LMFDB - Embedded newform 418.2.n.e.125.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			125.8
Character	$\chi$	$=$	418.125
Dual form			418.2.n.e.311.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 - 0.406737i) q^{2} +(1.97217 + 2.19032i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.204659 + 1.94720i) q^{5} +(2.69255 + 1.19880i) q^{6} +(-0.518534 - 1.59588i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.594450 + 5.65582i) q^{9} +O(q^{10})$	\(q+(0.913545 - 0.406737i) q^{2} +(1.97217 + 2.19032i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.204659 + 1.94720i) q^{5} +(2.69255 + 1.19880i) q^{6} +(-0.518534 - 1.59588i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.594450 + 5.65582i) q^{9} +(0.978965 + 1.69562i) q^{10} +(-2.33399 + 2.35637i) q^{11} +2.94737 q^{12} +(0.0425494 - 0.404831i) q^{13} +(-1.12281 - 1.24701i) q^{14} +(-3.86137 + 4.28849i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.663968 - 6.31723i) q^{17} +(1.75737 + 5.40863i) q^{18} +(1.82479 - 3.95855i) q^{19} +(1.58400 + 1.15084i) q^{20} +(2.47286 - 4.28311i) q^{21} +(-1.17379 + 3.10197i) q^{22} +(-2.06962 - 3.58469i) q^{23} +(2.69255 - 1.19880i) q^{24} +(1.14102 - 0.242532i) q^{25} +(-0.125789 - 0.387138i) q^{26} +(-6.40700 + 4.65496i) q^{27} +(-1.53294 - 0.682509i) q^{28} +(-1.26928 + 1.40968i) q^{29} +(-1.78325 + 5.48829i) q^{30} +(7.04121 + 5.11574i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-9.76424 - 0.465030i) q^{33} +(-3.17601 - 5.50102i) q^{34} +(3.00139 - 1.33630i) q^{35} +(3.80533 + 4.22624i) q^{36} +(1.37040 + 4.21765i) q^{37} +(0.0569431 - 4.35853i) q^{38} +(0.970624 - 0.705199i) q^{39} +(1.91514 + 0.407076i) q^{40} +(-4.81948 - 5.35258i) q^{41} +(0.516968 - 4.91862i) q^{42} +(-2.46726 + 4.27343i) q^{43} +(0.189376 + 3.31121i) q^{44} -11.1347 q^{45} +(-3.34872 - 2.43299i) q^{46} +(4.76679 - 1.01321i) q^{47} +(1.97217 - 2.19032i) q^{48} +(3.38515 - 2.45946i) q^{49} +(0.943730 - 0.685660i) q^{50} +(12.5273 - 13.9130i) q^{51} +(-0.272377 - 0.302505i) q^{52} +(-1.04745 + 9.96580i) q^{53} +(-3.95974 + 6.85847i) q^{54} +(-5.06600 - 4.06251i) q^{55} -1.67801 q^{56} +(12.2693 - 3.81007i) q^{57} +(-0.586176 + 1.80406i) q^{58} +(-11.0932 - 2.35792i) q^{59} +(0.603206 + 5.73912i) q^{60} +(7.59906 + 3.38332i) q^{61} +(8.51322 + 1.80954i) q^{62} +(9.33426 - 1.98406i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.796996 q^{65} +(-9.10922 + 3.54665i) q^{66} +(-3.81734 - 6.61183i) q^{67} +(-5.13890 - 3.73363i) q^{68} +(3.76997 - 11.6028i) q^{69} +(2.19838 - 2.44155i) q^{70} +(-1.37967 - 13.1267i) q^{71} +(5.19530 + 2.31310i) q^{72} +(-2.27692 - 0.483975i) q^{73} +(2.96739 + 3.29563i) q^{74} +(2.78152 + 2.02089i) q^{75} +(-1.72075 - 4.00487i) q^{76} +(4.97074 + 2.50293i) q^{77} +(0.599878 - 1.03902i) q^{78} +(-9.49291 + 4.22652i) q^{79} +(1.91514 - 0.407076i) q^{80} +(-6.14346 - 1.30583i) q^{81} +(-6.57990 - 2.92956i) q^{82} +(-10.0905 + 7.33120i) q^{83} +(-1.52831 - 4.70365i) q^{84} +(12.1650 - 2.58576i) q^{85} +(-0.515798 + 4.90749i) q^{86} -5.59088 q^{87} +(1.51980 + 2.94792i) q^{88} +(-2.50675 - 4.34182i) q^{89} +(-10.1720 + 4.52888i) q^{90} +(-0.668126 + 0.142015i) q^{91} +(-4.04880 - 0.860598i) q^{92} +(2.68138 + 25.5116i) q^{93} +(3.94257 - 2.86444i) q^{94} +(8.08157 + 2.74309i) q^{95} +(0.910786 - 2.80311i) q^{96} +(-4.50759 + 2.00691i) q^{97} +(2.09214 - 3.62369i) q^{98} +(-11.9397 - 14.6014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) $ 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$2$	0.913545	−	0.406737i	0.645974	−	0.287606i
$3$	1.97217	+	2.19032i	1.13863	+	1.26458i	0.959794	+	0.280704i	$0.0905679\pi$
$3$	1.97217	+	2.19032i	1.13863	+	1.26458i	0.178840	+	0.983878i	$0.442765\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	0.204659	+	1.94720i	0.0915264	+	0.870816i	0.939907	+	0.341430i	$0.110911\pi$
$5$	0.204659	+	1.94720i	0.0915264	+	0.870816i	−0.848381	+	0.529386i	$0.822422\pi$
$6$	2.69255	+	1.19880i	1.09923	+	0.489409i
$7$	−0.518534	−	1.59588i	−0.195987	−	0.603187i	−0.999964	−	0.00852582i	$-0.997286\pi$
$7$	−0.518534	−	1.59588i	−0.195987	−	0.603187i	0.803976	−	0.594661i	$-0.202714\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.594450	+	5.65582i	−0.198150	+	1.88527i
$10$	0.978965	+	1.69562i	0.309576	+	0.536201i
$11$	−2.33399	+	2.35637i	−0.703726	+	0.710472i
$11$	−2.33399	+	2.35637i	−0.703726	+	0.710472i
$12$	2.94737			0.850831
$13$	0.0425494	−	0.404831i	0.0118011	−	0.112280i	−0.987036	−	0.160502i	$-0.948689\pi$
$13$	0.0425494	−	0.404831i	0.0118011	−	0.112280i	0.998837	+	0.0482219i	$0.0153555\pi$
$14$	−1.12281	−	1.24701i	−0.300083	−	0.333276i
$15$	−3.86137	+	4.28849i	−0.997003	+	1.10728i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	−0.663968	−	6.31723i	−0.161036	−	1.53215i	−0.714711	−	0.699420i	$-0.753442\pi$
$17$	−0.663968	−	6.31723i	−0.161036	−	1.53215i	0.553675	−	0.832733i	$-0.313225\pi$
$18$	1.75737	+	5.40863i	0.414216	+	1.27483i
$19$	1.82479	−	3.95855i	0.418636	−	0.908154i
$19$	1.82479	−	3.95855i	0.418636	−	0.908154i
$20$	1.58400	+	1.15084i	0.354193	+	0.257336i
$21$	2.47286	−	4.28311i	0.539622	−	0.934652i
$22$	−1.17379	+	3.10197i	−0.250253	+	0.661342i
$23$	−2.06962	−	3.58469i	−0.431546	−	0.747460i	0.565460	−	0.824776i	$-0.308699\pi$
$23$	−2.06962	−	3.58469i	−0.431546	−	0.747460i	−0.997007	+	0.0773152i	$0.975365\pi$
$24$	2.69255	−	1.19880i	0.549615	−	0.244704i
$25$	1.14102	−	0.242532i	0.228205	−	0.0485064i
$26$	−0.125789	−	0.387138i	−0.0246692	−	0.0759239i
$27$	−6.40700	+	4.65496i	−1.23303	+	0.895847i
$28$	−1.53294	−	0.682509i	−0.289698	−	0.128982i
$29$	−1.26928	+	1.40968i	−0.235699	+	0.261770i	−0.849378	−	0.527786i	$-0.823022\pi$
$29$	−1.26928	+	1.40968i	−0.235699	+	0.261770i	0.613679	+	0.789556i	$0.289689\pi$
$30$	−1.78325	+	5.48829i	−0.325576	+	1.00202i
$31$	7.04121	+	5.11574i	1.26464	+	0.918813i	0.998976	−	0.0452526i	$-0.0144093\pi$
$31$	7.04121	+	5.11574i	1.26464	+	0.918813i	0.265663	+	0.964066i	$0.414409\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−9.76424	−	0.465030i	−1.69974	−	0.0809513i
$34$	−3.17601	−	5.50102i	−0.544682	−	0.943416i
$35$	3.00139	−	1.33630i	0.507327	−	0.225877i
$36$	3.80533	+	4.22624i	0.634221	+	0.704374i
$37$	1.37040	+	4.21765i	0.225292	+	0.693378i	0.998262	+	0.0589348i	$0.0187704\pi$
$37$	1.37040	+	4.21765i	0.225292	+	0.693378i	−0.772970	+	0.634443i	$0.781230\pi$
$38$	0.0569431	−	4.35853i	0.00923739	−	0.707046i
$39$	0.970624	−	0.705199i	0.155424	−	0.112922i
$40$	1.91514	+	0.407076i	0.302811	+	0.0643644i
$41$	−4.81948	−	5.35258i	−0.752676	−	0.835932i	0.238128	−	0.971234i	$-0.423466\pi$
$41$	−4.81948	−	5.35258i	−0.752676	−	0.835932i	−0.990804	+	0.135302i	$0.956800\pi$
$42$	0.516968	−	4.91862i	0.0797699	−	0.758960i
$43$	−2.46726	+	4.27343i	−0.376254	+	0.651691i	−0.990514	−	0.137413i	$-0.956121\pi$
$43$	−2.46726	+	4.27343i	−0.376254	+	0.651691i	0.614260	+	0.789104i	$0.289455\pi$
$44$	0.189376	+	3.31121i	0.0285494	+	0.499184i
$45$	−11.1347			−1.65986
$46$	−3.34872	−	2.43299i	−0.493742	−	0.358725i
$47$	4.76679	−	1.01321i	0.695307	−	0.147792i	0.153317	−	0.988177i	$-0.451004\pi$
$47$	4.76679	−	1.01321i	0.695307	−	0.147792i	0.541990	+	0.840385i	$0.317671\pi$
$48$	1.97217	−	2.19032i	0.284659	−	0.316145i
$49$	3.38515	−	2.45946i	0.483593	−	0.351351i
$50$	0.943730	−	0.685660i	0.133464	−	0.0969669i
$51$	12.5273	−	13.9130i	1.75417	−	1.94821i
$52$	−0.272377	−	0.302505i	−0.0377719	−	0.0419499i
$53$	−1.04745	+	9.96580i	−0.143878	+	1.36891i	0.649585	+	0.760289i	$0.274943\pi$
$53$	−1.04745	+	9.96580i	−0.143878	+	1.36891i	−0.793463	+	0.608619i	$0.791724\pi$
$54$	−3.95974	+	6.85847i	−0.538853	+	0.933320i
$55$	−5.06600	−	4.06251i	−0.683099	−	0.547789i
$56$	−1.67801			−0.224234
$57$	12.2693	−	3.81007i	1.62511	−	0.504656i
$58$	−0.586176	+	1.80406i	−0.0769687	+	0.236885i
$59$	−11.0932	−	2.35792i	−1.44421	−	0.306976i	−0.581858	−	0.813290i	$-0.697674\pi$
$59$	−11.0932	−	2.35792i	−1.44421	−	0.306976i	−0.862349	+	0.506315i	$0.831007\pi$
$60$	0.603206	+	5.73912i	0.0778736	+	0.740917i
$61$	7.59906	+	3.38332i	0.972960	+	0.433190i	0.830749	−	0.556647i	$-0.187912\pi$
$61$	7.59906	+	3.38332i	0.972960	+	0.433190i	0.142210	+	0.989836i	$0.454579\pi$
$62$	8.51322	+	1.80954i	1.08118	+	0.229812i
$63$	9.33426	−	1.98406i	1.17601	−	0.249968i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.796996			0.0988552
$66$	−9.10922	+	3.54665i	−1.12127	+	0.436562i
$67$	−3.81734	−	6.61183i	−0.466362	−	0.807763i	0.532899	−	0.846179i	$-0.321102\pi$
$67$	−3.81734	−	6.61183i	−0.466362	−	0.807763i	−0.999262	+	0.0384151i	$0.987769\pi$
$68$	−5.13890	−	3.73363i	−0.623183	−	0.452769i
$69$	3.76997	−	11.6028i	0.453851	−	1.39681i
$70$	2.19838	−	2.44155i	0.262757	−	0.291821i
$71$	−1.37967	−	13.1267i	−0.163736	−	1.55785i	−0.700214	−	0.713933i	$-0.746912\pi$
$71$	−1.37967	−	13.1267i	−0.163736	−	1.55785i	0.536478	−	0.843914i	$-0.319754\pi$
$72$	5.19530	+	2.31310i	0.612273	+	0.272601i
$73$	−2.27692	−	0.483975i	−0.266494	−	0.0566450i	0.0727268	−	0.997352i	$-0.476830\pi$
$73$	−2.27692	−	0.483975i	−0.266494	−	0.0566450i	−0.339220	+	0.940707i	$0.610163\pi$
$74$	2.96739	+	3.29563i	0.344953	+	0.383109i
$75$	2.78152	+	2.02089i	0.321182	+	0.233352i
$76$	−1.72075	−	4.00487i	−0.197384	−	0.459390i
$77$	4.97074	+	2.50293i	0.566469	+	0.285235i
$78$	0.599878	−	1.03902i	0.0679229	−	0.117646i
$79$	−9.49291	+	4.22652i	−1.06804	+	0.475520i	−0.864025	−	0.503448i	$-0.832064\pi$
$79$	−9.49291	+	4.22652i	−1.06804	+	0.475520i	−0.204011	+	0.978969i	$0.565398\pi$
$80$	1.91514	−	0.407076i	0.214120	−	0.0455125i
$81$	−6.14346	−	1.30583i	−0.682607	−	0.145093i
$82$	−6.57990	−	2.92956i	−0.726629	−	0.323516i
$83$	−10.0905	+	7.33120i	−1.10758	+	0.804703i	−0.982281	−	0.187416i	$-0.939989\pi$
$83$	−10.0905	+	7.33120i	−1.10758	+	0.804703i	−0.125299	+	0.992119i	$0.539989\pi$
$84$	−1.52831	−	4.70365i	−0.166752	−	0.513211i
$85$	12.1650	−	2.58576i	1.31948	−	0.280465i
$86$	−0.515798	+	4.90749i	−0.0556200	+	0.529189i
$87$	−5.59088			−0.599405
$88$	1.51980	+	2.94792i	0.162011	+	0.314249i
$89$	−2.50675	−	4.34182i	−0.265715	−	0.460232i	0.702036	−	0.712142i	$-0.252275\pi$
$89$	−2.50675	−	4.34182i	−0.265715	−	0.460232i	−0.967751	+	0.251910i	$0.918941\pi$
$90$	−10.1720	+	4.52888i	−1.07223	+	0.477386i
$91$	−0.668126	+	0.142015i	−0.0700386	+	0.0148872i
$92$	−4.04880	−	0.860598i	−0.422116	−	0.0897235i
$93$	2.68138	+	25.5116i	0.278046	+	2.64543i
$94$	3.94257	−	2.86444i	0.406645	−	0.295445i
$95$	8.08157	+	2.74309i	0.829151	+	0.281435i
$96$	0.910786	−	2.80311i	0.0929567	−	0.286091i
$97$	−4.50759	+	2.00691i	−0.457676	+	0.203771i	−0.622607	−	0.782535i	$-0.713927\pi$
$97$	−4.50759	+	2.00691i	−0.457676	+	0.203771i	0.164931	+	0.986305i	$0.447260\pi$
$98$	2.09214	−	3.62369i	0.211338	−	0.366048i
$99$	−11.9397	−	14.6014i	−1.19999	−	1.46749i
$100$	0.583257	−	1.01023i	0.0583257	−	0.101023i
$101$	−0.424396	+	4.03786i	−0.0422290	+	0.401782i	0.952906	+	0.303265i	$0.0980766\pi$
$101$	−0.424396	+	4.03786i	−0.0422290	+	0.401782i	−0.995135	+	0.0985173i	$0.968590\pi$
$102$	5.78534	−	17.8054i	0.572834	−	1.76300i
$103$	−0.273318	−	0.841188i	−0.0269309	−	0.0828847i	0.936688	−	0.350166i	$-0.113875\pi$
$103$	−0.273318	−	0.841188i	−0.0269309	−	0.0828847i	−0.963619	+	0.267281i	$0.913875\pi$
$104$	−0.371868	−	0.165566i	−0.0364647	−	0.0162351i
$105$	8.84619	+	3.93858i	0.863299	+	0.384366i
$106$	3.09656	+	9.53024i	0.300765	+	0.925659i
$107$	−1.36671	+	4.20631i	−0.132125	+	0.406640i	−0.995132	−	0.0985530i	$-0.968579\pi$
$107$	−1.36671	+	4.20631i	−0.132125	+	0.406640i	0.863007	+	0.505193i	$0.168579\pi$
$108$	−0.827811	+	7.87610i	−0.0796562	+	0.757878i
$109$	2.48284	−	4.30041i	0.237813	−	0.411905i	−0.722273	−	0.691608i	$-0.756903\pi$
$109$	2.48284	−	4.30041i	0.237813	−	0.411905i	0.960087	+	0.279703i	$0.0902360\pi$
$110$	−6.28039	−	1.65076i	−0.598812	−	0.157394i
$111$	−6.53534	+	11.3195i	−0.620307	+	1.07440i
$112$	−1.53294	+	0.682509i	−0.144849	+	0.0644910i
$113$	−0.898443	+	2.76512i	−0.0845184	+	0.260121i	−0.984381	−	0.176053i	$-0.943667\pi$
$113$	−0.898443	+	2.76512i	−0.0845184	+	0.260121i	0.899862	+	0.436174i	$0.143667\pi$
$114$	9.65887	−	8.47105i	0.904636	−	0.793386i
$115$	6.55656	−	4.76362i	0.611402	−	0.444210i
$116$	0.198281	+	1.88651i	0.0184099	+	0.175158i
$117$	2.26435	+	0.481303i	0.209340	+	0.0444965i
$118$	−11.0932	+	2.35792i	−1.02121	+	0.217065i
$119$	−9.73727	+	4.33531i	−0.892614	+	0.397417i
$120$	2.88537	+	4.99760i	0.263397	+	0.456217i
$121$	−0.104940	−	10.9995i	−0.00953997	−	0.999954i
$122$	8.31820			0.753095
$123$	2.21900	−	21.1124i	0.200081	−	1.90364i
$124$	8.51322	−	1.80954i	0.764510	−	0.162502i
$125$	3.73095	+	11.4827i	0.333706	+	1.02704i
$126$	7.72029	−	5.60912i	0.687778	−	0.499700i
$127$	−3.55467	−	1.58264i	−0.315426	−	0.140437i	0.242916	−	0.970047i	$-0.421896\pi$
$127$	−3.55467	−	1.58264i	−0.315426	−	0.140437i	−0.558343	+	0.829610i	$0.688563\pi$
$128$	−0.978148	−	0.207912i	−0.0864569	−	0.0183770i
$129$	−14.2260	+	3.02384i	−1.25253	+	0.266234i
$130$	0.728092	−	0.324167i	0.0638579	−	0.0284314i
$131$	6.47417	−	11.2136i	0.565651	−	0.979736i	−0.431338	−	0.902190i	$-0.641958\pi$
$131$	6.47417	−	11.2136i	0.565651	−	0.979736i	0.996989	−	0.0775455i	$-0.0247083\pi$
$132$	−6.87914	+	6.94508i	−0.598752	+	0.604492i
$133$	−7.26360	−	0.859513i	−0.629834	−	0.0745292i
$134$	−6.17659	−	4.48755i	−0.533576	−	0.387666i
$135$	−10.3754	−	11.5230i	−0.892972	−	0.991746i
$136$	−6.21322	−	1.32066i	−0.532779	−	0.113246i
$137$	−10.8136	−	4.81453i	−0.923869	−	0.411333i	−0.111027	−	0.993817i	$-0.535414\pi$
$137$	−10.8136	−	4.81453i	−0.923869	−	0.411333i	−0.812842	+	0.582484i	$0.802081\pi$
$138$	−1.27523	−	12.1330i	−0.108555	−	1.03283i
$139$	−7.34307	+	8.15530i	−0.622831	+	0.691724i	−0.969172	−	0.246385i	$-0.920757\pi$
$139$	−7.34307	+	8.15530i	−0.622831	+	0.691724i	0.346341	+	0.938109i	$0.387424\pi$
$140$	1.01525	−	3.12463i	0.0858045	−	0.264079i
$141$	11.6202	+	8.44256i	0.978596	+	0.710992i
$142$	−6.59948	−	11.4306i	−0.553816	−	0.959237i
$143$	0.854620	+	1.04513i	0.0714669	+	0.0873986i
$144$	5.68697			0.473914
$145$	−3.00469	−	2.18304i	−0.249526	−	0.181291i
$146$	−2.27692	+	0.483975i	−0.188439	+	0.0400540i
$147$	12.0631	+	2.56409i	0.994948	+	0.211483i
$148$	4.05130	+	1.80376i	0.333015	+	0.148268i
$149$	2.02665	+	19.2823i	0.166030	+	1.57967i	0.687362	+	0.726315i	$0.258768\pi$
$149$	2.02665	+	19.2823i	0.166030	+	1.57967i	−0.521333	+	0.853354i	$0.674565\pi$
$150$	3.36301	+	0.714830i	0.274589	+	0.0583657i
$151$	−0.651229	+	2.00428i	−0.0529962	+	0.163106i	−0.974052	−	0.226326i	$-0.927329\pi$
$151$	−0.651229	+	2.00428i	−0.0529962	+	0.163106i	0.921055	+	0.389432i	$0.127329\pi$
$152$	−3.20091	−	2.95874i	−0.259628	−	0.239986i
$153$	36.1238			2.92043
$154$	5.55903	+	0.264753i	0.447960	+	0.0213344i
$155$	−8.52033	+	14.7576i	−0.684369	+	1.18536i
$156$	0.125409	−	1.19318i	0.0100407	−	0.0955312i
$157$	−9.18359	−	10.1994i	−0.732930	−	0.814002i	0.255318	−	0.966857i	$-0.417820\pi$
$157$	−9.18359	−	10.1994i	−0.732930	−	0.814002i	−0.988249	+	0.152856i	$0.951153\pi$
$158$	−6.95313	+	7.72223i	−0.553161	+	0.614348i
$159$	−23.8940	+	17.3600i	−1.89492	+	1.37674i
$160$	1.58400	−	1.15084i	0.125226	−	0.0909820i
$161$	−4.64758	+	5.16166i	−0.366281	+	0.406796i
$162$	−6.14346	+	1.30583i	−0.482676	+	0.102596i
$163$	−17.5489	−	12.7500i	−1.37453	−	0.998657i	−0.997368	−	0.0725112i	$-0.976899\pi$
$163$	−17.5489	−	12.7500i	−1.37453	−	0.998657i	−0.377166	−	0.926146i	$-0.623101\pi$
$164$	−7.20260			−0.562429
$165$	−1.09284	−	19.1081i	−0.0850771	−	1.48757i
$166$	−6.23629	+	10.8016i	−0.484030	+	0.838364i
$167$	−2.22103	+	21.1317i	−0.171869	+	1.63522i	0.480270	+	0.877121i	$0.340539\pi$
$167$	−2.22103	+	21.1317i	−0.171869	+	1.63522i	−0.652138	+	0.758100i	$0.726128\pi$
$168$	−3.30933	−	3.67538i	−0.255320	−	0.283562i
$169$	12.5538	+	2.66840i	0.965680	+	0.205262i
$170$	10.0616	−	7.31018i	0.771689	−	0.560665i
$171$	21.3041	+	12.6739i	1.62916	+	0.969194i
$172$	1.52485	+	4.69301i	0.116269	+	0.357839i
$173$	−7.55915	−	8.39529i	−0.574712	−	0.638282i	0.383773	−	0.923428i	$-0.374625\pi$
$173$	−7.55915	−	8.39529i	−0.574712	−	0.638282i	−0.958484	+	0.285146i	$0.907958\pi$
$174$	−5.10752	+	2.27401i	−0.387200	+	0.172393i
$175$	−0.978712	−	1.69518i	−0.0739837	−	0.128143i
$176$	2.58743	+	2.07490i	0.195035	+	0.156402i
$177$	−16.7130	−	28.9478i	−1.25623	−	2.17585i
$178$	−4.05600	−	2.94686i	−0.304010	−	0.220876i
$179$	−3.34722	+	10.3017i	−0.250183	+	0.769983i	0.744558	+	0.667558i	$0.232660\pi$
$179$	−3.34722	+	10.3017i	−0.250183	+	0.769983i	−0.994741	+	0.102425i	$0.967340\pi$
$180$	−7.45056	+	8.27468i	−0.555332	+	0.616758i
$181$	17.6440	+	7.85561i	1.31147	+	0.583903i	0.938928	−	0.344113i	$-0.111820\pi$
$181$	17.6440	+	7.85561i	1.31147	+	0.583903i	0.372540	+	0.928016i	$0.378487\pi$
$182$	−0.552601	+	0.401488i	−0.0409615	+	0.0297603i
$183$	7.57611	+	23.3169i	0.560042	+	1.72363i
$184$	−4.04880	+	0.860598i	−0.298481	+	0.0634441i
$185$	−7.93216	+	3.53163i	−0.583184	+	0.259650i
$186$	12.8261	+	22.2154i	0.940453	+	1.62891i
$187$	16.4354	+	13.1798i	1.20188	+	0.963804i
$188$	2.43664	−	4.22038i	0.177710	−	0.307803i
$189$	10.7510	+	7.81107i	0.782021	+	0.568172i
$190$	8.49859	−	0.781133i	0.616553	−	0.0566694i
$191$	−2.36600	−	7.28180i	−0.171198	−	0.526892i	0.828242	−	0.560371i	$-0.189341\pi$
$191$	−2.36600	−	7.28180i	−0.171198	−	0.526892i	−0.999439	+	0.0334786i	$0.989341\pi$
$192$	−0.308084	−	2.93122i	−0.0222340	−	0.211543i
$193$	−0.205537	−	1.95555i	−0.0147949	−	0.140764i	0.984631	−	0.174648i	$-0.0558789\pi$
$193$	−0.205537	−	1.95555i	−0.0147949	−	0.140764i	−0.999426	+	0.0338844i	$0.989212\pi$
$194$	−3.30160	+	3.66680i	−0.237041	+	0.263261i
$195$	1.57181	+	1.74568i	0.112560	+	0.125010i
$196$	0.437376	−	4.16136i	0.0312412	−	0.297240i
$197$	16.0523			1.14368			0.571840	−	0.820365i	$-0.306230\pi$
$197$	16.0523			1.14368			0.571840	+	0.820365i	$0.306230\pi$
$198$	−16.8464	−	8.48270i	−1.19722	−	0.602839i
$199$	−1.45909	−	2.52722i	−0.103432	−	0.179150i	0.809664	−	0.586893i	$-0.199649\pi$
$199$	−1.45909	−	2.52722i	−0.103432	−	0.179150i	−0.913097	+	0.407743i	$0.866316\pi$
$200$	0.121934	−	1.16012i	0.00862203	−	0.0820331i
$201$	6.95356	−	21.4009i	0.490467	−	1.50950i
$202$	1.25464	+	3.86138i	0.0882762	+	0.271686i
$203$	2.90784	+	1.29465i	0.204090	+	0.0908669i
$204$	−1.95696	−	18.6192i	−0.137014	−	1.30360i
$205$	9.43620	−	10.4800i	0.659053	−	0.731952i
$206$	−0.591831	−	0.657295i	−0.0412348	−	0.0457959i
$207$	21.5047	−	9.57449i	1.49468	−	0.665473i
$208$	−0.407061			−0.0282246
$209$	5.06875	+	13.5391i	0.350613	+	0.936521i
$210$	9.68336			0.668215
$211$	6.89985	−	3.07201i	0.475005	−	0.211486i	−0.155248	−	0.987876i	$-0.549618\pi$
$211$	6.89985	−	3.07201i	0.475005	−	0.211486i	0.630253	+	0.776390i	$0.282951\pi$
$212$	6.70515	+	7.44682i	0.460512	+	0.511450i
$213$	26.0306	−	28.9099i	1.78359	−	1.98088i
$214$	0.462306	+	4.39855i	0.0316026	+	0.300679i
$215$	−8.82618	−	3.92967i	−0.601940	−	0.268001i
$216$	2.44725	+	7.53188i	0.166515	+	0.512479i
$217$	4.51301	−	13.8896i	0.306363	−	0.942890i
$218$	0.519056	−	4.93849i	0.0351549	−	0.334476i
$219$	−3.43042	−	5.94167i	−0.231807	−	0.401501i
$220$	−6.40885	+	1.04642i	−0.432085	+	0.0705498i
$221$	−2.58566			−0.173930
$222$	−1.36626	+	12.9991i	−0.0916973	+	0.872442i
$223$	4.47940	+	4.97487i	0.299962	+	0.333142i	0.874218	−	0.485534i	$-0.161375\pi$
$223$	4.47940	+	4.97487i	0.299962	+	0.333142i	−0.574255	+	0.818676i	$0.694708\pi$
$224$	−1.12281	+	1.24701i	−0.0750208	+	0.0833190i
$225$	0.693434	+	6.59759i	0.0462290	+	0.439839i
$226$	0.303908	+	2.89149i	0.0202157	+	0.192339i
$227$	8.07777	+	24.8608i	0.536140	+	1.65007i	0.741173	+	0.671314i	$0.234270\pi$
$227$	8.07777	+	24.8608i	0.536140	+	1.65007i	−0.205032	+	0.978755i	$0.565730\pi$
$228$	5.37833	−	11.6673i	0.356189	−	0.772686i
$229$	20.9482	+	15.2197i	1.38429	+	1.00575i	0.996464	+	0.0840169i	$0.0267750\pi$
$229$	20.9482	+	15.2197i	1.38429	+	1.00575i	0.387829	+	0.921731i	$0.373225\pi$
$230$	4.05218	−	7.01858i	0.267193	−	0.462791i
$231$	4.32096	+	15.8237i	0.284298	+	1.04112i
$232$	0.948453	+	1.64277i	0.0622690	+	0.107853i
$233$	23.7886	−	10.5914i	1.55844	−	0.693863i	0.566917	−	0.823775i	$-0.308136\pi$
$233$	23.7886	−	10.5914i	1.55844	−	0.693863i	0.991526	+	0.129912i	$0.0414695\pi$
$234$	2.26435	−	0.481303i	0.148025	−	0.0314638i
$235$	2.94850	+	9.07454i	0.192339	+	0.591958i
$236$	−9.17506	+	6.66607i	−0.597245	+	0.433924i
$237$	−27.9791	−	12.4571i	−1.81744	−	0.809175i
$238$	−7.13211	+	7.92101i	−0.462306	+	0.513443i
$239$	6.76560	−	20.8224i	0.437630	−	1.34689i	−0.452736	−	0.891644i	$-0.649552\pi$
$239$	6.76560	−	20.8224i	0.437630	−	1.34689i	0.890367	−	0.455244i	$-0.150448\pi$
$240$	4.66862	+	3.39195i	0.301358	+	0.218950i
$241$	10.8855	+	18.8543i	0.701198	+	1.21451i	0.968046	+	0.250772i	$0.0806844\pi$
$241$	10.8855	+	18.8543i	0.701198	+	1.21451i	−0.266848	+	0.963739i	$0.585982\pi$
$242$	−4.56977	−	10.0059i	−0.293756	−	0.643201i
$243$	2.62345	+	4.54394i	0.168294	+	0.291494i
$244$	7.59906	−	3.38332i	0.486480	−	0.216595i
$245$	5.48187	+	6.08823i	0.350224	+	0.388963i
$246$	−6.56003	−	20.1897i	−0.418252	−	1.28725i
$247$	−1.52490	−	0.907166i	−0.0970270	−	0.0577216i
$248$	7.04121	−	5.11574i	0.447117	−	0.324850i
$249$	−35.9579	−	7.64310i	−2.27874	−	0.484361i
$250$	8.07881	+	8.97243i	0.510949	+	0.567466i
$251$	−2.95071	+	28.0741i	−0.186247	+	1.77202i	0.358605	+	0.933489i	$0.383252\pi$
$251$	−2.95071	+	28.0741i	−0.186247	+	1.77202i	−0.544852	+	0.838532i	$0.683414\pi$
$252$	4.77140	−	8.26431i	0.300570	−	0.520602i
$253$	13.2773	+	3.48986i	0.834740	+	0.219406i
$254$	−3.89107			−0.244148
$255$	29.6552	+	21.5458i	1.85708	+	1.34925i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	18.0341	−	20.0289i	1.12494	−	1.24937i	0.159936	−	0.987127i	$-0.448871\pi$
$257$	18.0341	−	20.0289i	1.12494	−	1.24937i	0.965002	−	0.262243i	$-0.0844622\pi$
$258$	−11.7662	+	8.54867i	−0.732533	+	0.532217i
$259$	6.02028	−	4.37399i	0.374082	−	0.271787i
$260$	0.533294	−	0.592283i	0.0330735	−	0.0367319i
$261$	−7.21834	−	8.01678i	−0.446804	−	0.496226i
$262$	1.35347	−	12.8774i	0.0836176	−	0.795569i
$263$	−8.15167	+	14.1191i	−0.502653	+	0.870621i	0.497342	+	0.867555i	$0.334309\pi$
$263$	−8.15167	+	14.1191i	−0.502653	+	0.870621i	−0.999995	+	0.00306654i	$0.999024\pi$
$264$	−3.45959	+	9.14264i	−0.212923	+	0.562691i
$265$	−19.6198			−1.20523
$266$	−6.98523	+	2.16917i	−0.428292	+	0.133000i
$267$	4.56623	−	14.0534i	0.279448	−	0.860054i
$268$	−7.46785	−	1.58734i	−0.456171	−	0.0969622i
$269$	1.25226	+	11.9145i	0.0763518	+	0.726439i	0.963997	+	0.265912i	$0.0856730\pi$
$269$	1.25226	+	11.9145i	0.0763518	+	0.726439i	−0.887646	+	0.460527i	$0.847660\pi$
$270$	−14.1652	−	6.30677i	−0.862069	−	0.383818i
$271$	−18.2203	−	3.87284i	−1.10680	−	0.235258i	−0.381965	−	0.924177i	$-0.624752\pi$
$271$	−18.2203	−	3.87284i	−1.10680	−	0.235258i	−0.724839	+	0.688919i	$0.758086\pi$
$272$	−6.21322	+	1.32066i	−0.376732	+	0.0800768i
$273$	−1.62872	−	1.18333i	−0.0985745	−	0.0716185i
$274$	−11.8370			−0.715098
$275$	−2.09165	+	3.25474i	−0.126131	+	0.196268i
$276$	−6.09994	−	10.5654i	−0.367173	−	0.635963i
$277$	−8.62085	−	6.26342i	−0.517977	−	0.376332i	0.297864	−	0.954608i	$-0.403726\pi$
$277$	−8.62085	−	6.26342i	−0.517977	−	0.376332i	−0.815841	+	0.578276i	$0.803726\pi$
$278$	−3.39117	+	10.4369i	−0.203389	+	0.625966i
$279$	−33.1193	+	36.7827i	−1.98280	+	2.20212i
$280$	−0.343421	−	3.26743i	−0.0205233	−	0.195266i
$281$	−7.83127	−	3.48670i	−0.467174	−	0.207999i	0.159629	−	0.987177i	$-0.448970\pi$
$281$	−7.83127	−	3.48670i	−0.467174	−	0.207999i	−0.626803	+	0.779178i	$0.715637\pi$
$282$	14.0495	+	2.98631i	0.836633	+	0.177832i
$283$	−15.7846	−	17.5305i	−0.938296	−	1.04208i	−0.999035	−	0.0439293i	$-0.986012\pi$
$283$	−15.7846	−	17.5305i	−0.938296	−	1.04208i	0.0607389	−	0.998154i	$-0.480654\pi$
$284$	−10.6782	−	7.75815i	−0.633634	−	0.460362i
$285$	9.93001	+	23.1111i	0.588203	+	1.36898i
$286$	1.20583	+	0.607173i	0.0713022	+	0.0359029i
$287$	−6.04302	+	10.4668i	−0.356708	+	0.617837i
$288$	5.19530	−	2.31310i	0.306136	−	0.136301i
$289$	−22.8380	+	4.85437i	−1.34341	+	0.285551i
$290$	−3.63285	−	0.772185i	−0.213328	−	0.0453443i
$291$	−13.2855	−	5.91509i	−0.778811	−	0.346749i
$292$	−1.88322	+	1.36824i	−0.110207	+	0.0800702i
$293$	0.765986	+	2.35746i	0.0447494	+	0.137724i	0.970935	−	0.239344i	$-0.0769323\pi$
$293$	0.765986	+	2.35746i	0.0447494	+	0.137724i	−0.926186	+	0.377068i	$0.876932\pi$
$294$	12.0631	−	2.56409i	0.703535	−	0.149541i
$295$	2.32104	−	22.0832i	0.135136	−	1.28573i
$296$	4.43470			0.257762
$297$	3.98511	−	25.9619i	0.231239	−	1.50646i
$298$	9.69426	+	16.7909i	0.561573	+	0.972674i
$299$	−1.53926	+	0.685321i	−0.0890174	+	0.0396331i
$300$	3.36301	−	0.714830i	0.194164	−	0.0412708i
$301$	8.09925	+	1.72155i	0.466833	+	0.0992284i
$302$	0.220285	+	2.09588i	0.0126760	+	0.120604i
$303$	−9.68119	+	7.03379i	−0.556170	+	0.404081i
$304$	−4.12761	−	1.40102i	−0.236735	−	0.0803537i
$305$	−5.03279	+	15.4893i	−0.288177	+	0.886917i
$306$	33.0007	−	14.6929i	1.88653	−	0.839935i
$307$	2.66561	−	4.61698i	0.152135	−	0.263505i	−0.779877	−	0.625932i	$-0.784719\pi$
$307$	2.66561	−	4.61698i	0.152135	−	0.263505i	0.932012	+	0.362427i	$0.118052\pi$
$308$	5.18611	−	2.01920i	0.295506	−	0.115054i
$309$	1.30344	−	2.25762i	0.0741501	−	0.128432i
$310$	−1.78123	+	16.9473i	−0.101167	+	0.962543i
$311$	1.30117	−	4.00460i	0.0737828	−	0.227080i	−0.907363	−	0.420347i	$-0.861908\pi$
$311$	1.30117	−	4.00460i	0.0737828	−	0.227080i	0.981146	+	0.193267i	$0.0619083\pi$
$312$	−0.370745	−	1.14104i	−0.0209893	−	0.0645985i
$313$	8.20975	+	3.65522i	0.464043	+	0.206605i	0.625421	−	0.780287i	$-0.284927\pi$
$313$	8.20975	+	3.65522i	0.464043	+	0.206605i	−0.161378	+	0.986893i	$0.551594\pi$
$314$	−12.5381	−	5.58232i	−0.707566	−	0.315029i
$315$	5.77371	+	17.7697i	0.325312	+	1.00121i
$316$	−3.21108	+	9.88270i	−0.180638	+	0.555945i
$317$	1.06296	−	10.1134i	0.0597020	−	0.568027i	−0.923255	−	0.384189i	$-0.874481\pi$
$317$	1.06296	−	10.1134i	0.0597020	−	0.568027i	0.982957	−	0.183838i	$-0.0588522\pi$
$318$	−14.7673	+	25.5778i	−0.828110	+	1.43433i
$319$	−0.359228	−	6.28106i	−0.0201129	−	0.351672i
$320$	0.978965	−	1.69562i	0.0547258	−	0.0947878i
$321$	−11.9086	+	5.30204i	−0.664672	+	0.295931i
$322$	−2.14634	+	6.60576i	−0.119611	+	0.368124i
$323$	−26.2187	−	8.89928i	−1.45885	−	0.495169i
$324$	−5.08120	+	3.69171i	−0.282289	+	0.205095i
$325$	−0.0496345	−	0.472241i	−0.00275323	−	0.0261952i
$326$	−21.2176	−	4.50994i	−1.17513	−	0.249782i
$327$	14.3159	−	3.04293i	0.791670	−	0.168275i
$328$	−6.57990	+	2.92956i	−0.363314	+	0.161758i
$329$	−4.08871	−	7.08185i	−0.225418	−	0.390435i
$330$	−8.77033	−	17.0117i	−0.482791	−	0.936461i
$331$	20.3356			1.11774			0.558872	−	0.829254i	$-0.311234\pi$
$331$	20.3356			1.11774			0.558872	+	0.829254i	$0.311234\pi$
$332$	−1.30374	+	12.4043i	−0.0715520	+	0.680772i
$333$	−24.6689	+	5.24353i	−1.35185	+	0.287344i
$334$	6.56603	+	20.2082i	0.359277	+	1.10574i
$335$	12.0933	−	8.78631i	0.660729	−	0.480047i
$336$	−4.51813	−	2.01160i	−0.246484	−	0.109742i
$337$	22.3479	+	4.75020i	1.21737	+	0.258760i	0.771437	−	0.636306i	$-0.219538\pi$
$337$	22.3479	+	4.75020i	1.21737	+	0.258760i	0.445933	+	0.895066i	$0.352872\pi$
$338$	12.5538	−	2.66840i	0.682839	−	0.145142i
$339$	−7.82839	+	3.48542i	−0.425180	+	0.189302i
$340$	6.21841	−	10.7706i	0.337241	−	0.584118i
$341$	−28.4887	+	4.65157i	−1.54275	+	0.251897i
$342$	24.6172	+	2.91299i	1.33114	+	0.157516i
$343$	−15.1831	−	11.0312i	−0.819810	−	0.595627i
$344$	3.30184	+	3.66707i	0.178023	+	0.197715i
$345$	23.3645	+	4.96628i	1.25790	+	0.267376i
$346$	−10.3203	−	4.59489i	−0.554823	−	0.247023i
$347$	−2.29948	−	21.8781i	−0.123443	−	1.17448i	−0.864357	−	0.502878i	$-0.832274\pi$
$347$	−2.29948	−	21.8781i	−0.123443	−	1.17448i	0.740915	−	0.671599i	$-0.234392\pi$
$348$	−3.74103	+	4.15483i	−0.200540	+	0.222722i
$349$	−8.72339	+	26.8478i	−0.466952	+	1.43713i	0.389558	+	0.921002i	$0.372628\pi$
$349$	−8.72339	+	26.8478i	−0.466952	+	1.43713i	−0.856511	+	0.516130i	$0.827372\pi$
$350$	−1.58359	−	1.15054i	−0.0846464	−	0.0614992i
$351$	1.61185	+	2.79181i	0.0860345	+	0.149016i
$352$	3.20767	+	0.843115i	0.170969	+	0.0449382i
$353$	12.3116			0.655283			0.327641	−	0.944802i	$-0.393746\pi$
$353$	12.3116			0.655283			0.327641	+	0.944802i	$0.393746\pi$
$354$	−27.0423	−	19.6473i	−1.43728	−	1.04424i
$355$	25.2779	−	5.37298i	1.34161	−	0.285168i
$356$	−4.90394	−	1.04236i	−0.259908	−	0.0552452i
$357$	−28.6993	−	12.7778i	−1.51893	−	0.676271i
$358$	1.13223	+	10.7725i	0.0598404	+	0.569343i
$359$	−20.7926	−	4.41961i	−1.09739	−	0.233258i	−0.376577	−	0.926385i	$-0.622899\pi$
$359$	−20.7926	−	4.41961i	−1.09739	−	0.233258i	−0.720815	+	0.693127i	$0.756232\pi$
$360$	−3.44081	+	10.5897i	−0.181346	+	0.558127i
$361$	−12.3403	−	14.4471i	−0.649488	−	0.760372i
$362$	19.3138			1.01511
$363$	23.8855	−	21.9228i	1.25366	−	1.15065i
$364$	−0.341526	+	0.591541i	−0.0179008	+	0.0310052i
$365$	0.476404	−	4.53268i	0.0249361	−	0.237251i
$366$	16.4049	+	18.2195i	0.857500	+	0.952350i
$367$	8.91719	−	9.90355i	0.465474	−	0.516961i	−0.464007	−	0.885832i	$-0.653589\pi$
$367$	8.91719	−	9.90355i	0.465474	−	0.516961i	0.929481	+	0.368871i	$0.120255\pi$
$368$	−3.34872	+	2.43299i	−0.174564	+	0.126828i
$369$	33.1381	−	24.0763i	1.72510	−	1.25336i
$370$	−5.80995	+	6.45260i	−0.302045	+	0.335455i
$371$	16.4474	−	3.49600i	0.853906	−	0.181503i
$372$	20.7530	+	15.0780i	1.07599	+	0.781755i
$373$	10.7466			0.556440			0.278220	−	0.960517i	$-0.410256\pi$
$373$	10.7466			0.556440			0.278220	+	0.960517i	$0.410256\pi$
$374$	20.3752	+	5.35549i	1.05358	+	0.276926i
$375$	−17.7927	+	30.8178i	−0.918809	+	1.59142i
$376$	0.509396	−	4.84658i	0.0262701	−	0.249943i
$377$	0.516673	+	0.573824i	0.0266100	+	0.0295534i
$378$	12.9986	+	2.76293i	0.668575	+	0.142110i
$379$	21.3993	−	15.5475i	1.09921	−	0.798622i	0.118279	−	0.992980i	$-0.462262\pi$
$379$	21.3993	−	15.5475i	1.09921	−	0.798622i	0.980931	+	0.194358i	$0.0622623\pi$
$380$	7.44613	−	4.17029i	0.381979	−	0.213931i
$381$	−3.54394	−	10.9071i	−0.181561	−	0.558789i
$382$	−5.12322	−	5.68991i	−0.262127	−	0.291121i
$383$	−22.9738	+	10.2286i	−1.17391	+	0.522657i	−0.898630	−	0.438708i	$-0.855436\pi$
$383$	−22.9738	+	10.2286i	−1.17391	+	0.522657i	−0.275277	+	0.961365i	$0.588770\pi$
$384$	−1.47368	−	2.55249i	−0.0752036	−	0.130256i
$385$	−3.85640	+	10.1913i	−0.196540	+	0.519397i
$386$	−0.983163	−	1.70289i	−0.0500417	−	0.0866747i
$387$	−22.7030	−	16.4947i	−1.15406	−	0.838474i
$388$	−1.52474	+	4.69267i	−0.0774071	+	0.238234i
$389$	12.3225	−	13.6855i	0.624775	−	0.693883i	−0.344801	−	0.938676i	$-0.612053\pi$
$389$	12.3225	−	13.6855i	0.624775	−	0.693883i	0.969575	+	0.244793i	$0.0787201\pi$
$390$	2.14595	+	0.955440i	0.108665	+	0.0483806i
$391$	−21.2712	+	15.4544i	−1.07573	+	0.781563i
$392$	−1.29301	−	3.97949i	−0.0653070	−	0.200994i
$393$	37.3295	−	7.93464i	1.88303	−	0.400249i
$394$	14.6645	−	6.52907i	0.738788	−	0.328930i
$395$	−10.1727	−	17.6196i	−0.511844	−	0.886540i
$396$	−18.8402	−	0.897279i	−0.946755	−	0.0450899i
$397$	−9.26043	+	16.0395i	−0.464768	+	0.805002i	−0.999191	−	0.0402155i	$-0.987196\pi$
$397$	−9.26043	+	16.0395i	−0.464768	+	0.805002i	0.534423	+	0.845217i	$0.320529\pi$
$398$	−2.36086	−	1.71526i	−0.118339	−	0.0859784i
$399$	−12.4425	−	17.6047i	−0.622903	−	0.881339i
$400$	−0.360473	−	1.10942i	−0.0180236	−	0.0554710i
$401$	0.221679	+	2.10913i	0.0110701	+	0.105325i	0.998662	−	0.0517193i	$-0.0164701\pi$
$401$	0.221679	+	2.10913i	0.0110701	+	0.105325i	−0.987592	+	0.157044i	$0.949803\pi$
$402$	−2.35212	−	22.3789i	−0.117313	−	1.11616i
$403$	2.37061	−	2.63283i	0.118088	−	0.131150i
$404$	2.71674	+	3.01724i	0.135163	+	0.150113i
$405$	1.28541	−	12.2298i	0.0638723	−	0.607705i
$406$	3.18303			0.157971
$407$	−13.1368	−	6.61481i	−0.651169	−	0.327884i
$408$	−9.36087	−	16.2135i	−0.463432	−	0.802688i
$409$	−0.815543	+	7.75937i	−0.0403260	+	0.383676i	0.955681	+	0.294404i	$0.0951210\pi$
$409$	−0.815543	+	7.75937i	−0.0403260	+	0.383676i	−0.996007	+	0.0892728i	$0.971546\pi$
$410$	4.35781	−	13.4120i	0.215217	−	0.662370i
$411$	−10.7810	−	33.1804i	−0.531785	−	1.63667i
$412$	−0.808010	−	0.359749i	−0.0398078	−	0.0177236i
$413$	1.98921	+	18.9261i	0.0978826	+	0.931291i
$414$	15.7512	−	17.4935i	0.774128	−	0.859757i
$415$	−16.3405	−	18.1479i	−0.802121	−	0.890846i
$416$	−0.371868	+	0.165566i	−0.0182323	+	0.00811756i
$417$	−32.3445			−1.58392
$418$	10.1374	+	10.3070i	0.495836	+	0.504130i
$419$	−20.2694			−0.990227			−0.495113	−	0.868828i	$-0.664873\pi$
$419$	−20.2694			−0.990227			−0.495113	+	0.868828i	$0.664873\pi$
$420$	8.84619	−	3.93858i	0.431650	−	0.192183i
$421$	−3.00824	−	3.34098i	−0.146612	−	0.162830i	0.665365	−	0.746518i	$-0.268276\pi$
$421$	−3.00824	−	3.34098i	−0.146612	−	0.162830i	−0.811978	+	0.583688i	$0.801609\pi$
$422$	5.05383	−	5.61284i	0.246016	−	0.273229i
$423$	2.89692	+	27.5624i	0.140853	+	1.34013i
$424$	9.15436	+	4.07578i	0.444575	+	0.197937i
$425$	−2.28973	−	7.04707i	−0.111068	−	0.341833i
$426$	12.0214	−	36.9982i	0.582440	−	1.79257i
$427$	1.45901	−	13.8816i	0.0706066	−	0.671777i
$428$	2.21139	+	3.83024i	0.106892	+	0.185142i
$429$	−0.603721	+	3.93308i	−0.0291479	+	0.189891i
$430$	−9.66145			−0.465917
$431$	−2.06744	+	19.6704i	−0.0995852	+	0.947490i	0.824644	+	0.565652i	$0.191375\pi$
$431$	−2.06744	+	19.6704i	−0.0995852	+	0.947490i	−0.924229	+	0.381838i	$0.875291\pi$
$432$	5.29917	+	5.88532i	0.254956	+	0.283158i
$433$	12.3981	−	13.7695i	0.595814	−	0.661719i	−0.367522	−	0.930015i	$-0.619794\pi$
$433$	12.3981	−	13.7695i	0.595814	−	0.661719i	0.963337	+	0.268296i	$0.0864605\pi$
$434$	−1.52658	−	14.5244i	−0.0732781	−	0.697194i
$435$	−1.14423	−	10.8866i	−0.0548614	−	0.521971i
$436$	−1.53448	−	4.72265i	−0.0734884	−	0.226174i
$437$	−17.9668	+	1.65139i	−0.859470	+	0.0789967i
$438$	−5.55054	−	4.03271i	−0.265215	−	0.192690i
$439$	6.53448	−	11.3181i	0.311874	−	0.540181i	−0.666894	−	0.745152i	$-0.732377\pi$
$439$	6.53448	−	11.3181i	0.311874	−	0.540181i	0.978768	+	0.204971i	$0.0657101\pi$
$440$	−5.42916	+	3.56267i	−0.258825	+	0.169844i
$441$	11.8979	+	20.6078i	0.566568	+	0.981325i
$442$	−2.36212	+	1.05168i	−0.112354	+	0.0500234i
$443$	0.969289	−	0.206029i	0.0460523	−	0.00978872i	−0.184828	−	0.982771i	$-0.559173\pi$
$443$	0.969289	−	0.206029i	0.0460523	−	0.00978872i	0.230880	+	0.972982i	$0.425839\pi$
$444$	4.03907	+	12.4310i	0.191686	+	0.589947i
$445$	7.94137	−	5.76974i	0.376457	−	0.273512i
$446$	6.11559	+	2.72284i	0.289582	+	0.128930i
$447$	−38.2375	+	42.4671i	−1.80857	+	2.00862i
$448$	−0.518534	+	1.59588i	−0.0244984	+	0.0753984i
$449$	−8.64408	−	6.28030i	−0.407940	−	0.296385i	0.364828	−	0.931075i	$-0.381128\pi$
$449$	−8.64408	−	6.28030i	−0.407940	−	0.296385i	−0.772767	+	0.634690i	$0.781128\pi$
$450$	3.31696	+	5.74515i	0.156363	+	0.270829i
$451$	23.8613	+	1.13641i	1.12358	+	0.0535115i
$452$	1.45371	+	2.51790i	0.0683768	+	0.118432i
$453$	−5.67434	+	2.52638i	−0.266604	+	0.118700i
$454$	17.4912	+	19.4260i	0.820903	+	0.911705i
$455$	−0.413269	−	1.27191i	−0.0193744	−	0.0596282i
$456$	0.167832	−	12.8462i	0.00785946	−	0.601577i
$457$	1.12026	−	0.813914i	0.0524034	−	0.0380733i	−0.561275	−	0.827629i	$-0.689689\pi$
$457$	1.12026	−	0.813914i	0.0524034	−	0.0380733i	0.613679	+	0.789556i	$0.289689\pi$
$458$	25.3275	+	5.38353i	1.18348	+	0.251556i
$459$	33.6605	+	37.3837i	1.57114	+	1.74492i
$460$	0.847136	−	8.05996i	0.0394979	−	0.375797i
$461$	11.2558	−	19.4957i	0.524236	−	0.908004i	−0.475366	−	0.879788i	$-0.657684\pi$
$461$	11.2558	−	19.4957i	0.524236	−	0.908004i	0.999602	−	0.0282153i	$-0.00898241\pi$
$462$	10.3835	+	12.6982i	0.483083	+	0.590774i
$463$	27.1707			1.26273			0.631364	−	0.775487i	$-0.282495\pi$
$463$	27.1707			1.26273			0.631364	+	0.775487i	$0.282495\pi$
$464$	1.53463	+	1.11497i	0.0712434	+	0.0517613i
$465$	−49.1275	+	10.4424i	−2.27823	+	0.484254i
$466$	17.4241	−	19.3514i	0.807154	−	0.896435i
$467$	−23.0263	+	16.7296i	−1.06553	+	0.774155i	−0.975104	−	0.221748i	$-0.928824\pi$
$467$	−23.0263	+	16.7296i	−1.06553	+	0.774155i	−0.0904284	+	0.995903i	$0.528824\pi$
$468$	1.87283	−	1.36069i	0.0865715	−	0.0628978i
$469$	−8.57229	+	9.52049i	−0.395831	+	0.439615i
$470$	6.38453	+	7.09074i	0.294497	+	0.327072i
$471$	4.22834	−	40.2300i	0.194832	−	1.85370i
$472$	−5.67050	+	9.82159i	−0.261006	+	0.452075i
$473$	−4.31118	−	15.7879i	−0.198228	−	0.725930i
$474$	−30.6269			−1.40674
$475$	1.12206	−	4.95937i	0.0514834	−	0.227551i
$476$	−3.29374	+	10.1371i	−0.150968	+	0.464633i
$477$	−55.7421	−	11.8483i	−2.55225	−	0.542498i
$478$	−2.28854	−	21.7740i	−0.104675	−	0.995920i
$479$	−1.01928	−	0.453814i	−0.0465723	−	0.0207353i	0.383318	−	0.923616i	$-0.374781\pi$
$479$	−1.01928	−	0.453814i	−0.0465723	−	0.0207353i	−0.429891	+	0.902881i	$0.641448\pi$
$480$	5.64463	+	1.19980i	0.257641	+	0.0547633i
$481$	1.76574	−	0.375321i	0.0805110	−	0.0171131i
$482$	17.6131	+	12.7967i	0.802256	+	0.582873i
$483$	−20.4715			−0.931487
$484$	−8.24444	−	7.28212i	−0.374747	−	0.331005i
$485$	−4.83038	−	8.36646i	−0.219336	−	0.379901i
$486$	4.24482	+	3.08404i	0.192549	+	0.139895i
$487$	−0.707586	+	2.17773i	−0.0320638	+	0.0986822i	−0.965808	−	0.259260i	$-0.916521\pi$
$487$	−0.707586	+	2.17773i	−0.0320638	+	0.0986822i	0.933744	+	0.357942i	$0.116521\pi$
$488$	5.56596	−	6.18163i	0.251959	−	0.279829i
$489$	−6.68283	−	63.5828i	−0.302208	−	2.87532i
$490$	7.48424	+	3.33220i	0.338103	+	0.150533i
$491$	25.5923	+	5.43981i	1.15496	+	0.245495i	0.745292	−	0.666738i	$-0.232310\pi$
$491$	25.5923	+	5.43981i	1.15496	+	0.245495i	0.409672	+	0.912233i	$0.365643\pi$
$492$	−14.2048	−	15.7760i	−0.640401	−	0.711237i
$493$	9.74800	+	7.08234i	0.439028	+	0.318973i
$494$	−1.76204	−	0.208505i	−0.0792780	−	0.00938109i
$495$	25.9883	−	26.2374i	1.16809	−	1.17928i
$496$	4.35171	−	7.53738i	0.195397	−	0.338438i
$497$	−20.2332	+	9.00840i	−0.907583	+	0.404082i
$498$	−35.9579	+	7.64310i	−1.61131	+	0.342495i
$499$	13.3515	+	2.83796i	0.597697	+	0.127044i	0.496819	−	0.867854i	$-0.334501\pi$
$499$	13.3515	+	2.83796i	0.597697	+	0.127044i	0.100878	+	0.994899i	$0.467835\pi$
$500$	11.0298	+	4.91077i	0.493267	+	0.219616i
$501$	−50.6655	+	36.8106i	−2.26357	+	1.64458i
$502$	8.72316	+	26.8471i	0.389334	+	1.19825i
$503$	29.1843	−	6.20331i	1.30126	−	0.276592i	0.495385	−	0.868673i	$-0.335027\pi$
$503$	29.1843	−	6.20331i	1.30126	−	0.276592i	0.805878	+	0.592081i	$0.201694\pi$
$504$	0.997494	−	9.49052i	0.0444319	−	0.422741i
$505$	−7.94939			−0.353743
$506$	13.5489	−	2.21224i	0.602323	−	0.0983460i
$507$	18.9137	+	32.7595i	0.839987	+	1.45490i
$508$	−3.55467	+	1.58264i	−0.157713	+	0.0702184i
$509$	1.10712	−	0.235325i	0.0490722	−	0.0104306i	−0.183310	−	0.983055i	$-0.558681\pi$
$509$	1.10712	−	0.235325i	0.0490722	−	0.0104306i	0.232382	+	0.972625i	$0.425348\pi$
$510$	35.8548	+	7.62118i	1.58768	+	0.337472i
$511$	0.408294	+	3.88466i	0.0180619	+	0.171847i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	6.73544	+	33.8568i	0.297377	+	1.49481i
$514$	8.32850	−	25.6325i	0.367354	−	1.13060i
$515$	1.58203	−	0.704363i	0.0697124	−	0.0310380i
$516$	−7.27193	+	12.5954i	−0.320129	+	0.554479i
$517$	−8.73815	+	13.5971i	−0.384304	+	0.598001i
$518$	3.72074	−	6.44451i	0.163480	−	0.283155i
$519$	3.48041	−	33.1139i	0.152773	−	1.45354i
$520$	0.246285	−	0.757988i	0.0108003	−	0.0332400i
$521$	5.41869	+	16.6770i	0.237397	+	0.730633i	0.996794	+	0.0800056i	$0.0254938\pi$
$521$	5.41869	+	16.6770i	0.237397	+	0.730633i	−0.759398	+	0.650627i	$0.774506\pi$
$522$	−9.85500	−	4.38773i	−0.431342	−	0.192046i
$523$	−9.03327	−	4.02187i	−0.394997	−	0.175864i	0.199619	−	0.979874i	$-0.436029\pi$
$523$	−9.03327	−	4.02187i	−0.394997	−	0.175864i	−0.594617	+	0.804009i	$0.702696\pi$
$524$	−4.00126	−	12.3146i	−0.174796	−	0.537966i
$525$	1.78279	−	5.48688i	0.0778075	−	0.239467i
$526$	−1.70416	+	16.2140i	−0.0743050	+	0.706965i
$527$	27.6421	−	47.8776i	1.20411	−	2.08558i
$528$	0.558159	+	9.75936i	0.0242908	+	0.424722i
$529$	2.93331	−	5.08065i	0.127535	−	0.220898i
$530$	−17.9236	+	7.98009i	−0.778551	+	0.346633i
$531$	19.9303	−	61.3392i	0.864902	−	2.66190i
$532$	−5.49904	+	4.82278i	−0.238414	+	0.209094i
$533$	−2.37195	+	1.72332i	−0.102741	+	0.0746455i
$534$	−1.54458	−	14.6957i	−0.0668404	−	0.635944i
$535$	−8.47026	−	1.80041i	−0.366201	−	0.0778385i
$536$	−7.46785	+	1.58734i	−0.322562	+	0.0685626i
$537$	−29.1652	+	12.9852i	−1.25857	+	0.560353i
$538$	5.99006	+	10.3751i	0.258250	+	0.447302i
$539$	−2.10554	+	13.7170i	−0.0906921	+	0.590834i
$540$	−15.5058			−0.667263
$541$	−2.11747	+	20.1464i	−0.0910372	+	0.866161i	0.849755	+	0.527178i	$0.176750\pi$
$541$	−2.11747	+	20.1464i	−0.0910372	+	0.866161i	−0.940792	+	0.338984i	$0.889917\pi$
$542$	−18.2203	+	3.87284i	−0.782628	+	0.166353i
$543$	17.5907	+	54.1386i	0.754890	+	2.32331i
$544$	−5.13890	+	3.73363i	−0.220328	+	0.160078i
$545$	8.88191	+	3.95448i	0.380459	+	0.169391i
$546$	−1.96921	−	0.418569i	−0.0842745	−	0.0179131i
$547$	−7.61667	+	1.61897i	−0.325665	+	0.0692223i	−0.367843	−	0.929888i	$-0.619904\pi$
$547$	−7.61667	+	1.61897i	−0.325665	+	0.0692223i	0.0421780	+	0.999110i	$0.486570\pi$
$548$	−10.8136	+	4.81453i	−0.461935	+	0.205667i
$549$	−23.6527	+	40.9677i	−1.00947	+	1.74846i
$550$	−0.586993	+	3.82410i	−0.0250295	+	0.163060i
$551$	3.26411	+	7.59687i	0.139056	+	0.323637i
$552$	−9.86991	−	7.17091i	−0.420091	−	0.305214i
$553$	11.6674	+	12.9580i	0.496149	+	0.551030i
$554$	−10.4231	−	2.21550i	−0.442835	−	0.0941275i
$555$	−23.3790	−	10.4090i	−0.992383	−	0.441837i
$556$	1.14710	+	10.9139i	0.0486479	+	0.462854i
$557$	6.78151	−	7.53163i	0.287342	−	0.319125i	−0.582142	−	0.813087i	$-0.697785\pi$
$557$	6.78151	−	7.53163i	0.287342	−	0.319125i	0.869484	+	0.493962i	$0.164452\pi$
$558$	−15.2951	+	47.0735i	−0.647494	+	1.99278i
$559$	1.62503	+	1.18066i	0.0687316	+	0.0499364i
$560$	−1.64271	−	2.84526i	−0.0694173	−	0.120234i
$561$	3.54544	+	61.9917i	0.149689	+	2.61729i
$562$	−8.57239			−0.361604
$563$	−5.00047	−	3.63306i	−0.210745	−	0.153115i	0.477406	−	0.878683i	$-0.341577\pi$
$563$	−5.00047	−	3.63306i	−0.210745	−	0.153115i	−0.688151	+	0.725568i	$0.741577\pi$
$564$	14.0495	−	2.98631i	0.591589	−	0.125746i
$565$	−5.56813	−	1.18354i	−0.234253	−	0.0497920i
$566$	−21.5502	−	9.59479i	−0.905824	−	0.403299i
$567$	1.10164	+	10.4814i	0.0462644	+	0.440176i
$568$	−12.9105	−	2.74422i	−0.541714	−	0.115145i
$569$	−3.62548	+	11.1581i	−0.151988	+	0.467772i	−0.997843	−	0.0656412i	$-0.979091\pi$
$569$	−3.62548	+	11.1581i	−0.151988	+	0.467772i	0.845855	+	0.533413i	$0.179091\pi$
$570$	18.4716	+	17.0741i	0.773691	+	0.715156i
$571$	−5.76954			−0.241448			−0.120724	−	0.992686i	$-0.538522\pi$
$571$	−5.76954			−0.241448			−0.120724	+	0.992686i	$0.538522\pi$
$572$	1.34854	+	0.0642252i	0.0563852	+	0.00268539i
$573$	11.2833	−	19.5433i	0.471367	−	0.816431i
$574$	−1.26334	+	12.0198i	−0.0527306	+	0.501698i
$575$	−3.23089	−	3.58827i	−0.134737	−	0.149641i
$576$	3.80533	−	4.22624i	0.158555	−	0.176093i
$577$	−10.8045	+	7.84994i	−0.449798	+	0.326797i	−0.789516	−	0.613730i	$-0.789668\pi$
$577$	−10.8045	+	7.84994i	−0.449798	+	0.326797i	0.339718	+	0.940527i	$0.389668\pi$
$578$	−18.8891	+	13.7237i	−0.785684	+	0.570833i
$579$	3.87794	−	4.30688i	0.161162	−	0.178988i
$580$	−3.63285	+	0.772185i	−0.150846	+	0.0320633i
$581$	16.9320	+	12.3018i	0.702458	+	0.510366i
$582$	−14.5428			−0.602819
$583$	−21.0383	−	25.7283i	−0.871319	−	1.06556i
$584$	−1.16389	+	2.01593i	−0.0481623	+	0.0834196i
$585$	−0.473774	+	4.50766i	−0.0195882	+	0.186369i
$586$	1.65863	+	1.84209i	0.0685173	+	0.0760962i
$587$	−46.6746	−	9.92100i	−1.92647	−	0.409483i	−0.999402	−	0.0345859i	$-0.988989\pi$
$587$	−46.6746	−	9.92100i	−1.92647	−	0.409483i	−0.927066	−	0.374898i	$-0.877678\pi$
$588$	9.97729	−	7.24892i	0.411456	−	0.298941i
$589$	33.0997	−	18.5378i	1.36385	−	0.763838i
$590$	−6.86168	−	21.1181i	−0.282491	−	0.869417i
$591$	31.6580	+	35.1597i	1.30223	+	1.44628i
$592$	4.05130	−	1.80376i	0.166507	−	0.0741339i
$593$	−1.24277	−	2.15253i	−0.0510343	−	0.0883939i	0.839380	−	0.543545i	$-0.182918\pi$
$593$	−1.24277	−	2.15253i	−0.0510343	−	0.0883939i	−0.890414	+	0.455151i	$0.849585\pi$
$594$	−6.91907	−	25.3382i	−0.283893	−	1.03964i
$595$	−10.4346	−	18.0732i	−0.427775	−	0.740928i
$596$	15.6856	+	11.3963i	0.642509	+	0.466810i
$597$	2.65784	−	8.17998i	0.108778	−	0.334784i
$598$	−1.12743	+	1.25214i	−0.0461042	+	0.0512039i
$599$	24.1288	+	10.7428i	0.985875	+	0.438940i	0.835381	−	0.549671i	$-0.185247\pi$
$599$	24.1288	+	10.7428i	0.985875	+	0.438940i	0.150494	+	0.988611i	$0.451914\pi$
$600$	2.78152	−	2.02089i	0.113555	−	0.0825025i
$601$	10.2398	+	31.5148i	0.417689	+	1.28551i	0.909824	+	0.414995i	$0.136217\pi$
$601$	10.2398	+	31.5148i	0.417689	+	1.28551i	−0.492135	+	0.870519i	$0.663783\pi$
$602$	8.09925	−	1.72155i	0.330101	−	0.0701651i
$603$	39.6645	−	17.6598i	1.61526	−	0.719162i
$604$	1.05371	+	1.82508i	0.0428749	+	0.0742614i
$605$	21.3968	−	2.45549i	0.869903	−	0.0998298i
$606$	−5.98330	+	10.3634i	−0.243055	+	0.420984i
$607$	13.2991	+	9.66235i	0.539793	+	0.392183i	0.824008	−	0.566578i	$-0.191733\pi$
$607$	13.2991	+	9.66235i	0.539793	+	0.392183i	−0.284215	+	0.958761i	$0.591733\pi$
$608$	−4.34060	+	0.398959i	−0.176035	+	0.0161799i
$609$	2.89906	+	8.92239i	0.117476	+	0.361553i
$610$	1.70240	+	16.1972i	0.0689281	+	0.655807i
$611$	−0.207355	−	1.97285i	−0.00838869	−	0.0798131i
$612$	24.1715	−	26.8452i	0.977076	−	1.08515i
$613$	−29.5599	−	32.8296i	−1.19391	−	1.32597i	−0.932683	−	0.360697i	$-0.882539\pi$
$613$	−29.5599	−	32.8296i	−1.19391	−	1.32597i	−0.261229	−	0.965277i	$-0.584128\pi$
$614$	0.557265	−	5.30202i	0.0224894	−	0.213972i
$615$	41.5643			1.67603
$616$	3.91647	−	3.95401i	0.157799	−	0.159312i
$617$	−5.68252	−	9.84242i	−0.228770	−	0.396241i	0.728674	−	0.684861i	$-0.240137\pi$
$617$	−5.68252	−	9.84242i	−0.228770	−	0.396241i	−0.957444	+	0.288620i	$0.906804\pi$
$618$	0.272493	−	2.59260i	0.0109613	−	0.104290i
$619$	10.3438	−	31.8349i	0.415752	−	1.27955i	−0.495825	−	0.868422i	$-0.665134\pi$
$619$	10.3438	−	31.8349i	0.415752	−	1.27955i	0.911577	−	0.411130i	$-0.134866\pi$
$620$	5.26585	+	16.2066i	0.211482	+	0.650874i
$621$	29.9467	+	13.3331i	1.20172	+	0.535039i
$622$	−0.440137	−	4.18762i	−0.0176479	−	0.167908i
$623$	−5.62920	+	6.25186i	−0.225529	+	0.250475i
$624$	−0.802794	−	0.891593i	−0.0321375	−	0.0356923i
$625$	−16.2672	+	7.24263i	−0.650688	+	0.289705i
$626$	8.98670			0.359181
$627$	−19.6586	+	37.8037i	−0.785087	+	1.50973i
$628$	−13.7247			−0.547674
$629$	25.7340	−	11.4575i	1.02608	−	0.456841i
$630$	12.5021	+	13.8850i	0.498096	+	0.553192i
$631$	−16.3138	+	18.1183i	−0.649443	+	0.721280i	−0.974493	−	0.224417i	$-0.927952\pi$
$631$	−16.3138	+	18.1183i	−0.649443	+	0.721280i	0.325050	+	0.945697i	$0.394619\pi$
$632$	1.08619	+	10.3344i	0.0432061	+	0.411079i
$633$	20.3364	+	9.05434i	0.808299	+	0.359878i
$634$	−3.14244	−	9.67142i	−0.124802	−	0.384101i
$635$	2.35423	−	7.24557i	0.0934248	−	0.287532i
$636$	−3.08721	+	29.3729i	−0.122416	+	1.16471i
$637$	−0.851628	−	1.47506i	−0.0337427	−	0.0584441i
$638$	−2.88291	−	5.59192i	−0.114135	−	0.221386i
$639$	75.0621			2.96941
$640$	0.204659	−	1.94720i	0.00808987	−	0.0769700i
$641$	19.7030	+	21.8824i	0.778221	+	0.864302i	0.993684	−	0.112210i	$-0.0357930\pi$
$641$	19.7030	+	21.8824i	0.778221	+	0.864302i	−0.215464	+	0.976512i	$0.569126\pi$
$642$	−8.72249	+	9.68731i	−0.344249	+	0.382327i
$643$	−3.30278	−	31.4239i	−0.130249	−	1.23924i	−0.843036	−	0.537857i	$-0.819234\pi$
$643$	−3.30278	−	31.4239i	−0.130249	−	1.23924i	0.712787	−	0.701381i	$-0.247433\pi$
$644$	0.726024	+	6.90765i	0.0286093	+	0.272200i
$645$	−8.79952	−	27.0821i	−0.346481	−	1.06636i
$646$	−27.5716	+	2.53420i	−1.08479	+	0.0997067i
$647$	−14.0041	−	10.1746i	−0.550557	−	0.400003i	0.277434	−	0.960745i	$-0.410516\pi$
$647$	−14.0041	−	10.1746i	−0.550557	−	0.400003i	−0.827991	+	0.560742i	$0.810516\pi$
$648$	−3.14036	+	5.43926i	−0.123365	+	0.213674i
$649$	31.4475	−	20.6362i	1.23442	−	0.810041i
$650$	−0.237421	−	0.411225i	−0.00931242	−	0.0161296i
$651$	39.3232	−	17.5078i	1.54120	−	0.686185i
$652$	−21.2176	+	4.50994i	−0.830945	+	0.176623i
$653$	−5.36758	−	16.5197i	−0.210050	−	0.646466i	−0.999468	−	0.0326108i	$-0.989618\pi$
$653$	−5.36758	−	16.5197i	−0.210050	−	0.646466i	0.789419	−	0.613855i	$-0.210382\pi$
$654$	11.8405	−	8.60265i	0.463002	−	0.336390i
$655$	23.1601	+	10.3116i	0.904941	+	0.402906i
$656$	−4.81948	+	5.35258i	−0.188169	+	0.208983i
$657$	4.09079	−	12.5902i	0.159597	−	0.491189i
$658$	−6.61567	−	4.80656i	−0.257906	−	0.187379i
$659$	−14.9647	−	25.9196i	−0.582942	−	1.00969i	−0.995129	−	0.0985861i	$-0.968568\pi$
$659$	−14.9647	−	25.9196i	−0.582942	−	1.00969i	0.412186	−	0.911100i	$-0.364765\pi$
$660$	−14.9314	−	11.9737i	−0.581202	−	0.466076i
$661$	−12.1660	−	21.0722i	−0.473204	−	0.819614i	0.526325	−	0.850283i	$-0.323569\pi$
$661$	−12.1660	−	21.0722i	−0.473204	−	0.819614i	−0.999530	+	0.0306694i	$0.990236\pi$
$662$	18.5775	−	8.27122i	0.722034	−	0.321470i
$663$	−5.09937	−	5.66342i	−0.198043	−	0.219949i
$664$	3.85424	+	11.8621i	0.149573	+	0.460340i
$665$	0.187082	−	14.3196i	0.00725474	−	0.555291i
$666$	−20.4034	+	14.8239i	−0.790616	+	0.574416i
$667$	7.68018	+	1.63247i	0.297378	+	0.0632096i
$668$	14.2178	+	15.7904i	0.550102	+	0.610950i
$669$	−2.06242	+	19.6226i	−0.0797378	+	0.758654i
$670$	7.47408	−	12.9455i	0.288749	−	0.500128i
$671$	−25.7085	+	10.0095i	−0.992466	+	0.386414i
$672$	−4.94571			−0.190785
$673$	31.6694	+	23.0091i	1.22076	+	0.886938i	0.996163	−	0.0875132i	$-0.0278920\pi$
$673$	31.6694	+	23.0091i	1.22076	+	0.886938i	0.224601	+	0.974451i	$0.427892\pi$
$674$	22.3479	−	4.75020i	0.860811	−	0.182971i
$675$	−6.18155	+	6.86531i	−0.237928	+	0.264246i
$676$	10.3832	−	7.54381i	0.399353	−	0.290147i
$677$	19.0604	−	13.8482i	0.732549	−	0.532228i	−0.157820	−	0.987468i	$-0.550447\pi$
$677$	19.0604	−	13.8482i	0.732549	−	0.532228i	0.890369	+	0.455240i	$0.150447\pi$
$678$	−5.73394	+	6.36818i	−0.220211	+	0.244569i
$679$	5.54013	+	6.15293i	0.212611	+	0.236128i
$680$	1.30000	−	12.3687i	0.0498528	−	0.474317i
$681$	−38.5224	+	66.7227i	−1.47618	+	2.55682i
$682$	−24.1338	+	15.8368i	−0.924129	+	0.606423i
$683$	39.0100			1.49268			0.746339	−	0.665566i	$-0.231810\pi$
$683$	39.0100			1.49268			0.746339	+	0.665566i	$0.231810\pi$
$684$	23.6737	−	7.35156i	0.905188	−	0.281094i
$685$	7.16176	−	22.0416i	0.273637	−	0.842168i
$686$	−18.3572	−	3.90195i	−0.700882	−	0.148977i
$687$	7.97732	+	75.8991i	0.304354	+	2.89573i
$688$	4.50791	+	2.00705i	0.171863	+	0.0765182i
$689$	3.98989	+	0.848078i	0.152003	+	0.0323092i
$690$	23.3645	−	4.96628i	0.889472	−	0.189063i
$691$	−36.2439	−	26.3327i	−1.37878	−	1.00174i	−0.996993	−	0.0774953i	$-0.975308\pi$
$691$	−36.2439	−	26.3327i	−1.37878	−	1.00174i	−0.381790	−	0.924249i	$-0.624692\pi$
$692$	−11.2970			−0.429446
$693$	−17.1109	+	26.6257i	−0.649991	+	1.01143i
$694$	−10.9993	−	19.0514i	−0.417528	−	0.723179i
$695$	−17.3829	−	12.6294i	−0.659370	−	0.479060i
$696$	−1.72768	+	5.31724i	−0.0654874	+	0.201549i
$697$	−30.6135	+	33.9997i	−1.15957	+	1.28783i
$698$	2.95078	+	28.0748i	0.111689	+	1.06265i
$699$	70.1137	+	31.2166i	2.65194	+	1.18072i
$700$	−1.91465	−	0.406971i	−0.0723669	−	0.0153821i
$701$	34.4686	+	38.2812i	1.30186	+	1.44586i	0.823078	+	0.567928i	$0.192255\pi$
$701$	34.4686	+	38.2812i	1.30186	+	1.44586i	0.478782	+	0.877934i	$0.341079\pi$
$702$	2.60804	+	1.89485i	0.0984340	+	0.0715165i
$703$	19.1965	+	2.27155i	0.724009	+	0.0856731i
$704$	3.27328	−	0.534454i	0.123366	−	0.0201430i
$705$	−14.0612	+	24.3547i	−0.529575	+	0.917251i
$706$	11.2472	−	5.00760i	0.423296	−	0.188463i
$707$	6.66402	−	1.41648i	0.250626	−	0.0532722i
$708$	−32.6956	−	6.94967i	−1.22878	−	0.261185i
$709$	−17.9505	−	7.99210i	−0.674147	−	0.300150i	0.0409639	−	0.999161i	$-0.486957\pi$
$709$	−17.9505	−	7.99210i	−0.674147	−	0.300150i	−0.715111	+	0.699011i	$0.753624\pi$
$710$	20.9071	−	15.1899i	0.784630	−	0.570067i
$711$	−18.2613	−	56.2026i	−0.684854	−	2.10776i
$712$	−4.90394	+	1.04236i	−0.183783	+	0.0390643i
$713$	3.76570	−	35.8282i	0.141026	−	1.34178i
$714$	−31.4153			−1.17569
$715$	−1.86018	+	1.87802i	−0.0695669	+	0.0702338i
$716$	5.41591	+	9.38063i	0.202402	+	0.350571i
$717$	58.9506	−	26.2465i	2.20155	−	0.980194i
$718$	−20.7926	+	4.41961i	−0.775973	+	0.164938i
$719$	35.9582	+	7.64315i	1.34101	+	0.285041i	0.821884	−	0.569654i	$-0.192923\pi$
$719$	35.9582	+	7.64315i	1.34101	+	0.285041i	0.519129	+	0.854696i	$0.326256\pi$
$720$	1.16389	+	11.0737i	0.0433757	+	0.412692i
$721$	−1.20071	+	0.872369i	−0.0447169	+	0.0324887i
$722$	−17.1495	−	8.17882i	−0.638240	−	0.304384i
$723$	−19.8288	+	61.0267i	−0.737440	+	2.26961i
$724$	17.6440	−	7.85561i	0.655734	−	0.291952i
$725$	−1.10638	+	1.91631i	−0.0410901	+	0.0711701i
$726$	12.9037	−	29.7425i	0.478900	−	1.10385i
$727$	6.43834	−	11.1515i	0.238785	−	0.413587i	−0.721581	−	0.692330i	$-0.756584\pi$
$727$	6.43834	−	11.1515i	0.238785	−	0.413587i	0.960366	+	0.278743i	$0.0899176\pi$
$728$	−0.0713984	+	0.679310i	−0.00264620	+	0.0251769i
$729$	−10.6013	+	32.6276i	−0.392642	+	1.20843i
$730$	−1.40839	−	4.33458i	−0.0521269	−	0.160430i
$731$	28.6344	+	12.7489i	1.05908	+	0.471533i
$732$	22.3972	+	9.97188i	0.827825	+	0.368571i
$733$	−12.0339	−	37.0365i	−0.444482	−	1.36797i	−0.883051	−	0.469277i	$-0.844515\pi$
$733$	−12.0339	−	37.0365i	−0.444482	−	1.36797i	0.438569	−	0.898697i	$-0.355485\pi$
$734$	4.11813	−	12.6743i	0.152003	−	0.467817i
$735$	−2.52398	+	24.0141i	−0.0930985	+	0.885773i
$736$	−2.06962	+	3.58469i	−0.0762873	+	0.132134i
$737$	24.4896	+	6.43691i	0.902084	+	0.237107i
$738$	20.4805	−	35.4732i	0.753897	−	1.30579i
$739$	−7.59446	+	3.38127i	−0.279367	+	0.124382i	−0.541637	−	0.840612i	$-0.682195\pi$
$739$	−7.59446	+	3.38127i	−0.279367	+	0.124382i	0.262271	+	0.964994i	$0.415529\pi$
$740$	−2.68314	+	8.25786i	−0.0986343	+	0.303565i
$741$	−1.02038	−	5.12911i	−0.0374846	−	0.188422i
$742$	13.6035	−	9.88351i	0.499400	−	0.362835i
$743$	−2.10010	−	19.9811i	−0.0770451	−	0.733035i	−0.963043	−	0.269346i	$-0.913192\pi$
$743$	−2.10010	−	19.9811i	−0.0770451	−	0.733035i	0.885998	−	0.463688i	$-0.153474\pi$
$744$	25.0916	+	5.33338i	0.919902	+	0.195531i
$745$	−37.1318	+	7.89261i	−1.36040	+	0.289163i
$746$	9.81754	−	4.37105i	0.359446	−	0.160035i
$747$	−35.4656	−	61.4282i	−1.29762	−	2.24754i
$748$	20.7920	−	3.39487i	0.760229	−	0.124129i
$749$	7.42148			0.271175
$750$	−3.71968	+	35.3904i	−0.135823	+	1.29227i
$751$	−15.1874	+	3.22818i	−0.554196	+	0.117798i	−0.476492	−	0.879179i	$-0.658092\pi$
$751$	−15.1874	+	3.22818i	−0.554196	+	0.117798i	−0.0777033	+	0.996977i	$0.524759\pi$
$752$	−1.50593	−	4.63476i	−0.0549155	−	0.169012i
$753$	−67.3106	+	48.9040i	−2.45293	+	1.78216i
$754$	0.705399	+	0.314064i	0.0256891	+	0.0114375i
$755$	−4.03601	−	0.857881i	−0.146886	−	0.0312215i
$756$	12.9986	−	2.76293i	0.472754	−	0.100487i
$757$	−21.0796	+	9.38524i	−0.766151	+	0.341112i	−0.752325	−	0.658792i	$-0.771068\pi$
$757$	−21.0796	+	9.38524i	−0.766151	+	0.341112i	−0.0138257	+	0.999904i	$0.504401\pi$
$758$	13.2255	−	22.9073i	0.480372	−	0.832029i
$759$	18.5413	+	35.9642i	0.673007	+	1.30542i
$760$	5.10617	−	6.83836i	0.185220	−	0.248054i
$761$	−24.6452	−	17.9058i	−0.893388	−	0.649084i	0.0433715	−	0.999059i	$-0.486190\pi$
$761$	−24.6452	−	17.9058i	−0.893388	−	0.649084i	−0.936759	+	0.349975i	$0.886190\pi$
$762$	−7.67387	−	8.52270i	−0.277995	−	0.308745i
$763$	−8.15040	−	1.73242i	−0.295064	−	0.0627178i
$764$	−6.99459	−	3.11419i	−0.253055	−	0.112668i
$765$	7.39307	+	70.3403i	0.267297	+	2.54316i
$766$	−16.8273	+	18.6886i	−0.607994	+	0.675246i
$767$	−1.42657	+	4.39053i	−0.0515104	+	0.158533i
$768$	−2.38447	−	1.73242i	−0.0860421	−	0.0625133i
$769$	−12.1531	−	21.0499i	−0.438253	−	0.759077i	0.559301	−	0.828964i	$-0.311069\pi$
$769$	−12.1531	−	21.0499i	−0.438253	−	0.759077i	−0.997555	+	0.0698871i	$0.977736\pi$
$770$	0.622179	+	10.8788i	0.0224218	+	0.392043i
$771$	79.4362			2.86082
$772$	−1.59079	−	1.15578i	−0.0572538	−	0.0415973i
$773$	−10.0714	+	2.14075i	−0.362244	+	0.0769974i	−0.385438	−	0.922734i	$-0.625950\pi$
$773$	−10.0714	+	2.14075i	−0.362244	+	0.0769974i	0.0231941	+	0.999731i	$0.492616\pi$
$774$	−27.4493	−	5.83452i	−0.986644	−	0.209718i
$775$	9.27491	+	4.12946i	0.333165	+	0.148334i
$776$	0.515761	+	4.90714i	0.0185147	+	0.176156i
$777$	21.4535	+	4.56008i	0.769639	+	0.163592i
$778$	5.69075	−	17.5143i	0.204023	−	0.627919i
$779$	−29.9830	+	9.31082i	−1.07425	+	0.333595i
$780$	2.34904			0.0841091
$781$	34.1514	+	27.3865i	1.22203	+	0.979967i
$782$	−13.1463	+	22.7701i	−0.470111	+	0.814256i
$783$	1.57028	−	14.9402i	0.0561172	−	0.533920i
$784$	−2.79983	−	3.10953i	−0.0999939	−	0.111054i
$785$	17.9808	−	19.9697i	0.641763	−	0.712750i
$786$	30.8749	−	22.4319i	1.10127	−	0.800121i
$787$	−9.32895	+	6.77788i	−0.332541	+	0.241605i	−0.741508	−	0.670944i	$-0.765889\pi$
$787$	−9.32895	+	6.77788i	−0.332541	+	0.241605i	0.408967	+	0.912549i	$0.365889\pi$
$788$	10.7411	−	11.9292i	0.382636	−	0.424960i
$789$	−47.0019	+	9.99055i	−1.67331	+	0.355673i
$790$	−16.4598	−	11.9587i	−0.585613	−	0.425472i
$791$	4.87868			0.173466
$792$	−17.5763	+	6.84329i	−0.624548	+	0.243166i
$793$	1.69301	−	2.93237i	0.0601204	−	0.104132i
$794$	−1.93596	+	18.4194i	−0.0687046	+	0.653680i
$795$	−38.6936	−	42.9736i	−1.37232	−	1.52412i
$796$	−2.85441	−	0.606724i	−0.101172	−	0.0215048i
$797$	1.65329	−	1.20118i	0.0585624	−	0.0425481i	−0.558119	−	0.829761i	$-0.688477\pi$
$797$	1.65329	−	1.20118i	0.0585624	−	0.0425481i	0.616681	+	0.787213i	$0.288477\pi$
$798$	−18.5273	−	11.0219i	−0.655858	−	0.390171i
$799$	−9.56568	−	29.4401i	−0.338409	−	1.04152i
$800$	−0.780550	−	0.866889i	−0.0275966	−	0.0306491i
$801$	26.0466	−	11.5967i	0.920313	−	0.409750i
$802$	1.06038	+	1.83662i	0.0374432	+	0.0648535i
$803$	6.45475	−	4.23567i	0.227783	−	0.149474i
$804$	−11.2511	−	19.4875i	−0.396796	−	0.687271i
$805$	−11.0020	−	7.99341i	−0.387769	−	0.281731i
$806$	1.09479	−	3.36942i	0.0385623	−	0.118683i
$807$	−23.6269	+	26.2403i	−0.831705	+	0.923702i
$808$	3.70909	+	1.65139i	0.130485	+	0.0580958i
$809$	−2.17756	+	1.58209i	−0.0765589	+	0.0556233i	−0.625406	−	0.780299i	$-0.715067\pi$
$809$	−2.17756	+	1.58209i	−0.0765589	+	0.0556233i	0.548847	+	0.835923i	$0.315067\pi$
$810$	−3.80004	−	11.6953i	−0.133520	−	0.410932i
$811$	−27.9227	+	5.93514i	−0.980497	+	0.208411i	−0.670161	−	0.742216i	$-0.733775\pi$
$811$	−27.9227	+	5.93514i	−0.980497	+	0.208411i	−0.310336	+	0.950627i	$0.600442\pi$
$812$	2.90784	−	1.29465i	0.102045	−	0.0454335i
$813$	−27.4508	−	47.5462i	−0.962741	−	1.66752i
$814$	−14.6916	−	0.699698i	−0.514940	−	0.0245244i
$815$	21.2353	−	36.7806i	0.743840	−	1.28837i
$816$	−15.1462	−	11.0044i	−0.530224	−	0.385230i
$817$	12.4143	+	17.5649i	0.434322	+	0.614518i
$818$	2.41099	+	7.42025i	0.0842982	+	0.259443i
$819$	−0.406041	−	3.86322i	−0.0141882	−	0.134992i
$820$	−1.47408	−	14.0249i	−0.0514771	−	0.489772i
$821$	18.0606	−	20.0584i	0.630320	−	0.700041i	−0.340393	−	0.940283i	$-0.610560\pi$
$821$	18.0606	−	20.0584i	0.630320	−	0.700041i	0.970713	+	0.240242i	$0.0772267\pi$
$822$	−23.3446	−	25.9268i	−0.814235	−	0.904300i
$823$	−5.40420	+	51.4175i	−0.188379	+	1.79230i	0.337072	+	0.941479i	$0.390563\pi$
$823$	−5.40420	+	51.4175i	−0.188379	+	1.79230i	−0.525451	+	0.850824i	$0.676103\pi$
$824$	−0.884477			−0.0308122
$825$	−11.2540	+	1.83753i	−0.391814	+	0.0639746i
$826$	9.51516	+	16.4807i	0.331075	+	0.573438i
$827$	4.28229	−	40.7433i	0.148910	−	1.41678i	−0.623582	−	0.781758i	$-0.714323\pi$
$827$	4.28229	−	40.7433i	0.148910	−	1.41678i	0.772492	−	0.635025i	$-0.219010\pi$
$828$	7.27419	−	22.3877i	0.252796	−	0.778025i
$829$	1.19921	+	3.69078i	0.0416501	+	0.128186i	0.969719	−	0.244221i	$-0.0785324\pi$
$829$	1.19921	+	3.69078i	0.0416501	+	0.128186i	−0.928069	+	0.372407i	$0.878532\pi$
$830$	−22.3092	−	9.93268i	−0.774362	−	0.344768i
$831$	−3.28293	−	31.2350i	−0.113883	−	1.08353i
$832$	−0.272377	+	0.302505i	−0.00944296	+	0.0104875i
$833$	−17.7846	−	19.7518i	−0.616199	−	0.684359i
$834$	−29.5482	+	13.1557i	−1.02317	+	0.455545i
$835$	−41.6023			−1.43971
$836$	13.4532	+	5.29263i	0.465288	+	0.183049i
$837$	−68.9265			−2.38245
$838$	−18.5171	+	8.24432i	−0.639661	+	0.284795i
$839$	31.4956	+	34.9794i	1.08735	+	1.20762i	0.976890	+	0.213744i	$0.0685658\pi$
$839$	31.4956	+	34.9794i	1.08735	+	1.20762i	0.110460	+	0.993881i	$0.464768\pi$
$840$	6.47943	−	7.19614i	0.223562	−	0.248290i
$841$	2.65521	+	25.2626i	0.0915588	+	0.871124i
$842$	−4.10706	−	1.82858i	−0.141539	−	0.0630171i
$843$	−7.80761	−	24.0294i	−0.268909	−	0.827615i
$844$	2.33395	−	7.18316i	0.0803379	−	0.247255i
$845$	−2.62666	+	24.9910i	−0.0903598	+	0.859716i
$846$	13.8571	+	24.0012i	0.476417	+	0.825178i
$847$	−17.4995	+	5.87109i	−0.601290	+	0.201733i
$848$	10.0207			0.344112
$849$	7.26760	−	69.1466i	0.249423	−	2.37310i
$850$	−4.95808	−	5.50650i	−0.170061	−	0.188871i
$851$	12.2828	−	13.6414i	0.421048	−	0.467621i
$852$	−4.06638	−	38.6891i	−0.139312	−	1.32547i
$853$	4.80990	+	45.7631i	0.164688	+	1.56690i	0.694945	+	0.719063i	$0.255429\pi$
$853$	4.80990	+	45.7631i	0.164688	+	1.56690i	−0.530257	+	0.847837i	$0.677905\pi$
$854$	−4.31327	−	13.2749i	−0.147597	−	0.454257i
$855$	−20.3185	+	44.0772i	−0.694878	+	1.50741i
$856$	3.57810	+	2.59965i	0.122297	+	0.0888540i
$857$	4.97366	−	8.61463i	0.169897	−	0.294270i	−0.768487	−	0.639866i	$-0.778990\pi$
$857$	4.97366	−	8.61463i	0.169897	−	0.294270i	0.938383	+	0.345596i	$0.112323\pi$
$858$	1.04820	+	3.83860i	0.0357850	+	0.131048i
$859$	−28.6793	−	49.6741i	−0.978526	−	1.69486i	−0.667770	−	0.744368i	$-0.732751\pi$
$859$	−28.6793	−	49.6741i	−0.978526	−	1.69486i	−0.310757	−	0.950489i	$-0.600582\pi$
$860$	−8.82618	+	3.92967i	−0.300970	+	0.134001i
$861$	−34.8436	+	7.40623i	−1.18747	+	0.252404i
$862$	6.11197	+	18.8107i	0.208174	+	0.640695i
$863$	0.354726	−	0.257724i	0.0120750	−	0.00877302i	−0.581731	−	0.813381i	$-0.697625\pi$
$863$	0.354726	−	0.257724i	0.0120750	−	0.00877302i	0.593806	+	0.804608i	$0.297625\pi$
$864$	7.23481	+	3.22114i	0.246133	+	0.109586i
$865$	14.8003	−	16.4374i	0.503225	−	0.558888i
$866$	5.72567	−	17.6218i	0.194566	−	0.598813i
$867$	−55.6732	−	40.4489i	−1.89076	−	1.37372i
$868$	−7.30221	−	12.6478i	−0.247853	−	0.429294i
$869$	12.1972	−	32.2335i	0.413761	−	1.09345i
$870$	−5.47327	−	9.47998i	−0.185561	−	0.321401i
$871$	−2.83910	+	1.26405i	−0.0961991	+	0.0428306i
$872$	−3.32269	−	3.69023i	−0.112521	−	0.124967i
$873$	−8.67116	−	26.6871i	−0.293474	−	0.903221i
$874$	−15.7418	+	8.81639i	−0.532475	+	0.298219i
$875$	16.3904	−	11.9083i	0.554096	−	0.402574i
$876$	−6.71092	−	1.42645i	−0.226741	−	0.0481953i
$877$	−36.4257	−	40.4548i	−1.23001	−	1.36606i	−0.907805	−	0.419393i	$-0.862243\pi$
$877$	−36.4257	−	40.4548i	−1.23001	−	1.36606i	−0.322204	−	0.946670i	$-0.604424\pi$
$878$	1.36608	−	12.9974i	0.0461029	−	0.438640i
$879$	−3.65294	+	6.32708i	−0.123211	+	0.213407i
$880$	−3.51071	+	5.46290i	−0.118346	+	0.184154i
$881$	−37.3424			−1.25810			−0.629048	−	0.777366i	$-0.716555\pi$
$881$	−37.3424			−1.25810			−0.629048	+	0.777366i	$0.716555\pi$
$882$	19.2513	+	13.9869i	0.648224	+	0.470962i
$883$	15.4414	−	3.28217i	0.519644	−	0.110454i	0.0593794	−	0.998235i	$-0.481088\pi$
$883$	15.4414	−	3.28217i	0.519644	−	0.110454i	0.460265	+	0.887782i	$0.347754\pi$
$884$	−1.73014	+	1.92152i	−0.0581910	+	0.0646277i
$885$	52.9468	−	38.4681i	1.77979	−	1.29309i
$886$	0.801690	−	0.582462i	0.0269333	−	0.0195682i
$887$	24.4310	−	27.1334i	0.820313	−	0.911050i	−0.177007	−	0.984210i	$-0.556642\pi$
$887$	24.4310	−	27.1334i	0.820313	−	0.911050i	0.997320	+	0.0731594i	$0.0233082\pi$
$888$	8.74600	+	9.71342i	0.293496	+	0.325961i
$889$	−0.682494	+	6.49350i	−0.0228901	+	0.217785i
$890$	4.90804	−	8.50097i	0.164518	−	0.284953i
$891$	17.4158	−	11.4285i	0.583452	−	0.382868i
$892$	6.69435			0.224143
$893$	4.68755	−	20.7185i	0.156863	−	0.693317i
$894$	−17.6588	+	54.3482i	−0.590599	+	1.81768i
$895$	−20.7445	−	4.40938i	−0.693412	−	0.147389i
$896$	0.175400	+	1.66882i	0.00585970	+	0.0557513i
$897$	−4.53675	−	2.01989i	−0.151478	−	0.0674422i
$898$	−10.4512	−	2.22147i	−0.348761	−	0.0741314i
$899$	−16.1488	+	3.43253i	−0.538592	+	0.114481i
$900$	5.36696	+	3.89933i	0.178899	+	0.129978i
$901$	63.6517			2.12055
$902$	22.2606	−	8.66709i	0.741196	−	0.288583i
$903$	12.2024	+	21.1351i	0.406070	+	0.703333i
$904$	2.35215	+	1.70894i	0.0782314	+	0.0568385i
$905$	−11.6855	+	35.9642i	−0.388438	+	1.19549i
$906$	−4.15620	+	4.61593i	−0.138080	+	0.153354i
$907$	1.50729	+	14.3409i	0.0500487	+	0.476182i	0.990626	+	0.136602i	$0.0436181\pi$
$907$	1.50729	+	14.3409i	0.0500487	+	0.476182i	−0.940577	+	0.339580i	$0.889715\pi$
$908$	23.8803	+	10.6322i	0.792494	+	0.352841i
$909$	−22.5851	−	4.80061i	−0.749100	−	0.159226i
$910$	−0.894874	−	0.993858i	−0.0296648	−	0.0329461i
$911$	38.7890	+	28.1818i	1.28514	+	0.933706i	0.999695	−	0.0246908i	$-0.00786013\pi$
$911$	38.7890	+	28.1818i	1.28514	+	0.933706i	0.285440	+	0.958396i	$0.407860\pi$
$912$	−5.07169	−	11.8038i	−0.167940	−	0.390864i
$913$	6.27624	−	40.8880i	0.207713	−	1.35319i
$914$	0.692357	−	1.19920i	0.0229011	−	0.0396659i
$915$	−43.8521	+	19.5242i	−1.44971	+	0.645451i
$916$	25.3275	−	5.38353i	0.836845	−	0.177877i
$917$	−21.2527	−	4.51739i	−0.701825	−	0.149177i
$918$	45.9557	+	20.4608i	1.51676	+	0.675307i
$919$	5.17092	−	3.75690i	0.170573	−	0.123929i	−0.499223	−	0.866473i	$-0.666381\pi$
$919$	5.17092	−	3.75690i	0.170573	−	0.123929i	0.669797	+	0.742545i	$0.266381\pi$
$920$	−2.50438	−	7.70770i	−0.0825671	−	0.254115i
$921$	15.3697	−	3.26693i	0.506449	−	0.107649i
$922$	2.35311	−	22.3883i	0.0774955	−	0.737320i
$923$	−5.37278			−0.176847
$924$	14.6506	+	7.37704i	0.481969	+	0.242687i
$925$	2.58657	+	4.48007i	0.0850459	+	0.147304i
$926$	24.8216	−	11.0513i	0.815690	−	0.363169i
$927$	4.92008	−	1.04579i	0.161597	−	0.0343484i
$928$	1.85545	+	0.394389i	0.0609083	+	0.0129465i
$929$	−0.342057	−	3.25445i	−0.0112225	−	0.106775i	0.987477	−	0.157765i	$-0.0504289\pi$
$929$	−0.342057	−	3.25445i	−0.0112225	−	0.106775i	−0.998699	+	0.0509902i	$0.983762\pi$
$930$	−40.6329	+	29.5216i	−1.33241	+	0.968050i
$931$	−3.55869	−	17.8883i	−0.116631	−	0.586265i
$932$	8.04676	−	24.7654i	0.263580	−	0.811217i
$933$	11.3375	−	5.04778i	0.371173	−	0.165257i
$934$	−14.2311	+	24.6489i	−0.465655	+	0.806538i
$935$	−22.3001	+	34.7005i	−0.729293	+	1.13483i
$936$	1.15747	−	2.00480i	0.0378331	−	0.0655289i
$937$	−1.87208	+	17.8117i	−0.0611582	+	0.581881i	0.920435	+	0.390896i	$0.127835\pi$
$937$	−1.87208	+	17.8117i	−0.0611582	+	0.581881i	−0.981593	+	0.190985i	$0.938832\pi$
$938$	−3.95884	+	12.1841i	−0.129261	+	0.397824i
$939$	8.18496	+	25.1907i	0.267106	+	0.822068i
$940$	8.71663	+	3.88089i	0.284305	+	0.126581i
$941$	−16.1835	−	7.20538i	−0.527569	−	0.234889i	0.125627	−	0.992077i	$-0.459906\pi$
$941$	−16.1835	−	7.20538i	−0.527569	−	0.234889i	−0.653196	+	0.757189i	$0.726572\pi$
$942$	−12.5002	−	38.4718i	−0.407280	−	1.25348i
$943$	−9.21283	+	28.3542i	−0.300011	+	0.923339i
$944$	−1.18546	+	11.2789i	−0.0385833	+	0.367096i
$945$	−13.0094	+	22.5330i	−0.423197	+	0.732999i
$946$	−10.3600	−	12.6695i	−0.336832	−	0.411920i
$947$	−12.6602	+	21.9280i	−0.411400	+	0.712565i	−0.995043	−	0.0994447i	$-0.968293\pi$
$947$	−12.6602	+	21.9280i	−0.411400	+	0.712565i	0.583643	+	0.812010i	$0.301627\pi$
$948$	−27.9791	+	12.4571i	−0.908719	+	0.404588i
$949$	−0.292810	+	0.901175i	−0.00950500	+	0.0292534i
$950$	−0.992108	−	4.98699i	−0.0321882	−	0.161799i
$951$	24.2480	−	17.6172i	0.786295	−	0.571277i
$952$	1.11414	+	10.6004i	0.0361096	+	0.343560i
$953$	−26.0069	−	5.52794i	−0.842447	−	0.179068i	−0.233577	−	0.972338i	$-0.575043\pi$
$953$	−26.0069	−	5.52794i	−0.842447	−	0.179068i	−0.608869	+	0.793271i	$0.708377\pi$
$954$	−55.7421	+	11.8483i	−1.80472	+	0.383604i
$955$	13.6949	−	6.09737i	0.443157	−	0.197306i
$956$	−10.9470	−	18.9607i	−0.354050	−	0.613233i
$957$	13.0491	−	13.1742i	0.421817	−	0.425860i
$958$	−1.11575			−0.0360481
$959$	−2.07620	+	19.7538i	−0.0670441	+	0.637882i
$960$	5.64463	−	1.19980i	0.182180	−	0.0387235i
$961$	13.8283	+	42.5592i	0.446075	+	1.37288i
$962$	1.46043	−	1.06107i	0.0470862	−	0.0342101i
$963$	−22.9777	−	10.2303i	−0.740446	−	0.329668i
$964$	21.2953	+	4.52645i	0.685875	+	0.145787i
$965$	3.76580	−	0.800445i	0.121225	−	0.0257672i
$966$	−18.7017	+	8.32652i	−0.601717	+	0.267901i
$967$	−4.48085	+	7.76105i	−0.144094	+	0.249579i	−0.929035	−	0.369993i	$-0.879360\pi$
$967$	−4.48085	+	7.76105i	−0.144094	+	0.249579i	0.784940	+	0.619571i	$0.212694\pi$
$968$	−10.4936	−	3.29923i	−0.337276	−	0.106041i
$969$	−32.2155	−	74.9782i	−1.03491	−	2.40865i
$970$	−7.81571	−	5.67845i	−0.250947	−	0.182324i
$971$	34.9013	+	38.7618i	1.12003	+	1.24392i	0.966745	+	0.255743i	$0.0823201\pi$
$971$	34.9013	+	38.7618i	1.12003	+	1.24392i	0.153290	+	0.988181i	$0.451013\pi$
$972$	5.13223	+	1.09089i	0.164616	+	0.0349903i
$973$	16.8225	+	7.48988i	0.539306	+	0.240115i
$974$	0.239349	+	2.27725i	0.00766923	+	0.0729679i
$975$	0.936470	−	1.04006i	0.0299911	−	0.0333084i
$976$	2.57047	−	7.91108i	0.0822786	−	0.253228i
$977$	−33.9016	−	24.6310i	−1.08461	−	0.788015i	−0.106128	−	0.994352i	$-0.533845\pi$
$977$	−33.9016	−	24.6310i	−1.08461	−	0.788015i	−0.978481	+	0.206338i	$0.933845\pi$
$978$	−31.9665	−	55.3677i	−1.02218	−	1.77046i
$979$	16.0817	+	4.22695i	0.513972	+	0.135094i
$980$	8.19252			0.261700
$981$	22.8464	+	16.5989i	0.729430	+	0.529962i
$982$	25.5923	−	5.43981i	0.816683	−	0.173591i
$983$	27.4737	+	5.83971i	0.876275	+	0.186258i	0.624025	−	0.781404i	$-0.285496\pi$
$983$	27.4737	+	5.83971i	0.876275	+	0.186258i	0.252250	+	0.967662i	$0.418830\pi$
$984$	−19.3934	−	8.63449i	−0.618239	−	0.275258i
$985$	3.28526	+	31.2571i	0.104677	+	0.995935i
$986$	11.7859	+	2.50517i	0.375339	+	0.0797808i
$987$	7.44788	−	22.9222i	0.237069	−	0.729622i
$988$	−1.69451	+	0.526208i	−0.0539096	+	0.0167409i
$989$	20.4252			0.649484
$990$	13.0698	−	34.5395i	0.415384	−	1.09774i
$991$	22.2721	−	38.5765i	0.707497	−	1.22542i	−0.258285	−	0.966069i	$-0.583157\pi$
$991$	22.2721	−	38.5765i	0.707497	−	1.22542i	0.965783	−	0.259353i	$-0.0835092\pi$
$992$	0.909754	−	8.65573i	0.0288847	−	0.274820i
$993$	40.1053	+	44.5414i	1.27270	+	1.41348i
$994$	−14.8199	+	16.4592i	−0.470059	+	0.522053i
$995$	4.62239	−	3.35836i	0.146540	−	0.106467i
$996$	−29.7405	+	21.6077i	−0.942363	+	0.684667i
$997$	5.70535	−	6.33644i	0.180690	−	0.200677i	−0.645995	−	0.763342i	$-0.723557\pi$
$997$	5.70535	−	6.33644i	0.180690	−	0.200677i	0.826685	+	0.562665i	$0.190224\pi$
$998$	13.3515	−	2.83796i	0.422636	−	0.0898340i
$999$	−28.4131	−	20.6433i	−0.898951	−	0.653126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.e.125.8	✓	72
11.3	even	5	inner	418.2.n.e.201.2	yes	72
19.7	even	3	inner	418.2.n.e.235.2	yes	72
209.102	even	15	inner	418.2.n.e.311.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.e.125.8	✓	72	1.1	even	1	trivial
418.2.n.e.201.2	yes	72	11.3	even	5	inner
418.2.n.e.235.2	yes	72	19.7	even	3	inner
418.2.n.e.311.8	yes	72	209.102	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 - 0.406737i) q^{2} +(1.97217 + 2.19032i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.204659 + 1.94720i) q^{5} +(2.69255 + 1.19880i) q^{6} +(-0.518534 - 1.59588i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.594450 + 5.65582i) q^{9} +O(q^{10})\)	\(q+(0.913545 - 0.406737i) q^{2} +(1.97217 + 2.19032i) q^{3} +(0.669131 - 0.743145i) q^{4} +(0.204659 + 1.94720i) q^{5} +(2.69255 + 1.19880i) q^{6} +(-0.518534 - 1.59588i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.594450 + 5.65582i) q^{9} +(0.978965 + 1.69562i) q^{10} +(-2.33399 + 2.35637i) q^{11} +2.94737 q^{12} +(0.0425494 - 0.404831i) q^{13} +(-1.12281 - 1.24701i) q^{14} +(-3.86137 + 4.28849i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.663968 - 6.31723i) q^{17} +(1.75737 + 5.40863i) q^{18} +(1.82479 - 3.95855i) q^{19} +(1.58400 + 1.15084i) q^{20} +(2.47286 - 4.28311i) q^{21} +(-1.17379 + 3.10197i) q^{22} +(-2.06962 - 3.58469i) q^{23} +(2.69255 - 1.19880i) q^{24} +(1.14102 - 0.242532i) q^{25} +(-0.125789 - 0.387138i) q^{26} +(-6.40700 + 4.65496i) q^{27} +(-1.53294 - 0.682509i) q^{28} +(-1.26928 + 1.40968i) q^{29} +(-1.78325 + 5.48829i) q^{30} +(7.04121 + 5.11574i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-9.76424 - 0.465030i) q^{33} +(-3.17601 - 5.50102i) q^{34} +(3.00139 - 1.33630i) q^{35} +(3.80533 + 4.22624i) q^{36} +(1.37040 + 4.21765i) q^{37} +(0.0569431 - 4.35853i) q^{38} +(0.970624 - 0.705199i) q^{39} +(1.91514 + 0.407076i) q^{40} +(-4.81948 - 5.35258i) q^{41} +(0.516968 - 4.91862i) q^{42} +(-2.46726 + 4.27343i) q^{43} +(0.189376 + 3.31121i) q^{44} -11.1347 q^{45} +(-3.34872 - 2.43299i) q^{46} +(4.76679 - 1.01321i) q^{47} +(1.97217 - 2.19032i) q^{48} +(3.38515 - 2.45946i) q^{49} +(0.943730 - 0.685660i) q^{50} +(12.5273 - 13.9130i) q^{51} +(-0.272377 - 0.302505i) q^{52} +(-1.04745 + 9.96580i) q^{53} +(-3.95974 + 6.85847i) q^{54} +(-5.06600 - 4.06251i) q^{55} -1.67801 q^{56} +(12.2693 - 3.81007i) q^{57} +(-0.586176 + 1.80406i) q^{58} +(-11.0932 - 2.35792i) q^{59} +(0.603206 + 5.73912i) q^{60} +(7.59906 + 3.38332i) q^{61} +(8.51322 + 1.80954i) q^{62} +(9.33426 - 1.98406i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.796996 q^{65} +(-9.10922 + 3.54665i) q^{66} +(-3.81734 - 6.61183i) q^{67} +(-5.13890 - 3.73363i) q^{68} +(3.76997 - 11.6028i) q^{69} +(2.19838 - 2.44155i) q^{70} +(-1.37967 - 13.1267i) q^{71} +(5.19530 + 2.31310i) q^{72} +(-2.27692 - 0.483975i) q^{73} +(2.96739 + 3.29563i) q^{74} +(2.78152 + 2.02089i) q^{75} +(-1.72075 - 4.00487i) q^{76} +(4.97074 + 2.50293i) q^{77} +(0.599878 - 1.03902i) q^{78} +(-9.49291 + 4.22652i) q^{79} +(1.91514 - 0.407076i) q^{80} +(-6.14346 - 1.30583i) q^{81} +(-6.57990 - 2.92956i) q^{82} +(-10.0905 + 7.33120i) q^{83} +(-1.52831 - 4.70365i) q^{84} +(12.1650 - 2.58576i) q^{85} +(-0.515798 + 4.90749i) q^{86} -5.59088 q^{87} +(1.51980 + 2.94792i) q^{88} +(-2.50675 - 4.34182i) q^{89} +(-10.1720 + 4.52888i) q^{90} +(-0.668126 + 0.142015i) q^{91} +(-4.04880 - 0.860598i) q^{92} +(2.68138 + 25.5116i) q^{93} +(3.94257 - 2.86444i) q^{94} +(8.08157 + 2.74309i) q^{95} +(0.910786 - 2.80311i) q^{96} +(-4.50759 + 2.00691i) q^{97} +(2.09214 - 3.62369i) q^{98} +(-11.9397 - 14.6014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

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Database

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