LMFDB - Embedded newform 117.2.x.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(2,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("117.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (of order $12$, degree $4$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75301 - 1.75301i) q^{2} +(-1.71669 - 0.230184i) q^{3} -4.14611i q^{4} +(-0.542141 - 0.145266i) q^{5} +(-3.41289 + 2.60586i) q^{6} +(0.541135 + 0.144997i) q^{7} +(-3.76217 - 3.76217i) q^{8} +(2.89403 + 0.790307i) q^{9} +O(q^{10})$	\(q+(1.75301 - 1.75301i) q^{2} +(-1.71669 - 0.230184i) q^{3} -4.14611i q^{4} +(-0.542141 - 0.145266i) q^{5} +(-3.41289 + 2.60586i) q^{6} +(0.541135 + 0.144997i) q^{7} +(-3.76217 - 3.76217i) q^{8} +(2.89403 + 0.790307i) q^{9} +(-1.20503 + 0.695727i) q^{10} +(3.72918 + 3.72918i) q^{11} +(-0.954368 + 7.11758i) q^{12} +(-1.98995 - 3.00668i) q^{13} +(1.20280 - 0.694436i) q^{14} +(0.897249 + 0.374169i) q^{15} -4.89803 q^{16} +(-1.39921 + 2.42351i) q^{17} +(6.45869 - 3.68786i) q^{18} +(3.31532 - 0.888337i) q^{19} +(-0.602290 + 2.24778i) q^{20} +(-0.895584 - 0.373474i) q^{21} +13.0746 q^{22} +(-3.77915 + 6.54568i) q^{23} +(5.59247 + 7.32445i) q^{24} +(-4.05731 - 2.34249i) q^{25} +(-8.75915 - 1.78235i) q^{26} +(-4.78623 - 2.02287i) q^{27} +(0.601173 - 2.24361i) q^{28} -0.895922i q^{29} +(2.22881 - 0.916966i) q^{30} +(-1.57626 + 5.88269i) q^{31} +(-1.06198 + 1.06198i) q^{32} +(-5.54344 - 7.26024i) q^{33} +(1.79560 + 6.70128i) q^{34} +(-0.272308 - 0.157217i) q^{35} +(3.27670 - 11.9990i) q^{36} +(-0.0565841 - 0.0151617i) q^{37} +(4.25453 - 7.36906i) q^{38} +(2.72403 + 5.61958i) q^{39} +(1.49311 + 2.58614i) q^{40} +(-1.50730 - 5.62531i) q^{41} +(-2.22468 + 0.915264i) q^{42} +(9.03652 - 5.21724i) q^{43} +(15.4616 - 15.4616i) q^{44} +(-1.45417 - 0.848863i) q^{45} +(4.84977 + 18.0996i) q^{46} +(-10.6264 + 2.84732i) q^{47} +(8.40838 + 1.12745i) q^{48} +(-5.79037 - 3.34307i) q^{49} +(-11.2189 + 3.00611i) q^{50} +(2.95986 - 3.83833i) q^{51} +(-12.4660 + 8.25054i) q^{52} +5.68410i q^{53} +(-11.9364 + 4.84421i) q^{54} +(-1.48002 - 2.56347i) q^{55} +(-1.49034 - 2.58134i) q^{56} +(-5.89584 + 0.761864i) q^{57} +(-1.57056 - 1.57056i) q^{58} +(3.61546 + 3.61546i) q^{59} +(1.55135 - 3.72010i) q^{60} +(2.08491 + 3.61117i) q^{61} +(7.54922 + 13.0756i) q^{62} +(1.45147 + 0.847288i) q^{63} -6.07273i q^{64} +(0.642063 + 1.91912i) q^{65} +(-22.4450 - 3.00956i) q^{66} +(-6.36385 + 1.70519i) q^{67} +(10.0481 + 5.80130i) q^{68} +(7.99433 - 10.3670i) q^{69} +(-0.752964 + 0.201756i) q^{70} +(-0.573694 - 2.14106i) q^{71} +(-7.91455 - 13.8611i) q^{72} +(2.68642 - 2.68642i) q^{73} +(-0.125771 + 0.0726140i) q^{74} +(6.42593 + 4.95525i) q^{75} +(-3.68314 - 13.7457i) q^{76} +(1.47727 + 2.55871i) q^{77} +(14.6265 + 5.07595i) q^{78} +(2.61166 - 4.52353i) q^{79} +(2.65542 + 0.711518i) q^{80} +(7.75083 + 4.57435i) q^{81} +(-12.5035 - 7.21893i) q^{82} +(0.0375018 + 0.139959i) q^{83} +(-1.54847 + 3.71319i) q^{84} +(1.11063 - 1.11063i) q^{85} +(6.69526 - 24.9870i) q^{86} +(-0.206227 + 1.53802i) q^{87} -28.0596i q^{88} +(2.14168 - 7.99287i) q^{89} +(-4.03725 + 1.06111i) q^{90} +(-0.640871 - 1.91555i) q^{91} +(27.1391 + 15.6688i) q^{92} +(4.06005 - 9.73591i) q^{93} +(-13.6367 + 23.6195i) q^{94} -1.92642 q^{95} +(2.06753 - 1.57863i) q^{96} +(-0.238007 + 0.888254i) q^{97} +(-16.0111 + 4.29015i) q^{98} +(7.84517 + 13.7396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.75301	−	1.75301i	1.23957	−	1.23957i	0.279390	−	0.960178i	$-0.409868\pi$
$2$	1.75301	−	1.75301i	1.23957	−	1.23957i	0.960178	−	0.279390i	$-0.0901323\pi$
$3$	−1.71669	−	0.230184i	−0.991130	−	0.132897i
$3$	−1.71669	−	0.230184i	−0.991130	−	0.132897i
$4$		−	4.14611i		−	2.07306i
$5$	−0.542141	−	0.145266i	−0.242453	−	0.0649651i	0.135546	−	0.990771i	$-0.456721\pi$
$5$	−0.542141	−	0.145266i	−0.242453	−	0.0649651i	−0.377999	+	0.925806i	$0.623388\pi$
$6$	−3.41289	+	2.60586i	−1.39331	+	1.06384i
$7$	0.541135	+	0.144997i	0.204530	+	0.0548036i	0.359629	−	0.933095i	$-0.382903\pi$
$7$	0.541135	+	0.144997i	0.204530	+	0.0548036i	−0.155100	+	0.987899i	$0.549570\pi$
$8$	−3.76217	−	3.76217i	−1.33013	−	1.33013i
$9$	2.89403	+	0.790307i	0.964677	+	0.263436i
$10$	−1.20503	+	0.695727i	−0.381065	+	0.220008i
$11$	3.72918	+	3.72918i	1.12439	+	1.12439i	0.991073	+	0.133317i	$0.0425629\pi$
$11$	3.72918	+	3.72918i	1.12439	+	1.12439i	0.133317	+	0.991073i	$0.457437\pi$
$12$	−0.954368	+	7.11758i	−0.275502	+	2.05467i
$13$	−1.98995	−	3.00668i	−0.551912	−	0.833903i
$13$	−1.98995	−	3.00668i	−0.551912	−	0.833903i
$14$	1.20280	−	0.694436i	0.321461	−	0.185596i
$15$	0.897249	+	0.374169i	0.231669	+	0.0966100i
$16$	−4.89803			−1.22451
$17$	−1.39921	+	2.42351i	−0.339359	+	0.587787i	−0.984312	−	0.176435i	$-0.943544\pi$
$17$	−1.39921	+	2.42351i	−0.339359	+	0.587787i	0.644953	+	0.764222i	$0.276877\pi$
$18$	6.45869	−	3.68786i	1.52233	−	0.869236i
$19$	3.31532	−	0.888337i	0.760586	−	0.203798i	0.142377	−	0.989812i	$-0.454525\pi$
$19$	3.31532	−	0.888337i	0.760586	−	0.203798i	0.618209	+	0.786014i	$0.287859\pi$
$20$	−0.602290	+	2.24778i	−0.134676	+	0.502619i
$21$	−0.895584	−	0.373474i	−0.195432	−	0.0814988i
$22$	13.0746			2.78752
$23$	−3.77915	+	6.54568i	−0.788008	+	1.36487i	0.139178	+	0.990267i	$0.455554\pi$
$23$	−3.77915	+	6.54568i	−0.788008	+	1.36487i	−0.927186	+	0.374602i	$0.877779\pi$
$24$	5.59247	+	7.32445i	1.14156	+	1.49510i
$25$	−4.05731	−	2.34249i	−0.811462	−	0.468498i
$26$	−8.75915	−	1.78235i	−1.71781	−	0.349547i
$27$	−4.78623	−	2.02287i	−0.921110	−	0.389302i
$28$	0.601173	−	2.24361i	0.113611	−	0.424002i
$29$		−	0.895922i		−	0.166368i	−0.996534	−	0.0831842i	$-0.973491\pi$
$29$		−	0.895922i		−	0.166368i	0.996534	−	0.0831842i	$-0.0265090\pi$
$30$	2.22881	−	0.916966i	0.406924	−	0.167414i
$31$	−1.57626	+	5.88269i	−0.283105	+	1.05656i	0.667108	+	0.744961i	$0.267532\pi$
$31$	−1.57626	+	5.88269i	−0.283105	+	1.05656i	−0.950213	+	0.311601i	$0.899135\pi$
$32$	−1.06198	+	1.06198i	−0.187733	+	0.187733i
$33$	−5.54344	−	7.26024i	−0.964989	−	1.26384i
$34$	1.79560	+	6.70128i	0.307943	+	1.14926i
$35$	−0.272308	−	0.157217i	−0.0460285	−	0.0265746i
$36$	3.27670	−	11.9990i	0.546117	−	1.99983i
$37$	−0.0565841	−	0.0151617i	−0.00930236	−	0.00249256i	0.254165	−	0.967161i	$-0.418199\pi$
$37$	−0.0565841	−	0.0151617i	−0.00930236	−	0.00249256i	−0.263467	+	0.964668i	$0.584866\pi$
$38$	4.25453	−	7.36906i	0.690176	−	1.19542i
$39$	2.72403	+	5.61958i	0.436193	+	0.899853i
$40$	1.49311	+	2.58614i	0.236081	+	0.408905i
$41$	−1.50730	−	5.62531i	−0.235400	−	0.878525i	−0.977968	−	0.208754i	$-0.933059\pi$
$41$	−1.50730	−	5.62531i	−0.235400	−	0.878525i	0.742568	−	0.669771i	$-0.233608\pi$
$42$	−2.22468	+	0.915264i	−0.343275	+	0.141228i
$43$	9.03652	−	5.21724i	1.37806	−	0.795621i	0.386131	−	0.922444i	$-0.373811\pi$
$43$	9.03652	−	5.21724i	1.37806	−	0.795621i	0.991925	+	0.126822i	$0.0404778\pi$
$44$	15.4616	−	15.4616i	2.33093	−	2.33093i
$45$	−1.45417	−	0.848863i	−0.216775	−	0.126541i
$46$	4.84977	+	18.0996i	0.715059	+	2.66864i
$47$	−10.6264	+	2.84732i	−1.55001	+	0.415325i	−0.929485	−	0.368859i	$-0.879748\pi$
$47$	−10.6264	+	2.84732i	−1.55001	+	0.415325i	−0.620528	+	0.784184i	$0.713082\pi$
$48$	8.40838	+	1.12745i	1.21365	+	0.162733i
$49$	−5.79037	−	3.34307i	−0.827196	−	0.477582i
$50$	−11.2189	+	3.00611i	−1.58660	+	0.425128i
$51$	2.95986	−	3.83833i	0.414464	−	0.537474i
$52$	−12.4660	+	8.25054i	−1.72873	+	1.14414i
$53$			5.68410i			0.780771i	0.920652	+	0.390385i	$0.127658\pi$
$53$			5.68410i			0.780771i	−0.920652	+	0.390385i	$0.872342\pi$
$54$	−11.9364	+	4.84421i	−1.62434	+	0.659213i
$55$	−1.48002	−	2.56347i	−0.199566	−	0.345658i
$56$	−1.49034	−	2.58134i	−0.199155	−	0.344946i
$57$	−5.89584	+	0.761864i	−0.780924	+	0.100911i
$58$	−1.57056	−	1.57056i	−0.206225	−	0.206225i
$59$	3.61546	+	3.61546i	0.470692	+	0.470692i	0.902139	−	0.431446i	$-0.141997\pi$
$59$	3.61546	+	3.61546i	0.470692	+	0.470692i	−0.431446	+	0.902139i	$0.641997\pi$
$60$	1.55135	−	3.72010i	0.200278	−	0.480262i
$61$	2.08491	+	3.61117i	0.266945	+	0.462363i	0.968071	−	0.250675i	$-0.0806524\pi$
$61$	2.08491	+	3.61117i	0.266945	+	0.462363i	−0.701126	+	0.713037i	$0.747319\pi$
$62$	7.54922	+	13.0756i	0.958752	+	1.66061i
$63$	1.45147	+	0.847288i	0.182868	+	0.106748i
$64$		−	6.07273i		−	0.759091i
$65$	0.642063	+	1.91912i	0.0796381	+	0.238037i
$66$	−22.4450	−	3.00956i	−2.76279	−	0.370452i
$67$	−6.36385	+	1.70519i	−0.777468	+	0.208322i	−0.625668	−	0.780089i	$-0.715174\pi$
$67$	−6.36385	+	1.70519i	−0.777468	+	0.208322i	−0.151800	+	0.988411i	$0.548507\pi$
$68$	10.0481	+	5.80130i	1.21852	+	0.703511i
$69$	7.99433	−	10.3670i	0.962404	−	1.24804i
$70$	−0.752964	+	0.201756i	−0.0899965	+	0.0241145i
$71$	−0.573694	−	2.14106i	−0.0680850	−	0.254097i	0.923492	−	0.383619i	$-0.125322\pi$
$71$	−0.573694	−	2.14106i	−0.0680850	−	0.254097i	−0.991577	+	0.129522i	$0.958656\pi$
$72$	−7.91455	−	13.8611i	−0.932739	−	1.63355i
$73$	2.68642	−	2.68642i	0.314422	−	0.314422i	−0.532198	−	0.846620i	$-0.678634\pi$
$73$	2.68642	−	2.68642i	0.314422	−	0.314422i	0.846620	+	0.532198i	$0.178634\pi$
$74$	−0.125771	+	0.0726140i	−0.0146206	+	0.00844121i
$75$	6.42593	+	4.95525i	0.742003	+	0.572183i
$76$	−3.68314	−	13.7457i	−0.422486	−	1.57674i
$77$	1.47727	+	2.55871i	0.168351	+	0.291592i
$78$	14.6265	+	5.07595i	1.65612	+	0.574738i
$79$	2.61166	−	4.52353i	0.293835	−	0.508937i	−0.680878	−	0.732397i	$-0.738402\pi$
$79$	2.61166	−	4.52353i	0.293835	−	0.508937i	0.974713	+	0.223459i	$0.0717350\pi$
$80$	2.65542	+	0.711518i	0.296885	+	0.0795502i
$81$	7.75083	+	4.57435i	0.861203	+	0.508261i
$82$	−12.5035	−	7.21893i	−1.38079	−	0.797197i
$83$	0.0375018	+	0.139959i	0.00411636	+	0.0153625i	0.967953	−	0.251130i	$-0.0808020\pi$
$83$	0.0375018	+	0.139959i	0.00411636	+	0.0153625i	−0.963837	+	0.266492i	$0.914135\pi$
$84$	−1.54847	+	3.71319i	−0.168952	+	0.405142i
$85$	1.11063	−	1.11063i	0.120464	−	0.120464i
$86$	6.69526	−	24.9870i	0.721968	−	2.69442i
$87$	−0.206227	+	1.53802i	−0.0221098	+	0.164893i
$88$		−	28.0596i		−	2.99116i
$89$	2.14168	−	7.99287i	0.227018	−	0.847242i	−0.754568	−	0.656222i	$-0.772154\pi$
$89$	2.14168	−	7.99287i	0.227018	−	0.847242i	0.981586	−	0.191020i	$-0.0611797\pi$
$90$	−4.03725	+	1.06111i	−0.425563	+	0.111851i
$91$	−0.640871	−	1.91555i	−0.0671815	−	0.200805i
$92$	27.1391	+	15.6688i	2.82945	+	1.63358i
$93$	4.06005	−	9.73591i	0.421007	−	1.00957i
$94$	−13.6367	+	23.6195i	−1.40652	+	2.43617i
$95$	−1.92642			−0.197646
$96$	2.06753	−	1.57863i	0.211017	−	0.161119i
$97$	−0.238007	+	0.888254i	−0.0241659	+	0.0901885i	−0.976956	−	0.213443i	$-0.931532\pi$
$97$	−0.238007	+	0.888254i	−0.0241659	+	0.0901885i	0.952790	+	0.303631i	$0.0981990\pi$
$98$	−16.0111	+	4.29015i	−1.61736	+	0.433371i
$99$	7.84517	+	13.7396i	0.788469	+	1.38088i
$100$	−9.71223	+	16.8221i	−0.971223	+	1.68221i
$101$	13.8424			1.37737			0.688684	−	0.725062i	$-0.258189\pi$
$101$	13.8424			1.37737			0.688684	+	0.725062i	$0.258189\pi$
$102$	−1.53996	−	11.9173i	−0.152479	−	1.17999i
$103$	0.558610	−	0.322514i	0.0550415	−	0.0317782i	−0.472227	−	0.881477i	$-0.656550\pi$
$103$	0.558610	−	0.322514i	0.0550415	−	0.0317782i	0.527268	+	0.849699i	$0.323216\pi$
$104$	−3.82511	+	18.7981i	−0.375083	+	1.84331i
$105$	0.431279	+	0.332574i	0.0420886	+	0.0324559i
$106$	9.96430	+	9.96430i	0.967818	+	0.967818i
$107$	9.64434	−	5.56816i	0.932354	−	0.538295i	0.0447985	−	0.998996i	$-0.485735\pi$
$107$	9.64434	−	5.56816i	0.932354	−	0.538295i	0.887555	+	0.460701i	$0.152402\pi$
$108$	−8.38705	+	19.8443i	−0.807044	+	1.90951i
$109$	−12.1108	−	12.1108i	−1.16000	−	1.16000i	−0.984475	−	0.175526i	$-0.943837\pi$
$109$	−12.1108	−	12.1108i	−1.16000	−	1.16000i	−0.175526	−	0.984475i	$-0.556163\pi$
$110$	−7.08828	−	1.89930i	−0.675841	−	0.181091i
$111$	0.0936472	+	0.0390525i	0.00888859	+	0.00370670i
$112$	−2.65049	−	0.710198i	−0.250448	−	0.0671074i
$113$			6.62019i			0.622775i	0.950283	+	0.311387i	$0.100794\pi$
$113$			6.62019i			0.622775i	−0.950283	+	0.311387i	$0.899206\pi$
$114$	−8.99994	+	11.6711i	−0.842921	+	1.09309i
$115$	2.99970	−	2.99970i	0.279724	−	0.279724i
$116$	−3.71459			−0.344891
$117$	−3.38276	−	10.2741i	−0.312737	−	0.949840i
$118$	12.6759			1.16691
$119$	−1.10856	+	1.10856i	−0.101622	+	0.101622i
$120$	−1.96791	−	4.78328i	−0.179645	−	0.436652i
$121$			16.8136i			1.52851i
$122$	9.98530	+	2.67555i	0.904026	+	0.242233i
$123$	1.29270	+	10.0038i	0.116559	+	0.902016i
$124$	24.3903	+	6.53536i	2.19031	+	0.586893i
$125$	3.84373	+	3.84373i	0.343793	+	0.343793i
$126$	4.02975	−	1.05914i	0.358999	−	0.0943555i
$127$	−4.61182	+	2.66264i	−0.409233	+	0.236271i	−0.690460	−	0.723370i	$-0.742592\pi$
$127$	−4.61182	+	2.66264i	−0.409233	+	0.236271i	0.281227	+	0.959641i	$0.409259\pi$
$128$	−12.7695	−	12.7695i	−1.12868	−	1.12868i
$129$	−16.7138	+	6.87631i	−1.47157	+	0.605425i
$130$	4.48978	+	2.23869i	0.393780	+	0.196346i
$131$	−10.5429	+	6.08694i	−0.921137	+	0.531819i	−0.883998	−	0.467491i	$-0.845158\pi$
$131$	−10.5429	+	6.08694i	−0.921137	+	0.531819i	−0.0371394	+	0.999310i	$0.511825\pi$
$132$	−30.1018	+	22.9837i	−2.62002	+	2.00048i
$133$	1.92284			0.166731
$134$	−8.16670	+	14.1451i	−0.705495	+	1.22195i
$135$	2.30096	+	1.79196i	0.198035	+	0.154227i
$136$	14.3817	−	3.85357i	1.23322	−	0.330441i
$137$	1.70117	−	6.34886i	0.145341	−	0.542420i	−0.854399	−	0.519618i	$-0.826074\pi$
$137$	1.70117	−	6.34886i	0.145341	−	0.542420i	0.999740	−	0.0228025i	$-0.00725889\pi$
$138$	−4.15930	−	32.1876i	−0.354063	−	2.73999i
$139$	2.88509			0.244710			0.122355	−	0.992486i	$-0.460955\pi$
$139$	2.88509			0.244710			0.122355	+	0.992486i	$0.460955\pi$
$140$	−0.651841	+	1.12902i	−0.0550906	+	0.0954197i
$141$	18.8975	−	2.44195i	1.59146	−	0.205649i
$142$	−4.75900	−	2.74761i	−0.399366	−	0.230574i
$143$	3.79158	−	18.6333i	0.317068	−	1.55820i
$144$	−14.1750	−	3.87095i	−1.18125	−	0.322579i
$145$	−0.130147	+	0.485716i	−0.0108081	+	0.0403365i
$146$		−	9.41867i		−	0.779495i
$147$	9.17074	+	7.07186i	0.756390	+	0.583278i
$148$	−0.0628619	+	0.234604i	−0.00516722	+	0.0192843i
$149$	−0.214569	+	0.214569i	−0.0175782	+	0.0175782i	−0.715841	−	0.698263i	$-0.753957\pi$
$149$	−0.214569	+	0.214569i	−0.0175782	+	0.0175782i	0.698263	+	0.715841i	$0.253957\pi$
$150$	19.9514	−	2.57813i	1.62902	−	0.210503i
$151$	3.91822	+	14.6230i	0.318860	+	1.19000i	0.920341	+	0.391116i	$0.127911\pi$
$151$	3.91822	+	14.6230i	0.318860	+	1.19000i	−0.601481	+	0.798887i	$0.705422\pi$
$152$	−15.8148	−	9.13070i	−1.28275	−	0.740598i
$153$	−5.96468	+	5.90790i	−0.482216	+	0.477625i
$154$	7.07513	+	1.89577i	0.570130	+	0.152766i
$155$	1.70911	−	2.96027i	0.137279	−	0.237775i
$156$	23.2994	−	11.2941i	1.86545	−	0.904253i
$157$	2.96185	+	5.13007i	0.236381	+	0.409424i	0.959673	−	0.281118i	$-0.0907053\pi$
$157$	2.96185	+	5.13007i	0.236381	+	0.409424i	−0.723292	+	0.690542i	$0.757372\pi$
$158$	−3.35153	−	12.5081i	−0.266634	−	0.995091i
$159$	1.30839	−	9.75782i	0.103762	−	0.773845i
$160$	0.730011	−	0.421472i	0.0577125	−	0.0333203i
$161$	−2.99413	+	2.99413i	−0.235971	+	0.235971i
$162$	21.6062	−	5.56841i	1.69754	−	0.437496i
$163$	−3.97922	−	14.8506i	−0.311676	−	1.16319i	−0.927044	−	0.374952i	$-0.877659\pi$
$163$	−3.97922	−	14.8506i	−0.311676	−	1.16319i	0.615368	−	0.788240i	$-0.289007\pi$
$164$	−23.3232	+	6.24942i	−1.82123	+	0.487998i
$165$	1.95066	+	4.74135i	0.151859	+	0.369113i
$166$	0.311090	+	0.179608i	0.0241453	+	0.0139403i
$167$	1.89441	−	0.507605i	0.146594	−	0.0392797i	−0.184776	−	0.982781i	$-0.559156\pi$
$167$	1.89441	−	0.507605i	0.146594	−	0.0392797i	0.331370	+	0.943501i	$0.392489\pi$
$168$	1.96426	+	4.77441i	0.151546	+	0.368353i
$169$	−5.08023	+	11.9663i	−0.390787	+	0.920481i
$170$		−	3.89388i		−	0.298647i
$171$	10.2967	+	0.0492466i	0.787408	+	0.00376598i
$172$	−21.6313	−	37.4664i	−1.64937	−	2.85679i
$173$	−5.89508	−	10.2106i	−0.448194	−	0.776296i	0.550074	−	0.835116i	$-0.314599\pi$
$173$	−5.89508	−	10.2106i	−0.448194	−	0.776296i	−0.998269	+	0.0588202i	$0.981266\pi$
$174$	2.33465	+	3.05768i	0.176989	+	0.231802i
$175$	−1.85590	−	1.85590i	−0.140293	−	0.140293i
$176$	−18.2656	−	18.2656i	−1.37682	−	1.37682i
$177$	−5.37439	−	7.03883i	−0.403964	−	0.529071i
$178$	−10.2572	−	17.7660i	−0.768810	−	1.33162i
$179$	−7.29437	−	12.6342i	−0.545207	−	0.944326i	−0.998594	−	0.0530122i	$-0.983118\pi$
$179$	−7.29437	−	12.6342i	−0.545207	−	0.944326i	0.453387	−	0.891314i	$-0.350216\pi$
$180$	−3.51948	+	6.02915i	−0.262327	+	0.449386i
$181$			3.05362i			0.226974i	0.993539	+	0.113487i	$0.0362020\pi$
$181$			3.05362i			0.226974i	−0.993539	+	0.113487i	$0.963798\pi$
$182$	−4.48145	−	2.23454i	−0.332187	−	0.165635i
$183$	−2.74790	−	6.67916i	−0.203131	−	0.493738i
$184$	38.8437	−	10.4081i	2.86360	−	0.767299i
$185$	0.0284741	+	0.0164395i	0.00209345	+	0.00120866i
$186$	−9.94986	−	24.1845i	−0.729559	−	1.77329i
$187$	−14.2556	+	3.81978i	−1.04247	+	0.279330i
$188$	11.8053	+	44.0581i	0.860992	+	3.21327i
$189$	−2.29669	−	1.78863i	−0.167059	−	0.130104i
$190$	−3.37703	+	3.37703i	−0.244996	+	0.244996i
$191$	−11.6232	+	6.71063i	−0.841022	+	0.485564i	−0.857612	−	0.514298i	$-0.828053\pi$
$191$	−11.6232	+	6.71063i	−0.841022	+	0.485564i	0.0165893	+	0.999862i	$0.494719\pi$
$192$	−1.39784	+	10.4250i	−0.100881	+	0.752358i
$193$	−0.927596	−	3.46183i	−0.0667698	−	0.249188i	0.924472	−	0.381251i	$-0.124507\pi$
$193$	−0.927596	−	3.46183i	−0.0667698	−	0.249188i	−0.991241	+	0.132063i	$0.957840\pi$
$194$	1.13989	+	1.97435i	0.0818394	+	0.141750i
$195$	−0.660471	−	3.44231i	−0.0472973	−	0.246509i
$196$	−13.8608	+	24.0075i	−0.990055	+	1.71482i
$197$	−12.7045	−	3.40415i	−0.905155	−	0.242536i	−0.223926	−	0.974606i	$-0.571887\pi$
$197$	−12.7045	−	3.40415i	−0.905155	−	0.242536i	−0.681229	+	0.732071i	$0.738554\pi$
$198$	37.8383	+	10.3330i	2.68905	+	0.734332i
$199$	17.2174	+	9.94049i	1.22051	+	0.704662i	0.965027	−	0.262151i	$-0.0844318\pi$
$199$	17.2174	+	9.94049i	1.22051	+	0.704662i	0.255484	+	0.966813i	$0.417765\pi$
$200$	6.45144	+	24.0771i	0.456186	+	1.70251i
$201$	11.3172	−	1.46242i	0.798257	−	0.103151i
$202$	24.2659	−	24.2659i	1.70734	−	1.70734i
$203$	0.129906	−	0.484814i	0.00911759	−	0.0340273i
$204$	−15.9142	−	12.2719i	−1.11421	−	0.859207i
$205$			3.26867i			0.228294i
$206$	0.413880	−	1.54462i	0.0288364	−	0.107619i
$207$	−16.1101	+	15.9567i	−1.11973	+	1.10907i
$208$	9.74681	+	14.7268i	0.675820	+	1.02112i
$209$	15.6762	+	9.05065i	1.08434	+	0.626047i
$210$	1.33905	−	0.173032i	0.0924029	−	0.0119403i
$211$	2.79451	−	4.84023i	0.192382	−	0.333215i	−0.753657	−	0.657268i	$-0.771712\pi$
$211$	2.79451	−	4.84023i	0.192382	−	0.333215i	0.946039	+	0.324052i	$0.105045\pi$
$212$	23.5669			1.61858
$213$	0.492017	+	3.80758i	0.0337125	+	0.260891i
$214$	7.14560	−	26.6677i	0.488463	−	1.82297i
$215$	−5.65696	+	1.51578i	−0.385801	+	0.103375i
$216$	10.3962	+	25.6170i	0.707373	+	1.74301i
$217$	−1.70594	+	2.95478i	−0.115807	+	0.200583i
$218$	−42.4607			−2.87580
$219$	−5.23012	+	3.99338i	−0.353419	+	0.269847i
$220$	−10.6284	+	6.13632i	−0.716568	+	0.413711i
$221$	10.0711	−	0.615667i	0.677453	−	0.0414142i
$222$	0.232624	−	0.0957051i	0.0156127	−	0.00642330i
$223$	−11.6779	−	11.6779i	−0.782011	−	0.782011i	0.198159	−	0.980170i	$-0.436504\pi$
$223$	−11.6779	−	11.6779i	−0.782011	−	0.782011i	−0.980170	+	0.198159i	$0.936504\pi$
$224$	−0.728656	+	0.420690i	−0.0486854	+	0.0281085i
$225$	−9.89070	−	9.98576i	−0.659380	−	0.665718i
$226$	11.6053	+	11.6053i	0.771971	+	0.771971i
$227$	−3.26741	−	0.875500i	−0.216866	−	0.0581090i	0.148750	−	0.988875i	$-0.452475\pi$
$227$	−3.26741	−	0.875500i	−0.216866	−	0.0581090i	−0.365616	+	0.930766i	$0.619142\pi$
$228$	3.15877	+	24.4448i	0.209195	+	1.61890i
$229$	−16.5714	−	4.44029i	−1.09507	−	0.293423i	−0.334313	−	0.942462i	$-0.608504\pi$
$229$	−16.5714	−	4.44029i	−1.09507	−	0.293423i	−0.760755	+	0.649039i	$0.775171\pi$
$230$		−	10.5170i		−	0.693472i
$231$	−1.94704	−	4.73255i	−0.128106	−	0.311379i
$232$	−3.37060	+	3.37060i	−0.221291	+	0.221291i
$233$	2.96268			0.194092			0.0970459	−	0.995280i	$-0.469061\pi$
$233$	2.96268			0.194092			0.0970459	+	0.995280i	$0.469061\pi$
$234$	−23.9406	−	12.0806i	−1.56505	−	0.789733i
$235$	6.17460			0.402787
$236$	14.9901	−	14.9901i	0.975772	−	0.975772i
$237$	−5.52465	+	7.16433i	−0.358865	+	0.465373i
$238$			3.88665i			0.251934i
$239$	−24.9831	−	6.69421i	−1.61602	−	0.433012i	−0.666194	−	0.745778i	$-0.732078\pi$
$239$	−24.9831	−	6.69421i	−1.61602	−	0.433012i	−0.949830	+	0.312766i	$0.898744\pi$
$240$	−4.39475	−	1.83269i	−0.283680	−	0.118300i
$241$	5.70394	+	1.52837i	0.367423	+	0.0984507i	0.437806	−	0.899069i	$-0.355756\pi$
$241$	5.70394	+	1.52837i	0.367423	+	0.0984507i	−0.0703833	+	0.997520i	$0.522422\pi$
$242$	29.4744	+	29.4744i	1.89469	+	1.89469i
$243$	−12.2528	−	9.63684i	−0.786018	−	0.618204i
$244$	14.9723	−	8.64427i	0.958504	−	0.553392i
$245$	2.65356	+	2.65356i	0.169530	+	0.169530i
$246$	19.8030	+	15.2708i	1.26259	+	0.973628i
$247$	−9.26825	−	8.20035i	−0.589724	−	0.521776i
$248$	28.0618	−	16.2015i	1.78193	−	1.02880i
$249$	−0.0321626	−	0.248897i	−0.00203822	−	0.0157732i
$250$	13.4762			0.852310
$251$	1.51755	−	2.62847i	0.0957869	−	0.165908i	−0.814150	−	0.580655i	$-0.802797\pi$
$251$	1.51755	−	2.62847i	0.0957869	−	0.165908i	0.909937	+	0.414747i	$0.136130\pi$
$252$	3.51295	−	6.01796i	0.221295	−	0.379096i
$253$	−38.5032	+	10.3169i	−2.42067	+	0.648618i
$254$	−3.41695	+	12.7522i	−0.214398	+	0.800146i
$255$	−2.16224	+	1.65095i	−0.135405	+	0.103386i
$256$	−32.6249			−2.03905
$257$	9.66046	−	16.7324i	0.602603	−	1.04374i	−0.389822	−	0.920890i	$-0.627464\pi$
$257$	9.66046	−	16.7324i	0.602603	−	1.04374i	0.992425	−	0.122849i	$-0.0392031\pi$
$258$	−17.2453	+	41.3538i	−1.07364	+	2.57457i
$259$	−0.0284212	−	0.0164090i	−0.00176601	−	0.00101961i
$260$	7.95687	−	2.66206i	0.493464	−	0.165094i
$261$	0.708053	−	2.59282i	0.0438274	−	0.160492i
$262$	−7.81134	+	29.1523i	−0.482586	+	1.80104i
$263$			9.22129i			0.568609i	0.958734	+	0.284304i	$0.0917626\pi$
$263$			9.22129i			0.568609i	−0.958734	+	0.284304i	$0.908237\pi$
$264$	−6.45887	+	48.1695i	−0.397516	+	2.96463i
$265$	0.825708	−	3.08158i	0.0507228	−	0.189300i
$266$	3.37076	−	3.37076i	0.206675	−	0.206675i
$267$	−5.51643	+	13.2283i	−0.337600	+	0.809557i
$268$	7.06990	+	26.3852i	0.431863	+	1.61173i
$269$	21.9375	+	12.6656i	1.33755	+	0.772236i	0.986444	−	0.164099i	$-0.0524717\pi$
$269$	21.9375	+	12.6656i	1.33755	+	0.772236i	0.351108	+	0.936335i	$0.385805\pi$
$270$	7.17494	−	0.892281i	0.436653	−	0.0543025i
$271$	21.4503	+	5.74758i	1.30301	+	0.349141i	0.842588	−	0.538559i	$-0.181031\pi$
$271$	21.4503	+	5.74758i	1.30301	+	0.349141i	0.460423	+	0.887700i	$0.347698\pi$
$272$	6.85338	−	11.8704i	0.415548	−	0.719749i
$273$	0.659245	+	3.43593i	0.0398993	+	0.207952i
$274$	−8.14747	−	14.1118i	−0.492206	−	0.852526i
$275$	−6.39488	−	23.8660i	−0.385626	−	1.43918i
$276$	−42.9827	−	33.1454i	−2.58726	−	1.99512i
$277$	17.8165	−	10.2863i	1.07049	−	0.618046i	0.142173	−	0.989842i	$-0.454591\pi$
$277$	17.8165	−	10.2863i	1.07049	−	0.618046i	0.928315	+	0.371796i	$0.121258\pi$
$278$	5.05760	−	5.05760i	0.303335	−	0.303335i
$279$	−9.21088	+	15.7790i	−0.551441	+	0.944661i
$280$	0.432992	+	1.61595i	0.0258762	+	0.0965713i
$281$	−1.34049	+	0.359183i	−0.0799670	+	0.0214271i	−0.298581	−	0.954384i	$-0.596513\pi$
$281$	−1.34049	+	0.359183i	−0.0799670	+	0.0214271i	0.218614	+	0.975811i	$0.429847\pi$
$282$	28.8469	−	37.4084i	1.71781	−	2.22764i
$283$	28.8273	+	16.6434i	1.71360	+	0.989350i	0.929580	+	0.368621i	$0.120170\pi$
$283$	28.8273	+	16.6434i	1.71360	+	0.989350i	0.784025	+	0.620729i	$0.213163\pi$
$284$	−8.87706	+	2.37860i	−0.526757	+	0.141144i
$285$	3.30705	+	0.443430i	0.195893	+	0.0262665i
$286$	−26.0178	−	39.3111i	−1.53846	−	2.32452i
$287$		−	3.26260i		−	0.192585i
$288$	−3.91269	+	2.23411i	−0.230557	+	0.131646i
$289$	4.58440	+	7.94042i	0.269671	+	0.467084i
$290$	0.623317	+	1.07962i	0.0366024	+	0.0633973i
$291$	0.613045	−	1.47007i	0.0359373	−	0.0861769i
$292$	−11.1382	−	11.1382i	−0.651815	−	0.651815i
$293$	−6.75772	−	6.75772i	−0.394790	−	0.394790i	0.481601	−	0.876391i	$-0.340056\pi$
$293$	−6.75772	−	6.75772i	−0.394790	−	0.394790i	−0.876391	+	0.481601i	$0.840056\pi$
$294$	28.4735	−	3.67936i	1.66061	−	0.214585i
$295$	−1.43488	−	2.48529i	−0.0835422	−	0.144699i
$296$	0.155838	+	0.269919i	0.00905789	+	0.0156887i
$297$	−10.3051	−	25.3924i	−0.597961	−	1.47341i
$298$			0.752285i			0.0435787i
$299$	27.2011	−	1.66286i	1.57308	−	0.0961658i
$300$	20.5450	−	26.6426i	1.18617	−	1.53821i
$301$	5.64646	−	1.51296i	0.325457	−	0.0872058i
$302$	32.5030	+	18.7656i	1.87034	+	1.07984i
$303$	−23.7630	−	3.18629i	−1.36515	−	0.183048i
$304$	−16.2385	+	4.35110i	−0.931343	+	0.249553i
$305$	−0.605734	−	2.26063i	−0.0346842	−	0.129443i
$306$	−0.0995427	+	20.8128i	−0.00569048	+	1.18979i
$307$	22.8954	−	22.8954i	1.30671	−	1.30671i	0.382938	−	0.923774i	$-0.374912\pi$
$307$	22.8954	−	22.8954i	1.30671	−	1.30671i	0.923774	−	0.382938i	$-0.125088\pi$
$308$	10.6087	−	6.12493i	0.604487	−	0.349001i
$309$	−1.03320	+	0.425072i	−0.0587765	+	0.0241815i
$310$	−2.19330	−	8.18549i	−0.124571	−	0.464905i
$311$	8.44356	+	14.6247i	0.478790	+	0.829289i	0.999704	−	0.0243201i	$-0.00774210\pi$
$311$	8.44356	+	14.6247i	0.478790	+	0.829289i	−0.520914	+	0.853609i	$0.674409\pi$
$312$	10.8936	−	31.3900i	0.616726	−	1.77711i
$313$	−8.64294	+	14.9700i	−0.488528	+	0.846155i	−0.999913	−	0.0131968i	$-0.995799\pi$
$313$	−8.64294	+	14.9700i	−0.488528	+	0.846155i	0.511385	+	0.859352i	$0.329133\pi$
$314$	14.1852	+	3.80092i	0.800519	+	0.214498i
$315$	−0.663819	−	0.670199i	−0.0374020	−	0.0377614i
$316$	−18.7551	−	10.8282i	−1.05506	−	0.609137i
$317$	3.01849	+	11.2652i	0.169535	+	0.632715i	0.997418	+	0.0718135i	$0.0228786\pi$
$317$	3.01849	+	11.2652i	0.169535	+	0.632715i	−0.827883	+	0.560901i	$0.810455\pi$
$318$	−14.8120	−	19.3992i	−0.830614	−	1.08785i
$319$	3.34105	−	3.34105i	0.187063	−	0.187063i
$320$	−0.882163	+	3.29228i	−0.0493144	+	0.184044i
$321$	−17.8380	+	7.33882i	−0.995621	+	0.409613i
$322$			10.4975i			0.585003i
$323$	−2.48595	+	9.27767i	−0.138322	+	0.516224i
$324$	18.9658	−	32.1358i	1.05365	−	1.78532i
$325$	1.03072	+	16.8605i	0.0571739	+	0.935250i
$326$	−33.0090	−	19.0577i	−1.82820	−	1.05551i
$327$	18.0027	+	23.5781i	0.995551	+	1.30387i
$328$	−15.4926	+	26.8340i	−0.855437	+	1.48166i
$329$	−6.16314			−0.339785
$330$	11.7312	+	4.89211i	0.645780	+	0.269302i
$331$	1.91001	−	7.12824i	0.104983	−	0.391804i	−0.893360	−	0.449342i	$-0.851658\pi$
$331$	1.91001	−	7.12824i	0.104983	−	0.391804i	0.998343	+	0.0575384i	$0.0183252\pi$
$332$	0.580284	−	0.155487i	0.0318472	−	0.00853344i
$333$	−0.151774	−	0.0885971i	−0.00831714	−	0.00485509i
$334$	2.43109	−	4.21076i	0.133023	−	0.230403i
$335$	3.69781			0.202033
$336$	4.38659	+	1.82929i	0.239308	+	0.0997958i
$337$	20.3501	−	11.7491i	1.10854	−	0.640015i	0.170088	−	0.985429i	$-0.445595\pi$
$337$	20.3501	−	11.7491i	1.10854	−	0.640015i	0.938450	+	0.345414i	$0.112262\pi$
$338$	12.0713	+	29.8827i	0.656592	+	1.62541i
$339$	1.52386	−	11.3648i	0.0827647	−	0.617251i
$340$	−4.60478	−	4.60478i	−0.249729	−	0.249729i
$341$	−27.8158	+	16.0594i	−1.50631	+	0.869668i
$342$	18.1366	−	17.9639i	0.980713	−	0.971377i
$343$	−5.42161	−	5.42161i	−0.292739	−	0.292739i
$344$	−53.6250	−	14.3688i	−2.89127	−	0.774712i
$345$	−5.84003	+	4.45907i	−0.314417	+	0.240068i
$346$	−28.2334	−	7.56512i	−1.51784	−	0.406704i
$347$			23.5752i			1.26558i	0.774323	+	0.632790i	$0.218091\pi$
$347$			23.5752i			1.26558i	−0.774323	+	0.632790i	$0.781909\pi$
$348$	6.37679	+	0.855039i	0.341832	+	0.0458349i
$349$	−11.0873	+	11.0873i	−0.593491	+	0.593491i	−0.938573	−	0.345082i	$-0.887851\pi$
$349$	−11.0873	+	11.0873i	−0.593491	+	0.593491i	0.345082	+	0.938573i	$0.387851\pi$
$350$	−6.50684			−0.347805
$351$	3.44222	+	18.4161i	0.183732	+	0.982976i
$352$	−7.92061			−0.422170
$353$	1.18338	−	1.18338i	0.0629849	−	0.0629849i	−0.674913	−	0.737898i	$-0.735819\pi$
$353$	1.18338	−	1.18338i	0.0629849	−	0.0629849i	0.737898	+	0.674913i	$0.235819\pi$
$354$	−21.7605	−	2.91779i	−1.15656	−	0.155079i
$355$			1.24409i			0.0660296i
$356$	−33.1393	−	8.87966i	−1.75638	−	0.470621i
$357$	2.15823	−	1.64788i	0.114226	−	0.0872153i
$358$	−34.9351	−	9.36083i	−1.84638	−	0.494735i
$359$	−3.23316	−	3.23316i	−0.170640	−	0.170640i	0.616621	−	0.787260i	$-0.288501\pi$
$359$	−3.23316	−	3.23316i	−0.170640	−	0.170640i	−0.787260	+	0.616621i	$0.788501\pi$
$360$	2.27726	+	8.66439i	0.120022	+	0.456653i
$361$	−6.25229	+	3.60976i	−0.329068	+	0.189988i
$362$	5.35304	+	5.35304i	0.281349	+	0.281349i
$363$	3.87022	−	28.8637i	0.203134	−	1.51495i
$364$	−7.94210	+	2.65712i	−0.416279	+	0.139271i
$365$	−1.84667	+	1.06617i	−0.0966590	+	0.0558061i
$366$	−16.5258	−	6.89154i	−0.863816	−	0.360227i
$367$	−1.85971			−0.0970758			−0.0485379	−	0.998821i	$-0.515456\pi$
$367$	−1.85971			−0.0970758			−0.0485379	+	0.998821i	$0.515456\pi$
$368$	18.5104	−	32.0609i	0.964921	−	1.67129i
$369$	0.0835598	−	17.4710i	0.00434995	−	0.909506i
$370$	0.0787341	−	0.0210967i	0.00409319	−	0.00109677i
$371$	−0.824175	+	3.07586i	−0.0427890	+	0.159691i
$372$	−40.3662	−	16.8334i	−2.09289	−	0.872772i
$373$	25.8344			1.33765			0.668826	−	0.743419i	$-0.266797\pi$
$373$	25.8344			1.33765			0.668826	+	0.743419i	$0.266797\pi$
$374$	−18.2942	+	31.6864i	−0.945969	+	1.63847i
$375$	−5.71371	−	7.48324i	−0.295055	−	0.386433i
$376$	50.6902	+	29.2660i	2.61415	+	1.50928i
$377$	−2.69375	+	1.78284i	−0.138735	+	0.0918207i
$378$	−7.16162	+	0.890625i	−0.368354	+	0.0458088i
$379$	−9.87280	+	36.8458i	−0.507132	+	1.89264i	−0.0599419	+	0.998202i	$0.519092\pi$
$379$	−9.87280	+	36.8458i	−0.507132	+	1.89264i	−0.447190	+	0.894439i	$0.647575\pi$
$380$			7.98714i			0.409731i
$381$	8.52995	−	3.50935i	0.437003	−	0.179789i
$382$	−8.61172	+	32.1394i	−0.440614	+	1.64439i
$383$	10.5154	−	10.5154i	0.537311	−	0.537311i	−0.385427	−	0.922738i	$-0.625946\pi$
$383$	10.5154	−	10.5154i	0.537311	−	0.537311i	0.922738	+	0.385427i	$0.125946\pi$
$384$	18.9820	+	24.8606i	0.968669	+	1.26866i
$385$	−0.429195	−	1.60178i	−0.0218738	−	0.0816342i
$386$	−7.69473	−	4.44255i	−0.391651	−	0.226120i
$387$	30.2752	−	7.95722i	1.53897	−	0.404488i
$388$	3.68280	+	0.986803i	0.186966	+	0.0500973i
$389$	7.77391	−	13.4648i	0.394153	−	0.682692i	−0.598840	−	0.800869i	$-0.704371\pi$
$389$	7.77391	−	13.4648i	0.394153	−	0.682692i	0.992993	+	0.118176i	$0.0377048\pi$
$390$	−7.19224	−	4.87661i	−0.364193	−	0.246937i
$391$	−10.5757	−	18.3176i	−0.534835	−	0.926361i
$392$	9.20715	+	34.3615i	0.465031	+	1.73552i
$393$	19.5000	−	8.02257i	0.983643	−	0.404685i
$394$	−28.2386	+	16.3036i	−1.42264	+	0.821362i
$395$	−2.07301	+	2.07301i	−0.104304	+	0.104304i
$396$	56.9658	−	32.5269i	2.86264	−	1.63454i
$397$	−0.481208	−	1.79589i	−0.0241511	−	0.0901332i	0.952798	−	0.303604i	$-0.0981899\pi$
$397$	−0.481208	−	1.79589i	−0.0241511	−	0.0901332i	−0.976949	+	0.213471i	$0.931523\pi$
$398$	47.6082	−	12.7566i	2.38638	−	0.639429i
$399$	−3.30092	−	0.442607i	−0.165252	−	0.0221581i
$400$	19.8728	+	11.4736i	0.993641	+	0.573679i
$401$	−2.74656	+	0.735939i	−0.137157	+	0.0367510i	−0.326744	−	0.945113i	$-0.605952\pi$
$401$	−2.74656	+	0.735939i	−0.137157	+	0.0367510i	0.189588	+	0.981864i	$0.439285\pi$
$402$	17.2756	−	22.4029i	0.861631	−	1.11736i
$403$	20.8240	−	6.96692i	1.03732	−	0.347047i
$404$		−	57.3920i		−	2.85536i
$405$	−3.53754	−	3.60588i	−0.175782	−	0.179177i
$406$	−0.622160	−	1.07761i	−0.0308773	−	0.0534810i
$407$	−0.154472	−	0.267553i	−0.00765687	−	0.0132621i
$408$	−25.5759	+	3.30493i	−1.26620	+	0.163619i
$409$	8.34468	+	8.34468i	0.412618	+	0.412618i	0.882649	−	0.470032i	$-0.155758\pi$
$409$	8.34468	+	8.34468i	0.412618	+	0.412618i	−0.470032	+	0.882649i	$0.655758\pi$
$410$	5.73002	+	5.73002i	0.282986	+	0.282986i
$411$	−4.38179	+	10.5074i	−0.216138	+	0.518293i
$412$	−1.33718	−	2.31606i	−0.0658781	−	0.114104i
$413$	1.43222	+	2.48068i	0.0704750	+	0.122066i
$414$	−0.268856	+	56.2135i	−0.0132135	+	2.76274i
$415$		−	0.0813251i		−	0.00399209i
$416$	5.30630	+	1.07975i	0.260163	+	0.0529390i
$417$	−4.95280	−	0.664102i	−0.242540	−	0.0325212i
$418$	43.3465	−	11.6147i	2.12015	−	0.568091i
$419$	−19.5778	−	11.3033i	−0.956439	−	0.552201i	−0.0613641	−	0.998115i	$-0.519545\pi$
$419$	−19.5778	−	11.3033i	−0.956439	−	0.552201i	−0.895075	+	0.445915i	$0.852878\pi$
$420$	1.37889	−	1.78813i	0.0672829	−	0.0872520i
$421$	18.8345	−	5.04668i	0.917936	−	0.245960i	0.231233	−	0.972898i	$-0.425724\pi$
$421$	18.8345	−	5.04668i	0.917936	−	0.245960i	0.686703	+	0.726938i	$0.259057\pi$
$422$	−3.58618	−	13.3838i	−0.174573	−	0.651514i
$423$	−33.0033	−	0.157847i	−1.60467	−	0.00767477i
$424$	21.3845	−	21.3845i	1.03852	−	1.03852i
$425$	11.3541	−	6.55529i	0.550754	−	0.317978i
$426$	7.53725	+	5.81223i	0.365181	+	0.281603i
$427$	0.604610	+	2.25643i	0.0292591	+	0.109196i
$428$	−23.0862	−	39.9865i	−1.11592	−	1.93282i
$429$	−10.7980	+	31.1148i	−0.521335	+	1.50224i
$430$	−7.25955	+	12.5739i	−0.350086	+	0.606368i
$431$	−11.0205	−	2.95294i	−0.530840	−	0.142238i	−0.0165641	−	0.999863i	$-0.505273\pi$
$431$	−11.0205	−	2.95294i	−0.530840	−	0.142238i	−0.514276	+	0.857625i	$0.671939\pi$
$432$	23.4431	+	9.90807i	1.12791	+	0.476702i
$433$	24.9555	+	14.4081i	1.19929	+	0.692408i	0.960396	−	0.278639i	$-0.0898832\pi$
$433$	24.9555	+	14.4081i	1.19929	+	0.692408i	0.238890	+	0.971047i	$0.423217\pi$
$434$	2.18922	+	8.17030i	0.105086	+	0.392187i
$435$	0.335226	−	0.803865i	0.0160729	−	0.0385424i
$436$	−50.2126	+	50.2126i	−2.40475	+	2.40475i
$437$	−6.71432	+	25.0582i	−0.321189	+	1.19870i
$438$	−2.16803	+	16.1689i	−0.103592	+	0.772581i
$439$		−	23.2920i		−	1.11167i	−0.831294	−	0.555833i	$-0.812400\pi$
$439$		−	23.2920i		−	1.11167i	0.831294	−	0.555833i	$-0.187600\pi$
$440$	−4.07611	+	15.2123i	−0.194321	+	0.725216i
$441$	−14.1155	−	14.2511i	−0.672165	−	0.678626i
$442$	16.5754	−	18.7340i	0.788414	−	0.891085i
$443$	−15.9997	−	9.23744i	−0.760170	−	0.438884i	0.0691871	−	0.997604i	$-0.477959\pi$
$443$	−15.9997	−	9.23744i	−0.760170	−	0.438884i	−0.829357	+	0.558720i	$0.811293\pi$
$444$	0.161916	−	0.388272i	0.00768421	−	0.0184266i
$445$	−2.32219	+	4.02215i	−0.110082	+	0.190668i
$446$	−40.9431			−1.93871
$447$	0.417739	−	0.318958i	0.0197584	−	0.0150862i
$448$	0.880526	−	3.28617i	0.0416009	−	0.155257i
$449$	34.2960	−	9.18959i	1.61853	−	0.433684i	0.667960	−	0.744197i	$-0.267168\pi$
$449$	34.2960	−	9.18959i	1.61853	−	0.433684i	0.950569	+	0.310513i	$0.100501\pi$
$450$	−34.8437	−	0.166649i	−1.64255	−	0.00785592i
$451$	15.3568	−	26.5988i	0.723124	−	1.25249i
$452$	27.4480			1.29105
$453$	−3.36038	−	26.0050i	−0.157885	−	1.22182i
$454$	−7.26258	+	4.19305i	−0.340850	+	0.196790i
$455$	0.0691771	+	1.13160i	0.00324307	+	0.0530501i
$456$	25.0474	+	19.3149i	1.17295	+	0.904502i
$457$	12.3515	+	12.3515i	0.577780	+	0.577780i	0.934291	−	0.356511i	$-0.116034\pi$
$457$	12.3515	+	12.3515i	0.577780	+	0.577780i	−0.356511	+	0.934291i	$0.616034\pi$
$458$	−36.8337	+	21.2660i	−1.72113	+	0.993694i
$459$	11.5994	−	8.76904i	0.541414	−	0.409304i
$460$	−12.4371	−	12.4371i	−0.579883	−	0.579883i
$461$	4.57459	+	1.22576i	0.213060	+	0.0570892i	0.363770	−	0.931489i	$-0.381489\pi$
$461$	4.57459	+	1.22576i	0.213060	+	0.0570892i	−0.150710	+	0.988578i	$0.548156\pi$
$462$	−11.7094	−	4.88303i	−0.544771	−	0.227179i
$463$	2.18422	+	0.585260i	0.101509	+	0.0271993i	0.309216	−	0.950992i	$-0.399933\pi$
$463$	2.18422	+	0.585260i	0.101509	+	0.0271993i	−0.207707	+	0.978191i	$0.566600\pi$
$464$			4.38825i			0.203719i
$465$	−3.61542	+	4.68845i	−0.167661	+	0.217422i
$466$	5.19362	−	5.19362i	0.240590	−	0.240590i
$467$	13.8388			0.640383			0.320192	−	0.947353i	$-0.396253\pi$
$467$	13.8388			0.640383			0.320192	+	0.947353i	$0.396253\pi$
$468$	−42.5975	+	14.0253i	−1.96907	+	0.648321i
$469$	−3.69095			−0.170432
$470$	10.8242	−	10.8242i	0.499282	−	0.499282i
$471$	−3.90370	−	9.48849i	−0.179873	−	0.437206i
$472$		−	27.2039i		−	1.25216i
$473$	53.1549	+	14.2428i	2.44406	+	0.654885i
$474$	2.87437	+	22.2440i	0.132024	+	1.02170i
$475$	−15.5322	−	4.16184i	−0.712666	−	0.190958i
$476$	4.59623	+	4.59623i	0.210668	+	0.210668i
$477$	−4.49218	+	16.4499i	−0.205683	+	0.753191i
$478$	−55.5308	+	32.0607i	−2.53992	+	1.46642i
$479$	4.43161	+	4.43161i	0.202485	+	0.202485i	0.801064	−	0.598579i	$-0.204268\pi$
$479$	4.43161	+	4.43161i	0.202485	+	0.202485i	−0.598579	+	0.801064i	$0.704268\pi$
$480$	−1.35022	+	0.555499i	−0.0616287	+	0.0253550i
$481$	0.0670130	+	0.200301i	0.00305553	+	0.00913294i
$482$	12.6783	−	7.31984i	0.577482	−	0.333409i
$483$	5.82919	−	4.45079i	0.265237	−	0.202518i
$484$	69.7110			3.16868
$485$	0.258067	−	0.446984i	0.0117182	−	0.0202965i
$486$	−38.3729	+	4.58582i	−1.74063	+	0.208017i
$487$	−17.1218	+	4.58779i	−0.775865	+	0.207892i	−0.624961	−	0.780656i	$-0.714885\pi$
$487$	−17.1218	+	4.58779i	−0.775865	+	0.207892i	−0.150904	+	0.988548i	$0.548218\pi$
$488$	5.74204	−	21.4296i	0.259930	−	0.970071i
$489$	3.41269	+	26.4098i	0.154327	+	1.19429i
$490$	9.30347			0.420288
$491$	12.0817	−	20.9261i	0.545239	−	0.944381i	−0.453353	−	0.891331i	$-0.649772\pi$
$491$	12.0817	−	20.9261i	0.545239	−	0.944381i	0.998592	−	0.0530504i	$-0.0168944\pi$
$492$	41.4771	−	5.35969i	1.86993	−	0.241633i
$493$	2.17127	+	1.25359i	0.0977892	+	0.0564586i
$494$	−30.6227	+	1.87203i	−1.37778	+	0.0842268i
$495$	−2.25729	−	8.58842i	−0.101458	−	0.386021i
$496$	7.72057	−	28.8136i	0.346664	−	1.29377i
$497$		−	1.24178i		−	0.0557016i
$498$	−0.492702	−	0.379939i	−0.0220785	−	0.0170255i
$499$	2.49814	−	9.32320i	0.111832	−	0.417364i	−0.887198	−	0.461389i	$-0.847351\pi$
$499$	2.49814	−	9.32320i	0.111832	−	0.417364i	0.999030	+	0.0440247i	$0.0140180\pi$
$500$	15.9365	−	15.9365i	0.712703	−	0.712703i
$501$	−3.36895	+	0.435337i	−0.150514	+	0.0194494i
$502$	−1.94746	−	7.26804i	−0.0869196	−	0.324388i
$503$	−16.6315	−	9.60220i	−0.741562	−	0.428141i	0.0810753	−	0.996708i	$-0.474165\pi$
$503$	−16.6315	−	9.60220i	−0.741562	−	0.428141i	−0.822637	+	0.568567i	$0.807498\pi$
$504$	−2.27303	−	8.64830i	−0.101249	−	0.385226i
$505$	−7.50452	−	2.01083i	−0.333947	−	0.0894808i
$506$	−49.4109	+	85.5822i	−2.19658	+	3.80459i
$507$	11.4756	−	19.3729i	0.509649	−	0.860382i
$508$	11.0396	+	19.1211i	0.489803	+	0.848363i
$509$	−1.53691	−	5.73581i	−0.0681221	−	0.254235i	0.923464	−	0.383686i	$-0.125345\pi$
$509$	−1.53691	−	5.73581i	−0.0681221	−	0.254235i	−0.991586	+	0.129450i	$0.958679\pi$
$510$	−0.896309	+	6.68458i	−0.0396892	+	0.295998i
$511$	1.84324	−	1.06419i	0.0815401	−	0.0470772i
$512$	−31.6528	+	31.6528i	−1.39887	+	1.39887i
$513$	−17.6649	−	2.45467i	−0.779923	−	0.108376i
$514$	−12.3972	−	46.2671i	−0.546818	−	2.04075i
$515$	−0.349696	+	0.0937008i	−0.0154094	+	0.00412895i
$516$	28.5099	+	69.2973i	1.25508	+	3.05065i
$517$	−50.2458	−	29.0094i	−2.20981	−	1.27583i
$518$	−0.0785880	+	0.0210576i	−0.00345296	+	0.000925217i
$519$	7.76970	+	18.8853i	0.341052	+	0.828973i
$520$	4.80449	−	9.63558i	0.210691	−	0.422548i
$521$			13.0320i			0.570942i	0.958387	+	0.285471i	$0.0921500\pi$
$521$			13.0320i			0.570942i	−0.958387	+	0.285471i	$0.907850\pi$
$522$	−3.30403	−	5.78648i	−0.144613	−	0.253268i
$523$	6.02410	+	10.4340i	0.263415	+	0.456249i	0.967147	−	0.254217i	$-0.0818177\pi$
$523$	6.02410	+	10.4340i	0.263415	+	0.456249i	−0.703732	+	0.710466i	$0.748484\pi$
$524$	25.2372	+	43.7120i	1.10249	+	1.90957i
$525$	2.75880	+	3.61320i	0.120404	+	0.157693i
$526$	16.1650	+	16.1650i	0.704829	+	0.704829i
$527$	−12.0512	−	12.0512i	−0.524959	−	0.524959i
$528$	27.1519	+	35.5608i	1.18164	+	1.54759i
$529$	−17.0640	−	29.5557i	−0.741912	−	1.28503i
$530$	−3.95458	−	6.84953i	−0.171776	−	0.297525i
$531$	7.60592	+	13.3206i	0.330069	+	0.578063i
$532$		−	7.97231i		−	0.345644i
$533$	−13.9140	+	15.7260i	−0.602684	+	0.681169i
$534$	13.5190	+	32.8597i	0.585023	+	1.42198i
$535$	−6.03746	+	1.61773i	−0.261022	+	0.0699407i
$536$	30.3571	+	17.5267i	1.31122	+	0.757036i
$537$	9.61396	+	23.3681i	0.414873	+	1.00841i
$538$	60.6597	−	16.2537i	2.61522	−	0.700747i
$539$	−9.12643	−	34.0603i	−0.393103	−	1.46708i
$540$	7.42966	−	9.54003i	0.319722	−	0.410538i
$541$	5.96251	−	5.96251i	0.256348	−	0.256348i	−0.567219	−	0.823567i	$-0.691981\pi$
$541$	5.96251	−	5.96251i	0.256348	−	0.256348i	0.823567	+	0.567219i	$0.191981\pi$
$542$	47.6782	−	27.5270i	2.04795	−	1.18239i
$543$	0.702894	−	5.24211i	0.0301641	−	0.224961i
$544$	−1.08778	−	4.05965i	−0.0466381	−	0.174056i
$545$	4.80646	+	8.32503i	0.205886	+	0.356605i
$546$	7.17889	+	4.86756i	0.307228	+	0.208312i
$547$	−14.3308	+	24.8217i	−0.612740	+	1.06130i	0.378036	+	0.925791i	$0.376600\pi$
$547$	−14.3308	+	24.8217i	−0.612740	+	1.06130i	−0.990776	+	0.135507i	$0.956734\pi$
$548$	−26.3231	−	7.05326i	−1.12447	−	0.301300i
$549$	3.17986	+	12.0985i	0.135713	+	0.516353i
$550$	−53.0478	−	30.6271i	−2.26196	−	1.30595i
$551$	−0.795880	−	2.97026i	−0.0339056	−	0.126538i
$552$	−69.0783	+	8.92633i	−2.94017	+	0.379930i
$553$	2.06916	−	2.06916i	0.0879896	−	0.0879896i
$554$	13.2004	−	49.2646i	0.560832	−	2.09305i
$555$	−0.0450970	−	0.0347758i	−0.00191426	−	0.00147615i
$556$		−	11.9619i		−	0.507298i
$557$	−11.3445	+	42.3384i	−0.480683	+	1.79393i	0.118075	+	0.993005i	$0.462328\pi$
$557$	−11.3445	+	42.3384i	−0.480683	+	1.79393i	−0.598759	+	0.800930i	$0.704339\pi$
$558$	11.5139	+	43.8075i	0.487423	+	1.85452i
$559$	−33.6687	−	16.7879i	−1.42404	−	0.710052i
$560$	1.33377	+	0.770055i	0.0563622	+	0.0325408i
$561$	25.3517	−	3.27596i	1.07035	−	0.138311i
$562$	−1.72024	+	2.97955i	−0.0725642	+	0.125685i
$563$	−34.0602			−1.43546			−0.717732	−	0.696319i	$-0.754820\pi$
$563$	−34.0602			−1.43546			−0.717732	+	0.696319i	$0.754820\pi$
$564$	−10.1246	−	78.3513i	−0.426322	−	3.29919i
$565$	0.961690	−	3.58908i	0.0404586	−	0.150994i
$566$	79.7108	−	21.3585i	3.35050	−	0.897763i
$567$	3.53098	+	3.59918i	0.148287	+	0.151152i
$568$	−5.89668	+	10.2133i	−0.247419	+	0.428542i
$569$	−18.6327			−0.781122			−0.390561	−	0.920577i	$-0.627719\pi$
$569$	−18.6327			−0.781122			−0.390561	+	0.920577i	$0.627719\pi$
$570$	6.57465	−	5.01997i	0.275382	−	0.210263i
$571$	15.0722	−	8.70193i	0.630751	−	0.364164i	−0.150292	−	0.988642i	$-0.548021\pi$
$571$	15.0722	−	8.70193i	0.630751	−	0.364164i	0.781043	+	0.624477i	$0.214688\pi$
$572$	−77.2558	−	15.7203i	−3.23023	−	0.657299i
$573$	21.4980	−	8.84460i	0.898092	−	0.369488i
$574$	−5.71939	−	5.71939i	−0.238723	−	0.238723i
$575$	30.6664	−	17.7053i	1.27888	−	0.738360i
$576$	4.79933	−	17.5747i	0.199972	−	0.732278i
$577$	7.58470	+	7.58470i	0.315755	+	0.315755i	0.847134	−	0.531379i	$-0.178326\pi$
$577$	7.58470	+	7.58470i	0.315755	+	0.315755i	−0.531379	+	0.847134i	$0.678326\pi$
$578$	21.9562	+	5.88314i	0.913257	+	0.244706i
$579$	0.795533	+	6.15640i	0.0330612	+	0.255851i
$580$	2.01383	+	0.539605i	0.0836199	+	0.0224059i
$581$			0.0811741i			0.00336767i
$582$	−1.50237	−	3.65173i	−0.0622754	−	0.151369i
$583$	−21.1970	+	21.1970i	−0.877891	+	0.877891i
$584$	−20.2135			−0.836442
$585$	0.341457	+	6.06141i	0.0141175	+	0.250608i
$586$	−23.6928			−0.978739
$587$	−23.8893	+	23.8893i	−0.986016	+	0.986016i	−0.999904	−	0.0138873i	$-0.995579\pi$
$587$	−23.8893	+	23.8893i	−0.986016	+	0.986016i	0.0138873	+	0.999904i	$0.495579\pi$
$588$	29.3207	−	38.0229i	1.20917	−	1.56804i
$589$			20.9032i			0.861303i
$590$	−6.87212	−	1.84138i	−0.282921	−	0.0758084i
$591$	21.0260	+	8.76822i	0.864894	+	0.360676i
$592$	0.277150	+	0.0742622i	0.0113908	+	0.00305216i
$593$	−21.2686	−	21.2686i	−0.873399	−	0.873399i	0.119443	−	0.992841i	$-0.461889\pi$
$593$	−21.2686	−	21.2686i	−0.873399	−	0.873399i	−0.992841	+	0.119443i	$0.961889\pi$
$594$	−62.5781	−	26.4482i	−2.56761	−	1.08518i
$595$	0.762035	−	0.439961i	0.0312404	−	0.0180366i
$596$	0.889628	+	0.889628i	0.0364406	+	0.0364406i
$597$	−27.2688	−	21.0279i	−1.11604	−	0.860614i
$598$	44.7688	−	50.5989i	1.83073	−	2.06914i
$599$	3.06596	−	1.77013i	0.125272	−	0.0723256i	−0.436055	−	0.899920i	$-0.643625\pi$
$599$	3.06596	−	1.77013i	0.125272	−	0.0723256i	0.561326	+	0.827595i	$0.310291\pi$
$600$	−5.53295	−	42.8179i	−0.225882	−	1.74803i
$601$	−28.3664			−1.15709			−0.578544	−	0.815651i	$-0.696379\pi$
$601$	−28.3664			−1.15709			−0.578544	+	0.815651i	$0.696379\pi$
$602$	7.24607	−	12.5506i	0.295328	−	0.511523i
$603$	−19.7648	−	0.0945303i	−0.804885	−	0.00384957i
$604$	60.6286	−	16.2454i	2.46694	−	0.661016i
$605$	2.44245	−	9.11534i	0.0992996	−	0.370591i
$606$	−47.2425	+	36.0713i	−1.91910	+	1.46530i
$607$	−10.1601			−0.412387			−0.206193	−	0.978511i	$-0.566108\pi$
$607$	−10.1601			−0.412387			−0.206193	+	0.978511i	$0.566108\pi$
$608$	−2.57740	+	4.46419i	−0.104527	+	0.181047i
$609$	−0.334604	+	0.802373i	−0.0135588	+	0.0325138i
$610$	−5.02477	−	2.90105i	−0.203447	−	0.117460i
$611$	29.7069	+	26.2840i	1.20181	+	1.06334i
$612$	24.4948	+	24.7303i	0.990144	+	0.999661i
$613$	5.13413	−	19.1608i	0.207365	−	0.773898i	−0.781350	−	0.624093i	$-0.785469\pi$
$613$	5.13413	−	19.1608i	0.207365	−	0.773898i	0.988716	−	0.149805i	$-0.0478647\pi$
$614$		−	80.2721i		−	3.23952i
$615$	0.752395	−	5.61128i	0.0303395	−	0.226269i
$616$	4.06855	−	15.1840i	0.163926	−	0.611782i
$617$	4.00140	−	4.00140i	0.161090	−	0.161090i	−0.621959	−	0.783050i	$-0.713663\pi$
$617$	4.00140	−	4.00140i	0.161090	−	0.161090i	0.783050	+	0.621959i	$0.213663\pi$
$618$	−1.06605	+	2.55636i	−0.0428828	+	0.102832i
$619$	−5.87159	−	21.9131i	−0.235999	−	0.880761i	−0.977696	−	0.210025i	$-0.932645\pi$
$619$	−5.87159	−	21.9131i	−0.235999	−	0.880761i	0.741697	−	0.670735i	$-0.234021\pi$
$620$	−12.2736	−	7.08617i	−0.492920	−	0.284588i
$621$	31.3290	−	23.6844i	1.25719	−	0.950423i
$622$	40.4389	+	10.8356i	1.62145	+	0.434467i
$623$	2.31788	−	4.01468i	0.0928638	−	0.160845i
$624$	−13.3424	−	27.5249i	−0.534122	−	1.10188i
$625$	10.1870	+	17.6444i	0.407479	+	0.705774i
$626$	11.0914	+	41.3938i	0.443303	+	1.65443i
$627$	−24.8278	−	19.1455i	−0.991527	−	0.764599i
$628$	21.2698	−	12.2801i	0.848759	−	0.490031i
$629$	0.115918	−	0.115918i	0.00462194	−	0.00462194i
$630$	−2.33855	−	0.0111847i	−0.0931701	−	0.000445611i
$631$	5.55205	+	20.7205i	0.221024	+	0.824872i	0.983959	+	0.178397i	$0.0570910\pi$
$631$	5.55205	+	20.7205i	0.221024	+	0.824872i	−0.762935	+	0.646475i	$0.776242\pi$
$632$	−26.8438	+	7.19277i	−1.06779	+	0.286113i
$633$	−5.91144	+	7.66592i	−0.234959	+	0.304693i
$634$	25.0394	+	14.4565i	0.994444	+	0.574142i
$635$	2.88705	−	0.773583i	0.114569	−	0.0306987i
$636$	−40.4570	−	5.42472i	−1.60422	−	0.215104i
$637$	1.47098	+	24.0623i	0.0582825	+	0.953384i
$638$		−	11.7138i		−	0.463755i
$639$	0.0318038	−	6.64968i	0.00125814	−	0.263057i
$640$	5.06791	+	8.77787i	0.200327	+	0.346976i
$641$	−14.1441	−	24.4983i	−0.558658	−	0.967624i	−0.997609	−	0.0691131i	$-0.977983\pi$
$641$	−14.1441	−	24.4983i	−0.558658	−	0.967624i	0.438951	−	0.898511i	$-0.355350\pi$
$642$	−18.4052	+	44.1353i	−0.726397	+	1.74188i
$643$	20.2321	+	20.2321i	0.797877	+	0.797877i	0.982760	−	0.184883i	$-0.0591908\pi$
$643$	20.2321	+	20.2321i	0.797877	+	0.797877i	−0.184883	+	0.982760i	$0.559191\pi$
$644$	12.4140	+	12.4140i	0.489181	+	0.489181i
$645$	10.0601	−	1.29998i	0.396118	−	0.0511865i
$646$	11.9060	+	20.6218i	0.468435	+	0.811353i
$647$	−0.317553	−	0.550019i	−0.0124843	−	0.0216235i	0.859716	−	0.510773i	$-0.170641\pi$
$647$	−0.317553	−	0.550019i	−0.0124843	−	0.0216235i	−0.872200	+	0.489149i	$0.837307\pi$
$648$	−11.9504	−	46.3694i	−0.469458	−	1.82156i
$649$			26.9654i			1.05848i
$650$	31.3635	+	27.7498i	1.23018	+	1.08844i
$651$	3.60871	−	4.67975i	0.141436	−	0.183414i
$652$	−61.5724	+	16.4983i	−2.41136	+	0.646122i
$653$	−5.05334	−	2.91755i	−0.197753	−	0.114172i	0.397854	−	0.917449i	$-0.369755\pi$
$653$	−5.05334	−	2.91755i	−0.197753	−	0.114172i	−0.595607	+	0.803276i	$0.703088\pi$
$654$	72.8917	+	9.77376i	2.85029	+	0.382184i
$655$	6.59997	−	1.76846i	0.257882	−	0.0690993i
$656$	7.38278	+	27.5529i	0.288249	+	1.07576i
$657$	9.89769	−	5.65149i	0.386146	−	0.220486i
$658$	−10.8041	+	10.8041i	−0.421187	+	0.421187i
$659$	−0.0772408	+	0.0445950i	−0.00300888	+	0.00173718i	−0.501504	−	0.865156i	$-0.667220\pi$
$659$	−0.0772408	+	0.0445950i	−0.00300888	+	0.00173718i	0.498495	+	0.866893i	$0.333886\pi$
$660$	19.6582	−	8.08766i	0.765193	−	0.314812i
$661$	−9.42231	−	35.1645i	−0.366485	−	1.36774i	−0.865396	−	0.501088i	$-0.832933\pi$
$661$	−9.42231	−	35.1645i	−0.366485	−	1.36774i	0.498911	−	0.866653i	$-0.333734\pi$
$662$	−9.14764	−	15.8442i	−0.355533	−	0.615801i
$663$	−17.4306	−	1.26129i	−0.676948	−	0.0489845i
$664$	0.385459	−	0.667635i	0.0149587	−	0.0259093i
$665$	−1.04245	−	0.279324i	−0.0404245	−	0.0108317i
$666$	−0.421373	+	0.110749i	−0.0163279	+	0.00429145i
$667$	5.86442	+	3.38582i	0.227071	+	0.131100i
$668$	−2.10459	−	7.85443i	−0.0814290	−	0.303897i
$669$	17.3593	+	22.7354i	0.671148	+	0.879001i
$670$	6.48231	−	6.48231i	0.250434	−	0.250434i
$671$	−5.69170	+	21.2417i	−0.219725	+	0.820027i
$672$	1.34771	−	0.554468i	0.0519891	−	0.0213891i
$673$			20.2157i			0.779259i	0.920972	+	0.389630i	$0.127397\pi$
$673$			20.2157i			0.779259i	−0.920972	+	0.389630i	$0.872603\pi$
$674$	15.0776	−	56.2703i	0.580766	−	2.16745i
$675$	14.6807	+	19.4191i	0.565059	+	0.747442i
$676$	49.6134	+	21.0632i	1.90821	+	0.810123i
$677$	−11.6860	−	6.74691i	−0.449129	−	0.259305i	0.258333	−	0.966056i	$-0.416827\pi$
$677$	−11.6860	−	6.74691i	−0.449129	−	0.259305i	−0.707462	+	0.706751i	$0.750160\pi$
$678$	−17.2513	−	22.5940i	−0.662532	−	0.867716i
$679$	−0.257588	+	0.446155i	−0.00988530	+	0.0171219i
$680$	−8.35671			−0.320465
$681$	5.40760	+	2.25507i	0.207220	+	0.0864143i
$682$	−20.6090	+	76.9139i	−0.789160	+	2.94518i
$683$	32.8276	−	8.79612i	1.25611	−	0.336574i	0.431417	−	0.902153i	$-0.358014\pi$
$683$	32.8276	−	8.79612i	1.25611	−	0.336574i	0.824695	+	0.565578i	$0.191347\pi$
$684$	0.204182	−	42.6912i	0.00780710	−	1.63234i
$685$	−1.84455	+	3.19486i	−0.0704767	+	0.122069i
$686$	−19.0083			−0.725740
$687$	27.4258	+	11.4371i	1.04636	+	0.436351i
$688$	−44.2611	+	25.5542i	−1.68744	+	0.974244i
$689$	17.0902	−	11.3110i	0.651087	−	0.430916i
$690$	−2.42085	+	18.0545i	−0.0921602	+	0.687321i
$691$	7.26839	+	7.26839i	0.276503	+	0.276503i	0.831711	−	0.555208i	$-0.187362\pi$
$691$	7.26839	+	7.26839i	0.276503	+	0.276503i	−0.555208	+	0.831711i	$0.687362\pi$
$692$	−42.3342	+	24.4417i	−1.60930	+	0.929132i
$693$	2.25310	+	8.57248i	0.0855883	+	0.325642i
$694$	41.3276	+	41.3276i	1.56877	+	1.56877i
$695$	−1.56413	−	0.419107i	−0.0593307	−	0.0158976i
$696$	6.56213	−	5.01042i	0.248737	−	0.189919i
$697$	15.7420	+	4.21806i	0.596271	+	0.159770i
$698$			38.8725i			1.47134i
$699$	−5.08600	−	0.681962i	−0.192370	−	0.0257942i
$700$	−7.69477	+	7.69477i	−0.290835	+	0.290835i
$701$	−2.07594			−0.0784071			−0.0392036	−	0.999231i	$-0.512482\pi$
$701$	−2.07594			−0.0784071			−0.0392036	+	0.999231i	$0.512482\pi$
$702$	38.3179	+	26.2493i	1.44621	+	0.990717i
$703$	−0.201063			−0.00758323
$704$	22.6463	−	22.6463i	0.853515	−	0.853515i
$705$	−10.5999	−	1.42129i	−0.399214	−	0.0535290i
$706$		−	4.14896i		−	0.156148i
$707$	7.49059	+	2.00710i	0.281713	+	0.0754847i
$708$	−29.1838	+	22.2828i	−1.09679	+	0.837440i
$709$	−47.7752	−	12.8013i	−1.79424	−	0.480764i	−0.801182	−	0.598421i	$-0.795795\pi$
$709$	−47.7752	−	12.8013i	−1.79424	−	0.480764i	−0.993054	+	0.117657i	$0.962462\pi$
$710$	2.18091	+	2.18091i	0.0818482	+	0.0818482i
$711$	11.1332	−	11.0272i	0.417528	−	0.413553i
$712$	−38.1278	+	22.0131i	−1.42890	+	0.824977i
$713$	−32.5493	−	32.5493i	−1.21898	−	1.21898i
$714$	0.894645	−	6.67217i	0.0334813	−	0.249700i
$715$	−4.76236	+	9.55110i	−0.178102	+	0.357191i
$716$	−52.3829	+	30.2433i	−1.95764	+	1.13024i
$717$	41.3473	+	17.2426i	1.54414	+	0.643936i
$718$	−11.3356			−0.423039
$719$	−16.4531	+	28.4976i	−0.613597	+	1.06278i	0.377032	+	0.926200i	$0.376945\pi$
$719$	−16.4531	+	28.4976i	−0.613597	+	1.06278i	−0.990629	+	0.136581i	$0.956389\pi$
$720$	7.12256	+	4.15776i	0.265442	+	0.154950i
$721$	0.349047	−	0.0935268i	0.0129992	−	0.00348312i
$722$	−4.63239	+	17.2883i	−0.172400	+	0.643405i
$723$	−9.44007	−	3.93668i	−0.351080	−	0.146407i
$724$	12.6607			0.470530
$725$	−2.09869	+	3.63503i	−0.0779433	+	0.135002i
$726$	−43.8139	−	57.3830i	−1.62609	−	2.12968i
$727$	−14.8096	−	8.55034i	−0.549258	−	0.317115i	0.199564	−	0.979885i	$-0.436047\pi$
$727$	−14.8096	−	8.55034i	−0.549258	−	0.317115i	−0.748823	+	0.662770i	$0.769381\pi$
$728$	−4.79557	+	9.61769i	−0.177736	+	0.356455i
$729$	18.8160	+	19.3638i	0.696889	+	0.717179i
$730$	−1.36822	+	5.10625i	−0.0506399	+	0.188991i
$731$			29.2001i			1.08001i
$732$	−27.6925	+	11.3931i	−1.02355	+	0.421102i
$733$	−6.08699	+	22.7169i	−0.224828	+	0.839070i	0.757645	+	0.652667i	$0.226350\pi$
$733$	−6.08699	+	22.7169i	−0.224828	+	0.839070i	−0.982473	+	0.186403i	$0.940317\pi$
$734$	−3.26009	+	3.26009i	−0.120332	+	0.120332i
$735$	−3.94453	−	5.16615i	−0.145496	−	0.190556i
$736$	−2.93799	−	10.9647i	−0.108296	−	0.404166i
$737$	−30.0909	−	17.3730i	−1.10841	−	0.639942i
$738$	−30.4805	−	30.7734i	−1.12200	−	1.13279i
$739$	−23.5898	−	6.32087i	−0.867766	−	0.232517i	−0.202644	−	0.979252i	$-0.564954\pi$
$739$	−23.5898	−	6.32087i	−0.867766	−	0.232517i	−0.665121	+	0.746735i	$0.731620\pi$
$740$	0.0681601	−	0.118057i	0.00250561	−	0.00433985i
$741$	14.0231	+	16.2108i	0.515151	+	0.595520i
$742$	3.94724	+	6.83682i	0.144908	+	0.250988i
$743$	9.24450	+	34.5010i	0.339148	+	1.26572i	0.899302	+	0.437329i	$0.144075\pi$
$743$	9.24450	+	34.5010i	0.339148	+	1.26572i	−0.560154	+	0.828389i	$0.689258\pi$
$744$	−51.9027	+	21.3535i	−1.90284	+	0.782858i
$745$	0.147496	−	0.0851571i	0.00540385	−	0.00311992i
$746$	45.2880	−	45.2880i	1.65811	−	1.65811i
$747$	−0.00207898	+	0.434682i	−7.60660e−5	+	0.0159042i
$748$	15.8373	+	59.1054i	0.579067	+	2.16111i
$749$	6.02625	−	1.61473i	0.220195	−	0.0590010i
$750$	−23.1344	−	3.10201i	−0.844750	−	0.113269i
$751$	−2.10012	−	1.21250i	−0.0766343	−	0.0442448i	0.461193	−	0.887300i	$-0.347422\pi$
$751$	−2.10012	−	1.21250i	−0.0766343	−	0.0442448i	−0.537828	+	0.843055i	$0.680755\pi$
$752$	52.0482	−	13.9463i	1.89800	−	0.508568i
$753$	−3.21019	+	4.16295i	−0.116986	+	0.151706i
$754$	−1.59684	+	7.84751i	−0.0581535	+	0.285790i
$755$		−	8.49692i		−	0.309235i
$756$	−7.41587	+	9.52232i	−0.269713	+	0.346324i
$757$	−13.9450	−	24.1534i	−0.506838	−	0.877869i	−0.999969	−	0.00791399i	$-0.997481\pi$
$757$	−13.9450	−	24.1534i	−0.506838	−	0.877869i	0.493131	−	0.869955i	$-0.335852\pi$
$758$	47.2840	+	81.8983i	1.71743	+	2.97468i
$759$	68.4727	−	8.84807i	2.48540	−	0.321165i
$760$	7.24749	+	7.24749i	0.262894	+	0.262894i
$761$	23.6347	+	23.6347i	0.856759	+	0.856759i	0.990955	−	0.134196i	$-0.0428452\pi$
$761$	23.6347	+	23.6347i	0.856759	+	0.856759i	−0.134196	+	0.990955i	$0.542845\pi$
$762$	8.80119	−	21.1051i	0.318833	−	0.764556i
$763$	−4.79754	−	8.30958i	−0.173682	−	0.300827i
$764$	27.8230	+	48.1909i	1.00660	+	1.74349i
$765$	4.09192	−	2.33645i	0.147944	−	0.0844745i
$766$		−	36.8672i		−	1.33207i
$767$	3.67595	−	18.0651i	0.132731	−	0.652292i
$768$	56.0067	+	7.50972i	2.02097	+	0.270984i
$769$	−26.7023	+	7.15486i	−0.962909	+	0.258011i	−0.705831	−	0.708380i	$-0.749426\pi$
$769$	−26.7023	+	7.15486i	−0.962909	+	0.258011i	−0.257078	+	0.966391i	$0.582760\pi$
$770$	−3.56033	−	2.05556i	−0.128305	−	0.0740771i
$771$	−20.4355	+	26.5006i	−0.735967	+	0.954397i
$772$	−14.3532	+	3.84592i	−0.516581	+	0.138418i
$773$	9.46654	+	35.3296i	0.340488	+	1.27072i	0.897796	+	0.440412i	$0.145167\pi$
$773$	9.46654	+	35.3296i	0.340488	+	1.27072i	−0.557308	+	0.830306i	$0.688166\pi$
$774$	39.1237	−	67.0219i	1.40627	−	2.40905i
$775$	20.1755	−	20.1755i	0.724726	−	0.724726i
$776$	4.23718	−	2.44634i	0.152106	−	0.0878183i
$777$	0.0450133	+	0.0347112i	0.00161484	+	0.00124526i
$778$	−9.97621	−	37.2317i	−0.357665	−	1.33482i
$779$	−9.99433	−	17.3107i	−0.358084	−	0.620220i
$780$	−14.2722	+	2.73839i	−0.511028	+	0.0980500i
$781$	5.84498	−	10.1238i	0.209150	−	0.362258i
$782$	−50.6503	−	13.5717i	−1.81125	−	0.485324i
$783$	−1.81233	+	4.28809i	−0.0647675	+	0.153244i
$784$	28.3614	+	16.3745i	1.01291	+	0.584803i
$785$	−0.860512	−	3.21148i	−0.0307130	−	0.114623i
$786$	20.1200	−	48.2474i	0.717658	−	1.72093i
$787$	−1.54460	+	1.54460i	−0.0550589	+	0.0550589i	−0.734100	−	0.679041i	$-0.762396\pi$
$787$	−1.54460	+	1.54460i	−0.0550589	+	0.0550589i	0.679041	+	0.734100i	$0.262396\pi$
$788$	−14.1140	+	52.6741i	−0.502790	+	1.87644i
$789$	2.12259	−	15.8301i	0.0755663	−	0.563565i
$790$			7.26802i			0.258584i
$791$	−0.959905	+	3.58241i	−0.0341303	+	0.127376i
$792$	22.1757	−	81.2053i	0.787979	−	2.88551i
$793$	6.70876	−	13.4547i	0.238235	−	0.477790i
$794$	−3.99179	−	2.30466i	−0.141663	−	0.0817893i
$795$	−2.12681	+	5.10005i	−0.0754303	+	0.180880i
$796$	41.2144	−	71.3854i	1.46080	−	2.53019i
$797$	−11.6003			−0.410905			−0.205452	−	0.978667i	$-0.565867\pi$
$797$	−11.6003			−0.410905			−0.205452	+	0.978667i	$0.565867\pi$
$798$	−6.56244	+	5.01065i	−0.232308	+	0.177375i
$799$	7.96803	−	29.7371i	0.281888	−	1.05202i
$800$	6.79645	−	1.82110i	0.240291	−	0.0643857i
$801$	12.5149	−	21.4390i	0.442193	−	0.757510i
$802$	−3.52465	+	6.10487i	−0.124460	+	0.215570i
$803$	20.0363			0.707066
$804$	−6.06336	−	46.9226i	−0.213838	−	1.65483i
$805$	2.05819	−	1.18830i	0.0725416	−	0.0418819i
$806$	24.2917	−	48.7179i	0.855638	−	1.71602i
$807$	−34.7444	−	26.7925i	−1.22306	−	0.943142i
$808$	−52.0773	−	52.0773i	−1.83207	−	1.83207i
$809$	−15.4191	+	8.90221i	−0.542106	+	0.312985i	−0.745932	−	0.666022i	$-0.767996\pi$
$809$	−15.4191	+	8.90221i	−0.542106	+	0.312985i	0.203826	+	0.979007i	$0.434662\pi$
$810$	−12.5225	−	0.119787i	−0.439996	−	0.00420889i
$811$	−28.5606	−	28.5606i	−1.00290	−	1.00290i	−0.999996	−	0.00290204i	$-0.999076\pi$
$811$	−28.5606	−	28.5606i	−1.00290	−	1.00290i	−0.00290204	−	0.999996i	$-0.500924\pi$
$812$	−2.01010	−	0.538603i	−0.0705405	−	0.0189013i
$813$	−35.5004	−	14.8043i	−1.24505	−	0.519209i
$814$	−0.739814	−	0.198233i	−0.0259305	−	0.00694805i
$815$			8.62919i			0.302267i
$816$	−14.4975	+	18.8002i	−0.507514	+	0.658140i
$817$	25.3243	−	25.3243i	0.885984	−	0.885984i
$818$	29.2567			1.02294
$819$	−0.340823	−	6.05016i	−0.0119093	−	0.211410i
$820$	13.5523			0.473266
$821$	11.3212	−	11.3212i	0.395114	−	0.395114i	−0.481392	−	0.876506i	$-0.659869\pi$
$821$	11.3212	−	11.3212i	0.395114	−	0.395114i	0.876506	+	0.481392i	$0.159869\pi$
$822$	10.7383	+	26.1010i	0.374542	+	0.910377i
$823$			26.5436i			0.925250i	0.886554	+	0.462625i	$0.153092\pi$
$823$			26.5436i			0.925250i	−0.886554	+	0.462625i	$0.846908\pi$
$824$	−3.31493	−	0.888234i	−0.115481	−	0.0309431i
$825$	5.48444	+	42.4425i	0.190944	+	1.47766i
$826$	6.85937	+	1.83796i	0.238668	+	0.0639509i
$827$	−9.10200	−	9.10200i	−0.316508	−	0.316508i	0.530916	−	0.847424i	$-0.321848\pi$
$827$	−9.10200	−	9.10200i	−0.316508	−	0.316508i	−0.847424	+	0.530916i	$0.821848\pi$
$828$	66.1583	+	66.7942i	2.29916	+	2.32126i
$829$	15.4318	−	8.90953i	0.535967	−	0.309441i	−0.207476	−	0.978240i	$-0.566525\pi$
$829$	15.4318	−	8.90953i	0.535967	−	0.309441i	0.743443	+	0.668799i	$0.233191\pi$
$830$	−0.142564	−	0.142564i	−0.00494847	−	0.00494847i
$831$	−32.9530	+	13.5574i	−1.14313	+	0.470300i
$832$	−18.2588	+	12.0844i	−0.633008	+	0.418952i
$833$	16.2039	−	9.35535i	0.561433	−	0.324144i
$834$	−9.84651	+	7.51815i	−0.340957	+	0.260332i
$835$	−1.10077			−0.0380939
$836$	37.5250	−	64.9953i	1.29783	−	2.24791i
$837$	19.4443	−	24.9673i	0.672092	−	0.862997i
$838$	−54.1350	+	14.5054i	−1.87006	+	0.501081i
$839$	−4.96733	+	18.5383i	−0.171491	+	0.640014i	0.825631	+	0.564210i	$0.190819\pi$
$839$	−4.96733	+	18.5383i	−0.171491	+	0.640014i	−0.997123	+	0.0758043i	$0.975848\pi$
$840$	−0.371346	−	2.87374i	−0.0128127	−	0.0991535i
$841$	28.1973			0.972322
$842$	24.1702	−	41.8640i	0.832959	−	1.44273i
$843$	2.38388	−	0.308046i	0.0821052	−	0.0106097i
$844$	−20.0682	−	11.5864i	−0.690774	−	0.398819i
$845$	4.49250	−	5.74941i	0.154547	−	0.197786i
$846$	−58.1319	+	57.5785i	−1.99861	+	1.97959i
$847$	−2.43791	+	9.09842i	−0.0837677	+	0.312625i
$848$		−	27.8409i		−	0.956059i
$849$	−45.6564	−	35.2072i	−1.56692	−	1.20831i
$850$	8.41237	−	31.3954i	0.288542	−	1.07685i
$851$	0.313083	−	0.313083i	0.0107323	−	0.0107323i
$852$	15.7867	−	2.03996i	0.540842	−	0.0698878i
$853$	−4.35692	−	16.2603i	−0.149178	−	0.556741i	−0.999534	−	0.0305321i	$-0.990280\pi$
$853$	−4.35692	−	16.2603i	−0.149178	−	0.556741i	0.850356	−	0.526208i	$-0.176387\pi$
$854$	5.01545	+	2.89567i	0.171625	+	0.0990878i
$855$	−5.57511	−	1.52246i	−0.190665	−	0.0520671i
$856$	−57.2320	−	15.3353i	−1.95615	−	0.524148i
$857$	11.2337	−	19.4574i	0.383737	−	0.664653i	−0.607856	−	0.794047i	$-0.707970\pi$
$857$	11.2337	−	19.4574i	0.383737	−	0.664653i	0.991593	+	0.129395i	$0.0413035\pi$
$858$	35.6156	+	73.4738i	1.21590	+	2.50835i
$859$	−12.8127	−	22.1923i	−0.437165	−	0.757193i	0.560304	−	0.828287i	$-0.310684\pi$
$859$	−12.8127	−	22.1923i	−0.437165	−	0.757193i	−0.997470	+	0.0710943i	$0.977351\pi$
$860$	6.28459	+	23.4544i	0.214303	+	0.799788i
$861$	−0.750998	+	5.60087i	−0.0255940	+	0.190877i
$862$	−24.4957	+	14.1426i	−0.834327	+	0.481699i
$863$	−9.56910	+	9.56910i	−0.325736	+	0.325736i	−0.850962	−	0.525226i	$-0.823981\pi$
$863$	−9.56910	+	9.56910i	−0.325736	+	0.325736i	0.525226	+	0.850962i	$0.323981\pi$
$864$	7.23111	−	2.93463i	0.246007	−	0.0998380i
$865$	1.71271	+	6.39193i	0.0582340	+	0.217332i
$866$	69.0049	−	18.4898i	2.34488	−	0.628309i
$867$	−6.04223	−	14.6865i	−0.205205	−	0.498779i
$868$	12.2508	+	7.07302i	0.415820	+	0.240074i
$869$	26.6084	−	7.12971i	0.902629	−	0.241859i
$870$	−0.821530	−	1.99684i	−0.0278525	−	0.0676993i
$871$	17.7907	+	15.7408i	0.602814	+	0.533357i
$872$			91.1254i			3.08589i
$873$	−1.39079	+	2.38253i	−0.0470712	+	0.0806366i
$874$	32.1570	+	55.6976i	1.08773	+	1.88400i
$875$	1.52265	+	2.63730i	0.0514749	+	0.0891571i
$876$	16.5570	+	21.6847i	0.559409	+	0.732657i
$877$	−38.4144	−	38.4144i	−1.29716	−	1.29716i	−0.930260	−	0.366901i	$-0.880419\pi$
$877$	−38.4144	−	38.4144i	−1.29716	−	1.29716i	−0.366901	−	0.930260i	$-0.619581\pi$
$878$	−40.8311	−	40.8311i	−1.37798	−	1.37798i
$879$	10.0454	+	13.1564i	0.338822	+	0.443755i
$880$	7.24917	+	12.5559i	0.244369	+	0.423260i
$881$	−13.0677	−	22.6339i	−0.440261	−	0.762554i	0.557448	−	0.830212i	$-0.311781\pi$
$881$	−13.0677	−	22.6339i	−0.440261	−	0.762554i	−0.997709	+	0.0676577i	$0.978447\pi$
$882$	−49.7270	−	0.237833i	−1.67440	−	0.00800824i
$883$			47.1984i			1.58835i	0.607687	+	0.794177i	$0.292097\pi$
$883$			47.1984i			1.58835i	−0.607687	+	0.794177i	$0.707903\pi$
$884$	−2.55262	−	41.7558i	−0.0858541	−	1.40440i
$885$	1.89117	+	4.59676i	0.0635711	+	0.154518i
$886$	−44.2411	+	11.8544i	−1.48631	+	0.398255i
$887$	12.2665	+	7.08207i	0.411869	+	0.237793i	0.691592	−	0.722288i	$-0.256909\pi$
$887$	12.2665	+	7.08207i	0.411869	+	0.237793i	−0.279724	+	0.960081i	$0.590243\pi$
$888$	−0.205394	−	0.499238i	−0.00689257	−	0.0167533i
$889$	−2.88169	+	0.772147i	−0.0966488	+	0.0258970i
$890$	2.98005	+	11.1217i	0.0998916	+	0.372800i
$891$	11.8457	+	45.9628i	0.396845	+	1.53981i
$892$	−48.4180	+	48.4180i	−1.62115	+	1.62115i
$893$	−32.7004	+	18.8796i	−1.09428	+	0.631780i
$894$	0.173164	−	1.29144i	0.00579147	−	0.0431922i
$895$	2.11925	+	7.90916i	0.0708388	+	0.264374i
$896$	−5.05850	−	8.76158i	−0.168993	−	0.292704i
$897$	−47.0785	−	3.40663i	−1.57191	−	0.113744i
$898$	44.0119	−	76.2309i	1.46870	−	2.54386i
$899$	5.27043	+	1.41221i	0.175779	+	0.0470997i
$900$	−41.4021	+	41.0080i	−1.38007	+	1.36693i
$901$	−13.7755	−	7.95326i	−0.458927	−	0.264962i
$902$	−19.7073	−	73.5487i	−0.656182	−	2.44890i
$903$	−10.0415	+	1.29756i	−0.334159	+	0.0431802i
$904$	24.9062	−	24.9062i	0.828369	−	0.828369i
$905$	0.443588	−	1.65549i	0.0147454	−	0.0550305i
$906$	−51.4780	−	39.6964i	−1.71024	−	1.31882i
$907$			35.3813i			1.17482i	0.809291	+	0.587408i	$0.199852\pi$
$907$			35.3813i			1.17482i	−0.809291	+	0.587408i	$0.800148\pi$
$908$	−3.62992	+	13.5471i	−0.120463	+	0.449575i
$909$	40.0602	+	10.9397i	1.32871	+	0.362848i
$910$	2.10497	+	1.86244i	0.0697792	+	0.0617392i
$911$	19.1166	+	11.0370i	0.633362	+	0.365672i	0.782053	−	0.623212i	$-0.214173\pi$
$911$	19.1166	+	11.0370i	0.633362	+	0.365672i	−0.148691	+	0.988884i	$0.547506\pi$
$912$	28.8780	−	3.73163i	0.956246	−	0.123567i
$913$	−0.382080	+	0.661782i	−0.0126450	+	0.0219018i
$914$	43.3048			1.43240
$915$	0.519495	+	4.02022i	0.0171740	+	0.132905i
$916$	−18.4099	+	68.7068i	−0.608282	+	2.27014i
$917$	−6.58772	+	1.76517i	−0.217546	+	0.0582911i
$918$	4.96165	−	35.7062i	0.163759	−	1.17848i
$919$	−19.0623	+	33.0168i	−0.628807	+	1.08913i	0.358985	+	0.933343i	$0.383123\pi$
$919$	−19.0623	+	33.0168i	−0.628807	+	1.08913i	−0.987791	+	0.155782i	$0.950210\pi$
$920$	−22.5707			−0.744135
$921$	−44.5745	+	34.0342i	−1.46878	+	1.12146i
$922$	10.1681	−	5.87055i	0.334868	−	0.193336i
$923$	−5.29585	+	5.98550i	−0.174315	+	0.197015i
$924$	−19.6217	+	8.07265i	−0.645506	+	0.265571i
$925$	0.194063	+	0.194063i	0.00638076	+	0.00638076i
$926$	4.85493	−	2.80300i	0.159543	−	0.0921122i
$927$	1.87152	−	0.491891i	0.0614688	−	0.0161558i
$928$	0.951449	+	0.951449i	0.0312328	+	0.0312328i
$929$	−48.4979	−	12.9950i	−1.59117	−	0.426352i	−0.648806	−	0.760953i	$-0.724732\pi$
$929$	−48.4979	−	12.9950i	−1.59117	−	0.426352i	−0.942360	+	0.334602i	$0.891398\pi$
$930$	1.88103	+	14.5568i	0.0616816	+	0.477336i
$931$	−22.1667	−	5.93955i	−0.726485	−	0.194661i
$932$		−	12.2836i		−	0.402363i
$933$	−11.1286	−	27.0496i	−0.364334	−	0.885563i
$934$	24.2596	−	24.2596i	0.793798	−	0.793798i
$935$	8.28345			0.270898
$936$	−25.9263	+	51.3793i	−0.847428	+	1.67939i
$937$	51.0153			1.66660			0.833299	−	0.552822i	$-0.186449\pi$
$937$	51.0153			1.66660			0.833299	+	0.552822i	$0.186449\pi$
$938$	−6.47028	+	6.47028i	−0.211262	+	0.211262i
$939$	18.2831	−	23.7094i	0.596646	−	0.773726i
$940$		−	25.6006i		−	0.835000i
$941$	−25.7667	−	6.90418i	−0.839972	−	0.225070i	−0.186912	−	0.982377i	$-0.559848\pi$
$941$	−25.7667	−	6.90418i	−0.839972	−	0.225070i	−0.653059	+	0.757307i	$0.726515\pi$
$942$	−23.4767	−	9.79020i	−0.764912	−	0.318982i
$943$	42.5178	+	11.3926i	1.38457	+	0.370994i
$944$	−17.7086	−	17.7086i	−0.576366	−	0.576366i
$945$	0.985300	+	1.30332i	0.0320518	+	0.0423971i
$946$	118.149	−	68.2134i	3.84136	−	2.21781i
$947$	12.1604	+	12.1604i	0.395161	+	0.395161i	0.876522	−	0.481361i	$-0.159858\pi$
$947$	12.1604	+	12.1604i	0.395161	+	0.395161i	−0.481361	+	0.876522i	$0.659858\pi$
$948$	29.7041	+	22.9058i	0.964745	+	0.743947i
$949$	−13.4230	−	2.73137i	−0.435731	−	0.0886641i
$950$	−34.5239	+	19.9324i	−1.12010	+	0.646692i
$951$	−2.58875	−	20.0336i	−0.0839459	−	0.649633i
$952$	8.34120			0.270340
$953$	23.1429	−	40.0846i	0.749671	−	1.29847i	−0.198310	−	0.980139i	$-0.563545\pi$
$953$	23.1429	−	40.0846i	0.749671	−	1.29847i	0.947981	−	0.318328i	$-0.103121\pi$
$954$	20.9621	+	36.7118i	0.678674	+	1.18859i
$955$	7.27622	−	1.94966i	0.235453	−	0.0630894i
$956$	−27.7549	+	103.583i	−0.897659	+	3.35011i
$957$	−6.50460	+	4.96649i	−0.210264	+	0.160544i
$958$	15.5373			0.501988
$959$	1.84113	−	3.18893i	0.0594531	−	0.102976i
$960$	2.27223	−	5.44875i	0.0733358	−	0.175858i
$961$	−5.27464	−	3.04531i	−0.170150	−	0.0982359i
$962$	0.468605	+	0.233656i	0.0151084	+	0.00753336i
$963$	32.3116	−	8.49244i	1.04123	−	0.273665i
$964$	6.33678	−	23.6492i	0.204094	−	0.761689i
$965$			2.01155i			0.0647541i
$966$	2.41636	−	18.0209i	0.0777450	−	0.579814i
$967$	2.85708	−	10.6628i	0.0918776	−	0.342892i	−0.904650	−	0.426155i	$-0.859868\pi$
$967$	2.85708	−	10.6628i	0.0918776	−	0.342892i	0.996528	+	0.0832636i	$0.0265343\pi$
$968$	63.2555	−	63.2555i	2.03311	−	2.03311i
$969$	6.40316	−	15.3546i	0.205699	−	0.493262i
$970$	−0.331176	−	1.23596i	−0.0106334	−	0.0396844i
$971$	43.7777	+	25.2751i	1.40489	+	0.811116i	0.994890	−	0.100968i	$-0.0321940\pi$
$971$	43.7777	+	25.2751i	1.40489	+	0.811116i	0.410004	+	0.912084i	$0.365527\pi$
$972$	−39.9554	+	50.8015i	−1.28157	+	1.62946i
$973$	1.56122	+	0.418329i	0.0500505	+	0.0134110i
$974$	−21.9724	+	38.0573i	−0.704041	+	1.21943i
$975$	2.11159	−	29.1814i	0.0676249	−	0.934553i
$976$	−10.2119	−	17.6876i	−0.326876	−	0.566166i
$977$	−8.62900	−	32.2039i	−0.276066	−	1.03029i	−0.955123	−	0.296208i	$-0.904278\pi$
$977$	−8.62900	−	32.2039i	−0.276066	−	1.03029i	0.679057	−	0.734085i	$-0.262389\pi$
$978$	52.2793	+	40.3143i	1.67171	+	1.28911i
$979$	37.7936	−	21.8201i	1.20789	−	0.697374i
$980$	11.0020	−	11.0020i	0.351445	−	0.351445i
$981$	−25.4777	−	44.6201i	−0.813440	−	1.42461i
$982$	−15.5044	−	57.8631i	−0.494764	−	1.84649i
$983$	−27.3655	+	7.33255i	−0.872823	+	0.233872i	−0.667308	−	0.744782i	$-0.732554\pi$
$983$	−27.3655	+	7.33255i	−0.872823	+	0.233872i	−0.205515	+	0.978654i	$0.565887\pi$
$984$	32.7728	−	42.4995i	1.04476	−	1.35483i
$985$	6.39310	+	3.69106i	0.203701	+	0.117607i
$986$	6.00382	−	1.60872i	0.191201	−	0.0512321i
$987$	10.5802	+	1.41866i	0.336771	+	0.0451563i
$988$	−33.9996	+	38.4272i	−1.08167	+	1.22253i
$989$			78.8669i			2.50782i
$990$	−19.0127	−	11.0986i	−0.604263	−	0.352735i
$991$	−1.60816	−	2.78541i	−0.0510848	−	0.0884814i	0.839352	−	0.543588i	$-0.182935\pi$
$991$	−1.60816	−	2.78541i	−0.0510848	−	0.0884814i	−0.890437	+	0.455106i	$0.849601\pi$
$992$	−4.57333	−	7.92124i	−0.145203	−	0.251500i
$993$	−4.91969	+	11.7973i	−0.156122	+	0.374376i
$994$	−2.17686	−	2.17686i	−0.0690460	−	0.0690460i
$995$	−7.89026	−	7.89026i	−0.250138	−	0.250138i
$996$	−1.03196	+	0.133350i	−0.0326988	+	0.00422535i
$997$	−3.31747	−	5.74603i	−0.105065	−	0.181979i	0.808700	−	0.588222i	$-0.200172\pi$
$997$	−3.31747	−	5.74603i	−0.105065	−	0.181979i	−0.913765	+	0.406243i	$0.866839\pi$
$998$	−11.9644	−	20.7230i	−0.378727	−	0.655975i
$999$	0.240154	+	0.187029i	0.00759814	+	0.00591735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.12	✓	48
3.2	odd	2		351.2.ba.a.89.1		48
9.4	even	3		351.2.bf.a.206.12		48
9.5	odd	6		117.2.bc.a.50.1	yes	48
13.6	odd	12		117.2.bc.a.110.1	yes	48
39.32	even	12		351.2.bf.a.305.12		48
117.32	even	12	inner	117.2.x.a.32.12	yes	48
117.58	odd	12		351.2.ba.a.71.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.12	✓	48	1.1	even	1	trivial
117.2.x.a.32.12	yes	48	117.32	even	12	inner
117.2.bc.a.50.1	yes	48	9.5	odd	6
117.2.bc.a.110.1	yes	48	13.6	odd	12
351.2.ba.a.71.1		48	117.58	odd	12
351.2.ba.a.89.1		48	3.2	odd	2
351.2.bf.a.206.12		48	9.4	even	3
351.2.bf.a.305.12		48	39.32	even	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.75301 - 1.75301i) q^{2} +(-1.71669 - 0.230184i) q^{3} -4.14611i q^{4} +(-0.542141 - 0.145266i) q^{5} +(-3.41289 + 2.60586i) q^{6} +(0.541135 + 0.144997i) q^{7} +(-3.76217 - 3.76217i) q^{8} +(2.89403 + 0.790307i) q^{9} +O(q^{10})\)	\(q+(1.75301 - 1.75301i) q^{2} +(-1.71669 - 0.230184i) q^{3} -4.14611i q^{4} +(-0.542141 - 0.145266i) q^{5} +(-3.41289 + 2.60586i) q^{6} +(0.541135 + 0.144997i) q^{7} +(-3.76217 - 3.76217i) q^{8} +(2.89403 + 0.790307i) q^{9} +(-1.20503 + 0.695727i) q^{10} +(3.72918 + 3.72918i) q^{11} +(-0.954368 + 7.11758i) q^{12} +(-1.98995 - 3.00668i) q^{13} +(1.20280 - 0.694436i) q^{14} +(0.897249 + 0.374169i) q^{15} -4.89803 q^{16} +(-1.39921 + 2.42351i) q^{17} +(6.45869 - 3.68786i) q^{18} +(3.31532 - 0.888337i) q^{19} +(-0.602290 + 2.24778i) q^{20} +(-0.895584 - 0.373474i) q^{21} +13.0746 q^{22} +(-3.77915 + 6.54568i) q^{23} +(5.59247 + 7.32445i) q^{24} +(-4.05731 - 2.34249i) q^{25} +(-8.75915 - 1.78235i) q^{26} +(-4.78623 - 2.02287i) q^{27} +(0.601173 - 2.24361i) q^{28} -0.895922i q^{29} +(2.22881 - 0.916966i) q^{30} +(-1.57626 + 5.88269i) q^{31} +(-1.06198 + 1.06198i) q^{32} +(-5.54344 - 7.26024i) q^{33} +(1.79560 + 6.70128i) q^{34} +(-0.272308 - 0.157217i) q^{35} +(3.27670 - 11.9990i) q^{36} +(-0.0565841 - 0.0151617i) q^{37} +(4.25453 - 7.36906i) q^{38} +(2.72403 + 5.61958i) q^{39} +(1.49311 + 2.58614i) q^{40} +(-1.50730 - 5.62531i) q^{41} +(-2.22468 + 0.915264i) q^{42} +(9.03652 - 5.21724i) q^{43} +(15.4616 - 15.4616i) q^{44} +(-1.45417 - 0.848863i) q^{45} +(4.84977 + 18.0996i) q^{46} +(-10.6264 + 2.84732i) q^{47} +(8.40838 + 1.12745i) q^{48} +(-5.79037 - 3.34307i) q^{49} +(-11.2189 + 3.00611i) q^{50} +(2.95986 - 3.83833i) q^{51} +(-12.4660 + 8.25054i) q^{52} +5.68410i q^{53} +(-11.9364 + 4.84421i) q^{54} +(-1.48002 - 2.56347i) q^{55} +(-1.49034 - 2.58134i) q^{56} +(-5.89584 + 0.761864i) q^{57} +(-1.57056 - 1.57056i) q^{58} +(3.61546 + 3.61546i) q^{59} +(1.55135 - 3.72010i) q^{60} +(2.08491 + 3.61117i) q^{61} +(7.54922 + 13.0756i) q^{62} +(1.45147 + 0.847288i) q^{63} -6.07273i q^{64} +(0.642063 + 1.91912i) q^{65} +(-22.4450 - 3.00956i) q^{66} +(-6.36385 + 1.70519i) q^{67} +(10.0481 + 5.80130i) q^{68} +(7.99433 - 10.3670i) q^{69} +(-0.752964 + 0.201756i) q^{70} +(-0.573694 - 2.14106i) q^{71} +(-7.91455 - 13.8611i) q^{72} +(2.68642 - 2.68642i) q^{73} +(-0.125771 + 0.0726140i) q^{74} +(6.42593 + 4.95525i) q^{75} +(-3.68314 - 13.7457i) q^{76} +(1.47727 + 2.55871i) q^{77} +(14.6265 + 5.07595i) q^{78} +(2.61166 - 4.52353i) q^{79} +(2.65542 + 0.711518i) q^{80} +(7.75083 + 4.57435i) q^{81} +(-12.5035 - 7.21893i) q^{82} +(0.0375018 + 0.139959i) q^{83} +(-1.54847 + 3.71319i) q^{84} +(1.11063 - 1.11063i) q^{85} +(6.69526 - 24.9870i) q^{86} +(-0.206227 + 1.53802i) q^{87} -28.0596i q^{88} +(2.14168 - 7.99287i) q^{89} +(-4.03725 + 1.06111i) q^{90} +(-0.640871 - 1.91555i) q^{91} +(27.1391 + 15.6688i) q^{92} +(4.06005 - 9.73591i) q^{93} +(-13.6367 + 23.6195i) q^{94} -1.92642 q^{95} +(2.06753 - 1.57863i) q^{96} +(-0.238007 + 0.888254i) q^{97} +(-16.0111 + 4.29015i) q^{98} +(7.84517 + 13.7396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21} - 4 q^{22} - 6 q^{23} + 6 q^{24} - 48 q^{26} - 32 q^{27} + 42 q^{30} - 18 q^{31} + 54 q^{32} + 28 q^{33} + 6 q^{34} + 6 q^{35} + 24 q^{36} - 6 q^{37} + 36 q^{38} + 10 q^{39} - 12 q^{40} + 18 q^{41} - 70 q^{42} - 30 q^{43} + 12 q^{44} + 40 q^{45} - 12 q^{46} - 36 q^{47} - 14 q^{48} - 6 q^{49} - 60 q^{50} + 56 q^{52} + 34 q^{54} - 4 q^{55} - 6 q^{56} - 56 q^{57} + 50 q^{58} - 6 q^{59} + 44 q^{60} + 2 q^{61} + 18 q^{62} + 22 q^{63} + 72 q^{65} + 32 q^{66} + 26 q^{67} + 42 q^{68} + 30 q^{69} - 16 q^{70} - 48 q^{71} + 30 q^{72} - 22 q^{73} + 30 q^{74} - 24 q^{75} + 6 q^{76} + 72 q^{77} - 20 q^{78} + 8 q^{79} - 54 q^{80} + 82 q^{81} - 12 q^{82} + 54 q^{83} - 38 q^{84} - 24 q^{85} - 54 q^{86} + 2 q^{87} - 114 q^{90} - 16 q^{91} + 120 q^{92} + 52 q^{93} + 26 q^{94} - 12 q^{95} + 94 q^{96} - 24 q^{97} + 36 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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