LMFDB - Embedded newform 430.2.q.c.281.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			281.3
Character	$\chi$	$=$	430.281
Dual form			430.2.q.c.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 - 0.781831i) q^{2} +(0.396839 + 1.01113i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.543108 - 0.940691i) q^{6} +(0.223308 + 0.386780i) q^{7} +(0.900969 - 0.433884i) q^{8} +(1.33425 - 1.23801i) q^{9} +O(q^{10})$	\(q+(-0.623490 - 0.781831i) q^{2} +(0.396839 + 1.01113i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.543108 - 0.940691i) q^{6} +(0.223308 + 0.386780i) q^{7} +(0.900969 - 0.433884i) q^{8} +(1.33425 - 1.23801i) q^{9} +(-0.826239 + 0.563320i) q^{10} +(1.28267 + 5.61977i) q^{11} +(-1.07408 + 0.161892i) q^{12} +(0.373719 + 0.254797i) q^{13} +(0.163167 - 0.415742i) q^{14} +(1.03796 - 0.320168i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-0.296178 - 3.95222i) q^{17} +(-1.79981 - 0.271277i) q^{18} +(-0.327885 - 0.304233i) q^{19} +(0.955573 + 0.294755i) q^{20} +(-0.302468 + 0.379282i) q^{21} +(3.59398 - 4.50670i) q^{22} +(7.04037 + 2.17167i) q^{23} +(0.796253 + 0.738815i) q^{24} +(-0.988831 - 0.149042i) q^{25} +(-0.0338014 - 0.451049i) q^{26} +(4.71721 + 2.27169i) q^{27} +(-0.426773 + 0.131642i) q^{28} +(-2.44716 + 6.23526i) q^{29} +(-0.897474 - 0.611887i) q^{30} +(7.48974 - 1.12890i) q^{31} +(0.222521 + 0.974928i) q^{32} +(-5.17330 + 3.52710i) q^{33} +(-2.90530 + 2.69573i) q^{34} +(0.402386 - 0.193779i) q^{35} +(0.910067 + 1.57628i) q^{36} +(2.40228 - 4.16087i) q^{37} +(-0.0334259 + 0.446037i) q^{38} +(-0.109327 + 0.478992i) q^{39} +(-0.365341 - 0.930874i) q^{40} +(6.05421 + 7.59174i) q^{41} +0.485120 q^{42} +(-5.94596 + 2.76505i) q^{43} -5.76429 q^{44} +(-1.13484 - 1.42304i) q^{45} +(-2.69172 - 6.85839i) q^{46} +(0.856452 - 3.75236i) q^{47} +(0.0811730 - 1.08318i) q^{48} +(3.40027 - 5.88944i) q^{49} +(0.500000 + 0.866025i) q^{50} +(3.87867 - 1.86787i) q^{51} +(-0.331569 + 0.307651i) q^{52} +(0.0159456 - 0.0108715i) q^{53} +(-1.16505 - 5.10444i) q^{54} +(5.69991 - 0.859123i) q^{55} +(0.369011 + 0.251587i) q^{56} +(0.177501 - 0.452266i) q^{57} +(6.40070 - 1.97436i) q^{58} +(-7.61246 - 3.66597i) q^{59} +(0.0811730 + 1.08318i) q^{60} +(-3.03953 - 0.458135i) q^{61} +(-5.55238 - 5.15186i) q^{62} +(0.776785 + 0.239606i) q^{63} +(0.623490 - 0.781831i) q^{64} +(0.282013 - 0.353633i) q^{65} +(5.98309 + 1.84554i) q^{66} +(-9.95393 - 9.23589i) q^{67} +(3.91903 + 0.590699i) q^{68} +(0.598058 + 7.98053i) q^{69} +(-0.402386 - 0.193779i) q^{70} +(-9.82210 + 3.02972i) q^{71} +(0.664970 - 1.69432i) q^{72} +(-8.00951 - 5.46079i) q^{73} +(-4.75089 + 0.716082i) q^{74} +(-0.241706 - 1.05898i) q^{75} +(0.369567 - 0.251966i) q^{76} +(-1.88718 + 1.75105i) q^{77} +(0.442655 - 0.213172i) q^{78} +(5.58172 + 9.66782i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.0169417 + 0.226072i) q^{81} +(2.16072 - 9.46675i) q^{82} +(-0.964527 - 2.45757i) q^{83} +(-0.302468 - 0.379282i) q^{84} -3.96330 q^{85} +(5.86905 + 2.92476i) q^{86} -7.27579 q^{87} +(3.59398 + 4.50670i) q^{88} +(3.60004 + 9.17275i) q^{89} +(-0.405018 + 1.77450i) q^{90} +(-0.0150962 + 0.201445i) q^{91} +(-3.68385 + 6.38061i) q^{92} +(4.11368 + 7.12511i) q^{93} +(-3.46770 + 1.66996i) q^{94} +(-0.327885 + 0.304233i) q^{95} +(-0.897474 + 0.611887i) q^{96} +(-4.02232 - 17.6229i) q^{97} +(-6.72458 + 1.01357i) q^{98} +(8.66872 + 5.91023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{8}{21}\right)$

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 $

$2$	−0.623490	−	0.781831i	−0.440874	−	0.552838i
$2$	−0.623490	−	0.781831i	−0.440874	−	0.552838i
$3$	0.396839	+	1.01113i	0.229115	+	0.583776i	0.998485	−	0.0550278i	$-0.0175247\pi$
$3$	0.396839	+	1.01113i	0.229115	+	0.583776i	−0.769370	+	0.638804i	$0.779429\pi$
$4$	−0.222521	+	0.974928i	−0.111260	+	0.487464i
$5$	0.0747301	−	0.997204i	0.0334203	−	0.445963i
$5$	0.0747301	−	0.997204i	0.0334203	−	0.445963i
$6$	0.543108	−	0.940691i	0.221723	−	0.384035i
$7$	0.223308	+	0.386780i	0.0844023	+	0.146189i	0.905136	−	0.425121i	$-0.139769\pi$
$7$	0.223308	+	0.386780i	0.0844023	+	0.146189i	−0.820734	+	0.571310i	$0.806435\pi$
$8$	0.900969	−	0.433884i	0.318541	−	0.153401i
$9$	1.33425	−	1.23801i	0.444751	−	0.412669i
$10$	−0.826239	+	0.563320i	−0.261280	+	0.178137i
$11$	1.28267	+	5.61977i	0.386741	+	1.69442i	0.675778	+	0.737105i	$0.263808\pi$
$11$	1.28267	+	5.61977i	0.386741	+	1.69442i	−0.289037	+	0.957318i	$0.593335\pi$
$12$	−1.07408	+	0.161892i	−0.310061	+	0.0467342i
$13$	0.373719	+	0.254797i	0.103651	+	0.0706681i	0.614036	−	0.789278i	$-0.289545\pi$
$13$	0.373719	+	0.254797i	0.103651	+	0.0706681i	−0.510385	+	0.859946i	$0.670497\pi$
$14$	0.163167	−	0.415742i	0.0436082	−	0.111112i
$15$	1.03796	−	0.320168i	0.268000	−	0.0826670i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	−0.296178	−	3.95222i	−0.0718337	−	0.958554i	−0.910393	−	0.413744i	$-0.864221\pi$
$17$	−0.296178	−	3.95222i	−0.0718337	−	0.958554i	0.838560	−	0.544810i	$-0.183398\pi$
$18$	−1.79981	−	0.271277i	−0.424218	−	0.0639406i
$19$	−0.327885	−	0.304233i	−0.0752220	−	0.0697958i	0.641666	−	0.766984i	$-0.278244\pi$
$19$	−0.327885	−	0.304233i	−0.0752220	−	0.0697958i	−0.716888	+	0.697188i	$0.754434\pi$
$20$	0.955573	+	0.294755i	0.213673	+	0.0659093i
$21$	−0.302468	+	0.379282i	−0.0660039	+	0.0827662i
$22$	3.59398	−	4.50670i	0.766238	−	0.960832i
$23$	7.04037	+	2.17167i	1.46802	+	0.452824i	0.922737	−	0.385430i	$-0.125947\pi$
$23$	7.04037	+	2.17167i	1.46802	+	0.452824i	0.545281	+	0.838253i	$0.316423\pi$
$24$	0.796253	+	0.738815i	0.162534	+	0.150810i
$25$	−0.988831	−	0.149042i	−0.197766	−	0.0298085i
$26$	−0.0338014	−	0.451049i	−0.00662901	−	0.0884580i
$27$	4.71721	+	2.27169i	0.907827	+	0.437187i
$28$	−0.426773	+	0.131642i	−0.0806526	+	0.0248780i
$29$	−2.44716	+	6.23526i	−0.454426	+	1.15786i	0.501736	+	0.865021i	$0.332695\pi$
$29$	−2.44716	+	6.23526i	−0.454426	+	1.15786i	−0.956162	+	0.292838i	$0.905400\pi$
$30$	−0.897474	−	0.611887i	−0.163856	−	0.111715i
$31$	7.48974	−	1.12890i	1.34520	−	0.202756i	0.563345	−	0.826221i	$-0.309514\pi$
$31$	7.48974	−	1.12890i	1.34520	−	0.202756i	0.781851	+	0.623466i	$0.214276\pi$
$32$	0.222521	+	0.974928i	0.0393365	+	0.172345i
$33$	−5.17330	+	3.52710i	−0.900556	+	0.613988i
$34$	−2.90530	+	2.69573i	−0.498256	+	0.462314i
$35$	0.402386	−	0.193779i	0.0680157	−	0.0327546i
$36$	0.910067	+	1.57628i	0.151678	+	0.262714i
$37$	2.40228	−	4.16087i	0.394932	−	0.684043i	−0.598160	−	0.801376i	$-0.704101\pi$
$37$	2.40228	−	4.16087i	0.394932	−	0.684043i	0.993093	+	0.117334i	$0.0374348\pi$
$38$	−0.0334259	+	0.446037i	−0.00542239	+	0.0723568i
$39$	−0.109327	+	0.478992i	−0.0175063	+	0.0767001i
$40$	−0.365341	−	0.930874i	−0.0577655	−	0.147184i
$41$	6.05421	+	7.59174i	0.945509	+	1.18563i	0.982490	+	0.186315i	$0.0596544\pi$
$41$	6.05421	+	7.59174i	0.945509	+	1.18563i	−0.0369812	+	0.999316i	$0.511774\pi$
$42$	0.485120			0.0748557
$43$	−5.94596	+	2.76505i	−0.906751	+	0.421667i
$43$	−5.94596	+	2.76505i	−0.906751	+	0.421667i
$44$	−5.76429			−0.868999
$45$	−1.13484	−	1.42304i	−0.169171	−	0.212134i
$46$	−2.69172	−	6.85839i	−0.396872	−	1.01121i
$47$	0.856452	−	3.75236i	0.124926	−	0.547338i	−0.873266	−	0.487243i	$-0.838003\pi$
$47$	0.856452	−	3.75236i	0.124926	−	0.547338i	0.998193	−	0.0600949i	$-0.0191403\pi$
$48$	0.0811730	−	1.08318i	0.0117163	−	0.156343i
$49$	3.40027	−	5.88944i	0.485753	−	0.841348i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	3.87867	−	1.86787i	0.543123	−	0.261554i
$52$	−0.331569	+	0.307651i	−0.0459804	+	0.0426636i
$53$	0.0159456	−	0.0108715i	0.00219030	−	0.00149332i	−0.562224	−	0.826985i	$-0.690054\pi$
$53$	0.0159456	−	0.0108715i	0.00219030	−	0.00149332i	0.564415	+	0.825491i	$0.309102\pi$
$54$	−1.16505	−	5.10444i	−0.158544	−	0.694626i
$55$	5.69991	−	0.859123i	0.768575	−	0.115844i
$56$	0.369011	+	0.251587i	0.0493111	+	0.0336198i
$57$	0.177501	−	0.452266i	0.0235106	−	0.0599041i
$58$	6.40070	−	1.97436i	0.840454	−	0.259246i
$59$	−7.61246	−	3.66597i	−0.991058	−	0.477269i	−0.133164	−	0.991094i	$-0.542514\pi$
$59$	−7.61246	−	3.66597i	−0.991058	−	0.477269i	−0.857895	+	0.513825i	$0.828228\pi$
$60$	0.0811730	+	1.08318i	0.0104794	+	0.139838i
$61$	−3.03953	−	0.458135i	−0.389172	−	0.0586582i	−0.0484578	−	0.998825i	$-0.515431\pi$
$61$	−3.03953	−	0.458135i	−0.389172	−	0.0586582i	−0.340714	+	0.940167i	$0.610669\pi$
$62$	−5.55238	−	5.15186i	−0.705153	−	0.654286i
$63$	0.776785	+	0.239606i	0.0978657	+	0.0301876i
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	0.282013	−	0.353633i	0.0349794	−	0.0438628i
$66$	5.98309	+	1.84554i	0.736468	+	0.227170i
$67$	−9.95393	−	9.23589i	−1.21607	−	1.12834i	−0.987960	−	0.154708i	$-0.950556\pi$
$67$	−9.95393	−	9.23589i	−1.21607	−	1.12834i	−0.228105	−	0.973636i	$-0.573253\pi$
$68$	3.91903	+	0.590699i	0.475253	+	0.0716328i
$69$	0.598058	+	7.98053i	0.0719977	+	0.960743i
$70$	−0.402386	−	0.193779i	−0.0480944	−	0.0231610i
$71$	−9.82210	+	3.02972i	−1.16567	+	0.359561i	−0.816414	−	0.577466i	$-0.804041\pi$
$71$	−9.82210	+	3.02972i	−1.16567	+	0.359561i	−0.349255	+	0.937028i	$0.613565\pi$
$72$	0.664970	−	1.69432i	0.0783674	−	0.199677i
$73$	−8.00951	−	5.46079i	−0.937442	−	0.639137i	−0.00481879	−	0.999988i	$-0.501534\pi$
$73$	−8.00951	−	5.46079i	−0.937442	−	0.639137i	−0.932623	+	0.360851i	$0.882486\pi$
$74$	−4.75089	+	0.716082i	−0.552280	+	0.0832429i
$75$	−0.241706	−	1.05898i	−0.0279098	−	0.122281i
$76$	0.369567	−	0.251966i	0.0423922	−	0.0289025i
$77$	−1.88718	+	1.75105i	−0.215064	+	0.199551i
$78$	0.442655	−	0.213172i	0.0501208	−	0.0241369i
$79$	5.58172	+	9.66782i	0.627993	+	1.08772i	0.987954	+	0.154748i	$0.0494565\pi$
$79$	5.58172	+	9.66782i	0.627993	+	1.08772i	−0.359961	+	0.932967i	$0.617210\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.0169417	+	0.226072i	−0.00188242	+	0.0251191i
$82$	2.16072	−	9.46675i	0.238612	−	1.04543i
$83$	−0.964527	−	2.45757i	−0.105871	−	0.269754i	0.868115	−	0.496363i	$-0.165331\pi$
$83$	−0.964527	−	2.45757i	−0.105871	−	0.269754i	−0.973986	+	0.226609i	$0.927236\pi$
$84$	−0.302468	−	0.379282i	−0.0330019	−	0.0413831i
$85$	−3.96330			−0.429880
$86$	5.86905	+	2.92476i	0.632876	+	0.315385i
$87$	−7.27579			−0.780047
$88$	3.59398	+	4.50670i	0.383119	+	0.480416i
$89$	3.60004	+	9.17275i	0.381603	+	0.972310i	0.984640	+	0.174596i	$0.0558620\pi$
$89$	3.60004	+	9.17275i	0.381603	+	0.972310i	−0.603037	+	0.797713i	$0.706043\pi$
$90$	−0.405018	+	1.77450i	−0.0426927	+	0.187049i
$91$	−0.0150962	+	0.201445i	−0.00158252	+	0.0211172i
$92$	−3.68385	+	6.38061i	−0.384067	+	0.665224i
$93$	4.11368	+	7.12511i	0.426569	+	0.738839i
$94$	−3.46770	+	1.66996i	−0.357666	+	0.172243i
$95$	−0.327885	+	0.304233i	−0.0336403	+	0.0312136i
$96$	−0.897474	+	0.611887i	−0.0915980	+	0.0624505i
$97$	−4.02232	−	17.6229i	−0.408404	−	1.78934i	−0.591570	−	0.806254i	$-0.701491\pi$
$97$	−4.02232	−	17.6229i	−0.408404	−	1.78934i	0.183165	−	0.983082i	$-0.441366\pi$
$98$	−6.72458	+	1.01357i	−0.679285	+	0.102386i
$99$	8.66872	+	5.91023i	0.871239	+	0.594001i
$100$	0.365341	−	0.930874i	0.0365341	−	0.0930874i
$101$	−17.7937	+	5.48862i	−1.77054	+	0.546139i	−0.996236	−	0.0866786i	$-0.972375\pi$
$101$	−17.7937	+	5.48862i	−1.77054	+	0.546139i	−0.774301	+	0.632817i	$0.781898\pi$
$102$	−3.87867	−	1.86787i	−0.384046	−	0.184947i
$103$	−0.604963	−	8.07268i	−0.0596088	−	0.795424i	−0.944266	−	0.329183i	$-0.893227\pi$
$103$	−0.604963	−	8.07268i	−0.0596088	−	0.795424i	0.884657	−	0.466242i	$-0.154392\pi$
$104$	0.447262	+	0.0674138i	0.0438576	+	0.00661047i
$105$	0.355618	+	0.329966i	0.0347048	+	0.0322014i
$106$	−0.0184417	−	0.00568850i	−0.00179121	−	0.000552516i
$107$	1.43090	−	1.79429i	0.138330	−	0.173460i	−0.707841	−	0.706372i	$-0.750331\pi$
$107$	1.43090	−	1.79429i	0.138330	−	0.173460i	0.846171	+	0.532912i	$0.178902\pi$
$108$	−3.26441	+	4.09344i	−0.314118	+	0.393892i
$109$	−4.01217	−	1.23759i	−0.384296	−	0.118540i	0.0965866	−	0.995325i	$-0.469208\pi$
$109$	−4.01217	−	1.23759i	−0.384296	−	0.118540i	−0.480883	+	0.876785i	$0.659684\pi$
$110$	−4.22552	−	3.92071i	−0.402888	−	0.373825i
$111$	5.16050	+	0.777820i	0.489813	+	0.0738274i
$112$	−0.0333756	−	0.445366i	−0.00315370	−	0.0420832i
$113$	−0.283930	−	0.136734i	−0.0267099	−	0.0128628i	0.420481	−	0.907301i	$-0.361861\pi$
$113$	−0.283930	−	0.136734i	−0.0267099	−	0.0128628i	−0.447191	+	0.894438i	$0.647576\pi$
$114$	−0.464266	+	0.143207i	−0.0434825	+	0.0134126i
$115$	2.69172	−	6.85839i	0.251004	−	0.639548i
$116$	−5.53439	−	3.77328i	−0.513855	−	0.350340i
$117$	0.814076	−	0.122702i	0.0752614	−	0.0113438i
$118$	1.88012	+	8.23736i	0.173079	+	0.758310i
$119$	1.46250	−	0.997116i	0.134067	−	0.0914054i
$120$	0.796253	−	0.738815i	0.0726876	−	0.0674442i
$121$	−20.0259	+	9.64394i	−1.82053	+	0.876722i
$122$	1.53693	+	2.66204i	0.139147	+	0.241010i
$123$	−5.27369	+	9.13430i	−0.475512	+	0.823612i
$124$	−0.566031	+	7.55315i	−0.0508311	+	0.678293i
$125$	−0.222521	+	0.974928i	−0.0199029	+	0.0872002i
$126$	−0.296986	−	0.756707i	−0.0264576	−	0.0674128i
$127$	7.19610	+	9.02362i	0.638550	+	0.800717i	0.990821	−	0.135182i	$-0.0431618\pi$
$127$	7.19610	+	9.02362i	0.638550	+	0.800717i	−0.352271	+	0.935898i	$0.614590\pi$
$128$	−1.00000			−0.0883883
$129$	−5.15542	−	4.91486i	−0.453909	−	0.432729i
$130$	−0.452314			−0.0396705
$131$	−3.98335	−	4.99497i	−0.348027	−	0.436412i	0.576750	−	0.816920i	$-0.304321\pi$
$131$	−3.98335	−	4.99497i	−0.348027	−	0.436412i	−0.924778	+	0.380508i	$0.875749\pi$
$132$	−2.28750	−	5.82845i	−0.199101	−	0.507301i
$133$	0.0444520	−	0.194757i	0.00385448	−	0.0168876i
$134$	−1.01474	+	13.5408i	−0.0876603	+	1.16975i
$135$	2.61785	−	4.53426i	0.225309	−	0.390247i
$136$	−1.98165	−	3.43232i	−0.169925	−	0.294319i
$137$	−14.9424	+	7.19590i	−1.27662	+	0.614787i	−0.944519	−	0.328457i	$-0.893471\pi$
$137$	−14.9424	+	7.19590i	−1.27662	+	0.614787i	−0.332100	+	0.943244i	$0.607757\pi$
$138$	5.86654	−	5.44336i	0.499393	−	0.463369i
$139$	3.92808	−	2.67812i	0.333175	−	0.227155i	−0.385164	−	0.922848i	$-0.625855\pi$
$139$	3.92808	−	2.67812i	0.333175	−	0.227155i	0.718339	+	0.695693i	$0.244903\pi$
$140$	0.0993812	+	0.435417i	0.00839924	+	0.0367995i
$141$	4.13400	−	0.623100i	0.348145	−	0.0524745i
$142$	8.49271	+	5.79023i	0.712692	+	0.485905i
$143$	−0.952541	+	2.42704i	−0.0796555	+	0.202959i
$144$	−1.73927	+	0.536494i	−0.144939	+	0.0447078i
$145$	6.03495	+	2.90628i	0.501175	+	0.241353i
$146$	0.724429	+	9.66683i	0.0599542	+	0.800033i
$147$	7.30435	+	1.10095i	0.602452	+	0.0908051i
$148$	3.52199	+	3.26793i	0.289506	+	0.268622i
$149$	12.3609	+	3.81284i	1.01265	+	0.312360i	0.756300	−	0.654225i	$-0.227005\pi$
$149$	12.3609	+	3.81284i	1.01265	+	0.312360i	0.256346	+	0.966585i	$0.417481\pi$
$150$	−0.677245	+	0.849238i	−0.0552968	+	0.0693400i
$151$	8.05253	−	10.0976i	0.655306	−	0.821728i	−0.337517	−	0.941319i	$-0.609587\pi$
$151$	8.05253	−	10.0976i	0.655306	−	0.821728i	0.992823	+	0.119592i	$0.0381586\pi$
$152$	−0.427416	−	0.131840i	−0.0346680	−	0.0106937i
$153$	−5.28805	−	4.90659i	−0.427513	−	0.396674i
$154$	2.54566	+	0.383697i	0.205135	+	0.0309192i
$155$	−0.566031	−	7.55315i	−0.0454647	−	0.606684i
$156$	−0.442655	−	0.213172i	−0.0354408	−	0.0170674i
$157$	−2.82223	+	0.870542i	−0.225238	+	0.0694768i	−0.405320	−	0.914175i	$-0.632840\pi$
$157$	−2.82223	+	0.870542i	−0.225238	+	0.0694768i	0.180082	+	0.983652i	$0.442364\pi$
$158$	4.07846	−	10.3918i	0.324465	−	0.826724i
$159$	0.0173204	+	0.0118088i	0.00137360	+	0.000936502i
$160$	0.988831	−	0.149042i	0.0781739	−	0.0117828i
$161$	0.732210	+	3.20802i	0.0577062	+	0.252828i
$162$	0.187313	−	0.127708i	0.0147167	−	0.0100337i
$163$	−13.5201	+	12.5448i	−1.05897	+	0.982585i	−0.999877	−	0.0156672i	$-0.995013\pi$
$163$	−13.5201	+	12.5448i	−1.05897	+	0.982585i	−0.0590976	+	0.998252i	$0.518822\pi$
$164$	−8.74859	+	4.21310i	−0.683150	+	0.328988i
$165$	3.13063	+	5.42241i	0.243719	+	0.422134i
$166$	−1.32004	+	2.28637i	−0.102455	+	0.177457i
$167$	0.461067	−	6.15251i	0.0356784	−	0.476095i	−0.950535	−	0.310617i	$-0.899464\pi$
$167$	0.461067	−	6.15251i	0.0356784	−	0.476095i	0.986213	−	0.165478i	$-0.0529167\pi$
$168$	−0.107949	+	0.472957i	−0.00832848	+	0.0364895i
$169$	−4.67469	−	11.9109i	−0.359591	−	0.916224i
$170$	2.47108	+	3.09863i	0.189523	+	0.237654i
$171$	−0.814124			−0.0622576
$172$	−1.37263	−	6.41217i	−0.104662	−	0.488923i
$173$	5.56916			0.423416			0.211708	−	0.977333i	$-0.432097\pi$
$173$	5.56916			0.423416			0.211708	+	0.977333i	$0.432097\pi$
$174$	4.53638	+	5.68844i	0.343902	+	0.431240i
$175$	−0.163167	−	0.415742i	−0.0123343	−	0.0314272i
$176$	1.28267	−	5.61977i	0.0966853	−	0.423606i
$177$	0.685847	−	9.15199i	0.0515514	−	0.687906i
$178$	4.92696	−	8.53374i	0.369291	−	0.639631i
$179$	−7.96417	−	13.7944i	−0.595270	−	1.03104i	−0.993509	−	0.113756i	$-0.963712\pi$
$179$	−7.96417	−	13.7944i	−0.595270	−	1.03104i	0.398238	−	0.917282i	$-0.369622\pi$
$180$	1.63988	−	0.789727i	0.122230	−	0.0588628i
$181$	7.78768	−	7.22591i	0.578854	−	0.537098i	−0.335486	−	0.942045i	$-0.608901\pi$
$181$	7.78768	−	7.22591i	0.578854	−	0.537098i	0.914340	+	0.404947i	$0.132710\pi$
$182$	0.166909	−	0.113796i	0.0123721	−	0.00843514i
$183$	−0.742970	−	3.25516i	−0.0549219	−	0.240629i
$184$	7.28540	−	1.09810i	0.537087	−	0.0809528i
$185$	−3.96971	−	2.70650i	−0.291859	−	0.198986i
$186$	3.00579	−	7.65864i	0.220395	−	0.561558i
$187$	21.8306	−	6.73386i	1.59641	−	0.492429i
$188$	3.46770	+	1.66996i	0.252908	+	0.121794i
$189$	0.174745	+	2.33181i	0.0127108	+	0.169614i
$190$	0.442292	+	0.0666648i	0.0320872	+	0.00483637i
$191$	−12.7258	−	11.8078i	−0.920803	−	0.854380i	0.0688842	−	0.997625i	$-0.478056\pi$
$191$	−12.7258	−	11.8078i	−0.920803	−	0.854380i	−0.989687	+	0.143244i	$0.954247\pi$
$192$	1.03796	+	0.320168i	0.0749082	+	0.0231061i
$193$	−0.456601	+	0.572560i	−0.0328669	+	0.0412138i	−0.797993	−	0.602666i	$-0.794105\pi$
$193$	−0.456601	+	0.572560i	−0.0328669	+	0.0412138i	0.765126	+	0.643880i	$0.222676\pi$
$194$	−11.2703	+	14.1325i	−0.809159	+	1.01465i
$195$	0.469483	+	0.144816i	0.0336204	+	0.0103705i
$196$	4.98514	+	4.62554i	0.356082	+	0.330396i
$197$	15.6208	+	2.35446i	1.11294	+	0.167748i	0.679670	−	0.733518i	$-0.262123\pi$
$197$	15.6208	+	2.35446i	1.11294	+	0.167748i	0.433266	+	0.901266i	$0.357361\pi$
$198$	−0.784052	−	10.4624i	−0.0557201	−	0.743534i
$199$	22.1952	+	10.6886i	1.57337	+	0.757697i	0.998179	−	0.0603202i	$-0.0192122\pi$
$199$	22.1952	+	10.6886i	1.57337	+	0.757697i	0.575194	+	0.818017i	$0.304926\pi$
$200$	−0.955573	+	0.294755i	−0.0675692	+	0.0208423i
$201$	5.38858	−	13.7299i	0.380081	−	0.968431i
$202$	15.3854	+	10.4896i	1.08251	+	0.738043i
$203$	−2.95814	+	0.445868i	−0.207621	+	0.0312938i
$204$	0.957953	+	4.19707i	0.0670701	+	0.293853i
$205$	8.02294	−	5.46995i	0.560347	−	0.382038i
$206$	−5.93428	+	5.50621i	−0.413461	+	0.383636i
$207$	12.0822	−	5.81846i	0.839769	−	0.404411i
$208$	−0.226157	−	0.391715i	−0.0156812	−	0.0271606i
$209$	1.28915	−	2.23287i	0.0891722	−	0.154451i
$210$	0.0362531	−	0.483764i	0.00250170	−	0.0333829i
$211$	0.828872	−	3.63153i	0.0570619	−	0.250005i	−0.938350	−	0.345687i	$-0.887646\pi$
$211$	0.828872	−	3.63153i	0.0570619	−	0.250005i	0.995412	+	0.0956820i	$0.0305032\pi$
$212$	0.00705074	+	0.0179650i	0.000484247	+	0.00123384i
$213$	−6.96123	−	8.72911i	−0.476976	−	0.598109i
$214$	−2.29498			−0.156882
$215$	2.31298	+	6.13597i	0.157744	+	0.418470i
$216$	5.23571			0.356245
$217$	2.10915	+	2.64479i	0.143178	+	0.179540i
$218$	1.53396	+	3.90847i	0.103893	+	0.264715i
$219$	2.34308	−	10.2657i	0.158331	−	0.693693i
$220$	−0.430766	+	5.74817i	−0.0290422	+	0.387542i
$221$	0.896327	−	1.55248i	0.0602935	−	0.104431i
$222$	−2.60939	−	4.51960i	−0.175131	−	0.303336i
$223$	0.981983	−	0.472898i	0.0657584	−	0.0316676i	−0.400716	−	0.916203i	$-0.631238\pi$
$223$	0.981983	−	0.472898i	0.0657584	−	0.0316676i	0.466474	+	0.884535i	$0.345524\pi$
$224$	−0.327392	+	0.303775i	−0.0218748	+	0.0202968i
$225$	−1.50387	+	1.02532i	−0.100258	+	0.0683546i
$226$	0.0701250	+	0.307238i	0.00466464	+	0.0204371i
$227$	10.6743	−	1.60889i	0.708476	−	0.106786i	0.215087	−	0.976595i	$-0.430996\pi$
$227$	10.6743	−	1.60889i	0.708476	−	0.106786i	0.493388	+	0.869809i	$0.335758\pi$
$228$	0.401429	+	0.273690i	0.0265853	+	0.0181255i
$229$	−1.45080	+	3.69657i	−0.0958712	+	0.244276i	−0.970762	−	0.240045i	$-0.922838\pi$
$229$	−1.45080	+	3.69657i	−0.0958712	+	0.244276i	0.874891	+	0.484321i	$0.160933\pi$
$230$	−7.04037	+	2.17167i	−0.464228	+	0.143195i
$231$	−2.51945	−	1.21330i	−0.165767	−	0.0798294i
$232$	0.500564	+	6.67956i	0.0328636	+	0.438535i
$233$	−8.18456	−	1.23362i	−0.536188	−	0.0808174i	−0.124634	−	0.992203i	$-0.539776\pi$
$233$	−8.18456	−	1.23362i	−0.536188	−	0.0808174i	−0.411554	+	0.911385i	$0.635014\pi$
$234$	−0.603501	−	0.559967i	−0.0394521	−	0.0366062i
$235$	−3.67787	−	1.13447i	−0.239917	−	0.0740047i
$236$	5.26799	−	6.60585i	0.342917	−	0.430004i
$237$	−7.56038	+	9.48042i	−0.491100	+	0.615819i
$238$	−1.69143	−	0.521737i	−0.109639	−	0.0338192i
$239$	12.5554	+	11.6498i	0.812144	+	0.753560i	0.972351	−	0.233524i	$-0.0750256\pi$
$239$	12.5554	+	11.6498i	0.812144	+	0.753560i	−0.160207	+	0.987083i	$0.551216\pi$
$240$	−1.07408	−	0.161892i	−0.0693318	−	0.0104501i
$241$	0.868923	+	11.5950i	0.0559723	+	0.746898i	0.952622	+	0.304157i	$0.0983748\pi$
$241$	0.868923	+	11.5950i	0.0559723	+	0.746898i	−0.896650	+	0.442741i	$0.854006\pi$
$242$	20.0259	+	9.64394i	1.28731	+	0.619936i
$243$	14.7740	−	4.55717i	0.947752	−	0.292343i
$244$	1.12301	−	2.86138i	0.0718932	−	0.183181i
$245$	−5.61887	−	3.83088i	−0.358976	−	0.244746i
$246$	10.4296	−	1.57200i	0.664965	−	0.100227i
$247$	−0.0450192	−	0.197242i	−0.00286450	−	0.0125502i
$248$	6.25821	−	4.26677i	0.397397	−	0.270940i
$249$	2.10217	−	1.95052i	0.133219	−	0.123609i
$250$	0.900969	−	0.433884i	0.0569823	−	0.0274412i
$251$	3.95467	+	6.84969i	0.249617	+	0.432349i	0.963419	−	0.267998i	$-0.0863621\pi$
$251$	3.95467	+	6.84969i	0.249617	+	0.432349i	−0.713803	+	0.700347i	$0.753029\pi$
$252$	−0.406450	+	0.703992i	−0.0256039	+	0.0443473i
$253$	−3.17375	+	42.3508i	−0.199532	+	2.66257i
$254$	2.56826	−	11.2523i	0.161147	−	0.706030i
$255$	−1.57279	−	4.00741i	−0.0984921	−	0.250954i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	−8.72126			−0.544017			−0.272009	−	0.962295i	$-0.587688\pi$
$257$	−8.72126			−0.544017			−0.272009	+	0.962295i	$0.587688\pi$
$258$	−0.628241	+	7.09504i	−0.0391126	+	0.441718i
$259$	2.14579			0.133333
$260$	0.282013	+	0.353633i	0.0174897	+	0.0219314i
$261$	4.45416	+	11.3490i	0.275706	+	0.702487i
$262$	−1.42164	+	6.22862i	−0.0878294	+	0.384806i
$263$	−0.201849	+	2.69349i	−0.0124466	+	0.166088i	0.987517	+	0.157514i	$0.0503481\pi$
$263$	−0.201849	+	2.69349i	−0.0124466	+	0.166088i	−0.999963	+	0.00857335i	$0.997271\pi$
$264$	−3.13063	+	5.42241i	−0.192677	+	0.333726i
$265$	−0.00964953	−	0.0167135i	−0.000592766	−	0.00102670i
$266$	−0.179982	+	0.0866750i	−0.0110354	+	0.00531438i
$267$	−7.84621	+	7.28022i	−0.480180	+	0.445542i
$268$	11.2193	−	7.64918i	0.685327	−	0.467248i
$269$	−1.92701	−	8.44280i	−0.117492	−	0.514767i	−0.999086	−	0.0427570i	$-0.986386\pi$
$269$	−1.92701	−	8.44280i	−0.117492	−	0.514767i	0.881593	−	0.472010i	$-0.156471\pi$
$270$	−5.17723	+	0.780342i	−0.315076	+	0.0474901i
$271$	−20.5276	−	13.9955i	−1.24697	−	0.850167i	−0.253843	−	0.967245i	$-0.581695\pi$
$271$	−20.5276	−	13.9955i	−1.24697	−	0.850167i	−0.993123	+	0.117079i	$0.962647\pi$
$272$	−1.44796	+	3.68933i	−0.0877952	+	0.223699i
$273$	−0.209678	+	0.0646771i	−0.0126903	+	0.00391444i
$274$	14.9424	+	7.19590i	0.902706	+	0.434720i
$275$	−0.430766	−	5.74817i	−0.0259762	−	0.346628i
$276$	−7.91352	−	1.19277i	−0.476338	−	0.0717964i
$277$	−21.1566	−	19.6304i	−1.27118	−	1.17948i	−0.974472	−	0.224508i	$-0.927922\pi$
$277$	−21.1566	−	19.6304i	−1.27118	−	1.17948i	−0.296703	−	0.954970i	$-0.595887\pi$
$278$	−4.54295	−	1.40132i	−0.272468	−	0.0840453i
$279$	8.59562	−	10.7786i	0.514606	−	0.645296i
$280$	0.278460	−	0.349178i	0.0166412	−	0.0208674i
$281$	4.35079	+	1.34204i	0.259547	+	0.0800595i	0.421798	−	0.906690i	$-0.361399\pi$
$281$	4.35079	+	1.34204i	0.259547	+	0.0800595i	−0.162251	+	0.986750i	$0.551875\pi$
$282$	−3.06466	−	2.84359i	−0.182498	−	0.169334i
$283$	18.2460	+	2.75015i	1.08461	+	0.163479i	0.666935	−	0.745116i	$-0.267606\pi$
$283$	18.2460	+	2.75015i	1.08461	+	0.163479i	0.417678	+	0.908595i	$0.362844\pi$
$284$	−0.768133	−	10.2500i	−0.0455803	−	0.608227i
$285$	−0.437737	−	0.210803i	−0.0259293	−	0.0124869i
$286$	2.49143	−	0.768505i	0.147322	−	0.0454427i
$287$	−1.58438	+	4.03694i	−0.0935231	+	0.238293i
$288$	1.50387	+	1.02532i	0.0886161	+	0.0604175i
$289$	1.27782	−	0.192600i	0.0751657	−	0.0113294i
$290$	−1.49051	−	6.53035i	−0.0875258	−	0.383475i
$291$	16.2228	−	11.0605i	0.951000	−	0.648381i
$292$	7.10616	−	6.59355i	0.415857	−	0.385859i
$293$	−8.47082	+	4.07933i	−0.494871	+	0.238317i	−0.664636	−	0.747167i	$-0.731413\pi$
$293$	−8.47082	+	4.07933i	−0.494871	+	0.238317i	0.169765	+	0.985485i	$0.445699\pi$
$294$	−3.69343	−	6.39720i	−0.215405	−	0.373092i
$295$	−4.22460	+	7.31722i	−0.245966	+	0.426025i
$296$	0.359045	−	4.79112i	0.0208691	−	0.278478i
$297$	−6.71571	+	29.4235i	−0.389685	+	1.70732i
$298$	−4.72591	−	12.0414i	−0.273765	−	0.697541i
$299$	2.07778	+	2.60546i	0.120161	+	0.150678i
$300$	1.08622			0.0627127
$301$	−2.39725	−	1.68232i	−0.138175	−	0.0969675i
$302$	−12.9153			−0.743190
$303$	−12.6109	−	15.8136i	−0.724480	−	0.908469i
$304$	0.163413	+	0.416368i	0.00937236	+	0.0238804i
$305$	−0.683998	+	2.99679i	−0.0391656	+	0.171596i
$306$	−0.539083	+	7.19357i	−0.0308174	+	0.411229i
$307$	−10.7094	+	18.5493i	−0.611219	+	1.05866i	0.379816	+	0.925062i	$0.375987\pi$
$307$	−10.7094	+	18.5493i	−0.611219	+	1.05866i	−0.991035	+	0.133600i	$0.957346\pi$
$308$	−1.28721	−	2.22951i	−0.0733455	−	0.127038i
$309$	7.92245	−	3.81525i	0.450693	−	0.217042i
$310$	−5.55238	+	5.15186i	−0.315354	+	0.292606i
$311$	−7.57548	+	5.16487i	−0.429566	+	0.292873i	−0.758737	−	0.651397i	$-0.774183\pi$
$311$	−7.57548	+	5.16487i	−0.429566	+	0.292873i	0.329171	+	0.944270i	$0.393231\pi$
$312$	0.109327	+	0.478992i	0.00618941	+	0.0271176i
$313$	16.4585	−	2.48071i	0.930288	−	0.140218i	0.333621	−	0.942707i	$-0.391730\pi$
$313$	16.4585	−	2.48071i	0.930288	−	0.140218i	0.596667	+	0.802489i	$0.296491\pi$
$314$	2.44025	+	1.66373i	0.137711	+	0.0938898i
$315$	0.296986	−	0.756707i	0.0167332	−	0.0426356i
$316$	−10.6675	+	3.29048i	−0.600093	+	0.185104i
$317$	−2.66180	−	1.28186i	−0.149502	−	0.0719963i	0.357637	−	0.933861i	$-0.383583\pi$
$317$	−2.66180	−	1.28186i	−0.149502	−	0.0719963i	−0.507139	+	0.861864i	$0.669297\pi$
$318$	−0.00156656	−	0.0209043i	−8.78485e−5	−	0.00117226i
$319$	−38.1796	−	5.75465i	−2.13765	−	0.322199i
$320$	−0.733052	−	0.680173i	−0.0409788	−	0.0380228i
$321$	2.38209	+	0.734778i	0.132955	+	0.0410113i
$322$	2.05161	−	2.57263i	0.114332	−	0.143367i
$323$	−1.10528	+	1.38598i	−0.0614996	+	0.0771180i
$324$	−0.216634	−	0.0668227i	−0.0120352	−	0.00371237i
$325$	−0.331569	−	0.307651i	−0.0183922	−	0.0170654i
$326$	18.2376	+	2.74887i	1.01009	+	0.152246i
$327$	−0.340822	−	4.54795i	−0.0188475	−	0.251502i
$328$	8.74859	+	4.21310i	0.483060	+	0.232629i
$329$	1.64259	−	0.506672i	0.0905589	−	0.0279337i
$330$	2.28750	−	5.82845i	0.125923	−	0.320845i
$331$	−21.7172	−	14.8066i	−1.19369	−	0.813842i	−0.207299	−	0.978278i	$-0.566467\pi$
$331$	−21.7172	−	14.8066i	−1.19369	−	0.813842i	−0.986388	+	0.164436i	$0.947420\pi$
$332$	2.61059	−	0.393482i	0.143275	−	0.0215952i
$333$	−1.94593	−	8.52569i	−0.106636	−	0.467205i
$334$	−5.09769	+	3.47555i	−0.278933	+	0.190174i
$335$	−9.95393	+	9.23589i	−0.543841	+	0.504611i
$336$	0.437078	−	0.210486i	0.0238446	−	0.0114829i
$337$	−14.8980	−	25.8040i	−0.811544	−	1.40563i	−0.911783	−	0.410672i	$-0.865294\pi$
$337$	−14.8980	−	25.8040i	−0.811544	−	1.40563i	0.100240	−	0.994963i	$-0.468039\pi$
$338$	−6.39771	+	11.0812i	−0.347989	+	0.602735i
$339$	0.0255808	−	0.341352i	0.00138936	−	0.0185397i
$340$	0.881917	−	3.86393i	0.0478287	−	0.209551i
$341$	15.9510	+	40.6426i	0.863797	+	2.20092i
$342$	0.507598	+	0.636508i	0.0274478	+	0.0344184i
$343$	6.16353			0.332799
$344$	−4.15742	+	5.07108i	−0.224153	+	0.273414i
$345$	8.00291			0.430862
$346$	−3.47232	−	4.35415i	−0.186673	−	0.234080i
$347$	12.7983	+	32.6095i	0.687049	+	1.75057i	0.660384	+	0.750928i	$0.270393\pi$
$347$	12.7983	+	32.6095i	0.687049	+	1.75057i	0.0266645	+	0.999644i	$0.491511\pi$
$348$	1.61902	−	7.09337i	0.0867884	−	0.380245i
$349$	−0.241744	+	3.22585i	−0.0129403	+	0.172676i	0.986989	+	0.160787i	$0.0514033\pi$
$349$	−0.241744	+	3.22585i	−0.0129403	+	0.172676i	−0.999929	+	0.0118884i	$0.996216\pi$
$350$	−0.223308	+	0.386780i	−0.0119363	+	0.0206743i
$351$	1.18409	+	2.05091i	0.0632021	+	0.109469i
$352$	−5.19344	+	2.50103i	−0.276812	+	0.133305i
$353$	−11.4412	+	10.6159i	−0.608953	+	0.565026i	−0.923202	−	0.384314i	$-0.874438\pi$
$353$	−11.4412	+	10.6159i	−0.608953	+	0.565026i	0.314249	+	0.949341i	$0.398247\pi$
$354$	−7.58293	+	5.16996i	−0.403028	+	0.274780i
$355$	2.28724	+	10.0210i	0.121394	+	0.531862i
$356$	−9.74386	+	1.46865i	−0.516423	+	0.0778383i
$357$	1.58859	+	1.08308i	0.0840772	+	0.0573228i
$358$	−5.81928	+	14.8273i	−0.307558	+	0.783646i
$359$	−4.35441	+	1.34316i	−0.229817	+	0.0708892i	−0.407525	−	0.913194i	$-0.633608\pi$
$359$	−4.35441	+	1.34316i	−0.229817	+	0.0708892i	0.177708	+	0.984083i	$0.443132\pi$
$360$	−1.63988	−	0.789727i	−0.0864295	−	0.0416223i
$361$	−1.40492	−	18.7474i	−0.0739432	−	0.986703i
$362$	−10.5050	−	1.58337i	−0.552130	−	0.0832201i
$363$	−17.6983	−	16.4216i	−0.928921	−	0.861913i
$364$	−0.193035	−	0.0595435i	−0.0101178	−	0.00312093i
$365$	−6.04407	+	7.57903i	−0.316361	+	0.396704i
$366$	−2.08176	+	2.61044i	−0.108815	+	0.136450i
$367$	19.0998	+	5.89150i	0.997001	+	0.307534i	0.749969	−	0.661473i	$-0.230069\pi$
$367$	19.0998	+	5.89150i	0.997001	+	0.307534i	0.247032	+	0.969007i	$0.420545\pi$
$368$	−5.40090	−	5.01130i	−0.281541	−	0.261232i
$369$	17.4765	+	2.63415i	0.909789	+	0.137129i
$370$	0.359045	+	4.79112i	0.0186659	+	0.249079i
$371$	0.00776567	+	0.00373975i	0.000403174	+	0.000194158i
$372$	−7.86184	+	2.42506i	−0.407618	+	0.125733i
$373$	2.57971	−	6.57300i	0.133573	−	0.340337i	−0.848401	−	0.529353i	$-0.822435\pi$
$373$	2.57971	−	6.57300i	0.133573	−	0.340337i	0.981974	+	0.189016i	$0.0605298\pi$
$374$	−18.8759	−	12.8694i	−0.976051	−	0.665460i
$375$	−1.07408	+	0.161892i	−0.0554655	+	0.00836007i
$376$	−0.856452	−	3.75236i	−0.0441681	−	0.193513i
$377$	−2.50328	+	1.70671i	−0.128925	+	0.0878999i
$378$	1.71413	−	1.59048i	0.0881653	−	0.0818054i
$379$	1.60058	−	0.770798i	0.0822162	−	0.0395932i	−0.392324	−	0.919827i	$-0.628329\pi$
$379$	1.60058	−	0.770798i	0.0822162	−	0.0395932i	0.474540	+	0.880234i	$0.342614\pi$
$380$	−0.223644	−	0.387363i	−0.0114727	−	0.0198713i
$381$	−6.26836	+	10.8571i	−0.321138	+	0.556227i
$382$	−1.29731	+	17.3114i	−0.0663762	+	0.885729i
$383$	−2.21781	+	9.71687i	−0.113325	+	0.496509i	0.886128	+	0.463440i	$0.153385\pi$
$383$	−2.21781	+	9.71687i	−0.113325	+	0.496509i	−0.999453	+	0.0330687i	$0.989472\pi$
$384$	−0.396839	−	1.01113i	−0.0202511	−	0.0515990i
$385$	1.60512	+	2.01276i	0.0818047	+	0.102580i
$386$	0.732332			0.0372747
$387$	−4.51027	+	11.0504i	−0.229270	+	0.561724i
$388$	18.0761			0.917676
$389$	1.03761	+	1.30112i	0.0526090	+	0.0659696i	0.807440	−	0.589950i	$-0.200853\pi$
$389$	1.03761	+	1.30112i	0.0526090	+	0.0659696i	−0.754831	+	0.655919i	$0.772281\pi$
$390$	−0.179496	−	0.457348i	−0.00908912	−	0.0231587i
$391$	6.49770	−	28.4683i	0.328603	−	1.43970i
$392$	0.508205	−	6.78152i	0.0256682	−	0.342518i
$393$	3.46981	−	6.00989i	0.175029	−	0.303159i
$394$	−7.89862	−	13.6808i	−0.397927	−	0.689230i
$395$	10.0579	−	4.84364i	0.506069	−	0.243710i
$396$	−7.69102	+	7.13622i	−0.386488	+	0.358609i
$397$	−15.9343	+	10.8638i	−0.799721	+	0.545241i	−0.892819	−	0.450416i	$-0.851276\pi$
$397$	−15.9343	+	10.8638i	−0.799721	+	0.545241i	0.0930975	+	0.995657i	$0.470323\pi$
$398$	−5.48175	−	24.0171i	−0.274775	−	1.20387i
$399$	0.214565	−	0.0323405i	0.0107417	−	0.00161905i
$400$	0.826239	+	0.563320i	0.0413119	+	0.0281660i
$401$	6.57493	−	16.7526i	0.328336	−	0.836587i	−0.667431	−	0.744672i	$-0.732606\pi$
$401$	6.57493	−	16.7526i	0.328336	−	0.836587i	0.995767	−	0.0919150i	$-0.0292988\pi$
$402$	−14.0942	+	4.34748i	−0.702954	+	0.216832i
$403$	3.08670	+	1.48647i	0.153759	+	0.0740466i
$404$	−1.39155	−	18.5689i	−0.0692320	−	0.923837i
$405$	0.224174	+	0.0337887i	0.0111393	+	0.00167898i
$406$	2.19297	+	2.03478i	0.108835	+	0.100984i
$407$	26.4644	+	8.16320i	1.31179	+	0.404635i
$408$	2.68412	−	3.36578i	0.132884	−	0.166631i
$409$	21.3026	−	26.7126i	1.05335	−	1.32085i	0.108228	−	0.994126i	$-0.465482\pi$
$409$	21.3026	−	26.7126i	1.05335	−	1.32085i	0.945118	−	0.326728i	$-0.105946\pi$
$410$	−9.27880	−	2.86213i	−0.458247	−	0.141351i
$411$	−13.2057	−	12.2531i	−0.651391	−	0.604403i
$412$	8.00489	+	1.20654i	0.394373	+	0.0594421i
$413$	−0.281997	−	3.76299i	−0.0138762	−	0.185165i
$414$	−12.0822	−	5.81846i	−0.593806	−	0.285962i
$415$	−2.52278	+	0.778175i	−0.123839	+	0.0381991i
$416$	−0.165249	+	0.421047i	−0.00810199	+	0.0206435i
$417$	4.26674	+	2.90902i	0.208943	+	0.142455i
$418$	−2.54950	+	0.384275i	−0.124700	+	0.0187955i
$419$	−5.89480	−	25.8268i	−0.287980	−	1.26172i	−0.887293	−	0.461207i	$-0.847417\pi$
$419$	−5.89480	−	25.8268i	−0.287980	−	1.26172i	0.599313	−	0.800515i	$-0.295440\pi$
$420$	−0.400825	+	0.273278i	−0.0195583	+	0.0133346i
$421$	−22.5690	+	20.9410i	−1.09995	+	1.02060i	−0.100276	+	0.994960i	$0.531973\pi$
$421$	−22.5690	+	20.9410i	−1.09995	+	1.02060i	−0.999671	+	0.0256423i	$0.991837\pi$
$422$	−3.35603	+	1.61618i	−0.163369	+	0.0786745i
$423$	−3.50272	−	6.06689i	−0.170308	−	0.294982i
$424$	0.00964953	−	0.0167135i	0.000468622	−	0.000811678i
$425$	−0.296178	+	3.95222i	−0.0143667	+	0.191711i
$426$	−2.48444	+	10.8850i	−0.120371	+	0.527381i
$427$	−0.501552	−	1.27793i	−0.0242718	−	0.0618435i
$428$	1.43090	+	1.79429i	0.0691650	+	0.0867301i
$429$	−2.83205			−0.136733
$430$	3.35518	−	5.63407i	0.161801	−	0.271699i
$431$	34.3069			1.65251			0.826253	−	0.563300i	$-0.190468\pi$
$431$	34.3069			1.65251			0.826253	+	0.563300i	$0.190468\pi$
$432$	−3.26441	−	4.09344i	−0.157059	−	0.196946i
$433$	1.51032	+	3.84824i	0.0725815	+	0.184935i	0.962561	−	0.271067i	$-0.0873764\pi$
$433$	1.51032	+	3.84824i	0.0725815	+	0.184935i	−0.889979	+	0.456001i	$0.849281\pi$
$434$	0.752746	−	3.29800i	0.0361330	−	0.158309i
$435$	−0.543721	+	7.25545i	−0.0260694	+	0.347872i
$436$	2.09935	−	3.63619i	0.100541	−	0.174142i
$437$	−1.64774	−	2.85397i	−0.0788221	−	0.136524i
$438$	−9.48694	+	4.56867i	−0.453304	+	0.218300i
$439$	−15.2495	+	14.1495i	−0.727819	+	0.675318i	−0.954351	−	0.298686i	$-0.903452\pi$
$439$	−15.2495	+	14.1495i	−0.727819	+	0.675318i	0.226532	+	0.974004i	$0.427261\pi$
$440$	4.76268	−	3.24714i	0.227052	−	0.154801i
$441$	−2.75434	−	12.0675i	−0.131159	−	0.574645i
$442$	−1.77263	+	0.267181i	−0.0843155	+	0.0127085i
$443$	12.4949	+	8.51886i	0.593650	+	0.404743i	0.822539	−	0.568709i	$-0.192557\pi$
$443$	12.4949	+	8.51886i	0.593650	+	0.404743i	−0.228889	+	0.973452i	$0.573509\pi$
$444$	−1.90664	+	4.85803i	−0.0904850	+	0.230552i
$445$	9.41613	−	2.90449i	0.446368	−	0.137686i
$446$	−0.981983	−	0.472898i	−0.0464982	−	0.0223924i
$447$	1.05002	+	14.0116i	0.0496644	+	0.662725i
$448$	0.441627	+	0.0665645i	0.0208649	+	0.00314488i
$449$	−27.3337	−	25.3619i	−1.28996	−	1.19690i	−0.968227	−	0.250072i	$-0.919546\pi$
$449$	−27.3337	−	25.3619i	−1.28996	−	1.19690i	−0.321729	−	0.946832i	$-0.604264\pi$
$450$	1.73927	+	0.536494i	0.0819900	+	0.0252906i
$451$	−34.8982	+	43.7610i	−1.64329	+	2.06062i
$452$	0.196486	−	0.246385i	0.00924191	−	0.0115890i
$453$	13.4055	+	4.13505i	0.629846	+	0.194282i
$454$	−7.91317	−	7.34235i	−0.371384	−	0.344594i
$455$	0.199754	+	0.0301080i	0.00936460	+	0.00141149i
$456$	−0.0363077	−	0.484493i	−0.00170026	−	0.0226884i
$457$	6.71967	+	3.23602i	0.314333	+	0.151375i	0.584398	−	0.811467i	$-0.301331\pi$
$457$	6.71967	+	3.23602i	0.314333	+	0.151375i	−0.270065	+	0.962842i	$0.587045\pi$
$458$	3.79465	−	1.17049i	0.177312	−	0.0546936i
$459$	7.58108	−	19.3163i	0.353854	−	0.901606i
$460$	6.08747	+	4.15037i	0.283830	+	0.193512i
$461$	36.2268	−	5.46031i	1.68725	−	0.254312i	0.765876	−	0.642988i	$-0.222305\pi$
$461$	36.2268	−	5.46031i	1.68725	−	0.254312i	0.921375	+	0.388676i	$0.127067\pi$
$462$	0.622252	+	2.72626i	0.0289498	+	0.126837i
$463$	−9.42745	+	6.42753i	−0.438131	+	0.298712i	−0.762225	−	0.647312i	$-0.775893\pi$
$463$	−9.42745	+	6.42753i	−0.438131	+	0.298712i	0.324094	+	0.946025i	$0.394941\pi$
$464$	4.91019	−	4.55599i	0.227950	−	0.211507i
$465$	7.41260	−	3.56972i	0.343751	−	0.165542i
$466$	4.13850	+	7.16810i	0.191712	+	0.332056i
$467$	−8.69804	+	15.0655i	−0.402497	+	0.697146i	−0.994027	−	0.109137i	$-0.965191\pi$
$467$	−8.69804	+	15.0655i	−0.402497	+	0.697146i	0.591529	+	0.806284i	$0.298524\pi$
$468$	−0.0615232	+	0.820970i	−0.00284391	+	0.0379493i
$469$	1.34947	−	5.91242i	0.0623128	−	0.273010i
$470$	1.40615	+	3.58280i	0.0648607	+	0.165262i
$471$	−2.00020	−	2.50817i	−0.0921644	−	0.115571i
$472$	−8.44920			−0.388906
$473$	−23.1657	−	29.8683i	−1.06516	−	1.37334i
$474$	12.1259			0.556961
$475$	0.278879	+	0.349704i	0.0127959	+	0.0160455i
$476$	0.646679	+	1.64771i	0.0296405	+	0.0755227i
$477$	0.00781647	−	0.0342462i	0.000357891	−	0.00156802i
$478$	1.27995	−	17.0797i	0.0585435	−	0.781209i
$479$	−12.5692	+	21.7706i	−0.574303	+	0.994722i	0.421814	+	0.906682i	$0.361394\pi$
$479$	−12.5692	+	21.7706i	−0.574303	+	0.994722i	−0.996117	+	0.0880396i	$0.971940\pi$
$480$	0.543108	+	0.940691i	0.0247894	+	0.0429365i
$481$	1.95796	−	0.942902i	0.0892751	−	0.0429926i
$482$	8.52355	−	7.90870i	0.388237	−	0.360231i
$483$	−2.95316	+	2.01343i	−0.134373	+	0.0916142i
$484$	−4.94598	−	21.6697i	−0.224817	−	0.984988i
$485$	−17.8742	+	2.69411i	−0.811627	+	0.122333i
$486$	−12.7744	−	8.70942i	−0.579457	−	0.395067i
$487$	−10.5836	+	26.9665i	−0.479588	+	1.22197i	0.462505	+	0.886617i	$0.346951\pi$
$487$	−10.5836	+	26.9665i	−0.479588	+	1.22197i	−0.942093	+	0.335352i	$0.891145\pi$
$488$	−2.93730	+	0.906036i	−0.132965	+	0.0410143i
$489$	−18.0497	−	8.69229i	−0.816237	−	0.393079i
$490$	0.508205	+	6.78152i	0.0229583	+	0.306358i
$491$	−7.76768	−	1.17079i	−0.350550	−	0.0528370i	−0.0285931	−	0.999591i	$-0.509103\pi$
$491$	−7.76768	−	1.17079i	−0.350550	−	0.0528370i	−0.321957	+	0.946754i	$0.604341\pi$
$492$	−7.73177	−	7.17404i	−0.348575	−	0.323431i
$493$	25.3679	+	7.82497i	1.14251	+	0.352419i
$494$	−0.126141	+	0.158176i	−0.00567535	+	0.00711666i
$495$	6.54152	−	8.20281i	0.294019	−	0.368689i
$496$	−7.23783	−	2.23257i	−0.324988	−	0.100246i
$497$	−3.36518	−	3.12243i	−0.150949	−	0.140060i
$498$	−2.83566	−	0.427407i	−0.127069	−	0.0191526i
$499$	−0.436016	−	5.81823i	−0.0195187	−	0.260460i	−0.998423	−	0.0561397i	$-0.982121\pi$
$499$	−0.436016	−	5.81823i	−0.0195187	−	0.260460i	0.978904	−	0.204320i	$-0.0654983\pi$
$500$	−0.900969	−	0.433884i	−0.0402926	−	0.0194039i
$501$	6.40396	−	1.97536i	0.286108	−	0.0882525i
$502$	2.88961	−	7.36260i	0.128969	−	0.328609i
$503$	18.6841	+	12.7386i	0.833084	+	0.567987i	0.903037	−	0.429564i	$-0.141333\pi$
$503$	18.6841	+	12.7386i	0.833084	+	0.567987i	−0.0699531	+	0.997550i	$0.522285\pi$
$504$	0.803820	−	0.121156i	0.0358050	−	0.00539673i
$505$	4.14355	+	18.1541i	0.184386	+	0.807847i
$506$	35.0900	−	23.9239i	1.55994	−	1.06355i
$507$	10.1884	−	9.45344i	0.452482	−	0.419842i
$508$	−10.3987	+	5.00773i	−0.461366	+	0.222182i
$509$	−9.10562	−	15.7714i	−0.403600	−	0.699055i	0.590558	−	0.806995i	$-0.298908\pi$
$509$	−9.10562	−	15.7714i	−0.403600	−	0.699055i	−0.994157	+	0.107940i	$0.965574\pi$
$510$	−2.15250	+	3.72824i	−0.0953143	+	0.165089i
$511$	0.323541	−	4.31735i	0.0143126	−	0.190988i
$512$	0.222521	−	0.974928i	0.00983413	−	0.0430861i
$513$	−0.855581	−	2.17998i	−0.0377748	−	0.0962486i
$514$	5.43762	+	6.81855i	0.239843	+	0.300754i
$515$	−8.09531			−0.356722
$516$	5.93882	−	3.93250i	0.261442	−	0.173119i
$517$	22.1859			0.975736
$518$	−1.33788	−	1.67764i	−0.0587829	−	0.0737115i
$519$	2.21006	+	5.63115i	0.0970110	+	0.247180i
$520$	0.100649	−	0.440973i	0.00441376	−	0.0193380i
$521$	−1.22968	+	16.4089i	−0.0538732	+	0.718887i	0.903233	+	0.429150i	$0.141187\pi$
$521$	−1.22968	+	16.4089i	−0.0538732	+	0.718887i	−0.957106	+	0.289737i	$0.906432\pi$
$522$	6.09590	−	10.5584i	0.266810	−	0.462129i
$523$	4.08960	+	7.08339i	0.178826	+	0.309735i	0.941479	−	0.337073i	$-0.109437\pi$
$523$	4.08960	+	7.08339i	0.178826	+	0.309735i	−0.762653	+	0.646808i	$0.776104\pi$
$524$	5.75611	−	2.77200i	0.251457	−	0.121095i
$525$	0.355618	−	0.329966i	0.0155205	−	0.0144009i
$526$	2.23171	−	1.52155i	0.0973070	−	0.0663428i
$527$	−6.67994	−	29.2667i	−0.290983	−	1.27488i
$528$	6.19133	−	0.933193i	0.269443	−	0.0406120i
$529$	25.8471	+	17.6223i	1.12379	+	0.766186i
$530$	−0.00705074	+	0.0179650i	−0.000306264	+	0.000780349i
$531$	−14.6954	+	4.53295i	−0.637728	+	0.196713i
$532$	0.179982	+	0.0866750i	0.00780323	+	0.00375784i
$533$	0.328219	+	4.37977i	0.0142167	+	0.189709i
$534$	10.5839	+	1.59527i	0.458012	+	0.0690341i
$535$	−1.68234	−	1.56098i	−0.0727338	−	0.0674871i
$536$	−12.9755	−	4.00241i	−0.560455	−	0.172878i
$537$	10.7874	−	13.5270i	0.465510	−	0.583731i
$538$	−5.39937	+	6.77060i	−0.232784	+	0.291901i
$539$	37.4587	+	11.5545i	1.61346	+	0.497686i
$540$	3.83805	+	3.56119i	0.165163	+	0.153249i
$541$	5.14934	+	0.776138i	0.221388	+	0.0333688i	0.258799	−	0.965931i	$-0.416673\pi$
$541$	5.14934	+	0.776138i	0.221388	+	0.0333688i	−0.0374117	+	0.999300i	$0.511911\pi$
$542$	1.85665	+	24.7752i	0.0797498	+	1.06419i
$543$	10.3968	+	5.00683i	0.446169	+	0.214864i
$544$	3.78722	−	1.16820i	0.162376	−	0.0500863i
$545$	−1.53396	+	3.90847i	−0.0657076	+	0.167420i
$546$	0.181299	+	0.123607i	0.00775887	+	0.00528991i
$547$	−17.2530	+	2.60046i	−0.737683	+	0.111188i	−0.507127	−	0.861871i	$-0.669293\pi$
$547$	−17.2530	+	2.60046i	−0.737683	+	0.111188i	−0.230556	+	0.973059i	$0.574054\pi$
$548$	−3.69048	−	16.1690i	−0.157649	−	0.690707i
$549$	−4.62267	+	3.15169i	−0.197291	+	0.134511i
$550$	−4.22552	+	3.92071i	−0.180177	+	0.167180i
$551$	2.69936	−	1.29994i	0.114997	−	0.0553794i
$552$	4.00145	+	6.93072i	0.170313	+	0.294991i
$553$	−2.49288	+	4.31780i	−0.106008	+	0.183611i
$554$	−2.15678	+	28.7802i	−0.0916328	+	1.22276i
$555$	1.16129	−	5.08794i	0.0492940	−	0.215971i
$556$	1.73689	+	4.42553i	0.0736607	+	0.187684i
$557$	−10.5320	−	13.2067i	−0.446255	−	0.559585i	0.506925	−	0.861990i	$-0.330782\pi$
$557$	−10.5320	−	13.2067i	−0.446255	−	0.559585i	−0.953180	+	0.302405i	$0.902211\pi$
$558$	−13.7863			−0.583621
$559$	−2.92665	−	0.481663i	−0.123784	−	0.0203722i
$560$	−0.446615			−0.0188729
$561$	15.4721	+	19.4014i	0.653231	+	0.819126i
$562$	−1.66342	−	4.23834i	−0.0701673	−	0.178783i
$563$	4.92973	−	21.5985i	0.207763	−	0.910270i	−0.758288	−	0.651920i	$-0.773964\pi$
$563$	4.92973	−	21.5985i	0.207763	−	0.910270i	0.966051	−	0.258350i	$-0.0831789\pi$
$564$	−0.312424	+	4.16900i	−0.0131554	+	0.175547i
$565$	−0.157569	+	0.272918i	−0.00662899	+	0.0114818i
$566$	−9.22606	−	15.9800i	−0.387800	−	0.671690i
$567$	−0.0912233	+	0.0439308i	−0.00383102	+	0.00184492i
$568$	−7.53486	+	6.99133i	−0.316156	+	0.293350i
$569$	2.93909	−	2.00384i	0.123213	−	0.0840053i	−0.500145	−	0.865941i	$-0.666720\pi$
$569$	2.93909	−	2.00384i	0.123213	−	0.0840053i	0.623359	+	0.781936i	$0.285768\pi$
$570$	0.108112	+	0.473670i	0.00452832	+	0.0198398i
$571$	5.62658	−	0.848070i	0.235465	−	0.0354906i	−0.0302497	−	0.999542i	$-0.509630\pi$
$571$	5.62658	−	0.848070i	0.235465	−	0.0354906i	0.265715	+	0.964052i	$0.414392\pi$
$572$	−2.15422	−	1.46873i	−0.0900727	−	0.0614105i
$573$	6.88912	−	17.5532i	0.287797	−	0.733295i
$574$	4.14405	−	1.27827i	0.172969	−	0.0533540i
$575$	−6.63806	−	3.19672i	−0.276826	−	0.133313i
$576$	−0.136019	−	1.81505i	−0.00566745	−	0.0756269i
$577$	−45.2219	−	6.81610i	−1.88261	−	0.283758i	−0.895656	−	0.444748i	$-0.853293\pi$
$577$	−45.2219	−	6.81610i	−1.88261	−	0.283758i	−0.986956	+	0.160990i	$0.948531\pi$
$578$	−0.947286	−	0.878953i	−0.0394019	−	0.0365596i
$579$	−0.760130	−	0.234469i	−0.0315899	−	0.00974420i
$580$	−4.17632	+	5.23693i	−0.173412	+	0.217452i
$581$	0.735155	−	0.921855i	0.0304994	−	0.0382450i
$582$	−18.7623	−	5.78739i	−0.777721	−	0.239895i
$583$	0.0815486	+	0.0756660i	0.00337740	+	0.00313377i
$584$	−9.58567	−	1.44481i	−0.396658	−	0.0597865i
$585$	−0.0615232	−	0.820970i	−0.00254367	−	0.0339429i
$586$	8.47082	+	4.07933i	0.349926	+	0.168516i
$587$	−15.8270	+	4.88199i	−0.653251	+	0.201501i	−0.603627	−	0.797267i	$-0.706278\pi$
$587$	−15.8270	+	4.88199i	−0.653251	+	0.201501i	−0.0496237	+	0.998768i	$0.515802\pi$
$588$	−2.69872	+	6.87623i	−0.111293	+	0.283571i
$589$	−2.79922	−	1.90848i	−0.115340	−	0.0786374i
$590$	8.35483	−	1.25929i	0.343963	−	0.0518441i
$591$	3.81829	+	16.7290i	0.157063	+	0.688139i
$592$	−3.96971	+	2.70650i	−0.163154	+	0.111237i
$593$	33.9310	−	31.4833i	1.39338	−	1.29287i	0.485124	−	0.874446i	$-0.338775\pi$
$593$	33.9310	−	31.4833i	1.39338	−	1.29287i	0.908254	−	0.418420i	$-0.137416\pi$
$594$	27.1914	−	13.0947i	1.11567	−	0.537281i
$595$	−0.885035	−	1.53293i	−0.0362829	−	0.0628438i
$596$	−6.46781	+	11.2026i	−0.264932	+	0.458875i
$597$	−1.99968	+	26.6839i	−0.0818414	+	1.09210i
$598$	0.741553	−	3.24895i	0.0303243	−	0.132860i
$599$	−4.90538	−	12.4987i	−0.200428	−	0.510683i	0.794954	−	0.606669i	$-0.207495\pi$
$599$	−4.90538	−	12.4987i	−0.200428	−	0.510683i	−0.995383	+	0.0959861i	$0.969400\pi$
$600$	−0.677245	−	0.849238i	−0.0276484	−	0.0346700i
$601$	10.3765			0.423267			0.211633	−	0.977349i	$-0.432122\pi$
$601$	10.3765			0.423267			0.211633	+	0.977349i	$0.432122\pi$
$602$	0.179365	+	2.92315i	0.00731038	+	0.119139i
$603$	−24.7151			−1.00648
$604$	8.05253	+	10.0976i	0.327653	+	0.410864i
$605$	8.12044	+	20.6906i	0.330143	+	0.841191i
$606$	−4.50079	+	19.7193i	−0.182832	+	0.801041i
$607$	−1.57815	+	21.0590i	−0.0640553	+	0.854759i	0.868951	+	0.494898i	$0.164795\pi$
$607$	−1.57815	+	21.0590i	−0.0640553	+	0.854759i	−0.933006	+	0.359860i	$0.882824\pi$
$608$	0.223644	−	0.387363i	0.00906996	−	0.0157096i
$609$	−1.62474	−	2.81413i	−0.0658377	−	0.114034i
$610$	2.76945	−	1.33370i	0.112132	−	0.0539999i
$611$	1.27616	−	1.18411i	0.0516281	−	0.0479038i
$612$	5.96027	−	4.06364i	0.240930	−	0.164263i
$613$	0.735754	+	3.22355i	0.0297168	+	0.130198i	0.987610	−	0.156925i	$-0.0501582\pi$
$613$	0.735754	+	3.22355i	0.0297168	+	0.130198i	−0.957894	+	0.287123i	$0.907301\pi$
$614$	21.1796	−	3.19231i	0.854739	−	0.128831i
$615$	8.71465	+	5.94155i	0.351409	+	0.239586i
$616$	−0.940541	+	2.39646i	−0.0378955	+	0.0965561i
$617$	29.5472	−	9.11411i	1.18953	−	0.366920i	0.364062	−	0.931375i	$-0.381390\pi$
$617$	29.5472	−	9.11411i	1.18953	−	0.366920i	0.825464	+	0.564454i	$0.190913\pi$
$618$	−7.92245	−	3.81525i	−0.318688	−	0.153472i
$619$	3.09378	+	41.2837i	0.124350	+	1.65933i	0.615412	+	0.788206i	$0.288990\pi$
$619$	3.09378	+	41.2837i	0.124350	+	1.65933i	−0.491062	+	0.871125i	$0.663391\pi$
$620$	7.48974	+	1.12890i	0.300795	+	0.0453376i
$621$	28.2775	+	26.2377i	1.13474	+	1.05288i
$622$	8.76129	+	2.70250i	0.351296	+	0.108360i
$623$	−2.74392	+	3.44077i	−0.109933	+	0.137851i
$624$	0.306327	−	0.384122i	0.0122629	−	0.0153772i
$625$	0.955573	+	0.294755i	0.0382229	+	0.0117902i
$626$	−12.2012	−	11.3210i	−0.487658	−	0.452480i
$627$	2.76931	+	0.417406i	0.110595	+	0.0166696i
$628$	−0.220711	−	2.94518i	−0.00880732	−	0.117526i
$629$	−17.1562	−	8.26197i	−0.684061	−	0.329426i
$630$	−0.776785	+	0.239606i	−0.0309478	+	0.00954615i
$631$	11.3028	−	28.7991i	0.449959	−	1.14648i	−0.508454	−	0.861089i	$-0.669783\pi$
$631$	11.3028	−	28.7991i	0.449959	−	1.14648i	0.958413	−	0.285386i	$-0.0921220\pi$
$632$	9.22367	+	6.28859i	0.366898	+	0.250147i
$633$	4.00087	−	0.603035i	0.159020	−	0.0239685i
$634$	0.657411	+	2.88031i	0.0261091	+	0.114392i
$635$	9.53615	−	6.50164i	0.378431	−	0.258010i
$636$	−0.0153669	+	0.0142584i	−0.000609338	+	0.000565383i
$637$	2.77136	−	1.33462i	0.109805	−	0.0528794i
$638$	19.3054	+	33.4380i	0.764310	+	1.32382i
$639$	−9.35436	+	16.2022i	−0.370053	+	0.640950i
$640$	−0.0747301	+	0.997204i	−0.00295397	+	0.0394179i
$641$	−4.21817	+	18.4810i	−0.166608	+	0.729955i	0.820729	+	0.571317i	$0.193567\pi$
$641$	−4.21817	+	18.4810i	−0.166608	+	0.729955i	−0.987337	+	0.158638i	$0.949290\pi$
$642$	−0.910738	−	2.32052i	−0.0359439	−	0.0915837i
$643$	3.18958	+	3.99960i	0.125785	+	0.157729i	0.840736	−	0.541445i	$-0.182123\pi$
$643$	3.18958	+	3.99960i	0.125785	+	0.157729i	−0.714951	+	0.699174i	$0.753551\pi$
$644$	−3.29052			−0.129665
$645$	−5.28638	+	4.77372i	−0.208151	+	0.187965i
$646$	1.77274			0.0697474
$647$	12.3285	+	15.4594i	0.484683	+	0.607773i	0.962698	−	0.270578i	$-0.0872149\pi$
$647$	12.3285	+	15.4594i	0.484683	+	0.607773i	−0.478015	+	0.878352i	$0.658644\pi$
$648$	0.0828249	+	0.211034i	0.00325367	+	0.00829022i
$649$	10.8376	−	47.4825i	0.425412	−	1.86385i
$650$	−0.0338014	+	0.451049i	−0.00132580	+	0.0176916i
$651$	−1.83723	+	3.18218i	−0.0720068	+	0.124719i
$652$	−9.22178	−	15.9726i	−0.361153	−	0.625535i
$653$	6.69073	−	3.22209i	0.261829	−	0.126090i	−0.298365	−	0.954452i	$-0.596441\pi$
$653$	6.69073	−	3.22209i	0.261829	−	0.126090i	0.560193	+	0.828362i	$0.310727\pi$
$654$	−3.34323	+	3.10207i	−0.130731	+	0.121300i
$655$	−5.27868	+	3.59894i	−0.206255	+	0.140622i
$656$	−2.16072	−	9.46675i	−0.0843621	−	0.369614i
$657$	−17.4472	+	2.62974i	−0.680680	+	0.102596i
$658$	−1.42027	−	0.968324i	−0.0553679	−	0.0377492i
$659$	1.61773	−	4.12190i	0.0630177	−	0.160567i	−0.895896	−	0.444263i	$-0.853466\pi$
$659$	1.61773	−	4.12190i	0.0630177	−	0.160567i	0.958914	+	0.283696i	$0.0915608\pi$
$660$	−5.98309	+	1.84554i	−0.232892	+	0.0718375i
$661$	−13.8439	−	6.66688i	−0.538466	−	0.259312i	0.144825	−	0.989457i	$-0.453738\pi$
$661$	−13.8439	−	6.66688i	−0.538466	−	0.259312i	−0.683292	+	0.730146i	$0.739452\pi$
$662$	1.96424	+	26.2109i	0.0763423	+	1.01872i
$663$	1.92546	+	0.290217i	0.0747787	+	0.0112711i
$664$	−1.93531	−	1.79571i	−0.0751046	−	0.0696869i
$665$	−0.190890	−	0.0588819i	−0.00740241	−	0.00228334i
$666$	−5.45238	+	6.83707i	−0.211275	+	0.264931i
$667$	−30.7698	+	38.5841i	−1.19141	+	1.49398i
$668$	5.89565	+	1.81857i	0.228110	+	0.0703625i
$669$	0.867851	+	0.805248i	0.0335530	+	0.0311327i
$670$	13.4271	+	2.02381i	0.518733	+	0.0781865i
$671$	−1.32411	−	17.6691i	−0.0511169	−	0.682107i
$672$	−0.437078	−	0.210486i	−0.0168607	−	0.00811967i
$673$	−42.3786	+	13.0721i	−1.63358	+	0.503891i	−0.969771	−	0.244015i	$-0.921535\pi$
$673$	−42.3786	+	13.0721i	−1.63358	+	0.503891i	−0.663804	+	0.747907i	$0.731059\pi$
$674$	−10.8857	+	27.7362i	−0.419300	+	1.06836i
$675$	−4.32594	−	2.94938i	−0.166506	−	0.113522i
$676$	12.6525	−	1.90706i	0.486635	−	0.0733484i
$677$	0.0220073	+	0.0964202i	0.000845809	+	0.00370573i	0.975349	−	0.220668i	$-0.0708236\pi$
$677$	0.0220073	+	0.0964202i	0.000845809	+	0.00370573i	−0.974503	+	0.224373i	$0.927966\pi$
$678$	−0.282829	+	0.192829i	−0.0108620	+	0.00740557i
$679$	5.91798	−	5.49108i	0.227111	−	0.210728i
$680$	−3.57081	+	1.71961i	−0.136934	+	0.0659441i
$681$	5.86276	+	10.1546i	0.224661	+	0.389125i
$682$	21.8303	−	37.8112i	0.835926	−	1.44787i
$683$	3.20924	−	42.8244i	0.122798	−	1.63863i	−0.507054	−	0.861914i	$-0.669266\pi$
$683$	3.20924	−	42.8244i	0.122798	−	1.63863i	0.629852	−	0.776715i	$-0.283115\pi$
$684$	0.181160	−	0.793712i	0.00692681	−	0.0303483i
$685$	6.05913	+	15.4384i	0.231507	+	0.589871i
$686$	−3.84290	−	4.81884i	−0.146722	−	0.183984i
$687$	−4.31344			−0.164568
$688$	6.55684	+	0.0886307i	0.249977	+	0.00337901i
$689$	0.00872923			0.000332557
$690$	−4.98973	−	6.25692i	−0.189956	−	0.238197i
$691$	−9.09155	−	23.1649i	−0.345859	−	0.881234i	−0.992919	−	0.118795i	$-0.962097\pi$
$691$	−9.09155	−	23.1649i	−0.345859	−	0.881234i	0.647060	−	0.762439i	$-0.275998\pi$
$692$	−1.23926	+	5.42953i	−0.0471094	+	0.206400i
$693$	−0.350169	+	4.67269i	−0.0133018	+	0.177501i
$694$	17.5156	−	30.3378i	0.664881	−	1.15161i
$695$	−2.37708	−	4.11723i	−0.0901679	−	0.156175i
$696$	−6.55526	+	3.15685i	−0.248477	+	0.119660i
$697$	28.2111	−	26.1761i	1.06857	−	0.991489i
$698$	2.67280	−	1.82228i	0.101167	−	0.0689744i
$699$	−2.00060	−	8.76521i	−0.0756697	−	0.331531i
$700$	0.441627	−	0.0665645i	0.0166919	−	0.00251590i
$701$	28.4178	+	19.3749i	1.07332	+	0.731780i	0.964977	−	0.262333i	$-0.0844919\pi$
$701$	28.4178	+	19.3749i	1.07332	+	0.731780i	0.108347	+	0.994113i	$0.465444\pi$
$702$	0.865194	−	2.20448i	0.0326546	−	0.0832027i
$703$	−2.05355	+	0.633435i	−0.0774509	+	0.0238904i
$704$	5.19344	+	2.50103i	0.195735	+	0.0942612i
$705$	−0.312424	−	4.16900i	−0.0117666	−	0.157014i
$706$	15.4333	+	2.32620i	0.580840	+	0.0875475i
$707$	−6.09635	−	5.65659i	−0.229277	−	0.212738i
$708$	8.76992	+	2.70516i	0.329594	+	0.101666i
$709$	−4.63395	+	5.81080i	−0.174032	+	0.218229i	−0.861196	−	0.508273i	$-0.830284\pi$
$709$	−4.63395	+	5.81080i	−0.174032	+	0.218229i	0.687164	+	0.726502i	$0.258855\pi$
$710$	6.40870	−	8.03626i	0.240514	−	0.301595i
$711$	19.4163	+	5.98912i	0.728166	+	0.224610i
$712$	7.22343	+	6.70237i	0.270710	+	0.251182i
$713$	55.1821	+	8.31736i	2.06658	+	0.311487i
$714$	−0.143682	−	1.91730i	−0.00537716	−	0.0717532i
$715$	2.34907	+	1.13125i	0.0878501	+	0.0423064i
$716$	15.2207	−	4.69496i	0.568824	−	0.175459i
$717$	−6.79692	+	17.3183i	−0.253836	+	0.646763i
$718$	3.76506	+	2.56697i	0.140511	+	0.0957985i
$719$	31.9291	−	4.81254i	1.19076	−	0.179478i	0.476380	−	0.879240i	$-0.341949\pi$
$719$	31.9291	−	4.81254i	1.19076	−	0.179478i	0.714376	+	0.699762i	$0.246711\pi$
$720$	0.405018	+	1.77450i	0.0150941	+	0.0661317i
$721$	2.98726	−	2.03668i	0.111251	−	0.0758498i
$722$	−13.7813	+	12.7872i	−0.512888	+	0.475890i
$723$	−11.3792	+	5.47993i	−0.423197	+	0.203801i
$724$	5.31182	+	9.20034i	0.197412	+	0.341928i
$725$	3.34915	−	5.80089i	0.124384	−	0.215440i
$726$	−1.80423	+	24.0758i	−0.0669614	+	0.893538i
$727$	4.67024	−	20.4616i	0.173209	−	0.758880i	−0.811454	−	0.584416i	$-0.801324\pi$
$727$	4.67024	−	20.4616i	0.173209	−	0.758880i	0.984664	−	0.174464i	$-0.0558193\pi$
$728$	0.0738026	+	0.188046i	0.00273531	+	0.00696944i
$729$	10.8948	+	13.6617i	0.403513	+	0.505989i
$730$	9.69394			0.358789
$731$	12.6892	+	22.6808i	0.469325	+	0.838880i
$732$	3.33888			0.123408
$733$	−25.4211	−	31.8771i	−0.938950	−	1.17741i	−0.983954	−	0.178420i	$-0.942902\pi$
$733$	−25.4211	−	31.8771i	−0.938950	−	1.17741i	0.0450041	−	0.998987i	$-0.485670\pi$
$734$	−7.30236	−	18.6061i	−0.269535	−	0.686764i
$735$	1.64373	−	7.20165i	0.0606299	−	0.265637i
$736$	−0.550588	+	7.34709i	−0.0202950	+	0.270817i
$737$	39.1359	−	67.7854i	1.44159	−	2.49691i
$738$	−8.83694	−	15.3060i	−0.325292	−	0.563422i
$739$	−32.5782	+	15.6889i	−1.19841	+	0.577124i	−0.923222	−	0.384267i	$-0.874454\pi$
$739$	−32.5782	+	15.6889i	−1.19841	+	0.577124i	−0.275188	+	0.961391i	$0.588740\pi$
$740$	3.52199	−	3.26793i	0.129471	−	0.120131i
$741$	0.181572	−	0.123794i	0.00667021	−	0.00454767i
$742$	−0.00191796	−	0.00840315i	−7.04106e−5	−	0.000308489i
$743$	−31.6141	+	4.76505i	−1.15981	+	0.174813i	−0.700625	−	0.713529i	$-0.747095\pi$
$743$	−31.6141	+	4.76505i	−1.15981	+	0.174813i	−0.459182	+	0.888342i	$0.651857\pi$
$744$	6.79777	+	4.63464i	0.249218	+	0.169914i
$745$	4.72591	−	12.0414i	0.173144	−	0.441164i
$746$	−6.74741	+	2.08130i	−0.247040	+	0.0762018i
$747$	−4.32942	−	2.08494i	−0.158405	−	0.0762838i
$748$	1.70725	+	22.7817i	0.0624234	+	0.832982i
$749$	1.01352	+	0.152764i	0.0370334	+	0.00558188i
$750$	0.796253	+	0.738815i	0.0290750	+	0.0269777i
$751$	−7.18308	−	2.21569i	−0.262114	−	0.0808516i	0.160913	−	0.986969i	$-0.448556\pi$
$751$	−7.18308	−	2.21569i	−0.262114	−	0.0808516i	−0.423027	+	0.906117i	$0.639032\pi$
$752$	−2.39972	+	3.00916i	−0.0875090	+	0.109733i
$753$	−5.35656	+	6.71691i	−0.195204	+	0.244778i
$754$	2.89513	+	0.893028i	0.105434	+	0.0325222i
$755$	−9.46756	−	8.78461i	−0.344560	−	0.319705i
$756$	−2.31223	−	0.348512i	−0.0840949	−	0.0126753i
$757$	2.12327	+	28.3330i	0.0771715	+	1.02978i	0.892578	+	0.450893i	$0.148894\pi$
$757$	2.12327	+	28.3330i	0.0771715	+	1.02978i	−0.815406	+	0.578889i	$0.803486\pi$
$758$	−1.60058	−	0.770798i	−0.0581356	−	0.0279966i
$759$	−44.0816	+	13.5974i	−1.60006	+	0.493553i
$760$	−0.163413	+	0.416368i	−0.00592760	+	0.0151033i
$761$	−32.2334	−	21.9763i	−1.16846	−	0.796642i	−0.185895	−	0.982570i	$-0.559519\pi$
$761$	−32.2334	−	21.9763i	−1.16846	−	0.796642i	−0.982563	+	0.185928i	$0.940471\pi$
$762$	12.3967	−	1.86850i	0.449085	−	0.0676886i
$763$	−0.417272	−	1.82819i	−0.0151063	−	0.0661849i
$764$	14.3435	−	9.77921i	0.518929	−	0.353800i
$765$	−5.28805	+	4.90659i	−0.191190	+	0.177398i
$766$	8.97974	−	4.32442i	0.324451	−	0.156247i
$767$	−1.91084	−	3.30968i	−0.0689966	−	0.119506i
$768$	−0.543108	+	0.940691i	−0.0195977	+	0.0339443i
$769$	0.0822439	−	1.09747i	0.00296579	−	0.0395757i	−0.995525	−	0.0945032i	$-0.969874\pi$
$769$	0.0822439	−	1.09747i	0.00296579	−	0.0395757i	0.998490	+	0.0549275i	$0.0174928\pi$
$770$	0.572862	−	2.50987i	0.0206445	−	0.0904495i
$771$	−3.46094	−	8.81833i	−0.124643	−	0.317584i
$772$	−0.456601	−	0.572560i	−0.0164334	−	0.0206069i
$773$	16.7629			0.602918			0.301459	−	0.953479i	$-0.402526\pi$
$773$	16.7629			0.602918			0.301459	+	0.953479i	$0.402526\pi$
$774$	11.4517	−	3.36355i	0.411622	−	0.120900i
$775$	−7.57433			−0.272078
$776$	−11.2703	−	14.1325i	−0.404579	−	0.507327i
$777$	0.851533	+	2.16967i	0.0305486	+	0.0778365i
$778$	0.370319	−	1.62247i	0.0132766	−	0.0581685i
$779$	0.324572	−	4.33111i	0.0116290	−	0.155178i
$780$	−0.245655	+	0.425487i	−0.00879587	+	0.0152349i
$781$	−29.6249	−	51.3118i	−1.06006	−	1.83608i
$782$	−26.3086	+	12.6696i	−0.940795	+	0.453063i
$783$	−25.7083	+	23.8539i	−0.918741	+	0.852467i
$784$	−5.61887	+	3.83088i	−0.200674	+	0.136817i
$785$	0.657202	+	2.87939i	0.0234565	+	0.102770i
$786$	−6.86211	+	1.03430i	−0.244763	+	0.0368921i
$787$	2.29918	+	1.56755i	0.0819569	+	0.0558773i	0.603605	−	0.797283i	$-0.293730\pi$
$787$	2.29918	+	1.56755i	0.0819569	+	0.0558773i	−0.521648	+	0.853161i	$0.674683\pi$
$788$	−5.77138	+	14.7052i	−0.205597	+	0.523853i
$789$	−2.80357	+	0.864787i	−0.0998098	+	0.0307872i
$790$	−10.0579	−	4.84364i	−0.357844	−	0.172329i
$791$	−0.0105179	−	0.140352i	−0.000373975	−	0.00499035i
$792$	10.3746	+	1.56372i	0.368645	+	0.0555643i
$793$	−1.01920	−	0.945677i	−0.0361928	−	0.0335820i
$794$	18.4286	+	5.68447i	0.654006	+	0.201734i
$795$	0.0130702	−	0.0163895i	0.000463552	−	0.000581275i
$796$	−15.3595	+	19.2602i	−0.544404	+	0.682661i
$797$	39.2915	+	12.1198i	1.39178	+	0.429306i	0.897890	−	0.440220i	$-0.145099\pi$
$797$	39.2915	+	12.1198i	1.39178	+	0.429306i	0.493887	+	0.869526i	$0.335576\pi$
$798$	−0.159064	−	0.147590i	−0.00563080	−	0.00522462i
$799$	−15.0838	−	2.27352i	−0.533627	−	0.0804313i
$800$	−0.0747301	−	0.997204i	−0.00264211	−	0.0352565i
$801$	16.1593	+	7.78190i	0.570960	+	0.274960i
$802$	−17.1971	+	5.30462i	−0.607252	+	0.187312i
$803$	20.4148	−	52.0160i	0.720422	−	1.83560i
$804$	12.1866	+	8.30866i	0.429787	+	0.293024i
$805$	3.25377	−	0.490427i	0.114680	−	0.0172853i
$806$	−0.762351	−	3.34008i	−0.0268527	−	0.117649i
$807$	7.77205	−	5.29890i	0.273589	−	0.186530i
$808$	−13.6501	+	12.6655i	−0.480210	+	0.445570i
$809$	21.3165	−	10.2655i	0.749448	−	0.360915i	−0.0198522	−	0.999803i	$-0.506320\pi$
$809$	21.3165	−	10.2655i	0.749448	−	0.360915i	0.769300	+	0.638888i	$0.220605\pi$
$810$	−0.113353	−	0.196333i	−0.00398282	−	0.00689844i
$811$	−1.18563	+	2.05358i	−0.0416332	+	0.0721108i	−0.886091	−	0.463511i	$-0.846589\pi$
$811$	−1.18563	+	2.05358i	−0.0416332	+	0.0721108i	0.844458	+	0.535622i	$0.179923\pi$
$812$	0.223559	−	2.98319i	0.00784540	−	0.104690i
$813$	6.00511	−	26.3101i	0.210608	−	0.922735i
$814$	−10.1181	−	25.7804i	−0.354638	−	0.903603i
$815$	11.4994	+	14.4198i	0.402805	+	0.505102i
$816$	−4.30500			−0.150705
$817$	2.79081	+	0.902339i	0.0976382	+	0.0315688i
$818$	−34.1667			−1.19461
$819$	0.229248	+	0.287468i	0.00801058	+	0.0100449i
$820$	3.54753	+	9.03897i	0.123885	+	0.315655i
$821$	−3.35437	+	14.6965i	−0.117068	+	0.512910i	0.882059	+	0.471139i	$0.156157\pi$
$821$	−3.35437	+	14.6965i	−0.117068	+	0.512910i	−0.999127	+	0.0417709i	$0.986700\pi$
$822$	−1.34624	+	17.9644i	−0.0469556	+	0.626579i
$823$	3.90914	−	6.77084i	0.136264	−	0.236017i	−0.789815	−	0.613345i	$-0.789824\pi$
$823$	3.90914	−	6.77084i	0.136264	−	0.236017i	0.926080	+	0.377328i	$0.123157\pi$
$824$	−4.04766	−	7.01075i	−0.141007	−	0.244231i
$825$	5.64120	−	2.71666i	0.196401	−	0.0945820i
$826$	−2.76620	+	2.56666i	−0.0962484	+	0.0893055i
$827$	−28.8253	+	19.6528i	−1.00236	+	0.683394i	−0.949031	−	0.315183i	$-0.897934\pi$
$827$	−28.8253	+	19.6528i	−1.00236	+	0.683394i	−0.0533246	+	0.998577i	$0.516982\pi$
$828$	2.98405	+	13.0740i	0.103703	+	0.454352i
$829$	28.8740	−	4.35206i	1.00284	−	0.151153i	0.372959	−	0.927848i	$-0.378343\pi$
$829$	28.8740	−	4.35206i	1.00284	−	0.151153i	0.629878	+	0.776694i	$0.283105\pi$
$830$	2.18133	+	1.48721i	0.0757151	+	0.0516217i
$831$	11.4532	−	29.1822i	0.397306	−	1.01232i
$832$	0.432219	−	0.133322i	0.0149845	−	0.00462210i
$833$	−24.2834	−	11.6943i	−0.841371	−	0.405183i
$834$	−0.385910	−	5.14961i	−0.0133630	−	0.178317i
$835$	−6.10085	−	0.919555i	−0.211129	−	0.0318225i
$836$	1.89002	+	1.75369i	0.0653679	+	0.0606525i
$837$	37.8952	+	11.6891i	1.30985	+	0.404035i
$838$	−16.5169	+	20.7115i	−0.570565	+	0.715466i
$839$	7.91894	−	9.93004i	0.273392	−	0.342823i	−0.626114	−	0.779732i	$-0.715355\pi$
$839$	7.91894	−	9.93004i	0.273392	−	0.342823i	0.899506	+	0.436909i	$0.143927\pi$
$840$	0.463568	+	0.142992i	0.0159946	+	0.00493368i
$841$	−11.6314	−	10.7924i	−0.401083	−	0.372151i
$842$	30.4439	+	4.58868i	1.04917	+	0.158136i
$843$	0.369587	+	4.93179i	0.0127292	+	0.169860i
$844$	3.35603	+	1.61618i	0.115519	+	0.0556313i
$845$	−12.2269	+	3.77151i	−0.420620	+	0.129744i
$846$	−2.55938	+	6.52118i	−0.0879931	+	0.224203i
$847$	−8.20201	−	5.59203i	−0.281824	−	0.192145i
$848$	−0.0190835	+	0.00287637i	−0.000655330	+	9.87751e-5i
$849$	4.45998	+	19.5405i	0.153066	+	0.670627i
$850$	3.27463	−	2.23261i	0.112319	−	0.0765778i
$851$	25.9489	−	24.0771i	0.889518	−	0.825352i
$852$	10.0593	−	4.84429i	0.344625	−	0.165963i
$853$	16.9798	+	29.4098i	0.581377	+	1.00697i	0.995317	+	0.0966696i	$0.0308190\pi$
$853$	16.9798	+	29.4098i	0.581377	+	1.00697i	−0.413940	+	0.910304i	$0.635848\pi$
$854$	−0.686416	+	1.18891i	−0.0234887	+	0.0406836i
$855$	−0.0608396	+	0.811848i	−0.00208067	+	0.0277646i
$856$	0.510681	−	2.23744i	0.0174547	−	0.0764741i
$857$	−9.46350	−	24.1126i	−0.323267	−	0.823671i	−0.996449	−	0.0841946i	$-0.973168\pi$
$857$	−9.46350	−	24.1126i	−0.323267	−	0.823671i	0.673182	−	0.739477i	$-0.264927\pi$
$858$	1.76576	+	2.21419i	0.0602820	+	0.0755912i
$859$	−18.7596			−0.640071			−0.320035	−	0.947406i	$-0.603695\pi$
$859$	−18.7596			−0.640071			−0.320035	+	0.947406i	$0.603695\pi$
$860$	−6.49681	+	0.889605i	−0.221540	+	0.0303353i
$861$	−4.71062			−0.160537
$862$	−21.3900	−	26.8222i	−0.728546	−	0.913568i
$863$	−12.9016	−	32.8727i	−0.439174	−	1.11900i	−0.963554	−	0.267514i	$-0.913798\pi$
$863$	−12.9016	−	32.8727i	−0.439174	−	1.11900i	0.524380	−	0.851485i	$-0.324297\pi$
$864$	−1.16505	+	5.10444i	−0.0396360	+	0.173656i
$865$	0.416184	−	5.55359i	0.0141507	−	0.188828i
$866$	2.06701	−	3.58016i	0.0702397	−	0.121659i
$867$	0.701831	+	1.21561i	0.0238354	+	0.0412842i
$868$	−3.04781	+	1.46775i	−0.103449	+	0.0498186i
$869$	−47.1714	+	43.7686i	−1.60018	+	1.48475i
$870$	6.01154	−	4.09860i	0.203810	−	0.138956i
$871$	−1.36669	−	5.98786i	−0.0463085	−	0.202891i
$872$	−4.15181	+	0.625785i	−0.140598	+	0.0211917i
$873$	−27.1841	−	18.5338i	−0.920041	−	0.627273i
$874$	−1.20397	+	3.06767i	−0.0407250	+	0.103766i
$875$	−0.426773	+	0.131642i	−0.0144276	+	0.00445032i
$876$	9.48694	+	4.56867i	0.320534	+	0.154361i
$877$	−2.94890	−	39.3503i	−0.0995772	−	1.32877i	−0.793436	−	0.608654i	$-0.791710\pi$
$877$	−2.94890	−	39.3503i	−0.0995772	−	1.32877i	0.693859	−	0.720111i	$-0.255909\pi$
$878$	20.5704	+	3.10049i	0.694218	+	0.104637i
$879$	−7.48629	−	6.94626i	−0.252506	−	0.234292i
$880$	−5.50820	−	1.69905i	−0.185681	−	0.0572751i
$881$	−6.51338	+	8.16752i	−0.219441	+	0.275171i	−0.879351	−	0.476174i	$-0.842023\pi$
$881$	−6.51338	+	8.16752i	−0.219441	+	0.275171i	0.659910	+	0.751345i	$0.270595\pi$
$882$	−7.71749	+	9.67742i	−0.259861	+	0.325856i
$883$	44.4677	+	13.7165i	1.49646	+	0.461596i	0.931567	−	0.363570i	$-0.118442\pi$
$883$	44.4677	+	13.7165i	1.49646	+	0.461596i	0.564891	+	0.825166i	$0.308918\pi$
$884$	1.31411	+	1.21931i	0.0441983	+	0.0410100i
$885$	−9.07515	−	1.36786i	−0.305058	−	0.0459801i
$886$	−1.13011	−	15.0803i	−0.0379669	−	0.506633i
$887$	−33.0957	−	15.9380i	−1.11124	−	0.535147i	−0.214068	−	0.976819i	$-0.568671\pi$
$887$	−33.0957	−	15.9380i	−1.11124	−	0.535147i	−0.897177	+	0.441672i	$0.854386\pi$
$888$	4.98693	−	1.53826i	0.167350	−	0.0516208i
$889$	−1.88321	+	4.79835i	−0.0631609	+	0.160931i
$890$	−8.14169	−	5.55091i	−0.272910	−	0.186067i
$891$	−1.29220	+	0.194768i	−0.0432904	+	0.00652498i
$892$	0.242530	+	1.06259i	0.00812049	+	0.0355782i
$893$	−1.42241	+	0.969783i	−0.0475991	+	0.0324525i
$894$	10.3000	−	9.55702i	0.344484	−	0.319635i
$895$	−14.3509	+	6.91105i	−0.479699	+	0.231011i
$896$	−0.223308	−	0.386780i	−0.00746018	−	0.0129214i
$897$	−1.80991	+	3.13486i	−0.0604312	+	0.104670i
$898$	−2.78650	+	37.1832i	−0.0929867	+	1.24082i
$899$	−11.2896	+	49.4631i	−0.376530	+	1.64969i
$900$	−0.664970	−	1.69432i	−0.0221657	−	0.0564772i
$901$	−0.0476895	−	0.0598007i	−0.00158877	−	0.00199225i
$902$	55.9724			1.86368
$903$	0.749726	−	3.09154i	0.0249493	−	0.102880i
$904$	−0.315139			−0.0104814
$905$	−6.62373	−	8.30589i	−0.220180	−	0.276097i
$906$	−5.12528	−	13.0590i	−0.170276	−	0.433856i
$907$	6.24141	−	27.3454i	0.207242	−	0.907989i	−0.759150	−	0.650916i	$-0.774385\pi$
$907$	6.24141	−	27.3454i	0.207242	−	0.907989i	0.966392	−	0.257073i	$-0.0827579\pi$
$908$	−0.806699	+	10.7646i	−0.0267712	+	0.357237i
$909$	−16.9463	+	29.3519i	−0.562074	+	0.973541i
$910$	−0.101005	−	0.174946i	−0.00334828	−	0.00579940i
$911$	−48.8571	+	23.5283i	−1.61871	+	0.779529i	−0.999982	−	0.00607754i	$-0.998065\pi$
$911$	−48.8571	+	23.5283i	−1.61871	+	0.779529i	−0.618727	+	0.785606i	$0.712351\pi$
$912$	−0.356154	+	0.330463i	−0.0117934	+	0.0109427i
$913$	12.5738	−	8.57269i	0.416133	−	0.283714i
$914$	−1.65962	−	7.27128i	−0.0548954	−	0.240512i
$915$	−3.30158	+	0.497634i	−0.109147	+	0.0164513i
$916$	−3.28105	−	2.23698i	−0.108409	−	0.0739120i
$917$	1.04244	−	2.65610i	0.0344244	−	0.0877120i
$918$	−19.8288	+	6.11637i	−0.654448	+	0.201870i
$919$	17.7046	+	8.52609i	0.584021	+	0.281250i	0.702473	−	0.711710i	$-0.252079\pi$
$919$	17.7046	+	8.52609i	0.584021	+	0.281250i	−0.118452	+	0.992960i	$0.537793\pi$
$920$	−0.550588	−	7.34709i	−0.0181524	−	0.242226i
$921$	−23.0056	−	3.46754i	−0.758061	−	0.114259i
$922$	−26.8561	−	24.9188i	−0.884458	−	0.820657i
$923$	−4.44267	−	1.37038i	−0.146232	−	0.0451067i
$924$	1.74351	−	2.18629i	0.0573573	−	0.0719238i
$925$	−2.99559	+	3.75635i	−0.0984945	+	0.123508i
$926$	10.9032	+	3.36318i	0.358300	+	0.110521i
$927$	−10.8012	−	10.0220i	−0.354758	−	0.329167i
$928$	−6.62348	−	0.998328i	−0.217426	−	0.0327717i
$929$	0.437246	+	5.83464i	0.0143456	+	0.191428i	0.999773	+	0.0213291i	$0.00678979\pi$
$929$	0.437246	+	5.83464i	0.0143456	+	0.191428i	−0.985427	+	0.170099i	$0.945591\pi$
$930$	−7.41260	−	3.56972i	−0.243069	−	0.117056i
$931$	−2.90666	+	0.896585i	−0.0952619	+	0.0293844i
$932$	3.02393	−	7.70485i	0.0990521	−	0.252381i
$933$	−8.22860	−	5.61017i	−0.269392	−	0.183669i
$934$	17.2018	−	2.59275i	0.562860	−	0.0848375i
$935$	−5.08363	−	22.2728i	−0.166252	−	0.728399i
$936$	0.680219	−	0.463765i	0.0222337	−	0.0151586i
$937$	7.53359	−	6.99015i	0.246112	−	0.228358i	−0.547465	−	0.836829i	$-0.684407\pi$
$937$	7.53359	−	6.99015i	0.246112	−	0.228358i	0.793577	+	0.608470i	$0.208217\pi$
$938$	−5.46390	+	2.63128i	−0.178403	+	0.0859142i
$939$	9.03969	+	15.6572i	0.294999	+	0.510954i
$940$	1.92443	−	3.33321i	0.0627680	−	0.108717i
$941$	−2.85891	+	38.1496i	−0.0931979	+	1.24364i	0.732988	+	0.680242i	$0.238125\pi$
$941$	−2.85891	+	38.1496i	−0.0931979	+	1.24364i	−0.826186	+	0.563398i	$0.809494\pi$
$942$	−0.713863	+	3.12764i	−0.0232589	+	0.101904i
$943$	26.1371	+	66.5964i	0.851142	+	2.16868i
$944$	5.26799	+	6.60585i	0.171458	+	0.215002i
$945$	2.33835			0.0760664
$946$	−8.90838	+	36.7342i	−0.289636	+	1.19433i
$947$	−9.13168			−0.296740			−0.148370	−	0.988932i	$-0.547403\pi$
$947$	−9.13168			−0.296740			−0.148370	+	0.988932i	$0.547403\pi$
$948$	−7.56038	−	9.48042i	−0.245550	−	0.307910i
$949$	−1.60191	−	4.08160i	−0.0520002	−	0.132494i
$950$	0.0995309	−	0.436073i	0.00322921	−	0.0141481i
$951$	0.239816	−	3.20012i	0.00777657	−	0.103771i
$952$	0.885035	−	1.53293i	0.0286841	−	0.0496824i
$953$	−13.5543	−	23.4767i	−0.439066	−	0.760484i	0.558552	−	0.829470i	$-0.311357\pi$
$953$	−13.5543	−	23.4767i	−0.439066	−	0.760484i	−0.997618	+	0.0689853i	$0.978024\pi$
$954$	−0.0316482	+	0.0152410i	−0.00102465	+	0.000493445i
$955$	−12.7258	+	11.8078i	−0.411796	+	0.382091i
$956$	−14.1515	+	9.64834i	−0.457693	+	0.312050i
$957$	−9.33247	−	40.8882i	−0.301676	−	1.32173i
$958$	24.8577	−	3.74669i	0.803116	−	0.121050i
$959$	−6.11999	−	4.17254i	−0.197625	−	0.134738i
$960$	0.396839	−	1.01113i	0.0128079	−	0.0326341i
$961$	25.1990	−	7.77285i	0.812870	−	0.250737i
$962$	−1.95796	−	0.942902i	−0.0631270	−	0.0304004i
$963$	−0.312160	−	4.16549i	−0.0100592	−	0.134231i
$964$	−11.4976	−	1.73299i	−0.370313	−	0.0558157i
$965$	0.536837	+	0.498112i	0.0172814	+	0.0160348i
$966$	3.41543	+	1.05352i	0.109890	+	0.0338964i
$967$	−30.3197	+	38.0196i	−0.975014	+	1.22263i	−0.000111301		1.00000i	$0.500035\pi$
$967$	−30.3197	+	38.0196i	−0.975014	+	1.22263i	−0.974903	+	0.222629i	$0.928536\pi$
$968$	−13.8583	+	17.3778i	−0.445423	+	0.558543i
$969$	−1.84003	−	0.567573i	−0.0591102	−	0.0182331i
$970$	13.2507	+	12.2949i	0.425455	+	0.394765i
$971$	31.0807	+	4.68466i	0.997427	+	0.150338i	0.627412	−	0.778688i	$-0.284114\pi$
$971$	31.0807	+	4.68466i	0.997427	+	0.150338i	0.370015	+	0.929026i	$0.379352\pi$
$972$	1.15539	+	15.4176i	0.0370592	+	0.494521i
$973$	1.91301	+	0.921258i	0.0613283	+	0.0295342i
$974$	27.6820	−	8.53877i	0.886989	−	0.273600i
$975$	0.179496	−	0.457348i	0.00574847	−	0.0146469i
$976$	2.53974	+	1.73157i	0.0812952	+	0.0554261i
$977$	−45.5712	+	6.86875i	−1.45795	+	0.219751i	−0.829678	−	0.558242i	$-0.811476\pi$
$977$	−45.5712	+	6.86875i	−1.45795	+	0.219751i	−0.628273	+	0.777993i	$0.716238\pi$
$978$	4.45792	+	19.5314i	0.142548	+	0.624545i
$979$	−46.9310	+	31.9970i	−1.49992	+	1.02263i
$980$	4.98514	−	4.62554i	0.159245	−	0.147757i
$981$	−6.88539	+	3.31583i	−0.219834	+	0.105866i
$982$	3.92771	+	6.80299i	0.125338	+	0.217092i
$983$	−6.92263	+	11.9903i	−0.220798	+	0.382433i	−0.955050	−	0.296444i	$-0.904199\pi$
$983$	−6.92263	+	11.9903i	−0.220798	+	0.382433i	0.734253	+	0.678876i	$0.237533\pi$
$984$	−0.788206	+	10.5179i	−0.0251271	+	0.335298i
$985$	3.51522	−	15.4012i	0.112004	−	0.490722i
$986$	−9.69883	−	24.7122i	−0.308874	−	0.786997i
$987$	1.16416	+	1.45980i	0.0370555	+	0.0464661i
$988$	0.202314			0.00643648
$989$	−47.8665	+	6.55434i	−1.52207	+	0.208416i
$990$	−10.4918			−0.333451
$991$	3.11757	+	3.90931i	0.0990328	+	0.124183i	0.828878	−	0.559429i	$-0.188979\pi$
$991$	3.11757	+	3.90931i	0.0990328	+	0.124183i	−0.729846	+	0.683612i	$0.760408\pi$
$992$	2.76722	+	7.05075i	0.0878592	+	0.223862i
$993$	6.35310	−	27.8348i	0.201610	−	0.883309i
$994$	−0.343060	+	4.57781i	−0.0108812	+	0.145199i
$995$	12.3174	−	21.3343i	0.390487	−	0.676344i
$996$	1.43384	+	2.48349i	0.0454331	+	0.0786925i
$997$	36.1079	−	17.3887i	1.14355	−	0.550705i	0.236460	−	0.971641i	$-0.424013\pi$
$997$	36.1079	−	17.3887i	1.14355	−	0.550705i	0.907090	+	0.420937i	$0.138299\pi$
$998$	−4.27702	+	3.96850i	−0.135387	+	0.125621i
$999$	20.7842	−	14.1705i	0.657585	−	0.448334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.281.3	yes	48
43.15	even	21	inner	430.2.q.c.101.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.101.3	✓	48	43.15	even	21	inner
430.2.q.c.281.3	yes	48	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 - 0.781831i) q^{2} +(0.396839 + 1.01113i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.543108 - 0.940691i) q^{6} +(0.223308 + 0.386780i) q^{7} +(0.900969 - 0.433884i) q^{8} +(1.33425 - 1.23801i) q^{9} +O(q^{10})\)	\(q+(-0.623490 - 0.781831i) q^{2} +(0.396839 + 1.01113i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.543108 - 0.940691i) q^{6} +(0.223308 + 0.386780i) q^{7} +(0.900969 - 0.433884i) q^{8} +(1.33425 - 1.23801i) q^{9} +(-0.826239 + 0.563320i) q^{10} +(1.28267 + 5.61977i) q^{11} +(-1.07408 + 0.161892i) q^{12} +(0.373719 + 0.254797i) q^{13} +(0.163167 - 0.415742i) q^{14} +(1.03796 - 0.320168i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-0.296178 - 3.95222i) q^{17} +(-1.79981 - 0.271277i) q^{18} +(-0.327885 - 0.304233i) q^{19} +(0.955573 + 0.294755i) q^{20} +(-0.302468 + 0.379282i) q^{21} +(3.59398 - 4.50670i) q^{22} +(7.04037 + 2.17167i) q^{23} +(0.796253 + 0.738815i) q^{24} +(-0.988831 - 0.149042i) q^{25} +(-0.0338014 - 0.451049i) q^{26} +(4.71721 + 2.27169i) q^{27} +(-0.426773 + 0.131642i) q^{28} +(-2.44716 + 6.23526i) q^{29} +(-0.897474 - 0.611887i) q^{30} +(7.48974 - 1.12890i) q^{31} +(0.222521 + 0.974928i) q^{32} +(-5.17330 + 3.52710i) q^{33} +(-2.90530 + 2.69573i) q^{34} +(0.402386 - 0.193779i) q^{35} +(0.910067 + 1.57628i) q^{36} +(2.40228 - 4.16087i) q^{37} +(-0.0334259 + 0.446037i) q^{38} +(-0.109327 + 0.478992i) q^{39} +(-0.365341 - 0.930874i) q^{40} +(6.05421 + 7.59174i) q^{41} +0.485120 q^{42} +(-5.94596 + 2.76505i) q^{43} -5.76429 q^{44} +(-1.13484 - 1.42304i) q^{45} +(-2.69172 - 6.85839i) q^{46} +(0.856452 - 3.75236i) q^{47} +(0.0811730 - 1.08318i) q^{48} +(3.40027 - 5.88944i) q^{49} +(0.500000 + 0.866025i) q^{50} +(3.87867 - 1.86787i) q^{51} +(-0.331569 + 0.307651i) q^{52} +(0.0159456 - 0.0108715i) q^{53} +(-1.16505 - 5.10444i) q^{54} +(5.69991 - 0.859123i) q^{55} +(0.369011 + 0.251587i) q^{56} +(0.177501 - 0.452266i) q^{57} +(6.40070 - 1.97436i) q^{58} +(-7.61246 - 3.66597i) q^{59} +(0.0811730 + 1.08318i) q^{60} +(-3.03953 - 0.458135i) q^{61} +(-5.55238 - 5.15186i) q^{62} +(0.776785 + 0.239606i) q^{63} +(0.623490 - 0.781831i) q^{64} +(0.282013 - 0.353633i) q^{65} +(5.98309 + 1.84554i) q^{66} +(-9.95393 - 9.23589i) q^{67} +(3.91903 + 0.590699i) q^{68} +(0.598058 + 7.98053i) q^{69} +(-0.402386 - 0.193779i) q^{70} +(-9.82210 + 3.02972i) q^{71} +(0.664970 - 1.69432i) q^{72} +(-8.00951 - 5.46079i) q^{73} +(-4.75089 + 0.716082i) q^{74} +(-0.241706 - 1.05898i) q^{75} +(0.369567 - 0.251966i) q^{76} +(-1.88718 + 1.75105i) q^{77} +(0.442655 - 0.213172i) q^{78} +(5.58172 + 9.66782i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.0169417 + 0.226072i) q^{81} +(2.16072 - 9.46675i) q^{82} +(-0.964527 - 2.45757i) q^{83} +(-0.302468 - 0.379282i) q^{84} -3.96330 q^{85} +(5.86905 + 2.92476i) q^{86} -7.27579 q^{87} +(3.59398 + 4.50670i) q^{88} +(3.60004 + 9.17275i) q^{89} +(-0.405018 + 1.77450i) q^{90} +(-0.0150962 + 0.201445i) q^{91} +(-3.68385 + 6.38061i) q^{92} +(4.11368 + 7.12511i) q^{93} +(-3.46770 + 1.66996i) q^{94} +(-0.327885 + 0.304233i) q^{95} +(-0.897474 + 0.611887i) q^{96} +(-4.02232 - 17.6229i) q^{97} +(-6.72458 + 1.01357i) q^{98} +(8.66872 + 5.91023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

L-functions

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