LMFDB - Embedded newform 69.2.e.a.55.1

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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			55.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	69.55
Dual form			69.2.e.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41153 + 0.708089i) q^{2} +(0.654861 + 0.755750i) q^{3} +(3.63158 - 2.33387i) q^{4} +(0.108660 + 0.755750i) q^{5} +(-2.11435 - 1.35881i) q^{6} +(-2.00357 + 4.38721i) q^{7} +(-3.81329 + 4.40077i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-2.41153 + 0.708089i) q^{2} +(0.654861 + 0.755750i) q^{3} +(3.63158 - 2.33387i) q^{4} +(0.108660 + 0.755750i) q^{5} +(-2.11435 - 1.35881i) q^{6} +(-2.00357 + 4.38721i) q^{7} +(-3.81329 + 4.40077i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.797176 - 1.74557i) q^{10} +(3.23616 + 0.950224i) q^{11} +(4.14200 + 1.21620i) q^{12} +(-1.41718 - 3.10319i) q^{13} +(1.72514 - 11.9986i) q^{14} +(-0.500000 + 0.577031i) q^{15} +(2.49315 - 5.45923i) q^{16} +(0.774961 + 0.498037i) q^{17} +(-0.357685 - 2.48775i) q^{18} +(2.49611 - 1.60416i) q^{19} +(2.15843 + 2.49096i) q^{20} +(-4.62769 + 1.35881i) q^{21} -8.47695 q^{22} +(2.73939 - 3.93646i) q^{23} -5.82306 q^{24} +(4.23811 - 1.24442i) q^{25} +(5.61490 + 6.47994i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(2.96306 + 20.6086i) q^{28} +(-6.23737 - 4.00851i) q^{29} +(0.797176 - 1.74557i) q^{30} +(-0.311710 + 0.359733i) q^{31} +(-0.489262 + 3.40289i) q^{32} +(1.40111 + 3.06799i) q^{33} +(-2.22150 - 0.652290i) q^{34} +(-3.53334 - 1.03748i) q^{35} +(1.79329 + 3.92676i) q^{36} +(0.247817 - 1.72360i) q^{37} +(-4.88357 + 5.63594i) q^{38} +(1.41718 - 3.10319i) q^{39} +(-3.74024 - 2.40370i) q^{40} +(0.527961 + 3.67205i) q^{41} +(10.1977 - 6.55363i) q^{42} +(0.391457 + 0.451765i) q^{43} +(13.9701 - 4.10199i) q^{44} -0.763521 q^{45} +(-3.81876 + 11.4326i) q^{46} +5.02851 q^{47} +(5.75848 - 1.69084i) q^{48} +(-10.6493 - 12.2899i) q^{49} +(-9.33918 + 6.00192i) q^{50} +(0.131100 + 0.911821i) q^{51} +(-12.3890 - 7.96195i) q^{52} +(0.0367767 - 0.0805298i) q^{53} +(1.64589 - 1.89945i) q^{54} +(-0.366488 + 2.54898i) q^{55} +(-11.6669 - 25.5470i) q^{56} +(2.84695 + 0.835939i) q^{57} +(17.8800 + 5.25004i) q^{58} +(2.72548 + 5.96797i) q^{59} +(-0.469072 + 3.26247i) q^{60} +(3.85803 - 4.45240i) q^{61} +(0.496975 - 1.08822i) q^{62} +(-4.05742 - 2.60754i) q^{63} +(0.478549 + 3.32838i) q^{64} +(2.19124 - 1.40823i) q^{65} +(-5.55122 - 6.40645i) q^{66} +(9.60816 - 2.82121i) q^{67} +3.97669 q^{68} +(4.76890 - 0.507539i) q^{69} +9.25538 q^{70} +(-8.75112 + 2.56956i) q^{71} +(-3.81329 - 4.40077i) q^{72} +(-10.1506 + 6.52340i) q^{73} +(0.622847 + 4.33199i) q^{74} +(3.71585 + 2.38803i) q^{75} +(5.32094 - 11.6512i) q^{76} +(-10.6527 + 12.2939i) q^{77} +(-1.22023 + 8.48692i) q^{78} +(4.36916 + 9.56713i) q^{79} +(4.39672 + 1.29099i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-3.87333 - 8.48141i) q^{82} +(-0.420847 + 2.92705i) q^{83} +(-13.6345 + 15.7351i) q^{84} +(-0.292184 + 0.639793i) q^{85} +(-1.26390 - 0.812259i) q^{86} +(-1.05518 - 7.33891i) q^{87} +(-16.5222 + 10.6181i) q^{88} +(-6.39396 - 7.37902i) q^{89} +(1.84125 - 0.540641i) q^{90} +16.4537 q^{91} +(0.761114 - 20.6890i) q^{92} -0.475994 q^{93} +(-12.1264 + 3.56063i) q^{94} +(1.48357 + 1.71213i) q^{95} +(-2.89213 + 1.85866i) q^{96} +(-1.19327 - 8.29940i) q^{97} +(34.3834 + 22.0969i) q^{98} +(-1.40111 + 3.06799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	−2.41153	+	0.708089i	−1.70521	+	0.500694i	−0.981831	−	0.189758i	$-0.939230\pi$
$2$	−2.41153	+	0.708089i	−1.70521	+	0.500694i	−0.723378	+	0.690452i	$0.757411\pi$
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	3.63158	−	2.33387i	1.81579	−	1.16694i
$5$	0.108660	+	0.755750i	0.0485944	+	0.337981i	0.999586	+	0.0287654i	$0.00915756\pi$
$5$	0.108660	+	0.755750i	0.0485944	+	0.337981i	−0.950992	+	0.309216i	$0.899933\pi$
$6$	−2.11435	−	1.35881i	−0.863181	−	0.554733i
$7$	−2.00357	+	4.38721i	−0.757279	+	1.65821i	−0.00445196	+	0.999990i	$0.501417\pi$
$7$	−2.00357	+	4.38721i	−0.757279	+	1.65821i	−0.752827	+	0.658219i	$0.771310\pi$
$8$	−3.81329	+	4.40077i	−1.34820	+	1.55591i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	−0.797176	−	1.74557i	−0.252089	−	0.551998i
$11$	3.23616	+	0.950224i	0.975740	+	0.286503i	0.730465	−	0.682950i	$-0.239303\pi$
$11$	3.23616	+	0.950224i	0.975740	+	0.286503i	0.245275	+	0.969453i	$0.421122\pi$
$12$	4.14200	+	1.21620i	1.19569	+	0.351087i
$13$	−1.41718	−	3.10319i	−0.393055	−	0.860669i	−0.997928	−	0.0643475i	$-0.979503\pi$
$13$	−1.41718	−	3.10319i	−0.393055	−	0.860669i	0.604873	−	0.796322i	$-0.293224\pi$
$14$	1.72514	−	11.9986i	0.461062	−	3.20676i
$15$	−0.500000	+	0.577031i	−0.129099	+	0.148989i
$16$	2.49315	−	5.45923i	0.623287	−	1.36481i
$17$	0.774961	+	0.498037i	0.187956	+	0.120792i	0.631235	−	0.775592i	$-0.282549\pi$
$17$	0.774961	+	0.498037i	0.187956	+	0.120792i	−0.443279	+	0.896384i	$0.646185\pi$
$18$	−0.357685	−	2.48775i	−0.0843072	−	0.586369i
$19$	2.49611	−	1.60416i	0.572648	−	0.368018i	−0.222039	−	0.975038i	$-0.571271\pi$
$19$	2.49611	−	1.60416i	0.572648	−	0.368018i	0.794687	+	0.607019i	$0.207635\pi$
$20$	2.15843	+	2.49096i	0.482640	+	0.556996i
$21$	−4.62769	+	1.35881i	−1.00984	+	0.296517i
$22$	−8.47695			−1.80729
$23$	2.73939	−	3.93646i	0.571203	−	0.820809i
$23$	2.73939	−	3.93646i	0.571203	−	0.820809i
$24$	−5.82306			−1.18863
$25$	4.23811	−	1.24442i	0.847623	−	0.248885i
$26$	5.61490	+	6.47994i	1.10117	+	1.27082i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	2.96306	+	20.6086i	0.559966	+	3.89465i
$29$	−6.23737	−	4.00851i	−1.15825	−	0.744362i	−0.186985	−	0.982363i	$-0.559872\pi$
$29$	−6.23737	−	4.00851i	−1.15825	−	0.744362i	−0.971265	+	0.238001i	$0.923508\pi$
$30$	0.797176	−	1.74557i	0.145544	−	0.318696i
$31$	−0.311710	+	0.359733i	−0.0559848	+	0.0646099i	−0.783051	−	0.621957i	$-0.786338\pi$
$31$	−0.311710	+	0.359733i	−0.0559848	+	0.0646099i	0.727066	+	0.686567i	$0.240883\pi$
$32$	−0.489262	+	3.40289i	−0.0864901	+	0.601552i
$33$	1.40111	+	3.06799i	0.243901	+	0.534069i
$34$	−2.22150	−	0.652290i	−0.380983	−	0.111867i
$35$	−3.53334	−	1.03748i	−0.597243	−	0.175366i
$36$	1.79329	+	3.92676i	0.298882	+	0.654460i
$37$	0.247817	−	1.72360i	0.0407408	−	0.283358i	−0.959259	−	0.282529i	$-0.908827\pi$
$37$	0.247817	−	1.72360i	0.0407408	−	0.283358i	1.00000		0.000829807i	$-0.000264136\pi$
$38$	−4.88357	+	5.63594i	−0.792219	+	0.914270i
$39$	1.41718	−	3.10319i	0.226930	−	0.496908i
$40$	−3.74024	−	2.40370i	−0.591383	−	0.380059i
$41$	0.527961	+	3.67205i	0.0824537	+	0.573478i	0.988606	+	0.150526i	$0.0480969\pi$
$41$	0.527961	+	3.67205i	0.0824537	+	0.573478i	−0.906152	+	0.422952i	$0.860994\pi$
$42$	10.1977	−	6.55363i	1.57353	−	1.01125i
$43$	0.391457	+	0.451765i	0.0596966	+	0.0688936i	0.784812	−	0.619733i	$-0.212759\pi$
$43$	0.391457	+	0.451765i	0.0596966	+	0.0688936i	−0.725116	+	0.688627i	$0.758214\pi$
$44$	13.9701	−	4.10199i	2.10607	−	0.618398i
$45$	−0.763521			−0.113819
$46$	−3.81876	+	11.4326i	−0.563046	+	1.68565i
$47$	5.02851			0.733484			0.366742	−	0.930323i	$-0.380473\pi$
$47$	5.02851			0.733484			0.366742	+	0.930323i	$0.380473\pi$
$48$	5.75848	−	1.69084i	0.831164	−	0.244052i
$49$	−10.6493	−	12.2899i	−1.52133	−	1.75570i
$50$	−9.33918	+	6.00192i	−1.32076	+	0.848800i
$51$	0.131100	+	0.911821i	0.0183577	+	0.127681i
$52$	−12.3890	−	7.96195i	−1.71805	−	1.10412i
$53$	0.0367767	−	0.0805298i	0.00505167	−	0.0110616i	−0.907089	−	0.420938i	$-0.861701\pi$
$53$	0.0367767	−	0.0805298i	0.00505167	−	0.0110616i	0.912141	+	0.409877i	$0.134428\pi$
$54$	1.64589	−	1.89945i	0.223977	−	0.258483i
$55$	−0.366488	+	2.54898i	−0.0494173	+	0.343705i
$56$	−11.6669	−	25.5470i	−1.55906	−	3.41386i
$57$	2.84695	+	0.835939i	0.377087	+	0.110723i
$58$	17.8800	+	5.25004i	2.34776	+	0.689363i
$59$	2.72548	+	5.96797i	0.354827	+	0.776963i	0.999917	+	0.0128566i	$0.00409251\pi$
$59$	2.72548	+	5.96797i	0.354827	+	0.776963i	−0.645090	+	0.764106i	$0.723180\pi$
$60$	−0.469072	+	3.26247i	−0.0605569	+	0.421183i
$61$	3.85803	−	4.45240i	0.493970	−	0.570072i	−0.452952	−	0.891535i	$-0.649629\pi$
$61$	3.85803	−	4.45240i	0.493970	−	0.570072i	0.946922	+	0.321463i	$0.104175\pi$
$62$	0.496975	−	1.08822i	0.0631159	−	0.138205i
$63$	−4.05742	−	2.60754i	−0.511186	−	0.328519i
$64$	0.478549	+	3.32838i	0.0598186	+	0.416048i
$65$	2.19124	−	1.40823i	0.271790	−	0.174669i
$66$	−5.55122	−	6.40645i	−0.683308	−	0.788579i
$67$	9.60816	−	2.82121i	1.17382	−	0.344666i	0.364034	−	0.931386i	$-0.381399\pi$
$67$	9.60816	−	2.82121i	1.17382	−	0.344666i	0.809790	+	0.586720i	$0.199581\pi$
$68$	3.97669			0.482244
$69$	4.76890	−	0.507539i	0.574108	−	0.0611006i
$70$	9.25538			1.10623
$71$	−8.75112	+	2.56956i	−1.03857	+	0.304951i	−0.756190	−	0.654353i	$-0.772941\pi$
$71$	−8.75112	+	2.56956i	−1.03857	+	0.304951i	−0.282377	+	0.959303i	$0.591123\pi$
$72$	−3.81329	−	4.40077i	−0.449401	−	0.518636i
$73$	−10.1506	+	6.52340i	−1.18804	+	0.763506i	−0.976847	−	0.213939i	$-0.931371\pi$
$73$	−10.1506	+	6.52340i	−1.18804	+	0.763506i	−0.211192	+	0.977445i	$0.567734\pi$
$74$	0.622847	+	4.33199i	0.0724044	+	0.503584i
$75$	3.71585	+	2.38803i	0.429069	+	0.275746i
$76$	5.32094	−	11.6512i	0.610353	−	1.33649i
$77$	−10.6527	+	12.2939i	−1.21399	+	1.40102i
$78$	−1.22023	+	8.48692i	−0.138164	+	0.960954i
$79$	4.36916	+	9.56713i	0.491569	+	1.07639i	0.979118	+	0.203291i	$0.0651636\pi$
$79$	4.36916	+	9.56713i	0.491569	+	1.07639i	−0.487549	+	0.873095i	$0.662109\pi$
$80$	4.39672	+	1.29099i	0.491568	+	0.144337i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−3.87333	−	8.48141i	−0.427738	−	0.936615i
$83$	−0.420847	+	2.92705i	−0.0461939	+	0.321286i	0.953602	+	0.301071i	$0.0973441\pi$
$83$	−0.420847	+	2.92705i	−0.0461939	+	0.321286i	−0.999796	+	0.0202149i	$0.993565\pi$
$84$	−13.6345	+	15.7351i	−1.48765	+	1.71684i
$85$	−0.292184	+	0.639793i	−0.0316918	+	0.0693953i
$86$	−1.26390	−	0.812259i	−0.136290	−	0.0875882i
$87$	−1.05518	−	7.33891i	−0.113127	−	0.786813i
$88$	−16.5222	+	10.6181i	−1.76127	+	1.13190i
$89$	−6.39396	−	7.37902i	−0.677758	−	0.782175i	0.307811	−	0.951448i	$-0.400404\pi$
$89$	−6.39396	−	7.37902i	−0.677758	−	0.782175i	−0.985569	+	0.169273i	$0.945858\pi$
$90$	1.84125	−	0.540641i	0.194085	−	0.0569885i
$91$	16.4537			1.72482
$92$	0.761114	−	20.6890i	0.0793516	−	2.15697i
$93$	−0.475994			−0.0493583
$94$	−12.1264	+	3.56063i	−1.25074	+	0.367251i
$95$	1.48357	+	1.71213i	0.152211	+	0.175661i
$96$	−2.89213	+	1.85866i	−0.295177	+	0.189699i
$97$	−1.19327	−	8.29940i	−0.121159	−	0.842676i	−0.956247	−	0.292560i	$-0.905493\pi$
$97$	−1.19327	−	8.29940i	−0.121159	−	0.842676i	0.835088	−	0.550116i	$-0.185416\pi$
$98$	34.3834	+	22.0969i	3.47325	+	2.23212i
$99$	−1.40111	+	3.06799i	−0.140816	+	0.308345i
$100$	12.4867	−	14.4104i	1.24867	−	1.44104i
$101$	0.629480	−	4.37813i	0.0626356	−	0.435640i	−0.934240	−	0.356646i	$-0.883920\pi$
$101$	0.629480	−	4.37813i	0.0626356	−	0.435640i	0.996875	−	0.0789938i	$-0.0251707\pi$
$102$	−0.961802	−	2.10605i	−0.0952326	−	0.208530i
$103$	−15.5539	−	4.56703i	−1.53257	−	0.450002i	−0.596732	−	0.802440i	$-0.703535\pi$
$103$	−15.5539	−	4.56703i	−1.53257	−	0.450002i	−0.935835	+	0.352438i	$0.885353\pi$
$104$	19.0605	+	5.59668i	1.86904	+	0.548800i
$105$	−1.52977	−	3.34973i	−0.149290	−	0.326900i
$106$	−0.0316659	+	0.220241i	−0.00307567	+	0.0213917i
$107$	4.15860	−	4.79928i	0.402027	−	0.463964i	−0.518251	−	0.855228i	$-0.673417\pi$
$107$	4.15860	−	4.79928i	0.402027	−	0.463964i	0.920278	+	0.391265i	$0.127962\pi$
$108$	−1.79329	+	3.92676i	−0.172559	+	0.377852i
$109$	−2.07028	−	1.33049i	−0.198296	−	0.127437i	0.437725	−	0.899109i	$-0.355784\pi$
$109$	−2.07028	−	1.33049i	−0.198296	−	0.127437i	−0.636021	+	0.771672i	$0.719421\pi$
$110$	−0.921108	−	6.40645i	−0.0878242	−	0.610831i
$111$	1.46490	−	0.941432i	0.139042	−	0.0893568i
$112$	18.9556	+	21.8759i	1.79113	+	2.06708i
$113$	8.87992	−	2.60738i	0.835352	−	0.245282i	0.164038	−	0.986454i	$-0.447548\pi$
$113$	8.87992	−	2.60738i	0.835352	−	0.245282i	0.671315	+	0.741172i	$0.265730\pi$
$114$	−7.45741			−0.698451
$115$	3.27264	+	1.64256i	0.305175	+	0.153169i
$116$	−32.0068			−2.97176
$117$	3.27329	−	0.961124i	0.302616	−	0.0888559i
$118$	−10.7984	−	12.4620i	−0.994075	−	1.14722i
$119$	−3.73768	+	2.40206i	−0.342633	+	0.220197i
$120$	−0.632736	−	4.40077i	−0.0577606	−	0.401734i
$121$	0.316044	+	0.203109i	0.0287313	+	0.0184645i
$122$	−6.15105	+	13.4689i	−0.556890	+	1.21942i
$123$	−2.42941	+	2.80369i	−0.219052	+	0.252800i
$124$	−0.292429	+	2.03389i	−0.0262609	+	0.182649i
$125$	2.98688	+	6.54035i	0.267154	+	0.584987i
$126$	11.6309	+	3.41515i	1.03617	+	0.304246i
$127$	1.28204	+	0.376440i	0.113762	+	0.0334037i	0.338118	−	0.941104i	$-0.390210\pi$
$127$	1.28204	+	0.376440i	0.113762	+	0.0334037i	−0.224356	+	0.974507i	$0.572028\pi$
$128$	−6.36712	−	13.9420i	−0.562779	−	1.23231i
$129$	−0.0850717	+	0.591687i	−0.00749015	+	0.0520951i
$130$	−4.28709	+	4.94757i	−0.376003	+	0.433931i
$131$	−1.42534	+	3.12106i	−0.124533	+	0.272688i	−0.961622	−	0.274378i	$-0.911528\pi$
$131$	−1.42534	+	3.12106i	−0.124533	+	0.272688i	0.837089	+	0.547066i	$0.184255\pi$
$132$	12.2485	+	7.87165i	1.06610	+	0.685139i
$133$	2.03662	+	14.1650i	0.176597	+	1.22826i
$134$	−21.1727	+	13.6069i	−1.82904	+	1.17545i
$135$	−0.500000	−	0.577031i	−0.0430331	−	0.0496629i
$136$	−5.14690	+	1.51127i	−0.441343	+	0.129590i
$137$	−4.07129			−0.347833			−0.173917	−	0.984760i	$-0.555642\pi$
$137$	−4.07129			−0.347833			−0.173917	+	0.984760i	$0.555642\pi$
$138$	−11.1410	+	4.60075i	−0.948381	+	0.391642i
$139$	6.01342			0.510052			0.255026	−	0.966934i	$-0.417916\pi$
$139$	6.01342			0.510052			0.255026	+	0.966934i	$0.417916\pi$
$140$	−15.2529	+	4.47867i	−1.28911	+	0.378517i
$141$	3.29298	+	3.80030i	0.277319	+	0.320043i
$142$	19.2841	−	12.3931i	1.61829	−	1.04001i
$143$	−1.63750	−	11.3891i	−0.136935	−	0.952401i
$144$	5.04885	+	3.24470i	0.420738	+	0.270392i
$145$	2.35168	−	5.14945i	0.195296	−	0.427639i
$146$	19.8593	−	22.9189i	1.64357	−	1.89678i
$147$	2.31431	−	16.0964i	0.190881	−	1.32761i
$148$	−3.12270	−	6.83777i	−0.256685	−	0.562061i
$149$	14.5747	+	4.27953i	1.19401	+	0.350593i	0.817560	−	0.575844i	$-0.195326\pi$
$149$	14.5747	+	4.27953i	1.19401	+	0.350593i	0.376450	+	0.926437i	$0.377145\pi$
$150$	−10.6518	−	3.12765i	−0.869717	−	0.255372i
$151$	−0.248740	−	0.544665i	−0.0202422	−	0.0443242i	0.899241	−	0.437454i	$-0.144120\pi$
$151$	−0.248740	−	0.544665i	−0.0202422	−	0.0443242i	−0.919483	+	0.393130i	$0.871392\pi$
$152$	−2.45889	+	17.1019i	−0.199442	+	1.38715i
$153$	−0.603256	+	0.696195i	−0.0487704	+	0.0562840i
$154$	16.9842	−	37.1901i	1.36862	−	2.99687i
$155$	−0.305738	−	0.196486i	−0.0245575	−	0.0157821i
$156$	−2.09585	−	14.5770i	−0.167803	−	1.16709i
$157$	−2.89905	+	1.86310i	−0.231369	+	0.148692i	−0.651189	−	0.758915i	$-0.725730\pi$
$157$	−2.89905	+	1.86310i	−0.231369	+	0.148692i	0.419820	+	0.907607i	$0.362093\pi$
$158$	−17.3107	−	19.9777i	−1.37717	−	1.58934i
$159$	0.0849440	−	0.0249418i	0.00673650	−	0.00197801i
$160$	−2.62490			−0.207516
$161$	11.7815	+	19.9053i	0.928513	+	1.56875i
$162$	2.51334			0.197466
$163$	−13.7358	+	4.03318i	−1.07587	+	0.315903i	−0.771224	−	0.636564i	$-0.780355\pi$
$163$	−13.7358	+	4.03318i	−1.07587	+	0.315903i	−0.304643	+	0.952467i	$0.598537\pi$
$164$	10.4874	+	12.1031i	0.818931	+	0.945096i
$165$	−2.16639	+	1.39225i	−0.168653	+	0.108387i
$166$	−1.05773	−	7.35667i	−0.0820958	−	0.570989i
$167$	−19.1885	−	12.3317i	−1.48485	−	0.954257i	−0.996672	−	0.0815140i	$-0.974024\pi$
$167$	−19.1885	−	12.3317i	−1.48485	−	0.954257i	−0.488180	−	0.872743i	$-0.662339\pi$
$168$	11.6669	−	25.5470i	0.900122	−	1.97099i
$169$	0.891810	−	1.02920i	0.0686008	−	0.0791695i
$170$	0.251579	−	1.74977i	0.0192953	−	0.134201i
$171$	1.23259	+	2.69900i	0.0942588	+	0.206398i
$172$	2.47597	+	0.727010i	0.188791	+	0.0554340i
$173$	1.59528	+	0.468417i	0.121287	+	0.0356131i	0.341813	−	0.939768i	$-0.388959\pi$
$173$	1.59528	+	0.468417i	0.121287	+	0.0356131i	−0.220526	+	0.975381i	$0.570777\pi$
$174$	7.74118	+	16.9508i	0.586858	+	1.28504i
$175$	−3.03182	+	21.0868i	−0.229184	+	1.59401i
$176$	13.2557	−	15.2979i	0.999188	−	1.15312i
$177$	−2.72548	+	5.96797i	−0.204860	+	0.448580i
$178$	20.6442	+	13.2672i	1.54735	+	0.994421i
$179$	−3.46892	−	24.1268i	−0.259279	−	1.80333i	−0.537991	−	0.842950i	$-0.680817\pi$
$179$	−3.46892	−	24.1268i	−0.259279	−	1.80333i	0.278712	−	0.960375i	$-0.410092\pi$
$180$	−2.77279	+	1.78196i	−0.206671	+	0.132820i
$181$	6.93811	+	8.00700i	0.515705	+	0.595156i	0.952550	−	0.304381i	$-0.0984496\pi$
$181$	6.93811	+	8.00700i	0.515705	+	0.595156i	−0.436845	+	0.899537i	$0.643904\pi$
$182$	−39.6787	+	11.6507i	−2.94118	+	0.863609i
$183$	5.89137			0.435503
$184$	6.87737	+	27.0663i	0.507007	+	1.99536i
$185$	1.32954			0.0977497
$186$	1.14787	−	0.337046i	0.0841662	−	0.0247134i
$187$	2.03465	+	2.34812i	0.148789	+	0.171711i
$188$	18.2614	−	11.7359i	1.33185	−	0.855929i
$189$	−0.686393	−	4.77397i	−0.0499277	−	0.347255i
$190$	−4.79001	−	3.07835i	−0.347504	−	0.223327i
$191$	−7.13655	+	15.6269i	−0.516383	+	1.13072i	0.454408	+	0.890794i	$0.349851\pi$
$191$	−7.13655	+	15.6269i	−0.516383	+	1.13072i	−0.970791	+	0.239927i	$0.922877\pi$
$192$	−2.20204	+	2.54129i	−0.158919	+	0.183402i
$193$	2.01276	−	13.9991i	0.144882	−	1.00767i	−0.779554	−	0.626335i	$-0.784554\pi$
$193$	2.01276	−	13.9991i	0.144882	−	1.00767i	0.924435	−	0.381339i	$-0.124537\pi$
$194$	8.75432	+	19.1693i	0.628524	+	1.37628i
$195$	2.49922	+	0.733838i	0.178973	+	0.0525513i
$196$	−67.3568	−	19.7777i	−4.81120	−	1.41270i
$197$	−1.27802	−	2.79847i	−0.0910550	−	0.199383i	0.858625	−	0.512604i	$-0.171319\pi$
$197$	−1.27802	−	2.79847i	−0.0910550	−	0.199383i	−0.949680	+	0.313221i	$0.898592\pi$
$198$	1.20640	−	8.39066i	0.0857348	−	0.596299i
$199$	−10.3265	+	11.9174i	−0.732028	+	0.844805i	−0.992698	−	0.120623i	$-0.961511\pi$
$199$	−10.3265	+	11.9174i	−0.732028	+	0.844805i	0.260671	+	0.965428i	$0.416056\pi$
$200$	−10.6847	+	23.3963i	−0.755526	+	1.65437i
$201$	8.42414	+	5.41387i	0.594193	+	0.381865i
$202$	1.58209	+	11.0037i	0.111316	+	0.774218i
$203$	30.0832	−	19.3333i	2.11143	−	1.35693i
$204$	2.60418	+	3.00538i	0.182329	+	0.210419i
$205$	−2.71778	+	0.798013i	−0.189818	+	0.0557356i
$206$	40.7425			2.83866
$207$	3.50654	+	3.27173i	0.243721	+	0.227401i
$208$	−20.4743			−1.41963
$209$	9.60214	−	2.81944i	0.664194	−	0.195025i
$210$	6.06099	+	6.99475i	0.418248	+	0.482684i
$211$	−13.3259	+	8.56406i	−0.917395	+	0.589574i	−0.911901	−	0.410411i	$-0.865385\pi$
$211$	−13.3259	+	8.56406i	−0.917395	+	0.589574i	−0.00549464	+	0.999985i	$0.501749\pi$
$212$	−0.0543888	−	0.378282i	−0.00373544	−	0.0259805i
$213$	−7.67271	−	4.93095i	−0.525725	−	0.337863i
$214$	−6.63027	+	14.5183i	−0.453236	+	0.992448i
$215$	−0.298886	+	0.344932i	−0.0203838	+	0.0235242i
$216$	0.828708	−	5.76379i	0.0563864	−	0.392176i
$217$	−0.953688	−	2.08829i	−0.0647406	−	0.141762i
$218$	5.93463	+	1.74257i	0.401944	+	0.118021i
$219$	−11.5773	−	3.39940i	−0.782321	−	0.229710i
$220$	4.61807	+	10.1122i	0.311350	+	0.681762i
$221$	0.447245	−	3.11066i	0.0300850	−	0.209245i
$222$	−2.86602	+	3.30757i	−0.192355	+	0.221989i
$223$	−6.99135	+	15.3089i	−0.468176	+	1.02516i	0.517372	+	0.855761i	$0.326911\pi$
$223$	−6.99135	+	15.3089i	−0.468176	+	1.02516i	−0.985547	+	0.169401i	$0.945817\pi$
$224$	−13.9489	−	8.96442i	−0.932001	−	0.598961i
$225$	0.628610	+	4.37208i	0.0419073	+	0.291472i
$226$	−19.5679	+	12.5755i	−1.30164	+	0.836513i
$227$	14.1033	+	16.2761i	0.936068	+	1.08028i	0.996623	+	0.0821148i	$0.0261674\pi$
$227$	14.1033	+	16.2761i	0.936068	+	1.08028i	−0.0605553	+	0.998165i	$0.519287\pi$
$228$	12.2899	−	3.60863i	0.813917	−	0.238988i
$229$	−0.566524			−0.0374370			−0.0187185	−	0.999825i	$-0.505959\pi$
$229$	−0.566524			−0.0374370			−0.0187185	+	0.999825i	$0.505959\pi$
$230$	−9.05515	−	1.64375i	−0.597079	−	0.108386i
$231$	−16.2671			−1.07030
$232$	41.4255	−	12.1636i	2.71972	−	0.798580i
$233$	−5.27431	−	6.08688i	−0.345532	−	0.398765i	0.556209	−	0.831042i	$-0.312255\pi$
$233$	−5.27431	−	6.08688i	−0.345532	−	0.398765i	−0.901740	+	0.432278i	$0.857710\pi$
$234$	−7.21307	+	4.63556i	−0.471533	+	0.303036i
$235$	0.546400	+	3.80030i	0.0356432	+	0.247904i
$236$	23.8263	+	15.3122i	1.55096	+	0.996740i
$237$	−4.36916	+	9.56713i	−0.283808	+	0.621452i
$238$	7.31266	−	8.43926i	0.474009	−	0.547036i
$239$	0.983171	−	6.83811i	0.0635961	−	0.442320i	−0.933000	−	0.359877i	$-0.882819\pi$
$239$	0.983171	−	6.83811i	0.0635961	−	0.442320i	0.996596	−	0.0824432i	$-0.0262723\pi$
$240$	1.90357	+	4.16824i	0.122875	+	0.269059i
$241$	0.317423	+	0.0932039i	0.0204470	+	0.00600379i	0.291940	−	0.956437i	$-0.405699\pi$
$241$	0.317423	+	0.0932039i	0.0204470	+	0.00600379i	−0.271493	+	0.962440i	$0.587517\pi$
$242$	−0.905970	−	0.266017i	−0.0582379	−	0.0171002i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	3.61939	−	25.1734i	0.231707	−	1.61156i
$245$	8.13095	−	9.38361i	0.519467	−	0.599497i
$246$	3.87333	−	8.48141i	0.246955	−	0.540755i
$247$	−8.51543	−	5.47254i	−0.541824	−	0.348209i
$248$	−0.394460	−	2.74353i	−0.0250482	−	0.174214i
$249$	−2.48772	+	1.59876i	−0.157653	+	0.101317i
$250$	−11.8341	−	13.6573i	−0.748454	−	0.863762i
$251$	−26.2161	+	7.69773i	−1.65474	+	0.485877i	−0.970040	−	0.242945i	$-0.921886\pi$
$251$	−26.2161	+	7.69773i	−1.65474	+	0.485877i	−0.684704	+	0.728822i	$0.740068\pi$
$252$	−20.8205			−1.31157
$253$	12.6056	−	10.1360i	0.792510	−	0.637245i
$254$	−3.35822			−0.210714
$255$	−0.674863	+	0.198158i	−0.0422616	+	0.0124091i
$256$	20.8226	+	24.0306i	1.30141	+	1.50191i
$257$	3.13015	−	2.01162i	0.195253	−	0.125482i	−0.439361	−	0.898310i	$-0.644795\pi$
$257$	3.13015	−	2.01162i	0.195253	−	0.125482i	0.634615	+	0.772829i	$0.281159\pi$
$258$	−0.213814	−	1.48711i	−0.0133115	−	0.0925833i
$259$	7.06528	+	4.54058i	0.439015	+	0.282138i
$260$	4.67104	−	10.2282i	0.289686	−	0.634323i
$261$	4.85538	−	5.60341i	0.300541	−	0.346842i
$262$	1.22726	−	8.53580i	0.0758205	−	0.527343i
$263$	−7.67457	−	16.8050i	−0.473234	−	1.03624i	−0.984269	−	0.176678i	$-0.943465\pi$
$263$	−7.67457	−	16.8050i	−0.473234	−	1.03624i	0.511034	−	0.859560i	$-0.329262\pi$
$264$	−18.8444	−	5.53321i	−1.15979	−	0.340545i
$265$	0.0648566	+	0.0190436i	0.00398411	+	0.00116984i
$266$	−14.9415	−	32.7172i	−0.916120	−	2.00602i
$267$	1.38954	−	9.66446i	0.0850385	−	0.591455i
$268$	28.3084	−	32.6697i	1.72921	−	1.99562i
$269$	3.10328	−	6.79523i	0.189210	−	0.414313i	−0.791124	−	0.611655i	$-0.790504\pi$
$269$	3.10328	−	6.79523i	0.189210	−	0.414313i	0.980335	+	0.197343i	$0.0632312\pi$
$270$	1.61435	+	1.03748i	0.0982464	+	0.0631392i
$271$	−3.62528	−	25.2144i	−0.220220	−	1.53166i	−0.737205	−	0.675669i	$-0.763855\pi$
$271$	−3.62528	−	25.2144i	−0.220220	−	1.53166i	0.516985	−	0.855995i	$-0.327054\pi$
$272$	4.65099	−	2.98901i	0.282008	−	0.181235i
$273$	10.7749	+	12.4349i	0.652127	+	0.752595i
$274$	9.81803	−	2.88283i	0.593129	−	0.174158i
$275$	14.8977			0.898366
$276$	16.1341	−	12.9732i	0.971158	−	0.780893i
$277$	31.4086			1.88716			0.943579	−	0.331146i	$-0.107435\pi$
$277$	31.4086			1.88716			0.943579	+	0.331146i	$0.107435\pi$
$278$	−14.5015	+	4.25804i	−0.869744	+	0.255380i
$279$	−0.311710	−	0.359733i	−0.0186616	−	0.0215366i
$280$	18.0394	−	11.5932i	1.07806	−	0.692827i
$281$	0.760027	+	5.28610i	0.0453394	+	0.315342i	0.999853	+	0.0171736i	$0.00546678\pi$
$281$	0.760027	+	5.28610i	0.0453394	+	0.315342i	−0.954513	+	0.298169i	$0.903624\pi$
$282$	−10.6321	−	6.83281i	−0.633130	−	0.406888i
$283$	7.16662	−	15.6927i	0.426011	−	0.932835i	−0.567946	−	0.823066i	$-0.692262\pi$
$283$	7.16662	−	15.6927i	0.426011	−	0.932835i	0.993957	−	0.109769i	$-0.0350111\pi$
$284$	−25.7833	+	29.7556i	−1.52996	+	1.76567i
$285$	−0.322410	+	2.24241i	−0.0190979	+	0.132829i
$286$	12.0133	+	26.3056i	0.710364	+	1.55548i
$287$	−17.1679	−	5.04094i	−1.01339	−	0.297557i
$288$	−3.29862	−	0.968563i	−0.194373	−	0.0570731i
$289$	−6.70953	−	14.6918i	−0.394678	−	0.864225i
$290$	−2.02487	+	14.0833i	−0.118904	+	0.826997i
$291$	5.49084	−	6.33676i	0.321879	−	0.371468i
$292$	−21.6379	+	47.3804i	−1.26626	+	2.77273i
$293$	−27.6891	−	17.7947i	−1.61762	−	1.03958i	−0.957507	−	0.288409i	$-0.906874\pi$
$293$	−27.6891	−	17.7947i	−1.61762	−	1.03958i	−0.660109	−	0.751170i	$-0.729490\pi$
$294$	5.81664	+	40.4556i	0.339233	+	2.35942i
$295$	−4.21414	+	2.70826i	−0.245357	+	0.157681i
$296$	6.64019	+	7.66318i	0.385953	+	0.445414i
$297$	−3.23616	+	0.950224i	−0.187781	+	0.0551376i
$298$	−38.1777			−2.21158
$299$	−16.0978	−	2.92218i	−0.930959	−	0.168994i
$300$	19.0677			1.10088
$301$	−2.76630	+	0.812259i	−0.159447	+	0.0468178i
$302$	0.985515	+	1.13735i	0.0567100	+	0.0654469i
$303$	3.72099	−	2.39133i	0.213765	−	0.137379i
$304$	−2.53427	−	17.6263i	−0.145351	−	1.01094i
$305$	3.78412	+	2.43190i	0.216678	+	0.139250i
$306$	0.961802	−	2.10605i	0.0549826	−	0.120395i
$307$	−11.3883	+	13.1428i	−0.649964	+	0.750098i	−0.981104	−	0.193484i	$-0.938021\pi$
$307$	−11.3883	+	13.1428i	−0.649964	+	0.750098i	0.331140	+	0.943582i	$0.392567\pi$
$308$	−9.99378	+	69.5083i	−0.569448	+	3.96060i
$309$	−6.73409	−	14.7456i	−0.383089	−	0.838847i
$310$	0.876426	+	0.257342i	0.0497777	+	0.0146160i
$311$	10.7262	+	3.14949i	0.608226	+	0.178591i	0.571320	−	0.820727i	$-0.306432\pi$
$311$	10.7262	+	3.14949i	0.608226	+	0.178591i	0.0369063	+	0.999319i	$0.488250\pi$
$312$	8.25231	+	18.0700i	0.467195	+	1.02301i
$313$	−4.08868	+	28.4374i	−0.231106	+	1.60737i	0.462230	+	0.886760i	$0.347049\pi$
$313$	−4.08868	+	28.4374i	−0.231106	+	1.60737i	−0.693336	+	0.720615i	$0.743860\pi$
$314$	5.67189	−	6.54571i	0.320084	−	0.369396i
$315$	1.52977	−	3.34973i	0.0861927	−	0.188736i
$316$	38.1954	+	24.5467i	2.14866	+	1.38086i
$317$	2.68359	+	18.6648i	0.150726	+	1.04832i	0.915007	+	0.403437i	$0.132185\pi$
$317$	2.68359	+	18.6648i	0.150726	+	1.04832i	−0.764282	+	0.644882i	$0.776906\pi$
$318$	−0.187184	+	0.120296i	−0.0104968	+	0.00674586i
$319$	−16.3762	−	18.8991i	−0.916889	−	1.05815i
$320$	−2.46342	+	0.723326i	−0.137710	+	0.0404352i
$321$	6.35036			0.354442
$322$	−42.5062	−	39.6598i	−2.36878	−	2.21015i
$323$	2.73332			0.152086
$324$	−4.14200	+	1.21620i	−0.230111	+	0.0675667i
$325$	−9.86784	−	11.3881i	−0.547369	−	0.631698i
$326$	30.2683	−	19.4523i	1.67641	−	1.07736i
$327$	−0.350228	−	2.43589i	−0.0193677	−	0.134705i
$328$	−18.1731	−	11.6792i	−1.00344	−	0.644874i
$329$	−10.0750	+	22.0611i	−0.555452	+	1.21627i
$330$	4.23847	−	4.89146i	0.233320	−	0.269266i
$331$	1.22889	−	8.54715i	0.0675462	−	0.469794i	−0.927773	−	0.373146i	$-0.878279\pi$
$331$	1.22889	−	8.54715i	0.0675462	−	0.469794i	0.995319	−	0.0966475i	$-0.0308120\pi$
$332$	5.30303	+	11.6120i	0.291042	+	0.637293i
$333$	1.67079	+	0.490588i	0.0915588	+	0.0268841i
$334$	55.0056	+	16.1511i	3.00977	+	0.883750i
$335$	3.17616	+	6.95481i	0.173532	+	0.379982i
$336$	−4.11944	+	28.6514i	−0.224734	+	1.56306i
$337$	7.49057	−	8.64458i	0.408037	−	0.470900i	−0.514118	−	0.857719i	$-0.671881\pi$
$337$	7.49057	−	8.64458i	0.408037	−	0.470900i	0.922156	+	0.386819i	$0.126426\pi$
$338$	−1.42186	+	3.11343i	−0.0773389	+	0.169349i
$339$	7.78564	+	5.00352i	0.422858	+	0.271754i
$340$	0.432108	+	3.00538i	0.0234344	+	0.162990i
$341$	−1.35057	+	0.867959i	−0.0731375	+	0.0470026i
$342$	−4.88357	−	5.63594i	−0.264073	−	0.304757i
$343$	42.8612	−	12.5852i	2.31429	−	0.679536i
$344$	−3.48086			−0.187675
$345$	0.901763	+	3.54894i	0.0485493	+	0.191069i
$346$	−4.17875			−0.224651
$347$	26.7991	−	7.86893i	1.43865	−	0.422426i	0.532880	−	0.846191i	$-0.321110\pi$
$347$	26.7991	−	7.86893i	1.43865	−	0.422426i	0.905772	+	0.423764i	$0.139292\pi$
$348$	−20.9600	−	24.1892i	−1.12357	−	1.29667i
$349$	−15.0280	+	9.65788i	−0.804428	+	0.516975i	−0.877058	−	0.480384i	$-0.840497\pi$
$349$	−15.0280	+	9.65788i	−0.804428	+	0.516975i	0.0726298	+	0.997359i	$0.476861\pi$
$350$	−7.61999	−	52.9982i	−0.407306	−	2.83287i
$351$	2.86992	+	1.84438i	0.153185	+	0.0984459i
$352$	−4.81684	+	10.5474i	−0.256738	+	0.562178i
$353$	−5.38350	+	6.21289i	−0.286535	+	0.330679i	−0.880709	−	0.473658i	$-0.842933\pi$
$353$	−5.38350	+	6.21289i	−0.286535	+	0.330679i	0.594174	+	0.804336i	$0.297479\pi$
$354$	2.34672	−	16.3218i	0.124727	−	0.867494i
$355$	−2.89284	−	6.33445i	−0.153536	−	0.336198i
$356$	−40.4418	−	11.8748i	−2.14341	−	0.629363i
$357$	−4.26302	−	1.25174i	−0.225623	−	0.0662489i
$358$	25.4493	+	55.7263i	1.34504	+	2.94523i
$359$	0.690627	−	4.80342i	0.0364499	−	0.253515i	−0.963447	−	0.267900i	$-0.913670\pi$
$359$	0.690627	−	4.80342i	0.0364499	−	0.253515i	0.999897	+	0.0143857i	$0.00457928\pi$
$360$	2.91153	−	3.36008i	0.153451	−	0.177092i
$361$	−4.23561	+	9.27470i	−0.222927	+	0.488142i
$362$	−22.4011	−	14.3963i	−1.17738	−	0.756654i
$363$	0.0534652	+	0.371859i	0.00280620	+	0.0195175i
$364$	59.7530	−	38.4010i	3.13191	−	2.01276i
$365$	−6.03302	−	6.96248i	−0.315783	−	0.364433i
$366$	−14.2072	+	4.17161i	−0.742623	+	0.218054i
$367$	−10.9802			−0.573162			−0.286581	−	0.958056i	$-0.592519\pi$
$367$	−10.9802			−0.573162			−0.286581	+	0.958056i	$0.592519\pi$
$368$	−14.6603	−	24.7692i	−0.764223	−	1.29118i
$369$	−3.70981			−0.193125
$370$	−3.20622	+	0.941432i	−0.166684	+	0.0489427i
$371$	0.279616	+	0.322694i	0.0145170	+	0.0167535i
$372$	−1.72861	+	1.11091i	−0.0896242	+	0.0575980i
$373$	2.17383	+	15.1193i	0.112557	+	0.782850i	0.965417	+	0.260711i	$0.0839569\pi$
$373$	2.17383	+	15.1193i	0.112557	+	0.782850i	−0.852860	+	0.522140i	$0.825134\pi$
$374$	−6.56930	−	4.22184i	−0.339691	−	0.218306i
$375$	−2.98688	+	6.54035i	−0.154242	+	0.337742i
$376$	−19.1752	+	22.1293i	−0.988885	+	1.14123i
$377$	−3.59971	+	25.0365i	−0.185394	+	1.28945i
$378$	5.03565	+	11.0265i	0.259006	+	0.567144i
$379$	−0.0700264	−	0.0205616i	−0.00359701	−	0.00105618i	0.279934	−	0.960019i	$-0.409688\pi$
$379$	−0.0700264	−	0.0205616i	−0.00359701	−	0.00105618i	−0.283531	+	0.958963i	$0.591506\pi$
$380$	9.38358	+	2.75527i	0.481368	+	0.141342i
$381$	0.555061	+	1.21541i	0.0284367	+	0.0622676i
$382$	6.14479	−	42.7380i	0.314395	−	2.18666i
$383$	−17.3202	+	19.9885i	−0.885019	+	1.02137i	0.114590	+	0.993413i	$0.463445\pi$
$383$	−17.3202	+	19.9885i	−0.885019	+	1.02137i	−0.999609	+	0.0279538i	$0.991101\pi$
$384$	6.36712	−	13.9420i	0.324921	−	0.711477i
$385$	−10.4486	−	6.71492i	−0.532511	−	0.342224i
$386$	5.05875	+	35.1844i	0.257483	+	1.79084i
$387$	−0.502877	+	0.323180i	−0.0255627	+	0.0164281i
$388$	−23.7032	−	27.3549i	−1.20335	−	1.38874i
$389$	30.7724	−	9.03560i	1.56022	−	0.458123i	0.616088	−	0.787678i	$-0.288717\pi$
$389$	30.7724	−	9.03560i	1.56022	−	0.458123i	0.944137	+	0.329554i	$0.106899\pi$
$390$	−6.54657			−0.331499
$391$	4.08343	−	1.68628i	0.206508	−	0.0852791i
$392$	94.6940			4.78277
$393$	−3.29214	+	0.966659i	−0.166066	+	0.0487615i
$394$	5.06354	+	5.84364i	0.255097	+	0.294398i
$395$	−6.75560	+	4.34156i	−0.339911	+	0.218448i
$396$	2.07208	+	14.4117i	0.104126	+	0.724213i
$397$	15.4067	+	9.90129i	0.773241	+	0.496932i	0.866784	−	0.498684i	$-0.166183\pi$
$397$	15.4067	+	9.90129i	0.773241	+	0.496932i	−0.0935435	+	0.995615i	$0.529819\pi$
$398$	16.4641	−	36.0514i	0.825271	−	1.80709i
$399$	−9.37150	+	10.8153i	−0.469162	+	0.541442i
$400$	3.77265	−	26.2394i	0.188633	−	1.31197i
$401$	14.8518	+	32.5209i	0.741664	+	1.62402i	0.780798	+	0.624783i	$0.214813\pi$
$401$	14.8518	+	32.5209i	0.741664	+	1.62402i	−0.0391341	+	0.999234i	$0.512460\pi$
$402$	−24.1486	−	7.09066i	−1.20442	−	0.353650i
$403$	1.55807	+	0.457490i	0.0776128	+	0.0227892i
$404$	−7.93199	−	17.3686i	−0.394631	−	0.864122i
$405$	0.108660	−	0.755750i	0.00539938	−	0.0375535i
$406$	−58.8568	+	67.9244i	−2.92101	+	3.37103i
$407$	2.43978	−	5.34238i	0.120936	−	0.264812i
$408$	−4.51264	−	2.90010i	−0.223409	−	0.143576i
$409$	−1.57976	−	10.9875i	−0.0781143	−	0.543297i	−0.990873	−	0.134798i	$-0.956962\pi$
$409$	−1.57976	−	10.9875i	−0.0781143	−	0.543297i	0.912759	−	0.408499i	$-0.133948\pi$
$410$	5.98895	−	3.84886i	0.295773	−	0.190082i
$411$	−2.66613	−	3.07687i	−0.131510	−	0.151771i
$412$	−67.1439	+	19.7152i	−3.30794	+	0.971300i
$413$	−31.6434			−1.55707
$414$	−10.7728	−	5.40692i	−0.529454	−	0.265736i
$415$	−2.25785			−0.110833
$416$	11.2532	−	3.30423i	0.551732	−	0.162003i
$417$	3.93795	+	4.54464i	0.192842	+	0.222552i
$418$	−21.1594	+	13.5983i	−1.03494	+	0.665117i
$419$	5.42267	+	37.7155i	0.264915	+	1.84252i	0.494429	+	0.869218i	$0.335377\pi$
$419$	5.42267	+	37.7155i	0.264915	+	1.84252i	−0.229515	+	0.973305i	$0.573714\pi$
$420$	−13.3733	−	8.59450i	−0.652551	−	0.419369i
$421$	16.1314	−	35.3228i	0.786197	−	1.72153i	0.0989662	−	0.995091i	$-0.468446\pi$
$421$	16.1314	−	35.3228i	0.786197	−	1.72153i	0.687230	−	0.726440i	$-0.258826\pi$
$422$	26.0718	−	30.0884i	1.26915	−	1.46468i
$423$	−0.715632	+	4.97733i	−0.0347952	+	0.242006i
$424$	0.214153	+	0.468930i	0.0104002	+	0.0227733i
$425$	3.90414	+	1.14636i	0.189379	+	0.0556066i
$426$	21.9945	+	6.45817i	1.06564	+	0.312900i
$427$	11.8038	+	25.8467i	0.571225	+	1.25081i
$428$	3.90136	−	27.1346i	0.188580	−	1.31160i
$429$	7.53494	−	8.69579i	0.363791	−	0.419837i
$430$	0.476529	−	1.04345i	0.0229803	−	0.0503197i
$431$	11.3809	+	7.31405i	0.548198	+	0.352305i	0.785237	−	0.619195i	$-0.212541\pi$
$431$	11.3809	+	7.31405i	0.548198	+	0.352305i	−0.237040	+	0.971500i	$0.576177\pi$
$432$	0.854114	+	5.94049i	0.0410936	+	0.285812i
$433$	−0.875146	+	0.562422i	−0.0420569	+	0.0270283i	−0.561500	−	0.827477i	$-0.689776\pi$
$433$	−0.875146	+	0.562422i	−0.0420569	+	0.0270283i	0.519443	+	0.854505i	$0.326139\pi$
$434$	3.77854	+	4.36067i	0.181376	+	0.209319i
$435$	5.43172	−	1.59490i	0.260431	−	0.0764694i
$436$	−10.6235			−0.508776
$437$	0.523141	−	14.2203i	0.0250252	−	0.680248i
$438$	30.3261			1.44903
$439$	38.7399	−	11.3751i	1.84895	−	0.542902i	0.849061	−	0.528294i	$-0.177168\pi$
$439$	38.7399	−	11.3751i	1.84895	−	0.542902i	0.999893	−	0.0146080i	$-0.00465004\pi$
$440$	−9.81996	−	11.3328i	−0.468148	−	0.540272i
$441$	13.6804	−	8.79184i	0.651446	−	0.418659i
$442$	1.12408	+	7.81813i	0.0534669	+	0.371871i
$443$	−4.74472	−	3.04924i	−0.225428	−	0.144874i	0.423052	−	0.906105i	$-0.360959\pi$
$443$	−4.74472	−	3.04924i	−0.225428	−	0.144874i	−0.648480	+	0.761231i	$0.724595\pi$
$444$	3.12270	−	6.83777i	0.148197	−	0.324506i
$445$	4.88192	−	5.63404i	0.231425	−	0.267079i
$446$	6.01977	−	41.8684i	0.285044	−	1.98253i
$447$	6.31017	+	13.8174i	0.298461	+	0.653538i
$448$	−15.5611	−	4.56915i	−0.735193	−	0.215872i
$449$	−19.6683	−	5.77512i	−0.928203	−	0.272545i	−0.217519	−	0.976056i	$-0.569796\pi$
$449$	−19.6683	−	5.77512i	−0.928203	−	0.272545i	−0.710684	+	0.703511i	$0.751614\pi$
$450$	−4.61173	−	10.0983i	−0.217399	−	0.476037i
$451$	−1.78070	+	12.3850i	−0.0838499	+	0.583189i
$452$	26.1628	−	30.1935i	1.23060	−	1.42018i
$453$	0.248740	−	0.544665i	0.0116868	−	0.0255906i
$454$	−45.5354	−	29.2638i	−2.13708	−	1.37342i
$455$	1.78787	+	12.4349i	0.0838167	+	0.582958i
$456$	−14.5350	+	9.34109i	−0.680665	+	0.437437i
$457$	−6.82253	−	7.87362i	−0.319144	−	0.368312i	0.573397	−	0.819278i	$-0.305625\pi$
$457$	−6.82253	−	7.87362i	−0.319144	−	0.368312i	−0.892541	+	0.450965i	$0.851080\pi$
$458$	1.36619	−	0.401150i	0.0638379	−	0.0187445i
$459$	−0.921198			−0.0429978
$460$	15.7184	−	1.67286i	0.732873	−	0.0779974i
$461$	−17.5918			−0.819334			−0.409667	−	0.912235i	$-0.634355\pi$
$461$	−17.5918			−0.819334			−0.409667	+	0.912235i	$0.634355\pi$
$462$	39.2287	−	11.5186i	1.82508	−	0.535893i
$463$	3.41473	+	3.94081i	0.158696	+	0.183145i	0.829529	−	0.558463i	$-0.188609\pi$
$463$	3.41473	+	3.94081i	0.158696	+	0.183145i	−0.670833	+	0.741608i	$0.734063\pi$
$464$	−37.4341	+	24.0574i	−1.73783	+	1.11684i
$465$	−0.0517217	−	0.359733i	−0.00239854	−	0.0166822i
$466$	17.0292	+	10.9440i	0.788863	+	0.506971i
$467$	−0.104418	+	0.228644i	−0.00483191	+	0.0105804i	−0.912033	−	0.410118i	$-0.865488\pi$
$467$	−0.104418	+	0.228644i	−0.00483191	+	0.0105804i	0.907201	+	0.420698i	$0.138215\pi$
$468$	9.64405	−	11.1298i	0.445796	−	0.514477i
$469$	−6.87340	+	47.8055i	−0.317384	+	2.20745i
$470$	−4.00861	−	8.77762i	−0.184903	−	0.404882i
$471$	−3.30651	−	0.970880i	−0.152356	−	0.0447358i
$472$	−36.6567	−	10.7634i	−1.68726	−	0.495425i
$473$	0.837541	+	1.83396i	0.0385102	+	0.0843255i
$474$	3.76198	−	26.1652i	0.172794	−	1.20181i
$475$	8.58257	−	9.90481i	0.393795	−	0.454464i
$476$	−7.96757	+	17.4465i	−0.365193	+	0.799661i
$477$	0.0744763	+	0.0478630i	0.00341003	+	0.00219150i
$478$	2.47104	+	17.1865i	0.113023	+	0.786091i
$479$	−26.4674	+	17.0096i	−1.20933	+	0.777188i	−0.980546	−	0.196289i	$-0.937111\pi$
$479$	−26.4674	+	17.0096i	−1.20933	+	0.777188i	−0.228783	+	0.973478i	$0.573474\pi$
$480$	−1.71894	−	1.98376i	−0.0784586	−	0.0905460i
$481$	−5.69986	+	1.67363i	−0.259891	+	0.0763110i
$482$	−0.831472			−0.0378725
$483$	−7.32815	+	21.9390i	−0.333442	+	0.998261i
$484$	1.62177			0.0737169
$485$	6.14260	−	1.80363i	0.278921	−	0.0818987i
$486$	1.64589	+	1.89945i	0.0746589	+	0.0861610i
$487$	−3.08900	+	1.98518i	−0.139976	+	0.0899570i	−0.608755	−	0.793359i	$-0.708331\pi$
$487$	−3.08900	+	1.98518i	−0.139976	+	0.0899570i	0.468779	+	0.883316i	$0.344694\pi$
$488$	4.88222	+	33.9566i	0.221008	+	1.53714i
$489$	−12.0431	−	7.73962i	−0.544607	−	0.349998i
$490$	−12.9636	+	28.3863i	−0.585635	+	1.28236i
$491$	−10.6670	+	12.3103i	−0.481393	+	0.555558i	−0.943545	−	0.331243i	$-0.892532\pi$
$491$	−10.6670	+	12.3103i	−0.481393	+	0.555558i	0.462152	+	0.886801i	$0.347077\pi$
$492$	−2.27914	+	15.8517i	−0.102751	+	0.714652i
$493$	−2.83733	−	6.21288i	−0.127787	−	0.279814i
$494$	24.4103	+	7.16750i	1.09827	+	0.322481i
$495$	−2.47088	−	0.725516i	−0.111058	−	0.0326095i
$496$	1.18672	+	2.59856i	0.0532855	+	0.116679i
$497$	6.26029	−	43.5413i	0.280813	−	1.95309i
$498$	4.86714	−	5.61697i	0.218102	−	0.251703i
$499$	8.04026	−	17.6057i	0.359932	−	0.788140i	−0.639875	−	0.768479i	$-0.721014\pi$
$499$	8.04026	−	17.6057i	0.359932	−	0.788140i	0.999807	−	0.0196614i	$-0.00625883\pi$
$500$	26.1114	+	16.7808i	1.16774	+	0.750460i
$501$	−3.24612	−	22.5773i	−0.145026	−	1.00868i
$502$	57.7701	−	37.1266i	2.57841	−	1.65704i
$503$	23.3139	+	26.9057i	1.03952	+	1.19966i	0.979495	+	0.201467i	$0.0645710\pi$
$503$	23.3139	+	26.9057i	1.03952	+	1.19966i	0.0600201	+	0.998197i	$0.480884\pi$
$504$	26.9473	−	7.91245i	1.20033	−	0.352448i
$505$	3.37717			0.150282
$506$	−23.2217	+	33.3692i	−1.03233	+	1.48344i
$507$	1.36183			0.0604811
$508$	5.53438	−	1.62504i	0.245548	−	0.0720995i
$509$	−0.922120	−	1.06418i	−0.0408723	−	0.0471691i	0.734945	−	0.678126i	$-0.237208\pi$
$509$	−0.922120	−	1.06418i	−0.0408723	−	0.0471691i	−0.775818	+	0.630957i	$0.782662\pi$
$510$	1.48714	−	0.955726i	0.0658516	−	0.0423203i
$511$	−8.28205	−	57.6029i	−0.366376	−	2.54820i
$512$	−41.4422	−	26.6333i	−1.83150	−	1.17704i
$513$	−1.23259	+	2.69900i	−0.0544203	+	0.119164i
$514$	−6.12403	+	7.06751i	−0.270120	+	0.311735i
$515$	1.76144	−	12.2511i	0.0776183	−	0.539847i
$516$	1.07198	+	2.34730i	0.0471912	+	0.103334i
$517$	16.2731	+	4.77821i	0.715690	+	0.210145i
$518$	−20.2533	−	5.94690i	−0.889878	−	0.261292i
$519$	0.690682	+	1.51238i	0.0303176	+	0.0663862i
$520$	−2.15856	+	15.0131i	−0.0946592	+	0.658370i
$521$	25.1455	−	29.0195i	1.10164	−	1.27137i	0.142087	−	0.989854i	$-0.454619\pi$
$521$	25.1455	−	29.0195i	1.10164	−	1.27137i	0.959558	−	0.281512i	$-0.0908358\pi$
$522$	−7.74118	+	16.9508i	−0.338822	+	0.741918i
$523$	−3.95739	−	2.54326i	−0.173044	−	0.111209i	0.451252	−	0.892397i	$-0.350978\pi$
$523$	−3.95739	−	2.54326i	−0.173044	−	0.111209i	−0.624296	+	0.781188i	$0.714614\pi$
$524$	2.10792	+	14.6609i	0.0920851	+	0.640466i
$525$	−17.9217	+	11.5176i	−0.782169	+	0.502670i
$526$	30.4069	+	35.0914i	1.32580	+	1.53006i
$527$	−0.420723	+	0.123536i	−0.0183270	+	0.00538129i
$528$	20.2421			0.880922
$529$	−7.99146	−	21.5670i	−0.347455	−	0.937697i
$530$	−0.169888			−0.00737947
$531$	−6.29510	+	1.84841i	−0.273184	+	0.0802140i
$532$	40.4555	+	46.6881i	1.75397	+	2.02419i
$533$	10.6468	−	6.84231i	0.461166	−	0.296373i
$534$	3.49238	+	24.2901i	0.151130	+	1.05113i
$535$	4.07893	+	2.62137i	0.176347	+	0.113332i
$536$	−24.2232	+	53.0415i	−1.04628	+	2.29104i
$537$	15.9622	−	18.4214i	0.688820	−	0.794940i
$538$	−2.67202	+	18.5843i	−0.115199	+	0.801226i
$539$	−22.7846	−	49.8914i	−0.981404	−	2.14897i
$540$	−3.16250	−	0.928595i	−0.136093	−	0.0399604i
$541$	2.33038	+	0.684262i	0.100191	+	0.0294187i	0.331444	−	0.943475i	$-0.392464\pi$
$541$	2.33038	+	0.684262i	0.100191	+	0.0294187i	−0.231253	+	0.972894i	$0.574282\pi$
$542$	26.5965	+	58.2382i	1.14242	+	2.50154i
$543$	−1.50779	+	10.4869i	−0.0647057	+	0.450038i
$544$	−2.07392	+	2.39344i	−0.0889188	+	0.102618i
$545$	0.780557	−	1.70918i	0.0334354	−	0.0732133i
$546$	−34.7890	−	22.3576i	−1.48883	−	0.956815i
$547$	2.31498	+	16.1010i	0.0989814	+	0.688431i	0.977533	+	0.210783i	$0.0676013\pi$
$547$	2.31498	+	16.1010i	0.0989814	+	0.688431i	−0.878552	+	0.477648i	$0.841490\pi$
$548$	−14.7852	+	9.50186i	−0.631592	+	0.405899i
$549$	3.85803	+	4.45240i	0.164657	+	0.190024i
$550$	−35.9263	+	10.5489i	−1.53190	+	0.449807i
$551$	−21.9995			−0.937208
$552$	−15.9516	+	22.9222i	−0.678947	+	0.975636i
$553$	−50.7269			−2.15713
$554$	−75.7427	+	22.2401i	−3.21800	+	0.944890i
$555$	0.870663	+	1.00480i	0.0369576	+	0.0426513i
$556$	21.8382	−	14.0346i	0.926146	−	0.595198i
$557$	4.29622	+	29.8809i	0.182037	+	1.26609i	0.851938	+	0.523643i	$0.175427\pi$
$557$	4.29622	+	29.8809i	0.182037	+	1.26609i	−0.669901	+	0.742450i	$0.733663\pi$
$558$	1.00642	+	0.646787i	0.0426052	+	0.0273807i
$559$	0.847149	−	1.85500i	0.0358306	−	0.0784580i
$560$	−14.4730	+	16.7027i	−0.611596	+	0.705819i
$561$	−0.442173	+	3.07538i	−0.0186685	+	0.129843i
$562$	−5.57586	−	12.2094i	−0.235203	−	0.515024i
$563$	28.3538	+	8.32542i	1.19497	+	0.350875i	0.817927	−	0.575321i	$-0.195123\pi$
$563$	28.3538	+	8.32542i	1.19497	+	0.350875i	0.377042	+	0.926196i	$0.376941\pi$
$564$	20.8281	+	6.11568i	0.877021	+	0.257517i
$565$	2.93542	+	6.42768i	0.123494	+	0.270414i
$566$	−6.17068	+	42.9180i	−0.259373	+	1.80398i
$567$	3.15843	−	3.64502i	0.132642	−	0.153077i
$568$	22.0625	−	48.3102i	0.925723	−	2.02705i
$569$	−17.6455	−	11.3400i	−0.739736	−	0.475400i	0.115715	−	0.993282i	$-0.463084\pi$
$569$	−17.6455	−	11.3400i	−0.739736	−	0.475400i	−0.855452	+	0.517883i	$0.826720\pi$
$570$	−0.810326	−	5.63594i	−0.0339408	−	0.236063i
$571$	4.34206	−	2.79047i	0.181709	−	0.116778i	−0.446624	−	0.894722i	$-0.647374\pi$
$571$	4.34206	−	2.79047i	0.181709	−	0.116778i	0.628333	+	0.777944i	$0.283737\pi$
$572$	−32.5273	−	37.5385i	−1.36004	−	1.56956i
$573$	−16.4834	+	4.83998i	−0.688606	+	0.202193i
$574$	44.9702			1.87702
$575$	6.71124	−	20.0921i	0.279878	−	0.837900i
$576$	−3.36261			−0.140109
$577$	−21.7407	+	6.38365i	−0.905078	+	0.265755i	−0.700968	−	0.713193i	$-0.747248\pi$
$577$	−21.7407	+	6.38365i	−0.905078	+	0.265755i	−0.204110	+	0.978948i	$0.565430\pi$
$578$	26.5834	+	30.6788i	1.10572	+	1.27607i
$579$	11.8979	−	7.64629i	0.494458	−	0.317769i
$580$	−3.47788	−	24.1892i	−0.144411	−	1.00440i
$581$	−11.9984	−	7.71090i	−0.497777	−	0.319902i
$582$	−8.75432	+	19.1693i	−0.362878	+	0.794593i
$583$	0.195537	−	0.225662i	0.00809831	−	0.00934595i
$584$	9.99923	−	69.5462i	0.413771	−	2.87784i
$585$	1.08205	+	2.36935i	0.0447371	+	0.0979605i
$586$	79.3734	+	23.3061i	3.27888	+	0.962767i
$587$	−2.29196	−	0.672981i	−0.0945995	−	0.0277769i	0.234090	−	0.972215i	$-0.424789\pi$
$587$	−2.29196	−	0.672981i	−0.0945995	−	0.0277769i	−0.328690	+	0.944438i	$0.606607\pi$
$588$	−29.1623	−	63.8565i	−1.20263	−	2.63340i
$589$	−0.200997	+	1.39796i	−0.00828194	+	0.0576021i
$590$	8.24482	−	9.51503i	0.339434	−	0.391728i
$591$	1.27802	−	2.79847i	0.0525706	−	0.115114i
$592$	−8.79170	−	5.65008i	−0.361337	−	0.232217i
$593$	−5.12798	−	35.6659i	−0.210581	−	1.46462i	−0.771223	−	0.636565i	$-0.780355\pi$
$593$	−5.12798	−	35.6659i	−0.210581	−	1.46462i	0.560642	−	0.828058i	$-0.310554\pi$
$594$	7.13126	−	4.58298i	0.292599	−	0.188042i
$595$	−2.22150	−	2.56374i	−0.0910724	−	0.105103i
$596$	62.9172	−	18.4742i	2.57719	−	0.756731i
$597$	−15.7690			−0.645384
$598$	40.8894	−	4.35174i	1.67209	−	0.177956i
$599$	13.8880			0.567450			0.283725	−	0.958906i	$-0.408430\pi$
$599$	13.8880			0.567450			0.283725	+	0.958906i	$0.408430\pi$
$600$	−24.6788	+	7.24635i	−1.00751	+	0.295831i
$601$	−17.6880	−	20.4131i	−0.721509	−	0.832666i	0.269979	−	0.962866i	$-0.412983\pi$
$601$	−17.6880	−	20.4131i	−0.721509	−	0.832666i	−0.991488	+	0.130200i	$0.958438\pi$
$602$	6.09586	−	3.91757i	0.248449	−	0.159668i
$603$	1.42511	+	9.91187i	0.0580350	+	0.403642i
$604$	−2.17450	−	1.39746i	−0.0884791	−	0.0568620i
$605$	−0.119158	+	0.260920i	−0.00484448	+	0.0106079i
$606$	−7.28000	+	8.40156i	−0.295730	+	0.341290i
$607$	−2.52692	+	17.5751i	−0.102564	+	0.713351i	0.872043	+	0.489430i	$0.162795\pi$
$607$	−2.52692	+	17.5751i	−0.102564	+	0.713351i	−0.974607	+	0.223922i	$0.928114\pi$
$608$	4.23751	+	9.27885i	0.171854	+	0.376307i
$609$	34.3114	+	10.0747i	1.39037	+	0.408249i
$610$	−10.8475	−	3.18512i	−0.439203	−	0.128962i
$611$	−7.12630	−	15.6044i	−0.288299	−	0.631287i
$612$	−0.565941	+	3.93621i	−0.0228768	+	0.159112i
$613$	−1.90692	+	2.20070i	−0.0770198	+	0.0888856i	−0.792952	−	0.609285i	$-0.791457\pi$
$613$	−1.90692	+	2.20070i	−0.0770198	+	0.0888856i	0.715932	+	0.698170i	$0.246002\pi$
$614$	18.1569	−	39.7581i	0.732754	−	1.60451i
$615$	−2.38287	−	1.53138i	−0.0960865	−	0.0617510i
$616$	−13.4807	−	93.7604i	−0.543153	−	3.77771i
$617$	−4.67930	+	3.00721i	−0.188382	+	0.121066i	−0.631432	−	0.775431i	$-0.717533\pi$
$617$	−4.67930	+	3.00721i	−0.188382	+	0.121066i	0.443050	+	0.896497i	$0.353896\pi$
$618$	26.6806	+	30.7911i	1.07325	+	1.23860i
$619$	−30.9607	+	9.09087i	−1.24441	+	0.365393i	−0.836672	−	0.547704i	$-0.815502\pi$
$619$	−30.9607	+	9.09087i	−1.24441	+	0.365393i	−0.407742	+	0.913097i	$0.633684\pi$
$620$	−1.56889			−0.0630079
$621$	−0.176312	+	4.79259i	−0.00707515	+	0.192320i
$622$	−28.0966			−1.12657
$623$	45.1841	−	13.2672i	1.81026	−	0.531541i
$624$	−13.4078	−	15.4734i	−0.536741	−	0.619432i
$625$	13.9609	−	8.97214i	0.558437	−	0.358886i
$626$	−10.2762	−	71.4727i	−0.410720	−	2.85662i
$627$	8.41886	+	5.41047i	0.336217	+	0.216073i
$628$	−6.17986	+	13.5320i	−0.246603	+	0.539986i
$629$	1.05047	−	1.21230i	0.0418848	−	0.0483377i
$630$	−1.31718	+	9.16118i	−0.0524776	+	0.364990i
$631$	−14.7279	−	32.2497i	−0.586310	−	1.28384i	−0.937646	−	0.347590i	$-0.887000\pi$
$631$	−14.7279	−	32.2497i	−0.586310	−	1.28384i	0.351337	−	0.936249i	$-0.385727\pi$
$632$	−58.7637	−	17.2546i	−2.33749	−	0.686350i
$633$	−15.1989	−	4.46281i	−0.604103	−	0.177381i
$634$	−19.6879	−	43.1105i	−0.781906	−	1.71214i
$635$	−0.145188	+	1.00980i	−0.00576160	+	0.0400728i
$636$	0.250270	−	0.288827i	0.00992384	−	0.0114527i
$637$	−23.0460	+	50.4637i	−0.913116	+	1.99944i
$638$	52.8738	+	33.9800i	2.09330	+	1.34528i
$639$	−1.29799	−	9.02773i	−0.0513478	−	0.357132i
$640$	9.84484	−	6.32690i	0.389152	−	0.250093i
$641$	15.9578	+	18.4163i	0.630295	+	0.727399i	0.977628	−	0.210343i	$-0.0674580\pi$
$641$	15.9578	+	18.4163i	0.630295	+	0.727399i	−0.347333	+	0.937742i	$0.612913\pi$
$642$	−15.3141	+	4.49662i	−0.604398	+	0.177467i
$643$	16.2231			0.639777			0.319888	−	0.947455i	$-0.396355\pi$
$643$	16.2231			0.639777			0.319888	+	0.947455i	$0.396355\pi$
$644$	89.2418	+	44.7910i	3.51662	+	1.76501i
$645$	−0.456411			−0.0179712
$646$	−6.59148	+	1.93543i	−0.259338	+	0.0761486i
$647$	29.4336	+	33.9682i	1.15715	+	1.33543i	0.932577	+	0.360971i	$0.117555\pi$
$647$	29.4336	+	33.9682i	1.15715	+	1.33543i	0.224577	+	0.974456i	$0.427900\pi$
$648$	4.89867	−	3.14818i	0.192438	−	0.123672i
$649$	3.14920	+	21.9031i	0.123617	+	0.859773i
$650$	31.8604	+	20.4754i	1.24967	+	0.803112i
$651$	0.953688	−	2.08829i	0.0373780	−	0.0818464i
$652$	−40.4695	+	46.7043i	−1.58491	+	1.82908i
$653$	5.13339	−	35.7035i	0.200885	−	1.39719i	−0.600780	−	0.799414i	$-0.705143\pi$
$653$	5.13339	−	35.7035i	0.200885	−	1.39719i	0.801665	−	0.597773i	$-0.203948\pi$
$654$	2.56941	+	5.62623i	0.100472	+	0.220003i
$655$	−2.51362	−	0.738065i	−0.0982152	−	0.0288386i
$656$	21.3629	+	6.27270i	0.834079	+	0.244908i
$657$	−5.01242	−	10.9757i	−0.195553	−	0.428201i
$658$	8.67487	−	60.3350i	0.338182	−	2.35210i
$659$	−7.11106	+	8.20660i	−0.277007	+	0.319684i	−0.877157	−	0.480204i	$-0.840562\pi$
$659$	−7.11106	+	8.20660i	−0.277007	+	0.319684i	0.600149	+	0.799888i	$0.295108\pi$
$660$	−4.61807	+	10.1122i	−0.179758	+	0.393615i
$661$	37.5835	+	24.1535i	1.46183	+	0.939461i	0.998582	+	0.0532330i	$0.0169526\pi$
$661$	37.5835	+	24.1535i	1.46183	+	0.939461i	0.463248	+	0.886228i	$0.346684\pi$
$662$	3.08863	+	21.4819i	0.120043	+	0.834916i
$663$	2.64376	−	1.69904i	0.102675	−	0.0659853i
$664$	−11.2765	−	13.0138i	−0.437613	−	0.505032i
$665$	−10.4839	+	3.07835i	−0.406548	+	0.119373i
$666$	−4.37654			−0.169587
$667$	−32.8660	+	13.5723i	−1.27257	+	0.525520i
$668$	−98.4652			−3.80973
$669$	−16.1481	+	4.74150i	−0.624321	+	0.183317i
$670$	−12.5840	−	14.5227i	−0.486163	−	0.561062i
$671$	16.7160	−	10.7427i	0.645314	−	0.414718i
$672$	−2.35974	−	16.4123i	−0.0910289	−	0.633120i
$673$	9.46551	+	6.08312i	0.364869	+	0.234487i	0.710209	−	0.703991i	$-0.248600\pi$
$673$	9.46551	+	6.08312i	0.364869	+	0.234487i	−0.345341	+	0.938477i	$0.612237\pi$
$674$	−11.9426	+	26.1506i	−0.460012	+	1.00729i
$675$	−2.89254	+	3.33817i	−0.111334	+	0.128486i
$676$	0.836646	−	5.81900i	0.0321787	−	0.223808i
$677$	4.92928	+	10.7936i	0.189447	+	0.414832i	0.980392	−	0.197055i	$-0.0631378\pi$
$677$	4.92928	+	10.7936i	0.189447	+	0.414832i	−0.790945	+	0.611887i	$0.790411\pi$
$678$	−22.3182	−	6.55322i	−0.857126	−	0.251675i
$679$	38.8020	+	11.3933i	1.48908	+	0.437234i
$680$	−1.70140	−	3.72555i	−0.0652459	−	0.142868i
$681$	−3.06494	+	21.3171i	−0.117449	+	0.816873i
$682$	2.64235	−	3.04943i	0.101181	−	0.116769i
$683$	−7.12926	+	15.6109i	−0.272794	+	0.597335i	−0.995599	−	0.0937170i	$-0.970125\pi$
$683$	−7.12926	+	15.6109i	−0.272794	+	0.597335i	0.722805	+	0.691052i	$0.242852\pi$
$684$	10.7754	+	6.92492i	0.412007	+	0.264781i
$685$	−0.442388	−	3.07687i	−0.0169028	−	0.117561i
$686$	−94.4496	+	60.6991i	−3.60610	+	2.31750i
$687$	−0.370995	−	0.428150i	−0.0141543	−	0.0163350i
$688$	3.44225	−	1.01074i	0.131235	−	0.0385340i
$689$	−0.302018			−0.0115060
$690$	−4.68760	−	7.91986i	−0.178454	−	0.301504i
$691$	−21.3055			−0.810501			−0.405250	−	0.914206i	$-0.632816\pi$
$691$	−21.3055			−0.810501			−0.405250	+	0.914206i	$0.632816\pi$
$692$	6.88662	−	2.02209i	0.261790	−	0.0768685i
$693$	−10.6527	−	12.2939i	−0.404663	−	0.467006i
$694$	−59.0550	+	37.9523i	−2.24170	+	1.44065i
$695$	0.653420	+	4.54464i	0.0247857	+	0.172388i
$696$	36.3206	+	23.3418i	1.37673	+	0.884769i
$697$	−1.41967	+	3.10864i	−0.0537738	+	0.117748i
$698$	29.4017	−	33.9314i	1.11287	−	1.28432i
$699$	1.14622	−	7.97211i	0.0433539	−	0.301533i
$700$	38.2036	+	83.6541i	1.44396	+	3.16183i
$701$	−37.6974	−	11.0689i	−1.42381	−	0.418068i	−0.523019	−	0.852321i	$-0.675194\pi$
$701$	−37.6974	−	11.0689i	−1.42381	−	0.418068i	−0.900791	+	0.434253i	$0.857012\pi$
$702$	−8.22687	−	2.41563i	−0.310503	−	0.0911720i
$703$	−2.14635	−	4.69984i	−0.0809510	−	0.177258i
$704$	−1.61404	+	11.2259i	−0.0608315	+	0.423093i
$705$	−2.51426	+	2.90161i	−0.0946924	+	0.109281i
$706$	8.58318	−	18.7946i	0.323032	−	0.707342i
$707$	17.9465	+	11.5335i	0.674949	+	0.433764i
$708$	4.03069	+	28.0340i	0.151483	+	1.05358i
$709$	−16.0041	+	10.2852i	−0.601047	+	0.386269i	−0.805490	−	0.592609i	$-0.798098\pi$
$709$	−16.0041	+	10.2852i	−0.601047	+	0.386269i	0.204443	+	0.978878i	$0.434462\pi$
$710$	11.4615	+	13.2273i	0.430144	+	0.496412i
$711$	−10.0915	+	2.96315i	−0.378463	+	0.111127i
$712$	56.8554			2.13075
$713$	0.562177	+	2.21248i	0.0210537	+	0.0828581i
$714$	11.1667			0.417905
$715$	8.42935	−	2.47508i	0.315240	−	0.0925627i
$716$	−68.9066	−	79.5225i	−2.57516	−	2.97189i
$717$	5.81174	−	3.73498i	0.217043	−	0.139485i
$718$	1.73578	+	12.0726i	0.0647787	+	0.450546i
$719$	−3.40452	−	2.18795i	−0.126967	−	0.0815968i	0.475616	−	0.879653i	$-0.342225\pi$
$719$	−3.40452	−	2.18795i	−0.126967	−	0.0815968i	−0.602583	+	0.798056i	$0.705862\pi$
$720$	−1.90357	+	4.16824i	−0.0709419	+	0.155341i
$721$	51.1998	−	59.0877i	1.90678	−	2.20054i
$722$	3.64699	−	25.3654i	0.135727	−	0.944002i
$723$	0.137429	+	0.300928i	0.00511105	+	0.0111916i
$724$	43.8836	+	12.8854i	1.63092	+	0.478881i
$725$	−31.4230	−	9.22661i	−1.16702	−	0.342668i
$726$	−0.392242	−	0.858890i	−0.0145575	−	0.0318764i
$727$	−4.82536	+	33.5611i	−0.178963	+	1.24471i	0.680206	+	0.733021i	$0.261890\pi$
$727$	−4.82536	+	33.5611i	−0.178963	+	1.24471i	−0.859169	+	0.511692i	$0.829019\pi$
$728$	−62.7430	+	72.4092i	−2.32541	+	2.68366i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	19.4789	+	12.5183i	0.720945	+	0.463323i
$731$	0.0783679	+	0.545061i	0.00289854	+	0.0201598i
$732$	21.3950	−	13.7497i	0.790781	−	0.508204i
$733$	26.8279	+	30.9611i	0.990912	+	1.14357i	0.989640	+	0.143574i	$0.0458596\pi$
$733$	26.8279	+	30.9611i	0.990912	+	1.14357i	0.00127246	+	0.999999i	$0.499595\pi$
$734$	26.4791	−	7.77497i	0.977362	−	0.286979i
$735$	12.4163			0.457982
$736$	12.0551	+	11.2478i	0.444356	+	0.414600i
$737$	33.7744			1.24410
$738$	8.94632	−	2.62688i	0.329318	−	0.0966966i
$739$	−10.2508	−	11.8300i	−0.377081	−	0.435174i	0.535209	−	0.844720i	$-0.320233\pi$
$739$	−10.2508	−	11.8300i	−0.377081	−	0.435174i	−0.912290	+	0.409545i	$0.865687\pi$
$740$	4.82832	−	3.10298i	0.177493	−	0.114068i
$741$	−1.44056	−	10.0193i	−0.0529201	−	0.368068i
$742$	−0.902799	−	0.580194i	−0.0331428	−	0.0212996i
$743$	9.31220	−	20.3909i	0.341632	−	0.748069i	−0.658358	−	0.752705i	$-0.728749\pi$
$743$	9.31220	−	20.3909i	0.341632	−	0.748069i	0.999989	+	0.00463635i	$0.00147580\pi$
$744$	1.81511	−	2.09474i	0.0665450	−	0.0767970i
$745$	−1.65056	+	11.4799i	−0.0604717	+	0.420590i
$746$	−15.9481	−	34.9215i	−0.583902	−	1.27857i
$747$	−2.83737	−	0.833126i	−0.103814	−	0.0304825i
$748$	12.8692	+	3.77874i	0.470545	+	0.138164i
$749$	12.7234	+	27.8603i	0.464903	+	1.01799i
$750$	2.57179	−	17.8872i	0.0939086	−	0.653149i
$751$	−25.9577	+	29.9568i	−0.947211	+	1.09314i	0.0483318	+	0.998831i	$0.484610\pi$
$751$	−25.9577	+	29.9568i	−0.947211	+	1.09314i	−0.995543	+	0.0943087i	$0.969936\pi$
$752$	12.5368	−	27.4518i	0.457171	−	1.00106i
$753$	−22.9854	−	14.7718i	−0.837636	−	0.538316i
$754$	−9.04727	−	62.9252i	−0.329482	−	2.29160i
$755$	0.384602	−	0.247169i	0.0139971	−	0.00899539i
$756$	−13.6345	−	15.7351i	−0.495883	−	0.572279i
$757$	37.0396	−	10.8758i	1.34623	−	0.395288i	0.472340	−	0.881416i	$-0.343409\pi$
$757$	37.0396	−	10.8758i	1.34623	−	0.395288i	0.873888	+	0.486128i	$0.161591\pi$
$758$	0.183430			0.00666248
$759$	15.9152	+	2.88904i	0.577686	+	0.104866i
$760$	−13.1920			−0.478523
$761$	−39.2329	+	11.5198i	−1.42219	+	0.417593i	−0.900244	−	0.435386i	$-0.856612\pi$
$761$	−39.2329	+	11.5198i	−1.42219	+	0.417593i	−0.521946	+	0.852979i	$0.674794\pi$
$762$	−2.19917	−	2.53798i	−0.0796675	−	0.0919412i
$763$	9.98506	−	6.41701i	0.361483	−	0.232311i
$764$	10.5542	+	73.4060i	0.381837	+	2.65573i
$765$	−0.591699	−	0.380262i	−0.0213929	−	0.0137484i
$766$	27.6144	−	60.4672i	0.997750	−	2.18477i
$767$	14.6572	−	16.9153i	0.529242	−	0.610778i
$768$	−4.52519	+	31.4734i	−0.163289	+	1.13570i
$769$	6.21928	+	13.6183i	0.224273	+	0.491089i	0.988001	−	0.154449i	$-0.0493603\pi$
$769$	6.21928	+	13.6183i	0.224273	+	0.491089i	−0.763728	+	0.645538i	$0.776633\pi$
$770$	29.9519	+	8.79468i	1.07939	+	0.316938i
$771$	3.57009	+	1.04827i	0.128574	+	0.0377527i
$772$	−25.3625	−	55.5362i	−0.912817	−	1.99879i
$773$	4.82857	−	33.5834i	0.173672	−	1.20791i	−0.697373	−	0.716708i	$-0.745648\pi$
$773$	4.82857	−	33.5834i	0.173672	−	1.20791i	0.871045	−	0.491204i	$-0.163443\pi$
$774$	0.983863	−	1.13544i	0.0353642	−	0.0408125i
$775$	−0.873403	+	1.91249i	−0.0313736	+	0.0686985i
$776$	41.0741	+	26.3967i	1.47447	+	0.947586i
$777$	1.19523	+	8.31303i	0.0428788	+	0.298228i
$778$	−67.8106	+	43.5792i	−2.43113	+	1.56239i
$779$	7.20839	+	8.31893i	0.258267	+	0.298056i
$780$	10.7888	−	3.16788i	0.386301	−	0.113428i
$781$	−30.7617			−1.10074
$782$	−8.65326	+	6.95795i	−0.309440	+	0.248816i
$783$	7.41437			0.264968
$784$	−93.6437	+	27.4963i	−3.34442	+	0.982010i
$785$	−1.72305	−	1.98851i	−0.0614984	−	0.0709729i
$786$	7.25461	−	4.66225i	0.258763	−	0.166297i
$787$	−3.92180	−	27.2767i	−0.139797	−	0.972311i	−0.932105	−	0.362189i	$-0.882030\pi$
$787$	−3.92180	−	27.2767i	−0.139797	−	0.972311i	0.792307	−	0.610122i	$-0.208880\pi$
$788$	−11.1725	−	7.18012i	−0.398003	−	0.255781i
$789$	7.67457	−	16.8050i	0.273222	−	0.598273i
$790$	13.2171	−	15.2534i	0.470244	−	0.542690i
$791$	−6.35243	+	44.1821i	−0.225866	+	1.57094i
$792$	−8.15872	−	17.8651i	−0.289908	−	0.634809i
$793$	−19.2842	−	5.66234i	−0.684800	−	0.201076i
$794$	−44.1647	−	12.9679i	−1.56735	−	0.460215i
$795$	0.0280798	+	0.0614862i	0.000995889	+	0.00218069i
$796$	−9.68777	+	67.3799i	−0.343374	+	2.38822i
$797$	−0.630863	+	0.728055i	−0.0223463	+	0.0257890i	−0.766813	−	0.641871i	$-0.778159\pi$
$797$	−0.630863	+	0.728055i	−0.0223463	+	0.0257890i	0.744466	+	0.667660i	$0.232704\pi$
$798$	14.9415	−	32.7172i	0.528922	−	1.15818i
$799$	3.89690	+	2.50439i	0.137862	+	0.0885988i
$800$	2.16109	+	15.0307i	0.0764059	+	0.531415i
$801$	8.21387	−	5.27873i	0.290223	−	0.186515i
$802$	−58.8433	−	67.9088i	−2.07783	−	2.39794i
$803$	−39.0477	+	11.4654i	−1.37796	+	0.404607i
$804$	43.2282			1.52454
$805$	−13.7632	+	11.0668i	−0.485089	+	0.390053i
$806$	−4.08127			−0.143756
$807$	7.16771	−	2.10463i	0.252315	−	0.0740865i
$808$	16.8668	+	19.4653i	0.593370	+	0.684786i
$809$	−11.3145	+	7.27141i	−0.397798	+	0.255649i	−0.724212	−	0.689578i	$-0.757796\pi$
$809$	−11.3145	+	7.27141i	−0.397798	+	0.255649i	0.326414	+	0.945227i	$0.394160\pi$
$810$	0.273100	+	1.89945i	0.00959576	+	0.0667400i
$811$	20.0794	+	12.9043i	0.705085	+	0.453130i	0.843420	−	0.537255i	$-0.180539\pi$
$811$	20.0794	+	12.9043i	0.705085	+	0.453130i	−0.138335	+	0.990385i	$0.544175\pi$
$812$	64.1280	−	140.421i	2.25045	−	4.92780i
$813$	16.6817	−	19.2517i	0.585053	−	0.675187i
$814$	−2.10073	+	14.6109i	−0.0736305	+	0.512111i
$815$	−4.54061	−	9.94254i	−0.159051	−	0.348272i
$816$	5.30470	+	1.55760i	0.185702	+	0.0545269i
$817$	1.70182	+	0.499700i	0.0595393	+	0.0174823i
$818$	11.5898	+	25.3780i	0.405227	+	0.887323i
$819$	−2.34161	+	16.2863i	−0.0818226	+	0.569088i
$820$	−8.00737	+	9.24100i	−0.279630	+	0.322710i
$821$	7.68700	−	16.8322i	0.268278	−	0.587447i	−0.726766	−	0.686885i	$-0.758977\pi$
$821$	7.68700	−	16.8322i	0.268278	−	0.587447i	0.995044	+	0.0994386i	$0.0317047\pi$
$822$	8.60814	+	5.53211i	0.300243	+	0.192955i
$823$	0.236016	+	1.64153i	0.00822701	+	0.0572201i	0.993521	−	0.113645i	$-0.0362528\pi$
$823$	0.236016	+	1.64153i	0.00822701	+	0.0572201i	−0.985294	+	0.170865i	$0.945344\pi$
$824$	79.4099	−	51.0336i	2.76637	−	1.77784i
$825$	9.75593	+	11.2589i	0.339658	+	0.391986i
$826$	76.3090	−	22.4063i	2.65513	−	0.779616i
$827$	−38.8604			−1.35131			−0.675654	−	0.737219i	$-0.736139\pi$
$827$	−38.8604			−1.35131			−0.675654	+	0.737219i	$0.736139\pi$
$828$	20.3701	+	3.69771i	0.707908	+	0.128504i
$829$	−23.7245			−0.823986			−0.411993	−	0.911187i	$-0.635167\pi$
$829$	−23.7245			−0.823986			−0.411993	+	0.911187i	$0.635167\pi$
$830$	5.44487	−	1.59876i	0.188994	−	0.0554937i
$831$	20.5682	+	23.7370i	0.713505	+	0.823428i
$832$	9.65040	−	6.20194i	0.334567	−	0.215013i
$833$	−2.13194	−	14.8279i	−0.0738672	−	0.513758i
$834$	−12.7145	−	8.17111i	−0.440267	−	0.282942i
$835$	7.23466	−	15.8417i	0.250366	−	0.548224i
$836$	28.2907	−	32.6492i	0.978454	−	1.12920i
$837$	0.0677411	−	0.471149i	0.00234147	−	0.0162853i
$838$	−39.7829	−	87.1123i	−1.37428	−	3.00924i
$839$	−12.0022	−	3.52417i	−0.414363	−	0.121668i	0.0679048	−	0.997692i	$-0.478369\pi$
$839$	−12.0022	−	3.52417i	−0.414363	−	0.121668i	−0.482268	+	0.876024i	$0.660187\pi$
$840$	20.5748	+	6.04132i	0.709900	+	0.208445i
$841$	10.7895	+	23.6258i	0.372053	+	0.814683i
$842$	−13.8896	+	96.6046i	−0.478669	+	3.32921i
$843$	−3.49726	+	4.03605i	−0.120452	+	0.139009i
$844$	−28.4067	+	62.2021i	−0.977800	+	2.14108i
$845$	0.874724	+	0.562151i	0.0300914	+	0.0193386i
$846$	−1.79862	−	12.5097i	−0.0618380	−	0.430093i
$847$	−1.52430	+	0.979609i	−0.0523756	+	0.0336597i
$848$	−0.347941	−	0.401545i	−0.0119483	−	0.0137891i
$849$	16.5529	−	4.86037i	0.568094	−	0.166807i
$850$	−10.2267			−0.350772
$851$	−6.10603	−	5.69714i	−0.209312	−	0.195296i
$852$	−39.3722			−1.34887
$853$	7.10728	−	2.08689i	0.243349	−	0.0714536i	−0.157784	−	0.987474i	$-0.550435\pi$
$853$	7.10728	−	2.08689i	0.243349	−	0.0714536i	0.401132	+	0.916020i	$0.368617\pi$
$854$	−46.7669	−	53.9719i	−1.60033	−	1.84688i
$855$	−1.90584	+	1.22481i	−0.0651782	+	0.0418875i
$856$	5.26259	+	36.6021i	0.179872	+	1.25103i
$857$	30.3712	+	19.5184i	1.03746	+	0.666734i	0.944357	−	0.328922i	$-0.106685\pi$
$857$	30.3712	+	19.5184i	1.03746	+	0.666734i	0.0931019	+	0.995657i	$0.470322\pi$
$858$	−12.0133	+	26.3056i	−0.410129	+	0.898057i
$859$	−15.8185	+	18.2555i	−0.539721	+	0.622871i	−0.958457	−	0.285237i	$-0.907928\pi$
$859$	−15.8185	+	18.2555i	−0.539721	+	0.622871i	0.418736	+	0.908108i	$0.362473\pi$
$860$	−0.280398	+	1.95021i	−0.00956149	+	0.0665016i
$861$	−7.43287	−	16.2757i	−0.253312	−	0.554675i
$862$	−32.6243	−	9.57936i	−1.11119	−	0.326274i
$863$	51.9206	+	15.2453i	1.76740	+	0.518955i	0.993447	−	0.114290i	$-0.0364593\pi$
$863$	51.9206	+	15.2453i	1.76740	+	0.518955i	0.773951	+	0.633245i	$0.218277\pi$
$864$	−1.42815	−	3.12721i	−0.0485866	−	0.106390i
$865$	−0.180662	+	1.25653i	−0.00614270	+	0.0427234i
$866$	1.71220	−	1.97598i	0.0581828	−	0.0671465i
$867$	6.70953	−	14.6918i	0.227868	−	0.498961i
$868$	−8.33719	−	5.35798i	−0.282983	−	0.181862i
$869$	5.04841	+	35.1125i	0.171256	+	1.19111i
$870$	−11.9694	+	7.69228i	−0.405801	+	0.260793i
$871$	−22.3712	−	25.8178i	−0.758020	−	0.874802i
$872$	13.7497	−	4.03729i	0.465625	−	0.136720i
$873$	8.38474			0.283781
$874$	8.80764	+	34.6630i	0.297923	+	1.17249i
$875$	−34.6783			−1.17234
$876$	−49.9776	+	14.6747i	−1.68859	+	0.495814i
$877$	5.97534	+	6.89591i	0.201773	+	0.232858i	0.847614	−	0.530614i	$-0.178038\pi$
$877$	5.97534	+	6.89591i	0.201773	+	0.232858i	−0.645841	+	0.763472i	$0.723493\pi$
$878$	−85.3679	+	54.8626i	−2.88103	+	1.85152i
$879$	−4.68417	−	32.5791i	−0.157993	−	1.09887i
$880$	13.0018	+	8.35573i	0.438290	+	0.281672i
$881$	11.9030	−	26.0638i	0.401021	−	0.878113i	−0.596145	−	0.802877i	$-0.703302\pi$
$881$	11.9030	−	26.0638i	0.401021	−	0.878113i	0.997166	−	0.0752364i	$-0.0239711\pi$
$882$	−26.7652	+	30.8887i	−0.901232	+	1.04008i
$883$	6.00432	−	41.7610i	0.202061	−	1.40537i	−0.596093	−	0.802915i	$-0.703281\pi$
$883$	6.00432	−	41.7610i	0.202061	−	1.40537i	0.798154	−	0.602453i	$-0.205810\pi$
$884$	−5.63567	−	12.3404i	−0.189548	−	0.415053i
$885$	−4.80644	−	1.41130i	−0.161567	−	0.0474403i
$886$	13.6012	+	3.99366i	0.456940	+	0.134170i
$887$	−10.7798	−	23.6045i	−0.361951	−	0.792562i	−0.999750	−	0.0223595i	$-0.992882\pi$
$887$	−10.7798	−	23.6045i	−0.361951	−	0.792562i	0.637799	−	0.770203i	$-0.279845\pi$
$888$	−1.44305	+	10.0366i	−0.0484256	+	0.336807i
$889$	−4.22017	+	4.87034i	−0.141540	+	0.163346i
$890$	−7.78350	+	17.0435i	−0.260903	+	0.571299i
$891$	−2.83737	−	1.82347i	−0.0950554	−	0.0610884i
$892$	10.3395	+	71.9125i	0.346191	+	2.40781i
$893$	12.5517	−	8.06651i	0.420028	−	0.269936i
$894$	−25.0011	−	28.8528i	−0.836161	−	0.964982i
$895$	17.8569	−	5.24326i	0.596891	−	0.175263i
$896$	73.9236			2.46962
$897$	−8.33337	−	14.0795i	−0.278243	−	0.470101i
$898$	51.5199			1.71924
$899$	3.38624	−	0.994290i	0.112938	−	0.0331614i
$900$	12.4867	+	14.4104i	0.416224	+	0.480348i
$901$	0.0686074	−	0.0440913i	0.00228564	−	0.00146889i
$902$	−4.47550	−	31.1278i	−0.149018	−	1.03644i
$903$	−2.42541	−	1.55871i	−0.0807125	−	0.0518708i
$904$	−22.3872	+	49.0212i	−0.744588	+	1.63042i
$905$	−5.29739	+	6.11351i	−0.176091	+	0.203220i
$906$	−0.214173	+	1.48961i	−0.00711542	+	0.0494888i
$907$	−6.99794	−	15.3233i	−0.232363	−	0.508803i	0.757151	−	0.653239i	$-0.226590\pi$
$907$	−6.99794	−	15.3233i	−0.232363	−	0.508803i	−0.989514	+	0.144436i	$0.953863\pi$
$908$	89.2034	+	26.1925i	2.96032	+	0.869228i
$909$	4.24398	+	1.24614i	0.140764	+	0.0413320i
$910$	−13.1165	−	28.7212i	−0.434809	−	0.952098i
$911$	0.482231	−	3.35399i	0.0159770	−	0.111123i	−0.980272	−	0.197652i	$-0.936668\pi$
$911$	0.482231	−	3.35399i	0.0159770	−	0.111123i	0.996249	+	0.0865292i	$0.0275776\pi$
$912$	11.6614	−	13.4580i	0.386149	−	0.445640i
$913$	−4.14328	+	9.07253i	−0.137123	+	0.300257i
$914$	22.0279	+	14.1565i	0.728620	+	0.468256i
$915$	0.640159	+	4.45240i	0.0211630	+	0.147192i
$916$	−2.05738	+	1.32220i	−0.0679776	+	0.0436866i
$917$	−10.8370	−	12.5065i	−0.357868	−	0.413002i
$918$	2.22150	−	0.652290i	0.0733203	−	0.0215288i
$919$	29.9775			0.988867			0.494434	−	0.869215i	$-0.335376\pi$
$919$	29.9775			0.988867			0.494434	+	0.869215i	$0.335376\pi$
$920$	−19.7081	+	8.13861i	−0.649756	+	0.268322i
$921$	−17.3904			−0.573033
$922$	42.4233	−	12.4566i	1.39714	−	0.410236i
$923$	20.3757	+	23.5148i	0.670675	+	0.774001i
$924$	−59.0754	+	37.9654i	−1.94344	+	1.24897i
$925$	−1.09461	−	7.61321i	−0.0359907	−	0.250321i
$926$	−11.0252	−	7.08544i	−0.362309	−	0.232842i
$927$	6.73409	−	14.7456i	0.221176	−	0.484309i
$928$	16.6922	−	19.2639i	0.547949	−	0.632367i
$929$	−8.15732	+	56.7354i	−0.267633	+	1.86143i	0.203108	+	0.979156i	$0.434896\pi$
$929$	−8.15732	+	56.7354i	−0.267633	+	1.86143i	−0.470741	+	0.882272i	$0.656013\pi$
$930$	0.379451	+	0.830882i	0.0124427	+	0.0272457i
$931$	−46.2967	−	13.5940i	−1.51731	−	0.445524i
$932$	−33.3601	−	9.79540i	−1.09275	−	0.320859i
$933$	4.64393	+	10.1688i	0.152035	+	0.332911i
$934$	0.0899075	−	0.625320i	0.00294186	−	0.0204611i
$935$	−1.55350	+	1.79284i	−0.0508049	+	0.0586320i
$936$	−8.25231	+	18.0700i	−0.269735	+	0.590638i
$937$	−21.1351	−	13.5827i	−0.690453	−	0.443727i	0.147794	−	0.989018i	$-0.452783\pi$
$937$	−21.1351	−	13.5827i	−0.690453	−	0.443727i	−0.838247	+	0.545291i	$0.816419\pi$
$938$	−17.2752	−	120.151i	−0.564054	−	3.92308i
$939$	−24.1690	+	15.5325i	−0.788727	+	0.506884i
$940$	10.8537	+	12.5258i	0.354009	+	0.408548i
$941$	12.2897	−	3.60857i	0.400632	−	0.117636i	−0.0752086	−	0.997168i	$-0.523962\pi$
$941$	12.2897	−	3.60857i	0.400632	−	0.117636i	0.475840	+	0.879532i	$0.342144\pi$
$942$	8.66122			0.282198
$943$	15.9012	+	7.98089i	0.517814	+	0.259893i
$944$	39.3755			1.28156
$945$	3.53334	−	1.03748i	0.114940	−	0.0337493i
$946$	−3.31836	−	3.82959i	−0.107889	−	0.124511i
$947$	10.1103	−	6.49749i	0.328541	−	0.211140i	−0.365963	−	0.930629i	$-0.619260\pi$
$947$	10.1103	−	6.49749i	0.328541	−	0.211140i	0.694504	+	0.719489i	$0.255624\pi$
$948$	6.46152	+	44.9408i	0.209860	+	1.45961i
$949$	34.6286	+	22.2544i	1.12409	+	0.722409i
$950$	−13.6836	+	29.9630i	−0.443956	+	0.972127i
$951$	−12.3485	+	14.2510i	−0.400428	+	0.462119i
$952$	3.68194	−	25.6085i	0.119332	−	0.829975i
$953$	10.7991	+	23.6467i	0.349817	+	0.765992i	0.999981	+	0.00619817i	$0.00197295\pi$
$953$	10.7991	+	23.6467i	0.349817	+	0.765992i	−0.650164	+	0.759794i	$0.725300\pi$
$954$	−0.213493	−	0.0626872i	−0.00691209	−	0.00202957i
$955$	−12.5855	−	3.69542i	−0.407256	−	0.119581i
$956$	−12.3888	−	27.1277i	−0.400683	−	0.877373i
$957$	3.55888	−	24.7526i	0.115042	−	0.800136i
$958$	51.7827	−	59.7604i	1.67302	−	1.93077i
$959$	8.15711	−	17.8616i	0.263407	−	0.576781i
$960$	−2.15985	−	1.38805i	−0.0697089	−	0.0447992i
$961$	4.37952	+	30.4602i	0.141275	+	0.982587i
$962$	12.5603	−	8.07202i	0.404960	−	0.260252i
$963$	4.15860	+	4.79928i	0.134009	+	0.154655i
$964$	1.37027	−	0.402348i	0.0441335	−	0.0129588i
$965$	10.7985			0.347616
$966$	2.13725	−	58.0956i	0.0687648	−	1.86920i
$967$	36.2438			1.16552			0.582760	−	0.812644i	$-0.301973\pi$
$967$	36.2438			1.16552			0.582760	+	0.812644i	$0.301973\pi$
$968$	−2.09901	+	0.616324i	−0.0674647	+	0.0198094i
$969$	1.78994	+	2.06571i	0.0575013	+	0.0663600i
$970$	−13.5359	+	8.69902i	−0.434613	+	0.279309i
$971$	4.45032	+	30.9526i	0.142817	+	0.993317i	0.927608	+	0.373556i	$0.121862\pi$
$971$	4.45032	+	30.9526i	0.142817	+	0.993317i	−0.784790	+	0.619761i	$0.787229\pi$
$972$	−3.63158	−	2.33387i	−0.116483	−	0.0748590i
$973$	−12.0483	+	26.3821i	−0.386251	+	0.845772i
$974$	6.04353	−	6.97460i	0.193647	−	0.223481i
$975$	2.14449	−	14.9152i	0.0686785	−	0.477670i
$976$	−14.6881	−	32.1624i	−0.470153	−	1.02949i
$977$	−20.5363	−	6.02999i	−0.657013	−	0.192917i	−0.0638011	−	0.997963i	$-0.520322\pi$
$977$	−20.5363	−	6.02999i	−0.657013	−	0.192917i	−0.593212	+	0.805046i	$0.702141\pi$
$978$	34.5226	+	10.1367i	1.10391	+	0.324137i
$979$	−13.6802	−	29.9554i	−0.437220	−	0.957379i
$980$	7.62800	−	53.0539i	0.243668	−	1.69474i
$981$	1.61157	−	1.85986i	0.0514536	−	0.0593806i
$982$	17.0069	−	37.2399i	0.542712	−	1.18837i
$983$	−46.3451	−	29.7842i	−1.47818	−	0.949968i	−0.997319	−	0.0731704i	$-0.976688\pi$
$983$	−46.3451	−	29.7842i	−1.47818	−	0.949968i	−0.480860	−	0.876798i	$-0.659675\pi$
$984$	−3.07435	−	21.3826i	−0.0980067	−	0.681651i
$985$	1.97607	−	1.26994i	0.0629629	−	0.0404638i
$986$	11.2416	+	12.9735i	0.358005	+	0.413159i
$987$	−23.2704	+	6.83281i	−0.740705	+	0.217491i
$988$	−43.6967			−1.39018
$989$	2.85071	−	0.303392i	0.0906474	−	0.00964732i
$990$	6.47233			0.205704
$991$	−33.8884	+	9.95053i	−1.07650	+	0.316089i	−0.771478	−	0.636256i	$-0.780482\pi$
$991$	−33.8884	+	9.95053i	−1.07650	+	0.316089i	−0.305022	+	0.952345i	$0.598664\pi$
$992$	−1.07162	−	1.23672i	−0.0340240	−	0.0392658i
$993$	7.26426	−	4.66846i	0.230524	−	0.148149i
$994$	15.7342	+	109.434i	0.499059	+	3.47103i
$995$	−10.1287	−	6.50931i	−0.321101	−	0.206359i
$996$	−5.30303	+	11.6120i	−0.168033	+	0.367941i
$997$	7.79466	−	8.99552i	0.246859	−	0.284891i	−0.618774	−	0.785569i	$-0.712370\pi$
$997$	7.79466	−	8.99552i	0.246859	−	0.284891i	0.865634	+	0.500678i	$0.166916\pi$
$998$	−6.92292	+	48.1499i	−0.219141	+	1.52416i
$999$	0.723373	+	1.58397i	0.0228865	+	0.0501145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.a.55.1	✓	10
3.2	odd	2		207.2.i.b.55.1		10
23.8	even	11		1587.2.a.o.1.5		5
23.15	odd	22		1587.2.a.p.1.5		5
23.18	even	11	inner	69.2.e.a.64.1	yes	10
69.8	odd	22		4761.2.a.br.1.1		5
69.38	even	22		4761.2.a.bq.1.1		5
69.41	odd	22		207.2.i.b.64.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.a.55.1	✓	10	1.1	even	1	trivial
69.2.e.a.64.1	yes	10	23.18	even	11	inner
207.2.i.b.55.1		10	3.2	odd	2
207.2.i.b.64.1		10	69.41	odd	22
1587.2.a.o.1.5		5	23.8	even	11
1587.2.a.p.1.5		5	23.15	odd	22
4761.2.a.bq.1.1		5	69.38	even	22
4761.2.a.br.1.1		5	69.8	odd	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)

\(f(q)\)	\(=\)	\(q+(-2.41153 + 0.708089i) q^{2} +(0.654861 + 0.755750i) q^{3} +(3.63158 - 2.33387i) q^{4} +(0.108660 + 0.755750i) q^{5} +(-2.11435 - 1.35881i) q^{6} +(-2.00357 + 4.38721i) q^{7} +(-3.81329 + 4.40077i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-2.41153 + 0.708089i) q^{2} +(0.654861 + 0.755750i) q^{3} +(3.63158 - 2.33387i) q^{4} +(0.108660 + 0.755750i) q^{5} +(-2.11435 - 1.35881i) q^{6} +(-2.00357 + 4.38721i) q^{7} +(-3.81329 + 4.40077i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.797176 - 1.74557i) q^{10} +(3.23616 + 0.950224i) q^{11} +(4.14200 + 1.21620i) q^{12} +(-1.41718 - 3.10319i) q^{13} +(1.72514 - 11.9986i) q^{14} +(-0.500000 + 0.577031i) q^{15} +(2.49315 - 5.45923i) q^{16} +(0.774961 + 0.498037i) q^{17} +(-0.357685 - 2.48775i) q^{18} +(2.49611 - 1.60416i) q^{19} +(2.15843 + 2.49096i) q^{20} +(-4.62769 + 1.35881i) q^{21} -8.47695 q^{22} +(2.73939 - 3.93646i) q^{23} -5.82306 q^{24} +(4.23811 - 1.24442i) q^{25} +(5.61490 + 6.47994i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(2.96306 + 20.6086i) q^{28} +(-6.23737 - 4.00851i) q^{29} +(0.797176 - 1.74557i) q^{30} +(-0.311710 + 0.359733i) q^{31} +(-0.489262 + 3.40289i) q^{32} +(1.40111 + 3.06799i) q^{33} +(-2.22150 - 0.652290i) q^{34} +(-3.53334 - 1.03748i) q^{35} +(1.79329 + 3.92676i) q^{36} +(0.247817 - 1.72360i) q^{37} +(-4.88357 + 5.63594i) q^{38} +(1.41718 - 3.10319i) q^{39} +(-3.74024 - 2.40370i) q^{40} +(0.527961 + 3.67205i) q^{41} +(10.1977 - 6.55363i) q^{42} +(0.391457 + 0.451765i) q^{43} +(13.9701 - 4.10199i) q^{44} -0.763521 q^{45} +(-3.81876 + 11.4326i) q^{46} +5.02851 q^{47} +(5.75848 - 1.69084i) q^{48} +(-10.6493 - 12.2899i) q^{49} +(-9.33918 + 6.00192i) q^{50} +(0.131100 + 0.911821i) q^{51} +(-12.3890 - 7.96195i) q^{52} +(0.0367767 - 0.0805298i) q^{53} +(1.64589 - 1.89945i) q^{54} +(-0.366488 + 2.54898i) q^{55} +(-11.6669 - 25.5470i) q^{56} +(2.84695 + 0.835939i) q^{57} +(17.8800 + 5.25004i) q^{58} +(2.72548 + 5.96797i) q^{59} +(-0.469072 + 3.26247i) q^{60} +(3.85803 - 4.45240i) q^{61} +(0.496975 - 1.08822i) q^{62} +(-4.05742 - 2.60754i) q^{63} +(0.478549 + 3.32838i) q^{64} +(2.19124 - 1.40823i) q^{65} +(-5.55122 - 6.40645i) q^{66} +(9.60816 - 2.82121i) q^{67} +3.97669 q^{68} +(4.76890 - 0.507539i) q^{69} +9.25538 q^{70} +(-8.75112 + 2.56956i) q^{71} +(-3.81329 - 4.40077i) q^{72} +(-10.1506 + 6.52340i) q^{73} +(0.622847 + 4.33199i) q^{74} +(3.71585 + 2.38803i) q^{75} +(5.32094 - 11.6512i) q^{76} +(-10.6527 + 12.2939i) q^{77} +(-1.22023 + 8.48692i) q^{78} +(4.36916 + 9.56713i) q^{79} +(4.39672 + 1.29099i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-3.87333 - 8.48141i) q^{82} +(-0.420847 + 2.92705i) q^{83} +(-13.6345 + 15.7351i) q^{84} +(-0.292184 + 0.639793i) q^{85} +(-1.26390 - 0.812259i) q^{86} +(-1.05518 - 7.33891i) q^{87} +(-16.5222 + 10.6181i) q^{88} +(-6.39396 - 7.37902i) q^{89} +(1.84125 - 0.540641i) q^{90} +16.4537 q^{91} +(0.761114 - 20.6890i) q^{92} -0.475994 q^{93} +(-12.1264 + 3.56063i) q^{94} +(1.48357 + 1.71213i) q^{95} +(-2.89213 + 1.85866i) q^{96} +(-1.19327 - 8.29940i) q^{97} +(34.3834 + 22.0969i) q^{98} +(-1.40111 + 3.06799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} + 5 q^{5} - 7 q^{6} - 8 q^{7} - 15 q^{8} - q^{9} - 2 q^{10} + 7 q^{11} + 14 q^{12} - 30 q^{13} + q^{14} - 5 q^{15} + 12 q^{16} - 2 q^{17} - 4 q^{18} + 10 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - q^{23} - 18 q^{24} + 24 q^{25} + q^{26} + q^{27} + 9 q^{28} - 14 q^{29} + 2 q^{30} - 28 q^{31} + 23 q^{32} - 7 q^{33} - 8 q^{34} - 4 q^{35} - 3 q^{36} + 19 q^{37} - 15 q^{38} + 30 q^{39} - 13 q^{40} + 19 q^{41} + 21 q^{42} - 24 q^{43} + 54 q^{44} - 6 q^{45} + 18 q^{46} + 26 q^{47} + 10 q^{48} - 13 q^{49} - 36 q^{50} + 24 q^{51} - 57 q^{52} - q^{53} + 4 q^{54} - 24 q^{55} - 10 q^{56} + q^{57} + 10 q^{58} + 2 q^{59} + 7 q^{60} + 30 q^{61} - 24 q^{62} - 8 q^{63} + 13 q^{64} - 4 q^{65} - 28 q^{66} + 4 q^{67} - 50 q^{68} + q^{69} + 6 q^{70} - 14 q^{71} - 15 q^{72} - 26 q^{73} - 12 q^{74} - 13 q^{75} + 19 q^{76} - 43 q^{77} + 10 q^{78} + 20 q^{79} - 5 q^{80} - q^{81} + 10 q^{82} + 18 q^{83} - 42 q^{84} + 21 q^{85} + 14 q^{86} - 8 q^{87} - 38 q^{88} - 5 q^{89} + 9 q^{90} + 46 q^{91} + 52 q^{92} - 16 q^{93} - 6 q^{94} + 5 q^{95} - q^{96} + 15 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 + 5 * q^5 - 7 * q^6 - 8 * q^7 - 15 * q^8 - q^9 - 2 * q^10 + 7 * q^11 + 14 * q^12 - 30 * q^13 + q^14 - 5 * q^15 + 12 * q^16 - 2 * q^17 - 4 * q^18 + 10 * q^19 + 4 * q^20 - 3 * q^21 + 6 * q^22 - q^23 - 18 * q^24 + 24 * q^25 + q^26 + q^27 + 9 * q^28 - 14 * q^29 + 2 * q^30 - 28 * q^31 + 23 * q^32 - 7 * q^33 - 8 * q^34 - 4 * q^35 - 3 * q^36 + 19 * q^37 - 15 * q^38 + 30 * q^39 - 13 * q^40 + 19 * q^41 + 21 * q^42 - 24 * q^43 + 54 * q^44 - 6 * q^45 + 18 * q^46 + 26 * q^47 + 10 * q^48 - 13 * q^49 - 36 * q^50 + 24 * q^51 - 57 * q^52 - q^53 + 4 * q^54 - 24 * q^55 - 10 * q^56 + q^57 + 10 * q^58 + 2 * q^59 + 7 * q^60 + 30 * q^61 - 24 * q^62 - 8 * q^63 + 13 * q^64 - 4 * q^65 - 28 * q^66 + 4 * q^67 - 50 * q^68 + q^69 + 6 * q^70 - 14 * q^71 - 15 * q^72 - 26 * q^73 - 12 * q^74 - 13 * q^75 + 19 * q^76 - 43 * q^77 + 10 * q^78 + 20 * q^79 - 5 * q^80 - q^81 + 10 * q^82 + 18 * q^83 - 42 * q^84 + 21 * q^85 + 14 * q^86 - 8 * q^87 - 38 * q^88 - 5 * q^89 + 9 * q^90 + 46 * q^91 + 52 * q^92 - 16 * q^93 - 6 * q^94 + 5 * q^95 - q^96 + 15 * q^97 + 58 * q^98 + 7 * q^99

Introduction

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