LMFDB - Embedded newform 525.2.bg.a.16.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.15
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.a.361.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27220 - 0.566420i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.0405990 + 0.0450897i) q^{4} +(-0.413100 - 2.19758i) q^{5} +(-0.430336 + 1.32444i) q^{6} +(-0.306993 + 2.62788i) q^{7} +(-0.886782 + 2.72924i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(1.27220 - 0.566420i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.0405990 + 0.0450897i) q^{4} +(-0.413100 - 2.19758i) q^{5} +(-0.430336 + 1.32444i) q^{6} +(-0.306993 + 2.62788i) q^{7} +(-0.886782 + 2.72924i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.77030 - 2.56177i) q^{10} +(-0.596284 + 5.67327i) q^{11} +(-0.00634218 - 0.0603419i) q^{12} +(0.464497 - 0.337477i) q^{13} +(1.09793 + 3.51708i) q^{14} +(1.90954 + 1.16347i) q^{15} +(0.405045 + 3.85374i) q^{16} +(2.06829 - 0.439629i) q^{17} +(-0.696298 - 1.20602i) q^{18} +(4.20403 + 4.66905i) q^{19} +(0.115860 + 0.0705929i) q^{20} +(-1.74748 - 1.98654i) q^{21} +(2.45486 + 7.55528i) q^{22} +(2.13487 - 0.950503i) q^{23} +(-1.43484 - 2.48522i) q^{24} +(-4.65870 + 1.81564i) q^{25} +(0.399780 - 0.692439i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.106027 - 0.120532i) q^{28} +(-2.25636 - 6.94436i) q^{29} +(3.08833 + 0.398571i) q^{30} +(-6.04833 + 1.28561i) q^{31} +(-0.171553 - 0.297138i) q^{32} +(-3.81707 - 4.23928i) q^{33} +(2.38227 - 1.73082i) q^{34} +(5.90179 - 0.410936i) q^{35} +(0.0490865 + 0.0356634i) q^{36} +(0.815244 + 7.75653i) q^{37} +(7.99301 + 3.55872i) q^{38} +(-0.0600150 + 0.571005i) q^{39} +(6.36404 + 0.821326i) q^{40} +(1.14419 - 0.831301i) q^{41} +(-3.34835 - 1.53747i) q^{42} -5.48905 q^{43} +(-0.231598 - 0.257215i) q^{44} +(-2.14236 + 0.640547i) q^{45} +(2.17759 - 2.41846i) q^{46} +(8.12678 + 1.72740i) q^{47} +(-3.13492 - 2.27765i) q^{48} +(-6.81151 - 1.61348i) q^{49} +(-4.89838 + 4.94864i) q^{50} +(-1.05725 + 1.83121i) q^{51} +(-0.00364136 + 0.0346453i) q^{52} +(2.31447 - 2.57048i) q^{53} +(1.36217 + 0.289537i) q^{54} +(12.7138 - 1.03325i) q^{55} +(-6.89987 - 3.16822i) q^{56} -6.28282 q^{57} +(-6.80396 - 7.55657i) q^{58} +(-1.06529 - 0.474297i) q^{59} +(-0.129986 + 0.0388647i) q^{60} +(9.85346 - 4.38704i) q^{61} +(-6.96650 + 5.06146i) q^{62} +(2.64557 + 0.0306233i) q^{63} +(-6.65639 - 4.83615i) q^{64} +(-0.933515 - 0.881356i) q^{65} +(-7.25729 - 3.23115i) q^{66} +(0.346736 - 0.0737011i) q^{67} +(-0.0641478 + 0.111107i) q^{68} +(-0.722142 + 2.22252i) q^{69} +(7.27550 - 3.86569i) q^{70} +(3.65000 + 11.2335i) q^{71} +(2.80698 + 0.596642i) q^{72} +(1.38982 - 13.2232i) q^{73} +(5.43061 + 9.40608i) q^{74} +(1.76799 - 4.67699i) q^{75} -0.381206 q^{76} +(-14.7256 - 3.30862i) q^{77} +(0.247077 + 0.760426i) q^{78} +(-13.4519 - 2.85929i) q^{79} +(8.30158 - 2.48210i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.984770 - 1.70567i) q^{82} +(4.00436 - 12.3241i) q^{83} +(0.160518 + 0.00185805i) q^{84} +(-1.82053 - 4.36362i) q^{85} +(-6.98317 + 3.10911i) q^{86} +(6.67046 + 2.96988i) q^{87} +(-14.9549 - 6.65835i) q^{88} +(-5.26466 + 2.34398i) q^{89} +(-2.36269 + 2.02838i) q^{90} +(0.744251 + 1.32425i) q^{91} +(-0.0438154 + 0.134850i) q^{92} +(3.09173 - 5.35503i) q^{93} +(11.3173 - 2.40557i) q^{94} +(8.52391 - 11.1675i) q^{95} +(0.335608 + 0.0713357i) q^{96} +(0.178377 + 0.548987i) q^{97} +(-9.57952 + 1.80550i) q^{98} +5.70452 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.27220	−	0.566420i	0.899582	−	0.400520i	0.0957700	−	0.995403i	$-0.469469\pi$
$2$	1.27220	−	0.566420i	0.899582	−	0.400520i	0.803812	+	0.594884i	$0.202802\pi$
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$4$	−0.0405990	+	0.0450897i	−0.0202995	+	0.0225449i
$5$	−0.413100	−	2.19758i	−0.184744	−	0.982787i
$5$	−0.413100	−	2.19758i	−0.184744	−	0.982787i
$6$	−0.430336	+	1.32444i	−0.175684	+	0.540700i
$7$	−0.306993	+	2.62788i	−0.116033	+	0.993245i
$7$	−0.306993	+	2.62788i	−0.116033	+	0.993245i
$8$	−0.886782	+	2.72924i	−0.313525	+	0.964931i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−1.77030	−	2.56177i	−0.559818	−	0.810103i
$11$	−0.596284	+	5.67327i	−0.179786	+	1.71055i	0.417625	+	0.908619i	$0.362862\pi$
$11$	−0.596284	+	5.67327i	−0.179786	+	1.71055i	−0.597412	+	0.801935i	$0.703804\pi$
$12$	−0.00634218	−	0.0603419i	−0.00183083	−	0.0174192i
$13$	0.464497	−	0.337477i	0.128828	−	0.0935992i	−0.521505	−	0.853248i	$-0.674629\pi$
$13$	0.464497	−	0.337477i	0.128828	−	0.0935992i	0.650333	+	0.759649i	$0.274629\pi$
$14$	1.09793	+	3.51708i	0.293433	+	0.939979i
$15$	1.90954	+	1.16347i	0.493040	+	0.300408i
$16$	0.405045	+	3.85374i	0.101261	+	0.963436i
$17$	2.06829	−	0.439629i	0.501634	−	0.106626i	0.0498569	−	0.998756i	$-0.484123\pi$
$17$	2.06829	−	0.439629i	0.501634	−	0.106626i	0.451777	+	0.892131i	$0.350790\pi$
$18$	−0.696298	−	1.20602i	−0.164119	−	0.284263i
$19$	4.20403	+	4.66905i	0.964471	+	1.07115i	0.997426	+	0.0716964i	$0.0228413\pi$
$19$	4.20403	+	4.66905i	0.964471	+	1.07115i	−0.0329558	+	0.999457i	$0.510492\pi$
$20$	0.115860	+	0.0705929i	0.0259070	+	0.0157850i
$21$	−1.74748	−	1.98654i	−0.381331	−	0.433498i
$22$	2.45486	+	7.55528i	0.523378	+	1.61079i
$23$	2.13487	−	0.950503i	0.445150	−	0.198194i	−0.171905	−	0.985114i	$-0.554992\pi$
$23$	2.13487	−	0.950503i	0.445150	−	0.198194i	0.617055	+	0.786920i	$0.288326\pi$
$24$	−1.43484	−	2.48522i	−0.292886	−	0.507294i
$25$	−4.65870	+	1.81564i	−0.931739	+	0.363128i
$26$	0.399780	−	0.692439i	0.0784032	−	0.135798i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.106027	−	0.120532i	−0.0200372	−	0.0227783i
$29$	−2.25636	−	6.94436i	−0.418995	−	1.28953i	−0.908628	−	0.417606i	$-0.862869\pi$
$29$	−2.25636	−	6.94436i	−0.418995	−	1.28953i	0.489633	−	0.871929i	$-0.337131\pi$
$30$	3.08833	+	0.398571i	0.563849	+	0.0727688i
$31$	−6.04833	+	1.28561i	−1.08631	+	0.230903i	−0.716068	−	0.698031i	$-0.754060\pi$
$31$	−6.04833	+	1.28561i	−1.08631	+	0.230903i	−0.370245	+	0.928934i	$0.620726\pi$
$32$	−0.171553	−	0.297138i	−0.0303265	−	0.0525271i
$33$	−3.81707	−	4.23928i	−0.664466	−	0.737964i
$34$	2.38227	−	1.73082i	0.408555	−	0.296833i
$35$	5.90179	−	0.410936i	0.997585	−	0.0694609i
$36$	0.0490865	+	0.0356634i	0.00818108	+	0.00594390i
$37$	0.815244	+	7.75653i	0.134025	+	1.27516i	0.830270	+	0.557361i	$0.188186\pi$
$37$	0.815244	+	7.75653i	0.134025	+	1.27516i	−0.696245	+	0.717804i	$0.745147\pi$
$38$	7.99301	+	3.55872i	1.29664	+	0.577300i
$39$	−0.0600150	+	0.571005i	−0.00961009	+	0.0914339i
$40$	6.36404	+	0.821326i	1.00624	+	0.129863i
$41$	1.14419	−	0.831301i	0.178692	−	0.129827i	−0.494844	−	0.868982i	$-0.664775\pi$
$41$	1.14419	−	0.831301i	0.178692	−	0.129827i	0.673536	+	0.739155i	$0.264775\pi$
$42$	−3.34835	−	1.53747i	−0.516662	−	0.237236i
$43$	−5.48905			−0.837072			−0.418536	−	0.908200i	$-0.637457\pi$
$43$	−5.48905			−0.837072			−0.418536	+	0.908200i	$0.637457\pi$
$44$	−0.231598	−	0.257215i	−0.0349146	−	0.0387766i
$45$	−2.14236	+	0.640547i	−0.319364	+	0.0954871i
$46$	2.17759	−	2.41846i	0.321068	−	0.356583i
$47$	8.12678	+	1.72740i	1.18541	+	0.251967i	0.758101	−	0.652137i	$-0.226127\pi$
$47$	8.12678	+	1.72740i	1.18541	+	0.251967i	0.427312	+	0.904104i	$0.359461\pi$
$48$	−3.13492	−	2.27765i	−0.452486	−	0.328751i
$49$	−6.81151	−	1.61348i	−0.973073	−	0.230498i
$50$	−4.89838	+	4.94864i	−0.692736	+	0.699843i
$51$	−1.05725	+	1.83121i	−0.148044	+	0.256421i
$52$	−0.00364136	+	0.0346453i	−0.000504966	+	0.00480443i
$53$	2.31447	−	2.57048i	0.317917	−	0.353082i	−0.562912	−	0.826517i	$-0.690319\pi$
$53$	2.31447	−	2.57048i	0.317917	−	0.353082i	0.880829	+	0.473434i	$0.156986\pi$
$54$	1.36217	+	0.289537i	0.185367	+	0.0394010i
$55$	12.7138	−	1.03325i	1.71432	−	0.139323i
$56$	−6.89987	−	3.16822i	−0.922034	−	0.423371i
$57$	−6.28282			−0.832180
$58$	−6.80396	−	7.55657i	−0.893404	−	0.992226i
$59$	−1.06529	−	0.474297i	−0.138689	−	0.0617483i	0.336219	−	0.941784i	$-0.390852\pi$
$59$	−1.06529	−	0.474297i	−0.138689	−	0.0617483i	−0.474908	+	0.880036i	$0.657519\pi$
$60$	−0.129986	+	0.0388647i	−0.0167811	+	0.00501741i
$61$	9.85346	−	4.38704i	1.26161	−	0.561703i	0.336597	−	0.941649i	$-0.390724\pi$
$61$	9.85346	−	4.38704i	1.26161	−	0.561703i	0.925009	+	0.379945i	$0.124057\pi$
$62$	−6.96650	+	5.06146i	−0.884746	+	0.642806i
$63$	2.64557	+	0.0306233i	0.333311	+	0.00385818i
$64$	−6.65639	−	4.83615i	−0.832049	−	0.604519i
$65$	−0.933515	−	0.881356i	−0.115788	−	0.109319i
$66$	−7.25729	−	3.23115i	−0.893310	−	0.397727i
$67$	0.346736	−	0.0737011i	0.0423606	−	0.00900402i	−0.186683	−	0.982420i	$-0.559774\pi$
$67$	0.346736	−	0.0737011i	0.0423606	−	0.00900402i	0.229043	+	0.973416i	$0.426440\pi$
$68$	−0.0641478	+	0.111107i	−0.00777906	+	0.0134737i
$69$	−0.722142	+	2.22252i	−0.0869357	+	0.267561i
$70$	7.27550	−	3.86569i	0.869588	−	0.462038i
$71$	3.65000	+	11.2335i	0.433175	+	1.33318i	0.894945	+	0.446177i	$0.147215\pi$
$71$	3.65000	+	11.2335i	0.433175	+	1.33318i	−0.461770	+	0.887000i	$0.652785\pi$
$72$	2.80698	+	0.596642i	0.330806	+	0.0703149i
$73$	1.38982	−	13.2232i	0.162666	−	1.54766i	−0.543375	−	0.839490i	$-0.682854\pi$
$73$	1.38982	−	13.2232i	0.162666	−	1.54766i	0.706041	−	0.708171i	$-0.250479\pi$
$74$	5.43061	+	9.40608i	0.631295	+	1.09344i
$75$	1.76799	−	4.67699i	0.204150	−	0.540052i
$76$	−0.381206			−0.0437273
$77$	−14.7256	−	3.30862i	−1.67814	−	0.377052i
$78$	0.247077	+	0.760426i	0.0279760	+	0.0861013i
$79$	−13.4519	−	2.85929i	−1.51346	−	0.321695i	−0.624989	−	0.780633i	$-0.714897\pi$
$79$	−13.4519	−	2.85929i	−1.51346	−	0.321695i	−0.888468	+	0.458938i	$0.848230\pi$
$80$	8.30158	−	2.48210i	0.928144	−	0.277507i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	0.984770	−	1.70567i	0.108750	−	0.188360i
$83$	4.00436	−	12.3241i	0.439535	−	1.35275i	−0.448831	−	0.893617i	$-0.648160\pi$
$83$	4.00436	−	12.3241i	0.439535	−	1.35275i	0.888367	−	0.459135i	$-0.151840\pi$
$84$	0.160518	+	0.00185805i	0.0175140	+	0.000202730i
$85$	−1.82053	−	4.36362i	−0.197464	−	0.473301i
$86$	−6.98317	+	3.10911i	−0.753015	+	0.335264i
$87$	6.67046	+	2.96988i	0.715149	+	0.318405i
$88$	−14.9549	−	6.65835i	−1.59420	−	0.709783i
$89$	−5.26466	+	2.34398i	−0.558053	+	0.248461i	−0.666327	−	0.745660i	$-0.732134\pi$
$89$	−5.26466	+	2.34398i	−0.558053	+	0.248461i	0.108274	+	0.994121i	$0.465468\pi$
$90$	−2.36269	+	2.02838i	−0.249049	+	0.213810i
$91$	0.744251	+	1.32425i	0.0780187	+	0.138819i
$92$	−0.0438154	+	0.134850i	−0.00456807	+	0.0140591i
$93$	3.09173	−	5.35503i	0.320597	−	0.555291i
$94$	11.3173	−	2.40557i	1.16729	−	0.248116i
$95$	8.52391	−	11.1675i	0.874535	−	1.14576i
$96$	0.335608	+	0.0713357i	0.0342528	+	0.00728067i
$97$	0.178377	+	0.548987i	0.0181114	+	0.0557412i	0.959704	−	0.281014i	$-0.0906706\pi$
$97$	0.178377	+	0.548987i	0.0181114	+	0.0557412i	−0.941592	+	0.336755i	$0.890671\pi$
$98$	−9.57952	+	1.80550i	−0.967677	+	0.182383i
$99$	5.70452			0.573325
$100$	0.107272	−	0.283773i	0.0107272	−	0.0283773i
$101$	7.36291	+	12.7529i	0.732637	+	1.26896i	0.955752	+	0.294173i	$0.0950440\pi$
$101$	7.36291	+	12.7529i	0.732637	+	1.26896i	−0.223115	+	0.974792i	$0.571623\pi$
$102$	−0.307799	+	2.92851i	−0.0304766	+	0.289966i
$103$	7.17241	+	1.52454i	0.706718	+	0.150218i	0.547230	−	0.836982i	$-0.315682\pi$
$103$	7.17241	+	1.52454i	0.706718	+	0.150218i	0.159488	+	0.987200i	$0.449016\pi$
$104$	0.509146	+	1.56699i	0.0499259	+	0.153656i
$105$	−3.64368	+	4.66085i	−0.355587	+	0.454853i
$106$	1.48850	−	4.58112i	0.144576	−	0.444958i
$107$	6.11136	−	10.5852i	0.590808	−	1.02331i	−0.403316	−	0.915061i	$-0.632142\pi$
$107$	6.11136	−	10.5852i	0.590808	−	1.02331i	0.994124	−	0.108249i	$-0.0345242\pi$
$108$	−0.0593484	+	0.0126149i	−0.00571080	+	0.00121387i
$109$	16.6480	+	7.41219i	1.59459	+	0.709959i	0.995852	−	0.0909833i	$-0.0290010\pi$
$109$	16.6480	+	7.41219i	1.59459	+	0.709959i	0.598742	+	0.800942i	$0.295668\pi$
$110$	15.5892	−	8.51583i	1.48637	−	0.811952i
$111$	−6.30973	−	4.58428i	−0.598893	−	0.435121i
$112$	−10.2515	−	0.118664i	−0.968678	−	0.0112127i
$113$	12.6082	−	9.16038i	1.18608	−	0.861736i	0.193233	−	0.981153i	$-0.438103\pi$
$113$	12.6082	−	9.16038i	1.18608	−	0.861736i	0.992844	+	0.119417i	$0.0381026\pi$
$114$	−7.99301	+	3.55872i	−0.748614	+	0.333305i
$115$	−2.97072	−	4.29888i	−0.277021	−	0.400873i
$116$	0.404725	+	0.180195i	0.0375778	+	0.0167307i
$117$	−0.384181	−	0.426676i	−0.0355176	−	0.0394462i
$118$	−1.62391			−0.149493
$119$	0.520340	+	5.57018i	0.0476995	+	0.510618i
$120$	−4.86874	+	4.17983i	−0.444453	+	0.381564i
$121$	−21.0708	−	4.47873i	−1.91552	−	0.407157i
$122$	10.0507	−	11.1624i	0.909945	−	1.01060i
$123$	−0.147834	+	1.40655i	−0.0133297	+	0.126824i
$124$	0.187588	−	0.324912i	0.0168459	−	0.0291780i
$125$	5.91452	+	9.48781i	0.529011	+	0.848615i
$126$	3.38305	−	1.45955i	0.301386	−	0.130027i
$127$	5.61798	+	4.08170i	0.498515	+	0.362192i	0.808450	−	0.588565i	$-0.200307\pi$
$127$	5.61798	+	4.08170i	0.498515	+	0.362192i	−0.309934	+	0.950758i	$0.600307\pi$
$128$	−10.5363	−	2.23957i	−0.931289	−	0.197952i
$129$	3.67289	−	4.07916i	0.323380	−	0.359150i
$130$	−1.68684	−	0.592500i	−0.147945	−	0.0519657i
$131$	−3.53788	−	3.92921i	−0.309106	−	0.343297i	0.568497	−	0.822685i	$-0.307525\pi$
$131$	−3.53788	−	3.92921i	−0.309106	−	0.343297i	−0.877603	+	0.479389i	$0.840858\pi$
$132$	0.346117			0.0301256
$133$	−13.5603	+	9.61432i	−1.17583	+	0.833667i
$134$	0.399372	−	0.290161i	0.0345005	−	0.0250661i
$135$	0.957499	−	2.02069i	0.0824084	−	0.173913i
$136$	−0.634273	+	6.03471i	−0.0543885	+	0.517472i
$137$	11.4433	+	5.09487i	0.977664	+	0.435284i	0.832440	−	0.554115i	$-0.186943\pi$
$137$	11.4433	+	5.09487i	0.977664	+	0.435284i	0.145224	+	0.989399i	$0.453610\pi$
$138$	0.340173	+	3.23653i	0.0289575	+	0.275512i
$139$	−9.64995	−	7.01110i	−0.818498	−	0.594674i	0.0977836	−	0.995208i	$-0.468825\pi$
$139$	−9.64995	−	7.01110i	−0.818498	−	0.594674i	−0.916282	+	0.400534i	$0.868825\pi$
$140$	−0.221078	+	0.282794i	−0.0186845	+	0.0239004i
$141$	−6.72158	+	4.88352i	−0.566060	+	0.411266i
$142$	11.0064	+	12.2239i	0.923640	+	1.02581i
$143$	1.63762	+	2.83645i	0.136945	+	0.237196i
$144$	3.79029	−	0.805652i	0.315858	−	0.0671376i
$145$	−14.3287	+	7.82724i	−1.18993	+	0.650017i
$146$	−5.72177	−	17.6098i	−0.473537	−	1.45740i
$147$	5.75684	−	3.98231i	0.474816	−	0.328455i
$148$	−0.382838	−	0.278148i	−0.0314691	−	0.0228636i
$149$	5.41858	−	9.38525i	0.443907	−	0.768870i	−0.554068	−	0.832471i	$-0.686925\pi$
$149$	5.41858	−	9.38525i	0.443907	−	0.768870i	0.997975	+	0.0636013i	$0.0202586\pi$
$150$	−0.399897	−	6.95149i	−0.0326515	−	0.567587i
$151$	4.12029	+	7.13654i	0.335304	+	0.580764i	0.983543	−	0.180673i	$-0.0578276\pi$
$151$	4.12029	+	7.13654i	0.335304	+	0.580764i	−0.648239	+	0.761437i	$0.724494\pi$
$152$	−16.4710	+	7.33336i	−1.33597	+	0.594814i
$153$	−0.653416	−	2.01101i	−0.0528255	−	0.162580i
$154$	−20.6080	+	4.13165i	−1.66064	+	0.332938i
$155$	5.32380	+	12.7606i	0.427618	+	1.02496i
$156$	−0.0233099	−	0.0258883i	−0.00186629	−	0.00207272i
$157$	−1.13584	−	1.96733i	−0.0906499	−	0.157010i	0.817135	−	0.576446i	$-0.195561\pi$
$157$	−1.13584	−	1.96733i	−0.0906499	−	0.157010i	−0.907785	+	0.419436i	$0.862228\pi$
$158$	−18.7331	+	3.98184i	−1.49032	+	0.316778i
$159$	0.361555	+	3.43997i	0.0286732	+	0.272807i
$160$	−0.582116	+	0.499748i	−0.0460203	+	0.0395086i
$161$	1.84242	+	5.90197i	0.145203	+	0.465140i
$162$	−1.12663	+	0.818548i	−0.0885168	+	0.0643112i
$163$	−0.383978	−	3.65331i	−0.0300755	−	0.286149i	−0.999214	−	0.0396335i	$-0.987381\pi$
$163$	−0.383978	−	3.65331i	−0.0300755	−	0.286149i	0.969139	−	0.246516i	$-0.0792857\pi$
$164$	−0.00896971	+	0.0853411i	−0.000700416	+	0.00666402i
$165$	−7.73932	+	10.1395i	−0.602505	+	0.789363i
$166$	−1.88630	−	17.9469i	−0.146405	−	1.39295i
$167$	−2.85319	+	8.78121i	−0.220786	+	0.679510i	0.777906	+	0.628381i	$0.216282\pi$
$167$	−2.85319	+	8.78121i	−0.220786	+	0.679510i	−0.998692	+	0.0511294i	$0.983718\pi$
$168$	6.97136	−	3.00765i	0.537852	−	0.232045i
$169$	−3.91535	+	12.0502i	−0.301181	+	0.926940i
$170$	−4.78772	−	4.52021i	−0.367201	−	0.346685i
$171$	4.20403	−	4.66905i	0.321490	−	0.357051i
$172$	0.222850	−	0.247500i	0.0169921	−	0.0188717i
$173$	7.91252	−	3.52288i	0.601578	−	0.267840i	−0.0832685	−	0.996527i	$-0.526536\pi$
$173$	7.91252	−	3.52288i	0.601578	−	0.267840i	0.684846	+	0.728687i	$0.259869\pi$
$174$	10.1684			0.770862
$175$	−3.34109	−	12.7999i	−0.252563	−	0.967580i
$176$	−22.1048			−1.66621
$177$	1.06529	−	0.474297i	0.0800720	−	0.0356504i
$178$	−5.37003	+	5.96402i	−0.402500	+	0.447022i
$179$	−12.9191	+	14.3482i	−0.965622	+	1.07243i	0.0317143	+	0.999497i	$0.489903\pi$
$179$	−12.9191	+	14.3482i	−0.965622	+	1.07243i	−0.997337	+	0.0729353i	$0.976763\pi$
$180$	0.0580955	−	0.122604i	0.00433018	−	0.00913836i
$181$	1.53076	−	4.71121i	0.113781	−	0.350181i	−0.877910	−	0.478826i	$-0.841063\pi$
$181$	1.53076	−	4.71121i	0.113781	−	0.350181i	0.991691	+	0.128644i	$0.0410626\pi$
$182$	1.69692	+	1.26315i	0.125784	+	0.0936307i
$183$	−3.33304	+	10.2581i	−0.246386	+	0.758297i
$184$	0.700986	+	6.66944i	0.0516774	+	0.491678i
$185$	16.7088	−	4.99578i	1.22845	−	0.367297i
$186$	0.900101	−	8.56389i	0.0659986	−	0.627935i
$187$	1.26084	+	11.9961i	0.0922019	+	0.877242i
$188$	−0.407827	+	0.296304i	−0.0297438	+	0.0216102i
$189$	−1.79299	+	1.94555i	−0.130421	+	0.141518i
$190$	4.51865	−	19.0354i	0.327817	−	1.38097i
$191$	1.04163	+	9.91043i	0.0753696	+	0.717093i	0.965326	+	0.261048i	$0.0840680\pi$
$191$	1.04163	+	9.91043i	0.0753696	+	0.717093i	−0.889956	+	0.456046i	$0.849265\pi$
$192$	8.04795	−	1.71065i	0.580811	−	0.123455i
$193$	12.5042	+	21.6579i	0.900070	+	1.55897i	0.827401	+	0.561612i	$0.189818\pi$
$193$	12.5042	+	21.6579i	0.900070	+	1.55897i	0.0726695	+	0.997356i	$0.476848\pi$
$194$	0.537888	+	0.597385i	0.0386181	+	0.0428898i
$195$	1.27962	−	0.103994i	0.0916354	−	0.00744720i
$196$	0.349292	−	0.241623i	0.0249494	−	0.0172588i
$197$	0.600158	+	1.84709i	0.0427595	+	0.131600i	0.970157	−	0.242476i	$-0.0779597\pi$
$197$	0.600158	+	1.84709i	0.0427595	+	0.131600i	−0.927398	+	0.374077i	$0.877960\pi$
$198$	7.25729	−	3.23115i	0.515753	−	0.229628i
$199$	−6.24648	−	10.8192i	−0.442801	−	0.766955i	0.555095	−	0.831787i	$-0.312682\pi$
$199$	−6.24648	−	10.8192i	−0.442801	−	0.766955i	−0.997896	+	0.0648325i	$0.979349\pi$
$200$	−0.824058	−	14.3248i	−0.0582697	−	1.01291i
$201$	−0.177241	+	0.306991i	−0.0125016	+	0.0216535i
$202$	16.5906	+	12.0538i	1.16731	+	0.848102i
$203$	18.9416	−	3.79757i	1.32944	−	0.266537i
$204$	−0.0396455	−	0.122016i	−0.00277574	−	0.00854285i
$205$	−2.29951	−	2.17103i	−0.160605	−	0.151631i
$206$	9.98827	−	2.12307i	0.695916	−	0.147921i
$207$	−1.16845	−	2.02382i	−0.0812129	−	0.140665i
$208$	1.48869	+	1.65336i	0.103222	+	0.114640i
$209$	−28.9955	+	21.0665i	−2.00566	+	1.45720i
$210$	−1.99549	+	7.99340i	−0.137702	+	0.551597i
$211$	−0.272248	−	0.197799i	−0.0187423	−	0.0136171i	0.578375	−	0.815771i	$-0.303687\pi$
$211$	−0.272248	−	0.197799i	−0.0187423	−	0.0136171i	−0.597117	+	0.802154i	$0.703687\pi$
$212$	0.0219371	+	0.208718i	0.00150665	+	0.0143348i
$213$	−10.7905	−	4.80423i	−0.739351	−	0.329180i
$214$	1.77921	−	16.9281i	0.121625	−	1.15718i
$215$	2.26753	+	12.0626i	0.154644	+	0.822663i
$216$	−2.32163	+	1.68676i	−0.157967	+	0.114770i
$217$	−1.52164	−	16.2890i	−0.103296	−	1.10577i
$218$	25.3781			1.71882
$219$	8.89680	+	9.88090i	0.601190	+	0.667689i
$220$	−0.469577	+	0.615209i	−0.0316589	+	0.0414774i
$221$	0.812350	−	0.902206i	0.0546446	−	0.0606890i
$222$	−10.6239	−	2.25817i	−0.713027	−	0.151559i
$223$	−8.54840	−	6.21078i	−0.572443	−	0.415904i	0.263549	−	0.964646i	$-0.415107\pi$
$223$	−8.54840	−	6.21078i	−0.572443	−	0.415904i	−0.835992	+	0.548742i	$0.815107\pi$
$224$	0.833509	−	0.359601i	0.0556912	−	0.0240268i
$225$	2.29266	+	4.44339i	0.152844	+	0.296226i
$226$	10.8515	−	18.7954i	0.721832	−	1.25025i
$227$	2.57236	−	24.4744i	0.170734	−	1.62442i	−0.488554	−	0.872534i	$-0.662476\pi$
$227$	2.57236	−	24.4744i	0.170734	−	1.62442i	0.659288	−	0.751890i	$-0.270858\pi$
$228$	0.255076	−	0.283291i	0.0168928	−	0.0187614i
$229$	4.76522	+	1.01288i	0.314895	+	0.0669329i	0.362648	−	0.931926i	$-0.381873\pi$
$229$	4.76522	+	1.01288i	0.314895	+	0.0669329i	−0.0477533	+	0.998859i	$0.515206\pi$
$230$	−6.21432	−	3.78636i	−0.409760	−	0.249665i
$231$	12.3121	−	8.72936i	0.810079	−	0.574350i
$232$	20.9537			1.37568
$233$	0.427870	+	0.475198i	0.0280307	+	0.0311312i	0.756997	−	0.653418i	$-0.226666\pi$
$233$	0.427870	+	0.475198i	0.0280307	+	0.0311312i	−0.728966	+	0.684549i	$0.759999\pi$
$234$	−0.730434	−	0.325210i	−0.0477499	−	0.0212596i
$235$	0.438922	−	18.5728i	0.0286321	−	1.21156i
$236$	0.0646356	−	0.0287776i	0.00420742	−	0.00187326i
$237$	11.1259	−	8.08347i	0.722708	−	0.525078i
$238$	3.81704	+	6.79166i	0.247422	+	0.440238i
$239$	14.8161	+	10.7646i	0.958376	+	0.696301i	0.952773	−	0.303683i	$-0.0982165\pi$
$239$	14.8161	+	10.7646i	0.958376	+	0.696301i	0.00560310	+	0.999984i	$0.498216\pi$
$240$	−3.71028	+	7.83012i	−0.239497	+	0.505432i
$241$	13.0272	+	5.80010i	0.839158	+	0.373617i	0.780879	−	0.624683i	$-0.214772\pi$
$241$	13.0272	+	5.80010i	0.839158	+	0.373617i	0.0582799	+	0.998300i	$0.481438\pi$
$242$	−29.3431	+	6.23706i	−1.88624	+	0.400934i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.202230	+	0.622400i	−0.0129464	+	0.0398450i
$245$	−0.731920	+	15.6354i	−0.0467606	+	0.998906i
$246$	0.608621	+	1.87314i	0.0388043	+	0.119427i
$247$	3.52845	+	0.749996i	0.224510	+	0.0477211i
$248$	1.85482	−	17.6474i	0.117781	−	1.12061i
$249$	6.47919	+	11.2223i	0.410602	+	0.711183i
$250$	12.8985	+	8.72029i	0.815775	+	0.551520i
$251$	−4.64103			−0.292939			−0.146469	−	0.989215i	$-0.546791\pi$
$251$	−4.64103			−0.292939			−0.146469	+	0.989215i	$0.546791\pi$
$252$	−0.108788	+	0.118045i	−0.00685303	+	0.00743613i
$253$	4.11947	+	12.6784i	0.258989	+	0.797086i
$254$	9.45916	+	2.01061i	0.593520	+	0.126157i
$255$	4.46097	+	1.56691i	0.279357	+	0.0981240i
$256$	1.42304	−	0.302476i	0.0889398	−	0.0189047i
$257$	9.07654	−	15.7210i	0.566179	−	0.980650i	−0.430760	−	0.902466i	$-0.641755\pi$
$257$	9.07654	−	15.7210i	0.566179	−	0.980650i	0.996939	−	0.0781839i	$-0.0249121\pi$
$258$	2.36214	−	7.26991i	0.147060	−	0.452605i
$259$	−20.6335	−	0.238839i	−1.28210	−	0.0148407i
$260$	0.0776399	−	0.00630978i	0.00481502	−	0.000391316i
$261$	−6.67046	+	2.96988i	−0.412891	+	0.183831i
$262$	−6.72648	−	2.99482i	−0.415563	−	0.185021i
$263$	−3.66625	−	1.63232i	−0.226071	−	0.100653i	0.290576	−	0.956852i	$-0.406153\pi$
$263$	−3.66625	−	1.63232i	−0.226071	−	0.100653i	−0.516646	+	0.856199i	$0.672820\pi$
$264$	14.9549	−	6.65835i	0.920411	−	0.409793i
$265$	−6.60493	−	4.02436i	−0.405738	−	0.247214i
$266$	−11.8057	+	19.9122i	−0.723853	+	1.22089i
$267$	1.78083	−	5.48083i	0.108985	−	0.335421i
$268$	−0.0107540	+	0.0186264i	−0.000656904	+	0.00113779i
$269$	−8.55851	+	1.81917i	−0.521822	+	0.110917i	−0.461290	−	0.887250i	$-0.652613\pi$
$269$	−8.55851	+	1.81917i	−0.521822	+	0.110917i	−0.0605321	+	0.998166i	$0.519280\pi$
$270$	0.0735697	−	3.11307i	0.00447731	−	0.189456i
$271$	5.02589	+	1.06829i	0.305301	+	0.0648937i	0.358015	−	0.933716i	$-0.383454\pi$
$271$	5.02589	+	1.06829i	0.305301	+	0.0648937i	−0.0527138	+	0.998610i	$0.516787\pi$
$272$	2.53197	+	7.79259i	0.153523	+	0.472495i
$273$	−1.48211	−	0.333007i	−0.0897012	−	0.0201545i
$274$	17.4440			1.05383
$275$	−7.52270	−	27.5127i	−0.453636	−	1.65908i
$276$	−0.0708948	−	0.122793i	−0.00426737	−	0.00739130i
$277$	1.18621	−	11.2860i	0.0712725	−	0.678113i	−0.899305	−	0.437323i	$-0.855927\pi$
$277$	1.18621	−	11.2860i	0.0712725	−	0.678113i	0.970577	−	0.240790i	$-0.0774066\pi$
$278$	−16.2479	−	3.45360i	−0.974485	−	0.207133i
$279$	1.91079	+	5.88082i	0.114396	+	0.352075i
$280$	−4.11206	+	16.4718i	−0.245743	+	0.984378i
$281$	−1.43178	+	4.40657i	−0.0854129	+	0.262874i	−0.984637	−	0.174615i	$-0.944132\pi$
$281$	−1.43178	+	4.40657i	−0.0854129	+	0.262874i	0.899224	+	0.437489i	$0.144132\pi$
$282$	−5.78508	+	10.0201i	−0.344497	+	0.596686i
$283$	−22.2899	+	4.73787i	−1.32500	+	0.281637i	−0.815462	−	0.578811i	$-0.803517\pi$
$283$	−22.2899	+	4.73787i	−1.32500	+	0.281637i	−0.509538	+	0.860448i	$0.670184\pi$
$284$	−0.654704	−	0.291493i	−0.0388495	−	0.0172969i
$285$	2.59544	+	13.8070i	0.153740	+	0.817856i
$286$	3.69001	+	2.68095i	0.218195	+	0.158528i
$287$	1.83330	+	3.26199i	0.108216	+	0.192549i
$288$	−0.277578	+	0.201672i	−0.0163565	+	0.0118837i
$289$	−11.4457	+	5.09596i	−0.673278	+	0.299763i
$290$	−13.7954	+	18.0739i	−0.810095	+	1.06133i
$291$	−0.527334	−	0.234784i	−0.0309129	−	0.0137633i
$292$	0.539806	+	0.599516i	0.0315898	+	0.0350840i
$293$	18.6415			1.08905			0.544525	−	0.838744i	$-0.316710\pi$
$293$	18.6415			1.08905			0.544525	+	0.838744i	$0.316710\pi$
$294$	5.06820	−	8.32708i	0.295583	−	0.485645i
$295$	−0.602234	+	2.53699i	−0.0350634	+	0.147709i
$296$	−21.8923	−	4.65336i	−1.27247	−	0.270471i
$297$	−3.81707	+	4.23928i	−0.221489	+	0.245988i
$298$	1.57752	−	15.0091i	0.0913834	−	0.869455i
$299$	0.670866	−	1.16197i	0.0387972	−	0.0671986i
$300$	0.139105	+	0.269599i	0.00803125	+	0.0155653i
$301$	1.68510	−	14.4246i	0.0971276	−	0.831418i
$302$	9.28411	+	6.74530i	0.534241	+	0.388149i
$303$	−14.4040	−	3.06167i	−0.827490	−	0.175888i
$304$	−16.2905	+	18.0924i	−0.934324	+	1.03767i
$305$	−13.7113	−	19.8415i	−0.785109	−	1.13612i
$306$	−1.97035	−	2.18830i	−0.112637	−	0.125097i
$307$	8.64014			0.493119			0.246559	−	0.969128i	$-0.420700\pi$
$307$	8.64014			0.493119			0.246559	+	0.969128i	$0.420700\pi$
$308$	0.747029	−	0.529647i	0.0425660	−	0.0301795i
$309$	−5.93223	+	4.31002i	−0.337473	+	0.245188i
$310$	14.0008	+	13.2185i	0.795192	+	0.750762i
$311$	0.951103	−	9.04914i	0.0539321	−	0.513130i	−0.933892	−	0.357555i	$-0.883610\pi$
$311$	0.951103	−	9.04914i	0.0539321	−	0.513130i	0.987824	−	0.155575i	$-0.0497229\pi$
$312$	−1.50519	−	0.670152i	−0.0852144	−	0.0379399i
$313$	3.15735	+	30.0402i	0.178464	+	1.69797i	0.607205	+	0.794545i	$0.292291\pi$
$313$	3.15735	+	30.0402i	0.178464	+	1.69797i	−0.428741	+	0.903428i	$0.641043\pi$
$314$	−2.55935	−	1.85948i	−0.144433	−	0.104936i
$315$	−1.02559	−	5.82651i	−0.0577854	−	0.328286i
$316$	0.675058	−	0.490459i	0.0379750	−	0.0275904i
$317$	−13.3370	−	14.8123i	−0.749082	−	0.831940i	0.241278	−	0.970456i	$-0.422433\pi$
$317$	−13.3370	−	14.8123i	−0.749082	−	0.831940i	−0.990360	+	0.138516i	$0.955767\pi$
$318$	2.40844	+	4.17154i	0.135059	+	0.233928i
$319$	40.7426	−	8.66011i	2.28115	−	0.484873i
$320$	−7.87806	+	16.6257i	−0.440397	+	0.929407i
$321$	3.77703	+	11.6245i	0.210813	+	0.648817i
$322$	5.68692	+	6.46490i	0.316920	+	0.360275i
$323$	10.7478	+	7.80874i	0.598024	+	0.434490i
$324$	0.0303371	−	0.0525454i	0.00168540	−	0.00291919i
$325$	−1.55121	+	2.41556i	−0.0860459	+	0.133991i
$326$	−2.55780	−	4.43025i	−0.141664	−	0.245369i
$327$	−16.6480	+	7.41219i	−0.920639	+	0.409895i
$328$	1.25417	+	3.85994i	0.0692500	+	0.213129i
$329$	−7.03427	+	20.8259i	−0.387812	+	1.14817i
$330$	−4.10272	+	17.2832i	−0.225847	+	0.951411i
$331$	5.33041	+	5.92002i	0.292986	+	0.325394i	0.871609	−	0.490201i	$-0.163077\pi$
$331$	5.33041	+	5.92002i	0.292986	+	0.325394i	−0.578624	+	0.815595i	$0.696410\pi$
$332$	0.393120	+	0.680903i	0.0215753	+	0.0373694i
$333$	7.62882	−	1.62156i	0.418057	−	0.0888607i
$334$	1.34403	+	12.7876i	0.0735419	+	0.699704i
$335$	−0.305201	−	0.731534i	−0.0166749	−	0.0399680i
$336$	6.94779	−	7.53896i	0.379033	−	0.411284i
$337$	−8.26266	+	6.00318i	−0.450096	+	0.327014i	−0.789634	−	0.613579i	$-0.789729\pi$
$337$	−8.26266	+	6.00318i	−0.450096	+	0.327014i	0.339538	+	0.940592i	$0.389729\pi$
$338$	1.84437	+	17.5480i	0.100321	+	0.954487i
$339$	−1.62903	+	15.4992i	−0.0884768	+	0.841800i
$340$	0.270666	+	0.0950713i	0.0146789	+	0.00515597i
$341$	−3.68710	−	35.0804i	−0.199668	−	1.89971i
$342$	2.70373	−	8.32121i	0.146201	−	0.449960i
$343$	6.33113	−	17.4045i	0.341849	−	0.939755i
$344$	4.86759	−	14.9809i	0.262443	−	0.807716i
$345$	5.18249	+	0.668838i	0.279016	+	0.0360090i
$346$	8.07088	−	8.96362i	0.433893	−	0.481887i
$347$	14.7846	−	16.4199i	0.793677	−	0.881468i	−0.201507	−	0.979487i	$-0.564584\pi$
$347$	14.7846	−	16.4199i	0.793677	−	0.881468i	0.995185	+	0.0980190i	$0.0312506\pi$
$348$	−0.404725	+	0.180195i	−0.0216955	+	0.00965948i
$349$	−10.5671			−0.565644			−0.282822	−	0.959172i	$-0.591271\pi$
$349$	−10.5671			−0.565644			−0.282822	+	0.959172i	$0.591271\pi$
$350$	−11.5007	−	14.3916i	−0.614736	−	0.769261i
$351$	0.574150			0.0306458
$352$	1.78804	−	0.796086i	0.0953027	−	0.0424315i
$353$	−6.02265	+	6.68883i	−0.320553	+	0.356010i	−0.881788	−	0.471646i	$-0.843660\pi$
$353$	−6.02265	+	6.68883i	−0.320553	+	0.356010i	0.561235	+	0.827657i	$0.310327\pi$
$354$	1.08661	−	1.20680i	0.0577527	−	0.0641408i
$355$	23.1788	−	12.6617i	1.23020	−	0.672015i
$356$	0.108050	−	0.332545i	0.00572666	−	0.0176249i
$357$	−4.48763	−	3.34049i	−0.237511	−	0.176798i
$358$	−8.30865	+	25.5714i	−0.439126	+	1.35149i
$359$	0.487340	+	4.63673i	0.0257208	+	0.244717i	0.999827	+	0.0186243i	$0.00592864\pi$
$359$	0.487340	+	4.63673i	0.0257208	+	0.244717i	−0.974106	+	0.226093i	$0.927405\pi$
$360$	0.151603	−	6.41503i	0.00799019	−	0.338102i
$361$	−2.14010	+	20.3617i	−0.112637	+	1.07167i
$362$	−0.721084	−	6.86065i	−0.0378993	−	0.360588i
$363$	17.4274	−	12.6618i	0.914703	−	0.664571i
$364$	−0.0899257	−	0.0202049i	−0.00471339	−	0.00105903i
$365$	−29.6332	+	2.40828i	−1.55107	+	0.126055i
$366$	1.57007	+	14.9382i	0.0820688	+	0.780832i
$367$	9.59015	−	2.03845i	0.500602	−	0.106406i	0.0493116	−	0.998783i	$-0.484297\pi$
$367$	9.59015	−	2.03845i	0.500602	−	0.106406i	0.451290	+	0.892377i	$0.350964\pi$
$368$	4.52771	+	7.84222i	0.236023	+	0.408804i
$369$	−0.946347	−	1.05102i	−0.0492648	−	0.0547141i
$370$	18.4272	−	15.8198i	0.957985	−	0.822434i
$371$	6.04438	+	6.87127i	0.313809	+	0.356738i
$372$	0.115936	+	0.356814i	0.00601100	+	0.0185000i
$373$	2.11795	−	0.942973i	0.109663	−	0.0488253i	−0.351172	−	0.936311i	$-0.614217\pi$
$373$	2.11795	−	0.942973i	0.109663	−	0.0488253i	0.460835	+	0.887486i	$0.347550\pi$
$374$	8.39888	+	14.5473i	0.434296	+	0.752222i
$375$	−11.0084	−	1.95324i	−0.568471	−	0.100865i
$376$	−11.9212	+	20.6481i	−0.614787	+	1.06484i
$377$	−3.39163	−	2.46416i	−0.174678	−	0.126911i
$378$	−1.17904	+	3.49072i	−0.0606435	+	0.179543i
$379$	−4.82447	−	14.8482i	−0.247816	−	0.762700i	−0.995160	−	0.0982631i	$-0.968671\pi$
$379$	−4.82447	−	14.8482i	−0.247816	−	0.762700i	0.747344	−	0.664437i	$-0.231329\pi$
$380$	0.157476	+	0.837729i	0.00807835	+	0.0429746i
$381$	−6.79246	+	1.44378i	−0.347988	+	0.0739672i
$382$	6.93863	+	12.0181i	0.355011	+	0.614897i
$383$	7.39683	+	8.21501i	0.377960	+	0.419767i	0.901871	−	0.432006i	$-0.142194\pi$
$383$	7.39683	+	8.21501i	0.377960	+	0.419767i	−0.523911	+	0.851773i	$0.675527\pi$
$384$	8.71451	−	6.33146i	0.444710	−	0.323101i
$385$	−1.18780	+	33.7275i	−0.0605357	+	1.71891i
$386$	28.1753	+	20.4705i	1.43408	+	1.04192i
$387$	0.573762	+	5.45898i	0.0291660	+	0.277496i
$388$	−0.0319956	−	0.0142454i	−0.00162433	−	0.000723198i
$389$	2.30141	−	21.8965i	0.116686	−	1.11019i	−0.766848	−	0.641828i	$-0.778176\pi$
$389$	2.30141	−	21.8965i	0.116686	−	1.11019i	0.883535	−	0.468366i	$-0.155157\pi$
$390$	1.56903	−	0.857104i	0.0794508	−	0.0434011i
$391$	3.99765	−	2.90447i	0.202170	−	0.146885i
$392$	10.4439	−	17.1594i	0.527497	−	0.866681i
$393$	5.28728			0.266708
$394$	1.80975	+	2.00993i	0.0911740	+	0.101259i
$395$	−0.726529	+	30.7428i	−0.0365557	+	1.54684i
$396$	−0.231598	+	0.257215i	−0.0116382	+	0.0129255i
$397$	−22.1036	−	4.69826i	−1.10935	−	0.235799i	−0.383423	−	0.923573i	$-0.625255\pi$
$397$	−22.1036	−	4.69826i	−1.10935	−	0.235799i	−0.725925	+	0.687774i	$0.758588\pi$
$398$	−14.0750	−	10.2261i	−0.705516	−	0.512588i
$399$	1.92879	−	16.5105i	0.0965601	−	0.826559i
$400$	−8.88399	−	17.2180i	−0.444199	−	0.860900i
$401$	6.78546	−	11.7528i	0.338850	−	0.586905i	−0.645367	−	0.763873i	$-0.723295\pi$
$401$	6.78546	−	11.7528i	0.338850	−	0.586905i	0.984217	+	0.176968i	$0.0566288\pi$
$402$	−0.0516006	+	0.490947i	−0.00257360	+	0.0244862i
$403$	−2.37557	+	2.63834i	−0.118335	+	0.131425i
$404$	−0.873953	−	0.185765i	−0.0434808	−	0.00924213i
$405$	0.860975	+	2.06367i	0.0427822	+	0.102544i
$406$	21.9465	−	15.5602i	1.08919	−	0.772239i
$407$	−44.4909			−2.20533
$408$	−4.06025	−	4.50936i	−0.201012	−	0.223247i
$409$	−28.3738	−	12.6328i	−1.40300	−	0.624654i	−0.440947	−	0.897533i	$-0.645357\pi$
$409$	−28.3738	−	12.6328i	−1.40300	−	0.624654i	−0.962048	+	0.272879i	$0.912024\pi$
$410$	−4.15515	−	1.45950i	−0.205208	−	0.0720793i
$411$	−11.4433	+	5.09487i	−0.564454	+	0.251311i
$412$	−0.359934	+	0.261507i	−0.0177327	+	0.0128835i
$413$	1.57343	−	2.65385i	0.0774236	−	0.130587i
$414$	−2.63283	−	1.91287i	−0.129397	−	0.0940122i
$415$	−28.7375	−	3.70878i	−1.41067	−	0.182057i
$416$	−0.179963	−	0.0801247i	−0.00882341	−	0.00392844i
$417$	11.6673	−	2.47997i	0.571352	−	0.121445i
$418$	−24.9557	+	43.2245i	−1.22062	+	2.11418i
$419$	2.29582	−	7.06581i	0.112158	−	0.345187i	−0.879186	−	0.476480i	$-0.841913\pi$
$419$	2.29582	−	7.06581i	0.112158	−	0.345187i	0.991344	+	0.131292i	$0.0419126\pi$
$420$	−0.0622269	−	0.353519i	−0.00303636	−	0.0172499i
$421$	10.7212	+	32.9965i	0.522519	+	1.60815i	0.769169	+	0.639045i	$0.220670\pi$
$421$	10.7212	+	32.9965i	0.522519	+	1.60815i	−0.246650	+	0.969105i	$0.579330\pi$
$422$	−0.458391	−	0.0974340i	−0.0223141	−	0.00474301i
$423$	0.868458	−	8.26282i	0.0422259	−	0.401752i
$424$	4.96301	+	8.59618i	0.241025	+	0.417468i
$425$	−8.83733	+	5.80337i	−0.428674	+	0.281505i
$426$	−16.4489			−0.796950
$427$	8.50368	+	27.2405i	0.411522	+	1.31826i
$428$	0.229168	+	0.705308i	0.0110773	+	0.0340924i
$429$	−3.20367	−	0.680962i	−0.154675	−	0.0328772i
$430$	9.71726	+	14.0617i	0.468608	+	0.678115i
$431$	−22.0484	+	4.68654i	−1.06203	+	0.225742i	−0.705624	−	0.708587i	$-0.749333\pi$
$431$	−22.0484	+	4.68654i	−1.06203	+	0.225742i	−0.356411	+	0.934329i	$0.616000\pi$
$432$	−1.93749	+	3.35582i	−0.0932173	+	0.161457i
$433$	7.56482	−	23.2821i	0.363542	−	1.11887i	−0.587347	−	0.809335i	$-0.699828\pi$
$433$	7.56482	−	23.2821i	0.363542	−	1.11887i	0.950889	−	0.309532i	$-0.100172\pi$
$434$	−11.1622	−	19.8610i	−0.535804	−	0.953356i
$435$	3.77098	−	15.8857i	0.180804	−	0.761662i
$436$	−1.01011	+	0.449729i	−0.0483754	+	0.0215381i
$437$	13.4130	+	5.97185i	0.641630	+	0.285672i
$438$	16.9153	+	7.53115i	0.808242	+	0.359852i
$439$	28.1436	−	12.5303i	1.34322	−	0.598039i	0.395888	−	0.918299i	$-0.370437\pi$
$439$	28.1436	−	12.5303i	1.34322	−	0.598039i	0.947330	+	0.320259i	$0.103770\pi$
$440$	−8.45437	+	35.6151i	−0.403046	+	1.69788i
$441$	−0.892648	+	6.94285i	−0.0425071	+	0.330612i
$442$	0.522444	−	1.60792i	0.0248501	−	0.0764809i
$443$	6.68147	−	11.5727i	0.317446	−	0.549833i	−0.662508	−	0.749055i	$-0.730508\pi$
$443$	6.68147	−	11.5727i	0.317446	−	0.549833i	0.979954	+	0.199221i	$0.0638413\pi$
$444$	0.462873	−	0.0983866i	0.0219670	−	0.00466922i
$445$	7.32590	+	10.6012i	0.347281	+	0.502545i
$446$	−14.3932	−	3.05937i	−0.681537	−	0.144865i
$447$	3.34887	+	10.3068i	0.158396	+	0.487493i
$448$	14.7523	−	16.0075i	0.696980	−	0.756285i
$449$	−2.74848			−0.129709			−0.0648545	−	0.997895i	$-0.520658\pi$
$449$	−2.74848			−0.129709			−0.0648545	+	0.997895i	$0.520658\pi$
$450$	5.43355	+	4.35427i	0.256140	+	0.205262i
$451$	4.03393	+	6.98697i	0.189950	+	0.329003i
$452$	−0.0988402	+	0.940402i	−0.00464905	+	0.0442328i
$453$	−8.06050	−	1.71331i	−0.378715	−	0.0804984i
$454$	−10.5902	−	32.5934i	−0.497024	−	1.52968i
$455$	2.60268	−	2.18260i	0.122016	−	0.102322i
$456$	5.57150	−	17.1473i	0.260909	−	0.802996i
$457$	1.29064	−	2.23545i	0.0603735	−	0.104570i	−0.834259	−	0.551373i	$-0.814104\pi$
$457$	1.29064	−	2.23545i	0.0603735	−	0.104570i	0.894632	+	0.446803i	$0.147437\pi$
$458$	6.63603	−	1.41053i	0.310081	−	0.0659098i
$459$	1.93169	+	0.860044i	0.0901636	+	0.0401434i
$460$	0.314444	+	0.0405812i	0.0146610	+	0.00189211i
$461$	−27.1200	−	19.7038i	−1.26310	−	0.917698i	−0.264198	−	0.964468i	$-0.585107\pi$
$461$	−27.1200	−	19.7038i	−1.26310	−	0.917698i	−0.998906	+	0.0467700i	$0.985107\pi$
$462$	10.7190	−	18.0793i	0.498694	−	0.841127i
$463$	12.7174	−	9.23975i	0.591029	−	0.429407i	−0.251655	−	0.967817i	$-0.580975\pi$
$463$	12.7174	−	9.23975i	0.591029	−	0.429407i	0.842683	+	0.538410i	$0.180975\pi$
$464$	25.8478	−	11.5082i	1.19996	−	0.534255i
$465$	−13.0453	−	4.58215i	−0.604961	−	0.212492i
$466$	0.813498	+	0.362192i	0.0376845	+	0.0167782i
$467$	−20.1327	−	22.3596i	−0.931631	−	1.03468i	−0.999316	−	0.0369742i	$-0.988228\pi$
$467$	−20.1327	−	22.3596i	−0.931631	−	1.03468i	0.0676853	−	0.997707i	$-0.478439\pi$
$468$	0.0348361			0.00161030
$469$	0.0872318	+	0.933807i	0.00402799	+	0.0431192i
$470$	−9.96162	−	23.8770i	−0.459495	−	1.10136i
$471$	2.22204	+	0.472309i	0.102386	+	0.0217628i
$472$	2.23915	−	2.48683i	0.103065	−	0.114465i
$473$	3.27303	−	31.1408i	0.150494	−	1.43186i
$474$	9.57579	−	16.5858i	0.439831	−	0.761809i
$475$	−28.0626	−	14.1187i	−1.28760	−	0.647809i
$476$	−0.272283	−	0.202682i	−0.0124801	−	0.00928991i
$477$	−2.79832	−	2.03310i	−0.128126	−	0.0930893i
$478$	24.9464	+	5.30251i	1.14102	+	0.242531i
$479$	−15.0704	+	16.7374i	−0.688586	+	0.764752i	−0.981516	−	0.191382i	$-0.938703\pi$
$479$	−15.0704	+	16.7374i	−0.688586	+	0.764752i	0.292930	+	0.956134i	$0.405370\pi$
$480$	0.0181260	−	0.766993i	0.000827334	−	0.0350083i
$481$	2.99633	+	3.32776i	0.136621	+	0.151733i
$482$	19.8586			0.904532
$483$	−5.61884	−	2.58000i	−0.255666	−	0.117394i
$484$	1.05740	−	0.768243i	0.0480635	−	0.0349202i
$485$	1.13275	−	0.618783i	0.0514357	−	0.0280975i
$486$	0.145566	−	1.38497i	0.00660301	−	0.0628234i
$487$	−5.81067	−	2.58708i	−0.263307	−	0.117232i	0.270838	−	0.962625i	$-0.412699\pi$
$487$	−5.81067	−	2.58708i	−0.263307	−	0.117232i	−0.534144	+	0.845393i	$0.679366\pi$
$488$	3.23540	+	30.7828i	0.146460	+	1.39347i
$489$	2.97187	+	2.15919i	0.134393	+	0.0976419i
$490$	7.92503	+	20.3059i	0.358016	+	0.917326i
$491$	−6.54646	+	4.75628i	−0.295437	+	0.214648i	−0.725623	−	0.688093i	$-0.758448\pi$
$491$	−6.54646	+	4.75628i	−0.295437	+	0.214648i	0.430185	+	0.902741i	$0.358448\pi$
$492$	−0.0574189	−	0.0637701i	−0.00258864	−	0.00287498i
$493$	−7.71974	−	13.3710i	−0.347680	−	0.602199i
$494$	4.91371	−	1.04444i	0.221078	−	0.0469917i
$495$	−2.35654	−	12.5361i	−0.105918	−	0.563457i
$496$	−7.40427	−	22.7880i	−0.332461	−	1.02321i
$497$	−30.6409	+	6.14314i	−1.37443	+	0.275557i
$498$	14.5994	+	10.6071i	0.654213	+	0.475313i
$499$	4.09267	−	7.08871i	0.183213	−	0.317334i	−0.759760	−	0.650204i	$-0.774684\pi$
$499$	4.09267	−	7.08871i	0.183213	−	0.317334i	0.942973	+	0.332869i	$0.108017\pi$
$500$	−0.667926	−	0.118511i	−0.0298706	−	0.00529999i
$501$	−4.61655	−	7.99611i	−0.206252	−	0.357240i
$502$	−5.90432	+	2.62877i	−0.263522	+	0.117328i
$503$	6.31794	+	19.4446i	0.281703	+	0.866993i	0.987367	+	0.158447i	$0.0506487\pi$
$503$	6.31794	+	19.4446i	0.281703	+	0.866993i	−0.705664	+	0.708546i	$0.749351\pi$
$504$	−2.42963	+	7.19324i	−0.108224	+	0.320412i
$505$	24.9840	−	21.4488i	1.11177	−	0.954460i
$506$	12.4221	+	13.7961i	0.552230	+	0.613314i
$507$	−6.33518	−	10.9728i	−0.281355	−	0.487321i
$508$	−0.412127	+	0.0876003i	−0.0182852	+	0.00388664i
$509$	−2.12154	−	20.1851i	−0.0940357	−	0.894690i	−0.935250	−	0.353988i	$-0.884825\pi$
$509$	−2.12154	−	20.1851i	−0.0940357	−	0.894690i	0.841214	−	0.540702i	$-0.181841\pi$
$510$	6.56278	−	0.533356i	0.290605	−	0.0236174i
$511$	34.3224	+	7.71171i	1.51833	+	0.341146i
$512$	19.0681	−	13.8538i	0.842698	−	0.612256i
$513$	0.656734	+	6.24841i	0.0289955	+	0.275874i
$514$	2.64247	−	25.1414i	0.116554	−	1.10894i
$515$	0.387377	−	16.3917i	0.0170699	−	0.722305i
$516$	0.0348126	+	0.331219i	0.00153254	+	0.0145811i
$517$	−14.6459	+	45.0753i	−0.644125	+	1.98241i
$518$	−26.3852	+	11.3834i	−1.15930	+	0.500157i
$519$	−2.67650	+	8.23742i	−0.117485	+	0.361583i
$520$	3.23325	−	1.76621i	0.141788	−	0.0774535i
$521$	22.4013	−	24.8791i	0.981417	−	1.08997i	−0.0145171	−	0.999895i	$-0.504621\pi$
$521$	22.4013	−	24.8791i	0.981417	−	1.08997i	0.995935	−	0.0900799i	$-0.0287122\pi$
$522$	−6.80396	+	7.55657i	−0.297801	+	0.330742i
$523$	−21.5491	+	9.59426i	−0.942274	+	0.419528i	−0.819611	−	0.572921i	$-0.805810\pi$
$523$	−21.5491	+	9.59426i	−0.942274	+	0.419528i	−0.122664	+	0.992448i	$0.539144\pi$
$524$	0.320801			0.0140143
$525$	11.7478	+	6.08188i	0.512716	+	0.265435i
$526$	−5.58878			−0.243682
$527$	−11.9445	+	5.31804i	−0.520312	+	0.231658i
$528$	14.7910	−	16.4271i	0.643696	−	0.714897i
$529$	−11.7358	+	13.0339i	−0.510253	+	0.566693i
$530$	−10.6823	−	1.37863i	−0.464008	−	0.0598837i
$531$	−0.360346	+	1.10903i	−0.0156377	+	0.0481278i
$532$	0.117028	−	1.00176i	0.00507379	−	0.0434319i
$533$	0.250927	−	0.772273i	0.0108688	−	0.0334509i
$534$	−0.838880	−	7.98141i	−0.0363019	−	0.345390i
$535$	−25.7864	−	9.05745i	−1.11484	−	0.391588i
$536$	−0.106332	+	1.01168i	−0.00459284	+	0.0436980i
$537$	−2.01817	−	19.2016i	−0.0870904	−	0.828610i
$538$	−9.85773	+	7.16206i	−0.424997	+	0.308778i
$539$	13.2153	−	37.6814i	0.569224	−	1.62305i
$540$	0.0522390	+	0.125211i	0.00224801	+	0.00538824i
$541$	0.152516	+	1.45109i	0.00655718	+	0.0623874i	0.997311	−	0.0732833i	$-0.0233477\pi$
$541$	0.152516	+	1.45109i	0.00655718	+	0.0623874i	−0.990754	+	0.135671i	$0.956681\pi$
$542$	6.99904	−	1.48769i	0.300634	−	0.0639018i
$543$	2.47683	+	4.28999i	0.106291	+	0.184101i
$544$	−0.485452	−	0.539149i	−0.0208136	−	0.0231158i
$545$	9.41155	−	39.6474i	0.403147	−	1.69831i
$546$	−2.07416	+	0.415844i	−0.0887658	+	0.0177965i
$547$	−3.31139	−	10.1914i	−0.141585	−	0.435754i	0.854971	−	0.518676i	$-0.173575\pi$
$547$	−3.31139	−	10.1914i	−0.141585	−	0.435754i	−0.996556	+	0.0829220i	$0.973575\pi$
$548$	−0.694311	+	0.309127i	−0.0296595	+	0.0132053i
$549$	−5.39298	−	9.34091i	−0.230167	−	0.398660i
$550$	−25.1541	−	30.7406i	−1.07257	−	1.31078i
$551$	22.9377	−	39.7293i	0.977181	−	1.69253i
$552$	−5.42541	−	3.94179i	−0.230921	−	0.167774i
$553$	11.6435	−	34.4722i	0.495133	−	1.46591i
$554$	−4.88355	−	15.0300i	−0.207482	−	0.638564i
$555$	−7.46777	+	15.7599i	−0.316989	+	0.668970i
$556$	0.707907	−	0.150470i	0.0300219	−	0.00638136i
$557$	8.23406	+	14.2618i	0.348888	+	0.604292i	0.986052	−	0.166436i	$-0.0532260\pi$
$557$	8.23406	+	14.2618i	0.348888	+	0.604292i	−0.637164	+	0.770728i	$0.719893\pi$
$558$	5.76193	+	6.39927i	0.243922	+	0.270903i
$559$	−2.54965	+	1.85243i	−0.107839	+	0.0783493i
$560$	3.97413	+	22.5775i	0.167938	+	0.954075i
$561$	−9.75851	−	7.08997i	−0.412005	−	0.299339i
$562$	0.674457	+	6.41703i	0.0284503	+	0.270686i
$563$	−0.949824	−	0.422889i	−0.0400303	−	0.0178226i	0.386624	−	0.922237i	$-0.373641\pi$
$563$	−0.949824	−	0.422889i	−0.0400303	−	0.0178226i	−0.426654	+	0.904415i	$0.640308\pi$
$564$	0.0526930	−	0.501340i	0.00221878	−	0.0211102i
$565$	−25.3391	−	23.9233i	−1.06602	−	1.00646i
$566$	−25.6737	+	18.6530i	−1.07914	+	0.784044i
$567$	−0.246082	−	2.63428i	−0.0103345	−	0.110629i
$568$	−33.8957			−1.42223
$569$	−20.7725	−	23.0702i	−0.870830	−	0.967154i	0.128870	−	0.991662i	$-0.458865\pi$
$569$	−20.7725	−	23.0702i	−0.870830	−	0.967154i	−0.999700	+	0.0245072i	$0.992198\pi$
$570$	11.1225	+	16.0952i	0.465869	+	0.674152i
$571$	16.6059	−	18.4427i	0.694933	−	0.771802i	−0.287628	−	0.957742i	$-0.592867\pi$
$571$	16.6059	−	18.4427i	0.694933	−	0.771802i	0.982561	+	0.185941i	$0.0595332\pi$
$572$	−0.194380	−	0.0413168i	−0.00812746	−	0.00172754i
$573$	−8.06187	−	5.85729i	−0.336789	−	0.244692i
$574$	4.17998	+	3.11149i	0.174469	+	0.129871i
$575$	−8.21992	+	8.30425i	−0.342794	+	0.346311i
$576$	−4.11387	+	7.12544i	−0.171411	+	0.296893i
$577$	−2.40393	+	22.8719i	−0.100077	+	0.952169i	0.823127	+	0.567858i	$0.192228\pi$
$577$	−2.40393	+	22.8719i	−0.100077	+	0.952169i	−0.923204	+	0.384311i	$0.874439\pi$
$578$	−11.6748	+	12.9662i	−0.485607	+	0.539322i
$579$	−24.4619	−	5.19953i	−1.01660	−	0.216085i
$580$	0.228801	−	0.963854i	0.00950045	−	0.0400218i
$581$	31.1571	+	14.3064i	1.29261	+	0.593530i
$582$	−0.803861			−0.0333211
$583$	13.2029	+	14.6633i	0.546809	+	0.607293i
$584$	34.8568	+	15.5193i	1.44239	+	0.642191i
$585$	−0.778949	+	1.02053i	−0.0322056	+	0.0421936i
$586$	23.7158	−	10.5589i	0.979690	−	0.436186i
$587$	−17.3430	+	12.6004i	−0.715821	+	0.520075i	−0.885046	−	0.465503i	$-0.845874\pi$
$587$	−17.3430	+	12.6004i	−0.715821	+	0.520075i	0.169225	+	0.985577i	$0.445874\pi$
$588$	−0.0541607	+	0.421252i	−0.00223355	+	0.0173721i
$589$	−31.4300	−	22.8352i	−1.29505	−	0.940909i
$590$	0.670839	+	3.56868i	0.0276180	+	0.146920i
$591$	−1.77424	−	0.789944i	−0.0729826	−	0.0324939i
$592$	−29.5614	+	6.28348i	−1.21497	+	0.258249i
$593$	−13.7575	+	23.8287i	−0.564952	+	0.978526i	0.432102	+	0.901825i	$0.357772\pi$
$593$	−13.7575	+	23.8287i	−0.564952	+	0.978526i	−0.997054	+	0.0767011i	$0.975561\pi$
$594$	−2.45486	+	7.55528i	−0.100724	+	0.309997i
$595$	12.0260	−	3.44453i	0.493016	−	0.141212i
$596$	0.203190	+	0.625354i	0.00832298	+	0.0256155i
$597$	12.2200	+	2.59743i	0.500130	+	0.106306i
$598$	0.195310	−	1.85825i	0.00798684	−	0.0759897i
$599$	−1.64326	−	2.84620i	−0.0671416	−	0.116293i	0.830500	−	0.557018i	$-0.188055\pi$
$599$	−1.64326	−	2.84620i	−0.0671416	−	0.116293i	−0.897642	+	0.440725i	$0.854721\pi$
$600$	11.1968	+	8.97274i	0.457106	+	0.366311i
$601$	4.33569			0.176856			0.0884282	−	0.996083i	$-0.471816\pi$
$601$	4.33569			0.176856			0.0884282	+	0.996083i	$0.471816\pi$
$602$	−6.02658	−	19.3054i	−0.245625	−	0.786830i
$603$	−0.109541	−	0.337133i	−0.00446086	−	0.0137291i
$604$	−0.489064	−	0.103954i	−0.0198997	−	0.00422982i
$605$	−1.13802	+	48.1548i	−0.0462671	+	1.95777i
$606$	−20.0590	+	4.26367i	−0.814841	+	0.173200i
$607$	0.444769	−	0.770362i	0.0180526	−	0.0312680i	−0.856858	−	0.515553i	$-0.827587\pi$
$607$	0.444769	−	0.770362i	0.0180526	−	0.0312680i	0.874911	+	0.484285i	$0.160920\pi$
$608$	0.666139	−	2.05017i	0.0270155	−	0.0831452i
$609$	−9.85228	+	16.6174i	−0.399235	+	0.673373i
$610$	−28.6822	−	17.4759i	−1.16131	−	0.707580i
$611$	4.35782	−	1.94023i	0.176299	−	0.0784932i
$612$	0.117204	+	0.0521825i	0.00473768	+	0.00210935i
$613$	28.5427	+	12.7080i	1.15283	+	0.513272i	0.891965	−	0.452104i	$-0.149326\pi$
$613$	28.5427	+	12.7080i	1.15283	+	0.513272i	0.260862	+	0.965376i	$0.415993\pi$
$614$	10.9920	−	4.89395i	0.443600	−	0.197504i
$615$	3.15206	−	0.256168i	0.127103	−	0.0103297i
$616$	22.0884	−	37.2556i	0.889967	−	1.50107i
$617$	3.68557	−	11.3430i	0.148376	−	0.456653i	−0.849054	−	0.528306i	$-0.822827\pi$
$617$	3.68557	−	11.3430i	0.148376	−	0.456653i	0.997430	+	0.0716530i	$0.0228274\pi$
$618$	−5.10571	+	8.84335i	−0.205382	+	0.355732i
$619$	20.0746	−	4.26699i	0.806867	−	0.171505i	0.214030	−	0.976827i	$-0.431341\pi$
$619$	20.0746	−	4.26699i	0.806867	−	0.171505i	0.592837	+	0.805322i	$0.298008\pi$
$620$	−0.791513	−	0.278018i	−0.0317879	−	0.0111655i
$621$	2.28583	+	0.485869i	0.0917274	+	0.0194973i
$622$	−3.91562	−	12.0510i	−0.157002	−	0.483203i
$623$	−4.54348	−	14.5545i	−0.182031	−	0.583113i
$624$	−2.22481			−0.0890638
$625$	18.4069	−	16.9170i	0.736276	−	0.676681i
$626$	21.0322	+	36.4288i	0.840614	+	1.45599i
$627$	3.74635	−	35.6441i	0.149615	−	1.42349i
$628$	0.134820	+	0.0286570i	0.00537992	+	0.00114354i
$629$	5.09615	+	15.6843i	0.203197	+	0.625376i
$630$	−4.60501	−	6.83157i	−0.183468	−	0.272176i
$631$	−10.9123	+	33.5845i	−0.434410	+	1.33698i	0.459279	+	0.888292i	$0.348108\pi$
$631$	−10.9123	+	33.5845i	−0.434410	+	1.33698i	−0.893690	+	0.448686i	$0.851892\pi$
$632$	19.7326	−	34.1778i	0.784920	−	1.35952i
$633$	0.329163	−	0.0699657i	0.0130830	−	0.00278089i
$634$	−25.3573	−	11.2898i	−1.00707	−	0.448376i
$635$	6.64907	−	14.0321i	0.263860	−	0.556847i
$636$	−0.169786	−	0.123357i	−0.00673246	−	0.00489142i
$637$	−3.70844	+	1.54927i	−0.146934	+	0.0613842i
$638$	46.9275	−	34.0948i	1.85788	−	1.34983i
$639$	10.7905	−	4.80423i	0.426865	−	0.190052i
$640$	−0.569061	+	24.0796i	−0.0224941	+	0.951829i
$641$	33.6553	+	14.9843i	1.32930	+	0.591844i	0.943694	−	0.330819i	$-0.107325\pi$
$641$	33.6553	+	14.9843i	1.32930	+	0.591844i	0.385608	+	0.922663i	$0.373992\pi$
$642$	11.3895	+	12.6493i	0.449508	+	0.499229i
$643$	18.1620			0.716240			0.358120	−	0.933676i	$-0.383418\pi$
$643$	18.1620			0.716240			0.358120	+	0.933676i	$0.383418\pi$
$644$	−0.340919	−	0.156540i	−0.0134341	−	0.00616853i
$645$	−10.4815	−	6.38636i	−0.412710	−	0.251463i
$646$	18.0964	+	3.84651i	0.711993	+	0.151339i
$647$	10.7677	−	11.9588i	0.423322	−	0.470147i	−0.493324	−	0.869845i	$-0.664218\pi$
$647$	10.7677	−	11.9588i	0.423322	−	0.470147i	0.916647	+	0.399698i	$0.130885\pi$
$648$	0.299964	−	2.85397i	0.0117837	−	0.112114i
$649$	3.32603	−	5.76085i	0.130558	−	0.226133i
$650$	−0.605233	+	3.95172i	−0.0237392	+	0.154999i
$651$	13.1232	+	9.76865i	0.514340	+	0.382864i
$652$	0.180316	+	0.131007i	0.00706171	+	0.00513064i
$653$	−24.4168	−	5.18996i	−0.955505	−	0.203099i	−0.296328	−	0.955086i	$-0.595762\pi$
$653$	−24.4168	−	5.18996i	−0.955505	−	0.203099i	−0.659177	+	0.751988i	$0.729095\pi$
$654$	−16.9812	+	18.8596i	−0.664019	+	0.737468i
$655$	−7.17325	+	9.39792i	−0.280282	+	0.367207i
$656$	3.66707	+	4.07269i	0.143175	+	0.159012i
$657$	−13.2961			−0.518729
$658$	2.84721	+	30.4791i	0.110996	+	1.18820i
$659$	35.8969	−	26.0806i	1.39834	−	1.01596i	0.403453	−	0.915000i	$-0.367810\pi$
$659$	35.8969	−	26.0806i	1.39834	−	1.01596i	0.994891	−	0.100956i	$-0.0321902\pi$
$660$	−0.142981	−	0.760619i	−0.00556553	−	0.0296071i
$661$	−0.151709	+	1.44341i	−0.00590078	+	0.0561422i	−0.997076	−	0.0764157i	$-0.975652\pi$
$661$	−0.151709	+	1.44341i	−0.00590078	+	0.0561422i	0.991175	+	0.132558i	$0.0423190\pi$
$662$	10.1346	+	4.51220i	0.393891	+	0.175372i
$663$	0.126902	+	1.20739i	0.00492845	+	0.0468911i
$664$	30.0845	+	21.8577i	1.16751	+	0.848242i
$665$	26.7300	+	25.8282i	1.03654	+	1.00157i
$666$	8.78690	−	6.38406i	0.340486	−	0.247377i
$667$	−11.4177	−	12.6806i	−0.442093	−	0.490994i
$668$	−0.280106	−	0.485158i	−0.0108376	−	0.0187713i
$669$	10.3355	−	2.19688i	0.399594	−	0.0849363i
$670$	−0.802632	−	0.757786i	−0.0310084	−	0.0292758i
$671$	19.0134	+	58.5172i	0.734004	+	2.25903i
$672$	−0.290491	+	0.860038i	−0.0112059	+	0.0331767i
$673$	−7.02238	−	5.10206i	−0.270693	−	0.196670i	0.444155	−	0.895950i	$-0.353504\pi$
$673$	−7.02238	−	5.10206i	−0.270693	−	0.196670i	−0.714848	+	0.699280i	$0.753504\pi$
$674$	−7.11144	+	12.3174i	−0.273923	+	0.474448i
$675$	−4.83617	−	1.26943i	−0.186144	−	0.0488604i
$676$	−0.384382	−	0.665769i	−0.0147839	−	0.0256065i
$677$	−36.5901	+	16.2910i	−1.40627	+	0.626113i	−0.962810	−	0.270179i	$-0.912917\pi$
$677$	−36.5901	+	16.2910i	−1.40627	+	0.626113i	−0.443463	+	0.896292i	$0.646250\pi$
$678$	6.70660	+	20.6408i	0.257565	+	0.792705i
$679$	−1.49743	+	0.300217i	−0.0574662	+	0.0115213i
$680$	13.5238	−	1.09907i	0.518612	−	0.0421476i
$681$	16.4668	+	18.2882i	0.631009	+	0.700806i
$682$	−24.5610	−	42.5408i	−0.940488	−	1.62897i
$683$	−48.3067	+	10.2679i	−1.84840	+	0.392890i	−0.992294	−	0.123904i	$-0.960458\pi$
$683$	−48.3067	+	10.2679i	−1.84840	+	0.392890i	−0.856109	+	0.516795i	$0.827125\pi$
$684$	0.0398468	+	0.379117i	0.00152358	+	0.0144959i
$685$	6.46916	−	27.2521i	0.247174	−	1.04125i
$686$	−1.80380	−	25.7281i	−0.0688692	−	0.982303i
$687$	−3.94127	+	2.86350i	−0.150369	+	0.109249i
$688$	−2.22331	−	21.1534i	−0.0847629	−	0.806465i
$689$	0.207587	−	1.97506i	0.00790843	−	0.0752437i
$690$	6.97201	−	2.08457i	0.265420	−	0.0793582i
$691$	−2.22313	−	21.1516i	−0.0845717	−	0.804646i	−0.951797	−	0.306730i	$-0.900765\pi$
$691$	−2.22313	−	21.1516i	−0.0845717	−	0.804646i	0.867225	−	0.497917i	$-0.165901\pi$
$692$	−0.162395	+	0.499799i	−0.00617331	+	0.0189995i
$693$	−1.75125	+	14.9908i	−0.0665244	+	0.569453i
$694$	9.50836	−	29.2637i	0.360932	−	1.11084i
$695$	−11.4210	+	24.1028i	−0.433225	+	0.914272i
$696$	−14.0208	+	15.5716i	−0.531455	+	0.590241i
$697$	2.00105	−	2.22239i	0.0757951	−	0.0841790i
$698$	−13.4435	+	5.98542i	−0.508843	+	0.226552i
$699$	−0.639441			−0.0241859
$700$	0.712789	+	0.369013i	0.0269409	+	0.0139474i
$701$	−31.0925			−1.17435			−0.587175	−	0.809460i	$-0.699760\pi$
$701$	−31.0925			−1.17435			−0.587175	+	0.809460i	$0.699760\pi$
$702$	0.730434	−	0.325210i	0.0275684	−	0.0122743i
$703$	−32.7883	+	36.4151i	−1.23663	+	1.37342i
$704$	31.4059	−	34.8797i	1.18365	−	1.31458i
$705$	13.5086	+	12.7538i	0.508763	+	0.480337i
$706$	−3.87333	+	11.9209i	−0.145775	+	0.448648i
$707$	−35.7736	+	15.4338i	−1.34540	+	0.580447i
$708$	−0.0218637	+	0.0672896i	−0.000821689	+	0.00252890i
$709$	0.951895	+	9.05667i	0.0357492	+	0.340130i	0.997748	+	0.0670764i	$0.0213671\pi$
$709$	0.951895	+	9.05667i	0.0357492	+	0.340130i	−0.961999	+	0.273054i	$0.911966\pi$
$710$	22.3162	−	29.2372i	0.837511	−	1.09725i
$711$	−1.43752	+	13.6771i	−0.0539112	+	0.512931i
$712$	−1.72866	−	16.4471i	−0.0647842	−	0.616381i
$713$	−11.6904	+	8.49357i	−0.437809	+	0.318087i
$714$	−7.60129	−	1.70789i	−0.284471	−	0.0639163i
$715$	5.55681	−	4.77054i	0.207813	−	0.178408i
$716$	−0.122451	−	1.16504i	−0.00457620	−	0.0435397i
$717$	−17.9136	+	3.80764i	−0.668994	+	0.142199i
$718$	3.24633	+	5.62281i	0.121152	+	0.209841i
$719$	24.9713	+	27.7335i	0.931273	+	1.03428i	0.999330	+	0.0366019i	$0.0116534\pi$
$719$	24.9713	+	27.7335i	0.931273	+	1.03428i	−0.0680570	+	0.997681i	$0.521680\pi$
$720$	−3.33625	−	7.99665i	−0.124335	−	0.298017i
$721$	−6.20820	+	18.3802i	−0.231205	+	0.684515i
$722$	8.81065	+	27.1164i	0.327899	+	1.00917i
$723$	−13.0272	+	5.80010i	−0.484488	+	0.215708i
$724$	0.150280	+	0.260292i	0.00558510	+	0.00967367i
$725$	23.1201	+	28.2549i	0.858660	+	1.04936i
$726$	14.9993	−	25.9796i	0.556676	−	0.964192i
$727$	17.5637	+	12.7608i	0.651402	+	0.473271i	0.863748	−	0.503923i	$-0.168111\pi$
$727$	17.5637	+	12.7608i	0.651402	+	0.473271i	−0.212347	+	0.977194i	$0.568111\pi$
$728$	−4.27417	+	0.856919i	−0.158411	+	0.0317595i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−36.3353	+	19.8487i	−1.34483	+	0.734632i
$731$	−11.3529	+	2.41314i	−0.419904	+	0.0892533i
$732$	−0.327215	−	0.566753i	−0.0120942	−	0.0209478i
$733$	−11.7367	−	13.0349i	−0.433504	−	0.481455i	0.486323	−	0.873779i	$-0.338338\pi$
$733$	−11.7367	−	13.0349i	−0.433504	−	0.481455i	−0.919827	+	0.392324i	$0.871671\pi$
$734$	11.0460	−	8.02537i	0.407714	−	0.296222i
$735$	−11.1296	−	11.0060i	−0.410521	−	0.405963i
$736$	−0.648673	−	0.471288i	−0.0239104	−	0.0173719i
$737$	0.211372	+	2.01107i	0.00778600	+	0.0740788i
$738$	−1.79926	−	0.801084i	−0.0662318	−	0.0294883i
$739$	−3.61789	+	34.4220i	−0.133086	+	1.26623i	0.700423	+	0.713728i	$0.252995\pi$
$739$	−3.61789	+	34.4220i	−0.133086	+	1.26623i	−0.833510	+	0.552505i	$0.813672\pi$
$740$	−0.453101	+	0.956219i	−0.0166563	+	0.0351513i
$741$	−2.91835	+	2.12031i	−0.107208	+	0.0778914i
$742$	11.5817	+	5.31797i	0.425177	+	0.195229i
$743$	−14.9318			−0.547796			−0.273898	−	0.961759i	$-0.588313\pi$
$743$	−14.9318			−0.547796			−0.273898	+	0.961759i	$0.588313\pi$
$744$	11.8735	+	13.1868i	0.435302	+	0.483452i
$745$	−22.8632	−	8.03070i	−0.837644	−	0.294222i
$746$	2.16034	−	2.39930i	0.0790957	−	0.0878447i
$747$	−12.6752	−	2.69420i	−0.463762	−	0.0985756i
$748$	−0.592090	−	0.430179i	−0.0216490	−	0.0157289i
$749$	25.9405	+	19.3095i	0.947844	+	0.705555i
$750$	−15.1112	+	3.75047i	−0.551785	+	0.136948i
$751$	−8.95508	+	15.5106i	−0.326775	+	0.565992i	−0.981870	−	0.189555i	$-0.939295\pi$
$751$	−8.95508	+	15.5106i	−0.326775	+	0.565992i	0.655095	+	0.755547i	$0.272629\pi$
$752$	−3.36525	+	32.0182i	−0.122718	+	1.16758i
$753$	3.10545	−	3.44895i	0.113169	−	0.125687i
$754$	−5.71059	−	1.21382i	−0.207967	−	0.0442048i
$755$	13.9810	−	12.0028i	0.508821	−	0.436825i
$756$	−0.0149309	−	0.159833i	−0.000543030	−	0.00581307i
$757$	32.1193			1.16740			0.583698	−	0.811971i	$-0.301605\pi$
$757$	32.1193			1.16740			0.583698	+	0.811971i	$0.301605\pi$
$758$	−14.5480	−	16.1572i	−0.528407	−	0.586856i
$759$	−12.1784	−	5.42216i	−0.442047	−	0.196812i
$760$	22.9198	+	33.1669i	0.831388	+	1.20309i
$761$	2.82488	−	1.25772i	0.102402	−	0.0455923i	−0.354896	−	0.934906i	$-0.615484\pi$
$761$	2.82488	−	1.25772i	0.102402	−	0.0455923i	0.457298	+	0.889313i	$0.348817\pi$
$762$	−7.82358	+	5.68416i	−0.283418	+	0.205916i
$763$	−24.5892	+	41.4736i	−0.890188	+	1.50144i
$764$	−0.489148	−	0.355387i	−0.0176967	−	0.0128574i
$765$	−4.14942	+	2.26668i	−0.150023	+	0.0819520i
$766$	14.0634	+	6.26143i	0.508131	+	0.226234i
$767$	−0.654888	+	0.139201i	−0.0236466	+	0.00502625i
$768$	−0.727414	+	1.25992i	−0.0262483	+	0.0454634i
$769$	−12.6354	+	38.8876i	−0.455643	+	1.40232i	0.414737	+	0.909942i	$0.363874\pi$
$769$	−12.6354	+	38.8876i	−0.455643	+	1.40232i	−0.870379	+	0.492382i	$0.836126\pi$
$770$	17.5928	+	43.5809i	0.634000	+	1.57055i
$771$	5.60961	+	17.2646i	0.202025	+	0.621769i
$772$	−1.48420	−	0.315477i	−0.0534177	−	0.0113543i
$773$	0.335845	−	3.19535i	0.0120795	−	0.114929i	−0.986821	−	0.161818i	$-0.948264\pi$
$773$	0.335845	−	3.19535i	0.0120795	−	0.114929i	0.998900	+	0.0468895i	$0.0149309\pi$
$774$	3.82202	+	6.61993i	0.137380	+	0.237948i
$775$	25.8431	−	16.9709i	0.928313	−	0.609612i
$776$	−1.65650			−0.0594648
$777$	13.9840	−	15.1739i	0.501673	−	0.544359i
$778$	−9.47474	−	29.1602i	−0.339686	−	1.04545i
$779$	8.69158	+	1.84745i	0.311408	+	0.0661918i
$780$	−0.0472622	+	0.0619198i	−0.00169226	+	0.00221708i
$781$	−65.9073	+	14.0090i	−2.35835	+	0.501283i
$782$	3.44067	−	5.95941i	0.123038	−	0.213108i
$783$	2.25636	−	6.94436i	0.0806357	−	0.248171i
$784$	3.45898	−	26.9033i	0.123535	−	0.960834i
$785$	−3.85415	+	3.30880i	−0.137560	+	0.118096i
$786$	6.72648	−	2.99482i	0.239925	−	0.106822i
$787$	−15.8184	−	7.04279i	−0.563863	−	0.251048i	0.104951	−	0.994477i	$-0.466531\pi$
$787$	−15.8184	−	7.04279i	−0.563863	−	0.251048i	−0.668815	+	0.743429i	$0.733198\pi$
$788$	−0.107651	−	0.0479292i	−0.00383490	−	0.00170741i
$789$	3.66625	−	1.63232i	0.130522	−	0.0581121i
$790$	16.4890	+	39.5225i	0.586654	+	1.40615i
$791$	20.2017	+	35.9450i	0.718291	+	1.27806i
$792$	−5.05866	+	15.5690i	−0.179752	+	0.553219i
$793$	3.09638	−	5.36308i	0.109956	−	0.190449i
$794$	−30.7814	+	6.54279i	−1.09239	+	0.232195i
$795$	7.41024	−	2.21560i	0.262814	−	0.0785792i
$796$	0.741437	+	0.157597i	0.0262795	+	0.00558589i
$797$	5.53023	+	17.0203i	0.195891	+	0.602890i	0.999965	+	0.00836101i	$0.00266142\pi$
$797$	5.53023	+	17.0203i	0.195891	+	0.602890i	−0.804074	+	0.594529i	$0.797339\pi$
$798$	−6.89808	−	22.0972i	−0.244190	−	0.782232i
$799$	17.5680			0.621510
$800$	1.33871	+	1.07280i	0.0473305	+	0.0379292i
$801$	2.88144	+	4.99081i	0.101811	+	0.176341i
$802$	1.97547	−	18.7953i	0.0697561	−	0.663685i
$803$	74.1901	+	15.7696i	2.61811	+	0.556497i
$804$	−0.00664632	−	0.0204553i	−0.000234398	−	0.000721402i
$805$	12.2089	−	6.48696i	0.430308	−	0.228635i
$806$	−1.52779	+	4.70206i	−0.0538142	+	0.165623i
$807$	4.37486	−	7.57748i	0.154002	−	0.266740i
$808$	−41.3351	+	8.78604i	−1.45416	+	0.309092i
$809$	−28.0880	−	12.5056i	−0.987522	−	0.439673i	−0.151553	−	0.988449i	$-0.548427\pi$
$809$	−28.0880	−	12.5056i	−0.987522	−	0.439673i	−0.835969	+	0.548776i	$0.815094\pi$
$810$	2.26424	+	2.13772i	0.0795571	+	0.0751120i
$811$	9.86486	+	7.16724i	0.346402	+	0.251676i	0.747358	−	0.664421i	$-0.231322\pi$
$811$	9.86486	+	7.16724i	0.346402	+	0.251676i	−0.400956	+	0.916097i	$0.631322\pi$
$812$	−0.597780	+	1.00825i	−0.0209779	+	0.0353827i
$813$	−4.15687	+	3.02014i	−0.145788	+	0.105921i
$814$	−56.6014	+	25.2006i	−1.98388	+	0.883279i
$815$	−7.86981	+	2.35300i	−0.275667	+	0.0824222i
$816$	−7.48524	−	3.33264i	−0.262036	−	0.116666i
$817$	−23.0761	−	25.6286i	−0.807332	−	0.896632i
$818$	−43.2527			−1.51230
$819$	1.23920	−	0.878595i	0.0433010	−	0.0307006i
$820$	0.191249	−	0.0155428i	0.00667870	−	0.000542777i
$821$	51.5560	+	10.9586i	1.79932	+	0.382456i	0.981261	−	0.192685i	$-0.0617194\pi$
$821$	51.5560	+	10.9586i	1.79932	+	0.382456i	0.818054	+	0.575141i	$0.195053\pi$
$822$	−11.6723	+	12.9634i	−0.407118	+	0.452150i
$823$	0.811645	−	7.72229i	0.0282922	−	0.269182i	−0.971226	−	0.238158i	$-0.923456\pi$
$823$	0.811645	−	7.72229i	0.0282922	−	0.269182i	0.999519	−	0.0310242i	$-0.00987691\pi$
$824$	−10.5212	+	18.2233i	−0.366523	+	0.634837i
$825$	25.4796	+	12.8191i	0.887084	+	0.446304i
$826$	0.498531	−	4.26745i	0.0173461	−	0.148484i
$827$	−15.9302	−	11.5740i	−0.553949	−	0.402468i	0.275290	−	0.961361i	$-0.411226\pi$
$827$	−15.9302	−	11.5740i	−0.553949	−	0.402468i	−0.829239	+	0.558894i	$0.811226\pi$
$828$	0.138691	+	0.0294797i	0.00481985	+	0.00102449i
$829$	28.8331	−	32.0224i	1.00141	−	1.11218i	0.00773038	−	0.999970i	$-0.497539\pi$
$829$	28.8331	−	32.0224i	1.00141	−	1.11218i	0.993684	−	0.112213i	$-0.0357940\pi$
$830$	−38.6606	+	11.5592i	−1.34193	+	0.401225i
$831$	7.59344	+	8.43337i	0.263413	+	0.292550i
$832$	−4.72396			−0.163774
$833$	−14.7975	−	0.342617i	−0.512704	−	0.0118710i
$834$	13.4385	−	9.76364i	0.465337	−	0.338087i
$835$	20.4760	+	2.64258i	0.708603	+	0.0914504i
$836$	0.227307	−	2.16268i	0.00786157	−	0.0747979i
$837$	−5.64887	−	2.51504i	−0.195254	−	0.0869325i
$838$	−1.08147	−	10.2895i	−0.0373588	−	0.355446i
$839$	6.18507	+	4.49371i	0.213532	+	0.155140i	0.689410	−	0.724371i	$-0.257870\pi$
$839$	6.18507	+	4.49371i	0.213532	+	0.155140i	−0.475878	+	0.879511i	$0.657870\pi$
$840$	−9.48942	−	14.0776i	−0.327416	−	0.485725i
$841$	−19.6715	+	14.2921i	−0.678326	+	0.492833i
$842$	32.3294	+	35.9054i	1.11414	+	1.23738i
$843$	−2.31667	−	4.01259i	−0.0797904	−	0.138201i
$844$	0.0199717	−	0.00424512i	0.000687454	−	0.000146123i
$845$	28.0987	+	3.62635i	0.966626	+	0.124750i
$846$	−3.57538	−	11.0039i	−0.122924	−	0.378321i
$847$	18.2381	−	53.9965i	0.626670	−	1.85534i
$848$	10.8434	+	7.87821i	0.372365	+	0.270539i
$849$	11.3940	−	19.7349i	0.391040	−	0.677301i
$850$	−7.95571	+	12.3887i	−0.272879	+	0.424929i
$851$	9.11304	+	15.7842i	0.312391	+	0.541077i
$852$	0.654704	−	0.291493i	0.0224298	−	0.00998638i
$853$	2.86755	+	8.82542i	0.0981831	+	0.302176i	0.988070	−	0.154004i	$-0.0492170\pi$
$853$	2.86755	+	8.82542i	0.0981831	+	0.302176i	−0.889887	+	0.456181i	$0.849217\pi$
$854$	26.2480	+	29.8387i	0.898187	+	1.02106i
$855$	−11.9973	−	7.30990i	−0.410298	−	0.249993i
$856$	23.4700	+	26.0661i	0.802189	+	0.890922i
$857$	15.4531	+	26.7655i	0.527867	+	0.914293i	0.999472	+	0.0324830i	$0.0103415\pi$
$857$	15.4531	+	26.7655i	0.527867	+	0.914293i	−0.471605	+	0.881810i	$0.656325\pi$
$858$	−4.46143	+	0.948305i	−0.152311	+	0.0323746i
$859$	−4.03459	−	38.3866i	−0.137658	−	1.30973i	−0.817310	−	0.576198i	$-0.804536\pi$
$859$	−4.03459	−	38.3866i	−0.137658	−	1.30973i	0.679652	−	0.733535i	$-0.262131\pi$
$860$	−0.635959	−	0.387488i	−0.0216860	−	0.0132132i
$861$	−3.65085	−	0.820290i	−0.124421	−	0.0279554i
$862$	−25.3955	+	18.4509i	−0.864973	+	0.628439i
$863$	0.646982	+	6.15562i	0.0220235	+	0.209540i	1.00000		0.000823058i	$0.000261988\pi$
$863$	0.646982	+	6.15562i	0.0220235	+	0.209540i	−0.977976	+	0.208717i	$0.933071\pi$
$864$	0.0358643	−	0.341226i	0.00122013	−	0.0116087i
$865$	−11.0105	−	15.9331i	−0.374367	−	0.541741i
$866$	−3.56349	−	33.9044i	−0.121092	−	1.15212i
$867$	3.87164	−	11.9157i	0.131488	−	0.404678i
$868$	0.796243	+	0.592706i	0.0270262	+	0.0201177i
$869$	24.2427	−	74.6113i	0.822376	−	2.53101i
$870$	−4.20055	−	22.3458i	−0.142412	−	0.757593i
$871$	0.136186	−	0.151249i	0.00461447	−	0.00512489i
$872$	−34.9928	+	38.8635i	−1.18501	+	1.31608i
$873$	0.527334	−	0.234784i	0.0178476	−	0.00794624i
$874$	20.4466			0.691616
$875$	−26.7485	+	12.6300i	−0.904266	+	0.426970i
$876$	−0.806728			−0.0272568
$877$	39.3802	−	17.5332i	1.32978	−	0.592054i	0.385957	−	0.922517i	$-0.373871\pi$
$877$	39.3802	−	17.5332i	1.32978	−	0.592054i	0.943819	+	0.330462i	$0.107205\pi$
$878$	28.7068	−	31.8821i	0.968808	−	1.07597i
$879$	−12.4736	+	13.8534i	−0.420725	+	0.467262i
$880$	9.13151	+	48.5771i	0.307823	+	1.63753i
$881$	12.6489	−	38.9293i	0.426153	−	1.31156i	−0.475734	−	0.879589i	$-0.657817\pi$
$881$	12.6489	−	38.9293i	0.426153	−	1.31156i	0.901886	−	0.431974i	$-0.142183\pi$
$882$	2.79694	+	9.33831i	0.0941780	+	0.314437i
$883$	2.36178	−	7.26881i	0.0794802	−	0.244615i	−0.903419	−	0.428758i	$-0.858951\pi$
$883$	2.36178	−	7.26881i	0.0794802	−	0.244615i	0.982899	+	0.184144i	$0.0589511\pi$
$884$	0.00769966	+	0.0732573i	0.000258967	+	0.00246391i
$885$	−1.48238	−	2.14512i	−0.0498295	−	0.0721075i
$886$	1.94519	−	18.5073i	0.0653500	−	0.621763i
$887$	−0.432762	−	4.11745i	−0.0145307	−	0.138251i	0.984851	−	0.173401i	$-0.0554756\pi$
$887$	−0.432762	−	4.11745i	−0.0145307	−	0.138251i	−0.999382	+	0.0351504i	$0.988809\pi$
$888$	18.1069	−	13.1555i	0.607629	−	0.441469i
$889$	−12.4509	+	13.5103i	−0.417590	+	0.453122i
$890$	15.3248	+	9.33731i	0.513687	+	0.312987i
$891$	−0.596284	−	5.67327i	−0.0199763	−	0.190062i
$892$	0.627099	−	0.133294i	0.0209968	−	0.00446301i
$893$	26.0999	+	45.2064i	0.873400	+	1.51277i
$894$	10.0984	+	11.2154i	0.337740	+	0.375099i
$895$	36.8681	+	22.4636i	1.23237	+	0.750875i
$896$	9.11990	−	27.0007i	0.304674	−	0.902030i
$897$	0.414618	+	1.27606i	0.0138437	+	0.0426065i
$898$	−3.49662	+	1.55680i	−0.116684	+	0.0519510i
$899$	22.5750	+	39.1010i	0.752917	+	1.30409i
$900$	−0.293431	−	0.0770217i	−0.00978103	−	0.00256739i
$901$	3.65694	−	6.33400i	0.121830	−	0.211016i
$902$	9.08952	+	6.60393i	0.302648	+	0.219887i
$903$	9.59199	+	10.9042i	0.319201	+	0.362869i
$904$	13.8201	+	42.5339i	0.459650	+	1.41466i
$905$	−10.9856	−	1.41777i	−0.365174	−	0.0471283i
$906$	−11.2250	+	2.38595i	−0.372926	+	0.0792679i
$907$	11.0767	+	19.1854i	0.367796	+	0.637041i	0.989221	−	0.146433i	$-0.0467791\pi$
$907$	11.0767	+	19.1854i	0.367796	+	0.637041i	−0.621425	+	0.783474i	$0.713446\pi$
$908$	0.999110	+	1.10962i	0.0331566	+	0.0368242i
$909$	11.9134	−	8.65562i	0.395144	−	0.287089i
$910$	2.07487	−	4.25091i	0.0687812	−	0.140916i
$911$	−38.5275	−	27.9919i	−1.27647	−	0.927413i	−0.277034	−	0.960860i	$-0.589351\pi$
$911$	−38.5275	−	27.9919i	−1.27647	−	0.927413i	−0.999440	+	0.0334470i	$0.989351\pi$
$912$	−2.54482	−	24.2124i	−0.0842676	−	0.801752i
$913$	67.5304	+	30.0665i	2.23493	+	0.995055i
$914$	0.375746	−	3.57499i	0.0124286	−	0.118250i
$915$	23.9198	+	3.08702i	0.790763	+	0.102054i
$916$	−0.239134	+	0.173741i	−0.00790119	+	0.00574055i
$917$	11.4116	−	8.09088i	0.376844	−	0.267184i
$918$	2.94464			0.0971877
$919$	−17.5046	−	19.4408i	−0.577424	−	0.641294i	0.381698	−	0.924287i	$-0.375339\pi$
$919$	−17.5046	−	19.4408i	−0.577424	−	0.641294i	−0.959122	+	0.282993i	$0.908673\pi$
$920$	14.3670	−	4.29562i	0.473667	−	0.141622i
$921$	−5.78138	+	6.42087i	−0.190503	+	0.211575i
$922$	−45.6627	−	9.70591i	−1.50382	−	0.319647i
$923$	5.48647	+	3.98616i	0.180589	+	0.131206i
$924$	−0.106256	+	0.909554i	−0.00349555	+	0.0299221i
$925$	−17.8810	−	34.6551i	−0.587925	−	1.13945i
$926$	10.9455	−	18.9582i	0.359692	−	0.623006i
$927$	0.766470	−	7.29248i	0.0251742	−	0.239516i
$928$	−1.67635	+	1.86177i	−0.0550289	+	0.0611157i
$929$	−2.63267	−	0.559591i	−0.0863751	−	0.0183596i	0.164521	−	0.986374i	$-0.447392\pi$
$929$	−2.63267	−	0.559591i	−0.0863751	−	0.0183596i	−0.250896	+	0.968014i	$0.580725\pi$
$930$	−19.1916	+	1.55970i	−0.629319	+	0.0511447i
$931$	−21.1024	−	38.5864i	−0.691602	−	1.26462i
$932$	−0.0387976			−0.00127086
$933$	6.08841	+	6.76187i	0.199326	+	0.221374i
$934$	−38.2778	−	17.0424i	−1.25249	−	0.557644i
$935$	25.8415	−	7.72639i	0.845108	−	0.252680i
$936$	1.50519	−	0.670152i	0.0491985	−	0.0219046i
$937$	−46.9912	+	34.1411i	−1.53514	+	1.11534i	−0.581841	+	0.813303i	$0.697667\pi$
$937$	−46.9912	+	34.1411i	−1.53514	+	1.11534i	−0.953296	+	0.302039i	$0.902333\pi$
$938$	0.639904	+	1.13858i	0.0208936	+	0.0371760i
$939$	−24.4369	−	17.7545i	−0.797468	−	0.579395i
$940$	0.819624	+	0.773828i	0.0267332	+	0.0252395i
$941$	−35.1972	−	15.6708i	−1.14740	−	0.510853i	−0.257167	−	0.966367i	$-0.582789\pi$
$941$	−35.1972	−	15.6708i	−1.14740	−	0.510853i	−0.890229	+	0.455514i	$0.849456\pi$
$942$	3.09440	−	0.657735i	0.100821	−	0.0214302i
$943$	1.65253	−	2.86227i	0.0538138	−	0.0932083i
$944$	1.39633	−	4.29746i	0.0454467	−	0.139870i
$945$	5.01619	+	3.13653i	0.163177	+	0.102031i
$946$	−13.4748	−	41.4713i	−0.438105	−	1.34835i
$947$	47.5558	+	10.1083i	1.54536	+	0.328476i	0.900166	−	0.435547i	$-0.143445\pi$
$947$	47.5558	+	10.1083i	1.54536	+	0.328476i	0.645190	+	0.764022i	$0.276778\pi$
$948$	−0.0872204	+	0.829847i	−0.00283279	+	0.0269522i
$949$	−3.81696	−	6.61118i	−0.123904	−	0.214608i
$950$	−43.6984	−	2.06656i	−1.41776	−	0.0670480i
$951$	19.9319			0.646336
$952$	−15.6638	−	3.51941i	−0.507666	−	0.114065i
$953$	−17.2402	−	53.0598i	−0.558464	−	1.71878i	−0.686615	−	0.727021i	$-0.740904\pi$
$953$	−17.2402	−	53.0598i	−0.558464	−	1.71878i	0.128151	−	0.991755i	$-0.459096\pi$
$954$	−4.71162	−	1.00149i	−0.152544	−	0.0324243i
$955$	21.3486	−	6.38306i	0.690826	−	0.206551i
$956$	−1.08689	+	0.231026i	−0.0351526	+	0.00747191i
$957$	−20.8264	+	36.0724i	−0.673222	+	1.16606i
$958$	−9.69221	+	29.8295i	−0.313141	+	0.963749i
$959$	−16.9017	+	28.5074i	−0.545785	+	0.920553i
$960$	−7.08389	−	16.9793i	−0.228631	−	0.548006i
$961$	6.60964	−	2.94280i	0.213214	−	0.0949291i
$962$	5.69683	+	2.53639i	0.183673	+	0.0817766i
$963$	−11.1660	−	4.97143i	−0.359820	−	0.160202i
$964$	−0.790418	+	0.351917i	−0.0254576	+	0.0113345i
$965$	42.4294	−	36.4258i	1.36585	−	1.17259i
$966$	−8.60965	−	0.0996593i	−0.277011	−	0.00320649i
$967$	−11.5201	+	35.4551i	−0.370460	+	1.14016i	0.576031	+	0.817428i	$0.304601\pi$
$967$	−11.5201	+	35.4551i	−0.370460	+	1.14016i	−0.946491	+	0.322731i	$0.895399\pi$
$968$	30.9087	−	53.5354i	0.993443	−	1.72069i
$969$	−12.9947	+	2.76211i	−0.417450	+	0.0887318i
$970$	1.09060	−	1.42883i	0.0350170	−	0.0458770i
$971$	−10.7703	−	2.28930i	−0.345635	−	0.0734670i	0.0318233	−	0.999494i	$-0.489869\pi$
$971$	−10.7703	−	2.28930i	−0.345635	−	0.0734670i	−0.377459	+	0.926026i	$0.623202\pi$
$972$	0.0187494	+	0.0577046i	0.000601386	+	0.00185088i
$973$	21.3868	−	23.2066i	0.685630	−	0.743968i
$974$	−8.85771			−0.283819
$975$	−0.757147	−	2.76910i	−0.0242481	−	0.0886822i
$976$	20.8976	+	36.1958i	0.668917	+	1.15860i
$977$	−3.02582	+	28.7887i	−0.0968044	+	0.921033i	0.833073	+	0.553163i	$0.186579\pi$
$977$	−3.02582	+	28.7887i	−0.0968044	+	0.921033i	−0.929877	+	0.367869i	$0.880087\pi$
$978$	5.00382	+	1.06360i	0.160005	+	0.0340100i
$979$	−10.1588	−	31.2655i	−0.324676	−	0.999249i
$980$	−0.675279	−	0.667782i	−0.0215710	−	0.0213315i
$981$	5.63139	−	17.3316i	0.179796	−	0.553357i
$982$	−5.63435	+	9.75899i	−0.179799	+	0.311422i
$983$	−16.1066	+	3.42357i	−0.513721	+	0.109195i	−0.457476	−	0.889222i	$-0.651246\pi$
$983$	−16.1066	+	3.42357i	−0.513721	+	0.109195i	−0.0562457	+	0.998417i	$0.517913\pi$
$984$	−3.70770	−	1.65077i	−0.118197	−	0.0526247i
$985$	3.81121	−	2.08193i	0.121435	−	0.0663357i
$986$	−17.3947	−	12.6380i	−0.553959	−	0.402475i
$987$	−10.7698	−	19.1627i	−0.342807	−	0.609956i
$988$	−0.177069	+	0.128648i	−0.00563331	+	0.00409284i
$989$	−11.7184	+	5.21736i	−0.372623	+	0.165902i
$990$	−10.0987	−	14.6137i	−0.320958	−	0.464453i
$991$	26.5061	+	11.8013i	0.841993	+	0.374879i	0.781969	−	0.623318i	$-0.214216\pi$
$991$	26.5061	+	11.8013i	0.841993	+	0.374879i	0.0600240	+	0.998197i	$0.480882\pi$
$992$	1.41961	+	1.57664i	0.0450728	+	0.0500584i
$993$	−7.96617			−0.252799
$994$	−35.5018	+	25.1709i	−1.12605	+	0.798374i
$995$	−21.1957	+	18.1966i	−0.671948	+	0.576870i
$996$	−0.769058	−	0.163468i	−0.0243685	−	0.00517969i
$997$	8.97115	−	9.96347i	0.284119	−	0.315546i	−0.584144	−	0.811650i	$-0.698570\pi$
$997$	8.97115	−	9.96347i	0.284119	−	0.315546i	0.868263	+	0.496104i	$0.165236\pi$
$998$	1.19151	−	11.3364i	0.0377165	−	0.358848i
$999$	−3.89963	+	6.75435i	−0.123379	+	0.213698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.a.16.15	✓	160
7.4	even	3	inner	525.2.bg.a.466.6	yes	160
25.11	even	5	inner	525.2.bg.a.436.6	yes	160
175.11	even	15	inner	525.2.bg.a.361.15	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.15	✓	160	1.1	even	1	trivial
525.2.bg.a.361.15	yes	160	175.11	even	15	inner
525.2.bg.a.436.6	yes	160	25.11	even	5	inner
525.2.bg.a.466.6	yes	160	7.4	even	3	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27220 - 0.566420i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.0405990 + 0.0450897i) q^{4} +(-0.413100 - 2.19758i) q^{5} +(-0.430336 + 1.32444i) q^{6} +(-0.306993 + 2.62788i) q^{7} +(-0.886782 + 2.72924i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(1.27220 - 0.566420i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.0405990 + 0.0450897i) q^{4} +(-0.413100 - 2.19758i) q^{5} +(-0.430336 + 1.32444i) q^{6} +(-0.306993 + 2.62788i) q^{7} +(-0.886782 + 2.72924i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.77030 - 2.56177i) q^{10} +(-0.596284 + 5.67327i) q^{11} +(-0.00634218 - 0.0603419i) q^{12} +(0.464497 - 0.337477i) q^{13} +(1.09793 + 3.51708i) q^{14} +(1.90954 + 1.16347i) q^{15} +(0.405045 + 3.85374i) q^{16} +(2.06829 - 0.439629i) q^{17} +(-0.696298 - 1.20602i) q^{18} +(4.20403 + 4.66905i) q^{19} +(0.115860 + 0.0705929i) q^{20} +(-1.74748 - 1.98654i) q^{21} +(2.45486 + 7.55528i) q^{22} +(2.13487 - 0.950503i) q^{23} +(-1.43484 - 2.48522i) q^{24} +(-4.65870 + 1.81564i) q^{25} +(0.399780 - 0.692439i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.106027 - 0.120532i) q^{28} +(-2.25636 - 6.94436i) q^{29} +(3.08833 + 0.398571i) q^{30} +(-6.04833 + 1.28561i) q^{31} +(-0.171553 - 0.297138i) q^{32} +(-3.81707 - 4.23928i) q^{33} +(2.38227 - 1.73082i) q^{34} +(5.90179 - 0.410936i) q^{35} +(0.0490865 + 0.0356634i) q^{36} +(0.815244 + 7.75653i) q^{37} +(7.99301 + 3.55872i) q^{38} +(-0.0600150 + 0.571005i) q^{39} +(6.36404 + 0.821326i) q^{40} +(1.14419 - 0.831301i) q^{41} +(-3.34835 - 1.53747i) q^{42} -5.48905 q^{43} +(-0.231598 - 0.257215i) q^{44} +(-2.14236 + 0.640547i) q^{45} +(2.17759 - 2.41846i) q^{46} +(8.12678 + 1.72740i) q^{47} +(-3.13492 - 2.27765i) q^{48} +(-6.81151 - 1.61348i) q^{49} +(-4.89838 + 4.94864i) q^{50} +(-1.05725 + 1.83121i) q^{51} +(-0.00364136 + 0.0346453i) q^{52} +(2.31447 - 2.57048i) q^{53} +(1.36217 + 0.289537i) q^{54} +(12.7138 - 1.03325i) q^{55} +(-6.89987 - 3.16822i) q^{56} -6.28282 q^{57} +(-6.80396 - 7.55657i) q^{58} +(-1.06529 - 0.474297i) q^{59} +(-0.129986 + 0.0388647i) q^{60} +(9.85346 - 4.38704i) q^{61} +(-6.96650 + 5.06146i) q^{62} +(2.64557 + 0.0306233i) q^{63} +(-6.65639 - 4.83615i) q^{64} +(-0.933515 - 0.881356i) q^{65} +(-7.25729 - 3.23115i) q^{66} +(0.346736 - 0.0737011i) q^{67} +(-0.0641478 + 0.111107i) q^{68} +(-0.722142 + 2.22252i) q^{69} +(7.27550 - 3.86569i) q^{70} +(3.65000 + 11.2335i) q^{71} +(2.80698 + 0.596642i) q^{72} +(1.38982 - 13.2232i) q^{73} +(5.43061 + 9.40608i) q^{74} +(1.76799 - 4.67699i) q^{75} -0.381206 q^{76} +(-14.7256 - 3.30862i) q^{77} +(0.247077 + 0.760426i) q^{78} +(-13.4519 - 2.85929i) q^{79} +(8.30158 - 2.48210i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.984770 - 1.70567i) q^{82} +(4.00436 - 12.3241i) q^{83} +(0.160518 + 0.00185805i) q^{84} +(-1.82053 - 4.36362i) q^{85} +(-6.98317 + 3.10911i) q^{86} +(6.67046 + 2.96988i) q^{87} +(-14.9549 - 6.65835i) q^{88} +(-5.26466 + 2.34398i) q^{89} +(-2.36269 + 2.02838i) q^{90} +(0.744251 + 1.32425i) q^{91} +(-0.0438154 + 0.134850i) q^{92} +(3.09173 - 5.35503i) q^{93} +(11.3173 - 2.40557i) q^{94} +(8.52391 - 11.1675i) q^{95} +(0.335608 + 0.0713357i) q^{96} +(0.178377 + 0.548987i) q^{97} +(-9.57952 + 1.80550i) q^{98} +5.70452 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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