LMFDB - Embedded newform 966.2.r.b.113.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(113,966)]

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([11, 0, 13]))

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

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

chi := DirichletCharacter("966.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.r (of order $22$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.11
Character	$\chi$	$=$	966.113
Dual form			966.2.r.b.701.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 + 0.841254i) q^{2} +(1.71418 - 0.248176i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.707825 + 0.207836i) q^{5} +(-0.717976 + 1.57623i) q^{6} +(0.755750 + 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.87682 - 0.850837i) q^{9} +O(q^{10})$	\(q+(-0.540641 + 0.841254i) q^{2} +(1.71418 - 0.248176i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.707825 + 0.207836i) q^{5} +(-0.717976 + 1.57623i) q^{6} +(0.755750 + 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.87682 - 0.850837i) q^{9} +(-0.557522 + 0.483096i) q^{10} +(1.34909 - 0.867008i) q^{11} +(-0.937845 - 1.45618i) q^{12} +(0.599097 + 0.691395i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(1.26492 + 0.180603i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-3.27752 + 7.17677i) q^{17} +(-0.839555 + 2.88013i) q^{18} +(3.18030 - 1.45240i) q^{19} +(-0.104987 - 0.730199i) q^{20} +(1.45801 + 0.934989i) q^{21} +1.60367i q^{22} +(1.71568 - 4.47844i) q^{23} +(1.73205 - 0.00169721i) q^{24} +(-3.74845 - 2.40898i) q^{25} +(-0.905535 + 0.130196i) q^{26} +(4.72022 - 2.17244i) q^{27} +(0.281733 - 0.959493i) q^{28} +(7.61056 + 3.47563i) q^{29} +(-0.835800 + 0.966477i) q^{30} +(0.542626 - 3.77405i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(2.09741 - 1.82102i) q^{33} +(-4.26552 - 6.63728i) q^{34} +(0.398835 + 0.620599i) q^{35} +(-1.96902 - 2.26339i) q^{36} +(-0.714413 - 2.43307i) q^{37} +(-0.497569 + 3.46067i) q^{38} +(1.19855 + 1.03649i) q^{39} +(0.671043 + 0.306455i) q^{40} +(-2.62505 + 8.94010i) q^{41} +(-1.57482 + 0.721063i) q^{42} +(-1.27933 + 0.183940i) q^{43} +(-1.34909 - 0.867008i) q^{44} +(2.21312 - 0.00433720i) q^{45} +(2.83994 + 3.86455i) q^{46} +7.56101i q^{47} +(-0.934989 + 1.45801i) q^{48} +(0.142315 + 0.989821i) q^{49} +(4.05313 - 1.85100i) q^{50} +(-3.83715 + 13.1157i) q^{51} +(0.380041 - 0.832174i) q^{52} +(7.81766 - 9.02206i) q^{53} +(-0.724367 + 5.14541i) q^{54} +(1.13512 - 0.333300i) q^{55} +(0.654861 + 0.755750i) q^{56} +(5.09116 - 3.27894i) q^{57} +(-7.03847 + 4.52335i) q^{58} +(0.965031 - 0.836204i) q^{59} +(-0.361184 - 1.22564i) q^{60} +(-4.74293 - 0.681930i) q^{61} +(2.88157 + 2.49689i) q^{62} +(2.73133 + 1.24089i) q^{63} +(0.959493 + 0.281733i) q^{64} +(0.280359 + 0.613901i) q^{65} +(0.397992 + 2.74897i) q^{66} +(7.93711 - 12.3504i) q^{67} +7.88975 q^{68} +(1.82954 - 8.10264i) q^{69} -0.737708 q^{70} +(-5.65807 + 8.80413i) q^{71} +(2.96862 - 0.432763i) q^{72} +(-1.87353 - 4.10245i) q^{73} +(2.43307 + 0.714413i) q^{74} +(-7.02336 - 3.19915i) q^{75} +(-2.64229 - 2.28956i) q^{76} +(1.58734 + 0.228226i) q^{77} +(-1.51994 + 0.447912i) q^{78} +(-7.21102 + 6.24839i) q^{79} +(-0.620599 + 0.398835i) q^{80} +(7.55215 - 4.89541i) q^{81} +(-6.10168 - 7.04172i) q^{82} +(1.56050 - 0.458204i) q^{83} +(0.244816 - 1.71466i) q^{84} +(-3.81151 + 4.39871i) q^{85} +(0.536919 - 1.17569i) q^{86} +(13.9084 + 4.06909i) q^{87} +(1.45875 - 0.666187i) q^{88} +(-0.698943 - 4.86125i) q^{89} +(-1.19285 + 1.86414i) q^{90} +0.914847i q^{91} +(-4.78645 + 0.299773i) q^{92} +(-0.00647121 - 6.60406i) q^{93} +(-6.36073 - 4.08779i) q^{94} +(2.55296 - 0.367060i) q^{95} +(-0.721063 - 1.57482i) q^{96} +(2.03827 - 6.94171i) q^{97} +(-0.909632 - 0.415415i) q^{98} +(3.14340 - 3.64208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$3$	1.71418	−	0.248176i	0.989682	−	0.143285i
$3$	1.71418	−	0.248176i	0.989682	−	0.143285i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	0.707825	+	0.207836i	0.316549	+	0.0929472i	0.436148	−	0.899875i	$-0.356343\pi$
$5$	0.707825	+	0.207836i	0.316549	+	0.0929472i	−0.119598	+	0.992822i	$0.538161\pi$
$6$	−0.717976	+	1.57623i	−0.293112	+	0.643494i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	2.87682	−	0.850837i	0.958939	−	0.283612i
$10$	−0.557522	+	0.483096i	−0.176304	+	0.152768i
$11$	1.34909	−	0.867008i	0.406766	−	0.261413i	−0.321220	−	0.947005i	$-0.604093\pi$
$11$	1.34909	−	0.867008i	0.406766	−	0.261413i	0.727986	+	0.685592i	$0.240457\pi$
$12$	−0.937845	−	1.45618i	−0.270732	−	0.420362i
$13$	0.599097	+	0.691395i	0.166160	+	0.191759i	0.832723	−	0.553690i	$-0.186781\pi$
$13$	0.599097	+	0.691395i	0.166160	+	0.191759i	−0.666563	+	0.745449i	$0.732235\pi$
$14$	−0.959493	+	0.281733i	−0.256435	+	0.0752962i
$15$	1.26492	+	0.180603i	0.326601	+	0.0466315i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−3.27752	+	7.17677i	−0.794916	+	1.74062i	−0.132904	+	0.991129i	$0.542430\pi$
$17$	−3.27752	+	7.17677i	−0.794916	+	1.74062i	−0.662011	+	0.749494i	$0.730297\pi$
$18$	−0.839555	+	2.88013i	−0.197885	+	0.678853i
$19$	3.18030	−	1.45240i	0.729612	−	0.333203i	−0.0157379	−	0.999876i	$-0.505010\pi$
$19$	3.18030	−	1.45240i	0.729612	−	0.333203i	0.745350	+	0.666674i	$0.232282\pi$
$20$	−0.104987	−	0.730199i	−0.0234758	−	0.163277i
$21$	1.45801	+	0.934989i	0.318164	+	0.204031i
$22$			1.60367i			0.341903i
$23$	1.71568	−	4.47844i	0.357744	−	0.933820i
$23$	1.71568	−	4.47844i	0.357744	−	0.933820i
$24$	1.73205	−	0.00169721i	0.353553	−	0.000346441i
$25$	−3.74845	−	2.40898i	−0.749689	−	0.481796i
$26$	−0.905535	+	0.130196i	−0.177590	+	0.0255336i
$27$	4.72022	−	2.17244i	0.908407	−	0.418087i
$28$	0.281733	−	0.959493i	0.0532424	−	0.181327i
$29$	7.61056	+	3.47563i	1.41325	+	0.645408i	0.968218	−	0.250108i	$-0.0804663\pi$
$29$	7.61056	+	3.47563i	1.41325	+	0.645408i	0.445029	+	0.895516i	$0.353194\pi$
$30$	−0.835800	+	0.966477i	−0.152596	+	0.176454i
$31$	0.542626	−	3.77405i	0.0974586	−	0.677839i	−0.881260	−	0.472632i	$-0.843304\pi$
$31$	0.542626	−	3.77405i	0.0974586	−	0.677839i	0.978719	−	0.205207i	$-0.0657869\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	2.09741	−	1.82102i	0.365112	−	0.316999i
$34$	−4.26552	−	6.63728i	−0.731531	−	1.13828i
$35$	0.398835	+	0.620599i	0.0674154	+	0.104900i
$36$	−1.96902	−	2.26339i	−0.328170	−	0.377232i
$37$	−0.714413	−	2.43307i	−0.117449	−	0.399994i	0.879693	−	0.475541i	$-0.157748\pi$
$37$	−0.714413	−	2.43307i	−0.117449	−	0.399994i	−0.997142	+	0.0755475i	$0.975930\pi$
$38$	−0.497569	+	3.46067i	−0.0807163	+	0.561394i
$39$	1.19855	+	1.03649i	0.191921	+	0.165972i
$40$	0.671043	+	0.306455i	0.106101	+	0.0484548i
$41$	−2.62505	+	8.94010i	−0.409964	+	1.39621i	0.453256	+	0.891381i	$0.350262\pi$
$41$	−2.62505	+	8.94010i	−0.409964	+	1.39621i	−0.863220	+	0.504829i	$0.831556\pi$
$42$	−1.57482	+	0.721063i	−0.243000	+	0.111262i
$43$	−1.27933	+	0.183940i	−0.195097	+	0.0280506i	−0.239170	−	0.970978i	$-0.576875\pi$
$43$	−1.27933	+	0.183940i	−0.195097	+	0.0280506i	0.0440738	+	0.999028i	$0.485966\pi$
$44$	−1.34909	−	0.867008i	−0.203383	−	0.130706i
$45$	2.21312	−	0.00433720i	0.329912	−	0.000646552i
$46$	2.83994	+	3.86455i	0.418726	+	0.569797i
$47$			7.56101i			1.10289i	0.834212	+	0.551443i	$0.185923\pi$
$47$			7.56101i			1.10289i	−0.834212	+	0.551443i	$0.814077\pi$
$48$	−0.934989	+	1.45801i	−0.134954	+	0.210446i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	4.05313	−	1.85100i	0.573199	−	0.261771i
$51$	−3.83715	+	13.1157i	−0.537309	+	1.83656i
$52$	0.380041	−	0.832174i	0.0527022	−	0.115402i
$53$	7.81766	−	9.02206i	1.07384	−	1.23928i	0.104246	−	0.994552i	$-0.466757\pi$
$53$	7.81766	−	9.02206i	1.07384	−	1.23928i	0.969593	−	0.244724i	$-0.0786974\pi$
$54$	−0.724367	+	5.14541i	−0.0985739	+	0.700202i
$55$	1.13512	−	0.333300i	0.153059	−	0.0449422i
$56$	0.654861	+	0.755750i	0.0875094	+	0.100991i
$57$	5.09116	−	3.27894i	0.674341	−	0.434307i
$58$	−7.03847	+	4.52335i	−0.924196	+	0.593945i
$59$	0.965031	−	0.836204i	0.125636	−	0.108864i	−0.589776	−	0.807567i	$-0.700784\pi$
$59$	0.965031	−	0.836204i	0.125636	−	0.108864i	0.715413	+	0.698702i	$0.246239\pi$
$60$	−0.361184	−	1.22564i	−0.0466287	−	0.158229i
$61$	−4.74293	−	0.681930i	−0.607270	−	0.0873122i	−0.168181	−	0.985756i	$-0.553789\pi$
$61$	−4.74293	−	0.681930i	−0.607270	−	0.0873122i	−0.439088	+	0.898444i	$0.644698\pi$
$62$	2.88157	+	2.49689i	0.365959	+	0.317106i
$63$	2.73133	+	1.24089i	0.344116	+	0.156338i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	0.280359	+	0.613901i	0.0347743	+	0.0761451i
$66$	0.397992	+	2.74897i	0.0489894	+	0.338375i
$67$	7.93711	−	12.3504i	0.969673	−	1.50884i	0.112603	−	0.993640i	$-0.464081\pi$
$67$	7.93711	−	12.3504i	0.969673	−	1.50884i	0.857070	−	0.515200i	$-0.172282\pi$
$68$	7.88975			0.956773
$69$	1.82954	−	8.10264i	0.220251	−	0.975443i
$70$	−0.737708			−0.0881729
$71$	−5.65807	+	8.80413i	−0.671489	+	1.04486i	0.323630	+	0.946184i	$0.395097\pi$
$71$	−5.65807	+	8.80413i	−0.671489	+	1.04486i	−0.995120	+	0.0986744i	$0.968540\pi$
$72$	2.96862	−	0.432763i	0.349855	−	0.0510016i
$73$	−1.87353	−	4.10245i	−0.219280	−	0.480156i	0.767739	−	0.640763i	$-0.221382\pi$
$73$	−1.87353	−	4.10245i	−0.219280	−	0.480156i	−0.987018	+	0.160608i	$0.948655\pi$
$74$	2.43307	+	0.714413i	0.282838	+	0.0830488i
$75$	−7.02336	−	3.19915i	−0.810988	−	0.369406i
$76$	−2.64229	−	2.28956i	−0.303092	−	0.262631i
$77$	1.58734	+	0.228226i	0.180895	+	0.0260087i
$78$	−1.51994	+	0.447912i	−0.172099	+	0.0507161i
$79$	−7.21102	+	6.24839i	−0.811303	+	0.702998i	−0.958183	−	0.286156i	$-0.907622\pi$
$79$	−7.21102	+	6.24839i	−0.811303	+	0.702998i	0.146880	+	0.989154i	$0.453077\pi$
$80$	−0.620599	+	0.398835i	−0.0693851	+	0.0445911i
$81$	7.55215	−	4.89541i	0.839128	−	0.543934i
$82$	−6.10168	−	7.04172i	−0.673818	−	0.777628i
$83$	1.56050	−	0.458204i	0.171287	−	0.0502944i	−0.194964	−	0.980810i	$-0.562459\pi$
$83$	1.56050	−	0.458204i	0.171287	−	0.0502944i	0.366252	+	0.930516i	$0.380641\pi$
$84$	0.244816	−	1.71466i	0.0267117	−	0.187085i
$85$	−3.81151	+	4.39871i	−0.413416	+	0.477107i
$86$	0.536919	−	1.17569i	0.0578975	−	0.126778i
$87$	13.9084	+	4.06909i	1.49114	+	0.436252i
$88$	1.45875	−	0.666187i	0.155503	−	0.0710158i
$89$	−0.698943	−	4.86125i	−0.0740878	−	0.515292i	−0.992745	−	0.120237i	$-0.961635\pi$
$89$	−0.698943	−	4.86125i	−0.0740878	−	0.515292i	0.918657	−	0.395055i	$-0.129274\pi$
$90$	−1.19285	+	1.86414i	−0.125738	+	0.196498i
$91$			0.914847i			0.0959020i
$92$	−4.78645	+	0.299773i	−0.499022	+	0.0312535i
$93$	−0.00647121	−	6.60406i	−0.000671033	−	0.684809i
$94$	−6.36073	−	4.08779i	−0.656059	−	0.421623i
$95$	2.55296	−	0.367060i	0.261928	−	0.0376596i
$96$	−0.721063	−	1.57482i	−0.0735932	−	0.160730i
$97$	2.03827	−	6.94171i	0.206955	−	0.704824i	−0.788953	−	0.614453i	$-0.789377\pi$
$97$	2.03827	−	6.94171i	0.206955	−	0.704824i	0.995908	−	0.0903704i	$-0.0288051\pi$
$98$	−0.909632	−	0.415415i	−0.0918867	−	0.0419633i
$99$	3.14340	−	3.64208i	0.315924	−	0.366043i
$100$	−0.634125	+	4.41043i	−0.0634125	+	0.441043i
$101$	4.25834	+	14.5026i	0.423720	+	1.44306i	0.844333	+	0.535819i	$0.179997\pi$
$101$	4.25834	+	14.5026i	0.423720	+	1.44306i	−0.420613	+	0.907240i	$0.638185\pi$
$102$	−8.95908	−	10.3189i	−0.887081	−	1.02172i
$103$	3.62968	+	5.64790i	0.357643	+	0.556504i	0.972726	−	0.231959i	$-0.0745135\pi$
$103$	3.62968	+	5.64790i	0.357643	+	0.556504i	−0.615082	+	0.788463i	$0.710877\pi$
$104$	0.494604	+	0.769618i	0.0484999	+	0.0754673i
$105$	0.837692	+	0.964837i	0.0817504	+	0.0941584i
$106$	3.36330	+	11.4543i	0.326672	+	1.11254i
$107$	−1.15750	+	8.05057i	−0.111899	+	0.778278i	0.854170	+	0.519994i	$0.174066\pi$
$107$	−1.15750	+	8.05057i	−0.111899	+	0.778278i	−0.966069	+	0.258284i	$0.916843\pi$
$108$	−3.93698	−	3.39120i	−0.378836	−	0.326318i
$109$	−7.54678	−	3.44650i	−0.722850	−	0.330115i	0.0197909	−	0.999804i	$-0.493700\pi$
$109$	−7.54678	−	3.44650i	−0.722850	−	0.330115i	−0.742641	+	0.669689i	$0.766427\pi$
$110$	−0.333300	+	1.13512i	−0.0317789	+	0.108229i
$111$	−1.82846	−	3.99341i	−0.173550	−	0.379038i
$112$	−0.989821	+	0.142315i	−0.0935293	+	0.0134475i
$113$	−0.935785	−	0.601393i	−0.0880313	−	0.0565743i	0.495885	−	0.868388i	$-0.334844\pi$
$113$	−0.935785	−	0.601393i	−0.0880313	−	0.0565743i	−0.583916	+	0.811814i	$0.698480\pi$
$114$	0.00593387	+	6.05569i	0.000555757	+	0.567167i
$115$	2.14519	−	2.81337i	0.200040	−	0.262348i
$116$		−	8.36664i		−	0.776823i
$117$	2.31176	+	1.47928i	0.213722	+	0.136760i
$118$	0.181724	+	1.26392i	0.0167291	+	0.116353i
$119$	−7.17677	+	3.27752i	−0.657894	+	0.300450i
$120$	1.22634	+	0.358782i	0.111949	+	0.0327521i
$121$	−3.50122	+	7.66661i	−0.318293	+	0.696964i
$122$	3.13790	−	3.62133i	0.284092	−	0.327859i
$123$	−2.28108	+	15.9764i	−0.205678	+	1.44054i
$124$	−3.65841	+	1.07421i	−0.328535	+	0.0964666i
$125$	−4.56805	−	5.27181i	−0.408579	−	0.471525i
$126$	−2.52058	+	1.62687i	−0.224551	+	0.144933i
$127$	−10.2264	+	6.57208i	−0.907442	+	0.583178i	−0.908989	−	0.416821i	$-0.863144\pi$
$127$	−10.2264	+	6.57208i	−0.907442	+	0.583178i	0.00154616	+	0.999999i	$0.499508\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	−2.14736	+	0.632807i	−0.189064	+	0.0557155i
$130$	−0.668020	−	0.0960468i	−0.0585893	−	0.00842386i
$131$	−17.0962	−	14.8139i	−1.49370	−	1.29430i	−0.847048	−	0.531516i	$-0.821622\pi$
$131$	−17.0962	−	14.8139i	−1.49370	−	1.29430i	−0.646654	−	0.762784i	$-0.723832\pi$
$132$	−2.52775	−	1.15139i	−0.220013	−	0.100216i
$133$	3.35463	+	0.985009i	0.290883	+	0.0854111i
$134$	6.09868	+	13.3543i	0.526846	+	1.15363i
$135$	3.79261	−	0.556679i	0.326415	−	0.0479113i
$136$	−4.26552	+	6.63728i	−0.365765	+	0.569142i
$137$	−13.3036			−1.13660			−0.568302	−	0.822820i	$-0.692399\pi$
$137$	−13.3036			−1.13660			−0.568302	+	0.822820i	$0.692399\pi$
$138$	5.82725	+	5.91973i	0.496048	+	0.503921i
$139$	12.4565			1.05655			0.528273	−	0.849075i	$-0.322840\pi$
$139$	12.4565			1.05655			0.528273	+	0.849075i	$0.322840\pi$
$140$	0.398835	−	0.620599i	0.0337077	−	0.0524502i
$141$	1.87646	+	12.9609i	0.158027	+	1.09151i
$142$	−4.34752	−	9.51974i	−0.364836	−	0.798879i
$143$	1.40768	+	0.413333i	0.117716	+	0.0345646i
$144$	−1.24089	+	2.73133i	−0.103408	+	0.227611i
$145$	4.66459	+	4.04189i	0.387373	+	0.335661i
$146$	4.46411	+	0.641842i	0.369452	+	0.0531192i
$147$	0.489603	+	1.66141i	0.0403818	+	0.137031i
$148$	−1.91642	+	1.66059i	−0.157529	+	0.136499i
$149$	−12.1425	+	7.80348i	−0.994749	+	0.639286i	−0.933403	−	0.358830i	$-0.883176\pi$
$149$	−12.1425	+	7.80348i	−0.994749	+	0.639286i	−0.0613459	+	0.998117i	$0.519539\pi$
$150$	6.48841	−	4.17884i	0.529776	−	0.341201i
$151$	−4.68189	−	5.40319i	−0.381007	−	0.439706i	0.532561	−	0.846392i	$-0.321230\pi$
$151$	−4.68189	−	5.40319i	−0.381007	−	0.439706i	−0.913568	+	0.406686i	$0.866684\pi$
$152$	3.35463	−	0.985009i	0.272097	−	0.0798948i
$153$	−3.32257	+	23.4349i	−0.268614	+	1.89460i
$154$	−1.05018	+	1.21197i	−0.0846258	+	0.0976634i
$155$	1.16847	−	2.55859i	0.0938537	−	0.205511i
$156$	0.444933	−	1.52081i	0.0356231	−	0.121762i
$157$	8.94357	−	4.08439i	0.713775	−	0.325970i	−0.0252194	−	0.999682i	$-0.508028\pi$
$157$	8.94357	−	4.08439i	0.713775	−	0.325970i	0.738994	+	0.673712i	$0.235301\pi$
$158$	−1.35790	−	9.44443i	−0.108029	−	0.751359i
$159$	11.1618	−	17.4056i	0.885189	−	1.38035i
$160$		−	0.737708i		−	0.0583209i
$161$	4.22938	−	2.26105i	0.333322	−	0.178196i
$162$	0.0352757	+	8.99993i	0.00277152	+	0.707101i
$163$	11.4132	+	7.33483i	0.893952	+	0.574508i	0.904991	−	0.425431i	$-0.139877\pi$
$163$	11.4132	+	7.33483i	0.893952	+	0.574508i	−0.0110388	+	0.999939i	$0.503514\pi$
$164$	9.22269	−	1.32602i	0.720171	−	0.103545i
$165$	1.86307	−	0.853045i	0.145040	−	0.0664095i
$166$	−0.458204	+	1.56050i	−0.0355635	+	0.121118i
$167$	−3.05922	−	1.39710i	−0.236730	−	0.108111i	0.293518	−	0.955953i	$-0.405174\pi$
$167$	−3.05922	−	1.39710i	−0.236730	−	0.108111i	−0.530248	+	0.847843i	$0.677901\pi$
$168$	1.31011	+	1.13297i	0.101077	+	0.0874104i
$169$	1.73098	−	12.0393i	0.133153	−	0.926096i
$170$	−1.63978	−	5.58457i	−0.125765	−	0.428317i
$171$	7.91340	−	6.88420i	0.605153	−	0.526448i
$172$	0.698772	+	1.08731i	0.0532809	+	0.0829067i
$173$	−13.7876	−	21.4540i	−1.04825	−	1.63112i	−0.730459	−	0.682956i	$-0.760694\pi$
$173$	−13.7876	−	21.4540i	−1.04825	−	1.63112i	−0.317795	−	0.948159i	$-0.602942\pi$
$174$	−10.9426	+	9.50061i	−0.829556	+	0.720239i
$175$	−1.25534	−	4.27530i	−0.0948948	−	0.323182i
$176$	−0.228226	+	1.58734i	−0.0172032	+	0.119651i
$177$	1.44671	−	1.67290i	0.108741	−	0.125743i
$178$	4.46742	+	2.04020i	0.334847	+	0.152920i
$179$	5.01999	−	17.0965i	0.375212	−	1.27785i	−0.528215	−	0.849111i	$-0.677138\pi$
$179$	5.01999	−	17.0965i	0.375212	−	1.27785i	0.903427	−	0.428743i	$-0.141043\pi$
$180$	−0.923308	−	2.01132i	−0.0688193	−	0.149915i
$181$	−21.2823	+	3.05993i	−1.58190	+	0.227443i	−0.876513	−	0.481378i	$-0.840137\pi$
$181$	−21.2823	+	3.05993i	−1.58190	+	0.227443i	−0.705389	+	0.708821i	$0.749227\pi$
$182$	−0.769618	−	0.494604i	−0.0570479	−	0.0366625i
$183$	−8.29946	+	0.00813250i	−0.613514	+	0.000601172i
$184$	2.33557	−	4.18869i	0.172180	−	0.308794i
$185$		−	1.87067i		−	0.137534i
$186$	5.55919	+	3.56498i	0.407619	+	0.261397i
$187$	1.80064	+	12.5237i	0.131676	+	0.915827i
$188$	6.87774	−	3.14096i	0.501610	−	0.229078i
$189$	4.98995	+	1.44926i	0.362966	+	0.105418i
$190$	−1.07144	+	2.34614i	−0.0777307	+	0.170207i
$191$	−4.98303	+	5.75072i	−0.360559	+	0.416108i	−0.906827	−	0.421503i	$-0.861503\pi$
$191$	−4.98303	+	5.75072i	−0.360559	+	0.416108i	0.546268	+	0.837611i	$0.316048\pi$
$192$	1.71466	+	0.244816i	0.123745	+	0.0176681i
$193$	16.0509	−	4.71298i	1.15537	−	0.339248i	0.352739	−	0.935722i	$-0.385250\pi$
$193$	16.0509	−	4.71298i	1.15537	−	0.339248i	0.802632	+	0.596474i	$0.203432\pi$
$194$	4.73776	+	5.46767i	0.340152	+	0.392556i
$195$	0.632942	+	0.982758i	0.0453259	+	0.0703768i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	−10.1162	+	8.76574i	−0.720750	+	0.624533i	−0.935989	−	0.352028i	$-0.885492\pi$
$197$	−10.1162	+	8.76574i	−0.720750	+	0.624533i	0.215240	+	0.976561i	$0.430947\pi$
$198$	1.36446	+	4.61346i	0.0969679	+	0.327864i
$199$	−22.7266	−	3.26759i	−1.61104	−	0.231633i	−0.722817	−	0.691039i	$-0.757153\pi$
$199$	−22.7266	−	3.26759i	−1.61104	−	0.231633i	−0.888226	+	0.459406i	$0.848062\pi$
$200$	−3.36746	−	2.91792i	−0.238115	−	0.206328i
$201$	10.5406	−	23.1406i	0.743474	−	1.63221i
$202$	−14.5026	−	4.25834i	−1.02040	−	0.299616i
$203$	3.47563	+	7.61056i	0.243941	+	0.534157i
$204$	13.5244	−	1.95805i	0.946901	−	0.137091i
$205$	−3.71616	+	5.78245i	−0.259548	+	0.403864i
$206$	−6.71367			−0.467764
$207$	1.12528	−	14.3434i	0.0782122	−	0.996937i
$208$	−0.914847			−0.0634332
$209$	3.03128	−	4.71676i	0.209678	−	0.326265i
$210$	−1.26456	+	0.183082i	−0.0872631	+	0.0126338i
$211$	−2.43869	−	5.33999i	−0.167886	−	0.367620i	0.806924	−	0.590655i	$-0.201131\pi$
$211$	−2.43869	−	5.33999i	−0.167886	−	0.367620i	−0.974810	+	0.223035i	$0.928403\pi$
$212$	−11.4543	−	3.36330i	−0.786687	−	0.230992i
$213$	−7.51397	+	16.4961i	−0.514849	+	1.13029i
$214$	−6.14678	−	5.32621i	−0.420185	−	0.364093i
$215$	−0.943774	−	0.135694i	−0.0643649	−	0.00925427i
$216$	4.98135	−	1.47858i	0.338938	−	0.100604i
$217$	2.88157	−	2.49689i	0.195613	−	0.169500i
$218$	6.97948	−	4.48544i	0.472710	−	0.303792i
$219$	−4.22969	−	6.56737i	−0.285816	−	0.443782i
$220$	−0.774725	−	0.894080i	−0.0522319	−	0.0602789i
$221$	−6.92554	+	2.03352i	−0.465862	+	0.136789i
$222$	4.34801	+	0.620802i	0.291819	+	0.0416655i
$223$	−4.50570	+	5.19986i	−0.301724	+	0.348208i	−0.886284	−	0.463142i	$-0.846722\pi$
$223$	−4.50570	+	5.19986i	−0.301724	+	0.348208i	0.584560	+	0.811351i	$0.301267\pi$
$224$	0.415415	−	0.909632i	0.0277561	−	0.0607773i
$225$	−12.8332	−	3.74088i	−0.855550	−	0.249392i
$226$	1.01185	−	0.462095i	0.0673071	−	0.0307381i
$227$	−2.24613	−	15.6222i	−0.149081	−	1.03688i	−0.917729	−	0.397208i	$-0.869979\pi$
$227$	−2.24613	−	15.6222i	−0.149081	−	1.03688i	0.768648	−	0.639672i	$-0.220930\pi$
$228$	−5.09758	−	3.26896i	−0.337595	−	0.216492i
$229$		−	2.75813i		−	0.182263i	−0.995839	−	0.0911313i	$-0.970952\pi$
$229$		−	2.75813i		−	0.182263i	0.995839	−	0.0911313i	$-0.0290483\pi$
$230$	1.20699	+	3.32567i	0.0795863	+	0.219288i
$231$	2.77763	−	0.00272175i	0.182755	−	0.000179078i
$232$	7.03847	+	4.52335i	0.462098	+	0.296972i
$233$	20.3183	−	2.92133i	1.33109	−	0.191382i	0.560206	−	0.828353i	$-0.310722\pi$
$233$	20.3183	−	2.92133i	1.33109	−	0.191382i	0.770888	+	0.636971i	$0.219813\pi$
$234$	−2.49428	+	1.14501i	−0.163056	+	0.0748519i
$235$	−1.57145	+	5.35187i	−0.102510	+	0.349118i
$236$	−1.16153	−	0.530451i	−0.0756089	−	0.0345294i
$237$	−10.8103	+	12.5005i	−0.702203	+	0.811992i
$238$	1.12283	−	7.80945i	0.0727822	−	0.506211i
$239$	−0.933116	−	3.17790i	−0.0603582	−	0.205561i	0.923793	−	0.382892i	$-0.125072\pi$
$239$	−0.933116	−	3.17790i	−0.0603582	−	0.205561i	−0.984151	+	0.177331i	$0.943254\pi$
$240$	−0.964837	+	0.837692i	−0.0622799	+	0.0540728i
$241$	−10.9639	−	17.0601i	−0.706246	−	1.09894i	−0.990140	−	0.140084i	$-0.955263\pi$
$241$	−10.9639	−	17.0601i	−0.706246	−	1.09894i	0.283894	−	0.958856i	$-0.408374\pi$
$242$	−4.55666	−	7.09030i	−0.292913	−	0.455782i
$243$	11.7308	−	10.2659i	0.752532	−	0.658556i
$244$	1.34998	+	4.59760i	0.0864235	+	0.294331i
$245$	−0.104987	+	0.730199i	−0.00670736	+	0.0466507i
$246$	−12.2070	−	10.5565i	−0.778287	−	0.673056i
$247$	2.90949	+	1.32872i	0.185127	+	0.0845445i
$248$	1.07421	−	3.65841i	0.0682122	−	0.232309i
$249$	2.56126	−	1.17272i	0.162313	−	0.0743182i
$250$	6.90461	−	0.992733i	0.436686	−	0.0627859i
$251$	13.4999	+	8.67586i	0.852106	+	0.547615i	0.892231	−	0.451579i	$-0.149139\pi$
$251$	13.4999	+	8.67586i	0.852106	+	0.547615i	−0.0401248	+	0.999195i	$0.512776\pi$
$252$	−0.00587929	−	2.99999i	−0.000370361	−	0.188982i
$253$	−1.56823	−	7.52933i	−0.0985940	−	0.473365i
$254$		−	12.1561i		−	0.762741i
$255$	−5.44195	+	8.48611i	−0.340788	+	0.531421i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−4.06287	+	1.85545i	−0.253435	+	0.115740i	−0.538082	−	0.842893i	$-0.680851\pi$
$257$	−4.06287	+	1.85545i	−0.253435	+	0.115740i	0.284647	+	0.958632i	$0.408124\pi$
$258$	0.628597	−	2.14859i	0.0391348	−	0.133766i
$259$	1.05340	−	2.30663i	0.0654553	−	0.143327i
$260$	0.441959	−	0.510048i	0.0274091	−	0.0316318i
$261$	24.8514	+	3.52340i	1.53826	+	0.218093i
$262$	21.7052	−	6.37322i	1.34095	−	0.393739i
$263$	−16.0891	−	18.5678i	−0.992096	−	1.14494i	−0.989440	−	0.144943i	$-0.953700\pi$
$263$	−16.0891	−	18.5678i	−0.992096	−	1.14494i	−0.00265608	−	0.999996i	$-0.500845\pi$
$264$	2.33522	−	1.50399i	0.143723	−	0.0925642i
$265$	7.40865	−	4.76125i	0.455110	−	0.292481i
$266$	−2.64229	+	2.28956i	−0.162009	+	0.140382i
$267$	−2.40456	−	8.15959i	−0.147157	−	0.499359i
$268$	−14.5315	−	2.08932i	−0.887653	−	0.127625i
$269$	6.02374	+	5.21960i	0.367274	+	0.318245i	0.818871	−	0.573977i	$-0.194600\pi$
$269$	6.02374	+	5.21960i	0.367274	+	0.318245i	−0.451597	+	0.892222i	$0.649146\pi$
$270$	−1.58213	+	3.49151i	−0.0962853	+	0.212486i
$271$	20.4533	+	6.00563i	1.24245	+	0.364816i	0.835935	−	0.548829i	$-0.184926\pi$
$271$	20.4533	+	6.00563i	1.24245	+	0.364816i	0.406514	+	0.913645i	$0.366744\pi$
$272$	−3.27752	−	7.17677i	−0.198729	−	0.435156i
$273$	0.227043	+	1.56821i	0.0137413	+	0.0949125i
$274$	7.19247	−	11.1917i	0.434513	−	0.676116i
$275$	−7.14560			−0.430896
$276$	−8.13044	+	1.70175i	−0.489395	+	0.102433i
$277$	−20.1914			−1.21318			−0.606591	−	0.795014i	$-0.707463\pi$
$277$	−20.1914			−1.21318			−0.606591	+	0.795014i	$0.707463\pi$
$278$	−6.73449	+	10.4791i	−0.403908	+	0.628493i
$279$	−1.65006	−	11.3189i	−0.0987868	−	0.677647i
$280$	0.306455	+	0.671043i	0.0183142	+	0.0401025i
$281$	−28.0371	−	8.23244i	−1.67255	−	0.491106i	−0.698157	−	0.715944i	$-0.745996\pi$
$281$	−28.0371	−	8.23244i	−1.67255	−	0.491106i	−0.974396	+	0.224838i	$0.927815\pi$
$282$	−11.9179	−	5.42862i	−0.709701	−	0.323270i
$283$	−0.539942	−	0.467862i	−0.0320962	−	0.0278115i	0.638665	−	0.769485i	$-0.279487\pi$
$283$	−0.539942	−	0.467862i	−0.0320962	−	0.0278115i	−0.670761	+	0.741673i	$0.734032\pi$
$284$	10.3590	+	1.48939i	0.614692	+	0.0883793i
$285$	4.28514	−	1.26279i	0.253830	−	0.0748013i
$286$	−1.10877	+	0.960753i	−0.0655628	+	0.0568105i
$287$	−7.83840	+	5.03744i	−0.462686	+	0.297350i
$288$	−1.62687	−	2.52058i	−0.0958640	−	0.148526i
$289$	−29.6313	−	34.1963i	−1.74302	−	2.01155i
$290$	−5.92212	+	1.73889i	−0.347759	+	0.102111i
$291$	1.77119	−	12.4052i	0.103829	−	0.727204i
$292$	−2.95343	+	3.40844i	−0.172836	+	0.199464i
$293$	−2.32848	+	5.09866i	−0.136031	+	0.297867i	−0.965372	−	0.260876i	$-0.915989\pi$
$293$	−2.32848	+	5.09866i	−0.136031	+	0.297867i	0.829341	+	0.558743i	$0.188716\pi$
$294$	−1.66237	−	0.486346i	−0.0969513	−	0.0283643i
$295$	0.856867	−	0.391318i	0.0498887	−	0.0227834i
$296$	−0.360880	−	2.50997i	−0.0209757	−	0.145889i
$297$	4.48448	−	7.02329i	0.260216	−	0.407533i
$298$		−	14.4338i		−	0.836126i
$299$	4.12423	−	1.49681i	0.238511	−	0.0865627i
$300$	0.00756239	+	7.71765i	0.000436615	+	0.445579i
$301$	−1.08731	−	0.698772i	−0.0626716	−	0.0402766i
$302$	7.07668	−	1.01747i	0.407217	−	0.0585490i
$303$	10.8987	+	23.8032i	0.626116	+	1.36746i
$304$	−0.985009	+	3.35463i	−0.0564941	+	0.192401i
$305$	−3.21544	−	1.46844i	−0.184115	−	0.0840826i
$306$	−17.9184	−	15.4650i	−1.02433	−	0.884074i
$307$	−1.09475	+	7.61415i	−0.0624807	+	0.434562i	0.934438	+	0.356125i	$0.115902\pi$
$307$	−1.09475	+	7.61415i	−0.0624807	+	0.434562i	−0.996919	+	0.0784376i	$0.975007\pi$
$308$	−0.451805	−	1.53871i	−0.0257440	−	0.0876760i
$309$	7.62360	+	8.78070i	0.433692	+	0.499517i
$310$	1.52070	+	2.36626i	0.0863700	+	0.134394i
$311$	7.66182	+	11.9220i	0.434462	+	0.676036i	0.987589	−	0.157061i	$-0.0502019\pi$
$311$	7.66182	+	11.9220i	0.434462	+	0.676036i	−0.553127	+	0.833097i	$0.686566\pi$
$312$	1.03884	+	1.19651i	0.0588127	+	0.0677393i
$313$	−0.760273	−	2.58925i	−0.0429732	−	0.146353i	0.935212	−	0.354089i	$-0.115209\pi$
$313$	−0.760273	−	2.58925i	−0.0429732	−	0.146353i	−0.978185	+	0.207735i	$0.933391\pi$
$314$	−1.39925	+	9.73200i	−0.0789643	+	0.549209i
$315$	1.67540	+	1.44601i	0.0943983	+	0.0814733i
$316$	8.67930	+	3.96370i	0.488249	+	0.222976i
$317$	7.27256	−	24.7681i	0.408468	−	1.39111i	−0.456696	−	0.889623i	$-0.650967\pi$
$317$	7.27256	−	24.7681i	0.408468	−	1.39111i	0.865164	−	0.501490i	$-0.167215\pi$
$318$	8.60798	+	18.8001i	0.482712	+	1.05426i
$319$	13.2807	−	1.90948i	0.743578	−	0.106910i
$320$	0.620599	+	0.398835i	0.0346926	+	0.0222956i
$321$	0.0138040	+	14.0874i	0.000770463	+	0.786281i
$322$	−0.384462	+	4.78040i	−0.0214252	+	0.266401i
$323$			27.5846i			1.53485i
$324$	−7.59030	−	4.83605i	−0.421683	−	0.268670i
$325$	−0.580127	−	4.03487i	−0.0321797	−	0.223814i
$326$	−12.3409	+	5.63590i	−0.683499	+	0.312144i
$327$	−13.7919	−	4.03498i	−0.762692	−	0.223135i
$328$	−3.87064	+	8.47552i	−0.213720	+	0.467982i
$329$	−4.95141	+	5.71423i	−0.272980	+	0.315036i
$330$	−0.289627	+	2.02851i	−0.0159434	+	0.111666i
$331$	−11.3622	+	3.33625i	−0.624524	+	0.183377i	−0.578657	−	0.815571i	$-0.696423\pi$
$331$	−11.3622	+	3.33625i	−0.624524	+	0.183377i	−0.0458667	+	0.998948i	$0.514605\pi$
$332$	−1.06505	−	1.22914i	−0.0584523	−	0.0674575i
$333$	−4.12538	−	6.39164i	−0.226069	−	0.350260i
$334$	2.82925	−	1.81825i	0.154810	−	0.0994903i
$335$	8.18495	−	7.09230i	0.447192	−	0.387494i
$336$	−1.66141	+	0.489603i	−0.0906374	+	0.0267101i
$337$	−9.26514	−	1.33213i	−0.504705	−	0.0725656i	−0.114740	−	0.993396i	$-0.536604\pi$
$337$	−9.26514	−	1.33213i	−0.504705	−	0.0725656i	−0.389964	+	0.920830i	$0.627513\pi$
$338$	9.19222	+	7.96511i	0.499991	+	0.433245i
$339$	−1.75335	−	0.798655i	−0.0952292	−	0.0433770i
$340$	5.58457	+	1.63978i	0.302866	+	0.0889294i
$341$	−2.54008	−	5.56199i	−0.137553	−	0.301199i
$342$	1.51305	+	10.3791i	0.0818164	+	0.561235i
$343$	−0.540641	+	0.841254i	−0.0291919	+	0.0454234i
$344$	−1.29249			−0.0696863
$345$	2.97902	−	5.35501i	0.160385	−	0.288304i
$346$	25.5024			1.37102
$347$	11.3744	−	17.6989i	0.610610	−	0.950128i	−0.388973	−	0.921249i	$-0.627170\pi$
$347$	11.3744	−	17.6989i	0.610610	−	0.950128i	0.999583	−	0.0288789i	$-0.00919371\pi$
$348$	−2.07640	−	14.3419i	−0.111307	−	0.768808i
$349$	5.92163	+	12.9666i	0.316977	+	0.694084i	0.999317	−	0.0369517i	$-0.0117648\pi$
$349$	5.92163	+	12.9666i	0.316977	+	0.694084i	−0.682340	+	0.731035i	$0.739037\pi$
$350$	4.27530	+	1.25534i	0.228524	+	0.0671008i
$351$	4.32989	+	1.96203i	0.231112	+	0.104726i
$352$	−1.21197	−	1.05018i	−0.0645982	−	0.0559747i
$353$	17.2570	+	2.48119i	0.918499	+	0.132060i	0.585319	−	0.810803i	$-0.300969\pi$
$353$	17.2570	+	2.48119i	0.918499	+	0.132060i	0.333180	+	0.942863i	$0.391878\pi$
$354$	0.625184	+	2.12149i	0.0332281	+	0.112756i
$355$	−5.83474	+	5.05583i	−0.309676	+	0.268336i
$356$	−4.13160	+	2.65522i	−0.218974	+	0.140726i
$357$	−11.4889	+	7.39936i	−0.608055	+	0.391616i
$358$	11.6685	+	13.4662i	0.616699	+	0.711709i
$359$	−5.39208	+	1.58326i	−0.284583	+	0.0835612i	−0.420909	−	0.907103i	$-0.638289\pi$
$359$	−5.39208	+	1.58326i	−0.284583	+	0.0835612i	0.136326	+	0.990664i	$0.456471\pi$
$360$	2.19121	+	0.310667i	0.115487	+	0.0163736i
$361$	−4.43747	+	5.12111i	−0.233551	+	0.269532i
$362$	8.93191	−	19.5581i	0.469451	−	1.02795i
$363$	−4.09905	+	14.0109i	−0.215144	+	0.735379i
$364$	0.832174	−	0.380041i	0.0436178	−	0.0199196i
$365$	−0.473492	−	3.29321i	−0.0247837	−	0.172374i
$366$	4.48019	−	6.98635i	0.234183	−	0.365182i
$367$		−	9.09683i		−	0.474851i	−0.971406	−	0.237425i	$-0.923696\pi$
$367$		−	9.09683i		−	0.474851i	0.971406	−	0.237425i	$-0.0763035\pi$
$368$	2.26105	+	4.22938i	0.117865	+	0.220472i
$369$	0.0547805	+	27.9525i	0.00285176	+	1.45515i
$370$	1.57371	+	1.01136i	0.0818131	+	0.0525781i
$371$	11.8164	−	1.69894i	0.613476	−	0.0882046i
$372$	−6.00458	+	2.74931i	−0.311323	+	0.142545i
$373$	4.10589	−	13.9834i	0.212595	−	0.724033i	−0.782281	−	0.622926i	$-0.785944\pi$
$373$	4.10589	−	13.9834i	0.212595	−	0.724033i	0.994876	−	0.101106i	$-0.0322382\pi$
$374$	−11.5091	−	5.25605i	−0.595124	−	0.271784i
$375$	−9.13880	−	7.90315i	−0.471925	−	0.408117i
$376$	−1.07604	+	7.48405i	−0.0554927	+	0.385960i
$377$	2.15644	+	7.34415i	0.111062	+	0.378243i
$378$	−3.91697	+	3.41429i	−0.201467	+	0.175612i
$379$	10.2375	+	15.9299i	0.525866	+	0.818263i	0.997997	−	0.0632651i	$-0.0201514\pi$
$379$	10.2375	+	15.9299i	0.525866	+	0.818263i	−0.472131	+	0.881528i	$0.656515\pi$
$380$	−1.39443	−	2.16977i	−0.0715327	−	0.111307i
$381$	−15.8988	+	13.8037i	−0.814519	+	0.707183i
$382$	−2.14379	−	7.30107i	−0.109686	−	0.373555i
$383$	−5.39689	+	37.5362i	−0.275768	+	1.91801i	0.107178	+	0.994240i	$0.465819\pi$
$383$	−5.39689	+	37.5362i	−0.275768	+	1.91801i	−0.382946	+	0.923771i	$0.625090\pi$
$384$	−1.13297	+	1.31011i	−0.0578166	+	0.0668561i
$385$	1.07613	+	0.491452i	0.0548446	+	0.0250467i
$386$	−4.71298	+	16.0509i	−0.239884	+	0.816971i
$387$	−3.52390	+	1.61767i	−0.179130	+	0.0822307i
$388$	−7.16113	+	1.02961i	−0.363551	+	0.0522708i
$389$	−7.72312	−	4.96335i	−0.391578	−	0.251652i	0.330006	−	0.943979i	$-0.392949\pi$
$389$	−7.72312	−	4.96335i	−0.391578	−	0.251652i	−0.721584	+	0.692327i	$0.756586\pi$
$390$	−1.16894	+	0.00114543i	−0.0591917	+	5.80010e-5i
$391$	26.5176	+	26.9912i	1.34105	+	1.36501i
$392$			1.00000i			0.0505076i
$393$	−32.9824	−	21.1509i	−1.66374	−	1.06692i
$394$	−1.90498	−	13.2494i	−0.0959714	−	0.667496i
$395$	−6.40279	+	2.92405i	−0.322159	+	0.147125i
$396$	−4.61877	−	1.34637i	−0.232102	−	0.0676575i
$397$	−10.5348	+	23.0680i	−0.528727	+	1.15775i	0.437302	+	0.899315i	$0.355934\pi$
$397$	−10.5348	+	23.0680i	−0.528727	+	1.15775i	−0.966029	+	0.258435i	$0.916793\pi$
$398$	15.0358	−	17.3522i	0.753675	−	0.869788i
$399$	5.99489	+	0.855941i	0.300120	+	0.0428506i
$400$	4.27530	−	1.25534i	0.213765	−	0.0627670i
$401$	−15.0060	−	17.3179i	−0.749365	−	0.864814i	0.245141	−	0.969487i	$-0.421166\pi$
$401$	−15.0060	−	17.3179i	−0.749365	−	0.864814i	−0.994507	+	0.104674i	$0.966620\pi$
$402$	13.7684	+	21.3780i	0.686707	+	1.06624i
$403$	2.93445	−	1.88585i	0.146175	−	0.0939411i
$404$	11.4230	−	9.89810i	0.568316	−	0.492449i
$405$	6.36305	−	1.89548i	0.316182	−	0.0941872i
$406$	−8.28148	−	1.19070i	−0.411003	−	0.0590933i
$407$	−3.07330	−	2.66303i	−0.152338	−	0.132001i
$408$	−5.66465	+	12.4361i	−0.280442	+	0.615678i
$409$	−13.2723	−	3.89709i	−0.656271	−	0.192699i	−0.0633904	−	0.997989i	$-0.520191\pi$
$409$	−13.2723	−	3.89709i	−0.656271	−	0.192699i	−0.592881	+	0.805290i	$0.702010\pi$
$410$	−2.85540	−	6.25246i	−0.141018	−	0.308787i
$411$	−22.8048	+	3.30164i	−1.12488	+	0.162858i
$412$	3.62968	−	5.64790i	0.178822	−	0.278252i
$413$	1.27692			0.0628331
$414$	11.4581	+	8.70128i	0.563134	+	0.427645i
$415$	1.19979			0.0588955
$416$	0.494604	−	0.769618i	0.0242499	−	0.0377336i
$417$	21.3527	−	3.09141i	1.04564	−	0.151387i
$418$	2.32916	+	5.10015i	0.113923	+	0.249456i
$419$	0.537388	+	0.157791i	0.0262531	+	0.00770861i	0.294833	−	0.955549i	$-0.404736\pi$
$419$	0.537388	+	0.157791i	0.0262531	+	0.00770861i	−0.268580	+	0.963257i	$0.586554\pi$
$420$	0.529656	−	1.16280i	0.0258446	−	0.0567388i
$421$	−16.5359	−	14.3284i	−0.805910	−	0.698325i	0.151056	−	0.988525i	$-0.451733\pi$
$421$	−16.5359	−	14.3284i	−0.805910	−	0.698325i	−0.956966	+	0.290200i	$0.906278\pi$
$422$	5.81074	+	0.835458i	0.282862	+	0.0406695i
$423$	6.43319	+	21.7516i	0.312792	+	1.05760i
$424$	9.02206	−	7.81766i	0.438150	−	0.379659i
$425$	29.5743	−	19.0063i	1.43457	−	0.921939i
$426$	−9.81500	−	15.2396i	−0.475538	−	0.738361i
$427$	−3.13790	−	3.62133i	−0.151853	−	0.175248i
$428$	7.80390	−	2.29143i	0.377216	−	0.110760i
$429$	2.51560	+	0.359173i	0.121454	+	0.0173410i
$430$	0.624396	−	0.720592i	0.0301111	−	0.0347500i
$431$	0.801922	−	1.75596i	0.0386272	−	0.0845818i	−0.889335	−	0.457257i	$-0.848832\pi$
$431$	0.801922	−	1.75596i	0.0386272	−	0.0845818i	0.927962	+	0.372675i	$0.121559\pi$
$432$	−1.44926	+	4.98995i	−0.0697277	+	0.240079i
$433$	19.8600	−	9.06978i	0.954413	−	0.435866i	0.123547	−	0.992339i	$-0.460573\pi$
$433$	19.8600	−	9.06978i	0.954413	−	0.435866i	0.830866	+	0.556473i	$0.187846\pi$
$434$	0.542626	+	3.77405i	0.0260469	+	0.181160i
$435$	8.99904	+	5.77088i	0.431471	+	0.276693i
$436$			8.29652i			0.397331i
$437$	−1.04808	−	16.7347i	−0.0501366	−	0.800527i
$438$	7.81157	−	0.00765442i	0.373251	−	0.000365742i
$439$	2.70419	+	1.73788i	0.129064	+	0.0829443i	0.603580	−	0.797303i	$-0.293741\pi$
$439$	2.70419	+	1.73788i	0.129064	+	0.0829443i	−0.474516	+	0.880247i	$0.657377\pi$
$440$	1.17100	−	0.168364i	0.0558250	−	0.00802643i
$441$	1.25159	+	2.72645i	0.0595996	+	0.129831i
$442$	2.03352	−	6.92554i	0.0967248	−	0.329414i
$443$	−0.344780	−	0.157456i	−0.0163810	−	0.00748094i	0.407208	−	0.913336i	$-0.366503\pi$
$443$	−0.344780	−	0.157456i	−0.0163810	−	0.00748094i	−0.423589	+	0.905855i	$0.639230\pi$
$444$	−2.87296	+	3.32215i	−0.136345	+	0.157662i
$445$	0.515615	−	3.58618i	0.0244425	−	0.170001i
$446$	−1.93843	−	6.60170i	−0.0917875	−	0.312599i
$447$	−18.8777	+	16.3900i	−0.892884	+	0.775222i
$448$	0.540641	+	0.841254i	0.0255429	+	0.0397455i
$449$	4.56452	+	7.10253i	0.215413	+	0.335189i	0.932097	−	0.362209i	$-0.117977\pi$
$449$	4.56452	+	7.10253i	0.215413	+	0.335189i	−0.716684	+	0.697398i	$0.754341\pi$
$450$	10.0852	−	8.77354i	0.475421	−	0.413589i
$451$	4.20971	+	14.3369i	0.198227	+	0.675100i
$452$	−0.158307	+	1.10105i	−0.00744612	+	0.0517889i
$453$	−9.36655	−	8.10010i	−0.440079	−	0.380576i
$454$	14.3566	+	6.55642i	0.673787	+	0.307708i
$455$	−0.190138	+	0.647552i	−0.00891383	+	0.0303577i
$456$	5.50598	−	2.52102i	0.257841	−	0.118058i
$457$	28.8615	−	4.14966i	1.35008	−	0.194113i	0.570957	−	0.820980i	$-0.306572\pi$
$457$	28.8615	−	4.14966i	1.35008	−	0.194113i	0.779126	+	0.626867i	$0.215663\pi$
$458$	2.32029	+	1.49116i	0.108420	+	0.0696773i
$459$	0.120515	+	40.9962i	0.00562514	+	1.91354i
$460$	−3.45028	−	0.782612i	−0.160870	−	0.0364895i
$461$			20.2771i			0.944397i	0.881492	+	0.472198i	$0.156539\pi$
$461$			20.2771i			0.944397i	−0.881492	+	0.472198i	$0.843461\pi$
$462$	−1.49941	+	2.33816i	−0.0697589	+	0.108781i
$463$	2.53655	+	17.6421i	0.117884	+	0.819899i	0.959879	+	0.280414i	$0.0904718\pi$
$463$	2.53655	+	17.6421i	0.117884	+	0.819899i	−0.841996	+	0.539485i	$0.818619\pi$
$464$	−7.61056	+	3.47563i	−0.353312	+	0.161352i
$465$	1.36798	−	4.67587i	0.0634387	−	0.216838i
$466$	−8.52731	+	18.6722i	−0.395020	+	0.864973i
$467$	−3.48706	+	4.02428i	−0.161362	+	0.186222i	−0.830673	−	0.556761i	$-0.812044\pi$
$467$	−3.48706	+	4.02428i	−0.161362	+	0.186222i	0.669311	+	0.742982i	$0.266589\pi$
$468$	0.385264	−	2.71737i	0.0178088	−	0.125610i
$469$	14.0863	−	4.13610i	0.650443	−	0.190987i
$470$	−3.65269	−	4.21543i	−0.168486	−	0.194443i
$471$	14.3172	−	9.22096i	0.659703	−	0.424879i
$472$	1.07421	−	0.690354i	0.0494446	−	0.0317761i
$473$	−1.56646	+	1.35734i	−0.0720258	+	0.0624108i
$474$	−4.67157	−	15.8524i	−0.214573	−	0.728127i
$475$	−15.4200	−	2.21706i	−0.707518	−	0.101726i
$476$	5.96268	+	5.16669i	0.273299	+	0.236815i
$477$	14.8137	−	32.6064i	0.678272	−	1.49294i
$478$	3.17790	+	0.933116i	0.145354	+	0.0426797i
$479$	16.3510	+	35.8037i	0.747097	+	1.63591i	0.771513	+	0.636213i	$0.219500\pi$
$479$	16.3510	+	35.8037i	0.747097	+	1.63591i	−0.0244160	+	0.999702i	$0.507773\pi$
$480$	−0.183082	−	1.26456i	−0.00835649	−	0.0577191i
$481$	1.25421	−	1.95159i	0.0571870	−	0.0889847i
$482$	20.2794			0.923702
$483$	6.68878	−	4.92547i	0.304350	−	0.224117i
$484$	8.42825			0.383102
$485$	2.88548	−	4.48989i	0.131023	−	0.203875i
$486$	2.29404	+	15.4187i	0.104060	+	0.699408i
$487$	16.6854	+	36.5358i	0.756086	+	1.65560i	0.755111	+	0.655597i	$0.227583\pi$
$487$	16.6854	+	36.5358i	0.756086	+	1.65560i	0.000974635		1.00000i	$0.499690\pi$
$488$	−4.59760	−	1.34998i	−0.208124	−	0.0611106i
$489$	21.3846	+	9.74072i	0.967046	+	0.440490i
$490$	−0.557522	−	0.483096i	−0.0251863	−	0.0218240i
$491$	20.0317	+	2.88012i	0.904018	+	0.129978i	0.578618	−	0.815598i	$-0.303592\pi$
$491$	20.0317	+	2.88012i	0.904018	+	0.129978i	0.325400	+	0.945577i	$0.394501\pi$
$492$	15.4802	−	4.56189i	0.697903	−	0.205666i
$493$	−49.8876	+	43.2278i	−2.24682	+	1.94688i
$494$	−2.69078	+	1.72926i	−0.121064	+	0.0778031i
$495$	2.98194	−	1.92464i	0.134028	−	0.0865063i
$496$	2.49689	+	2.88157i	0.112114	+	0.129386i
$497$	−10.0416	+	2.94847i	−0.450426	+	0.132257i
$498$	−0.398164	+	2.78869i	−0.0178422	+	0.124964i
$499$	−0.554583	+	0.640023i	−0.0248266	+	0.0286514i	−0.768027	−	0.640417i	$-0.778761\pi$
$499$	−0.554583	+	0.640023i	−0.0248266	+	0.0286514i	0.743201	+	0.669069i	$0.233307\pi$
$500$	−2.89777	+	6.34524i	−0.129592	+	0.283768i
$501$	−5.59078	−	1.63565i	−0.249777	−	0.0730755i
$502$	−14.5972	+	6.66632i	−0.651505	+	0.297532i
$503$	−0.381351	−	2.65236i	−0.0170036	−	0.118263i	0.979552	−	0.201192i	$-0.0644815\pi$
$503$	−0.381351	−	2.65236i	−0.0170036	−	0.118263i	−0.996555	+	0.0829293i	$0.973572\pi$
$504$	2.52693	+	1.61697i	0.112559	+	0.0720257i
$505$			11.1503i			0.496183i
$506$	7.18193	+	2.75138i	0.319276	+	0.122314i
$507$	−0.0206432	−	21.0670i	−0.000916797	−	0.935619i
$508$	10.2264	+	6.57208i	0.453721	+	0.291589i
$509$	−19.8100	+	2.84825i	−0.878062	+	0.126246i	−0.566581	−	0.824006i	$-0.691734\pi$
$509$	−19.8100	+	2.84825i	−0.878062	+	0.126246i	−0.311481	+	0.950252i	$0.600825\pi$
$510$	−4.19683	−	9.16599i	−0.185839	−	0.405877i
$511$	1.27062	−	4.32732i	0.0562088	−	0.191430i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	11.8565	−	13.7647i	0.523477	−	0.607725i
$514$	0.635649	−	4.42104i	0.0280373	−	0.195004i
$515$	1.39534	+	4.75211i	0.0614862	+	0.209403i
$516$	1.46767	+	1.69043i	0.0646104	+	0.0744169i
$517$	6.55545	+	10.2005i	0.288309	+	0.448617i
$518$	1.37095	+	2.13324i	0.0602360	+	0.0937291i
$519$	−28.9588	−	33.3542i	−1.27115	−	1.46409i
$520$	0.190138	+	0.647552i	0.00833812	+	0.0283970i
$521$	−2.56892	+	17.8672i	−0.112546	+	0.782777i	0.852881	+	0.522105i	$0.174853\pi$
$521$	−2.56892	+	17.8672i	−0.112546	+	0.782777i	−0.965427	+	0.260672i	$0.916056\pi$
$522$	−16.3997	+	19.0014i	−0.717797	+	0.831670i
$523$	33.3171	+	15.2154i	1.45686	+	0.665324i	0.977237	−	0.212152i	$-0.0680474\pi$
$523$	33.3171	+	15.2154i	1.45686	+	0.665324i	0.479620	+	0.877476i	$0.340775\pi$
$524$	−6.37322	+	21.7052i	−0.278415	+	0.948195i
$525$	−3.21291	−	7.01708i	−0.140223	−	0.306250i
$526$	24.3187	−	3.49649i	1.06034	−	0.152454i
$527$	25.3070	+	16.2638i	1.10239	+	0.708464i
$528$	0.00272175	+	2.77763i	0.000118449	+	0.120881i
$529$	−17.1129	−	15.3672i	−0.744038	−	0.668137i
$530$			8.80668i			0.382538i
$531$	2.06474	−	3.22669i	0.0896022	−	0.140026i
$532$	−0.497569	−	3.46067i	−0.0215723	−	0.150039i
$533$	−7.75380	+	3.54104i	−0.335855	+	0.153380i
$534$	8.16429	+	2.38856i	0.353303	+	0.103363i
$535$	−2.49251	+	5.45783i	−0.107760	+	0.235962i
$536$	9.61397	−	11.0951i	0.415260	−	0.479236i
$537$	4.36221	−	30.5523i	0.188243	−	1.31843i
$538$	−7.64769	+	2.24556i	−0.329715	+	0.0968131i
$539$	1.05018	+	1.21197i	0.0452344	+	0.0522033i
$540$	−2.08188	−	3.21862i	−0.0895898	−	0.138507i
$541$	22.6324	−	14.5449i	0.973042	−	0.625336i	0.0454640	−	0.998966i	$-0.485523\pi$
$541$	22.6324	−	14.5449i	0.973042	−	0.625336i	0.927578	+	0.373630i	$0.121887\pi$
$542$	−16.1101	+	13.9595i	−0.691990	+	0.599612i
$543$	−35.7223	+	10.5270i	−1.53299	+	0.451759i
$544$	7.80945	+	1.12283i	0.334827	+	0.0481409i
$545$	−4.62549	−	4.00801i	−0.198134	−	0.171684i
$546$	−1.44201	−	0.656838i	−0.0617124	−	0.0281101i
$547$	4.24031	+	1.24507i	0.181303	+	0.0532352i	0.371124	−	0.928583i	$-0.378973\pi$
$547$	4.24031	+	1.24507i	0.181303	+	0.0532352i	−0.189821	+	0.981819i	$0.560791\pi$
$548$	5.52652	+	12.1014i	0.236081	+	0.516946i
$549$	−14.2247	+	2.07367i	−0.607097	+	0.0885021i
$550$	3.86320	−	6.01126i	0.164727	−	0.256321i
$551$	29.2519			1.24617
$552$	2.96405	−	7.75980i	0.126158	−	0.330279i
$553$	−9.54155			−0.405748
$554$	10.9163	−	16.9861i	0.463788	−	0.721669i
$555$	−0.464255	−	3.20666i	−0.0197065	−	0.136115i
$556$	−5.17462	−	11.3308i	−0.219453	−	0.480534i
$557$	23.1024	+	6.78348i	0.978881	+	0.287425i	0.731762	−	0.681560i	$-0.238698\pi$
$557$	23.1024	+	6.78348i	0.978881	+	0.287425i	0.247118	+	0.968985i	$0.420516\pi$
$558$	10.4142	+	4.73136i	0.440868	+	0.200294i
$559$	−0.893621	−	0.774327i	−0.0377961	−	0.0327505i
$560$	−0.730199	−	0.104987i	−0.0308565	−	0.00443650i
$561$	6.19472	+	21.0211i	0.261541	+	0.887510i
$562$	22.0836	−	19.1355i	0.931539	−	0.807183i
$563$	0.790456	−	0.507995i	0.0333138	−	0.0214095i	−0.523878	−	0.851793i	$-0.675515\pi$
$563$	0.790456	−	0.507995i	0.0333138	−	0.0214095i	0.557192	+	0.830384i	$0.311879\pi$
$564$	11.0102	−	7.09105i	0.463611	−	0.298587i
$565$	−0.537381	−	0.620171i	−0.0226078	−	0.0260908i
$566$	0.685505	−	0.201282i	0.0288139	−	0.00846053i
$567$	8.91334	+	1.24591i	0.374325	+	0.0523232i
$568$	−6.85344	+	7.90929i	−0.287564	+	0.331866i
$569$	−18.6056	+	40.7405i	−0.779986	+	1.70793i	−0.0766665	+	0.997057i	$0.524428\pi$
$569$	−18.6056	+	40.7405i	−0.779986	+	1.70793i	−0.703319	+	0.710874i	$0.748300\pi$
$570$	−1.25439	+	4.28760i	−0.0525407	+	0.179588i
$571$	−26.0815	+	11.9110i	−1.09148	+	0.498461i	−0.878085	−	0.478505i	$-0.841179\pi$
$571$	−26.0815	+	11.9110i	−1.09148	+	0.498461i	−0.213393	+	0.976966i	$0.568452\pi$
$572$	−0.208791	−	1.45218i	−0.00873001	−	0.0607186i
$573$	−7.11461	+	11.0944i	−0.297217	+	0.463477i
$574$		−	9.31753i		−	0.388906i
$575$	−17.2196	+	12.6542i	−0.718108	+	0.527715i
$576$	2.99999	−	0.00587929i	0.125000	−	0.000244971i
$577$	23.7360	+	15.2542i	0.988141	+	0.635040i	0.931648	−	0.363363i	$-0.118372\pi$
$577$	23.7360	+	15.2542i	0.988141	+	0.635040i	0.0564937	+	0.998403i	$0.482008\pi$
$578$	44.7876	−	6.43949i	1.86292	−	0.267847i
$579$	26.3445	−	12.0624i	1.09484	−	0.501294i
$580$	1.73889	−	5.92212i	0.0722036	−	0.245903i
$581$	1.47941	+	0.675622i	0.0613761	+	0.0280295i
$582$	9.47832	+	8.19676i	0.392889	+	0.339767i
$583$	2.72453	−	18.9496i	0.112839	−	0.784810i
$584$	−1.27062	−	4.32732i	−0.0525785	−	0.179066i
$585$	1.32887	+	1.52754i	0.0549421	+	0.0631561i
$586$	−3.03040	−	4.71539i	−0.125185	−	0.194791i
$587$	−3.11776	−	4.85133i	−0.128684	−	0.200236i	0.770933	−	0.636916i	$-0.219790\pi$
$587$	−3.11776	−	4.85133i	−0.128684	−	0.200236i	−0.899617	+	0.436680i	$0.856154\pi$
$588$	1.30788	−	1.13553i	0.0539363	−	0.0468286i
$589$	−3.75570	−	12.7907i	−0.154751	−	0.527033i
$590$	−0.134060	+	0.932405i	−0.00551914	+	0.0383865i
$591$	−15.1655	+	17.5367i	−0.623827	+	0.721361i
$592$	2.30663	+	1.05340i	0.0948019	+	0.0432946i
$593$	0.114932	−	0.391424i	0.00471971	−	0.0160739i	−0.957099	−	0.289760i	$-0.906425\pi$
$593$	0.114932	−	0.391424i	0.00471971	−	0.0160739i	0.961819	+	0.273686i	$0.0882428\pi$
$594$	3.48388	+	7.56966i	0.142945	+	0.310587i
$595$	−5.76109	+	0.828320i	−0.236182	+	0.0339578i
$596$	12.1425	+	7.80348i	0.497374	+	0.319643i
$597$	−39.7683	+	0.0389683i	−1.62761	+	0.00159487i
$598$	−0.970533	+	4.27876i	−0.0396881	+	0.174972i
$599$		−	36.9279i		−	1.50883i	−0.656396	−	0.754416i	$-0.727920\pi$
$599$		−	36.9279i		−	1.50883i	0.656396	−	0.754416i	$-0.272080\pi$
$600$	−6.49659	−	4.16611i	−0.265222	−	0.170081i
$601$	5.10919	+	35.5352i	0.208408	+	1.44951i	0.778353	+	0.627827i	$0.216055\pi$
$601$	5.10919	+	35.5352i	0.208408	+	1.44951i	−0.569945	+	0.821683i	$0.693035\pi$
$602$	1.17569	−	0.536919i	0.0479175	−	0.0218832i
$603$	12.3255	−	42.2830i	0.501931	−	1.72190i
$604$	−2.96999	+	6.50337i	−0.120847	+	0.264618i
$605$	−4.07165	+	4.69894i	−0.165536	+	0.191039i
$606$	−25.9168	−	3.70036i	−1.05280	−	0.150317i
$607$	16.0887	−	4.72406i	0.653019	−	0.191744i	0.0615908	−	0.998101i	$-0.480383\pi$
$607$	16.0887	−	4.72406i	0.653019	−	0.191744i	0.591428	+	0.806358i	$0.298564\pi$
$608$	−2.28956	−	2.64229i	−0.0928539	−	0.107159i
$609$	7.84661	+	12.1833i	0.317961	+	0.493692i
$610$	2.97373	−	1.91110i	0.120403	−	0.0773781i
$611$	−5.22765	+	4.52978i	−0.211488	+	0.183255i
$612$	22.6974	−	6.71289i	0.917487	−	0.271353i
$613$	14.9072	+	2.14333i	0.602097	+	0.0865685i	0.436621	−	0.899645i	$-0.356175\pi$
$613$	14.9072	+	2.14333i	0.602097	+	0.0865685i	0.165476	+	0.986214i	$0.447084\pi$
$614$	−5.81356	−	5.03748i	−0.234616	−	0.203296i
$615$	−4.93509	+	10.8344i	−0.199002	+	0.436886i
$616$	1.53871	+	0.451805i	0.0619963	+	0.0182037i
$617$	−15.4852	−	33.9079i	−0.623411	−	1.36508i	−0.913012	−	0.407933i	$-0.866250\pi$
$617$	−15.4852	−	33.9079i	−0.623411	−	1.36508i	0.289600	−	0.957148i	$-0.406478\pi$
$618$	−11.5084	+	1.66617i	−0.462937	+	0.0670233i
$619$	13.8890	−	21.6118i	0.558247	−	0.868650i	−0.441341	−	0.897339i	$-0.645497\pi$
$619$	13.8890	−	21.6118i	0.558247	−	0.868650i	0.999588	+	0.0286898i	$0.00913349\pi$
$620$	−2.81278			−0.112964
$621$	−1.63077	−	24.8665i	−0.0654406	−	0.997856i
$622$	−14.1717			−0.568235
$623$	2.65522	−	4.13160i	0.106379	−	0.165529i
$624$	−1.56821	+	0.227043i	−0.0627787	+	0.00908901i
$625$	7.11730	+	15.5847i	0.284692	+	0.623388i
$626$	2.58925	+	0.760273i	0.103487	+	0.0303866i
$627$	4.02557	−	8.83767i	0.160766	−	0.352942i
$628$	−7.43059	−	6.43864i	−0.296513	−	0.256930i
$629$	19.8031	+	2.84725i	0.789600	+	0.113527i
$630$	−2.12225	+	0.627669i	−0.0845525	+	0.0250069i
$631$	−22.9563	+	19.8917i	−0.913874	+	0.791876i	−0.978546	−	0.206030i	$-0.933945\pi$
$631$	−22.9563	+	19.8917i	−0.913874	+	0.791876i	0.0646715	+	0.997907i	$0.479400\pi$
$632$	−8.02686	+	5.15855i	−0.319291	+	0.205196i
$633$	−5.50561	−	8.54847i	−0.218828	−	0.339771i
$634$	16.9044	+	19.5087i	0.671358	+	0.774789i
$635$	−8.60439	+	2.52648i	−0.341455	+	0.100260i
$636$	−20.4695	−	2.92259i	−0.811667	−	0.115888i
$637$	−0.599097	+	0.691395i	−0.0237371	+	0.0273941i
$638$	−5.57375	+	12.2048i	−0.220667	+	0.483193i
$639$	−8.78635	+	30.1420i	−0.347583	+	1.19240i
$640$	−0.671043	+	0.306455i	−0.0265253	+	0.0121137i
$641$	−1.02995	−	7.16343i	−0.0406804	−	0.282938i	−1.00000		0.000615415i	$-0.999804\pi$
$641$	−1.02995	−	7.16343i	−0.0406804	−	0.282938i	0.959319	−	0.282323i	$-0.0911050\pi$
$642$	−11.8585	−	7.60460i	−0.468018	−	0.300130i
$643$			21.5316i			0.849123i	0.905399	+	0.424561i	$0.139572\pi$
$643$			21.5316i			0.849123i	−0.905399	+	0.424561i	$0.860428\pi$
$644$	−3.81367	−	2.90791i	−0.150280	−	0.114588i
$645$	−1.65147	+	0.00161825i	−0.0650267	+	6.37186e-5i
$646$	−23.2056	−	14.9134i	−0.913013	−	0.586758i
$647$	8.07071	−	1.16039i	0.317292	−	0.0456198i	0.0181712	−	0.999835i	$-0.494216\pi$
$647$	8.07071	−	1.16039i	0.317292	−	0.0456198i	0.299121	+	0.954215i	$0.403307\pi$
$648$	8.17197	−	3.77079i	0.321025	−	0.148131i
$649$	0.576918	−	1.96480i	0.0226460	−	0.0771253i
$650$	3.70799	+	1.69338i	0.145439	+	0.0664199i
$651$	4.31985	−	4.99525i	0.169308	−	0.195779i
$652$	1.93077	−	13.4288i	0.0756149	−	0.525913i
$653$	1.90658	+	6.49322i	0.0746103	+	0.254099i	0.988349	−	0.152202i	$-0.0486365\pi$
$653$	1.90658	+	6.49322i	0.0746103	+	0.254099i	−0.913739	+	0.406301i	$0.866818\pi$
$654$	10.8509	−	9.42098i	0.424303	−	0.368389i
$655$	−9.02225	−	14.0389i	−0.352528	−	0.548545i
$656$	−5.03744	−	7.83840i	−0.196679	−	0.306038i
$657$	−8.88031	−	10.2079i	−0.346454	−	0.398249i
$658$	−2.13018	−	7.25474i	−0.0830432	−	0.282819i
$659$	−3.11936	+	21.6956i	−0.121513	+	0.845142i	0.834330	+	0.551265i	$0.185855\pi$
$659$	−3.11936	+	21.6956i	−0.121513	+	0.845142i	−0.955843	+	0.293877i	$0.905054\pi$
$660$	−1.54991	−	1.34034i	−0.0603300	−	0.0521728i
$661$	13.7110	+	6.26160i	0.533296	+	0.243548i	0.663814	−	0.747898i	$-0.268937\pi$
$661$	13.7110	+	6.26160i	0.533296	+	0.243548i	−0.130518	+	0.991446i	$0.541664\pi$
$662$	3.33625	−	11.3622i	0.129667	−	0.441605i
$663$	−11.3669	+	5.20458i	−0.441455	+	0.202129i
$664$	1.60982	−	0.231458i	0.0624733	−	0.00898231i
$665$	2.16977	+	1.39443i	0.0841402	+	0.0540736i
$666$	7.60734	−	0.0149086i	0.294778	−	0.000577697i
$667$	28.6227	−	28.1204i	1.10828	−	1.08883i
$668$			3.36314i			0.130124i
$669$	−6.43310	+	10.0317i	−0.248718	+	0.387848i
$670$	1.54130	+	10.7200i	0.0595458	+	0.414150i
$671$	−6.98988	+	3.19217i	−0.269841	+	0.123232i
$672$	0.486346	−	1.66237i	0.0187612	−	0.0641272i
$673$	−3.99675	+	8.75167i	−0.154063	+	0.337352i	−0.970888	−	0.239534i	$-0.923005\pi$
$673$	−3.99675	+	8.75167i	−0.154063	+	0.337352i	0.816824	+	0.576886i	$0.195732\pi$
$674$	6.12977	−	7.07413i	0.236110	−	0.272485i
$675$	−22.9269	−	3.22763i	−0.882456	−	0.124231i
$676$	−11.6704	+	3.42673i	−0.448860	+	0.131797i
$677$	−19.1200	−	22.0657i	−0.734842	−	0.848052i	0.258166	−	0.966100i	$-0.416882\pi$
$677$	−19.1200	−	22.0657i	−0.734842	−	0.848052i	−0.993008	+	0.118048i	$0.962336\pi$
$678$	1.61981	−	1.04323i	0.0622083	−	0.0400650i
$679$	6.08627	−	3.91141i	0.233570	−	0.150106i
$680$	−4.39871	+	3.81151i	−0.168683	+	0.146165i
$681$	−7.72732	−	26.2218i	−0.296112	−	1.00482i
$682$	6.05232	+	0.870192i	0.231755	+	0.0333214i
$683$	24.2787	+	21.0376i	0.928998	+	0.804981i	0.981068	−	0.193662i	$-0.0620366\pi$
$683$	24.2787	+	21.0376i	0.928998	+	0.804981i	−0.0520706	+	0.998643i	$0.516582\pi$
$684$	−9.54944	−	4.33848i	−0.365132	−	0.165886i
$685$	−9.41663	−	2.76497i	−0.359791	−	0.105644i
$686$	−0.415415	−	0.909632i	−0.0158606	−	0.0347299i
$687$	−0.684503	−	4.72793i	−0.0261154	−	0.180382i
$688$	0.698772	−	1.08731i	0.0266404	−	0.0414533i
$689$	10.9214			0.416070
$690$	2.89434	+	5.40125i	0.110186	+	0.205622i
$691$	−30.9460			−1.17724			−0.588620	−	0.808410i	$-0.700329\pi$
$691$	−30.9460			−1.17724			−0.588620	+	0.808410i	$0.700329\pi$
$692$	−13.7876	+	21.4540i	−0.524127	+	0.815558i
$693$	4.76068	−	0.694008i	0.180843	−	0.0263632i
$694$	8.73981	+	19.1375i	0.331759	+	0.726451i
$695$	8.81703	+	2.58891i	0.334449	+	0.0982030i
$696$	13.1878	+	6.00705i	0.499881	+	0.227696i
$697$	−55.5574	−	48.1408i	−2.10439	−	1.82346i
$698$	−14.1096	−	2.02866i	−0.534057	−	0.0767859i
$699$	34.1041	−	10.0502i	1.28994	−	0.380133i
$700$	−3.36746	+	2.91792i	−0.127278	+	0.110287i
$701$	1.72888	−	1.11108i	0.0652988	−	0.0419650i	−0.507584	−	0.861602i	$-0.669461\pi$
$701$	1.72888	−	1.11108i	0.0652988	−	0.0419650i	0.572883	+	0.819637i	$0.305825\pi$
$702$	−3.99148	+	2.58178i	−0.150649	+	0.0974430i
$703$	−5.80583	−	6.70028i	−0.218971	−	0.252706i
$704$	1.53871	−	0.451805i	0.0579922	−	0.0170280i
$705$	−1.36554	+	9.56407i	−0.0514293	+	0.360204i
$706$	−11.4172	+	13.1761i	−0.429691	+	0.495889i
$707$	−6.27892	+	13.7489i	−0.236143	+	0.517082i
$708$	−2.12271	−	0.621025i	−0.0797763	−	0.0233395i
$709$	6.41574	−	2.92997i	0.240948	−	0.110037i	−0.291281	−	0.956637i	$-0.594082\pi$
$709$	6.41574	−	2.92997i	0.240948	−	0.110037i	0.532230	+	0.846600i	$0.321354\pi$
$710$	−1.09874	−	7.64189i	−0.0412349	−	0.286795i
$711$	−15.4284	+	24.1109i	−0.578611	+	0.904228i
$712$		−	4.91124i		−	0.184057i
$713$	−15.9709	−	8.90519i	−0.598114	−	0.333502i
$714$	−0.0133905	−	13.6654i	−0.000501128	−	0.511416i
$715$	0.910487	+	0.585135i	0.0340503	+	0.0218828i
$716$	−17.6369	+	2.53581i	−0.659123	+	0.0947675i
$717$	−2.38821	−	5.21591i	−0.0891892	−	0.194792i
$718$	1.58326	−	5.39208i	0.0590867	−	0.201231i
$719$	28.8539	+	13.1771i	1.07607	+	0.491424i	0.872990	−	0.487739i	$-0.162178\pi$
$719$	28.8539	+	13.1771i	1.07607	+	0.491424i	0.203078	+	0.979162i	$0.434905\pi$
$720$	−1.44601	+	1.67540i	−0.0538895	+	0.0624386i
$721$	−0.955455	+	6.64533i	−0.0355830	+	0.247485i
$722$	−1.90908	−	6.50172i	−0.0710485	−	0.241969i
$723$	−23.0280	−	26.5231i	−0.856420	−	0.986406i
$724$	11.6244	+	18.0879i	0.432018	+	0.672233i
$725$	−20.1551	−	31.3619i	−0.748541	−	1.16475i
$726$	−9.57057	−	11.0232i	−0.355197	−	0.409109i
$727$	−10.7686	−	36.6746i	−0.399387	−	1.36019i	−0.876524	−	0.481357i	$-0.840144\pi$
$727$	−10.7686	−	36.6746i	−0.399387	−	1.36019i	0.477138	−	0.878828i	$-0.341674\pi$
$728$	−0.130196	+	0.905535i	−0.00482540	+	0.0335614i
$729$	17.5610	−	20.5088i	0.650406	−	0.759587i
$730$	3.02641	+	1.38212i	0.112012	+	0.0511544i
$731$	2.87294	−	9.78435i	0.106260	−	0.361887i
$732$	3.45512	+	7.54608i	0.127705	+	0.278911i
$733$	25.9212	−	3.72690i	0.957421	−	0.137656i	0.354146	−	0.935190i	$-0.384771\pi$
$733$	25.9212	−	3.72690i	0.957421	−	0.137656i	0.603274	+	0.797534i	$0.293862\pi$
$734$	7.65274	+	4.91812i	0.282468	+	0.181531i
$735$	0.00125204	+	1.27775i	4.61823e−5	+	0.0471304i
$736$	−4.78040	−	0.384462i	−0.176208	−	0.0141714i
$737$		−	23.5433i		−	0.867230i
$738$	−23.5448	−	15.0662i	−0.866695	−	0.554594i
$739$	−0.961028	−	6.68409i	−0.0353520	−	0.245878i	0.964481	−	0.264152i	$-0.0850921\pi$
$739$	−0.961028	−	6.68409i	−0.0353520	−	0.245878i	−0.999833	+	0.0182737i	$0.994183\pi$
$740$	−1.70162	+	0.777103i	−0.0625528	+	0.0285669i
$741$	5.31715	+	1.55560i	0.195330	+	0.0571463i
$742$	−4.95918	+	10.8591i	−0.182057	+	0.398650i
$743$	−7.07765	+	8.16804i	−0.259654	+	0.299656i	−0.870576	−	0.492034i	$-0.836253\pi$
$743$	−7.07765	+	8.16804i	−0.259654	+	0.299656i	0.610922	+	0.791691i	$0.290799\pi$
$744$	0.933451	−	6.53776i	0.0342220	−	0.239686i
$745$	−10.2166	+	2.99986i	−0.374307	+	0.109906i
$746$	9.54376	+	11.0141i	0.349422	+	0.403254i
$747$	4.09941	−	2.64590i	0.149990	−	0.0968084i
$748$	10.6440	−	6.84048i	0.389183	−	0.250113i
$749$	−6.14678	+	5.32621i	−0.224598	+	0.194616i
$750$	11.5894	−	3.41528i	0.423183	−	0.124708i
$751$	12.7880	+	1.83864i	0.466642	+	0.0670930i	0.371626	−	0.928383i	$-0.378800\pi$
$751$	12.7880	+	1.83864i	0.466642	+	0.0670930i	0.0950166	+	0.995476i	$0.469710\pi$
$752$	−5.71423	−	4.95141i	−0.208377	−	0.180559i
$753$	25.2944	+	11.5216i	0.921779	+	0.419871i
$754$	−7.34415	−	2.15644i	−0.267458	−	0.0785328i
$755$	−2.19098	−	4.79759i	−0.0797381	−	0.174602i
$756$	−0.754606	−	5.14107i	−0.0274447	−	0.186979i
$757$	12.3161	−	19.1643i	0.447637	−	0.696537i	−0.541960	−	0.840404i	$-0.682317\pi$
$757$	12.3161	−	19.1643i	0.447637	−	0.696537i	0.989597	+	0.143867i	$0.0459538\pi$
$758$	−18.9359			−0.687783
$759$	−4.55684	−	12.5174i	−0.165403	−	0.454354i
$760$	2.57921			0.0935579
$761$	−1.89077	+	2.94210i	−0.0685405	+	0.106651i	−0.873832	−	0.486228i	$-0.838372\pi$
$761$	−1.89077	+	2.94210i	−0.0685405	+	0.106651i	0.805291	+	0.592879i	$0.202009\pi$
$762$	−3.01685	−	20.8377i	−0.109289	−	0.754871i
$763$	−3.44650	−	7.54678i	−0.124772	−	0.273212i
$764$	7.30107	+	2.14379i	0.264143	+	0.0775595i
$765$	−7.22242	+	15.8973i	−0.261127	+	0.574767i
$766$	−28.6597	−	24.8338i	−1.03552	−	0.897280i
$767$	1.15629	+	0.166250i	0.0417514	+	0.00600294i
$768$	−0.489603	−	1.66141i	−0.0176670	−	0.0599510i
$769$	19.9368	−	17.2753i	0.718940	−	0.622965i	−0.216569	−	0.976267i	$-0.569487\pi$
$769$	19.9368	−	17.2753i	0.718940	−	0.622965i	0.935509	+	0.353302i	$0.114941\pi$
$770$	−0.995234	+	0.639598i	−0.0358658	+	0.0230495i
$771$	−6.50401	+	4.18888i	−0.234236	+	0.150859i
$772$	−10.9549	−	12.6426i	−0.394275	−	0.455017i
$773$	−28.2135	+	8.28423i	−1.01477	+	0.297963i	−0.746503	−	0.665382i	$-0.768269\pi$
$773$	−28.2135	+	8.28423i	−1.01477	+	0.297963i	−0.268266	+	0.963345i	$0.586451\pi$
$774$	0.544299	−	3.83907i	0.0195644	−	0.137993i
$775$	−11.1256	+	12.8396i	−0.399644	+	0.461214i
$776$	3.00543	−	6.58097i	0.107889	−	0.236243i
$777$	1.23327	−	4.21541i	0.0442433	−	0.151227i
$778$	8.35087	−	3.81371i	0.299393	−	0.136728i
$779$	4.63611	+	32.2449i	0.166106	+	1.15529i
$780$	0.631015	−	0.983997i	0.0225939	−	0.0352327i
$781$			16.7832i			0.600549i
$782$	−37.0430	+	7.71543i	−1.32465	+	0.275903i
$783$	43.4742	−	0.127799i	1.55364	−	0.00456717i
$784$	−0.841254	−	0.540641i	−0.0300448	−	0.0193086i
$785$	7.17937	−	1.03224i	0.256243	−	0.0368422i
$786$	35.6249	−	16.3115i	1.27070	−	0.581814i
$787$	9.56046	−	32.5599i	0.340794	−	1.16064i	−0.593709	−	0.804680i	$-0.702337\pi$
$787$	9.56046	−	32.5599i	0.340794	−	1.16064i	0.934502	−	0.355957i	$-0.115845\pi$
$788$	12.1760	+	5.56060i	0.433753	+	0.198088i
$789$	−32.1877	−	27.8356i	−1.14591	−	0.990974i
$790$	1.00174	−	6.96723i	0.0356402	−	0.247883i
$791$	−0.313391	−	1.06731i	−0.0111429	−	0.0379492i
$792$	3.62973	−	3.15765i	0.128977	−	0.112202i
$793$	−2.36999	−	3.68778i	−0.0841609	−	0.130957i
$794$	−13.7105	−	21.3339i	−0.486567	−	0.757113i
$795$	11.5181	−	10.0003i	0.408506	−	0.354674i
$796$	6.46865	+	22.0302i	0.229275	+	0.780840i
$797$	4.99919	−	34.7702i	0.177081	−	1.23162i	−0.686394	−	0.727230i	$-0.740807\pi$
$797$	4.99919	−	34.7702i	0.177081	−	1.23162i	0.863475	−	0.504392i	$-0.168284\pi$
$798$	−3.96115	+	4.58047i	−0.140223	+	0.162147i
$799$	−54.2636	−	24.7814i	−1.91971	−	0.876702i
$800$	−1.25534	+	4.27530i	−0.0443830	+	0.151155i
$801$	−6.14686	−	13.3902i	−0.217189	−	0.473121i
$802$	22.6816	−	3.26112i	0.800915	−	0.115154i
$803$	−6.08441	−	3.91022i	−0.214714	−	0.137989i
$804$	−25.4281	+	0.0249166i	−0.896781	+	0.000878740i
$805$	3.46359	−	0.721408i	0.122076	−	0.0254263i
$806$			3.48818i			0.122866i
$807$	11.6211	+	7.45238i	0.409084	+	0.262336i
$808$	2.15106	+	14.9610i	0.0756741	+	0.526325i
$809$	−32.3018	+	14.7517i	−1.13567	+	0.518643i	−0.892369	−	0.451307i	$-0.850958\pi$
$809$	−32.3018	+	14.7517i	−1.13567	+	0.518643i	−0.243302	+	0.969951i	$0.578231\pi$
$810$	−1.84554	+	6.37771i	−0.0648458	+	0.224090i
$811$	13.5615	−	29.6956i	0.476209	−	1.04275i	−0.507280	−	0.861782i	$-0.669349\pi$
$811$	13.5615	−	29.6956i	0.476209	−	1.04275i	0.983489	−	0.180971i	$-0.0579239\pi$
$812$	5.47898	−	6.32309i	0.192275	−	0.221897i
$813$	36.5510	+	5.21870i	1.28190	+	0.183028i
$814$	3.90183	−	1.14568i	0.136759	−	0.0401561i
$815$	6.55412	+	7.56386i	0.229581	+	0.264950i
$816$	−7.39936	−	11.4889i	−0.259029	−	0.402191i
$817$	−3.80152	+	2.44309i	−0.132998	+	0.0854728i
$818$	10.4540	−	9.05841i	0.365514	−	0.316720i
$819$	0.778386	+	2.63185i	0.0271990	+	0.0919642i
$820$	6.80365	+	0.978217i	0.237594	+	0.0341608i
$821$	−8.65943	−	7.50344i	−0.302216	−	0.261872i	0.490529	−	0.871425i	$-0.336804\pi$
$821$	−8.65943	−	7.50344i	−0.302216	−	0.261872i	−0.792745	+	0.609553i	$0.791349\pi$
$822$	9.55167	−	20.9696i	0.333153	−	0.731398i
$823$	31.7752	+	9.33005i	1.10761	+	0.325225i	0.783873	−	0.620921i	$-0.213241\pi$
$823$	31.7752	+	9.33005i	1.10761	+	0.325225i	0.323741	+	0.946146i	$0.395059\pi$
$824$	2.78896	+	6.10697i	0.0971580	+	0.212746i
$825$	−12.2488	+	1.77337i	−0.426450	+	0.0617408i
$826$	−0.690354	+	1.07421i	−0.0240205	+	0.0373766i
$827$	19.0512			0.662474			0.331237	−	0.943548i	$-0.392534\pi$
$827$	19.0512			0.662474			0.331237	+	0.943548i	$0.392534\pi$
$828$	−13.5147	+	4.93488i	−0.469668	+	0.171499i
$829$	−3.85929			−0.134039			−0.0670193	−	0.997752i	$-0.521349\pi$
$829$	−3.85929			−0.134039			−0.0670193	+	0.997752i	$0.521349\pi$
$830$	−0.648657	+	1.00933i	−0.0225152	+	0.0350343i
$831$	−34.6116	+	5.01102i	−1.20066	+	0.173830i
$832$	0.380041	+	0.832174i	0.0131756	+	0.0288504i
$833$	−7.57016	−	2.22280i	−0.262291	−	0.0770155i
$834$	−8.94346	+	19.6343i	−0.309687	+	0.679882i
$835$	−1.87503	−	1.62472i	−0.0648879	−	0.0562257i
$836$	−5.54976	−	0.797935i	−0.191942	−	0.0275971i
$837$	−5.63760	−	18.9932i	−0.194864	−	0.656500i
$838$	−0.423277	+	0.366771i	−0.0146218	+	0.0126699i
$839$	−7.80922	+	5.01868i	−0.269604	+	0.173264i	−0.668457	−	0.743751i	$-0.733045\pi$
$839$	−7.80922	+	5.01868i	−0.269604	+	0.173264i	0.398853	+	0.917015i	$0.369408\pi$
$840$	0.691855	+	1.07423i	0.0238713	+	0.0370645i
$841$	26.8497	+	30.9863i	0.925853	+	1.06849i
$842$	20.9938	−	6.16435i	0.723495	−	0.212437i
$843$	−50.1037	−	7.15372i	−1.72566	−	0.246387i
$844$	−3.84435	+	4.43662i	−0.132328	+	0.152715i
$845$	3.72743	−	8.16193i	0.128227	−	0.280779i
$846$	−21.7767	−	6.34788i	−0.748698	−	0.218245i
$847$	−7.66661	+	3.50122i	−0.263428	+	0.120303i
$848$	1.69894	+	11.8164i	0.0583419	+	0.405777i
$849$	−1.04167	−	0.667999i	−0.0357500	−	0.0229257i
$850$			35.1551i			1.20581i
$851$	−12.1221	−	0.974912i	−0.415539	−	0.0334195i
$852$	18.1268	−	0.0177621i	0.621012	−	0.000608519i
$853$	18.8667	+	12.1249i	0.645983	+	0.415148i	0.822196	−	0.569204i	$-0.192748\pi$
$853$	18.8667	+	12.1249i	0.645983	+	0.415148i	−0.176213	+	0.984352i	$0.556385\pi$
$854$	4.74293	−	0.681930i	0.162300	−	0.0233352i
$855$	7.03209	−	3.22812i	0.240493	−	0.110399i
$856$	−2.29143	+	7.80390i	−0.0783195	+	0.266732i
$857$	−22.5789	−	10.3114i	−0.771281	−	0.352232i	−0.00940542	−	0.999956i	$-0.502994\pi$
$857$	−22.5789	−	10.3114i	−0.771281	−	0.352232i	−0.761875	+	0.647724i	$0.775721\pi$
$858$	−1.66219	+	1.92207i	−0.0567462	+	0.0656184i
$859$	−7.62138	+	53.0079i	−0.260038	+	1.80861i	0.272453	+	0.962169i	$0.412165\pi$
$859$	−7.62138	+	53.0079i	−0.260038	+	1.80861i	−0.532491	+	0.846436i	$0.678744\pi$
$860$	0.268626	+	0.914857i	0.00916008	+	0.0311964i
$861$	−12.1862	+	10.5804i	−0.415306	+	0.360578i
$862$	1.04366	+	1.62397i	0.0355472	+	0.0553125i
$863$	−4.66441	−	7.25797i	−0.158779	−	0.247064i	0.752745	−	0.658312i	$-0.228729\pi$
$863$	−4.66441	−	7.25797i	−0.158779	−	0.247064i	−0.911523	+	0.411248i	$0.865093\pi$
$864$	−3.41429	−	3.91697i	−0.116156	−	0.133258i
$865$	−5.30032	−	18.0512i	−0.180216	−	0.613761i
$866$	−3.10717	+	21.6108i	−0.105586	+	0.734365i
$867$	−59.2800	−	51.2648i	−2.01325	−	1.74104i
$868$	−3.46830	−	1.58392i	−0.117722	−	0.0537617i
$869$	−4.31092	+	14.6817i	−0.146238	+	0.498041i
$870$	−9.72002	+	4.45050i	−0.329540	+	0.150886i
$871$	13.2941	−	1.91140i	0.450454	−	0.0647654i
$872$	−6.97948	−	4.48544i	−0.236355	−	0.151896i
$873$	−0.0425353	−	21.7043i	−0.00143960	−	0.734578i
$874$	14.6447	+	8.16574i	0.495365	+	0.276210i
$875$		−	6.97561i		−	0.235819i
$876$	−4.21681	+	6.57565i	−0.142473	+	0.222170i
$877$	2.60510	+	18.1189i	0.0879681	+	0.611832i	0.985346	+	0.170568i	$0.0545604\pi$
$877$	2.60510	+	18.1189i	0.0879681	+	0.611832i	−0.897378	+	0.441263i	$0.854531\pi$
$878$	−2.92399	+	1.33534i	−0.0986798	+	0.0450656i
$879$	−2.72607	+	9.31790i	−0.0919479	+	0.314285i
$880$	−0.491452	+	1.07613i	−0.0165668	+	0.0362763i
$881$	0.438226	−	0.505740i	0.0147642	−	0.0170388i	−0.748319	−	0.663339i	$-0.769139\pi$
$881$	0.438226	−	0.505740i	0.0147642	−	0.0170388i	0.763084	+	0.646300i	$0.223684\pi$
$882$	−2.97030	−	0.421124i	−0.100015	−	0.0141800i
$883$	33.9372	−	9.96486i	1.14208	−	0.335344i	0.344634	−	0.938737i	$-0.388003\pi$
$883$	33.9372	−	9.96486i	1.14208	−	0.335344i	0.797444	+	0.603393i	$0.206185\pi$
$884$	4.72673	+	5.45494i	0.158977	+	0.183469i
$885$	1.37171	−	0.883443i	0.0461094	−	0.0296966i
$886$	0.318862	−	0.204920i	0.0107124	−	0.00688443i
$887$	5.86321	−	5.08050i	0.196867	−	0.170586i	−0.550849	−	0.834605i	$-0.685696\pi$
$887$	5.86321	−	5.08050i	0.196867	−	0.170586i	0.747716	+	0.664019i	$0.231150\pi$
$888$	−1.24153	−	4.21298i	−0.0416630	−	0.141378i
$889$	−12.0324	−	1.72999i	−0.403552	−	0.0580221i
$890$	2.73813	+	2.37260i	0.0917822	+	0.0795298i
$891$	5.94418	−	13.1521i	0.199138	−	0.440613i
$892$	6.60170	+	1.93843i	0.221041	+	0.0649035i
$893$	10.9816	+	24.0463i	0.367485	+	0.804679i
$894$	−3.58212	−	24.7421i	−0.119804	−	0.827498i
$895$	7.10655	−	11.0580i	0.237546	−	0.369629i
$896$	−1.00000			−0.0334077
$897$	6.69820	−	3.58933i	0.223646	−	0.119844i
$898$	−8.44279			−0.281739
$899$	17.2469	−	26.8367i	0.575216	−	0.895053i
$900$	1.92830	+	13.2275i	0.0642767	+	0.440918i
$901$	39.1267	+	85.6756i	1.30350	+	2.85427i
$902$	−14.3369	−	4.20971i	−0.477368	−	0.140168i
$903$	−2.03726	−	0.927976i	−0.0677959	−	0.0308811i
$904$	−0.840673	−	0.728448i	−0.0279604	−	0.0242278i
$905$	−15.7001	−	2.25734i	−0.521890	−	0.0750364i
$906$	11.8782	−	3.50039i	0.394626	−	0.116293i
$907$	−2.28353	+	1.97869i	−0.0758234	+	0.0657014i	−0.691948	−	0.721947i	$-0.743247\pi$
$907$	−2.28353	+	1.97869i	−0.0758234	+	0.0657014i	0.616125	+	0.787649i	$0.288702\pi$
$908$	−13.2774	+	8.53284i	−0.440625	+	0.283172i
$909$	24.5898	+	38.0981i	0.815591	+	1.26363i
$910$	−0.441959	−	0.510048i	−0.0146508	−	0.0169079i
$911$	16.1381	−	4.73857i	0.534679	−	0.156996i	−0.00323659	−	0.999995i	$-0.501030\pi$
$911$	16.1381	−	4.73857i	0.534679	−	0.156996i	0.537915	+	0.842999i	$0.319212\pi$
$912$	−0.855941	+	5.99489i	−0.0283430	+	0.198511i
$913$	1.70799	−	1.97112i	0.0565261	−	0.0652346i
$914$	−12.1128	+	26.5233i	−0.400655	+	0.877313i
$915$	−5.87626	−	1.71917i	−0.194263	−	0.0568341i
$916$	−2.50889	+	1.14577i	−0.0828959	+	0.0378573i
$917$	−3.21938	−	22.3913i	−0.106313	−	0.739424i
$918$	−34.5533	−	22.0628i	−1.14043	−	0.728182i
$919$		−	16.8432i		−	0.555606i	−0.960638	−	0.277803i	$-0.910394\pi$
$919$		−	16.8432i		−	0.555606i	0.960638	−	0.277803i	$-0.0896063\pi$
$920$	2.52374	−	2.47945i	0.0832051	−	0.0817449i
$921$	0.0130557	+	13.3237i	0.000430199	+	0.439031i
$922$	−17.0582	−	10.9626i	−0.561780	−	0.361034i
$923$	−9.47687	+	1.36257i	−0.311935	+	0.0448495i
$924$	−1.15635	−	2.52549i	−0.0380410	−	0.0830826i
$925$	−3.18327	+	10.8412i	−0.104665	+	0.356457i
$926$	−16.2129	−	7.40416i	−0.532787	−	0.243316i
$927$	15.2474	+	13.1597i	0.500790	+	0.432221i
$928$	1.19070	−	8.28148i	0.0390866	−	0.271853i
$929$	−5.63638	−	19.1958i	−0.184924	−	0.629793i	−0.998810	−	0.0487684i	$-0.984470\pi$
$929$	−5.63638	−	19.1958i	−0.184924	−	0.629793i	0.813886	−	0.581024i	$-0.197348\pi$
$930$	3.19400	+	3.67879i	0.104735	+	0.120632i
$931$	1.89022	+	2.94124i	0.0619494	+	0.0963951i
$932$	−11.0978	−	17.2686i	−0.363522	−	0.565651i
$933$	16.0925	+	18.5350i	0.526844	+	0.606808i
$934$	−1.50020	−	5.10920i	−0.0490879	−	0.167178i
$935$	−1.32835	+	9.23887i	−0.0434416	+	0.302143i
$936$	2.07770	+	1.79322i	0.0679119	+	0.0586134i
$937$	34.8237	+	15.9035i	1.13764	+	0.519544i	0.892994	−	0.450068i	$-0.148600\pi$
$937$	34.8237	+	15.9035i	1.13764	+	0.519544i	0.244648	+	0.969612i	$0.421328\pi$
$938$	−4.13610	+	14.0863i	−0.135048	+	0.459933i
$939$	−1.94583	−	4.24976i	−0.0634999	−	0.138686i
$940$	5.52104	−	0.793806i	0.180077	−	0.0258911i
$941$	39.0620	+	25.1037i	1.27339	+	0.818356i	0.990057	−	0.140667i	$-0.0449247\pi$
$941$	39.0620	+	25.1037i	1.27339	+	0.818356i	0.283329	+	0.959023i	$0.408561\pi$
$942$	0.0166871	+	17.0296i	0.000543694	+	0.554856i
$943$	35.5340	+	27.0945i	1.15715	+	0.882318i
$944$			1.27692i			0.0415602i
$945$	3.23081	+	2.06292i	0.105098	+	0.0671068i
$946$	−0.294979	−	2.05162i	−0.00959060	−	0.0667041i
$947$	20.8774	−	9.53439i	0.678424	−	0.309826i	−0.0462377	−	0.998930i	$-0.514723\pi$
$947$	20.8774	−	9.53439i	0.678424	−	0.309826i	0.724662	+	0.689104i	$0.241996\pi$
$948$	15.8616	+	4.64050i	0.515160	+	0.150716i
$949$	1.71399	−	3.75312i	0.0556385	−	0.121831i
$950$	10.2018	−	11.7735i	0.330990	−	0.381983i
$951$	6.31962	−	44.2618i	0.204928	−	1.43529i
$952$	−7.57016	+	2.22280i	−0.245350	+	0.0720414i
$953$	−25.9053	−	29.8963i	−0.839154	−	0.968435i	0.160674	−	0.987008i	$-0.448633\pi$
$953$	−25.9053	−	29.8963i	−0.839154	−	0.968435i	−0.999828	+	0.0185723i	$0.994088\pi$
$954$	19.4214	+	30.0904i	0.628790	+	0.974213i
$955$	−4.72233	+	3.03485i	−0.152811	+	0.0982056i
$956$	−2.50309	+	2.16894i	−0.0809557	+	0.0701485i
$957$	22.2917	−	6.56916i	0.720587	−	0.212351i
$958$	−38.9601	−	5.60161i	−1.25874	−	0.180980i
$959$	−10.0542	−	8.71201i	−0.324667	−	0.281326i
$960$	1.16280	+	0.529656i	0.0375292	+	0.0170946i
$961$	15.7953	+	4.63791i	0.509525	+	0.149610i
$962$	0.963702	+	2.11021i	0.0310710	+	0.0680360i
$963$	3.51982	+	24.1449i	0.113424	+	0.778057i
$964$	−10.9639	+	17.0601i	−0.353123	+	0.549470i
$965$	12.3408			0.397264
$966$	0.527345	+	8.28987i	0.0169671	+	0.266722i
$967$	36.7419			1.18154			0.590769	−	0.806840i	$-0.298824\pi$
$967$	36.7419			1.18154			0.590769	+	0.806840i	$0.298824\pi$
$968$	−4.55666	+	7.09030i	−0.146457	+	0.227891i
$969$	6.84584	+	47.2849i	0.219920	+	1.51901i
$970$	2.21713	+	4.85484i	0.0711877	+	0.155879i
$971$	16.8094	+	4.93567i	0.539438	+	0.158393i	0.540091	−	0.841606i	$-0.318390\pi$
$971$	16.8094	+	4.93567i	0.539438	+	0.158393i	−0.000653132		1.00000i	$0.500208\pi$
$972$	−14.2113	−	6.40613i	−0.455828	−	0.205477i
$973$	9.41399	+	8.15727i	0.301799	+	0.261510i
$974$	−39.7567	−	5.71615i	−1.27389	−	0.183157i
$975$	−1.99580	−	6.77252i	−0.0639168	−	0.216894i
$976$	3.62133	−	3.13790i	0.115916	−	0.100442i
$977$	11.5681	−	7.43440i	0.370098	−	0.237847i	−0.342350	−	0.939572i	$-0.611223\pi$
$977$	11.5681	−	7.43440i	0.370098	−	0.237847i	0.712448	+	0.701725i	$0.247586\pi$
$978$	−19.7558	+	12.7237i	−0.631721	+	0.406858i
$979$	−5.15768	−	5.95228i	−0.164840	−	0.190236i
$980$	0.707825	−	0.207836i	0.0226107	−	0.00663909i
$981$	−24.6431	−	3.49387i	−0.786794	−	0.111551i
$982$	−13.2529	+	15.2946i	−0.422916	+	0.488071i
$983$	9.46126	−	20.7173i	0.301767	−	0.660778i	−0.696627	−	0.717434i	$-0.745317\pi$
$983$	9.46126	−	20.7173i	0.301767	−	0.660778i	0.998394	+	0.0566559i	$0.0180438\pi$
$984$	−4.53155	+	15.4892i	−0.144460	+	0.493776i
$985$	−8.98235	+	4.10210i	−0.286201	+	0.130704i
$986$	−9.39431	−	65.3388i	−0.299176	−	2.08081i
$987$	−7.06946	+	11.0240i	−0.225023	+	0.350899i
$988$		−	3.19854i		−	0.101759i
$989$	−1.37116	+	6.04500i	−0.0436004	+	0.192220i
$990$	0.00695542	+	3.54911i	0.000221058	+	0.112798i
$991$	−6.63665	−	4.26512i	−0.210820	−	0.135486i	0.430970	−	0.902366i	$-0.358172\pi$
$991$	−6.63665	−	4.26512i	−0.210820	−	0.135486i	−0.641790	+	0.766880i	$0.721808\pi$
$992$	−3.77405	+	0.542626i	−0.119826	+	0.0172284i
$993$	−18.6489	+	8.53876i	−0.591805	+	0.270969i
$994$	2.94847	−	10.0416i	0.0935198	−	0.318499i
$995$	−15.4073	−	7.03629i	−0.488445	−	0.223065i
$996$	−2.13073	−	1.84264i	−0.0675148	−	0.0583862i
$997$	4.31436	−	30.0070i	0.136637	−	0.950332i	−0.799992	−	0.600010i	$-0.795163\pi$
$997$	4.31436	−	30.0070i	0.136637	−	0.950332i	0.936629	−	0.350322i	$-0.113928\pi$
$998$	−0.238591	−	0.812568i	−0.00755248	−	0.0257214i
$999$	−8.65789	−	9.93259i	−0.273924	−	0.314253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.r.b.113.11	yes	240
3.2	odd	2		966.2.r.a.113.13	✓	240
23.11	odd	22		966.2.r.a.701.13	yes	240
69.11	even	22	inner	966.2.r.b.701.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.r.a.113.13	✓	240	3.2	odd	2
966.2.r.a.701.13	yes	240	23.11	odd	22
966.2.r.b.113.11	yes	240	1.1	even	1	trivial
966.2.r.b.701.11	yes	240	69.11	even	22	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.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(1.71418 - 0.248176i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.707825 + 0.207836i) q^{5} +(-0.717976 + 1.57623i) q^{6} +(0.755750 + 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.87682 - 0.850837i) q^{9} +O(q^{10})\)	\(q+(-0.540641 + 0.841254i) q^{2} +(1.71418 - 0.248176i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(0.707825 + 0.207836i) q^{5} +(-0.717976 + 1.57623i) q^{6} +(0.755750 + 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.87682 - 0.850837i) q^{9} +(-0.557522 + 0.483096i) q^{10} +(1.34909 - 0.867008i) q^{11} +(-0.937845 - 1.45618i) q^{12} +(0.599097 + 0.691395i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(1.26492 + 0.180603i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-3.27752 + 7.17677i) q^{17} +(-0.839555 + 2.88013i) q^{18} +(3.18030 - 1.45240i) q^{19} +(-0.104987 - 0.730199i) q^{20} +(1.45801 + 0.934989i) q^{21} +1.60367i q^{22} +(1.71568 - 4.47844i) q^{23} +(1.73205 - 0.00169721i) q^{24} +(-3.74845 - 2.40898i) q^{25} +(-0.905535 + 0.130196i) q^{26} +(4.72022 - 2.17244i) q^{27} +(0.281733 - 0.959493i) q^{28} +(7.61056 + 3.47563i) q^{29} +(-0.835800 + 0.966477i) q^{30} +(0.542626 - 3.77405i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(2.09741 - 1.82102i) q^{33} +(-4.26552 - 6.63728i) q^{34} +(0.398835 + 0.620599i) q^{35} +(-1.96902 - 2.26339i) q^{36} +(-0.714413 - 2.43307i) q^{37} +(-0.497569 + 3.46067i) q^{38} +(1.19855 + 1.03649i) q^{39} +(0.671043 + 0.306455i) q^{40} +(-2.62505 + 8.94010i) q^{41} +(-1.57482 + 0.721063i) q^{42} +(-1.27933 + 0.183940i) q^{43} +(-1.34909 - 0.867008i) q^{44} +(2.21312 - 0.00433720i) q^{45} +(2.83994 + 3.86455i) q^{46} +7.56101i q^{47} +(-0.934989 + 1.45801i) q^{48} +(0.142315 + 0.989821i) q^{49} +(4.05313 - 1.85100i) q^{50} +(-3.83715 + 13.1157i) q^{51} +(0.380041 - 0.832174i) q^{52} +(7.81766 - 9.02206i) q^{53} +(-0.724367 + 5.14541i) q^{54} +(1.13512 - 0.333300i) q^{55} +(0.654861 + 0.755750i) q^{56} +(5.09116 - 3.27894i) q^{57} +(-7.03847 + 4.52335i) q^{58} +(0.965031 - 0.836204i) q^{59} +(-0.361184 - 1.22564i) q^{60} +(-4.74293 - 0.681930i) q^{61} +(2.88157 + 2.49689i) q^{62} +(2.73133 + 1.24089i) q^{63} +(0.959493 + 0.281733i) q^{64} +(0.280359 + 0.613901i) q^{65} +(0.397992 + 2.74897i) q^{66} +(7.93711 - 12.3504i) q^{67} +7.88975 q^{68} +(1.82954 - 8.10264i) q^{69} -0.737708 q^{70} +(-5.65807 + 8.80413i) q^{71} +(2.96862 - 0.432763i) q^{72} +(-1.87353 - 4.10245i) q^{73} +(2.43307 + 0.714413i) q^{74} +(-7.02336 - 3.19915i) q^{75} +(-2.64229 - 2.28956i) q^{76} +(1.58734 + 0.228226i) q^{77} +(-1.51994 + 0.447912i) q^{78} +(-7.21102 + 6.24839i) q^{79} +(-0.620599 + 0.398835i) q^{80} +(7.55215 - 4.89541i) q^{81} +(-6.10168 - 7.04172i) q^{82} +(1.56050 - 0.458204i) q^{83} +(0.244816 - 1.71466i) q^{84} +(-3.81151 + 4.39871i) q^{85} +(0.536919 - 1.17569i) q^{86} +(13.9084 + 4.06909i) q^{87} +(1.45875 - 0.666187i) q^{88} +(-0.698943 - 4.86125i) q^{89} +(-1.19285 + 1.86414i) q^{90} +0.914847i q^{91} +(-4.78645 + 0.299773i) q^{92} +(-0.00647121 - 6.60406i) q^{93} +(-6.36073 - 4.08779i) q^{94} +(2.55296 - 0.367060i) q^{95} +(-0.721063 - 1.57482i) q^{96} +(2.03827 - 6.94171i) q^{97} +(-0.909632 - 0.415415i) q^{98} +(3.14340 - 3.64208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Introduction

L-functions

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