197	−	0.0704361i	0.404239	+	0.914654i	$0.367537\pi$
$444$	−5.89525	−	37.1745i	−0.0132776	−	0.0837264i
$445$	−198.515	−	162.917i	−0.446101	−	0.366105i
$446$	−504.068	−	59.6109i	−1.13020	−	0.133657i
$447$	−501.914			−1.12285
$448$	135.822	+	172.083i	0.303173	+	0.384114i
$449$			487.456i			1.08565i	0.839846	+	0.542824i	$0.182645\pi$
$449$			487.456i			1.08565i	−0.839846	+	0.542824i	$0.817355\pi$
$450$	257.160	+	30.4117i	0.571468	+	0.0675815i
$451$	128.302	−	156.337i	0.284484	−	0.346645i
$452$	674.898	+	490.142i	1.49314	+	1.08439i
$453$	−100.390	−	330.940i	−0.221610	−	0.730552i
$454$	497.596	−	478.522i	1.09603	−	1.05401i
$455$	−150.712	−	29.9784i	−0.331234	−	0.0658866i
$456$	−338.289	+	81.3199i	−0.741861	+	0.178333i
$457$	−269.942	+	53.6949i	−0.590684	+	0.117494i	−0.481377	−	0.876514i	$-0.659863\pi$
$457$	−269.942	+	53.6949i	−0.590684	+	0.117494i	−0.109307	+	0.994008i	$0.534863\pi$
$458$	−716.133	+	127.957i	−1.56361	+	0.279381i
$459$	−164.592	−	16.2109i	−0.358587	−	0.0353178i
$460$	−55.1218	+	94.0885i	−0.119830	+	0.204540i
$461$	235.463	+	71.4270i	0.510766	+	0.154939i	0.535140	−	0.844764i	$-0.320259\pi$
$461$	235.463	+	71.4270i	0.510766	+	0.154939i	−0.0243732	+	0.999703i	$0.507759\pi$
$462$	199.834	+	64.9087i	0.432542	+	0.140495i
$463$	−6.49648	+	15.6839i	−0.0140313	+	0.0338745i	−0.930740	−	0.365682i	$-0.880836\pi$
$463$	−6.49648	+	15.6839i	−0.0140313	+	0.0338745i	0.916709	+	0.399556i	$0.130836\pi$
$464$	181.345	−	463.863i	0.390830	−	0.999705i
$465$	395.321	−	163.747i	0.850152	−	0.352145i
$466$	34.2934	+	435.200i	0.0735909	+	0.933905i
$467$	111.704	−	59.7070i	0.239195	−	0.127852i	−0.347445	−	0.937700i	$-0.612951\pi$
$467$	111.704	−	59.7070i	0.239195	−	0.127852i	0.586639	+	0.809848i	$0.300451\pi$
$468$	−164.108	+	473.545i	−0.350659	+	1.01185i
$469$	134.339	+	163.693i	0.286437	+	0.349025i
$470$	132.678	+	29.0970i	0.282293	+	0.0619084i
$471$	−341.186	+	510.622i	−0.724387	+	1.08412i
$472$	−354.471	−	398.667i	−0.750999	−	0.844633i
$473$	−137.162	−	205.277i	−0.289982	−	0.433989i
$474$	−74.4806	+	170.322i	−0.157132	+	0.359329i
$475$	184.706	+	98.7276i	0.388855	+	0.207848i
$476$	9.99831	−	255.737i	0.0210049	−	0.537263i
$477$	32.1618	−	3.16766i	0.0674251	−	0.00664079i
$478$	−2.29046	+	4.09084i	−0.00479175	+	0.00855823i
$479$	126.148	+	126.148i	0.263358	+	0.263358i	0.826417	−	0.563059i	$-0.190376\pi$
$479$	126.148	+	126.148i	0.263358	+	0.263358i	−0.563059	+	0.826417i	$0.690376\pi$
$480$	302.156	+	59.9504i	0.629491	+	0.124897i
$481$	−31.0069	−	31.0069i	−0.0644634	−	0.0644634i
$482$	−80.2943	−	284.597i	−0.166586	−	0.590450i
$483$	−152.245	+	14.9948i	−0.315207	+	0.0310452i
$484$	102.704	−	222.897i	0.212199	−	0.460530i
$485$	−202.832	−	108.416i	−0.418210	−	0.223538i
$486$	562.293	−	220.140i	1.15698	−	0.452963i
$487$	−221.039	−	330.808i	−0.453878	−	0.679276i	0.532000	−	0.846745i	$-0.321441\pi$
$487$	−221.039	−	330.808i	−0.453878	−	0.679276i	−0.985877	+	0.167468i	$0.946441\pi$
$488$	196.328	−	753.264i	0.402311	−	1.54357i
$489$	608.528	−	910.727i	1.24443	−	1.86243i
$490$	152.157	−	97.4226i	0.310524	−	0.198822i
$491$	−505.534	−	615.996i	−1.02960	−	1.25457i	−0.966527	−	0.256565i	$-0.917409\pi$
$491$	−505.534	−	615.996i	−1.02960	−	1.25457i	−0.0630747	−	0.998009i	$-0.520091\pi$
$492$	415.252	−	24.5694i	0.844007	−	0.0499378i
$493$	−512.787	+	274.090i	−1.04014	+	0.555964i
$494$	−263.219	+	308.250i	−0.532831	+	0.623987i
$495$	117.101	−	48.5047i	0.236567	−	0.0979894i
$496$	−676.302	+	220.033i	−1.36351	+	0.443616i
$497$	−149.310	+	360.466i	−0.300422	+	0.725283i
$498$	181.702	−	92.6038i	0.364863	−	0.185951i
$499$	494.592	+	150.033i	0.991165	+	0.300667i	0.743907	−	0.668283i	$-0.232970\pi$
$499$	494.592	+	150.033i	0.991165	+	0.300667i	0.247258	+	0.968950i	$0.420470\pi$
$500$	−258.290	−	341.073i	−0.516579	−	0.682146i
$501$	−570.691	−	56.2082i	−1.13910	−	0.112192i
$502$	100.523	+	70.0462i	0.200245	+	0.139534i
$503$	217.645	−	43.2923i	0.432694	−	0.0860682i	0.0260623	−	0.999660i	$-0.491703\pi$
$503$	217.645	−	43.2923i	0.432694	−	0.0860682i	0.406632	+	0.913592i	$0.366703\pi$
$504$	77.7232	+	168.466i	0.154213	+	0.334258i
$505$	−161.419	−	32.1083i	−0.319642	−	0.0635808i
$506$	3.39373	−	173.676i	0.00670698	−	0.343233i
$507$	199.981	+	659.249i	0.394440	+	1.30029i
$508$	414.291	+	99.3776i	0.815534	+	0.195625i
$509$	185.449	−	225.970i	0.364339	−	0.443948i	−0.558285	−	0.829649i	$-0.688540\pi$
$509$	185.449	−	225.970i	0.364339	−	0.443948i	0.922624	+	0.385701i	$0.126040\pi$
$510$	−222.668	−	282.397i	−0.436604	−	0.553720i
$511$			368.924i			0.721965i
$512$	−492.898	−	138.548i	−0.962692	−	0.270601i
$513$	96.9675			0.189020
$514$	626.550	−	494.031i	1.21897	−	0.961149i
$515$	303.099	+	248.747i	0.588543	+	0.483004i
$516$	118.447	−	493.787i	0.229548	−	0.956952i
$517$	−207.060	+	62.8110i	−0.400503	+	0.121491i
$518$	−16.2299	−	0.317142i	−0.0313319	−	0.000612244i
$519$	−113.073	+	568.457i	−0.217867	+	1.09529i
$520$	325.872	−	150.344i	0.626676	−	0.289122i
$521$	84.4672	+	424.645i	0.162125	+	0.815058i	0.973172	+	0.230077i	$0.0738979\pi$
$521$	84.4672	+	424.645i	0.162125	+	0.815058i	−0.811047	+	0.584981i	$0.801102\pi$
$522$	240.975	−	345.823i	0.461638	−	0.662495i
$523$	14.9611	−	151.903i	0.0286064	−	0.290446i	−0.970229	−	0.242191i	$-0.922134\pi$
$523$	14.9611	−	151.903i	0.0286064	−	0.290446i	0.998835	−	0.0482548i	$-0.0153660\pi$
$524$	−530.786	+	401.956i	−1.01295	+	0.767092i
$525$	75.5152	−	248.940i	0.143838	−	0.474172i
$526$	−75.0751	−	147.308i	−0.142728	−	0.280053i
$527$	767.074	+	317.732i	1.45555	+	0.602908i
$528$	−466.637	+	151.820i	−0.883783	+	0.287537i
$529$	−154.039	−	371.883i	−0.291189	−	0.702992i
$530$	−17.5986	−	15.0277i	−0.0332049	−	0.0283541i
$531$	−212.822	−	398.161i	−0.400794	−	0.749833i
$532$	8.86282	+	149.792i	0.0166594	+	0.281564i
$533$	374.620	−	307.442i	0.702851	−	0.576815i
$534$	453.712	+	708.617i	0.849648	+	1.32700i
$535$	−101.169	−	67.5987i	−0.189100	−	0.126353i
$536$	−478.575	−	124.734i	−0.892863	−	0.232712i
$537$	871.371	−	582.231i	1.62266	−	1.08423i
$538$	82.7652	+	211.403i	0.153839	+	0.392942i
$539$	−135.673	+	253.826i	−0.251712	+	0.470920i
$540$	−77.9737	−	35.9281i	−0.144396	−	0.0665335i
$541$	56.3616	+	572.248i	0.104180	+	1.05776i	0.895108	+	0.445850i	$0.147099\pi$
$541$	56.3616	+	572.248i	0.104180	+	1.05776i	−0.790927	+	0.611910i	$0.790401\pi$
$542$	451.387	−	127.352i	0.832818	−	0.234966i
$543$	328.481	−	328.481i	0.604937	−	0.604937i
$544$	332.320	+	496.831i	0.610883	+	0.913293i
$545$	−296.015	+	296.015i	−0.543147	+	0.543147i
$546$	439.305	+	245.967i	0.804589	+	0.450489i
$547$	−3.53133	−	35.8542i	−0.00645581	−	0.0655469i	0.991417	−	0.130737i	$-0.0417345\pi$
$547$	−3.53133	−	35.8542i	−0.00645581	−	0.0655469i	−0.997873	+	0.0651905i	$0.979234\pi$
$548$	142.915	+	5.58740i	0.260793	+	0.0101960i
$549$	310.548	−	580.994i	0.565661	−	1.05828i
$550$	270.643	+	118.350i	0.492078	+	0.215183i
$551$	283.449	−	189.395i	0.514427	−	0.343729i
$552$	267.006	−	237.406i	0.483707	−	0.430084i
$553$	66.6614	+	44.5417i	0.120545	+	0.0805456i
$554$	−1.83401	+	8.36281i	−0.00331048	+	0.0150953i
$555$	−17.6323	+	14.4704i	−0.0317699	+	0.0260728i
$556$	−236.788	−	82.0594i	−0.425877	−	0.147589i
$557$	364.972	+	682.815i	0.655246	+	1.22588i	0.961729	+	0.274003i	$0.0883478\pi$
$557$	364.972	+	682.815i	0.655246	+	1.22588i	−0.306483	+	0.951876i	$0.599152\pi$
$558$	−600.023	+	47.2813i	−1.07531	+	0.0847336i
$559$	−226.393	−	546.561i	−0.404996	−	0.977747i
$560$	48.3736	−	123.735i	0.0863815	−	0.220955i
$561$	529.269	+	219.230i	0.943438	+	0.390785i
$562$	272.188	−	837.986i	0.484321	−	1.49108i
$563$	196.714	−	648.479i	0.349403	−	1.15183i	−0.589535	−	0.807743i	$-0.700689\pi$
$563$	196.714	−	648.479i	0.349403	−	1.15183i	0.938938	−	0.344085i	$-0.111811\pi$
$564$	−384.001	−	224.967i	−0.680853	−	0.398877i
$565$	49.5457	−	503.046i	0.0876915	−	0.890346i
$566$	188.785	+	1056.57i	0.333543	+	1.86674i
$567$	−64.2171	−	322.841i	−0.113258	−	0.569384i
$568$	−212.979	−	885.987i	−0.374963	−	1.55984i
$569$	−2.08073	+	10.4606i	−0.00365682	+	0.0183841i	−0.982571	−	0.185890i	$-0.940483\pi$
$569$	−2.08073	+	10.4606i	−0.00365682	+	0.0183841i	0.978914	+	0.204274i	$0.0654833\pi$
$570$	146.151	+	151.977i	0.256406	+	0.266626i
$571$	175.863	−	53.3475i	0.307992	−	0.0934283i	−0.132505	−	0.991182i	$-0.542302\pi$
$571$	175.863	−	53.3475i	0.307992	−	0.0934283i	0.440497	+	0.897754i	$0.354802\pi$
$572$	−335.943	+	462.575i	−0.587313	+	0.808697i
$573$	936.347	+	768.440i	1.63411	+	1.34108i
$574$	21.0694	−	178.162i	0.0367062	−	0.310387i
$575$	−215.071			−0.374037
$576$	−378.180	−	211.502i	−0.656562	−	0.367191i
$577$		−	924.500i		−	1.60225i	−0.598495	−	0.801127i	$-0.704234\pi$
$577$		−	924.500i		−	1.60225i	0.598495	−	0.801127i	$-0.295766\pi$
$578$	14.0704	−	118.979i	0.0243433	−	0.205846i
$579$	−896.799	+	1092.75i	−1.54888	+	1.88731i
$580$	−298.102	+	47.2739i	−0.513969	+	0.0815068i
$581$	−25.5320	−	84.1677i	−0.0439449	−	0.144867i
$582$	522.330	+	543.150i	0.897474	+	0.933248i
$583$	36.1563	+	7.19193i	0.0620176	+	0.0123361i
$584$	−506.649	−	696.917i	−0.867550	−	1.19335i
$585$	297.884	−	59.2529i	0.509204	−	0.101287i
$586$	95.7697	+	535.993i	0.163430	+	0.914663i
$587$	−1049.71	−	103.388i	−1.78827	−	0.176129i	−0.851099	−	0.525006i	$-0.824063\pi$
$587$	−1049.71	−	103.388i	−1.78827	−	0.176129i	−0.937169	+	0.348877i	$0.886563\pi$
$588$	−572.762	+	149.579i	−0.974085	+	0.254386i
$589$	−465.832	−	141.308i	−0.790885	−	0.239912i
$590$	−99.8718	+	307.475i	−0.169274	+	0.521144i
$591$	198.836	−	480.032i	0.336440	−	0.812237i
$592$	31.0947	−	21.6897i	0.0525248	−	0.0366380i
$593$	115.944	−	48.0256i	0.195521	−	0.0809875i	−0.282774	−	0.959186i	$-0.591255\pi$
$593$	115.944	−	48.0256i	0.195521	−	0.0809875i	0.478296	+	0.878199i	$0.341255\pi$
$594$	136.340	−	10.7435i	0.229529	−	0.0180867i
$595$	−136.785	+	73.1133i	−0.229891	+	0.122879i
$596$	−220.717	−	454.829i	−0.370331	−	0.763137i
$597$	56.7218	+	69.1157i	0.0950113	+	0.115772i
$598$	89.1664	−	406.586i	0.149108	−	0.679909i
$599$	33.6776	−	50.4021i	0.0562230	−	0.0841437i	−0.802293	−	0.596930i	$-0.796387\pi$
$599$	33.6776	−	50.4021i	0.0562230	−	0.0841437i	0.858516	+	0.512787i	$0.171387\pi$
$600$	199.221	+	573.967i	0.332035	+	0.956611i
$601$	595.083	+	890.604i	0.990154	+	1.48187i	0.872379	+	0.488830i	$0.162576\pi$
$601$	595.083	+	890.604i	0.990154	+	1.48187i	0.117775	+	0.993040i	$0.462424\pi$
$602$	−200.656	−	87.7456i	−0.333316	−	0.145757i
$603$	−369.126	−	197.302i	−0.612149	−	0.327201i
$604$	255.748	−	236.503i	0.423424	−	0.391561i
$605$	−148.012	+	14.5780i	−0.244649	+	0.0240958i
$606$	470.517	+	263.442i	0.776431	+	0.434723i
$607$	300.370	+	300.370i	0.494843	+	0.494843i	0.909828	−	0.414985i	$-0.136213\pi$
$607$	300.370	+	300.370i	0.494843	+	0.494843i	−0.414985	+	0.909828i	$0.636213\pi$
$608$	−222.454	−	270.793i	−0.365878	−	0.445384i
$609$	−299.414	−	299.414i	−0.491649	−	0.491649i
$610$	−454.016	+	128.093i	−0.744289	+	0.209989i
$611$	−515.994	+	50.8210i	−0.844507	+	0.0831767i
$612$	175.177	+	474.555i	0.286237	+	0.775417i
$613$	−430.988	−	230.368i	−0.703079	−	0.375804i	0.0807887	−	0.996731i	$-0.474256\pi$
$613$	−430.988	−	230.368i	−0.703079	−	0.375804i	−0.783868	+	0.620928i	$0.786756\pi$
$614$	34.7332	+	88.7172i	0.0565687	+	0.144491i
$615$	−140.053	−	209.605i	−0.227729	−	0.340820i
$616$	29.0576	+	209.632i	0.0471715	+	0.340311i
$617$	239.650	−	358.662i	0.388412	−	0.581300i	−0.584809	−	0.811171i	$-0.698830\pi$
$617$	239.650	−	358.662i	0.388412	−	0.581300i	0.973221	+	0.229871i	$0.0738304\pi$
$618$	−692.744	−	1081.94i	−1.12094	−	1.75071i
$619$	−425.346	−	518.286i	−0.687150	−	0.837295i	0.306255	−	0.951949i	$-0.400924\pi$
$619$	−425.346	−	518.286i	−0.687150	−	0.837295i	−0.993405	+	0.114654i	$0.963424\pi$
$620$	322.228	+	286.228i	0.519723	+	0.461657i
$621$	−87.8187	+	46.9401i	−0.141415	+	0.0755879i
$622$	679.834	+	580.519i	1.09298	+	0.933311i
$623$	335.267	−	138.872i	0.538149	−	0.222909i
$624$	−1167.66	+	138.661i	−1.87125	+	0.222212i
$625$	83.7394	−	202.165i	0.133983	−	0.323464i
$626$	−41.9743	−	82.3596i	−0.0670517	−	0.131565i
$627$	−321.416	−	97.5006i	−0.512626	−	0.155503i
$628$	−612.757	−	84.6335i	−0.975727	−	0.134767i
$629$	−44.0468	−	4.33823i	−0.0700267	−	0.00689703i
$630$	64.2798	−	92.2477i	0.102031	−	0.146425i
$631$	−708.522	+	140.934i	−1.12286	+	0.223350i	−0.721393	−	0.692526i	$-0.756498\pi$
$631$	−708.522	+	140.934i	−1.12286	+	0.223350i	−0.401462	+	0.915876i	$0.631498\pi$
$632$	−187.097	+	7.40550i	−0.296039	+	0.0117176i
$633$	−1090.70	−	216.954i	−1.72307	−	0.342739i
$634$	−720.437	−	14.0777i	−1.13634	−	0.0222046i
$635$	−74.9484	−	247.072i	−0.118029	−	0.389089i
$636$	39.6302	+	64.6425i	0.0623117	+	0.101639i
$637$	−437.516	+	533.115i	−0.686839	+	0.836916i
$638$	377.557	−	297.701i	0.591783	−	0.466617i
$639$		−	771.169i		−	1.20684i
$640$	78.5467	+	300.174i	0.122729	+	0.469021i
$641$	674.946			1.05296			0.526479	−	0.850188i	$-0.323512\pi$
$641$	674.946			1.05296			0.526479	+	0.850188i	$0.323512\pi$
$642$	246.840	+	313.053i	0.384487	+	0.487622i
$643$	344.335	+	282.588i	0.535513	+	0.439484i	0.862877	−	0.505414i	$-0.168660\pi$
$643$	344.335	+	282.588i	0.535513	+	0.439484i	−0.327364	+	0.944898i	$0.606160\pi$
$644$	−80.5380	−	131.369i	−0.125059	−	0.203989i
$645$	−294.481	+	89.3298i	−0.456560	+	0.138496i
$646$	−7.99305	+	409.049i	−0.0123731	+	0.633203i
$647$	14.3609	−	72.1971i	0.0221961	−	0.111587i	−0.968099	−	0.250568i	$-0.919383\pi$
$647$	14.3609	−	72.1971i	0.0221961	−	0.111587i	0.990295	+	0.138981i	$0.0443826\pi$
$648$	564.671	+	521.673i	0.871407	+	0.805050i
$649$	−100.470	−	505.099i	−0.154808	−	0.778273i
$650$	580.736	+	404.667i	0.893440	+	0.622564i
$651$	−59.2658	+	601.736i	−0.0910381	+	0.924326i
$652$	1092.89	+	150.949i	1.67621	+	0.231518i
$653$	259.250	−	854.634i	0.397014	−	1.30878i	−0.499711	−	0.866192i	$-0.666560\pi$
$653$	259.250	−	854.634i	0.397014	−	1.30878i	0.896725	−	0.442588i	$-0.145940\pi$
$654$	1222.07	−	622.823i	1.86860	−	0.952329i
$655$	372.777	+	154.409i	0.569126	+	0.235740i
$656$	204.872	+	365.492i	0.312304	+	0.557153i
$657$	−279.047	−	673.680i	−0.424730	−	1.02539i
$658$	−124.641	+	145.965i	−0.189424	+	0.221831i
$659$	279.901	+	523.658i	0.424736	+	0.794625i	0.999723	−	0.0235378i	$-0.00749299\pi$
$659$	279.901	+	523.658i	0.424736	+	0.794625i	−0.574987	+	0.818162i	$0.694993\pi$
$660$	222.333	+	197.493i	0.336867	+	0.299231i
$661$	−214.224	+	175.809i	−0.324090	+	0.265974i	−0.782343	−	0.622848i	$-0.785975\pi$
$661$	−214.224	+	175.809i	−0.324090	+	0.265974i	0.458253	+	0.888822i	$0.348475\pi$
$662$	−552.205	+	353.565i	−0.834147	+	0.534086i
$663$	1141.40	+	762.657i	1.72156	+	1.15031i
$664$	163.820	+	123.934i	0.246717	+	0.186647i
$665$	75.6098	−	50.5208i	0.113699	−	0.0759712i
$666$	29.8768	−	11.6969i	0.0448601	−	0.0175629i
$667$	−165.024	+	308.738i	−0.247412	+	0.462876i
$668$	−200.026	−	541.872i	−0.299441	−	0.811185i
$669$	−98.7867	−	1003.00i	−0.147663	−	1.49925i
$670$	81.3822	+	288.453i	0.121466	+	0.430526i
$671$	531.374	−	531.374i	0.791914	−	0.791914i
$672$	−275.985	+	336.621i	−0.410692	+	0.500924i
$673$	−816.151	+	816.151i	−1.21271	+	1.21271i	−0.242572	+	0.970133i	$0.577991\pi$
$673$	−816.151	+	816.151i	−1.21271	+	1.21271i	−0.970133	+	0.242572i	$0.922009\pi$
$674$	98.4574	−	175.848i	0.146079	−	0.260902i
$675$	−16.5970	−	168.512i	−0.0245882	−	0.249648i
$676$	−509.463	+	471.126i	−0.753644	+	0.696932i
$677$	438.807	−	820.949i	0.648163	−	1.21263i	−0.316362	−	0.948639i	$-0.602461\pi$
$677$	438.807	−	820.949i	0.648163	−	1.21263i	0.964525	−	0.263990i	$-0.0850386\pi$
$678$	−663.570	+	1517.45i	−0.978717	+	2.23812i
$679$	270.222	−	180.557i	0.397971	−	0.265915i
$680$	157.987	−	325.964i	0.232334	−	0.479359i
$681$	1139.74	+	761.553i	1.67363	+	1.11829i
$682$	−670.634	−	147.074i	−0.983334	−	0.215650i
$683$	−308.460	+	253.146i	−0.451625	+	0.370639i	−0.832534	−	0.553973i	$-0.813111\pi$
$683$	−308.460	+	253.146i	−0.451625	+	0.370639i	0.380909	+	0.924612i	$0.375611\pi$
$684$	−129.484	−	266.826i	−0.189304	−	0.390097i
$685$	−40.8582	−	76.4403i	−0.0596470	−	0.111592i
$686$	46.4261	+	589.170i	0.0676766	+	0.858849i
$687$	−552.775	−	1334.52i	−0.804622	−	1.94253i
$688$	499.552	−	109.808i	0.726093	−	0.159605i
$689$	81.6121	+	33.8048i	0.118450	+	0.0490636i
$690$	−205.931	−	66.8889i	−0.298451	−	0.0969405i
$691$	−324.662	+	1070.27i	−0.469844	+	1.54887i	0.327206	+	0.944953i	$0.393893\pi$
$691$	−324.662	+	1070.27i	−0.469844	+	1.54887i	−0.797049	+	0.603914i	$0.793607\pi$
$692$	−564.854	+	147.513i	−0.816262	+	0.213170i
$693$	−17.5556	+	178.245i	−0.0253327	+	0.257207i
$694$	16.2578	−	2.90489i	0.0234262	−	0.00418573i
$695$	29.6283	+	148.952i	0.0426307	+	0.214319i
$696$	976.799	+	154.419i	1.40345	+	0.221866i
$697$	95.4285	−	479.751i	0.136913	−	0.688309i
$698$	568.617	−	546.821i	0.814637	−	0.783411i
$699$	−829.485	+	251.622i	−1.18667	+	0.359974i
$700$	258.795	−	41.0405i	0.369707	−	0.0586292i
$701$	−880.474	−	722.586i	−1.25603	−	1.03079i	−0.997906	−	0.0646809i	$-0.979397\pi$
$701$	−880.474	−	722.586i	−1.25603	−	1.03079i	−0.258120	−	0.966113i	$-0.583103\pi$
$702$	325.448	+	38.4873i	0.463601	+	0.0548252i
$703$	25.9497			0.0369128
$704$	−342.781	−	356.099i	−0.486905	−	0.505823i
$705$			269.706i			0.382561i
$706$	162.838	+	19.2571i	0.230649	+	0.0272764i
$707$	147.539	−	179.777i	0.208684	−	0.254282i
$708$	622.444	−	857.069i	0.879158	−	1.21055i
$709$	336.349	+	1108.79i	0.474399	+	1.56388i	0.788835	+	0.614605i	$0.210685\pi$
$709$	336.349	+	1108.79i	0.474399	+	1.56388i	−0.314436	+	0.949279i	$0.601815\pi$
$710$	−398.031	+	382.774i	−0.560607	+	0.539118i
$711$	−155.419	−	30.9147i	−0.218592	−	0.0434806i
$712$	−442.621	+	722.764i	−0.621659	+	1.01512i
$713$	490.285	−	97.5238i	0.687637	−	0.136780i
$714$	500.256	−	89.3844i	0.700639	−	0.125188i
$715$	344.787	+	33.9586i	0.482220	+	0.0474945i
$716$	910.798	+	533.591i	1.27206	+	0.745238i
$717$	−8.90843	−	2.70234i	−0.0124246	−	0.00376896i
$718$	−750.792	−	243.867i	−1.04567	−	0.339647i
$719$	−421.418	+	1017.39i	−0.586117	+	1.41501i	0.301070	+	0.953602i	$0.402656\pi$
$719$	−421.418	+	1017.39i	−0.586117	+	1.41501i	−0.887187	+	0.461410i	$0.847344\pi$
$720$	5.25733	+	262.537i	0.00730185	+	0.364635i
$721$	−511.898	+	212.035i	−0.709983	+	0.294085i
$722$	37.8739	+	480.638i	0.0524569	+	0.665703i
$723$	517.824	−	276.783i	0.716216	−	0.382825i
$724$	442.115	+	153.216i	0.610657	+	0.211625i
$725$	−377.650	−	460.168i	−0.520896	−	0.634714i
$726$	475.994	+	104.388i	0.655639	+	0.143785i
$727$	−226.678	+	339.247i	−0.311799	+	0.466640i	−0.953962	−	0.299928i	$-0.903037\pi$
$727$	−226.678	+	339.247i	−0.311799	+	0.466640i	0.642163	+	0.766568i	$0.278037\pi$
$728$	−29.7080	+	506.258i	−0.0408076	+	0.695409i
$729$	185.641	+	277.832i	0.254652	+	0.381114i
$730$	−209.206	+	478.412i	−0.286584	+	0.655359i
$731$	−526.611	−	281.479i	−0.720398	−	0.385061i
$732$	1544.47	+	60.3825i	2.10993	+	0.0824898i
$733$	−660.404	+	65.0441i	−0.900961	+	0.0887369i	−0.537881	−	0.843021i	$-0.680775\pi$
$733$	−660.404	+	65.0441i	−0.900961	+	0.0887369i	−0.363080	+	0.931758i	$0.618275\pi$
$734$	−670.610	+	1197.73i	−0.913637	+	1.63179i
$735$	253.670	+	253.670i	0.345130	+	0.345130i
$736$	332.551	+	137.559i	0.451836	+	0.186900i
$737$	−337.601	−	337.601i	−0.458074	−	0.458074i
$738$	96.2845	+	341.272i	0.130467	+	0.462429i
$739$	−115.552	+	11.3808i	−0.156362	+	0.0154003i	−0.175895	−	0.984409i	$-0.556282\pi$
$739$	−115.552	+	11.3808i	−0.156362	+	0.0154003i	0.0195331	+	0.999809i	$0.493782\pi$
$740$	−20.8667	−	9.61480i	−0.0281983	−	0.0129930i
$741$	−709.810	−	379.401i	−0.957909	−	0.512013i
$742$	30.4508	−	11.9216i	0.0410388	−	0.0160669i
$743$	221.939	+	332.156i	0.298707	+	0.447047i	0.950215	−	0.311595i	$-0.100863\pi$
$743$	221.939	+	332.156i	0.298707	+	0.447047i	−0.651508	+	0.758642i	$0.725863\pi$
$744$	−714.417	−	1218.10i	−0.960238	−	1.63723i
$745$	−170.213	+	254.741i	−0.228473	+	0.341934i
$746$	−145.140	+	92.9298i	−0.194557	+	0.124571i
$747$	110.286	+	134.384i	0.147638	+	0.179898i
$748$	34.0819	+	576.025i	0.0455641	+	0.770086i
$749$	151.634	−	81.0502i	0.202449	−	0.108211i
$750$	551.651	−	646.027i	0.735535	−	0.861370i
$751$	−182.510	+	75.5983i	−0.243023	+	0.100663i	−0.500871	−	0.865522i	$-0.666987\pi$
$751$	−182.510	+	75.5983i	−0.243023	+	0.100663i	0.257848	+	0.966186i	$0.416987\pi$
$752$	34.9981	−	446.907i	0.0465400	−	0.594291i
$753$	−93.0980	+	224.759i	−0.123636	+	0.298484i
$754$	1026.50	−	523.154i	1.36141	−	0.693838i
$755$	−202.010	−	61.2790i	−0.267562	−	0.0811642i
$756$	96.7147	−	73.2406i	0.127930	−	0.0968791i
$757$	−620.129	−	61.0774i	−0.819193	−	0.0806835i	−0.320266	−	0.947328i	$-0.603772\pi$
$757$	−620.129	−	61.0774i	−0.819193	−	0.0806835i	−0.498927	+	0.866644i	$0.666272\pi$
$758$	−1118.55	−	779.425i	−1.47566	−	1.02826i
$759$	338.289	−	67.2899i	0.445704	−	0.0886560i
$760$	−73.4497	+	199.272i	−0.0966444	+	0.262201i
$761$	819.531	+	163.015i	1.07691	+	0.214211i	0.701517	−	0.712653i	$-0.252507\pi$
$761$	819.531	+	163.015i	1.07691	+	0.214211i	0.375396	+	0.926864i	$0.377507\pi$
$762$	−16.5272	+	845.789i	−0.0216892	+	1.10996i
$763$	−171.720	−	566.085i	−0.225059	−	0.741920i
$764$	−284.593	+	1186.43i	−0.372505	+	1.55292i
$765$	194.477	−	236.971i	0.254219	−	0.309767i
$766$	−866.401	−	1098.81i	−1.13107	−	1.43447i
$767$		−	1234.05i		−	1.60893i
$768$	59.0631	−	1014.91i	0.0769050	−	1.32150i
$769$	58.7633			0.0764152			0.0382076	−	0.999270i	$-0.487835\pi$
$769$	58.7633			0.0764152			0.0382076	+	0.999270i	$0.487835\pi$
$770$	100.713	−	79.4115i	0.130796	−	0.103132i
$771$	1224.67	+	1005.06i	1.58842	+	1.30358i
$772$	−1384.61	−	332.132i	−1.79354	−	0.430222i
$773$	719.349	−	218.212i	0.930594	−	0.282293i	0.211638	−	0.977348i	$-0.432120\pi$
$773$	719.349	−	218.212i	0.930594	−	0.282293i	0.718956	+	0.695055i	$0.244620\pi$
$774$	432.780	+	8.45677i	0.559148	+	0.0109261i
$775$	−165.837	+	833.719i	−0.213983	+	1.07577i
$776$	−262.502	+	712.181i	−0.338276	+	0.917758i
$777$	−6.28820	−	31.6129i	−0.00809293	−	0.0406859i
$778$	−8.36535	+	12.0051i	−0.0107524	+	0.0154307i
$779$	−28.1103	+	285.409i	−0.0360852	+	0.366379i
$780$	430.200	+	568.082i	0.551538	+	0.728310i
$781$	255.357	−	841.799i	0.326961	−	1.07785i
$782$	−190.774	−	374.325i	−0.243956	−	0.478676i
$783$	−254.636	−	105.474i	−0.325206	−	0.134705i
$784$	−387.419	−	453.254i	−0.494157	−	0.578130i
$785$	143.455	+	346.331i	0.182745	+	0.441186i
$786$	−1005.36	−	858.492i	−1.27909	−	1.09223i
$787$	131.287	+	245.621i	0.166820	+	0.312098i	0.951416	−	0.307910i	$-0.0996295\pi$
$787$	131.287	+	245.621i	0.166820	+	0.312098i	−0.784596	+	0.620008i	$0.787130\pi$
$788$	522.438	−	30.9114i	0.662992	−	0.0392276i
$789$	253.772	−	208.265i	0.321637	−	0.263961i
$790$	61.1866	+	95.5625i	0.0774513	+	0.120965i
$791$	593.907	+	396.836i	0.750830	+	0.501689i
$792$	−211.623	−	360.822i	−0.267200	−	0.455584i
$793$	1497.24	−	1000.42i	1.88807	−	1.26157i
$794$	−275.033	−	702.504i	−0.346389	−	0.884765i
$795$	21.6608	−	40.5245i	0.0272463	−	0.0509743i
$796$	−37.6885	+	81.7943i	−0.0473473	+	0.102757i
$797$	76.1601	+	773.267i	0.0955585	+	0.970222i	0.916721	+	0.399527i	$0.130826\pi$
$797$	76.1601	+	773.267i	0.0955585	+	0.970222i	−0.821163	+	0.570694i	$0.806674\pi$
$798$	−286.753	+	80.9026i	−0.359339	+	0.101382i
$799$	−370.052	+	370.052i	−0.463144	+	0.463144i
$800$	−432.515	+	432.934i	−0.540644	+	0.541168i
$801$	−507.179	+	507.179i	−0.633183	+	0.633183i
$802$	−690.516	−	386.620i	−0.860993	−	0.482070i
$803$	−81.5293	−	827.781i	−0.101531	−	1.03086i
$804$	38.3631	−	981.253i	0.0477153	−	1.22046i
$805$	−44.0199	+	82.3555i	−0.0546831	+	0.102305i
$806$	−1507.36	−	659.160i	−1.87018	−	0.817817i
$807$	−374.814	+	250.442i	−0.464453	+	0.310338i
$808$	−31.8187	+	542.227i	−0.0393795	+	0.671073i
$809$	−182.556	−	121.980i	−0.225656	−	0.150779i	0.437603	−	0.899168i	$-0.355827\pi$
$809$	−182.556	−	121.980i	−0.225656	−	0.150779i	−0.663260	+	0.748389i	$0.730827\pi$
$810$	99.7988	−	455.068i	0.123208	−	0.561812i
$811$	689.753	−	566.065i	0.850497	−	0.697984i	−0.104525	−	0.994522i	$-0.533332\pi$
$811$	689.753	−	566.065i	0.850497	−	0.697984i	0.955021	+	0.296538i	$0.0958321\pi$
$812$	139.659	−	402.994i	0.171993	−	0.496298i
$813$	438.994	+	821.300i	0.539968	+	1.01021i
$814$	36.4863	−	2.87509i	0.0448235	−	0.00353205i
$815$	−255.861	−	617.703i	−0.313940	−	0.757918i
$816$	−822.256	+	855.861i	−1.00767	+	1.04885i
$817$	323.443	+	133.974i	0.395891	+	0.163983i
$818$	133.404	−	410.711i	0.163086	−	0.502092i
$819$	−124.585	+	410.702i	−0.152118	+	0.501467i
$820$	128.353	−	219.089i	0.156528	−	0.267181i
$821$	55.8674	−	567.231i	0.0680480	−	0.690903i	−0.899280	−	0.437374i	$-0.855909\pi$
$821$	55.8674	−	567.231i	0.0680480	−	0.690903i	0.967328	−	0.253529i	$-0.0815914\pi$
$822$	49.9510	+	279.560i	0.0607677	+	0.340097i
$823$	−77.9875	−	392.070i	−0.0947600	−	0.476391i	−0.998801	−	0.0489460i	$-0.984414\pi$
$823$	−77.9875	−	392.070i	−0.0947600	−	0.476391i	0.904041	−	0.427445i	$-0.140586\pi$
$824$	675.810	−	1103.54i	0.820158	−	1.33925i
$825$	−114.425	+	575.253i	−0.138697	+	0.697276i
$826$	−316.658	−	329.280i	−0.383363	−	0.398644i
$827$	−353.101	+	107.112i	−0.426966	+	0.129519i	−0.496452	−	0.868064i	$-0.665364\pi$
$827$	−353.101	+	107.112i	−0.426966	+	0.129519i	0.0694861	+	0.997583i	$0.477864\pi$
$828$	246.433	+	178.971i	0.297624	+	0.216148i
$829$	−641.774	−	526.691i	−0.774155	−	0.635332i	0.162052	−	0.986782i	$-0.448189\pi$
$829$	−641.774	−	526.691i	−0.774155	−	0.635332i	−0.936207	+	0.351450i	$0.885689\pi$
$830$	14.6198	−	123.625i	0.0176143	−	0.148946i
$831$	−16.9998			−0.0204570
$832$	−639.132	−	997.146i	−0.768187	−	1.19849i
$833$			696.102i			0.835656i
$834$	58.4384	−	494.154i	0.0700701	−	0.592511i
$835$	−222.064	+	270.586i	−0.265945	+	0.324055i
$836$	−52.9890	−	334.140i	−0.0633839	−	0.399689i
$837$	114.247	+	376.621i	0.136496	+	0.449966i
$838$	442.635	+	460.279i	0.528204	+	0.549259i
$839$	1561.46	+	310.594i	1.86110	+	0.370196i	0.992186	−	0.124770i	$-0.0398191\pi$
$839$	1561.46	+	310.594i	1.86110	+	0.370196i	0.868913	+	0.494965i	$0.164819\pi$
$840$	260.560	+	41.1910i	0.310190	+	0.0490369i
$841$	−125.507	+	24.9648i	−0.149235	+	0.0296847i
$842$	219.377	+	1227.79i	0.260543	+	1.45818i
$843$	1741.05	+	171.479i	2.06530	+	0.203415i
$844$	−283.035	−	1083.79i	−0.335349	−	1.28411i
$845$	402.414	+	122.071i	0.476229	+	0.144463i
$846$	117.198	−	360.818i	0.138532	−	0.426499i
$847$	80.4271	−	194.168i	0.0949552	−	0.229242i
$848$	−41.1510	+	64.3391i	−0.0485271	+	0.0758715i
$849$	−1968.93	+	815.557i	−2.31911	+	0.960609i
$850$	712.222	−	56.1225i	0.837909	−	0.0660265i
$851$	−23.5014	+	12.5618i	−0.0276162	+	0.0147612i
$852$	1627.79	−	789.923i	1.91055	−	0.927140i
$853$	262.390	+	319.723i	0.307608	+	0.374822i	0.903752	−	0.428056i	$-0.140801\pi$
$853$	262.390	+	319.723i	0.307608	+	0.374822i	−0.596144	+	0.802878i	$0.703301\pi$
$854$	142.797	−	651.134i	0.167210	−	0.762452i
$855$	−99.8554	+	149.444i	−0.116790	+	0.174789i
$856$	−175.137	+	361.349i	−0.204600	+	0.422137i
$857$	568.402	+	850.674i	0.663246	+	0.992618i	0.998721	+	0.0505687i	$0.0161034\pi$
$857$	568.402	+	850.674i	0.663246	+	0.992618i	−0.335474	+	0.942049i	$0.608897\pi$
$858$	−1040.06	−	454.810i	−1.21219	−	0.530082i
$859$	−677.560	−	362.163i	−0.788777	−	0.421610i	0.0272463	−	0.999629i	$-0.491326\pi$
$859$	−677.560	−	362.163i	−0.788777	−	0.421610i	−0.816024	+	0.578018i	$0.803826\pi$
$860$	−210.448	−	227.573i	−0.244707	−	0.264619i
$861$	354.508	−	34.9160i	0.411740	−	0.0405529i
$862$	43.8416	+	24.5469i	0.0508603	+	0.0284767i
$863$	19.4736	+	19.4736i	0.0225650	+	0.0225650i	0.718299	−	0.695734i	$-0.244921\pi$
$863$	19.4736	+	19.4736i	0.0225650	+	0.0225650i	−0.695734	+	0.718299i	$0.744921\pi$
$864$	−82.1166	+	271.175i	−0.0950424	+	0.313860i
$865$	250.168	+	250.168i	0.289211	+	0.289211i
$866$	88.3069	−	24.9143i	0.101971	−	0.0287695i
$867$	236.746	−	23.3174i	0.273063	−	0.0268944i
$868$	−571.349	+	210.908i	−0.658236	+	0.242981i
$869$	−159.416	−	85.2098i	−0.183448	−	0.0980550i
$870$	−218.484	−	558.063i	−0.251131	−	0.641451i
$871$	−635.604	−	951.249i	−0.729740	−	1.09213i
$872$	1101.80	+	833.538i	1.26353	+	0.955892i
$873$	−356.874	+	534.099i	−0.408790	+	0.611797i
$874$	132.824	+	207.448i	0.151973	+	0.237354i
$875$	−232.428	−	283.215i	−0.265632	−	0.323674i
$876$	1136.17	−	1279.08i	1.29700	−	1.46013i
$877$	−422.150	+	225.644i	−0.481357	+	0.257290i	−0.694182	−	0.719800i	$-0.744234\pi$
$877$	−422.150	+	225.644i	−0.481357	+	0.257290i	0.212825	+	0.977090i	$0.431734\pi$
$878$	−26.4706	−	22.6036i	−0.0301487	−	0.0257444i
$879$	−998.825	+	413.727i	−1.13632	+	0.470679i
$880$	−81.1949	+	288.323i	−0.0922669	+	0.327640i
$881$	−516.631	+	1247.26i	−0.586415	+	1.41573i	0.300493	+	0.953784i	$0.402849\pi$
$881$	−516.631	+	1247.26i	−0.586415	+	1.41573i	−0.886908	+	0.461947i	$0.847151\pi$
$882$	−229.135	−	449.596i	−0.259791	−	0.509746i
$883$	−34.3314	−	10.4143i	−0.0388804	−	0.0117942i	0.270785	−	0.962640i	$-0.412717\pi$
$883$	−34.3314	−	10.4143i	−0.0388804	−	0.0117942i	−0.309665	+	0.950846i	$0.600217\pi$
$884$	−189.182	+	1369.70i	−0.214007	+	1.54944i
$885$	−638.830	−	62.9192i	−0.721841	−	0.0710952i
$886$	−122.908	+	176.384i	−0.138722	+	0.199080i
$887$	−131.045	+	26.0665i	−0.147740	+	0.0293873i	−0.268406	−	0.963306i	$-0.586497\pi$
$887$	−131.045	+	26.0665i	−0.147740	+	0.0293873i	0.120666	+	0.992693i	$0.461497\pi$
$888$	55.2932	+	51.0828i	0.0622672	+	0.0575256i
$889$	357.833	+	71.1774i	0.402512	+	0.0800645i
$890$	513.517	+	10.0344i	0.576985	+	0.0112746i
$891$	215.434	+	710.189i	0.241789	+	0.797070i
$892$	865.465	−	530.588i	0.970252	−	0.594830i
$893$	194.652	−	237.184i	0.217975	−	0.265603i
$894$	788.263	−	621.541i	0.881726	−	0.695236i
$895$		−	639.705i		−	0.714754i
$896$	−426.407	−	102.066i	−0.475901	−	0.113912i
$897$	826.501			0.921406
$898$	−603.636	−	765.556i	−0.672201	−	0.852513i
$899$	1069.57	+	877.772i	1.18973	+	0.976387i
$900$	−441.534	+	270.690i	−0.490593	+	0.300767i
$901$	85.3220	−	25.8821i	0.0946970	−	0.0287260i
$902$	−7.90242	+	404.411i	−0.00876100	+	0.448349i
$903$	84.8352	−	426.495i	0.0939482	−	0.472309i
$904$	−1666.90	+	65.9779i	−1.84392	+	0.0729843i
$905$	−55.3202	−	278.113i	−0.0611273	−	0.307308i
$906$	567.479	+	395.429i	0.626357	+	0.436456i
$907$	−46.8359	+	475.533i	−0.0516383	+	0.524292i	0.934218	+	0.356701i	$0.116099\pi$
$907$	−46.8359	+	475.533i	−0.0516383	+	0.524292i	−0.985857	+	0.167591i	$0.946401\pi$
$908$	−188.908	+	1367.72i	−0.208049	+	1.50630i
$909$	−133.437	+	439.881i	−0.146795	+	0.483918i
$910$	273.818	−	139.551i	0.300899	−	0.153352i
$911$	417.843	+	173.076i	0.458664	+	0.189985i	0.600038	−	0.799971i	$-0.295152\pi$
$911$	417.843	+	173.076i	0.458664	+	0.189985i	−0.141374	+	0.989956i	$0.545152\pi$
$912$	430.585	−	546.630i	0.472133	−	0.599376i
$913$	75.8883	+	183.211i	0.0831197	+	0.200669i
$914$	357.456	−	418.609i	0.391089	−	0.457997i
$915$	−441.551	−	826.083i	−0.482569	−	0.902823i
$916$	966.242	−	1087.77i	1.05485	−	1.18753i
$917$	−440.745	+	361.710i	−0.480638	+	0.394450i
$918$	278.568	−	178.361i	0.303451	−	0.194293i
$919$	−41.5784	−	27.7818i	−0.0452431	−	0.0302305i	0.532743	−	0.846277i	$-0.321161\pi$
$919$	−41.5784	−	27.7818i	−0.0452431	−	0.0302305i	−0.577986	+	0.816047i	$0.696161\pi$
$920$	−29.9441	−	216.027i	−0.0325480	−	0.234812i
$921$	−157.294	+	105.100i	−0.170786	+	0.114116i
$922$	−458.249	+	179.407i	−0.497017	+	0.194584i
$923$	993.663	−	1859.01i	1.07656	−	2.01410i
$924$	−394.222	+	145.523i	−0.426647	+	0.157492i
$925$	−4.44157	−	45.0960i	−0.00480169	−	0.0487524i
$926$	−9.21917	−	32.6766i	−0.00995591	−	0.0352879i
$927$	774.380	−	774.380i	0.835361	−	0.835361i
$928$	289.615	+	953.071i	0.312085	+	1.02702i
$929$	694.414	−	694.414i	0.747485	−	0.747485i	−0.226521	−	0.974006i	$-0.572735\pi$
$929$	694.414	−	694.414i	0.747485	−	0.747485i	0.974006	+	0.226521i	$0.0727351\pi$
$930$	−418.082	+	746.709i	−0.449550	+	0.802913i
$931$	−40.0034	−	406.161i	−0.0429682	−	0.436263i
$932$	−592.783	−	641.020i	−0.636033	−	0.687790i
$933$	−836.757	+	1565.46i	−0.896845	+	1.67788i
$934$	−101.495	+	232.098i	−0.108667	+	0.248499i
$935$	290.757	−	194.278i	0.310970	−	0.207784i
$936$	−328.675	−	946.931i	−0.351149	−	1.01168i
$937$	−193.861	−	129.534i	−0.206896	−	0.138243i	0.447806	−	0.894131i	$-0.352206\pi$
$937$	−193.861	−	129.534i	−0.206896	−	0.138243i	−0.654701	+	0.755888i	$0.727206\pi$
$938$	−413.689	−	90.7241i	−0.441033	−	0.0967208i
$939$	141.883	−	116.441i	0.151100	−	0.124005i
$940$	−244.404	+	118.603i	−0.260005	+	0.126174i
$941$	−139.832	−	261.607i	−0.148599	−	0.278010i	0.796598	−	0.604509i	$-0.206631\pi$
$941$	−139.832	−	261.607i	−0.148599	−	0.278010i	−0.945197	+	0.326500i	$0.894131\pi$
$942$	−96.4851	−	1224.44i	−0.102426	−	1.29983i
$943$	−112.703	−	272.089i	−0.119515	−	0.288535i
$944$	1050.39	+	187.155i	1.11270	+	0.198258i
$945$	−67.9239	−	28.1350i	−0.0718772	−	0.0297725i
$946$	469.617	+	152.538i	0.496424	+	0.161245i
$947$	138.776	−	457.483i	0.146543	−	0.483087i	−0.852683	−	0.522429i	$-0.825026\pi$
$947$	138.776	−	457.483i	0.146543	−	0.483087i	0.999226	+	0.0393417i	$0.0125261\pi$
$948$	−93.9434	−	359.725i	−0.0990964	−	0.379457i
$949$	195.363	−	1983.56i	0.205862	−	2.09016i
$950$	−412.342	+	73.6762i	−0.434044	+	0.0775539i
$951$	−279.129	−	1403.28i	−0.293511	−	1.47558i
$952$	300.987	+	414.020i	0.316163	+	0.434895i
$953$	−184.697	+	928.536i	−0.193806	+	0.974330i	0.754337	+	0.656487i	$0.227958\pi$
$953$	−184.697	+	928.536i	−0.193806	+	0.974330i	−0.948143	+	0.317843i	$0.897042\pi$
$954$	−46.5879	+	44.8021i	−0.0488343	+	0.0469623i
$955$	707.554	−	214.634i	0.740894	−	0.224748i
$956$	−1.46865	−	9.26108i	−0.00153624	−	0.00968732i
$957$	737.985	+	605.649i	0.771144	+	0.632862i
$958$	−354.332	−	41.9032i	−0.369866	−	0.0437402i
$959$	122.479			0.127715
$960$	−548.779	+	280.019i	−0.571645	+	0.291686i
$961$		−	1014.78i		−	1.05596i
$962$	87.0939	+	10.2997i	0.0905342	+	0.0107065i
$963$	−215.589	+	262.696i	−0.223873	+	0.272789i
$964$	478.531	+	347.531i	0.496401	+	0.360510i
$965$	250.486	+	825.743i	0.259571	+	0.855692i
$966$	220.534	−	212.081i	0.228296	−	0.219545i
$967$	−946.751	−	188.320i	−0.979060	−	0.194747i	−0.320478	−	0.947256i	$-0.603843\pi$
$967$	−946.751	−	188.320i	−0.979060	−	0.194747i	−0.658582	+	0.752509i	$0.728843\pi$
$968$	114.723	+	477.245i	0.118516	+	0.493022i
$969$	−796.752	+	158.484i	−0.822242	+	0.163554i
$970$	452.806	−	80.9062i	0.466810	−	0.0834084i
$971$	1446.85	+	142.503i	1.49007	+	0.146759i	0.810016	−	0.586407i	$-0.199458\pi$
$971$	1446.85	+	142.503i	1.49007	+	0.146759i	0.680050	+	0.733166i	$0.261958\pi$
$972$	−610.481	+	1042.04i	−0.628067	+	1.07206i
$973$	−205.364	−	62.2965i	−0.211063	−	0.0640251i
$974$	756.796	+	245.817i	0.776998	+	0.252379i
$975$	−537.841	+	1298.46i	−0.551631	+	1.33176i
$976$	624.461	+	1426.13i	0.639817	+	1.46120i
$977$	−585.801	+	242.647i	−0.599591	+	0.248359i	−0.661771	−	0.749706i	$-0.730195\pi$
$977$	−585.801	+	242.647i	−0.599591	+	0.248359i	0.0621796	+	0.998065i	$0.480195\pi$
$978$	172.087	+	2183.87i	0.175959	+	2.23300i
$979$	−721.572	+	385.688i	−0.737050	+	0.393962i
$980$	−118.322	+	341.425i	−0.120737	+	0.348393i
$981$	741.748	+	903.823i	0.756114	+	0.921328i
$982$	1556.76	+	341.406i	1.58530	+	0.347664i
$983$	−309.764	+	463.594i	−0.315121	+	0.471612i	−0.954892	−	0.296954i	$-0.904029\pi$
$983$	−309.764	+	463.594i	−0.315121	+	0.471612i	0.639771	+	0.768566i	$0.279029\pi$
$984$	−621.733	+	552.809i	−0.631843	+	0.561798i
$985$	−176.204	−	263.709i	−0.178888	−	0.267724i
$986$	465.922	−	1065.47i	0.472538	−	1.08060i
$987$	−336.115	−	179.657i	−0.340542	−	0.182023i
$988$	31.6703	−	810.065i	0.0320550	−	0.819903i
$989$	−357.781	+	35.2383i	−0.361760	+	0.0356303i
$990$	−123.843	+	221.188i	−0.125094	+	0.223422i
$991$	422.055	+	422.055i	0.425888	+	0.425888i	0.887225	−	0.461337i	$-0.152630\pi$
$991$	422.055	+	422.055i	0.425888	+	0.425888i	−0.461337	+	0.887225i	$0.652630\pi$
$992$	789.665	−	1183.06i	0.796033	−	1.19260i
$993$	−920.618	−	920.618i	−0.927107	−	0.927107i
$994$	−211.886	−	751.013i	−0.213165	−	0.755546i
$995$	54.3148	−	5.34954i	0.0545877	−	0.00537642i
$996$	−170.690	+	370.444i	−0.171375	+	0.371932i
$997$	647.395	+	346.040i	0.649343	+	0.347081i	0.762962	−	0.646443i	$-0.223744\pi$
$997$	647.395	+	346.040i	0.649343	+	0.347081i	−0.113619	+	0.993524i	$0.536244\pi$
$998$	−962.554	+	376.844i	−0.964483	+	0.377599i
$999$	−11.6559	−	17.4444i	−0.0116676	−	0.0174618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.l.a.43.7	yes	496
128.3	odd	32	inner	128.3.l.a.3.7	✓	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.3.l.a.3.7	✓	496	128.3	odd	32	inner
128.3.l.a.43.7	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)

\(f(q)\)	\(=\)	\(q+(-1.57051 + 1.23834i) q^{2} +(-3.06977 - 2.51930i) q^{3} +(0.933028 - 3.88966i) q^{4} +(-2.31969 + 0.703669i) q^{5} +(7.94087 + 0.155169i) q^{6} +(0.668264 - 3.35959i) q^{7} +(3.35139 + 7.26417i) q^{8} +(1.32084 + 6.64029i) q^{9} +O(q^{10})\)	\(q+(-1.57051 + 1.23834i) q^{2} +(-3.06977 - 2.51930i) q^{3} +(0.933028 - 3.88966i) q^{4} +(-2.31969 + 0.703669i) q^{5} +(7.94087 + 0.155169i) q^{6} +(0.668264 - 3.35959i) q^{7} +(3.35139 + 7.26417i) q^{8} +(1.32084 + 6.64029i) q^{9} +(2.77172 - 3.97768i) q^{10} +(-0.756988 + 7.68583i) q^{11} +(-12.6634 + 9.58981i) q^{12} +(-5.37205 + 17.7093i) q^{13} +(3.11080 + 6.10382i) q^{14} +(8.89366 + 3.68388i) q^{15} +(-14.2589 - 7.25832i) q^{16} +(7.14813 + 17.2571i) q^{17} +(-10.2973 - 8.79303i) q^{18} +(-5.16252 - 9.65839i) q^{19} +(0.572702 + 9.67933i) q^{20} +(-10.5152 + 8.62963i) q^{21} +(-8.32881 - 13.0081i) q^{22} +(9.35088 + 6.24806i) q^{23} +(8.01261 - 30.7425i) q^{24} +(-15.9010 + 10.6247i) q^{25} +(-13.4932 - 34.4651i) q^{26} +(-4.17386 + 7.80874i) q^{27} +(-12.4442 - 5.73391i) q^{28} +(3.05110 + 30.9783i) q^{29} +(-18.5295 + 5.22780i) q^{30} +(31.4307 - 31.4307i) q^{31} +(31.3821 - 6.25809i) q^{32} +(21.6867 - 21.6867i) q^{33} +(-32.5964 - 18.2507i) q^{34} +(0.813877 + 8.26343i) q^{35} +(27.0609 + 1.05797i) q^{36} +(-1.11698 + 2.08972i) q^{37} +(20.0682 + 8.77569i) q^{38} +(61.1060 - 40.8297i) q^{39} +(-12.8857 - 14.4923i) q^{40} +(-21.7739 - 14.5488i) q^{41} +(5.82790 - 26.5744i) q^{42} +(-24.7111 + 20.2799i) q^{43} +(29.1890 + 10.1155i) q^{44} +(-7.73649 - 14.4740i) q^{45} +(-22.4229 + 1.76691i) q^{46} +(10.7217 + 25.8845i) q^{47} +(25.4858 + 58.2039i) q^{48} +(34.4298 + 14.2613i) q^{49} +(11.8157 - 36.3770i) q^{50} +(21.5327 - 70.9838i) q^{51} +(63.8708 + 37.4187i) q^{52} +(0.467870 - 4.75036i) q^{53} +(-3.11477 - 17.4324i) q^{54} +(-3.65230 - 18.3614i) q^{55} +(26.6442 - 6.40491i) q^{56} +(-8.48461 + 42.6550i) q^{57} +(-43.1535 - 44.8736i) q^{58} +(-63.8118 + 19.3571i) q^{59} +(22.6271 - 31.1562i) q^{60} +(-75.2167 - 61.7287i) q^{61} +(-10.4405 + 88.2842i) q^{62} +23.1913 q^{63} +(-41.5364 + 48.6901i) q^{64} -44.8601i q^{65} +(-7.20375 + 60.9147i) q^{66} +(-39.2184 + 47.7878i) q^{67} +(73.7938 - 11.7024i) q^{68} +(-12.9644 - 42.7378i) q^{69} +(-11.5111 - 11.9700i) q^{70} +(-111.715 - 22.2214i) q^{71} +(-43.8096 + 31.8490i) q^{72} +(-105.633 + 21.0117i) q^{73} +(-0.833552 - 4.66512i) q^{74} +(75.5791 + 7.44389i) q^{75} +(-42.3847 + 11.0689i) q^{76} +(25.3154 + 7.67933i) q^{77} +(-45.4067 + 139.794i) q^{78} +(-8.95686 + 21.6238i) q^{79} +(38.1837 + 6.80347i) q^{80} +(88.7805 - 36.7741i) q^{81} +(52.2126 - 4.11431i) q^{82} +(22.6453 - 12.1042i) q^{83} +(23.7553 + 48.9524i) q^{84} +(-28.7247 - 35.0012i) q^{85} +(13.6958 - 62.4506i) q^{86} +(68.6775 - 102.783i) q^{87} +(-58.3681 + 20.2593i) q^{88} +(58.8575 + 88.0865i) q^{89} +(30.0740 + 13.1511i) q^{90} +(55.9060 + 29.8824i) q^{91} +(33.0275 - 30.5421i) q^{92} +(-175.668 + 17.3018i) q^{93} +(-48.8924 - 27.3749i) q^{94} +(18.7717 + 18.7717i) q^{95} +(-112.102 - 59.8500i) q^{96} +(67.0884 + 67.0884i) q^{97} +(-71.7329 + 20.2383i) q^{98} +(-52.0360 + 5.12510i) 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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