LMFDB - Embedded newform 966.2.q.j.85.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.4
Character	$\chi$	$=$	966.85
Dual form			966.2.q.j.841.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(1.60548 + 3.51551i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(1.60548 + 3.51551i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-3.70821 - 1.08883i) q^{10} +(-3.67363 - 4.23960i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-5.89822 - 1.73187i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-3.25124 - 2.08945i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.914440 - 6.36007i) q^{17} +(0.415415 + 0.909632i) q^{18} +(0.225754 + 1.57015i) q^{19} +(3.25124 - 2.08945i) q^{20} +(-0.654861 + 0.755750i) q^{21} +5.60979 q^{22} +(-1.23777 - 4.63335i) q^{23} -1.00000 q^{24} +(-6.50692 + 7.50939i) q^{25} +(5.17138 - 3.32344i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.301766 + 2.09883i) q^{29} +(3.70821 - 1.08883i) q^{30} +(-9.10049 - 5.84853i) q^{31} +(0.415415 - 0.909632i) q^{32} +(5.38256 + 1.58046i) q^{33} +(4.20779 + 4.85605i) q^{34} +(2.53088 + 2.92079i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-3.52957 + 7.72867i) q^{37} +(-1.33448 - 0.857617i) q^{38} +(5.89822 - 1.73187i) q^{39} +(-0.550012 + 3.82542i) q^{40} +(-0.792187 - 1.73465i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(-5.79479 + 3.72409i) q^{43} +(-3.67363 + 4.23960i) q^{44} +3.86476 q^{45} +(4.31222 + 2.09875i) q^{46} +10.2611 q^{47} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-1.41409 - 9.83521i) q^{50} +(2.66924 + 5.84482i) q^{51} +(-0.874842 + 6.08466i) q^{52} +(-6.75719 + 1.98409i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(9.00640 - 19.7213i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-1.03880 - 1.19884i) q^{57} +(-1.38857 - 1.60250i) q^{58} +(-2.86437 - 0.841056i) q^{59} +(-1.60548 + 3.51551i) q^{60} +(1.93062 + 1.24073i) q^{61} +(10.3796 - 3.04772i) q^{62} +(0.142315 - 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-3.38105 - 23.5157i) q^{65} +(-4.71926 + 3.03288i) q^{66} +(4.84862 - 5.59561i) q^{67} -6.42547 q^{68} +(3.54626 + 3.22863i) q^{69} -3.86476 q^{70} +(-1.63768 + 1.88998i) q^{71} +(0.841254 - 0.540641i) q^{72} +(-0.628219 - 4.36936i) q^{73} +(-3.52957 - 7.72867i) q^{74} +(1.41409 - 9.83521i) q^{75} +(1.52204 - 0.446912i) q^{76} +(-4.71926 - 3.03288i) q^{77} +(-2.55365 + 5.59171i) q^{78} +(-2.07365 - 0.608878i) q^{79} +(-2.53088 - 2.92079i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(1.82973 + 0.537258i) q^{82} +(5.47310 - 11.9844i) q^{83} +(0.841254 + 0.540641i) q^{84} +(23.8270 - 6.99623i) q^{85} +(0.980305 - 6.81817i) q^{86} +(-0.880851 - 1.92880i) q^{87} +(-0.798357 - 5.55269i) q^{88} +(-2.09399 + 1.34572i) q^{89} +(-2.53088 + 2.92079i) q^{90} -6.14723 q^{91} +(-4.41003 + 1.88457i) q^{92} +10.8178 q^{93} +(-6.71960 + 7.75483i) q^{94} +(-5.15743 + 3.31448i) q^{95} +(0.142315 + 0.989821i) q^{96} +(0.470487 + 1.03022i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(-5.38256 + 1.58046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{14} - 7 q^{15} - 4 q^{16} + 5 q^{17} - 4 q^{18} + 44 q^{19} + 7 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 40 q^{24} + 2 q^{25} + 24 q^{26} + 4 q^{27} + 4 q^{28} + 35 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 11 q^{33} + 5 q^{34} - 7 q^{35} - 4 q^{36} + 20 q^{37} - 11 q^{38} + 20 q^{39} - 4 q^{40} + 11 q^{41} - 4 q^{42} - 42 q^{43} - 11 q^{44} - 4 q^{45} - 6 q^{46} + 40 q^{47} + 4 q^{48} - 4 q^{49} - 53 q^{50} + 17 q^{51} - 9 q^{52} - 32 q^{53} + 4 q^{54} + 29 q^{55} + 4 q^{56} - 11 q^{57} - 31 q^{58} - 25 q^{59} + 4 q^{60} - 30 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 80 q^{65} - 88 q^{67} - 28 q^{68} + 6 q^{69} + 4 q^{70} - 45 q^{71} - 4 q^{72} - 39 q^{73} + 20 q^{74} + 53 q^{75} - 22 q^{76} - 2 q^{78} + 26 q^{79} + 7 q^{80} - 4 q^{81} + 22 q^{83} - 4 q^{84} + 77 q^{85} - 31 q^{86} + 9 q^{87} - 11 q^{88} + 20 q^{89} + 7 q^{90} - 24 q^{91} - 17 q^{92} - 42 q^{93} - 26 q^{94} + 84 q^{95} + 4 q^{96} + 74 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 11 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^14 - 7 * q^15 - 4 * q^16 + 5 * q^17 - 4 * q^18 + 44 * q^19 + 7 * q^20 - 4 * q^21 + 22 * q^22 - 6 * q^23 - 40 * q^24 + 2 * q^25 + 24 * q^26 + 4 * q^27 + 4 * q^28 + 35 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 11 * q^33 + 5 * q^34 - 7 * q^35 - 4 * q^36 + 20 * q^37 - 11 * q^38 + 20 * q^39 - 4 * q^40 + 11 * q^41 - 4 * q^42 - 42 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 40 * q^47 + 4 * q^48 - 4 * q^49 - 53 * q^50 + 17 * q^51 - 9 * q^52 - 32 * q^53 + 4 * q^54 + 29 * q^55 + 4 * q^56 - 11 * q^57 - 31 * q^58 - 25 * q^59 + 4 * q^60 - 30 * q^61 - 24 * q^62 + 4 * q^63 - 4 * q^64 + 80 * q^65 - 88 * q^67 - 28 * q^68 + 6 * q^69 + 4 * q^70 - 45 * q^71 - 4 * q^72 - 39 * q^73 + 20 * q^74 + 53 * q^75 - 22 * q^76 - 2 * q^78 + 26 * q^79 + 7 * q^80 - 4 * q^81 + 22 * q^83 - 4 * q^84 + 77 * q^85 - 31 * q^86 + 9 * q^87 - 11 * q^88 + 20 * q^89 + 7 * q^90 - 24 * q^91 - 17 * q^92 - 42 * q^93 - 26 * q^94 + 84 * q^95 + 4 * q^96 + 74 * q^97 - 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	1.60548	+	3.51551i	0.717992	+	1.57218i	0.816698	+	0.577066i	$0.195802\pi$
$5$	1.60548	+	3.51551i	0.717992	+	1.57218i	−0.0987061	+	0.995117i	$0.531470\pi$
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−3.70821	−	1.08883i	−1.17264	−	0.344318i
$11$	−3.67363	−	4.23960i	−1.10764	−	1.27829i	−0.957124	−	0.289680i	$-0.906451\pi$
$11$	−3.67363	−	4.23960i	−1.10764	−	1.27829i	−0.150518	−	0.988607i	$-0.548094\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	−5.89822	−	1.73187i	−1.63587	−	0.480335i	−0.670652	−	0.741772i	$-0.733985\pi$
$13$	−5.89822	−	1.73187i	−1.63587	−	0.480335i	−0.965221	+	0.261437i	$0.915804\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	−3.25124	−	2.08945i	−0.839467	−	0.539492i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.914440	−	6.36007i	0.221784	−	1.54254i	−0.509500	−	0.860471i	$-0.670170\pi$
$17$	0.914440	−	6.36007i	0.221784	−	1.54254i	0.731284	−	0.682073i	$-0.238921\pi$
$18$	0.415415	+	0.909632i	0.0979143	+	0.214402i
$19$	0.225754	+	1.57015i	0.0517914	+	0.360217i	0.999193	+	0.0401696i	$0.0127898\pi$
$19$	0.225754	+	1.57015i	0.0517914	+	0.360217i	−0.947401	+	0.320048i	$0.896301\pi$
$20$	3.25124	−	2.08945i	0.726999	−	0.467214i
$21$	−0.654861	+	0.755750i	−0.142902	+	0.164918i
$22$	5.60979			1.19601
$23$	−1.23777	−	4.63335i	−0.258093	−	0.966120i
$23$	−1.23777	−	4.63335i	−0.258093	−	0.966120i
$24$	−1.00000			−0.204124
$25$	−6.50692	+	7.50939i	−1.30138	+	1.50188i
$26$	5.17138	−	3.32344i	1.01419	−	0.651781i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	−0.415415	−	0.909632i	−0.0785061	−	0.171904i
$29$	−0.301766	+	2.09883i	−0.0560366	+	0.389743i	0.942431	+	0.334401i	$0.108534\pi$
$29$	−0.301766	+	2.09883i	−0.0560366	+	0.389743i	−0.998467	+	0.0553419i	$0.982375\pi$
$30$	3.70821	−	1.08883i	0.677023	−	0.198792i
$31$	−9.10049	−	5.84853i	−1.63450	−	1.05043i	−0.945479	−	0.325683i	$-0.894406\pi$
$31$	−9.10049	−	5.84853i	−1.63450	−	1.05043i	−0.689018	−	0.724744i	$-0.741958\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	5.38256	+	1.58046i	0.936983	+	0.275123i
$34$	4.20779	+	4.85605i	0.721630	+	0.832805i
$35$	2.53088	+	2.92079i	0.427796	+	0.493703i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	−3.52957	+	7.72867i	−0.580257	+	1.27059i	0.360896	+	0.932606i	$0.382471\pi$
$37$	−3.52957	+	7.72867i	−0.580257	+	1.27059i	−0.941153	+	0.337980i	$0.890256\pi$
$38$	−1.33448	−	0.857617i	−0.216481	−	0.139124i
$39$	5.89822	−	1.73187i	0.944471	−	0.277322i
$40$	−0.550012	+	3.82542i	−0.0869646	+	0.604852i
$41$	−0.792187	−	1.73465i	−0.123719	−	0.270907i	0.837631	−	0.546237i	$-0.183940\pi$
$41$	−0.792187	−	1.73465i	−0.123719	−	0.270907i	−0.961350	+	0.275330i	$0.911213\pi$
$42$	−0.142315	−	0.989821i	−0.0219597	−	0.152733i
$43$	−5.79479	+	3.72409i	−0.883697	+	0.567918i	−0.901914	−	0.431916i	$-0.857838\pi$
$43$	−5.79479	+	3.72409i	−0.883697	+	0.567918i	0.0182163	+	0.999834i	$0.494201\pi$
$44$	−3.67363	+	4.23960i	−0.553821	+	0.639144i
$45$	3.86476			0.576124
$46$	4.31222	+	2.09875i	0.635802	+	0.309444i
$47$	10.2611			1.49674			0.748369	−	0.663283i	$-0.230837\pi$
$47$	10.2611			1.49674			0.748369	+	0.663283i	$0.230837\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−1.41409	−	9.83521i	−0.199982	−	1.39091i
$51$	2.66924	+	5.84482i	0.373768	+	0.818438i
$52$	−0.874842	+	6.08466i	−0.121319	+	0.843790i
$53$	−6.75719	+	1.98409i	−0.928171	+	0.272536i	−0.710671	−	0.703525i	$-0.751608\pi$
$53$	−6.75719	+	1.98409i	−0.928171	+	0.272536i	−0.217500	+	0.976060i	$0.569790\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	9.00640	−	19.7213i	1.21442	−	2.65921i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	−1.03880	−	1.19884i	−0.137593	−	0.158791i
$58$	−1.38857	−	1.60250i	−0.182329	−	0.210419i
$59$	−2.86437	−	0.841056i	−0.372910	−	0.109496i	0.0899069	−	0.995950i	$-0.471343\pi$
$59$	−2.86437	−	0.841056i	−0.372910	−	0.109496i	−0.462817	+	0.886454i	$0.653161\pi$
$60$	−1.60548	+	3.51551i	−0.207266	+	0.453850i
$61$	1.93062	+	1.24073i	0.247190	+	0.158860i	0.658369	−	0.752695i	$-0.271246\pi$
$61$	1.93062	+	1.24073i	0.247190	+	0.158860i	−0.411179	+	0.911555i	$0.634883\pi$
$62$	10.3796	−	3.04772i	1.31821	−	0.387061i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−3.38105	−	23.5157i	−0.419368	−	2.91677i
$66$	−4.71926	+	3.03288i	−0.580901	+	0.373322i
$67$	4.84862	−	5.59561i	0.592353	−	0.683612i	−0.377861	−	0.925863i	$-0.623340\pi$
$67$	4.84862	−	5.59561i	0.592353	−	0.683612i	0.970214	+	0.242250i	$0.0778856\pi$
$68$	−6.42547			−0.779203
$69$	3.54626	+	3.22863i	0.426919	+	0.388682i
$70$	−3.86476			−0.461927
$71$	−1.63768	+	1.88998i	−0.194356	+	0.224299i	−0.844560	−	0.535461i	$-0.820138\pi$
$71$	−1.63768	+	1.88998i	−0.194356	+	0.224299i	0.650204	+	0.759760i	$0.274683\pi$
$72$	0.841254	−	0.540641i	0.0991427	−	0.0637151i
$73$	−0.628219	−	4.36936i	−0.0735275	−	0.511395i	−0.992988	−	0.118213i	$-0.962283\pi$
$73$	−0.628219	−	4.36936i	−0.0735275	−	0.511395i	0.919461	−	0.393182i	$-0.128626\pi$
$74$	−3.52957	−	7.72867i	−0.410304	−	0.898440i
$75$	1.41409	−	9.83521i	0.163285	−	1.13567i
$76$	1.52204	−	0.446912i	0.174590	−	0.0512643i
$77$	−4.71926	−	3.03288i	−0.537809	−	0.345629i
$78$	−2.55365	+	5.59171i	−0.289144	+	0.633137i
$79$	−2.07365	−	0.608878i	−0.233304	−	0.0685041i	0.162991	−	0.986628i	$-0.447886\pi$
$79$	−2.07365	−	0.608878i	−0.233304	−	0.0685041i	−0.396295	+	0.918123i	$0.629704\pi$
$80$	−2.53088	−	2.92079i	−0.282961	−	0.326554i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	1.82973	+	0.537258i	0.202060	+	0.0593302i
$83$	5.47310	−	11.9844i	0.600750	−	1.31546i	−0.327973	−	0.944687i	$-0.606366\pi$
$83$	5.47310	−	11.9844i	0.600750	−	1.31546i	0.928724	−	0.370773i	$-0.120907\pi$
$84$	0.841254	+	0.540641i	0.0917883	+	0.0589887i
$85$	23.8270	−	6.99623i	2.58440	−	0.758848i
$86$	0.980305	−	6.81817i	0.105709	−	0.735222i
$87$	−0.880851	−	1.92880i	−0.0944372	−	0.206789i
$88$	−0.798357	−	5.55269i	−0.0851051	−	0.591919i
$89$	−2.09399	+	1.34572i	−0.221962	+	0.142646i	−0.646897	−	0.762578i	$-0.723933\pi$
$89$	−2.09399	+	1.34572i	−0.221962	+	0.142646i	0.424935	+	0.905224i	$0.360297\pi$
$90$	−2.53088	+	2.92079i	−0.266778	+	0.307878i
$91$	−6.14723			−0.644405
$92$	−4.41003	+	1.88457i	−0.459778	+	0.196480i
$93$	10.8178			1.12175
$94$	−6.71960	+	7.75483i	−0.693074	+	0.799850i
$95$	−5.15743	+	3.31448i	−0.529141	+	0.340059i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	0.470487	+	1.03022i	0.0477707	+	0.104603i	0.932013	−	0.362426i	$-0.118051\pi$
$97$	0.470487	+	1.03022i	0.0477707	+	0.104603i	−0.884242	+	0.467029i	$0.845324\pi$
$98$	−0.142315	+	0.989821i	−0.0143760	+	0.0999871i
$99$	−5.38256	+	1.58046i	−0.540967	+	0.158842i
$100$	8.35899	+	5.37199i	0.835899	+	0.537199i
$101$	0.413134	−	0.904638i	0.0411084	−	0.0900149i	−0.887964	−	0.459914i	$-0.847880\pi$
$101$	0.413134	−	0.904638i	0.0411084	−	0.0900149i	0.929072	+	0.369899i	$0.120608\pi$
$102$	−6.16520	−	1.81026i	−0.610445	−	0.179243i
$103$	1.10593	+	1.27631i	0.108970	+	0.125759i	0.807614	−	0.589711i	$-0.200758\pi$
$103$	1.10593	+	1.27631i	0.108970	+	0.125759i	−0.698644	+	0.715469i	$0.746213\pi$
$104$	−4.02558	−	4.64576i	−0.394740	−	0.455555i
$105$	−3.70821	−	1.08883i	−0.361884	−	0.106259i
$106$	2.92554	−	6.40604i	0.284154	−	0.622210i
$107$	1.06551	+	0.684759i	0.103006	+	0.0661982i	0.591130	−	0.806576i	$-0.298682\pi$
$107$	1.06551	+	0.684759i	0.103006	+	0.0661982i	−0.488123	+	0.872775i	$0.662318\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	−2.69162	+	18.7206i	−0.257810	+	1.79311i	0.290543	+	0.956862i	$0.406164\pi$
$109$	−2.69162	+	18.7206i	−0.257810	+	1.79311i	−0.548353	+	0.836247i	$0.684745\pi$
$110$	9.00640	+	19.7213i	0.858727	+	1.88035i
$111$	−1.20918	−	8.41000i	−0.114770	−	0.798242i
$112$	−0.841254	+	0.540641i	−0.0794910	+	0.0510858i
$113$	−9.30069	+	10.7336i	−0.874935	+	1.00973i	0.124910	+	0.992168i	$0.460136\pi$
$113$	−9.30069	+	10.7336i	−0.874935	+	1.00973i	−0.999846	+	0.0175613i	$0.994410\pi$
$114$	1.58630			0.148570
$115$	14.3014	−	11.7901i	1.33361	−	1.09944i
$116$	2.12041			0.196875
$117$	−4.02558	+	4.64576i	−0.372165	+	0.429501i
$118$	2.51139	−	1.61398i	0.231193	−	0.148578i
$119$	−0.914440	−	6.36007i	−0.0838266	−	0.583027i
$120$	−1.60548	−	3.51551i	−0.146559	−	0.320920i
$121$	−2.91315	+	20.2614i	−0.264832	+	1.84195i
$122$	−2.20197	+	0.646557i	−0.199357	+	0.0585365i
$123$	1.60425	+	1.03099i	0.144651	+	0.0929612i
$124$	−4.49387	+	9.84020i	−0.403561	+	0.883676i
$125$	−18.3050	−	5.37483i	−1.63725	−	0.480740i
$126$	0.654861	+	0.755750i	0.0583396	+	0.0673275i
$127$	−8.06970	−	9.31293i	−0.716070	−	0.826389i	0.274759	−	0.961513i	$-0.411402\pi$
$127$	−8.06970	−	9.31293i	−0.716070	−	0.826389i	−0.990829	+	0.135124i	$0.956857\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	2.86150	−	6.26580i	0.251941	−	0.551673i
$130$	19.9861	+	12.8443i	1.75290	+	1.12652i
$131$	5.66362	−	1.66299i	0.494833	−	0.145296i	−0.0247886	−	0.999693i	$-0.507891\pi$
$131$	5.66362	−	1.66299i	0.494833	−	0.145296i	0.519621	+	0.854397i	$0.326073\pi$
$132$	0.798357	−	5.55269i	0.0694880	−	0.483300i
$133$	0.658972	+	1.44295i	0.0571401	+	0.125119i
$134$	1.05371	+	7.32869i	0.0910263	+	0.633102i
$135$	−3.25124	+	2.08945i	−0.279822	+	0.179831i
$136$	4.20779	−	4.85605i	0.360815	−	0.416403i
$137$	11.6219			0.992930			0.496465	−	0.868057i	$-0.334631\pi$
$137$	11.6219			0.992930			0.496465	+	0.868057i	$0.334631\pi$
$138$	−4.76234	+	0.565778i	−0.405397	+	0.0481622i
$139$	−6.96779			−0.591000			−0.295500	−	0.955343i	$-0.595486\pi$
$139$	−6.96779			−0.591000			−0.295500	+	0.955343i	$0.595486\pi$
$140$	2.53088	−	2.92079i	0.213898	−	0.246852i
$141$	−8.63220	+	5.54758i	−0.726962	+	0.467190i
$142$	−0.355901	−	2.47535i	−0.0298665	−	0.207726i
$143$	14.3255	+	31.3684i	1.19795	+	2.62315i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−7.86293	+	2.30876i	−0.652981	+	0.191732i
$146$	3.71354	+	2.38655i	0.307335	+	0.197512i
$147$	−0.415415	+	0.909632i	−0.0342629	+	0.0750252i
$148$	8.15232	+	2.39374i	0.670116	+	0.196764i
$149$	−3.45442	−	3.98661i	−0.282997	−	0.326596i	0.596398	−	0.802689i	$-0.296598\pi$
$149$	−3.45442	−	3.98661i	−0.282997	−	0.326596i	−0.879395	+	0.476093i	$0.842053\pi$
$150$	6.50692	+	7.50939i	0.531288	+	0.613139i
$151$	−9.17969	−	2.69540i	−0.747033	−	0.219349i	−0.114008	−	0.993480i	$-0.536369\pi$
$151$	−9.17969	−	2.69540i	−0.747033	−	0.219349i	−0.633025	+	0.774131i	$0.718187\pi$
$152$	−0.658972	+	1.44295i	−0.0534497	+	0.117038i
$153$	−5.40545	−	3.47387i	−0.437005	−	0.280846i
$154$	5.38256	−	1.58046i	0.433739	−	0.127357i
$155$	5.94991	−	41.3825i	0.477908	−	3.32393i
$156$	−2.55365	−	5.59171i	−0.204456	−	0.447695i
$157$	−0.505940	−	3.51889i	−0.0403784	−	0.280838i	0.959622	−	0.281294i	$-0.0907638\pi$
$157$	−0.505940	−	3.51889i	−0.0403784	−	0.280838i	−1.00000		0.000456569i	$0.999855\pi$
$158$	1.81811	−	1.16843i	0.144641	−	0.0929552i
$159$	4.61183	−	5.32233i	0.365742	−	0.422088i
$160$	3.86476			0.305536
$161$	−2.49300	−	4.09695i	−0.196476	−	0.322885i
$162$	1.00000			0.0785674
$163$	4.08945	−	4.71947i	0.320310	−	0.369658i	−0.572645	−	0.819804i	$-0.694083\pi$
$163$	4.08945	−	4.71947i	0.320310	−	0.369658i	0.892955	+	0.450146i	$0.148628\pi$
$164$	−1.60425	+	1.03099i	−0.125271	+	0.0805068i
$165$	3.08545	+	21.4598i	0.240202	+	1.67064i
$166$	5.47310	+	11.9844i	0.424795	+	0.930170i
$167$	−1.55672	+	10.8272i	−0.120463	+	0.837837i	0.836571	+	0.547859i	$0.184557\pi$
$167$	−1.55672	+	10.8272i	−0.120463	+	0.837837i	−0.957033	+	0.289978i	$0.906352\pi$
$168$	−0.959493	+	0.281733i	−0.0740265	+	0.0217361i
$169$	20.8533	+	13.4016i	1.60410	+	1.03089i
$170$	−10.3160	+	22.5888i	−0.791198	+	1.73248i
$171$	1.52204	+	0.446912i	0.116393	+	0.0341762i
$172$	4.51087	+	5.20582i	0.343950	+	0.396940i
$173$	−4.12946	−	4.76565i	−0.313957	−	0.362326i	0.576736	−	0.816930i	$-0.304326\pi$
$173$	−4.12946	−	4.76565i	−0.313957	−	0.362326i	−0.890693	+	0.454604i	$0.849781\pi$
$174$	2.03452	+	0.597389i	0.154237	+	0.0452880i
$175$	−4.12771	+	9.03842i	−0.312025	+	0.683240i
$176$	4.71926	+	3.03288i	0.355727	+	0.228612i
$177$	2.86437	−	0.841056i	0.215300	−	0.0632177i
$178$	0.354239	−	2.46379i	0.0265514	−	0.184669i
$179$	4.63091	+	10.1403i	0.346130	+	0.757919i	0.999999	+	0.00131158i	$0.000417490\pi$
$179$	4.63091	+	10.1403i	0.346130	+	0.757919i	−0.653869	+	0.756608i	$0.726855\pi$
$180$	−0.550012	−	3.82542i	−0.0409955	−	0.285130i
$181$	−5.64321	+	3.62667i	−0.419457	+	0.269568i	−0.733298	−	0.679907i	$-0.762020\pi$
$181$	−5.64321	+	3.62667i	−0.419457	+	0.269568i	0.313842	+	0.949475i	$0.398384\pi$
$182$	4.02558	−	4.64576i	0.298396	−	0.344367i
$183$	−2.29493			−0.169646
$184$	1.46370	−	4.56701i	0.107905	−	0.336685i
$185$	−32.8368			−2.41421
$186$	−7.08414	+	8.17553i	−0.519434	+	0.599459i
$187$	−30.3235	+	19.4877i	−2.21747	+	1.42508i
$188$	−1.46031	−	10.1567i	−0.106504	−	0.740751i
$189$	0.415415	+	0.909632i	0.0302170	+	0.0661660i
$190$	0.872483	−	6.06825i	0.0632966	−	0.440237i
$191$	−10.3749	+	3.04636i	−0.750705	+	0.220427i	−0.634633	−	0.772814i	$-0.718849\pi$
$191$	−10.3749	+	3.04636i	−0.750705	+	0.220427i	−0.116072	+	0.993241i	$0.537030\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	8.37706	−	18.3432i	0.602994	−	1.32037i	−0.324270	−	0.945965i	$-0.605119\pi$
$193$	8.37706	−	18.3432i	0.602994	−	1.32037i	0.927264	−	0.374408i	$-0.122154\pi$
$194$	−1.08669	−	0.319082i	−0.0780201	−	0.0229088i
$195$	15.5579	+	17.9548i	1.11412	+	1.28577i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	3.17952	+	0.933592i	0.226531	+	0.0665156i	0.393028	−	0.919526i	$-0.371427\pi$
$197$	3.17952	+	0.933592i	0.226531	+	0.0665156i	−0.166497	+	0.986042i	$0.553246\pi$
$198$	2.33039	−	5.10285i	0.165614	−	0.362644i
$199$	20.3107	+	13.0529i	1.43979	+	0.925294i	0.999625	+	0.0273748i	$0.00871477\pi$
$199$	20.3107	+	13.0529i	1.43979	+	0.925294i	0.440160	+	0.897919i	$0.354922\pi$
$200$	−9.53386	+	2.79939i	−0.674145	+	0.197947i
$201$	−1.05371	+	7.32869i	−0.0743227	+	0.516926i
$202$	0.413134	+	0.904638i	0.0290680	+	0.0636501i
$203$	0.301766	+	2.09883i	0.0211798	+	0.147309i
$204$	5.40545	−	3.47387i	0.378457	−	0.243220i
$205$	4.82633	−	5.56988i	0.337085	−	0.389017i
$206$	−1.68880			−0.117664
$207$	−4.72883	−	0.798846i	−0.328676	−	0.0555237i
$208$	6.14723			0.426234
$209$	5.82747	−	6.72526i	0.403095	−	0.465196i
$210$	3.25124	−	2.08945i	0.224357	−	0.144185i
$211$	−0.0582374	−	0.405050i	−0.00400923	−	0.0278848i	0.987719	−	0.156243i	$-0.0499383\pi$
$211$	−0.0582374	−	0.405050i	−0.00400923	−	0.0278848i	−0.991728	+	0.128358i	$0.959029\pi$
$212$	2.92554	+	6.40604i	0.200927	+	0.439969i
$213$	0.355901	−	2.47535i	0.0243859	−	0.169608i
$214$	−1.21526	+	0.356834i	−0.0830738	+	0.0243927i
$215$	−22.3955	−	14.3927i	−1.52736	−	0.981573i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	−10.3796	−	3.04772i	−0.704612	−	0.206893i
$218$	−12.3855	−	14.2936i	−0.838849	−	0.968083i
$219$	2.89075	+	3.33610i	0.195339	+	0.225433i
$220$	−20.8023	−	6.10810i	−1.40249	−	0.411808i
$221$	−16.4084	+	35.9294i	−1.10375	+	2.41687i
$222$	7.14770	+	4.59355i	0.479722	+	0.308299i
$223$	2.50282	−	0.734895i	0.167601	−	0.0492122i	−0.196855	−	0.980433i	$-0.563073\pi$
$223$	2.50282	−	0.734895i	0.167601	−	0.0492122i	0.364457	+	0.931220i	$0.381255\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	4.12771	+	9.03842i	0.275181	+	0.602561i
$226$	−2.02123	−	14.0580i	−0.134450	−	0.935123i
$227$	12.6601	−	8.13613i	0.840278	−	0.540014i	−0.0482502	−	0.998835i	$-0.515364\pi$
$227$	12.6601	−	8.13613i	0.840278	−	0.540014i	0.888529	+	0.458821i	$0.151728\pi$
$228$	−1.03880	+	1.19884i	−0.0687965	+	0.0793953i
$229$	−27.7813			−1.83584			−0.917919	−	0.396768i	$-0.870132\pi$
$229$	−27.7813			−1.83584			−0.917919	+	0.396768i	$0.870132\pi$
$230$	−0.455007	+	18.5291i	−0.0300023	+	1.22178i
$231$	5.60979			0.369097
$232$	−1.38857	+	1.60250i	−0.0911644	+	0.105209i
$233$	18.0664	−	11.6106i	1.18357	−	0.760635i	0.207531	−	0.978228i	$-0.433457\pi$
$233$	18.0664	−	11.6106i	1.18357	−	0.760635i	0.976039	+	0.217594i	$0.0698208\pi$
$234$	−0.874842	−	6.08466i	−0.0571902	−	0.397767i
$235$	16.4740	+	36.0730i	1.07464	+	2.35314i
$236$	−0.424853	+	2.95491i	−0.0276555	+	0.192349i
$237$	2.07365	−	0.608878i	0.134698	−	0.0395509i
$238$	5.40545	+	3.47387i	0.350383	+	0.225178i
$239$	−5.91372	+	12.9492i	−0.382527	+	0.837617i	0.616220	+	0.787574i	$0.288663\pi$
$239$	−5.91372	+	12.9492i	−0.382527	+	0.837617i	−0.998747	+	0.0500431i	$0.984064\pi$
$240$	3.70821	+	1.08883i	0.239364	+	0.0702835i
$241$	5.43140	+	6.26817i	0.349867	+	0.403769i	0.903219	−	0.429179i	$-0.141197\pi$
$241$	5.43140	+	6.26817i	0.349867	+	0.403769i	−0.553352	+	0.832947i	$0.686652\pi$
$242$	−13.4049	−	15.4700i	−0.861697	−	0.994451i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	0.953349	−	2.08754i	0.0610319	−	0.133641i
$245$	3.25124	+	2.08945i	0.207714	+	0.133490i
$246$	−1.82973	+	0.537258i	−0.116659	+	0.0342543i
$247$	1.38776	−	9.65207i	0.0883010	−	0.614147i
$248$	−4.49387	−	9.84020i	−0.285361	−	0.624853i
$249$	1.87500	+	13.0409i	0.118823	+	0.826434i
$250$	16.0493	−	10.3142i	1.01504	−	0.652329i
$251$	12.6423	−	14.5900i	0.797973	−	0.920910i	−0.200295	−	0.979736i	$-0.564190\pi$
$251$	12.6423	−	14.5900i	0.797973	−	0.920910i	0.998268	+	0.0588253i	$0.0187355\pi$
$252$	−1.00000			−0.0629941
$253$	−15.0964	+	22.2689i	−0.949104	+	1.40003i
$254$	12.3228			0.773199
$255$	−16.2621	+	18.7674i	−1.01837	+	1.17526i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−2.54409	−	17.6945i	−0.158696	−	1.10376i	−0.901040	−	0.433736i	$-0.857195\pi$
$257$	−2.54409	−	17.6945i	−0.158696	−	1.10376i	0.742344	−	0.670019i	$-0.233714\pi$
$258$	2.86150	+	6.26580i	0.178149	+	0.390092i
$259$	−1.20918	+	8.41000i	−0.0751345	+	0.522572i
$260$	−22.7952	+	6.69327i	−1.41370	+	0.415099i
$261$	1.78380	+	1.14638i	0.110415	+	0.0709592i
$262$	−2.45208	+	5.36930i	−0.151490	+	0.331717i
$263$	9.49228	+	2.78719i	0.585319	+	0.171865i	0.560967	−	0.827838i	$-0.310429\pi$
$263$	9.49228	+	2.78719i	0.585319	+	0.171865i	0.0243523	+	0.999703i	$0.492248\pi$
$264$	3.67363	+	4.23960i	0.226096	+	0.260929i
$265$	−17.8236	−	20.5695i	−1.09489	−	1.26358i
$266$	−1.52204	−	0.446912i	−0.0933223	−	0.0274019i
$267$	1.03402	−	2.26419i	0.0632810	−	0.138566i
$268$	−6.22868	−	4.00293i	−0.380477	−	0.244518i
$269$	−17.5416	+	5.15069i	−1.06953	+	0.314043i	−0.768684	−	0.639629i	$-0.779088\pi$
$269$	−17.5416	+	5.15069i	−1.06953	+	0.314043i	−0.300849	+	0.953672i	$0.597270\pi$
$270$	0.550012	−	3.82542i	0.0334727	−	0.232808i
$271$	−1.31033	−	2.86922i	−0.0795967	−	0.174292i	0.865650	−	0.500650i	$-0.166906\pi$
$271$	−1.31033	−	2.86922i	−0.0795967	−	0.174292i	−0.945246	+	0.326358i	$0.894179\pi$
$272$	0.914440	+	6.36007i	0.0554461	+	0.385636i
$273$	5.17138	−	3.32344i	0.312986	−	0.201144i
$274$	−7.61076	+	8.78328i	−0.459783	+	0.530618i
$275$	55.7408			3.36130
$276$	2.69108	−	3.96964i	0.161984	−	0.238944i
$277$	−27.5484			−1.65523			−0.827613	−	0.561300i	$-0.810302\pi$
$277$	−27.5484			−1.65523			−0.827613	+	0.561300i	$0.810302\pi$
$278$	4.56293	−	5.26590i	0.273666	−	0.315828i
$279$	−9.10049	+	5.84853i	−0.544832	+	0.350142i
$280$	0.550012	+	3.82542i	0.0328695	+	0.228613i
$281$	6.04836	+	13.2441i	0.360815	+	0.790074i	0.999783	+	0.0208410i	$0.00663436\pi$
$281$	6.04836	+	13.2441i	0.360815	+	0.790074i	−0.638968	+	0.769233i	$0.720638\pi$
$282$	1.46031	−	10.1567i	0.0869601	−	0.604821i
$283$	8.50042	−	2.49595i	0.505297	−	0.148369i	−0.0191416	−	0.999817i	$-0.506093\pi$
$283$	8.50042	−	2.49595i	0.505297	−	0.148369i	0.524439	+	0.851448i	$0.324275\pi$
$284$	2.10381	+	1.35203i	0.124838	+	0.0802285i
$285$	2.54677	−	5.57664i	0.150857	−	0.330332i
$286$	−33.0878	−	9.71546i	−1.95652	−	0.574487i
$287$	−1.24880	−	1.44120i	−0.0737146	−	0.0850712i
$288$	−0.654861	−	0.755750i	−0.0385880	−	0.0445330i
$289$	−23.3029	−	6.84236i	−1.37076	−	0.402491i
$290$	3.40428	−	7.45432i	0.199906	−	0.437733i
$291$	−0.952780	−	0.612314i	−0.0558529	−	0.0358945i
$292$	−4.23548	+	1.24365i	−0.247863	+	0.0727791i
$293$	0.612217	−	4.25806i	0.0357661	−	0.248759i	−0.964093	−	0.265566i	$-0.914441\pi$
$293$	0.612217	−	4.25806i	0.0357661	−	0.248759i	0.999859	+	0.0168075i	$0.00535025\pi$
$294$	−0.415415	−	0.909632i	−0.0242275	−	0.0530508i
$295$	−1.64195	−	11.4200i	−0.0955981	−	0.664900i
$296$	−7.14770	+	4.59355i	−0.415451	+	0.266994i
$297$	3.67363	−	4.23960i	0.213166	−	0.246006i
$298$	5.27505			0.305575
$299$	−0.723728	+	29.4722i	−0.0418543	+	1.70442i
$300$	−9.93635			−0.573675
$301$	−4.51087	+	5.20582i	−0.260002	+	0.300058i
$302$	8.04847	−	5.17244i	0.463137	−	0.297640i
$303$	0.141534	+	0.984387i	0.00813089	+	0.0565516i
$304$	−0.658972	−	1.44295i	−0.0377946	−	0.0827587i
$305$	−1.26224	+	8.77908i	−0.0722757	+	0.502688i
$306$	6.16520	−	1.81026i	0.352441	−	0.103486i
$307$	−9.40945	−	6.04709i	−0.537026	−	0.345125i	0.243849	−	0.969813i	$-0.421590\pi$
$307$	−9.40945	−	6.04709i	−0.537026	−	0.345125i	−0.780875	+	0.624688i	$0.785226\pi$
$308$	−2.33039	+	5.10285i	−0.132786	+	0.290762i
$309$	−1.62039	−	0.475790i	−0.0921809	−	0.0270667i
$310$	27.3785	+	31.5964i	1.55499	+	1.79456i
$311$	−11.3265	−	13.0714i	−0.642265	−	0.741214i	0.337508	−	0.941323i	$-0.390416\pi$
$311$	−11.3265	−	13.0714i	−0.642265	−	0.741214i	−0.979774	+	0.200109i	$0.935870\pi$
$312$	5.89822	+	1.73187i	0.333921	+	0.0980481i
$313$	2.52178	−	5.52194i	0.142540	−	0.312118i	−0.824875	−	0.565315i	$-0.808755\pi$
$313$	2.52178	−	5.52194i	0.142540	−	0.312118i	0.967415	+	0.253197i	$0.0814819\pi$
$314$	2.99072	+	1.92202i	0.168776	+	0.108466i
$315$	3.70821	−	1.08883i	0.208934	−	0.0613485i
$316$	−0.307570	+	2.13919i	−0.0173021	+	0.120339i
$317$	−1.08633	−	2.37873i	−0.0610144	−	0.133603i	0.876669	−	0.481095i	$-0.159761\pi$
$317$	−1.08633	−	2.37873i	−0.0610144	−	0.133603i	−0.937683	+	0.347492i	$0.887033\pi$
$318$	1.00225	+	6.97077i	0.0562032	+	0.390902i
$319$	10.0068	−	6.43096i	0.560272	−	0.360065i
$320$	−2.53088	+	2.92079i	−0.141480	+	0.163277i
$321$	−1.26657			−0.0706930
$322$	4.72883	+	0.798846i	0.263527	+	0.0445180i
$323$	10.1927			0.567137
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	51.3846	−	33.0229i	2.85030	−	1.83178i
$326$	0.888722	+	6.18120i	0.0492218	+	0.342345i
$327$	−7.85679	−	17.2040i	−0.434482	−	0.951382i
$328$	0.271391	−	1.88757i	0.0149851	−	0.104223i
$329$	9.84547	−	2.89089i	0.542798	−	0.159380i
$330$	−18.2388	−	11.7214i	−1.00401	−	0.645239i
$331$	−13.6156	+	29.8140i	−0.748380	+	1.63872i	0.0208750	+	0.999782i	$0.493355\pi$
$331$	−13.6156	+	29.8140i	−0.748380	+	1.63872i	−0.769255	+	0.638942i	$0.779372\pi$
$332$	−12.6413	−	3.71183i	−0.693783	−	0.203713i
$333$	5.56401	+	6.42121i	0.304906	+	0.351880i
$334$	−7.16324	−	8.26682i	−0.391955	−	0.452340i
$335$	27.4557	+	8.06173i	1.50007	+	0.440460i
$336$	0.415415	−	0.909632i	0.0226627	−	0.0496245i
$337$	−28.5200	−	18.3287i	−1.55359	−	0.998429i	−0.984344	−	0.176258i	$-0.943601\pi$
$337$	−28.5200	−	18.3287i	−1.55359	−	0.998429i	−0.569242	−	0.822170i	$-0.692763\pi$
$338$	−23.7843	+	6.98370i	−1.29370	+	0.379863i
$339$	2.02123	−	14.0580i	0.109778	−	0.763525i
$340$	−10.3160	−	22.5888i	−0.559461	−	1.22505i
$341$	8.63645	+	60.0678i	0.467690	+	3.25285i
$342$	−1.33448	+	0.857617i	−0.0721603	+	0.0463746i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	−6.88828			−0.371391
$345$	−5.65684	+	17.6504i	−0.304554	+	0.950265i
$346$	6.30586			0.339005
$347$	14.2689	−	16.4672i	0.765995	−	0.884005i	−0.230021	−	0.973186i	$-0.573879\pi$
$347$	14.2689	−	16.4672i	0.765995	−	0.884005i	0.996015	+	0.0891806i	$0.0284248\pi$
$348$	−1.78380	+	1.14638i	−0.0956220	+	0.0614525i
$349$	−0.994767	−	6.91875i	−0.0532486	−	0.370352i	−0.998970	−	0.0453740i	$-0.985552\pi$
$349$	−0.994767	−	6.91875i	−0.0532486	−	0.370352i	0.945721	−	0.324978i	$-0.105357\pi$
$350$	−4.12771	−	9.03842i	−0.220635	−	0.483124i
$351$	0.874842	−	6.08466i	0.0466956	−	0.324775i
$352$	−5.38256	+	1.58046i	−0.286891	+	0.0842389i
$353$	−14.0975	−	9.05993i	−0.750336	−	0.482212i	0.108733	−	0.994071i	$-0.465321\pi$
$353$	−14.0975	−	9.05993i	−0.750336	−	0.482212i	−0.859069	+	0.511859i	$0.828957\pi$
$354$	−1.24014	+	2.71552i	−0.0659126	+	0.144329i
$355$	−9.27349	−	2.72294i	−0.492186	−	0.144519i
$356$	1.63003	+	1.88116i	0.0863914	+	0.0997010i
$357$	4.20779	+	4.85605i	0.222700	+	0.257009i
$358$	−10.6961	−	3.14066i	−0.565307	−	0.165989i
$359$	6.89566	−	15.0994i	0.363939	−	0.796916i	−0.635748	−	0.771897i	$-0.719308\pi$
$359$	6.89566	−	15.0994i	0.363939	−	0.796916i	0.999687	−	0.0250189i	$-0.00796459\pi$
$360$	3.25124	+	2.08945i	0.171355	+	0.110123i
$361$	15.8160	−	4.64398i	0.832419	−	0.244420i
$362$	0.954662	−	6.63982i	0.0501759	−	0.348981i
$363$	−8.50345	−	18.6200i	−0.446316	−	0.977295i
$364$	0.874842	+	6.08466i	0.0458542	+	0.318923i
$365$	14.3519	−	9.22342i	0.751214	−	0.482776i
$366$	1.50286	−	1.73439i	0.0785558	−	0.0906582i
$367$	−17.9516			−0.937068			−0.468534	−	0.883446i	$-0.655218\pi$
$367$	−17.9516			−0.937068			−0.468534	+	0.883446i	$0.655218\pi$
$368$	2.49300	+	4.09695i	0.129957	+	0.213568i
$369$	−1.90698			−0.0992733
$370$	21.5036	−	24.8164i	1.11792	−	1.29014i
$371$	−5.92449	+	3.80744i	−0.307584	+	0.197672i
$372$	−1.53953	−	10.7077i	−0.0798209	−	0.555167i
$373$	6.31608	+	13.8303i	0.327034	+	0.716105i	0.999716	−	0.0238271i	$-0.00758511\pi$
$373$	6.31608	+	13.8303i	0.327034	+	0.716105i	−0.672682	+	0.739932i	$0.734858\pi$
$374$	5.12982	−	35.6787i	0.265257	−	1.84490i
$375$	18.3050	−	5.37483i	0.945266	−	0.277555i
$376$	8.63220	+	5.54758i	0.445172	+	0.286094i
$377$	5.41479	−	11.8567i	0.278876	−	0.610653i
$378$	−0.959493	−	0.281733i	−0.0493510	−	0.0144908i
$379$	−8.75731	−	10.1065i	−0.449833	−	0.519135i	0.484860	−	0.874592i	$-0.338871\pi$
$379$	−8.75731	−	10.1065i	−0.449833	−	0.519135i	−0.934693	+	0.355457i	$0.884325\pi$
$380$	4.01472	+	4.63324i	0.205951	+	0.237680i
$381$	11.8236	+	3.47173i	0.605742	+	0.177862i
$382$	4.49186	−	9.83580i	0.229824	−	0.503243i
$383$	−21.1461	−	13.5898i	−1.08052	−	0.694407i	−0.125841	−	0.992050i	$-0.540163\pi$
$383$	−21.1461	−	13.5898i	−1.08052	−	0.694407i	−0.954677	+	0.297644i	$0.903799\pi$
$384$	0.959493	−	0.281733i	0.0489639	−	0.0143771i
$385$	3.08545	−	21.4598i	0.157249	−	1.09369i
$386$	8.37706	+	18.3432i	0.426381	+	0.933645i
$387$	0.980305	+	6.81817i	0.0498317	+	0.346587i
$388$	0.952780	−	0.612314i	0.0483701	−	0.0310856i
$389$	−9.43120	+	10.8842i	−0.478181	+	0.551850i	−0.942669	−	0.333729i	$-0.891693\pi$
$389$	−9.43120	+	10.8842i	−0.478181	+	0.551850i	0.464488	+	0.885579i	$0.346238\pi$
$390$	−23.7575			−1.20301
$391$	−30.6003	+	3.63539i	−1.54752	+	0.183850i
$392$	1.00000			0.0505076
$393$	−3.86546	+	4.46098i	−0.194987	+	0.225027i
$394$	−2.78770	+	1.79155i	−0.140443	+	0.0902569i
$395$	−1.18868	−	8.26747i	−0.0598091	−	0.415981i
$396$	2.33039	+	5.10285i	0.117107	+	0.256428i
$397$	−1.61917	+	11.2615i	−0.0812636	+	0.565201i	0.907990	+	0.418992i	$0.137616\pi$
$397$	−1.61917	+	11.2615i	−0.0812636	+	0.565201i	−0.989254	+	0.146209i	$0.953293\pi$
$398$	−23.1654	+	6.80197i	−1.16118	+	0.340952i
$399$	−1.33448	−	0.857617i	−0.0668075	−	0.0429345i
$400$	4.12771	−	9.03842i	0.206385	−	0.451921i
$401$	−13.1232	−	3.85331i	−0.655340	−	0.192425i	−0.0628748	−	0.998021i	$-0.520027\pi$
$401$	−13.1232	−	3.85331i	−0.655340	−	0.192425i	−0.592465	+	0.805596i	$0.701845\pi$
$402$	−4.84862	−	5.59561i	−0.241827	−	0.279083i
$403$	43.5478	+	50.2569i	2.16927	+	2.50347i
$404$	−0.954225	−	0.280186i	−0.0474745	−	0.0139398i
$405$	1.60548	−	3.51551i	0.0797768	−	0.174687i
$406$	−1.78380	−	1.14638i	−0.0885287	−	0.0568940i
$407$	45.7328	−	13.4284i	2.26689	−	0.665619i
$408$	−0.914440	+	6.36007i	−0.0452715	+	0.314870i
$409$	0.731666	+	1.60212i	0.0361785	+	0.0792200i	0.926858	−	0.375411i	$-0.122498\pi$
$409$	0.731666	+	1.60212i	0.0361785	+	0.0792200i	−0.890680	+	0.454631i	$0.849771\pi$
$410$	1.04886	+	7.29499i	0.0517996	+	0.360274i
$411$	−9.77701	+	6.28330i	−0.482264	+	0.309932i
$412$	1.10593	−	1.27631i	0.0544852	−	0.0628793i
$413$	−2.98530			−0.146897
$414$	3.70045	−	3.05068i	0.181867	−	0.149933i
$415$	50.9182			2.49948
$416$	−4.02558	+	4.64576i	−0.197370	+	0.227777i
$417$	5.86168	−	3.76707i	0.287048	−	0.184474i
$418$	1.26643	+	8.80822i	0.0619432	+	0.430824i
$419$	5.59452	+	12.2503i	0.273310	+	0.598466i	0.995660	−	0.0930615i	$-0.0296653\pi$
$419$	5.59452	+	12.2503i	0.273310	+	0.598466i	−0.722350	+	0.691528i	$0.756938\pi$
$420$	−0.550012	+	3.82542i	−0.0268379	+	0.186661i
$421$	24.7934	−	7.28000i	1.20836	−	0.354806i	0.385314	−	0.922785i	$-0.374093\pi$
$421$	24.7934	−	7.28000i	1.20836	−	0.354806i	0.823042	+	0.567980i	$0.192275\pi$
$422$	0.344254	+	0.221238i	0.0167580	+	0.0107697i
$423$	4.26262	−	9.33384i	0.207256	−	0.453827i
$424$	−6.75719	−	1.98409i	−0.328158	−	0.0963559i
$425$	41.8101	+	48.2514i	2.02809	+	2.34054i
$426$	1.63768	+	1.88998i	0.0793457	+	0.0915698i
$427$	2.20197	+	0.646557i	0.106561	+	0.0312891i
$428$	0.526152	−	1.15211i	0.0254325	−	0.0556894i
$429$	−29.0104	−	18.6438i	−1.40063	−	0.900132i
$430$	25.5432	−	7.50015i	1.23180	−	0.361690i
$431$	0.373594	−	2.59840i	0.0179954	−	0.125161i	−0.978843	−	0.204610i	$-0.934407\pi$
$431$	0.373594	−	2.59840i	0.0179954	−	0.125161i	0.996839	+	0.0794498i	$0.0253164\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	1.15255	+	8.01614i	0.0553879	+	0.385231i	0.998593	+	0.0530213i	$0.0168851\pi$
$433$	1.15255	+	8.01614i	0.0553879	+	0.385231i	−0.943206	+	0.332210i	$0.892206\pi$
$434$	9.10049	−	5.84853i	0.436838	−	0.280739i
$435$	5.36650	−	6.19328i	0.257304	−	0.296945i
$436$	18.9131			0.905774
$437$	6.99563	−	2.98948i	0.334646	−	0.143006i
$438$	−4.41429			−0.210923
$439$	12.3847	−	14.2927i	0.591091	−	0.682156i	−0.378860	−	0.925454i	$-0.623684\pi$
$439$	12.3847	−	14.2927i	0.591091	−	0.682156i	0.969952	+	0.243298i	$0.0782294\pi$
$440$	18.2388	−	11.7214i	0.869500	−	0.558794i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	−16.4084	−	35.9294i	−0.780469	−	1.70899i
$443$	0.460156	−	3.20046i	0.0218627	−	0.152058i	−0.975966	−	0.217924i	$-0.930072\pi$
$443$	0.460156	−	3.20046i	0.0218627	−	0.152058i	0.997829	+	0.0658652i	$0.0209807\pi$
$444$	−8.15232	+	2.39374i	−0.386892	+	0.113602i
$445$	−8.09274	−	5.20089i	−0.383633	−	0.246546i
$446$	−1.08360	+	2.37276i	−0.0513101	+	0.112354i
$447$	5.06137	+	1.48615i	0.239395	+	0.0702926i
$448$	0.654861	+	0.755750i	0.0309393	+	0.0357058i
$449$	10.8176	+	12.4841i	0.510512	+	0.589163i	0.951230	−	0.308483i	$-0.0998214\pi$
$449$	10.8176	+	12.4841i	0.510512	+	0.589163i	−0.440717	+	0.897646i	$0.645276\pi$
$450$	−9.53386	−	2.79939i	−0.449430	−	0.131965i
$451$	−4.44401	+	9.73102i	−0.209260	+	0.458216i
$452$	11.9479	+	7.67848i	0.561984	+	0.361165i
$453$	9.17969	−	2.69540i	0.431300	−	0.126641i
$454$	−2.14170	+	14.8959i	−0.100515	+	0.699098i
$455$	−9.86924	−	21.6106i	−0.462677	−	1.01312i
$456$	−0.225754	−	1.57015i	−0.0105719	−	0.0735290i
$457$	−2.37621	+	1.52710i	−0.111154	+	0.0714345i	−0.595037	−	0.803698i	$-0.702863\pi$
$457$	−2.37621	+	1.52710i	−0.111154	+	0.0714345i	0.483883	+	0.875133i	$0.339226\pi$
$458$	18.1929	−	20.9957i	0.850097	−	0.981064i
$459$	6.42547			0.299915
$460$	−13.7054	−	12.4779i	−0.639019	−	0.581784i
$461$	5.43503			0.253135			0.126567	−	0.991958i	$-0.459604\pi$
$461$	5.43503			0.253135			0.126567	+	0.991958i	$0.459604\pi$
$462$	−3.67363	+	4.23960i	−0.170913	+	0.197244i
$463$	−3.87765	+	2.49202i	−0.180210	+	0.115814i	−0.627636	−	0.778507i	$-0.715977\pi$
$463$	−3.87765	+	2.49202i	−0.180210	+	0.115814i	0.447426	+	0.894321i	$0.352341\pi$
$464$	−0.301766	−	2.09883i	−0.0140091	−	0.0974357i
$465$	17.3677	+	38.0300i	0.805408	+	1.76360i
$466$	−3.05630	+	21.2570i	−0.141580	+	0.984712i
$467$	−11.0035	+	3.23091i	−0.509179	+	0.149509i	−0.526224	−	0.850346i	$-0.676393\pi$
$467$	−11.0035	+	3.23091i	−0.509179	+	0.149509i	0.0170444	+	0.999855i	$0.494574\pi$
$468$	5.17138	+	3.32344i	0.239047	+	0.153626i
$469$	3.07575	−	6.73496i	0.142025	−	0.310992i
$470$	−38.0503	−	11.1726i	−1.75513	−	0.515353i
$471$	2.32808	+	2.68675i	0.107272	+	0.123799i
$472$	−1.95496	−	2.25614i	−0.0899841	−	0.103847i
$473$	37.0766	+	10.8867i	1.70478	+	0.500569i
$474$	−0.897792	+	1.96589i	−0.0412369	+	0.0902963i
$475$	−13.2598	−	8.52158i	−0.608403	−	0.390997i
$476$	−6.16520	+	1.81026i	−0.282581	+	0.0829734i
$477$	−1.00225	+	6.97077i	−0.0458897	+	0.319170i
$478$	−5.91372	−	12.9492i	−0.270487	−	0.592285i
$479$	2.44764	+	17.0237i	0.111835	+	0.777833i	0.966132	+	0.258047i	$0.0830790\pi$
$479$	2.44764	+	17.0237i	0.111835	+	0.777833i	−0.854297	+	0.519785i	$0.826012\pi$
$480$	−3.25124	+	2.08945i	−0.148398	+	0.0953697i
$481$	34.2033	−	39.4727i	1.55953	−	1.79980i
$482$	−8.29398			−0.377781
$483$	4.31222	+	2.09875i	0.196213	+	0.0954966i
$484$	20.4698			0.930444
$485$	−2.86640	+	3.30800i	−0.130157	+	0.150209i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−4.62711	−	32.1822i	−0.209674	−	1.45832i	−0.774221	−	0.632916i	$-0.781858\pi$
$487$	−4.62711	−	32.1822i	−0.209674	−	1.45832i	0.564547	−	0.825401i	$-0.309051\pi$
$488$	0.953349	+	2.08754i	0.0431561	+	0.0944986i
$489$	−0.888722	+	6.18120i	−0.0401894	+	0.279523i
$490$	−3.70821	+	1.08883i	−0.167520	+	0.0491882i
$491$	−13.6616	−	8.77976i	−0.616538	−	0.396225i	0.194765	−	0.980850i	$-0.437605\pi$
$491$	−13.6616	−	8.77976i	−0.616538	−	0.396225i	−0.811304	+	0.584625i	$0.801242\pi$
$492$	0.792187	−	1.73465i	0.0357146	−	0.0782040i
$493$	13.0728	+	3.83851i	0.588767	+	0.172878i
$494$	6.38576	+	7.36956i	0.287309	+	0.331572i
$495$	−14.1977	−	16.3850i	−0.638139	−	0.736452i
$496$	10.3796	+	3.04772i	0.466057	+	0.136847i
$497$	−1.03887	+	2.27481i	−0.0465997	+	0.102039i
$498$	−11.0835	−	7.12295i	−0.496664	−	0.319187i
$499$	−36.7539	+	10.7919i	−1.64533	+	0.483112i	−0.967660	−	0.252256i	$-0.918827\pi$
$499$	−36.7539	+	10.7919i	−1.64533	+	0.483112i	−0.677668	+	0.735368i	$0.737009\pi$
$500$	−2.71505	+	18.8836i	−0.121421	+	0.844500i
$501$	−4.54405	−	9.95008i	−0.203013	−	0.444537i
$502$	2.74743	+	19.1088i	0.122624	+	0.852867i
$503$	−14.9366	+	9.59918i	−0.665991	+	0.428006i	−0.829478	−	0.558539i	$-0.811362\pi$
$503$	−14.9366	+	9.59918i	−0.665991	+	0.428006i	0.163487	+	0.986545i	$0.447726\pi$
$504$	0.654861	−	0.755750i	0.0291698	−	0.0336638i
$505$	3.84354			0.171035
$506$	−6.94364	−	25.9921i	−0.308682	−	1.15549i
$507$	−24.7884			−1.10089
$508$	−8.06970	+	9.31293i	−0.358035	+	0.413194i
$509$	30.7373	−	19.7537i	1.36241	−	0.875567i	0.363969	−	0.931411i	$-0.381421\pi$
$509$	30.7373	−	19.7537i	1.36241	−	0.875567i	0.998439	+	0.0558445i	$0.0177851\pi$
$510$	−3.53409	−	24.5801i	−0.156492	−	1.08843i
$511$	−1.83376	−	4.01538i	−0.0811209	−	0.177630i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	−1.52204	+	0.446912i	−0.0671997	+	0.0197316i
$514$	15.0387	+	9.66477i	0.663327	+	0.426295i
$515$	−2.71133	+	5.93699i	−0.119476	+	0.261615i
$516$	−6.60926	−	1.94065i	−0.290956	−	0.0854325i
$517$	−37.6956	−	43.5030i	−1.65785	−	1.91326i
$518$	−5.56401	−	6.42121i	−0.244469	−	0.282132i
$519$	6.05043	+	1.77657i	0.265585	+	0.0779827i
$520$	9.86924	−	21.6106i	0.432795	−	0.947688i
$521$	−16.7297	−	10.7516i	−0.732944	−	0.471034i	0.120174	−	0.992753i	$-0.461655\pi$
$521$	−16.7297	−	10.7516i	−0.732944	−	0.471034i	−0.853118	+	0.521719i	$0.825291\pi$
$522$	−2.03452	+	0.597389i	−0.0890486	+	0.0261470i
$523$	4.54104	−	31.5836i	0.198566	−	1.38106i	−0.609884	−	0.792491i	$-0.708784\pi$
$523$	4.54104	−	31.5836i	0.198566	−	1.38106i	0.808450	−	0.588566i	$-0.200307\pi$
$524$	−2.45208	−	5.36930i	−0.107120	−	0.234559i
$525$	−1.41409	−	9.83521i	−0.0617159	−	0.429244i
$526$	−8.32254	+	5.34857i	−0.362880	+	0.233209i
$527$	−45.5189	+	52.5317i	−1.98284	+	2.28831i
$528$	−5.60979			−0.244135
$529$	−19.9358	+	11.4701i	−0.866776	+	0.498698i
$530$	27.2174			1.18225
$531$	−1.95496	+	2.25614i	−0.0848379	+	0.0979081i
$532$	1.33448	−	0.857617i	0.0578570	−	0.0371824i
$533$	1.66830	+	11.6033i	0.0722623	+	0.502595i
$534$	1.03402	+	2.26419i	0.0447464	+	0.0979810i
$535$	−0.696629	+	4.84516i	−0.0301179	+	0.209475i
$536$	7.10413	−	2.08596i	0.306852	−	0.0900998i
$537$	−9.37801	−	6.02688i	−0.404691	−	0.260079i
$538$	7.59470	−	16.6301i	0.327431	−	0.716973i
$539$	−5.38256	−	1.58046i	−0.231843	−	0.0680753i
$540$	2.53088	+	2.92079i	0.108912	+	0.125691i
$541$	5.02440	+	5.79846i	0.216016	+	0.249295i	0.853407	−	0.521245i	$-0.174532\pi$
$541$	5.02440	+	5.79846i	0.216016	+	0.249295i	−0.637392	+	0.770540i	$0.719987\pi$
$542$	3.02649	+	0.888658i	0.129999	+	0.0381711i
$543$	2.78664	−	6.10190i	0.119586	−	0.261858i
$544$	−5.40545	−	3.47387i	−0.231757	−	0.148941i
$545$	−70.1337	+	20.5931i	−3.00420	+	0.882113i
$546$	−0.874842	+	6.08466i	−0.0374398	+	0.260399i
$547$	7.29227	+	15.9678i	0.311795	+	0.682735i	0.999045	−	0.0436851i	$-0.0139098\pi$
$547$	7.29227	+	15.9678i	0.311795	+	0.682735i	−0.687251	+	0.726420i	$0.741183\pi$
$548$	−1.65398	−	11.5037i	−0.0706543	−	0.491412i
$549$	1.93062	−	1.24073i	0.0823968	−	0.0529532i
$550$	−36.5025	+	42.1261i	−1.55647	+	1.79626i
$551$	−3.36360			−0.143294
$552$	1.23777	+	4.63335i	0.0526830	+	0.197208i
$553$	−2.16119			−0.0919032
$554$	18.0404	−	20.8197i	0.766463	−	0.884545i
$555$	27.6241	−	17.7529i	1.17258	−	0.753570i
$556$	0.991620	+	6.89687i	0.0420540	+	0.292492i
$557$	−2.18640	−	4.78755i	−0.0926407	−	0.202855i	0.857639	−	0.514252i	$-0.171930\pi$
$557$	−2.18640	−	4.78755i	−0.0926407	−	0.202855i	−0.950280	+	0.311397i	$0.899203\pi$
$558$	1.53953	−	10.7077i	0.0651735	−	0.453292i
$559$	40.6286	−	11.9296i	1.71841	−	0.504570i
$560$	−3.25124	−	2.08945i	−0.137390	−	0.0882952i
$561$	14.9739	−	32.7882i	0.632197	−	1.38432i
$562$	−13.9700	−	4.10197i	−0.589290	−	0.173031i
$563$	1.07115	+	1.23617i	0.0451435	+	0.0520984i	0.777872	−	0.628422i	$-0.216299\pi$
$563$	1.07115	+	1.23617i	0.0451435	+	0.0520984i	−0.732729	+	0.680521i	$0.761754\pi$
$564$	6.71960	+	7.75483i	0.282946	+	0.326537i
$565$	−52.6660	−	15.4641i	−2.21568	−	0.650581i
$566$	−3.68028	+	8.05868i	−0.154694	+	0.338732i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	−2.39950	+	0.704557i	−0.100681	+	0.0295626i
$569$	3.03569	−	21.1137i	0.127263	−	0.885132i	−0.821740	−	0.569863i	$-0.806996\pi$
$569$	3.03569	−	21.1137i	0.127263	−	0.885132i	0.949002	−	0.315269i	$-0.102095\pi$
$570$	2.54677	+	5.57664i	0.106672	+	0.233580i
$571$	−4.67772	−	32.5343i	−0.195756	−	1.36152i	−0.816429	−	0.577446i	$-0.804049\pi$
$571$	−4.67772	−	32.5343i	−0.195756	−	1.36152i	0.620672	−	0.784070i	$-0.286860\pi$
$572$	29.0104	−	18.6438i	1.21298	−	0.779537i
$573$	7.08097	−	8.17188i	0.295812	−	0.341385i
$574$	1.90698			0.0795957
$575$	42.8477	+	20.8539i	1.78687	+	0.869669i
$576$	1.00000			0.0416667
$577$	−17.4311	+	20.1166i	−0.725666	+	0.837463i	−0.991976	−	0.126424i	$-0.959650\pi$
$577$	−17.4311	+	20.1166i	−0.725666	+	0.837463i	0.266310	+	0.963887i	$0.414195\pi$
$578$	20.4313	−	13.1304i	0.849829	−	0.546152i
$579$	2.86985	+	19.9603i	0.119267	+	0.829521i
$580$	3.40428	+	7.45432i	0.141355	+	0.309524i
$581$	1.87500	−	13.0409i	0.0777881	−	0.541028i
$582$	1.08669	−	0.319082i	0.0450449	−	0.0132264i
$583$	33.2352	+	21.3589i	1.37646	+	0.884597i
$584$	1.83376	−	4.01538i	0.0758816	−	0.166158i
$585$	−22.7952	−	6.69327i	−0.942465	−	0.276733i
$586$	2.81711	+	3.25112i	0.116374	+	0.134302i
$587$	−18.9215	−	21.8365i	−0.780972	−	0.901290i	0.216207	−	0.976348i	$-0.430631\pi$
$587$	−18.9215	−	21.8365i	−0.780972	−	0.901290i	−0.997179	+	0.0750576i	$0.976086\pi$
$588$	0.959493	+	0.281733i	0.0395688	+	0.0116185i
$589$	7.12861	−	15.6095i	0.293729	−	0.643177i
$590$	9.70593	+	6.23762i	0.399587	+	0.256799i
$591$	−3.17952	+	0.933592i	−0.130788	+	0.0384028i
$592$	1.20918	−	8.41000i	0.0496968	−	0.345649i
$593$	13.3155	+	29.1568i	0.546801	+	1.19733i	0.958260	+	0.285898i	$0.0922920\pi$
$593$	13.3155	+	29.1568i	0.546801	+	1.19733i	−0.411459	+	0.911428i	$0.634981\pi$
$594$	0.798357	+	5.55269i	0.0327570	+	0.227830i
$595$	20.8908	−	13.4257i	0.856438	−	0.550399i
$596$	−3.45442	+	3.98661i	−0.141499	+	0.163298i
$597$	−24.1433			−0.988121
$598$	−21.7996	−	19.8471i	−0.891454	−	0.811610i
$599$	−37.1568			−1.51819			−0.759093	−	0.650983i	$-0.774357\pi$
$599$	−37.1568			−1.51819			−0.759093	+	0.650983i	$0.774357\pi$
$600$	6.50692	−	7.50939i	0.265644	−	0.306570i
$601$	29.7493	−	19.1187i	1.21350	−	0.779868i	0.232258	−	0.972654i	$-0.425389\pi$
$601$	29.7493	−	19.1187i	1.21350	−	0.779868i	0.981241	+	0.192786i	$0.0617523\pi$
$602$	−0.980305	−	6.81817i	−0.0399542	−	0.277888i
$603$	−3.07575	−	6.73496i	−0.125254	−	0.274269i
$604$	−1.36156	+	9.46985i	−0.0554011	+	0.385323i
$605$	−75.9062	+	22.2881i	−3.08602	+	0.906139i
$606$	−0.836635	−	0.537673i	−0.0339860	−	0.0218415i
$607$	−6.43557	+	14.0919i	−0.261212	+	0.571974i	−0.994111	−	0.108363i	$-0.965439\pi$
$607$	−6.43557	+	14.0919i	−0.261212	+	0.571974i	0.732900	+	0.680337i	$0.238167\pi$
$608$	1.52204	+	0.446912i	0.0617269	+	0.0181247i
$609$	−1.38857	−	1.60250i	−0.0562679	−	0.0649366i
$610$	−5.80819	−	6.70301i	−0.235167	−	0.271397i
$611$	−60.5223	−	17.7710i	−2.44847	−	0.718936i
$612$	−2.66924	+	5.84482i	−0.107898	+	0.236263i
$613$	−14.1656	−	9.10370i	−0.572145	−	0.367695i	0.222349	−	0.974967i	$-0.428627\pi$
$613$	−14.1656	−	9.10370i	−0.572145	−	0.367695i	−0.794494	+	0.607272i	$0.792264\pi$
$614$	10.7320	−	3.15119i	0.433107	−	0.127172i
$615$	−1.04886	+	7.29499i	−0.0422942	+	0.294162i
$616$	−2.33039	−	5.10285i	−0.0938942	−	0.205600i
$617$	−5.33584	−	37.1116i	−0.214813	−	1.49406i	−0.756787	−	0.653662i	$-0.773232\pi$
$617$	−5.33584	−	37.1116i	−0.214813	−	1.49406i	0.541974	−	0.840395i	$-0.317677\pi$
$618$	1.42071	−	0.913034i	0.0571493	−	0.0367276i
$619$	32.5288	−	37.5403i	1.30744	−	1.50887i	0.609177	−	0.793034i	$-0.291500\pi$
$619$	32.5288	−	37.5403i	1.30744	−	1.50887i	0.698267	−	0.715837i	$-0.253955\pi$
$620$	−41.8081			−1.67905
$621$	4.41003	−	1.88457i	0.176969	−	0.0756251i
$622$	17.2960			0.693506
$623$	−1.63003	+	1.88116i	−0.0653058	+	0.0753669i
$624$	−5.17138	+	3.32344i	−0.207021	+	0.133044i
$625$	−3.42257	−	23.8045i	−0.136903	−	0.952179i
$626$	2.52178	+	5.52194i	0.100791	+	0.220701i
$627$	−1.26643	+	8.80822i	−0.0505764	+	0.351766i
$628$	−3.41107	+	1.00158i	−0.136116	+	0.0399674i
$629$	45.9273	+	29.5157i	1.83124	+	1.17687i
$630$	−1.60548	+	3.51551i	−0.0639638	+	0.140061i
$631$	23.9605	+	7.03542i	0.953851	+	0.280076i	0.721389	−	0.692530i	$-0.243504\pi$
$631$	23.9605	+	7.03542i	0.953851	+	0.280076i	0.232461	+	0.972606i	$0.425322\pi$
$632$	−1.41528	−	1.63332i	−0.0562968	−	0.0649700i
$633$	0.267979	+	0.309264i	0.0106512	+	0.0122921i
$634$	2.50912	+	0.736744i	0.0996499	+	0.0292599i
$635$	19.7839	−	43.3208i	0.785102	−	1.71913i
$636$	−5.92449	−	3.80744i	−0.234921	−	0.150975i
$637$	−5.89822	+	1.73187i	−0.233696	+	0.0686194i
$638$	−1.69285	+	11.7740i	−0.0670204	+	0.466137i
$639$	1.03887	+	2.27481i	0.0410971	+	0.0899900i
$640$	−0.550012	−	3.82542i	−0.0217411	−	0.151213i
$641$	7.90490	−	5.08017i	0.312225	−	0.200655i	−0.375138	−	0.926969i	$-0.622405\pi$
$641$	7.90490	−	5.08017i	0.312225	−	0.200655i	0.687363	+	0.726314i	$0.258768\pi$
$642$	0.829427	−	0.957209i	0.0327349	−	0.0377780i
$643$	−47.5343			−1.87457			−0.937285	−	0.348563i	$-0.886670\pi$
$643$	−47.5343			−1.87457			−0.937285	+	0.348563i	$0.886670\pi$
$644$	−3.70045	+	3.05068i	−0.145818	+	0.120214i
$645$	26.6215			1.04822
$646$	−6.67480	+	7.70314i	−0.262617	+	0.303076i
$647$	4.09486	−	2.63161i	0.160986	−	0.103459i	−0.457668	−	0.889123i	$-0.651315\pi$
$647$	4.09486	−	2.63161i	0.160986	−	0.103459i	0.618653	+	0.785664i	$0.287679\pi$
$648$	−0.142315	−	0.989821i	−0.00559065	−	0.0388839i
$649$	6.95692	+	15.2335i	0.273083	+	0.597968i
$650$	−8.69273	+	60.4593i	−0.340957	+	2.37141i
$651$	10.3796	−	3.04772i	0.406808	−	0.119450i
$652$	−5.25343	−	3.37617i	−0.205740	−	0.132221i
$653$	−0.418818	+	0.917084i	−0.0163896	+	0.0358883i	−0.917650	−	0.397390i	$-0.869916\pi$
$653$	−0.418818	+	0.917084i	−0.0163896	+	0.0358883i	0.901260	+	0.433278i	$0.142643\pi$
$654$	18.1470	+	5.32844i	0.709604	+	0.208358i
$655$	14.9391	+	17.2406i	0.583717	+	0.673646i
$656$	1.24880	+	1.44120i	0.0487576	+	0.0562693i
$657$	−4.23548	−	1.24365i	−0.165242	−	0.0485194i
$658$	−4.26262	+	9.33384i	−0.166174	+	0.363871i
$659$	4.54672	+	2.92200i	0.177115	+	0.113825i	0.626194	−	0.779667i	$-0.284612\pi$
$659$	4.54672	+	2.92200i	0.177115	+	0.113825i	−0.449079	+	0.893492i	$0.648248\pi$
$660$	20.8023	−	6.10810i	0.809727	−	0.237757i
$661$	−0.748506	+	5.20597i	−0.0291135	+	0.202489i	−0.999187	−	0.0403239i	$-0.987161\pi$
$661$	−0.748506	+	5.20597i	−0.0291135	+	0.202489i	0.970073	+	0.242813i	$0.0780701\pi$
$662$	−13.6156	−	29.8140i	−0.529185	−	1.15875i
$663$	−5.62127	−	39.0968i	−0.218312	−	1.51839i
$664$	11.0835	−	7.12295i	0.430124	−	0.276424i
$665$	−4.01472	+	4.63324i	−0.155684	+	0.179669i
$666$	−8.49648			−0.329232
$667$	10.0981	−	1.19968i	0.391001	−	0.0464519i
$668$	10.9386			0.423226
$669$	−1.70819	+	1.97136i	−0.0660426	+	0.0762172i
$670$	−24.0723	+	15.4704i	−0.929996	+	0.597672i
$671$	−1.83217	−	12.7431i	−0.0707303	−	0.491940i
$672$	0.415415	+	0.909632i	0.0160250	+	0.0350898i
$673$	−3.51906	+	24.4756i	−0.135650	+	0.943466i	0.802356	+	0.596846i	$0.203580\pi$
$673$	−3.51906	+	24.4756i	−0.135650	+	0.943466i	−0.938006	+	0.346620i	$0.887329\pi$
$674$	32.5286	−	9.55125i	1.25295	−	0.367900i
$675$	−8.35899	−	5.37199i	−0.321738	−	0.206768i
$676$	10.2975	−	22.5483i	0.396057	−	0.867243i
$677$	33.3136	+	9.78175i	1.28034	+	0.375943i	0.850029	−	0.526735i	$-0.176584\pi$
$677$	33.3136	+	9.78175i	1.28034	+	0.375943i	0.430315	+	0.902679i	$0.358402\pi$
$678$	9.30069	+	10.7336i	0.357191	+	0.412220i
$679$	0.741677	+	0.855940i	0.0284629	+	0.0328480i
$680$	23.8270	+	6.99623i	0.913723	+	0.268293i
$681$	−6.25160	+	13.6891i	−0.239562	+	0.524568i
$682$	−51.0519	−	32.8091i	−1.95488	−	1.25632i
$683$	31.6761	−	9.30095i	1.21205	−	0.355891i	0.387604	−	0.921826i	$-0.373303\pi$
$683$	31.6761	−	9.30095i	1.21205	−	0.355891i	0.824450	+	0.565935i	$0.191485\pi$
$684$	0.225754	−	1.57015i	0.00863190	−	0.0600362i
$685$	18.6588	+	40.8570i	0.712916	+	1.56107i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	23.3711	−	15.0197i	0.891663	−	0.573037i
$688$	4.51087	−	5.20582i	0.171975	−	0.198470i
$689$	43.2916			1.64928
$690$	−9.63483	−	15.8337i	−0.366792	−	0.602779i
$691$	−13.3300			−0.507097			−0.253548	−	0.967323i	$-0.581598\pi$
$691$	−13.3300			−0.507097			−0.253548	+	0.967323i	$0.581598\pi$
$692$	−4.12946	+	4.76565i	−0.156979	+	0.181163i
$693$	−4.71926	+	3.03288i	−0.179270	+	0.115210i
$694$	3.10093	+	21.5674i	0.117710	+	0.818689i
$695$	−11.1866	−	24.4953i	−0.424333	−	0.929160i
$696$	0.301766	−	2.09883i	0.0114384	−	0.0795559i
$697$	−11.7569	+	3.45214i	−0.445324	+	0.130759i
$698$	5.88028	+	3.77903i	0.222572	+	0.143038i
$699$	−8.92129	+	19.5349i	−0.337434	+	0.738877i
$700$	9.53386	+	2.79939i	0.360346	+	0.105807i
$701$	23.5452	+	27.1726i	0.889288	+	1.02629i	0.999476	+	0.0323825i	$0.0103095\pi$
$701$	23.5452	+	27.1726i	0.889288	+	1.02629i	−0.110187	+	0.993911i	$0.535145\pi$
$702$	4.02558	+	4.64576i	0.151936	+	0.175343i
$703$	−12.9320	−	3.79718i	−0.487739	−	0.143213i
$704$	2.33039	−	5.10285i	0.0878300	−	0.192321i
$705$	−33.3613	−	21.4400i	−1.25646	−	0.807479i
$706$	16.0790	−	4.72121i	0.605140	−	0.177685i
$707$	0.141534	−	0.984387i	0.00532292	−	0.0370217i
$708$	−1.24014	−	2.71552i	−0.0466073	−	0.102056i
$709$	4.97400	+	34.5950i	0.186803	+	1.29924i	0.840221	+	0.542244i	$0.182425\pi$
$709$	4.97400	+	34.5950i	0.186803	+	1.29924i	−0.653418	+	0.756997i	$0.726666\pi$
$710$	8.13070	−	5.22529i	0.305140	−	0.196101i
$711$	−1.41528	+	1.63332i	−0.0530771	+	0.0612543i
$712$	−2.48913			−0.0932839
$713$	−15.8340	+	49.4049i	−0.592987	+	1.85023i
$714$	−6.42547			−0.240467
$715$	−87.2765	+	100.722i	−3.26396	+	3.76681i
$716$	9.37801	−	6.02688i	0.350473	−	0.225235i
$717$	−2.02595	−	14.0908i	−0.0756605	−	0.526230i
$718$	6.89566	+	15.0994i	0.257344	+	0.563505i
$719$	−6.99281	+	48.6361i	−0.260788	+	1.81382i	0.266168	+	0.963927i	$0.414242\pi$
$719$	−6.99281	+	48.6361i	−0.260788	+	1.81382i	−0.526956	+	0.849892i	$0.676667\pi$
$720$	−3.70821	+	1.08883i	−0.138197	+	0.0405782i
$721$	1.42071	+	0.913034i	0.0529100	+	0.0340032i
$722$	−6.84756	+	14.9941i	−0.254840	+	0.558021i
$723$	−7.95802	−	2.33668i	−0.295962	−	0.0869022i
$724$	4.39287	+	5.06964i	0.163260	+	0.188412i
$725$	−13.7974	−	15.9230i	−0.512421	−	0.591366i
$726$	19.6406	+	5.76700i	0.728931	+	0.214034i
$727$	−12.7370	+	27.8901i	−0.472389	+	1.03439i	0.512097	+	0.858927i	$0.328869\pi$
$727$	−12.7370	+	27.8901i	−0.472389	+	1.03439i	−0.984486	+	0.175460i	$0.943859\pi$
$728$	−5.17138	−	3.32344i	−0.191664	−	0.123175i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−2.42791	+	16.8865i	−0.0898611	+	0.624998i
$731$	18.3865	+	40.2607i	0.680048	+	1.48910i
$732$	0.326603	+	2.27157i	0.0120716	+	0.0839597i
$733$	18.7744	−	12.0656i	0.693449	−	0.445652i	−0.145862	−	0.989305i	$-0.546595\pi$
$733$	18.7744	−	12.0656i	0.693449	−	0.445652i	0.839310	+	0.543653i	$0.182959\pi$
$734$	11.7558	−	13.5669i	0.433915	−	0.500765i
$735$	−3.86476			−0.142554
$736$	−4.72883	−	0.798846i	−0.174307	−	0.0294459i
$737$	−41.5352			−1.52997
$738$	1.24880	−	1.44120i	0.0459691	−	0.0530512i
$739$	−13.9690	+	8.97731i	−0.513857	+	0.330236i	−0.771738	−	0.635941i	$-0.780612\pi$
$739$	−13.9690	+	8.97731i	−0.513857	+	0.330236i	0.257881	+	0.966177i	$0.416976\pi$
$740$	4.67317	+	32.5026i	0.171789	+	1.19482i
$741$	4.05085	+	8.87012i	0.148812	+	0.325852i
$742$	1.00225	−	6.97077i	0.0367936	−	0.255905i
$743$	29.3603	−	8.62095i	1.07712	−	0.316272i	0.305396	−	0.952225i	$-0.401211\pi$
$743$	29.3603	−	8.62095i	1.07712	−	0.316272i	0.771728	+	0.635953i	$0.219393\pi$
$744$	9.10049	+	5.84853i	0.333640	+	0.214418i
$745$	8.46897	−	18.5445i	0.310279	−	0.679416i
$746$	−14.5884	−	4.28353i	−0.534118	−	0.156831i
$747$	−8.62779	−	9.95701i	−0.315674	−	0.364308i
$748$	23.6048	+	27.2414i	0.863078	+	0.996045i
$749$	1.21526	+	0.356834i	0.0444048	+	0.0130384i
$750$	−7.92520	+	17.3538i	−0.289387	+	0.633670i
$751$	−35.3634	−	22.7267i	−1.29043	−	0.829308i	−0.298292	−	0.954475i	$-0.596417\pi$
$751$	−35.3634	−	22.7267i	−1.29043	−	0.829308i	−0.992136	+	0.125167i	$0.960053\pi$
$752$	−9.84547	+	2.89089i	−0.359027	+	0.105420i
$753$	−2.74743	+	19.1088i	−0.100122	+	0.696363i
$754$	5.41479	+	11.8567i	0.197195	+	0.431797i
$755$	−5.26210	−	36.5987i	−0.191507	−	1.33196i
$756$	0.841254	−	0.540641i	0.0305961	−	0.0196629i
$757$	2.17607	−	2.51132i	0.0790908	−	0.0912756i	−0.714825	−	0.699303i	$-0.753494\pi$
$757$	2.17607	−	2.51132i	0.0790908	−	0.0912756i	0.793916	+	0.608028i	$0.208039\pi$
$758$	13.3728			0.485721
$759$	0.660454	−	26.8955i	0.0239730	−	0.976245i
$760$	−6.13065			−0.222382
$761$	4.67760	−	5.39824i	0.169563	−	0.195686i	−0.664608	−	0.747192i	$-0.731401\pi$
$761$	4.67760	−	5.39824i	0.169563	−	0.195686i	0.834171	+	0.551506i	$0.185947\pi$
$762$	−10.3666	+	6.66219i	−0.375541	+	0.241346i
$763$	2.69162	+	18.7206i	0.0974431	+	0.677731i
$764$	4.49186	+	9.83580i	0.162510	+	0.355847i
$765$	3.53409	−	24.5801i	0.127775	−	0.888696i
$766$	24.1183	−	7.08176i	0.871429	−	0.255875i
$767$	15.4381	+	9.92147i	0.557438	+	0.358244i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	47.0958	+	13.8286i	1.69832	+	0.498672i	0.980327	−	0.197380i	$-0.0632432\pi$
$769$	47.0958	+	13.8286i	1.69832	+	0.498672i	0.717992	+	0.696051i	$0.245061\pi$
$770$	14.1977	+	16.3850i	0.511650	+	0.590475i
$771$	11.7066	+	13.5102i	0.421604	+	0.486556i
$772$	−19.3487	−	5.68129i	−0.696374	−	0.204474i
$773$	9.87670	−	21.6270i	0.355240	−	0.777867i	−0.644670	−	0.764461i	$-0.723005\pi$
$773$	9.87670	−	21.6270i	0.355240	−	0.777867i	0.999910	−	0.0134065i	$-0.00426754\pi$
$774$	−5.79479	−	3.72409i	−0.208289	−	0.133860i
$775$	103.135	−	30.2832i	3.70472	−	1.08780i
$776$	−0.161182	+	1.12104i	−0.00578609	+	0.0402431i
$777$	−3.52957	−	7.72867i	−0.126623	−	0.277265i
$778$	−2.04960	−	14.2552i	−0.0734816	−	0.511075i
$779$	2.54482	−	1.63546i	0.0911776	−	0.0585963i
$780$	15.5579	−	17.9548i	0.557061	−	0.642883i
$781$	14.0290			0.501996
$782$	17.2915	−	25.5068i	0.618342	−	0.912123i
$783$	−2.12041			−0.0757774
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	11.5584	−	7.42813i	0.412537	−	0.265121i
$786$	−0.840045	−	5.84264i	−0.0299634	−	0.208400i
$787$	11.5870	+	25.3719i	0.413031	+	0.904412i	0.995781	+	0.0917603i	$0.0292493\pi$
$787$	11.5870	+	25.3719i	0.413031	+	0.904412i	−0.582750	+	0.812651i	$0.698023\pi$
$788$	0.471596	−	3.28002i	0.0167999	−	0.116846i
$789$	−9.49228	+	2.78719i	−0.337934	+	0.0992264i
$790$	7.02655	+	4.51569i	0.249994	+	0.160661i
$791$	−5.89995	+	12.9191i	−0.209778	+	0.459350i
$792$	−5.38256	−	1.58046i	−0.191261	−	0.0561592i
$793$	−9.23843	−	10.6617i	−0.328066	−	0.378609i
$794$	−7.45058	−	8.59843i	−0.264411	−	0.305147i
$795$	26.1149	+	7.66802i	0.926199	+	0.271957i
$796$	10.0295	−	21.9616i	0.355487	−	0.778407i
$797$	36.2219	+	23.2784i	1.28305	+	0.824563i	0.991260	−	0.131921i	$-0.0421145\pi$
$797$	36.2219	+	23.2784i	1.28305	+	0.824563i	0.291785	+	0.956484i	$0.405751\pi$
$798$	1.52204	−	0.446912i	0.0538797	−	0.0158205i
$799$	9.38317	−	65.2614i	0.331953	−	2.30878i
$800$	4.12771	+	9.03842i	0.145937	+	0.319556i
$801$	0.354239	+	2.46379i	0.0125164	+	0.0870537i
$802$	11.5060	−	7.39445i	0.406290	−	0.261107i
$803$	−16.2165	+	18.7148i	−0.572267	+	0.660432i
$804$	7.40405			0.261121
$805$	10.4004	−	15.3417i	0.366565	−	0.540724i
$806$	−66.4993			−2.34234
$807$	11.9723	−	13.8168i	0.421445	−	0.486373i
$808$	0.836635	−	0.537673i	0.0294327	−	0.0189153i
$809$	0.660191	+	4.59173i	0.0232111	+	0.161437i	0.998130	−	0.0611225i	$-0.0194680\pi$
$809$	0.660191	+	4.59173i	0.0232111	+	0.161437i	−0.974919	+	0.222559i	$0.928559\pi$
$810$	1.60548	+	3.51551i	0.0564107	+	0.123522i
$811$	3.18933	−	22.1823i	0.111993	−	0.778926i	−0.853985	−	0.520298i	$-0.825821\pi$
$811$	3.18933	−	22.1823i	0.111993	−	0.778926i	0.965977	−	0.258627i	$-0.0832702\pi$
$812$	2.03452	−	0.597389i	0.0713977	−	0.0209643i
$813$	2.65353	+	1.70532i	0.0930634	+	0.0598082i
$814$	−19.8001	+	43.3563i	−0.693995	+	1.51964i
$815$	23.1569	+	6.79947i	0.811149	+	0.238175i
$816$	−4.20779	−	4.85605i	−0.147302	−	0.169996i
$817$	−7.15557	−	8.25797i	−0.250342	−	0.288910i
$818$	−1.68994	−	0.496212i	−0.0590875	−	0.0173497i
$819$	−2.55365	+	5.59171i	−0.0892318	+	0.195390i
$820$	−6.20004	−	3.98453i	−0.216515	−	0.139146i
$821$	−46.1130	+	13.5400i	−1.60936	+	0.472550i	−0.958130	−	0.286334i	$-0.907563\pi$
$821$	−46.1130	+	13.5400i	−1.60936	+	0.472550i	−0.651226	+	0.758884i	$0.725745\pi$
$822$	1.65398	−	11.5037i	0.0576890	−	0.401236i
$823$	−1.89659	−	4.15296i	−0.0661111	−	0.144763i	0.873692	−	0.486479i	$-0.161719\pi$
$823$	−1.89659	−	4.15296i	−0.0661111	−	0.144763i	−0.939803	+	0.341716i	$0.888992\pi$
$824$	0.240341	+	1.67161i	0.00837268	+	0.0582333i
$825$	−46.8922	+	30.1358i	−1.63258	+	1.04919i
$826$	1.95496	−	2.25614i	0.0680216	−	0.0785011i
$827$	−12.6898			−0.441266			−0.220633	−	0.975357i	$-0.570812\pi$
$827$	−12.6898			−0.441266			−0.220633	+	0.975357i	$0.570812\pi$
$828$	−0.117732	+	4.79439i	−0.00409148	+	0.166616i
$829$	−27.7660			−0.964353			−0.482177	−	0.876074i	$-0.660154\pi$
$829$	−27.7660			−0.964353			−0.482177	+	0.876074i	$0.660154\pi$
$830$	−33.3443	+	38.4814i	−1.15740	+	1.33571i
$831$	23.1752	−	14.8938i	0.803940	−	0.516661i
$832$	−0.874842	−	6.08466i	−0.0303297	−	0.210948i
$833$	−2.66924	−	5.84482i	−0.0924836	−	0.202511i
$834$	−0.991620	+	6.89687i	−0.0343370	+	0.238819i
$835$	−40.5625	+	11.9102i	−1.40372	+	0.412170i
$836$	−7.48615	−	4.81105i	−0.258914	−	0.166394i
$837$	4.49387	−	9.84020i	0.155331	−	0.340127i
$838$	−12.9218	−	3.79418i	−0.446376	−	0.131068i
$839$	−24.9035	−	28.7402i	−0.859766	−	0.992222i	−0.999998	−	0.00210373i	$-0.999330\pi$
$839$	−24.9035	−	28.7402i	−0.859766	−	0.992222i	0.140232	−	0.990119i	$-0.455215\pi$
$840$	−2.53088	−	2.92079i	−0.0873236	−	0.100777i
$841$	23.5113	+	6.90353i	0.810734	+	0.238053i
$842$	−10.7344	+	23.5050i	−0.369931	+	0.810036i
$843$	−12.2485	−	7.87162i	−0.421860	−	0.271113i
$844$	−0.392639	+	0.115289i	−0.0135152	+	0.00396842i
$845$	−13.6339	+	94.8260i	−0.469021	+	3.26212i
$846$	4.26262	+	9.33384i	0.146552	+	0.320904i
$847$	2.91315	+	20.2614i	0.100097	+	0.696191i
$848$	5.92449	−	3.80744i	0.203448	−	0.130748i
$849$	−5.80159	+	6.69540i	−0.199110	+	0.229785i
$850$	−63.8457			−2.18989
$851$	40.1784	+	6.78738i	1.37730	+	0.232669i
$852$	−2.50080			−0.0856760
$853$	30.8958	−	35.6557i	1.05785	−	1.22083i	0.0833347	−	0.996522i	$-0.473443\pi$
$853$	30.8958	−	35.6557i	1.05785	−	1.22083i	0.974519	−	0.224306i	$-0.0720116\pi$
$854$	−1.93062	+	1.24073i	−0.0660644	+	0.0424570i
$855$	0.872483	+	6.06825i	0.0298383	+	0.207530i
$856$	0.526152	+	1.15211i	0.0179835	+	0.0393784i
$857$	−0.614610	+	4.27471i	−0.0209947	+	0.146021i	−0.997622	−	0.0689165i	$-0.978046\pi$
$857$	−0.614610	+	4.27471i	−0.0209947	+	0.146021i	0.976628	+	0.214938i	$0.0689549\pi$
$858$	33.0878	−	9.71546i	1.12960	−	0.331680i
$859$	−2.22014	−	1.42680i	−0.0757502	−	0.0486817i	0.502218	−	0.864741i	$-0.332518\pi$
$859$	−2.22014	−	1.42680i	−0.0757502	−	0.0486817i	−0.577968	+	0.816060i	$0.696154\pi$
$860$	−11.0590	+	24.2158i	−0.377108	+	0.825752i
$861$	1.82973	+	0.537258i	0.0623571	+	0.0183097i
$862$	1.71909	+	1.98393i	0.0585524	+	0.0675731i
$863$	−15.0657	−	17.3867i	−0.512841	−	0.591850i	0.438983	−	0.898496i	$-0.355339\pi$
$863$	−15.0657	−	17.3867i	−0.512841	−	0.591850i	−0.951824	+	0.306645i	$0.900793\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	10.1239	−	22.1683i	0.344224	−	0.753745i
$866$	−6.81295	−	4.37842i	−0.231514	−	0.148785i
$867$	23.3029	−	6.84236i	0.791409	−	0.232379i
$868$	−1.53953	+	10.7077i	−0.0522551	+	0.363442i
$869$	5.03642	+	11.0282i	0.170849	+	0.374107i
$870$	1.16625	+	8.11147i	0.0395397	+	0.275004i
$871$	−38.2891	+	24.6069i	−1.29738	+	0.833774i
$872$	−12.3855	+	14.2936i	−0.419424	+	0.484042i
$873$	1.13257			0.0383317
$874$	−2.32186	+	7.24464i	−0.0785381	+	0.245053i
$875$	−19.0778			−0.644947
$876$	2.89075	−	3.33610i	0.0976693	−	0.112716i
$877$	17.5593	−	11.2847i	0.592934	−	0.381056i	−0.209489	−	0.977811i	$-0.567180\pi$
$877$	17.5593	−	11.2847i	0.592934	−	0.381056i	0.802423	+	0.596755i	$0.203544\pi$
$878$	2.69146	+	18.7195i	0.0908324	+	0.631753i
$879$	1.78705	+	3.91310i	0.0602758	+	0.131986i
$880$	−3.08545	+	21.4598i	−0.104011	+	0.723410i
$881$	51.6205	−	15.1571i	1.73914	−	0.510657i	0.750486	−	0.660886i	$-0.229819\pi$
$881$	51.6205	−	15.1571i	1.73914	−	0.510657i	0.988651	+	0.150229i	$0.0480011\pi$
$882$	0.841254	+	0.540641i	0.0283265	+	0.0182043i
$883$	−13.4698	+	29.4948i	−0.453295	+	0.992579i	0.535669	+	0.844428i	$0.320059\pi$
$883$	−13.4698	+	29.4948i	−0.453295	+	0.992579i	−0.988965	+	0.148151i	$0.952668\pi$
$884$	37.8989	+	11.1281i	1.27468	+	0.374279i
$885$	7.55543	+	8.71943i	0.253973	+	0.293100i
$886$	2.11741	+	2.44362i	0.0711357	+	0.0820949i
$887$	8.74917	+	2.56899i	0.293768	+	0.0862582i	0.425296	−	0.905054i	$-0.360170\pi$
$887$	8.74917	+	2.56899i	0.293768	+	0.0862582i	−0.131528	+	0.991313i	$0.541988\pi$
$888$	3.52957	−	7.72867i	0.118445	−	0.259357i
$889$	−10.3666	−	6.66219i	−0.347684	−	0.223443i
$890$	9.23019	−	2.71023i	0.309397	−	0.0908471i
$891$	−0.798357	+	5.55269i	−0.0267460	+	0.186022i
$892$	−1.08360	−	2.37276i	−0.0362817	−	0.0794459i
$893$	2.31648	+	16.1115i	0.0775182	+	0.539151i
$894$	−4.43765	+	2.85190i	−0.148417	+	0.0953820i
$895$	−28.2134	+	32.5600i	−0.943069	+	1.08836i
$896$	−1.00000			−0.0334077
$897$	−15.3250	−	25.1849i	−0.511688	−	0.840898i
$898$	−16.5189			−0.551242
$899$	15.0213	−	17.3355i	0.500988	−	0.578171i
$900$	8.35899	−	5.37199i	0.278633	−	0.179066i
$901$	6.43990	+	44.7905i	0.214544	+	1.49219i
$902$	−4.44401	−	9.73102i	−0.147969	−	0.324007i
$903$	0.980305	−	6.81817i	0.0326225	−	0.226894i
$904$	−13.6272	+	4.00132i	−0.453235	+	0.133082i
$905$	−21.8096	−	14.0162i	−0.724977	−	0.465914i
$906$	−3.97437	+	8.70266i	−0.132040	+	0.289127i
$907$	−10.5746	−	3.10497i	−0.351123	−	0.103099i	0.101415	−	0.994844i	$-0.467663\pi$
$907$	−10.5746	−	3.10497i	−0.351123	−	0.103099i	−0.452538	+	0.891745i	$0.649481\pi$
$908$	−9.85504	−	11.3733i	−0.327051	−	0.377437i
$909$	−0.651266	−	0.751601i	−0.0216011	−	0.0249290i
$910$	22.7952	+	6.69327i	0.755653	+	0.221880i
$911$	−4.96965	+	10.8820i	−0.164652	+	0.360537i	−0.973916	−	0.226907i	$-0.927139\pi$
$911$	−4.96965	+	10.8820i	−0.164652	+	0.360537i	0.809265	+	0.587444i	$0.199866\pi$
$912$	1.33448	+	0.857617i	0.0441890	+	0.0283985i
$913$	−70.9152	+	20.8226i	−2.34695	+	0.689127i
$914$	0.401983	−	2.79585i	0.0132964	−	0.0924786i
$915$	−3.68446	−	8.06785i	−0.121805	−	0.266715i
$916$	3.95369	+	27.4985i	0.130633	+	0.908576i
$917$	4.96568	−	3.19125i	0.163981	−	0.105384i
$918$	−4.20779	+	4.85605i	−0.138878	+	0.160273i
$919$	−1.80819			−0.0596467			−0.0298233	−	0.999555i	$-0.509494\pi$
$919$	−1.80819			−0.0596467			−0.0298233	+	0.999555i	$0.509494\pi$
$920$	18.4053	−	2.18660i	0.606805	−	0.0720899i
$921$	11.1850			0.368559
$922$	−3.55919	+	4.10752i	−0.117216	+	0.135274i
$923$	12.9326	−	8.31127i	0.425681	−	0.273569i
$924$	−0.798357	−	5.55269i	−0.0262640	−	0.182670i
$925$	−35.0710	−	76.7948i	−1.15313	−	2.52500i
$926$	0.655983	−	4.56246i	0.0215569	−	0.149932i
$927$	1.62039	−	0.475790i	0.0532206	−	0.0156270i
$928$	1.78380	+	1.14638i	0.0585563	+	0.0376318i
$929$	5.15804	−	11.2945i	0.169230	−	0.370561i	−0.805948	−	0.591987i	$-0.798344\pi$
$929$	5.15804	−	11.2945i	0.169230	−	0.370561i	0.975177	+	0.221426i	$0.0710710\pi$
$930$	−40.1146	−	11.7787i	−1.31541	−	0.386239i
$931$	1.03880	+	1.19884i	0.0340454	+	0.0392905i
$932$	−14.0635	−	16.2302i	−0.460666	−	0.531637i
$933$	16.5954	+	4.87285i	0.543309	+	0.159530i
$934$	4.76398	−	10.4317i	0.155882	−	0.341334i
$935$	−117.193	−	75.3153i	−3.83262	−	2.46307i
$936$	−5.89822	+	1.73187i	−0.192789	+	0.0566081i
$937$	4.15257	−	28.8818i	0.135659	−	0.943526i	−0.802335	−	0.596874i	$-0.796409\pi$
$937$	4.15257	−	28.8818i	0.135659	−	0.943526i	0.937994	−	0.346652i	$-0.112682\pi$
$938$	3.07575	+	6.73496i	0.100427	+	0.219904i
$939$	0.863925	+	6.00873i	0.0281931	+	0.196087i
$940$	33.3613	−	21.4400i	1.08813	−	0.699297i
$941$	32.2062	−	37.1680i	1.04989	−	1.21164i	0.0731297	−	0.997322i	$-0.476701\pi$
$941$	32.2062	−	37.1680i	1.04989	−	1.21164i	0.976764	−	0.214319i	$-0.0687532\pi$
$942$	−3.55507			−0.115831
$943$	−7.05668	+	5.81758i	−0.229797	+	0.189446i
$944$	2.98530			0.0971633
$945$	−2.53088	+	2.92079i	−0.0823295	+	0.0950133i
$946$	−32.5076	+	20.8914i	−1.05691	+	0.679237i
$947$	1.09706	+	7.63024i	0.0356498	+	0.247950i	0.999852	−	0.0172194i	$-0.00548137\pi$
$947$	1.09706	+	7.63024i	0.0356498	+	0.247950i	−0.964202	+	0.265169i	$0.914572\pi$
$948$	−0.897792	−	1.96589i	−0.0291589	−	0.0638491i
$949$	−3.86181	+	26.8594i	−0.125360	+	0.871895i
$950$	15.1235	−	4.44067i	0.490672	−	0.144074i
$951$	2.19992	+	1.41380i	0.0713373	+	0.0458457i
$952$	2.66924	−	5.84482i	0.0865105	−	0.189432i
$953$	3.51901	+	1.03327i	0.113992	+	0.0334710i	0.338231	−	0.941063i	$-0.390172\pi$
$953$	3.51901	+	1.03327i	0.113992	+	0.0334710i	−0.224239	+	0.974534i	$0.571990\pi$
$954$	−4.61183	−	5.32233i	−0.149313	−	0.172317i
$955$	−27.3662	−	31.5823i	−0.885551	−	1.02198i
$956$	13.6590	+	4.01066i	0.441765	+	0.129714i
$957$	−4.94139	+	10.8201i	−0.159733	+	0.349765i
$958$	−14.4685	−	9.29835i	−0.467457	−	0.300416i
$959$	11.1512	−	3.27428i	0.360090	−	0.105732i
$960$	0.550012	−	3.82542i	0.0177516	−	0.123465i
$961$	35.7358	+	78.2505i	1.15277	+	2.52421i
$962$	7.43308	+	51.6982i	0.239652	+	1.66682i
$963$	1.06551	−	0.684759i	0.0343355	−	0.0220661i
$964$	5.43140	−	6.26817i	0.174934	−	0.201884i
$965$	77.9349			2.50881
$966$	−4.41003	+	1.88457i	−0.141891	+	0.0606349i
$967$	−37.7123			−1.21275			−0.606373	−	0.795180i	$-0.707376\pi$
$967$	−37.7123			−1.21275			−0.606373	+	0.795180i	$0.707376\pi$
$968$	−13.4049	+	15.4700i	−0.430848	+	0.497225i
$969$	−8.57465	+	5.51059i	−0.275458	+	0.177026i
$970$	−0.622928	−	4.33256i	−0.0200010	−	0.139110i
$971$	−21.2753	−	46.5864i	−0.682756	−	1.49503i	−0.859696	−	0.510806i	$-0.829347\pi$
$971$	−21.2753	−	46.5864i	−0.682756	−	1.49503i	0.176939	−	0.984222i	$-0.443380\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	−6.68554	+	1.96305i	−0.214329	+	0.0629326i
$974$	27.3518	+	17.5780i	0.876409	+	0.563234i
$975$	−25.3740	+	55.5612i	−0.812617	+	1.77938i
$976$	−2.20197	−	0.646557i	−0.0704834	−	0.0206958i
$977$	−35.9238	−	41.4582i	−1.14930	−	1.32637i	−0.937068	−	0.349147i	$-0.886471\pi$
$977$	−35.9238	−	41.4582i	−1.14930	−	1.32637i	−0.212235	−	0.977219i	$-0.568074\pi$
$978$	−4.08945	−	4.71947i	−0.130766	−	0.150912i
$979$	13.3979	+	3.93397i	0.428197	+	0.125730i
$980$	1.60548	−	3.51551i	0.0512851	−	0.112299i
$981$	15.9107	+	10.2252i	0.507990	+	0.326466i
$982$	15.5817	−	4.57521i	0.497233	−	0.146001i
$983$	5.14447	−	35.7805i	0.164083	−	1.14122i	−0.726754	−	0.686898i	$-0.758972\pi$
$983$	5.14447	−	35.7805i	0.164083	−	1.14122i	0.890837	−	0.454324i	$-0.150119\pi$
$984$	0.792187	+	1.73465i	0.0252540	+	0.0552986i
$985$	1.82260	+	12.6765i	0.0580730	+	0.403906i
$986$	−11.4618	+	7.36604i	−0.365018	+	0.234583i
$987$	−6.71960	+	7.75483i	−0.213887	+	0.246839i
$988$	−9.75133			−0.310231
$989$	24.4276	+	22.2397i	0.776753	+	0.707182i
$990$	21.6805			0.689051
$991$	−11.1698	+	12.8907i	−0.354821	+	0.409485i	−0.904898	−	0.425629i	$-0.860053\pi$
$991$	−11.1698	+	12.8907i	−0.354821	+	0.409485i	0.550077	+	0.835114i	$0.314598\pi$
$992$	−9.10049	+	5.84853i	−0.288941	+	0.185691i
$993$	−4.66449	−	32.4422i	−0.148023	−	1.02952i
$994$	−1.03887	−	2.27481i	−0.0329510	−	0.0721525i
$995$	−13.2791	+	92.3584i	−0.420977	+	2.92796i
$996$	12.6413	−	3.71183i	0.400556	−	0.117614i
$997$	11.2412	+	7.22430i	0.356013	+	0.228796i	0.706406	−	0.707807i	$-0.250315\pi$
$997$	11.2412	+	7.22430i	0.356013	+	0.228796i	−0.350392	+	0.936603i	$0.613952\pi$
$998$	15.9127	−	34.8439i	0.503707	−	1.10296i
$999$	−8.15232	−	2.39374i	−0.257928	−	0.0757345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.j.85.4	✓	40
23.13	even	11	inner	966.2.q.j.841.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.j.85.4	✓	40	1.1	even	1	trivial
966.2.q.j.841.4	yes	40	23.13	even	11	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(1.60548 + 3.51551i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(1.60548 + 3.51551i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-3.70821 - 1.08883i) q^{10} +(-3.67363 - 4.23960i) q^{11} +(0.654861 + 0.755750i) q^{12} +(-5.89822 - 1.73187i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(-3.25124 - 2.08945i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.914440 - 6.36007i) q^{17} +(0.415415 + 0.909632i) q^{18} +(0.225754 + 1.57015i) q^{19} +(3.25124 - 2.08945i) q^{20} +(-0.654861 + 0.755750i) q^{21} +5.60979 q^{22} +(-1.23777 - 4.63335i) q^{23} -1.00000 q^{24} +(-6.50692 + 7.50939i) q^{25} +(5.17138 - 3.32344i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(-0.301766 + 2.09883i) q^{29} +(3.70821 - 1.08883i) q^{30} +(-9.10049 - 5.84853i) q^{31} +(0.415415 - 0.909632i) q^{32} +(5.38256 + 1.58046i) q^{33} +(4.20779 + 4.85605i) q^{34} +(2.53088 + 2.92079i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-3.52957 + 7.72867i) q^{37} +(-1.33448 - 0.857617i) q^{38} +(5.89822 - 1.73187i) q^{39} +(-0.550012 + 3.82542i) q^{40} +(-0.792187 - 1.73465i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(-5.79479 + 3.72409i) q^{43} +(-3.67363 + 4.23960i) q^{44} +3.86476 q^{45} +(4.31222 + 2.09875i) q^{46} +10.2611 q^{47} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-1.41409 - 9.83521i) q^{50} +(2.66924 + 5.84482i) q^{51} +(-0.874842 + 6.08466i) q^{52} +(-6.75719 + 1.98409i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(9.00640 - 19.7213i) q^{55} +(0.959493 + 0.281733i) q^{56} +(-1.03880 - 1.19884i) q^{57} +(-1.38857 - 1.60250i) q^{58} +(-2.86437 - 0.841056i) q^{59} +(-1.60548 + 3.51551i) q^{60} +(1.93062 + 1.24073i) q^{61} +(10.3796 - 3.04772i) q^{62} +(0.142315 - 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-3.38105 - 23.5157i) q^{65} +(-4.71926 + 3.03288i) q^{66} +(4.84862 - 5.59561i) q^{67} -6.42547 q^{68} +(3.54626 + 3.22863i) q^{69} -3.86476 q^{70} +(-1.63768 + 1.88998i) q^{71} +(0.841254 - 0.540641i) q^{72} +(-0.628219 - 4.36936i) q^{73} +(-3.52957 - 7.72867i) q^{74} +(1.41409 - 9.83521i) q^{75} +(1.52204 - 0.446912i) q^{76} +(-4.71926 - 3.03288i) q^{77} +(-2.55365 + 5.59171i) q^{78} +(-2.07365 - 0.608878i) q^{79} +(-2.53088 - 2.92079i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(1.82973 + 0.537258i) q^{82} +(5.47310 - 11.9844i) q^{83} +(0.841254 + 0.540641i) q^{84} +(23.8270 - 6.99623i) q^{85} +(0.980305 - 6.81817i) q^{86} +(-0.880851 - 1.92880i) q^{87} +(-0.798357 - 5.55269i) q^{88} +(-2.09399 + 1.34572i) q^{89} +(-2.53088 + 2.92079i) q^{90} -6.14723 q^{91} +(-4.41003 + 1.88457i) q^{92} +10.8178 q^{93} +(-6.71960 + 7.75483i) q^{94} +(-5.15743 + 3.31448i) q^{95} +(0.142315 + 0.989821i) q^{96} +(0.470487 + 1.03022i) q^{97} +(-0.142315 + 0.989821i) q^{98} +(-5.38256 + 1.58046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{14} - 7 q^{15} - 4 q^{16} + 5 q^{17} - 4 q^{18} + 44 q^{19} + 7 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 40 q^{24} + 2 q^{25} + 24 q^{26} + 4 q^{27} + 4 q^{28} + 35 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 11 q^{33} + 5 q^{34} - 7 q^{35} - 4 q^{36} + 20 q^{37} - 11 q^{38} + 20 q^{39} - 4 q^{40} + 11 q^{41} - 4 q^{42} - 42 q^{43} - 11 q^{44} - 4 q^{45} - 6 q^{46} + 40 q^{47} + 4 q^{48} - 4 q^{49} - 53 q^{50} + 17 q^{51} - 9 q^{52} - 32 q^{53} + 4 q^{54} + 29 q^{55} + 4 q^{56} - 11 q^{57} - 31 q^{58} - 25 q^{59} + 4 q^{60} - 30 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 80 q^{65} - 88 q^{67} - 28 q^{68} + 6 q^{69} + 4 q^{70} - 45 q^{71} - 4 q^{72} - 39 q^{73} + 20 q^{74} + 53 q^{75} - 22 q^{76} - 2 q^{78} + 26 q^{79} + 7 q^{80} - 4 q^{81} + 22 q^{83} - 4 q^{84} + 77 q^{85} - 31 q^{86} + 9 q^{87} - 11 q^{88} + 20 q^{89} + 7 q^{90} - 24 q^{91} - 17 q^{92} - 42 q^{93} - 26 q^{94} + 84 q^{95} + 4 q^{96} + 74 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 11 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^14 - 7 * q^15 - 4 * q^16 + 5 * q^17 - 4 * q^18 + 44 * q^19 + 7 * q^20 - 4 * q^21 + 22 * q^22 - 6 * q^23 - 40 * q^24 + 2 * q^25 + 24 * q^26 + 4 * q^27 + 4 * q^28 + 35 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 11 * q^33 + 5 * q^34 - 7 * q^35 - 4 * q^36 + 20 * q^37 - 11 * q^38 + 20 * q^39 - 4 * q^40 + 11 * q^41 - 4 * q^42 - 42 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 40 * q^47 + 4 * q^48 - 4 * q^49 - 53 * q^50 + 17 * q^51 - 9 * q^52 - 32 * q^53 + 4 * q^54 + 29 * q^55 + 4 * q^56 - 11 * q^57 - 31 * q^58 - 25 * q^59 + 4 * q^60 - 30 * q^61 - 24 * q^62 + 4 * q^63 - 4 * q^64 + 80 * q^65 - 88 * q^67 - 28 * q^68 + 6 * q^69 + 4 * q^70 - 45 * q^71 - 4 * q^72 - 39 * q^73 + 20 * q^74 + 53 * q^75 - 22 * q^76 - 2 * q^78 + 26 * q^79 + 7 * q^80 - 4 * q^81 + 22 * q^83 - 4 * q^84 + 77 * q^85 - 31 * q^86 + 9 * q^87 - 11 * q^88 + 20 * q^89 + 7 * q^90 - 24 * q^91 - 17 * q^92 - 42 * q^93 - 26 * q^94 + 84 * q^95 + 4 * q^96 + 74 * q^97 - 4 * q^98 + 11 * q^99

Introduction

L-functions

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