LMFDB - Embedded newform 966.2.q.a.211.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	966.211
Dual form			966.2.q.a.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.114669 - 0.0736930i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.142315 + 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.114669 - 0.0736930i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.142315 + 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.0193985 - 0.134919i) q^{10} +(-0.794209 + 1.73907i) q^{11} +(0.415415 - 0.909632i) q^{12} +(-0.231487 + 1.61003i) q^{13} +(-0.841254 + 0.540641i) q^{14} +(0.130785 + 0.0384020i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-2.09514 - 2.41792i) q^{17} +(0.841254 + 0.540641i) q^{18} +(-2.38533 + 2.75282i) q^{19} +(0.130785 - 0.0384020i) q^{20} +(-0.415415 - 0.909632i) q^{21} -1.91184 q^{22} +(-3.50140 + 3.27723i) q^{23} +1.00000 q^{24} +(-2.06936 - 4.53126i) q^{25} +(-1.56070 + 0.458262i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-0.841254 - 0.540641i) q^{28} +(2.27351 + 2.62377i) q^{29} +(0.0193985 + 0.134919i) q^{30} +(4.47640 + 1.31439i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.272084 - 1.89238i) q^{33} +(1.32907 - 2.91025i) q^{34} +(0.0566239 - 0.123989i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-5.69755 + 3.66160i) q^{37} +(-3.49496 - 1.02621i) q^{38} +(-0.231487 - 1.61003i) q^{39} +(0.0892619 + 0.103014i) q^{40} +(-9.25980 - 5.95091i) q^{41} +(0.654861 - 0.755750i) q^{42} +(-2.86774 + 0.842045i) q^{43} +(-0.794209 - 1.73907i) q^{44} -0.136307 q^{45} +(-4.43560 - 1.82357i) q^{46} -10.3286 q^{47} +(0.415415 + 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(3.26214 - 3.76471i) q^{50} +(2.69148 + 1.72971i) q^{51} +(-1.06519 - 1.22929i) q^{52} +(0.287822 + 2.00184i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(0.219228 - 0.140889i) q^{55} +(0.142315 - 0.989821i) q^{56} +(1.51315 - 3.31334i) q^{57} +(-1.44222 + 3.15801i) q^{58} +(2.04547 - 14.2266i) q^{59} +(-0.114669 + 0.0736930i) q^{60} +(-7.00279 - 2.05620i) q^{61} +(0.663953 + 4.61789i) q^{62} +(0.654861 + 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.145192 - 0.167561i) q^{65} +(1.83440 - 0.538629i) q^{66} +(3.63081 + 7.95037i) q^{67} +3.19937 q^{68} +(2.43626 - 4.13094i) q^{69} +0.136307 q^{70} +(1.77683 + 3.89071i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(1.96318 - 2.26563i) q^{73} +(-5.69755 - 3.66160i) q^{74} +(3.26214 + 3.76471i) q^{75} +(-0.518382 - 3.60543i) q^{76} +(-1.83440 - 0.538629i) q^{77} +(1.36837 - 0.879398i) q^{78} +(-0.304200 + 2.11576i) q^{79} +(-0.0566239 + 0.123989i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.56648 - 10.8951i) q^{82} +(5.07208 - 3.25963i) q^{83} +(0.959493 + 0.281733i) q^{84} +(0.0620629 + 0.431657i) q^{85} +(-1.95725 - 2.25879i) q^{86} +(-2.92062 - 1.87697i) q^{87} +(1.25199 - 1.44488i) q^{88} +(-9.13618 + 2.68262i) q^{89} +(-0.0566239 - 0.123989i) q^{90} -1.62658 q^{91} +(-0.183838 - 4.79231i) q^{92} -4.66538 q^{93} +(-4.29067 - 9.39525i) q^{94} +(0.476386 - 0.139880i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(9.61893 + 6.18171i) q^{97} +(-0.654861 - 0.755750i) q^{98} +(0.272084 + 1.89238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 8 q^{10} - 4 q^{11} - q^{12} + 14 q^{13} + q^{14} - 3 q^{15} - q^{16} + 15 q^{17} - q^{18} - 11 q^{19} - 3 q^{20} + q^{21} - 26 q^{22} - q^{23} + 10 q^{24} + 7 q^{25} - 8 q^{26} - q^{27} + q^{28} + 19 q^{29} + 8 q^{30} - 5 q^{31} - q^{32} + 7 q^{33} - 18 q^{34} - 8 q^{35} - q^{36} - 2 q^{37} + 11 q^{38} + 14 q^{39} - 3 q^{40} + 2 q^{41} + q^{42} + 25 q^{43} - 4 q^{44} + 8 q^{45} - 23 q^{46} - 4 q^{47} - q^{48} - q^{49} - 15 q^{50} + 15 q^{51} - 8 q^{52} + 15 q^{53} - q^{54} + 54 q^{55} + q^{56} + 8 q^{58} - 17 q^{59} - 14 q^{60} + q^{61} - 16 q^{62} + q^{63} - q^{64} - 13 q^{65} - 4 q^{66} - 4 q^{67} + 26 q^{68} + 21 q^{69} - 8 q^{70} + 6 q^{71} - q^{72} - 25 q^{73} - 2 q^{74} - 15 q^{75} - 22 q^{76} + 4 q^{77} + 14 q^{78} + 3 q^{79} + 8 q^{80} - q^{81} + 2 q^{82} + 7 q^{83} + q^{84} + 12 q^{85} - 41 q^{86} + 8 q^{87} + 7 q^{88} - 41 q^{89} + 8 q^{90} + 30 q^{91} - q^{92} - 16 q^{93} - 15 q^{94} - 44 q^{95} - q^{96} - 4 q^{97} - q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9 + 8 * q^10 - 4 * q^11 - q^12 + 14 * q^13 + q^14 - 3 * q^15 - q^16 + 15 * q^17 - q^18 - 11 * q^19 - 3 * q^20 + q^21 - 26 * q^22 - q^23 + 10 * q^24 + 7 * q^25 - 8 * q^26 - q^27 + q^28 + 19 * q^29 + 8 * q^30 - 5 * q^31 - q^32 + 7 * q^33 - 18 * q^34 - 8 * q^35 - q^36 - 2 * q^37 + 11 * q^38 + 14 * q^39 - 3 * q^40 + 2 * q^41 + q^42 + 25 * q^43 - 4 * q^44 + 8 * q^45 - 23 * q^46 - 4 * q^47 - q^48 - q^49 - 15 * q^50 + 15 * q^51 - 8 * q^52 + 15 * q^53 - q^54 + 54 * q^55 + q^56 + 8 * q^58 - 17 * q^59 - 14 * q^60 + q^61 - 16 * q^62 + q^63 - q^64 - 13 * q^65 - 4 * q^66 - 4 * q^67 + 26 * q^68 + 21 * q^69 - 8 * q^70 + 6 * q^71 - q^72 - 25 * q^73 - 2 * q^74 - 15 * q^75 - 22 * q^76 + 4 * q^77 + 14 * q^78 + 3 * q^79 + 8 * q^80 - q^81 + 2 * q^82 + 7 * q^83 + q^84 + 12 * q^85 - 41 * q^86 + 8 * q^87 + 7 * q^88 - 41 * q^89 + 8 * q^90 + 30 * q^91 - q^92 - 16 * q^93 - 15 * q^94 - 44 * q^95 - q^96 - 4 * q^97 - q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	0.415415	+	0.909632i	0.293743	+	0.643207i
$2$	0.415415	+	0.909632i	0.293743	+	0.643207i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	−0.114669	−	0.0736930i	−0.0512813	−	0.0329565i	0.514749	−	0.857341i	$-0.327885\pi$
$5$	−0.114669	−	0.0736930i	−0.0512813	−	0.0329565i	−0.566030	+	0.824384i	$0.691521\pi$
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	0.142315	+	0.989821i	0.0537900	+	0.374117i
$7$	0.142315	+	0.989821i	0.0537900	+	0.374117i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.0193985	−	0.134919i	0.00613433	−	0.0426652i
$11$	−0.794209	+	1.73907i	−0.239463	+	0.524351i	−0.990762	−	0.135611i	$-0.956700\pi$
$11$	−0.794209	+	1.73907i	−0.239463	+	0.524351i	0.751299	+	0.659962i	$0.229428\pi$
$12$	0.415415	−	0.909632i	0.119920	−	0.262588i
$13$	−0.231487	+	1.61003i	−0.0642030	+	0.446542i	0.932210	+	0.361918i	$0.117878\pi$
$13$	−0.231487	+	1.61003i	−0.0642030	+	0.446542i	−0.996413	+	0.0846237i	$0.973031\pi$
$14$	−0.841254	+	0.540641i	−0.224834	+	0.144492i
$15$	0.130785	+	0.0384020i	0.0337686	+	0.00991536i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−2.09514	−	2.41792i	−0.508147	−	0.586433i	0.442476	−	0.896780i	$-0.354100\pi$
$17$	−2.09514	−	2.41792i	−0.508147	−	0.586433i	−0.950623	+	0.310348i	$0.899555\pi$
$18$	0.841254	+	0.540641i	0.198285	+	0.127430i
$19$	−2.38533	+	2.75282i	−0.547233	+	0.631540i	−0.960236	−	0.279189i	$-0.909934\pi$
$19$	−2.38533	+	2.75282i	−0.547233	+	0.631540i	0.413003	+	0.910729i	$0.364480\pi$
$20$	0.130785	−	0.0384020i	0.0292445	−	0.00858696i
$21$	−0.415415	−	0.909632i	−0.0906510	−	0.198498i
$22$	−1.91184			−0.407607
$23$	−3.50140	+	3.27723i	−0.730091	+	0.683350i
$23$	−3.50140	+	3.27723i	−0.730091	+	0.683350i
$24$	1.00000			0.204124
$25$	−2.06936	−	4.53126i	−0.413871	−	0.906252i
$26$	−1.56070	+	0.458262i	−0.306078	+	0.0898726i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	−0.841254	−	0.540641i	−0.158982	−	0.102172i
$29$	2.27351	+	2.62377i	0.422181	+	0.487222i	0.926500	−	0.376295i	$-0.122802\pi$
$29$	2.27351	+	2.62377i	0.422181	+	0.487222i	−0.504319	+	0.863517i	$0.668257\pi$
$30$	0.0193985	+	0.134919i	0.00354166	+	0.0246328i
$31$	4.47640	+	1.31439i	0.803985	+	0.236071i	0.657807	−	0.753187i	$-0.271484\pi$
$31$	4.47640	+	1.31439i	0.803985	+	0.236071i	0.146179	+	0.989258i	$0.453303\pi$
$32$	0.841254	−	0.540641i	0.148714	−	0.0955727i
$33$	0.272084	−	1.89238i	0.0473637	−	0.329422i
$34$	1.32907	−	2.91025i	0.227933	−	0.499104i
$35$	0.0566239	−	0.123989i	0.00957118	−	0.0209580i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	−5.69755	+	3.66160i	−0.936672	+	0.601963i	−0.917449	−	0.397853i	$-0.869756\pi$
$37$	−5.69755	+	3.66160i	−0.936672	+	0.601963i	−0.0192228	+	0.999815i	$0.506119\pi$
$38$	−3.49496	−	1.02621i	−0.566957	−	0.166473i
$39$	−0.231487	−	1.61003i	−0.0370676	−	0.257811i
$40$	0.0892619	+	0.103014i	0.0141135	+	0.0162879i
$41$	−9.25980	−	5.95091i	−1.44614	−	0.929376i	−0.999397	−	0.0347122i	$-0.988949\pi$
$41$	−9.25980	−	5.95091i	−1.44614	−	0.929376i	−0.446740	−	0.894664i	$-0.647415\pi$
$42$	0.654861	−	0.755750i	0.101047	−	0.116615i
$43$	−2.86774	+	0.842045i	−0.437326	+	0.128411i	−0.492982	−	0.870039i	$-0.664093\pi$
$43$	−2.86774	+	0.842045i	−0.437326	+	0.128411i	0.0556558	+	0.998450i	$0.482275\pi$
$44$	−0.794209	−	1.73907i	−0.119731	−	0.262175i
$45$	−0.136307			−0.0203194
$46$	−4.43560	−	1.82357i	−0.653994	−	0.268871i
$47$	−10.3286			−1.50658			−0.753292	−	0.657686i	$-0.771535\pi$
$47$	−10.3286			−1.50658			−0.753292	+	0.657686i	$0.771535\pi$
$48$	0.415415	+	0.909632i	0.0599600	+	0.131294i
$49$	−0.959493	+	0.281733i	−0.137070	+	0.0402475i
$50$	3.26214	−	3.76471i	0.461336	−	0.532410i
$51$	2.69148	+	1.72971i	0.376883	+	0.242208i
$52$	−1.06519	−	1.22929i	−0.147715	−	0.170472i
$53$	0.287822	+	2.00184i	0.0395354	+	0.274974i	0.999994	−	0.00344807i	$-0.00109756\pi$
$53$	0.287822	+	2.00184i	0.0395354	+	0.274974i	−0.960459	+	0.278422i	$0.910188\pi$
$54$	−0.959493	−	0.281733i	−0.130570	−	0.0383389i
$55$	0.219228	−	0.140889i	0.0295607	−	0.0189975i
$56$	0.142315	−	0.989821i	0.0190176	−	0.132270i
$57$	1.51315	−	3.31334i	0.200422	−	0.438862i
$58$	−1.44222	+	3.15801i	−0.189372	+	0.414668i
$59$	2.04547	−	14.2266i	0.266298	−	1.85214i	−0.216334	−	0.976319i	$-0.569410\pi$
$59$	2.04547	−	14.2266i	0.266298	−	1.85214i	0.482632	−	0.875823i	$-0.339681\pi$
$60$	−0.114669	+	0.0736930i	−0.0148036	+	0.00951372i
$61$	−7.00279	−	2.05620i	−0.896615	−	0.263270i	−0.199218	−	0.979955i	$-0.563840\pi$
$61$	−7.00279	−	2.05620i	−0.896615	−	0.263270i	−0.697397	+	0.716685i	$0.745658\pi$
$62$	0.663953	+	4.61789i	0.0843221	+	0.586473i
$63$	0.654861	+	0.755750i	0.0825047	+	0.0952155i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	0.145192	−	0.167561i	0.0180089	−	0.0207833i
$66$	1.83440	−	0.538629i	0.225799	−	0.0663006i
$67$	3.63081	+	7.95037i	0.443574	+	0.971292i	0.990928	+	0.134391i	$0.0429079\pi$
$67$	3.63081	+	7.95037i	0.443574	+	0.971292i	−0.547354	+	0.836901i	$0.684365\pi$
$68$	3.19937			0.387981
$69$	2.43626	−	4.13094i	0.293291	−	0.497306i
$70$	0.136307			0.0162918
$71$	1.77683	+	3.89071i	0.210871	+	0.461742i	0.985281	−	0.170941i	$-0.0546808\pi$
$71$	1.77683	+	3.89071i	0.210871	+	0.461742i	−0.774411	+	0.632683i	$0.781954\pi$
$72$	−0.959493	+	0.281733i	−0.113077	+	0.0332025i
$73$	1.96318	−	2.26563i	0.229773	−	0.265172i	−0.629142	−	0.777290i	$-0.716594\pi$
$73$	1.96318	−	2.26563i	0.229773	−	0.265172i	0.858915	+	0.512118i	$0.171139\pi$
$74$	−5.69755	−	3.66160i	−0.662327	−	0.425652i
$75$	3.26214	+	3.76471i	0.376679	+	0.434711i
$76$	−0.518382	−	3.60543i	−0.0594625	−	0.413571i
$77$	−1.83440	−	0.538629i	−0.209049	−	0.0613824i
$78$	1.36837	−	0.879398i	0.154937	−	0.0995722i
$79$	−0.304200	+	2.11576i	−0.0342252	+	0.238041i	−0.999752	−	0.0222616i	$-0.992913\pi$
$79$	−0.304200	+	2.11576i	−0.0342252	+	0.238041i	0.965527	+	0.260303i	$0.0838224\pi$
$80$	−0.0566239	+	0.123989i	−0.00633074	+	0.0138624i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	1.56648	−	10.8951i	0.172989	−	1.20316i
$83$	5.07208	−	3.25963i	0.556733	−	0.357791i	−0.231818	−	0.972759i	$-0.574468\pi$
$83$	5.07208	−	3.25963i	0.556733	−	0.357791i	0.788552	+	0.614968i	$0.210831\pi$
$84$	0.959493	+	0.281733i	0.104689	+	0.0307395i
$85$	0.0620629	+	0.431657i	0.00673167	+	0.0468198i
$86$	−1.95725	−	2.25879i	−0.211056	−	0.243572i
$87$	−2.92062	−	1.87697i	−0.313124	−	0.201232i
$88$	1.25199	−	1.44488i	0.133463	−	0.154024i
$89$	−9.13618	+	2.68262i	−0.968433	+	0.284358i	−0.727442	−	0.686170i	$-0.759291\pi$
$89$	−9.13618	+	2.68262i	−0.968433	+	0.284358i	−0.240991	+	0.970527i	$0.577473\pi$
$90$	−0.0566239	−	0.123989i	−0.00596868	−	0.0130696i
$91$	−1.62658			−0.170512
$92$	−0.183838	−	4.79231i	−0.0191665	−	0.499633i
$93$	−4.66538			−0.483778
$94$	−4.29067	−	9.39525i	−0.442548	−	0.969046i
$95$	0.476386	−	0.139880i	0.0488762	−	0.0143513i
$96$	−0.654861	+	0.755750i	−0.0668364	+	0.0771334i
$97$	9.61893	+	6.18171i	0.976654	+	0.627658i	0.928559	−	0.371185i	$-0.121048\pi$
$97$	9.61893	+	6.18171i	0.976654	+	0.627658i	0.0480955	+	0.998843i	$0.484685\pi$
$98$	−0.654861	−	0.755750i	−0.0661509	−	0.0763422i
$99$	0.272084	+	1.89238i	0.0273454	+	0.190192i
$100$	4.77964	+	1.40343i	0.477964	+	0.140343i
$101$	−7.28337	+	4.68074i	−0.724722	+	0.465751i	−0.850277	−	0.526336i	$-0.823565\pi$
$101$	−7.28337	+	4.68074i	−0.724722	+	0.465751i	0.125554	+	0.992087i	$0.459929\pi$
$102$	−0.455318	+	3.16681i	−0.0450832	+	0.313561i
$103$	−1.26110	+	2.76142i	−0.124260	+	0.272091i	−0.961531	−	0.274697i	$-0.911422\pi$
$103$	−1.26110	+	2.76142i	−0.124260	+	0.272091i	0.837271	+	0.546788i	$0.184150\pi$
$104$	0.675708	−	1.47959i	0.0662586	−	0.145086i
$105$	−0.0193985	+	0.134919i	−0.00189310	+	0.0131668i
$106$	−1.70138	+	1.09341i	−0.165252	+	0.106201i
$107$	9.30530	+	2.73228i	0.899577	+	0.264140i	0.698647	−	0.715466i	$-0.253786\pi$
$107$	9.30530	+	2.73228i	0.899577	+	0.264140i	0.200929	+	0.979606i	$0.435604\pi$
$108$	−0.142315	−	0.989821i	−0.0136943	−	0.0952456i
$109$	9.87387	+	11.3950i	0.945745	+	1.09145i	0.995694	+	0.0926960i	$0.0295485\pi$
$109$	9.87387	+	11.3950i	0.945745	+	1.09145i	−0.0499496	+	0.998752i	$0.515906\pi$
$110$	0.219228	+	0.140889i	0.0209026	+	0.0134333i
$111$	4.43517	−	5.11846i	0.420968	−	0.485823i
$112$	0.959493	−	0.281733i	0.0906636	−	0.0266212i
$113$	−3.37092	−	7.38130i	−0.317110	−	0.694374i	0.682213	−	0.731153i	$-0.261017\pi$
$113$	−3.37092	−	7.38130i	−0.317110	−	0.694374i	−0.999323	+	0.0367791i	$0.988290\pi$
$114$	3.64250			0.341152
$115$	0.643009	−	0.117767i	0.0599609	−	0.0109818i
$116$	−3.47175			−0.322344
$117$	0.675708	+	1.47959i	0.0624692	+	0.136788i
$118$	13.7907	−	4.04931i	1.26953	−	0.372769i
$119$	2.09514	−	2.41792i	0.192061	−	0.221651i
$120$	−0.114669	−	0.0736930i	−0.0104678	−	0.00672722i
$121$	4.80986	+	5.55087i	0.437260	+	0.504624i
$122$	−1.03867	−	7.22414i	−0.0940371	−	0.654043i
$123$	10.5613	+	3.10107i	0.952278	+	0.279614i
$124$	−3.92477	+	2.52230i	−0.352455	+	0.226509i
$125$	−0.193624	+	1.34669i	−0.0173183	+	0.120451i
$126$	−0.415415	+	0.909632i	−0.0370081	+	0.0810365i
$127$	1.22099	−	2.67359i	0.108345	−	0.237243i	−0.847692	−	0.530489i	$-0.822008\pi$
$127$	1.22099	−	2.67359i	0.108345	−	0.237243i	0.956037	+	0.293246i	$0.0947355\pi$
$128$	−0.142315	+	0.989821i	−0.0125790	+	0.0874887i
$129$	2.51435	−	1.61587i	0.221376	−	0.142270i
$130$	0.212733	+	0.0624642i	0.0186580	+	0.00547847i
$131$	2.84371	+	19.7784i	0.248456	+	1.72805i	0.607145	+	0.794591i	$0.292315\pi$
$131$	2.84371	+	19.7784i	0.248456	+	1.72805i	−0.358690	+	0.933457i	$0.616776\pi$
$132$	1.25199	+	1.44488i	0.108972	+	0.125760i
$133$	−3.06427	−	1.96929i	−0.265706	−	0.170759i
$134$	−5.72362	+	6.60541i	−0.494445	+	0.570620i
$135$	0.130785	−	0.0384020i	0.0112562	−	0.00330512i
$136$	1.32907	+	2.91025i	0.113967	+	0.249552i
$137$	−13.6415			−1.16547			−0.582736	−	0.812661i	$-0.698018\pi$
$137$	−13.6415			−1.16547			−0.582736	+	0.812661i	$0.698018\pi$
$138$	4.76969	+	0.500049i	0.406023	+	0.0425670i
$139$	−2.97477			−0.252317			−0.126158	−	0.992010i	$-0.540265\pi$
$139$	−2.97477			−0.252317			−0.126158	+	0.992010i	$0.540265\pi$
$140$	0.0566239	+	0.123989i	0.00478559	+	0.0104790i
$141$	9.91024	−	2.90991i	0.834593	−	0.245059i
$142$	−2.80099	+	3.23252i	−0.235054	+	0.271267i
$143$	−2.61611	−	1.68127i	−0.218770	−	0.140595i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	−0.0673466	−	0.468406i	−0.00559283	−	0.0388990i
$146$	2.87643	+	0.844595i	0.238055	+	0.0698992i
$147$	0.841254	−	0.540641i	0.0693854	−	0.0445913i
$148$	0.963855	−	6.70376i	0.0792284	−	0.551046i
$149$	7.37263	−	16.1438i	0.603989	−	1.32255i	−0.322621	−	0.946528i	$-0.604564\pi$
$149$	7.37263	−	16.1438i	0.603989	−	1.32255i	0.926610	−	0.376024i	$-0.122709\pi$
$150$	−2.06936	+	4.53126i	−0.168962	+	0.369976i
$151$	−2.67149	+	18.5806i	−0.217403	+	1.51207i	0.530170	+	0.847891i	$0.322128\pi$
$151$	−2.67149	+	18.5806i	−0.217403	+	1.51207i	−0.747573	+	0.664179i	$0.768781\pi$
$152$	3.06427	−	1.96929i	0.248545	−	0.159730i
$153$	−3.06977	−	0.901367i	−0.248177	−	0.0728712i
$154$	−0.272084	−	1.89238i	−0.0219251	−	0.152493i
$155$	−0.416441	−	0.480598i	−0.0334493	−	0.0386026i
$156$	1.36837	+	0.879398i	0.109557	+	0.0704082i
$157$	−2.74049	+	3.16269i	−0.218715	+	0.252410i	−0.854495	−	0.519460i	$-0.826133\pi$
$157$	−2.74049	+	3.16269i	−0.218715	+	0.252410i	0.635780	+	0.771870i	$0.280679\pi$
$158$	−2.05093	+	0.602208i	−0.163163	+	0.0479091i
$159$	−0.840148	−	1.83967i	−0.0666280	−	0.145895i
$160$	−0.136307			−0.0107760
$161$	−3.74217	−	2.99936i	−0.294924	−	0.236383i
$162$	1.00000			0.0785674
$163$	8.48793	+	18.5860i	0.664826	+	1.45577i	0.877956	+	0.478742i	$0.158907\pi$
$163$	8.48793	+	18.5860i	0.664826	+	1.45577i	−0.213130	+	0.977024i	$0.568366\pi$
$164$	10.5613	−	3.10107i	0.824697	−	0.242153i
$165$	−0.170655	+	0.196946i	−0.0132855	+	0.0153322i
$166$	5.07208	+	3.25963i	0.393670	+	0.252996i
$167$	−4.54145	−	5.24112i	−0.351428	−	0.405570i	0.552321	−	0.833631i	$-0.313742\pi$
$167$	−4.54145	−	5.24112i	−0.351428	−	0.405570i	−0.903750	+	0.428061i	$0.859197\pi$
$168$	0.142315	+	0.989821i	0.0109798	+	0.0763664i
$169$	9.93480	+	2.91712i	0.764216	+	0.224394i
$170$	−0.366867	+	0.235771i	−0.0281374	+	0.0180828i
$171$	−0.518382	+	3.60543i	−0.0396417	+	0.275714i
$172$	1.24160	−	2.71872i	0.0946708	−	0.207300i
$173$	3.00735	−	6.58518i	0.228645	−	0.500662i	−0.760186	−	0.649706i	$-0.774892\pi$
$173$	3.00735	−	6.58518i	0.228645	−	0.500662i	0.988831	+	0.149044i	$0.0476195\pi$
$174$	0.494081	−	3.43641i	0.0374562	−	0.260514i
$175$	4.19064	−	2.69316i	0.316782	−	0.203584i
$176$	1.83440	+	0.538629i	0.138273	+	0.0406007i
$177$	2.04547	+	14.2266i	0.153747	+	1.06934i
$178$	−6.23551	−	7.19616i	−0.467371	−	0.539375i
$179$	−8.30040	−	5.33435i	−0.620401	−	0.398708i	0.192343	−	0.981328i	$-0.438391\pi$
$179$	−8.30040	−	5.33435i	−0.620401	−	0.398708i	−0.812745	+	0.582620i	$0.802028\pi$
$180$	0.0892619	−	0.103014i	0.00665319	−	0.00767819i
$181$	18.9272	−	5.55753i	1.40685	−	0.413088i	0.511818	−	0.859094i	$-0.328972\pi$
$181$	18.9272	−	5.55753i	1.40685	−	0.413088i	0.895030	+	0.446007i	$0.147154\pi$
$182$	−0.675708	−	1.47959i	−0.0500868	−	0.109675i
$183$	7.29842			0.539515
$184$	4.28287	−	2.15802i	0.315737	−	0.159091i
$185$	0.923164			0.0678724
$186$	−1.93807	−	4.24378i	−0.142106	−	0.311169i
$187$	5.86893	−	1.72327i	0.429179	−	0.126018i
$188$	6.76381	−	7.80585i	0.493302	−	0.569300i
$189$	−0.841254	−	0.540641i	−0.0611922	−	0.0393258i
$190$	0.325137	+	0.375228i	0.0235879	+	0.0272219i
$191$	3.42778	+	23.8408i	0.248026	+	1.72506i	0.609596	+	0.792712i	$0.291332\pi$
$191$	3.42778	+	23.8408i	0.248026	+	1.72506i	−0.361570	+	0.932345i	$0.617759\pi$
$192$	−0.959493	−	0.281733i	−0.0692454	−	0.0203323i
$193$	−14.2128	+	9.13404i	−1.02306	+	0.657483i	−0.940742	−	0.339123i	$-0.889870\pi$
$193$	−14.2128	+	9.13404i	−1.02306	+	0.657483i	−0.0823213	+	0.996606i	$0.526233\pi$
$194$	−1.62723	+	11.3177i	−0.116829	+	0.812561i
$195$	−0.0921035	+	0.201679i	−0.00659567	+	0.0144425i
$196$	0.415415	−	0.909632i	0.0296725	−	0.0649737i
$197$	−0.929522	+	6.46497i	−0.0662257	+	0.460610i	0.929543	+	0.368714i	$0.120202\pi$
$197$	−0.929522	+	6.46497i	−0.0662257	+	0.460610i	−0.995769	+	0.0918960i	$0.970707\pi$
$198$	−1.60835	+	1.03362i	−0.114300	+	0.0734562i
$199$	22.0076	+	6.46202i	1.56008	+	0.458080i	0.944093	−	0.329678i	$-0.106940\pi$
$199$	22.0076	+	6.46202i	1.56008	+	0.458080i	0.615984	+	0.787758i	$0.288758\pi$
$200$	0.708930	+	4.93072i	0.0501289	+	0.348654i
$201$	−5.72362	−	6.60541i	−0.403713	−	0.465910i
$202$	−7.28337	−	4.68074i	−0.512456	−	0.329336i
$203$	−2.27351	+	2.62377i	−0.159569	+	0.184153i
$204$	−3.06977	+	0.901367i	−0.214927	+	0.0631083i
$205$	0.623267	+	1.36476i	0.0435308	+	0.0953193i
$206$	−3.03576			−0.211511
$207$	−1.17376	+	4.64998i	−0.0815818	+	0.323196i
$208$	1.62658			0.112783
$209$	−2.89291	−	6.33458i	−0.200107	−	0.438172i
$210$	−0.130785	+	0.0384020i	−0.00902505	+	0.00264999i
$211$	11.4965	−	13.2676i	0.791450	−	0.913382i	−0.206430	−	0.978461i	$-0.566185\pi$
$211$	11.4965	−	13.2676i	0.791450	−	0.913382i	0.997880	+	0.0650791i	$0.0207300\pi$
$212$	−1.70138	−	1.09341i	−0.116851	−	0.0750956i
$213$	−2.80099	−	3.23252i	−0.191921	−	0.221488i
$214$	1.38019	+	9.59943i	0.0943478	+	0.656203i
$215$	0.390892	+	0.114776i	0.0266586	+	0.00782768i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	−0.663953	+	4.61789i	−0.0450721	+	0.313483i
$218$	−6.26355	+	13.7153i	−0.424221	+	0.928915i
$219$	−1.24536	+	2.72695i	−0.0841534	+	0.184270i
$220$	−0.0370868	+	0.257945i	−0.00250039	+	0.0173906i
$221$	4.37792	−	2.81352i	0.294491	−	0.189258i
$222$	6.49835	+	1.90809i	0.436141	+	0.128063i
$223$	−0.163799	−	1.13925i	−0.0109688	−	0.0762898i	0.983602	−	0.180354i	$-0.0577243\pi$
$223$	−0.163799	−	1.13925i	−0.0109688	−	0.0762898i	−0.994571	+	0.104064i	$0.966815\pi$
$224$	0.654861	+	0.755750i	0.0437547	+	0.0504956i
$225$	−4.19064	−	2.69316i	−0.279376	−	0.179544i
$226$	5.31393	−	6.13260i	0.353477	−	0.407935i
$227$	12.9620	−	3.80600i	0.860320	−	0.252613i	0.178327	−	0.983971i	$-0.442931\pi$
$227$	12.9620	−	3.80600i	0.860320	−	0.252613i	0.681993	+	0.731358i	$0.261113\pi$
$228$	1.51315	+	3.31334i	0.100211	+	0.219431i
$229$	−12.0292			−0.794912			−0.397456	−	0.917621i	$-0.630107\pi$
$229$	−12.0292			−0.794912			−0.397456	+	0.917621i	$0.630107\pi$
$230$	0.374240	+	0.535979i	0.0246766	+	0.0353414i
$231$	1.91184			0.125790
$232$	−1.44222	−	3.15801i	−0.0946862	−	0.207334i
$233$	−14.3084	+	4.20133i	−0.937376	+	0.275238i	−0.714522	−	0.699613i	$-0.753356\pi$
$233$	−14.3084	+	4.20133i	−0.937376	+	0.275238i	−0.222854	+	0.974852i	$0.571537\pi$
$234$	−1.06519	+	1.22929i	−0.0696334	+	0.0803613i
$235$	1.18437	+	0.761147i	0.0772596	+	0.0496518i
$236$	9.41223	+	10.8623i	0.612684	+	0.707075i
$237$	−0.304200	−	2.11576i	−0.0197599	−	0.137433i
$238$	3.06977	+	0.901367i	0.198984	+	0.0584269i
$239$	−9.18292	+	5.90151i	−0.593994	+	0.381737i	−0.802825	−	0.596215i	$-0.796671\pi$
$239$	−9.18292	+	5.90151i	−0.593994	+	0.381737i	0.208831	+	0.977952i	$0.433034\pi$
$240$	0.0193985	−	0.134919i	0.00125217	−	0.00870900i
$241$	7.01909	−	15.3697i	0.452139	−	0.990047i	−0.537070	−	0.843538i	$-0.680469\pi$
$241$	7.01909	−	15.3697i	0.452139	−	0.990047i	0.989209	−	0.146510i	$-0.0468039\pi$
$242$	−3.05116	+	6.68111i	−0.196136	+	0.429478i
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$	6.13982	−	3.94583i	0.393062	−	0.252606i
$245$	0.130785	+	0.0384020i	0.00835557	+	0.00245342i
$246$	1.56648	+	10.8951i	0.0998751	+	0.694647i
$247$	−3.87994	−	4.47769i	−0.246875	−	0.284909i
$248$	−3.92477	−	2.52230i	−0.249223	−	0.160166i
$249$	−3.94828	+	4.55656i	−0.250212	+	0.288760i
$250$	−1.30542	+	0.383307i	−0.0825622	+	0.0242425i
$251$	1.51969	+	3.32766i	0.0959221	+	0.210040i	0.951510	−	0.307617i	$-0.0995316\pi$
$251$	1.51969	+	3.32766i	0.0959221	+	0.210040i	−0.855588	+	0.517657i	$0.826804\pi$
$252$	−1.00000			−0.0629941
$253$	−2.91851	−	8.69199i	−0.183485	−	0.546461i
$254$	2.93920			0.184422
$255$	−0.181161	−	0.396687i	−0.0113447	−	0.0248415i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−14.1030	+	16.2758i	−0.879722	+	1.01525i	0.120025	+	0.992771i	$0.461703\pi$
$257$	−14.1030	+	16.2758i	−0.879722	+	1.01525i	−0.999747	+	0.0224828i	$0.992843\pi$
$258$	2.51435	+	1.61587i	0.156536	+	0.100600i
$259$	−4.43517	−	5.11846i	−0.275588	−	0.318046i
$260$	0.0315533	+	0.219458i	0.00195685	+	0.0136102i
$261$	3.33112	+	0.978105i	0.206191	+	0.0605432i
$262$	−16.8098	+	10.8030i	−1.03851	+	0.667410i
$263$	−1.53584	+	10.6820i	−0.0947040	+	0.658681i	0.886073	+	0.463547i	$0.153423\pi$
$263$	−1.53584	+	10.6820i	−0.0947040	+	0.658681i	−0.980777	+	0.195134i	$0.937486\pi$
$264$	−0.794209	+	1.73907i	−0.0488802	+	0.107033i
$265$	0.114518	−	0.250759i	0.00703477	−	0.0154040i
$266$	0.518382	−	3.60543i	0.0317840	−	0.221063i
$267$	8.01032	−	5.14792i	0.490223	−	0.315047i
$268$	−8.38617	−	2.46240i	−0.512267	−	0.150415i
$269$	−2.98997	−	20.7957i	−0.182302	−	1.26794i	−0.851303	−	0.524675i	$-0.824187\pi$
$269$	−2.98997	−	20.7957i	−0.182302	−	1.26794i	0.669001	−	0.743261i	$-0.266722\pi$
$270$	0.0892619	+	0.103014i	0.00543231	+	0.00626922i
$271$	4.02078	+	2.58400i	0.244245	+	0.156967i	0.657036	−	0.753859i	$-0.271810\pi$
$271$	4.02078	+	2.58400i	0.244245	+	0.156967i	−0.412791	+	0.910826i	$0.635446\pi$
$272$	−2.09514	+	2.41792i	−0.127037	+	0.146608i
$273$	1.56070	−	0.458262i	0.0944577	−	0.0277353i
$274$	−5.66689	−	12.4088i	−0.342349	−	0.749640i
$275$	9.52370			0.574301
$276$	1.52654	+	4.54639i	0.0918869	+	0.273661i
$277$	24.1777			1.45270			0.726348	−	0.687327i	$-0.241216\pi$
$277$	24.1777			1.45270			0.726348	+	0.687327i	$0.241216\pi$
$278$	−1.23576	−	2.70594i	−0.0741162	−	0.162292i
$279$	4.47640	−	1.31439i	0.267995	−	0.0786905i
$280$	−0.0892619	+	0.103014i	−0.00533442	+	0.00615625i
$281$	17.8692	+	11.4838i	1.06599	+	0.685069i	0.951279	−	0.308330i	$-0.0997702\pi$
$281$	17.8692	+	11.4838i	1.06599	+	0.685069i	0.114709	+	0.993399i	$0.463407\pi$
$282$	6.76381	+	7.80585i	0.402779	+	0.464832i
$283$	0.881887	+	6.13366i	0.0524227	+	0.364608i	0.999100	+	0.0424239i	$0.0135080\pi$
$283$	0.881887	+	6.13366i	0.0524227	+	0.364608i	−0.946677	+	0.322184i	$0.895583\pi$
$284$	−4.10397	−	1.20504i	−0.243526	−	0.0715057i
$285$	−0.417680	+	0.268427i	−0.0247412	+	0.0159002i
$286$	0.442567	−	3.07812i	0.0261696	−	0.182013i
$287$	4.57253	−	10.0124i	0.269908	−	0.591016i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	0.962621	−	6.69518i	0.0566248	−	0.393834i
$290$	0.398100	−	0.255844i	0.0233773	−	0.0150237i
$291$	−10.9709	−	3.22134i	−0.643125	−	0.188838i
$292$	0.426640	+	2.96735i	0.0249672	+	0.173651i
$293$	−4.77665	−	5.51255i	−0.279055	−	0.322046i	0.598869	−	0.800847i	$-0.295617\pi$
$293$	−4.77665	−	5.51255i	−0.279055	−	0.322046i	−0.877924	+	0.478801i	$0.841072\pi$
$294$	0.841254	+	0.540641i	0.0490629	+	0.0315308i
$295$	−1.28295	+	1.48060i	−0.0746963	+	0.0862041i
$296$	6.49835	−	1.90809i	0.377709	−	0.110905i
$297$	−0.794209	−	1.73907i	−0.0460847	−	0.100911i
$298$	17.7476			1.02809
$299$	−4.46590	−	6.39598i	−0.258270	−	0.369889i
$300$	−4.98142			−0.287602
$301$	−1.24160	−	2.71872i	−0.0715644	−	0.156704i
$302$	−18.0113	+	5.28860i	−1.03643	+	0.304325i
$303$	5.66963	−	6.54310i	0.325712	−	0.375891i
$304$	3.06427	+	1.96929i	0.175748	+	0.112946i
$305$	0.651471	+	0.751838i	0.0373031	+	0.0430501i
$306$	−0.455318	−	3.16681i	−0.0260288	−	0.181034i
$307$	−9.57993	−	2.81292i	−0.546755	−	0.160542i	−0.00332253	−	0.999994i	$-0.501058\pi$
$307$	−9.57993	−	2.81292i	−0.546755	−	0.160542i	−0.543433	+	0.839453i	$0.682876\pi$
$308$	1.60835	−	1.03362i	0.0916440	−	0.0588960i
$309$	0.432034	−	3.00486i	0.0245775	−	0.170941i
$310$	0.264172	−	0.578456i	0.0150040	−	0.0328541i
$311$	6.29915	−	13.7932i	0.357192	−	0.782142i	−0.642680	−	0.766135i	$-0.722177\pi$
$311$	6.29915	−	13.7932i	0.357192	−	0.782142i	0.999872	−	0.0160069i	$-0.00509537\pi$
$312$	−0.231487	+	1.61003i	−0.0131054	+	0.0911499i
$313$	−9.13455	+	5.87042i	−0.516315	+	0.331816i	−0.772713	−	0.634756i	$-0.781101\pi$
$313$	−9.13455	+	5.87042i	−0.516315	+	0.331816i	0.256398	+	0.966571i	$0.417464\pi$
$314$	−4.01533	−	1.17901i	−0.226598	−	0.0665352i
$315$	−0.0193985	−	0.134919i	−0.00109298	−	0.00760184i
$316$	−1.39977	−	1.61543i	−0.0787435	−	0.0908748i
$317$	−11.4290	−	7.34500i	−0.641919	−	0.412537i	0.178786	−	0.983888i	$-0.442783\pi$
$317$	−11.4290	−	7.34500i	−0.641919	−	0.412537i	−0.820706	+	0.571351i	$0.806419\pi$
$318$	1.32441	−	1.52845i	0.0742692	−	0.0857112i
$319$	−6.36858	+	1.86998i	−0.356572	+	0.104699i
$320$	−0.0566239	−	0.123989i	−0.00316537	−	0.00693119i
$321$	−9.69814			−0.541297
$322$	1.17376	−	4.64998i	0.0654109	−	0.259133i
$323$	11.6537			0.648430
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	7.77449	−	2.28280i	0.431251	−	0.126627i
$326$	−13.3804	+	15.4418i	−0.741071	+	0.855241i
$327$	−12.6843	−	8.15168i	−0.701441	−	0.450789i
$328$	7.20815	+	8.31864i	0.398003	+	0.459320i
$329$	−1.46992	−	10.2235i	−0.0810391	−	0.563639i
$330$	−0.250041	−	0.0734187i	−0.0137643	−	0.00404157i
$331$	−10.1487	+	6.52219i	−0.557825	+	0.358492i	−0.788974	−	0.614426i	$-0.789388\pi$
$331$	−10.1487	+	6.52219i	−0.557825	+	0.358492i	0.231150	+	0.972918i	$0.425751\pi$
$332$	−0.858044	+	5.96783i	−0.0470913	+	0.327527i
$333$	−2.81348	+	6.16066i	−0.154178	+	0.337602i
$334$	2.88090	−	6.30829i	0.157636	−	0.345174i
$335$	0.169547	−	1.17922i	0.00926332	−	0.0644278i
$336$	−0.841254	+	0.540641i	−0.0458941	+	0.0294944i
$337$	−19.4225	−	5.70295i	−1.05801	−	0.310659i	−0.293960	−	0.955818i	$-0.594973\pi$
$337$	−19.4225	−	5.70295i	−1.05801	−	0.310659i	−0.764049	+	0.645158i	$0.776791\pi$
$338$	1.47356	+	10.2488i	0.0801511	+	0.557463i
$339$	5.31393	+	6.13260i	0.288613	+	0.333077i
$340$	−0.366867	−	0.235771i	−0.0198962	−	0.0127865i
$341$	−5.84102	+	6.74090i	−0.316309	+	0.365040i
$342$	−3.49496	+	1.02621i	−0.188986	+	0.0554912i
$343$	−0.415415	−	0.909632i	−0.0224303	−	0.0491155i
$344$	2.98881			0.161146
$345$	−0.583783	+	0.294153i	−0.0314298	+	0.0158367i
$346$	7.23939			0.389192
$347$	1.11610	+	2.44393i	0.0599156	+	0.131197i	0.937221	−	0.348735i	$-0.113389\pi$
$347$	1.11610	+	2.44393i	0.0599156	+	0.131197i	−0.877306	+	0.479932i	$0.840661\pi$
$348$	3.33112	−	0.978105i	0.178567	−	0.0524319i
$349$	−2.87655	+	3.31971i	−0.153978	+	0.177700i	−0.827498	−	0.561469i	$-0.810236\pi$
$349$	−2.87655	+	3.31971i	−0.153978	+	0.177700i	0.673520	+	0.739169i	$0.264782\pi$
$350$	4.19064	+	2.69316i	0.223999	+	0.143955i
$351$	−1.06519	−	1.22929i	−0.0568555	−	0.0656147i
$352$	0.272084	+	1.89238i	0.0145021	+	0.100864i
$353$	12.8939	+	3.78600i	0.686275	+	0.201509i	0.606238	−	0.795283i	$-0.292678\pi$
$353$	12.8939	+	3.78600i	0.686275	+	0.201509i	0.0800373	+	0.996792i	$0.474496\pi$
$354$	−12.0912	+	7.77056i	−0.642642	+	0.413001i
$355$	0.0829718	−	0.577081i	0.00440368	−	0.0306283i
$356$	3.95553	−	8.66141i	0.209643	−	0.459054i
$357$	−1.32907	+	2.91025i	−0.0703417	+	0.154027i
$358$	1.40418	−	9.76628i	0.0742132	−	0.516164i
$359$	6.21033	−	3.99114i	0.327769	−	0.210644i	−0.366398	−	0.930458i	$-0.619409\pi$
$359$	6.21033	−	3.99114i	0.327769	−	0.210644i	0.694167	+	0.719814i	$0.255773\pi$
$360$	0.130785	+	0.0384020i	0.00689299	+	0.00202397i
$361$	0.815774	+	5.67383i	0.0429355	+	0.298623i
$362$	12.9179	+	14.9081i	0.678952	+	0.783552i
$363$	−6.17888	−	3.97093i	−0.324307	−	0.208420i
$364$	1.06519	−	1.22929i	0.0558309	−	0.0644323i
$365$	−0.392076	+	0.115124i	−0.0205222	+	0.00602586i
$366$	3.03187	+	6.63888i	0.158479	+	0.347020i
$367$	−12.3711			−0.645767			−0.322884	−	0.946439i	$-0.604652\pi$
$367$	−12.3711			−0.645767			−0.322884	+	0.946439i	$0.604652\pi$
$368$	3.74217	+	2.99936i	0.195074	+	0.156352i
$369$	−11.0071			−0.573009
$370$	0.383496	+	0.839739i	0.0199370	+	0.0436560i
$371$	−1.94051	+	0.569784i	−0.100746	+	0.0295817i
$372$	3.05518	−	3.52586i	0.158403	−	0.182807i
$373$	11.3226	+	7.27659i	0.586262	+	0.376767i	0.799889	−	0.600148i	$-0.204892\pi$
$373$	11.3226	+	7.27659i	0.586262	+	0.376767i	−0.213628	+	0.976915i	$0.568528\pi$
$374$	4.00559	+	4.62269i	0.207124	+	0.239034i
$375$	−0.193624	−	1.34669i	−0.00999871	−	0.0695426i
$376$	9.91024	+	2.90991i	0.511082	+	0.150067i
$377$	−4.75064	+	3.05305i	−0.244670	+	0.157240i
$378$	0.142315	−	0.989821i	0.00731989	−	0.0509109i
$379$	9.28290	−	20.3267i	0.476831	−	1.04411i	−0.506492	−	0.862245i	$-0.669058\pi$
$379$	9.28290	−	20.3267i	0.476831	−	1.04411i	0.983323	−	0.181869i	$-0.0582146\pi$
$380$	−0.206253	+	0.451630i	−0.0105805	+	0.0231681i
$381$	−0.418292	+	2.90929i	−0.0214298	+	0.149047i
$382$	−20.2624	+	13.0218i	−1.03671	+	0.666255i
$383$	11.0253	+	3.23731i	0.563364	+	0.165419i	0.551000	−	0.834505i	$-0.314246\pi$
$383$	11.0253	+	3.23731i	0.563364	+	0.165419i	0.0123637	+	0.999924i	$0.496064\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	0.170655	+	0.196946i	0.00869738	+	0.0100373i
$386$	−14.2128	−	9.13404i	−0.723415	−	0.464911i
$387$	−1.95725	+	2.25879i	−0.0994928	+	0.114821i
$388$	−10.9709	+	3.22134i	−0.556962	+	0.163539i
$389$	−7.60829	−	16.6598i	−0.385755	−	0.844686i	−0.998518	−	0.0544195i	$-0.982669\pi$
$389$	−7.60829	−	16.6598i	−0.385755	−	0.844686i	0.612763	−	0.790267i	$-0.290058\pi$
$390$	−0.221714			−0.0112269
$391$	15.2600	+	1.59984i	0.771732	+	0.0809075i
$392$	1.00000			0.0505076
$393$	−8.30074	−	18.1761i	−0.418717	−	0.916862i
$394$	−6.26688	+	1.84012i	−0.315721	+	0.0927040i
$395$	0.190799	−	0.220193i	0.00960012	−	0.0110791i
$396$	−1.60835	−	1.03362i	−0.0808224	−	0.0519414i
$397$	−3.93548	−	4.54179i	−0.197516	−	0.227946i	0.648348	−	0.761344i	$-0.275460\pi$
$397$	−3.93548	−	4.54179i	−0.197516	−	0.227946i	−0.845864	+	0.533398i	$0.820915\pi$
$398$	3.26423	+	22.7032i	0.163621	+	1.13801i
$399$	3.49496	+	1.02621i	0.174967	+	0.0513748i
$400$	−4.19064	+	2.69316i	−0.209532	+	0.134658i
$401$	2.47761	−	17.2322i	0.123726	−	0.860534i	−0.829550	−	0.558433i	$-0.811403\pi$
$401$	2.47761	−	17.2322i	0.123726	−	0.860534i	0.953276	−	0.302101i	$-0.0976881\pi$
$402$	3.63081	−	7.95037i	0.181088	−	0.396528i
$403$	−3.15243	+	6.90287i	−0.157034	+	0.343856i
$404$	1.23213	−	8.56964i	0.0613006	−	0.426355i
$405$	−0.114669	+	0.0736930i	−0.00569792	+	0.00366183i
$406$	−3.33112	−	0.978105i	−0.165321	−	0.0485425i
$407$	−1.84274	−	12.8165i	−0.0913413	−	0.635292i
$408$	−2.09514	−	2.41792i	−0.103725	−	0.119705i
$409$	−21.5325	−	13.8381i	−1.06471	−	0.684250i	−0.113737	−	0.993511i	$-0.536282\pi$
$409$	−21.5325	−	13.8381i	−1.06471	−	0.684250i	−0.950977	+	0.309261i	$0.899918\pi$
$410$	−0.982519	+	1.13389i	−0.0485231	+	0.0559987i
$411$	13.0889	−	3.84326i	0.645629	−	0.189574i
$412$	−1.26110	−	2.76142i	−0.0621300	−	0.136046i
$413$	14.3729			0.707243
$414$	−4.71737	+	0.863983i	−0.231846	+	0.0424625i
$415$	−0.821820			−0.0403416
$416$	0.675708	+	1.47959i	0.0331293	+	0.0725430i
$417$	2.85427	−	0.838089i	0.139774	−	0.0410414i
$418$	4.56038	−	5.26296i	0.223056	−	0.257420i
$419$	7.34248	+	4.71872i	0.358704	+	0.230525i	0.707563	−	0.706650i	$-0.249795\pi$
$419$	7.34248	+	4.71872i	0.358704	+	0.230525i	−0.348859	+	0.937175i	$0.613431\pi$
$420$	−0.0892619	−	0.103014i	−0.00435554	−	0.00502656i
$421$	4.02540	+	27.9973i	0.196186	+	1.36450i	0.815225	+	0.579144i	$0.196613\pi$
$421$	4.02540	+	27.9973i	0.196186	+	1.36450i	−0.619039	+	0.785360i	$0.712478\pi$
$422$	16.8445	+	4.94599i	0.819977	+	0.240767i
$423$	−8.68899	+	5.58408i	−0.422473	+	0.271507i
$424$	0.287822	−	2.00184i	0.0139779	−	0.0972181i
$425$	−6.62064	+	14.4972i	−0.321148	+	0.703216i
$426$	1.77683	−	3.89071i	0.0860875	−	0.188505i
$427$	1.03867	−	7.22414i	0.0502650	−	0.349600i
$428$	−8.15859	+	5.24321i	−0.394360	+	0.253440i
$429$	2.98381	+	0.876125i	0.144060	+	0.0422997i
$430$	0.0579783	+	0.403248i	0.00279596	+	0.0194463i
$431$	17.1618	+	19.8058i	0.826655	+	0.954011i	0.999521	−	0.0309345i	$-0.00984832\pi$
$431$	17.1618	+	19.8058i	0.826655	+	0.954011i	−0.172866	+	0.984945i	$0.555303\pi$
$432$	0.841254	+	0.540641i	0.0404748	+	0.0260116i
$433$	14.4486	−	16.6746i	0.694357	−	0.801330i	−0.293622	−	0.955922i	$-0.594861\pi$
$433$	14.4486	−	16.6746i	0.694357	−	0.801330i	0.987979	+	0.154591i	$0.0494061\pi$
$434$	−4.47640	+	1.31439i	−0.214874	+	0.0630927i
$435$	0.196584	+	0.430459i	0.00942547	+	0.0206389i
$436$	−15.0778			−0.722096
$437$	−0.669631	−	17.4560i	−0.0320328	−	0.835033i
$438$	−2.99786			−0.143243
$439$	−14.2215	−	31.1408i	−0.678757	−	1.48627i	−0.863955	−	0.503569i	$-0.832020\pi$
$439$	−14.2215	−	31.1408i	−0.678757	−	1.48627i	0.185198	−	0.982701i	$-0.440707\pi$
$440$	−0.250041	+	0.0734187i	−0.0119202	+	0.00350010i
$441$	−0.654861	+	0.755750i	−0.0311838	+	0.0359881i
$442$	4.37792	+	2.81352i	0.208237	+	0.133826i
$443$	−18.0134	−	20.7886i	−0.855844	−	0.987697i	0.144154	−	0.989555i	$-0.453954\pi$
$443$	−18.0134	−	20.7886i	−0.855844	−	0.987697i	−0.999998	+	0.00185838i	$0.999408\pi$
$444$	0.963855	+	6.70376i	0.0457425	+	0.318146i
$445$	1.24532	+	0.365660i	0.0590340	+	0.0173339i
$446$	0.968253	−	0.622258i	0.0458481	−	0.0294648i
$447$	−2.52575	+	17.5670i	−0.119464	+	0.830890i
$448$	−0.415415	+	0.909632i	−0.0196265	+	0.0429761i
$449$	8.71756	−	19.0888i	0.411407	−	0.900856i	−0.584578	−	0.811338i	$-0.698740\pi$
$449$	8.71756	−	19.0888i	0.411407	−	0.900856i	0.995985	−	0.0895187i	$-0.0285329\pi$
$450$	0.708930	−	4.93072i	0.0334193	−	0.232436i
$451$	17.7033	−	11.3772i	0.833615	−	0.535732i
$452$	7.78590	+	2.28615i	0.366218	+	0.107531i
$453$	−2.67149	−	18.5806i	−0.125518	−	0.872994i
$454$	8.84668	+	10.2096i	0.415195	+	0.479161i
$455$	0.186518	+	0.119868i	0.00874410	+	0.00561949i
$456$	−2.38533	+	2.75282i	−0.111703	+	0.128913i
$457$	−17.7720	+	5.21832i	−0.831338	+	0.244103i	−0.669592	−	0.742729i	$-0.733531\pi$
$457$	−17.7720	+	5.21832i	−0.831338	+	0.244103i	−0.161746	+	0.986832i	$0.551713\pi$
$458$	−4.99711	−	10.9421i	−0.233500	−	0.511293i
$459$	3.19937			0.149334
$460$	−0.332079	+	0.563074i	−0.0154833	+	0.0262535i
$461$	−21.8897			−1.01951			−0.509753	−	0.860321i	$-0.670263\pi$
$461$	−21.8897			−1.01951			−0.509753	+	0.860321i	$0.670263\pi$
$462$	0.794209	+	1.73907i	0.0369499	+	0.0809091i
$463$	7.90548	−	2.32126i	0.367399	−	0.107878i	−0.0928215	−	0.995683i	$-0.529589\pi$
$463$	7.90548	−	2.32126i	0.367399	−	0.107878i	0.460220	+	0.887805i	$0.347770\pi$
$464$	2.27351	−	2.62377i	0.105545	−	0.121806i
$465$	0.534972	+	0.343806i	0.0248087	+	0.0159436i
$466$	−9.76560	−	11.2701i	−0.452383	−	0.522077i
$467$	5.88751	+	40.9486i	0.272442	+	1.89487i	0.422770	+	0.906237i	$0.361058\pi$
$467$	5.88751	+	40.9486i	0.272442	+	1.89487i	−0.150329	+	0.988636i	$0.548033\pi$
$468$	−1.56070	−	0.458262i	−0.0721432	−	0.0211832i
$469$	−7.35273	+	4.72531i	−0.339518	+	0.218195i
$470$	−0.200359	+	1.39353i	−0.00924189	+	0.0642788i
$471$	1.73845	−	3.80667i	0.0801034	−	0.175402i
$472$	−5.97071	+	13.0740i	−0.274824	+	0.601781i
$473$	0.813206	−	5.65597i	0.0373913	−	0.260062i
$474$	1.79819	−	1.15563i	0.0825937	−	0.0530797i
$475$	17.4098	+	5.11199i	0.798818	+	0.234554i
$476$	0.455318	+	3.16681i	0.0208695	+	0.145150i
$477$	1.32441	+	1.52845i	0.0606406	+	0.0699829i
$478$	−9.18292	−	5.90151i	−0.420017	−	0.269929i
$479$	1.60659	−	1.85410i	0.0734070	−	0.0847162i	−0.717858	−	0.696189i	$-0.754877\pi$
$479$	1.60659	−	1.85410i	0.0734070	−	0.0847162i	0.791265	+	0.611473i	$0.209423\pi$
$480$	0.130785	−	0.0384020i	0.00596951	−	0.00175281i
$481$	−4.57636	−	10.0208i	−0.208664	−	0.456911i
$482$	16.8966			0.769618
$483$	4.43560	+	1.82357i	0.201827	+	0.0829754i
$484$	−7.34485			−0.333857
$485$	−0.647440	−	1.41770i	−0.0293987	−	0.0643742i
$486$	−0.959493	+	0.281733i	−0.0435235	+	0.0127796i
$487$	−10.9280	+	12.6116i	−0.495197	+	0.571487i	−0.947247	−	0.320505i	$-0.896147\pi$
$487$	−10.9280	+	12.6116i	−0.495197	+	0.571487i	0.452050	+	0.891993i	$0.350693\pi$
$488$	6.13982	+	3.94583i	0.277937	+	0.178619i
$489$	−13.3804	−	15.4418i	−0.605082	−	0.698302i
$490$	0.0193985	+	0.134919i	0.000876333	+	0.00609503i
$491$	18.2475	+	5.35795i	0.823499	+	0.241801i	0.666222	−	0.745754i	$-0.267910\pi$
$491$	18.2475	+	5.35795i	0.823499	+	0.241801i	0.157277	+	0.987555i	$0.449729\pi$
$492$	−9.25980	+	5.95091i	−0.417464	+	0.268288i
$493$	1.58075	−	10.9944i	0.0711934	−	0.495161i
$494$	2.46127	−	5.38942i	0.110738	−	0.242482i
$495$	0.108256	−	0.237048i	0.00486574	−	0.0106545i
$496$	0.663953	−	4.61789i	0.0298124	−	0.207350i
$497$	−3.59824	+	2.31245i	−0.161403	+	0.103727i
$498$	−5.78497	−	1.69862i	−0.259231	−	0.0761170i
$499$	−2.66547	−	18.5388i	−0.119323	−	0.829910i	−0.958304	−	0.285749i	$-0.907757\pi$
$499$	−2.66547	−	18.5388i	−0.119323	−	0.829910i	0.838981	−	0.544160i	$-0.183152\pi$
$500$	−0.890961	−	1.02822i	−0.0398450	−	0.0459836i
$501$	5.83409	+	3.74934i	0.260648	+	0.167508i
$502$	−2.39564	+	2.76472i	−0.106923	+	0.123396i
$503$	−28.0139	+	8.22563i	−1.24908	+	0.366763i	−0.838419	−	0.545026i	$-0.816520\pi$
$503$	−28.0139	+	8.22563i	−1.24908	+	0.366763i	−0.410660	+	0.911789i	$0.634702\pi$
$504$	−0.415415	−	0.909632i	−0.0185041	−	0.0405182i
$505$	1.18011			0.0525142
$506$	6.69412	−	6.26555i	0.297590	−	0.278538i
$507$	−10.3542			−0.459847
$508$	1.22099	+	2.67359i	0.0541726	+	0.118622i
$509$	35.6368	−	10.4639i	1.57957	−	0.463804i	0.629803	−	0.776755i	$-0.283136\pi$
$509$	35.6368	−	10.4639i	1.57957	−	0.463804i	0.949769	+	0.312951i	$0.101318\pi$
$510$	0.285582	−	0.329579i	0.0126458	−	0.0145940i
$511$	2.52196	+	1.62077i	0.111565	+	0.0716985i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	−0.518382	−	3.60543i	−0.0228871	−	0.159183i
$514$	−20.6636	−	6.06737i	−0.911430	−	0.267620i
$515$	0.348106	−	0.223714i	0.0153394	−	0.00985803i
$516$	−0.425352	+	2.95839i	−0.0187251	+	0.130236i
$517$	8.20308	−	17.9622i	0.360771	−	0.789979i
$518$	2.81348	−	6.16066i	0.123617	−	0.270684i
$519$	−1.03027	+	7.16570i	−0.0452239	+	0.314539i
$520$	−0.186518	+	0.119868i	−0.00817936	+	0.00525655i
$521$	−9.36233	−	2.74903i	−0.410171	−	0.120437i	0.0701361	−	0.997537i	$-0.477657\pi$
$521$	−9.36233	−	2.74903i	−0.410171	−	0.120437i	−0.480307	+	0.877100i	$0.659475\pi$
$522$	0.494081	+	3.43641i	0.0216254	+	0.150408i
$523$	−0.113608	−	0.131111i	−0.00496775	−	0.00573309i	0.753260	−	0.657723i	$-0.228480\pi$
$523$	−0.113608	−	0.131111i	−0.00496775	−	0.00573309i	−0.758228	+	0.651989i	$0.773935\pi$
$524$	−16.8098	−	10.8030i	−0.734338	−	0.471930i
$525$	−3.26214	+	3.76471i	−0.142371	+	0.164305i
$526$	−10.3547	+	3.04042i	−0.451487	+	0.132568i
$527$	−6.20060	−	13.5774i	−0.270103	−	0.591442i
$528$	−1.91184			−0.0832023
$529$	1.51954	−	22.9497i	0.0660669	−	0.997815i
$530$	0.275671			0.0119744
$531$	−5.97071	−	13.0740i	−0.259107	−	0.567364i
$532$	3.49496	−	1.02621i	0.151526	−	0.0444919i
$533$	11.7247	−	13.5310i	0.507851	−	0.586092i
$534$	8.01032	+	5.14792i	0.346640	+	0.222772i
$535$	−0.865674	−	0.999042i	−0.0374264	−	0.0431923i
$536$	−1.24386	−	8.65124i	−0.0537266	−	0.373677i
$537$	9.46704	+	2.77977i	0.408533	+	0.119956i
$538$	17.6744	−	11.3586i	0.761996	−	0.489705i
$539$	0.272084	−	1.89238i	0.0117195	−	0.0815108i
$540$	−0.0566239	+	0.123989i	−0.00243670	+	0.00533563i
$541$	12.1054	−	26.5071i	0.520452	−	1.13963i	−0.448817	−	0.893624i	$-0.648154\pi$
$541$	12.1054	−	26.5071i	0.520452	−	1.13963i	0.969268	−	0.246006i	$-0.0791184\pi$
$542$	−0.680195	+	4.73086i	−0.0292169	+	0.203208i
$543$	−16.5948	+	10.6648i	−0.712150	+	0.457671i
$544$	−3.06977	−	0.901367i	−0.131615	−	0.0386458i
$545$	−0.292486	−	2.03429i	−0.0125287	−	0.0871393i
$546$	1.06519	+	1.22929i	0.0455858	+	0.0526088i
$547$	−14.4889	−	9.31145i	−0.619501	−	0.398129i	0.192908	−	0.981217i	$-0.438208\pi$
$547$	−14.4889	−	9.31145i	−0.619501	−	0.398129i	−0.812409	+	0.583088i	$0.801844\pi$
$548$	8.93329	−	10.3096i	0.381611	−	0.440403i
$549$	−7.00279	+	2.05620i	−0.298872	+	0.0877566i
$550$	3.95629	+	8.66306i	0.168697	+	0.369394i
$551$	−12.6459			−0.538732
$552$	−3.50140	+	3.27723i	−0.149029	+	0.139488i
$553$	−2.13751			−0.0908964
$554$	10.0438	+	21.9928i	0.426719	+	0.934384i
$555$	−0.885769	+	0.260085i	−0.0375988	+	0.0110400i
$556$	1.94806	−	2.24818i	0.0826161	−	0.0953441i
$557$	−18.6442	−	11.9819i	−0.789979	−	0.507689i	0.0823528	−	0.996603i	$-0.473757\pi$
$557$	−18.6442	−	11.9819i	−0.789979	−	0.507689i	−0.872332	+	0.488915i	$0.837393\pi$
$558$	3.05518	+	3.52586i	0.129336	+	0.149262i
$559$	−0.691871	−	4.81207i	−0.0292630	−	0.203529i
$560$	−0.130785	−	0.0384020i	−0.00552669	−	0.00162278i
$561$	−5.14569	+	3.30694i	−0.217251	+	0.139619i
$562$	−3.02293	+	21.0250i	−0.127515	+	0.886885i
$563$	−1.08323	+	2.37195i	−0.0456529	+	0.0999659i	−0.931084	−	0.364804i	$-0.881136\pi$
$563$	−1.08323	+	2.37195i	−0.0456529	+	0.0999659i	0.885431	+	0.464770i	$0.153863\pi$
$564$	−4.29067	+	9.39525i	−0.180670	+	0.395611i
$565$	−0.157411	+	1.09482i	−0.00662232	+	0.0460592i
$566$	−5.21302	+	3.35021i	−0.219120	+	0.140820i
$567$	0.959493	+	0.281733i	0.0402949	+	0.0118317i
$568$	−0.608714	−	4.23370i	−0.0255411	−	0.177642i
$569$	5.32733	+	6.14807i	0.223333	+	0.257741i	0.856348	−	0.516400i	$-0.172728\pi$
$569$	5.32733	+	6.14807i	0.223333	+	0.257741i	−0.633014	+	0.774140i	$0.718183\pi$
$570$	−0.417680	−	0.268427i	−0.0174947	−	0.0112432i
$571$	−26.9010	+	31.0454i	−1.12577	+	1.29921i	−0.176659	+	0.984272i	$0.556529\pi$
$571$	−26.9010	+	31.0454i	−1.12577	+	1.29921i	−0.949112	+	0.314937i	$0.898016\pi$
$572$	2.98381	−	0.876125i	0.124759	−	0.0366326i
$573$	−10.0057	−	21.9093i	−0.417992	−	0.915275i
$574$	11.0071			0.459429
$575$	22.0956	+	9.08397i	0.921451	+	0.378828i
$576$	1.00000			0.0416667
$577$	18.3635	+	40.2104i	0.764482	+	1.67398i	0.738439	+	0.674321i	$0.235563\pi$
$577$	18.3635	+	40.2104i	0.764482	+	1.67398i	0.0260430	+	0.999661i	$0.491709\pi$
$578$	6.49004	−	1.90565i	0.269950	−	0.0792644i
$579$	11.0638	−	12.7683i	0.459795	−	0.530631i
$580$	0.398100	+	0.255844i	0.0165302	+	0.0106233i
$581$	3.94828	+	4.55656i	0.163802	+	0.189038i
$582$	−1.62723	−	11.3177i	−0.0674510	−	0.469132i
$583$	−3.70995	−	1.08934i	−0.153650	−	0.0451158i
$584$	−2.52196	+	1.62077i	−0.104359	+	0.0670678i
$585$	0.0315533	−	0.219458i	0.00130457	−	0.00907346i
$586$	3.03010	−	6.63499i	0.125172	−	0.274089i
$587$	3.47958	−	7.61923i	0.143618	−	0.314479i	−0.824130	−	0.566401i	$-0.808335\pi$
$587$	3.47958	−	7.61923i	0.143618	−	0.314479i	0.967748	+	0.251922i	$0.0810626\pi$
$588$	−0.142315	+	0.989821i	−0.00586897	+	0.0408195i
$589$	−14.2960	+	9.18747i	−0.589056	+	0.378563i
$590$	−1.87976	−	0.551948i	−0.0773885	−	0.0227233i
$591$	−0.929522	−	6.46497i	−0.0382354	−	0.265933i
$592$	4.43517	+	5.11846i	0.182284	+	0.210367i
$593$	−8.21549	−	5.27978i	−0.337370	−	0.216814i	0.360976	−	0.932575i	$-0.382444\pi$
$593$	−8.21549	−	5.27978i	−0.337370	−	0.216814i	−0.698346	+	0.715761i	$0.746080\pi$
$594$	1.25199	−	1.44488i	0.0513698	−	0.0592840i
$595$	−0.418431	+	0.122862i	−0.0171540	+	0.00503687i
$596$	7.37263	+	16.1438i	0.301995	+	0.661276i
$597$	−22.9367			−0.938737
$598$	3.96279	−	6.71932i	0.162050	−	0.274773i
$599$	−10.7675			−0.439947			−0.219973	−	0.975506i	$-0.570597\pi$
$599$	−10.7675			−0.439947			−0.219973	+	0.975506i	$0.570597\pi$
$600$	−2.06936	−	4.53126i	−0.0844811	−	0.184988i
$601$	−42.9607	+	12.6144i	−1.75240	+	0.514552i	−0.991016	−	0.133744i	$-0.957300\pi$
$601$	−42.9607	+	12.6144i	−1.75240	+	0.514552i	−0.761388	+	0.648296i	$0.775482\pi$
$602$	1.95725	−	2.25879i	0.0797717	−	0.0920614i
$603$	7.35273	+	4.72531i	0.299426	+	0.192430i
$604$	−12.2929	−	14.1867i	−0.500189	−	0.577249i
$605$	−0.142479	−	0.990962i	−0.00579259	−	0.0402884i
$606$	8.30706	+	2.43917i	0.337451	+	0.0990846i
$607$	−34.6868	+	22.2918i	−1.40789	+	0.904797i	−0.999966	−	0.00821777i	$-0.997384\pi$
$607$	−34.6868	+	22.2918i	−1.40789	+	0.904797i	−0.407926	+	0.913015i	$0.633748\pi$
$608$	−0.518382	+	3.60543i	−0.0210232	+	0.146219i
$609$	1.44222	−	3.15801i	0.0584416	−	0.127969i
$610$	−0.413265	+	0.904924i	−0.0167326	+	0.0366393i
$611$	2.39094	−	16.6294i	0.0967272	−	0.672753i
$612$	2.69148	−	1.72971i	0.108797	−	0.0699194i
$613$	22.7311	+	6.67445i	0.918100	+	0.269578i	0.706447	−	0.707766i	$-0.250297\pi$
$613$	22.7311	+	6.67445i	0.918100	+	0.269578i	0.211653	+	0.977345i	$0.432115\pi$
$614$	−1.42092	−	9.88274i	−0.0573438	−	0.398835i
$615$	−0.982519	−	1.13389i	−0.0396190	−	0.0457227i
$616$	1.60835	+	1.03362i	0.0648021	+	0.0416458i
$617$	9.39207	−	10.8390i	0.378110	−	0.436363i	−0.534515	−	0.845159i	$-0.679506\pi$
$617$	9.39207	−	10.8390i	0.378110	−	0.436363i	0.912626	+	0.408796i	$0.134051\pi$
$618$	2.91279	−	0.855273i	0.117170	−	0.0344041i
$619$	−4.83410	−	10.5852i	−0.194299	−	0.425456i	0.787258	−	0.616623i	$-0.211500\pi$
$619$	−4.83410	−	10.5852i	−0.194299	−	0.425456i	−0.981557	+	0.191168i	$0.938773\pi$
$620$	0.635923			0.0255393
$621$	−0.183838	−	4.79231i	−0.00737718	−	0.192309i
$622$	15.1635			0.608002
$623$	−3.95553	−	8.66141i	−0.158475	−	0.347012i
$624$	−1.56070	+	0.458262i	−0.0624779	+	0.0183452i
$625$	−16.1892	+	18.6834i	−0.647570	+	0.747335i
$626$	−9.13455	−	5.87042i	−0.365090	−	0.234629i
$627$	4.56038	+	5.26296i	0.182124	+	0.210182i
$628$	−0.595565	−	4.14225i	−0.0237656	−	0.165294i
$629$	20.7906	+	6.10468i	0.828977	+	0.243410i
$630$	0.114669	−	0.0736930i	0.00456850	−	0.00293600i
$631$	3.40738	−	23.6989i	0.135646	−	0.943437i	−0.802366	−	0.596833i	$-0.796426\pi$
$631$	3.40738	−	23.6989i	0.135646	−	0.943437i	0.938012	−	0.346604i	$-0.112665\pi$
$632$	0.887956	−	1.94435i	0.0353210	−	0.0773422i
$633$	−7.29286	+	15.9691i	−0.289865	+	0.634717i
$634$	1.93345	−	13.4475i	0.0767872	−	0.534067i
$635$	−0.337034	+	0.216599i	−0.0133748	+	0.00859545i
$636$	1.94051	+	0.569784i	0.0769461	+	0.0225934i
$637$	−0.231487	−	1.61003i	−0.00917185	−	0.0637917i
$638$	−4.34660	−	5.01625i	−0.172084	−	0.198595i
$639$	3.59824	+	2.31245i	0.142344	+	0.0914790i
$640$	0.0892619	−	0.103014i	0.00352839	−	0.00407198i
$641$	14.1078	−	4.14243i	0.557226	−	0.163616i	0.00901928	−	0.999959i	$-0.497129\pi$
$641$	14.1078	−	4.14243i	0.557226	−	0.163616i	0.548206	+	0.836343i	$0.315311\pi$
$642$	−4.02875	−	8.82174i	−0.159002	−	0.348166i
$643$	−34.3156			−1.35327			−0.676637	−	0.736317i	$-0.736563\pi$
$643$	−34.3156			−1.35327			−0.676637	+	0.736317i	$0.736563\pi$
$644$	4.71737	−	0.863983i	0.185890	−	0.0340457i
$645$	−0.407395			−0.0160411
$646$	4.84113	+	10.6006i	0.190472	+	0.417075i
$647$	13.2870	−	3.90141i	0.522365	−	0.153380i	−0.00991157	−	0.999951i	$-0.503155\pi$
$647$	13.2870	−	3.90141i	0.522365	−	0.153380i	0.532276	+	0.846571i	$0.321337\pi$
$648$	−0.654861	+	0.755750i	−0.0257254	+	0.0296886i
$649$	23.1165	+	14.8561i	0.907404	+	0.583153i
$650$	5.30614	+	6.12361i	0.208124	+	0.240188i
$651$	−0.663953	−	4.61789i	−0.0260224	−	0.180990i
$652$	−19.6048	−	5.75648i	−0.767781	−	0.225441i
$653$	−22.5361	+	14.4830i	−0.881904	+	0.566765i	−0.901372	−	0.433045i	$-0.857439\pi$
$653$	−22.5361	+	14.4830i	−0.881904	+	0.566765i	0.0194682	+	0.999810i	$0.493803\pi$
$654$	2.14580	−	14.9243i	0.0839073	−	0.583588i
$655$	1.13145	−	2.47752i	0.0442093	−	0.0968048i
$656$	−4.57253	+	10.0124i	−0.178527	+	0.390920i
$657$	0.426640	−	2.96735i	0.0166448	−	0.115767i
$658$	8.68899	−	5.58408i	0.338732	−	0.217690i
$659$	−0.687236	−	0.201791i	−0.0267709	−	0.00786065i	0.268320	−	0.963330i	$-0.413532\pi$
$659$	−0.687236	−	0.201791i	−0.0267709	−	0.00786065i	−0.295091	+	0.955469i	$0.595350\pi$
$660$	−0.0370868	−	0.257945i	−0.00144360	−	0.0100405i
$661$	21.7988	+	25.1572i	0.847875	+	0.978500i	0.999951	−	0.00986886i	$-0.00314141\pi$
$661$	21.7988	+	25.1572i	0.847875	+	0.978500i	−0.152076	+	0.988369i	$0.548596\pi$
$662$	−10.1487	−	6.52219i	−0.394442	−	0.253492i
$663$	−3.40793	+	3.93296i	−0.132353	+	0.152743i
$664$	−5.78497	+	1.69862i	−0.224500	+	0.0659193i
$665$	0.206253	+	0.451630i	0.00799813	+	0.0175135i
$666$	−6.77270			−0.262437
$667$	−16.5592	−	1.73605i	−0.641174	−	0.0672200i
$668$	6.93499			0.268323
$669$	0.478128	+	1.04695i	0.0184855	+	0.0404776i
$670$	1.14309	−	0.335642i	0.0441615	−	0.0129670i
$671$	9.13756	−	10.5453i	0.352752	−	0.407097i
$672$	−0.841254	−	0.540641i	−0.0324521	−	0.0208557i
$673$	−12.6529	−	14.6022i	−0.487734	−	0.562875i	0.457525	−	0.889197i	$-0.348736\pi$
$673$	−12.6529	−	14.6022i	−0.487734	−	0.562875i	−0.945259	+	0.326322i	$0.894191\pi$
$674$	−2.88080	−	20.0364i	−0.110964	−	0.771773i
$675$	4.77964	+	1.40343i	0.183968	+	0.0540180i
$676$	−8.71053	+	5.59791i	−0.335020	+	0.215304i
$677$	−6.20694	+	43.1702i	−0.238552	+	1.65917i	0.420666	+	0.907216i	$0.361796\pi$
$677$	−6.20694	+	43.1702i	−0.238552	+	1.65917i	−0.659218	+	0.751952i	$0.729113\pi$
$678$	−3.37092	+	7.38130i	−0.129460	+	0.283477i
$679$	−4.74987	+	10.4008i	−0.182283	+	0.399145i
$680$	0.0620629	−	0.431657i	0.00238000	−	0.0165533i
$681$	−11.3647	+	7.30365i	−0.435497	+	0.279877i
$682$	−8.55818	−	2.51291i	−0.327710	−	0.0962242i
$683$	3.10984	+	21.6294i	0.118995	+	0.827626i	0.958666	+	0.284532i	$0.0918383\pi$
$683$	3.10984	+	21.6294i	0.118995	+	0.827626i	−0.839672	+	0.543094i	$0.817253\pi$
$684$	−2.38533	−	2.75282i	−0.0912054	−	0.105257i
$685$	1.56425	+	1.00528i	0.0597670	+	0.0384099i
$686$	0.654861	−	0.755750i	0.0250027	−	0.0288547i
$687$	11.5419	−	3.38902i	0.440352	−	0.129299i
$688$	1.24160	+	2.71872i	0.0473354	+	0.103650i
$689$	−3.28965			−0.125326
$690$	−0.510083	−	0.408833i	−0.0194185	−	0.0155640i
$691$	−9.10252			−0.346276			−0.173138	−	0.984898i	$-0.555391\pi$
$691$	−9.10252			−0.346276			−0.173138	+	0.984898i	$0.555391\pi$
$692$	3.00735	+	6.58518i	0.114322	+	0.250331i
$693$	−1.83440	+	0.538629i	−0.0696831	+	0.0204608i
$694$	−1.75943	+	2.03049i	−0.0667869	+	0.0770762i
$695$	0.341112	+	0.219220i	0.0129391	+	0.00831547i
$696$	2.27351	+	2.62377i	0.0861773	+	0.0994539i
$697$	5.01175	+	34.8575i	0.189834	+	1.32032i
$698$	−4.21467	−	1.23754i	−0.159528	−	0.0468416i
$699$	12.5452	−	8.06229i	0.474502	−	0.304944i
$700$	−0.708930	+	4.93072i	−0.0267950	+	0.186364i
$701$	−7.81411	+	17.1105i	−0.295135	+	0.646255i	−0.997873	−	0.0651939i	$-0.979233\pi$
$701$	−7.81411	+	17.1105i	−0.295135	+	0.646255i	0.702738	+	0.711449i	$0.251961\pi$
$702$	0.675708	−	1.47959i	0.0255029	−	0.0558437i
$703$	3.51084	−	24.4185i	0.132414	−	0.920960i
$704$	−1.60835	+	1.03362i	−0.0606168	+	0.0389561i
$705$	−1.35083	−	0.396640i	−0.0508753	−	0.0149383i
$706$	1.91247	+	13.3015i	0.0719767	+	0.500609i
$707$	−5.66963	−	6.54310i	−0.213228	−	0.246079i
$708$	−12.0912	−	7.77056i	−0.454416	−	0.292036i
$709$	−7.26728	+	8.38689i	−0.272928	+	0.314976i	−0.875622	−	0.482996i	$-0.839548\pi$
$709$	−7.26728	+	8.38689i	−0.272928	+	0.314976i	0.602694	+	0.797972i	$0.294094\pi$
$710$	0.559399	−	0.164254i	0.0209939	−	0.00616436i
$711$	0.887956	+	1.94435i	0.0333009	+	0.0729189i
$712$	9.52188			0.356848
$713$	−19.9812	+	10.0680i	−0.748302	+	0.377049i
$714$	−3.19937			−0.119733
$715$	0.176088	+	0.385578i	0.00658530	+	0.0144198i
$716$	9.46704	−	2.77977i	0.353800	−	0.103885i
$717$	7.14830	−	8.24958i	0.266958	−	0.308086i
$718$	6.21033	+	3.99114i	0.231768	+	0.148948i
$719$	23.3566	+	26.9549i	0.871053	+	1.00525i	0.999908	+	0.0135850i	$0.00432436\pi$
$719$	23.3566	+	26.9549i	0.871053	+	1.00525i	−0.128855	+	0.991663i	$0.541130\pi$
$720$	0.0193985	+	0.134919i	0.000722938	+	0.00502815i
$721$	−2.91279	−	0.855273i	−0.108478	−	0.0318520i
$722$	−4.82222	+	3.09905i	−0.179464	+	0.115335i
$723$	−2.40463	+	16.7246i	−0.0894293	+	0.621994i
$724$	−8.19458	+	17.9436i	−0.304549	+	0.666870i
$725$	7.18429	−	15.7314i	0.266818	−	0.584249i
$726$	1.04528	−	7.27009i	0.0387940	−	0.269818i
$727$	−28.3042	+	18.1900i	−1.04974	+	0.674630i	−0.947378	−	0.320117i	$-0.896278\pi$
$727$	−28.3042	+	18.1900i	−1.04974	+	0.674630i	−0.102367	+	0.994747i	$0.532642\pi$
$728$	1.56070	+	0.458262i	0.0578433	+	0.0169843i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−0.267595	−	0.308821i	−0.00990413	−	0.0114300i
$731$	8.04432	+	5.16977i	0.297530	+	0.191211i
$732$	−4.77945	+	5.51578i	−0.176654	+	0.203869i
$733$	20.5007	−	6.01955i	0.757211	−	0.222337i	0.119734	−	0.992806i	$-0.461796\pi$
$733$	20.5007	−	6.01955i	0.757211	−	0.222337i	0.637478	+	0.770469i	$0.279978\pi$
$734$	−5.13915	−	11.2532i	−0.189690	−	0.415362i
$735$	−0.136307			−0.00502775
$736$	−1.17376	+	4.64998i	−0.0432653	+	0.171400i
$737$	−16.7099			−0.615518
$738$	−4.57253	−	10.0124i	−0.168317	−	0.368563i
$739$	−6.40363	+	1.88028i	−0.235561	+	0.0691670i	−0.397383	−	0.917653i	$-0.630081\pi$
$739$	−6.40363	+	1.88028i	−0.235561	+	0.0691670i	0.161821	+	0.986820i	$0.448263\pi$
$740$	−0.604544	+	0.697681i	−0.0222235	+	0.0256473i
$741$	4.98429	+	3.20321i	0.183103	+	0.117673i
$742$	−1.32441	−	1.52845i	−0.0486206	−	0.0561112i
$743$	2.15905	+	15.0165i	0.0792077	+	0.550902i	0.990326	+	0.138758i	$0.0443109\pi$
$743$	2.15905	+	15.0165i	0.0792077	+	0.550902i	−0.911119	+	0.412144i	$0.864780\pi$
$744$	4.47640	+	1.31439i	0.164113	+	0.0481879i
$745$	−2.03509	+	1.30788i	−0.0745601	+	0.0479168i
$746$	−1.91544	+	13.3222i	−0.0701293	+	0.487760i
$747$	2.50462	−	5.48435i	0.0916392	−	0.200662i
$748$	−2.54097	+	5.56394i	−0.0929070	+	0.203438i
$749$	−1.38019	+	9.59943i	−0.0504310	+	0.350755i
$750$	1.14455	−	0.735561i	0.0417932	−	0.0268589i
$751$	−46.4273	−	13.6323i	−1.69416	−	0.497449i	−0.714756	−	0.699374i	$-0.753462\pi$
$751$	−46.4273	−	13.6323i	−1.69416	−	0.497449i	−0.979401	+	0.201924i	$0.935281\pi$
$752$	1.46992	+	10.2235i	0.0536023	+	0.372812i
$753$	−2.39564	−	2.76472i	−0.0873021	−	0.100752i
$754$	−4.75064	−	3.05305i	−0.173008	−	0.111186i
$755$	1.67560	−	1.93374i	0.0609813	−	0.0703761i
$756$	0.959493	−	0.281733i	0.0348964	−	0.0102465i
$757$	−4.70425	−	10.3009i	−0.170979	−	0.374392i	0.804672	−	0.593719i	$-0.202341\pi$
$757$	−4.70425	−	10.3009i	−0.170979	−	0.374392i	−0.975651	+	0.219327i	$0.929614\pi$
$758$	22.3461			0.811646
$759$	5.24910	+	7.51767i	0.190530	+	0.272874i
$760$	−0.496497			−0.0180099
$761$	0.560009	+	1.22625i	0.0203003	+	0.0444515i	0.919511	−	0.393065i	$-0.128585\pi$
$761$	0.560009	+	1.22625i	0.0203003	+	0.0444515i	−0.899210	+	0.437517i	$0.855858\pi$
$762$	−2.82014	+	0.828069i	−0.102163	+	0.0299978i
$763$	−9.87387	+	11.3950i	−0.357458	+	0.412528i
$764$	−20.2624	−	13.0218i	−0.733067	−	0.471113i
$765$	0.285582	+	0.329579i	0.0103252	+	0.0119160i
$766$	1.63530	+	11.3737i	0.0590857	+	0.410950i
$767$	22.4317	+	6.58654i	0.809962	+	0.237826i
$768$	0.841254	−	0.540641i	0.0303561	−	0.0195087i
$769$	−2.48708	+	17.2981i	−0.0896866	+	0.623784i	0.894555	+	0.446957i	$0.147492\pi$
$769$	−2.48708	+	17.2981i	−0.0896866	+	0.623784i	−0.984242	+	0.176827i	$0.943417\pi$
$770$	−0.108256	+	0.237048i	−0.00390127	+	0.00854260i
$771$	8.94634	−	19.5898i	0.322195	−	0.705508i
$772$	2.40439	−	16.7229i	0.0865358	−	0.601870i
$773$	11.0156	−	7.07928i	0.396202	−	0.254624i	−0.327336	−	0.944908i	$-0.606151\pi$
$773$	11.0156	−	7.07928i	0.396202	−	0.254624i	0.723538	+	0.690284i	$0.242514\pi$
$774$	−2.86774	−	0.842045i	−0.103079	−	0.0302667i
$775$	−3.30743	−	23.0037i	−0.118806	−	0.826316i
$776$	−7.48771	−	8.64127i	−0.268793	−	0.310204i
$777$	5.69755	+	3.66160i	0.204399	+	0.131359i
$778$	11.9937	−	13.8415i	0.429995	−	0.496241i
$779$	38.4695	−	11.2957i	1.37831	−	0.404709i
$780$	−0.0921035	−	0.201679i	−0.00329783	−	0.00722125i
$781$	−8.17740			−0.292610
$782$	4.88397	+	14.5456i	0.174650	+	0.520149i
$783$	−3.47175			−0.124070
$784$	0.415415	+	0.909632i	0.0148363	+	0.0324869i
$785$	0.547316	−	0.160706i	0.0195345	−	0.00573586i
$786$	13.0853	−	15.1012i	0.466737	−	0.538643i
$787$	24.6154	+	15.8193i	0.877443	+	0.563898i	0.900021	−	0.435847i	$-0.143551\pi$
$787$	24.6154	+	15.8193i	0.877443	+	0.563898i	−0.0225782	+	0.999745i	$0.507187\pi$
$788$	−4.27719	−	4.93614i	−0.152369	−	0.175843i
$789$	−1.53584	−	10.6820i	−0.0546774	−	0.380289i
$790$	0.279556	+	0.0820849i	0.00994614	+	0.00292045i
$791$	6.82643	−	4.38708i	0.242720	−	0.155987i
$792$	0.272084	−	1.89238i	0.00966808	−	0.0672429i
$793$	4.93160	−	10.7987i	0.175126	−	0.383473i
$794$	2.49650	−	5.46656i	0.0885973	−	0.194001i
$795$	−0.0392320	+	0.272865i	−0.00139142	+	0.00967752i
$796$	−19.2956	+	12.4005i	−0.683914	+	0.439525i
$797$	13.7699	+	4.04319i	0.487753	+	0.143217i	0.516357	−	0.856374i	$-0.327288\pi$
$797$	13.7699	+	4.04319i	0.487753	+	0.143217i	−0.0286035	+	0.999591i	$0.509106\pi$
$798$	0.518382	+	3.60543i	0.0183505	+	0.127631i
$799$	21.6399	+	24.9738i	0.765566	+	0.883510i
$800$	−4.19064	−	2.69316i	−0.148161	−	0.0952176i
$801$	−6.23551	+	7.19616i	−0.220321	+	0.254264i
$802$	16.7042	−	4.90479i	0.589845	−	0.173194i
$803$	2.38093	+	5.21350i	0.0840211	+	0.183981i
$804$	8.74021			0.308243
$805$	0.208078	+	0.619704i	0.00733378	+	0.0218417i
$806$	−7.58864			−0.267298
$807$	8.72768	+	19.1110i	0.307229	+	0.672737i
$808$	8.30706	−	2.43917i	0.292241	−	0.0858098i
$809$	20.1926	−	23.3035i	0.709932	−	0.819306i	−0.280126	−	0.959963i	$-0.590376\pi$
$809$	20.1926	−	23.3035i	0.709932	−	0.819306i	0.990058	+	0.140658i	$0.0449217\pi$
$810$	−0.114669	−	0.0736930i	−0.00402904	−	0.00258931i
$811$	0.869804	+	1.00381i	0.0305429	+	0.0352484i	0.770816	−	0.637058i	$-0.219849\pi$
$811$	0.869804	+	1.00381i	0.0305429	+	0.0352484i	−0.740273	+	0.672307i	$0.765304\pi$
$812$	−0.494081	−	3.43641i	−0.0173389	−	0.120594i
$813$	−4.58591	−	1.34654i	−0.160835	−	0.0472254i
$814$	10.8928	−	7.00040i	0.381794	−	0.245364i
$815$	0.396357	−	2.75673i	0.0138838	−	0.0965639i
$816$	1.32907	−	2.91025i	0.0465266	−	0.101879i
$817$	4.52252	−	9.90293i	0.158223	−	0.346460i
$818$	3.64266	−	25.3352i	0.127362	−	0.885825i
$819$	−1.36837	+	0.879398i	−0.0478147	+	0.0307287i
$820$	−1.43957	−	0.422697i	−0.0502721	−	0.0147612i
$821$	2.60323	+	18.1059i	0.0908535	+	0.631900i	0.983468	+	0.181080i	$0.0579593\pi$
$821$	2.60323	+	18.1059i	0.0908535	+	0.631900i	−0.892615	+	0.450820i	$0.851132\pi$
$822$	8.93329	+	10.3096i	0.311584	+	0.359587i
$823$	3.04550	+	1.95723i	0.106160	+	0.0682246i	0.592643	−	0.805465i	$-0.298084\pi$
$823$	3.04550	+	1.95723i	0.106160	+	0.0682246i	−0.486484	+	0.873690i	$0.661721\pi$
$824$	1.98800	−	2.29427i	0.0692553	−	0.0799248i
$825$	−9.13792	+	2.68314i	−0.318142	+	0.0934148i
$826$	5.97071	+	13.0740i	0.207747	+	0.454904i
$827$	29.0588			1.01047			0.505237	−	0.862981i	$-0.331405\pi$
$827$	29.0588			1.01047			0.505237	+	0.862981i	$0.331405\pi$
$828$	−2.74557	−	3.93215i	−0.0954152	−	0.136652i
$829$	30.5330			1.06045			0.530227	−	0.847856i	$-0.322107\pi$
$829$	30.5330			1.06045			0.530227	+	0.847856i	$0.322107\pi$
$830$	−0.341396	−	0.747554i	−0.0118500	−	0.0259480i
$831$	−23.1983	+	6.81164i	−0.804741	+	0.236293i
$832$	−1.06519	+	1.22929i	−0.0369287	+	0.0426180i
$833$	2.69148	+	1.72971i	0.0932543	+	0.0599309i
$834$	1.94806	+	2.24818i	0.0674558	+	0.0778481i
$835$	0.134528	+	0.935664i	0.00465554	+	0.0323800i
$836$	6.68181	+	1.96196i	0.231095	+	0.0678557i
$837$	−3.92477	+	2.52230i	−0.135660	+	0.0871833i
$838$	−1.24213	+	8.63918i	−0.0429086	+	0.298436i
$839$	11.1304	−	24.3721i	0.384263	−	0.841419i	−0.614363	−	0.789023i	$-0.710587\pi$
$839$	11.1304	−	24.3721i	0.384263	−	0.841419i	0.998626	−	0.0523954i	$-0.0166856\pi$
$840$	0.0566239	−	0.123989i	0.00195371	−	0.00427803i
$841$	2.41180	−	16.7745i	0.0831656	−	0.578430i
$842$	−23.7950	+	15.2921i	−0.820030	+	0.527001i
$843$	−20.3808	−	5.98433i	−0.701951	−	0.206111i
$844$	2.49842	+	17.3769i	0.0859993	+	0.598138i
$845$	−0.924238	−	1.06663i	−0.0317947	−	0.0366931i
$846$	−8.68899	−	5.58408i	−0.298734	−	0.191984i
$847$	−4.80986	+	5.55087i	−0.165269	+	0.190730i
$848$	1.94051	−	0.569784i	0.0666373	−	0.0195665i
$849$	−2.57422	−	5.63675i	−0.0883469	−	0.193453i
$850$	−15.9374			−0.546649
$851$	7.94950	−	31.4929i	0.272505	−	1.07956i
$852$	4.27723			0.146536
$853$	−0.190510	−	0.417159i	−0.00652295	−	0.0142833i	0.906342	−	0.422544i	$-0.138863\pi$
$853$	−0.190510	−	0.417159i	−0.00652295	−	0.0142833i	−0.912865	+	0.408261i	$0.866135\pi$
$854$	7.00279	−	2.05620i	0.239630	−	0.0703618i
$855$	0.325137	−	0.375228i	0.0111194	−	0.0128325i
$856$	−8.15859	−	5.24321i	−0.278855	−	0.179209i
$857$	−4.04926	−	4.67310i	−0.138320	−	0.159630i	0.682363	−	0.731013i	$-0.260952\pi$
$857$	−4.04926	−	4.67310i	−0.138320	−	0.159630i	−0.820683	+	0.571384i	$0.806407\pi$
$858$	0.442567	+	3.07812i	0.0151090	+	0.105085i
$859$	−19.4629	−	5.71483i	−0.664066	−	0.194987i	−0.0677070	−	0.997705i	$-0.521568\pi$
$859$	−19.4629	−	5.71483i	−0.664066	−	0.194987i	−0.596359	+	0.802718i	$0.703386\pi$
$860$	−0.342722	+	0.220254i	−0.0116867	+	0.00751061i
$861$	−1.56648	+	10.8951i	−0.0533855	+	0.371304i
$862$	−10.8867	+	23.8385i	−0.370802	+	0.811944i
$863$	17.7885	−	38.9515i	0.605529	−	1.32592i	−0.320061	−	0.947397i	$-0.603703\pi$
$863$	17.7885	−	38.9515i	0.605529	−	1.32592i	0.925590	−	0.378527i	$-0.123569\pi$
$864$	−0.142315	+	0.989821i	−0.00484165	+	0.0336744i
$865$	−0.830130	+	0.533492i	−0.0282253	+	0.0181393i
$866$	21.1699	+	6.21605i	0.719384	+	0.211230i
$867$	0.962621	+	6.69518i	0.0326923	+	0.227380i
$868$	−3.05518	−	3.52586i	−0.103699	−	0.119675i
$869$	−3.43786	−	2.20938i	−0.116622	−	0.0749481i
$870$	−0.309895	+	0.357638i	−0.0105064	+	0.0121251i
$871$	−13.6408	+	4.00530i	−0.462201	+	0.135715i
$872$	−6.26355	−	13.7153i	−0.212111	−	0.464457i
$873$	11.4340			0.386984
$874$	15.6003	−	7.86060i	0.527690	−	0.265889i
$875$	−1.36053			−0.0459945
$876$	−1.24536	−	2.72695i	−0.0420767	−	0.0921351i
$877$	39.6338	−	11.6375i	1.33834	−	0.392972i	0.467262	−	0.884119i	$-0.345241\pi$
$877$	39.6338	−	11.6375i	1.33834	−	0.392972i	0.871076	+	0.491148i	$0.163422\pi$
$878$	22.4189	−	25.8727i	0.756600	−	0.873163i
$879$	6.13623	+	3.94351i	0.206970	+	0.133011i
$880$	−0.170655	−	0.196946i	−0.00575277	−	0.00663906i
$881$	6.33435	+	44.0564i	0.213410	+	1.48430i	0.761657	+	0.647981i	$0.224386\pi$
$881$	6.33435	+	44.0564i	0.213410	+	1.48430i	−0.548247	+	0.836317i	$0.684705\pi$
$882$	−0.959493	−	0.281733i	−0.0323078	−	0.00948643i
$883$	−21.4591	+	13.7909i	−0.722157	+	0.464102i	−0.849387	−	0.527771i	$-0.823028\pi$
$883$	−21.4591	+	13.7909i	−0.722157	+	0.464102i	0.127230	+	0.991873i	$0.459391\pi$
$884$	−0.740613	+	5.15108i	−0.0249095	+	0.173250i
$885$	0.813848	−	1.78208i	0.0273572	−	0.0599039i
$886$	11.4269	−	25.0215i	0.383895	−	0.840614i
$887$	−5.21169	+	36.2481i	−0.174992	+	1.21709i	0.693156	+	0.720787i	$0.256220\pi$
$887$	−5.21169	+	36.2481i	−0.174992	+	1.21709i	−0.868148	+	0.496306i	$0.834690\pi$
$888$	−5.69755	+	3.66160i	−0.191197	+	0.122875i
$889$	2.82014	+	0.828069i	0.0945846	+	0.0277726i
$890$	0.184710	+	1.28469i	0.00619149	+	0.0430628i
$891$	1.25199	+	1.44488i	0.0419433	+	0.0484051i
$892$	0.968253	+	0.622258i	0.0324195	+	0.0208348i
$893$	24.6372	−	28.4328i	0.824452	−	0.951469i
$894$	−17.0287	+	5.00008i	−0.569526	+	0.167228i
$895$	0.558691	+	1.22336i	0.0186750	+	0.0408925i
$896$	−1.00000			−0.0334077
$897$	6.08696	+	4.87871i	0.203238	+	0.162895i
$898$	20.9852			0.700285
$899$	6.72849	+	14.7333i	0.224408	+	0.491385i
$900$	4.77964	−	1.40343i	0.159321	−	0.0467809i
$901$	4.23728	−	4.89008i	0.141164	−	0.162912i
$902$	17.7033	+	11.3772i	0.589455	+	0.378820i
$903$	1.95725	+	2.25879i	0.0651333	+	0.0751678i
$904$	1.15483	+	8.03200i	0.0384090	+	0.267140i
$905$	−2.57990	−	0.757528i	−0.0857589	−	0.0251811i
$906$	15.7918	−	10.1487i	0.524646	−	0.337170i
$907$	−7.36949	+	51.2559i	−0.244700	+	1.70193i	0.383228	+	0.923654i	$0.374812\pi$
$907$	−7.36949	+	51.2559i	−0.244700	+	1.70193i	−0.627928	+	0.778272i	$0.716097\pi$
$908$	−5.61195	+	12.2884i	−0.186239	+	0.407807i
$909$	−3.59656	+	7.87537i	−0.119290	+	0.261210i
$910$	−0.0315533	+	0.219458i	−0.00104598	+	0.00727495i
$911$	24.9774	−	16.0520i	0.827537	−	0.531826i	−0.0569576	−	0.998377i	$-0.518140\pi$
$911$	24.9774	−	16.0520i	0.827537	−	0.531826i	0.884494	+	0.466551i	$0.154504\pi$
$912$	−3.49496	−	1.02621i	−0.115730	−	0.0339813i
$913$	1.64045	+	11.4096i	0.0542909	+	0.377601i
$914$	−12.1295	−	13.9982i	−0.401208	−	0.463019i
$915$	−0.836899	−	0.537843i	−0.0276670	−	0.0177805i
$916$	7.87745	−	9.09106i	0.260278	−	0.300377i
$917$	−19.1724	+	5.62952i	−0.633128	+	0.185903i
$918$	1.32907	+	2.91025i	0.0438657	+	0.0960526i
$919$	15.3391			0.505989			0.252994	−	0.967468i	$-0.418585\pi$
$919$	15.3391			0.505989			0.252994	+	0.967468i	$0.418585\pi$
$920$	−0.650141	−	0.0681601i	−0.0214345	−	0.00224717i
$921$	9.98437			0.328996
$922$	−9.09332	−	19.9116i	−0.299473	−	0.655754i
$923$	−6.67546	+	1.96009i	−0.219726	+	0.0645172i
$924$	−1.25199	+	1.44488i	−0.0411875	+	0.0475329i
$925$	28.3819	+	18.2399i	0.933192	+	0.599726i
$926$	5.39555	+	6.22679i	0.177309	+	0.204625i
$927$	0.432034	+	3.00486i	0.0141898	+	0.0986926i
$928$	3.33112	+	0.978105i	0.109349	+	0.0321079i
$929$	−36.1523	+	23.2337i	−1.18612	+	0.762272i	−0.976501	−	0.215512i	$-0.930858\pi$
$929$	−36.1523	+	23.2337i	−1.18612	+	0.762272i	−0.209617	+	0.977784i	$0.567222\pi$
$930$	−0.0905013	+	0.629450i	−0.00296765	+	0.0206405i
$931$	1.51315	−	3.31334i	0.0495915	−	0.108590i
$932$	6.19487	−	13.5649i	0.202920	−	0.444332i
$933$	−2.15799	+	15.0092i	−0.0706495	+	0.491378i
$934$	−34.8024	+	22.3661i	−1.13877	+	0.731842i
$935$	−0.799974	−	0.234894i	−0.0261620	−	0.00768184i
$936$	−0.231487	−	1.61003i	−0.00756639	−	0.0526254i
$937$	20.2752	+	23.3989i	0.662363	+	0.764408i	0.983161	−	0.182739i	$-0.0584965\pi$
$937$	20.2752	+	23.3989i	0.662363	+	0.764408i	−0.320798	+	0.947148i	$0.603951\pi$
$938$	−7.35273	−	4.72531i	−0.240075	−	0.154287i
$939$	7.11065	−	8.20613i	0.232047	−	0.267797i
$940$	−1.35083	+	0.396640i	−0.0440593	+	0.0129370i
$941$	12.9001	+	28.2473i	0.420532	+	0.920837i	0.994769	+	0.102148i	$0.0325715\pi$
$941$	12.9001	+	28.2473i	0.420532	+	0.920837i	−0.574237	+	0.818689i	$0.694701\pi$
$942$	4.18484			0.136349
$943$	51.9247	−	9.50999i	1.69090	−	0.309688i
$944$	−14.3729			−0.467797
$945$	0.0566239	+	0.123989i	0.00184197	+	0.00403336i
$946$	5.48267	−	1.60986i	0.178257	−	0.0523410i
$947$	1.09107	−	1.25916i	0.0354549	−	0.0409172i	−0.737745	−	0.675079i	$-0.764109\pi$
$947$	1.09107	−	1.25916i	0.0354549	−	0.0409172i	0.773200	+	0.634162i	$0.218655\pi$
$948$	1.79819	+	1.15563i	0.0584026	+	0.0375330i
$949$	3.19328	+	3.68524i	0.103658	+	0.119628i
$950$	2.58228	+	17.9601i	0.0837802	+	0.582704i
$951$	13.0354	+	3.82754i	0.422702	+	0.124117i
$952$	−2.69148	+	1.72971i	−0.0872314	+	0.0560602i
$953$	−4.74558	+	33.0062i	−0.153724	+	1.06918i	0.756182	+	0.654362i	$0.227063\pi$
$953$	−4.74558	+	33.0062i	−0.153724	+	1.06918i	−0.909906	+	0.414814i	$0.863847\pi$
$954$	−0.840148	+	1.83967i	−0.0272008	+	0.0595614i
$955$	1.36384	−	2.98639i	0.0441328	−	0.0966373i
$956$	1.55347	−	10.8047i	0.0502430	−	0.349447i
$957$	5.58377	−	3.58847i	0.180498	−	0.115999i
$958$	2.35395	+	0.691184i	0.0760528	+	0.0223311i
$959$	−1.94139	−	13.5027i	−0.0626907	−	0.436024i
$960$	0.0892619	+	0.103014i	0.00288092	+	0.00332475i
$961$	−7.76831	−	4.99239i	−0.250591	−	0.161045i
$962$	7.21418	−	8.32561i	0.232595	−	0.268429i
$963$	9.30530	−	2.73228i	0.299859	−	0.0880465i
$964$	7.01909	+	15.3697i	0.226070	+	0.495024i
$965$	2.30288			0.0741324
$966$	0.183838	+	4.79231i	0.00591490	+	0.154190i
$967$	27.4986			0.884295			0.442148	−	0.896942i	$-0.354217\pi$
$967$	27.4986			0.884295			0.442148	+	0.896942i	$0.354217\pi$
$968$	−3.05116	−	6.68111i	−0.0980681	−	0.214739i
$969$	−11.1817	+	3.28323i	−0.359207	+	0.105473i
$970$	1.02062	−	1.17786i	0.0327703	−	0.0378189i
$971$	21.3635	+	13.7295i	0.685586	+	0.440600i	0.836514	−	0.547945i	$-0.184590\pi$
$971$	21.3635	+	13.7295i	0.685586	+	0.440600i	−0.150928	+	0.988545i	$0.548226\pi$
$972$	−0.654861	−	0.755750i	−0.0210047	−	0.0242407i
$973$	−0.423354	−	2.94449i	−0.0135721	−	0.0943960i
$974$	−16.0116	−	4.70143i	−0.513045	−	0.150644i
$975$	−6.81643	+	4.38065i	−0.218300	+	0.140293i
$976$	−1.03867	+	7.22414i	−0.0332471	+	0.231239i
$977$	13.3368	−	29.2035i	0.426681	−	0.934302i	−0.567172	−	0.823599i	$-0.691963\pi$
$977$	13.3368	−	29.2035i	0.426681	−	0.934302i	0.993854	−	0.110703i	$-0.0353102\pi$
$978$	8.48793	−	18.5860i	0.271414	−	0.594314i
$979$	2.59075	−	18.0191i	0.0828007	−	0.575892i
$980$	−0.114669	+	0.0736930i	−0.00366295	+	0.00235404i
$981$	14.4671	+	4.24791i	0.461897	+	0.135625i
$982$	2.70652	+	18.8243i	0.0863687	+	0.600707i
$983$	2.72470	+	3.14447i	0.0869045	+	0.100293i	0.797536	−	0.603271i	$-0.206136\pi$
$983$	2.72470	+	3.14447i	0.0869045	+	0.100293i	−0.710632	+	0.703564i	$0.751591\pi$
$984$	−9.25980	−	5.95091i	−0.295192	−	0.189708i
$985$	0.583010	−	0.672829i	0.0185762	−	0.0214381i
$986$	10.6575	−	3.12932i	0.339403	−	0.0996579i
$987$	4.29067	+	9.39525i	0.136573	+	0.299054i
$988$	5.92484			0.188494
$989$	7.28152	−	12.3466i	0.231539	−	0.392598i
$990$	0.260597			0.00828232
$991$	−17.3829	−	38.0633i	−0.552187	−	1.20912i	−0.955753	−	0.294171i	$-0.904956\pi$
$991$	−17.3829	−	38.0633i	−0.552187	−	1.20912i	0.403565	−	0.914951i	$-0.367771\pi$
$992$	4.47640	−	1.31439i	0.142126	−	0.0417319i
$993$	7.90012	−	9.11723i	0.250703	−	0.289326i
$994$	−3.59824	−	2.31245i	−0.114129	−	0.0733463i
$995$	−2.04737	−	2.36280i	−0.0649061	−	0.0749057i
$996$	−0.858044	−	5.96783i	−0.0271882	−	0.189098i
$997$	29.4801	+	8.65613i	0.933643	+	0.274142i	0.712961	−	0.701203i	$-0.247354\pi$
$997$	29.4801	+	8.65613i	0.933643	+	0.274142i	0.220682	+	0.975346i	$0.429172\pi$
$998$	15.7562	−	10.1259i	0.498753	−	0.320529i
$999$	0.963855	−	6.70376i	0.0304950	−	0.212098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.a.211.1	✓	10
23.6	even	11	inner	966.2.q.a.673.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.a.211.1	✓	10	1.1	even	1	trivial
966.2.q.a.673.1	yes	10	23.6	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)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.114669 - 0.0736930i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.142315 + 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.114669 - 0.0736930i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(0.142315 + 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.0193985 - 0.134919i) q^{10} +(-0.794209 + 1.73907i) q^{11} +(0.415415 - 0.909632i) q^{12} +(-0.231487 + 1.61003i) q^{13} +(-0.841254 + 0.540641i) q^{14} +(0.130785 + 0.0384020i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-2.09514 - 2.41792i) q^{17} +(0.841254 + 0.540641i) q^{18} +(-2.38533 + 2.75282i) q^{19} +(0.130785 - 0.0384020i) q^{20} +(-0.415415 - 0.909632i) q^{21} -1.91184 q^{22} +(-3.50140 + 3.27723i) q^{23} +1.00000 q^{24} +(-2.06936 - 4.53126i) q^{25} +(-1.56070 + 0.458262i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(-0.841254 - 0.540641i) q^{28} +(2.27351 + 2.62377i) q^{29} +(0.0193985 + 0.134919i) q^{30} +(4.47640 + 1.31439i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.272084 - 1.89238i) q^{33} +(1.32907 - 2.91025i) q^{34} +(0.0566239 - 0.123989i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-5.69755 + 3.66160i) q^{37} +(-3.49496 - 1.02621i) q^{38} +(-0.231487 - 1.61003i) q^{39} +(0.0892619 + 0.103014i) q^{40} +(-9.25980 - 5.95091i) q^{41} +(0.654861 - 0.755750i) q^{42} +(-2.86774 + 0.842045i) q^{43} +(-0.794209 - 1.73907i) q^{44} -0.136307 q^{45} +(-4.43560 - 1.82357i) q^{46} -10.3286 q^{47} +(0.415415 + 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(3.26214 - 3.76471i) q^{50} +(2.69148 + 1.72971i) q^{51} +(-1.06519 - 1.22929i) q^{52} +(0.287822 + 2.00184i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(0.219228 - 0.140889i) q^{55} +(0.142315 - 0.989821i) q^{56} +(1.51315 - 3.31334i) q^{57} +(-1.44222 + 3.15801i) q^{58} +(2.04547 - 14.2266i) q^{59} +(-0.114669 + 0.0736930i) q^{60} +(-7.00279 - 2.05620i) q^{61} +(0.663953 + 4.61789i) q^{62} +(0.654861 + 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.145192 - 0.167561i) q^{65} +(1.83440 - 0.538629i) q^{66} +(3.63081 + 7.95037i) q^{67} +3.19937 q^{68} +(2.43626 - 4.13094i) q^{69} +0.136307 q^{70} +(1.77683 + 3.89071i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(1.96318 - 2.26563i) q^{73} +(-5.69755 - 3.66160i) q^{74} +(3.26214 + 3.76471i) q^{75} +(-0.518382 - 3.60543i) q^{76} +(-1.83440 - 0.538629i) q^{77} +(1.36837 - 0.879398i) q^{78} +(-0.304200 + 2.11576i) q^{79} +(-0.0566239 + 0.123989i) q^{80} +(0.415415 - 0.909632i) q^{81} +(1.56648 - 10.8951i) q^{82} +(5.07208 - 3.25963i) q^{83} +(0.959493 + 0.281733i) q^{84} +(0.0620629 + 0.431657i) q^{85} +(-1.95725 - 2.25879i) q^{86} +(-2.92062 - 1.87697i) q^{87} +(1.25199 - 1.44488i) q^{88} +(-9.13618 + 2.68262i) q^{89} +(-0.0566239 - 0.123989i) q^{90} -1.62658 q^{91} +(-0.183838 - 4.79231i) q^{92} -4.66538 q^{93} +(-4.29067 - 9.39525i) q^{94} +(0.476386 - 0.139880i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(9.61893 + 6.18171i) q^{97} +(-0.654861 - 0.755750i) q^{98} +(0.272084 + 1.89238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 8 q^{10} - 4 q^{11} - q^{12} + 14 q^{13} + q^{14} - 3 q^{15} - q^{16} + 15 q^{17} - q^{18} - 11 q^{19} - 3 q^{20} + q^{21} - 26 q^{22} - q^{23} + 10 q^{24} + 7 q^{25} - 8 q^{26} - q^{27} + q^{28} + 19 q^{29} + 8 q^{30} - 5 q^{31} - q^{32} + 7 q^{33} - 18 q^{34} - 8 q^{35} - q^{36} - 2 q^{37} + 11 q^{38} + 14 q^{39} - 3 q^{40} + 2 q^{41} + q^{42} + 25 q^{43} - 4 q^{44} + 8 q^{45} - 23 q^{46} - 4 q^{47} - q^{48} - q^{49} - 15 q^{50} + 15 q^{51} - 8 q^{52} + 15 q^{53} - q^{54} + 54 q^{55} + q^{56} + 8 q^{58} - 17 q^{59} - 14 q^{60} + q^{61} - 16 q^{62} + q^{63} - q^{64} - 13 q^{65} - 4 q^{66} - 4 q^{67} + 26 q^{68} + 21 q^{69} - 8 q^{70} + 6 q^{71} - q^{72} - 25 q^{73} - 2 q^{74} - 15 q^{75} - 22 q^{76} + 4 q^{77} + 14 q^{78} + 3 q^{79} + 8 q^{80} - q^{81} + 2 q^{82} + 7 q^{83} + q^{84} + 12 q^{85} - 41 q^{86} + 8 q^{87} + 7 q^{88} - 41 q^{89} + 8 q^{90} + 30 q^{91} - q^{92} - 16 q^{93} - 15 q^{94} - 44 q^{95} - q^{96} - 4 q^{97} - q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9 + 8 * q^10 - 4 * q^11 - q^12 + 14 * q^13 + q^14 - 3 * q^15 - q^16 + 15 * q^17 - q^18 - 11 * q^19 - 3 * q^20 + q^21 - 26 * q^22 - q^23 + 10 * q^24 + 7 * q^25 - 8 * q^26 - q^27 + q^28 + 19 * q^29 + 8 * q^30 - 5 * q^31 - q^32 + 7 * q^33 - 18 * q^34 - 8 * q^35 - q^36 - 2 * q^37 + 11 * q^38 + 14 * q^39 - 3 * q^40 + 2 * q^41 + q^42 + 25 * q^43 - 4 * q^44 + 8 * q^45 - 23 * q^46 - 4 * q^47 - q^48 - q^49 - 15 * q^50 + 15 * q^51 - 8 * q^52 + 15 * q^53 - q^54 + 54 * q^55 + q^56 + 8 * q^58 - 17 * q^59 - 14 * q^60 + q^61 - 16 * q^62 + q^63 - q^64 - 13 * q^65 - 4 * q^66 - 4 * q^67 + 26 * q^68 + 21 * q^69 - 8 * q^70 + 6 * q^71 - q^72 - 25 * q^73 - 2 * q^74 - 15 * q^75 - 22 * q^76 + 4 * q^77 + 14 * q^78 + 3 * q^79 + 8 * q^80 - q^81 + 2 * q^82 + 7 * q^83 + q^84 + 12 * q^85 - 41 * q^86 + 8 * q^87 + 7 * q^88 - 41 * q^89 + 8 * q^90 + 30 * q^91 - q^92 - 16 * q^93 - 15 * q^94 - 44 * q^95 - q^96 - 4 * q^97 - q^98 + 7 * q^99

Introduction

L-functions

Modular forms

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