LMFDB - Embedded newform 46.2.c.a.39.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,2,Mod(3,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("46.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	46.c (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.367311849298$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			39.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	46.39
Dual form			46.2.c.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-2.71616 + 1.74557i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.985691 + 2.15836i) q^{5} +(0.459493 - 3.19584i) q^{6} +(0.381761 - 0.112095i) q^{7} +(0.841254 + 0.540641i) q^{8} +(3.08427 - 6.75361i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-2.71616 + 1.74557i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.985691 + 2.15836i) q^{5} +(0.459493 - 3.19584i) q^{6} +(0.381761 - 0.112095i) q^{7} +(0.841254 + 0.540641i) q^{8} +(3.08427 - 6.75361i) q^{9} +(-2.27667 - 0.668491i) q^{10} +(2.10260 + 2.42653i) q^{11} +(2.11435 + 2.44009i) q^{12} +(-0.149167 - 0.0437995i) q^{13} +(-0.165284 + 0.361922i) q^{14} +(-6.44487 - 4.14187i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.467137 + 3.24901i) q^{17} +(3.08427 + 6.75361i) q^{18} +(-0.404992 - 2.81678i) q^{19} +(1.99611 - 1.28282i) q^{20} +(-0.841254 + 0.970858i) q^{21} -3.21076 q^{22} +(1.27778 - 4.62248i) q^{23} -3.22871 q^{24} +(-0.412635 + 0.476206i) q^{25} +(0.130785 - 0.0840506i) q^{26} +(2.03305 + 14.1402i) q^{27} +(-0.165284 - 0.361922i) q^{28} +(-0.0538974 + 0.374864i) q^{29} +(7.35070 - 2.15836i) q^{30} +(2.31086 + 1.48510i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-9.94668 - 2.92061i) q^{33} +(-2.14953 - 2.48069i) q^{34} +(0.618239 + 0.713486i) q^{35} +(-7.12381 - 2.09174i) q^{36} +(2.66750 - 5.84100i) q^{37} +(2.39399 + 1.53853i) q^{38} +(0.481618 - 0.141416i) q^{39} +(-0.337683 + 2.34863i) q^{40} +(-1.66324 - 3.64198i) q^{41} +(-0.182822 - 1.27155i) q^{42} +(6.25061 - 4.01702i) q^{43} +(2.10260 - 2.42653i) q^{44} +17.6169 q^{45} +(2.65667 + 3.99276i) q^{46} +2.97017 q^{47} +(2.11435 - 2.44009i) q^{48} +(-5.75560 + 3.69890i) q^{49} +(-0.0896742 - 0.623698i) q^{50} +(-4.40255 - 9.64025i) q^{51} +(-0.0221250 + 0.153882i) q^{52} +(-12.5046 + 3.67168i) q^{53} +(-12.0178 - 7.72337i) q^{54} +(-3.16481 + 6.92998i) q^{55} +(0.381761 + 0.112095i) q^{56} +(6.01691 + 6.94388i) q^{57} +(-0.248008 - 0.286217i) q^{58} +(-8.29589 - 2.43589i) q^{59} +(-3.18251 + 6.96872i) q^{60} +(9.37463 + 6.02471i) q^{61} +(-2.63565 + 0.773896i) q^{62} +(0.420407 - 2.92399i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.0524978 - 0.365130i) q^{65} +(8.72094 - 5.60461i) q^{66} +(-5.50581 + 6.35404i) q^{67} +3.28242 q^{68} +(4.59821 + 14.7858i) q^{69} -0.944078 q^{70} +(-0.233571 + 0.269556i) q^{71} +(6.24593 - 4.01402i) q^{72} +(-0.802078 - 5.57857i) q^{73} +(2.66750 + 5.84100i) q^{74} +(0.289532 - 2.01374i) q^{75} +(-2.73047 + 0.801739i) q^{76} +(1.07469 + 0.690662i) q^{77} +(-0.208518 + 0.456590i) q^{78} +(7.23307 + 2.12382i) q^{79} +(-1.55384 - 1.79323i) q^{80} +(-15.6186 - 18.0249i) q^{81} +(3.84161 + 1.12800i) q^{82} +(5.56234 - 12.1798i) q^{83} +(1.08070 + 0.694523i) q^{84} +(-7.47299 + 2.19427i) q^{85} +(-1.05742 + 7.35448i) q^{86} +(-0.507959 - 1.11227i) q^{87} +(0.456938 + 3.17808i) q^{88} +(1.81771 - 1.16817i) q^{89} +(-11.5366 + 13.3139i) q^{90} -0.0618559 q^{91} +(-4.75727 - 0.606924i) q^{92} -8.86900 q^{93} +(-1.94505 + 2.24471i) q^{94} +(5.68043 - 3.65059i) q^{95} +(0.459493 + 3.19584i) q^{96} +(-1.09254 - 2.39234i) q^{97} +(0.973675 - 6.77206i) q^{98} +(22.8728 - 6.71606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9}+O(q^{10}) $ 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20} + q^{21} + 10 q^{22} - q^{23} - 4 q^{24} + 13 q^{25} - 3 q^{26} + 26 q^{27} + 3 q^{28} - 8 q^{29} + 20 q^{30} - 21 q^{31} - q^{32} - 15 q^{33} - 7 q^{34} + 7 q^{35} - 13 q^{36} + 28 q^{37} - 9 q^{38} - 12 q^{39} - 6 q^{40} - 31 q^{41} - 10 q^{42} + 11 q^{43} - 12 q^{44} + 10 q^{45} - 12 q^{46} + 18 q^{47} + 7 q^{48} - 24 q^{49} + 2 q^{50} - 17 q^{51} + 8 q^{52} - 21 q^{53} - 29 q^{54} + 5 q^{55} + 3 q^{56} + 19 q^{57} - 8 q^{58} - 5 q^{59} - 13 q^{60} + 37 q^{61} + q^{62} + 17 q^{63} - q^{64} + 37 q^{65} + 29 q^{66} - 13 q^{67} + 26 q^{68} - 15 q^{69} + 18 q^{70} + 49 q^{71} + 20 q^{72} - 8 q^{73} + 28 q^{74} + 8 q^{75} - 20 q^{76} - 8 q^{77} + 10 q^{78} + 8 q^{79} + 5 q^{80} - 11 q^{81} + 2 q^{82} - 7 q^{83} + q^{84} - 42 q^{85} + 22 q^{86} - 21 q^{87} - q^{88} - 13 q^{89} - 45 q^{90} - 24 q^{91} - 23 q^{92} - 40 q^{93} - 37 q^{94} - 10 q^{95} - 4 q^{96} - 32 q^{97} - 24 q^{98} + 20 q^{99}+O(q^{100}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	−2.71616	+	1.74557i	−1.56818	+	1.00781i	−0.588195	+	0.808719i	$0.700161\pi$
$3$	−2.71616	+	1.74557i	−1.56818	+	1.00781i	−0.979982	+	0.199087i	$0.936203\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.985691	+	2.15836i	0.440814	+	0.965249i	0.991448	+	0.130502i	$0.0416588\pi$
$5$	0.985691	+	2.15836i	0.440814	+	0.965249i	−0.550634	+	0.834747i	$0.685614\pi$
$6$	0.459493	−	3.19584i	0.187587	−	1.30470i
$7$	0.381761	−	0.112095i	0.144292	−	0.0423679i	−0.208789	−	0.977961i	$-0.566952\pi$
$7$	0.381761	−	0.112095i	0.144292	−	0.0423679i	0.353081	+	0.935593i	$0.385134\pi$
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	3.08427	−	6.75361i	1.02809	−	2.25120i
$10$	−2.27667	−	0.668491i	−0.719947	−	0.211395i
$11$	2.10260	+	2.42653i	0.633957	+	0.731626i	0.978294	−	0.207220i	$-0.0664417\pi$
$11$	2.10260	+	2.42653i	0.633957	+	0.731626i	−0.344337	+	0.938846i	$0.611896\pi$
$12$	2.11435	+	2.44009i	0.610361	+	0.704395i
$13$	−0.149167	−	0.0437995i	−0.0413716	−	0.0121478i	0.260981	−	0.965344i	$-0.415954\pi$
$13$	−0.149167	−	0.0437995i	−0.0413716	−	0.0121478i	−0.302353	+	0.953196i	$0.597772\pi$
$14$	−0.165284	+	0.361922i	−0.0441741	+	0.0967277i
$15$	−6.44487	−	4.14187i	−1.66406	−	1.06943i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.467137	+	3.24901i	−0.113297	+	0.788000i	0.851377	+	0.524554i	$0.175768\pi$
$17$	−0.467137	+	3.24901i	−0.113297	+	0.788000i	−0.964674	+	0.263446i	$0.915141\pi$
$18$	3.08427	+	6.75361i	0.726969	+	1.59184i
$19$	−0.404992	−	2.81678i	−0.0929114	−	0.646213i	−0.982056	−	0.188588i	$-0.939609\pi$
$19$	−0.404992	−	2.81678i	−0.0929114	−	0.646213i	0.889145	−	0.457626i	$-0.151300\pi$
$20$	1.99611	−	1.28282i	0.446345	−	0.286848i
$21$	−0.841254	+	0.970858i	−0.183577	+	0.211859i
$22$	−3.21076			−0.684536
$23$	1.27778	−	4.62248i	0.266435	−	0.963853i
$23$	1.27778	−	4.62248i	0.266435	−	0.963853i
$24$	−3.22871			−0.659057
$25$	−0.412635	+	0.476206i	−0.0825271	+	0.0952413i
$26$	0.130785	−	0.0840506i	0.0256491	−	0.0164837i
$27$	2.03305	+	14.1402i	0.391261	+	2.72128i
$28$	−0.165284	−	0.361922i	−0.0312358	−	0.0683968i
$29$	−0.0538974	+	0.374864i	−0.0100085	+	0.0696106i	−0.994214	−	0.107422i	$-0.965741\pi$
$29$	−0.0538974	+	0.374864i	−0.0100085	+	0.0696106i	0.984205	+	0.177032i	$0.0566496\pi$
$30$	7.35070	−	2.15836i	1.34205	−	0.394061i
$31$	2.31086	+	1.48510i	0.415042	+	0.266731i	0.731454	−	0.681891i	$-0.238842\pi$
$31$	2.31086	+	1.48510i	0.415042	+	0.266731i	−0.316412	+	0.948622i	$0.602478\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	−9.94668	−	2.92061i	−1.73149	−	0.508413i
$34$	−2.14953	−	2.48069i	−0.368641	−	0.425434i
$35$	0.618239	+	0.713486i	0.104502	+	0.120601i
$36$	−7.12381	−	2.09174i	−1.18730	−	0.348623i
$37$	2.66750	−	5.84100i	0.438534	−	0.960255i	−0.553331	−	0.832961i	$-0.686644\pi$
$37$	2.66750	−	5.84100i	0.438534	−	0.960255i	0.991865	−	0.127294i	$-0.0406290\pi$
$38$	2.39399	+	1.53853i	0.388357	+	0.249582i
$39$	0.481618	−	0.141416i	0.0771206	−	0.0226446i
$40$	−0.337683	+	2.34863i	−0.0533923	+	0.371352i
$41$	−1.66324	−	3.64198i	−0.259754	−	0.568782i	0.734156	−	0.678981i	$-0.237578\pi$
$41$	−1.66324	−	3.64198i	−0.259754	−	0.568782i	−0.993909	+	0.110200i	$0.964851\pi$
$42$	−0.182822	−	1.27155i	−0.0282100	−	0.196205i
$43$	6.25061	−	4.01702i	0.953209	−	0.612590i	0.0310980	−	0.999516i	$-0.490100\pi$
$43$	6.25061	−	4.01702i	0.953209	−	0.612590i	0.922111	+	0.386926i	$0.126463\pi$
$44$	2.10260	−	2.42653i	0.316979	−	0.365813i
$45$	17.6169			2.62617
$46$	2.65667	+	3.99276i	0.391704	+	0.588700i
$47$	2.97017			0.433244			0.216622	−	0.976256i	$-0.430496\pi$
$47$	2.97017			0.433244			0.216622	+	0.976256i	$0.430496\pi$
$48$	2.11435	−	2.44009i	0.305181	−	0.352197i
$49$	−5.75560	+	3.69890i	−0.822228	+	0.528414i
$50$	−0.0896742	−	0.623698i	−0.0126818	−	0.0882042i
$51$	−4.40255	−	9.64025i	−0.616481	−	1.34990i
$52$	−0.0221250	+	0.153882i	−0.00306818	+	0.0213397i
$53$	−12.5046	+	3.67168i	−1.71764	+	0.504344i	−0.984447	−	0.175679i	$-0.943788\pi$
$53$	−12.5046	+	3.67168i	−1.71764	+	0.504344i	−0.733191	+	0.680023i	$0.761970\pi$
$54$	−12.0178	−	7.72337i	−1.63541	−	1.05102i
$55$	−3.16481	+	6.92998i	−0.426743	+	0.934438i
$56$	0.381761	+	0.112095i	0.0510149	+	0.0149793i
$57$	6.01691	+	6.94388i	0.796959	+	0.919740i
$58$	−0.248008	−	0.286217i	−0.0325651	−	0.0375821i
$59$	−8.29589	−	2.43589i	−1.08003	−	0.317126i	−0.307141	−	0.951664i	$-0.599372\pi$
$59$	−8.29589	−	2.43589i	−1.08003	−	0.317126i	−0.772892	+	0.634538i	$0.781190\pi$
$60$	−3.18251	+	6.96872i	−0.410860	+	0.899658i
$61$	9.37463	+	6.02471i	1.20030	+	0.771385i	0.979008	−	0.203823i	$-0.0653367\pi$
$61$	9.37463	+	6.02471i	1.20030	+	0.771385i	0.221291	+	0.975208i	$0.428973\pi$
$62$	−2.63565	+	0.773896i	−0.334728	+	0.0982850i
$63$	0.420407	−	2.92399i	0.0529663	−	0.368389i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.0524978	−	0.365130i	−0.00651155	−	0.0452888i
$66$	8.72094	−	5.60461i	1.07347	−	0.689879i
$67$	−5.50581	+	6.35404i	−0.672642	+	0.776270i	−0.984787	−	0.173764i	$-0.944407\pi$
$67$	−5.50581	+	6.35404i	−0.672642	+	0.776270i	0.312145	+	0.950034i	$0.398952\pi$
$68$	3.28242			0.398052
$69$	4.59821	+	14.7858i	0.553560	+	1.78001i
$70$	−0.944078			−0.112839
$71$	−0.233571	+	0.269556i	−0.0277198	+	0.0319904i	−0.769440	−	0.638719i	$-0.779465\pi$
$71$	−0.233571	+	0.269556i	−0.0277198	+	0.0319904i	0.741720	+	0.670709i	$0.234010\pi$
$72$	6.24593	−	4.01402i	0.736090	−	0.473056i
$73$	−0.802078	−	5.57857i	−0.0938761	−	0.652923i	−0.981373	−	0.192110i	$-0.938467\pi$
$73$	−0.802078	−	5.57857i	−0.0938761	−	0.652923i	0.887497	−	0.460813i	$-0.152442\pi$
$74$	2.66750	+	5.84100i	0.310090	+	0.679003i
$75$	0.289532	−	2.01374i	0.0334323	−	0.232526i
$76$	−2.73047	+	0.801739i	−0.313206	+	0.0919657i
$77$	1.07469	+	0.690662i	0.122472	+	0.0787082i
$78$	−0.208518	+	0.456590i	−0.0236100	+	0.0516987i
$79$	7.23307	+	2.12382i	0.813784	+	0.238949i	0.662037	−	0.749471i	$-0.269692\pi$
$79$	7.23307	+	2.12382i	0.813784	+	0.238949i	0.151747	+	0.988419i	$0.451510\pi$
$80$	−1.55384	−	1.79323i	−0.173725	−	0.200489i
$81$	−15.6186	−	18.0249i	−1.73540	−	2.00276i
$82$	3.84161	+	1.12800i	0.424235	+	0.124567i
$83$	5.56234	−	12.1798i	0.610547	−	1.33691i	−0.311653	−	0.950196i	$-0.600883\pi$
$83$	5.56234	−	12.1798i	0.610547	−	1.33691i	0.922199	−	0.386715i	$-0.126390\pi$
$84$	1.08070	+	0.694523i	0.117914	+	0.0757787i
$85$	−7.47299	+	2.19427i	−0.810559	+	0.238002i
$86$	−1.05742	+	7.35448i	−0.114024	+	0.793054i
$87$	−0.507959	−	1.11227i	−0.0544589	−	0.119248i
$88$	0.456938	+	3.17808i	0.0487098	+	0.338784i
$89$	1.81771	−	1.16817i	0.192677	−	0.123826i	−0.440746	−	0.897632i	$-0.645286\pi$
$89$	1.81771	−	1.16817i	0.192677	−	0.123826i	0.633422	+	0.773806i	$0.281650\pi$
$90$	−11.5366	+	13.3139i	−1.21606	+	1.40341i
$91$	−0.0618559			−0.00648426
$92$	−4.75727	−	0.606924i	−0.495980	−	0.0632762i
$93$	−8.86900			−0.919672
$94$	−1.94505	+	2.24471i	−0.200617	+	0.231524i
$95$	5.68043	−	3.65059i	0.582800	−	0.374543i
$96$	0.459493	+	3.19584i	0.0468968	+	0.326174i
$97$	−1.09254	−	2.39234i	−0.110931	−	0.242905i	0.846022	−	0.533148i	$-0.178991\pi$
$97$	−1.09254	−	2.39234i	−0.110931	−	0.242905i	−0.956953	+	0.290243i	$0.906264\pi$
$98$	0.973675	−	6.77206i	0.0983560	−	0.684081i
$99$	22.8728	−	6.71606i	2.29880	−	0.674990i
$100$	0.530084	+	0.340664i	0.0530084	+	0.0340664i
$101$	−3.62945	+	7.94740i	−0.361144	+	0.790795i	0.638629	+	0.769514i	$0.279502\pi$
$101$	−3.62945	+	7.94740i	−0.361144	+	0.790795i	−0.999774	+	0.0212810i	$0.993226\pi$
$102$	10.1687	+	2.98579i	1.00685	+	0.295637i
$103$	−2.80497	−	3.23711i	−0.276382	−	0.318962i	0.600540	−	0.799595i	$-0.294952\pi$
$103$	−2.80497	−	3.23711i	−0.276382	−	0.318962i	−0.876922	+	0.480633i	$0.840407\pi$
$104$	−0.101808	−	0.117492i	−0.00998308	−	0.0115211i
$105$	−2.92468	−	0.858763i	−0.285419	−	0.0838067i
$106$	5.41390	−	11.8548i	0.525844	−	1.15144i
$107$	−15.1529	−	9.73821i	−1.46489	−	0.941428i	−0.998379	−	0.0569126i	$-0.981874\pi$
$107$	−15.1529	−	9.73821i	−1.46489	−	0.941428i	−0.466511	−	0.884515i	$-0.654489\pi$
$108$	13.7069	−	4.02471i	1.31895	−	0.387278i
$109$	1.35720	−	9.43952i	0.129996	−	0.904142i	−0.815558	−	0.578676i	$-0.803570\pi$
$109$	1.35720	−	9.43952i	0.129996	−	0.904142i	0.945554	−	0.325466i	$-0.105521\pi$
$110$	−3.16481	−	6.92998i	−0.301753	−	0.660747i
$111$	2.95053	+	20.5214i	0.280052	+	1.94781i
$112$	−0.334716	+	0.215109i	−0.0316277	+	0.0203259i
$113$	4.11470	−	4.74861i	0.387078	−	0.446712i	−0.528451	−	0.848964i	$-0.677227\pi$
$113$	4.11470	−	4.74861i	0.387078	−	0.446712i	0.915529	+	0.402252i	$0.131772\pi$
$114$	−9.18807			−0.860542
$115$	11.2365	−	1.79843i	1.04781	−	0.167704i
$116$	0.378719			0.0351632
$117$	−0.755877	+	0.872329i	−0.0698809	+	0.0806468i
$118$	7.27358	−	4.67444i	0.669587	−	0.430317i
$119$	0.185863	+	1.29271i	0.0170380	+	0.118502i
$120$	−3.18251	−	6.96872i	−0.290522	−	0.636154i
$121$	0.0983447	−	0.684003i	0.00894043	−	0.0621821i
$122$	−10.6922	+	3.13953i	−0.968031	+	0.284239i
$123$	10.8750	+	6.98891i	0.980561	+	0.630169i
$124$	1.14111	−	2.49869i	0.102475	−	0.224389i
$125$	9.94880	+	2.92123i	0.889848	+	0.261283i
$126$	1.93450	+	2.23253i	0.172339	+	0.198890i
$127$	5.80796	+	6.70274i	0.515373	+	0.594772i	0.952466	−	0.304644i	$-0.0985375\pi$
$127$	5.80796	+	6.70274i	0.515373	+	0.594772i	−0.437093	+	0.899416i	$0.643992\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	−9.96566	+	21.8218i	−0.877428	+	1.92130i
$130$	0.310326	+	0.199434i	0.0272174	+	0.0174915i
$131$	−4.99107	+	1.46551i	−0.436072	+	0.128042i	−0.492398	−	0.870370i	$-0.663880\pi$
$131$	−4.99107	+	1.46551i	−0.436072	+	0.128042i	0.0563262	+	0.998412i	$0.482061\pi$
$132$	−1.47532	+	10.2611i	−0.128410	+	0.893112i
$133$	−0.470357	−	1.02994i	−0.0407851	−	0.0893069i
$134$	−1.19653	−	8.32203i	−0.103364	−	0.718914i
$135$	−28.5157	+	18.3259i	−2.45424	+	1.57724i
$136$	−2.14953	+	2.48069i	−0.184320	+	0.212717i
$137$	−0.501086			−0.0428107			−0.0214053	−	0.999771i	$-0.506814\pi$
$137$	−0.501086			−0.0428107			−0.0214053	+	0.999771i	$0.506814\pi$
$138$	−14.1856	−	6.20757i	−1.20756	−	0.528424i
$139$	−15.7509			−1.33598			−0.667989	−	0.744171i	$-0.732845\pi$
$139$	−15.7509			−1.33598			−0.667989	+	0.744171i	$0.732845\pi$
$140$	0.618239	−	0.713486i	0.0522508	−	0.0603006i
$141$	−8.06747	+	5.18465i	−0.679404	+	0.436626i
$142$	−0.0507599	−	0.353043i	−0.00425968	−	0.0296267i
$143$	−0.207359	−	0.454052i	−0.0173402	−	0.0379697i
$144$	−1.05662	+	7.34898i	−0.0880520	+	0.612415i
$145$	−0.862219	+	0.253170i	−0.0716034	+	0.0210247i
$146$	4.74125	+	3.04702i	0.392389	+	0.252173i
$147$	9.17645	−	20.0936i	0.756860	−	1.65729i
$148$	−6.16117	−	1.80908i	−0.506445	−	0.148706i
$149$	2.53429	+	2.92473i	0.207617	+	0.239603i	0.850002	−	0.526779i	$-0.176600\pi$
$149$	2.53429	+	2.92473i	0.207617	+	0.239603i	−0.642385	+	0.766382i	$0.722055\pi$
$150$	1.33228	+	1.53753i	0.108780	+	0.125539i
$151$	15.2097	+	4.46596i	1.23774	+	0.363435i	0.834167	−	0.551511i	$-0.185949\pi$
$151$	15.2097	+	4.46596i	1.23774	+	0.363435i	0.403577	+	0.914946i	$0.367767\pi$
$152$	1.18216	−	2.58858i	0.0958862	−	0.209961i
$153$	20.5018	+	13.1757i	1.65747	+	1.06519i
$154$	−1.22574	+	0.359910i	−0.0987730	+	0.0290024i
$155$	−0.927587	+	6.45151i	−0.0745056	+	0.518198i
$156$	−0.208518	−	0.456590i	−0.0166948	−	0.0365565i
$157$	−2.97025	−	20.6585i	−0.237051	−	1.64873i	−0.666403	−	0.745592i	$-0.732167\pi$
$157$	−2.97025	−	20.6585i	−0.237051	−	1.64873i	0.429352	−	0.903137i	$-0.358742\pi$
$158$	−6.34173	+	4.07558i	−0.504521	+	0.324236i
$159$	27.5553	−	31.8005i	2.18528	−	2.52195i
$160$	2.37279			0.187585
$161$	−0.0303516	−	1.90791i	−0.00239204	−	0.150364i
$162$	23.8503			1.87386
$163$	−15.5752	+	17.9747i	−1.21994	+	1.40789i	−0.334976	+	0.942227i	$0.608728\pi$
$163$	−15.5752	+	17.9747i	−1.21994	+	1.40789i	−0.884964	+	0.465659i	$0.845817\pi$
$164$	−3.36821	+	2.16461i	−0.263013	+	0.169028i
$165$	−3.50062	−	24.3473i	−0.272523	−	1.89544i
$166$	5.56234	+	12.1798i	0.431722	+	0.945339i
$167$	−0.795161	+	5.53047i	−0.0615314	+	0.427960i	0.935650	+	0.352930i	$0.114815\pi$
$167$	−0.795161	+	5.53047i	−0.0615314	+	0.427960i	−0.997181	+	0.0750306i	$0.976095\pi$
$168$	−1.23259	+	0.361922i	−0.0950966	+	0.0279229i
$169$	−10.9160	−	7.01526i	−0.839689	−	0.539636i
$170$	3.23545	−	7.08464i	0.248148	−	0.543367i
$171$	−20.2725	−	5.95255i	−1.55028	−	0.455203i
$172$	−4.86569	−	5.61530i	−0.371005	−	0.428163i
$173$	14.9062	+	17.2026i	1.13329	+	1.30789i	0.945478	+	0.325687i	$0.105596\pi$
$173$	14.9062	+	17.2026i	1.13329	+	1.30789i	0.187817	+	0.982204i	$0.439859\pi$
$174$	1.17324	+	0.344495i	0.0889433	+	0.0261161i
$175$	−0.104147	+	0.228051i	−0.00787281	+	0.0172391i
$176$	−2.70106	−	1.73587i	−0.203600	−	0.130846i
$177$	26.7850	−	7.86478i	2.01328	−	0.591153i
$178$	−0.307502	+	2.13872i	−0.0230482	+	0.160304i
$179$	1.03536	+	2.26712i	0.0773864	+	0.169453i	0.944371	−	0.328883i	$-0.106672\pi$
$179$	1.03536	+	2.26712i	0.0773864	+	0.169453i	−0.866984	+	0.498335i	$0.833945\pi$
$180$	−2.50714	−	17.4376i	−0.186871	−	1.29972i
$181$	8.49697	−	5.46067i	0.631575	−	0.405888i	−0.185318	−	0.982679i	$-0.559331\pi$
$181$	8.49697	−	5.46067i	0.631575	−	0.405888i	0.816892	+	0.576790i	$0.195695\pi$
$182$	0.0405070	−	0.0467476i	0.00300258	−	0.00346516i
$183$	−35.9796			−2.65969
$184$	3.57403	−	3.19786i	0.263481	−	0.235749i
$185$	15.2363			1.12020
$186$	5.80796	−	6.70274i	0.425860	−	0.491469i
$187$	−8.86601	+	5.69784i	−0.648347	+	0.416667i
$188$	−0.422700	−	2.93994i	−0.0308285	−	0.214417i
$189$	2.36118	+	5.17027i	0.171751	+	0.376082i
$190$	−0.960958	+	6.68361i	−0.0697152	+	0.484880i
$191$	−2.46643	+	0.724209i	−0.178465	+	0.0524019i	−0.369744	−	0.929134i	$-0.620555\pi$
$191$	−2.46643	+	0.724209i	−0.178465	+	0.0524019i	0.191279	+	0.981536i	$0.438736\pi$
$192$	−2.71616	−	1.74557i	−0.196022	−	0.125976i
$193$	−9.38297	+	20.5458i	−0.675401	+	1.47892i	0.192043	+	0.981387i	$0.438489\pi$
$193$	−9.38297	+	20.5458i	−0.675401	+	1.47892i	−0.867444	+	0.497535i	$0.834239\pi$
$194$	2.52347	+	0.740958i	0.181175	+	0.0531977i
$195$	0.779953	+	0.900113i	0.0558536	+	0.0644585i
$196$	4.48036	+	5.17061i	0.320025	+	0.369329i
$197$	−0.491527	−	0.144325i	−0.0350198	−	0.0102828i	0.264176	−	0.964475i	$-0.414900\pi$
$197$	−0.491527	−	0.144325i	−0.0350198	−	0.0102828i	−0.299196	+	0.954192i	$0.596718\pi$
$198$	−9.90284	+	21.6842i	−0.703764	+	1.54103i
$199$	−1.10660	−	0.711170i	−0.0784449	−	0.0504135i	0.500830	−	0.865545i	$-0.333028\pi$
$199$	−1.10660	−	0.711170i	−0.0784449	−	0.0504135i	−0.579275	+	0.815132i	$0.696664\pi$
$200$	−0.604588	+	0.177523i	−0.0427508	+	0.0125528i
$201$	3.86324	−	26.8694i	0.272492	−	1.89522i
$202$	−3.62945	−	7.94740i	−0.255368	−	0.559177i
$203$	0.0214445	+	0.149150i	0.00150511	+	0.0104683i
$204$	−8.91558	+	5.72969i	−0.624215	+	0.401159i
$205$	6.22127	−	7.17973i	0.434513	−	0.501454i
$206$	4.28331			0.298433
$207$	−27.2774	−	22.8866i	−1.89591	−	1.59073i
$208$	0.155465			0.0107795
$209$	5.98346	−	6.90528i	0.413884	−	0.477648i
$210$	2.56427	−	1.64795i	0.176951	−	0.113720i
$211$	0.998177	+	6.94248i	0.0687174	+	0.477940i	0.994900	+	0.100865i	$0.0321610\pi$
$211$	0.998177	+	6.94248i	0.0687174	+	0.477940i	−0.926183	+	0.377075i	$0.876930\pi$
$212$	5.41390	+	11.8548i	0.371828	+	0.814190i
$213$	0.163889	−	1.13987i	0.0112295	−	0.0781028i
$214$	17.2827	−	5.07466i	1.18142	−	0.346897i
$215$	14.8314	+	9.53153i	1.01149	+	0.650045i
$216$	−5.93445	+	12.9946i	−0.403788	+	0.884172i
$217$	1.04867	+	0.307916i	0.0711880	+	0.0209027i
$218$	6.24514	+	7.20727i	0.422974	+	0.488138i
$219$	11.9164	+	13.7522i	0.805234	+	0.929289i
$220$	7.30984	+	2.14636i	0.492829	+	0.144708i
$221$	0.211986	−	0.464186i	0.0142598	−	0.0312245i
$222$	−17.4412	−	11.2088i	−1.17058	−	0.752285i
$223$	−12.3773	+	3.63430i	−0.828846	+	0.243371i	−0.668521	−	0.743693i	$-0.733072\pi$
$223$	−12.3773	+	3.63430i	−0.828846	+	0.243371i	−0.160325	+	0.987064i	$0.551254\pi$
$224$	0.0566239	−	0.393828i	0.00378334	−	0.0263137i
$225$	1.94343	+	4.25553i	0.129562	+	0.283702i
$226$	0.894209	+	6.21936i	0.0594819	+	0.413706i
$227$	−0.648126	+	0.416525i	−0.0430176	+	0.0276457i	−0.561973	−	0.827156i	$-0.689957\pi$
$227$	−0.648126	+	0.416525i	−0.0430176	+	0.0276457i	0.518955	+	0.854801i	$0.326321\pi$
$228$	6.01691	−	6.94388i	0.398479	−	0.459870i
$229$	−19.2701			−1.27341			−0.636703	−	0.771109i	$-0.719702\pi$
$229$	−19.2701			−1.27341			−0.636703	+	0.771109i	$0.719702\pi$
$230$	−5.99916	+	9.66968i	−0.395573	+	0.637600i
$231$	−4.12463			−0.271381
$232$	−0.248008	+	0.286217i	−0.0162825	+	0.0187911i
$233$	7.12327	−	4.57785i	0.466661	−	0.299905i	−0.286099	−	0.958200i	$-0.592359\pi$
$233$	7.12327	−	4.57785i	0.466661	−	0.299905i	0.752760	+	0.658295i	$0.228722\pi$
$234$	−0.164268	−	1.14251i	−0.0107385	−	0.0746881i
$235$	2.92767	+	6.41071i	0.190980	+	0.418189i
$236$	−1.23047	+	8.55811i	−0.0800968	+	0.557086i
$237$	−23.3535	+	6.85720i	−1.51697	+	0.445423i
$238$	−1.09868	−	0.706077i	−0.0712166	−	0.0457682i
$239$	3.30114	−	7.22848i	0.213533	−	0.467572i	−0.772310	−	0.635246i	$-0.780899\pi$
$239$	3.30114	−	7.22848i	0.213533	−	0.467572i	0.985842	+	0.167675i	$0.0536258\pi$
$240$	7.35070	+	2.15836i	0.474486	+	0.139322i
$241$	−8.80435	−	10.1608i	−0.567138	−	0.654512i	0.397651	−	0.917537i	$-0.369825\pi$
$241$	−8.80435	−	10.1608i	−0.567138	−	0.654512i	−0.964789	+	0.263025i	$0.915280\pi$
$242$	0.452533	+	0.522250i	0.0290899	+	0.0335715i
$243$	32.7657	+	9.62087i	2.10192	+	0.617179i
$244$	4.62924	−	10.1366i	0.296357	−	0.648930i
$245$	−13.6568	−	8.77669i	−0.872501	−	0.560722i
$246$	−12.4034	+	3.64198i	−0.790815	+	0.232204i
$247$	−0.0629619	+	0.437910i	−0.00400617	+	0.0278635i
$248$	1.14111	+	2.49869i	0.0724606	+	0.158667i
$249$	6.15254	+	42.7919i	0.389902	+	2.71182i
$250$	−8.72280	+	5.60580i	−0.551678	+	0.354542i
$251$	−9.85898	+	11.3779i	−0.622293	+	0.718165i	−0.976141	−	0.217138i	$-0.930328\pi$
$251$	−9.85898	+	11.3779i	−0.622293	+	0.718165i	0.353848	+	0.935303i	$0.384873\pi$
$252$	−2.95406			−0.186088
$253$	13.9032	−	6.61865i	0.874088	−	0.416111i
$254$	−8.86900			−0.556490
$255$	16.4676	−	19.0046i	1.03124	−	1.19011i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	0.669316	+	4.65520i	0.0417508	+	0.290383i	0.999990	+	0.00441617i	$0.00140572\pi$
$257$	0.669316	+	4.65520i	0.0417508	+	0.290383i	−0.958239	+	0.285967i	$0.907685\pi$
$258$	−9.96566	−	21.8218i	−0.620435	−	1.35856i
$259$	0.363598	−	2.52888i	0.0225929	−	0.157137i
$260$	−0.353942	+	0.103927i	−0.0219506	+	0.00644527i
$261$	2.36545	+	1.52019i	0.146418	+	0.0940971i
$262$	2.16090	−	4.73170i	0.133501	−	0.292326i
$263$	19.8270	+	5.82172i	1.22258	+	0.358983i	0.828446	−	0.560069i	$-0.189225\pi$
$263$	19.8270	+	5.82172i	1.22258	+	0.358983i	0.394137	+	0.919052i	$0.371044\pi$
$264$	−6.78868	−	7.83455i	−0.417814	−	0.482183i
$265$	−20.2505	−	23.3703i	−1.24398	−	1.43563i
$266$	1.08639	+	0.318994i	0.0666110	+	0.0195588i
$267$	−2.89806	+	6.34588i	−0.177359	+	0.388361i
$268$	7.07293	+	4.54549i	0.432048	+	0.277660i
$269$	−16.0994	+	4.72721i	−0.981598	+	0.288223i	−0.732884	−	0.680354i	$-0.761826\pi$
$269$	−16.0994	+	4.72721i	−0.981598	+	0.288223i	−0.248714	+	0.968577i	$0.580008\pi$
$270$	4.82399	−	33.5516i	0.293579	−	2.04189i
$271$	4.26445	+	9.33785i	0.259047	+	0.567234i	0.993810	−	0.111090i	$-0.0354340\pi$
$271$	4.26445	+	9.33785i	0.259047	+	0.567234i	−0.734763	+	0.678324i	$0.762707\pi$
$272$	−0.467137	−	3.24901i	−0.0283243	−	0.197000i
$273$	0.168011	−	0.107974i	0.0101685	−	0.00653488i
$274$	0.328142	−	0.378696i	0.0198238	−	0.0228778i
$275$	−2.02314			−0.122000
$276$	13.9810	−	6.65565i	0.841554	−	0.400623i
$277$	25.2836			1.51914			0.759572	−	0.650423i	$-0.225408\pi$
$277$	25.2836			1.51914			0.759572	+	0.650423i	$0.225408\pi$
$278$	10.3147	−	11.9038i	0.618633	−	0.713941i
$279$	17.1571	−	11.0262i	1.02717	−	0.660120i
$280$	0.134356	+	0.934468i	0.00802932	+	0.0558452i
$281$	−5.58559	−	12.2307i	−0.333208	−	0.729624i	0.666668	−	0.745355i	$-0.267720\pi$
$281$	−5.58559	−	12.2307i	−0.333208	−	0.729624i	−0.999876	+	0.0157304i	$0.994993\pi$
$282$	1.36477	−	9.49221i	0.0812711	−	0.565253i
$283$	4.21075	−	1.23639i	0.250303	−	0.0734957i	−0.154174	−	0.988044i	$-0.549272\pi$
$283$	4.21075	−	1.23639i	0.250303	−	0.0734957i	0.404477	+	0.914548i	$0.367453\pi$
$284$	0.300053	+	0.192832i	0.0178049	+	0.0114425i
$285$	−9.05660	+	19.8312i	−0.536467	+	1.17470i
$286$	0.478940	+	0.140630i	0.0283203	+	0.00831560i
$287$	−1.04321	−	1.20392i	−0.0615785	−	0.0710654i
$288$	−4.86205	−	5.61110i	−0.286499	−	0.330637i
$289$	5.97355	+	1.75399i	0.351385	+	0.103176i
$290$	0.373300	−	0.817413i	0.0219209	−	0.0480002i
$291$	7.14352	+	4.59086i	0.418760	+	0.269121i
$292$	−5.40764	+	1.58783i	−0.316458	+	0.0929206i
$293$	0.783862	−	5.45188i	0.0457937	−	0.318502i	−0.954030	−	0.299712i	$-0.903109\pi$
$293$	0.783862	−	5.45188i	0.0457937	−	0.318502i	0.999823	−	0.0187902i	$-0.00598145\pi$
$294$	9.17645	+	20.0936i	0.535181	+	1.17188i
$295$	−2.91964	−	20.3066i	−0.169988	−	1.18229i
$296$	5.40192	−	3.47161i	0.313980	−	0.201783i
$297$	−30.0369	+	34.6644i	−1.74291	+	2.01143i
$298$	−3.86997			−0.224181
$299$	−0.393065	+	0.633557i	−0.0227315	+	0.0366395i
$300$	−2.03445			−0.117459
$301$	1.93595	−	2.23420i	0.111586	−	0.128777i
$302$	−13.3354	+	8.57011i	−0.767363	+	0.493154i
$303$	−4.01456	−	27.9219i	−0.230630	−	1.60407i
$304$	1.18216	+	2.58858i	0.0678018	+	0.148465i
$305$	−3.76301	+	26.1723i	−0.215470	+	1.49862i
$306$	−23.3833	+	6.86596i	−1.33673	+	0.392501i
$307$	−21.4631	−	13.7935i	−1.22497	−	0.787238i	−0.241867	−	0.970309i	$-0.577760\pi$
$307$	−21.4631	−	13.7935i	−1.22497	−	0.787238i	−0.983100	+	0.183071i	$0.941396\pi$
$308$	0.530688	−	1.16204i	0.0302387	−	0.0662136i
$309$	13.2694	+	3.89624i	0.754868	+	0.221649i
$310$	−4.26828	−	4.92586i	−0.242422	−	0.279770i
$311$	−6.58523	−	7.59976i	−0.373414	−	0.430943i	0.537675	−	0.843152i	$-0.319303\pi$
$311$	−6.58523	−	7.59976i	−0.373414	−	0.430943i	−0.911089	+	0.412209i	$0.864757\pi$
$312$	0.481618	+	0.141416i	0.0272662	+	0.00800609i
$313$	−1.46099	+	3.19913i	−0.0825803	+	0.180826i	−0.946418	−	0.322945i	$-0.895327\pi$
$313$	−1.46099	+	3.19913i	−0.0825803	+	0.180826i	0.863837	+	0.503771i	$0.168054\pi$
$314$	17.5578	+	11.2837i	0.990842	+	0.636775i
$315$	6.72543	−	1.97476i	0.378935	−	0.111265i
$316$	1.07283	−	7.46170i	0.0603514	−	0.419753i
$317$	−14.5188	−	31.7918i	−0.815459	−	1.78561i	−0.581893	−	0.813265i	$-0.697688\pi$
$317$	−14.5188	−	31.7918i	−0.815459	−	1.78561i	−0.233566	−	0.972341i	$-0.575039\pi$
$318$	5.98834	+	41.6498i	0.335810	+	2.33561i
$319$	−1.02294	+	0.657406i	−0.0572739	+	0.0368077i
$320$	−1.55384	+	1.79323i	−0.0868625	+	0.100245i
$321$	58.1566			3.24598
$322$	1.46178	+	1.22648i	0.0814618	+	0.0683490i
$323$	9.34092			0.519743
$324$	−15.6186	+	18.0249i	−0.867702	+	1.00138i
$325$	0.0824093	−	0.0529613i	0.00457125	−	0.00293776i
$326$	−3.38480	−	23.5418i	−0.187467	−	1.30386i
$327$	12.7910	+	28.0084i	0.707343	+	1.54887i
$328$	0.569799	−	3.96304i	0.0314619	−	0.218822i
$329$	1.13390	−	0.332942i	0.0625137	−	0.0183557i
$330$	20.6929	+	13.2985i	1.13911	+	0.732060i
$331$	0.978864	−	2.14341i	0.0538033	−	0.117813i	−0.880821	−	0.473449i	$-0.843009\pi$
$331$	0.978864	−	2.14341i	0.0538033	−	0.117813i	0.934624	+	0.355637i	$0.115736\pi$
$332$	−12.8475	−	3.77236i	−0.705096	−	0.207035i
$333$	−31.2206	−	36.0305i	−1.71088	−	1.97446i
$334$	−3.65893	−	4.22263i	−0.200208	−	0.231052i
$335$	−19.1414	−	5.62041i	−1.04580	−	0.307076i
$336$	0.533654	−	1.16854i	0.0291132	−	0.0637491i
$337$	14.9883	+	9.63237i	0.816462	+	0.524708i	0.880950	−	0.473210i	$-0.156905\pi$
$337$	14.9883	+	9.63237i	0.816462	+	0.524708i	−0.0644874	+	0.997919i	$0.520541\pi$
$338$	12.4502	−	3.65571i	0.677203	−	0.198845i
$339$	−2.88714	+	20.0805i	−0.156808	+	1.09062i
$340$	3.23545	+	7.08464i	0.175467	+	0.384219i
$341$	1.25517	+	8.72992i	0.0679714	+	0.472752i
$342$	17.7743	−	11.4229i	0.961125	−	0.617677i
$343$	−3.60651	+	4.16214i	−0.194733	+	0.224734i
$344$	7.43011			0.400605
$345$	−27.3808	+	24.4989i	−1.47413	+	1.31897i
$346$	−22.7623			−1.22371
$347$	15.1382	−	17.4704i	0.812660	−	0.937859i	−0.186344	−	0.982485i	$-0.559664\pi$
$347$	15.1382	−	17.4704i	0.812660	−	0.937859i	0.999004	+	0.0446251i	$0.0142093\pi$
$348$	−1.02866	+	0.661081i	−0.0551421	+	0.0354377i
$349$	−1.41310	−	9.82834i	−0.0756416	−	0.526099i	−0.992049	−	0.125852i	$-0.959833\pi$
$349$	−1.41310	−	9.82834i	−0.0756416	−	0.526099i	0.916407	−	0.400247i	$-0.131076\pi$
$350$	−0.104147	−	0.228051i	−0.00556692	−	0.0121899i
$351$	0.316068	−	2.19830i	0.0168705	−	0.117337i
$352$	3.08070	−	0.904575i	0.164202	−	0.0482140i
$353$	−8.23891	−	5.29483i	−0.438513	−	0.281815i	0.302699	−	0.953086i	$-0.402112\pi$
$353$	−8.23891	−	5.29483i	−0.438513	−	0.281815i	−0.741212	+	0.671271i	$0.765749\pi$
$354$	−11.5966	+	25.3931i	−0.616354	+	1.34963i
$355$	−0.812028	−	0.238433i	−0.0430980	−	0.0126547i
$356$	−1.41497	−	1.63296i	−0.0749931	−	0.0865466i
$357$	−2.76135	−	3.18676i	−0.146146	−	0.168661i
$358$	−2.39139	−	0.702176i	−0.126389	−	0.0371112i
$359$	−11.1748	+	24.4694i	−0.589783	+	1.29144i	0.345790	+	0.938312i	$0.387611\pi$
$359$	−11.1748	+	24.4694i	−0.589783	+	1.29144i	−0.935573	+	0.353133i	$0.885116\pi$
$360$	14.8203	+	9.52440i	0.781096	+	0.501980i
$361$	10.4601	−	3.07138i	0.550534	−	0.161651i
$362$	−1.43743	+	9.99756i	−0.0755498	+	0.525460i
$363$	0.926855	+	2.02953i	0.0486473	+	0.106523i
$364$	0.00880302	+	0.0612263i	0.000461404	+	0.00320913i
$365$	11.2500	−	7.22992i	0.588851	−	0.378431i
$366$	23.5616	−	27.1915i	1.23158	−	1.42132i
$367$	20.9617			1.09419			0.547097	−	0.837069i	$-0.315733\pi$
$367$	20.9617			1.09419			0.547097	+	0.837069i	$0.315733\pi$
$368$	0.0762839	+	4.79522i	0.00397657	+	0.249968i
$369$	−29.7264			−1.54749
$370$	−9.97767	+	11.5148i	−0.518714	+	0.598628i
$371$	−4.36218	+	2.80341i	−0.226473	+	0.145546i
$372$	1.26219	+	8.77872i	0.0654415	+	0.455156i
$373$	11.3868	+	24.9337i	0.589588	+	1.29102i	0.935691	+	0.352820i	$0.114777\pi$
$373$	11.3868	+	24.9337i	0.589588	+	1.29102i	−0.346103	+	0.938196i	$0.612495\pi$
$374$	1.49986	−	10.4318i	0.0775561	−	0.539414i
$375$	−32.1218	+	9.43180i	−1.65876	+	0.487056i
$376$	2.49867	+	1.60580i	0.128859	+	0.0828127i
$377$	0.0244586	−	0.0535569i	0.00125968	−	0.00275832i
$378$	−5.45367	−	1.60134i	−0.280507	−	0.0823642i
$379$	2.66138	+	3.07140i	0.136706	+	0.157767i	0.819975	−	0.572400i	$-0.193988\pi$
$379$	2.66138	+	3.07140i	0.136706	+	0.157767i	−0.683268	+	0.730167i	$0.739442\pi$
$380$	−4.42184	−	5.10308i	−0.226836	−	0.261782i
$381$	−27.4755	−	8.06752i	−1.40761	−	0.413312i
$382$	1.06785	−	2.33826i	0.0546358	−	0.119636i
$383$	−14.6836	−	9.43657i	−0.750297	−	0.482186i	0.108759	−	0.994068i	$-0.465312\pi$
$383$	−14.6836	−	9.43657i	−0.750297	−	0.482186i	−0.859056	+	0.511882i	$0.828949\pi$
$384$	3.09792	−	0.909632i	0.158090	−	0.0464195i
$385$	−0.431385	+	3.00035i	−0.0219854	+	0.152912i
$386$	−9.38297	−	20.5458i	−0.477581	−	1.04576i
$387$	−7.85083	−	54.6037i	−0.399080	−	2.77566i
$388$	−2.21250	+	1.42189i	−0.112323	+	0.0721854i
$389$	−7.20827	+	8.31878i	−0.365474	+	0.421779i	−0.908466	−	0.417959i	$-0.862746\pi$
$389$	−7.20827	+	8.31878i	−0.365474	+	0.421779i	0.542992	+	0.839738i	$0.317291\pi$
$390$	−1.19102			−0.0603097
$391$	14.4216	+	6.31084i	0.729330	+	0.319153i
$392$	−6.84169			−0.345558
$393$	10.9984	−	12.6928i	0.554796	−	0.640268i
$394$	0.430955	−	0.276958i	0.0217112	−	0.0139530i
$395$	2.54560	+	17.7050i	0.128083	+	0.890836i
$396$	−9.90284	−	21.6842i	−0.497637	−	1.08967i
$397$	−3.19923	+	22.2511i	−0.160565	+	1.11675i	0.737007	+	0.675885i	$0.236238\pi$
$397$	−3.19923	+	22.2511i	−0.160565	+	1.11675i	−0.897572	+	0.440868i	$0.854671\pi$
$398$	1.26214	−	0.370597i	0.0632652	−	0.0185763i
$399$	3.07539	+	1.97643i	0.153962	+	0.0989455i
$400$	0.261758	−	0.573170i	0.0130879	−	0.0286585i
$401$	0.621311	+	0.182433i	0.0310268	+	0.00911029i	0.297209	−	0.954812i	$-0.403944\pi$
$401$	0.621311	+	0.182433i	0.0310268	+	0.00911029i	−0.266182	+	0.963923i	$0.585762\pi$
$402$	17.7767	+	20.5153i	0.886619	+	1.02321i
$403$	−0.279658	−	0.322742i	−0.0139307	−	0.0160769i
$404$	8.38303	+	2.46148i	0.417071	+	0.122463i
$405$	23.5090	−	51.4776i	1.16817	−	2.55794i
$406$	−0.126763	−	0.0814658i	−0.00629116	−	0.00404308i
$407$	19.7820	−	5.80853i	0.980559	−	0.287918i
$408$	1.50825	−	10.4901i	0.0746694	−	0.519337i
$409$	9.93727	+	21.7596i	0.491367	+	1.07594i	0.979180	+	0.202995i	$0.0650674\pi$
$409$	9.93727	+	21.7596i	0.491367	+	1.07594i	−0.487813	+	0.872948i	$0.662205\pi$
$410$	1.35201	+	9.40345i	0.0667711	+	0.464403i
$411$	1.36103	−	0.874681i	0.0671347	−	0.0431449i
$412$	−2.80497	+	3.23711i	−0.138191	+	0.159481i
$413$	−3.44009			−0.169276
$414$	35.1594	−	5.62736i	1.72799	−	0.276570i
$415$	31.7712			1.55959
$416$	−0.101808	+	0.117492i	−0.00499154	+	0.00576054i
$417$	42.7821	−	27.4944i	2.09505	−	1.34641i
$418$	1.30033	+	9.04399i	0.0636012	+	0.442356i
$419$	−13.5866	−	29.7505i	−0.663748	−	1.45340i	−0.878988	−	0.476844i	$-0.841781\pi$
$419$	−13.5866	−	29.7505i	−0.663748	−	1.45340i	0.215240	−	0.976561i	$-0.430947\pi$
$420$	−0.433797	+	3.01713i	−0.0211671	+	0.147221i
$421$	26.8578	−	7.88616i	1.30897	−	0.384348i	0.448468	−	0.893799i	$-0.351970\pi$
$421$	26.8578	−	7.88616i	1.30897	−	0.384348i	0.860500	+	0.509451i	$0.170151\pi$
$422$	−5.90044	−	3.79198i	−0.287229	−	0.184591i
$423$	9.16082	−	20.0594i	0.445414	−	0.975321i
$424$	−12.5046	−	3.67168i	−0.607277	−	0.178313i
$425$	−1.35444	−	1.56311i	−0.0657001	−	0.0758219i
$426$	0.754134	+	0.870317i	0.0365379	+	0.0421670i
$427$	4.25420	+	1.24915i	0.205875	+	0.0604505i
$428$	−7.48260	+	16.3846i	−0.361685	+	0.791980i
$429$	1.35580	+	0.871319i	0.0654586	+	0.0420677i
$430$	−16.9159	+	4.96696i	−0.815758	+	0.239528i
$431$	−0.854386	+	5.94238i	−0.0411543	+	0.286235i	0.958843	+	0.283937i	$0.0916405\pi$
$431$	−0.854386	+	5.94238i	−0.0411543	+	0.286235i	−0.999997	+	0.00229793i	$0.999269\pi$
$432$	−5.93445	−	12.9946i	−0.285521	−	0.625204i
$433$	−1.51859	−	10.5621i	−0.0729790	−	0.507580i	−0.993222	−	0.116233i	$-0.962918\pi$
$433$	−1.51859	−	10.5621i	−0.0729790	−	0.507580i	0.920243	−	0.391347i	$-0.127991\pi$
$434$	−0.919437	+	0.590886i	−0.0441344	+	0.0283635i
$435$	1.90000	−	2.19272i	0.0910980	−	0.105133i
$436$	−9.53659			−0.456720
$437$	−13.5380	−	1.72715i	−0.647609	−	0.0826208i
$438$	−18.1968			−0.869477
$439$	−21.5079	+	24.8215i	−1.02652	+	1.18466i	−0.0438973	+	0.999036i	$0.513977\pi$
$439$	−21.5079	+	24.8215i	−1.02652	+	1.18466i	−0.982620	+	0.185628i	$0.940568\pi$
$440$	−6.40904	+	4.11884i	−0.305539	+	0.196358i
$441$	7.22910	+	50.2795i	0.344243	+	2.39426i
$442$	0.211986	+	0.464186i	0.0100832	+	0.0220791i
$443$	0.0587614	−	0.408695i	0.00279184	−	0.0194177i	−0.988378	−	0.152017i	$-0.951423\pi$
$443$	0.0587614	−	0.408695i	0.00279184	−	0.0194177i	0.991170	+	0.132599i	$0.0423323\pi$
$444$	19.8926	−	5.84100i	0.944062	−	0.277202i
$445$	4.31303	+	2.77182i	0.204457	+	0.131397i
$446$	5.35879	−	11.7341i	0.253746	−	0.555626i
$447$	−11.9889	−	3.52025i	−0.567054	−	0.166502i
$448$	0.260554	+	0.300696i	0.0123100	+	0.0142065i
$449$	6.17485	+	7.12616i	0.291409	+	0.336304i	0.882510	−	0.470293i	$-0.155852\pi$
$449$	6.17485	+	7.12616i	0.291409	+	0.336304i	−0.591101	+	0.806598i	$0.701306\pi$
$450$	−4.48879	−	1.31803i	−0.211604	−	0.0621324i
$451$	5.34025	−	11.6935i	0.251462	−	0.550626i
$452$	−5.28586	−	3.39702i	−0.248626	−	0.159782i
$453$	−49.1075	+	14.4193i	−2.30727	+	0.677477i
$454$	0.109643	−	0.762586i	0.00514582	−	0.0357900i
$455$	−0.0609708	−	0.133507i	−0.00285836	−	0.00625893i
$456$	1.30760	+	9.09455i	0.0612339	+	0.425891i
$457$	−26.1069	+	16.7779i	−1.22123	+	0.784837i	−0.982502	−	0.186250i	$-0.940367\pi$
$457$	−26.1069	+	16.7779i	−1.22123	+	0.784837i	−0.238728	+	0.971087i	$0.576730\pi$
$458$	12.6193	−	14.5634i	0.589659	−	0.680503i
$459$	−46.8912			−2.18870
$460$	−3.37924	−	10.8662i	−0.157558	−	0.506637i
$461$	−33.0117			−1.53751			−0.768753	−	0.639546i	$-0.779122\pi$
$461$	−33.0117			−1.53751			−0.768753	+	0.639546i	$0.779122\pi$
$462$	2.70106	−	3.11719i	0.125665	−	0.145025i
$463$	−14.8651	+	9.55319i	−0.690838	+	0.443975i	−0.838384	−	0.545081i	$-0.816499\pi$
$463$	−14.8651	+	9.55319i	−0.690838	+	0.443975i	0.147546	+	0.989055i	$0.452863\pi$
$464$	−0.0538974	−	0.374864i	−0.00250212	−	0.0174026i
$465$	−8.74209	−	19.1425i	−0.405405	−	0.887712i
$466$	−1.20504	+	8.38126i	−0.0558225	+	0.388254i
$467$	10.6555	−	3.12873i	0.493076	−	0.144780i	−0.0257355	−	0.999669i	$-0.508193\pi$
$467$	10.6555	−	3.12873i	0.493076	−	0.144780i	0.518812	+	0.854889i	$0.326375\pi$
$468$	0.971022	+	0.624038i	0.0448855	+	0.0288462i
$469$	−1.38964	+	3.04290i	−0.0641678	+	0.140508i
$470$	−6.76211	−	1.98553i	−0.311913	−	0.0915859i
$471$	44.1286	+	50.9271i	2.03334	+	2.34660i
$472$	−5.66200	−	6.53430i	−0.260615	−	0.300766i
$473$	22.8899	+	6.72109i	1.05248	+	0.309036i
$474$	10.1109	−	22.1399i	0.464411	−	1.01692i
$475$	1.50848	+	0.969442i	0.0692139	+	0.0444811i
$476$	1.25310	−	0.367943i	0.0574356	−	0.0168646i
$477$	−13.7705	+	95.7756i	−0.630506	+	4.38526i
$478$	3.30114	+	7.22848i	0.150991	+	0.330623i
$479$	1.46637	+	10.1988i	0.0670002	+	0.465997i	0.995508	+	0.0946826i	$0.0301836\pi$
$479$	1.46637	+	10.1988i	0.0670002	+	0.465997i	−0.928507	+	0.371314i	$0.878907\pi$
$480$	−6.44487	+	4.14187i	−0.294167	+	0.189049i
$481$	−0.653736	+	0.754452i	−0.0298078	+	0.0344001i
$482$	13.4446			0.612385
$483$	3.41283	+	5.12921i	0.155289	+	0.233387i
$484$	−0.691036			−0.0314107
$485$	4.08662	−	4.71621i	0.185564	−	0.214152i
$486$	−28.7279	+	18.4623i	−1.30312	+	0.837467i
$487$	1.60654	+	11.1737i	0.0727994	+	0.506331i	0.993298	+	0.115584i	$0.0368740\pi$
$487$	1.60654	+	11.1737i	0.0727994	+	0.506331i	−0.920498	+	0.390747i	$0.872217\pi$
$488$	4.62924	+	10.1366i	0.209556	+	0.458863i
$489$	10.9285	−	76.0097i	0.494206	−	3.43728i
$490$	15.5763	−	4.57361i	0.703665	−	0.206615i
$491$	−7.70415	−	4.95115i	−0.347683	−	0.223442i	0.355130	−	0.934817i	$-0.384437\pi$
$491$	−7.70415	−	4.95115i	−0.347683	−	0.223442i	−0.702813	+	0.711375i	$0.748073\pi$
$492$	5.37010	−	11.7589i	0.242103	−	0.530132i
$493$	−1.19276	−	0.350226i	−0.0537192	−	0.0157734i
$494$	−0.289719	−	0.334353i	−0.0130351	−	0.0150433i
$495$	37.0412	+	42.7478i	1.66488	+	1.92137i
$496$	−2.63565	−	0.773896i	−0.118344	−	0.0347490i
$497$	−0.0589525	+	0.129088i	−0.00264438	+	0.00579039i
$498$	−36.3690	−	23.3729i	−1.62973	−	1.04737i
$499$	29.9602	−	8.79710i	1.34120	−	0.393812i	0.469103	−	0.883143i	$-0.344577\pi$
$499$	29.9602	−	8.79710i	1.34120	−	0.393812i	0.872098	+	0.489331i	$0.162759\pi$
$500$	1.47564	−	10.2633i	0.0659924	−	0.458987i
$501$	−7.49404	−	16.4097i	−0.334809	−	0.733129i
$502$	−2.14256	−	14.9018i	−0.0956272	−	0.665102i
$503$	14.3084	−	9.19543i	0.637979	−	0.410004i	−0.181277	−	0.983432i	$-0.558023\pi$
$503$	14.3084	−	9.19543i	0.637979	−	0.410004i	0.819256	+	0.573428i	$0.194387\pi$
$504$	1.93450	−	2.23253i	0.0861694	−	0.0994448i
$505$	−20.7309			−0.922512
$506$	−4.10263	+	14.8416i	−0.182384	+	0.659792i
$507$	41.8952			1.86063
$508$	5.80796	−	6.70274i	0.257686	−	0.297386i
$509$	15.4467	−	9.92700i	0.684663	−	0.440007i	−0.151522	−	0.988454i	$-0.548417\pi$
$509$	15.4467	−	9.92700i	0.684663	−	0.440007i	0.836185	+	0.548447i	$0.184781\pi$
$510$	3.57875	+	24.8907i	0.158470	+	1.10218i
$511$	−0.931532	−	2.03977i	−0.0412085	−	0.0902341i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	39.0064	−	11.4533i	1.72217	−	0.505676i
$514$	−3.95647	−	2.54267i	−0.174513	−	0.112152i
$515$	4.22202	−	9.24494i	0.186045	−	0.407381i
$516$	23.0179	+	6.75867i	1.01331	+	0.297534i
$517$	6.24508	+	7.20721i	0.274658	+	0.316973i
$518$	1.67309	+	1.93085i	0.0735114	+	0.0848367i
$519$	−70.5159	−	20.7053i	−3.09531	−	0.908864i
$520$	0.153240	−	0.335549i	0.00672003	−	0.0147148i
$521$	−22.1100	−	14.2092i	−0.968655	−	0.622517i	−0.0422744	−	0.999106i	$-0.513460\pi$
$521$	−22.1100	−	14.2092i	−0.968655	−	0.622517i	−0.926380	+	0.376589i	$0.877097\pi$
$522$	−2.69792	+	0.792181i	−0.118085	+	0.0346728i
$523$	4.87720	−	33.9217i	0.213265	−	1.48329i	−0.548888	−	0.835896i	$-0.684949\pi$
$523$	4.87720	−	33.9217i	0.213265	−	1.48329i	0.762153	−	0.647397i	$-0.224142\pi$
$524$	2.16090	+	4.73170i	0.0943992	+	0.206705i
$525$	−0.115198	−	0.801221i	−0.00502766	−	0.0349681i
$526$	−17.3837	+	11.1718i	−0.757964	+	0.487114i
$527$	−5.90457	+	6.81424i	−0.257207	+	0.296833i
$528$	10.3666			0.451148
$529$	−19.7346	−	11.8130i	−0.858025	−	0.513608i
$530$	30.9233			1.34322
$531$	−42.0378	+	48.5142i	−1.82429	+	2.10534i
$532$	−0.952515	+	0.612144i	−0.0412968	+	0.0265398i
$533$	0.0885838	+	0.616114i	0.00383699	+	0.0266868i
$534$	−2.89806	−	6.34588i	−0.125412	−	0.274613i
$535$	6.08245	−	42.3044i	0.262967	−	1.82898i
$536$	−8.06704	+	2.36870i	−0.348443	+	0.102312i
$537$	−6.76963	−	4.35057i	−0.292131	−	0.187741i
$538$	6.97028	−	15.2628i	0.300510	−	0.658025i
$539$	−21.0772	−	6.18882i	−0.907859	−	0.266572i
$540$	22.1976	+	25.6174i	0.955231	+	1.10240i
$541$	−5.25176	−	6.06086i	−0.225791	−	0.260577i	0.631539	−	0.775344i	$-0.282424\pi$
$541$	−5.25176	−	6.06086i	−0.225791	−	0.260577i	−0.857330	+	0.514768i	$0.827878\pi$
$542$	−9.84970	−	2.89213i	−0.423081	−	0.124228i
$543$	−13.5472	+	29.6641i	−0.581364	+	1.27301i
$544$	2.76135	+	1.77461i	0.118392	+	0.0760857i
$545$	21.7117	−	6.37512i	0.930026	−	0.273080i
$546$	−0.0284224	+	0.197682i	−0.00121637	+	0.00846001i
$547$	5.85916	+	12.8298i	0.250520	+	0.548562i	0.992555	−	0.121799i	$-0.0388665\pi$
$547$	5.85916	+	12.8298i	0.250520	+	0.548562i	−0.742035	+	0.670361i	$0.766139\pi$
$548$	0.0713120	+	0.495986i	0.00304630	+	0.0211875i
$549$	69.6024	−	44.7308i	2.97056	−	1.90906i
$550$	1.32487	−	1.52898i	0.0564927	−	0.0651961i
$551$	1.07774			0.0459132
$552$	−4.12557	+	14.9246i	−0.175596	+	0.635234i
$553$	2.99937			0.127546
$554$	−16.5572	+	19.1081i	−0.703450	+	0.811824i
$555$	−41.3843	+	26.5961i	−1.75667	+	1.12894i
$556$	2.24159	+	15.5906i	0.0950647	+	0.661190i
$557$	−2.71856	−	5.95281i	−0.115189	−	0.252229i	0.843253	−	0.537517i	$-0.180638\pi$
$557$	−2.71856	−	5.95281i	−0.115189	−	0.252229i	−0.958442	+	0.285289i	$0.907910\pi$
$558$	−2.90246	+	20.1871i	−0.122871	+	0.854586i
$559$	−1.10833	+	0.325435i	−0.0468774	+	0.0137644i
$560$	−0.794209	−	0.510407i	−0.0335614	−	0.0215686i
$561$	14.1355	−	30.9525i	0.596803	−	1.30682i
$562$	12.9012	+	3.78812i	0.544202	+	0.159792i
$563$	11.8897	+	13.7215i	0.501093	+	0.578292i	0.948796	−	0.315890i	$-0.102303\pi$
$563$	11.8897	+	13.7215i	0.501093	+	0.578292i	−0.447703	+	0.894183i	$0.647758\pi$
$564$	6.28000	+	7.24750i	0.264436	+	0.305175i
$565$	14.3050	+	4.20034i	0.601818	+	0.176710i
$566$	−1.82306	+	3.99194i	−0.0766288	+	0.167794i
$567$	−7.98308	−	5.13041i	−0.335258	−	0.215457i
$568$	−0.342226	+	0.100487i	−0.0143595	+	0.00421632i
$569$	0.552105	−	3.83998i	0.0231455	−	0.160980i	−0.974971	−	0.222334i	$-0.928633\pi$
$569$	0.552105	−	3.83998i	0.0231455	−	0.160980i	0.998116	+	0.0613534i	$0.0195417\pi$
$570$	−9.05660	−	19.8312i	−0.379339	−	0.830637i
$571$	−4.70574	−	32.7291i	−0.196929	−	1.36967i	−0.813130	−	0.582083i	$-0.802238\pi$
$571$	−4.70574	−	32.7291i	−0.196929	−	1.36967i	0.616200	−	0.787589i	$-0.288671\pi$
$572$	−0.419920	+	0.269866i	−0.0175577	+	0.0112837i
$573$	5.43506	−	6.27240i	0.227053	−	0.262033i
$574$	1.59302			0.0664913
$575$	1.67400	+	2.51588i	0.0698105	+	0.104920i
$576$	7.42455			0.309356
$577$	−13.0284	+	15.0356i	−0.542380	+	0.625940i	−0.959091	−	0.283099i	$-0.908637\pi$
$577$	−13.0284	+	15.0356i	−0.542380	+	0.625940i	0.416711	+	0.909039i	$0.363183\pi$
$578$	−5.23742	+	3.36589i	−0.217848	+	0.140002i
$579$	−10.3786	−	72.1844i	−0.431318	−	2.99988i
$580$	0.373300	+	0.817413i	0.0155004	+	0.0339412i
$581$	0.758185	−	5.27329i	0.0314548	−	0.218773i
$582$	−8.14755	+	2.39234i	−0.337727	+	0.0991655i
$583$	−35.2016	−	22.6227i	−1.45790	−	0.936936i
$584$	2.34125	−	5.12663i	0.0968818	−	0.212141i
$585$	−2.62786	−	0.771610i	−0.108649	−	0.0319022i
$586$	3.60693	+	4.16262i	0.149001	+	0.171956i
$587$	1.81135	+	2.09041i	0.0747623	+	0.0862803i	0.791898	−	0.610653i	$-0.209093\pi$
$587$	1.81135	+	2.09041i	0.0747623	+	0.0862803i	−0.717136	+	0.696933i	$0.754547\pi$
$588$	−21.1950	−	6.22342i	−0.874068	−	0.256650i
$589$	3.24731	−	7.11062i	0.133803	−	0.292988i
$590$	17.2586	+	11.0915i	0.710527	+	0.456628i
$591$	1.58700	−	0.465984i	0.0652803	−	0.0191680i
$592$	−0.913843	+	6.35592i	−0.0375587	+	0.261227i
$593$	17.7134	+	38.7869i	0.727401	+	1.59279i	0.803232	+	0.595666i	$0.203112\pi$
$593$	17.7134	+	38.7869i	0.727401	+	1.59279i	−0.0758313	+	0.997121i	$0.524161\pi$
$594$	−6.52763	−	45.4007i	−0.267832	−	1.86281i
$595$	−2.60692	+	1.67537i	−0.106873	+	0.0686834i
$596$	2.53429	−	2.92473i	0.103809	−	0.119802i
$597$	4.24711			0.173823
$598$	−0.221408	−	0.711950i	−0.00905403	−	0.0291138i
$599$	−20.1889			−0.824895			−0.412448	−	0.910981i	$-0.635326\pi$
$599$	−20.1889			−0.824895			−0.412448	+	0.910981i	$0.635326\pi$
$600$	1.33228	−	1.53753i	0.0543900	−	0.0627695i
$601$	−12.5371	+	8.05708i	−0.511397	+	0.328655i	−0.770761	−	0.637125i	$-0.780124\pi$
$601$	−12.5371	+	8.05708i	−0.511397	+	0.328655i	0.259363	+	0.965780i	$0.416487\pi$
$602$	0.420722	+	2.92618i	0.0171473	+	0.119262i
$603$	25.9313	+	56.7817i	1.05601	+	2.31233i
$604$	2.25594	−	15.6904i	0.0917930	−	0.638434i
$605$	1.57326	−	0.461952i	0.0639622	−	0.0187810i
$606$	23.7309	+	15.2509i	0.964003	+	0.619527i
$607$	12.7592	−	27.9387i	0.517879	−	1.13400i	−0.452357	−	0.891837i	$-0.649417\pi$
$607$	12.7592	−	27.9387i	0.517879	−	1.13400i	0.970236	−	0.242161i	$-0.0778561\pi$
$608$	−2.73047	−	0.801739i	−0.110735	−	0.0325148i
$609$	−0.318599	−	0.367683i	−0.0129103	−	0.0148993i
$610$	−17.3155	−	19.9831i	−0.701083	−	0.809093i
$611$	−0.443053	−	0.130092i	−0.0179240	−	0.00526296i
$612$	10.1239	−	22.1682i	0.409233	−	0.896095i
$613$	15.9162	+	10.2287i	0.642850	+	0.413135i	0.821047	−	0.570860i	$-0.193390\pi$
$613$	15.9162	+	10.2287i	0.642850	+	0.413135i	−0.178197	+	0.983995i	$0.557026\pi$
$614$	24.4798	−	7.18793i	0.987925	−	0.290081i
$615$	−4.36525	+	30.3610i	−0.176024	+	1.22427i
$616$	0.530688	+	1.16204i	0.0213820	+	0.0468201i
$617$	3.03989	+	21.1429i	0.122381	+	0.851181i	0.954846	+	0.297103i	$0.0960203\pi$
$617$	3.03989	+	21.1429i	0.122381	+	0.851181i	−0.832464	+	0.554079i	$0.813071\pi$
$618$	−11.6342	+	7.47683i	−0.467995	+	0.300762i
$619$	−5.27356	+	6.08601i	−0.211962	+	0.244618i	−0.851768	−	0.523919i	$-0.824469\pi$
$619$	−5.27356	+	6.08601i	−0.211962	+	0.244618i	0.639806	+	0.768537i	$0.279015\pi$
$620$	6.51785			0.261763
$621$	67.9604	+	8.67027i	2.72716	+	0.347926i
$622$	10.0559			0.403206
$623$	0.562983	−	0.649717i	0.0225554	−	0.0260304i
$624$	−0.422268	+	0.271375i	−0.0169042	+	0.0108637i
$625$	3.94974	+	27.4710i	0.157989	+	1.09884i
$626$	−1.46099	−	3.19913i	−0.0583931	−	0.127863i
$627$	−4.19838	+	29.2004i	−0.167667	+	1.16615i
$628$	−20.0255	+	5.88003i	−0.799106	+	0.234639i
$629$	17.7314	+	11.3953i	0.706996	+	0.454359i
$630$	−2.91179	+	6.37593i	−0.116009	+	0.254023i
$631$	−25.9629	−	7.62339i	−1.03357	−	0.303483i	−0.279406	−	0.960173i	$-0.590138\pi$
$631$	−25.9629	−	7.62339i	−1.03357	−	0.303483i	−0.754160	+	0.656690i	$0.771956\pi$
$632$	4.93662	+	5.69716i	0.196368	+	0.226621i
$633$	−14.8298	−	17.1145i	−0.589431	−	0.680240i
$634$	33.5345	+	9.84661i	1.33182	+	0.391059i
$635$	−8.74209	+	19.1425i	−0.346919	+	0.759647i
$636$	−35.3984	−	22.7492i	−1.40364	−	0.902063i
$637$	1.02056	−	0.299663i	0.0404360	−	0.0118731i
$638$	0.173051	−	1.20360i	0.00685117	−	0.0476509i
$639$	1.10008	+	2.40883i	0.0435184	+	0.0952920i
$640$	−0.337683	−	2.34863i	−0.0133481	−	0.0928379i
$641$	−33.4278	+	21.4827i	−1.32032	+	0.848517i	−0.995267	−	0.0971801i	$-0.969018\pi$
$641$	−33.4278	+	21.4827i	−1.32032	+	0.848517i	−0.325051	+	0.945697i	$0.605381\pi$
$642$	−38.0845	+	43.9518i	−1.50307	+	1.73464i
$643$	−1.75237			−0.0691066			−0.0345533	−	0.999403i	$-0.511001\pi$
$643$	−1.75237			−0.0691066			−0.0345533	+	0.999403i	$0.511001\pi$
$644$	−1.88417	+	0.301567i	−0.0742468	+	0.0118834i
$645$	−56.9223			−2.24131
$646$	−6.11700	+	7.05940i	−0.240670	+	0.277748i
$647$	7.48969	−	4.81333i	0.294450	−	0.189232i	−0.385072	−	0.922886i	$-0.625823\pi$
$647$	7.48969	−	4.81333i	0.294450	−	0.189232i	0.679522	+	0.733655i	$0.262187\pi$
$648$	−3.39425	−	23.6075i	−0.133339	−	0.927392i
$649$	−11.5322	−	25.2519i	−0.452677	−	0.991224i
$650$	−0.0139412	+	0.0969631i	−0.000546818	+	0.00380320i
$651$	−3.38583	+	0.994170i	−0.132701	+	0.0389646i
$652$	20.0083	+	12.8586i	0.783586	+	0.503580i
$653$	−9.55387	+	20.9200i	−0.373872	+	0.818665i	0.625393	+	0.780310i	$0.284939\pi$
$653$	−9.55387	+	20.9200i	−0.373872	+	0.818665i	−0.999264	+	0.0383544i	$0.987788\pi$
$654$	−29.5436	−	8.67479i	−1.15525	−	0.339211i
$655$	−8.08275	−	9.32799i	−0.315819	−	0.364475i
$656$	2.62193	+	3.02587i	0.102369	+	0.118140i
$657$	−40.1493	−	11.7889i	−1.56637	−	0.459929i
$658$	−0.490923	+	1.07497i	−0.0191382	+	0.0419067i
$659$	27.8796	+	17.9171i	1.08604	+	0.697953i	0.955944	−	0.293549i	$-0.0948365\pi$
$659$	27.8796	+	17.9171i	1.08604	+	0.697953i	0.130092	+	0.991502i	$0.458473\pi$
$660$	−23.6013	+	6.92998i	−0.918681	+	0.269749i
$661$	3.05748	−	21.2652i	0.118922	−	0.827121i	−0.839824	−	0.542858i	$-0.817342\pi$
$661$	3.05748	−	21.2652i	0.118922	−	0.827121i	0.958746	−	0.284263i	$-0.0917489\pi$
$662$	0.978864	+	2.14341i	0.0380446	+	0.0833062i
$663$	0.234479	+	1.63084i	0.00910643	+	0.0633366i
$664$	11.2643	−	7.23910i	0.437138	−	0.280932i
$665$	1.75935	−	2.03040i	0.0682247	−	0.0787355i
$666$	47.6751			1.84737
$667$	1.66393	+	0.728133i	0.0644278	+	0.0281934i
$668$	5.58734			0.216181
$669$	27.2748	−	31.4768i	1.05451	−	1.21696i
$670$	16.7825	−	10.7855i	0.648366	−	0.416680i
$671$	5.09196	+	35.4154i	0.196573	+	1.36719i
$672$	0.533654	+	1.16854i	0.0205862	+	0.0450774i
$673$	−3.63513	+	25.2829i	−0.140124	+	0.974583i	0.791503	+	0.611166i	$0.209299\pi$
$673$	−3.63513	+	25.2829i	−0.140124	+	0.974583i	−0.931627	+	0.363417i	$0.881610\pi$
$674$	−17.0949	+	5.01951i	−0.658470	+	0.193344i
$675$	−7.57255	−	4.86658i	−0.291468	−	0.187315i
$676$	−5.39035	+	11.8032i	−0.207321	+	0.453970i
$677$	46.2052	+	13.5671i	1.77581	+	0.521425i	0.994686	−	0.102952i	$-0.0328288\pi$
$677$	46.2052	+	13.5671i	1.77581	+	0.521425i	0.781123	+	0.624377i	$0.214647\pi$
$678$	−13.2852	−	15.3319i	−0.510213	−	0.588817i
$679$	−0.685259	−	0.790831i	−0.0262978	−	0.0303493i
$680$	−7.47299	−	2.19427i	−0.286576	−	0.0841463i
$681$	1.03334	−	2.26270i	0.0395977	−	0.0867068i
$682$	−7.41960	−	4.76828i	−0.284111	−	0.182587i
$683$	4.51551	−	1.32587i	0.172781	−	0.0507331i	−0.194198	−	0.980962i	$-0.562210\pi$
$683$	4.51551	−	1.32587i	0.172781	−	0.0507331i	0.366979	+	0.930229i	$0.380392\pi$
$684$	−3.00688	+	20.9133i	−0.114971	+	0.799640i
$685$	−0.493916	−	1.08153i	−0.0188716	−	0.0413230i
$686$	−0.783770	−	5.45124i	−0.0299245	−	0.208129i
$687$	52.3408	−	33.6374i	1.99693	−	1.28335i
$688$	−4.86569	+	5.61530i	−0.185503	+	0.214081i
$689$	2.02610			0.0771881
$690$	−0.584413	−	36.7364i	−0.0222482	−	1.39853i
$691$	−7.93027			−0.301682			−0.150841	−	0.988558i	$-0.548198\pi$
$691$	−7.93027			−0.301682			−0.150841	+	0.988558i	$0.548198\pi$
$692$	14.9062	−	17.2026i	0.566647	−	0.653946i
$693$	7.97910	−	5.12786i	0.303101	−	0.194791i
$694$	3.28984	+	22.8813i	0.124881	+	0.868564i
$695$	−15.5256	−	33.9962i	−0.588918	−	1.28955i
$696$	0.174019	−	1.21033i	0.00659617	−	0.0458774i
$697$	12.6098	−	3.70256i	0.477629	−	0.140245i
$698$	8.35315	+	5.36824i	0.316171	+	0.203191i
$699$	−11.3570	+	24.8683i	−0.429561	+	0.940607i
$700$	0.240552	+	0.0706324i	0.00909200	+	0.00266965i
$701$	−21.4018	−	24.6990i	−0.808335	−	0.932868i	0.190473	−	0.981692i	$-0.438998\pi$
$701$	−21.4018	−	24.6990i	−0.808335	−	0.932868i	−0.998807	+	0.0488247i	$0.984452\pi$
$702$	1.45438	+	1.67845i	0.0548922	+	0.0633490i
$703$	−17.5331	−	5.14819i	−0.661274	−	0.194168i
$704$	−1.33380	+	2.92061i	−0.0502694	+	0.110075i
$705$	−19.1424	−	12.3021i	−0.720944	−	0.463322i
$706$	9.39691	−	2.75918i	0.353657	−	0.103843i
$707$	−0.494719	+	3.44085i	−0.0186058	+	0.129406i
$708$	−11.5966	−	25.3931i	−0.435828	−	0.954331i
$709$	7.03916	+	48.9584i	0.264361	+	1.83867i	0.499016	+	0.866593i	$0.333695\pi$
$709$	7.03916	+	48.9584i	0.264361	+	1.83867i	−0.234655	+	0.972079i	$0.575396\pi$
$710$	0.711961	−	0.457550i	0.0267194	−	0.0171715i
$711$	36.6522	−	42.2989i	1.37456	−	1.58633i
$712$	2.16071			0.0809762
$713$	9.81758	−	8.78425i	0.367671	−	0.328973i
$714$	4.21669			0.157806
$715$	0.775617	−	0.895109i	0.0290064	−	0.0334752i
$716$	2.09670	−	1.34747i	0.0783573	−	0.0503572i
$717$	3.65141	+	25.3961i	0.136364	+	0.948435i
$718$	−11.1748	−	24.4694i	−0.417040	−	0.913189i
$719$	4.00200	−	27.8345i	0.149249	−	1.03805i	−0.768203	−	0.640207i	$-0.778849\pi$
$719$	4.00200	−	27.8345i	0.149249	−	1.03805i	0.917452	−	0.397846i	$-0.130242\pi$
$720$	−16.9033	+	4.96325i	−0.629947	+	0.184969i
$721$	−1.43369	−	0.921379i	−0.0533935	−	0.0343139i
$722$	−4.52875	+	9.91658i	−0.168543	+	0.369057i
$723$	41.6503	+	12.2296i	1.54899	+	0.454825i
$724$	−6.61433	−	7.63335i	−0.245820	−	0.283691i
$725$	−0.156273	−	0.180349i	−0.00580383	−	0.00669798i
$726$	−2.14078	−	0.628589i	−0.0794517	−	0.0233291i
$727$	6.50239	−	14.2382i	0.241160	−	0.528067i	−0.749889	−	0.661564i	$-0.769893\pi$
$727$	6.50239	−	14.2382i	0.241160	−	0.528067i	0.991049	+	0.133496i	$0.0426204\pi$
$728$	−0.0520365	−	0.0334418i	−0.00192860	−	0.00123944i
$729$	−37.1381	+	10.9047i	−1.37549	+	0.403879i
$730$	−1.90316	+	13.2368i	−0.0704391	+	0.489914i
$731$	10.1314	+	22.1848i	0.374725	+	0.820533i
$732$	5.12043	+	35.6133i	0.189256	+	1.31631i
$733$	−8.51386	+	5.47152i	−0.314466	+	0.202095i	−0.688347	−	0.725382i	$-0.741663\pi$
$733$	−8.51386	+	5.47152i	−0.314466	+	0.202095i	0.373881	+	0.927477i	$0.378027\pi$
$734$	−13.7270	+	15.8418i	−0.506674	+	0.584733i
$735$	52.4144			1.93334
$736$	−3.67394	−	3.08255i	−0.135423	−	0.113624i
$737$	−26.9948			−0.994366
$738$	19.4666	−	22.4657i	0.716577	−	0.826974i
$739$	10.7530	−	6.91052i	0.395554	−	0.254207i	−0.327710	−	0.944778i	$-0.606277\pi$
$739$	10.7530	−	6.91052i	0.395554	−	0.254207i	0.723265	+	0.690571i	$0.242641\pi$
$740$	−2.16835	−	15.0812i	−0.0797103	−	0.554397i
$741$	−0.593388	−	1.29934i	−0.0217987	−	0.0477324i
$742$	0.737950	−	5.13256i	0.0270910	−	0.188422i
$743$	34.6951	−	10.1874i	1.27284	−	0.373739i	0.425581	−	0.904921i	$-0.360070\pi$
$743$	34.6951	−	10.1874i	1.27284	−	0.373739i	0.847258	+	0.531181i	$0.178252\pi$
$744$	−7.46108	−	4.79494i	−0.273536	−	0.175791i
$745$	−3.81459	+	8.35280i	−0.139756	+	0.306023i
$746$	−26.3004	−	7.72250i	−0.962926	−	0.282741i
$747$	−65.1021	−	75.1318i	−2.38196	−	2.74893i
$748$	6.90161	+	7.96488i	0.252348	+	0.291225i
$749$	−6.87640	−	2.01909i	−0.251258	−	0.0737761i
$750$	13.9072	−	30.4525i	0.507819	−	1.11197i
$751$	14.8497	+	9.54330i	0.541872	+	0.348240i	0.782771	−	0.622310i	$-0.213806\pi$
$751$	14.8497	+	9.54330i	0.541872	+	0.348240i	−0.240899	+	0.970550i	$0.577442\pi$
$752$	−2.84986	+	0.836795i	−0.103924	+	0.0305148i
$753$	6.91770	−	48.1137i	0.252095	−	1.75336i
$754$	0.0244586	+	0.0535569i	0.000890730	+	0.00195043i
$755$	5.35287	+	37.2300i	0.194811	+	1.35494i
$756$	4.78161	−	3.07295i	0.173905	−	0.111762i
$757$	−32.4005	+	37.3921i	−1.17762	+	1.35904i	−0.258036	+	0.966135i	$0.583075\pi$
$757$	−32.4005	+	37.3921i	−1.17762	+	1.35904i	−0.919579	+	0.392905i	$0.871470\pi$
$758$	−4.06405			−0.147613
$759$	−26.2101	+	42.2464i	−0.951365	+	1.53345i
$760$	6.75234			0.244933
$761$	15.2253	−	17.5710i	0.551918	−	0.636947i	−0.409411	−	0.912350i	$-0.634266\pi$
$761$	15.2253	−	17.5710i	0.551918	−	0.636947i	0.961329	+	0.275403i	$0.0888112\pi$
$762$	24.0896	−	15.4815i	0.872675	−	0.560834i
$763$	−0.539999	−	3.75577i	−0.0195493	−	0.135968i
$764$	1.06785	+	2.33826i	0.0386334	+	0.0845953i
$765$	−8.22949	+	57.2373i	−0.297538	+	2.06942i
$766$	16.7474	−	4.91748i	0.605108	−	0.177676i
$767$	1.13079	+	0.726712i	0.0408303	+	0.0262400i
$768$	−1.34125	+	2.93694i	−0.0483983	+	0.105978i
$769$	−40.5167	−	11.8968i	−1.46107	−	0.429009i	−0.547886	−	0.836553i	$-0.684567\pi$
$769$	−40.5167	−	11.8968i	−1.46107	−	0.429009i	−0.913186	+	0.407544i	$0.866385\pi$
$770$	−1.98502	−	2.29083i	−0.0715350	−	0.0825558i
$771$	−9.94395	−	11.4759i	−0.358123	−	0.413296i
$772$	21.6720	+	6.36349i	0.779994	+	0.229027i
$773$	5.46707	−	11.9712i	0.196637	−	0.430574i	−0.785470	−	0.618900i	$-0.787579\pi$
$773$	5.46707	−	11.9712i	0.196637	−	0.430574i	0.982107	+	0.188325i	$0.0603060\pi$
$774$	46.4080	+	29.8246i	1.66810	+	1.07202i
$775$	−1.66075	+	0.487641i	−0.0596560	+	0.0175166i
$776$	0.374289	−	2.60324i	0.0134362	−	0.0934507i
$777$	3.42674	+	7.50352i	0.122934	+	0.269187i
$778$	−1.56651	−	10.8953i	−0.0561620	−	0.390615i
$779$	−9.58505	+	6.15994i	−0.343420	+	0.220703i
$780$	0.779953	−	0.900113i	0.0279268	−	0.0322292i
$781$	−1.14519			−0.0409782
$782$	−14.2135	+	6.76637i	−0.508275	+	0.241965i
$783$	−5.41023			−0.193346
$784$	4.48036	−	5.17061i	0.160013	−	0.184665i
$785$	41.6608	−	26.7738i	1.48694	−	0.955597i
$786$	2.39018	+	16.6241i	0.0852549	+	0.592961i
$787$	15.6368	+	34.2398i	0.557391	+	1.22052i	0.953244	+	0.302202i	$0.0977217\pi$
$787$	15.6368	+	34.2398i	0.557391	+	1.22052i	−0.395853	+	0.918314i	$0.629551\pi$
$788$	−0.0729047	+	0.507064i	−0.00259712	+	0.0180634i
$789$	−64.0155	+	18.7966i	−2.27901	+	0.669178i
$790$	−15.0476	−	9.67048i	−0.535368	−	0.344060i
$791$	1.03853	−	2.27407i	0.0369260	−	0.0808566i
$792$	22.8728	+	6.71606i	0.812750	+	0.238645i
$793$	−1.13451	−	1.30929i	−0.0402876	−	0.0464944i
$794$	−14.7212	−	16.9892i	−0.522437	−	0.602924i
$795$	95.7981	+	28.1289i	3.39761	+	0.997628i
$796$	−0.546445	+	1.19655i	−0.0193682	+	0.0424105i
$797$	5.36489	+	3.44780i	0.190034	+	0.122127i	0.632198	−	0.774807i	$-0.282153\pi$
$797$	5.36489	+	3.44780i	0.190034	+	0.122127i	−0.442164	+	0.896934i	$0.645789\pi$
$798$	−3.50764	+	1.02994i	−0.124169	+	0.0364594i
$799$	−1.38748	+	9.65012i	−0.0490854	+	0.341397i
$800$	0.261758	+	0.573170i	0.00925453	+	0.0202646i
$801$	−2.28306	−	15.8790i	−0.0806680	−	0.561058i
$802$	−0.544746	+	0.350087i	−0.0192357	+	0.0123620i
$803$	11.8501	−	13.6758i	0.418182	−	0.482607i
$804$	−27.1457			−0.957355
$805$	4.08805	−	1.94612i	0.144085	−	0.0685917i
$806$	0.427049			0.0150422
$807$	35.4769	−	40.9425i	1.24885	−	1.44125i
$808$	−7.34998	+	4.72354i	−0.258571	+	0.166174i
$809$	−3.74186	−	26.0252i	−0.131557	−	0.914998i	−0.943526	−	0.331298i	$-0.892514\pi$
$809$	−3.74186	−	26.0252i	−0.131557	−	0.914998i	0.811969	−	0.583700i	$-0.198396\pi$
$810$	23.5090	+	51.4776i	0.826023	+	1.80874i
$811$	1.80260	−	12.5374i	0.0632978	−	0.440246i	−0.933386	−	0.358874i	$-0.883161\pi$
$811$	1.80260	−	12.5374i	0.0632978	−	0.440246i	0.996684	−	0.0813719i	$-0.0259301\pi$
$812$	0.144580	−	0.0424525i	0.00507377	−	0.00148979i
$813$	−27.8828	−	17.9192i	−0.977894	−	0.628454i
$814$	−8.56468	+	18.7540i	−0.300192	+	0.657329i
$815$	−54.1482	−	15.8993i	−1.89673	−	0.556929i
$816$	6.94019	+	8.00941i	0.242955	+	0.280385i
$817$	−13.8465	−	15.9797i	−0.484428	−	0.559059i
$818$	−22.9523	−	6.73941i	−0.802510	−	0.235638i
$819$	−0.190780	+	0.417751i	−0.00666641	+	0.0145974i
$820$	−7.99203	−	5.13617i	−0.279094	−	0.179363i
$821$	−47.5748	+	13.9692i	−1.66037	+	0.487529i	−0.971437	−	0.237296i	$-0.923739\pi$
$821$	−47.5748	+	13.9692i	−1.66037	+	0.487529i	−0.688933	+	0.724825i	$0.741921\pi$
$822$	−0.230246	+	1.60139i	−0.00803074	+	0.0558550i
$823$	−12.4380	−	27.2354i	−0.433561	−	0.949365i	−0.992736	−	0.120316i	$-0.961609\pi$
$823$	−12.4380	−	27.2354i	−0.433561	−	0.949365i	0.559175	−	0.829050i	$-0.311118\pi$
$824$	−0.609579	−	4.23972i	−0.0212357	−	0.147698i
$825$	5.49516	−	3.53153i	0.191317	−	0.122952i
$826$	2.25278	−	2.59985i	0.0783843	−	0.0904603i
$827$	19.8427			0.689998			0.344999	−	0.938603i	$-0.387879\pi$
$827$	19.8427			0.689998			0.344999	+	0.938603i	$0.387879\pi$
$828$	−18.7716	+	30.2568i	−0.652360	+	1.05150i
$829$	38.9517			1.35285			0.676425	−	0.736512i	$-0.263528\pi$
$829$	38.9517			1.35285			0.676425	+	0.736512i	$0.263528\pi$
$830$	−20.8057	+	24.0111i	−0.722178	+	0.833438i
$831$	−68.6744	+	44.1343i	−2.38229	+	1.53100i
$832$	−0.0221250	−	0.153882i	−0.000767045	−	0.00533491i
$833$	−9.32910	−	20.4279i	−0.323234	−	0.707784i
$834$	−7.23745	+	50.3376i	−0.250612	+	1.74305i
$835$	−12.7205	+	3.73508i	−0.440212	+	0.129258i
$836$	−7.68653	−	4.93983i	−0.265844	−	0.170848i
$837$	−16.3014	+	35.6952i	−0.563460	+	1.23381i
$838$	31.3812	+	9.21435i	1.08405	+	0.318305i
$839$	30.6040	+	35.3190i	1.05657	+	1.21935i	0.974890	+	0.222687i	$0.0714828\pi$
$839$	30.6040	+	35.3190i	1.05657	+	1.21935i	0.0816792	+	0.996659i	$0.473972\pi$
$840$	−1.99611	−	2.30364i	−0.0688725	−	0.0794831i
$841$	27.6877	+	8.12984i	0.954748	+	0.280339i
$842$	−11.6281	+	25.4621i	−0.400732	+	0.877482i
$843$	36.5210	+	23.4706i	1.25785	+	0.808371i
$844$	6.72976	−	1.97603i	0.231648	−	0.0680179i
$845$	4.38171	−	30.4755i	0.150735	−	1.04839i
$846$	9.16082	+	20.0594i	0.314955	+	0.689656i
$847$	−0.0391291	−	0.272149i	−0.00134449	−	0.00935116i
$848$	10.9636	−	7.04590i	0.376493	−	0.241957i
$849$	−9.27888	+	10.7084i	−0.318450	+	0.367511i
$850$	2.06829			0.0709417
$851$	−23.5914	−	19.7939i	−0.808704	−	0.678527i
$852$	−1.15159			−0.0394530
$853$	−11.6361	+	13.4288i	−0.398414	+	0.459794i	−0.919141	−	0.393929i	$-0.871115\pi$
$853$	−11.6361	+	13.4288i	−0.398414	+	0.459794i	0.520727	+	0.853723i	$0.325661\pi$
$854$	−3.72995	+	2.39710i	−0.127636	+	0.0820269i
$855$	−7.13468	−	49.6228i	−0.244001	−	1.69706i
$856$	−7.48260	−	16.3846i	−0.255750	−	0.560014i
$857$	3.35722	−	23.3500i	0.114680	−	0.797620i	−0.848583	−	0.529062i	$-0.822544\pi$
$857$	3.35722	−	23.3500i	0.114680	−	0.797620i	0.963264	−	0.268558i	$-0.0865470\pi$
$858$	−1.54636	+	0.454052i	−0.0527918	+	0.0155011i
$859$	19.5067	+	12.5362i	0.665561	+	0.427730i	0.829323	−	0.558770i	$-0.188726\pi$
$859$	19.5067	+	12.5362i	0.665561	+	0.427730i	−0.163762	+	0.986500i	$0.552363\pi$
$860$	7.32379	−	16.0369i	0.249739	−	0.546853i
$861$	4.93505	+	1.44906i	0.168186	+	0.0493839i
$862$	−3.93145	−	4.53714i	−0.133906	−	0.154535i
$863$	−23.0756	−	26.6307i	−0.785502	−	0.906518i	0.211992	−	0.977272i	$-0.432005\pi$
$863$	−23.0756	−	26.6307i	−0.785502	−	0.906518i	−0.997494	+	0.0707535i	$0.977460\pi$
$864$	13.7069	+	4.02471i	0.466319	+	0.136924i
$865$	−22.4366	+	49.1294i	−0.762868	+	1.67045i
$866$	8.97674	+	5.76900i	0.305042	+	0.196039i
$867$	−19.2868	+	5.66313i	−0.655015	+	0.192330i
$868$	0.155541	−	1.08181i	0.00527941	−	0.0367191i
$869$	10.0547	+	22.0168i	0.341083	+	0.746869i
$870$	0.412909	+	2.87185i	0.0139989	+	0.0973648i
$871$	1.09959	−	0.706665i	0.0372582	−	0.0239444i
$872$	6.24514	−	7.20727i	0.211487	−	0.244069i
$873$	−19.5266			−0.660876
$874$	10.1708	−	9.10028i	0.344032	−	0.307821i
$875$	4.12551			0.139468
$876$	11.9164	−	13.7522i	0.402617	−	0.464645i
$877$	27.9357	−	17.9532i	0.943323	−	0.606237i	0.0239879	−	0.999712i	$-0.492364\pi$
$877$	27.9357	−	17.9532i	0.943323	−	0.606237i	0.919335	+	0.393475i	$0.128727\pi$
$878$	−4.67412	−	32.5092i	−0.157744	−	1.09713i
$879$	7.38754	+	16.1765i	0.249176	+	0.545619i
$880$	1.08422	−	7.54089i	0.0365489	−	0.254203i
$881$	−11.9769	+	3.51674i	−0.403512	+	0.118482i	−0.477190	−	0.878800i	$-0.658345\pi$
$881$	−11.9769	+	3.51674i	−0.403512	+	0.118482i	0.0736776	+	0.997282i	$0.476526\pi$
$882$	−42.7327	−	27.4627i	−1.43889	−	0.924716i
$883$	−8.57642	+	18.7797i	−0.288620	+	0.631989i	−0.997292	−	0.0735494i	$-0.976567\pi$
$883$	−8.57642	+	18.7797i	−0.288620	+	0.631989i	0.708672	+	0.705538i	$0.249295\pi$
$884$	−0.489630	−	0.143768i	−0.0164680	−	0.00483545i
$885$	43.3768	+	50.0595i	1.45809	+	1.68273i
$886$	0.270390	+	0.312047i	0.00908394	+	0.0104834i
$887$	−22.0294	−	6.46840i	−0.739674	−	0.217188i	−0.109874	−	0.993946i	$-0.535045\pi$
$887$	−22.0294	−	6.46840i	−0.739674	−	0.217188i	−0.629799	+	0.776758i	$0.716863\pi$
$888$	−8.61256	+	18.8589i	−0.289019	+	0.632863i
$889$	2.96859	+	1.90780i	0.0995634	+	0.0639855i
$890$	−4.91923	+	1.44442i	−0.164893	+	0.0484170i
$891$	10.8981	−	75.7981i	0.365101	−	2.53933i
$892$	5.35879	+	11.7341i	0.179425	+	0.392887i
$893$	−1.20289	−	8.36632i	−0.0402533	−	0.279968i
$894$	10.5115	−	6.75531i	0.351556	−	0.225931i
$895$	−3.87272	+	4.46936i	−0.129451	+	0.149394i
$896$	−0.397877			−0.0132922
$897$	−0.0382907	−	2.40697i	−0.00127849	−	0.0803662i
$898$	−9.42926			−0.314659
$899$	−0.681259	+	0.786215i	−0.0227213	+	0.0262217i
$900$	3.93563	−	2.52928i	0.131188	−	0.0843092i
$901$	−6.08796	−	42.3427i	−0.202819	−	1.41064i
$902$	5.34025	+	11.6935i	0.177811	+	0.389351i
$903$	−1.35839	+	9.44779i	−0.0452043	+	0.314403i
$904$	6.02880	−	1.77021i	0.200515	−	0.0588765i
$905$	20.1615	+	12.9570i	0.670191	+	0.430705i
$906$	21.2612	−	46.5556i	0.706357	−	1.54671i
$907$	−24.1820	−	7.10046i	−0.802949	−	0.235767i	−0.145590	−	0.989345i	$-0.546508\pi$
$907$	−24.1820	−	7.10046i	−0.802949	−	0.235767i	−0.657359	+	0.753578i	$0.728326\pi$
$908$	0.504523	+	0.582251i	0.0167432	+	0.0193227i
$909$	42.4794	+	49.0238i	1.40895	+	1.62602i
$910$	0.140826	+	0.0413501i	0.00466832	+	0.00137074i
$911$	12.0923	−	26.4784i	0.400636	−	0.877270i	−0.596570	−	0.802561i	$-0.703470\pi$
$911$	12.0923	−	26.4784i	0.400636	−	0.877270i	0.997205	−	0.0747088i	$-0.0238027\pi$
$912$	−7.72950	−	4.96745i	−0.255949	−	0.164489i
$913$	41.2501	−	12.1121i	1.36518	−	0.400853i
$914$	4.41651	−	30.7175i	0.146085	−	1.01604i
$915$	−35.4647	−	77.6569i	−1.17243	−	2.56726i
$916$	2.74243	+	19.0740i	0.0906123	+	0.630222i
$917$	−1.74112	+	1.11895i	−0.0574967	+	0.0369509i
$918$	30.7072	−	35.4380i	1.01349	−	1.16963i
$919$	22.9832			0.758147			0.379074	−	0.925367i	$-0.376243\pi$
$919$	22.9832			0.758147			0.379074	+	0.925367i	$0.376243\pi$
$920$	10.4250	+	4.56196i	0.343703	+	0.150403i
$921$	82.3750			2.71435
$922$	21.6180	−	24.9485i	0.711952	−	0.821637i
$923$	0.0466477	−	0.0299786i	0.00153543	−	0.000986759i
$924$	0.586997	+	4.08265i	0.0193108	+	0.134309i
$925$	1.68082	+	3.68048i	0.0552650	+	0.121014i
$926$	2.51472	−	17.4903i	0.0826389	−	0.574766i
$927$	−30.5135	+	8.95957i	−1.00219	+	0.294271i
$928$	0.318599	+	0.204751i	0.0104585	+	0.00672128i
$929$	−7.30034	+	15.9855i	−0.239516	+	0.524467i	−0.990771	−	0.135545i	$-0.956722\pi$
$929$	−7.30034	+	15.9855i	−0.239516	+	0.524467i	0.751255	+	0.660012i	$0.229449\pi$
$930$	20.1918	+	5.92884i	0.662115	+	0.194414i
$931$	12.7499	+	14.7142i	0.417863	+	0.482239i
$932$	−5.54500	−	6.39927i	−0.181632	−	0.209615i
$933$	31.1525	+	9.14719i	1.01989	+	0.299466i
$934$	−4.61331	+	10.1017i	−0.150952	+	0.330539i
$935$	−21.0371	−	13.5198i	−0.687988	−	0.442143i
$936$	−1.10750	+	0.325192i	−0.0361998	+	0.0106292i
$937$	−2.69350	+	18.7337i	−0.0879930	+	0.612004i	0.897337	+	0.441346i	$0.145499\pi$
$937$	−2.69350	+	18.7337i	−0.0879930	+	0.612004i	−0.985330	+	0.170659i	$0.945410\pi$
$938$	−1.38964	−	3.04290i	−0.0453735	−	0.0993541i
$939$	−1.61601	−	11.2396i	−0.0527367	−	0.366791i
$940$	5.92881	−	3.81021i	0.193376	−	0.124275i
$941$	26.6714	−	30.7804i	0.869463	−	1.00341i	−0.130465	−	0.991453i	$-0.541647\pi$
$941$	26.6714	−	30.7804i	0.869463	−	1.00341i	0.999928	−	0.0119609i	$-0.00380737\pi$
$942$	−67.3862			−2.19556
$943$	−18.9602	+	3.03463i	−0.617429	+	0.0988212i
$944$	8.64612			0.281407
$945$	−8.83191	+	10.1926i	−0.287302	+	0.331564i
$946$	−20.0692	+	12.8977i	−0.652505	+	0.419340i
$947$	2.24956	+	15.6460i	0.0731009	+	0.508428i	0.993170	+	0.116673i	$0.0372229\pi$
$947$	2.24956	+	15.6460i	0.0731009	+	0.508428i	−0.920069	+	0.391755i	$0.871868\pi$
$948$	10.1109	+	22.1399i	0.328388	+	0.719070i
$949$	−0.124695	+	0.867272i	−0.00404777	+	0.0281528i
$950$	−1.72050	+	0.505185i	−0.0558204	+	0.0163904i
$951$	94.9304	+	61.0080i	3.07833	+	1.97832i
$952$	−0.542532	+	1.18798i	−0.0175836	+	0.0385026i
$953$	15.5810	+	4.57498i	0.504717	+	0.148198i	0.524172	−	0.851613i	$-0.324375\pi$
$953$	15.5810	+	4.57498i	0.504717	+	0.148198i	−0.0194551	+	0.999811i	$0.506193\pi$
$954$	−63.3646	−	73.1267i	−2.05151	−	2.36756i
$955$	−3.99424	−	4.60960i	−0.129251	−	0.149163i
$956$	−7.62471	−	2.23882i	−0.246601	−	0.0724085i
$957$	1.63093	−	3.57124i	0.0527205	−	0.115442i
$958$	−8.66804	−	5.57061i	−0.280052	−	0.179978i
$959$	−0.191295	+	0.0561693i	−0.00617724	+	0.00181380i
$960$	1.09028	−	7.58305i	0.0351886	−	0.244742i
$961$	−9.74333	−	21.3349i	−0.314301	−	0.688223i
$962$	−0.142071	−	0.988122i	−0.00458054	−	0.0318583i
$963$	−112.504	+	72.3018i	−3.62538	+	2.32989i
$964$	−8.80435	+	10.1608i	−0.283569	+	0.327256i
$965$	−53.5941			−1.72525
$966$	−6.11133	−	0.779673i	−0.196629	−	0.0250856i
$967$	−22.9012			−0.736453			−0.368226	−	0.929736i	$-0.620035\pi$
$967$	−22.9012			−0.736453			−0.368226	+	0.929736i	$0.620035\pi$
$968$	0.452533	−	0.522250i	0.0145449	−	0.0167858i
$969$	−25.3714	+	16.3052i	−0.815048	+	0.523800i
$970$	0.888107	+	6.17692i	0.0285154	+	0.198329i
$971$	11.1988	+	24.5220i	0.359388	+	0.786949i	0.999821	+	0.0189350i	$0.00602757\pi$
$971$	11.1988	+	24.5220i	0.359388	+	0.786949i	−0.640433	+	0.768014i	$0.721245\pi$
$972$	4.85990	−	33.8013i	0.155881	−	1.08418i
$973$	−6.01309	+	1.76560i	−0.192771	+	0.0566026i
$974$	−9.49662	−	6.10311i	−0.304291	−	0.195556i
$975$	−0.131389	+	0.287703i	−0.00420783	+	0.00921386i
$976$	−10.6922	−	3.13953i	−0.342251	−	0.100494i
$977$	−18.1607	−	20.9585i	−0.581012	−	0.670523i	0.386810	−	0.922159i	$-0.373577\pi$
$977$	−18.1607	−	20.9585i	−0.581012	−	0.670523i	−0.967822	+	0.251636i	$0.919031\pi$
$978$	50.2876	+	58.0350i	1.60802	+	1.85575i
$979$	6.65651	+	1.95453i	0.212743	+	0.0624670i
$980$	−6.74379	+	14.7668i	−0.215423	+	0.471710i
$981$	−59.5649	−	38.2800i	−1.90176	−	1.22219i
$982$	8.78698	−	2.58009i	0.280404	−	0.0823339i
$983$	−6.36764	+	44.2879i	−0.203096	+	1.41256i	0.591930	+	0.805989i	$0.298366\pi$
$983$	−6.36764	+	44.2879i	−0.203096	+	1.41256i	−0.795026	+	0.606575i	$0.792543\pi$
$984$	5.37010	+	11.7589i	0.171193	+	0.374860i
$985$	−0.172987	−	1.20315i	−0.00551183	−	0.0383356i
$986$	1.04577	−	0.672079i	0.0333043	−	0.0214033i
$987$	−2.49867	+	2.88362i	−0.0795335	+	0.0917866i
$988$	0.442413			0.0140750
$989$	−10.5817	−	34.0261i	−0.336479	−	1.08197i
$990$	−56.5635			−1.79771
$991$	−1.42071	+	1.63959i	−0.0451305	+	0.0520833i	−0.777866	−	0.628430i	$-0.783698\pi$
$991$	−1.42071	+	1.63959i	−0.0451305	+	0.0520833i	0.732736	+	0.680514i	$0.238243\pi$
$992$	2.31086	−	1.48510i	0.0733697	−	0.0471519i
$993$	1.08273	+	7.53054i	0.0343593	+	0.238974i
$994$	−0.0589525	−	0.129088i	−0.00186986	−	0.00409442i
$995$	0.444195	−	3.08944i	0.0140819	−	0.0979419i
$996$	41.4807	−	12.1798i	1.31437	−	0.385933i
$997$	9.17431	+	5.89597i	0.290553	+	0.186727i	0.677795	−	0.735251i	$-0.262936\pi$
$997$	9.17431	+	5.89597i	0.290553	+	0.186727i	−0.387242	+	0.921978i	$0.626572\pi$
$998$	−12.9713	+	28.4033i	−0.410600	+	0.899090i
$999$	88.0159	+	25.8438i	2.78470	+	0.817662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.2.c.a.39.1	yes	10
3.2	odd	2		414.2.i.f.361.1		10
4.3	odd	2		368.2.m.b.177.1		10
23.6	even	11		1058.2.a.m.1.1		5
23.13	even	11	inner	46.2.c.a.13.1	✓	10
23.17	odd	22		1058.2.a.l.1.1		5
69.17	even	22		9522.2.a.bu.1.3		5
69.29	odd	22		9522.2.a.bp.1.3		5
69.59	odd	22		414.2.i.f.289.1		10
92.59	odd	22		368.2.m.b.289.1		10
92.63	even	22		8464.2.a.bw.1.5		5
92.75	odd	22		8464.2.a.bx.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.13.1	✓	10	23.13	even	11	inner
46.2.c.a.39.1	yes	10	1.1	even	1	trivial
368.2.m.b.177.1		10	4.3	odd	2
368.2.m.b.289.1		10	92.59	odd	22
414.2.i.f.289.1		10	69.59	odd	22
414.2.i.f.361.1		10	3.2	odd	2
1058.2.a.l.1.1		5	23.17	odd	22
1058.2.a.m.1.1		5	23.6	even	11
8464.2.a.bw.1.5		5	92.63	even	22
8464.2.a.bx.1.5		5	92.75	odd	22
9522.2.a.bp.1.3		5	69.29	odd	22
9522.2.a.bu.1.3		5	69.17	even	22

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:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-2.71616 + 1.74557i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.985691 + 2.15836i) q^{5} +(0.459493 - 3.19584i) q^{6} +(0.381761 - 0.112095i) q^{7} +(0.841254 + 0.540641i) q^{8} +(3.08427 - 6.75361i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-2.71616 + 1.74557i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.985691 + 2.15836i) q^{5} +(0.459493 - 3.19584i) q^{6} +(0.381761 - 0.112095i) q^{7} +(0.841254 + 0.540641i) q^{8} +(3.08427 - 6.75361i) q^{9} +(-2.27667 - 0.668491i) q^{10} +(2.10260 + 2.42653i) q^{11} +(2.11435 + 2.44009i) q^{12} +(-0.149167 - 0.0437995i) q^{13} +(-0.165284 + 0.361922i) q^{14} +(-6.44487 - 4.14187i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.467137 + 3.24901i) q^{17} +(3.08427 + 6.75361i) q^{18} +(-0.404992 - 2.81678i) q^{19} +(1.99611 - 1.28282i) q^{20} +(-0.841254 + 0.970858i) q^{21} -3.21076 q^{22} +(1.27778 - 4.62248i) q^{23} -3.22871 q^{24} +(-0.412635 + 0.476206i) q^{25} +(0.130785 - 0.0840506i) q^{26} +(2.03305 + 14.1402i) q^{27} +(-0.165284 - 0.361922i) q^{28} +(-0.0538974 + 0.374864i) q^{29} +(7.35070 - 2.15836i) q^{30} +(2.31086 + 1.48510i) q^{31} +(0.415415 - 0.909632i) q^{32} +(-9.94668 - 2.92061i) q^{33} +(-2.14953 - 2.48069i) q^{34} +(0.618239 + 0.713486i) q^{35} +(-7.12381 - 2.09174i) q^{36} +(2.66750 - 5.84100i) q^{37} +(2.39399 + 1.53853i) q^{38} +(0.481618 - 0.141416i) q^{39} +(-0.337683 + 2.34863i) q^{40} +(-1.66324 - 3.64198i) q^{41} +(-0.182822 - 1.27155i) q^{42} +(6.25061 - 4.01702i) q^{43} +(2.10260 - 2.42653i) q^{44} +17.6169 q^{45} +(2.65667 + 3.99276i) q^{46} +2.97017 q^{47} +(2.11435 - 2.44009i) q^{48} +(-5.75560 + 3.69890i) q^{49} +(-0.0896742 - 0.623698i) q^{50} +(-4.40255 - 9.64025i) q^{51} +(-0.0221250 + 0.153882i) q^{52} +(-12.5046 + 3.67168i) q^{53} +(-12.0178 - 7.72337i) q^{54} +(-3.16481 + 6.92998i) q^{55} +(0.381761 + 0.112095i) q^{56} +(6.01691 + 6.94388i) q^{57} +(-0.248008 - 0.286217i) q^{58} +(-8.29589 - 2.43589i) q^{59} +(-3.18251 + 6.96872i) q^{60} +(9.37463 + 6.02471i) q^{61} +(-2.63565 + 0.773896i) q^{62} +(0.420407 - 2.92399i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.0524978 - 0.365130i) q^{65} +(8.72094 - 5.60461i) q^{66} +(-5.50581 + 6.35404i) q^{67} +3.28242 q^{68} +(4.59821 + 14.7858i) q^{69} -0.944078 q^{70} +(-0.233571 + 0.269556i) q^{71} +(6.24593 - 4.01402i) q^{72} +(-0.802078 - 5.57857i) q^{73} +(2.66750 + 5.84100i) q^{74} +(0.289532 - 2.01374i) q^{75} +(-2.73047 + 0.801739i) q^{76} +(1.07469 + 0.690662i) q^{77} +(-0.208518 + 0.456590i) q^{78} +(7.23307 + 2.12382i) q^{79} +(-1.55384 - 1.79323i) q^{80} +(-15.6186 - 18.0249i) q^{81} +(3.84161 + 1.12800i) q^{82} +(5.56234 - 12.1798i) q^{83} +(1.08070 + 0.694523i) q^{84} +(-7.47299 + 2.19427i) q^{85} +(-1.05742 + 7.35448i) q^{86} +(-0.507959 - 1.11227i) q^{87} +(0.456938 + 3.17808i) q^{88} +(1.81771 - 1.16817i) q^{89} +(-11.5366 + 13.3139i) q^{90} -0.0618559 q^{91} +(-4.75727 - 0.606924i) q^{92} -8.86900 q^{93} +(-1.94505 + 2.24471i) q^{94} +(5.68043 - 3.65059i) q^{95} +(0.459493 + 3.19584i) q^{96} +(-1.09254 - 2.39234i) q^{97} +(0.973675 - 6.77206i) q^{98} +(22.8728 - 6.71606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9}+O(q^{10}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9	\( 10 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} + 3 q^{7} - q^{8} + 9 q^{9} - 6 q^{10} - 12 q^{11} + 7 q^{12} - 14 q^{13} + 3 q^{14} - 13 q^{15} - q^{16} + 15 q^{17} + 9 q^{18} + 2 q^{19} + 5 q^{20} + q^{21} + 10 q^{22} - q^{23} - 4 q^{24} + 13 q^{25} - 3 q^{26} + 26 q^{27} + 3 q^{28} - 8 q^{29} + 20 q^{30} - 21 q^{31} - q^{32} - 15 q^{33} - 7 q^{34} + 7 q^{35} - 13 q^{36} + 28 q^{37} - 9 q^{38} - 12 q^{39} - 6 q^{40} - 31 q^{41} - 10 q^{42} + 11 q^{43} - 12 q^{44} + 10 q^{45} - 12 q^{46} + 18 q^{47} + 7 q^{48} - 24 q^{49} + 2 q^{50} - 17 q^{51} + 8 q^{52} - 21 q^{53} - 29 q^{54} + 5 q^{55} + 3 q^{56} + 19 q^{57} - 8 q^{58} - 5 q^{59} - 13 q^{60} + 37 q^{61} + q^{62} + 17 q^{63} - q^{64} + 37 q^{65} + 29 q^{66} - 13 q^{67} + 26 q^{68} - 15 q^{69} + 18 q^{70} + 49 q^{71} + 20 q^{72} - 8 q^{73} + 28 q^{74} + 8 q^{75} - 20 q^{76} - 8 q^{77} + 10 q^{78} + 8 q^{79} + 5 q^{80} - 11 q^{81} + 2 q^{82} - 7 q^{83} + q^{84} - 42 q^{85} + 22 q^{86} - 21 q^{87} - q^{88} - 13 q^{89} - 45 q^{90} - 24 q^{91} - 23 q^{92} - 40 q^{93} - 37 q^{94} - 10 q^{95} - 4 q^{96} - 32 q^{97} - 24 q^{98} + 20 q^{99}+O(q^{100}) \) 10 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 + 3 * q^7 - q^8 + 9 * q^9 - 6 * q^10 - 12 * q^11 + 7 * q^12 - 14 * q^13 + 3 * q^14 - 13 * q^15 - q^16 + 15 * q^17 + 9 * q^18 + 2 * q^19 + 5 * q^20 + q^21 + 10 * q^22 - q^23 - 4 * q^24 + 13 * q^25 - 3 * q^26 + 26 * q^27 + 3 * q^28 - 8 * q^29 + 20 * q^30 - 21 * q^31 - q^32 - 15 * q^33 - 7 * q^34 + 7 * q^35 - 13 * q^36 + 28 * q^37 - 9 * q^38 - 12 * q^39 - 6 * q^40 - 31 * q^41 - 10 * q^42 + 11 * q^43 - 12 * q^44 + 10 * q^45 - 12 * q^46 + 18 * q^47 + 7 * q^48 - 24 * q^49 + 2 * q^50 - 17 * q^51 + 8 * q^52 - 21 * q^53 - 29 * q^54 + 5 * q^55 + 3 * q^56 + 19 * q^57 - 8 * q^58 - 5 * q^59 - 13 * q^60 + 37 * q^61 + q^62 + 17 * q^63 - q^64 + 37 * q^65 + 29 * q^66 - 13 * q^67 + 26 * q^68 - 15 * q^69 + 18 * q^70 + 49 * q^71 + 20 * q^72 - 8 * q^73 + 28 * q^74 + 8 * q^75 - 20 * q^76 - 8 * q^77 + 10 * q^78 + 8 * q^79 + 5 * q^80 - 11 * q^81 + 2 * q^82 - 7 * q^83 + q^84 - 42 * q^85 + 22 * q^86 - 21 * q^87 - q^88 - 13 * q^89 - 45 * q^90 - 24 * q^91 - 23 * q^92 - 40 * q^93 - 37 * q^94 - 10 * q^95 - 4 * q^96 - 32 * q^97 - 24 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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