LMFDB - Embedded newform 69.2.e.c.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.1
Root			$-0.591994 - 0.380451i$ of defining polynomial
Character	$\chi$	$=$	69.16
Dual form			69.2.e.c.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37624 + 1.58827i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.343924 - 2.39205i) q^{4} +(1.43308 + 3.13801i) q^{5} +(-0.299086 + 2.08019i) q^{6} +(-1.51768 + 0.445631i) q^{7} +(0.736612 + 0.473392i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.37624 + 1.58827i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.343924 - 2.39205i) q^{4} +(1.43308 + 3.13801i) q^{5} +(-0.299086 + 2.08019i) q^{6} +(-1.51768 + 0.445631i) q^{7} +(0.736612 + 0.473392i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-6.95628 - 2.04255i) q^{10} +(-0.903570 - 1.04278i) q^{11} +(-1.58257 - 1.82638i) q^{12} +(4.36913 + 1.28289i) q^{13} +(1.38092 - 3.02378i) q^{14} +(2.90212 + 1.86508i) q^{15} +(2.87188 - 0.843259i) q^{16} +(0.575735 - 4.00433i) q^{17} +(0.873028 + 1.91167i) q^{18} +(-0.869183 - 6.04530i) q^{19} +(7.01340 - 4.50724i) q^{20} +(-1.03583 + 1.19541i) q^{21} +2.89974 q^{22} +(-3.84094 + 2.87179i) q^{23} +0.875613 q^{24} +(-4.51910 + 5.21532i) q^{25} +(-8.05057 + 5.17378i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.58794 + 3.47710i) q^{28} +(1.43619 - 9.98890i) q^{29} +(-6.95628 + 2.04255i) q^{30} +(0.956733 + 0.614855i) q^{31} +(-3.34056 + 7.31481i) q^{32} +(-1.32390 - 0.388732i) q^{33} +(5.56760 + 6.42535i) q^{34} +(-3.57336 - 4.12388i) q^{35} +(-2.31875 - 0.680847i) q^{36} +(-3.43311 + 7.51746i) q^{37} +(10.7978 + 6.93931i) q^{38} +(4.36913 - 1.28289i) q^{39} +(-0.429884 + 2.98991i) q^{40} +(2.03647 + 4.45925i) q^{41} +(-0.473080 - 3.29035i) q^{42} +(-2.41809 + 1.55401i) q^{43} +(-2.18361 + 2.52002i) q^{44} +3.44976 q^{45} +(0.724889 - 10.0527i) q^{46} +4.66656 q^{47} +(1.96008 - 2.26205i) q^{48} +(-3.78401 + 2.43183i) q^{49} +(-2.06395 - 14.3551i) q^{50} +(-1.68056 - 3.67992i) q^{51} +(1.56609 - 10.8924i) q^{52} +(-6.27174 + 1.84155i) q^{53} +(1.76796 + 1.13620i) q^{54} +(1.97735 - 4.32980i) q^{55} +(-1.32890 - 0.390200i) q^{56} +(-3.99954 - 4.61571i) q^{57} +(13.8885 + 16.0282i) q^{58} +(-0.908902 - 0.266878i) q^{59} +(3.46325 - 7.58346i) q^{60} +(0.641360 + 0.412177i) q^{61} +(-2.29325 + 0.673360i) q^{62} +(-0.225107 + 1.56565i) q^{63} +(-4.53369 - 9.92740i) q^{64} +(2.23559 + 15.5489i) q^{65} +(2.43942 - 1.56772i) q^{66} +(1.82896 - 2.11073i) q^{67} -9.77655 q^{68} +(-1.67860 + 4.49247i) q^{69} +11.4676 q^{70} +(3.71613 - 4.28865i) q^{71} +(0.736612 - 0.473392i) q^{72} +(-0.129513 - 0.900780i) q^{73} +(-7.21496 - 15.7986i) q^{74} +(-0.982094 + 6.83061i) q^{75} +(-14.1617 + 4.15825i) q^{76} +(1.83602 + 1.17994i) q^{77} +(-3.97541 + 8.70493i) q^{78} +(-9.35234 - 2.74609i) q^{79} +(6.76179 + 7.80352i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-9.88516 - 2.90255i) q^{82} +(-2.01659 + 4.41571i) q^{83} +(3.21572 + 2.06662i) q^{84} +(13.3907 - 3.93187i) q^{85} +(0.859691 - 5.97928i) q^{86} +(-4.19221 - 9.17966i) q^{87} +(-0.171939 - 1.19586i) q^{88} +(-3.08440 + 1.98222i) q^{89} +(-4.74771 + 5.47915i) q^{90} -7.20264 q^{91} +(8.19045 + 8.20003i) q^{92} +1.13727 q^{93} +(-6.42232 + 7.41176i) q^{94} +(17.7246 - 11.3909i) q^{95} +(1.14443 + 7.95966i) q^{96} +(-0.708736 - 1.55192i) q^{97} +(1.34531 - 9.35682i) q^{98} +(-1.32390 + 0.388732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.37624	+	1.58827i	−0.973151	+	1.12308i	0.0192234	+	0.999815i	$0.493881\pi$
$2$	−1.37624	+	1.58827i	−0.973151	+	1.12308i	−0.992374	+	0.123261i	$0.960665\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	−0.343924	−	2.39205i	−0.171962	−	1.19602i
$5$	1.43308	+	3.13801i	0.640894	+	1.40336i	0.899303	+	0.437326i	$0.144075\pi$
$5$	1.43308	+	3.13801i	0.640894	+	1.40336i	−0.258409	+	0.966036i	$0.583198\pi$
$6$	−0.299086	+	2.08019i	−0.122101	+	0.849234i
$7$	−1.51768	+	0.445631i	−0.573629	+	0.168433i	−0.555666	−	0.831406i	$-0.687537\pi$
$7$	−1.51768	+	0.445631i	−0.573629	+	0.168433i	−0.0179637	+	0.999839i	$0.505718\pi$
$8$	0.736612	+	0.473392i	0.260432	+	0.167369i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−6.95628	−	2.04255i	−2.19977	−	0.645910i
$11$	−0.903570	−	1.04278i	−0.272437	−	0.314409i	0.603000	−	0.797741i	$-0.293972\pi$
$11$	−0.903570	−	1.04278i	−0.272437	−	0.314409i	−0.875437	+	0.483332i	$0.839426\pi$
$12$	−1.58257	−	1.82638i	−0.456847	−	0.527230i
$13$	4.36913	+	1.28289i	1.21178	+	0.355810i	0.824345	−	0.566087i	$-0.191543\pi$
$13$	4.36913	+	1.28289i	1.21178	+	0.355810i	0.387434	+	0.921898i	$0.373362\pi$
$14$	1.38092	−	3.02378i	0.369065	−	0.808140i
$15$	2.90212	+	1.86508i	0.749325	+	0.481562i
$16$	2.87188	−	0.843259i	0.717969	−	0.210815i
$17$	0.575735	−	4.00433i	0.139636	−	0.971192i	−0.792703	−	0.609608i	$-0.791327\pi$
$17$	0.575735	−	4.00433i	0.139636	−	0.971192i	0.932340	−	0.361584i	$-0.117764\pi$
$18$	0.873028	+	1.91167i	0.205775	+	0.450584i
$19$	−0.869183	−	6.04530i	−0.199404	−	1.38689i	−0.806018	−	0.591891i	$-0.798382\pi$
$19$	−0.869183	−	6.04530i	−0.199404	−	1.38689i	0.606614	−	0.794996i	$-0.292527\pi$
$20$	7.01340	−	4.50724i	1.56824	−	1.00785i
$21$	−1.03583	+	1.19541i	−0.226036	+	0.260860i
$22$	2.89974			0.618227
$23$	−3.84094	+	2.87179i	−0.800891	+	0.598810i
$23$	−3.84094	+	2.87179i	−0.800891	+	0.598810i
$24$	0.875613			0.178734
$25$	−4.51910	+	5.21532i	−0.903819	+	1.04306i
$26$	−8.05057	+	5.17378i	−1.57885	+	1.01466i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	1.58794	+	3.47710i	0.300092	+	0.657110i
$29$	1.43619	−	9.98890i	0.266693	−	1.85489i	−0.212471	−	0.977167i	$-0.568151\pi$
$29$	1.43619	−	9.98890i	0.266693	−	1.85489i	0.479164	−	0.877725i	$-0.340940\pi$
$30$	−6.95628	+	2.04255i	−1.27004	+	0.372917i
$31$	0.956733	+	0.614855i	0.171834	+	0.110431i	0.623731	−	0.781639i	$-0.285616\pi$
$31$	0.956733	+	0.614855i	0.171834	+	0.110431i	−0.451897	+	0.892070i	$0.649252\pi$
$32$	−3.34056	+	7.31481i	−0.590534	+	1.29309i
$33$	−1.32390	−	0.388732i	−0.230461	−	0.0676695i
$34$	5.56760	+	6.42535i	0.954835	+	1.10194i
$35$	−3.57336	−	4.12388i	−0.604008	−	0.697062i
$36$	−2.31875	−	0.680847i	−0.386459	−	0.113475i
$37$	−3.43311	+	7.51746i	−0.564400	+	1.23586i	0.385326	+	0.922780i	$0.374089\pi$
$37$	−3.43311	+	7.51746i	−0.564400	+	1.23586i	−0.949726	+	0.313082i	$0.898638\pi$
$38$	10.7978	+	6.93931i	1.75163	+	1.12570i
$39$	4.36913	−	1.28289i	0.699621	−	0.205427i
$40$	−0.429884	+	2.98991i	−0.0679706	+	0.472746i
$41$	2.03647	+	4.45925i	0.318043	+	0.696417i	0.999367	−	0.0355645i	$-0.0113229\pi$
$41$	2.03647	+	4.45925i	0.318043	+	0.696417i	−0.681324	+	0.731982i	$0.738596\pi$
$42$	−0.473080	−	3.29035i	−0.0729979	−	0.507712i
$43$	−2.41809	+	1.55401i	−0.368755	+	0.236985i	−0.711874	−	0.702307i	$-0.752153\pi$
$43$	−2.41809	+	1.55401i	−0.368755	+	0.236985i	0.343118	+	0.939292i	$0.388517\pi$
$44$	−2.18361	+	2.52002i	−0.329191	+	0.379907i
$45$	3.44976			0.514260
$46$	0.724889	−	10.0527i	0.106879	−	1.48219i
$47$	4.66656			0.680688			0.340344	−	0.940301i	$-0.389456\pi$
$47$	4.66656			0.680688			0.340344	+	0.940301i	$0.389456\pi$
$48$	1.96008	−	2.26205i	0.282913	−	0.326498i
$49$	−3.78401	+	2.43183i	−0.540573	+	0.347405i
$50$	−2.06395	−	14.3551i	−0.291887	−	2.03012i
$51$	−1.68056	−	3.67992i	−0.235326	−	0.515292i
$52$	1.56609	−	10.8924i	0.217177	−	1.51050i
$53$	−6.27174	+	1.84155i	−0.861490	+	0.252956i	−0.682492	−	0.730893i	$-0.739104\pi$
$53$	−6.27174	+	1.84155i	−0.861490	+	0.252956i	−0.178998	+	0.983849i	$0.557286\pi$
$54$	1.76796	+	1.13620i	0.240589	+	0.154617i
$55$	1.97735	−	4.32980i	0.266626	−	0.583830i
$56$	−1.32890	−	0.390200i	−0.177582	−	0.0521427i
$57$	−3.99954	−	4.61571i	−0.529752	−	0.611366i
$58$	13.8885	+	16.0282i	1.82365	+	2.10461i
$59$	−0.908902	−	0.266878i	−0.118329	−	0.0347445i	0.222032	−	0.975039i	$-0.428731\pi$
$59$	−0.908902	−	0.266878i	−0.118329	−	0.0347445i	−0.340361	+	0.940295i	$0.610549\pi$
$60$	3.46325	−	7.58346i	0.447104	−	0.979021i
$61$	0.641360	+	0.412177i	0.0821177	+	0.0527739i	0.581055	−	0.813864i	$-0.302640\pi$
$61$	0.641360	+	0.412177i	0.0821177	+	0.0527739i	−0.498938	+	0.866638i	$0.666276\pi$
$62$	−2.29325	+	0.673360i	−0.291243	+	0.0855168i
$63$	−0.225107	+	1.56565i	−0.0283608	+	0.197254i
$64$	−4.53369	−	9.92740i	−0.566712	−	1.24093i
$65$	2.23559	+	15.5489i	0.277291	+	1.92860i
$66$	2.43942	−	1.56772i	0.300271	−	0.192973i
$67$	1.82896	−	2.11073i	0.223443	−	0.257867i	−0.632949	−	0.774194i	$-0.718156\pi$
$67$	1.82896	−	2.11073i	0.223443	−	0.257867i	0.856392	+	0.516327i	$0.172701\pi$
$68$	−9.77655			−1.18558
$69$	−1.67860	+	4.49247i	−0.202079	+	0.540830i
$70$	11.4676			1.37064
$71$	3.71613	−	4.28865i	0.441024	−	0.508969i	−0.491103	−	0.871102i	$-0.663406\pi$
$71$	3.71613	−	4.28865i	0.441024	−	0.508969i	0.932126	+	0.362133i	$0.117951\pi$
$72$	0.736612	−	0.473392i	0.0868106	−	0.0557898i
$73$	−0.129513	−	0.900780i	−0.0151583	−	0.105428i	0.980838	−	0.194827i	$-0.0624145\pi$
$73$	−0.129513	−	0.900780i	−0.0151583	−	0.105428i	−0.995996	+	0.0893987i	$0.971505\pi$
$74$	−7.21496	−	15.7986i	−0.838722	−	1.83654i
$75$	−0.982094	+	6.83061i	−0.113402	+	0.788731i
$76$	−14.1617	+	4.15825i	−1.62446	+	0.476984i
$77$	1.83602	+	1.17994i	0.209234	+	0.134467i
$78$	−3.97541	+	8.70493i	−0.450126	+	0.985639i
$79$	−9.35234	−	2.74609i	−1.05222	−	0.308960i	−0.290506	−	0.956873i	$-0.593824\pi$
$79$	−9.35234	−	2.74609i	−1.05222	−	0.308960i	−0.761714	+	0.647913i	$0.775642\pi$
$80$	6.76179	+	7.80352i	0.755991	+	0.872460i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−9.88516	−	2.90255i	−1.09163	−	0.320532i
$83$	−2.01659	+	4.41571i	−0.221349	+	0.484687i	−0.987430	−	0.158057i	$-0.949477\pi$
$83$	−2.01659	+	4.41571i	−0.221349	+	0.484687i	0.766081	+	0.642744i	$0.222204\pi$
$84$	3.21572	+	2.06662i	0.350864	+	0.225487i
$85$	13.3907	−	3.93187i	1.45243	−	0.426471i
$86$	0.859691	−	5.97928i	0.0927028	−	0.644762i
$87$	−4.19221	−	9.17966i	−0.449452	−	0.984163i
$88$	−0.171939	−	1.19586i	−0.0183288	−	0.127479i
$89$	−3.08440	+	1.98222i	−0.326946	+	0.210115i	−0.693808	−	0.720160i	$-0.744068\pi$
$89$	−3.08440	+	1.98222i	−0.326946	+	0.210115i	0.366862	+	0.930275i	$0.380432\pi$
$90$	−4.74771	+	5.47915i	−0.500453	+	0.577553i
$91$	−7.20264			−0.755042
$92$	8.19045	+	8.20003i	0.853914	+	0.854912i
$93$	1.13727			0.117929
$94$	−6.42232	+	7.41176i	−0.662412	+	0.764464i
$95$	17.7246	−	11.3909i	1.81851	−	1.16868i
$96$	1.14443	+	7.95966i	0.116802	+	0.812379i
$97$	−0.708736	−	1.55192i	−0.0719613	−	0.157573i	0.870233	−	0.492640i	$-0.163968\pi$
$97$	−0.708736	−	1.55192i	−0.0719613	−	0.157573i	−0.942194	+	0.335067i	$0.891241\pi$
$98$	1.34531	−	9.35682i	0.135897	−	0.945181i
$99$	−1.32390	+	0.388732i	−0.133057	+	0.0390690i
$100$	14.0295	+	9.01622i	1.40295	+	0.901622i
$101$	2.86027	−	6.26312i	0.284608	−	0.623204i	−0.712292	−	0.701883i	$-0.752343\pi$
$101$	2.86027	−	6.26312i	0.284608	−	0.623204i	0.996900	+	0.0786790i	$0.0250702\pi$
$102$	8.15757	+	2.39528i	0.807719	+	0.237168i
$103$	−0.188331	−	0.217346i	−0.0185569	−	0.0214158i	0.746395	−	0.665503i	$-0.231783\pi$
$103$	−0.188331	−	0.217346i	−0.0185569	−	0.0214158i	−0.764952	+	0.644087i	$0.777237\pi$
$104$	2.61104	+	3.01331i	0.256034	+	0.295479i
$105$	−5.23564	−	1.53732i	−0.510946	−	0.150027i
$106$	5.70656	−	12.4956i	0.554271	−	1.21368i
$107$	6.97450	+	4.48224i	0.674250	+	0.433314i	0.832455	−	0.554092i	$-0.186934\pi$
$107$	6.97450	+	4.48224i	0.674250	+	0.433314i	−0.158205	+	0.987406i	$0.550571\pi$
$108$	−2.31875	+	0.680847i	−0.223122	+	0.0655146i
$109$	−2.92433	+	20.3392i	−0.280100	+	1.94814i	0.0358379	+	0.999358i	$0.488590\pi$
$109$	−2.92433	+	20.3392i	−0.280100	+	1.94814i	−0.315938	+	0.948780i	$0.602319\pi$
$110$	4.15557	+	9.09942i	0.396218	+	0.867596i
$111$	1.17613	+	8.18017i	0.111633	+	0.776427i
$112$	−3.98281	+	2.55959i	−0.376340	+	0.241859i
$113$	1.06272	−	1.22644i	0.0999719	−	0.115374i	−0.703559	−	0.710637i	$-0.748407\pi$
$113$	1.06272	−	1.22644i	0.0999719	−	0.115374i	0.803531	+	0.595263i	$0.202952\pi$
$114$	12.8353			1.20214
$115$	−14.5161	−	7.93740i	−1.35363	−	0.740167i
$116$	−24.3879			−2.26436
$117$	2.98196	−	3.44137i	0.275683	−	0.318155i
$118$	1.67474	−	1.07629i	0.154173	−	0.0990807i
$119$	0.910671	+	6.33385i	0.0834810	+	0.580623i
$120$	1.25483	+	2.74768i	0.114549	+	0.250828i
$121$	1.29452	−	9.00360i	0.117684	−	0.818509i
$122$	−1.53732	+	0.451397i	−0.139182	+	0.0408675i
$123$	4.12404	+	2.65036i	0.371852	+	0.238975i
$124$	1.14172	−	2.50001i	0.102529	−	0.224508i
$125$	−6.29186	−	1.84746i	−0.562761	−	0.165242i
$126$	−2.17688	−	2.51225i	−0.193932	−	0.223809i
$127$	−6.34610	−	7.32379i	−0.563126	−	0.649882i	0.400765	−	0.916181i	$-0.368744\pi$
$127$	−6.34610	−	7.32379i	−0.563126	−	0.649882i	−0.963890	+	0.266299i	$0.914199\pi$
$128$	6.57531	+	1.93069i	0.581181	+	0.170650i
$129$	−1.19406	+	2.61464i	−0.105132	+	0.230206i
$130$	−27.7725	−	17.8483i	−2.43581	−	1.56540i
$131$	−10.9926	+	3.22771i	−0.960425	+	0.282006i	−0.724121	−	0.689673i	$-0.757754\pi$
$131$	−10.9926	+	3.22771i	−0.960425	+	0.282006i	−0.236304	+	0.971679i	$0.575936\pi$
$132$	−0.474543	+	3.30052i	−0.0413037	+	0.287273i
$133$	4.01312	+	8.78750i	0.347981	+	0.761973i
$134$	0.835317	+	5.80976i	0.0721604	+	0.501886i
$135$	2.90212	−	1.86508i	0.249775	−	0.160521i
$136$	2.31971	−	2.67709i	0.198913	−	0.229558i
$137$	1.64372			0.140433			0.0702163	−	0.997532i	$-0.477631\pi$
$137$	1.64372			0.140433			0.0702163	+	0.997532i	$0.477631\pi$
$138$	−4.82510	−	8.84880i	−0.410740	−	0.753260i
$139$	−5.57603			−0.472952			−0.236476	−	0.971637i	$-0.575993\pi$
$139$	−5.57603			−0.472952			−0.236476	+	0.971637i	$0.575993\pi$
$140$	−8.63554	+	9.96594i	−0.729836	+	0.842276i
$141$	3.92576	−	2.52293i	0.330609	−	0.212469i
$142$	1.69722	+	11.8044i	0.142428	+	0.990607i
$143$	−2.61005	−	5.71520i	−0.218263	−	0.477929i
$144$	0.425965	−	2.96265i	0.0354971	−	0.246888i
$145$	33.4035	−	9.80815i	2.77401	−	0.814522i
$146$	1.60892	+	1.03399i	0.133155	+	0.0855737i
$147$	−1.86856	+	4.09158i	−0.154116	+	0.337468i
$148$	19.1628	+	5.62672i	1.57518	+	0.462513i
$149$	−3.98279	−	4.59639i	−0.326283	−	0.376551i	0.568781	−	0.822489i	$-0.307415\pi$
$149$	−3.98279	−	4.59639i	−0.326283	−	0.376551i	−0.895063	+	0.445939i	$0.852870\pi$
$150$	−9.49725	−	10.9604i	−0.775447	−	0.894914i
$151$	22.7086	+	6.66784i	1.84800	+	0.542621i	0.999919	+	0.0127498i	$0.00405850\pi$
$151$	22.7086	+	6.66784i	1.84800	+	0.542621i	0.848078	+	0.529871i	$0.177760\pi$
$152$	2.22155	−	4.86451i	0.180191	−	0.394564i
$153$	−3.40329	−	2.18716i	−0.275140	−	0.176822i
$154$	−4.40088	+	1.29221i	−0.354633	+	0.104130i
$155$	−0.558345	+	3.88338i	−0.0448474	+	0.311920i
$156$	−4.57139	−	10.0099i	−0.366004	−	0.801437i
$157$	−2.21713	−	15.4205i	−0.176946	−	1.23069i	−0.863778	−	0.503872i	$-0.831908\pi$
$157$	−2.21713	−	15.4205i	−0.176946	−	1.23069i	0.686832	−	0.726816i	$-0.259001\pi$
$158$	17.2326	−	11.0747i	1.37095	−	0.881059i
$159$	−4.28051	+	4.93997i	−0.339466	+	0.391765i
$160$	−27.7413			−2.19314
$161$	4.54956	−	6.07010i	0.358555	−	0.478391i
$162$	2.10158			0.165116
$163$	4.03515	−	4.65682i	0.316058	−	0.364750i	−0.575386	−	0.817882i	$-0.695148\pi$
$163$	4.03515	−	4.65682i	0.316058	−	0.364750i	0.891443	+	0.453132i	$0.149693\pi$
$164$	9.96633	−	6.40497i	0.778240	−	0.500144i
$165$	−0.677411	−	4.71149i	−0.0527363	−	0.366789i
$166$	−4.23802	−	9.27997i	−0.328934	−	0.720265i
$167$	−1.34398	+	9.34759i	−0.104000	+	0.723338i	0.869380	+	0.494144i	$0.164518\pi$
$167$	−1.34398	+	9.34759i	−0.104000	+	0.723338i	−0.973381	+	0.229195i	$0.926391\pi$
$168$	−1.32890	+	0.390200i	−0.102527	+	0.0301046i
$169$	6.50719	+	4.18192i	0.500553	+	0.321686i
$170$	−12.1840	+	26.6792i	−0.934470	+	2.04620i
$171$	−5.86007	−	1.72067i	−0.448131	−	0.131583i
$172$	4.54891	+	5.24972i	0.346851	+	0.400288i
$173$	−4.64554	−	5.36123i	−0.353194	−	0.407607i	0.551154	−	0.834403i	$-0.314188\pi$
$173$	−4.64554	−	5.36123i	−0.353194	−	0.407607i	−0.904348	+	0.426796i	$0.859642\pi$
$174$	20.3493	+	5.97509i	1.54267	+	0.452970i
$175$	4.53444	−	9.92903i	0.342771	−	0.750564i
$176$	−3.47427	−	2.23278i	−0.261883	−	0.168302i
$177$	−0.908902	+	0.266878i	−0.0683172	+	0.0200597i
$178$	1.09658	−	7.62688i	0.0821921	−	0.571659i
$179$	3.33449	+	7.30152i	0.249232	+	0.545741i	0.992355	−	0.123413i	$-0.0393839\pi$
$179$	3.33449	+	7.30152i	0.249232	+	0.545741i	−0.743124	+	0.669154i	$0.766657\pi$
$180$	−1.18646	−	8.25199i	−0.0884333	−	0.615067i
$181$	−9.91759	+	6.37365i	−0.737169	+	0.473750i	−0.854571	−	0.519335i	$-0.826180\pi$
$181$	−9.91759	+	6.37365i	−0.737169	+	0.473750i	0.117402	+	0.993084i	$0.462543\pi$
$182$	9.91259	−	11.4397i	0.734770	−	0.847970i
$183$	0.762386			0.0563572
$184$	−4.18877	+	0.297127i	−0.308800	+	0.0219045i
$185$	−28.5098			−2.09608
$186$	−1.56516	+	1.80629i	−0.114763	+	0.132444i
$187$	−4.69583	+	3.01783i	−0.343393	+	0.220685i
$188$	−1.60494	−	11.1626i	−0.117053	−	0.814119i
$189$	0.657084	+	1.43881i	0.0477958	+	0.104658i
$190$	−6.30154	+	43.8282i	−0.457162	+	3.17963i
$191$	25.3783	−	7.45175i	1.83631	−	0.539190i	0.836353	−	0.548192i	$-0.184684\pi$
$191$	25.3783	−	7.45175i	1.83631	−	0.539190i	0.999959	+	0.00900195i	$0.00286545\pi$
$192$	−9.18114	−	5.90036i	−0.662592	−	0.425822i
$193$	7.83014	−	17.1456i	0.563626	−	1.23417i	−0.386497	−	0.922291i	$-0.626315\pi$
$193$	7.83014	−	17.1456i	0.563626	−	1.23417i	0.950122	−	0.311877i	$-0.100958\pi$
$194$	3.44025	+	1.01015i	0.246996	+	0.0725245i
$195$	10.2871	+	11.8719i	0.736672	+	0.850164i
$196$	7.11847	+	8.21516i	0.508462	+	0.586797i
$197$	−8.46097	−	2.48436i	−0.602819	−	0.177004i	−0.0339386	−	0.999424i	$-0.510805\pi$
$197$	−8.46097	−	2.48436i	−0.602819	−	0.177004i	−0.568880	+	0.822420i	$0.692623\pi$
$198$	1.20460	−	2.63770i	0.0856069	−	0.187453i
$199$	12.6239	+	8.11290i	0.894885	+	0.575108i	0.905269	−	0.424838i	$-0.139669\pi$
$199$	12.6239	+	8.11290i	0.894885	+	0.575108i	−0.0103839	+	0.999946i	$0.503305\pi$
$200$	−5.79771	+	1.70236i	−0.409960	+	0.120375i
$201$	0.397471	−	2.76447i	0.0280354	−	0.194991i
$202$	6.01110	+	13.1625i	0.422939	+	0.926108i
$203$	2.27169	+	15.8000i	0.159442	+	1.10894i
$204$	−8.22455	+	5.28560i	−0.575834	+	0.370066i
$205$	−11.0747	+	12.7809i	−0.773494	+	0.892659i
$206$	0.604394			0.0421101
$207$	1.01669	+	4.68683i	0.0706648	+	0.325757i
$208$	13.6294			0.945030
$209$	−5.51852	+	6.36871i	−0.381724	+	0.440533i
$210$	9.64719	−	6.19987i	0.665719	−	0.427832i
$211$	3.80345	+	26.4536i	0.261840	+	1.82114i	0.519005	+	0.854771i	$0.326303\pi$
$211$	3.80345	+	26.4536i	0.261840	+	1.82114i	−0.257164	+	0.966368i	$0.582788\pi$
$212$	6.56208	+	14.3689i	0.450685	+	0.986863i
$213$	0.807593	−	5.61693i	0.0553354	−	0.384866i
$214$	−16.7176	+	4.90873i	−1.14279	+	0.335554i
$215$	−8.34184	−	5.36097i	−0.568908	−	0.365615i
$216$	0.363743	−	0.796485i	0.0247496	−	0.0541940i
$217$	−1.72601	−	0.506803i	−0.117169	−	0.0344040i
$218$	−28.2795	−	32.6362i	−1.91533	−	2.21041i
$219$	−0.595951	−	0.687764i	−0.0402706	−	0.0464748i
$220$	−11.0371	−	3.24080i	−0.744123	−	0.218494i
$221$	7.65258	−	16.7568i	0.514768	−	1.12719i
$222$	−14.6109	−	9.38989i	−0.980623	−	0.630208i
$223$	−11.7966	+	3.46380i	−0.789960	+	0.231953i	−0.651734	−	0.758447i	$-0.725958\pi$
$223$	−11.7966	+	3.46380i	−0.789960	+	0.231953i	−0.138226	+	0.990401i	$0.544140\pi$
$224$	1.81020	−	12.5902i	0.120949	−	0.841219i
$225$	2.86672	+	6.27724i	0.191114	+	0.418482i
$226$	0.485361	+	3.37576i	0.0322857	+	0.224552i
$227$	−13.8661	+	8.91123i	−0.920328	+	0.591459i	−0.912753	−	0.408512i	$-0.866048\pi$
$227$	−13.8661	+	8.91123i	−0.920328	+	0.591459i	−0.00757515	+	0.999971i	$0.502411\pi$
$228$	−9.66547	+	11.1545i	−0.640111	+	0.738728i
$229$	−0.636413			−0.0420554			−0.0210277	−	0.999779i	$-0.506694\pi$
$229$	−0.636413			−0.0420554			−0.0210277	+	0.999779i	$0.506694\pi$
$230$	32.5844	−	12.1317i	2.14855	−	0.799939i
$231$	2.18249			0.143597
$232$	5.78658	−	6.67807i	0.379908	−	0.438437i
$233$	0.541416	−	0.347947i	0.0354693	−	0.0227947i	−0.522786	−	0.852464i	$-0.675107\pi$
$233$	0.541416	−	0.347947i	0.0354693	−	0.0227947i	0.558255	+	0.829669i	$0.311471\pi$
$234$	1.36191	+	9.47232i	0.0890311	+	0.619225i
$235$	6.68757	+	14.6437i	0.436249	+	0.955252i
$236$	−0.325790	+	2.26592i	−0.0212071	+	0.147499i
$237$	−9.35234	+	2.74609i	−0.607500	+	0.178378i
$238$	−11.3132	−	7.27053i	−0.733324	−	0.471279i
$239$	−4.00001	+	8.75880i	−0.258739	+	0.566560i	−0.993767	−	0.111477i	$-0.964442\pi$
$239$	−4.00001	+	8.75880i	−0.258739	+	0.566560i	0.735028	+	0.678037i	$0.237169\pi$
$240$	9.90728	+	2.90904i	0.639512	+	0.187778i
$241$	3.90622	+	4.50802i	0.251622	+	0.290387i	0.867482	−	0.497468i	$-0.165737\pi$
$241$	3.90622	+	4.50802i	0.251622	+	0.290387i	−0.615860	+	0.787855i	$0.711191\pi$
$242$	12.5186	+	14.4472i	0.804723	+	0.928700i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	0.765367	−	1.67592i	0.0489976	−	0.107290i
$245$	−13.0539	−	8.38925i	−0.833984	−	0.535969i
$246$	−9.88516	+	2.90255i	−0.630255	+	0.185060i
$247$	3.95790	−	27.5278i	0.251835	−	1.75155i
$248$	0.413674	+	0.905819i	0.0262683	+	0.0575196i
$249$	0.690851	+	4.80498i	0.0437809	+	0.304503i
$250$	11.5934	−	7.45062i	0.733230	−	0.471218i
$251$	2.52430	−	2.91320i	0.159332	−	0.183879i	−0.670470	−	0.741936i	$-0.733908\pi$
$251$	2.52430	−	2.91320i	0.159332	−	0.183879i	0.829803	+	0.558057i	$0.188453\pi$
$252$	3.82253			0.240797
$253$	6.46519	+	1.41037i	0.406463	+	0.0886693i
$254$	20.3659			1.27787
$255$	9.13925	−	10.5473i	0.572322	−	0.660495i
$256$	6.24661	−	4.01445i	0.390413	−	0.250903i
$257$	1.68086	+	11.6906i	0.104849	+	0.729242i	0.972641	+	0.232314i	$0.0746297\pi$
$257$	1.68086	+	11.6906i	0.104849	+	0.729242i	−0.867792	+	0.496928i	$0.834461\pi$
$258$	−2.50942	−	5.49487i	−0.156230	−	0.342096i
$259$	1.86035	−	12.9390i	0.115596	−	0.803990i
$260$	36.4248	−	10.6953i	2.25897	−	0.663293i
$261$	−8.48961	−	5.45594i	−0.525494	−	0.337714i
$262$	10.0020	−	21.9013i	0.617924	−	1.35307i
$263$	−14.0599	−	4.12835i	−0.866968	−	0.254565i	−0.182143	−	0.983272i	$-0.558303\pi$
$263$	−14.0599	−	4.12835i	−0.866968	−	0.254565i	−0.684825	+	0.728707i	$0.740121\pi$
$264$	−0.791177	−	0.913067i	−0.0486936	−	0.0561954i
$265$	−14.7667	−	17.0417i	−0.907113	−	1.04686i
$266$	−19.4799	−	5.71983i	−1.19439	−	0.350705i
$267$	−1.52309	+	3.33511i	−0.0932117	+	0.204105i
$268$	−5.67799	−	3.64902i	−0.346838	−	0.222899i
$269$	26.1145	−	7.66790i	1.59223	−	0.467520i	0.638858	−	0.769324i	$-0.279407\pi$
$269$	26.1145	−	7.66790i	1.59223	−	0.467520i	0.953370	+	0.301804i	$0.0975888\pi$
$270$	−1.03178	+	7.17616i	−0.0627919	+	0.436727i
$271$	−1.77962	−	3.89682i	−0.108104	−	0.236715i	0.847847	−	0.530241i	$-0.177899\pi$
$271$	−1.77962	−	3.89682i	−0.108104	−	0.236715i	−0.955951	+	0.293526i	$0.905171\pi$
$272$	−1.72324	−	11.9854i	−0.104487	−	0.726723i
$273$	−6.05925	+	3.89404i	−0.366722	+	0.235678i
$274$	−2.26216	+	2.61067i	−0.136662	+	0.157717i
$275$	9.52172			0.574181
$276$	11.3235	+	2.47021i	0.681596	+	0.148689i
$277$	6.86176			0.412283			0.206142	−	0.978522i	$-0.433909\pi$
$277$	6.86176			0.412283			0.206142	+	0.978522i	$0.433909\pi$
$278$	7.67397	−	8.85623i	0.460254	−	0.531161i
$279$	0.956733	−	0.614855i	0.0572781	−	0.0368104i
$280$	−0.679970	−	4.72930i	−0.0406360	−	0.282629i
$281$	−5.52742	−	12.1034i	−0.329738	−	0.722025i	0.670056	−	0.742310i	$-0.266270\pi$
$281$	−5.52742	−	12.1034i	−0.329738	−	0.722025i	−0.999794	+	0.0202849i	$0.993543\pi$
$282$	−1.39570	+	9.70734i	−0.0831130	+	0.578064i
$283$	−18.4431	+	5.41539i	−1.09633	+	0.321912i	−0.779393	−	0.626535i	$-0.784473\pi$
$283$	−18.4431	+	5.41539i	−1.09633	+	0.321912i	−0.316937	+	0.948447i	$0.602654\pi$
$284$	−11.5367	−	7.41419i	−0.684578	−	0.439951i
$285$	8.75250	−	19.1653i	0.518454	−	1.13525i
$286$	12.6693	+	3.72005i	0.749154	+	0.219971i
$287$	−5.07789	−	5.86020i	−0.299738	−	0.345916i
$288$	5.26607	+	6.07737i	0.310306	+	0.358112i
$289$	0.608222	+	0.178590i	0.0357778	+	0.0105053i
$290$	−30.3933	+	66.5521i	−1.78476	+	3.90807i
$291$	−1.43526	−	0.922383i	−0.0841362	−	0.0540711i
$292$	−2.11016	+	0.619600i	−0.123488	+	0.0362594i
$293$	−1.94185	+	13.5058i	−0.113444	+	0.789019i	0.851082	+	0.525032i	$0.175947\pi$
$293$	−1.94185	+	13.5058i	−0.113444	+	0.789019i	−0.964526	+	0.263987i	$0.914962\pi$
$294$	−3.92693	−	8.59878i	−0.229023	−	0.501491i
$295$	−0.465066	−	3.23460i	−0.0270772	−	0.188326i
$296$	−6.08757	+	3.91225i	−0.353833	+	0.227395i
$297$	−0.903570	+	1.04278i	−0.0524304	+	0.0605079i
$298$	12.7816			0.740417
$299$	−20.4658	+	7.61972i	−1.18357	+	0.440660i
$300$	16.6769			0.962842
$301$	2.97737	−	3.43607i	0.171613	−	0.198052i
$302$	−41.8428	+	26.8908i	−2.40778	+	1.54739i
$303$	−0.979886	−	6.81525i	−0.0562930	−	0.391526i
$304$	−7.59394	−	16.6284i	−0.435542	−	0.953704i
$305$	−0.374295	+	2.60328i	−0.0214321	+	0.149063i
$306$	8.15757	−	2.39528i	0.466337	−	0.136929i
$307$	−21.3942	−	13.7492i	−1.22103	−	0.784709i	−0.238561	−	0.971128i	$-0.576676\pi$
$307$	−21.3942	−	13.7492i	−1.22103	−	0.784709i	−0.982470	+	0.186418i	$0.940312\pi$
$308$	2.19102	−	4.79766i	0.124845	−	0.273372i
$309$	−0.275941	−	0.0810235i	−0.0156977	−	0.00460927i
$310$	−5.39943	−	6.23128i	−0.306667	−	0.353913i
$311$	20.6138	+	23.7896i	1.16890	+	1.34898i	0.925358	+	0.379095i	$0.123764\pi$
$311$	20.6138	+	23.7896i	1.16890	+	1.34898i	0.243544	+	0.969890i	$0.421690\pi$
$312$	3.82567	+	1.12332i	0.216586	+	0.0635953i
$313$	5.59541	−	12.2522i	0.316271	−	0.692537i	−0.683011	−	0.730408i	$-0.739330\pi$
$313$	5.59541	−	12.2522i	0.316271	−	0.692537i	0.999283	+	0.0378702i	$0.0120574\pi$
$314$	27.5432	+	17.7009i	1.55435	+	0.998921i
$315$	−5.23564	+	1.53732i	−0.294995	+	0.0866182i
$316$	−3.35229	+	23.3157i	−0.188581	+	1.31161i
$317$	−1.59881	−	3.50090i	−0.0897980	−	0.196630i	0.859404	−	0.511297i	$-0.170835\pi$
$317$	−1.59881	−	3.50090i	−0.0897980	−	0.196630i	−0.949202	+	0.314666i	$0.898107\pi$
$318$	−1.95498	−	13.5972i	−0.109630	−	0.762493i
$319$	−11.7139	+	7.52805i	−0.655851	+	0.421490i
$320$	24.6552	−	28.4536i	1.37827	−	1.59060i
$321$	8.29060			0.462736
$322$	3.37966	+	15.5799i	0.188341	+	0.868232i
$323$	−24.7078			−1.37478
$324$	−1.58257	+	1.82638i	−0.0879203	+	0.101465i
$325$	−26.4352	+	16.9889i	−1.46636	+	0.942374i
$326$	1.84292	+	12.8178i	0.102070	+	0.709914i
$327$	8.53607	+	18.6914i	0.472046	+	1.03364i
$328$	−0.610883	+	4.24878i	−0.0337304	+	0.234600i
$329$	−7.08235	+	2.07957i	−0.390463	+	0.114650i
$330$	8.41540	+	5.40825i	0.463253	+	0.297714i
$331$	−8.39492	+	18.3823i	−0.461427	+	1.01038i	0.525733	+	0.850649i	$0.323791\pi$
$331$	−8.39492	+	18.3823i	−0.461427	+	1.01038i	−0.987160	+	0.159734i	$0.948936\pi$
$332$	11.2561	+	3.30510i	0.617760	+	0.181391i
$333$	5.41196	+	6.24573i	0.296573	+	0.342264i
$334$	−12.9969	−	14.9992i	−0.711156	−	0.820718i
$335$	9.24455	+	2.71444i	0.505084	+	0.148306i
$336$	−1.96673	+	4.30654i	−0.107294	+	0.234941i
$337$	9.26412	+	5.95369i	0.504649	+	0.324318i	0.768073	−	0.640362i	$-0.221216\pi$
$337$	9.26412	+	5.95369i	0.504649	+	0.324318i	−0.263425	+	0.964680i	$0.584852\pi$
$338$	−15.5975	+	4.57984i	−0.848392	+	0.249110i
$339$	0.230950	−	1.60629i	0.0125435	−	0.0872420i
$340$	−14.0106	−	30.6789i	−0.759831	−	1.66380i
$341$	−0.223320	−	1.55322i	−0.0120934	−	0.0841117i
$342$	10.7978	−	6.93931i	0.583877	−	0.375235i
$343$	11.9100	−	13.7449i	0.643080	−	0.742154i
$344$	−2.51685			−0.135700
$345$	−16.5030	+	1.17063i	−0.888492	+	0.0630245i
$346$	14.9085			0.801484
$347$	17.2640	−	19.9238i	0.926782	−	1.06956i	−0.0706185	−	0.997503i	$-0.522497\pi$
$347$	17.2640	−	19.9238i	0.926782	−	1.06956i	0.997400	−	0.0720598i	$-0.0229573\pi$
$348$	−20.5164	+	13.1851i	−1.09979	+	0.706794i
$349$	−2.66076	−	18.5060i	−0.142427	−	0.990602i	−0.928199	−	0.372085i	$-0.878643\pi$
$349$	−2.66076	−	18.5060i	−0.142427	−	0.990602i	0.785772	−	0.618517i	$-0.212266\pi$
$350$	9.52949	+	20.8667i	0.509373	+	1.11537i
$351$	0.648042	−	4.50723i	0.0345899	−	0.240578i
$352$	10.6461	−	3.12599i	0.567441	−	0.166616i
$353$	19.8432	+	12.7524i	1.05615	+	0.678744i	0.948928	−	0.315491i	$-0.102169\pi$
$353$	19.8432	+	12.7524i	1.05615	+	0.678744i	0.107218	+	0.994236i	$0.465806\pi$
$354$	0.826996	−	1.81087i	0.0439543	−	0.0962466i
$355$	18.7834	+	5.51529i	0.996917	+	0.292721i
$356$	5.80237	+	6.69630i	0.307525	+	0.354903i
$357$	4.19044	+	4.83603i	0.221782	+	0.255950i
$358$	−16.1859	−	4.75259i	−0.855449	−	0.251182i
$359$	−6.25424	+	13.6949i	−0.330086	+	0.722788i	−0.999803	−	0.0198281i	$-0.993688\pi$
$359$	−6.25424	+	13.6949i	−0.330086	+	0.722788i	0.669717	+	0.742616i	$0.266415\pi$
$360$	2.54114	+	1.63309i	0.133930	+	0.0860714i
$361$	−17.5598	+	5.15603i	−0.924201	+	0.271370i
$362$	3.52595	−	24.5235i	0.185320	−	1.28893i
$363$	−3.77869	−	8.27418i	−0.198330	−	0.434282i
$364$	2.47716	+	17.2291i	0.129839	+	0.903048i
$365$	2.64106	−	1.69730i	0.138239	−	0.0888409i
$366$	−1.04923	+	1.21087i	−0.0548441	+	0.0632934i
$367$	33.1504			1.73043			0.865217	−	0.501397i	$-0.167180\pi$
$367$	33.1504			1.73043			0.865217	+	0.501397i	$0.167180\pi$
$368$	−8.60904	+	11.4863i	−0.448777	+	0.598766i
$369$	4.90225			0.255201
$370$	39.2364	−	45.2813i	2.03981	−	2.35406i
$371$	8.69785	−	5.58977i	0.451570	−	0.290206i
$372$	−0.391135	−	2.72040i	−0.0202794	−	0.141046i
$373$	13.6829	+	29.9614i	0.708475	+	1.55134i	0.829383	+	0.558680i	$0.188692\pi$
$373$	13.6829	+	29.9614i	0.708475	+	1.55134i	−0.120908	+	0.992664i	$0.538581\pi$
$374$	1.66948	−	11.6115i	0.0863269	−	0.600417i
$375$	−6.29186	+	1.84746i	−0.324910	+	0.0954022i
$376$	3.43745	+	2.20911i	0.177273	+	0.113926i
$377$	19.0896	−	41.8003i	0.983163	−	2.15283i
$378$	−3.18953	−	0.936530i	−0.164052	−	0.0481699i
$379$	−14.4104	−	16.6305i	−0.740213	−	0.854252i	0.253368	−	0.967370i	$-0.418462\pi$
$379$	−14.4104	−	16.6305i	−0.740213	−	0.854252i	−0.993582	+	0.113118i	$0.963916\pi$
$380$	−33.3435	−	38.4805i	−1.71049	−	1.97401i
$381$	−9.29822	−	2.73020i	−0.476362	−	0.139873i
$382$	−23.0914	+	50.5631i	−1.18146	+	2.58703i
$383$	3.93919	+	2.53156i	0.201283	+	0.129357i	0.637400	−	0.770533i	$-0.280010\pi$
$383$	3.93919	+	2.53156i	0.201283	+	0.129357i	−0.436116	+	0.899890i	$0.643646\pi$
$384$	6.57531	−	1.93069i	0.335545	−	0.0985249i
$385$	−1.07150	+	7.45242i	−0.0546085	+	0.379810i
$386$	16.4557	+	36.0329i	0.837572	+	1.83403i
$387$	0.409068	+	2.84513i	0.0207941	+	0.144626i
$388$	−3.46850	+	2.22907i	−0.176087	+	0.113164i
$389$	9.18800	−	10.6035i	0.465850	−	0.537620i	−0.473402	−	0.880846i	$-0.656974\pi$
$389$	9.18800	−	10.6035i	0.465850	−	0.537620i	0.939253	+	0.343226i	$0.111520\pi$
$390$	−33.0133			−1.67169
$391$	9.28823	+	17.0338i	0.469726	+	0.861435i
$392$	−3.93856			−0.198927
$393$	−7.50251	+	8.65835i	−0.378451	+	0.436756i
$394$	15.5902	−	10.0192i	0.785422	−	0.504760i
$395$	−4.78539	−	33.2831i	−0.240779	−	1.67466i
$396$	1.38518	+	3.03313i	0.0696082	+	0.152421i
$397$	−1.60265	+	11.1467i	−0.0804348	+	0.559437i	0.909258	+	0.416232i	$0.136650\pi$
$397$	−1.60265	+	11.1467i	−0.0804348	+	0.559437i	−0.989693	+	0.143204i	$0.954259\pi$
$398$	−30.2590	+	8.88486i	−1.51675	+	0.445358i
$399$	8.12693	+	5.22286i	0.406855	+	0.261470i
$400$	−8.58042	+	18.7885i	−0.429021	+	0.939425i
$401$	16.4297	+	4.82419i	0.820459	+	0.240909i	0.664914	−	0.746920i	$-0.268468\pi$
$401$	16.4297	+	4.82419i	0.820459	+	0.240909i	0.155546	+	0.987829i	$0.450286\pi$
$402$	3.84370	+	4.43587i	0.191707	+	0.221241i
$403$	3.39130	+	3.91377i	0.168933	+	0.194959i
$404$	−15.9654	−	4.68786i	−0.794308	−	0.233230i
$405$	1.43308	−	3.13801i	0.0712104	−	0.155929i
$406$	−28.2210	−	18.1365i	−1.40059	−	0.900102i
$407$	10.9411	−	3.21259i	0.542329	−	0.159242i
$408$	0.504121	−	3.50624i	0.0249577	−	0.173585i
$409$	−3.73112	−	8.17001i	−0.184492	−	0.403981i	0.794676	−	0.607034i	$-0.207641\pi$
$409$	−3.73112	−	8.17001i	−0.184492	−	0.403981i	−0.979168	+	0.203053i	$0.934914\pi$
$410$	−5.05803	−	35.1793i	−0.249798	−	1.73738i
$411$	1.38279	−	0.888663i	0.0682078	−	0.0438345i
$412$	−0.455130	+	0.525248i	−0.0224227	+	0.0258771i
$413$	1.49835			0.0737290
$414$	−8.84315	−	4.83544i	−0.434617	−	0.237649i
$415$	−16.7465			−0.822052
$416$	−23.9795	+	27.6738i	−1.17569	+	1.35682i
$417$	−4.69085	+	3.01463i	−0.229712	+	0.147627i
$418$	−2.52040	−	17.5298i	−0.123277	−	0.857410i
$419$	−2.92531	−	6.40554i	−0.142911	−	0.312931i	0.824619	−	0.565689i	$-0.191390\pi$
$419$	−2.92531	−	6.40554i	−0.142911	−	0.312931i	−0.967530	+	0.252758i	$0.918662\pi$
$420$	−1.87668	+	13.0526i	−0.0915727	+	0.636902i
$421$	−11.7991	+	3.46454i	−0.575055	+	0.168851i	−0.556313	−	0.830973i	$-0.687784\pi$
$421$	−11.7991	+	3.46454i	−0.575055	+	0.168851i	−0.0187420	+	0.999824i	$0.505966\pi$
$422$	−47.2499	−	30.3656i	−2.30009	−	1.47818i
$423$	1.93856	−	4.24485i	0.0942560	−	0.206392i
$424$	−5.49162	−	1.61248i	−0.266696	−	0.0783091i
$425$	18.2820	+	21.0986i	0.886808	+	1.02343i
$426$	7.80976	+	9.01294i	0.378384	+	0.436678i
$427$	−1.15706	−	0.339743i	−0.0559940	−	0.0164413i
$428$	8.32302	−	18.2249i	0.402309	−	0.880933i
$429$	−5.28558	−	3.39684i	−0.255190	−	0.164001i
$430$	19.9951	−	5.87108i	0.964248	−	0.283129i
$431$	−0.717708	+	4.99177i	−0.0345708	+	0.240445i	−0.999779	−	0.0210388i	$-0.993303\pi$
$431$	−0.717708	+	4.99177i	−0.0345708	+	0.240445i	0.965208	+	0.261484i	$0.0842118\pi$
$432$	−1.24339	−	2.72264i	−0.0598224	−	0.130993i
$433$	0.126595	+	0.880491i	0.00608379	+	0.0423137i	0.992637	−	0.121125i	$-0.0386503\pi$
$433$	0.126595	+	0.880491i	0.00608379	+	0.0423137i	−0.986553	+	0.163439i	$0.947741\pi$
$434$	3.18035	−	2.04389i	0.152662	−	0.0981098i
$435$	22.7981	−	26.3104i	1.09309	−	1.26149i
$436$	49.6580			2.37818
$437$	20.6993	+	20.7235i	0.990183	+	0.991340i
$438$	1.91253			0.0913841
$439$	−26.1182	+	30.1421i	−1.24656	+	1.43860i	−0.391409	+	0.920217i	$0.628012\pi$
$439$	−26.1182	+	30.1421i	−1.24656	+	1.43860i	−0.855147	+	0.518385i	$0.826533\pi$
$440$	3.50623	−	2.25332i	0.167153	−	0.107423i
$441$	0.640140	+	4.45227i	0.0304829	+	0.212013i
$442$	16.0825	+	35.2158i	0.764968	+	1.67505i
$443$	−1.82310	+	12.6799i	−0.0866180	+	0.602441i	0.899566	+	0.436785i	$0.143883\pi$
$443$	−1.82310	+	12.6799i	−0.0866180	+	0.602441i	−0.986184	+	0.165656i	$0.947026\pi$
$444$	19.1628	−	5.62672i	0.909428	−	0.267032i
$445$	−10.6404	−	6.83820i	−0.504405	−	0.324162i
$446$	10.7336	−	23.5032i	0.508249	−	1.11291i
$447$	−5.83553	−	1.71347i	−0.276011	−	0.0810442i
$448$	11.3047	+	13.0463i	0.534095	+	0.616378i
$449$	8.73849	+	10.0848i	0.412395	+	0.475929i	0.923505	−	0.383586i	$-0.125311\pi$
$449$	8.73849	+	10.0848i	0.412395	+	0.475929i	−0.511110	+	0.859515i	$0.670766\pi$
$450$	−13.9152	−	4.08588i	−0.655971	−	0.192610i
$451$	2.80990	−	6.15282i	0.132313	−	0.289725i
$452$	−3.29920	−	2.12026i	−0.155181	−	0.0997288i
$453$	22.7086	−	6.66784i	1.06694	−	0.313282i
$454$	4.92975	−	34.2872i	0.231365	−	1.60918i
$455$	−10.3220	−	22.6020i	−0.483902	−	1.05960i
$456$	−0.761068	−	5.29334i	−0.0356403	−	0.247883i
$457$	19.4014	−	12.4685i	0.907559	−	0.583253i	−0.00146402	−	0.999999i	$-0.500466\pi$
$457$	19.4014	−	12.4685i	0.907559	−	0.583253i	0.909023	+	0.416746i	$0.136830\pi$
$458$	0.875860	−	1.01080i	0.0409262	−	0.0472314i
$459$	−4.04550			−0.188828
$460$	−13.9942	+	37.4531i	−0.652483	+	1.74626i
$461$	−7.59985			−0.353960			−0.176980	−	0.984214i	$-0.556633\pi$
$461$	−7.59985			−0.353960			−0.176980	+	0.984214i	$0.556633\pi$
$462$	−3.00363	+	3.46637i	−0.139742	+	0.161270i
$463$	8.55341	−	5.49694i	0.397511	−	0.255465i	−0.326580	−	0.945170i	$-0.605896\pi$
$463$	8.55341	−	5.49694i	0.397511	−	0.255465i	0.724090	+	0.689705i	$0.242260\pi$
$464$	−4.29868	−	29.8980i	−0.199561	−	1.38798i
$465$	1.62980	+	3.56877i	0.0755803	+	0.165498i
$466$	−0.192487	+	1.33877i	−0.00891677	+	0.0620175i
$467$	9.91443	−	2.91114i	0.458785	−	0.134711i	−0.0441700	−	0.999024i	$-0.514064\pi$
$467$	9.91443	−	2.91114i	0.458785	−	0.134711i	0.502955	+	0.864313i	$0.332246\pi$
$468$	−9.25748	−	5.94942i	−0.427927	−	0.275012i
$469$	−1.83517	+	4.01846i	−0.0847401	+	0.185555i
$470$	−32.4619	−	9.53168i	−1.49736	−	0.439664i
$471$	−10.2021	−	11.7739i	−0.470088	−	0.542511i
$472$	−0.543170	−	0.626852i	−0.0250014	−	0.0288532i
$473$	3.80540	+	1.11737i	0.174972	+	0.0513765i
$474$	8.50955	−	18.6333i	0.390857	−	0.855857i
$475$	35.4561	+	22.7862i	1.62684	+	1.04550i
$476$	14.8377	−	4.35673i	0.680084	−	0.199691i
$477$	−0.930243	+	6.46998i	−0.0425929	+	0.296240i
$478$	−8.40634	−	18.4073i	−0.384497	−	0.841932i
$479$	1.23975	+	8.62266i	0.0566457	+	0.393980i	0.998344	+	0.0575217i	$0.0183199\pi$
$479$	1.23975	+	8.62266i	0.0566457	+	0.393980i	−0.941699	+	0.336458i	$0.890771\pi$
$480$	−23.3374	+	14.9981i	−1.06520	+	0.684565i
$481$	−24.6438	+	28.4405i	−1.12366	+	1.29677i
$482$	−12.5359			−0.570993
$483$	0.545587	−	7.56617i	0.0248251	−	0.344273i
$484$	−21.9822			−0.999193
$485$	3.85426	−	4.44805i	0.175013	−	0.201975i
$486$	1.76796	−	1.13620i	0.0801964	−	0.0515391i
$487$	−3.24014	−	22.5356i	−0.146825	−	1.02119i	−0.921375	−	0.388675i	$-0.872933\pi$
$487$	−3.24014	−	22.5356i	−0.146825	−	1.02119i	0.774550	−	0.632512i	$-0.217976\pi$
$488$	0.277312	+	0.607229i	0.0125533	+	0.0274880i
$489$	0.876923	−	6.09913i	0.0396558	−	0.275812i
$490$	31.2898	−	9.18750i	1.41353	−	0.415049i
$491$	23.5914	+	15.1613i	1.06466	+	0.684219i	0.950966	−	0.309297i	$-0.100094\pi$
$491$	23.5914	+	15.1613i	1.06466	+	0.684219i	0.113699	+	0.993515i	$0.463730\pi$
$492$	4.92142	−	10.7764i	0.221875	−	0.485838i
$493$	−39.1720	−	11.5019i	−1.76422	−	0.518021i
$494$	38.2745	+	44.1711i	1.72205	+	1.98735i
$495$	−3.11710	−	3.59732i	−0.140103	−	0.161688i
$496$	3.26610	+	0.959013i	0.146652	+	0.0430610i
$497$	−3.72875	+	8.16482i	−0.167257	+	0.366242i
$498$	−8.58238	−	5.51556i	−0.384585	−	0.247158i
$499$	14.0554	−	4.12705i	0.629207	−	0.184752i	0.0484460	−	0.998826i	$-0.484573\pi$
$499$	14.0554	−	4.12705i	0.629207	−	0.184752i	0.580761	+	0.814074i	$0.302755\pi$
$500$	−2.25528	+	15.6858i	−0.100859	+	0.701491i
$501$	3.92306	+	8.59031i	0.175269	+	0.383787i
$502$	1.15289	+	8.01853i	0.0514560	+	0.357885i
$503$	−1.35700	+	0.872088i	−0.0605055	+	0.0388845i	−0.570544	−	0.821267i	$-0.693268\pi$
$503$	−1.35700	+	0.872088i	−0.0605055	+	0.0388845i	0.510038	+	0.860152i	$0.329631\pi$
$504$	−0.906984	+	1.04672i	−0.0404003	+	0.0466244i
$505$	23.7528			1.05698
$506$	−11.1377	+	8.32745i	−0.495132	+	0.370200i
$507$	7.73512			0.343529
$508$	−15.3363	+	17.6990i	−0.680437	+	0.785266i
$509$	−20.5963	+	13.2364i	−0.912914	+	0.586694i	−0.910594	−	0.413303i	$-0.864375\pi$
$509$	−20.5963	+	13.2364i	−0.912914	+	0.586694i	−0.00232071	+	0.999997i	$0.500739\pi$
$510$	4.17405	+	29.0312i	0.184830	+	1.28552i
$511$	0.597974	+	1.30938i	0.0264528	+	0.0579236i
$512$	−4.17136	+	29.0125i	−0.184350	+	1.28218i
$513$	−5.86007	+	1.72067i	−0.258728	+	0.0759695i
$514$	−20.8812	−	13.4195i	−0.921029	−	0.591909i
$515$	0.412140	−	0.902462i	0.0181611	−	0.0397672i
$516$	6.66500	+	1.95702i	0.293410	+	0.0861531i
$517$	−4.21656	−	4.86617i	−0.185444	−	0.214014i
$518$	17.9903	+	20.7619i	0.790450	+	0.912228i
$519$	−6.80658	−	1.99859i	−0.298776	−	0.0877284i
$520$	−5.71395	+	12.5118i	−0.250573	+	0.548679i
$521$	−30.5797	−	19.6524i	−1.33972	−	0.860986i	−0.342800	−	0.939408i	$-0.611375\pi$
$521$	−30.5797	−	19.6524i	−1.33972	−	0.860986i	−0.996920	+	0.0784221i	$0.975012\pi$
$522$	20.3493	−	5.97509i	0.890664	−	0.261522i
$523$	2.57768	−	17.9282i	0.112714	−	0.783943i	−0.852546	−	0.522652i	$-0.824943\pi$
$523$	2.57768	−	17.9282i	0.112714	−	0.783943i	0.965260	−	0.261291i	$-0.0841483\pi$
$524$	11.5014	+	25.1847i	0.502443	+	1.10020i
$525$	−1.55343	−	10.8043i	−0.0677972	−	0.471540i
$526$	25.9067	−	16.6492i	1.12959	−	0.725941i
$527$	3.01290	−	3.47708i	0.131244	−	0.151464i
$528$	−4.12987			−0.179730
$529$	6.50563	−	22.0608i	0.282854	−	0.959163i
$530$	47.3894			2.05847
$531$	−0.620332	+	0.715901i	−0.0269201	+	0.0310675i
$532$	19.6399	−	12.6218i	0.851498	−	0.547224i
$533$	3.17687	+	22.0956i	0.137605	+	0.957067i
$534$	−3.20090	−	7.00900i	−0.138517	−	0.303309i
$535$	−4.07029	+	28.3095i	−0.175974	+	1.22393i
$536$	2.34644	−	0.688976i	0.101351	−	0.0297592i
$537$	6.75265	+	4.33967i	0.291398	+	0.187270i
$538$	−23.7612	+	52.0297i	−1.02442	+	2.24316i
$539$	5.95497	+	1.74854i	0.256499	+	0.0753148i
$540$	−5.45947	−	6.30057i	−0.234938	−	0.271133i
$541$	−23.7651	−	27.4264i	−1.02174	−	1.17915i	−0.983689	−	0.179879i	$-0.942429\pi$
$541$	−23.7651	−	27.4264i	−1.02174	−	1.17915i	−0.0380547	−	0.999276i	$-0.512116\pi$
$542$	8.63840	+	2.53646i	0.371051	+	0.108950i
$543$	−4.89735	+	10.7237i	−0.210166	+	0.460198i
$544$	27.3676	+	17.5881i	1.17338	+	0.754083i
$545$	−68.0153	+	19.9711i	−2.91346	+	0.855468i
$546$	2.15421	−	14.9829i	0.0921917	−	0.641207i
$547$	−4.79518	−	10.5000i	−0.205027	−	0.448947i	0.778986	−	0.627041i	$-0.215734\pi$
$547$	−4.79518	−	10.5000i	−0.205027	−	0.448947i	−0.984013	+	0.178094i	$0.943007\pi$
$548$	−0.565316	−	3.93186i	−0.0241491	−	0.167961i
$549$	0.641360	−	0.412177i	0.0273726	−	0.0175913i
$550$	−13.1042	+	15.1231i	−0.558765	+	0.644849i
$551$	−61.6342			−2.62571
$552$	−3.36318	+	2.51458i	−0.143146	+	0.107027i
$553$	15.4176			0.655623
$554$	−9.44345	+	10.8983i	−0.401214	+	0.463025i
$555$	−23.9840	+	15.4136i	−1.01806	+	0.654270i
$556$	1.91773	+	13.3381i	0.0813299	+	0.565662i
$557$	7.05495	+	15.4482i	0.298928	+	0.654560i	0.998179	−	0.0603152i	$-0.0192106\pi$
$557$	7.05495	+	15.4482i	0.298928	+	0.654560i	−0.699252	+	0.714876i	$0.746483\pi$
$558$	−0.340142	+	2.36574i	−0.0143994	+	0.100150i
$559$	−12.5586	+	3.68753i	−0.531172	+	0.155966i
$560$	−13.7397	−	8.82999i	−0.580610	−	0.373135i
$561$	−2.31882	+	5.07751i	−0.0979008	+	0.214373i
$562$	26.8304	+	7.87813i	1.13177	+	0.332319i
$563$	−10.7487	−	12.4046i	−0.453002	−	0.522792i	0.482604	−	0.875839i	$-0.339691\pi$
$563$	−10.7487	−	12.4046i	−0.453002	−	0.522792i	−0.935606	+	0.353047i	$0.885146\pi$
$564$	−7.38514	−	8.52291i	−0.310971	−	0.358879i
$565$	5.37154	+	1.57723i	0.225983	+	0.0663545i
$566$	16.7811	−	36.7455i	0.705363	−	1.54453i
$567$	1.33066	+	0.855160i	0.0558823	+	0.0359133i
$568$	4.76756	−	1.39988i	0.200042	−	0.0587377i
$569$	0.107529	−	0.747877i	0.00450783	−	0.0313526i	−0.987443	−	0.157973i	$-0.949504\pi$
$569$	0.107529	−	0.747877i	0.00450783	−	0.0313526i	0.991951	+	0.126621i	$0.0404131\pi$
$570$	18.3941	+	40.2775i	0.770444	+	1.68704i
$571$	−3.85667	−	26.8237i	−0.161397	−	1.12254i	−0.896004	−	0.444046i	$-0.853543\pi$
$571$	−3.85667	−	26.8237i	−0.161397	−	1.12254i	0.734608	−	0.678492i	$-0.237366\pi$
$572$	−12.7734	+	8.20895i	−0.534082	+	0.343233i
$573$	17.3209	−	19.9894i	0.723591	−	0.835068i
$574$	16.2960			0.680181
$575$	2.38028	−	33.0096i	0.0992645	−	1.37660i
$576$	−10.9136			−0.454735
$577$	−6.23334	+	7.19365i	−0.259497	+	0.299476i	−0.870516	−	0.492141i	$-0.836215\pi$
$577$	−6.23334	+	7.19365i	−0.259497	+	0.299476i	0.611019	+	0.791616i	$0.290760\pi$
$578$	−1.12071	+	0.720237i	−0.0466154	+	0.0299579i
$579$	−2.68249	−	18.6571i	−0.111480	−	0.775362i
$580$	−34.9498	−	76.5294i	−1.45121	−	3.17771i
$581$	1.09276	−	7.60028i	0.0453352	−	0.315313i
$582$	3.44025	−	1.01015i	0.142603	−	0.0418721i
$583$	7.58728	+	4.87605i	0.314233	+	0.201945i
$584$	0.331021	−	0.724835i	0.0136978	−	0.0299939i
$585$	15.0725	+	4.42567i	0.623169	+	0.182979i
$586$	−18.7784	−	21.6715i	−0.775731	−	0.895241i
$587$	−27.9888	−	32.3008i	−1.15522	−	1.33320i	−0.933706	−	0.358040i	$-0.883445\pi$
$587$	−27.9888	−	32.3008i	−1.15522	−	1.33320i	−0.221515	−	0.975157i	$-0.571100\pi$
$588$	10.4299	+	3.06249i	0.430121	+	0.126295i
$589$	2.88541	−	6.31816i	0.118891	−	0.260335i
$590$	5.77746	+	3.71295i	0.237854	+	0.152860i
$591$	−8.46097	+	2.48436i	−0.348038	+	0.102193i
$592$	−3.52030	+	24.4842i	−0.144683	+	1.00629i
$593$	−5.31366	−	11.6353i	−0.218206	−	0.477805i	0.768596	−	0.639734i	$-0.220956\pi$
$593$	−5.31366	−	11.6353i	−0.218206	−	0.477805i	−0.986802	+	0.161930i	$0.948228\pi$
$594$	−0.412676	−	2.87022i	−0.0169323	−	0.117767i
$595$	−18.5706	+	11.9346i	−0.761322	+	0.489272i
$596$	−9.62499	+	11.1078i	−0.394255	+	0.454994i
$597$	15.0061			0.614158
$598$	16.0637	−	42.9917i	0.656894	−	1.75806i
$599$	27.4971			1.12350			0.561751	−	0.827306i	$-0.310128\pi$
$599$	27.4971			1.12350			0.561751	+	0.827306i	$0.310128\pi$
$600$	−3.95698	+	4.56660i	−0.161543	+	0.186431i
$601$	28.7319	−	18.4649i	1.17200	−	0.753198i	0.198100	−	0.980182i	$-0.436523\pi$
$601$	28.7319	−	18.4649i	1.17200	−	0.753198i	0.973899	+	0.226984i	$0.0728864\pi$
$602$	1.35982	+	9.45774i	0.0554220	+	0.385469i
$603$	−1.16021	−	2.54051i	−0.0472474	−	0.103457i
$604$	8.13975	−	56.6132i	0.331202	−	2.30356i
$605$	30.1086	−	8.84067i	1.22409	−	0.359424i
$606$	12.1730	+	7.82312i	0.494495	+	0.317793i
$607$	−12.4592	+	27.2819i	−0.505704	+	1.10734i	0.468869	+	0.883267i	$0.344661\pi$
$607$	−12.4592	+	27.2819i	−0.505704	+	1.10734i	−0.974573	+	0.224069i	$0.928066\pi$
$608$	47.1238	+	13.8368i	1.91112	+	0.561156i
$609$	10.4532	+	12.0636i	0.423584	+	0.488842i
$610$	−3.61959	−	4.17723i	−0.146553	−	0.169131i
$611$	20.3888	+	5.98670i	0.824843	+	0.242196i
$612$	−4.06132	+	8.89306i	−0.164169	+	0.359481i
$613$	5.60513	+	3.60220i	0.226389	+	0.145491i	0.648919	−	0.760858i	$-0.275221\pi$
$613$	5.60513	+	3.60220i	0.226389	+	0.145491i	−0.422530	+	0.906349i	$0.638858\pi$
$614$	51.2811	−	15.0575i	2.06954	−	0.607671i
$615$	−2.40677	+	16.7395i	−0.0970504	+	0.675000i
$616$	0.793863	+	1.73832i	0.0319857	+	0.0700388i
$617$	−4.06924	−	28.3022i	−0.163822	−	1.13940i	−0.891346	−	0.453323i	$-0.850239\pi$
$617$	−4.06924	−	28.3022i	−0.163822	−	1.13940i	0.727525	−	0.686081i	$-0.240671\pi$
$618$	0.508449	−	0.326760i	0.0204528	−	0.0131442i
$619$	1.97493	−	2.27919i	0.0793791	−	0.0916084i	−0.714671	−	0.699461i	$-0.753423\pi$
$619$	1.97493	−	2.27919i	0.0793791	−	0.0916084i	0.794050	+	0.607853i	$0.207969\pi$
$620$	9.48125			0.380776
$621$	3.38918	+	3.39315i	0.136003	+	0.136162i
$622$	−66.1539			−2.65253
$623$	3.79779	−	4.38289i	0.152155	−	0.175597i
$624$	11.4658	−	7.36862i	0.458999	−	0.294981i
$625$	1.69106	+	11.7616i	0.0676423	+	0.470462i
$626$	11.7592	+	25.7491i	0.469993	+	1.02914i
$627$	−1.19929	+	8.34124i	−0.0478950	+	0.333117i
$628$	−36.1240	+	10.6070i	−1.44150	+	0.423264i
$629$	28.1258	+	18.0754i	1.12145	+	0.720711i
$630$	4.76383	−	10.4313i	0.189795	−	0.415594i
$631$	25.2937	+	7.42689i	1.00692	+	0.295660i	0.743295	−	0.668964i	$-0.233262\pi$
$631$	25.2937	+	7.42689i	1.00692	+	0.295660i	0.263630	+	0.964624i	$0.415080\pi$
$632$	−5.58907	−	6.45013i	−0.222321	−	0.256572i
$633$	17.5015	+	20.1979i	0.695624	+	0.802793i
$634$	7.76073	+	2.27875i	0.308218	+	0.0905009i
$635$	13.8877	−	30.4098i	0.551115	−	1.20677i
$636$	13.2888	+	8.54020i	0.526935	+	0.338641i
$637$	−19.6526	+	5.77053i	−0.778665	+	0.228637i
$638$	4.16457	−	28.9652i	0.164877	−	1.14674i
$639$	−2.35735	−	5.16188i	−0.0932554	−	0.204201i
$640$	3.36445	+	23.4002i	0.132991	+	0.924976i
$641$	13.0722	−	8.40101i	0.516322	−	0.331820i	−0.256394	−	0.966572i	$-0.582534\pi$
$641$	13.0722	−	8.40101i	0.516322	−	0.331820i	0.772716	+	0.634752i	$0.218898\pi$
$642$	−11.4099	+	13.1677i	−0.450312	+	0.519688i
$643$	−40.0898			−1.58099			−0.790493	−	0.612471i	$-0.790176\pi$
$643$	−40.0898			−1.58099			−0.790493	+	0.612471i	$0.790176\pi$
$644$	−16.0847	−	8.79510i	−0.633825	−	0.346576i
$645$	−9.91596			−0.390441
$646$	34.0039	−	39.2426i	1.33787	−	1.54398i
$647$	−15.6948	+	10.0864i	−0.617025	+	0.396538i	−0.811486	−	0.584372i	$-0.801341\pi$
$647$	−15.6948	+	10.0864i	−0.617025	+	0.396538i	0.194460	+	0.980910i	$0.437704\pi$
$648$	−0.124613	−	0.866700i	−0.00489525	−	0.0340472i
$649$	0.542963	+	1.18892i	0.0213131	+	0.0466693i
$650$	9.39837	−	65.3671i	0.368634	−	2.56391i
$651$	−1.72601	+	0.506803i	−0.0676478	+	0.0198632i
$652$	−12.5271	−	8.05068i	−0.490599	−	0.315289i
$653$	−19.3948	+	42.4686i	−0.758976	+	1.66193i	−0.00944723	+	0.999955i	$0.503007\pi$
$653$	−19.3948	+	42.4686i	−0.758976	+	1.66193i	−0.749529	+	0.661971i	$0.769720\pi$
$654$	−41.4347	−	12.1663i	−1.62022	−	0.475741i
$655$	−25.8819	−	29.8693i	−1.01129	−	1.16709i
$656$	9.60879	+	11.0891i	0.375160	+	0.432958i
$657$	−0.873179	−	0.256389i	−0.0340660	−	0.0100027i
$658$	6.44413	−	14.1107i	0.251218	−	0.550091i
$659$	−10.3563	−	6.65560i	−0.403425	−	0.259266i	0.323157	−	0.946345i	$-0.395256\pi$
$659$	−10.3563	−	6.65560i	−0.403425	−	0.259266i	−0.726582	+	0.687080i	$0.758892\pi$
$660$	−11.0371	+	3.24080i	−0.429620	+	0.126148i
$661$	−5.03323	+	35.0069i	−0.195770	+	1.36161i	0.620622	+	0.784110i	$0.286880\pi$
$661$	−5.03323	+	35.0069i	−0.195770	+	1.36161i	−0.816391	+	0.577499i	$0.804029\pi$
$662$	−17.6426	−	38.6319i	−0.685700	−	1.50147i
$663$	−2.62166	−	18.2340i	−0.101817	−	0.708151i
$664$	−3.57580	+	2.29803i	−0.138768	+	0.0891808i
$665$	−21.8242	+	25.1864i	−0.846305	+	0.976688i
$666$	−17.3681			−0.672999
$667$	23.1697	+	42.4912i	0.897136	+	1.64527i
$668$	22.8221			0.883014
$669$	−8.05128	+	9.29167i	−0.311280	+	0.359237i
$670$	−17.0340	+	10.9471i	−0.658081	+	0.422923i
$671$	−0.149706	−	1.04122i	−0.00577932	−	0.0401960i
$672$	−5.28394	−	11.5702i	−0.203833	−	0.446331i
$673$	0.0996232	−	0.692895i	0.00384019	−	0.0267091i	−0.987811	−	0.155656i	$-0.950251\pi$
$673$	0.0996232	−	0.692895i	0.00384019	−	0.0267091i	0.991651	+	0.128947i	$0.0411598\pi$
$674$	−22.2057	+	6.52019i	−0.855333	+	0.251148i
$675$	5.80537	+	3.73088i	0.223449	+	0.143602i
$676$	7.76536	−	17.0038i	0.298668	−	0.653991i
$677$	10.9530	+	3.21609i	0.420958	+	0.123604i	0.485349	−	0.874320i	$-0.338692\pi$
$677$	10.9530	+	3.21609i	0.420958	+	0.123604i	−0.0643912	+	0.997925i	$0.520511\pi$
$678$	2.23338	+	2.57746i	0.0857726	+	0.0989869i
$679$	1.76722	+	2.03948i	0.0678196	+	0.0782680i
$680$	11.7251	+	3.44279i	0.449636	+	0.132025i
$681$	−6.84716	+	14.9932i	−0.262384	+	0.574541i
$682$	2.77428	+	1.78292i	0.106233	+	0.0682715i
$683$	−23.6595	+	6.94705i	−0.905305	+	0.265821i	−0.701063	−	0.713099i	$-0.747291\pi$
$683$	−23.6595	+	6.94705i	−0.905305	+	0.265821i	−0.204241	+	0.978921i	$0.565473\pi$
$684$	−2.10051	+	14.6093i	−0.0803149	+	0.558602i
$685$	2.35559	+	5.15802i	0.0900024	+	0.197078i
$686$	5.43951	+	37.8326i	0.207681	+	1.44446i
$687$	−0.535385	+	0.344071i	−0.0204262	+	0.0131271i
$688$	−5.63402	+	6.50201i	−0.214795	+	0.247887i
$689$	−29.7646			−1.13394
$690$	20.8529	−	27.8223i	0.793855	−	1.05918i
$691$	16.2668			0.618819			0.309410	−	0.950929i	$-0.399869\pi$
$691$	16.2668			0.618819			0.309410	+	0.950929i	$0.399869\pi$
$692$	−11.2266	+	12.9562i	−0.426772	+	0.492521i
$693$	1.83602	−	1.17994i	0.0697448	−	0.0448222i
$694$	7.88478	+	54.8399i	0.299302	+	2.08169i
$695$	−7.99091	−	17.4976i	−0.303112	−	0.663723i
$696$	1.25754	−	8.74641i	0.0476671	−	0.331532i
$697$	19.0287	−	5.58734i	0.720765	−	0.211636i
$698$	33.0543	+	21.2427i	1.25112	+	0.804048i
$699$	0.267354	−	0.585423i	0.0101122	−	0.0221427i
$700$	−25.3102	−	7.43175i	−0.956636	−	0.280894i
$701$	−15.8662	−	18.3105i	−0.599256	−	0.691579i	0.372374	−	0.928083i	$-0.378544\pi$
$701$	−15.8662	−	18.3105i	−0.599256	−	0.691579i	−0.971631	+	0.236504i	$0.923998\pi$
$702$	6.26684	+	7.23232i	0.236527	+	0.272966i
$703$	48.4293	+	14.2201i	1.82655	+	0.536322i
$704$	−6.25554	+	13.6977i	−0.235765	+	0.516252i
$705$	13.5429	+	8.70352i	0.510057	+	0.327794i
$706$	−47.5634	+	13.9659i	−1.79007	+	0.525612i
$707$	−1.54994	+	10.7800i	−0.0582914	+	0.405425i
$708$	0.950977	+	2.08235i	0.0357399	+	0.0782595i
$709$	2.90120	+	20.1783i	0.108957	+	0.757811i	0.968906	+	0.247431i	$0.0795863\pi$
$709$	2.90120	+	20.1783i	0.108957	+	0.757811i	−0.859949	+	0.510381i	$0.829505\pi$
$710$	−34.6102	+	22.2426i	−1.29890	+	0.834752i
$711$	−6.38304	+	7.36642i	−0.239383	+	0.276262i
$712$	−3.21038			−0.120314
$713$	−5.44049	+	0.385917i	−0.203748	+	0.0144527i
$714$	−13.4480			−0.503278
$715$	14.1940	−	16.3807i	0.530824	−	0.612604i
$716$	16.3188	−	10.4874i	0.609861	−	0.391934i
$717$	1.37034	+	9.53094i	0.0511764	+	0.355939i
$718$	−13.1438	−	28.7809i	−0.490522	−	1.07409i
$719$	3.34111	−	23.2379i	0.124602	−	0.866628i	−0.827634	−	0.561268i	$-0.810314\pi$
$719$	3.34111	−	23.2379i	0.124602	−	0.866628i	0.952237	−	0.305361i	$-0.0987770\pi$
$720$	9.90728	−	2.90904i	0.369223	−	0.108414i
$721$	0.382683	+	0.245936i	0.0142519	+	0.00915912i
$722$	15.9774	−	34.9857i	0.594618	−	1.30203i
$723$	5.72334	+	1.68052i	0.212853	+	0.0624994i
$724$	18.6570	+	21.5313i	0.693381	+	0.800204i
$725$	45.6050	+	52.6310i	1.69373	+	1.95467i
$726$	18.3420	+	5.38570i	0.680736	+	0.199882i
$727$	9.01408	−	19.7381i	0.334314	−	0.732045i	−0.665584	−	0.746323i	$-0.731818\pi$
$727$	9.01408	−	19.7381i	0.334314	−	0.732045i	0.999898	+	0.0142776i	$0.00454485\pi$
$728$	−5.30555	−	3.40967i	−0.196637	−	0.126371i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−0.938960	+	6.53061i	−0.0347525	+	0.241709i
$731$	4.83059	+	10.5775i	0.178666	+	0.391224i
$732$	−0.262203	−	1.82366i	−0.00969131	−	0.0674045i
$733$	27.2542	−	17.5152i	1.00666	−	0.646939i	0.0701305	−	0.997538i	$-0.477658\pi$
$733$	27.2542	−	17.5152i	1.00666	−	0.646939i	0.936526	+	0.350599i	$0.114022\pi$
$734$	−45.6229	+	52.6517i	−1.68397	+	1.94341i
$735$	−15.5172			−0.572362
$736$	−8.17571	−	37.6891i	−0.301361	−	1.38924i
$737$	−3.85361			−0.141949
$738$	−6.74669	+	7.78610i	−0.248349	+	0.286610i
$739$	30.7673	−	19.7730i	1.13179	−	0.727360i	0.165860	−	0.986149i	$-0.446960\pi$
$739$	30.7673	−	19.7730i	1.13179	−	0.727360i	0.965934	+	0.258789i	$0.0833236\pi$
$740$	9.80522	+	68.1968i	0.360447	+	2.50696i
$741$	−11.5530	−	25.2976i	−0.424412	−	0.929332i
$742$	−3.09230	+	21.5074i	−0.113522	+	0.789562i
$743$	−26.6770	+	7.83308i	−0.978685	+	0.287368i	−0.731681	−	0.681647i	$-0.761264\pi$
$743$	−26.6770	+	7.83308i	−0.978685	+	0.287368i	−0.247003	+	0.969015i	$0.579446\pi$
$744$	0.837727	+	0.538375i	0.0307126	+	0.0197378i
$745$	8.71585	−	19.0850i	0.319324	−	0.699222i
$746$	−66.4179	−	19.5020i	−2.43173	−	0.714021i
$747$	3.17895	+	3.66870i	0.116312	+	0.134231i
$748$	8.83379	+	10.1947i	0.322995	+	0.372757i
$749$	−12.5825	−	3.69455i	−0.459754	−	0.134996i
$750$	5.72487	−	12.5357i	0.209043	−	0.457740i
$751$	−20.6293	−	13.2576i	−0.752774	−	0.483778i	0.107123	−	0.994246i	$-0.465836\pi$
$751$	−20.6293	−	13.2576i	−0.752774	−	0.483778i	−0.859897	+	0.510467i	$0.829472\pi$
$752$	13.4018	−	3.93512i	0.488713	−	0.143499i
$753$	0.548583	−	3.81548i	0.0199915	−	0.139044i
$754$	40.1183	+	87.8468i	1.46102	+	3.19919i
$755$	11.6195	+	80.8153i	0.422877	+	2.94117i
$756$	3.21572	−	2.06662i	0.116955	−	0.0751622i
$757$	32.7294	−	37.7717i	1.18957	−	1.37284i	0.278578	−	0.960414i	$-0.410137\pi$
$757$	32.7294	−	37.7717i	1.18957	−	1.37284i	0.910992	−	0.412424i	$-0.135318\pi$
$758$	46.2460			1.67973
$759$	6.20137	−	2.30886i	0.225095	−	0.0838065i
$760$	18.4485			0.669199
$761$	0.591990	−	0.683192i	0.0214596	−	0.0247657i	−0.744918	−	0.667156i	$-0.767512\pi$
$761$	0.591990	−	0.683192i	0.0214596	−	0.0247657i	0.766378	+	0.642390i	$0.222057\pi$
$762$	17.1329	−	11.0107i	0.620660	−	0.398874i
$763$	−4.62556	−	32.1715i	−0.167457	−	1.16469i
$764$	−26.5532	−	58.1433i	−0.960660	−	2.10355i
$765$	1.98615	−	13.8140i	0.0718094	−	0.499445i
$766$	−9.44209	+	2.77245i	−0.341156	+	0.100173i
$767$	−3.62873	−	2.33205i	−0.131026	−	0.0842053i
$768$	3.08461	−	6.75434i	0.111306	−	0.243726i
$769$	−45.0748	−	13.2351i	−1.62544	−	0.477272i	−0.662965	−	0.748650i	$-0.730702\pi$
$769$	−45.0748	−	13.2351i	−1.62544	−	0.477272i	−0.962473	+	0.271379i	$0.912520\pi$
$770$	−10.3618	−	11.9582i	−0.373414	−	0.430942i
$771$	7.73447	+	8.92606i	0.278550	+	0.321464i
$772$	−43.7061	−	12.8333i	−1.57302	−	0.461879i
$773$	17.5403	−	38.4080i	0.630882	−	1.38144i	−0.276451	−	0.961028i	$-0.589158\pi$
$773$	17.5403	−	38.4080i	0.630882	−	1.38144i	0.907333	−	0.420412i	$-0.138114\pi$
$774$	−5.08181	−	3.26588i	−0.182662	−	0.117390i
$775$	−7.53023	+	2.21108i	−0.270494	+	0.0794242i
$776$	0.212601	−	1.47867i	0.00763192	−	0.0530812i
$777$	−5.43033	−	11.8908i	−0.194812	−	0.426579i
$778$	4.19632	+	29.1860i	0.150445	+	1.04637i
$779$	25.1874	−	16.1870i	0.902433	−	0.579958i
$780$	24.8602	−	28.6902i	0.890137	−	1.02727i
$781$	−7.82988			−0.280175
$782$	−39.8371	−	8.69040i	−1.42457	−	0.310768i
$783$	−10.0916			−0.360645
$784$	−8.81653	+	10.1748i	−0.314876	+	0.363387i
$785$	45.2123	−	29.0562i	1.61370	−	1.03706i
$786$	−3.42652	−	23.8320i	−0.122220	−	0.850059i
$787$	7.78645	+	17.0499i	0.277557	+	0.607765i	0.996150	−	0.0876659i	$-0.0279408\pi$
$787$	7.78645	+	17.0499i	0.277557	+	0.607765i	−0.718593	+	0.695431i	$0.755214\pi$
$788$	−3.03278	+	21.0935i	−0.108038	+	0.751423i
$789$	−14.0599	+	4.12835i	−0.500544	+	0.146973i
$790$	59.4485	+	38.2052i	2.11508	+	1.35928i
$791$	−1.06632	+	2.33492i	−0.0379141	+	0.0830203i
$792$	−1.15922	−	0.340378i	−0.0411912	−	0.0120948i
$793$	2.27341	+	2.62365i	0.0807310	+	0.0931686i
$794$	−15.4983	−	17.8860i	−0.550015	−	0.634751i
$795$	−21.6360	−	6.35290i	−0.767350	−	0.225314i
$796$	15.0648	−	32.9872i	0.533956	−	1.16920i
$797$	−40.5721	−	26.0741i	−1.43714	−	0.923593i	−0.999704	−	0.0243425i	$-0.992251\pi$
$797$	−40.5721	−	26.0741i	−1.43714	−	0.923593i	−0.437435	−	0.899250i	$-0.644113\pi$
$798$	−19.4799	+	5.71983i	−0.689582	+	0.202480i
$799$	2.68670	−	18.6864i	0.0950488	−	0.661079i
$800$	−23.0527	−	50.4784i	−0.815037	−	1.78468i
$801$	0.521788	+	3.62912i	0.0184365	+	0.128228i
$802$	−30.2734	+	19.4555i	−1.06899	+	0.686998i
$803$	−0.822287	+	0.948970i	−0.0290179	+	0.0334884i
$804$	−6.74944			−0.238034
$805$	25.5680	+	5.57762i	0.901152	+	0.196585i
$806$	−10.8834			−0.383350
$807$	17.8233	−	20.5692i	0.627411	−	0.724070i
$808$	5.07182	−	3.25946i	0.178426	−	0.114668i
$809$	7.57169	+	52.6623i	0.266206	+	1.85151i	0.483428	+	0.875384i	$0.339391\pi$
$809$	7.57169	+	52.6623i	0.266206	+	1.85151i	−0.217222	+	0.976122i	$0.569700\pi$
$810$	3.01174	+	6.59479i	0.105822	+	0.231717i
$811$	−0.523752	+	3.64278i	−0.0183914	+	0.127915i	−0.996949	−	0.0780599i	$-0.975127\pi$
$811$	−0.523752	+	3.64278i	−0.0183914	+	0.127915i	0.978557	+	0.205975i	$0.0660366\pi$
$812$	37.0130	−	10.8680i	1.29890	−	0.381392i
$813$	−3.60389	−	2.31608i	−0.126394	−	0.0812285i
$814$	−9.95512	+	21.7987i	−0.348927	+	0.764043i
$815$	20.3959	+	5.98876i	0.714436	+	0.209777i
$816$	−7.92949	−	9.15112i	−0.277588	−	0.320353i
$817$	11.4962	+	13.2674i	0.402202	+	0.464166i
$818$	18.1111	+	5.31790i	0.633240	+	0.185936i
$819$	−2.99209	+	6.55175i	−0.104552	+	0.228937i
$820$	34.3815	+	22.0956i	1.20065	+	0.771613i
$821$	−2.34866	+	0.689628i	−0.0819686	+	0.0240682i	−0.322460	−	0.946583i	$-0.604510\pi$
$821$	−2.34866	+	0.689628i	−0.0819686	+	0.0240682i	0.240491	+	0.970651i	$0.422692\pi$
$822$	−0.491615	+	3.41925i	−0.0171470	+	0.119260i
$823$	0.368876	+	0.807725i	0.0128582	+	0.0281555i	0.915952	−	0.401287i	$-0.131437\pi$
$823$	0.368876	+	0.807725i	0.0128582	+	0.0281555i	−0.903094	+	0.429443i	$0.858710\pi$
$824$	−0.0358374	−	0.249254i	−0.00124845	−	0.00868319i
$825$	8.01018	−	5.14783i	0.278879	−	0.179224i
$826$	−2.06210	+	2.37979i	−0.0717495	+	0.0828033i
$827$	25.9780			0.903343			0.451671	−	0.892184i	$-0.350828\pi$
$827$	25.9780			0.903343			0.451671	+	0.892184i	$0.350828\pi$
$828$	10.8614	−	4.04388i	0.377461	−	0.140535i
$829$	−18.5613			−0.644662			−0.322331	−	0.946627i	$-0.604466\pi$
$829$	−18.5613			−0.644662			−0.322331	+	0.946627i	$0.604466\pi$
$830$	23.0472	−	26.5979i	0.799981	−	0.923227i
$831$	5.77248	−	3.70975i	0.200245	−	0.128690i
$832$	−7.07250	−	49.1904i	−0.245195	−	1.70537i
$833$	7.55927	+	16.5525i	0.261913	+	0.573510i
$834$	1.66771	−	11.5992i	0.0577482	−	0.401647i
$835$	−31.2589	+	9.17844i	−1.08176	+	0.317633i
$836$	17.1322	+	11.0102i	0.592530	+	0.380796i
$837$	0.472439	−	1.03450i	0.0163299	−	0.0357575i
$838$	14.1997	+	4.16940i	0.490519	+	0.144029i
$839$	11.1414	+	12.8578i	0.384643	+	0.443902i	0.914745	−	0.404032i	$-0.132392\pi$
$839$	11.1414	+	12.8578i	0.384643	+	0.443902i	−0.530102	+	0.847934i	$0.677846\pi$
$840$	−3.12888	−	3.61092i	−0.107957	−	0.124588i
$841$	−69.8902	−	20.5216i	−2.41001	−	0.707642i
$842$	10.7359	−	23.5083i	0.369982	−	0.810148i
$843$	−11.1935	−	7.19364i	−0.385525	−	0.247762i
$844$	61.9701	−	18.1961i	2.13310	−	0.626334i
$845$	−3.79757	+	26.4127i	−0.130640	+	0.908624i
$846$	4.07404	+	8.92091i	0.140068	+	0.306707i
$847$	2.04761	+	14.2415i	0.0703568	+	0.489342i
$848$	−16.4588	+	10.5774i	−0.565196	+	0.363229i
$849$	−12.5876	+	14.5268i	−0.432004	+	0.498559i
$850$	−58.6707			−2.01239
$851$	−8.40221	−	38.7333i	−0.288024	−	1.32776i
$852$	−13.7137			−0.469824
$853$	−21.6663	+	25.0043i	−0.741841	+	0.856130i	−0.993751	−	0.111621i	$-0.964396\pi$
$853$	−21.6663	+	25.0043i	−0.741841	+	0.856130i	0.251910	+	0.967751i	$0.418941\pi$
$854$	2.13200	−	1.37015i	0.0729555	−	0.0468856i
$855$	−2.99847	−	20.8548i	−0.102546	−	0.713221i
$856$	3.01565	+	6.60334i	0.103073	+	0.225698i
$857$	1.42530	−	9.91317i	0.0486873	−	0.338628i	−0.950889	−	0.309531i	$-0.899828\pi$
$857$	1.42530	−	9.91317i	0.0486873	−	0.338628i	0.999577	−	0.0290964i	$-0.00926299\pi$
$858$	12.6693	−	3.72005i	0.432524	−	0.127001i
$859$	31.7908	+	20.4307i	1.08469	+	0.697087i	0.955636	−	0.294551i	$-0.0951699\pi$
$859$	31.7908	+	20.4307i	1.08469	+	0.697087i	0.129053	+	0.991638i	$0.458806\pi$
$860$	−9.95474	+	21.7978i	−0.339454	+	0.743300i
$861$	−7.44005	−	2.18460i	−0.253556	−	0.0744509i
$862$	−6.94053	−	8.00980i	−0.236395	−	0.272815i
$863$	−25.4019	−	29.3154i	−0.864691	−	0.997906i	−0.999975	−	0.00709937i	$-0.997740\pi$
$863$	−25.4019	−	29.3154i	−0.864691	−	0.997906i	0.135284	−	0.990807i	$-0.456805\pi$
$864$	7.71577	+	2.26555i	0.262496	+	0.0770757i
$865$	10.1662	−	22.2608i	0.345661	−	0.756891i
$866$	−1.57268	−	1.01070i	−0.0534419	−	0.0343450i
$867$	0.608222	−	0.178590i	0.0206563	−	0.00606524i
$868$	−0.618679	+	4.30301i	−0.0209993	+	0.146054i
$869$	5.58693	+	12.2337i	0.189524	+	0.414999i
$870$	10.4123	+	72.4191i	0.353010	+	2.45524i
$871$	10.6988	−	6.87570i	0.362515	−	0.232974i
$872$	−11.7825	+	13.5977i	−0.399005	+	0.460477i
$873$	−1.70609			−0.0577425
$874$	−61.4018	+	4.35549i	−2.07695	+	0.147327i
$875$	10.3723			0.350648
$876$	−1.44020	+	1.66208i	−0.0486599	+	0.0561565i
$877$	−19.9423	+	12.8161i	−0.673404	+	0.432770i	−0.832151	−	0.554549i	$-0.812891\pi$
$877$	−19.9423	+	12.8161i	−0.673404	+	0.432770i	0.158747	+	0.987319i	$0.449255\pi$
$878$	−11.9287	−	82.9656i	−0.402573	−	2.79995i
$879$	5.66822	+	12.4117i	0.191184	+	0.418635i
$880$	2.02757	−	14.1021i	0.0683494	−	0.475380i
$881$	−18.9632	+	5.56809i	−0.638885	+	0.187594i	−0.585103	−	0.810959i	$-0.698946\pi$
$881$	−18.9632	+	5.56809i	−0.638885	+	0.187594i	−0.0537823	+	0.998553i	$0.517128\pi$
$882$	−7.95240	−	5.11070i	−0.267771	−	0.172086i
$883$	11.0250	−	24.1413i	0.371020	−	0.812420i	−0.628385	−	0.777903i	$-0.716284\pi$
$883$	11.0250	−	24.1413i	0.371020	−	0.812420i	0.999404	−	0.0345167i	$-0.0109892\pi$
$884$	−42.7150	−	12.5423i	−1.43666	−	0.421842i
$885$	−2.14000	−	2.46969i	−0.0719352	−	0.0830176i
$886$	−17.6301	−	20.3462i	−0.592295	−	0.683545i
$887$	12.3340	+	3.62160i	0.414136	+	0.121601i	0.482162	−	0.876082i	$-0.339852\pi$
$887$	12.3340	+	3.62160i	0.414136	+	0.121601i	−0.0680256	+	0.997684i	$0.521670\pi$
$888$	−3.00607	+	6.58238i	−0.100877	+	0.220890i
$889$	12.8951	+	8.28716i	0.432487	+	0.277942i
$890$	25.5047	−	7.48887i	0.854921	−	0.251027i
$891$	−0.196364	+	1.36574i	−0.00657846	+	0.0457542i
$892$	12.3427	+	27.0268i	0.413265	+	0.904924i
$893$	−4.05610	−	28.2108i	−0.135732	−	0.944037i
$894$	10.7526	−	6.91025i	0.359619	−	0.231113i
$895$	−18.1337	+	20.9274i	−0.606141	+	0.699524i
$896$	−10.8396			−0.362125
$897$	−13.0974	+	17.4747i	−0.437308	+	0.583465i
$898$	−28.0436			−0.935827
$899$	7.51577	−	8.67366i	0.250665	−	0.289283i
$900$	14.0295	−	9.01622i	0.467650	−	0.300541i
$901$	3.76330	+	26.1743i	0.125374	+	0.871994i
$902$	5.90523	+	12.9307i	0.196623	+	0.430544i
$903$	0.647045	−	4.50030i	0.0215323	−	0.149760i
$904$	1.36340	−	0.400329i	0.0453459	−	0.0133148i
$905$	−34.2133	−	21.9876i	−1.13729	−	0.730891i
$906$	−20.6622	+	45.2439i	−0.686455	+	1.50313i
$907$	38.4349	+	11.2855i	1.27621	+	0.374729i	0.848504	−	0.529189i	$-0.177504\pi$
$907$	38.4349	+	11.2855i	1.27621	+	0.374729i	0.427706	+	0.903918i	$0.359322\pi$
$908$	26.0850	+	30.1037i	0.865660	+	0.999025i
$909$	−4.50894	−	5.20359i	−0.149552	−	0.172592i
$910$	50.1036	+	14.7117i	1.66092	+	0.487690i
$911$	−18.9746	+	41.5487i	−0.628658	+	1.37657i	0.280393	+	0.959885i	$0.409535\pi$
$911$	−18.9746	+	41.5487i	−0.628658	+	1.37657i	−0.909051	+	0.416684i	$0.863192\pi$
$912$	−15.3784	−	9.88311i	−0.509230	−	0.327263i
$913$	6.42671	−	1.88705i	0.212693	−	0.0624523i
$914$	−6.89767	+	47.9743i	−0.228155	+	1.58685i
$915$	1.09256	+	2.39238i	0.0361190	+	0.0790896i
$916$	0.218878	+	1.52233i	0.00723194	+	0.0502992i
$917$	15.2448	−	9.79726i	0.503429	−	0.323534i
$918$	5.56760	−	6.42535i	0.183758	−	0.212068i
$919$	9.12733			0.301083			0.150541	−	0.988604i	$-0.451898\pi$
$919$	9.12733			0.301083			0.150541	+	0.988604i	$0.451898\pi$
$920$	−6.93524	−	12.7186i	−0.228648	−	0.419320i
$921$	−25.4313			−0.837991
$922$	10.4592	−	12.0706i	0.344457	−	0.397524i
$923$	21.7381	−	13.9703i	0.715520	−	0.459837i
$924$	−0.750610	−	5.22061i	−0.0246933	−	0.171745i
$925$	−23.6914	−	51.8769i	−0.778967	−	1.70570i
$926$	−3.04095	+	21.1502i	−0.0999317	+	0.695040i
$927$	−0.275941	+	0.0810235i	−0.00906308	+	0.00266116i
$928$	68.2693	+	43.8740i	2.24105	+	1.44023i
$929$	0.242509	−	0.531021i	0.00795647	−	0.0174222i	−0.905612	−	0.424107i	$-0.860588\pi$
$929$	0.242509	−	0.531021i	0.00795647	−	0.0174222i	0.913569	+	0.406685i	$0.133315\pi$
$930$	−7.91117	−	2.32293i	−0.259418	−	0.0761719i
$931$	17.9902	+	20.7618i	0.589604	+	0.680439i
$932$	−1.01851	−	1.17542i	−0.0333624	−	0.0385023i
$933$	30.2031	+	8.86842i	0.988804	+	0.290339i
$934$	−9.02099	+	19.7532i	−0.295176	+	0.646345i
$935$	−16.1995	−	10.4108i	−0.529780	−	0.340469i
$936$	3.82567	−	1.12332i	0.125046	−	0.0367168i
$937$	7.47312	−	51.9767i	0.244136	−	1.69800i	−0.386795	−	0.922166i	$-0.626418\pi$
$937$	7.47312	−	51.9767i	0.244136	−	1.69800i	0.630931	−	0.775839i	$-0.282673\pi$
$938$	−3.85675	−	8.44511i	−0.125927	−	0.275743i
$939$	−1.91690	−	13.3323i	−0.0625557	−	0.435085i
$940$	32.7285	−	21.0333i	1.06749	−	0.686031i
$941$	34.9319	−	40.3135i	1.13875	−	1.31418i	0.196025	−	0.980599i	$-0.437197\pi$
$941$	34.9319	−	40.3135i	1.13875	−	1.31418i	0.942720	−	0.333584i	$-0.108258\pi$
$942$	32.7406			1.06675
$943$	−20.6280	−	11.2794i	−0.671739	−	0.367307i
$944$	−2.83530			−0.0922811
$945$	−3.57336	+	4.12388i	−0.116241	+	0.134150i
$946$	−7.01183	+	4.50623i	−0.227974	+	0.146510i
$947$	1.81889	+	12.6507i	0.0591060	+	0.411091i	0.997798	+	0.0663332i	$0.0211300\pi$
$947$	1.81889	+	12.6507i	0.0591060	+	0.411091i	−0.938692	+	0.344758i	$0.887961\pi$
$948$	9.78528	+	21.4268i	0.317811	+	0.695909i
$949$	0.589746	−	4.10177i	0.0191440	−	0.133149i
$950$	−84.9869	+	24.9544i	−2.75734	+	0.809627i
$951$	−3.23773	−	2.08077i	−0.104991	−	0.0674734i
$952$	−2.32758	+	5.09670i	−0.0754374	+	0.165185i
$953$	25.7813	+	7.57006i	0.835137	+	0.245218i	0.671222	−	0.741256i	$-0.265770\pi$
$953$	25.7813	+	7.57006i	0.835137	+	0.245218i	0.163915	+	0.986474i	$0.447588\pi$
$954$	−8.99584	−	10.3817i	−0.291251	−	0.336121i
$955$	59.7529	+	68.9586i	1.93356	+	2.23145i
$956$	22.3272	+	6.55584i	0.722112	+	0.212031i
$957$	−5.78437	+	12.6660i	−0.186982	+	0.409434i
$958$	−15.4013	−	9.89782i	−0.497594	−	0.319784i
$959$	−2.49464	+	0.732494i	−0.0805563	+	0.0236535i
$960$	5.35808	−	37.2663i	0.172931	−	1.20276i
$961$	−12.3406	−	27.0221i	−0.398083	−	0.871680i
$962$	−11.2552	−	78.2820i	−0.362884	−	2.52391i
$963$	6.97450	−	4.48224i	0.224750	−	0.144438i
$964$	9.43995	−	10.8943i	0.304040	−	0.350881i
$965$	65.0244			2.09321
$966$	11.2663	+	11.2794i	0.362486	+	0.362910i
$967$	12.5704			0.404236			0.202118	−	0.979361i	$-0.435218\pi$
$967$	12.5704			0.404236			0.202118	+	0.979361i	$0.435218\pi$
$968$	5.21579	−	6.01934i	0.167642	−	0.193469i
$969$	−20.7855	+	13.3580i	−0.667727	+	0.429122i
$970$	1.76031	+	12.2432i	0.0565200	+	0.393105i
$971$	−8.30513	−	18.1857i	−0.266524	−	0.583607i	0.728295	−	0.685263i	$-0.240313\pi$
$971$	−8.30513	−	18.1857i	−0.266524	−	0.583607i	−0.994820	+	0.101657i	$0.967586\pi$
$972$	−0.343924	+	2.39205i	−0.0110314	+	0.0767249i
$973$	8.46263	−	2.48485i	0.271299	−	0.0796607i
$974$	40.2519	+	25.8683i	1.28975	+	0.828874i
$975$	−13.0538	+	28.5839i	−0.418057	+	0.915418i
$976$	2.18948	+	0.642889i	0.0700835	+	0.0205784i
$977$	18.0952	+	20.8830i	0.578917	+	0.668106i	0.967372	−	0.253362i	$-0.0815364\pi$
$977$	18.0952	+	20.8830i	0.578917	+	0.668106i	−0.388454	+	0.921468i	$0.626991\pi$
$978$	8.48020	+	9.78668i	0.271167	+	0.312943i
$979$	4.85399	+	1.42526i	0.155134	+	0.0455515i
$980$	−15.5779	+	34.1109i	−0.497618	+	1.08963i
$981$	17.2863	+	11.1093i	0.551910	+	0.354691i
$982$	−56.5477	+	16.6039i	−1.80451	+	0.529852i
$983$	−3.34878	+	23.2913i	−0.106809	+	0.742876i	0.864081	+	0.503353i	$0.167900\pi$
$983$	−3.34878	+	23.2913i	−0.106809	+	0.742876i	−0.970891	+	0.239523i	$0.923009\pi$
$984$	1.78316	+	3.90457i	0.0568450	+	0.124473i
$985$	−4.32930	−	30.1109i	−0.137943	−	0.959414i
$986$	72.1783	−	46.3862i	2.29863	−	1.47724i
$987$	−4.83375	+	5.57845i	−0.153860	+	0.177564i
$988$	−67.2089			−2.13820
$989$	4.82494	−	12.9131i	0.153424	−	0.410613i
$990$	10.0034			0.317929
$991$	−28.0874	+	32.4146i	−0.892226	+	1.02968i	0.107146	+	0.994243i	$0.465829\pi$
$991$	−28.0874	+	32.4146i	−0.892226	+	1.02968i	−0.999372	+	0.0354405i	$0.988717\pi$
$992$	−7.69357	+	4.94436i	−0.244271	+	0.156984i
$993$	2.87597	+	20.0028i	0.0912662	+	0.634771i
$994$	−7.83627	−	17.1590i	−0.248551	−	0.544252i
$995$	−7.36726	+	51.2405i	−0.233558	+	1.62443i
$996$	11.2561	−	3.30510i	0.356664	−	0.104726i
$997$	−32.7183	−	21.0268i	−1.03620	−	0.665925i	−0.0921555	−	0.995745i	$-0.529376\pi$
$997$	−32.7183	−	21.0268i	−1.03620	−	0.665925i	−0.944044	+	0.329820i	$0.893012\pi$
$998$	−12.7888	+	28.0036i	−0.404823	+	0.886439i
$999$	7.92952	+	2.32832i	0.250879	+	0.0736647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.16.1	yes	20
3.2	odd	2		207.2.i.d.154.2		20
23.6	even	11		1587.2.a.u.1.10		10
23.13	even	11	inner	69.2.e.c.13.1	✓	20
23.17	odd	22		1587.2.a.t.1.10		10
69.17	even	22		4761.2.a.bu.1.1		10
69.29	odd	22		4761.2.a.bt.1.1		10
69.59	odd	22		207.2.i.d.82.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.13.1	✓	20	23.13	even	11	inner
69.2.e.c.16.1	yes	20	1.1	even	1	trivial
207.2.i.d.82.2		20	69.59	odd	22
207.2.i.d.154.2		20	3.2	odd	2
1587.2.a.t.1.10		10	23.17	odd	22
1587.2.a.u.1.10		10	23.6	even	11
4761.2.a.bt.1.1		10	69.29	odd	22
4761.2.a.bu.1.1		10	69.17	even	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37624 + 1.58827i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.343924 - 2.39205i) q^{4} +(1.43308 + 3.13801i) q^{5} +(-0.299086 + 2.08019i) q^{6} +(-1.51768 + 0.445631i) q^{7} +(0.736612 + 0.473392i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.37624 + 1.58827i) q^{2} +(0.841254 - 0.540641i) q^{3} +(-0.343924 - 2.39205i) q^{4} +(1.43308 + 3.13801i) q^{5} +(-0.299086 + 2.08019i) q^{6} +(-1.51768 + 0.445631i) q^{7} +(0.736612 + 0.473392i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-6.95628 - 2.04255i) q^{10} +(-0.903570 - 1.04278i) q^{11} +(-1.58257 - 1.82638i) q^{12} +(4.36913 + 1.28289i) q^{13} +(1.38092 - 3.02378i) q^{14} +(2.90212 + 1.86508i) q^{15} +(2.87188 - 0.843259i) q^{16} +(0.575735 - 4.00433i) q^{17} +(0.873028 + 1.91167i) q^{18} +(-0.869183 - 6.04530i) q^{19} +(7.01340 - 4.50724i) q^{20} +(-1.03583 + 1.19541i) q^{21} +2.89974 q^{22} +(-3.84094 + 2.87179i) q^{23} +0.875613 q^{24} +(-4.51910 + 5.21532i) q^{25} +(-8.05057 + 5.17378i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(1.58794 + 3.47710i) q^{28} +(1.43619 - 9.98890i) q^{29} +(-6.95628 + 2.04255i) q^{30} +(0.956733 + 0.614855i) q^{31} +(-3.34056 + 7.31481i) q^{32} +(-1.32390 - 0.388732i) q^{33} +(5.56760 + 6.42535i) q^{34} +(-3.57336 - 4.12388i) q^{35} +(-2.31875 - 0.680847i) q^{36} +(-3.43311 + 7.51746i) q^{37} +(10.7978 + 6.93931i) q^{38} +(4.36913 - 1.28289i) q^{39} +(-0.429884 + 2.98991i) q^{40} +(2.03647 + 4.45925i) q^{41} +(-0.473080 - 3.29035i) q^{42} +(-2.41809 + 1.55401i) q^{43} +(-2.18361 + 2.52002i) q^{44} +3.44976 q^{45} +(0.724889 - 10.0527i) q^{46} +4.66656 q^{47} +(1.96008 - 2.26205i) q^{48} +(-3.78401 + 2.43183i) q^{49} +(-2.06395 - 14.3551i) q^{50} +(-1.68056 - 3.67992i) q^{51} +(1.56609 - 10.8924i) q^{52} +(-6.27174 + 1.84155i) q^{53} +(1.76796 + 1.13620i) q^{54} +(1.97735 - 4.32980i) q^{55} +(-1.32890 - 0.390200i) q^{56} +(-3.99954 - 4.61571i) q^{57} +(13.8885 + 16.0282i) q^{58} +(-0.908902 - 0.266878i) q^{59} +(3.46325 - 7.58346i) q^{60} +(0.641360 + 0.412177i) q^{61} +(-2.29325 + 0.673360i) q^{62} +(-0.225107 + 1.56565i) q^{63} +(-4.53369 - 9.92740i) q^{64} +(2.23559 + 15.5489i) q^{65} +(2.43942 - 1.56772i) q^{66} +(1.82896 - 2.11073i) q^{67} -9.77655 q^{68} +(-1.67860 + 4.49247i) q^{69} +11.4676 q^{70} +(3.71613 - 4.28865i) q^{71} +(0.736612 - 0.473392i) q^{72} +(-0.129513 - 0.900780i) q^{73} +(-7.21496 - 15.7986i) q^{74} +(-0.982094 + 6.83061i) q^{75} +(-14.1617 + 4.15825i) q^{76} +(1.83602 + 1.17994i) q^{77} +(-3.97541 + 8.70493i) q^{78} +(-9.35234 - 2.74609i) q^{79} +(6.76179 + 7.80352i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-9.88516 - 2.90255i) q^{82} +(-2.01659 + 4.41571i) q^{83} +(3.21572 + 2.06662i) q^{84} +(13.3907 - 3.93187i) q^{85} +(0.859691 - 5.97928i) q^{86} +(-4.19221 - 9.17966i) q^{87} +(-0.171939 - 1.19586i) q^{88} +(-3.08440 + 1.98222i) q^{89} +(-4.74771 + 5.47915i) q^{90} -7.20264 q^{91} +(8.19045 + 8.20003i) q^{92} +1.13727 q^{93} +(-6.42232 + 7.41176i) q^{94} +(17.7246 - 11.3909i) q^{95} +(1.14443 + 7.95966i) q^{96} +(-0.708736 - 1.55192i) q^{97} +(1.34531 - 9.35682i) q^{98} +(-1.32390 + 0.388732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

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