LMFDB - Embedded newform 966.2.q.h.85.1

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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	966.85
Dual form			966.2.q.h.841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.480114 - 1.05130i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.480114 - 1.05130i) 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} +(-1.10893 - 0.325611i) q^{10} +(1.85127 + 2.13648i) q^{11} +(0.654861 + 0.755750i) q^{12} +(6.20055 + 1.82065i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(0.972274 + 0.624843i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.210309 - 1.46273i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(-0.363385 - 2.52740i) q^{19} +(-0.972274 + 0.624843i) q^{20} +(0.654861 - 0.755750i) q^{21} +2.82696 q^{22} +(-1.38159 - 4.59252i) q^{23} +1.00000 q^{24} +(2.39958 - 2.76926i) q^{25} +(5.43645 - 3.49379i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.415415 + 0.909632i) q^{28} +(0.556524 - 3.87071i) q^{29} +(1.10893 - 0.325611i) q^{30} +(-6.60855 - 4.24706i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-2.71245 - 0.796447i) q^{33} +(-0.967737 - 1.11683i) q^{34} +(0.756852 + 0.873454i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(1.38547 - 3.03376i) q^{37} +(-2.14805 - 1.38047i) q^{38} +(-6.20055 + 1.82065i) q^{39} +(-0.164480 + 1.14398i) q^{40} +(-1.34536 - 2.94592i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(7.78484 - 5.00301i) q^{43} +(1.85127 - 2.13648i) q^{44} -1.15574 q^{45} +(-4.37554 - 1.96332i) q^{46} -7.77501 q^{47} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.521478 - 3.62696i) q^{50} +(0.613890 + 1.34423i) q^{51} +(0.919684 - 6.39654i) q^{52} +(4.99792 - 1.46752i) q^{53} +(0.841254 + 0.540641i) q^{54} +(1.35726 - 2.97199i) q^{55} +(0.959493 + 0.281733i) q^{56} +(1.67211 + 1.92972i) q^{57} +(-2.56084 - 2.95537i) q^{58} +(7.13359 + 2.09461i) q^{59} +(0.480114 - 1.05130i) q^{60} +(5.31632 + 3.41659i) q^{61} +(-7.53739 + 2.21318i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-1.06292 - 7.39277i) q^{65} +(-2.37819 + 1.52837i) q^{66} +(3.69273 - 4.26163i) q^{67} -1.47778 q^{68} +(3.64517 + 3.11652i) q^{69} +1.15574 q^{70} +(-2.69105 + 3.10563i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(2.21245 + 15.3879i) q^{73} +(-1.38547 - 3.03376i) q^{74} +(-0.521478 + 3.62696i) q^{75} +(-2.44996 + 0.719373i) q^{76} +(-2.37819 - 1.52837i) q^{77} +(-2.68455 + 5.87833i) q^{78} +(6.76775 + 1.98719i) q^{79} +(0.756852 + 0.873454i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-3.10740 - 0.912415i) q^{82} +(-0.902325 + 1.97582i) q^{83} +(-0.841254 - 0.540641i) q^{84} +(-1.63875 + 0.481180i) q^{85} +(1.31696 - 9.15966i) q^{86} +(1.62449 + 3.55713i) q^{87} +(-0.402319 - 2.79819i) q^{88} +(6.03070 - 3.87569i) q^{89} +(-0.756852 + 0.873454i) q^{90} -6.46232 q^{91} +(-4.34915 + 2.02112i) q^{92} +7.85560 q^{93} +(-5.09155 + 5.87596i) q^{94} +(-2.48260 + 1.59547i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(4.73201 + 10.3616i) q^{97} +(0.142315 - 0.989821i) q^{98} +(2.71245 - 0.796447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * 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
$5$	−0.480114	−	1.05130i	−0.214713	−	0.470157i	0.771375	−	0.636381i	$-0.219570\pi$
$5$	−0.480114	−	1.05130i	−0.214713	−	0.470157i	−0.986088	+	0.166225i	$0.946842\pi$
$6$	−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
$10$	−1.10893	−	0.325611i	−0.350674	−	0.102967i
$11$	1.85127	+	2.13648i	0.558178	+	0.644172i	0.962769	−	0.270326i	$-0.0871315\pi$
$11$	1.85127	+	2.13648i	0.558178	+	0.644172i	−0.404591	+	0.914498i	$0.632586\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	6.20055	+	1.82065i	1.71972	+	0.504956i	0.984874	−	0.173273i	$-0.0554344\pi$
$13$	6.20055	+	1.82065i	1.71972	+	0.504956i	0.734850	+	0.678230i	$0.237253\pi$
$14$	−0.415415	+	0.909632i	−0.111024	+	0.243109i
$15$	0.972274	+	0.624843i	0.251040	+	0.161334i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.210309	−	1.46273i	0.0510075	−	0.354765i	−0.948294	−	0.317393i	$-0.897192\pi$
$17$	0.210309	−	1.46273i	0.0510075	−	0.354765i	0.999301	−	0.0373715i	$-0.0118985\pi$
$18$	−0.415415	−	0.909632i	−0.0979143	−	0.214402i
$19$	−0.363385	−	2.52740i	−0.0833663	−	0.579825i	−0.988096	−	0.153839i	$-0.950836\pi$
$19$	−0.363385	−	2.52740i	−0.0833663	−	0.579825i	0.904730	−	0.425986i	$-0.140073\pi$
$20$	−0.972274	+	0.624843i	−0.217407	+	0.139719i
$21$	0.654861	−	0.755750i	0.142902	−	0.164918i
$22$	2.82696			0.602710
$23$	−1.38159	−	4.59252i	−0.288082	−	0.957606i
$23$	−1.38159	−	4.59252i	−0.288082	−	0.957606i
$24$	1.00000			0.204124
$25$	2.39958	−	2.76926i	0.479915	−	0.553852i
$26$	5.43645	−	3.49379i	1.06618	−	0.685189i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	0.415415	+	0.909632i	0.0785061	+	0.171904i
$29$	0.556524	−	3.87071i	0.103344	−	0.718773i	−0.870601	−	0.491989i	$-0.836270\pi$
$29$	0.556524	−	3.87071i	0.103344	−	0.718773i	0.973945	−	0.226783i	$-0.0728210\pi$
$30$	1.10893	−	0.325611i	0.202462	−	0.0594482i
$31$	−6.60855	−	4.24706i	−1.18693	−	0.762794i	−0.210283	−	0.977641i	$-0.567439\pi$
$31$	−6.60855	−	4.24706i	−1.18693	−	0.762794i	−0.976648	+	0.214846i	$0.931075\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	−2.71245	−	0.796447i	−0.472177	−	0.138644i
$34$	−0.967737	−	1.11683i	−0.165965	−	0.191534i
$35$	0.756852	+	0.873454i	0.127931	+	0.147641i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	1.38547	−	3.03376i	0.227770	−	0.498748i	−0.760897	−	0.648873i	$-0.775241\pi$
$37$	1.38547	−	3.03376i	0.227770	−	0.498748i	0.988667	+	0.150126i	$0.0479678\pi$
$38$	−2.14805	−	1.38047i	−0.348459	−	0.223941i
$39$	−6.20055	+	1.82065i	−0.992883	+	0.291537i
$40$	−0.164480	+	1.14398i	−0.0260065	+	0.180879i
$41$	−1.34536	−	2.94592i	−0.210110	−	0.460076i	0.775009	−	0.631950i	$-0.217745\pi$
$41$	−1.34536	−	2.94592i	−0.210110	−	0.460076i	−0.985119	+	0.171874i	$0.945018\pi$
$42$	−0.142315	−	0.989821i	−0.0219597	−	0.152733i
$43$	7.78484	−	5.00301i	1.18718	−	0.762952i	0.210484	−	0.977597i	$-0.432496\pi$
$43$	7.78484	−	5.00301i	1.18718	−	0.762952i	0.976692	+	0.214645i	$0.0688596\pi$
$44$	1.85127	−	2.13648i	0.279089	−	0.322086i
$45$	−1.15574			−0.172288
$46$	−4.37554	−	1.96332i	−0.645139	−	0.289475i
$47$	−7.77501			−1.13410			−0.567051	−	0.823683i	$-0.691916\pi$
$47$	−7.77501			−1.13410			−0.567051	+	0.823683i	$0.691916\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−0.521478	−	3.62696i	−0.0737481	−	0.512929i
$51$	0.613890	+	1.34423i	0.0859618	+	0.188230i
$52$	0.919684	−	6.39654i	0.127537	−	0.887041i
$53$	4.99792	−	1.46752i	0.686517	−	0.201580i	0.0801718	−	0.996781i	$-0.474453\pi$
$53$	4.99792	−	1.46752i	0.686517	−	0.201580i	0.606345	+	0.795201i	$0.292635\pi$
$54$	0.841254	+	0.540641i	0.114480	+	0.0735719i
$55$	1.35726	−	2.97199i	0.183013	−	0.400743i
$56$	0.959493	+	0.281733i	0.128218	+	0.0376481i
$57$	1.67211	+	1.92972i	0.221477	+	0.255598i
$58$	−2.56084	−	2.95537i	−0.336255	−	0.388059i
$59$	7.13359	+	2.09461i	0.928714	+	0.272695i	0.710898	−	0.703295i	$-0.248289\pi$
$59$	7.13359	+	2.09461i	0.928714	+	0.272695i	0.217816	+	0.975990i	$0.430107\pi$
$60$	0.480114	−	1.05130i	0.0619824	−	0.135723i
$61$	5.31632	+	3.41659i	0.680685	+	0.437450i	0.834763	−	0.550609i	$-0.185604\pi$
$61$	5.31632	+	3.41659i	0.680685	+	0.437450i	−0.154078	+	0.988059i	$0.549241\pi$
$62$	−7.53739	+	2.21318i	−0.957250	+	0.281074i
$63$	−0.142315	+	0.989821i	−0.0179300	+	0.124706i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−1.06292	−	7.39277i	−0.131839	−	0.916961i
$66$	−2.37819	+	1.52837i	−0.292735	+	0.188130i
$67$	3.69273	−	4.26163i	0.451138	−	0.520641i	−0.483931	−	0.875106i	$-0.660791\pi$
$67$	3.69273	−	4.26163i	0.451138	−	0.520641i	0.935069	+	0.354465i	$0.115337\pi$
$68$	−1.47778			−0.179207
$69$	3.64517	+	3.11652i	0.438827	+	0.375185i
$70$	1.15574			0.138138
$71$	−2.69105	+	3.10563i	−0.319368	+	0.368571i	−0.892621	−	0.450808i	$-0.851136\pi$
$71$	−2.69105	+	3.10563i	−0.319368	+	0.368571i	0.573253	+	0.819379i	$0.305681\pi$
$72$	−0.841254	+	0.540641i	−0.0991427	+	0.0637151i
$73$	2.21245	+	15.3879i	0.258947	+	1.80102i	0.540364	+	0.841432i	$0.318287\pi$
$73$	2.21245	+	15.3879i	0.258947	+	1.80102i	−0.281417	+	0.959586i	$0.590804\pi$
$74$	−1.38547	−	3.03376i	−0.161058	−	0.352668i
$75$	−0.521478	+	3.62696i	−0.0602151	+	0.418805i
$76$	−2.44996	+	0.719373i	−0.281030	+	0.0825177i
$77$	−2.37819	−	1.52837i	−0.271020	−	0.174174i
$78$	−2.68455	+	5.87833i	−0.303965	+	0.665590i
$79$	6.76775	+	1.98719i	0.761432	+	0.223577i	0.639321	−	0.768940i	$-0.279215\pi$
$79$	6.76775	+	1.98719i	0.761432	+	0.223577i	0.122111	+	0.992516i	$0.461034\pi$
$80$	0.756852	+	0.873454i	0.0846186	+	0.0976551i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−3.10740	−	0.912415i	−0.343155	−	0.100759i
$83$	−0.902325	+	1.97582i	−0.0990431	+	0.216874i	−0.952667	−	0.304016i	$-0.901672\pi$
$83$	−0.902325	+	1.97582i	−0.0990431	+	0.216874i	0.853624	+	0.520890i	$0.174400\pi$
$84$	−0.841254	−	0.540641i	−0.0917883	−	0.0589887i
$85$	−1.63875	+	0.481180i	−0.177747	+	0.0521913i
$86$	1.31696	−	9.15966i	0.142012	−	0.987712i
$87$	1.62449	+	3.55713i	0.174163	+	0.381364i
$88$	−0.402319	−	2.79819i	−0.0428873	−	0.298288i
$89$	6.03070	−	3.87569i	0.639252	−	0.410823i	−0.180472	−	0.983580i	$-0.557763\pi$
$89$	6.03070	−	3.87569i	0.639252	−	0.410823i	0.819725	+	0.572757i	$0.194126\pi$
$90$	−0.756852	+	0.873454i	−0.0797792	+	0.0920701i
$91$	−6.46232			−0.677435
$92$	−4.34915	+	2.02112i	−0.453430	+	0.210716i
$93$	7.85560			0.814588
$94$	−5.09155	+	5.87596i	−0.525153	+	0.606059i
$95$	−2.48260	+	1.59547i	−0.254709	+	0.163691i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	4.73201	+	10.3616i	0.480462	+	1.05207i	0.982336	+	0.187125i	$0.0599170\pi$
$97$	4.73201	+	10.3616i	0.480462	+	1.05207i	−0.501874	+	0.864941i	$0.667356\pi$
$98$	0.142315	−	0.989821i	0.0143760	−	0.0999871i
$99$	2.71245	−	0.796447i	0.272612	−	0.0800460i
$100$	−3.08257	−	1.98105i	−0.308257	−	0.198105i
$101$	−2.93248	+	6.42123i	−0.291792	+	0.638936i	−0.997583	−	0.0694843i	$-0.977865\pi$
$101$	−2.93248	+	6.42123i	−0.291792	+	0.638936i	0.705791	+	0.708420i	$0.250592\pi$
$102$	1.41791	+	0.416337i	0.140394	+	0.0412235i
$103$	−2.69399	−	3.10903i	−0.265446	−	0.306342i	0.607342	−	0.794441i	$-0.292236\pi$
$103$	−2.69399	−	3.10903i	−0.265446	−	0.306342i	−0.872788	+	0.488099i	$0.837690\pi$
$104$	−4.23192	−	4.88390i	−0.414974	−	0.478905i
$105$	−1.10893	−	0.325611i	−0.108220	−	0.0317764i
$106$	2.16386	−	4.73820i	0.210173	−	0.460215i
$107$	−13.6823	−	8.79308i	−1.32272	−	0.850059i	−0.327230	−	0.944945i	$-0.606115\pi$
$107$	−13.6823	−	8.79308i	−1.32272	−	0.850059i	−0.995488	+	0.0948855i	$0.969752\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	0.485464	−	3.37647i	0.0464990	−	0.323408i	−0.953274	−	0.302107i	$-0.902310\pi$
$109$	0.485464	−	3.37647i	0.0464990	−	0.323408i	0.999773	−	0.0213009i	$-0.00678079\pi$
$110$	−1.35726	−	2.97199i	−0.129410	−	0.283368i
$111$	0.474642	+	3.30121i	0.0450510	+	0.313337i
$112$	0.841254	−	0.540641i	0.0794910	−	0.0510858i
$113$	10.7840	−	12.4454i	1.01447	−	1.17076i	0.0292331	−	0.999573i	$-0.490693\pi$
$113$	10.7840	−	12.4454i	1.01447	−	1.17076i	0.985238	−	0.171190i	$-0.0547610\pi$
$114$	2.55339			0.239147
$115$	−4.16480	+	3.65740i	−0.388370	+	0.341055i
$116$	−3.91051			−0.363082
$117$	4.23192	−	4.88390i	0.391241	−	0.451516i
$118$	6.25451	−	4.01953i	0.575774	−	0.370028i
$119$	0.210309	+	1.46273i	0.0192790	+	0.134089i
$120$	−0.480114	−	1.05130i	−0.0438282	−	0.0959703i
$121$	0.428123	−	2.97766i	0.0389203	−	0.270696i
$122$	6.06354	−	1.78042i	0.548967	−	0.161191i
$123$	2.72447	+	1.75091i	0.245657	+	0.157874i
$124$	−3.26334	+	7.14571i	−0.293056	+	0.641703i
$125$	−9.60804	−	2.82118i	−0.859369	−	0.252334i
$126$	0.654861	+	0.755750i	0.0583396	+	0.0673275i
$127$	8.46258	+	9.76633i	0.750932	+	0.866622i	0.994658	−	0.103222i	$-0.0329153\pi$
$127$	8.46258	+	9.76633i	0.750932	+	0.866622i	−0.243726	+	0.969844i	$0.578370\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	−3.84419	+	8.41760i	−0.338462	+	0.741128i
$130$	−6.28315	−	4.03793i	−0.551069	−	0.354150i
$131$	−4.97923	+	1.46203i	−0.435038	+	0.127739i	−0.491916	−	0.870643i	$-0.663703\pi$
$131$	−4.97923	+	1.46203i	−0.435038	+	0.127739i	0.0568786	+	0.998381i	$0.481885\pi$
$132$	−0.402319	+	2.79819i	−0.0350174	+	0.243551i
$133$	1.06072	+	2.32264i	0.0919758	+	0.201399i
$134$	−0.802506	−	5.58155i	−0.0693260	−	0.482173i
$135$	0.972274	−	0.624843i	0.0836801	−	0.0537779i
$136$	−0.967737	+	1.11683i	−0.0829827	+	0.0957672i
$137$	−19.1040			−1.63217			−0.816083	−	0.577935i	$-0.803859\pi$
$137$	−19.1040			−1.63217			−0.816083	+	0.577935i	$0.803859\pi$
$138$	4.74239	−	0.713949i	0.403699	−	0.0607754i
$139$	−14.0674			−1.19318			−0.596592	−	0.802544i	$-0.703479\pi$
$139$	−14.0674			−1.19318			−0.596592	+	0.802544i	$0.703479\pi$
$140$	0.756852	−	0.873454i	0.0639657	−	0.0738203i
$141$	6.54075	−	4.20349i	0.550831	−	0.353997i
$142$	0.584820	+	4.06751i	0.0490770	+	0.341338i
$143$	7.58911	+	16.6178i	0.634633	+	1.38965i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	−4.33648	+	1.27331i	−0.360125	+	0.105742i
$146$	13.0782	+	8.40488i	1.08236	+	0.695592i
$147$	−0.415415	+	0.909632i	−0.0342629	+	0.0750252i
$148$	−3.20006	−	0.939622i	−0.263043	−	0.0772364i
$149$	11.8800	+	13.7102i	0.973246	+	1.12319i	0.992361	+	0.123369i	$0.0393698\pi$
$149$	11.8800	+	13.7102i	0.973246	+	1.12319i	−0.0191147	+	0.999817i	$0.506085\pi$
$150$	2.39958	+	2.76926i	0.195925	+	0.226109i
$151$	4.47700	+	1.31457i	0.364333	+	0.106978i	0.458775	−	0.888552i	$-0.348288\pi$
$151$	4.47700	+	1.31457i	0.364333	+	0.106978i	−0.0944417	+	0.995530i	$0.530107\pi$
$152$	−1.06072	+	2.32264i	−0.0860355	+	0.188391i
$153$	−1.24318	−	0.798945i	−0.100505	−	0.0645909i
$154$	−2.71245	+	0.796447i	−0.218576	+	0.0641796i
$155$	−1.29209	+	8.98666i	−0.103783	+	0.721826i
$156$	2.68455	+	5.87833i	0.214936	+	0.470643i
$157$	1.03394	+	7.19118i	0.0825171	+	0.573919i	0.988571	+	0.150757i	$0.0481710\pi$
$157$	1.03394	+	7.19118i	0.0825171	+	0.573919i	−0.906054	+	0.423162i	$0.860920\pi$
$158$	5.93376	−	3.81339i	0.472064	−	0.303377i
$159$	−3.41112	+	3.93664i	−0.270519	+	0.312196i
$160$	1.15574			0.0913696
$161$	2.61949	+	4.01725i	0.206445	+	0.316603i
$162$	−1.00000			−0.0785674
$163$	−2.89387	+	3.33970i	−0.226665	+	0.261585i	−0.857678	−	0.514187i	$-0.828094\pi$
$163$	−2.89387	+	3.33970i	−0.226665	+	0.261585i	0.631013	+	0.775772i	$0.282639\pi$
$164$	−2.72447	+	1.75091i	−0.212746	+	0.136723i
$165$	0.464978	+	3.23399i	0.0361985	+	0.251766i
$166$	0.902325	+	1.97582i	0.0700340	+	0.153353i
$167$	−1.48374	+	10.3196i	−0.114815	+	0.798557i	0.848309	+	0.529501i	$0.177621\pi$
$167$	−1.48374	+	10.3196i	−0.114815	+	0.798557i	−0.963125	+	0.269056i	$0.913288\pi$
$168$	−0.959493	+	0.281733i	−0.0740265	+	0.0217361i
$169$	24.1958	+	15.5497i	1.86121	+	1.19613i
$170$	−0.709500	+	1.55359i	−0.0544162	+	0.119155i
$171$	−2.44996	−	0.719373i	−0.187353	−	0.0550118i
$172$	−6.05998	−	6.99359i	−0.462069	−	0.533257i
$173$	−14.6568	−	16.9149i	−1.11434	−	1.28602i	−0.954282	−	0.298908i	$-0.903378\pi$
$173$	−14.6568	−	16.9149i	−1.11434	−	1.28602i	−0.160057	−	0.987108i	$-0.551168\pi$
$174$	3.75211	+	1.10172i	0.284447	+	0.0835211i
$175$	−1.52219	+	3.33312i	−0.115066	+	0.251960i
$176$	−2.37819	−	1.52837i	−0.179263	−	0.115205i
$177$	−7.13359	+	2.09461i	−0.536193	+	0.157441i
$178$	1.02021	−	7.09573i	0.0764682	−	0.531848i
$179$	−4.75673	−	10.4158i	−0.355535	−	0.778512i	−0.999905	−	0.0137984i	$-0.995608\pi$
$179$	−4.75673	−	10.4158i	−0.355535	−	0.778512i	0.644370	−	0.764714i	$-0.277120\pi$
$180$	0.164480	+	1.14398i	0.0122596	+	0.0852673i
$181$	−3.17365	+	2.03958i	−0.235895	+	0.151601i	−0.653248	−	0.757144i	$-0.726594\pi$
$181$	−3.17365	+	2.03958i	−0.235895	+	0.151601i	0.417353	+	0.908744i	$0.362958\pi$
$182$	−4.23192	+	4.88390i	−0.313691	+	0.362018i
$183$	−6.31953			−0.467153
$184$	−1.32063	+	4.61042i	−0.0973581	+	0.339884i
$185$	−3.85459			−0.283395
$186$	5.14433	−	5.93687i	0.377200	−	0.435312i
$187$	3.51443	−	2.25859i	0.257001	−	0.165164i
$188$	1.10650	+	7.69587i	0.0806997	+	0.561279i
$189$	−0.415415	−	0.909632i	−0.0302170	−	0.0661660i
$190$	−0.419981	+	2.92103i	−0.0304686	+	0.211914i
$191$	9.29600	−	2.72955i	0.672635	−	0.197503i	0.0724587	−	0.997371i	$-0.476915\pi$
$191$	9.29600	−	2.72955i	0.672635	−	0.197503i	0.600176	+	0.799868i	$0.295097\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	5.35831	−	11.7331i	0.385700	−	0.844565i	−0.612822	−	0.790221i	$-0.709966\pi$
$193$	5.35831	−	11.7331i	0.385700	−	0.844565i	0.998522	−	0.0543441i	$-0.0173068\pi$
$194$	10.9296	+	3.20923i	0.784701	+	0.230409i
$195$	4.89102	+	5.64454i	0.350253	+	0.404214i
$196$	−0.654861	−	0.755750i	−0.0467758	−	0.0539821i
$197$	−16.5059	−	4.84658i	−1.17600	−	0.345304i	−0.365369	−	0.930863i	$-0.619057\pi$
$197$	−16.5059	−	4.84658i	−1.17600	−	0.345304i	−0.810630	+	0.585559i	$0.800875\pi$
$198$	1.17436	−	2.57150i	0.0834583	−	0.182748i
$199$	11.9864	+	7.70317i	0.849691	+	0.546063i	0.891478	−	0.453063i	$-0.149669\pi$
$199$	11.9864	+	7.70317i	0.849691	+	0.546063i	−0.0417875	+	0.999127i	$0.513305\pi$
$200$	−3.51583	+	1.03234i	−0.248606	+	0.0729974i
$201$	−0.802506	+	5.58155i	−0.0566044	+	0.393692i
$202$	2.93248	+	6.42123i	0.206328	+	0.451796i
$203$	0.556524	+	3.87071i	0.0390603	+	0.271671i
$204$	1.24318	−	0.798945i	0.0870403	−	0.0559374i
$205$	−2.45113	+	2.82876i	−0.171194	+	0.197569i
$206$	−4.11383			−0.286624
$207$	−4.75143	−	0.651057i	−0.330247	−	0.0452516i
$208$	−6.46232			−0.448081
$209$	4.72701	−	5.45526i	0.326974	−	0.377348i
$210$	−0.972274	+	0.624843i	−0.0670933	+	0.0431183i
$211$	4.09304	+	28.4677i	0.281776	+	1.95980i	0.280695	+	0.959797i	$0.409435\pi$
$211$	4.09304	+	28.4677i	0.281776	+	1.95980i	0.00108113	+	0.999999i	$0.499656\pi$
$212$	−2.16386	−	4.73820i	−0.148615	−	0.325421i
$213$	0.584820	−	4.06751i	0.0400712	−	0.278701i
$214$	−15.6054	+	4.58215i	−1.06676	+	0.313229i
$215$	−8.99728	−	5.78220i	−0.613610	−	0.394343i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	7.53739	+	2.21318i	0.511672	+	0.150240i
$218$	−2.23386	−	2.57801i	−0.151296	−	0.174605i
$219$	−10.1806	−	11.7490i	−0.687938	−	0.793923i
$220$	−3.13490	−	0.920490i	−0.211355	−	0.0620594i
$221$	3.96715	−	8.68685i	0.266860	−	0.584341i
$222$	2.80571	+	1.80312i	0.188307	+	0.121018i
$223$	−10.0261	+	2.94394i	−0.671401	+	0.197141i	−0.599627	−	0.800280i	$-0.704684\pi$
$223$	−10.0261	+	2.94394i	−0.671401	+	0.197141i	−0.0717740	+	0.997421i	$0.522866\pi$
$224$	0.142315	−	0.989821i	0.00950881	−	0.0661352i
$225$	−1.52219	−	3.33312i	−0.101479	−	0.222208i
$226$	−2.34358	−	16.3000i	−0.155893	−	1.08426i
$227$	−6.58606	+	4.23260i	−0.437132	+	0.280928i	−0.740641	−	0.671901i	$-0.765478\pi$
$227$	−6.58606	+	4.23260i	−0.437132	+	0.280928i	0.303509	+	0.952829i	$0.401842\pi$
$228$	1.67211	−	1.92972i	0.110738	−	0.127799i
$229$	2.56287			0.169359			0.0846795	−	0.996408i	$-0.473013\pi$
$229$	2.56287			0.169359			0.0846795	+	0.996408i	$0.473013\pi$
$230$	0.0367174	+	5.54264i	0.00242108	+	0.365471i
$231$	2.82696			0.186000
$232$	−2.56084	+	2.95537i	−0.168127	+	0.194029i
$233$	6.54412	−	4.20565i	0.428720	−	0.275521i	−0.308435	−	0.951245i	$-0.599805\pi$
$233$	6.54412	−	4.20565i	0.428720	−	0.275521i	0.737155	+	0.675724i	$0.236169\pi$
$234$	−0.919684	−	6.39654i	−0.0601216	−	0.418155i
$235$	3.73289	+	8.17388i	0.243507	+	0.533205i
$236$	1.05807	−	7.35907i	0.0688748	−	0.479035i
$237$	−6.76775	+	1.98719i	−0.439613	+	0.129082i
$238$	1.24318	+	0.798945i	0.0805836	+	0.0517879i
$239$	−12.2514	+	26.8267i	−0.792475	+	1.73528i	−0.123046	+	0.992401i	$0.539266\pi$
$239$	−12.2514	+	26.8267i	−0.792475	+	1.73528i	−0.669429	+	0.742876i	$0.733461\pi$
$240$	−1.10893	−	0.325611i	−0.0715811	−	0.0210181i
$241$	4.53285	+	5.23119i	0.291987	+	0.336971i	0.882723	−	0.469894i	$-0.155708\pi$
$241$	4.53285	+	5.23119i	0.291987	+	0.336971i	−0.590736	+	0.806865i	$0.701163\pi$
$242$	−1.97001	−	2.27351i	−0.126637	−	0.146147i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	2.62523	−	5.74844i	0.168063	−	0.368006i
$245$	−0.972274	−	0.624843i	−0.0621163	−	0.0399197i
$246$	3.10740	−	0.912415i	0.198121	−	0.0581735i
$247$	2.34831	−	16.3329i	0.149420	−	1.03924i
$248$	3.26334	+	7.14571i	0.207222	+	0.453753i
$249$	−0.309123	−	2.15000i	−0.0195899	−	0.136251i
$250$	−8.42403	+	5.41380i	−0.532783	+	0.342399i
$251$	8.72928	−	10.0741i	0.550987	−	0.635873i	−0.410126	−	0.912029i	$-0.634515\pi$
$251$	8.72928	−	10.0741i	0.550987	−	0.635873i	0.961113	+	0.276156i	$0.0890606\pi$
$252$	1.00000			0.0629941
$253$	7.25410	−	11.4537i	0.456061	−	0.720089i
$254$	12.9227			0.810843
$255$	1.11846	−	1.29077i	0.0700405	−	0.0808310i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−1.56335	−	10.8733i	−0.0975190	−	0.678260i	−0.978672	−	0.205429i	$-0.934141\pi$
$257$	−1.56335	−	10.8733i	−0.0975190	−	0.678260i	0.881153	−	0.472831i	$-0.156768\pi$
$258$	3.84419	+	8.41760i	0.239329	+	0.524057i
$259$	−0.474642	+	3.30121i	−0.0294928	+	0.205127i
$260$	−7.16626	+	2.10420i	−0.444432	+	0.130497i
$261$	−3.28973	−	2.11418i	−0.203629	−	0.130865i
$262$	−2.15577	+	4.72048i	−0.133184	+	0.291632i
$263$	14.7413	+	4.32843i	0.908985	+	0.266902i	0.702614	−	0.711572i	$-0.252016\pi$
$263$	14.7413	+	4.32843i	0.908985	+	0.266902i	0.206372	+	0.978474i	$0.433834\pi$
$264$	1.85127	+	2.13648i	0.113938	+	0.131491i
$265$	−3.94238	−	4.54975i	−0.242178	−	0.279489i
$266$	2.44996	+	0.719373i	0.150217	+	0.0441076i
$267$	−2.97799	+	6.52088i	−0.182250	+	0.399071i
$268$	−4.74379	−	3.04865i	−0.289773	−	0.186226i
$269$	17.9148	−	5.26026i	1.09228	−	0.320724i	0.314502	−	0.949257i	$-0.398163\pi$
$269$	17.9148	−	5.26026i	1.09228	−	0.320724i	0.777783	+	0.628533i	$0.216344\pi$
$270$	0.164480	−	1.14398i	0.0100099	−	0.0696205i
$271$	1.62933	+	3.56774i	0.0989748	+	0.216725i	0.952642	−	0.304095i	$-0.0983539\pi$
$271$	1.62933	+	3.56774i	0.0989748	+	0.216725i	−0.853667	+	0.520819i	$0.825627\pi$
$272$	0.210309	+	1.46273i	0.0127519	+	0.0886912i
$273$	5.43645	−	3.49379i	0.329029	−	0.211454i
$274$	−12.5105	+	14.4378i	−0.755785	+	0.872222i
$275$	10.3587			0.624654
$276$	2.56604	−	4.05160i	0.154457	−	0.243878i
$277$	−16.1554			−0.970681			−0.485341	−	0.874325i	$-0.661304\pi$
$277$	−16.1554			−0.970681			−0.485341	+	0.874325i	$0.661304\pi$
$278$	−9.21222	+	10.6315i	−0.552512	+	0.637633i
$279$	−6.60855	+	4.24706i	−0.395644	+	0.254265i
$280$	−0.164480	−	1.14398i	−0.00982954	−	0.0683659i
$281$	−1.73713	−	3.80378i	−0.103628	−	0.226915i	0.850714	−	0.525628i	$-0.176170\pi$
$281$	−1.73713	−	3.80378i	−0.103628	−	0.226915i	−0.954343	+	0.298714i	$0.903442\pi$
$282$	1.10650	−	7.69587i	0.0658910	−	0.458282i
$283$	−3.55264	+	1.04315i	−0.211183	+	0.0620088i	−0.385613	−	0.922661i	$-0.626010\pi$
$283$	−3.55264	+	1.04315i	−0.211183	+	0.0620088i	0.174430	+	0.984670i	$0.444192\pi$
$284$	3.45700	+	2.22168i	0.205135	+	0.131832i
$285$	1.22592	−	2.68438i	0.0726171	−	0.159009i
$286$	17.5287	+	5.14690i	1.03650	+	0.304343i
$287$	2.12082	+	2.44756i	0.125188	+	0.144475i
$288$	0.654861	+	0.755750i	0.0385880	+	0.0445330i
$289$	14.2160	+	4.17420i	0.836237	+	0.245541i
$290$	−1.87749	+	4.11113i	−0.110250	+	0.241414i
$291$	−9.58275	−	6.15846i	−0.561751	−	0.361015i
$292$	14.9164	−	4.37985i	0.872917	−	0.256311i
$293$	−3.70978	+	25.8021i	−0.216728	+	1.50737i	0.533276	+	0.845941i	$0.320961\pi$
$293$	−3.70978	+	25.8021i	−0.216728	+	1.50737i	−0.750004	+	0.661433i	$0.769948\pi$
$294$	0.415415	+	0.909632i	0.0242275	+	0.0530508i
$295$	−1.22286	−	8.50521i	−0.0711979	−	0.495192i
$296$	−2.80571	+	1.80312i	−0.163079	+	0.104804i
$297$	−1.85127	+	2.13648i	−0.107421	+	0.123971i
$298$	18.1412			1.05089
$299$	−0.205305	−	30.9915i	−0.0118731	−	1.79229i
$300$	3.66425			0.211556
$301$	−6.05998	+	6.99359i	−0.349292	+	0.403104i
$302$	3.92530	−	2.52263i	0.225875	−	0.145161i
$303$	−1.00462	−	6.98730i	−0.0577140	−	0.401410i
$304$	1.06072	+	2.32264i	0.0608363	+	0.133213i
$305$	1.03943	−	7.22942i	0.0595178	−	0.413955i
$306$	−1.41791	+	0.416337i	−0.0810568	+	0.0238004i
$307$	17.6487	+	11.3421i	1.00727	+	0.647331i	0.936684	−	0.350175i	$-0.113878\pi$
$307$	17.6487	+	11.3421i	1.00727	+	0.647331i	0.0705819	+	0.997506i	$0.477514\pi$
$308$	−1.17436	+	2.57150i	−0.0669155	+	0.146525i
$309$	3.94719	+	1.15900i	0.224548	+	0.0659332i
$310$	5.94553	+	6.86150i	0.337683	+	0.389707i
$311$	−17.3697	−	20.0457i	−0.984944	−	1.13669i	−0.990612	−	0.136702i	$-0.956350\pi$
$311$	−17.3697	−	20.0457i	−0.984944	−	1.13669i	0.00566777	−	0.999984i	$-0.498196\pi$
$312$	6.20055	+	1.82065i	0.351037	+	0.103074i
$313$	−5.77113	+	12.6370i	−0.326203	+	0.714286i	−0.999690	−	0.0249140i	$-0.992069\pi$
$313$	−5.77113	+	12.6370i	−0.326203	+	0.714286i	0.673486	+	0.739200i	$0.264796\pi$
$314$	6.11182	+	3.92783i	0.344910	+	0.221660i
$315$	1.10893	−	0.325611i	0.0624811	−	0.0183461i
$316$	1.00381	−	6.98168i	0.0564689	−	0.392750i
$317$	2.37999	+	5.21145i	0.133674	+	0.292704i	0.964618	−	0.263651i	$-0.0849267\pi$
$317$	2.37999	+	5.21145i	0.133674	+	0.292704i	−0.830945	+	0.556355i	$0.812199\pi$
$318$	0.741306	+	5.15590i	0.0415704	+	0.289128i
$319$	9.29995	−	5.97672i	0.520697	−	0.334632i
$320$	0.756852	−	0.873454i	0.0423093	−	0.0488275i
$321$	16.2642			0.907778
$322$	4.75143	+	0.651057i	0.264787	+	0.0362820i
$323$	−3.77334			−0.209954
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	19.9205	−	12.8022i	1.10499	−	0.710136i
$326$	0.628897	+	4.37408i	0.0348314	+	0.242258i
$327$	1.41706	+	3.10293i	0.0783637	+	0.171593i
$328$	−0.460899	+	3.20562i	−0.0254489	+	0.177001i
$329$	7.46006	−	2.19047i	0.411287	−	0.120765i
$330$	2.74858	+	1.76641i	0.151305	+	0.0972375i
$331$	−7.79755	+	17.0742i	−0.428592	+	0.938485i	0.564961	+	0.825117i	$0.308891\pi$
$331$	−7.79755	+	17.0742i	−0.428592	+	0.938485i	−0.993553	+	0.113368i	$0.963836\pi$
$332$	2.08412	+	0.611953i	0.114381	+	0.0335853i
$333$	−2.18406	−	2.52054i	−0.119686	−	0.138125i
$334$	6.82741	+	7.87925i	0.373579	+	0.431134i
$335$	−6.25319	−	1.83610i	−0.341648	−	0.100317i
$336$	−0.415415	+	0.909632i	−0.0226627	+	0.0496245i
$337$	−22.4417	−	14.4224i	−1.22247	−	0.785637i	−0.239772	−	0.970829i	$-0.577073\pi$
$337$	−22.4417	−	14.4224i	−1.22247	−	0.785637i	−0.982702	+	0.185192i	$0.940709\pi$
$338$	27.5965	−	8.10308i	1.50105	−	0.440749i
$339$	−2.34358	+	16.3000i	−0.127286	+	0.885293i
$340$	0.709500	+	1.55359i	0.0384780	+	0.0842552i
$341$	−3.16046	−	21.9815i	−0.171148	−	1.19036i
$342$	−2.14805	+	1.38047i	−0.116153	+	0.0746471i
$343$	−0.654861	+	0.755750i	−0.0353592	+	0.0408066i
$344$	−9.25385			−0.498934
$345$	1.52631	−	5.32846i	0.0821738	−	0.286875i
$346$	−22.3816			−1.20324
$347$	−6.26804	+	7.23370i	−0.336486	+	0.388325i	−0.898625	−	0.438717i	$-0.855433\pi$
$347$	−6.26804	+	7.23370i	−0.336486	+	0.388325i	0.562139	+	0.827043i	$0.309978\pi$
$348$	3.28973	−	2.11418i	0.176348	−	0.113332i
$349$	−2.43618	−	16.9440i	−0.130406	−	0.906991i	−0.945026	−	0.326996i	$-0.893964\pi$
$349$	−2.43618	−	16.9440i	−0.130406	−	0.906991i	0.814620	−	0.579995i	$-0.196945\pi$
$350$	1.52219	+	3.33312i	0.0813643	+	0.178163i
$351$	−0.919684	+	6.39654i	−0.0490891	+	0.341422i
$352$	−2.71245	+	0.796447i	−0.144574	+	0.0424508i
$353$	0.613741	+	0.394427i	0.0326661	+	0.0209933i	0.556872	−	0.830598i	$-0.312001\pi$
$353$	0.613741	+	0.394427i	0.0326661	+	0.0209933i	−0.524206	+	0.851592i	$0.675638\pi$
$354$	−3.08851	+	6.76288i	−0.164152	+	0.359443i
$355$	4.55697	+	1.33805i	0.241859	+	0.0710161i
$356$	−4.69450	−	5.41774i	−0.248808	−	0.287140i
$357$	−0.967737	−	1.11683i	−0.0512181	−	0.0591088i
$358$	−10.9867	−	3.22599i	−0.580666	−	0.170499i
$359$	−3.77491	+	8.26589i	−0.199232	+	0.436257i	−0.982707	−	0.185166i	$-0.940718\pi$
$359$	−3.77491	+	8.26589i	−0.199232	+	0.436257i	0.783475	+	0.621423i	$0.213445\pi$
$360$	0.972274	+	0.624843i	0.0512434	+	0.0329321i
$361$	11.9747	−	3.51608i	0.630246	−	0.185057i
$362$	−0.536886	+	3.73412i	−0.0282181	+	0.196261i
$363$	1.24969	+	2.73643i	0.0655915	+	0.143625i
$364$	0.919684	+	6.39654i	0.0482045	+	0.335270i
$365$	15.1151	−	9.71389i	0.791161	−	0.508448i
$366$	−4.13841	+	4.77598i	−0.216318	+	0.249644i
$367$	4.88171			0.254823			0.127412	−	0.991850i	$-0.459333\pi$
$367$	4.88171			0.254823			0.127412	+	0.991850i	$0.459333\pi$
$368$	2.61949	+	4.01725i	0.136550	+	0.209413i
$369$	−3.23859			−0.168594
$370$	−2.52422	+	2.91310i	−0.131228	+	0.151445i
$371$	−4.38202	+	2.81615i	−0.227503	+	0.146207i
$372$	−1.11797	−	7.77564i	−0.0579640	−	0.403148i
$373$	−6.20453	−	13.5860i	−0.321258	−	0.703458i	0.678249	−	0.734832i	$-0.262739\pi$
$373$	−6.20453	−	13.5860i	−0.321258	−	0.703458i	−0.999508	+	0.0313741i	$0.990012\pi$
$374$	0.594537	−	4.13509i	0.0307428	−	0.213821i
$375$	9.60804	−	2.82118i	0.496157	−	0.145685i
$376$	6.54075	+	4.20349i	0.337314	+	0.216778i
$377$	10.4979	−	22.9873i	0.540672	−	1.18391i
$378$	−0.959493	−	0.281733i	−0.0493510	−	0.0144908i
$379$	0.263966	+	0.304633i	0.0135590	+	0.0156479i	0.762489	−	0.647002i	$-0.223977\pi$
$379$	0.263966	+	0.304633i	0.0135590	+	0.0156479i	−0.748930	+	0.662650i	$0.769432\pi$
$380$	1.93254	+	2.23027i	0.0991371	+	0.114410i
$381$	−12.3993	−	3.64075i	−0.635233	−	0.186521i
$382$	4.02473	−	8.81292i	0.205923	−	0.450908i
$383$	−27.8327	−	17.8870i	−1.42218	−	0.913981i	−0.999972	−	0.00748285i	$-0.997618\pi$
$383$	−27.8327	−	17.8870i	−1.42218	−	0.913981i	−0.422210	−	0.906498i	$-0.638746\pi$
$384$	−0.959493	+	0.281733i	−0.0489639	+	0.0143771i
$385$	−0.464978	+	3.23399i	−0.0236975	+	0.164819i
$386$	−5.35831	−	11.7331i	−0.272731	−	0.597197i
$387$	−1.31696	−	9.15966i	−0.0669449	−	0.465612i
$388$	9.58275	−	6.15846i	0.486490	−	0.312648i
$389$	5.78896	−	6.68081i	0.293512	−	0.338731i	−0.589772	−	0.807570i	$-0.700782\pi$
$389$	5.78896	−	6.68081i	0.293512	−	0.338731i	0.883283	+	0.468839i	$0.155328\pi$
$390$	7.46879			0.378197
$391$	−7.00819	+	1.05506i	−0.354419	+	0.0533565i
$392$	−1.00000			−0.0505076
$393$	3.39836	−	3.92192i	0.171425	−	0.197835i
$394$	−14.4719	+	9.30052i	−0.729083	+	0.468553i
$395$	−1.16015	−	8.06904i	−0.0583736	−	0.405997i
$396$	−1.17436	−	2.57150i	−0.0590140	−	0.129223i
$397$	−1.88573	+	13.1155i	−0.0946419	+	0.658249i	0.886180	+	0.463342i	$0.153350\pi$
$397$	−1.88573	+	13.1155i	−0.0946419	+	0.658249i	−0.980822	+	0.194907i	$0.937559\pi$
$398$	13.6711	−	4.01419i	0.685269	−	0.201213i
$399$	−2.14805	−	1.38047i	−0.107537	−	0.0691098i
$400$	−1.52219	+	3.33312i	−0.0761093	+	0.166656i
$401$	−0.707327	−	0.207690i	−0.0353222	−	0.0103715i	0.264024	−	0.964516i	$-0.414950\pi$
$401$	−0.707327	−	0.207690i	−0.0353222	−	0.0103715i	−0.299346	+	0.954145i	$0.596768\pi$
$402$	3.69273	+	4.26163i	0.184176	+	0.212551i
$403$	−33.2443	−	38.3659i	−1.65602	−	1.91114i
$404$	6.77321	+	1.98879i	0.336980	+	0.0989461i
$405$	−0.480114	+	1.05130i	−0.0238570	+	0.0522396i
$406$	3.28973	+	2.11418i	0.163267	+	0.104925i
$407$	9.04644	−	2.65628i	0.448416	−	0.131667i
$408$	0.210309	−	1.46273i	0.0104119	−	0.0724161i
$409$	12.2505	+	26.8250i	0.605751	+	1.32641i	0.925443	+	0.378887i	$0.123693\pi$
$409$	12.2505	+	26.8250i	0.605751	+	1.32641i	−0.319692	+	0.947521i	$0.603580\pi$
$410$	0.532682	+	3.70488i	0.0263073	+	0.182971i
$411$	16.0713	−	10.3284i	0.792740	−	0.509463i
$412$	−2.69399	+	3.10903i	−0.132723	+	0.153171i
$413$	−7.43475			−0.365840
$414$	−3.60356	+	3.16454i	−0.177105	+	0.155529i
$415$	2.51040			0.123231
$416$	−4.23192	+	4.88390i	−0.207487	+	0.239453i
$417$	11.8343	−	7.60543i	0.579527	−	0.372440i
$418$	−1.02728	−	7.14487i	−0.0502457	−	0.349467i
$419$	16.5460	+	36.2306i	0.808323	+	1.76998i	0.614455	+	0.788952i	$0.289376\pi$
$419$	16.5460	+	36.2306i	0.808323	+	1.76998i	0.193868	+	0.981028i	$0.437897\pi$
$420$	−0.164480	+	1.14398i	−0.00802578	+	0.0558206i
$421$	−19.1517	+	5.62343i	−0.933395	+	0.274069i	−0.712857	−	0.701309i	$-0.752599\pi$
$421$	−19.1517	+	5.62343i	−0.933395	+	0.274069i	−0.220537	+	0.975379i	$0.570781\pi$
$422$	24.1948	+	15.5491i	1.17778	+	0.756916i
$423$	−3.22985	+	7.07239i	−0.157041	+	0.343872i
$424$	−4.99792	−	1.46752i	−0.242720	−	0.0712692i
$425$	−3.54603	−	4.09234i	−0.172008	−	0.198508i
$426$	−2.69105	−	3.10563i	−0.130382	−	0.150468i
$427$	−6.06354	−	1.78042i	−0.293435	−	0.0861604i
$428$	−6.75639	+	14.7944i	−0.326582	+	0.715115i
$429$	−15.3686	−	9.87683i	−0.742005	−	0.476858i
$430$	−10.2619	+	3.01316i	−0.494871	+	0.145307i
$431$	0.483985	−	3.36619i	0.0233128	−	0.162144i	−0.974839	−	0.222909i	$-0.928445\pi$
$431$	0.483985	−	3.36619i	0.0233128	−	0.162144i	0.998152	+	0.0607648i	$0.0193540\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	−3.98717	−	27.7314i	−0.191611	−	1.33268i	−0.827745	−	0.561105i	$-0.810376\pi$
$433$	−3.98717	−	27.7314i	−0.191611	−	1.33268i	0.636134	−	0.771579i	$-0.280533\pi$
$434$	6.60855	−	4.24706i	0.317221	−	0.203865i
$435$	2.95968	−	3.41565i	0.141906	−	0.163768i
$436$	−3.41119			−0.163367
$437$	−11.1051	+	5.16069i	−0.531228	+	0.246870i
$438$	−15.5461			−0.742823
$439$	−14.4608	+	16.6887i	−0.690177	+	0.796507i	−0.987390	−	0.158304i	$-0.949397\pi$
$439$	−14.4608	+	16.6887i	−0.690177	+	0.796507i	0.297213	+	0.954811i	$0.403943\pi$
$440$	−2.74858	+	1.76641i	−0.131034	+	0.0842102i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	−3.96715	−	8.68685i	−0.188698	−	0.413192i
$443$	−0.408185	+	2.83899i	−0.0193935	+	0.134885i	−0.997218	−	0.0745418i	$-0.976251\pi$
$443$	−0.408185	+	2.83899i	−0.0193935	+	0.134885i	0.977824	+	0.209426i	$0.0671597\pi$
$444$	3.20006	−	0.939622i	0.151868	−	0.0445925i
$445$	−6.96994	−	4.47931i	−0.330407	−	0.212340i
$446$	−4.34085	+	9.50513i	−0.205545	+	0.450081i
$447$	−17.4064	−	5.11098i	−0.823294	−	0.241741i
$448$	−0.654861	−	0.755750i	−0.0309393	−	0.0357058i
$449$	20.8855	+	24.1031i	0.985648	+	1.13750i	0.990500	+	0.137510i	$0.0439098\pi$
$449$	20.8855	+	24.1031i	0.985648	+	1.13750i	−0.00485288	+	0.999988i	$0.501545\pi$
$450$	−3.51583	−	1.03234i	−0.165738	−	0.0486650i
$451$	3.80328	−	8.32801i	0.179089	−	0.392151i
$452$	−13.8534	−	8.90305i	−0.651610	−	0.418764i
$453$	−4.47700	+	1.31457i	−0.210348	+	0.0617637i
$454$	−1.11416	+	7.74918i	−0.0522903	+	0.363687i
$455$	3.10265	+	6.79385i	0.145454	+	0.318501i
$456$	−0.363385	−	2.52740i	−0.0170171	−	0.118356i
$457$	−11.7912	+	7.57773i	−0.551568	+	0.354471i	−0.786548	−	0.617529i	$-0.788134\pi$
$457$	−11.7912	+	7.57773i	−0.551568	+	0.354471i	0.234980	+	0.972000i	$0.424498\pi$
$458$	1.67832	−	1.93689i	0.0784228	−	0.0905047i
$459$	1.47778			0.0689766
$460$	4.21289	+	3.60191i	0.196427	+	0.167940i
$461$	−37.8564			−1.76315			−0.881575	−	0.472045i	$-0.843516\pi$
$461$	−37.8564			−1.76315			−0.881575	+	0.472045i	$0.843516\pi$
$462$	1.85127	−	2.13648i	0.0861287	−	0.0993979i
$463$	−16.9772	+	10.9106i	−0.788999	+	0.507059i	−0.872009	−	0.489490i	$-0.837183\pi$
$463$	−16.9772	+	10.9106i	−0.788999	+	0.507059i	0.0830101	+	0.996549i	$0.473547\pi$
$464$	0.556524	+	3.87071i	0.0258360	+	0.179693i
$465$	−3.77158	−	8.25861i	−0.174903	−	0.382984i
$466$	1.10707	−	7.69983i	0.0512840	−	0.356688i
$467$	8.49892	−	2.49551i	0.393283	−	0.115478i	−0.0791109	−	0.996866i	$-0.525208\pi$
$467$	8.49892	−	2.49551i	0.393283	−	0.115478i	0.472394	+	0.881387i	$0.343390\pi$
$468$	−5.43645	−	3.49379i	−0.251300	−	0.161501i
$469$	−2.34250	+	5.12937i	−0.108167	+	0.236852i
$470$	8.62193	+	2.53163i	0.397700	+	0.116775i
$471$	−4.75765	−	5.49062i	−0.219221	−	0.252994i
$472$	−4.86872	−	5.61881i	−0.224101	−	0.258627i
$473$	25.1006	+	7.37021i	1.15413	+	0.338882i
$474$	−2.93012	+	6.41606i	−0.134585	+	0.294699i
$475$	−7.87099	−	5.05838i	−0.361146	−	0.232094i
$476$	1.41791	−	0.416337i	0.0649900	−	0.0190828i
$477$	0.741306	−	5.15590i	0.0339421	−	0.236072i
$478$	12.2514	+	26.8267i	0.560364	+	1.22703i
$479$	3.51426	+	24.4422i	0.160571	+	1.11679i	0.897561	+	0.440890i	$0.145337\pi$
$479$	3.51426	+	24.4422i	0.160571	+	1.11679i	−0.736990	+	0.675903i	$0.763754\pi$
$480$	−0.972274	+	0.624843i	−0.0443781	+	0.0285200i
$481$	14.1141	−	16.2885i	0.643548	−	0.742694i
$482$	6.92186			0.315282
$483$	−4.37554	−	1.96332i	−0.199094	−	0.0893341i
$484$	−3.00828			−0.136740
$485$	8.62133	−	9.94954i	0.391474	−	0.451785i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	−5.21520	−	36.2725i	−0.236323	−	1.64366i	−0.669831	−	0.742514i	$-0.733633\pi$
$487$	−5.21520	−	36.2725i	−0.236323	−	1.64366i	0.433507	−	0.901150i	$-0.357276\pi$
$488$	−2.62523	−	5.74844i	−0.118838	−	0.260220i
$489$	0.628897	−	4.37408i	0.0284397	−	0.197803i
$490$	−1.10893	+	0.325611i	−0.0500963	+	0.0147096i
$491$	−6.34513	−	4.07777i	−0.286352	−	0.184027i	0.389577	−	0.920994i	$-0.372621\pi$
$491$	−6.34513	−	4.07777i	−0.286352	−	0.184027i	−0.675929	+	0.736967i	$0.736257\pi$
$492$	1.34536	−	2.94592i	0.0606534	−	0.132812i
$493$	−5.54477	−	1.62809i	−0.249724	−	0.0733256i
$494$	−10.8057	−	12.4705i	−0.486173	−	0.561074i
$495$	−2.13959	−	2.46922i	−0.0961675	−	0.110983i
$496$	7.53739	+	2.21318i	0.338439	+	0.0993747i
$497$	1.70708	−	3.73799i	0.0765731	−	0.167672i
$498$	−1.82729	−	1.17433i	−0.0818829	−	0.0526229i
$499$	−5.38004	+	1.57972i	−0.240844	+	0.0707181i	−0.399927	−	0.916547i	$-0.630964\pi$
$499$	−5.38004	+	1.57972i	−0.240844	+	0.0707181i	0.159083	+	0.987265i	$0.449146\pi$
$500$	−1.42509	+	9.91174i	−0.0637321	+	0.443267i
$501$	−4.33101	−	9.48359i	−0.193495	−	0.423696i
$502$	−1.89705	−	13.1943i	−0.0846697	−	0.588890i
$503$	5.63992	−	3.62456i	0.251472	−	0.161611i	−0.408832	−	0.912610i	$-0.634064\pi$
$503$	5.63992	−	3.62456i	0.251472	−	0.161611i	0.660304	+	0.750999i	$0.270428\pi$
$504$	0.654861	−	0.755750i	0.0291698	−	0.0336638i
$505$	8.15858			0.363052
$506$	−3.90572	−	12.9829i	−0.173630	−	0.577159i
$507$	−28.7616			−1.27735
$508$	8.46258	−	9.76633i	0.375466	−	0.433311i
$509$	−16.1772	+	10.3965i	−0.717043	+	0.460816i	−0.847607	−	0.530624i	$-0.821958\pi$
$509$	−16.1772	+	10.3965i	−0.717043	+	0.460816i	0.130564	+	0.991440i	$0.458321\pi$
$510$	−0.243064	−	1.69055i	−0.0107631	−	0.0748587i
$511$	−6.45810	−	14.1413i	−0.285689	−	0.625573i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	2.44996	−	0.719373i	0.108168	−	0.0317611i
$514$	−9.24129	−	5.93902i	−0.407616	−	0.261959i
$515$	−1.97511	+	4.32488i	−0.0870336	+	0.190577i
$516$	8.87901	+	2.60711i	0.390876	+	0.114772i
$517$	−14.3936	−	16.6111i	−0.633030	−	0.730556i
$518$	2.18406	+	2.52054i	0.0959622	+	0.110746i
$519$	21.4750	+	6.30563i	0.942648	+	0.276786i
$520$	−3.10265	+	6.79385i	−0.136060	+	0.297930i
$521$	24.0532	+	15.4580i	1.05379	+	0.677229i	0.948359	−	0.317198i	$-0.102742\pi$
$521$	24.0532	+	15.4580i	1.05379	+	0.677229i	0.105429	+	0.994427i	$0.466378\pi$
$522$	−3.75211	+	1.10172i	−0.164225	+	0.0482209i
$523$	4.68519	−	32.5862i	0.204869	−	1.42489i	−0.584709	−	0.811243i	$-0.698791\pi$
$523$	4.68519	−	32.5862i	0.204869	−	1.42489i	0.789578	−	0.613651i	$-0.210300\pi$
$524$	2.15577	+	4.72048i	0.0941753	+	0.206215i
$525$	−0.521478	−	3.62696i	−0.0227592	−	0.158293i
$526$	12.9247	−	8.30619i	0.563543	−	0.362167i
$527$	−7.60216	+	8.77335i	−0.331155	+	0.382173i
$528$	2.82696			0.123028
$529$	−19.1824	+	12.6900i	−0.834017	+	0.551739i
$530$	−6.02018			−0.261500
$531$	4.86872	−	5.61881i	0.211285	−	0.243835i
$532$	2.14805	−	1.38047i	0.0931297	−	0.0598508i
$533$	−2.97848	−	20.7158i	−0.129012	−	0.897299i
$534$	2.97799	+	6.52088i	0.128870	+	0.282186i
$535$	−2.67513	+	18.6059i	−0.115656	+	0.804404i
$536$	−5.41053	+	1.58868i	−0.233699	+	0.0686203i
$537$	9.63281	+	6.19063i	0.415686	+	0.267145i
$538$	7.75626	−	16.9838i	0.334396	−	0.732225i
$539$	2.71245	+	0.796447i	0.116834	+	0.0343054i
$540$	−0.756852	−	0.873454i	−0.0325697	−	0.0375875i
$541$	−16.8349	−	19.4286i	−0.723791	−	0.835299i	0.267967	−	0.963428i	$-0.413648\pi$
$541$	−16.8349	−	19.4286i	−0.723791	−	0.835299i	−0.991758	+	0.128129i	$0.959103\pi$
$542$	3.76330	+	1.10500i	0.161648	+	0.0474640i
$543$	1.56716	−	3.43161i	0.0672534	−	0.147264i
$544$	1.24318	+	0.798945i	0.0533011	+	0.0342545i
$545$	−3.78277	+	1.11072i	−0.162036	+	0.0475781i
$546$	0.919684	−	6.39654i	0.0393588	−	0.273747i
$547$	14.2465	+	31.1955i	0.609137	+	1.33382i	0.923163	+	0.384409i	$0.125595\pi$
$547$	14.2465	+	31.1955i	0.609137	+	1.33382i	−0.314026	+	0.949414i	$0.601678\pi$
$548$	2.71878	+	18.9096i	0.116141	+	0.807776i
$549$	5.31632	−	3.41659i	0.226895	−	0.145817i
$550$	6.78351	−	7.82859i	0.289250	−	0.333812i
$551$	−9.98506			−0.425378
$552$	−1.38159	−	4.59252i	−0.0588046	−	0.195470i
$553$	−7.05347			−0.299944
$554$	−10.5795	+	12.2094i	−0.449480	+	0.518728i
$555$	3.24269	−	2.08395i	0.137644	−	0.0884586i
$556$	2.00201	+	13.9243i	0.0849040	+	0.590520i
$557$	2.65106	+	5.80500i	0.112329	+	0.245966i	0.957444	−	0.288618i	$-0.0931957\pi$
$557$	2.65106	+	5.80500i	0.112329	+	0.245966i	−0.845116	+	0.534584i	$0.820468\pi$
$558$	−1.11797	+	7.77564i	−0.0473274	+	0.329169i
$559$	57.3790	−	16.8480i	2.42687	−	0.712594i
$560$	−0.972274	−	0.624843i	−0.0410861	−	0.0264044i
$561$	−1.73544	+	3.80009i	−0.0732705	+	0.160440i
$562$	−4.01228	−	1.17811i	−0.169248	−	0.0496957i
$563$	19.5952	+	22.6141i	0.825840	+	0.953070i	0.999496	−	0.0317366i	$-0.0101038\pi$
$563$	19.5952	+	22.6141i	0.825840	+	0.953070i	−0.173657	+	0.984806i	$0.555558\pi$
$564$	−5.09155	−	5.87596i	−0.214393	−	0.247422i
$565$	−18.2614	−	5.36203i	−0.768262	−	0.225582i
$566$	−1.53813	+	3.36803i	−0.0646522	+	0.141569i
$567$	0.841254	+	0.540641i	0.0353293	+	0.0227048i
$568$	3.94288	−	1.15773i	0.165440	−	0.0485775i
$569$	−2.71823	+	18.9057i	−0.113954	+	0.792570i	0.850054	+	0.526696i	$0.176569\pi$
$569$	−2.71823	+	18.9057i	−0.113954	+	0.792570i	−0.964008	+	0.265873i	$0.914340\pi$
$570$	−1.22592	−	2.68438i	−0.0513480	−	0.112437i
$571$	−5.19457	−	36.1290i	−0.217386	−	1.51195i	−0.747635	−	0.664110i	$-0.768811\pi$
$571$	−5.19457	−	36.1290i	−0.217386	−	1.51195i	0.530249	−	0.847842i	$-0.322099\pi$
$572$	15.3686	−	9.87683i	0.642595	−	0.412971i
$573$	−6.34458	+	7.32204i	−0.265049	+	0.305883i
$574$	3.23859			0.135176
$575$	−16.0331	−	7.19410i	−0.668627	−	0.300015i
$576$	1.00000			0.0416667
$577$	28.9469	−	33.4065i	1.20507	−	1.39073i	0.306521	−	0.951864i	$-0.400835\pi$
$577$	28.9469	−	33.4065i	1.20507	−	1.39073i	0.898553	−	0.438865i	$-0.144619\pi$
$578$	12.4642	−	8.01023i	0.518441	−	0.333182i
$579$	1.83568	+	12.7674i	0.0762881	+	0.530595i
$580$	1.87749	+	4.11113i	0.0779586	+	0.170705i
$581$	0.309123	−	2.15000i	0.0128246	−	0.0891969i
$582$	−10.9296	+	3.20923i	−0.453047	+	0.133027i
$583$	12.3878	+	7.96116i	0.513051	+	0.329718i
$584$	6.45810	−	14.1413i	0.267238	−	0.585170i
$585$	−7.16626	−	2.10420i	−0.296288	−	0.0869981i
$586$	17.0705	+	19.7004i	0.705177	+	0.813818i
$587$	1.19846	+	1.38309i	0.0494656	+	0.0570864i	0.779943	−	0.625850i	$-0.215248\pi$
$587$	1.19846	+	1.38309i	0.0494656	+	0.0570864i	−0.730478	+	0.682937i	$0.760702\pi$
$588$	0.959493	+	0.281733i	0.0395688	+	0.0116185i
$589$	−8.33257	+	18.2458i	−0.343337	+	0.751804i
$590$	−7.22861	−	4.64555i	−0.297597	−	0.191254i
$591$	16.5059	−	4.84658i	0.678963	−	0.199362i
$592$	−0.474642	+	3.30121i	−0.0195077	+	0.135679i
$593$	−5.59200	−	12.2448i	−0.229636	−	0.502832i	0.759379	−	0.650648i	$-0.225503\pi$
$593$	−5.59200	−	12.2448i	−0.229636	−	0.502832i	−0.989015	+	0.147816i	$0.952776\pi$
$594$	0.402319	+	2.79819i	0.0165073	+	0.114811i
$595$	1.43680	−	0.923377i	0.0589032	−	0.0378548i
$596$	11.8800	−	13.7102i	0.486623	−	0.561593i
$597$	−14.2482			−0.583141
$598$	−23.5563	−	20.1400i	−0.963288	−	0.823585i
$599$	12.7292			0.520101			0.260050	−	0.965595i	$-0.416261\pi$
$599$	12.7292			0.520101			0.260050	+	0.965595i	$0.416261\pi$
$600$	2.39958	−	2.76926i	0.0979623	−	0.113054i
$601$	18.1528	−	11.6661i	0.740468	−	0.475870i	−0.115235	−	0.993338i	$-0.536762\pi$
$601$	18.1528	−	11.6661i	0.740468	−	0.475870i	0.855702	+	0.517469i	$0.173126\pi$
$602$	1.31696	+	9.15966i	0.0536753	+	0.373320i
$603$	−2.34250	−	5.12937i	−0.0953941	−	0.208884i
$604$	0.664042	−	4.61852i	0.0270195	−	0.187925i
$605$	−3.33597	+	0.979529i	−0.135626	+	0.0398235i
$606$	−5.93854	−	3.81646i	−0.241237	−	0.155033i
$607$	−6.86910	+	15.0412i	−0.278808	+	0.610504i	−0.996289	−	0.0860739i	$-0.972568\pi$
$607$	−6.86910	+	15.0412i	−0.278808	+	0.610504i	0.717481	+	0.696578i	$0.245295\pi$
$608$	2.44996	+	0.719373i	0.0993590	+	0.0291744i
$609$	−2.56084	−	2.95537i	−0.103771	−	0.119758i
$610$	−4.78294	−	5.51981i	−0.193656	−	0.223491i
$611$	−48.2093	−	14.1555i	−1.95034	−	0.572672i
$612$	−0.613890	+	1.34423i	−0.0248150	+	0.0543373i
$613$	29.0773	+	18.6869i	1.17442	+	0.754756i	0.974353	−	0.225026i	$-0.0722468\pi$
$613$	29.0773	+	18.6869i	1.17442	+	0.754756i	0.200070	+	0.979782i	$0.435883\pi$
$614$	20.1293	−	5.91049i	0.812352	−	0.238528i
$615$	0.532682	−	3.70488i	0.0214798	−	0.149395i
$616$	1.17436	+	2.57150i	0.0473164	+	0.103609i
$617$	−1.24093	−	8.63084i	−0.0499579	−	0.347465i	−0.999434	−	0.0336267i	$-0.989294\pi$
$617$	−1.24093	−	8.63084i	−0.0499579	−	0.347465i	0.949477	−	0.313838i	$-0.101615\pi$
$618$	3.46078	−	2.22411i	0.139213	−	0.0894667i
$619$	26.7887	−	30.9158i	1.07673	−	1.24261i	0.108091	−	0.994141i	$-0.465526\pi$
$619$	26.7887	−	30.9158i	1.07673	−	1.24261i	0.968639	−	0.248472i	$-0.0799283\pi$
$620$	9.07907			0.364624
$621$	4.34915	−	2.02112i	0.174525	−	0.0811046i
$622$	−26.5242			−1.06353
$623$	−4.69450	+	5.41774i	−0.188081	+	0.217057i
$624$	5.43645	−	3.49379i	0.217632	−	0.139864i
$625$	−0.960344	−	6.67934i	−0.0384138	−	0.267174i
$626$	5.77113	+	12.6370i	0.230661	+	0.505076i
$627$	−1.02728	+	7.14487i	−0.0410255	+	0.285338i
$628$	6.97084	−	2.04682i	0.278167	−	0.0816772i
$629$	−4.14621	−	2.66461i	−0.165320	−	0.106245i
$630$	0.480114	−	1.05130i	0.0191282	−	0.0418849i
$631$	12.9635	+	3.80644i	0.516070	+	0.151532i	0.529389	−	0.848379i	$-0.322421\pi$
$631$	12.9635	+	3.80644i	0.516070	+	0.151532i	−0.0133185	+	0.999911i	$0.504240\pi$
$632$	−4.61904	−	5.33066i	−0.183736	−	0.212042i
$633$	−18.8341	−	21.7357i	−0.748587	−	0.863916i
$634$	5.49712	+	1.61410i	0.218318	+	0.0641040i
$635$	6.20437	−	13.5857i	0.246213	−	0.539131i
$636$	4.38202	+	2.81615i	0.173758	+	0.111668i
$637$	6.20055	−	1.82065i	0.245675	−	0.0721366i
$638$	1.57327	−	10.9424i	0.0622865	−	0.433212i
$639$	1.70708	+	3.73799i	0.0675311	+	0.147873i
$640$	−0.164480	−	1.14398i	−0.00650163	−	0.0452198i
$641$	−5.38257	+	3.45917i	−0.212599	+	0.136629i	−0.642607	−	0.766196i	$-0.722147\pi$
$641$	−5.38257	+	3.45917i	−0.212599	+	0.136629i	0.430008	+	0.902825i	$0.358511\pi$
$642$	10.6508	−	12.2917i	0.420353	−	0.485113i
$643$	−41.3745			−1.63165			−0.815825	−	0.578299i	$-0.803717\pi$
$643$	−41.3745			−1.63165			−0.815825	+	0.578299i	$0.803717\pi$
$644$	3.60356	−	3.16454i	0.142000	−	0.124700i
$645$	10.6951			0.421119
$646$	−2.47101	+	2.85170i	−0.0972206	+	0.112199i
$647$	−11.8422	+	7.61054i	−0.465566	+	0.299201i	−0.752314	−	0.658805i	$-0.771062\pi$
$647$	−11.8422	+	7.61054i	−0.465566	+	0.299201i	0.286748	+	0.958006i	$0.407426\pi$
$648$	0.142315	+	0.989821i	0.00559065	+	0.0388839i
$649$	8.73109	+	19.1184i	0.342725	+	0.750464i
$650$	3.36996	−	23.4386i	0.132181	−	0.919336i
$651$	−7.53739	+	2.21318i	−0.295414	+	0.0867413i
$652$	3.71755	+	2.38912i	0.145590	+	0.0935652i
$653$	−14.8685	+	32.5575i	−0.581850	+	1.27407i	0.358393	+	0.933571i	$0.383325\pi$
$653$	−14.8685	+	32.5575i	−0.581850	+	1.27407i	−0.940243	+	0.340503i	$0.889403\pi$
$654$	3.27302	+	0.961045i	0.127985	+	0.0375798i
$655$	3.92764	+	4.53274i	0.153466	+	0.177109i
$656$	2.12082	+	2.44756i	0.0828043	+	0.0955612i
$657$	14.9164	+	4.37985i	0.581944	+	0.170874i
$658$	3.22985	−	7.07239i	0.125913	−	0.275711i
$659$	−2.73698	−	1.75895i	−0.106617	−	0.0685189i	0.486246	−	0.873822i	$-0.338366\pi$
$659$	−2.73698	−	1.75895i	−0.106617	−	0.0685189i	−0.592863	+	0.805303i	$0.702002\pi$
$660$	3.13490	−	0.920490i	0.122026	−	0.0358300i
$661$	0.327105	−	2.27506i	0.0127229	−	0.0884898i	−0.982471	−	0.186417i	$-0.940312\pi$
$661$	0.327105	−	2.27506i	0.0127229	−	0.0884898i	0.995194	+	0.0979277i	$0.0312214\pi$
$662$	7.79755	+	17.0742i	0.303060	+	0.663609i
$663$	1.35909	+	9.45265i	0.0527825	+	0.367111i
$664$	1.82729	−	1.17433i	0.0709127	−	0.0455728i
$665$	1.93254	−	2.23027i	0.0749406	−	0.0864861i
$666$	−3.33515			−0.129235
$667$	−18.5452	+	2.79191i	−0.718072	+	0.108103i
$668$	10.4257			0.403384
$669$	6.84292	−	7.89715i	0.264562	−	0.305321i
$670$	−5.48261	+	3.52346i	−0.211812	+	0.136123i
$671$	2.54246	+	17.6832i	0.0981507	+	0.682653i
$672$	0.415415	+	0.909632i	0.0160250	+	0.0350898i
$673$	−6.97337	+	48.5009i	−0.268804	+	1.86957i	0.191056	+	0.981579i	$0.438809\pi$
$673$	−6.97337	+	48.5009i	−0.268804	+	1.86957i	−0.459860	+	0.887991i	$0.652100\pi$
$674$	−25.5959	+	7.51562i	−0.985916	+	0.289491i
$675$	3.08257	+	1.98105i	0.118648	+	0.0762505i
$676$	11.9480	−	26.1625i	0.459538	−	1.00625i
$677$	−18.0726	−	5.30659i	−0.694586	−	0.203949i	−0.0846630	−	0.996410i	$-0.526981\pi$
$677$	−18.0726	−	5.30659i	−0.694586	−	0.203949i	−0.609923	+	0.792461i	$0.708800\pi$
$678$	10.7840	+	12.4454i	0.414156	+	0.477962i
$679$	−7.45954	−	8.60877i	−0.286271	−	0.330374i
$680$	1.63875	+	0.481180i	0.0628431	+	0.0184524i
$681$	3.25223	−	7.12139i	0.124626	−	0.272892i
$682$	−18.6821	−	12.0063i	−0.715376	−	0.459744i
$683$	17.6138	−	5.17188i	0.673973	−	0.197896i	0.0732016	−	0.997317i	$-0.476678\pi$
$683$	17.6138	−	5.17188i	0.673973	−	0.197896i	0.600771	+	0.799421i	$0.294860\pi$
$684$	−0.363385	+	2.52740i	−0.0138944	+	0.0966376i
$685$	9.17210	+	20.0841i	0.350448	+	0.767374i
$686$	0.142315	+	0.989821i	0.00543361	+	0.0377916i
$687$	−2.15602	+	1.38559i	−0.0822573	+	0.0528636i
$688$	−6.05998	+	6.99359i	−0.231035	+	0.266628i
$689$	33.6617			1.28241
$690$	−3.02746	−	4.64291i	−0.115254	−	0.176753i
$691$	38.6768			1.47133			0.735667	−	0.677343i	$-0.236869\pi$
$691$	38.6768			1.47133			0.735667	+	0.677343i	$0.236869\pi$
$692$	−14.6568	+	16.9149i	−0.557170	+	0.643008i
$693$	−2.37819	+	1.52837i	−0.0903401	+	0.0580580i
$694$	1.36217	+	9.47413i	0.0517074	+	0.359633i
$695$	6.75397	+	14.7891i	0.256193	+	0.560984i
$696$	0.556524	−	3.87071i	0.0210950	−	0.146719i
$697$	−4.59204	+	1.34834i	−0.173936	+	0.0510722i
$698$	−14.4008	−	9.25481i	−0.545077	−	0.350300i
$699$	−3.23152	+	7.07604i	−0.122227	+	0.267640i
$700$	3.51583	+	1.03234i	0.132886	+	0.0390188i
$701$	27.5864	+	31.8364i	1.04192	+	1.20245i	0.978880	+	0.204435i	$0.0655356\pi$
$701$	27.5864	+	31.8364i	1.04192	+	1.20245i	0.0630448	+	0.998011i	$0.479919\pi$
$702$	4.23192	+	4.88390i	0.159724	+	0.184331i
$703$	−8.17099	−	2.39922i	−0.308175	−	0.0904883i
$704$	−1.17436	+	2.57150i	−0.0442605	+	0.0969169i
$705$	−7.55944	−	4.85816i	−0.284705	−	0.182969i
$706$	0.700003	−	0.205539i	0.0263450	−	0.00773558i
$707$	1.00462	−	6.98730i	0.0377827	−	0.262784i
$708$	3.08851	+	6.76288i	0.116073	+	0.254165i
$709$	−6.70459	−	46.6315i	−0.251796	−	1.75128i	−0.587417	−	0.809284i	$-0.699855\pi$
$709$	−6.70459	−	46.6315i	−0.251796	−	1.75128i	0.335621	−	0.941997i	$-0.391054\pi$
$710$	3.99541	−	2.56769i	0.149945	−	0.0963638i
$711$	4.61904	−	5.33066i	0.173228	−	0.199915i
$712$	−7.16870			−0.268658
$713$	−10.3743	+	36.2176i	−0.388522	+	1.35636i
$714$	−1.47778			−0.0553043
$715$	13.8267	−	15.9569i	0.517090	−	0.596754i
$716$	−9.63281	+	6.19063i	−0.359995	+	0.231355i
$717$	−4.19713	−	29.1917i	−0.156745	−	1.09018i
$718$	3.77491	+	8.26589i	0.140878	+	0.308480i
$719$	−0.194021	+	1.34945i	−0.00723577	+	0.0503259i	−0.993119	−	0.117106i	$-0.962638\pi$
$719$	−0.194021	+	1.34945i	−0.00723577	+	0.0503259i	0.985884	+	0.167432i	$0.0535474\pi$
$720$	1.10893	−	0.325611i	0.0413273	−	0.0121348i
$721$	3.46078	+	2.22411i	0.128886	+	0.0828300i
$722$	5.18446	−	11.3524i	0.192946	−	0.422492i
$723$	−6.64147	−	1.95011i	−0.246999	−	0.0725255i
$724$	2.47048	+	2.85108i	0.0918145	+	0.105960i
$725$	−9.38357	−	10.8292i	−0.348497	−	0.402187i
$726$	2.88642	+	0.847531i	0.107125	+	0.0314548i
$727$	9.81258	−	21.4866i	0.363929	−	0.796892i	−0.635759	−	0.771888i	$-0.719313\pi$
$727$	9.81258	−	21.4866i	0.363929	−	0.796892i	0.999687	−	0.0250045i	$-0.00796002\pi$
$728$	5.43645	+	3.49379i	0.201488	+	0.129489i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	2.55702	−	17.7845i	0.0946397	−	0.658233i
$731$	−5.68085	−	12.4393i	−0.210114	−	0.460085i
$732$	0.899362	+	6.25520i	0.0332414	+	0.231199i
$733$	35.3300	−	22.7052i	1.30494	−	0.838636i	0.311202	−	0.950344i	$-0.399268\pi$
$733$	35.3300	−	22.7052i	1.30494	−	0.838636i	0.993741	+	0.111707i	$0.0356319\pi$
$734$	3.19684	−	3.68935i	0.117998	−	0.136176i
$735$	1.15574			0.0426303
$736$	4.75143	+	0.651057i	0.175140	+	0.0239983i
$737$	15.9411			0.587198
$738$	−2.12082	+	2.44756i	−0.0780686	+	0.0900960i
$739$	1.23930	−	0.796450i	0.0455884	−	0.0292979i	−0.517648	−	0.855594i	$-0.673192\pi$
$739$	1.23930	−	0.796450i	0.0455884	−	0.0292979i	0.563237	+	0.826296i	$0.309556\pi$
$740$	0.548565	+	3.81535i	0.0201656	+	0.140255i
$741$	6.85469	+	15.0097i	0.251813	+	0.551394i
$742$	−0.741306	+	5.15590i	−0.0272142	+	0.189279i
$743$	21.4475	−	6.29755i	0.786832	−	0.231035i	0.136455	−	0.990646i	$-0.456429\pi$
$743$	21.4475	−	6.29755i	0.786832	−	0.231035i	0.650377	+	0.759611i	$0.274611\pi$
$744$	−6.60855	−	4.24706i	−0.242281	−	0.155705i
$745$	8.70986	−	19.0719i	0.319104	−	0.698741i
$746$	−14.3307	−	4.20788i	−0.524686	−	0.154062i
$747$	1.42243	+	1.64157i	0.0520439	+	0.0600618i
$748$	−2.73576	−	3.15723i	−0.100029	−	0.115440i
$749$	15.6054	+	4.58215i	0.570208	+	0.167428i
$750$	4.15983	−	9.10875i	0.151895	−	0.332605i
$751$	18.2507	+	11.7290i	0.665977	+	0.427998i	0.829473	−	0.558546i	$-0.188641\pi$
$751$	18.2507	+	11.7290i	0.665977	+	0.427998i	−0.163496	+	0.986544i	$0.552277\pi$
$752$	7.46006	−	2.19047i	0.272041	−	0.0798783i
$753$	−1.89705	+	13.1943i	−0.0691325	+	0.480827i
$754$	−10.4979	−	22.9873i	−0.382313	−	0.837148i
$755$	−0.767463	−	5.33783i	−0.0279309	−	0.194263i
$756$	−0.841254	+	0.540641i	−0.0305961	+	0.0196629i
$757$	4.03634	−	4.65818i	0.146703	−	0.169304i	−0.677642	−	0.735392i	$-0.736998\pi$
$757$	4.03634	−	4.65818i	0.146703	−	0.169304i	0.824345	+	0.566087i	$0.191544\pi$
$758$	0.403087			0.0146408
$759$	0.0898112	+	13.5573i	0.00325994	+	0.492100i
$760$	2.95107			0.107046
$761$	21.6076	−	24.9365i	0.783276	−	0.903949i	−0.214065	−	0.976819i	$-0.568671\pi$
$761$	21.6076	−	24.9365i	0.783276	−	0.903949i	0.997341	+	0.0728707i	$0.0232160\pi$
$762$	−10.8713	+	6.98655i	−0.393825	+	0.253096i
$763$	0.485464	+	3.37647i	0.0175750	+	0.122237i
$764$	−4.02473	−	8.81292i	−0.145609	−	0.318840i
$765$	−0.243064	+	1.69055i	−0.00878799	+	0.0611218i
$766$	−31.7446	+	9.32105i	−1.14698	+	0.336783i
$767$	40.4186	+	25.9755i	1.45943	+	0.937920i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	−8.47291	−	2.48787i	−0.305541	−	0.0897149i	0.125368	−	0.992110i	$-0.459989\pi$
$769$	−8.47291	−	2.48787i	−0.305541	−	0.0897149i	−0.430909	+	0.902395i	$0.641807\pi$
$770$	2.13959	+	2.46922i	0.0771055	+	0.0889845i
$771$	7.19374	+	8.30202i	0.259076	+	0.298990i
$772$	−12.3762	−	3.63398i	−0.445430	−	0.130790i
$773$	−2.23114	+	4.88551i	−0.0802484	+	0.175720i	−0.945503	−	0.325613i	$-0.894429\pi$
$773$	−2.23114	+	4.88551i	−0.0802484	+	0.175720i	0.865255	+	0.501332i	$0.167157\pi$
$774$	−7.78484	−	5.00301i	−0.279820	−	0.179829i
$775$	−27.6189	+	8.10965i	−0.992101	+	0.291307i
$776$	1.62111	−	11.2751i	0.0581946	−	0.404752i
$777$	−1.38547	−	3.03376i	−0.0497036	−	0.108836i
$778$	−1.25806	−	8.75000i	−0.0451036	−	0.313703i
$779$	−6.95664	+	4.47076i	−0.249248	+	0.160182i
$780$	4.89102	−	5.64454i	0.175127	−	0.202107i
$781$	−11.6170			−0.415687
$782$	−3.79203	+	5.98735i	−0.135603	+	0.214107i
$783$	3.91051			0.139750
$784$	−0.654861	+	0.755750i	−0.0233879	+	0.0269911i
$785$	7.06370	−	4.53957i	0.252114	−	0.162024i
$786$	−0.738535	−	5.13662i	−0.0263427	−	0.183217i
$787$	−3.21148	−	7.03215i	−0.114477	−	0.250669i	0.843718	−	0.536787i	$-0.180362\pi$
$787$	−3.21148	−	7.03215i	−0.114477	−	0.250669i	−0.958194	+	0.286118i	$0.907635\pi$
$788$	−2.44821	+	17.0277i	−0.0872138	+	0.606585i
$789$	−14.7413	+	4.32843i	−0.524803	+	0.154096i
$790$	−6.85791	−	4.40731i	−0.243993	−	0.156805i
$791$	−6.84088	+	14.9794i	−0.243234	+	0.532608i
$792$	−2.71245	−	0.796447i	−0.0963827	−	0.0283005i
$793$	26.7437	+	30.8639i	0.949698	+	1.09601i
$794$	8.67716	+	10.0140i	0.307941	+	0.355383i
$795$	5.77632	+	1.69608i	0.204865	+	0.0601538i
$796$	5.91892	−	12.9606i	0.209791	−	0.459378i
$797$	−32.7450	−	21.0439i	−1.15989	−	0.745414i	−0.188304	−	0.982111i	$-0.560299\pi$
$797$	−32.7450	−	21.0439i	−1.15989	−	0.745414i	−0.971584	+	0.236697i	$0.923935\pi$
$798$	−2.44996	+	0.719373i	−0.0867276	+	0.0254655i
$799$	−1.63516	+	11.3728i	−0.0578477	+	0.402339i
$800$	1.52219	+	3.33312i	0.0538174	+	0.117844i
$801$	−1.02021	−	7.09573i	−0.0360474	−	0.250715i
$802$	−0.620162	+	0.398554i	−0.0218987	+	0.0140734i
$803$	−28.7800	+	33.2139i	−1.01563	+	1.17209i
$804$	5.63895			0.198870
$805$	2.96569	−	4.68261i	0.104527	−	0.165040i
$806$	−50.7654			−1.78814
$807$	−12.2270	+	14.1107i	−0.430410	+	0.496720i
$808$	5.93854	−	3.81646i	0.208917	−	0.134263i
$809$	7.46598	+	51.9271i	0.262490	+	1.82566i	0.513985	+	0.857799i	$0.328169\pi$
$809$	7.46598	+	51.9271i	0.262490	+	1.82566i	−0.251494	+	0.967859i	$0.580922\pi$
$810$	0.480114	+	1.05130i	0.0168695	+	0.0369390i
$811$	−0.909285	+	6.32422i	−0.0319293	+	0.222073i	−0.999538	−	0.0303799i	$-0.990328\pi$
$811$	−0.909285	+	6.32422i	−0.0319293	+	0.222073i	0.967609	+	0.252453i	$0.0812374\pi$
$812$	3.75211	−	1.10172i	0.131673	−	0.0386627i
$813$	−3.29954	−	2.12049i	−0.115720	−	0.0743688i
$814$	3.91668	−	8.57634i	0.137280	−	0.300600i
$815$	4.90042	+	1.43889i	0.171654	+	0.0504022i
$816$	−0.967737	−	1.11683i	−0.0338776	−	0.0390968i
$817$	−15.4735	−	17.8574i	−0.541349	−	0.624750i
$818$	28.2953	+	8.30826i	0.989324	+	0.290492i
$819$	−2.68455	+	5.87833i	−0.0938056	+	0.205406i
$820$	3.14880	+	2.02361i	0.109961	+	0.0706675i
$821$	0.428700	−	0.125878i	0.0149617	−	0.00439316i	−0.274243	−	0.961660i	$-0.588427\pi$
$821$	0.428700	−	0.125878i	0.0149617	−	0.00439316i	0.289205	+	0.957267i	$0.406609\pi$
$822$	2.71878	−	18.9096i	0.0948285	−	0.659547i
$823$	−19.3731	−	42.4212i	−0.675304	−	1.47871i	−0.867543	−	0.497362i	$-0.834302\pi$
$823$	−19.3731	−	42.4212i	−0.675304	−	1.47871i	0.192239	−	0.981348i	$-0.438425\pi$
$824$	0.585459	+	4.07196i	0.0203954	+	0.141853i
$825$	−8.71430	+	5.60034i	−0.303393	+	0.194979i
$826$	−4.86872	+	5.61881i	−0.169405	+	0.195503i
$827$	31.4263			1.09280			0.546399	−	0.837525i	$-0.315998\pi$
$827$	31.4263			1.09280			0.546399	+	0.837525i	$0.315998\pi$
$828$	0.0317695	+	4.79573i	0.00110407	+	0.166663i
$829$	−39.0400			−1.35591			−0.677957	−	0.735101i	$-0.737135\pi$
$829$	−39.0400			−1.35591			−0.677957	+	0.735101i	$0.737135\pi$
$830$	1.64396	−	1.89723i	0.0570628	−	0.0658539i
$831$	13.5908	−	8.73425i	0.471458	−	0.302988i
$832$	0.919684	+	6.39654i	0.0318843	+	0.221760i
$833$	−0.613890	−	1.34423i	−0.0212700	−	0.0465749i
$834$	2.00201	−	13.9243i	0.0693238	−	0.482158i
$835$	11.5614	−	3.39474i	0.400099	−	0.117480i
$836$	−6.07245	−	3.90253i	−0.210020	−	0.134972i
$837$	3.26334	−	7.14571i	0.112797	−	0.246992i
$838$	38.2165	+	11.2214i	1.32017	+	0.387636i
$839$	−5.36757	−	6.19450i	−0.185309	−	0.213858i	0.655492	−	0.755202i	$-0.272461\pi$
$839$	−5.36757	−	6.19450i	−0.185309	−	0.213858i	−0.840801	+	0.541344i	$0.817916\pi$
$840$	0.756852	+	0.873454i	0.0261139	+	0.0301370i
$841$	13.1526	+	3.86196i	0.453539	+	0.133171i
$842$	−8.29176	+	18.1564i	−0.285753	+	0.625712i
$843$	3.51784	+	2.26078i	0.121161	+	0.0778655i
$844$	27.5954	−	8.10275i	0.949874	−	0.278908i
$845$	4.73070	−	32.9027i	0.162741	−	1.13189i
$846$	3.22985	+	7.07239i	0.111045	+	0.243154i
$847$	0.428123	+	2.97766i	0.0147105	+	0.102314i
$848$	−4.38202	+	2.81615i	−0.150479	+	0.0967071i
$849$	2.42470	−	2.79826i	0.0832156	−	0.0960359i
$850$	−5.41494			−0.185731
$851$	−15.8468	−	2.17138i	−0.543220	−	0.0744338i
$852$	−4.10934			−0.140784
$853$	3.77922	−	4.36146i	0.129398	−	0.149333i	−0.687353	−	0.726324i	$-0.741227\pi$
$853$	3.77922	−	4.36146i	0.129398	−	0.149333i	0.816751	+	0.576990i	$0.195773\pi$
$854$	−5.31632	+	3.41659i	−0.181921	+	0.116913i
$855$	0.419981	+	2.92103i	0.0143630	+	0.0998971i
$856$	6.75639	+	14.7944i	0.230929	+	0.505663i
$857$	−0.995053	+	6.92075i	−0.0339904	+	0.236408i	−0.999733	−	0.0230923i	$-0.992649\pi$
$857$	−0.995053	+	6.92075i	−0.0339904	+	0.236408i	0.965743	+	0.259501i	$0.0835579\pi$
$858$	−17.5287	+	5.14690i	−0.598421	+	0.175712i
$859$	−11.2238	−	7.21309i	−0.382951	−	0.246108i	0.334975	−	0.942227i	$-0.391272\pi$
$859$	−11.2238	−	7.21309i	−0.382951	−	0.246108i	−0.717926	+	0.696119i	$0.754908\pi$
$860$	−4.44290	+	9.72860i	−0.151502	+	0.331742i
$861$	−3.10740	−	0.912415i	−0.105900	−	0.0310950i
$862$	−2.22706	−	2.57016i	−0.0758538	−	0.0875400i
$863$	25.1761	+	29.0548i	0.857004	+	0.989035i	1.00000		0.000687849i	$-0.000218949\pi$
$863$	25.1761	+	29.0548i	0.857004	+	0.989035i	−0.142996	+	0.989723i	$0.545673\pi$
$864$	−0.959493	−	0.281733i	−0.0326426	−	0.00958474i
$865$	−10.7457	+	23.5299i	−0.365366	+	0.800039i
$866$	−23.5690	−	15.1469i	−0.800907	−	0.514712i
$867$	−14.2160	+	4.17420i	−0.482801	+	0.141763i
$868$	1.11797	−	7.77564i	0.0379463	−	0.263923i
$869$	8.28333	+	18.1380i	0.280993	+	0.615288i
$870$	−0.643200	−	4.47355i	−0.0218065	−	0.151668i
$871$	30.6559	−	19.7013i	1.03873	−	0.667554i
$872$	−2.23386	+	2.57801i	−0.0756480	+	0.0873024i
$873$	11.3910			0.385528
$874$	−3.37208	+	11.7722i	−0.114062	+	0.398200i
$875$	10.0137			0.338524
$876$	−10.1806	+	11.7490i	−0.343969	+	0.396961i
$877$	−14.1758	+	9.11026i	−0.478684	+	0.307632i	−0.757640	−	0.652672i	$-0.773648\pi$
$877$	−14.1758	+	9.11026i	−0.478684	+	0.307632i	0.278956	+	0.960304i	$0.410012\pi$
$878$	3.14263	+	21.8575i	0.106059	+	0.737655i
$879$	−10.8288	−	23.7118i	−0.365246	−	0.799778i
$880$	−0.464978	+	3.23399i	−0.0156744	+	0.109018i
$881$	27.3340	−	8.02597i	0.920904	−	0.270402i	0.213280	−	0.976991i	$-0.431585\pi$
$881$	27.3340	−	8.02597i	0.920904	−	0.270402i	0.707624	+	0.706589i	$0.249767\pi$
$882$	−0.841254	−	0.540641i	−0.0283265	−	0.0182043i
$883$	−4.35700	+	9.54051i	−0.146625	+	0.321064i	−0.968667	−	0.248363i	$-0.920107\pi$
$883$	−4.35700	+	9.54051i	−0.146625	+	0.321064i	0.822042	+	0.569427i	$0.192835\pi$
$884$	−9.16302	−	2.69051i	−0.308186	−	0.0904915i
$885$	5.62700	+	6.49391i	0.189150	+	0.218290i
$886$	1.87826	+	2.16763i	0.0631015	+	0.0728230i
$887$	29.3002	+	8.60331i	0.983804	+	0.288871i	0.733794	−	0.679372i	$-0.237748\pi$
$887$	29.3002	+	8.60331i	0.983804	+	0.288871i	0.250010	+	0.968243i	$0.419566\pi$
$888$	1.38547	−	3.03376i	0.0464934	−	0.101806i
$889$	−10.8713	−	6.98655i	−0.364611	−	0.234321i
$890$	−7.94958	+	2.33421i	−0.266471	+	0.0782428i
$891$	0.402319	−	2.79819i	0.0134782	−	0.0937428i
$892$	4.34085	+	9.50513i	0.145342	+	0.318255i
$893$	2.82532	+	19.6506i	0.0945458	+	0.657581i
$894$	−15.2614	+	9.80789i	−0.510417	+	0.328025i
$895$	−8.66637	+	10.0015i	−0.289685	+	0.334314i
$896$	−1.00000			−0.0334077
$897$	16.9280	+	25.9607i	0.565209	+	0.866804i
$898$	31.8930			1.06428
$899$	−20.1169	+	23.2162i	−0.670938	+	0.774304i
$900$	−3.08257	+	1.98105i	−0.102752	+	0.0660348i
$901$	−1.09548	−	7.61926i	−0.0364959	−	0.253834i
$902$	−3.80328	−	8.32801i	−0.126635	−	0.277293i
$903$	1.31696	−	9.15966i	0.0438257	−	0.304814i
$904$	−15.8005	+	4.63946i	−0.525518	+	0.154306i
$905$	3.66793	+	2.35723i	0.121926	+	0.0783571i
$906$	−1.93833	+	4.24435i	−0.0643967	+	0.141009i
$907$	−28.9654	−	8.50499i	−0.961779	−	0.282404i	−0.237096	−	0.971486i	$-0.576196\pi$
$907$	−28.9654	−	8.50499i	−0.961779	−	0.282404i	−0.724683	+	0.689083i	$0.758014\pi$
$908$	5.12682	+	5.91666i	0.170139	+	0.196351i
$909$	4.62276	+	5.33495i	0.153327	+	0.176949i
$910$	7.16626	+	2.10420i	0.237559	+	0.0697536i
$911$	−5.04263	+	11.0418i	−0.167070	+	0.365832i	−0.974586	−	0.224013i	$-0.928084\pi$
$911$	−5.04263	+	11.0418i	−0.167070	+	0.365832i	0.807516	+	0.589845i	$0.200811\pi$
$912$	−2.14805	−	1.38047i	−0.0711290	−	0.0457118i
$913$	−5.89173	+	1.72997i	−0.194988	+	0.0572536i
$914$	−1.99471	+	13.8735i	−0.0659793	+	0.458896i
$915$	3.03409	+	6.64373i	0.100304	+	0.219635i
$916$	−0.364734	−	2.53678i	−0.0120512	−	0.0838176i
$917$	4.36564	−	2.80562i	0.144166	−	0.0926499i
$918$	0.967737	−	1.11683i	0.0319401	−	0.0368608i
$919$	−46.2652			−1.52615			−0.763075	−	0.646310i	$-0.776311\pi$
$919$	−46.2652			−1.52615			−0.763075	+	0.646310i	$0.776311\pi$
$920$	5.48099	−	0.825143i	0.180703	−	0.0272042i
$921$	−20.9791			−0.691284
$922$	−24.7907	+	28.6100i	−0.816438	+	0.942219i
$923$	−22.3402	+	14.3572i	−0.735337	+	0.472573i
$924$	−0.402319	−	2.79819i	−0.0132353	−	0.0920536i
$925$	−5.07673	−	11.1165i	−0.166922	−	0.365508i
$926$	−2.87204	+	19.9755i	−0.0943810	+	0.656434i
$927$	−3.94719	+	1.15900i	−0.129643	+	0.0380666i
$928$	3.28973	+	2.11418i	0.107991	+	0.0694015i
$929$	−17.5737	+	38.4810i	−0.576573	+	1.26252i	0.366650	+	0.930359i	$0.380505\pi$
$929$	−17.5737	+	38.4810i	−0.576573	+	1.26252i	−0.943223	+	0.332160i	$0.892223\pi$
$930$	−8.71130	−	2.55787i	−0.285655	−	0.0838759i
$931$	−1.67211	−	1.92972i	−0.0548013	−	0.0632441i
$932$	−5.09417	−	5.87898i	−0.166865	−	0.192573i
$933$	25.4498	+	7.47274i	0.833190	+	0.244647i
$934$	3.67963	−	8.05727i	0.120401	−	0.263642i
$935$	−4.06179	−	2.61035i	−0.132835	−	0.0853677i
$936$	−6.20055	+	1.82065i	−0.202671	+	0.0595097i
$937$	−3.55419	+	24.7200i	−0.116110	+	0.807566i	0.845663	+	0.533718i	$0.179206\pi$
$937$	−3.55419	+	24.7200i	−0.116110	+	0.807566i	−0.961773	+	0.273848i	$0.911704\pi$
$938$	2.34250	+	5.12937i	0.0764855	+	0.167480i
$939$	−1.97710	−	13.7510i	−0.0645202	−	0.448748i
$940$	7.55944	−	4.85816i	0.246562	−	0.158456i
$941$	30.4707	−	35.1650i	0.993316	−	1.14635i	0.00408410	−	0.999992i	$-0.498700\pi$
$941$	30.4707	−	35.1650i	0.993316	−	1.14635i	0.989232	−	0.146356i	$-0.0467546\pi$
$942$	−7.26513			−0.236711
$943$	−11.6705	+	10.2486i	−0.380042	+	0.333742i
$944$	−7.43475			−0.241980
$945$	−0.756852	+	0.873454i	−0.0246204	+	0.0284134i
$946$	22.0074	−	14.1433i	0.715524	−	0.459839i
$947$	−1.03245	−	7.18085i	−0.0335501	−	0.233346i	0.966146	−	0.257996i	$-0.0830621\pi$
$947$	−1.03245	−	7.18085i	−0.0335501	−	0.233346i	−0.999696	+	0.0246495i	$0.992153\pi$
$948$	2.93012	+	6.41606i	0.0951658	+	0.208384i
$949$	−14.2975	+	99.4415i	−0.464118	+	3.22801i
$950$	−8.97727	+	2.63597i	−0.291261	+	0.0855220i
$951$	−4.81970	−	3.09743i	−0.156289	−	0.100441i
$952$	0.613890	−	1.34423i	0.0198963	−	0.0435668i
$953$	−29.4384	−	8.64391i	−0.953605	−	0.280004i	−0.232318	−	0.972640i	$-0.574631\pi$
$953$	−29.4384	−	8.64391i	−0.953605	−	0.280004i	−0.721287	+	0.692636i	$0.756449\pi$
$954$	−3.41112	−	3.93664i	−0.110439	−	0.127453i
$955$	−7.33272	−	8.46241i	−0.237281	−	0.273837i
$956$	28.2972	+	8.30882i	0.915198	+	0.268726i
$957$	−4.59236	+	10.0559i	−0.148450	+	0.325060i
$958$	20.7736	+	13.3504i	0.671163	+	0.431330i
$959$	18.3302	−	5.38222i	0.591912	−	0.173801i
$960$	−0.164480	+	1.14398i	−0.00530856	+	0.0369218i
$961$	12.7576	+	27.9352i	0.411535	+	0.901137i
$962$	−3.06729	−	21.3335i	−0.0988934	−	0.687818i
$963$	−13.6823	+	8.79308i	−0.440906	+	0.283353i
$964$	4.53285	−	5.23119i	0.145993	−	0.168485i
$965$	−14.9076			−0.479893
$966$	−4.34915	+	2.02112i	−0.139932	+	0.0650283i
$967$	−12.3142			−0.395997			−0.197998	−	0.980202i	$-0.563444\pi$
$967$	−12.3142			−0.395997			−0.197998	+	0.980202i	$0.563444\pi$
$968$	−1.97001	+	2.27351i	−0.0633184	+	0.0730733i
$969$	3.17433	−	2.04002i	0.101974	−	0.0655349i
$970$	−1.87359	−	13.0311i	−0.0601574	−	0.418404i
$971$	24.0020	+	52.5571i	0.770262	+	1.68664i	0.726075	+	0.687616i	$0.241343\pi$
$971$	24.0020	+	52.5571i	0.770262	+	1.68664i	0.0441875	+	0.999023i	$0.485930\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	13.4976	−	3.96326i	0.432714	−	0.127056i
$974$	−30.8282	−	19.8121i	−0.987798	−	0.634819i
$975$	−9.83686	+	21.5397i	−0.315031	+	0.689823i
$976$	−6.06354	−	1.78042i	−0.194089	−	0.0569897i
$977$	22.9682	+	26.5067i	0.734818	+	0.848025i	0.993005	−	0.118070i	$-0.0376707\pi$
$977$	22.9682	+	26.5067i	0.734818	+	0.848025i	−0.258187	+	0.966095i	$0.583125\pi$
$978$	−2.89387	−	3.33970i	−0.0925356	−	0.106792i
$979$	19.4448	+	5.70949i	0.621457	+	0.182476i
$980$	−0.480114	+	1.05130i	−0.0153367	+	0.0335826i
$981$	−2.86968	−	1.84423i	−0.0916218	−	0.0588818i
$982$	−7.23695	+	2.12496i	−0.230940	+	0.0678102i
$983$	−3.34863	+	23.2902i	−0.106805	+	0.742842i	0.864090	+	0.503337i	$0.167894\pi$
$983$	−3.34863	+	23.2902i	−0.106805	+	0.742842i	−0.970895	+	0.239506i	$0.923015\pi$
$984$	−1.34536	−	2.94592i	−0.0428884	−	0.0939126i
$985$	2.82950	+	19.6796i	0.0901555	+	0.627045i
$986$	−4.86148	+	3.12429i	−0.154821	+	0.0994976i
$987$	−5.09155	+	5.87596i	−0.162066	+	0.187034i
$988$	−16.5008			−0.524961
$989$	−33.7319	−	28.8398i	−1.07261	−	0.917054i
$990$	−3.26725			−0.103840
$991$	9.40015	−	10.8483i	0.298605	−	0.344609i	−0.586543	−	0.809918i	$-0.699511\pi$
$991$	9.40015	−	10.8483i	0.298605	−	0.344609i	0.885148	+	0.465309i	$0.154057\pi$
$992$	6.60855	−	4.24706i	0.209822	−	0.134844i
$993$	−2.67132	−	18.5794i	−0.0847718	−	0.589601i
$994$	−1.70708	−	3.73799i	−0.0541453	−	0.118562i
$995$	2.34354	−	16.2997i	0.0742953	−	0.516735i
$996$	−2.08412	+	0.611953i	−0.0660379	+	0.0193905i
$997$	14.4427	+	9.28176i	0.457405	+	0.293956i	0.748981	−	0.662591i	$-0.230543\pi$
$997$	14.4427	+	9.28176i	0.457405	+	0.293956i	−0.291576	+	0.956548i	$0.594180\pi$
$998$	−2.32930	+	5.10046i	−0.0737328	+	0.161452i
$999$	3.20006	+	0.939622i	0.101245	+	0.0297283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.h.85.1	✓	30
23.13	even	11	inner	966.2.q.h.841.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.h.85.1	✓	30	1.1	even	1	trivial
966.2.q.h.841.1	yes	30	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)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.480114 - 1.05130i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.480114 - 1.05130i) 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} +(-1.10893 - 0.325611i) q^{10} +(1.85127 + 2.13648i) q^{11} +(0.654861 + 0.755750i) q^{12} +(6.20055 + 1.82065i) q^{13} +(-0.415415 + 0.909632i) q^{14} +(0.972274 + 0.624843i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.210309 - 1.46273i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(-0.363385 - 2.52740i) q^{19} +(-0.972274 + 0.624843i) q^{20} +(0.654861 - 0.755750i) q^{21} +2.82696 q^{22} +(-1.38159 - 4.59252i) q^{23} +1.00000 q^{24} +(2.39958 - 2.76926i) q^{25} +(5.43645 - 3.49379i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.415415 + 0.909632i) q^{28} +(0.556524 - 3.87071i) q^{29} +(1.10893 - 0.325611i) q^{30} +(-6.60855 - 4.24706i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-2.71245 - 0.796447i) q^{33} +(-0.967737 - 1.11683i) q^{34} +(0.756852 + 0.873454i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(1.38547 - 3.03376i) q^{37} +(-2.14805 - 1.38047i) q^{38} +(-6.20055 + 1.82065i) q^{39} +(-0.164480 + 1.14398i) q^{40} +(-1.34536 - 2.94592i) q^{41} +(-0.142315 - 0.989821i) q^{42} +(7.78484 - 5.00301i) q^{43} +(1.85127 - 2.13648i) q^{44} -1.15574 q^{45} +(-4.37554 - 1.96332i) q^{46} -7.77501 q^{47} +(0.654861 - 0.755750i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.521478 - 3.62696i) q^{50} +(0.613890 + 1.34423i) q^{51} +(0.919684 - 6.39654i) q^{52} +(4.99792 - 1.46752i) q^{53} +(0.841254 + 0.540641i) q^{54} +(1.35726 - 2.97199i) q^{55} +(0.959493 + 0.281733i) q^{56} +(1.67211 + 1.92972i) q^{57} +(-2.56084 - 2.95537i) q^{58} +(7.13359 + 2.09461i) q^{59} +(0.480114 - 1.05130i) q^{60} +(5.31632 + 3.41659i) q^{61} +(-7.53739 + 2.21318i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-1.06292 - 7.39277i) q^{65} +(-2.37819 + 1.52837i) q^{66} +(3.69273 - 4.26163i) q^{67} -1.47778 q^{68} +(3.64517 + 3.11652i) q^{69} +1.15574 q^{70} +(-2.69105 + 3.10563i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(2.21245 + 15.3879i) q^{73} +(-1.38547 - 3.03376i) q^{74} +(-0.521478 + 3.62696i) q^{75} +(-2.44996 + 0.719373i) q^{76} +(-2.37819 - 1.52837i) q^{77} +(-2.68455 + 5.87833i) q^{78} +(6.76775 + 1.98719i) q^{79} +(0.756852 + 0.873454i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-3.10740 - 0.912415i) q^{82} +(-0.902325 + 1.97582i) q^{83} +(-0.841254 - 0.540641i) q^{84} +(-1.63875 + 0.481180i) q^{85} +(1.31696 - 9.15966i) q^{86} +(1.62449 + 3.55713i) q^{87} +(-0.402319 - 2.79819i) q^{88} +(6.03070 - 3.87569i) q^{89} +(-0.756852 + 0.873454i) q^{90} -6.46232 q^{91} +(-4.34915 + 2.02112i) q^{92} +7.85560 q^{93} +(-5.09155 + 5.87596i) q^{94} +(-2.48260 + 1.59547i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(4.73201 + 10.3616i) q^{97} +(0.142315 - 0.989821i) q^{98} +(2.71245 - 0.796447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more