LMFDB - Embedded newform 117.2.x.a.11.11

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			11.11
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30379 - 1.30379i) q^{2} +(-0.407694 + 1.68339i) q^{3} -1.39974i q^{4} +(2.51024 + 0.672617i) q^{5} +(1.66324 + 2.72633i) q^{6} +(-2.72321 - 0.729681i) q^{7} +(0.782609 + 0.782609i) q^{8} +(-2.66757 - 1.37261i) q^{9} +O(q^{10})$	\(q+(1.30379 - 1.30379i) q^{2} +(-0.407694 + 1.68339i) q^{3} -1.39974i q^{4} +(2.51024 + 0.672617i) q^{5} +(1.66324 + 2.72633i) q^{6} +(-2.72321 - 0.729681i) q^{7} +(0.782609 + 0.782609i) q^{8} +(-2.66757 - 1.37261i) q^{9} +(4.14978 - 2.39588i) q^{10} +(-4.45189 - 4.45189i) q^{11} +(2.35631 + 0.570667i) q^{12} +(2.41762 - 2.67491i) q^{13} +(-4.50185 + 2.59914i) q^{14} +(-2.15568 + 3.95148i) q^{15} +4.84020 q^{16} +(-2.31896 + 4.01655i) q^{17} +(-5.26756 + 1.68836i) q^{18} +(0.390218 - 0.104559i) q^{19} +(0.941492 - 3.51370i) q^{20} +(2.33857 - 4.28672i) q^{21} -11.6087 q^{22} +(-2.13369 + 3.69565i) q^{23} +(-1.63650 + 0.998367i) q^{24} +(1.51877 + 0.876864i) q^{25} +(-0.335449 - 6.63959i) q^{26} +(3.39819 - 3.93095i) q^{27} +(-1.02137 + 3.81179i) q^{28} +6.03554i q^{29} +(2.34135 + 7.96247i) q^{30} +(0.608508 - 2.27098i) q^{31} +(4.74540 - 4.74540i) q^{32} +(9.30926 - 5.67924i) q^{33} +(2.21331 + 8.26018i) q^{34} +(-6.34511 - 3.66335i) q^{35} +(-1.92130 + 3.73392i) q^{36} +(1.60869 + 0.431046i) q^{37} +(0.372440 - 0.645085i) q^{38} +(3.51725 + 5.16033i) q^{39} +(1.43814 + 2.49093i) q^{40} +(0.432026 + 1.61234i) q^{41} +(-2.53998 - 8.63800i) q^{42} +(2.59028 - 1.49550i) q^{43} +(-6.23151 + 6.23151i) q^{44} +(-5.77301 - 5.23984i) q^{45} +(2.03648 + 7.60024i) q^{46} +(4.68901 - 1.25642i) q^{47} +(-1.97332 + 8.14793i) q^{48} +(0.821249 + 0.474148i) q^{49} +(3.12341 - 0.836916i) q^{50} +(-5.81598 - 5.54122i) q^{51} +(-3.74418 - 3.38405i) q^{52} +0.186317i q^{53} +(-0.694608 - 9.55566i) q^{54} +(-8.18091 - 14.1698i) q^{55} +(-1.56015 - 2.70226i) q^{56} +(0.0169230 + 0.699515i) q^{57} +(7.86908 + 7.86908i) q^{58} +(-2.93819 - 2.93819i) q^{59} +(5.53106 + 3.01741i) q^{60} +(-0.0475495 - 0.0823581i) q^{61} +(-2.16752 - 3.75426i) q^{62} +(6.26278 + 5.68438i) q^{63} -2.69361i q^{64} +(7.86800 - 5.08853i) q^{65} +(4.73279 - 19.5419i) q^{66} +(3.70116 - 0.991722i) q^{67} +(5.62214 + 3.24595i) q^{68} +(-5.35132 - 5.09851i) q^{69} +(-13.0490 + 3.49646i) q^{70} +(1.56243 + 5.83108i) q^{71} +(-1.01345 - 3.16188i) q^{72} +(-1.49562 + 1.49562i) q^{73} +(2.65938 - 1.53540i) q^{74} +(-2.09529 + 2.19919i) q^{75} +(-0.146355 - 0.546205i) q^{76} +(8.87497 + 15.3719i) q^{77} +(11.3137 + 2.14223i) q^{78} +(-2.84121 + 4.92112i) q^{79} +(12.1501 + 3.25561i) q^{80} +(5.23188 + 7.32308i) q^{81} +(2.66543 + 1.53889i) q^{82} +(4.04440 + 15.0939i) q^{83} +(-6.00031 - 3.27340i) q^{84} +(-8.52274 + 8.52274i) q^{85} +(1.42737 - 5.32701i) q^{86} +(-10.1601 - 2.46065i) q^{87} -6.96818i q^{88} +(-0.0313812 + 0.117116i) q^{89} +(-14.3585 + 0.695139i) q^{90} +(-8.53551 + 5.52023i) q^{91} +(5.17297 + 2.98661i) q^{92} +(3.57486 + 1.95022i) q^{93} +(4.47538 - 7.75159i) q^{94} +1.04987 q^{95} +(6.05367 + 9.92301i) q^{96} +(4.10452 - 15.3183i) q^{97} +(1.68893 - 0.452547i) q^{98} +(5.76503 + 17.9865i) 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 $

$2$	1.30379	−	1.30379i	0.921920	−	0.921920i	−0.0752453	−	0.997165i	$-0.523974\pi$
$2$	1.30379	−	1.30379i	0.921920	−	0.921920i	0.997165	+	0.0752453i	$0.0239740\pi$
$3$	−0.407694	+	1.68339i	−0.235382	+	0.971903i
$3$	−0.407694	+	1.68339i	−0.235382	+	0.971903i
$4$		−	1.39974i		−	0.699872i
$5$	2.51024	+	0.672617i	1.12261	+	0.300804i	0.771941	−	0.635694i	$-0.219286\pi$
$5$	2.51024	+	0.672617i	1.12261	+	0.300804i	0.350673	+	0.936498i	$0.385953\pi$
$6$	1.66324	+	2.72633i	0.679013	+	1.11302i
$7$	−2.72321	−	0.729681i	−1.02928	−	0.275794i	−0.295613	−	0.955308i	$-0.595524\pi$
$7$	−2.72321	−	0.729681i	−1.02928	−	0.275794i	−0.733663	+	0.679514i	$0.762191\pi$
$8$	0.782609	+	0.782609i	0.276694	+	0.276694i
$9$	−2.66757	−	1.37261i	−0.889191	−	0.457537i
$10$	4.14978	−	2.39588i	1.31228	−	0.757644i
$11$	−4.45189	−	4.45189i	−1.34230	−	1.34230i	−0.893769	−	0.448528i	$-0.851949\pi$
$11$	−4.45189	−	4.45189i	−1.34230	−	1.34230i	−0.448528	−	0.893769i	$-0.648051\pi$
$12$	2.35631	+	0.570667i	0.680208	+	0.164737i
$13$	2.41762	−	2.67491i	0.670527	−	0.741885i
$13$	2.41762	−	2.67491i	0.670527	−	0.741885i
$14$	−4.50185	+	2.59914i	−1.20317	+	0.694650i
$15$	−2.15568	+	3.95148i	−0.556595	+	1.02027i
$16$	4.84020			1.21005
$17$	−2.31896	+	4.01655i	−0.562430	+	0.974157i	0.434854	+	0.900501i	$0.356800\pi$
$17$	−2.31896	+	4.01655i	−0.562430	+	0.974157i	−0.997284	+	0.0736558i	$0.976533\pi$
$18$	−5.26756	+	1.68836i	−1.24157	+	0.397950i
$19$	0.390218	−	0.104559i	0.0895221	−	0.0239874i	−0.213780	−	0.976882i	$-0.568578\pi$
$19$	0.390218	−	0.104559i	0.0895221	−	0.0239874i	0.303302	+	0.952894i	$0.401911\pi$
$20$	0.941492	−	3.51370i	0.210524	−	0.785686i
$21$	2.33857	−	4.28672i	0.510318	−	0.935439i
$22$	−11.6087			−2.47498
$23$	−2.13369	+	3.69565i	−0.444904	+	0.770597i	−0.998046	−	0.0624908i	$-0.980096\pi$
$23$	−2.13369	+	3.69565i	−0.444904	+	0.770597i	0.553141	+	0.833087i	$0.313429\pi$
$24$	−1.63650	+	0.998367i	−0.334048	+	0.203791i
$25$	1.51877	+	0.876864i	0.303755	+	0.175373i
$26$	−0.335449	−	6.63959i	−0.0657869	−	1.30213i
$27$	3.39819	−	3.93095i	0.653981	−	0.756511i
$28$	−1.02137	+	3.81179i	−0.193020	+	0.720361i
$29$			6.03554i			1.12077i	0.828232	+	0.560386i	$0.189347\pi$
$29$			6.03554i			1.12077i	−0.828232	+	0.560386i	$0.810653\pi$
$30$	2.34135	+	7.96247i	0.427469	+	1.45374i
$31$	0.608508	−	2.27098i	0.109291	−	0.407881i	−0.889505	−	0.456925i	$-0.848951\pi$
$31$	0.608508	−	2.27098i	0.109291	−	0.407881i	0.998797	+	0.0490441i	$0.0156175\pi$
$32$	4.74540	−	4.74540i	0.838876	−	0.838876i
$33$	9.30926	−	5.67924i	1.62053	−	0.988629i
$34$	2.21331	+	8.26018i	0.379579	+	1.41661i
$35$	−6.34511	−	3.66335i	−1.07252	−	0.619220i
$36$	−1.92130	+	3.73392i	−0.320217	+	0.622320i
$37$	1.60869	+	0.431046i	0.264466	+	0.0708635i	0.388615	−	0.921400i	$-0.372953\pi$
$37$	1.60869	+	0.431046i	0.264466	+	0.0708635i	−0.124149	+	0.992264i	$0.539620\pi$
$38$	0.372440	−	0.645085i	0.0604178	−	0.104647i
$39$	3.51725	+	5.16033i	0.563211	+	0.826313i
$40$	1.43814	+	2.49093i	0.227390	+	0.393851i
$41$	0.432026	+	1.61234i	0.0674711	+	0.251806i	0.991421	−	0.130708i	$-0.0417251\pi$
$41$	0.432026	+	1.61234i	0.0674711	+	0.251806i	−0.923950	+	0.382514i	$0.875058\pi$
$42$	−2.53998	−	8.63800i	−0.391928	−	1.33287i
$43$	2.59028	−	1.49550i	0.395014	−	0.228062i	−0.289316	−	0.957234i	$-0.593428\pi$
$43$	2.59028	−	1.49550i	0.395014	−	0.228062i	0.684331	+	0.729172i	$0.260095\pi$
$44$	−6.23151	+	6.23151i	−0.939436	+	0.939436i
$45$	−5.77301	−	5.23984i	−0.860589	−	0.781109i
$46$	2.03648	+	7.60024i	0.300262	+	1.12059i
$47$	4.68901	−	1.25642i	0.683962	−	0.183267i	0.0999262	−	0.994995i	$-0.468139\pi$
$47$	4.68901	−	1.25642i	0.683962	−	0.183267i	0.584036	+	0.811728i	$0.301473\pi$
$48$	−1.97332	+	8.14793i	−0.284824	+	1.17605i
$49$	0.821249	+	0.474148i	0.117321	+	0.0677355i
$50$	3.12341	−	0.836916i	0.441717	−	0.118358i
$51$	−5.81598	−	5.54122i	−0.814400	−	0.775926i
$52$	−3.74418	−	3.38405i	−0.519225	−	0.469283i
$53$			0.186317i			0.0255926i	0.999918	+	0.0127963i	$0.00407330\pi$
$53$			0.186317i			0.0255926i	−0.999918	+	0.0127963i	$0.995927\pi$
$54$	−0.694608	−	9.55566i	−0.0945242	−	1.30036i
$55$	−8.18091	−	14.1698i	−1.10311	−	1.91065i
$56$	−1.56015	−	2.70226i	−0.208484	−	0.361105i
$57$	0.0169230	+	0.699515i	0.00224150	+	0.0926530i
$58$	7.86908	+	7.86908i	1.03326	+	1.03326i
$59$	−2.93819	−	2.93819i	−0.382520	−	0.382520i	0.489489	−	0.872009i	$-0.337183\pi$
$59$	−2.93819	−	2.93819i	−0.382520	−	0.382520i	−0.872009	+	0.489489i	$0.837183\pi$
$60$	5.53106	+	3.01741i	0.714057	+	0.389545i
$61$	−0.0475495	−	0.0823581i	−0.00608809	−	0.0105449i	0.862965	−	0.505263i	$-0.168605\pi$
$61$	−0.0475495	−	0.0823581i	−0.00608809	−	0.0105449i	−0.869053	+	0.494718i	$0.835271\pi$
$62$	−2.16752	−	3.75426i	−0.275276	−	0.476791i
$63$	6.26278	+	5.68438i	0.789037	+	0.716165i
$64$		−	2.69361i		−	0.336702i
$65$	7.86800	−	5.08853i	0.975905	−	0.631154i
$66$	4.73279	−	19.5419i	0.582566	−	2.40544i
$67$	3.70116	−	0.991722i	0.452168	−	0.121158i	−0.0255455	−	0.999674i	$-0.508132\pi$
$67$	3.70116	−	0.991722i	0.452168	−	0.121158i	0.477714	+	0.878516i	$0.341466\pi$
$68$	5.62214	+	3.24595i	0.681785	+	0.393629i
$69$	−5.35132	−	5.09851i	−0.644223	−	0.613788i
$70$	−13.0490	+	3.49646i	−1.55965	+	0.417907i
$71$	1.56243	+	5.83108i	0.185427	+	0.692022i	0.994539	+	0.104368i	$0.0332819\pi$
$71$	1.56243	+	5.83108i	0.185427	+	0.692022i	−0.809112	+	0.587655i	$0.800051\pi$
$72$	−1.01345	−	3.16188i	−0.119436	−	0.372631i
$73$	−1.49562	+	1.49562i	−0.175049	+	0.175049i	−0.789194	−	0.614144i	$-0.789501\pi$
$73$	−1.49562	+	1.49562i	−0.175049	+	0.175049i	0.614144	+	0.789194i	$0.289501\pi$
$74$	2.65938	−	1.53540i	0.309147	−	0.178486i
$75$	−2.09529	+	2.19919i	−0.241944	+	0.253940i
$76$	−0.146355	−	0.546205i	−0.0167881	−	0.0626540i
$77$	8.87497	+	15.3719i	1.01140	+	1.75179i
$78$	11.3137	+	2.14223i	1.28103	+	0.242560i
$79$	−2.84121	+	4.92112i	−0.319661	+	0.553669i	−0.980417	−	0.196931i	$-0.936902\pi$
$79$	−2.84121	+	4.92112i	−0.319661	+	0.553669i	0.660756	+	0.750601i	$0.270236\pi$
$80$	12.1501	+	3.25561i	1.35842	+	0.363988i
$81$	5.23188	+	7.32308i	0.581320	+	0.813675i
$82$	2.66543	+	1.53889i	0.294348	+	0.169942i
$83$	4.04440	+	15.0939i	0.443931	+	1.65677i	0.718743	+	0.695275i	$0.244718\pi$
$83$	4.04440	+	15.0939i	0.443931	+	1.65677i	−0.274812	+	0.961498i	$0.588616\pi$
$84$	−6.00031	−	3.27340i	−0.654688	−	0.357157i
$85$	−8.52274	+	8.52274i	−0.924421	+	0.924421i
$86$	1.42737	−	5.32701i	0.153917	−	0.574426i
$87$	−10.1601	−	2.46065i	−1.08928	−	0.263810i
$88$		−	6.96818i		−	0.742811i
$89$	−0.0313812	+	0.117116i	−0.00332640	+	0.0124143i	−0.967569	−	0.252607i	$-0.918712\pi$
$89$	−0.0313812	+	0.117116i	−0.00332640	+	0.0124143i	0.964243	+	0.265021i	$0.0853788\pi$
$90$	−14.3585	+	0.695139i	−1.51351	+	0.0732741i
$91$	−8.53551	+	5.52023i	−0.894764	+	0.578678i
$92$	5.17297	+	2.98661i	0.539319	+	0.311376i
$93$	3.57486	+	1.95022i	0.370695	+	0.202228i
$94$	4.47538	−	7.75159i	0.461601	−	0.799516i
$95$	1.04987			0.107714
$96$	6.05367	+	9.92301i	0.617850	+	1.01276i
$97$	4.10452	−	15.3183i	0.416750	−	1.55533i	−0.364553	−	0.931183i	$-0.618778\pi$
$97$	4.10452	−	15.3183i	0.416750	−	1.55533i	0.781303	−	0.624151i	$-0.214555\pi$
$98$	1.68893	−	0.452547i	0.170608	−	0.0457141i
$99$	5.76503	+	17.9865i	0.579407	+	1.80771i
$100$	1.22739	−	2.12589i	0.122739	−	0.212589i
$101$	−3.50102			−0.348365			−0.174182	−	0.984713i	$-0.555728\pi$
$101$	−3.50102			−0.348365			−0.174182	+	0.984713i	$0.555728\pi$
$102$	−14.8074	+	0.358228i	−1.46615	+	0.0354698i
$103$	10.5831	−	6.11018i	1.04279	−	0.602054i	0.122166	−	0.992510i	$-0.461016\pi$
$103$	10.5831	−	6.11018i	1.04279	−	0.602054i	0.920622	+	0.390456i	$0.127683\pi$
$104$	3.98545	−	0.201355i	0.390806	−	0.0197445i
$105$	8.75370	−	9.18775i	0.854274	−	0.896632i
$106$	0.242919	+	0.242919i	0.0235943	+	0.0235943i
$107$	−3.96991	+	2.29203i	−0.383786	+	0.221579i	−0.679464	−	0.733709i	$-0.737788\pi$
$107$	−3.96991	+	2.29203i	−0.383786	+	0.221579i	0.295678	+	0.955288i	$0.404454\pi$
$108$	−5.50232	−	4.75659i	−0.529461	−	0.457703i
$109$	−7.19868	−	7.19868i	−0.689508	−	0.689508i	0.272615	−	0.962123i	$-0.412111\pi$
$109$	−7.19868	−	7.19868i	−0.689508	−	0.689508i	−0.962123	+	0.272615i	$0.912111\pi$
$110$	−29.1406	−	7.80820i	−2.77845	−	0.744483i
$111$	−1.38147	+	2.53230i	−0.131123	+	0.240356i
$112$	−13.1809	−	3.53181i	−1.24548	−	0.333724i
$113$		−	15.5056i		−	1.45864i	−0.684171	−	0.729322i	$-0.739836\pi$
$113$		−	15.5056i		−	1.45864i	0.684171	−	0.729322i	$-0.260164\pi$
$114$	0.934086	+	0.889958i	0.0874851	+	0.0833522i
$115$	−7.84183	+	7.84183i	−0.731254	+	0.731254i
$116$	8.44821			0.784397
$117$	−10.1208	+	3.81705i	−0.935666	+	0.352887i
$118$	−7.66158			−0.705305
$119$	9.24580	−	9.24580i	0.847562	−	0.847562i
$120$	−4.77952	+	1.40541i	−0.436309	+	0.128296i
$121$			28.6387i			2.60352i
$122$	−0.169372	−	0.0453832i	−0.0153343	−	0.00410880i
$123$	−2.89033	+	0.0699241i	−0.260612	+	0.00630485i
$124$	−3.17880	−	0.851756i	−0.285464	−	0.0764899i
$125$	−5.96543	−	5.96543i	−0.533564	−	0.533564i
$126$	15.5766	−	0.754114i	1.38768	−	0.0671818i
$127$	2.41225	−	1.39271i	0.214052	−	0.123583i	−0.389141	−	0.921178i	$-0.627228\pi$
$127$	2.41225	−	1.39271i	0.214052	−	0.123583i	0.603193	+	0.797595i	$0.293895\pi$
$128$	5.97889	+	5.97889i	0.528464	+	0.528464i
$129$	1.46146	+	4.97015i	0.128674	+	0.437597i
$130$	3.62384	−	16.8926i	0.317832	−	1.48158i
$131$	−11.1980	+	6.46515i	−0.978370	+	0.564862i	−0.901778	−	0.432200i	$-0.857737\pi$
$131$	−11.1980	+	6.46515i	−0.978370	+	0.564862i	−0.0765926	+	0.997062i	$0.524404\pi$
$132$	−7.94949	−	13.0306i	−0.691914	−	1.13417i
$133$	−1.13894			−0.0987585
$134$	3.53254	−	6.11854i	0.305165	−	0.528561i
$135$	11.1743	−	7.58195i	0.961730	−	0.652550i
$136$	−4.95822	+	1.32855i	−0.425164	+	0.113922i
$137$	0.110132	−	0.411020i	0.00940925	−	0.0351158i	−0.961062	−	0.276334i	$-0.910880\pi$
$137$	0.110132	−	0.411020i	0.00940925	−	0.0351158i	0.970471	+	0.241218i	$0.0775470\pi$
$138$	−13.6244	+	0.329607i	−1.15979	+	0.0280580i
$139$	8.73505			0.740898			0.370449	−	0.928853i	$-0.379204\pi$
$139$	8.73505			0.740898			0.370449	+	0.928853i	$0.379204\pi$
$140$	−5.12776	+	8.88154i	−0.433375	+	0.750627i
$141$	0.203353	+	8.40564i	0.0171254	+	0.707883i
$142$	9.63961	+	5.56543i	0.808938	+	0.467040i
$143$	−22.6714	+	1.14542i	−1.89588	+	0.0957845i
$144$	−12.9116	−	6.64372i	−1.07597	−	0.553643i
$145$	−4.05961	+	15.1507i	−0.337132	+	1.25819i
$146$			3.89996i			0.322763i
$147$	−1.13299	+	1.18917i	−0.0934476	+	0.0980812i
$148$	0.603354	−	2.25175i	0.0495954	−	0.185093i
$149$	1.82689	−	1.82689i	0.149664	−	0.149664i	−0.628304	−	0.777968i	$-0.716250\pi$
$149$	1.82689	−	1.82689i	0.149664	−	0.149664i	0.777968	+	0.628304i	$0.216250\pi$
$150$	0.135456	+	5.59911i	0.0110599	+	0.457165i
$151$	−0.352316	−	1.31486i	−0.0286711	−	0.107002i	0.950107	−	0.311923i	$-0.100973\pi$
$151$	−0.352316	−	1.31486i	−0.0286711	−	0.107002i	−0.978779	+	0.204921i	$0.934306\pi$
$152$	0.387216	+	0.223559i	0.0314074	+	0.0181331i
$153$	11.6991	−	7.53141i	0.945820	−	0.608879i
$154$	31.6129	+	8.47064i	2.54744	+	0.682584i
$155$	3.05501	−	5.29143i	0.245384	−	0.425018i
$156$	7.22313	−	4.92325i	0.578314	−	0.394175i
$157$	−6.09285	−	10.5531i	−0.486263	−	0.842231i	0.513613	−	0.858022i	$-0.328307\pi$
$157$	−6.09285	−	10.5531i	−0.486263	−	0.842231i	−0.999875	+	0.0157906i	$0.994973\pi$
$158$	2.71177	+	10.1205i	0.215737	+	0.805140i
$159$	−0.313643	−	0.0759603i	−0.0248735	−	0.00602404i
$160$	15.1039	−	8.72026i	1.19407	−	0.689397i
$161$	8.50712	−	8.50712i	0.670455	−	0.670455i
$162$	16.3690	+	2.72649i	1.28607	+	0.214213i
$163$	6.32949	+	23.6220i	0.495764	+	1.85022i	0.525707	+	0.850666i	$0.323801\pi$
$163$	6.32949	+	23.6220i	0.495764	+	1.85022i	−0.0299426	+	0.999552i	$0.509532\pi$
$164$	2.25687	−	0.604726i	0.176232	−	0.0472212i
$165$	27.1885	−	7.99470i	2.11662	−	0.622387i
$166$	24.9524	+	14.4063i	1.93668	+	1.11814i
$167$	−7.44045	+	1.99366i	−0.575759	+	0.154274i	−0.534937	−	0.844892i	$-0.679665\pi$
$167$	−7.44045	+	1.99366i	−0.575759	+	0.154274i	−0.0408227	+	0.999166i	$0.512998\pi$
$168$	5.18501	−	1.52464i	0.400032	−	0.117629i
$169$	−1.31024	−	12.9338i	−0.100788	−	0.994908i
$170$			22.2238i			1.70448i
$171$	−1.18445	−	0.256700i	−0.0905774	−	0.0196303i
$172$	−2.09332	−	3.62573i	−0.159614	−	0.276460i
$173$	−5.80228	−	10.0498i	−0.441139	−	0.764076i	0.556635	−	0.830757i	$-0.312092\pi$
$173$	−5.80228	−	10.0498i	−0.441139	−	0.764076i	−0.997774	+	0.0666815i	$0.978759\pi$
$174$	−16.4549	+	10.0385i	−1.24744	+	0.761019i
$175$	−3.49610	−	3.49610i	−0.264281	−	0.264281i
$176$	−21.5481	−	21.5481i	−1.62425	−	1.62425i
$177$	6.14399	−	3.74823i	0.461811	−	0.281734i
$178$	0.111781	+	0.193610i	0.00837831	+	0.0145117i
$179$	−2.75530	−	4.77232i	−0.205941	−	0.356700i	0.744491	−	0.667632i	$-0.232692\pi$
$179$	−2.75530	−	4.77232i	−0.205941	−	0.356700i	−0.950432	+	0.310932i	$0.899359\pi$
$180$	−7.33444	+	8.08073i	−0.546677	+	0.602302i
$181$		−	9.65258i		−	0.717471i	−0.933439	−	0.358735i	$-0.883208\pi$
$181$		−	9.65258i		−	0.717471i	0.933439	−	0.358735i	$-0.116792\pi$
$182$	−3.93129	+	18.3258i	−0.291406	+	1.35840i
$183$	0.158026	−	0.0464672i	0.0116816	−	0.00343496i
$184$	−4.56209	+	1.22241i	−0.336322	+	0.0901171i
$185$	3.74826	+	2.16406i	0.275578	+	0.159105i
$186$	7.20355	−	2.11819i	0.528190	−	0.155313i
$187$	28.2050	−	7.55751i	2.06255	−	0.552660i
$188$	−1.75866	−	6.56341i	−0.128264	−	0.478686i
$189$	−12.1223	+	8.22519i	−0.881768	+	0.598295i
$190$	1.36881	−	1.36881i	0.0993040	−	0.0993040i
$191$	−6.30072	+	3.63772i	−0.455904	+	0.263216i	−0.710320	−	0.703878i	$-0.751450\pi$
$191$	−6.30072	+	3.63772i	−0.455904	+	0.263216i	0.254416	+	0.967095i	$0.418117\pi$
$192$	4.53439	+	1.09817i	0.327241	+	0.0792536i
$193$	−3.31894	−	12.3864i	−0.238902	−	0.891595i	−0.976351	−	0.216192i	$-0.930636\pi$
$193$	−3.31894	−	12.3864i	−0.238902	−	0.891595i	0.737449	−	0.675403i	$-0.236030\pi$
$194$	−14.6204	−	25.3233i	−1.04968	−	1.81810i
$195$	5.35822	+	15.3194i	0.383710	+	1.09705i
$196$	0.663686	−	1.14954i	0.0474062	−	0.0821099i
$197$	15.2346	+	4.08211i	1.08542	+	0.290838i	0.756816	−	0.653628i	$-0.226754\pi$
$197$	15.2346	+	4.08211i	1.08542	+	0.290838i	0.328608	+	0.944467i	$0.393421\pi$
$198$	30.9670	+	15.9342i	2.20073	+	1.13239i
$199$	−21.4175	−	12.3654i	−1.51825	−	0.876560i	−0.999770	−	0.0214686i	$-0.993166\pi$
$199$	−21.4175	−	12.3654i	−1.51825	−	0.876560i	−0.518477	−	0.855091i	$-0.673501\pi$
$200$	0.502364	+	1.87485i	0.0355225	+	0.132572i
$201$	0.160512	+	6.63479i	0.0113216	+	0.467982i
$202$	−4.56460	+	4.56460i	−0.321164	+	0.321164i
$203$	4.40402	−	16.4360i	0.309102	−	1.15358i
$204$	−7.75629	+	8.14088i	−0.543049	+	0.569976i
$205$			4.33796i			0.302976i
$206$	5.83181	−	21.7646i	0.406321	−	1.51641i
$207$	10.7645	−	6.92970i	0.748181	−	0.481647i
$208$	11.7018	−	12.9471i	0.811372	−	0.897719i
$209$	−2.20269	−	1.27173i	−0.152363	−	0.0879671i
$210$	−0.565907	−	23.3919i	−0.0390513	−	1.61419i
$211$	−7.20117	+	12.4728i	−0.495749	+	0.858662i	−0.999988	−	0.00490196i	$-0.998440\pi$
$211$	−7.20117	+	12.4728i	−0.495749	+	0.858662i	0.504239	+	0.863564i	$0.331773\pi$
$212$	0.260796			0.0179116
$213$	−10.4530	+	0.252883i	−0.716225	+	0.0173272i
$214$	−2.18761	+	8.16426i	−0.149542	+	0.558097i
$215$	7.50814	−	2.01180i	0.512051	−	0.137204i
$216$	5.73584	−	0.416943i	0.390275	−	0.0283694i
$217$	−3.31419	+	5.74035i	−0.224982	+	0.389680i
$218$	−18.7711			−1.27134
$219$	−1.90795	−	3.12746i	−0.128927	−	0.211334i
$220$	−19.8340	+	11.4512i	−1.33721	+	0.772038i
$221$	5.13754	+	15.9135i	0.345589	+	1.07046i
$222$	1.50045	+	5.10274i	0.100704	+	0.342473i
$223$	0.720687	+	0.720687i	0.0482608	+	0.0482608i	0.730825	−	0.682565i	$-0.239135\pi$
$223$	0.720687	+	0.720687i	0.0482608	+	0.0482608i	−0.682565	+	0.730825i	$0.739135\pi$
$224$	−16.3853	+	9.46008i	−1.09479	+	0.632078i
$225$	−2.84784	−	4.42378i	−0.189856	−	0.294919i
$226$	−20.2161	−	20.2161i	−1.34475	−	1.34475i
$227$	7.50412	+	2.01072i	0.498066	+	0.133456i	0.499102	−	0.866543i	$-0.333663\pi$
$227$	7.50412	+	2.01072i	0.498066	+	0.133456i	−0.00103641	+	0.999999i	$0.500330\pi$
$228$	0.979142	−	0.0236878i	0.0648453	−	0.00156877i
$229$	−15.1620	−	4.06263i	−1.00193	−	0.268466i	−0.279676	−	0.960094i	$-0.590227\pi$
$229$	−15.1620	−	4.06263i	−1.00193	−	0.268466i	−0.722254	+	0.691628i	$0.756894\pi$
$230$			20.4482i			1.34832i
$231$	−29.4951	+	8.67297i	−1.94063	+	0.570639i
$232$	−4.72346	+	4.72346i	−0.310111	+	0.310111i
$233$	9.38345			0.614730			0.307365	−	0.951592i	$-0.400553\pi$
$233$	9.38345			0.614730			0.307365	+	0.951592i	$0.400553\pi$
$234$	−8.21874	+	18.1720i	−0.537276	+	1.18794i
$235$	12.6156			0.822953
$236$	−4.11272	+	4.11272i	−0.267715	+	0.267715i
$237$	−7.12580	−	6.78916i	−0.462870	−	0.441003i
$238$		−	24.1092i		−	1.56277i
$239$	−17.2852	−	4.63155i	−1.11809	−	0.299590i	−0.347977	−	0.937503i	$-0.613131\pi$
$239$	−17.2852	−	4.63155i	−1.11809	−	0.299590i	−0.770108	+	0.637913i	$0.779798\pi$
$240$	−10.4340	+	19.1260i	−0.673509	+	1.23458i
$241$	14.6279	+	3.91954i	0.942268	+	0.252480i	0.697078	−	0.716995i	$-0.254483\pi$
$241$	14.6279	+	3.91954i	0.942268	+	0.252480i	0.245190	+	0.969475i	$0.421150\pi$
$242$	37.3389	+	37.3389i	2.40024	+	2.40024i
$243$	−14.4606	+	5.82169i	−0.927646	+	0.373462i
$244$	−0.115280	+	0.0665571i	−0.00738006	+	0.00426088i
$245$	1.74261	+	1.74261i	0.111331	+	0.111331i
$246$	−3.67722	+	3.85955i	−0.234451	+	0.246076i
$247$	0.663714	−	1.29658i	0.0422311	−	0.0824993i
$248$	2.25352	−	1.30107i	0.143098	−	0.0826179i
$249$	−27.0578	+	0.654593i	−1.71472	+	0.0414832i
$250$	−15.5553			−0.983807
$251$	8.02608	−	13.9016i	0.506602	−	0.877460i	−0.493369	−	0.869820i	$-0.664235\pi$
$251$	8.02608	−	13.9016i	0.506602	−	0.877460i	0.999971	−	0.00763991i	$-0.00243188\pi$
$252$	7.95668	−	8.76629i	0.501224	−	0.552225i
$253$	25.9516	−	6.95371i	1.63156	−	0.437176i
$254$	1.32926	−	4.96088i	0.0834054	−	0.311273i
$255$	−10.8724	−	17.8217i	−0.680856	−	1.11604i
$256$	20.9777			1.31110
$257$	7.17869	−	12.4339i	0.447794	−	0.775602i	−0.550448	−	0.834869i	$-0.685543\pi$
$257$	7.17869	−	12.4339i	0.447794	−	0.775602i	0.998242	+	0.0592672i	$0.0188764\pi$
$258$	8.38548	+	4.57460i	0.522057	+	0.284802i
$259$	−4.06626	−	2.34766i	−0.252665	−	0.145876i
$260$	−7.12264	−	11.0132i	−0.441727	−	0.683008i
$261$	8.28445	−	16.1002i	0.512795	−	0.996580i
$262$	−6.17060	+	23.0290i	−0.381221	+	1.42274i
$263$		−	18.1216i		−	1.11743i	−0.829360	−	0.558714i	$-0.811295\pi$
$263$		−	18.1216i		−	1.11743i	0.829360	−	0.558714i	$-0.188705\pi$
$264$	11.7301	+	2.84088i	0.721940	+	0.174844i
$265$	−0.125320	+	0.467701i	−0.00769835	+	0.0287306i
$266$	−1.48494	+	1.48494i	−0.0910475	+	0.0910475i
$267$	−0.184358	−	0.100574i	−0.0112825	−	0.00615504i
$268$	−1.38816	−	5.18067i	−0.0847952	−	0.316460i
$269$	2.52163	+	1.45587i	0.153747	+	0.0887657i	0.574900	−	0.818224i	$-0.305041\pi$
$269$	2.52163	+	1.45587i	0.153747	+	0.0887657i	−0.421153	+	0.906990i	$0.638374\pi$
$270$	4.68367	−	24.4542i	0.285039	−	1.48824i
$271$	13.0634	+	3.50032i	0.793544	+	0.212629i	0.632748	−	0.774358i	$-0.281927\pi$
$271$	13.0634	+	3.50032i	0.793544	+	0.212629i	0.160796	+	0.986988i	$0.448594\pi$
$272$	−11.2242	+	19.4409i	−0.680569	+	1.17878i
$273$	−5.81281	−	16.6191i	−0.351807	−	1.00583i
$274$	−0.392294	−	0.679474i	−0.0236994	−	0.0410485i
$275$	−2.85771	−	10.6651i	−0.172326	−	0.643131i
$276$	−7.13661	+	7.49047i	−0.429573	+	0.450873i
$277$	−21.8686	+	12.6259i	−1.31396	+	0.758615i	−0.982749	−	0.184942i	$-0.940790\pi$
$277$	−21.8686	+	12.6259i	−1.31396	+	0.758615i	−0.331210	+	0.943557i	$0.607457\pi$
$278$	11.3887	−	11.3887i	0.683048	−	0.683048i
$279$	−4.74042	+	5.22277i	−0.283801	+	0.312679i
$280$	−2.09877	−	7.83271i	−0.125425	−	0.468094i
$281$	−20.1864	+	5.40894i	−1.20422	+	0.322670i	−0.804492	−	0.593963i	$-0.797563\pi$
$281$	−20.1864	+	5.40894i	−1.20422	+	0.322670i	−0.399729	+	0.916633i	$0.630896\pi$
$282$	11.2243	+	10.6941i	0.668399	+	0.636823i
$283$	−1.87406	−	1.08199i	−0.111401	−	0.0643177i	0.443264	−	0.896391i	$-0.353820\pi$
$283$	−1.87406	−	1.08199i	−0.111401	−	0.0643177i	−0.554665	+	0.832073i	$0.687154\pi$
$284$	8.16203	−	2.18701i	0.484327	−	0.129775i
$285$	−0.428025	+	1.76733i	−0.0253540	+	0.104688i
$286$	−28.0654	+	31.0521i	−1.65954	+	1.83615i
$287$		−	4.70599i		−	0.277786i
$288$	−19.1723	+	6.14511i	−1.12974	+	0.362104i
$289$	−2.25512	−	3.90599i	−0.132654	−	0.229764i
$290$	14.4604	+	25.0462i	0.849145	+	1.47076i
$291$	24.1132	+	13.1546i	1.41354	+	0.771139i
$292$	2.09349	+	2.09349i	0.122512	+	0.122512i
$293$	22.6747	+	22.6747i	1.32467	+	1.32467i	0.909948	+	0.414723i	$0.136122\pi$
$293$	22.6747	+	22.6747i	1.32467	+	1.32467i	0.414723	+	0.909948i	$0.363878\pi$
$294$	0.0732455	+	3.02762i	0.00427176	+	0.176574i
$295$	−5.39929	−	9.35185i	−0.314359	−	0.544486i
$296$	0.921631	+	1.59631i	0.0535687	+	0.0927837i
$297$	−32.6285	+	2.37179i	−1.89330	+	0.137625i
$298$		−	4.76376i		−	0.275957i
$299$	4.72708	+	14.6421i	0.273374	+	0.846774i
$300$	3.07830	+	2.93288i	0.177726	+	0.169330i
$301$	−8.14512	+	2.18248i	−0.469477	+	0.125796i
$302$	−2.17365	−	1.25496i	−0.125080	−	0.0722147i
$303$	1.42734	−	5.89357i	0.0819988	−	0.338576i
$304$	1.88873	−	0.506085i	0.108326	−	0.0290260i
$305$	−0.0639652	−	0.238721i	−0.00366264	−	0.0136691i
$306$	5.43386	−	25.0726i	0.310633	−	1.43331i
$307$	18.5795	−	18.5795i	1.06039	−	1.06039i	0.0623341	−	0.998055i	$-0.480146\pi$
$307$	18.5795	−	18.5795i	1.06039	−	1.06039i	0.998055	−	0.0623341i	$-0.0198544\pi$
$308$	21.5167	−	12.4227i	1.22603	−	0.707848i
$309$	5.97110	+	20.3066i	0.339684	+	1.15520i
$310$	−2.91583	−	10.8820i	−0.165608	−	0.618057i
$311$	3.45338	+	5.98144i	0.195823	+	0.339176i	0.947170	−	0.320732i	$-0.103929\pi$
$311$	3.45338	+	5.98144i	0.195823	+	0.339176i	−0.751347	+	0.659908i	$0.770595\pi$
$312$	−1.28589	+	6.79114i	−0.0727989	+	0.384473i
$313$	−14.0998	+	24.4216i	−0.796969	+	1.38039i	0.124613	+	0.992205i	$0.460231\pi$
$313$	−14.0998	+	24.4216i	−0.796969	+	1.38039i	−0.921582	+	0.388185i	$0.873102\pi$
$314$	−21.7029	−	5.81527i	−1.22476	−	0.328175i
$315$	11.8977	+	18.4816i	0.670359	+	1.04132i
$316$	6.88831	+	3.97697i	0.387498	+	0.223722i
$317$	−0.187051	−	0.698082i	−0.0105058	−	0.0392082i	0.960474	−	0.278370i	$-0.0897941\pi$
$317$	−0.187051	−	0.698082i	−0.0105058	−	0.0392082i	−0.970980	+	0.239162i	$0.923127\pi$
$318$	−0.507962	+	0.309889i	−0.0284851	+	0.0173777i
$319$	26.8696	−	26.8696i	1.50441	−	1.50441i
$320$	1.81177	−	6.76162i	0.101281	−	0.377986i
$321$	−2.23986	−	7.61733i	−0.125017	−	0.425158i
$322$		−	22.1830i		−	1.23621i
$323$	−0.484934	+	1.80980i	−0.0269824	+	0.100700i
$324$	10.2504	−	7.32329i	0.569469	−	0.406849i
$325$	6.01734	−	1.94265i	0.333782	−	0.107759i
$326$	39.0505	+	22.5458i	2.16281	+	1.24870i
$327$	15.0530	−	9.18329i	0.832433	−	0.507837i
$328$	−0.923726	+	1.59994i	−0.0510043	+	0.0883420i
$329$	−13.6859			−0.754530
$330$	25.0246	−	45.8715i	1.37756	−	2.52514i
$331$	−1.25380	+	4.67925i	−0.0689151	+	0.257195i	−0.991785	−	0.127918i	$-0.959171\pi$
$331$	−1.25380	+	4.67925i	−0.0689151	+	0.257195i	0.922870	+	0.385112i	$0.125837\pi$
$332$	21.1276	−	5.66113i	1.15953	−	0.310695i
$333$	−3.69962	−	3.35795i	−0.202738	−	0.184014i
$334$	−7.10148	+	12.3001i	−0.388575	+	0.673032i
$335$	9.95785			0.544055
$336$	11.3192	−	20.7486i	0.617511	−	1.13193i
$337$	−21.7282	+	12.5448i	−1.18361	+	0.683359i	−0.956848	−	0.290590i	$-0.906148\pi$
$337$	−21.7282	+	12.5448i	−1.18361	+	0.683359i	−0.226765	+	0.973949i	$0.572815\pi$
$338$	−18.5713	−	15.1547i	−1.01014	−	0.824307i
$339$	26.1019	+	6.32153i	1.41766	+	0.343338i
$340$	11.9297	+	11.9297i	0.646977	+	0.646977i
$341$	−12.8192	+	7.40117i	−0.694198	+	0.400796i
$342$	−1.87896	+	1.20960i	−0.101603	+	0.0654075i
$343$	12.0642	+	12.0642i	0.651407	+	0.651407i
$344$	3.19757	+	0.856786i	0.172401	+	0.0461948i
$345$	−10.0038	−	16.3979i	−0.538584	−	0.882832i
$346$	−20.6679	−	5.53794i	−1.11111	−	0.297721i
$347$			27.4221i			1.47210i	0.676929	+	0.736048i	$0.263310\pi$
$347$			27.4221i			1.47210i	−0.676929	+	0.736048i	$0.736690\pi$
$348$	−3.44428	+	14.2216i	−0.184633	+	0.762357i
$349$	0.725891	−	0.725891i	0.0388561	−	0.0388561i	−0.687412	−	0.726268i	$-0.741253\pi$
$349$	0.725891	−	0.725891i	0.0388561	−	0.0388561i	0.726268	+	0.687412i	$0.241253\pi$
$350$	−9.11638			−0.487291
$351$	−2.29939	−	18.5934i	−0.122733	−	0.992440i
$352$	−42.2520			−2.25204
$353$	13.5642	−	13.5642i	0.721951	−	0.721951i	−0.247052	−	0.969002i	$-0.579462\pi$
$353$	13.5642	−	13.5642i	0.721951	−	0.721951i	0.969002	+	0.247052i	$0.0794617\pi$
$354$	3.12358	−	12.8974i	0.166016	−	0.685488i
$355$			15.6884i			0.832651i
$356$	0.163933	+	0.0439257i	0.00868842	+	0.00232806i
$357$	11.7948	+	19.3337i	0.624247	+	1.02325i
$358$	−9.81444	−	2.62977i	−0.518709	−	0.138988i
$359$	−18.1179	−	18.1179i	−0.956226	−	0.956226i	0.0428555	−	0.999081i	$-0.486354\pi$
$359$	−18.1179	−	18.1179i	−0.956226	−	0.956226i	−0.999081	+	0.0428555i	$0.986354\pi$
$360$	−0.417261	−	8.61875i	−0.0219916	−	0.454248i
$361$	−16.3131	+	9.41840i	−0.858587	+	0.495705i
$362$	−12.5850	−	12.5850i	−0.661451	−	0.661451i
$363$	−48.2100	−	11.6758i	−2.53037	−	0.612822i
$364$	7.72691	+	11.9475i	0.405000	+	0.626220i
$365$	−4.76035	+	2.74839i	−0.249168	+	0.143857i
$366$	0.145449	−	0.266617i	0.00760277	−	0.0139363i
$367$	23.3055			1.21654			0.608268	−	0.793732i	$-0.291865\pi$
$367$	23.3055			1.21654			0.608268	+	0.793732i	$0.291865\pi$
$368$	−10.3275	+	17.8877i	−0.538357	+	0.932461i
$369$	1.06066	−	4.89404i	0.0552157	−	0.254774i
$370$	7.70843	−	2.06547i	0.400742	−	0.107379i
$371$	0.135952	−	0.507380i	0.00705828	−	0.0263419i
$372$	2.72981	−	5.00388i	0.141534	−	0.259439i
$373$	7.02200			0.363585			0.181793	−	0.983337i	$-0.441810\pi$
$373$	7.02200			0.363585			0.181793	+	0.983337i	$0.441810\pi$
$374$	26.9200	−	46.6269i	1.39200	−	2.41102i
$375$	12.4742	−	7.61005i	0.644164	−	0.392981i
$376$	4.65294	+	2.68638i	0.239957	+	0.138539i
$377$	16.1445	+	14.5916i	0.831484	+	0.751507i
$378$	−5.08102	+	26.5289i	−0.261340	+	1.36450i
$379$	2.49511	−	9.31188i	0.128165	−	0.478319i	−0.871767	−	0.489920i	$-0.837026\pi$
$379$	2.49511	−	9.31188i	0.128165	−	0.478319i	0.999933	+	0.0116007i	$0.00369271\pi$
$380$		−	1.46955i		−	0.0753862i
$381$	1.36101	+	4.62854i	0.0697268	+	0.237128i
$382$	−3.47199	+	12.9577i	−0.177643	+	0.662971i
$383$	16.3640	−	16.3640i	0.836164	−	0.836164i	−0.152188	−	0.988352i	$-0.548632\pi$
$383$	16.3640	−	16.3640i	0.836164	−	0.836164i	0.988352	+	0.152188i	$0.0486319\pi$
$384$	−12.5023	+	7.62722i	−0.638007	+	0.389225i
$385$	11.9389	+	44.5566i	0.608463	+	2.27082i
$386$	−20.4765	−	11.8221i	−1.04223	−	0.601731i
$387$	−8.96251	+	0.433904i	−0.455590	+	0.0220566i
$388$	−21.4416	−	5.74527i	−1.08853	−	0.291672i
$389$	−2.26345	+	3.92041i	−0.114761	+	0.198772i	−0.917684	−	0.397310i	$-0.869944\pi$
$389$	−2.26345	+	3.92041i	−0.114761	+	0.198772i	0.802923	+	0.596083i	$0.203277\pi$
$390$	26.9593	+	12.9873i	1.36514	+	0.657639i
$391$	−9.89585	−	17.1401i	−0.500455	−	0.866813i
$392$	0.271644	+	1.01379i	0.0137201	+	0.0512041i
$393$	−6.31799	−	21.4863i	−0.318701	−	1.08384i
$394$	25.1850	−	14.5406i	1.26880	−	0.732544i
$395$	−10.4422	+	10.4422i	−0.525402	+	0.525402i
$396$	25.1764	−	8.06956i	1.26516	−	0.405511i
$397$	−2.03359	−	7.58947i	−0.102063	−	0.380905i	0.895932	−	0.444191i	$-0.146509\pi$
$397$	−2.03359	−	7.58947i	−0.102063	−	0.380905i	−0.997995	+	0.0632859i	$0.979842\pi$
$398$	−44.0459	+	11.8021i	−2.20782	+	0.591583i
$399$	0.464338	−	1.91727i	0.0232460	−	0.0959837i
$400$	7.35117	+	4.24420i	0.367559	+	0.212210i
$401$	−0.250322	+	0.0670735i	−0.0125005	+	0.00334949i	−0.265064	−	0.964231i	$-0.585393\pi$
$401$	−0.250322	+	0.0670735i	−0.0125005	+	0.00334949i	0.252563	+	0.967580i	$0.418726\pi$
$402$	8.85966	+	8.44111i	0.441880	+	0.421004i
$403$	−4.60353	−	7.11808i	−0.229318	−	0.354577i
$404$			4.90053i			0.243811i
$405$	8.20765	+	21.9017i	0.407841	+	1.08831i
$406$	−15.6872	−	27.1711i	−0.778544	−	1.34848i
$407$	−5.24273	−	9.08067i	−0.259872	−	0.450112i
$408$	−0.215028	−	8.88824i	−0.0106455	−	0.440034i
$409$	26.1162	+	26.1162i	1.29136	+	1.29136i	0.933943	+	0.357422i	$0.116344\pi$
$409$	26.1162	+	26.1162i	1.29136	+	1.29136i	0.357422	+	0.933943i	$0.383656\pi$
$410$	5.65579	+	5.65579i	0.279320	+	0.279320i
$411$	0.647004	+	0.352965i	0.0319144	+	0.0174105i
$412$	−8.55269	−	14.8137i	−0.421361	−	0.729818i
$413$	5.85736	+	10.1453i	0.288222	+	0.499215i
$414$	4.99972	−	23.0695i	0.245723	−	1.13380i
$415$			40.6097i			1.99345i
$416$	−1.22093	−	24.1661i	−0.0598611	−	1.18484i
$417$	−3.56123	+	14.7045i	−0.174394	+	0.720081i
$418$	−4.52992	+	1.21379i	−0.221565	+	0.0593683i
$419$	25.2077	+	14.5537i	1.23148	+	0.710993i	0.967338	−	0.253491i	$-0.0815790\pi$
$419$	25.2077	+	14.5537i	1.23148	+	0.710993i	0.264139	+	0.964485i	$0.414912\pi$
$420$	−12.8605	−	12.2529i	−0.627528	−	0.597882i
$421$	−7.04531	+	1.88779i	−0.343368	+	0.0920051i	−0.426382	−	0.904543i	$-0.640212\pi$
$421$	−7.04531	+	1.88779i	−0.343368	+	0.0920051i	0.0830142	+	0.996548i	$0.473545\pi$
$422$	6.87309	+	25.6507i	0.334577	+	1.24866i
$423$	−14.2328	−	3.08461i	−0.692024	−	0.149979i
$424$	−0.145813	+	0.145813i	−0.00708132	+	0.00708132i
$425$	−7.04394	+	4.06682i	−0.341681	+	0.197270i
$426$	−13.2988	+	13.9582i	−0.644327	+	0.676276i
$427$	0.0693920	+	0.258974i	0.00335811	+	0.0125326i
$428$	3.20825	+	5.55686i	0.155077	+	0.268601i
$429$	7.31480	−	38.6316i	0.353162	−	1.86515i
$430$	7.16608	−	12.4120i	0.345579	−	0.598560i
$431$	−14.6266	−	3.91918i	−0.704537	−	0.188780i	−0.111275	−	0.993790i	$-0.535494\pi$
$431$	−14.6266	−	3.91918i	−0.704537	−	0.188780i	−0.593262	+	0.805009i	$0.702160\pi$
$432$	16.4479	−	19.0266i	0.791351	−	0.915417i
$433$	26.0240	+	15.0250i	1.25063	+	0.722054i	0.971235	−	0.238121i	$-0.0765316\pi$
$433$	26.0240	+	15.0250i	1.25063	+	0.722054i	0.279399	+	0.960175i	$0.409865\pi$
$434$	3.16320	+	11.8052i	0.151838	+	0.566669i
$435$	−23.8493	−	13.0107i	−1.14349	−	0.623816i
$436$	−10.0763	+	10.0763i	−0.482567	+	0.482567i
$437$	−0.446190	+	1.66520i	−0.0213442	+	0.0796575i
$438$	−6.56513	−	1.58999i	−0.313694	−	0.0759726i
$439$		−	15.6785i		−	0.748293i	−0.927370	−	0.374146i	$-0.877936\pi$
$439$		−	15.6785i		−	0.748293i	0.927370	−	0.374146i	$-0.122064\pi$
$440$	4.68692	−	17.4918i	0.223440	−	0.833890i
$441$	−1.53992	−	2.39208i	−0.0733295	−	0.113909i
$442$	27.4461	+	14.0496i	1.30548	+	0.668270i
$443$	11.9145	+	6.87886i	0.566076	+	0.326824i	0.755581	−	0.655056i	$-0.227355\pi$
$443$	11.9145	+	6.87886i	0.566076	+	0.326824i	−0.189504	+	0.981880i	$0.560688\pi$
$444$	3.54458	+	1.93370i	0.168218	+	0.0917694i
$445$	−0.157549	+	0.272883i	−0.00746853	+	0.0129359i
$446$	1.87925			0.0889851
$447$	2.33054	+	3.82016i	0.110231	+	0.180688i
$448$	−1.96548	+	7.33527i	−0.0928602	+	0.346559i
$449$	11.5500	−	3.09482i	0.545079	−	0.146054i	0.0242366	−	0.999706i	$-0.492285\pi$
$449$	11.5500	−	3.09482i	0.545079	−	0.146054i	0.520843	+	0.853653i	$0.325618\pi$
$450$	−9.48068	−	2.05470i	−0.446924	−	0.0968594i
$451$	5.25465	−	9.10132i	0.247432	−	0.428564i
$452$	−21.7039			−1.02086
$453$	2.35705	−	0.0570229i	0.110744	−	0.00267917i
$454$	12.4054	−	7.16224i	0.582213	−	0.336141i
$455$	−25.1392	+	8.11599i	−1.17854	+	0.380484i
$456$	−0.534202	+	0.560690i	−0.0250163	+	0.0262567i
$457$	−27.8019	−	27.8019i	−1.30052	−	1.30052i	−0.928041	−	0.372478i	$-0.878508\pi$
$457$	−27.8019	−	27.8019i	−1.30052	−	1.30052i	−0.372478	−	0.928041i	$-0.621492\pi$
$458$	−25.0649	+	14.4712i	−1.17120	+	0.676195i
$459$	7.90860	+	22.7647i	0.369142	+	1.06256i
$460$	10.9765	+	10.9765i	0.511784	+	0.511784i
$461$	−17.3771	−	4.65619i	−0.809334	−	0.216860i	−0.169656	−	0.985503i	$-0.554266\pi$
$461$	−17.3771	−	4.65619i	−0.809334	−	0.216860i	−0.639678	+	0.768643i	$0.720932\pi$
$462$	−27.1477	+	49.7632i	−1.26303	+	2.31519i
$463$	32.6751	+	8.75526i	1.51854	+	0.406891i	0.919261	−	0.393649i	$-0.128787\pi$
$463$	32.6751	+	8.75526i	1.51854	+	0.406891i	0.599279	+	0.800540i	$0.295454\pi$
$464$			29.2132i			1.35619i
$465$	7.66200	+	7.30003i	0.355317	+	0.338531i
$466$	12.2341	−	12.2341i	0.566732	−	0.566732i
$467$	−15.4828			−0.716459			−0.358229	−	0.933634i	$-0.616619\pi$
$467$	−15.4828			−0.716459			−0.358229	+	0.933634i	$0.616619\pi$
$468$	5.34290	+	14.1665i	0.246976	+	0.654847i
$469$	−10.8027			−0.498821
$470$	16.4482	−	16.4482i	0.758697	−	0.758697i
$471$	20.2490	−	5.95417i	0.933025	−	0.274354i
$472$		−	4.59891i		−	0.211682i
$473$	−18.1895	−	4.87385i	−0.836353	−	0.224100i
$474$	−18.1422	+	0.438904i	−0.833299	+	0.0201595i
$475$	0.684336	+	0.183367i	0.0313995	+	0.00841347i
$476$	−12.9418	−	12.9418i	−0.593185	−	0.593185i
$477$	0.255741	−	0.497014i	0.0117096	−	0.0227567i
$478$	−28.5748	+	16.4977i	−1.30698	+	0.754587i
$479$	−21.8078	−	21.8078i	−0.996425	−	0.996425i	0.00356821	−	0.999994i	$-0.498864\pi$
$479$	−21.8078	−	21.8078i	−0.996425	−	0.996425i	−0.999994	+	0.00356821i	$0.998864\pi$
$480$	8.52178	+	28.9809i	0.388964	+	1.32279i
$481$	5.04219	−	3.26098i	0.229904	−	0.148688i
$482$	24.1820	−	13.9615i	1.10146	−	0.635929i
$483$	10.8525	+	17.7891i	0.493804	+	0.809430i
$484$	40.0869			1.82213
$485$	20.6067	−	35.6918i	0.935700	−	1.62068i
$486$	−11.2633	+	26.4438i	−0.510913	+	1.19952i
$487$	−36.9964	+	9.91314i	−1.67647	+	0.449207i	−0.966842	−	0.255374i	$-0.917801\pi$
$487$	−36.9964	+	9.91314i	−1.67647	+	0.449207i	−0.709623	+	0.704582i	$0.751135\pi$
$488$	0.0272415	−	0.101667i	0.00123317	−	0.00460224i
$489$	−42.3454	+	1.02444i	−1.91493	+	0.0463267i
$490$	4.54401			0.205277
$491$	−16.4396	+	28.4742i	−0.741909	+	1.28502i	0.209716	+	0.977762i	$0.432746\pi$
$491$	−16.4396	+	28.4742i	−0.741909	+	1.28502i	−0.951625	+	0.307261i	$0.900587\pi$
$492$	0.0978759	+	4.04572i	0.00441259	+	0.182395i
$493$	−24.2421	−	13.9962i	−1.09181	−	0.630355i
$494$	−0.825124	−	2.55581i	−0.0371241	−	0.114991i
$495$	2.37361	+	49.0280i	0.106686	+	2.20365i
$496$	2.94531	−	10.9920i	0.132248	−	0.493557i
$497$		−	17.0193i		−	0.763422i
$498$	−34.4242	+	36.1311i	−1.54259	+	1.61907i
$499$	4.99230	−	18.6315i	0.223486	−	0.834061i	−0.759520	−	0.650485i	$-0.774566\pi$
$499$	4.99230	−	18.6315i	0.223486	−	0.834061i	0.983005	−	0.183576i	$-0.0587675\pi$
$500$	−8.35007	+	8.35007i	−0.373427	+	0.373427i
$501$	−0.322678	−	13.3379i	−0.0144162	−	0.595896i
$502$	−7.66043	−	28.5891i	−0.341902	−	1.27599i
$503$	14.1918	+	8.19366i	0.632783	+	0.365337i	0.781829	−	0.623493i	$-0.214287\pi$
$503$	14.1918	+	8.19366i	0.632783	+	0.365337i	−0.149046	+	0.988830i	$0.547620\pi$
$504$	0.452661	+	9.34995i	0.0201631	+	0.416480i
$505$	−8.78841	−	2.35485i	−0.391079	−	0.104789i
$506$	24.7693	−	42.9016i	1.10113	−	1.90721i
$507$	22.3068	+	3.06739i	0.990678	+	0.136228i
$508$	−1.94944	−	3.37653i	−0.0864925	−	0.149809i
$509$	2.79747	+	10.4403i	0.123996	+	0.462758i	0.999802	−	0.0199051i	$-0.00633640\pi$
$509$	2.79747	+	10.4403i	0.123996	+	0.462758i	−0.875806	+	0.482663i	$0.839670\pi$
$510$	−37.4112	−	9.06049i	−1.65659	−	0.401205i
$511$	5.16422	−	2.98156i	0.228451	−	0.131897i
$512$	15.3927	−	15.3927i	0.680269	−	0.680269i
$513$	0.915019	−	1.88924i	0.0403991	−	0.0834118i
$514$	−6.85164	−	25.5707i	−0.302213	−	1.12787i
$515$	30.6761	−	8.21962i	1.35175	−	0.362200i
$516$	6.95694	−	2.04567i	0.306262	−	0.0900557i
$517$	−26.4684	−	15.2815i	−1.16408	−	0.672081i
$518$	−8.36241	+	2.24070i	−0.367423	+	0.0984507i
$519$	19.2833	−	5.67022i	0.846444	−	0.248895i
$520$	10.1399	+	2.17523i	0.444663	+	0.0953903i
$521$			18.8001i			0.823648i	0.911263	+	0.411824i	$0.135108\pi$
$521$			18.8001i			0.823648i	−0.911263	+	0.411824i	$0.864892\pi$
$522$	−10.1902	−	31.7925i	−0.446011	−	1.39152i
$523$	−1.02893	−	1.78216i	−0.0449919	−	0.0779283i	0.842652	−	0.538458i	$-0.180993\pi$
$523$	−1.02893	−	1.78216i	−0.0449919	−	0.0779283i	−0.887644	+	0.460530i	$0.847660\pi$
$524$	9.04955	+	15.6743i	0.395331	+	0.684734i
$525$	7.31063	−	4.45995i	0.319062	−	0.194648i
$526$	−23.6268	−	23.6268i	−1.03018	−	1.03018i
$527$	7.71042	+	7.71042i	0.335871	+	0.335871i
$528$	45.0587	−	27.4887i	1.96093	−	1.19629i
$529$	2.39477	+	4.14787i	0.104121	+	0.180342i
$530$	0.446393	+	0.773176i	0.0193901	+	0.0335846i
$531$	3.80484	+	11.8708i	0.165116	+	0.515150i
$532$			1.59422i			0.0691183i
$533$	5.35734	+	2.74240i	0.232052	+	0.118787i
$534$	−0.371492	+	0.109236i	−0.0160760	+	0.00472712i
$535$	−11.5071	+	3.08332i	−0.497495	+	0.133303i
$536$	3.67269	+	2.12043i	0.158636	+	0.0915885i
$537$	9.15696	−	2.69258i	0.395152	−	0.116194i
$538$	5.18583	−	1.38954i	0.223577	−	0.0599073i
$539$	−1.54526	−	5.76697i	−0.0665589	−	0.248401i
$540$	−10.6128	−	15.6411i	−0.456702	−	0.673088i
$541$	23.9398	−	23.9398i	1.02925	−	1.02925i	0.0296937	−	0.999559i	$-0.490547\pi$
$541$	23.9398	−	23.9398i	1.02925	−	1.02925i	0.999559	−	0.0296937i	$-0.00945319\pi$
$542$	21.5956	−	12.4682i	0.927611	−	0.535556i
$543$	16.2490	+	3.93530i	0.697312	+	0.168880i
$544$	8.05576	+	30.0645i	0.345388	+	1.28901i
$545$	−13.2285	−	22.9124i	−0.566645	−	0.981458i
$546$	−29.2465	−	14.0892i	−1.25164	−	0.602961i
$547$	−8.43825	+	14.6155i	−0.360793	+	0.624912i	−0.988092	−	0.153867i	$-0.950827\pi$
$547$	−8.43825	+	14.6155i	−0.360793	+	0.624912i	0.627298	+	0.778779i	$0.284161\pi$
$548$	−0.575322	−	0.154157i	−0.0245766	−	0.00658527i
$549$	0.0137960	+	0.284963i	0.000588798	+	0.0121619i
$550$	−17.6310	−	10.1792i	−0.751787	−	0.434044i
$551$	0.631067	+	2.35518i	0.0268844	+	0.100334i
$552$	−0.197849	−	8.17812i	−0.00842100	−	0.348084i
$553$	11.3281	−	11.3281i	0.481718	−	0.481718i
$554$	−12.0506	+	44.9736i	−0.511983	+	1.91075i
$555$	−5.17109	+	5.42749i	−0.219500	+	0.230384i
$556$		−	12.2268i		−	0.518533i
$557$	−6.49382	+	24.2353i	−0.275152	+	1.02688i	0.680587	+	0.732667i	$0.261725\pi$
$557$	−6.49382	+	24.2353i	−0.275152	+	1.02688i	−0.955739	+	0.294215i	$0.904942\pi$
$558$	0.628884	+	12.9899i	0.0266228	+	0.549907i
$559$	2.26199	−	10.5443i	0.0956721	−	0.445977i
$560$	−30.7117	−	17.7314i	−1.29780	−	0.749288i
$561$	1.22320	+	50.5610i	0.0516433	+	2.13469i
$562$	−19.2668	+	33.3710i	−0.812720	+	1.40767i
$563$	−8.00333			−0.337300			−0.168650	−	0.985676i	$-0.553941\pi$
$563$	−8.00333			−0.337300			−0.168650	+	0.985676i	$0.553941\pi$
$564$	11.7657	−	0.284642i	0.495427	−	0.0119856i
$565$	10.4293	−	38.9228i	0.438765	−	1.63749i
$566$	−3.85408	+	1.03270i	−0.161999	+	0.0434075i
$567$	−8.90398	−	23.7599i	−0.373932	−	0.997821i
$568$	−3.34068	+	5.78623i	−0.140172	+	0.242785i
$569$	6.86820			0.287930			0.143965	−	0.989583i	$-0.454015\pi$
$569$	6.86820			0.287930			0.143965	+	0.989583i	$0.454015\pi$
$570$	1.74618	+	2.86229i	0.0731394	+	0.119888i
$571$	8.78114	−	5.06979i	0.367479	−	0.212164i	−0.304877	−	0.952392i	$-0.598616\pi$
$571$	8.78114	−	5.06979i	0.367479	−	0.212164i	0.672357	+	0.740227i	$0.265282\pi$
$572$	1.60329	+	31.7341i	0.0670369	+	1.32687i
$573$	−3.55492	−	12.0896i	−0.148509	−	0.505051i
$574$	−6.13563	−	6.13563i	−0.256096	−	0.256096i
$575$	−6.48117	+	3.74191i	−0.270283	+	0.156048i
$576$	−3.69729	+	7.18541i	−0.154054	+	0.299392i
$577$	−6.26722	−	6.26722i	−0.260908	−	0.260908i	0.564515	−	0.825423i	$-0.309063\pi$
$577$	−6.26722	−	6.26722i	−0.260908	−	0.260908i	−0.825423	+	0.564515i	$0.809063\pi$
$578$	−8.03280	−	2.15238i	−0.334120	−	0.0895273i
$579$	22.2043	−	0.537175i	0.922777	−	0.0223242i
$580$	21.2071	+	5.68241i	0.880575	+	0.235949i
$581$		−	44.0550i		−	1.82771i
$582$	48.5894	−	14.2876i	2.01410	−	0.592241i
$583$	0.829464	−	0.829464i	0.0343529	−	0.0343529i
$584$	−2.34097			−0.0968701
$585$	−27.9730	+	2.77432i	−1.15654	+	0.114704i
$586$	59.1262			2.44248
$587$	8.13480	−	8.13480i	0.335759	−	0.335759i	−0.519009	−	0.854769i	$-0.673699\pi$
$587$	8.13480	−	8.13480i	0.335759	−	0.335759i	0.854769	+	0.519009i	$0.173699\pi$
$588$	1.66454	+	1.58590i	0.0686443	+	0.0654014i
$589$		−	0.949804i		−	0.0391360i
$590$	−19.2324	−	5.15331i	−0.791786	−	0.212158i
$591$	−13.0828	+	23.9815i	−0.538156	+	0.986468i
$592$	7.78637	+	2.08635i	0.320018	+	0.0857485i
$593$	12.5514	+	12.5514i	0.515426	+	0.515426i	0.916184	−	0.400758i	$-0.131253\pi$
$593$	12.5514	+	12.5514i	0.515426	+	0.515426i	−0.400758	+	0.916184i	$0.631253\pi$
$594$	−39.4485	+	45.6331i	−1.61859	+	1.87235i
$595$	29.4281	−	16.9903i	1.20643	−	0.696535i
$596$	−2.55717	−	2.55717i	−0.104746	−	0.104746i
$597$	29.5475	−	31.0126i	1.20930	−	1.26926i
$598$	25.2534	+	12.9271i	1.03269	+	0.528628i
$599$	37.6976	−	21.7647i	1.54028	−	0.889283i	0.541462	−	0.840725i	$-0.317871\pi$
$599$	37.6976	−	21.7647i	1.54028	−	0.889283i	0.998820	−	0.0485576i	$-0.0154625\pi$
$600$	−3.36090	+	0.0813084i	−0.137208	+	0.00331940i
$601$	28.4886			1.16207			0.581036	−	0.813878i	$-0.302647\pi$
$601$	28.4886			1.16207			0.581036	+	0.813878i	$0.302647\pi$
$602$	−7.77404	+	13.4650i	−0.316846	+	0.548794i
$603$	−11.2344	−	2.43476i	−0.457498	−	0.0991511i
$604$	−1.84047	+	0.493152i	−0.0748876	+	0.0200661i
$605$	−19.2629	+	71.8901i	−0.783148	+	2.92275i
$606$	−5.82302	−	9.54494i	−0.236544	−	0.387737i
$607$	29.6066			1.20170			0.600848	−	0.799363i	$-0.294830\pi$
$607$	29.6066			1.20170			0.600848	+	0.799363i	$0.294830\pi$
$608$	1.35557	−	2.34791i	0.0549755	−	0.0952204i
$609$	25.8727	+	14.1145i	1.04841	+	0.571950i
$610$	−0.394640	−	0.227846i	−0.0159785	−	0.00922520i
$611$	7.97544	−	15.5802i	0.322652	−	0.630307i
$612$	−10.5420	−	16.3758i	−0.426137	−	0.661953i
$613$	−8.67578	+	32.3784i	−0.350411	+	1.30775i	0.535750	+	0.844377i	$0.320029\pi$
$613$	−8.67578	+	32.3784i	−0.350411	+	1.30775i	−0.886161	+	0.463377i	$0.846638\pi$
$614$		−	48.4476i		−	1.95519i
$615$	−7.30246	−	1.76856i	−0.294463	−	0.0713152i
$616$	−5.08455	+	18.9758i	−0.204862	+	0.764557i
$617$	23.9642	−	23.9642i	0.964763	−	0.964763i	−0.0346374	−	0.999400i	$-0.511028\pi$
$617$	23.9642	−	23.9642i	0.964763	−	0.964763i	0.999400	+	0.0346374i	$0.0110276\pi$
$618$	34.2606	+	18.6905i	1.37816	+	0.751841i
$619$	6.95927	+	25.9724i	0.279717	+	1.04392i	0.952614	+	0.304181i	$0.0983829\pi$
$619$	6.95927	+	25.9724i	0.279717	+	1.04392i	−0.672897	+	0.739736i	$0.734950\pi$
$620$	−7.40664	−	4.27623i	−0.297458	−	0.171737i
$621$	7.27675	+	20.9459i	0.292006	+	0.840531i
$622$	12.3010	+	3.29605i	0.493227	+	0.132160i
$623$	0.170915	−	0.296034i	0.00684757	−	0.0118603i
$624$	17.0242	+	24.9770i	0.681514	+	0.999881i
$625$	−15.3465	−	26.5810i	−0.613862	−	1.06324i
$626$	13.4574	+	50.2239i	0.537868	+	2.00735i
$627$	3.03883	−	3.18951i	0.121359	−	0.127377i
$628$	−14.7717	+	8.52843i	−0.589454	+	0.340322i
$629$	−5.46179	+	5.46179i	−0.217776	+	0.217776i
$630$	39.6083	+	8.58409i	1.57803	+	0.341998i
$631$	−0.0679900	−	0.253742i	−0.00270664	−	0.0101013i	0.964559	−	0.263866i	$-0.0849977\pi$
$631$	−0.0679900	−	0.253742i	−0.00270664	−	0.0101013i	−0.967266	+	0.253765i	$0.918331\pi$
$632$	−6.07486	+	1.62776i	−0.241645	+	0.0647486i
$633$	−18.0606	−	17.2074i	−0.717846	−	0.683933i
$634$	−1.15403	−	0.666279i	−0.0458323	−	0.0264613i
$635$	6.99209	−	1.87353i	0.277473	−	0.0743486i
$636$	−0.106325	+	0.439021i	−0.00421606	+	0.0174083i
$637$	3.25377	−	1.05045i	0.128919	−	0.0416205i
$638$		−	70.0647i		−	2.77389i
$639$	3.83591	−	17.6995i	0.151746	−	0.700179i
$640$	10.9870	+	19.0300i	0.434297	+	0.752225i
$641$	15.6027	+	27.0246i	0.616268	+	1.06741i	0.990161	+	0.139935i	$0.0446894\pi$
$641$	15.6027	+	27.0246i	0.616268	+	1.06741i	−0.373893	+	0.927472i	$0.621977\pi$
$642$	−12.8517	−	7.01110i	−0.507217	−	0.276706i
$643$	−31.3478	−	31.3478i	−1.23624	−	1.23624i	−0.961527	−	0.274710i	$-0.911418\pi$
$643$	−31.3478	−	31.3478i	−1.23624	−	1.23624i	−0.274710	−	0.961527i	$-0.588582\pi$
$644$	−11.9078	−	11.9078i	−0.469233	−	0.469233i
$645$	0.325613	+	13.4593i	0.0128210	+	0.529959i
$646$	1.72735	+	2.99185i	0.0679615	+	0.117713i
$647$	−5.33648	−	9.24306i	−0.209799	−	0.363382i	0.741852	−	0.670563i	$-0.233948\pi$
$647$	−5.33648	−	9.24306i	−0.209799	−	0.363382i	−0.951651	+	0.307181i	$0.900614\pi$
$648$	−1.63659	+	9.82561i	−0.0642914	+	0.385987i
$649$			26.1610i			1.02691i
$650$	5.31255	−	10.3782i	0.208375	−	0.407066i
$651$	−8.31204	−	7.91936i	−0.325774	−	0.310384i
$652$	33.0647	−	8.85967i	1.29492	−	0.346972i
$653$	−30.4306	−	17.5691i	−1.19084	−	0.687532i	−0.232343	−	0.972634i	$-0.574639\pi$
$653$	−30.4306	−	17.5691i	−1.19084	−	0.687532i	−0.958497	+	0.285102i	$0.907972\pi$
$654$	7.65288	−	31.5991i	0.299251	−	1.23562i
$655$	−32.4582	+	8.69714i	−1.26825	+	0.339825i
$656$	2.09109	+	7.80407i	0.0816435	+	0.304698i
$657$	6.04259	−	1.93677i	0.235744	−	0.0755606i
$658$	−17.8436	+	17.8436i	−0.695616	+	0.695616i
$659$	−8.31698	+	4.80181i	−0.323983	+	0.187052i	−0.653167	−	0.757214i	$-0.726560\pi$
$659$	−8.31698	+	4.80181i	−0.323983	+	0.187052i	0.329183	+	0.944266i	$0.393227\pi$
$660$	−11.1905	−	38.0569i	−0.435591	−	1.48136i
$661$	3.00868	+	11.2285i	0.117024	+	0.436740i	0.999430	−	0.0337484i	$-0.0107445\pi$
$661$	3.00868	+	11.2285i	0.117024	+	0.436740i	−0.882406	+	0.470488i	$0.844078\pi$
$662$	4.46607	+	7.73546i	0.173579	+	0.300647i
$663$	−28.8831	+	2.16064i	−1.12173	+	0.0839122i
$664$	−8.64745	+	14.9778i	−0.335586	+	0.581252i
$665$	−2.85901	−	0.766070i	−0.110868	−	0.0297069i
$666$	−9.20160	+	0.445479i	−0.356555	+	0.0172620i
$667$	−22.3053	−	12.8779i	−0.863663	−	0.498636i
$668$	2.79062	+	10.4147i	0.107972	+	0.402958i
$669$	−1.50701	+	0.919374i	−0.0582645	+	0.0355451i
$670$	12.9830	−	12.9830i	0.501575	−	0.501575i
$671$	−0.154964	+	0.578335i	−0.00598233	+	0.0223264i
$672$	−9.24476	−	31.4397i	−0.356624	−	1.21281i
$673$			24.3131i			0.937201i	0.883410	+	0.468601i	$0.155242\pi$
$673$			24.3131i			0.937201i	−0.883410	+	0.468601i	$0.844758\pi$
$674$	−11.9733	+	44.6849i	−0.461194	+	1.72120i
$675$	8.60798	−	2.99047i	0.331321	−	0.115103i
$676$	−18.1040	+	1.83400i	−0.696308	+	0.0705386i
$677$	−36.2277	−	20.9161i	−1.39234	−	0.803871i	−0.398770	−	0.917051i	$-0.630563\pi$
$677$	−36.2277	−	20.9161i	−1.39234	−	0.803871i	−0.993574	+	0.113180i	$0.963896\pi$
$678$	42.2734	−	25.7894i	1.62350	−	0.990438i
$679$	−22.3549	+	38.7198i	−0.857902	+	1.48593i
$680$	−13.3399			−0.511564
$681$	−6.44420	+	11.8126i	−0.246942	+	0.452658i
$682$	−7.06398	+	26.3631i	−0.270494	+	1.00950i
$683$	−9.97708	+	2.67335i	−0.381763	+	0.102293i	−0.444596	−	0.895731i	$-0.646653\pi$
$683$	−9.97708	+	2.67335i	−0.381763	+	0.102293i	0.0628338	+	0.998024i	$0.479986\pi$
$684$	−0.359314	+	1.65793i	−0.0137387	+	0.0633926i
$685$	0.552918	−	0.957682i	0.0211259	−	0.0365911i
$686$	31.4585			1.20109
$687$	13.0204	−	23.8671i	0.496760	−	0.910587i
$688$	12.5375	−	7.23853i	0.477988	−	0.275966i
$689$	0.498381	+	0.450444i	0.0189868	+	0.0171605i
$690$	−34.4222	−	8.33661i	−1.31043	−	0.317369i
$691$	0.482794	+	0.482794i	0.0183664	+	0.0183664i	0.716230	−	0.697864i	$-0.245866\pi$
$691$	0.482794	+	0.482794i	0.0183664	+	0.0183664i	−0.697864	+	0.716230i	$0.745866\pi$
$692$	−14.0672	+	8.12171i	−0.534755	+	0.308741i
$693$	−2.57498	−	53.1875i	−0.0978154	−	2.02043i
$694$	35.7527	+	35.7527i	1.35715	+	1.35715i
$695$	21.9271	+	5.87535i	0.831742	+	0.222865i
$696$	−6.02568	−	9.87714i	−0.228403	−	0.374392i
$697$	−7.47791	−	2.00370i	−0.283246	−	0.0758955i
$698$		−	1.89282i		−	0.0716444i
$699$	−3.82557	+	15.7960i	−0.144697	+	0.597458i
$700$	−4.89365	+	4.89365i	−0.184963	+	0.184963i
$701$	−48.1896			−1.82010			−0.910049	−	0.414502i	$-0.863956\pi$
$701$	−48.1896			−1.82010			−0.910049	+	0.414502i	$0.863956\pi$
$702$	−27.2398	−	21.2439i	−1.02810	−	0.801800i
$703$	0.672807			0.0253754
$704$	−11.9917	+	11.9917i	−0.451954	+	0.451954i
$705$	−5.14331	+	21.2370i	−0.193708	+	0.799831i
$706$		−	35.3698i		−	1.33116i
$707$	9.53401	+	2.55463i	0.358563	+	0.0960767i
$708$	−5.24656	−	8.60001i	−0.197178	−	0.323208i
$709$	−17.9546	−	4.81091i	−0.674298	−	0.180678i	−0.0946079	−	0.995515i	$-0.530160\pi$
$709$	−17.9546	−	4.81091i	−0.674298	−	0.180678i	−0.579690	+	0.814837i	$0.696826\pi$
$710$	20.4543	+	20.4543i	0.767638	+	0.767638i
$711$	14.3339	−	9.22756i	0.537564	−	0.346061i
$712$	−0.116215	+	0.0670970i	−0.00435536	+	0.00251457i
$713$	7.09440	+	7.09440i	0.265687	+	0.265687i
$714$	40.5851	+	9.82917i	1.51886	+	0.367847i
$715$	−57.6811	−	12.3739i	−2.15715	−	0.462757i
$716$	−6.68002	+	3.85671i	−0.249644	+	0.144132i
$717$	14.8437	−	27.2094i	0.554350	−	1.01615i
$718$	−47.2439			−1.76313
$719$	17.7360	−	30.7196i	0.661439	−	1.14565i	−0.318798	−	0.947823i	$-0.603279\pi$
$719$	17.7360	−	30.7196i	0.661439	−	1.14565i	0.980238	−	0.197824i	$-0.0633875\pi$
$720$	−27.9425	−	25.3619i	−1.04136	−	0.945182i
$721$	−33.2786	+	8.91697i	−1.23936	+	0.332085i
$722$	−8.98931	+	33.5486i	−0.334548	+	1.24855i
$723$	−12.5618	+	23.0265i	−0.467179	+	0.856364i
$724$	−13.5111			−0.502138
$725$	−5.29235	+	9.16662i	−0.196553	+	0.340440i
$726$	−78.0786	+	47.6329i	−2.89777	+	1.76782i
$727$	0.212677	+	0.122789i	0.00788777	+	0.00455400i	0.503939	−	0.863739i	$-0.331884\pi$
$727$	0.212677	+	0.122789i	0.00788777	+	0.00455400i	−0.496051	+	0.868293i	$0.665217\pi$
$728$	−11.0001	−	2.35978i	−0.407692	−	0.0874592i
$729$	−3.90467	−	26.7162i	−0.144617	−	0.989488i
$730$	−2.62318	+	9.78984i	−0.0970882	+	0.362338i
$731$			13.8720i			0.513075i
$732$	−0.0650422	−	0.221196i	−0.00240403	−	0.00817564i
$733$	−0.228106	+	0.851305i	−0.00842530	+	0.0314437i	−0.970011	−	0.243063i	$-0.921848\pi$
$733$	−0.228106	+	0.851305i	−0.00842530	+	0.0314437i	0.961585	+	0.274507i	$0.0885145\pi$
$734$	30.3855	−	30.3855i	1.12155	−	1.12155i
$735$	−3.64394	+	2.22304i	−0.134409	+	0.0819980i
$736$	7.41215	+	27.6625i	0.273216	+	1.01965i
$737$	−20.8922	−	12.0621i	−0.769574	−	0.444314i
$738$	−4.99793	−	7.76369i	−0.183977	−	0.285785i
$739$	−19.4340	−	5.20731i	−0.714890	−	0.191554i	−0.116999	−	0.993132i	$-0.537328\pi$
$739$	−19.4340	−	5.20731i	−0.714890	−	0.191554i	−0.597890	+	0.801578i	$0.703994\pi$
$740$	3.02913	−	5.24661i	0.111353	−	0.192869i
$741$	1.91205	+	1.64589i	0.0702409	+	0.0604634i
$742$	−0.484265	−	0.838771i	−0.0177779	−	0.0307923i
$743$	−8.01669	−	29.9187i	−0.294104	−	1.09761i	−0.941926	−	0.335819i	$-0.890987\pi$
$743$	−8.01669	−	29.9187i	−0.294104	−	1.09761i	0.647823	−	0.761791i	$-0.275680\pi$
$744$	1.27145	+	4.32397i	0.0466138	+	0.158525i
$745$	5.81472	−	3.35713i	0.213035	−	0.122996i
$746$	9.15522	−	9.15522i	0.335197	−	0.335197i
$747$	9.92935	−	45.8155i	0.363296	−	1.67630i
$748$	−10.5786	−	39.4798i	−0.386791	−	1.44352i
$749$	12.4833	−	3.34490i	0.456131	−	0.122220i
$750$	6.34182	−	26.1856i	0.231570	−	0.956165i
$751$	−27.3543	−	15.7930i	−0.998172	−	0.576295i	−0.0904653	−	0.995900i	$-0.528835\pi$
$751$	−27.3543	−	15.7930i	−0.998172	−	0.576295i	−0.907707	+	0.419605i	$0.862169\pi$
$752$	22.6958	−	6.08131i	0.827629	−	0.221763i
$753$	20.1295	+	19.1786i	0.733561	+	0.698906i
$754$	40.0735	−	2.02462i	1.45939	−	0.0737321i
$755$		−	3.53759i		−	0.128746i
$756$	11.5132	+	16.9681i	0.418730	+	0.617125i
$757$	6.66044	+	11.5362i	0.242078	+	0.419291i	0.961306	−	0.275483i	$-0.0888377\pi$
$757$	6.66044	+	11.5362i	0.242078	+	0.419291i	−0.719228	+	0.694774i	$0.755504\pi$
$758$	−8.88764	−	15.3939i	−0.322814	−	0.559130i
$759$	1.12547	+	46.5215i	0.0408519	+	1.68862i
$760$	0.821637	+	0.821637i	0.0298039	+	0.0298039i
$761$	−5.09409	−	5.09409i	−0.184661	−	0.184661i	0.608722	−	0.793383i	$-0.291682\pi$
$761$	−5.09409	−	5.09409i	−0.184661	−	0.184661i	−0.793383	+	0.608722i	$0.791682\pi$
$762$	7.80913	+	4.26018i	0.282895	+	0.154330i
$763$	14.3508	+	24.8562i	0.519532	+	0.899856i
$764$	5.09188	+	8.81939i	0.184218	+	0.319074i
$765$	34.4334	−	11.0366i	1.24494	−	0.399030i
$766$		−	42.6706i		−	1.54175i
$767$	−14.9628	+	0.755959i	−0.540276	+	0.0272961i
$768$	−8.55247	+	35.3135i	−0.308611	+	1.27427i
$769$	38.1141	−	10.2126i	1.37443	−	0.368277i	0.505335	−	0.862923i	$-0.331369\pi$
$769$	38.1141	−	10.2126i	1.37443	−	0.368277i	0.869095	+	0.494646i	$0.164702\pi$
$770$	73.6584	+	42.5267i	2.65447	+	1.53256i
$771$	18.0043	+	17.1537i	0.648407	+	0.617775i
$772$	−17.3378	+	4.64566i	−0.624003	+	0.167201i
$773$	12.7625	+	47.6302i	0.459034	+	1.71314i	0.675950	+	0.736947i	$0.263733\pi$
$773$	12.7625	+	47.6302i	0.459034	+	1.71314i	−0.216916	+	0.976190i	$0.569600\pi$
$774$	−11.1195	+	12.2510i	−0.399683	+	0.440352i
$775$	2.91553	−	2.91553i	0.104729	−	0.104729i
$776$	15.2004	−	8.77597i	0.545664	−	0.315039i
$777$	5.60980	−	5.88796i	0.201250	−	0.211229i
$778$	2.16033	+	8.06245i	0.0774515	+	0.289053i
$779$	0.337169	+	0.583993i	0.0120803	+	0.0209237i
$780$	21.4433	−	7.50014i	0.767793	−	0.268548i
$781$	19.0036	−	32.9152i	0.680001	−	1.17780i
$782$	−35.2493	−	9.44501i	−1.26051	−	0.337753i
$783$	23.7254	+	20.5099i	0.847876	+	0.732963i
$784$	3.97501	+	2.29498i	0.141965	+	0.0819634i
$785$	−8.19632	−	30.5891i	−0.292539	−	1.09177i
$786$	−36.2510	−	19.7763i	−1.29303	−	0.705397i
$787$	−35.3034	+	35.3034i	−1.25843	+	1.25843i	−0.306590	+	0.951842i	$0.599188\pi$
$787$	−35.3034	+	35.3034i	−1.25843	+	1.25843i	−0.951842	+	0.306590i	$0.900812\pi$
$788$	5.71391	−	21.3246i	0.203550	−	0.759657i
$789$	30.5057	+	7.38808i	1.08603	+	0.263023i
$790$			27.2288i			0.968756i
$791$	−11.3141	+	42.2249i	−0.402285	+	1.50135i
$792$	−9.56460	+	18.5881i	−0.339863	+	0.660500i
$793$	−0.335257	−	0.0719201i	−0.0119053	−	0.00255396i
$794$	−12.5465	−	7.24371i	−0.445257	−	0.257070i
$795$	−0.736229	−	0.401641i	−0.0261113	−	0.0142447i
$796$	−17.3084	+	29.9790i	−0.613480	+	1.06258i
$797$	0.751305			0.0266126			0.0133063	−	0.999911i	$-0.495764\pi$
$797$	0.751305			0.0266126			0.0133063	+	0.999911i	$0.495764\pi$
$798$	−1.89432	−	3.10512i	−0.0670583	−	0.109920i
$799$	−5.82715	+	21.7472i	−0.206150	+	0.769361i
$800$	11.3683	−	3.04612i	0.401929	−	0.107696i
$801$	0.244467	−	0.269342i	0.00863781	−	0.00951673i
$802$	−0.238917	+	0.413817i	−0.00843647	+	0.0146124i
$803$	13.3167			0.469936
$804$	9.28701	−	0.224675i	0.327528	−	0.00792369i
$805$	27.0770	−	15.6329i	0.954337	−	0.550987i
$806$	−15.2825	−	3.27845i	−0.538304	−	0.115478i
$807$	−3.47884	+	3.65133i	−0.122461	+	0.128533i
$808$	−2.73993	−	2.73993i	−0.0963903	−	0.0963903i
$809$	24.5450	−	14.1711i	0.862958	−	0.498229i	−0.00204394	−	0.999998i	$-0.500651\pi$
$809$	24.5450	−	14.1711i	0.862958	−	0.498229i	0.865002	+	0.501769i	$0.167317\pi$
$810$	39.2564	+	17.8542i	1.37933	+	0.627334i
$811$	−14.9696	−	14.9696i	−0.525652	−	0.525652i	0.393621	−	0.919273i	$-0.371222\pi$
$811$	−14.9696	−	14.9696i	−0.525652	−	0.525652i	−0.919273	+	0.393621i	$0.871222\pi$
$812$	−23.0062	−	6.16450i	−0.807361	−	0.216332i
$813$	−11.2182	+	20.5636i	−0.393441	+	0.721198i
$814$	−18.6747	−	5.00388i	−0.654548	−	0.175386i
$815$			63.5542i			2.22621i
$816$	−28.1505	−	26.8206i	−0.985466	−	0.938910i
$817$	0.854407	−	0.854407i	0.0298919	−	0.0298919i
$818$	68.1002			2.38107
$819$	30.3462	−	3.00969i	1.06038	−	0.105167i
$820$	6.07203			0.212045
$821$	−27.6320	+	27.6320i	−0.964363	+	0.964363i	−0.999386	−	0.0350239i	$-0.988849\pi$
$821$	−27.6320	+	27.6320i	−0.964363	+	0.964363i	0.0350239	+	0.999386i	$0.488849\pi$
$822$	1.30375	−	0.383365i	0.0454736	−	0.0133714i
$823$			44.5571i			1.55316i	0.630016	+	0.776582i	$0.283048\pi$
$823$			44.5571i			1.55316i	−0.630016	+	0.776582i	$0.716952\pi$
$824$	13.0643	+	3.50058i	0.455118	+	0.121948i
$825$	19.1186	−	0.462525i	0.665624	−	0.0161031i
$826$	20.8641	+	5.59051i	0.725954	+	0.194519i
$827$	−6.18902	−	6.18902i	−0.215213	−	0.215213i	0.591265	−	0.806478i	$-0.298629\pi$
$827$	−6.18902	−	6.18902i	−0.215213	−	0.215213i	−0.806478	+	0.591265i	$0.798629\pi$
$828$	−9.69980	−	15.0675i	−0.337091	−	0.523631i
$829$	15.4468	−	8.91823i	0.536490	−	0.309743i	−0.207165	−	0.978306i	$-0.566424\pi$
$829$	15.4468	−	8.91823i	0.536490	−	0.309743i	0.743655	+	0.668563i	$0.233090\pi$
$830$	52.9466	+	52.9466i	1.83780	+	1.83780i
$831$	−12.3385	−	41.9608i	−0.428017	−	1.45560i
$832$	−7.20517	−	6.51213i	−0.249794	−	0.225768i
$833$	−3.80888	+	2.19906i	−0.131970	+	0.0761929i
$834$	14.5285	+	23.8146i	0.503079	+	0.824634i
$835$	−20.0183			−0.692762
$836$	−1.78009	+	3.08321i	−0.0615657	+	0.106635i
$837$	−6.85929	−	10.1092i	−0.237092	−	0.349426i
$838$	51.8405	−	13.8906i	1.79080	−	0.479844i
$839$	8.59411	−	32.0736i	0.296702	−	1.10731i	−0.643155	−	0.765736i	$-0.722375\pi$
$839$	8.59411	−	32.0736i	0.296702	−	1.10731i	0.939857	−	0.341569i	$-0.110958\pi$
$840$	14.0411	−	0.339689i	0.484465	−	0.0117204i
$841$	−7.42774			−0.256129
$842$	−6.72434	+	11.6469i	−0.231736	+	0.401379i
$843$	−0.875446	−	36.1867i	−0.0301519	−	1.24634i
$844$	17.4587	+	10.0798i	0.600954	+	0.346961i
$845$	5.41048	−	33.3483i	0.186126	−	1.14722i
$846$	−22.5783	+	14.5350i	−0.776259	+	0.499723i
$847$	20.8971	−	77.9892i	0.718034	−	2.67974i
$848$			0.901813i			0.0309684i
$849$	2.58545	−	2.71365i	0.0887324	−	0.0931322i
$850$	−3.88154	+	14.4861i	−0.133136	+	0.496870i
$851$	−5.02542	+	5.02542i	−0.172269	+	0.172269i
$852$	0.353971	+	14.6315i	0.0121268	+	0.501266i
$853$	−4.86849	−	18.1694i	−0.166694	−	0.622110i	−0.997818	−	0.0660230i	$-0.978969\pi$
$853$	−4.86849	−	18.1694i	−0.166694	−	0.622110i	0.831124	−	0.556087i	$-0.187698\pi$
$854$	0.428121	+	0.247176i	0.0146500	+	0.00845818i
$855$	−2.80060	−	1.44106i	−0.0957786	−	0.0492833i
$856$	−4.90065	−	1.31312i	−0.167501	−	0.0448817i
$857$	−16.1683	+	28.0043i	−0.552298	+	0.956607i	0.445811	+	0.895127i	$0.352915\pi$
$857$	−16.1683	+	28.0043i	−0.552298	+	0.956607i	−0.998108	+	0.0614802i	$0.980418\pi$
$858$	−40.8306	−	59.9046i	−1.39393	−	2.04511i
$859$	8.02856	+	13.9059i	0.273931	+	0.474462i	0.969865	−	0.243644i	$-0.0783427\pi$
$859$	8.02856	+	13.9059i	0.273931	+	0.474462i	−0.695934	+	0.718106i	$0.745009\pi$
$860$	−2.81600	−	10.5095i	−0.0960249	−	0.358370i
$861$	7.92199	+	1.91860i	0.269981	+	0.0653858i
$862$	−24.1798	+	13.9602i	−0.823567	+	0.475487i
$863$	−23.7439	+	23.7439i	−0.808250	+	0.808250i	−0.984369	−	0.176119i	$-0.943646\pi$
$863$	−23.7439	+	23.7439i	−0.808250	+	0.808250i	0.176119	+	0.984369i	$0.443646\pi$
$864$	−2.52816	−	34.7797i	−0.0860098	−	1.18323i
$865$	−7.80543	−	29.1303i	−0.265393	−	0.990458i
$866$	53.5193	−	14.3405i	1.81866	−	0.487308i
$867$	7.49468	−	2.20379i	0.254533	−	0.0748448i
$868$	8.03501	+	4.63902i	0.272726	+	0.157459i
$869$	34.5571	−	9.25954i	1.17227	−	0.314108i
$870$	−48.0578	+	14.1313i	−1.62931	+	0.479096i
$871$	6.29522	−	12.2979i	0.213306	−	0.416697i
$872$		−	11.2675i		−	0.381565i
$873$	−31.9751	+	35.2287i	−1.08219	+	1.19231i
$874$	1.58934	+	2.75282i	0.0537602	+	0.0931155i
$875$	11.8922	+	20.5980i	0.402031	+	0.696338i
$876$	−4.37765	+	2.67064i	−0.147907	+	0.0902327i
$877$	22.7606	+	22.7606i	0.768571	+	0.768571i	0.977855	−	0.209284i	$-0.0671132\pi$
$877$	22.7606	+	22.7606i	0.768571	+	0.768571i	−0.209284	+	0.977855i	$0.567113\pi$
$878$	−20.4415	−	20.4415i	−0.689866	−	0.689866i
$879$	−47.4146	+	28.9259i	−1.59926	+	0.975648i
$880$	−39.5973	−	68.5845i	−1.33482	−	2.31198i
$881$	21.3604	+	36.9973i	0.719650	+	1.24647i	0.961139	+	0.276066i	$0.0890309\pi$
$881$	21.3604	+	36.9973i	0.719650	+	1.24647i	−0.241489	+	0.970404i	$0.577636\pi$
$882$	−5.12651	−	1.11104i	−0.172619	−	0.0374107i
$883$		−	30.7720i		−	1.03556i	−0.855514	−	0.517780i	$-0.826759\pi$
$883$		−	30.7720i		−	1.03556i	0.855514	−	0.517780i	$-0.173241\pi$
$884$	22.2748	−	7.19125i	0.749183	−	0.241868i
$885$	17.9440	−	5.27640i	0.603182	−	0.177364i
$886$	24.5027	−	6.56547i	0.823183	−	0.220571i
$887$	−22.1434	−	12.7845i	−0.743504	−	0.429262i	0.0798379	−	0.996808i	$-0.474560\pi$
$887$	−22.1434	−	12.7845i	−0.743504	−	0.429262i	−0.823342	+	0.567546i	$0.807893\pi$
$888$	−3.06295	+	0.900653i	−0.102786	+	0.0302240i
$889$	−7.58529	+	2.03247i	−0.254403	+	0.0681670i
$890$	0.150371	+	0.561193i	0.00504045	+	0.0188112i
$891$	9.30980	−	55.8933i	0.311890	−	1.87250i
$892$	1.00878	−	1.00878i	0.0337764	−	0.0337764i
$893$	1.69837	−	0.980552i	0.0568337	−	0.0328129i
$894$	8.01924	+	1.94215i	0.268203	+	0.0649553i
$895$	−3.70652	−	13.8329i	−0.123895	−	0.462384i
$896$	−11.9191	−	20.6444i	−0.398188	−	0.689682i
$897$	−26.5755	+	1.98802i	−0.887329	+	0.0663779i
$898$	11.0238	−	19.0938i	0.367870	−	0.637169i
$899$	13.7066	+	3.67268i	0.457141	+	0.122491i
$900$	−6.19216	+	3.98625i	−0.206405	+	0.132875i
$901$	−0.748352	−	0.432061i	−0.0249312	−	0.0143940i
$902$	−5.01525	−	18.7172i	−0.166990	−	0.623214i
$903$	−0.353238	−	14.6012i	−0.0117550	−	0.485896i
$904$	12.1348	−	12.1348i	0.403598	−	0.403598i
$905$	6.49249	−	24.2303i	0.215818	−	0.805443i
$906$	2.99876	−	3.14745i	0.0996272	−	0.104567i
$907$			44.7134i			1.48468i	0.670022	+	0.742342i	$0.266285\pi$
$907$			44.7134i			1.48468i	−0.670022	+	0.742342i	$0.733715\pi$
$908$	2.81450	−	10.5038i	0.0934023	−	0.348582i
$909$	9.33922	+	4.80554i	0.309762	+	0.159390i
$910$	−22.1947	+	43.3578i	−0.735747	+	1.43730i
$911$	28.6386	+	16.5345i	0.948840	+	0.547813i	0.892720	−	0.450611i	$-0.148794\pi$
$911$	28.6386	+	16.5345i	0.948840	+	0.547813i	0.0561197	+	0.998424i	$0.482127\pi$
$912$	0.0819107	+	3.38580i	0.00271233	+	0.112115i
$913$	49.1913	−	85.2018i	1.62799	−	2.81977i
$914$	−72.4958			−2.39795
$915$	0.427938	−	0.0103529i	0.0141472	−	0.000342255i
$916$	−5.68665	+	21.2229i	−0.187892	+	0.701223i
$917$	35.2119	−	9.43499i	1.16280	−	0.311571i
$918$	39.9916	+	19.3692i	1.31992	+	0.639280i
$919$	−7.33901	+	12.7115i	−0.242092	+	0.419315i	−0.961310	−	0.275469i	$-0.911167\pi$
$919$	−7.33901	+	12.7115i	−0.242092	+	0.419315i	0.719218	+	0.694784i	$0.244500\pi$
$920$	−12.2742			−0.404667
$921$	23.7017	+	38.8512i	0.780999	+	1.28019i
$922$	−28.7269	+	16.5855i	−0.946069	+	0.546213i
$923$	19.3750	+	9.91797i	0.637735	+	0.326454i
$924$	12.1399	+	41.2856i	0.399374	+	1.35820i
$925$	2.06526	+	2.06526i	0.0679053	+	0.0679053i
$926$	54.0165	−	31.1865i	1.77509	−	1.02485i
$927$	−36.6182	+	1.77280i	−1.20270	+	0.0582265i
$928$	28.6411	+	28.6411i	0.940189	+	0.940189i
$929$	−48.2923	−	12.9399i	−1.58442	−	0.424544i	−0.644128	−	0.764918i	$-0.722780\pi$
$929$	−48.2923	−	12.9399i	−1.58442	−	0.424544i	−0.940290	+	0.340374i	$0.889446\pi$
$930$	19.5074	−	0.471931i	0.639672	−	0.0154752i
$931$	0.370042	+	0.0991526i	0.0121277	+	0.00324959i
$932$		−	13.1344i		−	0.430233i
$933$	−11.4770	+	3.37478i	−0.375740	+	0.110485i
$934$	−20.1863	+	20.1863i	−0.660517	+	0.660517i
$935$	75.8847			2.48170
$936$	−10.9079	−	4.93335i	−0.356535	−	0.161252i
$937$	12.7044			0.415036			0.207518	−	0.978231i	$-0.433462\pi$
$937$	12.7044			0.415036			0.207518	+	0.978231i	$0.433462\pi$
$938$	−14.0844	+	14.0844i	−0.459873	+	0.459873i
$939$	−35.3625	−	33.6919i	−1.15401	−	1.09950i
$940$		−	17.6587i		−	0.575962i
$941$	1.19444	+	0.320048i	0.0389375	+	0.0104333i	0.278235	−	0.960513i	$-0.410251\pi$
$941$	1.19444	+	0.320048i	0.0389375	+	0.0104333i	−0.239298	+	0.970946i	$0.576917\pi$
$942$	18.6375	−	34.1635i	0.607242	−	1.11311i
$943$	−6.88047	−	1.84362i	−0.224059	−	0.0600364i
$944$	−14.2214	−	14.2214i	−0.462869	−	0.462869i
$945$	−35.9623	+	12.4935i	−1.16985	+	0.406415i
$946$	−30.0698	+	17.3608i	−0.977653	+	0.564448i
$947$	−11.8787	−	11.8787i	−0.386005	−	0.386005i	0.487255	−	0.873260i	$-0.337998\pi$
$947$	−11.8787	−	11.8787i	−0.386005	−	0.386005i	−0.873260	+	0.487255i	$0.837998\pi$
$948$	−9.50309	+	9.97429i	−0.308646	+	0.323950i
$949$	0.384804	+	7.61649i	0.0124913	+	0.247242i
$950$	1.13130	−	0.653159i	0.0367044	−	0.0211913i
$951$	1.25140	−	0.0302744i	0.0405795	−	0.000981716i
$952$	14.4717			0.469030
$953$	3.87222	−	6.70688i	0.125433	−	0.217257i	−0.796469	−	0.604680i	$-0.793301\pi$
$953$	3.87222	−	6.70688i	0.125433	−	0.217257i	0.921902	+	0.387422i	$0.126635\pi$
$954$	−0.314570	−	0.981436i	−0.0101846	−	0.0317752i
$955$	−18.2631	+	4.89359i	−0.590981	+	0.158353i
$956$	−6.48299	+	24.1948i	−0.209675	+	0.782517i
$957$	34.2773	+	56.1864i	1.10803	+	1.81625i
$958$	−56.8657			−1.83725
$959$	−0.599827	+	1.03893i	−0.0193694	+	0.0335488i
$960$	10.6438	+	5.80658i	0.343526	+	0.187407i
$961$	22.0597	+	12.7362i	0.711603	+	0.410844i
$962$	2.32234	−	10.8256i	0.0748751	−	0.349031i
$963$	13.7361	−	0.665008i	0.442639	−	0.0214296i
$964$	5.48636	−	20.4754i	0.176704	−	0.659467i
$965$		−	33.3253i		−	1.07278i
$966$	37.3426	+	9.04388i	1.20148	+	0.290982i
$967$	−5.06094	+	18.8877i	−0.162749	+	0.607387i	0.835568	+	0.549387i	$0.185139\pi$
$967$	−5.06094	+	18.8877i	−0.162749	+	0.607387i	−0.998317	+	0.0579995i	$0.981528\pi$
$968$	−22.4129	+	22.4129i	−0.720378	+	0.720378i
$969$	−2.84888	−	1.55417i	−0.0915193	−	0.0499272i
$970$	−19.6678	−	73.4014i	−0.631497	−	2.35678i
$971$	−46.5819	−	26.8941i	−1.49489	−	0.863073i	−0.494903	−	0.868948i	$-0.664796\pi$
$971$	−46.5819	−	26.8941i	−1.49489	−	0.863073i	−0.999983	+	0.00587546i	$0.998130\pi$
$972$	8.14888	+	20.2411i	0.261375	+	0.649233i
$973$	−23.7874	−	6.37381i	−0.762588	−	0.204335i
$974$	−35.3109	+	61.1602i	−1.13143	+	1.95970i
$975$	0.816999	+	10.9215i	0.0261649	+	0.349768i
$976$	−0.230149	−	0.398630i	−0.00736690	−	0.0127598i
$977$	−11.4482	−	42.7252i	−0.366260	−	1.36690i	−0.865705	−	0.500554i	$-0.833130\pi$
$977$	−11.4482	−	42.7252i	−0.366260	−	1.36690i	0.499446	−	0.866345i	$-0.333537\pi$
$978$	−53.8739	+	56.5452i	−1.72270	+	1.80812i
$979$	0.661095	−	0.381683i	0.0211287	−	0.0121987i
$980$	2.43921	−	2.43921i	0.0779178	−	0.0779178i
$981$	9.32200	+	29.0840i	0.297629	+	0.928580i
$982$	15.6906	+	58.5583i	0.500708	+	1.86867i
$983$	−46.9456	+	12.5790i	−1.49733	+	0.401209i	−0.912206	−	0.409733i	$-0.865622\pi$
$983$	−46.9456	+	12.5790i	−1.49733	+	0.401209i	−0.585127	+	0.810942i	$0.698955\pi$
$984$	−2.31672	−	2.20727i	−0.0738543	−	0.0703653i
$985$	35.4969	+	20.4942i	1.13103	+	0.652998i
$986$	−49.8547	+	13.3585i	−1.58770	+	0.425422i
$987$	5.57967	−	23.0387i	0.177603	−	0.733330i
$988$	−1.81488	−	0.929029i	−0.0577390	−	0.0295564i
$989$			12.7637i			0.405862i
$990$	67.0170	+	60.8276i	2.12994	+	1.93323i
$991$	20.5994	+	35.6792i	0.654362	+	1.13339i	0.982053	+	0.188604i	$0.0603961\pi$
$991$	20.5994	+	35.6792i	0.654362	+	1.13339i	−0.327691	+	0.944785i	$0.606271\pi$
$992$	−7.88911	−	13.6643i	−0.250480	−	0.433843i
$993$	−7.36581	−	4.01833i	−0.233747	−	0.127518i
$994$	−22.1897	−	22.1897i	−0.703813	−	0.703813i
$995$	−45.4459	−	45.4459i	−1.44073	−	1.44073i
$996$	0.916263	+	37.8739i	0.0290329	+	1.20008i
$997$	15.0041	+	25.9878i	0.475183	+	0.823042i	0.999596	−	0.0284225i	$-0.00904838\pi$
$997$	15.0041	+	25.9878i	0.475183	+	0.823042i	−0.524413	+	0.851464i	$0.675715\pi$
$998$	−17.7827	−	30.8005i	−0.562901	−	0.974973i
$999$	7.16103	−	4.85888i	0.226565	−	0.153728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.11	✓	48
3.2	odd	2		351.2.ba.a.89.2		48
9.4	even	3		351.2.bf.a.206.11		48
9.5	odd	6		117.2.bc.a.50.2	yes	48
13.6	odd	12		117.2.bc.a.110.2	yes	48
39.32	even	12		351.2.bf.a.305.11		48
117.32	even	12	inner	117.2.x.a.32.11	yes	48
117.58	odd	12		351.2.ba.a.71.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.11	✓	48	1.1	even	1	trivial
117.2.x.a.32.11	yes	48	117.32	even	12	inner
117.2.bc.a.50.2	yes	48	9.5	odd	6
117.2.bc.a.110.2	yes	48	13.6	odd	12
351.2.ba.a.71.2		48	117.58	odd	12
351.2.ba.a.89.2		48	3.2	odd	2
351.2.bf.a.206.11		48	9.4	even	3
351.2.bf.a.305.11		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)

\(f(q)\)	\(=\)	\(q+(1.30379 - 1.30379i) q^{2} +(-0.407694 + 1.68339i) q^{3} -1.39974i q^{4} +(2.51024 + 0.672617i) q^{5} +(1.66324 + 2.72633i) q^{6} +(-2.72321 - 0.729681i) q^{7} +(0.782609 + 0.782609i) q^{8} +(-2.66757 - 1.37261i) q^{9} +O(q^{10})\)	\(q+(1.30379 - 1.30379i) q^{2} +(-0.407694 + 1.68339i) q^{3} -1.39974i q^{4} +(2.51024 + 0.672617i) q^{5} +(1.66324 + 2.72633i) q^{6} +(-2.72321 - 0.729681i) q^{7} +(0.782609 + 0.782609i) q^{8} +(-2.66757 - 1.37261i) q^{9} +(4.14978 - 2.39588i) q^{10} +(-4.45189 - 4.45189i) q^{11} +(2.35631 + 0.570667i) q^{12} +(2.41762 - 2.67491i) q^{13} +(-4.50185 + 2.59914i) q^{14} +(-2.15568 + 3.95148i) q^{15} +4.84020 q^{16} +(-2.31896 + 4.01655i) q^{17} +(-5.26756 + 1.68836i) q^{18} +(0.390218 - 0.104559i) q^{19} +(0.941492 - 3.51370i) q^{20} +(2.33857 - 4.28672i) q^{21} -11.6087 q^{22} +(-2.13369 + 3.69565i) q^{23} +(-1.63650 + 0.998367i) q^{24} +(1.51877 + 0.876864i) q^{25} +(-0.335449 - 6.63959i) q^{26} +(3.39819 - 3.93095i) q^{27} +(-1.02137 + 3.81179i) q^{28} +6.03554i q^{29} +(2.34135 + 7.96247i) q^{30} +(0.608508 - 2.27098i) q^{31} +(4.74540 - 4.74540i) q^{32} +(9.30926 - 5.67924i) q^{33} +(2.21331 + 8.26018i) q^{34} +(-6.34511 - 3.66335i) q^{35} +(-1.92130 + 3.73392i) q^{36} +(1.60869 + 0.431046i) q^{37} +(0.372440 - 0.645085i) q^{38} +(3.51725 + 5.16033i) q^{39} +(1.43814 + 2.49093i) q^{40} +(0.432026 + 1.61234i) q^{41} +(-2.53998 - 8.63800i) q^{42} +(2.59028 - 1.49550i) q^{43} +(-6.23151 + 6.23151i) q^{44} +(-5.77301 - 5.23984i) q^{45} +(2.03648 + 7.60024i) q^{46} +(4.68901 - 1.25642i) q^{47} +(-1.97332 + 8.14793i) q^{48} +(0.821249 + 0.474148i) q^{49} +(3.12341 - 0.836916i) q^{50} +(-5.81598 - 5.54122i) q^{51} +(-3.74418 - 3.38405i) q^{52} +0.186317i q^{53} +(-0.694608 - 9.55566i) q^{54} +(-8.18091 - 14.1698i) q^{55} +(-1.56015 - 2.70226i) q^{56} +(0.0169230 + 0.699515i) q^{57} +(7.86908 + 7.86908i) q^{58} +(-2.93819 - 2.93819i) q^{59} +(5.53106 + 3.01741i) q^{60} +(-0.0475495 - 0.0823581i) q^{61} +(-2.16752 - 3.75426i) q^{62} +(6.26278 + 5.68438i) q^{63} -2.69361i q^{64} +(7.86800 - 5.08853i) q^{65} +(4.73279 - 19.5419i) q^{66} +(3.70116 - 0.991722i) q^{67} +(5.62214 + 3.24595i) q^{68} +(-5.35132 - 5.09851i) q^{69} +(-13.0490 + 3.49646i) q^{70} +(1.56243 + 5.83108i) q^{71} +(-1.01345 - 3.16188i) q^{72} +(-1.49562 + 1.49562i) q^{73} +(2.65938 - 1.53540i) q^{74} +(-2.09529 + 2.19919i) q^{75} +(-0.146355 - 0.546205i) q^{76} +(8.87497 + 15.3719i) q^{77} +(11.3137 + 2.14223i) q^{78} +(-2.84121 + 4.92112i) q^{79} +(12.1501 + 3.25561i) q^{80} +(5.23188 + 7.32308i) q^{81} +(2.66543 + 1.53889i) q^{82} +(4.04440 + 15.0939i) q^{83} +(-6.00031 - 3.27340i) q^{84} +(-8.52274 + 8.52274i) q^{85} +(1.42737 - 5.32701i) q^{86} +(-10.1601 - 2.46065i) q^{87} -6.96818i q^{88} +(-0.0313812 + 0.117116i) q^{89} +(-14.3585 + 0.695139i) q^{90} +(-8.53551 + 5.52023i) q^{91} +(5.17297 + 2.98661i) q^{92} +(3.57486 + 1.95022i) q^{93} +(4.47538 - 7.75159i) q^{94} +1.04987 q^{95} +(6.05367 + 9.92301i) q^{96} +(4.10452 - 15.3183i) q^{97} +(1.68893 - 0.452547i) q^{98} +(5.76503 + 17.9865i) 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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