LMFDB - Embedded newform 81.2.g.a.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

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("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			31.5
Character	$\chi$	$=$	81.31
Dual form			81.2.g.a.34.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.130814 + 0.303261i) q^{2} +(-0.919544 + 1.46780i) q^{3} +(1.29763 - 1.37541i) q^{4} +(-0.175343 + 3.01052i) q^{5} +(-0.565415 - 0.0868526i) q^{6} +(0.00895493 - 0.00212236i) q^{7} +(1.20756 + 0.439517i) q^{8} +(-1.30888 - 2.69941i) q^{9} +(-0.935909 + 0.340643i) q^{10} +(2.97312 - 1.95545i) q^{11} +(0.825596 + 3.16941i) q^{12} +(-3.51646 + 0.411015i) q^{13} +(0.00181506 + 0.00243804i) q^{14} +(-4.25761 - 3.02567i) q^{15} +(-0.195217 - 3.35174i) q^{16} +(-3.09319 - 2.59549i) q^{17} +(0.647406 - 0.750053i) q^{18} +(5.54096 - 4.64941i) q^{19} +(3.91316 + 4.14770i) q^{20} +(-0.00511925 + 0.0150957i) q^{21} +(0.981937 + 0.645830i) q^{22} +(-5.00317 - 1.18577i) q^{23} +(-1.75553 + 1.36831i) q^{24} +(-4.06629 - 0.475281i) q^{25} +(-0.584647 - 1.01264i) q^{26} +(5.16577 + 0.561054i) q^{27} +(0.00870107 - 0.0150707i) q^{28} +(-2.83907 + 3.81353i) q^{29} +(0.360613 - 1.68696i) q^{30} +(2.59221 + 8.65858i) q^{31} +(3.28766 - 1.65112i) q^{32} +(0.136301 + 6.16207i) q^{33} +(0.382479 - 1.27757i) q^{34} +(0.00481921 + 0.0273311i) q^{35} +(-5.41123 - 1.70260i) q^{36} +(0.0241986 - 0.137237i) q^{37} +(2.13482 + 1.07215i) q^{38} +(2.63025 - 5.53941i) q^{39} +(-1.53491 + 3.55832i) q^{40} +(-1.42815 + 3.31082i) q^{41} +(-0.00524759 + 0.000422254i) q^{42} +(1.09801 + 0.551444i) q^{43} +(1.16847 - 6.62670i) q^{44} +(8.35614 - 3.46708i) q^{45} +(-0.294886 - 1.67238i) q^{46} +(0.298973 - 0.998641i) q^{47} +(5.09920 + 2.79553i) q^{48} +(-6.25535 + 3.14156i) q^{49} +(-0.387793 - 1.29532i) q^{50} +(6.65399 - 2.15352i) q^{51} +(-3.99775 + 5.36991i) q^{52} +(1.88778 - 3.26973i) q^{53} +(0.505609 + 1.63997i) q^{54} +(5.36561 + 9.29351i) q^{55} +(0.0117464 + 0.00137296i) q^{56} +(1.72926 + 12.4084i) q^{57} +(-1.52788 - 0.362115i) q^{58} +(-4.33615 - 2.85193i) q^{59} +(-9.68632 + 1.92974i) q^{60} +(-4.70281 - 4.98469i) q^{61} +(-2.28671 + 1.91878i) q^{62} +(-0.0174500 - 0.0213951i) q^{63} +(-4.21308 - 3.53519i) q^{64} +(-0.620784 - 10.6584i) q^{65} +(-1.85088 + 0.847419i) q^{66} +(4.97104 + 6.67727i) q^{67} +(-7.58367 + 0.886403i) q^{68} +(6.34111 - 6.25329i) q^{69} +(-0.00765804 + 0.00503677i) q^{70} +(-2.49894 + 0.909541i) q^{71} +(-0.394116 - 3.83498i) q^{72} +(2.10657 + 0.766729i) q^{73} +(0.0447841 - 0.0106140i) q^{74} +(4.43675 - 5.53146i) q^{75} +(0.795271 - 13.6543i) q^{76} +(0.0224739 - 0.0238210i) q^{77} +(2.02396 + 0.0730195i) q^{78} +(-1.63789 - 3.79706i) q^{79} +10.1247 q^{80} +(-5.57367 + 7.06641i) q^{81} -1.19086 q^{82} +(-5.10959 - 11.8454i) q^{83} +(0.0141198 + 0.0266296i) q^{84} +(8.35615 - 8.85700i) q^{85} +(-0.0235956 + 0.405121i) q^{86} +(-2.98686 - 7.67390i) q^{87} +(4.44968 - 1.05459i) q^{88} +(-9.21313 - 3.35330i) q^{89} +(2.14453 + 2.08055i) q^{90} +(-0.0306173 + 0.0111438i) q^{91} +(-8.12317 + 5.34270i) q^{92} +(-15.0927 - 4.15709i) q^{93} +(0.341958 - 0.0399692i) q^{94} +(13.0256 + 17.4964i) q^{95} +(-0.599623 + 6.34391i) q^{96} +(0.917855 + 15.7590i) q^{97} +(-1.77100 - 1.48604i) q^{98} +(-9.17003 - 5.46623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	0.130814	+	0.303261i	0.0924994	+	0.214438i	0.958184	−	0.286151i	$-0.0923760\pi$
$2$	0.130814	+	0.303261i	0.0924994	+	0.214438i	−0.865685	+	0.500589i	$0.833117\pi$
$3$	−0.919544	+	1.46780i	−0.530899	+	0.847435i
$3$	−0.919544	+	1.46780i	−0.530899	+	0.847435i
$4$	1.29763	−	1.37541i	0.648814	−	0.687703i
$5$	−0.175343	+	3.01052i	−0.0784157	+	1.34635i	0.697988	+	0.716109i	$0.254079\pi$
$5$	−0.175343	+	3.01052i	−0.0784157	+	1.34635i	−0.776404	+	0.630236i	$0.782958\pi$
$6$	−0.565415	−	0.0868526i	−0.230830	−	0.0354574i
$7$	0.00895493	−	0.00212236i	0.00338465	−	0.000802176i	−0.228923	−	0.973444i	$-0.573520\pi$
$7$	0.00895493	−	0.00212236i	0.00338465	−	0.000802176i	0.232308	+	0.972642i	$0.425372\pi$
$8$	1.20756	+	0.439517i	0.426938	+	0.155393i
$9$	−1.30888	−	2.69941i	−0.436293	−	0.899805i
$10$	−0.935909	+	0.340643i	−0.295961	+	0.107721i
$11$	2.97312	−	1.95545i	0.896429	−	0.589591i	−0.0155264	−	0.999879i	$-0.504942\pi$
$11$	2.97312	−	1.95545i	0.896429	−	0.589591i	0.911956	+	0.410289i	$0.134572\pi$
$12$	0.825596	+	3.16941i	0.238329	+	0.914929i
$13$	−3.51646	+	0.411015i	−0.975291	+	0.113995i	−0.588783	−	0.808291i	$-0.700393\pi$
$13$	−3.51646	+	0.411015i	−0.975291	+	0.113995i	−0.386508	+	0.922286i	$0.626319\pi$
$14$	0.00181506	+	0.00243804i	0.000485094	+	0.000651595i
$15$	−4.25761	−	3.02567i	−1.09931	−	0.781225i
$16$	−0.195217	−	3.35174i	−0.0488042	−	0.837936i
$17$	−3.09319	−	2.59549i	−0.750208	−	0.629500i	0.185350	−	0.982673i	$-0.440658\pi$
$17$	−3.09319	−	2.59549i	−0.750208	−	0.629500i	−0.935558	+	0.353173i	$0.885103\pi$
$18$	0.647406	−	0.750053i	0.152595	−	0.176789i
$19$	5.54096	−	4.64941i	1.27118	−	1.06665i	0.276786	−	0.960931i	$-0.410731\pi$
$19$	5.54096	−	4.64941i	1.27118	−	1.06665i	0.994396	−	0.105717i	$-0.0337139\pi$
$20$	3.91316	+	4.14770i	0.875008	+	0.927455i
$21$	−0.00511925	+	0.0150957i	−0.00111711	+	0.00329414i
$22$	0.981937	+	0.645830i	0.209350	+	0.137691i
$23$	−5.00317	−	1.18577i	−1.04323	−	0.247251i	−0.326936	−	0.945046i	$-0.606016\pi$
$23$	−5.00317	−	1.18577i	−1.04323	−	0.247251i	−0.716297	+	0.697796i	$0.754164\pi$
$24$	−1.75553	+	1.36831i	−0.358346	+	0.279304i
$25$	−4.06629	−	0.475281i	−0.813258	−	0.0950562i
$26$	−0.584647	−	1.01264i	−0.114659	−	0.198595i
$27$	5.16577	+	0.561054i	0.994154	+	0.107975i
$28$	0.00870107	−	0.0150707i	0.00164435	−	0.00284809i
$29$	−2.83907	+	3.81353i	−0.527202	+	0.708155i	−0.983345	−	0.181751i	$-0.941823\pi$
$29$	−2.83907	+	3.81353i	−0.527202	+	0.708155i	0.456142	+	0.889907i	$0.349231\pi$
$30$	0.360613	−	1.68696i	0.0658386	−	0.307996i
$31$	2.59221	+	8.65858i	0.465574	+	1.55513i	0.792376	+	0.610033i	$0.208844\pi$
$31$	2.59221	+	8.65858i	0.465574	+	1.55513i	−0.326801	+	0.945093i	$0.605971\pi$
$32$	3.28766	−	1.65112i	0.581181	−	0.291880i
$33$	0.136301	+	6.16207i	0.0237269	+	1.07268i
$34$	0.382479	−	1.27757i	0.0655946	−	0.219101i
$35$	0.00481921	+	0.0273311i	0.000814596	+	0.00461980i
$36$	−5.41123	−	1.70260i	−0.901871	−	0.283766i
$37$	0.0241986	−	0.137237i	0.00397822	−	0.0225616i	−0.982754	−	0.184918i	$-0.940798\pi$
$37$	0.0241986	−	0.137237i	0.00397822	−	0.0225616i	0.986732	+	0.162356i	$0.0519093\pi$
$38$	2.13482	+	1.07215i	0.346313	+	0.173925i
$39$	2.63025	−	5.53941i	0.421177	−	0.887016i
$40$	−1.53491	+	3.55832i	−0.242691	+	0.562620i
$41$	−1.42815	+	3.31082i	−0.223039	+	0.517063i	−0.992588	−	0.121525i	$-0.961222\pi$
$41$	−1.42815	+	3.31082i	−0.223039	+	0.517063i	0.769549	+	0.638587i	$0.220481\pi$
$42$	−0.00524759		0.000422254i	−0.000809720		6.51553e-5i
$43$	1.09801	+	0.551444i	0.167446	+	0.0840943i	0.530548	−	0.847655i	$-0.321986\pi$
$43$	1.09801	+	0.551444i	0.167446	+	0.0840943i	−0.363102	+	0.931749i	$0.618282\pi$
$44$	1.16847	−	6.62670i	0.176153	−	0.999012i
$45$	8.35614	−	3.46708i	1.24566	−	0.516842i
$46$	−0.294886	−	1.67238i	−0.0434785	−	0.246579i
$47$	0.298973	−	0.998641i	0.0436098	−	0.145667i	−0.933412	−	0.358807i	$-0.883184\pi$
$47$	0.298973	−	0.998641i	0.0436098	−	0.145667i	0.977022	+	0.213140i	$0.0683690\pi$
$48$	5.09920	+	2.79553i	0.736006	+	0.403500i
$49$	−6.25535	+	3.14156i	−0.893622	+	0.448794i
$50$	−0.387793	−	1.29532i	−0.0548422	−	0.183186i
$51$	6.65399	−	2.15352i	0.931745	−	0.301553i
$52$	−3.99775	+	5.36991i	−0.554388	+	0.744672i
$53$	1.88778	−	3.26973i	0.259307	−	0.449133i	−0.706750	−	0.707464i	$-0.749839\pi$
$53$	1.88778	−	3.26973i	0.259307	−	0.449133i	0.966056	+	0.258331i	$0.0831726\pi$
$54$	0.505609	+	1.63997i	0.0688047	+	0.223172i
$55$	5.36561	+	9.29351i	0.723499	+	1.25314i
$56$	0.0117464	+	0.00137296i	0.00156968	+	0.000183470i
$57$	1.72926	+	12.4084i	0.229047	+	1.64353i
$58$	−1.52788	−	0.362115i	−0.200621	−	0.0475481i
$59$	−4.33615	−	2.85193i	−0.564519	−	0.371290i	0.234941	−	0.972010i	$-0.424510\pi$
$59$	−4.33615	−	2.85193i	−0.564519	−	0.371290i	−0.799460	+	0.600720i	$0.794881\pi$
$60$	−9.68632	+	1.92974i	−1.25050	+	0.249128i
$61$	−4.70281	−	4.98469i	−0.602133	−	0.638224i	0.352569	−	0.935786i	$-0.385308\pi$
$61$	−4.70281	−	4.98469i	−0.602133	−	0.638224i	−0.954703	+	0.297562i	$0.903827\pi$
$62$	−2.28671	+	1.91878i	−0.290412	+	0.243685i
$63$	−0.0174500	−	0.0213951i	−0.00219850	−	0.00269554i
$64$	−4.21308	−	3.53519i	−0.526635	−	0.441899i
$65$	−0.620784	−	10.6584i	−0.0769987	−	1.32202i
$66$	−1.85088	+	0.847419i	−0.227828	+	0.104310i
$67$	4.97104	+	6.67727i	0.607310	+	0.815758i	0.994333	−	0.106312i	$-0.0339041\pi$
$67$	4.97104	+	6.67727i	0.607310	+	0.815758i	−0.387023	+	0.922070i	$0.626497\pi$
$68$	−7.58367	+	0.886403i	−0.919655	+	0.107492i
$69$	6.34111	−	6.25329i	0.763380	−	0.752807i
$70$	−0.00765804	+	0.00503677i	−0.000915310	+	0.000602009i
$71$	−2.49894	+	0.909541i	−0.296570	+	0.107943i	−0.486020	−	0.873948i	$-0.661552\pi$
$71$	−2.49894	+	0.909541i	−0.296570	+	0.107943i	0.189450	+	0.981890i	$0.439330\pi$
$72$	−0.394116	−	3.83498i	−0.0464470	−	0.451957i
$73$	2.10657	+	0.766729i	0.246555	+	0.0897388i	0.462342	−	0.886702i	$-0.347009\pi$
$73$	2.10657	+	0.766729i	0.246555	+	0.0897388i	−0.215786	+	0.976441i	$0.569232\pi$
$74$	0.0447841	−	0.0106140i	0.00520604	−	0.00123385i
$75$	4.43675	−	5.53146i	0.512311	−	0.638718i
$76$	0.795271	−	13.6543i	0.0912238	−	1.56625i
$77$	0.0224739	−	0.0238210i	0.00256114	−	0.00271465i
$78$	2.02396	+	0.0730195i	0.229168	+	0.00826783i
$79$	−1.63789	−	3.79706i	−0.184277	−	0.427203i	0.800887	−	0.598815i	$-0.204362\pi$
$79$	−1.63789	−	3.79706i	−0.184277	−	0.427203i	−0.985165	+	0.171612i	$0.945102\pi$
$80$	10.1247			1.13198
$81$	−5.57367	+	7.06641i	−0.619297	+	0.785157i
$82$	−1.19086			−0.131509
$83$	−5.10959	−	11.8454i	−0.560850	−	1.30020i	−0.928879	−	0.370382i	$-0.879227\pi$
$83$	−5.10959	−	11.8454i	−0.560850	−	1.30020i	0.368030	−	0.929814i	$-0.380033\pi$
$84$	0.0141198	+	0.0266296i	0.00154059	+	0.00290553i
$85$	8.35615	−	8.85700i	0.906352	−	0.960677i
$86$	−0.0235956	+	0.405121i	−0.00254438	+	0.0436853i
$87$	−2.98686	−	7.67390i	−0.320225	−	0.822728i
$88$	4.44968	−	1.05459i	0.474337	−	0.112420i
$89$	−9.21313	−	3.35330i	−0.976590	−	0.355450i	−0.196076	−	0.980589i	$-0.562820\pi$
$89$	−9.21313	−	3.35330i	−0.976590	−	0.355450i	−0.780513	+	0.625139i	$0.785042\pi$
$90$	2.14453	+	2.08055i	0.226053	+	0.219309i
$91$	−0.0306173	+	0.0111438i	−0.00320957	+	0.00116819i
$92$	−8.12317	+	5.34270i	−0.846899	+	0.557014i
$93$	−15.0927	−	4.15709i	−1.56504	−	0.431070i
$94$	0.341958	−	0.0399692i	0.0352703	−	0.00412251i
$95$	13.0256	+	17.4964i	1.33640	+	1.79509i
$96$	−0.599623	+	6.34391i	−0.0611988	+	0.647473i
$97$	0.917855	+	15.7590i	0.0931941	+	1.60008i	0.643719	+	0.765262i	$0.277390\pi$
$97$	0.917855	+	15.7590i	0.0931941	+	1.60008i	−0.550525	+	0.834819i	$0.685573\pi$
$98$	−1.77100	−	1.48604i	−0.178898	−	0.150113i
$99$	−9.17003	−	5.46623i	−0.921623	−	0.549377i
$100$	−5.93024	+	4.97606i	−0.593024	+	0.497606i
$101$	13.2093	+	14.0010i	1.31437	+	1.39315i	0.866600	+	0.499003i	$0.166300\pi$
$101$	13.2093	+	14.0010i	1.31437	+	1.39315i	0.447771	+	0.894149i	$0.352218\pi$
$102$	1.52351	+	1.73618i	0.150850	+	0.171908i
$103$	−7.29517	−	4.79811i	−0.718815	−	0.472772i	0.136659	−	0.990618i	$-0.456364\pi$
$103$	−7.29517	−	4.79811i	−0.718815	−	0.472772i	−0.855474	+	0.517846i	$0.826734\pi$
$104$	−4.42699	−	1.04922i	−0.434102	−	0.102884i
$105$	−0.0445481	−	0.0180585i	−0.00434745	−	0.00176233i
$106$	1.23853	+	0.144763i	0.120297	+	0.0140607i
$107$	7.06211	+	12.2319i	0.682720	+	1.18251i	0.974147	+	0.225913i	$0.0725365\pi$
$107$	7.06211	+	12.2319i	0.682720	+	1.18251i	−0.291427	+	0.956593i	$0.594130\pi$
$108$	7.47493	−	6.37700i	0.719276	−	0.613627i
$109$	−3.80056	+	6.58277i	−0.364028	+	0.630515i	−0.988620	−	0.150437i	$-0.951932\pi$
$109$	−3.80056	+	6.58277i	−0.364028	+	0.630515i	0.624592	+	0.780951i	$0.285265\pi$
$110$	−2.11646	+	2.84290i	−0.201797	+	0.271060i
$111$	0.179185	+	0.161714i	0.0170075	+	0.0153492i
$112$	−0.00886175	−	0.0296003i	−0.000837356	−	0.00279696i
$113$	17.2409	−	8.65873i	1.62189	−	0.814544i	0.622399	−	0.782701i	$-0.286158\pi$
$113$	17.2409	−	8.65873i	1.62189	−	0.814544i	0.999493	−	0.0318440i	$-0.0101380\pi$
$114$	−3.53676	+	2.14760i	−0.331248	+	0.201142i
$115$	4.44706	−	14.8542i	0.414691	−	1.38516i
$116$	1.56110	+	8.85342i	0.144944	+	0.822020i
$117$	5.71212	+	8.95441i	0.528086	+	0.827836i
$118$	0.297650	−	1.68806i	0.0274009	−	0.155398i
$119$	−0.0332078	−	0.0166776i	−0.00304416	−	0.00152883i
$120$	−3.81149	−	5.52498i	−0.347940	−	0.504359i
$121$	0.658773	−	1.52721i	0.0598885	−	0.138837i
$122$	0.896467	−	2.07824i	0.0811623	−	0.188155i
$123$	−3.54638	−	5.14067i	−0.319766	−	0.463519i
$124$	15.2728	+	7.67028i	1.37154	+	0.688811i
$125$	−0.474449	+	2.69073i	−0.0424360	+	0.240667i
$126$	0.00420560	−	0.00809070i	0.000374665	−	0.000720776i
$127$	−1.36077	−	7.71730i	−0.120749	−	0.684800i	−0.983742	−	0.179585i	$-0.942524\pi$
$127$	−1.36077	−	7.71730i	−0.120749	−	0.684800i	0.862994	−	0.505214i	$-0.168587\pi$
$128$	2.63124	−	8.78897i	0.232571	−	0.776842i
$129$	−1.81908	+	1.10459i	−0.160161	+	0.0972537i
$130$	3.15108	−	1.58253i	0.276368	−	0.138797i
$131$	−1.23950	−	4.14021i	−0.108295	−	0.361732i	0.886613	−	0.462511i	$-0.153052\pi$
$131$	−1.23950	−	4.14021i	−0.108295	−	0.361732i	−0.994909	+	0.100780i	$0.967866\pi$
$132$	8.65222	+	7.80861i	0.753079	+	0.679652i
$133$	0.0397512	−	0.0533951i	0.00344686	−	0.00462994i
$134$	−1.37467	+	2.38100i	−0.118754	+	0.205687i
$135$	−2.59484	+	15.4533i	−0.223329	+	1.33001i
$136$	−2.59445	−	4.49373i	−0.222473	−	0.385334i
$137$	−0.116944	−	0.0136688i	−0.00999123	−	0.00116781i	0.111096	−	0.993810i	$-0.464564\pi$
$137$	−0.116944	−	0.0136688i	−0.00999123	−	0.00116781i	−0.121087	+	0.992642i	$0.538638\pi$
$138$	2.72588	+	1.10499i	0.232042	+	0.0940632i
$139$	1.26696	+	0.300276i	0.107462	+	0.0254691i	0.283995	−	0.958826i	$-0.408340\pi$
$139$	1.26696	+	0.300276i	0.107462	+	0.0254691i	−0.176533	+	0.984295i	$0.556488\pi$
$140$	0.0438449	+	0.0288373i	0.00370557	+	0.00243719i
$141$	1.19089	+	1.35713i	0.100291	+	0.114291i
$142$	−0.602724	−	0.638851i	−0.0505795	−	0.0536111i
$143$	−9.65114	+	8.09827i	−0.807069	+	0.677211i
$144$	−8.79222	+	4.91400i	−0.732685	+	0.409500i
$145$	−10.9829	−	9.21575i	−0.912081	−	0.765326i
$146$	0.0430499	+	0.739139i	0.00356284	+	0.0611716i
$147$	1.14089	−	12.0704i	0.0940990	−	0.995551i
$148$	−0.157356	−	0.211365i	−0.0129346	−	0.0173741i
$149$	6.89069	−	0.805406i	0.564507	−	0.0659815i	0.170947	−	0.985280i	$-0.445317\pi$
$149$	6.89069	−	0.805406i	0.564507	−	0.0659815i	0.393560	+	0.919299i	$0.371243\pi$
$150$	2.25786	+	0.621899i	0.184354	+	0.0507778i
$151$	7.88747	−	5.18767i	0.641874	−	0.422167i	−0.186413	−	0.982471i	$-0.559686\pi$
$151$	7.88747	−	5.18767i	0.641874	−	0.422167i	0.828287	+	0.560305i	$0.189316\pi$
$152$	8.73454	−	3.17911i	0.708465	−	0.257860i
$153$	−2.95770	+	11.7470i	−0.239116	+	0.949687i
$154$	0.0101639	+	0.00369934i	0.000819027	+	0.000298102i
$155$	−26.5213	+	6.28567i	−2.13025	+	0.504877i
$156$	−4.20585	−	10.8058i	−0.336738	−	0.865153i
$157$	−0.356933	+	6.12831i	−0.0284864	+	0.489092i	0.953650	+	0.300920i	$0.0972936\pi$
$157$	−0.356933	+	6.12831i	−0.0284864	+	0.489092i	−0.982136	+	0.188173i	$0.939743\pi$
$158$	0.937241	−	0.993417i	0.0745629	−	0.0790320i
$159$	3.06342	+	5.77755i	0.242945	+	0.458190i
$160$	4.39427	+	10.1871i	0.347398	+	0.805359i
$161$	−0.0473197			−0.00372931
$162$	−2.87208	−	0.765890i	−0.225652	−	0.0601740i
$163$	1.40640			0.110158			0.0550788	−	0.998482i	$-0.482459\pi$
$163$	1.40640			0.110158			0.0550788	+	0.998482i	$0.482459\pi$
$164$	2.70051	+	6.26049i	0.210875	+	0.488862i
$165$	−18.5749	−	0.670138i	−1.44606	−	0.0521702i
$166$	2.92382	−	3.09907i	0.226933	−	0.240535i
$167$	0.855100	−	14.6815i	0.0661696	−	1.13609i	−0.787857	−	0.615859i	$-0.788809\pi$
$167$	0.855100	−	14.6815i	0.0661696	−	1.13609i	0.854026	−	0.520230i	$-0.174154\pi$
$168$	−0.0128166	+	0.0159789i	−0.000988822	+	0.00123280i
$169$	−0.453017	+	0.107367i	−0.0348475	+	0.00825900i
$170$	3.77908	+	1.37547i	0.289842	+	0.105494i
$171$	−19.8031	−	8.87181i	−1.51438	−	0.678444i
$172$	2.18327	−	0.794647i	0.166473	−	0.0605912i
$173$	6.40528	−	4.21282i	0.486984	−	0.320295i	−0.282163	−	0.959367i	$-0.591052\pi$
$173$	6.40528	−	4.21282i	0.486984	−	0.320295i	0.769147	+	0.639072i	$0.220681\pi$
$174$	1.93647	−	1.90965i	0.146803	−	0.144770i
$175$	−0.0374220	+	0.00437401i	−0.00282884	+	0.000330644i
$176$	−7.13457	−	9.58339i	−0.537789	−	0.722376i
$177$	8.17334	−	3.74213i	0.614346	−	0.281276i
$178$	−0.188280	−	3.23264i	−0.0141122	−	0.242296i
$179$	4.59366	+	3.85454i	0.343347	+	0.288102i	0.798112	−	0.602509i	$-0.205832\pi$
$179$	4.59366	+	3.85454i	0.343347	+	0.288102i	−0.454765	+	0.890611i	$0.650277\pi$
$180$	6.07452	−	15.9921i	0.452768	−	1.19198i
$181$	7.92436	−	6.64933i	0.589013	−	0.494241i	−0.298880	−	0.954291i	$-0.596613\pi$
$181$	7.92436	−	6.64933i	0.589013	−	0.494241i	0.887893	+	0.460050i	$0.152169\pi$
$182$	−0.00738465	−	0.00782727i	−0.000547387	−	0.000580196i
$183$	11.6410	−	2.31915i	0.860525	−	0.171437i
$184$	−5.52047	−	3.63087i	−0.406974	−	0.267671i
$185$	0.408911	+	0.0969138i	0.0300638	+	0.00712524i
$186$	−0.713654	−	5.12083i	−0.0523277	−	0.375478i
$187$	−14.2718	−	1.66813i	−1.04366	−	0.121986i
$188$	−0.985580	−	1.70707i	−0.0718808	−	0.124501i
$189$	0.0474499	−	0.00593942i	0.00345147	−	0.000432029i
$190$	−3.60204	+	6.23892i	−0.261320	+	0.452619i
$191$	−9.48044	+	12.7344i	−0.685981	+	0.921432i	−0.999605	−	0.0281152i	$-0.991049\pi$
$191$	−9.48044	+	12.7344i	−0.685981	+	0.921432i	0.313624	+	0.949547i	$0.398457\pi$
$192$	9.06306	−	2.93320i	0.654070	−	0.211685i
$193$	−5.63752	−	18.8306i	−0.405798	−	1.35546i	−0.879971	−	0.475027i	$-0.842438\pi$
$193$	−5.63752	−	18.8306i	−0.405798	−	1.35546i	0.474174	−	0.880431i	$-0.342747\pi$
$194$	−4.65901	+	2.33984i	−0.334497	+	0.167991i
$195$	16.2153	+	8.88971i	1.16120	+	0.636606i
$196$	−3.79621	+	12.6802i	−0.271158	+	0.905730i
$197$	−0.0147762	−	0.0837998i	−0.00105276	−	0.00597049i	0.984277	−	0.176633i	$-0.0565204\pi$
$197$	−0.0147762	−	0.0837998i	−0.00105276	−	0.00597049i	−0.985330	+	0.170662i	$0.945409\pi$
$198$	0.458126	−	3.49597i	0.0325576	−	0.248448i
$199$	−3.10186	+	17.5915i	−0.219885	+	1.24703i	0.652340	+	0.757927i	$0.273788\pi$
$199$	−3.10186	+	17.5915i	−0.219885	+	1.24703i	−0.872225	+	0.489105i	$0.837324\pi$
$200$	−4.70140	−	2.36113i	−0.332439	−	0.166957i
$201$	−14.3720	+	1.15646i	−1.01372	+	0.0815705i
$202$	−2.51800	+	5.83738i	−0.177166	+	0.410716i
$203$	−0.0173300	+	0.0401754i	−0.00121633	+	0.00281976i
$204$	5.67245	−	11.9464i	0.397151	−	0.836415i
$205$	−9.71686	−	4.87999i	−0.678655	−	0.340833i
$206$	0.500769	−	2.84000i	0.0348902	−	0.197872i
$207$	3.34765	+	15.0577i	0.232678	+	1.04658i
$208$	2.06409	+	11.7060i	0.143119	+	0.811667i
$209$	7.38222	−	24.6583i	0.510639	−	1.70565i
$210$	−0.000351078	−	0.0158720i	−2.42267e−5	−	0.00109527i
$211$	6.97370	−	3.50232i	0.480089	−	0.241110i	−0.192260	−	0.981344i	$-0.561582\pi$
$211$	6.97370	−	3.50232i	0.480089	−	0.241110i	0.672349	+	0.740234i	$0.265285\pi$
$212$	−2.04757	−	6.83937i	−0.140628	−	0.469730i
$213$	0.962862	−	4.50431i	0.0659742	−	0.308630i
$214$	−2.78564	+	3.74177i	−0.190423	+	0.255782i
$215$	−1.85266	+	3.20890i	−0.126350	+	0.218845i
$216$	5.99140	+	2.94795i	0.407663	+	0.200583i
$217$	0.0415896	+	0.0720354i	0.00282329	+	0.00489008i
$218$	−2.49346	−	0.291444i	−0.168879	−	0.0197391i
$219$	−3.06249	+	2.38698i	−0.206944	+	0.161297i
$220$	19.7449	+	4.67963i	1.33120	+	0.315501i
$221$	11.9439	+	7.85560i	0.803431	+	0.528425i
$222$	−0.0256016	+	0.0754942i	−0.00171827	+	0.00506684i
$223$	15.4174	+	16.3415i	1.03243	+	1.09431i	0.995478	+	0.0949935i	$0.0302830\pi$
$223$	15.4174	+	16.3415i	1.03243	+	1.09431i	0.0369509	+	0.999317i	$0.488235\pi$
$224$	0.0259365	−	0.0217633i	0.00173295	−	0.00145412i
$225$	4.03930	+	11.5987i	0.269287	+	0.773245i
$226$	4.88121	+	4.09582i	0.324693	+	0.272450i
$227$	−0.942461	−	16.1814i	−0.0625533	−	1.07400i	−0.872853	−	0.487983i	$-0.837733\pi$
$227$	−0.942461	−	16.1814i	−0.0625533	−	1.07400i	0.810300	−	0.586016i	$-0.199304\pi$
$228$	19.3105	+	13.7230i	1.27887	+	0.908828i
$229$	−8.71685	−	11.7088i	−0.576026	−	0.773737i	0.414650	−	0.909981i	$-0.363904\pi$
$229$	−8.71685	−	11.7088i	−0.576026	−	0.773737i	−0.990675	+	0.136245i	$0.956497\pi$
$230$	5.08644	−	0.594519i	0.335390	−	0.0392014i
$231$	0.0142987	+	0.0548916i	0.000940784	+	0.00361160i
$232$	−5.10446	+	3.35726i	−0.335125	+	0.220415i
$233$	−9.97733	+	3.63145i	−0.653637	+	0.237904i	−0.647487	−	0.762077i	$-0.724180\pi$
$233$	−9.97733	+	3.63145i	−0.653637	+	0.237904i	−0.00615012	+	0.999981i	$0.501958\pi$
$234$	−1.96830	+	2.90362i	−0.128672	+	0.189816i
$235$	2.95400	+	1.07517i	0.192698	+	0.0701363i
$236$	−9.54927	+	2.26322i	−0.621605	+	0.147323i
$237$	7.07945	+	1.08746i	0.459860	+	0.0706384i
$238$	0.000713615	−	0.0122523i	4.62568e−5	−	0.000794199i
$239$	−3.47849	+	3.68698i	−0.225005	+	0.238491i	−0.830035	−	0.557712i	$-0.811680\pi$
$239$	−3.47849	+	3.68698i	−0.225005	+	0.238491i	0.605030	+	0.796202i	$0.293161\pi$
$240$	−9.31011	+	14.8611i	−0.600965	+	0.959278i
$241$	−0.140741	−	0.326274i	−0.00906593	−	0.0210172i	0.913623	−	0.406562i	$-0.133273\pi$
$241$	−0.140741	−	0.326274i	−0.00906593	−	0.0210172i	−0.922689	+	0.385545i	$0.874013\pi$
$242$	0.549319			0.0353116
$243$	−5.24686	−	14.6789i	−0.336586	−	0.941653i
$244$	−12.9585			−0.829581
$245$	−8.36088	−	19.3827i	−0.534157	−	1.23832i
$246$	1.09505	−	1.74795i	0.0698178	−	0.111445i
$247$	−17.5736	+	18.6269i	−1.11818	+	1.18520i
$248$	−0.675337	+	11.5951i	−0.0428839	+	0.736289i
$249$	22.0851	+	3.39246i	1.39959	+	0.214988i
$250$	−0.878059	+	0.208104i	−0.0555333	+	0.0131616i
$251$	20.8143	+	7.57577i	1.31378	+	0.478179i	0.901462	−	0.432859i	$-0.142495\pi$
$251$	20.8143	+	7.57577i	1.31378	+	0.478179i	0.412323	+	0.911038i	$0.364717\pi$
$252$	−0.0520707	−	0.00376206i	−0.00328015	−	0.000236988i
$253$	−17.1937	+	6.25801i	−1.08096	+	0.393438i
$254$	2.16235	−	1.42220i	0.135678	−	0.0892366i
$255$	5.31647	+	20.4096i	0.332930	+	1.27810i
$256$	−7.91564	+	0.925205i	−0.494727	+	0.0578253i
$257$	−12.2561	−	16.4628i	−0.764513	−	1.02692i	−0.998504	−	0.0546803i	$-0.982586\pi$
$257$	−12.2561	−	16.4628i	−0.764513	−	1.02692i	0.233991	−	0.972239i	$-0.424821\pi$
$258$	−0.572940	−	0.407160i	−0.0356697	−	0.0253487i
$259$	−7.45693e−5	−	0.00128030i	−4.63351e−6	−	7.95543e-5i
$260$	−15.4652	−	12.9769i	−0.959113	−	0.804791i
$261$	14.0103	+	2.67237i	0.867216	+	0.165416i
$262$	1.09342	−	0.917488i	0.0675517	−	0.0566826i
$263$	15.2357	+	16.1489i	0.939472	+	0.995782i	0.999997	−	0.00238468i	$-0.000759067\pi$
$263$	15.2357	+	16.1489i	0.939472	+	0.995782i	−0.0605253	+	0.998167i	$0.519278\pi$
$264$	−2.54374	+	7.50099i	−0.156556	+	0.461654i
$265$	9.51259	+	6.25653i	0.584354	+	0.384336i
$266$	0.0213926	+	0.00507015i	0.00131167	+	0.000310871i
$267$	13.3939	−	10.4395i	0.819691	−	0.638889i
$268$	15.6345	+	1.82741i	0.955031	+	0.111627i
$269$	−8.77459	−	15.1980i	−0.534996	−	0.926641i	−0.999164	−	0.0408933i	$-0.986980\pi$
$269$	−8.77459	−	15.1980i	−0.534996	−	0.926641i	0.464167	−	0.885748i	$-0.346354\pi$
$270$	−5.02582	+	1.23459i	−0.305861	+	0.0751348i
$271$	11.7223	−	20.3037i	0.712082	−	1.23336i	−0.251992	−	0.967729i	$-0.581086\pi$
$271$	11.7223	−	20.3037i	0.712082	−	1.23336i	0.964074	−	0.265633i	$-0.0855809\pi$
$272$	−8.09558	+	10.8743i	−0.490867	+	0.659348i
$273$	0.0117971	−	0.0551874i	0.000713993	−	0.00334009i
$274$	−0.0111527	−	0.0372527i	−0.000673761	−	0.00225052i
$275$	−13.0190	+	6.53836i	−0.785072	+	0.394278i
$276$	−0.372402	−	16.8360i	−0.0224160	−	1.01341i
$277$	−0.0988045	+	0.330030i	−0.00593659	+	0.0198296i	−0.960906	−	0.276873i	$-0.910702\pi$
$277$	−0.0988045	+	0.330030i	−0.00593659	+	0.0198296i	0.954970	+	0.296703i	$0.0958870\pi$
$278$	0.0746746	+	0.423500i	0.00447868	+	0.0253999i
$279$	19.9802	−	18.3305i	1.19618	−	1.09742i
$280$	−0.00619298	+	0.0351222i	−0.000370102	+	0.00209895i
$281$	27.0285	+	13.5742i	1.61238	+	0.809770i	0.999813	+	0.0193542i	$0.00616100\pi$
$281$	27.0285	+	13.5742i	1.61238	+	0.809770i	0.612571	+	0.790415i	$0.290135\pi$
$282$	−0.255779	+	0.538680i	−0.0152314	+	0.0320780i
$283$	−2.19004	+	5.07708i	−0.130184	+	0.301801i	−0.970824	−	0.239794i	$-0.922920\pi$
$283$	−2.19004	+	5.07708i	−0.130184	+	0.301801i	0.840640	+	0.541595i	$0.182179\pi$
$284$	−1.99171	+	4.61731i	−0.118186	+	0.273987i
$285$	−37.6588	+	3.03027i	−2.23072	+	0.179498i
$286$	−3.71839	−	1.86745i	−0.219873	−	0.110424i
$287$	−0.00576222	+	0.0326792i	−0.000340133	+	0.00192899i
$288$	−8.76022	−	6.71363i	−0.516201	−	0.395604i
$289$	−0.120790	−	0.685032i	−0.00710527	−	0.0402960i
$290$	1.35806	−	4.53623i	0.0797479	−	0.266377i
$291$	−23.9750	−	13.1438i	−1.40544	−	0.770505i
$292$	3.78811	−	1.90246i	0.221682	−	0.111333i
$293$	5.73668	+	19.1618i	0.335140	+	1.11945i	0.945036	+	0.326965i	$0.106026\pi$
$293$	5.73668	+	19.1618i	0.335140	+	1.11945i	−0.609896	+	0.792481i	$0.708789\pi$
$294$	3.80973	−	1.23299i	0.222188	−	0.0719095i
$295$	9.34610	−	12.5540i	0.544151	−	0.730922i
$296$	0.0895392	−	0.155086i	0.00520436	−	0.00901421i
$297$	16.4556	−	8.43334i	0.954850	−	0.489352i
$298$	1.14565	+	1.98432i	0.0663655	+	0.114948i
$299$	18.0808	+	2.11334i	1.04564	+	0.122218i
$300$	−1.85075	−	13.2801i	−0.106853	−	0.766727i
$301$	0.0110030	+	0.00260776i	0.000634202	+	0.000150309i
$302$	2.60501	+	1.71334i	0.149901	+	0.0985917i
$303$	−32.6972	+	6.51404i	−1.87840	+	0.374222i
$304$	−16.6653	−	17.6642i	−0.955822	−	1.01311i
$305$	15.8311	−	13.2839i	0.906487	−	0.760632i
$306$	−3.94931	+	0.639715i	−0.225767	+	0.0365701i
$307$	0.858198	+	0.720114i	0.0489799	+	0.0410991i	0.666949	−	0.745103i	$-0.267600\pi$
$307$	0.858198	+	0.720114i	0.0489799	+	0.0410991i	−0.617969	+	0.786202i	$0.712044\pi$
$308$	−0.00360069	−	0.0618215i	−0.000205168	−	0.00352261i
$309$	13.7509	−	6.29579i	0.782262	−	0.358155i
$310$	−5.37556	−	7.22063i	−0.305311	−	0.410104i
$311$	0.819543	−	0.0957909i	0.0464720	−	0.00543180i	−0.0928251	−	0.995682i	$-0.529590\pi$
$311$	0.819543	−	0.0957909i	0.0464720	−	0.00543180i	0.139297	+	0.990251i	$0.455516\pi$
$312$	5.61085	−	5.53314i	0.317652	−	0.313253i
$313$	−0.974256	+	0.640778i	−0.0550682	+	0.0362189i	−0.576745	−	0.816925i	$-0.695677\pi$
$313$	−0.974256	+	0.640778i	−0.0550682	+	0.0362189i	0.521676	+	0.853143i	$0.325307\pi$
$314$	−1.90517	+	0.693424i	−0.107515	+	0.0391322i
$315$	0.0674702	−	0.0487822i	0.00380152	−	0.00274857i
$316$	−7.34788	−	2.67441i	−0.413351	−	0.150447i
$317$	−4.51524	+	1.07013i	−0.253601	+	0.0601045i	−0.355450	−	0.934695i	$-0.615672\pi$
$317$	−4.51524	+	1.07013i	−0.253601	+	0.0601045i	0.101849	+	0.994800i	$0.467524\pi$
$318$	−1.35137	+	1.68480i	−0.0757809	+	0.0944789i
$319$	−0.983716	+	16.8898i	−0.0550775	+	0.945645i
$320$	11.3815	−	12.0637i	0.636245	−	0.674380i
$321$	−24.4480	−	0.882023i	−1.36455	−	0.0492297i
$322$	−0.00619007	−	0.0143502i	−0.000344959	−	0.000799705i
$323$	−29.2067			−1.62511
$324$	2.48664	+	16.8356i	0.138146	+	0.935313i
$325$	14.4943			0.803999
$326$	0.183976	+	0.426505i	0.0101895	+	0.0236219i
$327$	−6.16741	−	11.6316i	−0.341059	−	0.643230i
$328$	−3.17973	+	3.37032i	−0.175571	+	0.186095i
$329$	0.000557814	−	0.00957729i	3.07533e−5	−	0.000528013i
$330$	−2.22663	−	5.72071i	−0.122572	−	0.314915i
$331$	−6.47768	+	1.53524i	−0.356046	+	0.0843844i	−0.404746	−	0.914429i	$-0.632640\pi$
$331$	−6.47768	+	1.53524i	−0.356046	+	0.0843844i	0.0487006	+	0.998813i	$0.484492\pi$
$332$	−22.9225	−	8.34311i	−1.25804	−	0.457888i
$333$	−0.402132	+	0.114305i	−0.0220367	+	0.00626386i
$334$	4.56418	−	1.66123i	0.249741	−	0.0908982i
$335$	−20.9737	+	13.7946i	−1.14591	+	0.753680i
$336$	0.0515961	+	0.0142115i	0.00281480	+	0.000775300i
$337$	16.4774	−	1.92593i	0.897581	−	0.104912i	0.345225	−	0.938520i	$-0.387803\pi$
$337$	16.4774	−	1.92593i	0.897581	−	0.104912i	0.552357	+	0.833608i	$0.313729\pi$
$338$	−0.0918211	−	0.123337i	−0.00499441	−	0.00670866i
$339$	−3.14451	+	33.2683i	−0.170786	+	1.80689i
$340$	−1.33879	−	22.9862i	−0.0726063	−	1.24660i
$341$	24.6384	+	20.6741i	1.33424	+	1.11956i
$342$	0.0999459	−	7.16607i	0.00540446	−	0.387497i
$343$	−0.0986981	+	0.0828175i	−0.00532920	+	0.00447173i
$344$	1.08355	+	1.14850i	0.0584212	+	0.0619228i
$345$	17.7138	+	20.1865i	0.953677	+	1.08680i
$346$	2.11548	+	1.39137i	0.113729	+	0.0748007i
$347$	13.3534	+	3.16483i	0.716851	+	0.169897i	0.572826	−	0.819677i	$-0.305847\pi$
$347$	13.3534	+	3.16483i	0.716851	+	0.169897i	0.144025	+	0.989574i	$0.453995\pi$
$348$	−14.4306	−	5.84973i	−0.773559	−	0.313578i
$349$	14.0327	+	1.64018i	0.751152	+	0.0877971i	0.483049	−	0.875593i	$-0.339529\pi$
$349$	14.0327	+	1.64018i	0.751152	+	0.0877971i	0.268103	+	0.963390i	$0.413603\pi$
$350$	−0.00622179	−	0.0107765i	−0.000332569	−	0.000576026i
$351$	−18.3958	+	0.150289i	−0.981898	+	0.00802181i
$352$	6.54591	−	11.3378i	0.348898	−	0.604309i
$353$	5.52814	−	7.42558i	0.294233	−	0.395224i	−0.630284	−	0.776365i	$-0.717061\pi$
$353$	5.52814	−	7.42558i	0.294233	−	0.395224i	0.924517	+	0.381141i	$0.124469\pi$
$354$	2.20403	+	1.98913i	0.117143	+	0.105721i
$355$	−2.30002	−	7.68260i	−0.122072	−	0.407750i
$356$	−16.5674	+	8.32045i	−0.878069	+	0.440983i
$357$	0.0550155	−	0.0334067i	0.00291173	−	0.00176807i
$358$	−0.568016	+	1.89731i	−0.0300206	+	0.100276i
$359$	−3.82037	−	21.6664i	−0.201631	−	1.14351i	−0.902653	−	0.430368i	$-0.858384\pi$
$359$	−3.82037	−	21.6664i	−0.201631	−	1.14351i	0.701022	−	0.713140i	$-0.252727\pi$
$360$	11.6144	−	0.514057i	0.612132	−	0.0270932i
$361$	5.78583	−	32.8131i	0.304517	−	1.72700i
$362$	3.05310	+	1.53332i	0.160467	+	0.0805897i
$363$	1.63587	+	2.37128i	0.0858607	+	0.124460i
$364$	−0.0244027	+	0.0565718i	−0.00127905	+	0.00296517i
$365$	−2.67762	+	6.20743i	−0.140153	+	0.324912i
$366$	2.22611	+	3.22687i	0.116361	+	0.168671i
$367$	−17.6586	−	8.86848i	−0.921772	−	0.462931i	−0.0763804	−	0.997079i	$-0.524336\pi$
$367$	−17.6586	−	8.86848i	−0.921772	−	0.462931i	−0.845391	+	0.534148i	$0.820633\pi$
$368$	−2.99770	+	17.0008i	−0.156266	+	0.886229i
$369$	10.8065	−	0.478301i	0.562566	−	0.0248993i
$370$	0.0241011	+	0.136684i	0.00125296	+	0.00710588i
$371$	0.00996541	−	0.0332868i	0.000517378	−	0.00172816i
$372$	−25.3024	+	15.3642i	−1.31187	+	0.796599i
$373$	6.63183	−	3.33063i	0.343383	−	0.172454i	−0.268746	−	0.963211i	$-0.586609\pi$
$373$	6.63183	−	3.33063i	0.343383	−	0.172454i	0.612130	+	0.790757i	$0.290313\pi$
$374$	−1.36107	−	4.54629i	−0.0703792	−	0.235083i
$375$	−3.51319	−	3.17064i	−0.181420	−	0.163731i
$376$	0.799948	−	1.07452i	0.0412542	−	0.0554140i
$377$	8.41606	−	14.5770i	0.433449	−	0.750756i
$378$	0.00800830	+	0.0136127i	0.000411902	+	0.000700163i
$379$	4.80243	+	8.31805i	0.246684	+	0.427269i	0.962604	−	0.270913i	$-0.0873257\pi$
$379$	4.80243	+	8.31805i	0.246684	+	0.427269i	−0.715920	+	0.698183i	$0.753992\pi$
$380$	40.9670	+	4.78836i	2.10156	+	0.245638i
$381$	12.5787	+	5.09906i	0.644429	+	0.261233i
$382$	−5.10203	−	1.20920i	−0.261043	−	0.0618682i
$383$	−7.63456	−	5.02133i	−0.390108	−	0.256578i	0.339270	−	0.940689i	$-0.389820\pi$
$383$	−7.63456	−	5.02133i	−0.390108	−	0.256578i	−0.729378	+	0.684111i	$0.760190\pi$
$384$	10.4809	+	11.9440i	0.534852	+	0.609514i
$385$	0.0677728	+	0.0718350i	0.00345402	+	0.00366105i
$386$	4.97312	−	4.17295i	0.253125	−	0.212397i
$387$	0.0514058	−	3.68577i	0.00261310	−	0.187358i
$388$	22.8660	+	19.1869i	1.16085	+	0.974065i
$389$	0.926398	+	15.9056i	0.0469702	+	0.806448i	0.936737	+	0.350033i	$0.113830\pi$
$389$	0.926398	+	15.9056i	0.0469702	+	0.806448i	−0.889767	+	0.456415i	$0.849133\pi$
$390$	−0.574713	+	6.08036i	−0.0291017	+	0.307891i
$391$	12.3981	+	16.6535i	0.626998	+	0.842204i
$392$	−8.93449	+	1.04429i	−0.451260	+	0.0527447i
$393$	7.21677	+	1.98777i	0.364038	+	0.100270i
$394$	0.0234803	−	0.0154432i	0.00118292	−	0.000778017i
$395$	11.7183	−	4.26512i	0.589613	−	0.214602i
$396$	−19.4176	+	5.51938i	−0.975770	+	0.277359i
$397$	−5.92327	−	2.15589i	−0.297280	−	0.108201i	0.189074	−	0.981963i	$-0.439451\pi$
$397$	−5.92327	−	2.15589i	−0.297280	−	0.108201i	−0.486354	+	0.873762i	$0.661674\pi$
$398$	−5.74059	+	1.36054i	−0.287750	+	0.0681980i
$399$	0.0418204	+	0.107446i	0.00209364	+	0.00537902i
$400$	−0.799211	+	13.7219i	−0.0399606	+	0.686097i
$401$	−21.9497	+	23.2654i	−1.09612	+	1.16182i	−0.110317	+	0.993896i	$0.535187\pi$
$401$	−21.9497	+	23.2654i	−1.09612	+	1.16182i	−0.985801	+	0.167920i	$0.946295\pi$
$402$	−2.23077	−	4.20718i	−0.111260	−	0.209835i
$403$	−12.6742	−	29.3821i	−0.631347	−	1.46363i
$404$	36.3978			1.81086
$405$	−20.2963	−	18.0187i	−1.00853	−	0.895355i
$406$	−0.0144506			−0.000717173
$407$	−0.196415	−	0.455341i	−0.00973593	−	0.0225704i
$408$	8.98161	+	0.324035i	0.444656	+	0.0160421i
$409$	−24.6088	+	26.0838i	−1.21683	+	1.28976i	−0.271958	+	0.962309i	$0.587671\pi$
$409$	−24.6088	+	26.0838i	−1.21683	+	1.28976i	−0.944868	+	0.327451i	$0.893810\pi$
$410$	0.208809	−	3.58511i	0.0103123	−	0.177056i
$411$	0.127599	−	0.159082i	0.00629397	−	0.00784693i
$412$	−16.0658	+	3.80766i	−0.791504	+	0.187590i
$413$	−0.0448827	−	0.0163360i	−0.00220853	−	0.000803841i
$414$	−4.12848	+	2.98496i	−0.202904	+	0.146703i
$415$	36.5566	−	13.3055i	1.79449	−	0.653142i
$416$	−10.8823	+	7.15739i	−0.533548	+	0.350920i
$417$	−1.60577	+	1.58353i	−0.0786350	+	0.0775460i
$418$	8.44360	−	0.986916i	0.412990	−	0.0482716i
$419$	−4.32862	−	5.81434i	−0.211467	−	0.284049i	0.683716	−	0.729748i	$-0.260363\pi$
$419$	−4.32862	−	5.81434i	−0.211467	−	0.284049i	−0.895183	+	0.445699i	$0.852955\pi$
$420$	−0.0826447	+	0.0378385i	−0.00403265	+	0.00184633i
$421$	0.169004	+	2.90168i	0.00823673	+	0.141419i	0.999919	+	0.0127108i	$0.00404607\pi$
$421$	0.169004	+	2.90168i	0.00823673	+	0.141419i	−0.991682	+	0.128708i	$0.958917\pi$
$422$	1.97437	+	1.65670i	0.0961111	+	0.0806467i
$423$	−3.08707	+	0.500048i	−0.150098	+	0.0243131i
$424$	3.71672	−	3.11870i	0.180500	−	0.151457i
$425$	11.3442	+	12.0242i	0.550275	+	0.583257i
$426$	1.49194	−	0.297229i	0.0722846	−	0.0144008i
$427$	−0.0526926	−	0.0346565i	−0.00254998	−	0.00167715i
$428$	25.9879	+	6.15924i	1.25617	+	0.297718i
$429$	−3.01200	−	21.6127i	−0.145421	−	1.04347i
$430$	−1.21549	−	0.142070i	−0.0586160	−	0.00685123i
$431$	−0.349866	−	0.605986i	−0.0168525	−	0.0291893i	0.857476	−	0.514524i	$-0.172031\pi$
$431$	−0.349866	−	0.605986i	−0.0168525	−	0.0291893i	−0.874329	+	0.485334i	$0.838698\pi$
$432$	0.872062	−	17.4239i	0.0419571	−	0.838306i
$433$	−8.81031	+	15.2599i	−0.423397	+	0.733344i	−0.996269	−	0.0863000i	$-0.972496\pi$
$433$	−8.81031	+	15.2599i	−0.423397	+	0.733344i	0.572873	+	0.819644i	$0.305829\pi$
$434$	−0.0164050	+	0.0220357i	−0.000787465	+	0.00105775i
$435$	23.6261	−	7.64643i	1.13279	−	0.366618i
$436$	4.12226	+	13.7693i	0.197420	+	0.659430i
$437$	−33.2355	+	16.6915i	−1.58987	+	0.798462i
$438$	−1.12449	−	0.616481i	−0.0537304	−	0.0294566i
$439$	−6.92464	+	23.1299i	−0.330495	+	1.10393i	0.617745	+	0.786378i	$0.288046\pi$
$439$	−6.92464	+	23.1299i	−0.330495	+	1.10393i	−0.948241	+	0.317553i	$0.897139\pi$
$440$	2.39465	+	13.5808i	0.114161	+	0.647437i
$441$	16.6679	+	12.7739i	0.793708	+	0.608279i
$442$	−0.819872	+	4.64973i	−0.0389974	+	0.221165i
$443$	−6.10266	−	3.06487i	−0.289946	−	0.145616i	0.297881	−	0.954603i	$-0.403720\pi$
$443$	−6.10266	−	3.06487i	−0.289946	−	0.145616i	−0.587827	+	0.808987i	$0.700016\pi$
$444$	0.454938	−	0.0366072i	0.0215904	−	0.00173730i
$445$	11.7106	−	27.1483i	0.555138	−	1.28695i
$446$	−2.93893	+	6.81321i	−0.139162	+	0.322615i
$447$	−5.15411	+	10.8548i	−0.243781	+	0.513413i
$448$	−0.0452307	−	0.0227157i	−0.00213695	−	0.00107322i
$449$	0.451728	−	2.56188i	0.0213184	−	0.120902i	−0.972291	−	0.233772i	$-0.924893\pi$
$449$	0.451728	−	2.56188i	0.0213184	−	0.120902i	0.993610	+	0.112870i	$0.0360042\pi$
$450$	−2.98903	+	2.74223i	−0.140904	+	0.129270i
$451$	2.22809	+	12.6361i	0.104917	+	0.595012i
$452$	10.4631	−	34.9491i	0.492142	−	1.64387i
$453$	0.361596	+	16.3475i	0.0169893	+	0.768074i
$454$	4.78390	−	2.40257i	0.224520	−	0.112758i
$455$	−0.0281801	−	0.0941281i	−0.00132110	−	0.00441279i
$456$	−3.36549	+	15.7439i	−0.157603	+	0.737276i
$457$	4.63782	−	6.22968i	0.216948	−	0.291412i	−0.680304	−	0.732930i	$-0.738152\pi$
$457$	4.63782	−	6.22968i	0.216948	−	0.291412i	0.897253	+	0.441518i	$0.145560\pi$
$458$	2.41052	−	4.17515i	0.112636	−	0.195092i
$459$	−14.5225	−	15.1432i	−0.677852	−	0.706823i
$460$	−14.6599	−	25.3918i	−0.683523	−	1.18390i
$461$	−0.674287	−	0.0788128i	−0.0314047	−	0.00367068i	0.100376	−	0.994950i	$-0.467995\pi$
$461$	−0.674287	−	0.0788128i	−0.0314047	−	0.00367068i	−0.131781	+	0.991279i	$0.542069\pi$
$462$	−0.0147760	+	0.0115168i	−0.000687442	+	0.000535811i
$463$	−19.6840	−	4.66519i	−0.914793	−	0.216810i	−0.253848	−	0.967244i	$-0.581696\pi$
$463$	−19.6840	−	4.66519i	−0.914793	−	0.216810i	−0.660945	+	0.750434i	$0.729844\pi$
$464$	13.3362	+	8.77137i	0.619118	+	0.407200i
$465$	15.1614	−	44.7080i	0.703093	−	2.07328i
$466$	−2.40645	−	2.55069i	−0.111477	−	0.118158i
$467$	6.20374	−	5.20555i	0.287075	−	0.240884i	−0.487866	−	0.872919i	$-0.662224\pi$
$467$	6.20374	−	5.20555i	0.287075	−	0.240884i	0.774940	+	0.632035i	$0.217780\pi$
$468$	19.7282	+	3.76301i	0.911935	+	0.173945i
$469$	0.0586869	+	0.0492442i	0.00270991	+	0.00227388i
$470$	0.0603681	+	1.03648i	0.00278457	+	0.0478093i
$471$	−8.66692	−	6.15915i	−0.399351	−	0.283799i
$472$	−3.98270	−	5.34969i	−0.183319	−	0.246240i
$473$	4.34285	−	0.507606i	0.199684	−	0.0233398i
$474$	0.596305	+	2.28917i	0.0273892	+	0.105145i
$475$	−24.7409	+	16.2723i	−1.13519	+	0.746627i
$476$	−0.0660299	+	0.0240329i	−0.00302648	+	0.00110155i
$477$	−11.2972	−	0.816217i	−0.517265	−	0.0373720i
$478$	−1.57315	−	0.572580i	−0.0719542	−	0.0261892i
$479$	−28.3209	+	6.71218i	−1.29401	+	0.306687i	−0.819256	−	0.573429i	$-0.805613\pi$
$479$	−28.3209	+	6.71218i	−1.29401	+	0.306687i	−0.474759	+	0.880116i	$0.657465\pi$
$480$	−18.9933	−	2.91754i	−0.866923	−	0.133167i
$481$	−0.0286869	+	0.492534i	−0.00130801	+	0.0224576i
$482$	0.0805353	−	0.0853625i	0.00366828	−	0.00388815i
$483$	0.0435125	−	0.0694558i	0.00197989	−	0.00316035i
$484$	−1.24569	−	2.88783i	−0.0566222	−	0.131265i
$485$	−47.6036			−2.16157
$486$	3.76518	−	3.51137i	0.170792	−	0.159279i
$487$	3.59484			0.162898			0.0814489	−	0.996678i	$-0.474045\pi$
$487$	3.59484			0.162898			0.0814489	+	0.996678i	$0.474045\pi$
$488$	−3.48808	−	8.08629i	−0.157898	−	0.366049i
$489$	−1.29324	+	2.06431i	−0.0584825	+	0.0933514i
$490$	4.78429	−	5.07106i	0.216132	−	0.229087i
$491$	1.95535	−	33.5720i	0.0882436	−	1.51508i	−0.606070	−	0.795411i	$-0.707255\pi$
$491$	1.95535	−	33.5720i	0.0882436	−	1.51508i	0.694314	−	0.719672i	$-0.255708\pi$
$492$	−11.6724	−	1.79298i	−0.526232	−	0.0808337i
$493$	18.6798	−	4.42719i	0.841295	−	0.199391i
$494$	−7.94768	−	2.89272i	−0.357583	−	0.130150i
$495$	18.0641	−	26.6481i	0.811920	−	1.19774i
$496$	28.5153	−	10.3787i	1.28037	−	0.466018i
$497$	−0.0204475	+	0.0134485i	−0.000917195	+	0.000603249i
$498$	1.86024	+	7.14133i	0.0833593	+	0.320010i
$499$	13.6291	−	1.59301i	0.610121	−	0.0713129i	0.194579	−	0.980887i	$-0.437666\pi$
$499$	13.6291	−	1.59301i	0.610121	−	0.0713129i	0.415542	+	0.909574i	$0.363592\pi$
$500$	3.08519	+	4.14413i	0.137974	+	0.185331i
$501$	20.7632	+	14.7554i	0.927632	+	0.659222i
$502$	0.425361	+	7.30316i	0.0189848	+	0.325956i
$503$	−2.12583	−	1.78378i	−0.0947859	−	0.0795348i	0.594163	−	0.804344i	$-0.297483\pi$
$503$	−2.12583	−	1.78378i	−0.0947859	−	0.0795348i	−0.688949	+	0.724810i	$0.741928\pi$
$504$	−0.0116685	−	0.0335056i	−0.000519756	−	0.00149246i
$505$	−44.4664	+	37.3118i	−1.97873	+	1.66035i
$506$	−4.14699	−	4.39555i	−0.184356	−	0.195406i
$507$	0.258975	−	0.763667i	0.0115015	−	0.0339157i
$508$	−12.3802	−	8.14258i	−0.549282	−	0.361268i
$509$	−7.12682	−	1.68909i	−0.315891	−	0.0748675i	0.0696121	−	0.997574i	$-0.477824\pi$
$509$	−7.12682	−	1.68909i	−0.315891	−	0.0748675i	−0.385503	+	0.922707i	$0.625972\pi$
$510$	−5.49395	+	4.28213i	−0.243276	+	0.189616i
$511$	0.0204915	+	0.00239511i	0.000906489	+	0.000105953i
$512$	−10.4904	−	18.1700i	−0.463616	−	0.803007i
$513$	31.2319	−	20.9090i	1.37892	−	0.923157i
$514$	3.38924	−	5.87034i	0.149493	−	0.258930i
$515$	15.7240	−	21.1209i	0.692881	−	0.930700i
$516$	−0.841232	+	3.93532i	−0.0370332	+	0.173243i
$517$	−1.06391	−	3.55371i	−0.0467907	−	0.156292i
$518$	0.000378511	0	0.000190096i	1.66308e−5	0	8.35232e-6i
$519$	0.293646	+	13.2755i	0.0128896	+	0.582732i
$520$	3.93493	−	13.1436i	0.172558	−	0.576384i
$521$	−6.17963	−	35.0464i	−0.270734	−	1.53541i	−0.752193	−	0.658942i	$-0.771004\pi$
$521$	−6.17963	−	35.0464i	−0.270734	−	1.53541i	0.481459	−	0.876469i	$-0.340107\pi$
$522$	1.02232	+	4.59836i	0.0447456	+	0.201265i
$523$	−5.30847	+	30.1059i	−0.232123	+	1.31644i	0.616465	+	0.787383i	$0.288564\pi$
$523$	−5.30847	+	30.1059i	−0.232123	+	1.31644i	−0.848588	+	0.529054i	$0.822547\pi$
$524$	−7.30287	−	3.66764i	−0.319028	−	0.160222i
$525$	0.0279910	−	0.0589502i	0.00122163	−	0.00257280i
$526$	−2.90428	+	6.73288i	−0.126633	+	0.293567i
$527$	14.4551	−	33.5107i	0.629674	−	1.45975i
$528$	20.6271	−	1.65978i	0.897678	−	0.0722329i
$529$	3.07209	+	1.54286i	0.133569	+	0.0670810i
$530$	−0.652980	+	3.70324i	−0.0283637	+	0.160858i
$531$	−2.02304	+	15.4379i	−0.0877926	+	0.669948i
$532$	−0.0218577	−	0.123961i	−0.000947650	−	0.00537439i
$533$	3.66123	−	12.2293i	0.158585	−	0.529712i
$534$	4.91800	+	2.69619i	0.212823	+	0.116676i
$535$	−38.0628	+	19.1158i	−1.64560	+	0.826450i
$536$	3.06807	+	10.2481i	0.132521	+	0.442649i
$537$	−9.88177	+	3.19817i	−0.426430	+	0.138011i
$538$	3.46113	−	4.64910i	0.149220	−	0.200437i
$539$	−12.4548	+	21.5723i	−0.536464	+	0.929183i
$540$	17.8874	+	23.6216i	0.769751	+	1.01651i
$541$	−14.2816	−	24.7364i	−0.614012	−	1.06350i	−0.990557	−	0.137102i	$-0.956221\pi$
$541$	−14.2816	−	24.7364i	−0.614012	−	1.06350i	0.376545	−	0.926398i	$-0.377112\pi$
$542$	7.69076	+	0.898921i	0.330347	+	0.0386120i
$543$	2.47310	+	17.7457i	0.106131	+	0.761542i
$544$	−14.4548	−	3.42586i	−0.619746	−	0.146882i
$545$	−19.1511	−	12.5959i	−0.820345	−	0.539549i
$546$	0.0182794	−	0.00364168i	0.000782286	−	0.000155850i
$547$	20.5203	+	21.7502i	0.877384	+	0.929973i	0.998031	−	0.0627227i	$-0.0199784\pi$
$547$	20.5203	+	21.7502i	0.877384	+	0.929973i	−0.120647	+	0.992695i	$0.538497\pi$
$548$	−0.170550	+	0.143109i	−0.00728555	+	0.00611331i
$549$	−7.30032	+	19.2192i	−0.311570	+	0.820255i
$550$	−3.68589	−	3.09283i	−0.157167	−	0.131879i
$551$	1.99953	+	34.3306i	0.0851829	+	1.46253i
$552$	10.4057	−	4.76421i	0.442896	−	0.202778i
$553$	−0.0227259	−	0.0305262i	−0.000966406	−	0.00129811i
$554$	−0.113010	+	0.0132090i	−0.00480134	+	0.000561196i
$555$	−0.518262	+	0.511084i	−0.0219990	+	0.0216943i
$556$	2.05705	−	1.35294i	0.0872383	−	0.0573775i
$557$	−11.4069	+	4.15178i	−0.483327	+	0.175917i	−0.572180	−	0.820128i	$-0.693902\pi$
$557$	−11.4069	+	4.15178i	−0.483327	+	0.175917i	0.0888529	+	0.996045i	$0.471680\pi$
$558$	8.17260	+	3.66133i	0.345974	+	0.154996i
$559$	−4.08778	−	1.48783i	−0.172895	−	0.0629285i
$560$	0.0906661	−	0.0214883i	0.00383134	−	0.000908045i
$561$	15.5720	−	19.4142i	0.657451	−	0.819669i
$562$	−0.580824	+	9.97237i	−0.0245006	+	0.420659i
$563$	12.6158	−	13.3720i	0.531694	−	0.563563i	−0.404729	−	0.914437i	$-0.632634\pi$
$563$	12.6158	−	13.3720i	0.531694	−	0.563563i	0.936423	+	0.350874i	$0.114115\pi$
$564$	3.41193	+	0.123094i	0.143668	+	0.00518320i
$565$	23.0442	+	53.4224i	0.969476	+	2.24750i
$566$	−1.82617			−0.0767595
$567$	−0.0349144	+	0.0751086i	−0.00146627	+	0.00315426i
$568$	−3.41739			−0.143390
$569$	3.37933	+	7.83416i	0.141669	+	0.328425i	0.974247	−	0.225482i	$-0.0723956\pi$
$569$	3.37933	+	7.83416i	0.141669	+	0.328425i	−0.832579	+	0.553907i	$0.813136\pi$
$570$	−5.84526	−	11.0240i	−0.244831	−	0.461746i
$571$	28.4066	−	30.1092i	1.18878	−	1.26003i	0.230862	−	0.972986i	$-0.425845\pi$
$571$	28.4066	−	30.1092i	1.18878	−	1.26003i	0.957917	−	0.287046i	$-0.0926732\pi$
$572$	−1.38519	+	23.7828i	−0.0579177	+	0.994408i
$573$	−9.97395	−	25.6253i	−0.416668	−	1.07051i
$574$	−0.0106641	+	0.00252743i	−0.000445110	+	0.000105493i
$575$	19.7808	+	7.19960i	0.824914	+	0.300244i
$576$	−4.02853	+	16.0000i	−0.167856	+	0.666666i
$577$	−41.2655	+	15.0194i	−1.71791	+	0.625266i	−0.997655	−	0.0684479i	$-0.978195\pi$
$577$	−41.2655	+	15.0194i	−1.71791	+	0.625266i	−0.720250	+	0.693714i	$0.755973\pi$
$578$	0.191942	−	0.126242i	0.00798375	−	0.00525099i
$579$	32.8236	+	9.04082i	1.36410	+	0.375724i
$580$	−26.9271	+	3.14733i	−1.11809	+	0.130686i
$581$	−0.0708961	−	0.0952299i	−0.00294126	−	0.00395080i
$582$	0.849738	−	8.99008i	0.0352228	−	0.372651i
$583$	−0.781206	−	13.4128i	−0.0323542	−	0.555501i
$584$	2.20682	+	1.85174i	0.0913190	+	0.0766258i
$585$	−27.9590	+	15.6264i	−1.15596	+	0.646071i
$586$	−5.06059	+	4.24634i	−0.209051	+	0.175415i
$587$	−9.02510	−	9.56605i	−0.372506	−	0.394833i	0.513818	−	0.857899i	$-0.328231\pi$
$587$	−9.02510	−	9.56605i	−0.372506	−	0.394833i	−0.886324	+	0.463066i	$0.846749\pi$
$588$	−15.1213	−	17.2321i	−0.623590	−	0.710640i
$589$	54.6206	+	35.9246i	2.25060	+	1.48025i
$590$	5.02973	+	1.19207i	0.207071	+	0.0490767i
$591$	0.136589	+	0.0553691i	0.00561851	+	0.00227758i
$592$	−0.464707	−	0.0543164i	−0.0190993	−	0.00223239i
$593$	10.7252	+	18.5766i	0.440432	+	0.762850i	0.997721	−	0.0674679i	$-0.0214920\pi$
$593$	10.7252	+	18.5766i	0.440432	+	0.762850i	−0.557290	+	0.830318i	$0.688159\pi$
$594$	4.71012	+	3.88713i	0.193259	+	0.159491i
$595$	0.0560310	−	0.0970486i	0.00229705	−	0.00397860i
$596$	7.83380	−	10.5226i	0.320885	−	0.431023i
$597$	−22.9686	−	20.7291i	−0.940042	−	0.848386i
$598$	1.72433	+	5.75966i	0.0705130	+	0.235530i
$599$	20.0409	−	10.0649i	0.818850	−	0.411242i	0.0105004	−	0.999945i	$-0.496658\pi$
$599$	20.0409	−	10.0649i	0.818850	−	0.411242i	0.808349	+	0.588703i	$0.200361\pi$
$600$	7.78881	−	4.72956i	0.317977	−	0.193083i
$601$	−2.72865	+	9.11434i	−0.111304	+	0.371782i	−0.995433	−	0.0954612i	$-0.969567\pi$
$601$	−2.72865	+	9.11434i	−0.111304	+	0.371782i	0.884129	+	0.467243i	$0.154753\pi$
$602$	0.000648515		0.00367791i	2.64315e−5		0.000149900i
$603$	11.5182	−	22.1586i	0.469058	−	0.902370i
$604$	3.09986	−	17.5802i	0.126131	−	0.715326i
$605$	4.48218	+	2.25103i	0.182226	+	0.0915176i
$606$	−6.25270	−	9.06364i	−0.253998	−	0.368185i
$607$	9.70931	−	22.5087i	0.394089	−	0.913601i	−0.599482	−	0.800388i	$-0.704627\pi$
$607$	9.70931	−	22.5087i	0.394089	−	0.913601i	0.993571	−	0.113212i	$-0.0361141\pi$
$608$	10.5400	−	24.4345i	0.427454	−	0.990950i
$609$	−0.0430339	−	0.0623801i	−0.00174382	−	0.00252777i
$610$	6.09941	+	3.06324i	0.246958	+	0.124027i
$611$	−0.640872	+	3.63457i	−0.0259269	+	0.147039i
$612$	12.3189	+	19.3113i	0.497961	+	0.780611i
$613$	−1.29645	−	7.35253i	−0.0523631	−	0.296966i	0.947368	−	0.320146i	$-0.103732\pi$
$613$	−1.29645	−	7.35253i	−0.0523631	−	0.296966i	−0.999731	+	0.0231801i	$0.992621\pi$
$614$	−0.106118	+	0.354459i	−0.00428257	+	0.0143048i
$615$	16.0979	−	9.77505i	0.649131	−	0.394168i
$616$	0.0376083	−	0.0188876i	0.00151528	−	0.000761004i
$617$	−4.10354	−	13.7068i	−0.165202	−	0.551814i	−0.999999	−	0.00125610i	$-0.999600\pi$
$617$	−4.10354	−	13.7068i	−0.165202	−	0.551814i	0.834797	−	0.550558i	$-0.185585\pi$
$618$	3.70808	+	3.34653i	0.149161	+	0.134617i
$619$	−2.49473	+	3.35100i	−0.100272	+	0.134688i	−0.849427	−	0.527706i	$-0.823052\pi$
$619$	−2.49473	+	3.35100i	−0.100272	+	0.134688i	0.749155	+	0.662394i	$0.230460\pi$
$620$	−25.7695	+	44.6341i	−1.03493	+	1.79255i
$621$	−25.1800	−	8.93248i	−1.01044	−	0.358448i
$622$	0.136257	+	0.236004i	0.00546342	+	0.00946292i
$623$	−0.0896198	−	0.0104751i	−0.00359054	−	0.000419674i
$624$	−19.0801	−	7.73453i	−0.763817	−	0.309629i
$625$	−27.9354	−	6.62081i	−1.11742	−	0.264832i
$626$	−0.321769	−	0.211631i	−0.0128605	−	0.00845847i
$627$	29.4053	+	33.5101i	1.17433	+	1.33826i
$628$	7.96575	+	8.44320i	0.317868	+	0.336920i
$629$	−0.431048	+	0.361692i	−0.0171870	+	0.0144216i
$630$	0.0236198	+	0.0140797i	0.000941034	+	0.000560948i
$631$	14.2403	+	11.9490i	0.566896	+	0.475683i	0.880614	−	0.473834i	$-0.157130\pi$
$631$	14.2403	+	11.9490i	0.566896	+	0.475683i	−0.313718	+	0.949516i	$0.601575\pi$
$632$	−0.308985	−	5.30507i	−0.0122908	−	0.211024i
$633$	−1.27191	+	13.4565i	−0.0505537	+	0.534850i
$634$	−0.915184	−	1.22931i	−0.0363466	−	0.0488220i
$635$	23.4717	−	2.74345i	0.931445	−	0.108870i
$636$	11.9217	+	3.28367i	0.472725	+	0.130206i
$637$	20.7055	−	13.6182i	0.820381	−	0.539573i
$638$	−5.25068	+	1.91109i	−0.207877	+	0.0756609i
$639$	5.72604	+	5.55520i	0.226519	+	0.219760i
$640$	25.9980	+	9.46249i	1.02766	+	0.374038i
$641$	−15.6267	+	3.70359i	−0.617216	+	0.146283i	−0.527318	−	0.849668i	$-0.676802\pi$
$641$	−15.6267	+	3.70359i	−0.617216	+	0.146283i	−0.0898984	+	0.995951i	$0.528654\pi$
$642$	−2.93065	−	7.52949i	−0.115664	−	0.297165i
$643$	1.55848	−	26.7581i	0.0614606	−	1.05524i	−0.816758	−	0.576980i	$-0.804231\pi$
$643$	1.55848	−	26.7581i	0.0614606	−	1.05524i	0.878219	−	0.478259i	$-0.158732\pi$
$644$	−0.0614033	+	0.0650837i	−0.00241963	+	0.00256466i
$645$	−3.00643	−	5.67006i	−0.118378	−	0.223258i
$646$	−3.82065	−	8.85726i	−0.150321	−	0.348484i
$647$	16.2621			0.639328			0.319664	−	0.947531i	$-0.396430\pi$
$647$	16.2621			0.639328			0.319664	+	0.947531i	$0.396430\pi$
$648$	−9.83636	+	6.08341i	−0.386409	+	0.238979i
$649$	−18.4687			−0.724960
$650$	1.89605	+	4.39555i	0.0743694	+	0.172408i
$651$	−0.143977	−	0.00519434i	−0.00564291	−	0.000203582i
$652$	1.82498	−	1.93437i	0.0714718	−	0.0757556i
$653$	−2.54255	+	43.6539i	−0.0994976	+	1.70831i	0.467010	+	0.884252i	$0.345331\pi$
$653$	−2.54255	+	43.6539i	−0.0994976	+	1.70831i	−0.566508	+	0.824057i	$0.691706\pi$
$654$	2.72063	−	3.39191i	0.106385	−	0.132634i
$655$	12.6815	−	3.00557i	0.495508	−	0.117437i
$656$	11.3758	+	4.14045i	0.444150	+	0.161657i
$657$	−0.687528	−	6.69006i	−0.0268230	−	0.261004i
$658$	0.00297738	−	0.00108368i	0.000116071	−	4.22462e-5i
$659$	−22.2684	+	14.6462i	−0.867455	+	0.570534i	−0.903390	−	0.428820i	$-0.858929\pi$
$659$	−22.2684	+	14.6462i	−0.867455	+	0.570534i	0.0359352	+	0.999354i	$0.488559\pi$
$660$	−25.0251	+	24.6785i	−0.974100	+	0.960609i
$661$	17.3882	−	2.03239i	0.676323	−	0.0790508i	0.229004	−	0.973425i	$-0.426453\pi$
$661$	17.3882	−	2.03239i	0.676323	−	0.0790508i	0.447319	+	0.894375i	$0.352379\pi$
$662$	−1.31295	−	1.76360i	−0.0510292	−	0.0685441i
$663$	−22.5134	+	10.3076i	−0.874347	+	0.400316i
$664$	−0.963913	−	16.5497i	−0.0374071	−	0.642255i
$665$	0.153777	+	0.129034i	0.00596321	+	0.00500373i
$666$	−0.0872686	−	0.106998i	−0.00338159	−	0.00414610i
$667$	18.7263	−	15.7133i	0.725086	−	0.608420i
$668$	−19.0834	−	20.2272i	−0.738360	−	0.782616i
$669$	−38.1631	+	7.60299i	−1.47547	+	0.293949i
$670$	−6.92701	−	4.55597i	−0.267614	−	0.176012i
$671$	−23.7293	−	5.62396i	−0.916061	−	0.217110i
$672$	0.00809446	+	0.0580819i	0.000312250	+	0.00224056i
$673$	−7.95363	−	0.929646i	−0.306590	−	0.0358352i	−0.0385930	−	0.999255i	$-0.512288\pi$
$673$	−7.95363	−	0.929646i	−0.306590	−	0.0358352i	−0.267997	+	0.963420i	$0.586362\pi$
$674$	2.73953	+	4.74501i	0.105523	+	0.182771i
$675$	−20.7389	−	4.73660i	−0.798239	−	0.182312i
$676$	−0.440175	+	0.762405i	−0.0169298	+	0.0293233i
$677$	−25.3648	+	34.0708i	−0.974847	+	1.30945i	−0.0240237	+	0.999711i	$0.507648\pi$
$677$	−25.3648	+	34.0708i	−0.974847	+	1.30945i	−0.950823	+	0.309735i	$0.899760\pi$
$678$	−10.5003	+	3.39836i	−0.403263	+	0.130513i
$679$	0.0416655	+	0.139172i	0.00159897	+	0.00534095i
$680$	13.9834	−	7.02271i	0.536238	−	0.269309i
$681$	24.6177	+	13.4962i	0.943354	+	0.517175i
$682$	−3.04659	+	10.1763i	−0.116660	+	0.389671i
$683$	3.92505	+	22.2600i	0.150188	+	0.851757i	0.963054	+	0.269307i	$0.0867947\pi$
$683$	3.92505	+	22.2600i	0.150188	+	0.851757i	−0.812867	+	0.582450i	$0.802094\pi$
$684$	−37.8995	+	15.7250i	−1.44912	+	0.601262i
$685$	0.0616556	−	0.349666i	0.00235574	−	0.0133601i
$686$	−0.0380264	−	0.0190976i	−0.00145185	−	0.000729148i
$687$	25.2016	−	2.02788i	0.961503	−	0.0773686i
$688$	1.63395	−	3.78791i	0.0622936	−	0.144413i
$689$	−5.29440	+	12.2738i	−0.201701	+	0.467595i
$690$	−3.80457	+	8.01257i	−0.144837	+	0.305033i
$691$	−7.58174	−	3.80769i	−0.288423	−	0.144851i	0.298705	−	0.954345i	$-0.403445\pi$
$691$	−7.58174	−	3.80769i	−0.288423	−	0.144851i	−0.587128	+	0.809494i	$0.699742\pi$
$692$	2.51734	−	14.2765i	0.0956948	−	0.542712i
$693$	−0.0937183	−	0.0294876i	−0.00356006	−	0.00112014i
$694$	0.787049	+	4.46358i	0.0298760	+	0.169435i
$695$	−1.12614	+	3.76157i	−0.0427169	+	0.142684i
$696$	−0.234011	−	10.5795i	−0.00887017	−	0.401014i
$697$	13.0107	−	6.53423i	0.492816	−	0.247502i
$698$	1.33827	+	4.47012i	0.0506541	+	0.169196i
$699$	3.84434	−	17.9840i	0.145406	−	0.680218i
$700$	−0.0425439	+	0.0571463i	−0.00160801	+	0.00215993i
$701$	18.1146	−	31.3755i	0.684181	−	1.18504i	−0.289513	−	0.957174i	$-0.593493\pi$
$701$	18.1146	−	31.3755i	0.684181	−	1.18504i	0.973694	−	0.227861i	$-0.0731733\pi$
$702$	−2.45201	−	5.55908i	−0.0925451	−	0.209814i
$703$	−0.503988	−	0.872933i	−0.0190083	−	0.0329233i
$704$	−19.4389	−	2.27208i	−0.732630	−	0.0856322i
$705$	−4.29447	+	3.34723i	−0.161739	+	0.126064i
$706$	2.97504	+	0.705099i	0.111967	+	0.0265367i
$707$	0.148003	+	0.0973432i	0.00556623	+	0.00366097i
$708$	5.45902	−	16.0976i	0.205162	−	0.604983i
$709$	7.03434	+	7.45597i	0.264180	+	0.280015i	0.845862	−	0.533402i	$-0.179087\pi$
$709$	7.03434	+	7.45597i	0.264180	+	0.280015i	−0.581682	+	0.813416i	$0.697605\pi$
$710$	2.02896	−	1.70250i	0.0761453	−	0.0638935i
$711$	−8.10604	+	9.39125i	−0.304000	+	0.352199i
$712$	−9.65159	−	8.09865i	−0.361709	−	0.303510i
$713$	−2.70215	−	46.3941i	−0.101196	−	1.73747i
$714$	0.0173277	+	0.0123140i	0.000648474	+	0.000460839i
$715$	−22.6877	−	30.4749i	−0.848473	−	1.13970i
$716$	11.2624	−	1.31639i	0.420897	−	0.0491958i
$717$	−2.21313	−	8.49606i	−0.0826510	−	0.317291i
$718$	6.07080	−	3.99283i	0.226560	−	0.149011i
$719$	34.8714	−	12.6922i	1.30048	−	0.473338i	0.403330	−	0.915055i	$-0.367853\pi$
$719$	34.8714	−	12.6922i	1.30048	−	0.473338i	0.897154	+	0.441717i	$0.145630\pi$
$720$	−13.2520	−	27.3308i	−0.493874	−	1.01856i
$721$	−0.0755111	−	0.0274838i	−0.00281218	−	0.00102355i
$722$	10.7078	−	2.53779i	0.398502	−	0.0944468i
$723$	0.608323	+	0.0934437i	0.0226238	+	0.00347521i
$724$	1.13735	−	19.5276i	0.0422693	−	0.725737i
$725$	13.3570	−	14.1576i	0.496066	−	0.525799i
$726$	−0.505123	+	0.806291i	−0.0187469	+	0.0299243i
$727$	−13.1970	−	30.5941i	−0.489450	−	1.13467i	−0.966702	−	0.255906i	$-0.917626\pi$
$727$	−13.1970	−	30.5941i	−0.489450	−	1.13467i	0.477252	−	0.878767i	$-0.341633\pi$
$728$	−0.0418702			−0.00155181
$729$	26.3704	+	5.79655i	0.976683	+	0.214687i
$730$	−2.23274			−0.0826374
$731$	−1.96510	−	4.55561i	−0.0726817	−	0.168495i
$732$	11.9159	−	19.0205i	0.440424	−	0.703016i
$733$	25.7806	−	27.3259i	0.952230	−	1.00930i	−0.0477158	−	0.998861i	$-0.515194\pi$
$733$	25.7806	−	27.3259i	0.952230	−	1.00930i	0.999945	−	0.0104436i	$-0.00332435\pi$
$734$	0.379472	−	6.51528i	0.0140066	−	0.240483i
$735$	36.1382	+	5.55113i	1.33298	+	0.204756i
$736$	−18.4066	+	4.36244i	−0.678475	+	0.160802i
$737$	27.8366	+	10.1317i	1.02537	+	0.373206i
$738$	1.55869	+	3.21463i	0.0573763	+	0.118332i
$739$	−12.4039	+	4.51464i	−0.456283	+	0.166074i	−0.559929	−	0.828541i	$-0.689172\pi$
$739$	−12.4039	+	4.51464i	−0.456283	+	0.166074i	0.103645	+	0.994614i	$0.466949\pi$
$740$	0.663911	−	0.436661i	0.0244058	−	0.0160520i
$741$	−11.1809	−	42.9228i	−0.410741	−	1.57681i
$742$	0.0113982	−	0.00133226i	0.000418441	−	4.89087e-5i
$743$	−4.10039	−	5.50778i	−0.150429	−	0.202061i	0.720521	−	0.693433i	$-0.243903\pi$
$743$	−4.10039	−	5.50778i	−0.150429	−	0.202061i	−0.870950	+	0.491372i	$0.836495\pi$
$744$	−16.3983	−	11.6534i	−0.601190	−	0.427236i
$745$	1.21646	+	20.8858i	0.0445676	+	0.765196i
$746$	1.87759	+	1.57548i	0.0687433	+	0.0576825i
$747$	−25.2877	+	29.2970i	−0.925228	+	1.07192i
$748$	−20.8138	+	17.4649i	−0.761029	+	0.638579i
$749$	0.0892013	+	0.0945478i	0.00325934	+	0.00345470i
$750$	0.501958	−	1.48018i	0.0183289	−	0.0540484i
$751$	−15.1165	−	9.94229i	−0.551610	−	0.362799i	0.242900	−	0.970051i	$-0.421901\pi$
$751$	−15.1165	−	9.94229i	−0.551610	−	0.362799i	−0.794509	+	0.607252i	$0.792272\pi$
$752$	−3.40555	−	0.807131i	−0.124188	−	0.0294330i
$753$	−30.2593	+	23.5849i	−1.10271	+	0.859483i
$754$	5.52158	+	0.645380i	0.201084	+	0.0235034i
$755$	14.2346	+	24.6550i	0.518049	+	0.897288i
$756$	0.0534032	−	0.0729700i	0.00194226	−	0.00265389i
$757$	−2.10262	+	3.64185i	−0.0764211	+	0.132365i	−0.901703	−	0.432355i	$-0.857683\pi$
$757$	−2.10262	+	3.64185i	−0.0764211	+	0.132365i	0.825282	+	0.564720i	$0.191016\pi$
$758$	−1.89431	+	2.54450i	−0.0688045	+	0.0924205i
$759$	6.62488	−	30.9915i	0.240468	−	1.12492i
$760$	8.03924	+	26.8529i	0.291614	+	0.974059i
$761$	17.4823	−	8.77996i	0.633735	−	0.318273i	−0.102771	−	0.994705i	$-0.532771\pi$
$761$	17.4823	−	8.77996i	0.633735	−	0.318273i	0.736505	+	0.676432i	$0.236475\pi$
$762$	0.0991314	+	4.48167i	0.00359115	+	0.162354i
$763$	−0.0200628	+	0.0670144i	−0.000726322	+	0.00242608i
$764$	5.21294	+	29.5640i	0.188597	+	1.06959i
$765$	−34.8459	−	10.9640i	−1.25986	−	0.396403i
$766$	0.524065	−	2.97212i	0.0189353	−	0.107387i
$767$	16.4201	+	8.24648i	0.592895	+	0.297763i
$768$	5.92075	−	12.4693i	0.213647	−	0.449949i
$769$	9.37175	−	21.7261i	0.337954	−	0.783465i	−0.661485	−	0.749959i	$-0.730073\pi$
$769$	9.37175	−	21.7261i	0.337954	−	0.783465i	0.999439	−	0.0335063i	$-0.0106674\pi$
$770$	−0.0129191	+	0.0299498i	−0.000465572	+	0.00107932i
$771$	35.4341	−	2.85125i	1.27613	−	0.102685i
$772$	−33.2152	−	16.6813i	−1.19544	−	0.600372i
$773$	−7.96472	+	45.1702i	−0.286471	+	1.62466i	0.413511	+	0.910499i	$0.364302\pi$
$773$	−7.96472	+	45.1702i	−0.286471	+	1.62466i	−0.699983	+	0.714160i	$0.746809\pi$
$774$	1.12447	−	0.466560i	0.0404184	−	0.0167702i
$775$	−6.42541	−	36.4403i	−0.230807	−	1.30897i
$776$	−5.81796	+	19.4333i	−0.208853	+	0.697616i
$777$	0.00194780	+	0.00106784i	6.98770e−5	+	3.83087e-5i
$778$	−4.70237	+	2.36162i	−0.168588	+	0.0846681i
$779$	7.48006	+	24.9851i	0.268001	+	0.895185i
$780$	33.2684	−	10.7671i	1.19120	−	0.385523i
$781$	−5.65109	+	7.59074i	−0.202212	+	0.271618i
$782$	−3.42851	+	5.93836i	−0.122603	+	0.212355i
$783$	−16.8056	+	18.1070i	−0.600583	+	0.647091i
$784$	11.7508	+	20.3530i	0.419673	+	0.726894i
$785$	−18.3868	−	2.14911i	−0.656253	−	0.0767050i
$786$	0.341243	+	2.44859i	0.0121717	+	0.0873384i
$787$	13.0689	+	3.09738i	0.465855	+	0.110410i	0.456838	−	0.889550i	$-0.348982\pi$
$787$	13.0689	+	3.09738i	0.465855	+	0.110410i	0.00901649	+	0.999959i	$0.497130\pi$
$788$	−0.134433	−	0.0884178i	−0.00478897	−	0.00314975i
$789$	−37.7132	+	7.51335i	−1.34263	+	0.267482i
$790$	2.82636	+	2.99577i	0.100558	+	0.106585i
$791$	0.136015	−	0.114130i	0.00483612	−	0.00405799i
$792$	−8.67088	−	10.6312i	−0.308106	−	0.377763i
$793$	18.5860	+	15.5955i	0.660010	+	0.553814i
$794$	−0.121048	−	2.07832i	−0.00429584	−	0.0737567i
$795$	−17.9306	+	8.20944i	−0.635932	+	0.291159i
$796$	20.1704	+	27.0936i	0.714922	+	0.960307i
$797$	−32.0603	+	3.74731i	−1.13563	+	0.132737i	−0.663069	−	0.748559i	$-0.730746\pi$
$797$	−32.0603	+	3.74731i	−1.13563	+	0.132737i	−0.472566	+	0.881295i	$0.656672\pi$
$798$	−0.0271134	+	0.0267379i	−0.000959805	+	0.000946512i
$799$	−3.51675	+	2.31300i	−0.124414	+	0.0818281i
$800$	−14.1533	+	5.15139i	−0.500395	+	0.182129i
$801$	3.00692	+	29.2591i	0.106244	+	1.03382i
$802$	−9.92680	−	3.61306i	−0.350527	−	0.127582i
$803$	7.76239	−	1.83972i	0.273929	−	0.0649223i
$804$	−17.0589	+	21.2680i	−0.601621	+	0.750064i
$805$	0.00829716	−	0.142457i	0.000292436	−	0.00502094i
$806$	7.25248	−	7.68718i	0.255458	−	0.270769i
$807$	30.3763	+	1.09590i	1.06930	+	0.0385776i
$808$	9.79733	+	22.7128i	0.344669	+	0.799032i
$809$	−17.1245			−0.602066			−0.301033	−	0.953614i	$-0.597332\pi$
$809$	−17.1245			−0.602066			−0.301033	+	0.953614i	$0.597332\pi$
$810$	2.80932	−	8.51216i	0.0987096	−	0.299087i
$811$	−12.0048			−0.421545			−0.210772	−	0.977535i	$-0.567598\pi$
$811$	−12.0048			−0.421545			−0.210772	+	0.977535i	$0.567598\pi$
$812$	0.0327696	+	0.0759686i	0.00114999	+	0.00266597i
$813$	19.0226	+	35.8762i	0.667151	+	1.25823i
$814$	0.112393	−	0.119130i	0.00393938	−	0.00417550i
$815$	−0.246602	+	4.23398i	−0.00863807	+	0.148310i
$816$	−8.51700	−	21.8821i	−0.298155	−	0.766025i
$817$	8.64794	−	2.04960i	0.302553	−	0.0717064i
$818$	−11.1294	−	4.05076i	−0.389129	−	0.141631i
$819$	0.0701561	+	0.0680630i	0.00245145	+	0.00237831i
$820$	−19.3208	+	7.03221i	−0.674713	+	0.245575i
$821$	30.2085	−	19.8684i	1.05428	−	0.693413i	0.100814	−	0.994905i	$-0.467855\pi$
$821$	30.2085	−	19.8684i	1.05428	−	0.693413i	0.953468	+	0.301493i	$0.0974849\pi$
$822$	0.0649349	+	0.0178855i	0.00226487	+	0.000623828i
$823$	−52.8276	+	6.17466i	−1.84145	+	0.215235i	−0.964271	−	0.264919i	$-0.914655\pi$
$823$	−52.8276	+	6.17466i	−1.84145	+	0.215235i	−0.877184	+	0.480154i	$0.840581\pi$
$824$	−6.70053	−	9.00037i	−0.233424	−	0.313543i
$825$	2.37448	−	25.1215i	0.0826686	−	0.874620i
$826$	−0.000917225	−	0.0157481i	−3.19143e−5	−	0.000547948i
$827$	14.2860	+	11.9874i	0.496773	+	0.416842i	0.856446	−	0.516236i	$-0.172667\pi$
$827$	14.2860	+	11.9874i	0.496773	+	0.416842i	−0.359673	+	0.933078i	$0.617112\pi$
$828$	25.0544	+	14.9349i	0.870701	+	0.519022i
$829$	34.9024	−	29.2866i	1.21221	−	1.01716i	0.213014	−	0.977049i	$-0.431672\pi$
$829$	34.9024	−	29.2866i	1.21221	−	1.01716i	0.999195	−	0.0401151i	$-0.0127725\pi$
$830$	8.81715	+	9.34563i	0.306048	+	0.324392i
$831$	−0.393563	−	0.448502i	−0.0136526	−	0.0155584i
$832$	16.2681	+	10.6997i	0.563996	+	0.370946i
$833$	27.5029	+	6.51830i	0.952918	+	0.225846i
$834$	−0.690281	−	0.279820i	−0.0239025	−	0.00968936i
$835$	44.0490	+	5.14859i	1.52438	+	0.178174i
$836$	−24.3358	−	42.1509i	−0.841673	−	1.45782i
$837$	8.53283	+	46.1826i	0.294938	+	1.59630i
$838$	1.19702	−	2.07330i	0.0413503	−	0.0716208i
$839$	3.98907	−	5.35824i	0.137718	−	0.184987i	−0.727914	−	0.685669i	$-0.759510\pi$
$839$	3.98907	−	5.35824i	0.137718	−	0.184987i	0.865632	+	0.500682i	$0.166917\pi$
$840$	−0.0458576	−	0.0413864i	−0.00158224	−	0.00142797i
$841$	1.83458	+	6.12792i	0.0632613	+	0.211307i
$842$	−0.857857	+	0.430832i	−0.0295637	+	0.0148474i
$843$	−44.7781	+	27.1903i	−1.54224	+	0.936485i
$844$	4.23216	−	14.1364i	0.145677	−	0.486595i
$845$	−0.243797	−	1.38264i	−0.00838688	−	0.0475643i
$846$	−0.555476	−	0.870772i	−0.0190977	−	0.0299378i
$847$	0.00265799	−	0.0150742i	9.13295e−5	−	0.000517955i
$848$	−11.3278	−	5.68905i	−0.388999	−	0.195363i
$849$	−5.43831	−	7.88314i	−0.186642	−	0.270549i
$850$	−2.16247	+	5.01318i	−0.0741723	+	0.171951i
$851$	−0.283801	+	0.657925i	−0.00972858	+	0.0225534i
$852$	−4.94582	−	7.16925i	−0.169441	−	0.245614i
$853$	41.7453	+	20.9653i	1.42933	+	0.717838i	0.984106	−	0.177580i	$-0.0568269\pi$
$853$	41.7453	+	20.9653i	1.42933	+	0.717838i	0.445226	+	0.895418i	$0.353123\pi$
$854$	0.00361702	−	0.0205132i	0.000123772	−	0.000701946i
$855$	30.1811	−	58.0621i	1.03217	−	1.98568i
$856$	3.15180	+	17.8747i	0.107726	+	0.610946i
$857$	−14.7882	+	49.3962i	−0.505157	+	1.68734i	0.201255	+	0.979539i	$0.435498\pi$
$857$	−14.7882	+	49.3962i	−0.505157	+	1.68734i	−0.706411	+	0.707802i	$0.749687\pi$
$858$	6.16026	−	3.74066i	0.210308	−	0.127704i
$859$	18.4183	−	9.25001i	0.628423	−	0.315606i	−0.105930	−	0.994374i	$-0.533782\pi$
$859$	18.4183	−	9.25001i	0.628423	−	0.315606i	0.734353	+	0.678767i	$0.237486\pi$
$860$	2.00948	+	6.71212i	0.0685226	+	0.228881i
$861$	−0.0426679	−	0.0385077i	−0.00145412	−	0.00131234i
$862$	0.138004	−	0.185372i	0.00470045	−	0.00631380i
$863$	26.9774	−	46.7263i	0.918322	−	1.59058i	0.116359	−	0.993207i	$-0.462878\pi$
$863$	26.9774	−	46.7263i	0.918322	−	1.59058i	0.801963	−	0.597373i	$-0.203789\pi$
$864$	17.9097	−	6.68478i	0.609299	−	0.227421i
$865$	11.5596	+	20.0219i	0.393040	+	0.680765i
$866$	−5.78024	−	0.675613i	−0.196421	−	0.0229583i
$867$	1.11656	+	0.452621i	0.0379204	+	0.0153718i
$868$	0.153046	+	0.0362725i	0.00519471	+	0.00123117i
$869$	−12.2946	−	8.08630i	−0.417067	−	0.274309i
$870$	5.40949	+	6.16462i	0.183399	+	0.209000i
$871$	−20.2249	−	21.4372i	−0.685296	−	0.726371i
$872$	−7.48265	+	6.27869i	−0.253395	+	0.212623i
$873$	41.3386	−	23.1043i	1.39910	−	0.781960i
$874$	−9.40954	−	7.89554i	−0.318282	−	0.267071i
$875$	0.00146204	+	0.0251023i	4.94260e−5	+	0.000848612i
$876$	−0.690898	+	7.30958i	−0.0233433	+	0.246968i
$877$	9.68370	+	13.0075i	0.326995	+	0.439231i	0.934971	−	0.354725i	$-0.115425\pi$
$877$	9.68370	+	13.0075i	0.326995	+	0.439231i	−0.607975	+	0.793956i	$0.708018\pi$
$878$	−7.92024	+	0.925743i	−0.267295	+	0.0312423i
$879$	−33.4009	−	9.19984i	−1.12658	−	0.310303i
$880$	30.1020	−	19.7984i	1.01474	−	0.667404i
$881$	−36.0488	+	13.1207i	−1.21451	+	0.442047i	−0.868267	−	0.496097i	$-0.834766\pi$
$881$	−36.0488	+	13.1207i	−1.21451	+	0.442047i	−0.346246	+	0.938144i	$0.612544\pi$
$882$	−1.69342	+	6.72571i	−0.0570205	+	0.226466i
$883$	−51.0003	−	18.5626i	−1.71630	−	0.624681i	−0.718788	−	0.695229i	$-0.755303\pi$
$883$	−51.0003	−	18.5626i	−1.71630	−	0.624681i	−0.997508	+	0.0705487i	$0.977525\pi$
$884$	26.3033	−	6.23401i	0.884677	−	0.209672i
$885$	9.83262	+	25.2622i	0.330520	+	0.849178i
$886$	0.131142	−	2.25163i	0.00440581	−	0.0756449i
$887$	2.56518	−	2.71893i	0.0861303	−	0.0912928i	−0.682875	−	0.730535i	$-0.739271\pi$
$887$	2.56518	−	2.71893i	0.0861303	−	0.0912928i	0.769005	+	0.639243i	$0.220752\pi$
$888$	0.145301	+	0.274034i	0.00487598	+	0.00919599i
$889$	−0.0285644	−	0.0662198i	−0.000958021	−	0.00222094i
$890$	9.76493			0.327321
$891$	−2.75315	+	31.9083i	−0.0922341	+	1.06897i
$892$	42.4824			1.42242
$893$	−2.98650	−	6.92348i	−0.0999393	−	0.231685i
$894$	−3.96605	−	0.143086i	−0.132645	−	0.00478550i
$895$	−12.4096	+	13.1534i	−0.414808	+	0.439671i
$896$	0.00490928	−	0.0842890i	0.000164007	−	0.00281590i
$897$	−19.7281	+	24.5957i	−0.658701	+	0.821228i
$898$	0.836009	−	0.198138i	0.0278980	−	0.00661194i
$899$	−40.3792	−	14.6968i	−1.34672	−	0.490167i
$900$	21.1944	+	9.49510i	0.706480	+	0.316503i
$901$	−14.3258	+	5.21418i	−0.477263	+	0.173710i
$902$	−3.54057	+	2.32867i	−0.117888	+	0.0775363i
$903$	−0.0139454	+	0.0137523i	−0.000464074	+	0.000457647i
$904$	24.6252	−	2.87827i	0.819021	−	0.0957298i
$905$	18.6285	+	25.0224i	0.619231	+	0.831771i
$906$	−4.91026	+	2.24814i	−0.163133	+	0.0746895i
$907$	1.10404	+	18.9556i	0.0366590	+	0.629411i	0.965736	+	0.259525i	$0.0835661\pi$
$907$	1.10404	+	18.9556i	0.0366590	+	0.629411i	−0.929077	+	0.369886i	$0.879397\pi$
$908$	−23.4790	−	19.7012i	−0.779178	−	0.653808i
$909$	20.5052	−	53.9829i	0.680113	−	1.79050i
$910$	0.0248590	−	0.0208592i	0.000824068	−	0.000691475i
$911$	−10.0667	−	10.6701i	−0.333524	−	0.353515i	0.538808	−	0.842429i	$-0.318875\pi$
$911$	−10.0667	−	10.6701i	−0.333524	−	0.353515i	−0.872332	+	0.488914i	$0.837393\pi$
$912$	41.2520	−	8.21837i	1.36599	−	0.272137i
$913$	−38.3544	−	25.2261i	−1.26935	−	0.834862i
$914$	2.49591	+	0.591541i	0.0825573	+	0.0195664i
$915$	4.94069	+	35.4520i	0.163334	+	1.17201i
$916$	−27.4155	−	3.20442i	−0.905834	−	0.105877i
$917$	−0.0198866	−	0.0344446i	−0.000656714	−	0.00113746i
$918$	2.69259	−	6.38504i	0.0888686	−	0.210738i
$919$	−14.0757	+	24.3798i	−0.464315	+	0.804216i	−0.999170	−	0.0407270i	$-0.987033\pi$
$919$	−14.0757	+	24.3798i	−0.464315	+	0.804216i	0.534856	+	0.844943i	$0.320366\pi$
$920$	11.8988	−	15.9828i	0.392291	−	0.526938i
$921$	−1.84613	+	0.597488i	−0.0608322	+	0.0196879i
$922$	−0.0643052	−	0.214794i	−0.00211778	−	0.00707388i
$923$	8.41360	−	4.22547i	0.276937	−	0.139083i
$924$	0.0940527	+	0.0515625i	0.00309411	+	0.00169628i
$925$	−0.163624	+	0.546544i	−0.00537994	+	0.0179702i
$926$	−1.16017	−	6.57965i	−0.0381256	−	0.216221i
$927$	−3.40358	+	25.9728i	−0.111788	+	0.853060i
$928$	−3.03728	+	17.2253i	−0.0997035	+	0.565447i
$929$	−33.7421	−	16.9459i	−1.10704	−	0.555977i	−0.201181	−	0.979554i	$-0.564478\pi$
$929$	−33.7421	−	16.9459i	−1.10704	−	0.555977i	−0.905860	+	0.423577i	$0.860774\pi$
$930$	15.5415	−	1.25057i	0.509626	−	0.0410077i
$931$	−20.0542	+	46.4910i	−0.657251	+	1.52368i
$932$	−7.95215	+	18.4352i	−0.260481	+	0.603864i
$933$	−0.613004	+	1.29101i	−0.0200688	+	0.0422658i
$934$	2.39017	+	1.20039i	0.0782089	+	0.0392780i
$935$	7.52440	−	42.6730i	0.246074	−	1.39556i
$936$	2.96213	+	13.3236i	0.0968203	+	0.435495i
$937$	4.74619	+	26.9170i	0.155051	+	0.879339i	0.958739	+	0.284288i	$0.0917572\pi$
$937$	4.74619	+	26.9170i	0.155051	+	0.879339i	−0.803688	+	0.595051i	$0.797132\pi$
$938$	−0.00725675	+	0.0242392i	−0.000236941	+	0.000791440i
$939$	−0.0446642	−	2.01924i	−0.00145756	−	0.0658953i
$940$	5.31200	−	2.66778i	0.173258	−	0.0870135i
$941$	−14.2198	−	47.4974i	−0.463551	−	1.54837i	−0.796029	−	0.605259i	$-0.793070\pi$
$941$	−14.2198	−	47.4974i	−0.463551	−	1.54837i	0.332477	−	0.943111i	$-0.392115\pi$
$942$	0.734076	−	3.43404i	0.0239175	−	0.111887i
$943$	11.0711	−	14.8711i	0.360526	−	0.484270i
$944$	−8.71245	+	15.0904i	−0.283566	+	0.491151i
$945$	0.00956074	+	0.143890i	0.000311011	+	0.00468075i
$946$	0.722042	+	1.25061i	0.0234756	+	0.0406610i
$947$	−6.59374	−	0.770698i	−0.214268	−	0.0250443i	0.00828174	−	0.999966i	$-0.497364\pi$
$947$	−6.59374	−	0.770698i	−0.214268	−	0.0250443i	−0.222549	+	0.974921i	$0.571438\pi$
$948$	10.6822	−	8.32599i	0.346942	−	0.270416i
$949$	−7.72281	−	1.83034i	−0.250693	−	0.0594153i
$950$	−8.17122	−	5.37429i	−0.265109	−	0.174365i
$951$	2.58122	−	7.61150i	0.0837017	−	0.246820i
$952$	−0.0327704	−	0.0347346i	−0.00106210	−	0.00112576i
$953$	−3.58202	+	3.00567i	−0.116033	+	0.0973632i	−0.698958	−	0.715163i	$-0.746353\pi$
$953$	−3.58202	+	3.00567i	−0.116033	+	0.0973632i	0.582925	+	0.812526i	$0.301908\pi$
$954$	−1.23031	−	3.53278i	−0.0398328	−	0.114378i
$955$	−36.6750	−	30.7739i	−1.18677	−	0.995822i
$956$	0.557311	+	9.56866i	0.0180247	+	0.309473i
$957$	−23.8862	−	16.9748i	−0.772132	−	0.548716i
$958$	−5.74031	−	7.71057i	−0.185461	−	0.249117i
$959$	−0.00107624		0.000125794i	−3.47535e−5		4.06211e-6i
$960$	7.24130	+	27.7988i	0.233712	+	0.897204i
$961$	−42.3513	+	27.8549i	−1.36617	+	0.898545i
$962$	−0.153119	+	0.0557307i	−0.00493675	+	0.00179683i
$963$	23.7756	−	35.0737i	0.766158	−	1.13023i
$964$	−0.631389	−	0.229807i	−0.0203357	−	0.00740158i
$965$	57.6785	−	13.6700i	1.85674	−	0.440054i
$966$	0.0267553	+	0.00410984i	0.000860837	+	0.000132232i
$967$	0.543701	−	9.33499i	0.0174843	−	0.300193i	−0.978218	−	0.207580i	$-0.933441\pi$
$967$	0.543701	−	9.33499i	0.0174843	−	0.300193i	0.995702	−	0.0926127i	$-0.0295218\pi$
$968$	1.46674	−	1.55466i	0.0471429	−	0.0499686i
$969$	26.8569	−	42.8697i	0.862767	−	1.37717i
$970$	−6.22721	−	14.4363i	−0.199944	−	0.463522i
$971$	33.5606			1.07701			0.538505	−	0.842622i	$-0.318989\pi$
$971$	33.5606			1.07701			0.538505	+	0.842622i	$0.318989\pi$
$972$	−26.9979	−	11.8312i	−0.865959	−	0.379486i
$973$	0.0119829			0.000384153
$974$	0.470255	+	1.09017i	0.0150679	+	0.0349314i
$975$	−13.3281	+	21.2747i	−0.426842	+	0.681337i
$976$	−15.7893	+	16.7357i	−0.505404	+	0.535697i
$977$	−0.410464	+	7.04739i	−0.0131319	+	0.225466i	0.985357	+	0.170506i	$0.0545402\pi$
$977$	−0.410464	+	7.04739i	−0.0131319	+	0.225466i	−0.998489	+	0.0549601i	$0.982497\pi$
$978$	−0.795199	−	0.122149i	−0.0254276	−	0.00390590i
$979$	−33.9490	+	8.04605i	−1.08501	+	0.257153i
$980$	−37.5084	−	13.6519i	−1.19816	−	0.436095i
$981$	22.7441	+	1.64324i	0.726163	+	0.0524647i
$982$	10.4369	−	3.79871i	0.333054	−	0.121222i
$983$	35.0570	−	23.0574i	1.11815	−	0.735416i	0.150722	−	0.988576i	$-0.451840\pi$
$983$	35.0570	−	23.0574i	1.11815	−	0.735416i	0.967424	+	0.253160i	$0.0814699\pi$
$984$	−2.02306	−	7.76637i	−0.0644927	−	0.247583i
$985$	0.254872	−	0.0297902i	0.00812089	−	0.000949196i
$986$	3.78617	+	5.08571i	0.120576	+	0.161962i
$987$	0.0135446	+	0.00962549i	0.000431130	+	0.000306383i
$988$	2.81558	+	48.3416i	0.0895755	+	1.53795i
$989$	−4.83966	−	4.06096i	−0.153892	−	0.129131i
$990$	10.4444	+	1.99219i	0.331943	+	0.0633159i
$991$	10.7027	−	8.98062i	0.339982	−	0.285279i	−0.456770	−	0.889585i	$-0.650994\pi$
$991$	10.7027	−	8.98062i	0.339982	−	0.285279i	0.796753	+	0.604306i	$0.206549\pi$
$992$	22.8187	+	24.1864i	0.724494	+	0.767919i
$993$	3.70309	−	10.9197i	0.117514	−	0.346525i
$994$	−0.00675322	−	0.00444167i	−0.000214199	−	0.000140881i
$995$	−52.4158	−	12.4228i	−1.66169	−	0.393828i
$996$	33.3243	−	25.9738i	1.05592	−	0.823012i
$997$	−17.4776	−	2.04284i	−0.553521	−	0.0646973i	−0.165265	−	0.986249i	$-0.552848\pi$
$997$	−17.4776	−	2.04284i	−0.553521	−	0.0646973i	−0.388255	+	0.921552i	$0.626922\pi$
$998$	2.26597	+	3.92477i	0.0717280	+	0.124237i
$999$	0.202002	−	0.695358i	0.00639105	−	0.0220002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.31.5	✓	144
3.2	odd	2		243.2.g.a.145.4		144
9.2	odd	6		729.2.g.a.190.4		144
9.4	even	3		729.2.g.c.433.4		144
9.5	odd	6		729.2.g.b.433.5		144
9.7	even	3		729.2.g.d.190.5		144
81.7	even	27		729.2.g.c.298.4		144
81.14	odd	54		6561.2.a.d.1.30		72
81.20	odd	54		729.2.g.a.541.4		144
81.34	even	27	inner	81.2.g.a.34.5	yes	144
81.47	odd	54		243.2.g.a.181.4		144
81.61	even	27		729.2.g.d.541.5		144
81.67	even	27		6561.2.a.c.1.43		72
81.74	odd	54		729.2.g.b.298.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.31.5	✓	144	1.1	even	1	trivial
81.2.g.a.34.5	yes	144	81.34	even	27	inner
243.2.g.a.145.4		144	3.2	odd	2
243.2.g.a.181.4		144	81.47	odd	54
729.2.g.a.190.4		144	9.2	odd	6
729.2.g.a.541.4		144	81.20	odd	54
729.2.g.b.298.5		144	81.74	odd	54
729.2.g.b.433.5		144	9.5	odd	6
729.2.g.c.298.4		144	81.7	even	27
729.2.g.c.433.4		144	9.4	even	3
729.2.g.d.190.5		144	9.7	even	3
729.2.g.d.541.5		144	81.61	even	27
6561.2.a.c.1.43		72	81.67	even	27
6561.2.a.d.1.30		72	81.14	odd	54

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.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.130814 + 0.303261i) q^{2} +(-0.919544 + 1.46780i) q^{3} +(1.29763 - 1.37541i) q^{4} +(-0.175343 + 3.01052i) q^{5} +(-0.565415 - 0.0868526i) q^{6} +(0.00895493 - 0.00212236i) q^{7} +(1.20756 + 0.439517i) q^{8} +(-1.30888 - 2.69941i) q^{9} +(-0.935909 + 0.340643i) q^{10} +(2.97312 - 1.95545i) q^{11} +(0.825596 + 3.16941i) q^{12} +(-3.51646 + 0.411015i) q^{13} +(0.00181506 + 0.00243804i) q^{14} +(-4.25761 - 3.02567i) q^{15} +(-0.195217 - 3.35174i) q^{16} +(-3.09319 - 2.59549i) q^{17} +(0.647406 - 0.750053i) q^{18} +(5.54096 - 4.64941i) q^{19} +(3.91316 + 4.14770i) q^{20} +(-0.00511925 + 0.0150957i) q^{21} +(0.981937 + 0.645830i) q^{22} +(-5.00317 - 1.18577i) q^{23} +(-1.75553 + 1.36831i) q^{24} +(-4.06629 - 0.475281i) q^{25} +(-0.584647 - 1.01264i) q^{26} +(5.16577 + 0.561054i) q^{27} +(0.00870107 - 0.0150707i) q^{28} +(-2.83907 + 3.81353i) q^{29} +(0.360613 - 1.68696i) q^{30} +(2.59221 + 8.65858i) q^{31} +(3.28766 - 1.65112i) q^{32} +(0.136301 + 6.16207i) q^{33} +(0.382479 - 1.27757i) q^{34} +(0.00481921 + 0.0273311i) q^{35} +(-5.41123 - 1.70260i) q^{36} +(0.0241986 - 0.137237i) q^{37} +(2.13482 + 1.07215i) q^{38} +(2.63025 - 5.53941i) q^{39} +(-1.53491 + 3.55832i) q^{40} +(-1.42815 + 3.31082i) q^{41} +(-0.00524759 + 0.000422254i) q^{42} +(1.09801 + 0.551444i) q^{43} +(1.16847 - 6.62670i) q^{44} +(8.35614 - 3.46708i) q^{45} +(-0.294886 - 1.67238i) q^{46} +(0.298973 - 0.998641i) q^{47} +(5.09920 + 2.79553i) q^{48} +(-6.25535 + 3.14156i) q^{49} +(-0.387793 - 1.29532i) q^{50} +(6.65399 - 2.15352i) q^{51} +(-3.99775 + 5.36991i) q^{52} +(1.88778 - 3.26973i) q^{53} +(0.505609 + 1.63997i) q^{54} +(5.36561 + 9.29351i) q^{55} +(0.0117464 + 0.00137296i) q^{56} +(1.72926 + 12.4084i) q^{57} +(-1.52788 - 0.362115i) q^{58} +(-4.33615 - 2.85193i) q^{59} +(-9.68632 + 1.92974i) q^{60} +(-4.70281 - 4.98469i) q^{61} +(-2.28671 + 1.91878i) q^{62} +(-0.0174500 - 0.0213951i) q^{63} +(-4.21308 - 3.53519i) q^{64} +(-0.620784 - 10.6584i) q^{65} +(-1.85088 + 0.847419i) q^{66} +(4.97104 + 6.67727i) q^{67} +(-7.58367 + 0.886403i) q^{68} +(6.34111 - 6.25329i) q^{69} +(-0.00765804 + 0.00503677i) q^{70} +(-2.49894 + 0.909541i) q^{71} +(-0.394116 - 3.83498i) q^{72} +(2.10657 + 0.766729i) q^{73} +(0.0447841 - 0.0106140i) q^{74} +(4.43675 - 5.53146i) q^{75} +(0.795271 - 13.6543i) q^{76} +(0.0224739 - 0.0238210i) q^{77} +(2.02396 + 0.0730195i) q^{78} +(-1.63789 - 3.79706i) q^{79} +10.1247 q^{80} +(-5.57367 + 7.06641i) q^{81} -1.19086 q^{82} +(-5.10959 - 11.8454i) q^{83} +(0.0141198 + 0.0266296i) q^{84} +(8.35615 - 8.85700i) q^{85} +(-0.0235956 + 0.405121i) q^{86} +(-2.98686 - 7.67390i) q^{87} +(4.44968 - 1.05459i) q^{88} +(-9.21313 - 3.35330i) q^{89} +(2.14453 + 2.08055i) q^{90} +(-0.0306173 + 0.0111438i) q^{91} +(-8.12317 + 5.34270i) q^{92} +(-15.0927 - 4.15709i) q^{93} +(0.341958 - 0.0399692i) q^{94} +(13.0256 + 17.4964i) q^{95} +(-0.599623 + 6.34391i) q^{96} +(0.917855 + 15.7590i) q^{97} +(-1.77100 - 1.48604i) q^{98} +(-9.17003 - 5.46623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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