LMFDB - Embedded newform 690.2.w.a.373.7

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			373.7
Character	$\chi$	$=$	690.373
Dual form			690.2.w.a.37.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.877679 - 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-1.94930 - 1.09554i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.266002 - 0.713180i) q^{7} +(0.0713392 - 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})$	\(q+(0.877679 - 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-1.94930 - 1.09554i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.266002 - 0.713180i) q^{7} +(0.0713392 - 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(-2.23590 - 0.0273353i) q^{10} +(-1.07796 - 3.67121i) q^{11} +(0.479249 - 0.877679i) q^{12} +(1.99930 - 0.745701i) q^{13} +(-0.108326 - 0.753424i) q^{14} +(-2.02249 - 0.953692i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(-3.59684 - 0.782446i) q^{17} +(0.800541 - 0.599278i) q^{18} +(0.402082 + 0.258402i) q^{19} +(-1.97550 + 1.04756i) q^{20} +(0.214447 - 0.730339i) q^{21} +(-2.70553 - 2.70553i) q^{22} +(2.66718 - 3.98574i) q^{23} -1.00000i q^{24} +(2.59956 + 4.27110i) q^{25} +(1.39737 - 1.61265i) q^{26} +(0.977147 - 0.212565i) q^{27} +(-0.456153 - 0.609350i) q^{28} +(1.30424 + 2.02944i) q^{29} +(-2.23215 + 0.132242i) q^{30} +(-1.58642 - 1.83082i) q^{31} +(-0.800541 - 0.599278i) q^{32} +(-1.33712 - 3.58495i) q^{33} +(-3.53186 + 1.03705i) q^{34} +(-1.29984 + 1.09879i) q^{35} +(0.415415 - 0.909632i) q^{36} +(2.32132 - 3.10092i) q^{37} +(0.476738 + 0.0340970i) q^{38} +(1.94101 - 0.886429i) q^{39} +(-1.23182 + 1.86618i) q^{40} +(0.610814 - 4.24831i) q^{41} +(-0.161799 - 0.743777i) q^{42} +(0.197108 + 2.75593i) q^{43} +(-3.67121 - 1.07796i) q^{44} +(-2.08537 - 0.806979i) q^{45} +(0.430764 - 4.77645i) q^{46} +(-3.20158 + 3.20158i) q^{47} +(-0.479249 - 0.877679i) q^{48} +(4.85238 + 4.20461i) q^{49} +(4.32850 + 2.50281i) q^{50} +(-3.64350 - 0.523856i) q^{51} +(0.453580 - 2.08507i) q^{52} +(1.42225 + 0.530471i) q^{53} +(0.755750 - 0.654861i) q^{54} +(-1.92069 + 8.33725i) q^{55} +(-0.692386 - 0.316202i) q^{56} +(0.419492 + 0.229060i) q^{57} +(2.11731 + 1.15614i) q^{58} +(7.27790 + 3.32370i) q^{59} +(-1.89574 + 1.18582i) q^{60} +(-3.67344 + 3.18305i) q^{61} +(-2.26978 - 0.846586i) q^{62} +(0.161799 - 0.743777i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(-4.71419 - 0.736727i) q^{65} +(-2.89164 - 2.50562i) q^{66} +(3.93580 + 7.20789i) q^{67} +(-2.60284 + 2.60284i) q^{68} +(2.37604 - 4.16586i) q^{69} +(-0.614250 + 1.58733i) q^{70} +(3.48967 + 1.02466i) q^{71} +(-0.0713392 - 0.997452i) q^{72} +(1.41187 + 6.49025i) q^{73} +(0.551261 - 3.83410i) q^{74} +(2.89764 + 4.07476i) q^{75} +(0.434764 - 0.198550i) q^{76} +(-2.90497 - 0.207768i) q^{77} +(1.27876 - 1.70823i) q^{78} +(2.14420 - 4.69513i) q^{79} +(-0.186773 + 2.22825i) q^{80} +(0.959493 - 0.281733i) q^{81} +(-1.49990 - 4.02138i) q^{82} +(0.565465 + 0.423302i) q^{83} +(-0.498462 - 0.575255i) q^{84} +(6.15413 + 5.46573i) q^{85} +(1.49378 + 2.32436i) q^{86} +(1.44570 + 1.93122i) q^{87} +(-3.73875 + 0.813316i) q^{88} +(0.972526 - 1.12236i) q^{89} +(-2.21703 + 0.291145i) q^{90} -1.62422i q^{91} +(-1.91103 - 4.39863i) q^{92} +(-1.71298 - 1.71298i) q^{93} +(-1.27561 + 4.34431i) q^{94} +(-0.500688 - 0.944203i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(8.22520 - 6.15731i) q^{97} +(6.27389 + 1.36480i) q^{98} +(-1.58946 - 3.48043i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{22}\right)$

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 $

$2$	0.877679	−	0.479249i	0.620613	−	0.338880i
$2$	0.877679	−	0.479249i	0.620613	−	0.338880i
$3$	0.997452	−	0.0713392i	0.575879	−	0.0411877i
$3$	0.997452	−	0.0713392i	0.575879	−	0.0411877i
$4$	0.540641	−	0.841254i	0.270320	−	0.420627i
$5$	−1.94930	−	1.09554i	−0.871755	−	0.489943i
$5$	−1.94930	−	1.09554i	−0.871755	−	0.489943i
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	0.266002	−	0.713180i	0.100539	−	0.269557i	−0.876936	−	0.480608i	$-0.840416\pi$
$7$	0.266002	−	0.713180i	0.100539	−	0.269557i	0.977475	+	0.211051i	$0.0676887\pi$
$8$	0.0713392	−	0.997452i	0.0252222	−	0.352653i
$9$	0.989821	−	0.142315i	0.329940	−	0.0474383i
$10$	−2.23590	−	0.0273353i	−0.707054	−	0.00864419i
$11$	−1.07796	−	3.67121i	−0.325018	−	1.10691i	−0.946291	−	0.323316i	$-0.895202\pi$
$11$	−1.07796	−	3.67121i	−0.325018	−	1.10691i	0.621273	−	0.783594i	$-0.286616\pi$
$12$	0.479249	−	0.877679i	0.138347	−	0.253364i
$13$	1.99930	−	0.745701i	0.554506	−	0.206820i	−0.0565606	−	0.998399i	$-0.518013\pi$
$13$	1.99930	−	0.745701i	0.554506	−	0.206820i	0.611067	+	0.791579i	$0.290741\pi$
$14$	−0.108326	−	0.753424i	−0.0289514	−	0.201361i
$15$	−2.02249	−	0.953692i	−0.522205	−	0.246242i
$16$	−0.415415	−	0.909632i	−0.103854	−	0.227408i
$17$	−3.59684	−	0.782446i	−0.872363	−	0.189771i	−0.245969	−	0.969278i	$-0.579106\pi$
$17$	−3.59684	−	0.782446i	−0.872363	−	0.189771i	−0.626394	+	0.779507i	$0.715470\pi$
$18$	0.800541	−	0.599278i	0.188689	−	0.141251i
$19$	0.402082	+	0.258402i	0.0922439	+	0.0592816i	0.585950	−	0.810347i	$-0.300722\pi$
$19$	0.402082	+	0.258402i	0.0922439	+	0.0592816i	−0.493706	+	0.869629i	$0.664358\pi$
$20$	−1.97550	+	1.04756i	−0.441736	+	0.234242i
$21$	0.214447	−	0.730339i	0.0467962	−	0.159373i
$22$	−2.70553	−	2.70553i	−0.576820	−	0.576820i
$23$	2.66718	−	3.98574i	0.556145	−	0.831085i
$23$	2.66718	−	3.98574i	0.556145	−	0.831085i
$24$		−	1.00000i		−	0.204124i
$25$	2.59956	+	4.27110i	0.519913	+	0.854219i
$26$	1.39737	−	1.61265i	0.274046	−	0.316266i
$27$	0.977147	−	0.212565i	0.188052	−	0.0409082i
$28$	−0.456153	−	0.609350i	−0.0862049	−	0.115156i
$29$	1.30424	+	2.02944i	0.242192	+	0.376857i	0.940975	−	0.338476i	$-0.109911\pi$
$29$	1.30424	+	2.02944i	0.242192	+	0.376857i	−0.698784	+	0.715333i	$0.746275\pi$
$30$	−2.23215	+	0.132242i	−0.407534	+	0.0241439i
$31$	−1.58642	−	1.83082i	−0.284929	−	0.328826i	0.595184	−	0.803589i	$-0.297079\pi$
$31$	−1.58642	−	1.83082i	−0.284929	−	0.328826i	−0.880113	+	0.474764i	$0.842534\pi$
$32$	−0.800541	−	0.599278i	−0.141517	−	0.105938i
$33$	−1.33712	−	3.58495i	−0.232762	−	0.624060i
$34$	−3.53186	+	1.03705i	−0.605709	+	0.177852i
$35$	−1.29984	+	1.09879i	−0.219713	+	0.185729i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	2.32132	−	3.10092i	0.381623	−	0.509788i	−0.568066	−	0.822983i	$-0.692308\pi$
$37$	2.32132	−	3.10092i	0.381623	−	0.509788i	0.949689	+	0.313194i	$0.101399\pi$
$38$	0.476738	+	0.0340970i	0.0773371	+	0.00553126i
$39$	1.94101	−	0.886429i	0.310810	−	0.141942i
$40$	−1.23182	+	1.86618i	−0.194767	+	0.295069i
$41$	0.610814	−	4.24831i	0.0953932	−	0.663474i	−0.884879	−	0.465821i	$-0.845759\pi$
$41$	0.610814	−	4.24831i	0.0953932	−	0.663474i	0.980272	−	0.197653i	$-0.0633319\pi$
$42$	−0.161799	−	0.743777i	−0.0249661	−	0.114767i
$43$	0.197108	+	2.75593i	0.0300587	+	0.420276i	0.990095	+	0.140400i	$0.0448388\pi$
$43$	0.197108	+	2.75593i	0.0300587	+	0.420276i	−0.960036	+	0.279876i	$0.909707\pi$
$44$	−3.67121	−	1.07796i	−0.553455	−	0.162509i
$45$	−2.08537	−	0.806979i	−0.310869	−	0.120297i
$46$	0.430764	−	4.77645i	0.0635127	−	0.704249i
$47$	−3.20158	+	3.20158i	−0.466999	+	0.466999i	−0.900941	−	0.433942i	$-0.857122\pi$
$47$	−3.20158	+	3.20158i	−0.466999	+	0.466999i	0.433942	+	0.900941i	$0.357122\pi$
$48$	−0.479249	−	0.877679i	−0.0691736	−	0.126682i
$49$	4.85238	+	4.20461i	0.693197	+	0.600659i
$50$	4.32850	+	2.50281i	0.612142	+	0.353951i
$51$	−3.64350	−	0.523856i	−0.510192	−	0.0733545i
$52$	0.453580	−	2.08507i	0.0629003	−	0.289148i
$53$	1.42225	+	0.530471i	0.195361	+	0.0728658i	0.445240	−	0.895411i	$-0.353118\pi$
$53$	1.42225	+	0.530471i	0.195361	+	0.0728658i	−0.249879	+	0.968277i	$0.580391\pi$
$54$	0.755750	−	0.654861i	0.102844	−	0.0891153i
$55$	−1.92069	+	8.33725i	−0.258986	+	1.12419i
$56$	−0.692386	−	0.316202i	−0.0925240	−	0.0422543i
$57$	0.419492	+	0.229060i	0.0555630	+	0.0303397i
$58$	2.11731	+	1.15614i	0.278017	+	0.151809i
$59$	7.27790	+	3.32370i	0.947501	+	0.432709i	0.828378	−	0.560170i	$-0.189264\pi$
$59$	7.27790	+	3.32370i	0.947501	+	0.432709i	0.119124	+	0.992879i	$0.461991\pi$
$60$	−1.89574	+	1.18582i	−0.244739	+	0.153089i
$61$	−3.67344	+	3.18305i	−0.470336	+	0.407548i	−0.857517	−	0.514455i	$-0.827994\pi$
$61$	−3.67344	+	3.18305i	−0.470336	+	0.407548i	0.387182	+	0.922004i	$0.373449\pi$
$62$	−2.26978	−	0.846586i	−0.288263	−	0.107517i
$63$	0.161799	−	0.743777i	0.0203847	−	0.0937071i
$64$	−0.989821	−	0.142315i	−0.123728	−	0.0177894i
$65$	−4.71419	−	0.736727i	−0.584723	−	0.0913798i
$66$	−2.89164	−	2.50562i	−0.355937	−	0.308421i
$67$	3.93580	+	7.20789i	0.480835	+	0.880584i	0.999669	+	0.0257089i	$0.00818431\pi$
$67$	3.93580	+	7.20789i	0.480835	+	0.880584i	−0.518834	+	0.854875i	$0.673634\pi$
$68$	−2.60284	+	2.60284i	−0.315640	+	0.315640i
$69$	2.37604	−	4.16586i	0.286042	−	0.501511i
$70$	−0.614250	+	1.58733i	−0.0734169	+	0.189722i
$71$	3.48967	+	1.02466i	0.414147	+	0.121605i	0.482167	−	0.876079i	$-0.339850\pi$
$71$	3.48967	+	1.02466i	0.414147	+	0.121605i	−0.0680196	+	0.997684i	$0.521668\pi$
$72$	−0.0713392	−	0.997452i	−0.00840740	−	0.117551i
$73$	1.41187	+	6.49025i	0.165247	+	0.759627i	0.982933	+	0.183963i	$0.0588927\pi$
$73$	1.41187	+	6.49025i	0.165247	+	0.759627i	−0.817686	+	0.575664i	$0.804744\pi$
$74$	0.551261	−	3.83410i	0.0640828	−	0.445706i
$75$	2.89764	+	4.07476i	0.334590	+	0.470513i
$76$	0.434764	−	0.198550i	0.0498708	−	0.0227752i
$77$	−2.90497	−	0.207768i	−0.331052	−	0.0236773i
$78$	1.27876	−	1.70823i	0.144791	−	0.193419i
$79$	2.14420	−	4.69513i	0.241241	−	0.528244i	−0.749822	−	0.661640i	$-0.769861\pi$
$79$	2.14420	−	4.69513i	0.241241	−	0.528244i	0.991063	+	0.133396i	$0.0425882\pi$
$80$	−0.186773	+	2.22825i	−0.0208819	+	0.249126i
$81$	0.959493	−	0.281733i	0.106610	−	0.0313036i
$82$	−1.49990	−	4.02138i	−0.165636	−	0.444087i
$83$	0.565465	+	0.423302i	0.0620679	+	0.0464634i	0.629861	−	0.776708i	$-0.283112\pi$
$83$	0.565465	+	0.423302i	0.0620679	+	0.0464634i	−0.567793	+	0.823171i	$0.692203\pi$
$84$	−0.498462	−	0.575255i	−0.0543866	−	0.0627655i
$85$	6.15413	+	5.46573i	0.667510	+	0.592841i
$86$	1.49378	+	2.32436i	0.161078	+	0.250642i
$87$	1.44570	+	1.93122i	0.154995	+	0.207049i
$88$	−3.73875	+	0.813316i	−0.398552	+	0.0866998i
$89$	0.972526	−	1.12236i	0.103088	−	0.118969i	−0.701861	−	0.712314i	$-0.747647\pi$
$89$	0.972526	−	1.12236i	0.103088	−	0.118969i	0.804949	+	0.593344i	$0.202193\pi$
$90$	−2.21703	+	0.291145i	−0.233696	+	0.0306894i
$91$		−	1.62422i		−	0.170264i
$92$	−1.91103	−	4.39863i	−0.199239	−	0.458589i
$93$	−1.71298	−	1.71298i	−0.177628	−	0.177628i
$94$	−1.27561	+	4.34431i	−0.131569	+	0.448082i
$95$	−0.500688	−	0.944203i	−0.0513695	−	0.0968732i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	8.22520	−	6.15731i	0.835143	−	0.625180i	−0.0937222	−	0.995598i	$-0.529877\pi$
$97$	8.22520	−	6.15731i	0.835143	−	0.625180i	0.928865	+	0.370418i	$0.120786\pi$
$98$	6.27389	+	1.36480i	0.633758	+	0.137866i
$99$	−1.58946	−	3.48043i	−0.159747	−	0.349796i
$100$	4.99851	+	0.122238i	0.499851	+	0.0122238i
$101$	1.96156	+	13.6430i	0.195183	+	1.35752i	0.818027	+	0.575179i	$0.195068\pi$
$101$	1.96156	+	13.6430i	0.195183	+	1.35752i	−0.622845	+	0.782345i	$0.714023\pi$
$102$	−3.44888	+	1.28637i	−0.341490	+	0.127369i
$103$	−4.79010	+	8.77241i	−0.471982	+	0.864371i	0.527904	+	0.849304i	$0.322978\pi$
$103$	−4.79010	+	8.77241i	−0.471982	+	0.864371i	−0.999886	+	0.0150670i	$0.995204\pi$
$104$	−0.601172	−	2.04740i	−0.0589498	−	0.200765i
$105$	−1.21814	+	1.18872i	−0.118878	+	0.116007i
$106$	1.50250	−	0.216028i	0.145936	−	0.0209825i
$107$	−0.525609	+	7.34898i	−0.0508126	+	0.710453i	0.906648	+	0.421888i	$0.138633\pi$
$107$	−0.525609	+	7.34898i	−0.0508126	+	0.710453i	−0.957460	+	0.288564i	$0.906822\pi$
$108$	0.349464	−	0.936950i	0.0336272	−	0.0901580i
$109$	3.03951	−	1.95337i	0.291132	−	0.187099i	−0.386920	−	0.922113i	$-0.626461\pi$
$109$	3.03951	−	1.95337i	0.291132	−	0.187099i	0.678052	+	0.735014i	$0.262825\pi$
$110$	2.30987	+	8.23792i	0.220237	+	0.785455i
$111$	2.09419	−	3.25862i	0.198772	−	0.309295i
$112$	−0.759233	+	0.0543014i	−0.0717407	+	0.00513100i
$113$	−11.9558	+	6.52834i	−1.12470	+	0.614134i	−0.930304	−	0.366788i	$-0.880457\pi$
$113$	−11.9558	+	6.52834i	−1.12470	+	0.614134i	−0.194399	+	0.980923i	$0.562276\pi$
$114$	0.477956			0.0447647
$115$	−9.56570	+	4.84741i	−0.892006	+	0.452023i
$116$	2.41240			0.223986
$117$	1.87283	−	1.02264i	0.173143	−	0.0945432i
$118$	7.98054	−	0.570779i	0.734668	−	0.0525445i
$119$	−1.51479	+	2.35706i	−0.138861	+	0.216072i
$120$	−1.09554	+	1.94930i	−0.100009	+	0.177946i
$121$	−3.06196	+	1.96780i	−0.278360	+	0.178891i
$122$	−1.69863	+	4.55419i	−0.153786	+	0.412317i
$123$	0.306187	−	4.28106i	0.0276080	−	0.386010i
$124$	−2.39787	+	0.344761i	−0.215335	+	0.0309605i
$125$	−0.388156	−	11.1736i	−0.0347178	−	0.999397i
$126$	−0.214447	−	0.730339i	−0.0191045	−	0.0650638i
$127$	5.32619	−	9.75419i	0.472623	−	0.865545i	−0.527252	−	0.849709i	$-0.676777\pi$
$127$	5.32619	−	9.75419i	0.472623	−	0.865545i	0.999875	−	0.0158353i	$-0.00504073\pi$
$128$	−0.936950	+	0.349464i	−0.0828154	+	0.0308886i
$129$	0.393212	+	2.73485i	0.0346204	+	0.240790i
$130$	−4.49062	+	1.61266i	−0.393854	+	0.141440i
$131$	−7.78879	−	17.0551i	−0.680510	−	1.49011i	−0.862102	−	0.506735i	$-0.830852\pi$
$131$	−7.78879	−	17.0551i	−0.680510	−	1.49011i	0.181592	−	0.983374i	$-0.441875\pi$
$132$	−3.73875	−	0.813316i	−0.325417	−	0.0707901i
$133$	0.291242	−	0.218021i	0.0252539	−	0.0189048i
$134$	6.90875	+	4.43998i	0.596825	+	0.383556i
$135$	−2.13763	−	0.656154i	−0.183978	−	0.0564728i
$136$	−1.03705	+	3.53186i	−0.0889261	+	0.302855i
$137$	−5.75959	−	5.75959i	−0.492075	−	0.492075i	0.416885	−	0.908959i	$-0.363122\pi$
$137$	−5.75959	−	5.75959i	−0.492075	−	0.492075i	−0.908959	+	0.416885i	$0.863122\pi$
$138$	0.0889186	−	4.79501i	0.00756926	−	0.408178i
$139$			11.6902i			0.991551i	0.868451	+	0.495775i	$0.165116\pi$
$139$			11.6902i			0.991551i	−0.868451	+	0.495775i	$0.834884\pi$
$140$	0.221611	+	1.68754i	0.0187296	+	0.142623i
$141$	−2.96503	+	3.42182i	−0.249700	+	0.288169i
$142$	3.55387	−	0.773098i	0.298235	−	0.0648769i
$143$	−4.89279	−	6.53601i	−0.409156	−	0.546568i
$144$	−0.540641	−	0.841254i	−0.0450534	−	0.0701045i
$145$	−0.319020	−	5.38485i	−0.0264931	−	0.447187i
$146$	4.34962	+	5.01972i	0.359977	+	0.415435i
$147$	5.13997	+	3.84773i	0.423937	+	0.317356i
$148$	−1.35366	−	3.62930i	−0.111270	−	0.298327i
$149$	10.3170	−	3.02936i	0.845205	−	0.248174i	0.169668	−	0.985501i	$-0.445730\pi$
$149$	10.3170	−	3.02936i	0.845205	−	0.248174i	0.675536	+	0.737327i	$0.263912\pi$
$150$	4.49602	+	2.18765i	0.367099	+	0.178621i
$151$	3.96417	−	8.68031i	0.322599	−	0.706394i	−0.676962	−	0.736018i	$-0.736704\pi$
$151$	3.96417	−	8.68031i	0.322599	−	0.706394i	0.999561	+	0.0296243i	$0.00943110\pi$
$152$	0.286428	−	0.382623i	0.0232324	−	0.0310349i
$153$	−3.67159	−	0.262597i	−0.296830	−	0.0212297i
$154$	−2.64920	+	1.20985i	−0.213479	+	0.0974926i
$155$	1.08666	+	5.30682i	0.0872825	+	0.426254i
$156$	0.303677	−	2.11212i	0.0243136	−	0.169105i
$157$	1.47772	+	6.79298i	0.117935	+	0.542139i	0.997763	+	0.0668471i	$0.0212940\pi$
$157$	1.47772	+	6.79298i	0.117935	+	0.542139i	−0.879828	+	0.475292i	$0.842342\pi$
$158$	−0.368223	−	5.14842i	−0.0292942	−	0.409587i
$159$	1.45647	+	0.427657i	0.115505	+	0.0339154i
$160$	0.903962	+	2.04520i	0.0714644	+	0.161687i
$161$	−2.13308	−	2.96240i	−0.168110	−	0.233470i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	10.1272	+	18.5465i	0.793221	+	1.45268i	0.889311	+	0.457303i	$0.151184\pi$
$163$	10.1272	+	18.5465i	0.793221	+	1.45268i	−0.0960904	+	0.995373i	$0.530634\pi$
$164$	−3.24367	−	2.81066i	−0.253288	−	0.219475i
$165$	−1.32103	+	8.45303i	−0.102842	+	0.658067i
$166$	0.699164	+	0.100525i	0.0542656	+	0.00780222i
$167$	1.70593	−	7.84206i	0.132009	−	0.606836i	−0.862841	−	0.505476i	$-0.831317\pi$
$167$	1.70593	−	7.84206i	0.132009	−	0.606836i	0.994850	−	0.101360i	$-0.0323195\pi$
$168$	−0.713180	−	0.266002i	−0.0550230	−	0.0205225i
$169$	−6.38361	+	5.53143i	−0.491047	+	0.425495i
$170$	8.02080	+	1.84779i	0.615167	+	0.141719i
$171$	0.434764	+	0.198550i	0.0332472	+	0.0151835i
$172$	2.42500	+	1.32415i	0.184905	+	0.100966i
$173$	−11.4585	−	6.25684i	−0.871177	−	0.475698i	−0.0195267	−	0.999809i	$-0.506216\pi$
$173$	−11.4585	−	6.25684i	−0.871177	−	0.475698i	−0.851650	+	0.524111i	$0.824398\pi$
$174$	2.19440	+	1.00215i	0.166357	+	0.0759725i
$175$	3.73755	−	0.717834i	0.282532	−	0.0542632i
$176$	−2.89164	+	2.50562i	−0.217966	+	0.188869i
$177$	7.49646	+	2.79604i	0.563469	+	0.210163i
$178$	0.315678	−	1.45115i	0.0236611	−	0.108768i
$179$	14.5315	+	2.08931i	1.08613	+	0.156163i	0.662050	−	0.749460i	$-0.269687\pi$
$179$	14.5315	+	2.08931i	1.08613	+	0.156163i	0.424085	+	0.905622i	$0.360596\pi$
$180$	−1.80631	+	1.31804i	−0.134635	+	0.0982411i
$181$	−11.4645	−	9.93407i	−0.852152	−	0.738394i	0.114790	−	0.993390i	$-0.463380\pi$
$181$	−11.4645	−	9.93407i	−0.852152	−	0.738394i	−0.966942	+	0.254996i	$0.917926\pi$
$182$	−0.778405	−	1.42554i	−0.0576992	−	0.105668i
$183$	−3.43700	+	3.43700i	−0.254071	+	0.254071i
$184$	−3.78531	−	2.94472i	−0.279057	−	0.217088i
$185$	−7.92216	+	3.50152i	−0.582449	+	0.257437i
$186$	−2.32440	−	0.682504i	−0.170433	−	0.0500437i
$187$	1.00475	+	14.0482i	0.0734744	+	1.02731i
$188$	0.962436	+	4.42425i	0.0701928	+	0.322671i
$189$	0.108326	−	0.753424i	0.00787956	−	0.0548036i
$190$	−0.891952	−	0.588753i	−0.0647090	−	0.0427126i
$191$	21.2098	−	9.68618i	1.53469	−	0.700868i	0.544261	−	0.838916i	$-0.316810\pi$
$191$	21.2098	−	9.68618i	1.53469	−	0.700868i	0.990425	+	0.138048i	$0.0440830\pi$
$192$	−0.997452	−	0.0713392i	−0.0719849	−	0.00514846i
$193$	−12.6623	+	16.9148i	−0.911449	+	1.21755i	0.0641383	+	0.997941i	$0.479570\pi$
$193$	−12.6623	+	16.9148i	−0.911449	+	1.21755i	−0.975587	+	0.219612i	$0.929521\pi$
$194$	4.26820	−	9.34606i	0.306439	−	0.671008i
$195$	−4.75474	−	0.398544i	−0.340494	−	0.0285403i
$196$	6.16054	−	1.80890i	0.440038	−	0.129207i
$197$	−0.0704870	−	0.188983i	−0.00502199	−	0.0134645i	0.934415	−	0.356187i	$-0.115924\pi$
$197$	−0.0704870	−	0.188983i	−0.00502199	−	0.0134645i	−0.939437	+	0.342723i	$0.888651\pi$
$198$	−3.06303	−	2.29295i	−0.217680	−	0.162953i
$199$	5.55458	+	6.41033i	0.393754	+	0.454416i	0.917664	−	0.397358i	$-0.130073\pi$
$199$	5.55458	+	6.41033i	0.393754	+	0.454416i	−0.523910	+	0.851774i	$0.675527\pi$
$200$	4.44567	−	2.28824i	0.314356	−	0.161803i
$201$	4.43998	+	6.90875i	0.313172	+	0.487305i
$202$	8.25999	+	11.0341i	0.581171	+	0.776354i
$203$	1.79429	−	0.390323i	0.125934	−	0.0273953i
$204$	−2.41052	+	2.78189i	−0.168770	+	0.194771i
$205$	−5.84487	+	7.61206i	−0.408224	+	0.531649i
$206$			9.99501i			0.696385i
$207$	2.07280	−	4.32475i	0.144070	−	0.300591i
$208$	−1.50885	−	1.50885i	−0.104620	−	0.104620i
$209$	0.515219	−	1.75467i	0.0356384	−	0.121373i
$210$	−0.499446	+	1.62710i	−0.0344651	+	0.112281i
$211$	2.11962	+	1.36220i	0.145921	+	0.0937775i	0.611564	−	0.791195i	$-0.290541\pi$
$211$	2.11962	+	1.36220i	0.145921	+	0.0937775i	−0.465643	+	0.884972i	$0.654177\pi$
$212$	1.21519	−	0.909677i	0.0834593	−	0.0624769i
$213$	3.55387	+	0.773098i	0.243507	+	0.0529718i
$214$	3.06067	+	6.70194i	0.209223	+	0.458135i
$215$	2.63502	−	5.58809i	0.179707	−	0.381104i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	−1.72770	+	0.644398i	−0.117284	+	0.0437446i
$218$	1.73156	−	3.17112i	0.117276	−	0.214775i
$219$	1.87128	+	6.37300i	0.126449	+	0.430647i
$220$	5.97534	+	6.12325i	0.402857	+	0.412829i
$221$	−7.77464	+	1.11782i	−0.522979	+	0.0751930i
$222$	0.276335	−	3.86366i	0.0185464	−	0.259312i
$223$	−0.741723	+	1.98864i	−0.0496694	+	0.133169i	−0.959416	−	0.281996i	$-0.909003\pi$
$223$	−0.741723	+	1.98864i	−0.0496694	+	0.133169i	0.909746	+	0.415165i	$0.136276\pi$
$224$	−0.640339	+	0.411521i	−0.0427844	+	0.0274959i
$225$	3.18094	+	3.85767i	0.212063	+	0.257178i
$226$	−7.36462	+	11.4596i	−0.489887	+	0.762279i
$227$	−16.7456	+	1.19767i	−1.11144	+	0.0794919i	−0.614962	−	0.788557i	$-0.710829\pi$
$227$	−16.7456	+	1.19767i	−1.11144	+	0.0794919i	−0.496479	+	0.868048i	$0.665374\pi$
$228$	0.419492	−	0.229060i	0.0277815	−	0.0151699i
$229$	24.4597			1.61634			0.808171	−	0.588948i	$-0.200458\pi$
$229$	24.4597			1.61634			0.808171	+	0.588948i	$0.200458\pi$
$230$	−6.07250	+	8.83882i	−0.400409	+	0.582815i
$231$	−2.91239			−0.191621
$232$	2.11731	−	1.15614i	0.139008	−	0.0759043i
$233$	−12.1534	+	0.869230i	−0.796198	+	0.0569452i	−0.463510	−	0.886092i	$-0.653410\pi$
$233$	−12.1534	+	0.869230i	−0.796198	+	0.0569452i	−0.332688	+	0.943037i	$0.607956\pi$
$234$	1.15364	−	1.79510i	0.0754159	−	0.117349i
$235$	9.74833	−	2.73337i	0.635911	−	0.178306i
$236$	6.73081	−	4.32563i	0.438138	−	0.281574i
$237$	1.80379	−	4.83614i	0.117168	−	0.314141i
$238$	−0.199882	+	2.79471i	−0.0129564	+	0.181154i
$239$	28.0439	−	4.03211i	1.81401	−	0.260815i	0.850019	−	0.526752i	$-0.176590\pi$
$239$	28.0439	−	4.03211i	1.81401	−	0.260815i	0.963991	+	0.265936i	$0.0856811\pi$
$240$	−0.0273353	+	2.23590i	−0.00176449	+	0.144327i
$241$	−3.22361	−	10.9786i	−0.207651	−	0.707194i	−0.995787	−	0.0916933i	$-0.970772\pi$
$241$	−3.22361	−	10.9786i	−0.207651	−	0.707194i	0.788136	−	0.615501i	$-0.211046\pi$
$242$	−1.74435	+	3.19454i	−0.112131	+	0.205353i
$243$	0.936950	−	0.349464i	0.0601054	−	0.0224181i
$244$	0.691744	+	4.81118i	0.0442843	+	0.308004i
$245$	−4.85242	−	13.5121i	−0.310010	−	0.863254i
$246$	−1.78296	−	3.90413i	−0.113677	−	0.248918i
$247$	0.996574	+	0.216791i	0.0634105	+	0.0137941i
$248$	−1.93933	+	1.45177i	−0.123148	+	0.0921872i
$249$	0.594222	+	0.381884i	0.0376573	+	0.0242009i
$250$	−5.69561	−	9.62081i	−0.360222	−	0.608473i
$251$	−2.53587	+	8.63636i	−0.160062	+	0.545122i	0.839935	+	0.542688i	$0.182593\pi$
$251$	−2.53587	+	8.63636i	−0.160062	+	0.545122i	−0.999997	+	0.00243486i	$0.999225\pi$
$252$	−0.538230	−	0.538230i	−0.0339053	−	0.0339053i
$253$	−17.5076	−	5.49528i	−1.10069	−	0.345485i
$254$		−	11.1136i		−	0.697331i
$255$	6.52838	+	5.01277i	0.408823	+	0.313912i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−18.7242	+	4.07320i	−1.16798	+	0.254079i	−0.754418	−	0.656395i	$-0.772081\pi$
$257$	−18.7242	+	4.07320i	−1.16798	+	0.254079i	−0.413566	+	0.910474i	$0.635717\pi$
$258$	1.65579	+	2.21187i	0.103085	+	0.137705i
$259$	−1.59404	−	2.48037i	−0.0990487	−	0.154123i
$260$	−3.16846	+	3.56752i	−0.196499	+	0.221248i
$261$	1.57979	+	1.82317i	0.0977863	+	0.112851i
$262$	−15.0097	−	11.2361i	−0.927302	−	0.694169i
$263$	−7.92785	−	21.2554i	−0.488852	−	1.31066i	−0.914064	−	0.405570i	$-0.867073\pi$
$263$	−7.92785	−	21.2554i	−0.488852	−	1.31066i	0.425212	−	0.905094i	$-0.360200\pi$
$264$	−3.67121	+	1.07796i	−0.225947	+	0.0663441i
$265$	−2.19124	−	2.59219i	−0.134607	−	0.159237i
$266$	0.151131	−	0.330930i	0.00926642	−	0.0202906i
$267$	0.889981	−	1.18887i	0.0544659	−	0.0727580i
$268$	8.19152	+	0.585869i	0.500377	+	0.0357876i
$269$	−10.7483	+	4.90859i	−0.655336	+	0.299282i	−0.715195	−	0.698925i	$-0.753662\pi$
$269$	−10.7483	+	4.90859i	−0.655336	+	0.299282i	0.0598591	+	0.998207i	$0.480935\pi$
$270$	−2.19061	+	0.448564i	−0.133317	+	0.0272988i
$271$	4.13826	−	28.7823i	0.251382	−	1.74840i	−0.338554	−	0.940947i	$-0.609938\pi$
$271$	4.13826	−	28.7823i	0.251382	−	1.74840i	0.589936	−	0.807450i	$-0.299153\pi$
$272$	0.782446	+	3.59684i	0.0474427	+	0.218091i
$273$	−0.115870	−	1.62008i	−0.00701280	−	0.0980518i
$274$	−7.81534	−	2.29479i	−0.472142	−	0.138633i
$275$	12.8778	−	14.1476i	0.776563	−	0.853133i
$276$	−2.21996	−	4.25109i	−0.133626	−	0.255886i
$277$	−0.981150	+	0.981150i	−0.0589516	+	0.0589516i	−0.735968	−	0.677016i	$-0.763273\pi$
$277$	−0.981150	+	0.981150i	−0.0589516	+	0.0589516i	0.677016	+	0.735968i	$0.263273\pi$
$278$	5.60252	+	10.2603i	0.336017	+	0.615369i
$279$	−1.83082	−	1.58642i	−0.109609	−	0.0949763i
$280$	1.00326	+	1.37491i	0.0599561	+	0.0821669i
$281$	−1.14077	−	0.164018i	−0.0680528	−	0.00978452i	0.108204	−	0.994129i	$-0.465490\pi$
$281$	−1.14077	−	0.164018i	−0.0680528	−	0.00978452i	−0.176257	+	0.984344i	$0.556399\pi$
$282$	−0.962436	+	4.42425i	−0.0573122	+	0.263460i
$283$	20.9687	+	7.82091i	1.24646	+	0.464905i	0.884172	−	0.467162i	$-0.154724\pi$
$283$	20.9687	+	7.82091i	1.24646	+	0.464905i	0.362286	+	0.932067i	$0.381996\pi$
$284$	2.74865	−	2.38172i	0.163103	−	0.141329i
$285$	−0.566771	−	0.906079i	−0.0335726	−	0.0536715i
$286$	−7.42668	−	3.39165i	−0.439149	−	0.200552i
$287$	−2.86733	−	1.56568i	−0.169253	−	0.0924192i
$288$	−0.877679	−	0.479249i	−0.0517177	−	0.0282400i
$289$	−3.13867	−	1.43338i	−0.184628	−	0.0843167i
$290$	−2.86068	−	4.57328i	−0.167985	−	0.268552i
$291$	7.76499	−	6.72840i	0.455192	−	0.394426i
$292$	6.22326	+	2.32116i	0.364189	+	0.135835i
$293$	−6.98427	+	32.1062i	−0.408026	+	1.87566i	0.0703726	+	0.997521i	$0.477581\pi$
$293$	−6.98427	+	32.1062i	−0.408026	+	1.87566i	−0.478398	+	0.878143i	$0.658782\pi$
$294$	6.35526	+	0.913749i	0.370647	+	0.0532909i
$295$	−10.5456	−	14.4522i	−0.613986	−	0.841438i
$296$	−2.92742	−	2.53662i	−0.170153	−	0.147438i
$297$	−1.83370	−	3.35817i	−0.106402	−	0.194861i
$298$	7.60323	−	7.60323i	0.440443	−	0.440443i
$299$	2.36032	−	9.95762i	0.136501	−	0.575864i
$300$	4.99449	−	0.234663i	0.288357	−	0.0135483i
$301$	2.01791	+	0.592511i	0.116310	+	0.0341518i
$302$	−0.680766	−	9.51835i	−0.0391737	−	0.547719i
$303$	2.92984	+	13.4683i	0.168315	+	0.773731i
$304$	0.0680202	−	0.473091i	0.00390123	−	0.0271336i
$305$	10.6478	−	2.18032i	0.609693	−	0.124845i
$306$	−3.34832	+	1.52913i	−0.191411	+	0.0874145i
$307$	−19.7503	−	1.41257i	−1.12721	−	0.0806194i	−0.504744	−	0.863269i	$-0.668413\pi$
$307$	−19.7503	−	1.41257i	−1.12721	−	0.0806194i	−0.622463	+	0.782650i	$0.713868\pi$
$308$	−1.74533	+	2.33149i	−0.0994495	+	0.132849i
$309$	−4.15208	+	9.09178i	−0.236203	+	0.517213i
$310$	3.49703	+	4.13690i	0.198618	+	0.234960i
$311$	24.9753	−	7.33341i	1.41622	−	0.415840i	0.517998	−	0.855382i	$-0.326677\pi$
$311$	24.9753	−	7.33341i	1.41622	−	0.415840i	0.898222	+	0.439542i	$0.144859\pi$
$312$	−0.745701	−	1.99930i	−0.0422170	−	0.113188i
$313$	−24.4909	−	18.3336i	−1.38431	−	1.03628i	−0.993260	−	0.115907i	$-0.963023\pi$
$313$	−24.4909	−	18.3336i	−1.38431	−	1.03628i	−0.391046	−	0.920371i	$-0.627887\pi$
$314$	4.55250	+	5.25386i	0.256912	+	0.296493i
$315$	−1.13024	+	1.27259i	−0.0636816	+	0.0717022i
$316$	−2.79056	−	4.34219i	−0.156981	−	0.244267i
$317$	−18.6170	−	24.8694i	−1.04564	−	1.39681i	−0.914097	−	0.405496i	$-0.867099\pi$
$317$	−18.6170	−	24.8694i	−1.04564	−	1.39681i	−0.131539	−	0.991311i	$-0.541992\pi$
$318$	1.48327	−	0.322665i	0.0831774	−	0.0180941i
$319$	6.04456	−	6.97580i	0.338431	−	0.390570i
$320$	1.77355	+	1.36181i	0.0991444	+	0.0761274i
$321$			7.36775i			0.411228i
$322$	−3.29188	−	1.57776i	−0.183449	−	0.0879250i
$323$	−1.24404	−	1.24404i	−0.0692203	−	0.0692203i
$324$	0.281733	−	0.959493i	0.0156518	−	0.0533052i
$325$	8.38227	+	6.60071i	0.464965	+	0.366142i
$326$	17.7768	+	11.4245i	0.984566	+	0.632742i
$327$	2.89241	−	2.16523i	0.159951	−	0.119738i
$328$	−4.19391	−	0.912329i	−0.231570	−	0.0503749i
$329$	1.43168	+	3.13493i	0.0789308	+	0.172834i
$330$	2.89167	+	8.05215i	0.159181	+	0.443256i
$331$	−0.256742	−	1.78568i	−0.0141118	−	0.0981498i	0.981548	−	0.191215i	$-0.0612427\pi$
$331$	−0.256742	−	1.78568i	−0.0141118	−	0.0981498i	−0.995660	+	0.0930649i	$0.970334\pi$
$332$	0.661818	−	0.246845i	0.0363220	−	0.0135474i
$333$	1.85639	−	3.39972i	0.101729	−	0.186303i
$334$	−2.26103	−	7.70037i	−0.123718	−	0.421346i
$335$	0.224490	−	18.3622i	0.0122652	−	1.00323i
$336$	−0.753424	+	0.108326i	−0.0411027	+	0.00590967i
$337$	0.0239514	−	0.334884i	0.00130472	−	0.0182423i	−0.996758	−	0.0804574i	$-0.974362\pi$
$337$	0.0239514	−	0.334884i	0.00130472	−	0.0182423i	0.998063	+	0.0622150i	$0.0198165\pi$
$338$	−2.95183	+	7.91416i	−0.160558	+	0.430474i
$339$	−11.4596	+	7.36462i	−0.622398	+	0.399991i
$340$	7.92524	−	2.22219i	0.429806	−	0.120515i
$341$	−5.01123	+	7.79762i	−0.271373	+	0.422265i
$342$	0.476738	−	0.0340970i	0.0257790	−	0.00184375i
$343$	8.96584	−	4.89572i	0.484110	−	0.264344i
$344$	2.76297			0.148969
$345$	−9.19552	+	5.51746i	−0.495070	+	0.297050i
$346$	−13.0555			−0.701868
$347$	−7.69316	+	4.20078i	−0.412990	+	0.225510i	−0.672291	−	0.740287i	$-0.734690\pi$
$347$	−7.69316	+	4.20078i	−0.412990	+	0.225510i	0.259301	+	0.965797i	$0.416508\pi$
$348$	2.40625	−	0.172099i	0.128989	−	0.00922545i
$349$	−12.8120	+	19.9358i	−0.685810	+	1.06714i	0.307487	+	0.951552i	$0.400512\pi$
$349$	−12.8120	+	19.9358i	−0.685810	+	1.06714i	−0.993297	+	0.115589i	$0.963125\pi$
$350$	2.93635	−	2.42125i	0.156954	−	0.129421i
$351$	1.79510	−	1.15364i	0.0958154	−	0.0615768i
$352$	−1.33712	+	3.58495i	−0.0712686	+	0.191079i
$353$	−2.11431	+	29.5619i	−0.112533	+	1.57342i	0.556920	+	0.830566i	$0.311983\pi$
$353$	−2.11431	+	29.5619i	−0.112533	+	1.57342i	−0.669453	+	0.742854i	$0.733472\pi$
$354$	7.91949	−	1.13865i	0.420916	−	0.0605186i
$355$	−5.67986	−	5.82046i	−0.301456	−	0.308918i
$356$	−0.418398	−	1.42493i	−0.0221750	−	0.0755213i
$357$	−1.34278	+	2.45912i	−0.0710676	+	0.130151i
$358$	13.7553	−	5.13046i	0.726989	−	0.271153i
$359$	−1.15549	−	8.03664i	−0.0609847	−	0.424158i	−0.997327	−	0.0730691i	$-0.976721\pi$
$359$	−1.15549	−	8.03664i	−0.0609847	−	0.424158i	0.936342	−	0.351089i	$-0.114188\pi$
$360$	−0.953692	+	2.02249i	−0.0502640	+	0.106595i
$361$	−7.79799	−	17.0752i	−0.410420	−	0.898695i
$362$	−14.8231	−	3.22456i	−0.779083	−	0.169479i
$363$	−2.91378	+	2.18123i	−0.152934	+	0.114485i
$364$	−1.36638	−	0.878119i	−0.0716178	−	0.0460259i
$365$	4.35821	−	14.1982i	0.228119	−	0.743170i
$366$	−1.36941	+	4.66377i	−0.0715800	+	0.243779i
$367$	−15.3107	−	15.3107i	−0.799211	−	0.799211i	0.183760	−	0.982971i	$-0.441173\pi$
$367$	−15.3107	−	15.3107i	−0.799211	−	0.799211i	−0.982971	+	0.183760i	$0.941173\pi$
$368$	−4.73355	−	0.770414i	−0.246753	−	0.0401606i
$369$		−	4.29199i		−	0.223432i
$370$	−5.27501	+	6.86990i	−0.274235	+	0.357149i
$371$	0.756643	−	0.873212i	0.0392829	−	0.0453349i
$372$	−2.36716	+	0.514945i	−0.122732	+	0.0266987i
$373$	−20.2441	−	27.0430i	−1.04820	−	1.40023i	−0.912306	−	0.409510i	$-0.865700\pi$
$373$	−20.2441	−	27.0430i	−1.04820	−	1.40023i	−0.135895	−	0.990723i	$-0.543391\pi$
$374$	7.61443	+	11.8483i	0.393733	+	0.612661i
$375$	−1.18428	−	11.1174i	−0.0611561	−	0.574102i
$376$	2.96503	+	3.42182i	0.152909	+	0.176467i
$377$	4.12092	+	3.08489i	0.212238	+	0.158880i
$378$	−0.266002	−	0.713180i	−0.0136817	−	0.0366820i
$379$	−12.6670	+	3.71938i	−0.650662	+	0.191052i	−0.590375	−	0.807129i	$-0.701020\pi$
$379$	−12.6670	+	3.71938i	−0.650662	+	0.191052i	−0.0602878	+	0.998181i	$0.519202\pi$
$380$	−1.06501	−	0.0892692i	−0.0546337	−	0.00457942i
$381$	4.61676	−	10.1093i	0.236524	−	0.517915i
$382$	13.9733	−	18.6661i	0.714936	−	0.955042i
$383$	14.6906	+	1.05069i	0.750656	+	0.0536880i	0.441424	−	0.897299i	$-0.354473\pi$
$383$	14.6906	+	1.05069i	0.750656	+	0.0536880i	0.309232	+	0.950987i	$0.399928\pi$
$384$	−0.909632	+	0.415415i	−0.0464195	+	0.0211991i
$385$	5.43505	+	3.58753i	0.276996	+	0.182837i
$386$	−3.00700	+	20.9141i	−0.153052	+	1.06450i
$387$	0.587312	+	2.69983i	0.0298547	+	0.137240i
$388$	−0.732978	−	10.2484i	−0.0372113	−	0.520282i
$389$	−34.0453	−	9.99660i	−1.72617	−	0.506848i	−0.739999	−	0.672608i	$-0.765174\pi$
$389$	−34.0453	−	9.99660i	−1.72617	−	0.506848i	−0.986166	+	0.165760i	$0.946992\pi$
$390$	−4.36413	+	1.92891i	−0.220987	+	0.0976741i
$391$	−12.7121	+	12.2492i	−0.642876	+	0.619468i
$392$	4.54006	−	4.54006i	0.229308	−	0.229308i
$393$	−8.98564	−	16.4560i	−0.453266	−	0.830094i
$394$	−0.152435	−	0.132086i	−0.00767956	−	0.00665438i
$395$	−9.32342	+	6.80317i	−0.469112	+	0.342305i
$396$	−3.78725	−	0.544524i	−0.190316	−	0.0273634i
$397$	7.13860	−	32.8156i	0.358276	−	1.64697i	−0.346876	−	0.937911i	$-0.612758\pi$
$397$	7.13860	−	32.8156i	0.358276	−	1.64697i	0.705152	−	0.709056i	$-0.250879\pi$
$398$	7.94728	+	2.96418i	0.398361	+	0.148581i
$399$	0.274947	−	0.238243i	0.0137646	−	0.0119271i
$400$	2.80523	−	4.13892i	0.140261	−	0.206946i
$401$	7.46094	+	3.40730i	0.372582	+	0.170152i	0.592901	−	0.805275i	$-0.297983\pi$
$401$	7.46094	+	3.40730i	0.372582	+	0.170152i	−0.220319	+	0.975428i	$0.570710\pi$
$402$	7.20789	+	3.93580i	0.359497	+	0.196300i
$403$	−4.53697	−	2.47737i	−0.226003	−	0.123407i
$404$	12.5377	+	5.72577i	0.623773	+	0.284868i
$405$	−2.17899	−	0.501986i	−0.108275	−	0.0249439i
$406$	1.38775	−	1.20249i	0.0688727	−	0.0596785i
$407$	−13.8864	−	5.17937i	−0.688324	−	0.256732i
$408$	−0.782446	+	3.59684i	−0.0387368	+	0.178070i
$409$	33.5296	+	4.82082i	1.65793	+	0.238374i	0.906733	−	0.421705i	$-0.138568\pi$
$409$	33.5296	+	4.82082i	1.65793	+	0.238374i	0.751196	+	0.660079i	$0.229477\pi$
$410$	−1.48185	+	9.48210i	−0.0731833	+	0.468287i
$411$	−6.15579	−	5.33403i	−0.303643	−	0.263108i
$412$	4.79010	+	8.77241i	0.235991	+	0.432185i
$413$	4.30634	−	4.30634i	0.211901	−	0.211901i
$414$	−0.253380	−	4.78913i	−0.0124529	−	0.235373i
$415$	−0.638516	−	1.44464i	−0.0313435	−	0.0709144i
$416$	−2.04740	−	0.601172i	−0.100382	−	0.0294749i
$417$	0.833970	+	11.6604i	0.0408397	+	0.571013i
$418$	−0.388729	−	1.78696i	−0.0190134	−	0.0874030i
$419$	−1.12235	+	7.80612i	−0.0548304	+	0.381354i	0.943867	+	0.330326i	$0.107159\pi$
$419$	−1.12235	+	7.80612i	−0.0548304	+	0.381354i	−0.998697	+	0.0510277i	$0.983750\pi$
$420$	0.341435	+	1.66743i	0.0166603	+	0.0813625i
$421$	13.0850	−	5.97573i	0.637725	−	0.291239i	−0.0701936	−	0.997533i	$-0.522362\pi$
$421$	13.0850	−	5.97573i	0.637725	−	0.291239i	0.707918	+	0.706294i	$0.249634\pi$
$422$	2.51318	+	0.179746i	0.122340	+	0.00874990i
$423$	−2.71336	+	3.62463i	−0.131928	+	0.176235i
$424$	0.630582	−	1.38078i	0.0306237	−	0.0670566i
$425$	−6.00832	−	17.3965i	−0.291446	−	0.843854i
$426$	3.48967	−	1.02466i	0.169075	−	0.0496449i
$427$	1.29295	+	3.46652i	0.0625700	+	0.167757i
$428$	5.89819	+	4.41533i	0.285100	+	0.213423i
$429$	−5.34660	−	6.17031i	−0.258136	−	0.297905i
$430$	−0.365380	−	6.16738i	−0.0176202	−	0.297417i
$431$	17.1350	+	26.6626i	0.825364	+	1.28429i	0.956149	+	0.292881i	$0.0946140\pi$
$431$	17.1350	+	26.6626i	0.825364	+	1.28429i	−0.130785	+	0.991411i	$0.541750\pi$
$432$	−0.599278	−	0.800541i	−0.0288328	−	0.0385161i
$433$	−6.59901	+	1.43553i	−0.317128	+	0.0689870i	−0.368312	−	0.929702i	$-0.620064\pi$
$433$	−6.59901	+	1.43553i	−0.317128	+	0.0689870i	0.0511838	+	0.998689i	$0.483701\pi$
$434$	−1.20754	+	1.39357i	−0.0579636	+	0.0668936i
$435$	−0.702357	−	5.34837i	−0.0336755	−	0.256435i
$436$		−	3.61307i		−	0.173035i
$437$	2.10235	−	0.913390i	0.100569	−	0.0436934i
$438$	4.69664	+	4.69664i	0.224414	+	0.224414i
$439$	6.42342	−	21.8762i	0.306573	−	1.04409i	−0.651756	−	0.758428i	$-0.725968\pi$
$439$	6.42342	−	21.8762i	0.306573	−	1.04409i	0.958330	−	0.285664i	$-0.0922143\pi$
$440$	8.17899	+	2.51057i	0.389918	+	0.119687i
$441$	5.40137	+	3.47125i	0.257208	+	0.165298i
$442$	−6.28792	+	4.70708i	−0.299086	+	0.223893i
$443$	32.7002	+	7.11349i	1.55363	+	0.337972i	0.905765	−	0.423780i	$-0.139297\pi$
$443$	32.7002	+	7.11349i	1.55363	+	0.337972i	0.647868	+	0.761752i	$0.275661\pi$
$444$	−1.60912	−	3.52349i	−0.0763656	−	0.167217i
$445$	−3.12534	+	1.12236i	−0.148155	+	0.0532052i
$446$	0.302057	+	2.10085i	0.0143028	+	0.0994783i
$447$	10.0746	−	3.75765i	0.476514	−	0.177731i
$448$	−0.364791	+	0.668065i	−0.0172348	+	0.0315631i
$449$	1.15769	+	3.94273i	0.0546348	+	0.186069i	0.982289	−	0.187371i	$-0.0599965\pi$
$449$	1.15769	+	3.94273i	0.0546348	+	0.186069i	−0.927655	+	0.373440i	$0.878178\pi$
$450$	4.64063	+	1.86133i	0.218761	+	0.0877439i
$451$	−16.2548	+	2.33709i	−0.765411	+	0.110049i
$452$	−0.971783	+	13.5873i	−0.0457088	+	0.639093i
$453$	3.33482	−	8.94100i	0.156683	−	0.420085i
$454$	−14.1232	+	9.07646i	−0.662837	+	0.425979i
$455$	−1.77940	+	3.16609i	−0.0834198	+	0.148429i
$456$	0.258402	−	0.402082i	0.0121008	−	0.0188292i
$457$	11.5847	−	0.828553i	0.541909	−	0.0387581i	0.202298	−	0.979324i	$-0.435159\pi$
$457$	11.5847	−	0.828553i	0.541909	−	0.0387581i	0.339611	+	0.940566i	$0.389705\pi$
$458$	21.4678	−	11.7223i	1.00312	−	0.547746i
$459$	−3.68097			−0.171813
$460$	−1.09371	+	10.6679i	−0.0509945	+	0.497393i
$461$	−2.76714			−0.128879			−0.0644393	−	0.997922i	$-0.520526\pi$
$461$	−2.76714			−0.128879			−0.0644393	+	0.997922i	$0.520526\pi$
$462$	−2.55615	+	1.39576i	−0.118923	+	0.0649367i
$463$	−16.5747	+	1.18544i	−0.770289	+	0.0550922i	−0.450951	−	0.892549i	$-0.648915\pi$
$463$	−16.5747	+	1.18544i	−0.770289	+	0.0550922i	−0.319338	+	0.947641i	$0.603461\pi$
$464$	1.30424	−	2.02944i	0.0605479	−	0.0942143i
$465$	1.46247	+	5.21578i	0.0678206	+	0.241876i
$466$	−10.2502	+	6.58742i	−0.474833	+	0.305157i
$467$	−9.81415	+	26.3127i	−0.454145	+	1.21761i	0.485130	+	0.874442i	$0.338772\pi$
$467$	−9.81415	+	26.3127i	−0.454145	+	1.21761i	−0.939275	+	0.343167i	$0.888500\pi$
$468$	0.152226	−	2.12840i	0.00703667	−	0.0983855i
$469$	6.18745	−	0.889622i	0.285710	−	0.0410789i
$470$	7.24593	−	7.07090i	0.334230	−	0.326156i
$471$	1.95856	+	6.67026i	0.0902459	+	0.307349i
$472$	3.83443	−	7.02224i	0.176494	−	0.323225i
$473$	9.90512	−	3.69442i	0.455438	−	0.169870i
$474$	−0.734569	−	5.10904i	−0.0337399	−	0.234666i
$475$	−0.0584244	+	2.38906i	−0.00268070	+	0.109618i
$476$	1.16393	+	2.54865i	0.0533486	+	0.116817i
$477$	1.48327	+	0.322665i	0.0679141	+	0.0147738i
$478$	22.6812	−	16.9789i	1.03741	−	0.776597i
$479$	−17.2771	−	11.1033i	−0.789410	−	0.507323i	0.0827346	−	0.996572i	$-0.473635\pi$
$479$	−17.2771	−	11.1033i	−0.789410	−	0.507323i	−0.872144	+	0.489249i	$0.837271\pi$
$480$	1.04756	+	1.97550i	0.0478144	+	0.0901690i
$481$	2.32866	−	7.93069i	0.106178	−	0.361608i
$482$	−8.09078	−	8.09078i	−0.368525	−	0.368525i
$483$	−2.33898	−	2.80268i	−0.106427	−	0.127526i
$484$			3.63976i			0.165444i
$485$	−22.7790	+	2.99138i	−1.03434	+	0.135832i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	4.24775	−	0.924041i	0.192484	−	0.0418723i	−0.115290	−	0.993332i	$-0.536780\pi$
$487$	4.24775	−	0.924041i	0.192484	−	0.0418723i	0.307774	+	0.951460i	$0.400416\pi$
$488$	2.91288	+	3.89116i	0.131860	+	0.176144i
$489$	11.4245	+	17.7768i	0.516632	+	0.803895i
$490$	−10.7345	−	9.53373i	−0.484935	−	0.430690i
$491$	14.6058	+	16.8560i	0.659149	+	0.760699i	0.982638	−	0.185533i	$-0.0594012\pi$
$491$	14.6058	+	16.8560i	0.659149	+	0.760699i	−0.323489	+	0.946232i	$0.604856\pi$
$492$	−3.43592	−	2.57210i	−0.154903	−	0.115959i
$493$	−3.10323	−	8.32007i	−0.139762	−	0.374717i
$494$	0.978569	−	0.287334i	0.0440279	−	0.0129278i
$495$	−0.714630	+	8.52573i	−0.0321202	+	0.383203i
$496$	−1.00635	+	2.20361i	−0.0451866	+	0.0989449i
$497$	1.65903	−	2.21620i	0.0744175	−	0.0994101i
$498$	0.704554	+	0.0503907i	0.0315718	+	0.00225806i
$499$	13.8248	−	6.31359i	0.618885	−	0.282635i	−0.0811968	−	0.996698i	$-0.525874\pi$
$499$	13.8248	−	6.31359i	0.618885	−	0.282635i	0.700082	+	0.714063i	$0.253147\pi$
$500$	−9.60968	−	5.71437i	−0.429758	−	0.255554i
$501$	1.14214	−	7.94377i	0.0510272	−	0.354902i
$502$	1.91329	+	8.79527i	0.0853944	+	0.392552i
$503$	1.79675	+	25.1218i	0.0801129	+	1.12012i	0.865430	+	0.501031i	$0.167046\pi$
$503$	1.79675	+	25.1218i	0.0801129	+	1.12012i	−0.785317	+	0.619094i	$0.787500\pi$
$504$	−0.730339	−	0.214447i	−0.0325319	−	0.00955223i
$505$	11.1228	−	28.7432i	0.494958	−	1.27906i
$506$	−17.9997	+	3.56741i	−0.800183	+	0.158591i
$507$	−5.97274	+	5.97274i	−0.265259	+	0.265259i
$508$	−5.32619	−	9.75419i	−0.236312	−	0.432772i
$509$	10.5960	+	9.18150i	0.469660	+	0.406963i	0.857275	−	0.514859i	$-0.172156\pi$
$509$	10.5960	+	9.18150i	0.469660	+	0.406963i	−0.387615	+	0.921821i	$0.626701\pi$
$510$	8.13218	+	1.27089i	0.360099	+	0.0562758i
$511$	5.00428	+	0.719507i	0.221376	+	0.0318291i
$512$	−0.212565	+	0.977147i	−0.00939415	+	0.0431842i
$513$	0.447821	+	0.167028i	0.0197718	+	0.00737449i
$514$	−14.4818	+	12.5485i	−0.638763	+	0.553491i
$515$	18.9479	−	11.8523i	0.834945	−	0.522275i
$516$	2.51329	+	1.14778i	0.110641	+	0.0505282i
$517$	15.2048	+	8.30248i	0.668708	+	0.365142i
$518$	−2.58777	−	1.41303i	−0.113700	−	0.0620849i
$519$	−11.8757	−	5.42345i	−0.521286	−	0.238063i
$520$	−1.07116	+	4.64962i	−0.0469733	+	0.203899i
$521$	−14.5269	+	12.5876i	−0.636434	+	0.551473i	−0.912197	−	0.409753i	$-0.865615\pi$
$521$	−14.5269	+	12.5876i	−0.636434	+	0.551473i	0.275763	+	0.961226i	$0.411070\pi$
$522$	2.26030	+	0.843047i	0.0989305	+	0.0368992i
$523$	3.61505	−	16.6181i	0.158075	−	0.726659i	−0.828050	−	0.560655i	$-0.810550\pi$
$523$	3.61505	−	16.6181i	0.158075	−	0.726659i	0.986125	−	0.166005i	$-0.0530868\pi$
$524$	−18.5586	−	2.66832i	−0.810735	−	0.116566i
$525$	3.67682	−	0.982639i	0.160470	−	0.0428859i
$526$	−17.1447	−	14.8560i	−0.747546	−	0.647752i
$527$	4.27358	+	7.82647i	0.186160	+	0.340926i
$528$	−2.70553	+	2.70553i	−0.117743	+	0.117743i
$529$	−8.77230	−	21.2614i	−0.381405	−	0.924408i
$530$	−3.16550	−	1.22496i	−0.137501	−	0.0532088i
$531$	7.67683	+	2.25412i	0.333146	+	0.0978205i
$532$	−0.0259537	−	0.362880i	−0.00112523	−	0.0157328i
$533$	−1.94676	−	8.94913i	−0.0843237	−	0.387630i
$534$	0.211350	−	1.46997i	0.00914602	−	0.0636119i
$535$	9.07571	−	13.7496i	0.392377	−	0.594445i
$536$	7.47030	−	3.41157i	0.322668	−	0.147357i
$537$	14.6435	+	1.04733i	0.631914	+	0.0451954i
$538$	−7.08113	+	9.45928i	−0.305289	+	0.407818i
$539$	10.2053	−	22.3465i	0.439574	−	0.962532i
$540$	−1.70768	+	1.44355i	−0.0734869	+	0.0621203i
$541$	−20.9839	+	6.16143i	−0.902169	+	0.264901i	−0.699741	−	0.714396i	$-0.746701\pi$
$541$	−20.9839	+	6.16143i	−0.902169	+	0.264901i	−0.202428	+	0.979297i	$0.564883\pi$
$542$	−10.1618	−	27.2448i	−0.436487	−	1.17027i
$543$	−12.1440	−	9.09089i	−0.521149	−	0.390127i
$544$	2.41052	+	2.78189i	0.103350	+	0.119272i
$545$	−8.06493	+	0.477799i	−0.345464	+	0.0204666i
$546$	−0.878119	−	1.36638i	−0.0375800	−	0.0584757i
$547$	14.0290	+	18.7405i	0.599836	+	0.801287i	0.992992	−	0.118185i	$-0.0377076\pi$
$547$	14.0290	+	18.7405i	0.599836	+	0.801287i	−0.393156	+	0.919472i	$0.628617\pi$
$548$	−7.95914	+	1.73140i	−0.339998	+	0.0739619i
$549$	−3.18305	+	3.67344i	−0.135849	+	0.156779i
$550$	4.52238	−	18.5888i	0.192835	−	0.792627i
$551$			1.15302i			0.0491203i
$552$	−3.98574	−	2.66718i	−0.169645	−	0.113523i
$553$	−2.77811	−	2.77811i	−0.118137	−	0.118137i
$554$	−0.390920	+	1.33135i	−0.0166086	+	0.0565636i
$555$	−7.65218	+	4.05776i	−0.324817	+	0.172242i
$556$	9.83443	+	6.32020i	0.417073	+	0.268036i
$557$	−4.99287	+	3.73761i	−0.211555	+	0.158368i	−0.699801	−	0.714338i	$-0.746728\pi$
$557$	−4.99287	+	3.73761i	−0.211555	+	0.158368i	0.488246	+	0.872706i	$0.337637\pi$
$558$	−2.36716	−	0.514945i	−0.100210	−	0.0217994i
$559$	2.44918	+	5.36295i	0.103589	+	0.226829i
$560$	1.53946	+	0.725924i	0.0650542	+	0.0306759i
$561$	2.00437	+	13.9407i	0.0846248	+	0.588578i
$562$	−1.07984	+	0.402759i	−0.0455502	+	0.0169894i
$563$	−16.3483	+	29.9397i	−0.689000	+	1.26181i	0.265647	+	0.964070i	$0.414415\pi$
$563$	−16.3483	+	29.9397i	−0.689000	+	1.26181i	−0.954647	+	0.297740i	$0.903767\pi$
$564$	1.27561	+	4.34431i	0.0537127	+	0.182929i
$565$	30.4575	+	0.372362i	1.28136	+	0.0156654i
$566$	22.1519	−	3.18497i	0.931115	−	0.133874i
$567$	0.0543014	−	0.759233i	0.00228044	−	0.0318848i
$568$	1.27100	−	3.40768i	0.0533299	−	0.142983i
$569$	−15.9159	+	10.2285i	−0.667227	+	0.428801i	−0.829925	−	0.557875i	$-0.811617\pi$
$569$	−15.9159	+	10.2285i	−0.667227	+	0.428801i	0.162698	+	0.986676i	$0.447980\pi$
$570$	−0.931681	−	0.523622i	−0.0390238	−	0.0219321i
$571$	8.32925	−	12.9606i	0.348568	−	0.542382i	−0.622059	−	0.782970i	$-0.713704\pi$
$571$	8.32925	−	12.9606i	0.348568	−	0.542382i	0.970627	+	0.240588i	$0.0773401\pi$
$572$	−8.14368	+	0.582448i	−0.340504	+	0.0243534i
$573$	20.4647	−	11.1746i	0.854927	−	0.466825i
$574$	−3.26694			−0.136360
$575$	23.9570	+	1.03059i	0.999076	+	0.0429787i
$576$	−1.00000			−0.0416667
$577$	−3.92949	+	2.14566i	−0.163587	+	0.0893252i	−0.558957	−	0.829197i	$-0.688798\pi$
$577$	−3.92949	+	2.14566i	−0.163587	+	0.0893252i	0.395370	+	0.918522i	$0.370616\pi$
$578$	−3.44170	+	0.246155i	−0.143156	+	0.0102387i
$579$	−11.4233	+	17.7750i	−0.474736	+	0.738704i
$580$	−4.70250	−	2.64289i	−0.195261	−	0.109740i
$581$	0.452305	−	0.290679i	0.0187648	−	0.0120594i
$582$	3.59059	−	9.62674i	0.148835	−	0.399041i
$583$	0.414337	−	5.79319i	0.0171601	−	0.239930i
$584$	6.57444	−	0.945262i	0.272052	−	0.0391152i
$585$	−4.77105	−	0.0583292i	−0.197259	−	0.00241161i
$586$	9.25691	+	31.5261i	0.382399	+	1.30233i
$587$	−8.57797	+	15.7094i	−0.354051	+	0.648395i	−0.992633	−	0.121158i	$-0.961339\pi$
$587$	−8.57797	+	15.7094i	−0.354051	+	0.648395i	0.638583	+	0.769553i	$0.279521\pi$
$588$	6.01580	−	2.24378i	0.248087	−	0.0925318i
$589$	−0.164781	−	1.14607i	−0.00678967	−	0.0472232i
$590$	−16.1818	−	7.63042i	−0.666194	−	0.314139i
$591$	−0.0837893	−	0.183473i	−0.00344663	−	0.00754707i
$592$	−3.78501	−	0.823378i	−0.155563	−	0.0338406i
$593$	6.72039	−	5.03082i	0.275973	−	0.206591i	−0.452322	−	0.891855i	$-0.649404\pi$
$593$	6.72039	−	5.03082i	0.275973	−	0.206591i	0.728295	+	0.685264i	$0.240313\pi$
$594$	−3.21880	−	2.06860i	−0.132069	−	0.0848755i
$595$	5.53506	−	2.93511i	0.226915	−	0.120328i
$596$	3.02936	−	10.3170i	0.124087	−	0.422602i
$597$	5.99773	+	5.99773i	0.245471	+	0.245471i
$598$	−2.70057	−	9.87077i	−0.110435	−	0.403646i
$599$		−	37.6820i		−	1.53965i	−0.638258	−	0.769823i	$-0.720345\pi$
$599$		−	37.6820i		−	1.53965i	0.638258	−	0.769823i	$-0.279655\pi$
$600$	4.27110	−	2.59956i	0.174367	−	0.106127i
$601$	−23.7827	+	27.4467i	−0.970117	+	1.11957i	0.0226774	+	0.999743i	$0.492781\pi$
$601$	−23.7827	+	27.4467i	−0.970117	+	1.11957i	−0.992794	+	0.119832i	$0.961765\pi$
$602$	2.05503	−	0.447045i	0.0837570	−	0.0182202i
$603$	4.92153	+	6.57440i	0.200420	+	0.267730i
$604$	−5.15915	−	8.02780i	−0.209923	−	0.326647i
$605$	8.12450	−	0.481328i	0.330308	−	0.0195688i
$606$	9.02611	+	10.4167i	0.366661	+	0.423149i
$607$	−7.53884	−	5.64351i	−0.305992	−	0.229063i	0.435235	−	0.900317i	$-0.356665\pi$
$607$	−7.53884	−	5.64351i	−0.305992	−	0.229063i	−0.741228	+	0.671254i	$0.765756\pi$
$608$	−0.167028	−	0.447821i	−0.00677390	−	0.0181615i
$609$	1.76187	−	0.517332i	0.0713946	−	0.0209633i
$610$	8.30045	−	7.01658i	0.336076	−	0.284093i
$611$	−4.01350	+	8.78834i	−0.162369	+	0.355538i
$612$	−2.20592	+	2.94677i	−0.0891691	+	0.119116i
$613$	6.75048	+	0.482804i	0.272649	+	0.0195003i	0.206994	−	0.978342i	$-0.433632\pi$
$613$	6.75048	+	0.482804i	0.272649	+	0.0195003i	0.0656548	+	0.997842i	$0.479086\pi$
$614$	−18.0114	+	8.22551i	−0.726879	+	0.331955i
$615$	−5.28694	+	8.00963i	−0.213190	+	0.322980i
$616$	−0.414477	+	2.88275i	−0.0166997	+	0.116149i
$617$	4.24715	+	19.5238i	0.170984	+	0.786000i	0.980124	+	0.198384i	$0.0635695\pi$
$617$	4.24715	+	19.5238i	0.170984	+	0.786000i	−0.809141	+	0.587615i	$0.800067\pi$
$618$	0.713036	+	9.96954i	0.0286825	+	0.401034i
$619$	13.9948	+	4.10924i	0.562498	+	0.165164i	0.550606	−	0.834765i	$-0.314397\pi$
$619$	13.9948	+	4.10924i	0.562498	+	0.165164i	0.0118916	+	0.999929i	$0.496215\pi$
$620$	5.05187	+	1.95493i	0.202888	+	0.0785118i
$621$	1.75900	−	4.46161i	0.0705861	−	0.179038i
$622$	18.4058	−	18.4058i	0.738004	−	0.738004i
$623$	−0.541747	−	0.992135i	−0.0217046	−	0.0397491i
$624$	−1.61265	−	1.39737i	−0.0645576	−	0.0559395i
$625$	−11.4845	+	22.2060i	−0.459382	+	0.888239i
$626$	−30.2815	−	4.35382i	−1.21029	−	0.174014i
$627$	0.388729	−	1.78696i	0.0155243	−	0.0713643i
$628$	6.51354	+	2.42942i	0.259919	+	0.0969446i
$629$	−10.7757	+	9.33723i	−0.429657	+	0.372300i
$630$	−0.382097	+	1.65859i	−0.0152231	+	0.0660797i
$631$	−9.80635	−	4.47841i	−0.390385	−	0.178283i	0.210546	−	0.977584i	$-0.432476\pi$
$631$	−9.80635	−	4.47841i	−0.390385	−	0.178283i	−0.600931	+	0.799301i	$0.705203\pi$
$632$	−4.53021	−	2.47368i	−0.180202	−	0.0983977i
$633$	2.21140	+	1.20751i	0.0878951	+	0.0479944i
$634$	−28.2584	−	12.9052i	−1.12229	−	0.512531i
$635$	−21.0685	+	13.1788i	−0.836078	+	0.522984i
$636$	1.14719	−	0.994049i	0.0454892	−	0.0394166i
$637$	12.8367	+	4.78786i	0.508610	+	0.189702i
$638$	1.96204	−	9.01936i	0.0776780	−	0.357080i
$639$	3.59997	+	0.517598i	0.142413	+	0.0204759i
$640$	2.20925	+	0.345259i	0.0873284	+	0.0136476i
$641$	32.1155	+	27.8283i	1.26849	+	1.09915i	0.990347	+	0.138609i	$0.0442632\pi$
$641$	32.1155	+	27.8283i	1.26849	+	1.09915i	0.278139	+	0.960541i	$0.410282\pi$
$642$	3.53099	+	6.46652i	0.139357	+	0.255213i
$643$	0.644128	−	0.644128i	0.0254019	−	0.0254019i	−0.694292	−	0.719694i	$-0.744282\pi$
$643$	0.644128	−	0.644128i	0.0254019	−	0.0254019i	0.719694	+	0.694292i	$0.244282\pi$
$644$	−3.64535	+	0.192866i	−0.143647	+	0.00759997i
$645$	2.22966	−	5.76183i	0.0877928	−	0.226872i
$646$	−1.68807	−	0.495663i	−0.0664164	−	0.0195016i
$647$	3.38172	+	47.2826i	0.132949	+	1.85887i	0.428498	+	0.903543i	$0.359043\pi$
$647$	3.38172	+	47.2826i	0.132949	+	1.85887i	−0.295549	+	0.955328i	$0.595503\pi$
$648$	−0.212565	−	0.977147i	−0.00835035	−	0.0383860i
$649$	4.35670	−	30.3015i	0.171015	−	1.18944i
$650$	10.5203	+	1.77611i	0.412641	+	0.0696649i
$651$	−1.67732	+	0.766008i	−0.0657395	+	0.0300222i
$652$	21.0775	+	1.50749i	0.825458	+	0.0590379i
$653$	−14.4590	+	19.3149i	−0.565824	+	0.755852i	−0.988630	−	0.150368i	$-0.951954\pi$
$653$	−14.4590	+	19.3149i	−0.565824	+	0.755852i	0.422806	+	0.906220i	$0.361045\pi$
$654$	1.50092	−	3.28657i	0.0586908	−	0.128515i
$655$	−3.50189	+	41.7785i	−0.136830	+	1.63242i
$656$	−4.11814	+	1.20919i	−0.160786	+	0.0472111i
$657$	2.32116	+	6.22326i	0.0905570	+	0.242793i
$658$	2.75896	+	2.06533i	0.107556	+	0.0805151i
$659$	−2.14135	−	2.47125i	−0.0834153	−	0.0962664i	0.712508	−	0.701664i	$-0.247559\pi$
$659$	−2.14135	−	2.47125i	−0.0834153	−	0.0962664i	−0.795923	+	0.605398i	$0.793014\pi$
$660$	6.39694	+	5.68137i	0.249000	+	0.221147i
$661$	9.01685	+	14.0305i	0.350715	+	0.545723i	0.971130	−	0.238551i	$-0.0766723\pi$
$661$	9.01685	+	14.0305i	0.350715	+	0.545723i	−0.620415	+	0.784273i	$0.713036\pi$
$662$	−1.08112	−	1.44421i	−0.0420190	−	0.0561308i
$663$	−7.67509	+	1.66961i	−0.298076	+	0.0648424i
$664$	0.462563	−	0.533826i	0.0179509	−	0.0207165i
$665$	−0.806571	+	0.105920i	−0.0312775	+	0.00410742i
$666$		−	3.87353i		−	0.150096i
$667$	11.5675	+	0.214507i	0.447894	+	0.00830575i
$668$	−5.67486	−	5.67486i	−0.219567	−	0.219567i
$669$	−0.597965	+	2.03648i	−0.0231187	+	0.0787350i
$670$	−8.60304	−	16.2237i	−0.332364	−	0.626777i
$671$	15.6455	+	10.0547i	0.603987	+	0.388159i
$672$	−0.609350	+	0.456153i	−0.0235062	+	0.0175965i
$673$	38.2149	+	8.31315i	1.47308	+	0.320448i	0.876225	−	0.481903i	$-0.160054\pi$
$673$	38.2149	+	8.31315i	1.47308	+	0.320448i	0.596852	+	0.802351i	$0.296418\pi$
$674$	−0.139471	−	0.305400i	−0.00537223	−	0.0117636i
$675$	3.44804	+	3.62091i	0.132715	+	0.139369i
$676$	1.20209	+	8.36075i	0.0462344	+	0.321567i
$677$	32.5375	−	12.1359i	1.25052	−	0.466419i	0.364993	−	0.931010i	$-0.381071\pi$
$677$	32.5375	−	12.1359i	1.25052	−	0.466419i	0.885525	+	0.464591i	$0.153799\pi$
$678$	−6.52834	+	11.9558i	−0.250719	+	0.459158i
$679$	−2.20335	−	7.50391i	−0.0845567	−	0.287974i
$680$	5.89083	−	5.74853i	0.225903	−	0.220446i
$681$	−16.6174	+	2.38923i	−0.636782	+	0.0915554i
$682$	−0.661247	+	9.24544i	−0.0253204	+	0.354026i
$683$	−5.70749	+	15.3024i	−0.218391	+	0.585529i	−0.999231	−	0.0392015i	$-0.987519\pi$
$683$	−5.70749	+	15.3024i	−0.218391	+	0.585529i	0.780840	+	0.624731i	$0.214791\pi$
$684$	0.402082	−	0.258402i	0.0153740	−	0.00988026i
$685$	4.91729	+	17.5371i	0.187880	+	0.670057i
$686$	5.52286	−	8.59374i	0.210864	−	0.328111i
$687$	24.3974	−	1.74494i	0.930818	−	0.0665734i
$688$	2.42500	−	1.32415i	0.0924523	−	0.0504828i
$689$	3.23907			0.123399
$690$	−5.42647	+	9.24951i	−0.206582	+	0.352123i
$691$	−22.7265			−0.864556			−0.432278	−	0.901740i	$-0.642290\pi$
$691$	−22.7265			−0.864556			−0.432278	+	0.901740i	$0.642290\pi$
$692$	−11.4585	+	6.25684i	−0.435588	+	0.237849i
$693$	−2.90497	+	0.207768i	−0.110351	+	0.00789244i
$694$	−4.73890	+	7.37387i	−0.179886	+	0.279908i
$695$	12.8071	−	22.7878i	0.485803	−	0.864389i
$696$	2.02944	−	1.30424i	0.0769257	−	0.0494371i
$697$	−5.52107	+	14.8026i	−0.209126	+	0.560687i
$698$	−1.69058	+	23.6374i	−0.0639894	+	0.894689i
$699$	−12.0605	+	1.73403i	−0.456168	+	0.0655871i
$700$	1.41679	−	3.53232i	0.0535497	−	0.133509i
$701$	9.73523	+	33.1552i	0.367695	+	1.25225i	0.910891	+	0.412647i	$0.135396\pi$
$701$	9.73523	+	33.1552i	0.367695	+	1.25225i	−0.543196	+	0.839606i	$0.682786\pi$
$702$	1.02264	−	1.87283i	0.0385971	−	0.0706853i
$703$	1.73465	−	0.646990i	0.0654235	−	0.0244017i
$704$	0.544524	+	3.78725i	0.0205225	+	0.142737i
$705$	9.52849	−	3.42185i	0.358864	−	0.128874i
$706$	12.3118	+	26.9591i	0.463361	+	1.01462i
$707$	10.2517	+	2.23011i	0.385553	+	0.0838720i
$708$	6.40507	−	4.79478i	0.240717	−	0.180199i
$709$	−22.3380	−	14.3557i	−0.838920	−	0.539141i	0.0491810	−	0.998790i	$-0.484339\pi$
$709$	−22.3380	−	14.3557i	−0.838920	−	0.539141i	−0.888101	+	0.459649i	$0.847975\pi$
$710$	−7.77454	−	2.38643i	−0.291773	−	0.0895610i
$711$	1.45418	−	4.95250i	0.0545362	−	0.185733i
$712$	−1.05012	−	1.05012i	−0.0393548	−	0.0393548i
$713$	−11.5285	+	1.43992i	−0.431744	+	0.0539254i
$714$			2.80185i			0.104857i
$715$	2.37705	+	18.1009i	0.0888965	+	0.676936i
$716$	9.61396	−	11.0951i	0.359291	−	0.414643i
$717$	27.6848	−	6.02246i	1.03391	−	0.224913i
$718$	−4.86571	−	6.49982i	−0.181587	−	0.242571i
$719$	23.4030	+	36.4158i	0.872786	+	1.35808i	0.932993	+	0.359895i	$0.117188\pi$
$719$	23.4030	+	36.4158i	0.872786	+	1.35808i	−0.0602071	+	0.998186i	$0.519176\pi$
$720$	0.132242	+	2.23215i	0.00492836	+	0.0831875i
$721$	4.98213	+	5.74968i	0.185544	+	0.214129i
$722$	−15.0274	−	11.2494i	−0.559262	−	0.418658i
$723$	−3.99860	−	10.7207i	−0.148709	−	0.398706i
$724$	−14.5553	+	4.27381i	−0.540942	+	0.158835i
$725$	−5.27747	+	10.8462i	−0.196000	+	0.402818i
$726$	−1.51201	+	3.31084i	−0.0561160	+	0.122877i
$727$	−16.9034	+	22.5802i	−0.626911	+	0.837455i	−0.995756	−	0.0920361i	$-0.970662\pi$
$727$	−16.9034	+	22.5802i	−0.626911	+	0.837455i	0.368845	+	0.929491i	$0.379753\pi$
$728$	−1.62008	−	0.115870i	−0.0600442	−	0.00429445i
$729$	0.909632	−	0.415415i	0.0336901	−	0.0153857i
$730$	−2.97938	−	14.5502i	−0.110272	−	0.538526i
$731$	1.44740	−	10.0669i	0.0535340	−	0.372337i
$732$	1.03321	+	4.74957i	0.0381884	+	0.175549i
$733$	1.79218	+	25.0579i	0.0661955	+	0.925534i	0.916703	+	0.399570i	$0.130841\pi$
$733$	1.79218	+	25.0579i	0.0661955	+	0.925534i	−0.850507	+	0.525964i	$0.823705\pi$
$734$	−20.7755	−	6.10024i	−0.766838	−	0.225164i
$735$	−5.80399	−	13.1315i	−0.214083	−	0.484361i
$736$	−4.52375	+	1.59237i	−0.166748	+	0.0586956i
$737$	22.2190	−	22.2190i	0.818447	−	0.818447i
$738$	−2.05693	−	3.76699i	−0.0757168	−	0.138665i
$739$	−29.2258	−	25.3243i	−1.07509	−	0.931571i	−0.0772338	−	0.997013i	$-0.524609\pi$
$739$	−29.2258	−	25.3243i	−1.07509	−	0.931571i	−0.997856	+	0.0654421i	$0.979154\pi$
$740$	−1.33737	+	8.55761i	−0.0491628	+	0.314584i
$741$	1.00950	+	0.145144i	0.0370849	+	0.00533201i
$742$	0.245603	−	1.12902i	0.00901638	−	0.0414476i
$743$	33.4810	+	12.4878i	1.22830	+	0.458131i	0.878069	−	0.478533i	$-0.158831\pi$
$743$	33.4810	+	12.4878i	1.22830	+	0.458131i	0.350228	+	0.936664i	$0.386104\pi$
$744$	−1.83082	+	1.58642i	−0.0671212	+	0.0581609i
$745$	−23.4298	−	5.39765i	−0.858402	−	0.197754i
$746$	−30.7282	−	14.0331i	−1.12504	−	0.513788i
$747$	0.619952	+	0.338519i	0.0226828	+	0.0123858i
$748$	12.3613	+	6.74979i	0.451974	+	0.246797i
$749$	5.10133	+	2.32970i	0.186399	+	0.0851254i
$750$	−6.36744	−	9.18998i	−0.232506	−	0.335571i
$751$	−25.5026	+	22.0981i	−0.930603	+	0.806372i	−0.981328	−	0.192340i	$-0.938392\pi$
$751$	−25.5026	+	22.0981i	−0.930603	+	0.806372i	0.0507251	+	0.998713i	$0.483847\pi$
$752$	4.24224	+	1.58228i	0.154699	+	0.0576997i
$753$	−1.91329	+	8.79527i	−0.0697243	+	0.320517i
$754$	5.09528	+	0.732590i	0.185559	+	0.0266794i
$755$	−17.2370	+	12.5776i	−0.627320	+	0.457747i
$756$	−0.575255	−	0.498462i	−0.0209218	−	0.0181289i
$757$	13.8870	+	25.4322i	0.504732	+	0.924348i	0.998500	+	0.0547545i	$0.0174376\pi$
$757$	13.8870	+	25.4322i	0.504732	+	0.924348i	−0.493767	+	0.869594i	$0.664381\pi$
$758$	−9.33509	+	9.33509i	−0.339066	+	0.339066i
$759$	−17.8550	−	4.23230i	−0.648097	−	0.153623i
$760$	−0.977516	+	0.432054i	−0.0354582	+	0.0156722i
$761$	−17.8673	−	5.24631i	−0.647688	−	0.190178i	−0.0586437	−	0.998279i	$-0.518678\pi$
$761$	−17.8673	−	5.24631i	−0.647688	−	0.190178i	−0.589045	+	0.808101i	$0.700496\pi$
$762$	−0.792837	−	11.0853i	−0.0287214	−	0.401578i
$763$	−0.584591	−	2.68732i	−0.0211636	−	0.0972875i
$764$	3.31834	−	23.0796i	0.120053	−	0.834989i
$765$	6.86935	+	4.53427i	0.248362	+	0.163937i
$766$	13.3972	−	6.11830i	0.484061	−	0.221063i
$767$	17.0292	+	1.21795i	0.614888	+	0.0439777i
$768$	−0.599278	+	0.800541i	−0.0216246	+	0.0288870i
$769$	−19.7746	+	43.3004i	−0.713092	+	1.56145i	0.110248	+	0.993904i	$0.464835\pi$
$769$	−19.7746	+	43.3004i	−0.713092	+	1.56145i	−0.823340	+	0.567549i	$0.807892\pi$
$770$	6.48955	+	0.543956i	0.233867	+	0.0196028i
$771$	−18.3859	+	5.39859i	−0.662153	+	0.194426i
$772$	7.38390	+	19.7970i	0.265752	+	0.712509i
$773$	16.4241	+	12.2950i	0.590735	+	0.442219i	0.852364	−	0.522950i	$-0.175168\pi$
$773$	16.4241	+	12.2950i	0.590735	+	0.442219i	−0.261628	+	0.965169i	$0.584259\pi$
$774$	1.80936	+	2.08811i	0.0650362	+	0.0750557i
$775$	3.69563	−	11.5351i	0.132751	−	0.414352i
$776$	−5.55484	−	8.64350i	−0.199407	−	0.310284i
$777$	−1.76692	−	2.36033i	−0.0633881	−	0.0846765i
$778$	−34.6717	+	7.54237i	−1.24304	+	0.270407i
$779$	1.34337	−	1.55033i	0.0481312	−	0.0555464i
$780$	−2.90588	+	3.78447i	−0.104047	+	0.135506i
$781$		−	13.9158i		−	0.497948i
$782$	−5.28670	+	16.8431i	−0.189052	+	0.602308i
$783$	1.70582	+	1.70582i	0.0609612	+	0.0609612i
$784$	1.80890	−	6.16054i	0.0646035	−	0.220019i
$785$	4.56149	−	14.8605i	0.162807	−	0.530394i
$786$	−15.7730	−	10.1367i	−0.562605	−	0.361564i
$787$	−11.0804	+	8.29470i	−0.394974	+	0.295674i	−0.778243	−	0.627963i	$-0.783889\pi$
$787$	−11.0804	+	8.29470i	−0.394974	+	0.295674i	0.383269	+	0.923637i	$0.374798\pi$
$788$	−0.197091	−	0.0428745i	−0.00702107	−	0.00152734i
$789$	−9.42399	−	20.6357i	−0.335503	−	0.734649i
$790$	−4.92255	+	10.4392i	−0.175137	+	0.371412i
$791$	1.47562	+	10.2632i	0.0524670	+	0.364916i
$792$	−3.58495	+	1.33712i	−0.127386	+	0.0475124i
$793$	−4.97070	+	9.10316i	−0.176515	+	0.323263i
$794$	−9.46144	−	32.2227i	−0.335774	−	1.14354i
$795$	−2.37058	−	2.42926i	−0.0840758	−	0.0861570i
$796$	8.39574	−	1.20713i	0.297579	−	0.0427854i
$797$	1.07110	−	14.9759i	0.0379402	−	0.530473i	−0.942571	−	0.334007i	$-0.891599\pi$
$797$	1.07110	−	14.9759i	0.0379402	−	0.530473i	0.980511	−	0.196466i	$-0.0629465\pi$
$798$	0.127137	−	0.340868i	0.00450061	−	0.0120666i
$799$	14.0207	−	9.01052i	0.496015	−	0.318769i
$800$	0.478516	−	4.97705i	0.0169181	−	0.175965i
$801$	0.802900	−	1.24934i	0.0283691	−	0.0441431i
$802$	8.18126	−	0.585135i	0.288890	−	0.0206618i
$803$	22.3051	−	12.1795i	0.787131	−	0.429806i
$804$	8.21244			0.289631
$805$	0.912574	+	8.11149i	0.0321640	+	0.285892i
$806$	−5.16928			−0.182080
$807$	−10.3707	+	5.66286i	−0.365068	+	0.199342i
$808$	13.7481	−	0.983286i	0.483658	−	0.0345919i
$809$	−6.13106	+	9.54011i	−0.215556	+	0.335412i	−0.932146	−	0.362083i	$-0.882066\pi$
$809$	−6.13106	+	9.54011i	−0.215556	+	0.335412i	0.716589	+	0.697495i	$0.245702\pi$
$810$	−2.15303	+	0.603698i	−0.0756498	+	0.0212118i
$811$	15.7650	−	10.1316i	0.553585	−	0.355768i	−0.233746	−	0.972298i	$-0.575098\pi$
$811$	15.7650	−	10.1316i	0.553585	−	0.355768i	0.787331	+	0.616530i	$0.211462\pi$
$812$	0.641704	−	1.72047i	0.0225194	−	0.0603768i
$813$	2.07442	−	29.0041i	0.0727530	−	1.01722i
$814$	−14.6700	+	2.10923i	−0.514184	+	0.0739285i
$815$	0.577631	−	47.2475i	0.0202335	−	1.65501i
$816$	1.03705	+	3.53186i	0.0363039	+	0.123640i
$817$	−0.632886	+	1.15904i	−0.0221419	+	0.0405498i
$818$	31.7386	−	11.8379i	1.10971	−	0.413901i
$819$	−0.231150	−	1.60769i	−0.00807705	−	0.0561771i
$820$	3.24370	+	9.03241i	0.113275	+	0.315425i
$821$	−6.38776	−	13.9872i	−0.222934	−	0.488158i	0.764807	−	0.644260i	$-0.222834\pi$
$821$	−6.38776	−	13.9872i	−0.222934	−	0.488158i	−0.987741	+	0.156102i	$0.950107\pi$
$822$	−7.95914	−	1.73140i	−0.277607	−	0.0603897i
$823$	24.1670	−	18.0912i	0.842410	−	0.630620i	−0.0884158	−	0.996084i	$-0.528180\pi$
$823$	24.1670	−	18.0912i	0.842410	−	0.630620i	0.930826	+	0.365464i	$0.119090\pi$
$824$	8.40833	+	5.40371i	0.292918	+	0.188247i
$825$	11.8358	−	15.0303i	0.412068	−	0.523287i
$826$	1.71577	−	5.84339i	0.0596994	−	0.203318i
$827$	25.6136	+	25.6136i	0.890671	+	0.890671i	0.994586	−	0.103915i	$-0.0331371\pi$
$827$	25.6136	+	25.6136i	0.890671	+	0.890671i	−0.103915	+	0.994586i	$0.533137\pi$
$828$	−2.51757	−	4.08189i	−0.0874917	−	0.141855i
$829$			34.6944i			1.20499i	0.798124	+	0.602494i	$0.205826\pi$
$829$			34.6944i			1.20499i	−0.798124	+	0.602494i	$0.794174\pi$
$830$	−1.25275	−	0.961918i	−0.0434837	−	0.0333887i
$831$	−0.908656	+	1.04864i	−0.0315209	+	0.0363771i
$832$	−2.08507	+	0.453580i	−0.0722870	+	0.0157251i
$833$	−14.1634	−	18.9201i	−0.490732	−	0.655541i
$834$	6.32020	+	9.83443i	0.218851	+	0.340538i
$835$	−11.9167	+	13.4176i	−0.412395	+	0.464336i
$836$	−1.19758	−	1.38208i	−0.0414191	−	0.0478002i
$837$	−1.93933	−	1.45177i	−0.0670331	−	0.0501804i
$838$	2.75601	+	7.38915i	0.0952048	+	0.255254i
$839$	−44.8884	+	13.1804i	−1.54972	+	0.455039i	−0.941017	−	0.338359i	$-0.890128\pi$
$839$	−44.8884	+	13.1804i	−1.54972	+	0.455039i	−0.608703	+	0.793398i	$0.708310\pi$
$840$	1.09879	+	1.29984i	0.0379117	+	0.0448487i
$841$	9.62946	−	21.0856i	0.332050	−	0.727089i
$842$	8.62059	−	11.5158i	0.297085	−	0.396859i
$843$	−1.14957	−	0.0822187i	−0.0395932	−	0.00283176i
$844$	2.29191	−	1.04668i	0.0788906	−	0.0360282i
$845$	18.5035	−	3.78890i	0.636540	−	0.130342i
$846$	−0.644362	+	4.48163i	−0.0221536	+	0.154082i
$847$	0.588909	+	2.70717i	0.0202351	+	0.0930194i
$848$	−0.108290	−	1.51409i	−0.00371868	−	0.0519940i
$849$	21.4732	+	6.30509i	0.736958	+	0.216390i
$850$	−13.6106	−	12.3891i	−0.466841	−	0.424941i
$851$	−6.16810	−	17.5229i	−0.211440	−	0.600677i
$852$	2.57174	−	2.57174i	0.0881064	−	0.0881064i
$853$	−4.27075	−	7.82129i	−0.146228	−	0.267796i	0.794291	−	0.607537i	$-0.207842\pi$
$853$	−4.27075	−	7.82129i	−0.146228	−	0.267796i	−0.940519	+	0.339741i	$0.889661\pi$
$854$	2.79612	+	2.42285i	0.0956812	+	0.0829082i
$855$	−0.629966	−	0.863337i	−0.0215444	−	0.0295255i
$856$	7.29276	+	1.04854i	0.249261	+	0.0358384i
$857$	7.37956	−	33.9233i	0.252081	−	1.15880i	−0.660797	−	0.750565i	$-0.729782\pi$
$857$	7.37956	−	33.9233i	0.252081	−	1.15880i	0.912878	−	0.408233i	$-0.133855\pi$
$858$	−7.64971	−	2.85319i	−0.261157	−	0.0974065i
$859$	−15.7869	+	13.6795i	−0.538643	+	0.466737i	−0.881189	−	0.472764i	$-0.843256\pi$
$859$	−15.7869	+	13.6795i	−0.538643	+	0.466737i	0.342546	+	0.939501i	$0.388711\pi$
$860$	−3.27640	−	5.23787i	−0.111724	−	0.178610i
$861$	−2.97172	−	1.35714i	−0.101276	−	0.0462511i
$862$	27.8171	+	15.1893i	0.947453	+	0.517348i
$863$	−28.1146	−	15.3518i	−0.957034	−	0.522580i	−0.0767617	−	0.997049i	$-0.524458\pi$
$863$	−28.1146	−	15.3518i	−0.957034	−	0.522580i	−0.880272	+	0.474470i	$0.842640\pi$
$864$	−0.909632	−	0.415415i	−0.0309463	−	0.0141327i
$865$	15.4815	+	24.7498i	0.526387	+	0.841519i
$866$	−5.10384	+	4.42250i	−0.173436	+	0.150283i
$867$	−3.23293	−	1.20582i	−0.109796	−	0.0409519i
$868$	−0.391962	+	1.80182i	−0.0133040	+	0.0611577i
$869$	−19.5482	−	2.81060i	−0.663126	−	0.0953432i
$870$	−3.17964	−	4.35755i	−0.107800	−	0.147735i
$871$	13.2438	+	11.4758i	0.448748	+	0.388843i
$872$	−1.73156	−	3.17112i	−0.0586381	−	0.107388i
$873$	7.26521	−	7.26521i	0.245890	−	0.245890i
$874$	1.40745	−	1.80921i	0.0476076	−	0.0611975i
$875$	−8.07204	−	2.69538i	−0.272885	−	0.0911204i
$876$	6.37300	+	1.87128i	0.215324	+	0.0632247i
$877$	0.0613163	+	0.857313i	0.00207050	+	0.0289494i	0.998382	−	0.0568570i	$-0.0181079\pi$
$877$	0.0613163	+	0.857313i	0.00207050	+	0.0289494i	−0.996312	+	0.0858064i	$0.972653\pi$
$878$	−4.84643	−	22.2787i	−0.163559	−	0.751869i
$879$	−4.67605	+	32.5226i	−0.157719	+	1.09696i
$880$	8.38171	−	1.71629i	0.282548	−	0.0578563i
$881$	35.2850	−	16.1141i	1.18878	−	0.542899i	0.279932	−	0.960020i	$-0.409688\pi$
$881$	35.2850	−	16.1141i	1.18878	−	0.542899i	0.908851	+	0.417121i	$0.136961\pi$
$882$	6.40426	+	0.458042i	0.215643	+	0.0154231i
$883$	13.7991	−	18.4334i	0.464377	−	0.620335i	−0.505824	−	0.862637i	$-0.668812\pi$
$883$	13.7991	−	18.4334i	0.464377	−	0.620335i	0.970201	+	0.242302i	$0.0779025\pi$
$884$	−3.26292	+	7.14479i	−0.109744	+	0.240305i
$885$	−11.5497	−	13.6630i	−0.388239	−	0.459278i
$886$	32.1094	−	9.42817i	1.07874	−	0.316746i
$887$	4.98117	+	13.3550i	0.167251	+	0.448418i	0.993354	−	0.115102i	$-0.0367195\pi$
$887$	4.98117	+	13.3550i	0.167251	+	0.448418i	−0.826102	+	0.563520i	$0.809447\pi$
$888$	−3.10092	−	2.32132i	−0.104060	−	0.0778984i
$889$	−5.53971	−	6.39317i	−0.185796	−	0.214420i
$890$	−2.20515	+	2.48289i	−0.0739169	+	0.0832267i
$891$	−2.06860	−	3.21880i	−0.0693006	−	0.107834i
$892$	1.27194	+	1.69911i	0.0425877	+	0.0568906i
$893$	−2.11459	+	0.460002i	−0.0707622	+	0.0153934i
$894$	7.04145	−	8.12627i	0.235501	−	0.271783i
$895$	−26.0373	−	19.9926i	−0.870332	−	0.668279i
$896$			0.761172i			0.0254290i
$897$	1.64394	−	10.1006i	0.0548896	−	0.337250i
$898$	2.90563	+	2.90563i	0.0969621	+	0.0969621i
$899$	1.64647	−	5.60737i	0.0549129	−	0.187016i
$900$	4.96502	−	0.590368i	0.165501	−	0.0196789i
$901$	−4.70054	−	3.02085i	−0.156598	−	0.100639i
$902$	−13.1465	+	9.84134i	−0.437730	+	0.327681i
$903$	2.05503	+	0.447045i	0.0683873	+	0.0148767i
$904$	5.65879	+	12.3910i	0.188209	+	0.412119i
$905$	11.4646	+	31.9244i	0.381097	+	1.06120i
$906$	−1.35806	−	9.44553i	−0.0451186	−	0.313807i
$907$	−5.36146	+	1.99972i	−0.178024	+	0.0663997i	−0.436896	−	0.899512i	$-0.643922\pi$
$907$	−5.36146	+	1.99972i	−0.178024	+	0.0663997i	0.258871	+	0.965912i	$0.416649\pi$
$908$	−8.04579	+	14.7348i	−0.267009	+	0.488990i
$909$	3.88319	+	13.2249i	0.128797	+	0.438643i
$910$	−0.0443985	+	3.63159i	−0.00147180	+	0.120386i
$911$	−30.6605	+	4.40831i	−1.01583	+	0.146054i	−0.630063	−	0.776544i	$-0.716971\pi$
$911$	−30.6605	+	4.40831i	−1.01583	+	0.146054i	−0.385763	+	0.922598i	$0.626062\pi$
$912$	0.0340970	−	0.476738i	0.00112906	−	0.0157864i
$913$	0.944478	−	2.53224i	0.0312576	−	0.0838050i
$914$	9.77055	−	6.27915i	0.323181	−	0.207696i
$915$	10.4652	−	2.93437i	0.345967	−	0.0970072i
$916$	13.2239	−	20.5768i	0.436930	−	0.679877i
$917$	−14.2352	+	1.01812i	−0.470087	+	0.0336213i
$918$	−3.23071	+	1.76410i	−0.106629	+	0.0582240i
$919$	−24.4692			−0.807163			−0.403582	−	0.914944i	$-0.632235\pi$
$919$	−24.4692			−0.807163			−0.403582	+	0.914944i	$0.632235\pi$
$920$	4.15265	+	9.88714i	0.136909	+	0.325969i
$921$	−19.8007			−0.652455
$922$	−2.42866	+	1.32615i	−0.0799837	+	0.0436744i
$923$	7.74098	−	0.553646i	0.254798	−	0.0182235i
$924$	−1.57456	+	2.45006i	−0.0517992	+	0.0806011i
$925$	19.2788	+	1.85355i	0.633882	+	0.0609442i
$926$	−13.9791	+	8.98382i	−0.459382	+	0.295227i
$927$	−3.49290	+	9.36482i	−0.114722	+	0.307581i
$928$	0.172099	−	2.40625i	0.00564941	−	0.0789891i
$929$	−6.38570	+	0.918125i	−0.209508	+	0.0301227i	−0.246270	−	0.969201i	$-0.579205\pi$
$929$	−6.38570	+	0.918125i	−0.209508	+	0.0301227i	0.0367616	+	0.999324i	$0.488296\pi$
$930$	3.78324	+	3.87689i	0.124057	+	0.127128i
$931$	0.864573	+	2.94446i	0.0283352	+	0.0965009i
$932$	−5.83940	+	10.6941i	−0.191276	+	0.350295i
$933$	24.3885	−	9.09645i	0.798444	−	0.297804i
$934$	3.99669	+	27.7976i	0.130776	+	0.909564i
$935$	13.4319	−	28.4850i	0.439270	−	0.931558i
$936$	−0.886429	−	1.94101i	−0.0289738	−	0.0634439i
$937$	−14.8067	−	3.22100i	−0.483714	−	0.105225i	−0.0359057	−	0.999355i	$-0.511432\pi$
$937$	−14.8067	−	3.22100i	−0.483714	−	0.105225i	−0.447808	+	0.894130i	$0.647795\pi$
$938$	5.00425	−	3.74613i	0.163395	−	0.122316i
$939$	−25.7364	−	16.5398i	−0.839875	−	0.539755i
$940$	2.97088	−	9.67859i	0.0968995	−	0.315681i
$941$	−11.4778	+	39.0899i	−0.374167	+	1.27429i	0.530322	+	0.847797i	$0.322071\pi$
$941$	−11.4778	+	39.0899i	−0.374167	+	1.27429i	−0.904488	+	0.426498i	$0.859747\pi$
$942$	4.91570	+	4.91570i	0.160162	+	0.160162i
$943$	−15.3035	−	13.7655i	−0.498351	−	0.448268i
$944$		−	8.00092i		−	0.260408i
$945$	−1.03657	+	1.34998i	−0.0337196	+	0.0439147i
$946$	6.92297	−	7.98953i	0.225085	−	0.259762i
$947$	35.3490	−	7.68971i	1.14869	−	0.249882i	0.402374	−	0.915475i	$-0.368185\pi$
$947$	35.3490	−	7.68971i	1.14869	−	0.249882i	0.746315	+	0.665593i	$0.231821\pi$
$948$	−3.09322	−	4.13205i	−0.100463	−	0.134203i
$949$	7.66254	+	11.9231i	0.248736	+	0.387041i
$950$	1.09368	+	2.12483i	0.0354836	+	0.0689386i
$951$	−20.3438	−	23.4779i	−0.659692	−	0.761325i
$952$	2.24300	+	1.67909i	0.0726959	+	0.0544195i
$953$	−14.9054	−	39.9629i	−0.482833	−	1.29452i	−0.918857	−	0.394590i	$-0.870887\pi$
$953$	−14.9054	−	39.9629i	−0.482833	−	1.29452i	0.436025	−	0.899935i	$-0.356386\pi$
$954$	1.45647	−	0.427657i	0.0471549	−	0.0138459i
$955$	−51.9559	−	4.35496i	−1.68125	−	0.140923i
$956$	11.7697	−	25.7720i	0.380658	−	0.833525i
$957$	5.53152	−	7.38924i	0.178809	−	0.238860i
$958$	−20.4850	−	1.46511i	−0.661839	−	0.0473357i
$959$	−5.63968	+	2.57556i	−0.182115	+	0.0831691i
$960$	1.86618	+	1.23182i	0.0602307	+	0.0397567i
$961$	3.57657	−	24.8756i	0.115373	−	0.802438i
$962$	−1.75696	−	8.07660i	−0.0566466	−	0.260400i
$963$	0.525609	+	7.34898i	0.0169375	+	0.236818i
$964$	−10.9786	−	3.22361i	−0.353597	−	0.103825i
$965$	43.2135	−	19.1000i	1.39109	−	0.614850i
$966$	−3.39605	−	1.33890i	−0.109266	−	0.0430783i
$967$	−10.6857	+	10.6857i	−0.343629	+	0.343629i	−0.857730	−	0.514101i	$-0.828126\pi$
$967$	−10.6857	+	10.6857i	−0.343629	+	0.343629i	0.514101	+	0.857730i	$0.328126\pi$
$968$	1.74435	+	3.19454i	0.0560656	+	0.102676i
$969$	−1.32962	−	1.15212i	−0.0427135	−	0.0370115i
$970$	−18.5591	+	13.5423i	−0.595895	+	0.434817i
$971$	−3.24092	−	0.465974i	−0.104006	−	0.0149538i	0.0901153	−	0.995931i	$-0.471276\pi$
$971$	−3.24092	−	0.465974i	−0.104006	−	0.0149538i	−0.194121	+	0.980978i	$0.562186\pi$
$972$	0.212565	−	0.977147i	0.00681803	−	0.0313420i
$973$	8.33722	+	3.10962i	0.267279	+	0.0996899i
$974$	3.28531	−	2.84674i	0.105268	−	0.0912155i
$975$	8.83180	+	5.98591i	0.282844	+	0.191703i
$976$	4.42141	+	2.01919i	0.141526	+	0.0646327i
$977$	24.4500	+	13.3507i	0.782225	+	0.427127i	0.820146	−	0.572154i	$-0.193892\pi$
$977$	24.4500	+	13.3507i	0.782225	+	0.427127i	−0.0379217	+	0.999281i	$0.512074\pi$
$978$	18.5465	+	10.1272i	0.593052	+	0.323831i
$979$	−5.16875	−	2.36049i	−0.165194	−	0.0754415i
$980$	−13.9905	−	3.22306i	−0.446909	−	0.102957i
$981$	2.73058	−	2.36606i	0.0871806	−	0.0755424i
$982$	20.8974	+	7.79432i	0.666862	+	0.248727i
$983$	2.73086	−	12.5536i	0.0871009	−	0.400396i	−0.912868	−	0.408254i	$-0.866138\pi$
$983$	2.73086	−	12.5536i	0.0871009	−	0.400396i	0.999969	+	0.00785800i	$0.00250130\pi$
$984$	−4.24831	−	0.610814i	−0.135431	−	0.0194720i
$985$	−0.0696388	+	0.445607i	−0.00221888	+	0.0141982i
$986$	−6.71102	−	5.81514i	−0.213723	−	0.185192i
$987$	1.65167	+	3.02481i	0.0525733	+	0.0962807i
$988$	0.721165	−	0.721165i	0.0229433	−	0.0229433i
$989$	11.5102	+	6.56494i	0.366002	+	0.208753i
$990$	3.45873	+	7.82534i	0.109926	+	0.248706i
$991$	48.8463	+	14.3426i	1.55165	+	0.455606i	0.941594	−	0.336750i	$-0.109328\pi$
$991$	48.8463	+	14.3426i	1.55165	+	0.455606i	0.610059	+	0.792356i	$0.291146\pi$
$992$	0.172821	+	2.41635i	0.00548707	+	0.0767193i
$993$	−0.383476	−	1.76281i	−0.0121693	−	0.0559412i
$994$	0.393981	−	2.74020i	0.0124963	−	0.0869138i
$995$	−3.80476	−	18.5810i	−0.120619	−	0.589056i
$996$	0.642522	−	0.293430i	0.0203591	−	0.00929768i
$997$	−28.2952	−	2.02371i	−0.896118	−	0.0640916i	−0.384322	−	0.923199i	$-0.625565\pi$
$997$	−28.2952	−	2.02371i	−0.896118	−	0.0640916i	−0.511796	+	0.859107i	$0.671019\pi$
$998$	9.10799	−	12.1668i	0.288308	−	0.385135i
$999$	1.60912	−	3.52349i	0.0509104	−	0.111478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.373.7	yes	240
5.2	odd	4	inner	690.2.w.a.97.7	yes	240
23.14	odd	22	inner	690.2.w.a.313.7	yes	240
115.37	even	44	inner	690.2.w.a.37.7	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.37.7	✓	240	115.37	even	44	inner
690.2.w.a.97.7	yes	240	5.2	odd	4	inner
690.2.w.a.313.7	yes	240	23.14	odd	22	inner
690.2.w.a.373.7	yes	240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.877679 - 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-1.94930 - 1.09554i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.266002 - 0.713180i) q^{7} +(0.0713392 - 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +O(q^{10})\)	\(q+(0.877679 - 0.479249i) q^{2} +(0.997452 - 0.0713392i) q^{3} +(0.540641 - 0.841254i) q^{4} +(-1.94930 - 1.09554i) q^{5} +(0.841254 - 0.540641i) q^{6} +(0.266002 - 0.713180i) q^{7} +(0.0713392 - 0.997452i) q^{8} +(0.989821 - 0.142315i) q^{9} +(-2.23590 - 0.0273353i) q^{10} +(-1.07796 - 3.67121i) q^{11} +(0.479249 - 0.877679i) q^{12} +(1.99930 - 0.745701i) q^{13} +(-0.108326 - 0.753424i) q^{14} +(-2.02249 - 0.953692i) q^{15} +(-0.415415 - 0.909632i) q^{16} +(-3.59684 - 0.782446i) q^{17} +(0.800541 - 0.599278i) q^{18} +(0.402082 + 0.258402i) q^{19} +(-1.97550 + 1.04756i) q^{20} +(0.214447 - 0.730339i) q^{21} +(-2.70553 - 2.70553i) q^{22} +(2.66718 - 3.98574i) q^{23} -1.00000i q^{24} +(2.59956 + 4.27110i) q^{25} +(1.39737 - 1.61265i) q^{26} +(0.977147 - 0.212565i) q^{27} +(-0.456153 - 0.609350i) q^{28} +(1.30424 + 2.02944i) q^{29} +(-2.23215 + 0.132242i) q^{30} +(-1.58642 - 1.83082i) q^{31} +(-0.800541 - 0.599278i) q^{32} +(-1.33712 - 3.58495i) q^{33} +(-3.53186 + 1.03705i) q^{34} +(-1.29984 + 1.09879i) q^{35} +(0.415415 - 0.909632i) q^{36} +(2.32132 - 3.10092i) q^{37} +(0.476738 + 0.0340970i) q^{38} +(1.94101 - 0.886429i) q^{39} +(-1.23182 + 1.86618i) q^{40} +(0.610814 - 4.24831i) q^{41} +(-0.161799 - 0.743777i) q^{42} +(0.197108 + 2.75593i) q^{43} +(-3.67121 - 1.07796i) q^{44} +(-2.08537 - 0.806979i) q^{45} +(0.430764 - 4.77645i) q^{46} +(-3.20158 + 3.20158i) q^{47} +(-0.479249 - 0.877679i) q^{48} +(4.85238 + 4.20461i) q^{49} +(4.32850 + 2.50281i) q^{50} +(-3.64350 - 0.523856i) q^{51} +(0.453580 - 2.08507i) q^{52} +(1.42225 + 0.530471i) q^{53} +(0.755750 - 0.654861i) q^{54} +(-1.92069 + 8.33725i) q^{55} +(-0.692386 - 0.316202i) q^{56} +(0.419492 + 0.229060i) q^{57} +(2.11731 + 1.15614i) q^{58} +(7.27790 + 3.32370i) q^{59} +(-1.89574 + 1.18582i) q^{60} +(-3.67344 + 3.18305i) q^{61} +(-2.26978 - 0.846586i) q^{62} +(0.161799 - 0.743777i) q^{63} +(-0.989821 - 0.142315i) q^{64} +(-4.71419 - 0.736727i) q^{65} +(-2.89164 - 2.50562i) q^{66} +(3.93580 + 7.20789i) q^{67} +(-2.60284 + 2.60284i) q^{68} +(2.37604 - 4.16586i) q^{69} +(-0.614250 + 1.58733i) q^{70} +(3.48967 + 1.02466i) q^{71} +(-0.0713392 - 0.997452i) q^{72} +(1.41187 + 6.49025i) q^{73} +(0.551261 - 3.83410i) q^{74} +(2.89764 + 4.07476i) q^{75} +(0.434764 - 0.198550i) q^{76} +(-2.90497 - 0.207768i) q^{77} +(1.27876 - 1.70823i) q^{78} +(2.14420 - 4.69513i) q^{79} +(-0.186773 + 2.22825i) q^{80} +(0.959493 - 0.281733i) q^{81} +(-1.49990 - 4.02138i) q^{82} +(0.565465 + 0.423302i) q^{83} +(-0.498462 - 0.575255i) q^{84} +(6.15413 + 5.46573i) q^{85} +(1.49378 + 2.32436i) q^{86} +(1.44570 + 1.93122i) q^{87} +(-3.73875 + 0.813316i) q^{88} +(0.972526 - 1.12236i) q^{89} +(-2.21703 + 0.291145i) q^{90} -1.62422i q^{91} +(-1.91103 - 4.39863i) q^{92} +(-1.71298 - 1.71298i) q^{93} +(-1.27561 + 4.34431i) q^{94} +(-0.500688 - 0.944203i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(8.22520 - 6.15731i) q^{97} +(6.27389 + 1.36480i) q^{98} +(-1.58946 - 3.48043i) 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

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