LMFDB - Embedded newform 675.2.y.a.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(19,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 27]))

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

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

chi := DirichletCharacter("675.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.y (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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	675.19
Dual form			675.2.y.a.604.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119971 - 0.564417i) q^{2} +(1.52292 + 0.678046i) q^{4} +(2.21766 - 0.286312i) q^{5} +(-3.44219 - 1.98735i) q^{7} +(1.24374 - 1.71186i) q^{8} +O(q^{10})$	\(q+(0.119971 - 0.564417i) q^{2} +(1.52292 + 0.678046i) q^{4} +(2.21766 - 0.286312i) q^{5} +(-3.44219 - 1.98735i) q^{7} +(1.24374 - 1.71186i) q^{8} +(0.104455 - 1.28604i) q^{10} +(3.70374 + 0.787255i) q^{11} +(-0.326987 - 1.53835i) q^{13} +(-1.53465 + 1.70441i) q^{14} +(1.41394 + 1.57034i) q^{16} +(2.58890 - 3.56332i) q^{17} +(-5.39444 - 3.91929i) q^{19} +(3.57145 + 1.06765i) q^{20} +(0.888681 - 1.99601i) q^{22} +(-0.0622737 - 0.0560715i) q^{23} +(4.83605 - 1.26989i) q^{25} -0.907503 q^{26} +(-3.89465 - 5.36053i) q^{28} +(0.460792 + 4.38415i) q^{29} +(-0.869869 + 8.27625i) q^{31} +(4.72094 - 2.72564i) q^{32} +(-1.70061 - 1.88872i) q^{34} +(-8.20261 - 3.42173i) q^{35} +(6.07159 + 1.97278i) q^{37} +(-2.85929 + 2.57451i) q^{38} +(2.26807 - 4.15243i) q^{40} +(3.17329 - 0.674503i) q^{41} +(3.86343 + 2.23055i) q^{43} +(5.10670 + 3.71023i) q^{44} +(-0.0391187 + 0.0284214i) q^{46} +(-4.52055 + 0.475129i) q^{47} +(4.39910 + 7.61946i) q^{49} +(-0.136562 - 2.88190i) q^{50} +(0.545101 - 2.56450i) q^{52} +(-1.75963 - 2.42193i) q^{53} +(8.43905 + 0.685440i) q^{55} +(-7.68326 + 3.42081i) q^{56} +(2.52977 + 0.265890i) q^{58} +(-8.99567 + 1.91209i) q^{59} +(-6.13333 - 1.30368i) q^{61} +(4.56690 + 1.48388i) q^{62} +(0.333946 + 1.02778i) q^{64} +(-1.16560 - 3.31793i) q^{65} +(-5.80254 - 0.609871i) q^{67} +(6.35878 - 3.67125i) q^{68} +(-2.91535 + 4.21919i) q^{70} +(11.3688 - 8.25994i) q^{71} +(-7.89126 + 2.56403i) q^{73} +(1.84188 - 3.19023i) q^{74} +(-5.55782 - 9.62643i) q^{76} +(-11.1844 - 10.0705i) q^{77} +(-1.28423 - 12.2187i) q^{79} +(3.58525 + 3.07766i) q^{80} -1.87198i q^{82} +(4.97724 + 11.1791i) q^{83} +(4.72110 - 8.64348i) q^{85} +(1.72246 - 1.91299i) q^{86} +(5.95417 - 5.36116i) q^{88} +(2.49240 + 7.67081i) q^{89} +(-1.93169 + 5.94514i) q^{91} +(-0.0568186 - 0.127617i) q^{92} +(-0.274162 + 2.60848i) q^{94} +(-13.0852 - 7.14716i) q^{95} +(-7.12501 + 0.748868i) q^{97} +(4.82832 - 1.56882i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	$ 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) $ 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.119971	−	0.564417i	0.0848320	−	0.399103i	−0.915160	−	0.403091i	$-0.867936\pi$
$2$	0.119971	−	0.564417i	0.0848320	−	0.399103i	0.999992	+	0.00398740i	$0.00126923\pi$
$3$		0			0
$3$		0			0
$4$	1.52292	+	0.678046i	0.761458	+	0.339023i
$5$	2.21766	−	0.286312i	0.991769	−	0.128043i
$5$	2.21766	−	0.286312i	0.991769	−	0.128043i
$6$		0			0
$7$	−3.44219	−	1.98735i	−1.30102	−	0.751147i	−0.320444	−	0.947267i	$-0.603832\pi$
$7$	−3.44219	−	1.98735i	−1.30102	−	0.751147i	−0.980580	+	0.196121i	$0.937166\pi$
$8$	1.24374	−	1.71186i	0.439729	−	0.605235i
$9$		0			0
$10$	0.104455	−	1.28604i	0.0330316	−	0.406680i
$11$	3.70374	+	0.787255i	1.11672	+	0.237366i	0.729069	−	0.684440i	$-0.239953\pi$
$11$	3.70374	+	0.787255i	1.11672	+	0.237366i	0.387651	+	0.921806i	$0.373287\pi$
$12$		0			0
$13$	−0.326987	−	1.53835i	−0.0906899	−	0.426663i	−0.999946	−	0.0104247i	$-0.996682\pi$
$13$	−0.326987	−	1.53835i	−0.0906899	−	0.426663i	0.909256	−	0.416238i	$-0.136652\pi$
$14$	−1.53465	+	1.70441i	−0.410154	+	0.455522i
$15$		0			0
$16$	1.41394	+	1.57034i	0.353485	+	0.392585i
$17$	2.58890	−	3.56332i	0.627902	−	0.864232i	−0.369997	−	0.929033i	$-0.620641\pi$
$17$	2.58890	−	3.56332i	0.627902	−	0.864232i	0.997898	+	0.0648006i	$0.0206411\pi$
$18$		0			0
$19$	−5.39444	−	3.91929i	−1.23757	−	0.899146i	−0.240135	−	0.970740i	$-0.577192\pi$
$19$	−5.39444	−	3.91929i	−1.23757	−	0.899146i	−0.997434	+	0.0715934i	$0.977192\pi$
$20$	3.57145	+	1.06765i	0.798600	+	0.238733i
$21$		0			0
$22$	0.888681	−	1.99601i	0.189467	−	0.425551i
$23$	−0.0622737	−	0.0560715i	−0.0129850	−	0.0116917i	0.662613	−	0.748962i	$-0.269448\pi$
$23$	−0.0622737	−	0.0560715i	−0.0129850	−	0.0116917i	−0.675598	+	0.737271i	$0.736114\pi$
$24$		0			0
$25$	4.83605	−	1.26989i	0.967210	−	0.253977i
$26$	−0.907503			−0.177976
$27$		0			0
$28$	−3.89465	−	5.36053i	−0.736020	−	1.01304i
$29$	0.460792	+	4.38415i	0.0855670	+	0.814116i	0.950185	+	0.311686i	$0.100894\pi$
$29$	0.460792	+	4.38415i	0.0855670	+	0.814116i	−0.864618	+	0.502430i	$0.832440\pi$
$30$		0			0
$31$	−0.869869	+	8.27625i	−0.156233	+	1.48646i	0.582705	+	0.812684i	$0.301994\pi$
$31$	−0.869869	+	8.27625i	−0.156233	+	1.48646i	−0.738938	+	0.673774i	$0.764672\pi$
$32$	4.72094	−	2.72564i	0.834553	−	0.481829i
$33$		0			0
$34$	−1.70061	−	1.88872i	−0.291652	−	0.323912i
$35$	−8.20261	−	3.42173i	−1.38649	−	0.578377i
$36$		0			0
$37$	6.07159	+	1.97278i	0.998163	+	0.324323i	0.762131	−	0.647422i	$-0.224153\pi$
$37$	6.07159	+	1.97278i	0.998163	+	0.324323i	0.236032	+	0.971745i	$0.424153\pi$
$38$	−2.85929	+	2.57451i	−0.463838	+	0.417641i
$39$		0			0
$40$	2.26807	−	4.15243i	0.358614	−	0.656557i
$41$	3.17329	−	0.674503i	0.495584	−	0.105340i	0.0466623	−	0.998911i	$-0.485142\pi$
$41$	3.17329	−	0.674503i	0.495584	−	0.105340i	0.448922	+	0.893571i	$0.351808\pi$
$42$		0			0
$43$	3.86343	+	2.23055i	0.589167	+	0.340156i	0.764768	−	0.644305i	$-0.222853\pi$
$43$	3.86343	+	2.23055i	0.589167	+	0.340156i	−0.175601	+	0.984461i	$0.556187\pi$
$44$	5.10670	+	3.71023i	0.769864	+	0.559339i
$45$		0			0
$46$	−0.0391187	+	0.0284214i	−0.00576774	+	0.00419051i
$47$	−4.52055	+	0.475129i	−0.659390	+	0.0693047i	−0.428313	−	0.903631i	$-0.640892\pi$
$47$	−4.52055	+	0.475129i	−0.659390	+	0.0693047i	−0.231078	+	0.972935i	$0.574225\pi$
$48$		0			0
$49$	4.39910	+	7.61946i	0.628443	+	1.08849i
$50$	−0.136562	−	2.88190i	−0.0193127	−	0.407562i
$51$		0			0
$52$	0.545101	−	2.56450i	0.0755919	−	0.355632i
$53$	−1.75963	−	2.42193i	−0.241704	−	0.332677i	0.670880	−	0.741566i	$-0.265916\pi$
$53$	−1.75963	−	2.42193i	−0.241704	−	0.332677i	−0.912584	+	0.408889i	$0.865916\pi$
$54$		0			0
$55$	8.43905	+	0.685440i	1.13792	+	0.0924247i
$56$	−7.68326	+	3.42081i	−1.02672	+	0.457125i
$57$		0			0
$58$	2.52977	+	0.265890i	0.332175	+	0.0349130i
$59$	−8.99567	+	1.91209i	−1.17114	+	0.248933i	−0.752108	−	0.659040i	$-0.770963\pi$
$59$	−8.99567	+	1.91209i	−1.17114	+	0.248933i	−0.419029	+	0.907973i	$0.637629\pi$
$60$		0			0
$61$	−6.13333	−	1.30368i	−0.785293	−	0.166919i	−0.202221	−	0.979340i	$-0.564816\pi$
$61$	−6.13333	−	1.30368i	−0.785293	−	0.166919i	−0.583072	+	0.812421i	$0.698149\pi$
$62$	4.56690	+	1.48388i	0.579997	+	0.188452i
$63$		0			0
$64$	0.333946	+	1.02778i	0.0417433	+	0.128473i
$65$	−1.16560	−	3.31793i	−0.144574	−	0.411538i
$66$		0			0
$67$	−5.80254	−	0.609871i	−0.708893	−	0.0745076i	−0.256782	−	0.966469i	$-0.582662\pi$
$67$	−5.80254	−	0.609871i	−0.708893	−	0.0745076i	−0.452111	+	0.891962i	$0.649329\pi$
$68$	6.35878	−	3.67125i	0.771116	−	0.445204i
$69$		0			0
$70$	−2.91535	+	4.21919i	−0.348451	+	0.504289i
$71$	11.3688	−	8.25994i	1.34923	−	0.980275i	0.350183	−	0.936681i	$-0.386119\pi$
$71$	11.3688	−	8.25994i	1.34923	−	0.980275i	0.999049	−	0.0435934i	$-0.0138806\pi$
$72$		0			0
$73$	−7.89126	+	2.56403i	−0.923602	+	0.300097i	−0.731944	−	0.681365i	$-0.761387\pi$
$73$	−7.89126	+	2.56403i	−0.923602	+	0.300097i	−0.191659	+	0.981462i	$0.561387\pi$
$74$	1.84188	−	3.19023i	0.214115	−	0.370857i
$75$		0			0
$76$	−5.55782	−	9.62643i	−0.637526	−	1.10423i
$77$	−11.1844	−	10.0705i	−1.27458	−	1.14764i
$78$		0			0
$79$	−1.28423	−	12.2187i	−0.144487	−	1.37471i	−0.791006	−	0.611808i	$-0.790442\pi$
$79$	−1.28423	−	12.2187i	−0.144487	−	1.37471i	0.646519	−	0.762898i	$-0.276224\pi$
$80$	3.58525	+	3.07766i	0.400843	+	0.344093i
$81$		0			0
$82$		−	1.87198i		−	0.206725i
$83$	4.97724	+	11.1791i	0.546323	+	1.22706i	0.950026	+	0.312171i	$0.101056\pi$
$83$	4.97724	+	11.1791i	0.546323	+	1.22706i	−0.403703	+	0.914890i	$0.632277\pi$
$84$		0			0
$85$	4.72110	−	8.64348i	0.512075	−	0.937517i
$86$	1.72246	−	1.91299i	0.185738	−	0.206283i
$87$		0			0
$88$	5.95417	−	5.36116i	0.634717	−	0.571502i
$89$	2.49240	+	7.67081i	0.264193	+	0.813104i	0.991878	+	0.127192i	$0.0405964\pi$
$89$	2.49240	+	7.67081i	0.264193	+	0.813104i	−0.727685	+	0.685912i	$0.759404\pi$
$90$		0			0
$91$	−1.93169	+	5.94514i	−0.202496	+	0.623220i
$92$	−0.0568186	−	0.127617i	−0.00592375	−	0.0133050i
$93$		0			0
$94$	−0.274162	+	2.60848i	−0.0282777	+	0.269044i
$95$	−13.0852	−	7.14716i	−1.34251	−	0.733284i
$96$		0			0
$97$	−7.12501	+	0.748868i	−0.723435	+	0.0760361i	−0.459087	−	0.888391i	$-0.651823\pi$
$97$	−7.12501	+	0.748868i	−0.723435	+	0.0760361i	−0.264348	+	0.964427i	$0.585157\pi$
$98$	4.82832	−	1.56882i	0.487734	−	0.158474i
$99$		0			0
$100$	8.22595	+	1.34514i	0.822595	+	0.134514i
$101$	0.954257	−	1.65282i	0.0949521	−	0.164462i	−0.814637	−	0.579972i	$-0.803064\pi$
$101$	0.954257	−	1.65282i	0.0949521	−	0.164462i	0.909589	+	0.415510i	$0.136397\pi$
$102$		0			0
$103$	−2.97736	+	6.68727i	−0.293368	+	0.658916i	−0.998754	−	0.0499079i	$-0.984107\pi$
$103$	−2.97736	+	6.68727i	−0.293368	+	0.658916i	0.705386	+	0.708824i	$0.250774\pi$
$104$	−3.04014	−	1.35356i	−0.298110	−	0.132727i
$105$		0			0
$106$	−1.57808	+	0.702607i	−0.153277	+	0.0682432i
$107$			2.89008i			0.279395i	0.990194	+	0.139697i	$0.0446130\pi$
$107$			2.89008i			0.279395i	−0.990194	+	0.139697i	$0.955387\pi$
$108$		0			0
$109$	0.524408	−	1.61396i	0.0502292	−	0.154590i	−0.922796	−	0.385290i	$-0.874102\pi$
$109$	0.524408	−	1.61396i	0.0502292	−	0.154590i	0.973025	+	0.230700i	$0.0741016\pi$
$110$	1.39931	−	4.68091i	0.133419	−	0.446308i
$111$		0			0
$112$	−1.74624	−	8.21540i	−0.165004	−	0.776283i
$113$	1.86854	+	8.79081i	0.175778	+	0.826970i	0.974344	+	0.225063i	$0.0722588\pi$
$113$	1.86854	+	8.79081i	0.175778	+	0.826970i	−0.798566	+	0.601907i	$0.794408\pi$
$114$		0			0
$115$	−0.154156	−	0.106518i	−0.0143751	−	0.00993285i
$116$	−2.27091	+	6.98913i	−0.210848	+	0.648924i
$117$		0			0
$118$			5.30671i			0.488522i
$119$	−15.9931	+	7.12057i	−1.46608	+	0.652741i
$120$		0			0
$121$	3.04894	+	1.35747i	0.277176	+	0.123407i
$122$	−1.47164	+	3.30536i	−0.133236	+	0.299253i
$123$		0			0
$124$	−6.93642	+	12.0142i	−0.622909	+	1.07891i
$125$	10.3611	−	4.20080i	0.926729	−	0.375731i
$126$		0			0
$127$	−12.2527	+	3.98114i	−1.08725	+	0.353269i	−0.797183	−	0.603738i	$-0.793677\pi$
$127$	−12.2527	+	3.98114i	−1.08725	+	0.353269i	−0.290066	+	0.957007i	$0.593677\pi$
$128$	11.4630	−	1.20481i	1.01319	−	0.106491i
$129$		0			0
$130$	−2.01253	+	0.259829i	−0.176511	+	0.0227885i
$131$	−1.99635	+	18.9940i	−0.174422	+	1.65952i	0.461036	+	0.887382i	$0.347478\pi$
$131$	−1.99635	+	18.9940i	−0.174422	+	1.65952i	−0.635458	+	0.772135i	$0.719189\pi$
$132$		0			0
$133$	10.7797	+	24.2115i	0.934716	+	2.09941i
$134$	−1.04036	+	3.20189i	−0.0898731	+	0.276601i
$135$		0			0
$136$	−2.87999	−	8.86371i	−0.246957	−	0.760057i
$137$	−4.91618	+	4.42654i	−0.420017	+	0.378185i	−0.851865	−	0.523761i	$-0.824528\pi$
$137$	−4.91618	+	4.42654i	−0.420017	+	0.378185i	0.431848	+	0.901946i	$0.357862\pi$
$138$		0			0
$139$	−3.08371	+	3.42481i	−0.261557	+	0.290489i	−0.859591	−	0.510982i	$-0.829282\pi$
$139$	−3.08371	+	3.42481i	−0.261557	+	0.290489i	0.598034	+	0.801470i	$0.295949\pi$
$140$	−10.1718	−	10.7728i	−0.859674	−	0.910464i
$141$		0			0
$142$	−3.29813	−	7.40772i	−0.276773	−	0.621642i
$143$		−	5.95509i		−	0.497990i
$144$		0			0
$145$	2.27711	+	9.59063i	0.189104	+	0.796458i
$146$	0.500462	+	4.76157i	0.0414185	+	0.394071i
$147$		0			0
$148$	7.90889	+	7.12120i	0.650107	+	0.585359i
$149$	−0.629430	−	1.09020i	−0.0515649	−	0.0893130i	0.839091	−	0.543991i	$-0.183088\pi$
$149$	−0.629430	−	1.09020i	−0.0515649	−	0.0893130i	−0.890656	+	0.454678i	$0.849754\pi$
$150$		0			0
$151$	−10.9968	+	19.0470i	−0.894905	+	1.55002i	−0.0609823	+	0.998139i	$0.519423\pi$
$151$	−10.9968	+	19.0470i	−0.894905	+	1.55002i	−0.833922	+	0.551882i	$0.813910\pi$
$152$	−13.4186	+	4.35996i	−1.08839	+	0.353639i
$153$		0			0
$154$	−7.02577	+	5.10452i	−0.566152	+	0.411334i
$155$	0.440513	+	18.6030i	0.0353828	+	1.49423i
$156$		0			0
$157$	−6.49560	+	3.75024i	−0.518405	+	0.299301i	−0.736282	−	0.676675i	$-0.763420\pi$
$157$	−6.49560	+	3.75024i	−0.518405	+	0.299301i	0.217877	+	0.975976i	$0.430087\pi$
$158$	−7.05049	−	0.741037i	−0.560907	−	0.0589537i
$159$		0			0
$160$	9.68908	−	7.39621i	0.765989	−	0.584722i
$161$	0.102924	+	0.316768i	0.00811156	+	0.0249648i
$162$		0			0
$163$	2.64517	+	0.859468i	0.207186	+	0.0673187i	0.410771	−	0.911738i	$-0.365259\pi$
$163$	2.64517	+	0.859468i	0.207186	+	0.0673187i	−0.203585	+	0.979057i	$0.565259\pi$
$164$	5.29000	+	1.12442i	0.413079	+	0.0878027i
$165$		0			0
$166$	6.90678	−	1.46808i	0.536070	−	0.113945i
$167$	−17.0556	−	1.79262i	−1.31980	−	0.138717i	−0.581698	−	0.813405i	$-0.697612\pi$
$167$	−17.0556	−	1.79262i	−1.31980	−	0.138717i	−0.738103	+	0.674688i	$0.764278\pi$
$168$		0			0
$169$	9.61648	−	4.28153i	0.739729	−	0.329349i
$170$	−4.31214	−	3.70163i	−0.330726	−	0.283902i
$171$		0			0
$172$	4.37126	+	6.01653i	0.333306	+	0.458756i
$173$	3.06460	−	14.4178i	0.232997	−	1.09617i	−0.693673	−	0.720290i	$-0.744009\pi$
$173$	3.06460	−	14.4178i	0.232997	−	1.09617i	0.926670	−	0.375876i	$-0.122658\pi$
$174$		0			0
$175$	−19.1703	−	5.23973i	−1.44914	−	0.396086i
$176$	4.00062	+	6.92927i	0.301558	+	0.522314i
$177$		0			0
$178$	4.62855	−	0.486480i	0.346925	−	0.0364632i
$179$	5.93941	−	4.31523i	0.443932	−	0.322536i	−0.343263	−	0.939239i	$-0.611532\pi$
$179$	5.93941	−	4.31523i	0.443932	−	0.322536i	0.787195	+	0.616704i	$0.211532\pi$
$180$		0			0
$181$	13.0147	+	9.45570i	0.967371	+	0.702836i	0.954851	−	0.297085i	$-0.0960145\pi$
$181$	13.0147	+	9.45570i	0.967371	+	0.702836i	0.0125204	+	0.999922i	$0.496015\pi$
$182$	3.12379	+	1.80352i	0.231551	+	0.133686i
$183$		0			0
$184$	−0.173439	+	0.0368656i	−0.0127861	+	0.00271777i
$185$	14.0296	+	2.63659i	1.03147	+	0.193846i
$186$		0			0
$187$	12.3939	−	11.1595i	0.906330	−	0.816063i
$188$	−7.20659	−	2.34156i	−0.525594	−	0.170776i
$189$		0			0
$190$	−5.60382	+	6.52805i	−0.406544	+	0.473595i
$191$	−0.251974	−	0.279845i	−0.0182322	−	0.0202489i	0.733960	−	0.679193i	$-0.237670\pi$
$191$	−0.251974	−	0.279845i	−0.0182322	−	0.0202489i	−0.752192	+	0.658944i	$0.771003\pi$
$192$		0			0
$193$	−6.86408	+	3.96298i	−0.494087	+	0.285261i	−0.726268	−	0.687411i	$-0.758747\pi$
$193$	−6.86408	+	3.96298i	−0.494087	+	0.285261i	0.232181	+	0.972673i	$0.425414\pi$
$194$	−0.432117	+	4.11132i	−0.0310242	+	0.295176i
$195$		0			0
$196$	1.53311	+	14.5866i	0.109508	+	1.04190i
$197$	0.640724	+	0.881881i	0.0456497	+	0.0628314i	0.831232	−	0.555926i	$-0.187636\pi$
$197$	0.640724	+	0.881881i	0.0456497	+	0.0628314i	−0.785582	+	0.618758i	$0.787636\pi$
$198$		0			0
$199$	−9.75032			−0.691182			−0.345591	−	0.938385i	$-0.612321\pi$
$199$	−9.75032			−0.691182			−0.345591	+	0.938385i	$0.612321\pi$
$200$	3.84093	−	9.85807i	0.271595	−	0.697071i
$201$		0			0
$202$	−0.818398	−	0.736889i	−0.0575823	−	0.0518473i
$203$	7.12669	−	16.0068i	0.500195	−	1.12346i
$204$		0			0
$205$	6.84416	−	2.40437i	0.478017	−	0.167928i
$206$	3.41721	+	2.48275i	0.238089	+	0.172981i
$207$		0			0
$208$	1.95340	−	2.68862i	0.135444	−	0.186423i
$209$	−16.8941	−	18.7628i	−1.16859	−	1.29785i
$210$		0			0
$211$	8.22151	−	9.13092i	0.565992	−	0.628598i	−0.390413	−	0.920640i	$-0.627668\pi$
$211$	8.22151	−	9.13092i	0.565992	−	0.628598i	0.956406	+	0.292042i	$0.0943345\pi$
$212$	−1.03760	−	4.88150i	−0.0712624	−	0.335263i
$213$		0			0
$214$	1.63121	+	0.346725i	0.111507	+	0.0237016i
$215$	9.20641	+	3.84047i	0.627872	+	0.261918i
$216$		0			0
$217$	19.4420	−	26.7597i	1.31981	−	1.81656i
$218$	−0.848035	−	0.489613i	−0.0574362	−	0.0331608i
$219$		0			0
$220$	12.3872	+	6.76593i	0.835146	+	0.456159i
$221$	−6.32819	−	2.81749i	−0.425680	−	0.189525i
$222$		0			0
$223$	2.51865	−	11.8493i	0.168661	−	0.793488i	−0.809743	−	0.586785i	$-0.800393\pi$
$223$	2.51865	−	11.8493i	0.168661	−	0.793488i	0.978404	−	0.206703i	$-0.0662734\pi$
$224$	−21.6672			−1.44770
$225$		0			0
$226$	5.18586			0.344958
$227$	2.01619	−	9.48542i	0.133819	−	0.629569i	−0.859202	−	0.511636i	$-0.829040\pi$
$227$	2.01619	−	9.48542i	0.133819	−	0.629569i	0.993021	−	0.117933i	$-0.0376270\pi$
$228$		0			0
$229$	−8.52141	−	3.79398i	−0.563111	−	0.250713i	0.105382	−	0.994432i	$-0.466393\pi$
$229$	−8.52141	−	3.79398i	−0.563111	−	0.250713i	−0.668493	+	0.743719i	$0.733060\pi$
$230$	−0.0786147	+	0.0742293i	−0.00518370	+	0.00489453i
$231$		0			0
$232$	8.07817	+	4.66393i	0.530358	+	0.306202i
$233$	5.80504	−	7.98995i	0.380301	−	0.523439i	−0.575363	−	0.817898i	$-0.695139\pi$
$233$	5.80504	−	7.98995i	0.380301	−	0.523439i	0.955664	+	0.294459i	$0.0951394\pi$
$234$		0			0
$235$	−9.88902	+	2.34796i	−0.645089	+	0.153164i
$236$	−14.9961	−	3.18753i	−0.976165	−	0.207490i
$237$		0			0
$238$	2.10027	+	9.88101i	0.136141	+	0.640491i
$239$	−4.46389	+	4.95765i	−0.288745	+	0.320684i	−0.870013	−	0.493028i	$-0.835890\pi$
$239$	−4.46389	+	4.95765i	−0.288745	+	0.320684i	0.581268	+	0.813712i	$0.302557\pi$
$240$		0			0
$241$	3.01817	+	3.35202i	0.194417	+	0.215922i	0.832470	−	0.554071i	$-0.186926\pi$
$241$	3.01817	+	3.35202i	0.194417	+	0.215922i	−0.638052	+	0.769993i	$0.720260\pi$
$242$	1.13197	−	1.55802i	0.0727655	−	0.100153i
$243$		0			0
$244$	−8.45660	−	6.14408i	−0.541378	−	0.393334i
$245$	11.9373	+	15.6379i	0.762643	+	0.999068i
$246$		0			0
$247$	−4.26534	+	9.58011i	−0.271397	+	0.609568i
$248$	13.0859	+	11.7826i	0.830957	+	0.748197i
$249$		0			0
$250$	−1.12797	−	6.35198i	−0.0713390	−	0.401735i
$251$	1.58877			0.100283			0.0501413	−	0.998742i	$-0.484033\pi$
$251$	1.58877			0.100283			0.0501413	+	0.998742i	$0.484033\pi$
$252$		0			0
$253$	−0.186503	−	0.256700i	−0.0117254	−	0.0161386i
$254$	0.777061	+	7.39324i	0.0487571	+	0.463893i
$255$		0			0
$256$	0.469285	−	4.46495i	0.0293303	−	0.279059i
$257$	−24.3360	+	14.0504i	−1.51804	+	0.876440i	−0.518264	+	0.855221i	$0.673422\pi$
$257$	−24.3360	+	14.0504i	−1.51804	+	0.876440i	−0.999775	+	0.0212197i	$0.993245\pi$
$258$		0			0
$259$	−16.9789	−	18.8570i	−1.05502	−	1.17172i
$260$	0.474603	−	5.84326i	0.0294337	−	0.362384i
$261$		0			0
$262$	10.4811	+	3.40550i	0.647522	+	0.210393i
$263$	−15.7064	+	14.1421i	−0.968495	+	0.872037i	−0.991814	−	0.127691i	$-0.959243\pi$
$263$	−15.7064	+	14.1421i	−0.968495	+	0.872037i	0.0233186	+	0.999728i	$0.492577\pi$
$264$		0			0
$265$	−4.59570	−	4.86721i	−0.282311	−	0.298990i
$266$	14.9587	−	3.17956i	0.917174	−	0.194951i
$267$		0			0
$268$	−8.42326	−	4.86317i	−0.514533	−	0.297066i
$269$	8.75136	+	6.35824i	0.533580	+	0.387669i	0.821695	−	0.569927i	$-0.193029\pi$
$269$	8.75136	+	6.35824i	0.533580	+	0.387669i	−0.288115	+	0.957596i	$0.593029\pi$
$270$		0			0
$271$	0.215924	−	0.156878i	0.0131165	−	0.00952967i	−0.581208	−	0.813755i	$-0.697420\pi$
$271$	0.215924	−	0.156878i	0.0131165	−	0.00952967i	0.594324	+	0.804226i	$0.297420\pi$
$272$	9.25619	−	0.972865i	0.561239	−	0.0589886i
$273$		0			0
$274$	1.90862	+	3.30583i	0.115304	+	0.199712i
$275$	18.9112	−	0.896125i	1.14039	−	0.0540384i
$276$		0			0
$277$	−2.69919	+	12.6987i	−0.162179	+	0.762990i	0.819596	+	0.572942i	$0.194198\pi$
$277$	−2.69919	+	12.6987i	−0.162179	+	0.762990i	−0.981775	+	0.190048i	$0.939135\pi$
$278$	1.56307	+	2.15138i	0.0937465	+	0.129031i
$279$		0			0
$280$	−16.0595	+	9.78600i	−0.959736	+	0.584826i
$281$	16.4071	−	7.30490i	0.978765	−	0.435774i	0.145929	−	0.989295i	$-0.453383\pi$
$281$	16.4071	−	7.30490i	0.978765	−	0.435774i	0.832835	+	0.553521i	$0.186716\pi$
$282$		0			0
$283$	24.7026	+	2.59634i	1.46841	+	0.154337i	0.804714	−	0.593662i	$-0.202318\pi$
$283$	24.7026	+	2.59634i	1.46841	+	0.154337i	0.663700	+	0.747999i	$0.268985\pi$
$284$	22.9144	−	4.87061i	1.35972	−	0.289017i
$285$		0			0
$286$	−3.36116	−	0.714436i	−0.198749	−	0.0422455i
$287$	−12.2635	−	3.98466i	−0.723892	−	0.235207i
$288$		0			0
$289$	−0.741545	−	2.28224i	−0.0436203	−	0.134249i
$290$	5.68630	−	0.134650i	0.333911	−	0.00790691i
$291$		0			0
$292$	−13.7563	−	1.44584i	−0.805025	−	0.0846115i
$293$	2.62262	−	1.51417i	0.153215	−	0.0884587i	−0.421432	−	0.906860i	$-0.638473\pi$
$293$	2.62262	−	1.51417i	0.153215	−	0.0884587i	0.574647	+	0.818401i	$0.305139\pi$
$294$		0			0
$295$	−19.4019	+	6.81593i	−1.12962	+	0.396839i
$296$	10.9286	−	7.94011i	0.635213	−	0.461509i
$297$		0			0
$298$	−0.690843	+	0.224469i	−0.0400195	+	0.0130031i
$299$	−0.0658951	+	0.114134i	−0.00381081	+	0.00660052i
$300$		0			0
$301$	−8.86576	−	15.3560i	−0.511014	−	0.885102i
$302$	9.43115	+	8.49185i	0.542702	+	0.488651i
$303$		0			0
$304$	−1.47280	−	14.0128i	−0.0844708	−	0.803686i
$305$	−13.9749	−	1.13508i	−0.800201	−	0.0649943i
$306$		0			0
$307$		−	19.0789i		−	1.08889i	−0.838797	−	0.544445i	$-0.816740\pi$
$307$		−	19.0789i		−	1.08889i	0.838797	−	0.544445i	$-0.183260\pi$
$308$	−10.2047	−	22.9201i	−0.581466	−	1.30599i
$309$		0			0
$310$	10.5527	+	1.98318i	0.599353	+	0.112637i
$311$	7.34268	−	8.15487i	0.416365	−	0.462420i	−0.498080	−	0.867131i	$-0.665961\pi$
$311$	7.34268	−	8.15487i	0.416365	−	0.462420i	0.914445	+	0.404711i	$0.132628\pi$
$312$		0			0
$313$	5.79703	−	5.21967i	0.327668	−	0.295033i	−0.488833	−	0.872377i	$-0.662577\pi$
$313$	5.79703	−	5.21967i	0.327668	−	0.295033i	0.816501	+	0.577344i	$0.195911\pi$
$314$	1.33742	+	4.11615i	0.0754748	+	0.232288i
$315$		0			0
$316$	6.32904	−	19.4788i	0.356036	−	1.09577i
$317$	−2.29289	−	5.14991i	−0.128781	−	0.289248i	0.837634	−	0.546231i	$-0.183938\pi$
$317$	−2.29289	−	5.14991i	−0.128781	−	0.289248i	−0.966416	+	0.256984i	$0.917271\pi$
$318$		0			0
$319$	−1.74478	+	16.6005i	−0.0976891	+	0.929450i
$320$	1.03485	+	2.18366i	0.0578496	+	0.122070i
$321$		0			0
$322$	0.191137	−	0.0200893i	0.0106517	−	0.00111953i
$323$	−27.9314	+	9.07545i	−1.55414	+	0.504972i
$324$		0			0
$325$	−3.53486	−	7.02432i	−0.196079	−	0.389639i
$326$	0.802441	−	1.38987i	0.0444431	−	0.0769777i
$327$		0			0
$328$	2.79209	−	6.27114i	0.154168	−	0.346266i
$329$	16.5048	+	7.34842i	0.909941	+	0.405132i
$330$		0			0
$331$	−29.4203	+	13.0988i	−1.61709	+	0.719974i	−0.997869	−	0.0652449i	$-0.979217\pi$
$331$	−29.4203	+	13.0988i	−1.61709	+	0.719974i	−0.619218	+	0.785219i	$0.712550\pi$
$332$			20.3996i			1.11957i
$333$		0			0
$334$	−3.05795	+	9.41141i	−0.167324	+	0.514970i
$335$	−13.0427	+	0.308847i	−0.712598	+	0.0168741i
$336$		0			0
$337$	−4.30314	−	20.2447i	−0.234407	−	1.10280i	−0.925121	−	0.379671i	$-0.876037\pi$
$337$	−4.30314	−	20.2447i	−0.234407	−	1.10280i	0.690714	−	0.723128i	$-0.257296\pi$
$338$	−1.26288	−	5.94137i	−0.0686914	−	0.323168i
$339$		0			0
$340$	13.0505	−	9.96218i	0.707763	−	0.540275i
$341$	−9.73728	+	29.9683i	−0.527304	+	1.62287i
$342$		0			0
$343$		−	7.14729i		−	0.385917i
$344$	8.62351	−	3.83943i	0.464949	−	0.207008i
$345$		0			0
$346$	−7.77001	−	3.45943i	−0.417718	−	0.185980i
$347$	10.7538	−	24.1534i	0.577293	−	1.29662i	−0.354983	−	0.934873i	$-0.615513\pi$
$347$	10.7538	−	24.1534i	0.577293	−	1.29662i	0.932276	−	0.361749i	$-0.117820\pi$
$348$		0			0
$349$	−8.19419	+	14.1928i	−0.438625	+	0.759721i	−0.997584	−	0.0694745i	$-0.977868\pi$
$349$	−8.19419	+	14.1928i	−0.438625	+	0.759721i	0.558959	+	0.829196i	$0.311201\pi$
$350$	−5.25727	+	10.1914i	−0.281013	+	0.544755i
$351$		0			0
$352$	19.6309	−	6.37848i	1.04633	−	0.339974i
$353$	13.9339	−	1.46451i	0.741628	−	0.0779482i	0.273823	−	0.961780i	$-0.411712\pi$
$353$	13.9339	−	1.46451i	0.741628	−	0.0779482i	0.467805	+	0.883832i	$0.345045\pi$
$354$		0			0
$355$	22.8473	−	21.5728i	1.21261	−	1.14496i
$356$	−1.40545	+	13.3720i	−0.0744887	+	0.708712i
$357$		0			0
$358$	−1.72304	−	3.87001i	−0.0910654	−	0.204536i
$359$	8.88728	−	27.3522i	0.469053	−	1.44360i	−0.384761	−	0.923016i	$-0.625716\pi$
$359$	8.88728	−	27.3522i	0.469053	−	1.44360i	0.853813	−	0.520579i	$-0.174284\pi$
$360$		0			0
$361$	7.86781	+	24.2146i	0.414095	+	1.27445i
$362$	6.89834	−	6.21129i	0.362568	−	0.326458i
$363$		0			0
$364$	−6.97289	+	7.74417i	−0.365479	+	0.405905i
$365$	−16.7660	+	7.94551i	−0.877575	+	0.415887i
$366$		0			0
$367$	8.50915	+	19.1119i	0.444174	+	0.997632i	0.987429	+	0.158064i	$0.0505251\pi$
$367$	8.50915	+	19.1119i	0.444174	+	0.997632i	−0.543255	+	0.839568i	$0.682808\pi$
$368$		−	0.177073i		−	0.00923056i
$369$		0			0
$370$	3.17127	−	7.60222i	0.164867	−	0.395220i
$371$	1.24377	+	11.8337i	0.0645735	+	0.614376i
$372$		0			0
$373$	−8.23671	−	7.41637i	−0.426481	−	0.384005i	0.427752	−	0.903896i	$-0.359306\pi$
$373$	−8.23671	−	7.41637i	−0.426481	−	0.384005i	−0.854232	+	0.519891i	$0.825972\pi$
$374$	−4.81171	−	8.33413i	−0.248808	−	0.430948i
$375$		0			0
$376$	−4.80904	+	8.32951i	−0.248008	+	0.429562i
$377$	6.59370	−	2.14242i	0.339593	−	0.110340i
$378$		0			0
$379$	21.6625	−	15.7387i	1.11273	−	0.808445i	0.129637	−	0.991561i	$-0.458619\pi$
$379$	21.6625	−	15.7387i	1.11273	−	0.808445i	0.983091	+	0.183117i	$0.0586187\pi$
$380$	−15.0815	−	19.7569i	−0.773666	−	1.01351i
$381$		0			0
$382$	−0.188179	+	0.108645i	−0.00962808	+	0.00555877i
$383$	0.535397	+	0.0562724i	0.0273575	+	0.00287539i	0.118197	−	0.992990i	$-0.462288\pi$
$383$	0.535397	+	0.0562724i	0.0273575	+	0.00287539i	−0.0908398	+	0.995866i	$0.528955\pi$
$384$		0			0
$385$	−27.6866	−	19.1307i	−1.41104	−	0.974993i
$386$	1.41329	+	4.34965i	0.0719343	+	0.221391i
$387$		0			0
$388$	−11.3586	−	3.69062i	−0.576644	−	0.187363i
$389$	32.5642	+	6.92173i	1.65107	+	0.350946i	0.937054	−	0.349185i	$-0.113541\pi$
$389$	32.5642	+	6.92173i	1.65107	+	0.350946i	0.714015	+	0.700130i	$0.246875\pi$
$390$		0			0
$391$	−0.361021	+	0.0767375i	−0.0182576	+	0.00388078i
$392$	18.5148	+	1.94599i	0.935140	+	0.0982872i
$393$		0			0
$394$	0.574617	−	0.255836i	0.0289488	−	0.0128888i
$395$	−6.34634	−	26.7292i	−0.319319	−	1.34489i
$396$		0			0
$397$	−14.9827	−	20.6220i	−0.751962	−	1.03499i	−0.997840	−	0.0656864i	$-0.979076\pi$
$397$	−14.9827	−	20.6220i	−0.751962	−	1.03499i	0.245878	−	0.969301i	$-0.420924\pi$
$398$	−1.16975	+	5.50325i	−0.0586344	+	0.275853i
$399$		0			0
$400$	8.83205	+	5.79871i	0.441602	+	0.289935i
$401$	2.20470	+	3.81866i	0.110098	+	0.190695i	0.915809	−	0.401613i	$-0.131550\pi$
$401$	2.20470	+	3.81866i	0.110098	+	0.190695i	−0.805712	+	0.592308i	$0.798217\pi$
$402$		0			0
$403$	13.0162	−	1.36806i	0.648385	−	0.0681480i
$404$	2.57394	−	1.87008i	0.128058	−	0.0930399i
$405$		0			0
$406$	−8.17953	−	5.94277i	−0.405943	−	0.294935i
$407$	20.9345	+	12.0866i	1.03769	+	0.599108i
$408$		0			0
$409$	19.1074	−	4.06140i	0.944800	−	0.200824i	0.290343	−	0.956923i	$-0.406231\pi$
$409$	19.1074	−	4.06140i	0.944800	−	0.200824i	0.654457	+	0.756099i	$0.272897\pi$
$410$	−0.535970	−	4.15142i	−0.0264696	−	0.205024i
$411$		0			0
$412$	−9.06855	+	8.16536i	−0.446776	+	0.402278i
$413$	34.7647	+	11.2958i	1.71066	+	0.555828i
$414$		0			0
$415$	14.2385	+	23.3663i	0.698942	+	1.14701i
$416$	−5.73669	−	6.37124i	−0.281264	−	0.312376i
$417$		0			0
$418$	−12.6169	+	7.28435i	−0.617111	+	0.356289i
$419$	−0.0914298	+	0.869897i	−0.00446664	+	0.0424972i	−0.996528	−	0.0832560i	$-0.973468\pi$
$419$	−0.0914298	+	0.869897i	−0.00446664	+	0.0424972i	0.992062	+	0.125753i	$0.0401348\pi$
$420$		0			0
$421$	−3.57646	−	34.0277i	−0.174306	−	1.65841i	−0.636236	−	0.771494i	$-0.719510\pi$
$421$	−3.57646	−	34.0277i	−0.174306	−	1.65841i	0.461930	−	0.886916i	$-0.347157\pi$
$422$	−4.16731	−	5.73581i	−0.202861	−	0.279215i
$423$		0			0
$424$	−6.33454			−0.307632
$425$	7.99506	−	20.5200i	0.387818	−	0.995367i
$426$		0			0
$427$	18.5212	+	16.6766i	0.896304	+	0.807036i
$428$	−1.95961	+	4.40136i	−0.0947213	+	0.212748i
$429$		0			0
$430$	3.27212	−	4.73552i	0.157796	−	0.228367i
$431$	−24.1797	−	17.5676i	−1.16470	−	0.846201i	−0.174332	−	0.984687i	$-0.555777\pi$
$431$	−24.1797	−	17.5676i	−1.16470	−	0.846201i	−0.990364	+	0.138486i	$0.955777\pi$
$432$		0			0
$433$	1.94879	−	2.68228i	0.0936530	−	0.128902i	−0.759619	−	0.650368i	$-0.774615\pi$
$433$	1.94879	−	2.68228i	0.0936530	−	0.128902i	0.853272	+	0.521466i	$0.174615\pi$
$434$	−12.7711	−	14.1838i	−0.613034	−	0.680844i
$435$		0			0
$436$	1.89297	−	2.10236i	0.0906569	−	0.100685i
$437$	0.116171	+	0.546543i	0.00555722	+	0.0261447i
$438$		0			0
$439$	18.9635	+	4.03081i	0.905076	+	0.192380i	0.636861	−	0.770979i	$-0.280233\pi$
$439$	18.9635	+	4.03081i	0.905076	+	0.192380i	0.268216	+	0.963359i	$0.413566\pi$
$440$	11.6694	−	13.5940i	0.556316	−	0.648068i
$441$		0			0
$442$	−2.34944	+	3.23372i	−0.111751	+	0.153813i
$443$	26.9071	+	15.5348i	1.27839	+	0.738081i	0.976553	−	0.215277i	$-0.0690653\pi$
$443$	26.9071	+	15.5348i	1.27839	+	0.738081i	0.301841	+	0.953358i	$0.402399\pi$
$444$		0			0
$445$	7.72353	+	16.2977i	0.366131	+	0.772583i
$446$	−6.38579	−	2.84314i	−0.302376	−	0.134626i
$447$		0			0
$448$	0.893052	−	4.20148i	0.0421928	−	0.198501i
$449$	−22.5328			−1.06339			−0.531694	−	0.846936i	$-0.678444\pi$
$449$	−22.5328			−1.06339			−0.531694	+	0.846936i	$0.678444\pi$
$450$		0			0
$451$	12.2840			0.578433
$452$	−3.11494	+	14.6546i	−0.146514	+	0.689296i
$453$		0			0
$454$	−5.11185	−	2.27594i	−0.239911	−	0.106815i
$455$	−2.58168	+	13.7374i	−0.121031	+	0.644018i
$456$		0			0
$457$	36.6544	+	21.1624i	1.71462	+	0.989936i	0.928067	+	0.372412i	$0.121469\pi$
$457$	36.6544	+	21.1624i	1.71462	+	0.989936i	0.786552	+	0.617524i	$0.211864\pi$
$458$	−3.16370	+	4.35447i	−0.147830	+	0.203471i
$459$		0			0
$460$	−0.162543	−	0.266743i	−0.00757859	−	0.0124369i
$461$	−5.83902	−	1.24112i	−0.271950	−	0.0578049i	0.0699177	−	0.997553i	$-0.477726\pi$
$461$	−5.83902	−	1.24112i	−0.271950	−	0.0578049i	−0.341868	+	0.939748i	$0.611060\pi$
$462$		0			0
$463$	−5.80209	−	27.2967i	−0.269646	−	1.26858i	−0.879434	−	0.476020i	$-0.842079\pi$
$463$	−5.80209	−	27.2967i	−0.269646	−	1.26858i	0.609789	−	0.792564i	$-0.291254\pi$
$464$	−6.23307	+	6.92253i	−0.289363	+	0.321370i
$465$		0			0
$466$	−3.81323	−	4.23502i	−0.176645	−	0.196184i
$467$	18.8801	−	25.9862i	0.873666	−	1.20250i	−0.104469	−	0.994528i	$-0.533314\pi$
$467$	18.8801	−	25.9862i	0.873666	−	1.20250i	0.978135	−	0.207970i	$-0.0666855\pi$
$468$		0			0
$469$	18.7614	+	13.6309i	0.866320	+	0.629419i
$470$	0.138839	+	5.86322i	0.00640418	+	0.270450i
$471$		0			0
$472$	−7.91505	+	17.7775i	−0.364320	+	0.818276i
$473$	12.5531	+	11.3029i	0.577194	+	0.519708i
$474$		0			0
$475$	−31.0648	−	12.1036i	−1.42535	−	0.555349i
$476$	−29.1842			−1.33765
$477$		0			0
$478$	2.26265	+	3.11427i	0.103491	+	0.142443i
$479$	−3.45990	−	32.9187i	−0.158087	−	1.50410i	−0.729811	−	0.683649i	$-0.760392\pi$
$479$	−3.45990	−	32.9187i	−0.158087	−	1.50410i	0.571724	−	0.820446i	$-0.306275\pi$
$480$		0			0
$481$	1.04950	−	9.98533i	0.0478531	−	0.455292i
$482$	2.25403	−	1.30136i	0.102668	−	0.0592755i
$483$		0			0
$484$	3.72285	+	4.13464i	0.169220	+	0.187938i
$485$	−15.5864	+	3.70071i	−0.707744	+	0.168041i
$486$		0			0
$487$	−31.5524	−	10.2520i	−1.42978	−	0.464563i	−0.511083	−	0.859531i	$-0.670755\pi$
$487$	−31.5524	−	10.2520i	−1.42978	−	0.464563i	−0.918695	+	0.394969i	$0.870755\pi$
$488$	−9.86000	+	8.87799i	−0.446341	+	0.401888i
$489$		0			0
$490$	10.2584	−	4.86151i	0.463428	−	0.219621i
$491$	2.96718	−	0.630694i	0.133907	−	0.0284628i	−0.140470	−	0.990085i	$-0.544862\pi$
$491$	2.96718	−	0.630694i	0.133907	−	0.0284628i	0.274378	+	0.961622i	$0.411528\pi$
$492$		0			0
$493$	16.8151	+	9.70819i	0.757313	+	0.437235i
$494$	4.89546	+	3.55676i	0.220257	+	0.160026i
$495$		0			0
$496$	−14.2265	+	10.3361i	−0.638788	+	0.464106i
$497$	−55.5490	+	5.83844i	−2.49171	+	0.261890i
$498$		0			0
$499$	10.3387	+	17.9072i	0.462826	+	0.801638i	0.999100	−	0.0424056i	$-0.0135022\pi$
$499$	10.3387	+	17.9072i	0.462826	+	0.801638i	−0.536275	+	0.844044i	$0.680169\pi$
$500$	18.6275	+	0.627872i	0.833047	+	0.0280793i
$501$		0			0
$502$	0.190606	−	0.896732i	0.00850717	−	0.0400231i
$503$	−7.23065	−	9.95214i	−0.322399	−	0.443744i	0.616799	−	0.787121i	$-0.288429\pi$
$503$	−7.23065	−	9.95214i	−0.322399	−	0.443744i	−0.939198	+	0.343377i	$0.888429\pi$
$504$		0			0
$505$	1.64300	−	3.93862i	0.0731124	−	0.175266i
$506$	−0.167261	+	0.0744692i	−0.00743564	+	0.00331056i
$507$		0			0
$508$	−21.3592	−	2.24494i	−0.947661	−	0.0996032i
$509$	−1.17440	+	0.249627i	−0.0520545	+	0.0110645i	−0.233865	−	0.972269i	$-0.575137\pi$
$509$	−1.17440	+	0.249627i	−0.0520545	+	0.0110645i	0.181811	+	0.983334i	$0.441804\pi$
$510$		0			0
$511$	32.2588	+	6.85682i	1.42705	+	0.303328i
$512$	19.4602	+	6.32301i	0.860028	+	0.279440i
$513$		0			0
$514$	5.01069	+	15.4213i	0.221012	+	0.680205i
$515$	−4.68814	+	15.6826i	−0.206584	+	0.691056i
$516$		0			0
$517$	−17.1170	−	1.79907i	−0.752805	−	0.0791230i
$518$	−12.6802	+	7.32092i	−0.557136	+	0.321663i
$519$		0			0
$520$	−7.12954	−	2.13131i	−0.312651	−	0.0934639i
$521$	−11.7503	+	8.53706i	−0.514788	+	0.374015i	−0.814637	−	0.579971i	$-0.803064\pi$
$521$	−11.7503	+	8.53706i	−0.514788	+	0.374015i	0.299849	+	0.953987i	$0.403064\pi$
$522$		0			0
$523$	−11.8008	+	3.83432i	−0.516013	+	0.167663i	−0.555435	−	0.831560i	$-0.687448\pi$
$523$	−11.8008	+	3.83432i	−0.516013	+	0.167663i	0.0394220	+	0.999223i	$0.487448\pi$
$524$	−15.9191	+	27.5727i	−0.695430	+	1.20452i
$525$		0			0
$526$	6.09773	+	10.5616i	0.265874	+	0.460506i
$527$	27.2389	+	24.5260i	1.18655	+	1.06837i
$528$		0			0
$529$	−2.40342	−	22.8670i	−0.104497	−	0.994218i
$530$	−3.29849	+	2.00997i	−0.143277	+	0.0873075i
$531$		0			0
$532$			44.1813i			1.91550i
$533$	−2.07525	−	4.66108i	−0.0898890	−	0.201894i
$534$		0			0
$535$	0.827465	+	6.40923i	0.0357744	+	0.277095i
$536$	−8.26088	+	9.17463i	−0.356816	+	0.396284i
$537$		0			0
$538$	4.63861	−	4.17662i	0.199985	−	0.180067i
$539$	10.2947	+	31.6837i	0.443423	+	1.36472i
$540$		0			0
$541$	−3.54465	+	10.9093i	−0.152396	+	0.469027i	−0.997888	−	0.0649614i	$-0.979308\pi$
$541$	−3.54465	+	10.9093i	−0.152396	+	0.469027i	0.845492	+	0.533989i	$0.179308\pi$
$542$	−0.0626402	−	0.140692i	−0.00269063	−	0.00604324i
$543$		0			0
$544$	2.50975	−	23.8787i	0.107605	−	1.02379i
$545$	0.700864	−	3.72937i	0.0300217	−	0.159749i
$546$		0			0
$547$	−8.01796	+	0.842721i	−0.342823	+	0.0360322i	−0.274376	−	0.961623i	$-0.588471\pi$
$547$	−8.01796	+	0.842721i	−0.342823	+	0.0360322i	−0.0684474	+	0.997655i	$0.521805\pi$
$548$	−10.4883	+	3.40786i	−0.448039	+	0.145577i
$549$		0			0
$550$	1.76300	−	10.7813i	0.0751746	−	0.459717i
$551$	14.6970	−	25.4560i	0.626114	−	1.08446i
$552$		0			0
$553$	−19.8621	+	44.6111i	−0.844624	+	1.89706i
$554$	6.84354	+	3.04694i	0.290754	+	0.129452i
$555$		0			0
$556$	−7.01842	+	3.12480i	−0.297647	+	0.132521i
$557$			17.2305i			0.730082i	0.930992	+	0.365041i	$0.118945\pi$
$557$			17.2305i			0.730082i	−0.930992	+	0.365041i	$0.881055\pi$
$558$		0			0
$559$	2.16809	−	6.67268i	0.0917003	−	0.282224i
$560$	−6.22473	−	17.7190i	−0.263043	−	0.748765i
$561$		0			0
$562$	−2.15465	−	10.1368i	−0.0908883	−	0.427596i
$563$	−3.76707	−	17.7226i	−0.158763	−	0.746921i	−0.983428	−	0.181299i	$-0.941970\pi$
$563$	−3.76707	−	17.7226i	−0.158763	−	0.746921i	0.824665	−	0.565621i	$-0.191364\pi$
$564$		0			0
$565$	6.66071	+	18.9601i	0.280218	+	0.797656i
$566$	4.42900	−	13.6311i	0.186165	−	0.572956i
$567$		0			0
$568$		−	29.7351i		−	1.24766i
$569$	8.67299	−	3.86147i	0.363591	−	0.161881i	−0.216806	−	0.976215i	$-0.569564\pi$
$569$	8.67299	−	3.86147i	0.363591	−	0.161881i	0.580397	+	0.814334i	$0.302897\pi$
$570$		0			0
$571$	12.6641	+	5.63842i	0.529976	+	0.235961i	0.654238	−	0.756289i	$-0.272990\pi$
$571$	12.6641	+	5.63842i	0.529976	+	0.235961i	−0.124262	+	0.992250i	$0.539656\pi$
$572$	4.03783	−	9.06911i	0.168830	−	0.379198i
$573$		0			0
$574$	−3.72027	+	6.44370i	−0.155281	+	0.268955i
$575$	−0.372363	−	0.192084i	−0.0155286	−	0.00801046i
$576$		0			0
$577$	7.51395	−	2.44143i	0.312810	−	0.101638i	−0.148405	−	0.988927i	$-0.547414\pi$
$577$	7.51395	−	2.44143i	0.312810	−	0.101638i	0.461215	+	0.887289i	$0.347414\pi$
$578$	−1.37710	+	0.144739i	−0.0572798	+	0.00602035i
$579$		0			0
$580$	−3.03503	+	16.1497i	−0.126023	+	0.670580i
$581$	5.08409	−	48.3719i	0.210924	−	2.00681i
$582$		0			0
$583$	−4.61055	−	10.3555i	−0.190950	−	0.428880i
$584$	−5.42543	+	16.6978i	−0.224506	+	0.690958i
$585$		0			0
$586$	−0.539987	−	1.66191i	−0.0223066	−	0.0686528i
$587$	18.3867	−	16.5554i	0.758900	−	0.683316i	−0.195881	−	0.980628i	$-0.562757\pi$
$587$	18.3867	−	16.5554i	0.758900	−	0.683316i	0.954781	+	0.297311i	$0.0960899\pi$
$588$		0			0
$589$	37.1294	−	41.2364i	1.52989	−	1.69912i
$590$	1.51937	+	11.7685i	0.0625516	+	0.484501i
$591$		0			0
$592$	5.48694	+	12.3239i	0.225512	+	0.506508i
$593$			0.857005i			0.0351930i	0.999845	+	0.0175965i	$0.00560143\pi$
$593$			0.857005i			0.0351930i	−0.999845	+	0.0175965i	$0.994399\pi$
$594$		0			0
$595$	−33.4285	+	20.3700i	−1.37043	+	0.835089i
$596$	−0.219360	−	2.08707i	−0.00898535	−	0.0854899i
$597$		0			0
$598$	0.0565135	+	0.0508850i	0.00231101	+	0.00208084i
$599$	−12.6975	−	21.9926i	−0.518804	−	0.898595i	−0.999761	−	0.0218507i	$-0.993044\pi$
$599$	−12.6975	−	21.9926i	−0.518804	−	0.898595i	0.480957	−	0.876744i	$-0.340289\pi$
$600$		0			0
$601$	16.2206	−	28.0949i	0.661652	−	1.14601i	−0.318530	−	0.947913i	$-0.603189\pi$
$601$	16.2206	−	28.0949i	0.661652	−	1.14601i	0.980181	−	0.198102i	$-0.0634776\pi$
$602$	−9.73080	+	3.16173i	−0.396598	+	0.128862i
$603$		0			0
$604$	−29.6619	+	21.5506i	−1.20693	+	0.876883i
$605$	7.15018	+	2.13747i	0.290696	+	0.0869007i
$606$		0			0
$607$	−22.0994	+	12.7591i	−0.896989	+	0.517877i	−0.876222	−	0.481908i	$-0.839944\pi$
$607$	−22.0994	+	12.7591i	−0.896989	+	0.517877i	−0.0207668	+	0.999784i	$0.506611\pi$
$608$	−36.1494	−	3.79945i	−1.46605	−	0.154088i
$609$		0			0
$610$	−2.31724	+	7.75151i	−0.0938221	+	0.313849i
$611$	2.20908	+	6.79885i	0.0893698	+	0.275052i
$612$		0			0
$613$	−6.98214	−	2.26864i	−0.282006	−	0.0916293i	0.164599	−	0.986361i	$-0.447367\pi$
$613$	−6.98214	−	2.26864i	−0.282006	−	0.0916293i	−0.446605	+	0.894731i	$0.647367\pi$
$614$	−10.7685	−	2.28891i	−0.434579	−	0.0923727i
$615$		0			0
$616$	−31.1499	+	6.62111i	−1.25506	+	0.266772i
$617$	20.3914	+	2.14323i	0.820928	+	0.0862830i	0.505674	−	0.862724i	$-0.331244\pi$
$617$	20.3914	+	2.14323i	0.820928	+	0.0862830i	0.315254	+	0.949007i	$0.397910\pi$
$618$		0			0
$619$	27.7882	−	12.3721i	1.11690	−	0.497277i	0.236561	−	0.971617i	$-0.423980\pi$
$619$	27.7882	−	12.3721i	1.11690	−	0.497277i	0.880342	+	0.474340i	$0.157313\pi$
$620$	−11.9428	+	28.6295i	−0.479635	+	1.14979i
$621$		0			0
$622$	−3.72184	−	5.12268i	−0.149232	−	0.205401i
$623$	6.66526	−	31.3576i	0.267038	−	1.25632i
$624$		0			0
$625$	21.7748	−	12.2825i	0.870991	−	0.491299i
$626$	−2.25060	−	3.89815i	−0.0899521	−	0.155802i
$627$		0			0
$628$	−12.4351	+	1.30698i	−0.496214	+	0.0521542i
$629$	22.7484	−	16.5277i	0.907039	−	0.659002i
$630$		0			0
$631$	16.2008	+	11.7706i	0.644943	+	0.468578i	0.861545	−	0.507682i	$-0.169497\pi$
$631$	16.2008	+	11.7706i	0.644943	+	0.468578i	−0.216602	+	0.976260i	$0.569497\pi$
$632$	−22.5139	−	12.9984i	−0.895556	−	0.517050i
$633$		0			0
$634$	−3.18178	+	0.676307i	−0.126364	+	0.0268596i
$635$	−26.0325	+	12.3369i	−1.03307	+	0.489575i
$636$		0			0
$637$	10.2830	−	9.25884i	0.407427	−	0.366849i
$638$	9.16029	+	2.97636i	0.362659	+	0.117835i
$639$		0			0
$640$	25.0761	−	5.95385i	0.991220	−	0.235347i
$641$	−1.94797	−	2.16344i	−0.0769403	−	0.0854509i	0.703445	−	0.710749i	$-0.251644\pi$
$641$	−1.94797	−	2.16344i	−0.0769403	−	0.0854509i	−0.780386	+	0.625298i	$0.784977\pi$
$642$		0			0
$643$	−16.6176	+	9.59419i	−0.655335	+	0.378358i	−0.790497	−	0.612466i	$-0.790178\pi$
$643$	−16.6176	+	9.59419i	−0.655335	+	0.378358i	0.135162	+	0.990823i	$0.456844\pi$
$644$	−0.0580384	+	0.552199i	−0.00228703	+	0.0217597i
$645$		0			0
$646$	1.77140	+	16.8537i	0.0696948	+	0.663101i
$647$	5.59274	+	7.69775i	0.219873	+	0.302630i	0.904677	−	0.426098i	$-0.140112\pi$
$647$	5.59274	+	7.69775i	0.219873	+	0.302630i	−0.684804	+	0.728728i	$0.740112\pi$
$648$		0			0
$649$	−34.8229			−1.36692
$650$	−4.38873	+	1.15242i	−0.172140	+	0.0452018i
$651$		0			0
$652$	3.44562	+	3.10245i	0.134941	+	0.121501i
$653$	−17.0140	+	38.2140i	−0.665808	+	1.49543i	0.191966	+	0.981402i	$0.438514\pi$
$653$	−17.0140	+	38.2140i	−0.665808	+	1.49543i	−0.857774	+	0.514027i	$0.828153\pi$
$654$		0			0
$655$	1.01098	+	42.6939i	0.0395022	+	1.66819i
$656$	5.54604	+	4.02944i	0.216537	+	0.157323i
$657$		0			0
$658$	6.12767	−	8.43402i	0.238882	−	0.328792i
$659$	27.4755	+	30.5147i	1.07030	+	1.18868i	0.981267	+	0.192654i	$0.0617095\pi$
$659$	27.4755	+	30.5147i	1.07030	+	1.18868i	0.0890283	+	0.996029i	$0.471624\pi$
$660$		0			0
$661$	−18.9810	+	21.0805i	−0.738274	+	0.819936i	−0.988968	−	0.148130i	$-0.952674\pi$
$661$	−18.9810	+	21.0805i	−0.738274	+	0.819936i	0.250694	+	0.968066i	$0.419341\pi$
$662$	3.86360	+	18.1768i	0.150163	+	0.706462i
$663$		0			0
$664$	25.3274	+	5.38351i	0.982895	+	0.208921i
$665$	30.8377	+	50.6067i	1.19584	+	1.96244i
$666$		0			0
$667$	0.217130	−	0.298854i	0.00840732	−	0.0115717i
$668$	−24.7588	−	14.2945i	−0.957946	−	0.553070i
$669$		0			0
$670$	−1.39042	+	7.39857i	−0.0537166	+	0.285832i
$671$	−21.6900	−	9.65699i	−0.837331	−	0.372804i
$672$		0			0
$673$	−2.05793	+	9.68178i	−0.0793272	+	0.373205i	−0.999847	−	0.0174906i	$-0.994432\pi$
$673$	−2.05793	+	9.68178i	−0.0793272	+	0.373205i	0.920520	+	0.390696i	$0.127766\pi$
$674$	−11.9427			−0.460016
$675$		0			0
$676$	17.5482			0.674930
$677$	−0.942183	+	4.43262i	−0.0362110	+	0.170360i	−0.992537	−	0.121942i	$-0.961088\pi$
$677$	−0.942183	+	4.43262i	−0.0362110	+	0.170360i	0.956326	+	0.292302i	$0.0944211\pi$
$678$		0			0
$679$	26.0139	+	11.5821i	0.998321	+	0.444481i
$680$	−8.92463	−	18.8321i	−0.342244	−	0.722179i
$681$		0			0
$682$	15.7464	+	9.09121i	0.602962	+	0.348120i
$683$	−11.1929	+	15.4057i	−0.428283	+	0.589481i	−0.967558	−	0.252648i	$-0.918698\pi$
$683$	−11.1929	+	15.4057i	−0.428283	+	0.589481i	0.539275	+	0.842130i	$0.318698\pi$
$684$		0			0
$685$	−9.63504	+	11.2241i	−0.368136	+	0.428852i
$686$	−4.03405	−	0.857464i	−0.154021	−	0.0327381i
$687$		0			0
$688$	1.95994	+	9.22077i	0.0747219	+	0.351539i
$689$	−3.15040	+	3.49888i	−0.120021	+	0.133297i
$690$		0			0
$691$	−3.46559	−	3.84893i	−0.131837	−	0.146420i	0.673611	−	0.739086i	$-0.264742\pi$
$691$	−3.46559	−	3.84893i	−0.131837	−	0.146420i	−0.805449	+	0.592666i	$0.798076\pi$
$692$	14.4431	−	19.8792i	0.549044	−	0.755694i
$693$		0			0
$694$	−12.3425	−	8.96732i	−0.468513	−	0.340395i
$695$	−5.85807	+	8.47797i	−0.222209	+	0.321588i
$696$		0			0
$697$	5.81187	−	13.0537i	0.220140	−	0.494443i
$698$	7.02758	+	6.32766i	0.265998	+	0.239505i
$699$		0			0
$700$	−25.6420	−	20.9780i	−0.969176	−	0.792895i
$701$	5.29123			0.199847			0.0999235	−	0.994995i	$-0.468140\pi$
$701$	5.29123			0.199847			0.0999235	+	0.994995i	$0.468140\pi$
$702$		0			0
$703$	−25.0209	−	34.4383i	−0.943682	−	1.29887i
$704$	0.427725	+	4.06954i	0.0161205	+	0.153376i
$705$		0			0
$706$	0.845064	−	8.04024i	0.0318044	−	0.302599i
$707$	−6.56946	+	3.79288i	−0.247070	+	0.142646i
$708$		0			0
$709$	−26.9583	−	29.9402i	−1.01244	−	1.12443i	−0.992203	−	0.124633i	$-0.960225\pi$
$709$	−26.9583	−	29.9402i	−1.01244	−	1.12443i	−0.0202369	−	0.999795i	$-0.506442\pi$
$710$	−9.43505	−	15.4835i	−0.354091	−	0.581086i
$711$		0			0
$712$	16.2313	+	5.27386i	0.608293	+	0.197646i
$713$	0.518231	−	0.466618i	0.0194079	−	0.0174750i
$714$		0			0
$715$	−1.70501	−	13.2064i	−0.0637638	−	0.493890i
$716$	11.9712	−	2.54455i	0.447383	−	0.0950942i
$717$		0			0
$718$	−14.3719	−	8.29760i	−0.536353	−	0.309664i
$719$	−28.5521	−	20.7443i	−1.06482	−	0.773634i	−0.0898421	−	0.995956i	$-0.528636\pi$
$719$	−28.5521	−	20.7443i	−1.06482	−	0.773634i	−0.974973	+	0.222322i	$0.928636\pi$
$720$		0			0
$721$	23.5386	−	17.1018i	0.876622	−	0.636903i
$722$	14.6111	−	1.53568i	0.543767	−	0.0571522i
$723$		0			0
$724$	13.4088	+	23.2248i	0.498335	+	0.863142i
$725$	7.79578	+	20.6168i	0.289528	+	0.765689i
$726$		0			0
$727$	−10.2062	+	48.0164i	−0.378527	+	1.78083i	0.215626	+	0.976476i	$0.430821\pi$
$727$	−10.2062	+	48.0164i	−0.378527	+	1.78083i	−0.594153	+	0.804352i	$0.702513\pi$
$728$	7.77474	+	10.7010i	0.288151	+	0.396606i
$729$		0			0
$730$	2.47315	+	10.4163i	0.0915354	+	0.385524i
$731$	17.9502	−	7.99196i	0.663913	−	0.295593i
$732$		0			0
$733$	−27.9553	−	2.93822i	−1.03255	−	0.108526i	−0.426935	−	0.904282i	$-0.640407\pi$
$733$	−27.9553	−	2.93822i	−1.03255	−	0.108526i	−0.605616	+	0.795757i	$0.707073\pi$
$734$	11.8079	−	2.50985i	0.435838	−	0.0926403i
$735$		0			0
$736$	−0.446821	−	0.0949748i	−0.0164701	−	0.00350082i
$737$	−21.0110	−	6.82688i	−0.773949	−	0.251471i
$738$		0			0
$739$	3.92501	+	12.0799i	0.144384	+	0.444367i	0.996931	−	0.0782824i	$-0.0249436\pi$
$739$	3.92501	+	12.0799i	0.144384	+	0.444367i	−0.852548	+	0.522650i	$0.824944\pi$
$740$	19.5781	+	13.5280i	0.719706	+	0.497299i
$741$		0			0
$742$	6.82837	+	0.717691i	0.250678	+	0.0263473i
$743$	−34.2613	+	19.7808i	−1.25692	+	0.725686i	−0.972475	−	0.233005i	$-0.925144\pi$
$743$	−34.2613	+	19.7808i	−1.25692	+	0.725686i	−0.284449	+	0.958691i	$0.591811\pi$
$744$		0			0
$745$	−1.70800	−	2.23749i	−0.0625763	−	0.0819754i
$746$	−5.17409	+	3.75920i	−0.189437	+	0.137634i
$747$		0			0
$748$	26.4415	−	8.59137i	0.966797	−	0.314131i
$749$	5.74360	−	9.94821i	0.209867	−	0.363500i
$750$		0			0
$751$	−2.75708	−	4.77540i	−0.100607	−	0.174257i	0.811328	−	0.584591i	$-0.198745\pi$
$751$	−2.75708	−	4.77540i	−0.100607	−	0.174257i	−0.911935	+	0.410335i	$0.865412\pi$
$752$	−7.13791	−	6.42701i	−0.260293	−	0.234369i
$753$		0			0
$754$	−0.418170	−	3.97862i	−0.0152289	−	0.144893i
$755$	−18.9338	+	45.3883i	−0.689070	+	1.65185i
$756$		0			0
$757$			13.9252i			0.506119i	0.967451	+	0.253060i	$0.0814369\pi$
$757$			13.9252i			0.506119i	−0.967451	+	0.253060i	$0.918563\pi$
$758$	−6.28435	−	14.1149i	−0.228258	−	0.512676i
$759$		0			0
$760$	−28.5096	+	13.5108i	−1.03415	+	0.490089i
$761$	−6.71753	+	7.46058i	−0.243510	+	0.270446i	−0.852494	−	0.522737i	$-0.824911\pi$
$761$	−6.71753	+	7.46058i	−0.243510	+	0.270446i	0.608983	+	0.793183i	$0.291578\pi$
$762$		0			0
$763$	−5.01262	+	4.51338i	−0.181469	+	0.163395i
$764$	−0.193987	−	0.597031i	−0.00701821	−	0.0215998i
$765$		0			0
$766$	0.0959930	−	0.295436i	0.00346837	−	0.0106745i
$767$	5.88294	+	13.2133i	0.212421	+	0.477104i
$768$		0			0
$769$	2.26575	−	21.5572i	0.0817050	−	0.777371i	−0.874570	−	0.484900i	$-0.838856\pi$
$769$	2.26575	−	21.5572i	0.0817050	−	0.777371i	0.956274	−	0.292471i	$-0.0944774\pi$
$770$	−14.1193	+	13.3317i	−0.508824	+	0.480440i
$771$		0			0
$772$	−13.1405	+	1.38112i	−0.472937	+	0.0497077i
$773$	−9.56391	+	3.10750i	−0.343990	+	0.111769i	−0.475917	−	0.879490i	$-0.657884\pi$
$773$	−9.56391	+	3.10750i	−0.343990	+	0.111769i	0.131927	+	0.991259i	$0.457884\pi$
$774$		0			0
$775$	6.30316	+	41.1290i	0.226416	+	1.47740i
$776$	−7.57971	+	13.1284i	−0.272096	+	0.471284i
$777$		0			0
$778$	7.81349	−	17.5494i	0.280127	−	0.629176i
$779$	−19.7617	−	8.79846i	−0.708035	−	0.315238i
$780$		0			0
$781$	48.6099	−	21.6425i	1.73940	−	0.774431i
$782$			0.212973i			0.00761590i
$783$		0			0
$784$	−5.74509	+	17.6816i	−0.205182	+	0.631484i
$785$	−13.3313	+	10.1765i	−0.475815	+	0.363216i
$786$		0			0
$787$	0.715489	+	3.36611i	0.0255044	+	0.119989i	0.989058	−	0.147526i	$-0.0471309\pi$
$787$	0.715489	+	3.36611i	0.0255044	+	0.119989i	−0.963554	+	0.267515i	$0.913798\pi$
$788$	0.377813	+	1.77747i	0.0134590	+	0.0633198i
$789$		0			0
$790$	−15.8478	+	0.375270i	−0.563839	+	0.0133515i
$791$	11.0385	−	33.9731i	0.392484	−	1.20794i
$792$		0			0
$793$			9.86152i			0.350193i
$794$	−13.4369	+	5.98249i	−0.476857	+	0.212311i
$795$		0			0
$796$	−14.8489	−	6.61117i	−0.526306	−	0.234327i
$797$	11.8910	−	26.7076i	0.421200	−	0.946030i	−0.570951	−	0.820984i	$-0.693425\pi$
$797$	11.8910	−	26.7076i	0.421200	−	0.946030i	0.992151	−	0.125046i	$-0.0399079\pi$
$798$		0			0
$799$	−10.0102	+	17.3382i	−0.354137	+	0.613383i
$800$	19.3695	−	19.1764i	0.684815	−	0.677988i
$801$		0			0
$802$	2.41981	−	0.786245i	0.0854466	−	0.0277633i
$803$	−31.2457	+	3.28406i	−1.10264	+	0.115892i
$804$		0			0
$805$	0.318945	+	0.673016i	0.0112413	+	0.0237207i
$806$	0.789408	−	7.51072i	0.0278057	−	0.264554i
$807$		0			0
$808$	−1.64256	−	3.68924i	−0.0577849	−	0.129787i
$809$	10.4348	−	32.1149i	0.366867	−	1.12910i	−0.581937	−	0.813234i	$-0.697705\pi$
$809$	10.4348	−	32.1149i	0.366867	−	1.12910i	0.948804	−	0.315867i	$-0.102295\pi$
$810$		0			0
$811$	−5.27105	−	16.2226i	−0.185092	−	0.569654i	0.814858	−	0.579660i	$-0.196815\pi$
$811$	−5.27105	−	16.2226i	−0.185092	−	0.569654i	−0.999950	+	0.0100067i	$0.996815\pi$
$812$	21.7067	−	19.5448i	0.761756	−	0.685888i
$813$		0			0
$814$	9.33339	−	10.3658i	0.327135	−	0.363320i
$815$	6.11217	+	1.14867i	0.214100	+	0.0402360i
$816$		0			0
$817$	−12.0988	−	27.1745i	−0.423285	−	0.950714i
$818$		−	11.2718i		−	0.394109i
$819$		0			0
$820$	12.0534	+	0.979003i	0.420922	+	0.0341883i
$821$	1.13532	+	10.8018i	0.0396229	+	0.376987i	0.996307	+	0.0858595i	$0.0273636\pi$
$821$	1.13532	+	10.8018i	0.0396229	+	0.376987i	−0.956684	+	0.291127i	$0.905970\pi$
$822$		0			0
$823$	−14.4013	−	12.9670i	−0.501997	−	0.452000i	0.378811	−	0.925474i	$-0.376333\pi$
$823$	−14.4013	−	12.9670i	−0.501997	−	0.452000i	−0.880808	+	0.473474i	$0.843000\pi$
$824$	7.74462	+	13.4141i	0.269797	+	0.467301i
$825$		0			0
$826$	10.5463	−	18.2667i	0.366952	−	0.635579i
$827$	−31.4930	+	10.2327i	−1.09512	+	0.355826i	−0.800223	−	0.599703i	$-0.795286\pi$
$827$	−31.4930	+	10.2327i	−1.09512	+	0.355826i	−0.294898	+	0.955529i	$0.595286\pi$
$828$		0			0
$829$	−13.1342	+	9.54259i	−0.456171	+	0.331428i	−0.792027	−	0.610485i	$-0.790974\pi$
$829$	−13.1342	+	9.54259i	−0.456171	+	0.331428i	0.335856	+	0.941913i	$0.390974\pi$
$830$	14.8966	−	5.23320i	0.517068	−	0.181647i
$831$		0			0
$832$	1.47189	−	0.849799i	0.0510288	−	0.0294615i
$833$	38.5394	+	4.05066i	1.33531	+	0.140347i
$834$		0			0
$835$	−38.3368	+	0.907803i	−1.32670	+	0.0314158i
$836$	−13.0063	−	40.0292i	−0.449832	−	1.38444i
$837$		0			0
$838$	0.480016	+	0.155967i	0.0165819	+	0.00538778i
$839$	9.37271	+	1.99223i	0.323582	+	0.0687795i	0.366839	−	0.930285i	$-0.380440\pi$
$839$	9.37271	+	1.99223i	0.323582	+	0.0687795i	−0.0432569	+	0.999064i	$0.513773\pi$
$840$		0			0
$841$	9.35787	−	1.98908i	0.322685	−	0.0685888i
$842$	−19.6349	−	2.06371i	−0.676664	−	0.0711202i
$843$		0			0
$844$	18.7119	−	8.33106i	0.644089	−	0.286767i
$845$	20.1002	−	12.2483i	0.691470	−	0.421354i
$846$		0			0
$847$	−7.79724	−	10.7320i	−0.267916	−	0.368755i
$848$	1.31523	−	6.18769i	0.0451653	−	0.212486i
$849$		0			0
$850$	−10.6227	−	6.97435i	−0.364355	−	0.239218i
$851$	−0.267484	−	0.463295i	−0.00916922	−	0.0158816i
$852$		0			0
$853$	11.7858	−	1.23873i	0.403537	−	0.0424135i	0.0994139	−	0.995046i	$-0.468303\pi$
$853$	11.7858	−	1.23873i	0.403537	−	0.0424135i	0.304123	+	0.952633i	$0.401637\pi$
$854$	11.6345	−	8.45299i	0.398126	−	0.289255i
$855$		0			0
$856$	4.94743	+	3.59452i	0.169100	+	0.122858i
$857$	31.5833	+	18.2346i	1.07886	+	0.622882i	0.930590	−	0.366064i	$-0.119295\pi$
$857$	31.5833	+	18.2346i	1.07886	+	0.622882i	0.148274	+	0.988946i	$0.452628\pi$
$858$		0			0
$859$	−27.8307	+	5.91560i	−0.949571	+	0.201838i	−0.656562	−	0.754272i	$-0.727990\pi$
$859$	−27.8307	+	5.91560i	−0.949571	+	0.201838i	−0.293009	+	0.956110i	$0.594657\pi$
$860$	11.4166	+	12.0911i	0.389303	+	0.412303i
$861$		0			0
$862$	−12.8163	+	11.5399i	−0.436525	+	0.393049i
$863$	−20.4628	−	6.64876i	−0.696561	−	0.226326i	−0.0607293	−	0.998154i	$-0.519343\pi$
$863$	−20.4628	−	6.64876i	−0.696561	−	0.226326i	−0.635831	+	0.771828i	$0.719343\pi$
$864$		0			0
$865$	2.66826	−	32.8513i	0.0907236	−	1.11698i
$866$	−1.28013	−	1.42173i	−0.0435005	−	0.0483123i
$867$		0			0
$868$	47.7529	−	27.5701i	1.62084	−	0.935791i
$869$	4.86273	−	46.2658i	0.164957	−	1.56946i
$870$		0			0
$871$	0.959158	+	9.12578i	0.0324998	+	0.309215i
$872$	−2.11066	−	2.90507i	−0.0714758	−	0.0983780i
$873$		0			0
$874$	0.322415			0.0109059
$875$	−44.0134	−	6.13127i	−1.48793	−	0.207275i
$876$		0			0
$877$	−20.5970	−	18.5456i	−0.695512	−	0.626242i	0.243591	−	0.969878i	$-0.421675\pi$
$877$	−20.5970	−	18.5456i	−0.695512	−	0.626242i	−0.939103	+	0.343636i	$0.888341\pi$
$878$	4.55011	−	10.2197i	0.153559	−	0.344899i
$879$		0			0
$880$	10.8560	+	14.2214i	0.365954	+	0.479402i
$881$	41.6453	+	30.2571i	1.40307	+	1.01939i	0.994285	+	0.106754i	$0.0340456\pi$
$881$	41.6453	+	30.2571i	1.40307	+	1.01939i	0.408780	+	0.912633i	$0.365954\pi$
$882$		0			0
$883$	12.1334	−	16.7002i	0.408321	−	0.562006i	−0.554487	−	0.832192i	$-0.687085\pi$
$883$	12.1334	−	16.7002i	0.408321	−	0.562006i	0.962808	+	0.270187i	$0.0870854\pi$
$884$	−7.72692	−	8.58161i	−0.259884	−	0.288631i
$885$		0			0
$886$	11.9962	−	13.3231i	0.403020	−	0.447599i
$887$	10.5848	+	49.7976i	0.355403	+	1.67204i	0.685485	+	0.728087i	$0.259590\pi$
$887$	10.5848	+	49.7976i	0.355403	+	1.67204i	−0.330082	+	0.943952i	$0.607076\pi$
$888$		0			0
$889$	50.0879	+	10.6465i	1.67989	+	0.357073i
$890$	10.1253	−	2.40406i	0.339400	−	0.0805842i
$891$		0			0
$892$	11.8701	−	16.3378i	0.397439	−	0.547028i
$893$	26.2480	+	15.1543i	0.878356	+	0.507119i
$894$		0			0
$895$	11.9361	−	11.2703i	0.398980	−	0.376723i
$896$	−41.8521	−	18.6338i	−1.39818	−	0.622510i
$897$		0			0
$898$	−2.70327	+	12.7179i	−0.0902094	+	0.424402i
$899$	−36.6851			−1.22352
$900$		0			0
$901$	−13.1856			−0.439277
$902$	1.47372	−	6.93333i	0.0490696	−	0.230855i
$903$		0			0
$904$	17.3727	+	7.73481i	0.577806	+	0.257256i
$905$	31.5694	+	17.2433i	1.04940	+	0.573186i
$906$		0			0
$907$	−44.8055	−	25.8684i	−1.48774	−	0.858948i	−0.487839	−	0.872934i	$-0.662215\pi$
$907$	−44.8055	−	25.8684i	−1.48774	−	0.858948i	−0.999902	+	0.0139860i	$0.995548\pi$
$908$	9.50204	−	13.0784i	0.315336	−	0.434023i
$909$		0			0
$910$	7.44389	+	3.10523i	0.246762	+	0.102937i
$911$	40.3818	+	8.58343i	1.33791	+	0.284382i	0.820642	−	0.571442i	$-0.193616\pi$
$911$	40.3818	+	8.58343i	1.33791	+	0.284382i	0.517268	+	0.855824i	$0.326949\pi$
$912$		0			0
$913$	9.63364	+	45.3227i	0.318827	+	1.49996i
$914$	16.3419	−	18.1495i	0.540541	−	0.600332i
$915$		0			0
$916$	−10.4049	−	11.5558i	−0.343788	−	0.381815i
$917$	44.6196	−	61.4136i	1.47347	−	2.02805i
$918$		0			0
$919$	15.8417	+	11.5097i	0.522569	+	0.379669i	0.817571	−	0.575828i	$-0.195320\pi$
$919$	15.8417	+	11.5097i	0.522569	+	0.379669i	−0.295002	+	0.955497i	$0.595320\pi$
$920$	−0.374074	+	0.131413i	−0.0123329	+	0.00433256i
$921$		0			0
$922$	−1.40102	+	3.14675i	−0.0461402	+	0.103633i
$923$	−16.4242	−	14.7884i	−0.540608	−	0.486766i
$924$		0			0
$925$	31.8677	+	1.83024i	1.04780	+	0.0601778i
$926$	−16.1028			−0.529171
$927$		0			0
$928$	14.1250	+	19.4414i	0.463675	+	0.638194i
$929$	2.51782	+	23.9554i	0.0826069	+	0.785952i	0.954892	+	0.296954i	$0.0959709\pi$
$929$	2.51782	+	23.9554i	0.0826069	+	0.785952i	−0.872285	+	0.488998i	$0.837362\pi$
$930$		0			0
$931$	6.13221	−	58.3440i	0.200975	−	1.91215i
$932$	14.2581	−	8.23195i	0.467041	−	0.269646i
$933$		0			0
$934$	−12.4020	−	13.7738i	−0.405806	−	0.450693i
$935$	24.2903	−	28.2965i	0.794379	−	0.925395i
$936$		0			0
$937$	22.8902	+	7.43748i	0.747791	+	0.242972i	0.658030	−	0.752991i	$-0.271390\pi$
$937$	22.8902	+	7.43748i	0.747791	+	0.242972i	0.0897606	+	0.995963i	$0.471390\pi$
$938$	9.94436	−	8.95394i	0.324695	−	0.292357i
$939$		0			0
$940$	−16.6522	−	3.12946i	−0.543135	−	0.102072i
$941$	−37.9203	+	8.06021i	−1.23617	+	0.262755i	−0.779227	−	0.626742i	$-0.784388\pi$
$941$	−37.9203	+	8.06021i	−1.23617	+	0.262755i	−0.456940	+	0.889497i	$0.651055\pi$
$942$		0			0
$943$	−0.235433	−	0.135927i	−0.00766674	−	0.00442640i
$944$	−15.7220	−	11.4227i	−0.511707	−	0.371777i
$945$		0			0
$946$	7.88556	−	5.72919i	0.256382	−	0.186272i
$947$	−38.1583	+	4.01060i	−1.23998	+	0.130327i	−0.701720	−	0.712453i	$-0.747584\pi$
$947$	−38.1583	+	4.01060i	−1.23998	+	0.130327i	−0.538259	+	0.842780i	$0.680918\pi$
$948$		0			0
$949$	6.52472	+	11.3012i	0.211801	+	0.366851i
$950$	−10.5583	+	16.0815i	−0.342557	+	0.521751i
$951$		0			0
$952$	−7.70179	+	36.2341i	−0.249616	+	1.17435i
$953$	21.3570	+	29.3953i	0.691820	+	0.952208i	1.00000		0.000880159i	$0.000280163\pi$
$953$	21.3570	+	29.3953i	0.691820	+	0.952208i	−0.308180	+	0.951328i	$0.599720\pi$
$954$		0			0
$955$	−0.638916	−	0.548460i	−0.0206748	−	0.0177477i
$956$	−10.1596	+	4.52337i	−0.328586	+	0.146296i
$957$		0			0
$958$	−18.9950	−	1.99645i	−0.613700	−	0.0645025i
$959$	25.7195	−	5.46684i	0.830525	−	0.176534i
$960$		0			0
$961$	−37.4170	−	7.95323i	−1.20700	−	0.256556i
$962$	−5.50998	−	1.79030i	−0.177649	−	0.0577216i
$963$		0			0
$964$	2.32360	+	7.15130i	0.0748381	+	0.230328i
$965$	−14.0876	+	10.7538i	−0.453495	+	0.346177i
$966$		0			0
$967$	22.5541	+	2.37053i	0.725291	+	0.0762312i	0.459977	−	0.887931i	$-0.347858\pi$
$967$	22.5541	+	2.37053i	0.725291	+	0.0762312i	0.265314	+	0.964162i	$0.414524\pi$
$968$	6.11591	−	3.53102i	0.196573	−	0.113491i
$969$		0			0
$970$	0.218830	+	9.24124i	0.00702619	+	0.296718i
$971$	40.5533	−	29.4637i	1.30142	−	0.945536i	0.301450	−	0.953482i	$-0.402530\pi$
$971$	40.5533	−	29.4637i	1.30142	−	0.945536i	0.999968	+	0.00794658i	$0.00252950\pi$
$972$		0			0
$973$	17.4210	−	5.66042i	0.558491	−	0.181465i
$974$	−9.57178	+	16.5788i	−0.306699	+	0.531219i
$975$		0			0
$976$	−6.62495	−	11.4748i	−0.212060	−	0.367298i
$977$	10.5779	+	9.52435i	0.338416	+	0.304711i	0.820763	−	0.571269i	$-0.193549\pi$
$977$	10.5779	+	9.52435i	0.338416	+	0.304711i	−0.482347	+	0.875980i	$0.660216\pi$
$978$		0			0
$979$	3.19231	+	30.3728i	0.102027	+	0.970720i
$980$	7.57624	+	31.9092i	0.242014	+	1.01930i
$981$		0			0
$982$		−	1.75040i		−	0.0558574i
$983$	18.3638	+	41.2458i	0.585714	+	1.31554i	0.926818	+	0.375510i	$0.122532\pi$
$983$	18.3638	+	41.2458i	0.585714	+	1.31554i	−0.341104	+	0.940026i	$0.610801\pi$
$984$		0			0
$985$	1.67340	+	1.77227i	0.0533190	+	0.0564691i
$986$	7.49678	−	8.32602i	0.238746	−	0.265155i
$987$		0			0
$988$	−12.9915	+	11.6976i	−0.413315	+	0.372151i
$989$	−0.115520	−	0.355533i	−0.00367331	−	0.0113053i
$990$		0			0
$991$	−4.55426	+	14.0166i	−0.144671	+	0.445251i	−0.996969	−	0.0778062i	$-0.975208\pi$
$991$	−4.55426	+	14.0166i	−0.144671	+	0.445251i	0.852298	+	0.523057i	$0.175208\pi$
$992$	18.4515	+	41.4427i	0.585834	+	1.31581i
$993$		0			0
$994$	−3.36893	+	32.0533i	−0.106856	+	1.01667i
$995$	−21.6229	+	2.79163i	−0.685492	+	0.0885007i
$996$		0			0
$997$	4.64867	−	0.488595i	0.147225	−	0.0154739i	−0.0306293	−	0.999531i	$-0.509751\pi$
$997$	4.64867	−	0.488595i	0.147225	−	0.0154739i	0.177854	+	0.984057i	$0.443084\pi$
$998$	11.3475	−	3.68703i	0.359199	−	0.116711i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.y.a.19.16		224
3.2	odd	2		225.2.u.a.169.13	yes	224
9.4	even	3	inner	675.2.y.a.469.16		224
9.5	odd	6		225.2.u.a.94.13	yes	224
25.4	even	10	inner	675.2.y.a.154.16		224
75.29	odd	10		225.2.u.a.79.13	yes	224
225.4	even	30	inner	675.2.y.a.604.16		224
225.104	odd	30		225.2.u.a.4.13	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.u.a.4.13	✓	224	225.104	odd	30
225.2.u.a.79.13	yes	224	75.29	odd	10
225.2.u.a.94.13	yes	224	9.5	odd	6
225.2.u.a.169.13	yes	224	3.2	odd	2
675.2.y.a.19.16		224	1.1	even	1	trivial
675.2.y.a.154.16		224	25.4	even	10	inner
675.2.y.a.469.16		224	9.4	even	3	inner
675.2.y.a.604.16		224	225.4	even	30	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.119971 - 0.564417i) q^{2} +(1.52292 + 0.678046i) q^{4} +(2.21766 - 0.286312i) q^{5} +(-3.44219 - 1.98735i) q^{7} +(1.24374 - 1.71186i) q^{8} +O(q^{10})\)	\(q+(0.119971 - 0.564417i) q^{2} +(1.52292 + 0.678046i) q^{4} +(2.21766 - 0.286312i) q^{5} +(-3.44219 - 1.98735i) q^{7} +(1.24374 - 1.71186i) q^{8} +(0.104455 - 1.28604i) q^{10} +(3.70374 + 0.787255i) q^{11} +(-0.326987 - 1.53835i) q^{13} +(-1.53465 + 1.70441i) q^{14} +(1.41394 + 1.57034i) q^{16} +(2.58890 - 3.56332i) q^{17} +(-5.39444 - 3.91929i) q^{19} +(3.57145 + 1.06765i) q^{20} +(0.888681 - 1.99601i) q^{22} +(-0.0622737 - 0.0560715i) q^{23} +(4.83605 - 1.26989i) q^{25} -0.907503 q^{26} +(-3.89465 - 5.36053i) q^{28} +(0.460792 + 4.38415i) q^{29} +(-0.869869 + 8.27625i) q^{31} +(4.72094 - 2.72564i) q^{32} +(-1.70061 - 1.88872i) q^{34} +(-8.20261 - 3.42173i) q^{35} +(6.07159 + 1.97278i) q^{37} +(-2.85929 + 2.57451i) q^{38} +(2.26807 - 4.15243i) q^{40} +(3.17329 - 0.674503i) q^{41} +(3.86343 + 2.23055i) q^{43} +(5.10670 + 3.71023i) q^{44} +(-0.0391187 + 0.0284214i) q^{46} +(-4.52055 + 0.475129i) q^{47} +(4.39910 + 7.61946i) q^{49} +(-0.136562 - 2.88190i) q^{50} +(0.545101 - 2.56450i) q^{52} +(-1.75963 - 2.42193i) q^{53} +(8.43905 + 0.685440i) q^{55} +(-7.68326 + 3.42081i) q^{56} +(2.52977 + 0.265890i) q^{58} +(-8.99567 + 1.91209i) q^{59} +(-6.13333 - 1.30368i) q^{61} +(4.56690 + 1.48388i) q^{62} +(0.333946 + 1.02778i) q^{64} +(-1.16560 - 3.31793i) q^{65} +(-5.80254 - 0.609871i) q^{67} +(6.35878 - 3.67125i) q^{68} +(-2.91535 + 4.21919i) q^{70} +(11.3688 - 8.25994i) q^{71} +(-7.89126 + 2.56403i) q^{73} +(1.84188 - 3.19023i) q^{74} +(-5.55782 - 9.62643i) q^{76} +(-11.1844 - 10.0705i) q^{77} +(-1.28423 - 12.2187i) q^{79} +(3.58525 + 3.07766i) q^{80} -1.87198i q^{82} +(4.97724 + 11.1791i) q^{83} +(4.72110 - 8.64348i) q^{85} +(1.72246 - 1.91299i) q^{86} +(5.95417 - 5.36116i) q^{88} +(2.49240 + 7.67081i) q^{89} +(-1.93169 + 5.94514i) q^{91} +(-0.0568186 - 0.127617i) q^{92} +(-0.274162 + 2.60848i) q^{94} +(-13.0852 - 7.14716i) q^{95} +(-7.12501 + 0.748868i) q^{97} +(4.82832 - 1.56882i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8}+O(q^{10}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8	\( 224 q + 5 q^{2} - 29 q^{4} + 20 q^{8} - 12 q^{10} - 5 q^{11} - 5 q^{13} + 23 q^{14} + 15 q^{16} + 20 q^{17} - 12 q^{19} + 17 q^{20} - 5 q^{22} + 5 q^{23} - 16 q^{25} - 72 q^{26} - 60 q^{28} + 15 q^{29} - 9 q^{31} - 7 q^{34} + 46 q^{35} - 20 q^{37} + 75 q^{38} - q^{40} - 13 q^{41} - 20 q^{44} - 4 q^{46} - 20 q^{47} + 56 q^{49} + 29 q^{50} - 15 q^{52} + 20 q^{53} - 44 q^{55} - 22 q^{56} - 5 q^{58} + 30 q^{59} - 3 q^{61} - 40 q^{62} - 12 q^{64} - 45 q^{65} + 10 q^{67} - 12 q^{70} + 106 q^{71} - 20 q^{73} - 82 q^{74} + 8 q^{76} + 115 q^{77} - 15 q^{79} + 22 q^{80} - 65 q^{83} - 21 q^{85} + 15 q^{86} - 5 q^{88} - 26 q^{89} - 54 q^{91} - 95 q^{92} + 41 q^{94} + 17 q^{95} - 5 q^{97} + 70 q^{98}+O(q^{100}) \) 224 * q + 5 * q^2 - 29 * q^4 + 20 * q^8 - 12 * q^10 - 5 * q^11 - 5 * q^13 + 23 * q^14 + 15 * q^16 + 20 * q^17 - 12 * q^19 + 17 * q^20 - 5 * q^22 + 5 * q^23 - 16 * q^25 - 72 * q^26 - 60 * q^28 + 15 * q^29 - 9 * q^31 - 7 * q^34 + 46 * q^35 - 20 * q^37 + 75 * q^38 - q^40 - 13 * q^41 - 20 * q^44 - 4 * q^46 - 20 * q^47 + 56 * q^49 + 29 * q^50 - 15 * q^52 + 20 * q^53 - 44 * q^55 - 22 * q^56 - 5 * q^58 + 30 * q^59 - 3 * q^61 - 40 * q^62 - 12 * q^64 - 45 * q^65 + 10 * q^67 - 12 * q^70 + 106 * q^71 - 20 * q^73 - 82 * q^74 + 8 * q^76 + 115 * q^77 - 15 * q^79 + 22 * q^80 - 65 * q^83 - 21 * q^85 + 15 * q^86 - 5 * q^88 - 26 * q^89 - 54 * q^91 - 95 * q^92 + 41 * q^94 + 17 * q^95 - 5 * q^97 + 70 * q^98

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