LMFDB - Embedded newform 891.2.u.d.431.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, degree $8$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			431.3
Character	$\chi$	$=$	891.431
Dual form			891.2.u.d.215.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.117667 + 0.130682i) q^{2} +(0.205825 - 1.95829i) q^{4} +(1.37458 + 1.23768i) q^{5} +(1.36208 + 3.05928i) q^{7} +(0.564664 - 0.410252i) q^{8} +O(q^{10})$	\(q+(0.117667 + 0.130682i) q^{2} +(0.205825 - 1.95829i) q^{4} +(1.37458 + 1.23768i) q^{5} +(1.36208 + 3.05928i) q^{7} +(0.564664 - 0.410252i) q^{8} +0.325266i q^{10} +(-1.20047 + 3.09174i) q^{11} +(-0.0815164 - 0.383504i) q^{13} +(-0.239522 + 0.537975i) q^{14} +(-3.73204 - 0.793270i) q^{16} +(2.21341 + 6.81217i) q^{17} +(1.85773 + 2.55694i) q^{19} +(2.70665 - 2.43708i) q^{20} +(-0.545291 + 0.206916i) q^{22} +(-5.54549 + 3.20169i) q^{23} +(-0.165018 - 1.57004i) q^{25} +(0.0405254 - 0.0557785i) q^{26} +(6.27130 - 2.03767i) q^{28} +(5.68449 - 2.53090i) q^{29} +(-0.562448 + 0.119552i) q^{31} +(-1.03343 - 1.78996i) q^{32} +(-0.629785 + 1.09082i) q^{34} +(-1.91411 + 5.89103i) q^{35} +(-8.33302 - 6.05429i) q^{37} +(-0.115554 + 0.543639i) q^{38} +(1.28393 + 0.134947i) q^{40} +(-0.393540 - 0.175215i) q^{41} +(1.89104 + 1.09179i) q^{43} +(5.80744 + 2.98722i) q^{44} +(-1.07092 - 0.347964i) q^{46} +(8.50024 - 0.893411i) q^{47} +(-2.82001 + 3.13194i) q^{49} +(0.185759 - 0.206307i) q^{50} +(-0.767791 + 0.0806981i) q^{52} +(8.20670 + 2.66652i) q^{53} +(-5.47672 + 2.76405i) q^{55} +(2.02419 + 1.16867i) q^{56} +(0.999619 + 0.445059i) q^{58} +(1.85422 + 0.194887i) q^{59} +(2.26208 - 10.6422i) q^{61} +(-0.0818047 - 0.0594346i) q^{62} +(-2.24574 + 6.91168i) q^{64} +(0.362604 - 0.628048i) q^{65} +(3.96966 + 6.87565i) q^{67} +(13.7958 - 2.93238i) q^{68} +(-0.995080 + 0.443038i) q^{70} +(0.678883 - 0.220583i) q^{71} +(1.27295 - 1.75207i) q^{73} +(-0.189331 - 1.80137i) q^{74} +(5.38960 - 3.11169i) q^{76} +(-11.0936 + 0.538628i) q^{77} +(6.85723 - 6.17428i) q^{79} +(-4.14817 - 5.70947i) q^{80} +(-0.0234091 - 0.0720457i) q^{82} +(-0.292948 - 0.0622681i) q^{83} +(-5.38876 + 12.1034i) q^{85} +(0.0798347 + 0.375593i) q^{86} +(0.590533 + 2.23829i) q^{88} +4.80386i q^{89} +(1.06221 - 0.771744i) q^{91} +(5.12844 + 11.5187i) q^{92} +(1.11695 + 1.00571i) q^{94} +(-0.611074 + 5.81399i) q^{95} +(8.94292 + 9.93212i) q^{97} -0.741110 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} + 15 q^{5}+O(q^{10}) $ 32 * q + 4 * q^4 + 15 * q^5	$ 32 q + 4 q^{4} + 15 q^{5} + 33 q^{11} - 12 q^{14} - 16 q^{16} - 36 q^{20} + 15 q^{22} + 18 q^{23} - 13 q^{25} - 10 q^{28} + 15 q^{29} + 8 q^{31} - 22 q^{34} + 18 q^{37} - 105 q^{38} - 15 q^{40} - 75 q^{41} + 40 q^{46} + 36 q^{47} + 12 q^{49} + 15 q^{50} + 40 q^{52} - 16 q^{55} + 60 q^{56} + 24 q^{58} - 39 q^{59} + 30 q^{61} + 48 q^{67} + 165 q^{68} + 41 q^{70} - 70 q^{73} - 15 q^{74} - 42 q^{77} + 60 q^{79} - 66 q^{82} - 60 q^{83} - 80 q^{85} + 6 q^{86} - 24 q^{88} - 60 q^{91} + 42 q^{92} - 100 q^{94} - 60 q^{95} - 24 q^{97}+O(q^{100}) $ 32 * q + 4 * q^4 + 15 * q^5 + 33 * q^11 - 12 * q^14 - 16 * q^16 - 36 * q^20 + 15 * q^22 + 18 * q^23 - 13 * q^25 - 10 * q^28 + 15 * q^29 + 8 * q^31 - 22 * q^34 + 18 * q^37 - 105 * q^38 - 15 * q^40 - 75 * q^41 + 40 * q^46 + 36 * q^47 + 12 * q^49 + 15 * q^50 + 40 * q^52 - 16 * q^55 + 60 * q^56 + 24 * q^58 - 39 * q^59 + 30 * q^61 + 48 * q^67 + 165 * q^68 + 41 * q^70 - 70 * q^73 - 15 * q^74 - 42 * q^77 + 60 * q^79 - 66 * q^82 - 60 * q^83 - 80 * q^85 + 6 * q^86 - 24 * q^88 - 60 * q^91 + 42 * q^92 - 100 * q^94 - 60 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.117667	+	0.130682i	0.0832030	+	0.0924063i	0.783309	−	0.621633i	$-0.213530\pi$
$2$	0.117667	+	0.130682i	0.0832030	+	0.0924063i	−0.700106	+	0.714039i	$0.746864\pi$
$3$		0			0
$3$		0			0
$4$	0.205825	−	1.95829i	0.102912	−	0.979145i
$5$	1.37458	+	1.23768i	0.614730	+	0.553506i	0.916581	−	0.399850i	$-0.130938\pi$
$5$	1.37458	+	1.23768i	0.614730	+	0.553506i	−0.301850	+	0.953355i	$0.597604\pi$
$6$		0			0
$7$	1.36208	+	3.05928i	0.514817	+	1.15630i	0.964734	+	0.263228i	$0.0847870\pi$
$7$	1.36208	+	3.05928i	0.514817	+	1.15630i	−0.449917	+	0.893071i	$0.648546\pi$
$8$	0.564664	−	0.410252i	0.199639	−	0.145046i
$9$		0			0
$10$			0.325266i			0.102858i
$11$	−1.20047	+	3.09174i	−0.361955	+	0.932196i
$11$	−1.20047	+	3.09174i	−0.361955	+	0.932196i
$12$		0			0
$13$	−0.0815164	−	0.383504i	−0.0226086	−	0.106365i	0.965396	−	0.260787i	$-0.0839819\pi$
$13$	−0.0815164	−	0.383504i	−0.0226086	−	0.106365i	−0.988005	+	0.154422i	$0.950649\pi$
$14$	−0.239522	+	0.537975i	−0.0640149	+	0.143780i
$15$		0			0
$16$	−3.73204	−	0.793270i	−0.933010	−	0.198317i
$17$	2.21341	+	6.81217i	0.536830	+	1.65219i	0.739661	+	0.672980i	$0.234986\pi$
$17$	2.21341	+	6.81217i	0.536830	+	1.65219i	−0.202830	+	0.979214i	$0.565014\pi$
$18$		0			0
$19$	1.85773	+	2.55694i	0.426192	+	0.586603i	0.967074	−	0.254496i	$-0.0819095\pi$
$19$	1.85773	+	2.55694i	0.426192	+	0.586603i	−0.540882	+	0.841098i	$0.681909\pi$
$20$	2.70665	−	2.43708i	0.605226	−	0.544948i
$21$		0			0
$22$	−0.545291	+	0.206916i	−0.116256	+	0.0441145i
$23$	−5.54549	+	3.20169i	−1.15632	+	0.667599i	−0.950418	−	0.310975i	$-0.899345\pi$
$23$	−5.54549	+	3.20169i	−1.15632	+	0.667599i	−0.205897	+	0.978574i	$0.566011\pi$
$24$		0			0
$25$	−0.165018	−	1.57004i	−0.0330036	−	0.314008i
$26$	0.0405254	−	0.0557785i	0.00794769	−	0.0109391i
$27$		0			0
$28$	6.27130	−	2.03767i	1.18516	−	0.385083i
$29$	5.68449	−	2.53090i	1.05558	−	0.469976i	0.195805	−	0.980643i	$-0.437268\pi$
$29$	5.68449	−	2.53090i	1.05558	−	0.469976i	0.859779	+	0.510667i	$0.170601\pi$
$30$		0			0
$31$	−0.562448	+	0.119552i	−0.101019	+	0.0214722i	−0.258144	−	0.966107i	$-0.583111\pi$
$31$	−0.562448	+	0.119552i	−0.101019	+	0.0214722i	0.157125	+	0.987579i	$0.449777\pi$
$32$	−1.03343	−	1.78996i	−0.182687	−	0.316423i
$33$		0			0
$34$	−0.629785	+	1.09082i	−0.108007	+	0.187074i
$35$	−1.91411	+	5.89103i	−0.323544	+	0.995766i
$36$		0			0
$37$	−8.33302	−	6.05429i	−1.36994	−	0.995320i	−0.997742	−	0.0671666i	$-0.978604\pi$
$37$	−8.33302	−	6.05429i	−1.36994	−	0.995320i	−0.372198	−	0.928153i	$-0.621396\pi$
$38$	−0.115554	+	0.543639i	−0.0187453	+	0.0881899i
$39$		0			0
$40$	1.28393	+	0.134947i	0.203008	+	0.0213370i
$41$	−0.393540	−	0.175215i	−0.0614607	−	0.0273641i	0.375776	−	0.926710i	$-0.377376\pi$
$41$	−0.393540	−	0.175215i	−0.0614607	−	0.0273641i	−0.437237	+	0.899346i	$0.644043\pi$
$42$		0			0
$43$	1.89104	+	1.09179i	0.288381	+	0.166497i	0.637211	−	0.770689i	$-0.280088\pi$
$43$	1.89104	+	1.09179i	0.288381	+	0.166497i	−0.348831	+	0.937186i	$0.613421\pi$
$44$	5.80744	+	2.98722i	0.875505	+	0.450341i
$45$		0			0
$46$	−1.07092	−	0.347964i	−0.157899	−	0.0513046i
$47$	8.50024	−	0.893411i	1.23989	−	0.130317i	0.538209	−	0.842811i	$-0.319101\pi$
$47$	8.50024	−	0.893411i	1.23989	−	0.130317i	0.701678	+	0.712494i	$0.252434\pi$
$48$		0			0
$49$	−2.82001	+	3.13194i	−0.402858	+	0.447419i
$50$	0.185759	−	0.206307i	0.0262703	−	0.0291761i
$51$		0			0
$52$	−0.767791	+	0.0806981i	−0.106473	+	0.0111908i
$53$	8.20670	+	2.66652i	1.12728	+	0.366274i	0.812541	−	0.582905i	$-0.198084\pi$
$53$	8.20670	+	2.66652i	1.12728	+	0.366274i	0.314736	+	0.949179i	$0.398084\pi$
$54$		0			0
$55$	−5.47672	+	2.76405i	−0.738480	+	0.372705i
$56$	2.02419	+	1.16867i	0.270494	+	0.156170i
$57$		0			0
$58$	0.999619	+	0.445059i	0.131256	+	0.0584391i
$59$	1.85422	+	0.194887i	0.241399	+	0.0253721i	0.224455	−	0.974484i	$-0.427940\pi$
$59$	1.85422	+	0.194887i	0.241399	+	0.0253721i	0.0169439	+	0.999856i	$0.494606\pi$
$60$		0			0
$61$	2.26208	−	10.6422i	0.289629	−	1.36260i	−0.557043	−	0.830483i	$-0.688064\pi$
$61$	2.26208	−	10.6422i	0.289629	−	1.36260i	0.846672	−	0.532115i	$-0.178602\pi$
$62$	−0.0818047	−	0.0594346i	−0.0103892	−	0.00754821i
$63$		0			0
$64$	−2.24574	+	6.91168i	−0.280718	+	0.863960i
$65$	0.362604	−	0.628048i	0.0449755	−	0.0778998i
$66$		0			0
$67$	3.96966	+	6.87565i	0.484971	+	0.839994i	0.999851	−	0.0172679i	$-0.00549682\pi$
$67$	3.96966	+	6.87565i	0.484971	+	0.839994i	−0.514880	+	0.857262i	$0.672163\pi$
$68$	13.7958	−	2.93238i	1.67298	−	0.355604i
$69$		0			0
$70$	−0.995080	+	0.443038i	−0.118935	+	0.0529532i
$71$	0.678883	−	0.220583i	0.0805686	−	0.0261783i	−0.268455	−	0.963292i	$-0.586513\pi$
$71$	0.678883	−	0.220583i	0.0805686	−	0.0261783i	0.349024	+	0.937114i	$0.386513\pi$
$72$		0			0
$73$	1.27295	−	1.75207i	0.148988	−	0.205064i	−0.727999	−	0.685578i	$-0.759550\pi$
$73$	1.27295	−	1.75207i	0.148988	−	0.205064i	0.876987	+	0.480514i	$0.159550\pi$
$74$	−0.189331	−	1.80137i	−0.0220093	−	0.209405i
$75$		0			0
$76$	5.38960	−	3.11169i	0.618230	−	0.356935i
$77$	−11.0936	+	0.538628i	−1.26424	+	0.0613824i
$78$		0			0
$79$	6.85723	−	6.17428i	0.771499	−	0.694660i	−0.186175	−	0.982517i	$-0.559609\pi$
$79$	6.85723	−	6.17428i	0.771499	−	0.694660i	0.957674	+	0.287856i	$0.0929425\pi$
$80$	−4.14817	−	5.70947i	−0.463780	−	0.638338i
$81$		0			0
$82$	−0.0234091	−	0.0720457i	−0.00258510	−	0.00795612i
$83$	−0.292948	−	0.0622681i	−0.0321553	−	0.00683481i	0.191806	−	0.981433i	$-0.438566\pi$
$83$	−0.292948	−	0.0622681i	−0.0321553	−	0.00683481i	−0.223961	+	0.974598i	$0.571899\pi$
$84$		0			0
$85$	−5.38876	+	12.1034i	−0.584493	+	1.31279i
$86$	0.0798347	+	0.375593i	0.00860880	+	0.0405012i
$87$		0			0
$88$	0.590533	+	2.23829i	0.0629511	+	0.238603i
$89$			4.80386i			0.509208i	0.967045	+	0.254604i	$0.0819451\pi$
$89$			4.80386i			0.509208i	−0.967045	+	0.254604i	$0.918055\pi$
$90$		0			0
$91$	1.06221	−	0.771744i	0.111350	−	0.0809008i
$92$	5.12844	+	11.5187i	0.534677	+	1.20090i
$93$		0			0
$94$	1.11695	+	1.00571i	0.115204	+	0.103731i
$95$	−0.611074	+	5.81399i	−0.0626949	+	0.596502i
$96$		0			0
$97$	8.94292	+	9.93212i	0.908016	+	1.00845i	0.999920	+	0.0126865i	$0.00403834\pi$
$97$	8.94292	+	9.93212i	0.908016	+	1.00845i	−0.0919031	+	0.995768i	$0.529295\pi$
$98$	−0.741110			−0.0748634
$99$		0			0
$100$	−3.10856			−0.310856
$101$	−11.4738	−	12.7429i	−1.14168	−	1.26797i	−0.958564	−	0.284878i	$-0.908047\pi$
$101$	−11.4738	−	12.7429i	−1.14168	−	1.26797i	−0.183120	−	0.983091i	$-0.558620\pi$
$102$		0			0
$103$	1.41651	−	13.4772i	0.139573	−	1.32795i	−0.670626	−	0.741796i	$-0.733974\pi$
$103$	1.41651	−	13.4772i	0.139573	−	1.32795i	0.810199	−	0.586155i	$-0.199359\pi$
$104$	−0.203363	−	0.183109i	−0.0199414	−	0.0179553i
$105$		0			0
$106$	0.617189	+	1.38623i	0.0599467	+	0.134643i
$107$	−11.0351	+	8.01744i	−1.06680	+	0.775075i	−0.975334	−	0.220734i	$-0.929155\pi$
$107$	−11.0351	+	8.01744i	−1.06680	+	0.775075i	−0.0914648	+	0.995808i	$0.529155\pi$
$108$		0			0
$109$		−	2.96385i		−	0.283885i	−0.989875	−	0.141943i	$-0.954665\pi$
$109$		−	2.96385i		−	0.283885i	0.989875	−	0.141943i	$-0.0453349\pi$
$110$	−1.00564	−	0.390472i	−0.0958840	−	0.0372301i
$111$		0			0
$112$	−2.65650	−	12.4978i	−0.251016	−	1.18094i
$113$	−4.26681	+	9.58342i	−0.401388	+	0.901532i	0.593897	+	0.804541i	$0.297589\pi$
$113$	−4.26681	+	9.58342i	−0.401388	+	0.901532i	−0.995285	+	0.0969913i	$0.969078\pi$
$114$		0			0
$115$	−11.5854	−	2.46255i	−1.08034	−	0.229634i
$116$	−3.78623	−	11.6528i	−0.351542	−	1.08194i
$117$		0			0
$118$	0.192712	+	0.265246i	0.0177406	+	0.0244178i
$119$	−17.8255	+	16.0501i	−1.63406	+	1.47131i
$120$		0			0
$121$	−8.11775	−	7.42308i	−0.737977	−	0.674826i
$122$	1.65692	−	0.956624i	0.150011	−	0.0866087i
$123$		0			0
$124$	0.118352	+	1.12604i	0.0106283	+	0.101122i
$125$	7.15244	−	9.84449i	0.639734	−	0.880518i
$126$		0			0
$127$	6.15614	−	2.00025i	0.546269	−	0.177494i	−0.0228645	−	0.999739i	$-0.507279\pi$
$127$	6.15614	−	2.00025i	0.546269	−	0.177494i	0.569134	+	0.822245i	$0.307279\pi$
$128$	−4.94384	+	2.20114i	−0.436978	+	0.194555i
$129$		0			0
$130$	0.124741	−	0.0265145i	0.0109405	−	0.00232548i
$131$	−9.59591	−	16.6206i	−0.838399	−	1.45215i	−0.891233	−	0.453546i	$-0.850159\pi$
$131$	−9.59591	−	16.6206i	−0.838399	−	1.45215i	0.0528345	−	0.998603i	$-0.483174\pi$
$132$		0			0
$133$	−5.29203	+	9.16606i	−0.458877	+	0.794798i
$134$	−0.431428	+	1.32780i	−0.0372697	+	0.114704i
$135$		0			0
$136$	4.04454	+	2.93853i	0.346817	+	0.251977i
$137$	2.43449	−	11.4534i	0.207992	−	0.978527i	−0.742995	−	0.669297i	$-0.766595\pi$
$137$	2.43449	−	11.4534i	0.207992	−	0.978527i	0.950987	−	0.309230i	$-0.100071\pi$
$138$		0			0
$139$	18.1025	+	1.90265i	1.53544	+	0.161381i	0.834166	−	0.551514i	$-0.185950\pi$
$139$	18.1025	+	1.90265i	1.53544	+	0.161381i	0.701271	+	0.712895i	$0.252616\pi$
$140$	11.1424	+	4.96091i	0.941703	+	0.419273i
$141$		0			0
$142$	0.108708	+	0.0627627i	0.00912259	+	0.00526693i
$143$	1.28355	+	0.208357i	0.107336	+	0.0174237i
$144$		0			0
$145$	10.9462	+	3.55664i	0.909034	+	0.295363i
$146$	0.378748	−	0.0398081i	0.0313454	−	0.00329454i
$147$		0			0
$148$	−13.5712	+	15.0723i	−1.11555	+	1.23894i
$149$	−5.79385	+	6.43472i	−0.474650	+	0.527153i	−0.932157	−	0.362053i	$-0.882076\pi$
$149$	−5.79385	+	6.43472i	−0.474650	+	0.527153i	0.457507	+	0.889206i	$0.348742\pi$
$150$		0			0
$151$	−13.5584	+	1.42504i	−1.10337	+	0.115968i	−0.638654	−	0.769494i	$-0.720509\pi$
$151$	−13.5584	+	1.42504i	−1.10337	+	0.115968i	−0.464711	+	0.885462i	$0.653842\pi$
$152$	2.09798	+	0.681676i	0.170169	+	0.0552912i
$153$		0			0
$154$	−1.37574	−	1.38636i	−0.110860	−	0.111716i
$155$	−0.921096	−	0.531795i	−0.0739842	−	0.0427148i
$156$		0			0
$157$	−7.46420	−	3.32328i	−0.595708	−	0.265226i	0.0866565	−	0.996238i	$-0.472382\pi$
$157$	−7.46420	−	3.32328i	−0.595708	−	0.265226i	−0.682365	+	0.731012i	$0.739048\pi$
$158$	1.61374	+	0.169610i	0.128382	+	0.0134935i
$159$		0			0
$160$	0.794855	−	3.73950i	0.0628388	−	0.295633i
$161$	−17.3483	−	12.6042i	−1.36723	−	0.993354i
$162$		0			0
$163$	−1.15567	+	3.55678i	−0.0905189	+	0.278588i	−0.986060	−	0.166390i	$-0.946789\pi$
$163$	−1.15567	+	3.55678i	−0.0905189	+	0.278588i	0.895541	+	0.444979i	$0.146789\pi$
$164$	−0.424123	+	0.734602i	−0.0331184	+	0.0573628i
$165$		0			0
$166$	−0.0263330	−	0.0456100i	−0.00204383	−	0.00354002i
$167$	7.49043	−	1.59214i	0.579626	−	0.123203i	0.0912371	−	0.995829i	$-0.470918\pi$
$167$	7.49043	−	1.59214i	0.579626	−	0.123203i	0.488389	+	0.872626i	$0.337585\pi$
$168$		0			0
$169$	11.7357	−	5.22505i	0.902743	−	0.401927i
$170$	−2.21577	+	0.719947i	−0.169942	+	0.0552174i
$171$		0			0
$172$	2.52727	−	3.47849i	0.192702	−	0.265232i
$173$	0.152390	+	1.44989i	0.0115860	+	0.110233i	0.998786	−	0.0492511i	$-0.0156835\pi$
$173$	0.152390	+	1.44989i	0.0115860	+	0.110233i	−0.987200	+	0.159485i	$0.949017\pi$
$174$		0			0
$175$	4.57842	−	2.64335i	0.346096	−	0.199819i
$176$	6.93278	−	10.5862i	0.522578	−	0.797966i
$177$		0			0
$178$	−0.627778	+	0.565254i	−0.0470540	+	0.0423676i
$179$	−11.5933	−	15.9568i	−0.866525	−	1.19267i	−0.979974	−	0.199126i	$-0.936190\pi$
$179$	−11.5933	−	15.9568i	−0.866525	−	1.19267i	0.113449	−	0.993544i	$-0.463810\pi$
$180$		0			0
$181$	−0.369642	−	1.13764i	−0.0274752	−	0.0845601i	0.936379	−	0.350992i	$-0.114155\pi$
$181$	−0.369642	−	1.13764i	−0.0274752	−	0.0845601i	−0.963854	+	0.266431i	$0.914155\pi$
$182$	0.225841	+	0.0480039i	0.0167404	+	0.00355829i
$183$		0			0
$184$	−1.81784	+	4.08293i	−0.134013	+	0.300998i
$185$	−3.96114	−	18.6357i	−0.291229	−	1.37012i
$186$		0			0
$187$	−23.7186	−	1.33451i	−1.73448	−	0.0975889i
$188$		−	16.8298i		−	1.22744i
$189$		0			0
$190$	−0.831687	+	0.604256i	−0.0603369	+	0.0438374i
$191$	−2.54523	−	5.71668i	−0.184166	−	0.413644i	0.797743	−	0.602998i	$-0.206027\pi$
$191$	−2.54523	−	5.71668i	−0.184166	−	0.413644i	−0.981909	+	0.189354i	$0.939361\pi$
$192$		0			0
$193$	−14.4096	−	12.9744i	−1.03722	−	0.933919i	−0.0393569	−	0.999225i	$-0.512531\pi$
$193$	−14.4096	−	12.9744i	−1.03722	−	0.933919i	−0.997865	+	0.0653062i	$0.979198\pi$
$194$	−0.245667	+	2.33736i	−0.0176378	+	0.167813i
$195$		0			0
$196$	5.55281	+	6.16702i	0.396629	+	0.440502i
$197$	12.1276			0.864053			0.432027	−	0.901861i	$-0.357799\pi$
$197$	12.1276			0.864053			0.432027	+	0.901861i	$0.357799\pi$
$198$		0			0
$199$	0.269305			0.0190905			0.00954527	−	0.999954i	$-0.496962\pi$
$199$	0.269305			0.0190905			0.00954527	+	0.999954i	$0.496962\pi$
$200$	−0.737293	−	0.818846i	−0.0521345	−	0.0579012i
$201$		0			0
$202$	0.315191	−	2.99884i	0.0221767	−	0.210997i
$203$	15.4854	+	13.9432i	1.08687	+	0.978618i
$204$		0			0
$205$	−0.324092	−	0.727923i	−0.0226356	−	0.0508404i
$206$	1.92791	−	1.40071i	0.134324	−	0.0975920i
$207$		0			0
$208$			1.49592i			0.103723i
$209$	−10.1356	+	2.67409i	−0.701091	+	0.184970i
$210$		0			0
$211$	0.177658	+	0.835816i	0.0122305	+	0.0575399i	0.983840	−	0.179052i	$-0.0573030\pi$
$211$	0.177658	+	0.835816i	0.0122305	+	0.0575399i	−0.971609	+	0.236592i	$0.923970\pi$
$212$	6.91096	−	15.5223i	0.474646	−	1.06607i
$213$		0			0
$214$	−2.34620	−	0.498699i	−0.160383	−	0.0340904i
$215$	1.24810	+	3.84125i	0.0851196	+	0.261971i
$216$		0			0
$217$	−1.13184	−	1.55785i	−0.0768344	−	0.105753i
$218$	0.387322	−	0.348747i	0.0262328	−	0.0236201i
$219$		0			0
$220$	4.28557	+	11.2939i	0.288933	+	0.761435i
$221$	2.43207	−	1.40416i	0.163599	−	0.0944537i
$222$		0			0
$223$	1.53124	+	14.5688i	0.102540	+	0.975600i	0.917945	+	0.396709i	$0.129848\pi$
$223$	1.53124	+	14.5688i	0.102540	+	0.975600i	−0.815405	+	0.578891i	$0.803486\pi$
$224$	4.06837	−	5.59963i	0.271829	−	0.374141i
$225$		0			0
$226$	−1.75444	+	0.570054i	−0.116704	+	0.0379194i
$227$	12.3294	−	5.48941i	0.818332	−	0.364345i	0.0455070	−	0.998964i	$-0.485510\pi$
$227$	12.3294	−	5.48941i	0.818332	−	0.364345i	0.772825	+	0.634619i	$0.218843\pi$
$228$		0			0
$229$	18.8681	−	4.01054i	1.24684	−	0.265024i	0.463208	−	0.886250i	$-0.346698\pi$
$229$	18.8681	−	4.01054i	1.24684	−	0.265024i	0.783632	+	0.621226i	$0.213365\pi$
$230$	−1.04140	−	1.80376i	−0.0686681	−	0.118937i
$231$		0			0
$232$	2.17152	−	3.76118i	0.142567	−	0.246934i
$233$	−0.648004	+	1.99435i	−0.0424521	+	0.130654i	−0.970036	−	0.242960i	$-0.921882\pi$
$233$	−0.648004	+	1.99435i	−0.0424521	+	0.130654i	0.927584	+	0.373614i	$0.121882\pi$
$234$		0			0
$235$	12.7900	+	9.29248i	0.834328	+	0.606175i
$236$	0.763290	−	3.59100i	0.0496859	−	0.233754i
$237$		0			0
$238$	−4.19493	−	0.440905i	−0.271917	−	0.0285796i
$239$	−5.95852	−	2.65290i	−0.385425	−	0.171602i	0.204872	−	0.978789i	$-0.434322\pi$
$239$	−5.95852	−	2.65290i	−0.385425	−	0.171602i	−0.590296	+	0.807187i	$0.700989\pi$
$240$		0			0
$241$	20.3150	+	11.7289i	1.30861	+	0.755524i	0.981864	−	0.189589i	$-0.0607156\pi$
$241$	20.3150	+	11.7289i	1.30861	+	0.755524i	0.326743	+	0.945113i	$0.394049\pi$
$242$	0.0148752	−	1.93430i	0.000956215	−	0.124341i
$243$		0			0
$244$	−20.3750	−	6.62023i	−1.30437	−	0.423817i
$245$	−7.75265	+	0.814836i	−0.495299	+	0.0520580i
$246$		0			0
$247$	0.829163	−	0.920879i	0.0527584	−	0.0585941i
$248$	−0.268548	+	0.298252i	−0.0170528	+	0.0189390i
$249$		0			0
$250$	2.12810	−	0.223673i	0.134593	−	0.0141463i
$251$	−2.91675	−	0.947710i	−0.184104	−	0.0598190i	0.215514	−	0.976501i	$-0.430857\pi$
$251$	−2.91675	−	0.947710i	−0.184104	−	0.0598190i	−0.399618	+	0.916682i	$0.630857\pi$
$252$		0			0
$253$	−3.24162	−	20.9888i	−0.203799	−	1.31955i
$254$	0.985771	+	0.569135i	0.0618528	+	0.0357107i
$255$		0			0
$256$	12.4088	+	5.52474i	0.775549	+	0.345296i
$257$	−24.6099	−	2.58660i	−1.53512	−	0.161348i	−0.701093	−	0.713070i	$-0.747304\pi$
$257$	−24.6099	−	2.58660i	−1.53512	−	0.161348i	−0.834028	+	0.551722i	$0.813971\pi$
$258$		0			0
$259$	7.17154	−	33.7394i	0.445618	−	2.09647i
$260$	−1.15527	−	0.839351i	−0.0716466	−	0.0520543i
$261$		0			0
$262$	1.04290	−	3.20971i	0.0644304	−	0.198296i
$263$	−9.84990	+	17.0605i	−0.607371	+	1.05200i	0.384301	+	0.923208i	$0.374443\pi$
$263$	−9.84990	+	17.0605i	−0.607371	+	1.05200i	−0.991672	+	0.128790i	$0.958891\pi$
$264$		0			0
$265$	7.98047	+	13.8226i	0.490236	+	0.849114i
$266$	−1.82054	+	0.386967i	−0.111624	+	0.0237265i
$267$		0			0
$268$	14.2816	−	6.35856i	0.872386	−	0.388411i
$269$	−24.0214	+	7.80503i	−1.46461	+	0.475881i	−0.929475	−	0.368885i	$-0.879739\pi$
$269$	−24.0214	+	7.80503i	−1.46461	+	0.475881i	−0.535136	+	0.844766i	$0.679739\pi$
$270$		0			0
$271$	5.91030	−	8.13484i	0.359025	−	0.494156i	−0.590851	−	0.806780i	$-0.701208\pi$
$271$	5.91030	−	8.13484i	0.359025	−	0.494156i	0.949877	+	0.312624i	$0.101208\pi$
$272$	−2.85664	−	27.1791i	−0.173209	−	1.64798i
$273$		0			0
$274$	1.78321	−	1.02954i	0.107728	−	0.0621966i
$275$	5.05226	+	1.37459i	0.304663	+	0.0828910i
$276$		0			0
$277$	6.61728	−	5.95822i	0.397594	−	0.357995i	−0.445948	−	0.895059i	$-0.647133\pi$
$277$	6.61728	−	5.95822i	0.397594	−	0.357995i	0.843541	+	0.537064i	$0.180467\pi$
$278$	1.88142	+	2.58956i	0.112840	+	0.155311i
$279$		0			0
$280$	1.33598	+	4.11172i	0.0798400	+	0.245722i
$281$	−8.00956	−	1.70249i	−0.477810	−	0.101562i	−0.0372903	−	0.999304i	$-0.511873\pi$
$281$	−8.00956	−	1.70249i	−0.477810	−	0.101562i	−0.440520	+	0.897743i	$0.645206\pi$
$282$		0			0
$283$	1.85250	−	4.16079i	0.110120	−	0.247333i	−0.850076	−	0.526659i	$-0.823444\pi$
$283$	1.85250	−	4.16079i	0.110120	−	0.247333i	0.960196	+	0.279326i	$0.0901110\pi$
$284$	−0.292234	−	1.37485i	−0.0173409	−	0.0815824i
$285$		0			0
$286$	0.123803	+	0.192254i	0.00732063	+	0.0113682i
$287$		−	1.44261i		−	0.0851543i
$288$		0			0
$289$	−27.7532	+	20.1639i	−1.63254	+	1.18611i
$290$	0.823216	+	1.84897i	0.0483409	+	0.108576i
$291$		0			0
$292$	−3.16905	−	2.85343i	−0.185455	−	0.166984i
$293$	0.256266	−	2.43820i	0.0149712	−	0.142441i	−0.984483	−	0.175481i	$-0.943852\pi$
$293$	0.256266	−	2.43820i	0.0149712	−	0.142441i	0.999454	+	0.0330394i	$0.0105187\pi$
$294$		0			0
$295$	2.30757	+	2.56282i	0.134352	+	0.149213i
$296$	−7.18914			−0.417861
$297$		0			0
$298$	−1.52265			−0.0882045
$299$	1.67991	+	1.86573i	0.0971518	+	0.107898i
$300$		0			0
$301$	−0.764352	+	7.27232i	−0.0440565	+	0.419170i
$302$	−1.78160	−	1.60416i	−0.102520	−	0.0923090i
$303$		0			0
$304$	−4.90477	−	11.0163i	−0.281308	−	0.631828i
$305$	16.2810	−	11.8289i	0.932250	−	0.677319i
$306$		0			0
$307$			30.9408i			1.76589i	0.469479	+	0.882944i	$0.344442\pi$
$307$			30.9408i			1.76589i	−0.469479	+	0.882944i	$0.655558\pi$
$308$	−1.22855	+	21.8354i	−0.0700032	+	1.24419i
$309$		0			0
$310$	−0.0388862	−	0.182945i	−0.00220859	−	0.0103906i
$311$	−10.0144	+	22.4926i	−0.567862	+	1.27544i	0.370194	+	0.928955i	$0.379291\pi$
$311$	−10.0144	+	22.4926i	−0.567862	+	1.27544i	−0.938056	+	0.346484i	$0.887375\pi$
$312$		0			0
$313$	−11.5535	−	2.45578i	−0.653043	−	0.138809i	−0.130536	−	0.991444i	$-0.541670\pi$
$313$	−11.5535	−	2.45578i	−0.653043	−	0.138809i	−0.522507	+	0.852635i	$0.675003\pi$
$314$	−0.443996	−	1.36648i	−0.0250561	−	0.0771148i
$315$		0			0
$316$	−10.6796	−	14.6993i	−0.600777	−	0.826898i
$317$	10.4417	−	9.40179i	0.586467	−	0.528057i	−0.321604	−	0.946874i	$-0.604222\pi$
$317$	10.4417	−	9.40179i	0.586467	−	0.528057i	0.908071	+	0.418817i	$0.137555\pi$
$318$		0			0
$319$	1.00083	+	20.6133i	0.0560359	+	1.15412i
$320$	−11.6414	+	6.72115i	−0.650773	+	0.375724i
$321$		0			0
$322$	−0.394163	−	3.75021i	−0.0219658	−	0.208991i
$323$	−13.3064	+	18.3147i	−0.740389	+	1.01906i
$324$		0			0
$325$	−0.588666	+	0.191269i	−0.0326533	+	0.0106097i
$326$	−0.600791	+	0.267489i	−0.0332747	+	0.0148149i
$327$		0			0
$328$	−0.294101	+	0.0625130i	−0.0162390	+	0.00345170i
$329$	14.3112	+	24.7877i	0.789001	+	1.36659i
$330$		0			0
$331$	−15.3072	+	26.5128i	−0.841359	+	1.45728i	0.0473865	+	0.998877i	$0.484911\pi$
$331$	−15.3072	+	26.5128i	−0.841359	+	1.45728i	−0.888746	+	0.458400i	$0.848423\pi$
$332$	−0.182235	+	0.560862i	−0.0100014	+	0.0307813i
$333$		0			0
$334$	1.08944	+	0.791523i	0.0596114	+	0.0433102i
$335$	−3.05322	+	14.3643i	−0.166815	+	0.784804i
$336$		0			0
$337$	−17.5900	−	1.84879i	−0.958190	−	0.100710i	−0.387495	−	0.921872i	$-0.626660\pi$
$337$	−17.5900	−	1.84879i	−0.958190	−	0.100710i	−0.570695	+	0.821162i	$0.693326\pi$
$338$	2.06372	+	0.918827i	0.112251	+	0.0499776i
$339$		0			0
$340$	22.5927	+	13.0439i	1.22526	+	0.707406i
$341$	0.305577	−	1.88246i	0.0165479	−	0.101941i
$342$		0			0
$343$	8.87173	+	2.88260i	0.479028	+	0.155646i
$344$	1.51571	−	0.159308i	0.0817217	−	0.00858930i
$345$		0			0
$346$	−0.171544	+	0.190519i	−0.00922226	+	0.0102424i
$347$	16.7948	−	18.6525i	0.901594	−	1.00132i	−0.0983872	−	0.995148i	$-0.531368\pi$
$347$	16.7948	−	18.6525i	0.901594	−	1.00132i	0.999981	−	0.00617310i	$-0.00196497\pi$
$348$		0			0
$349$	−24.7124	+	2.59738i	−1.32282	+	0.139034i	−0.739473	−	0.673186i	$-0.764925\pi$
$349$	−24.7124	+	2.59738i	−1.32282	+	0.139034i	−0.583350	+	0.812221i	$0.698259\pi$
$350$	0.884168	+	0.287283i	0.0472607	+	0.0153559i
$351$		0			0
$352$	6.77470	−	1.04632i	0.361093	−	0.0557691i
$353$	−11.1137	−	6.41647i	−0.591520	−	0.341514i	0.174178	−	0.984714i	$-0.444273\pi$
$353$	−11.1137	−	6.41647i	−0.591520	−	0.341514i	−0.765698	+	0.643200i	$0.777606\pi$
$354$		0			0
$355$	1.20619	+	0.537030i	0.0640178	+	0.0285026i
$356$	9.40734	+	0.988751i	0.498588	+	0.0524037i
$357$		0			0
$358$	0.721125	−	3.39263i	0.0381127	−	0.179306i
$359$	24.7483	+	17.9807i	1.30617	+	0.948985i	0.999996	−	0.00299211i	$-0.000952421\pi$
$359$	24.7483	+	17.9807i	1.30617	+	0.948985i	0.306170	+	0.951977i	$0.400952\pi$
$360$		0			0
$361$	2.78452	−	8.56987i	0.146554	−	0.451046i
$362$	0.105175	−	0.182168i	0.00552786	−	0.00957454i
$363$		0			0
$364$	−1.29267	−	2.23897i	−0.0677543	−	0.117354i
$365$	3.91827	−	0.832854i	0.205092	−	0.0435936i
$366$		0			0
$367$	15.5911	−	6.94161i	0.813850	−	0.362349i	0.0427678	−	0.999085i	$-0.486382\pi$
$367$	15.5911	−	6.94161i	0.813850	−	0.362349i	0.771082	+	0.636736i	$0.219716\pi$
$368$	23.2358	−	7.54977i	1.21125	−	0.393559i
$369$		0			0
$370$	1.96926	−	2.71045i	0.102377	−	0.140910i
$371$	3.02055	+	28.7386i	0.156819	+	1.49203i
$372$		0			0
$373$	5.75822	−	3.32451i	0.298149	−	0.172137i	−0.343462	−	0.939167i	$-0.611600\pi$
$373$	5.75822	−	3.32451i	0.298149	−	0.172137i	0.641611	+	0.767030i	$0.278266\pi$
$374$	−2.61650	−	3.25663i	−0.135296	−	0.168396i
$375$		0			0
$376$	4.43325	−	3.99172i	0.228628	−	0.205857i
$377$	−1.43399	−	1.97372i	−0.0738542	−	0.101652i
$378$		0			0
$379$	−4.59981	−	14.1568i	−0.236276	−	0.727184i	−0.996950	−	0.0780488i	$-0.975131\pi$
$379$	−4.59981	−	14.1568i	−0.236276	−	0.727184i	0.760673	−	0.649135i	$-0.224869\pi$
$380$	11.2597	+	2.39332i	0.577610	+	0.122775i
$381$		0			0
$382$	0.447579	−	1.00528i	0.0229001	−	0.0514346i
$383$	3.97701	+	18.7104i	0.203216	+	0.956056i	0.954991	+	0.296636i	$0.0958647\pi$
$383$	3.97701	+	18.7104i	0.203216	+	0.956056i	−0.751775	+	0.659420i	$0.770802\pi$
$384$		0			0
$385$	−15.9157	−	12.9899i	−0.811140	−	0.662029i
$386$		−	3.40973i		−	0.173551i
$387$		0			0
$388$	21.2907	−	15.4686i	1.08087	−	0.785297i
$389$	−3.18270	−	7.14846i	−0.161369	−	0.362441i	0.814706	−	0.579874i	$-0.196898\pi$
$389$	−3.18270	−	7.14846i	−0.161369	−	0.362441i	−0.976075	+	0.217433i	$0.930232\pi$
$390$		0			0
$391$	−34.0849	−	30.6902i	−1.72375	−	1.55207i
$392$	−0.307473	+	2.92541i	−0.0155297	+	0.147755i
$393$		0			0
$394$	1.42701	+	1.58486i	0.0718918	+	0.0798439i
$395$	17.0676			0.858762
$396$		0			0
$397$	1.05373			0.0528854			0.0264427	−	0.999650i	$-0.491582\pi$
$397$	1.05373			0.0528854			0.0264427	+	0.999650i	$0.491582\pi$
$398$	0.0316883	+	0.0351934i	0.00158839	+	0.00176408i
$399$		0			0
$400$	−0.629612	+	5.99036i	−0.0314806	+	0.299518i
$401$	−24.4102	−	21.9790i	−1.21899	−	1.09758i	−0.992332	−	0.123605i	$-0.960554\pi$
$401$	−24.4102	−	21.9790i	−1.21899	−	1.09758i	−0.226655	−	0.973975i	$-0.572779\pi$
$402$		0			0
$403$	0.0916974	+	0.205956i	0.00456777	+	0.0102594i
$404$	−27.3159	+	19.8462i	−1.35902	+	0.987385i
$405$		0			0
$406$			3.66432i			0.181857i
$407$	28.7219	−	18.4956i	1.42369	−	0.916791i
$408$		0			0
$409$	−1.18060	−	5.55429i	−0.0583770	−	0.274642i	0.939272	−	0.343174i	$-0.111502\pi$
$409$	−1.18060	−	5.55429i	−0.0583770	−	0.274642i	−0.997649	+	0.0685316i	$0.978169\pi$
$410$	0.0569917	−	0.128005i	0.00281462	−	0.00632174i
$411$		0			0
$412$	−26.1008	−	5.54789i	−1.28589	−	0.273325i
$413$	1.92939	+	5.93804i	0.0949388	+	0.292192i
$414$		0			0
$415$	−0.325613	−	0.448168i	−0.0159837	−	0.0219997i
$416$	−0.602216	+	0.542238i	−0.0295261	+	0.0265854i
$417$		0			0
$418$	−1.54207	−	1.00989i	−0.0754253	−	0.0493951i
$419$	15.8726	−	9.16403i	0.775426	−	0.447692i	−0.0593810	−	0.998235i	$-0.518913\pi$
$419$	15.8726	−	9.16403i	0.775426	−	0.447692i	0.834807	+	0.550543i	$0.185579\pi$
$420$		0			0
$421$	3.27802	+	31.1883i	0.159761	+	1.52002i	0.721328	+	0.692593i	$0.243532\pi$
$421$	3.27802	+	31.1883i	0.159761	+	1.52002i	−0.561567	+	0.827431i	$0.689801\pi$
$422$	−0.0883218	+	0.121564i	−0.00429944	+	0.00591767i
$423$		0			0
$424$	5.72797	−	1.86113i	0.278175	−	0.0903845i
$425$	10.3301	−	4.59927i	0.501085	−	0.223097i
$426$		0			0
$427$	35.6387	−	7.57523i	1.72468	−	0.366591i
$428$	13.4292	+	23.2600i	0.649124	+	1.12432i
$429$		0			0
$430$	−0.355123	+	0.615092i	−0.0171256	+	0.0296623i
$431$	−7.48774	+	23.0449i	−0.360672	+	1.11003i	0.591975	+	0.805956i	$0.298348\pi$
$431$	−7.48774	+	23.0449i	−0.360672	+	1.11003i	−0.952647	+	0.304078i	$0.901652\pi$
$432$		0			0
$433$	15.9525	+	11.5902i	0.766627	+	0.556987i	0.900936	−	0.433952i	$-0.142881\pi$
$433$	15.9525	+	11.5902i	0.766627	+	0.556987i	−0.134309	+	0.990940i	$0.542881\pi$
$434$	0.0704026	−	0.331218i	0.00337943	−	0.0158990i
$435$		0			0
$436$	−5.80408	−	0.610033i	−0.277965	−	0.0292153i
$437$	−18.4886	−	8.23164i	−0.884428	−	0.393773i
$438$		0			0
$439$	−0.989513	−	0.571296i	−0.0472269	−	0.0272665i	0.476201	−	0.879337i	$-0.342014\pi$
$439$	−0.989513	−	0.571296i	−0.0472269	−	0.0272665i	−0.523428	+	0.852070i	$0.675347\pi$
$440$	−1.95855	+	3.80760i	−0.0933700	+	0.181520i
$441$		0			0
$442$	0.469672	+	0.152606i	0.0223400	+	0.00725871i
$443$	9.25936	−	0.973198i	0.439925	−	0.0462380i	0.118023	−	0.993011i	$-0.462344\pi$
$443$	9.25936	−	0.973198i	0.439925	−	0.0462380i	0.321902	+	0.946773i	$0.395678\pi$
$444$		0			0
$445$	−5.94562	+	6.60328i	−0.281849	+	0.313025i
$446$	−1.72371	+	1.91437i	−0.0816199	+	0.0906481i
$447$		0			0
$448$	−24.2036	+	2.54390i	−1.14351	+	0.120188i
$449$	3.09428	+	1.00539i	0.146028	+	0.0474474i	0.381119	−	0.924526i	$-0.375539\pi$
$449$	3.09428	+	1.00539i	0.146028	+	0.0474474i	−0.235091	+	0.971973i	$0.575539\pi$
$450$		0			0
$451$	1.01415	−	1.00638i	0.0477546	−	0.0473888i
$452$	17.8889	+	10.3282i	0.841423	+	0.485796i
$453$		0			0
$454$	2.16813	+	0.965314i	0.101755	+	0.0453044i
$455$	2.41527	+	0.253855i	0.113230	+	0.0119009i
$456$		0			0
$457$	2.90130	−	13.6495i	0.135717	−	0.638498i	−0.856724	−	0.515775i	$-0.827504\pi$
$457$	2.90130	−	13.6495i	0.135717	−	0.638498i	0.992441	−	0.122723i	$-0.0391627\pi$
$458$	2.74426	+	1.99382i	0.128231	+	0.0931650i
$459$		0			0
$460$	−7.20694	+	22.1807i	−0.336025	+	1.03418i
$461$	16.8347	−	29.1586i	0.784071	−	1.35805i	−0.145482	−	0.989361i	$-0.546473\pi$
$461$	16.8347	−	29.1586i	0.784071	−	1.35805i	0.929553	−	0.368689i	$-0.120193\pi$
$462$		0			0
$463$	−9.10638	−	15.7727i	−0.423209	−	0.733020i	0.573042	−	0.819526i	$-0.305763\pi$
$463$	−9.10638	−	15.7727i	−0.423209	−	0.733020i	−0.996251	+	0.0865060i	$0.972430\pi$
$464$	−23.2224	+	4.93608i	−1.07807	+	0.229152i
$465$		0			0
$466$	−0.336875	+	0.149986i	−0.0156054	+	0.00694798i
$467$	22.5998	−	7.34311i	1.04579	−	0.339799i	0.264777	−	0.964310i	$-0.414702\pi$
$467$	22.5998	−	7.34311i	1.04579	−	0.339799i	0.781016	+	0.624511i	$0.214702\pi$
$468$		0			0
$469$	−15.6275	+	21.5095i	−0.721613	+	0.993215i
$470$	0.290597	+	2.76484i	0.0134042	+	0.127533i
$471$		0			0
$472$	1.12697	−	0.650654i	0.0518728	−	0.0299488i
$473$	−5.64567	+	4.53595i	−0.259588	+	0.208563i
$474$		0			0
$475$	3.70795	−	3.33865i	0.170132	−	0.153188i
$476$	27.7619	+	38.2110i	1.27246	+	1.75140i
$477$		0			0
$478$	−0.354432	−	1.09083i	−0.0162114	−	0.0498934i
$479$	10.8565	+	2.30761i	0.496044	+	0.105437i	0.449139	−	0.893462i	$-0.351731\pi$
$479$	10.8565	+	2.30761i	0.496044	+	0.105437i	0.0469052	+	0.998899i	$0.485064\pi$
$480$		0			0
$481$	−1.64257	+	3.68927i	−0.0748948	+	0.168216i
$482$	0.857647	+	4.03491i	0.0390648	+	0.183785i
$483$		0			0
$484$	−16.2074	+	14.3691i	−0.736699	+	0.653139i
$485$			24.7209i			1.12252i
$486$		0			0
$487$	−1.57754	+	1.14615i	−0.0714850	+	0.0519369i	−0.622954	−	0.782259i	$-0.714068\pi$
$487$	−1.57754	+	1.14615i	−0.0714850	+	0.0519369i	0.551469	+	0.834196i	$0.314068\pi$
$488$	−3.08869	−	6.93731i	−0.139818	−	0.314037i
$489$		0			0
$490$	−1.01871	−	0.917254i	−0.0460208	−	0.0414373i
$491$	−0.383211	+	3.64601i	−0.0172941	+	0.164542i	−0.999760	−	0.0218991i	$-0.993029\pi$
$491$	−0.383211	+	3.64601i	−0.0172941	+	0.164542i	0.982466	+	0.186441i	$0.0596954\pi$
$492$		0			0
$493$	29.8230	+	33.1218i	1.34316	+	1.49173i
$494$	0.217907			0.00980412
$495$		0			0
$496$	2.19392			0.0985097
$497$	1.59952	+	1.77644i	0.0717481	+	0.0796843i
$498$		0			0
$499$	0.474479	−	4.51436i	0.0212406	−	0.202091i	−0.978755	−	0.205033i	$-0.934270\pi$
$499$	0.474479	−	4.51436i	0.0212406	−	0.202091i	0.999996	+	0.00294223i	$0.000936543\pi$
$500$	−17.8062	−	16.0328i	−0.796318	−	0.717008i
$501$		0			0
$502$	−0.219356	−	0.492682i	−0.00979034	−	0.0219895i
$503$	15.1967	−	11.0411i	0.677589	−	0.492297i	−0.194968	−	0.980810i	$-0.562460\pi$
$503$	15.1967	−	11.0411i	0.677589	−	0.492297i	0.872557	+	0.488512i	$0.162460\pi$
$504$		0			0
$505$		−	31.7170i		−	1.41139i
$506$	2.36143	−	2.89330i	0.104978	−	0.128623i
$507$		0			0
$508$	−2.64999	−	12.4672i	−0.117574	−	0.553143i
$509$	0.0234176	−	0.0525968i	0.00103797	−	0.00233131i	−0.913026	−	0.407902i	$-0.866261\pi$
$509$	0.0234176	−	0.0525968i	0.00103797	−	0.00233131i	0.914064	+	0.405571i	$0.132927\pi$
$510$		0			0
$511$	7.09393	+	1.50786i	0.313817	+	0.0667038i
$512$	4.08273	+	12.5654i	0.180433	+	0.555316i
$513$		0			0
$514$	−2.55774	−	3.52043i	−0.112817	−	0.155279i
$515$	18.6276	−	16.7723i	0.820828	−	0.739077i
$516$		0			0
$517$	−7.44207	+	27.3531i	−0.327302	+	1.20299i
$518$	5.25300	−	3.03282i	0.230803	−	0.133254i
$519$		0			0
$520$	−0.0529090	−	0.503395i	−0.00232021	−	0.0220753i
$521$	−10.7802	+	14.8377i	−0.472289	+	0.650050i	−0.977000	−	0.213238i	$-0.931599\pi$
$521$	−10.7802	+	14.8377i	−0.472289	+	0.650050i	0.504711	+	0.863288i	$0.331599\pi$
$522$		0			0
$523$	0.656293	−	0.213243i	0.0286977	−	0.00932445i	−0.294633	−	0.955610i	$-0.595197\pi$
$523$	0.656293	−	0.213243i	0.0286977	−	0.00932445i	0.323331	+	0.946286i	$0.395197\pi$
$524$	−34.5230	+	15.3706i	−1.50815	+	0.671470i
$525$		0			0
$526$	−3.38851	+	0.720251i	−0.147746	+	0.0314044i
$527$	−2.05934	−	3.56687i	−0.0897061	−	0.155375i
$528$		0			0
$529$	9.00166	−	15.5913i	0.391377	−	0.677884i
$530$	−0.867329	+	2.66936i	−0.0376744	+	0.115950i
$531$		0			0
$532$	16.8606	+	12.2499i	0.730998	+	0.531101i
$533$	−0.0351159	+	0.165207i	−0.00152104	+	0.00715593i
$534$		0			0
$535$	−25.0915	−	2.63723i	−1.08480	−	0.114017i
$536$	5.06227	+	2.25387i	0.218657	+	0.0973524i
$537$		0			0
$538$	−3.84650	−	2.22078i	−0.165834	−	0.0957445i
$539$	−6.29781	−	12.4785i	−0.271266	−	0.537488i
$540$		0			0
$541$	36.9058	+	11.9914i	1.58670	+	0.515552i	0.963773	−	0.266725i	$-0.0859414\pi$
$541$	36.9058	+	11.9914i	1.58670	+	0.515552i	0.622932	+	0.782276i	$0.285941\pi$
$542$	1.75852	−	0.184828i	0.0755351	−	0.00793906i
$543$		0			0
$544$	9.90610	−	11.0018i	0.424721	−	0.471700i
$545$	3.66829	−	4.07405i	0.157132	−	0.174513i
$546$		0			0
$547$	38.6214	−	4.05927i	1.65133	−	0.173562i	0.767398	−	0.641172i	$-0.221551\pi$
$547$	38.6214	−	4.05927i	1.65133	−	0.173562i	0.883935	+	0.467610i	$0.154885\pi$
$548$	−21.9279	−	7.12482i	−0.936715	−	0.304357i
$549$		0			0
$550$	0.414849	+	0.821984i	0.0176892	+	0.0350495i
$551$	17.0316	+	9.83320i	0.725570	+	0.418908i
$552$		0			0
$553$	28.2289	+	12.5683i	1.20042	+	0.534459i
$554$	1.55727	+	0.163675i	0.0661619	+	0.00695390i
$555$		0			0
$556$	7.45189	−	35.0584i	0.316031	−	1.48681i
$557$	13.5054	+	9.81227i	0.572244	+	0.415759i	0.835920	−	0.548852i	$-0.184935\pi$
$557$	13.5054	+	9.81227i	0.572244	+	0.415759i	−0.263676	+	0.964611i	$0.584935\pi$
$558$		0			0
$559$	0.264556	−	0.814221i	0.0111895	−	0.0344379i
$560$	11.8167	−	20.4672i	0.499348	−	0.864895i
$561$		0			0
$562$	−0.719975	−	1.24703i	−0.0303703	−	0.0526029i
$563$	−34.5061	+	7.33450i	−1.45426	+	0.309113i	−0.866197	−	0.499703i	$-0.833443\pi$
$563$	−34.5061	+	7.33450i	−1.45426	+	0.309113i	−0.588063	+	0.808815i	$0.700109\pi$
$564$		0			0
$565$	−17.7262	+	7.89223i	−0.745749	+	0.332029i
$566$	0.761720	−	0.247498i	0.0320175	−	0.0104031i
$567$		0			0
$568$	0.292846	−	0.403068i	0.0122876	−	0.0169124i
$569$	2.61672	+	24.8964i	0.109698	+	1.04371i	0.901455	+	0.432874i	$0.142500\pi$
$569$	2.61672	+	24.8964i	0.109698	+	1.04371i	−0.791756	+	0.610837i	$0.790833\pi$
$570$		0			0
$571$	15.2940	−	8.83002i	0.640036	−	0.369525i	−0.144593	−	0.989491i	$-0.546187\pi$
$571$	15.2940	−	8.83002i	0.640036	−	0.369525i	0.784628	+	0.619967i	$0.212854\pi$
$572$	0.672211	−	2.47069i	0.0281066	−	0.103305i
$573$		0			0
$574$	0.188523	−	0.169747i	0.00786879	−	0.00708509i
$575$	5.94189	+	8.17831i	0.247794	+	0.341059i
$576$		0			0
$577$	−7.75725	−	23.8744i	−0.322938	−	0.993902i	−0.972363	−	0.233476i	$-0.924990\pi$
$577$	−7.75725	−	23.8744i	−0.322938	−	0.993902i	0.649424	−	0.760426i	$-0.275010\pi$
$578$	−5.90069	−	1.25423i	−0.245436	−	0.0521691i
$579$		0			0
$580$	9.21794	−	20.7038i	0.382754	−	0.859679i
$581$	−0.208523	−	0.981025i	−0.00865100	−	0.0406998i
$582$		0			0
$583$	−18.0961	+	22.1719i	−0.749463	+	0.918268i
$584$		−	1.51156i		−	0.0625489i
$585$		0			0
$586$	0.348784	−	0.253406i	0.0144081	−	0.0104681i
$587$	1.76213	+	3.95780i	0.0727308	+	0.163356i	0.946252	−	0.323430i	$-0.104836\pi$
$587$	1.76213	+	3.95780i	0.0727308	+	0.163356i	−0.873521	+	0.486786i	$0.838169\pi$
$588$		0			0
$589$	−1.35056	−	1.21605i	−0.0556490	−	0.0501065i
$590$	−0.0633901	+	0.603117i	−0.00260973	+	0.0248299i
$591$		0			0
$592$	26.2965	+	29.2052i	1.08078	+	1.20033i
$593$	−11.9330			−0.490031			−0.245015	−	0.969519i	$-0.578793\pi$
$593$	−11.9330			−0.490031			−0.245015	+	0.969519i	$0.578793\pi$
$594$		0			0
$595$	−44.3674			−1.81889
$596$	11.4085	+	12.6705i	0.467312	+	0.519002i
$597$		0			0
$598$	−0.0461480	+	0.439069i	−0.00188713	+	0.0179549i
$599$	28.5698	+	25.7244i	1.16733	+	1.05107i	0.997850	+	0.0655349i	$0.0208754\pi$
$599$	28.5698	+	25.7244i	1.16733	+	1.05107i	0.169480	+	0.985534i	$0.445791\pi$
$600$		0			0
$601$	−10.5928	−	23.7918i	−0.432089	−	0.970487i	−0.990062	−	0.140628i	$-0.955088\pi$
$601$	−10.5928	−	23.7918i	−0.432089	−	0.970487i	0.557974	−	0.829859i	$-0.311579\pi$
$602$	−1.04030	+	0.755823i	−0.0423995	+	0.0308051i
$603$		0			0
$604$			26.8446i			1.09229i
$605$	−1.97111	−	20.2508i	−0.0801372	−	0.823311i
$606$		0			0
$607$	7.47587	+	35.1712i	0.303436	+	1.42755i	0.820519	+	0.571619i	$0.193685\pi$
$607$	7.47587	+	35.1712i	0.303436	+	1.42755i	−0.517083	+	0.855935i	$0.672982\pi$
$608$	2.65699	−	5.96769i	0.107755	−	0.242022i
$609$		0			0
$610$	3.46156	+	0.735777i	0.140154	+	0.0297908i
$611$	−1.03554	−	3.18705i	−0.0418933	−	0.128934i
$612$		0			0
$613$	−8.69094	−	11.9621i	−0.351024	−	0.483143i	0.596597	−	0.802541i	$-0.296519\pi$
$613$	−8.69094	−	11.9621i	−0.351024	−	0.483143i	−0.947621	+	0.319398i	$0.896519\pi$
$614$	−4.04342	+	3.64071i	−0.163179	+	0.146927i
$615$		0			0
$616$	−6.04320	+	4.85533i	−0.243487	+	0.195627i
$617$	34.7254	−	20.0487i	1.39799	−	0.807132i	0.403811	−	0.914843i	$-0.367685\pi$
$617$	34.7254	−	20.0487i	1.39799	−	0.807132i	0.994182	+	0.107711i	$0.0343521\pi$
$618$		0			0
$619$	−1.44689	−	13.7662i	−0.0581553	−	0.553311i	−0.984345	−	0.176253i	$-0.943602\pi$
$619$	−1.44689	−	13.7662i	−0.0581553	−	0.553311i	0.926190	−	0.377058i	$-0.123064\pi$
$620$	−1.23099	+	1.69432i	−0.0494379	+	0.0680454i
$621$		0			0
$622$	−4.11774	+	1.33793i	−0.165106	+	0.0536463i
$623$	−14.6963	+	6.54323i	−0.588796	+	0.262149i
$624$		0			0
$625$	14.2949	−	3.03848i	0.571798	−	0.121539i
$626$	−1.03854	−	1.79880i	−0.0415083	−	0.0718946i
$627$		0			0
$628$	−8.04426	+	13.9331i	−0.321001	+	0.555990i
$629$	22.7985	−	70.1666i	0.909036	−	2.79772i
$630$		0			0
$631$	−28.6716	−	20.8311i	−1.14140	−	0.829274i	−0.154084	−	0.988058i	$-0.549243\pi$
$631$	−28.6716	−	20.8311i	−1.14140	−	0.829274i	−0.987313	+	0.158784i	$0.949243\pi$
$632$	1.33902	−	6.29959i	0.0532633	−	0.250584i
$633$		0			0
$634$	2.45729	+	0.258272i	0.0975916	+	0.0102573i
$635$	10.9378	+	4.86981i	0.434052	+	0.193252i
$636$		0			0
$637$	1.43099	+	0.826181i	0.0566978	+	0.0327345i
$638$	−2.57602	+	2.55629i	−0.101986	+	0.101204i
$639$		0			0
$640$	−9.51999	−	3.09323i	−0.376311	−	0.122271i
$641$	−18.5025	+	1.94469i	−0.730804	+	0.0768105i	−0.462619	−	0.886557i	$-0.653090\pi$
$641$	−18.5025	+	1.94469i	−0.730804	+	0.0768105i	−0.268184	+	0.963368i	$0.586424\pi$
$642$		0			0
$643$	−8.45910	+	9.39479i	−0.333595	+	0.370494i	−0.886483	−	0.462761i	$-0.846859\pi$
$643$	−8.45910	+	9.39479i	−0.333595	+	0.370494i	0.552889	+	0.833255i	$0.313526\pi$
$644$	−28.2535	+	31.3787i	−1.11334	+	1.23649i
$645$		0			0
$646$	−3.95913	+	0.416121i	−0.155770	+	0.0163721i
$647$	−20.3494	−	6.61193i	−0.800019	−	0.259942i	−0.119654	−	0.992816i	$-0.538179\pi$
$647$	−20.3494	−	6.61193i	−0.800019	−	0.259942i	−0.680365	+	0.732874i	$0.738179\pi$
$648$		0			0
$649$	−2.82848	+	5.49883i	−0.111027	+	0.215848i
$650$	−0.0942619	−	0.0544221i	−0.00369726	−	0.00213461i
$651$		0			0
$652$	6.72734	+	2.99520i	0.263463	+	0.117301i
$653$	12.6965	+	1.33446i	0.496853	+	0.0522214i	0.349641	−	0.936884i	$-0.386303\pi$
$653$	12.6965	+	1.33446i	0.496853	+	0.0522214i	0.147212	+	0.989105i	$0.452970\pi$
$654$		0			0
$655$	7.38059	−	34.7230i	0.288384	−	1.35674i
$656$	1.32972	+	0.966095i	0.0519167	+	0.0377197i
$657$		0			0
$658$	−1.55536	+	4.78690i	−0.0606342	+	0.186613i
$659$	−23.8138	+	41.2467i	−0.927653	+	1.60674i	−0.140415	+	0.990093i	$0.544844\pi$
$659$	−23.8138	+	41.2467i	−0.927653	+	1.60674i	−0.787238	+	0.616649i	$0.788490\pi$
$660$		0			0
$661$	12.9086	+	22.3584i	0.502087	+	0.869640i	0.999997	+	0.00241171i	$0.000767671\pi$
$661$	12.9086	+	22.3584i	0.502087	+	0.869640i	−0.497910	+	0.867229i	$0.665899\pi$
$662$	−5.26590	+	1.11930i	−0.204665	+	0.0435029i
$663$		0			0
$664$	−0.190963	+	0.0850222i	−0.00741080	+	0.00329950i
$665$	−18.6189	+	6.04966i	−0.722011	+	0.234596i
$666$		0			0
$667$	−23.4202	+	32.2351i	−0.906832	+	1.24815i
$668$	−1.57616	−	14.9961i	−0.0609833	−	0.580217i
$669$		0			0
$670$	−2.23642	+	1.29120i	−0.0864004	+	0.0498833i
$671$	30.1875	+	19.7694i	1.16538	+	0.763190i
$672$		0			0
$673$	32.6839	−	29.4287i	1.25987	−	1.13439i	0.274937	−	0.961462i	$-0.411343\pi$
$673$	32.6839	−	29.4287i	1.25987	−	1.13439i	0.984934	−	0.172930i	$-0.0553236\pi$
$674$	−1.82816	−	2.51625i	−0.0704181	−	0.0969222i
$675$		0			0
$676$	−7.81668	−	24.0573i	−0.300642	−	0.925280i
$677$	−22.3474	−	4.75009i	−0.858882	−	0.182561i	−0.242639	−	0.970117i	$-0.578013\pi$
$677$	−22.3474	−	4.75009i	−0.858882	−	0.182561i	−0.616243	+	0.787556i	$0.711346\pi$
$678$		0			0
$679$	−18.2042	+	40.8872i	−0.698612	+	1.56911i
$680$	1.92259	+	9.04508i	0.0737280	+	0.346863i
$681$		0			0
$682$	0.281961	−	0.181570i	0.0107968	−	0.00695267i
$683$		−	0.0146413i		−	0.000560235i	−1.00000		0.000280118i	$-0.999911\pi$
$683$		−	0.0146413i		−	0.000560235i	1.00000		0.000280118i	$-8.91642e-5\pi$
$684$		0			0
$685$	17.5220	−	12.7304i	0.669480	−	0.486405i
$686$	0.667203	+	1.49856i	0.0254739	+	0.0572154i
$687$		0			0
$688$	−6.19135	−	5.57472i	−0.236043	−	0.212534i
$689$	0.353641	−	3.36467i	0.0134727	−	0.128184i
$690$		0			0
$691$	−21.9950	−	24.4279i	−0.836728	−	0.929281i	0.161613	−	0.986854i	$-0.448330\pi$
$691$	−21.9950	−	24.4279i	−0.836728	−	0.929281i	−0.998341	+	0.0575732i	$0.981664\pi$
$692$	2.87068			0.109127
$693$		0			0
$694$	4.41375			0.167544
$695$	22.5285	+	25.0204i	0.854555	+	0.949079i
$696$		0			0
$697$	0.322532	−	3.06869i	0.0122168	−	0.116235i
$698$	−3.24726	−	2.92384i	−0.122910	−	0.110669i
$699$		0			0
$700$	−4.23410	−	9.50995i	−0.160034	−	0.359442i
$701$	29.3731	−	21.3408i	1.10941	−	0.806031i	0.126836	−	0.991924i	$-0.459518\pi$
$701$	29.3731	−	21.3408i	1.10941	−	0.806031i	0.982570	+	0.185893i	$0.0595177\pi$
$702$		0			0
$703$		−	32.5543i		−	1.22781i
$704$	−18.6732	−	15.2405i	−0.703773	−	0.574399i
$705$		0			0
$706$	−0.469189	−	2.20736i	−0.0176582	−	0.0830752i
$707$	23.3560	−	52.4583i	0.878391	−	1.97290i
$708$		0			0
$709$	−19.7997	−	4.20856i	−0.743594	−	0.158056i	−0.179490	−	0.983760i	$-0.557445\pi$
$709$	−19.7997	−	4.20856i	−0.743594	−	0.158056i	−0.564104	+	0.825704i	$0.690778\pi$
$710$	0.0717481	+	0.220818i	0.00269266	+	0.00828715i
$711$		0			0
$712$	1.97079	+	2.71256i	0.0738586	+	0.101658i
$713$	2.73628	−	2.46376i	0.102475	−	0.0922685i
$714$		0			0
$715$	1.50647	+	1.87503i	0.0563387	+	0.0701221i
$716$	−33.6343	+	19.4188i	−1.25697	+	0.725713i
$717$		0			0
$718$	0.562296	+	5.34989i	0.0209847	+	0.199656i
$719$	−6.94898	+	9.56445i	−0.259153	+	0.356694i	−0.918691	−	0.394978i	$-0.870752\pi$
$719$	−6.94898	+	9.56445i	−0.259153	+	0.356694i	0.659537	+	0.751672i	$0.270752\pi$
$720$		0			0
$721$	43.1600	−	14.0235i	1.60736	−	0.522263i
$722$	1.44757	−	0.644502i	0.0538732	−	0.0239859i
$723$		0			0
$724$	−2.30391	+	0.489711i	−0.0856241	+	0.0182000i
$725$	−4.91166	−	8.50724i	−0.182414	−	0.315951i
$726$		0			0
$727$	−7.56176	+	13.0973i	−0.280450	+	0.485754i	−0.971496	−	0.237057i	$-0.923817\pi$
$727$	−7.56176	+	13.0973i	−0.280450	+	0.485754i	0.691046	+	0.722811i	$0.257150\pi$
$728$	0.283184	−	0.871552i	0.0104955	−	0.0323019i
$729$		0			0
$730$	0.569889	+	0.414049i	0.0210925	+	0.0153246i
$731$	−3.25183	+	15.2987i	−0.120273	+	0.565842i
$732$		0			0
$733$	−5.37738	−	0.565185i	−0.198618	−	0.0208756i	0.00469699	−	0.999989i	$-0.498505\pi$
$733$	−5.37738	−	0.565185i	−0.198618	−	0.0208756i	−0.203315	+	0.979113i	$0.565172\pi$
$734$	2.74170	+	1.22068i	0.101198	+	0.0450563i
$735$		0			0
$736$	11.4618	+	6.61747i	0.422488	+	0.243923i
$737$	−26.0232	+	4.01916i	−0.958577	+	0.148048i
$738$		0			0
$739$	10.8856	+	3.53696i	0.400434	+	0.130109i	0.502309	−	0.864688i	$-0.332484\pi$
$739$	10.8856	+	3.53696i	0.400434	+	0.130109i	−0.101875	+	0.994797i	$0.532484\pi$
$740$	−37.3094	+	3.92137i	−1.37152	+	0.144153i
$741$		0			0
$742$	−3.40020	+	3.77631i	−0.124825	+	0.138633i
$743$	14.1011	−	15.6609i	0.517321	−	0.574543i	−0.426715	−	0.904386i	$-0.640329\pi$
$743$	14.1011	−	15.6609i	0.517321	−	0.574543i	0.944036	+	0.329843i	$0.106996\pi$
$744$		0			0
$745$	−15.9282	+	1.67412i	−0.583564	+	0.0613351i
$746$	1.11201	+	0.361312i	0.0407134	+	0.0132286i
$747$		0			0
$748$	−7.49523	+	46.1732i	−0.274053	+	1.68826i
$749$	−39.5582	−	22.8389i	−1.44542	−	0.834516i
$750$		0			0
$751$	−13.0979	−	5.83158i	−0.477951	−	0.212797i	0.153598	−	0.988133i	$-0.450914\pi$
$751$	−13.0979	−	5.83158i	−0.477951	−	0.212797i	−0.631549	+	0.775336i	$0.717581\pi$
$752$	−32.4320	−	3.40874i	−1.18267	−	0.124304i
$753$		0			0
$754$	0.0891968	−	0.419638i	0.00324836	−	0.0152823i
$755$	−20.4008	−	14.8221i	−0.742462	−	0.539430i
$756$		0			0
$757$	−1.66452	+	5.12287i	−0.0604981	+	0.186194i	−0.976738	−	0.214436i	$-0.931209\pi$
$757$	−1.66452	+	5.12287i	−0.0604981	+	0.186194i	0.916240	+	0.400630i	$0.131209\pi$
$758$	1.30879	−	2.26689i	0.0475374	−	0.0823373i
$759$		0			0
$760$	2.04015	+	3.53364i	0.0740040	+	0.128179i
$761$	−23.2406	+	4.93995i	−0.842472	+	0.179073i	−0.608881	−	0.793262i	$-0.708381\pi$
$761$	−23.2406	+	4.93995i	−0.842472	+	0.179073i	−0.233592	+	0.972335i	$0.575048\pi$
$762$		0			0
$763$	9.06724	−	4.03700i	0.328256	−	0.146149i
$764$	−11.7188	+	3.80766i	−0.423971	+	0.137756i
$765$		0			0
$766$	−1.97715	+	2.72131i	−0.0714374	+	0.0983251i
$767$	−0.0764097	−	0.726990i	−0.00275899	−	0.0262501i
$768$		0			0
$769$	25.2319	−	14.5677i	0.909887	−	0.525323i	0.0294919	−	0.999565i	$-0.490611\pi$
$769$	25.2319	−	14.5677i	0.909887	−	0.525323i	0.880395	+	0.474242i	$0.157278\pi$
$770$	−0.175198	−	3.60839i	−0.00631369	−	0.130037i
$771$		0			0
$772$	−28.3735	+	25.5476i	−1.02118	+	0.919479i
$773$	−6.21792	−	8.55823i	−0.223643	−	0.307818i	0.682421	−	0.730960i	$-0.260927\pi$
$773$	−6.21792	−	8.55823i	−0.223643	−	0.307818i	−0.906064	+	0.423142i	$0.860927\pi$
$774$		0			0
$775$	0.280516	+	0.863338i	0.0100764	+	0.0310120i
$776$	9.12442	+	1.93946i	0.327548	+	0.0696224i
$777$		0			0
$778$	0.559678	−	1.25706i	0.0200654	−	0.0450677i
$779$	−0.283075	−	1.33176i	−0.0101422	−	0.0477153i
$780$		0			0
$781$	−0.132994	+	2.36373i	−0.00475889	+	0.0845811i
$782$		−	8.06551i		−	0.288422i
$783$		0			0
$784$	13.0089	−	9.45149i	0.464602	−	0.337553i
$785$	−6.14700	−	13.8064i	−0.219396	−	0.492771i
$786$		0			0
$787$	−10.9534	−	9.86248i	−0.390446	−	0.351559i	0.450406	−	0.892824i	$-0.351279\pi$
$787$	−10.9534	−	9.86248i	−0.390446	−	0.351559i	−0.840853	+	0.541264i	$0.817946\pi$
$788$	2.49615	−	23.7493i	0.0889217	−	0.846033i
$789$		0			0
$790$	2.00828	+	2.23043i	0.0714516	+	0.0793550i
$791$	−35.1301			−1.24908
$792$		0			0
$793$	−4.26574			−0.151481
$794$	0.123989	+	0.137704i	0.00440022	+	0.00488694i
$795$		0			0
$796$	0.0554296	−	0.527377i	0.00196465	−	0.0186924i
$797$	2.33490	+	2.10236i	0.0827066	+	0.0744693i	0.709447	−	0.704759i	$-0.248945\pi$
$797$	2.33490	+	2.10236i	0.0827066	+	0.0744693i	−0.626741	+	0.779228i	$0.715611\pi$
$798$		0			0
$799$	24.9006	+	55.9276i	0.880919	+	1.97858i
$800$	−2.63978	+	1.91791i	−0.0933301	+	0.0678083i
$801$		0			0
$802$		−	5.77618i		−	0.203964i
$803$	3.88881	+	6.03895i	0.137233	+	0.213110i
$804$		0			0
$805$	−8.24657	−	38.7971i	−0.290653	−	1.36742i
$806$	−0.0161250	+	0.0362174i	−0.000567979	+	0.00127570i
$807$		0			0
$808$	−11.7066	−	2.48832i	−0.411838	−	0.0875390i
$809$	−13.5845	−	41.8088i	−0.477606	−	1.46992i	−0.842411	−	0.538836i	$-0.818864\pi$
$809$	−13.5845	−	41.8088i	−0.477606	−	1.46992i	0.364805	−	0.931084i	$-0.381136\pi$
$810$		0			0
$811$	12.4846	+	17.1835i	0.438392	+	0.603395i	0.969854	−	0.243687i	$-0.0783570\pi$
$811$	12.4846	+	17.1835i	0.438392	+	0.603395i	−0.531462	+	0.847082i	$0.678357\pi$
$812$	30.4920	−	27.4551i	1.07006	−	0.963487i
$813$		0			0
$814$	5.79665	+	1.57712i	0.203172	+	0.0552781i
$815$	−5.99070	+	3.45873i	−0.209845	+	0.121154i
$816$		0			0
$817$	0.721386	+	6.86353i	0.0252381	+	0.240125i
$818$	0.586929	−	0.807839i	0.0205215	−	0.0282454i
$819$		0			0
$820$	−1.49219	+	0.484842i	−0.0521096	+	0.0169314i
$821$	14.5734	−	6.48849i	0.508615	−	0.226450i	−0.136352	−	0.990660i	$-0.543538\pi$
$821$	14.5734	−	6.48849i	0.508615	−	0.226450i	0.644967	+	0.764211i	$0.276871\pi$
$822$		0			0
$823$	−23.9150	+	5.08330i	−0.833625	+	0.177193i	−0.604903	−	0.796299i	$-0.706788\pi$
$823$	−23.9150	+	5.08330i	−0.833625	+	0.177193i	−0.228722	+	0.973492i	$0.573455\pi$
$824$	−4.72921	−	8.19123i	−0.164750	−	0.285355i
$825$		0			0
$826$	−0.548971	+	0.950846i	−0.0191011	+	0.0330842i
$827$	10.3732	−	31.9255i	0.360712	−	1.11016i	−0.591910	−	0.806004i	$-0.701626\pi$
$827$	10.3732	−	31.9255i	0.360712	−	1.11016i	0.952623	−	0.304155i	$-0.0983739\pi$
$828$		0			0
$829$	−16.0411	−	11.6545i	−0.557130	−	0.404778i	0.273278	−	0.961935i	$-0.411892\pi$
$829$	−16.0411	−	11.6545i	−0.557130	−	0.404778i	−0.830407	+	0.557157i	$0.811892\pi$
$830$	0.0202537	−	0.0952863i	0.000703017	−	0.00330743i
$831$		0			0
$832$	2.83373	+	0.297837i	0.0982418	+	0.0103256i
$833$	−27.5771	−	12.2781i	−0.955490	−	0.425412i
$834$		0			0
$835$	12.2667	+	7.08220i	0.424508	+	0.245090i
$836$	3.15049	+	20.3987i	0.108962	+	0.705505i
$837$		0			0
$838$	3.06525	+	0.995960i	0.105887	+	0.0344049i
$839$	−28.7560	+	3.02238i	−0.992768	+	0.104344i	−0.586962	−	0.809615i	$-0.699676\pi$
$839$	−28.7560	+	3.02238i	−0.992768	+	0.104344i	−0.405807	+	0.913959i	$0.633009\pi$
$840$		0			0
$841$	6.50321	−	7.22255i	0.224249	−	0.249053i
$842$	−3.69004	+	4.09820i	−0.127167	+	0.141233i
$843$		0			0
$844$	1.67334	−	0.175875i	0.0575986	−	0.00605386i
$845$	22.5985	+	7.34270i	0.777413	+	0.252597i
$846$		0			0
$847$	11.6523	−	34.9453i	0.400376	−	1.20073i
$848$	−28.5125	−	16.4617i	−0.979122	−	0.565296i
$849$		0			0
$850$	1.81656	+	0.808783i	0.0623074	+	0.0277410i
$851$	65.5947	+	6.89428i	2.24856	+	0.236333i
$852$		0			0
$853$	3.35419	−	15.7802i	0.114845	−	0.540305i	−0.882678	−	0.469977i	$-0.844262\pi$
$853$	3.35419	−	15.7802i	0.114845	−	0.540305i	0.997524	−	0.0703280i	$-0.0224046\pi$
$854$	5.18343	+	3.76599i	0.177373	+	0.128869i
$855$		0			0
$856$	−2.94192	+	9.05431i	−0.100553	+	0.309470i
$857$	11.4918	−	19.9043i	0.392551	−	0.679919i	−0.600234	−	0.799825i	$-0.704926\pi$
$857$	11.4918	−	19.9043i	0.392551	−	0.679919i	0.992785	+	0.119906i	$0.0382592\pi$
$858$		0			0
$859$	−0.0655414	−	0.113521i	−0.00223624	−	0.00387329i	0.864905	−	0.501935i	$-0.167378\pi$
$859$	−0.0655414	−	0.113521i	−0.00223624	−	0.00387329i	−0.867141	+	0.498062i	$0.834045\pi$
$860$	7.77917	−	1.65351i	0.265267	−	0.0563843i
$861$		0			0
$862$	−3.89262	+	1.73310i	−0.132583	+	0.0590298i
$863$	3.92342	−	1.27480i	0.133555	−	0.0433945i	−0.241477	−	0.970407i	$-0.577632\pi$
$863$	3.92342	−	1.27480i	0.133555	−	0.0433945i	0.375032	+	0.927012i	$0.377632\pi$
$864$		0			0
$865$	−1.58503	+	2.18160i	−0.0538926	+	0.0741767i
$866$	0.362450	+	3.44848i	0.0123166	+	0.117184i
$867$		0			0
$868$	−3.28367	+	1.89583i	−0.111455	+	0.0643487i
$869$	10.8574	+	28.6128i	0.368312	+	0.970623i
$870$		0			0
$871$	2.31325	−	2.08286i	0.0783815	−	0.0705750i
$872$	−1.21593	−	1.67358i	−0.0411765	−	0.0566746i
$873$		0			0
$874$	−1.09976	−	3.38471i	−0.0372000	−	0.114490i
$875$	39.8592	+	8.47234i	1.34749	+	0.286417i
$876$		0			0
$877$	16.9390	−	38.0455i	0.571988	−	1.28471i	−0.363581	−	0.931563i	$-0.618446\pi$
$877$	16.9390	−	38.0455i	0.571988	−	1.28471i	0.935569	−	0.353144i	$-0.114887\pi$
$878$	−0.0417747	−	0.196534i	−0.00140983	−	0.00663271i
$879$		0			0
$880$	22.6320	−	5.97104i	0.762924	−	0.201284i
$881$			2.57715i			0.0868263i	0.999057	+	0.0434131i	$0.0138232\pi$
$881$			2.57715i			0.0868263i	−0.999057	+	0.0434131i	$0.986177\pi$
$882$		0			0
$883$	−10.4533	+	7.59475i	−0.351781	+	0.255584i	−0.749616	−	0.661873i	$-0.769762\pi$
$883$	−10.4533	+	7.59475i	−0.351781	+	0.255584i	0.397835	+	0.917457i	$0.369762\pi$
$884$	−2.24916	−	5.05170i	−0.0756476	−	0.169907i
$885$		0			0
$886$	1.21670	+	1.09552i	0.0408758	+	0.0368047i
$887$	5.37462	−	51.1361i	0.180462	−	1.71698i	−0.411833	−	0.911259i	$-0.635111\pi$
$887$	5.37462	−	51.1361i	0.180462	−	1.71698i	0.592295	−	0.805721i	$-0.298222\pi$
$888$		0			0
$889$	14.5045	+	16.1089i	0.486464	+	0.540274i
$890$	−1.56253			−0.0523762
$891$		0			0
$892$	28.8451			0.965806
$893$	18.0755	+	20.0749i	0.604875	+	0.671781i
$894$		0			0
$895$	3.81347	−	36.2827i	0.127470	−	1.21280i
$896$	−13.4678	−	12.1265i	−0.449927	−	0.405116i
$897$		0			0
$898$	0.232707	+	0.522669i	0.00776554	+	0.0174417i
$899$	−2.89466	+	2.10309i	−0.0965422	+	0.0701420i
$900$		0			0
$901$			61.8075i			2.05911i
$902$	0.250849	+	0.0141138i	0.00835235	+	0.000469938i
$903$		0			0
$904$	1.52230	+	7.16188i	0.0506311	+	0.238201i
$905$	0.899929	−	2.02127i	0.0299146	−	0.0671894i
$906$		0			0
$907$	−16.3205	−	3.46903i	−0.541913	−	0.115187i	−0.0711811	−	0.997463i	$-0.522677\pi$
$907$	−16.3205	−	3.46903i	−0.541913	−	0.115187i	−0.470732	+	0.882276i	$0.656010\pi$
$908$	−8.21216	−	25.2744i	−0.272530	−	0.838761i
$909$		0			0
$910$	0.251022	+	0.345503i	0.00832131	+	0.0114533i
$911$	−31.4901	+	28.3538i	−1.04331	+	0.939403i	−0.998224	−	0.0595801i	$-0.981024\pi$
$911$	−31.4901	+	28.3538i	−1.04331	+	0.939403i	−0.0450890	+	0.998983i	$0.514357\pi$
$912$		0			0
$913$	0.544192	−	0.830970i	0.0180101	−	0.0275011i
$914$	2.12514	−	1.22695i	0.0702933	−	0.0405839i
$915$		0			0
$916$	−3.97028	−	37.7747i	−0.131182	−	1.24811i
$917$	37.7767	−	51.9951i	1.24750	−	1.71703i
$918$		0			0
$919$	19.3770	−	6.29596i	0.639188	−	0.207685i	0.0285469	−	0.999592i	$-0.490912\pi$
$919$	19.3770	−	6.29596i	0.639188	−	0.207685i	0.610641	+	0.791908i	$0.290912\pi$
$920$	−7.55211	+	3.36242i	−0.248986	+	0.110856i
$921$		0			0
$922$	5.79139	−	1.23100i	0.190729	−	0.0405408i
$923$	−0.139934	−	0.242374i	−0.00460600	−	0.00797782i
$924$		0			0
$925$	−8.13039	+	14.0822i	−0.267326	+	0.463022i
$926$	0.989694	−	3.04597i	0.0325234	−	0.100097i
$927$		0			0
$928$	−10.4048	−	7.55950i	−0.341553	−	0.248153i
$929$	−0.734828	+	3.45709i	−0.0241089	+	0.113424i	−0.988557	−	0.150850i	$-0.951799\pi$
$929$	−0.734828	+	3.45709i	−0.0241089	+	0.113424i	0.964448	+	0.264274i	$0.0851322\pi$
$930$		0			0
$931$	−13.2470	−	1.39231i	−0.434152	−	0.0456313i
$932$	3.77214	+	1.67947i	0.123561	+	0.0550127i
$933$		0			0
$934$	3.61886	+	2.08935i	0.118413	+	0.0683655i
$935$	−30.9514	−	31.1904i	−1.01222	−	1.02003i
$936$		0			0
$937$	1.72416	+	0.560214i	0.0563259	+	0.0183014i	0.337044	−	0.941489i	$-0.390573\pi$
$937$	1.72416	+	0.560214i	0.0563259	+	0.0183014i	−0.280719	+	0.959790i	$0.590573\pi$
$938$	−4.64975	+	0.488708i	−0.151820	+	0.0159569i
$939$		0			0
$940$	20.8299	−	23.1339i	0.679396	−	0.754545i
$941$	15.9555	−	17.7204i	0.520134	−	0.577668i	−0.424651	−	0.905357i	$-0.639603\pi$
$941$	15.9555	−	17.7204i	0.520134	−	0.577668i	0.944786	+	0.327689i	$0.106270\pi$
$942$		0			0
$943$	2.74336	−	0.288339i	0.0893361	−	0.00938960i
$944$	−6.76544	−	2.19823i	−0.220196	−	0.0715461i
$945$		0			0
$946$	−1.25708	−	0.204059i	−0.0408710	−	0.00663453i
$947$	−16.6997	−	9.64156i	−0.542666	−	0.313309i	0.203493	−	0.979076i	$-0.434771\pi$
$947$	−16.6997	−	9.64156i	−0.542666	−	0.313309i	−0.746159	+	0.665768i	$0.768104\pi$
$948$		0			0
$949$	−0.775693	−	0.345361i	−0.0251800	−	0.0112109i
$950$	0.872604	+	0.0917144i	0.0283110	+	0.00297561i
$951$		0			0
$952$	−3.48080	+	16.3759i	−0.112813	+	0.530745i
$953$	−13.0109	−	9.45300i	−0.421466	−	0.306213i	0.356762	−	0.934195i	$-0.383881\pi$
$953$	−13.0109	−	9.45300i	−0.421466	−	0.306213i	−0.778227	+	0.627983i	$0.783881\pi$
$954$		0			0
$955$	3.57678	−	11.0082i	0.115742	−	0.356217i
$956$	−6.42156	+	11.1225i	−0.207688	+	0.359727i
$957$		0			0
$958$	0.975881	+	1.69027i	0.0315293	+	0.0546103i
$959$	38.3550	−	8.15260i	1.23855	−	0.263261i
$960$		0			0
$961$	−28.0179	+	12.4744i	−0.903802	+	0.402398i
$962$	−0.675398	+	0.219450i	−0.0217757	+	0.00707536i
$963$		0			0
$964$	27.1499	−	37.3686i	0.874439	−	1.20356i
$965$	−3.74893	−	35.6687i	−0.120682	−	1.14822i
$966$		0			0
$967$	−22.3887	+	12.9261i	−0.719972	+	0.415676i	−0.814742	−	0.579823i	$-0.803122\pi$
$967$	−22.3887	+	12.9261i	−0.719972	+	0.415676i	0.0947706	+	0.995499i	$0.469788\pi$
$968$	−7.62914	−	0.861221i	−0.245210	−	0.0276807i
$969$		0			0
$970$	−3.23059	+	2.90883i	−0.103728	+	0.0933970i
$971$	3.75618	+	5.16993i	0.120541	+	0.165911i	0.865023	−	0.501732i	$-0.167303\pi$
$971$	3.75618	+	5.16993i	0.120541	+	0.165911i	−0.744482	+	0.667643i	$0.767303\pi$
$972$		0			0
$973$	18.8363	+	57.9723i	0.603865	+	1.85851i
$974$	−0.335405	−	0.0712925i	−0.0107471	−	0.00228436i
$975$		0			0
$976$	−16.8843	+	37.9228i	−0.540454	+	1.21388i
$977$	0.167685	+	0.788894i	0.00536471	+	0.0252390i	0.980749	−	0.195275i	$-0.0625599\pi$
$977$	0.167685	+	0.788894i	0.00536471	+	0.0252390i	−0.975384	+	0.220514i	$0.929227\pi$
$978$		0			0
$979$	−14.8523	−	5.76688i	−0.474681	−	0.184310i
$980$			15.3496i			0.490326i
$981$		0			0
$982$	−0.521560	+	0.378936i	−0.0166437	+	0.0120923i
$983$	−3.55683	−	7.98877i	−0.113445	−	0.254802i	0.847896	−	0.530163i	$-0.177869\pi$
$983$	−3.55683	−	7.98877i	−0.113445	−	0.254802i	−0.961341	+	0.275361i	$0.911203\pi$
$984$		0			0
$985$	16.6703	+	15.0100i	0.531160	+	0.478259i
$986$	−0.819253	+	7.79467i	−0.0260903	+	0.248233i
$987$		0			0
$988$	−1.63269	−	1.81328i	−0.0519427	−	0.0576882i
$989$	−13.9823			−0.444612
$990$		0			0
$991$	12.8901			0.409466			0.204733	−	0.978818i	$-0.434367\pi$
$991$	12.8901			0.409466			0.204733	+	0.978818i	$0.434367\pi$
$992$	0.795246	+	0.883210i	0.0252491	+	0.0280420i
$993$		0			0
$994$	−0.0439395	+	0.418056i	−0.00139368	+	0.0132599i
$995$	0.370181	+	0.333313i	0.0117355	+	0.0105667i
$996$		0			0
$997$	1.59169	+	3.57501i	0.0504095	+	0.113222i	0.936994	−	0.349344i	$-0.113596\pi$
$997$	1.59169	+	3.57501i	0.0504095	+	0.113222i	−0.886585	+	0.462566i	$0.846929\pi$
$998$	0.645777	−	0.469185i	0.0204417	−	0.0148518i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.d.431.3		32
3.2	odd	2		891.2.u.b.431.2		32
9.2	odd	6		297.2.k.b.134.4	✓	32
9.4	even	3		891.2.u.b.134.2		32
9.5	odd	6	inner	891.2.u.d.134.3		32
9.7	even	3		297.2.k.b.134.5	yes	32
11.6	odd	10	inner	891.2.u.d.512.3		32
33.17	even	10		891.2.u.b.512.2		32
99.50	even	30	inner	891.2.u.d.215.3		32
99.61	odd	30		297.2.k.b.215.4	yes	32
99.83	even	30		297.2.k.b.215.5	yes	32
99.94	odd	30		891.2.u.b.215.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.b.134.4	✓	32	9.2	odd	6
297.2.k.b.134.5	yes	32	9.7	even	3
297.2.k.b.215.4	yes	32	99.61	odd	30
297.2.k.b.215.5	yes	32	99.83	even	30
891.2.u.b.134.2		32	9.4	even	3
891.2.u.b.215.2		32	99.94	odd	30
891.2.u.b.431.2		32	3.2	odd	2
891.2.u.b.512.2		32	33.17	even	10
891.2.u.d.134.3		32	9.5	odd	6	inner
891.2.u.d.215.3		32	99.50	even	30	inner
891.2.u.d.431.3		32	1.1	even	1	trivial
891.2.u.d.512.3		32	11.6	odd	10	inner

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.117667 + 0.130682i) q^{2} +(0.205825 - 1.95829i) q^{4} +(1.37458 + 1.23768i) q^{5} +(1.36208 + 3.05928i) q^{7} +(0.564664 - 0.410252i) q^{8} +O(q^{10})\)	\(q+(0.117667 + 0.130682i) q^{2} +(0.205825 - 1.95829i) q^{4} +(1.37458 + 1.23768i) q^{5} +(1.36208 + 3.05928i) q^{7} +(0.564664 - 0.410252i) q^{8} +0.325266i q^{10} +(-1.20047 + 3.09174i) q^{11} +(-0.0815164 - 0.383504i) q^{13} +(-0.239522 + 0.537975i) q^{14} +(-3.73204 - 0.793270i) q^{16} +(2.21341 + 6.81217i) q^{17} +(1.85773 + 2.55694i) q^{19} +(2.70665 - 2.43708i) q^{20} +(-0.545291 + 0.206916i) q^{22} +(-5.54549 + 3.20169i) q^{23} +(-0.165018 - 1.57004i) q^{25} +(0.0405254 - 0.0557785i) q^{26} +(6.27130 - 2.03767i) q^{28} +(5.68449 - 2.53090i) q^{29} +(-0.562448 + 0.119552i) q^{31} +(-1.03343 - 1.78996i) q^{32} +(-0.629785 + 1.09082i) q^{34} +(-1.91411 + 5.89103i) q^{35} +(-8.33302 - 6.05429i) q^{37} +(-0.115554 + 0.543639i) q^{38} +(1.28393 + 0.134947i) q^{40} +(-0.393540 - 0.175215i) q^{41} +(1.89104 + 1.09179i) q^{43} +(5.80744 + 2.98722i) q^{44} +(-1.07092 - 0.347964i) q^{46} +(8.50024 - 0.893411i) q^{47} +(-2.82001 + 3.13194i) q^{49} +(0.185759 - 0.206307i) q^{50} +(-0.767791 + 0.0806981i) q^{52} +(8.20670 + 2.66652i) q^{53} +(-5.47672 + 2.76405i) q^{55} +(2.02419 + 1.16867i) q^{56} +(0.999619 + 0.445059i) q^{58} +(1.85422 + 0.194887i) q^{59} +(2.26208 - 10.6422i) q^{61} +(-0.0818047 - 0.0594346i) q^{62} +(-2.24574 + 6.91168i) q^{64} +(0.362604 - 0.628048i) q^{65} +(3.96966 + 6.87565i) q^{67} +(13.7958 - 2.93238i) q^{68} +(-0.995080 + 0.443038i) q^{70} +(0.678883 - 0.220583i) q^{71} +(1.27295 - 1.75207i) q^{73} +(-0.189331 - 1.80137i) q^{74} +(5.38960 - 3.11169i) q^{76} +(-11.0936 + 0.538628i) q^{77} +(6.85723 - 6.17428i) q^{79} +(-4.14817 - 5.70947i) q^{80} +(-0.0234091 - 0.0720457i) q^{82} +(-0.292948 - 0.0622681i) q^{83} +(-5.38876 + 12.1034i) q^{85} +(0.0798347 + 0.375593i) q^{86} +(0.590533 + 2.23829i) q^{88} +4.80386i q^{89} +(1.06221 - 0.771744i) q^{91} +(5.12844 + 11.5187i) q^{92} +(1.11695 + 1.00571i) q^{94} +(-0.611074 + 5.81399i) q^{95} +(8.94292 + 9.93212i) q^{97} -0.741110 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} + 15 q^{5}+O(q^{10}) \) 32 * q + 4 * q^4 + 15 * q^5	\( 32 q + 4 q^{4} + 15 q^{5} + 33 q^{11} - 12 q^{14} - 16 q^{16} - 36 q^{20} + 15 q^{22} + 18 q^{23} - 13 q^{25} - 10 q^{28} + 15 q^{29} + 8 q^{31} - 22 q^{34} + 18 q^{37} - 105 q^{38} - 15 q^{40} - 75 q^{41} + 40 q^{46} + 36 q^{47} + 12 q^{49} + 15 q^{50} + 40 q^{52} - 16 q^{55} + 60 q^{56} + 24 q^{58} - 39 q^{59} + 30 q^{61} + 48 q^{67} + 165 q^{68} + 41 q^{70} - 70 q^{73} - 15 q^{74} - 42 q^{77} + 60 q^{79} - 66 q^{82} - 60 q^{83} - 80 q^{85} + 6 q^{86} - 24 q^{88} - 60 q^{91} + 42 q^{92} - 100 q^{94} - 60 q^{95} - 24 q^{97}+O(q^{100}) \) 32 * q + 4 * q^4 + 15 * q^5 + 33 * q^11 - 12 * q^14 - 16 * q^16 - 36 * q^20 + 15 * q^22 + 18 * q^23 - 13 * q^25 - 10 * q^28 + 15 * q^29 + 8 * q^31 - 22 * q^34 + 18 * q^37 - 105 * q^38 - 15 * q^40 - 75 * q^41 + 40 * q^46 + 36 * q^47 + 12 * q^49 + 15 * q^50 + 40 * q^52 - 16 * q^55 + 60 * q^56 + 24 * q^58 - 39 * q^59 + 30 * q^61 + 48 * q^67 + 165 * q^68 + 41 * q^70 - 70 * q^73 - 15 * q^74 - 42 * q^77 + 60 * q^79 - 66 * q^82 - 60 * q^83 - 80 * q^85 + 6 * q^86 - 24 * q^88 - 60 * q^91 + 42 * q^92 - 100 * q^94 - 60 * q^95 - 24 * q^97

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