LMFDB - Embedded newform 483.2.q.b.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			190.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	483.190
Dual form			483.2.q.b.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.570276 + 1.24873i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(0.0756100 + 0.0872586i) q^{4} +(-1.87491 + 1.20493i) q^{5} +(0.898983 - 1.03748i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-2.78644 + 0.818172i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.570276 + 1.24873i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(0.0756100 + 0.0872586i) q^{4} +(-1.87491 + 1.20493i) q^{5} +(0.898983 - 1.03748i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-2.78644 + 0.818172i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.435418 - 3.02840i) q^{10} +(1.84125 + 4.03178i) q^{11} +(-0.0479637 - 0.105026i) q^{12} +(-0.211799 - 1.47310i) q^{13} +(-1.15486 - 0.742184i) q^{14} +(2.13843 - 0.627899i) q^{15} +(0.534499 - 3.71752i) q^{16} +(0.654861 - 0.755750i) q^{17} +(-1.15486 + 0.742184i) q^{18} +(-4.72871 - 5.45722i) q^{19} +(-0.246902 - 0.0724971i) q^{20} +(0.415415 - 0.909632i) q^{21} -6.08463 q^{22} +(-4.28287 - 2.15802i) q^{23} +2.90407 q^{24} +(-0.0136519 + 0.0298935i) q^{25} +(1.96028 + 0.575591i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-0.0971309 + 0.0624222i) q^{28} +(-2.70829 + 3.12554i) q^{29} +(-0.435418 + 3.02840i) q^{30} +(1.91899 - 0.563465i) q^{31} +(-0.548755 - 0.352663i) q^{32} +(-0.630785 - 4.38721i) q^{33} +(0.570276 + 1.24873i) q^{34} +(-0.925839 - 2.02730i) q^{35} +(0.0164316 + 0.114284i) q^{36} +(-6.16820 - 3.96406i) q^{37} +(9.51126 - 2.79276i) q^{38} +(-0.211799 + 1.47310i) q^{39} +(4.23847 - 4.89146i) q^{40} +(-0.367883 + 0.236424i) q^{41} +(0.898983 + 1.03748i) q^{42} +(7.97252 + 2.34094i) q^{43} +(-0.212591 + 0.465508i) q^{44} -2.22871 q^{45} +(5.13720 - 4.11748i) q^{46} -9.42455 q^{47} +(-1.56019 + 3.41635i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.0295435 - 0.0340950i) q^{50} +(-0.841254 + 0.540641i) q^{51} +(0.112526 - 0.129862i) q^{52} +(0.833267 - 5.79550i) q^{53} +(1.31718 - 0.386758i) q^{54} +(-8.31020 - 5.34064i) q^{55} +(-0.413293 - 2.87451i) q^{56} +(2.99969 + 6.56839i) q^{57} +(-2.35848 - 5.16434i) q^{58} +(0.553567 + 3.85015i) q^{59} +(0.216476 + 0.139121i) q^{60} +(3.17500 - 0.932263i) q^{61} +(-0.390736 + 2.71763i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(7.07240 - 4.54515i) q^{64} +(2.17208 + 2.50672i) q^{65} +(5.83816 + 1.71424i) q^{66} +(-2.02434 + 4.43268i) q^{67} +0.115460 q^{68} +(3.50140 + 3.27723i) q^{69} +3.05954 q^{70} +(-2.45954 + 5.38564i) q^{71} +(-2.78644 - 0.818172i) q^{72} +(4.52265 + 5.21942i) q^{73} +(8.46761 - 5.44180i) q^{74} +(0.0215209 - 0.0248364i) q^{75} +(0.118652 - 0.825241i) q^{76} +(-4.25278 + 1.24873i) q^{77} +(-1.71872 - 1.10455i) q^{78} +(0.976839 + 6.79406i) q^{79} +(3.47722 + 7.61404i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.0854351 - 0.594214i) q^{82} +(-4.81541 - 3.09468i) q^{83} +(0.110783 - 0.0325288i) q^{84} +(-0.317178 + 2.20602i) q^{85} +(-7.46974 + 8.62053i) q^{86} +(3.47915 - 2.23592i) q^{87} +(-8.42923 - 9.72785i) q^{88} +(13.4780 + 3.95751i) q^{89} +(1.27098 - 2.78305i) q^{90} +1.48825 q^{91} +(-0.135522 - 0.536885i) q^{92} -2.00000 q^{93} +(5.37459 - 11.7687i) q^{94} +(15.4415 + 4.53402i) q^{95} +(0.427170 + 0.492980i) q^{96} +(-13.4363 + 8.63496i) q^{97} +(0.898983 - 1.03748i) q^{98} +(-0.630785 + 4.38721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9	\( 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9} + 3 q^{10} + 9 q^{11} - 12 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 5 q^{16} + q^{17} - 6 q^{18} - 19 q^{19} - 5 q^{20} - q^{21} - 12 q^{22} - 21 q^{23} + 6 q^{24} + 2 q^{25} - 13 q^{26} - q^{27} - q^{28} + 3 q^{30} + 2 q^{31} + 7 q^{32} - 2 q^{33} - 5 q^{34} - 5 q^{35} + 10 q^{36} - 27 q^{37} + 18 q^{38} - 15 q^{39} - 3 q^{40} + 10 q^{41} - 6 q^{42} + 15 q^{43} + 9 q^{44} + 6 q^{45} - 5 q^{46} - 18 q^{47} + 5 q^{48} - q^{49} + 34 q^{50} + q^{51} + 18 q^{52} + 19 q^{53} + 5 q^{54} - 21 q^{55} - 5 q^{56} + 3 q^{57} - 13 q^{59} + 6 q^{60} - 18 q^{61} - 10 q^{62} - q^{63} + 54 q^{64} + 2 q^{65} + 10 q^{66} - 18 q^{67} - 10 q^{68} + q^{69} - 8 q^{70} + 38 q^{71} + 6 q^{72} + 14 q^{73} + 14 q^{74} + 2 q^{75} + 3 q^{76} - 13 q^{77} + 9 q^{78} + 25 q^{79} + 25 q^{80} - q^{81} - 72 q^{82} - 19 q^{83} - q^{84} + 5 q^{85} + 2 q^{86} + 33 q^{87} + q^{88} - 17 q^{89} + 14 q^{90} - 4 q^{91} + 67 q^{92} - 20 q^{93} + 13 q^{94} + 37 q^{95} + 18 q^{96} - 49 q^{97} - 6 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9 + 3 * q^10 + 9 * q^11 - 12 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 5 * q^16 + q^17 - 6 * q^18 - 19 * q^19 - 5 * q^20 - q^21 - 12 * q^22 - 21 * q^23 + 6 * q^24 + 2 * q^25 - 13 * q^26 - q^27 - q^28 + 3 * q^30 + 2 * q^31 + 7 * q^32 - 2 * q^33 - 5 * q^34 - 5 * q^35 + 10 * q^36 - 27 * q^37 + 18 * q^38 - 15 * q^39 - 3 * q^40 + 10 * q^41 - 6 * q^42 + 15 * q^43 + 9 * q^44 + 6 * q^45 - 5 * q^46 - 18 * q^47 + 5 * q^48 - q^49 + 34 * q^50 + q^51 + 18 * q^52 + 19 * q^53 + 5 * q^54 - 21 * q^55 - 5 * q^56 + 3 * q^57 - 13 * q^59 + 6 * q^60 - 18 * q^61 - 10 * q^62 - q^63 + 54 * q^64 + 2 * q^65 + 10 * q^66 - 18 * q^67 - 10 * q^68 + q^69 - 8 * q^70 + 38 * q^71 + 6 * q^72 + 14 * q^73 + 14 * q^74 + 2 * q^75 + 3 * q^76 - 13 * q^77 + 9 * q^78 + 25 * q^79 + 25 * q^80 - q^81 - 72 * q^82 - 19 * q^83 - q^84 + 5 * q^85 + 2 * q^86 + 33 * q^87 + q^88 - 17 * q^89 + 14 * q^90 - 4 * q^91 + 67 * q^92 - 20 * q^93 + 13 * q^94 + 37 * q^95 + 18 * q^96 - 49 * q^97 - 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.570276	+	1.24873i	−0.403246	+	0.882985i	0.593685	+	0.804698i	$0.297673\pi$
$2$	−0.570276	+	1.24873i	−0.403246	+	0.882985i	−0.996931	+	0.0782877i	$0.975055\pi$
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	0.0756100	+	0.0872586i	0.0378050	+	0.0436293i
$5$	−1.87491	+	1.20493i	−0.838484	+	0.538861i	−0.887963	−	0.459914i	$-0.847880\pi$
$5$	−1.87491	+	1.20493i	−0.838484	+	0.538861i	0.0494791	+	0.998775i	$0.484244\pi$
$6$	0.898983	−	1.03748i	0.367008	−	0.423550i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$8$	−2.78644	+	0.818172i	−0.985154	+	0.289267i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.435418	−	3.02840i	−0.137691	−	0.957663i
$11$	1.84125	+	4.03178i	0.555159	+	1.21563i	0.954331	+	0.298752i	$0.0965704\pi$
$11$	1.84125	+	4.03178i	0.555159	+	1.21563i	−0.399172	+	0.916876i	$0.630702\pi$
$12$	−0.0479637	−	0.105026i	−0.0138459	−	0.0303183i
$13$	−0.211799	−	1.47310i	−0.0587426	−	0.408564i	−0.997883	−	0.0650308i	$-0.979285\pi$
$13$	−0.211799	−	1.47310i	−0.0587426	−	0.408564i	0.939141	−	0.343533i	$-0.111624\pi$
$14$	−1.15486	−	0.742184i	−0.308650	−	0.198357i
$15$	2.13843	−	0.627899i	0.552140	−	0.162123i
$16$	0.534499	−	3.71752i	0.133625	−	0.929380i
$17$	0.654861	−	0.755750i	0.158827	−	0.183296i	−0.670758	−	0.741676i	$-0.734031\pi$
$17$	0.654861	−	0.755750i	0.158827	−	0.183296i	0.829586	+	0.558380i	$0.188577\pi$
$18$	−1.15486	+	0.742184i	−0.272203	+	0.174934i
$19$	−4.72871	−	5.45722i	−1.08484	−	1.25197i	−0.965857	−	0.259076i	$-0.916582\pi$
$19$	−4.72871	−	5.45722i	−1.08484	−	1.25197i	−0.118983	−	0.992896i	$-0.537963\pi$
$20$	−0.246902	−	0.0724971i	−0.0552091	−	0.0162108i
$21$	0.415415	−	0.909632i	0.0906510	−	0.198498i
$22$	−6.08463			−1.29725
$23$	−4.28287	−	2.15802i	−0.893039	−	0.449979i
$23$	−4.28287	−	2.15802i	−0.893039	−	0.449979i
$24$	2.90407			0.592791
$25$	−0.0136519	+	0.0298935i	−0.00273038	+	0.00597869i
$26$	1.96028	+	0.575591i	0.384443	+	0.112883i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−0.0971309	+	0.0624222i	−0.0183560	+	0.0117967i
$29$	−2.70829	+	3.12554i	−0.502917	+	0.580398i	−0.949271	−	0.314459i	$-0.898177\pi$
$29$	−2.70829	+	3.12554i	−0.502917	+	0.580398i	0.446354	+	0.894857i	$0.352722\pi$
$30$	−0.435418	+	3.02840i	−0.0794960	+	0.552907i
$31$	1.91899	−	0.563465i	0.344660	−	0.101201i	−0.104821	−	0.994491i	$-0.533427\pi$
$31$	1.91899	−	0.563465i	0.344660	−	0.101201i	0.449481	+	0.893290i	$0.351609\pi$
$32$	−0.548755	−	0.352663i	−0.0970071	−	0.0623427i
$33$	−0.630785	−	4.38721i	−0.109806	−	0.763715i
$34$	0.570276	+	1.24873i	0.0978015	+	0.214155i
$35$	−0.925839	−	2.02730i	−0.156495	−	0.342677i
$36$	0.0164316	+	0.114284i	0.00273860	+	0.0190474i
$37$	−6.16820	−	3.96406i	−1.01405	−	0.651687i	−0.0756084	−	0.997138i	$-0.524090\pi$
$37$	−6.16820	−	3.96406i	−1.01405	−	0.651687i	−0.938437	+	0.345450i	$0.887726\pi$
$38$	9.51126	−	2.79276i	1.54293	−	0.453045i
$39$	−0.211799	+	1.47310i	−0.0339150	+	0.235884i
$40$	4.23847	−	4.89146i	0.670162	−	0.773408i
$41$	−0.367883	+	0.236424i	−0.0574537	+	0.0369233i	−0.569052	−	0.822301i	$-0.692690\pi$
$41$	−0.367883	+	0.236424i	−0.0574537	+	0.0369233i	0.511599	+	0.859225i	$0.329053\pi$
$42$	0.898983	+	1.03748i	0.138716	+	0.160087i
$43$	7.97252	+	2.34094i	1.21580	+	0.356990i	0.825873	−	0.563857i	$-0.190683\pi$
$43$	7.97252	+	2.34094i	1.21580	+	0.356990i	0.389924	+	0.920847i	$0.372501\pi$
$44$	−0.212591	+	0.465508i	−0.0320492	+	0.0701780i
$45$	−2.22871			−0.332236
$46$	5.13720	−	4.11748i	0.757439	−	0.607089i
$47$	−9.42455			−1.37471			−0.687356	−	0.726321i	$-0.741229\pi$
$47$	−9.42455			−1.37471			−0.687356	+	0.726321i	$0.741229\pi$
$48$	−1.56019	+	3.41635i	−0.225195	+	0.493108i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−0.0295435	−	0.0340950i	−0.00417809	−	0.00482177i
$51$	−0.841254	+	0.540641i	−0.117799	+	0.0757049i
$52$	0.112526	−	0.129862i	0.0156046	−	0.0180087i
$53$	0.833267	−	5.79550i	0.114458	−	0.796073i	−0.849034	−	0.528338i	$-0.822816\pi$
$53$	0.833267	−	5.79550i	0.114458	−	0.796073i	0.963492	−	0.267736i	$-0.0862754\pi$
$54$	1.31718	−	0.386758i	0.179245	−	0.0526312i
$55$	−8.31020	−	5.34064i	−1.12055	−	0.720132i
$56$	−0.413293	−	2.87451i	−0.0552286	−	0.384123i
$57$	2.99969	+	6.56839i	0.397318	+	0.870005i
$58$	−2.35848	−	5.16434i	−0.309683	−	0.678111i
$59$	0.553567	+	3.85015i	0.0720683	+	0.501246i	0.993601	+	0.112946i	$0.0360286\pi$
$59$	0.553567	+	3.85015i	0.0720683	+	0.501246i	−0.921533	+	0.388301i	$0.873062\pi$
$60$	0.216476	+	0.139121i	0.0279470	+	0.0179604i
$61$	3.17500	−	0.932263i	0.406517	−	0.119364i	−0.0720801	−	0.997399i	$-0.522964\pi$
$61$	3.17500	−	0.932263i	0.406517	−	0.119364i	0.478597	+	0.878035i	$0.341146\pi$
$62$	−0.390736	+	2.71763i	−0.0496235	+	0.345139i
$63$	−0.654861	+	0.755750i	−0.0825047	+	0.0952155i
$64$	7.07240	−	4.54515i	0.884050	−	0.568144i
$65$	2.17208	+	2.50672i	0.269414	+	0.310920i
$66$	5.83816	+	1.71424i	0.718628	+	0.211008i
$67$	−2.02434	+	4.43268i	−0.247312	+	0.541538i	−0.992054	−	0.125815i	$-0.959845\pi$
$67$	−2.02434	+	4.43268i	−0.247312	+	0.541538i	0.744742	+	0.667353i	$0.232573\pi$
$68$	0.115460			0.0140015
$69$	3.50140	+	3.27723i	0.421518	+	0.394532i
$70$	3.05954			0.365685
$71$	−2.45954	+	5.38564i	−0.291893	+	0.639157i	−0.997592	−	0.0693548i	$-0.977906\pi$
$71$	−2.45954	+	5.38564i	−0.291893	+	0.639157i	0.705699	+	0.708512i	$0.250633\pi$
$72$	−2.78644	−	0.818172i	−0.328385	−	0.0964225i
$73$	4.52265	+	5.21942i	0.529337	+	0.610887i	0.955944	−	0.293550i	$-0.0948367\pi$
$73$	4.52265	+	5.21942i	0.529337	+	0.610887i	−0.426607	+	0.904437i	$0.640291\pi$
$74$	8.46761	−	5.44180i	0.984340	−	0.632597i
$75$	0.0215209	−	0.0248364i	0.00248501	−	0.00286786i
$76$	0.118652	−	0.825241i	0.0136103	−	0.0946616i
$77$	−4.25278	+	1.24873i	−0.484650	+	0.142306i
$78$	−1.71872	−	1.10455i	−0.194606	−	0.125066i
$79$	0.976839	+	6.79406i	0.109903	+	0.764392i	0.968008	+	0.250918i	$0.0807325\pi$
$79$	0.976839	+	6.79406i	0.109903	+	0.764392i	−0.858105	+	0.513474i	$0.828358\pi$
$80$	3.47722	+	7.61404i	0.388765	+	0.851276i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.0854351	−	0.594214i	−0.00943473	−	0.0656200i
$83$	−4.81541	−	3.09468i	−0.528560	−	0.339685i	0.248990	−	0.968506i	$-0.419901\pi$
$83$	−4.81541	−	3.09468i	−0.528560	−	0.339685i	−0.777550	+	0.628821i	$0.783538\pi$
$84$	0.110783	−	0.0325288i	0.0120874	−	0.00354918i
$85$	−0.317178	+	2.20602i	−0.0344028	+	0.239277i
$86$	−7.46974	+	8.62053i	−0.805482	+	0.929576i
$87$	3.47915	−	2.23592i	0.373004	−	0.239715i
$88$	−8.42923	−	9.72785i	−0.898559	−	1.03699i
$89$	13.4780	+	3.95751i	1.42867	+	0.419495i	0.902428	−	0.430841i	$-0.141783\pi$
$89$	13.4780	+	3.95751i	1.42867	+	0.419495i	0.526240	+	0.850336i	$0.323601\pi$
$90$	1.27098	−	2.78305i	0.133973	−	0.293360i
$91$	1.48825			0.156010
$92$	−0.135522	−	0.536885i	−0.0141291	−	0.0559741i
$93$	−2.00000			−0.207390
$94$	5.37459	−	11.7687i	0.554347	−	1.21385i
$95$	15.4415	+	4.53402i	1.58426	+	0.465181i
$96$	0.427170	+	0.492980i	0.0435978	+	0.0503146i
$97$	−13.4363	+	8.63496i	−1.36424	+	0.876747i	−0.998542	−	0.0539847i	$-0.982808\pi$
$97$	−13.4363	+	8.63496i	−1.36424	+	0.876747i	−0.365703	+	0.930732i	$0.619171\pi$
$98$	0.898983	−	1.03748i	0.0908110	−	0.104802i
$99$	−0.630785	+	4.38721i	−0.0633963	+	0.440931i
$100$	−0.00364068	+	0.00106900i	−0.000364068	+	0.000106900i
$101$	3.86885	+	2.48636i	0.384965	+	0.247402i	0.718781	−	0.695236i	$-0.244700\pi$
$101$	3.86885	+	2.48636i	0.384965	+	0.247402i	−0.333817	+	0.942638i	$0.608337\pi$
$102$	−0.195368	−	1.35881i	−0.0193443	−	0.134542i
$103$	3.28998	+	7.20405i	0.324171	+	0.709836i	0.999620	−	0.0275708i	$-0.00877719\pi$
$103$	3.28998	+	7.20405i	0.324171	+	0.709836i	−0.675448	+	0.737407i	$0.736050\pi$
$104$	1.79541	+	3.93140i	0.176055	+	0.385506i
$105$	0.317178	+	2.20602i	0.0309534	+	0.215286i
$106$	6.76182	+	4.34556i	0.656766	+	0.422078i
$107$	−15.4647	+	4.54086i	−1.49503	+	0.438981i	−0.924144	−	0.382045i	$-0.875220\pi$
$107$	−15.4647	+	4.54086i	−1.49503	+	0.438981i	−0.570890	+	0.821027i	$0.693402\pi$
$108$	0.0164316	−	0.114284i	0.00158113	−	0.0109970i
$109$	−8.97611	+	10.3590i	−0.859755	+	0.992210i	0.140243	+	0.990117i	$0.455212\pi$
$109$	−8.97611	+	10.3590i	−0.859755	+	0.992210i	−0.999998	+	0.00209305i	$0.999334\pi$
$110$	11.4081	−	7.33155i	1.08772	−	0.699036i
$111$	4.80154	+	5.54127i	0.455742	+	0.525954i
$112$	3.60362	+	1.05812i	0.340510	+	0.0999827i
$113$	−1.05780	+	2.31627i	−0.0995099	+	0.217896i	−0.952839	−	0.303477i	$-0.901853\pi$
$113$	−1.05780	+	2.31627i	−0.0995099	+	0.217896i	0.853329	+	0.521373i	$0.174580\pi$
$114$	−9.91280			−0.928418
$115$	10.6302	−	1.11446i	0.991275	−	0.103924i
$116$	−0.477504			−0.0443351
$117$	0.618239	−	1.35376i	0.0571563	−	0.125155i
$118$	−5.12348	−	1.50439i	−0.471654	−	0.138490i
$119$	0.654861	+	0.755750i	0.0600310	+	0.0692794i
$120$	−5.44487	+	3.49920i	−0.497046	+	0.319432i
$121$	−5.66159	+	6.53382i	−0.514690	+	0.593984i
$122$	−0.646479	+	4.49636i	−0.0585295	+	0.407081i
$123$	0.419590	−	0.123203i	0.0378332	−	0.0111088i
$124$	0.194262	+	0.124844i	0.0174452	+	0.0112114i
$125$	−1.59631	−	11.1026i	−0.142779	−	0.993048i
$126$	−0.570276	−	1.24873i	−0.0508042	−	0.111246i
$127$	2.68655	+	5.88272i	0.238393	+	0.522007i	0.990579	−	0.136944i	$-0.0437279\pi$
$127$	2.68655	+	5.88272i	0.238393	+	0.522007i	−0.752186	+	0.658951i	$0.771001\pi$
$128$	1.45679	+	10.1322i	0.128763	+	0.895566i
$129$	−6.99005	−	4.49223i	−0.615440	−	0.395519i
$130$	−4.36890	+	1.28282i	−0.383178	+	0.112511i
$131$	−0.788029	+	5.48086i	−0.0688504	+	0.478865i	0.926001	+	0.377521i	$0.123223\pi$
$131$	−0.788029	+	5.48086i	−0.0688504	+	0.478865i	−0.994851	+	0.101344i	$0.967686\pi$
$132$	0.335128	−	0.386758i	0.0291692	−	0.0336630i
$133$	6.07464	−	3.90393i	0.526738	−	0.338514i
$134$	−4.38079	−	5.05570i	−0.378442	−	0.436746i
$135$	2.13843	+	0.627899i	0.184047	+	0.0540410i
$136$	−1.20640	+	2.64164i	−0.103448	+	0.226519i
$137$	16.6436			1.42196			0.710979	−	0.703213i	$-0.248252\pi$
$137$	16.6436			1.42196			0.710979	+	0.703213i	$0.248252\pi$
$138$	−6.08913	+	2.50337i	−0.518342	+	0.213101i
$139$	−23.2261			−1.97001			−0.985007	−	0.172512i	$-0.944812\pi$
$139$	−23.2261			−1.97001			−0.985007	+	0.172512i	$0.944812\pi$
$140$	0.106897	−	0.234072i	0.00903445	−	0.0197827i
$141$	9.04279	+	2.65520i	0.761540	+	0.223608i
$142$	−5.32259	−	6.14259i	−0.446662	−	0.515475i
$143$	5.54923	−	3.56627i	0.464050	−	0.298227i
$144$	2.45949	−	2.83841i	0.204958	−	0.236534i
$145$	1.31175	−	9.12340i	0.108935	−	0.757657i
$146$	−9.09681	+	2.67106i	−0.752857	+	0.221059i
$147$	0.841254	+	0.540641i	0.0693854	+	0.0445913i
$148$	−0.120479	−	0.837951i	−0.00990333	−	0.0688792i
$149$	0.214296	+	0.469243i	0.0175558	+	0.0384419i	0.918207	−	0.396101i	$-0.129637\pi$
$149$	0.214296	+	0.469243i	0.0175558	+	0.0384419i	−0.900651	+	0.434543i	$0.856910\pi$
$150$	0.0187411	+	0.0410373i	0.00153021	+	0.00335068i
$151$	1.76335	+	12.2644i	0.143499	+	0.998060i	0.926569	+	0.376126i	$0.122744\pi$
$151$	1.76335	+	12.2644i	0.143499	+	0.998060i	−0.783069	+	0.621935i	$0.786347\pi$
$152$	17.6412	+	11.3373i	1.43089	+	0.919577i
$153$	0.959493	−	0.281733i	0.0775704	−	0.0227767i
$154$	0.865933	−	6.02270i	0.0697789	−	0.485323i
$155$	−2.91899	+	3.36869i	−0.234459	+	0.270580i
$156$	−0.144555	+	0.0928996i	−0.0115736	+	0.00743792i
$157$	−11.0279	−	12.7269i	−0.880122	−	1.01571i	−0.999738	−	0.0228945i	$-0.992712\pi$
$157$	−11.0279	−	12.7269i	−0.880122	−	1.01571i	0.119616	−	0.992820i	$-0.461834\pi$
$158$	−9.04102	−	2.65468i	−0.719265	−	0.211195i
$159$	−2.43230	+	5.32598i	−0.192894	+	0.422378i
$160$	1.45380			0.114933
$161$	2.74557	−	3.93215i	0.216381	−	0.309897i
$162$	−1.37279			−0.107856
$163$	−2.74104	+	6.00203i	−0.214695	+	0.470115i	−0.986084	−	0.166248i	$-0.946835\pi$
$163$	−2.74104	+	6.00203i	−0.214695	+	0.470115i	0.771389	+	0.636363i	$0.219562\pi$
$164$	−0.0484457	−	0.0142250i	−0.00378298	−	0.00111078i
$165$	6.46894	+	7.46556i	0.503607	+	0.581193i
$166$	6.61053	−	4.24833i	0.513077	−	0.329734i
$167$	−6.13225	+	7.07699i	−0.474528	+	0.547634i	−0.941665	−	0.336550i	$-0.890740\pi$
$167$	−6.13225	+	7.07699i	−0.474528	+	0.547634i	0.467138	+	0.884185i	$0.345285\pi$
$168$	−0.413293	+	2.87451i	−0.0318862	+	0.221774i
$169$	10.3483	−	3.03852i	0.796019	−	0.233732i
$170$	−2.57385	−	1.65411i	−0.197405	−	0.126865i
$171$	−1.02765	−	7.14744i	−0.0785861	−	0.546578i
$172$	0.398535	+	0.872669i	0.0303880	+	0.0665404i
$173$	−7.13453	−	15.6224i	−0.542428	−	1.18775i	−0.960229	−	0.279213i	$-0.909926\pi$
$173$	−7.13453	−	15.6224i	−0.542428	−	1.18775i	0.417801	−	0.908539i	$-0.362801\pi$
$174$	0.807978	+	5.61961i	0.0612527	+	0.426022i
$175$	−0.0276463	−	0.0177672i	−0.00208987	−	0.00134308i
$176$	15.9724	−	4.68992i	1.20396	−	0.353516i
$177$	0.553567	−	3.85015i	0.0416087	−	0.289395i
$178$	−12.6280	+	14.5735i	−0.946512	+	1.09233i
$179$	−19.6049	+	12.5993i	−1.46534	+	0.941718i	−0.466995	+	0.884260i	$0.654663\pi$
$179$	−19.6049	+	12.5993i	−1.46534	+	0.941718i	−0.998348	+	0.0574583i	$0.981700\pi$
$180$	−0.168513	−	0.194474i	−0.0125602	−	0.0144952i
$181$	11.9433	+	3.50688i	0.887740	+	0.260664i	0.693644	−	0.720318i	$-0.256004\pi$
$181$	11.9433	+	3.50688i	0.887740	+	0.260664i	0.194097	+	0.980982i	$0.437822\pi$
$182$	−0.848710	+	1.85842i	−0.0629106	+	0.137755i
$183$	−3.30904			−0.244611
$184$	13.6996	+	2.50907i	1.00995	+	0.184971i
$185$	16.3412			1.20143
$186$	1.14055	−	2.49746i	0.0836293	−	0.183123i
$187$	4.25278	+	1.24873i	0.310994	+	0.0913162i
$188$	−0.712591	−	0.822373i	−0.0519710	−	0.0599777i
$189$	0.841254	−	0.540641i	0.0611922	−	0.0393258i
$190$	−14.4677	+	16.6966i	−1.04959	+	1.21130i
$191$	1.17807	−	8.19367i	0.0852423	−	0.592873i	−0.901769	−	0.432219i	$-0.857731\pi$
$191$	1.17807	−	8.19367i	0.0852423	−	0.592873i	0.987011	−	0.160654i	$-0.0513603\pi$
$192$	−8.06643	+	2.36852i	−0.582145	+	0.170933i
$193$	−1.62821	−	1.04639i	−0.117201	−	0.0753207i	0.480727	−	0.876870i	$-0.340373\pi$
$193$	−1.62821	−	1.04639i	−0.117201	−	0.0753207i	−0.597928	+	0.801550i	$0.704009\pi$
$194$	−3.12036	−	21.7026i	−0.224029	−	1.55815i
$195$	−1.37787	−	3.01713i	−0.0986717	−	0.216061i
$196$	−0.0479637	−	0.105026i	−0.00342598	−	0.00750185i
$197$	−2.16769	−	15.0766i	−0.154441	−	1.07416i	−0.908659	−	0.417539i	$-0.862893\pi$
$197$	−2.16769	−	15.0766i	−0.154441	−	1.07416i	0.754218	−	0.656624i	$-0.228016\pi$
$198$	−5.11872	−	3.28960i	−0.363771	−	0.233782i
$199$	7.07098	−	2.07623i	0.501248	−	0.147180i	−0.0213276	−	0.999773i	$-0.506789\pi$
$199$	7.07098	−	2.07623i	0.501248	−	0.147180i	0.522576	+	0.852593i	$0.324971\pi$
$200$	0.0135821	−	0.0944659i	0.000960402	−	0.00667975i
$201$	3.19117	−	3.68280i	0.225088	−	0.259765i
$202$	−5.31110	+	3.41323i	−0.373687	+	0.240154i
$203$	−2.70829	−	3.12554i	−0.190085	−	0.219370i
$204$	−0.110783	−	0.0325288i	−0.00775635	−	0.00227747i
$205$	0.404873	−	0.886548i	0.0282775	−	0.0619192i
$206$	−10.8721			−0.757496
$207$	−2.43626	−	4.13094i	−0.169332	−	0.287120i
$208$	−5.58948			−0.387560
$209$	13.2956	−	29.1132i	0.919674	−	2.01381i
$210$	−2.93560	−	0.861971i	−0.202576	−	0.0594817i
$211$	11.0780	+	12.7847i	0.762644	+	0.880138i	0.995730	−	0.0923179i	$-0.0294276\pi$
$211$	11.0780	+	12.7847i	0.762644	+	0.880138i	−0.233085	+	0.972456i	$0.574882\pi$
$212$	0.568711	−	0.365488i	0.0390592	−	0.0251018i
$213$	3.87722	−	4.47455i	0.265663	−	0.306591i
$214$	3.14886	−	21.9008i	0.215252	−	1.49711i
$215$	−17.7684	+	5.21727i	−1.21180	+	0.355815i
$216$	2.44306	+	1.57006i	0.166229	+	0.106829i
$217$	0.284630	+	1.97964i	0.0193219	+	0.134387i
$218$	−7.81671	−	17.1162i	−0.529414	−	1.15926i
$219$	−2.86897	−	6.28218i	−0.193867	−	0.424510i
$220$	−0.162317	−	1.12894i	−0.0109434	−	0.0761133i
$221$	−1.25199	−	0.804606i	−0.0842181	−	0.0541237i
$222$	−9.65775	+	2.83577i	−0.648186	+	0.190324i
$223$	−0.0731408	+	0.508705i	−0.00489787	+	0.0340654i	−0.992124	−	0.125261i	$-0.960023\pi$
$223$	−0.0731408	+	0.508705i	−0.00489787	+	0.0340654i	0.987226	+	0.159326i	$0.0509322\pi$
$224$	0.427170	−	0.492980i	0.0285415	−	0.0329386i
$225$	−0.0276463	+	0.0177672i	−0.00184309	+	0.00118448i
$226$	−2.28915	−	2.64182i	−0.152272	−	0.175731i
$227$	1.34312	+	0.394375i	0.0891459	+	0.0261756i	0.326001	−	0.945369i	$-0.394299\pi$
$227$	1.34312	+	0.394375i	0.0891459	+	0.0261756i	−0.236855	+	0.971545i	$0.576117\pi$
$228$	−0.346343	+	0.758385i	−0.0229371	+	0.0502253i
$229$	3.11346			0.205743			0.102872	−	0.994695i	$-0.467197\pi$
$229$	3.11346			0.205743			0.102872	+	0.994695i	$0.467197\pi$
$230$	−4.67051	+	13.9099i	−0.307964	+	0.917189i
$231$	4.43232			0.291625
$232$	4.98926	−	10.9250i	0.327561	−	0.717259i
$233$	18.5678	+	5.45199i	1.21642	+	0.357172i	0.826107	−	0.563513i	$-0.190550\pi$
$233$	18.5678	+	5.45199i	1.21642	+	0.357172i	0.390308	+	0.920684i	$0.372369\pi$
$234$	1.33791	+	1.54403i	0.0874618	+	0.100936i
$235$	17.6702	−	11.3559i	1.15267	−	0.740779i
$236$	−0.294103	+	0.339413i	−0.0191445	+	0.0220939i
$237$	0.976839	−	6.79406i	0.0634525	−	0.441322i
$238$	−1.31718	+	0.386758i	−0.0853800	+	0.0250698i
$239$	−4.89659	−	3.14685i	−0.316734	−	0.203553i	0.372608	−	0.927989i	$-0.378464\pi$
$239$	−4.89659	−	3.14685i	−0.316734	−	0.203553i	−0.689342	+	0.724436i	$0.742100\pi$
$240$	−1.19124	−	8.28527i	−0.0768943	−	0.534812i
$241$	−10.4189	−	22.8141i	−0.671138	−	1.46959i	−0.871768	−	0.489919i	$-0.837026\pi$
$241$	−10.4189	−	22.8141i	−0.671138	−	1.46959i	0.200630	−	0.979667i	$-0.435701\pi$
$242$	−4.93031	−	10.7959i	−0.316932	−	0.693985i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	0.321410	+	0.206557i	0.0205761	+	0.0132235i
$245$	2.13843	−	0.627899i	0.136619	−	0.0401150i
$246$	−0.0854351	+	0.594214i	−0.00544714	+	0.0378857i
$247$	−7.03748	+	8.12168i	−0.447784	+	0.516770i
$248$	−4.88612	+	3.14012i	−0.310269	+	0.199398i
$249$	3.74848	+	4.32598i	0.237551	+	0.274148i
$250$	14.7745	+	4.33818i	0.934421	+	0.274371i
$251$	9.43013	−	20.6491i	0.595224	−	1.30336i	−0.337009	−	0.941501i	$-0.609415\pi$
$251$	9.43013	−	20.6491i	0.595224	−	1.30336i	0.932233	−	0.361858i	$-0.117857\pi$
$252$	−0.115460			−0.00727328
$253$	0.814831	−	21.2411i	0.0512280	−	1.33541i
$254$	−8.87800			−0.557055
$255$	0.925839	−	2.02730i	0.0579783	−	0.126955i
$256$	2.64976	+	0.778038i	0.165610	+	0.0486274i
$257$	12.6770	+	14.6300i	0.790767	+	0.912594i	0.997837	−	0.0657322i	$-0.0209383\pi$
$257$	12.6770	+	14.6300i	0.790767	+	0.912594i	−0.207070	+	0.978326i	$0.566393\pi$
$258$	9.59584	−	6.16687i	0.597411	−	0.383933i
$259$	4.80154	−	5.54127i	0.298353	−	0.344318i
$260$	−0.0545015	+	0.379066i	−0.00338004	+	0.0235087i
$261$	−3.96815	+	1.16515i	−0.245623	+	0.0721213i
$262$	−6.39472	−	4.10964i	−0.395067	−	0.253894i
$263$	−3.89456	−	27.0873i	−0.240149	−	1.67027i	−0.651388	−	0.758745i	$-0.725813\pi$
$263$	−3.89456	−	27.0873i	−0.240149	−	1.67027i	0.411239	−	0.911528i	$-0.365096\pi$
$264$	5.34713	+	11.7086i	0.329093	+	0.720614i
$265$	5.42087	+	11.8701i	0.333002	+	0.729172i
$266$	1.41074	+	9.81190i	0.0864979	+	0.601606i
$267$	−11.8171	−	7.59440i	−0.723196	−	0.464770i
$268$	−0.539850	+	0.158514i	−0.0329766	+	0.00968279i
$269$	−0.637397	+	4.43319i	−0.0388628	+	0.270297i	−0.999983	−	0.00583371i	$-0.998143\pi$
$269$	−0.637397	+	4.43319i	−0.0388628	+	0.270297i	0.961120	+	0.276130i	$0.0890522\pi$
$270$	−2.00357	+	2.31224i	−0.121933	+	0.140719i
$271$	−15.6401	+	10.0513i	−0.950068	+	0.610572i	−0.921232	−	0.389013i	$-0.872816\pi$
$271$	−15.6401	+	10.0513i	−0.950068	+	0.610572i	−0.0288355	+	0.999584i	$0.509180\pi$
$272$	−2.45949	−	2.83841i	−0.149129	−	0.172104i
$273$	−1.42796	−	0.419287i	−0.0864241	−	0.0253764i
$274$	−9.49144	+	20.7834i	−0.573399	+	1.25557i
$275$	−0.145661			−0.00878366
$276$	−0.0212259	+	0.553318i	−0.00127765	+	0.0333058i
$277$	20.0249			1.20318			0.601591	−	0.798805i	$-0.294534\pi$
$277$	20.0249			1.20318			0.601591	+	0.798805i	$0.294534\pi$
$278$	13.2453	−	29.0032i	0.794400	−	1.73949i
$279$	1.91899	+	0.563465i	0.114887	+	0.0337338i
$280$	4.23847	+	4.89146i	0.253297	+	0.292321i
$281$	2.99789	−	1.92663i	0.178839	−	0.114933i	−0.448158	−	0.893954i	$-0.647920\pi$
$281$	2.99789	−	1.92663i	0.178839	−	0.114933i	0.626998	+	0.779021i	$0.284284\pi$
$282$	−8.47252	+	9.77780i	−0.504531	+	0.582260i
$283$	−1.44529	+	10.0522i	−0.0859137	+	0.597543i	0.900697	+	0.434448i	$0.143057\pi$
$283$	−1.44529	+	10.0522i	−0.0859137	+	0.597543i	−0.986610	+	0.163094i	$0.947852\pi$
$284$	−0.655909	+	0.192592i	−0.0389210	+	0.0114282i
$285$	−13.5386	−	8.70072i	−0.801957	−	0.515386i
$286$	1.28872	+	8.96325i	0.0762037	+	0.530008i
$287$	−0.181663	−	0.397786i	−0.0107232	−	0.0234805i
$288$	−0.270978	−	0.593359i	−0.0159675	−	0.0349640i
$289$	2.27704	+	15.8371i	0.133943	+	0.931597i
$290$	10.6446	+	6.84087i	0.625072	+	0.401710i
$291$	15.3247	−	4.49975i	0.898352	−	0.263780i
$292$	−0.113482	+	0.789281i	−0.00664100	+	0.0461892i
$293$	−15.5113	+	17.9010i	−0.906179	+	1.04579i	0.0925658	+	0.995707i	$0.470493\pi$
$293$	−15.5113	+	17.9010i	−0.906179	+	1.04579i	−0.998745	+	0.0500802i	$0.984052\pi$
$294$	−1.15486	+	0.742184i	−0.0673528	+	0.0432850i
$295$	−5.67705	−	6.55166i	−0.330530	−	0.381452i
$296$	20.4306	+	5.99896i	1.18750	+	0.348682i
$297$	1.84125	−	4.03178i	0.106840	−	0.233948i
$298$	−0.708165			−0.0410229
$299$	−2.27187	+	6.76615i	−0.131385	+	0.391296i
$300$	0.00379438			0.000219069
$301$	−3.45172	+	7.55822i	−0.198954	+	0.435648i
$302$	−16.3205	−	4.79213i	−0.939138	−	0.275756i
$303$	−3.01164	−	3.47562i	−0.173014	−	0.199669i
$304$	−22.8148	+	14.6622i	−1.30852	+	0.840934i
$305$	−4.82952	+	5.57356i	−0.276537	+	0.319141i
$306$	−0.195368	+	1.35881i	−0.0111684	+	0.0776781i
$307$	−25.2038	+	7.40050i	−1.43846	+	0.422369i	−0.905707	−	0.423904i	$-0.860659\pi$
$307$	−25.2038	+	7.40050i	−1.43846	+	0.422369i	−0.532749	+	0.846273i	$0.678841\pi$
$308$	−0.430515	−	0.276675i	−0.0245309	−	0.0157650i
$309$	−1.12710	−	7.83913i	−0.0641183	−	0.445953i
$310$	−2.54196	−	5.56611i	−0.144373	−	0.316134i
$311$	7.38129	+	16.1628i	0.418554	+	0.916506i	0.995047	+	0.0994040i	$0.0316936\pi$
$311$	7.38129	+	16.1628i	0.418554	+	0.916506i	−0.576493	+	0.817102i	$0.695579\pi$
$312$	−0.615081	−	4.27798i	−0.0348221	−	0.242193i
$313$	3.64401	+	2.34186i	0.205972	+	0.132370i	0.639560	−	0.768741i	$-0.279116\pi$
$313$	3.64401	+	2.34186i	0.205972	+	0.132370i	−0.433588	+	0.901111i	$0.642753\pi$
$314$	22.1814	−	6.51303i	1.25177	−	0.367552i
$315$	0.317178	−	2.20602i	0.0178710	−	0.124295i
$316$	−0.518982	+	0.598937i	−0.0291950	+	0.0336928i
$317$	−25.9086	+	16.6505i	−1.45517	+	0.935183i	−0.456200	+	0.889877i	$0.650790\pi$
$317$	−25.9086	+	16.6505i	−1.45517	+	0.935183i	−0.998973	+	0.0453053i	$0.985574\pi$
$318$	−5.26364	−	6.07456i	−0.295170	−	0.340644i
$319$	−17.5881	−	5.16434i	−0.984747	−	0.289148i
$320$	−7.78350	+	17.0435i	−0.435111	+	0.952760i
$321$	16.1176			0.899598
$322$	3.34447	+	5.67089i	0.186380	+	0.316026i
$323$	−7.22094			−0.401784
$324$	−0.0479637	+	0.105026i	−0.00266465	+	0.00583477i
$325$	0.0469274	+	0.0137791i	0.00260307	+	0.000764329i
$326$	−5.93177	−	6.84563i	−0.328530	−	0.379144i
$327$	11.5310	−	7.41051i	0.637664	−	0.409802i
$328$	0.831648	−	0.959774i	0.0459201	−	0.0529946i
$329$	1.34125	−	9.32862i	0.0739457	−	0.514304i
$330$	−13.0115	+	3.82054i	−0.716262	+	0.210314i
$331$	2.10525	+	1.35296i	0.115715	+	0.0743656i	0.597218	−	0.802079i	$-0.296273\pi$
$331$	2.10525	+	1.35296i	0.115715	+	0.0743656i	−0.481503	+	0.876444i	$0.659909\pi$
$332$	−0.0940562	−	0.654175i	−0.00516200	−	0.0359025i
$333$	−3.04589	−	6.66956i	−0.166913	−	0.365490i
$334$	−5.34018	−	11.6934i	−0.292202	−	0.639832i
$335$	−1.54562	−	10.7501i	−0.0844465	−	0.587338i
$336$	−3.15954	−	2.03051i	−0.172367	−	0.110773i
$337$	−10.8854	+	3.19625i	−0.592968	+	0.174111i	−0.564429	−	0.825482i	$-0.690904\pi$
$337$	−10.8854	+	3.19625i	−0.592968	+	0.174111i	−0.0285388	+	0.999593i	$0.509085\pi$
$338$	−2.10707	+	14.6550i	−0.114609	+	0.797125i
$339$	1.66752	−	1.92443i	0.0905675	−	0.104520i
$340$	−0.216476	+	0.139121i	−0.0117401	+	0.00754489i
$341$	5.80511	+	6.69945i	0.314364	+	0.362796i
$342$	9.51126	+	2.79276i	0.514310	+	0.151015i
$343$	0.415415	−	0.909632i	0.0224303	−	0.0491155i
$344$	−24.1302			−1.30101
$345$	−10.5136	−	1.92557i	−0.566035	−	0.103669i
$346$	23.5768			1.26750
$347$	11.3169	−	24.7806i	0.607524	−	1.33029i	−0.316731	−	0.948516i	$-0.602585\pi$
$347$	11.3169	−	24.7806i	0.607524	−	1.33029i	0.924255	−	0.381777i	$-0.124688\pi$
$348$	0.458162	+	0.134528i	0.0245600	+	0.00721148i
$349$	19.0761	+	22.0149i	1.02112	+	1.17843i	0.983826	+	0.179128i	$0.0573277\pi$
$349$	19.0761	+	22.0149i	1.02112	+	1.17843i	0.0372920	+	0.999304i	$0.488127\pi$
$350$	0.0379525	−	0.0243906i	0.00202865	−	0.00130373i
$351$	−0.974593	+	1.12474i	−0.0520199	+	0.0600342i
$352$	0.411465	−	2.86180i	0.0219312	−	0.152535i
$353$	12.0143	−	3.52773i	0.639459	−	0.187762i	0.0540991	−	0.998536i	$-0.482771\pi$
$353$	12.0143	−	3.52773i	0.639459	−	0.187762i	0.585360	+	0.810773i	$0.300953\pi$
$354$	4.49211	+	2.88690i	0.238753	+	0.153437i
$355$	−1.87791	−	13.0611i	−0.0996690	−	0.693213i
$356$	0.673747	+	1.47530i	0.0357085	+	0.0781908i
$357$	−0.415415	−	0.909632i	−0.0219861	−	0.0481428i
$358$	−4.55294	−	31.6664i	−0.240630	−	1.67362i
$359$	−28.9332	−	18.5942i	−1.52704	−	0.981366i	−0.990504	−	0.137485i	$-0.956098\pi$
$359$	−28.9332	−	18.5942i	−1.52704	−	0.981366i	−0.536531	−	0.843880i	$-0.680266\pi$
$360$	6.21015	−	1.82347i	0.327304	−	0.0961051i
$361$	−4.71659	+	32.8046i	−0.248241	+	1.72656i
$362$	−11.1901	+	12.9141i	−0.588140	+	0.678750i
$363$	7.27305	−	4.67410i	0.381736	−	0.245327i
$364$	0.112526	+	0.129862i	0.00589798	+	0.00680663i
$365$	−14.7686	−	4.33645i	−0.773024	−	0.226980i
$366$	1.88706	−	4.13209i	0.0986384	−	0.215988i
$367$	2.79169			0.145725			0.0728625	−	0.997342i	$-0.476787\pi$
$367$	2.79169			0.145725			0.0728625	+	0.997342i	$0.476787\pi$
$368$	−10.3117	+	14.7682i	−0.537533	+	0.769845i
$369$	−0.437304			−0.0227651
$370$	−9.31900	+	20.4058i	−0.484472	+	1.06085i
$371$	5.61792	+	1.64957i	0.291668	+	0.0856415i
$372$	−0.151220	−	0.174517i	−0.00784039	−	0.00904830i
$373$	6.19360	−	3.98038i	0.320692	−	0.206096i	−0.370383	−	0.928879i	$-0.620774\pi$
$373$	6.19360	−	3.98038i	0.320692	−	0.206096i	0.691075	+	0.722783i	$0.257137\pi$
$374$	−3.98458	+	4.59846i	−0.206038	+	0.237780i
$375$	−1.59631	+	11.1026i	−0.0824333	+	0.573336i
$376$	26.2609	−	7.71090i	1.35430	−	0.397659i
$377$	5.17783	+	3.32759i	0.266672	+	0.171380i
$378$	0.195368	+	1.35881i	0.0100486	+	0.0698898i
$379$	12.8485	+	28.1342i	0.659981	+	1.44516i	0.882539	+	0.470238i	$0.155832\pi$
$379$	12.8485	+	28.1342i	0.659981	+	1.44516i	−0.222558	+	0.974919i	$0.571441\pi$
$380$	0.771897	+	1.69022i	0.0395975	+	0.0867064i
$381$	−0.920370	−	6.40132i	−0.0471520	−	0.327949i
$382$	9.55985	+	6.14374i	0.489125	+	0.314341i
$383$	−12.0070	+	3.52559i	−0.613531	+	0.180149i	−0.573711	−	0.819058i	$-0.694497\pi$
$383$	−12.0070	+	3.52559i	−0.613531	+	0.180149i	−0.0398203	+	0.999207i	$0.512679\pi$
$384$	1.45679	−	10.1322i	0.0743413	−	0.517055i
$385$	6.46894	−	7.46556i	0.329688	−	0.380480i
$386$	2.23519	−	1.43647i	0.113768	−	0.0731143i
$387$	5.44130	+	6.27959i	0.276597	+	0.319210i
$388$	−1.76939	−	0.519540i	−0.0898272	−	0.0263756i
$389$	5.04923	−	11.0563i	0.256006	−	0.560576i	−0.737369	−	0.675490i	$-0.763932\pi$
$389$	5.04923	−	11.0563i	0.256006	−	0.560576i	0.993375	+	0.114915i	$0.0366594\pi$
$390$	4.55334			0.230567
$391$	−4.43560	+	1.82357i	−0.224318	+	0.0922219i
$392$	2.90407			0.146678
$393$	2.30024	−	5.03683i	0.116032	−	0.254075i
$394$	20.0628	+	5.89096i	1.01075	+	0.296782i
$395$	−10.0179	−	11.5612i	−0.504053	−	0.581708i
$396$	−0.430515	+	0.276675i	−0.0216342	+	0.0139035i
$397$	7.47627	−	8.62807i	0.375223	−	0.433031i	−0.536459	−	0.843926i	$-0.680238\pi$
$397$	7.47627	−	8.62807i	0.375223	−	0.433031i	0.911682	+	0.410896i	$0.134784\pi$
$398$	−1.43976	+	10.0138i	−0.0721687	+	0.501944i
$399$	−6.92844	+	2.03437i	−0.346856	+	0.101846i
$400$	0.103833	+	0.0667292i	0.00519164	+	0.00333646i
$401$	−0.847832	−	5.89680i	−0.0423387	−	0.294472i	−0.999979	−	0.00650460i	$-0.997930\pi$
$401$	−0.847832	−	5.89680i	−0.0423387	−	0.294472i	0.957640	−	0.287968i	$-0.0929796\pi$
$402$	2.77898	+	6.08512i	0.138603	+	0.303498i
$403$	−1.23648	−	2.70751i	−0.0615934	−	0.134871i
$404$	0.0755675	+	0.525584i	0.00375963	+	0.0261488i
$405$	−1.87491	−	1.20493i	−0.0931649	−	0.0598735i
$406$	5.44742	−	1.59951i	0.270351	−	0.0793822i
$407$	4.62501	−	32.1677i	0.229253	−	1.59449i
$408$	1.90176	−	2.19475i	0.0941513	−	0.108656i
$409$	−9.77702	+	6.28331i	−0.483443	+	0.310690i	−0.759563	−	0.650433i	$-0.774587\pi$
$409$	−9.77702	+	6.28331i	−0.483443	+	0.310690i	0.276121	+	0.961123i	$0.410951\pi$
$410$	0.876169	+	1.01115i	0.0432709	+	0.0499373i
$411$	−15.9694	−	4.68904i	−0.787713	−	0.231293i
$412$	−0.379860	+	0.831778i	−0.0187144	+	0.0409787i
$413$	−3.88974			−0.191401
$414$	6.54776	−	0.686460i	0.321805	−	0.0337377i
$415$	12.7573			0.626233
$416$	−0.403281	+	0.883063i	−0.0197725	+	0.0432957i
$417$	22.2853	+	6.54356i	1.09132	+	0.320439i
$418$	28.7724	+	33.2052i	1.40731	+	1.62412i
$419$	−28.3503	+	18.2197i	−1.38500	+	0.890089i	−0.999468	−	0.0326040i	$-0.989620\pi$
$419$	−28.3503	+	18.2197i	−1.38500	+	0.890089i	−0.385537	+	0.922693i	$0.625984\pi$
$420$	−0.168513	+	0.194474i	−0.00822257	+	0.00948936i
$421$	5.22125	−	36.3146i	0.254468	−	1.76987i	−0.316208	−	0.948690i	$-0.602410\pi$
$421$	5.22125	−	36.3146i	0.254468	−	1.76987i	0.570676	−	0.821175i	$-0.306681\pi$
$422$	−22.2822	+	6.54266i	−1.08468	+	0.318491i
$423$	−7.92844	−	5.09530i	−0.385494	−	0.247742i
$424$	2.41987	+	16.8306i	0.117519	+	0.817364i
$425$	0.0136519	+	0.0298935i	0.000662214	+	0.00145005i
$426$	3.37642	+	7.39332i	0.163588	+	0.358208i
$427$	0.470925	+	3.27536i	0.0227897	+	0.158506i
$428$	−1.56552	−	1.00610i	−0.0756722	−	0.0486316i
$429$	−6.32918	+	1.85842i	−0.305576	+	0.0897252i
$430$	3.61792	−	25.1632i	0.174472	−	1.21348i
$431$	−2.37167	+	2.73705i	−0.114239	+	0.131839i	−0.809989	−	0.586445i	$-0.800527\pi$
$431$	−2.37167	+	2.73705i	−0.114239	+	0.131839i	0.695749	+	0.718285i	$0.255072\pi$
$432$	−3.15954	+	2.03051i	−0.152013	+	0.0976930i
$433$	−20.4356	−	23.5840i	−0.982073	−	1.13337i	−0.991060	−	0.133413i	$-0.957406\pi$
$433$	−20.4356	−	23.5840i	−0.982073	−	1.13337i	0.00898707	−	0.999960i	$-0.497139\pi$
$434$	−2.63436	−	0.773517i	−0.126453	−	0.0371300i
$435$	−3.82897	+	8.38427i	−0.183585	+	0.401995i
$436$	−1.58259			−0.0757925
$437$	8.47563	+	33.5772i	0.405444	+	1.60621i
$438$	9.48085			0.453012
$439$	−7.39542	+	16.1937i	−0.352964	+	0.772884i	0.646982	+	0.762505i	$0.276031\pi$
$439$	−7.39542	+	16.1937i	−0.352964	+	0.772884i	−0.999946	+	0.0103786i	$0.996696\pi$
$440$	27.5254	+	8.08219i	1.31222	+	0.385303i
$441$	−0.654861	−	0.755750i	−0.0311838	−	0.0359881i
$442$	1.71872	−	1.10455i	0.0817510	−	0.0525382i
$443$	−6.01844	+	6.94565i	−0.285945	+	0.329998i	−0.880490	−	0.474064i	$-0.842787\pi$
$443$	−6.01844	+	6.94565i	−0.285945	+	0.329998i	0.594546	+	0.804062i	$0.297332\pi$
$444$	−0.120479	+	0.837951i	−0.00571769	+	0.0397674i
$445$	−30.0386	+	8.82012i	−1.42397	+	0.418114i
$446$	−0.593525	−	0.381435i	−0.0281042	−	0.0180615i
$447$	−0.0734145	−	0.510609i	−0.00347239	−	0.0241510i
$448$	3.49238	+	7.64725i	0.165000	+	0.361299i
$449$	11.3631	+	24.8818i	0.536260	+	1.17425i	0.962908	+	0.269828i	$0.0869670\pi$
$449$	11.3631	+	24.8818i	0.536260	+	1.17425i	−0.426648	+	0.904418i	$0.640306\pi$
$450$	−0.00642042	−	0.0446550i	−0.000302662	−	0.00210506i
$451$	−1.63058	−	1.04791i	−0.0767809	−	0.0493441i
$452$	−0.282095	+	0.0828306i	−0.0132686	+	0.00389602i
$453$	1.76335	−	12.2644i	0.0828494	−	0.576230i
$454$	−1.25842	+	1.45229i	−0.0590604	+	0.0681593i
$455$	−2.79032	+	1.79323i	−0.130812	+	0.0840680i
$456$	−13.7325	−	15.8482i	−0.643084	−	0.742158i
$457$	37.0248	+	10.8715i	1.73195	+	0.508546i	0.987294	−	0.158905i	$-0.0507965\pi$
$457$	37.0248	+	10.8715i	1.73195	+	0.508546i	0.744654	+	0.667451i	$0.232615\pi$
$458$	−1.77553	+	3.88787i	−0.0829651	+	0.181668i
$459$	−1.00000			−0.0466760
$460$	0.901000	+	0.843316i	0.0420093	+	0.0393198i
$461$	29.0494			1.35297			0.676484	−	0.736458i	$-0.263503\pi$
$461$	29.0494			1.35297			0.676484	+	0.736458i	$0.263503\pi$
$462$	−2.52765	+	5.53477i	−0.117597	+	0.257501i
$463$	33.9403	+	9.96578i	1.57734	+	0.463149i	0.949128	−	0.314892i	$-0.101968\pi$
$463$	33.9403	+	9.96578i	1.57734	+	0.463149i	0.628214	+	0.778041i	$0.283786\pi$
$464$	10.1717	+	11.7387i	0.472208	+	0.544957i
$465$	3.74982	−	2.40986i	0.173894	−	0.111755i
$466$	−17.3968	+	20.0770i	−0.805892	+	0.930049i
$467$	−4.48632	+	31.2030i	−0.207602	+	1.44390i	0.573349	+	0.819312i	$0.305644\pi$
$467$	−4.48632	+	31.2030i	−0.207602	+	1.44390i	−0.780951	+	0.624593i	$0.785265\pi$
$468$	0.164872	−	0.0484108i	0.00762121	−	0.00223779i
$469$	−4.09947	−	2.63457i	−0.189296	−	0.121653i
$470$	4.10362	+	28.5413i	0.189286	+	1.31651i
$471$	6.99561	+	15.3183i	0.322341	+	0.705828i
$472$	−4.69256	−	10.2753i	−0.215993	−	0.472958i
$473$	5.24125	+	36.4537i	0.240993	+	1.67614i
$474$	7.92688	+	5.09430i	0.364094	+	0.233989i
$475$	0.227691	−	0.0668561i	0.0104472	−	0.00306757i
$476$	−0.0164316	+	0.114284i	−0.000753142	+	0.00523822i
$477$	3.83427	−	4.42499i	0.175559	−	0.202606i
$478$	6.72197	−	4.31995i	0.307456	−	0.197590i
$479$	−12.1374	−	14.0073i	−0.554571	−	0.640009i	0.407371	−	0.913263i	$-0.366446\pi$
$479$	−12.1374	−	14.0073i	−0.554571	−	0.640009i	−0.961942	+	0.273254i	$0.911900\pi$
$480$	−1.39491	−	0.409583i	−0.0636687	−	0.0186948i
$481$	−4.53302	+	9.92594i	−0.206688	+	0.452584i
$482$	34.4303			1.56826
$483$	−3.74217	+	2.99936i	−0.170275	+	0.136476i
$484$	−0.998205			−0.0453730
$485$	14.7872	−	32.3795i	0.671453	−	1.47028i
$486$	1.31718	+	0.386758i	0.0597484	+	0.0175437i
$487$	2.24278	+	2.58831i	0.101630	+	0.117287i	0.804286	−	0.594243i	$-0.202548\pi$
$487$	2.24278	+	2.58831i	0.101630	+	0.117287i	−0.702656	+	0.711530i	$0.748003\pi$
$488$	−8.08418	+	5.19539i	−0.365954	+	0.235184i
$489$	4.32097	−	4.98667i	0.195401	−	0.225505i
$490$	−0.435418	+	3.02840i	−0.0196702	+	0.136809i
$491$	6.76538	−	1.98649i	0.305317	−	0.0896492i	−0.125485	−	0.992095i	$-0.540049\pi$
$491$	6.76538	−	1.98649i	0.305317	−	0.0896492i	0.430802	+	0.902446i	$0.358231\pi$
$492$	0.0424757	+	0.0272975i	0.00191495	+	0.00123067i
$493$	0.588568	+	4.09358i	0.0265078	+	0.184366i
$494$	−6.12848	−	13.4195i	−0.275733	−	0.603772i
$495$	−4.10362	−	8.98566i	−0.184444	−	0.403876i
$496$	−1.06900	−	7.43504i	−0.0479994	−	0.333843i
$497$	−4.98079	−	3.20096i	−0.223419	−	0.143583i
$498$	−7.53965	+	2.21384i	−0.337860	+	0.0992046i
$499$	5.13681	−	35.7273i	0.229955	−	1.59937i	−0.468330	−	0.883554i	$-0.655144\pi$
$499$	5.13681	−	35.7273i	0.229955	−	1.59937i	0.698285	−	0.715820i	$-0.253947\pi$
$500$	0.848101	−	0.978761i	0.0379282	−	0.0437715i
$501$	7.87767	−	5.06267i	0.351948	−	0.226183i
$502$	20.4074	+	23.5514i	0.910825	+	1.05115i
$503$	34.6528	+	10.1750i	1.54509	+	0.453680i	0.939629	−	0.342194i	$-0.111170\pi$
$503$	34.6528	+	10.1750i	1.54509	+	0.453680i	0.605463	+	0.795874i	$0.292988\pi$
$504$	1.20640	−	2.64164i	0.0537371	−	0.117668i
$505$	−10.2496			−0.456102
$506$	26.0597	+	13.1308i	1.15849	+	0.583733i
$507$	−10.7851			−0.478984
$508$	−0.310188	+	0.679217i	−0.0137624	+	0.0301354i
$509$	−16.1113	−	4.73070i	−0.714120	−	0.209685i	−0.0955619	−	0.995423i	$-0.530465\pi$
$509$	−16.1113	−	4.73070i	−0.714120	−	0.209685i	−0.618558	+	0.785739i	$0.712283\pi$
$510$	2.00357	+	2.31224i	0.0887196	+	0.102388i
$511$	−5.80994	+	3.73382i	−0.257016	+	0.165174i
$512$	−15.8894	+	18.3374i	−0.702220	+	0.810406i
$513$	−1.02765	+	7.14744i	−0.0453717	+	0.315567i
$514$	−25.4983	+	7.48697i	−1.12468	+	0.330236i
$515$	−14.8488	−	9.54274i	−0.654316	−	0.420503i
$516$	−0.136532	−	0.949600i	−0.00601048	−	0.0418038i
$517$	−17.3530	−	37.9977i	−0.763184	−	1.67114i
$518$	4.18135	+	9.15587i	0.183718	+	0.402286i
$519$	2.44418	+	16.9996i	0.107288	+	0.746202i
$520$	−8.10330	−	5.20768i	−0.355353	−	0.228372i
$521$	31.7713	−	9.32890i	1.39193	−	0.408706i	0.502022	−	0.864855i	$-0.332590\pi$
$521$	31.7713	−	9.32890i	1.39193	−	0.408706i	0.889904	+	0.456148i	$0.150771\pi$
$522$	0.807978	−	5.61961i	0.0353642	−	0.245964i
$523$	3.95004	−	4.55859i	0.172723	−	0.199333i	−0.662787	−	0.748808i	$-0.730627\pi$
$523$	3.95004	−	4.55859i	0.172723	−	0.199333i	0.835511	+	0.549474i	$0.185172\pi$
$524$	−0.537835	+	0.345646i	−0.0234954	+	0.0150996i
$525$	0.0215209	+	0.0248364i	0.000939247	+	0.00108395i
$526$	36.0457	+	10.5840i	1.57167	+	0.461483i
$527$	0.830830	−	1.81926i	0.0361915	−	0.0792484i
$528$	−16.6467			−0.724454
$529$	13.6859	+	18.4850i	0.595039	+	0.803697i
$530$	−17.9139			−0.778130
$531$	−1.61586	+	3.53823i	−0.0701222	+	0.153546i
$532$	0.799955	+	0.234888i	0.0346825	+	0.0101837i
$533$	0.426194	+	0.491854i	0.0184605	+	0.0213045i
$534$	16.2224	−	10.4255i	0.702010	−	0.451155i
$535$	23.5236	−	27.1476i	1.01701	−	1.17369i
$536$	2.01399	−	14.0076i	0.0869913	−	0.605038i
$537$	22.3605	−	6.56562i	0.964925	−	0.283327i
$538$	−5.17237	−	3.32408i	−0.222997	−	0.143311i
$539$	−0.630785	−	4.38721i	−0.0271698	−	0.188970i
$540$	0.106897	+	0.234072i	0.00460012	+	0.0100728i
$541$	−3.58148	−	7.84235i	−0.153980	−	0.337169i	0.816883	−	0.576803i	$-0.195700\pi$
$541$	−3.58148	−	7.84235i	−0.153980	−	0.337169i	−0.970863	+	0.239634i	$0.922973\pi$
$542$	−3.63216	−	25.2622i	−0.156015	−	1.08511i
$543$	−10.4715	−	6.72965i	−0.449377	−	0.288797i
$544$	−0.625883	+	0.183776i	−0.0268345	+	0.00787933i
$545$	4.34753	−	30.2377i	0.186228	−	1.29524i
$546$	1.33791	−	1.54403i	0.0572572	−	0.0660783i
$547$	−14.4569	+	9.29090i	−0.618134	+	0.397250i	−0.811899	−	0.583798i	$-0.801566\pi$
$547$	−14.4569	+	9.29090i	−0.618134	+	0.397250i	0.193766	+	0.981048i	$0.437930\pi$
$548$	1.25842	+	1.45230i	0.0537571	+	0.0620391i
$549$	3.17500	+	0.932263i	0.135506	+	0.0397880i
$550$	0.0830667	−	0.181891i	0.00354198	−	0.00775584i
$551$	29.8635			1.27223
$552$	−12.4378	−	6.26705i	−0.529386	−	0.266743i
$553$	−6.86393			−0.291884
$554$	−11.4197	+	25.0057i	−0.485178	+	1.06239i
$555$	−15.6793	−	4.60385i	−0.665549	−	0.195423i
$556$	−1.75613	−	2.02668i	−0.0744764	−	0.0859504i
$557$	10.0791	−	6.47747i	0.427067	−	0.274459i	−0.309401	−	0.950932i	$-0.600129\pi$
$557$	10.0791	−	6.47747i	0.427067	−	0.274459i	0.736468	+	0.676473i	$0.236492\pi$
$558$	−1.79797	+	2.07496i	−0.0761140	+	0.0878402i
$559$	1.75986	−	12.2401i	0.0744342	−	0.517701i
$560$	−8.03140	+	2.35823i	−0.339389	+	0.0996535i
$561$	−3.72871	−	2.39629i	−0.157426	−	0.101172i
$562$	0.696212	+	4.84226i	0.0293679	+	0.204258i
$563$	−1.15676	−	2.53295i	−0.0487516	−	0.106751i	0.883689	−	0.468075i	$-0.155052\pi$
$563$	−1.15676	−	2.53295i	−0.0487516	−	0.106751i	−0.932440	+	0.361324i	$0.882325\pi$
$564$	0.452036	+	0.989821i	0.0190342	+	0.0416790i
$565$	−0.807656	−	5.61737i	−0.0339783	−	0.236325i
$566$	−11.7283	−	7.53732i	−0.492977	−	0.316817i
$567$	−0.959493	+	0.281733i	−0.0402949	+	0.0118317i
$568$	2.44697	−	17.0191i	0.102673	−	0.714104i
$569$	29.6580	−	34.2272i	1.24333	−	1.43488i	0.384095	−	0.923293i	$-0.374513\pi$
$569$	29.6580	−	34.2272i	1.24333	−	1.43488i	0.859233	−	0.511584i	$-0.170941\pi$
$570$	18.5856	−	11.9442i	0.778464	−	0.500289i
$571$	−19.4478	−	22.4440i	−0.813867	−	0.939253i	0.185188	−	0.982703i	$-0.440710\pi$
$571$	−19.4478	−	22.4440i	−0.813867	−	0.939253i	−0.999056	+	0.0434502i	$0.986165\pi$
$572$	0.730766	+	0.214572i	0.0305548	+	0.00897171i
$573$	−3.43878	+	7.52987i	−0.143657	+	0.314565i
$574$	0.600325			0.0250571
$575$	0.122980	−	0.0985687i	0.00512862	−	0.00411060i
$576$	8.40698			0.350291
$577$	−17.2387	+	37.7474i	−0.717654	+	1.57144i	0.0995081	+	0.995037i	$0.468273\pi$
$577$	−17.2387	+	37.7474i	−0.717654	+	1.57144i	−0.817163	+	0.576407i	$0.804454\pi$
$578$	−21.0749	−	6.18813i	−0.876598	−	0.257392i
$579$	1.26746	+	1.46272i	0.0526737	+	0.0607887i
$580$	0.895276	−	0.575359i	0.0371743	−	0.0238905i
$581$	3.74848	−	4.32598i	0.155513	−	0.179472i
$582$	−3.12036	+	21.7026i	−0.129343	+	0.899600i
$583$	24.9005	−	7.31143i	1.03127	−	0.302809i
$584$	−16.8725	−	10.8433i	−0.698188	−	0.448698i
$585$	0.472039	+	3.28310i	0.0195164	+	0.135740i
$586$	−13.5078	−	29.5779i	−0.558001	−	1.22185i
$587$	13.3806	+	29.2995i	0.552277	+	1.20932i	0.955710	+	0.294309i	$0.0950896\pi$
$587$	13.3806	+	29.2995i	0.552277	+	1.20932i	−0.403433	+	0.915009i	$0.632183\pi$
$588$	0.0164316	+	0.114284i	0.000677629	+	0.00471301i
$589$	−12.1493	−	7.80787i	−0.500602	−	0.321717i
$590$	11.4187	−	3.35284i	0.470102	−	0.138034i
$591$	−2.16769	+	15.0766i	−0.0891668	+	0.620169i
$592$	−18.0334	+	20.8116i	−0.741167	+	0.855352i
$593$	−1.52349	+	0.979091i	−0.0625624	+	0.0402064i	−0.571548	−	0.820569i	$-0.693657\pi$
$593$	−1.52349	+	0.979091i	−0.0625624	+	0.0402064i	0.508986	+	0.860775i	$0.330021\pi$
$594$	3.98458	+	4.59846i	0.163489	+	0.188677i
$595$	−2.13843	−	0.627899i	−0.0876670	−	0.0257414i
$596$	−0.0247426	+	0.0541786i	−0.00101349	+	0.00221924i
$597$	−7.36949			−0.301613
$598$	−7.15350	−	6.69552i	−0.292528	−	0.273800i
$599$	5.25057			0.214533			0.107266	−	0.994230i	$-0.465790\pi$
$599$	5.25057			0.214533			0.107266	+	0.994230i	$0.465790\pi$
$600$	−0.0396461	+	0.0868128i	−0.00161854	+	0.00354412i
$601$	−14.4313	−	4.23740i	−0.588664	−	0.172847i	−0.0261823	−	0.999657i	$-0.508335\pi$
$601$	−14.4313	−	4.23740i	−0.588664	−	0.172847i	−0.562481	+	0.826810i	$0.690153\pi$
$602$	−7.46974	−	8.62053i	−0.304444	−	0.351347i
$603$	−4.09947	+	2.63457i	−0.166943	+	0.107288i
$604$	−0.936845	+	1.08118i	−0.0381197	+	0.0439925i
$605$	2.74216	−	19.0721i	0.111485	−	0.775393i
$606$	6.05758	−	1.77867i	0.246072	−	0.0722534i
$607$	−1.98313	−	1.27448i	−0.0804929	−	0.0517297i	0.499775	−	0.866155i	$-0.333416\pi$
$607$	−1.98313	−	1.27448i	−0.0804929	−	0.0517297i	−0.580268	+	0.814425i	$0.697052\pi$
$608$	0.670340	+	4.66232i	0.0271859	+	0.189082i
$609$	1.71802	+	3.76194i	0.0696178	+	0.152442i
$610$	−4.20571	−	9.20922i	−0.170284	−	0.372871i
$611$	1.99611	+	13.8833i	0.0807541	+	0.561657i
$612$	0.0971309	+	0.0624222i	0.00392628	+	0.00252327i
$613$	−17.7095	+	5.19997i	−0.715279	+	0.210025i	−0.619069	−	0.785336i	$-0.712490\pi$
$613$	−17.7095	+	5.19997i	−0.715279	+	0.210025i	−0.0962094	+	0.995361i	$0.530672\pi$
$614$	5.13189	−	35.6931i	0.207106	−	1.44045i
$615$	−0.638242	+	0.736571i	−0.0257364	+	0.0297014i
$616$	10.8284	−	6.95901i	0.436290	−	0.280387i
$617$	2.68637	+	3.10024i	0.108149	+	0.124811i	0.807243	−	0.590219i	$-0.200959\pi$
$617$	2.68637	+	3.10024i	0.108149	+	0.124811i	−0.699094	+	0.715030i	$0.746413\pi$
$618$	10.4317	+	3.06303i	0.419625	+	0.123213i
$619$	−16.2367	+	35.5534i	−0.652608	+	1.42901i	0.236645	+	0.971596i	$0.423952\pi$
$619$	−16.2367	+	35.5534i	−0.652608	+	1.42901i	−0.889253	+	0.457416i	$0.848775\pi$
$620$	−0.514652			−0.0206689
$621$	1.17376	+	4.64998i	0.0471013	+	0.186597i
$622$	−24.3923			−0.978042
$623$	−5.83535	+	12.7776i	−0.233788	+	0.511925i
$624$	5.36306	+	1.57474i	0.214694	+	0.0630400i
$625$	16.2632	+	18.7687i	0.650528	+	0.750750i
$626$	−5.00245	+	3.21488i	−0.199938	+	0.128492i
$627$	−20.9592	+	24.1882i	−0.837028	+	0.965982i
$628$	0.276710	−	1.92456i	0.0110419	−	0.0767982i
$629$	−7.03515	+	2.06571i	−0.280510	+	0.0823651i
$630$	2.57385	+	1.65411i	0.102545	+	0.0659014i
$631$	−4.15697	−	28.9124i	−0.165486	−	1.15098i	−0.888073	−	0.459702i	$-0.847956\pi$
$631$	−4.15697	−	28.9124i	−0.165486	−	1.15098i	0.722587	−	0.691280i	$-0.242953\pi$
$632$	−8.28061	−	18.1320i	−0.329385	−	0.721253i
$633$	−7.02743	−	15.3879i	−0.279315	−	0.611615i
$634$	−6.01686	−	41.8482i	−0.238960	−	1.66200i
$635$	−12.1253	−	7.79246i	−0.481178	−	0.309234i
$636$	−0.648644	+	0.190459i	−0.0257204	+	0.00755219i
$637$	−0.211799	+	1.47310i	−0.00839180	+	0.0583662i
$638$	16.4790	−	19.0177i	0.652408	−	0.752919i
$639$	−4.98079	+	3.20096i	−0.197037	+	0.126628i
$640$	−14.9399	−	17.2416i	−0.590551	−	0.681533i
$641$	−23.5321	−	6.90966i	−0.929463	−	0.272915i	−0.218251	−	0.975893i	$-0.570035\pi$
$641$	−23.5321	−	6.90966i	−0.929463	−	0.272915i	−0.711212	+	0.702978i	$0.751853\pi$
$642$	−9.19149	+	20.1266i	−0.362759	+	0.794332i
$643$	−8.73569			−0.344502			−0.172251	−	0.985053i	$-0.555104\pi$
$643$	−8.73569			−0.344502			−0.172251	+	0.985053i	$0.555104\pi$
$644$	0.550707	−	0.0577355i	0.0217009	−	0.00227510i
$645$	18.5185			0.729167
$646$	4.11792	−	9.01700i	0.162018	−	0.354769i
$647$	−15.9241	−	4.67572i	−0.626039	−	0.183822i	−0.0467009	−	0.998909i	$-0.514871\pi$
$647$	−15.9241	−	4.67572i	−0.626039	−	0.183822i	−0.579338	+	0.815087i	$0.696689\pi$
$648$	−1.90176	−	2.19475i	−0.0747083	−	0.0862180i
$649$	−14.5037	+	9.32096i	−0.569320	+	0.365880i
$650$	−0.0439680	+	0.0507418i	−0.00172457	+	0.00199026i
$651$	0.284630	−	1.97964i	0.0111555	−	0.0775883i
$652$	−0.730979	+	0.214635i	−0.0286273	+	0.00840575i
$653$	2.33784	+	1.50244i	0.0914869	+	0.0587950i	0.585584	−	0.810611i	$-0.300865\pi$
$653$	2.33784	+	1.50244i	0.0914869	+	0.0587950i	−0.494098	+	0.869406i	$0.664501\pi$
$654$	2.67788	+	18.6251i	0.104714	+	0.728299i
$655$	−5.12657	−	11.2256i	−0.200312	−	0.438622i
$656$	0.682279	+	1.49398i	0.0266385	+	0.0583302i
$657$	0.982867	+	6.83599i	0.0383453	+	0.266697i
$658$	10.8840	+	6.99475i	0.424304	+	0.272684i
$659$	37.1263	−	10.9013i	1.44624	−	0.424653i	0.537940	−	0.842983i	$-0.319203\pi$
$659$	37.1263	−	10.9013i	1.44624	−	0.424653i	0.908295	+	0.418330i	$0.137384\pi$
$660$	−0.162317	+	1.12894i	−0.00631820	+	0.0439440i
$661$	−10.2575	+	11.8378i	−0.398971	+	0.460437i	−0.919317	−	0.393519i	$-0.871258\pi$
$661$	−10.2575	+	11.8378i	−0.398971	+	0.460437i	0.520346	+	0.853956i	$0.325803\pi$
$662$	−2.89006	+	1.85733i	−0.112325	+	0.0721872i
$663$	0.974593	+	1.12474i	0.0378501	+	0.0436813i
$664$	15.9498	+	4.68329i	0.618973	+	0.181747i
$665$	−6.68542	+	14.6390i	−0.259249	+	0.567677i
$666$	10.0655			0.390029
$667$	18.3442	−	7.54170i	0.710291	−	0.292016i
$668$	−1.08119			−0.0418324
$669$	0.213497	−	0.467493i	0.00825427	−	0.0180743i
$670$	14.3053	+	4.20043i	0.552663	+	0.162277i
$671$	9.60466	+	11.0844i	0.370784	+	0.427907i
$672$	−0.548755	+	0.352663i	−0.0211687	+	0.0136043i
$673$	19.2951	−	22.2677i	0.743772	−	0.858358i	−0.250177	−	0.968200i	$-0.580489\pi$
$673$	19.2951	−	22.2677i	0.743772	−	0.858358i	0.993949	+	0.109842i	$0.0350344\pi$
$674$	2.21645	−	15.4157i	0.0853743	−	0.593791i
$675$	0.0315321	−	0.00925865i	0.00121367	−	0.000356366i
$676$	1.04757	+	0.673232i	0.0402911	+	0.0258935i
$677$	−1.96971	−	13.6996i	−0.0757020	−	0.526519i	−0.992021	−	0.126070i	$-0.959763\pi$
$677$	−1.96971	−	13.6996i	−0.0757020	−	0.526519i	0.916319	−	0.400448i	$-0.131146\pi$
$678$	1.45214	+	3.17974i	0.0557690	+	0.122117i
$679$	−6.63489	−	14.5284i	−0.254624	−	0.557548i
$680$	−0.921108	−	6.40645i	−0.0353229	−	0.245676i
$681$	−1.17760	−	0.756801i	−0.0451259	−	0.0290007i
$682$	−11.6763	+	3.42848i	−0.447109	+	0.131283i
$683$	−1.68490	+	11.7188i	−0.0644710	+	0.448406i	0.931860	+	0.362819i	$0.118186\pi$
$683$	−1.68490	+	11.7188i	−0.0644710	+	0.448406i	−0.996331	+	0.0855868i	$0.972723\pi$
$684$	0.545975	−	0.630089i	0.0208759	−	0.0240921i
$685$	−31.2052	+	20.0544i	−1.19229	+	0.766238i
$686$	0.898983	+	1.03748i	0.0343233	+	0.0396113i
$687$	−2.98734	−	0.877163i	−0.113974	−	0.0334659i
$688$	12.9638	−	28.3868i	0.494240	−	1.08224i
$689$	−8.71382			−0.331970
$690$	8.40018	−	12.0306i	0.319789	−	0.457996i
$691$	15.0735			0.573422			0.286711	−	0.958017i	$-0.407438\pi$
$691$	15.0735			0.573422			0.286711	+	0.958017i	$0.407438\pi$
$692$	0.823750	−	1.80376i	0.0313143	−	0.0685687i
$693$	−4.25278	−	1.24873i	−0.161550	−	0.0474353i
$694$	24.4905	+	28.2635i	0.929647	+	1.07287i
$695$	43.5469	−	27.9859i	1.65183	−	1.06156i
$696$	−7.86508	+	9.07678i	−0.298125	+	0.344055i
$697$	−0.0622348	+	0.432853i	−0.00235731	+	0.0163955i
$698$	−38.3693	+	11.2662i	−1.45230	+	0.426434i
$699$	−16.2796	−	10.4623i	−0.615753	−	0.395720i
$700$	−0.000539997	−	0.00375576i	−2.04100e−5	−	0.000141954i
$701$	−3.28532	−	7.19384i	−0.124085	−	0.271708i	0.837388	−	0.546610i	$-0.184082\pi$
$701$	−3.28532	−	7.19384i	−0.124085	−	0.271708i	−0.961472	+	0.274902i	$0.911355\pi$
$702$	−0.848710	−	1.85842i	−0.0320325	−	0.0701414i
$703$	7.53486	+	52.4061i	0.284183	+	1.97653i
$704$	31.3472	+	20.1456i	1.18144	+	0.759266i
$705$	−20.1537	+	5.91767i	−0.759034	+	0.222872i
$706$	−2.44631	+	17.0145i	−0.0920681	+	0.640347i
$707$	−3.01164	+	3.47562i	−0.113265	+	0.130714i
$708$	0.377814	−	0.242806i	0.0141991	−	0.00912521i
$709$	−1.57181	−	1.81396i	−0.0590305	−	0.0681249i	0.725466	−	0.688258i	$-0.241624\pi$
$709$	−1.57181	−	1.81396i	−0.0590305	−	0.0681249i	−0.784497	+	0.620133i	$0.787079\pi$
$710$	17.3808	+	5.10345i	0.652288	+	0.191529i
$711$	−2.85138	+	6.24365i	−0.106935	+	0.234155i
$712$	−40.7936			−1.52880
$713$	−9.43473	−	1.72797i	−0.353333	−	0.0647129i
$714$	1.37279			0.0513752
$715$	−6.10719	+	13.3729i	−0.228396	+	0.500117i
$716$	−2.58173	−	0.758065i	−0.0964838	−	0.0283302i
$717$	3.81168	+	4.39891i	0.142350	+	0.164280i
$718$	39.7191	−	25.5259i	1.48230	−	0.952618i
$719$	3.24077	−	3.74005i	0.120860	−	0.139480i	−0.692095	−	0.721807i	$-0.743312\pi$
$719$	3.24077	−	3.74005i	0.120860	−	0.139480i	0.812955	+	0.582326i	$0.197857\pi$
$720$	−1.19124	+	8.28527i	−0.0443950	+	0.308774i
$721$	−7.59894	+	2.23125i	−0.282999	+	0.0830961i
$722$	−38.2743	−	24.5974i	−1.42442	−	0.915420i
$723$	3.56934	+	24.8253i	0.132745	+	0.923263i
$724$	0.597030	+	1.30731i	0.0221884	+	0.0485859i
$725$	−0.0564598	−	0.123630i	−0.00209686	−	0.00459149i
$726$	1.68905	+	11.7476i	0.0626865	+	0.435994i
$727$	−16.1803	−	10.3984i	−0.600092	−	0.385656i	0.205038	−	0.978754i	$-0.434268\pi$
$727$	−16.1803	−	10.3984i	−0.600092	−	0.385656i	−0.805130	+	0.593098i	$0.797905\pi$
$728$	−4.14690	+	1.21764i	−0.153694	+	0.0451288i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	13.8372	−	15.9690i	0.512139	−	0.591040i
$731$	6.99005	−	4.49223i	0.258536	−	0.166151i
$732$	−0.250196	−	0.288742i	−0.00924752	−	0.0106722i
$733$	−28.1651	−	8.27003i	−1.04030	−	0.305460i	−0.283409	−	0.958999i	$-0.591466\pi$
$733$	−28.1651	−	8.27003i	−1.04030	−	0.305460i	−0.756893	+	0.653539i	$0.773284\pi$
$734$	−1.59203	+	3.48607i	−0.0587630	+	0.128673i
$735$	−2.22871			−0.0822071
$736$	1.58919	+	2.69463i	0.0585783	+	0.0993256i
$737$	−21.5989			−0.795606
$738$	0.249384	−	0.546074i	0.00917995	−	0.0201013i
$739$	−44.1359	−	12.9595i	−1.62357	−	0.476722i	−0.661593	−	0.749863i	$-0.730119\pi$
$739$	−44.1359	−	12.9595i	−1.62357	−	0.476722i	−0.961974	+	0.273141i	$0.911937\pi$
$740$	1.23556	+	1.42591i	0.0454201	+	0.0524176i
$741$	9.04055	−	5.81001i	0.332113	−	0.213436i
$742$	−5.26364	+	6.07456i	−0.193234	+	0.223004i
$743$	−6.52202	+	45.3617i	−0.239270	+	1.66416i	0.416454	+	0.909157i	$0.363273\pi$
$743$	−6.52202	+	45.3617i	−0.239270	+	1.66416i	−0.655723	+	0.755001i	$0.727636\pi$
$744$	5.57287	−	1.63634i	0.204311	−	0.0599913i
$745$	−0.967190	−	0.621575i	−0.0354351	−	0.0227728i
$746$	1.43836	+	10.0040i	0.0526623	+	0.366274i
$747$	−2.37787	−	5.20682i	−0.0870019	−	0.190508i
$748$	0.212591	+	0.465508i	0.00777308	+	0.0170207i
$749$	−2.29378	−	15.9536i	−0.0838128	−	0.582931i
$750$	−12.9538	−	8.32491i	−0.473007	−	0.303983i
$751$	−1.04715	+	0.307471i	−0.0382111	+	0.0112198i	−0.300782	−	0.953693i	$-0.597248\pi$
$751$	−1.04715	+	0.307471i	−0.0382111	+	0.0112198i	0.262571	+	0.964913i	$0.415430\pi$
$752$	−5.03741	+	35.0360i	−0.183696	+	1.27763i
$753$	−14.8657	+	17.1559i	−0.541735	+	0.625195i
$754$	−7.10805	+	4.56807i	−0.258860	+	0.166359i
$755$	−18.0838	−	20.8699i	−0.658138	−	0.759532i
$756$	0.110783	+	0.0325288i	0.00402913	+	0.00118306i
$757$	1.16729	−	2.55601i	0.0424259	−	0.0928997i	−0.887232	−	0.461323i	$-0.847375\pi$
$757$	1.16729	−	2.55601i	0.0424259	−	0.0928997i	0.929658	+	0.368423i	$0.120102\pi$
$758$	−42.4592			−1.54219
$759$	−6.76612	+	20.1511i	−0.245595	+	0.731438i
$760$	−46.7363			−1.69530
$761$	−1.89274	+	4.14452i	−0.0686118	+	0.150239i	−0.940831	−	0.338877i	$-0.889953\pi$
$761$	−1.89274	+	4.14452i	−0.0686118	+	0.150239i	0.872219	+	0.489115i	$0.162680\pi$
$762$	8.51838	+	2.50122i	0.308588	+	0.0906097i
$763$	−8.97611	−	10.3590i	−0.324957	−	0.375020i
$764$	0.804042	−	0.516727i	0.0290892	−	0.0186945i
$765$	−1.45949	+	1.68434i	−0.0527681	+	0.0608976i
$766$	2.44482	−	17.0041i	0.0883350	−	0.614383i
$767$	5.55439	−	1.63092i	0.200558	−	0.0588890i
$768$	−2.32322	−	1.49304i	−0.0838321	−	0.0538756i
$769$	−4.51307	−	31.3891i	−0.162746	−	1.13192i	−0.893429	−	0.449204i	$-0.851708\pi$
$769$	−4.51307	−	31.3891i	−0.162746	−	1.13192i	0.730684	−	0.682716i	$-0.239201\pi$
$770$	5.63338	+	12.3354i	0.203013	+	0.444537i
$771$	−8.04171	−	17.6089i	−0.289615	−	0.634169i
$772$	−0.0318028	−	0.221193i	−0.00114461	−	0.00796091i
$773$	0.174499	+	0.112144i	0.00627629	+	0.00403353i	0.543775	−	0.839231i	$-0.316994\pi$
$773$	0.174499	+	0.112144i	0.00627629	+	0.00403353i	−0.537499	+	0.843264i	$0.680631\pi$
$774$	−10.9446	+	3.21361i	−0.393394	+	0.115511i
$775$	−0.00935386	+	0.0650575i	−0.000336001	+	0.00233693i
$776$	30.3744	−	35.0539i	1.09038	−	1.25836i
$777$	−6.16820	+	3.96406i	−0.221283	+	0.142210i
$778$	10.9268	+	12.6103i	0.391746	+	0.452099i
$779$	3.02983	+	0.889639i	0.108555	+	0.0318746i
$780$	0.159089	−	0.348356i	0.00569630	−	0.0124732i
$781$	−26.2423			−0.939025
$782$	0.252371	−	6.57881i	0.00902475	−	0.235258i
$783$	4.13568			0.147797
$784$	−1.56019	+	3.41635i	−0.0557212	+	0.122013i
$785$	36.0113	+	10.5739i	1.28530	+	0.377397i
$786$	4.97787	+	5.74477i	0.177555	+	0.204909i
$787$	14.6988	−	9.44638i	0.523957	−	0.336727i	−0.251778	−	0.967785i	$-0.581015\pi$
$787$	14.6988	−	9.44638i	0.523957	−	0.336727i	0.775736	+	0.631058i	$0.217379\pi$
$788$	1.15166	−	1.32909i	0.0410263	−	0.0473469i
$789$	−3.89456	+	27.0873i	−0.138650	+	0.964333i
$790$	20.1498	−	5.91651i	0.716897	−	0.210500i
$791$	−2.14215	−	1.37668i	−0.0761661	−	0.0489490i
$792$	−1.83185	−	12.7408i	−0.0650918	−	0.452724i
$793$	−2.04578	−	4.47963i	−0.0726477	−	0.159076i
$794$	6.51060	+	14.2562i	0.231052	+	0.505934i
$795$	−1.85711	−	12.9165i	−0.0658649	−	0.458100i
$796$	0.715805	+	0.460020i	0.0253711	+	0.0163050i
$797$	−0.600250	+	0.176249i	−0.0212619	+	0.00624307i	−0.292346	−	0.956313i	$-0.594436\pi$
$797$	−0.600250	+	0.176249i	−0.0212619	+	0.00624307i	0.271084	+	0.962556i	$0.412618\pi$
$798$	1.41074	−	9.81190i	0.0499396	−	0.347337i
$799$	−6.17177	+	7.12260i	−0.218341	+	0.251980i
$800$	0.0180339	−	0.0115897i	0.000637594	−	0.000409757i
$801$	9.19885	+	10.6160i	0.325025	+	0.375099i
$802$	7.84701	+	2.30409i	0.277088	+	0.0813603i
$803$	−12.7162	+	27.8446i	−0.448746	+	0.982616i
$804$	0.562641			0.0198428
$805$	−0.409722	+	10.6806i	−0.0144408	+	0.376443i
$806$	4.08608			0.143926
$807$	1.86055	−	4.07404i	0.0654946	−	0.143413i
$808$	−12.8146	−	3.76270i	−0.450815	−	0.132371i
$809$	14.1123	+	16.2864i	0.496161	+	0.572601i	0.947502	−	0.319751i	$-0.103599\pi$
$809$	14.1123	+	16.2864i	0.496161	+	0.572601i	−0.451340	+	0.892352i	$0.649054\pi$
$810$	2.57385	−	1.65411i	0.0904358	−	0.0581195i
$811$	11.3064	−	13.0482i	0.397020	−	0.458185i	−0.521680	−	0.853141i	$-0.674695\pi$
$811$	11.3064	−	13.0482i	0.397020	−	0.458185i	0.918700	+	0.394956i	$0.129240\pi$
$812$	0.0679559	−	0.472644i	0.00238478	−	0.0165865i
$813$	17.8383	−	5.23781i	0.625618	−	0.183698i
$814$	37.5312	+	24.1198i	1.31547	+	0.845400i
$815$	−2.09284	−	14.5560i	−0.0733089	−	0.509875i
$816$	1.56019	+	3.41635i	0.0546177	+	0.119596i
$817$	−24.9247	−	54.5774i	−0.872003	−	1.90942i
$818$	−2.27056	−	15.7921i	−0.0793882	−	0.552157i
$819$	1.25199	+	0.804606i	0.0437481	+	0.0281152i
$820$	0.107971	−	0.0317033i	0.00377052	−	0.00110713i
$821$	−0.688769	+	4.79049i	−0.0240382	+	0.167189i	−0.998304	−	0.0582118i	$-0.981460\pi$
$821$	−0.688769	+	4.79049i	−0.0240382	+	0.167189i	0.974266	+	0.225401i	$0.0723692\pi$
$822$	14.9623	−	17.2674i	0.521871	−	0.602271i
$823$	29.7239	−	19.1024i	1.03611	−	0.665866i	0.0920872	−	0.995751i	$-0.470646\pi$
$823$	29.7239	−	19.1024i	1.03611	−	0.665866i	0.944021	+	0.329884i	$0.107010\pi$
$824$	−15.0615	−	17.3819i	−0.524691	−	0.605526i
$825$	0.139760	+	0.0410373i	0.00486583	+	0.00142874i
$826$	2.21822	−	4.85723i	0.0771819	−	0.169005i
$827$	54.2743			1.88730			0.943652	−	0.330941i	$-0.107366\pi$
$827$	54.2743			1.88730			0.943652	+	0.330941i	$0.107366\pi$
$828$	0.176254	−	0.524925i	0.00612525	−	0.0182424i
$829$	27.3727			0.950695			0.475347	−	0.879798i	$-0.342322\pi$
$829$	27.3727			0.950695			0.475347	+	0.879798i	$0.342322\pi$
$830$	−7.27520	+	15.9305i	−0.252526	+	0.552954i
$831$	−19.2138	−	5.64167i	−0.666518	−	0.195707i
$832$	−8.19338	−	9.45567i	−0.284054	−	0.327816i
$833$	−0.841254	+	0.540641i	−0.0291477	+	0.0187321i
$834$	−20.8799	+	24.0967i	−0.723012	+	0.834400i
$835$	2.97012	−	20.6576i	0.102785	−	0.714887i
$836$	3.54566	−	1.04110i	0.122629	−	0.0360072i
$837$	−1.68251	−	1.08128i	−0.0581560	−	0.0373746i
$838$	−6.58392	−	45.7921i	−0.227438	−	1.58186i
$839$	3.54839	+	7.76989i	0.122504	+	0.268246i	0.960942	−	0.276751i	$-0.0892578\pi$
$839$	3.54839	+	7.76989i	0.122504	+	0.268246i	−0.838438	+	0.544998i	$0.816531\pi$
$840$	−2.68870	−	5.88744i	−0.0927690	−	0.203136i
$841$	1.69300	+	11.7751i	0.0583794	+	0.406038i
$842$	42.3696	+	27.2293i	1.46015	+	0.938382i
$843$	−3.41925	+	1.00398i	−0.117765	+	0.0345790i
$844$	−0.277968	+	1.93331i	−0.00956806	+	0.0665473i
$845$	−15.7408	+	18.1659i	−0.541501	+	0.624925i
$846$	10.8840	−	6.99475i	0.374201	−	0.240484i
$847$	−5.66159	−	6.53382i	−0.194535	−	0.224505i
$848$	−21.0995	−	6.19538i	−0.724560	−	0.212750i
$849$	4.21879	−	9.23785i	0.144788	−	0.317042i
$850$	−0.0451142			−0.00154740
$851$	17.8630	+	30.2886i	0.612337	+	1.03828i
$852$	0.683599			0.0234197
$853$	−20.6290	+	45.1712i	−0.706323	+	1.54663i	0.125810	+	0.992054i	$0.459847\pi$
$853$	−20.6290	+	45.1712i	−0.706323	+	1.54663i	−0.832133	+	0.554576i	$0.812880\pi$
$854$	−4.35859	−	1.27980i	−0.149148	−	0.0437938i
$855$	10.5389	+	12.1625i	0.360423	+	0.415950i
$856$	39.3763	−	25.3056i	1.34586	−	0.864929i
$857$	−8.29698	+	9.57522i	−0.283419	+	0.327083i	−0.879552	−	0.475802i	$-0.842158\pi$
$857$	−8.29698	+	9.57522i	−0.283419	+	0.327083i	0.596133	+	0.802886i	$0.296703\pi$
$858$	1.28872	−	8.96325i	0.0439962	−	0.306000i
$859$	48.0738	−	14.1157i	1.64026	−	0.481623i	0.673899	−	0.738824i	$-0.264618\pi$
$859$	48.0738	−	14.1157i	1.64026	−	0.481623i	0.966358	+	0.257201i	$0.0828003\pi$
$860$	−1.79872	−	1.15597i	−0.0613359	−	0.0394182i
$861$	0.0622348	+	0.432853i	0.00212096	+	0.0147516i
$862$	−2.06533	−	4.52245i	−0.0703456	−	0.154035i
$863$	5.55015	+	12.1531i	0.188929	+	0.413697i	0.980266	−	0.197683i	$-0.0633417\pi$
$863$	5.55015	+	12.1531i	0.188929	+	0.413697i	−0.791337	+	0.611381i	$0.790614\pi$
$864$	0.0928329	+	0.645667i	0.00315824	+	0.0219660i
$865$	32.2005	+	20.6940i	1.09485	+	0.703618i
$866$	41.1039	−	12.0692i	1.39677	−	0.410128i
$867$	2.27704	−	15.8371i	0.0773322	−	0.537858i
$868$	−0.151220	+	0.174517i	−0.00513274	+	0.00592350i
$869$	−25.5936	+	16.4480i	−0.868203	+	0.557960i
$870$	−8.28612	−	9.56270i	−0.280926	−	0.324206i
$871$	6.95852	+	2.04321i	0.235780	+	0.0692314i
$872$	16.5359	−	36.2086i	0.559977	−	1.22618i
$873$	−15.9717			−0.540560
$874$	−46.7623	−	8.56449i	−1.58176	−	0.289698i
$875$	11.2168			0.379196
$876$	0.331251	−	0.725338i	0.0111919	−	0.0245069i
$877$	−22.2295	−	6.52716i	−0.750636	−	0.220407i	−0.116034	−	0.993245i	$-0.537018\pi$
$877$	−22.2295	−	6.52716i	−0.750636	−	0.220407i	−0.634603	+	0.772839i	$0.718836\pi$
$878$	−16.0041	−	18.4698i	−0.540114	−	0.623324i
$879$	19.9263	−	12.8058i	0.672096	−	0.431930i
$880$	−24.2957	+	28.0388i	−0.819009	+	0.945187i
$881$	4.21007	−	29.2817i	0.141841	−	0.986524i	−0.787240	−	0.616647i	$-0.788491\pi$
$881$	4.21007	−	29.2817i	0.141841	−	0.986524i	0.929081	−	0.369877i	$-0.120600\pi$
$882$	1.31718	−	0.386758i	0.0443517	−	0.0130228i
$883$	34.5800	+	22.2232i	1.16371	+	0.747870i	0.972322	−	0.233645i	$-0.0750653\pi$
$883$	34.5800	+	22.2232i	1.16371	+	0.747870i	0.191386	+	0.981515i	$0.438702\pi$
$884$	−0.0244543	−	0.170083i	−0.000822487	−	0.00572052i
$885$	3.60127	+	7.88568i	0.121055	+	0.265074i
$886$	−5.24107	−	11.4763i	−0.176077	−	0.385555i
$887$	−4.44256	−	30.8987i	−0.149166	−	1.03748i	−0.917588	−	0.397532i	$-0.869867\pi$
$887$	−4.44256	−	30.8987i	−0.149166	−	1.03748i	0.768422	−	0.639944i	$-0.221042\pi$
$888$	−17.9129	−	11.5119i	−0.601117	−	0.386315i
$889$	−6.20518	+	1.82200i	−0.208115	+	0.0611081i
$890$	6.11632	−	42.5400i	0.205020	−	1.42594i
$891$	−2.90255	+	3.34973i	−0.0972392	+	0.112220i
$892$	−0.0499191	+	0.0320811i	−0.00167141	+	0.00107415i
$893$	44.5659	+	51.4318i	1.49134	+	1.72110i
$894$	0.679479	+	0.199513i	0.0227252	+	0.00667272i
$895$	21.5762	−	47.2452i	0.721211	−	1.57923i
$896$	−10.2364			−0.341973
$897$	4.08608	−	5.85201i	0.136430	−	0.195393i
$898$	−37.5508			−1.25309
$899$	−3.43604	+	7.52389i	−0.114599	+	0.250936i
$900$	−0.00364068	−	0.00106900i	−0.000121356	−	3.56334e-5i
$901$	−3.83427	−	4.42499i	−0.127738	−	0.147418i
$902$	2.23843	−	1.43855i	0.0745317	−	0.0478986i
$903$	5.44130	−	6.27959i	0.181075	−	0.208972i
$904$	1.05240	−	7.31960i	0.0350023	−	0.243446i
$905$	−26.6182	+	7.81580i	−0.884818	+	0.259806i
$906$	14.3093	+	9.19602i	0.475394	+	0.305517i
$907$	−3.95458	−	27.5047i	−0.131310	−	0.913278i	−0.943850	−	0.330374i	$-0.892825\pi$
$907$	−3.95458	−	27.5047i	−0.131310	−	0.913278i	0.812541	−	0.582905i	$-0.198084\pi$
$908$	0.0671406	+	0.147017i	0.00222814	+	0.00487895i
$909$	1.91045	+	4.18331i	0.0633658	+	0.138752i
$910$	−0.648008	−	4.50700i	−0.0214813	−	0.149405i
$911$	45.8280	+	29.4519i	1.51835	+	0.975784i	0.992099	+	0.125455i	$0.0400389\pi$
$911$	45.8280	+	29.4519i	1.51835	+	0.975784i	0.526250	+	0.850330i	$0.323597\pi$
$912$	26.0215	−	7.64059i	0.861657	−	0.253005i
$913$	3.61067	−	25.1128i	0.119496	−	0.831112i
$914$	−34.6899	+	40.0342i	−1.14744	+	1.32422i
$915$	6.20414	−	3.98716i	0.205102	−	0.131811i
$916$	0.235409	+	0.271676i	0.00777813	+	0.00897643i
$917$	−5.31292	−	1.56002i	−0.175448	−	0.0515162i
$918$	0.570276	−	1.24873i	0.0188219	−	0.0412142i
$919$	−11.0116			−0.363240			−0.181620	−	0.983369i	$-0.558134\pi$
$919$	−11.0116			−0.363240			−0.181620	+	0.983369i	$0.558134\pi$
$920$	−28.7087	+	11.8027i	−0.946497	+	0.389125i
$921$	26.2678			0.865554
$922$	−16.5662	+	36.2749i	−0.545579	+	1.19465i
$923$	8.45449	+	2.48246i	0.278283	+	0.0817113i
$924$	0.335128	+	0.386758i	0.0110249	+	0.0127234i
$925$	0.202707	−	0.130272i	0.00666497	−	0.00428331i
$926$	−31.7999	+	36.6991i	−1.04501	+	1.20601i
$927$	−1.12710	+	7.83913i	−0.0370187	+	0.257471i
$928$	2.58845	−	0.760038i	0.0849701	−	0.0249495i
$929$	−14.9598	−	9.61408i	−0.490815	−	0.315428i	0.271718	−	0.962377i	$-0.412408\pi$
$929$	−14.9598	−	9.61408i	−0.490815	−	0.315428i	−0.762533	+	0.646949i	$0.776045\pi$
$930$	0.870835	+	6.05679i	0.0285558	+	0.198610i
$931$	2.99969	+	6.56839i	0.0983107	+	0.215270i
$932$	0.928177	+	2.03242i	0.0304034	+	0.0665742i
$933$	−2.52872	−	17.5876i	−0.0827864	−	0.575792i
$934$	−36.4057	−	23.3965i	−1.19123	−	0.765558i
$935$	−9.47821	+	2.78305i	−0.309971	+	0.0910156i
$936$	−0.615081	+	4.27798i	−0.0201045	+	0.139830i
$937$	30.0235	−	34.6490i	0.980826	−	1.13193i	−0.0104251	−	0.999946i	$-0.503318\pi$
$937$	30.0235	−	34.6490i	0.980826	−	1.13193i	0.991251	−	0.131988i	$-0.0421361\pi$
$938$	5.62769	−	3.61670i	0.183751	−	0.118089i
$939$	−2.83662	−	3.27364i	−0.0925697	−	0.106831i
$940$	2.32694	+	0.683252i	0.0758966	+	0.0222852i
$941$	−0.982132	+	2.15057i	−0.0320166	+	0.0701066i	−0.924965	−	0.380053i	$-0.875906\pi$
$941$	−0.982132	+	2.15057i	−0.0320166	+	0.0701066i	0.892948	+	0.450160i	$0.148633\pi$
$942$	−23.1178			−0.753218
$943$	2.08580	−	0.218674i	0.0679231	−	0.00712099i
$944$	14.6089			0.475479
$945$	−0.925839	+	2.02730i	−0.0301175	+	0.0659482i
$946$	−48.5098	−	14.2438i	−1.57719	−	0.463105i
$947$	−29.2629	−	33.7712i	−0.950916	−	1.09742i	−0.995148	−	0.0983942i	$-0.968629\pi$
$947$	−29.2629	−	33.7712i	−0.950916	−	1.09742i	0.0442316	−	0.999021i	$-0.485916\pi$
$948$	0.666699	−	0.428462i	0.0216534	−	0.0139158i
$949$	6.73082	−	7.76778i	0.218492	−	0.252153i
$950$	−0.0463614	+	0.322451i	−0.00150416	+	0.0104617i
$951$	29.5501	−	8.67670i	0.958228	−	0.281361i
$952$	−2.44306	−	1.57006i	−0.0791801	−	0.0508859i
$953$	2.73575	+	19.0276i	0.0886197	+	0.616363i	0.984932	+	0.172941i	$0.0553269\pi$
$953$	2.73575	+	19.0276i	0.0886197	+	0.616363i	−0.896313	+	0.443423i	$0.853764\pi$
$954$	3.33902	+	7.31143i	0.108105	+	0.236716i
$955$	7.66402	+	16.7819i	0.248002	+	0.543049i
$956$	−0.0956418	−	0.665203i	−0.00309328	−	0.0215142i
$957$	15.4207	+	9.91030i	0.498481	+	0.320355i
$958$	24.4129	−	7.16829i	0.788747	−	0.231597i
$959$	−2.36863	+	16.4742i	−0.0764871	+	0.531979i
$960$	12.2699	−	14.1602i	0.396010	−	0.457020i
$961$	−22.7138	+	14.5973i	−0.732705	+	0.470881i
$962$	−9.80974	−	11.3210i	−0.316279	−	0.365005i
$963$	−15.4647	−	4.54086i	−0.498344	−	0.146327i
$964$	1.20296	−	2.63411i	0.0387447	−	0.0848390i
$965$	4.31357			0.138859
$966$	−1.61132	−	6.38342i	−0.0518433	−	0.205383i
$967$	−9.81238			−0.315545			−0.157772	−	0.987476i	$-0.550431\pi$
$967$	−9.81238			−0.315545			−0.157772	+	0.987476i	$0.550431\pi$
$968$	10.4299	−	22.8382i	0.335229	−	0.734049i
$969$	6.92844	+	2.03437i	0.222573	+	0.0653535i
$970$	32.0004	+	36.9305i	1.02747	+	1.18577i
$971$	−29.5041	+	18.9611i	−0.946831	+	0.608491i	−0.920324	−	0.391157i	$-0.872075\pi$
$971$	−29.5041	+	18.9611i	−0.946831	+	0.608491i	−0.0265072	+	0.999649i	$0.508439\pi$
$972$	0.0756100	−	0.0872586i	0.00242519	−	0.00279882i
$973$	3.30542	−	22.9897i	0.105967	−	0.737017i
$974$	−4.51110	+	1.32458i	−0.144545	+	0.0424422i
$975$	−0.0411445	−	0.0264420i	−0.00131768	−	0.000846821i
$976$	−1.76868	−	12.3014i	−0.0566139	−	0.393759i
$977$	11.6507	+	25.5115i	0.372740	+	0.816187i	0.999322	+	0.0368309i	$0.0117263\pi$
$977$	11.6507	+	25.5115i	0.372740	+	0.816187i	−0.626582	+	0.779356i	$0.715546\pi$
$978$	3.76285	+	8.23950i	0.120323	+	0.263470i
$979$	8.86066	+	61.6273i	0.283188	+	1.96962i
$980$	0.216476	+	0.139121i	0.00691508	+	0.00444405i
$981$	−13.1517	+	3.86168i	−0.419900	+	0.123294i
$982$	−1.37754	+	9.58098i	−0.0439590	+	0.305741i
$983$	−15.5670	+	17.9653i	−0.496511	+	0.573004i	−0.947594	−	0.319478i	$-0.896492\pi$
$983$	−15.5670	+	17.9653i	−0.496511	+	0.573004i	0.451083	+	0.892482i	$0.351038\pi$
$984$	−1.06836	+	0.686593i	−0.0340581	+	0.0218878i
$985$	22.2305	+	25.6553i	0.708322	+	0.817447i
$986$	−5.44742	−	1.59951i	−0.173481	−	0.0509387i
$987$	−3.91510	+	8.57287i	−0.124619	+	0.272878i
$988$	−1.24079			−0.0394748
$989$	−29.0934	−	27.2308i	−0.925117	−	0.865889i
$990$	13.5609			0.430992
$991$	2.77482	−	6.07602i	0.0881452	−	0.193011i	−0.860426	−	0.509576i	$-0.829802\pi$
$991$	2.77482	−	6.07602i	0.0881452	−	0.193011i	0.948571	+	0.316565i	$0.102530\pi$
$992$	−1.25177	−	0.367552i	−0.0397436	−	0.0116698i
$993$	−1.63880	−	1.89128i	−0.0520058	−	0.0600179i
$994$	6.83755	−	4.39423i	0.216874	−	0.139377i
$995$	−10.7557	+	12.4128i	−0.340979	+	0.393511i
$996$	−0.0940562	+	0.654175i	−0.00298028	+	0.0207283i
$997$	26.2521	−	7.70832i	0.831413	−	0.244125i	0.161789	−	0.986825i	$-0.448273\pi$
$997$	26.2521	−	7.70832i	0.831413	−	0.244125i	0.669624	+	0.742700i	$0.266455\pi$
$998$	41.6843	+	26.7889i	1.31949	+	0.847988i
$999$	1.04347	+	7.25752i	0.0330141	+	0.229618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.b.190.1	✓	10
23.4	even	11	inner	483.2.q.b.211.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.b.190.1	✓	10	1.1	even	1	trivial
483.2.q.b.211.1	yes	10	23.4	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.570276 + 1.24873i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(0.0756100 + 0.0872586i) q^{4} +(-1.87491 + 1.20493i) q^{5} +(0.898983 - 1.03748i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-2.78644 + 0.818172i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.570276 + 1.24873i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(0.0756100 + 0.0872586i) q^{4} +(-1.87491 + 1.20493i) q^{5} +(0.898983 - 1.03748i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-2.78644 + 0.818172i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.435418 - 3.02840i) q^{10} +(1.84125 + 4.03178i) q^{11} +(-0.0479637 - 0.105026i) q^{12} +(-0.211799 - 1.47310i) q^{13} +(-1.15486 - 0.742184i) q^{14} +(2.13843 - 0.627899i) q^{15} +(0.534499 - 3.71752i) q^{16} +(0.654861 - 0.755750i) q^{17} +(-1.15486 + 0.742184i) q^{18} +(-4.72871 - 5.45722i) q^{19} +(-0.246902 - 0.0724971i) q^{20} +(0.415415 - 0.909632i) q^{21} -6.08463 q^{22} +(-4.28287 - 2.15802i) q^{23} +2.90407 q^{24} +(-0.0136519 + 0.0298935i) q^{25} +(1.96028 + 0.575591i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-0.0971309 + 0.0624222i) q^{28} +(-2.70829 + 3.12554i) q^{29} +(-0.435418 + 3.02840i) q^{30} +(1.91899 - 0.563465i) q^{31} +(-0.548755 - 0.352663i) q^{32} +(-0.630785 - 4.38721i) q^{33} +(0.570276 + 1.24873i) q^{34} +(-0.925839 - 2.02730i) q^{35} +(0.0164316 + 0.114284i) q^{36} +(-6.16820 - 3.96406i) q^{37} +(9.51126 - 2.79276i) q^{38} +(-0.211799 + 1.47310i) q^{39} +(4.23847 - 4.89146i) q^{40} +(-0.367883 + 0.236424i) q^{41} +(0.898983 + 1.03748i) q^{42} +(7.97252 + 2.34094i) q^{43} +(-0.212591 + 0.465508i) q^{44} -2.22871 q^{45} +(5.13720 - 4.11748i) q^{46} -9.42455 q^{47} +(-1.56019 + 3.41635i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.0295435 - 0.0340950i) q^{50} +(-0.841254 + 0.540641i) q^{51} +(0.112526 - 0.129862i) q^{52} +(0.833267 - 5.79550i) q^{53} +(1.31718 - 0.386758i) q^{54} +(-8.31020 - 5.34064i) q^{55} +(-0.413293 - 2.87451i) q^{56} +(2.99969 + 6.56839i) q^{57} +(-2.35848 - 5.16434i) q^{58} +(0.553567 + 3.85015i) q^{59} +(0.216476 + 0.139121i) q^{60} +(3.17500 - 0.932263i) q^{61} +(-0.390736 + 2.71763i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(7.07240 - 4.54515i) q^{64} +(2.17208 + 2.50672i) q^{65} +(5.83816 + 1.71424i) q^{66} +(-2.02434 + 4.43268i) q^{67} +0.115460 q^{68} +(3.50140 + 3.27723i) q^{69} +3.05954 q^{70} +(-2.45954 + 5.38564i) q^{71} +(-2.78644 - 0.818172i) q^{72} +(4.52265 + 5.21942i) q^{73} +(8.46761 - 5.44180i) q^{74} +(0.0215209 - 0.0248364i) q^{75} +(0.118652 - 0.825241i) q^{76} +(-4.25278 + 1.24873i) q^{77} +(-1.71872 - 1.10455i) q^{78} +(0.976839 + 6.79406i) q^{79} +(3.47722 + 7.61404i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.0854351 - 0.594214i) q^{82} +(-4.81541 - 3.09468i) q^{83} +(0.110783 - 0.0325288i) q^{84} +(-0.317178 + 2.20602i) q^{85} +(-7.46974 + 8.62053i) q^{86} +(3.47915 - 2.23592i) q^{87} +(-8.42923 - 9.72785i) q^{88} +(13.4780 + 3.95751i) q^{89} +(1.27098 - 2.78305i) q^{90} +1.48825 q^{91} +(-0.135522 - 0.536885i) q^{92} -2.00000 q^{93} +(5.37459 - 11.7687i) q^{94} +(15.4415 + 4.53402i) q^{95} +(0.427170 + 0.492980i) q^{96} +(-13.4363 + 8.63496i) q^{97} +(0.898983 - 1.03748i) q^{98} +(-0.630785 + 4.38721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9	\( 10 q + 5 q^{2} - q^{3} - q^{4} - 5 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - q^{9} + 3 q^{10} + 9 q^{11} - 12 q^{12} - 15 q^{13} - 6 q^{14} + 6 q^{15} + 5 q^{16} + q^{17} - 6 q^{18} - 19 q^{19} - 5 q^{20} - q^{21} - 12 q^{22} - 21 q^{23} + 6 q^{24} + 2 q^{25} - 13 q^{26} - q^{27} - q^{28} + 3 q^{30} + 2 q^{31} + 7 q^{32} - 2 q^{33} - 5 q^{34} - 5 q^{35} + 10 q^{36} - 27 q^{37} + 18 q^{38} - 15 q^{39} - 3 q^{40} + 10 q^{41} - 6 q^{42} + 15 q^{43} + 9 q^{44} + 6 q^{45} - 5 q^{46} - 18 q^{47} + 5 q^{48} - q^{49} + 34 q^{50} + q^{51} + 18 q^{52} + 19 q^{53} + 5 q^{54} - 21 q^{55} - 5 q^{56} + 3 q^{57} - 13 q^{59} + 6 q^{60} - 18 q^{61} - 10 q^{62} - q^{63} + 54 q^{64} + 2 q^{65} + 10 q^{66} - 18 q^{67} - 10 q^{68} + q^{69} - 8 q^{70} + 38 q^{71} + 6 q^{72} + 14 q^{73} + 14 q^{74} + 2 q^{75} + 3 q^{76} - 13 q^{77} + 9 q^{78} + 25 q^{79} + 25 q^{80} - q^{81} - 72 q^{82} - 19 q^{83} - q^{84} + 5 q^{85} + 2 q^{86} + 33 q^{87} + q^{88} - 17 q^{89} + 14 q^{90} - 4 q^{91} + 67 q^{92} - 20 q^{93} + 13 q^{94} + 37 q^{95} + 18 q^{96} - 49 q^{97} - 6 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - q^3 - q^4 - 5 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - q^9 + 3 * q^10 + 9 * q^11 - 12 * q^12 - 15 * q^13 - 6 * q^14 + 6 * q^15 + 5 * q^16 + q^17 - 6 * q^18 - 19 * q^19 - 5 * q^20 - q^21 - 12 * q^22 - 21 * q^23 + 6 * q^24 + 2 * q^25 - 13 * q^26 - q^27 - q^28 + 3 * q^30 + 2 * q^31 + 7 * q^32 - 2 * q^33 - 5 * q^34 - 5 * q^35 + 10 * q^36 - 27 * q^37 + 18 * q^38 - 15 * q^39 - 3 * q^40 + 10 * q^41 - 6 * q^42 + 15 * q^43 + 9 * q^44 + 6 * q^45 - 5 * q^46 - 18 * q^47 + 5 * q^48 - q^49 + 34 * q^50 + q^51 + 18 * q^52 + 19 * q^53 + 5 * q^54 - 21 * q^55 - 5 * q^56 + 3 * q^57 - 13 * q^59 + 6 * q^60 - 18 * q^61 - 10 * q^62 - q^63 + 54 * q^64 + 2 * q^65 + 10 * q^66 - 18 * q^67 - 10 * q^68 + q^69 - 8 * q^70 + 38 * q^71 + 6 * q^72 + 14 * q^73 + 14 * q^74 + 2 * q^75 + 3 * q^76 - 13 * q^77 + 9 * q^78 + 25 * q^79 + 25 * q^80 - q^81 - 72 * q^82 - 19 * q^83 - q^84 + 5 * q^85 + 2 * q^86 + 33 * q^87 + q^88 - 17 * q^89 + 14 * q^90 - 4 * q^91 + 67 * q^92 - 20 * q^93 + 13 * q^94 + 37 * q^95 + 18 * q^96 - 49 * q^97 - 6 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more