LMFDB - Embedded newform 81.2.g.a.22.5

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			22.5
Character	$\chi$	$=$	81.22
Dual form			81.2.g.a.70.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.259760 + 0.275329i) q^{2} +(-0.322104 - 1.70184i) q^{3} +(0.107959 - 1.85358i) q^{4} +(-1.27364 + 0.148867i) q^{5} +(0.384896 - 0.530753i) q^{6} +(1.70721 + 0.857394i) q^{7} +(1.11832 - 0.938383i) q^{8} +(-2.79250 + 1.09634i) q^{9} +(-0.371828 - 0.312001i) q^{10} +(1.93272 + 4.48054i) q^{11} +(-3.18926 + 0.413317i) q^{12} +(3.34705 + 0.793266i) q^{13} +(0.207399 + 0.692762i) q^{14} +(0.663593 + 2.11958i) q^{15} +(-3.13947 - 0.366951i) q^{16} +(0.0728119 - 0.412937i) q^{17} +(-1.02723 - 0.484072i) q^{18} +(-0.626542 - 3.55329i) q^{19} +(0.138437 + 2.37686i) q^{20} +(0.909245 - 3.18157i) q^{21} +(-0.731582 + 1.69600i) q^{22} +(-5.99966 + 3.01314i) q^{23} +(-1.95719 - 1.60094i) q^{24} +(-3.26522 + 0.773872i) q^{25} +(0.651020 + 1.12760i) q^{26} +(2.76526 + 4.39924i) q^{27} +(1.77356 - 3.07189i) q^{28} +(1.44045 - 4.81145i) q^{29} +(-0.411207 + 0.733287i) q^{30} +(5.54449 + 3.64667i) q^{31} +(-2.45802 - 3.30169i) q^{32} +(7.00261 - 4.73237i) q^{33} +(0.132607 - 0.0872170i) q^{34} +(-2.30201 - 0.837864i) q^{35} +(1.73067 + 5.29447i) q^{36} +(0.465059 - 0.169268i) q^{37} +(0.815575 - 1.09551i) q^{38} +(0.271909 - 5.95165i) q^{39} +(-1.28465 + 1.36164i) q^{40} +(4.16545 - 4.41512i) q^{41} +(1.11216 - 0.576101i) q^{42} +(-6.92694 + 9.30450i) q^{43} +(8.51368 - 3.09873i) q^{44} +(3.39343 - 1.81205i) q^{45} +(-2.38808 - 0.869188i) q^{46} +(-5.06765 + 3.33305i) q^{47} +(0.386745 + 5.46106i) q^{48} +(-2.00066 - 2.68735i) q^{49} +(-1.06124 - 0.697991i) q^{50} +(-0.726204 + 0.00909474i) q^{51} +(1.83172 - 6.11838i) q^{52} +(2.95007 - 5.10967i) q^{53} +(-0.492935 + 1.90410i) q^{54} +(-3.12859 - 5.41888i) q^{55} +(2.71378 - 0.643177i) q^{56} +(-5.84532 + 2.21080i) q^{57} +(1.69890 - 0.853222i) q^{58} +(2.23192 - 5.17418i) q^{59} +(4.00044 - 1.00119i) q^{60} +(0.161757 + 2.77726i) q^{61} +(0.436200 + 2.47381i) q^{62} +(-5.70738 - 0.522590i) q^{63} +(-0.827191 + 4.69124i) q^{64} +(-4.38103 - 0.512069i) q^{65} +(3.12196 + 0.698745i) q^{66} +(2.07542 + 6.93240i) q^{67} +(-0.757549 - 0.179542i) q^{68} +(7.06039 + 9.23990i) q^{69} +(-0.367282 - 0.851455i) q^{70} +(-11.9949 - 10.0649i) q^{71} +(-2.09412 + 3.84649i) q^{72} +(-5.04326 + 4.23179i) q^{73} +(0.167408 + 0.0840754i) q^{74} +(2.36875 + 5.30761i) q^{75} +(-6.65395 + 0.777735i) q^{76} +(-0.542032 + 9.30634i) q^{77} +(1.70929 - 1.47113i) q^{78} +(-2.62307 - 2.78030i) q^{79} +4.05318 q^{80} +(6.59609 - 6.12304i) q^{81} +2.29763 q^{82} +(3.32898 + 3.52851i) q^{83} +(-5.79912 - 2.02883i) q^{84} +(-0.0312634 + 0.536772i) q^{85} +(-4.36114 + 0.509744i) q^{86} +(-8.65228 - 0.901629i) q^{87} +(6.36586 + 3.19706i) q^{88} +(-7.97723 + 6.69369i) q^{89} +(1.38039 + 0.463612i) q^{90} +(5.03399 + 4.22402i) q^{91} +(4.93738 + 11.4461i) q^{92} +(4.42013 - 10.6104i) q^{93} +(-2.23406 - 0.529481i) q^{94} +(1.32696 + 4.43235i) q^{95} +(-4.82720 + 5.24663i) q^{96} +(2.14884 + 0.251163i) q^{97} +(0.220216 - 1.24891i) q^{98} +(-10.3093 - 10.3930i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	0.259760	+	0.275329i	0.183678	+	0.194687i	0.812669	−	0.582725i	$-0.198014\pi$
$2$	0.259760	+	0.275329i	0.183678	+	0.194687i	−0.628992	+	0.777412i	$0.716532\pi$
$3$	−0.322104	−	1.70184i	−0.185967	−	0.982556i
$3$	−0.322104	−	1.70184i	−0.185967	−	0.982556i
$4$	0.107959	−	1.85358i	0.0539793	−	0.926789i
$5$	−1.27364	+	0.148867i	−0.569590	+	0.0665755i	−0.396013	−	0.918245i	$-0.629606\pi$
$5$	−1.27364	+	0.148867i	−0.569590	+	0.0665755i	−0.173577	+	0.984820i	$0.555532\pi$
$6$	0.384896	−	0.530753i	0.157133	−	0.216679i
$7$	1.70721	+	0.857394i	0.645266	+	0.324065i	0.741161	−	0.671327i	$-0.234275\pi$
$7$	1.70721	+	0.857394i	0.645266	+	0.324065i	−0.0958958	+	0.995391i	$0.530572\pi$
$8$	1.11832	−	0.938383i	0.395386	−	0.331768i
$9$	−2.79250	+	1.09634i	−0.930833	+	0.365446i
$10$	−0.371828	−	0.312001i	−0.117582	−	0.0986633i
$11$	1.93272	+	4.48054i	0.582736	+	1.35093i	0.913353	+	0.407169i	$0.133484\pi$
$11$	1.93272	+	4.48054i	0.582736	+	1.35093i	−0.330617	+	0.943765i	$0.607257\pi$
$12$	−3.18926	+	0.413317i	−0.920660	+	0.119314i
$13$	3.34705	+	0.793266i	0.928305	+	0.220012i	0.666840	−	0.745201i	$-0.267646\pi$
$13$	3.34705	+	0.793266i	0.928305	+	0.220012i	0.261465	+	0.965213i	$0.415794\pi$
$14$	0.207399	+	0.692762i	0.0554298	+	0.185148i
$15$	0.663593	+	2.11958i	0.171339	+	0.547273i
$16$	−3.13947	−	0.366951i	−0.784867	−	0.0917379i
$17$	0.0728119	−	0.412937i	0.0176595	−	0.100152i	−0.974704	−	0.223499i	$-0.928252\pi$
$17$	0.0728119	−	0.412937i	0.0176595	−	0.100152i	0.992364	+	0.123348i	$0.0393630\pi$
$18$	−1.02723	−	0.484072i	−0.242121	−	0.114097i
$19$	−0.626542	−	3.55329i	−0.143739	−	0.815182i	−0.968371	−	0.249513i	$-0.919729\pi$
$19$	−0.626542	−	3.55329i	−0.143739	−	0.815182i	0.824633	−	0.565668i	$-0.191382\pi$
$20$	0.138437	+	2.37686i	0.0309554	+	0.531483i
$21$	0.909245	−	3.18157i	0.198413	−	0.694275i
$22$	−0.731582	+	1.69600i	−0.155974	+	0.361588i
$23$	−5.99966	+	3.01314i	−1.25102	+	0.628284i	−0.946032	−	0.324074i	$-0.894947\pi$
$23$	−5.99966	+	3.01314i	−1.25102	+	0.628284i	−0.304984	+	0.952358i	$0.598651\pi$
$24$	−1.95719	−	1.60094i	−0.399510	−	0.326791i
$25$	−3.26522	+	0.773872i	−0.653045	+	0.154774i
$26$	0.651020	+	1.12760i	0.127675	+	0.221140i
$27$	2.76526	+	4.39924i	0.532175	+	0.846634i
$28$	1.77356	−	3.07189i	0.335170	−	0.580532i
$29$	1.44045	−	4.81145i	0.267486	−	0.893464i	−0.713709	−	0.700443i	$-0.752986\pi$
$29$	1.44045	−	4.81145i	0.267486	−	0.893464i	0.981194	−	0.193022i	$-0.0618288\pi$
$30$	−0.411207	+	0.733287i	−0.0750758	+	0.133879i
$31$	5.54449	+	3.64667i	0.995819	+	0.654960i	0.939177	−	0.343434i	$-0.111590\pi$
$31$	5.54449	+	3.64667i	0.995819	+	0.654960i	0.0566423	+	0.998395i	$0.481961\pi$
$32$	−2.45802	−	3.30169i	−0.434520	−	0.583662i
$33$	7.00261	−	4.73237i	1.21900	−	0.823800i
$34$	0.132607	−	0.0872170i	0.0227419	−	0.0149576i
$35$	−2.30201	−	0.837864i	−0.389111	−	0.141625i
$36$	1.73067	+	5.29447i	0.288446	+	0.882412i
$37$	0.465059	−	0.169268i	0.0764552	−	0.0278274i	−0.303509	−	0.952828i	$-0.598158\pi$
$37$	0.465059	−	0.169268i	0.0764552	−	0.0278274i	0.379965	+	0.925001i	$0.375936\pi$
$38$	0.815575	−	1.09551i	0.132304	−	0.177715i
$39$	0.271909	−	5.95165i	0.0435403	−	0.953027i
$40$	−1.28465	+	1.36164i	−0.203120	+	0.215295i
$41$	4.16545	−	4.41512i	0.650535	−	0.689526i	−0.315210	−	0.949022i	$-0.602075\pi$
$41$	4.16545	−	4.41512i	0.650535	−	0.689526i	0.965744	+	0.259496i	$0.0835563\pi$
$42$	1.11216	−	0.576101i	0.171611	−	0.0888943i
$43$	−6.92694	+	9.30450i	−1.05635	+	1.41892i	−0.153920	+	0.988083i	$0.549190\pi$
$43$	−6.92694	+	9.30450i	−1.05635	+	1.41892i	−0.902429	+	0.430839i	$0.858218\pi$
$44$	8.51368	−	3.09873i	1.28349	−	0.467151i
$45$	3.39343	−	1.81205i	0.505863	−	0.270125i
$46$	−2.38808	−	0.869188i	−0.352102	−	0.128155i
$47$	−5.06765	+	3.33305i	−0.739193	+	0.486175i	−0.862413	−	0.506205i	$-0.831048\pi$
$47$	−5.06765	+	3.33305i	−0.739193	+	0.486175i	0.123221	+	0.992379i	$0.460678\pi$
$48$	0.386745	+	5.46106i	0.0558219	+	0.788236i
$49$	−2.00066	−	2.68735i	−0.285809	−	0.383908i
$50$	−1.06124	−	0.697991i	−0.150082	−	0.0987108i
$51$	−0.726204	+	0.00909474i	−0.101689	+	0.00127352i
$52$	1.83172	−	6.11838i	0.254014	−	0.848467i
$53$	2.95007	−	5.10967i	0.405223	−	0.701867i	−0.589124	−	0.808043i	$-0.700527\pi$
$53$	2.95007	−	5.10967i	0.405223	−	0.701867i	0.994347	+	0.106175i	$0.0338605\pi$
$54$	−0.492935	+	1.90410i	−0.0670800	+	0.259116i
$55$	−3.12859	−	5.41888i	−0.421859	−	0.730682i
$56$	2.71378	−	0.643177i	0.362644	−	0.0859481i
$57$	−5.84532	+	2.21080i	−0.774231	+	0.292828i
$58$	1.69890	−	0.853222i	0.223077	−	0.112034i
$59$	2.23192	−	5.17418i	0.290572	−	0.673621i	−0.708927	−	0.705282i	$-0.750820\pi$
$59$	2.23192	−	5.17418i	0.290572	−	0.673621i	0.999499	+	0.0316611i	$0.0100797\pi$
$60$	4.00044	−	1.00119i	0.516455	−	0.129254i
$61$	0.161757	+	2.77726i	0.0207109	+	0.355592i	0.992704	+	0.120581i	$0.0384757\pi$
$61$	0.161757	+	2.77726i	0.0207109	+	0.355592i	−0.971993	+	0.235011i	$0.924487\pi$
$62$	0.436200	+	2.47381i	0.0553975	+	0.314175i
$63$	−5.70738	−	0.522590i	−0.719062	−	0.0658401i
$64$	−0.827191	+	4.69124i	−0.103399	+	0.586404i
$65$	−4.38103	−	0.512069i	−0.543400	−	0.0635144i
$66$	3.12196	+	0.698745i	0.384286	+	0.0860095i
$67$	2.07542	+	6.93240i	0.253553	+	0.846928i	0.986092	+	0.166202i	$0.0531503\pi$
$67$	2.07542	+	6.93240i	0.253553	+	0.846928i	−0.732538	+	0.680726i	$0.761665\pi$
$68$	−0.757549	−	0.179542i	−0.0918664	−	0.0217727i
$69$	7.06039	+	9.23990i	0.849971	+	1.11235i
$70$	−0.367282	−	0.851455i	−0.0438986	−	0.101768i
$71$	−11.9949	−	10.0649i	−1.42353	−	1.19448i	−0.949418	−	0.314015i	$-0.898326\pi$
$71$	−11.9949	−	10.0649i	−1.42353	−	1.19448i	−0.474109	−	0.880466i	$-0.657230\pi$
$72$	−2.09412	+	3.84649i	−0.246795	+	0.453313i
$73$	−5.04326	+	4.23179i	−0.590268	+	0.495294i	−0.888301	−	0.459262i	$-0.848114\pi$
$73$	−5.04326	+	4.23179i	−0.590268	+	0.495294i	0.298033	+	0.954556i	$0.403670\pi$
$74$	0.167408	+	0.0840754i	0.0194608	+	0.00977357i
$75$	2.36875	+	5.30761i	0.273519	+	0.612870i
$76$	−6.65395	+	0.777735i	−0.763260	+	0.0892123i
$77$	−0.542032	+	9.30634i	−0.0617703	+	1.06056i
$78$	1.70929	−	1.47113i	0.193539	−	0.166573i
$79$	−2.62307	−	2.78030i	−0.295119	−	0.312808i	0.562800	−	0.826593i	$-0.309724\pi$
$79$	−2.62307	−	2.78030i	−0.295119	−	0.312808i	−0.857919	+	0.513786i	$0.828243\pi$
$80$	4.05318			0.453160
$81$	6.59609	−	6.12304i	0.732898	−	0.680338i
$82$	2.29763			0.253731
$83$	3.32898	+	3.52851i	0.365403	+	0.387304i	0.883823	−	0.467822i	$-0.154961\pi$
$83$	3.32898	+	3.52851i	0.365403	+	0.387304i	−0.518420	+	0.855126i	$0.673480\pi$
$84$	−5.79912	−	2.02883i	−0.632736	−	0.221364i
$85$	−0.0312634	+	0.536772i	−0.00339099	+	0.0582211i
$86$	−4.36114	+	0.509744i	−0.470274	+	0.0549671i
$87$	−8.65228	−	0.901629i	−0.927622	−	0.0966647i
$88$	6.36586	+	3.19706i	0.678603	+	0.340807i
$89$	−7.97723	+	6.69369i	−0.845585	+	0.709530i	−0.958813	−	0.284039i	$-0.908325\pi$
$89$	−7.97723	+	6.69369i	−0.845585	+	0.709530i	0.113228	+	0.993569i	$0.463881\pi$
$90$	1.38039	+	0.463612i	0.145506	+	0.0488690i
$91$	5.03399	+	4.22402i	0.527705	+	0.442797i
$92$	4.93738	+	11.4461i	0.514757	+	1.19334i
$93$	4.42013	−	10.6104i	0.458346	−	1.10025i
$94$	−2.23406	−	0.529481i	−0.230425	−	0.0546118i
$95$	1.32696	+	4.43235i	0.136143	+	0.454749i
$96$	−4.82720	+	5.24663i	−0.492674	+	0.535482i
$97$	2.14884	+	0.251163i	0.218182	+	0.0255018i	0.224481	−	0.974478i	$-0.427931\pi$
$97$	2.14884	+	0.251163i	0.218182	+	0.0255018i	−0.00629978	+	0.999980i	$0.502005\pi$
$98$	0.220216	−	1.24891i	0.0222452	−	0.126159i
$99$	−10.3093	−	10.3930i	−1.03612	−	1.04453i
$100$	1.08192	+	6.13589i	0.108192	+	0.613589i
$101$	−0.949061	−	16.2948i	−0.0944351	−	1.62139i	−0.629793	−	0.776763i	$-0.716860\pi$
$101$	−0.949061	−	16.2948i	−0.0944351	−	1.62139i	0.535358	−	0.844625i	$-0.320177\pi$
$102$	−0.191142	−	0.197583i	−0.0189259	−	0.0195636i
$103$	7.15634	−	16.5903i	0.705135	−	1.63469i	−0.0658471	−	0.997830i	$-0.520975\pi$
$103$	7.15634	−	16.5903i	0.705135	−	1.63469i	0.770982	−	0.636857i	$-0.219766\pi$
$104$	4.48747	−	2.25369i	0.440032	−	0.220993i
$105$	−0.684420	+	4.18753i	−0.0667926	+	0.408661i
$106$	2.17315	−	0.515046i	0.211075	−	0.0500257i
$107$	8.06607	+	13.9708i	0.779777	+	1.35061i	0.932070	+	0.362277i	$0.118001\pi$
$107$	8.06607	+	13.9708i	0.779777	+	1.35061i	−0.152294	+	0.988335i	$0.548666\pi$
$108$	8.45287	−	4.65070i	0.813378	−	0.447513i
$109$	4.04171	−	7.00045i	0.387126	−	0.670521i	−0.604936	−	0.796274i	$-0.706801\pi$
$109$	4.04171	−	7.00045i	0.387126	−	0.670521i	0.992062	+	0.125753i	$0.0401347\pi$
$110$	0.679294	−	2.26900i	0.0647681	−	0.216341i
$111$	−0.437864	−	0.736933i	−0.0415602	−	0.0699466i
$112$	−5.04512	−	3.31823i	−0.476719	−	0.313543i
$113$	−1.02756	−	1.38026i	−0.0966651	−	0.129844i	0.751159	−	0.660121i	$-0.229495\pi$
$113$	−1.02756	−	1.38026i	−0.0966651	−	0.129844i	−0.847824	+	0.530278i	$0.822088\pi$
$114$	−2.12708	−	1.03511i	−0.199219	−	0.0969468i
$115$	7.19285	−	4.73081i	0.670737	−	0.441151i
$116$	−8.76289	−	3.18943i	−0.813614	−	0.296131i
$117$	−10.2163	+	1.45431i	−0.944499	+	0.134451i
$118$	2.00437	−	0.729529i	0.184517	−	0.0671586i
$119$	0.478355	−	0.642542i	0.0438507	−	0.0589017i
$120$	2.73109	+	1.74767i	0.249313	+	0.159539i
$121$	−8.79120	+	9.31813i	−0.799200	+	0.847102i
$122$	−0.722644	+	0.765957i	−0.0654251	+	0.0693465i
$123$	−8.85553	−	5.66679i	−0.798476	−	0.510957i
$124$	7.35795	−	9.88345i	0.660764	−	0.887560i
$125$	10.0684	−	3.66460i	0.900546	−	0.327772i
$126$	−1.33866	−	1.70716i	−0.119258	−	0.152086i
$127$	−4.79894	−	1.74667i	−0.425837	−	0.154992i	0.120206	−	0.992749i	$-0.461644\pi$
$127$	−4.79894	−	1.74667i	−0.425837	−	0.154992i	−0.546044	+	0.837757i	$0.683867\pi$
$128$	−8.38455	+	5.51461i	−0.741097	+	0.487427i
$129$	18.0659	+	8.79151i	1.59062	+	0.774049i
$130$	−0.997028	−	1.33924i	−0.0874452	−	0.117459i
$131$	9.73457	+	6.40253i	0.850514	+	0.559392i	0.898258	−	0.439468i	$-0.144833\pi$
$131$	9.73457	+	6.40253i	0.850514	+	0.559392i	−0.0477446	+	0.998860i	$0.515203\pi$
$132$	−8.01582	−	13.4908i	−0.697688	−	1.17422i
$133$	1.97693	−	6.60342i	0.171422	−	0.572589i
$134$	−1.36958	+	2.37218i	−0.118314	+	0.204925i
$135$	−4.17686	−	5.19140i	−0.359487	−	0.446804i
$136$	−0.306066	−	0.530121i	−0.0262449	−	0.0454575i
$137$	4.82005	−	1.14237i	0.411805	−	0.0975995i	−0.0194912	−	0.999810i	$-0.506205\pi$
$137$	4.82005	−	1.14237i	0.411805	−	0.0975995i	0.431296	+	0.902210i	$0.358056\pi$
$138$	−0.710007	+	4.34408i	−0.0604398	+	0.369793i
$139$	15.0389	−	7.55284i	1.27559	−	0.640623i	0.323435	−	0.946250i	$-0.395162\pi$
$139$	15.0389	−	7.55284i	1.27559	−	0.640623i	0.952151	+	0.305627i	$0.0988660\pi$
$140$	−1.80157	+	4.17651i	−0.152260	+	0.352979i
$141$	7.30461	+	7.55072i	0.615159	+	0.635886i
$142$	−0.344625	−	5.91698i	−0.0289203	−	0.496542i
$143$	2.91464	+	16.5298i	0.243735	+	1.38229i
$144$	9.16927	−	2.41721i	0.764105	−	0.201434i
$145$	−1.11835	+	6.34250i	−0.0928742	+	0.526716i
$146$	−2.47517	−	0.289306i	−0.204847	−	0.0239431i
$147$	−3.92902	+	4.27041i	−0.324060	+	0.352217i
$148$	−0.263544	−	0.880297i	−0.0216632	−	0.0723600i
$149$	16.9579	+	4.01909i	1.38924	+	0.329257i	0.856119	−	0.516779i	$-0.172869\pi$
$149$	16.9579	+	4.01909i	1.38924	+	0.329257i	0.533126	+	0.846036i	$0.321017\pi$
$150$	−0.846035	+	2.03089i	−0.0690785	+	0.165821i
$151$	2.55693	+	5.92763i	0.208080	+	0.482384i	0.990013	−	0.140979i	$-0.0450251\pi$
$151$	2.55693	+	5.92763i	0.208080	+	0.482384i	−0.781932	+	0.623363i	$0.785766\pi$
$152$	−4.03503	−	3.38579i	−0.327284	−	0.274624i
$153$	0.249391	+	1.23295i	0.0201621	+	0.0996782i
$154$	−2.70310	+	2.26817i	−0.217822	+	0.182775i
$155$	−7.60455	−	3.81915i	−0.610812	−	0.306762i
$156$	−11.0025	−	1.14654i	−0.880904	−	0.0917964i
$157$	−12.6850	+	1.48266i	−1.01237	+	0.118329i	−0.606072	−	0.795410i	$-0.707256\pi$
$157$	−12.6850	+	1.48266i	−1.01237	+	0.118329i	−0.406301	+	0.913739i	$0.633181\pi$
$158$	0.0841277	−	1.44442i	0.00669284	−	0.114912i
$159$	−9.64606	−	3.37469i	−0.764982	−	0.267630i
$160$	3.62214	+	3.83925i	0.286356	+	0.303519i
$161$	−12.8261			−1.01084
$162$	3.39925	+	0.225575i	0.267070	+	0.0177229i
$163$	−0.599869			−0.0469853			−0.0234927	−	0.999724i	$-0.507479\pi$
$163$	−0.599869			−0.0469853			−0.0234927	+	0.999724i	$0.507479\pi$
$164$	−7.73408	−	8.19764i	−0.603930	−	0.640128i
$165$	−8.21432	+	7.06980i	−0.639484	+	0.550383i
$166$	−0.106768	+	1.83313i	−0.00828677	+	0.142278i
$167$	3.01391	−	0.352275i	0.233223	−	0.0272599i	0.00132163	−	0.999999i	$-0.499579\pi$
$167$	3.01391	−	0.352275i	0.233223	−	0.0272599i	0.231902	+	0.972739i	$0.425505\pi$
$168$	−1.96870	−	4.41123i	−0.151889	−	0.340334i
$169$	−1.04374	−	0.524184i	−0.0802874	−	0.0403219i
$170$	−0.155910	+	0.130824i	−0.0119578	+	0.0100337i
$171$	5.64523	+	9.23566i	0.431701	+	0.706269i
$172$	16.4988	+	13.8441i	1.25802	+	1.05560i
$173$	−3.82438	−	8.86591i	−0.290762	−	0.674063i	0.708745	−	0.705465i	$-0.249262\pi$
$173$	−3.82438	−	8.86591i	−0.290762	−	0.674063i	−0.999507	+	0.0314024i	$0.990003\pi$
$174$	−1.99927	−	2.61643i	−0.151564	−	0.198351i
$175$	−6.23795	−	1.47842i	−0.471544	−	0.111758i
$176$	−4.42357	−	14.7757i	−0.333439	−	1.11376i
$177$	−9.52452	−	2.13174i	−0.715907	−	0.160232i
$178$	−3.91513	−	0.457613i	−0.293451	−	0.0342995i
$179$	−4.48229	+	25.4203i	−0.335022	+	1.90001i	0.0919897	+	0.995760i	$0.470677\pi$
$179$	−4.48229	+	25.4203i	−0.335022	+	1.90001i	−0.427012	+	0.904246i	$0.640434\pi$
$180$	−2.99243	−	6.48561i	−0.223043	−	0.483409i
$181$	0.154861	+	0.878259i	0.0115107	+	0.0652805i	0.990022	−	0.140913i	$-0.0450036\pi$
$181$	0.154861	+	0.878259i	0.0115107	+	0.0652805i	−0.978511	+	0.206193i	$0.933893\pi$
$182$	0.144632	+	2.48323i	0.0107208	+	0.184069i
$183$	4.67435	−	1.16985i	0.345538	−	0.0864780i
$184$	−3.88206	+	8.99964i	−0.286190	+	0.663462i
$185$	−0.567120	+	0.284818i	−0.0416955	+	0.0209403i
$186$	4.06953	−	1.53917i	0.298392	−	0.112857i
$187$	1.99090	−	0.471853i	0.145589	−	0.0345053i
$188$	5.63096	+	9.75311i	0.410680	+	0.711319i
$189$	0.949009	+	9.88136i	0.0690303	+	0.718763i
$190$	−0.875665	+	1.51670i	−0.0635274	+	0.110033i
$191$	2.31577	−	7.73521i	0.167563	−	0.559700i	−0.832421	−	0.554143i	$-0.813046\pi$
$191$	2.31577	−	7.73521i	0.167563	−	0.559700i	0.999985	−	0.00555685i	$-0.00176881\pi$
$192$	8.25016	−	0.103322i	0.595404	−	0.00745665i
$193$	−0.162747	−	0.107041i	−0.0117148	−	0.00770494i	0.543638	−	0.839320i	$-0.317046\pi$
$193$	−0.162747	−	0.107041i	−0.0117148	−	0.00770494i	−0.555353	+	0.831615i	$0.687417\pi$
$194$	0.489029	+	0.656880i	0.0351102	+	0.0471612i
$195$	0.539691	+	7.62075i	0.0386481	+	0.545733i
$196$	−5.19721	+	3.41826i	−0.371229	+	0.244161i
$197$	−10.8405	−	3.94561i	−0.772351	−	0.281113i	−0.0743718	−	0.997231i	$-0.523695\pi$
$197$	−10.8405	−	3.94561i	−0.772351	−	0.281113i	−0.697980	+	0.716118i	$0.745917\pi$
$198$	0.183554	−	5.53813i	0.0130446	−	0.393578i
$199$	−1.65236	+	0.601410i	−0.117133	+	0.0426328i	−0.399922	−	0.916549i	$-0.630963\pi$
$199$	−1.65236	+	0.601410i	−0.117133	+	0.0426328i	0.282789	+	0.959182i	$0.408740\pi$
$200$	−2.92538	+	3.92947i	−0.206856	+	0.277855i
$201$	11.1293	−	5.76499i	0.785001	−	0.406631i
$202$	4.23989	−	4.49402i	0.298318	−	0.316198i
$203$	6.58447	−	6.97913i	0.462139	−	0.489839i
$204$	−0.0615421	+	1.34706i	−0.00430881	+	0.0943128i
$205$	−4.64803	+	6.24338i	−0.324632	+	0.436057i
$206$	6.42671	−	2.33913i	0.447770	−	0.162975i
$207$	13.4506	−	14.9918i	0.934882	−	1.04201i
$208$	−10.2169	−	3.71864i	−0.708413	−	0.257841i
$209$	14.7098	−	9.67476i	1.01749	−	0.669217i
$210$	−1.33073	+	0.899311i	−0.0918294	+	0.0620583i
$211$	−2.13583	−	2.86892i	−0.147037	−	0.197504i	0.722503	−	0.691368i	$-0.242992\pi$
$211$	−2.13583	−	2.86892i	−0.147037	−	0.197504i	−0.869539	+	0.493864i	$0.835584\pi$
$212$	−9.15269	−	6.01982i	−0.628609	−	0.413443i
$213$	−13.2652	+	23.6552i	−0.908915	+	1.62083i
$214$	−1.75134	+	5.84989i	−0.119719	+	0.399890i
$215$	7.43730	−	12.8818i	0.507220	−	0.878530i
$216$	7.22062	+	2.32489i	0.491301	+	0.158189i
$217$	6.33898	+	10.9794i	0.430318	+	0.745333i
$218$	2.97730	−	0.705633i	0.201648	−	0.0477915i
$219$	8.82628	+	7.21972i	0.596425	+	0.487863i
$220$	−10.3821	+	5.21408i	−0.699960	+	0.351533i
$221$	0.571274	−	1.32436i	0.0384280	−	0.0890862i
$222$	0.0891598	−	0.311982i	0.00598402	−	0.0209389i
$223$	0.381494	+	6.55001i	0.0255468	+	0.438621i	0.986694	+	0.162586i	$0.0519835\pi$
$223$	0.381494	+	6.55001i	0.0255468	+	0.438621i	−0.961148	+	0.276035i	$0.910979\pi$
$224$	−1.36551	−	7.74417i	−0.0912368	−	0.517429i
$225$	8.26971	−	5.74083i	0.551314	−	0.382722i
$226$	0.113106	−	0.641454i	0.00752367	−	0.0426689i
$227$	8.07328	+	0.943631i	0.535843	+	0.0626310i	0.379711	−	0.925105i	$-0.376023\pi$
$227$	8.07328	+	0.943631i	0.535843	+	0.0626310i	0.156132	+	0.987736i	$0.450098\pi$
$228$	3.46684	+	11.0734i	0.229597	+	0.733355i
$229$	−2.24705	−	7.50566i	−0.148489	−	0.495988i	0.851089	−	0.525021i	$-0.175942\pi$
$229$	−2.24705	−	7.50566i	−0.148489	−	0.495988i	−0.999578	+	0.0290329i	$0.990757\pi$
$230$	3.17094	+	0.751528i	0.209086	+	0.0495543i
$231$	16.0125	−	2.07516i	1.05354	−	0.136536i
$232$	−2.90409	−	6.73245i	−0.190663	−	0.442007i
$233$	−19.7955	−	16.6104i	−1.29685	−	1.08818i	−0.990681	−	0.136205i	$-0.956509\pi$
$233$	−19.7955	−	16.6104i	−1.29685	−	1.08818i	−0.306166	−	0.951978i	$-0.599046\pi$
$234$	−3.05420	−	2.43508i	−0.199659	−	0.159186i
$235$	5.95818	−	4.99951i	0.388669	−	0.326132i
$236$	−9.34979	−	4.69564i	−0.608619	−	0.305660i
$237$	−3.88671	+	5.35959i	−0.252469	+	0.348143i
$238$	0.301168	−	0.0352015i	0.0195218	−	0.00228177i
$239$	−0.0102090	+	0.175281i	−0.000660364	+	0.0113380i	−0.998622	−	0.0524749i	$-0.983289\pi$
$239$	−0.0102090	+	0.175281i	−0.000660364	+	0.0113380i	0.997962	+	0.0638129i	$0.0203261\pi$
$240$	−1.30555	−	6.89786i	−0.0842728	−	0.445255i
$241$	−13.2643	−	14.0594i	−0.854430	−	0.905643i	0.142017	−	0.989864i	$-0.454641\pi$
$241$	−13.2643	−	14.0594i	−0.854430	−	0.905643i	−0.996447	+	0.0842212i	$0.973160\pi$
$242$	−4.84915			−0.311715
$243$	−12.5450	−	9.25320i	−0.804765	−	0.593593i
$244$	5.16534			0.330677
$245$	2.94818	+	3.12489i	0.188352	+	0.199642i
$246$	−0.740076	−	3.91019i	−0.0471855	−	0.249305i
$247$	0.721640	−	12.3901i	0.0459168	−	0.788362i
$248$	9.62248	−	1.12471i	0.611028	−	0.0714190i
$249$	4.93267	−	6.80193i	0.312595	−	0.431055i
$250$	3.62434	+	1.82021i	0.229223	+	0.115120i
$251$	18.5138	−	15.5349i	1.16858	−	0.980554i	0.168592	−	0.985686i	$-0.446078\pi$
$251$	18.5138	−	15.5349i	1.16858	−	0.980554i	0.999987	+	0.00513137i	$0.00163337\pi$
$252$	−1.58482	+	10.5227i	−0.0998344	+	0.662865i
$253$	−25.0962	−	21.0582i	−1.57778	−	1.32392i
$254$	−0.765662	−	1.77500i	−0.0480419	−	0.111374i
$255$	0.923569	−	0.119691i	0.0578361	−	0.00749537i
$256$	5.57410	+	1.32109i	0.348381	+	0.0825679i
$257$	3.92685	+	13.1166i	0.244950	+	0.818191i	0.988723	+	0.149758i	$0.0478494\pi$
$257$	3.92685	+	13.1166i	0.244950	+	0.818191i	−0.743773	+	0.668433i	$0.766965\pi$
$258$	2.27224	+	7.25776i	0.141464	+	0.451848i
$259$	0.939084	+	0.109763i	0.0583518	+	0.00682035i
$260$	−1.42213	+	8.06530i	−0.0881968	+	0.500189i
$261$	1.25251	+	15.0152i	0.0775286	+	0.929417i
$262$	0.765846	+	4.34333i	0.0473141	+	0.268332i
$263$	0.844392	+	14.4977i	0.0520675	+	0.893964i	0.918685	+	0.394991i	$0.129252\pi$
$263$	0.844392	+	14.4977i	0.0520675	+	0.893964i	−0.866618	+	0.498973i	$0.833711\pi$
$264$	3.39040	−	11.8634i	0.208664	−	0.730144i
$265$	−2.99667	+	6.94706i	−0.184084	+	0.426754i
$266$	2.33164	−	1.17099i	0.142962	−	0.0717983i
$267$	13.9611	+	11.4199i	0.854403	+	0.698885i
$268$	13.0738	−	3.09855i	0.798610	−	0.189274i
$269$	0.0908847	+	0.157417i	0.00554134	+	0.00959788i	0.868783	−	0.495193i	$-0.164903\pi$
$269$	0.0908847	+	0.157417i	0.00554134	+	0.00959788i	−0.863241	+	0.504791i	$0.831569\pi$
$270$	0.344364	−	2.49853i	0.0209573	−	0.152055i
$271$	−10.1446	+	17.5709i	−0.616239	+	1.06736i	0.373927	+	0.927458i	$0.378011\pi$
$271$	−10.1446	+	17.5709i	−0.616239	+	1.06736i	−0.990166	+	0.139899i	$0.955322\pi$
$272$	−0.380118	+	1.26968i	−0.0230481	+	0.0769859i
$273$	5.56712	−	9.92760i	0.336937	−	0.600846i
$274$	1.56658	+	1.03036i	0.0946408	+	0.0622462i
$275$	−9.77812	−	13.1343i	−0.589643	−	0.792028i
$276$	17.8891	−	12.0895i	1.07680	−	0.727700i
$277$	9.30636	−	6.12089i	0.559165	−	0.367769i	−0.238246	−	0.971205i	$-0.576573\pi$
$277$	9.30636	−	6.12089i	0.559165	−	0.367769i	0.797411	+	0.603436i	$0.206202\pi$
$278$	5.98603	+	2.17874i	0.359018	+	0.130672i
$279$	−19.4809	−	4.10467i	−1.16629	−	0.245740i
$280$	−3.36063	+	1.22317i	−0.200836	+	0.0730983i
$281$	1.19622	−	1.60680i	0.0713603	−	0.0958535i	−0.765010	−	0.644018i	$-0.777266\pi$
$281$	1.19622	−	1.60680i	0.0713603	−	0.0958535i	0.836370	+	0.548165i	$0.184673\pi$
$282$	−0.181491	+	3.97255i	−0.0108076	+	0.236562i
$283$	−1.56990	+	1.66400i	−0.0933210	+	0.0989145i	−0.772351	−	0.635196i	$-0.780919\pi$
$283$	−1.56990	+	1.66400i	−0.0933210	+	0.0989145i	0.679030	+	0.734111i	$0.262401\pi$
$284$	−19.9510	+	21.1468i	−1.18387	+	1.25483i
$285$	7.11572	−	3.68595i	0.421499	−	0.218337i
$286$	−3.79402	+	5.09625i	−0.224345	+	0.301348i
$287$	10.8968	−	3.96612i	0.643219	−	0.234112i
$288$	10.4838	+	6.52514i	0.617762	+	0.384498i
$289$	15.8096	+	5.75421i	0.929974	+	0.338483i
$290$	−2.03678	+	1.33961i	−0.119604	+	0.0786646i
$291$	−0.264711	−	3.73787i	−0.0155177	−	0.219118i
$292$	7.29950	+	9.80492i	0.427171	+	0.573790i
$293$	−4.19171	−	2.75693i	−0.244882	−	0.161061i	0.421135	−	0.906998i	$-0.361632\pi$
$293$	−4.19171	−	2.75693i	−0.244882	−	0.161061i	−0.666017	+	0.745936i	$0.732002\pi$
$294$	−2.19637	+	0.0275066i	−0.128095	+	0.00160422i
$295$	−2.07240	+	6.92231i	−0.120660	+	0.403032i
$296$	0.361248	−	0.625699i	0.0209971	−	0.0363680i
$297$	−14.3665	+	20.8924i	−0.833629	+	1.21230i
$298$	3.29840	+	5.71300i	0.191071	+	0.330945i
$299$	−22.4714	+	5.32582i	−1.29955	+	0.308000i
$300$	10.0938	−	3.81765i	0.582766	−	0.220412i
$301$	−19.8034	+	9.94563i	−1.14145	+	0.573257i
$302$	−0.967862	+	2.24376i	−0.0556942	+	0.129114i
$303$	−27.4253	+	6.86376i	−1.57554	+	0.394313i
$304$	0.663122	+	11.3854i	0.0380327	+	0.652996i
$305$	−0.619464	−	3.51316i	−0.0354704	−	0.201163i
$306$	−0.274686	+	0.388935i	−0.0157027	+	0.0222340i
$307$	3.72532	−	21.1273i	0.212615	−	1.20580i	−0.672382	−	0.740204i	$-0.734729\pi$
$307$	3.72532	−	21.1273i	0.212615	−	1.20580i	0.884997	−	0.465596i	$-0.154160\pi$
$308$	17.1915	+	2.00940i	0.979577	+	0.114496i
$309$	−30.5390	−	6.83513i	−1.73730	−	0.388837i
$310$	−0.923833	−	3.08582i	−0.0524702	−	0.175263i
$311$	−11.7156	−	2.77665i	−0.664332	−	0.157450i	−0.115403	−	0.993319i	$-0.536816\pi$
$311$	−11.7156	−	2.77665i	−0.664332	−	0.157450i	−0.548929	+	0.835869i	$0.684964\pi$
$312$	−5.28085	−	6.91101i	−0.298969	−	0.391259i
$313$	3.68811	+	8.54999i	0.208464	+	0.483274i	0.990083	−	0.140482i	$-0.0448652\pi$
$313$	3.68811	+	8.54999i	0.208464	+	0.483274i	−0.781619	+	0.623756i	$0.785606\pi$
$314$	−3.70327	−	3.10741i	−0.208988	−	0.175361i
$315$	7.34695	−	0.184051i	0.413954	−	0.0103701i
$316$	−5.43668	+	4.56191i	−0.305837	+	0.256628i
$317$	14.6362	+	7.35057i	0.822051	+	0.412849i	0.809534	−	0.587072i	$-0.199720\pi$
$317$	14.6362	+	7.35057i	0.822051	+	0.412849i	0.0125161	+	0.999922i	$0.496016\pi$
$318$	−1.57651	−	3.53245i	−0.0884060	−	0.198090i
$319$	24.3419	−	2.84516i	1.36288	−	0.159298i
$320$	0.355173	−	6.09809i	0.0198548	−	0.340894i
$321$	21.1780	−	18.2272i	1.18204	−	1.01734i
$322$	−3.33171	−	3.53141i	−0.185669	−	0.196798i
$323$	−1.51290			−0.0841803
$324$	−10.6374	−	12.8874i	−0.590968	−	0.715966i
$325$	−11.5428			−0.640277
$326$	−0.155822	−	0.165161i	−0.00863016	−	0.00914744i
$327$	−13.2155	−	4.62346i	−0.730817	−	0.255678i
$328$	0.515239	−	8.84632i	0.0284493	−	0.488456i
$329$	−11.5093	+	1.34524i	−0.634528	+	0.0741656i
$330$	−4.08027	−	0.425193i	−0.224612	−	0.0234061i
$331$	−4.58340	−	2.30187i	−0.251926	−	0.126522i	0.318355	−	0.947972i	$-0.396870\pi$
$331$	−4.58340	−	2.30187i	−0.251926	−	0.126522i	−0.570281	+	0.821449i	$0.693166\pi$
$332$	6.89976	−	5.78959i	0.378673	−	0.317745i
$333$	−1.11310	+	0.982542i	−0.0609976	+	0.0538429i
$334$	0.879884	+	0.738310i	0.0481451	+	0.0403985i
$335$	−3.67535	−	8.52043i	−0.200806	−	0.465521i
$336$	−4.02203	+	9.65479i	−0.219420	+	0.526712i
$337$	12.1868	+	2.88834i	0.663860	+	0.157338i	0.548713	−	0.836011i	$-0.315118\pi$
$337$	12.1868	+	2.88834i	0.663860	+	0.157338i	0.115147	+	0.993348i	$0.463266\pi$
$338$	−0.126797	−	0.423533i	−0.00689687	−	0.0230372i
$339$	−2.01799	+	2.19333i	−0.109602	+	0.119126i
$340$	0.991574	+	0.115898i	0.0537756	+	0.00628547i
$341$	−5.62311	+	31.8903i	−0.304509	+	1.72695i
$342$	−1.07645	+	3.95335i	−0.0582075	+	0.213773i
$343$	−3.43362	−	19.4730i	−0.185398	−	1.05144i
$344$	0.984635	+	16.9055i	0.0530880	+	0.911486i
$345$	−10.3679	−	10.7172i	−0.558190	−	0.576997i
$346$	1.44762	−	3.35597i	0.0778247	−	0.180418i
$347$	−12.5791	+	6.31748i	−0.675284	+	0.339140i	−0.753174	−	0.657822i	$-0.771478\pi$
$347$	−12.5791	+	6.31748i	−0.675284	+	0.339140i	0.0778899	+	0.996962i	$0.475182\pi$
$348$	−2.60533	+	15.9403i	−0.139660	+	0.854492i
$349$	−14.9834	+	3.55113i	−0.802043	+	0.190088i	−0.611141	−	0.791522i	$-0.709289\pi$
$349$	−14.9834	+	3.55113i	−0.802043	+	0.190088i	−0.190902	+	0.981609i	$0.561141\pi$
$350$	−1.21331	−	2.10152i	−0.0648544	−	0.112331i
$351$	5.76572	+	16.9181i	0.307751	+	0.903020i
$352$	10.0427	−	17.3945i	0.535278	−	0.927129i
$353$	−9.63269	+	32.1754i	−0.512696	+	1.71252i	0.173255	+	0.984877i	$0.444572\pi$
$353$	−9.63269	+	32.1754i	−0.512696	+	1.71252i	−0.685951	+	0.727648i	$0.740614\pi$
$354$	−1.88715	−	3.17612i	−0.100301	−	0.168809i
$355$	16.7755	+	11.0334i	0.890349	+	0.585592i
$356$	11.5461	+	15.5091i	0.611940	+	0.821978i
$357$	−1.24758	−	0.607116i	−0.0660290	−	0.0321320i
$358$	−8.16328	+	5.36907i	−0.431443	+	0.283764i
$359$	11.6368	+	4.23546i	0.614168	+	0.223539i	0.630326	−	0.776330i	$-0.282921\pi$
$359$	11.6368	+	4.23546i	0.614168	+	0.223539i	−0.0161577	+	0.999869i	$0.505143\pi$
$360$	2.09455	−	5.21079i	0.110392	−	0.274633i
$361$	5.62081	−	2.04581i	0.295832	−	0.107674i
$362$	−0.201584	+	0.270774i	−0.0105950	+	0.0142316i
$363$	18.6896	+	11.9598i	0.980950	+	0.627725i
$364$	8.37301	−	8.87487i	0.438865	−	0.465169i
$365$	5.79332	−	6.14056i	0.303236	−	0.321412i
$366$	1.53630	+	0.983103i	0.0803037	+	0.0513876i
$367$	17.1370	−	23.0189i	0.894543	−	1.20158i	−0.0841921	−	0.996450i	$-0.526831\pi$
$367$	17.1370	−	23.0189i	0.894543	−	1.20158i	0.978735	−	0.205130i	$-0.0657617\pi$
$368$	19.9414	−	7.25809i	1.03952	−	0.378354i
$369$	−6.79155	+	16.8960i	−0.353554	+	0.879569i
$370$	−0.225734	−	0.0821603i	−0.0117353	−	0.00427131i
$371$	9.41740	−	6.19392i	0.488927	−	0.321572i
$372$	−19.1900	−	9.33853i	−0.994957	−	0.484180i
$373$	11.3384	+	15.2301i	0.587080	+	0.788586i	0.992063	−	0.125738i	$-0.0401300\pi$
$373$	11.3384	+	15.2301i	0.587080	+	0.788586i	−0.404983	+	0.914324i	$0.632723\pi$
$374$	0.647071	+	0.425586i	0.0334593	+	0.0220065i
$375$	−9.47964	−	15.9544i	−0.489526	−	0.823882i
$376$	−2.53959	+	8.48281i	−0.130969	+	0.437468i
$377$	8.63804	−	14.9615i	0.444882	−	0.770557i
$378$	−2.47411	+	2.82807i	−0.127255	+	0.145460i
$379$	−9.40390	−	16.2880i	−0.483046	−	0.836660i	0.516764	−	0.856128i	$-0.327136\pi$
$379$	−9.40390	−	16.2880i	−0.483046	−	0.836660i	−0.999810	+	0.0194673i	$0.993803\pi$
$380$	8.35896	−	1.98111i	0.428806	−	0.101629i
$381$	−1.42679	+	8.72963i	−0.0730968	+	0.447233i
$382$	2.73127	−	1.37170i	0.139744	−	0.0701821i
$383$	2.63824	−	6.11612i	0.134808	−	0.312519i	−0.837419	−	0.546562i	$-0.815936\pi$
$383$	2.63824	−	6.11612i	0.134808	−	0.312519i	0.972226	+	0.234043i	$0.0751955\pi$
$384$	12.0857	+	12.4929i	0.616744	+	0.637524i
$385$	−0.695054	−	11.9336i	−0.0354233	−	0.608194i
$386$	−0.0128038	−	0.0726138i	−0.000651695	−	0.00369595i
$387$	9.14259	−	33.5771i	0.464744	−	1.70682i
$388$	0.697536	−	3.95592i	0.0354120	−	0.200832i
$389$	−0.868765	−	0.101544i	−0.0440481	−	0.00514849i	0.0940403	−	0.995568i	$-0.470022\pi$
$389$	−0.868765	−	0.101544i	−0.0440481	−	0.00514849i	−0.138088	+	0.990420i	$0.544096\pi$
$390$	−1.95802	+	2.12815i	−0.0991484	+	0.107763i
$391$	0.807390	+	2.69687i	0.0408315	+	0.136387i
$392$	−4.75915	−	1.12794i	−0.240373	−	0.0569695i
$393$	7.76051	−	18.6289i	0.391466	−	0.939706i
$394$	−1.72958	−	4.00961i	−0.0871347	−	0.202001i
$395$	3.75475	+	3.15061i	0.188922	+	0.158524i
$396$	−20.3772	+	17.9871i	−1.02399	+	0.903884i
$397$	26.1379	−	21.9323i	1.31182	−	1.10075i	0.323854	−	0.946107i	$-0.395021\pi$
$397$	26.1379	−	21.9323i	1.31182	−	1.10075i	0.987970	−	0.154644i	$-0.0494231\pi$
$398$	−0.594802	−	0.298721i	−0.0298147	−	0.0149735i
$399$	−11.8747	−	1.23743i	−0.594480	−	0.0619490i
$400$	10.5350	−	1.23137i	0.526752	−	0.0615685i
$401$	0.244187	−	4.19252i	0.0121941	−	0.209364i	−0.986707	−	0.162507i	$-0.948042\pi$
$401$	0.244187	−	4.19252i	0.0121941	−	0.209364i	0.998902	−	0.0468580i	$-0.0149208\pi$
$402$	4.47822	+	1.56671i	0.223353	+	0.0781405i
$403$	15.6649	+	16.6038i	0.780325	+	0.827096i
$404$	−30.3060			−1.50778
$405$	−7.48953	+	8.78050i	−0.372157	+	0.436307i
$406$	3.63194			0.180250
$407$	1.65724	+	1.75657i	0.0821463	+	0.0870699i
$408$	−0.803595	+	0.691628i	−0.0397839	+	0.0342407i
$409$	−1.26061	+	21.6439i	−0.0623333	+	1.07022i	0.811612	+	0.584197i	$0.198590\pi$
$409$	−1.26061	+	21.6439i	−0.0623333	+	1.07022i	−0.873945	+	0.486025i	$0.838447\pi$
$410$	−2.92635	+	0.342042i	−0.144522	+	0.0168922i
$411$	−3.49669	−	7.83498i	−0.172479	−	0.386471i
$412$	−29.9787	−	15.0559i	−1.47695	−	0.741750i
$413$	8.24668	−	6.91978i	0.405792	−	0.340500i
$414$	7.62162	−	0.190931i	0.374582	−	0.00938376i
$415$	−4.76520	−	3.99848i	−0.233915	−	0.196278i
$416$	−5.60799	−	13.0008i	−0.274954	−	0.637416i
$417$	−17.6978	−	23.1610i	−0.866665	−	1.13420i
$418$	6.48474	+	1.53691i	0.317179	+	0.0751728i
$419$	1.20046	+	4.00981i	0.0586462	+	0.195892i	0.982292	−	0.187354i	$-0.0599912\pi$
$419$	1.20046	+	4.00981i	0.0586462	+	0.195892i	−0.923646	+	0.383246i	$0.874806\pi$
$420$	7.68803	+	1.72071i	0.375137	+	0.0839618i
$421$	−4.93643	−	0.576986i	−0.240587	−	0.0281206i	−0.00505515	−	0.999987i	$-0.501609\pi$
$421$	−4.93643	−	0.576986i	−0.240587	−	0.0281206i	−0.235532	+	0.971867i	$0.575683\pi$
$422$	0.235094	−	1.33328i	0.0114442	−	0.0649033i
$423$	10.4973	−	14.8634i	0.510394	−	0.722682i
$424$	−1.49570	−	8.48255i	−0.0726377	−	0.411949i
$425$	0.0818132	+	1.40468i	0.00396852	+	0.0681369i
$426$	−9.95873	+	2.49238i	−0.482502	+	0.120756i
$427$	−2.10506	+	4.88007i	−0.101871	+	0.236163i
$428$	26.7668	−	13.4428i	1.29382	−	0.649783i
$429$	27.1921	−	10.2846i	1.31285	−	0.496543i
$430$	5.47864	−	1.29846i	0.264204	−	0.0626174i
$431$	−13.2418	−	22.9355i	−0.637837	−	1.10477i	−0.985907	−	0.167297i	$-0.946496\pi$
$431$	−13.2418	−	22.9355i	−0.637837	−	1.10477i	0.348070	−	0.937469i	$-0.386837\pi$
$432$	−7.06716	−	14.8260i	−0.340019	−	0.713316i
$433$	−10.6919	+	18.5189i	−0.513820	+	0.889962i	0.486052	+	0.873930i	$0.338437\pi$
$433$	−10.6919	+	18.5189i	−0.513820	+	0.889962i	−0.999871	+	0.0160319i	$0.994897\pi$
$434$	−1.37635	+	4.59732i	−0.0660668	+	0.220679i
$435$	11.1541	−	0.139691i	0.534799	−	0.00669766i
$436$	−12.5395	−	8.24738i	−0.600535	−	0.394978i
$437$	14.4656	+	19.4307i	0.691984	+	0.929496i
$438$	0.304912	+	4.30552i	0.0145692	+	0.205726i
$439$	−26.9943	+	17.7544i	−1.28837	+	0.847372i	−0.994112	−	0.108355i	$-0.965442\pi$
$439$	−26.9943	+	17.7544i	−1.28837	+	0.847372i	−0.294255	+	0.955727i	$0.595071\pi$
$440$	−8.58376	−	3.12423i	−0.409215	−	0.148942i
$441$	8.53309	+	5.31103i	0.406338	+	0.252906i
$442$	0.513029	−	0.186727i	0.0244023	−	0.00888171i
$443$	−19.4171	+	26.0817i	−0.922535	+	1.23918i	0.0481536	+	0.998840i	$0.484666\pi$
$443$	−19.4171	+	26.0817i	−0.922535	+	1.23918i	−0.970689	+	0.240340i	$0.922741\pi$
$444$	−1.41323	+	0.732056i	−0.0670691	+	0.0347418i
$445$	9.16365	−	9.71291i	0.434399	−	0.460436i
$446$	−1.70431	+	1.80646i	−0.0807015	+	0.0855385i
$447$	1.37763	−	30.1541i	0.0651598	−	1.42624i
$448$	−5.43443	+	7.29971i	−0.256753	+	0.344879i
$449$	15.0197	−	5.46673i	0.708825	−	0.257991i	0.0376508	−	0.999291i	$-0.488013\pi$
$449$	15.0197	−	5.46673i	0.708825	−	0.257991i	0.671174	+	0.741300i	$0.265790\pi$
$450$	3.72875	+	0.785656i	0.175775	+	0.0370362i
$451$	27.8328	+	10.1303i	1.31059	+	0.477017i
$452$	−2.66935	+	1.75566i	−0.125556	+	0.0825793i
$453$	9.26427	−	6.26080i	0.435273	−	0.294158i
$454$	1.83730	+	2.46793i	0.0862289	+	0.115826i
$455$	−7.04031	−	4.63049i	−0.330055	−	0.217081i
$456$	−4.46236	+	7.95753i	−0.208969	+	0.372646i
$457$	−5.53279	+	18.4808i	−0.258813	+	0.864495i	0.725524	+	0.688197i	$0.241597\pi$
$457$	−5.53279	+	18.4808i	−0.258813	+	0.864495i	−0.984337	+	0.176298i	$0.943588\pi$
$458$	1.48283	−	2.56834i	0.0692883	−	0.120011i
$459$	2.01795	−	0.821562i	0.0941899	−	0.0383472i
$460$	−7.99240	−	13.8432i	−0.372648	−	0.645445i
$461$	14.4202	−	3.41765i	0.671615	−	0.159176i	0.119360	−	0.992851i	$-0.461916\pi$
$461$	14.4202	−	3.41765i	0.671615	−	0.159176i	0.552255	+	0.833675i	$0.313767\pi$
$462$	4.73074	+	3.86965i	0.220094	+	0.180033i
$463$	2.47485	−	1.24292i	0.115016	−	0.0577632i	−0.390361	−	0.920662i	$-0.627650\pi$
$463$	2.47485	−	1.24292i	0.115016	−	0.0577632i	0.505377	+	0.862899i	$0.331353\pi$
$464$	−6.28783	+	14.5768i	−0.291905	+	0.676713i
$465$	−4.05011	+	14.1719i	−0.187819	+	0.657205i
$466$	−0.568746	−	9.76499i	−0.0263466	−	0.452354i
$467$	3.42252	+	19.4101i	0.158375	+	0.898191i	0.955635	+	0.294554i	$0.0951712\pi$
$467$	3.42252	+	19.4101i	0.158375	+	0.898191i	−0.797259	+	0.603637i	$0.793718\pi$
$468$	1.59273	+	19.0938i	0.0736240	+	0.882609i
$469$	−2.40061	+	13.6145i	−0.110850	+	0.628661i
$470$	2.92421	+	0.341791i	0.134884	+	0.0157656i
$471$	6.60914	+	21.1102i	0.304533	+	0.972707i
$472$	−2.35935	−	7.88079i	−0.108598	−	0.362743i
$473$	−55.0770	−	13.0535i	−2.53244	−	0.600200i
$474$	−2.48526	+	0.322081i	−0.114152	+	0.0147937i
$475$	4.79560	+	11.1174i	0.220037	+	0.510103i
$476$	−1.13936	−	0.956036i	−0.0522224	−	0.0438198i
$477$	−2.63614	+	17.5030i	−0.120700	+	0.801408i
$478$	−0.0509120	+	0.0427202i	−0.00232866	+	0.00195398i
$479$	16.6577	+	8.36582i	0.761110	+	0.382244i	0.786625	−	0.617431i	$-0.211826\pi$
$479$	16.6577	+	8.36582i	0.761110	+	0.382244i	−0.0255152	+	0.999674i	$0.508123\pi$
$480$	5.36707	−	7.40094i	0.244972	−	0.337805i
$481$	1.69085	−	0.197632i	0.0770962	−	0.00901125i
$482$	0.425416	−	7.30411i	0.0193772	−	0.332693i
$483$	4.13136	+	21.8280i	0.187983	+	0.993209i
$484$	16.3228	+	17.3011i	0.741945	+	0.786415i
$485$	−2.77424			−0.125972
$486$	−0.711020	−	5.85763i	−0.0322525	−	0.265707i
$487$	−5.34343			−0.242134			−0.121067	−	0.992644i	$-0.538632\pi$
$487$	−5.34343			−0.242134			−0.121067	+	0.992644i	$0.538632\pi$
$488$	2.78703	+	2.95408i	0.126163	+	0.133725i
$489$	0.193220	+	1.02088i	0.00873772	+	0.0461657i
$490$	−0.0945547	+	1.62344i	−0.00427155	+	0.0733396i
$491$	−3.67611	+	0.429676i	−0.165901	+	0.0193910i	−0.198638	−	0.980073i	$-0.563652\pi$
$491$	−3.67611	+	0.429676i	−0.165901	+	0.0193910i	0.0327371	+	0.999464i	$0.489578\pi$
$492$	−11.4599	+	15.8026i	−0.516651	+	0.712438i
$493$	−1.88194	−	0.945147i	−0.0847584	−	0.0425673i
$494$	3.59880	−	3.01975i	0.161918	−	0.135865i
$495$	14.6775	+	11.7022i	0.659705	+	0.525976i
$496$	−16.0686	−	13.4832i	−0.721501	−	0.605411i
$497$	−11.8482	−	27.4672i	−0.531464	−	1.23207i
$498$	3.15408	−	0.408758i	0.141338	−	0.0183169i
$499$	−27.1971	−	6.44583i	−1.21751	−	0.288555i	−0.428844	−	0.903379i	$-0.641079\pi$
$499$	−27.1971	−	6.44583i	−1.21751	−	0.288555i	−0.788664	+	0.614824i	$0.789227\pi$
$500$	−5.70565	−	19.0582i	−0.255165	−	0.852309i
$501$	−1.57031	−	5.01571i	−0.0701562	−	0.224086i
$502$	9.08634	+	1.06204i	0.405543	+	0.0474012i
$503$	−1.72317	+	9.77258i	−0.0768323	+	0.435738i	0.921990	+	0.387214i	$0.126563\pi$
$503$	−1.72317	+	9.77258i	−0.0768323	+	0.435738i	−0.998822	+	0.0485234i	$0.984548\pi$
$504$	−6.87307	+	4.77128i	−0.306151	+	0.212530i
$505$	3.63452	+	20.6124i	0.161734	+	0.917239i
$506$	−0.721039	−	12.3798i	−0.0320541	−	0.550348i
$507$	−0.555884	+	1.94511i	−0.0246877	+	0.0863854i
$508$	−3.75568	+	8.70665i	−0.166631	+	0.386295i
$509$	−0.0252818	+	0.0126970i	−0.00112059	+	0.000562784i	−0.449359	−	0.893351i	$-0.648348\pi$
$509$	−0.0252818	+	0.0126970i	−0.00112059	+	0.000562784i	0.448239	+	0.893914i	$0.352051\pi$
$510$	0.272860	+	0.223194i	0.0120825	+	0.00988322i
$511$	−12.2382	+	2.90051i	−0.541387	+	0.128311i
$512$	11.1197	+	19.2599i	0.491426	+	0.851176i
$513$	13.8992	−	12.5821i	0.613667	−	0.555513i
$514$	−2.59134	+	4.48834i	−0.114299	+	0.197972i
$515$	−6.64486	+	22.1954i	−0.292808	+	0.978045i
$516$	18.2461	−	32.5375i	0.803240	−	1.43238i
$517$	−24.7282	−	16.2640i	−1.08754	−	0.715289i
$518$	0.213715	+	0.287069i	0.00939010	+	0.0126131i
$519$	−13.8565	+	9.36422i	−0.608232	+	0.411044i
$520$	−5.37992	+	3.53843i	−0.235925	+	0.155170i
$521$	−2.11604	−	0.770177i	−0.0927056	−	0.0337421i	0.295251	−	0.955420i	$-0.404597\pi$
$521$	−2.11604	−	0.770177i	−0.0927056	−	0.0337421i	−0.387957	+	0.921678i	$0.626819\pi$
$522$	−3.80877	+	4.24519i	−0.166705	+	0.185807i
$523$	−11.5433	+	4.20142i	−0.504753	+	0.183715i	−0.581831	−	0.813310i	$-0.697663\pi$
$523$	−11.5433	+	4.20142i	−0.504753	+	0.183715i	0.0770775	+	0.997025i	$0.475441\pi$
$524$	12.9185	−	17.3526i	0.564348	−	0.758051i
$525$	−0.506761	+	11.0922i	−0.0221169	+	0.484102i
$526$	−3.77229	+	3.99839i	−0.164480	+	0.174338i
$527$	1.90955	−	2.02400i	0.0831811	−	0.0881669i
$528$	−23.7210	+	12.2875i	−1.03233	+	0.534745i
$529$	13.1822	−	17.7068i	0.573141	−	0.769862i
$530$	−2.69114	+	0.979495i	−0.116896	+	0.0425465i
$531$	−0.559991	+	16.8958i	−0.0243015	+	0.733216i
$532$	−12.0265	−	4.37730i	−0.521416	−	0.189780i
$533$	17.4444	−	11.4733i	0.755599	−	0.496965i
$534$	0.482297	+	6.81031i	0.0208710	+	0.294711i
$535$	−12.3531	−	16.5931i	−0.534070	−	0.717381i
$536$	8.82624	+	5.80511i	0.381235	+	0.250742i
$537$	44.7050	−	0.559872i	1.92917	−	0.0241602i
$538$	−0.0197333	+	0.0659138i	−0.000850762	+	0.00284174i
$539$	8.17409	−	14.1579i	0.352083	−	0.609826i
$540$	−10.0736	+	7.18167i	−0.433498	+	0.309050i
$541$	19.8474	+	34.3766i	0.853304	+	1.47797i	0.878209	+	0.478277i	$0.158738\pi$
$541$	19.8474	+	34.3766i	0.853304	+	1.47797i	−0.0249047	+	0.999690i	$0.507928\pi$
$542$	−7.47294	+	1.77112i	−0.320990	+	0.0760761i
$543$	1.44477	−	0.546439i	0.0620011	−	0.0234499i
$544$	−1.54236	+	0.774603i	−0.0661282	+	0.0332108i
$545$	−4.10555	+	9.51773i	−0.175862	+	0.407695i
$546$	4.17947	−	1.04600i	0.178865	−	0.0447647i
$547$	−0.472894	−	8.11928i	−0.0202195	−	0.347155i	−0.993212	−	0.116318i	$-0.962891\pi$
$547$	−0.472894	−	8.11928i	−0.0202195	−	0.347155i	0.972992	−	0.230837i	$-0.0741464\pi$
$548$	−1.59711	−	9.05767i	−0.0682252	−	0.386924i
$549$	−3.49653	−	7.57816i	−0.149228	−	0.323428i
$550$	1.07629	−	6.10396i	0.0458933	−	0.260274i
$551$	−17.9990	−	2.10378i	−0.766784	−	0.0896242i
$552$	16.5663	+	3.70782i	0.705110	+	0.157815i
$553$	−2.09433	−	6.99556i	−0.0890601	−	0.297482i
$554$	4.10268	+	0.972352i	0.174306	+	0.0413113i
$555$	0.667386	+	0.873404i	0.0283290	+	0.0370740i
$556$	−12.3762	−	28.6912i	−0.524867	−	1.21678i
$557$	−16.2629	−	13.6462i	−0.689081	−	0.578207i	0.229563	−	0.973294i	$-0.426270\pi$
$557$	−16.2629	−	13.6462i	−0.689081	−	0.578207i	−0.918644	+	0.395086i	$0.870715\pi$
$558$	−3.93023	−	6.42990i	−0.166380	−	0.272199i
$559$	−30.5658	+	25.6477i	−1.29279	+	1.08478i
$560$	6.91965	+	3.47518i	0.292408	+	0.146853i
$561$	−1.44430	−	3.23621i	−0.0609782	−	0.136633i
$562$	0.753127	−	0.0880279i	0.0317687	−	0.00371323i
$563$	2.62696	−	45.1032i	0.110713	−	1.90087i	−0.250078	−	0.968226i	$-0.580456\pi$
$563$	2.62696	−	45.1032i	0.110713	−	1.90087i	0.360791	−	0.932647i	$-0.382507\pi$
$564$	14.7844	−	12.7245i	0.622538	−	0.535798i
$565$	1.51422	+	1.60498i	0.0637038	+	0.0675221i
$566$	−0.865945			−0.0363984
$567$	16.5108	−	4.79789i	0.693388	−	0.201492i
$568$	−22.8588			−0.959134
$569$	−3.93683	−	4.17280i	−0.165041	−	0.174933i	0.639575	−	0.768728i	$-0.279110\pi$
$569$	−3.93683	−	4.17280i	−0.165041	−	0.174933i	−0.804616	+	0.593796i	$0.797629\pi$
$570$	2.86322	+	1.00170i	0.119927	+	0.0419568i
$571$	−2.52145	+	43.2916i	−0.105519	+	1.81170i	0.366831	+	0.930287i	$0.380443\pi$
$571$	−2.52145	+	43.2916i	−0.105519	+	1.81170i	−0.472351	+	0.881411i	$0.656594\pi$
$572$	30.9539	−	3.61799i	1.29425	−	0.151276i
$573$	−13.9100	−	1.44952i	−0.581098	−	0.0605545i
$574$	3.92254	+	1.96997i	0.163724	+	0.0822251i
$575$	17.2584	−	14.4816i	0.719727	−	0.603923i
$576$	−2.83325	−	14.0071i	−0.118052	−	0.583631i
$577$	10.1857	+	8.54680i	0.424035	+	0.355808i	0.829696	−	0.558216i	$-0.188514\pi$
$577$	10.1857	+	8.54680i	0.424035	+	0.355808i	−0.405660	+	0.914024i	$0.632958\pi$
$578$	2.52238	+	5.84754i	0.104917	+	0.243226i
$579$	−0.129744	+	0.311447i	−0.00539197	+	0.0129433i
$580$	11.6356	+	2.75768i	0.483141	+	0.114507i
$581$	2.65795	+	8.87816i	0.110270	+	0.368328i
$582$	0.960384	−	1.04383i	0.0398092	−	0.0432682i
$583$	28.5957	+	3.34236i	1.18431	+	0.138427i
$584$	−1.66894	+	9.46501i	−0.0690611	+	0.391665i
$585$	12.7954	−	3.37314i	0.529026	−	0.139462i
$586$	−0.329773	−	1.87024i	−0.0136228	−	0.0772588i
$587$	−0.719217	−	12.3485i	−0.0296853	−	0.509677i	−0.980077	−	0.198620i	$-0.936354\pi$
$587$	−0.719217	−	12.3485i	−0.0296853	−	0.509677i	0.950391	−	0.311057i	$-0.100683\pi$
$588$	7.49136	+	7.74376i	0.308938	+	0.319347i
$589$	9.48382	−	21.9860i	0.390774	−	0.905916i
$590$	−2.44424	+	1.22754i	−0.100628	+	0.0505371i
$591$	−3.22302	+	19.7196i	−0.132577	+	0.811156i
$592$	−1.52215	+	0.360757i	−0.0625601	+	0.0148270i
$593$	0.572367	+	0.991369i	0.0235043	+	0.0407106i	0.877538	−	0.479507i	$-0.159184\pi$
$593$	0.572367	+	0.991369i	0.0235043	+	0.0407106i	−0.854034	+	0.520217i	$0.825851\pi$
$594$	−9.48411	+	1.47148i	−0.389138	+	0.0603754i
$595$	−0.513599	+	0.889579i	−0.0210555	+	0.0364692i
$596$	9.28045	−	30.9989i	0.380142	−	1.26976i
$597$	1.55573	+	2.61833i	0.0636720	+	0.107161i
$598$	−7.30351	−	4.80360i	−0.298663	−	0.196434i
$599$	1.44868	+	1.94591i	0.0591913	+	0.0795078i	0.830733	−	0.556671i	$-0.187922\pi$
$599$	1.44868	+	1.94591i	0.0591913	+	0.0795078i	−0.771542	+	0.636179i	$0.780514\pi$
$600$	7.62959	+	3.71282i	0.311477	+	0.151575i
$601$	32.7732	−	21.5553i	1.33685	−	0.879259i	0.338748	−	0.940877i	$-0.389996\pi$
$601$	32.7732	−	21.5553i	1.33685	−	0.879259i	0.998100	+	0.0616181i	$0.0196261\pi$
$602$	−7.88244	−	2.86897i	−0.321264	−	0.116931i
$603$	−13.3959	−	17.0833i	−0.545522	−	0.695688i
$604$	11.2634	−	4.09953i	0.458300	−	0.166808i
$605$	9.80967	−	13.1767i	0.398820	−	0.535708i
$606$	−9.01378	−	5.76806i	−0.366160	−	0.234311i
$607$	4.86035	−	5.15167i	0.197276	−	0.209100i	−0.621183	−	0.783666i	$-0.713348\pi$
$607$	4.86035	−	5.15167i	0.197276	−	0.209100i	0.818458	+	0.574566i	$0.194829\pi$
$608$	−10.1918	+	10.8027i	−0.413333	+	0.438107i
$609$	−13.9982	−	8.95769i	−0.567237	−	0.362984i
$610$	0.806362	−	1.08313i	0.0326487	−	0.0438548i
$611$	−19.6057	+	7.13588i	−0.793161	+	0.288687i
$612$	2.31229	−	0.329158i	0.0934689	−	0.0133054i
$613$	19.4482	+	7.07855i	0.785503	+	0.285900i	0.703466	−	0.710729i	$-0.251635\pi$
$613$	19.4482	+	7.07855i	0.785503	+	0.285900i	0.0820378	+	0.996629i	$0.473857\pi$
$614$	6.78466	−	4.46234i	0.273806	−	0.180085i
$615$	12.1224	+	5.89916i	0.488821	+	0.237877i
$616$	8.12674	+	10.9161i	0.327436	+	0.439822i
$617$	19.9175	+	13.1000i	0.801849	+	0.527385i	0.883031	−	0.469315i	$-0.155499\pi$
$617$	19.9175	+	13.1000i	0.801849	+	0.527385i	−0.0811816	+	0.996699i	$0.525869\pi$
$618$	−6.05089	−	10.1838i	−0.243402	−	0.409651i
$619$	0.190902	−	0.637658i	0.00767301	−	0.0256296i	−0.954067	−	0.299592i	$-0.903149\pi$
$619$	0.190902	−	0.637658i	0.00767301	−	0.0256296i	0.961740	+	0.273963i	$0.0883345\pi$
$620$	−7.90007	+	13.6833i	−0.317274	+	0.549535i
$621$	−29.8462	−	18.0618i	−1.19769	−	0.724795i
$622$	−2.27875	−	3.94691i	−0.0913696	−	0.158257i
$623$	−19.3580	+	4.58792i	−0.775560	+	0.183811i
$624$	−3.03762	+	18.5853i	−0.121602	+	0.744006i
$625$	2.71571	−	1.36388i	0.108628	−	0.0545552i
$626$	−1.39604	+	3.23639i	−0.0557970	+	0.129352i
$627$	−21.2029	−	21.9173i	−0.846764	−	0.875293i
$628$	1.37878	+	23.6727i	0.0550192	+	0.944643i
$629$	−0.0360350	−	0.204365i	−0.00143681	−	0.00814855i
$630$	1.95912	+	1.97502i	0.0780530	+	0.0786867i
$631$	4.06193	−	23.0363i	0.161703	−	0.917062i	−0.790696	−	0.612209i	$-0.790281\pi$
$631$	4.06193	−	23.0363i	0.161703	−	0.917062i	0.952399	−	0.304854i	$-0.0986076\pi$
$632$	−5.54242	−	0.647816i	−0.220466	−	0.0257687i
$633$	−4.19447	+	4.55892i	−0.166715	+	0.181201i
$634$	1.77807	+	5.93915i	0.0706160	+	0.235874i
$635$	6.37216	+	1.51023i	0.252871	+	0.0599316i
$636$	−7.29663	+	17.5154i	−0.289330	+	0.694530i
$637$	−4.56453	−	10.5818i	−0.180853	−	0.419265i
$638$	7.10640	+	5.96298i	0.281345	+	0.236077i
$639$	44.5301	+	14.9557i	1.76158	+	0.591639i
$640$	9.85797	−	8.27182i	0.389670	−	0.326972i
$641$	6.36402	+	3.19613i	0.251364	+	0.126240i	0.570020	−	0.821631i	$-0.306935\pi$
$641$	6.36402	+	3.19613i	0.251364	+	0.126240i	−0.318657	+	0.947870i	$0.603232\pi$
$642$	10.5197	+	1.09622i	0.415178	+	0.0432645i
$643$	−15.3703	+	1.79653i	−0.606144	+	0.0708481i	−0.413628	−	0.910446i	$-0.635739\pi$
$643$	−15.3703	+	1.79653i	−0.606144	+	0.0708481i	−0.192516	+	0.981294i	$0.561665\pi$
$644$	−1.38469	+	23.7743i	−0.0545645	+	0.936837i
$645$	−24.3183	−	8.50780i	−0.957531	−	0.334994i
$646$	−0.392992	−	0.416547i	−0.0154620	−	0.0163888i
$647$	−15.3916			−0.605107			−0.302554	−	0.953132i	$-0.597839\pi$
$647$	−15.3916			−0.605107			−0.302554	+	0.953132i	$0.597839\pi$
$648$	1.63078	−	13.0372i	0.0640633	−	0.512149i
$649$	27.4968			1.07934
$650$	−2.99834	−	3.17806i	−0.117605	−	0.124654i
$651$	16.6434	−	14.3244i	0.652307	−	0.561419i
$652$	−0.0647610	+	1.11190i	−0.00253624	+	0.0435455i
$653$	1.22345	−	0.143001i	0.0478773	−	0.00559605i	−0.0921206	−	0.995748i	$-0.529365\pi$
$653$	1.22345	−	0.143001i	0.0478773	−	0.00559605i	0.139998	+	0.990152i	$0.455290\pi$
$654$	−2.15987	−	4.83959i	−0.0844577	−	0.189243i
$655$	−13.3515	−	6.70537i	−0.521686	−	0.262000i
$656$	−14.6975	+	12.3326i	−0.573839	+	0.481508i
$657$	9.44380	−	17.3464i	0.368438	−	0.676747i
$658$	−3.36003	−	2.81940i	−0.130988	−	0.109912i
$659$	2.73379	+	6.33763i	0.106493	+	0.246879i	0.963128	−	0.269045i	$-0.0867080\pi$
$659$	2.73379	+	6.33763i	0.106493	+	0.246879i	−0.856634	+	0.515924i	$0.827449\pi$
$660$	12.2176	+	15.9891i	0.475570	+	0.622376i
$661$	−34.9734	−	8.28885i	−1.36031	−	0.322399i	−0.515235	−	0.857049i	$-0.672295\pi$
$661$	−34.9734	−	8.28885i	−1.36031	−	0.322399i	−0.845073	+	0.534650i	$0.820443\pi$
$662$	−0.556810	−	1.85987i	−0.0216410	−	0.0722861i
$663$	−2.43786	−	0.545632i	−0.0946785	−	0.0211906i
$664$	7.03396	+	0.822152i	0.272971	+	0.0319057i
$665$	−1.53487	+	8.70469i	−0.0595198	+	0.337553i
$666$	−0.559661	−	0.0512447i	−0.0216864	−	0.00198569i
$667$	5.85536	+	33.2074i	0.226720	+	1.28579i
$668$	−0.327592	−	5.62455i	−0.0126749	−	0.217620i
$669$	11.0242	−	2.75903i	0.426219	−	0.106670i
$670$	1.39121	−	3.22519i	0.0537473	−	0.124600i
$671$	−12.1310	+	6.09242i	−0.468313	+	0.235195i
$672$	−12.7395	+	4.81830i	−0.491436	+	0.185870i
$673$	8.46457	−	2.00614i	0.326285	−	0.0773310i	−0.0642089	−	0.997936i	$-0.520452\pi$
$673$	8.46457	−	2.00614i	0.326285	−	0.0773310i	0.390494	+	0.920606i	$0.372304\pi$
$674$	2.37041	+	4.10567i	0.0913047	+	0.158144i
$675$	−12.4337	−	12.2245i	−0.478572	−	0.470523i
$676$	−1.08430	+	1.87806i	−0.0417037	+	0.0722329i
$677$	0.165536	−	0.552928i	0.00636206	−	0.0212508i	−0.954750	−	0.297411i	$-0.903877\pi$
$677$	0.165536	−	0.552928i	0.00636206	−	0.0212508i	0.961112	+	0.276160i	$0.0890620\pi$
$678$	−1.12808	+	0.0141277i	−0.0433237	+	0.000542572i
$679$	3.45318	+	2.27119i	0.132521	+	0.0871603i
$680$	0.468735	+	0.629621i	0.0179752	+	0.0241449i
$681$	−0.994532	−	14.0434i	−0.0381106	−	0.538143i
$682$	−10.2410	+	6.73560i	−0.392147	+	0.257919i
$683$	33.8572	+	12.3230i	1.29551	+	0.471528i	0.895532	−	0.444997i	$-0.146795\pi$
$683$	33.8572	+	12.3230i	1.29551	+	0.471528i	0.399979	+	0.916524i	$0.369017\pi$
$684$	17.7285	−	9.46680i	0.677865	−	0.361972i
$685$	−5.96895	+	2.17252i	−0.228062	+	0.0830078i
$686$	4.46957	−	6.00367i	0.170649	−	0.229221i
$687$	−12.0496	+	6.24171i	−0.459722	+	0.238136i
$688$	25.1612	−	26.6693i	0.959263	−	1.01676i
$689$	13.9274	−	14.7621i	0.530590	−	0.562393i
$690$	0.257603	−	5.63850i	0.00980676	−	0.214654i
$691$	−8.76512	+	11.7736i	−0.333441	+	0.447889i	−0.936948	−	0.349469i	$-0.886362\pi$
$691$	−8.76512	+	11.7736i	−0.333441	+	0.447889i	0.603507	+	0.797357i	$0.293769\pi$
$692$	−16.8465	+	6.13164i	−0.640409	+	0.233090i
$693$	−8.68927	−	26.5822i	−0.330078	−	1.00977i
$694$	−5.00694	−	1.82238i	−0.190061	−	0.0691765i
$695$	−18.0298	+	11.8584i	−0.683911	+	0.449815i
$696$	−10.5221	+	7.11084i	−0.398839	+	0.269536i
$697$	−1.51987	−	2.04154i	−0.0575692	−	0.0773289i
$698$	−4.86981	−	3.20293i	−0.184325	−	0.121233i
$699$	−21.8920	+	39.0390i	−0.828030	+	1.47659i
$700$	−3.41381	+	11.4029i	−0.129030	+	0.430989i
$701$	−15.3027	+	26.5051i	−0.577976	+	1.00108i	0.417735	+	0.908569i	$0.362824\pi$
$701$	−15.3027	+	26.5051i	−0.577976	+	1.00108i	−0.995711	+	0.0925152i	$0.970509\pi$
$702$	−3.16034	+	5.98210i	−0.119279	+	0.225780i
$703$	−0.892837	−	1.54644i	−0.0336740	−	0.0583250i
$704$	−22.6180	+	5.36056i	−0.852448	+	0.202034i
$705$	−10.4275	−	8.52949i	−0.392723	−	0.321239i
$706$	−11.3610	+	5.70572i	−0.427577	+	0.214737i
$707$	12.3508	−	28.6323i	0.464499	−	1.07683i
$708$	−4.97961	+	17.4243i	−0.187145	+	0.654845i
$709$	−2.68046	−	46.0217i	−0.100667	−	1.72838i	−0.550128	−	0.835080i	$-0.685421\pi$
$709$	−2.68046	−	46.0217i	−0.100667	−	1.72838i	0.449462	−	0.893300i	$-0.351616\pi$
$710$	1.31977	+	7.48480i	0.0495302	+	0.280900i
$711$	10.3731	+	4.88819i	0.389020	+	0.183322i
$712$	−2.63986	+	14.9714i	−0.0989329	+	0.561077i
$713$	−44.2529	−	5.17243i	−1.65729	−	0.193709i
$714$	−0.156915	−	0.501200i	−0.00587238	−	0.0187569i
$715$	−6.17295	−	20.6191i	−0.230855	−	0.771110i
$716$	46.6347	+	11.0526i	1.74282	+	0.413056i
$717$	0.301589	−	0.0390849i	0.0112630	−	0.00145965i
$718$	1.85663	+	4.30416i	0.0692889	+	0.160630i
$719$	15.5899	+	13.0815i	0.581404	+	0.487856i	0.885408	−	0.464815i	$-0.153879\pi$
$719$	15.5899	+	13.0815i	0.581404	+	0.487856i	−0.304004	+	0.952671i	$0.598324\pi$
$720$	−11.3185	+	4.44366i	−0.421816	+	0.165605i
$721$	26.4418	−	22.1873i	0.984743	−	0.826298i
$722$	2.02333	+	1.01616i	0.0753006	+	0.0378174i
$723$	−19.6542	+	27.1023i	−0.730949	+	1.00795i
$724$	1.64464	−	0.192231i	0.0611226	−	0.00714421i
$725$	−0.979956	+	16.8252i	−0.0363947	+	0.624872i
$726$	1.56193	+	8.25246i	0.0579687	+	0.306278i
$727$	16.6791	+	17.6788i	0.618593	+	0.655670i	0.958601	−	0.284752i	$-0.0919114\pi$
$727$	16.6791	+	17.6788i	0.618593	+	0.655670i	−0.340008	+	0.940422i	$0.610430\pi$
$728$	9.59336			0.355554
$729$	−11.7066	+	24.3301i	−0.433579	+	0.901116i
$730$	3.19555			0.118272
$731$	3.33780	+	3.53787i	0.123453	+	0.130853i
$732$	−1.66378	−	8.79056i	−0.0614950	−	0.324908i
$733$	2.31961	−	39.8261i	0.0856767	−	1.47101i	−0.632180	−	0.774821i	$-0.717840\pi$
$733$	2.31961	−	39.8261i	0.0856767	−	1.47101i	0.717857	−	0.696191i	$-0.245123\pi$
$734$	10.7893	−	1.26109i	0.398240	−	0.0465475i
$735$	4.36843	−	6.02387i	0.161132	−	0.222194i
$736$	24.6957	+	12.4027i	0.910296	+	0.457168i
$737$	−27.0497	+	22.6974i	−0.996389	+	0.836069i
$738$	−6.41612	+	2.51898i	−0.236181	+	0.0927248i
$739$	6.20932	+	5.21024i	0.228413	+	0.191662i	0.749811	−	0.661652i	$-0.230145\pi$
$739$	6.20932	+	5.21024i	0.228413	+	0.191662i	−0.521397	+	0.853314i	$0.674589\pi$
$740$	0.466707	+	1.08195i	0.0171565	+	0.0397733i
$741$	−21.3183	+	2.76278i	−0.783148	+	0.101493i
$742$	4.15163	+	0.983954i	0.152411	+	0.0361221i
$743$	7.11485	+	23.7653i	0.261019	+	0.871863i	0.983567	+	0.180543i	$0.0577854\pi$
$743$	7.11485	+	23.7653i	0.261019	+	0.871863i	−0.722548	+	0.691320i	$0.757029\pi$
$744$	−5.01351	−	16.0136i	−0.183804	−	0.587088i
$745$	−22.1966	−	2.59441i	−0.813220	−	0.0950517i
$746$	−1.24804	+	7.07796i	−0.0456938	+	0.259143i
$747$	−13.1646	−	6.20367i	−0.481668	−	0.226980i
$748$	−0.659681	−	3.74124i	−0.0241203	−	0.136793i
$749$	1.79197	+	30.7670i	0.0654773	+	1.12420i
$750$	1.93029	−	6.75433i	0.0704841	−	0.246633i
$751$	−12.5408	+	29.0728i	−0.457619	+	1.06088i	0.520693	+	0.853744i	$0.325674\pi$
$751$	−12.5408	+	29.0728i	−0.457619	+	1.06088i	−0.978312	+	0.207137i	$0.933586\pi$
$752$	17.1328	−	8.60441i	0.624769	−	0.313771i
$753$	−32.4012	−	26.5036i	−1.18077	−	0.965844i
$754$	6.36316	−	1.50810i	0.231732	−	0.0549216i
$755$	−4.13904	−	7.16903i	−0.150635	−	0.260908i
$756$	18.4183	−	0.692285i	0.669868	−	0.0251782i
$757$	−7.21394	+	12.4949i	−0.262195	+	0.454135i	−0.966825	−	0.255440i	$-0.917780\pi$
$757$	−7.21394	+	12.4949i	−0.262195	+	0.454135i	0.704630	+	0.709575i	$0.251113\pi$
$758$	2.04182	−	6.82014i	0.0741621	−	0.247719i
$759$	−27.7540	+	49.4925i	−1.00741	+	1.79646i
$760$	5.64321	+	3.71160i	0.204701	+	0.134634i
$761$	13.3336	+	17.9101i	0.483342	+	0.649241i	0.975172	−	0.221451i	$-0.0710792\pi$
$761$	13.3336	+	17.9101i	0.483342	+	0.649241i	−0.491830	+	0.870691i	$0.663672\pi$
$762$	−2.77414	+	1.87477i	−0.100497	+	0.0679157i
$763$	12.9022	−	8.48591i	0.467091	−	0.307211i
$764$	−14.0878	−	5.12754i	−0.509679	−	0.185508i
$765$	−0.501181	−	1.53321i	−0.0181202	−	0.0554333i
$766$	2.36925	−	0.862338i	0.0856046	−	0.0311575i
$767$	11.5749	−	15.5477i	0.417944	−	0.561396i
$768$	0.452831	−	9.91174i	0.0163401	−	0.357659i
$769$	−18.7216	+	19.8437i	−0.675118	+	0.715583i	−0.970850	−	0.239688i	$-0.922955\pi$
$769$	−18.7216	+	19.8437i	−0.675118	+	0.715583i	0.295732	+	0.955271i	$0.404436\pi$
$770$	3.10513	−	3.29124i	0.111901	−	0.118608i
$771$	21.0574	−	10.9078i	0.758365	−	0.392834i
$772$	−0.215978	+	0.290109i	−0.00777321	+	0.0104412i
$773$	7.11832	−	2.59086i	0.256028	−	0.0931867i	−0.210817	−	0.977525i	$-0.567613\pi$
$773$	7.11832	−	2.59086i	0.256028	−	0.0931867i	0.466846	+	0.884339i	$0.345390\pi$
$774$	11.6196	−	6.20474i	0.417659	−	0.223025i
$775$	−20.9260	−	7.61646i	−0.751686	−	0.273591i
$776$	2.63878	−	1.73555i	0.0947267	−	0.0623027i
$777$	−0.115684	−	1.63352i	−0.00415014	−	0.0586023i
$778$	−0.197712	−	0.265573i	−0.00708832	−	0.00952126i
$779$	−18.2981	−	12.0348i	−0.655596	−	0.431192i
$780$	14.1839	−	0.177635i	0.507865	−	0.00636034i
$781$	21.9134	−	73.1960i	0.784124	−	2.61916i
$782$	−0.532800	+	0.922836i	−0.0190529	+	0.0330006i
$783$	25.1500	−	6.96803i	0.898787	−	0.249017i
$784$	5.29489	+	9.17101i	0.189103	+	0.327536i
$785$	15.9354	−	3.77676i	0.568759	−	0.134798i
$786$	7.14496	−	2.70235i	0.254852	−	0.0963897i
$787$	−7.15801	+	3.59489i	−0.255155	+	0.128144i	−0.571780	−	0.820407i	$-0.693747\pi$
$787$	−7.15801	+	3.59489i	−0.255155	+	0.128144i	0.316624	+	0.948551i	$0.397451\pi$
$788$	−8.48381	+	19.6677i	−0.302223	+	0.700632i
$789$	24.4007	−	6.10678i	0.868687	−	0.217407i
$790$	0.107878	+	1.85219i	0.00383812	+	0.0658980i
$791$	−0.570845	−	3.23742i	−0.0202969	−	0.115109i
$792$	−21.2817	−	1.94863i	−0.756212	−	0.0692417i
$793$	−1.66170	+	9.42396i	−0.0590087	+	0.334655i
$794$	12.8282	+	1.49940i	0.455255	+	0.0532117i
$795$	12.7880	+	2.86216i	0.453543	+	0.101510i
$796$	0.936374	+	3.12771i	0.0331889	+	0.110859i
$797$	13.3001	+	3.15217i	0.471113	+	0.111656i	0.459313	−	0.888275i	$-0.348096\pi$
$797$	13.3001	+	3.15217i	0.471113	+	0.111656i	0.0117999	+	0.999930i	$0.496244\pi$
$798$	−2.74387	−	3.59089i	−0.0971321	−	0.127116i
$799$	1.00735	+	2.33530i	0.0356375	+	0.0826171i
$800$	10.5811	+	8.87856i	0.374097	+	0.313905i
$801$	14.9378	−	27.4379i	0.527803	−	0.969469i
$802$	1.21775	−	1.02182i	0.0430003	−	0.0360816i
$803$	−28.7079	−	14.4177i	−1.01308	−	0.508788i
$804$	−9.48435	−	21.2514i	−0.334487	−	0.749480i
$805$	16.3359	−	1.90939i	0.575765	−	0.0672973i
$806$	−0.502408	+	8.62601i	−0.0176966	+	0.303838i
$807$	0.238624	−	0.205376i	0.00839995	−	0.00722956i
$808$	−16.3521	−	17.3322i	−0.575264	−	0.609744i
$809$	6.31109			0.221886			0.110943	−	0.993827i	$-0.464613\pi$
$809$	6.31109			0.221886			0.110943	+	0.993827i	$0.464613\pi$
$810$	−4.36300	+	0.218735i	−0.153300	+	0.00768556i
$811$	−29.8809			−1.04926			−0.524631	−	0.851330i	$-0.675797\pi$
$811$	−29.8809			−1.04926			−0.524631	+	0.851330i	$0.675797\pi$
$812$	−12.2255	−	12.9583i	−0.429031	−	0.454747i
$813$	33.1704	+	11.6047i	1.16334	+	0.406996i
$814$	−0.0531513	+	0.912572i	−0.00186295	+	0.0319856i
$815$	0.764017	−	0.0893008i	0.0267624	−	0.00312807i
$816$	2.28323	+	0.237929i	0.0799291	+	0.00832917i
$817$	37.4016	+	18.7838i	1.30852	+	0.657162i
$818$	−6.28665	+	5.27513i	−0.219808	+	0.184440i
$819$	−18.6883	−	6.27661i	−0.653024	−	0.219322i
$820$	11.0708	+	9.28950i	0.386609	+	0.324403i
$821$	12.5829	+	29.1705i	0.439147	+	1.01806i	0.983780	+	0.179382i	$0.0574097\pi$
$821$	12.5829	+	29.1705i	0.439147	+	1.01806i	−0.544633	+	0.838675i	$0.683331\pi$
$822$	1.24890	−	2.99795i	0.0435603	−	0.104566i
$823$	25.0358	+	5.93360i	0.872694	+	0.206832i	0.642475	−	0.766307i	$-0.277908\pi$
$823$	25.0358	+	5.93360i	0.872694	+	0.206832i	0.230219	+	0.973139i	$0.426056\pi$
$824$	−7.56493	−	25.2686i	−0.263537	−	0.880274i
$825$	−19.2029	+	20.8714i	−0.668558	+	0.726648i
$826$	4.04737	+	0.473070i	0.140826	+	0.0164602i
$827$	3.15225	−	17.8773i	0.109615	−	0.621655i	−0.879662	−	0.475600i	$-0.842231\pi$
$827$	3.15225	−	17.8773i	0.109615	−	0.621655i	0.989276	−	0.146056i	$-0.0466578\pi$
$828$	−26.3364	−	26.5503i	−0.915255	−	0.922685i
$829$	−4.93669	−	27.9974i	−0.171458	−	0.972389i	−0.942153	−	0.335184i	$-0.891202\pi$
$829$	−4.93669	−	27.9974i	−0.171458	−	0.972389i	0.770694	−	0.637205i	$-0.219910\pi$
$830$	−0.136909	−	2.35064i	−0.00475219	−	0.0815920i
$831$	−13.4144	−	13.8663i	−0.465339	−	0.481018i
$832$	−6.49005	+	15.0456i	−0.225002	+	0.521613i
$833$	−1.25538	+	0.630475i	−0.0434963	+	0.0218447i
$834$	1.77973	−	10.8890i	0.0616269	−	0.377056i
$835$	−3.78620	+	0.897345i	−0.131027	+	0.0310539i
$836$	−16.3449	−	28.3101i	−0.565299	−	0.979127i
$837$	−0.710592	+	34.4755i	−0.0245616	+	1.19165i
$838$	−0.792187	+	1.37211i	−0.0273656	+	0.0473987i
$839$	8.56334	−	28.6036i	0.295639	−	0.987504i	−0.673126	−	0.739527i	$-0.735049\pi$
$839$	8.56334	−	28.6036i	0.295639	−	0.987504i	0.968766	−	0.247977i	$-0.0797658\pi$
$840$	3.16411	+	5.32525i	0.109172	+	0.183739i
$841$	3.15398	+	2.07441i	0.108758	+	0.0715312i
$842$	−1.12342	−	1.50902i	−0.0387158	−	0.0520043i
$843$	−3.11981	−	1.51821i	−0.107452	−	0.0522899i
$844$	−5.54834	+	3.64920i	−0.190982	+	0.125611i
$845$	1.40738	+	0.512244i	0.0484153	+	0.0176217i
$846$	6.81908	−	0.970706i	0.234445	−	0.0333735i
$847$	−22.9977	+	8.37050i	−0.790212	+	0.287614i
$848$	−11.1367	+	14.9591i	−0.382434	+	0.513698i
$849$	3.33753	+	2.13574i	0.114544	+	0.0732983i
$850$	−0.365497	+	0.387404i	−0.0125364	+	0.0132879i
$851$	−2.28017	+	2.41684i	−0.0781632	+	0.0828481i
$852$	42.4147	+	27.1418i	1.45310	+	0.929864i
$853$	−3.04813	+	4.09435i	−0.104366	+	0.140188i	−0.851238	−	0.524780i	$-0.824147\pi$
$853$	−3.04813	+	4.09435i	−0.104366	+	0.140188i	0.746872	+	0.664968i	$0.231555\pi$
$854$	−1.89043	+	0.688062i	−0.0646893	+	0.0235450i
$855$	−8.56488	−	10.9225i	−0.292913	−	0.373543i
$856$	22.1305	+	8.05483i	0.756403	+	0.275308i
$857$	−11.8982	+	7.82555i	−0.406434	+	0.267316i	−0.736223	−	0.676739i	$-0.763393\pi$
$857$	−11.8982	+	7.82555i	−0.406434	+	0.267316i	0.329790	+	0.944054i	$0.393022\pi$
$858$	9.89506	+	4.81528i	0.337812	+	0.164391i
$859$	−25.0637	−	33.6664i	−0.855162	−	1.14868i	−0.987522	−	0.157480i	$-0.949663\pi$
$859$	−25.0637	−	33.6664i	−0.855162	−	1.14868i	0.132361	−	0.991202i	$-0.457744\pi$
$860$	−23.0745	−	15.1763i	−0.786833	−	0.517508i
$861$	−10.2596	−	17.2671i	−0.349646	−	0.588461i
$862$	2.87513	−	9.60359i	0.0979272	−	0.327100i
$863$	12.5420	−	21.7234i	0.426934	−	0.739472i	−0.569665	−	0.821877i	$-0.692927\pi$
$863$	12.5420	−	21.7234i	0.426934	−	0.739472i	0.996599	+	0.0824054i	$0.0262602\pi$
$864$	7.72786	−	19.9434i	0.262907	−	0.678490i
$865$	6.19073	+	10.7227i	0.210491	+	0.364582i
$866$	−7.87612	+	1.86667i	−0.267641	+	0.0634322i
$867$	4.70040	−	28.7587i	0.159634	−	0.976698i
$868$	21.0356	−	10.5645i	0.713995	−	0.358582i
$869$	7.38757	−	17.1263i	0.250606	−	0.580970i
$870$	2.93585	+	3.03477i	0.0995347	+	0.102888i
$871$	1.44732	+	24.8495i	0.0490405	+	0.841992i
$872$	−2.04917	−	11.6214i	−0.0693936	−	0.393551i
$873$	−6.27599	+	1.65448i	−0.212410	+	0.0559957i
$874$	−1.59225	+	9.03012i	−0.0538588	+	0.305448i
$875$	20.3309	+	2.37634i	0.687311	+	0.0803351i
$876$	14.3352	−	15.5808i	0.484341	−	0.526425i
$877$	9.14104	+	30.5332i	0.308671	+	1.03103i	0.961792	+	0.273780i	$0.0882739\pi$
$877$	9.14104	+	30.5332i	0.308671	+	1.03103i	−0.653121	+	0.757253i	$0.726541\pi$
$878$	−11.9003	−	2.82043i	−0.401617	−	0.0951849i
$879$	−3.34168	+	8.02162i	−0.112712	+	0.270563i
$880$	7.83366	+	18.1605i	0.264073	+	0.612189i
$881$	−4.45428	−	3.73758i	−0.150068	−	0.125922i	0.564662	−	0.825322i	$-0.309006\pi$
$881$	−4.45428	−	3.73758i	−0.150068	−	0.125922i	−0.714731	+	0.699400i	$0.753451\pi$
$882$	0.754271	+	3.72900i	0.0253976	+	0.125562i
$883$	−0.930865	+	0.781089i	−0.0313261	+	0.0262857i	−0.658316	−	0.752741i	$-0.728731\pi$
$883$	−0.930865	+	0.781089i	−0.0313261	+	0.0262857i	0.626990	+	0.779027i	$0.284287\pi$
$884$	−2.39313	−	1.20188i	−0.0804897	−	0.0404235i
$885$	12.4482	+	1.29719i	0.418441	+	0.0436044i
$886$	−12.2248	+	1.42888i	−0.410702	+	0.0480041i
$887$	−0.151446	+	2.60022i	−0.00508505	+	0.0873069i	−0.999896	−	0.0144357i	$-0.995405\pi$
$887$	−0.151446	+	2.60022i	−0.00508505	+	0.0873069i	0.994811	+	0.101743i	$0.0324418\pi$
$888$	−1.18120	−	0.413244i	−0.0396384	−	0.0138676i
$889$	−6.69523	−	7.09653i	−0.224551	−	0.238010i
$890$	5.05459			0.169430
$891$	40.1829	+	17.7199i	1.34618	+	0.593640i
$892$	12.1821			0.407888
$893$	15.0184	+	15.9186i	0.502571	+	0.532694i
$894$	8.66016	−	7.45352i	0.289639	−	0.249283i
$895$	1.92457	−	33.0437i	0.0643314	−	1.10453i
$896$	−19.0424	+	2.22574i	−0.636162	+	0.0743567i
$897$	16.3018	+	36.5272i	0.544302	+	1.21961i
$898$	5.40667	+	2.71533i	0.180423	+	0.0906118i
$899$	25.5323	−	21.4242i	0.851551	−	0.714536i
$900$	−9.74828	−	15.9483i	−0.324943	−	0.531610i
$901$	−1.89517	−	1.59024i	−0.0631373	−	0.0529785i
$902$	4.44067	+	10.2946i	0.147858	+	0.342773i
$903$	23.3046	+	30.4986i	0.775529	+	1.01493i
$904$	−2.44436	−	0.579323i	−0.0812981	−	0.0192680i
$905$	−0.327981	−	1.09553i	−0.0109025	−	0.0364168i
$906$	4.13026	+	0.924420i	0.137219	+	0.0307118i
$907$	−13.3542	−	1.56088i	−0.443419	−	0.0518282i	−0.108546	−	0.994091i	$-0.534619\pi$
$907$	−13.3542	−	1.56088i	−0.443419	−	0.0518282i	−0.334873	+	0.942263i	$0.608693\pi$
$908$	2.62067	−	14.8626i	0.0869701	−	0.493232i
$909$	20.5148	+	44.4626i	0.680433	+	1.47473i
$910$	−0.553881	−	3.14122i	−0.0183610	−	0.104130i
$911$	−1.63910	−	28.1423i	−0.0543058	−	0.932395i	−0.909921	−	0.414782i	$-0.863858\pi$
$911$	−1.63910	−	28.1423i	−0.0543058	−	0.932395i	0.855615	−	0.517613i	$-0.173179\pi$
$912$	19.1624	−	4.79580i	0.634532	−	0.158805i
$913$	−9.37566	+	21.7352i	−0.310289	+	0.719331i
$914$	−6.52549	+	3.27723i	−0.215844	+	0.108401i
$915$	−5.77929	+	2.18583i	−0.191057	+	0.0722613i
$916$	−14.1549	+	3.35477i	−0.467691	+	0.110845i
$917$	11.1295	+	19.2768i	0.367528	+	0.636578i
$918$	0.750382	+	0.342192i	0.0247663	+	0.0112940i
$919$	13.5339	−	23.4413i	0.446441	−	0.773258i	−0.551710	−	0.834036i	$-0.686025\pi$
$919$	13.5339	−	23.4413i	0.446441	−	0.773258i	0.998151	+	0.0607774i	$0.0193580\pi$
$920$	3.60461	−	12.0402i	0.118840	−	0.396954i
$921$	−37.1552	+	0.465320i	−1.22431	+	0.0153328i
$922$	4.68676	+	3.08253i	0.154350	+	0.101518i
$923$	−32.1633	−	43.2028i	−1.05867	−	1.42204i
$924$	−2.11779	−	29.9044i	−0.0696701	−	0.983781i
$925$	−1.38753	+	0.912593i	−0.0456217	+	0.0300059i
$926$	0.985077	+	0.358539i	0.0323716	+	0.0117823i
$927$	−1.79553	+	54.1740i	−0.0589729	+	1.77931i
$928$	−19.4266	+	7.07070i	−0.637709	+	0.232107i
$929$	28.7357	−	38.5987i	0.942787	−	1.26638i	−0.0210192	−	0.999779i	$-0.506691\pi$
$929$	28.7357	−	38.5987i	0.942787	−	1.26638i	0.963806	−	0.266604i	$-0.0859015\pi$
$930$	−4.95399	+	2.56617i	−0.162448	+	0.0841479i
$931$	−8.29546	+	8.79268i	−0.271873	+	0.288168i
$932$	−32.9258	+	34.8993i	−1.07852	+	1.14316i
$933$	−0.951759	+	20.8324i	−0.0311592	+	0.682024i
$934$	−4.45513	+	5.98427i	−0.145776	+	0.195811i
$935$	−2.46545	+	0.897352i	−0.0806290	+	0.0293465i
$936$	−10.0604	+	11.2132i	−0.328836	+	0.366515i
$937$	−48.7239	−	17.7340i	−1.59174	−	0.579346i	−0.614026	−	0.789286i	$-0.710451\pi$
$937$	−48.7239	−	17.7340i	−1.59174	−	0.579346i	−0.977714	+	0.209940i	$0.932673\pi$
$938$	−4.37206	+	2.87555i	−0.142753	+	0.0938900i
$939$	13.3627	−	9.03054i	0.436076	−	0.294701i
$940$	−8.62374	−	11.5837i	−0.281275	−	0.377819i
$941$	37.8323	+	24.8827i	1.23330	+	0.811153i	0.987416	−	0.158146i	$-0.0505517\pi$
$941$	37.8323	+	24.8827i	1.23330	+	0.811153i	0.245883	+	0.969300i	$0.420922\pi$
$942$	−4.09547	+	7.30327i	−0.133438	+	0.237953i
$943$	−11.6879	+	39.0403i	−0.380611	+	1.27133i
$944$	−8.90573	+	15.4252i	−0.289857	+	0.502047i
$945$	−2.67971	−	12.4440i	−0.0871709	−	0.404804i
$946$	−10.7128	−	18.5551i	−0.348302	−	0.603277i
$947$	20.4431	−	4.84509i	0.664310	−	0.157444i	0.115391	−	0.993320i	$-0.463188\pi$
$947$	20.4431	−	4.84509i	0.664310	−	0.157444i	0.548919	+	0.835876i	$0.315040\pi$
$948$	9.51481	+	7.78292i	0.309027	+	0.252778i
$949$	−20.2370	+	10.1634i	−0.656920	+	0.329918i
$950$	−1.81525	+	4.20823i	−0.0588946	+	0.136533i
$951$	7.79510	−	27.2761i	0.252773	−	0.884487i
$952$	−0.0679961	−	1.16745i	−0.00220377	−	0.0378372i
$953$	−1.52233	−	8.63357i	−0.0493132	−	0.279669i	0.950173	−	0.311723i	$-0.100906\pi$
$953$	−1.52233	−	8.63357i	−0.0493132	−	0.279669i	−0.999486	+	0.0320543i	$0.989795\pi$
$954$	−5.50385	+	3.82077i	−0.178194	+	0.123702i
$955$	−1.79794	+	10.1966i	−0.0581800	+	0.329955i
$956$	0.323796	+	0.0378463i	0.0104723	+	0.00122404i
$957$	−12.6826	−	40.5095i	−0.409971	−	1.30949i
$958$	2.02365	+	6.75945i	0.0653811	+	0.218388i
$959$	9.20832	+	2.18241i	0.297352	+	0.0704737i
$960$	−10.4924	+	1.35977i	−0.338639	+	0.0438865i
$961$	5.16468	+	11.9731i	0.166603	+	0.386228i
$962$	0.493629	+	0.414204i	0.0159152	+	0.0133545i
$963$	−37.8413	−	30.1704i	−1.21942	−	0.972228i
$964$	−27.4921	+	23.0686i	−0.885461	+	0.742990i
$965$	0.223216	+	0.112103i	0.00718559	+	0.00360874i
$966$	−4.93673	+	6.80752i	−0.158837	+	0.219028i
$967$	22.4843	−	2.62804i	0.723047	−	0.0845120i	0.253394	−	0.967363i	$-0.418453\pi$
$967$	22.4843	−	2.62804i	0.723047	−	0.0845120i	0.469653	+	0.882851i	$0.344379\pi$
$968$	−1.08741	+	18.6702i	−0.0349508	+	0.600082i
$969$	0.487313	+	2.57472i	0.0156548	+	0.0827118i
$970$	−0.720635	−	0.763829i	−0.0231382	−	0.0245251i
$971$	13.1781			0.422905			0.211453	−	0.977388i	$-0.432181\pi$
$971$	13.1781			0.422905			0.211453	+	0.977388i	$0.432181\pi$
$972$	−18.5059	+	22.2543i	−0.593576	+	0.713806i
$973$	32.1504			1.03070
$974$	−1.38801	−	1.47120i	−0.0444746	−	0.0471403i
$975$	3.71797	+	19.6439i	0.119070	+	0.629108i
$976$	0.511289	−	8.77849i	0.0163660	−	0.280993i
$977$	−39.4606	+	4.61228i	−1.26246	+	0.147560i	−0.720861	−	0.693079i	$-0.756254\pi$
$977$	−39.4606	+	4.61228i	−1.26246	+	0.147560i	−0.541595	+	0.840639i	$0.682179\pi$
$978$	−0.230887	+	0.318382i	−0.00738294	+	0.0101807i
$979$	−45.4091	−	22.8053i	−1.45128	−	0.728860i
$980$	6.11051	−	5.12733i	0.195193	−	0.163786i
$981$	−3.61161	+	23.9798i	−0.115310	+	0.765616i
$982$	−1.07321	−	0.900528i	−0.0342474	−	0.0287370i
$983$	23.2360	+	53.8671i	0.741113	+	1.71809i	0.694840	+	0.719165i	$0.255475\pi$
$983$	23.2360	+	53.8671i	0.741113	+	1.71809i	0.0462734	+	0.998929i	$0.485265\pi$
$984$	−15.2209	+	1.97258i	−0.485226	+	0.0628837i
$985$	14.3942	+	3.41150i	0.458639	+	0.108699i
$986$	−0.228626	−	0.763665i	−0.00728094	−	0.0243200i
$987$	5.99657	+	19.1536i	0.190873	+	0.609666i
$988$	−22.8881	−	2.67523i	−0.728166	−	0.0851104i
$989$	13.5235	−	76.6957i	0.430023	−	2.43878i
$990$	0.590664	+	7.08091i	0.0187725	+	0.225046i
$991$	3.30423	+	18.7392i	0.104962	+	0.595270i	0.991235	+	0.132108i	$0.0421744\pi$
$991$	3.30423	+	18.7392i	0.104962	+	0.595270i	−0.886273	+	0.463163i	$0.846714\pi$
$992$	−1.58828	−	27.2697i	−0.0504280	−	0.865815i
$993$	−2.44107	+	8.54163i	−0.0774651	+	0.271061i
$994$	4.48484	−	10.3970i	0.142250	−	0.329773i
$995$	2.01498	−	1.01196i	0.0638793	−	0.0320814i
$996$	−12.0754	−	9.87741i	−0.382623	−	0.312978i
$997$	−5.53844	+	1.31264i	−0.175404	+	0.0415716i	−0.317379	−	0.948299i	$-0.602803\pi$
$997$	−5.53844	+	1.31264i	−0.175404	+	0.0415716i	0.141975	+	0.989870i	$0.454655\pi$
$998$	−5.28998	−	9.16251i	−0.167451	−	0.290034i
$999$	2.03066	+	1.57784i	0.0642473	+	0.0499206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.22.5	✓	144
3.2	odd	2		243.2.g.a.199.4		144
9.2	odd	6		729.2.g.a.352.4		144
9.4	even	3		729.2.g.c.595.4		144
9.5	odd	6		729.2.g.b.595.5		144
9.7	even	3		729.2.g.d.352.5		144
81.11	odd	54		243.2.g.a.127.4		144
81.16	even	27		729.2.g.d.379.5		144
81.31	even	27		6561.2.a.c.1.34		72
81.38	odd	54		729.2.g.b.136.5		144
81.43	even	27		729.2.g.c.136.4		144
81.50	odd	54		6561.2.a.d.1.39		72
81.65	odd	54		729.2.g.a.379.4		144
81.70	even	27	inner	81.2.g.a.70.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.5	✓	144	1.1	even	1	trivial
81.2.g.a.70.5	yes	144	81.70	even	27	inner
243.2.g.a.127.4		144	81.11	odd	54
243.2.g.a.199.4		144	3.2	odd	2
729.2.g.a.352.4		144	9.2	odd	6
729.2.g.a.379.4		144	81.65	odd	54
729.2.g.b.136.5		144	81.38	odd	54
729.2.g.b.595.5		144	9.5	odd	6
729.2.g.c.136.4		144	81.43	even	27
729.2.g.c.595.4		144	9.4	even	3
729.2.g.d.352.5		144	9.7	even	3
729.2.g.d.379.5		144	81.16	even	27
6561.2.a.c.1.34		72	81.31	even	27
6561.2.a.d.1.39		72	81.50	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+(0.259760 + 0.275329i) q^{2} +(-0.322104 - 1.70184i) q^{3} +(0.107959 - 1.85358i) q^{4} +(-1.27364 + 0.148867i) q^{5} +(0.384896 - 0.530753i) q^{6} +(1.70721 + 0.857394i) q^{7} +(1.11832 - 0.938383i) q^{8} +(-2.79250 + 1.09634i) q^{9} +(-0.371828 - 0.312001i) q^{10} +(1.93272 + 4.48054i) q^{11} +(-3.18926 + 0.413317i) q^{12} +(3.34705 + 0.793266i) q^{13} +(0.207399 + 0.692762i) q^{14} +(0.663593 + 2.11958i) q^{15} +(-3.13947 - 0.366951i) q^{16} +(0.0728119 - 0.412937i) q^{17} +(-1.02723 - 0.484072i) q^{18} +(-0.626542 - 3.55329i) q^{19} +(0.138437 + 2.37686i) q^{20} +(0.909245 - 3.18157i) q^{21} +(-0.731582 + 1.69600i) q^{22} +(-5.99966 + 3.01314i) q^{23} +(-1.95719 - 1.60094i) q^{24} +(-3.26522 + 0.773872i) q^{25} +(0.651020 + 1.12760i) q^{26} +(2.76526 + 4.39924i) q^{27} +(1.77356 - 3.07189i) q^{28} +(1.44045 - 4.81145i) q^{29} +(-0.411207 + 0.733287i) q^{30} +(5.54449 + 3.64667i) q^{31} +(-2.45802 - 3.30169i) q^{32} +(7.00261 - 4.73237i) q^{33} +(0.132607 - 0.0872170i) q^{34} +(-2.30201 - 0.837864i) q^{35} +(1.73067 + 5.29447i) q^{36} +(0.465059 - 0.169268i) q^{37} +(0.815575 - 1.09551i) q^{38} +(0.271909 - 5.95165i) q^{39} +(-1.28465 + 1.36164i) q^{40} +(4.16545 - 4.41512i) q^{41} +(1.11216 - 0.576101i) q^{42} +(-6.92694 + 9.30450i) q^{43} +(8.51368 - 3.09873i) q^{44} +(3.39343 - 1.81205i) q^{45} +(-2.38808 - 0.869188i) q^{46} +(-5.06765 + 3.33305i) q^{47} +(0.386745 + 5.46106i) q^{48} +(-2.00066 - 2.68735i) q^{49} +(-1.06124 - 0.697991i) q^{50} +(-0.726204 + 0.00909474i) q^{51} +(1.83172 - 6.11838i) q^{52} +(2.95007 - 5.10967i) q^{53} +(-0.492935 + 1.90410i) q^{54} +(-3.12859 - 5.41888i) q^{55} +(2.71378 - 0.643177i) q^{56} +(-5.84532 + 2.21080i) q^{57} +(1.69890 - 0.853222i) q^{58} +(2.23192 - 5.17418i) q^{59} +(4.00044 - 1.00119i) q^{60} +(0.161757 + 2.77726i) q^{61} +(0.436200 + 2.47381i) q^{62} +(-5.70738 - 0.522590i) q^{63} +(-0.827191 + 4.69124i) q^{64} +(-4.38103 - 0.512069i) q^{65} +(3.12196 + 0.698745i) q^{66} +(2.07542 + 6.93240i) q^{67} +(-0.757549 - 0.179542i) q^{68} +(7.06039 + 9.23990i) q^{69} +(-0.367282 - 0.851455i) q^{70} +(-11.9949 - 10.0649i) q^{71} +(-2.09412 + 3.84649i) q^{72} +(-5.04326 + 4.23179i) q^{73} +(0.167408 + 0.0840754i) q^{74} +(2.36875 + 5.30761i) q^{75} +(-6.65395 + 0.777735i) q^{76} +(-0.542032 + 9.30634i) q^{77} +(1.70929 - 1.47113i) q^{78} +(-2.62307 - 2.78030i) q^{79} +4.05318 q^{80} +(6.59609 - 6.12304i) q^{81} +2.29763 q^{82} +(3.32898 + 3.52851i) q^{83} +(-5.79912 - 2.02883i) q^{84} +(-0.0312634 + 0.536772i) q^{85} +(-4.36114 + 0.509744i) q^{86} +(-8.65228 - 0.901629i) q^{87} +(6.36586 + 3.19706i) q^{88} +(-7.97723 + 6.69369i) q^{89} +(1.38039 + 0.463612i) q^{90} +(5.03399 + 4.22402i) q^{91} +(4.93738 + 11.4461i) q^{92} +(4.42013 - 10.6104i) q^{93} +(-2.23406 - 0.529481i) q^{94} +(1.32696 + 4.43235i) q^{95} +(-4.82720 + 5.24663i) q^{96} +(2.14884 + 0.251163i) q^{97} +(0.220216 - 1.24891i) q^{98} +(-10.3093 - 10.3930i) 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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