LMFDB - Embedded newform 483.2.q.c.64.1

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			64.1
Root			$2.10485 - 0.618040i$ of defining polynomial
Character	$\chi$	$=$	483.64
Dual form			483.2.q.c.400.1

$q$-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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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	0.376858	−	0.926271i	$-0.377005\pi$
$2$	0.273100	+	0.0801894i	0.193111	+	0.0567025i	−0.183747	+	0.982974i	$0.558823\pi$
$3$	−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	−0.996695	−	0.0812406i	$-0.974112\pi$
$5$	−0.0390977	+	0.271930i	−0.0174850	+	0.121611i	0.979210	+	0.202852i	$0.0650209\pi$
$6$	−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	0.430997	−	0.902353i	$-0.358162\pi$
$11$	4.25000	−	1.24791i	1.28142	−	0.376260i	0.850427	+	0.526093i	$0.176344\pi$
$12$	1.84125	−	0.540641i	0.531524	−	0.156070i
$13$	0.917944	−	2.01002i	0.254592	−	0.557479i	−0.738576	−	0.674170i	$-0.764502\pi$
$13$	0.917944	−	2.01002i	0.254592	−	0.557479i	0.993168	+	0.116691i	$0.0372288\pi$
$14$	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	−0.758194	−	0.652029i	$-0.773918\pi$
$17$	−1.97931	+	1.27203i	−0.480053	+	0.308512i	0.278141	+	0.960540i	$0.410282\pi$
$18$	0.0405070	−	0.281733i	0.00954760	−	0.0664050i
$19$	4.49442	+	2.88839i	1.03109	+	0.662641i	0.942768	−	0.333451i	$-0.108213\pi$
$19$	4.49442	+	2.88839i	1.03109	+	0.662641i	0.0883225	+	0.996092i	$0.471849\pi$
$20$	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	−0.448660	−	0.893703i	$-0.648098\pi$
$29$	0.958025	−	0.615686i	0.177901	−	0.114330i	0.626561	+	0.779373i	$0.284462\pi$
$30$	−0.0324835	−	0.0711290i	−0.00593066	−	0.0129863i
$31$	2.03278	+	2.34596i	0.365099	+	0.421346i	0.908342	−	0.418229i	$-0.137349\pi$
$31$	2.03278	+	2.34596i	0.365099	+	0.421346i	−0.543243	+	0.839576i	$0.682804\pi$
$32$	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	−0.745017	−	0.667046i	$-0.767559\pi$
$37$	−1.32669	−	9.22735i	−0.218107	−	1.51697i	0.526910	−	0.849921i	$-0.323350\pi$
$38$	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	−0.906999	−	0.421134i	$-0.861632\pi$
$41$	0.524462	−	3.64772i	0.0819072	−	0.569677i	0.988906	−	0.148544i	$-0.0474586\pi$
$42$	−0.239446	−	0.153882i	−0.0369473	−	0.0237446i
$43$	6.99339	−	8.07080i	1.06648	−	1.23079i	0.0945510	−	0.995520i	$-0.469858\pi$
$43$	6.99339	−	8.07080i	1.06648	−	1.23079i	0.971931	−	0.235266i	$-0.0755961\pi$
$44$	−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	0.844489	+	0.535573i	$0.179904\pi$
$53$	5.06860	+	11.0987i	0.696225	+	1.52452i	−0.148264	+	0.988948i	$0.547369\pi$
$54$	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	−0.892751	−	0.450549i	$-0.851228\pi$
$59$	0.248707	−	0.544593i	0.0323789	−	0.0709000i	0.925130	+	0.379649i	$0.123955\pi$
$60$	0.0750279	+	0.521831i	0.00968606	+	0.0673681i
$61$	9.18014	+	10.5944i	1.17540	+	1.35648i	0.921087	+	0.389356i	$0.127303\pi$
$61$	9.18014	+	10.5944i	1.17540	+	1.35648i	0.254309	+	0.967123i	$0.418152\pi$
$62$	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	−0.105298	−	0.994441i	$-0.533580\pi$
$67$	−5.98771	−	1.75815i	−0.731515	−	0.214792i	−0.626217	+	0.779649i	$0.715398\pi$
$68$	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	−0.706724	−	0.707489i	$-0.749828\pi$
$71$	−14.1876	−	4.16585i	−1.68376	−	0.494395i	−0.977032	+	0.213094i	$0.931646\pi$
$72$	−0.730471	+	0.843008i	−0.0860868	+	0.0993495i
$73$	−6.05644	−	3.89224i	−0.708853	−	0.455552i	0.135891	−	0.990724i	$-0.456610\pi$
$73$	−6.05644	−	3.89224i	−0.708853	−	0.455552i	−0.844743	+	0.535172i	$0.820247\pi$
$74$	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	−0.922778	−	0.385331i	$-0.874087\pi$
$79$	−0.242409	+	0.530803i	−0.0272732	+	0.0597200i	0.895505	+	0.445051i	$0.146814\pi$
$80$	−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	−0.988481	−	0.151348i	$-0.951639\pi$
$83$	−0.753251	−	5.23898i	−0.0826801	−	0.575053i	0.905800	−	0.423705i	$-0.139271\pi$
$84$	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	0.0198996	+	0.999802i	$0.493665\pi$
$89$	−9.17509	+	10.5886i	−0.972558	+	1.12239i	−0.992457	+	0.122590i	$0.960880\pi$
$90$	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	−0.651195	−	0.758910i	$-0.725732\pi$
$97$	1.84599	−	12.8391i	0.187432	−	1.30362i	0.838627	−	0.544706i	$-0.183359\pi$
$98$	−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	0.644335	+	0.764744i	$0.277134\pi$
$101$	2.42758	+	16.8842i	0.241553	+	1.68004i	−0.402782	+	0.915296i	$0.631957\pi$
$102$	0.278195	−	0.609162i	0.0275454	−	0.0603161i
$103$	18.6491	−	5.47587i	1.83755	−	0.539554i	0.837574	−	0.546324i	$-0.183973\pi$
$103$	18.6491	−	5.47587i	1.83755	−	0.539554i	0.999977	+	0.00677092i	$0.00215527\pi$
$104$	−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	0.176527	−	0.984296i	$-0.443514\pi$
$107$	−8.51186	−	9.82321i	−0.822872	−	0.949645i	−0.999399	+	0.0346506i	$0.988968\pi$
$108$	−0.797176	−	1.74557i	−0.0767083	−	0.167968i
$109$	−1.65587	+	1.06416i	−0.158603	+	0.101928i	−0.617535	−	0.786543i	$-0.711869\pi$
$109$	−1.65587	+	1.06416i	−0.158603	+	0.101928i	0.458932	+	0.888472i	$0.348232\pi$
$110$	−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	0.494656	−	0.869089i	$-0.335294\pi$
$113$	4.68706	+	1.37624i	0.440921	+	0.129466i	−0.0537343	+	0.998555i	$0.517112\pi$
$114$	−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	−0.0543824	−	0.998520i	$-0.517319\pi$
$127$	4.95527	−	1.45500i	0.439709	−	0.129110i	0.494091	+	0.869410i	$0.335501\pi$
$128$	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	0.992788	+	0.119886i	$0.0382529\pi$
$131$	4.95882	+	10.8583i	0.433254	+	0.948694i	−0.559534	+	0.828808i	$0.689020\pi$
$132$	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	−0.843396	−	0.537293i	$-0.819447\pi$
$149$	−15.4098	+	4.52474i	−1.26242	+	0.370681i	−0.419027	+	0.907974i	$0.637629\pi$
$150$	−1.34489	+	0.394895i	−0.109810	+	0.0322430i
$151$	4.00277	−	8.76484i	0.325741	−	0.713273i	−0.673934	−	0.738792i	$-0.735397\pi$
$151$	4.00277	−	8.76484i	0.325741	−	0.713273i	0.999674	+	0.0255193i	$0.00812391\pi$
$152$	−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	0.876336	−	0.481700i	$-0.159981\pi$
$157$	10.0517	+	6.45981i	0.802210	+	0.515549i	−0.0741265	+	0.997249i	$0.523617\pi$
$158$	−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	0.508343	−	0.861154i	$-0.330258\pi$
$163$	6.00584	+	1.76347i	0.470414	+	0.138126i	−0.0379295	+	0.999280i	$0.512076\pi$
$164$	−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	−0.362378	−	0.932031i	$-0.618035\pi$
$167$	4.32773	−	2.78126i	0.334890	−	0.215220i	0.697268	+	0.716811i	$0.254399\pi$
$168$	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	−0.487172	−	0.873306i	$-0.661971\pi$
$173$	−5.58819	+	1.64084i	−0.424862	+	0.124751i	0.0623098	+	0.998057i	$0.480153\pi$
$174$	−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	−0.800234	−	0.599688i	$-0.795291\pi$
$179$	1.82673	−	12.7052i	0.136536	−	0.949632i	0.936770	−	0.349944i	$-0.113800\pi$
$180$	−0.443506	−	0.285024i	−0.0330570	−	0.0212444i
$181$	−12.8280	+	14.8043i	−0.953494	+	1.10039i	0.0413668	+	0.999144i	$0.486829\pi$
$181$	−12.8280	+	14.8043i	−0.953494	+	1.10039i	−0.994861	+	0.101247i	$0.967717\pi$
$182$	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	−0.948296	−	0.317388i	$-0.897194\pi$
$191$	−7.83831	−	17.1635i	−0.567160	−	1.24191i	0.381135	−	0.924519i	$-0.375533\pi$
$192$	4.00825	+	4.62576i	0.289270	+	0.333836i
$193$	1.98983	+	13.8396i	0.143231	+	0.996196i	0.926978	+	0.375115i	$0.122397\pi$
$193$	1.98983	+	13.8396i	0.143231	+	0.996196i	−0.783747	+	0.621080i	$0.786694\pi$
$194$	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	−0.260580	−	0.965452i	$-0.583914\pi$
$197$	8.97867	−	19.6605i	0.639704	−	1.40076i	0.900284	−	0.435303i	$-0.143359\pi$
$198$	−0.179423	−	1.24791i	−0.0127510	−	0.0886853i
$199$	11.4900	+	13.2602i	0.814506	+	0.939990i	0.999082	−	0.0428284i	$-0.0136369\pi$
$199$	11.4900	+	13.2602i	0.814506	+	0.939990i	−0.184577	+	0.982818i	$0.559091\pi$
$200$	−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	0.412086	−	0.911145i	$-0.364800\pi$
$211$	−3.56659	−	2.29211i	−0.245534	−	0.157795i	−0.657620	+	0.753350i	$0.728437\pi$
$212$	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	0.730851	−	0.682537i	$-0.239123\pi$
$223$	−3.93611	−	8.61887i	−0.263581	−	0.577162i	−0.994433	+	0.105374i	$0.966396\pi$
$224$	−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	−0.833361	−	0.552730i	$-0.813586\pi$
$227$	−2.52601	+	2.91517i	−0.167657	+	0.193487i	0.665703	+	0.746216i	$0.268132\pi$
$228$	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	−0.800285	−	0.599620i	$-0.795318\pi$
$233$	−1.41769	+	1.63610i	−0.0928761	+	0.107185i	0.707409	+	0.706804i	$0.249864\pi$
$234$	−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	0.349983	+	0.936756i	$0.386187\pi$
$239$	4.29919	+	29.9015i	0.278091	+	1.93417i	−0.0718918	+	0.997412i	$0.522904\pi$
$240$	0.401777	−	0.879769i	0.0259346	−	0.0567888i
$241$	0.590606	−	0.173418i	0.0380443	−	0.0111708i	−0.262655	−	0.964890i	$-0.584598\pi$
$241$	0.590606	−	0.173418i	0.0380443	−	0.0111708i	0.300699	+	0.953719i	$0.402780\pi$
$242$	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	−0.0450004	−	0.998987i	$-0.514329\pi$
$251$	−9.86939	−	2.89791i	−0.622950	−	0.182915i	−0.577950	+	0.816072i	$0.696147\pi$
$252$	−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	0.884642	−	0.466271i	$-0.154403\pi$
$257$	13.2739	+	8.53059i	0.828000	+	0.532123i	−0.0566418	+	0.998395i	$0.518039\pi$
$258$	−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	−0.888060	−	0.459728i	$-0.847947\pi$
$263$	0.663850	−	1.45363i	0.0409347	−	0.0896346i	0.928995	+	0.370093i	$0.120674\pi$
$264$	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	−0.996802	−	0.0799094i	$-0.974537\pi$
$269$	−6.63310	−	14.5245i	−0.404427	−	0.885572i	0.592375	−	0.805662i	$-0.298190\pi$
$270$	−0.0657822	+	0.0422756i	−0.00400337	+	0.00257281i
$271$	−1.80538	+	12.5567i	−0.109669	+	0.762764i	0.858563	+	0.512709i	$0.171358\pi$
$271$	−1.80538	+	12.5567i	−0.109669	+	0.762764i	−0.968232	+	0.250055i	$0.919551\pi$
$272$	−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	−0.824786	−	0.565446i	$-0.808704\pi$
$281$	2.11038	−	14.6780i	0.125895	−	0.875618i	0.950680	−	0.310172i	$-0.100387\pi$
$282$	2.36938	−	1.52271i	0.141095	−	0.0906760i
$283$	−7.11331	−	15.5760i	−0.422843	−	0.925896i	−0.994434	−	0.105358i	$-0.966401\pi$
$283$	−7.11331	−	15.5760i	−0.422843	−	0.925896i	0.571592	−	0.820538i	$-0.306326\pi$
$284$	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	−0.885173	−	0.465262i	$-0.845960\pi$
$293$	−14.2017	+	9.12685i	−0.829670	+	0.533196i	0.0555032	+	0.998459i	$0.482324\pi$
$294$	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	0.696818	−	0.717248i	$-0.254598\pi$
$307$	−1.96760	−	2.27073i	−0.112297	−	0.129597i	−0.809115	+	0.587651i	$0.800053\pi$
$308$	−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	0.343183	−	0.939268i	$-0.388495\pi$
$311$	20.0987	−	5.90152i	1.13969	−	0.334644i	0.796511	+	0.604624i	$0.206677\pi$
$312$	1.02393	−	2.24209i	0.0579686	−	0.126934i
$313$	−0.837199	−	5.82285i	−0.0473213	−	0.329127i	−0.999706	−	0.0242292i	$-0.992287\pi$
$313$	−0.837199	−	5.82285i	−0.0473213	−	0.329127i	0.952385	−	0.304898i	$-0.0986222\pi$
$314$	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	−0.992274	−	0.124066i	$-0.960406\pi$
$317$	−0.0933044	+	0.648946i	−0.00524050	+	0.0364485i	0.987033	+	0.160515i	$0.0513155\pi$
$318$	−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	−0.994783	−	0.102009i	$-0.967473\pi$
$331$	−1.25598	−	8.73555i	−0.0690351	−	0.480149i	0.925748	−	0.378140i	$-0.123436\pi$
$332$	−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	0.839558	−	0.543270i	$-0.182814\pi$
$337$	3.34724	+	3.86292i	0.182336	+	0.210426i	−0.657222	+	0.753697i	$0.728269\pi$
$338$	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	0.562102	−	0.827068i	$-0.309993\pi$
$347$	10.9500	+	3.21520i	0.587825	+	0.172601i	0.0257231	+	0.999669i	$0.491811\pi$
$348$	1.43110	−	1.65158i	0.0767152	−	0.0885340i
$349$	−11.0800	−	7.12066i	−0.593097	−	0.381160i	0.209388	−	0.977833i	$-0.432853\pi$
$349$	−11.0800	−	7.12066i	−0.593097	−	0.381160i	−0.802485	+	0.596672i	$0.796489\pi$
$350$	−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	0.674043	−	0.738692i	$-0.264556\pi$
$353$	−2.87567	−	3.31870i	−0.153056	−	0.176637i	−0.827100	+	0.562055i	$0.810011\pi$
$354$	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	−0.994633	−	0.103465i	$-0.967007\pi$
$359$	−1.31568	−	9.15076i	−0.0694390	−	0.482959i	0.925194	−	0.379494i	$-0.123902\pi$
$360$	−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	−0.991504	−	0.130076i	$-0.958478\pi$
$373$	−0.0679100	+	0.472324i	−0.00351625	+	0.0244560i	0.987988	+	0.154532i	$0.0493870\pi$
$374$	−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	−0.751817	−	0.659372i	$-0.770822\pi$
$379$	−20.0092	+	5.87523i	−1.02780	+	0.301790i	−0.275986	+	0.961162i	$0.589004\pi$
$380$	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	0.228812	−	0.973471i	$-0.426516\pi$
$383$	−15.0166	−	17.3301i	−0.767314	−	0.885528i	−0.996125	+	0.0879432i	$0.971971\pi$
$384$	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	−0.0378911	−	0.999282i	$-0.512064\pi$
$389$	−12.0315	−	3.53276i	−0.610020	−	0.179118i	−0.572129	+	0.820164i	$0.693882\pi$
$390$	−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	−0.912407	−	0.409284i	$-0.865779\pi$
$397$	−18.3137	+	11.7695i	−0.919137	+	0.590694i	−0.00673020	+	0.999977i	$0.502142\pi$
$398$	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	−0.916191	−	0.400743i	$-0.868752\pi$
$401$	−0.267373	+	0.585465i	−0.0133520	+	0.0292367i	0.902839	+	0.429980i	$0.141479\pi$
$402$	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	−0.217121	−	0.976145i	$-0.569667\pi$
$409$	5.38390	−	37.4459i	0.266217	−	1.85158i	0.483338	−	0.875434i	$-0.339424\pi$
$410$	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	−0.999856	−	0.0169869i	$-0.994593\pi$
$419$	−0.731076	+	5.08475i	−0.0357154	+	0.248406i	0.964140	+	0.265393i	$0.0855017\pi$
$420$	−0.443506	+	0.285024i	−0.0216409	+	0.0139078i
$421$	5.76077	+	12.6143i	0.280763	+	0.614784i	0.996501	−	0.0835846i	$-0.0266369\pi$
$421$	5.76077	+	12.6143i	0.280763	+	0.614784i	−0.715738	+	0.698369i	$0.753910\pi$
$422$	−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	−0.597547	−	0.801834i	$-0.703858\pi$
$431$	−2.41661	+	1.55306i	−0.116404	+	0.0748083i	0.481143	+	0.876642i	$0.340222\pi$
$432$	−0.501016	+	3.48465i	−0.0241052	+	0.167655i
$433$	−16.8115	−	10.8041i	−0.807911	−	0.519213i	0.0702774	−	0.997527i	$-0.477612\pi$
$433$	−16.8115	−	10.8041i	−0.807911	−	0.519213i	−0.878189	+	0.478314i	$0.841248\pi$
$434$	−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	0.646452	−	0.762955i	$-0.276252\pi$
$439$	16.2967	+	4.78513i	0.777797	+	0.228382i	0.131346	+	0.991337i	$0.458070\pi$
$440$	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	−0.610013	+	0.792392i	$0.708836\pi$
$443$	−33.3437	+	21.4287i	−1.58421	+	1.01811i	−0.974193	+	0.225716i	$0.927528\pi$
$444$	−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	0.123700	−	0.992320i	$-0.460524\pi$
$449$	16.1942	−	4.75505i	0.764252	−	0.224405i	0.640552	+	0.767915i	$0.278706\pi$
$450$	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	−0.988011	−	0.154381i	$-0.950662\pi$
$457$	−14.8487	+	17.1363i	−0.694593	+	0.801603i	0.293418	+	0.955984i	$0.405207\pi$
$458$	−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	−0.0437617	−	0.999042i	$-0.513934\pi$
$463$	20.4704	−	23.6241i	0.951339	−	1.09790i	0.995101	−	0.0988623i	$-0.0315203\pi$
$464$	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	−0.982997	−	0.183623i	$-0.941217\pi$
$467$	−10.3306	−	22.6209i	−0.478044	−	1.04677i	0.504953	−	0.863147i	$-0.331510\pi$
$468$	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	0.0895870	−	0.995979i	$-0.471445\pi$
$479$	−17.0530	−	10.9593i	−0.779172	−	0.500743i	−0.868759	+	0.495236i	$0.835082\pi$
$480$	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	0.269360	−	0.963040i	$-0.413188\pi$
$487$	−10.9183	−	7.01678i	−0.494756	−	0.317960i	−0.764116	+	0.645079i	$0.776824\pi$
$488$	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	0.794502	−	0.607261i	$-0.207732\pi$
$491$	1.78049	+	2.05479i	0.0803523	+	0.0927315i	−0.714150	+	0.699993i	$0.753186\pi$
$492$	−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	0.999225	−	0.0393638i	$-0.0125331\pi$
$499$	7.03931	+	15.4139i	0.315123	+	0.690022i	−0.684102	+	0.729386i	$0.739806\pi$
$500$	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	−0.839532	−	0.543310i	$-0.817171\pi$
$503$	−4.08797	+	4.71777i	−0.182274	+	0.210355i	0.657258	+	0.753666i	$0.271716\pi$
$504$	−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	−0.240791	+	0.970577i	$0.577407\pi$
$509$	−26.3337	+	30.3907i	−1.16722	+	1.34704i	−0.926430	+	0.376468i	$0.877139\pi$
$510$	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	0.566039	−	0.824378i	$-0.308475\pi$
$521$	−7.54390	−	8.70612i	−0.330504	−	0.381422i	−0.896543	+	0.442956i	$0.853930\pi$
$522$	−0.134652	−	0.294847i	−0.00589355	−	0.0129051i
$523$	5.81239	−	3.73540i	0.254158	−	0.163337i	−0.407358	−	0.913269i	$-0.633550\pi$
$523$	5.81239	−	3.73540i	0.254158	−	0.163337i	0.661516	+	0.749931i	$0.269913\pi$
$524$	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	0.640813	−	0.767697i	$-0.278597\pi$
$541$	37.0975	−	10.8928i	1.59495	−	0.468319i	0.954135	+	0.299378i	$0.0967790\pi$
$542$	−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	−0.955469	−	0.295092i	$-0.904650\pi$
$547$	1.03922	−	7.22795i	0.0444340	−	0.309045i	0.999903	−	0.0139525i	$-0.00444136\pi$
$548$	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	0.729364	+	0.684126i	$0.239816\pi$
$557$	−3.85157	+	26.7883i	−0.163196	+	1.13505i	−0.892560	+	0.450929i	$0.851093\pi$
$558$	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	−0.998884	−	0.0472294i	$-0.984961\pi$
$563$	−43.0339	+	12.6359i	−1.81366	+	0.532540i	−0.814781	+	0.579769i	$0.803143\pi$
$564$	−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	−0.626241	−	0.779630i	$-0.715407\pi$
$569$	−4.22722	+	2.71667i	−0.177214	+	0.113889i	0.449026	+	0.893518i	$0.351771\pi$
$570$	0.0594536	−	0.413509i	0.00249024	−	0.0173200i
$571$	8.37221	+	5.38049i	0.350366	+	0.225167i	0.703972	−	0.710228i	$-0.251408\pi$
$571$	8.37221	+	5.38049i	0.350366	+	0.225167i	−0.353606	+	0.935395i	$0.615044\pi$
$572$	−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	−0.771079	−	0.636740i	$-0.780283\pi$
$577$	−42.3727	−	12.4418i	−1.76400	−	0.517957i	−0.992920	+	0.118783i	$0.962101\pi$
$578$	−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	0.0363749	−	0.999338i	$-0.488419\pi$
$587$	14.7127	−	4.32004i	0.607258	−	0.178307i	0.570884	+	0.821031i	$0.306601\pi$
$588$	−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	−0.937721	−	0.347388i	$-0.887069\pi$
$593$	1.45833	−	10.1429i	0.0598863	−	0.416518i	0.997608	−	0.0691300i	$-0.0220223\pi$
$594$	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	−0.645219	−	0.763997i	$-0.723234\pi$
$601$	4.97233	−	5.73838i	0.202826	−	0.234073i	0.848045	+	0.529924i	$0.177780\pi$
$602$	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	0.995903	−	0.0904319i	$-0.0288248\pi$
$607$	0.366196	+	2.54695i	0.0148634	+	0.103377i	−0.981039	+	0.193809i	$0.937916\pi$
$608$	−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	−0.999072	−	0.0430694i	$-0.986286\pi$
$613$	−22.2711	−	25.7022i	−0.899520	−	1.03810i	0.0995517	−	0.995032i	$-0.468259\pi$
$614$	−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	−0.258144	−	0.966106i	$-0.583111\pi$
$617$	−30.9049	−	19.8613i	−1.24418	−	0.799588i	−0.986038	+	0.166519i	$0.946747\pi$
$618$	−3.62281	+	4.18094i	−0.145731	+	0.168182i
$619$	6.71964	+	1.97306i	0.270085	+	0.0793042i	0.413971	−	0.910290i	$-0.364142\pi$
$619$	6.71964	+	1.97306i	0.270085	+	0.0793042i	−0.143886	+	0.989594i	$0.545960\pi$
$620$	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	−0.959253	−	0.282547i	$-0.908821\pi$
$631$	−2.95260	+	6.46530i	−0.117541	+	0.257380i	0.841712	+	0.539926i	$0.181548\pi$
$632$	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	−0.741910	−	0.670500i	$-0.766080\pi$
$641$	0.692460	−	0.799141i	0.0273505	−	0.0315642i	0.769260	+	0.638936i	$0.220625\pi$
$642$	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	−0.0395286	−	0.999218i	$-0.512586\pi$
$647$	24.2952	−	28.0382i	0.955145	−	1.10230i	0.994673	−	0.103077i	$-0.0328689\pi$
$648$	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	0.811966	+	0.583705i	$0.198397\pi$
$653$	5.04277	+	35.0733i	0.197339	+	1.37252i	−0.614627	+	0.788818i	$0.710693\pi$
$654$	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	0.513600	−	0.858030i	$-0.328312\pi$
$659$	−10.4940	−	12.1107i	−0.408789	−	0.471768i	−0.922389	+	0.386262i	$0.873766\pi$
$660$	0.970068	+	2.12415i	0.0377599	+	0.0826825i
$661$	−3.05667	+	1.96440i	−0.118891	+	0.0764063i	−0.598735	−	0.800947i	$-0.704330\pi$
$661$	−3.05667	+	1.96440i	−0.118891	+	0.0764063i	0.479844	+	0.877354i	$0.340693\pi$
$662$	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	0.186705	−	0.982416i	$-0.440219\pi$
$673$	30.0386	−	19.3046i	1.15790	−	0.744139i	0.971197	+	0.238277i	$0.0765827\pi$
$674$	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	−0.893623	−	0.448818i	$-0.851845\pi$
$677$	0.800595	−	1.75306i	0.0307694	−	0.0673755i	0.924393	+	0.381442i	$0.124572\pi$
$678$	−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	0.921281	−	0.388896i	$-0.127144\pi$
$683$	0.628845	+	1.37698i	0.0240621	+	0.0526886i	−0.897219	+	0.441585i	$0.854416\pi$
$684$	−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	0.198033	−	0.980195i	$-0.436545\pi$
$701$	23.6848	−	6.95448i	0.894562	−	0.262667i	0.696529	+	0.717528i	$0.254727\pi$
$702$	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	0.631157	−	0.775655i	$-0.282580\pi$
$709$	5.00027	+	3.21348i	0.187789	+	0.120685i	−0.443368	+	0.896340i	$0.646217\pi$
$710$	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	−0.0418441	−	0.999124i	$-0.513323\pi$
$719$	22.7816	−	14.6408i	0.849609	−	0.546010i	0.891453	+	0.453114i	$0.149687\pi$
$720$	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	0.987245	+	0.159209i	$0.0508945\pi$
$727$	2.28766	+	15.9111i	0.0848448	+	0.590108i	−0.902400	+	0.430899i	$0.858196\pi$
$728$	−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	−0.558865	−	0.829258i	$-0.688763\pi$
$733$	9.24541	−	10.6698i	0.341487	−	0.394097i	0.900353	+	0.435161i	$0.143309\pi$
$734$	−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	−0.411780	−	0.911283i	$-0.635093\pi$
$739$	14.9197	−	17.2183i	0.548830	−	0.633384i	0.960610	+	0.277899i	$0.0896382\pi$
$740$	−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	−0.978897	−	0.204352i	$-0.934491\pi$
$743$	−13.4190	−	29.3835i	−0.492295	−	1.07798i	0.486602	−	0.873624i	$-0.338236\pi$
$744$	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	0.859053	−	0.511887i	$-0.171053\pi$
$751$	6.30631	+	7.27787i	0.230121	+	0.265573i	−0.628932	+	0.777460i	$0.716508\pi$
$752$	−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	0.909949	−	0.414720i	$-0.136121\pi$
$757$	39.9287	+	11.7241i	1.45123	+	0.426120i	0.541283	+	0.840840i	$0.317939\pi$
$758$	−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	0.995849	−	0.0910257i	$-0.0290145\pi$
$761$	49.2248	+	14.4537i	1.78440	+	0.523946i	0.788549	+	0.614972i	$0.210833\pi$
$762$	−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	−0.276383	−	0.961048i	$-0.589136\pi$
$769$	17.4960	−	38.3108i	0.630921	−	1.38152i	0.907303	−	0.420476i	$-0.138137\pi$
$770$	−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	0.991196	+	0.132400i	$0.0422683\pi$
$773$	2.15338	+	14.9771i	0.0774517	+	0.538689i	−0.913745	+	0.406289i	$0.866823\pi$
$774$	−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	−0.999335	−	0.0364500i	$-0.988395\pi$
$787$	−0.847523	+	5.89465i	−0.0302109	+	0.210122i	0.969125	+	0.246572i	$0.0793041\pi$
$788$	−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	0.819614	+	0.572916i	$0.194188\pi$
$797$	35.8552	+	41.3791i	1.27006	+	1.46572i	0.450442	+	0.892806i	$0.351267\pi$
$798$	−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	0.470117	−	0.882604i	$-0.344212\pi$
$809$	−3.90903	−	2.51218i	−0.137434	−	0.0883235i	−0.607551	+	0.794281i	$0.707848\pi$
$810$	0.0111284	−	0.0773995i	0.000391011	−	0.00271954i
$811$	4.66619	−	2.99878i	0.163852	−	0.105301i	−0.456145	−	0.889906i	$-0.650770\pi$
$811$	4.66619	−	2.99878i	0.163852	−	0.105301i	0.619997	+	0.784604i	$0.287134\pi$
$812$	−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	0.994657	+	0.103234i	$0.0329189\pi$
$821$	12.0720	+	26.4339i	0.421314	+	0.922549i	−0.573343	+	0.819315i	$0.694354\pi$
$822$	0.979964	−	0.629784i	0.0341802	−	0.0219663i
$823$	2.44556	−	17.0092i	0.0852467	−	0.592904i	−0.901762	−	0.432234i	$-0.857725\pi$
$823$	2.44556	−	17.0092i	0.0852467	−	0.592904i	0.987008	−	0.160670i	$-0.0513654\pi$
$824$	−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	−0.786766	−	0.617251i	$-0.788246\pi$
$839$	−32.2944	+	9.48248i	−1.11492	+	0.327371i	−0.328159	+	0.944623i	$0.606428\pi$
$840$	−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	0.349533	−	0.936924i	$-0.386340\pi$
$853$	4.00242	+	1.17522i	0.137040	+	0.0402386i	−0.212493	+	0.977163i	$0.568158\pi$
$854$	−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	−0.413237	−	0.910624i	$-0.635602\pi$
$857$	7.12633	−	4.57981i	0.243431	−	0.156443i	0.656668	+	0.754180i	$0.271965\pi$
$858$	1.15729	+	2.53412i	0.0395094	+	0.0865134i
$859$	−9.61855	−	11.1004i	−0.328181	−	0.378741i	0.567549	−	0.823340i	$-0.307892\pi$
$859$	−9.61855	−	11.1004i	−0.328181	−	0.378741i	−0.895730	+	0.444599i	$0.853346\pi$
$860$	−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	−0.513861	−	0.857874i	$-0.671785\pi$
$863$	−14.1698	+	4.16063i	−0.482346	+	0.141630i	0.0315145	+	0.999503i	$0.489967\pi$
$864$	−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	−0.405653	+	0.914027i	$0.632956\pi$
$877$	−37.0961	+	42.8112i	−1.25265	+	1.44563i	−0.846993	+	0.531604i	$0.821589\pi$
$878$	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	−0.928202	−	0.372076i	$-0.878646\pi$
$881$	−17.8552	−	39.0973i	−0.601555	−	1.31722i	0.326647	−	0.945146i	$-0.394081\pi$
$882$	0.186393	+	0.215109i	0.00627617	+	0.00724309i
$883$	5.80018	+	40.3411i	0.195191	+	1.35759i	0.818003	+	0.575214i	$0.195081\pi$
$883$	5.80018	+	40.3411i	0.195191	+	1.35759i	−0.622811	+	0.782372i	$0.714010\pi$
$884$	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	0.0417409	+	0.999128i	$0.486710\pi$
$887$	−22.0595	+	48.3035i	−0.740684	+	1.62187i	−0.782425	+	0.622744i	$0.786018\pi$
$888$	−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	−0.472722	−	0.881212i	$-0.656729\pi$
$907$	15.1432	−	33.1589i	0.502820	−	1.10102i	0.975542	−	0.219811i	$-0.0705442\pi$
$908$	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	0.983447	+	0.181197i	$0.0579971\pi$
$911$	2.74318	+	19.0792i	0.0908855	+	0.632123i	−0.892561	+	0.450926i	$0.851094\pi$
$912$	−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	0.934880	+	0.354965i	$0.115507\pi$
$929$	4.20234	+	29.2279i	0.137874	+	0.958937i	−0.797005	+	0.603972i	$0.793584\pi$
$930$	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	−0.829404	−	0.558650i	$-0.811320\pi$
$937$	−20.3800	+	13.0974i	−0.665784	+	0.427874i	0.163619	+	0.986524i	$0.447683\pi$
$938$	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	0.693127	−	0.720816i	$-0.256233\pi$
$941$	27.1946	+	7.98506i	0.886520	+	0.260306i	0.193393	+	0.981121i	$0.438051\pi$
$942$	−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	0.965193	−	0.261537i	$-0.0842293\pi$
$947$	34.7200	+	22.3132i	1.12825	+	0.725080i	0.163054	+	0.986617i	$0.447866\pi$
$948$	−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	0.650179	+	0.759781i	$0.274694\pi$
$953$	−10.7986	+	23.6457i	−0.349802	+	0.765959i	−0.999981	+	0.00617816i	$0.998033\pi$
$954$	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	−0.0840328	−	0.996463i	$-0.526780\pi$
$971$	8.64191	−	60.1058i	0.277332	−	1.92889i	0.361365	−	0.932424i	$-0.382311\pi$
$972$	−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	−0.398158	−	0.917317i	$-0.630351\pi$
$977$	−7.41328	+	2.17673i	−0.237172	+	0.0696399i	0.160987	+	0.986957i	$0.448532\pi$
$978$	−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	−0.170129	−	0.985422i	$-0.554418\pi$
$983$	20.5539	−	13.2092i	0.655568	−	0.421308i	0.825697	+	0.564114i	$0.190782\pi$
$984$	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	0.998734	−	0.0502963i	$-0.0160166\pi$
$991$	57.0336	+	16.7466i	1.81173	+	0.531972i	0.812997	+	0.582268i	$0.197835\pi$
$992$	−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	0.583959	−	0.811783i	$-0.301503\pi$
$997$	−9.55680	−	11.0291i	−0.302667	−	0.349296i	−0.886626	+	0.462487i	$0.846957\pi$
$998$	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.64.1	✓	20
23.9	even	11	inner	483.2.q.c.400.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.64.1	✓	20	1.1	even	1	trivial
483.2.q.c.400.1	yes	20	23.9	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
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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