LMFDB - Embedded newform 690.2.m.e.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
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} - 6 x^{19} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 21x^18 - 47x^17 + 44x^16 + 232x^15 - 1084x^14 + 1484x^13 + 2670x^12 - 12826x^11 + 18393x^10 - 2728x^9 - 12654x^8 - 6818x^7 + 39054x^6 + 33738x^5 + 67716x^4 + 45635x^3 + 32892x^2 + 9761*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			151.1
Root			$0.909132 - 1.99072i$ of defining polynomial
Character	$\chi$	$=$	690.151
Dual form			690.2.m.e.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.28976 - 0.672335i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.28976 - 0.672335i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(0.959493 - 0.281733i) q^{10} +(-2.98888 + 3.44935i) q^{11} +(0.654861 - 0.755750i) q^{12} +(-1.03405 + 0.303624i) q^{13} +(-0.991359 - 2.17077i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.0307658 + 0.213981i) q^{17} +(-0.415415 + 0.909632i) q^{18} +(-0.801398 + 5.57385i) q^{19} +(0.841254 + 0.540641i) q^{20} +(1.56278 + 1.80354i) q^{21} -4.56415 q^{22} +(-2.92281 + 3.80226i) q^{23} +1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-0.906620 - 0.582649i) q^{26} +(0.142315 - 0.989821i) q^{27} +(0.991359 - 2.17077i) q^{28} +(0.113058 + 0.786335i) q^{29} +(-0.959493 - 0.281733i) q^{30} +(-4.68265 + 3.00935i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(4.37927 - 1.28587i) q^{33} +(-0.141569 + 0.163379i) q^{34} +(-1.56278 + 1.80354i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-2.14119 - 4.68854i) q^{37} +(-4.73724 + 3.04444i) q^{38} +(1.03405 + 0.303624i) q^{39} +(0.142315 + 0.989821i) q^{40} +(-0.401760 + 0.879732i) q^{41} +(-0.339625 + 2.36214i) q^{42} +(5.15916 + 3.31559i) q^{43} +(-2.98888 - 3.44935i) q^{44} +1.00000 q^{45} +(-4.78759 + 0.281042i) q^{46} +2.66714 q^{47} +(0.654861 + 0.755750i) q^{48} +(-1.09779 - 0.705508i) q^{49} +(0.142315 - 0.989821i) q^{50} +(0.0898049 - 0.196645i) q^{51} +(-0.153373 - 1.06673i) q^{52} +(-3.38723 - 0.994581i) q^{53} +(0.841254 - 0.540641i) q^{54} +(1.89602 + 4.15170i) q^{55} +(2.28976 - 0.672335i) q^{56} +(3.68763 - 4.25575i) q^{57} +(-0.520235 + 0.600384i) q^{58} +(5.22968 - 1.53557i) q^{59} +(-0.415415 - 0.909632i) q^{60} +(-9.10999 + 5.85463i) q^{61} +(-5.34080 - 1.56820i) q^{62} +(-0.339625 - 2.36214i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.153373 + 1.06673i) q^{65} +(3.83961 + 2.46757i) q^{66} +(-9.12366 - 10.5293i) q^{67} -0.216181 q^{68} +(4.51448 - 1.61848i) q^{69} -2.38643 q^{70} +(-2.21848 - 2.56026i) q^{71} +(-0.841254 - 0.540641i) q^{72} +(1.94089 - 13.4992i) q^{73} +(2.14119 - 4.68854i) q^{74} +(0.142315 + 0.989821i) q^{75} +(-5.40306 - 1.58648i) q^{76} +(9.16296 - 5.88867i) q^{77} +(0.447693 + 0.980312i) q^{78} +(-0.0557307 + 0.0163640i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-0.927954 + 0.272472i) q^{82} +(6.91098 + 15.1329i) q^{83} +(-2.00759 + 1.29020i) q^{84} +(0.207424 + 0.0609053i) q^{85} +(0.872774 + 6.07028i) q^{86} +(0.330015 - 0.722631i) q^{87} +(0.649546 - 4.51769i) q^{88} +(1.58913 + 1.02127i) q^{89} +(0.654861 + 0.755750i) q^{90} +2.57186 q^{91} +(-3.34760 - 3.43418i) q^{92} +5.56627 q^{93} +(1.74661 + 2.01569i) q^{94} +(4.73724 + 3.04444i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(3.73646 - 8.18170i) q^{97} +(-0.185713 - 1.29167i) q^{98} +(-4.37927 - 1.28587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.654861	+	0.755750i	0.463056	+	0.534396i
$2$	0.654861	+	0.755750i	0.463056	+	0.534396i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−2.28976	−	0.672335i	−0.865449	−	0.254119i	−0.181271	−	0.983433i	$-0.558021\pi$
$7$	−2.28976	−	0.672335i	−0.865449	−	0.254119i	−0.684179	+	0.729314i	$0.739839\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	0.959493	−	0.281733i	0.303418	−	0.0890917i
$11$	−2.98888	+	3.44935i	−0.901182	+	1.04002i	0.0978134	+	0.995205i	$0.468815\pi$
$11$	−2.98888	+	3.44935i	−0.901182	+	1.04002i	−0.998995	+	0.0448146i	$0.985730\pi$
$12$	0.654861	−	0.755750i	0.189042	−	0.218166i
$13$	−1.03405	+	0.303624i	−0.286793	+	0.0842100i	−0.421965	−	0.906612i	$-0.638659\pi$
$13$	−1.03405	+	0.303624i	−0.286793	+	0.0842100i	0.135172	+	0.990822i	$0.456841\pi$
$14$	−0.991359	−	2.17077i	−0.264952	−	0.580164i
$15$	−0.841254	+	0.540641i	−0.217211	+	0.139593i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.0307658	+	0.213981i	0.00746180	+	0.0518980i	0.993212	−	0.116317i	$-0.0371088\pi$
$17$	0.0307658	+	0.213981i	0.00746180	+	0.0518980i	−0.985750	+	0.168215i	$0.946200\pi$
$18$	−0.415415	+	0.909632i	−0.0979143	+	0.214402i
$19$	−0.801398	+	5.57385i	−0.183853	+	1.27873i	0.663692	+	0.748006i	$0.268988\pi$
$19$	−0.801398	+	5.57385i	−0.183853	+	1.27873i	−0.847546	+	0.530722i	$0.821921\pi$
$20$	0.841254	+	0.540641i	0.188110	+	0.120891i
$21$	1.56278	+	1.80354i	0.341027	+	0.393566i
$22$	−4.56415			−0.973080
$23$	−2.92281	+	3.80226i	−0.609447	+	0.792826i
$23$	−2.92281	+	3.80226i	−0.609447	+	0.792826i
$24$	1.00000			0.204124
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	−0.906620	−	0.582649i	−0.177803	−	0.114267i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	0.991359	−	2.17077i	0.187349	−	0.410238i
$29$	0.113058	+	0.786335i	0.0209943	+	0.146019i	0.997622	−	0.0689178i	$-0.0219546\pi$
$29$	0.113058	+	0.786335i	0.0209943	+	0.146019i	−0.976628	+	0.214937i	$0.931046\pi$
$30$	−0.959493	−	0.281733i	−0.175179	−	0.0514371i
$31$	−4.68265	+	3.00935i	−0.841028	+	0.540496i	−0.888765	−	0.458364i	$-0.848436\pi$
$31$	−4.68265	+	3.00935i	−0.841028	+	0.540496i	0.0477364	+	0.998860i	$0.484799\pi$
$32$	−0.415415	−	0.909632i	−0.0734357	−	0.160802i
$33$	4.37927	−	1.28587i	0.762333	−	0.223841i
$34$	−0.141569	+	0.163379i	−0.0242788	+	0.0280192i
$35$	−1.56278	+	1.80354i	−0.264158	+	0.304855i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−2.14119	−	4.68854i	−0.352009	−	0.770792i	−0.999959	−	0.00910862i	$-0.997101\pi$
$37$	−2.14119	−	4.68854i	−0.352009	−	0.770792i	0.647950	−	0.761683i	$-0.275627\pi$
$38$	−4.73724	+	3.04444i	−0.768481	+	0.493873i
$39$	1.03405	+	0.303624i	0.165580	+	0.0486187i
$40$	0.142315	+	0.989821i	0.0225020	+	0.156505i
$41$	−0.401760	+	0.879732i	−0.0627444	+	0.137391i	−0.938407	−	0.345533i	$-0.887698\pi$
$41$	−0.401760	+	0.879732i	−0.0627444	+	0.137391i	0.875662	+	0.482924i	$0.160425\pi$
$42$	−0.339625	+	2.36214i	−0.0524052	+	0.364486i
$43$	5.15916	+	3.31559i	0.786764	+	0.505622i	0.871272	−	0.490800i	$-0.163296\pi$
$43$	5.15916	+	3.31559i	0.786764	+	0.505622i	−0.0845082	+	0.996423i	$0.526932\pi$
$44$	−2.98888	−	3.44935i	−0.450591	−	0.520010i
$45$	1.00000			0.149071
$46$	−4.78759	+	0.281042i	−0.705892	+	0.0414373i
$47$	2.66714			0.389042			0.194521	−	0.980898i	$-0.437685\pi$
$47$	2.66714			0.389042			0.194521	+	0.980898i	$0.437685\pi$
$48$	0.654861	+	0.755750i	0.0945210	+	0.109083i
$49$	−1.09779	−	0.705508i	−0.156827	−	0.100787i
$50$	0.142315	−	0.989821i	0.0201264	−	0.139982i
$51$	0.0898049	−	0.196645i	0.0125752	−	0.0275358i
$52$	−0.153373	−	1.06673i	−0.0212690	−	0.147929i
$53$	−3.38723	−	0.994581i	−0.465272	−	0.136616i	0.0406903	−	0.999172i	$-0.487044\pi$
$53$	−3.38723	−	0.994581i	−0.465272	−	0.136616i	−0.505962	+	0.862556i	$0.668862\pi$
$54$	0.841254	−	0.540641i	0.114480	−	0.0735719i
$55$	1.89602	+	4.15170i	0.255659	+	0.559815i
$56$	2.28976	−	0.672335i	0.305983	−	0.0898446i
$57$	3.68763	−	4.25575i	0.488438	−	0.563688i
$58$	−0.520235	+	0.600384i	−0.0683103	+	0.0788342i
$59$	5.22968	−	1.53557i	0.680847	−	0.199915i	0.0770193	−	0.997030i	$-0.475460\pi$
$59$	5.22968	−	1.53557i	0.680847	−	0.199915i	0.603828	+	0.797115i	$0.293642\pi$
$60$	−0.415415	−	0.909632i	−0.0536298	−	0.117433i
$61$	−9.10999	+	5.85463i	−1.16641	+	0.749609i	−0.972840	−	0.231477i	$-0.925644\pi$
$61$	−9.10999	+	5.85463i	−1.16641	+	0.749609i	−0.193574	+	0.981086i	$0.562008\pi$
$62$	−5.34080	−	1.56820i	−0.678282	−	0.199162i
$63$	−0.339625	−	2.36214i	−0.0427887	−	0.297602i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−0.153373	+	1.06673i	−0.0190236	+	0.132312i
$66$	3.83961	+	2.46757i	0.472623	+	0.303736i
$67$	−9.12366	−	10.5293i	−1.11463	−	1.28635i	−0.954154	−	0.299315i	$-0.903242\pi$
$67$	−9.12366	−	10.5293i	−1.11463	−	1.28635i	−0.160478	−	0.987039i	$-0.551304\pi$
$68$	−0.216181			−0.0262158
$69$	4.51448	−	1.61848i	0.543480	−	0.194842i
$70$	−2.38643			−0.285233
$71$	−2.21848	−	2.56026i	−0.263285	−	0.303847i	0.608680	−	0.793416i	$-0.291699\pi$
$71$	−2.21848	−	2.56026i	−0.263285	−	0.303847i	−0.871964	+	0.489569i	$0.837154\pi$
$72$	−0.841254	−	0.540641i	−0.0991427	−	0.0637151i
$73$	1.94089	−	13.4992i	0.227164	−	1.57996i	−0.482807	−	0.875727i	$-0.660383\pi$
$73$	1.94089	−	13.4992i	0.227164	−	1.57996i	0.709971	−	0.704231i	$-0.248708\pi$
$74$	2.14119	−	4.68854i	0.248908	−	0.545032i
$75$	0.142315	+	0.989821i	0.0164331	+	0.114295i
$76$	−5.40306	−	1.58648i	−0.619774	−	0.181982i
$77$	9.16296	−	5.88867i	1.04422	−	0.671077i
$78$	0.447693	+	0.980312i	0.0506913	+	0.110998i
$79$	−0.0557307	+	0.0163640i	−0.00627020	+	0.00184110i	−0.284866	−	0.958567i	$-0.591949\pi$
$79$	−0.0557307	+	0.0163640i	−0.00627020	+	0.00184110i	0.278596	+	0.960408i	$0.410131\pi$
$80$	−0.654861	+	0.755750i	−0.0732157	+	0.0844954i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−0.927954	+	0.272472i	−0.102475	+	0.0300895i
$83$	6.91098	+	15.1329i	0.758578	+	1.66105i	0.750308	+	0.661089i	$0.229905\pi$
$83$	6.91098	+	15.1329i	0.758578	+	1.66105i	0.00827078	+	0.999966i	$0.497367\pi$
$84$	−2.00759	+	1.29020i	−0.219046	+	0.140773i
$85$	0.207424	+	0.0609053i	0.0224983	+	0.00660610i
$86$	0.872774	+	6.07028i	0.0941137	+	0.654575i
$87$	0.330015	−	0.722631i	0.0353813	−	0.0774742i
$88$	0.649546	−	4.51769i	0.0692419	−	0.481588i
$89$	1.58913	+	1.02127i	0.168447	+	0.108255i	0.622148	−	0.782900i	$-0.286260\pi$
$89$	1.58913	+	1.02127i	0.168447	+	0.108255i	−0.453701	+	0.891154i	$0.649897\pi$
$90$	0.654861	+	0.755750i	0.0690284	+	0.0796630i
$91$	2.57186			0.269604
$92$	−3.34760	−	3.43418i	−0.349012	−	0.358038i
$93$	5.56627			0.577196
$94$	1.74661	+	2.01569i	0.180149	+	0.207903i
$95$	4.73724	+	3.04444i	0.486030	+	0.312353i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	3.73646	−	8.18170i	0.379380	−	0.830726i	−0.619571	−	0.784940i	$-0.712694\pi$
$97$	3.73646	−	8.18170i	0.379380	−	0.830726i	0.998951	−	0.0457859i	$-0.0145792\pi$
$98$	−0.185713	−	1.29167i	−0.0187599	−	0.130478i
$99$	−4.37927	−	1.28587i	−0.440133	−	0.129235i
$100$	0.841254	−	0.540641i	0.0841254	−	0.0540641i
$101$	4.73960	+	10.3783i	0.471607	+	1.03268i	0.984686	+	0.174335i	$0.0557775\pi$
$101$	4.73960	+	10.3783i	0.471607	+	1.03268i	−0.513079	+	0.858341i	$0.671495\pi$
$102$	0.207424	−	0.0609053i	0.0205381	−	0.00603052i
$103$	−9.24056	+	10.6642i	−0.910500	+	1.05077i	0.0880056	+	0.996120i	$0.471951\pi$
$103$	−9.24056	+	10.6642i	−0.910500	+	1.05077i	−0.998505	+	0.0546528i	$0.982595\pi$
$104$	0.705744	−	0.814472i	0.0692039	−	0.0798656i
$105$	2.28976	−	0.672335i	0.223458	−	0.0656132i
$106$	−1.46651	−	3.21121i	−0.142440	−	0.311900i
$107$	9.95433	−	6.39726i	0.962321	−	0.618446i	0.0376815	−	0.999290i	$-0.488003\pi$
$107$	9.95433	−	6.39726i	0.962321	−	0.618446i	0.924639	+	0.380844i	$0.124366\pi$
$108$	0.959493	+	0.281733i	0.0923273	+	0.0271097i
$109$	−0.781942	−	5.43853i	−0.0748965	−	0.520916i	−0.992387	−	0.123159i	$-0.960698\pi$
$109$	−0.781942	−	5.43853i	−0.0748965	−	0.520916i	0.917491	−	0.397758i	$-0.130212\pi$
$110$	−1.89602	+	4.15170i	−0.180778	+	0.395849i
$111$	−0.733538	+	5.10187i	−0.0696243	+	0.484248i
$112$	2.00759	+	1.29020i	0.189700	+	0.121913i
$113$	13.0297	+	15.0371i	1.22573	+	1.41457i	0.879149	+	0.476547i	$0.158112\pi$
$113$	13.0297	+	15.0371i	1.22573	+	1.41457i	0.346580	+	0.938020i	$0.387343\pi$
$114$	5.63116			0.527407
$115$	2.24448	+	4.23820i	0.209299	+	0.395214i
$116$	−0.794422			−0.0737602
$117$	−0.705744	−	0.814472i	−0.0652461	−	0.0752980i
$118$	4.58522	+	2.94674i	0.422104	+	0.271270i
$119$	0.0734204	−	0.510650i	0.00673044	−	0.0468112i
$120$	0.415415	−	0.909632i	0.0379220	−	0.0830377i
$121$	−1.39916	−	9.73139i	−0.127197	−	0.884672i
$122$	−10.3904	−	3.05090i	−0.940703	−	0.276215i
$123$	0.813601	−	0.522870i	0.0733600	−	0.0471456i
$124$	−2.31231	−	5.06326i	−0.207652	−	0.454694i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	1.56278	−	1.80354i	0.139223	−	0.160672i
$127$	1.53170	−	1.76768i	0.135916	−	0.156856i	−0.683711	−	0.729753i	$-0.739635\pi$
$127$	1.53170	−	1.76768i	0.135916	−	0.156856i	0.819627	+	0.572897i	$0.194181\pi$
$128$	0.959493	−	0.281733i	0.0848080	−	0.0249019i
$129$	−2.54762	−	5.57850i	−0.224305	−	0.491160i
$130$	−0.906620	+	0.582649i	−0.0795158	+	0.0511017i
$131$	9.02562	+	2.65016i	0.788572	+	0.231546i	0.651132	−	0.758964i	$-0.274294\pi$
$131$	9.02562	+	2.65016i	0.788572	+	0.231546i	0.137440	+	0.990510i	$0.456113\pi$
$132$	0.649546	+	4.51769i	0.0565357	+	0.393215i
$133$	5.58251	−	12.2240i	0.484065	−	1.05995i
$134$	1.98276	−	13.7904i	0.171284	−	1.19131i
$135$	−0.841254	−	0.540641i	−0.0724036	−	0.0465310i
$136$	−0.141569	−	0.163379i	−0.0121394	−	0.0140096i
$137$	6.88297			0.588052			0.294026	−	0.955797i	$-0.405005\pi$
$137$	6.88297			0.588052			0.294026	+	0.955797i	$0.405005\pi$
$138$	4.17952	+	2.35194i	0.355784	+	0.200210i
$139$	−5.96041			−0.505555			−0.252778	−	0.967524i	$-0.581344\pi$
$139$	−5.96041			−0.505555			−0.252778	+	0.967524i	$0.581344\pi$
$140$	−1.56278	−	1.80354i	−0.132079	−	0.152427i
$141$	−2.24374	−	1.44197i	−0.188957	−	0.121435i
$142$	0.482121	−	3.35323i	0.0404587	−	0.281396i
$143$	2.04334	−	4.47429i	0.170873	−	0.374159i
$144$	−0.142315	−	0.989821i	−0.0118596	−	0.0824851i
$145$	0.762242	+	0.223814i	0.0633007	+	0.0185868i
$146$	11.4730	−	7.37325i	0.949512	−	0.610214i
$147$	0.542095	+	1.18702i	0.0447112	+	0.0979040i
$148$	4.94554	−	1.45214i	0.406521	−	0.119365i
$149$	−5.62093	+	6.48690i	−0.460484	+	0.531427i	−0.937740	−	0.347337i	$-0.887086\pi$
$149$	−5.62093	+	6.48690i	−0.460484	+	0.531427i	0.477256	+	0.878764i	$0.341631\pi$
$150$	−0.654861	+	0.755750i	−0.0534692	+	0.0617067i
$151$	16.9357	−	4.97278i	1.37821	−	0.404679i	0.493065	−	0.869993i	$-0.335877\pi$
$151$	16.9357	−	4.97278i	1.37821	−	0.404679i	0.885146	+	0.465314i	$0.154058\pi$
$152$	−2.33927	−	5.12229i	−0.189740	−	0.415472i
$153$	−0.181863	+	0.116876i	−0.0147028	+	0.00944889i
$154$	10.4508	+	3.06864i	0.842151	+	0.247278i
$155$	0.792163	+	5.50962i	0.0636281	+	0.442543i
$156$	−0.447693	+	0.980312i	−0.0358442	+	0.0784878i
$157$	−0.0744313	+	0.517681i	−0.00594027	+	0.0413155i	−0.992576	−	0.121626i	$-0.961189\pi$
$157$	−0.0744313	+	0.517681i	−0.00594027	+	0.0413155i	0.986636	+	0.162942i	$0.0520982\pi$
$158$	−0.0488630	−	0.0314023i	−0.00388733	−	0.00249823i
$159$	2.31181	+	2.66797i	0.183338	+	0.211584i
$160$	−1.00000			−0.0790569
$161$	9.24893	−	6.74117i	0.728918	−	0.531279i
$162$	−1.00000			−0.0785674
$163$	−5.87500	−	6.78012i	−0.460166	−	0.531060i	0.477484	−	0.878640i	$-0.341549\pi$
$163$	−5.87500	−	6.78012i	−0.460166	−	0.531060i	−0.937650	+	0.347581i	$0.887003\pi$
$164$	−0.813601	−	0.522870i	−0.0635316	−	0.0408293i
$165$	0.649546	−	4.51769i	0.0505671	−	0.351702i
$166$	−6.91098	+	15.1329i	−0.536396	+	1.17454i
$167$	−1.01954	−	7.09108i	−0.0788946	−	0.548724i	−0.990485	−	0.137624i	$-0.956054\pi$
$167$	−1.01954	−	7.09108i	−0.0788946	−	0.548724i	0.911590	−	0.411101i	$-0.134856\pi$
$168$	−2.28976	−	0.672335i	−0.176659	−	0.0518718i
$169$	−9.95923	+	6.40041i	−0.766095	+	0.492339i
$170$	0.0898049	+	0.196645i	0.00688772	+	0.0150820i
$171$	−5.40306	+	1.58648i	−0.413182	+	0.121321i
$172$	−4.01606	+	4.63479i	−0.306222	+	0.353399i
$173$	−5.18837	+	5.98770i	−0.394464	+	0.455236i	−0.917890	−	0.396835i	$-0.870108\pi$
$173$	−5.18837	+	5.98770i	−0.394464	+	0.455236i	0.523425	+	0.852072i	$0.324654\pi$
$174$	0.762242	−	0.223814i	0.0577854	−	0.0169673i
$175$	0.991359	+	2.17077i	0.0749397	+	0.164095i
$176$	3.83961	−	2.46757i	0.289421	−	0.186000i
$177$	−5.22968	−	1.53557i	−0.393087	−	0.115421i
$178$	0.268833	+	1.86977i	0.0201499	+	0.140146i
$179$	2.48532	−	5.44209i	0.185762	−	0.406761i	−0.793723	−	0.608279i	$-0.791860\pi$
$179$	2.48532	−	5.44209i	0.185762	−	0.406761i	0.979485	+	0.201518i	$0.0645875\pi$
$180$	−0.142315	+	0.989821i	−0.0106075	+	0.0737769i
$181$	19.2316	+	12.3594i	1.42947	+	0.918666i	0.999878	+	0.0156445i	$0.00498001\pi$
$181$	19.2316	+	12.3594i	1.42947	+	0.918666i	0.429595	+	0.903022i	$0.358656\pi$
$182$	1.68421	+	1.94368i	0.124842	+	0.144075i
$183$	10.8291			0.800507
$184$	0.403164	−	4.77886i	0.0297216	−	0.352302i
$185$	−5.15433			−0.378954
$186$	3.64513	+	4.20671i	0.267274	+	0.308451i
$187$	−0.830051	−	0.533441i	−0.0606993	−	0.0390091i
$188$	−0.379574	+	2.63999i	−0.0276833	+	0.192541i
$189$	−0.991359	+	2.17077i	−0.0721108	+	0.157901i
$190$	0.801398	+	5.57385i	0.0581395	+	0.404369i
$191$	−18.8376	−	5.53121i	−1.36304	−	0.400224i	−0.483205	−	0.875507i	$-0.660528\pi$
$191$	−18.8376	−	5.53121i	−1.36304	−	0.400224i	−0.879833	+	0.475283i	$0.842346\pi$
$192$	−0.841254	+	0.540641i	−0.0607122	+	0.0390174i
$193$	−2.12509	−	4.65331i	−0.152968	−	0.334952i	0.817598	−	0.575790i	$-0.195305\pi$
$193$	−2.12509	−	4.65331i	−0.152968	−	0.334952i	−0.970566	+	0.240837i	$0.922578\pi$
$194$	8.63018	−	2.53405i	0.619611	−	0.181934i
$195$	0.705744	−	0.814472i	0.0505394	−	0.0583256i
$196$	0.854559	−	0.986214i	0.0610400	−	0.0704439i
$197$	7.29077	−	2.14076i	0.519446	−	0.152523i	−0.0114916	−	0.999934i	$-0.503658\pi$
$197$	7.29077	−	2.14076i	0.519446	−	0.152523i	0.530938	+	0.847411i	$0.321840\pi$
$198$	−1.89602	−	4.15170i	−0.134744	−	0.295048i
$199$	−17.7722	+	11.4215i	−1.25984	+	0.809647i	−0.988262	−	0.152770i	$-0.951181\pi$
$199$	−17.7722	+	11.4215i	−1.25984	+	0.809647i	−0.271574	+	0.962418i	$0.587544\pi$
$200$	0.959493	+	0.281733i	0.0678464	+	0.0199215i
$201$	1.98276	+	13.7904i	0.139853	+	0.972700i
$202$	−4.73960	+	10.3783i	−0.333477	+	0.730212i
$203$	0.269805	−	1.87654i	0.0189366	−	0.131707i
$204$	0.181863	+	0.116876i	0.0127330	+	0.00818298i
$205$	0.633335	+	0.730908i	0.0442341	+	0.0510488i
$206$	−14.1107			−0.983141
$207$	−4.67284	−	1.07916i	−0.324785	−	0.0750070i
$208$	1.07770			0.0747252
$209$	−16.8309	−	19.4239i	−1.16422	−	1.34358i
$210$	2.00759	+	1.29020i	0.138537	+	0.0890324i
$211$	0.235314	−	1.63664i	0.0161997	−	0.112671i	−0.980117	−	0.198420i	$-0.936419\pi$
$211$	0.235314	−	1.63664i	0.0161997	−	0.112671i	0.996317	+	0.0857486i	$0.0273282\pi$
$212$	1.46651	−	3.21121i	0.100720	−	0.220547i
$213$	0.482121	+	3.35323i	0.0330344	+	0.229759i
$214$	11.3534	+	3.33367i	0.776104	+	0.227885i
$215$	5.15916	−	3.31559i	0.351852	−	0.226121i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	12.7454	−	3.74240i	0.865217	−	0.254051i
$218$	3.59810	−	4.15243i	0.243694	−	0.281238i
$219$	−8.93098	+	10.3069i	−0.603500	+	0.696476i
$220$	−4.37927	+	1.28587i	−0.295250	+	0.0866933i
$221$	−0.0967829	−	0.211925i	−0.00651032	−	0.0142556i
$222$	−4.33610	+	2.78664i	−0.291020	+	0.187027i
$223$	−23.3921	−	6.86855i	−1.56645	−	0.459952i	−0.620486	−	0.784217i	$-0.713065\pi$
$223$	−23.3921	−	6.86855i	−1.56645	−	0.459952i	−0.945966	+	0.324265i	$0.894883\pi$
$224$	0.339625	+	2.36214i	0.0226921	+	0.157827i
$225$	0.415415	−	0.909632i	0.0276943	−	0.0606421i
$226$	−2.83162	+	19.6944i	−0.188357	+	1.31005i
$227$	17.8032	+	11.4414i	1.18164	+	0.759395i	0.975688	−	0.219166i	$-0.0703336\pi$
$227$	17.8032	+	11.4414i	1.18164	+	0.759395i	0.205955	+	0.978561i	$0.433970\pi$
$228$	3.68763	+	4.25575i	0.244219	+	0.281844i
$229$	6.65161			0.439551			0.219775	−	0.975551i	$-0.429468\pi$
$229$	6.65161			0.439551			0.219775	+	0.975551i	$0.429468\pi$
$230$	−1.73319	+	4.47169i	−0.114283	+	0.294855i
$231$	−10.8920			−0.716643
$232$	−0.520235	−	0.600384i	−0.0341551	−	0.0394171i
$233$	−2.84358	−	1.82746i	−0.186289	−	0.119721i	0.444172	−	0.895941i	$-0.353498\pi$
$233$	−2.84358	−	1.82746i	−0.186289	−	0.119721i	−0.630461	+	0.776221i	$0.717134\pi$
$234$	0.153373	−	1.06673i	0.0100263	−	0.0697345i
$235$	1.10797	−	2.42612i	0.0722760	−	0.158262i
$236$	0.775682	+	5.39499i	0.0504926	+	0.351184i
$237$	0.0557307	+	0.0163640i	0.00362010	+	0.00106296i
$238$	0.434004	−	0.278917i	0.0281323	−	0.0180795i
$239$	5.11313	+	11.1962i	0.330741	+	0.724221i	0.999820	−	0.0189699i	$-0.00603866\pi$
$239$	5.11313	+	11.1962i	0.330741	+	0.724221i	−0.669079	+	0.743191i	$0.733311\pi$
$240$	0.959493	−	0.281733i	0.0619350	−	0.0181858i
$241$	−12.5458	+	14.4786i	−0.808144	+	0.932648i	−0.998798	−	0.0490093i	$-0.984394\pi$
$241$	−12.5458	+	14.4786i	−0.808144	+	0.932648i	0.190654	+	0.981657i	$0.438939\pi$
$242$	6.43824	−	7.43012i	0.413866	−	0.477626i
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$	−4.49855	−	9.85046i	−0.287990	−	0.630611i
$245$	−1.09779	+	0.705508i	−0.0701354	+	0.0450733i
$246$	0.927954	+	0.272472i	0.0591642	+	0.0173722i
$247$	−0.863668	−	6.00694i	−0.0549539	−	0.382213i
$248$	2.31231	−	5.06326i	0.146832	−	0.321517i
$249$	2.36760	−	16.4670i	0.150040	−	1.04355i
$250$	−0.841254	−	0.540641i	−0.0532055	−	0.0341931i
$251$	10.0578	+	11.6074i	0.634844	+	0.732649i	0.978454	−	0.206463i	$-0.0661953\pi$
$251$	10.0578	+	11.6074i	0.634844	+	0.732649i	−0.343610	+	0.939112i	$0.611650\pi$
$252$	2.38643			0.150331
$253$	−4.37942	−	21.4463i	−0.275332	−	1.34832i
$254$	2.33897			0.146760
$255$	−0.141569	−	0.163379i	−0.00886537	−	0.0102312i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	0.669696	−	4.65784i	0.0417745	−	0.290548i	−0.958215	−	0.286048i	$-0.907658\pi$
$257$	0.669696	−	4.65784i	0.0417745	−	0.290548i	0.999990	−	0.00450034i	$-0.00143251\pi$
$258$	2.54762	−	5.57850i	0.158608	−	0.347302i
$259$	1.75054	+	12.1752i	0.108773	+	0.756533i
$260$	−1.03405	−	0.303624i	−0.0641289	−	0.0188299i
$261$	−0.668310	+	0.429497i	−0.0413673	+	0.0265852i
$262$	3.90767	+	8.55660i	0.241416	+	0.528628i
$263$	−24.0722	+	7.06823i	−1.48435	+	0.435846i	−0.920735	−	0.390189i	$-0.872410\pi$
$263$	−24.0722	+	7.06823i	−1.48435	+	0.435846i	−0.563619	+	0.826035i	$0.690591\pi$
$264$	−2.98888	+	3.44935i	−0.183953	+	0.212293i
$265$	−2.31181	+	2.66797i	−0.142013	+	0.163892i
$266$	12.8940	−	3.78603i	0.790584	−	0.232136i
$267$	−0.784720	−	1.71830i	−0.0480241	−	0.105158i
$268$	11.7205	−	7.53232i	0.715945	−	0.460110i
$269$	−4.55977	−	1.33887i	−0.278014	−	0.0816323i	0.139753	−	0.990186i	$-0.455369\pi$
$269$	−4.55977	−	1.33887i	−0.278014	−	0.0816323i	−0.417767	+	0.908554i	$0.637187\pi$
$270$	−0.142315	−	0.989821i	−0.00866101	−	0.0602386i
$271$	−8.64602	+	18.9321i	−0.525208	+	1.15005i	0.442221	+	0.896906i	$0.354191\pi$
$271$	−8.64602	+	18.9321i	−0.525208	+	1.15005i	−0.967430	+	0.253140i	$0.918537\pi$
$272$	0.0307658	−	0.213981i	0.00186545	−	0.0129745i
$273$	−2.16359	−	1.39045i	−0.130946	−	0.0841540i
$274$	4.50739	+	5.20180i	0.272301	+	0.314252i
$275$	4.56415			0.275229
$276$	0.959526	+	4.69886i	0.0577567	+	0.282838i
$277$	−8.81798			−0.529821			−0.264911	−	0.964273i	$-0.585342\pi$
$277$	−8.81798			−0.529821			−0.264911	+	0.964273i	$0.585342\pi$
$278$	−3.90324	−	4.50457i	−0.234101	−	0.270166i
$279$	−4.68265	−	3.00935i	−0.280343	−	0.180165i
$280$	0.339625	−	2.36214i	0.0202964	−	0.141165i
$281$	−8.38830	+	18.3678i	−0.500404	+	1.09573i	0.475934	+	0.879481i	$0.342110\pi$
$281$	−8.38830	+	18.3678i	−0.500404	+	1.09573i	−0.976338	+	0.216251i	$0.930617\pi$
$282$	−0.379574	−	2.63999i	−0.0226033	−	0.157209i
$283$	−5.41410	−	1.58972i	−0.321835	−	0.0944993i	0.116825	−	0.993153i	$-0.462728\pi$
$283$	−5.41410	−	1.58972i	−0.321835	−	0.0944993i	−0.438660	+	0.898653i	$0.644547\pi$
$284$	2.84992	−	1.83153i	0.169112	−	0.108681i
$285$	−2.33927	−	5.12229i	−0.138566	−	0.303418i
$286$	4.71954	−	1.38578i	0.279073	−	0.0819431i
$287$	1.51141	−	1.74426i	0.0892158	−	0.102960i
$288$	0.654861	−	0.755750i	0.0385880	−	0.0445330i
$289$	16.2665	−	4.77629i	0.956855	−	0.280958i
$290$	0.330015	+	0.722631i	0.0193791	+	0.0424344i
$291$	−7.56667	+	4.86281i	−0.443566	+	0.285063i
$292$	13.0855	+	3.84226i	0.765774	+	0.224851i
$293$	−2.15408	−	14.9819i	−0.125843	−	0.875254i	−0.950744	−	0.309977i	$-0.899679\pi$
$293$	−2.15408	−	14.9819i	−0.125843	−	0.875254i	0.824901	−	0.565277i	$-0.191231\pi$
$294$	−0.542095	+	1.18702i	−0.0316156	+	0.0692286i
$295$	0.775682	−	5.39499i	0.0451620	−	0.314108i
$296$	4.33610	+	2.78664i	0.252031	+	0.161970i
$297$	2.98888	+	3.44935i	0.173433	+	0.200152i
$298$	−8.58339			−0.497223
$299$	1.86786	−	4.81915i	0.108021	−	0.278699i
$300$	−1.00000			−0.0577350
$301$	−9.58406	−	11.0606i	−0.552416	−	0.637522i
$302$	14.8487	+	9.54270i	0.854448	+	0.549120i
$303$	1.62371	−	11.2932i	0.0932799	−	0.648776i
$304$	2.33927	−	5.12229i	0.134166	−	0.293783i
$305$	1.54114	+	10.7188i	0.0882452	+	0.613759i
$306$	−0.207424	−	0.0609053i	−0.0118577	−	0.00348172i
$307$	0.781519	−	0.502251i	0.0446036	−	0.0286650i	−0.518149	−	0.855290i	$-0.673379\pi$
$307$	0.781519	−	0.502251i	0.0446036	−	0.0286650i	0.562753	+	0.826625i	$0.309742\pi$
$308$	4.52471	+	9.90774i	0.257819	+	0.564546i
$309$	13.5391	−	3.97545i	0.770215	−	0.226156i
$310$	−3.64513	+	4.20671i	−0.207030	+	0.238925i
$311$	11.0027	−	12.6977i	0.623903	−	0.720023i	−0.352540	−	0.935797i	$-0.614682\pi$
$311$	11.0027	−	12.6977i	0.623903	−	0.720023i	0.976443	+	0.215774i	$0.0692274\pi$
$312$	−1.03405	+	0.303624i	−0.0585414	+	0.0171893i
$313$	2.17751	+	4.76809i	0.123080	+	0.269508i	0.961135	−	0.276077i	$-0.0890346\pi$
$313$	2.17751	+	4.76809i	0.123080	+	0.269508i	−0.838055	+	0.545586i	$0.816307\pi$
$314$	−0.439980	+	0.282758i	−0.0248295	+	0.0159569i
$315$	−2.28976	−	0.672335i	−0.129014	−	0.0378818i
$316$	−0.00826615	−	0.0574923i	−0.000465007	−	0.00323420i
$317$	2.81947	−	6.17377i	0.158357	−	0.346753i	−0.813778	−	0.581176i	$-0.802593\pi$
$317$	2.81947	−	6.17377i	0.158357	−	0.346753i	0.972135	+	0.234423i	$0.0753200\pi$
$318$	−0.502404	+	3.49430i	−0.0281734	+	0.195950i
$319$	−3.05027	−	1.96029i	−0.170782	−	0.109755i
$320$	−0.654861	−	0.755750i	−0.0366078	−	0.0422477i
$321$	−11.8327			−0.660439
$322$	11.1514	+	2.57535i	0.621443	+	0.143518i
$323$	−1.21735			−0.0677352
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	0.906620	+	0.582649i	0.0502902	+	0.0323196i
$326$	1.27676	−	8.88006i	0.0707132	−	0.491821i
$327$	−2.28248	+	4.99793i	−0.126221	+	0.276386i
$328$	−0.137637	−	0.957286i	−0.00759973	−	0.0528573i
$329$	−6.10712	−	1.79321i	−0.336696	−	0.0988630i
$330$	3.83961	−	2.46757i	0.211363	−	0.135835i
$331$	−0.738329	−	1.61672i	−0.0405822	−	0.0888627i	0.888255	−	0.459351i	$-0.151918\pi$
$331$	−0.738329	−	1.61672i	−0.0405822	−	0.0888627i	−0.928837	+	0.370488i	$0.879191\pi$
$332$	−15.9624	+	4.68699i	−0.876052	+	0.257232i
$333$	3.37537	−	3.89538i	0.184969	−	0.213466i
$334$	4.69142	−	5.41419i	0.256703	−	0.296251i
$335$	−13.3679	+	3.92516i	−0.730364	+	0.214454i
$336$	−0.991359	−	2.17077i	−0.0540831	−	0.118425i
$337$	7.96254	−	5.11721i	0.433747	−	0.278752i	−0.305493	−	0.952194i	$-0.598821\pi$
$337$	7.96254	−	5.11721i	0.433747	−	0.278752i	0.739240	+	0.673442i	$0.235185\pi$
$338$	−11.3590	−	3.33531i	−0.617849	−	0.181417i
$339$	−2.83162	−	19.6944i	−0.153793	−	1.06965i
$340$	−0.0898049	+	0.196645i	−0.00487035	+	0.0106646i
$341$	3.61555	−	25.1467i	0.195793	−	1.36177i
$342$	−4.73724	−	3.04444i	−0.256160	−	0.164624i
$343$	12.9788	+	14.9783i	0.700790	+	0.808754i
$344$	−6.13270			−0.330653
$345$	0.403164	−	4.77886i	0.0217056	−	0.257285i
$346$	−7.92286			−0.425936
$347$	−16.8769	−	19.4770i	−0.906000	−	1.04558i	−0.998755	−	0.0498910i	$-0.984113\pi$
$347$	−16.8769	−	19.4770i	−0.906000	−	1.04558i	0.0927544	−	0.995689i	$-0.470433\pi$
$348$	0.668310	+	0.429497i	0.0358252	+	0.0230234i
$349$	−2.03785	+	14.1736i	−0.109084	+	0.758694i	0.859702	+	0.510796i	$0.170649\pi$
$349$	−2.03785	+	14.1736i	−0.109084	+	0.758694i	−0.968786	+	0.247899i	$0.920260\pi$
$350$	−0.991359	+	2.17077i	−0.0529904	+	0.116033i
$351$	0.153373	+	1.06673i	0.00818644	+	0.0569379i
$352$	4.37927	+	1.28587i	0.233416	+	0.0685371i
$353$	−17.7077	+	11.3800i	−0.942484	+	0.605698i	−0.919098	−	0.394029i	$-0.871081\pi$
$353$	−17.7077	+	11.3800i	−0.942484	+	0.605698i	−0.0233858	+	0.999727i	$0.507445\pi$
$354$	−2.26421	−	4.95792i	−0.120341	−	0.263510i
$355$	−3.25048	+	0.954428i	−0.172518	+	0.0506558i
$356$	−1.23703	+	1.42761i	−0.0655626	+	0.0756633i
$357$	−0.337844	+	0.389892i	−0.0178806	+	0.0206353i
$358$	5.74040	−	1.68553i	0.303389	−	0.0890832i
$359$	−9.14599	−	20.0269i	−0.482707	−	1.05698i	−0.981710	−	0.190381i	$-0.939028\pi$
$359$	−9.14599	−	20.0269i	−0.482707	−	1.05698i	0.499004	−	0.866600i	$-0.333699\pi$
$360$	−0.841254	+	0.540641i	−0.0443380	+	0.0284943i
$361$	−12.1952	−	3.58082i	−0.641851	−	0.188464i
$362$	3.25341	+	22.6279i	0.170995	+	1.18930i
$363$	−4.08414	+	8.94301i	−0.214362	+	0.469386i
$364$	−0.366014	+	2.54568i	−0.0191843	+	0.133430i
$365$	−11.4730	−	7.37325i	−0.600524	−	0.385934i
$366$	7.09153	+	8.18406i	0.370680	+	0.427788i
$367$	−35.9390			−1.87600			−0.938000	−	0.346634i	$-0.887324\pi$
$367$	−35.9390			−1.87600			−0.938000	+	0.346634i	$0.887324\pi$
$368$	3.87563	−	2.82479i	0.202031	−	0.147253i
$369$	−0.967130			−0.0503468
$370$	−3.37537	−	3.89538i	−0.175477	−	0.202511i
$371$	7.08727	+	4.55471i	0.367952	+	0.236469i
$372$	−0.792163	+	5.50962i	−0.0410718	+	0.285660i
$373$	8.09314	−	17.7215i	0.419047	−	0.917585i	−0.575932	−	0.817498i	$-0.695361\pi$
$373$	8.09314	−	17.7215i	0.419047	−	0.917585i	0.994979	−	0.100087i	$-0.0319121\pi$
$374$	−0.140420	−	0.976640i	−0.00726093	−	0.0505009i
$375$	0.959493	+	0.281733i	0.0495480	+	0.0145486i
$376$	−2.24374	+	1.44197i	−0.115712	+	0.0743637i
$377$	−0.355657	−	0.778781i	−0.0183173	−	0.0401092i
$378$	−2.28976	+	0.672335i	−0.117773	+	0.0345812i
$379$	−11.4942	+	13.2650i	−0.590415	+	0.681375i	−0.969811	−	0.243859i	$-0.921587\pi$
$379$	−11.4942	+	13.2650i	−0.590415	+	0.681375i	0.379396	+	0.925235i	$0.376132\pi$
$380$	−3.68763	+	4.25575i	−0.189171	+	0.218315i
$381$	−2.24422	+	0.658964i	−0.114975	+	0.0337597i
$382$	−8.15577	−	17.8587i	−0.417286	−	0.913728i
$383$	−5.40666	+	3.47465i	−0.276268	+	0.177546i	−0.671437	−	0.741062i	$-0.734322\pi$
$383$	−5.40666	+	3.47465i	−0.276268	+	0.177546i	0.395169	+	0.918608i	$0.370686\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	−1.55010	−	10.7812i	−0.0790003	−	0.549459i
$386$	2.12509	−	4.65331i	0.108164	−	0.236847i
$387$	−0.872774	+	6.07028i	−0.0443656	+	0.308570i
$388$	7.56667	+	4.86281i	0.384140	+	0.246872i
$389$	1.02817	+	1.18657i	0.0521301	+	0.0601613i	0.781216	−	0.624261i	$-0.214600\pi$
$389$	1.02817	+	1.18657i	0.0521301	+	0.0601613i	−0.729086	+	0.684422i	$0.760054\pi$
$390$	1.07770			0.0545715
$391$	−0.903533	−	0.508445i	−0.0456936	−	0.0257132i
$392$	1.30495			0.0659098
$393$	−6.16005	−	7.10908i	−0.310733	−	0.358606i
$394$	6.39232	+	4.10810i	0.322041	+	0.206963i
$395$	−0.00826615	+	0.0574923i	−0.000415915	+	0.00289275i
$396$	1.89602	−	4.15170i	0.0952784	−	0.208631i
$397$	3.66451	+	25.4873i	0.183917	+	1.27917i	0.847391	+	0.530970i	$0.178172\pi$
$397$	3.66451	+	25.4873i	0.183917	+	1.27917i	−0.663474	+	0.748199i	$0.730919\pi$
$398$	−20.2701	−	5.95183i	−1.01605	−	0.298338i
$399$	−11.3051	+	7.26534i	−0.565962	+	0.363722i
$400$	0.415415	+	0.909632i	0.0207708	+	0.0454816i
$401$	−9.28246	+	2.72558i	−0.463544	+	0.136109i	−0.505161	−	0.863025i	$-0.668567\pi$
$401$	−9.28246	+	2.72558i	−0.463544	+	0.136109i	0.0416176	+	0.999134i	$0.486749\pi$
$402$	−9.12366	+	10.5293i	−0.455047	+	0.525152i
$403$	3.92837	−	4.53358i	0.195686	−	0.225834i
$404$	−10.9471	+	3.21437i	−0.544641	+	0.159921i
$405$	0.415415	+	0.909632i	0.0206421	+	0.0452000i
$406$	1.59488	−	1.02496i	0.0791523	−	0.0508681i
$407$	22.5722	+	6.62779i	1.11886	+	0.328528i
$408$	0.0307658	+	0.213981i	0.00152313	+	0.0105936i
$409$	8.70612	−	19.0637i	0.430490	−	0.942641i	−0.562757	−	0.826622i	$-0.690259\pi$
$409$	8.70612	−	19.0637i	0.430490	−	0.942641i	0.993247	−	0.116019i	$-0.0370134\pi$
$410$	−0.137637	+	0.957286i	−0.00679740	+	0.0472770i
$411$	−5.79032	−	3.72121i	−0.285615	−	0.183554i
$412$	−9.24056	−	10.6642i	−0.455250	−	0.525386i
$413$	−13.0072			−0.640041
$414$	−2.24448	−	4.23820i	−0.110310	−	0.208296i
$415$	16.6363			0.816645
$416$	0.705744	+	0.814472i	0.0346020	+	0.0399328i
$417$	5.01421	+	3.22244i	0.245547	+	0.157804i
$418$	3.65770	−	25.4399i	0.178904	−	1.24430i
$419$	−12.4274	+	27.2123i	−0.607120	+	1.32941i	0.317406	+	0.948290i	$0.397188\pi$
$419$	−12.4274	+	27.2123i	−0.607120	+	1.32941i	−0.924526	+	0.381118i	$0.875539\pi$
$420$	0.339625	+	2.36214i	0.0165720	+	0.115261i
$421$	28.1651	+	8.27003i	1.37268	+	0.403057i	0.883217	−	0.468965i	$-0.155373\pi$
$421$	28.1651	+	8.27003i	1.37268	+	0.403057i	0.489468	+	0.872021i	$0.337191\pi$
$422$	1.39099	−	0.893935i	0.0677123	−	0.0435161i
$423$	1.10797	+	2.42612i	0.0538714	+	0.117962i
$424$	3.38723	−	0.994581i	0.164498	−	0.0483011i
$425$	0.141569	−	0.163379i	0.00686708	−	0.00792504i
$426$	−2.21848	+	2.56026i	−0.107486	+	0.124045i
$427$	24.7960	−	7.28076i	1.19996	−	0.352341i
$428$	4.91549	+	10.7634i	0.237599	+	0.520270i
$429$	−4.13795	+	2.65930i	−0.199782	+	0.128392i
$430$	5.88428	+	1.72778i	0.283765	+	0.0833210i
$431$	−0.105007	−	0.730340i	−0.00505801	−	0.0351792i	0.987136	−	0.159882i	$-0.0511114\pi$
$431$	−0.105007	−	0.730340i	−0.00505801	−	0.0351792i	−0.992194	+	0.124703i	$0.960202\pi$
$432$	−0.415415	+	0.909632i	−0.0199867	+	0.0437647i
$433$	−0.978848	+	6.80804i	−0.0470405	+	0.327174i	0.952690	+	0.303945i	$0.0983038\pi$
$433$	−0.978848	+	6.80804i	−0.0470405	+	0.327174i	−0.999730	+	0.0232290i	$0.992605\pi$
$434$	11.1748	+	7.18162i	0.536408	+	0.344729i
$435$	−0.520235	−	0.600384i	−0.0249434	−	0.0287862i
$436$	5.49445			0.263137
$437$	−18.8509	−	19.3384i	−0.901761	−	0.925081i
$438$	−13.6380			−0.651648
$439$	−18.0886	−	20.8754i	−0.863322	−	0.996327i	−0.999984	−	0.00570888i	$-0.998183\pi$
$439$	−18.0886	−	20.8754i	−0.863322	−	0.996327i	0.136662	−	0.990618i	$-0.456363\pi$
$440$	−3.83961	−	2.46757i	−0.183046	−	0.117637i
$441$	0.185713	−	1.29167i	0.00884350	−	0.0615079i
$442$	0.0967829	−	0.211925i	0.00460349	−	0.0100802i
$443$	5.35912	+	37.2735i	0.254619	+	1.77092i	0.569701	+	0.821852i	$0.307059\pi$
$443$	5.35912	+	37.2735i	0.254619	+	1.77092i	−0.315081	+	0.949065i	$0.602032\pi$
$444$	−4.94554	−	1.45214i	−0.234705	−	0.0689156i
$445$	1.58913	−	1.02127i	0.0753320	−	0.0484129i
$446$	−10.1277	−	22.1765i	−0.479560	−	1.05009i
$447$	8.23571	−	2.41822i	0.389536	−	0.114378i
$448$	−1.56278	+	1.80354i	−0.0738344	+	0.0852094i
$449$	−13.4199	+	15.4874i	−0.633325	+	0.730896i	−0.978180	−	0.207760i	$-0.933383\pi$
$449$	−13.4199	+	15.4874i	−0.633325	+	0.730896i	0.344855	+	0.938656i	$0.387928\pi$
$450$	0.959493	−	0.281733i	0.0452309	−	0.0132810i
$451$	−1.83369	−	4.01523i	−0.0863453	−	0.189070i
$452$	−16.7383	+	10.7571i	−0.787304	+	0.505970i
$453$	−16.9357	−	4.97278i	−0.795710	−	0.233642i
$454$	3.01177	+	20.9473i	0.141350	+	0.983108i
$455$	1.06839	−	2.33945i	0.0500869	−	0.109675i
$456$	−0.801398	+	5.57385i	−0.0375289	+	0.261019i
$457$	32.2948	+	20.7546i	1.51069	+	0.970859i	0.993357	+	0.115072i	$0.0367098\pi$
$457$	32.2948	+	20.7546i	1.51069	+	0.970859i	0.517328	+	0.855787i	$0.326927\pi$
$458$	4.35588	+	5.02695i	0.203537	+	0.234894i
$459$	0.216181			0.0100905
$460$	−4.51448	+	1.61848i	−0.210489	+	0.0754619i
$461$	34.8125			1.62138			0.810691	−	0.585475i	$-0.199092\pi$
$461$	34.8125			1.62138			0.810691	+	0.585475i	$0.199092\pi$
$462$	−7.13276	−	8.23164i	−0.331846	−	0.382971i
$463$	16.9100	+	10.8674i	0.785875	+	0.505051i	0.870979	−	0.491321i	$-0.163486\pi$
$463$	16.9100	+	10.8674i	0.785875	+	0.505051i	−0.0851036	+	0.996372i	$0.527122\pi$
$464$	0.113058	−	0.786335i	0.00524858	−	0.0365047i
$465$	2.31231	−	5.06326i	0.107231	−	0.234803i
$466$	−0.481048	−	3.34576i	−0.0222841	−	0.154989i
$467$	−31.7964	−	9.33626i	−1.47136	−	0.432031i	−0.554820	−	0.831970i	$-0.687213\pi$
$467$	−31.7964	−	9.33626i	−1.47136	−	0.432031i	−0.916542	+	0.399940i	$0.869031\pi$
$468$	0.906620	−	0.582649i	0.0419085	−	0.0269330i
$469$	13.8118	+	30.2437i	0.637771	+	1.39652i
$470$	2.55910	−	0.751420i	0.118043	−	0.0346604i
$471$	0.342495	−	0.395261i	0.0157814	−	0.0182126i
$472$	−3.56930	+	4.11919i	−0.164290	+	0.189601i
$473$	−26.8567	+	7.88585i	−1.23487	+	0.362592i
$474$	0.0241288	+	0.0528346i	0.00110827	+	0.00242677i
$475$	4.73724	−	3.04444i	0.217359	−	0.139688i
$476$	0.495004	+	0.145346i	0.0226885	+	0.00666193i
$477$	−0.502404	−	3.49430i	−0.0230035	−	0.159993i
$478$	−5.11313	+	11.1962i	−0.233869	+	0.512102i
$479$	0.264370	−	1.83874i	0.0120794	−	0.0840140i	−0.982890	−	0.184194i	$-0.941033\pi$
$479$	0.264370	−	1.83874i	0.0120794	−	0.0840140i	0.994969	+	0.100180i	$0.0319418\pi$
$480$	0.841254	+	0.540641i	0.0383978	+	0.0246768i
$481$	3.63764	+	4.19806i	0.165862	+	0.191415i
$482$	−19.1579			−0.872619
$483$	−11.4253	+	0.670687i	−0.519867	+	0.0305173i
$484$	9.83146			0.446885
$485$	−5.89016	−	6.79761i	−0.267458	−	0.308663i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	2.44513	−	17.0062i	0.110799	−	0.770627i	−0.856346	−	0.516403i	$-0.827271\pi$
$487$	2.44513	−	17.0062i	0.110799	−	0.770627i	0.967145	−	0.254224i	$-0.0818201\pi$
$488$	4.49855	−	9.85046i	0.203640	−	0.445909i
$489$	1.27676	+	8.88006i	0.0577371	+	0.401570i
$490$	−1.25209	−	0.367646i	−0.0565636	−	0.0166086i
$491$	2.94699	−	1.89392i	0.132996	−	0.0854713i	−0.472451	−	0.881357i	$-0.656631\pi$
$491$	2.94699	−	1.89392i	0.132996	−	0.0854713i	0.605447	+	0.795886i	$0.292994\pi$
$492$	0.401760	+	0.879732i	0.0181128	+	0.0396614i
$493$	−0.164782	+	0.0483845i	−0.00742142	+	0.00217913i
$494$	3.97416	−	4.58643i	0.178806	−	0.206353i
$495$	−2.98888	+	3.44935i	−0.134340	+	0.155037i
$496$	5.34080	−	1.56820i	0.239809	−	0.0704143i
$497$	3.35844	+	7.35395i	0.150646	+	0.329870i
$498$	13.9954	−	8.99427i	0.627147	−	0.403043i
$499$	35.3335	+	10.3748i	1.58174	+	0.464442i	0.950392	−	0.311055i	$-0.100682\pi$
$499$	35.3335	+	10.3748i	1.58174	+	0.464442i	0.631351	+	0.775497i	$0.282501\pi$
$500$	−0.142315	−	0.989821i	−0.00636451	−	0.0442662i
$501$	−2.97603	+	6.51660i	−0.132959	+	0.291140i
$502$	−2.18577	+	15.2024i	−0.0975559	+	0.678516i
$503$	−4.68662	−	3.01190i	−0.208966	−	0.134294i	0.431972	−	0.901887i	$-0.357818\pi$
$503$	−4.68662	−	3.01190i	−0.208966	−	0.134294i	−0.640938	+	0.767593i	$0.721454\pi$
$504$	1.56278	+	1.80354i	0.0696117	+	0.0803362i
$505$	11.4093			0.507707
$506$	13.3401	−	17.3541i	0.593041	−	0.771483i
$507$	11.8386			0.525769
$508$	1.53170	+	1.76768i	0.0679582	+	0.0784279i
$509$	31.0831	+	19.9759i	1.37773	+	0.885415i	0.999193	−	0.0401698i	$-0.0127899\pi$
$509$	31.0831	+	19.9759i	1.37773	+	0.885415i	0.378540	+	0.925585i	$0.376426\pi$
$510$	0.0307658	−	0.213981i	0.00136233	−	0.00947523i
$511$	−13.5201	+	29.6050i	−0.598096	+	1.30965i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	5.40306	+	1.58648i	0.238551	+	0.0700449i
$514$	3.95872	−	2.54411i	0.174612	−	0.112216i
$515$	5.86181	+	12.8356i	0.258302	+	0.565603i
$516$	5.88428	−	1.72778i	0.259041	−	0.0760613i
$517$	−7.97177	+	9.19991i	−0.350598	+	0.404612i
$518$	−8.05508	+	9.29606i	−0.353920	+	0.408445i
$519$	7.60193	−	2.23213i	0.333688	−	0.0979795i
$520$	−0.447693	−	0.980312i	−0.0196327	−	0.0429895i
$521$	−8.15841	+	5.24309i	−0.357426	+	0.229704i	−0.707014	−	0.707200i	$-0.749958\pi$
$521$	−8.15841	+	5.24309i	−0.357426	+	0.229704i	0.349587	+	0.936904i	$0.386322\pi$
$522$	−0.762242	−	0.223814i	−0.0333624	−	0.00979609i
$523$	−1.07384	−	7.46871i	−0.0469557	−	0.326584i	−0.999737	−	0.0229271i	$-0.992701\pi$
$523$	−1.07384	−	7.46871i	−0.0469557	−	0.326584i	0.952781	−	0.303657i	$-0.0982077\pi$
$524$	−3.90767	+	8.55660i	−0.170707	+	0.373797i
$525$	0.339625	−	2.36214i	0.0148224	−	0.103092i
$526$	−21.1057	−	13.5638i	−0.920254	−	0.591411i
$527$	−0.788009	−	0.909411i	−0.0343262	−	0.0396146i
$528$	−4.56415			−0.198629
$529$	−5.91439	−	22.2266i	−0.257148	−	0.966372i
$530$	−3.53023			−0.153343
$531$	3.56930	+	4.11919i	0.154894	+	0.178758i
$532$	11.3051	+	7.26534i	0.490138	+	0.314992i
$533$	0.148332	−	1.03167i	0.00642495	−	0.0446865i
$534$	0.784720	−	1.71830i	0.0339581	−	0.0743580i
$535$	−1.68397	−	11.7123i	−0.0728045	−	0.506366i
$536$	13.3679	+	3.92516i	0.577404	+	0.169541i
$537$	−5.03300	+	3.23451i	−0.217190	+	0.139580i
$538$	−1.97417	−	4.32282i	−0.0851123	−	0.186370i
$539$	5.71472	−	1.67799i	0.246150	−	0.0722763i
$540$	0.654861	−	0.755750i	0.0281807	−	0.0325223i
$541$	18.2233	−	21.0308i	0.783481	−	0.904186i	−0.213874	−	0.976861i	$-0.568608\pi$
$541$	18.2233	−	21.0308i	0.783481	−	0.904186i	0.997356	+	0.0726755i	$0.0231537\pi$
$542$	−19.9699	+	5.86369i	−0.857781	+	0.251867i
$543$	−9.49665	−	20.7948i	−0.407540	−	0.892389i
$544$	0.181863	−	0.116876i	0.00779732	−	0.00501103i
$545$	−5.27189	−	1.54797i	−0.225823	−	0.0663076i
$546$	−0.366014	−	2.54568i	−0.0156639	−	0.108945i
$547$	−15.5907	+	34.1390i	−0.666612	+	1.45968i	0.209618	+	0.977783i	$0.432778\pi$
$547$	−15.5907	+	34.1390i	−0.666612	+	1.45968i	−0.876230	+	0.481893i	$0.839949\pi$
$548$	−0.979548	+	6.81291i	−0.0418442	+	0.291033i
$549$	−9.10999	−	5.85463i	−0.388805	−	0.249870i
$550$	2.98888	+	3.44935i	0.127446	+	0.147081i
$551$	−4.47352			−0.190578
$552$	−2.92281	+	3.80226i	−0.124403	+	0.161835i
$553$	0.138612			0.00589439
$554$	−5.77455	−	6.66419i	−0.245337	−	0.283134i
$555$	4.33610	+	2.78664i	0.184057	+	0.118286i
$556$	0.848254	−	5.89974i	0.0359740	−	0.250205i
$557$	−7.18733	+	15.7381i	−0.304537	+	0.666843i	−0.998590	−	0.0530808i	$-0.983096\pi$
$557$	−7.18733	+	15.7381i	−0.304537	+	0.666843i	0.694053	+	0.719924i	$0.255823\pi$
$558$	−0.792163	−	5.50962i	−0.0335349	−	0.233241i
$559$	−6.34150	−	1.86203i	−0.268217	−	0.0787556i
$560$	2.00759	−	1.29020i	0.0848363	−	0.0545210i
$561$	0.409883	+	0.897519i	0.0173053	+	0.0378933i
$562$	−19.3746	+	5.68891i	−0.817270	+	0.239972i
$563$	−23.1052	+	26.6648i	−0.973769	+	1.12379i	0.0185184	+	0.999829i	$0.494105\pi$
$563$	−23.1052	+	26.6648i	−0.973769	+	1.12379i	−0.992287	+	0.123960i	$0.960440\pi$
$564$	1.74661	−	2.01569i	0.0735454	−	0.0848759i
$565$	19.0909	−	5.60560i	0.803161	−	0.235829i
$566$	−2.34405	−	5.13275i	−0.0985278	−	0.215746i
$567$	2.00759	−	1.29020i	0.0843110	−	0.0541834i
$568$	3.25048	+	0.954428i	0.136387	+	0.0400469i
$569$	2.75322	+	19.1491i	0.115421	+	0.802771i	0.962496	+	0.271297i	$0.0874525\pi$
$569$	2.75322	+	19.1491i	0.115421	+	0.802771i	−0.847075	+	0.531474i	$0.821638\pi$
$570$	2.33927	−	5.12229i	0.0979812	−	0.214549i
$571$	2.19297	−	15.2525i	0.0917730	−	0.638295i	−0.891072	−	0.453862i	$-0.850046\pi$
$571$	2.19297	−	15.2525i	0.0917730	−	0.638295i	0.982845	−	0.184433i	$-0.0590450\pi$
$572$	4.13795	+	2.65930i	0.173016	+	0.111191i
$573$	12.8568	+	14.8375i	0.537099	+	0.619846i
$574$	2.30799			0.0963336
$575$	4.78759	−	0.281042i	0.199656	−	0.0117202i
$576$	1.00000			0.0416667
$577$	4.78318	+	5.52009i	0.199126	+	0.229804i	0.846527	−	0.532346i	$-0.178689\pi$
$577$	4.78318	+	5.52009i	0.199126	+	0.229804i	−0.647401	+	0.762150i	$0.724144\pi$
$578$	14.2620	+	9.16563i	0.593221	+	0.381240i
$579$	−0.728025	+	5.06352i	−0.0302557	+	0.210433i
$580$	−0.330015	+	0.722631i	−0.0137031	+	0.0300056i
$581$	−5.65010	−	39.2973i	−0.234406	−	1.63033i
$582$	−8.63018	−	2.53405i	−0.357732	−	0.105040i
$583$	13.5547	−	8.71107i	0.561378	−	0.360776i
$584$	5.66542	+	12.4055i	0.234437	+	0.513345i
$585$	−1.03405	+	0.303624i	−0.0427526	+	0.0125533i
$586$	9.91197	−	11.4390i	0.409460	−	0.472542i
$587$	11.2926	−	13.0324i	0.466096	−	0.537904i	−0.473225	−	0.880941i	$-0.656910\pi$
$587$	11.2926	−	13.0324i	0.466096	−	0.537904i	0.939322	+	0.343037i	$0.111456\pi$
$588$	−1.25209	+	0.367646i	−0.0516353	+	0.0151615i
$589$	−13.0210	−	28.5120i	−0.536522	−	1.17482i
$590$	4.58522	−	2.94674i	0.188771	−	0.121316i
$591$	−7.29077	−	2.14076i	−0.299902	−	0.0880593i
$592$	0.733538	+	5.10187i	0.0301482	+	0.209685i
$593$	−6.63553	+	14.5298i	−0.272489	+	0.596667i	−0.995562	−	0.0941039i	$-0.970001\pi$
$593$	−6.63553	+	14.5298i	−0.272489	+	0.596667i	0.723074	+	0.690771i	$0.242729\pi$
$594$	−0.649546	+	4.51769i	−0.0266512	+	0.185363i
$595$	−0.434004	−	0.278917i	−0.0177924	−	0.0114345i
$596$	−5.62093	−	6.48690i	−0.230242	−	0.265714i
$597$	21.1258			0.864622
$598$	4.86526	−	1.74424i	0.198955	−	0.0713271i
$599$	27.6350			1.12913			0.564567	−	0.825387i	$-0.309043\pi$
$599$	27.6350			1.12913			0.564567	+	0.825387i	$0.309043\pi$
$600$	−0.654861	−	0.755750i	−0.0267346	−	0.0308533i
$601$	−10.7281	−	6.89452i	−0.437607	−	0.281233i	0.303230	−	0.952917i	$-0.401935\pi$
$601$	−10.7281	−	6.89452i	−0.437607	−	0.281233i	−0.740838	+	0.671684i	$0.765571\pi$
$602$	2.08282	−	14.4863i	0.0848892	−	0.590417i
$603$	5.78765	−	12.6732i	0.235691	−	0.516092i
$604$	2.51196	+	17.4711i	0.102210	+	0.710887i
$605$	−9.43322	−	2.76984i	−0.383515	−	0.112610i
$606$	9.59812	−	6.16834i	0.389897	−	0.250572i
$607$	−13.3634	−	29.2618i	−0.542404	−	1.18770i	−0.960240	−	0.279177i	$-0.909938\pi$
$607$	−13.3634	−	29.2618i	−0.542404	−	1.18770i	0.417836	−	0.908523i	$-0.362789\pi$
$608$	5.40306	−	1.58648i	0.219123	−	0.0643403i
$609$	−1.24151	+	1.43277i	−0.0503084	+	0.0580589i
$610$	−7.09153	+	8.18406i	−0.287128	+	0.331363i
$611$	−2.75795	+	0.809807i	−0.111575	+	0.0327613i
$612$	−0.0898049	−	0.196645i	−0.00363015	−	0.00794892i
$613$	−7.41911	+	4.76797i	−0.299655	+	0.192577i	−0.681825	−	0.731516i	$-0.738813\pi$
$613$	−7.41911	+	4.76797i	−0.299655	+	0.192577i	0.382170	+	0.924092i	$0.375177\pi$
$614$	0.891362	+	0.261728i	0.0359724	+	0.0105625i
$615$	−0.137637	−	0.957286i	−0.00555006	−	0.0386015i
$616$	−4.52471	+	9.90774i	−0.182306	+	0.399194i
$617$	1.38712	−	9.64763i	0.0558433	−	0.388399i	−0.942662	−	0.333748i	$-0.891686\pi$
$617$	1.38712	−	9.64763i	0.0558433	−	0.388399i	0.998506	−	0.0546506i	$-0.0174045\pi$
$618$	11.8707	+	7.62884i	0.477510	+	0.306877i
$619$	3.86149	+	4.45640i	0.155206	+	0.179118i	0.828027	−	0.560688i	$-0.189463\pi$
$619$	3.86149	+	4.45640i	0.155206	+	0.179118i	−0.672821	+	0.739805i	$0.734918\pi$
$620$	−5.56627			−0.223547
$621$	3.34760	+	3.43418i	0.134335	+	0.137809i
$622$	16.8015			0.673680
$623$	−2.95209	−	3.40690i	−0.118273	−	0.136494i
$624$	−0.906620	−	0.582649i	−0.0362939	−	0.0233246i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−2.17751	+	4.76809i	−0.0870309	+	0.190571i
$627$	3.65770	+	25.4399i	0.146075	+	1.01597i
$628$	−0.501819	−	0.147347i	−0.0200248	−	0.00587980i
$629$	0.937383	−	0.602419i	0.0373759	−	0.0240200i
$630$	−0.991359	−	2.17077i	−0.0394967	−	0.0864857i
$631$	15.8154	−	4.64381i	0.629600	−	0.184867i	0.0486624	−	0.998815i	$-0.484504\pi$
$631$	15.8154	−	4.64381i	0.629600	−	0.184867i	0.580938	+	0.813948i	$0.302686\pi$
$632$	0.0380366	−	0.0438966i	0.00151302	−	0.00174611i
$633$	−1.08279	+	1.24961i	−0.0430372	+	0.0496676i
$634$	6.51218	−	1.91215i	0.258632	−	0.0759411i
$635$	−0.971643	−	2.12760i	−0.0385585	−	0.0844313i
$636$	−2.96982	+	1.90859i	−0.117761	+	0.0756804i
$637$	1.34938	+	0.396213i	0.0534643	+	0.0156985i
$638$	−0.516013	−	3.58895i	−0.0204292	−	0.142088i
$639$	1.40730	−	3.08157i	0.0556721	−	0.121905i
$640$	0.142315	−	0.989821i	0.00562549	−	0.0391261i
$641$	−5.89635	−	3.78935i	−0.232892	−	0.149670i	0.418991	−	0.907991i	$-0.362384\pi$
$641$	−5.89635	−	3.78935i	−0.232892	−	0.149670i	−0.651882	+	0.758320i	$0.726020\pi$
$642$	−7.74879	−	8.94258i	−0.305820	−	0.352935i
$643$	47.1751			1.86040			0.930202	−	0.367048i	$-0.119632\pi$
$643$	47.1751			1.86040			0.930202	+	0.367048i	$0.119632\pi$
$644$	5.35630	+	10.1142i	0.211068	+	0.398554i
$645$	−6.13270			−0.241475
$646$	−0.797196	−	0.920013i	−0.0313652	−	0.0361974i
$647$	20.6258	+	13.2554i	0.810882	+	0.521122i	0.879150	−	0.476545i	$-0.158111\pi$
$647$	20.6258	+	13.2554i	0.810882	+	0.521122i	−0.0682682	+	0.997667i	$0.521747\pi$
$648$	0.142315	−	0.989821i	0.00559065	−	0.0388839i
$649$	−10.3342	+	22.6287i	−0.405652	+	0.888253i
$650$	0.153373	+	1.06673i	0.00601578	+	0.0418407i
$651$	−12.7454	−	3.74240i	−0.499534	−	0.146676i
$652$	7.54720	−	4.85029i	0.295571	−	0.189952i
$653$	1.39201	+	3.04807i	0.0544735	+	0.119280i	0.934911	−	0.354881i	$-0.115479\pi$
$653$	1.39201	+	3.04807i	0.0544735	+	0.119280i	−0.880438	+	0.474161i	$0.842751\pi$
$654$	−5.27189	+	1.54797i	−0.206147	+	0.0605303i
$655$	6.16005	−	7.10908i	0.240693	−	0.277775i
$656$	0.633335	−	0.730908i	0.0247276	−	0.0285372i
$657$	13.0855	−	3.84226i	0.510516	−	0.149901i
$658$	−2.64409	−	5.78976i	−0.103078	−	0.225708i
$659$	35.7456	−	22.9723i	1.39245	−	0.894875i	0.392759	−	0.919641i	$-0.371521\pi$
$659$	35.7456	−	22.9723i	1.39245	−	0.894875i	0.999693	+	0.0247662i	$0.00788414\pi$
$660$	4.37927	+	1.28587i	0.170463	+	0.0500524i
$661$	3.63300	+	25.2681i	0.141307	+	0.982814i	0.929877	+	0.367869i	$0.119913\pi$
$661$	3.63300	+	25.2681i	0.141307	+	0.982814i	−0.788570	+	0.614945i	$0.789178\pi$
$662$	0.738329	−	1.61672i	0.0286960	−	0.0628354i
$663$	−0.0331563	+	0.230607i	−0.00128769	+	0.00895605i
$664$	−13.9954	−	8.99427i	−0.543125	−	0.349046i
$665$	−8.80027	−	10.1561i	−0.341260	−	0.393835i
$666$	5.15433			0.199726
$667$	−3.32030	−	1.86843i	−0.128563	−	0.0723459i
$668$	7.16400			0.277183
$669$	15.9653	+	18.4249i	0.617254	+	0.712349i
$670$	−11.7205	−	7.53232i	−0.452803	−	0.290999i
$671$	7.03398	−	48.9224i	0.271544	−	1.88863i
$672$	0.991359	−	2.17077i	0.0382425	−	0.0837394i
$673$	−1.73037	−	12.0350i	−0.0667009	−	0.463915i	−0.995609	−	0.0936055i	$-0.970161\pi$
$673$	−1.73037	−	12.0350i	−0.0667009	−	0.463915i	0.928908	−	0.370309i	$-0.120748\pi$
$674$	9.08169	+	2.66662i	0.349813	+	0.102715i
$675$	−0.841254	+	0.540641i	−0.0323799	+	0.0208093i
$676$	−4.91792	−	10.7687i	−0.189151	−	0.414182i
$677$	29.8278	−	8.75823i	1.14638	−	0.336606i	0.347251	−	0.937772i	$-0.387115\pi$
$677$	29.8278	−	8.75823i	1.14638	−	0.336606i	0.799124	+	0.601166i	$0.205297\pi$
$678$	13.0297	−	15.0371i	0.500402	−	0.577495i
$679$	−14.0565	+	16.2220i	−0.539437	+	0.622544i
$680$	−0.207424	+	0.0609053i	−0.00795436	+	0.00233561i
$681$	−8.79132	−	19.2503i	−0.336884	−	0.737674i
$682$	21.3723	−	13.7351i	0.818388	−	0.525946i
$683$	8.52737	+	2.50386i	0.326291	+	0.0958077i	0.440776	−	0.897617i	$-0.354703\pi$
$683$	8.52737	+	2.50386i	0.326291	+	0.0958077i	−0.114485	+	0.993425i	$0.536522\pi$
$684$	−0.801398	−	5.57385i	−0.0306422	−	0.213121i
$685$	2.85929	−	6.26097i	0.109248	−	0.239219i
$686$	−2.82056	+	19.6175i	−0.107690	+	0.748998i
$687$	−5.59569	−	3.59613i	−0.213489	−	0.137201i
$688$	−4.01606	−	4.63479i	−0.153111	−	0.176700i
$689$	3.80453			0.144941
$690$	3.87563	−	2.82479i	0.147543	−	0.107538i
$691$	27.8764			1.06047			0.530234	−	0.847852i	$-0.322104\pi$
$691$	27.8764			1.06047			0.530234	+	0.847852i	$0.322104\pi$
$692$	−5.18837	−	5.98770i	−0.197232	−	0.227618i
$693$	9.16296	+	5.88867i	0.348072	+	0.223692i
$694$	3.66770	−	25.5094i	0.139224	−	0.968325i
$695$	−2.47604	+	5.42178i	−0.0939216	+	0.205660i
$696$	0.113058	+	0.786335i	0.00428545	+	0.0298060i
$697$	−0.200606	−	0.0589033i	−0.00759850	−	0.00223112i
$698$	−12.0462	+	7.74162i	−0.455955	+	0.293024i
$699$	1.40417	+	3.07471i	0.0531107	+	0.116296i
$700$	−2.28976	+	0.672335i	−0.0865449	+	0.0254119i
$701$	−4.55345	+	5.25496i	−0.171981	+	0.198477i	−0.835196	−	0.549952i	$-0.814646\pi$
$701$	−4.55345	+	5.25496i	−0.171981	+	0.198477i	0.663215	+	0.748429i	$0.269191\pi$
$702$	−0.705744	+	0.814472i	−0.0266366	+	0.0307403i
$703$	27.8492	−	8.17725i	1.05035	−	0.308411i
$704$	1.89602	+	4.15170i	0.0714588	+	0.156473i
$705$	−2.24374	+	1.44197i	−0.0845042	+	0.0543075i
$706$	−20.1965	−	5.93023i	−0.760105	−	0.223187i
$707$	−3.87488	−	26.9504i	−0.145730	−	1.01357i
$708$	2.26421	−	4.95792i	0.0850941	−	0.186330i
$709$	−5.70092	+	39.6508i	−0.214103	+	1.48912i	0.545160	+	0.838332i	$0.316469\pi$
$709$	−5.70092	+	39.6508i	−0.214103	+	1.48912i	−0.759263	+	0.650784i	$0.774440\pi$
$710$	−2.84992	−	1.83153i	−0.106956	−	0.0687362i
$711$	−0.0380366	−	0.0438966i	−0.00142648	−	0.00164625i
$712$	−1.88900			−0.0707933
$713$	2.24412	−	26.6004i	0.0840430	−	0.996193i
$714$	−0.515901			−0.0193071
$715$	−3.22112	−	3.71737i	−0.120463	−	0.139022i
$716$	5.03300	+	3.23451i	0.188092	+	0.120879i
$717$	1.75168	−	12.1832i	0.0654177	−	0.454990i
$718$	9.14599	−	20.0269i	0.341325	−	0.747398i
$719$	−6.27651	−	43.6541i	−0.234074	−	1.62802i	−0.680183	−	0.733043i	$-0.738099\pi$
$719$	−6.27651	−	43.6541i	−0.234074	−	1.62802i	0.446108	−	0.894979i	$-0.352810\pi$
$720$	−0.959493	−	0.281733i	−0.0357582	−	0.0104996i
$721$	28.3286	−	18.2057i	1.05501	−	0.678015i
$722$	−5.27993	−	11.5614i	−0.196499	−	0.430272i
$723$	18.3819	−	5.39741i	0.683630	−	0.200732i
$724$	−14.9705	+	17.2769i	−0.556375	+	0.642091i
$725$	0.520235	−	0.600384i	0.0193211	−	0.0222977i
$726$	−9.43322	+	2.76984i	−0.350099	+	0.102798i
$727$	−8.29687	−	18.1676i	−0.307714	−	0.673799i	0.691086	−	0.722772i	$-0.257132\pi$
$727$	−8.29687	−	18.1676i	−0.307714	−	0.673799i	−0.998800	+	0.0489730i	$0.984405\pi$
$728$	−2.16359	+	1.39045i	−0.0801878	+	0.0515336i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−1.94089	−	13.4992i	−0.0718355	−	0.499627i
$731$	−0.550747	+	1.20597i	−0.0203701	+	0.0446043i
$732$	−1.54114	+	10.7188i	−0.0569620	+	0.396180i
$733$	0.698986	+	0.449211i	0.0258176	+	0.0165920i	0.553486	−	0.832858i	$-0.313297\pi$
$733$	0.698986	+	0.449211i	0.0258176	+	0.0165920i	−0.527668	+	0.849450i	$0.676934\pi$
$734$	−23.5350	−	27.1609i	−0.868694	−	1.00253i
$735$	1.30495			0.0481337
$736$	4.67284	+	1.07916i	0.172243	+	0.0397785i
$737$	63.5887			2.34232
$738$	−0.633335	−	0.730908i	−0.0233134	−	0.0269051i
$739$	−27.7564	−	17.8380i	−1.02104	−	0.656180i	−0.0808091	−	0.996730i	$-0.525750\pi$
$739$	−27.7564	−	17.8380i	−1.02104	−	0.656180i	−0.940226	+	0.340550i	$0.889387\pi$
$740$	0.733538	−	5.10187i	0.0269654	−	0.187548i
$741$	−2.52103	+	5.52030i	−0.0926125	+	0.202793i
$742$	1.19895	+	8.33890i	0.0440149	+	0.306131i
$743$	0.998183	+	0.293093i	0.0366198	+	0.0107525i	0.299991	−	0.953942i	$-0.403016\pi$
$743$	0.998183	+	0.293093i	0.0366198	+	0.0107525i	−0.263371	+	0.964695i	$0.584834\pi$
$744$	−4.68265	+	3.00935i	−0.171674	+	0.110328i
$745$	3.56567	+	7.80773i	0.130636	+	0.286053i
$746$	18.6929	−	5.48873i	0.684396	−	0.200957i
$747$	−10.8945	+	12.5729i	−0.398608	+	0.460018i
$748$	0.646140	−	0.745685i	0.0236252	−	0.0272650i
$749$	−27.0942	+	7.95556i	−0.989999	+	0.290690i
$750$	0.415415	+	0.909632i	0.0151688	+	0.0332151i
$751$	−15.1423	+	9.73137i	−0.552551	+	0.355103i	−0.786930	−	0.617042i	$-0.788331\pi$
$751$	−15.1423	+	9.73137i	−0.552551	+	0.355103i	0.234379	+	0.972145i	$0.424694\pi$
$752$	−2.55910	−	0.751420i	−0.0933209	−	0.0274015i
$753$	−2.18577	−	15.2024i	−0.0796541	−	0.554006i
$754$	0.355657	−	0.778781i	0.0129523	−	0.0283615i
$755$	2.51196	−	17.4711i	0.0914195	−	0.635837i
$756$	−2.00759	−	1.29020i	−0.0730155	−	0.0469242i
$757$	25.4806	+	29.4062i	0.926109	+	1.06879i	0.997452	+	0.0713351i	$0.0227260\pi$
$757$	25.4806	+	29.4062i	0.926109	+	1.06879i	−0.0713433	+	0.997452i	$0.522729\pi$
$758$	−17.5521			−0.637520
$759$	−7.91055	+	20.4095i	−0.287135	+	0.740817i
$760$	−5.63116			−0.204264
$761$	3.91284	+	4.51566i	0.141840	+	0.163693i	0.822225	−	0.569163i	$-0.192733\pi$
$761$	3.91284	+	4.51566i	0.141840	+	0.163693i	−0.680384	+	0.732855i	$0.738187\pi$
$762$	−1.96767	−	1.26454i	−0.0712810	−	0.0458095i
$763$	−1.86605	+	12.9787i	−0.0675556	+	0.469859i
$764$	8.15577	−	17.8587i	0.295066	−	0.646103i
$765$	0.0307658	+	0.213981i	0.00111234	+	0.00773649i
$766$	−6.16658	−	1.81067i	−0.222808	−	0.0654222i
$767$	−4.94150	+	3.17571i	−0.178427	+	0.114668i
$768$	−0.415415	−	0.909632i	−0.0149900	−	0.0328235i
$769$	18.5440	−	5.44500i	0.668712	−	0.196352i	0.0702828	−	0.997527i	$-0.477610\pi$
$769$	18.5440	−	5.44500i	0.668712	−	0.196352i	0.598429	+	0.801175i	$0.295792\pi$
$770$	7.13276	−	8.23164i	0.257047	−	0.296648i
$771$	−3.08160	+	3.55636i	−0.110981	+	0.128079i
$772$	4.90838	−	1.44123i	0.176656	−	0.0518710i
$773$	7.29550	+	15.9749i	0.262401	+	0.574578i	0.994274	−	0.106864i	$-0.0340808\pi$
$773$	7.29550	+	15.9749i	0.262401	+	0.574578i	−0.731873	+	0.681441i	$0.761354\pi$
$774$	−5.15916	+	3.31559i	−0.185442	+	0.119176i
$775$	5.34080	+	1.56820i	0.191847	+	0.0563314i
$776$	1.28005	+	8.90297i	0.0459513	+	0.319598i
$777$	5.10979	−	11.1889i	0.183313	−	0.401399i
$778$	−0.223442	+	1.55407i	−0.00801078	+	0.0557162i
$779$	−4.58152	−	2.94437i	−0.164150	−	0.105493i
$780$	0.705744	+	0.814472i	0.0252697	+	0.0291628i
$781$	15.4620			0.553274
$782$	−0.207431	−	1.01581i	−0.00741773	−	0.0363251i
$783$	0.794422			0.0283903
$784$	0.854559	+	0.986214i	0.0305200	+	0.0352219i
$785$	0.439980	+	0.282758i	0.0157035	+	0.0100921i
$786$	1.33871	−	9.31091i	0.0477501	−	0.332109i
$787$	−21.1908	+	46.4014i	−0.755370	+	1.65403i	0.00109818	+	0.999999i	$0.499650\pi$
$787$	−21.1908	+	46.4014i	−0.755370	+	1.65403i	−0.756468	+	0.654030i	$0.773077\pi$
$788$	1.08139	+	7.52123i	0.0385229	+	0.267933i
$789$	24.0722	+	7.06823i	0.856992	+	0.251636i
$790$	−0.0488630	+	0.0314023i	−0.00173847	+	0.00111724i
$791$	−19.7249	−	43.1916i	−0.701338	−	1.53572i
$792$	4.37927	−	1.28587i	0.155611	−	0.0456914i
$793$	7.64255	−	8.81997i	0.271395	−	0.313206i
$794$	−16.8622	+	19.4601i	−0.598418	+	0.690612i
$795$	3.38723	−	0.994581i	0.120133	−	0.0352741i
$796$	−8.77598	−	19.2167i	−0.311056	−	0.681119i
$797$	−46.8624	+	30.1167i	−1.65995	+	1.06679i	−0.741749	+	0.670677i	$0.766004\pi$
$797$	−46.8624	+	30.1167i	−1.65995	+	1.06679i	−0.918203	+	0.396109i	$0.870360\pi$
$798$	−12.8940	−	3.78603i	−0.456444	−	0.134024i
$799$	0.0820567	+	0.570717i	0.00290296	+	0.0201905i
$800$	−0.415415	+	0.909632i	−0.0146871	+	0.0321603i
$801$	−0.268833	+	1.86977i	−0.00949875	+	0.0660652i
$802$	−8.13857	−	5.23034i	−0.287383	−	0.184690i
$803$	40.7623	+	47.0422i	1.43847	+	1.66008i
$804$	−13.9322			−0.491351
$805$	−2.28984	−	11.2135i	−0.0807064	−	0.395224i
$806$	5.99878			0.211298
$807$	3.11208	+	3.59153i	0.109550	+	0.126428i
$808$	−9.59812	−	6.16834i	−0.337661	−	0.217001i
$809$	4.92008	−	34.2199i	0.172981	−	1.20311i	−0.699562	−	0.714571i	$-0.746622\pi$
$809$	4.92008	−	34.2199i	0.172981	−	1.20311i	0.872543	−	0.488537i	$-0.162469\pi$
$810$	−0.415415	+	0.909632i	−0.0145962	+	0.0319612i
$811$	−5.42530	−	37.7338i	−0.190508	−	1.32501i	−0.830667	−	0.556769i	$-0.812041\pi$
$811$	−5.42530	−	37.7338i	−0.190508	−	1.32501i	0.640159	−	0.768242i	$-0.278868\pi$
$812$	1.81904	+	0.534118i	0.0638357	+	0.0187439i
$813$	17.5090	−	11.2523i	0.614067	−	0.394637i
$814$	9.77269	+	21.3992i	0.342533	+	0.750042i
$815$	−8.60798	+	2.52753i	−0.301524	+	0.0885355i
$816$	−0.141569	+	0.163379i	−0.00495589	+	0.00571940i
$817$	−22.6151	+	26.0992i	−0.791203	+	0.913097i
$818$	20.1087	−	5.90445i	0.703085	−	0.206444i
$819$	1.06839	+	2.33945i	0.0373325	+	0.0817469i
$820$	−0.813601	+	0.522870i	−0.0284122	+	0.0182594i
$821$	−7.18009	−	2.10826i	−0.250587	−	0.0735789i	0.154027	−	0.988067i	$-0.450776\pi$
$821$	−7.18009	−	2.10826i	−0.250587	−	0.0735789i	−0.404614	+	0.914488i	$0.632594\pi$
$822$	−0.979548	−	6.81291i	−0.0341657	−	0.237627i
$823$	−14.9657	+	32.7703i	−0.521671	+	1.14230i	0.447132	+	0.894468i	$0.352445\pi$
$823$	−14.9657	+	32.7703i	−0.521671	+	1.14230i	−0.968803	+	0.247832i	$0.920282\pi$
$824$	2.00817	−	13.9671i	0.0699578	−	0.486567i
$825$	−3.83961	−	2.46757i	−0.133678	−	0.0859096i
$826$	−8.51788	−	9.83016i	−0.296375	−	0.342035i
$827$	6.16601			0.214413			0.107207	−	0.994237i	$-0.465809\pi$
$827$	6.16601			0.214413			0.107207	+	0.994237i	$0.465809\pi$
$828$	1.73319	−	4.47169i	0.0602326	−	0.155402i
$829$	−14.5485			−0.505290			−0.252645	−	0.967559i	$-0.581300\pi$
$829$	−14.5485			−0.505290			−0.252645	+	0.967559i	$0.581300\pi$
$830$	10.8945	+	12.5729i	0.378153	+	0.436411i
$831$	7.41816	+	4.76736i	0.257333	+	0.165378i
$832$	−0.153373	+	1.06673i	−0.00531725	+	0.0369823i
$833$	0.117191	−	0.256612i	0.00406042	−	0.00889108i
$834$	0.848254	+	5.89974i	0.0293726	+	0.204291i
$835$	−6.87381	−	2.01833i	−0.237878	−	0.0698472i
$836$	21.6215	−	13.8953i	0.747794	−	0.480578i
$837$	2.31231	+	5.06326i	0.0799252	+	0.175012i
$838$	−28.7039	+	8.42823i	−0.991560	+	0.291148i
$839$	−21.7508	+	25.1018i	−0.750922	+	0.866610i	−0.994657	−	0.103232i	$-0.967082\pi$
$839$	−21.7508	+	25.1018i	−0.750922	+	0.866610i	0.243736	+	0.969842i	$0.421627\pi$
$840$	−1.56278	+	1.80354i	−0.0539210	+	0.0622282i
$841$	27.2198	−	7.99244i	0.938612	−	0.275601i
$842$	12.1942	+	26.7015i	0.420239	+	0.920195i
$843$	16.9871	−	10.9169i	0.585066	−	0.375999i
$844$	1.58650	+	0.465837i	0.0546094	+	0.0160348i
$845$	1.68480	+	11.7181i	0.0579590	+	0.403114i
$846$	−1.10797	+	2.42612i	−0.0380928	+	0.0834116i
$847$	−3.33900	+	23.2233i	−0.114730	+	0.797962i
$848$	2.96982	+	1.90859i	0.101984	+	0.0655411i
$849$	3.69516	+	4.26445i	0.126818	+	0.146355i
$850$	0.216181			0.00741495
$851$	24.0853	+	5.56236i	0.825635	+	0.190675i
$852$	−3.38771			−0.116061
$853$	10.7663	+	12.4250i	0.368632	+	0.425424i	0.909513	−	0.415675i	$-0.136455\pi$
$853$	10.7663	+	12.4250i	0.368632	+	0.425424i	−0.540881	+	0.841099i	$0.681909\pi$
$854$	21.7404	+	13.9717i	0.743939	+	0.478101i
$855$	−0.801398	+	5.57385i	−0.0274072	+	0.190622i
$856$	−4.91549	+	10.7634i	−0.168008	+	0.367886i
$857$	2.90629	+	20.2137i	0.0992768	+	0.690486i	0.977299	+	0.211865i	$0.0679538\pi$
$857$	2.90629	+	20.2137i	0.0992768	+	0.690486i	−0.878022	+	0.478620i	$0.841137\pi$
$858$	−4.71954	−	1.38578i	−0.161123	−	0.0473099i
$859$	28.6920	−	18.4392i	0.978957	−	0.629138i	0.0497755	−	0.998760i	$-0.484149\pi$
$859$	28.6920	−	18.4392i	0.978957	−	0.629138i	0.929182	+	0.369623i	$0.120513\pi$
$860$	2.54762	+	5.57850i	0.0868730	+	0.190225i
$861$	−2.21450	+	0.650235i	−0.0754699	+	0.0221600i
$862$	0.483189	−	0.557630i	0.0164575	−	0.0189929i
$863$	22.7352	−	26.2378i	0.773915	−	0.893145i	−0.222740	−	0.974878i	$-0.571500\pi$
$863$	22.7352	−	26.2378i	0.773915	−	0.893145i	0.996654	+	0.0817328i	$0.0260454\pi$
$864$	−0.959493	+	0.281733i	−0.0326426	+	0.00958474i
$865$	3.29127	+	7.20689i	0.111907	+	0.245041i
$866$	−5.78618	+	3.71855i	−0.196623	+	0.126362i
$867$	−16.2665	−	4.77629i	−0.552441	−	0.162211i
$868$	1.89044	+	13.1483i	0.0641658	+	0.446283i
$869$	0.110127	−	0.241145i	0.00373581	−	0.00818029i
$870$	0.113058	−	0.786335i	0.00383302	−	0.0266593i
$871$	12.6312	+	8.11760i	0.427993	+	0.275054i
$872$	3.59810	+	4.15243i	0.121847	+	0.140619i
$873$	8.99452			0.304418
$874$	2.27028	−	26.9105i	0.0767934	−	0.910262i
$875$	2.38643			0.0806761
$876$	−8.93098	−	10.3069i	−0.301750	−	0.348238i
$877$	−32.2574	−	20.7305i	−1.08925	−	0.700021i	−0.132577	−	0.991173i	$-0.542325\pi$
$877$	−32.2574	−	20.7305i	−1.08925	−	0.700021i	−0.956677	+	0.291152i	$0.905961\pi$
$878$	3.93103	−	27.3409i	0.132666	−	0.922711i
$879$	−6.28772	+	13.7682i	−0.212080	+	0.464389i
$880$	−0.649546	−	4.51769i	−0.0218962	−	0.152291i
$881$	−35.2643	−	10.3545i	−1.18808	−	0.348853i	−0.372798	−	0.927913i	$-0.621602\pi$
$881$	−35.2643	−	10.3545i	−1.18808	−	0.348853i	−0.815285	+	0.579060i	$0.803420\pi$
$882$	1.09779	−	0.705508i	0.0369646	−	0.0237557i
$883$	23.9573	+	52.4592i	0.806227	+	1.76539i	0.622838	+	0.782351i	$0.285979\pi$
$883$	23.9573	+	52.4592i	0.806227	+	1.76539i	0.183389	+	0.983040i	$0.441293\pi$
$884$	0.223541	−	0.0656377i	0.00751851	−	0.00220763i
$885$	−3.56930	+	4.11919i	−0.119981	+	0.138465i
$886$	−24.6600	+	28.4591i	−0.828467	+	0.956102i
$887$	12.7425	−	3.74155i	0.427853	−	0.125629i	−0.0607145	−	0.998155i	$-0.519338\pi$
$887$	12.7425	−	3.74155i	0.427853	−	0.125629i	0.488567	+	0.872526i	$0.337520\pi$
$888$	−2.14119	−	4.68854i	−0.0718535	−	0.157337i
$889$	−4.69570	+	3.01774i	−0.157489	+	0.101212i
$890$	1.81248	+	0.532193i	0.0607546	+	0.0178392i
$891$	−0.649546	−	4.51769i	−0.0217606	−	0.151348i
$892$	10.1277	−	22.1765i	0.339100	−	0.742525i
$893$	−2.13744	+	14.8662i	−0.0715268	+	0.497479i
$894$	7.22081	+	4.64053i	0.241500	+	0.155203i
$895$	−3.91786	−	4.52145i	−0.130960	−	0.151135i
$896$	−2.38643			−0.0797251
$897$	−4.17678	+	3.04428i	−0.139459	+	0.101646i
$898$	−20.4928			−0.683853
$899$	−2.89577	−	3.34190i	−0.0965794	−	0.111459i
$900$	0.841254	+	0.540641i	0.0280418	+	0.0180214i
$901$	0.108610	−	0.755401i	0.00361833	−	0.0251661i
$902$	1.83369	−	4.01523i	0.0610553	−	0.133693i
$903$	2.08282	+	14.4863i	0.0693118	+	0.482074i
$904$	−19.0909	−	5.60560i	−0.634954	−	0.186439i
$905$	19.2316	−	12.3594i	0.639280	−	0.410840i
$906$	−7.33237	−	16.0557i	−0.243602	−	0.533413i
$907$	−26.7839	+	7.86447i	−0.889346	+	0.261136i	−0.694323	−	0.719663i	$-0.744296\pi$
$907$	−26.7839	+	7.86447i	−0.889346	+	0.261136i	−0.195023	+	0.980799i	$0.562478\pi$
$908$	−13.8587	+	15.9937i	−0.459916	+	0.530771i
$909$	−7.47151	+	8.62258i	−0.247814	+	0.285993i
$910$	2.46768	−	0.724577i	0.0818028	−	0.0240195i
$911$	−5.72622	−	12.5387i	−0.189718	−	0.415424i	0.790740	−	0.612152i	$-0.209696\pi$
$911$	−5.72622	−	12.5387i	−0.189718	−	0.415424i	−0.980458	+	0.196727i	$0.936969\pi$
$912$	−4.73724	+	3.04444i	−0.156866	+	0.100811i
$913$	−72.8549	−	21.3921i	−2.41115	−	0.707976i
$914$	5.46331	+	37.9981i	0.180710	+	1.25687i
$915$	4.49855	−	9.85046i	0.148718	−	0.325646i
$916$	−0.946622	+	6.58390i	−0.0312773	+	0.217538i
$917$	−18.8847	−	12.1365i	−0.623629	−	0.400782i
$918$	0.141569	+	0.163379i	0.00467246	+	0.00539230i
$919$	−4.51877			−0.149061			−0.0745303	−	0.997219i	$-0.523746\pi$
$919$	−4.51877			−0.149061			−0.0745303	+	0.997219i	$0.523746\pi$
$920$	−4.17952	−	2.35194i	−0.137795	−	0.0775411i
$921$	−0.928993			−0.0306114
$922$	22.7974	+	26.3096i	0.750791	+	0.866459i
$923$	3.07136	+	1.97385i	0.101095	+	0.0649699i
$924$	1.55010	−	10.7812i	0.0509944	−	0.354674i
$925$	−2.14119	+	4.68854i	−0.0704018	+	0.154158i
$926$	2.86067	+	19.8964i	0.0940073	+	0.653835i
$927$	−13.5391	−	3.97545i	−0.444684	−	0.130571i
$928$	0.668310	−	0.429497i	0.0219383	−	0.0140989i
$929$	21.5969	+	47.2907i	0.708572	+	1.55156i	0.829258	+	0.558866i	$0.188763\pi$
$929$	21.5969	+	47.2907i	0.708572	+	1.55156i	−0.120686	+	0.992691i	$0.538509\pi$
$930$	5.34080	−	1.56820i	0.175132	−	0.0514233i
$931$	4.81216	−	5.55353i	0.157712	−	0.182010i
$932$	2.21354	−	2.55456i	0.0725069	−	0.0836774i
$933$	−16.1209	+	4.73354i	−0.527776	+	0.154969i
$934$	−13.7663	−	30.1441i	−0.450448	−	0.986344i
$935$	−0.830051	+	0.533441i	−0.0271456	+	0.0174454i
$936$	1.03405	+	0.303624i	0.0337989	+	0.00992425i
$937$	−3.18606	−	22.1595i	−0.104084	−	0.723920i	−0.973308	−	0.229502i	$-0.926290\pi$
$937$	−3.18606	−	22.1595i	−0.104084	−	0.723920i	0.869224	−	0.494418i	$-0.164619\pi$
$938$	−13.8118	+	30.2437i	−0.450972	+	0.987491i
$939$	0.745983	−	5.18842i	0.0243442	−	0.169318i
$940$	2.24374	+	1.44197i	0.0731828	+	0.0470317i
$941$	−3.99233	−	4.60740i	−0.130146	−	0.150197i	0.686936	−	0.726718i	$-0.258955\pi$
$941$	−3.99233	−	4.60740i	−0.130146	−	0.150197i	−0.817082	+	0.576521i	$0.804410\pi$
$942$	0.523005			0.0170404
$943$	−2.17070	−	4.09889i	−0.0706879	−	0.133478i
$944$	−5.45047			−0.177398
$945$	1.56278	+	1.80354i	0.0508372	+	0.0586693i
$946$	−23.5472	−	15.1328i	−0.765584	−	0.492011i
$947$	−8.25301	+	57.4010i	−0.268187	+	1.86528i	0.197462	+	0.980311i	$0.436730\pi$
$947$	−8.25301	+	57.4010i	−0.268187	+	1.86528i	−0.465648	+	0.884970i	$0.654179\pi$
$948$	−0.0241288	+	0.0528346i	−0.000783666	+	0.00171599i
$949$	2.09170	+	14.5481i	0.0678994	+	0.472250i
$950$	5.40306	+	1.58648i	0.175298	+	0.0514723i
$951$	−5.70968	+	3.66939i	−0.185149	+	0.118988i
$952$	0.214313	+	0.469280i	0.00694593	+	0.0152095i
$953$	−53.7403	+	15.7796i	−1.74082	+	0.511151i	−0.988961	−	0.148174i	$-0.952660\pi$
$953$	−53.7403	+	15.7796i	−1.74082	+	0.511151i	−0.751858	+	0.659325i	$0.770842\pi$
$954$	2.31181	−	2.66797i	0.0748476	−	0.0863787i
$955$	−12.8568	+	14.8375i	−0.416035	+	0.480130i
$956$	−11.8099	+	3.46770i	−0.381959	+	0.112153i
$957$	1.50624	+	3.29820i	0.0486897	+	0.106616i
$958$	1.56275	−	1.00432i	0.0504901	−	0.0324480i
$959$	−15.7604	−	4.62766i	−0.508929	−	0.149435i
$960$	0.142315	+	0.989821i	0.00459319	+	0.0319463i
$961$	−0.00689732	+	0.0151030i	−0.000222494	+	0.000487194i
$962$	−0.790534	+	5.49829i	−0.0254879	+	0.177272i
$963$	9.95433	+	6.39726i	0.320774	+	0.206149i
$964$	−12.5458	−	14.4786i	−0.404072	−	0.466324i
$965$	−5.11559			−0.164677
$966$	−7.98882	−	8.19542i	−0.257036	−	0.263683i
$967$	11.9178			0.383249			0.191625	−	0.981468i	$-0.438624\pi$
$967$	11.9178			0.383249			0.191625	+	0.981468i	$0.438624\pi$
$968$	6.43824	+	7.43012i	0.206933	+	0.238813i
$969$	1.02410	+	0.658150i	0.0328989	+	0.0211428i
$970$	1.28005	−	8.90297i	0.0411001	−	0.285857i
$971$	21.7560	−	47.6391i	0.698185	−	1.52881i	−0.143974	−	0.989581i	$-0.545988\pi$
$971$	21.7560	−	47.6391i	0.698185	−	1.52881i	0.842159	−	0.539230i	$-0.181284\pi$
$972$	0.142315	+	0.989821i	0.00456475	+	0.0317485i
$973$	13.6479	+	4.00739i	0.437532	+	0.128471i
$974$	14.4537	−	9.28882i	0.463126	−	0.297633i
$975$	−0.447693	−	0.980312i	−0.0143377	−	0.0313951i
$976$	10.3904	−	3.05090i	0.332589	−	0.0976569i
$977$	−24.4403	+	28.2056i	−0.781913	+	0.902376i	−0.997246	−	0.0741647i	$-0.976371\pi$
$977$	−24.4403	+	28.2056i	−0.781913	+	0.902376i	0.215333	+	0.976541i	$0.430916\pi$
$978$	−5.87500	+	6.78012i	−0.187862	+	0.216804i
$979$	−8.27245	+	2.42901i	−0.264389	+	0.0776315i
$980$	−0.542095	−	1.18702i	−0.0173166	−	0.0379180i
$981$	4.62223	−	2.97053i	0.147576	−	0.0948416i
$982$	3.36120	+	0.986936i	0.107260	+	0.0314944i
$983$	−6.52579	−	45.3878i	−0.208140	−	1.44765i	−0.779219	−	0.626752i	$-0.784384\pi$
$983$	−6.52579	−	45.3878i	−0.208140	−	1.44765i	0.571079	−	0.820895i	$-0.306525\pi$
$984$	−0.401760	+	0.879732i	−0.0128076	+	0.0280448i
$985$	1.08139	−	7.52123i	0.0344559	−	0.239646i
$986$	−0.144476	−	0.0928491i	−0.00460105	−	0.00295692i
$987$	4.16815	+	4.81031i	0.132674	+	0.153114i
$988$	6.06871			0.193071
$989$	−27.6860	+	9.92564i	−0.880362	+	0.315617i
$990$	−4.56415			−0.145058
$991$	−36.9131	−	42.6000i	−1.17258	−	1.35323i	−0.922963	−	0.384889i	$-0.874240\pi$
$991$	−36.9131	−	42.6000i	−1.17258	−	1.35323i	−0.249621	−	0.968344i	$-0.580306\pi$
$992$	4.68265	+	3.00935i	0.148674	+	0.0955471i
$993$	−0.252940	+	1.75924i	−0.00802682	+	0.0558278i
$994$	−3.35844	+	7.35395i	−0.106523	+	0.233253i
$995$	3.00652	+	20.9108i	0.0953130	+	0.662917i
$996$	15.9624	+	4.68699i	0.505789	+	0.148513i
$997$	−28.1327	+	18.0798i	−0.890971	+	0.572592i	−0.904100	−	0.427321i	$-0.859457\pi$
$997$	−28.1327	+	18.0798i	−0.890971	+	0.572592i	0.0131286	+	0.999914i	$0.495821\pi$
$998$	15.2977	+	33.4973i	0.484241	+	1.06034i
$999$	−4.94554	+	1.45214i	−0.156470	+	0.0459438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.e.151.1	✓	20
23.16	even	11	inner	690.2.m.e.361.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.e.151.1	✓	20	1.1	even	1	trivial
690.2.m.e.361.1	yes	20	23.16	even	11	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.28976 - 0.672335i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.415415 - 0.909632i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.28976 - 0.672335i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(0.959493 - 0.281733i) q^{10} +(-2.98888 + 3.44935i) q^{11} +(0.654861 - 0.755750i) q^{12} +(-1.03405 + 0.303624i) q^{13} +(-0.991359 - 2.17077i) q^{14} +(-0.841254 + 0.540641i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.0307658 + 0.213981i) q^{17} +(-0.415415 + 0.909632i) q^{18} +(-0.801398 + 5.57385i) q^{19} +(0.841254 + 0.540641i) q^{20} +(1.56278 + 1.80354i) q^{21} -4.56415 q^{22} +(-2.92281 + 3.80226i) q^{23} +1.00000 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-0.906620 - 0.582649i) q^{26} +(0.142315 - 0.989821i) q^{27} +(0.991359 - 2.17077i) q^{28} +(0.113058 + 0.786335i) q^{29} +(-0.959493 - 0.281733i) q^{30} +(-4.68265 + 3.00935i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(4.37927 - 1.28587i) q^{33} +(-0.141569 + 0.163379i) q^{34} +(-1.56278 + 1.80354i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-2.14119 - 4.68854i) q^{37} +(-4.73724 + 3.04444i) q^{38} +(1.03405 + 0.303624i) q^{39} +(0.142315 + 0.989821i) q^{40} +(-0.401760 + 0.879732i) q^{41} +(-0.339625 + 2.36214i) q^{42} +(5.15916 + 3.31559i) q^{43} +(-2.98888 - 3.44935i) q^{44} +1.00000 q^{45} +(-4.78759 + 0.281042i) q^{46} +2.66714 q^{47} +(0.654861 + 0.755750i) q^{48} +(-1.09779 - 0.705508i) q^{49} +(0.142315 - 0.989821i) q^{50} +(0.0898049 - 0.196645i) q^{51} +(-0.153373 - 1.06673i) q^{52} +(-3.38723 - 0.994581i) q^{53} +(0.841254 - 0.540641i) q^{54} +(1.89602 + 4.15170i) q^{55} +(2.28976 - 0.672335i) q^{56} +(3.68763 - 4.25575i) q^{57} +(-0.520235 + 0.600384i) q^{58} +(5.22968 - 1.53557i) q^{59} +(-0.415415 - 0.909632i) q^{60} +(-9.10999 + 5.85463i) q^{61} +(-5.34080 - 1.56820i) q^{62} +(-0.339625 - 2.36214i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.153373 + 1.06673i) q^{65} +(3.83961 + 2.46757i) q^{66} +(-9.12366 - 10.5293i) q^{67} -0.216181 q^{68} +(4.51448 - 1.61848i) q^{69} -2.38643 q^{70} +(-2.21848 - 2.56026i) q^{71} +(-0.841254 - 0.540641i) q^{72} +(1.94089 - 13.4992i) q^{73} +(2.14119 - 4.68854i) q^{74} +(0.142315 + 0.989821i) q^{75} +(-5.40306 - 1.58648i) q^{76} +(9.16296 - 5.88867i) q^{77} +(0.447693 + 0.980312i) q^{78} +(-0.0557307 + 0.0163640i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-0.927954 + 0.272472i) q^{82} +(6.91098 + 15.1329i) q^{83} +(-2.00759 + 1.29020i) q^{84} +(0.207424 + 0.0609053i) q^{85} +(0.872774 + 6.07028i) q^{86} +(0.330015 - 0.722631i) q^{87} +(0.649546 - 4.51769i) q^{88} +(1.58913 + 1.02127i) q^{89} +(0.654861 + 0.755750i) q^{90} +2.57186 q^{91} +(-3.34760 - 3.43418i) q^{92} +5.56627 q^{93} +(1.74661 + 2.01569i) q^{94} +(4.73724 + 3.04444i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(3.73646 - 8.18170i) q^{97} +(-0.185713 - 1.29167i) q^{98} +(-4.37927 - 1.28587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Introduction

L-functions

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