LMFDB - Embedded newform 69.2.e.c.52.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			52.1
Root			$0.545935 - 0.160301i$ of defining polynomial
Character	$\chi$	$=$	69.52
Dual form			69.2.e.c.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10489 + 2.41937i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-3.32285 - 3.83478i) q^{4} +(-2.44470 + 1.57111i) q^{5} +(1.74175 - 2.01009i) q^{6} +(-0.326826 + 2.27313i) q^{7} +(7.84516 - 2.30355i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-1.10489 + 2.41937i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-3.32285 - 3.83478i) q^{4} +(-2.44470 + 1.57111i) q^{5} +(1.74175 - 2.01009i) q^{6} +(-0.326826 + 2.27313i) q^{7} +(7.84516 - 2.30355i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-1.09998 - 7.65055i) q^{10} +(0.0494206 + 0.108216i) q^{11} +(2.10787 + 4.61560i) q^{12} +(0.614381 + 4.27311i) q^{13} +(-5.13843 - 3.30227i) q^{14} +(2.78831 - 0.818721i) q^{15} +(-1.65065 + 11.4805i) q^{16} +(-1.68604 + 1.94579i) q^{17} +(-2.23750 + 1.43796i) q^{18} +(-1.13103 - 1.30528i) q^{19} +(14.1483 + 4.15430i) q^{20} +(0.954001 - 2.08897i) q^{21} -0.316419 q^{22} +(4.00915 - 2.63187i) q^{23} -8.17636 q^{24} +(1.43109 - 3.13366i) q^{25} +(-11.0171 - 3.23490i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(9.80293 - 6.29996i) q^{28} +(-0.933494 + 1.07731i) q^{29} +(-1.09998 + 7.65055i) q^{30} +(5.49527 - 1.61356i) q^{31} +(-12.1951 - 7.83731i) q^{32} +(-0.0169307 - 0.117756i) q^{33} +(-2.84470 - 6.22903i) q^{34} +(-2.77235 - 6.07060i) q^{35} +(-0.722125 - 5.02249i) q^{36} +(5.79948 + 3.72710i) q^{37} +(4.40762 - 1.29419i) q^{38} +(0.614381 - 4.27311i) q^{39} +(-15.5599 + 17.9571i) q^{40} +(-5.48180 + 3.52294i) q^{41} +(3.99993 + 4.61617i) q^{42} +(-8.28385 - 2.43236i) q^{43} +(0.250767 - 0.549102i) q^{44} -2.90602 q^{45} +(1.93781 + 12.6075i) q^{46} +5.91880 q^{47} +(4.81823 - 10.5504i) q^{48} +(1.65616 + 0.486293i) q^{49} +(6.00028 + 6.92469i) q^{50} +(2.16593 - 1.39196i) q^{51} +(14.3449 - 16.5549i) q^{52} +(-0.514895 + 3.58117i) q^{53} +(2.55199 - 0.749331i) q^{54} +(-0.290838 - 0.186910i) q^{55} +(2.67225 + 18.5859i) q^{56} +(0.717477 + 1.57106i) q^{57} +(-1.57500 - 3.44878i) q^{58} +(0.386194 + 2.68604i) q^{59} +(-12.4048 - 7.97205i) q^{60} +(-12.0589 + 3.54081i) q^{61} +(-2.16787 + 15.0779i) q^{62} +(-1.50389 + 1.73558i) q^{63} +(12.9209 - 8.30375i) q^{64} +(-8.21553 - 9.48123i) q^{65} +(0.303602 + 0.0891454i) q^{66} +(-0.0349839 + 0.0766041i) q^{67} +13.0641 q^{68} +(-4.58823 + 1.39575i) q^{69} +17.7502 q^{70} +(6.43563 - 14.0921i) q^{71} +(7.84516 + 2.30355i) q^{72} +(0.455430 + 0.525595i) q^{73} +(-15.4250 + 9.91306i) q^{74} +(-2.25598 + 2.60354i) q^{75} +(-1.24721 + 8.67450i) q^{76} +(-0.262140 + 0.0769714i) q^{77} +(9.65942 + 6.20774i) q^{78} +(1.05210 + 7.31752i) q^{79} +(-14.0019 - 30.6598i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-2.46651 - 17.1550i) q^{82} +(2.33903 + 1.50321i) q^{83} +(-11.1807 + 3.28296i) q^{84} +(1.06480 - 7.40583i) q^{85} +(15.0375 - 17.3542i) q^{86} +(1.19919 - 0.770675i) q^{87} +(0.636992 + 0.735128i) q^{88} +(12.7468 + 3.74281i) q^{89} +(3.21083 - 7.03075i) q^{90} -9.91413 q^{91} +(-23.4144 - 6.62886i) q^{92} -5.72727 q^{93} +(-6.53962 + 14.3198i) q^{94} +(4.81578 + 1.41404i) q^{95} +(9.49308 + 10.9556i) q^{96} +(-7.16897 + 4.60722i) q^{97} +(-3.00640 + 3.46957i) q^{98} +(-0.0169307 + 0.117756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.10489	+	2.41937i	−0.781275	+	1.71075i	−0.0811848	+	0.996699i	$0.525870\pi$
$2$	−1.10489	+	2.41937i	−0.781275	+	1.71075i	−0.700090	+	0.714054i	$0.746857\pi$
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−3.32285	−	3.83478i	−1.66143	−	1.91739i
$5$	−2.44470	+	1.57111i	−1.09330	+	0.702624i	−0.957593	−	0.288125i	$-0.906968\pi$
$5$	−2.44470	+	1.57111i	−1.09330	+	0.702624i	−0.135711	+	0.990748i	$0.543332\pi$
$6$	1.74175	−	2.01009i	0.711066	−	0.820614i
$7$	−0.326826	+	2.27313i	−0.123529	+	0.859161i	0.829979	+	0.557794i	$0.188352\pi$
$7$	−0.326826	+	2.27313i	−0.123529	+	0.859161i	−0.953508	+	0.301367i	$0.902557\pi$
$8$	7.84516	−	2.30355i	2.77368	−	0.814426i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−1.09998	−	7.65055i	−0.347845	−	2.41932i
$11$	0.0494206	+	0.108216i	0.0149009	+	0.0326283i	0.916936	−	0.399034i	$-0.130654\pi$
$11$	0.0494206	+	0.108216i	0.0149009	+	0.0326283i	−0.902035	+	0.431662i	$0.857927\pi$
$12$	2.10787	+	4.61560i	0.608490	+	1.33241i
$13$	0.614381	+	4.27311i	0.170399	+	1.18515i	0.878044	+	0.478580i	$0.158849\pi$
$13$	0.614381	+	4.27311i	0.170399	+	1.18515i	−0.707645	+	0.706568i	$0.750242\pi$
$14$	−5.13843	−	3.30227i	−1.37330	−	0.882568i
$15$	2.78831	−	0.818721i	0.719938	−	0.211393i
$16$	−1.65065	+	11.4805i	−0.412663	+	2.87013i
$17$	−1.68604	+	1.94579i	−0.408924	+	0.471923i	−0.922431	−	0.386162i	$-0.873800\pi$
$17$	−1.68604	+	1.94579i	−0.408924	+	0.471923i	0.513507	+	0.858085i	$0.328346\pi$
$18$	−2.23750	+	1.43796i	−0.527384	+	0.338929i
$19$	−1.13103	−	1.30528i	−0.259476	−	0.299452i	0.611031	−	0.791606i	$-0.290755\pi$
$19$	−1.13103	−	1.30528i	−0.259476	−	0.299452i	−0.870508	+	0.492155i	$0.836209\pi$
$20$	14.1483	+	4.15430i	3.16365	+	0.928931i
$21$	0.954001	−	2.08897i	0.208180	−	0.455851i
$22$	−0.316419			−0.0674607
$23$	4.00915	−	2.63187i	0.835965	−	0.548783i
$23$	4.00915	−	2.63187i	0.835965	−	0.548783i
$24$	−8.17636			−1.66899
$25$	1.43109	−	3.13366i	0.286219	−	0.626731i
$26$	−11.0171	−	3.23490i	−2.16063	−	0.634417i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	9.80293	−	6.29996i	1.85258	−	1.19058i
$29$	−0.933494	+	1.07731i	−0.173345	+	0.200051i	−0.835774	−	0.549074i	$-0.814980\pi$
$29$	−0.933494	+	1.07731i	−0.173345	+	0.200051i	0.662428	+	0.749125i	$0.269526\pi$
$30$	−1.09998	+	7.65055i	−0.200829	+	1.39679i
$31$	5.49527	−	1.61356i	0.986980	−	0.289803i	0.251877	−	0.967759i	$-0.418952\pi$
$31$	5.49527	−	1.61356i	0.986980	−	0.289803i	0.735103	+	0.677956i	$0.237134\pi$
$32$	−12.1951	−	7.83731i	−2.15581	−	1.38545i
$33$	−0.0169307	−	0.117756i	−0.00294726	−	0.0204987i
$34$	−2.84470	−	6.22903i	−0.487862	−	1.06827i
$35$	−2.77235	−	6.07060i	−0.468613	−	1.02612i
$36$	−0.722125	−	5.02249i	−0.120354	−	0.837081i
$37$	5.79948	+	3.72710i	0.953429	+	0.612731i	0.922172	−	0.386780i	$-0.126413\pi$
$37$	5.79948	+	3.72710i	0.953429	+	0.612731i	0.0312566	+	0.999511i	$0.490049\pi$
$38$	4.40762	−	1.29419i	0.715010	−	0.209946i
$39$	0.614381	−	4.27311i	0.0983797	−	0.684246i
$40$	−15.5599	+	17.9571i	−2.46024	+	2.83927i
$41$	−5.48180	+	3.52294i	−0.856113	+	0.550190i	−0.893476	−	0.449111i	$-0.851741\pi$
$41$	−5.48180	+	3.52294i	−0.856113	+	0.550190i	0.0373628	+	0.999302i	$0.488104\pi$
$42$	3.99993	+	4.61617i	0.617203	+	0.712290i
$43$	−8.28385	−	2.43236i	−1.26327	−	0.370931i	−0.419562	−	0.907726i	$-0.637816\pi$
$43$	−8.28385	−	2.43236i	−1.26327	−	0.370931i	−0.843712	+	0.536796i	$0.819635\pi$
$44$	0.250767	−	0.549102i	0.0378045	−	0.0827803i
$45$	−2.90602			−0.433204
$46$	1.93781	+	12.6075i	0.285714	+	1.85888i
$47$	5.91880			0.863345			0.431673	−	0.902030i	$-0.357924\pi$
$47$	5.91880			0.863345			0.431673	+	0.902030i	$0.357924\pi$
$48$	4.81823	−	10.5504i	0.695451	−	1.52283i
$49$	1.65616	+	0.486293i	0.236595	+	0.0694704i
$50$	6.00028	+	6.92469i	0.848567	+	0.979299i
$51$	2.16593	−	1.39196i	0.303291	−	0.194913i
$52$	14.3449	−	16.5549i	1.98929	−	2.29576i
$53$	−0.514895	+	3.58117i	−0.0707263	+	0.491912i	0.923413	+	0.383807i	$0.125387\pi$
$53$	−0.514895	+	3.58117i	−0.0707263	+	0.491912i	−0.994140	+	0.108105i	$0.965522\pi$
$54$	2.55199	−	0.749331i	0.347281	−	0.101971i
$55$	−0.290838	−	0.186910i	−0.0392166	−	0.0252030i
$56$	2.67225	+	18.5859i	0.357094	+	2.48364i
$57$	0.717477	+	1.57106i	0.0950321	+	0.208091i
$58$	−1.57500	−	3.44878i	−0.206808	−	0.452846i
$59$	0.386194	+	2.68604i	0.0502782	+	0.349692i	0.999395	+	0.0347692i	$0.0110696\pi$
$59$	0.386194	+	2.68604i	0.0502782	+	0.349692i	−0.949117	+	0.314923i	$0.898021\pi$
$60$	−12.4048	−	7.97205i	−1.60145	−	1.02919i
$61$	−12.0589	+	3.54081i	−1.54398	+	0.453354i	−0.939296	−	0.343109i	$-0.888520\pi$
$61$	−12.0589	+	3.54081i	−1.54398	+	0.453354i	−0.604687	+	0.796463i	$0.706702\pi$
$62$	−2.16787	+	15.0779i	−0.275320	+	1.91490i
$63$	−1.50389	+	1.73558i	−0.189472	+	0.218663i
$64$	12.9209	−	8.30375i	1.61511	−	1.03797i
$65$	−8.21553	−	9.48123i	−1.01901	−	1.17600i
$66$	0.303602	+	0.0891454i	0.0373708	+	0.0109730i
$67$	−0.0349839	+	0.0766041i	−0.00427397	+	0.00935868i	−0.911757	−	0.410730i	$-0.865274\pi$
$67$	−0.0349839	+	0.0766041i	−0.00427397	+	0.00935868i	0.907483	+	0.420089i	$0.138001\pi$
$68$	13.0641			1.58426
$69$	−4.58823	+	1.39575i	−0.552358	+	0.168029i
$70$	17.7502			2.12155
$71$	6.43563	−	14.0921i	0.763769	−	1.67242i	0.0238577	−	0.999715i	$-0.492405\pi$
$71$	6.43563	−	14.0921i	0.763769	−	1.67242i	0.739911	−	0.672705i	$-0.234868\pi$
$72$	7.84516	+	2.30355i	0.924561	+	0.271475i
$73$	0.455430	+	0.525595i	0.0533041	+	0.0615162i	0.781775	−	0.623560i	$-0.214314\pi$
$73$	0.455430	+	0.525595i	0.0533041	+	0.0615162i	−0.728471	+	0.685076i	$0.759769\pi$
$74$	−15.4250	+	9.91306i	−1.79312	+	1.15237i
$75$	−2.25598	+	2.60354i	−0.260498	+	0.300630i
$76$	−1.24721	+	8.67450i	−0.143064	+	0.995034i
$77$	−0.262140	+	0.0769714i	−0.0298737	+	0.00877170i
$78$	9.65942	+	6.20774i	1.09371	+	0.702888i
$79$	1.05210	+	7.31752i	0.118371	+	0.823285i	0.959350	+	0.282218i	$0.0910702\pi$
$79$	1.05210	+	7.31752i	0.118371	+	0.823285i	−0.840980	+	0.541067i	$0.818021\pi$
$80$	−14.0019	−	30.6598i	−1.56546	−	3.42787i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−2.46651	−	17.1550i	−0.272381	−	1.89445i
$83$	2.33903	+	1.50321i	0.256742	+	0.164998i	0.662680	−	0.748902i	$-0.269419\pi$
$83$	2.33903	+	1.50321i	0.256742	+	0.164998i	−0.405938	+	0.913901i	$0.633055\pi$
$84$	−11.1807	+	3.28296i	−1.21992	+	0.358201i
$85$	1.06480	−	7.40583i	0.115493	−	0.803275i
$86$	15.0375	−	17.3542i	1.62154	−	1.87135i
$87$	1.19919	−	0.770675i	0.128567	−	0.0826250i
$88$	0.636992	+	0.735128i	0.0679036	+	0.0783649i
$89$	12.7468	+	3.74281i	1.35116	+	0.396737i	0.875638	−	0.482967i	$-0.160441\pi$
$89$	12.7468	+	3.74281i	1.35116	+	0.396737i	0.475522	+	0.879704i	$0.342259\pi$
$90$	3.21083	−	7.03075i	0.338452	−	0.741106i
$91$	−9.91413			−1.03928
$92$	−23.4144	−	6.62886i	−2.44112	−	0.691107i
$93$	−5.72727			−0.593890
$94$	−6.53962	+	14.3198i	−0.674510	+	1.47697i
$95$	4.81578	+	1.41404i	0.494089	+	0.145077i
$96$	9.49308	+	10.9556i	0.968883	+	1.11815i
$97$	−7.16897	+	4.60722i	−0.727898	+	0.467792i	−0.851376	−	0.524555i	$-0.824232\pi$
$97$	−7.16897	+	4.60722i	−0.727898	+	0.467792i	0.123478	+	0.992347i	$0.460595\pi$
$98$	−3.00640	+	3.46957i	−0.303692	+	0.350479i
$99$	−0.0169307	+	0.117756i	−0.00170160	+	0.0118349i
$100$	−16.7722	+	4.92476i	−1.67722	+	0.492476i
$101$	5.88248	+	3.78044i	0.585328	+	0.376168i	0.799534	−	0.600621i	$-0.205080\pi$
$101$	5.88248	+	3.78044i	0.585328	+	0.376168i	−0.214206	+	0.976789i	$0.568716\pi$
$102$	0.974551	+	6.77815i	0.0964949	+	0.671137i
$103$	5.73944	+	12.5676i	0.565523	+	1.23832i	0.949147	+	0.314834i	$0.101949\pi$
$103$	5.73944	+	12.5676i	0.565523	+	1.23832i	−0.383623	+	0.923490i	$0.625324\pi$
$104$	14.6632	+	32.1080i	1.43785	+	3.14845i
$105$	0.949765	+	6.60576i	0.0926875	+	0.644656i
$106$	−8.09528	−	5.20252i	−0.786283	−	0.505314i
$107$	−7.88971	+	2.31663i	−0.762727	+	0.223957i	−0.639886	−	0.768469i	$-0.721019\pi$
$107$	−7.88971	+	2.31663i	−0.762727	+	0.223957i	−0.122841	+	0.992426i	$0.539200\pi$
$108$	−0.722125	+	5.02249i	−0.0694865	+	0.483289i
$109$	11.3104	−	13.0529i	1.08334	−	1.25024i	0.116958	−	0.993137i	$-0.462686\pi$
$109$	11.3104	−	13.0529i	1.08334	−	1.25024i	0.966383	−	0.257106i	$-0.0827688\pi$
$110$	0.773550	−	0.497130i	0.0737551	−	0.0473995i
$111$	−4.51451	−	5.21003i	−0.428499	−	0.494514i
$112$	−25.5572	−	7.50428i	−2.41493	−	0.709088i
$113$	3.11467	−	6.82019i	0.293004	−	0.641589i	−0.704686	−	0.709519i	$-0.748912\pi$
$113$	3.11467	−	6.82019i	0.293004	−	0.641589i	0.997690	+	0.0679300i	$0.0216395\pi$
$114$	−4.59370			−0.430239
$115$	−5.66620	+	12.7330i	−0.528376	+	1.18736i
$116$	7.23310			0.671577
$117$	−1.79337	+	3.92693i	−0.165797	+	0.363045i
$118$	−6.92522	−	2.03343i	−0.637518	−	0.187192i
$119$	−3.87198	−	4.46851i	−0.354944	−	0.409627i
$120$	19.9888	−	12.8460i	1.82472	−	1.17267i
$121$	7.19420	−	8.30255i	0.654018	−	0.754777i
$122$	4.75721	−	33.0871i	0.430698	−	2.99557i
$123$	6.25227	−	1.83583i	0.563748	−	0.165531i
$124$	−24.4476	−	15.7115i	−2.19546	−	1.41094i
$125$	−0.643114	−	4.47295i	−0.0575218	−	0.400073i
$126$	−2.53738	−	5.55609i	−0.226048	−	0.494976i
$127$	−0.834395	−	1.82707i	−0.0740406	−	0.162126i	0.868992	−	0.494825i	$-0.164768\pi$
$127$	−0.834395	−	1.82707i	−0.0740406	−	0.162126i	−0.943033	+	0.332699i	$0.892041\pi$
$128$	1.68761	+	11.7376i	0.149165	+	1.03747i
$129$	7.26302	+	4.66766i	0.639473	+	0.410964i
$130$	32.0159	−	9.40071i	2.80798	−	0.824496i
$131$	0.699047	−	4.86198i	0.0610760	−	0.424793i	−0.936227	−	0.351396i	$-0.885707\pi$
$131$	0.699047	−	4.86198i	0.0610760	−	0.424793i	0.997303	−	0.0733967i	$-0.0233839\pi$
$132$	−0.395309	+	0.456211i	−0.0344072	+	0.0397080i
$133$	3.33672	−	2.14438i	0.289330	−	0.185941i
$134$	−0.146680	−	0.169278i	−0.0126712	−	0.0146234i
$135$	2.78831	+	0.818721i	0.239979	+	0.0704643i
$136$	−8.74500	+	19.1489i	−0.749877	+	1.64200i
$137$	7.93152			0.677636			0.338818	−	0.940852i	$-0.389973\pi$
$137$	7.93152			0.677636			0.338818	+	0.940852i	$0.389973\pi$
$138$	1.69264	−	12.6428i	0.144087	−	1.07623i
$139$	10.7987			0.915936			0.457968	−	0.888969i	$-0.348577\pi$
$139$	10.7987			0.915936			0.457968	+	0.888969i	$0.348577\pi$
$140$	−14.0673	+	30.8030i	−1.18890	+	2.60333i
$141$	−5.67904	−	1.66752i	−0.478262	−	0.140430i
$142$	26.9833	+	31.1403i	2.26439	+	2.61324i
$143$	−0.432056	+	0.277665i	−0.0361303	+	0.0232196i
$144$	−7.59546	+	8.76563i	−0.632955	+	0.730469i
$145$	0.589538	−	4.10033i	0.0489585	−	0.340514i
$146$	−1.77481	+	0.521131i	−0.146884	+	0.0431291i
$147$	−1.45207	−	0.933189i	−0.119765	−	0.0769682i
$148$	−4.97822	−	34.6243i	−0.409207	−	2.84610i
$149$	6.87613	+	15.0566i	0.563315	+	1.23349i	0.950281	+	0.311393i	$0.100796\pi$
$149$	6.87613	+	15.0566i	0.563315	+	1.23349i	−0.386967	+	0.922094i	$0.626477\pi$
$150$	−3.80631	−	8.33466i	−0.310784	−	0.680522i
$151$	−2.68982	−	18.7081i	−0.218895	−	1.52245i	−0.742128	−	0.670258i	$-0.766184\pi$
$151$	−2.68982	−	18.7081i	−0.218895	−	1.52245i	0.523234	−	0.852189i	$-0.324726\pi$
$152$	−11.8799	−	7.63474i	−0.963586	−	0.619259i
$153$	−2.47036	+	0.725362i	−0.199716	+	0.0586420i
$154$	0.103414	−	0.719260i	0.00833333	−	0.0579596i
$155$	−10.8992	+	12.5784i	−0.875446	+	1.01032i
$156$	−18.4279	+	11.8429i	−1.47542	+	0.948192i
$157$	−4.95301	−	5.71608i	−0.395293	−	0.456193i	0.522860	−	0.852419i	$-0.324865\pi$
$157$	−4.95301	−	5.71608i	−0.395293	−	0.456193i	−0.918153	+	0.396226i	$0.870320\pi$
$158$	−18.8662	−	5.53963i	−1.50092	−	0.440709i
$159$	1.50297	−	3.29105i	0.119193	−	0.260997i
$160$	42.1267			3.33041
$161$	4.67228	+	9.97346i	0.368227	+	0.786019i
$162$	−2.65972			−0.208968
$163$	0.693430	−	1.51840i	0.0543136	−	0.118930i	−0.880529	−	0.473992i	$-0.842813\pi$
$163$	0.693430	−	1.51840i	0.0543136	−	0.118930i	0.934843	+	0.355061i	$0.115540\pi$
$164$	31.7249	+	9.31527i	2.47730	+	0.727400i
$165$	0.226398	+	0.261278i	0.0176251	+	0.0203404i
$166$	−6.22119	+	3.99811i	−0.482858	+	0.310314i
$167$	−14.0362	+	16.1987i	−1.08615	+	1.25349i	−0.120764	+	0.992681i	$0.538535\pi$
$167$	−14.0362	+	16.1987i	−1.08615	+	1.25349i	−0.965391	+	0.260808i	$0.916011\pi$
$168$	2.67225	−	18.5859i	0.206168	−	1.43393i
$169$	−5.40863	+	1.58812i	−0.416049	+	0.122163i
$170$	16.7410	+	10.7588i	1.28397	+	0.825159i
$171$	−0.245797	−	1.70955i	−0.0187965	−	0.130733i
$172$	18.1985	+	39.8491i	1.38762	+	3.03846i
$173$	−2.62976	−	5.75836i	−0.199937	−	0.437800i	0.782932	−	0.622107i	$-0.213723\pi$
$173$	−2.62976	−	5.75836i	−0.199937	−	0.437800i	−0.982869	+	0.184307i	$0.940996\pi$
$174$	0.539572	+	3.75281i	0.0409048	+	0.284499i
$175$	6.65548	+	4.27722i	0.503107	+	0.323327i
$176$	−1.32395	+	0.388747i	−0.0997966	+	0.0293029i
$177$	0.386194	−	2.68604i	0.0290281	−	0.201895i
$178$	−23.1391	+	26.7039i	−1.73435	+	2.00154i
$179$	6.89203	−	4.42924i	0.515134	−	0.331057i	−0.257110	−	0.966382i	$-0.582770\pi$
$179$	6.89203	−	4.42924i	0.515134	−	0.331057i	0.772245	+	0.635325i	$0.219134\pi$
$180$	9.65629	+	11.1439i	0.719737	+	0.830621i
$181$	−6.05668	−	1.77840i	−0.450189	−	0.132188i	0.0487755	−	0.998810i	$-0.484468\pi$
$181$	−6.05668	−	1.77840i	−0.450189	−	0.132188i	−0.498965	+	0.866622i	$0.666286\pi$
$182$	10.9540	−	23.9859i	0.811966	−	1.77796i
$183$	12.5680			0.929052
$184$	25.3897	−	29.8827i	1.87176	−	2.20298i
$185$	−20.0337			−1.47291
$186$	6.32800	−	13.8564i	0.463991	−	1.01600i
$187$	−0.293890	−	0.0862939i	−0.0214914	−	0.00631044i
$188$	−19.6673	−	22.6973i	−1.43438	−	1.65537i
$189$	1.93194	−	1.24158i	0.140528	−	0.0903118i
$190$	−8.74199	+	10.0888i	−0.634211	+	0.731918i
$191$	−1.84244	+	12.8144i	−0.133314	+	0.927221i	0.807878	+	0.589350i	$0.200616\pi$
$191$	−1.84244	+	12.8144i	−0.133314	+	0.927221i	−0.941192	+	0.337871i	$0.890293\pi$
$192$	−14.7369	+	4.32716i	−1.06355	+	0.312286i
$193$	10.6093	+	6.81818i	0.763674	+	0.490784i	0.863579	−	0.504213i	$-0.168217\pi$
$193$	10.6093	+	6.81818i	0.763674	+	0.490784i	−0.0999048	+	0.994997i	$0.531854\pi$
$194$	−3.22565	−	22.4349i	−0.231588	−	1.61073i
$195$	5.21157	+	11.4118i	0.373209	+	0.817213i
$196$	−3.63836	−	7.96689i	−0.259883	−	0.569064i
$197$	2.06820	+	14.3847i	0.147353	+	1.02486i	0.920530	+	0.390673i	$0.127758\pi$
$197$	2.06820	+	14.3847i	0.147353	+	1.02486i	−0.773176	+	0.634191i	$0.781333\pi$
$198$	−0.266188	−	0.171069i	−0.0189172	−	0.0121573i
$199$	−19.3561	+	5.68347i	−1.37212	+	0.402890i	−0.883019	−	0.469337i	$-0.844493\pi$
$199$	−19.3561	+	5.68347i	−1.37212	+	0.402890i	−0.489100	+	0.872228i	$0.662675\pi$
$200$	4.00863	−	27.8806i	0.283453	−	1.97146i
$201$	0.0551487	−	0.0636450i	0.00388989	−	0.00448917i
$202$	−15.6458	+	10.0549i	−1.10083	+	0.707462i
$203$	−2.14377	−	2.47404i	−0.150463	−	0.173644i
$204$	−12.5349	−	3.68058i	−0.877620	−	0.257692i
$205$	7.86642	−	17.2251i	0.549415	−	1.20305i
$206$	−36.7472			−2.56030
$207$	4.79561	−	0.0465625i	0.333318	−	0.00323631i
$208$	−50.0717			−3.47185
$209$	0.0853558	−	0.186903i	0.00590419	−	0.0129284i
$210$	−17.0312	−	5.00080i	−1.17526	−	0.345088i
$211$	−4.88121	−	5.63321i	−0.336036	−	0.387806i	0.562433	−	0.826843i	$-0.309865\pi$
$211$	−4.88121	−	5.63321i	−0.336036	−	0.387806i	−0.898469	+	0.439036i	$0.855320\pi$
$212$	15.4439	−	9.92520i	1.06069	−	0.681666i
$213$	−10.1451	+	11.7081i	−0.695133	+	0.802226i
$214$	3.11248	−	21.6478i	0.212765	−	1.47981i
$215$	24.0731	−	7.06849i	1.64177	−	0.482067i
$216$	−6.87839	−	4.42047i	−0.468015	−	0.300775i
$217$	1.87182	+	13.0188i	0.127067	+	0.883774i
$218$	19.0831	+	41.7861i	1.29247	+	2.83011i
$219$	−0.288905	−	0.632614i	−0.0195224	−	0.0427481i
$220$	0.249653	+	1.73637i	0.0168316	+	0.117066i
$221$	−9.35044	−	6.00917i	−0.628979	−	0.404220i
$222$	17.5930	−	5.16578i	1.18077	−	0.346704i
$223$	−0.239369	+	1.66485i	−0.0160293	+	0.111486i	−0.996265	−	0.0863458i	$-0.972481\pi$
$223$	−0.239369	+	1.66485i	−0.0160293	+	0.111486i	0.980236	+	0.197832i	$0.0633901\pi$
$224$	21.8009	−	25.1596i	1.45663	−	1.68104i
$225$	2.89809	−	1.86249i	0.193206	−	0.124166i
$226$	13.0592	+	15.0711i	0.868684	+	1.00252i
$227$	−10.3447	−	3.03747i	−0.686601	−	0.201604i	−0.0802184	−	0.996777i	$-0.525562\pi$
$227$	−10.3447	−	3.03747i	−0.686601	−	0.201604i	−0.606383	+	0.795173i	$0.707380\pi$
$228$	3.64057	−	7.97175i	0.241103	−	0.527942i
$229$	21.9077			1.44770			0.723852	−	0.689955i	$-0.242370\pi$
$229$	21.9077			1.44770			0.723852	+	0.689955i	$0.242370\pi$
$230$	−24.5453	−	27.7772i	−1.61847	−	1.83157i
$231$	0.273207			0.0179757
$232$	−4.84177	+	10.6020i	−0.317878	+	0.696056i
$233$	−23.8637	−	7.00702i	−1.56336	−	0.459045i	−0.618304	−	0.785939i	$-0.712180\pi$
$233$	−23.8637	−	7.00702i	−1.56336	−	0.459045i	−0.945061	+	0.326894i	$0.893998\pi$
$234$	−7.51923	−	8.67765i	−0.491547	−	0.567276i
$235$	−14.4697	+	9.29911i	−0.943899	+	0.606607i
$236$	9.01709	−	10.4063i	0.586962	−	0.677391i
$237$	1.05210	−	7.31752i	0.0683412	−	0.475324i
$238$	15.0891	−	4.43056i	0.978080	−	0.287190i
$239$	3.53060	+	2.26898i	0.228375	+	0.146768i	0.649825	−	0.760084i	$-0.274842\pi$
$239$	3.53060	+	2.26898i	0.228375	+	0.146768i	−0.421450	+	0.906852i	$0.638479\pi$
$240$	4.79683	+	33.3627i	0.309634	+	2.15355i
$241$	−11.3946	−	24.9507i	−0.733991	−	1.60722i	−0.793193	−	0.608971i	$-0.791583\pi$
$241$	−11.3946	−	24.9507i	−0.733991	−	1.60722i	0.0592012	−	0.998246i	$-0.481145\pi$
$242$	12.1381	+	26.5788i	0.780270	+	1.70855i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	53.6481	+	34.4776i	3.43447	+	2.20720i
$245$	−4.81284	+	1.41318i	−0.307481	+	0.0902847i
$246$	−2.46651	+	17.1550i	−0.157259	+	1.09376i
$247$	4.88272	−	5.63496i	0.310680	−	0.358544i
$248$	39.3944	−	25.3172i	2.50154	−	1.60764i
$249$	−1.82078	−	2.10130i	−0.115388	−	0.133164i
$250$	11.5323	+	3.38619i	0.729367	+	0.214161i
$251$	−5.36870	+	11.7558i	−0.338869	+	0.742020i	−0.999966	−	0.00828064i	$-0.997364\pi$
$251$	−5.36870	+	11.7558i	−0.338869	+	0.742020i	0.661096	+	0.750301i	$0.270091\pi$
$252$	11.6528			0.734055
$253$	0.482945	+	0.303785i	0.0303625	+	0.0190988i
$254$	5.34227			0.335204
$255$	−3.10813	+	6.80585i	−0.194639	+	0.426199i
$256$	−0.788305	−	0.231467i	−0.0492691	−	0.0144667i
$257$	0.940093	+	1.08493i	0.0586414	+	0.0676758i	0.784312	−	0.620366i	$-0.213016\pi$
$257$	0.940093	+	1.08493i	0.0586414	+	0.0676758i	−0.725671	+	0.688042i	$0.758471\pi$
$258$	−19.3176	+	12.4147i	−1.20266	+	0.772905i
$259$	−10.3676	+	11.9648i	−0.644211	+	0.743459i
$260$	−9.05939	+	63.0095i	−0.561840	+	3.90768i
$261$	−1.36774	+	0.401605i	−0.0846611	+	0.0248587i
$262$	10.9906	+	7.06320i	0.678999	+	0.436366i
$263$	−2.04437	−	14.2189i	−0.126061	−	0.876774i	−0.950478	−	0.310791i	$-0.899406\pi$
$263$	−2.04437	−	14.2189i	−0.126061	−	0.876774i	0.824417	−	0.565983i	$-0.191503\pi$
$264$	−0.404080	−	0.884812i	−0.0248694	−	0.0544564i
$265$	−4.36767	−	9.56386i	−0.268304	−	0.587503i
$266$	1.50134	+	10.4421i	0.0920531	+	0.640244i
$267$	−11.1760	−	7.18239i	−0.683961	−	0.439555i
$268$	0.410006	−	0.120389i	0.0250451	−	0.00735390i
$269$	2.75934	−	19.1916i	0.168240	−	1.17013i	−0.714281	−	0.699859i	$-0.753246\pi$
$269$	2.75934	−	19.1916i	0.168240	−	1.17013i	0.882520	−	0.470274i	$-0.155845\pi$
$270$	−5.06156	+	5.84136i	−0.308037	+	0.355494i
$271$	13.7459	−	8.83395i	0.835004	−	0.536624i	−0.0518607	−	0.998654i	$-0.516515\pi$
$271$	13.7459	−	8.83395i	0.835004	−	0.536624i	0.886864	+	0.462030i	$0.152879\pi$
$272$	−19.5556	−	22.5684i	−1.18573	−	1.36841i
$273$	9.51253	+	2.79313i	0.575725	+	0.169048i
$274$	−8.76346	+	19.1893i	−0.529420	+	1.15927i
$275$	0.409837			0.0247141
$276$	20.5984	+	12.9570i	1.23988	+	0.779917i
$277$	20.1827			1.21266			0.606332	−	0.795212i	$-0.292640\pi$
$277$	20.1827			1.21266			0.606332	+	0.795212i	$0.292640\pi$
$278$	−11.9314	+	26.1261i	−0.715598	+	1.56694i
$279$	5.49527	+	1.61356i	0.328993	+	0.0966011i
$280$	−35.7334	−	41.2386i	−2.13548	−	2.46448i
$281$	7.16101	−	4.60210i	0.427190	−	0.274538i	−0.309329	−	0.950955i	$-0.600104\pi$
$281$	7.16101	−	4.60210i	0.427190	−	0.274538i	0.736519	+	0.676417i	$0.236468\pi$
$282$	10.3091	−	11.8973i	0.613896	−	0.708473i
$283$	0.480803	−	3.34406i	0.0285808	−	0.198784i	−0.970528	−	0.240987i	$-0.922529\pi$
$283$	0.480803	−	3.34406i	0.0285808	−	0.198784i	0.999109	+	0.0422038i	$0.0134379\pi$
$284$	−75.4246	+	22.1466i	−4.47562	+	1.31416i
$285$	−4.22232	−	2.71352i	−0.250109	−	0.160735i
$286$	−0.194402	−	1.35209i	−0.0114952	−	0.0799509i
$287$	−6.21649	−	13.6122i	−0.366948	−	0.803503i
$288$	−6.02199	−	13.1863i	−0.354849	−	0.777012i
$289$	1.47597	+	10.2656i	0.0868220	+	0.603861i
$290$	9.26883	+	5.95672i	0.544285	+	0.349791i
$291$	8.17658	−	2.40086i	0.479319	−	0.140741i
$292$	0.502210	−	3.49295i	0.0293896	−	0.204409i
$293$	2.70239	−	3.11873i	0.157876	−	0.182198i	−0.671301	−	0.741185i	$-0.734264\pi$
$293$	2.70239	−	3.11873i	0.157876	−	0.182198i	0.829177	+	0.558987i	$0.188810\pi$
$294$	3.86211	−	2.48203i	0.225243	−	0.144755i
$295$	−5.16420	−	5.95981i	−0.300671	−	0.346993i
$296$	54.0834	+	15.8803i	3.14353	+	0.923024i
$297$	0.0494206	−	0.108216i	0.00286767	−	0.00627932i
$298$	−44.0249			−2.55030
$299$	13.7094	+	15.5146i	0.792837	+	0.897231i
$300$	17.4803			1.00922
$301$	8.23643	−	18.0353i	0.474740	−	1.03954i
$302$	48.2339	+	14.1627i	2.77555	+	0.814975i
$303$	−4.57912	−	5.28459i	−0.263064	−	0.303592i
$304$	16.8522	−	10.8303i	0.966542	−	0.621159i
$305$	23.9174	−	27.6021i	1.36951	−	1.58049i
$306$	0.974551	−	6.77815i	0.0557114	−	0.387481i
$307$	−9.98433	+	2.93166i	−0.569836	+	0.167319i	−0.553943	−	0.832555i	$-0.686877\pi$
$307$	−9.98433	+	2.93166i	−0.569836	+	0.167319i	−0.0158931	+	0.999874i	$0.505059\pi$
$308$	1.16622	+	0.749485i	0.0664517	+	0.0427059i
$309$	−1.96624	−	13.6755i	−0.111856	−	0.777973i
$310$	−18.3893	−	40.2670i	−1.04444	−	2.28701i
$311$	5.48023	+	12.0000i	0.310756	+	0.680460i	0.998986	−	0.0450328i	$-0.0143392\pi$
$311$	5.48023	+	12.0000i	0.310756	+	0.680460i	−0.688230	+	0.725493i	$0.741612\pi$
$312$	−5.02340	−	34.9385i	−0.284394	−	1.97800i
$313$	−11.5760	−	7.43943i	−0.654313	−	0.420501i	0.170927	−	0.985284i	$-0.445324\pi$
$313$	−11.5760	−	7.43943i	−0.654313	−	0.420501i	−0.825240	+	0.564782i	$0.808960\pi$
$314$	19.3018	−	5.66753i	1.08927	−	0.319837i
$315$	0.949765	−	6.60576i	0.0535132	−	0.372192i
$316$	24.5651	−	28.3496i	1.38189	−	1.59479i
$317$	−12.0651	+	7.75378i	−0.677645	+	0.435496i	−0.833674	−	0.552257i	$-0.813767\pi$
$317$	−12.0651	+	7.75378i	−0.677645	+	0.435496i	0.156029	+	0.987752i	$0.450131\pi$
$318$	6.30165	+	7.27249i	0.353379	+	0.407821i
$319$	−0.162716	−	0.0477777i	−0.00911033	−	0.00267504i
$320$	−18.5416	+	40.6004i	−1.03651	+	2.26963i
$321$	8.22279			0.458952
$322$	−29.2919	+	0.284406i	−1.63237	+	0.0158493i
$323$	4.44676			0.247424
$324$	2.10787	−	4.61560i	0.117104	−	0.256422i
$325$	14.2697	+	4.18996i	0.791541	+	0.232417i
$326$	2.90741	+	3.35533i	0.161026	+	0.185834i
$327$	−14.5297	+	9.33767i	−0.803494	+	0.516374i
$328$	−34.8903	+	40.2656i	−1.92650	+	2.22329i
$329$	−1.93442	+	13.4542i	−0.106648	+	0.741753i
$330$	−0.882273	+	0.259059i	−0.0485675	+	0.0142607i
$331$	−9.95577	−	6.39818i	−0.547219	−	0.351676i	0.237638	−	0.971354i	$-0.423627\pi$
$331$	−9.95577	−	6.39818i	−0.547219	−	0.351676i	−0.784856	+	0.619678i	$0.787263\pi$
$332$	−2.00781	−	13.9646i	−0.110193	−	0.766407i
$333$	2.86381	+	6.27087i	0.156936	+	0.343642i
$334$	−23.6821	−	51.8565i	−1.29583	−	2.83746i
$335$	−0.0348286	−	0.242238i	−0.00190289	−	0.0132349i
$336$	22.4078	+	14.4006i	1.22244	+	0.785617i
$337$	−25.6791	+	7.54006i	−1.39883	+	0.410733i	−0.892281	−	0.451480i	$-0.850896\pi$
$337$	−25.6791	+	7.54006i	−1.39883	+	0.410733i	−0.506547	+	0.862213i	$0.669078\pi$
$338$	2.13370	−	14.8402i	0.116058	−	0.807199i
$339$	−4.90998	+	5.66642i	−0.266673	+	0.307757i
$340$	−31.9379	+	20.5252i	−1.73207	+	1.11314i
$341$	0.446192	+	0.514933i	0.0241626	+	0.0278852i
$342$	4.40762	+	1.29419i	0.238337	+	0.0699820i
$343$	−8.32469	+	18.2285i	−0.449491	+	0.984248i
$344$	−70.5911			−3.80602
$345$	9.02397	−	10.6208i	0.485834	−	0.571807i
$346$	16.8372			0.905174
$347$	−3.67463	+	8.04631i	−0.197264	+	0.431948i	−0.982253	−	0.187562i	$-0.939942\pi$
$347$	−3.67463	+	8.04631i	−0.197264	+	0.431948i	0.784989	+	0.619510i	$0.212669\pi$
$348$	−6.94011	−	2.03780i	−0.372029	−	0.109238i
$349$	19.5011	+	22.5054i	1.04387	+	1.20469i	0.978376	+	0.206834i	$0.0663160\pi$
$349$	19.5011	+	22.5054i	1.04387	+	1.20469i	0.0654913	+	0.997853i	$0.479139\pi$
$350$	−17.7017	+	11.3762i	−0.946198	+	0.608084i
$351$	2.82707	−	3.26261i	0.150898	−	0.174145i
$352$	0.245433	−	1.70703i	0.0130816	−	0.0909849i
$353$	16.5145	−	4.84909i	0.878978	−	0.258091i	0.189048	−	0.981968i	$-0.439460\pi$
$353$	16.5145	−	4.84909i	0.878978	−	0.258091i	0.689930	+	0.723877i	$0.257641\pi$
$354$	6.07182	+	3.90212i	0.322713	+	0.207395i
$355$	6.40705	+	44.5620i	0.340051	+	2.36511i
$356$	−28.0030	−	61.3180i	−1.48416	−	3.24985i
$357$	2.45622	+	5.37836i	0.129997	+	0.284653i
$358$	3.10104	+	21.5682i	0.163895	+	1.13991i
$359$	−5.99586	−	3.85331i	−0.316449	−	0.203370i	0.372767	−	0.927925i	$-0.378409\pi$
$359$	−5.99586	−	3.85331i	−0.316449	−	0.203370i	−0.689217	+	0.724555i	$0.742045\pi$
$360$	−22.7982	+	6.69416i	−1.20157	+	0.352813i
$361$	2.27946	−	15.8540i	0.119972	−	0.834420i
$362$	10.9946	−	12.6884i	0.577862	−	0.666888i
$363$	−9.24188	+	5.93940i	−0.485073	+	0.311738i
$364$	32.9432	+	38.0185i	1.72669	+	1.99271i
$365$	−1.93916	−	0.569389i	−0.101500	−	0.0298032i
$366$	−13.8862	+	30.4066i	−0.725845	+	1.58938i
$367$	13.5836			0.709060			0.354530	−	0.935045i	$-0.384641\pi$
$367$	13.5836			0.709060			0.354530	+	0.935045i	$0.384641\pi$
$368$	23.5976	+	50.3714i	1.23011	+	2.62579i
$369$	−6.51623			−0.339221
$370$	22.1350	−	48.4690i	1.15075	−	2.51978i
$371$	−7.97218	−	2.34084i	−0.413895	−	0.121531i
$372$	19.0309	+	21.9628i	0.986704	+	1.13872i
$373$	15.7544	−	10.1247i	0.815733	−	0.524240i	−0.0649821	−	0.997886i	$-0.520699\pi$
$373$	15.7544	−	10.1247i	0.815733	−	0.524240i	0.880715	+	0.473647i	$0.157063\pi$
$374$	0.533493	−	0.615684i	0.0275863	−	0.0318363i
$375$	−0.643114	+	4.47295i	−0.0332102	+	0.230982i
$376$	46.4339	−	13.6342i	2.39465	−	0.703131i
$377$	−5.17699	−	3.32705i	−0.266628	−	0.171352i
$378$	0.869268	+	6.04589i	0.0447103	+	0.310967i
$379$	−4.16129	−	9.11196i	−0.213751	−	0.468050i	0.772137	−	0.635456i	$-0.219188\pi$
$379$	−4.16129	−	9.11196i	−0.213751	−	0.468050i	−0.985888	+	0.167406i	$0.946461\pi$
$380$	−10.5796	−	23.1661i	−0.542722	−	1.18839i
$381$	0.285851	+	1.98814i	0.0146446	+	0.101855i
$382$	−28.9672	−	18.6161i	−1.48209	−	0.952482i
$383$	27.9432	−	8.20488i	1.42783	−	0.419250i	0.525686	−	0.850679i	$-0.323809\pi$
$383$	27.9432	−	8.20488i	1.42783	−	0.419250i	0.902147	+	0.431429i	$0.141990\pi$
$384$	1.68761	−	11.7376i	0.0861204	−	0.598981i
$385$	0.519924	−	0.600025i	0.0264978	−	0.0305801i
$386$	−28.2178	+	18.1345i	−1.43625	+	0.923022i
$387$	−5.65378	−	6.52481i	−0.287398	−	0.331675i
$388$	41.4891	+	12.1823i	2.10629	+	0.618462i
$389$	1.82086	−	3.98712i	0.0923211	−	0.202155i	−0.857838	−	0.513920i	$-0.828193\pi$
$389$	1.82086	−	3.98712i	0.0923211	−	0.202155i	0.950159	+	0.311765i	$0.100920\pi$
$390$	−33.3675			−1.68963
$391$	−1.63850	+	12.2384i	−0.0828624	+	0.618921i
$392$	14.1130			0.712816
$393$	−2.04051	+	4.46809i	−0.102930	+	0.225385i
$394$	−37.0869	−	10.8897i	−1.86841	−	0.548616i
$395$	−14.0687	−	16.2362i	−0.707875	−	0.816931i
$396$	0.507825	−	0.326360i	0.0255192	−	0.0164002i
$397$	−0.0954283	+	0.110130i	−0.00478941	+	0.00552727i	−0.758139	−	0.652093i	$-0.773891\pi$
$397$	−0.0954283	+	0.110130i	−0.00478941	+	0.00552727i	0.753350	+	0.657620i	$0.228437\pi$
$398$	7.63595	−	53.1092i	0.382756	−	2.66213i
$399$	−3.80570	+	1.11745i	−0.190523	+	0.0559426i
$400$	33.6138	+	21.6023i	1.68069	+	1.08011i
$401$	4.79060	+	33.3194i	0.239231	+	1.66389i	0.655912	+	0.754837i	$0.272284\pi$
$401$	4.79060	+	33.3194i	0.239231	+	1.66389i	−0.416681	+	0.909053i	$0.636807\pi$
$402$	0.0930476	+	0.203746i	0.00464079	+	0.0101619i
$403$	10.2711	+	22.4906i	0.511640	+	1.12034i
$404$	−5.04947	−	35.1198i	−0.251220	−	1.74728i
$405$	−2.44470	−	1.57111i	−0.121478	−	0.0780693i
$406$	8.35425	−	2.45303i	0.414615	−	0.121742i
$407$	−0.116718	+	0.811791i	−0.00578549	+	0.0402390i
$408$	13.7856	−	15.9095i	0.682490	−	0.787636i
$409$	−25.4633	+	16.3642i	−1.25908	+	0.809160i	−0.988158	−	0.153442i	$-0.950964\pi$
$409$	−25.4633	+	16.3642i	−1.25908	+	0.809160i	−0.270920	+	0.962602i	$0.587328\pi$
$410$	32.9823	+	38.0636i	1.62888	+	1.87983i
$411$	−7.61024	−	2.23457i	−0.375386	−	0.110223i
$412$	29.1227	−	63.7698i	1.43477	−	3.14171i
$413$	−6.23192			−0.306653
$414$	−5.18596	+	11.6538i	−0.254876	+	0.572753i
$415$	−8.07995			−0.396629
$416$	25.9973	−	56.9261i	1.27462	−	2.79103i
$417$	−10.3613	−	3.04235i	−0.507395	−	0.148985i
$418$	0.357879	+	0.413015i	0.0175045	+	0.0202012i
$419$	15.7624	−	10.1299i	0.770044	−	0.494877i	−0.0956719	−	0.995413i	$-0.530500\pi$
$419$	15.7624	−	10.1299i	0.770044	−	0.494877i	0.865716	+	0.500536i	$0.166864\pi$
$420$	22.1757	−	25.5921i	1.08206	−	1.24877i
$421$	−5.57819	+	38.7972i	−0.271864	+	1.89086i	0.157173	+	0.987571i	$0.449762\pi$
$421$	−5.57819	+	38.7972i	−0.271864	+	1.89086i	−0.429038	+	0.903287i	$0.641147\pi$
$422$	19.0220	−	5.58537i	0.925978	−	0.271892i
$423$	4.97921	+	3.19994i	0.242097	+	0.155587i
$424$	4.20996	+	29.2809i	0.204454	+	1.42201i
$425$	3.68456	+	8.06806i	0.178727	+	0.391358i
$426$	−17.1170	−	37.4810i	−0.829322	−	1.81596i
$427$	−4.10755	−	28.5686i	−0.198778	−	1.38253i
$428$	35.1001	+	22.5575i	1.69663	+	1.09036i
$429$	0.492782	−	0.144694i	0.0237917	−	0.00698589i
$430$	−9.49678	+	66.0515i	−0.457975	+	3.18529i
$431$	−14.0594	+	16.2254i	−0.677217	+	0.781550i	−0.985487	−	0.169749i	$-0.945704\pi$
$431$	−14.0594	+	16.2254i	−0.677217	+	0.781550i	0.308271	+	0.951299i	$0.400250\pi$
$432$	9.75735	−	6.27067i	0.469451	−	0.301698i
$433$	0.496613	+	0.573122i	0.0238657	+	0.0275425i	0.767557	−	0.640981i	$-0.221472\pi$
$433$	0.496613	+	0.573122i	0.0238657	+	0.0275425i	−0.743691	+	0.668523i	$0.766927\pi$
$434$	−33.5655	−	9.85571i	−1.61119	−	0.473089i
$435$	−1.72085	+	3.76814i	−0.0825086	+	0.180669i
$436$	−87.6378			−4.19709
$437$	−7.96980	−	2.25633i	−0.381247	−	0.107935i
$438$	1.84974			0.0883838
$439$	5.44584	−	11.9247i	0.259916	−	0.569136i	−0.734016	−	0.679132i	$-0.762357\pi$
$439$	5.44584	−	11.9247i	0.259916	−	0.569136i	0.993932	+	0.109996i	$0.0350838\pi$
$440$	−2.71223	−	0.796382i	−0.129300	−	0.0379660i
$441$	1.13034	+	1.30448i	0.0538258	+	0.0621183i
$442$	24.8696	−	15.9827i	1.18293	−	0.760221i
$443$	2.00368	−	2.31237i	0.0951976	−	0.109864i	−0.706152	−	0.708061i	$-0.749570\pi$
$443$	2.00368	−	2.31237i	0.0951976	−	0.109864i	0.801349	+	0.598197i	$0.204116\pi$
$444$	−4.97822	+	34.6243i	−0.236256	+	1.64320i
$445$	−37.0426	+	10.8767i	−1.75599	+	0.515604i
$446$	−3.76340	−	2.41859i	−0.178202	−	0.114524i
$447$	−2.35566	−	16.3840i	−0.111419	−	0.774935i
$448$	14.6526	+	32.0847i	0.692270	+	1.51586i
$449$	−3.18597	−	6.97630i	−0.150355	−	0.329232i	0.819435	−	0.573172i	$-0.194287\pi$
$449$	−3.18597	−	6.97630i	−0.150355	−	0.329232i	−0.969790	+	0.243940i	$0.921560\pi$
$450$	1.30398	+	9.06941i	0.0614704	+	0.427536i
$451$	−0.652151	−	0.419112i	−0.0307086	−	0.0197352i
$452$	−36.5035	+	10.7184i	−1.71698	+	0.504151i
$453$	−2.68982	+	18.7081i	−0.126379	+	0.878985i
$454$	18.7785	−	21.6716i	0.881319	−	1.01710i
$455$	24.2371	−	15.5762i	1.13625	−	0.730225i
$456$	9.24771	+	10.6724i	0.433064	+	0.499782i
$457$	−8.60068	−	2.52539i	−0.402323	−	0.118133i	0.0743097	−	0.997235i	$-0.476325\pi$
$457$	−8.60068	−	2.52539i	−0.402323	−	0.118133i	−0.476633	+	0.879103i	$0.658143\pi$
$458$	−24.2056	+	53.0030i	−1.13106	+	2.47667i
$459$	2.57465			0.120174
$460$	67.6560	−	20.5812i	3.15448	−	0.959602i
$461$	−7.53704			−0.351035			−0.175517	−	0.984476i	$-0.556160\pi$
$461$	−7.53704			−0.351035			−0.175517	+	0.984476i	$0.556160\pi$
$462$	−0.301864	+	0.660990i	−0.0140440	+	0.0307520i
$463$	31.6291	+	9.28715i	1.46993	+	0.431610i	0.916076	−	0.401004i	$-0.131339\pi$
$463$	31.6291	+	9.28715i	1.46993	+	0.431610i	0.553853	+	0.832614i	$0.313157\pi$
$464$	−10.8272	−	12.4953i	−0.502640	−	0.580078i
$465$	14.0015	−	8.99819i	0.649302	−	0.417281i
$466$	43.3194	−	49.9932i	2.00673	−	2.31589i
$467$	1.91901	−	13.3470i	0.0888010	−	0.617624i	−0.896015	−	0.444024i	$-0.853551\pi$
$467$	1.91901	−	13.3470i	0.0888010	−	0.617624i	0.984816	−	0.173601i	$-0.0555402\pi$
$468$	21.0180	−	6.17144i	0.971558	−	0.285275i
$469$	−0.162697	−	0.104559i	−0.00751265	−	0.00482809i
$470$	−6.51058	−	45.2821i	−0.300311	−	2.08871i
$471$	3.14197	+	6.87996i	0.144774	+	0.317012i
$472$	9.21716	+	20.1828i	0.424254	+	0.928987i
$473$	−0.146173	−	1.01665i	−0.00672102	−	0.0467457i
$474$	16.5413	+	10.6305i	0.759769	+	0.488274i
$475$	−5.70891	+	1.67629i	−0.261943	+	0.0769133i
$476$	−4.26969	+	29.6964i	−0.195701	+	1.36113i
$477$	−2.36929	+	2.73430i	−0.108482	+	0.125195i
$478$	−9.39042	+	6.03486i	−0.429508	+	0.276028i
$479$	13.6684	+	15.7742i	0.624524	+	0.720740i	0.976560	−	0.215247i	$-0.0690557\pi$
$479$	13.6684	+	15.7742i	0.624524	+	0.720740i	−0.352035	+	0.935987i	$0.614510\pi$
$480$	−40.4203	−	11.8685i	−1.84492	−	0.541719i
$481$	−12.3632	+	27.0717i	−0.563715	+	1.23436i
$482$	72.9548			3.32300
$483$	−1.67317	−	10.8858i	−0.0761320	−	0.495321i
$484$	−55.7437			−2.53380
$485$	10.2875	−	22.5265i	0.467133	−	1.02288i
$486$	2.55199	+	0.749331i	0.115760	+	0.0339903i
$487$	5.41275	+	6.24665i	0.245275	+	0.283063i	0.865016	−	0.501744i	$-0.167308\pi$
$487$	5.41275	+	6.24665i	0.245275	+	0.283063i	−0.619741	+	0.784806i	$0.712762\pi$
$488$	−86.4475	+	55.5564i	−3.91329	+	2.51492i
$489$	−1.09312	+	1.26153i	−0.0494328	+	0.0570485i
$490$	1.89866	−	13.2055i	0.0857727	−	0.596562i
$491$	10.6572	−	3.12922i	0.480951	−	0.141220i	−0.0322652	−	0.999479i	$-0.510272\pi$
$491$	10.6572	−	3.12922i	0.480951	−	0.141220i	0.513216	+	0.858259i	$0.328454\pi$
$492$	−27.8154	−	17.8759i	−1.25401	−	0.805906i
$493$	−0.522312	−	3.63276i	−0.0235238	−	0.163611i
$494$	8.23820	+	18.0391i	0.370654	+	0.811619i
$495$	−0.143617	−	0.314478i	−0.00645512	−	0.0141347i
$496$	9.45372	+	65.7520i	0.424484	+	2.95235i
$497$	29.9297	+	19.2347i	1.34253	+	0.862792i
$498$	7.09558	−	2.08345i	0.317961	−	0.0933617i
$499$	0.865761	−	6.02150i	0.0387568	−	0.269559i	−0.961224	−	0.275769i	$-0.911067\pi$
$499$	0.865761	−	6.02150i	0.0387568	−	0.269559i	0.999981	+	0.00620960i	$0.00197659\pi$
$500$	−15.0158	+	17.3292i	−0.671527	+	0.774984i
$501$	18.0313	−	11.5880i	0.805581	−	0.517715i
$502$	−22.5099	−	25.9778i	−1.00466	−	1.15944i
$503$	7.54921	+	2.21665i	0.336602	+	0.0988354i	0.445666	−	0.895199i	$-0.352967\pi$
$503$	7.54921	+	2.21665i	0.336602	+	0.0988354i	−0.109063	+	0.994035i	$0.534785\pi$
$504$	−7.80025	+	17.0802i	−0.347451	+	0.760811i
$505$	−20.3204			−0.904246
$506$	−1.26857	+	0.832773i	−0.0563948	+	0.0370213i
$507$	5.63697			0.250347
$508$	−4.23383	+	9.27080i	−0.187846	+	0.411325i
$509$	−28.5327	−	8.37797i	−1.26469	−	0.371347i	−0.420453	−	0.907315i	$-0.638129\pi$
$509$	−28.5327	−	8.37797i	−1.26469	−	0.371347i	−0.844238	+	0.535968i	$0.819947\pi$
$510$	−13.0317	−	15.0394i	−0.577055	−	0.665957i
$511$	−1.34359	+	0.863473i	−0.0594369	+	0.0381978i
$512$	−14.1000	+	16.2723i	−0.623140	+	0.719142i
$513$	−0.245797	+	1.70955i	−0.0108522	+	0.0754786i
$514$	−3.66354	+	1.07571i	−0.161592	+	0.0474476i
$515$	−33.7764	−	21.7068i	−1.48836	−	0.956514i
$516$	−6.23451	−	43.3620i	−0.274459	−	1.90891i
$517$	0.292510	+	0.640508i	0.0128646	+	0.0281695i
$518$	−17.4923	−	38.3029i	−0.768569	−	1.68293i
$519$	0.900914	+	6.26600i	0.0395457	+	0.275047i
$520$	−86.2926	−	55.4569i	−3.78418	−	2.43194i
$521$	18.2067	−	5.34598i	0.797651	−	0.234211i	0.142584	−	0.989783i	$-0.454459\pi$
$521$	18.2067	−	5.34598i	0.797651	−	0.234211i	0.655066	+	0.755571i	$0.272641\pi$
$522$	0.539572	−	3.75281i	0.0236164	−	0.164256i
$523$	17.3500	−	20.0229i	0.758661	−	0.875542i	−0.236717	−	0.971579i	$-0.576071\pi$
$523$	17.3500	−	20.0229i	0.758661	−	0.875542i	0.995378	+	0.0960371i	$0.0306168\pi$
$524$	−20.9674	+	13.4749i	−0.915966	+	0.588656i
$525$	−5.18085	−	5.97902i	−0.226111	−	0.260946i
$526$	36.6595	+	10.7642i	1.59843	+	0.469342i
$527$	−6.12558	+	13.4131i	−0.266834	+	0.584286i
$528$	1.37985			0.0600501
$529$	9.14651	−	21.1031i	0.397674	−	0.917527i
$530$	27.9643			1.21469
$531$	−1.12729	+	2.46843i	−0.0489204	+	0.107121i
$532$	−19.3106	−	5.67011i	−0.837222	−	0.245831i
$533$	−18.4218	−	21.2599i	−0.797938	−	0.920869i
$534$	29.7251	−	19.1032i	1.28633	−	0.826676i
$535$	15.6483	−	18.0591i	0.676535	−	0.780763i
$536$	−0.0979933	+	0.681558i	−0.00423266	+	0.0294388i
$537$	−7.86071	+	2.30811i	−0.339215	+	0.0996024i
$538$	43.3829	+	27.8805i	1.87037	+	1.20201i
$539$	0.0292238	+	0.203256i	0.00125876	+	0.00875485i
$540$	−6.12553	−	13.4130i	−0.263601	−	0.577205i
$541$	13.5708	+	29.7159i	0.583454	+	1.27759i	0.939318	+	0.343049i	$0.111460\pi$
$541$	13.5708	+	29.7159i	0.583454	+	1.27759i	−0.355863	+	0.934538i	$0.615813\pi$
$542$	6.18490	+	43.0170i	0.265664	+	1.84774i
$543$	5.31031	+	3.41273i	0.227887	+	0.146454i
$544$	35.8111	−	10.5151i	1.53539	−	0.450831i
$545$	−7.14297	+	49.6805i	−0.305971	+	2.12808i
$546$	−17.2679	+	19.9282i	−0.738999	+	0.852850i
$547$	38.2357	−	24.5726i	1.63484	−	1.05065i	0.689639	−	0.724153i	$-0.257769\pi$
$547$	38.2357	−	24.5726i	1.63484	−	1.05065i	0.945199	−	0.326494i	$-0.105867\pi$
$548$	−26.3553	−	30.4156i	−1.12584	−	1.29929i
$549$	−12.0589	−	3.54081i	−0.514661	−	0.151118i
$550$	−0.452824	+	0.991547i	−0.0193085	+	0.0422797i
$551$	2.46200			0.104885
$552$	−32.7802	+	21.5191i	−1.39522	+	0.915914i
$553$	−16.9775			−0.721957
$554$	−22.2997	+	48.8295i	−0.947424	+	2.07457i
$555$	19.2222	+	5.64415i	0.815937	+	0.239581i
$556$	−35.8826	−	41.4107i	−1.52176	−	1.75620i
$557$	12.6601	−	8.13615i	0.536425	−	0.344740i	−0.244214	−	0.969721i	$-0.578530\pi$
$557$	12.6601	−	8.13615i	0.536425	−	0.344740i	0.780639	+	0.624982i	$0.214894\pi$
$558$	−9.97546	+	11.5123i	−0.422295	+	0.487354i
$559$	5.30430	−	36.8922i	0.224348	−	1.56037i
$560$	74.2699	−	21.8076i	3.13848	−	0.921539i
$561$	0.257674	+	0.165597i	0.0108790	+	0.00699150i
$562$	3.22206	+	22.4099i	0.135915	+	0.945307i
$563$	−14.1960	−	31.0849i	−0.598290	−	1.31007i	−0.930301	−	0.366796i	$-0.880455\pi$
$563$	−14.1960	−	31.0849i	−0.598290	−	1.31007i	0.332012	−	0.943275i	$-0.392273\pi$
$564$	12.4761	+	27.3188i	0.525337	+	1.15033i
$565$	3.10084	+	21.5668i	0.130453	+	0.907324i
$566$	7.55928	+	4.85805i	0.317740	+	0.204199i
$567$	−2.20348	+	0.646999i	−0.0925373	+	0.0271714i
$568$	18.0268	−	125.379i	0.756388	−	5.26079i
$569$	12.0761	−	13.9366i	0.506257	−	0.584252i	−0.443879	−	0.896087i	$-0.646398\pi$
$569$	12.0761	−	13.9366i	0.506257	−	0.584252i	0.950136	+	0.311835i	$0.100944\pi$
$570$	11.2302	−	7.21723i	0.470382	−	0.302296i
$571$	−4.34404	−	5.01329i	−0.181792	−	0.209799i	0.657538	−	0.753422i	$-0.271598\pi$
$571$	−4.34404	−	5.01329i	−0.181792	−	0.209799i	−0.839330	+	0.543622i	$0.817053\pi$
$572$	2.50044	+	0.734196i	0.104549	+	0.0306983i
$573$	5.37805	−	11.7763i	0.224671	−	0.491962i
$574$	39.8015			1.66128
$575$	−2.50992	−	16.3297i	−0.104671	−	0.680997i
$576$	15.3591			0.639962
$577$	−5.22293	+	11.4366i	−0.217433	+	0.476112i	−0.986646	−	0.162881i	$-0.947921\pi$
$577$	−5.22293	+	11.4366i	−0.217433	+	0.476112i	0.769213	+	0.638993i	$0.220649\pi$
$578$	−26.4672	−	7.77146i	−1.10089	−	0.323250i
$579$	−8.25865	−	9.53099i	−0.343218	−	0.396094i
$580$	−17.6828	+	11.3640i	−0.734237	+	0.471866i
$581$	−4.18144	+	4.82563i	−0.173475	+	0.200201i
$582$	−3.22565	+	22.4349i	−0.133707	+	0.929955i
$583$	−0.412986	+	0.121264i	−0.0171041	+	0.00502223i
$584$	4.78365	+	3.07427i	0.197949	+	0.127214i
$585$	−1.78541	−	12.4178i	−0.0738174	−	0.513412i
$586$	4.55952	+	9.98395i	0.188352	+	0.412433i
$587$	0.454966	+	0.996237i	0.0187785	+	0.0411191i	0.918789	−	0.394749i	$-0.129169\pi$
$587$	0.454966	+	0.996237i	0.0187785	+	0.0411191i	−0.900010	+	0.435868i	$0.856441\pi$
$588$	1.24645	+	8.66922i	0.0514025	+	0.357513i
$589$	−8.32147	−	5.34788i	−0.342880	−	0.220356i
$590$	20.1249	−	5.90919i	0.828527	−	0.243278i
$591$	2.06820	−	14.3847i	0.0850744	−	0.591706i
$592$	−52.3620	+	60.4290i	−2.15206	+	2.48361i
$593$	1.95340	−	1.25538i	0.0802167	−	0.0515521i	−0.499918	−	0.866073i	$-0.666636\pi$
$593$	1.95340	−	1.25538i	0.0802167	−	0.0515521i	0.580134	+	0.814521i	$0.303000\pi$
$594$	0.207210	+	0.239133i	0.00850194	+	0.00981176i
$595$	16.4864	+	4.84084i	0.675876	+	0.198455i
$596$	34.8904	−	76.3994i	1.42917	−	3.12944i
$597$	20.1733			0.825637
$598$	−52.6829	+	16.0263i	−2.15436	+	0.655364i
$599$	−43.0508			−1.75901			−0.879504	−	0.475892i	$-0.842125\pi$
$599$	−43.0508			−1.75901			−0.879504	+	0.475892i	$0.842125\pi$
$600$	−11.7011	+	25.6219i	−0.477696	+	1.04601i
$601$	−12.7347	−	3.73926i	−0.519461	−	0.152527i	0.0114837	−	0.999934i	$-0.496345\pi$
$601$	−12.7347	−	3.73926i	−0.519461	−	0.152527i	−0.530944	+	0.847407i	$0.678163\pi$
$602$	34.5337	+	39.8540i	1.40749	+	1.62433i
$603$	−0.0708456	+	0.0455297i	−0.00288506	+	0.00185411i
$604$	−62.8036	+	72.4793i	−2.55544	+	2.94914i
$605$	−4.54342	+	31.6002i	−0.184716	+	1.28473i
$606$	17.8448	−	5.23971i	0.724896	−	0.212849i
$607$	−27.6867	−	17.7932i	−1.12377	−	0.722203i	−0.159520	−	0.987195i	$-0.550995\pi$
$607$	−27.6867	−	17.7932i	−1.12377	−	0.722203i	−0.964251	+	0.264991i	$0.914631\pi$
$608$	3.56315	+	24.7822i	0.144505	+	1.00505i
$609$	1.35991	+	2.97780i	0.0551065	+	0.120666i
$610$	40.3537	+	88.3623i	1.63387	+	3.57769i
$611$	3.63640	+	25.2917i	0.147113	+	1.02319i
$612$	10.9902	+	7.06299i	0.444254	+	0.285504i
$613$	38.7731	−	11.3848i	1.56603	−	0.459828i	0.620188	−	0.784454i	$-0.287057\pi$
$613$	38.7731	−	11.3848i	1.56603	−	0.459828i	0.945843	+	0.324626i	$0.105238\pi$
$614$	3.93880	−	27.3950i	0.158957	−	1.10557i
$615$	−12.4006	+	14.3111i	−0.500042	+	0.577079i
$616$	−1.87923	+	1.20770i	−0.0757162	+	0.0486598i
$617$	−19.6464	−	22.6732i	−0.790935	−	0.912788i	0.206913	−	0.978359i	$-0.433658\pi$
$617$	−19.6464	−	22.6732i	−0.790935	−	0.912788i	−0.997848	+	0.0655717i	$0.979113\pi$
$618$	35.2586	+	10.3529i	1.41831	+	0.416454i
$619$	11.0046	−	24.0967i	0.442313	−	0.968530i	−0.548855	−	0.835918i	$-0.684936\pi$
$619$	11.0046	−	24.0967i	0.442313	−	0.968530i	0.991168	−	0.132613i	$-0.0423366\pi$
$620$	84.4517			3.39166
$621$	−4.61447	−	1.30640i	−0.185172	−	0.0524241i
$622$	−35.0876			−1.40688
$623$	−12.6739	+	27.7519i	−0.507768	+	1.11186i
$624$	48.0435	+	14.1068i	1.92328	+	0.564726i
$625$	19.8796	+	22.9423i	0.795185	+	0.917692i
$626$	30.7889	−	19.7868i	1.23057	−	0.790841i
$627$	−0.134555	+	0.155285i	−0.00537361	+	0.00620148i
$628$	−5.46176	+	37.9874i	−0.217948	+	1.51586i
$629$	−17.0303	+	5.00054i	−0.679041	+	0.199385i
$630$	14.9324	+	9.59647i	0.594921	+	0.382332i
$631$	−2.28418	−	15.8868i	−0.0909316	−	0.632443i	−0.983416	−	0.181365i	$-0.941948\pi$
$631$	−2.28418	−	15.8868i	−0.0909316	−	0.632443i	0.892484	−	0.451079i	$-0.148961\pi$
$632$	25.1101	+	54.9835i	0.998827	+	2.18713i
$633$	3.09642	+	6.78022i	0.123072	+	0.269490i
$634$	−5.42865	−	37.7571i	−0.215599	−	1.49953i
$635$	4.91038	+	3.15571i	0.194863	+	0.125231i
$636$	−17.6146	+	5.17211i	−0.698464	+	0.205087i
$637$	−1.06047	+	7.37574i	−0.0420174	+	0.292237i
$638$	0.295375	−	0.340881i	0.0116940	−	0.0134956i
$639$	13.0327	−	8.37563i	0.515567	−	0.331335i
$640$	−22.5668	−	26.0435i	−0.892031	−	1.02946i
$641$	44.9585	+	13.2010i	1.77575	+	0.521408i	0.994678	−	0.103030i	$-0.0328537\pi$
$641$	44.9585	+	13.2010i	1.77575	+	0.521408i	0.781074	+	0.624438i	$0.214672\pi$
$642$	−9.08528	+	19.8940i	−0.358567	+	0.785153i
$643$	−27.2328			−1.07396			−0.536979	−	0.843596i	$-0.680435\pi$
$643$	−27.2328			−1.07396			−0.536979	+	0.843596i	$0.680435\pi$
$644$	22.7207	−	51.0575i	0.895321	−	2.01195i
$645$	−25.0893			−0.987892
$646$	−4.91317	+	10.7584i	−0.193306	+	0.423282i
$647$	−23.7997	−	6.98823i	−0.935664	−	0.274736i	−0.221858	−	0.975079i	$-0.571212\pi$
$647$	−23.7997	−	6.98823i	−0.935664	−	0.274736i	−0.713806	+	0.700343i	$0.753030\pi$
$648$	5.35437	+	6.17928i	0.210340	+	0.242745i
$649$	−0.271586	+	0.174538i	−0.0106607	+	0.00685121i
$650$	−25.9035	+	29.8943i	−1.01602	+	1.17255i
$651$	1.87182	−	13.0188i	0.0733624	−	0.510247i
$652$	−8.12689	+	2.38627i	−0.318274	+	0.0934535i
$653$	−24.7733	−	15.9208i	−0.969455	−	0.623031i	−0.0428558	−	0.999081i	$-0.513646\pi$
$653$	−24.7733	−	15.9208i	−0.969455	−	0.623031i	−0.926599	+	0.376050i	$0.877282\pi$
$654$	−6.53757	−	45.4698i	−0.255639	−	1.77801i
$655$	5.92976	+	12.9844i	0.231695	+	0.507341i
$656$	−31.3967	−	68.7491i	−1.22583	−	2.68420i
$657$	0.0989745	+	0.688383i	0.00386136	+	0.0268564i
$658$	−30.4133	−	19.5455i	−1.18563	−	0.761961i
$659$	−13.4131	+	3.93844i	−0.522500	+	0.153420i	−0.532338	−	0.846532i	$-0.678687\pi$
$659$	−13.4131	+	3.93844i	−0.522500	+	0.153420i	0.00983813	+	0.999952i	$0.496868\pi$
$660$	0.249653	−	1.73637i	0.00971773	−	0.0675883i
$661$	16.2537	−	18.7578i	0.632196	−	0.729593i	−0.345779	−	0.938316i	$-0.612385\pi$
$661$	16.2537	−	18.7578i	0.632196	−	0.729593i	0.977975	+	0.208723i	$0.0669308\pi$
$662$	26.4796	−	17.0174i	1.02916	−	0.661400i
$663$	7.27871	+	8.40008i	0.282682	+	0.326232i
$664$	21.8128	+	6.40481i	0.846501	+	0.248555i
$665$	−4.78822	+	10.4847i	−0.185679	+	0.406580i
$666$	−18.3358			−0.710496
$667$	−0.907174	+	6.77593i	−0.0351259	+	0.262365i
$668$	108.758			4.20799
$669$	0.698714	−	1.52997i	0.0270138	−	0.0591521i
$670$	0.624545	+	0.183383i	0.0241283	+	0.00708470i
$671$	−0.979129	−	1.12998i	−0.0377989	−	0.0436222i
$672$	−28.0061	+	17.9984i	−1.08036	+	0.694303i
$673$	−5.82979	+	6.72793i	−0.224722	+	0.259343i	−0.856903	−	0.515478i	$-0.827614\pi$
$673$	−5.82979	+	6.72793i	−0.224722	+	0.259343i	0.632181	+	0.774821i	$0.282160\pi$
$674$	10.1303	−	70.4581i	0.390206	−	2.71395i
$675$	−3.30543	+	0.970561i	−0.127226	+	0.0373569i
$676$	24.0622	+	15.4638i	0.925468	+	0.594762i
$677$	−0.401463	−	2.79223i	−0.0154295	−	0.107314i	0.980651	−	0.195763i	$-0.0627182\pi$
$677$	−0.401463	−	2.79223i	−0.0154295	−	0.107314i	−0.996081	+	0.0884485i	$0.971809\pi$
$678$	−8.28418	−	18.1398i	−0.318152	−	0.696656i
$679$	−8.12978	−	17.8017i	−0.311992	−	0.683168i
$680$	−8.70616	−	60.5527i	−0.333866	−	2.32209i
$681$	9.06990	+	5.82887i	0.347559	+	0.223363i
$682$	−1.73881	+	0.510560i	−0.0665823	+	0.0195503i
$683$	−2.95100	+	20.5247i	−0.112917	+	0.785355i	0.852140	+	0.523314i	$0.175305\pi$
$683$	−2.95100	+	20.5247i	−0.112917	+	0.785355i	−0.965057	+	0.262041i	$0.915604\pi$
$684$	−5.73901	+	6.62317i	−0.219436	+	0.253243i
$685$	−19.3902	+	12.4613i	−0.740862	+	0.476123i
$686$	−34.9037	−	40.2810i	−1.33263	−	1.53794i
$687$	−21.0203	−	6.17212i	−0.801975	−	0.235481i
$688$	41.5985	−	91.0880i	1.58593	−	3.47270i
$689$	−15.6191			−0.595040
$690$	15.7253	+	33.5672i	0.598651	+	1.27788i
$691$	1.36601			0.0519655			0.0259827	−	0.999662i	$-0.491729\pi$
$691$	1.36601			0.0519655			0.0259827	+	0.999662i	$0.491729\pi$
$692$	−13.3437	+	29.2187i	−0.507253	+	1.11073i
$693$	−0.262140	−	0.0769714i	−0.00995789	−	0.00292390i
$694$	−15.4069	−	17.7806i	−0.584840	−	0.674941i
$695$	−26.3997	+	16.9660i	−1.00140	+	0.643558i
$696$	7.63258	−	8.80846i	0.289312	−	0.333884i
$697$	2.38761	−	16.6062i	0.0904373	−	0.629005i
$698$	−75.9955	+	22.3143i	−2.87647	+	0.844608i
$699$	20.9230	+	13.4464i	0.791380	+	0.508589i
$700$	−5.71301	−	39.7348i	−0.215931	−	1.50184i
$701$	12.5045	+	27.3810i	0.472288	+	1.03417i	0.984512	+	0.175315i	$0.0560945\pi$
$701$	12.5045	+	27.3810i	0.472288	+	1.03417i	−0.512224	+	0.858852i	$0.671178\pi$
$702$	4.76987	+	10.4446i	0.180027	+	0.394204i
$703$	−1.69449	−	11.7854i	−0.0639087	−	0.444495i
$704$	1.53716	+	0.987870i	0.0579337	+	0.0372317i
$705$	16.5034	−	4.84585i	0.621555	−	0.182505i
$706$	−6.51494	+	45.3124i	−0.245193	+	1.70535i
$707$	−10.5160	+	12.1361i	−0.395493	+	0.456424i
$708$	−11.5836	+	7.44434i	−0.435339	+	0.279775i
$709$	25.9980	+	30.0033i	0.976375	+	1.12680i	0.991913	+	0.126918i	$0.0405085\pi$
$709$	25.9980	+	30.0033i	0.976375	+	1.12680i	−0.0155379	+	0.999879i	$0.504946\pi$
$710$	−114.891	−	33.7351i	−4.31179	−	1.26605i
$711$	−3.07107	+	6.72469i	−0.115174	+	0.252196i
$712$	108.623			4.07080
$713$	17.7847	−	20.9318i	0.666041	−	0.783903i
$714$	−15.7261			−0.588535
$715$	0.620004	−	1.35762i	0.0231868	−	0.0507721i
$716$	−39.8863	−	11.7117i	−1.49062	−	0.437686i
$717$	−2.74834	−	3.17175i	−0.102639	−	0.118451i
$718$	15.9473	−	10.2487i	0.595149	−	0.382479i
$719$	6.00668	−	6.93208i	0.224011	−	0.258523i	−0.632608	−	0.774473i	$-0.718015\pi$
$719$	6.00668	−	6.93208i	0.224011	−	0.258523i	0.856619	+	0.515950i	$0.172561\pi$
$720$	4.79683	−	33.3627i	0.178767	−	1.24335i
$721$	−30.4436	+	8.93904i	−1.13378	+	0.332907i
$722$	35.8381	+	23.0318i	1.33376	+	0.857153i
$723$	3.90362	+	27.1503i	0.145177	+	1.00973i
$724$	13.3057	+	29.1354i	0.494502	+	1.08281i
$725$	2.04000	+	4.46698i	0.0757637	+	0.165899i
$726$	−4.15834	−	28.9219i	−0.154331	−	1.07339i
$727$	−3.19987	−	2.05643i	−0.118676	−	0.0762687i	0.479956	−	0.877293i	$-0.340653\pi$
$727$	−3.19987	−	2.05643i	−0.118676	−	0.0762687i	−0.598632	+	0.801024i	$0.704289\pi$
$728$	−77.7779	+	22.8376i	−2.88264	+	0.846419i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	3.52012	−	4.06244i	0.130286	−	0.150358i
$731$	18.6997	−	12.0176i	0.691634	−	0.444486i
$732$	−41.7616	−	48.1954i	−1.54355	−	1.78135i
$733$	−39.2138	−	11.5142i	−1.44839	−	0.425287i	−0.539384	−	0.842060i	$-0.681343\pi$
$733$	−39.2138	−	11.5142i	−1.44839	−	0.425287i	−0.909011	+	0.416773i	$0.863161\pi$
$734$	−15.0084	+	32.8638i	−0.553971	+	1.21303i
$735$	5.01603			0.185019
$736$	−69.5187	+	0.674985i	−2.56249	+	0.0248803i
$737$	−0.0100187			−0.000369044
$738$	7.19971	−	15.7652i	0.265025	−	0.580324i
$739$	28.0767	+	8.24407i	1.03282	+	0.303263i	0.753856	−	0.657039i	$-0.228191\pi$
$739$	28.0767	+	8.24407i	1.03282	+	0.303263i	0.278962	+	0.960302i	$0.410010\pi$
$740$	66.5690	+	76.8248i	2.44713	+	2.82413i
$741$	−6.27249	+	4.03109i	−0.230426	+	0.148086i
$742$	14.4717	−	16.7013i	0.531274	−	0.613123i
$743$	1.23262	−	8.57306i	0.0452204	−	0.314515i	−0.954639	−	0.297765i	$-0.903759\pi$
$743$	1.23262	−	8.57306i	0.0452204	−	0.314515i	0.999860	−	0.0167502i	$-0.00533200\pi$
$744$	−44.9313	+	13.1930i	−1.64726	+	0.483680i
$745$	−40.4658	−	26.0058i	−1.48255	−	0.952778i
$746$	7.08863	+	49.3025i	0.259533	+	1.80509i
$747$	1.15503	+	2.52915i	0.0422602	+	0.0925369i
$748$	0.645636	+	1.41374i	0.0236068	+	0.0516916i
$749$	−2.68742	−	18.6914i	−0.0981964	−	0.682971i
$750$	−10.1112	−	6.49805i	−0.369207	−	0.237275i
$751$	−6.59622	+	1.93683i	−0.240700	+	0.0706758i	−0.399857	−	0.916577i	$-0.630940\pi$
$751$	−6.59622	+	1.93683i	−0.240700	+	0.0706758i	0.159158	+	0.987253i	$0.449122\pi$
$752$	−9.76987	+	67.9509i	−0.356270	+	2.47792i
$753$	8.46323	−	9.76708i	0.308417	−	0.355932i
$754$	13.7694	−	8.84903i	0.501450	−	0.322263i
$755$	35.9685	+	41.5098i	1.30903	+	1.51070i
$756$	−11.1807	−	3.28296i	−0.406640	−	0.119400i
$757$	−1.31155	+	2.87190i	−0.0476692	+	0.104381i	−0.931968	−	0.362540i	$-0.881910\pi$
$757$	−1.31155	+	2.87190i	−0.0476692	+	0.104381i	0.884299	+	0.466921i	$0.154637\pi$
$758$	26.6430			0.967717
$759$	−0.377796	−	0.427541i	−0.0137131	−	0.0155187i
$760$	41.0378			1.48860
$761$	7.11532	−	15.5804i	0.257930	−	0.564788i	−0.735722	−	0.677284i	$-0.763157\pi$
$761$	7.11532	−	15.5804i	0.257930	−	0.564788i	0.993652	+	0.112495i	$0.0358843\pi$
$762$	−5.12587	−	1.50509i	−0.185691	−	0.0545238i
$763$	25.9744	+	29.9760i	0.940336	+	1.08521i
$764$	55.2627	−	35.5152i	1.99933	−	1.28489i
$765$	4.89966	−	5.65451i	0.177147	−	0.204439i
$766$	−11.0236	+	76.6706i	−0.398298	+	2.77022i
$767$	−11.2405	+	3.30050i	−0.405870	+	0.119174i
$768$	0.691162	+	0.444183i	0.0249401	+	0.0160281i
$769$	3.01514	+	20.9707i	0.108729	+	0.756224i	0.969120	+	0.246590i	$0.0793101\pi$
$769$	3.01514	+	20.9707i	0.108729	+	0.756224i	−0.860391	+	0.509634i	$0.829781\pi$
$770$	0.877223	+	1.92085i	0.0316129	+	0.0692227i
$771$	−0.596354	−	1.30583i	−0.0214772	−	0.0470284i
$772$	−9.10694	−	63.3401i	−0.327766	−	2.27966i
$773$	4.49268	+	2.88727i	0.161590	+	0.103848i	0.618937	−	0.785441i	$-0.287564\pi$
$773$	4.49268	+	2.88727i	0.161590	+	0.103848i	−0.457346	+	0.889289i	$0.651200\pi$
$774$	22.0328	−	6.46940i	0.791951	−	0.232538i
$775$	2.80791	−	19.5294i	0.100863	−	0.701518i
$776$	−45.6287	+	52.6584i	−1.63798	+	1.89033i
$777$	13.3185	−	8.55929i	0.477799	−	0.307063i
$778$	7.63448	+	8.81066i	0.273709	+	0.315877i
$779$	10.7985	+	3.17073i	0.386897	+	0.113603i
$780$	26.4442	−	57.9048i	0.946856	−	2.07332i
$781$	1.84304			0.0659491
$782$	−27.7988	−	17.4862i	−0.994084	−	0.625305i
$783$	1.42548			0.0509427
$784$	−8.31664	+	18.2109i	−0.297023	+	0.650390i
$785$	21.0893	+	6.19236i	0.752708	+	0.221015i
$786$	−8.55543	−	9.87349i	−0.305162	−	0.352176i
$787$	36.6862	−	23.5768i	1.30772	−	0.840423i	0.313693	−	0.949525i	$-0.398434\pi$
$787$	36.6862	−	23.5768i	1.30772	−	0.840423i	0.994031	+	0.109102i	$0.0347975\pi$
$788$	48.2896	−	55.7292i	1.72025	−	1.98527i
$789$	−2.04437	+	14.2189i	−0.0727814	+	0.506206i
$790$	54.8257	−	16.0983i	1.95061	−	0.572751i
$791$	14.4852	+	9.30907i	0.515034	+	0.330992i
$792$	0.138432	+	0.962813i	0.00491895	+	0.0342121i
$793$	−22.5390	−	49.3536i	−0.800385	−	1.75260i
$794$	−0.161008	−	0.352558i	−0.00571396	−	0.0125118i
$795$	1.49630	+	10.4070i	0.0530682	+	0.369097i
$796$	86.1124	+	55.3410i	3.05217	+	1.96151i
$797$	11.1289	−	3.26774i	0.394205	−	0.115749i	−0.0786214	−	0.996905i	$-0.525052\pi$
$797$	11.1289	−	3.26774i	0.394205	−	0.115749i	0.472827	+	0.881155i	$0.343234\pi$
$798$	1.50134	−	10.4421i	0.0531469	−	0.369645i
$799$	−9.97930	+	11.5167i	−0.353042	+	0.407432i
$800$	−42.0117	+	26.9993i	−1.48534	+	0.954570i
$801$	8.69980	+	10.0401i	0.307392	+	0.354750i
$802$	−85.9050	−	25.2240i	−3.03341	−	0.890690i
$803$	−0.0343701	+	0.0752600i	−0.00121289	+	0.00265587i
$804$	−0.427315			−0.0150702
$805$	−27.0918	−	17.0415i	−0.954860	−	0.600632i
$806$	−65.7615			−2.31635
$807$	−8.05447	+	17.6368i	−0.283531	+	0.620846i
$808$	54.8574	+	16.1076i	1.92988	+	0.566663i
$809$	5.11925	+	5.90793i	0.179983	+	0.207712i	0.838571	−	0.544792i	$-0.183391\pi$
$809$	5.11925	+	5.90793i	0.179983	+	0.207712i	−0.658588	+	0.752504i	$0.728846\pi$
$810$	6.50224	−	4.17873i	0.228465	−	0.146826i
$811$	−7.54232	+	8.70430i	−0.264847	+	0.305649i	−0.872560	−	0.488507i	$-0.837542\pi$
$811$	−7.54232	+	8.70430i	−0.264847	+	0.305649i	0.607713	+	0.794157i	$0.292087\pi$
$812$	−2.36397	+	16.4418i	−0.0829590	+	0.576993i
$813$	−15.6779	+	4.60345i	−0.549848	+	0.161450i
$814$	−1.83506	−	1.17932i	−0.0643189	−	0.0413353i
$815$	0.690351	+	4.80149i	0.0241819	+	0.168189i
$816$	12.4052	+	27.1637i	0.434270	+	0.950919i
$817$	6.19438	+	13.5638i	0.216714	+	0.474538i
$818$	−11.4571	−	79.6858i	−0.400588	−	2.78615i
$819$	−8.34029	−	5.35998i	−0.291433	−	0.187293i
$820$	−92.1932	+	27.0704i	−3.21953	+	0.945339i
$821$	0.0743036	−	0.516793i	0.00259321	−	0.0180362i	−0.988484	−	0.151327i	$-0.951645\pi$
$821$	0.0743036	−	0.516793i	0.00259321	−	0.0180362i	0.991077	+	0.133291i	$0.0425544\pi$
$822$	13.8147	−	15.9430i	0.481844	−	0.556078i
$823$	−28.0088	+	18.0002i	−0.976327	+	0.627447i	−0.928470	−	0.371407i	$-0.878876\pi$
$823$	−28.0088	+	18.0002i	−0.976327	+	0.627447i	−0.0478569	+	0.998854i	$0.515239\pi$
$824$	73.9768	+	85.3738i	2.57711	+	2.97414i
$825$	−0.393236	−	0.115464i	−0.0136907	−	0.00401995i
$826$	6.88558	−	15.0773i	0.239580	−	0.524607i
$827$	24.2079			0.841791			0.420895	−	0.907109i	$-0.361716\pi$
$827$	24.2079			0.841791			0.420895	+	0.907109i	$0.361716\pi$
$828$	−16.1136	−	18.2354i	−0.559988	−	0.633722i
$829$	26.4851			0.919866			0.459933	−	0.887954i	$-0.347873\pi$
$829$	26.4851			0.919866			0.459933	+	0.887954i	$0.347873\pi$
$830$	8.92746	−	19.5484i	0.309876	−	0.678535i
$831$	−19.3652	−	5.68614i	−0.671771	−	0.197250i
$832$	43.4212	+	50.1108i	1.50536	+	1.73728i
$833$	−3.73857	+	2.40263i	−0.129534	+	0.0832463i
$834$	18.8087	−	21.7064i	0.651291	−	0.751630i
$835$	8.86442	−	61.6534i	0.306766	−	2.13360i
$836$	−1.00036	+	0.293731i	−0.0345981	+	0.0101589i
$837$	−4.81808	−	3.09639i	−0.166537	−	0.107027i
$838$	7.09223	+	49.3275i	0.244997	+	1.70399i
$839$	−16.0962	−	35.2458i	−0.555703	−	1.21682i	−0.954067	−	0.299593i	$-0.903149\pi$
$839$	−16.0962	−	35.2458i	−0.555703	−	1.21682i	0.398364	−	0.917228i	$-0.369578\pi$
$840$	22.6677	+	49.6354i	0.782111	+	1.71258i
$841$	3.83795	+	26.6935i	0.132343	+	0.920465i
$842$	−87.7014	−	56.3623i	−3.02239	−	1.94237i
$843$	−8.16750	+	2.39819i	−0.281304	+	0.0825982i
$844$	−5.38258	+	37.4367i	−0.185276	+	1.28862i
$845$	10.7274	−	12.3801i	0.369033	−	0.425887i
$846$	−13.2433	+	8.51097i	−0.455315	+	0.292613i
$847$	16.5215	+	19.0668i	0.567685	+	0.655144i
$848$	−40.2638	−	11.8225i	−1.38267	−	0.405987i
$849$	−1.40346	+	3.07314i	−0.0481665	+	0.105470i
$850$	−23.5907			−0.809153
$851$	33.0602	−	0.320995i	1.13329	−	0.0110036i
$852$	78.6088			2.69309
$853$	3.66776	−	8.03127i	0.125582	−	0.274985i	−0.836390	−	0.548135i	$-0.815338\pi$
$853$	3.66776	−	8.03127i	0.125582	−	0.274985i	0.961972	+	0.273149i	$0.0880654\pi$
$854$	73.6565	+	21.6275i	2.52047	+	0.740078i
$855$	3.28680	+	3.79317i	0.112406	+	0.129724i
$856$	−56.5596	+	36.3486i	−1.93317	+	1.24237i
$857$	0.448206	−	0.517257i	0.0153104	−	0.0176692i	−0.748043	−	0.663651i	$-0.769006\pi$
$857$	0.448206	−	0.517257i	0.0153104	−	0.0176692i	0.763353	+	0.645981i	$0.223552\pi$
$858$	−0.194402	+	1.35209i	−0.00663676	+	0.0461597i
$859$	−12.1210	+	3.55905i	−0.413563	+	0.121433i	−0.481894	−	0.876230i	$-0.660051\pi$
$859$	−12.1210	+	3.55905i	−0.413563	+	0.121433i	0.0683306	+	0.997663i	$0.478233\pi$
$860$	−107.097	−	68.8272i	−3.65199	−	2.34699i
$861$	2.12967	+	14.8122i	0.0725791	+	0.504799i
$862$	−23.7212	−	51.9421i	−0.807946	−	1.76916i
$863$	−2.36065	−	5.16909i	−0.0803573	−	0.175958i	0.865189	−	0.501446i	$-0.167199\pi$
$863$	−2.36065	−	5.16909i	−0.0803573	−	0.175958i	−0.945546	+	0.325488i	$0.894471\pi$
$864$	2.06304	+	14.3488i	0.0701862	+	0.488155i
$865$	15.4760	+	9.94583i	0.526200	+	0.338168i
$866$	−1.93530	+	0.568255i	−0.0657641	+	0.0193101i
$867$	1.47597	−	10.2656i	0.0501267	−	0.348639i
$868$	43.7044	−	50.4376i	1.48342	−	1.71196i
$869$	−0.739876	+	0.475490i	−0.0250986	+	0.0161299i
$870$	−7.21518	−	8.32676i	−0.244618	−	0.282304i
$871$	−0.348831	−	0.102426i	−0.0118197	−	0.00347058i
$872$	58.6640	−	128.456i	1.98661	−	4.35008i
$873$	−8.52177			−0.288418
$874$	14.2646	−	16.7889i	0.482509	−	0.567893i
$875$	10.3778			0.350833
$876$	−1.46594	+	3.20997i	−0.0495297	+	0.108455i
$877$	21.7361	+	6.38228i	0.733974	+	0.215514i	0.627298	−	0.778779i	$-0.284161\pi$
$877$	21.7361	+	6.38228i	0.733974	+	0.215514i	0.106677	+	0.994294i	$0.465979\pi$
$878$	22.8333	+	26.3510i	0.770585	+	0.889303i
$879$	−3.47158	+	2.23105i	−0.117093	+	0.0752513i
$880$	2.62590	−	3.03045i	0.0885191	−	0.102157i
$881$	3.21562	−	22.3652i	0.108337	−	0.753501i	−0.861149	−	0.508353i	$-0.830254\pi$
$881$	3.21562	−	22.3652i	0.108337	−	0.753501i	0.969486	−	0.245148i	$-0.0788365\pi$
$882$	−4.40493	+	1.29341i	−0.148322	+	0.0435512i
$883$	34.5835	+	22.2255i	1.16383	+	0.747947i	0.972345	−	0.233549i	$-0.0750341\pi$
$883$	34.5835	+	22.2255i	1.16383	+	0.747947i	0.191483	+	0.981496i	$0.438670\pi$
$884$	8.02634	+	55.8244i	0.269955	+	1.87758i
$885$	3.27594	+	7.17332i	0.110120	+	0.241128i
$886$	3.38063	+	7.40255i	0.113575	+	0.248693i
$887$	0.776455	+	5.40036i	0.0260708	+	0.181326i	0.998696	−	0.0510534i	$-0.0162579\pi$
$887$	0.776455	+	5.40036i	0.0260708	+	0.181326i	−0.972625	+	0.232380i	$0.925349\pi$
$888$	−47.4186	−	30.4741i	−1.59126	−	1.02264i
$889$	4.42586	−	1.29955i	0.148439	−	0.0435855i
$890$	14.6132	−	101.637i	0.489837	−	3.40689i
$891$	−0.0779066	+	0.0899090i	−0.00260997	+	0.00301207i
$892$	7.17970	−	4.61411i	0.240394	−	0.154492i
$893$	−6.69434	−	7.72569i	−0.224018	−	0.258530i
$894$	42.2416	+	12.4033i	1.41277	+	0.414827i
$895$	−9.89011	+	21.6563i	−0.330590	+	0.723891i
$896$	−27.2326			−0.909776
$897$	−8.78314	−	18.7485i	−0.293261	−	0.625995i
$898$	20.3984			0.680703
$899$	−3.39150	+	7.42635i	−0.113113	+	0.247683i
$900$	−16.7722	−	4.92476i	−0.559073	−	0.164159i
$901$	−6.10007	−	7.03986i	−0.203223	−	0.234532i
$902$	1.73454	−	1.11472i	0.0577540	−	0.0371162i
$903$	−12.9839	+	14.9842i	−0.432078	+	0.498645i
$904$	8.72450	−	60.6802i	0.290173	−	2.01819i
$905$	17.6008	−	5.16807i	0.585072	−	0.171793i
$906$	−42.2900	−	27.1781i	−1.40499	−	0.902932i
$907$	−4.00188	−	27.8337i	−0.132880	−	0.924202i	−0.941774	−	0.336247i	$-0.890842\pi$
$907$	−4.00188	−	27.8337i	−0.132880	−	0.924202i	0.808894	−	0.587955i	$-0.200067\pi$
$908$	22.7258	+	49.7626i	0.754183	+	1.65143i
$909$	2.90480	+	6.36061i	0.0963460	+	0.210968i
$910$	10.9054	+	75.8485i	0.361509	+	2.51435i
$911$	−48.0980	−	30.9107i	−1.59356	−	1.02412i	−0.970239	−	0.242151i	$-0.922147\pi$
$911$	−48.0980	−	30.9107i	−1.59356	−	1.02412i	−0.623320	−	0.781967i	$-0.714217\pi$
$912$	−19.2208	+	5.64375i	−0.636466	+	0.186883i
$913$	−0.0470745	+	0.327410i	−0.00155794	+	0.0108357i
$914$	15.6127	−	18.0180i	0.516421	−	0.595981i
$915$	−30.7250	+	19.7457i	−1.01574	+	0.652774i
$916$	−72.7962	−	84.0113i	−2.40525	−	2.77581i
$917$	10.8234	+	3.17804i	0.357421	+	0.104948i
$918$	−2.84470	+	6.22903i	−0.0938891	+	0.205588i
$919$	16.3674			0.539909			0.269955	−	0.962873i	$-0.412991\pi$
$919$	16.3674			0.539909			0.269955	+	0.962873i	$0.412991\pi$
$920$	−15.1212	+	112.944i	−0.498532	+	3.72367i
$921$	10.4058			0.342884
$922$	8.32759	−	18.2349i	0.274255	−	0.600534i
$923$	64.1709	+	18.8423i	2.11221	+	0.620201i
$924$	−0.907827	−	1.04769i	−0.0298653	−	0.0344664i
$925$	19.9790	−	12.8397i	0.656907	−	0.422168i
$926$	−57.4157	+	66.2613i	−1.88680	+	2.17748i
$927$	−1.96624	+	13.6755i	−0.0645799	+	0.449163i
$928$	19.8272	−	5.82181i	0.650861	−	0.191110i
$929$	32.1390	+	20.6545i	1.05445	+	0.677651i	0.948518	−	0.316723i	$-0.102582\pi$
$929$	32.1390	+	20.6545i	1.05445	+	0.677651i	0.105928	+	0.994374i	$0.466219\pi$
$930$	6.29989	+	43.8167i	0.206582	+	1.43681i
$931$	−1.23842	−	2.71177i	−0.0405877	−	0.0888746i
$932$	52.4253	+	114.795i	1.71725	+	3.76025i
$933$	−1.87744	−	13.0579i	−0.0614648	−	0.427497i
$934$	30.1710	+	19.3897i	0.987225	+	0.634451i
$935$	0.854051	−	0.250772i	0.0279305	−	0.00820112i
$936$	−5.02340	+	34.9385i	−0.164195	+	1.14200i
$937$	−9.21800	+	10.6381i	−0.301139	+	0.347533i	−0.886071	−	0.463549i	$-0.846576\pi$
$937$	−9.21800	+	10.6381i	−0.301139	+	0.347533i	0.584932	+	0.811082i	$0.301121\pi$
$938$	0.432730	−	0.278098i	0.0141291	−	0.00908023i
$939$	9.01114	+	10.3994i	0.294067	+	0.339372i
$940$	83.7407	+	24.5885i	2.73132	+	0.801988i
$941$	−18.0891	+	39.6097i	−0.589689	+	1.29124i	0.345940	+	0.938256i	$0.387560\pi$
$941$	−18.0891	+	39.6097i	−0.589689	+	1.29124i	−0.935630	+	0.352983i	$0.885167\pi$
$942$	−20.1167			−0.655438
$943$	−12.7054	+	28.5514i	−0.413745	+	0.929760i
$944$	−31.4746			−1.02441
$945$	−2.77235	+	6.07060i	−0.0901845	+	0.197477i
$946$	2.62116	+	0.769643i	0.0852214	+	0.0250233i
$947$	−20.1689	−	23.2762i	−0.655403	−	0.756375i	0.326616	−	0.945157i	$-0.394092\pi$
$947$	−20.1689	−	23.2762i	−0.655403	−	0.756375i	−0.982019	+	0.188782i	$0.939546\pi$
$948$	−31.5570	+	20.2805i	−1.02492	+	0.658679i
$949$	−1.96612	+	2.26902i	−0.0638229	+	0.0736556i
$950$	2.25215	−	15.6641i	0.0730695	−	0.508210i
$951$	13.7609	−	4.04056i	0.446228	−	0.131024i
$952$	−40.6697	−	26.1368i	−1.31811	−	0.847100i
$953$	−7.63117	−	53.0760i	−0.247198	−	1.71930i	−0.614261	−	0.789103i	$-0.710546\pi$
$953$	−7.63117	−	53.0760i	−0.247198	−	1.71930i	0.367063	−	0.930196i	$-0.380363\pi$
$954$	−3.99749	−	8.75328i	−0.129424	−	0.283398i
$955$	−15.6288	−	34.2222i	−0.505734	−	1.10740i
$956$	−3.03063	−	21.0785i	−0.0980177	−	0.681728i
$957$	0.142664	+	0.0916847i	0.00461168	+	0.00296374i
$958$	−53.2656	+	15.6402i	−1.72093	+	0.505312i
$959$	−2.59223	+	18.0294i	−0.0837075	+	0.582198i
$960$	29.2290	−	33.7320i	0.943361	−	1.08870i
$961$	1.51558	−	0.974001i	0.0488895	−	0.0314194i
$962$	−51.8365	−	59.8225i	−1.67127	−	1.92875i
$963$	−7.88971	−	2.31663i	−0.254242	−	0.0746523i
$964$	−57.8178	+	126.603i	−1.86219	+	4.07762i
$965$	−36.6487			−1.17976
$966$	28.1855	+	7.97958i	0.906852	+	0.256739i
$967$	−35.8006			−1.15127			−0.575635	−	0.817707i	$-0.695245\pi$
$967$	−35.8006			−1.15127			−0.575635	+	0.817707i	$0.695245\pi$
$968$	37.3143	−	81.7070i	1.19933	−	2.62616i
$969$	−4.26663	−	1.25280i	−0.137064	−	0.0402456i
$970$	43.1335	+	49.7787i	1.38493	+	1.59830i
$971$	−17.7167	+	11.3859i	−0.568557	+	0.365390i	−0.793116	−	0.609071i	$-0.791542\pi$
$971$	−17.7167	+	11.3859i	−0.568557	+	0.365390i	0.224558	+	0.974461i	$0.427906\pi$
$972$	−3.32285	+	3.83478i	−0.106581	+	0.123001i
$973$	−3.52931	+	24.5469i	−0.113144	+	0.786937i
$974$	−21.0934	+	6.19359i	−0.675878	+	0.198456i
$975$	−12.5112	−	8.04048i	−0.400680	−	0.257501i
$976$	−20.7454	−	144.287i	−0.664043	−	4.61852i
$977$	−17.6014	−	38.5417i	−0.563119	−	1.23306i	−0.950381	−	0.311088i	$-0.899307\pi$
$977$	−17.6014	−	38.5417i	−0.563119	−	1.23306i	0.387262	−	0.921970i	$-0.373421\pi$
$978$	−1.84433	−	4.03853i	−0.0589753	−	0.129138i
$979$	0.224924	+	1.56438i	0.00718860	+	0.0499978i
$980$	21.4116	+	13.7604i	0.683968	+	0.439560i
$981$	16.5719	−	4.86594i	0.529099	−	0.155357i
$982$	−4.20423	+	29.2411i	−0.134162	+	0.933120i
$983$	−18.1016	+	20.8903i	−0.577351	+	0.666299i	−0.967033	−	0.254651i	$-0.918039\pi$
$983$	−18.1016	+	20.8903i	−0.577351	+	0.666299i	0.389682	+	0.920949i	$0.372585\pi$
$984$	44.8211	−	28.8048i	1.42885	−	0.918263i
$985$	−27.6561	−	31.9168i	−0.881196	−	1.01695i
$986$	9.36610	+	2.75013i	0.298277	+	0.0875821i
$987$	5.64654	−	12.3642i	0.179731	−	0.393557i
$988$	−37.8334			−1.20364
$989$	−39.6128	+	12.0503i	−1.25961	+	0.383179i
$990$	0.919520			0.0292243
$991$	−18.8737	+	41.3276i	−0.599543	+	1.31282i	0.329958	+	0.943996i	$0.392966\pi$
$991$	−18.8737	+	41.3276i	−0.599543	+	1.31282i	−0.929501	+	0.368820i	$0.879762\pi$
$992$	−79.6613	−	23.3907i	−2.52925	−	0.742654i
$993$	7.74991	+	8.94388i	0.245936	+	0.283825i
$994$	−79.6048	+	51.1589i	−2.52491	+	1.62266i
$995$	38.3906	−	44.3051i	1.21706	−	1.40457i
$996$	−2.00781	+	13.9646i	−0.0636198	+	0.442485i
$997$	12.5546	−	3.68635i	0.397607	−	0.116748i	−0.0768154	−	0.997045i	$-0.524475\pi$
$997$	12.5546	−	3.68635i	0.397607	−	0.116748i	0.474422	+	0.880297i	$0.342657\pi$
$998$	13.6117	+	8.74769i	0.430870	+	0.276903i
$999$	−0.981098	−	6.82368i	−0.0310406	−	0.215892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.52.1	yes	20
3.2	odd	2		207.2.i.d.190.2		20
23.2	even	11		1587.2.a.u.1.1		10
23.4	even	11	inner	69.2.e.c.4.1	✓	20
23.21	odd	22		1587.2.a.t.1.1		10
69.2	odd	22		4761.2.a.bt.1.10		10
69.44	even	22		4761.2.a.bu.1.10		10
69.50	odd	22		207.2.i.d.73.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.4.1	✓	20	23.4	even	11	inner
69.2.e.c.52.1	yes	20	1.1	even	1	trivial
207.2.i.d.73.2		20	69.50	odd	22
207.2.i.d.190.2		20	3.2	odd	2
1587.2.a.t.1.1		10	23.21	odd	22
1587.2.a.u.1.1		10	23.2	even	11
4761.2.a.bt.1.10		10	69.2	odd	22
4761.2.a.bu.1.10		10	69.44	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10489 + 2.41937i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-3.32285 - 3.83478i) q^{4} +(-2.44470 + 1.57111i) q^{5} +(1.74175 - 2.01009i) q^{6} +(-0.326826 + 2.27313i) q^{7} +(7.84516 - 2.30355i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-1.10489 + 2.41937i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-3.32285 - 3.83478i) q^{4} +(-2.44470 + 1.57111i) q^{5} +(1.74175 - 2.01009i) q^{6} +(-0.326826 + 2.27313i) q^{7} +(7.84516 - 2.30355i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-1.09998 - 7.65055i) q^{10} +(0.0494206 + 0.108216i) q^{11} +(2.10787 + 4.61560i) q^{12} +(0.614381 + 4.27311i) q^{13} +(-5.13843 - 3.30227i) q^{14} +(2.78831 - 0.818721i) q^{15} +(-1.65065 + 11.4805i) q^{16} +(-1.68604 + 1.94579i) q^{17} +(-2.23750 + 1.43796i) q^{18} +(-1.13103 - 1.30528i) q^{19} +(14.1483 + 4.15430i) q^{20} +(0.954001 - 2.08897i) q^{21} -0.316419 q^{22} +(4.00915 - 2.63187i) q^{23} -8.17636 q^{24} +(1.43109 - 3.13366i) q^{25} +(-11.0171 - 3.23490i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(9.80293 - 6.29996i) q^{28} +(-0.933494 + 1.07731i) q^{29} +(-1.09998 + 7.65055i) q^{30} +(5.49527 - 1.61356i) q^{31} +(-12.1951 - 7.83731i) q^{32} +(-0.0169307 - 0.117756i) q^{33} +(-2.84470 - 6.22903i) q^{34} +(-2.77235 - 6.07060i) q^{35} +(-0.722125 - 5.02249i) q^{36} +(5.79948 + 3.72710i) q^{37} +(4.40762 - 1.29419i) q^{38} +(0.614381 - 4.27311i) q^{39} +(-15.5599 + 17.9571i) q^{40} +(-5.48180 + 3.52294i) q^{41} +(3.99993 + 4.61617i) q^{42} +(-8.28385 - 2.43236i) q^{43} +(0.250767 - 0.549102i) q^{44} -2.90602 q^{45} +(1.93781 + 12.6075i) q^{46} +5.91880 q^{47} +(4.81823 - 10.5504i) q^{48} +(1.65616 + 0.486293i) q^{49} +(6.00028 + 6.92469i) q^{50} +(2.16593 - 1.39196i) q^{51} +(14.3449 - 16.5549i) q^{52} +(-0.514895 + 3.58117i) q^{53} +(2.55199 - 0.749331i) q^{54} +(-0.290838 - 0.186910i) q^{55} +(2.67225 + 18.5859i) q^{56} +(0.717477 + 1.57106i) q^{57} +(-1.57500 - 3.44878i) q^{58} +(0.386194 + 2.68604i) q^{59} +(-12.4048 - 7.97205i) q^{60} +(-12.0589 + 3.54081i) q^{61} +(-2.16787 + 15.0779i) q^{62} +(-1.50389 + 1.73558i) q^{63} +(12.9209 - 8.30375i) q^{64} +(-8.21553 - 9.48123i) q^{65} +(0.303602 + 0.0891454i) q^{66} +(-0.0349839 + 0.0766041i) q^{67} +13.0641 q^{68} +(-4.58823 + 1.39575i) q^{69} +17.7502 q^{70} +(6.43563 - 14.0921i) q^{71} +(7.84516 + 2.30355i) q^{72} +(0.455430 + 0.525595i) q^{73} +(-15.4250 + 9.91306i) q^{74} +(-2.25598 + 2.60354i) q^{75} +(-1.24721 + 8.67450i) q^{76} +(-0.262140 + 0.0769714i) q^{77} +(9.65942 + 6.20774i) q^{78} +(1.05210 + 7.31752i) q^{79} +(-14.0019 - 30.6598i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-2.46651 - 17.1550i) q^{82} +(2.33903 + 1.50321i) q^{83} +(-11.1807 + 3.28296i) q^{84} +(1.06480 - 7.40583i) q^{85} +(15.0375 - 17.3542i) q^{86} +(1.19919 - 0.770675i) q^{87} +(0.636992 + 0.735128i) q^{88} +(12.7468 + 3.74281i) q^{89} +(3.21083 - 7.03075i) q^{90} -9.91413 q^{91} +(-23.4144 - 6.62886i) q^{92} -5.72727 q^{93} +(-6.53962 + 14.3198i) q^{94} +(4.81578 + 1.41404i) q^{95} +(9.49308 + 10.9556i) q^{96} +(-7.16897 + 4.60722i) q^{97} +(-3.00640 + 3.46957i) q^{98} +(-0.0169307 + 0.117756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Introduction

L-functions

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