LMFDB - Embedded newform 27.2.e.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,2,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$0.215596085457$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	27.25
Dual form			27.2.e.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.417037 + 2.36514i) q^{2} +(-0.210069 - 1.71926i) q^{3} +(-3.54056 - 1.28866i) q^{4} +(0.0713060 - 0.0598329i) q^{5} +(4.15390 + 0.220155i) q^{6} +(0.544891 - 0.198324i) q^{7} +(2.12277 - 3.67675i) q^{8} +(-2.91174 + 0.722330i) q^{9} +(0.111776 + 0.193601i) q^{10} +(-2.36944 - 1.98820i) q^{11} +(-1.47178 + 6.35787i) q^{12} +(0.729623 + 4.13790i) q^{13} +(0.241824 + 1.37145i) q^{14} +(-0.117848 - 0.110025i) q^{15} +(2.03816 + 1.71022i) q^{16} +(0.995493 + 1.72424i) q^{17} +(-0.494102 - 7.18790i) q^{18} +(1.92271 - 3.33023i) q^{19} +(-0.329567 + 0.119953i) q^{20} +(-0.455437 - 0.895151i) q^{21} +(5.69050 - 4.77489i) q^{22} +(4.18428 + 1.52295i) q^{23} +(-6.76724 - 2.87724i) q^{24} +(-0.866736 + 4.91551i) q^{25} -10.0910 q^{26} +(1.85354 + 4.85432i) q^{27} -2.18479 q^{28} +(1.11126 - 6.30229i) q^{29} +(0.309371 - 0.232841i) q^{30} +(-1.55754 - 0.566898i) q^{31} +(1.60967 - 1.35067i) q^{32} +(-2.92049 + 4.49135i) q^{33} +(-4.49323 + 1.63540i) q^{34} +(0.0269877 - 0.0467441i) q^{35} +(11.2400 + 1.19479i) q^{36} +(-2.01505 - 3.49016i) q^{37} +(7.07461 + 5.93630i) q^{38} +(6.96087 - 2.12366i) q^{39} +(-0.0686240 - 0.389186i) q^{40} +(-0.190345 - 1.07950i) q^{41} +(2.30709 - 0.703859i) q^{42} +(-5.28657 - 4.43596i) q^{43} +(5.82704 + 10.0927i) q^{44} +(-0.164406 + 0.225724i) q^{45} +(-5.34699 + 9.26126i) q^{46} +(-3.37650 + 1.22894i) q^{47} +(2.51217 - 3.86340i) q^{48} +(-5.10474 + 4.28338i) q^{49} +(-11.2644 - 4.09990i) q^{50} +(2.75531 - 2.07373i) q^{51} +(2.74906 - 15.5907i) q^{52} +5.40034 q^{53} +(-12.2541 + 2.35945i) q^{54} -0.287915 q^{55} +(0.427492 - 2.42443i) q^{56} +(-6.12946 - 2.60607i) q^{57} +(14.4423 + 5.25657i) q^{58} +(-7.87850 + 6.61085i) q^{59} +(0.275462 + 0.541415i) q^{60} +(12.4005 - 4.51341i) q^{61} +(1.99034 - 3.44738i) q^{62} +(-1.44333 + 0.971060i) q^{63} +(5.18386 + 8.97871i) q^{64} +(0.299609 + 0.251402i) q^{65} +(-9.40470 - 8.78041i) q^{66} +(-1.53458 - 8.70304i) q^{67} +(-1.30264 - 7.38764i) q^{68} +(1.73937 - 7.51381i) q^{69} +(0.0993013 + 0.0833237i) q^{70} +(-0.572473 - 0.991553i) q^{71} +(-3.52514 + 12.2391i) q^{72} +(-0.0977361 + 0.169284i) q^{73} +(9.09506 - 3.31033i) q^{74} +(8.63313 + 0.457552i) q^{75} +(-11.0990 + 9.31317i) q^{76} +(-1.68539 - 0.613433i) q^{77} +(2.11980 + 17.3491i) q^{78} +(-1.25166 + 7.09849i) q^{79} +0.247661 q^{80} +(7.95648 - 4.20647i) q^{81} +2.63255 q^{82} +(-2.58744 + 14.6741i) q^{83} +(0.458958 + 3.75624i) q^{84} +(0.174151 + 0.0633858i) q^{85} +(12.6963 - 10.6535i) q^{86} +(-11.0687 - 0.586638i) q^{87} +(-12.3399 + 4.49135i) q^{88} +(0.776563 - 1.34505i) q^{89} +(-0.465305 - 0.482977i) q^{90} +(1.21821 + 2.11000i) q^{91} +(-12.8521 - 10.7842i) q^{92} +(-0.647457 + 2.79691i) q^{93} +(-1.49850 - 8.49839i) q^{94} +(-0.0621565 - 0.352507i) q^{95} +(-2.66030 - 2.48371i) q^{96} +(4.05661 + 3.40390i) q^{97} +(-8.00191 - 13.8597i) q^{98} +(8.33533 + 4.07760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23}+ \cdots - 27 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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	0.372760	+	0.927928i	$0.378411\pi$
$2$	−0.417037	+	2.36514i	−0.294890	+	1.67240i	−0.667650	+	0.744475i	$0.732700\pi$
$3$	−0.210069	−	1.71926i	−0.121284	−	0.992618i
$3$	−0.210069	−	1.71926i	−0.121284	−	0.992618i
$4$	−3.54056	−	1.28866i	−1.77028	−	0.644329i
$5$	0.0713060	−	0.0598329i	0.0318890	−	0.0267581i	−0.626704	−	0.779258i	$-0.715596\pi$
$5$	0.0713060	−	0.0598329i	0.0318890	−	0.0267581i	0.658593	+	0.752499i	$0.271152\pi$
$6$	4.15390	+	0.220155i	1.69582	+	0.0898778i
$7$	0.544891	−	0.198324i	0.205950	−	0.0749595i	−0.236986	−	0.971513i	$-0.576159\pi$
$7$	0.544891	−	0.198324i	0.205950	−	0.0749595i	0.442935	+	0.896554i	$0.353937\pi$
$8$	2.12277	−	3.67675i	0.750514	−	1.29993i
$9$	−2.91174	+	0.722330i	−0.970581	+	0.240777i
$10$	0.111776	+	0.193601i	0.0353465	+	0.0612220i
$11$	−2.36944	−	1.98820i	−0.714413	−	0.599464i	0.211421	−	0.977395i	$-0.432191\pi$
$11$	−2.36944	−	1.98820i	−0.714413	−	0.599464i	−0.925834	+	0.377932i	$0.876635\pi$
$12$	−1.47178	+	6.35787i	−0.424867	+	1.83536i
$13$	0.729623	+	4.13790i	0.202361	+	1.14765i	0.901539	+	0.432699i	$0.142439\pi$
$13$	0.729623	+	4.13790i	0.202361	+	1.14765i	−0.699178	+	0.714948i	$0.746450\pi$
$14$	0.241824	+	1.37145i	0.0646301	+	0.366536i
$15$	−0.117848	−	0.110025i	−0.0304282	−	0.0284083i
$16$	2.03816	+	1.71022i	0.509540	+	0.427555i
$17$	0.995493	+	1.72424i	0.241443	+	0.418191i	0.961125	−	0.276112i	$-0.0890461\pi$
$17$	0.995493	+	1.72424i	0.241443	+	0.418191i	−0.719683	+	0.694303i	$0.755713\pi$
$18$	−0.494102	−	7.18790i	−0.116461	−	1.69420i
$19$	1.92271	−	3.33023i	0.441100	−	0.764008i	−0.556671	−	0.830733i	$-0.687922\pi$
$19$	1.92271	−	3.33023i	0.441100	−	0.764008i	0.997771	+	0.0667249i	$0.0212550\pi$
$20$	−0.329567	+	0.119953i	−0.0736935	+	0.0268222i
$21$	−0.455437	−	0.895151i	−0.0993845	−	0.195338i
$22$	5.69050	−	4.77489i	1.21322	−	1.01801i
$23$	4.18428	+	1.52295i	0.872482	+	0.317558i	0.739172	−	0.673517i	$-0.235217\pi$
$23$	4.18428	+	1.52295i	0.872482	+	0.317558i	0.133310	+	0.991074i	$0.457439\pi$
$24$	−6.76724	−	2.87724i	−1.38136	−	0.587314i
$25$	−0.866736	+	4.91551i	−0.173347	+	0.983101i
$26$	−10.0910			−1.97900
$27$	1.85354	+	4.85432i	0.356715	+	0.934213i
$28$	−2.18479			−0.412887
$29$	1.11126	−	6.30229i	0.206356	−	1.17031i	−0.688935	−	0.724823i	$-0.741921\pi$
$29$	1.11126	−	6.30229i	0.206356	−	1.17031i	0.895291	−	0.445482i	$-0.146968\pi$
$30$	0.309371	−	0.232841i	0.0564831	−	0.0425108i
$31$	−1.55754	−	0.566898i	−0.279743	−	0.101818i	0.198339	−	0.980134i	$-0.436445\pi$
$31$	−1.55754	−	0.566898i	−0.279743	−	0.101818i	−0.478081	+	0.878316i	$0.658668\pi$
$32$	1.60967	−	1.35067i	0.284552	−	0.238767i
$33$	−2.92049	+	4.49135i	−0.508392	+	0.781844i
$34$	−4.49323	+	1.63540i	−0.770582	+	0.280469i
$35$	0.0269877	−	0.0467441i	0.00456176	−	0.00790120i
$36$	11.2400	+	1.19479i	1.87334	+	0.199132i
$37$	−2.01505	−	3.49016i	−0.331272	−	0.573779i	0.651490	−	0.758657i	$-0.274144\pi$
$37$	−2.01505	−	3.49016i	−0.331272	−	0.573779i	−0.982761	+	0.184878i	$0.940811\pi$
$38$	7.07461	+	5.93630i	1.14765	+	0.962996i
$39$	6.96087	−	2.12366i	1.11463	−	0.340058i
$40$	−0.0686240	−	0.389186i	−0.0108504	−	0.0615358i
$41$	−0.190345	−	1.07950i	−0.0297270	−	0.168590i	0.966330	−	0.257306i	$-0.0828348\pi$
$41$	−0.190345	−	1.07950i	−0.0297270	−	0.168590i	−0.996057	+	0.0887159i	$0.971724\pi$
$42$	2.30709	−	0.703859i	0.355991	−	0.108608i
$43$	−5.28657	−	4.43596i	−0.806194	−	0.676477i	0.143502	−	0.989650i	$-0.454164\pi$
$43$	−5.28657	−	4.43596i	−0.806194	−	0.676477i	−0.949696	+	0.313173i	$0.898608\pi$
$44$	5.82704	+	10.0927i	0.878459	+	1.52154i
$45$	−0.164406	+	0.225724i	−0.0245082	+	0.0336490i
$46$	−5.34699	+	9.26126i	−0.788370	+	1.36550i
$47$	−3.37650	+	1.22894i	−0.492513	+	0.179260i	−0.576323	−	0.817222i	$-0.695513\pi$
$47$	−3.37650	+	1.22894i	−0.492513	+	0.179260i	0.0838106	+	0.996482i	$0.473291\pi$
$48$	2.51217	−	3.86340i	0.362600	−	0.557634i
$49$	−5.10474	+	4.28338i	−0.729248	+	0.611912i
$50$	−11.2644	−	4.09990i	−1.59302	−	0.579813i
$51$	2.75531	−	2.07373i	0.385821	−	0.290380i
$52$	2.74906	−	15.5907i	0.381226	−	2.16204i
$53$	5.40034			0.741793			0.370897	−	0.928674i	$-0.379050\pi$
$53$	5.40034			0.741793			0.370897	+	0.928674i	$0.379050\pi$
$54$	−12.2541	+	2.35945i	−1.66757	+	0.321081i
$55$	−0.287915			−0.0388224
$56$	0.427492	−	2.42443i	0.0571260	−	0.323978i
$57$	−6.12946	−	2.60607i	−0.811866	−	0.345182i
$58$	14.4423	+	5.25657i	1.89637	+	0.690222i
$59$	−7.87850	+	6.61085i	−1.02569	+	0.860659i	−0.990332	−	0.138715i	$-0.955703\pi$
$59$	−7.87850	+	6.61085i	−1.02569	+	0.860659i	−0.0353615	+	0.999375i	$0.511258\pi$
$60$	0.275462	+	0.541415i	0.0355620	+	0.0698964i
$61$	12.4005	−	4.51341i	1.58772	−	0.577883i	0.610855	−	0.791742i	$-0.290826\pi$
$61$	12.4005	−	4.51341i	1.58772	−	0.577883i	0.976864	+	0.213860i	$0.0686036\pi$
$62$	1.99034	−	3.44738i	0.252774	−	0.437817i
$63$	−1.44333	+	0.971060i	−0.181842	+	0.122342i
$64$	5.18386	+	8.97871i	0.647982	+	1.12234i
$65$	0.299609	+	0.251402i	0.0371619	+	0.0311825i
$66$	−9.40470	−	8.78041i	−1.15764	−	1.08079i
$67$	−1.53458	−	8.70304i	−0.187479	−	1.06324i	−0.922729	−	0.385449i	$-0.874046\pi$
$67$	−1.53458	−	8.70304i	−0.187479	−	1.06324i	0.735250	−	0.677796i	$-0.237065\pi$
$68$	−1.30264	−	7.38764i	−0.157968	−	0.895883i
$69$	1.73937	−	7.51381i	0.209396	−	0.904556i
$70$	0.0993013	+	0.0833237i	0.0118688	+	0.00995909i
$71$	−0.572473	−	0.991553i	−0.0679401	−	0.117676i	0.830054	−	0.557683i	$-0.188309\pi$
$71$	−0.572473	−	0.991553i	−0.0679401	−	0.117676i	−0.897994	+	0.440007i	$0.854976\pi$
$72$	−3.52514	+	12.2391i	−0.415442	+	1.44239i
$73$	−0.0977361	+	0.169284i	−0.0114391	+	0.0198132i	−0.871688	−	0.490061i	$-0.836975\pi$
$73$	−0.0977361	+	0.169284i	−0.0114391	+	0.0198132i	0.860249	+	0.509874i	$0.170308\pi$
$74$	9.09506	−	3.31033i	1.05728	−	0.384818i
$75$	8.63313	+	0.457552i	0.996868	+	0.0528336i
$76$	−11.0990	+	9.31317i	−1.27314	+	1.06829i
$77$	−1.68539	−	0.613433i	−0.192069	−	0.0699072i
$78$	2.11980	+	17.3491i	0.240020	+	1.96439i
$79$	−1.25166	+	7.09849i	−0.140822	+	0.798642i	0.829805	+	0.558054i	$0.188452\pi$
$79$	−1.25166	+	7.09849i	−0.140822	+	0.798642i	−0.970627	+	0.240589i	$0.922659\pi$
$80$	0.247661			0.0276893
$81$	7.95648	−	4.20647i	0.884053	−	0.467386i
$82$	2.63255			0.290717
$83$	−2.58744	+	14.6741i	−0.284008	+	1.61069i	0.424800	+	0.905287i	$0.360344\pi$
$83$	−2.58744	+	14.6741i	−0.284008	+	1.61069i	−0.708808	+	0.705402i	$0.750767\pi$
$84$	0.458958	+	3.75624i	0.0500764	+	0.409839i
$85$	0.174151	+	0.0633858i	0.0188893	+	0.00687516i
$86$	12.6963	−	10.6535i	1.36908	−	1.14879i
$87$	−11.0687	−	0.586638i	−1.18669	−	0.0628942i
$88$	−12.3399	+	4.49135i	−1.31544	+	0.478780i
$89$	0.776563	−	1.34505i	0.0823155	−	0.142575i	−0.821929	−	0.569590i	$-0.807102\pi$
$89$	0.776563	−	1.34505i	0.0823155	−	0.142575i	0.904244	+	0.427016i	$0.140435\pi$
$90$	−0.465305	−	0.482977i	−0.0490475	−	0.0509103i
$91$	1.21821	+	2.11000i	0.127703	+	0.221189i
$92$	−12.8521	−	10.7842i	−1.33993	−	1.12433i
$93$	−0.647457	+	2.79691i	−0.0671381	+	0.290026i
$94$	−1.49850	−	8.49839i	−0.154558	−	0.876542i
$95$	−0.0621565	−	0.352507i	−0.00637712	−	0.0361665i
$96$	−2.66030	−	2.48371i	−0.271516	−	0.253492i
$97$	4.05661	+	3.40390i	0.411887	+	0.345614i	0.825067	−	0.565035i	$-0.191137\pi$
$97$	4.05661	+	3.40390i	0.411887	+	0.345614i	−0.413180	+	0.910649i	$0.635582\pi$
$98$	−8.00191	−	13.8597i	−0.808315	−	1.40004i
$99$	8.33533	+	4.07760i	0.837732	+	0.409814i
$100$	9.40314	−	16.2867i	0.940314	−	1.62867i
$101$	6.83061	−	2.48614i	0.679671	−	0.247380i	0.0209647	−	0.999780i	$-0.493326\pi$
$101$	6.83061	−	2.48614i	0.679671	−	0.247380i	0.658706	+	0.752400i	$0.271104\pi$
$102$	3.75558	+	7.38150i	0.371858	+	0.730878i
$103$	4.90374	−	4.11472i	0.483179	−	0.405436i	−0.368395	−	0.929669i	$-0.620093\pi$
$103$	4.90374	−	4.11472i	0.483179	−	0.405436i	0.851574	+	0.524234i	$0.175648\pi$
$104$	16.7629	+	6.10118i	1.64373	+	0.598270i
$105$	−0.0860348	−	0.0365796i	−0.00839614	−	0.00356980i
$106$	−2.25214	+	12.7725i	−0.218747	+	1.24058i
$107$	−5.54365			−0.535925			−0.267963	−	0.963429i	$-0.586350\pi$
$107$	−5.54365			−0.535925			−0.267963	+	0.963429i	$0.586350\pi$
$108$	−0.307026	−	19.5756i	−0.0295436	−	1.88366i
$109$	−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
$111$	−5.57722	+	4.19758i	−0.529366	+	0.398416i
$112$	1.44975	+	0.527668i	0.136989	+	0.0498599i
$113$	−9.07301	+	7.61316i	−0.853517	+	0.716186i	−0.960561	−	0.278068i	$-0.910306\pi$
$113$	−9.07301	+	7.61316i	−0.853517	+	0.716186i	0.107044	+	0.994254i	$0.465861\pi$
$114$	8.71992	−	13.4102i	0.816695	−	1.25598i
$115$	0.389487	−	0.141762i	0.0363198	−	0.0132193i
$116$	−12.0560	+	20.8816i	−1.11937	+	1.93881i
$117$	−5.11340	−	11.5215i	−0.472734	−	1.06516i
$118$	−12.3499	−	21.3907i	−1.13690	−	1.96917i
$119$	0.884395	+	0.742096i	0.0810724	+	0.0680278i
$120$	−0.654698	+	0.199739i	−0.0597655	+	0.0182336i
$121$	−0.248809	−	1.41107i	−0.0226190	−	0.128279i
$122$	5.50336	+	31.2111i	0.498250	+	2.82572i
$123$	−1.81597	+	0.554025i	−0.163740	+	0.0499547i
$124$	4.78403	+	4.01427i	0.429618	+	0.360492i
$125$	0.465014	+	0.805428i	0.0415921	+	0.0720396i
$126$	−1.69477	−	3.81863i	−0.150982	−	0.340191i
$127$	−5.76469	+	9.98473i	−0.511533	+	0.886002i	0.488377	+	0.872633i	$0.337589\pi$
$127$	−5.76469	+	9.98473i	−0.511533	+	0.886002i	−0.999911	+	0.0133693i	$0.995744\pi$
$128$	−19.4486	+	7.07872i	−1.71903	+	0.625676i
$129$	−6.51604	+	10.0209i	−0.573705	+	0.882288i
$130$	−0.719547	+	0.603772i	−0.0631085	+	0.0529543i
$131$	8.46830	+	3.08221i	0.739879	+	0.269294i	0.684340	−	0.729163i	$-0.260090\pi$
$131$	8.46830	+	3.08221i	0.739879	+	0.269294i	0.0555383	+	0.998457i	$0.482312\pi$
$132$	16.1280	−	12.1384i	1.40376	−	1.05651i
$133$	0.387203	−	2.19594i	0.0335747	−	0.190412i
$134$	21.2238			1.83346
$135$	0.422616	+	0.235239i	0.0363730	+	0.0202462i
$136$	8.45283			0.724824
$137$	2.00047	−	11.3452i	0.170911	−	0.969287i	−0.771846	−	0.635809i	$-0.780667\pi$
$137$	2.00047	−	11.3452i	0.170911	−	0.969287i	0.942758	−	0.333478i	$-0.108222\pi$
$138$	17.0458	+	7.24738i	1.45103	+	0.616938i
$139$	−1.60108	−	0.582746i	−0.135802	−	0.0494279i	0.273225	−	0.961950i	$-0.411910\pi$
$139$	−1.60108	−	0.582746i	−0.135802	−	0.0494279i	−0.409027	+	0.912522i	$0.634132\pi$
$140$	−0.155789	+	0.130722i	−0.0131666	+	0.0110481i
$141$	2.82218	+	5.54693i	0.237670	+	0.467136i
$142$	2.58390	−	0.940462i	0.216836	−	0.0789219i
$143$	6.49816	−	11.2551i	0.543403	−	0.941202i
$144$	−7.16994	−	3.50750i	−0.597495	−	0.292291i
$145$	−0.297844	−	0.515881i	−0.0247346	−	0.0428416i
$146$	−0.359620	−	0.301757i	−0.0297623	−	0.0249736i
$147$	8.43662	+	7.87659i	0.695840	+	0.649650i
$148$	2.63677	+	14.9538i	0.216741	+	1.22920i
$149$	−3.75996	−	21.3238i	−0.308028	−	1.74691i	−0.608897	−	0.793249i	$-0.708388\pi$
$149$	−3.75996	−	21.3238i	−0.308028	−	1.74691i	0.300869	−	0.953666i	$-0.402723\pi$
$150$	−4.68251	+	20.2277i	−0.382325	+	1.65159i
$151$	−3.63222	−	3.04779i	−0.295586	−	0.248026i	0.482918	−	0.875665i	$-0.339577\pi$
$151$	−3.63222	−	3.04779i	−0.295586	−	0.248026i	−0.778504	+	0.627640i	$0.784021\pi$
$152$	−8.16296	−	14.1387i	−0.662104	−	1.14680i
$153$	−4.14409	−	4.30148i	−0.335030	−	0.347754i
$154$	2.15373	−	3.73036i	0.173552	−	0.300601i
$155$	−0.144981	+	0.0527688i	−0.0116452	+	0.00423849i
$156$	−27.3821	−	1.45124i	−2.19232	−	0.116192i
$157$	−0.160261	+	0.134475i	−0.0127902	+	0.0107323i	−0.649160	−	0.760652i	$-0.724880\pi$
$157$	−0.160261	+	0.134475i	−0.0127902	+	0.0107323i	0.636370	+	0.771384i	$0.280435\pi$
$158$	−16.2669	−	5.92067i	−1.29412	−	0.471023i
$159$	−1.13444	−	9.28461i	−0.0899673	−	0.736317i
$160$	0.0339644	−	0.192622i	0.00268513	−	0.0152281i
$161$	2.58202			0.203491
$162$	6.63073	+	20.5724i	0.520960	+	1.61632i
$163$	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
$165$	0.0604821	+	0.495002i	0.00470852	+	0.0385358i
$166$	−33.6271	−	12.2393i	−2.60997	−	0.949951i
$167$	12.7780	−	10.7220i	0.988791	−	0.829695i	0.00339914	−	0.999994i	$-0.498918\pi$
$167$	12.7780	−	10.7220i	0.988791	−	0.829695i	0.985392	+	0.170300i	$0.0544736\pi$
$168$	−4.25804	−	0.225674i	−0.328515	−	0.0174111i
$169$	−4.37386	+	1.59195i	−0.336451	+	0.122458i
$170$	−0.222544	+	0.385457i	−0.0170683	+	0.0295632i
$171$	−3.19291	+	11.0856i	−0.244168	+	0.847738i
$172$	13.0010	+	22.5183i	0.991315	+	1.71701i
$173$	14.5565	+	12.2143i	1.10671	+	0.928639i	0.997858	−	0.0654187i	$-0.0208383\pi$
$173$	14.5565	+	12.2143i	1.10671	+	0.928639i	0.108851	+	0.994058i	$0.465283\pi$
$174$	6.00355	−	25.9344i	0.455128	−	1.96608i
$175$	0.502587	+	2.85031i	0.0379920	+	0.215463i
$176$	−1.42905	−	8.10453i	−0.107718	−	0.610902i
$177$	13.0208	+	12.1565i	0.978706	+	0.913738i
$178$	2.85736	+	2.39761i	0.214168	+	0.179709i
$179$	−8.11761	−	14.0601i	−0.606739	−	1.05090i	−0.991774	−	0.128001i	$-0.959144\pi$
$179$	−8.11761	−	14.0601i	−0.606739	−	1.05090i	0.385035	−	0.922902i	$-0.374189\pi$
$180$	0.872970	−	0.587328i	0.0650673	−	0.0437768i
$181$	1.49579	−	2.59078i	0.111181	−	0.192571i	−0.805066	−	0.593186i	$-0.797870\pi$
$181$	1.49579	−	2.59078i	0.111181	−	0.192571i	0.916247	+	0.400614i	$0.131203\pi$
$182$	−5.49848	+	2.00128i	−0.407575	+	0.148345i
$183$	−10.3647	−	20.3716i	−0.766181	−	1.50591i
$184$	14.4818	−	12.1517i	1.06761	−	0.895833i
$185$	−0.352512	−	0.128304i	−0.0259172	−	0.00943308i
$186$	−6.34506	−	2.69774i	−0.465242	−	0.197808i
$187$	1.06938	−	6.06473i	0.0782005	−	0.443497i
$188$	13.5384			0.987388
$189$	1.97271	+	2.27747i	0.143493	+	0.165662i
$190$	0.859649			0.0623655
$191$	−0.391371	+	2.21958i	−0.0283186	+	0.160603i	−0.995688	−	0.0927685i	$-0.970428\pi$
$191$	−0.391371	+	2.21958i	−0.0283186	+	0.160603i	0.967369	+	0.253371i	$0.0815395\pi$
$192$	14.3478	−	10.7986i	1.03546	−	0.779320i
$193$	0.827186	+	0.301071i	0.0595422	+	0.0216716i	0.371620	−	0.928385i	$-0.378803\pi$
$193$	0.827186	+	0.301071i	0.0595422	+	0.0216716i	−0.312077	+	0.950057i	$0.601025\pi$
$194$	−9.74245	+	8.17489i	−0.699467	+	0.586923i
$195$	0.369287	−	0.567919i	0.0264452	−	0.0406695i
$196$	23.5934	−	8.58731i	1.68525	−	0.613379i
$197$	−10.1383	+	17.5600i	−0.722322	+	1.25110i	0.237744	+	0.971328i	$0.423592\pi$
$197$	−10.1383	+	17.5600i	−0.722322	+	1.25110i	−0.960067	+	0.279771i	$0.909741\pi$
$198$	−13.1202	+	18.0137i	−0.932413	+	1.28018i
$199$	9.50472	+	16.4627i	0.673772	+	1.16701i	0.976826	+	0.214034i	$0.0686603\pi$
$199$	9.50472	+	16.4627i	0.673772	+	1.16701i	−0.303054	+	0.952973i	$0.598006\pi$
$200$	16.2332	+	13.6213i	1.14786	+	0.963170i
$201$	−14.6405	+	4.46659i	−1.03266	+	0.315049i
$202$	3.03144	+	17.1921i	0.213291	+	1.20963i
$203$	−0.644379	−	3.65445i	−0.0452265	−	0.256492i
$204$	−12.4277	+	3.79150i	−0.870110	+	0.265458i
$205$	−0.0781625	−	0.0655862i	−0.00545911	−	0.00458074i
$206$	7.68684	+	13.3140i	0.535567	+	0.927630i
$207$	−13.2836	−	1.41202i	−0.923275	−	0.0981420i
$208$	−5.58963	+	9.68152i	−0.387571	+	0.671293i
$209$	−11.1769	+	4.06806i	−0.773123	+	0.281394i
$210$	0.122395	−	0.188229i	0.00844608	−	0.0129890i
$211$	12.3977	−	10.4029i	0.853494	−	0.716166i	−0.107062	−	0.994252i	$-0.534144\pi$
$211$	12.3977	−	10.4029i	0.853494	−	0.716166i	0.960556	+	0.278086i	$0.0897000\pi$
$212$	−19.1202	−	6.95919i	−1.31318	−	0.477959i
$213$	−1.58448	+	1.19253i	−0.108567	+	0.0817107i
$214$	2.31191	−	13.1115i	0.158039	−	0.896283i
$215$	−0.642380			−0.0438100
$216$	21.7828	+	3.48960i	1.48213	+	0.237437i
$217$	−0.961120			−0.0652451
$218$	2.59871	−	14.7380i	0.176007	−	0.998186i
$219$	0.311575	+	0.132473i	0.0210543	+	0.00895168i
$220$	1.01938	+	0.371024i	0.0687265	+	0.0250144i
$221$	−6.40842	+	5.37730i	−0.431077	+	0.361716i
$222$	−7.60193	−	14.9414i	−0.510208	−	1.00280i
$223$	−20.1633	+	7.33883i	−1.35023	+	0.491444i	−0.913020	−	0.407914i	$-0.866256\pi$
$223$	−20.1633	+	7.33883i	−1.35023	+	0.491444i	−0.437212	+	0.899359i	$0.644034\pi$
$224$	0.609223	−	1.05520i	0.0407054	−	0.0705038i
$225$	−1.02690	−	14.9388i	−0.0684602	−	0.995917i
$226$	−14.2224	−	24.6339i	−0.946058	−	1.63862i
$227$	−14.6424	−	12.2864i	−0.971848	−	0.815477i	0.0109918	−	0.999940i	$-0.496501\pi$
$227$	−14.6424	−	12.2864i	−0.971848	−	0.815477i	−0.982840	+	0.184462i	$0.940946\pi$
$228$	18.3434	+	17.1257i	1.21482	+	1.13418i
$229$	3.90190	+	22.1288i	0.257845	+	1.46231i	0.788663	+	0.614826i	$0.210774\pi$
$229$	3.90190	+	22.1288i	0.257845	+	1.46231i	−0.530818	+	0.847486i	$0.678115\pi$
$230$	0.172855	+	0.980309i	0.0113977	+	0.0646397i
$231$	−0.700605	+	3.02650i	−0.0460964	+	0.199129i
$232$	−20.8130	−	17.4642i	−1.36644	−	1.14658i
$233$	8.84074	+	15.3126i	0.579176	+	1.00316i	0.995574	+	0.0939796i	$0.0299589\pi$
$233$	8.84074	+	15.3126i	0.579176	+	1.00316i	−0.416398	+	0.909182i	$0.636708\pi$
$234$	29.3823	−	7.28901i	1.92078	−	0.476497i
$235$	−0.167233	+	0.289657i	−0.0109091	+	0.0188951i
$236$	36.4134	−	13.2534i	2.37031	−	0.862723i
$237$	12.4671	+	0.660752i	0.809826	+	0.0429204i
$238$	−2.12398	+	1.78223i	−0.137677	+	0.115525i
$239$	14.4904	+	5.27406i	0.937303	+	0.341151i	0.765100	−	0.643911i	$-0.222689\pi$
$239$	14.4904	+	5.27406i	0.937303	+	0.341151i	0.172203	+	0.985061i	$0.444912\pi$
$240$	−0.0520259	−	0.425794i	−0.00335826	−	0.0274849i
$241$	2.28373	−	12.9516i	0.147108	−	0.834289i	−0.818543	−	0.574445i	$-0.805218\pi$
$241$	2.28373	−	12.9516i	0.147108	−	0.834289i	0.965651	−	0.259844i	$-0.0836711\pi$
$242$	3.44113			0.221204
$243$	−8.90345	−	12.7956i	−0.571157	−	0.820841i
$244$	−49.7209			−3.18305
$245$	−0.107711	+	0.610862i	−0.00688143	+	0.0390265i
$246$	−0.553018	−	4.52605i	−0.0352592	−	0.288571i
$247$	15.1830	+	5.52617i	0.966073	+	0.351622i
$248$	−5.39065	+	4.52329i	−0.342307	+	0.287229i
$249$	25.7722	+	1.36591i	1.63324	+	0.0865612i
$250$	−2.09887	+	0.763927i	−0.132744	+	0.0483150i
$251$	−8.70830	+	15.0832i	−0.549663	+	0.952045i	0.448634	+	0.893716i	$0.351911\pi$
$251$	−8.70830	+	15.0832i	−0.549663	+	0.952045i	−0.998297	+	0.0583292i	$0.981423\pi$
$252$	6.36155	−	1.57814i	0.400740	−	0.0994135i
$253$	−6.88646	−	11.9277i	−0.432948	−	0.749889i
$254$	−21.2112	−	17.7983i	−1.33091	−	1.11676i
$255$	0.0723932	−	0.312727i	0.00453344	−	0.0195837i
$256$	−5.03066	−	28.5303i	−0.314416	−	1.78314i
$257$	1.94270	+	11.0176i	0.121182	+	0.687260i	0.983502	+	0.180896i	$0.0578997\pi$
$257$	1.94270	+	11.0176i	0.121182	+	0.687260i	−0.862320	+	0.506364i	$0.830989\pi$
$258$	−20.9833	−	19.5904i	−1.30636	−	1.21964i
$259$	−1.79017	−	1.50213i	−0.111236	−	0.0933377i
$260$	−0.736812	−	1.27620i	−0.0456952	−	0.0791463i
$261$	1.31662	+	19.1533i	0.0814965	+	1.18556i
$262$	−10.8214	+	18.7433i	−0.668550	+	1.15796i
$263$	19.4619	−	7.08354i	1.20007	−	0.436790i	0.336821	−	0.941569i	$-0.390648\pi$
$263$	19.4619	−	7.08354i	1.20007	−	0.436790i	0.863249	+	0.504779i	$0.168426\pi$
$264$	10.3141	+	20.2720i	0.634786	+	1.24766i
$265$	0.385077	−	0.323118i	0.0236551	−	0.0198490i
$266$	5.03221	+	1.83157i	0.308544	+	0.112301i
$267$	−2.47562	−	1.05256i	−0.151506	−	0.0644159i
$268$	−5.78197	+	32.7912i	−0.353190	+	2.00304i
$269$	−28.2449			−1.72212			−0.861060	−	0.508504i	$-0.830199\pi$
$269$	−28.2449			−1.72212			−0.861060	+	0.508504i	$0.830199\pi$
$270$	−0.732619	+	0.901441i	−0.0445858	+	0.0548600i
$271$	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
$273$	3.37175	−	2.53767i	0.204067	−	0.153587i
$274$	25.9987	+	9.46275i	1.57064	+	0.571666i
$275$	11.8267	−	9.92375i	0.713175	−	0.598425i
$276$	−15.8411	+	24.3616i	−0.953520	+	1.46640i
$277$	−4.85725	+	1.76789i	−0.291844	+	0.106222i	−0.483793	−	0.875182i	$-0.660741\pi$
$277$	−4.85725	+	1.76789i	−0.291844	+	0.106222i	0.191949	+	0.981405i	$0.438519\pi$
$278$	2.04598	−	3.54375i	0.122710	−	0.212540i
$279$	4.94464	+	0.525604i	0.296028	+	0.0314671i
$280$	−0.114578	−	0.198454i	−0.00684733	−	0.0118599i
$281$	−2.52522	−	2.11891i	−0.150642	−	0.126404i	0.564352	−	0.825534i	$-0.309126\pi$
$281$	−2.52522	−	2.11891i	−0.150642	−	0.126404i	−0.714994	+	0.699131i	$0.753571\pi$
$282$	−14.2962	+	4.36156i	−0.851326	+	0.259727i
$283$	−1.58553	−	8.99200i	−0.0942501	−	0.534519i	−0.994975	−	0.100128i	$-0.968075\pi$
$283$	−1.58553	−	8.99200i	−0.0942501	−	0.534519i	0.900724	−	0.434391i	$-0.143036\pi$
$284$	0.749103	+	4.24837i	0.0444511	+	0.252095i
$285$	−0.592996	+	0.180914i	−0.0351260	+	0.0107164i
$286$	23.9099	+	20.0628i	1.41382	+	1.18634i
$287$	−0.317809	−	0.550462i	−0.0187597	−	0.0324927i
$288$	−3.71130	+	5.09551i	−0.218691	+	0.300256i
$289$	6.51799	−	11.2895i	0.383411	−	0.664087i
$290$	1.34434	−	0.489300i	0.0789424	−	0.0287327i
$291$	5.00004	−	7.68945i	0.293108	−	0.450764i
$292$	0.564189	−	0.473411i	0.0330167	−	0.0277043i
$293$	2.65598	+	0.966697i	0.155164	+	0.0564750i	0.418434	−	0.908247i	$-0.362579\pi$
$293$	2.65598	+	0.966697i	0.155164	+	0.0564750i	−0.263271	+	0.964722i	$0.584801\pi$
$294$	−22.1476	+	16.6689i	−1.29167	+	0.972151i
$295$	−0.166239	+	0.942787i	−0.00967880	+	0.0548912i
$296$	−17.1100			−0.994496
$297$	5.25947	−	15.1872i	0.305185	−	0.881251i
$298$	52.0017			3.01238
$299$	−3.24888	+	18.4253i	−0.187887	+	1.06556i
$300$	−29.9765	−	12.7451i	−1.73069	−	0.735841i
$301$	−3.76036	−	1.36866i	−0.216744	−	0.0788882i
$302$	8.72321	−	7.31964i	0.501964	−	0.421198i
$303$	−5.70923	−	11.2214i	−0.327987	−	0.644650i
$304$	9.61423	−	3.49929i	0.551414	−	0.200698i
$305$	0.614179	−	1.06379i	0.0351678	−	0.0609124i
$306$	11.9018	−	8.00746i	0.680382	−	0.457756i
$307$	−3.14723	−	5.45116i	−0.179622	−	0.311114i	0.762129	−	0.647425i	$-0.224154\pi$
$307$	−3.14723	−	5.45116i	−0.179622	−	0.311114i	−0.941751	+	0.336311i	$0.890821\pi$
$308$	5.17673	+	4.34380i	0.294972	+	0.247511i
$309$	−8.10442	−	7.56644i	−0.461045	−	0.430440i
$310$	−0.0643429	−	0.364907i	−0.00365443	−	0.0207253i
$311$	−1.28029	−	7.26088i	−0.0725985	−	0.411727i	−0.999350	−	0.0360515i	$-0.988522\pi$
$311$	−1.28029	−	7.26088i	−0.0725985	−	0.411727i	0.926751	−	0.375675i	$-0.122589\pi$
$312$	6.96818	−	30.1015i	0.394496	−	1.70416i
$313$	−3.27159	−	2.74519i	−0.184921	−	0.155167i	0.545628	−	0.838028i	$-0.316291\pi$
$313$	−3.27159	−	2.74519i	−0.184921	−	0.155167i	−0.730549	+	0.682860i	$0.760736\pi$
$314$	−0.251217	−	0.435120i	−0.0141770	−	0.0245552i
$315$	−0.0448167	+	0.155601i	−0.00252513	+	0.00876712i
$316$	13.5791	−	23.5197i	0.763883	−	1.32308i
$317$	−15.1738	+	5.52279i	−0.852243	+	0.310191i	−0.730954	−	0.682426i	$-0.760925\pi$
$317$	−15.1738	+	5.52279i	−0.852243	+	0.310191i	−0.121288	+	0.992617i	$0.538703\pi$
$318$	22.4325	+	1.18891i	1.25795	+	0.0666708i
$319$	−15.1632	+	12.7235i	−0.848979	+	0.712378i
$320$	0.906862	+	0.330071i	0.0506951	+	0.0184515i
$321$	1.16455	+	9.53101i	0.0649989	+	0.531969i
$322$	−1.07680	+	6.10682i	−0.0600075	+	0.340320i
$323$	7.65618			0.426001
$324$	−33.5911	+	4.64009i	−1.86617	+	0.257783i
$325$	−20.9723			−1.16333
$326$	−2.34535	+	13.3012i	−0.129897	+	0.736683i
$327$	1.30902	+	10.7134i	0.0723890	+	0.592451i
$328$	−4.37313	−	1.59169i	−0.241465	−	0.0878862i
$329$	−1.59610	+	1.33928i	−0.0879956	+	0.0738371i
$330$	−1.19597	−	0.0633858i	−0.0658359	−	0.00348928i
$331$	−18.0686	+	6.57644i	−0.993142	+	0.361474i	−0.786936	−	0.617035i	$-0.788334\pi$
$331$	−18.0686	+	6.57644i	−0.993142	+	0.361474i	−0.206206	+	0.978509i	$0.566112\pi$
$332$	28.0708	−	48.6201i	1.54059	−	2.66838i
$333$	8.38834	+	8.70693i	0.459678	+	0.477137i
$334$	20.0301	+	34.6932i	1.09600	+	1.89833i
$335$	−0.630152	−	0.528761i	−0.0344289	−	0.0288893i
$336$	0.602651	−	2.60336i	0.0328773	−	0.142025i
$337$	−5.11615	−	29.0152i	−0.278695	−	1.58056i	−0.726976	−	0.686663i	$-0.759075\pi$
$337$	−5.11615	−	29.0152i	−0.278695	−	1.58056i	0.448281	−	0.893893i	$-0.352036\pi$
$338$	−1.94112	−	11.0087i	−0.105583	−	0.598792i
$339$	14.9950	+	13.9996i	0.814417	+	0.760355i
$340$	−0.534910	−	0.448843i	−0.0290096	−	0.0243419i
$341$	2.56339	+	4.43993i	0.138815	+	0.240435i
$342$	−24.8874	−	12.1748i	−1.34576	−	0.658337i
$343$	−3.96154	+	6.86159i	−0.213903	+	0.370491i
$344$	−27.5321	+	10.0209i	−1.48443	+	0.540289i
$345$	−0.325545	−	0.639851i	−0.0175268	−	0.0344484i
$346$	−34.9592	+	29.3342i	−1.87942	+	1.57702i
$347$	−10.7097	−	3.89801i	−0.574927	−	0.209256i	0.0381600	−	0.999272i	$-0.487850\pi$
$347$	−10.7097	−	3.89801i	−0.574927	−	0.209256i	−0.613087	+	0.790015i	$0.710073\pi$
$348$	38.4336	+	16.3408i	2.06025	+	0.875961i
$349$	4.89021	−	27.7338i	0.261767	−	1.48456i	−0.516318	−	0.856397i	$-0.672698\pi$
$349$	4.89021	−	27.7338i	0.261767	−	1.48456i	0.778085	−	0.628158i	$-0.216191\pi$
$350$	−6.95097			−0.371545
$351$	−18.7343	+	11.2116i	−0.999962	+	0.598431i
$352$	−6.49941			−0.346419
$353$	4.97573	−	28.2188i	0.264831	−	1.50193i	−0.504683	−	0.863305i	$-0.668391\pi$
$353$	4.97573	−	28.2188i	0.264831	−	1.50193i	0.769515	−	0.638629i	$-0.220498\pi$
$354$	−34.1819	+	25.7263i	−1.81675	+	1.36734i
$355$	−0.100148	−	0.0364510i	−0.00531532	−	0.00193462i
$356$	−4.48277	+	3.76149i	−0.237586	+	0.199359i
$357$	1.09007	−	1.67640i	0.0576929	−	0.0887245i
$358$	36.6394	−	13.3357i	1.93645	−	0.704812i
$359$	15.5161	−	26.8747i	0.818909	−	1.41839i	−0.0875770	−	0.996158i	$-0.527912\pi$
$359$	15.5161	−	26.8747i	0.818909	−	1.41839i	0.906486	−	0.422235i	$-0.138754\pi$
$360$	0.480936	+	1.08364i	0.0253476	+	0.0571129i
$361$	2.10636	+	3.64833i	0.110861	+	0.192017i
$362$	5.50376	+	4.61820i	0.289271	+	0.242727i
$363$	−2.37373	+	0.724191i	−0.124589	+	0.0380102i
$364$	−1.59408	−	9.04045i	−0.0835523	−	0.473848i
$365$	0.00315957	+	0.0179188i	0.000165379	+	0.000937912i
$366$	52.5040	−	16.0182i	2.74443	−	0.837286i
$367$	18.4802	+	15.5067i	0.964660	+	0.809446i	0.981705	−	0.190409i	$-0.0609814\pi$
$367$	18.4802	+	15.5067i	0.964660	+	0.809446i	−0.0170450	+	0.999855i	$0.505426\pi$
$368$	5.92365	+	10.2601i	0.308791	+	0.534843i
$369$	1.33399	+	3.00574i	0.0694449	+	0.156473i
$370$	0.450466	−	0.780230i	0.0234186	−	0.0405622i
$371$	2.94260	−	1.07102i	0.152772	−	0.0556045i
$372$	5.89662	−	9.06828i	0.305726	−	0.470169i
$373$	−9.64114	+	8.08988i	−0.499199	+	0.418878i	−0.857309	−	0.514801i	$-0.827866\pi$
$373$	−9.64114	+	8.08988i	−0.499199	+	0.418878i	0.358110	+	0.933679i	$0.383421\pi$
$374$	13.8979	+	5.05843i	0.718645	+	0.261565i
$375$	1.28706	−	0.968677i	0.0664634	−	0.0500223i
$376$	−2.64902	+	15.0233i	−0.136613	+	0.774769i
$377$	26.8890			1.38486
$378$	−6.20922	+	3.71593i	−0.319368	+	0.191127i
$379$	−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
$381$	18.3774	+	7.81354i	0.941502	+	0.400300i
$382$	−5.08638	−	1.85129i	−0.260242	−	0.0947203i
$383$	−13.6828	+	11.4812i	−0.699159	+	0.586664i	−0.921534	−	0.388297i	$-0.873063\pi$
$383$	−13.6828	+	11.4812i	−0.699159	+	0.586664i	0.222376	+	0.974961i	$0.428619\pi$
$384$	16.2557	+	31.9503i	0.829548	+	1.63046i
$385$	−0.156882	+	0.0571005i	−0.00799546	+	0.00291011i
$386$	−1.05704	+	1.83085i	−0.0538020	+	0.0931878i
$387$	18.5973	+	9.09771i	0.945356	+	0.462463i
$388$	−9.97622	−	17.2793i	−0.506466	−	0.877224i
$389$	20.9808	+	17.6050i	1.06377	+	0.892607i	0.994473	−	0.104989i	$-0.0334809\pi$
$389$	20.9808	+	17.6050i	1.06377	+	0.892607i	0.0692941	+	0.997596i	$0.477925\pi$
$390$	1.18920	+	1.11026i	0.0602174	+	0.0562201i
$391$	1.53948	+	8.73081i	0.0778547	+	0.441536i
$392$	4.91274	+	27.8615i	0.248131	+	1.40722i
$393$	3.52020	−	15.2067i	0.177571	−	0.767078i
$394$	−37.3038	−	31.3016i	−1.87934	−	1.57695i
$395$	0.335472	+	0.581055i	0.0168794	+	0.0292361i
$396$	−24.2571	−	25.1784i	−1.21896	−	1.26526i
$397$	−2.10799	+	3.65115i	−0.105797	+	0.183246i	−0.914064	−	0.405571i	$-0.867073\pi$
$397$	−2.10799	+	3.65115i	−0.105797	+	0.183246i	0.808266	+	0.588817i	$0.200406\pi$
$398$	−42.9002	+	15.6144i	−2.15039	+	0.782680i
$399$	−3.85673	−	0.204405i	−0.193078	−	0.0102331i
$400$	−10.1731	+	8.53628i	−0.508657	+	0.426814i
$401$	−14.2575	−	5.18930i	−0.711985	−	0.259141i	−0.0394656	−	0.999221i	$-0.512566\pi$
$401$	−14.2575	−	5.18930i	−0.711985	−	0.259141i	−0.672519	+	0.740080i	$0.734788\pi$
$402$	−4.45848	−	36.4894i	−0.222369	−	1.81993i
$403$	1.20935	−	6.85857i	0.0602420	−	0.341650i
$404$	−27.3880			−1.36260
$405$	0.315660	−	0.776006i	0.0156853	−	0.0385600i
$406$	8.91200			0.442295
$407$	−2.16460	+	12.2760i	−0.107295	+	0.608501i
$408$	−1.77568	−	14.5326i	−0.0879093	−	0.719473i
$409$	−4.42559	−	1.61078i	−0.218831	−	0.0796481i	0.230278	−	0.973125i	$-0.426036\pi$
$409$	−4.42559	−	1.61078i	−0.218831	−	0.0796481i	−0.449109	+	0.893477i	$0.648259\pi$
$410$	0.187717	−	0.157513i	0.00927067	−	0.00777902i
$411$	−19.9257	−	1.05605i	−0.982860	−	0.0520912i
$412$	−22.6644	+	8.24918i	−1.11660	+	0.406408i
$413$	−2.98184	+	5.16469i	−0.146727	+	0.254138i
$414$	8.87937	−	30.8287i	0.436397	−	1.51515i
$415$	0.693492	+	1.20116i	0.0340422	+	0.0589628i
$416$	6.76339	+	5.67516i	0.331602	+	0.278248i
$417$	−0.665556	+	2.87510i	−0.0325924	+	0.140794i
$418$	−4.96033	−	28.1314i	−0.242618	−	1.37595i
$419$	3.43669	+	19.4905i	0.167894	+	0.952171i	0.946031	+	0.324077i	$0.105054\pi$
$419$	3.43669	+	19.4905i	0.167894	+	0.952171i	−0.778137	+	0.628094i	$0.783835\pi$
$420$	0.257473	+	0.240382i	0.0125634	+	0.0117294i
$421$	21.5915	+	18.1174i	1.05231	+	0.882989i	0.993334	−	0.115270i	$-0.0367734\pi$
$421$	21.5915	+	18.1174i	1.05231	+	0.882989i	0.0589715	+	0.998260i	$0.481218\pi$
$422$	19.4340	+	33.6607i	0.946032	+	1.63858i
$423$	8.94379	−	6.01731i	0.434862	−	0.292572i
$424$	11.4637	−	19.8557i	0.556726	−	0.964278i
$425$	−9.33836	+	3.39889i	−0.452977	+	0.164870i
$426$	−2.15970	−	4.24484i	−0.104638	−	0.205663i
$427$	5.86180	−	4.91863i	0.283672	−	0.238029i
$428$	19.6276	+	7.14387i	0.948737	+	0.345312i
$429$	−20.7156	−	8.80769i	−1.00016	−	0.425239i
$430$	0.267896	−	1.51932i	0.0129191	−	0.0732679i
$431$	−5.19681			−0.250321			−0.125161	−	0.992136i	$-0.539945\pi$
$431$	−5.19681			−0.250321			−0.125161	+	0.992136i	$0.539945\pi$
$432$	−4.52413	+	13.0638i	−0.217667	+	0.628534i
$433$	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
$435$	−0.824368	+	0.620444i	−0.0395254	+	0.0297480i
$436$	22.0625	+	8.03011i	1.05660	+	0.384572i
$437$	13.1169	−	11.0064i	0.627469	−	0.526509i
$438$	−0.443254	+	0.681671i	−0.0211795	+	0.0325715i
$439$	14.7167	−	5.35646i	0.702392	−	0.255650i	0.0339602	−	0.999423i	$-0.489188\pi$
$439$	14.7167	−	5.35646i	0.702392	−	0.255650i	0.668432	+	0.743773i	$0.266966\pi$
$440$	−0.611178	+	1.05859i	−0.0291368	+	0.0504664i
$441$	11.7697	−	16.1594i	0.560460	−	0.769496i
$442$	−10.0455	−	17.3993i	−0.477815	−	0.827600i
$443$	−13.9833	−	11.7333i	−0.664365	−	0.557468i	0.247027	−	0.969009i	$-0.420546\pi$
$443$	−13.9833	−	11.7333i	−0.664365	−	0.557468i	−0.911391	+	0.411541i	$0.864991\pi$
$444$	25.1557	−	7.67464i	1.19384	−	0.364222i
$445$	−0.0251044	−	0.142374i	−0.00119006	−	0.00674917i
$446$	−8.94849	−	50.7494i	−0.423723	−	2.40305i
$447$	−35.8714	+	10.9439i	−1.69666	+	0.517626i
$448$	4.60534	+	3.86434i	0.217582	+	0.182573i
$449$	−14.3608	−	24.8737i	−0.677729	−	1.17386i	−0.975663	−	0.219274i	$-0.929631\pi$
$449$	−14.3608	−	24.8737i	−0.677729	−	1.17386i	0.297934	−	0.954586i	$-0.403702\pi$
$450$	35.7604	+	3.80125i	1.68576	+	0.179193i
$451$	−1.69525	+	2.93626i	−0.0798262	+	0.138263i
$452$	41.9343	−	15.2628i	1.97242	−	0.717904i
$453$	−4.47694	+	6.88499i	−0.210345	+	0.323485i
$454$	35.1654	−	29.5073i	1.65039	−	1.38485i
$455$	0.213113	+	0.0775669i	0.00999091	+	0.00363639i
$456$	−22.5933	+	17.0044i	−1.05803	+	0.796304i
$457$	−6.14505	+	34.8503i	−0.287453	+	1.63023i	0.408936	+	0.912563i	$0.365900\pi$
$457$	−6.14505	+	34.8503i	−0.287453	+	1.63023i	−0.696389	+	0.717665i	$0.745211\pi$
$458$	−53.9648			−2.52161
$459$	−6.52484	+	8.02840i	−0.304553	+	0.374734i
$460$	−1.56168			−0.0728139
$461$	0.395350	−	2.24214i	0.0184133	−	0.104427i	−0.974216	−	0.225617i	$-0.927560\pi$
$461$	0.395350	−	2.24214i	0.0184133	−	0.104427i	0.992629	+	0.121190i	$0.0386712\pi$
$462$	−6.86591	−	2.91919i	−0.319431	−	0.135813i
$463$	−17.2664	−	6.28446i	−0.802438	−	0.292064i	−0.0919417	−	0.995764i	$-0.529307\pi$
$463$	−17.2664	−	6.28446i	−0.802438	−	0.292064i	−0.710496	+	0.703701i	$0.751530\pi$
$464$	13.0432	−	10.9446i	0.605517	−	0.508089i
$465$	0.121180	+	0.238176i	0.00561957	+	0.0110451i
$466$	−39.9033	+	14.5236i	−1.84848	+	0.672793i
$467$	−2.32935	+	4.03455i	−0.107789	+	0.186697i	−0.914874	−	0.403738i	$-0.867711\pi$
$467$	−2.32935	+	4.03455i	−0.107789	+	0.186697i	0.807085	+	0.590435i	$0.201044\pi$
$468$	3.25707	+	47.3819i	0.150558	+	2.19023i
$469$	−2.56220	−	4.43786i	−0.118312	−	0.204922i
$470$	−0.615335	−	0.516327i	−0.0283833	−	0.0238164i
$471$	0.264864	+	0.247282i	0.0122043	+	0.0113941i
$472$	7.58218	+	43.0007i	0.348998	+	1.97927i
$473$	3.70665	+	21.0215i	0.170432	+	0.966568i
$474$	−6.76202	+	29.2109i	−0.310590	+	1.34170i
$475$	14.7033	+	12.3375i	0.674634	+	0.566085i
$476$	−2.17495	−	3.76712i	−0.0996885	−	0.172666i
$477$	−15.7244	+	3.90082i	−0.719970	+	0.178606i
$478$	−18.5169	+	32.0722i	−0.846942	+	1.46695i
$479$	13.3210	−	4.84844i	0.608651	−	0.221531i	−0.0192617	−	0.999814i	$-0.506132\pi$
$479$	13.3210	−	4.84844i	0.608651	−	0.221531i	0.627913	+	0.778283i	$0.283909\pi$
$480$	−0.338303	−	0.0179299i	−0.0154413	−	0.000818385i
$481$	12.9717	−	10.8846i	0.591460	−	0.496294i
$482$	29.6800	+	10.8026i	1.35189	+	0.492047i
$483$	−0.542402	−	4.43917i	−0.0246802	−	0.201989i
$484$	−0.937459	+	5.31660i	−0.0426118	+	0.241663i
$485$	0.492926			0.0223826
$486$	33.9765	−	15.7216i	1.54121	−	0.713147i
$487$	−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
$489$	−1.18140	−	9.66888i	−0.0534246	−	0.437242i
$490$	−1.39985	−	0.509504i	−0.0632389	−	0.0230171i
$491$	−10.7919	+	9.05550i	−0.487033	+	0.408669i	−0.852961	−	0.521974i	$-0.825196\pi$
$491$	−10.7919	+	9.05550i	−0.487033	+	0.408669i	0.365929	+	0.930643i	$0.380751\pi$
$492$	7.14348	+	0.378601i	0.322053	+	0.0170687i
$493$	11.9729	−	4.35779i	0.539234	−	0.196265i
$494$	−19.4020	+	33.6053i	−0.872938	+	1.51197i
$495$	0.838333	−	0.207969i	0.0376803	−	0.00934753i
$496$	−2.20500	−	3.81917i	−0.0990073	−	0.171486i
$497$	−0.508585	−	0.426753i	−0.0228131	−	0.0191425i
$498$	−13.9785	+	60.3850i	−0.626392	+	2.70592i
$499$	2.58898	+	14.6828i	0.115899	+	0.657294i	0.986301	+	0.164953i	$0.0527473\pi$
$499$	2.58898	+	14.6828i	0.115899	+	0.657294i	−0.870403	+	0.492340i	$0.836142\pi$
$500$	−0.608488	−	3.45091i	−0.0272124	−	0.154329i
$501$	−21.1182	−	19.7164i	−0.943494	−	0.880864i
$502$	−32.0422	−	26.8866i	−1.43011	−	1.20001i
$503$	7.93153	+	13.7378i	0.353650	+	0.612539i	0.986886	−	0.161420i	$-0.0516072\pi$
$503$	7.93153	+	13.7378i	0.353650	+	0.612539i	−0.633236	+	0.773958i	$0.718274\pi$
$504$	0.506490	+	7.36810i	0.0225608	+	0.328201i
$505$	0.338311	−	0.585972i	0.0150546	−	0.0260754i
$506$	31.0826	−	11.3131i	1.38179	−	0.502930i
$507$	3.65580	+	7.18540i	0.162360	+	0.319115i
$508$	33.2771	−	27.9228i	1.47643	−	1.23888i
$509$	−31.8807	−	11.6036i	−1.41309	−	0.514321i	−0.481052	−	0.876692i	$-0.659745\pi$
$509$	−31.8807	−	11.6036i	−1.41309	−	0.514321i	−0.932034	+	0.362371i	$0.881967\pi$
$510$	0.709452	+	0.301639i	0.0314151	+	0.0133568i
$511$	−0.0196825	+	0.111625i	−0.000870700	+	0.00493799i
$512$	28.1824			1.24550
$513$	19.7298	+	3.16072i	0.871093	+	0.139549i
$514$	−26.8683			−1.18511
$515$	0.103470	−	0.586809i	0.00455945	−	0.0258579i
$516$	35.9839	−	27.0825i	1.58410	−	1.19224i
$517$	10.4438	+	3.80123i	0.459317	+	0.167178i
$518$	4.29930	−	3.60754i	0.188900	−	0.158506i
$519$	17.9418	−	27.5923i	0.787558	−	1.21117i
$520$	1.56034	−	0.567919i	0.0684256	−	0.0249049i
$521$	21.3899	−	37.0484i	0.937108	−	1.62312i	0.166277	−	0.986079i	$-0.446825\pi$
$521$	21.3899	−	37.0484i	0.937108	−	1.62312i	0.770831	−	0.637040i	$-0.219841\pi$
$522$	−45.8493	−	4.87367i	−2.00677	−	0.213315i
$523$	1.38893	+	2.40569i	0.0607335	+	0.105193i	0.894793	−	0.446480i	$-0.147323\pi$
$523$	1.38893	+	2.40569i	0.0607335	+	0.105193i	−0.834060	+	0.551674i	$0.813989\pi$
$524$	−26.0106	−	21.8255i	−1.13628	−	0.953451i
$525$	4.79486	−	1.46284i	0.209265	−	0.0638437i
$526$	8.63721	+	48.9840i	0.376600	+	2.13581i
$527$	−0.573049	−	3.24992i	−0.0249624	−	0.141569i
$528$	−13.6336	+	4.15942i	−0.593327	+	0.181016i
$529$	−2.43023	−	2.03920i	−0.105662	−	0.0886609i
$530$	0.603626	+	1.04551i	0.0262198	+	0.0454141i
$531$	18.1650	−	24.9400i	0.788292	−	1.08230i
$532$	−4.20073	+	7.27587i	−0.182125	+	0.315449i
$533$	4.32799	−	1.57526i	0.187466	−	0.0682321i
$534$	3.52188	−	5.41622i	0.152407	−	0.234383i
$535$	−0.395296	+	0.331693i	−0.0170901	+	0.0143403i
$536$	−35.2565	−	12.8323i	−1.52285	−	0.554271i
$537$	−22.4678	+	16.9099i	−0.969557	+	0.729717i
$538$	11.7792	−	66.8029i	0.507835	−	2.88008i
$539$	20.6116			0.887803
$540$	−1.19316	−	1.37749i	−0.0513452	−	0.0592776i
$541$	−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
$543$	−4.76846	−	2.02741i	−0.204634	−	0.0870047i
$544$	3.93130	+	1.43088i	0.168553	+	0.0613483i
$545$	−0.444334	+	0.372841i	−0.0190332	+	0.0159707i
$546$	4.59580	+	9.03294i	0.196682	+	0.386574i
$547$	37.1985	−	13.5392i	1.59049	−	0.578892i	0.613042	−	0.790051i	$-0.289946\pi$
$547$	37.1985	−	13.5392i	1.59049	−	0.578892i	0.977452	+	0.211158i	$0.0677235\pi$
$548$	−21.7029	+	37.5905i	−0.927101	+	1.60579i
$549$	−32.8468	+	22.0991i	−1.40187	+	0.943167i
$550$	18.5389	+	32.1102i	0.790499	+	1.36919i
$551$	−18.8514	−	15.8182i	−0.803099	−	0.673880i
$552$	−23.9341	−	22.3453i	−1.01870	−	0.951081i
$553$	0.725786	+	4.11614i	0.0308636	+	0.175036i
$554$	−2.15566	−	12.2253i	−0.0915850	−	0.519405i
$555$	−0.146536	+	0.633013i	−0.00622011	+	0.0268699i
$556$	4.91776	+	4.12649i	0.208560	+	0.175002i
$557$	5.71731	+	9.90267i	0.242250	+	0.419590i	0.961355	−	0.275312i	$-0.0887812\pi$
$557$	5.71731	+	9.90267i	0.242250	+	0.419590i	−0.719105	+	0.694902i	$0.755448\pi$
$558$	−3.30522	+	11.4756i	−0.139921	+	0.485799i
$559$	14.4983	−	25.1119i	0.613214	−	1.06212i
$560$	0.134948	−	0.0491171i	0.00570260	−	0.00207558i
$561$	−10.6515	−	0.564526i	−0.449707	−	0.0238343i
$562$	6.06462	−	5.08882i	0.255821	−	0.214659i
$563$	−13.6357	−	4.96298i	−0.574676	−	0.209165i	0.0383005	−	0.999266i	$-0.487806\pi$
$563$	−13.6357	−	4.96298i	−0.574676	−	0.209165i	−0.612976	+	0.790101i	$0.710028\pi$
$564$	−2.84400	−	23.2761i	−0.119754	−	0.980099i
$565$	−0.191443	+	1.08573i	−0.00805408	+	0.0456770i
$566$	21.9285			0.921725
$567$	3.50117	−	3.87003i	0.147035	−	0.162526i
$568$	−4.86093			−0.203960
$569$	−0.225601	+	1.27945i	−0.00945767	+	0.0536371i	−0.989171	−	0.146765i	$-0.953114\pi$
$569$	−0.225601	+	1.27945i	−0.00945767	+	0.0536371i	0.979714	+	0.200402i	$0.0642249\pi$
$570$	−0.180586	−	1.47796i	−0.00756391	−	0.0619051i
$571$	−15.0890	−	5.49193i	−0.631453	−	0.229830i	0.00641065	−	0.999979i	$-0.497959\pi$
$571$	−15.0890	−	5.49193i	−0.631453	−	0.229830i	−0.637864	+	0.770149i	$0.720182\pi$
$572$	−37.5111	+	31.4756i	−1.56842	+	1.31606i
$573$	3.89825	+	0.206606i	0.162852	+	0.00863108i
$574$	1.43445	−	0.522099i	0.0598730	−	0.0217920i
$575$	−11.1127	+	19.2478i	−0.463434	+	0.802691i
$576$	−21.5796	−	22.3992i	−0.899152	−	0.933301i
$577$	4.23017	+	7.32686i	0.176104	+	0.305021i	0.940543	−	0.339675i	$-0.110317\pi$
$577$	4.23017	+	7.32686i	0.176104	+	0.305021i	−0.764439	+	0.644696i	$0.776984\pi$
$578$	23.9829	+	20.1241i	0.997558	+	0.837050i
$579$	0.343854	−	1.48540i	0.0142901	−	0.0617310i
$580$	0.389740	+	2.21033i	0.0161831	+	0.0917788i
$581$	1.50035	+	8.50893i	0.0622452	+	0.353010i
$582$	16.1014	+	15.0326i	0.667424	+	0.623120i
$583$	−12.7958	−	10.7369i	−0.529947	−	0.444678i
$584$	0.414943	+	0.718703i	0.0171705	+	0.0297401i
$585$	−1.05398	−	0.515601i	−0.0435767	−	0.0213175i
$586$	−3.39401	+	5.87860i	−0.140205	+	0.242843i
$587$	17.2764	−	6.28811i	0.713075	−	0.259538i	0.0400919	−	0.999196i	$-0.487235\pi$
$587$	17.2764	−	6.28811i	0.713075	−	0.259538i	0.672983	+	0.739658i	$0.265013\pi$
$588$	−19.7201	−	38.7594i	−0.813244	−	1.59841i
$589$	−4.88260	+	4.09699i	−0.201184	+	0.168814i
$590$	−2.16049	−	0.786354i	−0.0889460	−	0.0323737i
$591$	32.3200	+	13.7416i	1.32947	+	0.565252i
$592$	1.86196	−	10.5597i	0.0765260	−	0.434001i
$593$	13.5128			0.554905			0.277452	−	0.960739i	$-0.410510\pi$
$593$	13.5128			0.554905			0.277452	+	0.960739i	$0.410510\pi$
$594$	33.7264	+	18.7730i	1.38381	+	0.770265i
$595$	0.107464			0.00440561
$596$	−14.1667	+	80.3435i	−0.580292	+	3.29100i
$597$	26.3070	−	19.7994i	1.07667	−	0.810337i
$598$	−42.2234	−	15.3681i	−1.72664	−	0.628447i
$599$	8.44772	−	7.08848i	0.345165	−	0.289627i	−0.453680	−	0.891164i	$-0.649889\pi$
$599$	8.44772	−	7.08848i	0.345165	−	0.289627i	0.798845	+	0.601537i	$0.205445\pi$
$600$	20.0085	−	30.7706i	0.816843	−	1.25620i
$601$	−24.2421	+	8.82341i	−0.988856	+	0.359914i	−0.785277	−	0.619144i	$-0.787480\pi$
$601$	−24.2421	+	8.82341i	−0.988856	+	0.359914i	−0.203579	+	0.979058i	$0.565257\pi$
$602$	4.80528	−	8.32298i	0.195848	−	0.339219i
$603$	10.7548	+	24.2325i	0.437968	+	0.986824i
$604$	8.93252	+	15.4716i	0.363459	+	0.629529i
$605$	−0.102170	−	0.0857306i	−0.00415379	−	0.00348545i
$606$	28.9210	−	8.82338i	1.17484	−	0.358425i
$607$	−2.56823	−	14.5652i	−0.104241	−	0.591182i	−0.991521	−	0.129950i	$-0.958518\pi$
$607$	−2.56823	−	14.5652i	−0.104241	−	0.591182i	0.887279	−	0.461233i	$-0.152593\pi$
$608$	−1.40312	−	7.95752i	−0.0569042	−	0.322720i
$609$	−6.14761	+	1.87555i	−0.249114	+	0.0760009i
$610$	2.25987	+	1.89626i	0.0914995	+	0.0767772i
$611$	−7.54882	−	13.0749i	−0.305393	−	0.528956i
$612$	9.12926	+	20.5700i	0.369029	+	0.831492i
$613$	−18.1370	+	31.4141i	−0.732545	+	1.26880i	0.223248	+	0.974762i	$0.428334\pi$
$613$	−18.1370	+	31.4141i	−0.732545	+	1.26880i	−0.955792	+	0.294043i	$0.904999\pi$
$614$	14.2053	−	5.17029i	0.573277	−	0.208656i
$615$	−0.0963404	+	0.148160i	−0.00388482	+	0.00597438i
$616$	−5.83316	+	4.89460i	−0.235025	+	0.197209i
$617$	37.9387	+	13.8086i	1.52736	+	0.555912i	0.962972	−	0.269601i	$-0.0868918\pi$
$617$	37.9387	+	13.8086i	1.52736	+	0.555912i	0.564383	+	0.825513i	$0.309114\pi$
$618$	21.2755	−	16.0126i	0.855826	−	0.644120i
$619$	−1.19701	+	6.78858i	−0.0481119	+	0.272856i	−0.999368	−	0.0355458i	$-0.988683\pi$
$619$	−1.19701	+	6.78858i	−0.0481119	+	0.272856i	0.951256	+	0.308402i	$0.0997941\pi$
$620$	0.581315			0.0233462
$621$	0.362848	+	23.1347i	0.0145606	+	0.928362i
$622$	17.7069			0.709981
$623$	0.156387	−	0.886916i	0.00626552	−	0.0355335i
$624$	17.8193	+	7.57626i	0.713343	+	0.303293i
$625$	−23.3703	−	8.50608i	−0.934810	−	0.340243i
$626$	7.85711	−	6.59290i	0.314033	−	0.263505i
$627$	9.34200	+	18.3615i	0.373083	+	0.733287i
$628$	0.740705	−	0.269595i	0.0295574	−	0.0107580i
$629$	4.01193	−	6.94887i	0.159966	−	0.277070i
$630$	−0.349327	−	0.170889i	−0.0139175	−	0.00680837i
$631$	−14.9095	−	25.8241i	−0.593539	−	1.02804i	−0.993751	−	0.111617i	$-0.964397\pi$
$631$	−14.9095	−	25.8241i	−0.593539	−	1.02804i	0.400212	−	0.916423i	$-0.368936\pi$
$632$	23.4424	+	19.6705i	0.932489	+	0.782451i
$633$	−20.4897	−	19.1296i	−0.814394	−	0.760334i
$634$	−6.73414	−	38.1912i	−0.267447	−	1.51677i
$635$	0.186358	+	1.05689i	0.00739540	+	0.0419414i
$636$	−7.94811	+	34.3346i	−0.315163	+	1.36146i
$637$	−21.4487	−	17.9976i	−0.849830	−	0.713092i
$638$	−23.7691	−	41.1693i	−0.941028	−	1.62991i
$639$	2.38312	+	2.47363i	0.0942749	+	0.0978554i
$640$	−0.963264	+	1.66842i	−0.0380763	+	0.0659502i
$641$	−40.2947	+	14.6661i	−1.59155	+	0.579275i	−0.977673	−	0.210131i	$-0.932611\pi$
$641$	−40.2947	+	14.6661i	−1.59155	+	0.579275i	−0.613872	+	0.789406i	$0.710389\pi$
$642$	−23.0278	−	1.22046i	−0.908834	−	0.0481678i
$643$	−20.9998	+	17.6209i	−0.828150	+	0.694901i	−0.954866	−	0.297038i	$-0.904001\pi$
$643$	−20.9998	+	17.6209i	−0.828150	+	0.694901i	0.126715	+	0.991939i	$0.459557\pi$
$644$	−9.14178	−	3.32734i	−0.360237	−	0.131115i
$645$	0.134944	+	1.10442i	0.00531343	+	0.0434865i
$646$	−3.19291	+	18.1079i	−0.125623	+	0.712446i
$647$	−16.1623			−0.635407			−0.317703	−	0.948190i	$-0.602912\pi$
$647$	−16.1623			−0.635407			−0.317703	+	0.948190i	$0.602912\pi$
$648$	1.42365	−	38.1834i	0.0559261	−	1.49999i
$649$	31.8113			1.24870
$650$	8.74621	−	49.6022i	0.343055	−	1.94556i
$651$	0.201902	+	1.65242i	0.00791316	+	0.0647634i
$652$	−19.9116	−	7.24721i	−0.779797	−	0.283823i
$653$	24.7021	−	20.7275i	0.966668	−	0.811130i	−0.0153573	−	0.999882i	$-0.504889\pi$
$653$	24.7021	−	20.7275i	0.966668	−	0.811130i	0.982025	+	0.188752i	$0.0604441\pi$
$654$	−25.8845	−	1.37187i	−1.01216	−	0.0536442i
$655$	0.788258	−	0.286903i	0.0307998	−	0.0112102i
$656$	1.45823	−	2.52573i	0.0569344	−	0.0986133i
$657$	0.162303	−	0.563508i	0.00633206	−	0.0219846i
$658$	−2.50195	−	4.33351i	−0.0975363	−	0.168938i
$659$	21.3103	+	17.8814i	0.830130	+	0.696562i	0.955321	−	0.295571i	$-0.0955098\pi$
$659$	21.3103	+	17.8814i	0.830130	+	0.696562i	−0.125191	+	0.992133i	$0.539954\pi$
$660$	0.423748	−	1.83052i	0.0164944	−	0.0712530i
$661$	5.34639	+	30.3209i	0.207950	+	1.17934i	0.892729	+	0.450594i	$0.148788\pi$
$661$	5.34639	+	30.3209i	0.207950	+	1.17934i	−0.684779	+	0.728751i	$0.740101\pi$
$662$	−8.01889	−	45.4774i	−0.311663	−	1.76753i
$663$	10.5912	+	9.88816i	0.411329	+	0.384024i
$664$	48.4604	+	40.6631i	1.88063	+	1.57803i
$665$	−0.103779	−	0.179751i	−0.00402439	−	0.00697044i
$666$	−24.0913	+	16.2085i	−0.933519	+	0.628065i
$667$	14.2479	−	24.6781i	0.551682	−	0.955540i
$668$	−59.0583	+	21.4955i	−2.28503	+	0.831684i
$669$	16.8531	+	33.1243i	0.651577	+	1.28066i
$670$	1.51339	−	1.26988i	0.0584673	−	0.0490598i
$671$	−38.3557	−	13.9603i	−1.48071	−	0.538933i
$672$	−1.94216	−	0.825749i	−0.0749203	−	0.0318540i
$673$	−4.53753	+	25.7336i	−0.174909	+	0.991959i	0.763340	+	0.645997i	$0.223558\pi$
$673$	−4.53753	+	25.7336i	−0.174909	+	0.991959i	−0.938249	+	0.345961i	$0.887553\pi$
$674$	70.7584			2.72551
$675$	−25.4679	+	4.90369i	−0.980262	+	0.188743i
$676$	17.5374			0.674515
$677$	3.15944	−	17.9181i	0.121427	−	0.688648i	−0.861939	−	0.507012i	$-0.830750\pi$
$677$	3.15944	−	17.9181i	0.121427	−	0.688648i	0.983366	−	0.181635i	$-0.0581391\pi$
$678$	−39.3645	+	29.6269i	−1.51178	+	1.13781i
$679$	2.88549	+	1.05023i	0.110735	+	0.0403042i
$680$	0.602738	−	0.505757i	0.0231139	−	0.0193949i
$681$	−18.0477	+	27.7551i	−0.691588	+	1.06358i
$682$	−11.5701	+	4.21116i	−0.443040	+	0.161253i
$683$	−11.7486	+	20.3491i	−0.449546	+	0.778636i	−0.998356	−	0.0573104i	$-0.981748\pi$
$683$	−11.7486	+	20.3491i	−0.449546	+	0.778636i	0.548811	+	0.835947i	$0.315081\pi$
$684$	25.5903	−	35.1347i	0.978468	−	1.34341i
$685$	−0.536171	−	0.928676i	−0.0204860	−	0.0354829i
$686$	−14.5765	−	12.2311i	−0.556533	−	0.466987i
$687$	37.2256	−	11.3570i	1.42024	−	0.433296i
$688$	−3.18841	−	18.0824i	−0.121557	−	0.689384i
$689$	3.94021	+	22.3460i	0.150110	+	0.851317i
$690$	1.64910	−	0.503116i	0.0627801	−	0.0191533i
$691$	−34.1180	−	28.6284i	−1.29791	−	1.08908i	−0.990502	−	0.137499i	$-0.956094\pi$
$691$	−34.1180	−	28.6284i	−1.29791	−	1.08908i	−0.307409	−	0.951577i	$-0.599462\pi$
$692$	−35.7980	−	62.0039i	−1.36084	−	2.35704i
$693$	5.35054	+	0.568750i	0.203250	+	0.0216050i
$694$	13.6857	−	23.7043i	0.519501	−	0.899802i
$695$	−0.149034	+	0.0542440i	−0.00565318	+	0.00205759i
$696$	−25.6534	+	39.4517i	−0.972388	+	1.49541i
$697$	1.67184	−	1.40284i	0.0633254	−	0.0531363i
$698$	63.5547	+	23.1320i	2.40558	+	0.875560i
$699$	24.4692	−	18.4163i	0.925512	−	0.696567i
$700$	1.89364	−	10.7394i	0.0715728	−	0.405910i
$701$	−25.2567			−0.953934			−0.476967	−	0.878921i	$-0.658264\pi$
$701$	−25.2567			−0.953934			−0.476967	+	0.878921i	$0.658264\pi$
$702$	−18.7041	−	48.9848i	−0.705939	−	1.84881i
$703$	−15.4974			−0.584496
$704$	5.56859	−	31.5810i	0.209874	−	1.19025i
$705$	0.533127	+	0.226670i	0.0200787	+	0.00853690i
$706$	64.6662	+	23.5366i	2.43374	+	0.885810i
$707$	3.22888	−	2.70935i	0.121434	−	0.101896i
$708$	−30.4355	−	59.8202i	−1.14383	−	2.24818i
$709$	14.7382	−	5.36425i	0.553503	−	0.201459i	−0.0500991	−	0.998744i	$-0.515954\pi$
$709$	14.7382	−	5.36425i	0.553503	−	0.201459i	0.603602	+	0.797286i	$0.293731\pi$
$710$	0.127977	−	0.221663i	0.00480289	−	0.00831886i
$711$	−1.48295	−	21.5731i	−0.0556150	−	0.809053i
$712$	−3.29694	−	5.71046i	−0.123558	−	0.214009i
$713$	−5.65382	−	4.74412i	−0.211737	−	0.177669i
$714$	3.51031	+	3.27730i	0.131370	+	0.122650i
$715$	−0.210069	−	1.19136i	−0.00785615	−	0.0445544i
$716$	10.6222	+	60.2415i	0.396970	+	2.25133i
$717$	6.02352	−	26.0207i	0.224953	−	0.971760i
$718$	57.0915	+	47.9055i	2.13064	+	1.78782i
$719$	26.5804	+	46.0385i	0.991280	+	1.71695i	0.609757	+	0.792588i	$0.291267\pi$
$719$	26.5804	+	46.0385i	0.991280	+	1.71695i	0.381523	+	0.924359i	$0.375400\pi$
$720$	−0.721124	+	0.178893i	−0.0268747	+	0.00666693i
$721$	1.85595	−	3.21461i	0.0691194	−	0.119718i
$722$	−9.50721	+	3.46034i	−0.353822	+	0.128781i
$723$	−22.7471	−	1.20558i	−0.845972	−	0.0448361i
$724$	−8.63457	+	7.24526i	−0.320901	+	0.269268i
$725$	30.0158	+	10.9248i	1.11476	+	0.405738i
$726$	−0.722875	−	5.91621i	−0.0268284	−	0.219571i
$727$	0.0814709	−	0.462044i	0.00302159	−	0.0171363i	−0.983260	−	0.182210i	$-0.941675\pi$
$727$	0.0814709	−	0.462044i	0.00302159	−	0.0171363i	0.986281	+	0.165073i	$0.0527861\pi$
$728$	10.3440			0.383372
$729$	−20.1288	+	17.9954i	−0.745509	+	0.666495i
$730$	−0.0436980			−0.00161734
$731$	2.38593	−	13.5313i	0.0882469	−	0.500473i
$732$	10.4448	+	85.4834i	0.386052	+	3.15956i
$733$	43.6076	+	15.8719i	1.61068	+	0.586241i	0.981575	−	0.191075i	$-0.0611975\pi$
$733$	43.6076	+	15.8719i	1.61068	+	0.586241i	0.629109	+	0.777317i	$0.283420\pi$
$734$	−44.3825	+	37.2413i	−1.63819	+	1.37460i
$735$	1.07286	+	0.0568611i	0.0395731	+	0.00209735i
$736$	8.79230	−	3.20014i	0.324088	−	0.117959i
$737$	−13.6672	+	23.6724i	−0.503439	+	0.871983i
$738$	−7.66531	+	1.90157i	−0.282164	+	0.0699977i
$739$	−12.9047	−	22.3515i	−0.474706	−	0.822214i	0.524875	−	0.851179i	$-0.324112\pi$
$739$	−12.9047	−	22.3515i	−0.474706	−	0.822214i	−0.999580	+	0.0289653i	$0.990779\pi$
$740$	1.08275	+	0.908534i	0.0398026	+	0.0333984i
$741$	6.31146	−	27.2645i	0.231857	−	1.00159i
$742$	1.30593	+	7.40629i	0.0479422	+	0.271894i
$743$	6.02726	+	34.1823i	0.221119	+	1.25403i	0.869967	+	0.493110i	$0.164140\pi$
$743$	6.02726	+	34.1823i	0.221119	+	1.25403i	−0.648848	+	0.760918i	$0.724749\pi$
$744$	8.90915	+	8.31775i	0.326625	+	0.304944i
$745$	−1.54397	−	1.29555i	−0.0565668	−	0.0474652i
$746$	−15.1129	−	26.1764i	−0.553324	−	0.958385i
$747$	−3.06557	−	44.5961i	−0.112163	−	1.63169i
$748$	−11.6015	+	20.0945i	−0.424195	+	0.734727i
$749$	−3.02069	+	1.09944i	−0.110374	+	0.0401727i
$750$	1.75430	+	3.44804i	0.0640581	+	0.125905i
$751$	18.3742	−	15.4178i	0.670485	−	0.562604i	−0.242724	−	0.970095i	$-0.578041\pi$
$751$	18.3742	−	15.4178i	0.670485	−	0.562604i	0.913209	+	0.407492i	$0.133596\pi$
$752$	−8.98361	−	3.26977i	−0.327599	−	0.119236i
$753$	27.7614	+	11.8034i	1.01168	+	0.430138i
$754$	−11.2137	+	63.5962i	−0.408380	+	2.31604i
$755$	−0.441357			−0.0160626
$756$	−4.04961	−	10.6057i	−0.147283	−	0.385725i
$757$	−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
$759$	−19.0603	+	14.3453i	−0.691843	+	0.520701i
$760$	−1.42803	−	0.519759i	−0.0517999	−	0.0188536i
$761$	10.5361	−	8.84082i	0.381933	−	0.320479i	−0.431528	−	0.902100i	$-0.642025\pi$
$761$	10.5361	−	8.84082i	0.381933	−	0.320479i	0.813461	+	0.581620i	$0.197581\pi$
$762$	−26.1441	+	40.2065i	−0.947102	+	1.45653i
$763$	−3.39542	+	1.23583i	−0.122922	+	0.0447401i
$764$	4.24595	−	7.35420i	0.153613	−	0.266066i
$765$	−0.552869	−	0.0587687i	−0.0199890	−	0.00212479i
$766$	−21.4484	−	37.1498i	−0.774963	−	1.34228i
$767$	−33.1034	−	27.7770i	−1.19529	−	1.00297i
$768$	−47.9943	+	14.6424i	−1.73185	+	0.528361i
$769$	−5.44525	−	30.8815i	−0.196361	−	1.11362i	−0.910468	−	0.413580i	$-0.864278\pi$
$769$	−5.44525	−	30.8815i	−0.196361	−	1.11362i	0.714107	−	0.700036i	$-0.246833\pi$
$770$	−0.0696246	−	0.394861i	−0.00250910	−	0.0142298i
$771$	18.5341	−	5.65448i	0.667489	−	0.203641i
$772$	−2.54072	−	2.13192i	−0.0914426	−	0.0767295i
$773$	−14.0607	−	24.3539i	−0.505729	−	0.875948i	−0.999978	−	0.00662776i	$-0.997890\pi$
$773$	−14.0607	−	24.3539i	−0.505729	−	0.875948i	0.494249	−	0.869320i	$-0.335443\pi$
$774$	−29.2731	+	40.1911i	−1.05220	+	1.44464i
$775$	4.13657	−	7.16475i	0.148590	−	0.257365i
$776$	21.1266	−	7.68945i	0.758400	−	0.276035i
$777$	−2.20650	+	3.39332i	−0.0791576	+	0.121735i
$778$	−50.3879	+	42.2804i	−1.80649	+	1.51583i
$779$	−3.96098	−	1.44168i	−0.141917	−	0.0516535i
$780$	−2.03934	+	1.53486i	−0.0730200	+	0.0549570i
$781$	−0.614960	+	3.48761i	−0.0220050	+	0.124797i
$782$	−21.2916			−0.761385
$783$	32.6531	−	6.28714i	1.16693	−	0.224684i
$784$	−17.7298			−0.633207
$785$	−0.00338155	+	0.0191777i	−0.000120693	+	0.000684483i
$786$	34.4979	+	14.6675i	1.23050	+	0.523173i
$787$	34.0170	+	12.3812i	1.21258	+	0.441342i	0.867597	−	0.497269i	$-0.165664\pi$
$787$	34.0170	+	12.3812i	1.21258	+	0.441342i	0.344979	+	0.938610i	$0.387886\pi$
$788$	58.5240	−	49.1075i	2.08483	−	1.74938i
$789$	−16.2668	−	31.9721i	−0.579114	−	1.13824i
$790$	−1.51418	+	0.551116i	−0.0538721	+	0.0196078i
$791$	−3.43393	+	5.94775i	−0.122097	+	0.211478i
$792$	32.6863	−	21.9911i	1.16146	−	0.781421i
$793$	27.7237	+	48.0189i	0.984498	+	1.70520i
$794$	−7.75636	−	6.50836i	−0.275263	−	0.230973i
$795$	−0.636417	−	0.594171i	−0.0225714	−	0.0210731i
$796$	−12.4373	−	70.5354i	−0.440828	−	2.50006i
$797$	−5.14000	−	29.1504i	−0.182068	−	1.03256i	−0.929665	−	0.368407i	$-0.879903\pi$
$797$	−5.14000	−	29.1504i	−0.182068	−	1.03256i	0.747596	−	0.664153i	$-0.231208\pi$
$798$	2.09185	−	9.03645i	0.0740506	−	0.319887i
$799$	−5.48028	−	4.59850i	−0.193878	−	0.162683i
$800$	5.24407	+	9.08300i	0.185406	+	0.321133i
$801$	−1.28958	+	4.47736i	−0.0455652	+	0.158200i
$802$	18.2193	−	31.5568i	0.643346	−	1.11431i
$803$	0.568149	−	0.206789i	0.0200495	−	0.00729744i
$804$	57.5913	+	3.05231i	2.03109	+	0.107647i
$805$	0.184113	−	0.154489i	0.00648914	−	0.00544504i
$806$	15.7171	+	5.72055i	0.553611	+	0.201498i
$807$	5.93338	+	48.5604i	0.208865	+	1.70941i
$808$	5.35892	−	30.3920i	0.188526	−	1.06919i
$809$	−5.75943			−0.202491			−0.101245	−	0.994861i	$-0.532283\pi$
$809$	−5.75943			−0.202491			−0.101245	+	0.994861i	$0.532283\pi$
$810$	1.70372	+	1.07020i	0.0598625	+	0.0376030i
$811$	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
$813$	−3.62635	−	29.6791i	−0.127182	−	1.04089i
$814$	−28.1318	−	10.2391i	−0.986018	−	0.358881i
$815$	0.401014	−	0.336491i	0.0140469	−	0.0117868i
$816$	9.16230	+	0.485598i	0.320744	+	0.0169993i
$817$	−24.9373	+	9.07644i	−0.872446	+	0.317544i
$818$	5.65535	−	9.79536i	0.197735	−	0.342487i
$819$	−5.07123	−	5.26384i	−0.177203	−	0.183933i
$820$	0.192221	+	0.332936i	0.00671265	+	0.0116266i
$821$	32.9911	+	27.6828i	1.15140	+	0.966136i	0.999751	−	0.0222995i	$-0.00709873\pi$
$821$	32.9911	+	27.6828i	1.15140	+	0.966136i	0.151644	+	0.988435i	$0.451543\pi$
$822$	10.8074	−	46.6865i	0.376953	−	1.62838i
$823$	1.78581	+	10.1279i	0.0622496	+	0.353035i	0.999984	+	0.00568141i	$0.00180846\pi$
$823$	1.78581	+	10.1279i	0.0622496	+	0.353035i	−0.937734	+	0.347353i	$0.887080\pi$
$824$	−4.71930	−	26.7645i	−0.164404	−	0.932384i
$825$	−19.5460	−	18.2485i	−0.680504	−	0.635331i
$826$	−10.9717	−	9.20632i	−0.381753	−	0.320329i
$827$	−3.04731	−	5.27810i	−0.105965	−	0.183538i	0.808167	−	0.588954i	$-0.200460\pi$
$827$	−3.04731	−	5.27810i	−0.105965	−	0.183538i	−0.914132	+	0.405416i	$0.867127\pi$
$828$	45.2118	+	22.1174i	1.57122	+	0.768632i
$829$	16.8489	−	29.1832i	0.585188	−	1.01358i	−0.409664	−	0.912236i	$-0.634354\pi$
$829$	16.8489	−	29.1832i	0.585188	−	1.01358i	0.994852	−	0.101339i	$-0.0323126\pi$
$830$	−3.13013	+	1.13927i	−0.108648	+	0.0395447i
$831$	4.05984	+	7.97952i	0.140834	+	0.276806i
$832$	−33.3707	+	28.0014i	−1.15692	+	0.970772i
$833$	−12.4673	−	4.53774i	−0.431967	−	0.157223i
$834$	−6.52244	−	2.77315i	−0.225853	−	0.0960264i
$835$	0.269620	−	1.52909i	0.00933057	−	0.0529163i
$836$	44.8148			1.54995
$837$	−0.135065	−	8.61156i	−0.00466853	−	0.297659i
$838$	−47.5308			−1.64192
$839$	−7.33250	+	41.5847i	−0.253146	+	1.43566i	0.547641	+	0.836714i	$0.315526\pi$
$839$	−7.33250	+	41.5847i	−0.253146	+	1.43566i	−0.800787	+	0.598950i	$0.795585\pi$
$840$	−0.317126	+	0.238679i	−0.0109419	+	0.00823520i
$841$	−11.2328	−	4.08841i	−0.387339	−	0.140980i
$842$	−51.8546	+	43.5112i	−1.78703	+	1.49949i
$843$	−3.11250	+	4.78664i	−0.107200	+	0.164861i
$844$	−57.3007	+	20.8557i	−1.97237	+	0.717884i
$845$	−0.216631	+	0.375216i	−0.00745234	+	0.0129078i
$846$	10.5019	+	23.6627i	0.361062	+	0.813541i
$847$	−0.415423	−	0.719533i	−0.0142741	−	0.0247235i
$848$	11.0068	+	9.23576i	0.377973	+	0.317157i
$849$	−15.1266	+	4.61489i	−0.519142	+	0.158383i
$850$	−4.14438	−	23.5040i	−0.142151	−	0.806179i
$851$	−3.11616	−	17.6726i	−0.106821	−	0.605810i
$852$	7.14672	−	2.18036i	0.244842	−	0.0746979i
$853$	−27.3705	−	22.9665i	−0.937147	−	0.786359i	0.0399399	−	0.999202i	$-0.487283\pi$
$853$	−27.3705	−	22.9665i	−0.937147	−	0.786359i	−0.977086	+	0.212843i	$0.931728\pi$
$854$	9.18865	+	15.9152i	0.314429	+	0.544607i
$855$	0.435610	+	0.981512i	0.0148975	+	0.0335670i
$856$	−11.7679	+	20.3826i	−0.402219	+	0.696664i
$857$	−7.43170	+	2.70492i	−0.253862	+	0.0923983i	−0.465817	−	0.884881i	$-0.654239\pi$
$857$	−7.43170	+	2.70492i	−0.253862	+	0.0923983i	0.211954	+	0.977280i	$0.432017\pi$
$858$	29.4706	−	45.3221i	1.00611	−	1.54727i
$859$	−34.2569	+	28.7449i	−1.16883	+	0.980764i	−0.999988	−	0.00487963i	$-0.998447\pi$
$859$	−34.2569	+	28.7449i	−1.16883	+	0.980764i	−0.168841	+	0.985643i	$0.554002\pi$
$860$	2.27438	+	0.827808i	0.0775559	+	0.0282280i
$861$	−0.879627	+	0.662033i	−0.0299776	+	0.0225620i
$862$	2.16726	−	12.2911i	0.0738172	−	0.418638i
$863$	−22.9170			−0.780103			−0.390052	−	0.920793i	$-0.627543\pi$
$863$	−22.9170			−0.780103			−0.390052	+	0.920793i	$0.627543\pi$
$864$	9.54017	+	5.31030i	0.324563	+	0.180660i
$865$	1.76878			0.0601405
$866$	−10.5629	+	59.9053i	−0.358943	+	2.03567i
$867$	−20.7788	−	8.83457i	−0.705686	−	0.300038i
$868$	3.40290	+	1.23856i	0.115502	+	0.0420393i
$869$	17.0789	−	14.3309i	0.579362	−	0.486143i
$870$	−1.12364	−	2.20849i	−0.0380950	−	0.0748748i
$871$	34.8926	−	12.6999i	1.18229	−	0.430319i
$872$	−13.2278	+	22.9112i	−0.447950	+	0.775871i
$873$	−14.2706	−	6.98108i	−0.482985	−	0.236274i
$874$	20.5614	+	35.6134i	0.695501	+	1.20464i
$875$	0.413118	+	0.346647i	0.0139659	+	0.0117188i
$876$	−0.932438	−	0.870542i	−0.0315041	−	0.0294129i
$877$	−3.84416	−	21.8013i	−0.129808	−	0.736178i	−0.978335	−	0.207026i	$-0.933621\pi$
$877$	−3.84416	−	21.8013i	−0.129808	−	0.736178i	0.848527	−	0.529152i	$-0.177490\pi$
$878$	6.53132	+	37.0409i	0.220421	+	1.25007i
$879$	1.10407	−	4.76940i	0.0372393	−	0.160868i
$880$	−0.586817	−	0.492398i	−0.0197816	−	0.0165987i
$881$	−4.93202	−	8.54251i	−0.166164	−	0.287804i	0.770904	−	0.636951i	$-0.219805\pi$
$881$	−4.93202	−	8.54251i	−0.166164	−	0.287804i	−0.937068	+	0.349147i	$0.886471\pi$
$882$	33.3108	+	34.5759i	1.12163	+	1.16423i
$883$	−23.7865	+	41.1995i	−0.800481	+	1.38647i	0.118819	+	0.992916i	$0.462089\pi$
$883$	−23.7865	+	41.1995i	−0.800481	+	1.38647i	−0.919300	+	0.393558i	$0.871244\pi$
$884$	29.6189	−	10.7804i	0.996191	−	0.362584i
$885$	1.65582	+	0.0877578i	0.0556598	+	0.00294995i
$886$	33.5825	−	28.1791i	1.12823	−	0.946694i
$887$	−12.5517	−	4.56846i	−0.421446	−	0.153394i	0.122587	−	0.992458i	$-0.460881\pi$
$887$	−12.5517	−	4.56846i	−0.421446	−	0.153394i	−0.544033	+	0.839064i	$0.683103\pi$
$888$	3.59428	+	29.4165i	0.120616	+	0.987155i
$889$	−1.16091	+	6.58387i	−0.0389358	+	0.220816i
$890$	0.347203			0.0116383
$891$	−27.2157	−	5.85205i	−0.911760	−	0.196051i
$892$	80.8465			2.70694
$893$	−2.39936	+	13.6074i	−0.0802914	+	0.455355i
$894$	−10.9240	−	89.4048i	−0.365352	−	2.99014i
$895$	−1.42009	−	0.516871i	−0.0474684	−	0.0172771i
$896$	−9.19350	+	7.71427i	−0.307133	+	0.257716i
$897$	32.3605	+	1.71509i	1.08048	+	0.0572652i
$898$	64.8186	−	23.5920i	2.16302	−	0.787276i
$899$	−5.30359	+	9.18609i	−0.176885	+	0.306373i
$900$	−15.6151	+	54.2149i	−0.520505	+	1.80716i
$901$	5.37600	+	9.31150i	0.179100	+	0.310211i
$902$	−6.23767	−	5.23403i	−0.207692	−	0.174274i
$903$	−1.56315	+	6.75257i	−0.0520184	+	0.224712i
$904$	8.73176	+	49.5203i	0.290414	+	1.64702i
$905$	−0.0483552	−	0.274236i	−0.00160738	−	0.00911591i
$906$	−14.4169	−	13.4599i	−0.478969	−	0.447174i
$907$	28.3135	+	23.7578i	0.940134	+	0.788866i	0.977609	−	0.210431i	$-0.0674869\pi$
$907$	28.3135	+	23.7578i	0.940134	+	0.788866i	−0.0374746	+	0.999298i	$0.511931\pi$
$908$	36.0092	+	62.3697i	1.19501	+	2.06981i
$909$	−18.0932	+	12.1729i	−0.600112	+	0.403751i
$910$	−0.272332	+	0.471694i	−0.00902773	+	0.0156365i
$911$	45.4916	−	16.5576i	1.50720	−	0.548577i	0.549288	−	0.835633i	$-0.314899\pi$
$911$	45.4916	−	16.5576i	1.50720	−	0.548577i	0.957914	+	0.287056i	$0.0926766\pi$
$912$	−8.03587	−	15.7943i	−0.266094	−	0.523002i
$913$	35.3057	−	29.6250i	1.16845	−	0.980445i
$914$	−79.8629	−	29.0677i	−2.64163	−	0.961475i
$915$	−1.95796	−	0.832467i	−0.0647280	−	0.0275205i
$916$	14.7015	−	83.3765i	0.485752	−	2.75484i
$917$	5.22558			0.172564
$918$	−16.2671	−	18.7803i	−0.536896	−	0.619841i
$919$	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
$921$	−8.71086	+	6.55604i	−0.287032	+	0.216029i
$922$	5.13809	+	1.87011i	0.169214	+	0.0615889i
$923$	3.68526	−	3.09230i	0.121302	−	0.101784i
$924$	6.38066	−	9.81267i	0.209908	−	0.322813i
$925$	18.9024	−	6.87992i	0.621508	−	0.226211i
$926$	22.0643	−	38.2165i	0.725079	−	1.25587i
$927$	−11.3062	+	15.5231i	−0.371345	+	0.509846i
$928$	−6.72355	−	11.6455i	−0.220711	−	0.382283i
$929$	−4.78330	−	4.01366i	−0.156935	−	0.131684i	0.560939	−	0.827857i	$-0.310440\pi$
$929$	−4.78330	−	4.01366i	−0.156935	−	0.131684i	−0.717874	+	0.696173i	$0.754885\pi$
$930$	−0.613855	+	0.187278i	−0.0201291	+	0.00614109i
$931$	4.44973	+	25.2357i	0.145834	+	0.827066i
$932$	−11.5684	−	65.6079i	−0.378937	−	2.14906i
$933$	−12.2144	+	3.72644i	−0.399882	+	0.121998i
$934$	−8.57084	−	7.19179i	−0.280446	−	0.235322i
$935$	−0.286617	−	0.496435i	−0.00937338	−	0.0162352i
$936$	−53.2162	−	5.65676i	−1.73943	−	0.184897i
$937$	−22.9212	+	39.7006i	−0.748802	+	1.29696i	0.199595	+	0.979878i	$0.436037\pi$
$937$	−22.9212	+	39.7006i	−0.748802	+	1.29696i	−0.948397	+	0.317085i	$0.897296\pi$
$938$	11.5647	−	4.20920i	0.377600	−	0.137435i
$939$	−4.03244	+	6.20140i	−0.131594	+	0.202375i
$940$	0.965368	−	0.810040i	0.0314868	−	0.0264206i
$941$	4.09014	+	1.48869i	0.133335	+	0.0485298i	0.407826	−	0.913060i	$-0.366287\pi$
$941$	4.09014	+	1.48869i	0.133335	+	0.0485298i	−0.274491	+	0.961590i	$0.588509\pi$
$942$	−0.695313	+	0.523313i	−0.0226545	+	0.0170505i
$943$	0.847573	−	4.80683i	0.0276008	−	0.156532i
$944$	−27.3637			−0.890612
$945$	0.276934	+	0.0443647i	0.00900865	+	0.00144318i
$946$	−51.2644			−1.66675
$947$	0.350202	−	1.98610i	0.0113800	−	0.0645395i	−0.978589	−	0.205825i	$-0.934012\pi$
$947$	0.350202	−	1.98610i	0.0113800	−	0.0645395i	0.989969	+	0.141285i	$0.0451235\pi$
$948$	−43.2891	−	18.4053i	−1.40596	−	0.597776i
$949$	−0.771790	−	0.280909i	−0.0250534	−	0.00911868i
$950$	−35.3118	+	29.6301i	−1.14566	+	0.961327i
$951$	12.6827	+	24.9275i	0.411264	+	0.808331i
$952$	4.60587	−	1.67640i	0.149277	−	0.0543325i
$953$	17.8644	−	30.9420i	0.578684	−	1.00231i	−0.416947	−	0.908931i	$-0.636900\pi$
$953$	17.8644	−	30.9420i	0.578684	−	1.00231i	0.995631	−	0.0933786i	$-0.0297667\pi$
$954$	−2.66832	−	38.8171i	−0.0863900	−	1.25675i
$955$	0.104896	+	0.181686i	0.00339437	+	0.00587922i
$956$	−44.5075	−	37.3462i	−1.43948	−	1.20786i
$957$	25.0604	+	23.3968i	0.810086	+	0.756312i
$958$	5.91188	+	33.5279i	0.191004	+	1.08324i
$959$	−1.15999	−	6.57865i	−0.0374581	−	0.212436i
$960$	0.376975	−	1.62847i	0.0121668	−	0.0525588i
$961$	−21.6428	−	18.1605i	−0.698155	−	0.585822i
$962$	20.3338	+	35.2191i	0.655587	+	1.13551i
$963$	16.1417	−	4.00434i	0.520159	−	0.129038i
$964$	−24.7759	+	42.9131i	−0.797978	+	1.38214i
$965$	0.0769973	−	0.0280247i	0.00247863	−	0.000902148i
$966$	10.7254	+	0.568443i	0.345085	+	0.0182894i
$967$	−0.531112	+	0.445656i	−0.0170794	+	0.0143313i	−0.651287	−	0.758831i	$-0.725771\pi$
$967$	−0.531112	+	0.445656i	−0.0170794	+	0.0143313i	0.634208	+	0.773163i	$0.281326\pi$
$968$	−5.71631	−	2.08057i	−0.183729	−	0.0668719i
$969$	−1.60833	−	13.1630i	−0.0516670	−	0.422857i
$970$	−0.205569	+	1.16584i	−0.00660041	+	0.0374328i
$971$	47.4942			1.52416			0.762081	−	0.647482i	$-0.224178\pi$
$971$	47.4942			1.52416			0.762081	+	0.647482i	$0.224178\pi$
$972$	15.0340	+	56.7772i	0.482216	+	1.82113i
$973$	−0.987988			−0.0316734
$974$	8.93869	−	50.6938i	0.286414	−	1.62434i
$975$	4.40563	+	36.0569i	0.141093	+	1.15474i
$976$	32.9931	+	12.0085i	1.05608	+	0.384383i
$977$	−9.65470	+	8.10126i	−0.308881	+	0.259182i	−0.784029	−	0.620724i	$-0.786839\pi$
$977$	−9.65470	+	8.10126i	−0.308881	+	0.259182i	0.475148	+	0.879906i	$0.342394\pi$
$978$	23.3609	+	1.23812i	0.746999	+	0.0395906i
$979$	−4.51423	+	1.64305i	−0.144276	+	0.0525120i
$980$	1.16855	−	2.02399i	0.0373280	−	0.0646540i
$981$	18.1441	−	4.50110i	0.579298	−	0.143709i
$982$	−16.9168	−	29.3008i	−0.539838	−	0.935027i
$983$	8.84400	+	7.42100i	0.282080	+	0.236693i	0.772839	−	0.634602i	$-0.218836\pi$
$983$	8.84400	+	7.42100i	0.282080	+	0.236693i	−0.490759	+	0.871295i	$0.663280\pi$
$984$	−1.81787	+	7.85292i	−0.0579517	+	0.250342i
$985$	0.327745	+	1.85874i	0.0104428	+	0.0592243i
$986$	5.31361	+	30.1350i	0.169220	+	0.959693i
$987$	2.63787	+	2.46277i	0.0839644	+	0.0783908i
$988$	−46.6351	−	39.1315i	−1.48366	−	1.24494i
$989$	−15.3647	−	26.6125i	−0.488569	−	0.846227i
$990$	0.142259	+	2.06950i	0.00452130	+	0.0657731i
$991$	−9.34676	+	16.1891i	−0.296910	+	0.514263i	−0.975427	−	0.220322i	$-0.929289\pi$
$991$	−9.34676	+	16.1891i	−0.296910	+	0.514263i	0.678518	+	0.734584i	$0.262623\pi$
$992$	−3.27281	+	1.19121i	−0.103912	+	0.0378209i
$993$	15.1023	+	29.6832i	0.479257	+	0.941969i
$994$	1.22143	−	1.02490i	0.0387413	−	0.0325079i
$995$	1.66275	+	0.605192i	0.0527128	+	0.0191859i
$996$	−89.4877	−	38.0476i	−2.83553	−	1.20558i
$997$	0.583250	−	3.30778i	0.0184717	−	0.104758i	−0.974178	−	0.225782i	$-0.927506\pi$
$997$	0.583250	−	3.30778i	0.0184717	−	0.104758i	0.992650	+	0.121023i	$0.0386175\pi$
$998$	−35.8066			−1.13344
$999$	13.2074	−	16.2508i	0.417863	−	0.514154i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.1	✓	12	27.13	even	9	inner
27.2.e.a.25.1	yes	12	1.1	even	1	trivial
81.2.e.a.10.2		12	27.14	odd	18
81.2.e.a.73.2		12	3.2	odd	2
243.2.e.a.55.1		12	9.2	odd	6
243.2.e.a.190.1		12	27.5	odd	18
243.2.e.b.109.2		12	27.23	odd	18
243.2.e.b.136.2		12	9.5	odd	6
243.2.e.c.109.1		12	27.4	even	9
243.2.e.c.136.1		12	9.4	even	3
243.2.e.d.55.2		12	9.7	even	3
243.2.e.d.190.2		12	27.22	even	9
432.2.u.c.241.1		12	4.3	odd	2
432.2.u.c.337.1		12	108.67	odd	18
675.2.l.c.376.2		12	5.4	even	2
675.2.l.c.526.2		12	135.94	even	18
675.2.u.b.349.1		24	5.2	odd	4
675.2.u.b.349.4		24	5.3	odd	4
675.2.u.b.499.1		24	135.13	odd	36
675.2.u.b.499.4		24	135.67	odd	36
729.2.a.a.1.1		6	27.16	even	9
729.2.a.d.1.6		6	27.11	odd	18
729.2.c.b.244.1		12	27.20	odd	18
729.2.c.b.487.1		12	27.2	odd	18
729.2.c.e.244.6		12	27.7	even	9
729.2.c.e.487.6		12	27.25	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.417037 + 2.36514i) q^{2} +(-0.210069 - 1.71926i) q^{3} +(-3.54056 - 1.28866i) q^{4} +(0.0713060 - 0.0598329i) q^{5} +(4.15390 + 0.220155i) q^{6} +(0.544891 - 0.198324i) q^{7} +(2.12277 - 3.67675i) q^{8} +(-2.91174 + 0.722330i) q^{9} +(0.111776 + 0.193601i) q^{10} +(-2.36944 - 1.98820i) q^{11} +(-1.47178 + 6.35787i) q^{12} +(0.729623 + 4.13790i) q^{13} +(0.241824 + 1.37145i) q^{14} +(-0.117848 - 0.110025i) q^{15} +(2.03816 + 1.71022i) q^{16} +(0.995493 + 1.72424i) q^{17} +(-0.494102 - 7.18790i) q^{18} +(1.92271 - 3.33023i) q^{19} +(-0.329567 + 0.119953i) q^{20} +(-0.455437 - 0.895151i) q^{21} +(5.69050 - 4.77489i) q^{22} +(4.18428 + 1.52295i) q^{23} +(-6.76724 - 2.87724i) q^{24} +(-0.866736 + 4.91551i) q^{25} -10.0910 q^{26} +(1.85354 + 4.85432i) q^{27} -2.18479 q^{28} +(1.11126 - 6.30229i) q^{29} +(0.309371 - 0.232841i) q^{30} +(-1.55754 - 0.566898i) q^{31} +(1.60967 - 1.35067i) q^{32} +(-2.92049 + 4.49135i) q^{33} +(-4.49323 + 1.63540i) q^{34} +(0.0269877 - 0.0467441i) q^{35} +(11.2400 + 1.19479i) q^{36} +(-2.01505 - 3.49016i) q^{37} +(7.07461 + 5.93630i) q^{38} +(6.96087 - 2.12366i) q^{39} +(-0.0686240 - 0.389186i) q^{40} +(-0.190345 - 1.07950i) q^{41} +(2.30709 - 0.703859i) q^{42} +(-5.28657 - 4.43596i) q^{43} +(5.82704 + 10.0927i) q^{44} +(-0.164406 + 0.225724i) q^{45} +(-5.34699 + 9.26126i) q^{46} +(-3.37650 + 1.22894i) q^{47} +(2.51217 - 3.86340i) q^{48} +(-5.10474 + 4.28338i) q^{49} +(-11.2644 - 4.09990i) q^{50} +(2.75531 - 2.07373i) q^{51} +(2.74906 - 15.5907i) q^{52} +5.40034 q^{53} +(-12.2541 + 2.35945i) q^{54} -0.287915 q^{55} +(0.427492 - 2.42443i) q^{56} +(-6.12946 - 2.60607i) q^{57} +(14.4423 + 5.25657i) q^{58} +(-7.87850 + 6.61085i) q^{59} +(0.275462 + 0.541415i) q^{60} +(12.4005 - 4.51341i) q^{61} +(1.99034 - 3.44738i) q^{62} +(-1.44333 + 0.971060i) q^{63} +(5.18386 + 8.97871i) q^{64} +(0.299609 + 0.251402i) q^{65} +(-9.40470 - 8.78041i) q^{66} +(-1.53458 - 8.70304i) q^{67} +(-1.30264 - 7.38764i) q^{68} +(1.73937 - 7.51381i) q^{69} +(0.0993013 + 0.0833237i) q^{70} +(-0.572473 - 0.991553i) q^{71} +(-3.52514 + 12.2391i) q^{72} +(-0.0977361 + 0.169284i) q^{73} +(9.09506 - 3.31033i) q^{74} +(8.63313 + 0.457552i) q^{75} +(-11.0990 + 9.31317i) q^{76} +(-1.68539 - 0.613433i) q^{77} +(2.11980 + 17.3491i) q^{78} +(-1.25166 + 7.09849i) q^{79} +0.247661 q^{80} +(7.95648 - 4.20647i) q^{81} +2.63255 q^{82} +(-2.58744 + 14.6741i) q^{83} +(0.458958 + 3.75624i) q^{84} +(0.174151 + 0.0633858i) q^{85} +(12.6963 - 10.6535i) q^{86} +(-11.0687 - 0.586638i) q^{87} +(-12.3399 + 4.49135i) q^{88} +(0.776563 - 1.34505i) q^{89} +(-0.465305 - 0.482977i) q^{90} +(1.21821 + 2.11000i) q^{91} +(-12.8521 - 10.7842i) q^{92} +(-0.647457 + 2.79691i) q^{93} +(-1.49850 - 8.49839i) q^{94} +(-0.0621565 - 0.352507i) q^{95} +(-2.66030 - 2.48371i) q^{96} +(4.05661 + 3.40390i) q^{97} +(-8.00191 - 13.8597i) q^{98} +(8.33533 + 4.07760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 3 q^{5} - 6 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 12 q^{12} - 6 q^{13} + 15 q^{14} + 9 q^{15} + 9 q^{17} + 9 q^{18} - 3 q^{19} - 3 q^{20} - 12 q^{21} + 3 q^{22} - 12 q^{23}+ \cdots - 27 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Introduction

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