LMFDB - Embedded newform 67.2.e.c.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,2,Mod(9,67)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("67.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	67.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:	$0.534997693543$
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} + 39 x^{18} - 148 x^{17} + 492 x^{16} - 1282 x^{15} + 2921 x^{14} - 4316 x^{13} + \cdots + 4489 $ x^20 - 7x^19 + 39x^18 - 148x^17 + 492x^16 - 1282x^15 + 2921x^14 - 4316x^13 + 2696x^12 + 9361x^11 - 20998x^10 + 10813x^9 + 44155x^8 - 46933x^7 - 36976x^6 - 49131x^5 + 105828x^4 + 108234x^3 + 143215x^2 + 41004*x + 4489
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			64.2
Root			$2.28033 + 1.46548i$ of defining polynomial
Character	$\chi$	$=$	67.64
Dual form			67.2.e.c.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25667 + 0.368991i) q^{2} +(0.0280790 - 0.195293i) q^{3} +(-0.239446 - 0.153882i) q^{4} +(0.681980 + 1.49333i) q^{5} +(0.107348 - 0.235058i) q^{6} +(-3.00345 - 0.881891i) q^{7} +(-1.95949 - 2.26138i) q^{8} +(2.84113 + 0.834230i) q^{9} +O(q^{10})$	\(q+(1.25667 + 0.368991i) q^{2} +(0.0280790 - 0.195293i) q^{3} +(-0.239446 - 0.153882i) q^{4} +(0.681980 + 1.49333i) q^{5} +(0.107348 - 0.235058i) q^{6} +(-3.00345 - 0.881891i) q^{7} +(-1.95949 - 2.26138i) q^{8} +(2.84113 + 0.834230i) q^{9} +(0.305998 + 2.12826i) q^{10} +(-0.886770 - 1.94175i) q^{11} +(-0.0367756 + 0.0424413i) q^{12} +(-3.83253 + 4.42298i) q^{13} +(-3.44893 - 2.21649i) q^{14} +(0.310786 - 0.0912551i) q^{15} +(-1.39153 - 3.04702i) q^{16} +(1.43888 - 0.924714i) q^{17} +(3.26253 + 2.09670i) q^{18} +(4.99642 - 1.46708i) q^{19} +(0.0664997 - 0.462516i) q^{20} +(-0.256561 + 0.561791i) q^{21} +(-0.397885 - 2.76735i) q^{22} +(-0.305697 + 2.12617i) q^{23} +(-0.496652 + 0.319179i) q^{24} +(1.50937 - 1.74191i) q^{25} +(-6.44826 + 4.14405i) q^{26} +(0.488582 - 1.06985i) q^{27} +(0.583455 + 0.673342i) q^{28} -3.38215 q^{29} +0.424228 q^{30} +(4.27688 + 4.93579i) q^{31} +(0.227312 + 1.58099i) q^{32} +(-0.404112 + 0.118658i) q^{33} +(2.14941 - 0.631124i) q^{34} +(-0.731337 - 5.08656i) q^{35} +(-0.551923 - 0.636953i) q^{36} +7.19471 q^{37} +6.82018 q^{38} +(0.756165 + 0.872661i) q^{39} +(2.04064 - 4.46838i) q^{40} +(-1.44801 + 0.930581i) q^{41} +(-0.529708 + 0.611316i) q^{42} +(-7.43197 + 4.77624i) q^{43} +(-0.0864687 + 0.601403i) q^{44} +(0.691813 + 4.81166i) q^{45} +(-1.16870 + 2.55909i) q^{46} +(1.31320 - 9.13354i) q^{47} +(-0.634135 + 0.186199i) q^{48} +(2.35418 + 1.51294i) q^{49} +(2.53953 - 1.63206i) q^{50} +(-0.140188 - 0.306969i) q^{51} +(1.59830 - 0.469304i) q^{52} +(-7.51933 - 4.83238i) q^{53} +(1.00875 - 1.16416i) q^{54} +(2.29492 - 2.64848i) q^{55} +(3.89094 + 8.51998i) q^{56} +(-0.146217 - 1.01696i) q^{57} +(-4.25024 - 1.24798i) q^{58} +(-2.14217 - 2.47220i) q^{59} +(-0.0884590 - 0.0259739i) q^{60} +(-1.10760 + 2.42530i) q^{61} +(3.55336 + 7.78078i) q^{62} +(-7.79747 - 5.01113i) q^{63} +(-1.25115 + 8.70192i) q^{64} +(-9.21867 - 2.70684i) q^{65} -0.551618 q^{66} +(-2.29104 - 7.85819i) q^{67} -0.486831 q^{68} +(0.406643 + 0.119401i) q^{69} +(0.957847 - 6.66198i) q^{70} +(-11.1416 - 7.16030i) q^{71} +(-3.68066 - 8.05953i) q^{72} +(-5.26444 + 11.5275i) q^{73} +(9.04137 + 2.65479i) q^{74} +(-0.297802 - 0.343682i) q^{75} +(-1.42213 - 0.417575i) q^{76} +(0.950948 + 6.61399i) q^{77} +(0.628245 + 1.37566i) q^{78} +(1.65220 - 1.90674i) q^{79} +(3.60120 - 4.15601i) q^{80} +(7.27782 + 4.67717i) q^{81} +(-2.16305 + 0.635128i) q^{82} +(2.55909 + 5.60363i) q^{83} +(0.147882 - 0.0950381i) q^{84} +(2.36219 + 1.51809i) q^{85} +(-11.1019 + 3.25981i) q^{86} +(-0.0949671 + 0.660511i) q^{87} +(-2.65342 + 5.81017i) q^{88} +(-1.26829 - 8.82113i) q^{89} +(-0.906082 + 6.30194i) q^{90} +(15.4114 - 9.90430i) q^{91} +(0.400378 - 0.462060i) q^{92} +(1.08402 - 0.696656i) q^{93} +(5.02046 - 10.9933i) q^{94} +(5.59829 + 6.46077i) q^{95} +0.315140 q^{96} +8.00699 q^{97} +(2.40016 + 2.76993i) q^{98} +(-0.899555 - 6.25654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	1.25667	+	0.368991i	0.888599	+	0.260916i	0.694007	−	0.719968i	$-0.255844\pi$
$2$	1.25667	+	0.368991i	0.888599	+	0.260916i	0.194592	+	0.980884i	$0.437662\pi$
$3$	0.0280790	−	0.195293i	0.0162114	−	0.112753i	−0.980109	−	0.198460i	$-0.936406\pi$
$3$	0.0280790	−	0.195293i	0.0162114	−	0.112753i	0.996320	+	0.0857074i	$0.0273150\pi$
$4$	−0.239446	−	0.153882i	−0.119723	−	0.0769412i
$5$	0.681980	+	1.49333i	0.304991	+	0.667836i	0.998621	−	0.0524946i	$-0.0167172\pi$
$5$	0.681980	+	1.49333i	0.304991	+	0.667836i	−0.693631	+	0.720331i	$0.743990\pi$
$6$	0.107348	−	0.235058i	0.0438244	−	0.0959621i
$7$	−3.00345	−	0.881891i	−1.13520	−	0.333323i	−0.340448	−	0.940263i	$-0.610579\pi$
$7$	−3.00345	−	0.881891i	−1.13520	−	0.333323i	−0.794748	+	0.606940i	$0.792397\pi$
$8$	−1.95949	−	2.26138i	−0.692785	−	0.799517i
$9$	2.84113	+	0.834230i	0.947043	+	0.278077i
$10$	0.305998	+	2.12826i	0.0967650	+	0.673016i
$11$	−0.886770	−	1.94175i	−0.267371	−	0.585461i	0.727557	−	0.686047i	$-0.240656\pi$
$11$	−0.886770	−	1.94175i	−0.267371	−	0.585461i	−0.994928	+	0.100586i	$0.967928\pi$
$12$	−0.0367756	+	0.0424413i	−0.0106162	+	0.0122518i
$13$	−3.83253	+	4.42298i	−1.06295	+	1.22671i	−0.0899445	+	0.995947i	$0.528669\pi$
$13$	−3.83253	+	4.42298i	−1.06295	+	1.22671i	−0.973009	+	0.230767i	$0.925876\pi$
$14$	−3.44893	−	2.21649i	−0.921764	−	0.592382i
$15$	0.310786	−	0.0912551i	0.0802447	−	0.0235620i
$16$	−1.39153	−	3.04702i	−0.347882	−	0.761755i
$17$	1.43888	−	0.924714i	0.348980	−	0.224276i	−0.354393	−	0.935097i	$-0.615313\pi$
$17$	1.43888	−	0.924714i	0.348980	−	0.224276i	0.703373	+	0.710820i	$0.251676\pi$
$18$	3.26253	+	2.09670i	0.768986	+	0.494197i
$19$	4.99642	−	1.46708i	1.14626	−	0.336571i	0.347179	−	0.937799i	$-0.387140\pi$
$19$	4.99642	−	1.46708i	1.14626	−	0.336571i	0.799078	+	0.601227i	$0.205321\pi$
$20$	0.0664997	−	0.462516i	0.0148698	−	0.103422i
$21$	−0.256561	+	0.561791i	−0.0559862	+	0.122593i
$22$	−0.397885	−	2.76735i	−0.0848294	−	0.590002i
$23$	−0.305697	+	2.12617i	−0.0637422	+	0.443337i	0.932810	+	0.360369i	$0.117349\pi$
$23$	−0.305697	+	2.12617i	−0.0637422	+	0.443337i	−0.996552	+	0.0829682i	$0.973560\pi$
$24$	−0.496652	+	0.319179i	−0.101379	+	0.0651522i
$25$	1.50937	−	1.74191i	0.301875	−	0.348382i
$26$	−6.44826	+	4.14405i	−1.26461	+	0.812715i
$27$	0.488582	−	1.06985i	0.0940276	−	0.205892i
$28$	0.583455	+	0.673342i	0.110263	+	0.127250i
$29$	−3.38215			−0.628049			−0.314024	−	0.949415i	$-0.601677\pi$
$29$	−3.38215			−0.628049			−0.314024	+	0.949415i	$0.601677\pi$
$30$	0.424228			0.0774530
$31$	4.27688	+	4.93579i	0.768151	+	0.886493i	0.996195	−	0.0871575i	$-0.0277783\pi$
$31$	4.27688	+	4.93579i	0.768151	+	0.886493i	−0.228044	+	0.973651i	$0.573233\pi$
$32$	0.227312	+	1.58099i	0.0401835	+	0.279482i
$33$	−0.404112	+	0.118658i	−0.0703468	+	0.0206557i
$34$	2.14941	−	0.631124i	0.368621	−	0.108237i
$35$	−0.731337	−	5.08656i	−0.123618	−	0.859785i
$36$	−0.551923	−	0.636953i	−0.0919871	−	0.106159i
$37$	7.19471			1.18280			0.591402	−	0.806377i	$-0.298575\pi$
$37$	7.19471			1.18280			0.591402	+	0.806377i	$0.298575\pi$
$38$	6.82018			1.10638
$39$	0.756165	+	0.872661i	0.121083	+	0.139738i
$40$	2.04064	−	4.46838i	0.322653	−	0.706512i
$41$	−1.44801	+	0.930581i	−0.226142	+	0.145332i	−0.648806	−	0.760954i	$-0.724731\pi$
$41$	−1.44801	+	0.930581i	−0.226142	+	0.145332i	0.422664	+	0.906286i	$0.361095\pi$
$42$	−0.529708	+	0.611316i	−0.0817357	+	0.0943281i
$43$	−7.43197	+	4.77624i	−1.13336	+	0.728369i	−0.966260	−	0.257570i	$-0.917078\pi$
$43$	−7.43197	+	4.77624i	−1.13336	+	0.728369i	−0.167105	+	0.985939i	$0.553442\pi$
$44$	−0.0864687	+	0.601403i	−0.0130357	+	0.0906649i
$45$	0.691813	+	4.81166i	0.103129	+	0.717280i
$46$	−1.16870	+	2.55909i	−0.172315	+	0.377317i
$47$	1.31320	−	9.13354i	0.191551	−	1.33226i	−0.636355	−	0.771396i	$-0.719559\pi$
$47$	1.31320	−	9.13354i	0.191551	−	1.33226i	0.827906	−	0.560867i	$-0.189532\pi$
$48$	−0.634135	+	0.186199i	−0.0915296	+	0.0268755i
$49$	2.35418	+	1.51294i	0.336311	+	0.216134i
$50$	2.53953	−	1.63206i	0.359144	−	0.230808i
$51$	−0.140188	−	0.306969i	−0.0196303	−	0.0429843i
$52$	1.59830	−	0.469304i	0.221645	−	0.0650808i
$53$	−7.51933	−	4.83238i	−1.03286	−	0.663778i	−0.0896482	−	0.995973i	$-0.528574\pi$
$53$	−7.51933	−	4.83238i	−1.03286	−	0.663778i	−0.943211	+	0.332195i	$0.892211\pi$
$54$	1.00875	−	1.16416i	0.137273	−	0.158422i
$55$	2.29492	−	2.64848i	0.309447	−	0.357120i
$56$	3.89094	+	8.51998i	0.519949	+	1.13853i
$57$	−0.146217	−	1.01696i	−0.0193669	−	0.134700i
$58$	−4.25024	−	1.24798i	−0.558083	−	0.163868i
$59$	−2.14217	−	2.47220i	−0.278887	−	0.321853i	0.598974	−	0.800769i	$-0.295575\pi$
$59$	−2.14217	−	2.47220i	−0.278887	−	0.321853i	−0.877861	+	0.478916i	$0.841030\pi$
$60$	−0.0884590	−	0.0259739i	−0.0114200	−	0.00335322i
$61$	−1.10760	+	2.42530i	−0.141813	+	0.310528i	−0.967190	−	0.254055i	$-0.918236\pi$
$61$	−1.10760	+	2.42530i	−0.141813	+	0.310528i	0.825376	+	0.564583i	$0.190963\pi$
$62$	3.55336	+	7.78078i	0.451278	+	0.988160i
$63$	−7.79747	−	5.01113i	−0.982389	−	0.631343i
$64$	−1.25115	+	8.70192i	−0.156393	+	1.08774i
$65$	−9.21867	−	2.70684i	−1.14343	−	0.335743i
$66$	−0.551618			−0.0678995
$67$	−2.29104	−	7.85819i	−0.279895	−	0.960031i
$67$	−2.29104	−	7.85819i	−0.279895	−	0.960031i
$68$	−0.486831			−0.0590370
$69$	0.406643	+	0.119401i	0.0489541	+	0.0143742i
$70$	0.957847	−	6.66198i	0.114485	−	0.796258i
$71$	−11.1416	−	7.16030i	−1.32227	−	0.849771i	−0.326822	−	0.945086i	$-0.605978\pi$
$71$	−11.1416	−	7.16030i	−1.32227	−	0.849771i	−0.995447	+	0.0953153i	$0.969614\pi$
$72$	−3.68066	−	8.05953i	−0.433770	−	0.949824i
$73$	−5.26444	+	11.5275i	−0.616156	+	1.34919i	0.302127	+	0.953268i	$0.402303\pi$
$73$	−5.26444	+	11.5275i	−0.616156	+	1.34919i	−0.918283	+	0.395925i	$0.870424\pi$
$74$	9.04137	+	2.65479i	1.05104	+	0.308612i
$75$	−0.297802	−	0.343682i	−0.0343872	−	0.0396850i
$76$	−1.42213	−	0.417575i	−0.163129	−	0.0478991i
$77$	0.950948	+	6.61399i	0.108371	+	0.753734i
$78$	0.628245	+	1.37566i	0.0711347	+	0.155763i
$79$	1.65220	−	1.90674i	0.185887	−	0.214525i	−0.655155	−	0.755494i	$-0.727397\pi$
$79$	1.65220	−	1.90674i	0.185887	−	0.214525i	0.841043	+	0.540969i	$0.181942\pi$
$80$	3.60120	−	4.15601i	0.402627	−	0.464656i
$81$	7.27782	+	4.67717i	0.808647	+	0.519686i
$82$	−2.16305	+	0.635128i	−0.238869	+	0.0701382i
$83$	2.55909	+	5.60363i	0.280897	+	0.615078i	0.996515	−	0.0834133i	$-0.0265822\pi$
$83$	2.55909	+	5.60363i	0.280897	+	0.615078i	−0.715618	+	0.698492i	$0.753855\pi$
$84$	0.147882	−	0.0950381i	0.0161353	−	0.0103695i
$85$	2.36219	+	1.51809i	0.256215	+	0.164660i
$86$	−11.1019	+	3.25981i	−1.19715	+	0.351515i
$87$	−0.0949671	+	0.660511i	−0.0101815	+	0.0708142i
$88$	−2.65342	+	5.81017i	−0.282855	+	0.619367i
$89$	−1.26829	−	8.82113i	−0.134438	−	0.935038i	−0.939671	−	0.342079i	$-0.888869\pi$
$89$	−1.26829	−	8.82113i	−0.134438	−	0.935038i	0.805233	−	0.592958i	$-0.202040\pi$
$90$	−0.906082	+	6.30194i	−0.0955094	+	0.664283i
$91$	15.4114	−	9.90430i	1.61555	−	1.03825i
$92$	0.400378	−	0.462060i	0.0417423	−	0.0481731i
$93$	1.08402	−	0.696656i	0.112407	−	0.0722398i
$94$	5.02046	−	10.9933i	0.517821	−	1.13387i
$95$	5.59829	+	6.46077i	0.574372	+	0.662861i
$96$	0.315140			0.0321638
$97$	8.00699			0.812987			0.406493	−	0.913654i	$-0.366751\pi$
$97$	8.00699			0.812987			0.406493	+	0.913654i	$0.366751\pi$
$98$	2.40016	+	2.76993i	0.242453	+	0.279805i
$99$	−0.899555	−	6.25654i	−0.0904087	−	0.628806i
$100$	−0.629462	+	0.184827i	−0.0629462	+	0.0184827i
$101$	11.5689	−	3.39692i	1.15114	−	0.338006i	0.350159	−	0.936690i	$-0.386128\pi$
$101$	11.5689	−	3.39692i	1.15114	−	0.338006i	0.800985	+	0.598684i	$0.204310\pi$
$102$	−0.0629011	−	0.437487i	−0.00622814	−	0.0433177i
$103$	6.85501	+	7.91110i	0.675444	+	0.779504i	0.985218	−	0.171306i	$-0.0547988\pi$
$103$	6.85501	+	7.91110i	0.675444	+	0.779504i	−0.309774	+	0.950810i	$0.600253\pi$
$104$	17.5118			1.71718
$105$	−1.01391			−0.0989472
$106$	−7.66620	−	8.84726i	−0.744607	−	0.859322i
$107$	−7.07456	+	15.4911i	−0.683924	+	1.49758i	0.174508	+	0.984656i	$0.444166\pi$
$107$	−7.07456	+	15.4911i	−0.683924	+	1.49758i	−0.858432	+	0.512928i	$0.828561\pi$
$108$	−0.281619	+	0.180986i	−0.0270988	+	0.0174154i
$109$	−5.23520	+	6.04174i	−0.501441	+	0.578694i	−0.948886	−	0.315618i	$-0.897788\pi$
$109$	−5.23520	+	6.04174i	−0.501441	+	0.578694i	0.447446	+	0.894311i	$0.352334\pi$
$110$	3.86121	−	2.48145i	0.368152	−	0.236597i
$111$	0.202020	−	1.40508i	0.0191749	−	0.133364i
$112$	1.49224	+	10.3787i	0.141003	+	0.980698i
$113$	6.69947	−	14.6698i	0.630233	−	1.38002i	−0.277604	−	0.960696i	$-0.589540\pi$
$113$	6.69947	−	14.6698i	0.630233	−	1.38002i	0.907837	−	0.419323i	$-0.137732\pi$
$114$	0.191504	−	1.33194i	0.0179360	−	0.124747i
$115$	−3.38354	+	0.993498i	−0.315517	+	0.0926442i
$116$	0.809840	+	0.520453i	0.0751918	+	0.0483228i
$117$	−14.5785	+	9.36903i	−1.34778	+	0.866167i
$118$	−1.77978	−	3.89718i	−0.163842	−	0.358764i
$119$	−5.13710	+	1.50839i	−0.470917	+	0.138274i
$120$	−0.815346	−	0.523991i	−0.0744305	−	0.0478336i
$121$	4.21942	−	4.86947i	0.383583	−	0.442679i
$122$	−2.28680	+	2.63911i	−0.207037	+	0.238934i
$123$	0.141078	+	0.308917i	0.0127206	+	0.0278541i
$124$	−0.264551	−	1.83999i	−0.0237573	−	0.165236i
$125$	11.5065	+	3.37862i	1.02917	+	0.302193i
$126$	−7.94977	−	9.17453i	−0.708222	−	0.817332i
$127$	−4.74530	−	1.39335i	−0.421077	−	0.123639i	0.0643277	−	0.997929i	$-0.479510\pi$
$127$	−4.74530	−	1.39335i	−0.421077	−	0.123639i	−0.485405	+	0.874289i	$0.661328\pi$
$128$	−3.45617	+	7.56795i	−0.305485	+	0.668919i
$129$	0.724086	+	1.58553i	0.0637522	+	0.139598i
$130$	−10.5860	−	6.80321i	−0.928454	−	0.596681i
$131$	−1.76413	+	12.2698i	−0.154133	+	1.07202i	0.755065	+	0.655650i	$0.227605\pi$
$131$	−1.76413	+	12.2698i	−0.154133	+	1.07202i	−0.909197	+	0.416366i	$0.863304\pi$
$132$	0.115022	+	0.0337736i	0.0100114	+	0.00293961i
$133$	−16.3003			−1.41341
$134$	0.0205287	−	10.7205i	0.00177341	−	0.926111i
$135$	1.93083			0.166180
$136$	−4.91061	−	1.44188i	−0.421081	−	0.123641i
$137$	−0.260175	+	1.80956i	−0.0222283	+	0.154601i	−0.997913	−	0.0645796i	$-0.979429\pi$
$137$	−0.260175	+	1.80956i	−0.0222283	+	0.154601i	0.975684	+	0.219181i	$0.0703384\pi$
$138$	0.466958	+	0.300095i	0.0397501	+	0.0255458i
$139$	0.205421	+	0.449810i	0.0174236	+	0.0381523i	0.918144	−	0.396247i	$-0.129688\pi$
$139$	0.205421	+	0.449810i	0.0174236	+	0.0381523i	−0.900720	+	0.434400i	$0.856960\pi$
$140$	−0.607617	+	1.33049i	−0.0513530	+	0.112447i
$141$	−1.74685	−	0.512921i	−0.147111	−	0.0431957i
$142$	−11.3593	−	13.1093i	−0.953248	−	1.10011i
$143$	11.9869	+	3.51968i	1.00240	+	0.294330i
$144$	−1.41159	−	9.81782i	−0.117632	−	0.818152i
$145$	−2.30655	−	5.05065i	−0.191549	−	0.419434i
$146$	−10.8692	+	12.5437i	−0.899542	+	1.03813i
$147$	0.361570	−	0.417274i	0.0298218	−	0.0344161i
$148$	−1.72274	−	1.10714i	−0.141609	−	0.0910063i
$149$	21.1426	−	6.20802i	1.73207	−	0.508581i	0.744750	−	0.667343i	$-0.232569\pi$
$149$	21.1426	−	6.20802i	1.73207	−	0.508581i	0.987317	+	0.158763i	$0.0507505\pi$
$150$	−0.247423	−	0.541780i	−0.0202020	−	0.0442362i
$151$	−0.0664710	+	0.0427183i	−0.00540934	+	0.00347637i	−0.543343	−	0.839511i	$-0.682842\pi$
$151$	−0.0664710	+	0.0427183i	−0.00540934	+	0.00347637i	0.537933	+	0.842987i	$0.319205\pi$
$152$	−13.1081	−	8.42404i	−1.06320	−	0.683280i
$153$	4.85947	−	1.42687i	0.392865	−	0.115356i
$154$	−1.24548	+	8.66248i	−0.100363	+	0.698043i
$155$	−4.45400	+	9.75289i	−0.357754	+	0.783371i
$156$	−0.0467733	−	0.325316i	−0.00374486	−	0.0260461i
$157$	−1.92154	+	13.3646i	−0.153356	+	1.06661i	0.757187	+	0.653199i	$0.226573\pi$
$157$	−1.92154	+	13.3646i	−0.153356	+	1.06661i	−0.910543	+	0.413415i	$0.864336\pi$
$158$	2.77984	−	1.78650i	0.221152	−	0.142126i
$159$	−1.15487	+	1.33279i	−0.0915869	+	0.105697i
$160$	−2.20591	+	1.41765i	−0.174393	+	0.112075i
$161$	2.79319	−	6.11624i	0.220134	−	0.482027i
$162$	7.41997	+	8.56311i	0.582968	+	0.672781i
$163$	−2.58830			−0.202732			−0.101366	−	0.994849i	$-0.532321\pi$
$163$	−2.58830			−0.202732			−0.101366	+	0.994849i	$0.532321\pi$
$164$	0.489920			0.0382564
$165$	−0.452791	−	0.522549i	−0.0352497	−	0.0406804i
$166$	1.14824	+	7.98619i	0.0891208	+	0.619849i
$167$	10.6398	−	3.12412i	0.823331	−	0.241752i	0.157181	−	0.987570i	$-0.449759\pi$
$167$	10.6398	−	3.12412i	0.823331	−	0.241752i	0.666150	+	0.745818i	$0.267941\pi$
$168$	1.77315	−	0.520644i	0.136801	−	0.0401685i
$169$	−3.02434	−	21.0348i	−0.232642	−	1.61806i
$170$	2.40833	+	2.77936i	0.184710	+	0.213167i
$171$	15.4193			1.17915
$172$	2.51453			0.191731
$173$	−12.8621	−	14.8436i	−0.977884	−	1.12854i	−0.991692	−	0.128633i	$-0.958941\pi$
$173$	−12.8621	−	14.8436i	−0.977884	−	1.12854i	0.0138086	−	0.999905i	$-0.495604\pi$
$174$	−0.363065	+	0.795001i	−0.0275239	+	0.0602689i
$175$	−6.06949	+	3.90063i	−0.458811	+	0.294860i
$176$	−4.68260	+	5.40401i	−0.352964	+	0.407342i
$177$	−0.542954	+	0.348935i	−0.0408109	+	0.0262276i
$178$	1.66110	−	11.5532i	0.124505	−	0.865950i
$179$	0.992880	+	6.90563i	0.0742113	+	0.516151i	0.992691	+	0.120683i	$0.0385085\pi$
$179$	0.992880	+	6.90563i	0.0742113	+	0.516151i	−0.918480	+	0.395468i	$0.870582\pi$
$180$	0.574779	−	1.25859i	0.0428415	−	0.0938097i
$181$	−3.12312	+	21.7218i	−0.232140	+	1.61457i	0.456678	+	0.889632i	$0.349039\pi$
$181$	−3.12312	+	21.7218i	−0.232140	+	1.61457i	−0.688818	+	0.724935i	$0.741870\pi$
$182$	23.0216	−	6.75975i	1.70648	−	0.501066i
$183$	0.442546	+	0.284407i	0.0327139	+	0.0210240i
$184$	5.40708	−	3.47492i	0.398615	−	0.256174i
$185$	4.90665	+	10.7441i	0.360744	+	0.789919i
$186$	1.61931	−	0.475472i	0.118734	−	0.0348633i
$187$	−3.07153	−	1.97395i	−0.224612	−	0.144349i
$188$	−1.71993	+	1.98491i	−0.125439	+	0.144764i
$189$	−2.41092	+	2.78235i	−0.175368	+	0.202386i
$190$	4.65123	+	10.1848i	0.337435	+	0.738880i
$191$	−2.35394	−	16.3720i	−0.170325	−	1.18464i	−0.878198	−	0.478298i	$-0.841254\pi$
$191$	−2.35394	−	16.3720i	−0.170325	−	1.18464i	0.707872	−	0.706340i	$-0.249655\pi$
$192$	1.66430	+	0.488682i	0.120110	+	0.0352676i
$193$	−4.65033	−	5.36676i	−0.334738	−	0.386308i	0.563281	−	0.826266i	$-0.309539\pi$
$193$	−4.65033	−	5.36676i	−0.334738	−	0.386308i	−0.898019	+	0.439958i	$0.854993\pi$
$194$	10.0621	+	2.95451i	0.722419	+	0.212121i
$195$	−0.787480	+	1.72434i	−0.0563926	+	0.123483i
$196$	−0.330883	−	0.724533i	−0.0236345	−	0.0517523i
$197$	−7.27115	−	4.67288i	−0.518048	−	0.332929i	0.255351	−	0.966848i	$-0.417809\pi$
$197$	−7.27115	−	4.67288i	−0.518048	−	0.332929i	−0.773399	+	0.633919i	$0.781445\pi$
$198$	1.17817	−	8.19433i	0.0837287	−	0.582346i
$199$	−0.357953	−	0.105104i	−0.0253746	−	0.00745066i	0.269021	−	0.963134i	$-0.413300\pi$
$199$	−0.357953	−	0.105104i	−0.0253746	−	0.00745066i	−0.294395	+	0.955684i	$0.595118\pi$
$200$	−6.89672			−0.487672
$201$	−1.59898	+	0.226775i	−0.112784	+	0.0159955i
$202$	15.7916			1.11110
$203$	10.1581	+	2.98268i	0.712958	+	0.209343i
$204$	−0.0136697	+	0.0950750i	−0.000957072	+	0.00665658i
$205$	−2.37718	−	1.52772i	−0.166029	−	0.106701i
$206$	5.69535	+	12.4711i	0.396814	+	0.868900i
$207$	−2.64224	+	5.78569i	−0.183648	+	0.402134i
$208$	18.8100	+	5.52311i	1.30424	+	0.382959i
$209$	−7.27938	−	8.40086i	−0.503525	−	0.581099i
$210$	−1.27414	−	0.374123i	−0.0879244	−	0.0258169i
$211$	0.657748	+	4.57474i	0.0452812	+	0.314938i	0.999856	+	0.0169666i	$0.00540091\pi$
$211$	0.657748	+	4.57474i	0.0452812	+	0.314938i	−0.954575	+	0.297971i	$0.903690\pi$
$212$	1.05685	+	2.31418i	0.0725849	+	0.158939i
$213$	−1.71120	+	1.97484i	−0.117250	+	0.135313i
$214$	−14.6065	+	16.8568i	−0.998477	+	1.15230i
$215$	−12.2009	−	7.84107i	−0.832097	−	0.534756i
$216$	−3.37669	+	0.991487i	−0.229755	+	0.0674621i
$217$	−8.49256	−	18.5961i	−0.576512	−	1.26239i
$218$	−8.80825	+	5.66072i	−0.596570	+	0.383392i
$219$	2.10343	+	1.35179i	0.142136	+	0.0913456i
$220$	−0.957062	+	0.281019i	−0.0645251	+	0.0189463i
$221$	−1.42458	+	9.90814i	−0.0958274	+	0.666494i
$222$	0.772334	−	1.69118i	0.0518357	−	0.113504i
$223$	−1.35837	−	9.44764i	−0.0909629	−	0.632661i	−0.983395	−	0.181479i	$-0.941912\pi$
$223$	−1.35837	−	9.44764i	−0.0909629	−	0.632661i	0.892432	−	0.451182i	$-0.148997\pi$
$224$	0.711542	−	4.94888i	0.0475419	−	0.330661i
$225$	5.74148	−	3.68982i	0.382765	−	0.245988i
$226$	13.8320	−	15.9630i	0.920094	−	1.06184i
$227$	−10.9487	+	7.03628i	−0.726688	+	0.467014i	−0.850958	−	0.525234i	$-0.823978\pi$
$227$	−10.9487	+	7.03628i	−0.726688	+	0.467014i	0.124269	+	0.992249i	$0.460341\pi$
$228$	−0.121482	+	0.266007i	−0.00804531	+	0.0176168i
$229$	11.6156	+	13.4051i	0.767579	+	0.885833i	0.996147	−	0.0876946i	$-0.0279500\pi$
$229$	11.6156	+	13.4051i	0.767579	+	0.885833i	−0.228569	+	0.973528i	$0.573405\pi$
$230$	−4.61859			−0.304541
$231$	1.31837			0.0867424
$232$	6.62729	+	7.64830i	0.435103	+	0.502135i
$233$	−0.0461732	−	0.321142i	−0.00302491	−	0.0210387i	0.988253	−	0.152826i	$-0.0488375\pi$
$233$	−0.0461732	−	0.321142i	−0.00302491	−	0.0210387i	−0.991278	+	0.131787i	$0.957928\pi$
$234$	−21.7774	+	6.39443i	−1.42364	+	0.418017i
$235$	14.5349	−	4.26784i	0.948155	−	0.278403i
$236$	0.132506	+	0.921600i	0.00862541	+	0.0599910i
$237$	−0.325982	−	0.376203i	−0.0211748	−	0.0244370i
$238$	−7.01222			−0.454535
$239$	8.32723			0.538643			0.269322	−	0.963050i	$-0.413200\pi$
$239$	8.32723			0.538643			0.269322	+	0.963050i	$0.413200\pi$
$240$	−0.710524	−	0.819988i	−0.0458641	−	0.0529300i
$241$	12.1482	−	26.6009i	0.782536	−	1.71352i	0.0856598	−	0.996324i	$-0.472700\pi$
$241$	12.1482	−	26.6009i	0.782536	−	1.71352i	0.696877	−	0.717191i	$-0.254573\pi$
$242$	7.09920	−	4.56238i	0.456354	−	0.293281i
$243$	3.42838	−	3.95656i	0.219931	−	0.253813i
$244$	0.638421	−	0.410288i	0.0408707	−	0.0262660i
$245$	−0.653810	+	4.54735i	−0.0417704	+	0.290519i
$246$	0.0633002	+	0.440263i	0.00403588	+	0.0280701i
$247$	−12.6601	+	27.7217i	−0.805541	+	1.76389i
$248$	2.78114	−	19.3433i	0.176603	−	1.22830i
$249$	1.16621	−	0.342430i	0.0739055	−	0.0217006i
$250$	13.2132	+	8.49161i	0.835676	+	0.537057i
$251$	−6.05109	+	3.88880i	−0.381942	+	0.245459i	−0.717497	−	0.696562i	$-0.754712\pi$
$251$	−6.05109	+	3.88880i	−0.381942	+	0.245459i	0.335556	+	0.942020i	$0.391076\pi$
$252$	1.09595	+	2.39979i	0.0690381	+	0.151172i
$253$	4.39958	−	1.29183i	0.276599	−	0.0812169i
$254$	−5.44914	−	3.50195i	−0.341909	−	0.219732i
$255$	0.362800	−	0.418694i	0.0227194	−	0.0262196i
$256$	4.37853	−	5.05309i	0.273658	−	0.315818i
$257$	−10.2241	−	22.3876i	−0.637761	−	1.39650i	−0.901869	−	0.432009i	$-0.857805\pi$
$257$	−10.2241	−	22.3876i	−0.637761	−	1.39650i	0.264108	−	0.964493i	$-0.414922\pi$
$258$	0.324890	+	2.25966i	0.0202268	+	0.140680i
$259$	−21.6089	−	6.34495i	−1.34271	−	0.394256i
$260$	1.79083	+	2.06673i	0.111063	+	0.128173i
$261$	−9.60911	−	2.82149i	−0.594789	−	0.174646i
$262$	−6.74437	+	14.7681i	−0.416668	+	0.912376i
$263$	11.5295	+	25.2460i	0.710937	+	1.55673i	0.826186	+	0.563398i	$0.190506\pi$
$263$	11.5295	+	25.2460i	0.710937	+	1.55673i	−0.115249	+	0.993337i	$0.536766\pi$
$264$	1.06018	+	0.681339i	0.0652498	+	0.0419335i
$265$	2.08829	−	14.5244i	0.128283	−	0.892227i
$266$	−20.4840	−	6.01466i	−1.25596	−	0.368782i
$267$	−1.75832			−0.107607
$268$	−0.660658	+	2.23416i	−0.0403561	+	0.136473i
$269$	−15.9850			−0.974622			−0.487311	−	0.873229i	$-0.662022\pi$
$269$	−15.9850			−0.974622			−0.487311	+	0.873229i	$0.662022\pi$
$270$	2.42642	+	0.712460i	0.147667	+	0.0433589i
$271$	2.06951	−	14.3938i	0.125714	−	0.874359i	−0.825186	−	0.564861i	$-0.808930\pi$
$271$	2.06951	−	14.3938i	0.125714	−	0.874359i	0.950900	−	0.309498i	$-0.100161\pi$
$272$	−4.81986	−	3.09754i	−0.292247	−	0.187816i
$273$	−1.50151	−	3.28785i	−0.0908755	−	0.198990i
$274$	−0.994666	+	2.17801i	−0.0600900	+	0.131579i
$275$	−4.72083	−	1.38616i	−0.284677	−	0.0835886i
$276$	−0.0789952	−	0.0911653i	−0.00475495	−	0.00548751i
$277$	−8.05860	−	2.36622i	−0.484194	−	0.142172i	0.0305197	−	0.999534i	$-0.490284\pi$
$277$	−8.05860	−	2.36622i	−0.484194	−	0.142172i	−0.514714	+	0.857362i	$0.672102\pi$
$278$	0.0921705	+	0.641060i	0.00552802	+	0.0384482i
$279$	8.03359	+	17.5911i	0.480958	+	1.05315i
$280$	−10.0696	+	11.6209i	−0.601772	+	0.694482i
$281$	−0.564487	+	0.651453i	−0.0336745	+	0.0388624i	−0.772337	−	0.635213i	$-0.780912\pi$
$281$	−0.564487	+	0.651453i	−0.0336745	+	0.0388624i	0.738662	+	0.674075i	$0.235458\pi$
$282$	−2.00594	−	1.28914i	−0.119452	−	0.0767673i
$283$	−5.57497	+	1.63696i	−0.331397	+	0.0973071i	−0.443198	−	0.896424i	$-0.646156\pi$
$283$	−5.57497	+	1.63696i	−0.331397	+	0.0973071i	0.111801	+	0.993731i	$0.464338\pi$
$284$	1.56597	+	3.42900i	0.0929234	+	0.203474i
$285$	1.41894	−	0.911897i	0.0840508	−	0.0540161i
$286$	13.7649	+	8.84613i	0.813933	+	0.523083i
$287$	5.16970	−	1.51796i	0.305158	−	0.0896024i
$288$	−0.673088	+	4.68143i	−0.0396621	+	0.275856i
$289$	−5.84677	+	12.8026i	−0.343927	+	0.753096i
$290$	−1.03493	−	7.19809i	−0.0607731	−	0.422686i
$291$	0.224828	−	1.56371i	0.0131797	−	0.0916665i
$292$	3.03443	−	1.95011i	0.177576	−	0.114121i
$293$	7.10284	−	8.19711i	0.414952	−	0.478880i	−0.509340	−	0.860565i	$-0.670111\pi$
$293$	7.10284	−	8.19711i	0.414952	−	0.478880i	0.924293	+	0.381685i	$0.124656\pi$
$294$	0.608343	−	0.390959i	0.0354793	−	0.0228012i
$295$	2.23088	−	4.88495i	0.129887	−	0.284413i
$296$	−14.0980	−	16.2699i	−0.819429	−	0.945671i
$297$	−2.51064			−0.145682
$298$	28.8599			1.67181
$299$	−8.23240	−	9.50070i	−0.476092	−	0.549440i
$300$	0.0184208	+	0.128120i	0.00106353	+	0.00739699i
$301$	26.5336	−	7.79098i	1.52937	−	0.449064i
$302$	−0.0992947	+	0.0291556i	−0.00571377	+	0.00167771i
$303$	−0.338555	−	2.35470i	−0.0194495	−	0.135274i
$304$	−11.4229	−	13.1827i	−0.655147	−	0.756079i
$305$	−4.37713			−0.250634
$306$	6.63325			0.379198
$307$	2.11470	+	2.44050i	0.120693	+	0.139287i	0.812880	−	0.582431i	$-0.197898\pi$
$307$	2.11470	+	2.44050i	0.120693	+	0.139287i	−0.692188	+	0.721718i	$0.743353\pi$
$308$	0.790076	−	1.73003i	0.0450188	−	0.0985774i
$309$	1.73747	−	1.11660i	0.0988411	−	0.0635213i
$310$	−9.19593	+	10.6127i	−0.522294	+	0.602759i
$311$	−22.9703	+	14.7621i	−1.30253	+	0.837083i	−0.993485	−	0.113965i	$-0.963645\pi$
$311$	−22.9703	+	14.7621i	−1.30253	+	0.837083i	−0.309042	+	0.951048i	$0.600008\pi$
$312$	0.491714	−	3.41995i	0.0278378	−	0.193616i
$313$	2.23364	+	15.5353i	0.126253	+	0.878109i	0.950244	+	0.311506i	$0.100833\pi$
$313$	2.23364	+	15.5353i	0.126253	+	0.878109i	−0.823991	+	0.566603i	$0.808257\pi$
$314$	−7.34618	+	16.0859i	−0.414569	+	0.907779i
$315$	2.16554	−	15.0617i	0.122014	−	0.848629i
$316$	−0.689027	+	0.202316i	−0.0387608	+	0.0113812i
$317$	0.409770	+	0.263343i	0.0230149	+	0.0147908i	0.552098	−	0.833779i	$-0.313828\pi$
$317$	0.409770	+	0.263343i	0.0230149	+	0.0147908i	−0.529083	+	0.848570i	$0.677464\pi$
$318$	−1.94307	+	1.24874i	−0.108962	+	0.0700256i
$319$	2.99918	+	6.56730i	0.167922	+	0.367698i
$320$	−13.8481	+	4.06616i	−0.774131	+	0.227305i
$321$	2.82667	+	1.81659i	0.157769	+	0.101392i
$322$	5.76696	−	6.65542i	0.321380	−	0.370892i
$323$	5.83263	−	6.73121i	0.324536	−	0.374535i
$324$	−1.02291	−	2.23986i	−0.0568283	−	0.124437i
$325$	1.91971	+	13.3519i	0.106486	+	0.740628i
$326$	−3.25264	−	0.955061i	−0.180147	−	0.0528959i
$327$	1.03291	+	1.19205i	0.0571202	+	0.0659203i
$328$	4.94176	+	1.45103i	0.272863	+	0.0801199i
$329$	−11.9989	+	26.2740i	−0.661522	+	1.44853i
$330$	−0.376192	−	0.823746i	−0.0207087	−	0.0453457i
$331$	26.3110	+	16.9091i	1.44618	+	0.929406i	0.999395	+	0.0347670i	$0.0110689\pi$
$331$	26.3110	+	16.9091i	1.44618	+	0.929406i	0.446789	+	0.894639i	$0.352567\pi$
$332$	0.249537	−	1.73556i	0.0136951	−	0.0952515i
$333$	20.4411	+	6.00205i	1.12017	+	0.328910i
$334$	14.5235			0.794688
$335$	10.1724	−	8.78039i	0.555778	−	0.479724i
$336$	2.06880			0.112862
$337$	17.1423	+	5.03343i	0.933801	+	0.274189i	0.713027	−	0.701136i	$-0.247324\pi$
$337$	17.1423	+	5.03343i	0.933801	+	0.274189i	0.220774	+	0.975325i	$0.429142\pi$
$338$	3.96104	−	27.5497i	0.215452	−	1.49850i
$339$	−2.67680	−	1.72028i	−0.145384	−	0.0934325i
$340$	−0.332009	−	0.726999i	−0.0180057	−	0.0394270i
$341$	5.79148	−	12.6816i	0.313626	−	0.686745i
$342$	19.3770	+	5.68960i	1.04779	+	0.307658i
$343$	8.61271	+	9.93960i	0.465043	+	0.536688i
$344$	25.3638	+	7.44747i	1.36752	+	0.401541i
$345$	0.0990173	+	0.688681i	0.00533091	+	0.0370773i
$346$	−10.6862	−	23.3995i	−0.574493	−	1.25796i
$347$	16.6198	−	19.1802i	0.892195	−	1.02965i	−0.107178	−	0.994240i	$-0.534181\pi$
$347$	16.6198	−	19.1802i	0.892195	−	1.02965i	0.999373	−	0.0354081i	$-0.0112731\pi$
$348$	0.124380	−	0.143543i	0.00666749	−	0.00769470i
$349$	−11.0843	−	7.12347i	−0.593331	−	0.381311i	0.209243	−	0.977864i	$-0.432900\pi$
$349$	−11.0843	−	7.12347i	−0.593331	−	0.381311i	−0.802574	+	0.596553i	$0.796536\pi$
$350$	−9.06664	+	2.66221i	−0.484632	+	0.142301i
$351$	2.85940	+	6.26121i	0.152623	+	0.334198i
$352$	2.86832	−	1.84336i	0.152882	−	0.0982514i
$353$	−4.26483	−	2.74084i	−0.226994	−	0.145880i	0.422201	−	0.906502i	$-0.361258\pi$
$353$	−4.26483	−	2.74084i	−0.226994	−	0.145880i	−0.649195	+	0.760622i	$0.724894\pi$
$354$	−0.811068	+	0.238151i	−0.0431078	+	0.0126576i
$355$	3.09429	−	21.5213i	0.164228	−	1.14223i
$356$	−1.05373	+	2.30735i	−0.0558476	+	0.122289i
$357$	0.150334	+	1.04560i	0.00795652	+	0.0553388i
$358$	−1.30040	+	9.04445i	−0.0687281	+	0.478014i
$359$	−9.34999	+	6.00887i	−0.493473	+	0.317136i	−0.763601	−	0.645688i	$-0.776571\pi$
$359$	−9.34999	+	6.00887i	−0.493473	+	0.317136i	0.270128	+	0.962825i	$0.412934\pi$
$360$	9.52537	−	10.9929i	0.502031	−	0.579375i
$361$	6.82805	−	4.38812i	0.359371	−	0.230954i
$362$	−11.9399	+	26.1447i	−0.627546	+	1.37413i
$363$	−0.832498	−	0.960754i	−0.0436948	−	0.0504265i
$364$	−5.21429			−0.273303
$365$	−20.8046			−1.08896
$366$	0.451189	+	0.520700i	0.0235841	+	0.0272174i
$367$	0.272148	+	1.89283i	0.0142060	+	0.0988049i	0.995691	−	0.0927350i	$-0.0295609\pi$
$367$	0.272148	+	1.89283i	0.0142060	+	0.0988049i	−0.981485	+	0.191540i	$0.938652\pi$
$368$	6.90386	−	2.02716i	0.359889	−	0.105673i
$369$	−4.89031	+	1.43592i	−0.254579	+	0.0747512i
$370$	2.20157	+	15.3122i	0.114454	+	0.796045i
$371$	18.3223	+	21.1450i	0.951244	+	1.09779i
$372$	−0.366766			−0.0190160
$373$	−20.0706			−1.03922			−0.519609	−	0.854404i	$-0.673922\pi$
$373$	−20.0706			−1.03922			−0.519609	+	0.854404i	$0.673922\pi$
$374$	−3.13152	−	3.61397i	−0.161927	−	0.186874i
$375$	0.982913	−	2.15228i	0.0507574	−	0.111143i
$376$	−23.2276	+	14.9275i	−1.19787	+	0.769825i
$377$	12.9622	−	14.9592i	0.667586	−	0.770436i
$378$	−4.05638	+	2.60688i	−0.208638	+	0.134083i
$379$	1.12802	−	7.84555i	0.0579425	−	0.402999i	−0.940123	−	0.340834i	$-0.889291\pi$
$379$	1.12802	−	7.84555i	0.0579425	−	0.402999i	0.998066	−	0.0621646i	$-0.0198004\pi$
$380$	−0.346287	−	2.40848i	−0.0177642	−	0.123552i
$381$	−0.405355	+	0.887603i	−0.0207669	+	0.0454733i
$382$	3.08301	−	21.4428i	0.157740	−	1.09711i
$383$	−15.4044	+	4.52313i	−0.787126	+	0.231121i	−0.650505	−	0.759502i	$-0.725443\pi$
$383$	−15.4044	+	4.52313i	−0.787126	+	0.231121i	−0.136621	+	0.990623i	$0.543624\pi$
$384$	1.38093	+	0.887467i	0.0704701	+	0.0452884i
$385$	−9.22832	+	5.93068i	−0.470319	+	0.302256i
$386$	−3.86363	−	8.46017i	−0.196654	−	0.430611i
$387$	−25.0997	+	7.36992i	−1.27589	+	0.374634i
$388$	−1.91724	−	1.23214i	−0.0973331	−	0.0625522i
$389$	13.9108	−	16.0539i	0.705303	−	0.813964i	−0.284155	−	0.958778i	$-0.591713\pi$
$389$	13.9108	−	16.0539i	0.705303	−	0.813964i	0.989459	+	0.144815i	$0.0462586\pi$
$390$	−1.62587	+	1.87635i	−0.0823290	+	0.0950127i
$391$	1.52624	+	3.34199i	0.0771850	+	0.169012i
$392$	−1.19167	−	8.28827i	−0.0601886	−	0.418621i
$393$	2.34667	+	0.689046i	0.118374	+	0.0347578i
$394$	−7.41317	−	8.55525i	−0.373470	−	0.431007i
$395$	3.97416	+	1.16692i	0.199962	+	0.0587140i
$396$	−0.747377	+	1.63653i	−0.0375571	+	0.0822386i
$397$	1.81538	+	3.97512i	0.0911111	+	0.199505i	0.949701	−	0.313157i	$-0.101387\pi$
$397$	1.81538	+	3.97512i	0.0911111	+	0.199505i	−0.858590	+	0.512662i	$0.828659\pi$
$398$	−0.411046	−	0.264163i	−0.0206039	−	0.0132413i
$399$	−0.457695	+	3.18334i	−0.0229134	+	0.159366i
$400$	−7.40796	−	2.17517i	−0.370398	−	0.108759i
$401$	9.75212			0.486998			0.243499	−	0.969901i	$-0.421705\pi$
$401$	9.75212			0.486998			0.243499	+	0.969901i	$0.421705\pi$
$402$	−2.09307	−	0.305030i	−0.104393	−	0.0152135i
$403$	−38.2222			−1.90398
$404$	−3.29284	−	0.966865i	−0.163825	−	0.0481033i
$405$	−2.02122	+	14.0579i	−0.100435	+	0.698543i
$406$	11.6648	+	7.49649i	0.578913	+	0.372045i
$407$	−6.38005	−	13.9704i	−0.316247	−	0.692485i
$408$	−0.419475	+	0.918523i	−0.0207671	+	0.0454736i
$409$	−2.36549	−	0.694570i	−0.116966	−	0.0343443i	0.222726	−	0.974881i	$-0.428505\pi$
$409$	−2.36549	−	0.694570i	−0.116966	−	0.0343443i	−0.339692	+	0.940537i	$0.610323\pi$
$410$	−2.42361	−	2.79699i	−0.119694	−	0.138134i
$411$	0.346090	+	0.101621i	0.0170713	+	0.00501260i
$412$	−0.424023	−	2.94914i	−0.0208901	−	0.145294i
$413$	4.25369	+	9.31427i	0.209310	+	0.458325i
$414$	−5.45529	+	6.29574i	−0.268113	+	0.309419i
$415$	−6.62281	+	7.64313i	−0.325101	+	0.375186i
$416$	−7.86387	−	5.05380i	−0.385558	−	0.247783i
$417$	0.0936129	−	0.0274872i	0.00458424	−	0.00134606i
$418$	−6.04793	−	13.2431i	−0.295814	−	0.647742i
$419$	−30.0054	+	19.2833i	−1.46586	+	0.942050i	−0.467546	+	0.883969i	$0.654862\pi$
$419$	−30.0054	+	19.2833i	−1.46586	+	0.942050i	−0.998312	+	0.0580807i	$0.981502\pi$
$420$	0.242776	+	0.156022i	0.0118462	+	0.00761312i
$421$	−14.2798	+	4.19293i	−0.695955	+	0.204351i	−0.610529	−	0.791994i	$-0.709043\pi$
$421$	−14.2798	+	4.19293i	−0.695955	+	0.204351i	−0.0854258	+	0.996345i	$0.527225\pi$
$422$	−0.861467	+	5.99163i	−0.0419356	+	0.291668i
$423$	11.3505	−	24.8540i	0.551878	−	1.20844i
$424$	3.80625	+	26.4730i	0.184848	+	1.28564i
$425$	0.561043	−	3.90214i	0.0272146	−	0.189282i
$426$	−2.87911	+	1.85029i	−0.139494	+	0.0896470i
$427$	5.46546	−	6.30748i	0.264492	−	0.305240i
$428$	4.07779	−	2.62063i	0.197107	−	0.126673i
$429$	1.02395	−	2.24214i	0.0494368	−	0.108251i
$430$	−12.4392	−	14.3557i	−0.599874	−	0.692291i
$431$	9.89620			0.476683			0.238342	−	0.971181i	$-0.423396\pi$
$431$	9.89620			0.476683			0.238342	+	0.971181i	$0.423396\pi$
$432$	−3.93971			−0.189550
$433$	−3.80093	−	4.38651i	−0.182661	−	0.210802i	0.657033	−	0.753862i	$-0.271811\pi$
$433$	−3.80093	−	4.38651i	−0.182661	−	0.210802i	−0.839694	+	0.543060i	$0.817266\pi$
$434$	−3.81053	−	26.5028i	−0.182911	−	1.27218i
$435$	−1.05112	+	0.308638i	−0.0503976	+	0.0147981i
$436$	2.18326	−	0.641064i	0.104559	−	0.0307014i
$437$	1.59187	+	11.0717i	0.0761495	+	0.529632i
$438$	2.14451	+	2.47490i	0.102469	+	0.118255i
$439$	−5.55478			−0.265115			−0.132558	−	0.991175i	$-0.542319\pi$
$439$	−5.55478			−0.265115			−0.132558	+	0.991175i	$0.542319\pi$
$440$	−10.4861			−0.499904
$441$	5.42638	+	6.26237i	0.258399	+	0.298208i
$442$	−5.44624	+	11.9256i	−0.259051	+	0.567243i
$443$	15.4202	−	9.90999i	0.732638	−	0.470838i	−0.120374	−	0.992729i	$-0.538409\pi$
$443$	15.4202	−	9.90999i	0.732638	−	0.470838i	0.853012	+	0.521891i	$0.174773\pi$
$444$	−0.264590	+	0.305353i	−0.0125569	+	0.0144914i
$445$	12.3079	−	7.90980i	0.583450	−	0.374960i
$446$	1.77908	−	12.3738i	0.0842419	−	0.585915i
$447$	−0.618724	−	4.30332i	−0.0292646	−	0.203540i
$448$	11.4319	−	25.0324i	0.540106	−	1.18267i
$449$	−5.41332	+	37.6505i	−0.255470	+	1.77684i	0.308683	+	0.951165i	$0.400112\pi$
$449$	−5.41332	+	37.6505i	−0.255470	+	1.77684i	−0.564153	+	0.825670i	$0.690797\pi$
$450$	8.57665	−	2.51833i	0.404307	−	0.118715i
$451$	3.09101	+	1.98647i	0.145550	+	0.0935394i
$452$	−3.86158	+	2.48169i	−0.181634	+	0.116729i
$453$	0.00647617	+	0.0141808i	0.000304277	+	0.000666274i
$454$	−16.3552	+	4.80231i	−0.767586	+	0.225384i
$455$	25.3006	+	16.2597i	1.18611	+	0.762267i
$456$	−2.01322	+	2.32338i	−0.0942777	+	0.108802i
$457$	23.0329	−	26.5814i	1.07744	−	1.24343i	0.109032	−	0.994038i	$-0.465225\pi$
$457$	23.0329	−	26.5814i	1.07744	−	1.24343i	0.968403	−	0.249389i	$-0.0802297\pi$
$458$	9.65057	+	21.1318i	0.450941	+	0.987424i
$459$	−0.286289	−	1.99118i	−0.0133628	−	0.0929403i
$460$	0.963057	+	0.282779i	0.0449028	+	0.0131846i
$461$	−15.9590	−	18.4177i	−0.743286	−	0.857798i	0.250613	−	0.968087i	$-0.419368\pi$
$461$	−15.9590	−	18.4177i	−0.743286	−	0.857798i	−0.993900	+	0.110289i	$0.964822\pi$
$462$	1.65675	+	0.486467i	0.0770792	+	0.0226325i
$463$	12.0278	−	26.3373i	0.558981	−	1.22400i	−0.393479	−	0.919333i	$-0.628729\pi$
$463$	12.0278	−	26.3373i	0.558981	−	1.22400i	0.952460	−	0.304664i	$-0.0985440\pi$
$464$	4.70635	+	10.3055i	0.218487	+	0.478419i
$465$	1.77961	+	1.14369i	0.0825276	+	0.0530373i
$466$	0.0604740	−	0.420606i	0.00280140	−	0.0194842i
$467$	32.3460	+	9.49764i	1.49679	+	0.439498i	0.924702	−	0.380691i	$-0.124314\pi$
$467$	32.3460	+	9.49764i	1.49679	+	0.439498i	0.572092	+	0.820190i	$0.306132\pi$
$468$	4.93249			0.228004
$469$	−0.0490637	+	25.6221i	−0.00226555	+	1.18312i
$470$	19.8404			0.915169
$471$	2.55607	+	0.750530i	0.117778	+	0.0345826i
$472$	−1.39300	+	9.68851i	−0.0641179	+	0.445950i
$473$	15.8647	+	10.1956i	0.729461	+	0.468796i
$474$	−0.270836	−	0.593048i	−0.0124399	−	0.0272396i
$475$	4.98594	−	10.9177i	0.228771	−	0.500938i
$476$	1.46217	+	0.429332i	0.0670185	+	0.0196784i
$477$	−17.3320	−	20.0023i	−0.793580	−	0.915840i
$478$	10.4646	+	3.07267i	0.478638	+	0.140541i
$479$	0.889252	+	6.18488i	0.0406310	+	0.282595i	1.00000		0.000439898i	$0.000140024\pi$
$479$	0.889252	+	6.18488i	0.0406310	+	0.282595i	−0.959369	+	0.282155i	$0.908951\pi$
$480$	0.214919	+	0.470607i	0.00980966	+	0.0214802i
$481$	−27.5740	+	31.8221i	−1.25726	+	1.45096i
$482$	25.0818	−	28.9459i	1.14244	−	1.31845i
$483$	−1.11603	−	0.717230i	−0.0507812	−	0.0326351i
$484$	−1.75965	+	0.516679i	−0.0799839	+	0.0234854i
$485$	5.46061	+	11.9571i	0.247953	+	0.542942i
$486$	5.76827	−	3.70704i	0.261654	−	0.168155i
$487$	−26.7673	−	17.2023i	−1.21294	−	0.779511i	−0.231794	−	0.972765i	$-0.574459\pi$
$487$	−26.7673	−	17.2023i	−1.21294	−	0.779511i	−0.981149	+	0.193254i	$0.938096\pi$
$488$	7.65485	−	2.24767i	0.346519	−	0.101747i
$489$	−0.0726769	+	0.505479i	−0.00328656	+	0.0228585i
$490$	−2.49955	+	5.47326i	−0.112918	+	0.247257i
$491$	−1.81680	−	12.6361i	−0.0819910	−	0.570260i	−0.988860	−	0.148848i	$-0.952444\pi$
$491$	−1.81680	−	12.6361i	−0.0819910	−	0.570260i	0.906869	−	0.421412i	$-0.138465\pi$
$492$	0.0137565	−	0.0956783i	0.000620189	−	0.00431351i
$493$	−4.86651	+	3.12752i	−0.219177	+	0.140856i
$494$	−26.1386	+	30.1655i	−1.17603	+	1.35721i
$495$	8.72959	−	5.61017i	0.392366	−	0.252158i
$496$	9.08804	−	19.9000i	0.408065	−	0.893537i
$497$	27.1487	+	31.3313i	1.21779	+	1.40540i
$498$	1.59189			0.0713344
$499$	−13.2811			−0.594546			−0.297273	−	0.954793i	$-0.596077\pi$
$499$	−13.2811			−0.594546			−0.297273	+	0.954793i	$0.596077\pi$
$500$	−2.23528	−	2.57965i	−0.0999646	−	0.115365i
$501$	−0.311367	−	2.16560i	−0.0139108	−	0.0967520i
$502$	−9.03915	+	2.65413i	−0.403437	+	0.118460i
$503$	−1.02041	+	0.299618i	−0.0454977	+	0.0133593i	−0.304402	−	0.952544i	$-0.598457\pi$
$503$	−1.02041	+	0.299618i	−0.0454977	+	0.0133593i	0.258905	+	0.965903i	$0.416638\pi$
$504$	3.94704	+	27.4523i	0.175815	+	1.22282i
$505$	12.9624	+	14.9595i	0.576821	+	0.665687i
$506$	6.00549			0.266977
$507$	−4.19287			−0.186212
$508$	0.921831	+	1.06385i	0.0408996	+	0.0472007i
$509$	1.40898	−	3.08523i	0.0624518	−	0.136750i	−0.875833	−	0.482615i	$-0.839687\pi$
$509$	1.40898	−	3.08523i	0.0624518	−	0.136750i	0.938284	+	0.345865i	$0.112414\pi$
$510$	0.610414	−	0.392289i	0.0270296	−	0.0173709i
$511$	25.9775	−	29.9796i	1.14918	−	1.32622i
$512$	21.3650	−	13.7305i	0.944209	−	0.606806i
$513$	0.871610	−	6.06218i	0.0384825	−	0.267652i
$514$	−4.58745	−	31.9064i	−0.202344	−	1.40733i
$515$	−7.13889	+	15.6320i	−0.314577	+	0.688827i
$516$	0.0706054	−	0.491072i	0.00310823	−	0.0216182i
$517$	−18.8996	+	5.54942i	−0.831204	+	0.244063i
$518$	−24.8140	−	15.9470i	−1.09027	−	0.700671i
$519$	−3.26001	+	2.09508i	−0.143099	+	0.0919639i
$520$	11.9427	+	26.1509i	0.523723	+	1.14679i
$521$	11.4640	−	3.36613i	0.502247	−	0.147473i	−0.0207888	−	0.999784i	$-0.506618\pi$
$521$	11.4640	−	3.36613i	0.502247	−	0.147473i	0.523035	+	0.852311i	$0.324800\pi$
$522$	−11.0344	−	7.09135i	−0.482961	−	0.310380i
$523$	1.70225	−	1.96450i	0.0744342	−	0.0859017i	−0.717311	−	0.696753i	$-0.754627\pi$
$523$	1.70225	−	1.96450i	0.0744342	−	0.0859017i	0.791745	+	0.610851i	$0.209173\pi$
$524$	2.31052	−	2.66648i	0.100935	−	0.116486i
$525$	0.591342	+	1.29486i	0.0258083	+	0.0565123i
$526$	5.17316	+	35.9801i	0.225560	+	1.56881i
$527$	10.7181	+	3.14713i	0.466889	+	0.137091i
$528$	0.923885	+	1.06622i	0.0402069	+	0.0464013i
$529$	17.6412	+	5.17992i	0.767009	+	0.225214i
$530$	7.98367	−	17.4818i	0.346788	−	0.759361i
$531$	−4.02380	−	8.81090i	−0.174618	−	0.382360i
$532$	3.90303	+	2.50833i	0.169218	+	0.108750i
$533$	1.43362	−	9.97101i	0.0620968	−	0.431893i
$534$	−2.20963	−	0.648805i	−0.0956199	−	0.0280765i
$535$	−27.9580			−1.20873
$536$	−13.2810	+	20.5790i	−0.573654	+	0.888876i
$537$	1.37650			0.0594005
$538$	−20.0878	−	5.89832i	−0.866048	−	0.254295i
$539$	0.850141	−	5.91286i	0.0366182	−	0.254685i
$540$	−0.462330	−	0.297121i	−0.0198955	−	0.0127861i
$541$	−6.82793	−	14.9511i	−0.293556	−	0.642797i	0.704183	−	0.710019i	$-0.251314\pi$
$541$	−6.82793	−	14.9511i	−0.293556	−	0.642797i	−0.997738	+	0.0672221i	$0.978586\pi$
$542$	7.91186	−	17.3246i	0.339844	−	0.744154i
$543$	4.15443	+	1.21985i	0.178284	+	0.0523488i
$544$	1.78904	+	2.06466i	0.0767044	+	0.0885216i
$545$	−12.5926	−	3.69752i	−0.539407	−	0.158384i
$546$	−0.673713	−	4.68578i	−0.0288323	−	0.200533i
$547$	7.35265	+	16.1001i	0.314377	+	0.688389i	0.999186	−	0.0403330i	$-0.0128419\pi$
$547$	7.35265	+	16.1001i	0.314377	+	0.688389i	−0.684810	+	0.728722i	$0.740115\pi$
$548$	0.340757	−	0.393255i	0.0145564	−	0.0167990i
$549$	−5.17009	+	5.96660i	−0.220654	+	0.254648i
$550$	−5.42104	−	3.48389i	−0.231154	−	0.148553i
$551$	−16.8986	+	4.96188i	−0.719905	+	0.211383i
$552$	−0.526803	−	1.15354i	−0.0224222	−	0.0490979i
$553$	−6.64384	+	4.26973i	−0.282525	+	0.181568i
$554$	−9.25388	−	5.94711i	−0.393160	−	0.252668i
$555$	2.23602	−	0.656554i	0.0949137	−	0.0278692i
$556$	0.0200306	−	0.139316i	0.000849485	−	0.00590830i
$557$	2.41871	−	5.29623i	0.102484	−	0.224408i	−0.851443	−	0.524447i	$-0.824272\pi$
$557$	2.41871	−	5.29623i	0.102484	−	0.224408i	0.953927	+	0.300038i	$0.0969995\pi$
$558$	3.60460	+	25.0705i	0.152595	+	1.06132i
$559$	7.35807	−	51.1765i	0.311213	−	2.16454i
$560$	−14.4812	+	9.30648i	−0.611941	+	0.393271i
$561$	−0.471745	+	0.544422i	−0.0199171	+	0.0229855i
$562$	−0.949754	+	0.610370i	−0.0400629	+	0.0257469i
$563$	−15.6565	+	34.2830i	−0.659844	+	1.44486i	0.222824	+	0.974859i	$0.428473\pi$
$563$	−15.6565	+	34.2830i	−0.659844	+	1.44486i	−0.882668	+	0.469998i	$0.844255\pi$
$564$	0.339346	+	0.391626i	0.0142890	+	0.0164904i
$565$	26.4757			1.11384
$566$	−7.60991			−0.319868
$567$	−17.7338	−	20.4659i	−0.744749	−	0.859486i
$568$	5.63984	+	39.2260i	0.236643	+	1.64589i
$569$	−6.91184	+	2.02950i	−0.289759	+	0.0850810i	−0.423382	−	0.905951i	$-0.639157\pi$
$569$	−6.91184	+	2.02950i	−0.289759	+	0.0850810i	0.133623	+	0.991032i	$0.457339\pi$
$570$	2.11962	−	0.622376i	0.0887811	−	0.0260685i
$571$	−2.75702	−	19.1755i	−0.115378	−	0.802470i	−0.962541	−	0.271137i	$-0.912600\pi$
$571$	−2.75702	−	19.1755i	−0.115378	−	0.802470i	0.847163	−	0.531333i	$-0.178309\pi$
$572$	−2.32860	−	2.68735i	−0.0973636	−	0.112364i
$573$	−3.26345			−0.136332
$574$	7.05671			0.294541
$575$	3.24218	+	3.74168i	0.135208	+	0.156039i
$576$	−10.8141	+	23.6795i	−0.450586	+	0.986647i
$577$	−17.7373	+	11.3991i	−0.738412	+	0.474549i	−0.854998	−	0.518632i	$-0.826442\pi$
$577$	−17.7373	+	11.3991i	−0.738412	+	0.474549i	0.116585	+	0.993181i	$0.462805\pi$
$578$	−12.0715	+	13.9313i	−0.502109	+	0.579464i
$579$	−1.17867	+	0.757485i	−0.0489839	+	0.0314800i
$580$	−0.224912	+	1.56429i	−0.00933895	+	0.0649538i
$581$	−2.74430	−	19.0870i	−0.113853	−	0.791864i
$582$	0.859531	−	1.88211i	0.0356287	−	0.0780160i
$583$	−2.71538	+	18.8859i	−0.112460	+	0.782174i
$584$	36.3837	−	10.6832i	1.50557	−	0.442074i
$585$	−23.9333	−	15.3810i	−0.989519	−	0.635925i
$586$	11.9506	−	7.68017i	0.493674	−	0.317265i
$587$	−5.66511	−	12.4049i	−0.233824	−	0.512003i	0.755953	−	0.654626i	$-0.227174\pi$
$587$	−5.66511	−	12.4049i	−0.233824	−	0.512003i	−0.989777	+	0.142622i	$0.954447\pi$
$588$	−0.150787	+	0.0442752i	−0.00621837	+	0.00182588i
$589$	28.6103	+	18.3867i	1.17887	+	0.757612i
$590$	4.60599	−	5.31559i	0.189625	−	0.218839i
$591$	−1.11675	+	1.28880i	−0.0459369	+	0.0530141i
$592$	−10.0116	−	21.9224i	−0.411476	−	0.901006i
$593$	−2.00287	−	13.9303i	−0.0822481	−	0.572048i	−0.988719	−	0.149781i	$-0.952143\pi$
$593$	−2.00287	−	13.9303i	−0.0822481	−	0.572048i	0.906471	−	0.422268i	$-0.138766\pi$
$594$	−3.15504	−	0.926403i	−0.129453	−	0.0380108i
$595$	−5.75592	−	6.64268i	−0.235970	−	0.272324i
$596$	−6.01780	−	1.76699i	−0.246499	−	0.0723786i
$597$	−0.0305772	+	0.0669546i	−0.00125144	+	0.00274027i
$598$	−6.83973	−	14.9769i	−0.279697	−	0.612452i
$599$	−36.1845	−	23.2543i	−1.47846	−	0.950147i	−0.997294	−	0.0735156i	$-0.976578\pi$
$599$	−36.1845	−	23.2543i	−1.47846	−	0.950147i	−0.481163	−	0.876631i	$-0.659785\pi$
$600$	−0.193653	+	1.34688i	−0.00790584	+	0.0549863i
$601$	−12.5113	−	3.67366i	−0.510348	−	0.149852i	0.0164128	−	0.999865i	$-0.494775\pi$
$601$	−12.5113	−	3.67366i	−0.510348	−	0.149852i	−0.526761	+	0.850014i	$0.676594\pi$
$602$	36.2188			1.47617
$603$	0.0464121	−	24.2374i	0.00189005	−	0.987022i
$604$	0.0224898			0.000915097
$605$	10.1493	+	2.98009i	0.412626	+	0.121158i
$606$	0.443413	−	3.08401i	0.0180124	−	0.125279i
$607$	18.3445	+	11.7893i	0.744579	+	0.478512i	0.857108	−	0.515137i	$-0.172259\pi$
$607$	18.3445	+	11.7893i	0.744579	+	0.478512i	−0.112529	+	0.993648i	$0.535895\pi$
$608$	3.45519	+	7.56580i	0.140126	+	0.306834i
$609$	0.867727	−	1.90006i	0.0351621	−	0.0769942i
$610$	−5.50060	−	1.61512i	−0.222713	−	0.0653944i
$611$	35.3646	+	40.8129i	1.43070	+	1.65111i
$612$	−1.38315	−	0.406130i	−0.0559105	−	0.0164168i
$613$	−3.34341	−	23.2539i	−0.135039	−	0.939218i	−0.938848	−	0.344331i	$-0.888106\pi$
$613$	−3.34341	−	23.2539i	−0.135039	−	0.939218i	0.803809	−	0.594887i	$-0.202803\pi$
$614$	1.75696	+	3.84721i	0.0709051	+	0.155261i
$615$	−0.365102	+	0.421350i	−0.0147223	+	0.0169905i
$616$	13.0933	−	15.1105i	0.527546	−	0.608820i
$617$	12.7463	+	8.19152i	0.513145	+	0.329778i	0.771455	−	0.636284i	$-0.219529\pi$
$617$	12.7463	+	8.19152i	0.513145	+	0.329778i	−0.258310	+	0.966062i	$0.583166\pi$
$618$	2.59544	−	0.762089i	0.104404	−	0.0306557i
$619$	8.15643	+	17.8601i	0.327835	+	0.717858i	0.999741	−	0.0227789i	$-0.00725137\pi$
$619$	8.15643	+	17.8601i	0.327835	+	0.717858i	−0.671906	+	0.740636i	$0.734524\pi$
$620$	2.56729	−	1.64990i	0.103105	−	0.0662615i
$621$	2.12531	+	1.36586i	0.0852859	+	0.0548099i
$622$	−34.3132	+	10.0753i	−1.37583	+	0.403981i
$623$	−3.97004	+	27.6123i	−0.159056	+	1.10626i
$624$	1.60679	−	3.51838i	0.0643231	−	0.140848i
$625$	1.16174	+	8.08007i	0.0464695	+	0.323203i
$626$	−2.92545	+	20.3470i	−0.116925	+	0.813228i
$627$	−1.84503	+	1.18573i	−0.0736834	+	0.0473534i
$628$	2.51669	−	2.90441i	0.100427	−	0.115899i
$629$	10.3523	−	6.65305i	0.412775	−	0.265274i
$630$	8.27899	−	18.1285i	0.329843	−	0.722255i
$631$	−10.7889	−	12.4511i	−0.429500	−	0.495670i	0.499207	−	0.866483i	$-0.333625\pi$
$631$	−10.7889	−	12.4511i	−0.429500	−	0.495670i	−0.928708	+	0.370813i	$0.879079\pi$
$632$	−7.54934			−0.300296
$633$	0.911886			0.0362442
$634$	0.417773	+	0.482136i	0.0165919	+	0.0191481i
$635$	−1.15548	−	8.03652i	−0.0458537	−	0.318920i
$636$	0.481620	−	0.141417i	0.0190975	−	0.00560753i
$637$	−15.7142	+	4.61409i	−0.622617	+	0.182817i
$638$	1.34571	+	9.35959i	0.0532770	+	0.370550i
$639$	−25.6815	−	29.6380i	−1.01594	−	1.17246i
$640$	−13.6585			−0.539898
$641$	−17.9037			−0.707152			−0.353576	−	0.935406i	$-0.615034\pi$
$641$	−17.9037			−0.707152			−0.353576	+	0.935406i	$0.615034\pi$
$642$	2.88188	+	3.32587i	0.113739	+	0.131262i
$643$	1.42256	−	3.11496i	0.0561001	−	0.122842i	−0.879506	−	0.475888i	$-0.842127\pi$
$643$	1.42256	−	3.11496i	0.0561001	−	0.122842i	0.935606	+	0.353046i	$0.114854\pi$
$644$	−1.61000	+	1.03468i	−0.0634429	+	0.0407723i
$645$	−1.87390	+	2.16259i	−0.0737847	+	0.0851521i
$646$	9.81344	−	6.30672i	0.386105	−	0.248134i
$647$	−1.42966	+	9.94350i	−0.0562057	+	0.390919i	0.942228	+	0.334972i	$0.108727\pi$
$647$	−1.42966	+	9.94350i	−0.0562057	+	0.390919i	−0.998434	+	0.0559471i	$0.982182\pi$
$648$	−3.68400	−	25.6228i	−0.144721	−	1.00656i
$649$	−2.90079	+	6.35184i	−0.113866	+	0.249332i
$650$	−2.51428	+	17.4872i	−0.0986182	+	0.685905i
$651$	−3.87016	+	1.13638i	−0.151684	+	0.0445383i
$652$	0.619758	+	0.398294i	0.0242716	+	0.0155984i
$653$	7.27764	−	4.67705i	0.284796	−	0.183027i	−0.390441	−	0.920628i	$-0.627678\pi$
$653$	7.27764	−	4.67705i	0.284796	−	0.183027i	0.675237	+	0.737601i	$0.264041\pi$
$654$	0.858175	+	1.87914i	0.0335573	+	0.0734803i
$655$	−19.5259	+	5.73332i	−0.762940	+	0.224019i
$656$	4.85045	+	3.11719i	0.189378	+	0.121706i
$657$	−24.5735	+	28.3594i	−0.958705	+	1.10640i
$658$	−24.7735	+	28.5902i	−0.965773	+	1.11456i
$659$	−14.1306	−	30.9418i	−0.550451	−	1.20532i	−0.956571	−	0.291500i	$-0.905846\pi$
$659$	−14.1306	−	30.9418i	−0.550451	−	1.20532i	0.406120	−	0.913820i	$-0.366882\pi$
$660$	0.0280078	+	0.194799i	0.00109020	+	0.00758253i
$661$	18.2460	+	5.35750i	0.709687	+	0.208383i	0.616602	−	0.787275i	$-0.288509\pi$
$661$	18.2460	+	5.35750i	0.709687	+	0.208383i	0.0930850	+	0.995658i	$0.470327\pi$
$662$	26.8249	+	30.9576i	1.04258	+	1.20320i
$663$	1.89500	+	0.556421i	0.0735955	+	0.0216096i
$664$	7.65739	−	16.7673i	0.297164	−	0.650699i
$665$	−11.1165	−	24.3416i	−0.431078	−	0.943929i
$666$	23.4730	+	15.0852i	0.909559	+	0.584538i
$667$	1.03391	−	7.19101i	0.0400332	−	0.278437i
$668$	−3.02840	−	0.889218i	−0.117172	−	0.0344049i
$669$	−1.88320			−0.0728089
$670$	16.0232	−	7.28052i	0.619032	−	0.281271i
$671$	5.69153			0.219719
$672$	−0.946505	−	0.277919i	−0.0365122	−	0.0107210i
$673$	−3.48267	+	24.2225i	−0.134247	+	0.933709i	0.805684	+	0.592345i	$0.201798\pi$
$673$	−3.48267	+	24.2225i	−0.134247	+	0.933709i	−0.939931	+	0.341364i	$0.889111\pi$
$674$	19.6849	+	12.6507i	0.758234	+	0.487287i
$675$	−1.12612	−	2.46586i	−0.0433444	−	0.0949111i
$676$	−2.51271	+	5.50207i	−0.0966428	+	0.211618i
$677$	−8.27735	−	2.43045i	−0.318124	−	0.0934097i	0.118772	−	0.992922i	$-0.462104\pi$
$677$	−8.27735	−	2.43045i	−0.318124	−	0.0934097i	−0.436896	+	0.899512i	$0.643922\pi$
$678$	−2.72909	−	3.14953i	−0.104810	−	0.120957i
$679$	−24.0486	−	7.06129i	−0.922899	−	0.270988i
$680$	−1.19573	−	8.31648i	−0.0458541	−	0.318922i
$681$	1.06671	+	2.33577i	0.0408765	+	0.0895070i
$682$	11.9574	−	13.7995i	0.457871	−	0.528411i
$683$	14.0762	−	16.2448i	0.538612	−	0.621591i	−0.419580	−	0.907718i	$-0.637823\pi$
$683$	14.0762	−	16.2448i	0.538612	−	0.621591i	0.958192	+	0.286127i	$0.0923681\pi$
$684$	−3.69210	−	2.37277i	−0.141171	−	0.0907250i
$685$	−2.87970	+	0.845556i	−0.110028	+	0.0323070i
$686$	7.15570	+	15.6688i	0.273206	+	0.598238i
$687$	2.94408	−	1.89205i	0.112324	−	0.0721860i
$688$	24.8951	+	15.9991i	0.949115	+	0.609959i
$689$	50.1916	−	14.7376i	1.91215	−	0.561457i
$690$	−0.129685	+	0.901980i	−0.00493703	+	0.0343378i
$691$	3.70631	−	8.11568i	0.140995	−	0.308735i	−0.825941	−	0.563757i	$-0.809355\pi$
$691$	3.70631	−	8.11568i	0.140995	−	0.308735i	0.966935	+	0.255022i	$0.0820827\pi$
$692$	0.795594	+	5.53348i	0.0302440	+	0.210351i
$693$	−2.81583	+	19.5845i	−0.106964	+	0.743954i
$694$	27.9629	−	17.9706i	1.06146	−	0.682156i
$695$	−0.531620	+	0.613522i	−0.0201655	+	0.0232722i
$696$	1.67975	−	1.07951i	0.0636708	−	0.0409187i
$697$	−1.22300	+	2.67799i	−0.0463244	+	0.101436i
$698$	−11.3008	−	13.0419i	−0.427743	−	0.493642i
$699$	−0.0640133			−0.00242121
$700$	2.05355			0.0776170
$701$	−5.22789	−	6.03330i	−0.197455	−	0.227875i	0.648384	−	0.761313i	$-0.275445\pi$
$701$	−5.22789	−	6.03330i	−0.197455	−	0.227875i	−0.845839	+	0.533438i	$0.820900\pi$
$702$	1.28298	+	8.92335i	0.0484231	+	0.336790i
$703$	35.9478	−	10.5552i	1.35580	−	0.398098i
$704$	18.0065	−	5.28718i	0.678645	−	0.199268i
$705$	−0.425356	−	2.95842i	−0.0160198	−	0.111420i
$706$	−4.34813	−	5.01801i	−0.163644	−	0.188855i
$707$	−37.7421			−1.41944
$708$	0.183703			0.00690398
$709$	17.3371	+	20.0081i	0.651110	+	0.751421i	0.981298	−	0.192494i	$-0.0616578\pi$
$709$	17.3371	+	20.0081i	0.651110	+	0.751421i	−0.330188	+	0.943915i	$0.607112\pi$
$710$	11.8297	−	25.9034i	0.443960	−	0.972136i
$711$	6.28478	−	4.03898i	0.235698	−	0.151474i
$712$	−17.4627	+	20.1530i	−0.654442	+	0.755266i
$713$	−11.8017	+	7.58452i	−0.441979	+	0.284042i
$714$	−0.196896	+	1.36944i	−0.00736864	+	0.0512500i
$715$	2.91881	+	20.3007i	0.109157	+	0.759205i
$716$	0.824914	−	1.80631i	0.0308285	−	0.0675050i
$717$	0.233820	−	1.62625i	0.00873216	−	0.0607335i
$718$	−13.9671	+	4.10110i	−0.521246	+	0.153052i
$719$	26.9870	+	17.3435i	1.00644	+	0.646802i	0.936470	−	0.350747i	$-0.114072\pi$
$719$	26.9870	+	17.3435i	1.00644	+	0.646802i	0.0699736	+	0.997549i	$0.477708\pi$
$720$	13.6985	−	8.80352i	0.510515	−	0.328088i
$721$	−13.6119	−	29.8059i	−0.506934	−	1.11003i
$722$	10.1998	−	2.99492i	0.379596	−	0.111460i
$723$	−4.85388	−	3.11940i	−0.180518	−	0.116012i
$724$	4.09042	−	4.72059i	0.152019	−	0.175439i
$725$	−5.10492	+	5.89139i	−0.189592	+	0.218801i
$726$	−0.691664	−	1.51453i	−0.0256701	−	0.0562096i
$727$	−0.371540	−	2.58411i	−0.0137796	−	0.0958395i	0.981771	−	0.190068i	$-0.0608708\pi$
$727$	−0.371540	−	2.58411i	−0.0137796	−	0.0958395i	−0.995551	+	0.0942282i	$0.969962\pi$
$728$	−52.5959	−	15.4435i	−1.94933	−	0.572375i
$729$	16.3195	+	18.8337i	0.604426	+	0.697545i
$730$	−26.1445	−	7.67671i	−0.967650	−	0.284128i
$731$	−6.27708	+	13.7449i	−0.232166	+	0.508373i
$732$	−0.0622004	−	0.136200i	−0.00229899	−	0.00503410i
$733$	33.9048	+	21.7893i	1.25230	+	0.804806i	0.987211	−	0.159417i	$-0.0509614\pi$
$733$	33.9048	+	21.7893i	1.25230	+	0.804806i	0.265092	+	0.964223i	$0.414598\pi$
$734$	−0.356438	+	2.47908i	−0.0131564	+	0.0915045i
$735$	0.869709	+	0.255370i	0.0320797	+	0.00941945i
$736$	−3.43094			−0.126466
$737$	−13.2271	+	11.4170i	−0.487225	+	0.420552i
$738$	−6.67534			−0.245723
$739$	11.7218	+	3.44184i	0.431195	+	0.126610i	0.490125	−	0.871652i	$-0.336951\pi$
$739$	11.7218	+	3.44184i	0.431195	+	0.126610i	−0.0589309	+	0.998262i	$0.518769\pi$
$740$	0.478446	−	3.32767i	0.0175880	−	0.122327i
$741$	5.05838	+	3.25083i	0.185824	+	0.119422i
$742$	15.2227	+	33.3330i	0.558842	+	1.22369i
$743$	6.96716	−	15.2560i	0.255600	−	0.559687i	−0.737716	−	0.675111i	$-0.764096\pi$
$743$	6.96716	−	15.2560i	0.255600	−	0.559687i	0.993316	+	0.115425i	$0.0368228\pi$
$744$	−3.69952	−	1.08628i	−0.135631	−	0.0398249i
$745$	23.6894	+	27.3390i	0.867913	+	1.00162i
$746$	−25.2221	−	7.40588i	−0.923447	−	0.271149i
$747$	2.59599	+	18.0555i	0.0949823	+	0.660616i
$748$	0.431707	+	0.945307i	0.0157848	+	0.0345639i
$749$	34.9095	−	40.2878i	1.27557	−	1.47208i
$750$	2.02937	−	2.34202i	0.0741021	−	0.0855183i
$751$	33.9887	+	21.8432i	1.24027	+	0.797070i	0.985458	−	0.169922i	$-0.0543514\pi$
$751$	33.9887	+	21.8432i	1.24027	+	0.797070i	0.254808	+	0.966992i	$0.417988\pi$
$752$	−29.6574	+	8.70820i	−1.08149	+	0.317556i
$753$	0.589549	+	1.29093i	0.0214844	+	0.0470442i
$754$	21.8090	−	14.0158i	0.794236	−	0.510424i
$755$	−0.109124	−	0.0701300i	−0.00397144	−	0.00255229i
$756$	1.00544	−	0.295223i	0.0365674	−	0.0107372i
$757$	4.02913	−	28.0232i	0.146441	−	1.01852i	−0.775543	−	0.631295i	$-0.782524\pi$
$757$	4.02913	−	28.0232i	0.146441	−	1.01852i	0.921984	−	0.387227i	$-0.126567\pi$
$758$	4.31248	−	9.44302i	0.156636	−	0.342986i
$759$	−0.128751	−	0.895483i	−0.00467336	−	0.0325040i
$760$	3.64042	−	25.3197i	0.132052	−	0.918441i
$761$	−27.5693	+	17.7177i	−0.999388	+	0.642267i	−0.934626	−	0.355633i	$-0.884265\pi$
$761$	−27.5693	+	17.7177i	−0.999388	+	0.642267i	−0.0647620	+	0.997901i	$0.520629\pi$
$762$	−0.836914	+	0.965850i	−0.0303182	+	0.0349891i
$763$	21.0518	−	13.5292i	0.762126	−	0.489788i
$764$	−1.95573	+	4.28244i	−0.0707557	+	0.154933i
$765$	5.44485	+	6.28369i	0.196859	+	0.227187i
$766$	−21.0272			−0.759743
$767$	19.1444			0.691265
$768$	−0.863891	−	0.996983i	−0.0311730	−	0.0359755i
$769$	−4.28519	−	29.8042i	−0.154528	−	1.07477i	−0.908508	−	0.417868i	$-0.862777\pi$
$769$	−4.28519	−	29.8042i	−0.154528	−	1.07477i	0.753980	−	0.656898i	$-0.228132\pi$
$770$	−13.7853	+	4.04773i	−0.496788	+	0.145870i
$771$	−4.65924	+	1.36808i	−0.167798	+	0.0492701i
$772$	0.287650	+	2.00065i	0.0103528	+	0.0720050i
$773$	−12.3394	−	14.2405i	−0.443818	−	0.512193i	0.489127	−	0.872213i	$-0.337316\pi$
$773$	−12.3394	−	14.2405i	−0.443818	−	0.512193i	−0.932945	+	0.360019i	$0.882770\pi$
$774$	−34.2614			−1.23150
$775$	15.0531			0.540724
$776$	−15.6896	−	18.1068i	−0.563225	−	0.649997i
$777$	−1.84588	+	4.04192i	−0.0662207	+	0.145003i
$778$	23.4049	−	15.0414i	0.839108	−	0.539262i
$779$	−5.86964	+	6.77392i	−0.210302	+	0.242701i
$780$	0.453904	−	0.291707i	0.0162524	−	0.0104448i
$781$	−4.02347	+	27.9839i	−0.143971	+	1.00134i
$782$	0.684807	+	4.76294i	0.0244887	+	0.170322i
$783$	−1.65246	+	3.61837i	−0.0590539	+	0.129310i
$784$	1.33405	−	9.27851i	0.0476446	−	0.331375i
$785$	−21.2682	+	6.24491i	−0.759096	+	0.222891i
$786$	2.69474	+	1.73180i	0.0961182	+	0.0617714i
$787$	9.90970	−	6.36858i	0.353243	−	0.227015i	−0.351970	−	0.936011i	$-0.614488\pi$
$787$	9.90970	−	6.36858i	0.353243	−	0.227015i	0.705212	+	0.708996i	$0.250852\pi$
$788$	1.02197	+	2.23780i	0.0364062	+	0.0797184i
$789$	5.25411	−	1.54275i	0.187051	−	0.0549232i
$790$	4.56362	+	2.93286i	0.162366	+	0.104346i
$791$	−33.0587	+	38.1517i	−1.17543	+	1.35652i
$792$	−12.3857	+	14.2939i	−0.440107	+	0.507911i
$793$	−6.48215	−	14.1939i	−0.230188	−	0.504042i
$794$	0.814542	+	5.66526i	0.0289070	+	0.201053i
$795$	−2.77788	−	0.815660i	−0.0985214	−	0.0289285i
$796$	0.0695366	+	0.0802495i	0.00246466	+	0.00284437i
$797$	−3.71390	−	1.09050i	−0.131553	−	0.0386275i	0.215293	−	0.976549i	$-0.430929\pi$
$797$	−3.71390	−	1.09050i	−0.131553	−	0.0386275i	−0.346846	+	0.937922i	$0.612747\pi$
$798$	−1.74979	+	3.83151i	−0.0619420	+	0.135634i
$799$	−6.55636	−	14.3564i	−0.231947	−	0.507894i
$800$	3.09704	+	1.99035i	0.109497	+	0.0703694i
$801$	3.75549	−	26.1200i	0.132694	−	0.922905i
$802$	12.2552	+	3.59845i	0.432746	+	0.127066i
$803$	27.0519			0.954642
$804$	0.417766	+	0.191755i	0.0147335	+	0.00676268i
$805$	11.0384			0.389054
$806$	−48.0326	−	14.1036i	−1.69188	−	0.496780i
$807$	−0.448842	+	3.12176i	−0.0158000	+	0.109891i
$808$	−30.3508	−	19.5053i	−1.06774	−	0.686193i
$809$	2.15443	+	4.71755i	0.0757458	+	0.165860i	0.943717	−	0.330755i	$-0.107303\pi$
$809$	2.15443	+	4.71755i	0.0757458	+	0.165860i	−0.867971	+	0.496615i	$0.834576\pi$
$810$	−7.72725	+	16.9203i	−0.271508	+	0.594519i
$811$	−46.4942	−	13.6519i	−1.63263	−	0.479385i	−0.668260	−	0.743928i	$-0.732961\pi$
$811$	−46.4942	−	13.6519i	−1.63263	−	0.479385i	−0.964374	+	0.264543i	$0.914779\pi$
$812$	−1.97333	−	2.27734i	−0.0692502	−	0.0799190i
$813$	−2.75290	−	0.808324i	−0.0965484	−	0.0283492i
$814$	−2.86267	−	19.9103i	−0.100337	−	0.697856i
$815$	−1.76517	−	3.86518i	−0.0618312	−	0.135391i
$816$	−0.740266	+	0.854312i	−0.0259145	+	0.0299069i
$817$	−30.1261	+	34.7674i	−1.05398	+	1.21636i
$818$	−2.71634	−	1.74569i	−0.0949748	−	0.0610366i
$819$	52.0482	−	15.2827i	1.81871	−	0.534022i
$820$	0.334116	+	0.731612i	0.0116678	+	0.0255490i
$821$	−10.3283	+	6.63760i	−0.360460	+	0.231654i	−0.708318	−	0.705894i	$-0.750546\pi$
$821$	−10.3283	+	6.63760i	−0.360460	+	0.231654i	0.347857	+	0.937547i	$0.386909\pi$
$822$	0.397423	+	0.255408i	0.0138617	+	0.00890838i
$823$	−41.2799	+	12.1209i	−1.43893	+	0.422507i	−0.905864	−	0.423570i	$-0.860777\pi$
$823$	−41.2799	+	12.1209i	−1.43893	+	0.422507i	−0.533062	+	0.846076i	$0.678959\pi$
$824$	4.45763	−	31.0035i	0.155289	−	1.08006i
$825$	−0.403264	+	0.883025i	−0.0140399	+	0.0307430i
$826$	1.90859	+	13.2745i	0.0664083	+	0.461880i
$827$	0.817712	−	5.68731i	0.0284346	−	0.197767i	−0.970652	−	0.240486i	$-0.922693\pi$
$827$	0.817712	−	5.68731i	0.0284346	−	0.197767i	0.999087	+	0.0427193i	$0.0136021\pi$
$828$	1.52299	−	0.978766i	0.0529275	−	0.0340145i
$829$	−10.9239	+	12.6068i	−0.379401	+	0.437852i	−0.913046	−	0.407856i	$-0.866276\pi$
$829$	−10.9239	+	12.6068i	−0.379401	+	0.437852i	0.533645	+	0.845709i	$0.320822\pi$
$830$	−11.1429	+	7.16112i	−0.386776	+	0.248566i
$831$	−0.688384	+	1.50735i	−0.0238798	+	0.0522894i
$832$	−33.6933	−	38.8842i	−1.16811	−	1.34807i
$833$	4.78642			0.165840
$834$	0.127783			0.00442476
$835$	11.9215	+	13.7581i	0.412559	+	0.476118i
$836$	0.450273	+	3.13172i	0.0155730	+	0.108313i
$837$	7.37014	−	2.16407i	0.254749	−	0.0748011i
$838$	−44.8221	+	13.1610i	−1.54836	+	0.454638i
$839$	−0.901661	−	6.27119i	−0.0311288	−	0.216506i	0.968320	−	0.249714i	$-0.0803366\pi$
$839$	−0.901661	−	6.27119i	−0.0311288	−	0.216506i	−0.999448	+	0.0332084i	$0.989427\pi$
$840$	1.98674	+	2.29282i	0.0685492	+	0.0791100i
$841$	−17.5611			−0.605555
$842$	−19.4921			−0.671743
$843$	0.111374	+	0.128533i	0.00383593	+	0.00442690i
$844$	0.546477	−	1.19662i	0.0188105	−	0.0411893i
$845$	29.3492	−	18.8616i	1.00964	−	0.648859i
$846$	23.4347	−	27.0451i	0.805701	−	0.929829i
$847$	−16.9671	+	10.9041i	−0.582997	+	0.374670i
$848$	−4.26100	+	29.6359i	−0.146323	+	1.01770i
$849$	0.163148	+	1.13472i	0.00559922	+	0.0389434i
$850$	2.14490	−	4.69668i	0.0735695	−	0.161095i
$851$	−2.19940	+	15.2972i	−0.0753945	+	0.524380i
$852$	0.713633	−	0.209542i	0.0244487	−	0.00717878i
$853$	−21.8926	−	14.0695i	−0.749589	−	0.481731i	0.109227	−	0.994017i	$-0.465163\pi$
$853$	−21.8926	−	14.0695i	−0.749589	−	0.481731i	−0.858815	+	0.512286i	$0.828799\pi$
$854$	9.19568	−	5.90971i	0.314670	−	0.202226i
$855$	10.5157	+	23.0261i	0.359629	+	0.787477i
$856$	48.8938	−	14.3565i	1.67116	−	0.490696i
$857$	−11.3922	−	7.32133i	−0.389151	−	0.250092i	0.331406	−	0.943488i	$-0.392477\pi$
$857$	−11.3922	−	7.32133i	−0.389151	−	0.250092i	−0.720556	+	0.693396i	$0.756113\pi$
$858$	2.11409	−	2.43980i	0.0721740	−	0.0832932i
$859$	−24.4804	+	28.2519i	−0.835262	+	0.963943i	−0.999748	−	0.0224360i	$-0.992858\pi$
$859$	−24.4804	+	28.2519i	−0.835262	+	0.963943i	0.164487	+	0.986379i	$0.447403\pi$
$860$	1.71486	+	3.75502i	0.0584762	+	0.128045i
$861$	−0.151288	−	1.05223i	−0.00515588	−	0.0358599i
$862$	12.4362	+	3.65161i	0.423580	+	0.124374i
$863$	36.8427	+	42.5187i	1.25414	+	1.44735i	0.844898	+	0.534928i	$0.179661\pi$
$863$	36.8427	+	42.5187i	1.25414	+	1.44735i	0.409242	+	0.912426i	$0.365793\pi$
$864$	1.80248	+	0.529255i	0.0613215	+	0.0180056i
$865$	13.3947	−	29.3303i	0.455433	−	0.997260i
$866$	−3.15793	−	6.91490i	−0.107311	−	0.234978i
$867$	2.33610	+	1.50132i	0.0793381	+	0.0509875i
$868$	−0.828108	+	5.75961i	−0.0281078	+	0.195494i
$869$	−5.16755	−	1.51733i	−0.175297	−	0.0514719i
$870$	−1.43480			−0.0486443
$871$	43.5371	+	19.9836i	1.47520	+	0.677117i
$872$	23.9210			0.810066
$873$	22.7489	+	6.67968i	0.769933	+	0.226073i
$874$	−2.08491	+	14.5009i	−0.0705231	+	0.490499i
$875$	−31.5796	−	20.2950i	−1.06759	−	0.686096i
$876$	−0.295640	−	0.647361i	−0.00998875	−	0.0218723i
$877$	1.27311	−	2.78772i	0.0429899	−	0.0941347i	−0.886919	−	0.461926i	$-0.847159\pi$
$877$	1.27311	−	2.78772i	0.0429899	−	0.0941347i	0.929908	+	0.367791i	$0.119886\pi$
$878$	−6.98052	−	2.04966i	−0.235581	−	0.0691728i
$879$	−1.40140	−	1.61730i	−0.0472681	−	0.0545503i
$880$	−11.2634	−	3.30723i	−0.379689	−	0.111487i
$881$	3.46473	+	24.0977i	0.116730	+	0.811873i	0.961117	+	0.276141i	$0.0890555\pi$
$881$	3.46473	+	24.0977i	0.116730	+	0.811873i	−0.844388	+	0.535733i	$0.820035\pi$
$882$	4.50840	+	9.87201i	0.151806	+	0.332408i
$883$	−9.38048	+	10.8257i	−0.315678	+	0.364312i	−0.891308	−	0.453398i	$-0.850212\pi$
$883$	−9.38048	+	10.8257i	−0.315678	+	0.364312i	0.575630	+	0.817710i	$0.304757\pi$
$884$	1.86580	−	2.15325i	0.0627536	−	0.0724215i
$885$	−0.891359	−	0.572841i	−0.0299627	−	0.0192559i
$886$	23.0348	−	6.76364i	0.773871	−	0.227229i
$887$	−7.40661	−	16.2182i	−0.248690	−	0.544554i	0.743581	−	0.668646i	$-0.233126\pi$
$887$	−7.40661	−	16.2182i	−0.248690	−	0.544554i	−0.992271	+	0.124091i	$0.960398\pi$
$888$	−3.57327	+	2.29640i	−0.119911	+	0.0770622i
$889$	13.0235	+	8.36968i	0.436793	+	0.280710i
$890$	18.3856	−	5.39849i	0.616286	−	0.180958i
$891$	2.62817	−	18.2793i	0.0880470	−	0.612380i
$892$	−1.12857	+	2.47123i	−0.0377873	+	0.0827427i
$893$	−6.83832	−	47.5616i	−0.228836	−	1.59159i
$894$	0.810356	−	5.63615i	0.0271024	−	0.188501i
$895$	−9.63524	+	6.19219i	−0.322071	+	0.206982i
$896$	17.0545	−	19.6820i	0.569751	−	0.657528i
$897$	−2.08658	+	1.34097i	−0.0696690	+	0.0447735i
$898$	−20.6954	+	45.3167i	−0.690616	+	1.51224i
$899$	−14.4650	−	16.6935i	−0.482436	−	0.556761i
$900$	−1.94257			−0.0647524
$901$	−15.2880			−0.509317
$902$	3.15139	+	3.63690i	0.104930	+	0.121095i
$903$	−0.776490	−	5.40061i	−0.0258400	−	0.179721i
$904$	−46.3015	+	13.5953i	−1.53996	+	0.452174i
$905$	−34.5676	+	10.1500i	−1.14907	+	0.337396i
$906$	0.00290580	+	0.0202103i	9.65387e−5	+	0.000671441i
$907$	12.0668	+	13.9258i	0.400670	+	0.462398i	0.919852	−	0.392266i	$-0.128309\pi$
$907$	12.0668	+	13.9258i	0.400670	+	0.462398i	−0.519182	+	0.854664i	$0.673763\pi$
$908$	3.70437			0.122934
$909$	35.7024			1.18417
$910$	25.7948	+	29.7688i	0.855089	+	0.986826i
$911$	−2.23950	+	4.90382i	−0.0741979	+	0.162471i	−0.943096	−	0.332520i	$-0.892101\pi$
$911$	−2.23950	+	4.90382i	−0.0741979	+	0.162471i	0.868898	+	0.494990i	$0.164828\pi$
$912$	−2.89524	+	1.86066i	−0.0958709	+	0.0616125i
$913$	8.61155	−	9.93826i	0.285001	−	0.328908i
$914$	38.7531	−	24.9051i	1.28184	−	0.823787i
$915$	−0.122905	+	0.854825i	−0.00406312	+	0.0282596i
$916$	−0.718492	−	4.99722i	−0.0237397	−	0.165113i
$917$	16.1191	−	35.2959i	0.532299	−	1.16557i
$918$	0.374958	−	2.60789i	0.0123755	−	0.0860732i
$919$	9.72917	−	2.85674i	0.320936	−	0.0942352i	−0.117297	−	0.993097i	$-0.537423\pi$
$919$	9.72917	−	2.85674i	0.320936	−	0.0942352i	0.438232	+	0.898862i	$0.355605\pi$
$920$	8.87670	+	5.70471i	0.292656	+	0.188079i
$921$	0.535992	−	0.344461i	0.0176615	−	0.0113504i
$922$	−13.2592	−	29.0337i	−0.436670	−	0.956174i
$923$	74.3705	−	21.8372i	2.44794	−	0.718779i
$924$	−0.315678	−	0.202874i	−0.0103850	−	0.00667407i
$925$	10.8595	−	12.5325i	0.357058	−	0.412067i
$926$	24.8332	−	28.6591i	0.816070	−	0.941795i
$927$	12.8763	+	28.1951i	0.422912	+	0.926049i
$928$	−0.768803	−	5.34714i	−0.0252372	−	0.175528i
$929$	52.2858	+	15.3525i	1.71544	+	0.503699i	0.983994	−	0.178201i	$-0.0570276\pi$
$929$	52.2858	+	15.3525i	1.71544	+	0.503699i	0.731446	+	0.681899i	$0.238846\pi$
$930$	1.81437	+	2.09390i	0.0594956	+	0.0686616i
$931$	13.9821	+	4.10550i	0.458243	+	0.134552i
$932$	−0.0383621	+	0.0840012i	−0.00125659	+	0.00275155i
$933$	2.23796	+	4.90046i	0.0732676	+	0.160434i
$934$	37.1436	+	23.8708i	1.21538	+	0.781075i
$935$	0.853035	−	5.93299i	0.0278972	−	0.194029i
$936$	49.7534	+	14.6089i	1.62624	+	0.477507i
$937$	−19.5488			−0.638631			−0.319316	−	0.947648i	$-0.603453\pi$
$937$	−19.5488			−0.638631			−0.319316	+	0.947648i	$0.603453\pi$
$938$	−9.51598	+	32.1804i	−0.310708	+	1.05073i
$939$	3.09667			0.101056
$940$	−4.13708	−	1.21476i	−0.134937	−	0.0396209i
$941$	−5.19809	+	36.1535i	−0.169453	+	1.17857i	0.710566	+	0.703631i	$0.248439\pi$
$941$	−5.19809	+	36.1535i	−0.169453	+	1.17857i	−0.880019	+	0.474939i	$0.842470\pi$
$942$	2.93519	+	1.88633i	0.0956338	+	0.0614601i
$943$	−1.53592	−	3.36319i	−0.0500164	−	0.109521i
$944$	−4.55194	+	9.96737i	−0.148153	+	0.324410i
$945$	−5.79915	−	1.70278i	−0.188646	−	0.0553916i
$946$	16.1746	+	18.6665i	0.525882	+	0.606900i
$947$	0.362705	+	0.106500i	0.0117863	+	0.00346078i	0.287620	−	0.957744i	$-0.407136\pi$
$947$	0.362705	+	0.106500i	0.0117863	+	0.00346078i	−0.275834	+	0.961205i	$0.588954\pi$
$948$	0.0201639	+	0.140243i	0.000654894	+	0.00455489i
$949$	−30.8098	−	67.4641i	−1.00013	−	2.18998i
$950$	10.2942	−	11.8801i	0.333988	−	0.385443i
$951$	0.0629350	−	0.0726309i	0.00204081	−	0.00235522i
$952$	13.4772	+	8.66124i	0.436797	+	0.280712i
$953$	−39.7100	+	11.6599i	−1.28633	+	0.377702i	−0.852233	−	0.523163i	$-0.824752\pi$
$953$	−39.7100	+	11.6599i	−1.28633	+	0.377702i	−0.434101	+	0.900864i	$0.642934\pi$
$954$	−14.4000	−	31.5316i	−0.466217	−	1.02087i
$955$	22.8435	−	14.6806i	0.739197	−	0.475053i
$956$	−1.99392	−	1.28141i	−0.0644879	−	0.0414439i
$957$	1.36676	−	0.401318i	0.0441812	−	0.0129728i
$958$	−1.16467	+	8.10047i	−0.0376289	+	0.261714i
$959$	2.37726	−	5.20547i	0.0767656	−	0.168093i
$960$	0.405255	+	2.81861i	0.0130796	+	0.0909703i
$961$	−1.65850	+	11.5351i	−0.0534999	+	0.372100i
$962$	−46.3934	+	29.8152i	−1.49578	+	0.961282i
$963$	−33.0229	+	38.1105i	−1.06415	+	1.22809i
$964$	−7.00226	+	4.50008i	−0.225527	+	0.144938i
$965$	4.84291	−	10.6045i	0.155899	−	0.341370i
$966$	−1.13783	−	1.31313i	−0.0366091	−	0.0422491i
$967$	38.5742			1.24046			0.620232	−	0.784418i	$-0.287038\pi$
$967$	38.5742			1.24046			0.620232	+	0.784418i	$0.287038\pi$
$968$	−19.2796			−0.619670
$969$	−1.15079	−	1.32808i	−0.0369686	−	0.0426641i
$970$	2.45012	+	17.0410i	0.0786687	+	0.547153i
$971$	−27.3954	+	8.04401i	−0.879160	+	0.258145i	−0.690007	−	0.723803i	$-0.742392\pi$
$971$	−27.3954	+	8.04401i	−0.879160	+	0.258145i	−0.189153	+	0.981948i	$0.560574\pi$
$972$	−1.42976	+	0.419814i	−0.0458594	+	0.0134655i
$973$	−0.220288	−	1.53214i	−0.00706211	−	0.0491181i
$974$	−27.2901	−	31.4945i	−0.874432	−	1.00915i
$975$	2.66143			0.0852341
$976$	8.93119			0.285881
$977$	22.3001	+	25.7356i	0.713442	+	0.823356i	0.990502	−	0.137497i	$-0.0439056\pi$
$977$	22.3001	+	25.7356i	0.713442	+	0.823356i	−0.277060	+	0.960853i	$0.589360\pi$
$978$	−0.277848	+	0.608402i	−0.00888460	+	0.0194546i
$979$	−16.0038	+	10.2850i	−0.511483	+	0.328710i
$980$	0.856309	−	0.988233i	0.0273538	−	0.0315680i
$981$	−19.9141	+	12.7980i	−0.635807	+	0.408608i
$982$	2.37950	−	16.5498i	0.0759329	−	0.528125i
$983$	3.81929	+	26.5638i	0.121817	+	0.847253i	0.955496	+	0.295004i	$0.0953210\pi$
$983$	3.81929	+	26.5638i	0.121817	+	0.847253i	−0.833679	+	0.552249i	$0.813770\pi$
$984$	0.422137	−	0.924351i	0.0134572	−	0.0294672i
$985$	2.01937	−	14.0450i	0.0643424	−	0.447511i
$986$	−7.26962	+	2.13455i	−0.231512	+	0.0679780i
$987$	4.79422	+	3.08106i	0.152602	+	0.0980711i
$988$	7.29728	−	4.68968i	0.232157	−	0.149199i
$989$	−7.88315	−	17.2617i	−0.250670	−	0.548890i
$990$	13.0403	−	3.82898i	0.414448	−	0.121693i
$991$	−40.4513	−	25.9964i	−1.28498	−	0.825804i	−0.293484	−	0.955964i	$-0.594815\pi$
$991$	−40.4513	−	25.9964i	−1.28498	−	0.825804i	−0.991493	+	0.130160i	$0.958451\pi$
$992$	−6.83124	+	7.88368i	−0.216892	+	0.250307i
$993$	4.04102	−	4.66358i	0.128238	−	0.147994i
$994$	22.5560	+	49.3906i	0.715431	+	1.56658i
$995$	−0.0871613	−	0.606220i	−0.00276320	−	0.0192185i
$996$	−0.331938	−	0.0974657i	−0.0105179	−	0.00308832i
$997$	−6.28413	−	7.25228i	−0.199020	−	0.229682i	0.647463	−	0.762097i	$-0.275830\pi$
$997$	−6.28413	−	7.25228i	−0.199020	−	0.229682i	−0.846483	+	0.532415i	$0.821285\pi$
$998$	−16.6900	−	4.90062i	−0.528312	−	0.155127i
$999$	3.51521	−	7.69723i	0.111216	−	0.243530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.2.e.c.64.2	yes	20
3.2	odd	2		603.2.u.c.64.1		20
67.22	even	11	inner	67.2.e.c.22.2	✓	20
67.25	even	11		4489.2.a.l.1.3		10
67.42	odd	22		4489.2.a.m.1.8		10
201.89	odd	22		603.2.u.c.424.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.c.22.2	✓	20	67.22	even	11	inner
67.2.e.c.64.2	yes	20	1.1	even	1	trivial
603.2.u.c.64.1		20	3.2	odd	2
603.2.u.c.424.1		20	201.89	odd	22
4489.2.a.l.1.3		10	67.25	even	11
4489.2.a.m.1.8		10	67.42	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:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	67.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25667 + 0.368991i) q^{2} +(0.0280790 - 0.195293i) q^{3} +(-0.239446 - 0.153882i) q^{4} +(0.681980 + 1.49333i) q^{5} +(0.107348 - 0.235058i) q^{6} +(-3.00345 - 0.881891i) q^{7} +(-1.95949 - 2.26138i) q^{8} +(2.84113 + 0.834230i) q^{9} +O(q^{10})\)	\(q+(1.25667 + 0.368991i) q^{2} +(0.0280790 - 0.195293i) q^{3} +(-0.239446 - 0.153882i) q^{4} +(0.681980 + 1.49333i) q^{5} +(0.107348 - 0.235058i) q^{6} +(-3.00345 - 0.881891i) q^{7} +(-1.95949 - 2.26138i) q^{8} +(2.84113 + 0.834230i) q^{9} +(0.305998 + 2.12826i) q^{10} +(-0.886770 - 1.94175i) q^{11} +(-0.0367756 + 0.0424413i) q^{12} +(-3.83253 + 4.42298i) q^{13} +(-3.44893 - 2.21649i) q^{14} +(0.310786 - 0.0912551i) q^{15} +(-1.39153 - 3.04702i) q^{16} +(1.43888 - 0.924714i) q^{17} +(3.26253 + 2.09670i) q^{18} +(4.99642 - 1.46708i) q^{19} +(0.0664997 - 0.462516i) q^{20} +(-0.256561 + 0.561791i) q^{21} +(-0.397885 - 2.76735i) q^{22} +(-0.305697 + 2.12617i) q^{23} +(-0.496652 + 0.319179i) q^{24} +(1.50937 - 1.74191i) q^{25} +(-6.44826 + 4.14405i) q^{26} +(0.488582 - 1.06985i) q^{27} +(0.583455 + 0.673342i) q^{28} -3.38215 q^{29} +0.424228 q^{30} +(4.27688 + 4.93579i) q^{31} +(0.227312 + 1.58099i) q^{32} +(-0.404112 + 0.118658i) q^{33} +(2.14941 - 0.631124i) q^{34} +(-0.731337 - 5.08656i) q^{35} +(-0.551923 - 0.636953i) q^{36} +7.19471 q^{37} +6.82018 q^{38} +(0.756165 + 0.872661i) q^{39} +(2.04064 - 4.46838i) q^{40} +(-1.44801 + 0.930581i) q^{41} +(-0.529708 + 0.611316i) q^{42} +(-7.43197 + 4.77624i) q^{43} +(-0.0864687 + 0.601403i) q^{44} +(0.691813 + 4.81166i) q^{45} +(-1.16870 + 2.55909i) q^{46} +(1.31320 - 9.13354i) q^{47} +(-0.634135 + 0.186199i) q^{48} +(2.35418 + 1.51294i) q^{49} +(2.53953 - 1.63206i) q^{50} +(-0.140188 - 0.306969i) q^{51} +(1.59830 - 0.469304i) q^{52} +(-7.51933 - 4.83238i) q^{53} +(1.00875 - 1.16416i) q^{54} +(2.29492 - 2.64848i) q^{55} +(3.89094 + 8.51998i) q^{56} +(-0.146217 - 1.01696i) q^{57} +(-4.25024 - 1.24798i) q^{58} +(-2.14217 - 2.47220i) q^{59} +(-0.0884590 - 0.0259739i) q^{60} +(-1.10760 + 2.42530i) q^{61} +(3.55336 + 7.78078i) q^{62} +(-7.79747 - 5.01113i) q^{63} +(-1.25115 + 8.70192i) q^{64} +(-9.21867 - 2.70684i) q^{65} -0.551618 q^{66} +(-2.29104 - 7.85819i) q^{67} -0.486831 q^{68} +(0.406643 + 0.119401i) q^{69} +(0.957847 - 6.66198i) q^{70} +(-11.1416 - 7.16030i) q^{71} +(-3.68066 - 8.05953i) q^{72} +(-5.26444 + 11.5275i) q^{73} +(9.04137 + 2.65479i) q^{74} +(-0.297802 - 0.343682i) q^{75} +(-1.42213 - 0.417575i) q^{76} +(0.950948 + 6.61399i) q^{77} +(0.628245 + 1.37566i) q^{78} +(1.65220 - 1.90674i) q^{79} +(3.60120 - 4.15601i) q^{80} +(7.27782 + 4.67717i) q^{81} +(-2.16305 + 0.635128i) q^{82} +(2.55909 + 5.60363i) q^{83} +(0.147882 - 0.0950381i) q^{84} +(2.36219 + 1.51809i) q^{85} +(-11.1019 + 3.25981i) q^{86} +(-0.0949671 + 0.660511i) q^{87} +(-2.65342 + 5.81017i) q^{88} +(-1.26829 - 8.82113i) q^{89} +(-0.906082 + 6.30194i) q^{90} +(15.4114 - 9.90430i) q^{91} +(0.400378 - 0.462060i) q^{92} +(1.08402 - 0.696656i) q^{93} +(5.02046 - 10.9933i) q^{94} +(5.59829 + 6.46077i) q^{95} +0.315140 q^{96} +8.00699 q^{97} +(2.40016 + 2.76993i) q^{98} +(-0.899555 - 6.25654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9	\( 20 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + q^{5} + 3 q^{6} - 8 q^{7} - 22 q^{8} + 10 q^{9} - 9 q^{10} + 3 q^{12} + 12 q^{13} + 6 q^{14} - 11 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 4 q^{19} + 2 q^{20} - 53 q^{21} + 2 q^{23} + 11 q^{24} - 3 q^{25} - 31 q^{26} + 47 q^{27} - 5 q^{28} - 6 q^{29} + 44 q^{30} + 16 q^{32} + q^{33} - 8 q^{34} + 34 q^{35} + 9 q^{36} + 24 q^{37} - 14 q^{38} - 22 q^{39} - 11 q^{40} - 6 q^{41} + 59 q^{42} - 22 q^{43} - 22 q^{44} - 46 q^{45} + 15 q^{46} + 16 q^{47} + 5 q^{48} + 42 q^{49} - 17 q^{50} + 22 q^{51} + 2 q^{52} - q^{53} - 60 q^{54} + 20 q^{55} + 11 q^{56} - 52 q^{57} + 10 q^{58} - 26 q^{59} + 44 q^{60} - 26 q^{61} + 11 q^{62} - 42 q^{63} - 6 q^{64} + 9 q^{65} + 2 q^{66} - 22 q^{67} - 52 q^{68} + 62 q^{69} - 42 q^{70} + 20 q^{71} + 11 q^{72} - 55 q^{73} + 37 q^{74} - 70 q^{75} - 3 q^{76} - 70 q^{77} + 22 q^{78} - 34 q^{79} + 40 q^{80} + 42 q^{81} - 12 q^{82} + 56 q^{83} - 29 q^{84} + 41 q^{85} - 33 q^{86} - 10 q^{87} + 11 q^{88} - 3 q^{89} + 18 q^{90} + 12 q^{91} - 18 q^{92} - 69 q^{93} + 32 q^{94} + 74 q^{95} - 12 q^{96} - 14 q^{97} + 95 q^{98} + 81 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + q^5 + 3 * q^6 - 8 * q^7 - 22 * q^8 + 10 * q^9 - 9 * q^10 + 3 * q^12 + 12 * q^13 + 6 * q^14 - 11 * q^15 + 8 * q^16 - 4 * q^17 - 2 * q^18 + 4 * q^19 + 2 * q^20 - 53 * q^21 + 2 * q^23 + 11 * q^24 - 3 * q^25 - 31 * q^26 + 47 * q^27 - 5 * q^28 - 6 * q^29 + 44 * q^30 + 16 * q^32 + q^33 - 8 * q^34 + 34 * q^35 + 9 * q^36 + 24 * q^37 - 14 * q^38 - 22 * q^39 - 11 * q^40 - 6 * q^41 + 59 * q^42 - 22 * q^43 - 22 * q^44 - 46 * q^45 + 15 * q^46 + 16 * q^47 + 5 * q^48 + 42 * q^49 - 17 * q^50 + 22 * q^51 + 2 * q^52 - q^53 - 60 * q^54 + 20 * q^55 + 11 * q^56 - 52 * q^57 + 10 * q^58 - 26 * q^59 + 44 * q^60 - 26 * q^61 + 11 * q^62 - 42 * q^63 - 6 * q^64 + 9 * q^65 + 2 * q^66 - 22 * q^67 - 52 * q^68 + 62 * q^69 - 42 * q^70 + 20 * q^71 + 11 * q^72 - 55 * q^73 + 37 * q^74 - 70 * q^75 - 3 * q^76 - 70 * q^77 + 22 * q^78 - 34 * q^79 + 40 * q^80 + 42 * q^81 - 12 * q^82 + 56 * q^83 - 29 * q^84 + 41 * q^85 - 33 * q^86 - 10 * q^87 + 11 * q^88 - 3 * q^89 + 18 * q^90 + 12 * q^91 - 18 * q^92 - 69 * q^93 + 32 * q^94 + 74 * q^95 - 12 * q^96 - 14 * q^97 + 95 * q^98 + 81 * q^99

Introduction

L-functions

Modular forms

Varieties

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