LMFDB - Embedded newform 570.2.bh.b.67.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			67.7
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.b.553.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.137857 - 2.23181i) q^{5} +(0.766044 + 0.642788i) q^{6} +(3.36188 - 0.900812i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(0.819152 + 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.137857 - 2.23181i) q^{5} +(0.766044 + 0.642788i) q^{6} +(3.36188 - 0.900812i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(1.16719 - 1.90727i) q^{10} +(-2.47956 - 4.29473i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-0.461531 - 5.27533i) q^{13} +(3.27057 + 1.19039i) q^{14} +(0.0571834 - 2.23534i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-1.24295 + 1.77512i) q^{17} +(0.707107 + 0.707107i) q^{18} +(2.98013 + 3.18101i) q^{19} +(2.05007 - 0.892868i) q^{20} +(3.42759 - 0.604377i) q^{21} +(0.432216 - 4.94025i) q^{22} +(-3.76759 + 8.07962i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(-4.96199 + 0.615341i) q^{25} +(2.64774 - 4.58602i) q^{26} +(0.965926 + 0.258819i) q^{27} +(1.99632 + 2.85103i) q^{28} +(-1.01235 + 5.74133i) q^{29} +(1.32898 - 1.79828i) q^{30} +(5.57358 + 3.21791i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-2.09582 - 4.49449i) q^{33} +(-2.03634 + 0.741166i) q^{34} +(-2.47390 - 7.37890i) q^{35} +(0.173648 + 0.984808i) q^{36} +(2.22642 - 2.22642i) q^{37} +(0.616622 + 4.31506i) q^{38} -5.29548i q^{39} +(2.19145 + 0.444477i) q^{40} +(3.72188 + 4.43556i) q^{41} +(3.15438 + 1.47091i) q^{42} +(-2.57232 + 1.19949i) q^{43} +(3.18766 - 3.79891i) q^{44} +(0.251788 - 2.22185i) q^{45} +(-7.72050 + 4.45744i) q^{46} +(4.93978 - 3.45887i) q^{47} +(-0.819152 + 0.573576i) q^{48} +(4.42857 - 2.55683i) q^{49} +(-4.41757 - 2.34202i) q^{50} +(-1.39294 + 1.66004i) q^{51} +(4.79933 - 2.23797i) q^{52} +(1.42248 + 0.663316i) q^{53} +(0.642788 + 0.766044i) q^{54} +(-9.24321 + 6.12598i) q^{55} +3.48047i q^{56} +(2.69154 + 3.42864i) q^{57} +(-4.12236 + 4.12236i) q^{58} +(-1.77463 - 10.0644i) q^{59} +(2.12009 - 0.710795i) q^{60} +(-2.73303 + 0.994743i) q^{61} +(2.71989 + 5.83283i) q^{62} +(3.46723 - 0.303343i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-11.7099 + 1.75729i) q^{65} +(0.861143 - 4.88379i) q^{66} +(4.13406 + 5.90405i) q^{67} +(-2.09318 - 0.560867i) q^{68} +(-4.45744 + 7.72050i) q^{69} +(2.20586 - 7.46341i) q^{70} +(-4.58689 + 12.6024i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(-0.623799 + 7.13005i) q^{73} +(3.10080 - 0.546755i) q^{74} +(-4.99674 + 0.180533i) q^{75} +(-1.96991 + 3.88837i) q^{76} +(-12.2047 - 12.2047i) q^{77} +(3.03736 - 4.33780i) q^{78} +(-2.42883 + 2.03803i) q^{79} +(1.54019 + 1.62106i) q^{80} +(0.939693 + 0.342020i) q^{81} +(0.504651 + 5.76819i) q^{82} +(1.56537 + 5.84206i) q^{83} +(1.74023 + 3.01418i) q^{84} +(4.13309 + 2.52933i) q^{85} +(-2.79512 - 0.492856i) q^{86} +(-1.50889 + 5.63125i) q^{87} +(4.79015 - 1.28352i) q^{88} +(-11.5493 - 9.69100i) q^{89} +(1.48065 - 1.67561i) q^{90} +(-6.30369 - 17.3192i) q^{91} +(-8.88095 - 0.776982i) q^{92} +(5.27191 + 3.69143i) q^{93} +6.03036 q^{94} +(6.68860 - 7.08961i) q^{95} -1.00000 q^{96} +(2.33163 + 1.63262i) q^{97} +(5.09421 + 0.445686i) q^{98} +(-1.69612 - 4.66005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^5 + 12 * q^7	$ 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	0.996195	+	0.0871557i	0.575153	+	0.0503194i
$3$	0.996195	+	0.0871557i	0.575153	+	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−0.137857	−	2.23181i	−0.0616513	−	0.998098i
$5$	−0.137857	−	2.23181i	−0.0616513	−	0.998098i
$6$	0.766044	+	0.642788i	0.312736	+	0.262417i
$7$	3.36188	−	0.900812i	1.27067	−	0.340475i	0.440382	−	0.897810i	$-0.354843\pi$
$7$	3.36188	−	0.900812i	1.27067	−	0.340475i	0.830287	+	0.557336i	$0.188176\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	1.16719	−	1.90727i	0.369098	−	0.603131i
$11$	−2.47956	−	4.29473i	−0.747616	−	1.29491i	−0.948962	−	0.315389i	$-0.897865\pi$
$11$	−2.47956	−	4.29473i	−0.747616	−	1.29491i	0.201346	−	0.979520i	$-0.435468\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	−0.461531	−	5.27533i	−0.128006	−	1.46311i	−0.740190	−	0.672398i	$-0.765264\pi$
$13$	−0.461531	−	5.27533i	−0.128006	−	1.46311i	0.612184	−	0.790715i	$-0.290291\pi$
$14$	3.27057	+	1.19039i	0.874097	+	0.318145i
$15$	0.0571834	−	2.23534i	0.0147647	−	0.577161i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−1.24295	+	1.77512i	−0.301461	+	0.430530i	−0.941092	−	0.338152i	$-0.890198\pi$
$17$	−1.24295	+	1.77512i	−0.301461	+	0.430530i	0.639631	+	0.768682i	$0.279087\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	2.98013	+	3.18101i	0.683688	+	0.729775i
$19$	2.98013	+	3.18101i	0.683688	+	0.729775i
$20$	2.05007	−	0.892868i	0.458410	−	0.199651i
$21$	3.42759	−	0.604377i	0.747962	−	0.131886i
$22$	0.432216	−	4.94025i	0.0921488	−	1.05327i
$23$	−3.76759	+	8.07962i	−0.785596	+	1.68472i	−0.0583936	+	0.998294i	$0.518598\pi$
$23$	−3.76759	+	8.07962i	−0.785596	+	1.68472i	−0.727203	+	0.686423i	$0.759180\pi$
$24$	−0.342020	+	0.939693i	−0.0698146	+	0.191814i
$25$	−4.96199	+	0.615341i	−0.992398	+	0.123068i
$26$	2.64774	−	4.58602i	0.519264	−	0.899392i
$27$	0.965926	+	0.258819i	0.185893	+	0.0498097i
$28$	1.99632	+	2.85103i	0.377268	+	0.538795i
$29$	−1.01235	+	5.74133i	−0.187989	+	1.06614i	0.734066	+	0.679078i	$0.237620\pi$
$29$	−1.01235	+	5.74133i	−0.187989	+	1.06614i	−0.922055	+	0.387059i	$0.873491\pi$
$30$	1.32898	−	1.79828i	0.242637	−	0.328320i
$31$	5.57358	+	3.21791i	1.00104	+	0.577954i	0.908557	−	0.417760i	$-0.137185\pi$
$31$	5.57358	+	3.21791i	1.00104	+	0.577954i	0.0924876	+	0.995714i	$0.470518\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	−2.09582	−	4.49449i	−0.364835	−	0.782391i
$34$	−2.03634	+	0.741166i	−0.349229	+	0.127109i
$35$	−2.47390	−	7.37890i	−0.418166	−	1.24726i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	2.22642	−	2.22642i	0.366022	−	0.366022i	−0.500002	−	0.866024i	$-0.666667\pi$
$37$	2.22642	−	2.22642i	0.366022	−	0.366022i	0.866024	+	0.500002i	$0.166667\pi$
$38$	0.616622	+	4.31506i	0.100029	+	0.699996i
$39$		−	5.29548i		−	0.847955i
$40$	2.19145	+	0.444477i	0.346498	+	0.0702780i
$41$	3.72188	+	4.43556i	0.581260	+	0.692719i	0.973901	−	0.226973i	$-0.0728829\pi$
$41$	3.72188	+	4.43556i	0.581260	+	0.692719i	−0.392641	+	0.919692i	$0.628438\pi$
$42$	3.15438	+	1.47091i	0.486731	+	0.226966i
$43$	−2.57232	+	1.19949i	−0.392275	+	0.182921i	−0.608741	−	0.793369i	$-0.708325\pi$
$43$	−2.57232	+	1.19949i	−0.392275	+	0.182921i	0.216465	+	0.976290i	$0.430547\pi$
$44$	3.18766	−	3.79891i	0.480558	−	0.572707i
$45$	0.251788	−	2.22185i	0.0375344	−	0.331213i
$46$	−7.72050	+	4.45744i	−1.13833	+	0.657213i
$47$	4.93978	−	3.45887i	0.720541	−	0.504528i	−0.154854	−	0.987937i	$-0.549491\pi$
$47$	4.93978	−	3.45887i	0.720541	−	0.504528i	0.875394	+	0.483409i	$0.160602\pi$
$48$	−0.819152	+	0.573576i	−0.118234	+	0.0827886i
$49$	4.42857	−	2.55683i	0.632653	−	0.365262i
$50$	−4.41757	−	2.34202i	−0.624739	−	0.331212i
$51$	−1.39294	+	1.66004i	−0.195050	+	0.232452i
$52$	4.79933	−	2.23797i	0.665548	−	0.310350i
$53$	1.42248	+	0.663316i	0.195393	+	0.0911134i	0.517852	−	0.855470i	$-0.326732\pi$
$53$	1.42248	+	0.663316i	0.195393	+	0.0911134i	−0.322459	+	0.946583i	$0.604509\pi$
$54$	0.642788	+	0.766044i	0.0874723	+	0.104245i
$55$	−9.24321	+	6.12598i	−1.24635	+	0.826027i
$56$			3.48047i			0.465097i
$57$	2.69154	+	3.42864i	0.356504	+	0.454135i
$58$	−4.12236	+	4.12236i	−0.541292	+	0.541292i
$59$	−1.77463	−	10.0644i	−0.231037	−	1.31027i	−0.850801	−	0.525487i	$-0.823883\pi$
$59$	−1.77463	−	10.0644i	−0.231037	−	1.31027i	0.619765	−	0.784788i	$-0.287228\pi$
$60$	2.12009	−	0.710795i	0.273702	−	0.0917633i
$61$	−2.73303	+	0.994743i	−0.349929	+	0.127364i	−0.511004	−	0.859578i	$-0.670726\pi$
$61$	−2.73303	+	0.994743i	−0.349929	+	0.127364i	0.161075	+	0.986942i	$0.448504\pi$
$62$	2.71989	+	5.83283i	0.345427	+	0.740770i
$63$	3.46723	−	0.303343i	0.436829	−	0.0382176i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−11.7099	+	1.75729i	−1.45244	+	0.217965i
$66$	0.861143	−	4.88379i	0.105999	−	0.601152i
$67$	4.13406	+	5.90405i	0.505056	+	0.721295i	0.988017	−	0.154347i	$-0.0493275\pi$
$67$	4.13406	+	5.90405i	0.505056	+	0.721295i	−0.482961	+	0.875642i	$0.660439\pi$
$68$	−2.09318	−	0.560867i	−0.253836	−	0.0680151i
$69$	−4.45744	+	7.72050i	−0.536612	+	0.929440i
$70$	2.20586	−	7.46341i	0.263651	−	0.892048i
$71$	−4.58689	+	12.6024i	−0.544364	+	1.49563i	0.296850	+	0.954924i	$0.404064\pi$
$71$	−4.58689	+	12.6024i	−0.544364	+	1.49563i	−0.841214	+	0.540703i	$0.818158\pi$
$72$	−0.422618	+	0.906308i	−0.0498060	+	0.106809i
$73$	−0.623799	+	7.13005i	−0.0730101	+	0.834510i	0.868096	+	0.496397i	$0.165344\pi$
$73$	−0.623799	+	7.13005i	−0.0730101	+	0.834510i	−0.941106	+	0.338112i	$0.890212\pi$
$74$	3.10080	−	0.546755i	0.360461	−	0.0635590i
$75$	−4.99674	+	0.180533i	−0.576974	+	0.0208462i
$76$	−1.96991	+	3.88837i	−0.225964	+	0.446027i
$77$	−12.2047	−	12.2047i	−1.39086	−	1.39086i
$78$	3.03736	−	4.33780i	0.343914	−	0.491159i
$79$	−2.42883	+	2.03803i	−0.273265	+	0.229297i	−0.769113	−	0.639113i	$-0.779302\pi$
$79$	−2.42883	+	2.03803i	−0.273265	+	0.229297i	0.495848	+	0.868409i	$0.334857\pi$
$80$	1.54019	+	1.62106i	0.172198	+	0.181240i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	0.504651	+	5.76819i	0.0557294	+	0.636989i
$83$	1.56537	+	5.84206i	0.171822	+	0.641249i	0.997071	+	0.0764800i	$0.0243681\pi$
$83$	1.56537	+	5.84206i	0.171822	+	0.641249i	−0.825249	+	0.564769i	$0.808965\pi$
$84$	1.74023	+	3.01418i	0.189875	+	0.328873i
$85$	4.13309	+	2.52933i	0.448297	+	0.274344i
$86$	−2.79512	−	0.492856i	−0.301406	−	0.0531460i
$87$	−1.50889	+	5.63125i	−0.161770	+	0.603733i
$88$	4.79015	−	1.28352i	0.510631	−	0.136823i
$89$	−11.5493	−	9.69100i	−1.22422	−	1.02724i	−0.998593	−	0.0530302i	$-0.983112\pi$
$89$	−11.5493	−	9.69100i	−1.22422	−	1.02724i	−0.225628	−	0.974213i	$-0.572443\pi$
$90$	1.48065	−	1.67561i	0.156074	−	0.176625i
$91$	−6.30369	−	17.3192i	−0.660806	−	1.81555i
$92$	−8.88095	−	0.776982i	−0.925903	−	0.0810060i
$93$	5.27191	+	3.69143i	0.546672	+	0.382784i
$94$	6.03036			0.621984
$95$	6.68860	−	7.08961i	0.686236	−	0.727379i
$96$	−1.00000			−0.102062
$97$	2.33163	+	1.63262i	0.236741	+	0.165768i	0.685927	−	0.727671i	$-0.259397\pi$
$97$	2.33163	+	1.63262i	0.236741	+	0.165768i	−0.449186	+	0.893438i	$0.648286\pi$
$98$	5.09421	+	0.445686i	0.514593	+	0.0450211i
$99$	−1.69612	−	4.66005i	−0.170467	−	0.468353i
$100$	−2.27533	−	4.45229i	−0.227533	−	0.445229i
$101$	−0.981825	−	0.823849i	−0.0976952	−	0.0819760i	0.592632	−	0.805473i	$-0.298089\pi$
$101$	−0.981825	−	0.823849i	−0.0976952	−	0.0819760i	−0.690327	+	0.723497i	$0.742533\pi$
$102$	−2.09318	+	0.560867i	−0.207256	+	0.0555341i
$103$	1.91135	−	7.13326i	0.188331	−	0.702861i	−0.805562	−	0.592512i	$-0.798136\pi$
$103$	1.91135	−	7.13326i	0.188331	−	0.702861i	0.993893	−	0.110349i	$-0.0351970\pi$
$104$	5.21503	+	0.919550i	0.511376	+	0.0901693i
$105$	−1.82137	−	7.56644i	−0.177748	−	0.738408i
$106$	0.784769	+	1.35926i	0.0762235	+	0.132023i
$107$	−1.32651	−	4.95059i	−0.128238	−	0.478592i	0.871696	−	0.490047i	$-0.163020\pi$
$107$	−1.32651	−	4.95059i	−0.128238	−	0.478592i	−0.999934	+	0.0114549i	$0.996354\pi$
$108$	0.0871557	+	0.996195i	0.00838657	+	0.0958589i
$109$	−7.29685	−	2.65584i	−0.698911	−	0.254383i	−0.0319654	−	0.999489i	$-0.510177\pi$
$109$	−7.29685	−	2.65584i	−0.698911	−	0.254383i	−0.666946	+	0.745106i	$0.732399\pi$
$110$	−11.0853	−	0.283580i	−1.05694	−	0.0270383i
$111$	2.41200	−	2.02391i	0.228937	−	0.192101i
$112$	−1.99632	+	2.85103i	−0.188634	+	0.269397i
$113$	−8.63880	−	8.63880i	−0.812670	−	0.812670i	0.172363	−	0.985033i	$-0.444860\pi$
$113$	−8.63880	−	8.63880i	−0.812670	−	0.812670i	−0.985033	+	0.172363i	$0.944860\pi$
$114$	0.238193	+	4.35239i	0.0223088	+	0.407638i
$115$	18.5516	+	7.29473i	1.72994	+	0.680237i
$116$	−5.74133	+	1.01235i	−0.533069	+	0.0939944i
$117$	0.461531	−	5.27533i	0.0426686	−	0.487704i
$118$	4.31902	−	9.26217i	0.397598	−	0.852652i
$119$	−2.57961	+	7.08741i	−0.236472	+	0.649702i
$120$	2.14437	+	0.633783i	0.195753	+	0.0578562i
$121$	−6.79646	+	11.7718i	−0.617860	+	1.07017i
$122$	−2.80933	−	0.752758i	−0.254345	−	0.0681515i
$123$	3.32113	+	4.74307i	0.299456	+	0.427668i
$124$	−1.11757	+	6.33804i	−0.100361	+	0.569173i
$125$	2.05737	+	10.9894i	0.184017	+	0.982923i
$126$	3.01418	+	1.74023i	0.268524	+	0.155032i
$127$	1.41517	−	0.123811i	0.125576	−	0.0109864i	−0.0241946	−	0.999707i	$-0.507702\pi$
$127$	1.41517	−	0.123811i	0.125576	−	0.0109864i	0.149770	+	0.988721i	$0.452147\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	−2.66708	+	0.970736i	−0.234823	+	0.0854686i
$130$	−10.6002	−	5.27705i	−0.929695	−	0.462828i
$131$	−3.24975	−	18.4302i	−0.283932	−	1.61026i	−0.709077	−	0.705131i	$-0.750888\pi$
$131$	−3.24975	−	18.4302i	−0.283932	−	1.61026i	0.425146	−	0.905125i	$-0.360223\pi$
$132$	3.50663	−	3.50663i	0.305213	−	0.305213i
$133$	12.8843	+	8.00964i	1.11721	+	0.694524i
$134$			7.20752i			0.622635i
$135$	0.444477	−	2.19145i	0.0382545	−	0.188610i
$136$	−1.39294	−	1.66004i	−0.119443	−	0.142347i
$137$	13.1237	+	6.11970i	1.12124	+	0.522841i	0.892681	−	0.450689i	$-0.148822\pi$
$137$	13.1237	+	6.11970i	1.12124	+	0.522841i	0.228556	+	0.973531i	$0.426600\pi$
$138$	−8.07962	+	3.76759i	−0.687783	+	0.320718i
$139$	10.6743	−	12.7211i	0.905381	−	1.07899i	−0.0911558	−	0.995837i	$-0.529056\pi$
$139$	10.6743	−	12.7211i	0.905381	−	1.07899i	0.996537	−	0.0831543i	$-0.0264994\pi$
$140$	6.08777	−	4.84844i	0.514511	−	0.409768i
$141$	5.22244	−	3.01518i	0.439809	−	0.253924i
$142$	−10.9858	+	7.69233i	−0.921907	+	0.645526i
$143$	−21.5117	+	15.0627i	−1.79890	+	1.25960i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	12.9531	+	1.46790i	1.07570	+	0.121902i
$146$	−4.60062	+	5.48280i	−0.380750	+	0.453760i
$147$	4.63456	−	2.16113i	0.382252	−	0.178247i
$148$	2.85364	+	1.33067i	0.234567	+	0.109381i
$149$	−2.10956	−	2.51407i	−0.172822	−	0.205961i	0.672680	−	0.739933i	$-0.265143\pi$
$149$	−2.10956	−	2.51407i	−0.172822	−	0.205961i	−0.845502	+	0.533973i	$0.820699\pi$
$150$	−4.19664	−	2.71813i	−0.342654	−	0.221934i
$151$		−	19.1680i		−	1.55987i	−0.625860	−	0.779935i	$-0.715252\pi$
$151$		−	19.1680i		−	1.55987i	0.625860	−	0.779935i	$-0.284748\pi$
$152$	−3.84394	+	2.05527i	−0.311784	+	0.166705i
$153$	−1.53232	+	1.53232i	−0.123881	+	0.123881i
$154$	−2.99718	−	16.9979i	−0.241520	−	1.36973i
$155$	6.41342	−	12.8828i	0.515138	−	1.03477i
$156$	4.97612	−	1.81116i	0.398409	−	0.145009i
$157$	6.37097	+	13.6626i	0.508458	+	1.09039i	0.978215	+	0.207596i	$0.0665641\pi$
$157$	6.37097	+	13.6626i	0.508458	+	1.09039i	−0.469756	+	0.882796i	$0.655658\pi$
$158$	−3.15855	+	0.276338i	−0.251281	+	0.0219842i
$159$	1.35926	+	0.784769i	0.107796	+	0.0622362i
$160$	0.331847	+	2.21131i	0.0262348	+	0.174819i
$161$	−5.38794	+	30.5566i	−0.424630	+	2.40819i
$162$	0.573576	+	0.819152i	0.0450644	+	0.0643587i
$163$	−8.36182	−	2.24054i	−0.654949	−	0.175493i	−0.0839833	−	0.996467i	$-0.526764\pi$
$163$	−8.36182	−	2.24054i	−0.654949	−	0.175493i	−0.570965	+	0.820974i	$0.693431\pi$
$164$	−2.89511	+	5.01448i	−0.226070	+	0.391565i
$165$	−9.74195	+	5.29707i	−0.758410	+	0.412376i
$166$	−2.06859	+	5.68340i	−0.160553	+	0.441117i
$167$	−4.04687	+	8.67854i	−0.313156	+	0.671566i	−0.998388	−	0.0567594i	$-0.981923\pi$
$167$	−4.04687	+	8.67854i	−0.313156	+	0.671566i	0.685232	+	0.728325i	$0.259701\pi$
$168$	−0.303343	+	3.46723i	−0.0234034	+	0.267502i
$169$	−14.8136	+	2.61203i	−1.13951	+	0.200926i
$170$	1.93487	+	4.44255i	0.148398	+	0.340728i
$171$	2.38247	+	3.65018i	0.182192	+	0.279136i
$172$	−2.00694	−	2.00694i	−0.153028	−	0.153028i
$173$	−7.44595	+	10.6339i	−0.566105	+	0.808481i	−0.995513	−	0.0946292i	$-0.969833\pi$
$173$	−7.44595	+	10.6339i	−0.566105	+	0.808481i	0.429408	+	0.903111i	$0.358722\pi$
$174$	−4.46596	+	3.74738i	−0.338564	+	0.284089i
$175$	−16.1273	+	6.53852i	−1.21911	+	0.494266i
$176$	4.66005	+	1.69612i	0.351265	+	0.127850i
$177$	−0.890703	−	10.1808i	−0.0669493	−	0.765235i
$178$	−3.90209	−	14.5628i	−0.292474	−	1.09153i
$179$	−9.46891	−	16.4006i	−0.707740	−	1.22584i	−0.965694	−	0.259684i	$-0.916382\pi$
$179$	−9.46891	−	16.4006i	−0.707740	−	1.22584i	0.257954	−	0.966157i	$-0.416952\pi$
$180$	2.17397	−	0.523313i	0.162038	−	0.0390054i
$181$	−9.40383	−	1.65815i	−0.698981	−	0.123249i	−0.187145	−	0.982332i	$-0.559923\pi$
$181$	−9.40383	−	1.65815i	−0.698981	−	0.123249i	−0.511836	+	0.859083i	$0.671035\pi$
$182$	4.77023	−	17.8027i	0.353593	−	1.31963i
$183$	−2.80933	+	0.752758i	−0.207672	+	0.0556455i
$184$	−6.82919	−	5.73037i	−0.503454	−	0.422448i
$185$	−5.27589	−	4.66204i	−0.387891	−	0.342760i
$186$	2.20118	+	6.04769i	0.161398	+	0.443438i
$187$	10.7057	+	0.936623i	0.782875	+	0.0684927i
$188$	4.93978	+	3.45887i	0.360270	+	0.252264i
$189$	3.48047			0.253167
$190$	9.54542	−	1.97105i	0.692497	−	0.142995i
$191$	13.6931			0.990800			0.495400	−	0.868665i	$-0.335021\pi$
$191$	13.6931			0.990800			0.495400	+	0.868665i	$0.335021\pi$
$192$	−0.819152	−	0.573576i	−0.0591172	−	0.0413943i
$193$	12.8346	+	1.12289i	0.923857	+	0.0808270i	0.539148	−	0.842211i	$-0.318746\pi$
$193$	12.8346	+	1.12289i	0.923857	+	0.0808270i	0.384709	+	0.923038i	$0.374302\pi$
$194$	0.973523	+	2.67473i	0.0698949	+	0.192035i
$195$	−11.8185	+	0.730017i	−0.846342	+	0.0522776i
$196$	3.91730	+	3.28700i	0.279807	+	0.234786i
$197$	18.5877	−	4.98056i	1.32432	−	0.354850i	0.473725	−	0.880673i	$-0.342909\pi$
$197$	18.5877	−	4.98056i	1.32432	−	0.354850i	0.850594	+	0.525822i	$0.176242\pi$
$198$	1.28352	−	4.79015i	0.0912155	−	0.340421i
$199$	−21.9422	−	3.86900i	−1.55544	−	0.274266i	−0.671192	−	0.741284i	$-0.734217\pi$
$199$	−21.9422	−	3.86900i	−1.55544	−	0.274266i	−0.884248	+	0.467018i	$0.845328\pi$
$200$	0.689884	−	4.95218i	0.0487822	−	0.350172i
$201$	3.60376	+	6.24189i	0.254190	+	0.440269i
$202$	−0.331724	−	1.23801i	−0.0233400	−	0.0871060i
$203$	1.76846	+	20.2136i	0.124121	+	1.41871i
$204$	−2.03634	−	0.741166i	−0.142572	−	0.0518920i
$205$	9.38627	−	8.91802i	0.655566	−	0.622861i
$206$	5.65716	−	4.74692i	0.394153	−	0.330734i
$207$	−5.11336	+	7.30263i	−0.355403	+	0.507568i
$208$	3.74447	+	3.74447i	0.259632	+	0.259632i
$209$	6.27218	−	20.6864i	0.433856	−	1.43091i
$210$	2.84795	−	7.24276i	0.196527	−	0.499798i
$211$	8.02794	−	1.41554i	0.552666	−	0.0974499i	0.109661	−	0.993969i	$-0.465023\pi$
$211$	8.02794	−	1.41554i	0.552666	−	0.0974499i	0.443005	+	0.896519i	$0.353912\pi$
$212$	−0.136794	+	1.56357i	−0.00939507	+	0.107386i
$213$	−5.66781	+	12.1546i	−0.388352	+	0.832823i
$214$	1.75293	−	4.81614i	0.119828	−	0.329225i
$215$	3.03166	+	5.57559i	0.206757	+	0.380252i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	21.6364	+	5.79746i	1.46878	+	0.393557i
$218$	−4.45390	−	6.36083i	−0.301656	−	0.430810i
$219$	−1.24285	+	7.04855i	−0.0839840	+	0.476297i
$220$	−8.91790	−	6.59057i	−0.601245	−	0.444336i
$221$	9.93802	+	5.73772i	0.668503	+	0.385961i
$222$	3.13666	−	0.274422i	0.210519	−	0.0184180i
$223$	−6.47447	−	13.8845i	−0.433563	−	0.929778i	−0.994774	−	0.102105i	$-0.967442\pi$
$223$	−6.47447	−	13.8845i	−0.433563	−	0.929778i	0.561211	−	0.827673i	$-0.310336\pi$
$224$	−3.27057	+	1.19039i	−0.218524	+	0.0795363i
$225$	−4.99346	−	0.255648i	−0.332897	−	0.0170432i
$226$	−2.12148	−	12.0315i	−0.141119	−	0.800324i
$227$	16.3093	−	16.3093i	1.08249	−	1.08249i	0.0862104	−	0.996277i	$-0.472524\pi$
$227$	16.3093	−	16.3093i	1.08249	−	1.08249i	0.996277	−	0.0862104i	$-0.0274757\pi$
$228$	−2.30131	+	3.70189i	−0.152408	+	0.245164i
$229$			21.4178i			1.41533i	0.706548	+	0.707665i	$0.250251\pi$
$229$			21.4178i			1.41533i	−0.706548	+	0.707665i	$0.749749\pi$
$230$	11.0125	+	16.6162i	0.726142	+	1.09564i
$231$	−11.0946	−	13.2220i	−0.729969	−	0.869943i
$232$	−5.28368	−	2.46382i	−0.346891	−	0.161758i
$233$	−7.00994	+	3.26879i	−0.459236	+	0.214145i	−0.638448	−	0.769665i	$-0.720423\pi$
$233$	−7.00994	+	3.26879i	−0.459236	+	0.214145i	0.179212	+	0.983811i	$0.442645\pi$
$234$	3.40387	−	4.05657i	0.222518	−	0.265186i
$235$	−8.40054	−	10.5478i	−0.547991	−	0.688065i
$236$	8.85050	−	5.10984i	0.576118	−	0.332622i
$237$	−2.59722	+	1.81859i	−0.168707	+	0.118130i
$238$	−6.17826	+	4.32606i	−0.400477	+	0.280417i
$239$	−0.657773	+	0.379765i	−0.0425478	+	0.0245650i	−0.521123	−	0.853482i	$-0.674487\pi$
$239$	−0.657773	+	0.379765i	−0.0425478	+	0.0245650i	0.478575	+	0.878047i	$0.341153\pi$
$240$	1.39304	+	1.74912i	0.0899205	+	0.112905i
$241$	−9.68459	+	11.5416i	−0.623839	+	0.743463i	−0.981725	−	0.190303i	$-0.939053\pi$
$241$	−9.68459	+	11.5416i	−0.623839	+	0.743463i	0.357886	+	0.933765i	$0.383498\pi$
$242$	−12.3194	+	5.74462i	−0.791919	+	0.369278i
$243$	0.906308	+	0.422618i	0.0581397	+	0.0271110i
$244$	−1.86951	−	2.22799i	−0.119683	−	0.142632i
$245$	−6.31689	−	9.53126i	−0.403571	−	0.608930i
$246$			5.79022i			0.369171i
$247$	15.4055	−	17.1893i	0.980226	−	1.09373i
$248$	−4.55081	+	4.55081i	−0.288977	+	0.288977i
$249$	1.05025	+	5.95626i	0.0665568	+	0.377463i
$250$	−4.61797	+	10.1821i	−0.292066	+	0.643970i
$251$	−9.37664	+	3.41282i	−0.591848	+	0.215415i	−0.620542	−	0.784173i	$-0.713087\pi$
$251$	−9.37664	+	3.41282i	−0.591848	+	0.215415i	0.0286939	+	0.999588i	$0.490865\pi$
$252$	1.47091	+	3.15438i	0.0926586	+	0.198707i
$253$	44.0417	−	3.85315i	2.76888	−	0.242246i
$254$	1.23025	+	0.710286i	0.0771928	+	0.0445673i
$255$	3.89692	+	2.87993i	0.244035	+	0.180348i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.53197	+	2.18788i	0.0955618	+	0.136476i	0.864086	−	0.503345i	$-0.167897\pi$
$257$	1.53197	+	2.18788i	0.0955618	+	0.136476i	−0.768524	+	0.639821i	$0.779008\pi$
$258$	−2.74153	−	0.734592i	−0.170680	−	0.0457337i
$259$	5.47937	−	9.49055i	0.340472	−	0.589714i
$260$	−5.65635	−	10.4027i	−0.350792	−	0.645148i
$261$	−1.99394	+	5.47831i	−0.123422	+	0.339099i
$262$	7.90910	−	16.9611i	0.488626	−	1.04786i
$263$	1.91082	−	21.8408i	0.117826	−	1.34676i	−0.675227	−	0.737610i	$-0.735954\pi$
$263$	1.91082	−	21.8408i	0.117826	−	1.34676i	0.793053	−	0.609152i	$-0.208490\pi$
$264$	4.88379	−	0.861143i	0.300576	−	0.0529997i
$265$	1.28430	−	3.26616i	0.0788938	−	0.200639i
$266$	5.96007	+	13.9512i	0.365435	+	0.855406i
$267$	−10.6607	−	10.6607i	−0.652425	−	0.652425i
$268$	−4.13406	+	5.90405i	−0.252528	+	0.360647i
$269$	−12.4900	+	10.4803i	−0.761526	+	0.638996i	−0.938524	−	0.345215i	$-0.887806\pi$
$269$	−12.4900	+	10.4803i	−0.761526	+	0.638996i	0.176998	+	0.984211i	$0.443361\pi$
$270$	1.62106	−	1.54019i	0.0986544	−	0.0937328i
$271$	−4.81506	−	1.75254i	−0.292494	−	0.106459i	0.191606	−	0.981472i	$-0.438631\pi$
$271$	−4.81506	−	1.75254i	−0.292494	−	0.106459i	−0.484100	+	0.875013i	$0.660853\pi$
$272$	−0.188869	−	2.15878i	−0.0114518	−	0.130895i
$273$	−4.77023	−	17.8027i	−0.288707	−	1.07747i
$274$	7.24022	+	12.5404i	0.437398	+	0.757596i
$275$	14.9463	+	19.7846i	0.901295	+	1.19306i
$276$	−8.77943	−	1.54805i	−0.528460	−	0.0931817i
$277$	1.51938	−	5.67042i	0.0912909	−	0.340702i	−0.905140	−	0.425113i	$-0.860234\pi$
$277$	1.51938	−	5.67042i	0.0912909	−	0.340702i	0.996431	+	0.0844110i	$0.0269009\pi$
$278$	16.0404	−	4.29801i	0.962039	−	0.257778i
$279$	4.93012	+	4.13686i	0.295159	+	0.247668i
$280$	7.76776	−	0.479806i	0.464213	−	0.0286739i
$281$	3.41499	+	9.38262i	0.203721	+	0.559720i	0.998912	−	0.0466399i	$-0.0148513\pi$
$281$	3.41499	+	9.38262i	0.203721	+	0.559720i	−0.795190	+	0.606360i	$0.792629\pi$
$282$	6.00741	+	0.525580i	0.357736	+	0.0312978i
$283$	25.7443	+	18.0263i	1.53034	+	1.07155i	0.969944	+	0.243327i	$0.0782388\pi$
$283$	25.7443	+	18.0263i	1.53034	+	1.07155i	0.560393	+	0.828227i	$0.310650\pi$
$284$	−13.4112			−0.795807
$285$	7.28105	−	6.47968i	0.431292	−	0.383823i
$286$	−26.2609			−1.55284
$287$	16.5081	+	11.5591i	0.974443	+	0.682312i
$288$	−0.996195	−	0.0871557i	−0.0587013	−	0.00513570i
$289$	4.20822	+	11.5620i	0.247542	+	0.680117i
$290$	9.76863	+	8.63205i	0.573634	+	0.506891i
$291$	2.18046	+	1.82962i	0.127821	+	0.107254i
$292$	−6.91341	+	1.85244i	−0.404577	+	0.108406i
$293$	−2.62865	+	9.81025i	−0.153567	+	0.573121i	0.845656	+	0.533728i	$0.179209\pi$
$293$	−2.62865	+	9.81025i	−0.153567	+	0.573121i	−0.999224	+	0.0393934i	$0.987457\pi$
$294$	5.03598	+	0.887979i	0.293704	+	0.0517880i
$295$	−22.2173	+	5.34808i	−1.29354	+	0.311378i
$296$	1.57432	+	2.72680i	0.0915055	+	0.158492i
$297$	−1.28352	−	4.79015i	−0.0744772	−	0.277953i
$298$	−0.286035	−	3.26940i	−0.0165696	−	0.189391i
$299$	44.3615	+	16.1463i	2.56549	+	0.933762i
$300$	−1.87863	−	4.63365i	−0.108463	−	0.267524i
$301$	−7.56731	+	6.34973i	−0.436172	+	0.365992i
$302$	10.9943	−	15.7015i	0.632652	−	0.903521i
$303$	−0.906286	−	0.906286i	−0.0520648	−	0.0520648i
$304$	−4.32763	−	0.521209i	−0.248206	−	0.0298934i
$305$	2.59685	+	5.96249i	0.148695	+	0.341411i
$306$	−2.13410	+	0.376300i	−0.121999	+	0.0215116i
$307$	0.461440	−	5.27429i	0.0263358	−	0.301019i	−0.971591	−	0.236665i	$-0.923946\pi$
$307$	0.461440	−	5.27429i	0.0263358	−	0.301019i	0.997927	−	0.0643544i	$-0.0204988\pi$
$308$	7.29443	−	15.6430i	0.415639	−	0.891340i
$309$	2.52578	−	6.93953i	0.143687	−	0.394776i
$310$	12.6428	−	6.87439i	0.718065	−	0.390439i
$311$	11.4346	−	19.8053i	0.648396	−	1.12305i	−0.335111	−	0.942179i	$-0.608774\pi$
$311$	11.4346	−	19.8053i	0.648396	−	1.12305i	0.983506	−	0.180875i	$-0.0578930\pi$
$312$	5.11504	+	1.37057i	0.289582	+	0.0775933i
$313$	5.95511	+	8.50478i	0.336603	+	0.480719i	0.951396	−	0.307969i	$-0.0996495\pi$
$313$	5.95511	+	8.50478i	0.336603	+	0.480719i	−0.614793	+	0.788688i	$0.710761\pi$
$314$	−2.61774	+	14.8460i	−0.147728	+	0.837806i
$315$	−1.15499	−	7.69639i	−0.0650760	−	0.433642i
$316$	−2.74584	−	1.58531i	−0.154465	−	0.0891806i
$317$	−4.28752	+	0.375109i	−0.240811	+	0.0210682i	−0.206922	−	0.978357i	$-0.566345\pi$
$317$	−4.28752	+	0.375109i	−0.240811	+	0.0210682i	−0.0338888	+	0.999426i	$0.510789\pi$
$318$	0.663316	+	1.42248i	0.0371969	+	0.0797690i
$319$	27.1676	−	9.88821i	1.52110	−	0.553633i
$320$	−0.996520	+	2.00174i	−0.0557072	+	0.111900i
$321$	−0.889987	−	5.04737i	−0.0496742	−	0.281717i
$322$	−21.9401	+	21.9401i	−1.22267	+	1.22267i
$323$	−9.35085	+	1.33624i	−0.520295	+	0.0743501i
$324$			1.00000i			0.0555556i
$325$	5.53624	+	25.8921i	0.307095	+	1.43624i
$326$	−5.56448	−	6.63149i	−0.308188	−	0.367284i
$327$	−7.03761	−	3.28169i	−0.389181	−	0.181478i
$328$	−5.24772	+	2.44705i	−0.289757	+	0.135116i
$329$	13.4911	−	16.0781i	0.743790	−	0.886415i
$330$	−11.0184	−	1.24865i	−0.606544	−	0.0687359i
$331$	−19.8298	+	11.4487i	−1.08994	+	0.629279i	−0.933562	−	0.358417i	$-0.883317\pi$
$331$	−19.8298	+	11.4487i	−1.08994	+	0.629279i	−0.156382	+	0.987697i	$0.549983\pi$
$332$	−4.95435	+	3.46907i	−0.271905	+	0.190390i
$333$	2.57921	−	1.80599i	0.141340	−	0.0989674i
$334$	−8.29281	+	4.78786i	−0.453762	+	0.261980i
$335$	12.6068	−	10.0404i	0.688785	−	0.548564i
$336$	−2.23720	+	2.66619i	−0.122049	+	0.145453i
$337$	0.564418	−	0.263192i	0.0307458	−	0.0143370i	−0.407185	−	0.913346i	$-0.633489\pi$
$337$	0.564418	−	0.263192i	0.0307458	−	0.0143370i	0.437930	+	0.899009i	$0.355712\pi$
$338$	−13.6328	−	6.35707i	−0.741525	−	0.345779i
$339$	−7.85301	−	9.35885i	−0.426517	−	0.508303i
$340$	−0.963192	+	4.74892i	−0.0522364	+	0.257546i
$341$		−	31.9160i		−	1.72835i
$342$	−0.142049	+	4.35658i	−0.00768111	+	0.235577i
$343$	−4.64238	+	4.64238i	−0.250665	+	0.250665i
$344$	−0.492856	−	2.79512i	−0.0265730	−	0.150703i
$345$	17.8452	+	8.88385i	0.960754	+	0.478290i
$346$	−12.1987	+	4.43997i	−0.655807	+	0.238694i
$347$	−5.95236	−	12.7649i	−0.319539	−	0.685254i	0.679278	−	0.733881i	$-0.262293\pi$
$347$	−5.95236	−	12.7649i	−0.319539	−	0.685254i	−0.998817	+	0.0486269i	$0.984515\pi$
$348$	−5.80771	+	0.508109i	−0.311326	+	0.0272375i
$349$	−15.0579	−	8.69370i	−0.806033	−	0.465363i	0.0395434	−	0.999218i	$-0.487410\pi$
$349$	−15.0579	−	8.69370i	−0.806033	−	0.465363i	−0.845576	+	0.533854i	$0.820743\pi$
$350$	−16.9610	−	3.89419i	−0.906606	−	0.208153i
$351$	0.919550	−	5.21503i	0.0490820	−	0.278358i
$352$	2.84444	+	4.06228i	0.151609	+	0.216520i
$353$	18.8428	+	5.04892i	1.00290	+	0.268727i	0.722661	−	0.691203i	$-0.242919\pi$
$353$	18.8428	+	5.04892i	1.00290	+	0.268727i	0.280241	+	0.959930i	$0.409585\pi$
$354$	5.10984	−	8.85050i	0.271585	−	0.470399i
$355$	28.7585	+	8.49977i	1.52634	+	0.451121i
$356$	5.15647	−	14.1673i	0.273292	−	0.750865i
$357$	−3.18750	+	6.83561i	−0.168700	+	0.361779i
$358$	1.65054	−	18.8658i	0.0872337	−	0.997086i
$359$	−32.0683	+	5.65450i	−1.69250	+	0.298433i	−0.935064	−	0.354478i	$-0.884659\pi$
$359$	−32.0683	+	5.65450i	−1.69250	+	0.298433i	−0.757435	+	0.652911i	$0.773548\pi$
$360$	2.08097	+	0.818265i	0.109677	+	0.0431264i
$361$	−1.23769	+	18.9596i	−0.0651418	+	0.997876i
$362$	−6.75209	−	6.75209i	−0.354882	−	0.354882i
$363$	−7.79658	+	11.1347i	−0.409214	+	0.584419i
$364$	14.1188	−	11.8471i	0.740025	−	0.620955i
$365$	15.9990	+	0.409278i	0.837423	+	0.0214226i
$366$	−2.73303	−	0.994743i	−0.142858	−	0.0519961i
$367$	2.72506	+	31.1476i	0.142247	+	1.62589i	0.646905	+	0.762571i	$0.276063\pi$
$367$	2.72506	+	31.1476i	0.142247	+	1.62589i	−0.504658	+	0.863319i	$0.668381\pi$
$368$	−2.30734	−	8.61110i	−0.120278	−	0.448885i
$369$	2.89511	+	5.01448i	0.150713	+	0.261043i
$370$	−1.64772	−	6.84505i	−0.0856610	−	0.355857i
$371$	5.37974	+	0.948593i	0.279302	+	0.0492485i
$372$	−1.66571	+	6.21652i	−0.0863632	+	0.322312i
$373$	−24.4694	+	6.55654i	−1.26698	+	0.339485i	−0.828871	−	0.559439i	$-0.811016\pi$
$373$	−24.4694	+	6.55654i	−1.26698	+	0.339485i	−0.438104	+	0.898924i	$0.644350\pi$
$374$	8.23233	+	6.90775i	0.425684	+	0.357191i
$375$	1.09175	+	11.1269i	0.0563777	+	0.574591i
$376$	2.06250	+	5.66668i	0.106365	+	0.292237i
$377$	30.7546	+	2.69068i	1.58394	+	0.138577i
$378$	2.85103	+	1.99632i	0.146641	+	0.102679i
$379$	−25.1101			−1.28982			−0.644909	−	0.764259i	$-0.723105\pi$
$379$	−25.1101			−1.28982			−0.644909	+	0.764259i	$0.723105\pi$
$380$	8.94969	+	3.86044i	0.459110	+	0.198036i
$381$	1.42057			0.0727781
$382$	11.2168	+	7.85406i	0.573899	+	0.401848i
$383$	16.1762	+	1.41523i	0.826563	+	0.0723149i	0.492583	−	0.870265i	$-0.336053\pi$
$383$	16.1762	+	1.41523i	0.826563	+	0.0723149i	0.333980	+	0.942580i	$0.391608\pi$
$384$	−0.342020	−	0.939693i	−0.0174536	−	0.0479535i
$385$	−25.5562	+	28.9212i	−1.30246	+	1.47396i
$386$	9.86946	+	8.28146i	0.502342	+	0.421515i
$387$	−2.74153	+	0.734592i	−0.139360	+	0.0373414i
$388$	−0.736700	+	2.74940i	−0.0374003	+	0.139580i
$389$	−8.02384	−	1.41482i	−0.406825	−	0.0717342i	−0.0335089	−	0.999438i	$-0.510668\pi$
$389$	−8.02384	−	1.41482i	−0.406825	−	0.0717342i	−0.373316	+	0.927704i	$0.621779\pi$
$390$	−10.0999	−	6.18083i	−0.511428	−	0.312979i
$391$	−9.65937	−	16.7305i	−0.488495	−	0.846099i
$392$	1.32352	+	4.93943i	0.0668476	+	0.249479i
$393$	−1.63108	−	18.6433i	−0.0822771	−	0.940431i
$394$	18.0829	+	6.58163i	0.911003	+	0.331578i
$395$	4.88334	+	5.13975i	0.245708	+	0.258609i
$396$	3.79891	−	3.18766i	0.190902	−	0.160186i
$397$	−5.30297	+	7.57343i	−0.266148	+	0.380099i	−0.929875	−	0.367876i	$-0.880085\pi$
$397$	−5.30297	+	7.57343i	−0.266148	+	0.380099i	0.663726	+	0.747975i	$0.268974\pi$
$398$	−15.7548	−	15.7548i	−0.789718	−	0.789718i
$399$	12.1372	+	9.10210i	0.607620	+	0.455675i
$400$	3.40557	−	3.66088i	0.170279	−	0.183044i
$401$	23.6849	−	4.17629i	1.18277	−	0.208554i	0.452531	−	0.891749i	$-0.350521\pi$
$401$	23.6849	−	4.17629i	1.18277	−	0.208554i	0.730236	+	0.683195i	$0.239410\pi$
$402$	−0.628177	+	7.18009i	−0.0313306	+	0.358110i
$403$	14.4031	−	30.8876i	0.717472	−	1.53862i
$404$	0.438361	−	1.20439i	0.0218093	−	0.0599205i
$405$	0.633783	−	2.14437i	0.0314929	−	0.106555i
$406$	−10.1454	+	17.5723i	−0.503507	+	0.872100i
$407$	−15.0824	−	4.04133i	−0.747609	−	0.200321i
$408$	−1.24295	−	1.77512i	−0.0615354	−	0.0878817i
$409$	4.54142	−	25.7556i	0.224559	−	1.27353i	−0.638969	−	0.769233i	$-0.720639\pi$
$409$	4.54142	−	25.7556i	0.224559	−	1.27353i	0.863527	−	0.504302i	$-0.168250\pi$
$410$	12.8039	−	1.92147i	0.632342	−	0.0948946i
$411$	12.5404	+	7.24022i	0.618574	+	0.357134i
$412$	7.35680	−	0.643636i	0.362443	−	0.0317097i
$413$	−15.0322	−	32.2367i	−0.739687	−	1.58626i
$414$	−8.37724	+	3.04907i	−0.411719	+	0.149853i
$415$	12.8226	−	4.29899i	0.629436	−	0.211029i
$416$	0.919550	+	5.21503i	0.0450847	+	0.255688i
$417$	11.7424	−	11.7424i	0.575027	−	0.575027i
$418$	17.0031	−	13.3477i	0.831648	−	0.652857i
$419$			19.4643i			0.950891i	0.879745	+	0.475446i	$0.157713\pi$
$419$			19.4643i			0.950891i	−0.879745	+	0.475446i	$0.842287\pi$
$420$	6.48718	−	4.29941i	0.316542	−	0.209789i
$421$	−11.7040	−	13.9483i	−0.570418	−	0.679798i	0.401298	−	0.915947i	$-0.368559\pi$
$421$	−11.7040	−	13.9483i	−0.570418	−	0.679798i	−0.971717	+	0.236149i	$0.924115\pi$
$422$	7.38802	+	3.44509i	0.359643	+	0.167704i
$423$	5.46536	−	2.54854i	0.265735	−	0.123914i
$424$	−1.00888	+	1.20234i	−0.0489955	+	0.0583906i
$425$	5.07522	−	9.57298i	0.246184	−	0.464358i
$426$	−11.6144	+	6.70559i	−0.562720	+	0.324887i
$427$	−8.29204	+	5.80615i	−0.401280	+	0.280979i
$428$	4.19834	−	2.93971i	0.202935	−	0.142096i
$429$	−22.7426	+	13.1305i	−1.09803	+	0.633945i
$430$	−0.714636	+	6.30614i	−0.0344628	+	0.304109i
$431$	12.6244	−	15.0452i	0.608097	−	0.724702i	−0.370878	−	0.928682i	$-0.620943\pi$
$431$	12.6244	−	15.0452i	0.608097	−	0.724702i	0.978975	+	0.203980i	$0.0653877\pi$
$432$	−0.906308	+	0.422618i	−0.0436048	+	0.0203332i
$433$	−19.4076	−	9.04989i	−0.932667	−	0.434910i	−0.103953	−	0.994582i	$-0.533149\pi$
$433$	−19.4076	−	9.04989i	−0.932667	−	0.434910i	−0.828714	+	0.559672i	$0.810927\pi$
$434$	14.3982	+	17.1591i	0.691137	+	0.823665i
$435$	12.7759	+	2.59125i	0.612558	+	0.124241i
$436$		−	7.76514i		−	0.371883i
$437$	−36.9293	+	12.0935i	−1.76657	+	0.578512i
$438$	−5.06097	+	5.06097i	−0.241822	+	0.241822i
$439$	−4.54241	−	25.7613i	−0.216797	−	1.22952i	−0.877760	−	0.479100i	$-0.840963\pi$
$439$	−4.54241	−	25.7613i	−0.216797	−	1.22952i	0.660963	−	0.750418i	$-0.270148\pi$
$440$	−3.52492	−	10.5138i	−0.168044	−	0.501225i
$441$	4.80528	−	1.74898i	0.228823	−	0.0832847i
$442$	4.84973	+	10.4003i	0.230678	+	0.494691i
$443$	10.8810	−	0.951966i	0.516973	−	0.0452293i	0.174316	−	0.984690i	$-0.444229\pi$
$443$	10.8810	−	0.951966i	0.516973	−	0.0452293i	0.342657	+	0.939461i	$0.388673\pi$
$444$	2.72680	+	1.57432i	0.129408	+	0.0747139i
$445$	−20.0364	+	27.1118i	−0.949815	+	1.28522i
$446$	2.66027	−	15.0872i	0.125968	−	0.714398i
$447$	−1.88241	−	2.68836i	−0.0890351	−	0.127155i
$448$	−3.36188	−	0.900812i	−0.158834	−	0.0425594i
$449$	19.3336	−	33.4867i	0.912407	−	1.58034i	0.101754	−	0.994810i	$-0.467554\pi$
$449$	19.3336	−	33.4867i	0.912407	−	1.58034i	0.810653	−	0.585527i	$-0.199112\pi$
$450$	−3.94377	−	3.07355i	−0.185911	−	0.144888i
$451$	9.82091	−	26.9827i	0.462449	−	1.27057i
$452$	5.16317	−	11.0725i	0.242855	−	0.520805i
$453$	1.67060	−	19.0951i	0.0784918	−	0.897165i
$454$	22.7144	−	4.00517i	1.06604	−	0.187972i
$455$	−37.7843	+	16.4562i	−1.77136	+	0.771480i
$456$	−4.00844	+	1.71243i	−0.187712	+	0.0801920i
$457$	−10.3428	−	10.3428i	−0.483818	−	0.483818i	0.422531	−	0.906349i	$-0.361142\pi$
$457$	−10.3428	−	10.3428i	−0.483818	−	0.483818i	−0.906349	+	0.422531i	$0.861142\pi$
$458$	−12.2848	+	17.5445i	−0.574029	+	0.819799i
$459$	−1.66004	+	1.39294i	−0.0774839	+	0.0650167i
$460$	−0.509783	+	19.9277i	−0.0237688	+	0.929136i
$461$	−15.2600	−	5.55420i	−0.710731	−	0.258685i	−0.0387452	−	0.999249i	$-0.512336\pi$
$461$	−15.2600	−	5.55420i	−0.710731	−	0.258685i	−0.671985	+	0.740564i	$0.734558\pi$
$462$	−1.50432	−	17.1944i	−0.0699871	−	0.799956i
$463$	−4.15183	−	15.4949i	−0.192952	−	0.720107i	−0.992787	−	0.119888i	$-0.961747\pi$
$463$	−4.15183	−	15.4949i	−0.192952	−	0.720107i	0.799835	−	0.600219i	$-0.204920\pi$
$464$	−2.91495	−	5.04884i	−0.135323	−	0.234386i
$465$	7.51183	−	12.2748i	0.348353	−	0.569231i
$466$	−7.61710	−	1.34310i	−0.352855	−	0.0622179i
$467$	−5.33589	+	19.9138i	−0.246915	+	0.921501i	0.725496	+	0.688227i	$0.241611\pi$
$467$	−5.33589	+	19.9138i	−0.246915	+	0.921501i	−0.972411	+	0.233274i	$0.925056\pi$
$468$	5.11504	−	1.37057i	0.236443	−	0.0633547i
$469$	19.2166	+	16.1247i	0.887342	+	0.744568i
$470$	−0.831324	−	13.4586i	−0.0383461	−	0.620801i
$471$	5.15595	+	14.1659i	0.237574	+	0.652728i
$472$	10.1808	+	0.890703i	0.468609	+	0.0409979i
$473$	11.5297	+	8.07321i	0.530138	+	0.371206i
$474$	−3.17062			−0.145631
$475$	−16.7448	−	13.9504i	−0.768303	−	0.640087i
$476$	−7.54226			−0.345699
$477$	1.28569	+	0.900250i	0.0588677	+	0.0412196i
$478$	−0.756641	−	0.0661975i	−0.0346079	−	0.00302780i
$479$	13.3449	+	36.6647i	0.609743	+	1.67525i	0.730786	+	0.682607i	$0.239154\pi$
$479$	13.3449	+	36.6647i	0.609743	+	1.67525i	−0.121043	+	0.992647i	$0.538624\pi$
$480$	0.137857	+	2.23181i	0.00629226	+	0.101868i
$481$	−12.7727	−	10.7176i	−0.582384	−	0.488678i
$482$	−14.5532	+	3.89951i	−0.662879	+	0.177618i
$483$	−8.03062	+	29.9707i	−0.365406	+	1.36371i
$484$	−13.3864	−	2.36039i	−0.608474	−	0.107290i
$485$	3.32228	−	5.42882i	0.150857	−	0.246510i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−9.72368	−	36.2893i	−0.440622	−	1.64442i	−0.727244	−	0.686379i	$-0.759199\pi$
$487$	−9.72368	−	36.2893i	−0.440622	−	1.64442i	0.286622	−	0.958044i	$-0.407468\pi$
$488$	−0.253487	−	2.89737i	−0.0114748	−	0.131158i
$489$	−8.13473	−	2.96080i	−0.367865	−	0.133892i
$490$	0.292417	−	11.4308i	0.0132101	−	0.516390i
$491$	2.13364	−	1.79033i	0.0962896	−	0.0807966i	−0.593372	−	0.804928i	$-0.702204\pi$
$491$	2.13364	−	1.79033i	0.0962896	−	0.0807966i	0.689662	+	0.724132i	$0.257759\pi$
$492$	−3.32113	+	4.74307i	−0.149728	+	0.213834i
$493$	−8.93325	−	8.93325i	−0.402333	−	0.402333i
$494$	22.4788	−	5.24442i	1.01137	−	0.235958i
$495$	−10.1666	+	4.42785i	−0.456953	+	0.199017i
$496$	−6.33804	+	1.11757i	−0.284587	+	0.0501803i
$497$	−4.06818	+	46.4996i	−0.182483	+	2.08579i
$498$	−2.55606	+	5.48148i	−0.114540	+	0.245631i
$499$	4.89237	−	13.4417i	0.219012	−	0.601732i	−0.780720	−	0.624882i	$-0.785147\pi$
$499$	4.89237	−	13.4417i	0.219012	−	0.601732i	0.999732	+	0.0231498i	$0.00736946\pi$
$500$	−9.62301	+	5.69190i	−0.430354	+	0.254549i
$501$	−4.78786	+	8.29281i	−0.213906	+	0.370496i
$502$	−9.63840	−	2.58260i	−0.430183	−	0.115267i
$503$	0.0401622	+	0.0573576i	0.00179075	+	0.00255745i	0.820046	−	0.572297i	$-0.193948\pi$
$503$	0.0401622	+	0.0573576i	0.00179075	+	0.00255745i	−0.818256	+	0.574854i	$0.805059\pi$
$504$	−0.604377	+	3.42759i	−0.0269211	+	0.152677i
$505$	−1.70333	+	2.30482i	−0.0757971	+	0.102563i
$506$	38.2870	+	22.1050i	1.70206	+	0.982686i
$507$	−14.9849	+	1.31101i	−0.665501	+	0.0582238i
$508$	0.600359	+	1.28747i	0.0266366	+	0.0571225i
$509$	−11.7779	+	4.28679i	−0.522045	+	0.190009i	−0.589583	−	0.807708i	$-0.700708\pi$
$509$	−11.7779	+	4.28679i	−0.522045	+	0.190009i	0.0675381	+	0.997717i	$0.478486\pi$
$510$	1.54031	+	4.59428i	0.0682061	+	0.203438i
$511$	4.32570	+	24.5323i	0.191358	+	1.08524i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	2.05527	+	3.84394i	0.0907426	+	0.169714i
$514$			2.67091i			0.117809i
$515$	−16.1836	−	3.28242i	−0.713135	−	0.144641i
$516$	−1.82439	−	2.17422i	−0.0803142	−	0.0957147i
$517$	−27.1034	−	12.6385i	−1.19201	−	0.555842i
$518$	9.93200	−	4.63137i	0.436387	−	0.203491i
$519$	−8.34442	+	9.94449i	−0.366279	+	0.436515i
$520$	1.33334	−	11.7657i	0.0584708	−	0.515962i
$521$	14.9911	−	8.65512i	0.656772	−	0.379188i	−0.134274	−	0.990944i	$-0.542870\pi$
$521$	14.9911	−	8.65512i	0.656772	−	0.379188i	0.791046	+	0.611757i	$0.209537\pi$
$522$	−4.77557	+	3.34389i	−0.209021	+	0.146358i
$523$	0.0443256	−	0.0310371i	0.00193822	−	0.00135716i	−0.572607	−	0.819830i	$-0.694068\pi$
$523$	0.0443256	−	0.0310371i	0.00193822	−	0.00135716i	0.574545	+	0.818473i	$0.305179\pi$
$524$	16.2073	−	9.35727i	0.708018	−	0.408774i
$525$	−16.6358	+	5.10805i	−0.726045	+	0.222934i
$526$	14.0926	−	16.7949i	0.614468	−	0.732294i
$527$	−12.6399	+	5.89408i	−0.550602	+	0.256750i
$528$	4.49449	+	2.09582i	0.195598	+	0.0912087i
$529$	−36.3014	−	43.2623i	−1.57832	−	1.88097i
$530$	2.92543	−	1.93884i	0.127073	−	0.0842179i
$531$		−	10.2197i		−	0.443496i
$532$	−3.11990	+	14.8467i	−0.135265	+	0.643688i
$533$	21.6813	−	21.6813i	0.939121	−	0.939121i
$534$	−2.61801	−	14.8475i	−0.113292	−	0.642513i
$535$	−10.8659	+	3.64299i	−0.469776	+	0.157500i
$536$	−6.77285	+	2.46512i	−0.292543	+	0.106477i
$537$	−8.00347	−	17.1635i	−0.345375	−	0.740659i
$538$	−16.2424	+	1.42103i	−0.700261	+	0.0612649i
$539$	−21.9618	−	12.6797i	−0.945963	−	0.546152i
$540$	2.21131	−	0.331847i	0.0951595	−	0.0142804i
$541$	−6.85964	+	38.9029i	−0.294919	+	1.67257i	0.372614	+	0.927987i	$0.378462\pi$
$541$	−6.85964	+	38.9029i	−0.294919	+	1.67257i	−0.667532	+	0.744581i	$0.732649\pi$
$542$	−2.93905	−	4.19740i	−0.126243	−	0.180294i
$543$	−9.22353	−	2.47144i	−0.395820	−	0.106060i
$544$	1.08351	−	1.87670i	0.0464552	−	0.0804628i
$545$	−4.92141	+	16.6513i	−0.210810	+	0.713265i
$546$	6.30369	−	17.3192i	0.269773	−	0.741195i
$547$	−10.7208	+	22.9908i	−0.458389	+	0.983018i	0.532260	+	0.846581i	$0.321343\pi$
$547$	−10.7208	+	22.9908i	−0.458389	+	0.983018i	−0.990649	+	0.136437i	$0.956435\pi$
$548$	−1.26205	+	14.4253i	−0.0539123	+	0.616220i
$549$	−2.86425	+	0.505044i	−0.122243	+	0.0215548i
$550$	0.895286	+	24.7795i	0.0381751	+	1.05660i
$551$	−21.2802	+	13.8896i	−0.906566	+	0.591716i
$552$	−6.30377	−	6.30377i	−0.268306	−	0.268306i
$553$	−6.32955	+	9.03954i	−0.269160	+	0.384400i
$554$	4.49702	−	3.77345i	0.191060	−	0.160319i
$555$	−4.84949	−	5.10412i	−0.205850	−	0.216658i
$556$	15.6048	+	5.67967i	0.661789	+	0.240872i
$557$	0.110787	+	1.26630i	0.00469419	+	0.0536549i	0.998180	−	0.0602967i	$-0.0192047\pi$
$557$	0.110787	+	1.26630i	0.00469419	+	0.0536549i	−0.993486	+	0.113952i	$0.963649\pi$
$558$	1.66571	+	6.21652i	0.0705152	+	0.263166i
$559$	7.51493	+	13.0162i	0.317848	+	0.550528i
$560$	6.63818	+	4.06237i	0.280514	+	0.171667i
$561$	10.5833	+	1.86612i	0.446827	+	0.0787876i
$562$	−2.58425	+	9.64455i	−0.109010	+	0.406831i
$563$	16.3088	−	4.36994i	0.687336	−	0.184171i	0.101784	−	0.994806i	$-0.467545\pi$
$563$	16.3088	−	4.36994i	0.687336	−	0.184171i	0.585551	+	0.810635i	$0.300878\pi$
$564$	4.61952	+	3.87624i	0.194517	+	0.163219i
$565$	−18.0893	+	20.4711i	−0.761022	+	0.861226i
$566$	10.7490	+	29.5326i	0.451814	+	1.24135i
$567$	3.46723	+	0.303343i	0.145610	+	0.0127392i
$568$	−10.9858	−	7.69233i	−0.460953	−	0.322763i
$569$	−12.4389			−0.521465			−0.260733	−	0.965411i	$-0.583964\pi$
$569$	−12.4389			−0.521465			−0.260733	+	0.965411i	$0.583964\pi$
$570$	9.68088	−	1.13161i	0.405487	−	0.0473978i
$571$	44.5279			1.86344			0.931718	−	0.363184i	$-0.118310\pi$
$571$	44.5279			1.86344			0.931718	+	0.363184i	$0.118310\pi$
$572$	−21.5117	−	15.0627i	−0.899450	−	0.629801i
$573$	13.6410	+	1.19343i	0.569862	+	0.0498565i
$574$	6.89262	+	18.9373i	0.287693	+	0.790429i
$575$	13.7230	−	42.4093i	0.572289	−	1.76859i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−21.0303	+	5.63505i	−0.875502	+	0.234590i	−0.668466	−	0.743743i	$-0.733049\pi$
$577$	−21.0303	+	5.63505i	−0.875502	+	0.234590i	−0.207037	+	0.978333i	$0.566382\pi$
$578$	−3.18451	+	11.8848i	−0.132458	+	0.494341i
$579$	12.6879	+	2.23722i	0.527292	+	0.0929759i
$580$	3.05086	+	12.6740i	0.126680	+	0.526260i
$581$	10.5252	+	18.2302i	0.436658	+	0.756315i
$582$	0.736700	+	2.74940i	0.0305372	+	0.113966i
$583$	−0.678380	−	7.75392i	−0.0280956	−	0.321134i
$584$	−6.72565	−	2.44794i	−0.278309	−	0.101296i
$585$	−11.8372	−	0.302814i	−0.489407	−	0.0125198i
$586$	−7.78019	+	6.52836i	−0.321397	+	0.269684i
$587$	0.422928	−	0.604004i	0.0174561	−	0.0249299i	−0.810329	−	0.585975i	$-0.800712\pi$
$587$	0.422928	−	0.604004i	0.0174561	−	0.0249299i	0.827785	+	0.561045i	$0.189601\pi$
$588$	3.61591	+	3.61591i	0.149118	+	0.149118i
$589$	6.37377	+	27.3194i	0.262626	+	1.12568i
$590$	−21.2668	−	8.36240i	−0.875542	−	0.344275i
$591$	18.9511	−	3.34158i	0.779543	−	0.137454i
$592$	−0.274422	+	3.13666i	−0.0112787	+	0.128916i
$593$	−15.9520	+	34.2091i	−0.655068	+	1.40480i	0.245204	+	0.969471i	$0.421145\pi$
$593$	−15.9520	+	34.2091i	−0.655068	+	1.40480i	−0.900272	+	0.435327i	$0.856633\pi$
$594$	1.69612	−	4.66005i	0.0695927	−	0.191204i
$595$	16.1734	+	4.78016i	0.663045	+	0.195967i
$596$	1.64094	−	2.84220i	0.0672157	−	0.116421i
$597$	−21.5215	−	5.76666i	−0.880816	−	0.236014i
$598$	27.0777	+	38.6709i	1.10729	+	1.58137i
$599$	−4.52724	+	25.6753i	−0.184978	+	1.04906i	0.741006	+	0.671499i	$0.234349\pi$
$599$	−4.52724	+	25.6753i	−0.184978	+	1.04906i	−0.925984	+	0.377564i	$0.876762\pi$
$600$	1.11887	−	4.87321i	0.0456777	−	0.198948i
$601$	−4.12248	−	2.38011i	−0.168159	−	0.0970868i	0.413558	−	0.910478i	$-0.364286\pi$
$601$	−4.12248	−	2.38011i	−0.168159	−	0.0970868i	−0.581718	+	0.813391i	$0.697619\pi$
$602$	−9.84083	+	0.860961i	−0.401082	+	0.0350902i
$603$	3.04603	+	6.53223i	0.124044	+	0.266013i
$604$	18.0120	−	6.55585i	0.732900	−	0.266754i
$605$	27.2095	+	13.5456i	1.10622	+	0.550708i
$606$	−0.222562	−	1.26221i	−0.00904095	−	0.0512738i
$607$	−12.5128	+	12.5128i	−0.507880	+	0.507880i	−0.913875	−	0.405995i	$-0.866925\pi$
$607$	−12.5128	+	12.5128i	−0.507880	+	0.507880i	0.405995	+	0.913875i	$0.366925\pi$
$608$	−3.24603	−	2.90917i	−0.131644	−	0.117983i
$609$			20.2908i			0.822224i
$610$	−1.29273	+	6.37368i	−0.0523412	+	0.258063i
$611$	−20.5265	−	24.4626i	−0.830415	−	0.989650i
$612$	−1.96399	−	0.915824i	−0.0793896	−	0.0370200i
$613$	−26.5061	+	12.3600i	−1.07057	+	0.499216i	−0.876317	−	0.481735i	$-0.840007\pi$
$613$	−26.5061	+	12.3600i	−1.07057	+	0.499216i	−0.194255	+	0.980951i	$0.562229\pi$
$614$	3.40320	−	4.05577i	0.137342	−	0.163678i
$615$	10.1278	−	8.06602i	0.408393	−	0.325253i
$616$	14.9477	−	8.63004i	0.602259	−	0.347714i
$617$	20.9486	−	14.6684i	0.843361	−	0.590528i	−0.0700606	−	0.997543i	$-0.522319\pi$
$617$	20.9486	−	14.6684i	0.843361	−	0.590528i	0.913421	+	0.407015i	$0.133430\pi$
$618$	6.04935	−	4.23580i	0.243341	−	0.170389i
$619$	14.0496	−	8.11155i	0.564702	−	0.326031i	−0.190329	−	0.981720i	$-0.560955\pi$
$619$	14.0496	−	8.11155i	0.564702	−	0.326031i	0.755031	+	0.655690i	$0.227622\pi$
$620$	14.2994	+	1.62046i	0.574278	+	0.0650794i
$621$	−5.73037	+	6.82919i	−0.229952	+	0.274046i
$622$	20.7265	−	9.66492i	0.831057	−	0.387528i
$623$	−47.5570	−	22.1762i	−1.90533	−	0.888471i
$624$	3.40387	+	4.05657i	0.136264	+	0.162393i
$625$	24.2427	−	6.10663i	0.969708	−	0.244265i
$626$			10.3824i			0.414965i
$627$	8.05125	−	20.0610i	0.321536	−	0.801158i
$628$	−10.6596	+	10.6596i	−0.425365	+	0.425365i
$629$	1.18483	+	6.71952i	0.0472424	+	0.267925i
$630$	3.46836	−	6.96698i	0.138183	−	0.277571i
$631$	−4.75491	+	1.73064i	−0.189290	+	0.0688959i	−0.434926	−	0.900466i	$-0.643225\pi$
$631$	−4.75491	+	1.73064i	−0.189290	+	0.0688959i	0.245636	+	0.969362i	$0.421003\pi$
$632$	−1.33996	−	2.87356i	−0.0533008	−	0.114304i
$633$	8.12076	−	0.710475i	0.322771	−	0.0282388i
$634$	−3.72729	−	2.15195i	−0.148029	−	0.0854648i
$635$	−0.471413	−	3.14132i	−0.0187075	−	0.124659i
$636$	−0.272547	+	1.54569i	−0.0108072	+	0.0612907i
$637$	−15.5321	−	22.1821i	−0.615403	−	0.878886i
$638$	27.9261	+	7.48277i	1.10560	+	0.296246i
$639$	−6.70559	+	11.6144i	−0.265269	+	0.459459i
$640$	−1.96445	+	1.06815i	−0.0776517	+	0.0422222i
$641$	5.44286	−	14.9541i	0.214980	−	0.590653i	−0.784589	−	0.620016i	$-0.787126\pi$
$641$	5.44286	−	14.9541i	0.214980	−	0.590653i	0.999569	+	0.0293638i	$0.00934814\pi$
$642$	2.16602	−	4.64504i	0.0854859	−	0.183325i
$643$	2.61371	−	29.8748i	0.103074	−	1.17815i	−0.751828	−	0.659359i	$-0.770828\pi$
$643$	2.61371	−	29.8748i	0.103074	−	1.17815i	0.854903	−	0.518788i	$-0.173617\pi$
$644$	−30.5566	+	5.38794i	−1.20410	+	0.212315i
$645$	2.53418	+	5.81860i	0.0997832	+	0.229107i
$646$	−8.42620	−	4.26885i	−0.331524	−	0.167956i
$647$	−4.29310	−	4.29310i	−0.168779	−	0.168779i	0.617663	−	0.786443i	$-0.288079\pi$
$647$	−4.29310	−	4.29310i	−0.168779	−	0.168779i	−0.786443	+	0.617663i	$0.788079\pi$
$648$	−0.573576	+	0.819152i	−0.0225322	+	0.0321793i
$649$	−38.8236	+	32.5769i	−1.52396	+	1.27875i
$650$	−10.3161	+	24.3850i	−0.404631	+	0.956460i
$651$	21.0488	+	7.66114i	0.824968	+	0.300264i
$652$	−0.754490	−	8.62385i	−0.0295481	−	0.337736i
$653$	−2.04974	−	7.64975i	−0.0802127	−	0.299358i	0.914152	−	0.405372i	$-0.132858\pi$
$653$	−2.04974	−	7.64975i	−0.0802127	−	0.299358i	−0.994365	+	0.106014i	$0.966191\pi$
$654$	−3.88257	−	6.72481i	−0.151821	−	0.262961i
$655$	−40.6848	+	9.79356i	−1.58969	+	0.382666i
$656$	−5.70225	−	1.00546i	−0.222636	−	0.0392567i
$657$	−1.85244	+	6.91341i	−0.0722707	+	0.269718i
$658$	20.2733	−	5.43222i	0.790336	−	0.211770i
$659$	−3.49655	−	2.93395i	−0.136206	−	0.114291i	0.572139	−	0.820156i	$-0.306114\pi$
$659$	−3.49655	−	2.93395i	−0.136206	−	0.114291i	−0.708345	+	0.705866i	$0.750558\pi$
$660$	−8.30956	−	7.34274i	−0.323449	−	0.285816i
$661$	−0.136990	−	0.376377i	−0.00532829	−	0.0146394i	0.937000	−	0.349329i	$-0.113591\pi$
$661$	−0.136990	−	0.376377i	−0.00532829	−	0.0146394i	−0.942328	+	0.334690i	$0.891368\pi$
$662$	−22.8103	−	1.99565i	−0.886549	−	0.0775630i
$663$	9.40012	+	6.58204i	0.365071	+	0.255625i
$664$	−6.04814			−0.234713
$665$	16.0998	−	29.8596i	0.624325	−	1.15790i
$666$	3.14864			0.122007
$667$	−42.5736	−	29.8104i	−1.64846	−	1.15426i
$668$	−9.53928	−	0.834578i	−0.369086	−	0.0322908i
$669$	−5.23972	−	14.3960i	−0.202579	−	0.556581i
$670$	16.0858	−	0.993604i	0.621450	−	0.0383863i
$671$	11.0489	+	9.27111i	0.426537	+	0.357907i
$672$	−3.36188	+	0.900812i	−0.129687	+	0.0347496i
$673$	6.13069	−	22.8800i	0.236321	−	0.881961i	−0.741228	−	0.671253i	$-0.765756\pi$
$673$	6.13069	−	22.8800i	0.236321	−	0.881961i	0.977549	−	0.210708i	$-0.0675768\pi$
$674$	0.613305	+	0.108142i	0.0236236	+	0.00416548i
$675$	−4.95218	−	0.689884i	−0.190609	−	0.0265537i
$676$	−7.52105	−	13.0268i	−0.289271	−	0.501032i
$677$	4.49768	+	16.7856i	0.172860	+	0.645122i	0.996906	+	0.0785995i	$0.0250448\pi$
$677$	4.49768	+	16.7856i	0.172860	+	0.645122i	−0.824046	+	0.566522i	$0.808289\pi$
$678$	−1.06479	−	12.1706i	−0.0408931	−	0.467410i
$679$	9.30932	+	3.38832i	0.357259	+	0.130032i
$680$	−3.51287	+	3.33762i	−0.134712	+	0.127992i
$681$	17.6687	−	14.8258i	0.677066	−	0.568126i
$682$	18.3063	−	26.1441i	0.700984	−	1.00111i
$683$	18.0618	+	18.0618i	0.691115	+	0.691115i	0.962477	−	0.271362i	$-0.0874742\pi$
$683$	18.0618	+	18.0618i	0.691115	+	0.691115i	−0.271362	+	0.962477i	$0.587474\pi$
$684$	−2.61519	+	3.48723i	−0.0999944	+	0.133338i
$685$	11.8488	−	30.1334i	0.452721	−	1.15134i
$686$	−6.46557	+	1.14006i	−0.246857	+	0.0435275i
$687$	−1.86669	+	21.3363i	−0.0712186	+	0.814032i
$688$	1.19949	−	2.57232i	0.0457303	−	0.0980689i
$689$	2.84269	−	7.81021i	0.108298	−	0.297545i
$690$	9.52238	+	17.5128i	0.362511	+	0.666702i
$691$	15.5473	−	26.9288i	0.591448	−	1.02442i	−0.402589	−	0.915381i	$-0.631890\pi$
$691$	15.5473	−	26.9288i	0.591448	−	1.02442i	0.994038	−	0.109038i	$-0.0347770\pi$
$692$	−12.5393	−	3.35989i	−0.476672	−	0.127724i
$693$	−9.89998	−	14.1386i	−0.376069	−	0.537082i
$694$	2.44574	−	13.8705i	0.0928392	−	0.526517i
$695$	−29.8627	−	22.0693i	−1.13276	−	0.837137i
$696$	−5.04884	−	2.91495i	−0.191376	−	0.110491i
$697$	−12.4998	+	1.09359i	−0.473464	+	0.0414227i
$698$	−7.34824	−	15.7583i	−0.278135	−	0.596462i
$699$	−7.26815	+	2.64539i	−0.274907	+	0.100058i
$700$	−11.6601	−	12.9184i	−0.440709	−	0.488269i
$701$	0.782045	+	4.43520i	0.0295374	+	0.167515i	0.996008	−	0.0892615i	$-0.0284507\pi$
$701$	0.782045	+	4.43520i	0.0295374	+	0.167515i	−0.966471	+	0.256777i	$0.917340\pi$
$702$	3.74447	−	3.74447i	0.141326	−	0.141326i
$703$	13.7173	+	0.447260i	0.517358	+	0.0168687i
$704$			4.95913i			0.186904i
$705$	−7.44927	−	11.2399i	−0.280556	−	0.423318i
$706$	12.5392	+	14.9436i	0.471919	+	0.562411i
$707$	−4.04291	−	1.88524i	−0.152049	−	0.0709017i
$708$	9.26217	−	4.31902i	0.348094	−	0.162319i
$709$	1.96257	−	2.33890i	0.0737058	−	0.0878392i	−0.727931	−	0.685650i	$-0.759518\pi$
$709$	1.96257	−	2.33890i	0.0737058	−	0.0878392i	0.801637	+	0.597811i	$0.203963\pi$
$710$	18.6823	+	23.4578i	0.701135	+	0.880356i
$711$	−2.74584	+	1.58531i	−0.102977	+	0.0594537i
$712$	12.3500	−	8.64753i	0.462834	−	0.324080i
$713$	−46.9984	+	32.9087i	−1.76011	+	1.23244i
$714$	−6.53179	+	3.77113i	−0.244446	+	0.141131i
$715$	36.5826	+	45.9337i	1.36811	+	1.71782i
$716$	12.1730	−	14.5072i	0.454926	−	0.542160i
$717$	−0.688369	+	0.320992i	−0.0257076	+	0.0119877i
$718$	−29.5121	−	13.7617i	−1.10138	−	0.513583i
$719$	13.0792	+	15.5871i	0.487770	+	0.581302i	0.952649	−	0.304072i	$-0.0983465\pi$
$719$	13.0792	+	15.5871i	0.487770	+	0.581302i	−0.464879	+	0.885374i	$0.653902\pi$
$720$	1.23529	+	1.86388i	0.0460367	+	0.0694627i
$721$		−	25.7029i		−	0.957227i
$722$	−11.8887	+	14.8209i	−0.442450	+	0.551578i
$723$	−10.6537	+	10.6537i	−0.396214	+	0.396214i
$724$	−1.65815	−	9.40383i	−0.0616246	−	0.349491i
$725$	1.49040	−	29.1114i	0.0553522	−	1.08117i
$726$	−12.7732	+	4.64905i	−0.474057	+	0.172543i
$727$	17.2685	+	37.0324i	0.640454	+	1.37346i	0.911664	+	0.410937i	$0.134798\pi$
$727$	17.2685	+	37.0324i	0.640454	+	1.37346i	−0.271210	+	0.962520i	$0.587424\pi$
$728$	18.3606	−	1.60635i	0.680490	−	0.0595351i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	12.8708	+	9.51188i	0.476370	+	0.352051i
$731$	1.06803	−	6.05710i	0.0395025	−	0.224030i
$732$	−1.66821	−	2.38245i	−0.0616588	−	0.0880579i
$733$	11.8524	+	3.17585i	0.437780	+	0.117303i	0.470976	−	0.882146i	$-0.343902\pi$
$733$	11.8524	+	3.17585i	0.437780	+	0.117303i	−0.0331959	+	0.999449i	$0.510569\pi$
$734$	−15.6333	+	27.0776i	−0.577035	+	0.999453i
$735$	−5.46215	−	10.0455i	−0.201474	−	0.370536i
$736$	3.04907	−	8.37724i	0.112390	−	0.308789i
$737$	15.1056	−	32.3941i	0.556423	−	1.19325i
$738$	−0.504651	+	5.76819i	−0.0185765	+	0.212330i
$739$	50.3133	−	8.87159i	1.85081	−	0.326347i	0.866005	−	0.500036i	$-0.166680\pi$
$739$	50.3133	−	8.87159i	1.85081	−	0.326347i	0.984801	+	0.173689i	$0.0555688\pi$
$740$	2.57642	−	6.55223i	0.0947111	−	0.240865i
$741$	16.8450	−	15.7812i	0.618816	−	0.579737i
$742$	3.86273	+	3.86273i	0.141805	+	0.141805i
$743$	−5.55405	+	7.93201i	−0.203758	+	0.290997i	−0.908006	−	0.418957i	$-0.862396\pi$
$743$	−5.55405	+	7.93201i	−0.203758	+	0.290997i	0.704248	+	0.709955i	$0.251285\pi$
$744$	−4.93012	+	4.13686i	−0.180747	+	0.151665i
$745$	−5.32012	+	5.05472i	−0.194914	+	0.185191i
$746$	−23.8048	−	8.66424i	−0.871556	−	0.317220i
$747$	0.527130	+	6.02513i	0.0192867	+	0.220448i
$748$	2.78141	+	10.3804i	0.101698	+	0.379544i
$749$	−8.91911	−	15.4483i	−0.325897	−	0.564470i
$750$	−5.48782	+	9.74083i	−0.200387	+	0.355685i
$751$	−35.5572	−	6.26969i	−1.29750	−	0.228784i	−0.518105	−	0.855317i	$-0.673362\pi$
$751$	−35.5572	−	6.26969i	−1.29750	−	0.228784i	−0.779395	+	0.626532i	$0.784474\pi$
$752$	−1.56077	+	5.82488i	−0.0569155	+	0.212411i
$753$	−9.63840	+	2.58260i	−0.351243	+	0.0941153i
$754$	23.6494	+	19.8442i	0.861260	+	0.722683i
$755$	−42.7795	+	2.64244i	−1.55690	+	0.0961681i
$756$	1.19039	+	3.27057i	0.0432941	+	0.118950i
$757$	28.4940	+	2.49290i	1.03563	+	0.0906060i	0.592272	−	0.805738i	$-0.298231\pi$
$757$	28.4940	+	2.49290i	1.03563	+	0.0906060i	0.443359	+	0.896344i	$0.353787\pi$
$758$	−20.5690	−	14.4026i	−0.747099	−	0.523124i
$759$	44.2100			1.60472
$760$	5.11690	+	8.29562i	0.185610	+	0.300914i
$761$	−14.5219			−0.526418			−0.263209	−	0.964739i	$-0.584781\pi$
$761$	−14.5219			−0.526418			−0.263209	+	0.964739i	$0.584781\pi$
$762$	1.16366	+	0.814806i	0.0421551	+	0.0295173i
$763$	−26.9235	−	2.35550i	−0.974696	−	0.0852749i
$764$	4.68333	+	12.8673i	0.169437	+	0.465524i
$765$	3.63109	+	3.20861i	0.131282	+	0.116007i
$766$	12.4390	+	10.4376i	0.449439	+	0.377124i
$767$	−52.2740	+	14.0068i	−1.88751	+	0.505756i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	44.9481	+	7.92556i	1.62087	+	0.285803i	0.909090	−	0.416600i	$-0.136778\pi$
$769$	44.9481	+	7.92556i	1.62087	+	0.285803i	0.711780	+	0.702403i	$0.247889\pi$
$770$	−37.5229	+	9.03242i	−1.35223	+	0.325506i
$771$	1.33546	+	2.31308i	0.0480953	+	0.0833035i
$772$	3.33454	+	12.4447i	0.120013	+	0.447893i
$773$	−2.38727	−	27.2867i	−0.0858643	−	0.981433i	−0.909881	−	0.414868i	$-0.863828\pi$
$773$	−2.38727	−	27.2867i	−0.0858643	−	0.981433i	0.824017	−	0.566565i	$-0.191728\pi$
$774$	−2.66708	−	0.970736i	−0.0958661	−	0.0348924i
$775$	−29.6362	−	12.5376i	−1.06456	−	0.450363i
$776$	−2.18046	+	1.82962i	−0.0782740	+	0.0656797i
$777$	6.28568	−	8.97688i	0.225497	−	0.322044i
$778$	−5.76124	−	5.76124i	−0.206550	−	0.206550i
$779$	−3.01792	+	25.0579i	−0.108128	+	0.897792i
$780$	−4.72817	−	10.8561i	−0.169295	−	0.388711i
$781$	65.4973	−	11.5489i	2.34368	−	0.413254i
$782$	1.68374	−	19.2452i	0.0602104	−	0.688208i
$783$	−2.46382	+	5.28368i	−0.0880498	+	0.188823i
$784$	−1.74898	+	4.80528i	−0.0624635	+	0.171617i
$785$	29.6141	−	16.1023i	1.05697	−	0.574715i
$786$	9.35727	−	16.2073i	0.333763	−	0.578094i
$787$	−10.7742	−	2.88693i	−0.384057	−	0.102908i	0.0616244	−	0.998099i	$-0.480372\pi$
$787$	−10.7742	−	2.88693i	−0.384057	−	0.102908i	−0.445681	+	0.895192i	$0.647039\pi$
$788$	11.0376	+	15.7633i	0.393197	+	0.561544i
$789$	3.80711	−	21.5912i	0.135537	−	0.768666i
$790$	1.05216	+	7.01121i	0.0374342	+	0.249448i
$791$	−36.8245	−	21.2606i	−1.30933	−	0.755941i
$792$	4.94025	−	0.432216i	0.175544	−	0.0153581i
$793$	6.50898	+	13.9585i	0.231141	+	0.495683i
$794$	−8.68788	+	3.16213i	−0.308321	+	0.112220i
$795$	1.56408	−	3.14180i	0.0554721	−	0.111428i
$796$	−3.86900	−	21.9422i	−0.137133	−	0.777720i
$797$	13.2341	−	13.2341i	0.468778	−	0.468778i	−0.432741	−	0.901518i	$-0.642453\pi$
$797$	13.2341	−	13.2341i	0.468778	−	0.468778i	0.901518	+	0.432741i	$0.142453\pi$
$798$	4.72146	+	14.4176i	0.167138	+	0.510378i
$799$			13.0679i			0.462310i
$800$	4.88948	−	1.04547i	0.172869	−	0.0369628i
$801$	−9.69100	−	11.5493i	−0.342415	−	0.408074i
$802$	21.7969	+	10.1641i	0.769677	+	0.358906i
$803$	32.1684	−	15.0004i	1.13520	−	0.529351i
$804$	−4.63290	+	5.52128i	−0.163390	+	0.194720i
$805$	68.9393	+	7.81247i	2.42979	+	0.275353i
$806$	29.5148	−	17.0404i	1.03961	−	0.600221i
$807$	−13.3558	+	9.35186i	−0.470148	+	0.329201i
$808$	1.04989	−	0.735142i	0.0369351	−	0.0258622i
$809$	3.51004	−	2.02652i	0.123406	−	0.0712488i	−0.437026	−	0.899449i	$-0.643968\pi$
$809$	3.51004	−	2.02652i	0.123406	−	0.0712488i	0.560433	+	0.828200i	$0.310635\pi$
$810$	1.74912	−	1.39304i	0.0614580	−	0.0489465i
$811$	−6.88597	+	8.20638i	−0.241799	+	0.288165i	−0.873272	−	0.487233i	$-0.838006\pi$
$811$	−6.88597	+	8.20638i	−0.241799	+	0.288165i	0.631473	+	0.775398i	$0.282451\pi$
$812$	−18.3897	+	8.57525i	−0.645352	+	0.300932i
$813$	−4.64399	−	2.16553i	−0.162872	−	0.0759484i
$814$	−10.0368	−	11.9614i	−0.351790	−	0.419247i
$815$	−3.84775	+	18.9709i	−0.134781	+	0.664522i
$816$		−	2.16702i		−	0.0758610i
$817$	−11.4815	−	4.60795i	−0.401685	−	0.161212i
$818$	18.4929	−	18.4929i	0.646591	−	0.646591i
$819$	−3.20047	−	18.1508i	−0.111833	−	0.634239i
$820$	11.5905	+	5.77007i	0.404757	+	0.201500i
$821$	−19.2470	+	7.00532i	−0.671724	+	0.244487i	−0.655290	−	0.755377i	$-0.727454\pi$
$821$	−19.2470	+	7.00532i	−0.671724	+	0.244487i	−0.0164339	+	0.999865i	$0.505231\pi$
$822$	6.11970	+	13.1237i	0.213449	+	0.457743i
$823$	27.4533	−	2.40185i	0.956960	−	0.0837232i	0.402036	−	0.915624i	$-0.368303\pi$
$823$	27.4533	−	2.40185i	0.956960	−	0.0837232i	0.554925	+	0.831901i	$0.312747\pi$
$824$	6.39551	+	3.69245i	0.222798	+	0.128633i
$825$	13.1651	+	21.0120i	0.458349	+	0.731544i
$826$	6.17654	−	35.0289i	0.214909	−	1.21881i
$827$	25.5329	+	36.4647i	0.887865	+	1.26800i	0.962635	+	0.270802i	$0.0872890\pi$
$827$	25.5329	+	36.4647i	0.887865	+	1.26800i	−0.0747697	+	0.997201i	$0.523822\pi$
$828$	−8.61110	−	2.30734i	−0.299257	−	0.0801855i
$829$	19.3754	−	33.5591i	0.672935	−	1.16556i	−0.304133	−	0.952629i	$-0.598367\pi$
$829$	19.3754	−	33.5591i	0.672935	−	1.16556i	0.977068	−	0.212928i	$-0.0682999\pi$
$830$	12.9695	+	3.83321i	0.450176	+	0.133053i
$831$	2.00781	−	5.51642i	0.0696502	−	0.191362i
$832$	−2.23797	+	4.79933i	−0.0775875	+	0.166387i
$833$	−0.965812	+	11.0393i	−0.0334634	+	0.382488i
$834$	16.3540	−	2.88364i	0.566291	−	0.0998524i
$835$	19.9268	+	7.83547i	0.689595	+	0.271158i
$836$	21.5840	−	1.18123i	0.746499	−	0.0408537i
$837$	4.55081	+	4.55081i	0.157299	+	0.157299i
$838$	−11.1642	+	15.9442i	−0.385662	+	0.550783i
$839$	28.9988	−	24.3329i	1.00115	−	0.840064i	0.0140065	−	0.999902i	$-0.495541\pi$
$839$	28.9988	−	24.3329i	1.00115	−	0.840064i	0.987143	+	0.159837i	$0.0510970\pi$
$840$	7.78002	+	0.199025i	0.268436	+	0.00686702i
$841$	−4.68689	−	1.70589i	−0.161617	−	0.0588238i
$842$	−1.58695	−	18.1389i	−0.0546899	−	0.625108i
$843$	2.58425	+	9.64455i	0.0890063	+	0.332176i
$844$	4.07589	+	7.05965i	0.140298	+	0.243003i
$845$	7.87172	+	32.7011i	0.270795	+	1.12495i
$846$	5.93874	+	1.04716i	0.204178	+	0.0360021i
$847$	−12.2447	+	45.6977i	−0.420732	+	1.57019i
$848$	−1.51606	+	0.406226i	−0.0520616	+	0.0139499i
$849$	24.0752	+	20.2015i	0.826259	+	0.693313i
$850$	9.64822	−	4.93070i	0.330931	−	0.169122i
$851$	9.60041	+	26.3769i	0.329098	+	0.904189i
$852$	−13.3601	−	1.16886i	−0.457711	−	0.0400445i
$853$	−29.4767	−	20.6398i	−1.00926	−	0.706693i	−0.0528164	−	0.998604i	$-0.516820\pi$
$853$	−29.4767	−	20.6398i	−1.00926	−	0.706693i	−0.956445	+	0.291912i	$0.905709\pi$
$854$	−10.1227			−0.346392
$855$	7.81809	−	5.82044i	0.267373	−	0.199055i
$856$	5.12523			0.175177
$857$	−4.90131	−	3.43194i	−0.167426	−	0.117233i	0.486861	−	0.873480i	$-0.338142\pi$
$857$	−4.90131	−	3.43194i	−0.167426	−	0.117233i	−0.654286	+	0.756247i	$0.727031\pi$
$858$	−26.1610	−	2.28879i	−0.893122	−	0.0781381i
$859$	−10.3472	−	28.4286i	−0.353040	−	0.969971i	−0.981388	−	0.192037i	$-0.938490\pi$
$859$	−10.3472	−	28.4286i	−0.353040	−	0.969971i	0.628347	−	0.777933i	$-0.283732\pi$
$860$	−4.20245	+	4.75579i	−0.143302	+	0.162171i
$861$	15.4378	+	12.9539i	0.526120	+	0.441468i
$862$	18.9709	−	5.08324i	0.646151	−	0.173136i
$863$	−1.32049	+	4.92812i	−0.0449499	+	0.167755i	−0.984752	−	0.173964i	$-0.944342\pi$
$863$	−1.32049	+	4.92812i	−0.0449499	+	0.167755i	0.939802	+	0.341719i	$0.111009\pi$
$864$	−0.984808	−	0.173648i	−0.0335038	−	0.00590763i
$865$	24.7594	+	15.1520i	0.841845	+	0.515184i
$866$	−10.7069	−	18.5450i	−0.363836	−	0.630183i
$867$	3.18451	+	11.8848i	0.108152	+	0.403627i
$868$	1.95226	+	22.3144i	0.0662640	+	0.757401i
$869$	14.7753	+	5.37775i	0.501216	+	0.182428i
$870$	8.97913	+	9.45059i	0.304421	+	0.320405i
$871$	29.2378	−	24.5334i	0.990686	−	0.831284i
$872$	4.45390	−	6.36083i	0.150828	−	0.215405i
$873$	2.01270	+	2.01270i	0.0681196	+	0.0681196i
$874$	−37.1872	−	11.2753i	−1.25788	−	0.381393i
$875$	16.8160	+	35.0917i	0.568485	+	1.18632i
$876$	−7.04855	+	1.24285i	−0.238149	+	0.0419920i
$877$	3.27378	−	37.4195i	0.110548	−	1.26357i	−0.714955	−	0.699170i	$-0.753553\pi$
$877$	3.27378	−	37.4195i	0.110548	−	1.26357i	0.825503	−	0.564397i	$-0.190891\pi$
$878$	11.0551	−	23.7078i	0.373093	−	0.800100i
$879$	−3.47367	+	9.54382i	−0.117164	+	0.321905i
$880$	3.14301	−	10.6342i	0.105951	−	0.358479i
$881$	4.10730	−	7.11406i	0.138379	−	0.239679i	−0.788504	−	0.615029i	$-0.789144\pi$
$881$	4.10730	−	7.11406i	0.138379	−	0.239679i	0.926883	+	0.375350i	$0.122478\pi$
$882$	4.93943	+	1.32352i	0.166319	+	0.0445651i
$883$	8.87748	+	12.6784i	0.298751	+	0.426661i	0.940261	−	0.340454i	$-0.110581\pi$
$883$	8.87748	+	12.6784i	0.298751	+	0.426661i	−0.641510	+	0.767114i	$0.721692\pi$
$884$	−1.99269	+	11.3011i	−0.0670213	+	0.380097i
$885$	−22.5988	+	3.39137i	−0.759651	+	0.114000i
$886$	9.45924	+	5.46129i	0.317789	+	0.183476i
$887$	20.2687	−	1.77328i	0.680558	−	0.0595411i	0.258365	−	0.966047i	$-0.416816\pi$
$887$	20.2687	−	1.77328i	0.680558	−	0.0595411i	0.422192	+	0.906506i	$0.361261\pi$
$888$	1.33067	+	2.85364i	0.0446544	+	0.0957618i
$889$	4.64608	−	1.69103i	0.155825	−	0.0567155i
$890$	−31.9635	+	10.7163i	−1.07142	+	0.359212i
$891$	−0.861143	−	4.88379i	−0.0288494	−	0.163613i
$892$	10.8328	−	10.8328i	0.362709	−	0.362709i
$893$	25.7239	+	5.40563i	0.860817	+	0.180893i
$894$		−	3.28189i		−	0.109763i
$895$	−35.2978	+	23.3938i	−1.17988	+	0.781968i
$896$	−2.23720	−	2.66619i	−0.0747397	−	0.0890713i
$897$	42.7854	+	19.9512i	1.42856	+	0.666150i
$898$	35.0443	−	16.3414i	1.16944	−	0.545321i
$899$	−24.1175	+	28.7421i	−0.804363	+	0.958603i
$900$	−1.46763	−	4.77975i	−0.0489211	−	0.159325i
$901$	−2.94555	+	1.70061i	−0.0981305	+	0.0566557i
$902$	23.5215	−	16.4699i	0.783179	−	0.548388i
$903$	−8.09193	+	5.66603i	−0.269283	+	0.188554i
$904$	10.5803	−	6.10855i	0.351896	−	0.203168i
$905$	−2.40430	+	21.2162i	−0.0799217	+	0.705250i
$906$	12.3210	−	14.6836i	0.409337	−	0.487828i
$907$	13.4491	−	6.27144i	0.446571	−	0.208240i	−0.186306	−	0.982492i	$-0.559652\pi$
$907$	13.4491	−	6.27144i	0.446571	−	0.208240i	0.632877	+	0.774252i	$0.281874\pi$
$908$	20.9039	+	9.74763i	0.693719	+	0.323486i
$909$	−0.823849	−	0.981825i	−0.0273253	−	0.0325651i
$910$	−40.3900	−	8.19204i	−1.33892	−	0.271564i
$911$		−	12.9043i		−	0.427538i	−0.976884	−	0.213769i	$-0.931426\pi$
$911$		−	12.9043i		−	0.427538i	0.976884	−	0.213769i	$-0.0685739\pi$
$912$	−4.26573	−	0.896403i	−0.141252	−	0.0296829i
$913$	21.2086	−	21.2086i	0.701903	−	0.701903i
$914$	−2.53995	−	14.4048i	−0.0840141	−	0.476468i
$915$	2.06730	+	6.16613i	0.0683429	+	0.203846i
$916$	−20.1262	+	7.32533i	−0.664988	+	0.242036i
$917$	−27.5274	−	59.0327i	−0.909035	−	1.94943i
$918$	−2.15878	+	0.188869i	−0.0712503	+	0.00623359i
$919$	−48.5529	−	28.0320i	−1.60161	−	0.924692i	−0.991165	−	0.132635i	$-0.957656\pi$
$919$	−48.5529	−	28.0320i	−1.60161	−	0.924692i	−0.610448	−	0.792057i	$-0.709010\pi$
$920$	−11.8477	+	16.0314i	−0.390606	+	0.528541i
$921$	0.919369	−	5.21400i	0.0302942	−	0.171807i
$922$	−9.31453	−	13.3025i	−0.306758	−	0.438095i
$923$	68.5987	+	18.3810i	2.25795	+	0.605017i
$924$	8.63004	−	14.9477i	0.283908	−	0.491742i
$925$	−9.67749	+	12.4175i	−0.318194	+	0.408285i
$926$	5.48650	−	15.0740i	0.180298	−	0.495364i
$927$	3.12099	−	6.69299i	0.102507	−	0.219827i
$928$	0.508109	−	5.80771i	0.0166795	−	0.190647i
$929$	−27.8649	+	4.91334i	−0.914218	+	0.161201i	−0.610918	−	0.791694i	$-0.709200\pi$
$929$	−27.8649	+	4.91334i	−0.914218	+	0.161201i	−0.303300	+	0.952895i	$0.598088\pi$
$930$	13.1939	−	5.74634i	0.432644	−	0.188430i
$931$	21.3310	+	6.46764i	0.699096	+	0.211968i
$932$	−5.46919	−	5.46919i	−0.179149	−	0.179149i
$933$	13.1172	−	18.7333i	0.429438	−	0.613301i
$934$	−15.7930	+	13.2519i	−0.516762	+	0.433615i
$935$	0.614524	−	24.0221i	0.0200971	−	0.785608i
$936$	4.97612	+	1.81116i	0.162650	+	0.0591996i
$937$	0.778215	+	8.89503i	0.0254232	+	0.290588i	0.998254	+	0.0590703i	$0.0188136\pi$
$937$	0.778215	+	8.89503i	0.0254232	+	0.290588i	−0.972831	+	0.231518i	$0.925631\pi$
$938$	6.49262	+	24.2308i	0.211991	+	0.791163i
$939$	5.19121	+	8.99144i	0.169409	+	0.293425i
$940$	7.03858	−	11.5015i	0.229573	−	0.375137i
$941$	−24.6154	−	4.34036i	−0.802439	−	0.141492i	−0.242636	−	0.970117i	$-0.578012\pi$
$941$	−24.6154	−	4.34036i	−0.802439	−	0.141492i	−0.559803	+	0.828626i	$0.689123\pi$
$942$	−3.90169	+	14.5613i	−0.127124	+	0.474434i
$943$	−49.8602	+	13.3600i	−1.62367	+	0.435061i
$944$	7.82872	+	6.56908i	0.254803	+	0.213805i
$945$	−0.479806	−	7.76776i	−0.0156081	−	0.252685i
$946$	4.81400	+	13.2264i	0.156517	+	0.430026i
$947$	42.6417	+	3.73067i	1.38567	+	0.121230i	0.755460	−	0.655195i	$-0.227414\pi$
$947$	42.6417	+	3.73067i	1.38567	+	0.121230i	0.630209	+	0.776425i	$0.282969\pi$
$948$	−2.59722	−	1.81859i	−0.0843537	−	0.0590651i
$949$	37.9013			1.23033
$950$	−5.71491	−	21.0319i	−0.185416	−	0.682364i
$951$	−4.30390			−0.139563
$952$	−6.17826	−	4.32606i	−0.200239	−	0.140209i
$953$	−55.1045	−	4.82102i	−1.78501	−	0.156168i	−0.853787	−	0.520622i	$-0.825700\pi$
$953$	−55.1045	−	4.82102i	−1.78501	−	0.156168i	−0.931222	+	0.364454i	$0.881256\pi$
$954$	0.536814	+	1.47488i	0.0173800	+	0.0477511i
$955$	−1.88769	−	30.5605i	−0.0610842	−	0.988915i
$956$	−0.581834	−	0.488217i	−0.0188179	−	0.0157901i
$957$	27.9261	−	7.48277i	0.902721	−	0.241883i
$958$	−10.0985	+	37.6883i	−0.326269	+	1.21765i
$959$	49.6331	+	8.75165i	1.60274	+	0.282606i
$960$	−1.16719	+	1.90727i	−0.0376709	+	0.0615568i
$961$	5.20988	+	9.02378i	0.168061	+	0.291090i
$962$	−4.31543	−	16.1054i	−0.139135	−	0.519259i
$963$	−0.446693	−	5.10573i	−0.0143945	−	0.164530i
$964$	−14.1579	−	5.15306i	−0.455996	−	0.165969i
$965$	0.736732	−	28.7993i	0.0237162	−	0.927083i
$966$	−23.7688	+	19.9444i	−0.764748	+	0.641700i
$967$	5.85513	−	8.36200i	0.188288	−	0.268904i	−0.713898	−	0.700249i	$-0.753072\pi$
$967$	5.85513	−	8.36200i	0.188288	−	0.268904i	0.902187	+	0.431346i	$0.141961\pi$
$968$	−9.61165	−	9.61165i	−0.308930	−	0.308930i
$969$	−9.43173	+	0.516170i	−0.302991	+	0.0165818i
$970$	5.83530	−	2.54145i	0.187360	−	0.0816011i
$971$	−51.7641	+	9.12742i	−1.66119	+	0.292913i	−0.923892	−	0.382654i	$-0.875010\pi$
$971$	−51.7641	+	9.12742i	−1.66119	+	0.292913i	−0.737299	+	0.675567i	$0.763899\pi$
$972$	−0.0871557	+	0.996195i	−0.00279552	+	0.0319530i
$973$	24.4263	−	52.3823i	0.783071	−	1.67930i
$974$	12.8495	−	35.3037i	0.411724	−	1.13120i
$975$	3.25852	+	26.2761i	0.104356	+	0.841509i
$976$	1.45422	−	2.51878i	0.0465484	−	0.0806241i
$977$	28.7723	+	7.70952i	0.920507	+	0.246649i	0.687802	−	0.725898i	$-0.258576\pi$
$977$	28.7723	+	7.70952i	0.920507	+	0.246649i	0.232705	+	0.972547i	$0.425242\pi$
$978$	−4.96533	−	7.09123i	−0.158774	−	0.226753i
$979$	−12.9830	+	73.6305i	−0.414940	+	2.35324i
$980$	6.79596	−	9.19582i	0.217089	−	0.293750i
$981$	−6.72481	−	3.88257i	−0.214707	−	0.123961i
$982$	2.77467	−	0.242752i	0.0885431	−	0.00774652i
$983$	8.66357	+	18.5791i	0.276325	+	0.592581i	0.994670	−	0.103106i	$-0.0328780\pi$
$983$	8.66357	+	18.5791i	0.276325	+	0.592581i	−0.718345	+	0.695687i	$0.755100\pi$
$984$	−5.44103	+	1.98037i	−0.173454	+	0.0631319i
$985$	−13.6781	−	40.7977i	−0.435821	−	1.29992i
$986$	−2.19379	−	12.4416i	−0.0698645	−	0.396221i
$987$	14.8411	−	14.8411i	0.472397	−	0.472397i
$988$	21.4216	+	8.59732i	0.681513	+	0.273517i
$989$		−	25.3026i		−	0.804575i
$990$	−10.8677	−	2.20422i	−0.345397	−	0.0700546i
$991$	10.4939	+	12.5062i	0.333351	+	0.397272i	0.906519	−	0.422166i	$-0.138730\pi$
$991$	10.4939	+	12.5062i	0.333351	+	0.397272i	−0.573168	+	0.819438i	$0.694286\pi$
$992$	−5.83283	−	2.71989i	−0.185193	−	0.0863567i
$993$	−20.7522	+	9.67689i	−0.658550	+	0.307087i
$994$	−30.0035	+	35.7568i	−0.951654	+	1.13414i
$995$	−5.61001	+	49.5042i	−0.177849	+	1.56939i
$996$	−5.23785	+	3.02407i	−0.165968	+	0.0958214i
$997$	7.88730	−	5.52275i	0.249793	−	0.174907i	−0.441973	−	0.897028i	$-0.645721\pi$
$997$	7.88730	−	5.52275i	0.249793	−	0.174907i	0.691767	+	0.722121i	$0.256833\pi$
$998$	11.7174	−	8.20463i	0.370908	−	0.259713i
$999$	2.72680	−	1.57432i	0.0862722	−	0.0498093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.67.7	✓	120
5.3	odd	4	inner	570.2.bh.b.523.7	yes	120
19.2	odd	18	inner	570.2.bh.b.97.7	yes	120
95.78	even	36	inner	570.2.bh.b.553.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.67.7	✓	120	1.1	even	1	trivial
570.2.bh.b.97.7	yes	120	19.2	odd	18	inner
570.2.bh.b.523.7	yes	120	5.3	odd	4	inner
570.2.bh.b.553.7	yes	120	95.78	even	36	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.137857 - 2.23181i) q^{5} +(0.766044 + 0.642788i) q^{6} +(3.36188 - 0.900812i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(0.819152 + 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-0.137857 - 2.23181i) q^{5} +(0.766044 + 0.642788i) q^{6} +(3.36188 - 0.900812i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(1.16719 - 1.90727i) q^{10} +(-2.47956 - 4.29473i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-0.461531 - 5.27533i) q^{13} +(3.27057 + 1.19039i) q^{14} +(0.0571834 - 2.23534i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-1.24295 + 1.77512i) q^{17} +(0.707107 + 0.707107i) q^{18} +(2.98013 + 3.18101i) q^{19} +(2.05007 - 0.892868i) q^{20} +(3.42759 - 0.604377i) q^{21} +(0.432216 - 4.94025i) q^{22} +(-3.76759 + 8.07962i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(-4.96199 + 0.615341i) q^{25} +(2.64774 - 4.58602i) q^{26} +(0.965926 + 0.258819i) q^{27} +(1.99632 + 2.85103i) q^{28} +(-1.01235 + 5.74133i) q^{29} +(1.32898 - 1.79828i) q^{30} +(5.57358 + 3.21791i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-2.09582 - 4.49449i) q^{33} +(-2.03634 + 0.741166i) q^{34} +(-2.47390 - 7.37890i) q^{35} +(0.173648 + 0.984808i) q^{36} +(2.22642 - 2.22642i) q^{37} +(0.616622 + 4.31506i) q^{38} -5.29548i q^{39} +(2.19145 + 0.444477i) q^{40} +(3.72188 + 4.43556i) q^{41} +(3.15438 + 1.47091i) q^{42} +(-2.57232 + 1.19949i) q^{43} +(3.18766 - 3.79891i) q^{44} +(0.251788 - 2.22185i) q^{45} +(-7.72050 + 4.45744i) q^{46} +(4.93978 - 3.45887i) q^{47} +(-0.819152 + 0.573576i) q^{48} +(4.42857 - 2.55683i) q^{49} +(-4.41757 - 2.34202i) q^{50} +(-1.39294 + 1.66004i) q^{51} +(4.79933 - 2.23797i) q^{52} +(1.42248 + 0.663316i) q^{53} +(0.642788 + 0.766044i) q^{54} +(-9.24321 + 6.12598i) q^{55} +3.48047i q^{56} +(2.69154 + 3.42864i) q^{57} +(-4.12236 + 4.12236i) q^{58} +(-1.77463 - 10.0644i) q^{59} +(2.12009 - 0.710795i) q^{60} +(-2.73303 + 0.994743i) q^{61} +(2.71989 + 5.83283i) q^{62} +(3.46723 - 0.303343i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-11.7099 + 1.75729i) q^{65} +(0.861143 - 4.88379i) q^{66} +(4.13406 + 5.90405i) q^{67} +(-2.09318 - 0.560867i) q^{68} +(-4.45744 + 7.72050i) q^{69} +(2.20586 - 7.46341i) q^{70} +(-4.58689 + 12.6024i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(-0.623799 + 7.13005i) q^{73} +(3.10080 - 0.546755i) q^{74} +(-4.99674 + 0.180533i) q^{75} +(-1.96991 + 3.88837i) q^{76} +(-12.2047 - 12.2047i) q^{77} +(3.03736 - 4.33780i) q^{78} +(-2.42883 + 2.03803i) q^{79} +(1.54019 + 1.62106i) q^{80} +(0.939693 + 0.342020i) q^{81} +(0.504651 + 5.76819i) q^{82} +(1.56537 + 5.84206i) q^{83} +(1.74023 + 3.01418i) q^{84} +(4.13309 + 2.52933i) q^{85} +(-2.79512 - 0.492856i) q^{86} +(-1.50889 + 5.63125i) q^{87} +(4.79015 - 1.28352i) q^{88} +(-11.5493 - 9.69100i) q^{89} +(1.48065 - 1.67561i) q^{90} +(-6.30369 - 17.3192i) q^{91} +(-8.88095 - 0.776982i) q^{92} +(5.27191 + 3.69143i) q^{93} +6.03036 q^{94} +(6.68860 - 7.08961i) q^{95} -1.00000 q^{96} +(2.33163 + 1.63262i) q^{97} +(5.09421 + 0.445686i) q^{98} +(-1.69612 - 4.66005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^5 + 12 * q^7	\( 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more