LMFDB - Embedded newform 690.2.w.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	690.7
Dual form			690.2.w.a.493.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.11721 - 0.719325i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-2.05801 + 3.76897i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.11721 - 0.719325i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-2.05801 + 3.76897i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(2.16313 + 0.566452i) q^{10} +(2.64636 - 2.29308i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(0.896834 - 0.489708i) q^{13} +(1.78389 - 3.90618i) q^{14} +(-1.15293 + 1.91592i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-0.279315 - 0.373122i) q^{17} +(0.936950 + 0.349464i) q^{18} +(0.218004 + 1.51625i) q^{19} +(-2.19803 - 0.410693i) q^{20} +(3.24537 + 2.81213i) q^{21} +(-2.47603 + 2.47603i) q^{22} +(4.68188 + 1.03924i) q^{23} +1.00000i q^{24} +(3.96514 + 3.04592i) q^{25} +(-0.859613 + 0.552440i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(-1.50068 + 4.02349i) q^{28} +(7.70426 + 1.10771i) q^{29} +(1.01331 - 1.99329i) q^{30} +(4.48357 + 2.88141i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-1.67815 - 3.07331i) q^{33} +(0.305222 + 0.352245i) q^{34} +(7.06835 - 6.49931i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.203874 + 0.546607i) q^{37} +(-0.325617 - 1.49684i) q^{38} +(-0.287881 - 0.980433i) q^{39} +(2.22173 + 0.252841i) q^{40} +(-3.64571 - 7.98298i) q^{41} +(-3.43772 - 2.57344i) q^{42} +(2.91987 + 0.635179i) q^{43} +(2.29308 - 2.64636i) q^{44} +(1.62706 + 1.53384i) q^{45} +(-4.74409 - 0.702595i) q^{46} +(-0.989385 - 0.989385i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(-6.18520 - 9.62437i) q^{49} +(-4.17233 - 2.75529i) q^{50} +(-0.423967 + 0.193619i) q^{51} +(0.818013 - 0.612357i) q^{52} +(9.95488 + 5.43578i) q^{53} +(0.540641 - 0.841254i) q^{54} +(-7.25237 + 2.95134i) q^{55} +(1.20983 - 4.12029i) q^{56} +(1.52794 + 0.109281i) q^{57} +(-7.76365 - 0.555267i) q^{58} +(-0.205474 + 0.699779i) q^{59} +(-0.868532 + 2.06050i) q^{60} +(3.11627 - 4.84901i) q^{61} +(-4.67770 - 2.55422i) q^{62} +(3.43772 - 2.57344i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-2.25104 + 0.391700i) q^{65} +(1.89313 + 2.94576i) q^{66} +(0.845557 + 11.8224i) q^{67} +(-0.329573 - 0.329573i) q^{68} +(2.01070 - 4.35397i) q^{69} +(-6.58668 + 6.98700i) q^{70} +(9.63328 - 11.1174i) q^{71} +(0.977147 + 0.212565i) q^{72} +(-2.52325 - 1.88888i) q^{73} +(-0.242349 - 0.530670i) q^{74} +(3.81917 - 3.22707i) q^{75} +(0.431571 + 1.46979i) q^{76} +(3.19631 + 14.6932i) q^{77} +(0.357091 + 0.957398i) q^{78} +(8.14319 + 2.39106i) q^{79} +(-2.23410 - 0.0937008i) q^{80} +(0.654861 + 0.755750i) q^{81} +(4.20592 + 7.70256i) q^{82} +(-9.19453 + 3.42938i) q^{83} +(3.61255 + 2.32164i) q^{84} +(0.322973 + 0.990895i) q^{85} +(-2.95775 - 0.425260i) q^{86} +(2.72005 - 7.29273i) q^{87} +(-2.09845 + 2.80320i) q^{88} +(1.85091 - 1.18951i) q^{89} +(-1.73234 - 1.41386i) q^{90} +4.38796i q^{91} +(4.78212 + 0.362365i) q^{92} +(3.76862 - 3.76862i) q^{93} +(1.05745 + 0.916282i) q^{94} +(0.629118 - 3.36704i) q^{95} +(0.142315 + 0.989821i) q^{96} +(13.2709 + 4.94979i) q^{97} +(6.85604 + 9.15860i) q^{98} +(-3.35979 + 0.986524i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$2$	−0.997452	+	0.0713392i	−0.705305	+	0.0504444i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$3$	0.212565	−	0.977147i	0.122725	−	0.564156i
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	−2.11721	−	0.719325i	−0.946844	−	0.321692i
$5$	−2.11721	−	0.719325i	−0.946844	−	0.321692i
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	−2.05801	+	3.76897i	−0.777855	+	1.42453i	0.123903	+	0.992294i	$0.460459\pi$
$7$	−2.05801	+	3.76897i	−0.777855	+	1.42453i	−0.901758	+	0.432241i	$0.857723\pi$
$8$	−0.977147	+	0.212565i	−0.345474	+	0.0751532i
$9$	−0.909632	−	0.415415i	−0.303211	−	0.138472i
$10$	2.16313	+	0.566452i	0.684042	+	0.179128i
$11$	2.64636	−	2.29308i	0.797907	−	0.691391i	−0.157227	−	0.987562i	$-0.550256\pi$
$11$	2.64636	−	2.29308i	0.797907	−	0.691391i	0.955135	+	0.296172i	$0.0957101\pi$
$12$	0.0713392	−	0.997452i	0.0205938	−	0.287940i
$13$	0.896834	−	0.489708i	0.248737	−	0.135821i	−0.350045	−	0.936733i	$-0.613834\pi$
$13$	0.896834	−	0.489708i	0.248737	−	0.135821i	0.598782	+	0.800912i	$0.295652\pi$
$14$	1.78389	−	3.90618i	0.476765	−	1.04397i
$15$	−1.15293	+	1.91592i	−0.297686	+	0.494688i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−0.279315	−	0.373122i	−0.0677439	−	0.0904953i	0.765390	−	0.643567i	$-0.222546\pi$
$17$	−0.279315	−	0.373122i	−0.0677439	−	0.0904953i	−0.833133	+	0.553072i	$0.813455\pi$
$18$	0.936950	+	0.349464i	0.220841	+	0.0823695i
$19$	0.218004	+	1.51625i	0.0500136	+	0.347852i	0.999428	+	0.0338256i	$0.0107691\pi$
$19$	0.218004	+	1.51625i	0.0500136	+	0.347852i	−0.949414	+	0.314027i	$0.898322\pi$
$20$	−2.19803	−	0.410693i	−0.491494	−	0.0918338i
$21$	3.24537	+	2.81213i	0.708198	+	0.613657i
$22$	−2.47603	+	2.47603i	−0.527891	+	0.527891i
$23$	4.68188	+	1.03924i	0.976239	+	0.216697i
$23$	4.68188	+	1.03924i	0.976239	+	0.216697i
$24$			1.00000i			0.204124i
$25$	3.96514	+	3.04592i	0.793029	+	0.609184i
$26$	−0.859613	+	0.552440i	−0.168584	+	0.108342i
$27$	−0.599278	+	0.800541i	−0.115331	+	0.154064i
$28$	−1.50068	+	4.02349i	−0.283603	+	0.760368i
$29$	7.70426	+	1.10771i	1.43064	+	0.205696i	0.813688	−	0.581302i	$-0.197456\pi$
$29$	7.70426	+	1.10771i	1.43064	+	0.205696i	0.616957	+	0.786997i	$0.288365\pi$
$30$	1.01331	−	1.99329i	0.185005	−	0.363923i
$31$	4.48357	+	2.88141i	0.805273	+	0.517517i	0.877332	−	0.479883i	$-0.159321\pi$
$31$	4.48357	+	2.88141i	0.805273	+	0.517517i	−0.0720599	+	0.997400i	$0.522957\pi$
$32$	−0.936950	+	0.349464i	−0.165631	+	0.0617771i
$33$	−1.67815	−	3.07331i	−0.292129	−	0.534995i
$34$	0.305222	+	0.352245i	0.0523451	+	0.0604095i
$35$	7.06835	−	6.49931i	1.19477	−	1.09858i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	0.203874	+	0.546607i	0.0335167	+	0.0898616i	0.952630	−	0.304131i	$-0.0983662\pi$
$37$	0.203874	+	0.546607i	0.0335167	+	0.0898616i	−0.919113	+	0.393993i	$0.871093\pi$
$38$	−0.325617	−	1.49684i	−0.0528221	−	0.242819i
$39$	−0.287881	−	0.980433i	−0.0460979	−	0.156995i
$40$	2.22173	+	0.252841i	0.351286	+	0.0399777i
$41$	−3.64571	−	7.98298i	−0.569364	−	1.24673i	−0.947136	−	0.320834i	$-0.896037\pi$
$41$	−3.64571	−	7.98298i	−0.569364	−	1.24673i	0.377772	−	0.925899i	$-0.376690\pi$
$42$	−3.43772	−	2.57344i	−0.530451	−	0.397091i
$43$	2.91987	+	0.635179i	0.445276	+	0.0968639i	0.429612	−	0.903013i	$-0.358650\pi$
$43$	2.91987	+	0.635179i	0.445276	+	0.0968639i	0.0156639	+	0.999877i	$0.495014\pi$
$44$	2.29308	−	2.64636i	0.345695	−	0.398954i
$45$	1.62706	+	1.53384i	0.242548	+	0.228652i
$46$	−4.74409	−	0.702595i	−0.699477	−	0.103592i
$47$	−0.989385	−	0.989385i	−0.144317	−	0.144317i	0.631257	−	0.775574i	$-0.282539\pi$
$47$	−0.989385	−	0.989385i	−0.144317	−	0.144317i	−0.775574	+	0.631257i	$0.782539\pi$
$48$	−0.0713392	−	0.997452i	−0.0102969	−	0.143970i
$49$	−6.18520	−	9.62437i	−0.883601	−	1.37491i
$50$	−4.17233	−	2.75529i	−0.590057	−	0.389657i
$51$	−0.423967	+	0.193619i	−0.0593673	+	0.0271121i
$52$	0.818013	−	0.612357i	0.113438	−	0.0849186i
$53$	9.95488	+	5.43578i	1.36741	+	0.746662i	0.984210	−	0.177004i	$-0.0566407\pi$
$53$	9.95488	+	5.43578i	1.36741	+	0.746662i	0.383198	+	0.923666i	$0.374823\pi$
$54$	0.540641	−	0.841254i	0.0735719	−	0.114480i
$55$	−7.25237	+	2.95134i	−0.977909	+	0.397959i
$56$	1.20983	−	4.12029i	0.161670	−	0.550597i
$57$	1.52794	+	0.109281i	0.202381	+	0.0144746i
$58$	−7.76365	−	0.555267i	−1.01942	−	0.0729102i
$59$	−0.205474	+	0.699779i	−0.0267504	+	0.0911035i	−0.971786	−	0.235863i	$-0.924208\pi$
$59$	−0.205474	+	0.699779i	−0.0267504	+	0.0911035i	0.945036	+	0.326967i	$0.106026\pi$
$60$	−0.868532	+	2.06050i	−0.112127	+	0.266009i
$61$	3.11627	−	4.84901i	0.398997	−	0.620852i	−0.582386	−	0.812912i	$-0.697881\pi$
$61$	3.11627	−	4.84901i	0.398997	−	0.620852i	0.981383	+	0.192061i	$0.0615171\pi$
$62$	−4.67770	−	2.55422i	−0.594069	−	0.324386i
$63$	3.43772	−	2.57344i	0.433112	−	0.324223i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−2.25104	+	0.391700i	−0.279208	+	0.0485843i
$66$	1.89313	+	2.94576i	0.233028	+	0.362598i
$67$	0.845557	+	11.8224i	0.103301	+	1.44434i	0.739678	+	0.672961i	$0.234978\pi$
$67$	0.845557	+	11.8224i	0.103301	+	1.44434i	−0.636377	+	0.771379i	$0.719568\pi$
$68$	−0.329573	−	0.329573i	−0.0399666	−	0.0399666i
$69$	2.01070	−	4.35397i	0.242060	−	0.524157i
$70$	−6.58668	+	6.98700i	−0.787259	+	0.835106i
$71$	9.63328	−	11.1174i	1.14326	−	1.31939i	0.202904	−	0.979199i	$-0.434962\pi$
$71$	9.63328	−	11.1174i	1.14326	−	1.31939i	0.940356	−	0.340193i	$-0.110492\pi$
$72$	0.977147	+	0.212565i	0.115158	+	0.0250511i
$73$	−2.52325	−	1.88888i	−0.295324	−	0.221076i	0.441333	−	0.897343i	$-0.354506\pi$
$73$	−2.52325	−	1.88888i	−0.295324	−	0.221076i	−0.736657	+	0.676267i	$0.763597\pi$
$74$	−0.242349	−	0.530670i	−0.0281725	−	0.0616891i
$75$	3.81917	−	3.22707i	0.440999	−	0.372630i
$76$	0.431571	+	1.46979i	0.0495046	+	0.168597i
$77$	3.19631	+	14.6932i	0.364254	+	1.67445i
$78$	0.357091	+	0.957398i	0.0404326	+	0.108404i
$79$	8.14319	+	2.39106i	0.916181	+	0.269015i	0.705640	−	0.708570i	$-0.250659\pi$
$79$	8.14319	+	2.39106i	0.916181	+	0.269015i	0.210540	+	0.977585i	$0.432478\pi$
$80$	−2.23410	−	0.0937008i	−0.249780	−	0.0104761i
$81$	0.654861	+	0.755750i	0.0727623	+	0.0839722i
$82$	4.20592	+	7.70256i	0.464466	+	0.850606i
$83$	−9.19453	+	3.42938i	−1.00923	+	0.376424i	−0.799067	−	0.601242i	$-0.794673\pi$
$83$	−9.19453	+	3.42938i	−1.00923	+	0.376424i	−0.210164	+	0.977666i	$0.567400\pi$
$84$	3.61255	+	2.32164i	0.394161	+	0.253312i
$85$	0.322973	+	0.990895i	0.0350314	+	0.107478i
$86$	−2.95775	−	0.425260i	−0.318942	−	0.0458569i
$87$	2.72005	−	7.29273i	0.291620	−	0.781863i
$88$	−2.09845	+	2.80320i	−0.223696	+	0.298822i
$89$	1.85091	−	1.18951i	0.196196	−	0.126087i	−0.438855	−	0.898558i	$-0.644616\pi$
$89$	1.85091	−	1.18951i	0.196196	−	0.126087i	0.635050	+	0.772471i	$0.280979\pi$
$90$	−1.73234	−	1.41386i	−0.182605	−	0.149034i
$91$			4.38796i			0.459983i
$92$	4.78212	+	0.362365i	0.498571	+	0.0377792i
$93$	3.76862	−	3.76862i	0.390787	−	0.390787i
$94$	1.05745	+	0.916282i	0.109067	+	0.0945073i
$95$	0.629118	−	3.36704i	0.0645462	−	0.345451i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	13.2709	+	4.94979i	1.34746	+	0.502575i	0.916586	−	0.399838i	$-0.130934\pi$
$97$	13.2709	+	4.94979i	1.34746	+	0.502575i	0.430871	+	0.902414i	$0.358206\pi$
$98$	6.85604	+	9.15860i	0.692565	+	0.925158i
$99$	−3.35979	+	0.986524i	−0.337672	+	0.0991494i
$100$	4.35826	+	2.45062i	0.435826	+	0.245062i
$101$	−8.23439	+	18.0308i	−0.819352	+	1.79413i	−0.258998	+	0.965878i	$0.583392\pi$
$101$	−8.23439	+	18.0308i	−0.819352	+	1.79413i	−0.560354	+	0.828253i	$0.689335\pi$
$102$	0.409075	−	0.223372i	0.0405044	−	0.0221171i
$103$	0.336759	−	4.70851i	0.0331819	−	0.463943i	−0.953512	−	0.301355i	$-0.902561\pi$
$103$	0.336759	−	4.70851i	0.0331819	−	0.463943i	0.986694	−	0.162588i	$-0.0519843\pi$
$104$	−0.772243	+	0.669153i	−0.0757247	+	0.0656158i
$105$	−4.84829	−	8.28834i	−0.473145	−	0.808859i
$106$	−10.3173	−	4.71176i	−1.00211	−	0.457646i
$107$	8.57301	−	1.86494i	0.828784	−	0.180291i	0.221888	−	0.975072i	$-0.428778\pi$
$107$	8.57301	−	1.86494i	0.828784	−	0.180291i	0.606896	+	0.794781i	$0.292414\pi$
$108$	−0.479249	+	0.877679i	−0.0461158	+	0.0844547i
$109$	−0.941118	+	6.54562i	−0.0901427	+	0.626957i	0.893799	+	0.448467i	$0.148030\pi$
$109$	−0.941118	+	6.54562i	−0.0901427	+	0.626957i	−0.983942	+	0.178489i	$0.942879\pi$
$110$	7.02334	−	3.46120i	0.669649	−	0.330013i
$111$	0.577452	−	0.0830250i	0.0548093	−	0.00788039i
$112$	−0.912807	+	4.19610i	−0.0862521	+	0.396495i
$113$	−17.2541	+	1.23404i	−1.62313	+	0.116088i	−0.853039	−	0.521847i	$-0.825243\pi$
$113$	−17.2541	+	1.23404i	−1.62313	+	0.116088i	−0.770090	+	0.637936i	$0.779789\pi$
$114$	−1.53185			−0.143470
$115$	−9.16495	−	5.56809i	−0.854636	−	0.519227i
$116$	7.78348			0.722678
$117$	−1.01922	+	0.0728961i	−0.0942270	+	0.00673925i
$118$	0.155029	−	0.712655i	0.0142715	−	0.0656052i
$119$	1.98112	−	0.284842i	0.181609	−	0.0261114i
$120$	0.719325	−	2.11721i	0.0656651	−	0.193274i
$121$	0.179522	−	1.24860i	0.0163202	−	0.113510i
$122$	−2.76240	+	5.05896i	−0.250096	+	0.458017i
$123$	−8.57550	+	1.86549i	−0.773226	+	0.168205i
$124$	4.84800	+	2.21401i	0.435363	+	0.198824i
$125$	−6.20403	−	9.30108i	−0.554905	−	0.831914i
$126$	−3.24537	+	2.81213i	−0.289121	+	0.250524i
$127$	0.867350	−	12.1271i	0.0769649	−	1.07611i	−0.801403	−	0.598125i	$-0.795913\pi$
$127$	0.867350	−	12.1271i	0.0769649	−	1.07611i	0.878368	−	0.477985i	$-0.158633\pi$
$128$	−0.877679	+	0.479249i	−0.0775766	+	0.0423600i
$129$	1.24133	−	2.71813i	0.109293	−	0.239318i
$130$	2.21736	−	0.551289i	0.194476	−	0.0483513i
$131$	−1.92181	+	0.564295i	−0.167910	+	0.0493027i	−0.364607	−	0.931162i	$-0.618797\pi$
$131$	−1.92181	+	0.564295i	−0.167910	+	0.0493027i	0.196697	+	0.980464i	$0.436978\pi$
$132$	−2.09845	−	2.80320i	−0.182647	−	0.243987i
$133$	−6.16336	−	2.29881i	−0.534431	−	0.199333i
$134$	−1.68681	−	11.7320i	−0.145718	−	1.01349i
$135$	1.84465	−	1.26384i	0.158762	−	0.108774i
$136$	0.352245	+	0.305222i	0.0302048	+	0.0261726i
$137$	−14.3078	+	14.3078i	−1.22240	+	1.22240i	−0.255622	+	0.966777i	$0.582280\pi$
$137$	−14.3078	+	14.3078i	−1.22240	+	1.22240i	−0.966777	+	0.255622i	$0.917720\pi$
$138$	−1.69497	+	4.48632i	−0.144285	+	0.381901i
$139$			3.17705i			0.269474i	0.990881	+	0.134737i	$0.0430189\pi$
$139$			3.17705i			0.269474i	−0.990881	+	0.134737i	$0.956981\pi$
$140$	6.07146	−	7.43908i	0.513132	−	0.628717i
$141$	−1.17708	+	0.756466i	−0.0991283	+	0.0637059i
$142$	−8.81563	+	11.7763i	−0.739791	+	0.988245i
$143$	1.25040	−	3.35246i	0.104564	−	0.280347i
$144$	−0.989821	−	0.142315i	−0.0824851	−	0.0118596i
$145$	−15.5147	−	7.88711i	−1.28843	−	0.654989i
$146$	2.65157	+	1.70406i	0.219445	+	0.141029i
$147$	−10.7192	+	3.99805i	−0.884103	+	0.329753i
$148$	0.279589	+	0.512029i	0.0229821	+	0.0420885i
$149$	−8.12511	−	9.37688i	−0.665635	−	0.768184i	0.318052	−	0.948073i	$-0.396971\pi$
$149$	−8.12511	−	9.37688i	−0.665635	−	0.768184i	−0.983687	+	0.179890i	$0.942426\pi$
$150$	−3.57922	+	3.49130i	−0.292242	+	0.285064i
$151$	12.6768	+	3.72225i	1.03163	+	0.302913i	0.753372	−	0.657595i	$-0.228426\pi$
$151$	12.6768	+	3.72225i	1.03163	+	0.302913i	0.278254	+	0.960508i	$0.410244\pi$
$152$	−0.535325	−	1.43526i	−0.0434206	−	0.116415i
$153$	0.0990739	+	0.455435i	0.00800965	+	0.0368198i
$154$	−4.23637	−	14.4278i	−0.341377	−	1.16262i
$155$	−7.41997	−	9.32570i	−0.595987	−	0.749058i
$156$	−0.424481	−	0.929484i	−0.0339857	−	0.0744183i
$157$	5.38395	+	4.03037i	0.429686	+	0.321659i	0.792136	−	0.610344i	$-0.208969\pi$
$157$	5.38395	+	4.03037i	0.429686	+	0.321659i	−0.362450	+	0.932003i	$0.618060\pi$
$158$	−8.29302	−	1.80404i	−0.659757	−	0.143521i
$159$	7.42762	−	8.57193i	0.589048	−	0.679798i
$160$	2.23510	−	0.0659171i	0.176700	−	0.00521120i
$161$	−13.5522	+	15.5071i	−1.06807	+	1.22213i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−0.0922857	−	1.29032i	−0.00722838	−	0.101066i	0.992557	−	0.121781i	$-0.0388604\pi$
$163$	−0.0922857	−	1.29032i	−0.00722838	−	0.101066i	−0.999785	+	0.0207146i	$0.993406\pi$
$164$	−4.74469	−	7.38289i	−0.370498	−	0.576507i
$165$	1.34229	+	7.71398i	0.104497	+	0.600532i
$166$	8.92646	−	4.07658i	0.692827	−	0.316404i
$167$	1.44788	−	1.08387i	0.112040	−	0.0838720i	−0.541789	−	0.840515i	$-0.682253\pi$
$167$	1.44788	−	1.08387i	0.112040	−	0.0838720i	0.653829	+	0.756643i	$0.273162\pi$
$168$	−3.76897	−	2.05801i	−0.290782	−	0.158779i
$169$	−6.46383	+	10.0579i	−0.497218	+	0.773686i
$170$	−0.392840	−	0.965330i	−0.0301294	−	0.0740374i
$171$	0.431571	−	1.46979i	0.0330030	−	0.112398i
$172$	2.98055	+	0.213173i	0.227265	+	0.0162543i
$173$	−9.72762	−	0.695733i	−0.739577	−	0.0528956i	−0.303533	−	0.952821i	$-0.598166\pi$
$173$	−9.72762	−	0.695733i	−0.739577	−	0.0528956i	−0.436044	+	0.899925i	$0.643621\pi$
$174$	−2.19286	+	7.46820i	−0.166240	+	0.566163i
$175$	−19.6403	+	8.67594i	−1.48467	+	0.655840i
$176$	1.89313	−	2.94576i	0.142700	−	0.222045i
$177$	0.640111	+	0.349527i	0.0481137	+	0.0262721i
$178$	−1.76133	+	1.31852i	−0.132018	+	0.0988271i
$179$	17.9069	−	8.17780i	1.33842	−	0.611238i	0.387846	−	0.921724i	$-0.373219\pi$
$179$	17.9069	−	8.17780i	1.33842	−	0.611238i	0.950578	+	0.310486i	$0.100492\pi$
$180$	1.82879	+	1.28667i	0.136310	+	0.0959030i
$181$	−1.30004	−	2.02290i	−0.0966311	−	0.150361i	0.789572	−	0.613658i	$-0.210303\pi$
$181$	−1.30004	−	2.02290i	−0.0966311	−	0.150361i	−0.886203	+	0.463297i	$0.846666\pi$
$182$	−0.313034	−	4.37678i	−0.0232036	−	0.324429i
$183$	−4.07578	−	4.07578i	−0.301290	−	0.301290i
$184$	−4.79579	−	0.0202895i	−0.353550	−	0.00149576i
$185$	−0.0384553	−	1.30393i	−0.00282729	−	0.0958670i
$186$	−3.49016	+	4.02786i	−0.255911	+	0.295337i
$187$	−1.59477	−	0.346921i	−0.116621	−	0.0253693i
$188$	−1.12012	−	0.838511i	−0.0816931	−	0.0611547i
$189$	−1.78389	−	3.90618i	−0.129759	−	0.284133i
$190$	−0.387314	+	3.40334i	−0.0280987	+	0.246904i
$191$	−0.0241154	−	0.0821296i	−0.00174493	−	0.00594269i	0.958616	−	0.284703i	$-0.0918948\pi$
$191$	−0.0241154	−	0.0821296i	−0.00174493	−	0.00594269i	−0.960361	+	0.278760i	$0.910077\pi$
$192$	−0.212565	−	0.977147i	−0.0153406	−	0.0705195i
$193$	−7.68643	−	20.6081i	−0.553282	−	1.48341i	−0.849137	−	0.528173i	$-0.822877\pi$
$193$	−7.68643	−	20.6081i	−0.553282	−	1.48341i	0.295855	−	0.955233i	$-0.404395\pi$
$194$	−13.5902	−	3.99045i	−0.975720	−	0.286497i
$195$	−0.0957458	+	2.28286i	−0.00685650	+	0.163479i
$196$	−7.49194	−	8.64616i	−0.535138	−	0.617583i
$197$	11.7820	+	21.5771i	0.839432	+	1.53731i	0.843383	+	0.537313i	$0.180561\pi$
$197$	11.7820	+	21.5771i	0.839432	+	1.53731i	−0.00395021	+	0.999992i	$0.501257\pi$
$198$	3.28086	−	1.22370i	0.233160	−	0.0869643i
$199$	13.6796	+	8.79136i	0.969723	+	0.623203i	0.926672	−	0.375870i	$-0.122656\pi$
$199$	13.6796	+	8.79136i	0.969723	+	0.623203i	0.0430505	+	0.999073i	$0.486292\pi$
$200$	−4.52198	−	2.13346i	−0.319753	−	0.150859i
$201$	11.7320	+	1.68681i	0.827511	+	0.118978i
$202$	6.92710	−	18.5723i	0.487389	−	1.30674i
$203$	−20.0303	+	26.7574i	−1.40585	+	1.87800i
$204$	−0.392097	+	0.251986i	−0.0274523	+	0.0176425i
$205$	1.97636	+	19.5241i	0.138035	+	1.36362i
$206$			4.72054i			0.328895i
$207$	−3.82707	−	2.89025i	−0.266000	−	0.200886i
$208$	0.722539	−	0.722539i	0.0500991	−	0.0500991i
$209$	4.05381	+	3.51265i	0.280408	+	0.242975i
$210$	5.42722	+	7.92135i	0.374514	+	0.546625i
$211$	−0.0604568	−	0.420486i	−0.00416201	−	0.0289474i	0.987635	−	0.156773i	$-0.0501092\pi$
$211$	−0.0604568	−	0.420486i	−0.00416201	−	0.0289474i	−0.991797	+	0.127826i	$0.959200\pi$
$212$	10.6271	+	3.96372i	0.729876	+	0.272230i
$213$	−8.81563	−	11.7763i	−0.604037	−	0.806899i
$214$	−8.41813	+	2.47178i	−0.575451	+	0.168968i
$215$	−5.72508	−	3.44514i	−0.390447	−	0.234957i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−20.0872	+	10.9684i	−1.36361	+	0.744585i
$218$	0.471761	−	6.59608i	0.0319517	−	0.446743i
$219$	−2.38207	+	2.06407i	−0.160965	+	0.139477i
$220$	−6.75853	+	3.95342i	−0.455660	+	0.266540i
$221$	−0.433220	−	0.197845i	−0.0291416	−	0.0133085i
$222$	−0.570058	+	0.124008i	−0.0382598	+	0.00832290i
$223$	4.05731	−	7.43040i	0.271697	−	0.497577i	−0.705831	−	0.708380i	$-0.749426\pi$
$223$	4.05731	−	7.43040i	0.271697	−	0.497577i	0.977528	+	0.210804i	$0.0676080\pi$
$224$	0.611134	−	4.25053i	0.0408331	−	0.284001i
$225$	−2.34150	−	4.41785i	−0.156100	−	0.294523i
$226$	17.1221	−	2.46179i	1.13895	−	0.163756i
$227$	1.05135	−	4.83296i	0.0697803	−	0.320775i	−0.929004	−	0.370070i	$-0.879334\pi$
$227$	1.05135	−	4.83296i	0.0697803	−	0.320775i	0.998784	+	0.0492948i	$0.0156974\pi$
$228$	1.52794	−	0.109281i	0.101190	−	0.00723728i
$229$	17.0077			1.12390			0.561949	−	0.827172i	$-0.310052\pi$
$229$	17.0077			1.12390			0.561949	+	0.827172i	$0.310052\pi$
$230$	9.53883	+	4.90008i	0.628972	+	0.323102i
$231$	15.0369			0.989353
$232$	−7.76365	+	0.555267i	−0.509709	+	0.0364551i
$233$	5.15653	−	23.7042i	0.337815	−	1.55291i	−0.424331	−	0.905507i	$-0.639491\pi$
$233$	5.15653	−	23.7042i	0.337815	−	1.55291i	0.762146	−	0.647405i	$-0.224146\pi$
$234$	1.01142	−	0.145421i	0.0661188	−	0.00950645i
$235$	1.38305	+	2.80642i	0.0902199	+	0.183071i
$236$	−0.103793	+	0.721899i	−0.00675637	+	0.0469916i
$237$	4.06737	−	7.44884i	0.264204	−	0.483854i
$238$	−1.95575	+	0.425447i	−0.126772	+	0.0275776i
$239$	−21.6988	−	9.90953i	−1.40358	−	0.640994i	−0.437497	−	0.899220i	$-0.644135\pi$
$239$	−21.6988	−	9.90953i	−1.40358	−	0.640994i	−0.966085	+	0.258226i	$0.916862\pi$
$240$	−0.566452	+	2.16313i	−0.0365643	+	0.139629i
$241$	−20.0686	+	17.3895i	−1.29273	+	1.12016i	−0.307022	+	0.951702i	$0.599333\pi$
$241$	−20.0686	+	17.3895i	−1.29273	+	1.12016i	−0.985709	+	0.168456i	$0.946122\pi$
$242$	−0.0899904	+	1.25823i	−0.00578480	+	0.0808821i
$243$	0.877679	−	0.479249i	0.0563031	−	0.0307438i
$244$	2.39446	−	5.24314i	0.153290	−	0.335658i
$245$	6.17232	+	24.8260i	0.394335	+	1.58607i
$246$	8.42056	−	2.47250i	0.536876	−	0.157641i
$247$	0.938036	+	1.25307i	0.0596858	+	0.0797309i
$248$	−4.99359	−	1.86251i	−0.317093	−	0.118270i
$249$	1.39657	+	9.71338i	0.0885042	+	0.615560i
$250$	6.85175	+	8.83479i	0.433343	+	0.558761i
$251$	−12.3253	−	10.6799i	−0.777964	−	0.674110i	0.172477	−	0.985014i	$-0.444823\pi$
$251$	−12.3253	−	10.6799i	−0.777964	−	0.674110i	−0.950441	+	0.310904i	$0.899368\pi$
$252$	3.03649	−	3.03649i	0.191281	−	0.191281i
$253$	14.7730	−	7.98572i	0.928770	−	0.502058i
$254$			12.1581i			0.762868i
$255$	1.03690	−	0.104962i	0.0649334	−	0.00657299i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−2.87727	+	3.84358i	−0.179479	+	0.239756i	−0.881254	−	0.472643i	$-0.843300\pi$
$257$	−2.87727	+	3.84358i	−0.179479	+	0.239756i	0.701775	+	0.712398i	$0.252391\pi$
$258$	−1.04426	+	2.79976i	−0.0650125	+	0.174305i
$259$	−2.47972	−	0.356529i	−0.154082	−	0.0221537i
$260$	−2.17239	+	0.708070i	−0.134726	+	0.0439126i
$261$	−6.54788	−	4.20807i	−0.405304	−	0.260473i
$262$	1.87666	−	0.699958i	0.115941	−	0.0432436i
$263$	−0.425214	−	0.778721i	−0.0262198	−	0.0480180i	0.864241	−	0.503079i	$-0.167799\pi$
$263$	−0.425214	−	0.778721i	−0.0262198	−	0.0480180i	−0.890460	+	0.455061i	$0.849618\pi$
$264$	2.29308	+	2.64636i	0.141129	+	0.162872i
$265$	−17.1665	−	18.6695i	−1.05453	−	1.14686i
$266$	6.31165	+	1.85327i	0.386992	+	0.113631i
$267$	−0.768884	−	2.06146i	−0.0470549	−	0.126159i
$268$	2.51946	+	11.5818i	0.153900	+	0.707469i
$269$	1.30709	+	4.45155i	0.0796948	+	0.271416i	0.989695	−	0.143193i	$-0.0457368\pi$
$269$	1.30709	+	4.45155i	0.0796948	+	0.271416i	−0.910000	+	0.414608i	$0.863919\pi$
$270$	−1.74978	+	1.39221i	−0.106488	+	0.0847274i
$271$	0.660947	+	1.44727i	0.0401496	+	0.0879155i	0.928644	−	0.370972i	$-0.120975\pi$
$271$	0.660947	+	1.44727i	0.0401496	+	0.0879155i	−0.888494	+	0.458887i	$0.848248\pi$
$272$	−0.373122	−	0.279315i	−0.0226238	−	0.0169360i
$273$	4.28768	+	0.932728i	0.259502	+	0.0564513i
$274$	13.2506	−	15.2921i	0.800501	−	0.923827i
$275$	17.4777	−	1.03180i	1.05395	−	0.0622198i
$276$	1.37060	−	4.59581i	0.0825003	−	0.276635i
$277$	−12.3269	−	12.3269i	−0.740654	−	0.740654i	0.232050	−	0.972704i	$-0.425457\pi$
$277$	−12.3269	−	12.3269i	−0.740654	−	0.740654i	−0.972704	+	0.232050i	$0.925457\pi$
$278$	−0.226648	−	3.16895i	−0.0135934	−	0.190061i
$279$	−2.88141	−	4.48357i	−0.172506	−	0.268424i
$280$	−5.52529	+	7.85326i	−0.330199	+	0.469322i
$281$	0.989054	−	0.451686i	0.0590020	−	0.0269453i	−0.385695	−	0.922626i	$-0.626038\pi$
$281$	0.989054	−	0.451686i	0.0590020	−	0.0269453i	0.444697	+	0.895681i	$0.353311\pi$
$282$	1.12012	−	0.838511i	0.0667021	−	0.0499326i
$283$	14.8622	+	8.11537i	0.883466	+	0.482409i	0.855858	−	0.517210i	$-0.173029\pi$
$283$	14.8622	+	8.11537i	0.883466	+	0.482409i	0.0276072	+	0.999619i	$0.491211\pi$
$284$	7.95305	−	12.3752i	0.471927	−	0.734333i
$285$	−3.15636	−	1.33046i	−0.186967	−	0.0788095i
$286$	−1.00805	+	3.43312i	−0.0596075	+	0.203005i
$287$	37.5905	+	2.68852i	2.21890	+	0.158699i
$288$	0.997452	+	0.0713392i	0.0587754	+	0.00420370i
$289$	4.72825	−	16.1029i	0.278132	−	0.947232i
$290$	16.0378	+	6.76021i	0.941775	+	0.396973i
$291$	7.65761	−	11.9155i	0.448897	−	0.698497i
$292$	−2.76638	−	1.51056i	−0.161890	−	0.0883986i
$293$	−9.32593	+	6.98130i	−0.544827	+	0.407852i	−0.835927	−	0.548840i	$-0.815069\pi$
$293$	−9.32593	+	6.98130i	−0.544827	+	0.407852i	0.291101	+	0.956692i	$0.405979\pi$
$294$	10.4066	−	4.75256i	0.606928	−	0.277175i
$295$	0.938400	−	1.33378i	0.0546357	−	0.0776555i
$296$	−0.315404	−	0.490779i	−0.0183325	−	0.0285259i
$297$	0.249804	+	3.49271i	0.0144951	+	0.202668i
$298$	8.77335	+	8.77335i	0.508226	+	0.508226i
$299$	4.70779	−	1.36072i	0.272259	−	0.0786928i
$300$	3.32103	−	3.73775i	0.191740	−	0.215799i
$301$	−8.40310	+	9.69769i	−0.484346	+	0.558966i
$302$	−12.9101	−	2.80841i	−0.742891	−	0.161606i
$303$	15.8684	+	11.8789i	0.911615	+	0.682426i
$304$	0.636352	+	1.39342i	0.0364973	+	0.0799179i
$305$	−10.0858	+	8.02475i	−0.577511	+	0.459496i
$306$	−0.131312	−	0.447207i	−0.00750660	−	0.0255651i
$307$	−6.95721	−	31.9818i	−0.397069	−	1.82530i	−0.547660	−	0.836701i	$-0.684481\pi$
$307$	−6.95721	−	31.9818i	−0.397069	−	1.82530i	0.150591	−	0.988596i	$-0.451882\pi$
$308$	5.25484	+	14.0888i	0.299423	+	0.802783i
$309$	−4.52932	−	1.32993i	−0.257664	−	0.0756570i
$310$	8.06636	+	8.77260i	0.458138	+	0.498250i
$311$	22.1693	+	25.5847i	1.25710	+	1.45077i	0.840615	+	0.541633i	$0.182194\pi$
$311$	22.1693	+	25.5847i	1.25710	+	1.45077i	0.416488	+	0.909141i	$0.363261\pi$
$312$	0.489708	+	0.896834i	0.0277243	+	0.0507732i
$313$	11.2309	−	4.18891i	0.634809	−	0.236771i	−0.0113966	−	0.999935i	$-0.503628\pi$
$313$	11.2309	−	4.18891i	0.634809	−	0.236771i	0.646205	+	0.763164i	$0.276355\pi$
$314$	−5.65775	−	3.63602i	−0.319286	−	0.205192i
$315$	−9.12951	+	2.97568i	−0.514389	+	0.167660i
$316$	8.40059	+	1.20782i	0.472570	+	0.0679453i
$317$	4.02163	−	10.7824i	0.225877	−	0.605600i	−0.773733	−	0.633512i	$-0.781613\pi$
$317$	4.02163	−	10.7824i	0.225877	−	0.605600i	0.999610	+	0.0279114i	$0.00888562\pi$
$318$	−6.79718	+	9.07997i	−0.381167	+	0.509179i
$319$	22.9283	−	14.7351i	1.28374	−	0.825008i
$320$	−2.22470	+	0.225199i	−0.124364	+	0.0125890i
$321$		−	8.77351i		−	0.489690i
$322$	12.4114	−	16.4343i	0.691662	−	0.915851i
$323$	0.504855	−	0.504855i	0.0280909	−	0.0280909i
$324$	0.755750	+	0.654861i	0.0419861	+	0.0363812i
$325$	5.04769	+	0.789923i	0.279995	+	0.0438170i
$326$	0.184101	+	1.28045i	0.0101964	+	0.0709177i
$327$	6.19598	+	2.31098i	0.342639	+	0.127798i
$328$	5.25929	+	7.02560i	0.290396	+	0.387924i
$329$	5.76512	−	1.69279i	0.317842	−	0.0933267i
$330$	−1.88918	−	7.59857i	−0.103996	−	0.418287i
$331$	2.85749	−	6.25704i	0.157062	−	0.343918i	−0.814699	−	0.579884i	$-0.803098\pi$
$331$	2.85749	−	6.25704i	0.157062	−	0.343918i	0.971761	+	0.235966i	$0.0758253\pi$
$332$	−8.61289	+	4.70300i	−0.472694	+	0.258110i
$333$	0.0416186	−	0.581903i	0.00228068	−	0.0318881i
$334$	−1.36686	+	1.18439i	−0.0747915	+	0.0648072i
$335$	6.71395	−	25.6388i	0.366822	−	1.40080i
$336$	3.90618	+	1.78389i	0.213100	+	0.0973193i
$337$	−20.8025	+	4.52532i	−1.13319	+	0.246510i	−0.739776	−	0.672853i	$-0.765069\pi$
$337$	−20.8025	+	4.52532i	−1.13319	+	0.246510i	−0.393411	+	0.919363i	$0.628705\pi$
$338$	5.72984	−	10.4934i	0.311662	−	0.570767i
$339$	−2.46179	+	17.1221i	−0.133706	+	0.929945i
$340$	0.460705	+	0.934845i	0.0249852	+	0.0506991i
$341$	18.4724	−	2.65594i	1.00034	−	0.143827i
$342$	−0.325617	+	1.49684i	−0.0176074	+	0.0809397i
$343$	19.0200	−	1.36034i	1.02698	−	0.0734514i
$344$	−2.98816			−0.161111
$345$	−7.38899	+	7.77192i	−0.397810	+	0.418426i
$346$	9.75247			0.524296
$347$	27.2204	−	1.94684i	1.46127	−	0.104512i	0.682067	−	0.731290i	$-0.261081\pi$
$347$	27.2204	−	1.94684i	1.46127	−	0.104512i	0.779198	+	0.626778i	$0.215627\pi$
$348$	1.65450	−	7.60561i	0.0886904	−	0.407703i
$349$	0.0222219	−	0.00319503i	0.00118951	−	0.000171026i	−0.141720	−	0.989907i	$-0.545263\pi$
$349$	0.0222219	−	0.00319503i	0.00118951	−	0.000171026i	0.142910	+	0.989736i	$0.454354\pi$
$350$	18.9713	−	10.0550i	1.01406	−	0.537460i
$351$	−0.145421	+	1.01142i	−0.00776199	+	0.0539858i
$352$	−1.67815	+	3.07331i	−0.0894460	+	0.163808i
$353$	8.13441	−	1.76953i	0.432951	−	0.0941828i	0.00919220	−	0.999958i	$-0.497074\pi$
$353$	8.13441	−	1.76953i	0.432951	−	0.0941828i	0.423759	+	0.905775i	$0.360710\pi$
$354$	−0.663415	−	0.302971i	−0.0352601	−	0.0161027i
$355$	−28.3927	+	16.6084i	−1.50693	+	0.881481i
$356$	1.66278	−	1.44081i	0.0881274	−	0.0763628i
$357$	0.142785	−	1.99639i	0.00755696	−	0.105660i
$358$	−17.2779	+	9.43443i	−0.913164	+	0.498625i
$359$	−5.55506	+	12.1639i	−0.293185	+	0.641985i	−0.997706	−	0.0676982i	$-0.978435\pi$
$359$	−5.55506	+	12.1639i	−0.293185	+	0.641985i	0.704521	+	0.709683i	$0.251162\pi$
$360$	−1.91592	−	1.15293i	−0.100978	−	0.0607648i
$361$	15.9789	−	4.69182i	0.840993	−	0.246938i
$362$	1.44104	+	1.92500i	0.0757393	+	0.101176i
$363$	−1.18191	−	0.440830i	−0.0620342	−	0.0231376i
$364$	0.624472	+	4.34330i	0.0327312	+	0.227651i
$365$	3.98352	+	5.81418i	0.208507	+	0.304328i
$366$	4.35616	+	3.77463i	0.227700	+	0.197303i
$367$	11.7369	−	11.7369i	0.612661	−	0.612661i	−0.330978	−	0.943639i	$-0.607378\pi$
$367$	11.7369	−	11.7369i	0.612661	−	0.612661i	0.943639	+	0.330978i	$0.107378\pi$
$368$	4.78502	−	0.321890i	0.249436	−	0.0167797i
$369$			8.77606i			0.456863i
$370$	0.131379	+	1.29787i	0.00683006	+	0.0674729i
$371$	−40.9745	+	26.3327i	−2.12729	+	1.36713i
$372$	3.19393	−	4.26659i	0.165597	−	0.221212i
$373$	−9.78748	+	26.2412i	−0.506776	+	1.35872i	0.391860	+	0.920025i	$0.371832\pi$
$373$	−9.78748	+	26.2412i	−0.506776	+	1.35872i	−0.898636	+	0.438695i	$0.855441\pi$
$374$	1.61545	+	0.232267i	0.0835331	+	0.0120102i
$375$	−10.4073	+	4.08516i	−0.537430	+	0.210957i
$376$	1.17708	+	0.756466i	0.0607035	+	0.0390117i
$377$	7.45189	−	2.77941i	0.383792	−	0.143147i
$378$	2.05801	+	3.76897i	0.105853	+	0.193855i
$379$	12.4163	+	14.3291i	0.637781	+	0.736038i	0.978981	−	0.203952i	$-0.0653788\pi$
$379$	12.4163	+	14.3291i	0.637781	+	0.736038i	−0.341200	+	0.939991i	$0.610833\pi$
$380$	0.143535	−	3.42230i	0.00736320	−	0.175560i
$381$	−11.6656	−	3.42534i	−0.597648	−	0.175485i
$382$	0.0299130	+	0.0802000i	0.00153048	+	0.00410339i
$383$	4.35968	+	20.0411i	0.222769	+	1.02405i	0.943637	+	0.330982i	$0.107380\pi$
$383$	4.35968	+	20.0411i	0.222769	+	1.02405i	−0.720868	+	0.693073i	$0.756256\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	3.80194	−	33.4078i	0.193765	−	1.70262i
$386$	9.13702	+	20.0073i	0.465062	+	1.01834i
$387$	−2.39215	−	1.79074i	−0.121600	−	0.0910283i
$388$	13.8403	+	3.01076i	0.702633	+	0.152848i
$389$	−9.85952	+	11.3785i	−0.499897	+	0.576912i	−0.948483	−	0.316827i	$-0.897382\pi$
$389$	−9.85952	+	11.3785i	−0.499897	+	0.576912i	0.448586	+	0.893740i	$0.351928\pi$
$390$	−0.0673557	−	2.28388i	−0.00341069	−	0.115649i
$391$	−0.919956	−	2.03719i	−0.0465242	−	0.103025i
$392$	8.08966	+	8.08966i	0.408589	+	0.408589i
$393$	0.142889	+	1.99784i	0.00720778	+	0.100778i
$394$	−13.2913	−	20.6816i	−0.669604	−	1.04192i
$395$	−15.5209	−	10.9200i	−0.780941	−	0.549443i
$396$	−3.18520	+	1.45463i	−0.160062	+	0.0730980i
$397$	−12.2385	+	9.16160i	−0.614231	+	0.459808i	−0.860539	−	0.509384i	$-0.829873\pi$
$397$	−12.2385	+	9.16160i	−0.614231	+	0.459808i	0.246308	+	0.969192i	$0.420782\pi$
$398$	−14.2719	−	7.79307i	−0.715388	−	0.390631i
$399$	−3.55640	+	5.53386i	−0.178042	+	0.277040i
$400$	4.66266	+	1.80543i	0.233133	+	0.0902716i
$401$	−6.20905	+	21.1461i	−0.310065	+	1.05599i	0.646123	+	0.763233i	$0.276389\pi$
$401$	−6.20905	+	21.1461i	−0.310065	+	1.05599i	−0.956188	+	0.292752i	$0.905429\pi$
$402$	−11.8224	−	0.845557i	−0.589649	−	0.0421725i
$403$	5.43207	+	0.388509i	0.270591	+	0.0193530i
$404$	−5.58452	+	19.0191i	−0.277840	+	0.946238i
$405$	−0.842847	−	2.07114i	−0.0418814	−	0.102916i
$406$	18.0705	−	28.1182i	0.896822	−	1.39548i
$407$	1.79294	+	0.979018i	0.0888727	+	0.0485281i
$408$	0.373122	−	0.279315i	0.0184723	−	0.0138282i
$409$	22.3803	−	10.2208i	1.10664	−	0.505384i	0.223596	−	0.974682i	$-0.428220\pi$
$409$	22.3803	−	10.2208i	1.10664	−	0.505384i	0.883040	+	0.469298i	$0.155493\pi$
$410$	−3.36416	−	19.3333i	−0.166144	−	0.954806i
$411$	10.9395	+	17.0222i	0.539605	+	0.839642i
$412$	−0.336759	−	4.70851i	−0.0165909	−	0.231972i
$413$	−2.21458	−	2.21458i	−0.108972	−	0.108972i
$414$	4.02350	+	2.60987i	0.197744	+	0.128268i
$415$	21.9336	−	0.646861i	1.07668	−	0.0317532i
$416$	−0.669153	+	0.772243i	−0.0328079	+	0.0378623i
$417$	3.10444	+	0.675330i	0.152025	+	0.0330711i
$418$	−4.29407	−	3.21450i	−0.210030	−	0.157226i
$419$	3.51016	+	7.68619i	0.171483	+	0.375495i	0.975787	−	0.218723i	$-0.0701891\pi$
$419$	3.51016	+	7.68619i	0.171483	+	0.375495i	−0.804304	+	0.594218i	$0.797462\pi$
$420$	−5.97850	−	7.51399i	−0.291721	−	0.366645i
$421$	−10.5814	−	36.0371i	−0.515708	−	1.75634i	−0.644435	−	0.764659i	$-0.722908\pi$
$421$	−10.5814	−	36.0371i	−0.515708	−	1.75634i	0.128728	−	0.991680i	$-0.458911\pi$
$422$	0.0902998	+	0.415102i	0.00439573	+	0.0202068i
$423$	0.488971	+	1.31098i	0.0237746	+	0.0637421i
$424$	−10.8828	−	3.19549i	−0.528518	−	0.155187i
$425$	0.0289742	−	2.33025i	0.00140546	−	0.113034i
$426$	9.63328	+	11.1174i	0.466734	+	0.538639i
$427$	11.8624	+	21.7244i	0.574063	+	1.05132i
$428$	8.22034	−	3.06603i	0.397345	−	0.148202i
$429$	−3.01005	−	1.93444i	−0.145327	−	0.0933958i
$430$	5.95626	+	3.02794i	0.287237	+	0.146020i
$431$	−30.0560	−	4.32140i	−1.44775	−	0.208155i	−0.626809	−	0.779173i	$-0.715640\pi$
$431$	−30.0560	−	4.32140i	−1.44775	−	0.208155i	−0.820938	+	0.571018i	$0.806549\pi$
$432$	−0.349464	+	0.936950i	−0.0168136	+	0.0450790i
$433$	5.95973	−	7.96127i	0.286407	−	0.382594i	−0.634146	−	0.773213i	$-0.718648\pi$
$433$	5.95973	−	7.96127i	0.286407	−	0.382594i	0.920552	+	0.390619i	$0.127739\pi$
$434$	19.2535	−	12.3735i	0.924199	−	0.593946i
$435$	−11.0048	+	13.4836i	−0.527638	+	0.646491i
$436$			6.61293i			0.316702i
$437$	−0.555088	+	7.32547i	−0.0265534	+	0.350425i
$438$	2.22875	−	2.22875i	0.106494	−	0.106494i
$439$	2.35093	+	2.03709i	0.112204	+	0.0972250i	0.709156	−	0.705052i	$-0.249076\pi$
$439$	2.35093	+	2.03709i	0.112204	+	0.0972250i	−0.596952	+	0.802277i	$0.703622\pi$
$440$	6.45927	−	4.42550i	0.307934	−	0.210977i
$441$	1.62815	+	11.3241i	0.0775311	+	0.539241i
$442$	0.446231	+	0.166435i	0.0212250	+	0.00791653i
$443$	13.0405	+	17.4201i	0.619575	+	0.827656i	0.995071	−	0.0991687i	$-0.0316184\pi$
$443$	13.0405	+	17.4201i	0.619575	+	0.827656i	−0.375495	+	0.926824i	$0.622527\pi$
$444$	0.559758	−	0.164360i	0.0265650	−	0.00780018i
$445$	−4.77440	+	1.18703i	−0.226328	+	0.0562705i
$446$	−3.51689	+	7.70092i	−0.166530	+	0.364649i
$447$	−10.8897	+	5.94623i	−0.515065	+	0.281247i
$448$	−0.306348	+	4.28330i	−0.0144736	+	0.202367i
$449$	−9.15725	+	7.93480i	−0.432157	+	0.374466i	−0.843603	−	0.536968i	$-0.819570\pi$
$449$	−9.15725	+	7.93480i	−0.432157	+	0.374466i	0.411445	+	0.911434i	$0.365024\pi$
$450$	2.65070	+	4.23955i	0.124955	+	0.199854i
$451$	−27.9535	−	12.7659i	−1.31628	−	0.601124i
$452$	−16.9029	+	3.67699i	−0.795043	+	0.172951i
$453$	6.33184	−	11.5959i	0.297496	−	0.544823i
$454$	−0.703888	+	4.89565i	−0.0330351	+	0.229764i
$455$	3.15637	−	9.29023i	0.147973	−	0.435533i
$456$	−1.51625	+	0.218004i	−0.0710051	+	0.0102090i
$457$	5.74776	−	26.4220i	0.268869	−	1.23597i	−0.622474	−	0.782641i	$-0.713872\pi$
$457$	5.74776	−	26.4220i	0.268869	−	1.23597i	0.891343	−	0.453330i	$-0.149764\pi$
$458$	−16.9643	+	1.21331i	−0.792692	+	0.0566944i
$459$	0.466087			0.0217551
$460$	−9.86409	−	4.20710i	−0.459916	−	0.196157i
$461$	−24.6984			−1.15032			−0.575160	−	0.818041i	$-0.695060\pi$
$461$	−24.6984			−1.15032			−0.575160	+	0.818041i	$0.695060\pi$
$462$	−14.9985	+	1.07272i	−0.697796	+	0.0499073i
$463$	4.24089	−	19.4951i	0.197091	−	0.906012i	−0.767250	−	0.641348i	$-0.778375\pi$
$463$	4.24089	−	19.4951i	0.197091	−	0.906012i	0.964341	−	0.264664i	$-0.0852610\pi$
$464$	7.70426	−	1.10771i	0.357661	−	0.0514239i
$465$	−10.6898	+	5.26808i	−0.495728	+	0.244302i
$466$	−3.45235	+	24.0116i	−0.159927	+	1.11232i
$467$	13.5841	−	24.8775i	0.628598	−	1.15119i	−0.348279	−	0.937391i	$-0.613234\pi$
$467$	13.5841	−	24.8775i	0.628598	−	1.15119i	0.976877	−	0.213801i	$-0.0685843\pi$
$468$	−0.998473	+	0.217204i	−0.0461544	+	0.0100403i
$469$	−46.2985	−	21.1438i	−2.13787	−	0.976331i
$470$	−1.57973	−	2.70061i	−0.0728675	−	0.124570i
$471$	5.08271	−	4.40419i	0.234199	−	0.202934i
$472$	0.0520292	−	0.727464i	0.00239484	−	0.0334842i
$473$	9.18355	−	5.01460i	0.422260	−	0.230571i
$474$	−3.52562	+	7.72002i	−0.161937	+	0.354592i
$475$	−3.75397	+	6.67618i	−0.172244	+	0.306324i
$476$	1.92041	−	0.563885i	0.0880221	−	0.0258456i
$477$	−6.79718	−	9.07997i	−0.311221	−	0.415743i
$478$	22.3505	+	8.33630i	1.02229	+	0.381294i
$479$	−0.0829013	−	0.576591i	−0.00378786	−	0.0263451i	0.987840	−	0.155475i	$-0.0496907\pi$
$479$	−0.0829013	−	0.576591i	−0.00378786	−	0.0263451i	−0.991628	+	0.129130i	$0.958782\pi$
$480$	0.410693	−	2.19803i	0.0187455	−	0.100326i
$481$	0.450519	+	0.390377i	0.0205419	+	0.0177997i
$482$	18.7769	−	18.7769i	0.855264	−	0.855264i
$483$	12.2719	+	16.5388i	0.558392	+	0.752540i
$484$		−	1.26144i		−	0.0573384i
$485$	−24.5368	−	20.0258i	−1.11416	−	0.909326i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	20.1871	−	26.9669i	0.914767	−	1.22199i	−0.0598731	−	0.998206i	$-0.519070\pi$
$487$	20.1871	−	26.9669i	0.914767	−	1.22199i	0.974640	−	0.223779i	$-0.0718395\pi$
$488$	−2.01432	+	5.40060i	−0.0911840	+	0.244474i
$489$	−1.28045	−	0.184101i	−0.0579040	−	0.00832535i
$490$	−7.92766	−	24.3224i	−0.358135	−	1.09877i
$491$	10.6704	+	6.85744i	0.481548	+	0.309472i	0.758798	−	0.651326i	$-0.225787\pi$
$491$	10.6704	+	6.85744i	0.481548	+	0.309472i	−0.277250	+	0.960798i	$0.589423\pi$
$492$	−8.22272	+	3.06692i	−0.370709	+	0.138267i
$493$	−1.73861	−	3.18402i	−0.0783030	−	0.143401i
$494$	−1.02504	−	1.18296i	−0.0461187	−	0.0532238i
$495$	7.82302	+	0.328106i	0.351618	+	0.0147473i
$496$	5.11374	+	1.50153i	0.229614	+	0.0674207i
$497$	22.0757	+	59.1872i	0.990230	+	2.65491i
$498$	−2.08596	−	9.58900i	−0.0934740	−	0.429693i
$499$	1.86240	+	6.34274i	0.0833723	+	0.283940i	0.990618	−	0.136661i	$-0.0436373\pi$
$499$	1.86240	+	6.34274i	0.0833723	+	0.283940i	−0.907246	+	0.420601i	$0.861819\pi$
$500$	−7.46456	−	8.32348i	−0.333825	−	0.372237i
$501$	−0.751328	−	1.64518i	−0.0335669	−	0.0735012i
$502$	13.0558	+	9.77342i	0.582707	+	0.436209i
$503$	−25.4152	−	5.52875i	−1.13321	−	0.246515i	−0.393424	−	0.919357i	$-0.628710\pi$
$503$	−25.4152	−	5.52875i	−1.13321	−	0.246515i	−0.739786	+	0.672842i	$0.765073\pi$
$504$	−2.81213	+	3.24537i	−0.125262	+	0.144560i
$505$	30.4039	−	32.2517i	1.35296	−	1.43518i
$506$	−14.1657	+	9.01927i	−0.629741	+	0.400955i
$507$	8.45408	+	8.45408i	0.375459	+	0.375459i
$508$	−0.867350	−	12.1271i	−0.0384824	−	0.538055i
$509$	−13.9127	−	21.6486i	−0.616671	−	0.959559i	−0.999363	−	0.0356827i	$-0.988639\pi$
$509$	−13.9127	−	21.6486i	−0.616671	−	0.959559i	0.382692	−	0.923876i	$-0.374997\pi$
$510$	−1.02677	+	0.178667i	−0.0454663	+	0.00791149i
$511$	12.3120	−	5.62269i	0.544650	−	0.248733i
$512$	−0.800541	+	0.599278i	−0.0353793	+	0.0264846i
$513$	−1.34447	−	0.734135i	−0.0593597	−	0.0324129i
$514$	2.59574	−	4.03905i	0.114493	−	0.178155i
$515$	−4.09994	+	9.72666i	−0.180665	+	0.428608i
$516$	0.841862	−	2.86712i	0.0370609	−	0.126218i
$517$	−4.88701	−	0.349526i	−0.214930	−	0.0153721i
$518$	2.49883	+	0.178720i	0.109792	+	0.00785251i
$519$	−2.74759	+	9.35743i	−0.120606	+	0.410745i
$520$	2.11634	−	0.861242i	0.0928076	−	0.0377679i
$521$	22.9511	−	35.7126i	1.00551	−	1.56460i	0.193373	−	0.981125i	$-0.438057\pi$
$521$	22.9511	−	35.7126i	1.00551	−	1.56460i	0.812133	−	0.583473i	$-0.198306\pi$
$522$	6.83140	+	3.73023i	0.299002	+	0.163268i
$523$	32.1110	−	24.0380i	1.40412	−	1.05111i	0.414089	−	0.910237i	$-0.364100\pi$
$523$	32.1110	−	24.0380i	1.40412	−	1.05111i	0.990028	−	0.140872i	$-0.0449906\pi$
$524$	−1.82194	+	0.832054i	−0.0795920	+	0.0363485i
$525$	4.30283	+	21.0356i	0.187791	+	0.918071i
$526$	0.479684	+	0.746403i	0.0209152	+	0.0325447i
$527$	−0.177211	−	2.47774i	−0.00771945	−	0.107932i
$528$	−2.47603	−	2.47603i	−0.107755	−	0.107755i
$529$	20.8399	+	9.73123i	0.906085	+	0.423097i
$530$	18.4546	+	17.3973i	0.801617	+	0.755689i
$531$	0.477604	−	0.551185i	0.0207263	−	0.0239194i
$532$	−6.42778	−	1.39828i	−0.278680	−	0.0606231i
$533$	−7.17893	−	5.37408i	−0.310954	−	0.232777i
$534$	0.913987	+	2.00135i	0.0395521	+	0.0866070i
$535$	−19.4924	−	2.21831i	−0.842728	−	0.0959057i
$536$	−3.33927	−	11.3725i	−0.144235	−	0.491218i
$537$	−4.18453	−	19.2360i	−0.180576	−	0.830094i
$538$	−1.62133	−	4.34696i	−0.0699005	−	0.187411i
$539$	−38.4377	−	11.2863i	−1.65563	−	0.486137i
$540$	1.64601	−	1.51349i	0.0708328	−	0.0651304i
$541$	−0.709833	−	0.819190i	−0.0305181	−	0.0352197i	0.740285	−	0.672293i	$-0.234690\pi$
$541$	−0.709833	−	0.819190i	−0.0305181	−	0.0352197i	−0.770803	+	0.637073i	$0.780145\pi$
$542$	−0.762510	−	1.39643i	−0.0327526	−	0.0599819i
$543$	−2.25301	+	0.840330i	−0.0966860	+	0.0360620i
$544$	0.392097	+	0.251986i	0.0168110	+	0.0108038i
$545$	6.70097	−	13.1815i	0.287038	−	0.564632i
$546$	−4.34330	−	0.624472i	−0.185876	−	0.0267249i
$547$	−8.46613	+	22.6986i	−0.361986	+	0.970521i	0.620504	+	0.784203i	$0.286928\pi$
$547$	−8.46613	+	22.6986i	−0.361986	+	0.970521i	−0.982490	+	0.186318i	$0.940345\pi$
$548$	−12.1260	+	16.1984i	−0.517996	+	0.691961i
$549$	−4.84901	+	3.11627i	−0.206951	+	0.132999i
$550$	−17.3596	+	2.27602i	−0.740216	+	0.0970497i
$551$			11.9231i			0.507941i
$552$	−1.03924	+	4.68188i	−0.0442332	+	0.199274i
$553$	−25.7706	+	25.7706i	−1.09588	+	1.09588i
$554$	13.1749	+	11.4161i	0.559749	+	0.485025i
$555$	−1.28231	−	0.239594i	−0.0544309	−	0.0101702i
$556$	0.452141	+	3.14471i	0.0191751	+	0.133365i
$557$	8.04781	+	3.00168i	0.340997	+	0.127185i	0.514128	−	0.857714i	$-0.328116\pi$
$557$	8.04781	+	3.00168i	0.340997	+	0.127185i	−0.173131	+	0.984899i	$0.555388\pi$
$558$	3.19393	+	4.26659i	0.135210	+	0.180619i
$559$	2.92969	−	0.860235i	0.123913	−	0.0363841i
$560$	4.95096	−	8.22742i	0.209216	−	0.347672i
$561$	−0.677985	+	1.48458i	−0.0286245	+	0.0626790i
$562$	−0.954311	+	0.521093i	−0.0402552	+	0.0219810i
$563$	0.805941	−	11.2685i	0.0339664	−	0.474912i	−0.951792	−	0.306744i	$-0.900760\pi$
$563$	0.805941	−	11.2685i	0.0339664	−	0.474912i	0.985758	−	0.168168i	$-0.0537850\pi$
$564$	−1.05745	+	0.916282i	−0.0445265	+	0.0385825i
$565$	37.4182	+	9.79859i	1.57420	+	0.412230i
$566$	−15.4033	−	7.03444i	−0.647448	−	0.295679i
$567$	−4.19610	+	0.912807i	−0.176220	+	0.0383343i
$568$	−7.04995	+	12.9110i	−0.295809	+	0.541735i
$569$	1.18613	−	8.24969i	0.0497250	−	0.345845i	−0.949737	−	0.313049i	$-0.898650\pi$
$569$	1.18613	−	8.24969i	0.0497250	−	0.345845i	0.999462	−	0.0327962i	$-0.0104412\pi$
$570$	3.24324	+	1.10189i	0.135844	+	0.0461533i
$571$	−34.7345	+	4.99406i	−1.45359	+	0.208995i	−0.823407	−	0.567451i	$-0.807930\pi$
$571$	−34.7345	+	4.99406i	−1.45359	+	0.208995i	−0.630184	+	0.776446i	$0.717021\pi$
$572$	0.760570	−	3.49629i	0.0318010	−	0.146187i
$573$	−0.0853788	+	0.00610641i	−0.00356675	+	0.000255099i
$574$	−37.6865			−1.57300
$575$	15.3989	+	18.3814i	0.642177	+	0.766557i
$576$	−1.00000			−0.0416667
$577$	−47.4243	+	3.39185i	−1.97430	+	0.141205i	−0.997376	−	0.0723927i	$-0.976937\pi$
$577$	−47.4243	+	3.39185i	−1.97430	+	0.141205i	−0.976922	+	0.213597i	$0.931482\pi$
$578$	−3.56743	+	16.3992i	−0.148386	+	0.682118i
$579$	−21.7710	+	3.13020i	−0.904773	+	0.130087i
$580$	−16.4793	−	5.59885i	−0.684264	−	0.232480i
$581$	5.99722	−	41.7116i	0.248807	−	1.73049i
$582$	−6.78806	+	12.4314i	−0.281374	+	0.515298i
$583$	38.8089	−	8.44236i	1.60730	−	0.349647i
$584$	2.86709	+	1.30936i	0.118641	+	0.0541816i
$585$	2.21034	+	0.578815i	0.0913863	+	0.0239311i
$586$	8.80413	−	7.62882i	0.363695	−	0.315144i
$587$	2.82476	−	39.4954i	0.116591	−	1.63015i	−0.516652	−	0.856195i	$-0.672822\pi$
$587$	2.82476	−	39.4954i	0.116591	−	1.63015i	0.633243	−	0.773953i	$-0.281723\pi$
$588$	−10.0411	+	5.48285i	−0.414088	+	0.226109i
$589$	−3.39152	+	7.42638i	−0.139745	+	0.305999i
$590$	−0.840858	+	1.39732i	−0.0346176	+	0.0575269i
$591$	23.5885	−	6.92619i	0.970299	−	0.284906i
$592$	0.349612	+	0.467028i	0.0143690	+	0.0191947i
$593$	−13.5547	−	5.05562i	−0.556623	−	0.207610i	0.0553797	−	0.998465i	$-0.482363\pi$
$593$	−13.5547	−	5.05562i	−0.556623	−	0.207610i	−0.612003	+	0.790856i	$0.709636\pi$
$594$	−0.498335	−	3.46599i	−0.0204469	−	0.142211i
$595$	−4.39933	−	0.821998i	−0.180355	−	0.0336986i
$596$	−9.37688	−	8.12511i	−0.384092	−	0.332818i
$597$	11.4983	−	11.4983i	0.470593	−	0.470593i
$598$	−4.59872	+	1.69311i	−0.188056	+	0.0692363i
$599$		−	4.80779i		−	0.196441i	−0.995165	−	0.0982204i	$-0.968685\pi$
$599$		−	4.80779i		−	0.196441i	0.995165	−	0.0982204i	$-0.0313150\pi$
$600$	−3.04592	+	3.96514i	−0.124349	+	0.161876i
$601$	−23.1937	+	14.9057i	−0.946089	+	0.608015i	−0.920115	−	0.391648i	$-0.871905\pi$
$601$	−23.1937	+	14.9057i	−0.946089	+	0.608015i	−0.0259743	+	0.999663i	$0.508269\pi$
$602$	7.68986	−	10.2725i	0.313415	−	0.418674i
$603$	4.14207	−	11.1053i	0.168678	−	0.452244i
$604$	13.0775	+	1.88026i	0.532117	+	0.0765069i
$605$	−1.27824	+	2.51442i	−0.0519678	+	0.102226i
$606$	−16.6754	−	10.7166i	−0.677391	−	0.435333i
$607$	−21.2399	+	7.92208i	−0.862102	+	0.321547i	−0.741336	−	0.671134i	$-0.765808\pi$
$607$	−21.2399	+	7.92208i	−0.862102	+	0.321547i	−0.120766	+	0.992681i	$0.538535\pi$
$608$	−0.734135	−	1.34447i	−0.0297731	−	0.0545254i
$609$	21.8882	+	25.2603i	0.886953	+	1.02360i
$610$	9.48762	−	8.72382i	0.384143	−	0.353217i
$611$	−1.37182	−	0.402804i	−0.0554981	−	0.0162957i
$612$	0.162881	+	0.436700i	0.00658406	+	0.0176525i
$613$	1.43310	+	6.58784i	0.0578823	+	0.266080i	0.996989	−	0.0775457i	$-0.0247084\pi$
$613$	1.43310	+	6.58784i	0.0578823	+	0.266080i	−0.939107	+	0.343626i	$0.888345\pi$
$614$	9.22104	+	31.4040i	0.372131	+	1.26736i
$615$	19.4980	+	2.21895i	0.786235	+	0.0894767i
$616$	−6.24654	−	13.6780i	−0.251680	−	0.551103i
$617$	16.5807	+	12.4121i	0.667513	+	0.499694i	0.878468	−	0.477802i	$-0.158566\pi$
$617$	16.5807	+	12.4121i	0.667513	+	0.499694i	−0.210955	+	0.977496i	$0.567657\pi$
$618$	4.61266	+	1.00342i	0.185548	+	0.0403636i
$619$	−20.9512	+	24.1789i	−0.842099	+	0.971834i	−0.999878	−	0.0156407i	$-0.995021\pi$
$619$	−20.9512	+	24.1789i	−0.842099	+	0.971834i	0.157779	+	0.987474i	$0.449567\pi$
$620$	−8.67163	−	8.17480i	−0.348261	−	0.328308i
$621$	−3.63770	+	3.12524i	−0.145976	+	0.125412i
$622$	−23.9380	−	23.9380i	−0.959825	−	0.959825i
$623$	0.674019	+	9.42402i	0.0270040	+	0.377566i
$624$	−0.552440	−	0.859613i	−0.0221153	−	0.0344121i
$625$	6.44472	+	24.1550i	0.257789	+	0.966201i
$626$	−10.9035	+	4.97944i	−0.435790	+	0.199019i
$627$	4.29407	−	3.21450i	0.171489	−	0.128375i
$628$	5.90273	+	3.22313i	0.235545	+	0.128617i
$629$	0.147006	−	0.228745i	0.00586151	−	0.00912068i
$630$	8.89396	−	3.61939i	0.354344	−	0.144200i
$631$	−5.91586	+	20.1476i	−0.235506	+	0.802061i	0.753912	+	0.656975i	$0.228164\pi$
$631$	−5.91586	+	20.1476i	−0.235506	+	0.802061i	−0.989419	+	0.145087i	$0.953654\pi$
$632$	−8.46535	−	0.605454i	−0.336734	−	0.0240837i
$633$	−0.423728	−	0.0303056i	−0.0168417	−	0.00120454i
$634$	−3.24217	+	11.0418i	−0.128763	+	0.438527i
$635$	−10.5597	+	25.0518i	−0.419050	+	0.994149i
$636$	6.13210	−	9.54174i	0.243154	−	0.378354i
$637$	−10.2602	−	5.60251i	−0.406525	−	0.221980i
$638$	−21.8187	+	16.3333i	−0.863810	+	0.646640i
$639$	−13.3811	+	6.11093i	−0.529347	+	0.241745i
$640$	2.20297	−	0.383333i	0.0870798	−	0.0151526i
$641$	−13.7283	−	21.3616i	−0.542233	−	0.843731i	0.456714	−	0.889614i	$-0.349026\pi$
$641$	−13.7283	−	21.3616i	−0.542233	−	0.843731i	−0.998947	+	0.0458824i	$0.985390\pi$
$642$	0.625895	+	8.75116i	0.0247021	+	0.345381i
$643$	−21.0881	−	21.0881i	−0.831635	−	0.831635i	0.156105	−	0.987740i	$-0.450106\pi$
$643$	−21.0881	−	21.0881i	−0.831635	−	0.831635i	−0.987740	+	0.156105i	$0.950106\pi$
$644$	−11.2074	+	17.2779i	−0.441633	+	0.680845i
$645$	−4.58336	+	4.86192i	−0.180470	+	0.191438i
$646$	−0.467553	+	0.539585i	−0.0183956	+	0.0212297i
$647$	−7.83855	−	1.70517i	−0.308165	−	0.0670372i	0.0558234	−	0.998441i	$-0.482222\pi$
$647$	−7.83855	−	1.70517i	−0.308165	−	0.0670372i	−0.363989	+	0.931403i	$0.618585\pi$
$648$	−0.800541	−	0.599278i	−0.0314482	−	0.0235419i
$649$	1.06090	+	2.32304i	0.0416438	+	0.0911871i
$650$	−5.09118	−	0.427812i	−0.199692	−	0.0167802i
$651$	6.44793	+	21.9596i	0.252714	+	0.860666i
$652$	−0.274979	−	1.26406i	−0.0107690	−	0.0495043i
$653$	−0.238181	−	0.638588i	−0.00932074	−	0.0249899i	0.932206	−	0.361928i	$-0.117881\pi$
$653$	−0.238181	−	0.638588i	−0.00932074	−	0.0249899i	−0.941527	+	0.336938i	$0.890609\pi$
$654$	−6.34506	−	1.86308i	−0.248111	−	0.0728521i
$655$	4.47479	+	0.187678i	0.174845	+	0.00733318i
$656$	−5.74709	−	6.63250i	−0.224386	−	0.258956i
$657$	1.51056	+	2.76638i	0.0589324	+	0.107927i
$658$	−5.62967	+	2.09976i	−0.219467	+	0.0818571i
$659$	32.5525	+	20.9202i	1.26807	+	0.814937i	0.989367	−	0.145441i	$-0.0464602\pi$
$659$	32.5525	+	20.9202i	1.26807	+	0.814937i	0.278700	+	0.960378i	$0.410097\pi$
$660$	2.42644	+	7.44443i	0.0944492	+	0.289774i
$661$	43.8092	+	6.29881i	1.70398	+	0.244995i	0.924432	−	0.381346i	$-0.124540\pi$
$661$	43.8092	+	6.29881i	1.70398	+	0.244995i	0.779548	+	0.626342i	$0.215449\pi$
$662$	−2.40384	+	6.44495i	−0.0934279	+	0.250490i
$663$	−0.285411	+	0.381265i	−0.0110845	+	0.0148071i
$664$	8.25544	−	5.30545i	0.320373	−	0.205891i
$665$	11.3955	+	9.30053i	0.441899	+	0.360659i
$666$			0.583390i			0.0226059i
$667$	34.9192	+	13.1927i	1.35208	+	0.510825i
$668$	1.27889	−	1.27889i	0.0494816	−	0.0494816i
$669$	−6.39815	−	5.54403i	−0.247367	−	0.214345i
$670$	−4.86779	+	26.0524i	−0.188059	+	1.00649i
$671$	−2.87241	−	19.9781i	−0.110888	−	0.771245i
$672$	−4.02349	−	1.50068i	−0.155209	−	0.0578901i
$673$	−11.5271	−	15.3984i	−0.444338	−	0.593567i	0.521327	−	0.853357i	$-0.325437\pi$
$673$	−11.5271	−	15.3984i	−0.444338	−	0.593567i	−0.965665	+	0.259791i	$0.916346\pi$
$674$	20.4267	−	5.99782i	0.786808	−	0.231028i
$675$	−4.81461	+	1.34891i	−0.185314	+	0.0519195i
$676$	−4.96665	+	10.8754i	−0.191025	+	0.418286i
$677$	−20.9461	+	11.4374i	−0.805024	+	0.439576i	−0.828391	−	0.560151i	$-0.810743\pi$
$677$	−20.9461	+	11.4374i	−0.805024	+	0.439576i	0.0233669	+	0.999727i	$0.492561\pi$
$678$	1.23404	−	17.2541i	0.0473929	−	0.662640i
$679$	−45.9673	+	39.8309i	−1.76406	+	1.52857i
$680$	−0.526222	−	0.899597i	−0.0201797	−	0.0344980i
$681$	−4.49903	−	2.05464i	−0.172403	−	0.0787340i
$682$	−18.2359	+	3.96698i	−0.698289	+	0.151904i
$683$	18.2936	−	33.5023i	0.699986	−	1.28193i	−0.249577	−	0.968355i	$-0.580292\pi$
$683$	18.2936	−	33.5023i	0.699986	−	1.28193i	0.949564	−	0.313574i	$-0.101526\pi$
$684$	0.218004	−	1.51625i	0.00833560	−	0.0579754i
$685$	40.5846	−	20.0006i	1.55066	−	0.764186i
$686$	−18.8745	+	2.71374i	−0.720632	+	0.103611i
$687$	3.61524	−	16.6190i	0.137930	−	0.634054i
$688$	2.98055	−	0.213173i	0.113632	−	0.00812714i
$689$	11.5898			0.441537
$690$	6.81572	−	8.27925i	0.259470	−	0.315186i
$691$	−15.7276			−0.598307			−0.299153	−	0.954205i	$-0.596704\pi$
$691$	−15.7276			−0.598307			−0.299153	+	0.954205i	$0.596704\pi$
$692$	−9.72762	+	0.695733i	−0.369789	+	0.0264478i
$693$	3.19631	−	14.6932i	0.121418	−	0.558149i
$694$	−27.0121	+	3.88376i	−1.02537	+	0.147425i
$695$	2.28533	−	6.72647i	0.0866875	−	0.255150i
$696$	−1.10771	+	7.70426i	−0.0419875	+	0.292029i
$697$	−1.96032	+	3.59006i	−0.0742525	+	0.135983i
$698$	−0.0219374	+	0.00477219i	−0.000830343	+	0.000180630i
$699$	−22.0664	−	10.0774i	−0.834626	−	0.381161i
$700$	−18.2057	+	11.3827i	−0.688109	+	0.430227i
$701$	5.83026	−	5.05195i	0.220206	−	0.190809i	−0.537771	−	0.843091i	$-0.680733\pi$
$701$	5.83026	−	5.05195i	0.220206	−	0.190809i	0.757977	+	0.652282i	$0.226188\pi$
$702$	0.0728961	−	1.01922i	0.00275129	−	0.0384680i
$703$	−0.784349	+	0.428287i	−0.0295823	+	0.0161532i
$704$	1.45463	−	3.18520i	0.0548235	−	0.120047i
$705$	3.03628	−	0.754890i	0.114353	−	0.0284308i
$706$	−7.98745	+	2.34533i	−0.300612	+	0.0882676i
$707$	−51.0110	−	68.1427i	−1.91847	−	2.56277i
$708$	0.683338	+	0.254872i	0.0256814	+	0.00957868i
$709$	4.22562	+	29.3898i	0.158696	+	1.10376i	0.901039	+	0.433738i	$0.142806\pi$
$709$	4.22562	+	29.3898i	0.158696	+	1.10376i	−0.742343	+	0.670020i	$0.766285\pi$
$710$	27.1355	−	18.5916i	1.01838	−	0.697729i
$711$	−6.41403	−	5.55779i	−0.240545	−	0.208433i
$712$	−1.55576	+	1.55576i	−0.0583046	+	0.0583046i
$713$	17.9970	+	18.1499i	0.673994	+	0.679721i
$714$			2.00149i			0.0749038i
$715$	−5.05887	+	6.19841i	−0.189191	+	0.231807i
$716$	16.5608	−	10.6430i	0.618906	−	0.397747i
$717$	−14.2955	+	19.0965i	−0.533875	+	0.713173i
$718$	4.67314	−	12.5292i	0.174400	−	0.467585i
$719$	−45.1501	−	6.49160i	−1.68381	−	0.242096i	−0.767068	−	0.641566i	$-0.778285\pi$
$719$	−45.1501	−	6.49160i	−1.68381	−	0.242096i	−0.916746	+	0.399470i	$0.869194\pi$
$720$	1.99329	+	1.01331i	0.0742854	+	0.0377640i
$721$	17.0532	+	10.9594i	0.635093	+	0.408149i
$722$	−15.6034	+	5.81978i	−0.580700	+	0.216590i
$723$	12.7262	+	23.3064i	0.473294	+	0.866773i
$724$	−1.57469	−	1.81729i	−0.0585231	−	0.0675392i
$725$	27.1745	+	27.8588i	1.00924	+	1.03465i
$726$	1.21035	+	0.355390i	0.0449202	+	0.0131898i
$727$	−8.31397	−	22.2906i	−0.308348	−	0.826714i	−0.995014	−	0.0997399i	$-0.968199\pi$
$727$	−8.31397	−	22.2906i	−0.308348	−	0.826714i	0.686665	−	0.726974i	$-0.259074\pi$
$728$	−0.932728	−	4.28768i	−0.0345692	−	0.158912i
$729$	−0.281733	−	0.959493i	−0.0104345	−	0.0355368i
$730$	−4.38815	−	5.51519i	−0.162413	−	0.204126i
$731$	−0.578566	−	1.26688i	−0.0213990	−	0.0468574i
$732$	−4.61434	−	3.45425i	−0.170551	−	0.127673i
$733$	−25.9501	−	5.64509i	−0.958488	−	0.208506i	−0.294000	−	0.955805i	$-0.594987\pi$
$733$	−25.9501	−	5.64509i	−0.958488	−	0.208506i	−0.664488	+	0.747299i	$0.731350\pi$
$734$	−10.8697	+	12.5443i	−0.401208	+	0.463018i
$735$	25.5706	−	0.754124i	0.943187	−	0.0278163i
$736$	−4.74986	+	0.662429i	−0.175082	+	0.0244175i
$737$	29.3475	+	29.3475i	1.08103	+	1.08103i
$738$	−0.626077	−	8.75370i	−0.0230462	−	0.322228i
$739$	−10.5595	−	16.4309i	−0.388438	−	0.604421i	0.590877	−	0.806761i	$-0.298782\pi$
$739$	−10.5595	−	16.4309i	−0.388438	−	0.604421i	−0.979315	+	0.202340i	$0.935145\pi$
$740$	−0.223633	−	1.28519i	−0.00822091	−	0.0472444i
$741$	1.42383	−	0.650240i	0.0523056	−	0.0238871i
$742$	38.9916	−	29.1887i	1.43143	−	1.07155i
$743$	27.7695	+	15.1633i	1.01876	+	0.556286i	0.899658	−	0.436595i	$-0.143816\pi$
$743$	27.7695	+	15.1633i	1.01876	+	0.556286i	0.119105	+	0.992882i	$0.461998\pi$
$744$	−2.88141	+	4.48357i	−0.105638	+	0.164376i
$745$	10.4575	+	25.6974i	0.383134	+	0.941480i
$746$	7.89051	−	26.8726i	0.288892	−	0.983876i
$747$	9.78826	+	0.700070i	0.358134	+	0.0256142i
$748$	−1.62791	−	0.116430i	−0.0595222	−	0.00425711i
$749$	−10.6144	+	36.1495i	−0.387843	+	1.32087i
$750$	10.0893	−	4.81720i	0.368410	−	0.175899i
$751$	−8.86939	+	13.8010i	−0.323649	+	0.503607i	−0.964509	−	0.264050i	$-0.914941\pi$
$751$	−8.86939	+	13.8010i	−0.323649	+	0.503607i	0.640860	+	0.767658i	$0.278578\pi$
$752$	−1.22805	−	0.670566i	−0.0447824	−	0.0244530i
$753$	−13.0558	+	9.77342i	−0.475779	+	0.356163i
$754$	−7.23462	+	3.30394i	−0.263469	+	0.120322i
$755$	−24.1620	−	16.9995i	−0.879344	−	0.618677i
$756$	−2.32164	−	3.61255i	−0.0844373	−	0.131387i
$757$	1.96839	+	27.5217i	0.0715423	+	1.00029i	0.898768	+	0.438424i	$0.144463\pi$
$757$	1.96839	+	27.5217i	0.0715423	+	1.00029i	−0.827226	+	0.561869i	$0.810082\pi$
$758$	−13.4069	−	13.4069i	−0.486959	−	0.486959i
$759$	−4.66299	−	16.1329i	−0.169256	−	0.585586i
$760$	0.100975	+	3.42382i	0.00366274	+	0.124195i
$761$	−0.00239754	+	0.00276691i	−8.69107e−5	+	0.000100300i	−0.755793	−	0.654811i	$-0.772748\pi$
$761$	−0.00239754	+	0.00276691i	−8.69107e−5	+	0.000100300i	0.755706	+	0.654911i	$0.227294\pi$
$762$	11.8803	+	2.58439i	0.430377	+	0.0936227i
$763$	−22.7334	−	17.0180i	−0.823003	−	0.616093i
$764$	−0.0355582	−	0.0778617i	−0.00128645	−	0.00281694i
$765$	0.117846	−	1.03552i	0.00426073	−	0.0374392i
$766$	−5.77830	−	19.6791i	−0.208778	−	0.711034i
$767$	0.158412	+	0.728208i	0.00571993	+	0.0262941i
$768$	−0.349464	−	0.936950i	−0.0126102	−	0.0338093i
$769$	36.0384	+	10.5818i	1.29958	+	0.381591i	0.857082	−	0.515179i	$-0.172275\pi$
$769$	36.0384	+	10.5818i	1.29958	+	0.381591i	0.442497	+	0.896770i	$0.354093\pi$
$770$	−1.40897	+	33.5939i	−0.0507756	+	1.21064i
$771$	3.14413	+	3.62852i	0.113233	+	0.130678i
$772$	−10.5410	−	19.3045i	−0.379380	−	0.694783i
$773$	32.6880	−	12.1920i	1.17571	−	0.438516i	0.315730	−	0.948849i	$-0.397751\pi$
$773$	32.6880	−	12.1920i	1.17571	−	0.438516i	0.859977	+	0.510333i	$0.170478\pi$
$774$	2.51380	+	1.61552i	0.0903567	+	0.0580687i
$775$	9.00142	+	25.0818i	0.323341	+	0.900965i
$776$	−14.0198	−	2.01574i	−0.503281	−	0.0723608i
$777$	−0.875483	+	2.34726i	−0.0314078	+	0.0842075i
$778$	9.02267	−	12.0529i	0.323478	−	0.432116i
$779$	11.3094	−	7.26814i	0.405203	−	0.260408i
$780$	0.230114	+	2.27325i	0.00823940	+	0.0813955i
$781$		−	51.5105i		−	1.84319i
$782$	1.06294	+	1.96637i	0.0380108	+	0.0703172i
$783$	−5.50375	+	5.50375i	−0.196688	+	0.196688i
$784$	−8.64616	−	7.49194i	−0.308791	−	0.267569i
$785$	−8.49979	−	12.4059i	−0.303371	−	0.442787i
$786$	−0.285049	−	1.98256i	−0.0101674	−	0.0707156i
$787$	−29.1783	−	10.8829i	−1.04009	−	0.387935i	−0.229354	−	0.973343i	$-0.573661\pi$
$787$	−29.1783	−	10.8829i	−1.04009	−	0.387935i	−0.810739	+	0.585408i	$0.800934\pi$
$788$	14.7328	+	19.6807i	0.524835	+	0.701097i
$789$	−0.851311	+	0.249967i	−0.0303075	+	0.00889908i
$790$	16.2604	+	9.78490i	0.578518	+	0.348131i
$791$	30.8581	−	67.5697i	1.09719	−	2.40250i
$792$	3.07331	−	1.67815i	0.109205	−	0.0596306i
$793$	0.420175	−	5.87482i	0.0149209	−	0.208621i
$794$	11.5537	−	10.0113i	0.410026	−	0.355289i
$795$	−21.8918	+	12.8057i	−0.776423	+	0.454171i
$796$	14.7915	+	6.75506i	0.524272	+	0.239427i
$797$	1.43296	−	0.311722i	0.0507581	−	0.0110417i	−0.187115	−	0.982338i	$-0.559914\pi$
$797$	1.43296	−	0.311722i	0.0507581	−	0.0110417i	0.237873	+	0.971296i	$0.423550\pi$
$798$	3.15255	−	5.77347i	0.111599	−	0.204379i
$799$	−0.0928106	+	0.645512i	−0.00328340	+	0.0228366i
$800$	−4.77958	−	1.46820i	−0.168984	−	0.0519087i
$801$	−2.17778	+	0.313118i	−0.0769482	+	0.0110635i
$802$	4.68469	−	21.5352i	0.165422	−	0.760433i
$803$	−11.0088	+	0.787363i	−0.388491	+	0.0277854i
$804$	11.8526			0.418010
$805$	39.8475	−	23.0832i	1.40444	−	0.813576i
$806$	−5.44594			−0.191825
$807$	4.62766	−	0.330976i	0.162901	−	0.0116509i
$808$	4.21348	−	19.3691i	0.148230	−	0.681402i
$809$	20.1209	−	2.89295i	0.707413	−	0.101711i	0.220788	−	0.975322i	$-0.429137\pi$
$809$	20.1209	−	2.89295i	0.707413	−	0.101711i	0.486625	+	0.873611i	$0.338228\pi$
$810$	0.988453	+	2.00573i	0.0347307	+	0.0704742i
$811$	−1.83964	+	12.7950i	−0.0645984	+	0.449292i	0.931693	+	0.363247i	$0.118332\pi$
$811$	−1.83964	+	12.7950i	−0.0645984	+	0.449292i	−0.996291	+	0.0860448i	$0.972577\pi$
$812$	−16.0185	+	29.3357i	−0.562139	+	1.02948i
$813$	1.55469	−	0.338202i	0.0545254	−	0.0118613i
$814$	−1.85821	−	0.848617i	−0.0651303	−	0.0297440i
$815$	−0.732774	+	2.79827i	−0.0256679	+	0.0980190i
$816$	−0.352245	+	0.305222i	−0.0123310	+	0.0106849i
$817$	−0.326548	+	4.56574i	−0.0114245	+	0.159735i
$818$	−21.5942	+	11.7913i	−0.755022	+	0.412273i
$819$	1.82282	−	3.99143i	0.0636946	−	0.139472i
$820$	4.73481	+	19.0441i	0.165347	+	0.665049i
$821$	−31.8952	+	9.36527i	−1.11315	+	0.326850i	−0.786064	−	0.618145i	$-0.787885\pi$
$821$	−31.8952	+	9.36527i	−1.11315	+	0.326850i	−0.327085	+	0.944995i	$0.606066\pi$
$822$	−12.1260	−	16.1984i	−0.422942	−	0.564984i
$823$	26.9453	+	10.0501i	0.939255	+	0.350324i	0.772024	−	0.635594i	$-0.219245\pi$
$823$	26.9453	+	10.0501i	0.939255	+	0.350324i	0.167231	+	0.985918i	$0.446517\pi$
$824$	0.671802	+	4.67249i	0.0234033	+	0.162774i
$825$	2.70694	−	17.2976i	0.0942437	−	0.602227i
$826$	2.36692	+	2.05095i	0.0823557	+	0.0713616i
$827$	−15.8409	+	15.8409i	−0.550843	+	0.550843i	−0.926684	−	0.375841i	$-0.877354\pi$
$827$	−15.8409	+	15.8409i	−0.550843	+	0.550843i	0.375841	+	0.926684i	$0.377354\pi$
$828$	−4.19944	−	2.31618i	−0.145941	−	0.0804930i
$829$			50.3935i			1.75024i	0.483907	+	0.875120i	$0.339217\pi$
$829$			50.3935i			1.75024i	−0.483907	+	0.875120i	$0.660783\pi$
$830$	−21.8316	+	2.20994i	−0.757784	+	0.0767080i
$831$	−14.6655	+	9.42495i	−0.508741	+	0.326948i
$832$	0.612357	−	0.818013i	0.0212296	−	0.0283595i
$833$	−1.86344	+	4.99607i	−0.0645643	+	0.173103i
$834$	−3.14471	−	0.452141i	−0.108892	−	0.0156564i
$835$	−3.84510	+	1.25328i	−0.133065	+	0.0433714i
$836$	4.51245	+	2.89998i	0.156066	+	0.100298i
$837$	−4.99359	+	1.86251i	−0.172604	+	0.0643779i
$838$	−4.04955	−	7.41619i	−0.139889	−	0.256188i
$839$	−5.47304	−	6.31622i	−0.188950	−	0.218060i	0.653368	−	0.757040i	$-0.273355\pi$
$839$	−5.47304	−	6.31622i	−0.188950	−	0.218060i	−0.842319	+	0.538980i	$0.818810\pi$
$840$	6.49931	+	7.06835i	0.224247	+	0.243881i
$841$	30.3033	+	8.89785i	1.04494	+	0.306822i
$842$	13.1253	+	35.1904i	0.452329	+	1.21274i
$843$	−0.231125	−	1.06246i	−0.00796036	−	0.0365932i
$844$	−0.119683	−	0.407602i	−0.00411965	−	0.0140302i
$845$	20.9202	−	16.6451i	0.719677	−	0.572609i
$846$	−0.581250	−	1.27276i	−0.0199838	−	0.0437584i
$847$	4.33649	+	3.24625i	0.149004	+	0.111543i
$848$	11.0831	+	2.41098i	0.380594	+	0.0827933i
$849$	11.0891	−	12.7975i	0.380577	−	0.439209i
$850$	0.137338	+	2.32638i	0.00471066	+	0.0797943i
$851$	0.386454	+	2.77102i	0.0132475	+	0.0949894i
$852$	−10.4018	−	10.4018i	−0.356361	−	0.356361i
$853$	0.718321	+	10.0434i	0.0245949	+	0.343881i	0.994818	+	0.101669i	$0.0324183\pi$
$853$	0.718321	+	10.0434i	0.0245949	+	0.343881i	−0.970223	+	0.242212i	$0.922127\pi$
$854$	−13.3820	−	20.8228i	−0.457923	−	0.712542i
$855$	−1.97099	+	2.80142i	−0.0674063	+	0.0958066i
$856$	−7.98067	+	3.64465i	−0.272774	+	0.124572i
$857$	3.07162	−	2.29939i	0.104925	−	0.0785456i	−0.545527	−	0.838093i	$-0.683671\pi$
$857$	3.07162	−	2.29939i	0.104925	−	0.0785456i	0.650452	+	0.759548i	$0.274580\pi$
$858$	3.14038	+	1.71478i	0.107211	+	0.0585416i
$859$	10.0450	−	15.6303i	0.342730	−	0.533298i	−0.626511	−	0.779413i	$-0.715518\pi$
$859$	10.0450	−	15.6303i	0.342730	−	0.533298i	0.969241	+	0.246115i	$0.0791540\pi$
$860$	−6.15710	−	2.59531i	−0.209955	−	0.0884995i
$861$	10.6175	−	36.1599i	0.361844	−	1.23233i
$862$	30.2877	+	2.16622i	1.03160	+	0.0737817i
$863$	0.424591	+	0.0303674i	0.0144533	+	0.00103372i	0.0785639	−	0.996909i	$-0.474967\pi$
$863$	0.424591	+	0.0303674i	0.0144533	+	0.00103372i	−0.0641107	+	0.997943i	$0.520421\pi$
$864$	0.281733	−	0.959493i	0.00958474	−	0.0326426i
$865$	20.0949	+	8.47034i	0.683249	+	0.288000i
$866$	−5.37660	+	8.36615i	−0.182704	+	0.284293i
$867$	−14.7299	−	8.04312i	−0.500253	−	0.273159i
$868$	−18.3217	+	13.7155i	−0.621881	+	0.465534i
$869$	27.0327	−	12.3454i	0.917021	−	0.418790i
$870$	10.0148	−	14.2343i	0.339534	−	0.482590i
$871$	6.54787	+	10.1887i	0.221866	+	0.345230i
$872$	−0.471761	−	6.59608i	−0.0159758	−	0.223371i
$873$	−10.0154	−	10.0154i	−0.338971	−	0.338971i
$874$	0.0310804	−	7.34641i	0.00105131	−	0.248496i
$875$	47.8234	−	4.24104i	1.61673	−	0.143373i
$876$	−2.06407	+	2.38207i	−0.0697385	+	0.0804825i
$877$	33.4323	+	7.27276i	1.12893	+	0.245584i	0.737976	−	0.674827i	$-0.235782\pi$
$877$	33.4323	+	7.27276i	1.12893	+	0.245584i	0.390954	+	0.920410i	$0.372145\pi$
$878$	−2.49026	−	1.86419i	−0.0840423	−	0.0629133i
$879$	4.83939	+	10.5968i	0.163229	+	0.357421i
$880$	−6.12710	+	4.87502i	−0.206545	+	0.164337i
$881$	1.88608	+	6.42339i	0.0635436	+	0.216410i	0.985144	−	0.171731i	$-0.0549358\pi$
$881$	1.88608	+	6.42339i	0.0635436	+	0.216410i	−0.921600	+	0.388140i	$0.873118\pi$
$882$	−2.43185	−	11.1791i	−0.0818848	−	0.376418i
$883$	0.155955	+	0.418131i	0.00524830	+	0.0140712i	0.939547	−	0.342419i	$-0.111246\pi$
$883$	0.155955	+	0.418131i	0.00524830	+	0.0140712i	−0.934299	+	0.356490i	$0.883973\pi$
$884$	−0.456967	−	0.134178i	−0.0153695	−	0.00451288i
$885$	−1.10382	−	1.20047i	−0.0371046	−	0.0403533i
$886$	−14.2501	−	16.4454i	−0.478740	−	0.552496i
$887$	22.4173	+	41.0543i	0.752700	+	1.37847i	0.919744	+	0.392518i	$0.128396\pi$
$887$	22.4173	+	41.0543i	0.752700	+	1.37847i	−0.167044	+	0.985949i	$0.553422\pi$
$888$	−0.546607	+	0.203874i	−0.0183429	+	0.00684156i
$889$	43.9217	+	28.2268i	1.47309	+	0.946696i
$890$	4.67755	−	1.52461i	0.156792	−	0.0511049i
$891$	3.46599	+	0.498335i	0.116115	+	0.0166948i
$892$	2.95855	−	7.93219i	0.0990597	−	0.265589i
$893$	1.28447	−	1.71585i	0.0429831	−	0.0574187i
$894$	10.4378	−	6.70794i	0.349091	−	0.224347i
$895$	−43.7951	+	4.43324i	−1.46391	+	0.148187i
$896$		−	4.29424i		−	0.143461i
$897$	−0.328915	−	4.88945i	−0.0109821	−	0.163254i
$898$	8.56786	−	8.56786i	0.285913	−	0.285913i
$899$	31.3508	+	27.1656i	1.04561	+	0.906024i
$900$	−2.94639	−	4.03965i	−0.0982130	−	0.134655i
$901$	−0.752346	−	5.23268i	−0.0250643	−	0.174326i
$902$	28.7930	+	10.7392i	0.958701	+	0.357577i
$903$	7.68986	+	10.2725i	0.255903	+	0.341846i
$904$	16.5975	−	4.87346i	0.552024	−	0.162089i
$905$	1.29733	+	5.21805i	0.0431247	+	0.173454i
$906$	−5.48846	+	12.0181i	−0.182342	+	0.399273i
$907$	7.81537	−	4.26752i	0.259505	−	0.141701i	−0.344230	−	0.938885i	$-0.611860\pi$
$907$	7.81537	−	4.26752i	0.259505	−	0.141701i	0.603736	+	0.797185i	$0.293678\pi$
$908$	0.352843	−	4.93339i	0.0117095	−	0.163720i
$909$	14.9805	−	12.9807i	0.496873	−	0.430543i
$910$	−2.48557	+	9.49173i	−0.0823959	+	0.314648i
$911$	−13.8066	−	6.30526i	−0.457433	−	0.208903i	0.173352	−	0.984860i	$-0.444540\pi$
$911$	−13.8066	−	6.30526i	−0.457433	−	0.208903i	−0.630786	+	0.775957i	$0.717267\pi$
$912$	1.49684	−	0.325617i	0.0495653	−	0.0107823i
$913$	−16.4682	+	30.1592i	−0.545017	+	0.998124i
$914$	−3.84819	+	26.7648i	−0.127287	+	0.885299i
$915$	5.69747	+	11.5611i	0.188352	+	0.382198i
$916$	16.8346	−	2.42044i	0.556230	−	0.0799737i
$917$	1.82830	−	8.40458i	0.0603759	−	0.277544i
$918$	−0.464899	+	0.0332503i	−0.0153440	+	0.00109742i
$919$	−10.4913			−0.346076			−0.173038	−	0.984915i	$-0.555358\pi$
$919$	−10.4913			−0.346076			−0.173038	+	0.984915i	$0.555358\pi$
$920$	10.1391	+	3.49269i	0.334276	+	0.115151i
$921$	−32.7298			−1.07848
$922$	24.6355	−	1.76197i	0.811327	−	0.0580272i
$923$	3.19517	−	14.6879i	0.105170	−	0.483460i
$924$	14.8838	−	2.13997i	0.489641	−	0.0703998i
$925$	−0.856533	+	2.78836i	−0.0281626	+	0.0916807i
$926$	−2.83932	+	19.7479i	−0.0933060	+	0.648957i
$927$	−2.26231	+	4.14312i	−0.0743041	+	0.136078i
$928$	−7.60561	+	1.65450i	−0.249666	+	0.0543116i
$929$	−30.9668	−	14.1421i	−1.01599	−	0.463986i	−0.163395	−	0.986561i	$-0.552244\pi$
$929$	−30.9668	−	14.1421i	−1.01599	−	0.463986i	−0.852594	+	0.522575i	$0.824972\pi$
$930$	10.2867	−	6.01726i	0.337316	−	0.197314i
$931$	13.2446	−	11.4765i	0.434073	−	0.376127i
$932$	1.73059	−	24.1968i	0.0566872	−	0.792591i
$933$	29.7124	−	16.2242i	0.972740	−	0.531156i
$934$	−11.7748	+	25.7832i	−0.385282	+	0.843651i
$935$	3.12691	+	1.88166i	0.102261	+	0.0615368i
$936$	0.980433	−	0.287881i	0.0320465	−	0.00940969i
$937$	−24.5954	−	32.8555i	−0.803495	−	1.07334i	−0.995759	−	0.0920006i	$-0.970674\pi$
$937$	−24.5954	−	32.8555i	−0.803495	−	1.07334i	0.192264	−	0.981343i	$-0.438417\pi$
$938$	47.6889	+	17.7870i	1.55710	+	0.580768i
$939$	−1.70588	−	11.8647i	−0.0556693	−	0.387189i
$940$	1.76836	+	2.58103i	0.0576777	+	0.0841840i
$941$	20.5427	+	17.8004i	0.669673	+	0.580275i	0.921917	−	0.387389i	$-0.126623\pi$
$941$	20.5427	+	17.8004i	0.669673	+	0.580275i	−0.252243	+	0.967664i	$0.581168\pi$
$942$	−4.75557	+	4.75557i	−0.154945	+	0.154945i
$943$	−8.77248	−	41.1641i	−0.285671	−	1.34049i
$944$			0.729322i			0.0237374i
$945$	0.967059	+	9.55339i	0.0314584	+	0.310772i
$946$	−8.80241	+	5.65697i	−0.286191	+	0.183924i
$947$	−14.5916	+	19.4921i	−0.474164	+	0.633410i	−0.972313	−	0.233682i	$-0.924922\pi$
$947$	−14.5916	+	19.4921i	−0.474164	+	0.633410i	0.498149	+	0.867092i	$0.334013\pi$
$948$	2.96589	−	7.95187i	0.0963277	−	0.258265i
$949$	−3.18793	−	0.458355i	−0.103485	−	0.0148788i
$950$	3.26813	−	6.92698i	0.106032	−	0.224741i
$951$	−9.68113	−	6.22169i	−0.313932	−	0.201752i
$952$	−1.87529	+	0.699449i	−0.0607786	+	0.0226693i
$953$	−14.5823	−	26.7055i	−0.472368	−	0.865077i	−0.999879	−	0.0155290i	$-0.995057\pi$
$953$	−14.5823	−	26.7055i	−0.472368	−	0.865077i	0.527512	−	0.849548i	$-0.323125\pi$
$954$	7.42762	+	8.57193i	0.240478	+	0.277526i
$955$	−0.00802050	+	0.191232i	−0.000259537	+	0.00618813i
$956$	−22.8883	−	6.72060i	−0.740259	−	0.217360i
$957$	−9.52461	−	25.5365i	−0.307887	−	0.825477i
$958$	0.123824	+	0.569208i	0.00400056	+	0.0183903i
$959$	−24.4800	−	83.3713i	−0.790501	−	2.69220i
$960$	−0.252841	+	2.22173i	−0.00816042	+	0.0717059i
$961$	−1.07803	−	2.36056i	−0.0347753	−	0.0761472i
$962$	−0.477220	−	0.357243i	−0.0153862	−	0.0115180i
$963$	−8.57301	−	1.86494i	−0.276261	−	0.0600970i
$964$	−17.3895	+	20.0686i	−0.560079	+	0.646366i
$965$	1.44984	+	49.1607i	0.0466720	+	1.58254i
$966$	−13.4205	−	15.6212i	−0.431799	−	0.502603i
$967$	26.8907	+	26.8907i	0.864746	+	0.864746i	0.991885	−	0.127139i	$-0.0405793\pi$
$967$	26.8907	+	26.8907i	0.864746	+	0.864746i	−0.127139	+	0.991885i	$0.540579\pi$
$968$	0.0899904	+	1.25823i	0.00289240	+	0.0404411i
$969$	−0.386003	−	0.600632i	−0.0124002	−	0.0192951i
$970$	25.9029	+	18.2244i	0.831691	+	0.585150i
$971$	−29.9838	+	13.6932i	−0.962227	+	0.439434i	−0.833667	−	0.552267i	$-0.813763\pi$
$971$	−29.9838	+	13.6932i	−0.962227	+	0.439434i	−0.128560	+	0.991702i	$0.541035\pi$
$972$	0.800541	−	0.599278i	0.0256774	−	0.0192218i
$973$	−11.9742	−	6.53840i	−0.383875	−	0.209611i
$974$	−18.2119	+	28.3383i	−0.583547	+	0.908017i
$975$	1.84483	−	4.76442i	0.0590820	−	0.152584i
$976$	1.62391	−	5.53054i	0.0519802	−	0.177028i
$977$	−37.0978	−	2.65329i	−1.18686	−	0.0848862i	−0.536093	−	0.844159i	$-0.680100\pi$
$977$	−37.0978	−	2.65329i	−1.18686	−	0.0848862i	−0.650772	+	0.759273i	$0.725555\pi$
$978$	1.29032	+	0.0922857i	0.0412600	+	0.00295097i
$979$	2.17053	−	7.39215i	0.0693704	−	0.236254i
$980$	9.64260	+	23.6949i	0.308021	+	0.756904i
$981$	3.57522	−	5.56315i	0.114148	−	0.177618i
$982$	−11.1324	−	6.07876i	−0.355249	−	0.193981i
$983$	4.47312	−	3.34853i	0.142670	−	0.106802i	−0.525559	−	0.850757i	$-0.676144\pi$
$983$	4.47312	−	3.34853i	0.142670	−	0.106802i	0.668229	+	0.743956i	$0.267053\pi$
$984$	7.98298	−	3.64571i	0.254488	−	0.116221i
$985$	−9.42398	−	54.1583i	−0.300273	−	1.72563i
$986$	1.96133	+	3.05188i	0.0624613	+	0.0971917i
$987$	−0.428642	−	5.99320i	−0.0136438	−	0.190766i
$988$	1.10682	+	1.10682i	0.0352126	+	0.0352126i
$989$	13.0104	+	6.00829i	0.413706	+	0.191053i
$990$	−7.82649	+	0.230817i	−0.248742	+	0.00733586i
$991$	2.78345	−	3.21227i	0.0884192	−	0.102041i	−0.709816	−	0.704387i	$-0.751222\pi$
$991$	2.78345	−	3.21227i	0.0884192	−	0.102041i	0.798235	+	0.602346i	$0.205767\pi$
$992$	−5.20783	−	1.13289i	−0.165349	−	0.0359694i
$993$	−5.50664	−	4.12222i	−0.174748	−	0.130815i
$994$	−26.2418	−	57.4615i	−0.832339	−	1.82257i
$995$	−22.6388	−	28.4532i	−0.717697	−	0.902028i
$996$	2.76472	+	9.41576i	0.0876034	+	0.298350i
$997$	−10.1448	−	46.6348i	−0.321289	−	1.47694i	−0.800549	−	0.599268i	$-0.795459\pi$
$997$	−10.1448	−	46.6348i	−0.321289	−	1.47694i	0.479260	−	0.877673i	$-0.340905\pi$
$998$	−2.31014	−	6.19372i	−0.0731261	−	0.196059i
$999$	−0.559758	−	0.164360i	−0.0177100	−	0.00520012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.7.2	✓	240
5.3	odd	4	inner	690.2.w.a.283.10	yes	240
23.10	odd	22	inner	690.2.w.a.217.10	yes	240
115.33	even	44	inner	690.2.w.a.493.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.2	✓	240	1.1	even	1	trivial
690.2.w.a.217.10	yes	240	23.10	odd	22	inner
690.2.w.a.283.10	yes	240	5.3	odd	4	inner
690.2.w.a.493.2	yes	240	115.33	even	44	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.11721 - 0.719325i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-2.05801 + 3.76897i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.212565 - 0.977147i) q^{3} +(0.989821 - 0.142315i) q^{4} +(-2.11721 - 0.719325i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-2.05801 + 3.76897i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(-0.909632 - 0.415415i) q^{9} +(2.16313 + 0.566452i) q^{10} +(2.64636 - 2.29308i) q^{11} +(0.0713392 - 0.997452i) q^{12} +(0.896834 - 0.489708i) q^{13} +(1.78389 - 3.90618i) q^{14} +(-1.15293 + 1.91592i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-0.279315 - 0.373122i) q^{17} +(0.936950 + 0.349464i) q^{18} +(0.218004 + 1.51625i) q^{19} +(-2.19803 - 0.410693i) q^{20} +(3.24537 + 2.81213i) q^{21} +(-2.47603 + 2.47603i) q^{22} +(4.68188 + 1.03924i) q^{23} +1.00000i q^{24} +(3.96514 + 3.04592i) q^{25} +(-0.859613 + 0.552440i) q^{26} +(-0.599278 + 0.800541i) q^{27} +(-1.50068 + 4.02349i) q^{28} +(7.70426 + 1.10771i) q^{29} +(1.01331 - 1.99329i) q^{30} +(4.48357 + 2.88141i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-1.67815 - 3.07331i) q^{33} +(0.305222 + 0.352245i) q^{34} +(7.06835 - 6.49931i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.203874 + 0.546607i) q^{37} +(-0.325617 - 1.49684i) q^{38} +(-0.287881 - 0.980433i) q^{39} +(2.22173 + 0.252841i) q^{40} +(-3.64571 - 7.98298i) q^{41} +(-3.43772 - 2.57344i) q^{42} +(2.91987 + 0.635179i) q^{43} +(2.29308 - 2.64636i) q^{44} +(1.62706 + 1.53384i) q^{45} +(-4.74409 - 0.702595i) q^{46} +(-0.989385 - 0.989385i) q^{47} +(-0.0713392 - 0.997452i) q^{48} +(-6.18520 - 9.62437i) q^{49} +(-4.17233 - 2.75529i) q^{50} +(-0.423967 + 0.193619i) q^{51} +(0.818013 - 0.612357i) q^{52} +(9.95488 + 5.43578i) q^{53} +(0.540641 - 0.841254i) q^{54} +(-7.25237 + 2.95134i) q^{55} +(1.20983 - 4.12029i) q^{56} +(1.52794 + 0.109281i) q^{57} +(-7.76365 - 0.555267i) q^{58} +(-0.205474 + 0.699779i) q^{59} +(-0.868532 + 2.06050i) q^{60} +(3.11627 - 4.84901i) q^{61} +(-4.67770 - 2.55422i) q^{62} +(3.43772 - 2.57344i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-2.25104 + 0.391700i) q^{65} +(1.89313 + 2.94576i) q^{66} +(0.845557 + 11.8224i) q^{67} +(-0.329573 - 0.329573i) q^{68} +(2.01070 - 4.35397i) q^{69} +(-6.58668 + 6.98700i) q^{70} +(9.63328 - 11.1174i) q^{71} +(0.977147 + 0.212565i) q^{72} +(-2.52325 - 1.88888i) q^{73} +(-0.242349 - 0.530670i) q^{74} +(3.81917 - 3.22707i) q^{75} +(0.431571 + 1.46979i) q^{76} +(3.19631 + 14.6932i) q^{77} +(0.357091 + 0.957398i) q^{78} +(8.14319 + 2.39106i) q^{79} +(-2.23410 - 0.0937008i) q^{80} +(0.654861 + 0.755750i) q^{81} +(4.20592 + 7.70256i) q^{82} +(-9.19453 + 3.42938i) q^{83} +(3.61255 + 2.32164i) q^{84} +(0.322973 + 0.990895i) q^{85} +(-2.95775 - 0.425260i) q^{86} +(2.72005 - 7.29273i) q^{87} +(-2.09845 + 2.80320i) q^{88} +(1.85091 - 1.18951i) q^{89} +(-1.73234 - 1.41386i) q^{90} +4.38796i q^{91} +(4.78212 + 0.362365i) q^{92} +(3.76862 - 3.76862i) q^{93} +(1.05745 + 0.916282i) q^{94} +(0.629118 - 3.36704i) q^{95} +(0.142315 + 0.989821i) q^{96} +(13.2709 + 4.94979i) q^{97} +(6.85604 + 9.15860i) q^{98} +(-3.35979 + 0.986524i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more