LMFDB - Embedded newform 483.2.q.c.400.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 40 x^{18} - 117 x^{17} + 295 x^{16} - 575 x^{15} + 1777 x^{14} - 1560 x^{13} + \cdots + 2374681 $ x^20 - 8x^19 + 40x^18 - 117x^17 + 295x^16 - 575x^15 + 1777x^14 - 1560x^13 + 4383x^12 - 6446x^11 + 7261x^10 + 7700x^9 + 7852x^8 - 39430x^7 - 101709x^6 + 156742x^5 + 999838x^4 + 2029154x^3 + 3616480x^2 + 4299390*x + 2374681
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			400.1
Root			$2.10485 + 0.618040i$ of defining polynomial
Character	$\chi$	$=$	483.400
Dual form			483.2.q.c.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.273100 - 0.0801894i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.61435 + 1.03748i) q^{4} +(-0.0390977 - 0.271930i) q^{5} +(-0.239446 - 0.153882i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.730471 + 0.843008i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.273100 - 0.0801894i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.61435 + 1.03748i) q^{4} +(-0.0390977 - 0.271930i) q^{5} +(-0.239446 - 0.153882i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.730471 + 0.843008i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.0324835 - 0.0711290i) q^{10} +(4.25000 + 1.24791i) q^{11} +(1.84125 + 0.540641i) q^{12} +(0.917944 + 2.01002i) q^{13} +(0.0405070 - 0.281733i) q^{14} +(-0.179908 + 0.207625i) q^{15} +(1.46246 - 3.20234i) q^{16} +(-1.97931 - 1.27203i) q^{17} +(0.0405070 + 0.281733i) q^{18} +(4.49442 - 2.88839i) q^{19} +(0.345241 + 0.398429i) q^{20} +(-0.959493 + 0.281733i) q^{21} +1.26075 q^{22} +(4.62992 - 1.25052i) q^{23} +1.11546 q^{24} +(4.72505 - 1.38740i) q^{25} +(0.411873 + 0.475327i) q^{26} +(0.841254 - 0.540641i) q^{27} +(0.273100 + 1.89945i) q^{28} +(0.958025 + 0.615686i) q^{29} +(-0.0324835 + 0.0711290i) q^{30} +(2.03278 - 2.34596i) q^{31} +(0.460097 - 3.20005i) q^{32} +(-1.84005 - 4.02915i) q^{33} +(-0.642553 - 0.188671i) q^{34} +(-0.263598 - 0.0773995i) q^{35} +(-0.797176 - 1.74557i) q^{36} +(-1.32669 + 9.22735i) q^{37} +(0.995808 - 1.14922i) q^{38} +(0.917944 - 2.01002i) q^{39} +(0.257799 + 0.165678i) q^{40} +(0.524462 + 3.64772i) q^{41} +(-0.239446 + 0.153882i) q^{42} +(6.99339 + 8.07080i) q^{43} +(-8.15569 + 2.39473i) q^{44} +0.274727 q^{45} +(1.16415 - 0.712788i) q^{46} -9.89528 q^{47} +(-3.37787 + 0.991834i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(1.17916 - 0.757798i) q^{50} +(0.334840 + 2.32886i) q^{51} +(-3.56724 - 2.29253i) q^{52} +(5.06860 - 11.0987i) q^{53} +(0.186393 - 0.215109i) q^{54} +(0.173180 - 1.20450i) q^{55} +(0.463379 + 1.01466i) q^{56} +(-5.12611 - 1.50516i) q^{57} +(0.311008 + 0.0913203i) q^{58} +(0.248707 + 0.544593i) q^{59} +(0.0750279 - 0.521831i) q^{60} +(9.18014 - 10.5944i) q^{61} +(0.367033 - 0.803689i) q^{62} +(0.841254 + 0.540641i) q^{63} +(0.871076 + 6.05846i) q^{64} +(0.510695 - 0.328204i) q^{65} +(-0.825613 - 0.952808i) q^{66} +(-5.98771 + 1.75815i) q^{67} +4.51501 q^{68} +(-3.97703 - 2.68015i) q^{69} -0.0781954 q^{70} +(-14.1876 + 4.16585i) q^{71} +(-0.730471 - 0.843008i) q^{72} +(-6.05644 + 3.89224i) q^{73} +(0.377616 + 2.62638i) q^{74} +(-4.14277 - 2.66240i) q^{75} +(-4.25893 + 9.32576i) q^{76} +(2.90066 - 3.34754i) q^{77} +(0.0895085 - 0.622546i) q^{78} +(-0.242409 - 0.530803i) q^{79} +(-0.927993 - 0.272483i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.435739 + 0.954135i) q^{82} +(-0.753251 + 5.23898i) q^{83} +(1.25667 - 1.45027i) q^{84} +(-0.268516 + 0.587968i) q^{85} +(2.55709 + 1.64334i) q^{86} +(-0.162069 - 1.12722i) q^{87} +(-4.15650 + 2.67122i) q^{88} +(-9.17509 - 10.5886i) q^{89} +(0.0750279 - 0.0220302i) q^{90} +2.20970 q^{91} +(-6.17695 + 6.82224i) q^{92} -3.10415 q^{93} +(-2.70240 + 0.793497i) q^{94} +(-0.961162 - 1.10924i) q^{95} +(-2.71973 + 1.74787i) q^{96} +(1.84599 + 12.8391i) q^{97} +(-0.239446 - 0.153882i) q^{98} +(-1.84005 + 4.02915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.273100	−	0.0801894i	0.193111	−	0.0567025i	−0.183747	−	0.982974i	$-0.558823\pi$
$2$	0.273100	−	0.0801894i	0.193111	−	0.0567025i	0.376858	+	0.926271i	$0.377005\pi$
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$	−1.61435	+	1.03748i	−0.807177	+	0.518741i
$5$	−0.0390977	−	0.271930i	−0.0174850	−	0.121611i	0.979210	−	0.202852i	$-0.0650209\pi$
$5$	−0.0390977	−	0.271930i	−0.0174850	−	0.121611i	−0.996695	+	0.0812406i	$0.974112\pi$
$6$	−0.239446	−	0.153882i	−0.0977533	−	0.0628222i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$8$	−0.730471	+	0.843008i	−0.258260	+	0.298048i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	−0.0324835	−	0.0711290i	−0.0102722	−	0.0224930i
$11$	4.25000	+	1.24791i	1.28142	+	0.376260i	0.850427	−	0.526093i	$-0.176344\pi$
$11$	4.25000	+	1.24791i	1.28142	+	0.376260i	0.430997	+	0.902353i	$0.358162\pi$
$12$	1.84125	+	0.540641i	0.531524	+	0.156070i
$13$	0.917944	+	2.01002i	0.254592	+	0.557479i	0.993168	−	0.116691i	$-0.0372288\pi$
$13$	0.917944	+	2.01002i	0.254592	+	0.557479i	−0.738576	+	0.674170i	$0.764502\pi$
$14$	0.0405070	−	0.281733i	0.0108260	−	0.0752962i
$15$	−0.179908	+	0.207625i	−0.0464520	+	0.0536085i
$16$	1.46246	−	3.20234i	0.365615	−	0.800585i
$17$	−1.97931	−	1.27203i	−0.480053	−	0.308512i	0.278141	−	0.960540i	$-0.410282\pi$
$17$	−1.97931	−	1.27203i	−0.480053	−	0.308512i	−0.758194	+	0.652029i	$0.773918\pi$
$18$	0.0405070	+	0.281733i	0.00954760	+	0.0664050i
$19$	4.49442	−	2.88839i	1.03109	−	0.662641i	0.0883225	−	0.996092i	$-0.471849\pi$
$19$	4.49442	−	2.88839i	1.03109	−	0.662641i	0.942768	+	0.333451i	$0.108213\pi$
$20$	0.345241	+	0.398429i	0.0771981	+	0.0890914i
$21$	−0.959493	+	0.281733i	−0.209379	+	0.0614791i
$22$	1.26075			0.268792
$23$	4.62992	−	1.25052i	0.965406	−	0.260751i
$23$	4.62992	−	1.25052i	0.965406	−	0.260751i
$24$	1.11546			0.227692
$25$	4.72505	−	1.38740i	0.945009	−	0.277480i
$26$	0.411873	+	0.475327i	0.0807749	+	0.0932192i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	0.273100	+	1.89945i	0.0516111	+	0.358963i
$29$	0.958025	+	0.615686i	0.177901	+	0.114330i	0.626561	−	0.779373i	$-0.284462\pi$
$29$	0.958025	+	0.615686i	0.177901	+	0.114330i	−0.448660	+	0.893703i	$0.648098\pi$
$30$	−0.0324835	+	0.0711290i	−0.00593066	+	0.0129863i
$31$	2.03278	−	2.34596i	0.365099	−	0.421346i	−0.543243	−	0.839576i	$-0.682804\pi$
$31$	2.03278	−	2.34596i	0.365099	−	0.421346i	0.908342	+	0.418229i	$0.137349\pi$
$32$	0.460097	−	3.20005i	0.0813344	−	0.565693i
$33$	−1.84005	−	4.02915i	−0.320311	−	0.701384i
$34$	−0.642553	−	0.188671i	−0.110197	−	0.0323568i
$35$	−0.263598	−	0.0773995i	−0.0445563	−	0.0130829i
$36$	−0.797176	−	1.74557i	−0.132863	−	0.290929i
$37$	−1.32669	+	9.22735i	−0.218107	+	1.51697i	0.526910	+	0.849921i	$0.323350\pi$
$37$	−1.32669	+	9.22735i	−0.218107	+	1.51697i	−0.745017	+	0.667046i	$0.767559\pi$
$38$	0.995808	−	1.14922i	0.161541	−	0.186429i
$39$	0.917944	−	2.01002i	0.146989	−	0.321860i
$40$	0.257799	+	0.165678i	0.0407617	+	0.0261959i
$41$	0.524462	+	3.64772i	0.0819072	+	0.569677i	0.988906	+	0.148544i	$0.0474586\pi$
$41$	0.524462	+	3.64772i	0.0819072	+	0.569677i	−0.906999	+	0.421134i	$0.861632\pi$
$42$	−0.239446	+	0.153882i	−0.0369473	+	0.0237446i
$43$	6.99339	+	8.07080i	1.06648	+	1.23079i	0.971931	+	0.235266i	$0.0755961\pi$
$43$	6.99339	+	8.07080i	1.06648	+	1.23079i	0.0945510	+	0.995520i	$0.469858\pi$
$44$	−8.15569	+	2.39473i	−1.22952	+	0.361019i
$45$	0.274727			0.0409539
$46$	1.16415	−	0.712788i	0.171645	−	0.105095i
$47$	−9.89528			−1.44337			−0.721687	−	0.692219i	$-0.756633\pi$
$47$	−9.89528			−1.44337			−0.721687	+	0.692219i	$0.756633\pi$
$48$	−3.37787	+	0.991834i	−0.487554	+	0.143159i
$49$	−0.654861	−	0.755750i	−0.0935515	−	0.107964i
$50$	1.17916	−	0.757798i	0.166758	−	0.107169i
$51$	0.334840	+	2.32886i	0.0468870	+	0.326106i
$52$	−3.56724	−	2.29253i	−0.494688	−	0.317916i
$53$	5.06860	−	11.0987i	0.696225	−	1.52452i	−0.148264	−	0.988948i	$-0.547369\pi$
$53$	5.06860	−	11.0987i	0.696225	−	1.52452i	0.844489	−	0.535573i	$-0.179904\pi$
$54$	0.186393	−	0.215109i	0.0253648	−	0.0292726i
$55$	0.173180	−	1.20450i	0.0233516	−	0.162414i
$56$	0.463379	+	1.01466i	0.0619216	+	0.135589i
$57$	−5.12611	−	1.50516i	−0.678970	−	0.199364i
$58$	0.311008	+	0.0913203i	0.0408374	+	0.0119909i
$59$	0.248707	+	0.544593i	0.0323789	+	0.0709000i	0.925130	−	0.379649i	$-0.123955\pi$
$59$	0.248707	+	0.544593i	0.0323789	+	0.0709000i	−0.892751	+	0.450549i	$0.851228\pi$
$60$	0.0750279	−	0.521831i	0.00968606	−	0.0673681i
$61$	9.18014	−	10.5944i	1.17540	−	1.35648i	0.254309	−	0.967123i	$-0.418152\pi$
$61$	9.18014	−	10.5944i	1.17540	−	1.35648i	0.921087	−	0.389356i	$-0.127303\pi$
$62$	0.367033	−	0.803689i	0.0466132	−	0.102069i
$63$	0.841254	+	0.540641i	0.105988	+	0.0681143i
$64$	0.871076	+	6.05846i	0.108884	+	0.757308i
$65$	0.510695	−	0.328204i	0.0633440	−	0.0407087i
$66$	−0.825613	−	0.952808i	−0.101626	−	0.117283i
$67$	−5.98771	+	1.75815i	−0.731515	+	0.214792i	−0.626217	−	0.779649i	$-0.715398\pi$
$67$	−5.98771	+	1.75815i	−0.731515	+	0.214792i	−0.105298	+	0.994441i	$0.533580\pi$
$68$	4.51501			0.547526
$69$	−3.97703	−	2.68015i	−0.478779	−	0.322652i
$70$	−0.0781954			−0.00934614
$71$	−14.1876	+	4.16585i	−1.68376	+	0.494395i	−0.977032	−	0.213094i	$-0.931646\pi$
$71$	−14.1876	+	4.16585i	−1.68376	+	0.494395i	−0.706724	+	0.707489i	$0.749828\pi$
$72$	−0.730471	−	0.843008i	−0.0860868	−	0.0993495i
$73$	−6.05644	+	3.89224i	−0.708853	+	0.455552i	−0.844743	−	0.535172i	$-0.820247\pi$
$73$	−6.05644	+	3.89224i	−0.708853	+	0.455552i	0.135891	+	0.990724i	$0.456610\pi$
$74$	0.377616	+	2.62638i	0.0438970	+	0.305310i
$75$	−4.14277	−	2.66240i	−0.478366	−	0.307427i
$76$	−4.25893	+	9.32576i	−0.488533	+	1.06974i
$77$	2.90066	−	3.34754i	0.330560	−	0.381487i
$78$	0.0895085	−	0.622546i	0.0101348	−	0.0704894i
$79$	−0.242409	−	0.530803i	−0.0272732	−	0.0597200i	0.895505	−	0.445051i	$-0.146814\pi$
$79$	−0.242409	−	0.530803i	−0.0272732	−	0.0597200i	−0.922778	+	0.385331i	$0.874087\pi$
$80$	−0.927993	−	0.272483i	−0.103753	−	0.0304646i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	0.435739	+	0.954135i	0.0481193	+	0.105367i
$83$	−0.753251	+	5.23898i	−0.0826801	+	0.575053i	0.905800	+	0.423705i	$0.139271\pi$
$83$	−0.753251	+	5.23898i	−0.0826801	+	0.575053i	−0.988481	+	0.151348i	$0.951639\pi$
$84$	1.25667	−	1.45027i	0.137114	−	0.158238i
$85$	−0.268516	+	0.587968i	−0.0291247	+	0.0637741i
$86$	2.55709	+	1.64334i	0.275738	+	0.177206i
$87$	−0.162069	−	1.12722i	−0.0173756	−	0.120850i
$88$	−4.15650	+	2.67122i	−0.443085	+	0.284753i
$89$	−9.17509	−	10.5886i	−0.972558	−	1.12239i	−0.992457	−	0.122590i	$-0.960880\pi$
$89$	−9.17509	−	10.5886i	−0.972558	−	1.12239i	0.0198996	−	0.999802i	$-0.493665\pi$
$90$	0.0750279	−	0.0220302i	0.00790864	−	0.00232219i
$91$	2.20970			0.231640
$92$	−6.17695	+	6.82224i	−0.643991	+	0.711268i
$93$	−3.10415			−0.321885
$94$	−2.70240	+	0.793497i	−0.278732	+	0.0818430i
$95$	−0.961162	−	1.10924i	−0.0986131	−	0.113806i
$96$	−2.71973	+	1.74787i	−0.277582	+	0.178391i
$97$	1.84599	+	12.8391i	0.187432	+	1.30362i	0.838627	+	0.544706i	$0.183359\pi$
$97$	1.84599	+	12.8391i	0.187432	+	1.30362i	−0.651195	+	0.758910i	$0.725732\pi$
$98$	−0.239446	−	0.153882i	−0.0241877	−	0.0155445i
$99$	−1.84005	+	4.02915i	−0.184932	+	0.404944i
$100$	−6.18850	+	7.14191i	−0.618850	+	0.714191i
$101$	2.42758	−	16.8842i	0.241553	−	1.68004i	−0.402782	−	0.915296i	$-0.631957\pi$
$101$	2.42758	−	16.8842i	0.241553	−	1.68004i	0.644335	−	0.764744i	$-0.277134\pi$
$102$	0.278195	+	0.609162i	0.0275454	+	0.0603161i
$103$	18.6491	+	5.47587i	1.83755	+	0.539554i	0.999977	−	0.00677092i	$-0.00215527\pi$
$103$	18.6491	+	5.47587i	1.83755	+	0.539554i	0.837574	+	0.546324i	$0.183973\pi$
$104$	−2.36499	−	0.694424i	−0.231907	−	0.0680939i
$105$	0.114126	+	0.249900i	0.0111375	+	0.0243878i
$106$	0.494238	−	3.43750i	0.0480046	−	0.333879i
$107$	−8.51186	+	9.82321i	−0.822872	+	0.949645i	−0.999399	−	0.0346506i	$-0.988968\pi$
$107$	−8.51186	+	9.82321i	−0.822872	+	0.949645i	0.176527	+	0.984296i	$0.443514\pi$
$108$	−0.797176	+	1.74557i	−0.0767083	+	0.167968i
$109$	−1.65587	−	1.06416i	−0.158603	−	0.101928i	0.458932	−	0.888472i	$-0.348232\pi$
$109$	−1.65587	−	1.06416i	−0.158603	−	0.101928i	−0.617535	+	0.786543i	$0.711869\pi$
$110$	−0.0492922	−	0.342835i	−0.00469983	−	0.0326880i
$111$	7.84236	−	5.03998i	0.744364	−	0.478374i
$112$	−2.30542	−	2.66060i	−0.217842	−	0.251403i
$113$	4.68706	−	1.37624i	0.440921	−	0.129466i	−0.0537343	−	0.998555i	$-0.517112\pi$
$113$	4.68706	−	1.37624i	0.440921	−	0.129466i	0.494656	+	0.869089i	$0.335294\pi$
$114$	−1.52064			−0.142421
$115$	−0.521073	−	1.21013i	−0.0485903	−	0.112845i
$116$	−2.18535			−0.202905
$117$	−2.12020	+	0.622546i	−0.196012	+	0.0575544i
$118$	0.111593	+	0.128785i	0.0102729	+	0.0118556i
$119$	−1.97931	+	1.27203i	−0.181443	+	0.116606i
$120$	−0.0436119	−	0.303327i	−0.00398120	−	0.0276899i
$121$	7.25144	+	4.66021i	0.659221	+	0.423656i
$122$	1.65753	−	3.62949i	0.150066	−	0.328599i
$123$	2.41331	−	2.78511i	0.217601	−	0.251125i
$124$	−0.847743	+	5.89618i	−0.0761296	+	0.529493i
$125$	−1.13264	−	2.48014i	−0.101307	−	0.221831i
$126$	0.273100	+	0.0801894i	0.0243297	+	0.00714384i
$127$	4.95527	+	1.45500i	0.439709	+	0.129110i	0.494091	−	0.869410i	$-0.335501\pi$
$127$	4.95527	+	1.45500i	0.439709	+	0.129110i	−0.0543824	+	0.998520i	$0.517319\pi$
$128$	3.40975	+	7.46631i	0.301382	+	0.659935i
$129$	1.51981	−	10.5705i	0.133812	−	0.930681i
$130$	0.113153	−	0.130585i	0.00992413	−	0.0114531i
$131$	4.95882	−	10.8583i	0.433254	−	0.948694i	−0.559534	−	0.828808i	$-0.689020\pi$
$131$	4.95882	−	10.8583i	0.433254	−	0.948694i	0.992788	−	0.119886i	$-0.0382529\pi$
$132$	7.15066	+	4.59545i	0.622385	+	0.399982i
$133$	−0.760320	−	5.28815i	−0.0659281	−	0.458540i
$134$	−1.49426	+	0.960302i	−0.129084	+	0.0829575i
$135$	−0.179908	−	0.207625i	−0.0154840	−	0.0178695i
$136$	2.51816	−	0.739398i	0.215930	−	0.0634028i
$137$	−4.09263			−0.349657			−0.174829	−	0.984599i	$-0.555937\pi$
$137$	−4.09263			−0.349657			−0.174829	+	0.984599i	$0.555937\pi$
$138$	−1.30105	−	0.413033i	−0.110753	−	0.0351597i
$139$	−11.0090			−0.933767			−0.466884	−	0.884319i	$-0.654623\pi$
$139$	−11.0090			−0.933767			−0.466884	+	0.884319i	$0.654623\pi$
$140$	0.505842	−	0.148529i	0.0427514	−	0.0125530i
$141$	6.48003	+	7.47835i	0.545717	+	0.629791i
$142$	−3.54057	+	2.27539i	−0.297118	+	0.190946i
$143$	1.39294	+	9.68809i	0.116483	+	0.810159i
$144$	2.96162	+	1.90331i	0.246801	+	0.158610i
$145$	0.129967	−	0.284588i	0.0107932	−	0.0236338i
$146$	−1.34190	+	1.54863i	−0.111056	+	0.128166i
$147$	−0.142315	+	0.989821i	−0.0117379	+	0.0816391i
$148$	−7.43146	−	16.2726i	−0.610862	−	1.33760i
$149$	−15.4098	−	4.52474i	−1.26242	−	0.370681i	−0.419027	−	0.907974i	$-0.637629\pi$
$149$	−15.4098	−	4.52474i	−1.26242	−	0.370681i	−0.843396	+	0.537293i	$0.819447\pi$
$150$	−1.34489	−	0.394895i	−0.109810	−	0.0322430i
$151$	4.00277	+	8.76484i	0.325741	+	0.713273i	0.999674	−	0.0255193i	$-0.00812391\pi$
$151$	4.00277	+	8.76484i	0.325741	+	0.713273i	−0.673934	+	0.738792i	$0.735397\pi$
$152$	−0.848107	+	5.89871i	−0.0687905	+	0.478449i
$153$	1.54076	−	1.77814i	0.124563	−	0.143754i
$154$	0.523733	−	1.14681i	0.0422036	−	0.0924129i
$155$	−0.717415	−	0.461054i	−0.0576241	−	0.0370328i
$156$	0.603471	+	4.19723i	0.0483163	+	0.336047i
$157$	10.0517	−	6.45981i	0.802210	−	0.515549i	−0.0741265	−	0.997249i	$-0.523617\pi$
$157$	10.0517	−	6.45981i	0.802210	−	0.515549i	0.876336	+	0.481700i	$0.159981\pi$
$158$	−0.108767	−	0.125524i	−0.00865303	−	0.00998612i
$159$	−11.7070	+	3.43750i	−0.928429	+	0.272611i
$160$	−0.888179			−0.0702167
$161$	0.785829	−	4.73101i	0.0619320	−	0.372856i
$162$	−0.284630			−0.0223626
$163$	6.00584	−	1.76347i	0.470414	−	0.138126i	−0.0379295	−	0.999280i	$-0.512076\pi$
$163$	6.00584	−	1.76347i	0.470414	−	0.138126i	0.508343	+	0.861154i	$0.330258\pi$
$164$	−4.63111	−	5.34458i	−0.361629	−	0.417342i
$165$	−1.02371	+	0.657896i	−0.0796954	+	0.0512171i
$166$	0.214398	+	1.49117i	0.0166405	+	0.115737i
$167$	4.32773	+	2.78126i	0.334890	+	0.215220i	0.697268	−	0.716811i	$-0.254399\pi$
$167$	4.32773	+	2.78126i	0.334890	+	0.215220i	−0.362378	+	0.932031i	$0.618035\pi$
$168$	0.463379	−	1.01466i	0.0357504	−	0.0782826i
$169$	5.31564	−	6.13458i	0.408895	−	0.471891i
$170$	−0.0261829	+	0.182106i	−0.00200814	+	0.0139669i
$171$	2.21936	+	4.85973i	0.169719	+	0.371633i
$172$	−19.6631	−	5.77361i	−1.49930	−	0.440234i
$173$	−5.58819	−	1.64084i	−0.424862	−	0.124751i	0.0623098	−	0.998057i	$-0.480153\pi$
$173$	−5.58819	−	1.64084i	−0.424862	−	0.124751i	−0.487172	+	0.873306i	$0.661971\pi$
$174$	−0.134652	−	0.294847i	−0.0102079	−	0.0223523i
$175$	0.700833	−	4.87440i	0.0529780	−	0.368470i
$176$	10.2117	−	11.7849i	0.769736	−	0.888322i
$177$	0.248707	−	0.544593i	0.0186940	−	0.0409341i
$178$	−3.35481	−	2.15601i	−0.251454	−	0.161600i
$179$	1.82673	+	12.7052i	0.136536	+	0.949632i	0.936770	+	0.349944i	$0.113800\pi$
$179$	1.82673	+	12.7052i	0.136536	+	0.949632i	−0.800234	+	0.599688i	$0.795291\pi$
$180$	−0.443506	+	0.285024i	−0.0330570	+	0.0212444i
$181$	−12.8280	−	14.8043i	−0.953494	−	1.10039i	−0.994861	−	0.101247i	$-0.967717\pi$
$181$	−12.8280	−	14.8043i	−0.953494	−	1.10039i	0.0413668	−	0.999144i	$-0.486829\pi$
$182$	0.603471	−	0.177195i	0.0447322	−	0.0131346i
$183$	−14.0185			−1.03627
$184$	−2.32783	+	4.81653i	−0.171610	+	0.355079i
$185$	2.56107			0.188293
$186$	−0.847743	+	0.248920i	−0.0621595	+	0.0182517i
$187$	−6.82470	−	7.87612i	−0.499071	−	0.575959i
$188$	15.9745	−	10.2662i	1.16506	−	0.748738i
$189$	−0.142315	−	0.989821i	−0.0103519	−	0.0719989i
$190$	−0.351443	−	0.225859i	−0.0254963	−	0.0163855i
$191$	−7.83831	+	17.1635i	−0.567160	+	1.24191i	0.381135	+	0.924519i	$0.375533\pi$
$191$	−7.83831	+	17.1635i	−0.567160	+	1.24191i	−0.948296	+	0.317388i	$0.897194\pi$
$192$	4.00825	−	4.62576i	0.289270	−	0.333836i
$193$	1.98983	−	13.8396i	0.143231	−	0.996196i	−0.783747	−	0.621080i	$-0.786694\pi$
$193$	1.98983	−	13.8396i	0.143231	−	0.996196i	0.926978	−	0.375115i	$-0.122397\pi$
$194$	1.53370	+	3.35834i	0.110113	+	0.241115i
$195$	−0.582474	−	0.171030i	−0.0417119	−	0.0122477i
$196$	1.84125	+	0.540641i	0.131518	+	0.0386172i
$197$	8.97867	+	19.6605i	0.639704	+	1.40076i	0.900284	+	0.435303i	$0.143359\pi$
$197$	8.97867	+	19.6605i	0.639704	+	1.40076i	−0.260580	+	0.965452i	$0.583914\pi$
$198$	−0.179423	+	1.24791i	−0.0127510	+	0.0886853i
$199$	11.4900	−	13.2602i	0.814506	−	0.939990i	−0.184577	−	0.982818i	$-0.559091\pi$
$199$	11.4900	−	13.2602i	0.814506	−	0.939990i	0.999082	+	0.0428284i	$0.0136369\pi$
$200$	−2.28192	+	4.99671i	−0.161356	+	0.353321i
$201$	5.24984	+	3.37386i	0.370295	+	0.237974i
$202$	−0.690961	−	4.80574i	−0.0486159	−	0.338131i
$203$	0.958025	−	0.615686i	0.0672402	−	0.0432127i
$204$	−2.95670	−	3.41222i	−0.207011	−	0.238903i
$205$	0.971420	−	0.285235i	0.0678469	−	0.0199216i
$206$	5.53218			0.385445
$207$	0.578882	+	4.76077i	0.0402351	+	0.330896i
$208$	7.77922			0.539392
$209$	22.7057	−	6.66701i	1.57059	−	0.461166i
$210$	0.0512071	+	0.0590961i	0.00353363	+	0.00407802i
$211$	−3.56659	+	2.29211i	−0.245534	+	0.157795i	−0.657620	−	0.753350i	$-0.728437\pi$
$211$	−3.56659	+	2.29211i	−0.245534	+	0.157795i	0.412086	+	0.911145i	$0.364800\pi$
$212$	3.33217	+	23.1758i	0.228855	+	1.59172i
$213$	12.4392	+	7.99421i	0.852322	+	0.547754i
$214$	−1.53687	+	3.36528i	−0.105058	+	0.230046i
$215$	1.92127	−	2.21727i	0.131030	−	0.151216i
$216$	−0.158746	+	1.10411i	−0.0108013	+	0.0751249i
$217$	−1.28951	−	2.82363i	−0.0875376	−	0.191681i
$218$	−0.537553	−	0.157840i	−0.0364077	−	0.0106903i
$219$	6.90768	+	2.02828i	0.466778	+	0.137058i
$220$	0.970068	+	2.12415i	0.0654020	+	0.143210i
$221$	0.739897	−	5.14610i	0.0497709	−	0.346164i
$222$	1.73760	−	2.00529i	0.116620	−	0.134587i
$223$	−3.93611	+	8.61887i	−0.263581	+	0.577162i	−0.994433	−	0.105374i	$-0.966396\pi$
$223$	−3.93611	+	8.61887i	−0.263581	+	0.577162i	0.730851	+	0.682537i	$0.239123\pi$
$224$	−2.71973	−	1.74787i	−0.181720	−	0.116784i
$225$	0.700833	+	4.87440i	0.0467222	+	0.324960i
$226$	1.16968	−	0.751705i	0.0778057	−	0.0500027i
$227$	−2.52601	−	2.91517i	−0.167657	−	0.193487i	0.665703	−	0.746216i	$-0.268132\pi$
$227$	−2.52601	−	2.91517i	−0.167657	−	0.193487i	−0.833361	+	0.552730i	$0.813586\pi$
$228$	9.83694	−	2.88839i	0.651467	−	0.191288i
$229$	−13.6964			−0.905080			−0.452540	−	0.891744i	$-0.649482\pi$
$229$	−13.6964			−0.905080			−0.452540	+	0.891744i	$0.649482\pi$
$230$	−0.239344	−	0.288701i	−0.0157819	−	0.0190364i
$231$	−4.42942			−0.291435
$232$	−1.21884	+	0.357883i	−0.0800206	+	0.0234962i
$233$	−1.41769	−	1.63610i	−0.0928761	−	0.107185i	0.707409	−	0.706804i	$-0.249864\pi$
$233$	−1.41769	−	1.63610i	−0.0928761	−	0.107185i	−0.800285	+	0.599620i	$0.795318\pi$
$234$	−0.529104	+	0.340035i	−0.0345886	+	0.0222288i
$235$	0.386883	+	2.69083i	0.0252374	+	0.175530i
$236$	−0.966507	−	0.621136i	−0.0629142	−	0.0404325i
$237$	−0.242409	+	0.530803i	−0.0157462	+	0.0344793i
$238$	−0.438547	+	0.506110i	−0.0284268	+	0.0328063i
$239$	4.29919	−	29.9015i	0.278091	−	1.93417i	−0.0718918	−	0.997412i	$-0.522904\pi$
$239$	4.29919	−	29.9015i	0.278091	−	1.93417i	0.349983	−	0.936756i	$-0.386187\pi$
$240$	0.401777	+	0.879769i	0.0259346	+	0.0567888i
$241$	0.590606	+	0.173418i	0.0380443	+	0.0111708i	0.300699	−	0.953719i	$-0.402780\pi$
$241$	0.590606	+	0.173418i	0.0380443	+	0.0111708i	−0.262655	+	0.964890i	$0.584598\pi$
$242$	2.35407	+	0.691217i	0.151325	+	0.0444331i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	−3.82844	+	26.6274i	−0.245091	+	1.70465i
$245$	−0.179908	+	0.207625i	−0.0114939	+	0.0132647i
$246$	0.435739	−	0.954135i	0.0277817	−	0.0608334i
$247$	9.93133	+	6.38248i	0.631916	+	0.406107i
$248$	0.492772	+	3.42731i	0.0312911	+	0.217634i
$249$	4.45263	−	2.86153i	0.282174	−	0.181342i
$250$	−0.508206	−	0.586501i	−0.0321418	−	0.0370936i
$251$	−9.86939	+	2.89791i	−0.622950	+	0.182915i	−0.577950	−	0.816072i	$-0.696147\pi$
$251$	−9.86939	+	2.89791i	−0.622950	+	0.182915i	−0.0450004	+	0.998987i	$0.514329\pi$
$252$	−1.91899			−0.120885
$253$	21.2377	+	0.463041i	1.33520	+	0.0291112i
$254$	1.46996			0.0922335
$255$	0.620197	−	0.182106i	0.0388383	−	0.0114039i
$256$	−6.48657	−	7.48590i	−0.405411	−	0.467869i
$257$	13.2739	−	8.53059i	0.828000	−	0.532123i	−0.0566418	−	0.998395i	$-0.518039\pi$
$257$	13.2739	−	8.53059i	0.828000	−	0.532123i	0.884642	+	0.466271i	$0.154403\pi$
$258$	−0.432583	−	3.00868i	−0.0269314	−	0.187312i
$259$	7.84236	+	5.03998i	0.487301	+	0.313169i
$260$	−0.483937	+	1.05967i	−0.0300125	+	0.0657182i
$261$	−0.745760	+	0.860653i	−0.0461614	+	0.0532731i
$262$	0.483533	−	3.36305i	0.0298728	−	0.207770i
$263$	0.663850	+	1.45363i	0.0409347	+	0.0896346i	0.928995	−	0.370093i	$-0.120674\pi$
$263$	0.663850	+	1.45363i	0.0409347	+	0.0896346i	−0.888060	+	0.459728i	$0.847947\pi$
$264$	4.74071	+	1.39200i	0.291770	+	0.0856715i
$265$	−3.21624	−	0.944373i	−0.197572	−	0.0580124i
$266$	−0.631697	−	1.38322i	−0.0387318	−	0.0848109i
$267$	−1.99394	+	13.8681i	−0.122027	+	0.848717i
$268$	7.84223	−	9.05042i	0.479040	−	0.552842i
$269$	−6.63310	+	14.5245i	−0.404427	+	0.885572i	0.592375	+	0.805662i	$0.298190\pi$
$269$	−6.63310	+	14.5245i	−0.404427	+	0.885572i	−0.996802	+	0.0799094i	$0.974537\pi$
$270$	−0.0657822	−	0.0422756i	−0.00400337	−	0.00257281i
$271$	−1.80538	−	12.5567i	−0.109669	−	0.762764i	−0.968232	−	0.250055i	$-0.919551\pi$
$271$	−1.80538	−	12.5567i	−0.109669	−	0.762764i	0.858563	−	0.512709i	$-0.171358\pi$
$272$	−6.96812	+	4.47814i	−0.422505	+	0.271527i
$273$	−1.44705	−	1.66998i	−0.0875793	−	0.101072i
$274$	−1.11770	+	0.328186i	−0.0675227	+	0.0198264i
$275$	21.8128			1.31536
$276$	9.20095	+	0.200606i	0.553832	+	0.0120751i
$277$	−18.3178			−1.10061			−0.550305	−	0.834964i	$-0.685488\pi$
$277$	−18.3178			−1.10061			−0.550305	+	0.834964i	$0.685488\pi$
$278$	−3.00655	+	0.882802i	−0.180321	+	0.0529469i
$279$	2.03278	+	2.34596i	0.121700	+	0.140449i
$280$	0.257799	−	0.165678i	0.0154065	−	0.00990113i
$281$	2.11038	+	14.6780i	0.125895	+	0.875618i	0.950680	+	0.310172i	$0.100387\pi$
$281$	2.11038	+	14.6780i	0.125895	+	0.875618i	−0.824786	+	0.565446i	$0.808704\pi$
$282$	2.36938	+	1.52271i	0.141095	+	0.0906760i
$283$	−7.11331	+	15.5760i	−0.422843	+	0.925896i	0.571592	+	0.820538i	$0.306326\pi$
$283$	−7.11331	+	15.5760i	−0.422843	+	0.925896i	−0.994434	+	0.105358i	$0.966401\pi$
$284$	18.5818	−	21.4445i	1.10263	−	1.27250i
$285$	−0.208880	+	1.45280i	−0.0123730	+	0.0860562i
$286$	1.15729	+	2.53412i	0.0684322	+	0.149846i
$287$	3.53595	+	1.03825i	0.208720	+	0.0612858i
$288$	3.10199	+	0.910828i	0.182787	+	0.0536710i
$289$	−4.76243	−	10.4283i	−0.280143	−	0.613428i
$290$	0.0126731	−	0.0881431i	0.000744188	−	0.00517594i
$291$	8.49430	−	9.80295i	0.497945	−	0.574659i
$292$	5.73911	−	12.5669i	0.335856	−	0.735422i
$293$	−14.2017	−	9.12685i	−0.829670	−	0.533196i	0.0555032	−	0.998459i	$-0.482324\pi$
$293$	−14.2017	−	9.12685i	−0.829670	−	0.533196i	−0.885173	+	0.465262i	$0.845960\pi$
$294$	0.0405070	+	0.281733i	0.00236242	+	0.0164310i
$295$	0.138368	−	0.0889234i	0.00805607	−	0.00517732i
$296$	−6.80962	−	7.85872i	−0.395801	−	0.456779i
$297$	4.25000	−	1.24791i	0.246610	−	0.0724113i
$298$	−4.57127			−0.264806
$299$	6.76358	+	8.15832i	0.391148	+	0.471808i
$300$	9.45009			0.545601
$301$	10.2466	−	3.00868i	0.590605	−	0.173417i
$302$	1.79600	+	2.07270i	0.103348	+	0.119270i
$303$	−14.3499	+	9.22215i	−0.824383	+	0.529799i
$304$	−2.67669	−	18.6168i	−0.153519	−	1.06775i
$305$	−3.23987	−	2.08214i	−0.185515	−	0.119223i
$306$	0.278195	−	0.609162i	0.0159034	−	0.0348235i
$307$	−1.96760	+	2.27073i	−0.112297	+	0.129597i	−0.809115	−	0.587651i	$-0.800053\pi$
$307$	−1.96760	+	2.27073i	−0.112297	+	0.129597i	0.696818	+	0.717248i	$0.254598\pi$
$308$	−1.20968	+	8.41348i	−0.0689277	+	0.479403i
$309$	−8.07418	−	17.6800i	−0.459324	−	1.00578i
$310$	−0.232898	−	0.0683849i	−0.0132277	−	0.00388400i
$311$	20.0987	+	5.90152i	1.13969	+	0.334644i	0.796511	−	0.604624i	$-0.206677\pi$
$311$	20.0987	+	5.90152i	1.13969	+	0.334644i	0.343183	+	0.939268i	$0.388495\pi$
$312$	1.02393	+	2.24209i	0.0579686	+	0.126934i
$313$	−0.837199	+	5.82285i	−0.0473213	+	0.329127i	0.952385	+	0.304898i	$0.0986222\pi$
$313$	−0.837199	+	5.82285i	−0.0473213	+	0.329127i	−0.999706	+	0.0242292i	$0.992287\pi$
$314$	2.22710	−	2.57021i	0.125683	−	0.145045i
$315$	0.114126	−	0.249900i	0.00643025	−	0.0140803i
$316$	0.942033	+	0.605408i	0.0529935	+	0.0340568i
$317$	−0.0933044	−	0.648946i	−0.00524050	−	0.0364485i	0.987033	−	0.160515i	$-0.0513155\pi$
$317$	−0.0933044	−	0.648946i	−0.00524050	−	0.0364485i	−0.992274	+	0.124066i	$0.960406\pi$
$318$	−2.92154	+	1.87756i	−0.163832	+	0.105288i
$319$	3.30329	+	3.81220i	0.184949	+	0.213442i
$320$	1.61342	−	0.473744i	0.0901931	−	0.0264831i
$321$	12.9980			0.725476
$322$	−0.164767	−	1.35506i	−0.00918211	−	0.0755143i
$323$	−12.5700			−0.699411
$324$	1.84125	−	0.540641i	0.102292	−	0.0300356i
$325$	7.12603	+	8.22387i	0.395281	+	0.456178i
$326$	1.49878	−	0.963211i	0.0830100	−	0.0533473i
$327$	0.280123	+	1.94830i	0.0154909	+	0.107741i
$328$	−3.45816	−	2.22242i	−0.190945	−	0.122713i
$329$	−4.11065	+	9.00106i	−0.226627	+	0.496245i
$330$	−0.226818	+	0.261762i	−0.0124859	+	0.0144095i
$331$	−1.25598	+	8.73555i	−0.0690351	+	0.480149i	0.925748	+	0.378140i	$0.123436\pi$
$331$	−1.25598	+	8.73555i	−0.0690351	+	0.480149i	−0.994783	+	0.102009i	$0.967473\pi$
$332$	−4.21933	−	9.23905i	−0.231566	−	0.507059i
$333$	−8.94462	−	2.62638i	−0.490162	−	0.143925i
$334$	1.40493	+	0.412525i	0.0768744	+	0.0225724i
$335$	0.712200	+	1.55950i	0.0389116	+	0.0852046i
$336$	−0.501016	+	3.48465i	−0.0273327	+	0.190103i
$337$	3.34724	−	3.86292i	0.182336	−	0.210426i	−0.657222	−	0.753697i	$-0.728269\pi$
$337$	3.34724	−	3.86292i	0.182336	−	0.210426i	0.839558	+	0.543270i	$0.182814\pi$
$338$	0.959774	−	2.10161i	0.0522048	−	0.114313i
$339$	−4.10947	−	2.64099i	−0.223196	−	0.143439i
$340$	−0.176527	−	1.22777i	−0.00957350	−	0.0665851i
$341$	11.5669	−	7.43359i	0.626382	−	0.402551i
$342$	0.995808	+	1.14922i	0.0538471	+	0.0621429i
$343$	−0.959493	+	0.281733i	−0.0518078	+	0.0152121i
$344$	−11.9122			−0.642264
$345$	−0.573321	+	1.18626i	−0.0308666	+	0.0638663i
$346$	−1.65771			−0.0891192
$347$	10.9500	−	3.21520i	0.587825	−	0.172601i	0.0257231	−	0.999669i	$-0.491811\pi$
$347$	10.9500	−	3.21520i	0.587825	−	0.172601i	0.562102	+	0.827068i	$0.309993\pi$
$348$	1.43110	+	1.65158i	0.0767152	+	0.0885340i
$349$	−11.0800	+	7.12066i	−0.593097	+	0.381160i	−0.802485	−	0.596672i	$-0.796489\pi$
$349$	−11.0800	+	7.12066i	−0.593097	+	0.381160i	0.209388	+	0.977833i	$0.432853\pi$
$350$	−0.199478	−	1.38740i	−0.0106625	−	0.0741596i
$351$	1.85892	+	1.19466i	0.0992219	+	0.0637660i
$352$	5.94879	−	13.0260i	0.317072	−	0.694290i
$353$	−2.87567	+	3.31870i	−0.153056	+	0.176637i	−0.827100	−	0.562055i	$-0.810011\pi$
$353$	−2.87567	+	3.31870i	−0.153056	+	0.176637i	0.674043	+	0.738692i	$0.264556\pi$
$354$	0.0242514	−	0.168672i	0.00128895	−	0.00896482i
$355$	1.68752	+	3.69516i	0.0895644	+	0.196119i
$356$	25.7973	+	7.57479i	1.36726	+	0.401463i
$357$	2.25751	+	0.662864i	0.119480	+	0.0350825i
$358$	1.51771	+	3.32331i	0.0802132	+	0.175642i
$359$	−1.31568	+	9.15076i	−0.0694390	+	0.482959i	0.925194	+	0.379494i	$0.123902\pi$
$359$	−1.31568	+	9.15076i	−0.0694390	+	0.482959i	−0.994633	+	0.103465i	$0.967007\pi$
$360$	−0.200680	+	0.231597i	−0.0105768	+	0.0122062i
$361$	3.96413	−	8.68022i	0.208638	−	0.456854i
$362$	−4.69046	−	3.01438i	−0.246525	−	0.158432i
$363$	−1.22673	−	8.53206i	−0.0643864	−	0.447817i
$364$	−3.56724	+	2.29253i	−0.186974	+	0.120161i
$365$	1.29521	+	1.49475i	0.0677944	+	0.0782389i
$366$	−3.82844	+	1.12413i	−0.200116	+	0.0587593i
$367$	−27.8744			−1.45503			−0.727515	−	0.686092i	$-0.759325\pi$
$367$	−27.8744			−1.45503			−0.727515	+	0.686092i	$0.759325\pi$
$368$	2.76650	−	16.6554i	0.144214	−	0.868224i
$369$	−3.68523			−0.191845
$370$	0.699428	−	0.205371i	0.0363615	−	0.0106767i
$371$	−7.99014	−	9.22111i	−0.414827	−	0.478736i
$372$	5.01119	−	3.22050i	0.259818	−	0.166975i
$373$	−0.0679100	−	0.472324i	−0.00351625	−	0.0244560i	0.987988	−	0.154532i	$-0.0493870\pi$
$373$	−0.0679100	−	0.472324i	−0.00351625	−	0.0244560i	−0.991504	+	0.130076i	$0.958478\pi$
$374$	−2.49541	−	1.60370i	−0.129034	−	0.0829254i
$375$	−1.13264	+	2.48014i	−0.0584894	+	0.128074i
$376$	7.22821	−	8.34180i	0.372767	−	0.430196i
$377$	−0.358125	+	2.49081i	−0.0184444	+	0.128283i
$378$	−0.118239	−	0.258908i	−0.00608158	−	0.0133168i
$379$	−20.0092	−	5.87523i	−1.02780	−	0.301790i	−0.275986	−	0.961162i	$-0.589004\pi$
$379$	−20.0092	−	5.87523i	−1.02780	−	0.301790i	−0.751817	+	0.659372i	$0.770822\pi$
$380$	2.70247	+	0.793517i	0.138634	+	0.0407066i
$381$	−2.14540	−	4.69776i	−0.109912	−	0.240674i
$382$	−0.764312	+	5.31591i	−0.0391056	+	0.271985i
$383$	−15.0166	+	17.3301i	−0.767314	+	0.885528i	−0.996125	−	0.0879432i	$-0.971971\pi$
$383$	−15.0166	+	17.3301i	−0.767314	+	0.885528i	0.228812	+	0.973471i	$0.426516\pi$
$384$	3.40975	−	7.46631i	0.174003	−	0.381014i
$385$	−1.02371	−	0.657896i	−0.0521729	−	0.0335295i
$386$	−0.566366	−	3.93916i	−0.0288273	−	0.200498i
$387$	−8.98392	+	5.77361i	−0.456678	+	0.293489i
$388$	−16.3004	−	18.8117i	−0.827530	−	0.955020i
$389$	−12.0315	+	3.53276i	−0.610020	+	0.179118i	−0.572129	−	0.820164i	$-0.693882\pi$
$389$	−12.0315	+	3.53276i	−0.610020	+	0.179118i	−0.0378911	+	0.999282i	$0.512064\pi$
$390$	−0.172789			−0.00874949
$391$	−10.7548	−	3.41422i	−0.543891	−	0.172665i
$392$	1.11546			0.0563392
$393$	−11.4535	+	3.36305i	−0.577752	+	0.169643i
$394$	4.02864	+	4.64930i	0.202960	+	0.234228i
$395$	−0.134864	+	0.0866717i	−0.00678573	+	0.00436093i
$396$	−1.20968	−	8.41348i	−0.0607885	−	0.422794i
$397$	−18.3137	−	11.7695i	−0.919137	−	0.590694i	−0.00673020	−	0.999977i	$-0.502142\pi$
$397$	−18.3137	−	11.7695i	−0.919137	−	0.590694i	−0.912407	+	0.409284i	$0.865779\pi$
$398$	2.07460	−	4.54274i	0.103990	−	0.227707i
$399$	−3.49861	+	4.03761i	−0.175150	+	0.202133i
$400$	2.46727	−	17.1602i	0.123363	−	0.858011i
$401$	−0.267373	−	0.585465i	−0.0133520	−	0.0292367i	0.902839	−	0.429980i	$-0.141479\pi$
$401$	−0.267373	−	0.585465i	−0.0133520	−	0.0292367i	−0.916191	+	0.400743i	$0.868752\pi$
$402$	1.70428	+	0.500422i	0.0850017	+	0.0249588i
$403$	6.58140	+	1.93247i	0.327843	+	0.0962633i
$404$	13.5981	+	29.7756i	0.676529	+	1.48139i
$405$	−0.0390977	+	0.271930i	−0.00194278	+	0.0135123i
$406$	0.212265	−	0.244967i	0.0105346	−	0.0121575i
$407$	−17.1534	+	37.5606i	−0.850261	+	1.86181i
$408$	−2.20784	−	1.41889i	−0.109304	−	0.0702457i
$409$	5.38390	+	37.4459i	0.266217	+	1.85158i	0.483338	+	0.875434i	$0.339424\pi$
$409$	5.38390	+	37.4459i	0.266217	+	1.85158i	−0.217121	+	0.976145i	$0.569667\pi$
$410$	0.242422	−	0.155795i	0.0119724	−	0.00769418i
$411$	2.68010	+	3.09301i	0.132200	+	0.152567i
$412$	−35.7874	+	10.5081i	−1.76312	+	0.517698i
$413$	0.598696			0.0294599
$414$	0.539856	+	1.25375i	0.0265325	+	0.0616182i
$415$	1.45409			0.0713784
$416$	6.85449	−	2.01266i	0.336069	−	0.0986788i
$417$	7.20933	+	8.32001i	0.353043	+	0.407433i
$418$	5.66632	−	3.64152i	0.277149	−	0.178113i
$419$	−0.731076	−	5.08475i	−0.0357154	−	0.248406i	0.964140	−	0.265393i	$-0.0855017\pi$
$419$	−0.731076	−	5.08475i	−0.0357154	−	0.248406i	−0.999856	+	0.0169869i	$0.994593\pi$
$420$	−0.443506	−	0.285024i	−0.0216409	−	0.0139078i
$421$	5.76077	−	12.6143i	0.280763	−	0.614784i	−0.715738	−	0.698369i	$-0.753910\pi$
$421$	5.76077	−	12.6143i	0.280763	−	0.614784i	0.996501	+	0.0835846i	$0.0266369\pi$
$422$	−0.790233	+	0.911977i	−0.0384679	+	0.0443944i
$423$	1.40824	−	9.79456i	0.0684712	−	0.476228i
$424$	5.65381	+	12.3801i	0.274573	+	0.601232i
$425$	−11.1171	−	3.26429i	−0.539261	−	0.158341i
$426$	4.03821	+	1.18572i	0.195652	+	0.0574485i
$427$	−5.82348	−	12.7516i	−0.281818	−	0.617095i
$428$	3.54975	−	24.6890i	0.171583	−	1.19339i
$429$	6.40959	−	7.39706i	0.309458	−	0.357134i
$430$	0.346898	−	0.759601i	0.0167289	−	0.0366312i
$431$	−2.41661	−	1.55306i	−0.116404	−	0.0748083i	0.481143	−	0.876642i	$-0.340222\pi$
$431$	−2.41661	−	1.55306i	−0.116404	−	0.0748083i	−0.597547	+	0.801834i	$0.703858\pi$
$432$	−0.501016	−	3.48465i	−0.0241052	−	0.167655i
$433$	−16.8115	+	10.8041i	−0.807911	+	0.519213i	−0.878189	−	0.478314i	$-0.841248\pi$
$433$	−16.8115	+	10.8041i	−0.807911	+	0.519213i	0.0702774	+	0.997527i	$0.477612\pi$
$434$	−0.578591	−	0.667729i	−0.0277732	−	0.0320520i
$435$	−0.300188	+	0.0881431i	−0.0143929	+	0.00422614i
$436$	3.77721			0.180895
$437$	17.1968	−	18.9934i	0.822636	−	0.908576i
$438$	2.04914			0.0979115
$439$	16.2967	−	4.78513i	0.777797	−	0.228382i	0.131346	−	0.991337i	$-0.458070\pi$
$439$	16.2967	−	4.78513i	0.777797	−	0.228382i	0.646452	+	0.762955i	$0.276252\pi$
$440$	0.888896	+	1.02584i	0.0423765	+	0.0489051i
$441$	0.841254	−	0.540641i	0.0400597	−	0.0257448i
$442$	−0.210597	−	1.46473i	−0.0100171	−	0.0696702i
$443$	−33.3437	−	21.4287i	−1.58421	−	1.01811i	−0.974193	−	0.225716i	$-0.927528\pi$
$443$	−33.3437	−	21.4287i	−1.58421	−	1.01811i	−0.610013	−	0.792392i	$-0.708836\pi$
$444$	−7.43146	+	16.2726i	−0.352681	+	0.772264i
$445$	−2.52064	+	2.90898i	−0.119490	+	0.137899i
$446$	−0.383809	+	2.66945i	−0.0181739	+	0.126402i
$447$	6.67173	+	14.6091i	0.315562	+	0.690985i
$448$	5.87283	+	1.72442i	0.277465	+	0.0814711i
$449$	16.1942	+	4.75505i	0.764252	+	0.224405i	0.640552	−	0.767915i	$-0.278706\pi$
$449$	16.1942	+	4.75505i	0.764252	+	0.224405i	0.123700	+	0.992320i	$0.460524\pi$
$450$	0.582273	+	1.27500i	0.0274486	+	0.0601041i
$451$	−2.32307	+	16.1573i	−0.109389	+	0.760816i
$452$	−6.13874	+	7.08448i	−0.288742	+	0.333226i
$453$	4.00277	−	8.76484i	0.188066	−	0.411808i
$454$	−0.923620	−	0.593574i	−0.0433476	−	0.0278578i
$455$	−0.0863943	−	0.600886i	−0.00405023	−	0.0281700i
$456$	5.01334	−	3.22188i	0.234771	−	0.150878i
$457$	−14.8487	−	17.1363i	−0.694593	−	0.801603i	0.293418	−	0.955984i	$-0.405207\pi$
$457$	−14.8487	−	17.1363i	−0.694593	−	0.801603i	−0.988011	+	0.154381i	$0.950662\pi$
$458$	−3.74048	+	1.09830i	−0.174781	+	0.0513203i
$459$	−2.35281			−0.109820
$460$	2.09668	+	1.41297i	0.0977582	+	0.0658799i
$461$	−7.65994			−0.356759			−0.178380	−	0.983962i	$-0.557085\pi$
$461$	−7.65994			−0.356759			−0.178380	+	0.983962i	$0.557085\pi$
$462$	−1.20968	+	0.355193i	−0.0562792	+	0.0165251i
$463$	20.4704	+	23.6241i	0.951339	+	1.09790i	0.995101	+	0.0988623i	$0.0315203\pi$
$463$	20.4704	+	23.6241i	0.951339	+	1.09790i	−0.0437617	+	0.999042i	$0.513934\pi$
$464$	3.37271	−	2.16751i	0.156574	−	0.100624i
$465$	0.121365	+	0.844112i	0.00562817	+	0.0391448i
$466$	−0.518370	−	0.333136i	−0.0240130	−	0.0154322i
$467$	−10.3306	+	22.6209i	−0.478044	+	1.04677i	0.504953	+	0.863147i	$0.331510\pi$
$467$	−10.3306	+	22.6209i	−0.478044	+	1.04677i	−0.982997	+	0.183623i	$0.941217\pi$
$468$	2.77687	−	3.20467i	0.128361	−	0.148136i
$469$	−0.888115	+	6.17697i	−0.0410093	+	0.285226i
$470$	0.321434	+	0.703842i	0.0148266	+	0.0324658i
$471$	−11.4644	−	3.36626i	−0.528253	−	0.155109i
$472$	−0.640770	−	0.188147i	−0.0294938	−	0.00866017i
$473$	19.6503	+	43.0281i	0.903520	+	1.97843i
$474$	−0.0236373	+	0.164401i	−0.00108570	+	0.00755119i
$475$	17.2290	−	19.8833i	0.790520	−	0.912309i
$476$	1.87560	−	4.10700i	0.0859682	−	0.188244i
$477$	10.2644	+	6.59651i	0.469973	+	0.302033i
$478$	−1.22368	−	8.51086i	−0.0559697	−	0.389278i
$479$	−17.0530	+	10.9593i	−0.779172	+	0.500743i	−0.868759	−	0.495236i	$-0.835082\pi$
$479$	−17.0530	+	10.9593i	−0.779172	+	0.500743i	0.0895870	+	0.995979i	$0.471445\pi$
$480$	0.581633	+	0.671241i	0.0265478	+	0.0306378i
$481$	−19.7650	+	5.80352i	−0.901205	+	0.264618i
$482$	0.175201			0.00798019
$483$	−4.09007	+	2.50426i	−0.186105	+	0.113948i
$484$	−16.5413			−0.751876
$485$	3.41918	−	1.00396i	0.155257	−	0.0455875i
$486$	0.186393	+	0.215109i	0.00845495	+	0.00975753i
$487$	−10.9183	+	7.01678i	−0.494756	+	0.317960i	−0.764116	−	0.645079i	$-0.776824\pi$
$487$	−10.9183	+	7.01678i	−0.494756	+	0.317960i	0.269360	+	0.963040i	$0.413188\pi$
$488$	2.22538	+	15.4779i	0.100738	+	0.700650i
$489$	−5.26574	−	3.38408i	−0.238125	−	0.153034i
$490$	−0.0324835	+	0.0711290i	−0.00146746	+	0.00321328i
$491$	1.78049	−	2.05479i	0.0803523	−	0.0927315i	−0.714150	−	0.699993i	$-0.753186\pi$
$491$	1.78049	−	2.05479i	0.0803523	−	0.0927315i	0.794502	+	0.607261i	$0.207732\pi$
$492$	−1.00644	+	6.99991i	−0.0453736	+	0.315580i
$493$	−1.11306	−	2.43727i	−0.0501298	−	0.109769i
$494$	3.22406	+	0.946668i	0.145057	+	0.0425926i
$495$	1.16759	+	0.342835i	0.0524792	+	0.0154093i
$496$	−4.53969	−	9.94054i	−0.203838	−	0.446343i
$497$	−2.10434	+	14.6360i	−0.0943927	+	0.656516i
$498$	0.986550	−	1.13854i	0.0442083	−	0.0510191i
$499$	7.03931	−	15.4139i	0.315123	−	0.690022i	−0.684102	−	0.729386i	$-0.739806\pi$
$499$	7.03931	−	15.4139i	0.315123	−	0.690022i	0.999225	+	0.0393638i	$0.0125331\pi$
$500$	4.40159	+	2.82873i	0.196845	+	0.126505i
$501$	−0.732121	−	5.09202i	−0.0327088	−	0.227495i
$502$	−2.46295	+	1.58284i	−0.109927	+	0.0706457i
$503$	−4.08797	−	4.71777i	−0.182274	−	0.210355i	0.657258	−	0.753666i	$-0.271716\pi$
$503$	−4.08797	−	4.71777i	−0.182274	−	0.210355i	−0.839532	+	0.543310i	$0.817171\pi$
$504$	−1.07028	+	0.314261i	−0.0476739	+	0.0139983i
$505$	−4.68624			−0.208535
$506$	5.83716	−	1.57658i	0.259493	−	0.0700877i
$507$	−8.11721			−0.360498
$508$	−9.50909	+	2.79212i	−0.421898	+	0.123880i
$509$	−26.3337	−	30.3907i	−1.16722	−	1.34704i	−0.926430	−	0.376468i	$-0.877139\pi$
$509$	−26.3337	−	30.3907i	−1.16722	−	1.34704i	−0.240791	−	0.970577i	$-0.577407\pi$
$510$	0.154773	−	0.0994666i	0.00685346	−	0.00440445i
$511$	1.02457	+	7.12603i	0.0453242	+	0.315237i
$512$	−16.1819	−	10.3995i	−0.715145	−	0.459596i
$513$	2.21936	−	4.85973i	0.0979873	−	0.214562i
$514$	2.94103	−	3.39413i	0.129723	−	0.149709i
$515$	0.759919	−	5.28535i	0.0334860	−	0.232900i
$516$	8.51320	+	18.6413i	0.374773	+	0.820638i
$517$	−42.0549	−	12.3484i	−1.84957	−	0.543084i
$518$	2.54590	+	0.747545i	0.111861	+	0.0328452i
$519$	2.41942	+	5.29779i	0.106201	+	0.232547i
$520$	−0.0963694	+	0.670264i	−0.00422608	+	0.0293930i
$521$	−7.54390	+	8.70612i	−0.330504	+	0.381422i	−0.896543	−	0.442956i	$-0.853930\pi$
$521$	−7.54390	+	8.70612i	−0.330504	+	0.381422i	0.566039	+	0.824378i	$0.308475\pi$
$522$	−0.134652	+	0.294847i	−0.00589355	+	0.0129051i
$523$	5.81239	+	3.73540i	0.254158	+	0.163337i	0.661516	−	0.749931i	$-0.269913\pi$
$523$	5.81239	+	3.73540i	0.254158	+	0.163337i	−0.407358	+	0.913269i	$0.633550\pi$
$524$	3.26000	+	22.6738i	0.142414	+	0.990510i
$525$	−4.14277	+	2.66240i	−0.180805	+	0.116197i
$526$	0.297863	+	0.343752i	0.0129875	+	0.0149883i
$527$	−7.00763	+	2.05763i	−0.305257	+	0.0896316i
$528$	−15.5937			−0.678628
$529$	19.8724	−	11.5796i	0.864018	−	0.503461i
$530$	−0.954084			−0.0414428
$531$	−0.574445	+	0.168672i	−0.0249288	+	0.00731975i
$532$	6.71378	+	7.74812i	0.291079	+	0.335924i
$533$	−6.85054	+	4.40258i	−0.296730	+	0.190697i
$534$	0.567534	+	3.94729i	0.0245596	+	0.170816i
$535$	3.00402	+	1.93057i	0.129875	+	0.0834657i
$536$	2.89171	−	6.33196i	0.124903	−	0.273499i
$537$	8.40570	−	9.70070i	0.362733	−	0.418616i
$538$	−0.646792	+	4.49854i	−0.0278852	+	0.193946i
$539$	−1.84005	−	4.02915i	−0.0792565	−	0.173548i
$540$	0.505842	+	0.148529i	0.0217680	+	0.00639165i
$541$	37.0975	+	10.8928i	1.59495	+	0.468319i	0.954135	−	0.299378i	$-0.0967790\pi$
$541$	37.0975	+	10.8928i	1.59495	+	0.468319i	0.640813	+	0.767697i	$0.278597\pi$
$542$	−1.49996	−	3.28446i	−0.0644289	−	0.141080i
$543$	−2.78778	+	19.3894i	−0.119635	+	0.832081i
$544$	−4.98122	+	5.74863i	−0.213568	+	0.246470i
$545$	−0.224638	+	0.491888i	−0.00962241	+	0.0210701i
$546$	−0.529104	−	0.340035i	−0.0226436	−	0.0145521i
$547$	1.03922	+	7.22795i	0.0444340	+	0.309045i	0.999903	+	0.0139525i	$0.00444136\pi$
$547$	1.03922	+	7.22795i	0.0444340	+	0.309045i	−0.955469	+	0.295092i	$0.904650\pi$
$548$	6.60696	−	4.24603i	0.282235	−	0.181382i
$549$	9.18014	+	10.5944i	0.391799	+	0.452160i
$550$	5.95708	−	1.74916i	0.254011	−	0.0745843i
$551$	6.08410			0.259192
$552$	5.16449	−	1.39490i	0.219815	−	0.0593710i
$553$	−0.583536			−0.0248145
$554$	−5.00259	+	1.46889i	−0.212540	+	0.0624073i
$555$	−1.67714	−	1.93553i	−0.0711907	−	0.0821585i
$556$	17.7723	−	11.4216i	0.753715	−	0.484383i
$557$	−3.85157	−	26.7883i	−0.163196	−	1.13505i	−0.892560	−	0.450929i	$-0.851093\pi$
$557$	−3.85157	−	26.7883i	−0.163196	−	1.13505i	0.729364	−	0.684126i	$-0.239816\pi$
$558$	0.743275	+	0.477674i	0.0314653	+	0.0202215i
$559$	−9.80291	+	21.4654i	−0.414619	+	0.907889i
$560$	−0.633362	+	0.730938i	−0.0267644	+	0.0308878i
$561$	−1.48315	+	10.3155i	−0.0626186	+	0.435522i
$562$	1.75337	+	3.83934i	0.0739614	+	0.161953i
$563$	−43.0339	−	12.6359i	−1.81366	−	0.532540i	−0.814781	−	0.579769i	$-0.803143\pi$
$563$	−43.0339	−	12.6359i	−1.81366	−	0.532540i	−0.998884	+	0.0472294i	$0.984961\pi$
$564$	−18.2197	−	5.34979i	−0.767188	−	0.225267i
$565$	−0.557496	−	1.22075i	−0.0234540	−	0.0513571i
$566$	−0.693618	+	4.82422i	−0.0291549	+	0.202777i
$567$	−0.654861	+	0.755750i	−0.0275016	+	0.0317385i
$568$	6.85177	−	15.0033i	0.287494	−	0.629524i
$569$	−4.22722	−	2.71667i	−0.177214	−	0.113889i	0.449026	−	0.893518i	$-0.351771\pi$
$569$	−4.22722	−	2.71667i	−0.177214	−	0.113889i	−0.626241	+	0.779630i	$0.715407\pi$
$570$	0.0594536	+	0.413509i	0.00249024	+	0.0173200i
$571$	8.37221	−	5.38049i	0.350366	−	0.225167i	−0.353606	−	0.935395i	$-0.615044\pi$
$571$	8.37221	−	5.38049i	0.350366	−	0.225167i	0.703972	+	0.710228i	$0.251408\pi$
$572$	−12.2999	−	14.1949i	−0.514285	−	0.593517i
$573$	18.1043	−	5.31591i	0.756319	−	0.222075i
$574$	1.04892			0.0437813
$575$	20.1416	−	12.3323i	0.839965	−	0.514293i
$576$	−6.12076			−0.255032
$577$	−42.3727	+	12.4418i	−1.76400	+	0.517957i	−0.992920	−	0.118783i	$-0.962101\pi$
$577$	−42.3727	+	12.4418i	−1.76400	+	0.517957i	−0.771079	+	0.636740i	$0.780283\pi$
$578$	−2.13686	−	2.46607i	−0.0888816	−	0.102575i
$579$	−11.7623	+	7.55919i	−0.488826	+	0.314149i
$580$	0.0854423	+	0.594265i	0.00354780	+	0.0246755i
$581$	4.45263	+	2.86153i	0.184726	+	0.118716i
$582$	1.53370	−	3.35834i	0.0635740	−	0.139208i
$583$	35.3917	−	40.8442i	1.46578	−	1.69159i
$584$	1.14286	−	7.94879i	0.0472921	−	0.328923i
$585$	0.252184	+	0.552206i	0.0104265	+	0.0228309i
$586$	−4.61035	−	1.35372i	−0.190452	−	0.0559217i
$587$	14.7127	+	4.32004i	0.607258	+	0.178307i	0.570884	−	0.821031i	$-0.306601\pi$
$587$	14.7127	+	4.32004i	0.607258	+	0.178307i	0.0363749	+	0.999338i	$0.488419\pi$
$588$	−0.797176	−	1.74557i	−0.0328750	−	0.0719861i
$589$	2.36015	−	16.4152i	0.0972481	−	0.676376i
$590$	0.0306575	−	0.0353806i	0.00126215	−	0.00145660i
$591$	8.97867	−	19.6605i	0.369333	−	0.808727i
$592$	27.6089	+	17.7431i	1.13472	+	0.729239i
$593$	1.45833	+	10.1429i	0.0598863	+	0.416518i	0.997608	+	0.0691300i	$0.0220223\pi$
$593$	1.45833	+	10.1429i	0.0598863	+	0.416518i	−0.937721	+	0.347388i	$0.887069\pi$
$594$	1.06061	−	0.681611i	0.0435172	−	0.0279668i
$595$	0.423289	+	0.488502i	0.0173532	+	0.0200266i
$596$	29.5713	−	8.68291i	1.21129	−	0.355666i
$597$	−17.5457			−0.718099
$598$	2.50135	+	1.68567i	0.102288	+	0.0689323i
$599$	3.61642			0.147763			0.0738815	−	0.997267i	$-0.476461\pi$
$599$	3.61642			0.147763			0.0738815	+	0.997267i	$0.476461\pi$
$600$	5.27060	−	1.54759i	0.215171	−	0.0631800i
$601$	4.97233	+	5.73838i	0.202826	+	0.234073i	0.848045	−	0.529924i	$-0.177780\pi$
$601$	4.97233	+	5.73838i	0.202826	+	0.234073i	−0.645219	+	0.763997i	$0.723234\pi$
$602$	2.55709	−	1.64334i	0.104219	−	0.0669776i
$603$	−0.888115	−	6.17697i	−0.0361668	−	0.251546i
$604$	−15.5553	−	9.99675i	−0.632934	−	0.406762i
$605$	0.983740	−	2.15409i	0.0399947	−	0.0875762i
$606$	−3.17945	+	3.66929i	−0.129156	+	0.149055i
$607$	0.366196	−	2.54695i	0.0148634	−	0.103377i	−0.981039	−	0.193809i	$-0.937916\pi$
$607$	0.366196	−	2.54695i	0.0148634	−	0.103377i	0.995903	+	0.0904319i	$0.0288248\pi$
$608$	−7.17510	−	15.7113i	−0.290989	−	0.637176i
$609$	−1.09268	−	0.320839i	−0.0442775	−	0.0130011i
$610$	−1.05178	−	0.308829i	−0.0425852	−	0.0125041i
$611$	−9.08331	−	19.8897i	−0.367472	−	0.804650i
$612$	−0.642553	+	4.46906i	−0.0259737	+	0.180651i
$613$	−22.2711	+	25.7022i	−0.899520	+	1.03810i	0.0995517	+	0.995032i	$0.468259\pi$
$613$	−22.2711	+	25.7022i	−0.899520	+	1.03810i	−0.999072	+	0.0430694i	$0.986286\pi$
$614$	−0.355263	+	0.777917i	−0.0143372	+	0.0313942i
$615$	−0.851710	−	0.547361i	−0.0343443	−	0.0220717i
$616$	0.703155	+	4.89055i	0.0283309	+	0.197046i
$617$	−30.9049	+	19.8613i	−1.24418	+	0.799588i	−0.986038	−	0.166519i	$-0.946747\pi$
$617$	−30.9049	+	19.8613i	−1.24418	+	0.799588i	−0.258144	+	0.966106i	$0.583111\pi$
$618$	−3.62281	−	4.18094i	−0.145731	−	0.168182i
$619$	6.71964	−	1.97306i	0.270085	−	0.0793042i	−0.143886	−	0.989594i	$-0.545960\pi$
$619$	6.71964	−	1.97306i	0.270085	−	0.0793042i	0.413971	+	0.910290i	$0.364142\pi$
$620$	1.63650			0.0657233
$621$	3.21886	−	3.55513i	0.129168	−	0.142662i
$622$	5.96221			0.239063
$623$	−13.4432	+	3.94729i	−0.538591	+	0.158145i
$624$	−5.09430	−	5.87914i	−0.203935	−	0.235354i
$625$	20.0837	−	12.9070i	0.803349	−	0.516281i
$626$	0.238292	+	1.65735i	0.00952405	+	0.0662412i
$627$	−19.9077	−	12.7939i	−0.795036	−	0.510939i
$628$	−9.52500	+	20.8568i	−0.380089	+	0.832278i
$629$	14.3634	−	16.5762i	0.572705	−	0.660937i
$630$	0.0111284	−	0.0773995i	0.000443365	−	0.00308367i
$631$	−2.95260	−	6.46530i	−0.117541	−	0.257380i	0.841712	−	0.539926i	$-0.181548\pi$
$631$	−2.95260	−	6.46530i	−0.117541	−	0.257380i	−0.959253	+	0.282547i	$0.908821\pi$
$632$	0.624544	+	0.183383i	0.0248430	+	0.00729457i
$633$	4.06788	+	1.19444i	0.161684	+	0.0474746i
$634$	−0.0775201	−	0.169745i	−0.00307872	−	0.00674145i
$635$	0.201919	−	1.40438i	0.00801290	−	0.0557309i
$636$	15.3330	−	17.6952i	0.607992	−	0.701660i
$637$	0.917944	−	2.01002i	0.0363703	−	0.0796398i
$638$	1.20783	+	0.776223i	0.0478183	+	0.0307310i
$639$	−2.10434	−	14.6360i	−0.0832466	−	0.578992i
$640$	1.89700	−	1.21913i	0.0749857	−	0.0481904i
$641$	0.692460	+	0.799141i	0.0273505	+	0.0315642i	0.769260	−	0.638936i	$-0.220625\pi$
$641$	0.692460	+	0.799141i	0.0273505	+	0.0315642i	−0.741910	+	0.670500i	$0.766080\pi$
$642$	3.54975	−	1.04230i	0.140097	−	0.0411363i
$643$	11.9177			0.469987			0.234994	−	0.971997i	$-0.424493\pi$
$643$	11.9177			0.469987			0.234994	+	0.971997i	$0.424493\pi$
$644$	3.63973	+	8.45281i	0.143426	+	0.333087i
$645$	−2.93386			−0.115521
$646$	−3.43286	+	1.00798i	−0.135064	+	0.0396583i
$647$	24.2952	+	28.0382i	0.955145	+	1.10230i	0.994673	+	0.103077i	$0.0328689\pi$
$647$	24.2952	+	28.0382i	0.955145	+	1.10230i	−0.0395286	+	0.999218i	$0.512586\pi$
$648$	0.938384	−	0.603063i	0.0368632	−	0.0236906i
$649$	0.377402	+	2.62489i	0.0148143	+	0.103036i
$650$	2.60559	+	1.67451i	0.102200	+	0.0656796i
$651$	−1.28951	+	2.82363i	−0.0505399	+	0.110667i
$652$	−7.86598	+	9.07783i	−0.308056	+	0.355515i
$653$	5.04277	−	35.0733i	0.197339	−	1.37252i	−0.614627	−	0.788818i	$-0.710693\pi$
$653$	5.04277	−	35.0733i	0.197339	−	1.37252i	0.811966	−	0.583705i	$-0.198397\pi$
$654$	0.232735	+	0.509618i	0.00910065	+	0.0199277i
$655$	−3.14658	−	0.923919i	−0.122947	−	0.0361005i
$656$	12.4482	+	3.65513i	0.486022	+	0.142709i
$657$	−2.99070	−	6.54872i	−0.116678	−	0.255490i
$658$	−0.400828	+	2.78782i	−0.0156259	+	0.108681i
$659$	−10.4940	+	12.1107i	−0.408789	+	0.471768i	−0.922389	−	0.386262i	$-0.873766\pi$
$659$	−10.4940	+	12.1107i	−0.408789	+	0.471768i	0.513600	+	0.858030i	$0.328312\pi$
$660$	0.970068	−	2.12415i	0.0377599	−	0.0826825i
$661$	−3.05667	−	1.96440i	−0.118891	−	0.0764063i	0.479844	−	0.877354i	$-0.340693\pi$
$661$	−3.05667	−	1.96440i	−0.118891	−	0.0764063i	−0.598735	+	0.800947i	$0.704330\pi$
$662$	0.357490	+	2.48640i	0.0138942	+	0.0966366i
$663$	−4.37369	+	2.81080i	−0.169860	+	0.109162i
$664$	−3.86627	−	4.46192i	−0.150041	−	0.173156i
$665$	−1.40828	+	0.413509i	−0.0546108	+	0.0160352i
$666$	−2.65338			−0.102817
$667$	5.20551	+	1.65255i	0.201558	+	0.0639870i
$668$	−9.87199			−0.381959
$669$	9.09131	−	2.66945i	0.351490	−	0.103207i
$670$	0.319557	+	0.368789i	0.0123456	+	0.0142476i
$671$	52.2365	−	33.5704i	2.01657	−	1.29597i
$672$	0.460097	+	3.20005i	0.0177486	+	0.123444i
$673$	30.0386	+	19.3046i	1.15790	+	0.744139i	0.971197	−	0.238277i	$-0.0765827\pi$
$673$	30.0386	+	19.3046i	1.15790	+	0.744139i	0.186705	+	0.982416i	$0.440219\pi$
$674$	0.604366	−	1.32338i	0.0232793	−	0.0509745i
$675$	3.22488	−	3.72171i	0.124126	−	0.143249i
$676$	−2.21681	+	15.4183i	−0.0852620	+	0.593010i
$677$	0.800595	+	1.75306i	0.0307694	+	0.0673755i	0.924393	−	0.381442i	$-0.124572\pi$
$677$	0.800595	+	1.75306i	0.0307694	+	0.0673755i	−0.893623	+	0.448818i	$0.851845\pi$
$678$	−1.33408	−	0.391720i	−0.0512349	−	0.0150439i
$679$	12.4457	+	3.65440i	0.477624	+	0.140243i
$680$	−0.299519	−	0.655855i	−0.0114860	−	0.0251509i
$681$	−0.548954	+	3.81806i	−0.0210360	+	0.146308i
$682$	2.56282	−	2.95766i	0.0981356	−	0.113254i
$683$	0.628845	−	1.37698i	0.0240621	−	0.0526886i	−0.897219	−	0.441585i	$-0.854416\pi$
$683$	0.628845	−	1.37698i	0.0240621	−	0.0526886i	0.921281	+	0.388896i	$0.127144\pi$
$684$	−8.62472	−	5.54277i	−0.329775	−	0.211933i
$685$	0.160013	+	1.11291i	0.00611376	+	0.0425222i
$686$	−0.239446	+	0.153882i	−0.00914208	+	0.00587526i
$687$	8.96920	+	10.3510i	0.342196	+	0.394916i
$688$	36.0730	−	10.5920i	1.37527	−	0.403816i
$689$	26.9612			1.02714
$690$	−0.0614482	+	0.369943i	−0.00233929	+	0.0140835i
$691$	−35.0152			−1.33204			−0.666020	−	0.745934i	$-0.732003\pi$
$691$	−35.0152			−1.33204			−0.666020	+	0.745934i	$0.732003\pi$
$692$	10.7237	−	3.14875i	0.407652	−	0.119697i
$693$	2.90066	+	3.34754i	0.110187	+	0.127162i
$694$	2.73261	−	1.75614i	0.103728	−	0.0666623i
$695$	0.430425	+	2.99367i	0.0163269	+	0.113556i
$696$	1.06864	+	0.686772i	0.0405067	+	0.0260320i
$697$	3.60191	−	7.88709i	0.136432	−	0.298745i
$698$	−2.45494	+	2.83315i	−0.0929208	+	0.107236i
$699$	−0.308094	+	2.14284i	−0.0116532	+	0.0810496i
$700$	3.92571	+	8.59611i	0.148378	+	0.324902i
$701$	23.6848	+	6.95448i	0.894562	+	0.262667i	0.696529	−	0.717528i	$-0.254727\pi$
$701$	23.6848	+	6.95448i	0.894562	+	0.262667i	0.198033	+	0.980195i	$0.436545\pi$
$702$	0.603471	+	0.177195i	0.0227765	+	0.00668779i
$703$	20.6894	+	45.3036i	0.780317	+	1.70866i
$704$	−3.85836	+	26.8355i	−0.145418	+	1.01140i
$705$	1.78024	−	2.05450i	0.0670476	−	0.0773771i
$706$	−0.519221	+	1.13694i	−0.0195411	+	0.0427891i
$707$	−14.3499	−	9.22215i	−0.539685	−	0.346835i
$708$	0.163504	+	1.13720i	0.00614486	+	0.0427384i
$709$	5.00027	−	3.21348i	0.187789	−	0.120685i	−0.443368	−	0.896340i	$-0.646217\pi$
$709$	5.00027	−	3.21348i	0.187789	−	0.120685i	0.631157	+	0.775655i	$0.282580\pi$
$710$	0.757176	+	0.873827i	0.0284163	+	0.0327942i
$711$	0.559898	−	0.164401i	0.0209978	−	0.00616552i
$712$	15.6284			0.585700
$713$	6.47798	−	13.4036i	0.242602	−	0.501970i
$714$	0.669680			0.0250621
$715$	2.58003	−	0.757564i	0.0964875	−	0.0283313i
$716$	−16.1304	−	18.6155i	−0.602822	−	0.695694i
$717$	−25.4134	+	16.3322i	−0.949082	+	0.609938i
$718$	0.374482	+	2.60458i	0.0139755	+	0.0972020i
$719$	22.7816	+	14.6408i	0.849609	+	0.546010i	0.891453	−	0.453114i	$-0.149687\pi$
$719$	22.7816	+	14.6408i	0.849609	+	0.546010i	−0.0418441	+	0.999124i	$0.513323\pi$
$720$	0.401777	−	0.879769i	0.0149733	−	0.0327870i
$721$	12.7281	−	14.6891i	0.474021	−	0.547049i
$722$	0.386541	−	2.68845i	0.0143856	−	0.100054i
$723$	−0.255705	−	0.559915i	−0.00950976	−	0.0208235i
$724$	36.0680	+	10.5905i	1.34046	+	0.393594i
$725$	5.38092	+	1.57998i	0.199842	+	0.0586790i
$726$	−1.01920	−	2.23174i	−0.0378261	−	0.0828275i
$727$	2.28766	−	15.9111i	0.0848448	−	0.590108i	−0.902400	−	0.430899i	$-0.858196\pi$
$727$	2.28766	−	15.9111i	0.0848448	−	0.590108i	0.987245	−	0.159209i	$-0.0508945\pi$
$728$	−1.61412	+	1.86280i	−0.0598234	+	0.0690399i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	0.473586	+	0.304355i	0.0175282	+	0.0112647i
$731$	−3.57582	−	24.8704i	−0.132257	−	0.919865i
$732$	22.6307	−	14.5439i	0.836457	−	0.537558i
$733$	9.24541	+	10.6698i	0.341487	+	0.394097i	0.900353	−	0.435161i	$-0.143309\pi$
$733$	9.24541	+	10.6698i	0.341487	+	0.394097i	−0.558865	+	0.829258i	$0.688763\pi$
$734$	−7.61249	+	2.23523i	−0.280982	+	0.0825038i
$735$	0.274727			0.0101335
$736$	−1.87150	−	15.3913i	−0.0689844	−	0.567332i
$737$	−27.6418			−1.01820
$738$	−1.00644	+	0.295516i	−0.0370474	+	0.0108781i
$739$	14.9197	+	17.2183i	0.548830	+	0.633384i	0.960610	−	0.277899i	$-0.0896382\pi$
$739$	14.9197	+	17.2183i	0.548830	+	0.633384i	−0.411780	+	0.911283i	$0.635093\pi$
$740$	−4.13447	+	2.65706i	−0.151986	+	0.0976755i
$741$	−1.68008	−	11.6852i	−0.0617194	−	0.429268i
$742$	−2.92154	−	1.87756i	−0.107253	−	0.0689275i
$743$	−13.4190	+	29.3835i	−0.492295	+	1.07798i	0.486602	+	0.873624i	$0.338236\pi$
$743$	−13.4190	+	29.3835i	−0.492295	+	1.07798i	−0.978897	+	0.204352i	$0.934491\pi$
$744$	2.26749	−	2.61682i	0.0831302	−	0.0959373i
$745$	−0.627925	+	4.36731i	−0.0230054	+	0.160006i
$746$	−0.0564217	−	0.123546i	−0.00206574	−	0.00452335i
$747$	−5.07845	−	1.49117i	−0.185811	−	0.0545590i
$748$	19.1888	+	5.63434i	0.701612	+	0.206012i
$749$	5.39955	+	11.8234i	0.197295	+	0.432016i
$750$	−0.110444	+	0.768153i	−0.00403284	+	0.0280490i
$751$	6.30631	−	7.27787i	0.230121	−	0.265573i	−0.628932	−	0.777460i	$-0.716508\pi$
$751$	6.30631	−	7.27787i	0.230121	−	0.265573i	0.859053	+	0.511887i	$0.171053\pi$
$752$	−14.4714	+	31.6880i	−0.527719	+	1.15554i
$753$	8.65317	+	5.56106i	0.315339	+	0.202656i
$754$	0.101933	+	0.708959i	0.00371218	+	0.0258188i
$755$	2.22693	−	1.43116i	0.0810462	−	0.0520852i
$756$	1.25667	+	1.45027i	0.0457046	+	0.0527459i
$757$	39.9287	−	11.7241i	1.45123	−	0.426120i	0.541283	−	0.840840i	$-0.317939\pi$
$757$	39.9287	−	11.7241i	1.45123	−	0.426120i	0.909949	+	0.414720i	$0.136121\pi$
$758$	−5.93564			−0.215592
$759$	−13.5578	−	16.3536i	−0.492117	−	0.593599i
$760$	1.63720			0.0593874
$761$	49.2248	−	14.4537i	1.78440	−	0.523946i	0.788549	−	0.614972i	$-0.210833\pi$
$761$	49.2248	−	14.4537i	1.78440	−	0.523946i	0.995849	+	0.0910257i	$0.0290145\pi$
$762$	−0.962619	−	1.11092i	−0.0348720	−	0.0402445i
$763$	−1.65587	+	1.06416i	−0.0599465	+	0.0385253i
$764$	−5.15303	−	35.8401i	−0.186430	−	1.29665i
$765$	−0.543770	−	0.349460i	−0.0196600	−	0.0126347i
$766$	−2.71135	+	5.93703i	−0.0979651	+	0.214514i
$767$	−0.866342	+	0.999812i	−0.0312818	+	0.0361011i
$768$	−1.40967	+	9.80445i	−0.0508670	+	0.353788i
$769$	17.4960	+	38.3108i	0.630921	+	1.38152i	0.907303	+	0.420476i	$0.138137\pi$
$769$	17.4960	+	38.3108i	0.630921	+	1.38152i	−0.276383	+	0.961048i	$0.589136\pi$
$770$	−0.332331	−	0.0975810i	−0.0119764	−	0.00351658i
$771$	−15.1395	−	4.44536i	−0.545236	−	0.160096i
$772$	11.1460	+	24.4064i	0.401155	+	0.878406i
$773$	2.15338	−	14.9771i	0.0774517	−	0.538689i	−0.913745	−	0.406289i	$-0.866823\pi$
$773$	2.15338	−	14.9771i	0.0774517	−	0.538689i	0.991196	−	0.132400i	$-0.0422683\pi$
$774$	−1.99053	+	2.29719i	−0.0715480	+	0.0825708i
$775$	6.35022	−	13.9050i	0.228107	−	0.499484i
$776$	−12.1719	−	7.82243i	−0.436947	−	0.280809i
$777$	−1.32669	−	9.22735i	−0.0475948	−	0.331029i
$778$	−3.00251	+	1.92959i	−0.107645	+	0.0691793i
$779$	12.8932	+	14.8795i	0.461946	+	0.533114i
$780$	1.11776	−	0.328204i	0.0400222	−	0.0117516i
$781$	−65.4958			−2.34363
$782$	−3.21091	−	0.0700068i	−0.114822	−	0.00250344i
$783$	1.13881			0.0406976
$784$	−3.37787	+	0.991834i	−0.120638	+	0.0354226i
$785$	−2.14962	−	2.48079i	−0.0767231	−	0.0885431i
$786$	−2.85827	+	1.83690i	−0.101951	+	0.0655200i
$787$	−0.847523	−	5.89465i	−0.0302109	−	0.210122i	0.969125	−	0.246572i	$-0.0793041\pi$
$787$	−0.847523	−	5.89465i	−0.0302109	−	0.210122i	−0.999335	+	0.0364500i	$0.988395\pi$
$788$	−34.8922	−	22.4239i	−1.24298	−	0.798817i
$789$	0.663850	−	1.45363i	0.0236337	−	0.0517505i
$790$	−0.0298812	+	0.0344847i	−0.00106312	+	0.00122691i
$791$	0.695198	−	4.83521i	0.0247184	−	0.171920i
$792$	−2.05250	−	4.49435i	−0.0729324	−	0.159700i
$793$	29.7219	+	8.72713i	1.05545	+	0.309909i
$794$	−5.94526	−	1.74569i	−0.210989	−	0.0619521i
$795$	1.39248	+	3.04910i	0.0493861	+	0.108141i
$796$	−4.79175	+	33.3273i	−0.169839	+	1.18126i
$797$	35.8552	−	41.3791i	1.27006	−	1.46572i	0.450442	−	0.892806i	$-0.351267\pi$
$797$	35.8552	−	41.3791i	1.27006	−	1.46572i	0.819614	−	0.572916i	$-0.194188\pi$
$798$	−0.631697	+	1.38322i	−0.0223618	+	0.0489656i
$799$	19.5858	+	12.5871i	0.692897	+	0.445298i
$800$	−2.26576	−	15.7587i	−0.0801067	−	0.557154i
$801$	11.7866	−	7.57479i	0.416459	−	0.267642i
$802$	−0.119968	−	0.138450i	−0.00423620	−	0.00488884i
$803$	−30.5971	+	8.98410i	−1.07975	+	0.317042i
$804$	−11.9754			−0.422340
$805$	−1.31723	−	0.0287193i	−0.0464263	−	0.00101222i
$806$	1.95234			0.0687684
$807$	15.3206	−	4.49854i	0.539311	−	0.158356i
$808$	12.4602	+	14.3799i	0.438350	+	0.505882i
$809$	−3.90903	+	2.51218i	−0.137434	+	0.0883235i	−0.607551	−	0.794281i	$-0.707848\pi$
$809$	−3.90903	+	2.51218i	−0.137434	+	0.0883235i	0.470117	+	0.882604i	$0.344212\pi$
$810$	0.0111284	+	0.0773995i	0.000391011	+	0.00271954i
$811$	4.66619	+	2.99878i	0.163852	+	0.105301i	0.619997	−	0.784604i	$-0.287134\pi$
$811$	4.66619	+	2.99878i	0.163852	+	0.105301i	−0.456145	+	0.889906i	$0.650770\pi$
$812$	−0.907829	+	1.98787i	−0.0318586	+	0.0697605i
$813$	−8.30743	+	9.58729i	−0.291354	+	0.336241i
$814$	−1.67262	+	11.6333i	−0.0586253	+	0.407748i
$815$	−0.714357	−	1.56422i	−0.0250228	−	0.0547924i
$816$	7.94750	+	2.33360i	0.278218	+	0.0816923i
$817$	54.7428	+	16.0739i	1.91521	+	0.562356i
$818$	4.47311	+	9.79474i	0.156399	+	0.342465i
$819$	−0.314474	+	2.18721i	−0.0109886	+	0.0764274i
$820$	−1.27229	+	1.46830i	−0.0444303	+	0.0512753i
$821$	12.0720	−	26.4339i	0.421314	−	0.922549i	−0.573343	−	0.819315i	$-0.694354\pi$
$821$	12.0720	−	26.4339i	0.421314	−	0.922549i	0.994657	−	0.103234i	$-0.0329189\pi$
$822$	0.979964	+	0.629784i	0.0341802	+	0.0219663i
$823$	2.44556	+	17.0092i	0.0852467	+	0.592904i	0.987008	+	0.160670i	$0.0513654\pi$
$823$	2.44556	+	17.0092i	0.0852467	+	0.592904i	−0.901762	+	0.432234i	$0.857725\pi$
$824$	−18.2388	+	11.7214i	−0.635380	+	0.408334i
$825$	−14.2844	−	16.4850i	−0.497317	−	0.573935i
$826$	0.163504	−	0.0480091i	0.00568903	−	0.00167045i
$827$	30.5803			1.06338			0.531691	−	0.846938i	$-0.321557\pi$
$827$	30.5803			1.06338			0.531691	+	0.846938i	$0.321557\pi$
$828$	−5.87373	−	7.08498i	−0.204126	−	0.246220i
$829$	10.2250			0.355129			0.177565	−	0.984109i	$-0.443178\pi$
$829$	10.2250			0.355129			0.177565	+	0.984109i	$0.443178\pi$
$830$	0.397112	−	0.116603i	0.0137840	−	0.00404733i
$831$	11.9956	+	13.8437i	0.416123	+	0.480231i
$832$	−11.3780	+	7.31221i	−0.394462	+	0.253505i
$833$	0.334840	+	2.32886i	0.0116015	+	0.0806903i
$834$	2.63605	+	1.69408i	0.0912788	+	0.0586614i
$835$	0.587106	−	1.28558i	0.0203176	−	0.0444894i
$836$	−29.7382	+	34.3197i	−1.02852	+	1.18697i
$837$	0.441766	−	3.07255i	0.0152697	−	0.106203i
$838$	−0.607400	−	1.33002i	−0.0209823	−	0.0459448i
$839$	−32.2944	−	9.48248i	−1.11492	−	0.327371i	−0.328159	−	0.944623i	$-0.606428\pi$
$839$	−32.2944	−	9.48248i	−1.11492	−	0.327371i	−0.786766	+	0.617251i	$0.788246\pi$
$840$	−0.294033	−	0.0863360i	−0.0101451	−	0.00297888i
$841$	−11.5083	−	25.1996i	−0.396838	−	0.868953i
$842$	0.561731	−	3.90692i	0.0193585	−	0.134642i
$843$	9.71091	−	11.2070i	0.334461	−	0.385989i
$844$	3.37971	−	7.40054i	0.116335	−	0.254737i
$845$	−1.87601	−	1.20564i	−0.0645366	−	0.0414752i
$846$	−0.400828	−	2.78782i	−0.0137808	−	0.0958473i
$847$	7.25144	−	4.66021i	0.249162	−	0.160127i
$848$	−28.1291	−	32.4627i	−0.965958	−	1.11477i
$849$	16.4298	−	4.82422i	0.563868	−	0.165567i
$850$	−3.29786			−0.113116
$851$	5.39648	+	44.3810i	0.184989	+	1.52136i
$852$	−28.3752			−0.972117
$853$	4.00242	−	1.17522i	0.137040	−	0.0402386i	−0.212493	−	0.977163i	$-0.568158\pi$
$853$	4.00242	−	1.17522i	0.137040	−	0.0402386i	0.349533	+	0.936924i	$0.386340\pi$
$854$	−2.61294	−	3.01549i	−0.0894130	−	0.103188i
$855$	1.23474	−	0.793517i	0.0422271	−	0.0271377i
$856$	−2.06338	−	14.3511i	−0.0705249	−	0.490511i
$857$	7.12633	+	4.57981i	0.243431	+	0.156443i	0.656668	−	0.754180i	$-0.271965\pi$
$857$	7.12633	+	4.57981i	0.243431	+	0.156443i	−0.413237	+	0.910624i	$0.635602\pi$
$858$	1.15729	−	2.53412i	0.0395094	−	0.0865134i
$859$	−9.61855	+	11.1004i	−0.328181	+	0.378741i	−0.895730	−	0.444599i	$-0.853346\pi$
$859$	−9.61855	+	11.1004i	−0.328181	+	0.378741i	0.567549	+	0.823340i	$0.307892\pi$
$860$	−0.801239	+	5.57274i	−0.0273220	+	0.190029i
$861$	−1.53090	−	3.35220i	−0.0521729	−	0.114243i
$862$	−0.784515	−	0.230354i	−0.0267207	−	0.00784590i
$863$	−14.1698	−	4.16063i	−0.482346	−	0.141630i	0.0315145	−	0.999503i	$-0.489967\pi$
$863$	−14.1698	−	4.16063i	−0.482346	−	0.141630i	−0.513861	+	0.857874i	$0.671785\pi$
$864$	−1.34302	−	2.94080i	−0.0456904	−	0.100048i
$865$	−0.227709	+	1.58375i	−0.00774234	+	0.0538492i
$866$	−3.72486	+	4.29872i	−0.126576	+	0.146076i
$867$	−4.76243	+	10.4283i	−0.161741	+	0.354163i
$868$	5.01119	+	3.22050i	0.170091	+	0.109311i
$869$	−0.367845	−	2.55842i	−0.0124783	−	0.0867884i
$870$	−0.0749132	+	0.0481438i	−0.00253979	+	0.00163223i
$871$	−9.03029	−	10.4215i	−0.305980	−	0.353120i
$872$	2.10666	−	0.618572i	0.0713406	−	0.0209475i
$873$	−12.9712			−0.439007
$874$	3.17339	−	6.56610i	0.107342	−	0.222101i
$875$	−2.72653			−0.0921736
$876$	−13.2557	+	3.89224i	−0.447870	+	0.131507i
$877$	−37.0961	−	42.8112i	−1.25265	−	1.44563i	−0.846993	−	0.531604i	$-0.821589\pi$
$877$	−37.0961	−	42.8112i	−1.25265	−	1.44563i	−0.405653	−	0.914027i	$-0.632956\pi$
$878$	4.06691	−	2.61364i	0.137251	−	0.0882061i
$879$	2.40249	+	16.7097i	0.0810341	+	0.563605i
$880$	−3.60393	−	2.31611i	−0.121489	−	0.0780760i
$881$	−17.8552	+	39.0973i	−0.601555	+	1.31722i	0.326647	+	0.945146i	$0.394081\pi$
$881$	−17.8552	+	39.0973i	−0.601555	+	1.31722i	−0.928202	+	0.372076i	$0.878646\pi$
$882$	0.186393	−	0.215109i	0.00627617	−	0.00724309i
$883$	5.80018	−	40.3411i	0.195191	−	1.35759i	−0.622811	−	0.782372i	$-0.714010\pi$
$883$	5.80018	−	40.3411i	0.195191	−	1.35759i	0.818003	−	0.575214i	$-0.195081\pi$
$884$	4.14453	+	9.07525i	0.139396	+	0.305234i
$885$	−0.157815	−	0.0463388i	−0.00530490	−	0.00155766i
$886$	−10.8245	−	3.17837i	−0.363657	−	0.106779i
$887$	−22.0595	−	48.3035i	−0.740684	−	1.62187i	−0.782425	−	0.622744i	$-0.786018\pi$
$887$	−22.0595	−	48.3035i	−0.740684	−	1.62187i	0.0417409	−	0.999128i	$-0.486710\pi$
$888$	−1.47987	+	10.2927i	−0.0496612	+	0.345402i
$889$	3.38201	−	3.90304i	0.113429	−	0.130904i
$890$	−0.455119	+	0.996571i	−0.0152556	+	0.0334051i
$891$	−3.72627	−	2.39473i	−0.124835	−	0.0802264i
$892$	−2.58766	−	17.9975i	−0.0866411	−	0.602602i
$893$	−44.4735	+	28.5814i	−1.48825	+	0.956440i
$894$	2.99354	+	3.45473i	0.100119	+	0.115544i
$895$	3.38351	−	0.993489i	0.113098	−	0.0332087i
$896$	8.20806			0.274212
$897$	1.73645	−	10.4541i	0.0579784	−	0.349053i
$898$	4.80394			0.160310
$899$	3.39183	−	0.995932i	0.113124	−	0.0332162i
$900$	−6.18850	−	7.14191i	−0.206283	−	0.238064i
$901$	−24.1501	+	15.5203i	−0.804558	+	0.517058i
$902$	0.661213	+	4.59884i	0.0220160	+	0.153125i
$903$	−8.98392	−	5.77361i	−0.298966	−	0.192134i
$904$	−2.26357	+	4.95653i	−0.0752853	+	0.164852i
$905$	−3.52418	+	4.06712i	−0.117148	+	0.135196i
$906$	0.390309	−	2.71466i	0.0129672	−	0.0901885i
$907$	15.1432	+	33.1589i	0.502820	+	1.10102i	0.975542	+	0.219811i	$0.0705442\pi$
$907$	15.1432	+	33.1589i	0.502820	+	1.10102i	−0.472722	+	0.881212i	$0.656729\pi$
$908$	7.10231	+	2.08543i	0.235698	+	0.0692073i
$909$	16.3669	+	4.80574i	0.542854	+	0.159396i
$910$	−0.0717790	−	0.157174i	−0.00237945	−	0.00521027i
$911$	2.74318	−	19.0792i	0.0908855	−	0.632123i	−0.892561	−	0.450926i	$-0.851094\pi$
$911$	2.74318	−	19.0792i	0.0908855	−	0.632123i	0.983447	−	0.181197i	$-0.0579971\pi$
$912$	−12.3168	+	14.2143i	−0.407849	+	0.470683i
$913$	−9.73911	+	21.3257i	−0.322317	+	0.705777i
$914$	−5.42933	−	3.48922i	−0.179586	−	0.115413i
$915$	0.548089	+	3.81205i	0.0181193	+	0.126022i
$916$	22.1108	−	14.2097i	0.730560	−	0.469502i
$917$	−7.81709	−	9.02140i	−0.258143	−	0.297913i
$918$	−0.642553	+	0.188671i	−0.0212074	+	0.00622706i
$919$	−55.7057			−1.83756			−0.918781	−	0.394769i	$-0.870825\pi$
$919$	−55.7057			−1.83756			−0.918781	+	0.394769i	$0.870825\pi$
$920$	1.40077	+	0.444692i	0.0461822	+	0.0146611i
$921$	3.00460			0.0990051
$922$	−2.09193	+	0.614246i	−0.0688941	+	0.0202291i
$923$	−21.3968	−	24.6933i	−0.704285	−	0.812789i
$924$	7.15066	−	4.59545i	0.235239	−	0.151179i
$925$	6.53333	+	45.4403i	0.214815	+	1.49407i
$926$	7.48487	+	4.81023i	0.245968	+	0.158074i
$927$	−8.07418	+	17.6800i	−0.265191	+	0.580687i
$928$	2.41101	−	2.78245i	0.0791452	−	0.0913384i
$929$	4.20234	−	29.2279i	0.137874	−	0.958937i	−0.797005	−	0.603972i	$-0.793584\pi$
$929$	4.20234	−	29.2279i	0.137874	−	0.958937i	0.934880	−	0.354965i	$-0.115507\pi$
$930$	0.100834	+	0.220795i	0.00330647	+	0.00724015i
$931$	−5.12611	−	1.50516i	−0.168002	−	0.0493297i
$932$	3.98608	+	1.17042i	0.130569	+	0.0383384i
$933$	−8.70180	−	19.0543i	−0.284884	−	0.623809i
$934$	−1.00734	+	7.00618i	−0.0329611	+	0.229249i
$935$	−1.87493	+	2.16378i	−0.0613167	+	0.0707632i
$936$	1.02393	−	2.24209i	0.0334682	−	0.0732851i
$937$	−20.3800	−	13.0974i	−0.665784	−	0.427874i	0.163619	−	0.986524i	$-0.447683\pi$
$937$	−20.3800	−	13.0974i	−0.665784	−	0.427874i	−0.829404	+	0.558650i	$0.811320\pi$
$938$	0.252784	+	1.75815i	0.00825368	+	0.0574056i
$939$	4.94886	−	3.18044i	0.161500	−	0.103790i
$940$	−3.41625	−	3.94256i	−0.111426	−	0.128592i
$941$	27.1946	−	7.98506i	0.886520	−	0.260306i	0.193393	−	0.981121i	$-0.438051\pi$
$941$	27.1946	−	7.98506i	0.886520	−	0.260306i	0.693127	+	0.720816i	$0.256233\pi$
$942$	−3.40088			−0.110807
$943$	6.98975	+	16.2328i	0.227618	+	0.528613i
$944$	2.10770			0.0685997
$945$	−0.263598	+	0.0773995i	−0.00857486	+	0.00251781i
$946$	8.81689	+	10.1752i	0.286662	+	0.330825i
$947$	34.7200	−	22.3132i	1.12825	−	0.725080i	0.163054	−	0.986617i	$-0.447866\pi$
$947$	34.7200	−	22.3132i	1.12825	−	0.725080i	0.965193	+	0.261537i	$0.0842293\pi$
$948$	−0.159364	−	1.10840i	−0.00517589	−	0.0359991i
$949$	−13.3829	−	8.60069i	−0.434429	−	0.279190i
$950$	3.11081	−	6.81172i	0.100928	−	0.221001i
$951$	−0.429339	+	0.495484i	−0.0139223	+	0.0160672i
$952$	0.373501	−	2.59775i	0.0121052	−	0.0841937i
$953$	−10.7986	−	23.6457i	−0.349802	−	0.765959i	−0.999981	−	0.00617816i	$-0.998033\pi$
$953$	−10.7986	−	23.6457i	−0.349802	−	0.765959i	0.650179	−	0.759781i	$-0.274694\pi$
$954$	3.33217	+	0.978414i	0.107883	+	0.0316773i
$955$	4.97374	+	1.46042i	0.160946	+	0.0472581i
$956$	24.0819	+	52.7320i	0.778864	+	1.70547i
$957$	0.717873	−	4.99292i	0.0232055	−	0.161398i
$958$	−3.77836	+	4.36046i	−0.122073	+	0.140880i
$959$	−1.70014	+	3.72279i	−0.0549004	+	0.120215i
$960$	−1.41460	−	0.909108i	−0.0456560	−	0.0293413i
$961$	3.04045	+	21.1468i	0.0980791	+	0.682155i
$962$	−4.93243	+	3.16988i	−0.159028	+	0.102201i
$963$	−8.51186	−	9.82321i	−0.274291	−	0.316548i
$964$	−1.13337	+	0.332786i	−0.0365032	+	0.0107183i
$965$	−3.84121			−0.123653
$966$	−0.916183	+	1.01190i	−0.0294777	+	0.0325572i
$967$	−11.6612			−0.374998			−0.187499	−	0.982265i	$-0.560038\pi$
$967$	−11.6612			−0.374998			−0.187499	+	0.982265i	$0.560038\pi$
$968$	−9.22556	+	2.70887i	−0.296521	+	0.0870664i
$969$	8.23157	+	9.49974i	0.264436	+	0.305176i
$970$	0.853271	−	0.548364i	0.0273969	−	0.0176069i
$971$	8.64191	+	60.1058i	0.277332	+	1.92889i	0.361365	+	0.932424i	$0.382311\pi$
$971$	8.64191	+	60.1058i	0.277332	+	1.92889i	−0.0840328	+	0.996463i	$0.526780\pi$
$972$	−1.61435	−	1.03748i	−0.0517804	−	0.0332773i
$973$	−4.57329	+	10.0141i	−0.146613	+	0.321037i
$974$	−2.41912	+	2.79182i	−0.0775137	+	0.0894556i
$975$	1.54863	−	10.7710i	0.0495960	−	0.344947i
$976$	−20.5014	−	44.8919i	−0.656235	−	1.43695i
$977$	−7.41328	−	2.17673i	−0.237172	−	0.0696399i	0.160987	−	0.986957i	$-0.448532\pi$
$977$	−7.41328	−	2.17673i	−0.237172	−	0.0696399i	−0.398158	+	0.917317i	$0.630351\pi$
$978$	−1.70944	−	0.501937i	−0.0546619	−	0.0160502i
$979$	−25.7805	−	56.4514i	−0.823948	−	1.80419i
$980$	0.0750279	−	0.521831i	0.00239668	−	0.0166693i
$981$	1.28899	−	1.48757i	0.0411541	−	0.0474944i
$982$	0.321479	−	0.703940i	0.0102588	−	0.0224636i
$983$	20.5539	+	13.2092i	0.655568	+	0.421308i	0.825697	−	0.564114i	$-0.190782\pi$
$983$	20.5539	+	13.2092i	0.655568	+	0.421308i	−0.170129	+	0.985422i	$0.554418\pi$
$984$	0.585017	+	4.06888i	0.0186496	+	0.129711i
$985$	4.99525	−	3.21025i	0.159162	−	0.102287i
$986$	−0.499421	−	0.576362i	−0.0159048	−	0.0183551i
$987$	9.49445	−	2.78782i	0.302212	−	0.0887374i
$988$	−22.6544			−0.720732
$989$	42.4716	+	28.6219i	1.35052	+	0.910122i
$990$	0.346361			0.0110081
$991$	57.0336	−	16.7466i	1.81173	−	0.531972i	0.812997	−	0.582268i	$-0.197835\pi$
$991$	57.0336	−	16.7466i	1.81173	−	0.531972i	0.998734	+	0.0502963i	$0.0160166\pi$
$992$	−6.57189	−	7.58437i	−0.208658	−	0.240804i
$993$	7.42439	−	4.77136i	0.235606	−	0.151415i
$994$	0.598959	+	4.16585i	0.0189978	+	0.132133i
$995$	−4.05508	−	2.60604i	−0.128555	−	0.0826171i
$996$	−4.21933	+	9.23905i	−0.133695	+	0.292750i
$997$	−9.55680	+	11.0291i	−0.302667	+	0.349296i	−0.886626	−	0.462487i	$-0.846957\pi$
$997$	−9.55680	+	11.0291i	−0.302667	+	0.349296i	0.583959	+	0.811783i	$0.301503\pi$
$998$	0.686401	−	4.77403i	0.0217277	−	0.151119i
$999$	3.87260	+	8.47980i	0.122524	+	0.268289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.c.400.1	yes	20
23.18	even	11	inner	483.2.q.c.64.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.64.1	✓	20	23.18	even	11	inner
483.2.q.c.400.1	yes	20	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.273100 - 0.0801894i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.61435 + 1.03748i) q^{4} +(-0.0390977 - 0.271930i) q^{5} +(-0.239446 - 0.153882i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.730471 + 0.843008i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.273100 - 0.0801894i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.61435 + 1.03748i) q^{4} +(-0.0390977 - 0.271930i) q^{5} +(-0.239446 - 0.153882i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.730471 + 0.843008i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.0324835 - 0.0711290i) q^{10} +(4.25000 + 1.24791i) q^{11} +(1.84125 + 0.540641i) q^{12} +(0.917944 + 2.01002i) q^{13} +(0.0405070 - 0.281733i) q^{14} +(-0.179908 + 0.207625i) q^{15} +(1.46246 - 3.20234i) q^{16} +(-1.97931 - 1.27203i) q^{17} +(0.0405070 + 0.281733i) q^{18} +(4.49442 - 2.88839i) q^{19} +(0.345241 + 0.398429i) q^{20} +(-0.959493 + 0.281733i) q^{21} +1.26075 q^{22} +(4.62992 - 1.25052i) q^{23} +1.11546 q^{24} +(4.72505 - 1.38740i) q^{25} +(0.411873 + 0.475327i) q^{26} +(0.841254 - 0.540641i) q^{27} +(0.273100 + 1.89945i) q^{28} +(0.958025 + 0.615686i) q^{29} +(-0.0324835 + 0.0711290i) q^{30} +(2.03278 - 2.34596i) q^{31} +(0.460097 - 3.20005i) q^{32} +(-1.84005 - 4.02915i) q^{33} +(-0.642553 - 0.188671i) q^{34} +(-0.263598 - 0.0773995i) q^{35} +(-0.797176 - 1.74557i) q^{36} +(-1.32669 + 9.22735i) q^{37} +(0.995808 - 1.14922i) q^{38} +(0.917944 - 2.01002i) q^{39} +(0.257799 + 0.165678i) q^{40} +(0.524462 + 3.64772i) q^{41} +(-0.239446 + 0.153882i) q^{42} +(6.99339 + 8.07080i) q^{43} +(-8.15569 + 2.39473i) q^{44} +0.274727 q^{45} +(1.16415 - 0.712788i) q^{46} -9.89528 q^{47} +(-3.37787 + 0.991834i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(1.17916 - 0.757798i) q^{50} +(0.334840 + 2.32886i) q^{51} +(-3.56724 - 2.29253i) q^{52} +(5.06860 - 11.0987i) q^{53} +(0.186393 - 0.215109i) q^{54} +(0.173180 - 1.20450i) q^{55} +(0.463379 + 1.01466i) q^{56} +(-5.12611 - 1.50516i) q^{57} +(0.311008 + 0.0913203i) q^{58} +(0.248707 + 0.544593i) q^{59} +(0.0750279 - 0.521831i) q^{60} +(9.18014 - 10.5944i) q^{61} +(0.367033 - 0.803689i) q^{62} +(0.841254 + 0.540641i) q^{63} +(0.871076 + 6.05846i) q^{64} +(0.510695 - 0.328204i) q^{65} +(-0.825613 - 0.952808i) q^{66} +(-5.98771 + 1.75815i) q^{67} +4.51501 q^{68} +(-3.97703 - 2.68015i) q^{69} -0.0781954 q^{70} +(-14.1876 + 4.16585i) q^{71} +(-0.730471 - 0.843008i) q^{72} +(-6.05644 + 3.89224i) q^{73} +(0.377616 + 2.62638i) q^{74} +(-4.14277 - 2.66240i) q^{75} +(-4.25893 + 9.32576i) q^{76} +(2.90066 - 3.34754i) q^{77} +(0.0895085 - 0.622546i) q^{78} +(-0.242409 - 0.530803i) q^{79} +(-0.927993 - 0.272483i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.435739 + 0.954135i) q^{82} +(-0.753251 + 5.23898i) q^{83} +(1.25667 - 1.45027i) q^{84} +(-0.268516 + 0.587968i) q^{85} +(2.55709 + 1.64334i) q^{86} +(-0.162069 - 1.12722i) q^{87} +(-4.15650 + 2.67122i) q^{88} +(-9.17509 - 10.5886i) q^{89} +(0.0750279 - 0.0220302i) q^{90} +2.20970 q^{91} +(-6.17695 + 6.82224i) q^{92} -3.10415 q^{93} +(-2.70240 + 0.793497i) q^{94} +(-0.961162 - 1.10924i) q^{95} +(-2.71973 + 1.74787i) q^{96} +(1.84599 + 12.8391i) q^{97} +(-0.239446 - 0.153882i) q^{98} +(-1.84005 + 4.02915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Introduction

L-functions

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