LMFDB - Embedded newform 961.2.g.j.547.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			547.2
Root			$0.176392i$ of defining polynomial
Character	$\chi$	$=$	961.547
Dual form			961.2.g.j.448.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.380762 + 1.17187i) q^{2} +(-1.38843 - 1.54201i) q^{3} +(0.389745 - 0.283166i) q^{4} +(0.772811 + 1.33855i) q^{5} +(1.27836 - 2.21419i) q^{6} +(0.397601 + 3.78292i) q^{7} +(2.47393 + 1.79742i) q^{8} +(-0.136464 + 1.29837i) q^{9} +O(q^{10})$	\(q+(0.380762 + 1.17187i) q^{2} +(-1.38843 - 1.54201i) q^{3} +(0.389745 - 0.283166i) q^{4} +(0.772811 + 1.33855i) q^{5} +(1.27836 - 2.21419i) q^{6} +(0.397601 + 3.78292i) q^{7} +(2.47393 + 1.79742i) q^{8} +(-0.136464 + 1.29837i) q^{9} +(-1.27434 + 1.41530i) q^{10} +(3.43632 + 1.52995i) q^{11} +(-0.977778 - 0.207833i) q^{12} +(-2.57748 + 0.547860i) q^{13} +(-4.28168 + 1.90633i) q^{14} +(0.991057 - 3.05016i) q^{15} +(-0.866611 + 2.66715i) q^{16} +(-3.44803 + 1.53516i) q^{17} +(-1.57347 + 0.334452i) q^{18} +(-5.96505 - 1.26791i) q^{19} +(0.680232 + 0.302859i) q^{20} +(5.28125 - 5.86542i) q^{21} +(-0.484473 + 4.60946i) q^{22} +(0.736082 + 0.534795i) q^{23} +(-0.663250 - 6.31040i) q^{24} +(1.30553 - 2.26124i) q^{25} +(-1.62343 - 2.81186i) q^{26} +(-2.84451 + 2.06665i) q^{27} +(1.22616 + 1.36179i) q^{28} +(2.10397 + 6.47535i) q^{29} +3.95173 q^{30} +2.66037 q^{32} +(-2.41190 - 7.42306i) q^{33} +(-3.11188 - 3.45610i) q^{34} +(-4.75635 + 3.45569i) q^{35} +(0.314468 + 0.544675i) q^{36} +(-0.907032 + 1.57103i) q^{37} +(-0.785445 - 7.47301i) q^{38} +(4.42345 + 3.21383i) q^{39} +(-0.494046 + 4.70054i) q^{40} +(0.225594 - 0.250547i) q^{41} +(8.88438 + 3.95558i) q^{42} +(3.79912 + 0.807528i) q^{43} +(1.77252 - 0.376761i) q^{44} +(-1.84339 + 0.820730i) q^{45} +(-0.346435 + 1.06622i) q^{46} +(-0.367467 + 1.13095i) q^{47} +(5.31600 - 2.36684i) q^{48} +(-7.30537 + 1.55280i) q^{49} +(3.14696 + 0.668907i) q^{50} +(7.15458 + 3.18542i) q^{51} +(-0.849425 + 0.943382i) q^{52} +(-0.245028 + 2.33128i) q^{53} +(-3.50492 - 2.54647i) q^{54} +(0.607718 + 5.78205i) q^{55} +(-5.81584 + 10.0733i) q^{56} +(6.32692 + 10.9586i) q^{57} +(-6.78713 + 4.93114i) q^{58} +(5.20505 + 5.78080i) q^{59} +(-0.477443 - 1.46942i) q^{60} +2.72343 q^{61} -4.96588 q^{63} +(2.74619 + 8.45191i) q^{64} +(-2.72524 - 3.02669i) q^{65} +(7.78047 - 5.65284i) q^{66} +(3.71059 + 6.42693i) q^{67} +(-0.909147 + 1.57469i) q^{68} +(-0.197340 - 1.87757i) q^{69} +(-5.86065 - 4.25801i) q^{70} +(0.532905 - 5.07025i) q^{71} +(-2.67131 + 2.96679i) q^{72} +(-4.92560 - 2.19302i) q^{73} +(-2.18639 - 0.464732i) q^{74} +(-5.29947 + 1.12644i) q^{75} +(-2.68388 + 1.19494i) q^{76} +(-4.42139 + 13.6076i) q^{77} +(-2.08189 + 6.40740i) q^{78} +(8.89540 - 3.96049i) q^{79} +(-4.23984 + 0.901206i) q^{80} +(10.9672 + 2.33114i) q^{81} +(0.379505 + 0.168967i) q^{82} +(5.61745 - 6.23881i) q^{83} +(0.397451 - 3.78149i) q^{84} +(-4.71957 - 3.42897i) q^{85} +(0.500247 + 4.75953i) q^{86} +(7.06383 - 12.2349i) q^{87} +(5.75127 + 9.96149i) q^{88} +(4.12243 - 2.99512i) q^{89} +(-1.66368 - 1.84770i) q^{90} +(-3.09732 - 9.53258i) q^{91} +0.438320 q^{92} -1.46523 q^{94} +(-2.91270 - 8.96437i) q^{95} +(-3.69374 - 4.10231i) q^{96} +(-8.82979 + 6.41522i) q^{97} +(-4.60129 - 7.96966i) q^{98} +(-2.45537 + 4.25283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9	\( 16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} + 7 q^{11} + 10 q^{12} - 8 q^{13} - 21 q^{14} - 14 q^{15} - 2 q^{16} - 9 q^{17} + 12 q^{18} - 29 q^{19} - 8 q^{20} + 6 q^{21} + 21 q^{22} - q^{23} + 5 q^{24} - 13 q^{25} - 9 q^{26} - 9 q^{27} + 45 q^{28} + 14 q^{29} + 22 q^{30} - 42 q^{32} - 13 q^{33} + 17 q^{34} - 9 q^{35} + q^{36} + 8 q^{37} + 23 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 51 q^{42} + 37 q^{43} + 6 q^{44} - 70 q^{45} - 34 q^{46} + 14 q^{47} - 4 q^{48} - 43 q^{49} + 3 q^{50} + 33 q^{51} + 46 q^{52} + 9 q^{53} + 46 q^{54} - 8 q^{55} - 30 q^{56} + 17 q^{57} + 15 q^{58} - 11 q^{59} + 75 q^{60} + 60 q^{61} - 46 q^{63} + 23 q^{64} - 18 q^{65} - 30 q^{66} + 13 q^{67} - 30 q^{68} - 37 q^{69} + 12 q^{70} + 31 q^{71} - 38 q^{72} + 13 q^{73} - 43 q^{74} + 17 q^{75} - 12 q^{76} - 18 q^{77} - 15 q^{78} + 12 q^{79} + 6 q^{80} - 22 q^{81} - q^{82} - 44 q^{83} - 23 q^{84} - 37 q^{85} - 19 q^{86} + 15 q^{87} + 17 q^{88} - q^{89} + 7 q^{90} - 8 q^{91} + 64 q^{92} + 44 q^{94} - 22 q^{95} - 8 q^{96} + 3 q^{97} - 10 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 + 7 * q^11 + 10 * q^12 - 8 * q^13 - 21 * q^14 - 14 * q^15 - 2 * q^16 - 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 + 6 * q^21 + 21 * q^22 - q^23 + 5 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 45 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 17 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 51 * q^42 + 37 * q^43 + 6 * q^44 - 70 * q^45 - 34 * q^46 + 14 * q^47 - 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 + 46 * q^52 + 9 * q^53 + 46 * q^54 - 8 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 - 11 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 - 18 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 + 13 * q^73 - 43 * q^74 + 17 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 + 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 - 44 * q^83 - 23 * q^84 - 37 * q^85 - 19 * q^86 + 15 * q^87 + 17 * q^88 - q^89 + 7 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	0.380762	+	1.17187i	0.269240	+	0.828634i	0.990686	+	0.136164i	$0.0434774\pi$
$2$	0.380762	+	1.17187i	0.269240	+	0.828634i	−0.721447	+	0.692470i	$0.756523\pi$
$3$	−1.38843	−	1.54201i	−0.801610	−	0.890278i	0.194271	−	0.980948i	$-0.437766\pi$
$3$	−1.38843	−	1.54201i	−0.801610	−	0.890278i	−0.995881	+	0.0906699i	$0.971099\pi$
$4$	0.389745	−	0.283166i	0.194873	−	0.141583i
$5$	0.772811	+	1.33855i	0.345612	+	0.598617i	0.985465	−	0.169880i	$-0.0543381\pi$
$5$	0.772811	+	1.33855i	0.345612	+	0.598617i	−0.639853	+	0.768497i	$0.721005\pi$
$6$	1.27836	−	2.21419i	0.521890	−	0.903939i
$7$	0.397601	+	3.78292i	0.150279	+	1.42981i	0.766504	+	0.642239i	$0.221995\pi$
$7$	0.397601	+	3.78292i	0.150279	+	1.42981i	−0.616225	+	0.787570i	$0.711339\pi$
$8$	2.47393	+	1.79742i	0.874666	+	0.635482i
$9$	−0.136464	+	1.29837i	−0.0454880	+	0.432789i
$10$	−1.27434	+	1.41530i	−0.402982	+	0.447557i
$11$	3.43632	+	1.52995i	1.03609	+	0.461297i	0.853062	−	0.521810i	$-0.174743\pi$
$11$	3.43632	+	1.52995i	1.03609	+	0.461297i	0.183029	+	0.983108i	$0.441410\pi$
$12$	−0.977778	−	0.207833i	−0.282260	−	0.0599963i
$13$	−2.57748	+	0.547860i	−0.714865	+	0.151949i	−0.550966	−	0.834528i	$-0.685740\pi$
$13$	−2.57748	+	0.547860i	−0.714865	+	0.151949i	−0.163899	+	0.986477i	$0.552407\pi$
$14$	−4.28168	+	1.90633i	−1.14433	+	0.509488i
$15$	0.991057	−	3.05016i	0.255890	−	0.787548i
$16$	−0.866611	+	2.66715i	−0.216653	+	0.666789i
$17$	−3.44803	+	1.53516i	−0.836270	+	0.372332i	−0.779766	−	0.626071i	$-0.784662\pi$
$17$	−3.44803	+	1.53516i	−0.836270	+	0.372332i	−0.0565041	+	0.998402i	$0.517995\pi$
$18$	−1.57347	+	0.334452i	−0.370871	+	0.0788311i
$19$	−5.96505	−	1.26791i	−1.36848	−	0.290879i	−0.535663	−	0.844432i	$-0.679938\pi$
$19$	−5.96505	−	1.26791i	−1.36848	−	0.290879i	−0.832814	+	0.553553i	$0.813272\pi$
$20$	0.680232	+	0.302859i	0.152104	+	0.0677212i
$21$	5.28125	−	5.86542i	1.15246	−	1.27994i
$22$	−0.484473	+	4.60946i	−0.103290	+	0.982739i
$23$	0.736082	+	0.534795i	0.153484	+	0.111512i	0.661877	−	0.749613i	$-0.269760\pi$
$23$	0.736082	+	0.534795i	0.153484	+	0.111512i	−0.508393	+	0.861125i	$0.669760\pi$
$24$	−0.663250	−	6.31040i	−0.135385	−	1.28811i
$25$	1.30553	−	2.26124i	0.261105	−	0.452247i
$26$	−1.62343	−	2.81186i	−0.318380	−	0.551450i
$27$	−2.84451	+	2.06665i	−0.547425	+	0.397728i
$28$	1.22616	+	1.36179i	0.231722	+	0.257354i
$29$	2.10397	+	6.47535i	0.390697	+	1.20244i	0.932262	+	0.361784i	$0.117832\pi$
$29$	2.10397	+	6.47535i	0.390697	+	1.20244i	−0.541565	+	0.840659i	$0.682168\pi$
$30$	3.95173			0.721485
$31$		0			0
$31$		0			0
$32$	2.66037			0.470292
$33$	−2.41190	−	7.42306i	−0.419858	−	1.29219i
$34$	−3.11188	−	3.45610i	−0.533684	−	0.592716i
$35$	−4.75635	+	3.45569i	−0.803970	+	0.584119i
$36$	0.314468	+	0.544675i	0.0524114	+	0.0907792i
$37$	−0.907032	+	1.57103i	−0.149115	+	0.258275i	−0.930901	−	0.365272i	$-0.880976\pi$
$37$	−0.907032	+	1.57103i	−0.149115	+	0.258275i	0.781786	+	0.623547i	$0.214309\pi$
$38$	−0.785445	−	7.47301i	−0.127416	−	1.21228i
$39$	4.42345	+	3.21383i	0.708320	+	0.514624i
$40$	−0.494046	+	4.70054i	−0.0781156	+	0.743220i
$41$	0.225594	−	0.250547i	0.0352318	−	0.0391289i	−0.725271	−	0.688463i	$-0.758286\pi$
$41$	0.225594	−	0.250547i	0.0352318	−	0.0391289i	0.760503	+	0.649334i	$0.224952\pi$
$42$	8.88438	+	3.95558i	1.37089	+	0.610360i
$43$	3.79912	+	0.807528i	0.579360	+	0.123147i	0.488265	−	0.872695i	$-0.337630\pi$
$43$	3.79912	+	0.807528i	0.579360	+	0.123147i	0.0910953	+	0.995842i	$0.470963\pi$
$44$	1.77252	−	0.376761i	0.267218	−	0.0567989i
$45$	−1.84339	+	0.820730i	−0.274796	+	0.122347i
$46$	−0.346435	+	1.06622i	−0.0510791	+	0.157205i
$47$	−0.367467	+	1.13095i	−0.0536005	+	0.164965i	−0.974273	−	0.225370i	$-0.927641\pi$
$47$	−0.367467	+	1.13095i	−0.0536005	+	0.164965i	0.920673	+	0.390335i	$0.127641\pi$
$48$	5.31600	−	2.36684i	0.767298	−	0.341623i
$49$	−7.30537	+	1.55280i	−1.04362	+	0.221829i
$50$	3.14696	+	0.668907i	0.445047	+	0.0945977i
$51$	7.15458	+	3.18542i	1.00184	+	0.446048i
$52$	−0.849425	+	0.943382i	−0.117794	+	0.130824i
$53$	−0.245028	+	2.33128i	−0.0336572	+	0.320227i	0.964720	+	0.263278i	$0.0848037\pi$
$53$	−0.245028	+	2.33128i	−0.0336572	+	0.320227i	−0.998377	+	0.0569483i	$0.981863\pi$
$54$	−3.50492	−	2.54647i	−0.476959	−	0.346531i
$55$	0.607718	+	5.78205i	0.0819446	+	0.779651i
$56$	−5.81584	+	10.0733i	−0.777175	+	1.34611i
$57$	6.32692	+	10.9586i	0.838022	+	1.45150i
$58$	−6.78713	+	4.93114i	−0.891194	+	0.647490i
$59$	5.20505	+	5.78080i	0.677640	+	0.752596i	0.979651	−	0.200709i	$-0.0643245\pi$
$59$	5.20505	+	5.78080i	0.677640	+	0.752596i	−0.302011	+	0.953305i	$0.597658\pi$
$60$	−0.477443	−	1.46942i	−0.0616377	−	0.189701i
$61$	2.72343			0.348700			0.174350	−	0.984684i	$-0.444218\pi$
$61$	2.72343			0.348700			0.174350	+	0.984684i	$0.444218\pi$
$62$		0			0
$63$	−4.96588			−0.625642
$64$	2.74619	+	8.45191i	0.343274	+	1.05649i
$65$	−2.72524	−	3.02669i	−0.338025	−	0.375415i
$66$	7.78047	−	5.65284i	0.957709	−	0.695817i
$67$	3.71059	+	6.42693i	0.453321	+	0.785175i	0.998590	−	0.0530864i	$-0.0169059\pi$
$67$	3.71059	+	6.42693i	0.453321	+	0.785175i	−0.545269	+	0.838261i	$0.683573\pi$
$68$	−0.909147	+	1.57469i	−0.110250	+	0.190959i
$69$	−0.197340	−	1.87757i	−0.0237570	−	0.226033i
$70$	−5.86065	−	4.25801i	−0.700481	−	0.508929i
$71$	0.532905	−	5.07025i	0.0632442	−	0.601728i	−0.916299	−	0.400495i	$-0.868838\pi$
$71$	0.532905	−	5.07025i	0.0632442	−	0.601728i	0.979543	−	0.201234i	$-0.0644950\pi$
$72$	−2.67131	+	2.96679i	−0.314817	+	0.349640i
$73$	−4.92560	−	2.19302i	−0.576498	−	0.256674i	0.0977099	−	0.995215i	$-0.468848\pi$
$73$	−4.92560	−	2.19302i	−0.576498	−	0.256674i	−0.674208	+	0.738541i	$0.735515\pi$
$74$	−2.18639	−	0.464732i	−0.254163	−	0.0540240i
$75$	−5.29947	+	1.12644i	−0.611930	+	0.130070i
$76$	−2.68388	+	1.19494i	−0.307862	+	0.137069i
$77$	−4.42139	+	13.6076i	−0.503865	+	1.55074i
$78$	−2.08189	+	6.40740i	−0.235728	+	0.725495i
$79$	8.89540	−	3.96049i	1.00081	−	0.445590i	0.160115	−	0.987098i	$-0.448813\pi$
$79$	8.89540	−	3.96049i	1.00081	−	0.445590i	0.840695	+	0.541509i	$0.182147\pi$
$80$	−4.23984	+	0.901206i	−0.474029	+	0.100758i
$81$	10.9672	+	2.33114i	1.21857	+	0.259016i
$82$	0.379505	+	0.168967i	0.0419094	+	0.0186592i
$83$	5.61745	−	6.23881i	0.616595	−	0.684798i	−0.351268	−	0.936275i	$-0.614249\pi$
$83$	5.61745	−	6.23881i	0.616595	−	0.684798i	0.967863	+	0.251477i	$0.0809162\pi$
$84$	0.397451	−	3.78149i	0.0433654	−	0.412595i
$85$	−4.71957	−	3.42897i	−0.511909	−	0.371924i
$86$	0.500247	+	4.75953i	0.0539430	+	0.513234i
$87$	7.06383	−	12.2349i	0.757322	−	1.31172i
$88$	5.75127	+	9.96149i	0.613087	+	1.06190i
$89$	4.12243	−	2.99512i	0.436976	−	0.317482i	−0.347456	−	0.937696i	$-0.612954\pi$
$89$	4.12243	−	2.99512i	0.436976	−	0.317482i	0.784432	+	0.620214i	$0.212954\pi$
$90$	−1.66368	−	1.84770i	−0.175367	−	0.194765i
$91$	−3.09732	−	9.53258i	−0.324688	−	0.999285i
$92$	0.438320			0.0456980
$93$		0			0
$94$	−1.46523			−0.151127
$95$	−2.91270	−	8.96437i	−0.298837	−	0.919725i
$96$	−3.69374	−	4.10231i	−0.376991	−	0.418690i
$97$	−8.82979	+	6.41522i	−0.896530	+	0.651367i	−0.937572	−	0.347791i	$-0.886932\pi$
$97$	−8.82979	+	6.41522i	−0.896530	+	0.651367i	0.0410427	+	0.999157i	$0.486932\pi$
$98$	−4.60129	−	7.96966i	−0.464800	−	0.805057i
$99$	−2.45537	+	4.25283i	−0.246774	+	0.427426i
$100$	−0.131484	−	1.25099i	−0.0131484	−	0.125099i
$101$	0.322577	+	0.234366i	0.0320976	+	0.0233203i	0.603718	−	0.797198i	$-0.293685\pi$
$101$	0.322577	+	0.234366i	0.0320976	+	0.0233203i	−0.571621	+	0.820518i	$0.693685\pi$
$102$	−1.00869	+	9.59709i	−0.0998757	+	0.950253i
$103$	2.19261	−	2.43514i	0.216044	−	0.239941i	−0.625375	−	0.780324i	$-0.715054\pi$
$103$	2.19261	−	2.43514i	0.216044	−	0.239941i	0.841419	+	0.540383i	$0.181721\pi$
$104$	−7.36124	−	3.27743i	−0.721829	−	0.321379i
$105$	11.9326	+	2.53634i	1.16450	+	0.247522i
$106$	−2.82525	+	0.600525i	−0.274412	+	0.0583282i
$107$	2.88392	−	1.28401i	0.278799	−	0.124129i	−0.262574	−	0.964912i	$-0.584571\pi$
$107$	2.88392	−	1.28401i	0.278799	−	0.124129i	0.541373	+	0.840782i	$0.317905\pi$
$108$	−0.523425	+	1.61094i	−0.0503666	+	0.155013i
$109$	2.14959	−	6.61576i	0.205893	−	0.633675i	−0.793782	−	0.608202i	$-0.791891\pi$
$109$	2.14959	−	6.61576i	0.205893	−	0.633675i	0.999676	−	0.0254724i	$-0.00810899\pi$
$110$	−6.54439	+	2.91375i	−0.623983	+	0.277815i
$111$	3.68188	−	0.782608i	0.349469	−	0.0742819i
$112$	−10.4342	−	2.21786i	−0.985939	−	0.209568i
$113$	−13.9286	−	6.20143i	−1.31030	−	0.583381i	−0.371685	−	0.928359i	$-0.621220\pi$
$113$	−13.9286	−	6.20143i	−1.31030	−	0.583381i	−0.938611	+	0.344978i	$0.887886\pi$
$114$	−10.4329	+	11.5869i	−0.977130	+	1.08521i
$115$	−0.146996	+	1.39858i	−0.0137075	+	0.130418i
$116$	2.65362	+	1.92796i	0.246382	+	0.179007i
$117$	−0.359591	−	3.42128i	−0.0332442	−	0.316298i
$118$	−4.79243	+	8.30073i	−0.441179	+	0.764144i
$119$	−7.17834	−	12.4332i	−0.658037	−	1.13975i
$120$	7.93421	−	5.76454i	0.724291	−	0.526228i
$121$	2.10714	+	2.34021i	0.191558	+	0.212747i
$122$	1.03698	+	3.19150i	0.0938838	+	0.288945i
$123$	−0.699567			−0.0630778
$124$		0			0
$125$	11.7638			1.05219
$126$	−1.89082	−	5.81935i	−0.168448	−	0.518429i
$127$	13.5341	+	15.0311i	1.20096	+	1.33380i	0.928367	+	0.371666i	$0.121213\pi$
$127$	13.5341	+	15.0311i	1.20096	+	1.33380i	0.272589	+	0.962131i	$0.412120\pi$
$128$	−4.55428	+	3.30888i	−0.402545	+	0.292466i
$129$	−4.02960	−	6.97946i	−0.354786	−	0.614508i
$130$	2.50920	−	4.34607i	0.220072	−	0.381175i
$131$	−1.32242	−	12.5820i	−0.115540	−	1.09929i	−0.886602	−	0.462532i	$-0.846941\pi$
$131$	−1.32242	−	12.5820i	−0.115540	−	1.09929i	0.771062	−	0.636760i	$-0.219726\pi$
$132$	−3.04199	−	2.21013i	−0.264771	−	0.192367i
$133$	2.42470	−	23.0694i	0.210248	−	2.00037i
$134$	−6.11865	+	6.79545i	−0.528571	+	0.587037i
$135$	−4.96458	−	2.21038i	−0.427283	−	0.190239i
$136$	−11.2895	−	2.39966i	−0.968067	−	0.205769i
$137$	−9.66215	+	2.05375i	−0.825494	+	0.175464i	−0.601242	−	0.799067i	$-0.705327\pi$
$137$	−9.66215	+	2.05375i	−0.825494	+	0.175464i	−0.224252	+	0.974531i	$0.571994\pi$
$138$	2.12512	−	0.946163i	0.180902	−	0.0805427i
$139$	4.78945	−	14.7404i	0.406236	−	1.25026i	−0.513623	−	0.858016i	$-0.671697\pi$
$139$	4.78945	−	14.7404i	0.406236	−	1.25026i	0.919859	−	0.392249i	$-0.128303\pi$
$140$	−0.875229	+	2.69368i	−0.0739704	+	0.227657i
$141$	2.25413	−	1.00360i	0.189832	−	0.0845186i
$142$	6.14456	−	1.30607i	0.515640	−	0.109603i
$143$	−9.69526	−	2.06079i	−0.810758	−	0.172332i
$144$	−3.34469	−	1.48915i	−0.278724	−	0.124096i
$145$	−7.04160	+	7.82049i	−0.584773	+	0.649457i
$146$	0.694441	−	6.60716i	0.0574723	−	0.546813i
$147$	12.5374	+	9.10897i	1.03407	+	0.751295i
$148$	0.0913504	+	0.869141i	0.00750895	+	0.0714429i
$149$	7.62162	−	13.2010i	0.624388	−	1.08147i	−0.364271	−	0.931293i	$-0.618682\pi$
$149$	7.62162	−	13.2010i	0.624388	−	1.08147i	0.988659	−	0.150178i	$-0.0479848\pi$
$150$	−3.33787	−	5.78136i	−0.272536	−	0.472046i
$151$	−0.211823	+	0.153899i	−0.0172379	+	0.0125241i	−0.596371	−	0.802709i	$-0.703391\pi$
$151$	−0.211823	+	0.153899i	−0.0172379	+	0.0125241i	0.579133	+	0.815233i	$0.303391\pi$
$152$	−12.4782	−	13.8584i	−1.01211	−	1.12406i
$153$	−1.52267	−	4.68631i	−0.123101	−	0.378866i
$154$	−17.6298			−1.42065
$155$		0			0
$156$	2.63407			0.210894
$157$	4.92157	+	15.1470i	0.392784	+	1.20886i	0.930674	+	0.365850i	$0.119222\pi$
$157$	4.92157	+	15.1470i	0.392784	+	1.20886i	−0.537890	+	0.843015i	$0.680778\pi$
$158$	8.02819	+	8.91621i	0.638688	+	0.709335i
$159$	3.93506	−	2.85899i	0.312071	−	0.226733i
$160$	2.05597	+	3.56104i	0.162538	+	0.281525i
$161$	−1.73042	+	2.99717i	−0.136376	+	0.236210i
$162$	1.44410	+	13.7397i	0.113459	+	1.07949i
$163$	0.107741	+	0.0782785i	0.00843894	+	0.00613125i	0.591997	−	0.805940i	$-0.298340\pi$
$163$	0.107741	+	0.0782785i	0.00843894	+	0.00613125i	−0.583558	+	0.812072i	$0.698340\pi$
$164$	0.0169775	−	0.161530i	0.00132572	−	0.0126134i
$165$	8.07218	−	8.96507i	0.628419	−	0.697930i
$166$	9.44996	+	4.20739i	0.733459	+	0.326557i
$167$	−3.86249	−	0.820997i	−0.298888	−	0.0635307i	0.0560266	−	0.998429i	$-0.482157\pi$
$167$	−3.86249	−	0.820997i	−0.298888	−	0.0635307i	−0.354915	+	0.934899i	$0.615490\pi$
$168$	23.6080	−	5.01804i	1.82140	−	0.387150i
$169$	−5.53283	+	2.46338i	−0.425603	+	0.189491i
$170$	2.22125	−	6.83632i	0.170362	−	0.524322i
$171$	2.46023	−	7.57181i	0.188139	−	0.579031i
$172$	1.70935	−	0.761053i	0.130337	−	0.0580298i
$173$	14.1410	−	3.00577i	1.07512	−	0.228524i	0.363862	−	0.931453i	$-0.381458\pi$
$173$	14.1410	−	3.00577i	1.07512	−	0.228524i	0.711260	+	0.702929i	$0.248125\pi$
$174$	17.0273	+	3.61926i	1.29084	+	0.274376i
$175$	9.07316	+	4.03963i	0.685866	+	0.305367i
$176$	−7.05857	+	7.83933i	−0.532060	+	0.590912i
$177$	1.68718	−	16.0525i	0.126816	−	1.20658i
$178$	5.07954	+	3.69050i	0.380727	+	0.276615i
$179$	−1.85223	−	17.6228i	−0.138442	−	1.31719i	−0.814423	−	0.580272i	$-0.802946\pi$
$179$	−1.85223	−	17.6228i	−0.138442	−	1.31719i	0.675981	−	0.736919i	$-0.263720\pi$
$180$	−0.486049	+	0.841862i	−0.0362280	+	0.0627487i
$181$	−6.02958	−	10.4435i	−0.448175	−	0.776262i	0.550092	−	0.835104i	$-0.314593\pi$
$181$	−6.02958	−	10.4435i	−0.448175	−	0.776262i	−0.998267	+	0.0588418i	$0.981259\pi$
$182$	9.99155	−	7.25929i	0.740623	−	0.538094i
$183$	−3.78129	−	4.19955i	−0.279521	−	0.310440i
$184$	0.859766	+	2.64609i	0.0633828	+	0.195072i
$185$	−2.80386			−0.206144
$186$		0			0
$187$	−14.1973			−1.03821
$188$	0.177028	+	0.544835i	0.0129111	+	0.0397362i
$189$	−8.94897	−	9.93884i	−0.650942	−	0.722944i
$190$	9.39599	−	6.82658i	0.681656	−	0.495252i
$191$	−2.53576	−	4.39207i	−0.183481	−	0.317799i	0.759583	−	0.650411i	$-0.225403\pi$
$191$	−2.53576	−	4.39207i	−0.183481	−	0.317799i	−0.943064	+	0.332612i	$0.892070\pi$
$192$	9.22001	−	15.9695i	0.665397	−	1.15250i
$193$	2.09493	+	19.9320i	0.150797	+	1.43473i	0.764208	+	0.644970i	$0.223130\pi$
$193$	2.09493	+	19.9320i	0.150797	+	1.43473i	−0.613411	+	0.789764i	$0.710203\pi$
$194$	−10.8798	−	7.90466i	−0.781126	−	0.567521i
$195$	−0.883369	+	8.40469i	−0.0632593	+	0.601872i
$196$	−2.40753	+	2.67383i	−0.171966	+	0.190988i
$197$	−19.8316	−	8.82959i	−1.41294	−	0.629082i	−0.448597	−	0.893734i	$-0.648076\pi$
$197$	−19.8316	−	8.82959i	−1.41294	−	0.629082i	−0.964344	+	0.264652i	$0.914743\pi$
$198$	−5.91866	−	1.25805i	−0.420621	−	0.0894057i
$199$	14.8341	−	3.15309i	1.05156	−	0.223516i	0.350460	−	0.936578i	$-0.386025\pi$
$199$	14.8341	−	3.15309i	1.05156	−	0.223516i	0.701102	+	0.713061i	$0.252692\pi$
$200$	7.29416	−	3.24757i	0.515775	−	0.229638i
$201$	4.75848	−	14.6451i	0.335637	−	1.03299i
$202$	−0.151820	+	0.467255i	−0.0106820	+	0.0328759i
$203$	−23.6592	+	10.5338i	−1.66055	+	0.739325i
$204$	3.69047	−	0.784433i	0.258384	−	0.0549213i
$205$	0.509711	+	0.108342i	0.0355998	+	0.00756697i
$206$	3.68852	+	1.64223i	0.256991	+	0.114420i
$207$	−0.794809	+	0.882725i	−0.0552431	+	0.0613536i
$208$	0.772445	−	7.34932i	0.0535594	−	0.509584i
$209$	−18.5580	−	13.4832i	−1.28368	−	0.932651i
$210$	1.57121	+	14.9491i	0.108424	+	1.03159i
$211$	−3.15220	+	5.45978i	−0.217007	+	0.375867i	−0.953891	−	0.300152i	$-0.902963\pi$
$211$	−3.15220	+	5.45978i	−0.217007	+	0.375867i	0.736885	+	0.676018i	$0.236296\pi$
$212$	0.564643	+	0.977990i	0.0387798	+	0.0671687i
$213$	−8.55826	+	6.21794i	−0.586403	+	0.426046i
$214$	2.60277	+	2.89067i	0.177922	+	0.197602i
$215$	1.85509	+	5.70937i	0.126516	+	0.389376i
$216$	−10.7517			−0.731564
$217$		0			0
$218$	8.57126			0.580519
$219$	3.45720	+	10.6402i	0.233616	+	0.718996i
$220$	1.87414	+	2.08144i	0.126354	+	0.140331i
$221$	8.04618	−	5.84589i	0.541245	−	0.393237i
$222$	2.31903	+	4.01668i	0.155643	+	0.269582i
$223$	3.69455	−	6.39915i	0.247406	−	0.428519i	−0.715400	−	0.698716i	$-0.753755\pi$
$223$	3.69455	−	6.39915i	0.247406	−	0.428519i	0.962805	+	0.270196i	$0.0870887\pi$
$224$	1.05777	+	10.0640i	0.0706750	+	0.672428i
$225$	2.75776	+	2.00363i	0.183851	+	0.133575i
$226$	1.96374	−	18.6838i	0.130626	−	1.24282i
$227$	12.8739	−	14.2979i	0.854473	−	0.948988i	−0.144707	−	0.989474i	$-0.546224\pi$
$227$	12.8739	−	14.2979i	0.854473	−	0.948988i	0.999180	+	0.0404864i	$0.0128908\pi$
$228$	5.56898	+	2.47947i	0.368815	+	0.164207i
$229$	−5.95409	−	1.26558i	−0.393457	−	0.0836319i	0.00693463	−	0.999976i	$-0.497793\pi$
$229$	−5.95409	−	1.26558i	−0.393457	−	0.0836319i	−0.400392	+	0.916344i	$0.631126\pi$
$230$	−1.69491	+	0.360265i	−0.111759	+	0.0237552i
$231$	27.1219	−	12.0754i	1.78449	−	0.794505i
$232$	−6.43383	+	19.8013i	−0.422401	+	1.30002i
$233$	5.41646	−	16.6702i	0.354844	−	1.09210i	−0.601255	−	0.799057i	$-0.705333\pi$
$233$	5.41646	−	16.6702i	0.354844	−	1.09210i	0.956100	−	0.293042i	$-0.0946675\pi$
$234$	3.87236	−	1.72409i	0.253144	−	0.112707i
$235$	−1.79781	+	0.382136i	−0.117276	+	0.0249278i
$236$	3.66557	+	0.779142i	0.238608	+	0.0507178i
$237$	−18.4577	−	8.21791i	−1.19896	−	0.533811i
$238$	11.8369	−	13.1462i	0.767269	−	0.852139i
$239$	−2.91760	+	27.7591i	−0.188724	+	1.79559i	0.333468	+	0.942761i	$0.391781\pi$
$239$	−2.91760	+	27.7591i	−0.188724	+	1.79559i	−0.522192	+	0.852828i	$0.674886\pi$
$240$	7.27639	+	5.28660i	0.469689	+	0.341249i
$241$	2.37799	+	22.6251i	0.153180	+	1.45741i	0.753393	+	0.657571i	$0.228416\pi$
$241$	2.37799	+	22.6251i	0.153180	+	1.45741i	−0.600213	+	0.799841i	$0.704917\pi$
$242$	−1.94010	+	3.36034i	−0.124714	+	0.216011i
$243$	−6.35849	−	11.0132i	−0.407897	−	0.706499i
$244$	1.06144	−	0.771185i	0.0679520	−	0.0493701i
$245$	−7.72418	−	8.57857i	−0.493480	−	0.548065i
$246$	−0.266369	−	0.819798i	−0.0169830	−	0.0522684i
$247$	16.0694			1.02247
$248$		0			0
$249$	−17.4197			−1.10393
$250$	4.47921	+	13.7856i	0.283290	+	0.871878i
$251$	10.8630	+	12.0646i	0.685666	+	0.761510i	0.981026	−	0.193876i	$-0.0621061\pi$
$251$	10.8630	+	12.0646i	0.685666	+	0.761510i	−0.295359	+	0.955386i	$0.595439\pi$
$252$	−1.93543	+	1.40617i	−0.121921	+	0.0885805i
$253$	1.71121	+	2.96390i	0.107583	+	0.186339i
$254$	−12.4612	+	21.5834i	−0.781884	+	1.35426i
$255$	1.26530	+	12.0385i	0.0792359	+	0.753879i
$256$	8.76759	+	6.37002i	0.547974	+	0.398126i
$257$	−2.44096	+	23.2242i	−0.152263	+	1.44868i	0.605339	+	0.795968i	$0.293037\pi$
$257$	−2.44096	+	23.2242i	−0.152263	+	1.44868i	−0.757602	+	0.652717i	$0.773629\pi$
$258$	6.64468	−	7.37966i	0.413679	−	0.459438i
$259$	−6.30370	−	2.80659i	−0.391693	−	0.174393i
$260$	−1.91921	−	0.407940i	−0.119024	−	0.0252994i
$261$	−8.69451	+	1.84808i	−0.538177	+	0.114393i
$262$	14.2409	−	6.34044i	0.879803	−	0.391714i
$263$	3.21203	−	9.88562i	0.198062	−	0.609574i	−0.801865	−	0.597506i	$-0.796159\pi$
$263$	3.21203	−	9.88562i	0.198062	−	0.609574i	0.999927	−	0.0120680i	$-0.00384144\pi$
$264$	7.37545	−	22.6993i	0.453928	−	1.39705i
$265$	−3.30990	+	1.47366i	−0.203325	+	0.0905263i
$266$	27.9575	−	5.94255i	1.71419	−	0.364361i
$267$	−10.3422	−	2.19830i	−0.632932	−	0.134534i
$268$	3.26608	+	1.45415i	0.199507	+	0.0888264i
$269$	2.95625	−	3.28325i	0.180246	−	0.200183i	−0.646251	−	0.763125i	$-0.723664\pi$
$269$	2.95625	−	3.28325i	0.180246	−	0.200183i	0.826496	+	0.562942i	$0.190331\pi$
$270$	0.699937	−	6.65945i	0.0425968	−	0.405281i
$271$	4.97777	+	3.61656i	0.302378	+	0.219691i	0.728619	−	0.684919i	$-0.240162\pi$
$271$	4.97777	+	3.61656i	0.302378	+	0.219691i	−0.426241	+	0.904610i	$0.640162\pi$
$272$	−1.10641	−	10.5268i	−0.0670862	−	0.638282i
$273$	−10.3989	+	18.0114i	−0.629369	+	1.09010i
$274$	−6.08571	−	10.5408i	−0.367651	−	0.636790i
$275$	7.94578	−	5.77295i	0.479149	−	0.348122i
$276$	−0.608577	−	0.675893i	−0.0366320	−	0.0406840i
$277$	−6.81302	−	20.9683i	−0.409355	−	1.25987i	−0.917204	−	0.398419i	$-0.869559\pi$
$277$	−6.81302	−	20.9683i	−0.409355	−	1.25987i	0.507849	−	0.861446i	$-0.330441\pi$
$278$	19.0974			1.14539
$279$		0			0
$280$	−17.9782			−1.07440
$281$	−9.50955	−	29.2674i	−0.567292	−	1.74595i	−0.661040	−	0.750351i	$-0.729885\pi$
$281$	−9.50955	−	29.2674i	−0.567292	−	1.74595i	0.0937474	−	0.995596i	$-0.470115\pi$
$282$	2.03437	+	2.25940i	0.121145	+	0.134545i
$283$	17.2687	−	12.5464i	1.02652	−	0.745807i	0.0589075	−	0.998263i	$-0.481238\pi$
$283$	17.2687	−	12.5464i	1.02652	−	0.745807i	0.967608	+	0.252456i	$0.0812383\pi$
$284$	−1.22803	−	2.12701i	−0.0728701	−	0.126215i
$285$	−9.77904	+	16.9378i	−0.579260	+	1.00331i
$286$	−1.27662	−	12.1462i	−0.0754880	−	0.718220i
$287$	1.03750	+	0.753786i	0.0612415	+	0.0444946i
$288$	−0.363045	+	3.45414i	−0.0213926	+	0.203537i
$289$	−1.84303	+	2.04689i	−0.108413	+	0.120405i
$290$	−11.8457	−	5.27406i	−0.695606	−	0.309704i
$291$	22.1519	+	4.70852i	1.29856	+	0.276018i
$292$	−2.54072	+	0.540047i	−0.148684	+	0.0316038i
$293$	−1.64349	+	0.731730i	−0.0960139	+	0.0427481i	−0.454182	−	0.890909i	$-0.650068\pi$
$293$	−1.64349	+	0.731730i	−0.0960139	+	0.0427481i	0.358168	+	0.933657i	$0.383402\pi$
$294$	−5.90071	+	18.1605i	−0.344136	+	1.05914i
$295$	−3.71535	+	11.4347i	−0.216316	+	0.665753i
$296$	−5.06772	+	2.25629i	−0.294555	+	0.131144i
$297$	−12.9365	+	2.74974i	−0.750653	+	0.159556i
$298$	18.3719	+	3.90506i	1.06425	+	0.226214i
$299$	−2.19023	−	0.975153i	−0.126664	−	0.0563946i
$300$	−1.74647	+	1.93966i	−0.100833	+	0.111986i
$301$	−1.54428	+	14.6928i	−0.0890108	+	0.846882i
$302$	−0.261003	−	0.189630i	−0.0150190	−	0.0109120i
$303$	−0.0864815	−	0.822816i	−0.00496823	−	0.0472696i
$304$	8.55109	−	14.8109i	0.490439	−	0.849465i
$305$	2.10470	+	3.64545i	0.120515	+	0.208738i
$306$	4.91195	−	3.56874i	0.280797	−	0.204011i
$307$	17.9122	+	19.8935i	1.02230	+	1.13538i	0.990725	+	0.135883i	$0.0433872\pi$
$307$	17.9122	+	19.8935i	1.02230	+	1.13538i	0.0315799	+	0.999501i	$0.489946\pi$
$308$	2.13001	+	6.55551i	0.121369	+	0.373535i
$309$	−6.79928			−0.386798
$310$		0			0
$311$	4.18114			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$311$	4.18114			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$312$	5.16673	+	15.9016i	0.292509	+	0.900249i
$313$	7.58983	+	8.42936i	0.429003	+	0.476456i	0.918427	−	0.395590i	$-0.129460\pi$
$313$	7.58983	+	8.42936i	0.429003	+	0.476456i	−0.489425	+	0.872046i	$0.662793\pi$
$314$	−15.8763	+	11.5348i	−0.895953	+	0.650948i
$315$	−3.83769	−	6.64708i	−0.216229	−	0.374520i
$316$	2.34546	−	4.06246i	0.131943	−	0.228531i
$317$	−2.70534	−	25.7396i	−0.151947	−	1.44568i	−0.759038	−	0.651046i	$-0.774331\pi$
$317$	−2.70534	−	25.7396i	−0.151947	−	1.44568i	0.607092	−	0.794632i	$-0.292336\pi$
$318$	4.84867	+	3.52277i	0.271900	+	0.197547i
$319$	−2.67704	+	25.4704i	−0.149886	+	1.42607i
$320$	−9.19100	+	10.2076i	−0.513793	+	0.570624i
$321$	−5.98407	−	2.66428i	−0.333998	−	0.148706i
$322$	−4.17116	−	0.886608i	−0.232450	−	0.0494087i
$323$	22.5141	−	4.78553i	1.25272	−	0.266274i
$324$	4.93450	−	2.19698i	0.274139	−	0.122055i
$325$	−2.12612	+	6.54354i	−0.117936	+	0.362970i
$326$	−0.0507081	+	0.156064i	−0.00280846	+	0.00864356i
$327$	−13.1861	+	5.87083i	−0.729193	+	0.324657i
$328$	1.00844	−	0.214351i	0.0556818	−	0.0118355i
$329$	−4.42439	−	0.940432i	−0.243924	−	0.0518477i
$330$	13.5794	+	6.04595i	0.747523	+	0.332819i
$331$	−0.512412	+	0.569091i	−0.0281647	+	0.0312801i	−0.757063	−	0.653342i	$-0.773366\pi$
$331$	−0.512412	+	0.569091i	−0.0281647	+	0.0312801i	0.728898	+	0.684622i	$0.240033\pi$
$332$	0.422752	−	4.02222i	0.0232015	−	0.220748i
$333$	−1.91599	−	1.39205i	−0.104996	−	0.0762839i
$334$	−0.508591	−	4.83892i	−0.0278289	−	0.264774i
$335$	−5.73517	+	9.93361i	−0.313346	+	0.542731i
$336$	11.0672	+	19.1689i	0.603765	+	1.04575i
$337$	1.93706	−	1.40736i	0.105519	−	0.0766637i	−0.533775	−	0.845627i	$-0.679227\pi$
$337$	1.93706	−	1.40736i	0.105519	−	0.0766637i	0.639293	+	0.768963i	$0.279227\pi$
$338$	−4.99344	−	5.54578i	−0.271607	−	0.301650i
$339$	9.77628	+	30.0883i	0.530974	+	1.63417i
$340$	−2.81040			−0.152415
$341$		0			0
$342$	9.80991			0.530459
$343$	−0.550776	−	1.69511i	−0.0297391	−	0.0915276i
$344$	7.94729	+	8.82636i	0.428489	+	0.475886i
$345$	2.36071	−	1.71516i	0.127096	−	0.0923408i
$346$	8.90672	+	15.4269i	0.478828	+	0.829355i
$347$	2.82890	−	4.89980i	0.151863	−	0.263035i	−0.780049	−	0.625718i	$-0.784806\pi$
$347$	2.82890	−	4.89980i	0.151863	−	0.263035i	0.931912	+	0.362683i	$0.118139\pi$
$348$	−0.711423	−	6.76873i	−0.0381363	−	0.362842i
$349$	−23.5162	−	17.0855i	−1.25879	−	0.914566i	−0.260095	−	0.965583i	$-0.583754\pi$
$349$	−23.5162	−	17.0855i	−1.25879	−	0.914566i	−0.998698	+	0.0510167i	$0.983754\pi$
$350$	−1.27919	+	12.1707i	−0.0683754	+	0.650549i
$351$	6.19942	−	6.88516i	0.330901	−	0.367502i
$352$	9.14190	+	4.07024i	0.487265	+	0.216944i
$353$	−18.8540	−	4.00754i	−1.00350	−	0.213300i	−0.323274	−	0.946305i	$-0.604784\pi$
$353$	−18.8540	−	4.00754i	−1.00350	−	0.213300i	−0.680223	+	0.733006i	$0.738117\pi$
$354$	19.4537	−	4.13502i	1.03395	−	0.219774i
$355$	7.19861	−	3.20503i	0.382063	−	0.170105i
$356$	0.758579	−	2.33467i	0.0402046	−	0.123737i
$357$	−9.20553	+	28.3317i	−0.487209	+	1.49947i
$358$	19.9463	−	8.88067i	1.05420	−	0.469358i
$359$	−10.1182	+	2.15069i	−0.534019	+	0.113509i	−0.467025	−	0.884244i	$-0.654674\pi$
$359$	−10.1182	+	2.15069i	−0.534019	+	0.113509i	−0.0669943	+	0.997753i	$0.521341\pi$
$360$	−6.03561	−	1.28291i	−0.318105	−	0.0676152i
$361$	16.6169	+	7.39831i	0.874573	+	0.389385i
$362$	9.94259	−	11.0424i	0.522571	−	0.580374i
$363$	0.683013	−	6.49844i	0.0358489	−	0.341079i
$364$	−3.90647	−	2.83822i	−0.204755	−	0.148763i
$365$	−0.871099	−	8.28795i	−0.0455954	−	0.433811i
$366$	3.48154	−	6.03020i	0.181983	−	0.315203i
$367$	−0.0682819	−	0.118268i	−0.00356428	−	0.00617352i	0.864238	−	0.503084i	$-0.167801\pi$
$367$	−0.0682819	−	0.118268i	−0.00356428	−	0.00617352i	−0.867802	+	0.496910i	$0.834468\pi$
$368$	−2.06428	+	1.49978i	−0.107608	+	0.0781817i
$369$	0.294517	+	0.327095i	0.0153320	+	0.0170279i
$370$	−1.06760	−	3.28574i	−0.0555020	−	0.170818i
$371$	−8.91649			−0.462921
$372$		0			0
$373$	−7.36393			−0.381290			−0.190645	−	0.981659i	$-0.561058\pi$
$373$	−7.36393			−0.381290			−0.190645	+	0.981659i	$0.561058\pi$
$374$	−5.40578	−	16.6373i	−0.279526	−	0.860294i
$375$	−16.3332	−	18.1399i	−0.843444	−	0.936739i
$376$	−2.94187	+	2.13739i	−0.151715	+	0.110228i
$377$	−8.97053	−	15.5374i	−0.462006	−	0.800218i
$378$	8.23955	−	14.2713i	0.423797	−	0.734038i
$379$	0.481681	+	4.58289i	0.0247423	+	0.235407i	0.999903	+	0.0139098i	$0.00442778\pi$
$379$	0.481681	+	4.58289i	0.0247423	+	0.235407i	−0.975161	+	0.221497i	$0.928906\pi$
$380$	−3.67362	−	2.66904i	−0.188453	−	0.136919i
$381$	4.38698	−	41.7393i	0.224752	−	2.13837i
$382$	4.18139	−	4.64390i	0.213938	−	0.237603i
$383$	29.5028	+	13.1355i	1.50752	+	0.671191i	0.983565	−	0.180555i	$-0.0577893\pi$
$383$	29.5028	+	13.1355i	1.50752	+	0.671191i	0.523955	+	0.851746i	$0.324456\pi$
$384$	11.4256	+	2.42859i	0.583061	+	0.123933i
$385$	−21.6314	+	4.59790i	−1.10244	+	0.234330i
$386$	−22.5599	+	10.0443i	−1.14827	+	0.511242i
$387$	−1.56691	+	4.82246i	−0.0796506	+	0.245139i
$388$	−1.62479	+	5.00060i	−0.0824864	+	0.253867i
$389$	32.2219	−	14.3461i	1.63372	−	0.727377i	0.634744	−	0.772722i	$-0.281105\pi$
$389$	32.2219	−	14.3461i	1.63372	−	0.727377i	0.998971	+	0.0453451i	$0.0144387\pi$
$390$	−10.1855	+	2.16500i	−0.515764	+	0.109629i
$391$	−3.35903	−	0.713984i	−0.169873	−	0.0361077i
$392$	−20.8640	−	9.28925i	−1.05379	−	0.469178i
$393$	−17.5654	+	19.5084i	−0.886058	+	0.984067i
$394$	2.79597	−	26.6019i	0.140859	−	1.34018i
$395$	12.1758	+	8.84621i	0.612629	+	0.445101i
$396$	0.247289	+	2.35280i	0.0124268	+	0.118233i
$397$	2.01701	−	3.49356i	0.101231	−	0.175337i	−0.810961	−	0.585100i	$-0.801055\pi$
$397$	2.01701	−	3.49356i	0.101231	−	0.175337i	0.912192	+	0.409763i	$0.134389\pi$
$398$	9.34326	+	16.1830i	0.468335	+	0.811181i
$399$	−38.9398	+	28.2914i	−1.94943	+	1.41634i
$400$	4.89968	+	5.44165i	0.244984	+	0.272083i
$401$	−7.68933	−	23.6653i	−0.383987	−	1.18179i	−0.937212	−	0.348759i	$-0.886603\pi$
$401$	−7.68933	−	23.6653i	−0.383987	−	1.18179i	0.553225	−	0.833032i	$-0.313397\pi$
$402$	18.9739			0.946334
$403$		0			0
$404$	0.192087			0.00955671
$405$	5.35520	+	16.4816i	0.266102	+	0.818978i
$406$	−21.3527	−	23.7146i	−1.05972	−	1.17693i
$407$	−5.52044	+	4.01084i	−0.273638	+	0.198810i
$408$	11.9744	+	20.7403i	0.592821	+	1.02680i
$409$	1.75361	−	3.03734i	0.0867105	−	0.150187i	−0.819408	−	0.573210i	$-0.805698\pi$
$409$	1.75361	−	3.03734i	0.0867105	−	0.150187i	0.906119	+	0.423023i	$0.139031\pi$
$410$	0.0671160	+	0.638566i	0.00331462	+	0.0315365i
$411$	16.5821	+	12.0476i	0.817936	+	0.594265i
$412$	0.165009	−	1.56996i	0.00812942	−	0.0773462i
$413$	−19.7988	+	21.9888i	−0.974234	+	1.08200i
$414$	−1.33707	−	0.595301i	−0.0657133	−	0.0292575i
$415$	12.6922	+	2.69781i	0.623034	+	0.132430i
$416$	−6.85706	+	1.45751i	−0.336195	+	0.0714604i
$417$	−29.3796	+	13.0806i	−1.43873	+	0.640562i
$418$	8.73429	−	26.8814i	0.427208	−	1.31481i
$419$	1.27325	−	3.91865i	0.0622022	−	0.191439i	−0.915126	−	0.403167i	$-0.867909\pi$
$419$	1.27325	−	3.91865i	0.0622022	−	0.191439i	0.977328	+	0.211729i	$0.0679093\pi$
$420$	5.36886	−	2.39037i	0.261974	−	0.116638i
$421$	−26.9982	+	5.73865i	−1.31581	+	0.279685i	−0.811762	−	0.583989i	$-0.801491\pi$
$421$	−26.9982	+	5.73865i	−1.31581	+	0.279685i	−0.504052	+	0.863673i	$0.668158\pi$
$422$	−7.59836	−	1.61508i	−0.369883	−	0.0786210i
$423$	−1.41824	−	0.631441i	−0.0689571	−	0.0307017i
$424$	−4.79647	+	5.32702i	−0.232937	+	0.258703i
$425$	−1.03013	+	9.80100i	−0.0499685	+	0.475419i
$426$	−10.5453	−	7.66158i	−0.510919	−	0.371205i
$427$	1.08284	+	10.3025i	0.0524023	+	0.498574i
$428$	0.760408	−	1.31706i	0.0367557	−	0.0636627i
$429$	10.2834	+	17.8114i	0.496488	+	0.859943i
$430$	−5.98427	+	4.34783i	−0.288587	+	0.209671i
$431$	−9.95261	−	11.0535i	−0.479400	−	0.532428i	0.454126	−	0.890938i	$-0.349952\pi$
$431$	−9.95261	−	11.0535i	−0.479400	−	0.532428i	−0.933526	+	0.358510i	$0.883285\pi$
$432$	−3.04701	−	9.37772i	−0.146599	−	0.451186i
$433$	−9.26195			−0.445101			−0.222550	−	0.974921i	$-0.571438\pi$
$433$	−9.26195			−0.445101			−0.222550	+	0.974921i	$0.571438\pi$
$434$		0			0
$435$	21.8360			1.04696
$436$	−1.03557	−	3.18715i	−0.0495947	−	0.152637i
$437$	−3.71269	−	4.12336i	−0.177602	−	0.197247i
$438$	−11.1525	+	8.10275i	−0.532886	+	0.387164i
$439$	−8.85909	−	15.3444i	−0.422821	−	0.732348i	0.573393	−	0.819281i	$-0.305627\pi$
$439$	−8.85909	−	15.3444i	−0.422821	−	0.732348i	−0.996214	+	0.0869324i	$0.972294\pi$
$440$	−8.88929	+	15.3967i	−0.423780	+	0.734009i
$441$	−1.01919	−	9.69696i	−0.0485329	−	0.461760i
$442$	9.91428	+	7.20314i	0.471574	+	0.342619i
$443$	1.92857	−	18.3492i	0.0916293	−	0.871795i	−0.848091	−	0.529851i	$-0.822248\pi$
$443$	1.92857	−	18.3492i	0.0916293	−	0.871795i	0.939720	−	0.341944i	$-0.111085\pi$
$444$	1.21339	−	1.34760i	0.0575848	−	0.0639544i
$445$	7.19497	+	3.20341i	0.341074	+	0.151856i
$446$	8.90569	+	1.89296i	0.421697	+	0.0896344i
$447$	−30.9382	+	6.57611i	−1.46333	+	0.311039i
$448$	−30.8810	+	13.7491i	−1.45899	+	0.649584i
$449$	−7.01784	+	21.5987i	−0.331192	+	1.01931i	0.637375	+	0.770554i	$0.280020\pi$
$449$	−7.01784	+	21.5987i	−0.331192	+	1.01931i	−0.968567	+	0.248752i	$0.919980\pi$
$450$	−1.29793	+	3.99463i	−0.0611852	+	0.188309i
$451$	1.15854	−	0.515814i	0.0545534	−	0.0242888i
$452$	−7.18465	+	1.52715i	−0.337938	+	0.0718309i
$453$	0.531414	+	0.112956i	0.0249680	+	0.00530712i
$454$	21.6572	+	9.64240i	1.01642	+	0.452540i
$455$	10.3662	−	11.5128i	0.485974	−	0.539728i
$456$	−4.04471	+	38.4828i	−0.189411	+	1.80212i
$457$	−13.0752	−	9.49970i	−0.611633	−	0.444377i	0.238356	−	0.971178i	$-0.423392\pi$
$457$	−13.0752	−	9.49970i	−0.611633	−	0.444377i	−0.849989	+	0.526800i	$0.823392\pi$
$458$	−0.784001	−	7.45927i	−0.0366340	−	0.348549i
$459$	6.63529	−	11.4927i	0.309709	−	0.536432i
$460$	0.338739	+	0.586713i	0.0157938	+	0.0273556i
$461$	17.4252	−	12.6602i	0.811573	−	0.589642i	−0.102713	−	0.994711i	$-0.532752\pi$
$461$	17.4252	−	12.6602i	0.811573	−	0.589642i	0.914286	+	0.405069i	$0.132752\pi$
$462$	24.4778	+	27.1853i	1.13881	+	1.26478i
$463$	5.41083	+	16.6528i	0.251462	+	0.773922i	0.994506	+	0.104679i	$0.0333815\pi$
$463$	5.41083	+	16.6528i	0.251462	+	0.773922i	−0.743044	+	0.669243i	$0.766619\pi$
$464$	−19.0941			−0.886421
$465$		0			0
$466$	21.5976			1.00049
$467$	−3.64845	−	11.2288i	−0.168830	−	0.519605i	0.830468	−	0.557066i	$-0.188073\pi$
$467$	−3.64845	−	11.2288i	−0.168830	−	0.519605i	−0.999298	+	0.0374608i	$0.988073\pi$
$468$	−1.10894	−	1.23160i	−0.0512608	−	0.0569309i
$469$	−22.8372	+	16.5922i	−1.05453	+	0.766158i
$470$	−1.13235	−	1.96129i	−0.0522314	−	0.0904674i
$471$	16.5236	−	28.6197i	0.761366	−	1.31872i
$472$	2.48644	+	23.6569i	0.114448	+	1.08890i
$473$	11.8195	+	8.58739i	0.543463	+	0.394849i
$474$	2.60228	−	24.7590i	0.119527	−	1.13722i
$475$	−10.6546	+	11.8331i	−0.488865	+	0.542940i
$476$	−6.31840	−	2.81313i	−0.289603	−	0.128940i
$477$	−2.99343	−	0.636273i	−0.137060	−	0.0291329i
$478$	−33.6409	+	7.15059i	−1.53870	+	0.327060i
$479$	−14.4420	+	6.42999i	−0.659871	+	0.293794i	−0.709219	−	0.704988i	$-0.750952\pi$
$479$	−14.4420	+	6.42999i	−0.659871	+	0.293794i	0.0493480	+	0.998782i	$0.484286\pi$
$480$	2.63658	−	8.11456i	0.120343	−	0.370377i
$481$	1.47715	−	4.54621i	0.0673525	−	0.207290i
$482$	−25.6081	+	11.4015i	−1.16642	+	0.519323i
$483$	7.02423	−	1.49305i	0.319613	−	0.0679359i
$484$	1.48392	+	0.315416i	0.0674507	+	0.0143371i
$485$	−15.4108	−	6.86135i	−0.699770	−	0.311558i
$486$	10.4849	−	11.6447i	0.475607	−	0.528215i
$487$	1.33709	−	12.7216i	0.0605894	−	0.576469i	−0.921543	−	0.388277i	$-0.873070\pi$
$487$	1.33709	−	12.7216i	0.0605894	−	0.576469i	0.982132	−	0.188192i	$-0.0602629\pi$
$488$	6.73758	+	4.89514i	0.304996	+	0.221593i
$489$	−0.0288849	−	0.274822i	−0.00130622	−	0.0124279i
$490$	7.11185	−	12.3181i	0.321281	−	0.556475i
$491$	−9.26410	−	16.0459i	−0.418083	−	0.724141i	0.577664	−	0.816275i	$-0.303964\pi$
$491$	−9.26410	−	16.0459i	−0.418083	−	0.724141i	−0.995747	+	0.0921341i	$0.970631\pi$
$492$	−0.272653	+	0.198094i	−0.0122921	+	0.00893076i
$493$	−17.1953	−	19.0973i	−0.774436	−	0.860098i
$494$	6.11864	+	18.8312i	0.275290	+	0.847257i
$495$	−7.59016			−0.341152
$496$		0			0
$497$	19.3922			0.869861
$498$	−6.63277	−	20.4136i	−0.297221	−	0.914754i
$499$	−27.3589	−	30.3852i	−1.22475	−	1.36023i	−0.911894	−	0.410427i	$-0.865380\pi$
$499$	−27.3589	−	30.3852i	−1.22475	−	1.36023i	−0.312860	−	0.949799i	$-0.601287\pi$
$500$	4.58489	−	3.33112i	0.205042	−	0.148972i
$501$	4.09681	+	7.09588i	0.183032	+	0.317021i
$502$	−10.0018	+	17.3237i	−0.446404	+	0.773195i
$503$	−2.09863	−	19.9671i	−0.0935732	−	0.890290i	−0.936123	−	0.351672i	$-0.885613\pi$
$503$	−2.09863	−	19.9671i	−0.0935732	−	0.890290i	0.842550	−	0.538618i	$-0.181053\pi$
$504$	−12.2852	−	8.92575i	−0.547228	−	0.397585i
$505$	−0.0644190	+	0.612906i	−0.00286661	+	0.0272739i
$506$	−2.82172	+	3.13384i	−0.125441	+	0.139316i
$507$	11.4805	+	5.11144i	0.509867	+	0.227007i
$508$	9.53115	+	2.02591i	0.422877	+	0.0898852i
$509$	−31.2139	+	6.63471i	−1.38353	+	0.294079i	−0.838758	−	0.544505i	$-0.816718\pi$
$509$	−31.2139	+	6.63471i	−1.38353	+	0.294079i	−0.544773	+	0.838583i	$0.683384\pi$
$510$	−13.6257	+	6.06655i	−0.603356	+	0.268631i
$511$	6.33760	−	19.5051i	0.280359	−	0.862855i
$512$	−7.60561	+	23.4076i	−0.336123	+	1.03448i
$513$	19.5880	−	8.72112i	0.864830	−	0.385047i
$514$	−28.1450	+	5.98241i	−1.24142	+	0.263873i
$515$	4.95402	+	1.05301i	0.218300	+	0.0464012i
$516$	−3.54687	−	1.57917i	−0.156142	−	0.0695189i
$517$	−2.99303	+	3.32409i	−0.131633	+	0.146193i
$518$	0.888733	−	8.45573i	0.0390487	−	0.371524i
$519$	−24.2687	−	17.6323i	−1.06528	−	0.773970i
$520$	−1.30184	−	12.3862i	−0.0570896	−	0.543171i
$521$	−1.05378	+	1.82520i	−0.0461670	+	0.0799635i	−0.888185	−	0.459485i	$-0.848034\pi$
$521$	−1.05378	+	1.82520i	−0.0461670	+	0.0799635i	0.842019	+	0.539449i	$0.181367\pi$
$522$	−5.47624	−	9.48512i	−0.239688	−	0.415152i
$523$	3.97047	−	2.88471i	0.173616	−	0.126140i	−0.497584	−	0.867416i	$-0.665779\pi$
$523$	3.97047	−	2.88471i	0.173616	−	0.126140i	0.671200	+	0.741276i	$0.265779\pi$
$524$	−4.07820	−	4.52930i	−0.178157	−	0.197863i
$525$	−6.36830	−	19.5996i	−0.277935	−	0.855397i
$526$	12.8076			0.558440
$527$		0			0
$528$	21.8886			0.952580
$529$	−6.85158	−	21.0870i	−0.297895	−	0.916826i
$530$	−2.98722	−	3.31764i	−0.129756	−	0.144109i
$531$	−8.21591	+	5.96921i	−0.356540	+	0.259042i
$532$	−5.58748	−	9.67780i	−0.242248	−	0.419586i
$533$	−0.444199	+	0.769375i	−0.0192404	+	0.0333253i
$534$	−1.36180	−	12.9567i	−0.0589309	−	0.560690i
$535$	3.94743	+	2.86798i	0.170662	+	0.123993i
$536$	−2.37212	+	22.5692i	−0.102460	+	0.974843i
$537$	−24.6028	+	27.3242i	−1.06169	+	1.17913i
$538$	4.97315	+	2.21419i	0.214408	+	0.0954605i
$539$	−27.4793	−	5.84091i	−1.18362	−	0.251586i
$540$	−2.56083	+	0.544321i	−0.110200	+	0.0234238i
$541$	−11.3618	+	5.05859i	−0.488481	+	0.217486i	−0.636171	−	0.771548i	$-0.719483\pi$
$541$	−11.3618	+	5.05859i	−0.488481	+	0.217486i	0.147690	+	0.989034i	$0.452816\pi$
$542$	−2.34278	+	7.21033i	−0.100631	+	0.309710i
$543$	−7.73236	+	23.7978i	−0.331827	+	1.02126i
$544$	−9.17304	+	4.08410i	−0.393291	+	0.175104i
$545$	10.5167	−	2.23540i	0.450488	−	0.0957541i
$546$	−25.0664	−	5.32804i	−1.07274	−	0.228019i
$547$	−12.7577	−	5.68008i	−0.545479	−	0.242863i	0.115448	−	0.993314i	$-0.463170\pi$
$547$	−12.7577	−	5.68008i	−0.545479	−	0.242863i	−0.660926	+	0.750451i	$0.729836\pi$
$548$	−3.18422	+	3.53644i	−0.136023	+	0.151069i
$549$	−0.371651	+	3.53602i	−0.0158617	+	0.150914i
$550$	9.79058	+	7.11327i	0.417472	+	0.303311i
$551$	−4.34012	−	41.2935i	−0.184895	−	1.75916i
$552$	2.88656	−	4.99967i	0.122860	−	0.212800i
$553$	18.5190	+	32.0759i	0.787509	+	1.36401i
$554$	21.9779	−	15.9679i	0.933752	−	0.678411i
$555$	3.89296	+	4.32357i	0.165247	+	0.183525i
$556$	−2.30732	−	7.10121i	−0.0978523	−	0.301159i
$557$	37.2207			1.57709			0.788546	−	0.614976i	$-0.210834\pi$
$557$	37.2207			1.57709			0.788546	+	0.614976i	$0.210834\pi$
$558$		0			0
$559$	−10.2346			−0.432876
$560$	−5.09496	−	15.6807i	−0.215301	−	0.662629i
$561$	19.7119	+	21.8923i	0.832237	+	0.924293i
$562$	30.6766	−	22.2878i	1.29401	−	0.940156i
$563$	15.0134	+	26.0039i	0.632738	+	1.09593i	0.986990	+	0.160784i	$0.0514023\pi$
$563$	15.0134	+	26.0039i	0.632738	+	1.09593i	−0.354252	+	0.935150i	$0.615264\pi$
$564$	0.594349	−	1.02944i	0.0250266	−	0.0433474i
$565$	−2.46329	−	23.4367i	−0.103632	−	0.985989i
$566$	21.2780	+	15.4594i	0.894380	+	0.649805i
$567$	−4.45797	+	42.4148i	−0.187217	+	1.78125i
$568$	10.4317	−	11.5856i	0.437705	−	0.486121i
$569$	36.8810	+	16.4205i	1.54613	+	0.688383i	0.989785	−	0.142567i	$-0.0455355\pi$
$569$	36.8810	+	16.4205i	1.54613	+	0.688383i	0.556348	+	0.830949i	$0.312202\pi$
$570$	−23.5723	−	5.01045i	−0.987335	−	0.209865i
$571$	41.6706	−	8.85736i	1.74386	−	0.370669i	0.777705	−	0.628630i	$-0.216384\pi$
$571$	41.6706	−	8.85736i	1.74386	−	0.370669i	0.966155	+	0.257961i	$0.0830505\pi$
$572$	−4.36223	+	1.94219i	−0.182394	+	0.0812070i
$573$	−3.25187	+	10.0082i	−0.135849	+	0.418100i
$574$	−0.488296	+	1.50282i	−0.0203811	+	0.0627265i
$575$	2.17027	−	0.966267i	0.0905065	−	0.0402961i
$576$	−11.3484	+	2.41219i	−0.472852	+	0.100508i
$577$	6.39490	+	1.35928i	0.266223	+	0.0565875i	0.339089	−	0.940754i	$-0.389881\pi$
$577$	6.39490	+	1.35928i	0.266223	+	0.0565875i	−0.0728659	+	0.997342i	$0.523215\pi$
$578$	−3.10044	−	1.38040i	−0.128961	−	0.0574172i
$579$	27.8265	−	30.9045i	1.15643	−	1.28435i
$580$	−0.529930	+	5.04195i	−0.0220041	+	0.209355i
$581$	25.8344	+	18.7698i	1.07179	+	0.778703i
$582$	2.91683	+	27.7518i	0.120907	+	1.15035i
$583$	−4.40874	+	7.63617i	−0.182591	+	0.316258i
$584$	−8.24383	−	14.2787i	−0.341132	−	0.590858i
$585$	4.30166	−	3.12534i	0.177852	−	0.129217i
$586$	−1.48327	−	1.64734i	−0.0612733	−	0.0680509i
$587$	6.60607	+	20.3314i	0.272662	+	0.839167i	0.989829	+	0.142265i	$0.0454386\pi$
$587$	6.60607	+	20.3314i	0.272662	+	0.839167i	−0.717167	+	0.696902i	$0.754561\pi$
$588$	7.46576			0.307883
$589$		0			0
$590$	−14.8146			−0.609907
$591$	13.9195	+	42.8397i	0.572570	+	1.76219i
$592$	−3.40412	−	3.78066i	−0.139909	−	0.155384i
$593$	−21.0268	+	15.2769i	−0.863468	+	0.627347i	−0.928826	−	0.370515i	$-0.879181\pi$
$593$	−21.0268	+	15.2769i	−0.863468	+	0.627347i	0.0653579	+	0.997862i	$0.479181\pi$
$594$	−8.14807	−	14.1129i	−0.334319	−	0.579058i
$595$	11.0950	−	19.2171i	0.454851	−	0.787824i
$596$	−0.767600	−	7.30323i	−0.0314421	−	0.299152i
$597$	−25.4582	−	18.4965i	−1.04193	−	0.757010i
$598$	0.308792	−	2.93796i	0.0126274	−	0.120142i
$599$	−6.14794	+	6.82798i	−0.251198	+	0.278984i	−0.855535	−	0.517745i	$-0.826772\pi$
$599$	−6.14794	+	6.82798i	−0.251198	+	0.278984i	0.604337	+	0.796729i	$0.293438\pi$
$600$	−15.1352	−	6.73862i	−0.617892	−	0.275103i
$601$	32.5909	+	6.92742i	1.32941	+	0.282575i	0.817235	−	0.576305i	$-0.195506\pi$
$601$	32.5909	+	6.92742i	1.32941	+	0.282575i	0.512177	+	0.858880i	$0.328839\pi$
$602$	−17.8060	+	3.78479i	−0.725720	+	0.154257i
$603$	−8.85089	+	3.94067i	−0.360436	+	0.160476i
$604$	−0.0389782	+	0.119962i	−0.00158600	+	0.00488120i
$605$	−1.50407	+	4.62905i	−0.0611491	+	0.188197i
$606$	0.931301	−	0.414642i	0.0378315	−	0.0168437i
$607$	47.6365	−	10.1255i	1.93351	−	0.410980i	0.935112	−	0.354353i	$-0.115299\pi$
$607$	47.6365	−	10.1255i	1.93351	−	0.410980i	0.998395	−	0.0566271i	$-0.0180346\pi$
$608$	−15.8693	−	3.37311i	−0.643583	−	0.136798i
$609$	49.0923	+	21.8573i	1.98932	+	0.885702i
$610$	−3.47058	+	3.85447i	−0.140520	+	0.156063i
$611$	0.327538	−	3.11631i	0.0132508	−	0.126073i
$612$	−1.92046	−	1.39530i	−0.0776300	−	0.0564015i
$613$	2.18611	+	20.7994i	0.0882961	+	0.840081i	0.945613	+	0.325293i	$0.105463\pi$
$613$	2.18611	+	20.7994i	0.0882961	+	0.840081i	−0.857317	+	0.514788i	$0.827870\pi$
$614$	−16.4923	+	28.5654i	−0.665573	+	1.15281i
$615$	−0.540633	−	0.936404i	−0.0218004	−	0.0377594i
$616$	−35.3968	+	25.7173i	−1.42618	+	1.03618i
$617$	30.3678	+	33.7269i	1.22256	+	1.35779i	0.913546	+	0.406735i	$0.133333\pi$
$617$	30.3678	+	33.7269i	1.22256	+	1.35779i	0.309015	+	0.951057i	$0.400001\pi$
$618$	−2.58891	−	7.96784i	−0.104141	−	0.320514i
$619$	10.2462			0.411832			0.205916	−	0.978570i	$-0.433983\pi$
$619$	10.2462			0.411832			0.205916	+	0.978570i	$0.433983\pi$
$620$		0			0
$621$	−3.19902			−0.128372
$622$	1.59202	+	4.89973i	0.0638341	+	0.196461i
$623$	12.9694	+	14.4039i	0.519607	+	0.577082i
$624$	−12.4052	+	9.01290i	−0.496605	+	0.360805i
$625$	2.56358	+	4.44025i	0.102543	+	0.177610i
$626$	−6.98816	+	12.1038i	−0.279303	+	0.483767i
$627$	4.97532	+	47.3370i	0.198695	+	1.89046i
$628$	6.20729	+	4.50986i	0.247698	+	0.179963i
$629$	0.715695	−	6.80938i	0.0285366	−	0.271508i
$630$	6.32823	−	7.02821i	0.252123	−	0.280011i
$631$	9.75390	+	4.34271i	0.388296	+	0.172881i	0.591594	−	0.806236i	$-0.298499\pi$
$631$	9.75390	+	4.34271i	0.388296	+	0.172881i	−0.203297	+	0.979117i	$0.565166\pi$
$632$	29.1252	+	6.19076i	1.15854	+	0.246255i
$633$	12.7956	−	2.71979i	0.508580	−	0.108102i
$634$	29.1332	−	12.9709i	1.15703	−	0.515142i
$635$	−9.66059	+	29.7322i	−0.383369	+	1.17989i
$636$	0.724101	−	2.22855i	0.0287125	−	0.0883679i
$637$	17.9787	−	8.00465i	0.712343	−	0.317156i
$638$	−30.8672	+	6.56102i	−1.22204	+	0.259753i
$639$	6.51033	+	1.38381i	0.257545	+	0.0547428i
$640$	−7.94869	−	3.53899i	−0.314200	−	0.139891i
$641$	−15.9669	+	17.7330i	−0.630653	+	0.700411i	−0.970781	−	0.239968i	$-0.922863\pi$
$641$	−15.9669	+	17.7330i	−0.630653	+	0.700411i	0.340128	+	0.940379i	$0.389530\pi$
$642$	0.843669	−	8.02698i	0.0332970	−	0.316800i
$643$	−6.42300	−	4.66658i	−0.253298	−	0.184032i	0.453889	−	0.891058i	$-0.350036\pi$
$643$	−6.42300	−	4.66658i	−0.253298	−	0.184032i	−0.707187	+	0.707026i	$0.750036\pi$
$644$	0.174277	+	1.65813i	0.00686746	+	0.0653395i
$645$	6.22823	−	10.7876i	0.245237	−	0.424762i
$646$	14.1805	+	24.5614i	0.557925	+	0.966355i
$647$	2.00443	−	1.45630i	0.0788023	−	0.0572532i	−0.547687	−	0.836684i	$-0.684491\pi$
$647$	2.00443	−	1.45630i	0.0788023	−	0.0572532i	0.626489	+	0.779430i	$0.284491\pi$
$648$	22.9420	+	25.4796i	0.901245	+	1.00093i
$649$	9.04192	+	27.8282i	0.354926	+	1.09235i
$650$	−8.47769			−0.332523
$651$		0			0
$652$	0.0641574			0.00251260
$653$	6.95104	+	21.3931i	0.272015	+	0.837177i	0.989994	+	0.141112i	$0.0450677\pi$
$653$	6.95104	+	21.3931i	0.272015	+	0.837177i	−0.717978	+	0.696065i	$0.754932\pi$
$654$	−11.9006	−	13.2169i	−0.465350	−	0.516823i
$655$	15.8196	−	11.4936i	0.618123	−	0.449093i
$656$	0.472746	+	0.818821i	0.0184576	+	0.0319696i
$657$	3.51952	−	6.09598i	0.137309	−	0.237827i
$658$	−0.582579	−	5.54287i	−0.0227113	−	0.216083i
$659$	9.67555	+	7.02970i	0.376906	+	0.273838i	0.760069	−	0.649843i	$-0.225165\pi$
$659$	9.67555	+	7.02970i	0.376906	+	0.273838i	−0.383163	+	0.923681i	$0.625165\pi$
$660$	0.607488	−	5.77986i	0.0236464	−	0.224981i
$661$	15.9494	−	17.7136i	0.620359	−	0.688978i	−0.348297	−	0.937384i	$-0.613240\pi$
$661$	15.9494	−	17.7136i	0.620359	−	0.688978i	0.968656	+	0.248406i	$0.0799067\pi$
$662$	−0.862005	−	0.383790i	−0.0335028	−	0.0149164i
$663$	−20.1860	−	4.29066i	−0.783957	−	0.166635i
$664$	25.1109	−	5.33749i	0.974492	−	0.207135i
$665$	32.7534	−	14.5828i	1.27012	−	0.565495i
$666$	0.901758	−	2.77533i	0.0349424	−	0.107542i
$667$	−1.91429	+	5.89158i	−0.0741216	+	0.228123i
$668$	−1.73787	+	0.773748i	−0.0672400	+	0.0299372i
$669$	−14.9972	+	3.18775i	−0.579824	+	0.123245i
$670$	−13.8246	−	2.93851i	−0.534091	−	0.113524i
$671$	9.35860	+	4.16672i	0.361285	+	0.160854i
$672$	14.0501	−	15.6042i	0.541994	−	0.601945i
$673$	0.365235	−	3.47498i	0.0140788	−	0.133951i	−0.985225	−	0.171266i	$-0.945214\pi$
$673$	0.365235	−	3.47498i	0.0140788	−	0.133951i	0.999304	+	0.0373159i	$0.0118808\pi$
$674$	2.38679	+	1.73411i	0.0919359	+	0.0667953i
$675$	0.959619	+	9.13017i	0.0369358	+	0.351420i
$676$	−1.45885	+	2.52680i	−0.0561096	+	0.0971847i
$677$	−9.62287	−	16.6673i	−0.369837	−	0.640576i	0.619703	−	0.784836i	$-0.287253\pi$
$677$	−9.62287	−	16.6673i	−0.369837	−	0.640576i	−0.989540	+	0.144260i	$0.953920\pi$
$678$	−31.5370	+	22.9130i	−1.21117	+	0.879967i
$679$	−27.7790	−	30.8517i	−1.06606	−	1.18398i
$680$	−5.51260	−	16.9660i	−0.211399	−	0.650618i
$681$	−39.9221			−1.52982
$682$		0			0
$683$	−39.8738			−1.52573			−0.762865	−	0.646558i	$-0.776208\pi$
$683$	−39.8738			−1.52573			−0.762865	+	0.646558i	$0.776208\pi$
$684$	−1.18522	−	3.64773i	−0.0453180	−	0.139475i
$685$	−10.2161	−	11.3461i	−0.390336	−	0.433512i
$686$	1.77673	−	1.29087i	0.0678359	−	0.0492857i
$687$	6.31529	+	10.9384i	0.240944	+	0.417326i
$688$	−5.44616	+	9.43303i	−0.207633	+	0.359631i
$689$	−0.645664	−	6.14308i	−0.0245978	−	0.234033i
$690$	2.90880	+	2.11337i	0.110736	+	0.0804545i
$691$	−4.01498	+	38.2000i	−0.152737	+	1.45320i	0.602695	+	0.797971i	$0.294093\pi$
$691$	−4.01498	+	38.2000i	−0.152737	+	1.45320i	−0.755433	+	0.655226i	$0.772573\pi$
$692$	4.66026	−	5.17575i	0.177157	−	0.196752i
$693$	−17.0644	−	7.59755i	−0.648222	−	0.288607i
$694$	6.81904	+	1.44943i	0.258847	+	0.0550197i
$695$	23.4321	−	4.98064i	0.888830	−	0.188927i
$696$	39.4666	−	17.5717i	1.49598	−	0.666052i
$697$	−0.393224	+	1.21022i	−0.0148944	+	0.0458403i
$698$	11.0678	−	34.0633i	0.418924	−	1.28932i
$699$	−33.2259	+	14.7931i	−1.25672	+	0.559527i
$700$	4.68011	−	0.994787i	0.176891	−	0.0375994i
$701$	34.6513	+	7.36537i	1.30876	+	0.278186i	0.808914	−	0.587927i	$-0.200056\pi$
$701$	34.6513	+	7.36537i	1.30876	+	0.278186i	0.499849	+	0.866113i	$0.333389\pi$
$702$	10.4290	+	4.64328i	0.393616	+	0.175249i
$703$	7.40241	−	8.22121i	0.279187	−	0.310069i
$704$	−3.49419	+	33.2450i	−0.131692	+	1.25297i
$705$	3.08539	+	2.24166i	0.116202	+	0.0844260i
$706$	−2.48259	−	23.6203i	−0.0934335	−	0.888960i
$707$	−0.758331	+	1.31347i	−0.0285200	+	0.0493980i
$708$	−3.88795	−	6.73412i	−0.146118	−	0.253084i
$709$	−20.8801	+	15.1703i	−0.784170	+	0.569733i	−0.906228	−	0.422790i	$-0.861051\pi$
$709$	−20.8801	+	15.1703i	−0.784170	+	0.569733i	0.122057	+	0.992523i	$0.461051\pi$
$710$	6.49682	+	7.21545i	0.243821	+	0.270791i
$711$	3.92827	+	12.0900i	0.147322	+	0.453409i
$712$	15.5821			0.583962
$713$		0			0
$714$	−36.7061			−1.37369
$715$	−4.73414	−	14.5702i	−0.177047	−	0.544894i
$716$	−5.71209	−	6.34392i	−0.213471	−	0.237083i
$717$	46.8557	−	34.0426i	1.74986	−	1.27135i
$718$	−6.37296	−	11.0383i	−0.237837	−	0.411945i
$719$	−19.5234	+	33.8155i	−0.728099	+	1.26110i	0.229587	+	0.973288i	$0.426262\pi$
$719$	−19.5234	+	33.8155i	−0.728099	+	1.26110i	−0.957686	+	0.287816i	$0.907071\pi$
$720$	−0.591512	−	5.62786i	−0.0220443	−	0.209738i
$721$	10.0837	+	7.32625i	0.375537	+	0.272844i
$722$	−2.34275	+	22.2897i	−0.0871880	+	0.829538i
$723$	31.5864	−	35.0802i	1.17471	−	1.30465i
$724$	−5.30726	−	2.36294i	−0.197243	−	0.0878181i
$725$	17.3891	+	3.69617i	0.645815	+	0.137272i
$726$	7.87536	−	1.67396i	0.292282	−	0.0621264i
$727$	22.8237	−	10.1618i	0.846484	−	0.376879i	0.0627904	−	0.998027i	$-0.480000\pi$
$727$	22.8237	−	10.1618i	0.846484	−	0.376879i	0.783693	+	0.621148i	$0.213333\pi$
$728$	9.47144	−	29.1501i	0.351035	−	1.08037i
$729$	2.24010	−	6.89433i	0.0829668	−	0.255345i
$730$	9.38068	−	4.17655i	0.347195	−	0.154581i
$731$	−14.3392	+	3.04788i	−0.530353	+	0.112730i
$732$	−2.66291	−	0.566020i	−0.0984241	−	0.0209207i
$733$	−15.4837	−	6.89380i	−0.571904	−	0.254628i	0.100345	−	0.994953i	$-0.468005\pi$
$733$	−15.4837	−	6.89380i	−0.571904	−	0.254628i	−0.672250	+	0.740324i	$0.734672\pi$
$734$	0.112595	−	0.125049i	0.00415594	−	0.00461564i
$735$	−2.50374	+	23.8215i	−0.0923517	+	0.878668i
$736$	1.95825	+	1.42275i	0.0721821	+	0.0524434i
$737$	2.91791	+	27.7620i	0.107482	+	1.02263i
$738$	−0.271170	+	0.469680i	−0.00998190	+	0.0172892i
$739$	7.19107	+	12.4553i	0.264528	+	0.458175i	0.967440	−	0.253101i	$-0.0814506\pi$
$739$	7.19107	+	12.4553i	0.264528	+	0.458175i	−0.702912	+	0.711277i	$0.748117\pi$
$740$	−1.09279	+	0.793959i	−0.0401718	+	0.0291865i
$741$	−22.3113	−	24.7792i	−0.819626	−	0.910286i
$742$	−3.39506	−	10.4489i	−0.124637	−	0.383592i
$743$	27.7705			1.01880			0.509400	−	0.860530i	$-0.329867\pi$
$743$	27.7705			1.01880			0.509400	+	0.860530i	$0.329867\pi$
$744$		0			0
$745$	23.5603			0.863183
$746$	−2.80390	−	8.62953i	−0.102658	−	0.315950i
$747$	7.33369	+	8.14489i	0.268326	+	0.298006i
$748$	−5.53332	+	4.02019i	−0.202318	+	0.146993i
$749$	6.00394	+	10.3991i	0.219379	+	0.379976i
$750$	15.0384	−	26.0473i	0.549126	−	0.951113i
$751$	4.55433	+	43.3315i	0.166190	+	1.58119i	0.686447	+	0.727180i	$0.259169\pi$
$751$	4.55433	+	43.3315i	0.166190	+	1.58119i	−0.520257	+	0.854010i	$0.674164\pi$
$752$	−2.69796	−	1.96018i	−0.0983844	−	0.0714804i
$753$	3.52116	−	33.5016i	0.128318	−	1.22087i
$754$	14.7921	−	16.4283i	0.538697	−	0.598284i
$755$	−0.369700	−	0.164601i	−0.0134548	−	0.00599045i
$756$	−6.30216	−	1.33957i	−0.229207	−	0.0487195i
$757$	24.6660	−	5.24293i	0.896503	−	0.190558i	0.263456	−	0.964671i	$-0.415138\pi$
$757$	24.6660	−	5.24293i	0.896503	−	0.190558i	0.633046	+	0.774114i	$0.281804\pi$
$758$	−5.18713	+	2.30946i	−0.188405	+	0.0838833i
$759$	2.19446	−	6.75385i	0.0796538	−	0.245149i
$760$	8.90688	−	27.4125i	0.323086	−	0.994358i
$761$	2.38977	−	1.06399i	0.0866292	−	0.0385698i	−0.362965	−	0.931803i	$-0.618235\pi$
$761$	2.38977	−	1.06399i	0.0866292	−	0.0385698i	0.449594	+	0.893233i	$0.351569\pi$
$762$	50.5832	−	10.7518i	1.83244	−	0.389497i
$763$	25.8816	+	5.50130i	0.936975	+	0.199160i
$764$	−2.23199	−	0.993744i	−0.0807504	−	0.0359524i
$765$	5.09611	−	5.65981i	0.184250	−	0.204631i
$766$	−4.15947	+	39.5747i	−0.150288	+	1.42989i
$767$	−16.5830	−	12.0483i	−0.598777	−	0.435037i
$768$	−2.35055	−	22.3640i	−0.0848182	−	0.806991i
$769$	−5.67534	+	9.82998i	−0.204658	+	0.354478i	−0.950024	−	0.312178i	$-0.898942\pi$
$769$	−5.67534	+	9.82998i	−0.204658	+	0.354478i	0.745366	+	0.666656i	$0.232275\pi$
$770$	−13.6245	−	23.5984i	−0.490994	−	0.850427i
$771$	39.2009	−	28.4811i	1.41179	−	1.02572i
$772$	6.46055	+	7.17517i	0.232520	+	0.258240i
$773$	3.52816	+	10.8586i	0.126899	+	0.390556i	0.994242	−	0.107155i	$-0.0341741\pi$
$773$	3.52816	+	10.8586i	0.126899	+	0.390556i	−0.867343	+	0.497711i	$0.834174\pi$
$774$	−6.24789			−0.224576
$775$		0			0
$776$	−33.3751			−1.19810
$777$	4.42446	+	13.6171i	0.158727	+	0.488511i
$778$	29.0806	+	32.2973i	1.04259	+	1.15791i
$779$	−1.66335	+	1.20849i	−0.0595957	+	0.0432988i
$780$	2.03564	+	3.52583i	0.0728875	+	0.126245i
$781$	9.58846	−	16.6077i	0.343102	−	0.594270i
$782$	−0.442298	−	4.20819i	−0.0158166	−	0.150484i
$783$	−19.3671	−	14.0710i	−0.692123	−	0.502857i
$784$	2.18935	−	20.8302i	0.0781909	−	0.743937i
$785$	−16.4716	+	18.2936i	−0.587896	+	0.652925i
$786$	−29.5494	−	13.1562i	−1.05399	−	0.469268i
$787$	−26.4972	−	5.63216i	−0.944525	−	0.200765i	−0.290189	−	0.956969i	$-0.593718\pi$
$787$	−26.4972	−	5.63216i	−0.944525	−	0.200765i	−0.654336	+	0.756204i	$0.727052\pi$
$788$	−10.2295	+	2.17435i	−0.364411	+	0.0774579i
$789$	−19.7034	+	8.77251i	−0.701459	+	0.312310i
$790$	−5.73050	+	17.6367i	−0.203882	+	0.627484i
$791$	17.9215	−	55.1566i	0.637214	−	1.96114i
$792$	−13.7185	+	6.10788i	−0.487467	+	0.217034i
$793$	−7.01960	+	1.49206i	−0.249273	+	0.0529846i
$794$	4.86199	+	1.03345i	0.172545	+	0.0366757i
$795$	6.86795	+	3.05781i	0.243581	+	0.108449i
$796$	4.88867	−	5.42942i	0.173274	−	0.192441i
$797$	5.08592	−	48.3893i	0.180152	−	1.71404i	−0.414496	−	0.910051i	$-0.636042\pi$
$797$	5.08592	−	48.3893i	0.180152	−	1.71404i	0.594649	−	0.803985i	$-0.297291\pi$
$798$	−47.9805	−	34.8599i	−1.69849	−	1.23403i
$799$	−0.469149	−	4.46366i	−0.0165973	−	0.157913i
$800$	3.47318	−	6.01573i	0.122796	−	0.212688i
$801$	3.32620	+	5.76115i	0.117526	+	0.203560i
$802$	24.8048	−	18.0217i	0.875887	−	0.636369i
$803$	−13.5708	−	15.0719i	−0.478902	−	0.531874i
$804$	−2.29240	−	7.05530i	−0.0808469	−	0.248821i
$805$	−5.34915			−0.188533
$806$		0			0
$807$	−9.16733			−0.322705
$808$	0.376780	+	1.15961i	0.0132551	+	0.0407949i
$809$	12.5858	+	13.9779i	0.442492	+	0.491437i	0.922592	−	0.385776i	$-0.126066\pi$
$809$	12.5858	+	13.9779i	0.442492	+	0.491437i	−0.480100	+	0.877214i	$0.659400\pi$
$810$	−17.2752	+	12.5512i	−0.606988	+	0.441002i
$811$	19.7693	+	34.2414i	0.694193	+	1.20238i	0.970452	+	0.241294i	$0.0775720\pi$
$811$	19.7693	+	34.2414i	0.694193	+	1.20238i	−0.276259	+	0.961083i	$0.589095\pi$
$812$	−6.23826	+	10.8050i	−0.218920	+	0.379180i
$813$	−1.33452	−	12.6971i	−0.0468036	−	0.445307i
$814$	−6.80214	−	4.94204i	−0.238415	−	0.173219i
$815$	−0.0215160	+	0.204711i	−0.000753673	+	0.00717072i
$816$	−14.6962	+	16.3218i	−0.514472	+	0.571379i
$817$	−21.6381	−	9.63389i	−0.757020	−	0.337047i
$818$	4.22707	+	0.898491i	0.147796	+	0.0314150i
$819$	12.7995	−	2.72061i	0.447250	−	0.0950658i
$820$	0.229336	−	0.102107i	0.00800878	−	0.00356574i
$821$	4.52299	−	13.9203i	0.157854	−	0.485823i	−0.840585	−	0.541679i	$-0.817789\pi$
$821$	4.52299	−	13.9203i	0.157854	−	0.485823i	0.998439	+	0.0558559i	$0.0177887\pi$
$822$	−7.80434	+	24.0193i	−0.272208	+	0.837769i
$823$	−38.1741	+	16.9962i	−1.33066	+	0.592450i	−0.944053	−	0.329793i	$-0.893021\pi$
$823$	−38.1741	+	16.9962i	−1.33066	+	0.592450i	−0.386611	+	0.922243i	$0.626354\pi$
$824$	9.80132	−	2.08333i	0.341445	−	0.0725764i
$825$	−19.9341	−	4.23712i	−0.694016	−	0.147518i
$826$	−33.3065	−	14.8290i	−1.15888	−	0.515967i
$827$	6.29393	−	6.99012i	0.218861	−	0.243070i	−0.623709	−	0.781657i	$-0.714375\pi$
$827$	6.29393	−	6.99012i	0.218861	−	0.243070i	0.842570	+	0.538587i	$0.181042\pi$
$828$	−0.0598149	+	0.569101i	−0.00207871	+	0.0197776i
$829$	32.6283	+	23.7058i	1.13323	+	0.823337i	0.986161	−	0.165790i	$-0.0530173\pi$
$829$	32.6283	+	23.7058i	1.13323	+	0.823337i	0.147065	+	0.989127i	$0.453017\pi$
$830$	1.67124	+	15.9007i	0.0580094	+	0.551923i
$831$	−22.8739	+	39.6188i	−0.793487	+	1.37436i
$832$	−11.7087	−	20.2801i	−0.405927	−	0.703086i
$833$	22.8053	−	16.5690i	0.790158	−	0.574083i
$834$	−26.5154	−	29.4483i	−0.918153	−	1.01971i
$835$	−1.88603	−	5.80460i	−0.0652688	−	0.200877i
$836$	−11.0509			−0.382203
$837$		0			0
$838$	5.07693			0.175380
$839$	2.20936	+	6.79972i	0.0762757	+	0.234752i	0.981923	−	0.189278i	$-0.0606149\pi$
$839$	2.20936	+	6.79972i	0.0762757	+	0.234752i	−0.905648	+	0.424031i	$0.860615\pi$
$840$	24.9615	+	27.7225i	0.861252	+	0.956517i
$841$	−14.0420	+	10.2021i	−0.484208	+	0.351798i
$842$	−17.0048	−	29.4532i	−0.586025	−	1.01503i
$843$	−31.9272	+	55.2995i	−1.09963	+	1.90462i
$844$	0.317469	+	3.02052i	0.0109277	+	0.103971i
$845$	−7.57319	−	5.50224i	−0.260526	−	0.189283i
$846$	0.199952	−	1.90241i	0.00687448	−	0.0654063i
$847$	−8.01504	+	8.90160i	−0.275400	+	0.305863i
$848$	−6.00555	−	2.67384i	−0.206231	−	0.0918202i
$849$	−43.3230	−	9.20859i	−1.48684	−	0.316038i
$850$	−11.8777	+	2.52468i	−0.407401	+	0.0865959i
$851$	−1.50783	+	0.671327i	−0.0516876	+	0.0230128i
$852$	−1.57483	+	4.84683i	−0.0539528	+	0.166050i
$853$	0.348160	−	1.07153i	0.0119208	−	0.0366884i	−0.944919	−	0.327304i	$-0.893860\pi$
$853$	0.348160	−	1.07153i	0.0119208	−	0.0366884i	0.956840	+	0.290615i	$0.0938600\pi$
$854$	−11.6609	+	5.19176i	−0.399027	+	0.177658i
$855$	12.0365	−	2.55844i	0.411641	−	0.0874969i
$856$	9.44251	+	2.00707i	0.322738	+	0.0686002i
$857$	−21.7917	−	9.70231i	−0.744392	−	0.331425i	−0.000747156	−	1.00000i	$-0.500238\pi$
$857$	−21.7917	−	9.70231i	−0.744392	−	0.331425i	−0.743645	+	0.668575i	$0.766904\pi$
$858$	−16.9570	+	18.8327i	−0.578904	+	0.642938i
$859$	3.39359	−	32.2878i	0.115788	−	1.10165i	−0.770157	−	0.637855i	$-0.779822\pi$
$859$	3.39359	−	32.2878i	0.115788	−	1.10165i	0.885944	−	0.463792i	$-0.153511\pi$
$860$	2.33971	+	1.69990i	0.0797836	+	0.0579662i
$861$	−0.278148	−	2.64641i	−0.00947927	−	0.0901892i
$862$	9.16363	−	15.8719i	0.312114	−	0.540598i
$863$	−11.9209	−	20.6476i	−0.405793	−	0.702853i	0.588621	−	0.808409i	$-0.299671\pi$
$863$	−11.9209	−	20.6476i	−0.405793	−	0.702853i	−0.994413	+	0.105556i	$0.966338\pi$
$864$	−7.56744	+	5.49807i	−0.257450	+	0.187048i
$865$	14.9517	+	16.6056i	0.508373	+	0.564606i
$866$	−3.52660	−	10.8538i	−0.119839	−	0.368826i
$867$	5.71523			0.194099
$868$		0			0
$869$	36.6268			1.24248
$870$	8.31433	+	25.5889i	0.281882	+	0.867544i
$871$	−13.0850	−	14.5324i	−0.443370	−	0.492412i
$872$	17.2092	−	12.5032i	0.582777	−	0.423412i
$873$	−7.12437	−	12.3398i	−0.241123	−	0.417638i
$874$	3.41837	−	5.92080i	0.115628	−	0.200274i
$875$	4.67730	+	44.5016i	0.158122	+	1.50443i
$876$	4.36037	+	3.16799i	0.147323	+	0.107036i
$877$	−3.06003	+	29.1143i	−0.103330	+	0.983119i	0.812883	+	0.582427i	$0.197897\pi$
$877$	−3.06003	+	29.1143i	−0.103330	+	0.983119i	−0.916213	+	0.400692i	$0.868770\pi$
$878$	14.6084	−	16.2242i	0.493008	−	0.547541i
$879$	3.41021	+	1.51832i	0.115023	+	0.0512117i
$880$	−15.9483	−	3.38991i	−0.537616	−	0.114274i
$881$	8.83275	−	1.87746i	0.297583	−	0.0632532i	−0.0567007	−	0.998391i	$-0.518058\pi$
$881$	8.83275	−	1.87746i	0.297583	−	0.0632532i	0.354284	+	0.935138i	$0.384725\pi$
$882$	10.9755	−	4.88659i	0.369563	−	0.164540i
$883$	−6.61531	+	20.3598i	−0.222623	+	0.685162i	0.775901	+	0.630854i	$0.217295\pi$
$883$	−6.61531	+	20.3598i	−0.222623	+	0.685162i	−0.998524	+	0.0543083i	$0.982705\pi$
$884$	1.48060	−	4.55682i	0.0497979	−	0.153262i
$885$	22.7909	−	10.1471i	0.766107	−	0.341093i
$886$	22.2371	−	4.72664i	0.747069	−	0.158794i
$887$	−24.0575	−	5.11359i	−0.807773	−	0.171698i	−0.214527	−	0.976718i	$-0.568821\pi$
$887$	−24.0575	−	5.11359i	−0.807773	−	0.171698i	−0.593247	+	0.805021i	$0.702154\pi$
$888$	10.5154	+	4.68175i	0.352873	+	0.157109i
$889$	−51.4804	+	57.1748i	−1.72660	+	1.91758i
$890$	−1.01439	+	9.65127i	−0.0340024	+	0.323511i
$891$	34.1202	+	24.7898i	1.14307	+	0.830489i
$892$	−0.372091	−	3.54021i	−0.0124585	−	0.118535i
$893$	3.62590	−	6.28024i	0.121336	−	0.210160i
$894$	−19.4864	−	33.7514i	−0.651723	−	1.12882i
$895$	22.1576	−	16.0984i	0.740646	−	0.538111i
$896$	−14.3280	−	15.9129i	−0.478665	−	0.531612i
$897$	1.53729	+	4.73128i	0.0513285	+	0.157973i
$898$	−27.9829			−0.933801
$899$		0			0
$900$	1.64218			0.0547395
$901$	−2.73404	−	8.41450i	−0.0910839	−	0.280328i
$902$	1.04559	+	1.16125i	0.0348144	+	0.0386653i
$903$	24.8006	−	18.0187i	0.825312	−	0.599624i
$904$	−23.3119	−	40.3774i	−0.775343	−	1.34293i
$905$	9.31946	−	16.1418i	0.309789	−	0.536571i
$906$	0.0699737	+	0.665755i	0.00232472	+	0.0221182i
$907$	15.9913	+	11.6183i	0.530981	+	0.385781i	0.820725	−	0.571324i	$-0.193570\pi$
$907$	15.9913	+	11.6183i	0.530981	+	0.385781i	−0.289743	+	0.957104i	$0.593570\pi$
$908$	0.968853	−	9.21802i	0.0321525	−	0.305911i
$909$	−0.348313	+	0.386841i	−0.0115528	+	0.0128307i
$910$	17.4385	+	7.76412i	0.578081	+	0.257378i
$911$	−34.8432	−	7.40614i	−1.15441	−	0.245376i	−0.409349	−	0.912378i	$-0.634244\pi$
$911$	−34.8432	−	7.40614i	−1.15441	−	0.245376i	−0.745057	+	0.667001i	$0.767578\pi$
$912$	−34.7111	+	7.37808i	−1.14940	+	0.244313i
$913$	28.8484	−	12.8442i	0.954744	−	0.425079i
$914$	6.15383	−	18.9395i	0.203550	−	0.626464i
$915$	2.69908	−	8.30691i	0.0892287	−	0.274618i
$916$	−2.67895	+	1.19274i	−0.0885149	+	0.0394094i
$917$	47.0708	−	10.0052i	1.55442	−	0.330401i
$918$	15.9943	+	3.39970i	0.527891	+	0.112207i
$919$	−15.6731	−	6.97811i	−0.517007	−	0.230187i	0.131609	−	0.991302i	$-0.457986\pi$
$919$	−15.6731	−	6.97811i	−0.517007	−	0.230187i	−0.648617	+	0.761115i	$0.724652\pi$
$920$	−2.87748	+	3.19577i	−0.0948677	+	0.105361i
$921$	5.80612	−	55.2415i	0.191318	−	1.82027i
$922$	21.4709	+	15.5995i	0.707105	+	0.513742i
$923$	1.40424	+	13.3604i	0.0462211	+	0.439764i
$924$	7.15126	−	12.3863i	0.235259	−	0.407481i
$925$	2.36831	+	4.10203i	0.0778694	+	0.134874i
$926$	−17.4546	+	12.6815i	−0.573594	+	0.416741i
$927$	2.86250	+	3.17912i	0.0940167	+	0.104416i
$928$	5.59734	+	17.2268i	0.183742	+	0.565499i
$929$	−45.5222			−1.49353			−0.746767	−	0.665086i	$-0.768395\pi$
$929$	−45.5222			−1.49353			−0.746767	+	0.665086i	$0.768395\pi$
$930$		0			0
$931$	45.5457			1.49270
$932$	−2.60939	−	8.03088i	−0.0854734	−	0.263060i
$933$	−5.80521	−	6.44734i	−0.190054	−	0.211076i
$934$	11.7694	−	8.55098i	0.385107	−	0.279797i
$935$	−10.9718	−	19.0037i	−0.358817	−	0.621489i
$936$	5.25986	−	9.11035i	0.171924	−	0.297781i
$937$	−2.67776	−	25.4771i	−0.0874785	−	0.832302i	−0.947007	−	0.321214i	$-0.895909\pi$
$937$	−2.67776	−	25.4771i	−0.0874785	−	0.832302i	0.859528	−	0.511088i	$-0.170757\pi$
$938$	−28.1394	−	20.4445i	−0.918784	−	0.667536i
$939$	2.46019	−	23.4072i	0.0802853	−	0.763864i
$940$	−0.592479	+	0.658015i	−0.0193245	+	0.0214621i
$941$	−11.0757	−	4.93121i	−0.361057	−	0.160753i	0.218187	−	0.975907i	$-0.429986\pi$
$941$	−11.0757	−	4.93121i	−0.361057	−	0.160753i	−0.579244	+	0.815154i	$0.696652\pi$
$942$	39.8300	+	8.46612i	1.29773	+	0.275841i
$943$	0.300047	−	0.0637769i	0.00977087	−	0.00207686i
$944$	−19.9290	+	8.87298i	−0.648635	+	0.288791i
$945$	6.38775	−	19.6595i	0.207794	−	0.639523i
$946$	−5.56284	+	17.1207i	−0.180863	+	0.556640i
$947$	24.8494	−	11.0637i	0.807497	−	0.359521i	0.0388914	−	0.999243i	$-0.487617\pi$
$947$	24.8494	−	11.0637i	0.807497	−	0.359521i	0.768606	+	0.639722i	$0.220951\pi$
$948$	−9.52085	+	2.02372i	−0.309223	+	0.0657273i
$949$	13.8971	+	2.95392i	0.451120	+	0.0958884i
$950$	−17.9237	−	7.98013i	−0.581520	−	0.258910i
$951$	−35.9344	+	39.9092i	−1.16525	+	1.29414i
$952$	4.58900	−	43.6614i	0.148730	−	1.41507i
$953$	20.1386	+	14.6316i	0.652353	+	0.473962i	0.864072	−	0.503368i	$-0.167906\pi$
$953$	20.1386	+	14.6316i	0.652353	+	0.473962i	−0.211719	+	0.977331i	$0.567906\pi$
$954$	−0.394158	−	3.75016i	−0.0127613	−	0.121416i
$955$	3.91933	−	6.78848i	0.126826	−	0.219670i
$956$	6.72333	+	11.6452i	0.217448	+	0.376631i
$957$	42.9924	−	31.2358i	1.38975	−	1.00971i
$958$	−13.0340	−	14.4758i	−0.421111	−	0.467691i
$959$	−11.6109	−	35.7346i	−0.374935	−	1.15393i
$960$	28.5013			0.919876
$961$		0			0
$962$	5.89000			0.189901
$963$	1.27356	+	3.91961i	0.0410399	+	0.126308i
$964$	7.33348	+	8.14466i	0.236196	+	0.262322i
$965$	−25.0609	+	18.2078i	−0.806739	+	0.586130i
$966$	4.42421	+	7.66295i	0.142347	+	0.246551i
$967$	26.0999	−	45.2064i	0.839316	−	1.45374i	−0.0511507	−	0.998691i	$-0.516289\pi$
$967$	26.0999	−	45.2064i	0.839316	−	1.45374i	0.890467	−	0.455048i	$-0.150378\pi$
$968$	1.00657	+	9.57692i	0.0323525	+	0.307814i
$969$	−38.6386	−	28.0726i	−1.24125	−	0.901821i
$970$	2.17271	−	20.6720i	0.0697616	−	0.663737i
$971$	−13.3564	+	14.8338i	−0.428627	+	0.476039i	−0.918310	−	0.395862i	$-0.870446\pi$
$971$	−13.3564	+	14.8338i	−0.428627	+	0.476039i	0.489683	+	0.871901i	$0.337113\pi$
$972$	−5.59677	−	2.49184i	−0.179516	−	0.0799258i
$973$	57.6661	+	12.2573i	1.84869	+	0.392951i
$974$	15.4171	−	3.27700i	0.493995	−	0.105002i
$975$	13.0422	−	5.80674i	0.417683	−	0.185965i
$976$	−2.36016	+	7.26382i	−0.0755468	+	0.232509i
$977$	−18.6185	+	57.3017i	−0.595657	+	1.83324i	−0.0442310	+	0.999021i	$0.514084\pi$
$977$	−18.6185	+	57.3017i	−0.595657	+	1.83324i	−0.551426	+	0.834224i	$0.685916\pi$
$978$	0.311056	−	0.138491i	0.00994647	−	0.00442845i
$979$	18.7484	−	3.98509i	0.599200	−	0.127364i
$980$	−5.43962	−	1.15623i	−0.173762	−	0.0369343i
$981$	8.29635	+	3.69377i	0.264882	+	0.117933i
$982$	15.2762	−	16.9659i	0.487483	−	0.541405i
$983$	−1.20613	+	11.4755i	−0.0384694	+	0.366012i	0.958304	+	0.285750i	$0.0922425\pi$
$983$	−1.20613	+	11.4755i	−0.0384694	+	0.366012i	−0.996774	+	0.0802625i	$0.974424\pi$
$984$	−1.73068	−	1.25741i	−0.0551720	−	0.0400848i
$985$	−3.50724	−	33.3691i	−0.111750	−	1.06323i
$986$	15.8321	−	27.4221i	0.504198	−	0.873297i
$987$	4.69279	+	8.12816i	0.149373	+	0.258722i
$988$	6.26299	−	4.55033i	0.199252	−	0.144765i
$989$	2.36460	+	2.62616i	0.0751900	+	0.0835069i
$990$	−2.89005	−	8.89465i	−0.0918517	−	0.282690i
$991$	−37.3423			−1.18622			−0.593109	−	0.805122i	$-0.702100\pi$
$991$	−37.3423			−1.18622			−0.593109	+	0.805122i	$0.702100\pi$
$992$		0			0
$993$	1.58899			0.0504251
$994$	7.38383	+	22.7251i	0.234201	+	0.720796i
$995$	15.6845	+	17.4194i	0.497233	+	0.552233i
$996$	−6.78925	+	4.93268i	−0.215126	+	0.156298i
$997$	−10.4012	−	18.0154i	−0.329410	−	0.570555i	0.652985	−	0.757371i	$-0.273516\pi$
$997$	−10.4012	−	18.0154i	−0.329410	−	0.570555i	−0.982395	+	0.186816i	$0.940183\pi$
$998$	25.1901	−	43.6305i	0.797378	−	1.38110i
$999$	−0.666709	−	6.34331i	−0.0210937	−	0.200694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.j.547.2		16
31.2	even	5		961.2.g.n.235.1		16
31.3	odd	30		961.2.c.j.521.5		16
31.4	even	5		961.2.g.m.816.1		16
31.5	even	3		961.2.d.n.531.3		16
31.6	odd	6		31.2.g.a.7.2	✓	16
31.7	even	15		961.2.g.n.732.1		16
31.8	even	5		961.2.g.l.846.2		16
31.9	even	15		961.2.d.n.628.3		16
31.10	even	15		961.2.d.q.388.2		16
31.11	odd	30		961.2.d.p.374.2		16
31.12	odd	30		961.2.g.s.338.1		16
31.13	odd	30		961.2.a.i.1.5		8
31.14	even	15	inner	961.2.g.j.448.2		16
31.15	odd	10		961.2.c.j.439.5		16
31.16	even	5		961.2.c.i.439.5		16
31.17	odd	30		961.2.g.k.448.2		16
31.18	even	15		961.2.a.j.1.5		8
31.19	even	15		961.2.g.m.338.1		16
31.20	even	15		961.2.d.q.374.2		16
31.21	odd	30		961.2.d.p.388.2		16
31.22	odd	30		961.2.d.o.628.3		16
31.23	odd	10		31.2.g.a.9.2	yes	16
31.24	odd	30		961.2.g.t.732.1		16
31.25	even	3		961.2.g.l.844.2		16
31.26	odd	6		961.2.d.o.531.3		16
31.27	odd	10		961.2.g.s.816.1		16
31.28	even	15		961.2.c.i.521.5		16
31.29	odd	10		961.2.g.t.235.1		16
31.30	odd	2		961.2.g.k.547.2		16
93.23	even	10		279.2.y.c.226.1		16
93.44	even	30		8649.2.a.bf.1.4		8
93.68	even	6		279.2.y.c.100.1		16
93.80	odd	30		8649.2.a.be.1.4		8
124.23	even	10		496.2.bg.c.257.2		16
124.99	even	6		496.2.bg.c.193.2		16
155.23	even	20		775.2.ck.a.474.2		32
155.37	even	12		775.2.ck.a.224.2		32
155.54	odd	10		775.2.bl.a.226.1		16
155.68	even	12		775.2.ck.a.224.3		32
155.99	odd	6		775.2.bl.a.751.1		16
155.147	even	20		775.2.ck.a.474.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.2	✓	16	31.6	odd	6
31.2.g.a.9.2	yes	16	31.23	odd	10
279.2.y.c.100.1		16	93.68	even	6
279.2.y.c.226.1		16	93.23	even	10
496.2.bg.c.193.2		16	124.99	even	6
496.2.bg.c.257.2		16	124.23	even	10
775.2.bl.a.226.1		16	155.54	odd	10
775.2.bl.a.751.1		16	155.99	odd	6
775.2.ck.a.224.2		32	155.37	even	12
775.2.ck.a.224.3		32	155.68	even	12
775.2.ck.a.474.2		32	155.23	even	20
775.2.ck.a.474.3		32	155.147	even	20
961.2.a.i.1.5		8	31.13	odd	30
961.2.a.j.1.5		8	31.18	even	15
961.2.c.i.439.5		16	31.16	even	5
961.2.c.i.521.5		16	31.28	even	15
961.2.c.j.439.5		16	31.15	odd	10
961.2.c.j.521.5		16	31.3	odd	30
961.2.d.n.531.3		16	31.5	even	3
961.2.d.n.628.3		16	31.9	even	15
961.2.d.o.531.3		16	31.26	odd	6
961.2.d.o.628.3		16	31.22	odd	30
961.2.d.p.374.2		16	31.11	odd	30
961.2.d.p.388.2		16	31.21	odd	30
961.2.d.q.374.2		16	31.20	even	15
961.2.d.q.388.2		16	31.10	even	15
961.2.g.j.448.2		16	31.14	even	15	inner
961.2.g.j.547.2		16	1.1	even	1	trivial
961.2.g.k.448.2		16	31.17	odd	30
961.2.g.k.547.2		16	31.30	odd	2
961.2.g.l.844.2		16	31.25	even	3
961.2.g.l.846.2		16	31.8	even	5
961.2.g.m.338.1		16	31.19	even	15
961.2.g.m.816.1		16	31.4	even	5
961.2.g.n.235.1		16	31.2	even	5
961.2.g.n.732.1		16	31.7	even	15
961.2.g.s.338.1		16	31.12	odd	30
961.2.g.s.816.1		16	31.27	odd	10
961.2.g.t.235.1		16	31.29	odd	10
961.2.g.t.732.1		16	31.24	odd	30
8649.2.a.be.1.4		8	93.80	odd	30
8649.2.a.bf.1.4		8	93.44	even	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.380762 + 1.17187i) q^{2} +(-1.38843 - 1.54201i) q^{3} +(0.389745 - 0.283166i) q^{4} +(0.772811 + 1.33855i) q^{5} +(1.27836 - 2.21419i) q^{6} +(0.397601 + 3.78292i) q^{7} +(2.47393 + 1.79742i) q^{8} +(-0.136464 + 1.29837i) q^{9} +O(q^{10})\)	\(q+(0.380762 + 1.17187i) q^{2} +(-1.38843 - 1.54201i) q^{3} +(0.389745 - 0.283166i) q^{4} +(0.772811 + 1.33855i) q^{5} +(1.27836 - 2.21419i) q^{6} +(0.397601 + 3.78292i) q^{7} +(2.47393 + 1.79742i) q^{8} +(-0.136464 + 1.29837i) q^{9} +(-1.27434 + 1.41530i) q^{10} +(3.43632 + 1.52995i) q^{11} +(-0.977778 - 0.207833i) q^{12} +(-2.57748 + 0.547860i) q^{13} +(-4.28168 + 1.90633i) q^{14} +(0.991057 - 3.05016i) q^{15} +(-0.866611 + 2.66715i) q^{16} +(-3.44803 + 1.53516i) q^{17} +(-1.57347 + 0.334452i) q^{18} +(-5.96505 - 1.26791i) q^{19} +(0.680232 + 0.302859i) q^{20} +(5.28125 - 5.86542i) q^{21} +(-0.484473 + 4.60946i) q^{22} +(0.736082 + 0.534795i) q^{23} +(-0.663250 - 6.31040i) q^{24} +(1.30553 - 2.26124i) q^{25} +(-1.62343 - 2.81186i) q^{26} +(-2.84451 + 2.06665i) q^{27} +(1.22616 + 1.36179i) q^{28} +(2.10397 + 6.47535i) q^{29} +3.95173 q^{30} +2.66037 q^{32} +(-2.41190 - 7.42306i) q^{33} +(-3.11188 - 3.45610i) q^{34} +(-4.75635 + 3.45569i) q^{35} +(0.314468 + 0.544675i) q^{36} +(-0.907032 + 1.57103i) q^{37} +(-0.785445 - 7.47301i) q^{38} +(4.42345 + 3.21383i) q^{39} +(-0.494046 + 4.70054i) q^{40} +(0.225594 - 0.250547i) q^{41} +(8.88438 + 3.95558i) q^{42} +(3.79912 + 0.807528i) q^{43} +(1.77252 - 0.376761i) q^{44} +(-1.84339 + 0.820730i) q^{45} +(-0.346435 + 1.06622i) q^{46} +(-0.367467 + 1.13095i) q^{47} +(5.31600 - 2.36684i) q^{48} +(-7.30537 + 1.55280i) q^{49} +(3.14696 + 0.668907i) q^{50} +(7.15458 + 3.18542i) q^{51} +(-0.849425 + 0.943382i) q^{52} +(-0.245028 + 2.33128i) q^{53} +(-3.50492 - 2.54647i) q^{54} +(0.607718 + 5.78205i) q^{55} +(-5.81584 + 10.0733i) q^{56} +(6.32692 + 10.9586i) q^{57} +(-6.78713 + 4.93114i) q^{58} +(5.20505 + 5.78080i) q^{59} +(-0.477443 - 1.46942i) q^{60} +2.72343 q^{61} -4.96588 q^{63} +(2.74619 + 8.45191i) q^{64} +(-2.72524 - 3.02669i) q^{65} +(7.78047 - 5.65284i) q^{66} +(3.71059 + 6.42693i) q^{67} +(-0.909147 + 1.57469i) q^{68} +(-0.197340 - 1.87757i) q^{69} +(-5.86065 - 4.25801i) q^{70} +(0.532905 - 5.07025i) q^{71} +(-2.67131 + 2.96679i) q^{72} +(-4.92560 - 2.19302i) q^{73} +(-2.18639 - 0.464732i) q^{74} +(-5.29947 + 1.12644i) q^{75} +(-2.68388 + 1.19494i) q^{76} +(-4.42139 + 13.6076i) q^{77} +(-2.08189 + 6.40740i) q^{78} +(8.89540 - 3.96049i) q^{79} +(-4.23984 + 0.901206i) q^{80} +(10.9672 + 2.33114i) q^{81} +(0.379505 + 0.168967i) q^{82} +(5.61745 - 6.23881i) q^{83} +(0.397451 - 3.78149i) q^{84} +(-4.71957 - 3.42897i) q^{85} +(0.500247 + 4.75953i) q^{86} +(7.06383 - 12.2349i) q^{87} +(5.75127 + 9.96149i) q^{88} +(4.12243 - 2.99512i) q^{89} +(-1.66368 - 1.84770i) q^{90} +(-3.09732 - 9.53258i) q^{91} +0.438320 q^{92} -1.46523 q^{94} +(-2.91270 - 8.96437i) q^{95} +(-3.69374 - 4.10231i) q^{96} +(-8.82979 + 6.41522i) q^{97} +(-4.60129 - 7.96966i) q^{98} +(-2.45537 + 4.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9	\( 16 q - 6 q^{2} - 3 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} + 7 q^{11} + 10 q^{12} - 8 q^{13} - 21 q^{14} - 14 q^{15} - 2 q^{16} - 9 q^{17} + 12 q^{18} - 29 q^{19} - 8 q^{20} + 6 q^{21} + 21 q^{22} - q^{23} + 5 q^{24} - 13 q^{25} - 9 q^{26} - 9 q^{27} + 45 q^{28} + 14 q^{29} + 22 q^{30} - 42 q^{32} - 13 q^{33} + 17 q^{34} - 9 q^{35} + q^{36} + 8 q^{37} + 23 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 51 q^{42} + 37 q^{43} + 6 q^{44} - 70 q^{45} - 34 q^{46} + 14 q^{47} - 4 q^{48} - 43 q^{49} + 3 q^{50} + 33 q^{51} + 46 q^{52} + 9 q^{53} + 46 q^{54} - 8 q^{55} - 30 q^{56} + 17 q^{57} + 15 q^{58} - 11 q^{59} + 75 q^{60} + 60 q^{61} - 46 q^{63} + 23 q^{64} - 18 q^{65} - 30 q^{66} + 13 q^{67} - 30 q^{68} - 37 q^{69} + 12 q^{70} + 31 q^{71} - 38 q^{72} + 13 q^{73} - 43 q^{74} + 17 q^{75} - 12 q^{76} - 18 q^{77} - 15 q^{78} + 12 q^{79} + 6 q^{80} - 22 q^{81} - q^{82} - 44 q^{83} - 23 q^{84} - 37 q^{85} - 19 q^{86} + 15 q^{87} + 17 q^{88} - q^{89} + 7 q^{90} - 8 q^{91} + 64 q^{92} + 44 q^{94} - 22 q^{95} - 8 q^{96} + 3 q^{97} - 10 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 3 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 + 7 * q^11 + 10 * q^12 - 8 * q^13 - 21 * q^14 - 14 * q^15 - 2 * q^16 - 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 + 6 * q^21 + 21 * q^22 - q^23 + 5 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 + 45 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 17 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 51 * q^42 + 37 * q^43 + 6 * q^44 - 70 * q^45 - 34 * q^46 + 14 * q^47 - 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 + 46 * q^52 + 9 * q^53 + 46 * q^54 - 8 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 - 11 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 - 18 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 + 13 * q^73 - 43 * q^74 + 17 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 + 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 - 44 * q^83 - 23 * q^84 - 37 * q^85 - 19 * q^86 + 15 * q^87 + 17 * q^88 - q^89 + 7 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 - 22 * q^95 - 8 * q^96 + 3 * q^97 - 10 * q^98 - 6 * q^99

Introduction

L-functions

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