LMFDB - Embedded newform 81.2.e.a.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.2
Root			$0.500000 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	81.10
Dual form			81.2.e.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.417037 + 2.36514i) q^{2} +(-3.54056 + 1.28866i) q^{4} +(-0.0713060 - 0.0598329i) q^{5} +(0.544891 + 0.198324i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(0.111776 - 0.193601i) q^{10} +(2.36944 - 1.98820i) q^{11} +(0.729623 - 4.13790i) q^{13} +(-0.241824 + 1.37145i) q^{14} +(2.03816 - 1.71022i) q^{16} +(-0.995493 + 1.72424i) q^{17} +(1.92271 + 3.33023i) q^{19} +(0.329567 + 0.119953i) q^{20} +(5.69050 + 4.77489i) q^{22} +(-4.18428 + 1.52295i) q^{23} +(-0.866736 - 4.91551i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(-1.11126 - 6.30229i) q^{29} +(-1.55754 + 0.566898i) q^{31} +(-1.60967 - 1.35067i) q^{32} +(-4.49323 - 1.63540i) q^{34} +(-0.0269877 - 0.0467441i) q^{35} +(-2.01505 + 3.49016i) q^{37} +(-7.07461 + 5.93630i) q^{38} +(-0.0686240 + 0.389186i) q^{40} +(0.190345 - 1.07950i) q^{41} +(-5.28657 + 4.43596i) q^{43} +(-5.82704 + 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(3.37650 + 1.22894i) q^{47} +(-5.10474 - 4.28338i) q^{49} +(11.2644 - 4.09990i) q^{50} +(2.74906 + 15.5907i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(-0.427492 - 2.42443i) q^{56} +(14.4423 - 5.25657i) q^{58} +(7.87850 + 6.61085i) q^{59} +(12.4005 + 4.51341i) q^{61} +(-1.99034 - 3.44738i) q^{62} +(5.18386 - 8.97871i) q^{64} +(-0.299609 + 0.251402i) q^{65} +(-1.53458 + 8.70304i) q^{67} +(1.30264 - 7.38764i) q^{68} +(0.0993013 - 0.0833237i) q^{70} +(0.572473 - 0.991553i) q^{71} +(-0.0977361 - 0.169284i) q^{73} +(-9.09506 - 3.31033i) q^{74} +(-11.0990 - 9.31317i) q^{76} +(1.68539 - 0.613433i) q^{77} +(-1.25166 - 7.09849i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(2.58744 + 14.6741i) q^{83} +(0.174151 - 0.0633858i) q^{85} +(-12.6963 - 10.6535i) q^{86} +(-12.3399 - 4.49135i) q^{88} +(-0.776563 - 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(12.8521 - 10.7842i) q^{92} +(-1.49850 + 8.49839i) q^{94} +(0.0621565 - 0.352507i) q^{95} +(4.05661 - 3.40390i) q^{97} +(8.00191 - 13.8597i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29}+ \cdots + 45 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.417037	+	2.36514i	0.294890	+	1.67240i	0.667650	+	0.744475i	$0.267300\pi$
$2$	0.417037	+	2.36514i	0.294890	+	1.67240i	−0.372760	+	0.927928i	$0.621589\pi$
$3$		0			0
$3$		0			0
$4$	−3.54056	+	1.28866i	−1.77028	+	0.644329i
$5$	−0.0713060	−	0.0598329i	−0.0318890	−	0.0267581i	0.626704	−	0.779258i	$-0.284404\pi$
$5$	−0.0713060	−	0.0598329i	−0.0318890	−	0.0267581i	−0.658593	+	0.752499i	$0.728848\pi$
$6$		0			0
$7$	0.544891	+	0.198324i	0.205950	+	0.0749595i	0.442935	−	0.896554i	$-0.353937\pi$
$7$	0.544891	+	0.198324i	0.205950	+	0.0749595i	−0.236986	+	0.971513i	$0.576159\pi$
$8$	−2.12277	−	3.67675i	−0.750514	−	1.29993i
$9$		0			0
$10$	0.111776	−	0.193601i	0.0353465	−	0.0612220i
$11$	2.36944	−	1.98820i	0.714413	−	0.599464i	−0.211421	−	0.977395i	$-0.567809\pi$
$11$	2.36944	−	1.98820i	0.714413	−	0.599464i	0.925834	+	0.377932i	$0.123365\pi$
$12$		0			0
$13$	0.729623	−	4.13790i	0.202361	−	1.14765i	−0.699178	−	0.714948i	$-0.746450\pi$
$13$	0.729623	−	4.13790i	0.202361	−	1.14765i	0.901539	−	0.432699i	$-0.142439\pi$
$14$	−0.241824	+	1.37145i	−0.0646301	+	0.366536i
$15$		0			0
$16$	2.03816	−	1.71022i	0.509540	−	0.427555i
$17$	−0.995493	+	1.72424i	−0.241443	+	0.418191i	−0.961125	−	0.276112i	$-0.910954\pi$
$17$	−0.995493	+	1.72424i	−0.241443	+	0.418191i	0.719683	+	0.694303i	$0.244287\pi$
$18$		0			0
$19$	1.92271	+	3.33023i	0.441100	+	0.764008i	0.997771	−	0.0667249i	$-0.0212550\pi$
$19$	1.92271	+	3.33023i	0.441100	+	0.764008i	−0.556671	+	0.830733i	$0.687922\pi$
$20$	0.329567	+	0.119953i	0.0736935	+	0.0268222i
$21$		0			0
$22$	5.69050	+	4.77489i	1.21322	+	1.01801i
$23$	−4.18428	+	1.52295i	−0.872482	+	0.317558i	−0.739172	−	0.673517i	$-0.764783\pi$
$23$	−4.18428	+	1.52295i	−0.872482	+	0.317558i	−0.133310	+	0.991074i	$0.542561\pi$
$24$		0			0
$25$	−0.866736	−	4.91551i	−0.173347	−	0.983101i
$26$	10.0910			1.97900
$27$		0			0
$28$	−2.18479			−0.412887
$29$	−1.11126	−	6.30229i	−0.206356	−	1.17031i	−0.895291	−	0.445482i	$-0.853032\pi$
$29$	−1.11126	−	6.30229i	−0.206356	−	1.17031i	0.688935	−	0.724823i	$-0.258079\pi$
$30$		0			0
$31$	−1.55754	+	0.566898i	−0.279743	+	0.101818i	−0.478081	−	0.878316i	$-0.658668\pi$
$31$	−1.55754	+	0.566898i	−0.279743	+	0.101818i	0.198339	+	0.980134i	$0.436445\pi$
$32$	−1.60967	−	1.35067i	−0.284552	−	0.238767i
$33$		0			0
$34$	−4.49323	−	1.63540i	−0.770582	−	0.280469i
$35$	−0.0269877	−	0.0467441i	−0.00456176	−	0.00790120i
$36$		0			0
$37$	−2.01505	+	3.49016i	−0.331272	+	0.573779i	−0.982761	−	0.184878i	$-0.940811\pi$
$37$	−2.01505	+	3.49016i	−0.331272	+	0.573779i	0.651490	+	0.758657i	$0.274144\pi$
$38$	−7.07461	+	5.93630i	−1.14765	+	0.962996i
$39$		0			0
$40$	−0.0686240	+	0.389186i	−0.0108504	+	0.0615358i
$41$	0.190345	−	1.07950i	0.0297270	−	0.168590i	−0.966330	−	0.257306i	$-0.917165\pi$
$41$	0.190345	−	1.07950i	0.0297270	−	0.168590i	0.996057	+	0.0887159i	$0.0282763\pi$
$42$		0			0
$43$	−5.28657	+	4.43596i	−0.806194	+	0.676477i	−0.949696	−	0.313173i	$-0.898608\pi$
$43$	−5.28657	+	4.43596i	−0.806194	+	0.676477i	0.143502	+	0.989650i	$0.454164\pi$
$44$	−5.82704	+	10.0927i	−0.878459	+	1.52154i
$45$		0			0
$46$	−5.34699	−	9.26126i	−0.788370	−	1.36550i
$47$	3.37650	+	1.22894i	0.492513	+	0.179260i	0.576323	−	0.817222i	$-0.304487\pi$
$47$	3.37650	+	1.22894i	0.492513	+	0.179260i	−0.0838106	+	0.996482i	$0.526709\pi$
$48$		0			0
$49$	−5.10474	−	4.28338i	−0.729248	−	0.611912i
$50$	11.2644	−	4.09990i	1.59302	−	0.579813i
$51$		0			0
$52$	2.74906	+	15.5907i	0.381226	+	2.16204i
$53$	−5.40034			−0.741793			−0.370897	−	0.928674i	$-0.620950\pi$
$53$	−5.40034			−0.741793			−0.370897	+	0.928674i	$0.620950\pi$
$54$		0			0
$55$	−0.287915			−0.0388224
$56$	−0.427492	−	2.42443i	−0.0571260	−	0.323978i
$57$		0			0
$58$	14.4423	−	5.25657i	1.89637	−	0.690222i
$59$	7.87850	+	6.61085i	1.02569	+	0.860659i	0.990332	−	0.138715i	$-0.0442973\pi$
$59$	7.87850	+	6.61085i	1.02569	+	0.860659i	0.0353615	+	0.999375i	$0.488742\pi$
$60$		0			0
$61$	12.4005	+	4.51341i	1.58772	+	0.577883i	0.976864	−	0.213860i	$-0.0686036\pi$
$61$	12.4005	+	4.51341i	1.58772	+	0.577883i	0.610855	+	0.791742i	$0.290826\pi$
$62$	−1.99034	−	3.44738i	−0.252774	−	0.437817i
$63$		0			0
$64$	5.18386	−	8.97871i	0.647982	−	1.12234i
$65$	−0.299609	+	0.251402i	−0.0371619	+	0.0311825i
$66$		0			0
$67$	−1.53458	+	8.70304i	−0.187479	+	1.06324i	0.735250	+	0.677796i	$0.237065\pi$
$67$	−1.53458	+	8.70304i	−0.187479	+	1.06324i	−0.922729	+	0.385449i	$0.874046\pi$
$68$	1.30264	−	7.38764i	0.157968	−	0.895883i
$69$		0			0
$70$	0.0993013	−	0.0833237i	0.0118688	−	0.00995909i
$71$	0.572473	−	0.991553i	0.0679401	−	0.117676i	−0.830054	−	0.557683i	$-0.811691\pi$
$71$	0.572473	−	0.991553i	0.0679401	−	0.117676i	0.897994	+	0.440007i	$0.145024\pi$
$72$		0			0
$73$	−0.0977361	−	0.169284i	−0.0114391	−	0.0198132i	0.860249	−	0.509874i	$-0.170308\pi$
$73$	−0.0977361	−	0.169284i	−0.0114391	−	0.0198132i	−0.871688	+	0.490061i	$0.836975\pi$
$74$	−9.09506	−	3.31033i	−1.05728	−	0.384818i
$75$		0			0
$76$	−11.0990	−	9.31317i	−1.27314	−	1.06829i
$77$	1.68539	−	0.613433i	0.192069	−	0.0699072i
$78$		0			0
$79$	−1.25166	−	7.09849i	−0.140822	−	0.798642i	−0.970627	−	0.240589i	$-0.922659\pi$
$79$	−1.25166	−	7.09849i	−0.140822	−	0.798642i	0.829805	−	0.558054i	$-0.188452\pi$
$80$	−0.247661			−0.0276893
$81$		0			0
$82$	2.63255			0.290717
$83$	2.58744	+	14.6741i	0.284008	+	1.61069i	0.708808	+	0.705402i	$0.249233\pi$
$83$	2.58744	+	14.6741i	0.284008	+	1.61069i	−0.424800	+	0.905287i	$0.639656\pi$
$84$		0			0
$85$	0.174151	−	0.0633858i	0.0188893	−	0.00687516i
$86$	−12.6963	−	10.6535i	−1.36908	−	1.14879i
$87$		0			0
$88$	−12.3399	−	4.49135i	−1.31544	−	0.478780i
$89$	−0.776563	−	1.34505i	−0.0823155	−	0.142575i	0.821929	−	0.569590i	$-0.192898\pi$
$89$	−0.776563	−	1.34505i	−0.0823155	−	0.142575i	−0.904244	+	0.427016i	$0.859565\pi$
$90$		0			0
$91$	1.21821	−	2.11000i	0.127703	−	0.221189i
$92$	12.8521	−	10.7842i	1.33993	−	1.12433i
$93$		0			0
$94$	−1.49850	+	8.49839i	−0.154558	+	0.876542i
$95$	0.0621565	−	0.352507i	0.00637712	−	0.0361665i
$96$		0			0
$97$	4.05661	−	3.40390i	0.411887	−	0.345614i	−0.413180	−	0.910649i	$-0.635582\pi$
$97$	4.05661	−	3.40390i	0.411887	−	0.345614i	0.825067	+	0.565035i	$0.191137\pi$
$98$	8.00191	−	13.8597i	0.808315	−	1.40004i
$99$		0			0
$100$	9.40314	+	16.2867i	0.940314	+	1.62867i
$101$	−6.83061	−	2.48614i	−0.679671	−	0.247380i	−0.0209647	−	0.999780i	$-0.506674\pi$
$101$	−6.83061	−	2.48614i	−0.679671	−	0.247380i	−0.658706	+	0.752400i	$0.728896\pi$
$102$		0			0
$103$	4.90374	+	4.11472i	0.483179	+	0.405436i	0.851574	−	0.524234i	$-0.175648\pi$
$103$	4.90374	+	4.11472i	0.483179	+	0.405436i	−0.368395	+	0.929669i	$0.620093\pi$
$104$	−16.7629	+	6.10118i	−1.64373	+	0.598270i
$105$		0			0
$106$	−2.25214	−	12.7725i	−0.218747	−	1.24058i
$107$	5.54365			0.535925			0.267963	−	0.963429i	$-0.413650\pi$
$107$	5.54365			0.535925			0.267963	+	0.963429i	$0.413650\pi$
$108$		0			0
$109$	−6.23137			−0.596857			−0.298428	−	0.954432i	$-0.596462\pi$
$109$	−6.23137			−0.596857			−0.298428	+	0.954432i	$0.596462\pi$
$110$	−0.120071	−	0.680957i	−0.0114483	−	0.0649267i
$111$		0			0
$112$	1.44975	−	0.527668i	0.136989	−	0.0498599i
$113$	9.07301	+	7.61316i	0.853517	+	0.716186i	0.960561	−	0.278068i	$-0.0896941\pi$
$113$	9.07301	+	7.61316i	0.853517	+	0.716186i	−0.107044	+	0.994254i	$0.534139\pi$
$114$		0			0
$115$	0.389487	+	0.141762i	0.0363198	+	0.0132193i
$116$	12.0560	+	20.8816i	1.11937	+	1.93881i
$117$		0			0
$118$	−12.3499	+	21.3907i	−1.13690	+	1.96917i
$119$	−0.884395	+	0.742096i	−0.0810724	+	0.0680278i
$120$		0			0
$121$	−0.248809	+	1.41107i	−0.0226190	+	0.128279i
$122$	−5.50336	+	31.2111i	−0.498250	+	2.82572i
$123$		0			0
$124$	4.78403	−	4.01427i	0.429618	−	0.360492i
$125$	−0.465014	+	0.805428i	−0.0415921	+	0.0720396i
$126$		0			0
$127$	−5.76469	−	9.98473i	−0.511533	−	0.886002i	−0.999911	−	0.0133693i	$-0.995744\pi$
$127$	−5.76469	−	9.98473i	−0.511533	−	0.886002i	0.488377	−	0.872633i	$-0.337589\pi$
$128$	19.4486	+	7.07872i	1.71903	+	0.625676i
$129$		0			0
$130$	−0.719547	−	0.603772i	−0.0631085	−	0.0529543i
$131$	−8.46830	+	3.08221i	−0.739879	+	0.269294i	−0.684340	−	0.729163i	$-0.739910\pi$
$131$	−8.46830	+	3.08221i	−0.739879	+	0.269294i	−0.0555383	+	0.998457i	$0.517688\pi$
$132$		0			0
$133$	0.387203	+	2.19594i	0.0335747	+	0.190412i
$134$	−21.2238			−1.83346
$135$		0			0
$136$	8.45283			0.724824
$137$	−2.00047	−	11.3452i	−0.170911	−	0.969287i	−0.942758	−	0.333478i	$-0.891778\pi$
$137$	−2.00047	−	11.3452i	−0.170911	−	0.969287i	0.771846	−	0.635809i	$-0.219333\pi$
$138$		0			0
$139$	−1.60108	+	0.582746i	−0.135802	+	0.0494279i	−0.409027	−	0.912522i	$-0.634132\pi$
$139$	−1.60108	+	0.582746i	−0.135802	+	0.0494279i	0.273225	+	0.961950i	$0.411910\pi$
$140$	0.155789	+	0.130722i	0.0131666	+	0.0110481i
$141$		0			0
$142$	2.58390	+	0.940462i	0.216836	+	0.0789219i
$143$	−6.49816	−	11.2551i	−0.543403	−	0.941202i
$144$		0			0
$145$	−0.297844	+	0.515881i	−0.0247346	+	0.0428416i
$146$	0.359620	−	0.301757i	0.0297623	−	0.0249736i
$147$		0			0
$148$	2.63677	−	14.9538i	0.216741	−	1.22920i
$149$	3.75996	−	21.3238i	0.308028	−	1.74691i	−0.300869	−	0.953666i	$-0.597277\pi$
$149$	3.75996	−	21.3238i	0.308028	−	1.74691i	0.608897	−	0.793249i	$-0.291612\pi$
$150$		0			0
$151$	−3.63222	+	3.04779i	−0.295586	+	0.248026i	−0.778504	−	0.627640i	$-0.784021\pi$
$151$	−3.63222	+	3.04779i	−0.295586	+	0.248026i	0.482918	+	0.875665i	$0.339577\pi$
$152$	8.16296	−	14.1387i	0.662104	−	1.14680i
$153$		0			0
$154$	2.15373	+	3.73036i	0.173552	+	0.300601i
$155$	0.144981	+	0.0527688i	0.0116452	+	0.00423849i
$156$		0			0
$157$	−0.160261	−	0.134475i	−0.0127902	−	0.0107323i	0.636370	−	0.771384i	$-0.280435\pi$
$157$	−0.160261	−	0.134475i	−0.0127902	−	0.0107323i	−0.649160	+	0.760652i	$0.724880\pi$
$158$	16.2669	−	5.92067i	1.29412	−	0.471023i
$159$		0			0
$160$	0.0339644	+	0.192622i	0.00268513	+	0.0152281i
$161$	−2.58202			−0.203491
$162$		0			0
$163$	5.62384			0.440493			0.220247	−	0.975444i	$-0.429314\pi$
$163$	5.62384			0.440493			0.220247	+	0.975444i	$0.429314\pi$
$164$	0.717181	+	4.06733i	0.0560024	+	0.317605i
$165$		0			0
$166$	−33.6271	+	12.2393i	−2.60997	+	0.949951i
$167$	−12.7780	−	10.7220i	−0.988791	−	0.829695i	−0.00339914	−	0.999994i	$-0.501082\pi$
$167$	−12.7780	−	10.7220i	−0.988791	−	0.829695i	−0.985392	+	0.170300i	$0.945526\pi$
$168$		0			0
$169$	−4.37386	−	1.59195i	−0.336451	−	0.122458i
$170$	0.222544	+	0.385457i	0.0170683	+	0.0295632i
$171$		0			0
$172$	13.0010	−	22.5183i	0.991315	−	1.71701i
$173$	−14.5565	+	12.2143i	−1.10671	+	0.928639i	−0.997858	−	0.0654187i	$-0.979162\pi$
$173$	−14.5565	+	12.2143i	−1.10671	+	0.928639i	−0.108851	+	0.994058i	$0.534717\pi$
$174$		0			0
$175$	0.502587	−	2.85031i	0.0379920	−	0.215463i
$176$	1.42905	−	8.10453i	0.107718	−	0.610902i
$177$		0			0
$178$	2.85736	−	2.39761i	0.214168	−	0.179709i
$179$	8.11761	−	14.0601i	0.606739	−	1.05090i	−0.385035	−	0.922902i	$-0.625811\pi$
$179$	8.11761	−	14.0601i	0.606739	−	1.05090i	0.991774	−	0.128001i	$-0.0408560\pi$
$180$		0			0
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	0.916247	−	0.400614i	$-0.131203\pi$
$181$	1.49579	+	2.59078i	0.111181	+	0.192571i	−0.805066	+	0.593186i	$0.797870\pi$
$182$	5.49848	+	2.00128i	0.407575	+	0.148345i
$183$		0			0
$184$	14.4818	+	12.1517i	1.06761	+	0.895833i
$185$	0.352512	−	0.128304i	0.0259172	−	0.00943308i
$186$		0			0
$187$	1.06938	+	6.06473i	0.0782005	+	0.443497i
$188$	−13.5384			−0.987388
$189$		0			0
$190$	0.859649			0.0623655
$191$	0.391371	+	2.21958i	0.0283186	+	0.160603i	0.995688	−	0.0927685i	$-0.0295716\pi$
$191$	0.391371	+	2.21958i	0.0283186	+	0.160603i	−0.967369	+	0.253371i	$0.918461\pi$
$192$		0			0
$193$	0.827186	−	0.301071i	0.0595422	−	0.0216716i	−0.312077	−	0.950057i	$-0.601025\pi$
$193$	0.827186	−	0.301071i	0.0595422	−	0.0216716i	0.371620	+	0.928385i	$0.378803\pi$
$194$	9.74245	+	8.17489i	0.699467	+	0.586923i
$195$		0			0
$196$	23.5934	+	8.58731i	1.68525	+	0.613379i
$197$	10.1383	+	17.5600i	0.722322	+	1.25110i	0.960067	+	0.279771i	$0.0902586\pi$
$197$	10.1383	+	17.5600i	0.722322	+	1.25110i	−0.237744	+	0.971328i	$0.576408\pi$
$198$		0			0
$199$	9.50472	−	16.4627i	0.673772	−	1.16701i	−0.303054	−	0.952973i	$-0.598006\pi$
$199$	9.50472	−	16.4627i	0.673772	−	1.16701i	0.976826	−	0.214034i	$-0.0686603\pi$
$200$	−16.2332	+	13.6213i	−1.14786	+	0.963170i
$201$		0			0
$202$	3.03144	−	17.1921i	0.213291	−	1.20963i
$203$	0.644379	−	3.65445i	0.0452265	−	0.256492i
$204$		0			0
$205$	−0.0781625	+	0.0655862i	−0.00545911	+	0.00458074i
$206$	−7.68684	+	13.3140i	−0.535567	+	0.927630i
$207$		0			0
$208$	−5.58963	−	9.68152i	−0.387571	−	0.671293i
$209$	11.1769	+	4.06806i	0.773123	+	0.281394i
$210$		0			0
$211$	12.3977	+	10.4029i	0.853494	+	0.716166i	0.960556	−	0.278086i	$-0.0897000\pi$
$211$	12.3977	+	10.4029i	0.853494	+	0.716166i	−0.107062	+	0.994252i	$0.534144\pi$
$212$	19.1202	−	6.95919i	1.31318	−	0.477959i
$213$		0			0
$214$	2.31191	+	13.1115i	0.158039	+	0.896283i
$215$	0.642380			0.0438100
$216$		0			0
$217$	−0.961120			−0.0652451
$218$	−2.59871	−	14.7380i	−0.176007	−	0.998186i
$219$		0			0
$220$	1.01938	−	0.371024i	0.0687265	−	0.0250144i
$221$	6.40842	+	5.37730i	0.431077	+	0.361716i
$222$		0			0
$223$	−20.1633	−	7.33883i	−1.35023	−	0.491444i	−0.437212	−	0.899359i	$-0.644034\pi$
$223$	−20.1633	−	7.33883i	−1.35023	−	0.491444i	−0.913020	+	0.407914i	$0.866256\pi$
$224$	−0.609223	−	1.05520i	−0.0407054	−	0.0705038i
$225$		0			0
$226$	−14.2224	+	24.6339i	−0.946058	+	1.63862i
$227$	14.6424	−	12.2864i	0.971848	−	0.815477i	−0.0109918	−	0.999940i	$-0.503499\pi$
$227$	14.6424	−	12.2864i	0.971848	−	0.815477i	0.982840	+	0.184462i	$0.0590544\pi$
$228$		0			0
$229$	3.90190	−	22.1288i	0.257845	−	1.46231i	−0.530818	−	0.847486i	$-0.678115\pi$
$229$	3.90190	−	22.1288i	0.257845	−	1.46231i	0.788663	−	0.614826i	$-0.210774\pi$
$230$	−0.172855	+	0.980309i	−0.0113977	+	0.0646397i
$231$		0			0
$232$	−20.8130	+	17.4642i	−1.36644	+	1.14658i
$233$	−8.84074	+	15.3126i	−0.579176	+	1.00316i	0.416398	+	0.909182i	$0.363292\pi$
$233$	−8.84074	+	15.3126i	−0.579176	+	1.00316i	−0.995574	+	0.0939796i	$0.970041\pi$
$234$		0			0
$235$	−0.167233	−	0.289657i	−0.0109091	−	0.0188951i
$236$	−36.4134	−	13.2534i	−2.37031	−	0.862723i
$237$		0			0
$238$	−2.12398	−	1.78223i	−0.137677	−	0.115525i
$239$	−14.4904	+	5.27406i	−0.937303	+	0.341151i	−0.765100	−	0.643911i	$-0.777311\pi$
$239$	−14.4904	+	5.27406i	−0.937303	+	0.341151i	−0.172203	+	0.985061i	$0.555088\pi$
$240$		0			0
$241$	2.28373	+	12.9516i	0.147108	+	0.834289i	0.965651	+	0.259844i	$0.0836711\pi$
$241$	2.28373	+	12.9516i	0.147108	+	0.834289i	−0.818543	+	0.574445i	$0.805218\pi$
$242$	−3.44113			−0.221204
$243$		0			0
$244$	−49.7209			−3.18305
$245$	0.107711	+	0.610862i	0.00688143	+	0.0390265i
$246$		0			0
$247$	15.1830	−	5.52617i	0.966073	−	0.351622i
$248$	5.39065	+	4.52329i	0.342307	+	0.287229i
$249$		0			0
$250$	−2.09887	−	0.763927i	−0.132744	−	0.0483150i
$251$	8.70830	+	15.0832i	0.549663	+	0.952045i	0.998297	+	0.0583292i	$0.0185773\pi$
$251$	8.70830	+	15.0832i	0.549663	+	0.952045i	−0.448634	+	0.893716i	$0.648089\pi$
$252$		0			0
$253$	−6.88646	+	11.9277i	−0.432948	+	0.749889i
$254$	21.2112	−	17.7983i	1.33091	−	1.11676i
$255$		0			0
$256$	−5.03066	+	28.5303i	−0.314416	+	1.78314i
$257$	−1.94270	+	11.0176i	−0.121182	+	0.687260i	0.862320	+	0.506364i	$0.169011\pi$
$257$	−1.94270	+	11.0176i	−0.121182	+	0.687260i	−0.983502	+	0.180896i	$0.942100\pi$
$258$		0			0
$259$	−1.79017	+	1.50213i	−0.111236	+	0.0933377i
$260$	0.736812	−	1.27620i	0.0456952	−	0.0791463i
$261$		0			0
$262$	−10.8214	−	18.7433i	−0.668550	−	1.15796i
$263$	−19.4619	−	7.08354i	−1.20007	−	0.436790i	−0.336821	−	0.941569i	$-0.609352\pi$
$263$	−19.4619	−	7.08354i	−1.20007	−	0.436790i	−0.863249	+	0.504779i	$0.831574\pi$
$264$		0			0
$265$	0.385077	+	0.323118i	0.0236551	+	0.0198490i
$266$	−5.03221	+	1.83157i	−0.308544	+	0.112301i
$267$		0			0
$268$	−5.78197	−	32.7912i	−0.353190	−	2.00304i
$269$	28.2449			1.72212			0.861060	−	0.508504i	$-0.169801\pi$
$269$	28.2449			1.72212			0.861060	+	0.508504i	$0.169801\pi$
$270$		0			0
$271$	17.2626			1.04863			0.524316	−	0.851524i	$-0.324321\pi$
$271$	17.2626			1.04863			0.524316	+	0.851524i	$0.324321\pi$
$272$	0.919863	+	5.21680i	0.0557749	+	0.316315i
$273$		0			0
$274$	25.9987	−	9.46275i	1.57064	−	0.571666i
$275$	−11.8267	−	9.92375i	−0.713175	−	0.598425i
$276$		0			0
$277$	−4.85725	−	1.76789i	−0.291844	−	0.106222i	0.191949	−	0.981405i	$-0.438519\pi$
$277$	−4.85725	−	1.76789i	−0.291844	−	0.106222i	−0.483793	+	0.875182i	$0.660741\pi$
$278$	−2.04598	−	3.54375i	−0.122710	−	0.212540i
$279$		0			0
$280$	−0.114578	+	0.198454i	−0.00684733	+	0.0118599i
$281$	2.52522	−	2.11891i	0.150642	−	0.126404i	−0.564352	−	0.825534i	$-0.690874\pi$
$281$	2.52522	−	2.11891i	0.150642	−	0.126404i	0.714994	+	0.699131i	$0.246429\pi$
$282$		0			0
$283$	−1.58553	+	8.99200i	−0.0942501	+	0.534519i	0.900724	+	0.434391i	$0.143036\pi$
$283$	−1.58553	+	8.99200i	−0.0942501	+	0.534519i	−0.994975	+	0.100128i	$0.968075\pi$
$284$	−0.749103	+	4.24837i	−0.0444511	+	0.252095i
$285$		0			0
$286$	23.9099	−	20.0628i	1.41382	−	1.18634i
$287$	0.317809	−	0.550462i	0.0187597	−	0.0324927i
$288$		0			0
$289$	6.51799	+	11.2895i	0.383411	+	0.664087i
$290$	−1.34434	−	0.489300i	−0.0789424	−	0.0287327i
$291$		0			0
$292$	0.564189	+	0.473411i	0.0330167	+	0.0277043i
$293$	−2.65598	+	0.966697i	−0.155164	+	0.0564750i	−0.418434	−	0.908247i	$-0.637421\pi$
$293$	−2.65598	+	0.966697i	−0.155164	+	0.0564750i	0.263271	+	0.964722i	$0.415199\pi$
$294$		0			0
$295$	−0.166239	−	0.942787i	−0.00967880	−	0.0548912i
$296$	17.1100			0.994496
$297$		0			0
$298$	52.0017			3.01238
$299$	3.24888	+	18.4253i	0.187887	+	1.06556i
$300$		0			0
$301$	−3.76036	+	1.36866i	−0.216744	+	0.0788882i
$302$	−8.72321	−	7.31964i	−0.501964	−	0.421198i
$303$		0			0
$304$	9.61423	+	3.49929i	0.551414	+	0.200698i
$305$	−0.614179	−	1.06379i	−0.0351678	−	0.0609124i
$306$		0			0
$307$	−3.14723	+	5.45116i	−0.179622	+	0.311114i	−0.941751	−	0.336311i	$-0.890821\pi$
$307$	−3.14723	+	5.45116i	−0.179622	+	0.311114i	0.762129	+	0.647425i	$0.224154\pi$
$308$	−5.17673	+	4.34380i	−0.294972	+	0.247511i
$309$		0			0
$310$	−0.0643429	+	0.364907i	−0.00365443	+	0.0207253i
$311$	1.28029	−	7.26088i	0.0725985	−	0.411727i	−0.926751	−	0.375675i	$-0.877411\pi$
$311$	1.28029	−	7.26088i	0.0725985	−	0.411727i	0.999350	−	0.0360515i	$-0.0114780\pi$
$312$		0			0
$313$	−3.27159	+	2.74519i	−0.184921	+	0.155167i	−0.730549	−	0.682860i	$-0.760736\pi$
$313$	−3.27159	+	2.74519i	−0.184921	+	0.155167i	0.545628	+	0.838028i	$0.316291\pi$
$314$	0.251217	−	0.435120i	0.0141770	−	0.0245552i
$315$		0			0
$316$	13.5791	+	23.5197i	0.763883	+	1.32308i
$317$	15.1738	+	5.52279i	0.852243	+	0.310191i	0.730954	−	0.682426i	$-0.239075\pi$
$317$	15.1738	+	5.52279i	0.852243	+	0.310191i	0.121288	+	0.992617i	$0.461297\pi$
$318$		0			0
$319$	−15.1632	−	12.7235i	−0.848979	−	0.712378i
$320$	−0.906862	+	0.330071i	−0.0506951	+	0.0184515i
$321$		0			0
$322$	−1.07680	−	6.10682i	−0.0600075	−	0.340320i
$323$	−7.65618			−0.426001
$324$		0			0
$325$	−20.9723			−1.16333
$326$	2.34535	+	13.3012i	0.129897	+	0.736683i
$327$		0			0
$328$	−4.37313	+	1.59169i	−0.241465	+	0.0878862i
$329$	1.59610	+	1.33928i	0.0879956	+	0.0738371i
$330$		0			0
$331$	−18.0686	−	6.57644i	−0.993142	−	0.361474i	−0.206206	−	0.978509i	$-0.566112\pi$
$331$	−18.0686	−	6.57644i	−0.993142	−	0.361474i	−0.786936	+	0.617035i	$0.788334\pi$
$332$	−28.0708	−	48.6201i	−1.54059	−	2.66838i
$333$		0			0
$334$	20.0301	−	34.6932i	1.09600	−	1.89833i
$335$	0.630152	−	0.528761i	0.0344289	−	0.0288893i
$336$		0			0
$337$	−5.11615	+	29.0152i	−0.278695	+	1.58056i	0.448281	+	0.893893i	$0.352036\pi$
$337$	−5.11615	+	29.0152i	−0.278695	+	1.58056i	−0.726976	+	0.686663i	$0.759075\pi$
$338$	1.94112	−	11.0087i	0.105583	−	0.598792i
$339$		0			0
$340$	−0.534910	+	0.448843i	−0.0290096	+	0.0243419i
$341$	−2.56339	+	4.43993i	−0.138815	+	0.240435i
$342$		0			0
$343$	−3.96154	−	6.86159i	−0.213903	−	0.370491i
$344$	27.5321	+	10.0209i	1.48443	+	0.540289i
$345$		0			0
$346$	−34.9592	−	29.3342i	−1.87942	−	1.57702i
$347$	10.7097	−	3.89801i	0.574927	−	0.209256i	−0.0381600	−	0.999272i	$-0.512150\pi$
$347$	10.7097	−	3.89801i	0.574927	−	0.209256i	0.613087	+	0.790015i	$0.289927\pi$
$348$		0			0
$349$	4.89021	+	27.7338i	0.261767	+	1.48456i	0.778085	+	0.628158i	$0.216191\pi$
$349$	4.89021	+	27.7338i	0.261767	+	1.48456i	−0.516318	+	0.856397i	$0.672698\pi$
$350$	6.95097			0.371545
$351$		0			0
$352$	−6.49941			−0.346419
$353$	−4.97573	−	28.2188i	−0.264831	−	1.50193i	−0.769515	−	0.638629i	$-0.779502\pi$
$353$	−4.97573	−	28.2188i	−0.264831	−	1.50193i	0.504683	−	0.863305i	$-0.331609\pi$
$354$		0			0
$355$	−0.100148	+	0.0364510i	−0.00531532	+	0.00193462i
$356$	4.48277	+	3.76149i	0.237586	+	0.199359i
$357$		0			0
$358$	36.6394	+	13.3357i	1.93645	+	0.704812i
$359$	−15.5161	−	26.8747i	−0.818909	−	1.41839i	−0.906486	−	0.422235i	$-0.861246\pi$
$359$	−15.5161	−	26.8747i	−0.818909	−	1.41839i	0.0875770	−	0.996158i	$-0.472088\pi$
$360$		0			0
$361$	2.10636	−	3.64833i	0.110861	−	0.192017i
$362$	−5.50376	+	4.61820i	−0.289271	+	0.242727i
$363$		0			0
$364$	−1.59408	+	9.04045i	−0.0835523	+	0.473848i
$365$	−0.00315957	+	0.0179188i	−0.000165379	+	0.000937912i
$366$		0			0
$367$	18.4802	−	15.5067i	0.964660	−	0.809446i	−0.0170450	−	0.999855i	$-0.505426\pi$
$367$	18.4802	−	15.5067i	0.964660	−	0.809446i	0.981705	+	0.190409i	$0.0609814\pi$
$368$	−5.92365	+	10.2601i	−0.308791	+	0.534843i
$369$		0			0
$370$	0.450466	+	0.780230i	0.0234186	+	0.0405622i
$371$	−2.94260	−	1.07102i	−0.152772	−	0.0556045i
$372$		0			0
$373$	−9.64114	−	8.08988i	−0.499199	−	0.418878i	0.358110	−	0.933679i	$-0.383421\pi$
$373$	−9.64114	−	8.08988i	−0.499199	−	0.418878i	−0.857309	+	0.514801i	$0.827866\pi$
$374$	−13.8979	+	5.05843i	−0.718645	+	0.261565i
$375$		0			0
$376$	−2.64902	−	15.0233i	−0.136613	−	0.774769i
$377$	−26.8890			−1.38486
$378$		0			0
$379$	−7.70522			−0.395790			−0.197895	−	0.980223i	$-0.563411\pi$
$379$	−7.70522			−0.395790			−0.197895	+	0.980223i	$0.563411\pi$
$380$	0.234192	+	1.32817i	0.0120138	+	0.0681337i
$381$		0			0
$382$	−5.08638	+	1.85129i	−0.260242	+	0.0947203i
$383$	13.6828	+	11.4812i	0.699159	+	0.586664i	0.921534	−	0.388297i	$-0.126937\pi$
$383$	13.6828	+	11.4812i	0.699159	+	0.586664i	−0.222376	+	0.974961i	$0.571381\pi$
$384$		0			0
$385$	−0.156882	−	0.0571005i	−0.00799546	−	0.00291011i
$386$	1.05704	+	1.83085i	0.0538020	+	0.0931878i
$387$		0			0
$388$	−9.97622	+	17.2793i	−0.506466	+	0.877224i
$389$	−20.9808	+	17.6050i	−1.06377	+	0.892607i	−0.994473	−	0.104989i	$-0.966519\pi$
$389$	−20.9808	+	17.6050i	−1.06377	+	0.892607i	−0.0692941	+	0.997596i	$0.522075\pi$
$390$		0			0
$391$	1.53948	−	8.73081i	0.0778547	−	0.441536i
$392$	−4.91274	+	27.8615i	−0.248131	+	1.40722i
$393$		0			0
$394$	−37.3038	+	31.3016i	−1.87934	+	1.57695i
$395$	−0.335472	+	0.581055i	−0.0168794	+	0.0292361i
$396$		0			0
$397$	−2.10799	−	3.65115i	−0.105797	−	0.183246i	0.808266	−	0.588817i	$-0.200406\pi$
$397$	−2.10799	−	3.65115i	−0.105797	−	0.183246i	−0.914064	+	0.405571i	$0.867073\pi$
$398$	42.9002	+	15.6144i	2.15039	+	0.782680i
$399$		0			0
$400$	−10.1731	−	8.53628i	−0.508657	−	0.426814i
$401$	14.2575	−	5.18930i	0.711985	−	0.259141i	0.0394656	−	0.999221i	$-0.487434\pi$
$401$	14.2575	−	5.18930i	0.711985	−	0.259141i	0.672519	+	0.740080i	$0.265212\pi$
$402$		0			0
$403$	1.20935	+	6.85857i	0.0602420	+	0.341650i
$404$	27.3880			1.36260
$405$		0			0
$406$	8.91200			0.442295
$407$	2.16460	+	12.2760i	0.107295	+	0.608501i
$408$		0			0
$409$	−4.42559	+	1.61078i	−0.218831	+	0.0796481i	−0.449109	−	0.893477i	$-0.648259\pi$
$409$	−4.42559	+	1.61078i	−0.218831	+	0.0796481i	0.230278	+	0.973125i	$0.426036\pi$
$410$	−0.187717	−	0.157513i	−0.00927067	−	0.00777902i
$411$		0			0
$412$	−22.6644	−	8.24918i	−1.11660	−	0.406408i
$413$	2.98184	+	5.16469i	0.146727	+	0.254138i
$414$		0			0
$415$	0.693492	−	1.20116i	0.0340422	−	0.0589628i
$416$	−6.76339	+	5.67516i	−0.331602	+	0.278248i
$417$		0			0
$418$	−4.96033	+	28.1314i	−0.242618	+	1.37595i
$419$	−3.43669	+	19.4905i	−0.167894	+	0.952171i	0.778137	+	0.628094i	$0.216165\pi$
$419$	−3.43669	+	19.4905i	−0.167894	+	0.952171i	−0.946031	+	0.324077i	$0.894946\pi$
$420$		0			0
$421$	21.5915	−	18.1174i	1.05231	−	0.882989i	0.0589715	−	0.998260i	$-0.481218\pi$
$421$	21.5915	−	18.1174i	1.05231	−	0.882989i	0.993334	+	0.115270i	$0.0367734\pi$
$422$	−19.4340	+	33.6607i	−0.946032	+	1.63858i
$423$		0			0
$424$	11.4637	+	19.8557i	0.556726	+	0.964278i
$425$	9.33836	+	3.39889i	0.452977	+	0.164870i
$426$		0			0
$427$	5.86180	+	4.91863i	0.283672	+	0.238029i
$428$	−19.6276	+	7.14387i	−0.948737	+	0.345312i
$429$		0			0
$430$	0.267896	+	1.51932i	0.0129191	+	0.0732679i
$431$	5.19681			0.250321			0.125161	−	0.992136i	$-0.460055\pi$
$431$	5.19681			0.250321			0.125161	+	0.992136i	$0.460055\pi$
$432$		0			0
$433$	25.3285			1.21721			0.608605	−	0.793473i	$-0.291730\pi$
$433$	25.3285			1.21721			0.608605	+	0.793473i	$0.291730\pi$
$434$	−0.400823	−	2.27318i	−0.0192401	−	0.109116i
$435$		0			0
$436$	22.0625	−	8.03011i	1.05660	−	0.384572i
$437$	−13.1169	−	11.0064i	−0.627469	−	0.526509i
$438$		0			0
$439$	14.7167	+	5.35646i	0.702392	+	0.255650i	0.668432	−	0.743773i	$-0.266966\pi$
$439$	14.7167	+	5.35646i	0.702392	+	0.255650i	0.0339602	+	0.999423i	$0.489188\pi$
$440$	0.611178	+	1.05859i	0.0291368	+	0.0504664i
$441$		0			0
$442$	−10.0455	+	17.3993i	−0.477815	+	0.827600i
$443$	13.9833	−	11.7333i	0.664365	−	0.557468i	−0.247027	−	0.969009i	$-0.579454\pi$
$443$	13.9833	−	11.7333i	0.664365	−	0.557468i	0.911391	+	0.411541i	$0.135009\pi$
$444$		0			0
$445$	−0.0251044	+	0.142374i	−0.00119006	+	0.00674917i
$446$	8.94849	−	50.7494i	0.423723	−	2.40305i
$447$		0			0
$448$	4.60534	−	3.86434i	0.217582	−	0.182573i
$449$	14.3608	−	24.8737i	0.677729	−	1.17386i	−0.297934	−	0.954586i	$-0.596298\pi$
$449$	14.3608	−	24.8737i	0.677729	−	1.17386i	0.975663	−	0.219274i	$-0.0703690\pi$
$450$		0			0
$451$	−1.69525	−	2.93626i	−0.0798262	−	0.138263i
$452$	−41.9343	−	15.2628i	−1.97242	−	0.717904i
$453$		0			0
$454$	35.1654	+	29.5073i	1.65039	+	1.38485i
$455$	−0.213113	+	0.0775669i	−0.00999091	+	0.00363639i
$456$		0			0
$457$	−6.14505	−	34.8503i	−0.287453	−	1.63023i	−0.696389	−	0.717665i	$-0.745211\pi$
$457$	−6.14505	−	34.8503i	−0.287453	−	1.63023i	0.408936	−	0.912563i	$-0.365900\pi$
$458$	53.9648			2.52161
$459$		0			0
$460$	−1.56168			−0.0728139
$461$	−0.395350	−	2.24214i	−0.0184133	−	0.104427i	0.974216	−	0.225617i	$-0.0724399\pi$
$461$	−0.395350	−	2.24214i	−0.0184133	−	0.104427i	−0.992629	+	0.121190i	$0.961329\pi$
$462$		0			0
$463$	−17.2664	+	6.28446i	−0.802438	+	0.292064i	−0.710496	−	0.703701i	$-0.751530\pi$
$463$	−17.2664	+	6.28446i	−0.802438	+	0.292064i	−0.0919417	+	0.995764i	$0.529307\pi$
$464$	−13.0432	−	10.9446i	−0.605517	−	0.508089i
$465$		0			0
$466$	−39.9033	−	14.5236i	−1.84848	−	0.672793i
$467$	2.32935	+	4.03455i	0.107789	+	0.186697i	0.914874	−	0.403738i	$-0.132289\pi$
$467$	2.32935	+	4.03455i	0.107789	+	0.186697i	−0.807085	+	0.590435i	$0.798956\pi$
$468$		0			0
$469$	−2.56220	+	4.43786i	−0.118312	+	0.204922i
$470$	0.615335	−	0.516327i	0.0283833	−	0.0238164i
$471$		0			0
$472$	7.58218	−	43.0007i	0.348998	−	1.97927i
$473$	−3.70665	+	21.0215i	−0.170432	+	0.966568i
$474$		0			0
$475$	14.7033	−	12.3375i	0.674634	−	0.566085i
$476$	2.17495	−	3.76712i	0.0996885	−	0.172666i
$477$		0			0
$478$	−18.5169	−	32.0722i	−0.846942	−	1.46695i
$479$	−13.3210	−	4.84844i	−0.608651	−	0.221531i	0.0192617	−	0.999814i	$-0.493868\pi$
$479$	−13.3210	−	4.84844i	−0.608651	−	0.221531i	−0.627913	+	0.778283i	$0.716091\pi$
$480$		0			0
$481$	12.9717	+	10.8846i	0.591460	+	0.496294i
$482$	−29.6800	+	10.8026i	−1.35189	+	0.492047i
$483$		0			0
$484$	−0.937459	−	5.31660i	−0.0426118	−	0.241663i
$485$	−0.492926			−0.0223826
$486$		0			0
$487$	−21.4338			−0.971258			−0.485629	−	0.874165i	$-0.661409\pi$
$487$	−21.4338			−0.971258			−0.485629	+	0.874165i	$0.661409\pi$
$488$	−9.72875	−	55.1745i	−0.440400	−	2.49763i
$489$		0			0
$490$	−1.39985	+	0.509504i	−0.0632389	+	0.0230171i
$491$	10.7919	+	9.05550i	0.487033	+	0.408669i	0.852961	−	0.521974i	$-0.174804\pi$
$491$	10.7919	+	9.05550i	0.487033	+	0.408669i	−0.365929	+	0.930643i	$0.619249\pi$
$492$		0			0
$493$	11.9729	+	4.35779i	0.539234	+	0.196265i
$494$	19.4020	+	33.6053i	0.872938	+	1.51197i
$495$		0			0
$496$	−2.20500	+	3.81917i	−0.0990073	+	0.171486i
$497$	0.508585	−	0.426753i	0.0228131	−	0.0191425i
$498$		0			0
$499$	2.58898	−	14.6828i	0.115899	−	0.657294i	−0.870403	−	0.492340i	$-0.836142\pi$
$499$	2.58898	−	14.6828i	0.115899	−	0.657294i	0.986301	−	0.164953i	$-0.0527473\pi$
$500$	0.608488	−	3.45091i	0.0272124	−	0.154329i
$501$		0			0
$502$	−32.0422	+	26.8866i	−1.43011	+	1.20001i
$503$	−7.93153	+	13.7378i	−0.353650	+	0.612539i	−0.986886	−	0.161420i	$-0.948393\pi$
$503$	−7.93153	+	13.7378i	−0.353650	+	0.612539i	0.633236	+	0.773958i	$0.281726\pi$
$504$		0			0
$505$	0.338311	+	0.585972i	0.0150546	+	0.0260754i
$506$	−31.0826	−	11.3131i	−1.38179	−	0.502930i
$507$		0			0
$508$	33.2771	+	27.9228i	1.47643	+	1.23888i
$509$	31.8807	−	11.6036i	1.41309	−	0.514321i	0.481052	−	0.876692i	$-0.340255\pi$
$509$	31.8807	−	11.6036i	1.41309	−	0.514321i	0.932034	+	0.362371i	$0.118033\pi$
$510$		0			0
$511$	−0.0196825	−	0.111625i	−0.000870700	−	0.00493799i
$512$	−28.1824			−1.24550
$513$		0			0
$514$	−26.8683			−1.18511
$515$	−0.103470	−	0.586809i	−0.00455945	−	0.0258579i
$516$		0			0
$517$	10.4438	−	3.80123i	0.459317	−	0.167178i
$518$	−4.29930	−	3.60754i	−0.188900	−	0.158506i
$519$		0			0
$520$	1.56034	+	0.567919i	0.0684256	+	0.0249049i
$521$	−21.3899	−	37.0484i	−0.937108	−	1.62312i	−0.770831	−	0.637040i	$-0.780159\pi$
$521$	−21.3899	−	37.0484i	−0.937108	−	1.62312i	−0.166277	−	0.986079i	$-0.553175\pi$
$522$		0			0
$523$	1.38893	−	2.40569i	0.0607335	−	0.105193i	−0.834060	−	0.551674i	$-0.813989\pi$
$523$	1.38893	−	2.40569i	0.0607335	−	0.105193i	0.894793	+	0.446480i	$0.147323\pi$
$524$	26.0106	−	21.8255i	1.13628	−	0.953451i
$525$		0			0
$526$	8.63721	−	48.9840i	0.376600	−	2.13581i
$527$	0.573049	−	3.24992i	0.0249624	−	0.141569i
$528$		0			0
$529$	−2.43023	+	2.03920i	−0.105662	+	0.0886609i
$530$	−0.603626	+	1.04551i	−0.0262198	+	0.0454141i
$531$		0			0
$532$	−4.20073	−	7.27587i	−0.182125	−	0.315449i
$533$	−4.32799	−	1.57526i	−0.187466	−	0.0682321i
$534$		0			0
$535$	−0.395296	−	0.331693i	−0.0170901	−	0.0143403i
$536$	35.2565	−	12.8323i	1.52285	−	0.554271i
$537$		0			0
$538$	11.7792	+	66.8029i	0.507835	+	2.88008i
$539$	−20.6116			−0.887803
$540$		0			0
$541$	−3.59390			−0.154514			−0.0772570	−	0.997011i	$-0.524616\pi$
$541$	−3.59390			−0.154514			−0.0772570	+	0.997011i	$0.524616\pi$
$542$	7.19917	+	40.8285i	0.309231	+	1.75373i
$543$		0			0
$544$	3.93130	−	1.43088i	0.168553	−	0.0613483i
$545$	0.444334	+	0.372841i	0.0190332	+	0.0159707i
$546$		0			0
$547$	37.1985	+	13.5392i	1.59049	+	0.578892i	0.977452	−	0.211158i	$-0.0677235\pi$
$547$	37.1985	+	13.5392i	1.59049	+	0.578892i	0.613042	+	0.790051i	$0.289946\pi$
$548$	21.7029	+	37.5905i	0.927101	+	1.60579i
$549$		0			0
$550$	18.5389	−	32.1102i	0.790499	−	1.36919i
$551$	18.8514	−	15.8182i	0.803099	−	0.673880i
$552$		0			0
$553$	0.725786	−	4.11614i	0.0308636	−	0.175036i
$554$	2.15566	−	12.2253i	0.0915850	−	0.519405i
$555$		0			0
$556$	4.91776	−	4.12649i	0.208560	−	0.175002i
$557$	−5.71731	+	9.90267i	−0.242250	+	0.419590i	−0.961355	−	0.275312i	$-0.911219\pi$
$557$	−5.71731	+	9.90267i	−0.242250	+	0.419590i	0.719105	+	0.694902i	$0.244552\pi$
$558$		0			0
$559$	14.4983	+	25.1119i	0.613214	+	1.06212i
$560$	−0.134948	−	0.0491171i	−0.00570260	−	0.00207558i
$561$		0			0
$562$	6.06462	+	5.08882i	0.255821	+	0.214659i
$563$	13.6357	−	4.96298i	0.574676	−	0.209165i	−0.0383005	−	0.999266i	$-0.512194\pi$
$563$	13.6357	−	4.96298i	0.574676	−	0.209165i	0.612976	+	0.790101i	$0.289972\pi$
$564$		0			0
$565$	−0.191443	−	1.08573i	−0.00805408	−	0.0456770i
$566$	−21.9285			−0.921725
$567$		0			0
$568$	−4.86093			−0.203960
$569$	0.225601	+	1.27945i	0.00945767	+	0.0536371i	0.989171	−	0.146765i	$-0.0468862\pi$
$569$	0.225601	+	1.27945i	0.00945767	+	0.0536371i	−0.979714	+	0.200402i	$0.935775\pi$
$570$		0			0
$571$	−15.0890	+	5.49193i	−0.631453	+	0.229830i	−0.637864	−	0.770149i	$-0.720182\pi$
$571$	−15.0890	+	5.49193i	−0.631453	+	0.229830i	0.00641065	+	0.999979i	$0.497959\pi$
$572$	37.5111	+	31.4756i	1.56842	+	1.31606i
$573$		0			0
$574$	1.43445	+	0.522099i	0.0598730	+	0.0217920i
$575$	11.1127	+	19.2478i	0.463434	+	0.802691i
$576$		0			0
$577$	4.23017	−	7.32686i	0.176104	−	0.305021i	−0.764439	−	0.644696i	$-0.776984\pi$
$577$	4.23017	−	7.32686i	0.176104	−	0.305021i	0.940543	+	0.339675i	$0.110317\pi$
$578$	−23.9829	+	20.1241i	−0.997558	+	0.837050i
$579$		0			0
$580$	0.389740	−	2.21033i	0.0161831	−	0.0917788i
$581$	−1.50035	+	8.50893i	−0.0622452	+	0.353010i
$582$		0			0
$583$	−12.7958	+	10.7369i	−0.529947	+	0.444678i
$584$	−0.414943	+	0.718703i	−0.0171705	+	0.0297401i
$585$		0			0
$586$	−3.39401	−	5.87860i	−0.140205	−	0.242843i
$587$	−17.2764	−	6.28811i	−0.713075	−	0.259538i	−0.0400919	−	0.999196i	$-0.512765\pi$
$587$	−17.2764	−	6.28811i	−0.713075	−	0.259538i	−0.672983	+	0.739658i	$0.734987\pi$
$588$		0			0
$589$	−4.88260	−	4.09699i	−0.201184	−	0.168814i
$590$	2.16049	−	0.786354i	0.0889460	−	0.0323737i
$591$		0			0
$592$	1.86196	+	10.5597i	0.0765260	+	0.434001i
$593$	−13.5128			−0.554905			−0.277452	−	0.960739i	$-0.589490\pi$
$593$	−13.5128			−0.554905			−0.277452	+	0.960739i	$0.589490\pi$
$594$		0			0
$595$	0.107464			0.00440561
$596$	14.1667	+	80.3435i	0.580292	+	3.29100i
$597$		0			0
$598$	−42.2234	+	15.3681i	−1.72664	+	0.628447i
$599$	−8.44772	−	7.08848i	−0.345165	−	0.289627i	0.453680	−	0.891164i	$-0.350111\pi$
$599$	−8.44772	−	7.08848i	−0.345165	−	0.289627i	−0.798845	+	0.601537i	$0.794555\pi$
$600$		0			0
$601$	−24.2421	−	8.82341i	−0.988856	−	0.359914i	−0.203579	−	0.979058i	$-0.565257\pi$
$601$	−24.2421	−	8.82341i	−0.988856	−	0.359914i	−0.785277	+	0.619144i	$0.787480\pi$
$602$	−4.80528	−	8.32298i	−0.195848	−	0.339219i
$603$		0			0
$604$	8.93252	−	15.4716i	0.363459	−	0.629529i
$605$	0.102170	−	0.0857306i	0.00415379	−	0.00348545i
$606$		0			0
$607$	−2.56823	+	14.5652i	−0.104241	+	0.591182i	0.887279	+	0.461233i	$0.152593\pi$
$607$	−2.56823	+	14.5652i	−0.104241	+	0.591182i	−0.991521	+	0.129950i	$0.958518\pi$
$608$	1.40312	−	7.95752i	0.0569042	−	0.322720i
$609$		0			0
$610$	2.25987	−	1.89626i	0.0914995	−	0.0767772i
$611$	7.54882	−	13.0749i	0.305393	−	0.528956i
$612$		0			0
$613$	−18.1370	−	31.4141i	−0.732545	−	1.26880i	−0.955792	−	0.294043i	$-0.904999\pi$
$613$	−18.1370	−	31.4141i	−0.732545	−	1.26880i	0.223248	−	0.974762i	$-0.428334\pi$
$614$	−14.2053	−	5.17029i	−0.573277	−	0.208656i
$615$		0			0
$616$	−5.83316	−	4.89460i	−0.235025	−	0.197209i
$617$	−37.9387	+	13.8086i	−1.52736	+	0.555912i	−0.962972	−	0.269601i	$-0.913108\pi$
$617$	−37.9387	+	13.8086i	−1.52736	+	0.555912i	−0.564383	+	0.825513i	$0.690886\pi$
$618$		0			0
$619$	−1.19701	−	6.78858i	−0.0481119	−	0.272856i	0.951256	−	0.308402i	$-0.0997941\pi$
$619$	−1.19701	−	6.78858i	−0.0481119	−	0.272856i	−0.999368	+	0.0355458i	$0.988683\pi$
$620$	−0.581315			−0.0233462
$621$		0			0
$622$	17.7069			0.709981
$623$	−0.156387	−	0.886916i	−0.00626552	−	0.0355335i
$624$		0			0
$625$	−23.3703	+	8.50608i	−0.934810	+	0.340243i
$626$	−7.85711	−	6.59290i	−0.314033	−	0.263505i
$627$		0			0
$628$	0.740705	+	0.269595i	0.0295574	+	0.0107580i
$629$	−4.01193	−	6.94887i	−0.159966	−	0.277070i
$630$		0			0
$631$	−14.9095	+	25.8241i	−0.593539	+	1.02804i	0.400212	+	0.916423i	$0.368936\pi$
$631$	−14.9095	+	25.8241i	−0.593539	+	1.02804i	−0.993751	+	0.111617i	$0.964397\pi$
$632$	−23.4424	+	19.6705i	−0.932489	+	0.782451i
$633$		0			0
$634$	−6.73414	+	38.1912i	−0.267447	+	1.51677i
$635$	−0.186358	+	1.05689i	−0.00739540	+	0.0419414i
$636$		0			0
$637$	−21.4487	+	17.9976i	−0.849830	+	0.713092i
$638$	23.7691	−	41.1693i	0.941028	−	1.62991i
$639$		0			0
$640$	−0.963264	−	1.66842i	−0.0380763	−	0.0659502i
$641$	40.2947	+	14.6661i	1.59155	+	0.579275i	0.977673	−	0.210131i	$-0.0673889\pi$
$641$	40.2947	+	14.6661i	1.59155	+	0.579275i	0.613872	+	0.789406i	$0.289611\pi$
$642$		0			0
$643$	−20.9998	−	17.6209i	−0.828150	−	0.694901i	0.126715	−	0.991939i	$-0.459557\pi$
$643$	−20.9998	−	17.6209i	−0.828150	−	0.694901i	−0.954866	+	0.297038i	$0.904001\pi$
$644$	9.14178	−	3.32734i	0.360237	−	0.131115i
$645$		0			0
$646$	−3.19291	−	18.1079i	−0.125623	−	0.712446i
$647$	16.1623			0.635407			0.317703	−	0.948190i	$-0.397088\pi$
$647$	16.1623			0.635407			0.317703	+	0.948190i	$0.397088\pi$
$648$		0			0
$649$	31.8113			1.24870
$650$	−8.74621	−	49.6022i	−0.343055	−	1.94556i
$651$		0			0
$652$	−19.9116	+	7.24721i	−0.779797	+	0.283823i
$653$	−24.7021	−	20.7275i	−0.966668	−	0.811130i	0.0153573	−	0.999882i	$-0.495111\pi$
$653$	−24.7021	−	20.7275i	−0.966668	−	0.811130i	−0.982025	+	0.188752i	$0.939556\pi$
$654$		0			0
$655$	0.788258	+	0.286903i	0.0307998	+	0.0112102i
$656$	−1.45823	−	2.52573i	−0.0569344	−	0.0986133i
$657$		0			0
$658$	−2.50195	+	4.33351i	−0.0975363	+	0.168938i
$659$	−21.3103	+	17.8814i	−0.830130	+	0.696562i	−0.955321	−	0.295571i	$-0.904490\pi$
$659$	−21.3103	+	17.8814i	−0.830130	+	0.696562i	0.125191	+	0.992133i	$0.460046\pi$
$660$		0			0
$661$	5.34639	−	30.3209i	0.207950	−	1.17934i	−0.684779	−	0.728751i	$-0.740101\pi$
$661$	5.34639	−	30.3209i	0.207950	−	1.17934i	0.892729	−	0.450594i	$-0.148788\pi$
$662$	8.01889	−	45.4774i	0.311663	−	1.76753i
$663$		0			0
$664$	48.4604	−	40.6631i	1.88063	−	1.57803i
$665$	0.103779	−	0.179751i	0.00402439	−	0.00697044i
$666$		0			0
$667$	14.2479	+	24.6781i	0.551682	+	0.955540i
$668$	59.0583	+	21.4955i	2.28503	+	0.831684i
$669$		0			0
$670$	1.51339	+	1.26988i	0.0584673	+	0.0490598i
$671$	38.3557	−	13.9603i	1.48071	−	0.538933i
$672$		0			0
$673$	−4.53753	−	25.7336i	−0.174909	−	0.991959i	−0.938249	−	0.345961i	$-0.887553\pi$
$673$	−4.53753	−	25.7336i	−0.174909	−	0.991959i	0.763340	−	0.645997i	$-0.223558\pi$
$674$	−70.7584			−2.72551
$675$		0			0
$676$	17.5374			0.674515
$677$	−3.15944	−	17.9181i	−0.121427	−	0.688648i	−0.983366	−	0.181635i	$-0.941861\pi$
$677$	−3.15944	−	17.9181i	−0.121427	−	0.688648i	0.861939	−	0.507012i	$-0.169250\pi$
$678$		0			0
$679$	2.88549	−	1.05023i	0.110735	−	0.0403042i
$680$	−0.602738	−	0.505757i	−0.0231139	−	0.0193949i
$681$		0			0
$682$	−11.5701	−	4.21116i	−0.443040	−	0.161253i
$683$	11.7486	+	20.3491i	0.449546	+	0.778636i	0.998356	−	0.0573104i	$-0.0182525\pi$
$683$	11.7486	+	20.3491i	0.449546	+	0.778636i	−0.548811	+	0.835947i	$0.684919\pi$
$684$		0			0
$685$	−0.536171	+	0.928676i	−0.0204860	+	0.0354829i
$686$	14.5765	−	12.2311i	0.556533	−	0.466987i
$687$		0			0
$688$	−3.18841	+	18.0824i	−0.121557	+	0.689384i
$689$	−3.94021	+	22.3460i	−0.150110	+	0.851317i
$690$		0			0
$691$	−34.1180	+	28.6284i	−1.29791	+	1.08908i	−0.307409	+	0.951577i	$0.599462\pi$
$691$	−34.1180	+	28.6284i	−1.29791	+	1.08908i	−0.990502	+	0.137499i	$0.956094\pi$
$692$	35.7980	−	62.0039i	1.36084	−	2.35704i
$693$		0			0
$694$	13.6857	+	23.7043i	0.519501	+	0.899802i
$695$	0.149034	+	0.0542440i	0.00565318	+	0.00205759i
$696$		0			0
$697$	1.67184	+	1.40284i	0.0633254	+	0.0531363i
$698$	−63.5547	+	23.1320i	−2.40558	+	0.875560i
$699$		0			0
$700$	1.89364	+	10.7394i	0.0715728	+	0.405910i
$701$	25.2567			0.953934			0.476967	−	0.878921i	$-0.341736\pi$
$701$	25.2567			0.953934			0.476967	+	0.878921i	$0.341736\pi$
$702$		0			0
$703$	−15.4974			−0.584496
$704$	−5.56859	−	31.5810i	−0.209874	−	1.19025i
$705$		0			0
$706$	64.6662	−	23.5366i	2.43374	−	0.885810i
$707$	−3.22888	−	2.70935i	−0.121434	−	0.101896i
$708$		0			0
$709$	14.7382	+	5.36425i	0.553503	+	0.201459i	0.603602	−	0.797286i	$-0.293731\pi$
$709$	14.7382	+	5.36425i	0.553503	+	0.201459i	−0.0500991	+	0.998744i	$0.515954\pi$
$710$	−0.127977	−	0.221663i	−0.00480289	−	0.00831886i
$711$		0			0
$712$	−3.29694	+	5.71046i	−0.123558	+	0.214009i
$713$	5.65382	−	4.74412i	0.211737	−	0.177669i
$714$		0			0
$715$	−0.210069	+	1.19136i	−0.00785615	+	0.0445544i
$716$	−10.6222	+	60.2415i	−0.396970	+	2.25133i
$717$		0			0
$718$	57.0915	−	47.9055i	2.13064	−	1.78782i
$719$	−26.5804	+	46.0385i	−0.991280	+	1.71695i	−0.381523	+	0.924359i	$0.624600\pi$
$719$	−26.5804	+	46.0385i	−0.991280	+	1.71695i	−0.609757	+	0.792588i	$0.708733\pi$
$720$		0			0
$721$	1.85595	+	3.21461i	0.0691194	+	0.119718i
$722$	9.50721	+	3.46034i	0.353822	+	0.128781i
$723$		0			0
$724$	−8.63457	−	7.24526i	−0.320901	−	0.269268i
$725$	−30.0158	+	10.9248i	−1.11476	+	0.405738i
$726$		0			0
$727$	0.0814709	+	0.462044i	0.00302159	+	0.0171363i	0.986281	−	0.165073i	$-0.0527861\pi$
$727$	0.0814709	+	0.462044i	0.00302159	+	0.0171363i	−0.983260	+	0.182210i	$0.941675\pi$
$728$	−10.3440			−0.383372
$729$		0			0
$730$	−0.0436980			−0.00161734
$731$	−2.38593	−	13.5313i	−0.0882469	−	0.500473i
$732$		0			0
$733$	43.6076	−	15.8719i	1.61068	−	0.586241i	0.629109	−	0.777317i	$-0.283420\pi$
$733$	43.6076	−	15.8719i	1.61068	−	0.586241i	0.981575	+	0.191075i	$0.0611975\pi$
$734$	44.3825	+	37.2413i	1.63819	+	1.37460i
$735$		0			0
$736$	8.79230	+	3.20014i	0.324088	+	0.117959i
$737$	13.6672	+	23.6724i	0.503439	+	0.871983i
$738$		0			0
$739$	−12.9047	+	22.3515i	−0.474706	+	0.822214i	−0.999580	−	0.0289653i	$-0.990779\pi$
$739$	−12.9047	+	22.3515i	−0.474706	+	0.822214i	0.524875	+	0.851179i	$0.324112\pi$
$740$	−1.08275	+	0.908534i	−0.0398026	+	0.0333984i
$741$		0			0
$742$	1.30593	−	7.40629i	0.0479422	−	0.271894i
$743$	−6.02726	+	34.1823i	−0.221119	+	1.25403i	0.648848	+	0.760918i	$0.275251\pi$
$743$	−6.02726	+	34.1823i	−0.221119	+	1.25403i	−0.869967	+	0.493110i	$0.835860\pi$
$744$		0			0
$745$	−1.54397	+	1.29555i	−0.0565668	+	0.0474652i
$746$	15.1129	−	26.1764i	0.553324	−	0.958385i
$747$		0			0
$748$	−11.6015	−	20.0945i	−0.424195	−	0.734727i
$749$	3.02069	+	1.09944i	0.110374	+	0.0401727i
$750$		0			0
$751$	18.3742	+	15.4178i	0.670485	+	0.562604i	0.913209	−	0.407492i	$-0.133596\pi$
$751$	18.3742	+	15.4178i	0.670485	+	0.562604i	−0.242724	+	0.970095i	$0.578041\pi$
$752$	8.98361	−	3.26977i	0.327599	−	0.119236i
$753$		0			0
$754$	−11.2137	−	63.5962i	−0.408380	−	2.31604i
$755$	0.441357			0.0160626
$756$		0			0
$757$	−8.78780			−0.319398			−0.159699	−	0.987166i	$-0.551052\pi$
$757$	−8.78780			−0.319398			−0.159699	+	0.987166i	$0.551052\pi$
$758$	−3.21336	−	18.2239i	−0.116715	−	0.661921i
$759$		0			0
$760$	−1.42803	+	0.519759i	−0.0517999	+	0.0188536i
$761$	−10.5361	−	8.84082i	−0.381933	−	0.320479i	0.431528	−	0.902100i	$-0.357975\pi$
$761$	−10.5361	−	8.84082i	−0.381933	−	0.320479i	−0.813461	+	0.581620i	$0.802419\pi$
$762$		0			0
$763$	−3.39542	−	1.23583i	−0.122922	−	0.0447401i
$764$	−4.24595	−	7.35420i	−0.153613	−	0.266066i
$765$		0			0
$766$	−21.4484	+	37.1498i	−0.774963	+	1.34228i
$767$	33.1034	−	27.7770i	1.19529	−	1.00297i
$768$		0			0
$769$	−5.44525	+	30.8815i	−0.196361	+	1.11362i	0.714107	+	0.700036i	$0.246833\pi$
$769$	−5.44525	+	30.8815i	−0.196361	+	1.11362i	−0.910468	+	0.413580i	$0.864278\pi$
$770$	0.0696246	−	0.394861i	0.00250910	−	0.0142298i
$771$		0			0
$772$	−2.54072	+	2.13192i	−0.0914426	+	0.0767295i
$773$	14.0607	−	24.3539i	0.505729	−	0.875948i	−0.494249	−	0.869320i	$-0.664557\pi$
$773$	14.0607	−	24.3539i	0.505729	−	0.875948i	0.999978	−	0.00662776i	$-0.00210970\pi$
$774$		0			0
$775$	4.13657	+	7.16475i	0.148590	+	0.257365i
$776$	−21.1266	−	7.68945i	−0.758400	−	0.276035i
$777$		0			0
$778$	−50.3879	−	42.2804i	−1.80649	−	1.51583i
$779$	3.96098	−	1.44168i	0.141917	−	0.0516535i
$780$		0			0
$781$	−0.614960	−	3.48761i	−0.0220050	−	0.124797i
$782$	21.2916			0.761385
$783$		0			0
$784$	−17.7298			−0.633207
$785$	0.00338155	+	0.0191777i	0.000120693	+	0.000684483i
$786$		0			0
$787$	34.0170	−	12.3812i	1.21258	−	0.441342i	0.344979	−	0.938610i	$-0.387886\pi$
$787$	34.0170	−	12.3812i	1.21258	−	0.441342i	0.867597	+	0.497269i	$0.165664\pi$
$788$	−58.5240	−	49.1075i	−2.08483	−	1.74938i
$789$		0			0
$790$	−1.51418	−	0.551116i	−0.0538721	−	0.0196078i
$791$	3.43393	+	5.94775i	0.122097	+	0.211478i
$792$		0			0
$793$	27.7237	−	48.0189i	0.984498	−	1.70520i
$794$	7.75636	−	6.50836i	0.275263	−	0.230973i
$795$		0			0
$796$	−12.4373	+	70.5354i	−0.440828	+	2.50006i
$797$	5.14000	−	29.1504i	0.182068	−	1.03256i	−0.747596	−	0.664153i	$-0.768792\pi$
$797$	5.14000	−	29.1504i	0.182068	−	1.03256i	0.929665	−	0.368407i	$-0.120097\pi$
$798$		0			0
$799$	−5.48028	+	4.59850i	−0.193878	+	0.162683i
$800$	−5.24407	+	9.08300i	−0.185406	+	0.321133i
$801$		0			0
$802$	18.2193	+	31.5568i	0.643346	+	1.11431i
$803$	−0.568149	−	0.206789i	−0.0200495	−	0.00729744i
$804$		0			0
$805$	0.184113	+	0.154489i	0.00648914	+	0.00544504i
$806$	−15.7171	+	5.72055i	−0.553611	+	0.201498i
$807$		0			0
$808$	5.35892	+	30.3920i	0.188526	+	1.06919i
$809$	5.75943			0.202491			0.101245	−	0.994861i	$-0.467717\pi$
$809$	5.75943			0.202491			0.101245	+	0.994861i	$0.467717\pi$
$810$		0			0
$811$	12.4896			0.438569			0.219284	−	0.975661i	$-0.429628\pi$
$811$	12.4896			0.438569			0.219284	+	0.975661i	$0.429628\pi$
$812$	2.42788	+	13.7692i	0.0852019	+	0.483204i
$813$		0			0
$814$	−28.1318	+	10.2391i	−0.986018	+	0.358881i
$815$	−0.401014	−	0.336491i	−0.0140469	−	0.0117868i
$816$		0			0
$817$	−24.9373	−	9.07644i	−0.872446	−	0.317544i
$818$	−5.65535	−	9.79536i	−0.197735	−	0.342487i
$819$		0			0
$820$	0.192221	−	0.332936i	0.00671265	−	0.0116266i
$821$	−32.9911	+	27.6828i	−1.15140	+	0.966136i	−0.999751	−	0.0222995i	$-0.992901\pi$
$821$	−32.9911	+	27.6828i	−1.15140	+	0.966136i	−0.151644	+	0.988435i	$0.548457\pi$
$822$		0			0
$823$	1.78581	−	10.1279i	0.0622496	−	0.353035i	−0.937734	−	0.347353i	$-0.887080\pi$
$823$	1.78581	−	10.1279i	0.0622496	−	0.353035i	0.999984	−	0.00568141i	$-0.00180846\pi$
$824$	4.71930	−	26.7645i	0.164404	−	0.932384i
$825$		0			0
$826$	−10.9717	+	9.20632i	−0.381753	+	0.320329i
$827$	3.04731	−	5.27810i	0.105965	−	0.183538i	−0.808167	−	0.588954i	$-0.799540\pi$
$827$	3.04731	−	5.27810i	0.105965	−	0.183538i	0.914132	+	0.405416i	$0.132873\pi$
$828$		0			0
$829$	16.8489	+	29.1832i	0.585188	+	1.01358i	0.994852	+	0.101339i	$0.0323126\pi$
$829$	16.8489	+	29.1832i	0.585188	+	1.01358i	−0.409664	+	0.912236i	$0.634354\pi$
$830$	3.13013	+	1.13927i	0.108648	+	0.0395447i
$831$		0			0
$832$	−33.3707	−	28.0014i	−1.15692	−	0.970772i
$833$	12.4673	−	4.53774i	0.431967	−	0.157223i
$834$		0			0
$835$	0.269620	+	1.52909i	0.00933057	+	0.0529163i
$836$	−44.8148			−1.54995
$837$		0			0
$838$	−47.5308			−1.64192
$839$	7.33250	+	41.5847i	0.253146	+	1.43566i	0.800787	+	0.598950i	$0.204415\pi$
$839$	7.33250	+	41.5847i	0.253146	+	1.43566i	−0.547641	+	0.836714i	$0.684474\pi$
$840$		0			0
$841$	−11.2328	+	4.08841i	−0.387339	+	0.140980i
$842$	51.8546	+	43.5112i	1.78703	+	1.49949i
$843$		0			0
$844$	−57.3007	−	20.8557i	−1.97237	−	0.717884i
$845$	0.216631	+	0.375216i	0.00745234	+	0.0129078i
$846$		0			0
$847$	−0.415423	+	0.719533i	−0.0142741	+	0.0247235i
$848$	−11.0068	+	9.23576i	−0.377973	+	0.317157i
$849$		0			0
$850$	−4.14438	+	23.5040i	−0.142151	+	0.806179i
$851$	3.11616	−	17.6726i	0.106821	−	0.605810i
$852$		0			0
$853$	−27.3705	+	22.9665i	−0.937147	+	0.786359i	−0.977086	−	0.212843i	$-0.931728\pi$
$853$	−27.3705	+	22.9665i	−0.937147	+	0.786359i	0.0399399	+	0.999202i	$0.487283\pi$
$854$	−9.18865	+	15.9152i	−0.314429	+	0.544607i
$855$		0			0
$856$	−11.7679	−	20.3826i	−0.402219	−	0.696664i
$857$	7.43170	+	2.70492i	0.253862	+	0.0923983i	0.465817	−	0.884881i	$-0.345761\pi$
$857$	7.43170	+	2.70492i	0.253862	+	0.0923983i	−0.211954	+	0.977280i	$0.567983\pi$
$858$		0			0
$859$	−34.2569	−	28.7449i	−1.16883	−	0.980764i	−0.168841	−	0.985643i	$-0.554002\pi$
$859$	−34.2569	−	28.7449i	−1.16883	−	0.980764i	−0.999988	+	0.00487963i	$0.998447\pi$
$860$	−2.27438	+	0.827808i	−0.0775559	+	0.0282280i
$861$		0			0
$862$	2.16726	+	12.2911i	0.0738172	+	0.418638i
$863$	22.9170			0.780103			0.390052	−	0.920793i	$-0.372457\pi$
$863$	22.9170			0.780103			0.390052	+	0.920793i	$0.372457\pi$
$864$		0			0
$865$	1.76878			0.0601405
$866$	10.5629	+	59.9053i	0.358943	+	2.03567i
$867$		0			0
$868$	3.40290	−	1.23856i	0.115502	−	0.0420393i
$869$	−17.0789	−	14.3309i	−0.579362	−	0.486143i
$870$		0			0
$871$	34.8926	+	12.6999i	1.18229	+	0.430319i
$872$	13.2278	+	22.9112i	0.447950	+	0.775871i
$873$		0			0
$874$	20.5614	−	35.6134i	0.695501	−	1.20464i
$875$	−0.413118	+	0.346647i	−0.0139659	+	0.0117188i
$876$		0			0
$877$	−3.84416	+	21.8013i	−0.129808	+	0.736178i	0.848527	+	0.529152i	$0.177490\pi$
$877$	−3.84416	+	21.8013i	−0.129808	+	0.736178i	−0.978335	+	0.207026i	$0.933621\pi$
$878$	−6.53132	+	37.0409i	−0.220421	+	1.25007i
$879$		0			0
$880$	−0.586817	+	0.492398i	−0.0197816	+	0.0165987i
$881$	4.93202	−	8.54251i	0.166164	−	0.287804i	−0.770904	−	0.636951i	$-0.780195\pi$
$881$	4.93202	−	8.54251i	0.166164	−	0.287804i	0.937068	+	0.349147i	$0.113529\pi$
$882$		0			0
$883$	−23.7865	−	41.1995i	−0.800481	−	1.38647i	−0.919300	−	0.393558i	$-0.871244\pi$
$883$	−23.7865	−	41.1995i	−0.800481	−	1.38647i	0.118819	−	0.992916i	$-0.462089\pi$
$884$	−29.6189	−	10.7804i	−0.996191	−	0.362584i
$885$		0			0
$886$	33.5825	+	28.1791i	1.12823	+	0.946694i
$887$	12.5517	−	4.56846i	0.421446	−	0.153394i	−0.122587	−	0.992458i	$-0.539119\pi$
$887$	12.5517	−	4.56846i	0.421446	−	0.153394i	0.544033	+	0.839064i	$0.316897\pi$
$888$		0			0
$889$	−1.16091	−	6.58387i	−0.0389358	−	0.220816i
$890$	−0.347203			−0.0116383
$891$		0			0
$892$	80.8465			2.70694
$893$	2.39936	+	13.6074i	0.0802914	+	0.455355i
$894$		0			0
$895$	−1.42009	+	0.516871i	−0.0474684	+	0.0172771i
$896$	9.19350	+	7.71427i	0.307133	+	0.257716i
$897$		0			0
$898$	64.8186	+	23.5920i	2.16302	+	0.787276i
$899$	5.30359	+	9.18609i	0.176885	+	0.306373i
$900$		0			0
$901$	5.37600	−	9.31150i	0.179100	−	0.310211i
$902$	6.23767	−	5.23403i	0.207692	−	0.174274i
$903$		0			0
$904$	8.73176	−	49.5203i	0.290414	−	1.64702i
$905$	0.0483552	−	0.274236i	0.00160738	−	0.00911591i
$906$		0			0
$907$	28.3135	−	23.7578i	0.940134	−	0.788866i	−0.0374746	−	0.999298i	$-0.511931\pi$
$907$	28.3135	−	23.7578i	0.940134	−	0.788866i	0.977609	+	0.210431i	$0.0674869\pi$
$908$	−36.0092	+	62.3697i	−1.19501	+	2.06981i
$909$		0			0
$910$	−0.272332	−	0.471694i	−0.00902773	−	0.0156365i
$911$	−45.4916	−	16.5576i	−1.50720	−	0.548577i	−0.549288	−	0.835633i	$-0.685101\pi$
$911$	−45.4916	−	16.5576i	−1.50720	−	0.548577i	−0.957914	+	0.287056i	$0.907323\pi$
$912$		0			0
$913$	35.3057	+	29.6250i	1.16845	+	0.980445i
$914$	79.8629	−	29.0677i	2.64163	−	0.961475i
$915$		0			0
$916$	14.7015	+	83.3765i	0.485752	+	2.75484i
$917$	−5.22558			−0.172564
$918$		0			0
$919$	8.93459			0.294725			0.147363	−	0.989083i	$-0.452922\pi$
$919$	8.93459			0.294725			0.147363	+	0.989083i	$0.452922\pi$
$920$	−0.305570	−	1.73297i	−0.0100744	−	0.0571345i
$921$		0			0
$922$	5.13809	−	1.87011i	0.169214	−	0.0615889i
$923$	−3.68526	−	3.09230i	−0.121302	−	0.101784i
$924$		0			0
$925$	18.9024	+	6.87992i	0.621508	+	0.226211i
$926$	−22.0643	−	38.2165i	−0.725079	−	1.25587i
$927$		0			0
$928$	−6.72355	+	11.6455i	−0.220711	+	0.382283i
$929$	4.78330	−	4.01366i	0.156935	−	0.131684i	−0.560939	−	0.827857i	$-0.689560\pi$
$929$	4.78330	−	4.01366i	0.156935	−	0.131684i	0.717874	+	0.696173i	$0.245115\pi$
$930$		0			0
$931$	4.44973	−	25.2357i	0.145834	−	0.827066i
$932$	11.5684	−	65.6079i	0.378937	−	2.14906i
$933$		0			0
$934$	−8.57084	+	7.19179i	−0.280446	+	0.235322i
$935$	0.286617	−	0.496435i	0.00937338	−	0.0162352i
$936$		0			0
$937$	−22.9212	−	39.7006i	−0.748802	−	1.29696i	−0.948397	−	0.317085i	$-0.897296\pi$
$937$	−22.9212	−	39.7006i	−0.748802	−	1.29696i	0.199595	−	0.979878i	$-0.436037\pi$
$938$	−11.5647	−	4.20920i	−0.377600	−	0.137435i
$939$		0			0
$940$	0.965368	+	0.810040i	0.0314868	+	0.0264206i
$941$	−4.09014	+	1.48869i	−0.133335	+	0.0485298i	−0.407826	−	0.913060i	$-0.633713\pi$
$941$	−4.09014	+	1.48869i	−0.133335	+	0.0485298i	0.274491	+	0.961590i	$0.411491\pi$
$942$		0			0
$943$	0.847573	+	4.80683i	0.0276008	+	0.156532i
$944$	27.3637			0.890612
$945$		0			0
$946$	−51.2644			−1.66675
$947$	−0.350202	−	1.98610i	−0.0113800	−	0.0645395i	0.978589	−	0.205825i	$-0.0659877\pi$
$947$	−0.350202	−	1.98610i	−0.0113800	−	0.0645395i	−0.989969	+	0.141285i	$0.954877\pi$
$948$		0			0
$949$	−0.771790	+	0.280909i	−0.0250534	+	0.00911868i
$950$	35.3118	+	29.6301i	1.14566	+	0.961327i
$951$		0			0
$952$	4.60587	+	1.67640i	0.149277	+	0.0543325i
$953$	−17.8644	−	30.9420i	−0.578684	−	1.00231i	−0.995631	−	0.0933786i	$-0.970233\pi$
$953$	−17.8644	−	30.9420i	−0.578684	−	1.00231i	0.416947	−	0.908931i	$-0.363100\pi$
$954$		0			0
$955$	0.104896	−	0.181686i	0.00339437	−	0.00587922i
$956$	44.5075	−	37.3462i	1.43948	−	1.20786i
$957$		0			0
$958$	5.91188	−	33.5279i	0.191004	−	1.08324i
$959$	1.15999	−	6.57865i	0.0374581	−	0.212436i
$960$		0			0
$961$	−21.6428	+	18.1605i	−0.698155	+	0.585822i
$962$	−20.3338	+	35.2191i	−0.655587	+	1.13551i
$963$		0			0
$964$	−24.7759	−	42.9131i	−0.797978	−	1.38214i
$965$	−0.0769973	−	0.0280247i	−0.00247863	−	0.000902148i
$966$		0			0
$967$	−0.531112	−	0.445656i	−0.0170794	−	0.0143313i	0.634208	−	0.773163i	$-0.281326\pi$
$967$	−0.531112	−	0.445656i	−0.0170794	−	0.0143313i	−0.651287	+	0.758831i	$0.725771\pi$
$968$	5.71631	−	2.08057i	0.183729	−	0.0668719i
$969$		0			0
$970$	−0.205569	−	1.16584i	−0.00660041	−	0.0374328i
$971$	−47.4942			−1.52416			−0.762081	−	0.647482i	$-0.775822\pi$
$971$	−47.4942			−1.52416			−0.762081	+	0.647482i	$0.775822\pi$
$972$		0			0
$973$	−0.987988			−0.0316734
$974$	−8.93869	−	50.6938i	−0.286414	−	1.62434i
$975$		0			0
$976$	32.9931	−	12.0085i	1.05608	−	0.384383i
$977$	9.65470	+	8.10126i	0.308881	+	0.259182i	0.784029	−	0.620724i	$-0.213161\pi$
$977$	9.65470	+	8.10126i	0.308881	+	0.259182i	−0.475148	+	0.879906i	$0.657606\pi$
$978$		0			0
$979$	−4.51423	−	1.64305i	−0.144276	−	0.0525120i
$980$	−1.16855	−	2.02399i	−0.0373280	−	0.0646540i
$981$		0			0
$982$	−16.9168	+	29.3008i	−0.539838	+	0.935027i
$983$	−8.84400	+	7.42100i	−0.282080	+	0.236693i	−0.772839	−	0.634602i	$-0.781164\pi$
$983$	−8.84400	+	7.42100i	−0.282080	+	0.236693i	0.490759	+	0.871295i	$0.336720\pi$
$984$		0			0
$985$	0.327745	−	1.85874i	0.0104428	−	0.0592243i
$986$	−5.31361	+	30.1350i	−0.169220	+	0.959693i
$987$		0			0
$988$	−46.6351	+	39.1315i	−1.48366	+	1.24494i
$989$	15.3647	−	26.6125i	0.488569	−	0.846227i
$990$		0			0
$991$	−9.34676	−	16.1891i	−0.296910	−	0.514263i	0.678518	−	0.734584i	$-0.262623\pi$
$991$	−9.34676	−	16.1891i	−0.296910	−	0.514263i	−0.975427	+	0.220322i	$0.929289\pi$
$992$	3.27281	+	1.19121i	0.103912	+	0.0378209i
$993$		0			0
$994$	1.22143	+	1.02490i	0.0387413	+	0.0325079i
$995$	−1.66275	+	0.605192i	−0.0527128	+	0.0191859i
$996$		0			0
$997$	0.583250	+	3.30778i	0.0184717	+	0.104758i	0.992650	−	0.121023i	$-0.0386175\pi$
$997$	0.583250	+	3.30778i	0.0184717	+	0.104758i	−0.974178	+	0.225782i	$0.927506\pi$
$998$	35.8066			1.13344
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.e.a.10.2		12
3.2	odd	2		27.2.e.a.13.1	✓	12
9.2	odd	6		243.2.e.c.109.1		12
9.4	even	3		243.2.e.a.190.1		12
9.5	odd	6		243.2.e.d.190.2		12
9.7	even	3		243.2.e.b.109.2		12
12.11	even	2		432.2.u.c.337.1		12
15.2	even	4		675.2.u.b.499.4		24
15.8	even	4		675.2.u.b.499.1		24
15.14	odd	2		675.2.l.c.526.2		12
27.2	odd	18		27.2.e.a.25.1	yes	12
27.4	even	9		729.2.c.b.487.1		12
27.5	odd	18		729.2.a.a.1.1		6
27.7	even	9		243.2.e.b.136.2		12
27.11	odd	18		243.2.e.d.55.2		12
27.13	even	9		729.2.c.b.244.1		12
27.14	odd	18		729.2.c.e.244.6		12
27.16	even	9		243.2.e.a.55.1		12
27.20	odd	18		243.2.e.c.136.1		12
27.22	even	9		729.2.a.d.1.6		6
27.23	odd	18		729.2.c.e.487.6		12
27.25	even	9	inner	81.2.e.a.73.2		12
108.83	even	18		432.2.u.c.241.1		12
135.2	even	36		675.2.u.b.349.1		24
135.29	odd	18		675.2.l.c.376.2		12
135.83	even	36		675.2.u.b.349.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.1	✓	12	3.2	odd	2
27.2.e.a.25.1	yes	12	27.2	odd	18
81.2.e.a.10.2		12	1.1	even	1	trivial
81.2.e.a.73.2		12	27.25	even	9	inner
243.2.e.a.55.1		12	27.16	even	9
243.2.e.a.190.1		12	9.4	even	3
243.2.e.b.109.2		12	9.7	even	3
243.2.e.b.136.2		12	27.7	even	9
243.2.e.c.109.1		12	9.2	odd	6
243.2.e.c.136.1		12	27.20	odd	18
243.2.e.d.55.2		12	27.11	odd	18
243.2.e.d.190.2		12	9.5	odd	6
432.2.u.c.241.1		12	108.83	even	18
432.2.u.c.337.1		12	12.11	even	2
675.2.l.c.376.2		12	135.29	odd	18
675.2.l.c.526.2		12	15.14	odd	2
675.2.u.b.349.1		24	135.2	even	36
675.2.u.b.349.4		24	135.83	even	36
675.2.u.b.499.1		24	15.8	even	4
675.2.u.b.499.4		24	15.2	even	4
729.2.a.a.1.1		6	27.5	odd	18
729.2.a.d.1.6		6	27.22	even	9
729.2.c.b.244.1		12	27.13	even	9
729.2.c.b.487.1		12	27.4	even	9
729.2.c.e.244.6		12	27.14	odd	18
729.2.c.e.487.6		12	27.23	odd	18

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.417037 + 2.36514i) q^{2} +(-3.54056 + 1.28866i) q^{4} +(-0.0713060 - 0.0598329i) q^{5} +(0.544891 + 0.198324i) q^{7} +(-2.12277 - 3.67675i) q^{8} +(0.111776 - 0.193601i) q^{10} +(2.36944 - 1.98820i) q^{11} +(0.729623 - 4.13790i) q^{13} +(-0.241824 + 1.37145i) q^{14} +(2.03816 - 1.71022i) q^{16} +(-0.995493 + 1.72424i) q^{17} +(1.92271 + 3.33023i) q^{19} +(0.329567 + 0.119953i) q^{20} +(5.69050 + 4.77489i) q^{22} +(-4.18428 + 1.52295i) q^{23} +(-0.866736 - 4.91551i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(-1.11126 - 6.30229i) q^{29} +(-1.55754 + 0.566898i) q^{31} +(-1.60967 - 1.35067i) q^{32} +(-4.49323 - 1.63540i) q^{34} +(-0.0269877 - 0.0467441i) q^{35} +(-2.01505 + 3.49016i) q^{37} +(-7.07461 + 5.93630i) q^{38} +(-0.0686240 + 0.389186i) q^{40} +(0.190345 - 1.07950i) q^{41} +(-5.28657 + 4.43596i) q^{43} +(-5.82704 + 10.0927i) q^{44} +(-5.34699 - 9.26126i) q^{46} +(3.37650 + 1.22894i) q^{47} +(-5.10474 - 4.28338i) q^{49} +(11.2644 - 4.09990i) q^{50} +(2.74906 + 15.5907i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(-0.427492 - 2.42443i) q^{56} +(14.4423 - 5.25657i) q^{58} +(7.87850 + 6.61085i) q^{59} +(12.4005 + 4.51341i) q^{61} +(-1.99034 - 3.44738i) q^{62} +(5.18386 - 8.97871i) q^{64} +(-0.299609 + 0.251402i) q^{65} +(-1.53458 + 8.70304i) q^{67} +(1.30264 - 7.38764i) q^{68} +(0.0993013 - 0.0833237i) q^{70} +(0.572473 - 0.991553i) q^{71} +(-0.0977361 - 0.169284i) q^{73} +(-9.09506 - 3.31033i) q^{74} +(-11.0990 - 9.31317i) q^{76} +(1.68539 - 0.613433i) q^{77} +(-1.25166 - 7.09849i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(2.58744 + 14.6741i) q^{83} +(0.174151 - 0.0633858i) q^{85} +(-12.6963 - 10.6535i) q^{86} +(-12.3399 - 4.49135i) q^{88} +(-0.776563 - 1.34505i) q^{89} +(1.21821 - 2.11000i) q^{91} +(12.8521 - 10.7842i) q^{92} +(-1.49850 + 8.49839i) q^{94} +(0.0621565 - 0.352507i) q^{95} +(4.05661 - 3.40390i) q^{97} +(8.00191 - 13.8597i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29}+ \cdots + 45 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more