LMFDB - Embedded newform 243.2.g.a.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(10,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(54))

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

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

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

chi := DirichletCharacter("243.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	243.127
Dual form			243.2.g.a.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.259760 + 0.275329i) q^{2} +(0.107959 + 1.85358i) q^{4} +(1.27364 + 0.148867i) q^{5} +(1.70721 - 0.857394i) q^{7} +(-1.11832 - 0.938383i) q^{8} +(-0.371828 + 0.312001i) q^{10} +(-1.93272 + 4.48054i) q^{11} +(3.34705 - 0.793266i) q^{13} +(-0.207399 + 0.692762i) q^{14} +(-3.13947 + 0.366951i) q^{16} +(-0.0728119 - 0.412937i) q^{17} +(-0.626542 + 3.55329i) q^{19} +(-0.138437 + 2.37686i) q^{20} +(-0.731582 - 1.69600i) q^{22} +(5.99966 + 3.01314i) q^{23} +(-3.26522 - 0.773872i) q^{25} +(-0.651020 + 1.12760i) q^{26} +(1.77356 + 3.07189i) q^{28} +(-1.44045 - 4.81145i) q^{29} +(5.54449 - 3.64667i) q^{31} +(2.45802 - 3.30169i) q^{32} +(0.132607 + 0.0872170i) q^{34} +(2.30201 - 0.837864i) q^{35} +(0.465059 + 0.169268i) q^{37} +(-0.815575 - 1.09551i) q^{38} +(-1.28465 - 1.36164i) q^{40} +(-4.16545 - 4.41512i) q^{41} +(-6.92694 - 9.30450i) q^{43} +(-8.51368 - 3.09873i) q^{44} +(-2.38808 + 0.869188i) q^{46} +(5.06765 + 3.33305i) q^{47} +(-2.00066 + 2.68735i) q^{49} +(1.06124 - 0.697991i) q^{50} +(1.83172 + 6.11838i) q^{52} +(-2.95007 - 5.10967i) q^{53} +(-3.12859 + 5.41888i) q^{55} +(-2.71378 - 0.643177i) q^{56} +(1.69890 + 0.853222i) q^{58} +(-2.23192 - 5.17418i) q^{59} +(0.161757 - 2.77726i) q^{61} +(-0.436200 + 2.47381i) q^{62} +(-0.827191 - 4.69124i) q^{64} +(4.38103 - 0.512069i) q^{65} +(2.07542 - 6.93240i) q^{67} +(0.757549 - 0.179542i) q^{68} +(-0.367282 + 0.851455i) q^{70} +(11.9949 - 10.0649i) q^{71} +(-5.04326 - 4.23179i) q^{73} +(-0.167408 + 0.0840754i) q^{74} +(-6.65395 - 0.777735i) q^{76} +(0.542032 + 9.30634i) q^{77} +(-2.62307 + 2.78030i) q^{79} -4.05318 q^{80} +2.29763 q^{82} +(-3.32898 + 3.52851i) q^{83} +(-0.0312634 - 0.536772i) q^{85} +(4.36114 + 0.509744i) q^{86} +(6.36586 - 3.19706i) q^{88} +(7.97723 + 6.69369i) q^{89} +(5.03399 - 4.22402i) q^{91} +(-4.93738 + 11.4461i) q^{92} +(-2.23406 + 0.529481i) q^{94} +(-1.32696 + 4.43235i) q^{95} +(2.14884 - 0.251163i) q^{97} +(-0.220216 - 1.24891i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

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	$-0.801986\pi$
$2$	−0.259760	+	0.275329i	−0.183678	+	0.194687i	0.628992	+	0.777412i	$0.283468\pi$
$3$		0			0
$3$		0			0
$4$	0.107959	+	1.85358i	0.0539793	+	0.926789i
$5$	1.27364	+	0.148867i	0.569590	+	0.0665755i	0.396013	−	0.918245i	$-0.370394\pi$
$5$	1.27364	+	0.148867i	0.569590	+	0.0665755i	0.173577	+	0.984820i	$0.444468\pi$
$6$		0			0
$7$	1.70721	−	0.857394i	0.645266	−	0.324065i	−0.0958958	−	0.995391i	$-0.530572\pi$
$7$	1.70721	−	0.857394i	0.645266	−	0.324065i	0.741161	+	0.671327i	$0.234275\pi$
$8$	−1.11832	−	0.938383i	−0.395386	−	0.331768i
$9$		0			0
$10$	−0.371828	+	0.312001i	−0.117582	+	0.0986633i
$11$	−1.93272	+	4.48054i	−0.582736	+	1.35093i	0.330617	+	0.943765i	$0.392743\pi$
$11$	−1.93272	+	4.48054i	−0.582736	+	1.35093i	−0.913353	+	0.407169i	$0.866516\pi$
$12$		0			0
$13$	3.34705	−	0.793266i	0.928305	−	0.220012i	0.261465	−	0.965213i	$-0.415794\pi$
$13$	3.34705	−	0.793266i	0.928305	−	0.220012i	0.666840	+	0.745201i	$0.267646\pi$
$14$	−0.207399	+	0.692762i	−0.0554298	+	0.185148i
$15$		0			0
$16$	−3.13947	+	0.366951i	−0.784867	+	0.0917379i
$17$	−0.0728119	−	0.412937i	−0.0176595	−	0.100152i	0.974704	−	0.223499i	$-0.0717481\pi$
$17$	−0.0728119	−	0.412937i	−0.0176595	−	0.100152i	−0.992364	+	0.123348i	$0.960637\pi$
$18$		0			0
$19$	−0.626542	+	3.55329i	−0.143739	+	0.815182i	0.824633	+	0.565668i	$0.191382\pi$
$19$	−0.626542	+	3.55329i	−0.143739	+	0.815182i	−0.968371	+	0.249513i	$0.919729\pi$
$20$	−0.138437	+	2.37686i	−0.0309554	+	0.531483i
$21$		0			0
$22$	−0.731582	−	1.69600i	−0.155974	−	0.361588i
$23$	5.99966	+	3.01314i	1.25102	+	0.628284i	0.946032	−	0.324074i	$-0.105053\pi$
$23$	5.99966	+	3.01314i	1.25102	+	0.628284i	0.304984	+	0.952358i	$0.401349\pi$
$24$		0			0
$25$	−3.26522	−	0.773872i	−0.653045	−	0.154774i
$26$	−0.651020	+	1.12760i	−0.127675	+	0.221140i
$27$		0			0
$28$	1.77356	+	3.07189i	0.335170	+	0.580532i
$29$	−1.44045	−	4.81145i	−0.267486	−	0.893464i	−0.981194	−	0.193022i	$-0.938171\pi$
$29$	−1.44045	−	4.81145i	−0.267486	−	0.893464i	0.713709	−	0.700443i	$-0.247014\pi$
$30$		0			0
$31$	5.54449	−	3.64667i	0.995819	−	0.654960i	0.0566423	−	0.998395i	$-0.481961\pi$
$31$	5.54449	−	3.64667i	0.995819	−	0.654960i	0.939177	+	0.343434i	$0.111590\pi$
$32$	2.45802	−	3.30169i	0.434520	−	0.583662i
$33$		0			0
$34$	0.132607	+	0.0872170i	0.0227419	+	0.0149576i
$35$	2.30201	−	0.837864i	0.389111	−	0.141625i
$36$		0			0
$37$	0.465059	+	0.169268i	0.0764552	+	0.0278274i	0.379965	−	0.925001i	$-0.375936\pi$
$37$	0.465059	+	0.169268i	0.0764552	+	0.0278274i	−0.303509	+	0.952828i	$0.598158\pi$
$38$	−0.815575	−	1.09551i	−0.132304	−	0.177715i
$39$		0			0
$40$	−1.28465	−	1.36164i	−0.203120	−	0.215295i
$41$	−4.16545	−	4.41512i	−0.650535	−	0.689526i	0.315210	−	0.949022i	$-0.397925\pi$
$41$	−4.16545	−	4.41512i	−0.650535	−	0.689526i	−0.965744	+	0.259496i	$0.916444\pi$
$42$		0			0
$43$	−6.92694	−	9.30450i	−1.05635	−	1.41892i	−0.902429	−	0.430839i	$-0.858218\pi$
$43$	−6.92694	−	9.30450i	−1.05635	−	1.41892i	−0.153920	−	0.988083i	$-0.549190\pi$
$44$	−8.51368	−	3.09873i	−1.28349	−	0.467151i
$45$		0			0
$46$	−2.38808	+	0.869188i	−0.352102	+	0.128155i
$47$	5.06765	+	3.33305i	0.739193	+	0.486175i	0.862413	−	0.506205i	$-0.168952\pi$
$47$	5.06765	+	3.33305i	0.739193	+	0.486175i	−0.123221	+	0.992379i	$0.539322\pi$
$48$		0			0
$49$	−2.00066	+	2.68735i	−0.285809	+	0.383908i
$50$	1.06124	−	0.697991i	0.150082	−	0.0987108i
$51$		0			0
$52$	1.83172	+	6.11838i	0.254014	+	0.848467i
$53$	−2.95007	−	5.10967i	−0.405223	−	0.701867i	0.589124	−	0.808043i	$-0.299473\pi$
$53$	−2.95007	−	5.10967i	−0.405223	−	0.701867i	−0.994347	+	0.106175i	$0.966140\pi$
$54$		0			0
$55$	−3.12859	+	5.41888i	−0.421859	+	0.730682i
$56$	−2.71378	−	0.643177i	−0.362644	−	0.0859481i
$57$		0			0
$58$	1.69890	+	0.853222i	0.223077	+	0.112034i
$59$	−2.23192	−	5.17418i	−0.290572	−	0.673621i	0.708927	−	0.705282i	$-0.249180\pi$
$59$	−2.23192	−	5.17418i	−0.290572	−	0.673621i	−0.999499	+	0.0316611i	$0.989920\pi$
$60$		0			0
$61$	0.161757	−	2.77726i	0.0207109	−	0.355592i	−0.971993	−	0.235011i	$-0.924487\pi$
$61$	0.161757	−	2.77726i	0.0207109	−	0.355592i	0.992704	−	0.120581i	$-0.0384757\pi$
$62$	−0.436200	+	2.47381i	−0.0553975	+	0.314175i
$63$		0			0
$64$	−0.827191	−	4.69124i	−0.103399	−	0.586404i
$65$	4.38103	−	0.512069i	0.543400	−	0.0635144i
$66$		0			0
$67$	2.07542	−	6.93240i	0.253553	−	0.846928i	−0.732538	−	0.680726i	$-0.761665\pi$
$67$	2.07542	−	6.93240i	0.253553	−	0.846928i	0.986092	−	0.166202i	$-0.0531503\pi$
$68$	0.757549	−	0.179542i	0.0918664	−	0.0217727i
$69$		0			0
$70$	−0.367282	+	0.851455i	−0.0438986	+	0.101768i
$71$	11.9949	−	10.0649i	1.42353	−	1.19448i	0.474109	−	0.880466i	$-0.342770\pi$
$71$	11.9949	−	10.0649i	1.42353	−	1.19448i	0.949418	−	0.314015i	$-0.101674\pi$
$72$		0			0
$73$	−5.04326	−	4.23179i	−0.590268	−	0.495294i	0.298033	−	0.954556i	$-0.403670\pi$
$73$	−5.04326	−	4.23179i	−0.590268	−	0.495294i	−0.888301	+	0.459262i	$0.848114\pi$
$74$	−0.167408	+	0.0840754i	−0.0194608	+	0.00977357i
$75$		0			0
$76$	−6.65395	−	0.777735i	−0.763260	−	0.0892123i
$77$	0.542032	+	9.30634i	0.0617703	+	1.06056i
$78$		0			0
$79$	−2.62307	+	2.78030i	−0.295119	+	0.312808i	−0.857919	−	0.513786i	$-0.828243\pi$
$79$	−2.62307	+	2.78030i	−0.295119	+	0.312808i	0.562800	+	0.826593i	$0.309724\pi$
$80$	−4.05318			−0.453160
$81$		0			0
$82$	2.29763			0.253731
$83$	−3.32898	+	3.52851i	−0.365403	+	0.387304i	−0.883823	−	0.467822i	$-0.845039\pi$
$83$	−3.32898	+	3.52851i	−0.365403	+	0.387304i	0.518420	+	0.855126i	$0.326520\pi$
$84$		0			0
$85$	−0.0312634	−	0.536772i	−0.00339099	−	0.0582211i
$86$	4.36114	+	0.509744i	0.470274	+	0.0549671i
$87$		0			0
$88$	6.36586	−	3.19706i	0.678603	−	0.340807i
$89$	7.97723	+	6.69369i	0.845585	+	0.709530i	0.958813	−	0.284039i	$-0.0916746\pi$
$89$	7.97723	+	6.69369i	0.845585	+	0.709530i	−0.113228	+	0.993569i	$0.536119\pi$
$90$		0			0
$91$	5.03399	−	4.22402i	0.527705	−	0.442797i
$92$	−4.93738	+	11.4461i	−0.514757	+	1.19334i
$93$		0			0
$94$	−2.23406	+	0.529481i	−0.230425	+	0.0546118i
$95$	−1.32696	+	4.43235i	−0.136143	+	0.454749i
$96$		0			0
$97$	2.14884	−	0.251163i	0.218182	−	0.0255018i	−0.00629978	−	0.999980i	$-0.502005\pi$
$97$	2.14884	−	0.251163i	0.218182	−	0.0255018i	0.224481	+	0.974478i	$0.427931\pi$
$98$	−0.220216	−	1.24891i	−0.0222452	−	0.126159i
$99$		0			0
$100$	1.08192	−	6.13589i	0.108192	−	0.613589i
$101$	0.949061	−	16.2948i	0.0944351	−	1.62139i	−0.535358	−	0.844625i	$-0.679823\pi$
$101$	0.949061	−	16.2948i	0.0944351	−	1.62139i	0.629793	−	0.776763i	$-0.283140\pi$
$102$		0			0
$103$	7.15634	+	16.5903i	0.705135	+	1.63469i	0.770982	+	0.636857i	$0.219766\pi$
$103$	7.15634	+	16.5903i	0.705135	+	1.63469i	−0.0658471	+	0.997830i	$0.520975\pi$
$104$	−4.48747	−	2.25369i	−0.440032	−	0.220993i
$105$		0			0
$106$	2.17315	+	0.515046i	0.211075	+	0.0500257i
$107$	−8.06607	+	13.9708i	−0.779777	+	1.35061i	0.152294	+	0.988335i	$0.451334\pi$
$107$	−8.06607	+	13.9708i	−0.779777	+	1.35061i	−0.932070	+	0.362277i	$0.881999\pi$
$108$		0			0
$109$	4.04171	+	7.00045i	0.387126	+	0.670521i	0.992062	−	0.125753i	$-0.0401347\pi$
$109$	4.04171	+	7.00045i	0.387126	+	0.670521i	−0.604936	+	0.796274i	$0.706801\pi$
$110$	−0.679294	−	2.26900i	−0.0647681	−	0.216341i
$111$		0			0
$112$	−5.04512	+	3.31823i	−0.476719	+	0.313543i
$113$	1.02756	−	1.38026i	0.0966651	−	0.129844i	−0.751159	−	0.660121i	$-0.770505\pi$
$113$	1.02756	−	1.38026i	0.0966651	−	0.129844i	0.847824	+	0.530278i	$0.177912\pi$
$114$		0			0
$115$	7.19285	+	4.73081i	0.670737	+	0.441151i
$116$	8.76289	−	3.18943i	0.813614	−	0.296131i
$117$		0			0
$118$	2.00437	+	0.729529i	0.184517	+	0.0671586i
$119$	−0.478355	−	0.642542i	−0.0438507	−	0.0589017i
$120$		0			0
$121$	−8.79120	−	9.31813i	−0.799200	−	0.847102i
$122$	0.722644	+	0.765957i	0.0654251	+	0.0693465i
$123$		0			0
$124$	7.35795	+	9.88345i	0.660764	+	0.887560i
$125$	−10.0684	−	3.66460i	−0.900546	−	0.327772i
$126$		0			0
$127$	−4.79894	+	1.74667i	−0.425837	+	0.154992i	−0.546044	−	0.837757i	$-0.683867\pi$
$127$	−4.79894	+	1.74667i	−0.425837	+	0.154992i	0.120206	+	0.992749i	$0.461644\pi$
$128$	8.38455	+	5.51461i	0.741097	+	0.487427i
$129$		0			0
$130$	−0.997028	+	1.33924i	−0.0874452	+	0.117459i
$131$	−9.73457	+	6.40253i	−0.850514	+	0.559392i	−0.898258	−	0.439468i	$-0.855167\pi$
$131$	−9.73457	+	6.40253i	−0.850514	+	0.559392i	0.0477446	+	0.998860i	$0.484797\pi$
$132$		0			0
$133$	1.97693	+	6.60342i	0.171422	+	0.572589i
$134$	1.36958	+	2.37218i	0.118314	+	0.204925i
$135$		0			0
$136$	−0.306066	+	0.530121i	−0.0262449	+	0.0454575i
$137$	−4.82005	−	1.14237i	−0.411805	−	0.0975995i	0.0194912	−	0.999810i	$-0.493795\pi$
$137$	−4.82005	−	1.14237i	−0.411805	−	0.0975995i	−0.431296	+	0.902210i	$0.641944\pi$
$138$		0			0
$139$	15.0389	+	7.55284i	1.27559	+	0.640623i	0.952151	−	0.305627i	$-0.0988660\pi$
$139$	15.0389	+	7.55284i	1.27559	+	0.640623i	0.323435	+	0.946250i	$0.395162\pi$
$140$	1.80157	+	4.17651i	0.152260	+	0.352979i
$141$		0			0
$142$	−0.344625	+	5.91698i	−0.0289203	+	0.496542i
$143$	−2.91464	+	16.5298i	−0.243735	+	1.38229i
$144$		0			0
$145$	−1.11835	−	6.34250i	−0.0928742	−	0.526716i
$146$	2.47517	−	0.289306i	0.204847	−	0.0239431i
$147$		0			0
$148$	−0.263544	+	0.880297i	−0.0216632	+	0.0723600i
$149$	−16.9579	+	4.01909i	−1.38924	+	0.329257i	−0.856119	−	0.516779i	$-0.827131\pi$
$149$	−16.9579	+	4.01909i	−1.38924	+	0.329257i	−0.533126	+	0.846036i	$0.678983\pi$
$150$		0			0
$151$	2.55693	−	5.92763i	0.208080	−	0.482384i	−0.781932	−	0.623363i	$-0.785766\pi$
$151$	2.55693	−	5.92763i	0.208080	−	0.482384i	0.990013	+	0.140979i	$0.0450251\pi$
$152$	4.03503	−	3.38579i	0.327284	−	0.274624i
$153$		0			0
$154$	−2.70310	−	2.26817i	−0.217822	−	0.182775i
$155$	7.60455	−	3.81915i	0.610812	−	0.306762i
$156$		0			0
$157$	−12.6850	−	1.48266i	−1.01237	−	0.118329i	−0.406301	−	0.913739i	$-0.633181\pi$
$157$	−12.6850	−	1.48266i	−1.01237	−	0.118329i	−0.606072	+	0.795410i	$0.707256\pi$
$158$	−0.0841277	−	1.44442i	−0.00669284	−	0.114912i
$159$		0			0
$160$	3.62214	−	3.83925i	0.286356	−	0.303519i
$161$	12.8261			1.01084
$162$		0			0
$163$	−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
$165$		0			0
$166$	−0.106768	−	1.83313i	−0.00828677	−	0.142278i
$167$	−3.01391	−	0.352275i	−0.233223	−	0.0272599i	−0.00132163	−	0.999999i	$-0.500421\pi$
$167$	−3.01391	−	0.352275i	−0.233223	−	0.0272599i	−0.231902	+	0.972739i	$0.574495\pi$
$168$		0			0
$169$	−1.04374	+	0.524184i	−0.0802874	+	0.0403219i
$170$	0.155910	+	0.130824i	0.0119578	+	0.0100337i
$171$		0			0
$172$	16.4988	−	13.8441i	1.25802	−	1.05560i
$173$	3.82438	−	8.86591i	0.290762	−	0.674063i	−0.708745	−	0.705465i	$-0.750738\pi$
$173$	3.82438	−	8.86591i	0.290762	−	0.674063i	0.999507	+	0.0314024i	$0.00999735\pi$
$174$		0			0
$175$	−6.23795	+	1.47842i	−0.471544	+	0.111758i
$176$	4.42357	−	14.7757i	0.333439	−	1.11376i
$177$		0			0
$178$	−3.91513	+	0.457613i	−0.293451	+	0.0342995i
$179$	4.48229	+	25.4203i	0.335022	+	1.90001i	0.427012	+	0.904246i	$0.359566\pi$
$179$	4.48229	+	25.4203i	0.335022	+	1.90001i	−0.0919897	+	0.995760i	$0.529323\pi$
$180$		0			0
$181$	0.154861	−	0.878259i	0.0115107	−	0.0652805i	−0.978511	−	0.206193i	$-0.933893\pi$
$181$	0.154861	−	0.878259i	0.0115107	−	0.0652805i	0.990022	+	0.140913i	$0.0450036\pi$
$182$	−0.144632	+	2.48323i	−0.0107208	+	0.184069i
$183$		0			0
$184$	−3.88206	−	8.99964i	−0.286190	−	0.663462i
$185$	0.567120	+	0.284818i	0.0416955	+	0.0209403i
$186$		0			0
$187$	1.99090	+	0.471853i	0.145589	+	0.0345053i
$188$	−5.63096	+	9.75311i	−0.410680	+	0.711319i
$189$		0			0
$190$	−0.875665	−	1.51670i	−0.0635274	−	0.110033i
$191$	−2.31577	−	7.73521i	−0.167563	−	0.559700i	−0.999985	−	0.00555685i	$-0.998231\pi$
$191$	−2.31577	−	7.73521i	−0.167563	−	0.559700i	0.832421	−	0.554143i	$-0.186954\pi$
$192$		0			0
$193$	−0.162747	+	0.107041i	−0.0117148	+	0.00770494i	−0.555353	−	0.831615i	$-0.687417\pi$
$193$	−0.162747	+	0.107041i	−0.0117148	+	0.00770494i	0.543638	+	0.839320i	$0.317046\pi$
$194$	−0.489029	+	0.656880i	−0.0351102	+	0.0471612i
$195$		0			0
$196$	−5.19721	−	3.41826i	−0.371229	−	0.244161i
$197$	10.8405	−	3.94561i	0.772351	−	0.281113i	0.0743718	−	0.997231i	$-0.476305\pi$
$197$	10.8405	−	3.94561i	0.772351	−	0.281113i	0.697980	+	0.716118i	$0.254083\pi$
$198$		0			0
$199$	−1.65236	−	0.601410i	−0.117133	−	0.0426328i	0.282789	−	0.959182i	$-0.408740\pi$
$199$	−1.65236	−	0.601410i	−0.117133	−	0.0426328i	−0.399922	+	0.916549i	$0.630963\pi$
$200$	2.92538	+	3.92947i	0.206856	+	0.277855i
$201$		0			0
$202$	4.23989	+	4.49402i	0.298318	+	0.316198i
$203$	−6.58447	−	6.97913i	−0.462139	−	0.489839i
$204$		0			0
$205$	−4.64803	−	6.24338i	−0.324632	−	0.436057i
$206$	−6.42671	−	2.33913i	−0.447770	−	0.162975i
$207$		0			0
$208$	−10.2169	+	3.71864i	−0.708413	+	0.257841i
$209$	−14.7098	−	9.67476i	−1.01749	−	0.669217i
$210$		0			0
$211$	−2.13583	+	2.86892i	−0.147037	+	0.197504i	−0.869539	−	0.493864i	$-0.835584\pi$
$211$	−2.13583	+	2.86892i	−0.147037	+	0.197504i	0.722503	+	0.691368i	$0.242992\pi$
$212$	9.15269	−	6.01982i	0.628609	−	0.413443i
$213$		0			0
$214$	−1.75134	−	5.84989i	−0.119719	−	0.399890i
$215$	−7.43730	−	12.8818i	−0.507220	−	0.878530i
$216$		0			0
$217$	6.33898	−	10.9794i	0.430318	−	0.745333i
$218$	−2.97730	−	0.705633i	−0.201648	−	0.0477915i
$219$		0			0
$220$	−10.3821	−	5.21408i	−0.699960	−	0.351533i
$221$	−0.571274	−	1.32436i	−0.0384280	−	0.0890862i
$222$		0			0
$223$	0.381494	−	6.55001i	0.0255468	−	0.438621i	−0.961148	−	0.276035i	$-0.910979\pi$
$223$	0.381494	−	6.55001i	0.0255468	−	0.438621i	0.986694	−	0.162586i	$-0.0519835\pi$
$224$	1.36551	−	7.74417i	0.0912368	−	0.517429i
$225$		0			0
$226$	0.113106	+	0.641454i	0.00752367	+	0.0426689i
$227$	−8.07328	+	0.943631i	−0.535843	+	0.0626310i	−0.379711	−	0.925105i	$-0.623977\pi$
$227$	−8.07328	+	0.943631i	−0.535843	+	0.0626310i	−0.156132	+	0.987736i	$0.549902\pi$
$228$		0			0
$229$	−2.24705	+	7.50566i	−0.148489	+	0.495988i	−0.999578	−	0.0290329i	$-0.990757\pi$
$229$	−2.24705	+	7.50566i	−0.148489	+	0.495988i	0.851089	+	0.525021i	$0.175942\pi$
$230$	−3.17094	+	0.751528i	−0.209086	+	0.0495543i
$231$		0			0
$232$	−2.90409	+	6.73245i	−0.190663	+	0.442007i
$233$	19.7955	−	16.6104i	1.29685	−	1.08818i	0.306166	−	0.951978i	$-0.400954\pi$
$233$	19.7955	−	16.6104i	1.29685	−	1.08818i	0.990681	−	0.136205i	$-0.0434907\pi$
$234$		0			0
$235$	5.95818	+	4.99951i	0.388669	+	0.326132i
$236$	9.34979	−	4.69564i	0.608619	−	0.305660i
$237$		0			0
$238$	0.301168	+	0.0352015i	0.0195218	+	0.00228177i
$239$	0.0102090	+	0.175281i	0.000660364	+	0.0113380i	0.998622	−	0.0524749i	$-0.0167110\pi$
$239$	0.0102090	+	0.175281i	0.000660364	+	0.0113380i	−0.997962	+	0.0638129i	$0.979674\pi$
$240$		0			0
$241$	−13.2643	+	14.0594i	−0.854430	+	0.905643i	−0.996447	−	0.0842212i	$-0.973160\pi$
$241$	−13.2643	+	14.0594i	−0.854430	+	0.905643i	0.142017	+	0.989864i	$0.454641\pi$
$242$	4.84915			0.311715
$243$		0			0
$244$	5.16534			0.330677
$245$	−2.94818	+	3.12489i	−0.188352	+	0.199642i
$246$		0			0
$247$	0.721640	+	12.3901i	0.0459168	+	0.788362i
$248$	−9.62248	−	1.12471i	−0.611028	−	0.0714190i
$249$		0			0
$250$	3.62434	−	1.82021i	0.229223	−	0.115120i
$251$	−18.5138	−	15.5349i	−1.16858	−	0.980554i	−0.168592	−	0.985686i	$-0.553922\pi$
$251$	−18.5138	−	15.5349i	−1.16858	−	0.980554i	−0.999987	+	0.00513137i	$0.998367\pi$
$252$		0			0
$253$	−25.0962	+	21.0582i	−1.57778	+	1.32392i
$254$	0.765662	−	1.77500i	0.0480419	−	0.111374i
$255$		0			0
$256$	5.57410	−	1.32109i	0.348381	−	0.0825679i
$257$	−3.92685	+	13.1166i	−0.244950	+	0.818191i	0.743773	+	0.668433i	$0.233035\pi$
$257$	−3.92685	+	13.1166i	−0.244950	+	0.818191i	−0.988723	+	0.149758i	$0.952151\pi$
$258$		0			0
$259$	0.939084	−	0.109763i	0.0583518	−	0.00682035i
$260$	1.42213	+	8.06530i	0.0881968	+	0.500189i
$261$		0			0
$262$	0.765846	−	4.34333i	0.0473141	−	0.268332i
$263$	−0.844392	+	14.4977i	−0.0520675	+	0.893964i	0.866618	+	0.498973i	$0.166289\pi$
$263$	−0.844392	+	14.4977i	−0.0520675	+	0.893964i	−0.918685	+	0.394991i	$0.870748\pi$
$264$		0			0
$265$	−2.99667	−	6.94706i	−0.184084	−	0.426754i
$266$	−2.33164	−	1.17099i	−0.142962	−	0.0717983i
$267$		0			0
$268$	13.0738	+	3.09855i	0.798610	+	0.189274i
$269$	−0.0908847	+	0.157417i	−0.00554134	+	0.00959788i	−0.868783	−	0.495193i	$-0.835097\pi$
$269$	−0.0908847	+	0.157417i	−0.00554134	+	0.00959788i	0.863241	+	0.504791i	$0.168431\pi$
$270$		0			0
$271$	−10.1446	−	17.5709i	−0.616239	−	1.06736i	−0.990166	−	0.139899i	$-0.955322\pi$
$271$	−10.1446	−	17.5709i	−0.616239	−	1.06736i	0.373927	−	0.927458i	$-0.378011\pi$
$272$	0.380118	+	1.26968i	0.0230481	+	0.0769859i
$273$		0			0
$274$	1.56658	−	1.03036i	0.0946408	−	0.0622462i
$275$	9.77812	−	13.1343i	0.589643	−	0.792028i
$276$		0			0
$277$	9.30636	+	6.12089i	0.559165	+	0.367769i	0.797411	−	0.603436i	$-0.206202\pi$
$277$	9.30636	+	6.12089i	0.559165	+	0.367769i	−0.238246	+	0.971205i	$0.576573\pi$
$278$	−5.98603	+	2.17874i	−0.359018	+	0.130672i
$279$		0			0
$280$	−3.36063	−	1.22317i	−0.200836	−	0.0730983i
$281$	−1.19622	−	1.60680i	−0.0713603	−	0.0958535i	0.765010	−	0.644018i	$-0.222734\pi$
$281$	−1.19622	−	1.60680i	−0.0713603	−	0.0958535i	−0.836370	+	0.548165i	$0.815327\pi$
$282$		0			0
$283$	−1.56990	−	1.66400i	−0.0933210	−	0.0989145i	0.679030	−	0.734111i	$-0.262401\pi$
$283$	−1.56990	−	1.66400i	−0.0933210	−	0.0989145i	−0.772351	+	0.635196i	$0.780919\pi$
$284$	19.9510	+	21.1468i	1.18387	+	1.25483i
$285$		0			0
$286$	−3.79402	−	5.09625i	−0.224345	−	0.301348i
$287$	−10.8968	−	3.96612i	−0.643219	−	0.234112i
$288$		0			0
$289$	15.8096	−	5.75421i	0.929974	−	0.338483i
$290$	2.03678	+	1.33961i	0.119604	+	0.0786646i
$291$		0			0
$292$	7.29950	−	9.80492i	0.427171	−	0.573790i
$293$	4.19171	−	2.75693i	0.244882	−	0.161061i	−0.421135	−	0.906998i	$-0.638368\pi$
$293$	4.19171	−	2.75693i	0.244882	−	0.161061i	0.666017	+	0.745936i	$0.267998\pi$
$294$		0			0
$295$	−2.07240	−	6.92231i	−0.120660	−	0.403032i
$296$	−0.361248	−	0.625699i	−0.0209971	−	0.0363680i
$297$		0			0
$298$	3.29840	−	5.71300i	0.191071	−	0.330945i
$299$	22.4714	+	5.32582i	1.29955	+	0.308000i
$300$		0			0
$301$	−19.8034	−	9.94563i	−1.14145	−	0.573257i
$302$	0.967862	+	2.24376i	0.0556942	+	0.129114i
$303$		0			0
$304$	0.663122	−	11.3854i	0.0380327	−	0.652996i
$305$	0.619464	−	3.51316i	0.0354704	−	0.201163i
$306$		0			0
$307$	3.72532	+	21.1273i	0.212615	+	1.20580i	0.884997	+	0.465596i	$0.154160\pi$
$307$	3.72532	+	21.1273i	0.212615	+	1.20580i	−0.672382	+	0.740204i	$0.734729\pi$
$308$	−17.1915	+	2.00940i	−0.979577	+	0.114496i
$309$		0			0
$310$	−0.923833	+	3.08582i	−0.0524702	+	0.175263i
$311$	11.7156	−	2.77665i	0.664332	−	0.157450i	0.115403	−	0.993319i	$-0.463184\pi$
$311$	11.7156	−	2.77665i	0.664332	−	0.157450i	0.548929	+	0.835869i	$0.315036\pi$
$312$		0			0
$313$	3.68811	−	8.54999i	0.208464	−	0.483274i	−0.781619	−	0.623756i	$-0.785606\pi$
$313$	3.68811	−	8.54999i	0.208464	−	0.483274i	0.990083	+	0.140482i	$0.0448652\pi$
$314$	3.70327	−	3.10741i	0.208988	−	0.175361i
$315$		0			0
$316$	−5.43668	−	4.56191i	−0.305837	−	0.256628i
$317$	−14.6362	+	7.35057i	−0.822051	+	0.412849i	−0.809534	−	0.587072i	$-0.800280\pi$
$317$	−14.6362	+	7.35057i	−0.822051	+	0.412849i	−0.0125161	+	0.999922i	$0.503984\pi$
$318$		0			0
$319$	24.3419	+	2.84516i	1.36288	+	0.159298i
$320$	−0.355173	−	6.09809i	−0.0198548	−	0.340894i
$321$		0			0
$322$	−3.33171	+	3.53141i	−0.185669	+	0.196798i
$323$	1.51290			0.0841803
$324$		0			0
$325$	−11.5428			−0.640277
$326$	0.155822	−	0.165161i	0.00863016	−	0.00914744i
$327$		0			0
$328$	0.515239	+	8.84632i	0.0284493	+	0.488456i
$329$	11.5093	+	1.34524i	0.634528	+	0.0741656i
$330$		0			0
$331$	−4.58340	+	2.30187i	−0.251926	+	0.126522i	−0.570281	−	0.821449i	$-0.693166\pi$
$331$	−4.58340	+	2.30187i	−0.251926	+	0.126522i	0.318355	+	0.947972i	$0.396870\pi$
$332$	−6.89976	−	5.78959i	−0.378673	−	0.317745i
$333$		0			0
$334$	0.879884	−	0.738310i	0.0481451	−	0.0403985i
$335$	3.67535	−	8.52043i	0.200806	−	0.465521i
$336$		0			0
$337$	12.1868	−	2.88834i	0.663860	−	0.157338i	0.115147	−	0.993348i	$-0.463266\pi$
$337$	12.1868	−	2.88834i	0.663860	−	0.157338i	0.548713	+	0.836011i	$0.315118\pi$
$338$	0.126797	−	0.423533i	0.00689687	−	0.0230372i
$339$		0			0
$340$	0.991574	−	0.115898i	0.0537756	−	0.00628547i
$341$	5.62311	+	31.8903i	0.304509	+	1.72695i
$342$		0			0
$343$	−3.43362	+	19.4730i	−0.185398	+	1.05144i
$344$	−0.984635	+	16.9055i	−0.0530880	+	0.911486i
$345$		0			0
$346$	1.44762	+	3.35597i	0.0778247	+	0.180418i
$347$	12.5791	+	6.31748i	0.675284	+	0.339140i	0.753174	−	0.657822i	$-0.228522\pi$
$347$	12.5791	+	6.31748i	0.675284	+	0.339140i	−0.0778899	+	0.996962i	$0.524818\pi$
$348$		0			0
$349$	−14.9834	−	3.55113i	−0.802043	−	0.190088i	−0.190902	−	0.981609i	$-0.561141\pi$
$349$	−14.9834	−	3.55113i	−0.802043	−	0.190088i	−0.611141	+	0.791522i	$0.709289\pi$
$350$	1.21331	−	2.10152i	0.0648544	−	0.112331i
$351$		0			0
$352$	10.0427	+	17.3945i	0.535278	+	0.927129i
$353$	9.63269	+	32.1754i	0.512696	+	1.71252i	0.685951	+	0.727648i	$0.259386\pi$
$353$	9.63269	+	32.1754i	0.512696	+	1.71252i	−0.173255	+	0.984877i	$0.555428\pi$
$354$		0			0
$355$	16.7755	−	11.0334i	0.890349	−	0.585592i
$356$	−11.5461	+	15.5091i	−0.611940	+	0.821978i
$357$		0			0
$358$	−8.16328	−	5.36907i	−0.431443	−	0.283764i
$359$	−11.6368	+	4.23546i	−0.614168	+	0.223539i	−0.630326	−	0.776330i	$-0.717079\pi$
$359$	−11.6368	+	4.23546i	−0.614168	+	0.223539i	0.0161577	+	0.999869i	$0.494857\pi$
$360$		0			0
$361$	5.62081	+	2.04581i	0.295832	+	0.107674i
$362$	0.201584	+	0.270774i	0.0105950	+	0.0142316i
$363$		0			0
$364$	8.37301	+	8.87487i	0.438865	+	0.465169i
$365$	−5.79332	−	6.14056i	−0.303236	−	0.321412i
$366$		0			0
$367$	17.1370	+	23.0189i	0.894543	+	1.20158i	0.978735	+	0.205130i	$0.0657617\pi$
$367$	17.1370	+	23.0189i	0.894543	+	1.20158i	−0.0841921	+	0.996450i	$0.526831\pi$
$368$	−19.9414	−	7.25809i	−1.03952	−	0.378354i
$369$		0			0
$370$	−0.225734	+	0.0821603i	−0.0117353	+	0.00427131i
$371$	−9.41740	−	6.19392i	−0.488927	−	0.321572i
$372$		0			0
$373$	11.3384	−	15.2301i	0.587080	−	0.788586i	−0.404983	−	0.914324i	$-0.632723\pi$
$373$	11.3384	−	15.2301i	0.587080	−	0.788586i	0.992063	+	0.125738i	$0.0401300\pi$
$374$	−0.647071	+	0.425586i	−0.0334593	+	0.0220065i
$375$		0			0
$376$	−2.53959	−	8.48281i	−0.130969	−	0.437468i
$377$	−8.63804	−	14.9615i	−0.444882	−	0.770557i
$378$		0			0
$379$	−9.40390	+	16.2880i	−0.483046	+	0.836660i	−0.999810	−	0.0194673i	$-0.993803\pi$
$379$	−9.40390	+	16.2880i	−0.483046	+	0.836660i	0.516764	+	0.856128i	$0.327136\pi$
$380$	−8.35896	−	1.98111i	−0.428806	−	0.101629i
$381$		0			0
$382$	2.73127	+	1.37170i	0.139744	+	0.0701821i
$383$	−2.63824	−	6.11612i	−0.134808	−	0.312519i	0.837419	−	0.546562i	$-0.184064\pi$
$383$	−2.63824	−	6.11612i	−0.134808	−	0.312519i	−0.972226	+	0.234043i	$0.924804\pi$
$384$		0			0
$385$	−0.695054	+	11.9336i	−0.0354233	+	0.608194i
$386$	0.0128038	−	0.0726138i	0.000651695	−	0.00369595i
$387$		0			0
$388$	0.697536	+	3.95592i	0.0354120	+	0.200832i
$389$	0.868765	−	0.101544i	0.0440481	−	0.00514849i	−0.0940403	−	0.995568i	$-0.529978\pi$
$389$	0.868765	−	0.101544i	0.0440481	−	0.00514849i	0.138088	+	0.990420i	$0.455904\pi$
$390$		0			0
$391$	0.807390	−	2.69687i	0.0408315	−	0.136387i
$392$	4.75915	−	1.12794i	0.240373	−	0.0569695i
$393$		0			0
$394$	−1.72958	+	4.00961i	−0.0871347	+	0.202001i
$395$	−3.75475	+	3.15061i	−0.188922	+	0.158524i
$396$		0			0
$397$	26.1379	+	21.9323i	1.31182	+	1.10075i	0.987970	+	0.154644i	$0.0494231\pi$
$397$	26.1379	+	21.9323i	1.31182	+	1.10075i	0.323854	+	0.946107i	$0.395021\pi$
$398$	0.594802	−	0.298721i	0.0298147	−	0.0149735i
$399$		0			0
$400$	10.5350	+	1.23137i	0.526752	+	0.0615685i
$401$	−0.244187	−	4.19252i	−0.0121941	−	0.209364i	−0.998902	−	0.0468580i	$-0.985079\pi$
$401$	−0.244187	−	4.19252i	−0.0121941	−	0.209364i	0.986707	−	0.162507i	$-0.0519579\pi$
$402$		0			0
$403$	15.6649	−	16.6038i	0.780325	−	0.827096i
$404$	30.3060			1.50778
$405$		0			0
$406$	3.63194			0.180250
$407$	−1.65724	+	1.75657i	−0.0821463	+	0.0870699i
$408$		0			0
$409$	−1.26061	−	21.6439i	−0.0623333	−	1.07022i	−0.873945	−	0.486025i	$-0.838447\pi$
$409$	−1.26061	−	21.6439i	−0.0623333	−	1.07022i	0.811612	−	0.584197i	$-0.198590\pi$
$410$	2.92635	+	0.342042i	0.144522	+	0.0168922i
$411$		0			0
$412$	−29.9787	+	15.0559i	−1.47695	+	0.741750i
$413$	−8.24668	−	6.91978i	−0.405792	−	0.340500i
$414$		0			0
$415$	−4.76520	+	3.99848i	−0.233915	+	0.196278i
$416$	5.60799	−	13.0008i	0.274954	−	0.637416i
$417$		0			0
$418$	6.48474	−	1.53691i	0.317179	−	0.0751728i
$419$	−1.20046	+	4.00981i	−0.0586462	+	0.195892i	−0.982292	−	0.187354i	$-0.940009\pi$
$419$	−1.20046	+	4.00981i	−0.0586462	+	0.195892i	0.923646	+	0.383246i	$0.125194\pi$
$420$		0			0
$421$	−4.93643	+	0.576986i	−0.240587	+	0.0281206i	−0.235532	−	0.971867i	$-0.575683\pi$
$421$	−4.93643	+	0.576986i	−0.240587	+	0.0281206i	−0.00505515	+	0.999987i	$0.501609\pi$
$422$	−0.235094	−	1.33328i	−0.0114442	−	0.0649033i
$423$		0			0
$424$	−1.49570	+	8.48255i	−0.0726377	+	0.411949i
$425$	−0.0818132	+	1.40468i	−0.00396852	+	0.0681369i
$426$		0			0
$427$	−2.10506	−	4.88007i	−0.101871	−	0.236163i
$428$	−26.7668	−	13.4428i	−1.29382	−	0.649783i
$429$		0			0
$430$	5.47864	+	1.29846i	0.264204	+	0.0626174i
$431$	13.2418	−	22.9355i	0.637837	−	1.10477i	−0.348070	−	0.937469i	$-0.613163\pi$
$431$	13.2418	−	22.9355i	0.637837	−	1.10477i	0.985907	−	0.167297i	$-0.0535039\pi$
$432$		0			0
$433$	−10.6919	−	18.5189i	−0.513820	−	0.889962i	−0.999871	−	0.0160319i	$-0.994897\pi$
$433$	−10.6919	−	18.5189i	−0.513820	−	0.889962i	0.486052	−	0.873930i	$-0.338437\pi$
$434$	1.37635	+	4.59732i	0.0660668	+	0.220679i
$435$		0			0
$436$	−12.5395	+	8.24738i	−0.600535	+	0.394978i
$437$	−14.4656	+	19.4307i	−0.691984	+	0.929496i
$438$		0			0
$439$	−26.9943	−	17.7544i	−1.28837	−	0.847372i	−0.294255	−	0.955727i	$-0.595071\pi$
$439$	−26.9943	−	17.7544i	−1.28837	−	0.847372i	−0.994112	+	0.108355i	$0.965442\pi$
$440$	8.58376	−	3.12423i	0.409215	−	0.148942i
$441$		0			0
$442$	0.513029	+	0.186727i	0.0244023	+	0.00888171i
$443$	19.4171	+	26.0817i	0.922535	+	1.23918i	0.970689	+	0.240340i	$0.0772589\pi$
$443$	19.4171	+	26.0817i	0.922535	+	1.23918i	−0.0481536	+	0.998840i	$0.515334\pi$
$444$		0			0
$445$	9.16365	+	9.71291i	0.434399	+	0.460436i
$446$	1.70431	+	1.80646i	0.0807015	+	0.0855385i
$447$		0			0
$448$	−5.43443	−	7.29971i	−0.256753	−	0.344879i
$449$	−15.0197	−	5.46673i	−0.708825	−	0.257991i	−0.0376508	−	0.999291i	$-0.511987\pi$
$449$	−15.0197	−	5.46673i	−0.708825	−	0.257991i	−0.671174	+	0.741300i	$0.734210\pi$
$450$		0			0
$451$	27.8328	−	10.1303i	1.31059	−	0.477017i
$452$	2.66935	+	1.75566i	0.125556	+	0.0825793i
$453$		0			0
$454$	1.83730	−	2.46793i	0.0862289	−	0.115826i
$455$	7.04031	−	4.63049i	0.330055	−	0.217081i
$456$		0			0
$457$	−5.53279	−	18.4808i	−0.258813	−	0.864495i	−0.984337	−	0.176298i	$-0.943588\pi$
$457$	−5.53279	−	18.4808i	−0.258813	−	0.864495i	0.725524	−	0.688197i	$-0.241597\pi$
$458$	−1.48283	−	2.56834i	−0.0692883	−	0.120011i
$459$		0			0
$460$	−7.99240	+	13.8432i	−0.372648	+	0.645445i
$461$	−14.4202	−	3.41765i	−0.671615	−	0.159176i	−0.119360	−	0.992851i	$-0.538084\pi$
$461$	−14.4202	−	3.41765i	−0.671615	−	0.159176i	−0.552255	+	0.833675i	$0.686233\pi$
$462$		0			0
$463$	2.47485	+	1.24292i	0.115016	+	0.0577632i	0.505377	−	0.862899i	$-0.331353\pi$
$463$	2.47485	+	1.24292i	0.115016	+	0.0577632i	−0.390361	+	0.920662i	$0.627650\pi$
$464$	6.28783	+	14.5768i	0.291905	+	0.676713i
$465$		0			0
$466$	−0.568746	+	9.76499i	−0.0263466	+	0.452354i
$467$	−3.42252	+	19.4101i	−0.158375	+	0.898191i	0.797259	+	0.603637i	$0.206282\pi$
$467$	−3.42252	+	19.4101i	−0.158375	+	0.898191i	−0.955635	+	0.294554i	$0.904829\pi$
$468$		0			0
$469$	−2.40061	−	13.6145i	−0.110850	−	0.628661i
$470$	−2.92421	+	0.341791i	−0.134884	+	0.0157656i
$471$		0			0
$472$	−2.35935	+	7.88079i	−0.108598	+	0.362743i
$473$	55.0770	−	13.0535i	2.53244	−	0.600200i
$474$		0			0
$475$	4.79560	−	11.1174i	0.220037	−	0.510103i
$476$	1.13936	−	0.956036i	0.0522224	−	0.0438198i
$477$		0			0
$478$	−0.0509120	−	0.0427202i	−0.00232866	−	0.00195398i
$479$	−16.6577	+	8.36582i	−0.761110	+	0.382244i	−0.786625	−	0.617431i	$-0.788174\pi$
$479$	−16.6577	+	8.36582i	−0.761110	+	0.382244i	0.0255152	+	0.999674i	$0.491877\pi$
$480$		0			0
$481$	1.69085	+	0.197632i	0.0770962	+	0.00901125i
$482$	−0.425416	−	7.30411i	−0.0193772	−	0.332693i
$483$		0			0
$484$	16.3228	−	17.3011i	0.741945	−	0.786415i
$485$	2.77424			0.125972
$486$		0			0
$487$	−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			0
$490$	−0.0945547	−	1.62344i	−0.00427155	−	0.0733396i
$491$	3.67611	+	0.429676i	0.165901	+	0.0193910i	0.198638	−	0.980073i	$-0.436348\pi$
$491$	3.67611	+	0.429676i	0.165901	+	0.0193910i	−0.0327371	+	0.999464i	$0.510422\pi$
$492$		0			0
$493$	−1.88194	+	0.945147i	−0.0847584	+	0.0425673i
$494$	−3.59880	−	3.01975i	−0.161918	−	0.135865i
$495$		0			0
$496$	−16.0686	+	13.4832i	−0.721501	+	0.605411i
$497$	11.8482	−	27.4672i	0.531464	−	1.23207i
$498$		0			0
$499$	−27.1971	+	6.44583i	−1.21751	+	0.288555i	−0.788664	−	0.614824i	$-0.789227\pi$
$499$	−27.1971	+	6.44583i	−1.21751	+	0.288555i	−0.428844	+	0.903379i	$0.641079\pi$
$500$	5.70565	−	19.0582i	0.255165	−	0.852309i
$501$		0			0
$502$	9.08634	−	1.06204i	0.405543	−	0.0474012i
$503$	1.72317	+	9.77258i	0.0768323	+	0.435738i	0.998822	+	0.0485234i	$0.0154516\pi$
$503$	1.72317	+	9.77258i	0.0768323	+	0.435738i	−0.921990	+	0.387214i	$0.873437\pi$
$504$		0			0
$505$	3.63452	−	20.6124i	0.161734	−	0.917239i
$506$	0.721039	−	12.3798i	0.0320541	−	0.550348i
$507$		0			0
$508$	−3.75568	−	8.70665i	−0.166631	−	0.386295i
$509$	0.0252818	+	0.0126970i	0.00112059	+	0.000562784i	0.449359	−	0.893351i	$-0.351652\pi$
$509$	0.0252818	+	0.0126970i	0.00112059	+	0.000562784i	−0.448239	+	0.893914i	$0.647949\pi$
$510$		0			0
$511$	−12.2382	−	2.90051i	−0.541387	−	0.128311i
$512$	−11.1197	+	19.2599i	−0.491426	+	0.851176i
$513$		0			0
$514$	−2.59134	−	4.48834i	−0.114299	−	0.197972i
$515$	6.64486	+	22.1954i	0.292808	+	0.978045i
$516$		0			0
$517$	−24.7282	+	16.2640i	−1.08754	+	0.715289i
$518$	−0.213715	+	0.287069i	−0.00939010	+	0.0126131i
$519$		0			0
$520$	−5.37992	−	3.53843i	−0.235925	−	0.155170i
$521$	2.11604	−	0.770177i	0.0927056	−	0.0337421i	−0.295251	−	0.955420i	$-0.595403\pi$
$521$	2.11604	−	0.770177i	0.0927056	−	0.0337421i	0.387957	+	0.921678i	$0.373181\pi$
$522$		0			0
$523$	−11.5433	−	4.20142i	−0.504753	−	0.183715i	0.0770775	−	0.997025i	$-0.475441\pi$
$523$	−11.5433	−	4.20142i	−0.504753	−	0.183715i	−0.581831	+	0.813310i	$0.697663\pi$
$524$	−12.9185	−	17.3526i	−0.564348	−	0.758051i
$525$		0			0
$526$	−3.77229	−	3.99839i	−0.164480	−	0.174338i
$527$	−1.90955	−	2.02400i	−0.0831811	−	0.0881669i
$528$		0			0
$529$	13.1822	+	17.7068i	0.573141	+	0.769862i
$530$	2.69114	+	0.979495i	0.116896	+	0.0425465i
$531$		0			0
$532$	−12.0265	+	4.37730i	−0.521416	+	0.189780i
$533$	−17.4444	−	11.4733i	−0.755599	−	0.496965i
$534$		0			0
$535$	−12.3531	+	16.5931i	−0.534070	+	0.717381i
$536$	−8.82624	+	5.80511i	−0.381235	+	0.250742i
$537$		0			0
$538$	−0.0197333	−	0.0659138i	−0.000850762	−	0.00284174i
$539$	−8.17409	−	14.1579i	−0.352083	−	0.609826i
$540$		0			0
$541$	19.8474	−	34.3766i	0.853304	−	1.47797i	−0.0249047	−	0.999690i	$-0.507928\pi$
$541$	19.8474	−	34.3766i	0.853304	−	1.47797i	0.878209	−	0.478277i	$-0.158738\pi$
$542$	7.47294	+	1.77112i	0.320990	+	0.0760761i
$543$		0			0
$544$	−1.54236	−	0.774603i	−0.0661282	−	0.0332108i
$545$	4.10555	+	9.51773i	0.175862	+	0.407695i
$546$		0			0
$547$	−0.472894	+	8.11928i	−0.0202195	+	0.347155i	0.972992	+	0.230837i	$0.0741464\pi$
$547$	−0.472894	+	8.11928i	−0.0202195	+	0.347155i	−0.993212	+	0.116318i	$0.962891\pi$
$548$	1.59711	−	9.05767i	0.0682252	−	0.386924i
$549$		0			0
$550$	1.07629	+	6.10396i	0.0458933	+	0.260274i
$551$	17.9990	−	2.10378i	0.766784	−	0.0896242i
$552$		0			0
$553$	−2.09433	+	6.99556i	−0.0890601	+	0.297482i
$554$	−4.10268	+	0.972352i	−0.174306	+	0.0413113i
$555$		0			0
$556$	−12.3762	+	28.6912i	−0.524867	+	1.21678i
$557$	16.2629	−	13.6462i	0.689081	−	0.578207i	−0.229563	−	0.973294i	$-0.573730\pi$
$557$	16.2629	−	13.6462i	0.689081	−	0.578207i	0.918644	+	0.395086i	$0.129285\pi$
$558$		0			0
$559$	−30.5658	−	25.6477i	−1.29279	−	1.08478i
$560$	−6.91965	+	3.47518i	−0.292408	+	0.146853i
$561$		0			0
$562$	0.753127	+	0.0880279i	0.0317687	+	0.00371323i
$563$	−2.62696	−	45.1032i	−0.110713	−	1.90087i	−0.360791	−	0.932647i	$-0.617493\pi$
$563$	−2.62696	−	45.1032i	−0.110713	−	1.90087i	0.250078	−	0.968226i	$-0.419544\pi$
$564$		0			0
$565$	1.51422	−	1.60498i	0.0637038	−	0.0675221i
$566$	0.865945			0.0363984
$567$		0			0
$568$	−22.8588			−0.959134
$569$	3.93683	−	4.17280i	0.165041	−	0.174933i	−0.639575	−	0.768728i	$-0.720890\pi$
$569$	3.93683	−	4.17280i	0.165041	−	0.174933i	0.804616	+	0.593796i	$0.202371\pi$
$570$		0			0
$571$	−2.52145	−	43.2916i	−0.105519	−	1.81170i	−0.472351	−	0.881411i	$-0.656594\pi$
$571$	−2.52145	−	43.2916i	−0.105519	−	1.81170i	0.366831	−	0.930287i	$-0.380443\pi$
$572$	−30.9539	−	3.61799i	−1.29425	−	0.151276i
$573$		0			0
$574$	3.92254	−	1.96997i	0.163724	−	0.0822251i
$575$	−17.2584	−	14.4816i	−0.719727	−	0.603923i
$576$		0			0
$577$	10.1857	−	8.54680i	0.424035	−	0.355808i	−0.405660	−	0.914024i	$-0.632958\pi$
$577$	10.1857	−	8.54680i	0.424035	−	0.355808i	0.829696	+	0.558216i	$0.188514\pi$
$578$	−2.52238	+	5.84754i	−0.104917	+	0.243226i
$579$		0			0
$580$	11.6356	−	2.75768i	0.483141	−	0.114507i
$581$	−2.65795	+	8.87816i	−0.110270	+	0.368328i
$582$		0			0
$583$	28.5957	−	3.34236i	1.18431	−	0.138427i
$584$	1.66894	+	9.46501i	0.0690611	+	0.391665i
$585$		0			0
$586$	−0.329773	+	1.87024i	−0.0136228	+	0.0772588i
$587$	0.719217	−	12.3485i	0.0296853	−	0.509677i	−0.950391	−	0.311057i	$-0.899317\pi$
$587$	0.719217	−	12.3485i	0.0296853	−	0.509677i	0.980077	−	0.198620i	$-0.0636459\pi$
$588$		0			0
$589$	9.48382	+	21.9860i	0.390774	+	0.905916i
$590$	2.44424	+	1.22754i	0.100628	+	0.0505371i
$591$		0			0
$592$	−1.52215	−	0.360757i	−0.0625601	−	0.0148270i
$593$	−0.572367	+	0.991369i	−0.0235043	+	0.0407106i	−0.877538	−	0.479507i	$-0.840816\pi$
$593$	−0.572367	+	0.991369i	−0.0235043	+	0.0407106i	0.854034	+	0.520217i	$0.174149\pi$
$594$		0			0
$595$	−0.513599	−	0.889579i	−0.0210555	−	0.0364692i
$596$	−9.28045	−	30.9989i	−0.380142	−	1.26976i
$597$		0			0
$598$	−7.30351	+	4.80360i	−0.298663	+	0.196434i
$599$	−1.44868	+	1.94591i	−0.0591913	+	0.0795078i	−0.830733	−	0.556671i	$-0.812078\pi$
$599$	−1.44868	+	1.94591i	−0.0591913	+	0.0795078i	0.771542	+	0.636179i	$0.219486\pi$
$600$		0			0
$601$	32.7732	+	21.5553i	1.33685	+	0.879259i	0.998100	−	0.0616181i	$-0.0196261\pi$
$601$	32.7732	+	21.5553i	1.33685	+	0.879259i	0.338748	+	0.940877i	$0.389996\pi$
$602$	7.88244	−	2.86897i	0.321264	−	0.116931i
$603$		0			0
$604$	11.2634	+	4.09953i	0.458300	+	0.166808i
$605$	−9.80967	−	13.1767i	−0.398820	−	0.535708i
$606$		0			0
$607$	4.86035	+	5.15167i	0.197276	+	0.209100i	0.818458	−	0.574566i	$-0.194829\pi$
$607$	4.86035	+	5.15167i	0.197276	+	0.209100i	−0.621183	+	0.783666i	$0.713348\pi$
$608$	10.1918	+	10.8027i	0.413333	+	0.438107i
$609$		0			0
$610$	0.806362	+	1.08313i	0.0326487	+	0.0438548i
$611$	19.6057	+	7.13588i	0.793161	+	0.288687i
$612$		0			0
$613$	19.4482	−	7.07855i	0.785503	−	0.285900i	0.0820378	−	0.996629i	$-0.473857\pi$
$613$	19.4482	−	7.07855i	0.785503	−	0.285900i	0.703466	+	0.710729i	$0.251635\pi$
$614$	−6.78466	−	4.46234i	−0.273806	−	0.180085i
$615$		0			0
$616$	8.12674	−	10.9161i	0.327436	−	0.439822i
$617$	−19.9175	+	13.1000i	−0.801849	+	0.527385i	−0.883031	−	0.469315i	$-0.844501\pi$
$617$	−19.9175	+	13.1000i	−0.801849	+	0.527385i	0.0811816	+	0.996699i	$0.474131\pi$
$618$		0			0
$619$	0.190902	+	0.637658i	0.00767301	+	0.0256296i	0.961740	−	0.273963i	$-0.0883345\pi$
$619$	0.190902	+	0.637658i	0.00767301	+	0.0256296i	−0.954067	+	0.299592i	$0.903149\pi$
$620$	7.90007	+	13.6833i	0.317274	+	0.549535i
$621$		0			0
$622$	−2.27875	+	3.94691i	−0.0913696	+	0.158257i
$623$	19.3580	+	4.58792i	0.775560	+	0.183811i
$624$		0			0
$625$	2.71571	+	1.36388i	0.108628	+	0.0545552i
$626$	1.39604	+	3.23639i	0.0557970	+	0.129352i
$627$		0			0
$628$	1.37878	−	23.6727i	0.0550192	−	0.944643i
$629$	0.0360350	−	0.204365i	0.00143681	−	0.00814855i
$630$		0			0
$631$	4.06193	+	23.0363i	0.161703	+	0.917062i	0.952399	+	0.304854i	$0.0986076\pi$
$631$	4.06193	+	23.0363i	0.161703	+	0.917062i	−0.790696	+	0.612209i	$0.790281\pi$
$632$	5.54242	−	0.647816i	0.220466	−	0.0257687i
$633$		0			0
$634$	1.77807	−	5.93915i	0.0706160	−	0.235874i
$635$	−6.37216	+	1.51023i	−0.252871	+	0.0599316i
$636$		0			0
$637$	−4.56453	+	10.5818i	−0.180853	+	0.419265i
$638$	−7.10640	+	5.96298i	−0.281345	+	0.236077i
$639$		0			0
$640$	9.85797	+	8.27182i	0.389670	+	0.326972i
$641$	−6.36402	+	3.19613i	−0.251364	+	0.126240i	−0.570020	−	0.821631i	$-0.693065\pi$
$641$	−6.36402	+	3.19613i	−0.251364	+	0.126240i	0.318657	+	0.947870i	$0.396768\pi$
$642$		0			0
$643$	−15.3703	−	1.79653i	−0.606144	−	0.0708481i	−0.192516	−	0.981294i	$-0.561665\pi$
$643$	−15.3703	−	1.79653i	−0.606144	−	0.0708481i	−0.413628	+	0.910446i	$0.635739\pi$
$644$	1.38469	+	23.7743i	0.0545645	+	0.936837i
$645$		0			0
$646$	−0.392992	+	0.416547i	−0.0154620	+	0.0163888i
$647$	15.3916			0.605107			0.302554	−	0.953132i	$-0.402161\pi$
$647$	15.3916			0.605107			0.302554	+	0.953132i	$0.402161\pi$
$648$		0			0
$649$	27.4968			1.07934
$650$	2.99834	−	3.17806i	0.117605	−	0.124654i
$651$		0			0
$652$	−0.0647610	−	1.11190i	−0.00253624	−	0.0435455i
$653$	−1.22345	−	0.143001i	−0.0478773	−	0.00559605i	0.0921206	−	0.995748i	$-0.470635\pi$
$653$	−1.22345	−	0.143001i	−0.0478773	−	0.00559605i	−0.139998	+	0.990152i	$0.544710\pi$
$654$		0			0
$655$	−13.3515	+	6.70537i	−0.521686	+	0.262000i
$656$	14.6975	+	12.3326i	0.573839	+	0.481508i
$657$		0			0
$658$	−3.36003	+	2.81940i	−0.130988	+	0.109912i
$659$	−2.73379	+	6.33763i	−0.106493	+	0.246879i	−0.963128	−	0.269045i	$-0.913292\pi$
$659$	−2.73379	+	6.33763i	−0.106493	+	0.246879i	0.856634	+	0.515924i	$0.172551\pi$
$660$		0			0
$661$	−34.9734	+	8.28885i	−1.36031	+	0.322399i	−0.845073	−	0.534650i	$-0.820443\pi$
$661$	−34.9734	+	8.28885i	−1.36031	+	0.322399i	−0.515235	+	0.857049i	$0.672295\pi$
$662$	0.556810	−	1.85987i	0.0216410	−	0.0722861i
$663$		0			0
$664$	7.03396	−	0.822152i	0.272971	−	0.0319057i
$665$	1.53487	+	8.70469i	0.0595198	+	0.337553i
$666$		0			0
$667$	5.85536	−	33.2074i	0.226720	−	1.28579i
$668$	0.327592	−	5.62455i	0.0126749	−	0.217620i
$669$		0			0
$670$	1.39121	+	3.22519i	0.0537473	+	0.124600i
$671$	12.1310	+	6.09242i	0.468313	+	0.235195i
$672$		0			0
$673$	8.46457	+	2.00614i	0.326285	+	0.0773310i	0.390494	−	0.920606i	$-0.372304\pi$
$673$	8.46457	+	2.00614i	0.326285	+	0.0773310i	−0.0642089	+	0.997936i	$0.520452\pi$
$674$	−2.37041	+	4.10567i	−0.0913047	+	0.158144i
$675$		0			0
$676$	−1.08430	−	1.87806i	−0.0417037	−	0.0722329i
$677$	−0.165536	−	0.552928i	−0.00636206	−	0.0212508i	0.954750	−	0.297411i	$-0.0961231\pi$
$677$	−0.165536	−	0.552928i	−0.00636206	−	0.0212508i	−0.961112	+	0.276160i	$0.910938\pi$
$678$		0			0
$679$	3.45318	−	2.27119i	0.132521	−	0.0871603i
$680$	−0.468735	+	0.629621i	−0.0179752	+	0.0241449i
$681$		0			0
$682$	−10.2410	−	6.73560i	−0.392147	−	0.257919i
$683$	−33.8572	+	12.3230i	−1.29551	+	0.471528i	−0.895532	−	0.444997i	$-0.853205\pi$
$683$	−33.8572	+	12.3230i	−1.29551	+	0.471528i	−0.399979	+	0.916524i	$0.630983\pi$
$684$		0			0
$685$	−5.96895	−	2.17252i	−0.228062	−	0.0830078i
$686$	−4.46957	−	6.00367i	−0.170649	−	0.229221i
$687$		0			0
$688$	25.1612	+	26.6693i	0.959263	+	1.01676i
$689$	−13.9274	−	14.7621i	−0.530590	−	0.562393i
$690$		0			0
$691$	−8.76512	−	11.7736i	−0.333441	−	0.447889i	0.603507	−	0.797357i	$-0.293769\pi$
$691$	−8.76512	−	11.7736i	−0.333441	−	0.447889i	−0.936948	+	0.349469i	$0.886362\pi$
$692$	16.8465	+	6.13164i	0.640409	+	0.233090i
$693$		0			0
$694$	−5.00694	+	1.82238i	−0.190061	+	0.0691765i
$695$	18.0298	+	11.8584i	0.683911	+	0.449815i
$696$		0			0
$697$	−1.51987	+	2.04154i	−0.0575692	+	0.0773289i
$698$	4.86981	−	3.20293i	0.184325	−	0.121233i
$699$		0			0
$700$	−3.41381	−	11.4029i	−0.129030	−	0.430989i
$701$	15.3027	+	26.5051i	0.577976	+	1.00108i	0.995711	+	0.0925152i	$0.0294907\pi$
$701$	15.3027	+	26.5051i	0.577976	+	1.00108i	−0.417735	+	0.908569i	$0.637176\pi$
$702$		0			0
$703$	−0.892837	+	1.54644i	−0.0336740	+	0.0583250i
$704$	22.6180	+	5.36056i	0.852448	+	0.202034i
$705$		0			0
$706$	−11.3610	−	5.70572i	−0.427577	−	0.214737i
$707$	−12.3508	−	28.6323i	−0.464499	−	1.07683i
$708$		0			0
$709$	−2.68046	+	46.0217i	−0.100667	+	1.72838i	0.449462	+	0.893300i	$0.351616\pi$
$709$	−2.68046	+	46.0217i	−0.100667	+	1.72838i	−0.550128	+	0.835080i	$0.685421\pi$
$710$	−1.31977	+	7.48480i	−0.0495302	+	0.280900i
$711$		0			0
$712$	−2.63986	−	14.9714i	−0.0989329	−	0.561077i
$713$	44.2529	−	5.17243i	1.65729	−	0.193709i
$714$		0			0
$715$	−6.17295	+	20.6191i	−0.230855	+	0.771110i
$716$	−46.6347	+	11.0526i	−1.74282	+	0.413056i
$717$		0			0
$718$	1.85663	−	4.30416i	0.0692889	−	0.160630i
$719$	−15.5899	+	13.0815i	−0.581404	+	0.487856i	−0.885408	−	0.464815i	$-0.846121\pi$
$719$	−15.5899	+	13.0815i	−0.581404	+	0.487856i	0.304004	+	0.952671i	$0.401676\pi$
$720$		0			0
$721$	26.4418	+	22.1873i	0.984743	+	0.826298i
$722$	−2.02333	+	1.01616i	−0.0753006	+	0.0378174i
$723$		0			0
$724$	1.64464	+	0.192231i	0.0611226	+	0.00714421i
$725$	0.979956	+	16.8252i	0.0363947	+	0.624872i
$726$		0			0
$727$	16.6791	−	17.6788i	0.618593	−	0.655670i	−0.340008	−	0.940422i	$-0.610430\pi$
$727$	16.6791	−	17.6788i	0.618593	−	0.655670i	0.958601	+	0.284752i	$0.0919114\pi$
$728$	−9.59336			−0.355554
$729$		0			0
$730$	3.19555			0.118272
$731$	−3.33780	+	3.53787i	−0.123453	+	0.130853i
$732$		0			0
$733$	2.31961	+	39.8261i	0.0856767	+	1.47101i	0.717857	+	0.696191i	$0.245123\pi$
$733$	2.31961	+	39.8261i	0.0856767	+	1.47101i	−0.632180	+	0.774821i	$0.717840\pi$
$734$	−10.7893	−	1.26109i	−0.398240	−	0.0465475i
$735$		0			0
$736$	24.6957	−	12.4027i	0.910296	−	0.457168i
$737$	27.0497	+	22.6974i	0.996389	+	0.836069i
$738$		0			0
$739$	6.20932	−	5.21024i	0.228413	−	0.191662i	−0.521397	−	0.853314i	$-0.674589\pi$
$739$	6.20932	−	5.21024i	0.228413	−	0.191662i	0.749811	+	0.661652i	$0.230145\pi$
$740$	−0.466707	+	1.08195i	−0.0171565	+	0.0397733i
$741$		0			0
$742$	4.15163	−	0.983954i	0.152411	−	0.0361221i
$743$	−7.11485	+	23.7653i	−0.261019	+	0.871863i	0.722548	+	0.691320i	$0.242971\pi$
$743$	−7.11485	+	23.7653i	−0.261019	+	0.871863i	−0.983567	+	0.180543i	$0.942215\pi$
$744$		0			0
$745$	−22.1966	+	2.59441i	−0.813220	+	0.0950517i
$746$	1.24804	+	7.07796i	0.0456938	+	0.259143i
$747$		0			0
$748$	−0.659681	+	3.74124i	−0.0241203	+	0.136793i
$749$	−1.79197	+	30.7670i	−0.0654773	+	1.12420i
$750$		0			0
$751$	−12.5408	−	29.0728i	−0.457619	−	1.06088i	−0.978312	−	0.207137i	$-0.933586\pi$
$751$	−12.5408	−	29.0728i	−0.457619	−	1.06088i	0.520693	−	0.853744i	$-0.325674\pi$
$752$	−17.1328	−	8.60441i	−0.624769	−	0.313771i
$753$		0			0
$754$	6.36316	+	1.50810i	0.231732	+	0.0549216i
$755$	4.13904	−	7.16903i	0.150635	−	0.260908i
$756$		0			0
$757$	−7.21394	−	12.4949i	−0.262195	−	0.454135i	0.704630	−	0.709575i	$-0.251113\pi$
$757$	−7.21394	−	12.4949i	−0.262195	−	0.454135i	−0.966825	+	0.255440i	$0.917780\pi$
$758$	−2.04182	−	6.82014i	−0.0741621	−	0.247719i
$759$		0			0
$760$	5.64321	−	3.71160i	0.204701	−	0.134634i
$761$	−13.3336	+	17.9101i	−0.483342	+	0.649241i	−0.975172	−	0.221451i	$-0.928921\pi$
$761$	−13.3336	+	17.9101i	−0.483342	+	0.649241i	0.491830	+	0.870691i	$0.336328\pi$
$762$		0			0
$763$	12.9022	+	8.48591i	0.467091	+	0.307211i
$764$	14.0878	−	5.12754i	0.509679	−	0.185508i
$765$		0			0
$766$	2.36925	+	0.862338i	0.0856046	+	0.0311575i
$767$	−11.5749	−	15.5477i	−0.417944	−	0.561396i
$768$		0			0
$769$	−18.7216	−	19.8437i	−0.675118	−	0.715583i	0.295732	−	0.955271i	$-0.404436\pi$
$769$	−18.7216	−	19.8437i	−0.675118	−	0.715583i	−0.970850	+	0.239688i	$0.922955\pi$
$770$	−3.10513	−	3.29124i	−0.111901	−	0.118608i
$771$		0			0
$772$	−0.215978	−	0.290109i	−0.00777321	−	0.0104412i
$773$	−7.11832	−	2.59086i	−0.256028	−	0.0931867i	0.210817	−	0.977525i	$-0.432387\pi$
$773$	−7.11832	−	2.59086i	−0.256028	−	0.0931867i	−0.466846	+	0.884339i	$0.654610\pi$
$774$		0			0
$775$	−20.9260	+	7.61646i	−0.751686	+	0.273591i
$776$	−2.63878	−	1.73555i	−0.0947267	−	0.0623027i
$777$		0			0
$778$	−0.197712	+	0.265573i	−0.00708832	+	0.00952126i
$779$	18.2981	−	12.0348i	0.655596	−	0.431192i
$780$		0			0
$781$	21.9134	+	73.1960i	0.784124	+	2.61916i
$782$	0.532800	+	0.922836i	0.0190529	+	0.0330006i
$783$		0			0
$784$	5.29489	−	9.17101i	0.189103	−	0.327536i
$785$	−15.9354	−	3.77676i	−0.568759	−	0.134798i
$786$		0			0
$787$	−7.15801	−	3.59489i	−0.255155	−	0.128144i	0.316624	−	0.948551i	$-0.397451\pi$
$787$	−7.15801	−	3.59489i	−0.255155	−	0.128144i	−0.571780	+	0.820407i	$0.693747\pi$
$788$	8.48381	+	19.6677i	0.302223	+	0.700632i
$789$		0			0
$790$	0.107878	−	1.85219i	0.00383812	−	0.0658980i
$791$	0.570845	−	3.23742i	0.0202969	−	0.115109i
$792$		0			0
$793$	−1.66170	−	9.42396i	−0.0590087	−	0.334655i
$794$	−12.8282	+	1.49940i	−0.455255	+	0.0532117i
$795$		0			0
$796$	0.936374	−	3.12771i	0.0331889	−	0.110859i
$797$	−13.3001	+	3.15217i	−0.471113	+	0.111656i	−0.459313	−	0.888275i	$-0.651904\pi$
$797$	−13.3001	+	3.15217i	−0.471113	+	0.111656i	−0.0117999	+	0.999930i	$0.503756\pi$
$798$		0			0
$799$	1.00735	−	2.33530i	0.0356375	−	0.0826171i
$800$	−10.5811	+	8.87856i	−0.374097	+	0.313905i
$801$		0			0
$802$	1.21775	+	1.02182i	0.0430003	+	0.0360816i
$803$	28.7079	−	14.4177i	1.01308	−	0.508788i
$804$		0			0
$805$	16.3359	+	1.90939i	0.575765	+	0.0672973i
$806$	0.502408	+	8.62601i	0.0176966	+	0.303838i
$807$		0			0
$808$	−16.3521	+	17.3322i	−0.575264	+	0.609744i
$809$	−6.31109			−0.221886			−0.110943	−	0.993827i	$-0.535387\pi$
$809$	−6.31109			−0.221886			−0.110943	+	0.993827i	$0.535387\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	−0.0531513	−	0.912572i	−0.00186295	−	0.0319856i
$815$	−0.764017	−	0.0893008i	−0.0267624	−	0.00312807i
$816$		0			0
$817$	37.4016	−	18.7838i	1.30852	−	0.657162i
$818$	6.28665	+	5.27513i	0.219808	+	0.184440i
$819$		0			0
$820$	11.0708	−	9.28950i	0.386609	−	0.324403i
$821$	−12.5829	+	29.1705i	−0.439147	+	1.01806i	0.544633	+	0.838675i	$0.316669\pi$
$821$	−12.5829	+	29.1705i	−0.439147	+	1.01806i	−0.983780	+	0.179382i	$0.942590\pi$
$822$		0			0
$823$	25.0358	−	5.93360i	0.872694	−	0.206832i	0.230219	−	0.973139i	$-0.426056\pi$
$823$	25.0358	−	5.93360i	0.872694	−	0.206832i	0.642475	+	0.766307i	$0.277908\pi$
$824$	7.56493	−	25.2686i	0.263537	−	0.880274i
$825$		0			0
$826$	4.04737	−	0.473070i	0.140826	−	0.0164602i
$827$	−3.15225	−	17.8773i	−0.109615	−	0.621655i	−0.989276	−	0.146056i	$-0.953342\pi$
$827$	−3.15225	−	17.8773i	−0.109615	−	0.621655i	0.879662	−	0.475600i	$-0.157769\pi$
$828$		0			0
$829$	−4.93669	+	27.9974i	−0.171458	+	0.972389i	0.770694	+	0.637205i	$0.219910\pi$
$829$	−4.93669	+	27.9974i	−0.171458	+	0.972389i	−0.942153	+	0.335184i	$0.891202\pi$
$830$	0.136909	−	2.35064i	0.00475219	−	0.0815920i
$831$		0			0
$832$	−6.49005	−	15.0456i	−0.225002	−	0.521613i
$833$	1.25538	+	0.630475i	0.0434963	+	0.0218447i
$834$		0			0
$835$	−3.78620	−	0.897345i	−0.131027	−	0.0310539i
$836$	16.3449	−	28.3101i	0.565299	−	0.979127i
$837$		0			0
$838$	−0.792187	−	1.37211i	−0.0273656	−	0.0473987i
$839$	−8.56334	−	28.6036i	−0.295639	−	0.987504i	−0.968766	−	0.247977i	$-0.920234\pi$
$839$	−8.56334	−	28.6036i	−0.295639	−	0.987504i	0.673126	−	0.739527i	$-0.264951\pi$
$840$		0			0
$841$	3.15398	−	2.07441i	0.108758	−	0.0715312i
$842$	1.12342	−	1.50902i	0.0387158	−	0.0520043i
$843$		0			0
$844$	−5.54834	−	3.64920i	−0.190982	−	0.125611i
$845$	−1.40738	+	0.512244i	−0.0484153	+	0.0176217i
$846$		0			0
$847$	−22.9977	−	8.37050i	−0.790212	−	0.287614i
$848$	11.1367	+	14.9591i	0.382434	+	0.513698i
$849$		0			0
$850$	−0.365497	−	0.387404i	−0.0125364	−	0.0132879i
$851$	2.28017	+	2.41684i	0.0781632	+	0.0828481i
$852$		0			0
$853$	−3.04813	−	4.09435i	−0.104366	−	0.140188i	0.746872	−	0.664968i	$-0.231555\pi$
$853$	−3.04813	−	4.09435i	−0.104366	−	0.140188i	−0.851238	+	0.524780i	$0.824147\pi$
$854$	1.89043	+	0.688062i	0.0646893	+	0.0235450i
$855$		0			0
$856$	22.1305	−	8.05483i	0.756403	−	0.275308i
$857$	11.8982	+	7.82555i	0.406434	+	0.267316i	0.736223	−	0.676739i	$-0.236607\pi$
$857$	11.8982	+	7.82555i	0.406434	+	0.267316i	−0.329790	+	0.944054i	$0.606978\pi$
$858$		0			0
$859$	−25.0637	+	33.6664i	−0.855162	+	1.14868i	0.132361	+	0.991202i	$0.457744\pi$
$859$	−25.0637	+	33.6664i	−0.855162	+	1.14868i	−0.987522	+	0.157480i	$0.949663\pi$
$860$	23.0745	−	15.1763i	0.786833	−	0.517508i
$861$		0			0
$862$	2.87513	+	9.60359i	0.0979272	+	0.327100i
$863$	−12.5420	−	21.7234i	−0.426934	−	0.739472i	0.569665	−	0.821877i	$-0.307073\pi$
$863$	−12.5420	−	21.7234i	−0.426934	−	0.739472i	−0.996599	+	0.0824054i	$0.973740\pi$
$864$		0			0
$865$	6.19073	−	10.7227i	0.210491	−	0.364582i
$866$	7.87612	+	1.86667i	0.267641	+	0.0634322i
$867$		0			0
$868$	21.0356	+	10.5645i	0.713995	+	0.358582i
$869$	−7.38757	−	17.1263i	−0.250606	−	0.580970i
$870$		0			0
$871$	1.44732	−	24.8495i	0.0490405	−	0.841992i
$872$	2.04917	−	11.6214i	0.0693936	−	0.393551i
$873$		0			0
$874$	−1.59225	−	9.03012i	−0.0538588	−	0.305448i
$875$	−20.3309	+	2.37634i	−0.687311	+	0.0803351i
$876$		0			0
$877$	9.14104	−	30.5332i	0.308671	−	1.03103i	−0.653121	−	0.757253i	$-0.726541\pi$
$877$	9.14104	−	30.5332i	0.308671	−	1.03103i	0.961792	−	0.273780i	$-0.0882739\pi$
$878$	11.9003	−	2.82043i	0.401617	−	0.0951849i
$879$		0			0
$880$	7.83366	−	18.1605i	0.264073	−	0.612189i
$881$	4.45428	−	3.73758i	0.150068	−	0.125922i	−0.564662	−	0.825322i	$-0.690994\pi$
$881$	4.45428	−	3.73758i	0.150068	−	0.125922i	0.714731	+	0.699400i	$0.246549\pi$
$882$		0			0
$883$	−0.930865	−	0.781089i	−0.0313261	−	0.0262857i	0.626990	−	0.779027i	$-0.284287\pi$
$883$	−0.930865	−	0.781089i	−0.0313261	−	0.0262857i	−0.658316	+	0.752741i	$0.728731\pi$
$884$	2.39313	−	1.20188i	0.0804897	−	0.0404235i
$885$		0			0
$886$	−12.2248	−	1.42888i	−0.410702	−	0.0480041i
$887$	0.151446	+	2.60022i	0.00508505	+	0.0873069i	0.999896	−	0.0144357i	$-0.00459520\pi$
$887$	0.151446	+	2.60022i	0.00508505	+	0.0873069i	−0.994811	+	0.101743i	$0.967558\pi$
$888$		0			0
$889$	−6.69523	+	7.09653i	−0.224551	+	0.238010i
$890$	−5.05459			−0.169430
$891$		0			0
$892$	12.1821			0.407888
$893$	−15.0184	+	15.9186i	−0.502571	+	0.532694i
$894$		0			0
$895$	1.92457	+	33.0437i	0.0643314	+	1.10453i
$896$	19.0424	+	2.22574i	0.636162	+	0.0743567i
$897$		0			0
$898$	5.40667	−	2.71533i	0.180423	−	0.0906118i
$899$	−25.5323	−	21.4242i	−0.851551	−	0.714536i
$900$		0			0
$901$	−1.89517	+	1.59024i	−0.0631373	+	0.0529785i
$902$	−4.44067	+	10.2946i	−0.147858	+	0.342773i
$903$		0			0
$904$	−2.44436	+	0.579323i	−0.0812981	+	0.0192680i
$905$	0.327981	−	1.09553i	0.0109025	−	0.0364168i
$906$		0			0
$907$	−13.3542	+	1.56088i	−0.443419	+	0.0518282i	−0.334873	−	0.942263i	$-0.608693\pi$
$907$	−13.3542	+	1.56088i	−0.443419	+	0.0518282i	−0.108546	+	0.994091i	$0.534619\pi$
$908$	−2.62067	−	14.8626i	−0.0869701	−	0.493232i
$909$		0			0
$910$	−0.553881	+	3.14122i	−0.0183610	+	0.104130i
$911$	1.63910	−	28.1423i	0.0543058	−	0.932395i	−0.855615	−	0.517613i	$-0.826821\pi$
$911$	1.63910	−	28.1423i	0.0543058	−	0.932395i	0.909921	−	0.414782i	$-0.136142\pi$
$912$		0			0
$913$	−9.37566	−	21.7352i	−0.310289	−	0.719331i
$914$	6.52549	+	3.27723i	0.215844	+	0.108401i
$915$		0			0
$916$	−14.1549	−	3.35477i	−0.467691	−	0.110845i
$917$	−11.1295	+	19.2768i	−0.367528	+	0.636578i
$918$		0			0
$919$	13.5339	+	23.4413i	0.446441	+	0.773258i	0.998151	−	0.0607774i	$-0.0193580\pi$
$919$	13.5339	+	23.4413i	0.446441	+	0.773258i	−0.551710	+	0.834036i	$0.686025\pi$
$920$	−3.60461	−	12.0402i	−0.118840	−	0.396954i
$921$		0			0
$922$	4.68676	−	3.08253i	0.154350	−	0.101518i
$923$	32.1633	−	43.2028i	1.05867	−	1.42204i
$924$		0			0
$925$	−1.38753	−	0.912593i	−0.0456217	−	0.0300059i
$926$	−0.985077	+	0.358539i	−0.0323716	+	0.0117823i
$927$		0			0
$928$	−19.4266	−	7.07070i	−0.637709	−	0.232107i
$929$	−28.7357	−	38.5987i	−0.942787	−	1.26638i	−0.963806	−	0.266604i	$-0.914099\pi$
$929$	−28.7357	−	38.5987i	−0.942787	−	1.26638i	0.0210192	−	0.999779i	$-0.493309\pi$
$930$		0			0
$931$	−8.29546	−	8.79268i	−0.271873	−	0.288168i
$932$	32.9258	+	34.8993i	1.07852	+	1.14316i
$933$		0			0
$934$	−4.45513	−	5.98427i	−0.145776	−	0.195811i
$935$	2.46545	+	0.897352i	0.0806290	+	0.0293465i
$936$		0			0
$937$	−48.7239	+	17.7340i	−1.59174	+	0.579346i	−0.977714	−	0.209940i	$-0.932673\pi$
$937$	−48.7239	+	17.7340i	−1.59174	+	0.579346i	−0.614026	+	0.789286i	$0.710451\pi$
$938$	4.37206	+	2.87555i	0.142753	+	0.0938900i
$939$		0			0
$940$	−8.62374	+	11.5837i	−0.281275	+	0.377819i
$941$	−37.8323	+	24.8827i	−1.23330	+	0.811153i	−0.987416	−	0.158146i	$-0.949448\pi$
$941$	−37.8323	+	24.8827i	−1.23330	+	0.811153i	−0.245883	+	0.969300i	$0.579078\pi$
$942$		0			0
$943$	−11.6879	−	39.0403i	−0.380611	−	1.27133i
$944$	8.90573	+	15.4252i	0.289857	+	0.502047i
$945$		0			0
$946$	−10.7128	+	18.5551i	−0.348302	+	0.603277i
$947$	−20.4431	−	4.84509i	−0.664310	−	0.157444i	−0.115391	−	0.993320i	$-0.536812\pi$
$947$	−20.4431	−	4.84509i	−0.664310	−	0.157444i	−0.548919	+	0.835876i	$0.684960\pi$
$948$		0			0
$949$	−20.2370	−	10.1634i	−0.656920	−	0.329918i
$950$	1.81525	+	4.20823i	0.0588946	+	0.136533i
$951$		0			0
$952$	−0.0679961	+	1.16745i	−0.00220377	+	0.0378372i
$953$	1.52233	−	8.63357i	0.0493132	−	0.279669i	−0.950173	−	0.311723i	$-0.899094\pi$
$953$	1.52233	−	8.63357i	0.0493132	−	0.279669i	0.999486	+	0.0320543i	$0.0102050\pi$
$954$		0			0
$955$	−1.79794	−	10.1966i	−0.0581800	−	0.329955i
$956$	−0.323796	+	0.0378463i	−0.0104723	+	0.00122404i
$957$		0			0
$958$	2.02365	−	6.75945i	0.0653811	−	0.218388i
$959$	−9.20832	+	2.18241i	−0.297352	+	0.0704737i
$960$		0			0
$961$	5.16468	−	11.9731i	0.166603	−	0.386228i
$962$	−0.493629	+	0.414204i	−0.0159152	+	0.0133545i
$963$		0			0
$964$	−27.4921	−	23.0686i	−0.885461	−	0.742990i
$965$	−0.223216	+	0.112103i	−0.00718559	+	0.00360874i
$966$		0			0
$967$	22.4843	+	2.62804i	0.723047	+	0.0845120i	0.469653	−	0.882851i	$-0.344379\pi$
$967$	22.4843	+	2.62804i	0.723047	+	0.0845120i	0.253394	+	0.967363i	$0.418453\pi$
$968$	1.08741	+	18.6702i	0.0349508	+	0.600082i
$969$		0			0
$970$	−0.720635	+	0.763829i	−0.0231382	+	0.0245251i
$971$	−13.1781			−0.422905			−0.211453	−	0.977388i	$-0.567819\pi$
$971$	−13.1781			−0.422905			−0.211453	+	0.977388i	$0.567819\pi$
$972$		0			0
$973$	32.1504			1.03070
$974$	1.38801	−	1.47120i	0.0444746	−	0.0471403i
$975$		0			0
$976$	0.511289	+	8.77849i	0.0163660	+	0.280993i
$977$	39.4606	+	4.61228i	1.26246	+	0.147560i	0.720861	−	0.693079i	$-0.243746\pi$
$977$	39.4606	+	4.61228i	1.26246	+	0.147560i	0.541595	+	0.840639i	$0.317821\pi$
$978$		0			0
$979$	−45.4091	+	22.8053i	−1.45128	+	0.728860i
$980$	−6.11051	−	5.12733i	−0.195193	−	0.163786i
$981$		0			0
$982$	−1.07321	+	0.900528i	−0.0342474	+	0.0287370i
$983$	−23.2360	+	53.8671i	−0.741113	+	1.71809i	−0.0462734	+	0.998929i	$0.514735\pi$
$983$	−23.2360	+	53.8671i	−0.741113	+	1.71809i	−0.694840	+	0.719165i	$0.744525\pi$
$984$		0			0
$985$	14.3942	−	3.41150i	0.458639	−	0.108699i
$986$	0.228626	−	0.763665i	0.00728094	−	0.0243200i
$987$		0			0
$988$	−22.8881	+	2.67523i	−0.728166	+	0.0851104i
$989$	−13.5235	−	76.6957i	−0.430023	−	2.43878i
$990$		0			0
$991$	3.30423	−	18.7392i	0.104962	−	0.595270i	−0.886273	−	0.463163i	$-0.846714\pi$
$991$	3.30423	−	18.7392i	0.104962	−	0.595270i	0.991235	−	0.132108i	$-0.0421744\pi$
$992$	1.58828	−	27.2697i	0.0504280	−	0.865815i
$993$		0			0
$994$	4.48484	+	10.3970i	0.142250	+	0.329773i
$995$	−2.01498	−	1.01196i	−0.0638793	−	0.0320814i
$996$		0			0
$997$	−5.53844	−	1.31264i	−0.175404	−	0.0415716i	0.141975	−	0.989870i	$-0.454655\pi$
$997$	−5.53844	−	1.31264i	−0.175404	−	0.0415716i	−0.317379	+	0.948299i	$0.602803\pi$
$998$	5.28998	−	9.16251i	0.167451	−	0.290034i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.127.4		144
3.2	odd	2		81.2.g.a.70.5	yes	144
9.2	odd	6		729.2.g.c.136.4		144
9.4	even	3		729.2.g.a.379.4		144
9.5	odd	6		729.2.g.d.379.5		144
9.7	even	3		729.2.g.b.136.5		144
81.5	odd	54		729.2.g.d.352.5		144
81.22	even	27	inner	243.2.g.a.199.4		144
81.32	odd	54		729.2.g.c.595.4		144
81.34	even	27		6561.2.a.d.1.39		72
81.47	odd	54		6561.2.a.c.1.34		72
81.49	even	27		729.2.g.b.595.5		144
81.59	odd	54		81.2.g.a.22.5	✓	144
81.76	even	27		729.2.g.a.352.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.5	✓	144	81.59	odd	54
81.2.g.a.70.5	yes	144	3.2	odd	2
243.2.g.a.127.4		144	1.1	even	1	trivial
243.2.g.a.199.4		144	81.22	even	27	inner
729.2.g.a.352.4		144	81.76	even	27
729.2.g.a.379.4		144	9.4	even	3
729.2.g.b.136.5		144	9.7	even	3
729.2.g.b.595.5		144	81.49	even	27
729.2.g.c.136.4		144	9.2	odd	6
729.2.g.c.595.4		144	81.32	odd	54
729.2.g.d.352.5		144	81.5	odd	54
729.2.g.d.379.5		144	9.5	odd	6
6561.2.a.c.1.34		72	81.47	odd	54
6561.2.a.d.1.39		72	81.34	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.259760 + 0.275329i) q^{2} +(0.107959 + 1.85358i) q^{4} +(1.27364 + 0.148867i) q^{5} +(1.70721 - 0.857394i) q^{7} +(-1.11832 - 0.938383i) q^{8} +(-0.371828 + 0.312001i) q^{10} +(-1.93272 + 4.48054i) q^{11} +(3.34705 - 0.793266i) q^{13} +(-0.207399 + 0.692762i) q^{14} +(-3.13947 + 0.366951i) q^{16} +(-0.0728119 - 0.412937i) q^{17} +(-0.626542 + 3.55329i) q^{19} +(-0.138437 + 2.37686i) q^{20} +(-0.731582 - 1.69600i) q^{22} +(5.99966 + 3.01314i) q^{23} +(-3.26522 - 0.773872i) q^{25} +(-0.651020 + 1.12760i) q^{26} +(1.77356 + 3.07189i) q^{28} +(-1.44045 - 4.81145i) q^{29} +(5.54449 - 3.64667i) q^{31} +(2.45802 - 3.30169i) q^{32} +(0.132607 + 0.0872170i) q^{34} +(2.30201 - 0.837864i) q^{35} +(0.465059 + 0.169268i) q^{37} +(-0.815575 - 1.09551i) q^{38} +(-1.28465 - 1.36164i) q^{40} +(-4.16545 - 4.41512i) q^{41} +(-6.92694 - 9.30450i) q^{43} +(-8.51368 - 3.09873i) q^{44} +(-2.38808 + 0.869188i) q^{46} +(5.06765 + 3.33305i) q^{47} +(-2.00066 + 2.68735i) q^{49} +(1.06124 - 0.697991i) q^{50} +(1.83172 + 6.11838i) q^{52} +(-2.95007 - 5.10967i) q^{53} +(-3.12859 + 5.41888i) q^{55} +(-2.71378 - 0.643177i) q^{56} +(1.69890 + 0.853222i) q^{58} +(-2.23192 - 5.17418i) q^{59} +(0.161757 - 2.77726i) q^{61} +(-0.436200 + 2.47381i) q^{62} +(-0.827191 - 4.69124i) q^{64} +(4.38103 - 0.512069i) q^{65} +(2.07542 - 6.93240i) q^{67} +(0.757549 - 0.179542i) q^{68} +(-0.367282 + 0.851455i) q^{70} +(11.9949 - 10.0649i) q^{71} +(-5.04326 - 4.23179i) q^{73} +(-0.167408 + 0.0840754i) q^{74} +(-6.65395 - 0.777735i) q^{76} +(0.542032 + 9.30634i) q^{77} +(-2.62307 + 2.78030i) q^{79} -4.05318 q^{80} +2.29763 q^{82} +(-3.32898 + 3.52851i) q^{83} +(-0.0312634 - 0.536772i) q^{85} +(4.36114 + 0.509744i) q^{86} +(6.36586 - 3.19706i) q^{88} +(7.97723 + 6.69369i) q^{89} +(5.03399 - 4.22402i) q^{91} +(-4.93738 + 11.4461i) q^{92} +(-2.23406 + 0.529481i) q^{94} +(-1.32696 + 4.43235i) q^{95} +(2.14884 - 0.251163i) q^{97} +(-0.220216 - 1.24891i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

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