LMFDB - Embedded newform 342.2.u.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(55,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("342.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	342.289
Dual form			342.2.u.c.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-1.53209 + 1.28558i) q^{5} +(-2.53209 + 4.38571i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-1.53209 + 1.28558i) q^{5} +(-2.53209 + 4.38571i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.87939 + 0.684040i) q^{10} +(-0.705737 - 1.22237i) q^{11} +(-0.226682 + 1.28558i) q^{13} +(-3.87939 + 3.25519i) q^{14} +(0.173648 + 0.984808i) q^{16} +(2.24510 + 0.817150i) q^{17} +(2.23396 - 3.74292i) q^{19} -2.00000 q^{20} +(-0.245100 - 1.39003i) q^{22} +(2.34730 + 1.96962i) q^{23} +(-0.173648 + 0.984808i) q^{25} +(-0.652704 + 1.13052i) q^{26} +(-4.75877 + 1.73205i) q^{28} +(7.94356 - 2.89122i) q^{29} +(-0.184793 + 0.320070i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.83022 + 1.53574i) q^{34} +(-1.75877 - 9.97448i) q^{35} +4.82295 q^{37} +(3.37939 - 2.75314i) q^{38} +(-1.87939 - 0.684040i) q^{40} +(0.266044 + 1.50881i) q^{41} +(-0.581252 + 0.487728i) q^{43} +(0.245100 - 1.39003i) q^{44} +(1.53209 + 2.65366i) q^{46} +(-9.59627 + 3.49276i) q^{47} +(-9.32295 - 16.1478i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.00000 + 0.839100i) q^{52} +(-1.28312 - 1.07666i) q^{53} +(2.65270 + 0.965505i) q^{55} -5.06418 q^{56} +8.45336 q^{58} +(0.673648 + 0.245188i) q^{59} +(7.47565 + 6.27282i) q^{61} +(-0.283119 + 0.237565i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-1.30541 - 2.26103i) q^{65} +(1.31908 - 0.480105i) q^{67} +(1.19459 + 2.06910i) q^{68} +(1.75877 - 9.97448i) q^{70} +(4.87939 - 4.09429i) q^{71} +(-0.791737 - 4.49016i) q^{73} +(4.53209 + 1.64955i) q^{74} +(4.11721 - 1.43128i) q^{76} +7.14796 q^{77} +(-0.389185 - 2.20718i) q^{79} +(-1.53209 - 1.28558i) q^{80} +(-0.266044 + 1.50881i) q^{82} +(-1.99273 + 3.45150i) q^{83} +(-4.49020 + 1.63430i) q^{85} +(-0.713011 + 0.259515i) q^{86} +(0.705737 - 1.22237i) q^{88} +(1.84864 - 10.4842i) q^{89} +(-5.06418 - 4.24935i) q^{91} +(0.532089 + 3.01763i) q^{92} -10.2121 q^{94} +(1.38919 + 8.60640i) q^{95} +(1.43969 + 0.524005i) q^{97} +(-3.23783 - 18.3626i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 6 * q^7 + 3 * q^8	$ 6 q - 6 q^{7} + 3 q^{8} + 6 q^{11} + 12 q^{13} - 12 q^{14} + 12 q^{17} + 18 q^{19} - 12 q^{20} + 12 q^{23} - 6 q^{26} - 6 q^{28} + 18 q^{29} + 6 q^{31} - 12 q^{34} + 12 q^{35} - 12 q^{37} + 9 q^{38} - 3 q^{41} - 6 q^{43} - 30 q^{47} - 15 q^{49} - 3 q^{50} - 6 q^{52} - 24 q^{53} + 18 q^{55} - 12 q^{56} + 24 q^{58} + 3 q^{59} + 6 q^{61} - 18 q^{62} - 3 q^{64} - 12 q^{65} - 9 q^{67} + 3 q^{68} - 12 q^{70} + 18 q^{71} - 30 q^{73} + 18 q^{74} - 6 q^{76} + 12 q^{77} + 6 q^{79} + 3 q^{82} + 6 q^{83} - 24 q^{85} - 12 q^{86} - 6 q^{88} - 12 q^{91} - 6 q^{92} - 12 q^{94} + 3 q^{97}+O(q^{100}) $ 6 * q - 6 * q^7 + 3 * q^8 + 6 * q^11 + 12 * q^13 - 12 * q^14 + 12 * q^17 + 18 * q^19 - 12 * q^20 + 12 * q^23 - 6 * q^26 - 6 * q^28 + 18 * q^29 + 6 * q^31 - 12 * q^34 + 12 * q^35 - 12 * q^37 + 9 * q^38 - 3 * q^41 - 6 * q^43 - 30 * q^47 - 15 * q^49 - 3 * q^50 - 6 * q^52 - 24 * q^53 + 18 * q^55 - 12 * q^56 + 24 * q^58 + 3 * q^59 + 6 * q^61 - 18 * q^62 - 3 * q^64 - 12 * q^65 - 9 * q^67 + 3 * q^68 - 12 * q^70 + 18 * q^71 - 30 * q^73 + 18 * q^74 - 6 * q^76 + 12 * q^77 + 6 * q^79 + 3 * q^82 + 6 * q^83 - 24 * q^85 - 12 * q^86 - 6 * q^88 - 12 * q^91 - 6 * q^92 - 12 * q^94 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−1.53209	+	1.28558i	−0.685171	+	0.574927i	−0.917512	−	0.397708i	$-0.869806\pi$
$5$	−1.53209	+	1.28558i	−0.685171	+	0.574927i	0.232341	+	0.972634i	$0.425361\pi$
$6$		0			0
$7$	−2.53209	+	4.38571i	−0.957040	+	1.65764i	−0.227410	+	0.973799i	$0.573026\pi$
$7$	−2.53209	+	4.38571i	−0.957040	+	1.65764i	−0.729630	+	0.683842i	$0.760308\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	−1.87939	+	0.684040i	−0.594314	+	0.216313i
$11$	−0.705737	−	1.22237i	−0.212788	−	0.368559i	0.739798	−	0.672829i	$-0.234921\pi$
$11$	−0.705737	−	1.22237i	−0.212788	−	0.368559i	−0.952586	+	0.304270i	$0.901588\pi$
$12$		0			0
$13$	−0.226682	+	1.28558i	−0.0628702	+	0.356554i	0.937102	+	0.349056i	$0.113498\pi$
$13$	−0.226682	+	1.28558i	−0.0628702	+	0.356554i	−0.999972	+	0.00749804i	$0.997613\pi$
$14$	−3.87939	+	3.25519i	−1.03681	+	0.869986i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	2.24510	+	0.817150i	0.544517	+	0.198188i	0.599609	−	0.800293i	$-0.295323\pi$
$17$	2.24510	+	0.817150i	0.544517	+	0.198188i	−0.0550919	+	0.998481i	$0.517545\pi$
$18$		0			0
$19$	2.23396	−	3.74292i	0.512505	−	0.858685i
$19$	2.23396	−	3.74292i	0.512505	−	0.858685i
$20$	−2.00000			−0.447214
$21$		0			0
$22$	−0.245100	−	1.39003i	−0.0522555	−	0.296356i
$23$	2.34730	+	1.96962i	0.489445	+	0.410693i	0.853827	−	0.520556i	$-0.174275\pi$
$23$	2.34730	+	1.96962i	0.489445	+	0.410693i	−0.364382	+	0.931249i	$0.618720\pi$
$24$		0			0
$25$	−0.173648	+	0.984808i	−0.0347296	+	0.196962i
$26$	−0.652704	+	1.13052i	−0.128006	+	0.221712i
$27$		0			0
$28$	−4.75877	+	1.73205i	−0.899323	+	0.327327i
$29$	7.94356	−	2.89122i	1.47508	−	0.536886i	0.525607	−	0.850727i	$-0.323838\pi$
$29$	7.94356	−	2.89122i	1.47508	−	0.536886i	0.949475	+	0.313841i	$0.101616\pi$
$30$		0			0
$31$	−0.184793	+	0.320070i	−0.0331897	+	0.0574863i	−0.882143	−	0.470981i	$-0.843900\pi$
$31$	−0.184793	+	0.320070i	−0.0331897	+	0.0574863i	0.848953	+	0.528468i	$0.177233\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$		0			0
$34$	1.83022	+	1.53574i	0.313881	+	0.263377i
$35$	−1.75877	−	9.97448i	−0.297286	−	1.68600i
$36$		0			0
$37$	4.82295			0.792888			0.396444	−	0.918059i	$-0.370244\pi$
$37$	4.82295			0.792888			0.396444	+	0.918059i	$0.370244\pi$
$38$	3.37939	−	2.75314i	0.548209	−	0.446618i
$39$		0			0
$40$	−1.87939	−	0.684040i	−0.297157	−	0.108156i
$41$	0.266044	+	1.50881i	0.0415492	+	0.235637i	0.998509	−	0.0545825i	$-0.0173828\pi$
$41$	0.266044	+	1.50881i	0.0415492	+	0.235637i	−0.956960	+	0.290220i	$0.906272\pi$
$42$		0			0
$43$	−0.581252	+	0.487728i	−0.0886401	+	0.0743779i	−0.686031	−	0.727572i	$-0.740649\pi$
$43$	−0.581252	+	0.487728i	−0.0886401	+	0.0743779i	0.597391	+	0.801950i	$0.296204\pi$
$44$	0.245100	−	1.39003i	0.0369502	−	0.209555i
$45$		0			0
$46$	1.53209	+	2.65366i	0.225894	+	0.391260i
$47$	−9.59627	+	3.49276i	−1.39976	+	0.509471i	−0.928107	−	0.372314i	$-0.878565\pi$
$47$	−9.59627	+	3.49276i	−1.39976	+	0.509471i	−0.471652	+	0.881785i	$0.656342\pi$
$48$		0			0
$49$	−9.32295	−	16.1478i	−1.33185	−	2.30683i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	−1.00000	+	0.839100i	−0.138675	+	0.116362i
$53$	−1.28312	−	1.07666i	−0.176250	−	0.147891i	0.550395	−	0.834904i	$-0.314477\pi$
$53$	−1.28312	−	1.07666i	−0.176250	−	0.147891i	−0.726645	+	0.687013i	$0.758922\pi$
$54$		0			0
$55$	2.65270	+	0.965505i	0.357690	+	0.130189i
$56$	−5.06418			−0.676729
$57$		0			0
$58$	8.45336			1.10998
$59$	0.673648	+	0.245188i	0.0877015	+	0.0319207i	0.385498	−	0.922709i	$-0.374030\pi$
$59$	0.673648	+	0.245188i	0.0877015	+	0.0319207i	−0.297797	+	0.954629i	$0.596252\pi$
$60$		0			0
$61$	7.47565	+	6.27282i	0.957159	+	0.803152i	0.980489	−	0.196576i	$-0.0629822\pi$
$61$	7.47565	+	6.27282i	0.957159	+	0.803152i	−0.0233295	+	0.999728i	$0.507427\pi$
$62$	−0.283119	+	0.237565i	−0.0359561	+	0.0301707i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.30541	−	2.26103i	−0.161916	−	0.280446i
$66$		0			0
$67$	1.31908	−	0.480105i	0.161151	−	0.0586542i	−0.260185	−	0.965559i	$-0.583784\pi$
$67$	1.31908	−	0.480105i	0.161151	−	0.0586542i	0.421336	+	0.906905i	$0.361561\pi$
$68$	1.19459	+	2.06910i	0.144866	+	0.250915i
$69$		0			0
$70$	1.75877	−	9.97448i	0.210213	−	1.19218i
$71$	4.87939	−	4.09429i	0.579076	−	0.485903i	−0.305567	−	0.952171i	$-0.598846\pi$
$71$	4.87939	−	4.09429i	0.579076	−	0.485903i	0.884644	+	0.466268i	$0.154402\pi$
$72$		0			0
$73$	−0.791737	−	4.49016i	−0.0926658	−	0.525534i	−0.995438	−	0.0954141i	$-0.969582\pi$
$73$	−0.791737	−	4.49016i	−0.0926658	−	0.525534i	0.902772	−	0.430120i	$-0.141529\pi$
$74$	4.53209	+	1.64955i	0.526845	+	0.191756i
$75$		0			0
$76$	4.11721	−	1.43128i	0.472277	−	0.164179i
$77$	7.14796			0.814585
$78$		0			0
$79$	−0.389185	−	2.20718i	−0.0437868	−	0.248327i	0.955056	−	0.296426i	$-0.0957948\pi$
$79$	−0.389185	−	2.20718i	−0.0437868	−	0.248327i	−0.998843	+	0.0480989i	$0.984684\pi$
$80$	−1.53209	−	1.28558i	−0.171293	−	0.143732i
$81$		0			0
$82$	−0.266044	+	1.50881i	−0.0293797	+	0.166621i
$83$	−1.99273	+	3.45150i	−0.218730	+	0.378852i	−0.954420	−	0.298467i	$-0.903525\pi$
$83$	−1.99273	+	3.45150i	−0.218730	+	0.378852i	0.735690	+	0.677319i	$0.236858\pi$
$84$		0			0
$85$	−4.49020	+	1.63430i	−0.487031	+	0.177265i
$86$	−0.713011	+	0.259515i	−0.0768860	+	0.0279842i
$87$		0			0
$88$	0.705737	−	1.22237i	0.0752318	−	0.130305i
$89$	1.84864	−	10.4842i	0.195956	−	1.11132i	−0.715096	−	0.699026i	$-0.753617\pi$
$89$	1.84864	−	10.4842i	0.195956	−	1.11132i	0.911051	−	0.412293i	$-0.135272\pi$
$90$		0			0
$91$	−5.06418	−	4.24935i	−0.530870	−	0.445453i
$92$	0.532089	+	3.01763i	0.0554741	+	0.314609i
$93$		0			0
$94$	−10.2121			−1.05330
$95$	1.38919	+	8.60640i	0.142527	+	0.882998i
$96$		0			0
$97$	1.43969	+	0.524005i	0.146179	+	0.0532047i	0.414073	−	0.910244i	$-0.364106\pi$
$97$	1.43969	+	0.524005i	0.146179	+	0.0532047i	−0.267895	+	0.963448i	$0.586328\pi$
$98$	−3.23783	−	18.3626i	−0.327070	−	1.85491i
$99$		0			0
$100$	−0.766044	+	0.642788i	−0.0766044	+	0.0642788i
$101$	−1.53209	+	8.68891i	−0.152449	+	0.864579i	0.808633	+	0.588314i	$0.200208\pi$
$101$	−1.53209	+	8.68891i	−0.152449	+	0.864579i	−0.961081	+	0.276265i	$0.910903\pi$
$102$		0			0
$103$	3.57398	+	6.19031i	0.352155	+	0.609950i	0.986627	−	0.162996i	$-0.0521158\pi$
$103$	3.57398	+	6.19031i	0.352155	+	0.609950i	−0.634472	+	0.772946i	$0.718782\pi$
$104$	−1.22668	+	0.446476i	−0.120286	+	0.0437805i
$105$		0			0
$106$	−0.837496	−	1.45059i	−0.0813448	−	0.140893i
$107$	−4.68479	+	8.11430i	−0.452896	+	0.784439i	−0.998565	−	0.0535622i	$-0.982942\pi$
$107$	−4.68479	+	8.11430i	−0.452896	+	0.784439i	0.545669	+	0.838001i	$0.316276\pi$
$108$		0			0
$109$	8.47565	−	7.11192i	0.811820	−	0.681198i	−0.139221	−	0.990261i	$-0.544460\pi$
$109$	8.47565	−	7.11192i	0.811820	−	0.681198i	0.951041	+	0.309063i	$0.100015\pi$
$110$	2.16250	+	1.81456i	0.206187	+	0.173011i
$111$		0			0
$112$	−4.75877	−	1.73205i	−0.449662	−	0.163663i
$113$	13.2986			1.25103			0.625514	−	0.780213i	$-0.284890\pi$
$113$	13.2986			1.25103			0.625514	+	0.780213i	$0.284890\pi$
$114$		0			0
$115$	−6.12836			−0.571472
$116$	7.94356	+	2.89122i	0.737541	+	0.268443i
$117$		0			0
$118$	0.549163	+	0.460802i	0.0505546	+	0.0424203i
$119$	−9.26857	+	7.77725i	−0.849648	+	0.712940i
$120$		0			0
$121$	4.50387	−	7.80093i	0.409443	−	0.709176i
$122$	4.87939	+	8.45134i	0.441759	+	0.765149i
$123$		0			0
$124$	−0.347296	+	0.126406i	−0.0311881	+	0.0113516i
$125$	−6.00000	−	10.3923i	−0.536656	−	0.929516i
$126$		0			0
$127$	−0.992259	+	5.62738i	−0.0880488	+	0.499349i	0.908608	+	0.417650i	$0.137146\pi$
$127$	−0.992259	+	5.62738i	−0.0880488	+	0.499349i	−0.996657	+	0.0816999i	$0.973965\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$		0			0
$130$	−0.453363	−	2.57115i	−0.0397626	−	0.225505i
$131$	−9.28359	−	3.37895i	−0.811111	−	0.295220i	−0.0970281	−	0.995282i	$-0.530934\pi$
$131$	−9.28359	−	3.37895i	−0.811111	−	0.295220i	−0.714083	+	0.700062i	$0.753156\pi$
$132$		0			0
$133$	10.7588	+	19.2749i	0.932904	+	1.67134i
$134$	1.40373			0.121264
$135$		0			0
$136$	0.414878	+	2.35289i	0.0355755	+	0.201759i
$137$	−4.13429	−	3.46908i	−0.353216	−	0.296383i	0.448864	−	0.893600i	$-0.351829\pi$
$137$	−4.13429	−	3.46908i	−0.353216	−	0.296383i	−0.802080	+	0.597217i	$0.796273\pi$
$138$		0			0
$139$	−0.406260	+	2.30401i	−0.0344585	+	0.195424i	−0.997178	−	0.0750794i	$-0.976079\pi$
$139$	−0.406260	+	2.30401i	−0.0344585	+	0.195424i	0.962719	+	0.270503i	$0.0871901\pi$
$140$	5.06418	−	8.77141i	0.428001	−	0.741320i
$141$		0			0
$142$	5.98545	−	2.17853i	0.502288	−	0.182818i
$143$	1.73143	−	0.630189i	0.144789	−	0.0526990i
$144$		0			0
$145$	−8.45336	+	14.6417i	−0.702014	+	1.21592i
$146$	0.791737	−	4.49016i	0.0655246	−	0.371608i
$147$		0			0
$148$	3.69459	+	3.10013i	0.303694	+	0.254829i
$149$	2.49525	+	14.1513i	0.204419	+	1.15932i	0.898351	+	0.439278i	$0.144766\pi$
$149$	2.49525	+	14.1513i	0.204419	+	1.15932i	−0.693932	+	0.720040i	$0.744123\pi$
$150$		0			0
$151$	−20.8384			−1.69581			−0.847904	−	0.530150i	$-0.822135\pi$
$151$	−20.8384			−1.69581			−0.847904	+	0.530150i	$0.822135\pi$
$152$	4.35844	+	0.0632028i	0.353516	+	0.00512642i
$153$		0			0
$154$	6.71688	+	2.44474i	0.541262	+	0.197003i
$155$	−0.128356	−	0.727940i	−0.0103098	−	0.0584696i
$156$		0			0
$157$	4.87939	−	4.09429i	0.389417	−	0.326760i	−0.426969	−	0.904266i	$-0.640419\pi$
$157$	4.87939	−	4.09429i	0.389417	−	0.326760i	0.816386	+	0.577506i	$0.195974\pi$
$158$	0.389185	−	2.20718i	0.0309619	−	0.175594i
$159$		0			0
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	−14.5817	+	5.30731i	−1.14920	+	0.418275i
$162$		0			0
$163$	−2.36571	−	4.09754i	−0.185297	−	0.320944i	0.758380	−	0.651813i	$-0.225991\pi$
$163$	−2.36571	−	4.09754i	−0.185297	−	0.320944i	−0.943677	+	0.330869i	$0.892658\pi$
$164$	−0.766044	+	1.32683i	−0.0598180	+	0.103608i
$165$		0			0
$166$	−3.05303	+	2.56180i	−0.236961	+	0.198834i
$167$	−13.2344	−	11.1050i	−1.02411	−	0.859331i	−0.0339719	−	0.999423i	$-0.510816\pi$
$167$	−13.2344	−	11.1050i	−1.02411	−	0.859331i	−0.990138	+	0.140092i	$0.955260\pi$
$168$		0			0
$169$	10.6147	+	3.86343i	0.816514	+	0.297187i
$170$	−4.77837			−0.366484
$171$		0			0
$172$	−0.758770			−0.0578557
$173$	17.6878	+	6.43783i	1.34478	+	0.489459i	0.911314	−	0.411712i	$-0.135069\pi$
$173$	17.6878	+	6.43783i	1.34478	+	0.489459i	0.433463	+	0.901171i	$0.357291\pi$
$174$		0			0
$175$	−3.87939	−	3.25519i	−0.293254	−	0.246069i
$176$	1.08125	−	0.907278i	0.0815024	−	0.0683887i
$177$		0			0
$178$	5.32295	−	9.21962i	0.398972	−	0.691039i
$179$	−6.91400	−	11.9754i	−0.516777	−	0.895083i	−0.999810	−	0.0194816i	$-0.993798\pi$
$179$	−6.91400	−	11.9754i	−0.516777	−	0.895083i	0.483034	−	0.875602i	$-0.339535\pi$
$180$		0			0
$181$	−11.5175	+	4.19204i	−0.856092	+	0.311592i	−0.732522	−	0.680744i	$-0.761657\pi$
$181$	−11.5175	+	4.19204i	−0.856092	+	0.311592i	−0.123570	+	0.992336i	$0.539434\pi$
$182$	−3.30541	−	5.72513i	−0.245013	−	0.424375i
$183$		0			0
$184$	−0.532089	+	3.01763i	−0.0392261	+	0.222462i
$185$	−7.38919	+	6.20026i	−0.543264	+	0.455852i
$186$		0			0
$187$	−0.585589	−	3.32104i	−0.0428225	−	0.242859i
$188$	−9.59627	−	3.49276i	−0.699880	−	0.254735i
$189$		0			0
$190$	−1.63816	+	8.56250i	−0.118844	+	0.621189i
$191$	20.0993			1.45433			0.727166	−	0.686462i	$-0.240837\pi$
$191$	20.0993			1.45433			0.727166	+	0.686462i	$0.240837\pi$
$192$		0			0
$193$	2.89734	+	16.4316i	0.208555	+	1.18277i	0.891747	+	0.452535i	$0.149480\pi$
$193$	2.89734	+	16.4316i	0.208555	+	1.18277i	−0.683192	+	0.730239i	$0.739409\pi$
$194$	1.17365	+	0.984808i	0.0842630	+	0.0707051i
$195$		0			0
$196$	3.23783	−	18.3626i	0.231273	−	1.31162i
$197$	6.49525	−	11.2501i	0.462768	−	0.801537i	−0.536330	−	0.844008i	$-0.680190\pi$
$197$	6.49525	−	11.2501i	0.462768	−	0.801537i	0.999098	+	0.0424714i	$0.0135231\pi$
$198$		0			0
$199$	−16.1557	+	5.88019i	−1.14525	+	0.416836i	−0.843806	−	0.536649i	$-0.819690\pi$
$199$	−16.1557	+	5.88019i	−1.14525	+	0.416836i	−0.301441	+	0.953485i	$0.597468\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$		0			0
$202$	−4.41147	+	7.64090i	−0.310390	+	0.537612i
$203$	−7.43376	+	42.1590i	−0.521748	+	2.95898i
$204$		0			0
$205$	−2.34730	−	1.96962i	−0.163942	−	0.137564i
$206$	1.24123	+	7.03936i	0.0864806	+	0.490456i
$207$		0			0
$208$	−1.30541			−0.0905137
$209$	−6.15183	−	0.0892091i	−0.425531	−	0.00617072i
$210$		0			0
$211$	15.1373	+	5.50952i	1.04209	+	0.379291i	0.805673	−	0.592360i	$-0.201804\pi$
$211$	15.1373	+	5.50952i	1.04209	+	0.379291i	0.236420	+	0.971651i	$0.424026\pi$
$212$	−0.290859	−	1.64955i	−0.0199763	−	0.113291i
$213$		0			0
$214$	−7.17752	+	6.02265i	−0.490645	+	0.411700i
$215$	0.263518	−	1.49449i	0.0179718	−	0.101923i
$216$		0			0
$217$	−0.935822	−	1.62089i	−0.0635278	−	0.110033i
$218$	10.3969	−	3.78417i	0.704169	−	0.256296i
$219$		0			0
$220$	1.41147	+	2.44474i	0.0951616	+	0.164825i
$221$	−1.55943	+	2.70101i	−0.104899	+	0.181690i
$222$		0			0
$223$	3.12836	−	2.62500i	0.209490	−	0.175783i	−0.532005	−	0.846741i	$-0.678561\pi$
$223$	3.12836	−	2.62500i	0.209490	−	0.175783i	0.741495	+	0.670958i	$0.234117\pi$
$224$	−3.87939	−	3.25519i	−0.259202	−	0.217497i
$225$		0			0
$226$	12.4966	+	4.54839i	0.831261	+	0.302554i
$227$	−13.6604			−0.906676			−0.453338	−	0.891339i	$-0.649767\pi$
$227$	−13.6604			−0.906676			−0.453338	+	0.891339i	$0.649767\pi$
$228$		0			0
$229$	−5.22163			−0.345055			−0.172527	−	0.985005i	$-0.555193\pi$
$229$	−5.22163			−0.345055			−0.172527	+	0.985005i	$0.555193\pi$
$230$	−5.75877	−	2.09602i	−0.379722	−	0.138208i
$231$		0			0
$232$	6.47565	+	5.43372i	0.425147	+	0.356741i
$233$	20.7160	−	17.3828i	1.35715	−	1.13878i	0.380300	−	0.924863i	$-0.375821\pi$
$233$	20.7160	−	17.3828i	1.35715	−	1.13878i	0.976851	−	0.213921i	$-0.0686236\pi$
$234$		0			0
$235$	10.2121	−	17.6879i	0.666166	−	1.15383i
$236$	0.358441	+	0.620838i	0.0233325	+	0.0404131i
$237$		0			0
$238$	−11.3696	+	4.13819i	−0.736981	+	0.268239i
$239$	−0.142903	−	0.247516i	−0.00924366	−	0.0160105i	0.861367	−	0.507984i	$-0.169609\pi$
$239$	−0.142903	−	0.247516i	−0.00924366	−	0.0160105i	−0.870610	+	0.491973i	$0.836276\pi$
$240$		0			0
$241$	0.538485	−	3.05390i	0.0346869	−	0.196719i	−0.962540	−	0.271139i	$-0.912600\pi$
$241$	0.538485	−	3.05390i	0.0346869	−	0.196719i	0.997227	+	0.0744203i	$0.0237106\pi$
$242$	6.90033	−	5.79006i	0.443570	−	0.372199i
$243$		0			0
$244$	1.69459	+	9.61051i	0.108485	+	0.615250i
$245$	35.0428	+	12.7545i	2.23880	+	0.814858i
$246$		0			0
$247$	4.30541	+	3.72037i	0.273947	+	0.236721i
$248$	−0.369585			−0.0234687
$249$		0			0
$250$	−2.08378	−	11.8177i	−0.131790	−	0.747417i
$251$	9.69640	+	8.13625i	0.612032	+	0.513555i	0.895287	−	0.445489i	$-0.146970\pi$
$251$	9.69640	+	8.13625i	0.612032	+	0.513555i	−0.283256	+	0.959044i	$0.591415\pi$
$252$		0			0
$253$	0.751030	−	4.25930i	0.0472168	−	0.267780i
$254$	−2.85710	+	4.94864i	−0.179270	+	0.310505i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−28.5599	+	10.3950i	−1.78152	+	0.648419i	−0.781828	+	0.623494i	$0.785713\pi$
$257$	−28.5599	+	10.3950i	−1.78152	+	0.648419i	−0.999689	+	0.0249253i	$0.992065\pi$
$258$		0			0
$259$	−12.2121	+	21.1520i	−0.758825	+	1.31432i
$260$	0.453363	−	2.57115i	0.0281164	−	0.159456i
$261$		0			0
$262$	−7.56805	−	6.35035i	−0.467556	−	0.392326i
$263$	−3.80335	−	21.5699i	−0.234524	−	1.33005i	−0.843613	−	0.536952i	$-0.819576\pi$
$263$	−3.80335	−	21.5699i	−0.234524	−	1.33005i	0.609088	−	0.793102i	$-0.291535\pi$
$264$		0			0
$265$	3.34998			0.205788
$266$	3.51754	+	21.7922i	0.215674	+	1.33616i
$267$		0			0
$268$	1.31908	+	0.480105i	0.0805755	+	0.0293271i
$269$	0.248970	+	1.41198i	0.0151800	+	0.0860900i	0.991457	−	0.130437i	$-0.0416381\pi$
$269$	0.248970	+	1.41198i	0.0151800	+	0.0860900i	−0.976277	+	0.216527i	$0.930527\pi$
$270$		0			0
$271$	12.3892	−	10.3958i	0.752589	−	0.631498i	−0.183597	−	0.983002i	$-0.558774\pi$
$271$	12.3892	−	10.3958i	0.752589	−	0.631498i	0.936186	+	0.351504i	$0.114330\pi$
$272$	−0.414878	+	2.35289i	−0.0251557	+	0.142665i
$273$		0			0
$274$	−2.69846	−	4.67388i	−0.163020	−	0.282359i
$275$	1.32635	−	0.482753i	0.0799820	−	0.0291111i
$276$		0			0
$277$	−5.55438	−	9.62046i	−0.333730	−	0.578038i	0.649510	−	0.760353i	$-0.274974\pi$
$277$	−5.55438	−	9.62046i	−0.333730	−	0.578038i	−0.983240	+	0.182315i	$0.941641\pi$
$278$	−1.16978	+	2.02611i	−0.0701586	+	0.121518i
$279$		0			0
$280$	7.75877	−	6.51038i	0.463675	−	0.389070i
$281$	−3.25490	−	2.73119i	−0.194171	−	0.162929i	0.540519	−	0.841332i	$-0.318228\pi$
$281$	−3.25490	−	2.73119i	−0.194171	−	0.162929i	−0.734690	+	0.678403i	$0.762672\pi$
$282$		0			0
$283$	5.12701	+	1.86608i	0.304769	+	0.110927i	0.489878	−	0.871791i	$-0.337041\pi$
$283$	5.12701	+	1.86608i	0.304769	+	0.110927i	−0.185108	+	0.982718i	$0.559264\pi$
$284$	6.36959			0.377965
$285$		0			0
$286$	1.84255			0.108952
$287$	−7.29086	−	2.65366i	−0.430366	−	0.156640i
$288$		0			0
$289$	−8.65002	−	7.25822i	−0.508824	−	0.426954i
$290$	−12.9513	+	10.8674i	−0.760527	+	0.638158i
$291$		0			0
$292$	2.27972	−	3.94858i	0.133410	−	0.231073i
$293$	8.90673	+	15.4269i	0.520337	+	0.901249i	0.999720	+	0.0236440i	$0.00752682\pi$
$293$	8.90673	+	15.4269i	0.520337	+	0.901249i	−0.479384	+	0.877605i	$0.659140\pi$
$294$		0			0
$295$	−1.34730	+	0.490376i	−0.0784426	+	0.0285508i
$296$	2.41147	+	4.17680i	0.140164	+	0.242771i
$297$		0			0
$298$	−2.49525	+	14.1513i	−0.144546	+	0.819762i
$299$	−3.06418	+	2.57115i	−0.177206	+	0.148693i
$300$		0			0
$301$	−0.667252	−	3.78417i	−0.0384597	−	0.218116i
$302$	−19.5817	−	7.12716i	−1.12680	−	0.410122i
$303$		0			0
$304$	4.07398	+	1.55007i	0.233659	+	0.0889024i
$305$	−19.5175			−1.11757
$306$		0			0
$307$	−4.97653	−	28.2233i	−0.284026	−	1.61079i	−0.708746	−	0.705464i	$-0.750739\pi$
$307$	−4.97653	−	28.2233i	−0.284026	−	1.61079i	0.424720	−	0.905325i	$-0.360373\pi$
$308$	5.47565	+	4.59462i	0.312004	+	0.261803i
$309$		0			0
$310$	0.128356	−	0.727940i	0.00729011	−	0.0413442i
$311$	7.90673	−	13.6949i	0.448349	−	0.776564i	−0.549929	−	0.835211i	$-0.685345\pi$
$311$	7.90673	−	13.6949i	0.448349	−	0.776564i	0.998279	+	0.0586473i	$0.0186787\pi$
$312$		0			0
$313$	−12.3478	+	4.49422i	−0.697937	+	0.254028i	−0.666530	−	0.745478i	$-0.732221\pi$
$313$	−12.3478	+	4.49422i	−0.697937	+	0.254028i	−0.0314071	+	0.999507i	$0.509999\pi$
$314$	5.98545	−	2.17853i	0.337779	−	0.122941i
$315$		0			0
$316$	1.12061	−	1.94096i	0.0630395	−	0.109188i
$317$	3.71688	−	21.0795i	0.208761	−	1.18394i	−0.682650	−	0.730746i	$-0.739173\pi$
$317$	3.71688	−	21.0795i	0.208761	−	1.18394i	0.891411	−	0.453196i	$-0.149716\pi$
$318$		0			0
$319$	−9.14022	−	7.66955i	−0.511754	−	0.429412i
$320$	−0.347296	−	1.96962i	−0.0194145	−	0.110105i
$321$		0			0
$322$	−15.5175			−0.864759
$323$	8.07398	−	6.57775i	0.449248	−	0.365996i
$324$		0			0
$325$	−1.22668	−	0.446476i	−0.0680441	−	0.0247660i
$326$	−0.821604	−	4.65955i	−0.0455044	−	0.258069i
$327$		0			0
$328$	−1.17365	+	0.984808i	−0.0648039	+	0.0543769i
$329$	8.98040	−	50.9304i	0.495105	−	2.80788i
$330$		0			0
$331$	12.6989	+	21.9952i	0.697996	+	1.20897i	0.969160	+	0.246432i	$0.0792582\pi$
$331$	12.6989	+	21.9952i	0.697996	+	1.20897i	−0.271164	+	0.962533i	$0.587409\pi$
$332$	−3.74510	+	1.36310i	−0.205539	+	0.0748101i
$333$		0			0
$334$	−8.63816	−	14.9617i	−0.472659	−	0.818669i
$335$	−1.40373	+	2.43134i	−0.0766941	+	0.132838i
$336$		0			0
$337$	20.2062	−	16.9550i	1.10070	−	0.923599i	0.103230	−	0.994658i	$-0.467082\pi$
$337$	20.2062	−	16.9550i	1.10070	−	0.923599i	0.997472	+	0.0710588i	$0.0226378\pi$
$338$	8.65317	+	7.26087i	0.470670	+	0.394939i
$339$		0			0
$340$	−4.49020	−	1.63430i	−0.243515	−	0.0886323i
$341$	0.521660			0.0282495
$342$		0			0
$343$	58.9769			3.18445
$344$	−0.713011	−	0.259515i	−0.0384430	−	0.0139921i
$345$		0			0
$346$	14.4192	+	12.0992i	0.775182	+	0.650455i
$347$	19.6348	−	16.4755i	1.05405	−	0.884452i	0.0605352	−	0.998166i	$-0.480719\pi$
$347$	19.6348	−	16.4755i	1.05405	−	0.884452i	0.993514	+	0.113714i	$0.0362748\pi$
$348$		0			0
$349$	2.92127	−	5.05980i	0.156372	−	0.270845i	−0.777186	−	0.629271i	$-0.783353\pi$
$349$	2.92127	−	5.05980i	0.156372	−	0.270845i	0.933558	+	0.358427i	$0.116687\pi$
$350$	−2.53209	−	4.38571i	−0.135346	−	0.234426i
$351$		0			0
$352$	1.32635	−	0.482753i	0.0706948	−	0.0257308i
$353$	−11.2049	−	19.4074i	−0.596375	−	1.03295i	−0.993351	−	0.115122i	$-0.963274\pi$
$353$	−11.2049	−	19.4074i	−0.596375	−	1.03295i	0.396977	−	0.917829i	$-0.370059\pi$
$354$		0			0
$355$	−2.21213	+	12.5456i	−0.117408	+	0.665853i
$356$	8.15523	−	6.84305i	0.432226	−	0.362681i
$357$		0			0
$358$	−2.40121	−	13.6179i	−0.126908	−	0.719730i
$359$	9.03684	+	3.28914i	0.476946	+	0.173594i	0.569296	−	0.822132i	$-0.307216\pi$
$359$	9.03684	+	3.28914i	0.476946	+	0.173594i	−0.0923503	+	0.995727i	$0.529438\pi$
$360$		0			0
$361$	−9.01889	−	16.7230i	−0.474678	−	0.880159i
$362$	−12.2567			−0.644198
$363$		0			0
$364$	−1.14796	−	6.51038i	−0.0601692	−	0.341237i
$365$	6.98545	+	5.86149i	0.365635	+	0.306804i
$366$		0			0
$367$	4.05644	−	23.0052i	0.211744	−	1.20086i	−0.674723	−	0.738071i	$-0.735737\pi$
$367$	4.05644	−	23.0052i	0.211744	−	1.20086i	0.886468	−	0.462791i	$-0.153152\pi$
$368$	−1.53209	+	2.65366i	−0.0798657	+	0.138331i
$369$		0			0
$370$	−9.06418	+	3.29909i	−0.471224	+	0.171512i
$371$	7.97090	−	2.90117i	0.413829	−	0.150621i
$372$		0			0
$373$	12.9709	−	22.4663i	0.671608	−	1.16326i	−0.305840	−	0.952083i	$-0.598937\pi$
$373$	12.9709	−	22.4663i	0.671608	−	1.16326i	0.977448	−	0.211176i	$-0.0677294\pi$
$374$	0.585589	−	3.32104i	0.0302801	−	0.171727i
$375$		0			0
$376$	−7.82295	−	6.56423i	−0.403438	−	0.338524i
$377$	1.91622	+	10.8674i	0.0986904	+	0.559701i
$378$		0			0
$379$	9.47834			0.486870			0.243435	−	0.969917i	$-0.421726\pi$
$379$	9.47834			0.486870			0.243435	+	0.969917i	$0.421726\pi$
$380$	−4.46791	+	7.48584i	−0.229199	+	0.384015i
$381$		0			0
$382$	18.8871	+	6.87435i	0.966349	+	0.351722i
$383$	2.34224	+	13.2835i	0.119683	+	0.678756i	0.984324	+	0.176367i	$0.0564345\pi$
$383$	2.34224	+	13.2835i	0.119683	+	0.678756i	−0.864641	+	0.502390i	$0.832454\pi$
$384$		0			0
$385$	−10.9513	+	9.18923i	−0.558130	+	0.468327i
$386$	−2.89734	+	16.4316i	−0.147471	+	0.836347i
$387$		0			0
$388$	0.766044	+	1.32683i	0.0388900	+	0.0673595i
$389$	−23.6313	+	8.60111i	−1.19816	+	0.436093i	−0.862581	−	0.505920i	$-0.831153\pi$
$389$	−23.6313	+	8.60111i	−1.19816	+	0.436093i	−0.335576	+	0.942013i	$0.608931\pi$
$390$		0			0
$391$	3.66044	+	6.34008i	0.185117	+	0.320631i
$392$	9.32295	−	16.1478i	0.470880	−	0.815588i
$393$		0			0
$394$	9.95130	−	8.35014i	0.501339	−	0.420674i
$395$	3.43376	+	2.88127i	0.172771	+	0.144972i
$396$		0			0
$397$	−6.17024	−	2.24579i	−0.309676	−	0.112713i	0.182507	−	0.983205i	$-0.441579\pi$
$397$	−6.17024	−	2.24579i	−0.309676	−	0.112713i	−0.492183	+	0.870492i	$0.663801\pi$
$398$	−17.1925			−0.861784
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−27.7310	−	10.0933i	−1.38482	−	0.504034i	−0.461185	−	0.887304i	$-0.652575\pi$
$401$	−27.7310	−	10.0933i	−1.38482	−	0.504034i	−0.923636	+	0.383270i	$0.874798\pi$
$402$		0			0
$403$	−0.369585	−	0.310119i	−0.0184103	−	0.0154481i
$404$	−6.75877	+	5.67128i	−0.336261	+	0.282157i
$405$		0			0
$406$	−21.4047	+	37.0740i	−1.06230	+	1.83995i
$407$	−3.40373	−	5.89544i	−0.168717	−	0.292226i
$408$		0			0
$409$	−19.8567	+	7.22724i	−0.981850	+	0.357364i	−0.782559	−	0.622576i	$-0.786086\pi$
$409$	−19.8567	+	7.22724i	−0.981850	+	0.357364i	−0.199291	+	0.979940i	$0.563864\pi$
$410$	−1.53209	−	2.65366i	−0.0756645	−	0.131055i
$411$		0			0
$412$	−1.24123	+	7.03936i	−0.0611510	+	0.346804i
$413$	−2.78106	+	2.33359i	−0.136847	+	0.114828i
$414$		0			0
$415$	−1.38413	−	7.84981i	−0.0679444	−	0.385332i
$416$	−1.22668	−	0.446476i	−0.0601430	−	0.0218903i
$417$		0			0
$418$	−5.75031	−	2.18788i	−0.281257	−	0.107013i
$419$	27.8830			1.36217			0.681087	−	0.732202i	$-0.261508\pi$
$419$	27.8830			1.36217			0.681087	+	0.732202i	$0.261508\pi$
$420$		0			0
$421$	−0.00774079	−	0.0439002i	−0.000377263	−	0.00213956i	0.984619	−	0.174718i	$-0.0559013\pi$
$421$	−0.00774079	−	0.0439002i	−0.000377263	−	0.00213956i	−0.984996	+	0.172578i	$0.944790\pi$
$422$	12.3400	+	10.3545i	0.600703	+	0.504050i
$423$		0			0
$424$	0.290859	−	1.64955i	0.0141254	−	0.0801090i
$425$	−1.19459	+	2.06910i	−0.0579463	+	0.100366i
$426$		0			0
$427$	−46.4397	+	16.9027i	−2.24738	+	0.817978i
$428$	−8.80453	+	3.20459i	−0.425583	+	0.154900i
$429$		0			0
$430$	0.758770	−	1.31423i	0.0365912	−	0.0633778i
$431$	2.04694	−	11.6088i	0.0985977	−	0.559175i	−0.894988	−	0.446091i	$-0.852816\pi$
$431$	2.04694	−	11.6088i	0.0985977	−	0.559175i	0.993585	−	0.113084i	$-0.0360731\pi$
$432$		0			0
$433$	21.1780	+	17.7704i	1.01775	+	0.853993i	0.989343	−	0.145604i	$-0.0465124\pi$
$433$	21.1780	+	17.7704i	1.01775	+	0.853993i	0.0284060	+	0.999596i	$0.490957\pi$
$434$	−0.325008	−	1.84321i	−0.0156009	−	0.0884769i
$435$		0			0
$436$	11.0642			0.529878
$437$	12.6159	−	4.38571i	0.603499	−	0.209797i
$438$		0			0
$439$	−35.1908	−	12.8084i	−1.67956	−	0.611311i	−0.686314	−	0.727305i	$-0.740773\pi$
$439$	−35.1908	−	12.8084i	−1.67956	−	0.611311i	−0.993250	+	0.115994i	$0.962995\pi$
$440$	0.490200	+	2.78006i	0.0233694	+	0.132534i
$441$		0			0
$442$	−2.38919	+	2.00476i	−0.113642	+	0.0953569i
$443$	−3.64455	+	20.6693i	−0.173158	+	0.982027i	0.767091	+	0.641539i	$0.221704\pi$
$443$	−3.64455	+	20.6693i	−0.173158	+	0.982027i	−0.940249	+	0.340489i	$0.889408\pi$
$444$		0			0
$445$	10.6459	+	18.4392i	0.504664	+	0.874104i
$446$	3.83750	−	1.39673i	0.181711	−	0.0661373i
$447$		0			0
$448$	−2.53209	−	4.38571i	−0.119630	−	0.207205i
$449$	−10.9474	+	18.9615i	−0.516641	+	0.894849i	0.483172	+	0.875525i	$0.339485\pi$
$449$	−10.9474	+	18.9615i	−0.516641	+	0.894849i	−0.999813	+	0.0193235i	$0.993849\pi$
$450$		0			0
$451$	1.65657	−	1.39003i	0.0780050	−	0.0654540i
$452$	10.1873	+	8.54818i	0.479171	+	0.402072i
$453$		0			0
$454$	−12.8366	−	4.67215i	−0.602452	−	0.219275i
$455$	13.2216			0.619840
$456$		0			0
$457$	−13.0496			−0.610436			−0.305218	−	0.952283i	$-0.598729\pi$
$457$	−13.0496			−0.610436			−0.305218	+	0.952283i	$0.598729\pi$
$458$	−4.90673	−	1.78590i	−0.229276	−	0.0834497i
$459$		0			0
$460$	−4.69459	−	3.93923i	−0.218887	−	0.183668i
$461$	−3.37733	+	2.83391i	−0.157298	+	0.131988i	−0.718040	−	0.696002i	$-0.754960\pi$
$461$	−3.37733	+	2.83391i	−0.157298	+	0.131988i	0.560742	+	0.827991i	$0.310516\pi$
$462$		0			0
$463$	−13.3327	+	23.0930i	−0.619625	+	1.07322i	0.369929	+	0.929060i	$0.379382\pi$
$463$	−13.3327	+	23.0930i	−0.619625	+	1.07322i	−0.989554	+	0.144162i	$0.953951\pi$
$464$	4.22668	+	7.32083i	0.196219	+	0.339861i
$465$		0			0
$466$	25.4119	−	9.24919i	1.17719	−	0.428460i
$467$	15.0569	+	26.0793i	0.696750	+	1.20681i	0.969587	+	0.244747i	$0.0787048\pi$
$467$	15.0569	+	26.0793i	0.696750	+	1.20681i	−0.272837	+	0.962060i	$0.587962\pi$
$468$		0			0
$469$	−1.23442	+	7.00076i	−0.0570003	+	0.323265i
$470$	15.6459	−	13.1285i	0.721691	−	0.605571i
$471$		0			0
$472$	0.124485	+	0.705990i	0.00572989	+	0.0324958i
$473$	1.00640	+	0.366298i	0.0462742	+	0.0168424i
$474$		0			0
$475$	3.29813	+	2.84997i	0.151329	+	0.130765i
$476$	−12.0993			−0.554569
$477$		0			0
$478$	−0.0496299	−	0.281465i	−0.00227002	−	0.0128739i
$479$	−6.25671	−	5.25000i	−0.285876	−	0.239879i	0.488560	−	0.872530i	$-0.337522\pi$
$479$	−6.25671	−	5.25000i	−0.285876	−	0.239879i	−0.774437	+	0.632651i	$0.781967\pi$
$480$		0			0
$481$	−1.09327	+	6.20026i	−0.0498490	+	0.282708i
$482$	1.55051	−	2.68556i	0.0706237	−	0.122324i
$483$		0			0
$484$	8.46451	−	3.08083i	0.384750	−	0.140038i
$485$	−2.87939	+	1.04801i	−0.130746	+	0.0475877i
$486$		0			0
$487$	−13.2935	+	23.0251i	−0.602388	+	1.04337i	0.390070	+	0.920785i	$0.372451\pi$
$487$	−13.2935	+	23.0251i	−0.602388	+	1.04337i	−0.992458	+	0.122582i	$0.960883\pi$
$488$	−1.69459	+	9.61051i	−0.0767106	+	0.435047i
$489$		0			0
$490$	28.5672	+	23.9707i	1.29053	+	1.08289i
$491$	−6.74257	−	38.2390i	−0.304288	−	1.72570i	−0.626837	−	0.779151i	$-0.715651\pi$
$491$	−6.74257	−	38.2390i	−0.304288	−	1.72570i	0.322549	−	0.946553i	$-0.395460\pi$
$492$		0			0
$493$	20.1967			0.909611
$494$	2.77332	+	4.96854i	0.124777	+	0.223545i
$495$		0			0
$496$	−0.347296	−	0.126406i	−0.0155941	−	0.00567578i
$497$	5.60132	+	31.7667i	0.251253	+	1.42493i
$498$		0			0
$499$	15.8255	−	13.2791i	0.708446	−	0.594456i	−0.215717	−	0.976456i	$-0.569209\pi$
$499$	15.8255	−	13.2791i	0.708446	−	0.594456i	0.924163	+	0.382000i	$0.124764\pi$
$500$	2.08378	−	11.8177i	0.0931894	−	0.528503i
$501$		0			0
$502$	6.32888	+	10.9619i	0.282472	+	0.489255i
$503$	0.0692302	−	0.0251977i	0.00308682	−	0.00112351i	−0.340476	−	0.940253i	$-0.610588\pi$
$503$	0.0692302	−	0.0251977i	0.00308682	−	0.00112351i	0.343563	+	0.939130i	$0.388366\pi$
$504$		0			0
$505$	−8.82295	−	15.2818i	−0.392616	−	0.680031i
$506$	2.16250	−	3.74557i	0.0961350	−	0.166511i
$507$		0			0
$508$	−4.37733	+	3.67301i	−0.194212	+	0.162964i
$509$	−11.5057	−	9.65441i	−0.509980	−	0.427924i	0.351142	−	0.936322i	$-0.385793\pi$
$509$	−11.5057	−	9.65441i	−0.509980	−	0.427924i	−0.861122	+	0.508398i	$0.830238\pi$
$510$		0			0
$511$	21.6973	+	7.89716i	0.959831	+	0.349350i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−30.3928			−1.34057
$515$	−13.4338	−	4.88949i	−0.591962	−	0.215457i
$516$		0			0
$517$	11.0419	+	9.26525i	0.485622	+	0.407485i
$518$	−18.7101	+	15.6996i	−0.822073	+	0.689802i
$519$		0			0
$520$	1.30541	−	2.26103i	0.0572459	−	0.0991528i
$521$	22.5856	+	39.1194i	0.989493	+	1.71385i	0.619959	+	0.784634i	$0.287149\pi$
$521$	22.5856	+	39.1194i	0.989493	+	1.71385i	0.369533	+	0.929217i	$0.379518\pi$
$522$		0			0
$523$	−0.157451	+	0.0573076i	−0.00688487	+	0.00250589i	−0.345460	−	0.938433i	$-0.612277\pi$
$523$	−0.157451	+	0.0573076i	−0.00688487	+	0.00250589i	0.338575	+	0.940939i	$0.390055\pi$
$524$	−4.93969	−	8.55580i	−0.215791	−	0.373762i
$525$		0			0
$526$	3.80335	−	21.5699i	0.165834	−	0.940490i
$527$	−0.676423	+	0.567586i	−0.0294654	+	0.0247244i
$528$		0			0
$529$	−2.36349	−	13.4040i	−0.102761	−	0.582784i
$530$	3.14796	+	1.14576i	0.136738	+	0.0497687i
$531$		0			0
$532$	−4.14796	+	21.6810i	−0.179837	+	0.939991i
$533$	−2.00000			−0.0866296
$534$		0			0
$535$	−3.25402	−	18.4545i	−0.140684	−	0.797857i
$536$	1.07532	+	0.902302i	0.0464468	+	0.0389735i
$537$		0			0
$538$	−0.248970	+	1.41198i	−0.0107339	+	0.0608748i
$539$	−13.1591	+	22.7922i	−0.566803	+	0.981731i
$540$		0			0
$541$	0.921274	−	0.335316i	0.0396087	−	0.0144164i	−0.322140	−	0.946692i	$-0.604402\pi$
$541$	0.921274	−	0.335316i	0.0396087	−	0.0144164i	0.361749	+	0.932276i	$0.382180\pi$
$542$	15.1976	−	5.53147i	0.652792	−	0.237597i
$543$		0			0
$544$	−1.19459	+	2.06910i	−0.0512177	+	0.0887117i
$545$	−3.84255	+	21.7922i	−0.164597	+	0.933474i
$546$		0			0
$547$	21.7592	+	18.2582i	0.930358	+	0.780663i	0.975882	−	0.218300i	$-0.0700512\pi$
$547$	21.7592	+	18.2582i	0.930358	+	0.780663i	−0.0455238	+	0.998963i	$0.514496\pi$
$548$	−0.937166	−	5.31493i	−0.0400338	−	0.227043i
$549$		0			0
$550$	1.41147			0.0601855
$551$	6.92396	−	36.1910i	0.294971	−	1.54179i
$552$		0			0
$553$	10.6655	+	3.88192i	0.453543	+	0.165076i
$554$	−1.92902	−	10.9400i	−0.0819560	−	0.464796i
$555$		0			0
$556$	−1.79220	+	1.50384i	−0.0760064	+	0.0637769i
$557$	−6.18748	+	35.0909i	−0.262172	+	1.48685i	0.514797	+	0.857312i	$0.327867\pi$
$557$	−6.18748	+	35.0909i	−0.262172	+	1.48685i	−0.776969	+	0.629539i	$0.783244\pi$
$558$		0			0
$559$	−0.495252	−	0.857802i	−0.0209469	−	0.0362812i
$560$	9.51754	−	3.46410i	0.402190	−	0.146385i
$561$		0			0
$562$	−2.12449	−	3.67972i	−0.0896160	−	0.155219i
$563$	4.31386	−	7.47183i	0.181808	−	0.314900i	−0.760688	−	0.649117i	$-0.775139\pi$
$563$	4.31386	−	7.47183i	0.181808	−	0.314900i	0.942496	+	0.334217i	$0.108472\pi$
$564$		0			0
$565$	−20.3746	+	17.0964i	−0.857167	+	0.719249i
$566$	4.17958	+	3.50708i	0.175681	+	0.147414i
$567$		0			0
$568$	5.98545	+	2.17853i	0.251144	+	0.0914089i
$569$	−22.3310			−0.936164			−0.468082	−	0.883685i	$-0.655055\pi$
$569$	−22.3310			−0.936164			−0.468082	+	0.883685i	$0.655055\pi$
$570$		0			0
$571$	−9.56448			−0.400261			−0.200131	−	0.979769i	$-0.564137\pi$
$571$	−9.56448			−0.400261			−0.200131	+	0.979769i	$0.564137\pi$
$572$	1.73143	+	0.630189i	0.0723947	+	0.0263495i
$573$		0			0
$574$	−5.94356	−	4.98724i	−0.248080	−	0.208163i
$575$	−2.34730	+	1.96962i	−0.0978890	+	0.0821386i
$576$		0			0
$577$	−11.2378	+	19.4645i	−0.467837	+	0.810317i	−0.999325	−	0.0367489i	$-0.988300\pi$
$577$	−11.2378	+	19.4645i	−0.467837	+	0.810317i	0.531488	+	0.847066i	$0.321633\pi$
$578$	−5.64590	−	9.77898i	−0.234838	−	0.406752i
$579$		0			0
$580$	−15.8871	+	5.78244i	−0.659677	+	0.240103i
$581$	−10.0915	−	17.4790i	−0.418667	−	0.725152i
$582$		0			0
$583$	−0.410540	+	2.32829i	−0.0170028	+	0.0964279i
$584$	3.49273	−	2.93075i	0.144530	−	0.121275i
$585$		0			0
$586$	3.09327	+	17.5428i	0.127782	+	0.724687i
$587$	3.89780	+	1.41868i	0.160880	+	0.0585554i	0.421205	−	0.906966i	$-0.361607\pi$
$587$	3.89780	+	1.41868i	0.160880	+	0.0585554i	−0.260325	+	0.965521i	$0.583830\pi$
$588$		0			0
$589$	0.785178	+	1.40669i	0.0323527	+	0.0579615i
$590$	−1.43376			−0.0590271
$591$		0			0
$592$	0.837496	+	4.74968i	0.0344209	+	0.195211i
$593$	−7.98024	−	6.69621i	−0.327709	−	0.274981i	0.464057	−	0.885806i	$-0.346393\pi$
$593$	−7.98024	−	6.69621i	−0.327709	−	0.274981i	−0.791766	+	0.610825i	$0.790838\pi$
$594$		0			0
$595$	4.20203	−	23.8309i	0.172266	−	0.976971i
$596$	−7.18479	+	12.4444i	−0.294301	+	0.509744i
$597$		0			0
$598$	−3.75877	+	1.36808i	−0.153708	+	0.0559450i
$599$	−37.2645	+	13.5632i	−1.52258	+	0.554175i	−0.961792	−	0.273781i	$-0.911726\pi$
$599$	−37.2645	+	13.5632i	−1.52258	+	0.554175i	−0.560792	+	0.827957i	$0.689503\pi$
$600$		0			0
$601$	−11.9324	+	20.6676i	−0.486734	+	0.843047i	−0.999884	−	0.0152517i	$-0.995145\pi$
$601$	−11.9324	+	20.6676i	−0.486734	+	0.843047i	0.513150	+	0.858299i	$0.328478\pi$
$602$	0.667252	−	3.78417i	0.0271951	−	0.154231i
$603$		0			0
$604$	−15.9632	−	13.3947i	−0.649532	−	0.545022i
$605$	3.12836	+	17.7418i	0.127186	+	0.721306i
$606$		0			0
$607$	−29.9317			−1.21489			−0.607445	−	0.794362i	$-0.707806\pi$
$607$	−29.9317			−1.21489			−0.607445	+	0.794362i	$0.707806\pi$
$608$	3.29813	+	2.84997i	0.133757	+	0.115581i
$609$		0			0
$610$	−18.3405	−	6.67539i	−0.742585	−	0.270279i
$611$	−2.31490	−	13.1285i	−0.0936509	−	0.531121i
$612$		0			0
$613$	−27.2540	+	22.8688i	−1.10078	+	0.923664i	−0.997477	−	0.0709862i	$-0.977385\pi$
$613$	−27.2540	+	22.8688i	−1.10078	+	0.923664i	−0.103302	+	0.994650i	$0.532941\pi$
$614$	4.97653	−	28.2233i	0.200836	−	1.13900i
$615$		0			0
$616$	3.57398	+	6.19031i	0.144000	+	0.249415i
$617$	11.3068	−	4.11532i	0.455193	−	0.165677i	−0.104240	−	0.994552i	$-0.533241\pi$
$617$	11.3068	−	4.11532i	0.455193	−	0.165677i	0.559433	+	0.828876i	$0.311019\pi$
$618$		0			0
$619$	8.55644	+	14.8202i	0.343912	+	0.595673i	0.985156	−	0.171664i	$-0.0549144\pi$
$619$	8.55644	+	14.8202i	0.343912	+	0.595673i	−0.641243	+	0.767338i	$0.721581\pi$
$620$	0.369585	−	0.640140i	0.0148429	−	0.0257086i
$621$		0			0
$622$	12.1138	−	10.1647i	0.485719	−	0.407567i
$623$	41.2995	+	34.6544i	1.65463	+	1.38840i
$624$		0			0
$625$	17.8542	+	6.49838i	0.714166	+	0.259935i
$626$	−13.1402			−0.525189
$627$		0			0
$628$	6.36959			0.254174
$629$	10.8280	+	3.94107i	0.431741	+	0.157141i
$630$		0			0
$631$	14.0496	+	11.7890i	0.559307	+	0.469314i	0.878078	−	0.478517i	$-0.158826\pi$
$631$	14.0496	+	11.7890i	0.559307	+	0.469314i	−0.318771	+	0.947832i	$0.603270\pi$
$632$	1.71688	−	1.44063i	0.0682939	−	0.0573054i
$633$		0			0
$634$	10.7023	−	18.5370i	0.425044	−	0.736198i
$635$	−5.71419	−	9.89727i	−0.226761	−	0.392761i
$636$		0			0
$637$	22.8726	−	8.32494i	0.906245	−	0.329846i
$638$	−5.96585	−	10.3332i	−0.236190	−	0.409094i
$639$		0			0
$640$	0.347296	−	1.96962i	0.0137281	−	0.0778559i
$641$	23.8837	−	20.0408i	0.943350	−	0.791565i	−0.0348149	−	0.999394i	$-0.511084\pi$
$641$	23.8837	−	20.0408i	0.943350	−	0.791565i	0.978165	+	0.207829i	$0.0666397\pi$
$642$		0			0
$643$	−5.54798	−	31.4642i	−0.218791	−	1.24083i	−0.874206	−	0.485556i	$-0.838617\pi$
$643$	−5.54798	−	31.4642i	−0.218791	−	1.24083i	0.655414	−	0.755269i	$-0.272494\pi$
$644$	−14.5817	−	5.30731i	−0.574600	−	0.209137i
$645$		0			0
$646$	9.83678	−	3.41960i	0.387023	−	0.134542i
$647$	−2.99588			−0.117780			−0.0588901	−	0.998264i	$-0.518756\pi$
$647$	−2.99588			−0.117780			−0.0588901	+	0.998264i	$0.518756\pi$
$648$		0			0
$649$	−0.175708	−	0.996487i	−0.00689713	−	0.0391155i
$650$	−1.00000	−	0.839100i	−0.0392232	−	0.0329122i
$651$		0			0
$652$	0.821604	−	4.65955i	0.0321765	−	0.182482i
$653$	0.467911	−	0.810446i	0.0183108	−	0.0317152i	−0.856725	−	0.515774i	$-0.827505\pi$
$653$	0.467911	−	0.810446i	0.0183108	−	0.0317152i	0.875036	+	0.484059i	$0.160838\pi$
$654$		0			0
$655$	18.5672	−	6.75790i	0.725479	−	0.264053i
$656$	−1.43969	+	0.524005i	−0.0562106	+	0.0204590i
$657$		0			0
$658$	25.8580	−	44.7874i	1.00805	−	1.74600i
$659$	2.12495	−	12.0512i	0.0827764	−	0.469448i	−0.915038	−	0.403368i	$-0.867840\pi$
$659$	2.12495	−	12.0512i	0.0827764	−	0.469448i	0.997814	−	0.0660804i	$-0.0210494\pi$
$660$		0			0
$661$	−9.15839	−	7.68480i	−0.356220	−	0.298904i	0.447062	−	0.894503i	$-0.352470\pi$
$661$	−9.15839	−	7.68480i	−0.356220	−	0.298904i	−0.803282	+	0.595599i	$0.796915\pi$
$662$	4.41029	+	25.0120i	0.171411	+	0.972119i
$663$		0			0
$664$	−3.98545			−0.154666
$665$	−41.2627	−	15.6996i	−1.60010	−	0.608805i
$666$		0			0
$667$	24.3405	+	8.85921i	0.942468	+	0.343030i
$668$	−3.00000	−	17.0138i	−0.116073	−	0.658285i
$669$		0			0
$670$	−2.15064	+	1.80460i	−0.0830866	+	0.0697180i
$671$	2.39187	−	13.5650i	0.0923373	−	0.523671i
$672$		0			0
$673$	−22.4317	−	38.8529i	−0.864679	−	1.49767i	−0.867366	−	0.497671i	$-0.834189\pi$
$673$	−22.4317	−	38.8529i	−0.864679	−	1.49767i	0.00268731	−	0.999996i	$-0.499145\pi$
$674$	24.7866	−	9.02158i	0.954743	−	0.347498i
$675$		0			0
$676$	5.64796	+	9.78255i	0.217229	+	0.376252i
$677$	0.472964	−	0.819197i	0.0181775	−	0.0314843i	−0.856794	−	0.515660i	$-0.827547\pi$
$677$	0.472964	−	0.819197i	0.0181775	−	0.0314843i	0.874971	+	0.484175i	$0.160880\pi$
$678$		0			0
$679$	−5.94356	+	4.98724i	−0.228093	+	0.191393i
$680$	−3.66044	−	3.07148i	−0.140372	−	0.117786i
$681$		0			0
$682$	0.490200	+	0.178418i	0.0187707	+	0.00683198i
$683$	5.92221			0.226607			0.113303	−	0.993560i	$-0.463857\pi$
$683$	5.92221			0.226607			0.113303	+	0.993560i	$0.463857\pi$
$684$		0			0
$685$	10.7939			0.412412
$686$	55.4201	+	20.1713i	2.11595	+	0.770143i
$687$		0			0
$688$	−0.581252	−	0.487728i	−0.0221600	−	0.0185945i
$689$	1.67499	−	1.40549i	0.0638121	−	0.0535447i
$690$		0			0
$691$	−0.103074	+	0.178529i	−0.00392111	+	0.00679156i	−0.867979	−	0.496600i	$-0.834581\pi$
$691$	−0.103074	+	0.178529i	−0.00392111	+	0.00679156i	0.864058	+	0.503392i	$0.167915\pi$
$692$	9.41147	+	16.3012i	0.357771	+	0.619677i
$693$		0			0
$694$	24.0856	−	8.76644i	0.914276	−	0.332769i
$695$	−2.33956	−	4.05223i	−0.0887444	−	0.153710i
$696$		0			0
$697$	−0.635630	+	3.60483i	−0.0240762	+	0.136543i
$698$	4.47565	−	3.75552i	0.169406	−	0.142148i
$699$		0			0
$700$	−0.879385	−	4.98724i	−0.0332376	−	0.188500i
$701$	4.10607	+	1.49449i	0.155084	+	0.0564460i	0.418396	−	0.908265i	$-0.362593\pi$
$701$	4.10607	+	1.49449i	0.155084	+	0.0564460i	−0.263312	+	0.964711i	$0.584815\pi$
$702$		0			0
$703$	10.7743	−	18.0519i	0.406359	−	0.680840i
$704$	1.41147			0.0531969
$705$		0			0
$706$	−3.89141	−	22.0693i	−0.146455	−	0.830588i
$707$	−34.2276	−	28.7204i	−1.28726	−	1.08014i
$708$		0			0
$709$	1.52023	−	8.62165i	0.0570934	−	0.323793i	−0.942863	−	0.333182i	$-0.891878\pi$
$709$	1.52023	−	8.62165i	0.0570934	−	0.323793i	0.999956	+	0.00938924i	$0.00298873\pi$
$710$	−6.36959	+	11.0324i	−0.239046	+	0.414040i
$711$		0			0
$712$	10.0039	−	3.64111i	0.374911	−	0.136456i
$713$	−1.06418	+	0.387329i	−0.0398538	+	0.0145056i
$714$		0			0
$715$	−1.84255	+	3.19139i	−0.0689074	+	0.119351i
$716$	2.40121	−	13.6179i	0.0897373	−	0.508926i
$717$		0			0
$718$	7.36690	+	6.18156i	0.274930	+	0.230694i
$719$	4.79385	+	27.1873i	0.178781	+	1.01391i	0.933689	+	0.358085i	$0.116570\pi$
$719$	4.79385	+	27.1873i	0.178781	+	1.01391i	−0.754909	+	0.655830i	$0.772319\pi$
$720$		0			0
$721$	−36.1985			−1.34810
$722$	−2.75537	−	18.7991i	−0.102544	−	0.699632i
$723$		0			0
$724$	−11.5175	−	4.19204i	−0.428046	−	0.155796i
$725$	1.46791	+	8.32494i	0.0545169	+	0.309180i
$726$		0			0
$727$	21.9368	−	18.4071i	0.813589	−	0.682682i	−0.137872	−	0.990450i	$-0.544026\pi$
$727$	21.9368	−	18.4071i	0.813589	−	0.682682i	0.951462	+	0.307768i	$0.0995819\pi$
$728$	1.14796	−	6.51038i	0.0425461	−	0.241291i
$729$		0			0
$730$	4.55943	+	7.89716i	0.168752	+	0.292287i
$731$	−1.70352	+	0.620029i	−0.0630068	+	0.0229326i
$732$		0			0
$733$	−18.4807	−	32.0095i	−0.682600	−	1.18230i	−0.974184	−	0.225753i	$-0.927516\pi$
$733$	−18.4807	−	32.0095i	−0.682600	−	1.18230i	0.291584	−	0.956545i	$-0.405818\pi$
$734$	11.6800	−	20.2304i	0.431118	−	0.746719i
$735$		0			0
$736$	−2.34730	+	1.96962i	−0.0865225	+	0.0726010i
$737$	−1.51779	−	1.27358i	−0.0559085	−	0.0469128i
$738$		0			0
$739$	−43.2508	−	15.7420i	−1.59101	−	0.579079i	−0.613446	−	0.789737i	$-0.710217\pi$
$739$	−43.2508	−	15.7420i	−1.59101	−	0.579079i	−0.977560	+	0.210658i	$0.932439\pi$
$740$	−9.64590			−0.354590
$741$		0			0
$742$	8.48246			0.311401
$743$	24.8179	+	9.03298i	0.910480	+	0.331388i	0.754445	−	0.656364i	$-0.227906\pi$
$743$	24.8179	+	9.03298i	0.910480	+	0.331388i	0.156036	+	0.987751i	$0.450129\pi$
$744$		0			0
$745$	−22.0155	−	18.4732i	−0.806585	−	0.676805i
$746$	19.8726	−	16.6751i	0.727587	−	0.610518i
$747$		0			0
$748$	1.68614	−	2.92047i	0.0616513	−	0.106783i
$749$	−23.7246	−	41.0923i	−0.866879	−	1.50148i
$750$		0			0
$751$	25.5381	−	9.29510i	0.931898	−	0.339183i	0.168936	−	0.985627i	$-0.445967\pi$
$751$	25.5381	−	9.29510i	0.931898	−	0.339183i	0.762961	+	0.646444i	$0.223745\pi$
$752$	−5.10607	−	8.84397i	−0.186199	−	0.322506i
$753$		0			0
$754$	−1.91622	+	10.8674i	−0.0697847	+	0.395769i
$755$	31.9263	−	26.7894i	1.16192	−	0.974965i
$756$		0			0
$757$	3.36959	+	19.1099i	0.122470	+	0.694560i	0.982779	+	0.184787i	$0.0591595\pi$
$757$	3.36959	+	19.1099i	0.122470	+	0.694560i	−0.860309	+	0.509773i	$0.829729\pi$
$758$	8.90673	+	3.24178i	0.323507	+	0.117747i
$759$		0			0
$760$	−6.75877	+	5.50627i	−0.245166	+	0.199733i
$761$	−40.2645			−1.45959			−0.729793	−	0.683669i	$-0.760383\pi$
$761$	−40.2645			−1.45959			−0.729793	+	0.683669i	$0.760383\pi$
$762$		0			0
$763$	9.72967	+	55.1797i	0.352238	+	1.99764i
$764$	15.3969	+	12.9196i	0.557041	+	0.467413i
$765$		0			0
$766$	−2.34224	+	13.2835i	−0.0846287	+	0.479953i
$767$	−0.467911	+	0.810446i	−0.0168953	+	0.0292635i
$768$		0			0
$769$	36.5933	−	13.3189i	1.31959	−	0.480291i	0.416263	−	0.909244i	$-0.363340\pi$
$769$	36.5933	−	13.3189i	1.31959	−	0.480291i	0.903327	+	0.428953i	$0.141117\pi$
$770$	−13.4338	+	4.88949i	−0.484119	+	0.176205i
$771$		0			0
$772$	−8.34255	+	14.4497i	−0.300255	+	0.520057i
$773$	1.17436	−	6.66015i	0.0422389	−	0.239549i	−0.956378	−	0.292133i	$-0.905635\pi$
$773$	1.17436	−	6.66015i	0.0422389	−	0.239549i	0.998616	+	0.0525847i	$0.0167460\pi$
$774$		0			0
$775$	−0.283119	−	0.237565i	−0.0101699	−	0.00853358i
$776$	0.266044	+	1.50881i	0.00955044	+	0.0541632i
$777$		0			0
$778$	−25.1480			−0.901598
$779$	6.24170	+	2.37484i	0.223632	+	0.0850874i
$780$		0			0
$781$	−8.44831	−	3.07493i	−0.302304	−	0.110030i
$782$	1.27126	+	7.20967i	0.0454601	+	0.257817i
$783$		0			0
$784$	14.2836	−	11.9854i	0.510128	−	0.428048i
$785$	−2.21213	+	12.5456i	−0.0789544	+	0.447773i
$786$		0			0
$787$	−2.90239	−	5.02709i	−0.103459	−	0.179196i	0.809649	−	0.586915i	$-0.199658\pi$
$787$	−2.90239	−	5.02709i	−0.103459	−	0.179196i	−0.913108	+	0.407719i	$0.866324\pi$
$788$	12.2071	−	4.44301i	0.434859	−	0.158276i
$789$		0			0
$790$	2.24123	+	3.88192i	0.0797394	+	0.138113i
$791$	−33.6732	+	58.3238i	−1.19728	+	2.07375i
$792$		0			0
$793$	−9.75877	+	8.18858i	−0.346544	+	0.290785i
$794$	−5.03003	−	4.22070i	−0.178509	−	0.149787i
$795$		0			0
$796$	−16.1557	−	5.88019i	−0.572623	−	0.208418i
$797$	39.2181			1.38918			0.694589	−	0.719407i	$-0.255586\pi$
$797$	39.2181			1.38918			0.694589	+	0.719407i	$0.255586\pi$
$798$		0			0
$799$	−24.3987			−0.863163
$800$	−0.939693	−	0.342020i	−0.0332232	−	0.0120922i
$801$		0			0
$802$	−22.6065	−	18.9691i	−0.798264	−	0.669823i
$803$	−4.92989	+	4.13667i	−0.173972	+	0.145980i
$804$		0			0
$805$	15.5175	−	26.8772i	0.546921	−	0.947296i
$806$	−0.241230	−	0.417822i	−0.00849695	−	0.0147171i
$807$		0			0
$808$	−8.29086	+	3.01763i	−0.291671	+	0.106160i
$809$	3.50134	+	6.06451i	0.123101	+	0.213217i	0.920989	−	0.389589i	$-0.127383\pi$
$809$	3.50134	+	6.06451i	0.123101	+	0.213217i	−0.797888	+	0.602805i	$0.794050\pi$
$810$		0			0
$811$	7.58584	−	43.0214i	0.266375	−	1.51069i	−0.498717	−	0.866765i	$-0.666195\pi$
$811$	7.58584	−	43.0214i	0.266375	−	1.51069i	0.765092	−	0.643921i	$-0.222694\pi$
$812$	−32.7939	+	27.5173i	−1.15084	+	0.965668i
$813$		0			0
$814$	−1.18210	−	6.70405i	−0.0414327	−	0.234977i
$815$	8.89218	+	3.23649i	0.311479	+	0.113369i
$816$		0			0
$817$	0.527036	+	3.26514i	0.0184387	+	0.114233i
$818$	−21.1310			−0.738830
$819$		0			0
$820$	−0.532089	−	3.01763i	−0.0185813	−	0.105380i
$821$	−9.48751	−	7.96097i	−0.331116	−	0.277840i	0.462038	−	0.886860i	$-0.347118\pi$
$821$	−9.48751	−	7.96097i	−0.331116	−	0.277840i	−0.793155	+	0.609020i	$0.791563\pi$
$822$		0			0
$823$	−2.22762	+	12.6334i	−0.0776498	+	0.440374i	0.921052	+	0.389439i	$0.127331\pi$
$823$	−2.22762	+	12.6334i	−0.0776498	+	0.440374i	−0.998702	+	0.0509347i	$0.983780\pi$
$824$	−3.57398	+	6.19031i	−0.124505	+	0.215650i
$825$		0			0
$826$	−3.41147	+	1.24168i	−0.118700	+	0.0432034i
$827$	23.5831	−	8.58353i	0.820063	−	0.298479i	0.102289	−	0.994755i	$-0.467383\pi$
$827$	23.5831	−	8.58353i	0.820063	−	0.298479i	0.717774	+	0.696276i	$0.245161\pi$
$828$		0			0
$829$	−14.1634	+	24.5318i	−0.491917	+	0.852024i	−0.999957	−	0.00930899i	$-0.997037\pi$
$829$	−14.1634	+	24.5318i	−0.491917	+	0.852024i	0.508040	+	0.861333i	$0.330370\pi$
$830$	1.38413	−	7.84981i	0.0480440	−	0.272471i
$831$		0			0
$832$	−1.00000	−	0.839100i	−0.0346688	−	0.0290905i
$833$	−7.73577	−	43.8717i	−0.268028	−	1.52006i
$834$		0			0
$835$	34.5526			1.19574
$836$	−4.65523	−	4.02266i	−0.161004	−	0.139126i
$837$		0			0
$838$	26.2015	+	9.53655i	0.905114	+	0.329435i
$839$	5.26682	+	29.8696i	0.181831	+	1.03121i	0.929960	+	0.367660i	$0.119841\pi$
$839$	5.26682	+	29.8696i	0.181831	+	1.03121i	−0.748129	+	0.663553i	$0.769048\pi$
$840$		0			0
$841$	32.5257	−	27.2923i	1.12158	−	0.941115i
$842$	0.00774079	−	0.0439002i	0.000266765	−	0.00151290i
$843$		0			0
$844$	8.05438	+	13.9506i	0.277243	+	0.480199i
$845$	−21.2294	+	7.72686i	−0.730313	+	0.265812i
$846$		0			0
$847$	22.8084	+	39.5053i	0.783706	+	1.35742i
$848$	0.837496	−	1.45059i	0.0287597	−	0.0498133i
$849$		0			0
$850$	−1.83022	+	1.53574i	−0.0627761	+	0.0526754i
$851$	11.3209	+	9.49935i	0.388075	+	0.325634i
$852$		0			0
$853$	41.0009	+	14.9231i	1.40385	+	0.510958i	0.929317	−	0.369283i	$-0.120397\pi$
$853$	41.0009	+	14.9231i	1.40385	+	0.510958i	0.474528	+	0.880240i	$0.342619\pi$
$854$	−49.4201			−1.69112
$855$		0			0
$856$	−9.36959			−0.320246
$857$	−29.6095	−	10.7770i	−1.01144	−	0.368135i	−0.217456	−	0.976070i	$-0.569776\pi$
$857$	−29.6095	−	10.7770i	−1.01144	−	0.368135i	−0.793987	+	0.607935i	$0.791998\pi$
$858$		0			0
$859$	−14.3234	−	12.0188i	−0.488709	−	0.410075i	0.364855	−	0.931065i	$-0.381119\pi$
$859$	−14.3234	−	12.0188i	−0.488709	−	0.410075i	−0.853563	+	0.520989i	$0.825563\pi$
$860$	1.16250	−	0.975457i	0.0396411	−	0.0332628i
$861$		0			0
$862$	5.89393	−	10.2086i	0.200748	−	0.347706i
$863$	5.31315	+	9.20264i	0.180862	+	0.313262i	0.942174	−	0.335123i	$-0.108778\pi$
$863$	5.31315	+	9.20264i	0.180862	+	0.313262i	−0.761313	+	0.648385i	$0.775445\pi$
$864$		0			0
$865$	−35.3756	+	12.8757i	−1.20281	+	0.437785i
$866$	13.8229	+	23.9420i	0.469723	+	0.813584i
$867$		0			0
$868$	0.325008	−	1.84321i	0.0110315	−	0.0625626i
$869$	−2.42333	+	2.03342i	−0.0822060	+	0.0689790i
$870$		0			0
$871$	0.318201	+	1.80460i	0.0107818	+	0.0611467i
$872$	10.3969	+	3.78417i	0.352084	+	0.128148i
$873$		0			0
$874$	13.3550	+	0.193665i	0.451741	+	0.00655080i
$875$	60.7701			2.05441
$876$		0			0
$877$	7.79654	+	44.2164i	0.263270	+	1.49308i	0.773915	+	0.633289i	$0.218296\pi$
$877$	7.79654	+	44.2164i	0.263270	+	1.49308i	−0.510645	+	0.859792i	$0.670593\pi$
$878$	−28.6878	−	24.0719i	−0.968166	−	0.812388i
$879$		0			0
$880$	−0.490200	+	2.78006i	−0.0165246	+	0.0937158i
$881$	−9.00821	+	15.6027i	−0.303494	+	0.525667i	−0.976925	−	0.213583i	$-0.931487\pi$
$881$	−9.00821	+	15.6027i	−0.303494	+	0.525667i	0.673431	+	0.739250i	$0.264820\pi$
$882$		0			0
$883$	43.7879	−	15.9375i	1.47358	−	0.536340i	0.524511	−	0.851404i	$-0.324248\pi$
$883$	43.7879	−	15.9375i	1.47358	−	0.536340i	0.949070	+	0.315064i	$0.102026\pi$
$884$	−2.93077	+	1.06671i	−0.0985725	+	0.0358774i
$885$		0			0
$886$	−10.4941	+	18.1763i	−0.352555	+	0.610643i
$887$	−1.22937	+	6.97210i	−0.0412782	+	0.234100i	−0.998466	−	0.0553671i	$-0.982367\pi$
$887$	−1.22937	+	6.97210i	−0.0412782	+	0.234100i	0.957188	+	0.289467i	$0.0934782\pi$
$888$		0			0
$889$	−22.1676	−	18.6008i	−0.743476	−	0.623850i
$890$	3.69728	+	20.9683i	0.123933	+	0.702860i
$891$		0			0
$892$	4.08378			0.136735
$893$	−8.36453	+	43.7207i	−0.279908	+	1.46306i
$894$		0			0
$895$	25.9881	+	9.45891i	0.868688	+	0.316176i
$896$	−0.879385	−	4.98724i	−0.0293782	−	0.166612i
$897$		0			0
$898$	−16.7724	+	14.0737i	−0.559704	+	0.469647i
$899$	−0.542518	+	3.07677i	−0.0180940	+	0.102616i
$900$		0			0
$901$	−2.00093	−	3.46572i	−0.0666608	−	0.115460i
$902$	2.03209	−	0.739620i	0.0676612	−	0.0246266i
$903$		0			0
$904$	6.64930	+	11.5169i	0.221152	+	0.383047i
$905$	12.2567	−	21.2292i	0.407427	−	0.705684i
$906$		0			0
$907$	11.5792	−	9.71610i	0.384481	−	0.322618i	−0.429978	−	0.902840i	$-0.641479\pi$
$907$	11.5792	−	9.71610i	0.384481	−	0.322618i	0.814458	+	0.580222i	$0.197034\pi$
$908$	−10.4645	−	8.78076i	−0.347277	−	0.291400i
$909$		0			0
$910$	12.4243	+	4.52206i	0.411860	+	0.149905i
$911$	12.8366			0.425294			0.212647	−	0.977129i	$-0.431792\pi$
$911$	12.8366			0.425294			0.212647	+	0.977129i	$0.431792\pi$
$912$		0			0
$913$	5.62536			0.186172
$914$	−12.2626	−	4.46324i	−0.405612	−	0.147631i
$915$		0			0
$916$	−4.00000	−	3.35640i	−0.132164	−	0.110899i
$917$	38.3259	−	32.1593i	1.26563	−	1.06199i
$918$		0			0
$919$	10.3396	−	17.9086i	0.341070	−	0.590751i	−0.643561	−	0.765395i	$-0.722544\pi$
$919$	10.3396	−	17.9086i	0.341070	−	0.590751i	0.984632	+	0.174643i	$0.0558772\pi$
$920$	−3.06418	−	5.30731i	−0.101023	−	0.174977i
$921$		0			0
$922$	−4.14290	+	1.50789i	−0.136439	+	0.0496598i
$923$	4.15745	+	7.20092i	0.136844	+	0.237021i
$924$		0			0
$925$	−0.837496	+	4.74968i	−0.0275367	+	0.156168i
$926$	−20.4270	+	17.1403i	−0.671271	+	0.563264i
$927$		0			0
$928$	1.46791	+	8.32494i	0.0481865	+	0.273279i
$929$	−17.1493	−	6.24183i	−0.562650	−	0.204788i	0.0450079	−	0.998987i	$-0.485669\pi$
$929$	−17.1493	−	6.24183i	−0.562650	−	0.204788i	−0.607658	+	0.794199i	$0.707891\pi$
$930$		0			0
$931$	−81.2670	−	1.17847i	−2.66342	−	0.0386229i
$932$	27.0428			0.885817
$933$		0			0
$934$	5.22921	+	29.6563i	0.171105	+	0.970384i
$935$	5.16662	+	4.33531i	0.168967	+	0.141780i
$936$		0			0
$937$	−0.824292	+	4.67479i	−0.0269285	+	0.152719i	−0.995307	−	0.0967660i	$-0.969150\pi$
$937$	−0.824292	+	4.67479i	−0.0269285	+	0.152719i	0.968379	+	0.249485i	$0.0802613\pi$
$938$	−3.55438	+	6.15636i	−0.116055	+	0.201012i
$939$		0			0
$940$	19.1925	−	6.98551i	0.625991	−	0.227842i
$941$	44.1857	−	16.0823i	1.44041	−	0.524268i	0.500517	−	0.865727i	$-0.333143\pi$
$941$	44.1857	−	16.0823i	1.44041	−	0.524268i	0.939897	+	0.341459i	$0.110921\pi$
$942$		0			0
$943$	−2.34730	+	4.06564i	−0.0764385	+	0.132395i
$944$	−0.124485	+	0.705990i	−0.00405165	+	0.0229780i
$945$		0			0
$946$	0.820422	+	0.688416i	0.0266742	+	0.0223823i
$947$	−6.42427	−	36.4338i	−0.208761	−	1.18394i	−0.891411	−	0.453195i	$-0.850284\pi$
$947$	−6.42427	−	36.4338i	−0.208761	−	1.18394i	0.682651	−	0.730745i	$-0.260827\pi$
$948$		0			0
$949$	5.95191			0.193207
$950$	2.12449	+	3.80612i	0.0689274	+	0.123487i
$951$		0			0
$952$	−11.3696	−	4.13819i	−0.368490	−	0.134120i
$953$	6.54814	+	37.1364i	0.212115	+	1.20296i	0.885843	+	0.463985i	$0.153581\pi$
$953$	6.54814	+	37.1364i	0.212115	+	1.20296i	−0.673728	+	0.738980i	$0.735308\pi$
$954$		0			0
$955$	−30.7939	+	25.8391i	−0.996466	+	0.836134i
$956$	0.0496299	−	0.281465i	0.00160514	−	0.00910322i
$957$		0			0
$958$	−4.08378	−	7.07331i	−0.131941	−	0.228528i
$959$	25.6827	−	9.34775i	0.829339	−	0.301855i
$960$		0			0
$961$	15.4317	+	26.7285i	0.497797	+	0.862209i
$962$	−3.14796	+	5.45242i	−0.101494	+	0.175793i
$963$		0			0
$964$	2.37551	−	1.99329i	0.0765102	−	0.0641997i
$965$	−25.5631	−	21.4499i	−0.822904	−	0.690498i
$966$		0			0
$967$	−38.0702	−	13.8564i	−1.22425	−	0.445592i	−0.352628	−	0.935764i	$-0.614712\pi$
$967$	−38.0702	−	13.8564i	−1.22425	−	0.445592i	−0.871626	+	0.490172i	$0.836934\pi$
$968$	9.00774			0.289520
$969$		0			0
$970$	−3.06418			−0.0983848
$971$	−13.2289	−	4.81493i	−0.424536	−	0.154518i	0.120912	−	0.992663i	$-0.461418\pi$
$971$	−13.2289	−	4.81493i	−0.424536	−	0.154518i	−0.545448	+	0.838145i	$0.683640\pi$
$972$		0			0
$973$	−9.07604	−	7.61570i	−0.290964	−	0.244148i
$974$	−20.3669	+	17.0899i	−0.652597	+	0.547594i
$975$		0			0
$976$	−4.87939	+	8.45134i	−0.156185	+	0.270521i
$977$	−17.6028	−	30.4890i	−0.563164	−	0.975429i	−0.997218	−	0.0745421i	$-0.976250\pi$
$977$	−17.6028	−	30.4890i	−0.563164	−	0.975429i	0.434054	−	0.900887i	$-0.357083\pi$
$978$		0			0
$979$	−14.1202	+	5.13933i	−0.451284	+	0.164254i
$980$	18.6459	+	32.2956i	0.595621	+	1.03165i
$981$		0			0
$982$	6.74257	−	38.2390i	0.215164	−	1.22026i
$983$	−17.1898	+	14.4240i	−0.548271	+	0.460054i	−0.874355	−	0.485287i	$-0.838715\pi$
$983$	−17.1898	+	14.4240i	−0.548271	+	0.460054i	0.326084	+	0.945341i	$0.394271\pi$
$984$		0			0
$985$	4.51155	+	25.5863i	0.143750	+	0.815247i
$986$	18.9786	+	6.90766i	0.604403	+	0.219985i
$987$		0			0
$988$	0.906726	+	5.61743i	0.0288468	+	0.178714i
$989$	−2.32501			−0.0739309
$990$		0			0
$991$	4.70645	+	26.6916i	0.149505	+	0.847887i	0.963639	+	0.267209i	$0.0861014\pi$
$991$	4.70645	+	26.6916i	0.149505	+	0.847887i	−0.814133	+	0.580678i	$0.802787\pi$
$992$	−0.283119	−	0.237565i	−0.00898902	−	0.00754269i
$993$		0			0
$994$	−5.60132	+	31.7667i	−0.177663	+	1.00758i
$995$	17.1925	−	29.7783i	0.545040	−	0.944037i
$996$		0			0
$997$	−26.2618	+	9.55850i	−0.831718	+	0.302721i	−0.722564	−	0.691304i	$-0.757037\pi$
$997$	−26.2618	+	9.55850i	−0.831718	+	0.302721i	−0.109154	+	0.994025i	$0.534814\pi$
$998$	19.4128	−	7.06569i	0.614502	−	0.223660i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.c.289.1		6
3.2	odd	2		38.2.e.a.23.1	yes	6
12.11	even	2		304.2.u.c.289.1		6
15.2	even	4		950.2.u.b.99.2		12
15.8	even	4		950.2.u.b.99.1		12
15.14	odd	2		950.2.l.d.251.1		6
19.5	even	9	inner	342.2.u.c.271.1		6
19.9	even	9		6498.2.a.bl.1.3		3
19.10	odd	18		6498.2.a.bq.1.3		3
57.2	even	18		722.2.e.a.415.1		6
57.5	odd	18		38.2.e.a.5.1	✓	6
57.8	even	6		722.2.e.l.389.1		6
57.11	odd	6		722.2.e.b.389.1		6
57.14	even	18		722.2.e.k.423.1		6
57.17	odd	18		722.2.e.m.415.1		6
57.23	odd	18		722.2.c.k.653.3		6
57.26	odd	6		722.2.e.m.595.1		6
57.29	even	18		722.2.a.k.1.3		3
57.32	even	18		722.2.c.l.429.1		6
57.35	odd	18		722.2.e.b.245.1		6
57.41	even	18		722.2.e.l.245.1		6
57.44	odd	18		722.2.c.k.429.3		6
57.47	odd	18		722.2.a.l.1.1		3
57.50	even	6		722.2.e.a.595.1		6
57.53	even	18		722.2.c.l.653.1		6
57.56	even	2		722.2.e.k.99.1		6
228.47	even	18		5776.2.a.bn.1.3		3
228.119	even	18		304.2.u.c.81.1		6
228.143	odd	18		5776.2.a.bo.1.1		3
285.62	even	36		950.2.u.b.499.1		12
285.119	odd	18		950.2.l.d.651.1		6
285.233	even	36		950.2.u.b.499.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.5.1	✓	6	57.5	odd	18
38.2.e.a.23.1	yes	6	3.2	odd	2
304.2.u.c.81.1		6	228.119	even	18
304.2.u.c.289.1		6	12.11	even	2
342.2.u.c.271.1		6	19.5	even	9	inner
342.2.u.c.289.1		6	1.1	even	1	trivial
722.2.a.k.1.3		3	57.29	even	18
722.2.a.l.1.1		3	57.47	odd	18
722.2.c.k.429.3		6	57.44	odd	18
722.2.c.k.653.3		6	57.23	odd	18
722.2.c.l.429.1		6	57.32	even	18
722.2.c.l.653.1		6	57.53	even	18
722.2.e.a.415.1		6	57.2	even	18
722.2.e.a.595.1		6	57.50	even	6
722.2.e.b.245.1		6	57.35	odd	18
722.2.e.b.389.1		6	57.11	odd	6
722.2.e.k.99.1		6	57.56	even	2
722.2.e.k.423.1		6	57.14	even	18
722.2.e.l.245.1		6	57.41	even	18
722.2.e.l.389.1		6	57.8	even	6
722.2.e.m.415.1		6	57.17	odd	18
722.2.e.m.595.1		6	57.26	odd	6
950.2.l.d.251.1		6	15.14	odd	2
950.2.l.d.651.1		6	285.119	odd	18
950.2.u.b.99.1		12	15.8	even	4
950.2.u.b.99.2		12	15.2	even	4
950.2.u.b.499.1		12	285.62	even	36
950.2.u.b.499.2		12	285.233	even	36
5776.2.a.bn.1.3		3	228.47	even	18
5776.2.a.bo.1.1		3	228.143	odd	18
6498.2.a.bl.1.3		3	19.9	even	9
6498.2.a.bq.1.3		3	19.10	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-1.53209 + 1.28558i) q^{5} +(-2.53209 + 4.38571i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-1.53209 + 1.28558i) q^{5} +(-2.53209 + 4.38571i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.87939 + 0.684040i) q^{10} +(-0.705737 - 1.22237i) q^{11} +(-0.226682 + 1.28558i) q^{13} +(-3.87939 + 3.25519i) q^{14} +(0.173648 + 0.984808i) q^{16} +(2.24510 + 0.817150i) q^{17} +(2.23396 - 3.74292i) q^{19} -2.00000 q^{20} +(-0.245100 - 1.39003i) q^{22} +(2.34730 + 1.96962i) q^{23} +(-0.173648 + 0.984808i) q^{25} +(-0.652704 + 1.13052i) q^{26} +(-4.75877 + 1.73205i) q^{28} +(7.94356 - 2.89122i) q^{29} +(-0.184793 + 0.320070i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.83022 + 1.53574i) q^{34} +(-1.75877 - 9.97448i) q^{35} +4.82295 q^{37} +(3.37939 - 2.75314i) q^{38} +(-1.87939 - 0.684040i) q^{40} +(0.266044 + 1.50881i) q^{41} +(-0.581252 + 0.487728i) q^{43} +(0.245100 - 1.39003i) q^{44} +(1.53209 + 2.65366i) q^{46} +(-9.59627 + 3.49276i) q^{47} +(-9.32295 - 16.1478i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.00000 + 0.839100i) q^{52} +(-1.28312 - 1.07666i) q^{53} +(2.65270 + 0.965505i) q^{55} -5.06418 q^{56} +8.45336 q^{58} +(0.673648 + 0.245188i) q^{59} +(7.47565 + 6.27282i) q^{61} +(-0.283119 + 0.237565i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-1.30541 - 2.26103i) q^{65} +(1.31908 - 0.480105i) q^{67} +(1.19459 + 2.06910i) q^{68} +(1.75877 - 9.97448i) q^{70} +(4.87939 - 4.09429i) q^{71} +(-0.791737 - 4.49016i) q^{73} +(4.53209 + 1.64955i) q^{74} +(4.11721 - 1.43128i) q^{76} +7.14796 q^{77} +(-0.389185 - 2.20718i) q^{79} +(-1.53209 - 1.28558i) q^{80} +(-0.266044 + 1.50881i) q^{82} +(-1.99273 + 3.45150i) q^{83} +(-4.49020 + 1.63430i) q^{85} +(-0.713011 + 0.259515i) q^{86} +(0.705737 - 1.22237i) q^{88} +(1.84864 - 10.4842i) q^{89} +(-5.06418 - 4.24935i) q^{91} +(0.532089 + 3.01763i) q^{92} -10.2121 q^{94} +(1.38919 + 8.60640i) q^{95} +(1.43969 + 0.524005i) q^{97} +(-3.23783 - 18.3626i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 6 * q^7 + 3 * q^8	\( 6 q - 6 q^{7} + 3 q^{8} + 6 q^{11} + 12 q^{13} - 12 q^{14} + 12 q^{17} + 18 q^{19} - 12 q^{20} + 12 q^{23} - 6 q^{26} - 6 q^{28} + 18 q^{29} + 6 q^{31} - 12 q^{34} + 12 q^{35} - 12 q^{37} + 9 q^{38} - 3 q^{41} - 6 q^{43} - 30 q^{47} - 15 q^{49} - 3 q^{50} - 6 q^{52} - 24 q^{53} + 18 q^{55} - 12 q^{56} + 24 q^{58} + 3 q^{59} + 6 q^{61} - 18 q^{62} - 3 q^{64} - 12 q^{65} - 9 q^{67} + 3 q^{68} - 12 q^{70} + 18 q^{71} - 30 q^{73} + 18 q^{74} - 6 q^{76} + 12 q^{77} + 6 q^{79} + 3 q^{82} + 6 q^{83} - 24 q^{85} - 12 q^{86} - 6 q^{88} - 12 q^{91} - 6 q^{92} - 12 q^{94} + 3 q^{97}+O(q^{100}) \) 6 * q - 6 * q^7 + 3 * q^8 + 6 * q^11 + 12 * q^13 - 12 * q^14 + 12 * q^17 + 18 * q^19 - 12 * q^20 + 12 * q^23 - 6 * q^26 - 6 * q^28 + 18 * q^29 + 6 * q^31 - 12 * q^34 + 12 * q^35 - 12 * q^37 + 9 * q^38 - 3 * q^41 - 6 * q^43 - 30 * q^47 - 15 * q^49 - 3 * q^50 - 6 * q^52 - 24 * q^53 + 18 * q^55 - 12 * q^56 + 24 * q^58 + 3 * q^59 + 6 * q^61 - 18 * q^62 - 3 * q^64 - 12 * q^65 - 9 * q^67 + 3 * q^68 - 12 * q^70 + 18 * q^71 - 30 * q^73 + 18 * q^74 - 6 * q^76 + 12 * q^77 + 6 * q^79 + 3 * q^82 + 6 * q^83 - 24 * q^85 - 12 * q^86 - 6 * q^88 - 12 * q^91 - 6 * q^92 - 12 * q^94 + 3 * q^97

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