LMFDB - Embedded newform 690.2.m.c.541.1

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} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
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			541.1
Root			$2.21300 - 1.42221i$ of defining polynomial
Character	$\chi$	$=$	690.541
Dual form			690.2.m.c.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-2.29325 - 2.64655i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-2.29325 - 2.64655i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(-2.35891 - 1.51598i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(0.0353321 - 0.0407754i) q^{13} +(-3.36004 - 0.986596i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.10199 + 2.41302i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(-0.969650 + 2.12324i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(-2.94598 + 1.89326i) q^{21} -2.80404 q^{22} +(-3.56616 + 3.20664i) q^{23} -1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.00767840 - 0.0534044i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-3.36004 + 0.986596i) q^{28} +(-3.79793 - 8.31630i) q^{29} +(0.654861 + 0.755750i) q^{30} +(-1.07875 - 7.50285i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.83626 + 2.11915i) q^{33} +(2.23163 + 1.43418i) q^{34} +(2.94598 + 1.89326i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(3.72883 + 1.09488i) q^{37} +(0.332187 + 2.31041i) q^{38} +(-0.0353321 - 0.0407754i) q^{39} +(0.415415 + 0.909632i) q^{40} +(10.3379 - 3.03549i) q^{41} +(-1.45474 + 3.18543i) q^{42} +(1.39046 - 9.67083i) q^{43} +(-2.35891 + 1.51598i) q^{44} +1.00000 q^{45} +(-1.26640 + 4.62561i) q^{46} -12.8659 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-0.749034 + 5.20965i) q^{49} +(0.415415 - 0.909632i) q^{50} +(2.54528 - 0.747363i) q^{51} +(-0.0224131 - 0.0490779i) q^{52} +(8.43650 + 9.73624i) q^{53} +(0.142315 + 0.989821i) q^{54} +(2.69046 + 0.789989i) q^{55} +(-2.29325 + 2.64655i) q^{56} +(1.96363 + 1.26195i) q^{57} +(-7.69115 - 4.94280i) q^{58} +(2.72523 - 3.14508i) q^{59} +(0.959493 + 0.281733i) q^{60} +(-0.713737 - 4.96415i) q^{61} +(-4.96384 - 5.72858i) q^{62} +(1.45474 + 3.18543i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.0224131 + 0.0490779i) q^{65} +(-0.399057 + 2.77550i) q^{66} +(-5.39356 + 3.46623i) q^{67} +2.65274 q^{68} +(2.66648 + 3.98621i) q^{69} +3.50189 q^{70} +(0.0178062 - 0.0114433i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(5.60079 - 12.2640i) q^{73} +(3.72883 - 1.09488i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(1.52856 + 1.76405i) q^{76} +(1.39745 + 9.71949i) q^{77} +(-0.0517681 - 0.0152005i) q^{78} +(4.03792 - 4.66000i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(7.05571 - 8.14272i) q^{82} +(9.07850 + 2.66569i) q^{83} +(0.498371 + 3.46624i) q^{84} +(-1.73717 - 2.00481i) q^{85} +(-4.05872 - 8.88736i) q^{86} +(-8.77215 + 2.57574i) q^{87} +(-1.16484 + 2.55064i) q^{88} +(-1.08850 + 7.57069i) q^{89} +(0.841254 - 0.540641i) q^{90} -0.188939 q^{91} +(1.43543 + 4.57598i) q^{92} -7.58000 q^{93} +(-10.8235 + 6.95581i) q^{94} +(0.332187 - 2.31041i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(-8.12729 + 2.38639i) q^{97} +(2.18642 + 4.78759i) q^{98} +(1.83626 + 2.11915i) 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	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 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 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.415415	−	0.909632i	−0.169592	−	0.371356i
$7$	−2.29325	−	2.64655i	−0.866767	−	1.00030i	−0.999958	−	0.00921159i	$-0.997068\pi$
$7$	−2.29325	−	2.64655i	−0.866767	−	1.00030i	0.133191	−	0.991090i	$-0.457478\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−0.654861	+	0.755750i	−0.207085	+	0.238989i
$11$	−2.35891	−	1.51598i	−0.711238	−	0.457085i	0.134341	−	0.990935i	$-0.457108\pi$
$11$	−2.35891	−	1.51598i	−0.711238	−	0.457085i	−0.845579	+	0.533850i	$0.820745\pi$
$12$	−0.841254	−	0.540641i	−0.242849	−	0.156070i
$13$	0.0353321	−	0.0407754i	0.00979936	−	0.0113091i	−0.750829	−	0.660497i	$-0.770346\pi$
$13$	0.0353321	−	0.0407754i	0.00979936	−	0.0113091i	0.760628	+	0.649188i	$0.224891\pi$
$14$	−3.36004	−	0.986596i	−0.898008	−	0.263679i
$15$	0.142315	+	0.989821i	0.0367455	+	0.255571i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	1.10199	+	2.41302i	0.267271	+	0.585242i	0.994916	−	0.100712i	$-0.0321122\pi$
$17$	1.10199	+	2.41302i	0.267271	+	0.585242i	−0.727644	+	0.685955i	$0.759385\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	−0.969650	+	2.12324i	−0.222453	+	0.487104i	−0.987647	−	0.156696i	$-0.949916\pi$
$19$	−0.969650	+	2.12324i	−0.222453	+	0.487104i	0.765194	+	0.643800i	$0.222643\pi$
$20$	−0.142315	+	0.989821i	−0.0318226	+	0.221331i
$21$	−2.94598	+	1.89326i	−0.642865	+	0.413144i
$22$	−2.80404			−0.597823
$23$	−3.56616	+	3.20664i	−0.743595	+	0.668630i
$23$	−3.56616	+	3.20664i	−0.743595	+	0.668630i
$24$	−1.00000			−0.204124
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.00767840	−	0.0534044i	0.00150586	−	0.0104735i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−3.36004	+	0.986596i	−0.634987	+	0.186449i
$29$	−3.79793	−	8.31630i	−0.705257	−	1.54430i	−0.833479	−	0.552552i	$-0.813654\pi$
$29$	−3.79793	−	8.31630i	−0.705257	−	1.54430i	0.128221	−	0.991746i	$-0.459073\pi$
$30$	0.654861	+	0.755750i	0.119561	+	0.137980i
$31$	−1.07875	−	7.50285i	−0.193749	−	1.34755i	−0.821976	−	0.569522i	$-0.807128\pi$
$31$	−1.07875	−	7.50285i	−0.193749	−	1.34755i	0.628228	−	0.778029i	$-0.283781\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−1.83626	+	2.11915i	−0.319651	+	0.368897i
$34$	2.23163	+	1.43418i	0.382721	+	0.245960i
$35$	2.94598	+	1.89326i	0.497961	+	0.320020i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	3.72883	+	1.09488i	0.613016	+	0.179998i	0.573479	−	0.819220i	$-0.305593\pi$
$37$	3.72883	+	1.09488i	0.613016	+	0.179998i	0.0395373	+	0.999218i	$0.487412\pi$
$38$	0.332187	+	2.31041i	0.0538879	+	0.374799i
$39$	−0.0353321	−	0.0407754i	−0.00565766	−	0.00652929i
$40$	0.415415	+	0.909632i	0.0656829	+	0.143825i
$41$	10.3379	−	3.03549i	1.61451	−	0.474064i	0.654977	−	0.755649i	$-0.272678\pi$
$41$	10.3379	−	3.03549i	1.61451	−	0.474064i	0.959536	+	0.281585i	$0.0908601\pi$
$42$	−1.45474	+	3.18543i	−0.224471	+	0.491522i
$43$	1.39046	−	9.67083i	0.212042	−	1.47479i	−0.554279	−	0.832331i	$-0.687006\pi$
$43$	1.39046	−	9.67083i	0.212042	−	1.47479i	0.766322	−	0.642457i	$-0.222085\pi$
$44$	−2.35891	+	1.51598i	−0.355619	+	0.228542i
$45$	1.00000			0.149071
$46$	−1.26640	+	4.62561i	−0.186721	+	0.682008i
$47$	−12.8659			−1.87668			−0.938339	−	0.345716i	$-0.887636\pi$
$47$	−12.8659			−1.87668			−0.938339	+	0.345716i	$0.887636\pi$
$48$	−0.841254	+	0.540641i	−0.121424	+	0.0780348i
$49$	−0.749034	+	5.20965i	−0.107005	+	0.744235i
$50$	0.415415	−	0.909632i	0.0587486	−	0.128641i
$51$	2.54528	−	0.747363i	0.356411	−	0.104652i
$52$	−0.0224131	−	0.0490779i	−0.00310814	−	0.00680588i
$53$	8.43650	+	9.73624i	1.15884	+	1.33738i	0.931578	+	0.363543i	$0.118433\pi$
$53$	8.43650	+	9.73624i	1.15884	+	1.33738i	0.227265	+	0.973833i	$0.427022\pi$
$54$	0.142315	+	0.989821i	0.0193666	+	0.134698i
$55$	2.69046	+	0.789989i	0.362781	+	0.106522i
$56$	−2.29325	+	2.64655i	−0.306448	+	0.353660i
$57$	1.96363	+	1.26195i	0.260089	+	0.167149i
$58$	−7.69115	−	4.94280i	−1.00990	−	0.649021i
$59$	2.72523	−	3.14508i	0.354795	−	0.409455i	−0.550094	−	0.835103i	$-0.685408\pi$
$59$	2.72523	−	3.14508i	0.354795	−	0.409455i	0.904889	+	0.425647i	$0.139954\pi$
$60$	0.959493	+	0.281733i	0.123870	+	0.0363715i
$61$	−0.713737	−	4.96415i	−0.0913846	−	0.635594i	−0.983110	−	0.183017i	$-0.941414\pi$
$61$	−0.713737	−	4.96415i	−0.0913846	−	0.635594i	0.891725	−	0.452577i	$-0.149495\pi$
$62$	−4.96384	−	5.72858i	−0.630409	−	0.727531i
$63$	1.45474	+	3.18543i	0.183280	+	0.401326i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−0.0224131	+	0.0490779i	−0.00278001	+	0.00608737i
$66$	−0.399057	+	2.77550i	−0.0491205	+	0.341640i
$67$	−5.39356	+	3.46623i	−0.658928	+	0.423467i	−0.826919	−	0.562321i	$-0.809908\pi$
$67$	−5.39356	+	3.46623i	−0.658928	+	0.423467i	0.167991	+	0.985789i	$0.446272\pi$
$68$	2.65274			0.321692
$69$	2.66648	+	3.98621i	0.321007	+	0.479883i
$70$	3.50189			0.418556
$71$	0.0178062	−	0.0114433i	0.00211320	−	0.00135807i	−0.539584	−	0.841932i	$-0.681418\pi$
$71$	0.0178062	−	0.0114433i	0.00211320	−	0.00135807i	0.541697	+	0.840574i	$0.317782\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	5.60079	−	12.2640i	0.655523	−	1.43540i	−0.231112	−	0.972927i	$-0.574236\pi$
$73$	5.60079	−	12.2640i	0.655523	−	1.43540i	0.886636	−	0.462469i	$-0.153036\pi$
$74$	3.72883	−	1.09488i	0.433468	−	0.127278i
$75$	−0.415415	−	0.909632i	−0.0479680	−	0.105035i
$76$	1.52856	+	1.76405i	0.175338	+	0.202350i
$77$	1.39745	+	9.71949i	0.159254	+	1.10764i
$78$	−0.0517681	−	0.0152005i	−0.00586158	−	0.00172112i
$79$	4.03792	−	4.66000i	0.454301	−	0.524291i	−0.481677	−	0.876349i	$-0.659972\pi$
$79$	4.03792	−	4.66000i	0.454301	−	0.524291i	0.935978	+	0.352057i	$0.114518\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	7.05571	−	8.14272i	0.779173	−	0.899213i
$83$	9.07850	+	2.66569i	0.996495	+	0.292597i	0.739017	−	0.673687i	$-0.235290\pi$
$83$	9.07850	+	2.66569i	0.996495	+	0.292597i	0.257478	+	0.966284i	$0.417109\pi$
$84$	0.498371	+	3.46624i	0.0543767	+	0.378198i
$85$	−1.73717	−	2.00481i	−0.188423	−	0.217452i
$86$	−4.05872	−	8.88736i	−0.437663	−	0.958348i
$87$	−8.77215	+	2.57574i	−0.940473	+	0.276148i
$88$	−1.16484	+	2.55064i	−0.124172	+	0.271900i
$89$	−1.08850	+	7.57069i	−0.115381	+	0.802491i	0.847157	+	0.531343i	$0.178312\pi$
$89$	−1.08850	+	7.57069i	−0.115381	+	0.802491i	−0.962538	+	0.271148i	$0.912597\pi$
$90$	0.841254	−	0.540641i	0.0886759	−	0.0569885i
$91$	−0.188939			−0.0198062
$92$	1.43543	+	4.57598i	0.149653	+	0.477078i
$93$	−7.58000			−0.786009
$94$	−10.8235	+	6.95581i	−1.11635	+	0.717437i
$95$	0.332187	−	2.31041i	0.0340817	−	0.237044i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	−8.12729	+	2.38639i	−0.825201	+	0.242301i	−0.666954	−	0.745099i	$-0.732402\pi$
$97$	−8.12729	+	2.38639i	−0.825201	+	0.242301i	−0.158247	+	0.987400i	$0.550584\pi$
$98$	2.18642	+	4.78759i	0.220862	+	0.483620i
$99$	1.83626	+	2.11915i	0.184551	+	0.212983i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	15.1111	+	4.43703i	1.50361	+	0.441501i	0.926857	−	0.375415i	$-0.122500\pi$
$101$	15.1111	+	4.43703i	1.50361	+	0.441501i	0.576757	+	0.816916i	$0.304318\pi$
$102$	1.73717	−	2.00481i	0.172006	−	0.198505i
$103$	9.52817	+	6.12338i	0.938838	+	0.603355i	0.918065	−	0.396429i	$-0.129751\pi$
$103$	9.52817	+	6.12338i	0.938838	+	0.603355i	0.0207732	+	0.999784i	$0.493387\pi$
$104$	−0.0453887	−	0.0291695i	−0.00445072	−	0.00286031i
$105$	2.29325	−	2.64655i	0.223798	−	0.258277i
$106$	12.3610	+	3.62953i	1.20061	+	0.352531i
$107$	0.685864	+	4.77029i	0.0663050	+	0.461161i	0.995742	+	0.0921810i	$0.0293838\pi$
$107$	0.685864	+	4.77029i	0.0663050	+	0.461161i	−0.929437	+	0.368980i	$0.879707\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	−7.75374	−	16.9783i	−0.742673	−	1.62623i	−0.779107	−	0.626891i	$-0.784327\pi$
$109$	−7.75374	−	16.9783i	−0.742673	−	1.62623i	0.0364336	−	0.999336i	$-0.488400\pi$
$110$	2.69046	−	0.789989i	0.256525	−	0.0753225i
$111$	1.61441	−	3.53506i	0.153233	−	0.335533i
$112$	−0.498371	+	3.46624i	−0.0470916	+	0.327529i
$113$	3.09467	−	1.98882i	0.291122	−	0.187093i	−0.386925	−	0.922111i	$-0.626463\pi$
$113$	3.09467	−	1.98882i	0.291122	−	0.187093i	0.678047	+	0.735018i	$0.262826\pi$
$114$	2.33417			0.218615
$115$	2.51829	−	4.08145i	0.234832	−	0.380597i
$116$	−9.14248			−0.848858
$117$	−0.0453887	+	0.0291695i	−0.00419618	+	0.00269672i
$118$	0.592249	−	4.11919i	0.0545210	−	0.379202i
$119$	3.85904	−	8.45011i	0.353757	−	0.774620i
$120$	0.959493	−	0.281733i	0.0875893	−	0.0257185i
$121$	−1.30331	−	2.85384i	−0.118482	−	0.259440i
$122$	−3.28426	−	3.79023i	−0.297343	−	0.343152i
$123$	−1.53335	−	10.6647i	−0.138258	−	0.961604i
$124$	−7.27296	−	2.13553i	−0.653131	−	0.191777i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	2.94598	+	1.89326i	0.262448	+	0.168665i
$127$	2.94308	+	1.89141i	0.261157	+	0.167835i	0.664667	−	0.747140i	$-0.268574\pi$
$127$	2.94308	+	1.89141i	0.261157	+	0.167835i	−0.403510	+	0.914975i	$0.632210\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	−9.37451	−	2.75261i	−0.825380	−	0.242353i
$130$	0.00767840	+	0.0534044i	0.000673440	+	0.00468388i
$131$	3.32781	+	3.84050i	0.290752	+	0.335546i	0.882268	−	0.470747i	$-0.156016\pi$
$131$	3.32781	+	3.84050i	0.290752	+	0.335546i	−0.591516	+	0.806294i	$0.701470\pi$
$132$	1.16484	+	2.55064i	0.101386	+	0.222005i
$133$	7.84291	−	2.30289i	0.680066	−	0.199685i
$134$	−2.66336	+	5.83195i	−0.230080	+	0.503804i
$135$	0.142315	−	0.989821i	0.0122485	−	0.0851903i
$136$	2.23163	−	1.43418i	0.191360	−	0.122980i
$137$	−9.42533			−0.805260			−0.402630	−	0.915363i	$-0.631904\pi$
$137$	−9.42533			−0.805260			−0.402630	+	0.915363i	$0.631904\pi$
$138$	4.39830	+	1.91180i	0.374408	+	0.162744i
$139$	−1.15277			−0.0977764			−0.0488882	−	0.998804i	$-0.515568\pi$
$139$	−1.15277			−0.0977764			−0.0488882	+	0.998804i	$0.515568\pi$
$140$	2.94598	−	1.89326i	0.248980	−	0.160010i
$141$	−1.83100	+	12.7349i	−0.154198	+	1.07247i
$142$	0.00879278	−	0.0192535i	0.000737873	−	0.00161572i
$143$	−0.145160	+	0.0426228i	−0.0121389	+	0.00356429i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	5.98705	+	6.90943i	0.497198	+	0.573797i
$146$	−1.91875	−	13.3452i	−0.158797	−	1.10445i
$147$	5.05002	+	1.48282i	0.416519	+	0.122301i
$148$	2.54495	−	2.93703i	0.209194	−	0.241423i
$149$	1.38231	+	0.888357i	0.113243	+	0.0727770i	0.596036	−	0.802957i	$-0.296741\pi$
$149$	1.38231	+	0.888357i	0.113243	+	0.0727770i	−0.482793	+	0.875734i	$0.660378\pi$
$150$	−0.841254	−	0.540641i	−0.0686881	−	0.0441431i
$151$	3.84498	−	4.43734i	0.312900	−	0.361106i	−0.577415	−	0.816451i	$-0.695939\pi$
$151$	3.84498	−	4.43734i	0.312900	−	0.361106i	0.890315	+	0.455345i	$0.150484\pi$
$152$	2.23962	+	0.657612i	0.181657	+	0.0533394i
$153$	−0.377524	−	2.62574i	−0.0305210	−	0.212278i
$154$	6.43036	+	7.42103i	0.518173	+	0.598004i
$155$	3.14885	+	6.89501i	0.252921	+	0.553821i
$156$	−0.0517681	+	0.0152005i	−0.00414476	+	0.00121701i
$157$	2.08852	−	4.57322i	0.166682	−	0.364982i	−0.807797	−	0.589460i	$-0.799340\pi$
$157$	2.08852	−	4.57322i	0.166682	−	0.364982i	0.974479	+	0.224478i	$0.0720677\pi$
$158$	0.877523	−	6.10331i	0.0698120	−	0.485553i
$159$	10.8378	−	6.96502i	0.859492	−	0.552362i
$160$	1.00000			0.0790569
$161$	16.6646	+	2.08439i	1.31336	+	0.164273i
$162$	1.00000			0.0785674
$163$	5.38784	−	3.46256i	0.422008	−	0.271208i	−0.312354	−	0.949966i	$-0.601118\pi$
$163$	5.38784	−	3.46256i	0.422008	−	0.271208i	0.734363	+	0.678757i	$0.237481\pi$
$164$	1.53335	−	10.6647i	0.119735	−	0.832773i
$165$	1.16484	−	2.55064i	0.0906827	−	0.198567i
$166$	9.07850	−	2.66569i	0.704628	−	0.206898i
$167$	−9.08758	−	19.8990i	−0.703218	−	1.53983i	−0.836025	−	0.548691i	$-0.815126\pi$
$167$	−9.08758	−	19.8990i	−0.703218	−	1.53983i	0.132807	−	0.991142i	$-0.457601\pi$
$168$	2.29325	+	2.64655i	0.176928	+	0.204186i
$169$	1.84968	+	12.8648i	0.142283	+	0.989600i
$170$	−2.54528	−	0.747363i	−0.195214	−	0.0573201i
$171$	1.52856	−	1.76405i	0.116892	−	0.134900i
$172$	−8.21928	−	5.28221i	−0.626714	−	0.402765i
$173$	3.55741	+	2.28621i	0.270465	+	0.173817i	0.668842	−	0.743405i	$-0.266790\pi$
$173$	3.55741	+	2.28621i	0.270465	+	0.173817i	−0.398378	+	0.917222i	$0.630427\pi$
$174$	−5.98705	+	6.90943i	−0.453877	+	0.523802i
$175$	−3.36004	−	0.986596i	−0.253995	−	0.0745796i
$176$	0.399057	+	2.77550i	0.0300800	+	0.209211i
$177$	−2.72523	−	3.14508i	−0.204841	−	0.236399i
$178$	3.17732	+	6.95736i	0.238150	+	0.521476i
$179$	−8.86308	+	2.60244i	−0.662458	+	0.194515i	−0.595642	−	0.803250i	$-0.703102\pi$
$179$	−8.86308	+	2.60244i	−0.662458	+	0.194515i	−0.0668161	+	0.997765i	$0.521284\pi$
$180$	0.415415	−	0.909632i	0.0309632	−	0.0678000i
$181$	−0.255491	+	1.77698i	−0.0189905	+	0.132082i	−0.997111	−	0.0759568i	$-0.975799\pi$
$181$	−0.255491	+	1.77698i	−0.0189905	+	0.132082i	0.978121	+	0.208039i	$0.0667080\pi$
$182$	−0.158946	+	0.102148i	−0.0117819	+	0.00757174i
$183$	−5.01520			−0.370734
$184$	3.68152	+	3.07351i	0.271405	+	0.226582i
$185$	−3.88625			−0.285723
$186$	−6.37670	+	4.09806i	−0.467562	+	0.300484i
$187$	1.05859	−	7.36267i	0.0774119	−	0.538412i
$188$	−5.34467	+	11.7032i	−0.389800	+	0.853543i
$189$	3.36004	−	0.986596i	0.244407	−	0.0717643i
$190$	−0.969650	−	2.12324i	−0.0703458	−	0.154036i
$191$	−4.58316	−	5.28925i	−0.331626	−	0.382716i	0.565309	−	0.824879i	$-0.308757\pi$
$191$	−4.58316	−	5.28925i	−0.331626	−	0.382716i	−0.896935	+	0.442163i	$0.854211\pi$
$192$	0.142315	+	0.989821i	0.0102707	+	0.0714342i
$193$	7.95558	+	2.33597i	0.572655	+	0.168147i	0.555223	−	0.831701i	$-0.312633\pi$
$193$	7.95558	+	2.33597i	0.572655	+	0.168147i	0.0174318	+	0.999848i	$0.494451\pi$
$194$	−5.54693	+	6.40150i	−0.398246	+	0.459601i
$195$	0.0453887	+	0.0291695i	0.00325035	+	0.00208887i
$196$	4.42770	+	2.84551i	0.316264	+	0.203251i
$197$	−9.82172	+	11.3349i	−0.699768	+	0.807576i	−0.988721	−	0.149768i	$-0.952147\pi$
$197$	−9.82172	+	11.3349i	−0.699768	+	0.807576i	0.288953	+	0.957343i	$0.406693\pi$
$198$	2.69046	+	0.789989i	0.191202	+	0.0561421i
$199$	0.122713	+	0.853487i	0.00869889	+	0.0605021i	0.993709	−	0.111997i	$-0.0357248\pi$
$199$	0.122713	+	0.853487i	0.00869889	+	0.0605021i	−0.985010	+	0.172499i	$0.944816\pi$
$200$	−0.654861	−	0.755750i	−0.0463056	−	0.0534396i
$201$	2.66336	+	5.83195i	0.187859	+	0.411354i
$202$	15.1111	−	4.43703i	1.06322	−	0.312188i
$203$	−13.2999	+	29.1227i	−0.933471	+	2.04402i
$204$	0.377524	−	2.62574i	0.0264320	−	0.183838i
$205$	−9.06397	+	5.82506i	−0.633055	+	0.406840i
$206$	11.3262			0.789131
$207$	4.32512	−	2.07204i	0.300616	−	0.144017i
$208$	−0.0539536			−0.00374101
$209$	5.50610	−	3.53856i	0.380865	−	0.244767i
$210$	0.498371	−	3.46624i	0.0343908	−	0.239194i
$211$	6.24702	−	13.6791i	0.430062	−	0.941705i	−0.563254	−	0.826284i	$-0.690451\pi$
$211$	6.24702	−	13.6791i	0.430062	−	0.941705i	0.993317	−	0.115422i	$-0.0368219\pi$
$212$	12.3610	−	3.62953i	0.848960	−	0.249277i
$213$	−0.00879278	−	0.0192535i	−0.000602471	−	0.00131923i
$214$	3.15600	+	3.64222i	0.215740	+	0.248977i
$215$	1.39046	+	9.67083i	0.0948283	+	0.659545i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	−17.3828	+	20.0609i	−1.18002	+	1.36182i
$218$	−15.7020	−	10.0911i	−1.06348	−	0.683454i
$219$	−11.3421	−	7.28914i	−0.766429	−	0.492554i
$220$	1.83626	−	2.11915i	0.123800	−	0.142873i
$221$	0.137327	+	0.0403229i	0.00923763	+	0.00271241i
$222$	−0.553071	−	3.84670i	−0.0371197	−	0.258173i
$223$	−12.5808	−	14.5190i	−0.842472	−	0.972265i	0.157411	−	0.987533i	$-0.449685\pi$
$223$	−12.5808	−	14.5190i	−0.842472	−	0.972265i	−0.999883	+	0.0152685i	$0.995140\pi$
$224$	1.45474	+	3.18543i	0.0971987	+	0.212835i
$225$	−0.959493	+	0.281733i	−0.0639662	+	0.0187822i
$226$	1.52816	−	3.34621i	0.101652	−	0.222587i
$227$	−2.27244	+	15.8052i	−0.150827	+	1.04903i	0.764010	+	0.645205i	$0.223228\pi$
$227$	−2.27244	+	15.8052i	−0.150827	+	1.04903i	−0.914837	+	0.403823i	$0.867681\pi$
$228$	1.96363	−	1.26195i	0.130045	−	0.0835746i
$229$	−9.19489			−0.607615			−0.303808	−	0.952733i	$-0.598258\pi$
$229$	−9.19489			−0.607615			−0.303808	+	0.952733i	$0.598258\pi$
$230$	−0.0880794	−	4.79502i	−0.00580779	−	0.316174i
$231$	9.81943			0.646071
$232$	−7.69115	+	4.94280i	−0.504949	+	0.324511i
$233$	−3.76532	+	26.1884i	−0.246674	+	1.71566i	0.370502	+	0.928832i	$0.379186\pi$
$233$	−3.76532	+	26.1884i	−0.246674	+	1.71566i	−0.617176	+	0.786825i	$0.711723\pi$
$234$	−0.0224131	+	0.0490779i	−0.00146519	+	0.00320832i
$235$	12.3447	−	3.62473i	0.805280	−	0.236451i
$236$	−1.72877	−	3.78547i	−0.112533	−	0.246413i
$237$	−4.03792	−	4.66000i	−0.262291	−	0.302700i
$238$	−1.32205	−	9.19504i	−0.0856956	−	0.596026i
$239$	12.6857	+	3.72485i	0.820567	+	0.240940i	0.664960	−	0.746879i	$-0.268448\pi$
$239$	12.6857	+	3.72485i	0.820567	+	0.240940i	0.155607	+	0.987819i	$0.450267\pi$
$240$	0.654861	−	0.755750i	0.0422711	−	0.0487834i
$241$	11.5038	+	7.39304i	0.741024	+	0.476227i	0.855893	−	0.517153i	$-0.173008\pi$
$241$	11.5038	+	7.39304i	0.741024	+	0.476227i	−0.114868	+	0.993381i	$0.536645\pi$
$242$	−2.63931	−	1.69618i	−0.169662	−	0.109035i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	−4.81205	−	1.41294i	−0.308060	−	0.0904545i
$245$	−0.749034	−	5.20965i	−0.0478540	−	0.332832i
$246$	−7.05571	−	8.14272i	−0.449856	−	0.519161i
$247$	0.0523161	+	0.114556i	0.00332880	+	0.00728905i
$248$	−7.27296	+	2.13553i	−0.461833	+	0.135606i
$249$	3.93056	−	8.60673i	0.249089	−	0.545429i
$250$	−0.142315	+	0.989821i	−0.00900078	+	0.0626018i
$251$	9.78104	−	6.28589i	0.617374	−	0.396762i	−0.194242	−	0.980954i	$-0.562225\pi$
$251$	9.78104	−	6.28589i	0.617374	−	0.396762i	0.811616	+	0.584192i	$0.198588\pi$
$252$	3.50189			0.220598
$253$	13.2734	−	2.15795i	0.834494	−	0.135669i
$254$	3.49845			0.219512
$255$	−2.23163	+	1.43418i	−0.139750	+	0.0898117i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	0.932963	−	2.04290i	0.0581966	−	0.127433i	−0.878299	−	0.478111i	$-0.841322\pi$
$257$	0.932963	−	2.04290i	0.0581966	−	0.127433i	0.936496	+	0.350678i	$0.114049\pi$
$258$	−9.37451	+	2.75261i	−0.583632	+	0.171370i
$259$	−5.65347	−	12.3794i	−0.351290	−	0.769217i
$260$	0.0353321	+	0.0407754i	0.00219120	+	0.00252878i
$261$	1.30111	+	9.04943i	0.0805368	+	0.560145i
$262$	4.87587	+	1.43168i	0.301232	+	0.0884497i
$263$	−12.9022	+	14.8900i	−0.795586	+	0.918155i	−0.998131	−	0.0611180i	$-0.980533\pi$
$263$	−12.9022	+	14.8900i	−0.795586	+	0.918155i	0.202545	+	0.979273i	$0.435079\pi$
$264$	2.35891	+	1.51598i	0.145181	+	0.0933020i
$265$	−10.8378	−	6.96502i	−0.665759	−	0.427858i
$266$	5.35284	−	6.17751i	0.328204	−	0.378767i
$267$	7.33872	+	2.15484i	0.449122	+	0.131874i
$268$	0.912428	+	6.34608i	0.0557354	+	0.387648i
$269$	−9.39592	−	10.8435i	−0.572879	−	0.661138i	0.393179	−	0.919462i	$-0.371375\pi$
$269$	−9.39592	−	10.8435i	−0.572879	−	0.661138i	−0.966058	+	0.258324i	$0.916830\pi$
$270$	−0.415415	−	0.909632i	−0.0252814	−	0.0553584i
$271$	18.9373	−	5.56048i	1.15036	−	0.337775i	0.349678	−	0.936870i	$-0.386291\pi$
$271$	18.9373	−	5.56048i	1.15036	−	0.337775i	0.800678	+	0.599095i	$0.204473\pi$
$272$	1.10199	−	2.41302i	0.0668178	−	0.146311i
$273$	−0.0268889	+	0.187016i	−0.00162739	+	0.0113187i
$274$	−7.92909	+	5.09572i	−0.479014	+	0.307844i
$275$	−2.80404			−0.169090
$276$	4.73368	−	0.769586i	0.284934	−	0.0463236i
$277$	−15.8720			−0.953658			−0.476829	−	0.878996i	$-0.658214\pi$
$277$	−15.8720			−0.953658			−0.476829	+	0.878996i	$0.658214\pi$
$278$	−0.969769	+	0.623233i	−0.0581629	+	0.0373790i
$279$	−1.07875	+	7.50285i	−0.0645829	+	0.449184i
$280$	1.45474	−	3.18543i	0.0869372	−	0.190366i
$281$	−16.6904	+	4.90075i	−0.995667	+	0.292354i	−0.738677	−	0.674060i	$-0.764549\pi$
$281$	−16.6904	+	4.90075i	−0.995667	+	0.292354i	−0.256990	+	0.966414i	$0.582731\pi$
$282$	5.34467	+	11.7032i	0.318271	+	0.696915i
$283$	0.662448	+	0.764506i	0.0393784	+	0.0454451i	0.775097	−	0.631842i	$-0.217701\pi$
$283$	0.662448	+	0.764506i	0.0393784	+	0.0454451i	−0.735719	+	0.677287i	$0.763155\pi$
$284$	−0.00301227	−	0.0209508i	−0.000178745	−	0.00124320i
$285$	−2.23962	−	0.657612i	−0.132664	−	0.0389536i
$286$	−0.0990726	+	0.114336i	−0.00585829	+	0.00676082i
$287$	−31.7410	−	20.3987i	−1.87361	−	1.20410i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	6.52436	−	7.52952i	0.383786	−	0.442913i
$290$	8.77215	+	2.57574i	0.515118	+	0.151252i
$291$	1.20546	+	8.38418i	0.0706655	+	0.491489i
$292$	−8.82910	−	10.1893i	−0.516684	−	0.596285i
$293$	−1.07886	−	2.36238i	−0.0630277	−	0.138011i	0.875497	−	0.483224i	$-0.160534\pi$
$293$	−1.07886	−	2.36238i	−0.0630277	−	0.138011i	−0.938525	+	0.345212i	$0.887807\pi$
$294$	5.05002	−	1.48282i	0.294523	−	0.0864798i
$295$	−1.72877	+	3.78547i	−0.100653	+	0.220399i
$296$	0.553071	−	3.84670i	0.0321466	−	0.223585i
$297$	2.35891	−	1.51598i	0.136878	−	0.0879660i
$298$	1.64315			0.0951854
$299$	0.00475220	+	0.258709i	0.000274827	+	0.0149615i
$300$	−1.00000			−0.0577350
$301$	−28.7830	+	18.4977i	−1.65902	+	1.06619i
$302$	0.835593	−	5.81168i	0.0480830	−	0.334425i
$303$	6.54240	−	14.3259i	0.375851	−	0.822999i
$304$	2.23962	−	0.657612i	0.128451	−	0.0377167i
$305$	2.08339	+	4.56198i	0.119294	+	0.261218i
$306$	−1.73717	−	2.00481i	−0.0993076	−	0.114607i
$307$	−3.06290	−	21.3029i	−0.174809	−	1.21582i	−0.868551	−	0.495600i	$-0.834948\pi$
$307$	−3.06290	−	21.3029i	−0.174809	−	1.21582i	0.693742	−	0.720224i	$-0.255961\pi$
$308$	9.42168	+	2.76645i	0.536850	+	0.157633i
$309$	7.41706	−	8.55974i	0.421942	−	0.486946i
$310$	6.37670	+	4.09806i	0.362172	+	0.232754i
$311$	−13.2187	−	8.49514i	−0.749563	−	0.481715i	0.109243	−	0.994015i	$-0.465157\pi$
$311$	−13.2187	−	8.49514i	−0.749563	−	0.481715i	−0.858807	+	0.512300i	$0.828794\pi$
$312$	−0.0353321	+	0.0407754i	−0.00200029	+	0.00230845i
$313$	−19.0182	−	5.58426i	−1.07497	−	0.315641i	−0.304108	−	0.952638i	$-0.598358\pi$
$313$	−19.0182	−	5.58426i	−1.07497	−	0.315641i	−0.770867	+	0.636996i	$0.780177\pi$
$314$	−0.715494	−	4.97637i	−0.0403777	−	0.280833i
$315$	−2.29325	−	2.64655i	−0.129210	−	0.149116i
$316$	−2.56148	−	5.60885i	−0.144094	−	0.315523i
$317$	31.0182	−	9.10777i	1.74216	−	0.511543i	0.752951	−	0.658076i	$-0.228630\pi$
$317$	31.0182	−	9.10777i	1.74216	−	0.511543i	0.989206	+	0.146533i	$0.0468114\pi$
$318$	5.35175	−	11.7187i	0.300111	−	0.657152i
$319$	−3.64837	+	25.3750i	−0.204269	+	1.42072i
$320$	0.841254	−	0.540641i	0.0470275	−	0.0302227i
$321$	4.81934			0.268989
$322$	15.1461	−	7.25607i	0.844058	−	0.404365i
$323$	−6.19195			−0.344529
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	0.00767840	−	0.0534044i	0.000425921	−	0.00296234i
$326$	2.66054	−	5.82577i	0.147354	−	0.322660i
$327$	−17.9090	+	5.25855i	−0.990368	+	0.290798i
$328$	−4.47583	−	9.80071i	−0.247137	−	0.541154i
$329$	29.5046	+	34.0501i	1.62664	+	1.87725i
$330$	−0.399057	−	2.77550i	−0.0219673	−	0.152786i
$331$	27.5677	+	8.09460i	1.51526	+	0.444920i	0.930501	−	0.366290i	$-0.119372\pi$
$331$	27.5677	+	8.09460i	1.51526	+	0.444920i	0.584756	+	0.811209i	$0.301190\pi$
$332$	6.19614	−	7.15073i	0.340057	−	0.392447i
$333$	−3.26932	−	2.10107i	−0.179158	−	0.115138i
$334$	−18.4032	−	11.8270i	−1.00698	−	0.647145i
$335$	4.19853	−	4.84536i	0.229390	−	0.264730i
$336$	3.36004	+	0.986596i	0.183305	+	0.0538232i
$337$	4.16236	+	28.9498i	0.226738	+	1.57700i	0.711713	+	0.702470i	$0.247920\pi$
$337$	4.16236	+	28.9498i	0.226738	+	1.57700i	−0.484975	+	0.874528i	$0.661171\pi$
$338$	8.51128	+	9.82254i	0.462953	+	0.534276i
$339$	−1.52816	−	3.34621i	−0.0829984	−	0.181741i
$340$	−2.54528	+	0.747363i	−0.138037	+	0.0405314i
$341$	−8.82949	+	19.3339i	−0.478144	+	1.04699i
$342$	0.332187	−	2.31041i	0.0179626	−	0.124933i
$343$	−5.11651	+	3.28818i	−0.276266	+	0.177545i
$344$	−9.77028			−0.526778
$345$	−3.68152	−	3.07351i	−0.198206	−	0.165472i
$346$	4.22870			0.227336
$347$	−7.10740	+	4.56765i	−0.381545	+	0.245204i	−0.717329	−	0.696735i	$-0.754635\pi$
$347$	−7.10740	+	4.56765i	−0.381545	+	0.245204i	0.335783	+	0.941939i	$0.390999\pi$
$348$	−1.30111	+	9.04943i	−0.0697469	+	0.485100i
$349$	−8.66099	+	18.9649i	−0.463612	+	1.01517i	0.523037	+	0.852310i	$0.324799\pi$
$349$	−8.66099	+	18.9649i	−0.463612	+	1.01517i	−0.986649	+	0.162859i	$0.947928\pi$
$350$	−3.36004	+	0.986596i	−0.179602	+	0.0527358i
$351$	0.0224131	+	0.0490779i	0.00119632	+	0.00261959i
$352$	1.83626	+	2.11915i	0.0978728	+	0.112951i
$353$	−4.87061	−	33.8759i	−0.259237	−	1.80303i	−0.538295	−	0.842756i	$-0.680932\pi$
$353$	−4.87061	−	33.8759i	−0.259237	−	1.80303i	0.279059	−	0.960274i	$-0.409978\pi$
$354$	−3.99297	−	1.17244i	−0.212224	−	0.0623146i
$355$	−0.0138609	+	0.0159964i	−0.000735663	+	0.000849000i
$356$	6.43436	+	4.13511i	0.341020	+	0.219161i
$357$	−7.81490	−	5.02233i	−0.413608	−	0.265810i
$358$	−6.04912	+	6.98105i	−0.319706	+	0.368960i
$359$	−22.3415	−	6.56005i	−1.17914	−	0.346226i	−0.367297	−	0.930104i	$-0.619717\pi$
$359$	−22.3415	−	6.56005i	−1.17914	−	0.346226i	−0.811842	+	0.583877i	$0.801535\pi$
$360$	−0.142315	−	0.989821i	−0.00750065	−	0.0521682i
$361$	8.87444	+	10.2416i	0.467076	+	0.539034i
$362$	0.745775	+	1.63302i	0.0391970	+	0.0858296i
$363$	−3.01027	+	0.883896i	−0.157998	+	0.0463925i
$364$	−0.0784883	+	0.171865i	−0.00411390	+	0.00900819i
$365$	−1.91875	+	13.3452i	−0.100432	+	0.698518i
$366$	−4.21905	+	2.71142i	−0.220533	+	0.141728i
$367$	−1.38970			−0.0725419			−0.0362709	−	0.999342i	$-0.511548\pi$
$367$	−1.38970			−0.0725419			−0.0362709	+	0.999342i	$0.511548\pi$
$368$	4.75875	+	0.595220i	0.248067	+	0.0310280i
$369$	−10.7744			−0.560891
$370$	−3.26932	+	2.10107i	−0.169964	+	0.109229i
$371$	6.42046	−	44.6552i	0.333333	−	2.31838i
$372$	−3.14885	+	6.89501i	−0.163260	+	0.357490i
$373$	−34.3894	+	10.0976i	−1.78061	+	0.522835i	−0.995350	−	0.0963267i	$-0.969291\pi$
$373$	−34.3894	+	10.0976i	−1.78061	+	0.522835i	−0.785263	+	0.619162i	$0.787472\pi$
$374$	−3.09002	−	6.76619i	−0.159781	−	0.349871i
$375$	0.654861	+	0.755750i	0.0338169	+	0.0390267i
$376$	1.83100	+	12.7349i	0.0944268	+	0.656753i
$377$	−0.473289	−	0.138970i	−0.0243756	−	0.00715733i
$378$	2.29325	−	2.64655i	0.117952	−	0.136124i
$379$	17.9679	+	11.5473i	0.922949	+	0.593143i	0.913512	−	0.406812i	$-0.133360\pi$
$379$	17.9679	+	11.5473i	0.922949	+	0.593143i	0.00943690	+	0.999955i	$0.496996\pi$
$380$	−1.96363	−	1.26195i	−0.100732	−	0.0647366i
$381$	2.29100	−	2.64395i	0.117371	−	0.135454i
$382$	−6.71518	−	1.97175i	−0.343578	−	0.100884i
$383$	−3.37738	−	23.4902i	−0.172576	−	1.20029i	−0.873416	−	0.486975i	$-0.838100\pi$
$383$	−3.37738	−	23.4902i	−0.172576	−	1.20029i	0.700839	−	0.713319i	$-0.252809\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	−4.07914	−	8.93207i	−0.207892	−	0.455221i
$386$	7.95558	−	2.33597i	0.404928	−	0.118898i
$387$	−4.05872	+	8.88736i	−0.206316	+	0.451770i
$388$	−1.20546	+	8.38418i	−0.0611981	+	0.425642i
$389$	−1.22839	+	0.789436i	−0.0622817	+	0.0400260i	−0.571411	−	0.820664i	$-0.693604\pi$
$389$	−1.22839	+	0.789436i	−0.0622817	+	0.0400260i	0.509129	+	0.860690i	$0.329967\pi$
$390$	0.0539536			0.00273205
$391$	−11.6675	−	5.07152i	−0.590052	−	0.256478i
$392$	5.26322			0.265833
$393$	4.27501	−	2.74738i	0.215646	−	0.138587i
$394$	−2.13446	+	14.8455i	−0.107533	+	0.747906i
$395$	−2.56148	+	5.60885i	−0.128882	+	0.282212i
$396$	2.69046	−	0.789989i	0.135201	−	0.0396985i
$397$	8.29522	+	18.1640i	0.416325	+	0.911625i	0.995351	+	0.0963159i	$0.0307059\pi$
$397$	8.29522	+	18.1640i	0.416325	+	0.911625i	−0.579025	+	0.815309i	$0.696567\pi$
$398$	0.564663	+	0.651656i	0.0283040	+	0.0326645i
$399$	−1.16328	−	8.09081i	−0.0582370	−	0.405047i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−16.2712	+	18.7779i	−0.812543	+	0.937725i	−0.998999	−	0.0447386i	$-0.985755\pi$
$401$	−16.2712	+	18.7779i	−0.812543	+	0.937725i	0.186456	+	0.982463i	$0.440300\pi$
$402$	5.39356	+	3.46623i	0.269006	+	0.172880i
$403$	−0.344046	−	0.221105i	−0.0171382	−	0.0110140i
$404$	10.3135	−	11.9024i	0.513113	−	0.592164i
$405$	−0.959493	−	0.281733i	−0.0476776	−	0.0139994i
$406$	4.55635	+	31.6901i	0.226128	+	1.57275i
$407$	−7.13615	−	8.23556i	−0.353726	−	0.408222i
$408$	−1.10199	−	2.41302i	−0.0545565	−	0.119462i
$409$	−11.3965	+	3.34630i	−0.563519	+	0.165464i	−0.551071	−	0.834458i	$-0.685781\pi$
$409$	−11.3965	+	3.34630i	−0.563519	+	0.165464i	−0.0124480	+	0.999923i	$0.503962\pi$
$410$	−4.47583	+	9.80071i	−0.221046	+	0.484023i
$411$	−1.34136	+	9.32939i	−0.0661646	+	0.460185i
$412$	9.52817	−	6.12338i	0.469419	−	0.301677i
$413$	−14.5733			−0.717103
$414$	2.51829	−	4.08145i	0.123767	−	0.200592i
$415$	−9.46177			−0.464460
$416$	−0.0453887	+	0.0291695i	−0.00222536	+	0.00143015i
$417$	−0.164056	+	1.14103i	−0.00803385	+	0.0558767i
$418$	2.71894	−	5.95365i	0.132988	−	0.291202i
$419$	25.8326	−	7.58512i	1.26200	−	0.370557i	0.418763	−	0.908095i	$-0.362464\pi$
$419$	25.8326	−	7.58512i	1.26200	−	0.370557i	0.843240	+	0.537538i	$0.180646\pi$
$420$	−1.45474	−	3.18543i	−0.0709839	−	0.155433i
$421$	−1.71090	−	1.97449i	−0.0833843	−	0.0962306i	0.712524	−	0.701648i	$-0.247552\pi$
$421$	−1.71090	−	1.97449i	−0.0833843	−	0.0962306i	−0.795909	+	0.605417i	$0.793006\pi$
$422$	−2.14013	−	14.8850i	−0.104180	−	0.724588i
$423$	12.3447	+	3.62473i	0.600220	+	0.176240i
$424$	8.43650	−	9.73624i	0.409713	−	0.472834i
$425$	2.23163	+	1.43418i	0.108250	+	0.0695679i
$426$	−0.0178062	−	0.0114433i	−0.000862712	−	0.000554432i
$427$	−11.5011	+	13.2730i	−0.556577	+	0.642324i
$428$	4.62412	+	1.35777i	0.223515	+	0.0656301i
$429$	0.0215305	+	0.149748i	0.00103950	+	0.00722991i
$430$	6.39817	+	7.38388i	0.308547	+	0.356082i
$431$	−10.3334	−	22.6270i	−0.497742	−	1.08990i	−0.977197	−	0.212336i	$-0.931893\pi$
$431$	−10.3334	−	22.6270i	−0.497742	−	1.08990i	0.479455	−	0.877567i	$-0.340834\pi$
$432$	0.959493	−	0.281733i	0.0461636	−	0.0135549i
$433$	16.2530	−	35.5890i	0.781068	−	1.71030i	0.0804553	−	0.996758i	$-0.474363\pi$
$433$	16.2530	−	35.5890i	0.781068	−	1.71030i	0.700613	−	0.713542i	$-0.252910\pi$
$434$	−3.77765	+	26.2741i	−0.181333	+	1.26120i
$435$	7.69115	−	4.94280i	0.368762	−	0.236989i
$436$	−18.6650			−0.893893
$437$	−3.35053	−	10.6811i	−0.160278	−	0.510947i
$438$	−13.4824			−0.644214
$439$	−15.9906	+	10.2766i	−0.763192	+	0.490474i	−0.863417	−	0.504491i	$-0.831680\pi$
$439$	−15.9906	+	10.2766i	−0.763192	+	0.490474i	0.100225	+	0.994965i	$0.468044\pi$
$440$	0.399057	−	2.77550i	0.0190243	−	0.132317i
$441$	2.18642	−	4.78759i	0.104115	−	0.227981i
$442$	0.137327	−	0.0403229i	0.00653199	−	0.00191796i
$443$	−0.111292	−	0.243696i	−0.00528765	−	0.0115783i	0.906970	−	0.421196i	$-0.138389\pi$
$443$	−0.111292	−	0.243696i	−0.00528765	−	0.0115783i	−0.912257	+	0.409617i	$0.865662\pi$
$444$	−2.54495	−	2.93703i	−0.120778	−	0.139385i
$445$	−1.08850	−	7.57069i	−0.0515999	−	0.358885i
$446$	−18.4332	−	5.41248i	−0.872837	−	0.256288i
$447$	1.07604	−	1.24181i	0.0508948	−	0.0587358i
$448$	2.94598	+	1.89326i	0.139184	+	0.0894483i
$449$	−0.949082	−	0.609938i	−0.0447899	−	0.0287847i	0.518054	−	0.855348i	$-0.326657\pi$
$449$	−0.949082	−	0.609938i	−0.0447899	−	0.0287847i	−0.562844	+	0.826563i	$0.690293\pi$
$450$	−0.654861	+	0.755750i	−0.0308704	+	0.0356264i
$451$	−28.9880	−	8.51164i	−1.36499	−	0.400797i
$452$	−0.523525	−	3.64120i	−0.0246246	−	0.171268i
$453$	−3.84498	−	4.43734i	−0.180653	−	0.208484i
$454$	6.63323	+	14.5248i	0.311313	+	0.681681i
$455$	0.181286	−	0.0532304i	0.00849882	−	0.00249548i
$456$	0.969650	−	2.12324i	0.0454080	−	0.0994297i
$457$	−0.186119	+	1.29449i	−0.00870628	+	0.0605535i	−0.993711	−	0.111971i	$-0.964283\pi$
$457$	−0.186119	+	1.29449i	−0.00870628	+	0.0605535i	0.985005	+	0.172525i	$0.0551926\pi$
$458$	−7.73523	+	4.97113i	−0.361444	+	0.232286i
$459$	−2.65274			−0.123819
$460$	−2.66648	−	3.98621i	−0.124325	−	0.185858i
$461$	19.3398			0.900743			0.450371	−	0.892841i	$-0.351292\pi$
$461$	19.3398			0.900743			0.450371	+	0.892841i	$0.351292\pi$
$462$	8.26063	−	5.30879i	0.384319	−	0.246987i
$463$	−2.23151	+	15.5205i	−0.103707	+	0.721297i	0.869927	+	0.493181i	$0.164166\pi$
$463$	−2.23151	+	15.5205i	−0.103707	+	0.721297i	−0.973634	+	0.228117i	$0.926743\pi$
$464$	−3.79793	+	8.31630i	−0.176314	+	0.386074i
$465$	7.27296	−	2.13553i	0.337275	−	0.0990330i
$466$	10.9909	+	24.0667i	0.509144	+	1.11487i
$467$	19.8013	+	22.8519i	0.916293	+	1.05746i	0.998149	+	0.0608139i	$0.0193696\pi$
$467$	19.8013	+	22.8519i	0.916293	+	1.05746i	−0.0818565	+	0.996644i	$0.526085\pi$
$468$	0.00767840	+	0.0534044i	0.000354934	+	0.00246862i
$469$	21.5423	+	6.32539i	0.994732	+	0.292080i
$470$	8.42535	−	9.72337i	0.388632	−	0.448506i
$471$	−4.22944	−	2.71810i	−0.194882	−	0.125243i
$472$	−3.50091	−	2.24990i	−0.161143	−	0.103560i
$473$	−17.9407	+	20.7047i	−0.824916	+	0.952003i
$474$	−5.91630	−	1.73718i	−0.271745	−	0.0797914i
$475$	0.332187	+	2.31041i	0.0152418	+	0.106009i
$476$	−6.08339	−	7.02060i	−0.278832	−	0.321789i
$477$	−5.35175	−	11.7187i	−0.245040	−	0.536562i
$478$	12.6857	−	3.72485i	0.580229	−	0.170371i
$479$	13.5805	−	29.7372i	0.620510	−	1.35873i	−0.294638	−	0.955609i	$-0.595199\pi$
$479$	13.5805	−	29.7372i	0.620510	−	1.35873i	0.915148	−	0.403118i	$-0.132074\pi$
$480$	0.142315	−	0.989821i	0.00649575	−	0.0451790i
$481$	0.176392	−	0.113360i	0.00804277	−	0.00516878i
$482$	13.6746			0.622860
$483$	4.43480	−	16.1984i	0.201790	−	0.737051i
$484$	−3.13736			−0.142607
$485$	7.12575	−	4.57944i	0.323564	−	0.207942i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	−6.73349	+	14.7443i	−0.305124	+	0.668128i	−0.998630	−	0.0523226i	$-0.983338\pi$
$487$	−6.73349	+	14.7443i	−0.305124	+	0.668128i	0.693507	+	0.720450i	$0.256065\pi$
$488$	−4.81205	+	1.41294i	−0.217831	+	0.0639610i
$489$	−2.66054	−	5.82577i	−0.120314	−	0.263451i
$490$	−3.44668	−	3.97768i	−0.155705	−	0.179693i
$491$	0.0250799	+	0.174435i	0.00113184	+	0.00787213i	0.990380	−	0.138378i	$-0.0441888\pi$
$491$	0.0250799	+	0.174435i	0.00113184	+	0.00787213i	−0.989248	+	0.146250i	$0.953280\pi$
$492$	−10.3379	−	3.03549i	−0.466070	−	0.136850i
$493$	15.8821	−	18.3289i	0.715293	−	0.825492i
$494$	0.105945	+	0.0680867i	0.00476669	+	0.00306337i
$495$	−2.35891	−	1.51598i	−0.106025	−	0.0681382i
$496$	−4.96384	+	5.72858i	−0.222883	+	0.257221i
$497$	−0.0711194	−	0.0208825i	−0.00319014	−	0.000936710i
$498$	−1.34655	−	9.36546i	−0.0603403	−	0.419676i
$499$	11.4620	+	13.2278i	0.513108	+	0.592159i	0.951892	−	0.306434i	$-0.0991359\pi$
$499$	11.4620	+	13.2278i	0.513108	+	0.592159i	−0.438783	+	0.898593i	$0.644590\pi$
$500$	0.415415	+	0.909632i	0.0185779	+	0.0406800i
$501$	−20.9898	+	6.16316i	−0.937754	+	0.275350i
$502$	4.82993	−	10.5761i	0.215570	−	0.472033i
$503$	−1.44475	+	10.0484i	−0.0644180	+	0.448037i	0.931929	+	0.362641i	$0.118125\pi$
$503$	−1.44475	+	10.0484i	−0.0644180	+	0.448037i	−0.996347	+	0.0853966i	$0.972784\pi$
$504$	2.94598	−	1.89326i	0.131224	−	0.0843327i
$505$	−15.7491			−0.700825
$506$	9.99965	−	8.99154i	0.444538	−	0.399723i
$507$	12.9971			0.577221
$508$	2.94308	−	1.89141i	0.130578	−	0.0839176i
$509$	4.39873	−	30.5938i	0.194970	−	1.35605i	−0.623646	−	0.781707i	$-0.714349\pi$
$509$	4.39873	−	30.5938i	0.194970	−	1.35605i	0.818616	−	0.574341i	$-0.194742\pi$
$510$	−1.10199	+	2.41302i	−0.0487968	+	0.106850i
$511$	−45.3014	+	13.3017i	−2.00401	+	0.588432i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	−1.52856	−	1.76405i	−0.0674875	−	0.0778847i
$514$	−0.319619	−	2.22300i	−0.0140978	−	0.0980522i
$515$	−10.8674	−	3.19095i	−0.478873	−	0.140610i
$516$	−6.39817	+	7.38388i	−0.281664	+	0.325057i
$517$	30.3494	+	19.5044i	1.33476	+	0.857801i
$518$	−11.4488	−	7.35770i	−0.503032	−	0.323279i
$519$	2.76921	−	3.19584i	0.121555	−	0.140282i
$520$	0.0517681	+	0.0152005i	0.00227018	+	0.000666585i
$521$	−3.60336	−	25.0619i	−0.157866	−	1.09798i	−0.902556	−	0.430572i	$-0.858312\pi$
$521$	−3.60336	−	25.0619i	−0.157866	−	1.09798i	0.744690	−	0.667410i	$-0.232597\pi$
$522$	5.98705	+	6.90943i	0.262046	+	0.302417i
$523$	2.95032	+	6.46030i	0.129009	+	0.282489i	0.963103	−	0.269132i	$-0.0867367\pi$
$523$	2.95032	+	6.46030i	0.129009	+	0.282489i	−0.834095	+	0.551621i	$0.814009\pi$
$524$	4.87587	−	1.43168i	0.213003	−	0.0625434i
$525$	−1.45474	+	3.18543i	−0.0634899	+	0.139024i
$526$	−2.80392	+	19.5017i	−0.122257	+	0.850315i
$527$	16.9157	−	10.8711i	0.736860	−	0.473551i
$528$	2.80404			0.122030
$529$	2.43495	−	22.8707i	0.105867	−	0.994380i
$530$	−12.8829			−0.559597
$531$	−3.50091	+	2.24990i	−0.151927	+	0.0976374i
$532$	1.16328	−	8.09081i	0.0504347	−	0.350781i
$533$	0.241487	−	0.528783i	0.0104600	−	0.0229042i
$534$	7.33872	−	2.15484i	0.317577	−	0.0932492i
$535$	−2.00203	−	4.38383i	−0.0865552	−	0.189529i
$536$	4.19853	+	4.84536i	0.181349	+	0.209288i
$537$	1.31460	+	9.14324i	0.0567291	+	0.394560i
$538$	−13.7668	−	4.04229i	−0.593528	−	0.174275i
$539$	9.66462	−	11.1536i	0.416284	−	0.480418i
$540$	−0.841254	−	0.540641i	−0.0362018	−	0.0232655i
$541$	13.8020	+	8.86998i	0.593392	+	0.381350i	0.802597	−	0.596522i	$-0.203451\pi$
$541$	13.8020	+	8.86998i	0.593392	+	0.381350i	−0.209205	+	0.977872i	$0.567087\pi$
$542$	12.9248	−	14.9160i	0.555168	−	0.640698i
$543$	1.72253	+	0.505781i	0.0739209	+	0.0217051i
$544$	−0.377524	−	2.62574i	−0.0161862	−	0.112578i
$545$	12.2230	+	14.1061i	0.523576	+	0.604239i
$546$	0.0784883	+	0.171865i	0.00335899	+	0.00735516i
$547$	−6.48398	+	1.90387i	−0.277235	+	0.0814035i	−0.417394	−	0.908725i	$-0.637057\pi$
$547$	−6.48398	+	1.90387i	−0.277235	+	0.0814035i	0.140159	+	0.990129i	$0.455238\pi$
$548$	−3.91542	+	8.57358i	−0.167259	+	0.366245i
$549$	−0.713737	+	4.96415i	−0.0304615	+	0.211865i
$550$	−2.35891	+	1.51598i	−0.100584	+	0.0646415i
$551$	21.3401			0.909120
$552$	3.56616	−	3.20664i	0.151786	−	0.136484i
$553$	−21.5929			−0.918223
$554$	−13.3524	+	8.58107i	−0.567289	+	0.364575i
$555$	−0.553071	+	3.84670i	−0.0234766	+	0.163283i
$556$	−0.478877	+	1.04859i	−0.0203089	+	0.0444703i
$557$	19.9983	−	5.87203i	0.847355	−	0.248806i	0.170898	−	0.985289i	$-0.445333\pi$
$557$	19.9983	−	5.87203i	0.847355	−	0.248806i	0.676456	+	0.736483i	$0.263515\pi$
$558$	3.14885	+	6.89501i	0.133301	+	0.291889i
$559$	−0.345204	−	0.398387i	−0.0146006	−	0.0168500i
$560$	−0.498371	−	3.46624i	−0.0210600	−	0.146476i
$561$	−7.13708	−	2.09563i	−0.301328	−	0.0884778i
$562$	−11.3913	+	13.1463i	−0.480514	+	0.554543i
$563$	22.8101	+	14.6591i	0.961330	+	0.617809i	0.924366	−	0.381508i	$-0.124595\pi$
$563$	22.8101	+	14.6591i	0.961330	+	0.617809i	0.0369638	+	0.999317i	$0.488231\pi$
$564$	10.8235	+	6.95581i	0.455749	+	0.292892i
$565$	−2.40900	+	2.78013i	−0.101347	+	0.116961i
$566$	0.970610	+	0.284997i	0.0407978	+	0.0119793i
$567$	−0.498371	−	3.46624i	−0.0209296	−	0.145569i
$568$	−0.0138609	−	0.0159964i	−0.000581592	−	0.000671193i
$569$	12.2813	+	26.8922i	0.514858	+	1.12738i	0.971350	+	0.237654i	$0.0763783\pi$
$569$	12.2813	+	26.8922i	0.514858	+	1.12738i	−0.456492	+	0.889727i	$0.650894\pi$
$570$	−2.23962	+	0.657612i	−0.0938075	+	0.0275444i
$571$	−3.43877	+	7.52985i	−0.143908	+	0.315114i	−0.967837	−	0.251579i	$-0.919050\pi$
$571$	−3.43877	+	7.52985i	−0.143908	+	0.315114i	0.823929	+	0.566693i	$0.191778\pi$
$572$	−0.0215305	+	0.149748i	−0.000900237	+	0.00626128i
$573$	−5.88766	+	3.78377i	−0.245961	+	0.158069i
$574$	−37.7306			−1.57485
$575$	−1.26640	+	4.62561i	−0.0528126	+	0.192901i
$576$	1.00000			0.0416667
$577$	−23.9951	+	15.4207i	−0.998928	+	0.641972i	−0.934505	−	0.355951i	$-0.884157\pi$
$577$	−23.9951	+	15.4207i	−0.998928	+	0.641972i	−0.0644230	+	0.997923i	$0.520521\pi$
$578$	1.41788	−	9.86157i	0.0589760	−	0.410187i
$579$	3.44439	−	7.54216i	0.143144	−	0.313441i
$580$	8.77215	−	2.57574i	0.364244	−	0.106952i
$581$	−13.7644	−	30.1398i	−0.571043	−	1.25041i
$582$	5.54693	+	6.40150i	0.229928	+	0.265351i
$583$	−5.14100	−	35.7565i	−0.212919	−	1.48088i
$584$	−12.9363	−	3.79843i	−0.535307	−	0.157180i
$585$	0.0353321	−	0.0407754i	0.00146080	−	0.00168586i
$586$	−2.18479	−	1.40408i	−0.0902529	−	0.0580020i
$587$	7.59641	+	4.88191i	0.313537	+	0.201498i	0.687939	−	0.725768i	$-0.258516\pi$
$587$	7.59641	+	4.88191i	0.313537	+	0.201498i	−0.374402	+	0.927267i	$0.622152\pi$
$588$	3.44668	−	3.97768i	0.142138	−	0.164037i
$589$	16.9763	+	4.98470i	0.699498	+	0.205391i
$590$	0.592249	+	4.11919i	0.0243825	+	0.169584i
$591$	9.82172	+	11.3349i	0.404011	+	0.466254i
$592$	−1.61441	−	3.53506i	−0.0663517	−	0.145290i
$593$	19.0535	−	5.59462i	0.782435	−	0.229744i	0.133967	−	0.990986i	$-0.457228\pi$
$593$	19.0535	−	5.59462i	0.782435	−	0.229744i	0.648468	+	0.761242i	$0.275410\pi$
$594$	1.16484	−	2.55064i	0.0477940	−	0.104654i
$595$	−1.32205	+	9.19504i	−0.0541986	+	0.376960i
$596$	1.38231	−	0.888357i	0.0566216	−	0.0363885i
$597$	0.862264			0.0352901
$598$	0.143866	+	0.215070i	0.00588313	+	0.00879488i
$599$	−32.8806			−1.34346			−0.671732	−	0.740794i	$-0.734449\pi$
$599$	−32.8806			−1.34346			−0.671732	+	0.740794i	$0.734449\pi$
$600$	−0.841254	+	0.540641i	−0.0343440	+	0.0220716i
$601$	−0.722995	+	5.02854i	−0.0294916	+	0.205119i	−0.999240	−	0.0389896i	$-0.987586\pi$
$601$	−0.722995	+	5.02854i	−0.0294916	+	0.205119i	0.969748	+	0.244108i	$0.0784952\pi$
$602$	−14.2132	+	31.1225i	−0.579286	+	1.26846i
$603$	6.15163	−	1.80628i	0.250514	−	0.0735575i
$604$	−2.43908	−	5.34085i	−0.0992450	−	0.217316i
$605$	2.05453	+	2.37106i	0.0835287	+	0.0963972i
$606$	−2.24133	−	15.5888i	−0.0910477	−	0.633251i
$607$	29.3081	+	8.60562i	1.18958	+	0.349292i	0.815859	−	0.578251i	$-0.196264\pi$
$607$	29.3081	+	8.60562i	1.18958	+	0.349292i	0.373719	+	0.927542i	$0.378083\pi$
$608$	1.52856	−	1.76405i	0.0619912	−	0.0715417i
$609$	26.9335	+	17.3091i	1.09140	+	0.701401i
$610$	4.21905	+	2.71142i	0.170824	+	0.109782i
$611$	−0.454578	+	0.524611i	−0.0183902	+	0.0212235i
$612$	−2.54528	−	0.747363i	−0.102887	−	0.0302103i
$613$	−4.07850	−	28.3666i	−0.164729	−	1.14572i	−0.889570	−	0.456799i	$-0.848996\pi$
$613$	−4.07850	−	28.3666i	−0.164729	−	1.14572i	0.724841	−	0.688917i	$-0.241913\pi$
$614$	−14.0939	−	16.2653i	−0.568784	−	0.656412i
$615$	4.47583	+	9.80071i	0.180483	+	0.395203i
$616$	9.42168	−	2.76645i	0.379610	−	0.111464i
$617$	−5.63360	+	12.3359i	−0.226800	+	0.496623i	−0.988484	−	0.151326i	$-0.951646\pi$
$617$	−5.63360	+	12.3359i	−0.226800	+	0.496623i	0.761684	+	0.647949i	$0.224373\pi$
$618$	1.61188	−	11.2109i	0.0648393	−	0.450967i
$619$	20.5699	−	13.2195i	0.826773	−	0.531335i	−0.0574777	−	0.998347i	$-0.518306\pi$
$619$	20.5699	−	13.2195i	0.826773	−	0.531335i	0.884251	+	0.467012i	$0.154669\pi$
$620$	7.58000			0.304420
$621$	−1.43543	−	4.57598i	−0.0576016	−	0.183628i
$622$	−15.7131			−0.630038
$623$	22.5324	−	14.4807i	0.902742	−	0.580157i
$624$	−0.00767840	+	0.0534044i	−0.000307382	+	0.00213789i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−19.0182	+	5.58426i	−0.760122	+	0.223192i
$627$	−2.71894	−	5.95365i	−0.108584	−	0.237766i
$628$	−3.29234	−	3.79956i	−0.131379	−	0.151619i
$629$	1.46715	+	10.2043i	0.0584992	+	0.406871i
$630$	−3.36004	−	0.986596i	−0.133867	−	0.0393069i
$631$	−3.36678	+	3.88548i	−0.134030	+	0.154678i	−0.818797	−	0.574084i	$-0.805358\pi$
$631$	−3.36678	+	3.88548i	−0.134030	+	0.154678i	0.684767	+	0.728762i	$0.259904\pi$
$632$	−5.18723	−	3.33363i	−0.206337	−	0.132605i
$633$	−12.6508	−	8.13017i	−0.502824	−	0.323145i
$634$	21.1702	−	24.4317i	0.840774	−	0.970305i
$635$	−3.35674	−	0.985628i	−0.133208	−	0.0391134i
$636$	−1.83343	−	12.7518i	−0.0727001	−	0.505640i
$637$	0.185961	+	0.214610i	0.00736802	+	0.00850315i
$638$	10.6495	+	23.3192i	0.421619	+	0.923217i
$639$	−0.0203089	+	0.00596322i	−0.000803406	+	0.000235901i
$640$	0.415415	−	0.909632i	0.0164207	−	0.0359564i
$641$	0.978869	−	6.80819i	0.0386630	−	0.268907i	−0.961316	−	0.275449i	$-0.911173\pi$
$641$	0.978869	−	6.80819i	0.0386630	−	0.268907i	0.999979	+	0.00654217i	$0.00208245\pi$
$642$	4.05429	−	2.60553i	0.160010	−	0.102832i
$643$	11.6642			0.459992			0.229996	−	0.973192i	$-0.426129\pi$
$643$	11.6642			0.459992			0.229996	+	0.973192i	$0.426129\pi$
$644$	8.81876	−	14.2928i	0.347508	−	0.563214i
$645$	9.77028			0.384704
$646$	−5.20900	+	3.34762i	−0.204945	+	0.131710i
$647$	−2.35810	+	16.4010i	−0.0927066	+	0.644788i	0.889493	+	0.456949i	$0.151058\pi$
$647$	−2.35810	+	16.4010i	−0.0927066	+	0.644788i	−0.982200	+	0.187840i	$0.939851\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	−11.1965	+	3.28758i	−0.439499	+	0.129049i
$650$	−0.0224131	−	0.0490779i	−0.000879115	−	0.00192499i
$651$	17.3828	+	20.0609i	0.681287	+	0.786247i
$652$	−0.911461	−	6.33935i	−0.0356956	−	0.248268i
$653$	35.3695	+	10.3854i	1.38412	+	0.406413i	0.887200	−	0.461385i	$-0.152647\pi$
$653$	35.3695	+	10.3854i	1.38412	+	0.406413i	0.496916	+	0.867799i	$0.334466\pi$
$654$	−12.2230	+	14.1061i	−0.477957	+	0.551592i
$655$	−4.27501	−	2.74738i	−0.167038	−	0.107349i
$656$	−9.06397	−	5.82506i	−0.353889	−	0.227430i
$657$	−8.82910	+	10.1893i	−0.344456	+	0.397523i
$658$	43.2298	+	12.6934i	1.68527	+	0.494840i
$659$	−1.85590	−	12.9081i	−0.0722956	−	0.502827i	−0.993508	−	0.113766i	$-0.963709\pi$
$659$	−1.85590	−	12.9081i	−0.0722956	−	0.502827i	0.921212	−	0.389061i	$-0.127201\pi$
$660$	−1.83626	−	2.11915i	−0.0714762	−	0.0824879i
$661$	−5.33151	−	11.6744i	−0.207372	−	0.454081i	0.777156	−	0.629307i	$-0.216661\pi$
$661$	−5.33151	−	11.6744i	−0.207372	−	0.454081i	−0.984528	+	0.175227i	$0.943934\pi$
$662$	27.5677	−	8.09460i	1.07145	−	0.314606i
$663$	0.0594562	−	0.130191i	0.00230909	−	0.00505619i
$664$	1.34655	−	9.36546i	0.0522563	−	0.363450i
$665$	−6.87642	+	4.41920i	−0.266656	+	0.171369i
$666$	−3.88625			−0.150589
$667$	40.2113	+	17.4786i	1.55699	+	0.676776i
$668$	−21.8759			−0.846404
$669$	−16.1617	+	10.3865i	−0.624846	+	0.401564i
$670$	0.912428	−	6.34608i	0.0352502	−	0.245170i
$671$	−5.84190	+	12.7920i	−0.225524	+	0.493829i
$672$	3.36004	−	0.986596i	0.129616	−	0.0380588i
$673$	7.00251	+	15.3334i	0.269927	+	0.591058i	0.995250	−	0.0973509i	$-0.0310369\pi$
$673$	7.00251	+	15.3334i	0.269927	+	0.591058i	−0.725323	+	0.688409i	$0.758310\pi$
$674$	19.1531	+	22.1038i	0.737749	+	0.851407i
$675$	0.142315	+	0.989821i	0.00547770	+	0.0380982i
$676$	12.4706	+	3.66170i	0.479639	+	0.140835i
$677$	27.6881	−	31.9537i	1.06414	−	1.22808i	0.0914883	−	0.995806i	$-0.470838\pi$
$677$	27.6881	−	31.9537i	1.06414	−	1.22808i	0.972650	−	0.232275i	$-0.0746170\pi$
$678$	−3.09467	−	1.98882i	−0.118850	−	0.0763803i
$679$	24.9536	+	16.0367i	0.957631	+	0.615432i
$680$	−1.73717	+	2.00481i	−0.0666176	+	0.0768808i
$681$	15.3209	+	4.49863i	0.587099	+	0.172388i
$682$	3.02485	+	21.0383i	0.115827	+	0.805598i
$683$	13.6215	+	15.7201i	0.521214	+	0.601513i	0.953934	−	0.300015i	$-0.0969918\pi$
$683$	13.6215	+	15.7201i	0.521214	+	0.601513i	−0.432721	+	0.901528i	$0.642446\pi$
$684$	−0.969650	−	2.12324i	−0.0370755	−	0.0811840i
$685$	9.04354	−	2.65542i	0.345536	−	0.101458i
$686$	−2.52656	+	5.53239i	−0.0964645	+	0.211228i
$687$	−1.30857	+	9.10130i	−0.0499250	+	0.347236i
$688$	−8.21928	+	5.28221i	−0.313357	+	0.201382i
$689$	0.695078			0.0264804
$690$	−4.75875	−	0.595220i	−0.181163	−	0.0226596i
$691$	33.7099			1.28238			0.641192	−	0.767380i	$-0.278440\pi$
$691$	33.7099			1.28238			0.641192	+	0.767380i	$0.278440\pi$
$692$	3.55741	−	2.28621i	0.135232	−	0.0869085i
$693$	1.39745	−	9.71949i	0.0530848	−	0.369213i
$694$	−3.50967	+	7.68511i	−0.133225	+	0.291723i
$695$	1.10607	−	0.324772i	0.0419557	−	0.0123193i
$696$	3.79793	+	8.31630i	0.143960	+	0.315228i
$697$	18.7170	+	21.6005i	0.708955	+	0.818178i
$698$	2.96712	+	20.6368i	0.112307	+	0.781114i
$699$	25.3859	+	7.45398i	0.960184	+	0.281936i
$700$	−2.29325	+	2.64655i	−0.0866767	+	0.100030i
$701$	−9.44536	−	6.07016i	−0.356746	−	0.229267i	0.349975	−	0.936759i	$-0.386190\pi$
$701$	−9.44536	−	6.07016i	−0.356746	−	0.229267i	−0.706721	+	0.707492i	$0.749826\pi$
$702$	0.0453887	+	0.0291695i	0.00171308	+	0.00110093i
$703$	−5.94036	+	6.85554i	−0.224045	+	0.258562i
$704$	2.69046	+	0.789989i	0.101400	+	0.0297738i
$705$	−1.83100	−	12.7349i	−0.0689596	−	0.479624i
$706$	−22.4121	−	25.8649i	−0.843490	−	0.973440i
$707$	−22.9108	−	50.1676i	−0.861648	−	1.88675i
$708$	−3.99297	+	1.17244i	−0.150065	+	0.0440631i
$709$	5.39051	−	11.8036i	0.202445	−	0.443293i	−0.780992	−	0.624540i	$-0.785286\pi$
$709$	5.39051	−	11.8036i	0.202445	−	0.443293i	0.983437	+	0.181248i	$0.0580136\pi$
$710$	−0.00301227	+	0.0209508i	−0.000113049	+	0.000786270i
$711$	−5.18723	+	3.33363i	−0.194536	+	0.125021i
$712$	7.64854			0.286641
$713$	27.9059	+	23.2972i	1.04508	+	0.872486i
$714$	−9.28959			−0.347654
$715$	0.127272	−	0.0817925i	0.00475969	−	0.00305887i
$716$	−1.31460	+	9.14324i	−0.0491289	+	0.341699i
$717$	5.49229	−	12.0264i	0.205113	−	0.449136i
$718$	−22.3415	+	6.56005i	−0.833777	+	0.244819i
$719$	−11.9499	−	26.1667i	−0.445658	−	0.975855i	−0.990525	−	0.137332i	$-0.956147\pi$
$719$	−11.9499	−	26.1667i	−0.445658	−	0.975855i	0.544867	−	0.838522i	$-0.316580\pi$
$720$	−0.654861	−	0.755750i	−0.0244052	−	0.0281651i
$721$	−5.64462	−	39.2592i	−0.210217	−	1.46209i
$722$	13.0027	+	3.81794i	0.483910	+	0.142089i
$723$	8.95495	−	10.3346i	0.333038	−	0.384346i
$724$	1.51026	+	0.970587i	0.0561285	+	0.0360716i
$725$	−7.69115	−	4.94280i	−0.285642	−	0.183571i
$726$	−2.05453	+	2.37106i	−0.0762509	+	0.0879982i
$727$	22.7058	+	6.66704i	0.842113	+	0.247267i	0.674213	−	0.738537i	$-0.264483\pi$
$727$	22.7058	+	6.66704i	0.842113	+	0.247267i	0.167900	+	0.985804i	$0.446301\pi$
$728$	0.0268889	+	0.187016i	0.000996568	+	0.00693129i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	5.60079	+	12.2640i	0.207295	+	0.453912i
$731$	24.8681	−	7.30194i	0.919781	−	0.270072i
$732$	−2.08339	+	4.56198i	−0.0770042	+	0.168616i
$733$	−2.95236	+	20.5341i	−0.109048	+	0.758445i	0.859772	+	0.510678i	$0.170606\pi$
$733$	−2.95236	+	20.5341i	−0.109048	+	0.758445i	−0.968820	+	0.247767i	$0.920303\pi$
$734$	−1.16909	+	0.751330i	−0.0431520	+	0.0277321i
$735$	−5.26322			−0.194137
$736$	4.32512	−	2.07204i	0.159426	−	0.0763766i
$737$	17.9776			0.662215
$738$	−9.06397	+	5.82506i	−0.333650	+	0.214424i
$739$	−0.413063	+	2.87292i	−0.0151948	+	0.105682i	−0.996007	−	0.0892709i	$-0.971546\pi$
$739$	−0.413063	+	2.87292i	−0.0151948	+	0.105682i	0.980813	+	0.194953i	$0.0624554\pi$
$740$	−1.61441	+	3.53506i	−0.0593468	+	0.129951i
$741$	0.120836	−	0.0354806i	0.00443901	−	0.00130341i
$742$	−18.7412	−	41.0375i	−0.688012	−	1.50654i
$743$	33.1747	+	38.2856i	1.21706	+	1.40456i	0.887740	+	0.460346i	$0.152275\pi$
$743$	33.1747	+	38.2856i	1.21706	+	1.40456i	0.329322	+	0.944218i	$0.393180\pi$
$744$	1.07875	+	7.50285i	0.0395488	+	0.275068i
$745$	−1.57660	−	0.462930i	−0.0577620	−	0.0169604i
$746$	−23.4710	+	27.0870i	−0.859333	+	0.991724i
$747$	−7.95975	−	5.11542i	−0.291232	−	0.187163i
$748$	−6.25757	−	4.02149i	−0.228799	−	0.147040i
$749$	11.0519	−	12.7546i	0.403829	−	0.466044i
$750$	0.959493	+	0.281733i	0.0350357	+	0.0102874i
$751$	−3.08909	−	21.4851i	−0.112723	−	0.784002i	−0.965252	−	0.261322i	$-0.915841\pi$
$751$	−3.08909	−	21.4851i	−0.112723	−	0.784002i	0.852529	−	0.522680i	$-0.175068\pi$
$752$	8.42535	+	9.72337i	0.307241	+	0.354575i
$753$	−4.82993	−	10.5761i	−0.176012	−	0.385413i
$754$	−0.473289	+	0.138970i	−0.0172362	+	0.00506100i
$755$	−2.43908	+	5.34085i	−0.0887674	+	0.194373i
$756$	0.498371	−	3.46624i	0.0181256	−	0.126066i
$757$	20.4352	−	13.1329i	0.742728	−	0.477323i	−0.113747	−	0.993510i	$-0.536285\pi$
$757$	20.4352	−	13.1329i	0.742728	−	0.477323i	0.856476	+	0.516187i	$0.172649\pi$
$758$	21.3585			0.775775
$759$	−0.246978	−	13.4454i	−0.00896474	−	0.488038i
$760$	−2.33417			−0.0846693
$761$	−7.66108	+	4.92348i	−0.277714	+	0.178476i	−0.672082	−	0.740477i	$-0.734600\pi$
$761$	−7.66108	+	4.92348i	−0.277714	+	0.178476i	0.394368	+	0.918953i	$0.370963\pi$
$762$	0.497882	−	3.46284i	0.0180363	−	0.125446i
$763$	−27.1527	+	59.4561i	−0.982994	+	2.15246i
$764$	−6.71518	+	1.97175i	−0.242947	+	0.0713356i
$765$	1.10199	+	2.41302i	0.0398424	+	0.0872428i
$766$	−15.5410	−	17.9353i	−0.561520	−	0.648028i
$767$	−0.0319540	−	0.222245i	−0.00115379	−	0.00802480i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	13.2851	−	15.3318i	0.479072	−	0.552879i	−0.463841	−	0.885919i	$-0.653529\pi$
$769$	13.2851	−	15.3318i	0.479072	−	0.552879i	0.942913	+	0.333040i	$0.108074\pi$
$770$	−8.26063	−	5.30879i	−0.297693	−	0.191315i
$771$	−1.88934	−	1.21420i	−0.0680428	−	0.0437284i
$772$	5.42974	−	6.26625i	0.195421	−	0.225527i
$773$	−12.8635	−	3.77707i	−0.462669	−	0.135852i	0.0420870	−	0.999114i	$-0.486599\pi$
$773$	−12.8635	−	3.77707i	−0.462669	−	0.135852i	−0.504756	+	0.863262i	$0.668418\pi$
$774$	1.39046	+	9.67083i	0.0499789	+	0.347611i
$775$	−4.96384	−	5.72858i	−0.178307	−	0.205777i
$776$	3.51873	+	7.70494i	0.126315	+	0.276591i
$777$	−13.0580	+	3.83416i	−0.468451	+	0.137550i
$778$	−0.606583	+	1.32823i	−0.0217471	+	0.0476194i
$779$	−3.57911	+	24.8933i	−0.128235	+	0.891893i
$780$	0.0453887	−	0.0291695i	0.00162517	−	0.00104444i
$781$	−0.0593510			−0.00212375
$782$	−12.5572	+	2.04151i	−0.449045	+	0.0730042i
$783$	9.14248			0.326726
$784$	4.42770	−	2.84551i	0.158132	−	0.101625i
$785$	−0.715494	+	4.97637i	−0.0255371	+	0.177614i
$786$	2.11102	−	4.62249i	0.0752976	−	0.164879i
$787$	24.9456	−	7.32470i	0.889216	−	0.261097i	0.194947	−	0.980814i	$-0.437546\pi$
$787$	24.9456	−	7.32470i	0.889216	−	0.261097i	0.694268	+	0.719716i	$0.255728\pi$
$788$	6.23047	+	13.6428i	0.221951	+	0.486005i
$789$	12.9022	+	14.8900i	0.459332	+	0.530097i
$790$	0.877523	+	6.10331i	0.0312209	+	0.217146i
$791$	−12.3604	−	3.62933i	−0.439484	−	0.129044i
$792$	1.83626	−	2.11915i	0.0652485	−	0.0753008i
$793$	−0.227633	−	0.146291i	−0.00808349	−	0.00519494i
$794$	16.7986	+	10.7958i	0.596160	+	0.383129i
$795$	−8.43650	+	9.73624i	−0.299212	+	0.345309i
$796$	0.827336	+	0.242928i	0.0293242	+	0.00861035i
$797$	−3.74353	−	26.0368i	−0.132603	−	0.922272i	−0.942144	−	0.335209i	$-0.891193\pi$
$797$	−3.74353	−	26.0368i	−0.132603	−	0.922272i	0.809541	−	0.587063i	$-0.199716\pi$
$798$	−5.35284	−	6.17751i	−0.189488	−	0.218681i
$799$	−14.1780	−	31.0455i	−0.501582	−	1.09831i
$800$	−0.959493	+	0.281733i	−0.0339232	+	0.00996075i
$801$	3.17732	−	6.95736i	0.112265	−	0.245826i
$802$	−3.53606	+	24.5939i	−0.124863	+	0.868439i
$803$	−31.8038	+	20.4390i	−1.12233	+	0.721278i
$804$	6.41133			0.226110
$805$	−16.5768	+	2.69500i	−0.584256	+	0.0949864i
$806$	−0.408968			−0.0144053
$807$	−12.0703	+	7.75710i	−0.424894	+	0.273063i
$808$	2.24133	−	15.5888i	0.0788496	−	0.548411i
$809$	18.6669	−	40.8748i	0.656292	−	1.43708i	−0.229645	−	0.973275i	$-0.573756\pi$
$809$	18.6669	−	40.8748i	0.656292	−	1.43708i	0.885937	−	0.463805i	$-0.153516\pi$
$810$	−0.959493	+	0.281733i	−0.0337131	+	0.00989907i
$811$	−12.5856	−	27.5586i	−0.441941	−	0.967715i	−0.991238	−	0.132088i	$-0.957832\pi$
$811$	−12.5856	−	27.5586i	−0.441941	−	0.967715i	0.549297	−	0.835627i	$-0.314895\pi$
$812$	20.9660	+	24.1960i	0.735762	+	0.849115i
$813$	−2.80883	−	19.5358i	−0.0985100	−	0.685152i
$814$	−10.4558	−	3.07010i	−0.366475	−	0.107607i
$815$	−4.19408	+	4.84023i	−0.146912	+	0.169546i
$816$	−2.23163	−	1.43418i	−0.0781225	−	0.0502063i
$817$	19.1852	+	12.3296i	0.671206	+	0.431358i
$818$	−7.77817	+	8.97648i	−0.271957	+	0.313855i
$819$	0.181286	+	0.0532304i	0.00633465	+	0.00186002i
$820$	1.53335	+	10.6647i	0.0535470	+	0.372427i
$821$	13.2190	+	15.2555i	0.461346	+	0.532422i	0.937984	−	0.346678i	$-0.112690\pi$
$821$	13.2190	+	15.2555i	0.461346	+	0.532422i	−0.476638	+	0.879100i	$0.658145\pi$
$822$	3.91542	+	8.57358i	0.136566	+	0.299038i
$823$	37.2473	−	10.9368i	1.29836	−	0.381233i	0.441722	−	0.897152i	$-0.354368\pi$
$823$	37.2473	−	10.9368i	1.29836	−	0.381233i	0.856637	+	0.515920i	$0.172550\pi$
$824$	4.70506	−	10.3026i	0.163908	−	0.358909i
$825$	−0.399057	+	2.77550i	−0.0138934	+	0.0966305i
$826$	−12.2598	+	7.87890i	−0.426573	+	0.274142i
$827$	22.3917			0.778636			0.389318	−	0.921103i	$-0.372711\pi$
$827$	22.3917			0.778636			0.389318	+	0.921103i	$0.372711\pi$
$828$	−0.0880794	−	4.79502i	−0.00306097	−	0.166639i
$829$	46.9559			1.63085			0.815423	−	0.578865i	$-0.196504\pi$
$829$	46.9559			1.63085			0.815423	+	0.578865i	$0.196504\pi$
$830$	−7.95975	+	5.11542i	−0.276287	+	0.177559i
$831$	−2.25882	+	15.7105i	−0.0783578	+	0.544990i
$832$	−0.0224131	+	0.0490779i	−0.000777036	+	0.00170147i
$833$	−13.3964	+	3.93353i	−0.464157	+	0.136289i
$834$	0.478877	+	1.04859i	0.0165821	+	0.0363098i
$835$	14.3257	+	16.5327i	0.495760	+	0.572138i
$836$	−0.931467	−	6.47849i	−0.0322155	−	0.224063i
$837$	7.27296	+	2.13553i	0.251390	+	0.0738148i
$838$	17.6309	−	20.3471i	0.609049	−	0.702880i
$839$	−36.2708	−	23.3099i	−1.25221	−	0.804746i	−0.265011	−	0.964245i	$-0.585376\pi$
$839$	−36.2708	−	23.3099i	−1.25221	−	0.804746i	−0.987198	+	0.159500i	$0.949012\pi$
$840$	−2.94598	−	1.89326i	−0.101646	−	0.0653238i
$841$	−35.7456	+	41.2526i	−1.23261	+	1.42250i
$842$	−2.50679	−	0.736060i	−0.0863897	−	0.0253663i
$843$	2.47557	+	17.2180i	0.0852632	+	0.593019i
$844$	−9.84781	−	11.3650i	−0.338975	−	0.391199i
$845$	−5.39919	−	11.8226i	−0.185738	−	0.406709i
$846$	12.3447	−	3.62473i	0.424420	−	0.124621i
$847$	−4.56403	+	9.99384i	−0.156822	+	0.343392i
$848$	1.83343	−	12.7518i	0.0629601	−	0.437897i
$849$	0.851000	−	0.546905i	0.0292063	−	0.0187697i
$850$	2.65274			0.0909882
$851$	−16.8085	+	8.05249i	−0.576188	+	0.276036i
$852$	−0.0211662			−0.000725144
$853$	27.0624	−	17.3920i	0.926600	−	0.595490i	0.0120346	−	0.999928i	$-0.496169\pi$
$853$	27.0624	−	17.3920i	0.926600	−	0.595490i	0.914565	+	0.404438i	$0.132533\pi$
$854$	−2.49943	+	17.3839i	−0.0855286	+	0.594865i
$855$	−0.969650	+	2.12324i	−0.0331613	+	0.0726132i
$856$	4.62412	−	1.35777i	0.158049	−	0.0464075i
$857$	−10.6344	−	23.2860i	−0.363263	−	0.795436i	−0.999709	−	0.0241145i	$-0.992323\pi$
$857$	−10.6344	−	23.2860i	−0.363263	−	0.795436i	0.636446	−	0.771321i	$-0.280404\pi$
$858$	0.0990726	+	0.114336i	0.00338228	+	0.00390336i
$859$	3.97355	+	27.6367i	0.135576	+	0.942951i	0.938108	+	0.346342i	$0.112576\pi$
$859$	3.97355	+	27.6367i	0.135576	+	0.942951i	−0.802532	+	0.596609i	$0.796515\pi$
$860$	9.37451	+	2.75261i	0.319668	+	0.0938631i
$861$	−24.7083	+	28.5149i	−0.842057	+	0.971785i
$862$	−20.9261	−	13.4484i	−0.712745	−	0.458053i
$863$	−39.1503	−	25.1604i	−1.33269	−	0.856469i	−0.336334	−	0.941743i	$-0.609187\pi$
$863$	−39.1503	−	25.1604i	−1.33269	−	0.856469i	−0.996358	+	0.0852735i	$0.972824\pi$
$864$	0.654861	−	0.755750i	0.0222788	−	0.0257111i
$865$	−4.05740	−	1.19136i	−0.137956	−	0.0405075i
$866$	−5.56802	−	38.7264i	−0.189209	−	1.31598i
$867$	−6.52436	−	7.52952i	−0.221579	−	0.255716i
$868$	11.0269	+	24.1456i	0.374278	+	0.819554i
$869$	−16.5895	+	4.87113i	−0.562762	+	0.165242i
$870$	3.79793	−	8.31630i	0.128762	−	0.281949i
$871$	−0.0492288	+	0.342394i	−0.00166805	+	0.0116016i
$872$	−15.7020	+	10.0911i	−0.531738	+	0.341727i
$873$	8.47040			0.286679
$874$	−8.59329	−	7.17409i	−0.290673	−	0.242667i
$875$	3.50189			0.118385
$876$	−11.3421	+	7.28914i	−0.383215	+	0.246277i
$877$	4.73649	−	32.9430i	0.159940	−	1.11241i	−0.738800	−	0.673924i	$-0.764607\pi$
$877$	4.73649	−	32.9430i	0.159940	−	1.11241i	0.898740	−	0.438482i	$-0.144484\pi$
$878$	−7.89626	+	17.2904i	−0.266486	+	0.583522i
$879$	−2.49187	+	0.731678i	−0.0840486	+	0.0246789i
$880$	−1.16484	−	2.55064i	−0.0392668	−	0.0859822i
$881$	−0.666935	−	0.769684i	−0.0224696	−	0.0259313i	0.744404	−	0.667730i	$-0.232734\pi$
$881$	−0.666935	−	0.769684i	−0.0224696	−	0.0259313i	−0.766873	+	0.641799i	$0.778188\pi$
$882$	−0.749034	−	5.20965i	−0.0252213	−	0.175418i
$883$	11.5510	+	3.39168i	0.388722	+	0.114139i	0.470253	−	0.882532i	$-0.344163\pi$
$883$	11.5510	+	3.39168i	0.388722	+	0.114139i	−0.0815310	+	0.996671i	$0.525981\pi$
$884$	0.0937268	−	0.108166i	0.00315237	−	0.00363803i
$885$	3.50091	+	2.24990i	0.117682	+	0.0756296i
$886$	−0.225377	−	0.144841i	−0.00757168	−	0.00486602i
$887$	6.46262	−	7.45826i	0.216993	−	0.250424i	−0.636808	−	0.771022i	$-0.719746\pi$
$887$	6.46262	−	7.45826i	0.216993	−	0.250424i	0.853802	+	0.520599i	$0.174291\pi$
$888$	−3.72883	−	1.09488i	−0.125131	−	0.0367419i
$889$	−1.74353	−	12.1265i	−0.0584760	−	0.406709i
$890$	−5.00873	−	5.78038i	−0.167893	−	0.193759i
$891$	−1.16484	−	2.55064i	−0.0390236	−	0.0854498i
$892$	−18.4332	+	5.41248i	−0.617189	+	0.181223i
$893$	12.4754	−	27.3173i	0.417473	−	0.914138i
$894$	0.233845	−	1.62643i	0.00782096	−	0.0543959i
$895$	7.77088	−	4.99404i	0.259752	−	0.166932i
$896$	3.50189			0.116990
$897$	0.256752	+	0.0321143i	0.00857269	+	0.00107226i
$898$	−1.12818			−0.0376477
$899$	−58.2989	+	37.4664i	−1.94438	+	1.24958i
$900$	−0.142315	+	0.989821i	−0.00474383	+	0.0329940i
$901$	−14.1968	+	31.0866i	−0.472963	+	1.03565i
$902$	−28.9880	+	8.51164i	−0.965194	+	0.283406i
$903$	14.2132	+	31.1225i	0.472985	+	1.03569i
$904$	−2.40900	−	2.78013i	−0.0801221	−	0.0924658i
$905$	−0.255491	−	1.77698i	−0.00849281	−	0.0590688i
$906$	−5.63361	−	1.65418i	−0.187164	−	0.0549563i
$907$	29.1570	−	33.6490i	0.968143	−	1.11730i	−0.0249176	−	0.999690i	$-0.507932\pi$
$907$	29.1570	−	33.6490i	0.968143	−	1.11730i	0.993060	−	0.117607i	$-0.0375222\pi$
$908$	13.4329	+	8.63281i	0.445787	+	0.286490i
$909$	−13.2490	−	8.51459i	−0.439440	−	0.282411i
$910$	0.123729	−	0.142791i	0.00410158	−	0.00473347i
$911$	−20.1926	−	5.92908i	−0.669011	−	0.196439i	−0.0704482	−	0.997515i	$-0.522443\pi$
$911$	−20.1926	−	5.92908i	−0.669011	−	0.196439i	−0.598562	+	0.801076i	$0.704261\pi$
$912$	−0.332187	−	2.31041i	−0.0109998	−	0.0765055i
$913$	−17.3742	−	20.0509i	−0.575003	−	0.663589i
$914$	0.543279	+	1.18961i	0.0179701	+	0.0393489i
$915$	4.81205	−	1.41294i	0.159081	−	0.0467105i
$916$	−3.81969	+	8.36397i	−0.126206	+	0.276353i
$917$	2.53258	−	17.6145i	0.0836330	−	0.581680i
$918$	−2.23163	+	1.43418i	−0.0736546	+	0.0473349i
$919$	19.5603			0.645236			0.322618	−	0.946529i	$-0.395437\pi$
$919$	19.5603			0.645236			0.322618	+	0.946529i	$0.395437\pi$
$920$	−4.39830	−	1.91180i	−0.145008	−	0.0630303i
$921$	−21.5220			−0.709174
$922$	16.2697	−	10.4559i	0.535812	−	0.344346i
$923$	0.000162523	−	0.00113037i	5.34951e−6	−	3.72066e-5i
$924$	4.07914	−	8.93207i	0.134194	−	0.293844i
$925$	3.72883	−	1.09488i	0.122603	−	0.0359996i
$926$	6.51373	+	14.2631i	0.214055	+	0.468714i
$927$	−7.41706	−	8.55974i	−0.243608	−	0.281139i
$928$	1.30111	+	9.04943i	0.0427111	+	0.297062i
$929$	−29.7306	−	8.72969i	−0.975429	−	0.286412i	−0.245093	−	0.969500i	$-0.578818\pi$
$929$	−29.7306	−	8.72969i	−0.975429	−	0.286412i	−0.730336	+	0.683088i	$0.760637\pi$
$930$	4.96384	−	5.72858i	0.162771	−	0.187848i
$931$	−10.3350	−	6.64191i	−0.338717	−	0.217680i
$932$	22.2576	+	14.3041i	0.729072	+	0.468546i
$933$	−10.2899	+	11.8752i	−0.336876	+	0.388775i
$934$	29.0125	+	8.51884i	0.949319	+	0.278745i
$935$	1.05859	+	7.36267i	0.0346197	+	0.240785i
$936$	0.0353321	+	0.0407754i	0.00115487	+	0.00133279i
$937$	−12.9078	−	28.2641i	−0.421679	−	0.923348i	−0.994604	−	0.103741i	$-0.966919\pi$
$937$	−12.9078	−	28.2641i	−0.421679	−	0.923348i	0.572925	−	0.819607i	$-0.305808\pi$
$938$	21.5423	−	6.32539i	0.703382	−	0.206531i
$939$	−8.23400	+	18.0299i	−0.268706	+	0.588385i
$940$	1.83100	−	12.7349i	0.0597207	−	0.415367i
$941$	−15.0979	+	9.70285i	−0.492178	+	0.316304i	−0.763081	−	0.646303i	$-0.776314\pi$
$941$	−15.0979	+	9.70285i	−0.492178	+	0.316304i	0.270903	+	0.962607i	$0.412678\pi$
$942$	−5.02754			−0.163806
$943$	−27.1330	+	43.9750i	−0.883571	+	1.43202i
$944$	−4.16154			−0.135447
$945$	−2.94598	+	1.89326i	−0.0958326	+	0.0615879i
$946$	−3.89889	+	27.1174i	−0.126764	+	0.881663i
$947$	−5.95656	+	13.0430i	−0.193562	+	0.423842i	−0.981383	−	0.192063i	$-0.938482\pi$
$947$	−5.95656	+	13.0430i	−0.193562	+	0.423842i	0.787820	+	0.615905i	$0.211209\pi$
$948$	−5.91630	+	1.73718i	−0.192152	+	0.0564211i
$949$	−0.302183	−	0.661688i	−0.00980927	−	0.0214793i
$950$	1.52856	+	1.76405i	0.0495930	+	0.0572333i
$951$	−4.60072	−	31.9987i	−0.149188	−	1.03763i
$952$	−8.91330	−	2.61718i	−0.288882	−	0.0848233i
$953$	−7.32540	+	8.45396i	−0.237293	+	0.273851i	−0.861889	−	0.507098i	$-0.830718\pi$
$953$	−7.32540	+	8.45396i	−0.237293	+	0.273851i	0.624596	+	0.780948i	$0.285264\pi$
$954$	−10.8378	−	6.96502i	−0.350886	−	0.225501i
$955$	5.88766	+	3.78377i	0.190520	+	0.122440i
$956$	8.65805	−	9.99193i	0.280021	−	0.323162i
$957$	24.5975	+	7.22247i	0.795123	+	0.233469i
$958$	−4.65248	−	32.3587i	−0.150315	−	1.04546i
$959$	21.6146	+	24.9446i	0.697973	+	0.805503i
$960$	−0.415415	−	0.909632i	−0.0134075	−	0.0293582i
$961$	−25.3847	+	7.45363i	−0.818862	+	0.240440i
$962$	0.0871031	−	0.190729i	0.00280832	−	0.00614936i
$963$	0.685864	−	4.77029i	0.0221017	−	0.153720i
$964$	11.5038	−	7.39304i	0.370512	−	0.238114i
$965$	−8.29144			−0.266911
$966$	−5.02670	−	16.0246i	−0.161731	−	0.515582i
$967$	−47.4301			−1.52525			−0.762625	−	0.646841i	$-0.776090\pi$
$967$	−47.4301			−1.52525			−0.762625	+	0.646841i	$0.776090\pi$
$968$	−2.63931	+	1.69618i	−0.0848308	+	0.0545174i
$969$	−0.881206	+	6.12892i	−0.0283084	+	0.196889i
$970$	3.51873	−	7.70494i	0.112980	−	0.247391i
$971$	−41.3553	+	12.1430i	−1.32715	+	0.389688i	−0.867069	−	0.498188i	$-0.833999\pi$
$971$	−41.3553	+	12.1430i	−1.32715	+	0.389688i	−0.460085	+	0.887875i	$0.652181\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	2.64358	+	3.05086i	0.0847493	+	0.0978060i
$974$	2.30679	+	16.0441i	0.0739144	+	0.514086i
$975$	−0.0517681	−	0.0152005i	−0.00165791	−	0.000486805i
$976$	−3.28426	+	3.79023i	−0.105126	+	0.121322i
$977$	−18.4748	−	11.8730i	−0.591060	−	0.379851i	0.210652	−	0.977561i	$-0.432441\pi$
$977$	−18.4748	−	11.8730i	−0.591060	−	0.379851i	−0.801713	+	0.597710i	$0.796078\pi$
$978$	−5.38784	−	3.46256i	−0.172284	−	0.110720i
$979$	14.0447	−	16.2084i	0.448870	−	0.518023i
$980$	−5.05002	−	1.48282i	−0.161317	−	0.0473670i
$981$	2.65631	+	18.4751i	0.0848095	+	0.589863i
$982$	0.115405	+	0.133185i	0.00368273	+	0.00425009i
$983$	10.7054	+	23.4415i	0.341448	+	0.747668i	0.999988	−	0.00487840i	$-0.00155285\pi$
$983$	10.7054	+	23.4415i	0.341448	+	0.747668i	−0.658540	+	0.752546i	$0.728826\pi$
$984$	−10.3379	+	3.03549i	−0.329561	+	0.0967679i
$985$	6.23047	−	13.6428i	0.198519	−	0.434696i
$986$	3.45151	−	24.0058i	0.109918	−	0.764499i
$987$	37.9025	−	24.3585i	1.20645	−	0.775338i
$988$	0.125937			0.00400659
$989$	26.0523	+	38.9464i	0.828414	+	1.23842i
$990$	−2.80404			−0.0891182
$991$	−48.9060	+	31.4300i	−1.55355	+	0.998405i	−0.569195	+	0.822202i	$0.692745\pi$
$991$	−48.9060	+	31.4300i	−1.55355	+	0.998405i	−0.984354	+	0.176203i	$0.943618\pi$
$992$	−1.07875	+	7.50285i	−0.0342502	+	0.238216i
$993$	11.9355	−	26.1351i	0.378762	−	0.829372i
$994$	−0.0711194	+	0.0208825i	−0.00225577	+	0.000662354i
$995$	−0.358197	−	0.784343i	−0.0113556	−	0.0248653i
$996$	−6.19614	−	7.15073i	−0.196332	−	0.226579i
$997$	−0.831939	−	5.78626i	−0.0263478	−	0.183253i	0.972398	−	0.233330i	$-0.0749623\pi$
$997$	−0.831939	−	5.78626i	−0.0263478	−	0.183253i	−0.998745	+	0.0500774i	$0.984053\pi$
$998$	16.7939	+	4.93114i	0.531603	+	0.156093i
$999$	−2.54495	+	2.93703i	−0.0805188	+	0.0929236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.c.541.1	yes	20
23.2	even	11	inner	690.2.m.c.301.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.c.301.1	✓	20	23.2	even	11	inner
690.2.m.c.541.1	yes	20	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-2.29325 - 2.64655i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-2.29325 - 2.64655i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-0.654861 + 0.755750i) q^{10} +(-2.35891 - 1.51598i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(0.0353321 - 0.0407754i) q^{13} +(-3.36004 - 0.986596i) q^{14} +(0.142315 + 0.989821i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.10199 + 2.41302i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(-0.969650 + 2.12324i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(-2.94598 + 1.89326i) q^{21} -2.80404 q^{22} +(-3.56616 + 3.20664i) q^{23} -1.00000 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.00767840 - 0.0534044i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-3.36004 + 0.986596i) q^{28} +(-3.79793 - 8.31630i) q^{29} +(0.654861 + 0.755750i) q^{30} +(-1.07875 - 7.50285i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.83626 + 2.11915i) q^{33} +(2.23163 + 1.43418i) q^{34} +(2.94598 + 1.89326i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(3.72883 + 1.09488i) q^{37} +(0.332187 + 2.31041i) q^{38} +(-0.0353321 - 0.0407754i) q^{39} +(0.415415 + 0.909632i) q^{40} +(10.3379 - 3.03549i) q^{41} +(-1.45474 + 3.18543i) q^{42} +(1.39046 - 9.67083i) q^{43} +(-2.35891 + 1.51598i) q^{44} +1.00000 q^{45} +(-1.26640 + 4.62561i) q^{46} -12.8659 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-0.749034 + 5.20965i) q^{49} +(0.415415 - 0.909632i) q^{50} +(2.54528 - 0.747363i) q^{51} +(-0.0224131 - 0.0490779i) q^{52} +(8.43650 + 9.73624i) q^{53} +(0.142315 + 0.989821i) q^{54} +(2.69046 + 0.789989i) q^{55} +(-2.29325 + 2.64655i) q^{56} +(1.96363 + 1.26195i) q^{57} +(-7.69115 - 4.94280i) q^{58} +(2.72523 - 3.14508i) q^{59} +(0.959493 + 0.281733i) q^{60} +(-0.713737 - 4.96415i) q^{61} +(-4.96384 - 5.72858i) q^{62} +(1.45474 + 3.18543i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.0224131 + 0.0490779i) q^{65} +(-0.399057 + 2.77550i) q^{66} +(-5.39356 + 3.46623i) q^{67} +2.65274 q^{68} +(2.66648 + 3.98621i) q^{69} +3.50189 q^{70} +(0.0178062 - 0.0114433i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(5.60079 - 12.2640i) q^{73} +(3.72883 - 1.09488i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(1.52856 + 1.76405i) q^{76} +(1.39745 + 9.71949i) q^{77} +(-0.0517681 - 0.0152005i) q^{78} +(4.03792 - 4.66000i) q^{79} +(0.841254 + 0.540641i) q^{80} +(0.841254 + 0.540641i) q^{81} +(7.05571 - 8.14272i) q^{82} +(9.07850 + 2.66569i) q^{83} +(0.498371 + 3.46624i) q^{84} +(-1.73717 - 2.00481i) q^{85} +(-4.05872 - 8.88736i) q^{86} +(-8.77215 + 2.57574i) q^{87} +(-1.16484 + 2.55064i) q^{88} +(-1.08850 + 7.57069i) q^{89} +(0.841254 - 0.540641i) q^{90} -0.188939 q^{91} +(1.43543 + 4.57598i) q^{92} -7.58000 q^{93} +(-10.8235 + 6.95581i) q^{94} +(0.332187 - 2.31041i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(-8.12729 + 2.38639i) q^{97} +(2.18642 + 4.78759i) q^{98} +(1.83626 + 2.11915i) 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	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 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 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

L-functions

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