LMFDB - Embedded newform 900.2.bj.f.127.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.13
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.319851 - 1.37757i) q^{2} +(-1.79539 + 0.881234i) q^{4} +(-1.31656 - 1.80739i) q^{5} +(-1.89964 + 1.89964i) q^{7} +(1.78822 + 2.19141i) q^{8} +O(q^{10})$	\(q+(-0.319851 - 1.37757i) q^{2} +(-1.79539 + 0.881234i) q^{4} +(-1.31656 - 1.80739i) q^{5} +(-1.89964 + 1.89964i) q^{7} +(1.78822 + 2.19141i) q^{8} +(-2.06871 + 2.39175i) q^{10} +(0.371763 + 0.511688i) q^{11} +(-1.67521 + 0.265328i) q^{13} +(3.22449 + 2.00929i) q^{14} +(2.44685 - 3.16432i) q^{16} +(0.541217 - 1.06220i) q^{17} +(0.913372 + 2.81107i) q^{19} +(3.95647 + 2.08478i) q^{20} +(0.585977 - 0.675794i) q^{22} +(4.19377 + 0.664227i) q^{23} +(-1.53335 + 4.75908i) q^{25} +(0.901327 + 2.22286i) q^{26} +(1.73657 - 5.08463i) q^{28} +(5.22865 + 1.69889i) q^{29} +(7.39865 - 2.40397i) q^{31} +(-5.14170 - 2.35859i) q^{32} +(-1.63636 - 0.405818i) q^{34} +(5.93440 + 0.932412i) q^{35} +(0.788923 + 4.98106i) q^{37} +(3.58030 - 2.15736i) q^{38} +(1.60644 - 6.11713i) q^{40} +(-6.93315 - 5.03723i) q^{41} +(6.55061 + 6.55061i) q^{43} +(-1.11838 - 0.591069i) q^{44} +(-0.426363 - 5.98966i) q^{46} +(3.03945 + 5.96526i) q^{47} -0.217294i q^{49} +(7.04640 + 0.590090i) q^{50} +(2.77385 - 1.95262i) q^{52} +(-4.62574 - 9.07852i) q^{53} +(0.435374 - 1.34559i) q^{55} +(-7.55988 - 0.765918i) q^{56} +(0.667949 - 7.74622i) q^{58} +(-5.41851 - 3.93677i) q^{59} +(10.3079 - 7.48916i) q^{61} +(-5.67809 - 9.42323i) q^{62} +(-1.60455 + 7.83744i) q^{64} +(2.68507 + 2.67845i) q^{65} +(4.48471 + 2.28507i) q^{67} +(-0.0356501 + 2.38400i) q^{68} +(-0.613664 - 8.47327i) q^{70} +(10.6460 + 3.45911i) q^{71} +(-1.16618 + 7.36296i) q^{73} +(6.60942 - 2.68000i) q^{74} +(-4.11707 - 4.24207i) q^{76} +(-1.67824 - 0.265808i) q^{77} +(-2.84085 + 8.74324i) q^{79} +(-8.94060 - 0.256412i) q^{80} +(-4.72155 + 11.1621i) q^{82} +(1.18719 - 2.32999i) q^{83} +(-2.63235 + 0.420254i) q^{85} +(6.92870 - 11.1191i) q^{86} +(-0.456524 + 1.72970i) q^{88} +(9.57838 + 13.1835i) q^{89} +(2.67828 - 3.68634i) q^{91} +(-8.11479 + 2.50314i) q^{92} +(7.24538 - 6.09505i) q^{94} +(3.87820 - 5.35176i) q^{95} +(-14.4118 + 7.34318i) q^{97} +(-0.299338 + 0.0695018i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−0.319851	−	1.37757i	−0.226169	−	0.974088i
$2$	−0.319851	−	1.37757i	−0.226169	−	0.974088i
$3$		0			0
$3$		0			0
$4$	−1.79539	+	0.881234i	−0.897695	+	0.440617i
$5$	−1.31656	−	1.80739i	−0.588783	−	0.808291i
$5$	−1.31656	−	1.80739i	−0.588783	−	0.808291i
$6$		0			0
$7$	−1.89964	+	1.89964i	−0.717998	+	0.717998i	−0.968195	−	0.250197i	$-0.919505\pi$
$7$	−1.89964	+	1.89964i	−0.717998	+	0.717998i	0.250197	+	0.968195i	$0.419505\pi$
$8$	1.78822	+	2.19141i	0.632231	+	0.774780i
$9$		0			0
$10$	−2.06871	+	2.39175i	−0.654182	+	0.756337i
$11$	0.371763	+	0.511688i	0.112091	+	0.154280i	0.861376	−	0.507967i	$-0.169603\pi$
$11$	0.371763	+	0.511688i	0.112091	+	0.154280i	−0.749286	+	0.662247i	$0.769603\pi$
$12$		0			0
$13$	−1.67521	+	0.265328i	−0.464621	+	0.0735887i	−0.384356	−	0.923185i	$-0.625577\pi$
$13$	−1.67521	+	0.265328i	−0.464621	+	0.0735887i	−0.0802646	+	0.996774i	$0.525577\pi$
$14$	3.22449	+	2.00929i	0.861782	+	0.537004i
$15$		0			0
$16$	2.44685	−	3.16432i	0.611713	−	0.791080i
$17$	0.541217	−	1.06220i	0.131264	−	0.257621i	−0.816014	−	0.578032i	$-0.803821\pi$
$17$	0.541217	−	1.06220i	0.131264	−	0.257621i	0.947279	+	0.320411i	$0.103821\pi$
$18$		0			0
$19$	0.913372	+	2.81107i	0.209542	+	0.644904i	0.999496	+	0.0317382i	$0.0101043\pi$
$19$	0.913372	+	2.81107i	0.209542	+	0.644904i	−0.789954	+	0.613166i	$0.789896\pi$
$20$	3.95647	+	2.08478i	0.884695	+	0.466171i
$21$		0			0
$22$	0.585977	−	0.675794i	0.124931	−	0.144080i
$23$	4.19377	+	0.664227i	0.874461	+	0.138501i	0.577502	−	0.816389i	$-0.304028\pi$
$23$	4.19377	+	0.664227i	0.874461	+	0.138501i	0.296959	+	0.954890i	$0.404028\pi$
$24$		0			0
$25$	−1.53335	+	4.75908i	−0.306669	+	0.951816i
$26$	0.901327	+	2.22286i	0.176765	+	0.435938i
$27$		0			0
$28$	1.73657	−	5.08463i	0.328181	−	0.960905i
$29$	5.22865	+	1.69889i	0.970936	+	0.315476i	0.751194	−	0.660082i	$-0.229478\pi$
$29$	5.22865	+	1.69889i	0.970936	+	0.315476i	0.219742	+	0.975558i	$0.429478\pi$
$30$		0			0
$31$	7.39865	−	2.40397i	1.32884	−	0.431765i	0.443316	−	0.896366i	$-0.353802\pi$
$31$	7.39865	−	2.40397i	1.32884	−	0.431765i	0.885520	+	0.464601i	$0.153802\pi$
$32$	−5.14170	−	2.35859i	−0.908932	−	0.416944i
$33$		0			0
$34$	−1.63636	−	0.405818i	−0.280633	−	0.0695972i
$35$	5.93440	+	0.932412i	1.00310	+	0.157606i
$36$		0			0
$37$	0.788923	+	4.98106i	0.129698	+	0.818882i	0.963674	+	0.267081i	$0.0860592\pi$
$37$	0.788923	+	4.98106i	0.129698	+	0.818882i	−0.833976	+	0.551801i	$0.813941\pi$
$38$	3.58030	−	2.15736i	0.580801	−	0.349970i
$39$		0			0
$40$	1.60644	−	6.11713i	0.254001	−	0.967204i
$41$	−6.93315	−	5.03723i	−1.08278	−	0.786683i	−0.104612	−	0.994513i	$-0.533360\pi$
$41$	−6.93315	−	5.03723i	−1.08278	−	0.786683i	−0.978165	+	0.207830i	$0.933360\pi$
$42$		0			0
$43$	6.55061	+	6.55061i	0.998959	+	0.998959i	0.999999	−	0.00104006i	$-0.000331061\pi$
$43$	6.55061	+	6.55061i	0.998959	+	0.998959i	−0.00104006	+	0.999999i	$0.500331\pi$
$44$	−1.11838	−	0.591069i	−0.168602	−	0.0891071i
$45$		0			0
$46$	−0.426363	−	5.98966i	−0.0628639	−	0.883127i
$47$	3.03945	+	5.96526i	0.443349	+	0.870122i	0.999244	+	0.0388697i	$0.0123757\pi$
$47$	3.03945	+	5.96526i	0.443349	+	0.870122i	−0.555895	+	0.831253i	$0.687624\pi$
$48$		0			0
$49$		−	0.217294i		−	0.0310420i
$50$	7.04640	+	0.590090i	0.996512	+	0.0834513i
$51$		0			0
$52$	2.77385	−	1.95262i	0.384663	−	0.270780i
$53$	−4.62574	−	9.07852i	−0.635394	−	1.24703i	−0.954188	−	0.299207i	$-0.903278\pi$
$53$	−4.62574	−	9.07852i	−0.635394	−	1.24703i	0.318794	−	0.947824i	$-0.396722\pi$
$54$		0			0
$55$	0.435374	−	1.34559i	0.0587058	−	0.181439i
$56$	−7.55988	−	0.765918i	−1.01023	−	0.102350i
$57$		0			0
$58$	0.667949	−	7.74622i	0.0877060	−	1.01713i
$59$	−5.41851	−	3.93677i	−0.705429	−	0.512524i	0.176267	−	0.984342i	$-0.443598\pi$
$59$	−5.41851	−	3.93677i	−0.705429	−	0.512524i	−0.881696	+	0.471818i	$0.843598\pi$
$60$		0			0
$61$	10.3079	−	7.48916i	1.31980	−	0.958889i	0.319863	−	0.947464i	$-0.396363\pi$
$61$	10.3079	−	7.48916i	1.31980	−	0.958889i	0.999935	−	0.0114249i	$-0.00363674\pi$
$62$	−5.67809	−	9.42323i	−0.721119	−	1.19675i
$63$		0			0
$64$	−1.60455	+	7.83744i	−0.200568	+	0.979680i
$65$	2.68507	+	2.67845i	0.333042	+	0.332221i
$66$		0			0
$67$	4.48471	+	2.28507i	0.547894	+	0.279166i	0.705947	−	0.708265i	$-0.250522\pi$
$67$	4.48471	+	2.28507i	0.547894	+	0.279166i	−0.158053	+	0.987431i	$0.550522\pi$
$68$	−0.0356501	+	2.38400i	−0.00432321	+	0.289102i
$69$		0			0
$70$	−0.613664	−	8.47327i	−0.0733469	−	1.01275i
$71$	10.6460	+	3.45911i	1.26345	+	0.410520i	0.862723	−	0.505677i	$-0.168757\pi$
$71$	10.6460	+	3.45911i	1.26345	+	0.410520i	0.400728	+	0.916197i	$0.368757\pi$
$72$		0			0
$73$	−1.16618	+	7.36296i	−0.136491	+	0.861770i	0.820499	+	0.571648i	$0.193696\pi$
$73$	−1.16618	+	7.36296i	−0.136491	+	0.861770i	−0.956990	+	0.290121i	$0.906304\pi$
$74$	6.60942	−	2.68000i	0.768329	−	0.311543i
$75$		0			0
$76$	−4.11707	−	4.24207i	−0.472261	−	0.486599i
$77$	−1.67824	−	0.265808i	−0.191254	−	0.0302916i
$78$		0			0
$79$	−2.84085	+	8.74324i	−0.319621	+	0.983691i	0.654190	+	0.756330i	$0.273010\pi$
$79$	−2.84085	+	8.74324i	−0.319621	+	0.983691i	−0.973811	+	0.227361i	$0.926990\pi$
$80$	−8.94060	−	0.256412i	−0.999589	−	0.0286678i
$81$		0			0
$82$	−4.72155	+	11.1621i	−0.521408	+	1.23264i
$83$	1.18719	−	2.32999i	0.130311	−	0.255749i	−0.816627	−	0.577165i	$-0.804159\pi$
$83$	1.18719	−	2.32999i	0.130311	−	0.255749i	0.946938	+	0.321416i	$0.104159\pi$
$84$		0			0
$85$	−2.63235	+	0.420254i	−0.285519	+	0.0455830i
$86$	6.92870	−	11.1191i	0.747141	−	1.19901i
$87$		0			0
$88$	−0.456524	+	1.72970i	−0.0486656	+	0.184386i
$89$	9.57838	+	13.1835i	1.01531	+	1.39745i	0.915443	+	0.402447i	$0.131840\pi$
$89$	9.57838	+	13.1835i	1.01531	+	1.39745i	0.0998628	+	0.995001i	$0.468160\pi$
$90$		0			0
$91$	2.67828	−	3.68634i	0.280760	−	0.386433i
$92$	−8.11479	+	2.50314i	−0.846025	+	0.260971i
$93$		0			0
$94$	7.24538	−	6.09505i	0.747304	−	0.628656i
$95$	3.87820	−	5.35176i	0.397895	−	0.549079i
$96$		0			0
$97$	−14.4118	+	7.34318i	−1.46330	+	0.745587i	−0.990748	−	0.135716i	$-0.956666\pi$
$97$	−14.4118	+	7.34318i	−1.46330	+	0.745587i	−0.472550	+	0.881304i	$0.656666\pi$
$98$	−0.299338	+	0.0695018i	−0.0302377	+	0.00702075i
$99$		0			0
$100$	−1.44091	−	9.89564i	−0.144091	−	0.989564i
$101$	5.68594			0.565772			0.282886	−	0.959154i	$-0.408708\pi$
$101$	5.68594			0.565772			0.282886	+	0.959154i	$0.408708\pi$
$102$		0			0
$103$	6.63638	−	3.38140i	0.653902	−	0.333180i	−0.0953702	−	0.995442i	$-0.530403\pi$
$103$	6.63638	−	3.38140i	0.653902	−	0.333180i	0.749272	+	0.662262i	$0.230403\pi$
$104$	−3.57709	−	3.19661i	−0.350763	−	0.313454i
$105$		0			0
$106$	−11.0267	+	9.27605i	−1.07101	+	0.900970i
$107$	−12.5222	+	12.5222i	−1.21057	+	1.21057i	−0.239731	+	0.970839i	$0.577059\pi$
$107$	−12.5222	+	12.5222i	−1.21057	+	1.21057i	−0.970839	+	0.239731i	$0.922941\pi$
$108$		0			0
$109$	8.30989	−	11.4376i	0.795943	−	1.09552i	−0.197400	−	0.980323i	$-0.563250\pi$
$109$	8.30989	−	11.4376i	0.795943	−	1.09552i	0.993343	−	0.115198i	$-0.0367504\pi$
$110$	−1.99290	−	0.169369i	−0.190015	−	0.0161487i
$111$		0			0
$112$	1.36293	+	10.6592i	0.128785	+	1.00720i
$113$	−13.0323	+	2.06411i	−1.22598	+	0.194175i	−0.735649	−	0.677363i	$-0.763123\pi$
$113$	−13.0323	+	2.06411i	−1.22598	+	0.194175i	−0.490327	+	0.871539i	$0.663123\pi$
$114$		0			0
$115$	−4.32082	−	8.45428i	−0.402919	−	0.788366i
$116$	−10.8846	+	1.55749i	−1.01061	+	0.144610i
$117$		0			0
$118$	−3.69006	+	8.72355i	−0.339698	+	0.803068i
$119$	0.989679	+	3.04592i	0.0907237	+	0.279219i
$120$		0			0
$121$	3.27557	−	10.0812i	0.297779	−	0.916470i
$122$	−13.6138	−	11.8045i	−1.23254	−	1.06873i
$123$		0			0
$124$	−11.1650	+	10.8360i	−1.00265	+	0.973101i
$125$	10.6203	−	3.49425i	0.949906	−	0.312535i
$126$		0			0
$127$	0.370148	−	2.33702i	0.0328453	−	0.207377i	−0.965808	−	0.259259i	$-0.916522\pi$
$127$	0.370148	−	2.33702i	0.0328453	−	0.207377i	0.998653	+	0.0518815i	$0.0165218\pi$
$128$	11.3098	−	0.296442i	0.999657	−	0.0262020i
$129$		0			0
$130$	2.83093	−	4.55557i	0.248289	−	0.399550i
$131$	−6.46861	+	2.10178i	−0.565165	+	0.183633i	−0.577644	−	0.816289i	$-0.696028\pi$
$131$	−6.46861	+	2.10178i	−0.565165	+	0.183633i	0.0124790	+	0.999922i	$0.496028\pi$
$132$		0			0
$133$	−7.07512	−	3.60495i	−0.613490	−	0.312589i
$134$	1.71340	−	6.90888i	0.148016	−	0.596836i
$135$		0			0
$136$	3.29553	−	0.713415i	0.282589	−	0.0611748i
$137$	2.37978	+	15.0253i	0.203318	+	1.28370i	0.852364	+	0.522950i	$0.175168\pi$
$137$	2.37978	+	15.0253i	0.203318	+	1.28370i	−0.649046	+	0.760749i	$0.724832\pi$
$138$		0			0
$139$	7.83437	−	5.69201i	0.664503	−	0.482790i	−0.203678	−	0.979038i	$-0.565289\pi$
$139$	7.83437	−	5.69201i	0.664503	−	0.482790i	0.868181	+	0.496248i	$0.165289\pi$
$140$	−11.4762	+	3.55555i	−0.969919	+	0.300499i
$141$		0			0
$142$	1.36001	−	15.7720i	0.114129	−	1.32356i
$143$	−0.758548	−	0.758548i	−0.0634330	−	0.0634330i
$144$		0			0
$145$	−3.81326	−	11.6869i	−0.316674	−	0.970546i
$146$	10.5160	−	0.748563i	0.870309	−	0.0619515i
$147$		0			0
$148$	−5.80591	−	8.24773i	−0.477243	−	0.677959i
$149$			1.52894i			0.125256i	0.998037	+	0.0626280i	$0.0199482\pi$
$149$			1.52894i			0.125256i	−0.998037	+	0.0626280i	$0.980052\pi$
$150$		0			0
$151$			21.1225i			1.71893i	0.511199	+	0.859463i	$0.329202\pi$
$151$			21.1225i			1.71893i	−0.511199	+	0.859463i	$0.670798\pi$
$152$	−4.52690	+	7.02838i	−0.367180	+	0.570077i
$153$		0			0
$154$	0.170620	+	2.39691i	0.0137490	+	0.193149i
$155$	−14.0857	−	10.2073i	−1.13139	−	0.819870i
$156$		0			0
$157$	−10.5994	−	10.5994i	−0.845925	−	0.845925i	0.143697	−	0.989622i	$-0.454101\pi$
$157$	−10.5994	−	10.5994i	−0.845925	−	0.845925i	−0.989622	+	0.143697i	$0.954101\pi$
$158$	12.9531	+	1.11693i	1.03049	+	0.0888581i
$159$		0			0
$160$	2.50644	+	12.3983i	0.198151	+	0.980171i
$161$	−9.22846	+	6.70487i	−0.727305	+	0.528418i
$162$		0			0
$163$	1.90252	+	12.0120i	0.149017	+	0.940854i	0.942971	+	0.332876i	$0.108019\pi$
$163$	1.90252	+	12.0120i	0.149017	+	0.940854i	−0.793954	+	0.607978i	$0.791981\pi$
$164$	16.8867	+	2.93406i	1.31863	+	0.229112i
$165$		0			0
$166$	−3.58944	−	0.890183i	−0.278595	−	0.0690916i
$167$	8.22079	+	4.18870i	0.636144	+	0.324132i	0.742150	−	0.670234i	$-0.233806\pi$
$167$	8.22079	+	4.18870i	0.636144	+	0.324132i	−0.106006	+	0.994366i	$0.533806\pi$
$168$		0			0
$169$	−9.62779	+	3.12826i	−0.740599	+	0.240635i
$170$	1.42089	+	3.49183i	0.108977	+	0.267811i
$171$		0			0
$172$	−17.5335	−	5.98828i	−1.33692	−	0.456602i
$173$	−1.12169	+	7.08206i	−0.0852803	+	0.538439i	0.907649	+	0.419730i	$0.137875\pi$
$173$	−1.12169	+	7.08206i	−0.0852803	+	0.538439i	−0.992929	+	0.118708i	$0.962125\pi$
$174$		0			0
$175$	−6.12775	−	11.9534i	−0.463214	−	0.903590i
$176$	2.52879	+	0.0756476i	0.190615	+	0.00570216i
$177$		0			0
$178$	15.0975	−	17.4116i	1.13161	−	1.30506i
$179$	0.835280	−	2.57073i	0.0624318	−	0.192145i	−0.914976	−	0.403509i	$-0.867790\pi$
$179$	0.835280	−	2.57073i	0.0624318	−	0.192145i	0.977407	+	0.211364i	$0.0677904\pi$
$180$		0			0
$181$	1.34525	+	4.14024i	0.0999914	+	0.307742i	0.988522	−	0.151075i	$-0.0482735\pi$
$181$	1.34525	+	4.14024i	0.0999914	+	0.307742i	−0.888531	+	0.458817i	$0.848273\pi$
$182$	−5.93483	−	2.51044i	−0.439919	−	0.186086i
$183$		0			0
$184$	6.04378	+	10.3780i	0.445553	+	0.765080i
$185$	7.96408	−	7.98376i	0.585531	−	0.586978i
$186$		0			0
$187$	0.744719	−	0.117952i	0.0544592	−	0.00862550i
$188$	−10.7138	−	8.03150i	−0.781383	−	0.585757i
$189$		0			0
$190$	−8.61287	−	3.63072i	−0.624843	−	0.263400i
$191$	10.3534	−	14.2503i	0.749148	−	1.03111i	−0.248892	−	0.968531i	$-0.580066\pi$
$191$	10.3534	−	14.2503i	0.749148	−	1.03111i	0.998040	−	0.0625824i	$-0.0199336\pi$
$192$		0			0
$193$	5.57116	−	5.57116i	0.401021	−	0.401021i	−0.477572	−	0.878593i	$-0.658483\pi$
$193$	5.57116	−	5.57116i	0.401021	−	0.401021i	0.878593	+	0.477572i	$0.158483\pi$
$194$	14.7254	+	17.5045i	1.05722	+	1.25675i
$195$		0			0
$196$	0.191487	+	0.390128i	0.0136777	+	0.0278663i
$197$	−6.63385	+	3.38011i	−0.472642	+	0.240823i	−0.674052	−	0.738684i	$-0.735448\pi$
$197$	−6.63385	+	3.38011i	−0.472642	+	0.240823i	0.201410	+	0.979507i	$0.435448\pi$
$198$		0			0
$199$	−11.2356			−0.796467			−0.398234	−	0.917284i	$-0.630377\pi$
$199$	−11.2356			−0.796467			−0.398234	+	0.917284i	$0.630377\pi$
$200$	−13.1710	+	5.15009i	−0.931334	+	0.364166i
$201$		0			0
$202$	−1.81866	−	7.83277i	−0.127960	−	0.551112i
$203$	−13.1599	+	6.70529i	−0.923642	+	0.470619i
$204$		0			0
$205$	0.0236448	+	19.1628i	0.00165143	+	1.33838i
$206$	−6.78077	−	8.06052i	−0.472439	−	0.561603i
$207$		0			0
$208$	−3.25942	+	5.95013i	−0.226000	+	0.412567i
$209$	−1.09883	+	1.51241i	−0.0760079	+	0.104616i
$210$		0			0
$211$	8.18653	+	11.2678i	0.563584	+	0.775706i	0.991777	−	0.127981i	$-0.0408496\pi$
$211$	8.18653	+	11.2678i	0.563584	+	0.775706i	−0.428193	+	0.903687i	$0.640850\pi$
$212$	16.3053	+	12.2231i	1.11985	+	0.839488i
$213$		0			0
$214$	21.2555	+	13.2450i	1.45300	+	0.905409i
$215$	3.21527	−	20.4638i	0.219280	−	1.39562i
$216$		0			0
$217$	−9.48811	+	18.6215i	−0.644095	+	1.26411i
$218$	−18.4140	−	7.78911i	−1.24715	−	0.527545i
$219$		0			0
$220$	0.404114	+	2.79953i	0.0272454	+	0.188744i
$221$	−0.624824	+	1.92301i	−0.0420302	+	0.129356i
$222$		0			0
$223$	−21.4198	−	3.39257i	−1.43438	−	0.227183i	−0.609631	−	0.792685i	$-0.708682\pi$
$223$	−21.4198	−	3.39257i	−1.43438	−	0.227183i	−0.824747	+	0.565502i	$0.808682\pi$
$224$	14.2479	−	5.28690i	0.951977	−	0.353246i
$225$		0			0
$226$	7.01186	+	17.2927i	0.466422	+	1.15029i
$227$	−0.210388	+	1.32834i	−0.0139640	+	0.0881651i	−0.993686	−	0.112196i	$-0.964212\pi$
$227$	−0.210388	+	1.32834i	−0.0139640	+	0.0881651i	0.979722	+	0.200361i	$0.0642115\pi$
$228$		0			0
$229$	12.7082	+	4.12914i	0.839781	+	0.272862i	0.697160	−	0.716916i	$-0.254447\pi$
$229$	12.7082	+	4.12914i	0.839781	+	0.272862i	0.142622	+	0.989777i	$0.454447\pi$
$230$	−10.2643	+	8.65634i	−0.676810	+	0.570782i
$231$		0			0
$232$	5.62701	+	14.4961i	0.369431	+	0.951716i
$233$	−12.2616	−	6.24760i	−0.803284	−	0.409294i	0.00360719	−	0.999993i	$-0.498852\pi$
$233$	−12.2616	−	6.24760i	−0.803284	−	0.409294i	−0.806891	+	0.590700i	$0.798852\pi$
$234$		0			0
$235$	6.77995	−	13.3471i	0.442275	−	0.870669i
$236$	13.1976	+	2.29307i	0.859088	+	0.149266i
$237$		0			0
$238$	3.87941	−	2.33759i	0.251465	−	0.151524i
$239$	−23.3147	+	16.9391i	−1.50810	+	1.09570i	−0.541089	+	0.840965i	$0.681988\pi$
$239$	−23.3147	+	16.9391i	−1.50810	+	1.09570i	−0.967011	+	0.254734i	$0.918012\pi$
$240$		0			0
$241$	15.2138	+	11.0535i	0.980007	+	0.712017i	0.957710	−	0.287734i	$-0.0929021\pi$
$241$	15.2138	+	11.0535i	0.980007	+	0.712017i	0.0222970	+	0.999751i	$0.492902\pi$
$242$	−14.9352	−	1.28785i	−0.960071	−	0.0827859i
$243$		0			0
$244$	−11.9071	+	22.5297i	−0.762273	+	1.44232i
$245$	−0.392736	+	0.286081i	−0.0250910	+	0.0182770i
$246$		0			0
$247$	−2.27595	−	4.46680i	−0.144815	−	0.284216i
$248$	18.4985	+	11.9146i	1.17465	+	0.756580i
$249$		0			0
$250$	−8.21048	−	13.5125i	−0.519276	−	0.854606i
$251$		−	5.19716i		−	0.328042i	−0.986457	−	0.164021i	$-0.947554\pi$
$251$		−	5.19716i		−	0.328042i	0.986457	−	0.164021i	$-0.0524465\pi$
$252$		0			0
$253$	1.21921	+	2.39284i	0.0766511	+	0.150436i
$254$	−3.33780	+	0.237596i	−0.209432	+	0.0149081i
$255$		0			0
$256$	−4.02583	−	15.4852i	−0.251615	−	0.967828i
$257$	2.26286	+	2.26286i	0.141153	+	0.141153i	0.774152	−	0.632999i	$-0.218176\pi$
$257$	2.26286	+	2.26286i	0.141153	+	0.141153i	−0.632999	+	0.774152i	$0.718176\pi$
$258$		0			0
$259$	−10.9609	−	7.96358i	−0.681079	−	0.494833i
$260$	−7.18109	−	2.44269i	−0.445352	−	0.151489i
$261$		0			0
$262$	4.96433	+	8.23869i	0.306698	+	0.508988i
$263$	3.31222	+	20.9126i	0.204240	+	1.28952i	0.850325	+	0.526258i	$0.176405\pi$
$263$	3.31222	+	20.9126i	0.204240	+	1.28952i	−0.646085	+	0.763266i	$0.723595\pi$
$264$		0			0
$265$	−10.3184	+	20.3129i	−0.633855	+	1.24781i
$266$	−2.70308	+	10.8995i	−0.165737	+	0.668292i
$267$		0			0
$268$	−10.0655	−	0.150518i	−0.614848	−	0.00919438i
$269$	1.93497	−	0.628710i	0.117977	−	0.0383331i	−0.249433	−	0.968392i	$-0.580244\pi$
$269$	1.93497	−	0.628710i	0.117977	−	0.0383331i	0.367411	+	0.930059i	$0.380244\pi$
$270$		0			0
$271$	−6.63734	−	2.15660i	−0.403190	−	0.131004i	0.100400	−	0.994947i	$-0.467988\pi$
$271$	−6.63734	−	2.15660i	−0.403190	−	0.131004i	−0.503590	+	0.863943i	$0.667988\pi$
$272$	−2.03686	−	4.31163i	−0.123503	−	0.261431i
$273$		0			0
$274$	19.9372	−	8.08417i	1.20445	−	0.488383i
$275$	−3.00521	+	0.984657i	−0.181221	+	0.0593770i
$276$		0			0
$277$	16.9639	+	2.68682i	1.01926	+	0.161435i	0.643633	−	0.765335i	$-0.277427\pi$
$277$	16.9639	+	2.68682i	1.01926	+	0.161435i	0.375629	+	0.926770i	$0.377427\pi$
$278$	−10.3470	−	8.97179i	−0.620570	−	0.538092i
$279$		0			0
$280$	8.56871	+	14.6720i	0.512078	+	0.876823i
$281$	4.69025	+	14.4351i	0.279797	+	0.861126i	0.987910	+	0.155027i	$0.0495465\pi$
$281$	4.69025	+	14.4351i	0.279797	+	0.861126i	−0.708113	+	0.706099i	$0.750454\pi$
$282$		0			0
$283$	3.45853	−	6.78774i	0.205588	−	0.403489i	−0.765072	−	0.643945i	$-0.777297\pi$
$283$	3.45853	−	6.78774i	0.205588	−	0.403489i	0.970660	+	0.240455i	$0.0772967\pi$
$284$	−22.1621	+	3.17121i	−1.31508	+	0.188176i
$285$		0			0
$286$	−0.802329	+	1.28757i	−0.0474427	+	0.0761359i
$287$	22.7395	−	3.60158i	1.34227	−	0.212594i
$288$		0			0
$289$	9.15700	+	12.6035i	0.538647	+	0.741384i
$290$	−14.8799	+	8.99111i	−0.873776	+	0.527976i
$291$		0			0
$292$	−4.39475	−	14.2471i	−0.257183	−	0.833747i
$293$	9.90518	−	9.90518i	0.578667	−	0.578667i	−0.355869	−	0.934536i	$-0.615815\pi$
$293$	9.90518	−	9.90518i	0.578667	−	0.578667i	0.934536	+	0.355869i	$0.115815\pi$
$294$		0			0
$295$	0.0184793	+	14.9764i	0.00107591	+	0.871958i
$296$	−9.50478	+	10.6361i	−0.552454	+	0.618210i
$297$		0			0
$298$	2.10623	−	0.489035i	0.122010	−	0.0283290i
$299$	−7.20169			−0.416485
$300$		0			0
$301$	−24.8877			−1.43450
$302$	29.0977	−	6.75606i	1.67438	−	0.388768i
$303$		0			0
$304$	11.1300	+	3.98807i	0.638350	+	0.228732i
$305$	−27.1069	−	8.77060i	−1.55214	−	0.502203i
$306$		0			0
$307$	−0.395752	+	0.395752i	−0.0225868	+	0.0225868i	−0.718310	−	0.695723i	$-0.755084\pi$
$307$	−0.395752	+	0.395752i	−0.0225868	+	0.0225868i	0.695723	+	0.718310i	$0.255084\pi$
$308$	3.24734	−	1.00170i	0.185034	−	0.0570770i
$309$		0			0
$310$	−9.55594	+	22.6688i	−0.542741	+	1.28750i
$311$	−7.94526	−	10.9357i	−0.450535	−	0.620108i	0.521978	−	0.852959i	$-0.325194\pi$
$311$	−7.94526	−	10.9357i	−0.450535	−	0.620108i	−0.972512	+	0.232851i	$0.925194\pi$
$312$		0			0
$313$	24.5092	−	3.88187i	1.38534	−	0.219416i	0.581154	−	0.813793i	$-0.302601\pi$
$313$	24.5092	−	3.88187i	1.38534	−	0.219416i	0.804187	+	0.594377i	$0.202601\pi$
$314$	−11.2112	+	17.9916i	−0.632683	+	1.01533i
$315$		0			0
$316$	−2.60441	−	18.2010i	−0.146509	−	1.02389i
$317$	9.93010	−	19.4889i	0.557730	−	1.09461i	−0.424236	−	0.905551i	$-0.639457\pi$
$317$	9.93010	−	19.4889i	0.557730	−	1.09461i	0.981966	−	0.189055i	$-0.0605425\pi$
$318$		0			0
$319$	1.07452	+	3.30703i	0.0601614	+	0.185158i
$320$	16.2778	−	7.41840i	0.909958	−	0.414701i
$321$		0			0
$322$	12.1882	+	10.5683i	0.679219	+	0.588947i
$323$	3.48025	+	0.551217i	0.193646	+	0.0306705i
$324$		0			0
$325$	1.30596	−	8.37932i	0.0724419	−	0.464801i
$326$	15.9389	−	6.46291i	0.882772	−	0.357947i
$327$		0			0
$328$	−1.35936	−	24.2011i	−0.0750583	−	1.33628i
$329$	−17.1057	−	5.55799i	−0.943070	−	0.306422i
$330$		0			0
$331$	23.9793	−	7.79135i	1.31802	−	0.428251i	0.436207	−	0.899846i	$-0.356322\pi$
$331$	23.9793	−	7.79135i	1.31802	−	0.428251i	0.881815	+	0.471595i	$0.156322\pi$
$332$	−0.0782004	+	5.22943i	−0.00429180	+	0.287002i
$333$		0			0
$334$	3.14079	−	12.6645i	0.171857	−	0.692969i
$335$	−1.77436	−	11.1141i	−0.0969434	−	0.607226i
$336$		0			0
$337$	−1.74034	−	10.9881i	−0.0948026	−	0.598560i	−0.988656	−	0.150200i	$-0.952008\pi$
$337$	−1.74034	−	10.9881i	−0.0948026	−	0.598560i	0.893853	−	0.448360i	$-0.147992\pi$
$338$	7.38885	+	12.2624i	0.401901	+	0.666985i
$339$		0			0
$340$	4.35576	−	3.07424i	0.236224	−	0.166724i
$341$	3.98063	+	2.89209i	0.215563	+	0.156616i
$342$		0			0
$343$	−12.8847	−	12.8847i	−0.695710	−	0.695710i
$344$	−2.64114	+	26.0690i	−0.142401	+	1.40555i
$345$		0			0
$346$	10.1148	−	0.720004i	0.543775	−	0.0387077i
$347$	−3.35501	−	6.58458i	−0.180106	−	0.353479i	0.783248	−	0.621709i	$-0.213561\pi$
$347$	−3.35501	−	6.58458i	−0.180106	−	0.353479i	−0.963355	+	0.268230i	$0.913561\pi$
$348$		0			0
$349$		−	16.4473i		−	0.880406i	−0.897898	−	0.440203i	$-0.854907\pi$
$349$		−	16.4473i		−	0.880406i	0.897898	−	0.440203i	$-0.145093\pi$
$350$	−14.5066	+	12.2647i	−0.775411	+	0.655576i
$351$		0			0
$352$	−0.704629	−	3.50778i	−0.0375568	−	0.186965i
$353$	−5.94902	−	11.6756i	−0.316634	−	0.621430i	0.676757	−	0.736206i	$-0.263385\pi$
$353$	−5.94902	−	11.6756i	−0.316634	−	0.621430i	−0.993391	+	0.114777i	$0.963385\pi$
$354$		0			0
$355$	−7.76416	−	23.7957i	−0.412079	−	1.26294i
$356$	−28.8147	−	15.2287i	−1.52717	−	0.807122i
$357$		0			0
$358$	−3.80852	−	0.328405i	−0.201286	−	0.0173567i
$359$	−22.2780	−	16.1859i	−1.17579	−	0.854259i	−0.184097	−	0.982908i	$-0.558936\pi$
$359$	−22.2780	−	16.1859i	−1.17579	−	0.854259i	−0.991690	+	0.128649i	$0.958936\pi$
$360$		0			0
$361$	8.30345	−	6.03281i	0.437024	−	0.317516i
$362$	5.27319	−	3.17743i	0.277153	−	0.167002i
$363$		0			0
$364$	−1.56003	+	8.97861i	−0.0817679	+	0.470607i
$365$	14.8431	−	7.58603i	0.776924	−	0.397071i
$366$		0			0
$367$	−25.1586	−	12.8189i	−1.31327	−	0.669143i	−0.349763	−	0.936838i	$-0.613738\pi$
$367$	−25.1586	−	12.8189i	−1.31327	−	0.669143i	−0.963504	+	0.267696i	$0.913738\pi$
$368$	12.3634	−	11.6452i	0.644484	−	0.607046i
$369$		0			0
$370$	−13.5455	−	8.41745i	−0.704197	−	0.437602i
$371$	26.0332	+	8.45871i	1.35158	+	0.439154i
$372$		0			0
$373$	1.69813	−	10.7216i	0.0879257	−	0.555141i	−0.903921	−	0.427700i	$-0.859324\pi$
$373$	1.69813	−	10.7216i	0.0879257	−	0.555141i	0.991846	−	0.127440i	$-0.0406762\pi$
$374$	−0.400686	−	0.988174i	−0.0207190	−	0.0510973i
$375$		0			0
$376$	−7.63712	+	17.3279i	−0.393854	+	0.893616i
$377$	−9.20987	−	1.45870i	−0.474333	−	0.0751269i
$378$		0			0
$379$	−1.53707	+	4.73061i	−0.0789539	+	0.242995i	−0.982741	−	0.184988i	$-0.940776\pi$
$379$	−1.53707	+	4.73061i	−0.0789539	+	0.242995i	0.903787	+	0.427983i	$0.140776\pi$
$380$	−2.24673	+	13.0261i	−0.115255	+	0.668226i
$381$		0			0
$382$	−22.9423	−	9.70459i	−1.17383	−	0.496530i
$383$	−10.6272	+	20.8571i	−0.543025	+	1.06575i	0.442587	+	0.896725i	$0.354061\pi$
$383$	−10.6272	+	20.8571i	−0.543025	+	1.06575i	−0.985612	+	0.169021i	$0.945939\pi$
$384$		0			0
$385$	1.72909	+	3.38320i	0.0881224	+	0.172424i
$386$	−9.45660	−	5.89271i	−0.481328	−	0.299931i
$387$		0			0
$388$	19.4038	−	25.8841i	0.985077	−	1.31406i
$389$	−16.0951	−	22.1530i	−0.816053	−	1.12320i	−0.990361	−	0.138510i	$-0.955769\pi$
$389$	−16.0951	−	22.1530i	−0.816053	−	1.12320i	0.174308	−	0.984691i	$-0.444231\pi$
$390$		0			0
$391$	2.97528	−	4.09512i	0.150466	−	0.207099i
$392$	0.476180	−	0.388570i	0.0240507	−	0.0196257i
$393$		0			0
$394$	6.77818	+	8.05744i	0.341480	+	0.405928i
$395$	19.5426	−	6.37645i	0.983296	−	0.320834i
$396$		0			0
$397$	14.3256	−	7.29924i	0.718980	−	0.366338i	−0.0559093	−	0.998436i	$-0.517806\pi$
$397$	14.3256	−	7.29924i	0.718980	−	0.366338i	0.774889	+	0.632097i	$0.217806\pi$
$398$	3.59371	+	15.4777i	0.180136	+	0.775829i
$399$		0			0
$400$	11.3074	+	16.4968i	0.565369	+	0.824838i
$401$	27.2043			1.35852			0.679259	−	0.733898i	$-0.262301\pi$
$401$	27.2043			1.35852			0.679259	+	0.733898i	$0.262301\pi$
$402$		0			0
$403$	−11.7565	+	5.99022i	−0.585632	+	0.298394i
$404$	−10.2085	+	5.01064i	−0.507891	+	0.249289i
$405$		0			0
$406$	13.4462	+	15.9839i	0.667323	+	0.793269i
$407$	−2.25546	+	2.25546i	−0.111799	+	0.111799i
$408$		0			0
$409$	7.09641	−	9.76738i	0.350895	−	0.482966i	−0.596689	−	0.802473i	$-0.703517\pi$
$409$	7.09641	−	9.76738i	0.350895	−	0.482966i	0.947584	+	0.319507i	$0.103517\pi$
$410$	26.3904	−	6.16181i	1.30333	−	0.304310i
$411$		0			0
$412$	−8.93508	+	11.9191i	−0.440200	+	0.587214i
$413$	17.7717	−	2.81476i	0.874488	−	0.138505i
$414$		0			0
$415$	−5.77421	+	0.921849i	−0.283445	+	0.0452518i
$416$	9.23924	+	2.58691i	0.452991	+	0.126834i
$417$		0			0
$418$	2.43492	+	1.02997i	0.119096	+	0.0503775i
$419$	−3.46650	−	10.6688i	−0.169350	−	0.521205i	0.829981	−	0.557792i	$-0.188351\pi$
$419$	−3.46650	−	10.6688i	−0.169350	−	0.521205i	−0.999330	+	0.0365872i	$0.988351\pi$
$420$		0			0
$421$	−0.470464	+	1.44794i	−0.0229290	+	0.0705682i	−0.961866	−	0.273520i	$-0.911812\pi$
$421$	−0.470464	+	1.44794i	−0.0229290	+	0.0705682i	0.938937	+	0.344088i	$0.111812\pi$
$422$	12.9037	−	14.8815i	0.628141	−	0.724421i
$423$		0			0
$424$	11.6229	−	26.3713i	0.564459	−	1.28070i
$425$	4.22522	+	4.20441i	0.204953	+	0.203944i
$426$		0			0
$427$	−5.35469	+	33.8082i	−0.259132	+	1.63609i
$428$	11.4473	−	33.5173i	0.553325	−	1.62012i
$429$		0			0
$430$	−29.2187	+	2.11612i	−1.40905	+	0.102048i
$431$	36.0071	−	11.6994i	1.73440	−	0.563541i	0.740326	−	0.672248i	$-0.234671\pi$
$431$	36.0071	−	11.6994i	1.73440	−	0.563541i	0.994074	+	0.108708i	$0.0346713\pi$
$432$		0			0
$433$	−33.3181	−	16.9764i	−1.60116	−	0.815834i	−0.999859	−	0.0168151i	$-0.994647\pi$
$433$	−33.3181	−	16.9764i	−1.60116	−	0.815834i	−0.601306	−	0.799019i	$-0.705353\pi$
$434$	28.6871	+	7.11442i	1.37703	+	0.341503i
$435$		0			0
$436$	−4.84030	+	27.8579i	−0.231808	+	1.33415i
$437$	1.96328	+	12.3957i	0.0939165	+	0.592965i
$438$		0			0
$439$	−3.13332	+	2.27649i	−0.149545	+	0.108651i	−0.660042	−	0.751229i	$-0.729462\pi$
$439$	−3.13332	+	2.27649i	−0.149545	+	0.108651i	0.510497	+	0.859880i	$0.329462\pi$
$440$	3.72728	−	1.45213i	0.177691	−	0.0692275i
$441$		0			0
$442$	2.84893	+	0.245660i	0.135510	+	0.0116849i
$443$	−14.4860	−	14.4860i	−0.688250	−	0.688250i	0.273595	−	0.961845i	$-0.411787\pi$
$443$	−14.4860	−	14.4860i	−0.688250	−	0.688250i	−0.961845	+	0.273595i	$0.911787\pi$
$444$		0			0
$445$	11.2173	−	34.6688i	0.531750	−	1.64346i
$446$	2.17767	+	30.5924i	0.103116	+	1.44859i
$447$		0			0
$448$	−11.8403	−	17.9364i	−0.559400	−	0.847416i
$449$		−	23.1164i		−	1.09093i	−0.838134	−	0.545465i	$-0.816353\pi$
$449$		−	23.1164i		−	1.09093i	0.838134	−	0.545465i	$-0.183647\pi$
$450$		0			0
$451$		−	5.42027i		−	0.255231i
$452$	21.5791	−	15.1904i	1.01500	−	0.714496i
$453$		0			0
$454$	1.89717	−	0.135047i	0.0890388	−	0.00633807i
$455$	−10.1888	+	0.0125719i	−0.477657	+	0.000589379i
$456$		0			0
$457$	−5.45027	−	5.45027i	−0.254953	−	0.254953i	0.568045	−	0.822998i	$-0.307700\pi$
$457$	−5.45027	−	5.45027i	−0.254953	−	0.254953i	−0.822998	+	0.568045i	$0.807700\pi$
$458$	1.62344	−	18.8271i	0.0758586	−	0.879734i
$459$		0			0
$460$	15.2078	+	11.3711i	0.709066	+	0.530179i
$461$	11.7401	−	8.52968i	0.546791	−	0.397267i	−0.279810	−	0.960055i	$-0.590272\pi$
$461$	11.7401	−	8.52968i	0.546791	−	0.397267i	0.826601	+	0.562789i	$0.190272\pi$
$462$		0			0
$463$	−0.0468495	−	0.295796i	−0.00217728	−	0.0137468i	0.986576	−	0.163304i	$-0.0522152\pi$
$463$	−0.0468495	−	0.295796i	−0.00217728	−	0.0137468i	−0.988753	+	0.149557i	$0.952215\pi$
$464$	18.1696	−	12.3882i	0.843501	−	0.575107i
$465$		0			0
$466$	−4.68460	+	18.8895i	−0.217010	+	0.875039i
$467$	24.4141	+	12.4396i	1.12975	+	0.575636i	0.915970	−	0.401246i	$-0.131423\pi$
$467$	24.4141	+	12.4396i	1.12975	+	0.575636i	0.213779	+	0.976882i	$0.431423\pi$
$468$		0			0
$469$	−12.8602	+	4.17852i	−0.593828	+	0.192946i
$470$	−20.5551	−	5.07076i	−0.948137	−	0.233897i
$471$		0			0
$472$	−1.06239	−	18.9140i	−0.0489005	−	0.870586i
$473$	−0.916595	+	5.78715i	−0.0421451	+	0.266093i
$474$		0			0
$475$	−14.7786	+	0.0364706i	−0.678090	+	0.00167339i
$476$	−4.46103	−	4.59647i	−0.204471	−	0.210679i
$477$		0			0
$478$	30.7920	+	26.6996i	1.40839	+	1.22121i
$479$	0.998874	−	3.07422i	0.0456397	−	0.140465i	−0.925640	−	0.378406i	$-0.876472\pi$
$479$	0.998874	−	3.07422i	0.0456397	−	0.140465i	0.971280	+	0.237941i	$0.0764725\pi$
$480$		0			0
$481$	−2.64323	−	8.13502i	−0.120521	−	0.370925i
$482$	10.3608	−	24.4935i	0.471920	−	1.11565i
$483$		0			0
$484$	3.00295	+	20.9862i	0.136498	+	0.953917i
$485$	32.2460	+	16.3801i	1.46422	+	0.743781i
$486$		0			0
$487$	8.61334	−	1.36422i	0.390308	−	0.0618187i	0.0418035	−	0.999126i	$-0.486690\pi$
$487$	8.61334	−	1.36422i	0.390308	−	0.0618187i	0.348504	+	0.937307i	$0.386690\pi$
$488$	34.8447	+	9.19667i	1.57734	+	0.416314i
$489$		0			0
$490$	0.519713	+	0.449518i	0.0234782	+	0.0203071i
$491$	−9.14226	+	12.5832i	−0.412585	+	0.567874i	−0.963846	−	0.266458i	$-0.914147\pi$
$491$	−9.14226	+	12.5832i	−0.412585	+	0.567874i	0.551262	+	0.834332i	$0.314147\pi$
$492$		0			0
$493$	4.63440	−	4.63440i	0.208723	−	0.208723i
$494$	−5.42536	+	4.56399i	−0.244099	+	0.205344i
$495$		0			0
$496$	10.4965	−	29.2938i	0.471306	−	1.31533i
$497$	−26.7947	+	13.6526i	−1.20191	+	0.612403i
$498$		0			0
$499$	−17.8406			−0.798657			−0.399328	−	0.916808i	$-0.630757\pi$
$499$	−17.8406			−0.798657			−0.399328	+	0.916808i	$0.630757\pi$
$500$	−15.9883	+	15.6325i	−0.715018	+	0.699106i
$501$		0			0
$502$	−7.15945	+	1.66232i	−0.319542	+	0.0741929i
$503$	6.24965	−	3.18436i	0.278658	−	0.141983i	−0.309076	−	0.951037i	$-0.600020\pi$
$503$	6.24965	−	3.18436i	0.278658	−	0.141983i	0.587735	+	0.809054i	$0.300020\pi$
$504$		0			0
$505$	−7.48587	−	10.2767i	−0.333117	−	0.457308i
$506$	2.90633	−	2.44490i	0.129202	−	0.108689i
$507$		0			0
$508$	1.39490	+	4.52205i	0.0618889	+	0.200634i
$509$	16.3845	−	22.5514i	0.726231	−	0.999571i	−0.273063	−	0.961996i	$-0.588037\pi$
$509$	16.3845	−	22.5514i	0.726231	−	0.999571i	0.999294	−	0.0375751i	$-0.0119633\pi$
$510$		0			0
$511$	−11.7717	−	16.2023i	−0.520749	−	0.716749i
$512$	−20.0443	+	10.4988i	−0.885842	+	0.463987i
$513$		0			0
$514$	2.39346	−	3.84102i	0.105571	−	0.169420i
$515$	−14.8487	−	7.54273i	−0.654313	−	0.332373i
$516$		0			0
$517$	−1.92240	+	3.77291i	−0.0845469	+	0.165933i
$518$	−7.46451	+	17.6466i	−0.327972	+	0.775346i
$519$		0			0
$520$	−1.06809	+	10.6737i	−0.0468389	+	0.468075i
$521$	−3.19880	+	9.84488i	−0.140142	+	0.431312i	−0.996354	−	0.0853117i	$-0.972811\pi$
$521$	−3.19880	+	9.84488i	−0.140142	+	0.431312i	0.856213	+	0.516624i	$0.172811\pi$
$522$		0			0
$523$	21.5896	+	3.41946i	0.944049	+	0.149523i	0.609438	−	0.792834i	$-0.291395\pi$
$523$	21.5896	+	3.41946i	0.944049	+	0.149523i	0.334611	+	0.942356i	$0.391395\pi$
$524$	9.76151	−	9.47387i	0.426434	−	0.413868i
$525$		0			0
$526$	27.7491	−	11.2517i	1.20992	−	0.490599i
$527$	1.45078	−	9.15990i	0.0631972	−	0.399011i
$528$		0			0
$529$	−4.72781	−	1.53616i	−0.205557	−	0.0667896i
$530$	31.2828	+	7.71719i	1.35884	+	0.335214i
$531$		0			0
$532$	15.8794	+	0.237459i	0.688459	+	0.0102952i
$533$	12.9510	+	6.59888i	0.560972	+	0.285829i
$534$		0			0
$535$	39.1189	+	6.14635i	1.69126	+	0.265730i
$536$	3.01211	+	13.9140i	0.130103	+	0.600995i
$537$		0			0
$538$	−1.48499	−	2.46446i	−0.0640226	−	0.106250i
$539$	0.111187	−	0.0807820i	0.00478916	−	0.00347953i
$540$		0			0
$541$	21.4851	+	15.6098i	0.923715	+	0.671118i	0.944446	−	0.328667i	$-0.106599\pi$
$541$	21.4851	+	15.6098i	0.923715	+	0.671118i	−0.0207309	+	0.999785i	$0.506599\pi$
$542$	−0.847905	+	9.83318i	−0.0364206	+	0.422371i
$543$		0			0
$544$	−5.28807	+	4.18499i	−0.226724	+	0.179430i
$545$	−31.6127	+	0.0390067i	−1.35414	+	0.00167087i
$546$		0			0
$547$	5.65554	+	11.0996i	0.241814	+	0.474586i	0.979734	−	0.200302i	$-0.0641922\pi$
$547$	5.65554	+	11.0996i	0.241814	+	0.474586i	−0.737921	+	0.674887i	$0.764192\pi$
$548$	−17.5134	−	24.8792i	−0.748137	−	1.06278i
$549$		0			0
$550$	2.31765	+	3.82493i	0.0988250	+	0.163096i
$551$			16.2498i			0.692266i
$552$		0			0
$553$	−11.2124	−	22.0056i	−0.476801	−	0.935775i
$554$	−1.72465	−	24.2283i	−0.0732734	−	1.02936i
$555$		0			0
$556$	−9.04977	+	17.1233i	−0.383796	+	0.726189i
$557$	25.7954	+	25.7954i	1.09299	+	1.09299i	0.995208	+	0.0977791i	$0.0311739\pi$
$557$	25.7954	+	25.7954i	1.09299	+	1.09299i	0.0977791	+	0.995208i	$0.468826\pi$
$558$		0			0
$559$	−12.7117	−	9.23562i	−0.537649	−	0.390625i
$560$	17.4710	−	16.4969i	0.738286	−	0.697119i
$561$		0			0
$562$	18.3852	−	11.0782i	0.775531	−	0.467307i
$563$	6.27661	+	39.6289i	0.264527	+	1.67016i	0.659681	+	0.751545i	$0.270691\pi$
$563$	6.27661	+	39.6289i	0.264527	+	1.67016i	−0.395154	+	0.918615i	$0.629309\pi$
$564$		0			0
$565$	20.8885	+	20.8370i	0.878784	+	0.876618i
$566$	−10.4568	−	2.59329i	−0.439532	−	0.109004i
$567$		0			0
$568$	11.4571	+	29.5154i	0.480730	+	1.23844i
$569$	10.0584	−	3.26818i	0.421671	−	0.137009i	−0.0904926	−	0.995897i	$-0.528844\pi$
$569$	10.0584	−	3.26818i	0.421671	−	0.137009i	0.512164	+	0.858888i	$0.328844\pi$
$570$		0			0
$571$	−33.2285	−	10.7966i	−1.39057	−	0.451823i	−0.484439	−	0.874825i	$-0.660976\pi$
$571$	−33.2285	−	10.7966i	−1.39057	−	0.451823i	−0.906129	+	0.423002i	$0.860976\pi$
$572$	2.03035	+	0.693431i	0.0848931	+	0.0289938i
$573$		0			0
$574$	−12.2347	−	30.1732i	−0.510665	−	1.25941i
$575$	−9.59161	+	18.9400i	−0.399998	+	0.789852i
$576$		0			0
$577$	42.9968	+	6.81002i	1.78998	+	0.283505i	0.961156	−	0.276005i	$-0.0890107\pi$
$577$	42.9968	+	6.81002i	1.78998	+	0.283505i	0.828824	+	0.559510i	$0.189011\pi$
$578$	14.4333	−	16.6457i	0.600348	−	0.692368i
$579$		0			0
$580$	17.1452	+	17.6222i	0.711916	+	0.731723i
$581$	2.17091	+	6.68138i	0.0900646	+	0.277190i
$582$		0			0
$583$	2.92569	−	5.74200i	0.121170	−	0.237809i
$584$	−18.2206	+	10.6110i	−0.753976	+	0.439087i
$585$		0			0
$586$	−16.8133	−	10.4769i	−0.694549	−	0.432796i
$587$	−13.4305	+	2.12719i	−0.554338	+	0.0877985i	−0.427317	−	0.904102i	$-0.640541\pi$
$587$	−13.4305	+	2.12719i	−0.554338	+	0.0877985i	−0.127020	+	0.991900i	$0.540541\pi$
$588$		0			0
$589$	13.5154	+	18.6024i	0.556894	+	0.766499i
$590$	20.6251	−	4.81567i	0.849121	−	0.198258i
$591$		0			0
$592$	17.6921	+	9.69152i	0.727139	+	0.398319i
$593$	−8.49730	+	8.49730i	−0.348942	+	0.348942i	−0.859715	−	0.510773i	$-0.829359\pi$
$593$	−8.49730	+	8.49730i	−0.348942	+	0.348942i	0.510773	+	0.859715i	$0.329359\pi$
$594$		0			0
$595$	4.20220	−	5.79887i	0.172274	−	0.237731i
$596$	−1.34736	−	2.74505i	−0.0551900	−	0.112442i
$597$		0			0
$598$	2.30347	+	9.92083i	0.0941960	+	0.405693i
$599$	−32.3191			−1.32052			−0.660261	−	0.751036i	$-0.729554\pi$
$599$	−32.3191			−1.32052			−0.660261	+	0.751036i	$0.729554\pi$
$600$		0			0
$601$	−29.2439			−1.19288			−0.596441	−	0.802657i	$-0.703419\pi$
$601$	−29.2439			−1.19288			−0.596441	+	0.802657i	$0.703419\pi$
$602$	7.96036	+	34.2845i	0.324440	+	1.39733i
$603$		0			0
$604$	−18.6139	−	37.9231i	−0.757388	−	1.54307i
$605$	−22.5331	+	7.35221i	−0.916102	+	0.298910i
$606$		0			0
$607$	−3.02390	+	3.02390i	−0.122737	+	0.122737i	−0.765807	−	0.643070i	$-0.777660\pi$
$607$	−3.02390	+	3.02390i	−0.122737	+	0.122737i	0.643070	+	0.765807i	$0.277660\pi$
$608$	1.93389	−	16.6079i	0.0784297	−	0.673541i
$609$		0			0
$610$	−3.41192	+	40.1469i	−0.138145	+	1.62550i
$611$	−6.67448	−	9.18663i	−0.270020	−	0.371651i
$612$		0			0
$613$	−30.0602	+	4.76106i	−1.21412	+	0.192297i	−0.730458	−	0.682958i	$-0.760693\pi$
$613$	−30.0602	+	4.76106i	−1.21412	+	0.192297i	−0.483661	+	0.875255i	$0.660693\pi$
$614$	0.671758	+	0.418594i	0.0271099	+	0.0168931i
$615$		0			0
$616$	−2.41857	−	4.15304i	−0.0974471	−	0.167331i
$617$	6.53005	−	12.8160i	0.262890	−	0.515951i	−0.721398	−	0.692521i	$-0.756500\pi$
$617$	6.53005	−	12.8160i	0.262890	−	0.515951i	0.984288	+	0.176570i	$0.0565001\pi$
$618$		0			0
$619$	0.651133	+	2.00398i	0.0261713	+	0.0805469i	0.963289	−	0.268466i	$-0.0865168\pi$
$619$	0.651133	+	2.00398i	0.0261713	+	0.0805469i	−0.937118	+	0.349013i	$0.886517\pi$
$620$	34.2843	+	5.91332i	1.37689	+	0.237485i
$621$		0			0
$622$	−12.5234	+	14.4429i	−0.502142	+	0.579110i
$623$	−43.2395	−	6.84846i	−1.73235	−	0.274378i
$624$		0			0
$625$	−20.2977	−	14.5946i	−0.811908	−	0.583785i
$626$	−13.1868	−	32.5215i	−0.527052	−	1.29982i
$627$		0			0
$628$	28.3706	+	9.68951i	1.13211	+	0.386653i
$629$	5.71786	+	1.85784i	0.227986	+	0.0740771i
$630$		0			0
$631$	28.3045	−	9.19668i	1.12678	−	0.366114i	0.314431	−	0.949280i	$-0.398186\pi$
$631$	28.3045	−	9.19668i	1.12678	−	0.366114i	0.812353	+	0.583166i	$0.198186\pi$
$632$	−24.2401	+	9.40936i	−0.964218	+	0.374284i
$633$		0			0
$634$	−30.0235	−	7.44584i	−1.19238	−	0.295712i
$635$	−4.71124	+	2.40782i	−0.186960	+	0.0955516i
$636$		0			0
$637$	0.0576542	+	0.364014i	0.00228434	+	0.0144228i
$638$	4.21197	−	2.53798i	0.166753	−	0.100480i
$639$		0			0
$640$	−15.4258	−	20.0510i	−0.609760	−	0.792586i
$641$	−10.3700	−	7.53427i	−0.409592	−	0.297586i	0.363845	−	0.931460i	$-0.381464\pi$
$641$	−10.3700	−	7.53427i	−0.409592	−	0.297586i	−0.773437	+	0.633874i	$0.781464\pi$
$642$		0			0
$643$	1.49163	+	1.49163i	0.0588243	+	0.0588243i	0.735907	−	0.677083i	$-0.236756\pi$
$643$	1.49163	+	1.49163i	0.0588243	+	0.0588243i	−0.677083	+	0.735907i	$0.736756\pi$
$644$	10.6601	−	20.1703i	0.420068	−	0.794821i
$645$		0			0
$646$	−0.353823	−	4.97059i	−0.0139210	−	0.195565i
$647$	10.0385	+	19.7017i	0.394654	+	0.774552i	0.999767	−	0.0215874i	$-0.00687201\pi$
$647$	10.0385	+	19.7017i	0.394654	+	0.774552i	−0.605113	+	0.796140i	$0.706872\pi$
$648$		0			0
$649$		−	4.23613i		−	0.166283i
$650$	−11.9608	+	0.881080i	−0.469141	+	0.0345588i
$651$		0			0
$652$	−14.0012	−	19.8897i	−0.548328	−	0.778941i
$653$	−10.1505	−	19.9215i	−0.397220	−	0.779589i	0.602610	−	0.798036i	$-0.294128\pi$
$653$	−10.1505	−	19.9215i	−0.397220	−	0.779589i	−0.999830	+	0.0184475i	$0.994128\pi$
$654$		0			0
$655$	12.3150	+	8.92420i	0.481188	+	0.348698i
$656$	−32.9038	+	9.61336i	−1.28468	+	0.375338i
$657$		0			0
$658$	−2.18522	+	25.3421i	−0.0851887	+	0.987936i
$659$	21.7105	+	15.7736i	0.845720	+	0.614451i	0.923962	−	0.382483i	$-0.124931\pi$
$659$	21.7105	+	15.7736i	0.845720	+	0.614451i	−0.0782429	+	0.996934i	$0.524931\pi$
$660$		0			0
$661$	−26.7479	+	19.4335i	−1.04037	+	0.755875i	−0.970358	−	0.241671i	$-0.922304\pi$
$661$	−26.7479	+	19.4335i	−1.04037	+	0.755875i	−0.0700142	+	0.997546i	$0.522304\pi$
$662$	−18.4029	−	30.5411i	−0.715250	−	1.18701i
$663$		0			0
$664$	7.22890	−	1.56491i	0.280536	−	0.0607304i
$665$	2.79924	+	17.5337i	0.108550	+	0.679926i
$666$		0			0
$667$	20.7993	+	10.5978i	0.805352	+	0.410347i
$668$	−18.4508	−	0.275911i	−0.713881	−	0.0106753i
$669$		0			0
$670$	−14.7429	+	5.99915i	−0.569566	+	0.231767i
$671$	7.66423	+	2.49026i	0.295874	+	0.0961354i
$672$		0			0
$673$	−0.968440	+	6.11449i	−0.0373306	+	0.235696i	−0.999298	−	0.0374688i	$-0.988071\pi$
$673$	−0.968440	+	6.11449i	−0.0373306	+	0.235696i	0.961967	+	0.273165i	$0.0880705\pi$
$674$	−14.5802	+	5.91200i	−0.561609	+	0.227722i
$675$		0			0
$676$	14.5289	−	14.1008i	0.558804	−	0.542338i
$677$	−37.8109	−	5.98865i	−1.45319	−	0.230163i	−0.620632	−	0.784102i	$-0.713124\pi$
$677$	−37.8109	−	5.98865i	−1.45319	−	0.230163i	−0.832557	+	0.553939i	$0.813124\pi$
$678$		0			0
$679$	13.4279	−	41.3267i	0.515315	−	1.58598i
$680$	−5.62818	−	5.01706i	−0.215831	−	0.192395i
$681$		0			0
$682$	2.71085	−	6.40862i	0.103804	−	0.245399i
$683$	21.0947	−	41.4007i	0.807166	−	1.58415i	−0.00447006	−	0.999990i	$-0.501423\pi$
$683$	21.0947	−	41.4007i	0.807166	−	1.58415i	0.811636	−	0.584163i	$-0.198577\pi$
$684$		0			0
$685$	24.0235	−	24.0829i	0.917892	−	0.920160i
$686$	−13.6284	+	21.8708i	−0.520335	+	0.835031i
$687$		0			0
$688$	36.7566	−	4.69985i	1.40133	−	0.179180i
$689$	10.1579	+	13.9811i	0.386985	+	0.532639i
$690$		0			0
$691$	20.3465	−	28.0045i	0.774016	−	1.06534i	−0.221901	−	0.975069i	$-0.571226\pi$
$691$	20.3465	−	28.0045i	0.774016	−	1.06534i	0.995917	−	0.0902726i	$-0.0287738\pi$
$692$	−4.22708	−	13.7035i	−0.160690	−	0.520930i
$693$		0			0
$694$	−7.99760	+	6.72784i	−0.303585	+	0.255385i
$695$	−20.6021	−	6.66594i	−0.781483	−	0.252853i
$696$		0			0
$697$	−9.10288	+	4.63815i	−0.344796	+	0.175682i
$698$	−22.6573	+	5.26070i	−0.857593	+	0.199121i
$699$		0			0
$700$	21.5354	+	16.0610i	0.813962	+	0.607048i
$701$	1.62441			0.0613530			0.0306765	−	0.999529i	$-0.490234\pi$
$701$	1.62441			0.0613530			0.0306765	+	0.999529i	$0.490234\pi$
$702$		0			0
$703$	−13.2815	+	6.76729i	−0.500923	+	0.255233i
$704$	−4.60684	+	2.09264i	−0.173627	+	0.0788695i
$705$		0			0
$706$	−14.1811	+	11.9296i	−0.533714	+	0.448978i
$707$	−10.8013	+	10.8013i	−0.406223	+	0.406223i
$708$		0			0
$709$	−8.33878	+	11.4774i	−0.313170	+	0.431041i	−0.936366	−	0.351024i	$-0.885834\pi$
$709$	−8.33878	+	11.4774i	−0.313170	+	0.431041i	0.623197	+	0.782065i	$0.285834\pi$
$710$	−30.2968	+	18.3067i	−1.13702	+	0.687040i
$711$		0			0
$712$	−11.7622	+	44.5651i	−0.440808	+	1.67015i
$713$	32.6250	−	5.16729i	1.22181	−	0.193516i
$714$		0			0
$715$	−0.372322	+	2.36967i	−0.0139240	+	0.0886206i
$716$	0.765760	+	5.35154i	0.0286178	+	0.199996i
$717$		0			0
$718$	−15.1716	+	35.8665i	−0.566197	+	1.33853i
$719$	5.07697	+	15.6253i	0.189339	+	0.582725i	0.999996	−	0.00279590i	$-0.000889965\pi$
$719$	5.07697	+	15.6253i	0.189339	+	0.582725i	−0.810657	+	0.585521i	$0.800890\pi$
$720$		0			0
$721$	−6.18329	+	19.0302i	−0.230278	+	0.708723i
$722$	−10.9665	−	9.50897i	−0.408130	−	0.353887i
$723$		0			0
$724$	−6.06377	−	6.24787i	−0.225358	−	0.232200i
$725$	−16.1025	+	22.2786i	−0.598032	+	0.827406i
$726$		0			0
$727$	1.57474	−	9.94253i	0.0584039	−	0.368748i	−0.941125	−	0.338059i	$-0.890230\pi$
$727$	1.57474	−	9.94253i	0.0584039	−	0.368748i	0.999529	−	0.0306893i	$-0.00977024\pi$
$728$	12.8676	−	0.722769i	0.476906	−	0.0267876i
$729$		0			0
$730$	−15.1979	−	18.0210i	−0.562498	−	0.666987i
$731$	10.5034	−	3.41275i	0.388481	−	0.126225i
$732$		0			0
$733$	30.7430	+	15.6644i	1.13552	+	0.578576i	0.917645	−	0.397400i	$-0.130088\pi$
$733$	30.7430	+	15.6644i	1.13552	+	0.578576i	0.217875	+	0.975977i	$0.430088\pi$
$734$	−9.61195	+	38.7578i	−0.354784	+	1.43058i
$735$		0			0
$736$	−19.9964	−	13.3067i	−0.737078	−	0.490490i
$737$	0.498005	+	3.14428i	0.0183442	+	0.115821i
$738$		0			0
$739$	−33.3131	+	24.2034i	−1.22544	+	0.890335i	−0.996540	−	0.0831141i	$-0.973513\pi$
$739$	−33.3131	+	24.2034i	−1.22544	+	0.890335i	−0.228902	+	0.973450i	$0.573513\pi$
$740$	−7.26307	+	21.3522i	−0.266996	+	0.784922i
$741$		0			0
$742$	3.32569	−	38.5681i	0.122090	−	1.41588i
$743$	−11.4340	−	11.4340i	−0.419473	−	0.419473i	0.465549	−	0.885022i	$-0.345857\pi$
$743$	−11.4340	−	11.4340i	−0.419473	−	0.419473i	−0.885022	+	0.465549i	$0.845857\pi$
$744$		0			0
$745$	2.76341	−	2.01295i	0.101243	−	0.0737486i
$746$	−15.3128	+	1.09002i	−0.560642	+	0.0399083i
$747$		0			0
$748$	−1.23312	+	0.868042i	−0.0450873	+	0.0317387i
$749$		−	47.5756i		−	1.73837i
$750$		0			0
$751$			39.8961i			1.45583i	0.685668	+	0.727915i	$0.259510\pi$
$751$			39.8961i			1.45583i	−0.685668	+	0.727915i	$0.740490\pi$
$752$	26.3131	+	4.97831i	0.959539	+	0.181540i
$753$		0			0
$754$	0.936331	+	13.1538i	0.0340991	+	0.479033i
$755$	38.1767	−	27.8090i	1.38939	−	1.01207i
$756$		0			0
$757$	−2.42176	−	2.42176i	−0.0880204	−	0.0880204i	0.661726	−	0.749746i	$-0.269824\pi$
$757$	−2.42176	−	2.42176i	−0.0880204	−	0.0880204i	−0.749746	+	0.661726i	$0.769824\pi$
$758$	7.00837	+	0.604325i	0.254555	+	0.0219501i
$759$		0			0
$760$	18.6630	−	1.07139i	0.676978	−	0.0388636i
$761$	−16.8140	+	12.2161i	−0.609507	+	0.442833i	−0.849241	−	0.528006i	$-0.822940\pi$
$761$	−16.8140	+	12.2161i	−0.609507	+	0.442833i	0.239733	+	0.970839i	$0.422940\pi$
$762$		0			0
$763$	5.94150	+	37.5132i	0.215097	+	1.35807i
$764$	−6.03062	+	34.7086i	−0.218180	+	1.25571i
$765$		0			0
$766$	32.1312	+	7.96854i	1.16095	+	0.287915i
$767$	10.1217	+	5.15726i	0.365473	+	0.186218i
$768$		0			0
$769$	−9.52824	+	3.09591i	−0.343597	+	0.111641i	−0.475732	−	0.879590i	$-0.657817\pi$
$769$	−9.52824	+	3.09591i	−0.343597	+	0.111641i	0.132135	+	0.991232i	$0.457817\pi$
$770$	4.10754	−	3.46406i	0.148025	−	0.124836i
$771$		0			0
$772$	−5.09291	+	14.9119i	−0.183298	+	0.536691i
$773$	−4.80098	+	30.3122i	−0.172679	+	1.09025i	0.737289	+	0.675577i	$0.236106\pi$
$773$	−4.80098	+	30.3122i	−0.172679	+	1.09025i	−0.909968	+	0.414677i	$0.863894\pi$
$774$		0			0
$775$	0.0959895	+	38.8969i	0.00344804	+	1.39722i
$776$	−41.8634	−	18.4510i	−1.50281	−	0.662351i
$777$		0			0
$778$	−25.3692	+	29.2577i	−0.909531	+	1.04894i
$779$	7.82747	−	24.0905i	0.280448	−	0.863130i
$780$		0			0
$781$	2.18782	+	6.73342i	0.0782863	+	0.240941i
$782$	−6.59296	−	2.78882i	−0.235764	−	0.0997281i
$783$		0			0
$784$	−0.687588	−	0.531687i	−0.0245567	−	0.0189888i
$785$	−5.20256	+	33.1120i	−0.185687	+	1.18182i
$786$		0			0
$787$	34.3093	−	5.43407i	1.22300	−	0.193704i	0.488651	−	0.872480i	$-0.337489\pi$
$787$	34.3093	−	5.43407i	1.22300	−	0.193704i	0.734345	+	0.678776i	$0.237489\pi$
$788$	8.93167	−	11.9146i	0.318178	−	0.424440i
$789$		0			0
$790$	−15.0347	−	24.8818i	−0.534912	−	0.885254i
$791$	20.8356	−	28.6778i	0.740830	−	1.01967i
$792$		0			0
$793$	−15.2809	+	15.2809i	−0.542642	+	0.542642i
$794$	−14.6373	−	17.3998i	−0.519457	−	0.617495i
$795$		0			0
$796$	20.1722	−	9.90115i	0.714985	−	0.350937i
$797$	18.2016	−	9.27416i	0.644732	−	0.328508i	−0.100869	−	0.994900i	$-0.532162\pi$
$797$	18.2016	−	9.27416i	0.644732	−	0.328508i	0.745601	+	0.666392i	$0.232162\pi$
$798$		0			0
$799$	7.98129			0.282358
$800$	19.1087	−	20.8532i	0.675596	−	0.737272i
$801$		0			0
$802$	−8.70134	−	37.4758i	−0.307255	−	1.32332i
$803$	−4.20108	+	2.14056i	−0.148253	+	0.0755387i
$804$		0			0
$805$	24.2682	+	7.85211i	0.855340	+	0.276750i
$806$	12.0123	+	14.2794i	0.423114	+	0.502969i
$807$		0			0
$808$	10.1677	+	12.4602i	0.357698	+	0.438349i
$809$	−20.5456	+	28.2786i	−0.722344	+	0.994222i	0.277098	+	0.960842i	$0.410627\pi$
$809$	−20.5456	+	28.2786i	−0.722344	+	0.994222i	−0.999443	+	0.0333800i	$0.989373\pi$
$810$		0			0
$811$	−20.4028	−	28.0820i	−0.716438	−	0.986093i	−0.999635	−	0.0270307i	$-0.991395\pi$
$811$	−20.4028	−	28.0820i	−0.716438	−	0.986093i	0.283196	−	0.959062i	$-0.408605\pi$
$812$	17.7182	−	23.6355i	0.621786	−	0.829445i
$813$		0			0
$814$	3.82846	+	2.38564i	0.134188	+	0.0836166i
$815$	19.2057	−	19.2531i	0.672745	−	0.674408i
$816$		0			0
$817$	−12.4311	+	24.3974i	−0.434909	+	0.853557i
$818$	−15.7250	−	6.65169i	−0.549813	−	0.232571i
$819$		0			0
$820$	−16.9293	−	34.3838i	−0.591198	−	1.20073i
$821$	11.4445	−	35.2226i	0.399416	−	1.22928i	−0.526053	−	0.850452i	$-0.676329\pi$
$821$	11.4445	−	35.2226i	0.399416	−	1.22928i	0.925469	−	0.378824i	$-0.123671\pi$
$822$		0			0
$823$	39.2887	+	6.22271i	1.36952	+	0.216910i	0.797494	−	0.603327i	$-0.206159\pi$
$823$	39.2887	+	6.22271i	1.36952	+	0.216910i	0.572023	+	0.820237i	$0.306159\pi$
$824$	19.2773	+	8.49633i	0.671558	+	0.295984i
$825$		0			0
$826$	−9.56183	−	23.5814i	−0.332699	−	0.820503i
$827$	−0.257318	+	1.62464i	−0.00894782	+	0.0564943i	−0.991758	−	0.128123i	$-0.959105\pi$
$827$	−0.257318	+	1.62464i	−0.00894782	+	0.0564943i	0.982810	+	0.184618i	$0.0591047\pi$
$828$		0			0
$829$	−35.6026	−	11.5680i	−1.23653	−	0.401773i	−0.383454	−	0.923560i	$-0.625265\pi$
$829$	−35.6026	−	11.5680i	−1.23653	−	0.401773i	−0.853076	+	0.521787i	$0.825265\pi$
$830$	3.11680	+	7.65951i	0.108186	+	0.265865i
$831$		0			0
$832$	0.608469	−	13.5551i	0.0210949	−	0.469939i
$833$	−0.230809	−	0.117603i	−0.00799708	−	0.00407471i
$834$		0			0
$835$	−3.25252	−	20.3729i	−0.112558	−	0.705033i
$836$	0.640043	−	3.68370i	0.0221364	−	0.127404i
$837$		0			0
$838$	−13.5882	+	8.18777i	−0.469398	+	0.282842i
$839$	24.8408	−	18.0479i	0.857600	−	0.623083i	−0.0696306	−	0.997573i	$-0.522182\pi$
$839$	24.8408	−	18.0479i	0.857600	−	0.623083i	0.927231	+	0.374490i	$0.122182\pi$
$840$		0			0
$841$	0.991078	+	0.720060i	0.0341751	+	0.0248297i
$842$	2.14511	+	0.184971i	0.0739255	+	0.00637452i
$843$		0			0
$844$	−24.6276	−	13.0158i	−0.847716	−	0.448023i
$845$	18.3296	+	13.2827i	0.630556	+	0.456938i
$846$		0			0
$847$	12.9282	+	25.3730i	0.444219	+	0.871828i
$848$	−40.0458	−	7.57649i	−1.37518	−	0.260178i
$849$		0			0
$850$	4.44043	−	7.16531i	0.152305	−	0.245768i
$851$			21.4134i			0.734044i
$852$		0			0
$853$	3.51179	+	6.89228i	0.120241	+	0.235987i	0.943280	−	0.331999i	$-0.107723\pi$
$853$	3.51179	+	6.89228i	0.120241	+	0.235987i	−0.823038	+	0.567986i	$0.807723\pi$
$854$	48.2858	−	3.43714i	1.65231	−	0.117617i
$855$		0			0
$856$	−49.8339	−	5.04884i	−1.70329	−	0.172566i
$857$	−15.0616	−	15.0616i	−0.514495	−	0.514495i	0.401406	−	0.915900i	$-0.368522\pi$
$857$	−15.0616	−	15.0616i	−0.514495	−	0.514495i	−0.915900	+	0.401406i	$0.868522\pi$
$858$		0			0
$859$	−6.76410	−	4.91440i	−0.230788	−	0.167677i	0.466381	−	0.884584i	$-0.345557\pi$
$859$	−6.76410	−	4.91440i	−0.230788	−	0.167677i	−0.697169	+	0.716906i	$0.745557\pi$
$860$	12.2607	+	39.5739i	0.418088	+	1.34946i
$861$		0			0
$862$	−27.6336	−	45.8601i	−0.941206	−	1.56200i
$863$	5.82961	+	36.8067i	0.198442	+	1.25291i	0.862818	+	0.505515i	$0.168698\pi$
$863$	5.82961	+	36.8067i	0.198442	+	1.25291i	−0.664375	+	0.747399i	$0.731302\pi$
$864$		0			0
$865$	14.2768	−	7.29661i	0.485427	−	0.248092i
$866$	−12.7293	+	51.3279i	−0.432560	+	1.74419i
$867$		0			0
$868$	0.624985	−	41.7941i	0.0212134	−	1.41858i
$869$	−5.52994	+	1.79679i	−0.187590	+	0.0609518i
$870$		0			0
$871$	−8.11914	−	2.63807i	−0.275107	−	0.0893875i
$872$	39.9243	−	2.24253i	1.35201	−	0.0759417i
$873$		0			0
$874$	16.4479	−	6.66932i	0.556359	−	0.225593i
$875$	−13.5369	+	26.8126i	−0.457631	+	0.906430i
$876$		0			0
$877$	22.5291	+	3.56825i	0.760753	+	0.120491i	0.524745	−	0.851260i	$-0.324161\pi$
$877$	22.5291	+	3.56825i	0.760753	+	0.120491i	0.236008	+	0.971751i	$0.424161\pi$
$878$	4.13822	+	3.58823i	0.139658	+	0.121097i
$879$		0			0
$880$	−3.19258	−	4.67012i	−0.107622	−	0.157430i
$881$	5.60391	+	17.2470i	0.188800	+	0.581068i	0.999993	−	0.00371110i	$-0.00118128\pi$
$881$	5.60391	+	17.2470i	0.188800	+	0.581068i	−0.811193	+	0.584779i	$0.801181\pi$
$882$		0			0
$883$	−12.3251	+	24.1893i	−0.414772	+	0.814035i	0.585223	+	0.810872i	$0.301007\pi$
$883$	−12.3251	+	24.1893i	−0.414772	+	0.814035i	−0.999995	+	0.00316320i	$0.998993\pi$
$884$	−0.572820	−	4.00317i	−0.0192660	−	0.134641i
$885$		0			0
$886$	−15.3221	+	24.5888i	−0.514755	+	0.826077i
$887$	−12.4877	+	1.97785i	−0.419295	+	0.0664098i	−0.362517	−	0.931977i	$-0.618083\pi$
$887$	−12.4877	+	1.97785i	−0.419295	+	0.0664098i	−0.0567776	+	0.998387i	$0.518083\pi$
$888$		0			0
$889$	3.73636	+	5.14266i	0.125313	+	0.172479i
$890$	−51.3465	−	4.36373i	−1.72114	−	0.146273i
$891$		0			0
$892$	41.4466	−	12.7849i	1.38773	−	0.428070i
$893$	−13.9926	+	13.9926i	−0.468245	+	0.468245i
$894$		0			0
$895$	−5.74601	+	1.87483i	−0.192068	+	0.0626688i
$896$	−20.9215	+	22.0478i	−0.698938	+	0.736564i
$897$		0			0
$898$	−31.8444	+	7.39380i	−1.06266	+	0.246734i
$899$	42.7690			1.42643
$900$		0			0
$901$	−12.1467			−0.404666
$902$	−7.46680	+	1.73368i	−0.248617	+	0.0577253i
$903$		0			0
$904$	−27.8279	−	24.8680i	−0.925543	−	0.827098i
$905$	5.71195	−	7.88226i	0.189872	−	0.262015i
$906$		0			0
$907$	18.7242	−	18.7242i	0.621728	−	0.621728i	−0.324245	−	0.945973i	$-0.605110\pi$
$907$	18.7242	−	18.7242i	0.621728	−	0.621728i	0.945973	+	0.324245i	$0.105110\pi$
$908$	−0.792850	−	2.57029i	−0.0263117	−	0.0852981i
$909$		0			0
$910$	3.27621	+	14.0317i	0.108605	+	0.465147i
$911$	14.3129	+	19.7000i	0.474207	+	0.652690i	0.977379	−	0.211497i	$-0.0678337\pi$
$911$	14.3129	+	19.7000i	0.474207	+	0.652690i	−0.503172	+	0.864186i	$0.667834\pi$
$912$		0			0
$913$	1.63358	−	0.258734i	0.0540636	−	0.00856283i
$914$	−5.76485	+	9.25140i	−0.190684	+	0.306009i
$915$		0			0
$916$	−26.4549	+	3.78548i	−0.874095	+	0.125076i
$917$	8.29542	−	16.2807i	0.273939	−	0.537635i
$918$		0			0
$919$	10.9466	+	33.6902i	0.361095	+	1.11134i	0.952390	+	0.304881i	$0.0986167\pi$
$919$	10.9466	+	33.6902i	0.361095	+	1.11134i	−0.591296	+	0.806455i	$0.701383\pi$
$920$	10.8002	−	24.5868i	0.356073	−	0.810603i
$921$		0			0
$922$	−15.5053	−	13.4446i	−0.510640	−	0.442773i
$923$	−18.7522	−	2.97005i	−0.617235	−	0.0977605i
$924$		0			0
$925$	−24.9150	−	3.88314i	−0.819200	−	0.127677i
$926$	−0.392494	+	0.159149i	−0.0128982	+	0.00522997i
$927$		0			0
$928$	−22.8771	−	21.0675i	−0.750979	−	0.691573i
$929$	−13.7959	−	4.48257i	−0.452630	−	0.147068i	0.0738256	−	0.997271i	$-0.476479\pi$
$929$	−13.7959	−	4.48257i	−0.452630	−	0.147068i	−0.526455	+	0.850203i	$0.676479\pi$
$930$		0			0
$931$	0.610829	−	0.198471i	0.0200191	−	0.00650461i
$932$	27.5200	+	0.411531i	0.901446	+	0.0134801i
$933$		0			0
$934$	9.32752	−	37.6109i	0.305206	−	1.23067i
$935$	−1.19365	−	1.19071i	−0.0390366	−	0.0389404i
$936$		0			0
$937$	2.14371	+	13.5349i	0.0700320	+	0.442165i	0.997643	+	0.0686172i	$0.0218587\pi$
$937$	2.14371	+	13.5349i	0.0700320	+	0.442165i	−0.927611	+	0.373547i	$0.878141\pi$
$938$	9.86955	+	16.3793i	0.322252	+	0.534802i
$939$		0			0
$940$	−0.410742	+	29.9380i	−0.0133969	+	0.976469i
$941$	−16.3885	−	11.9070i	−0.534251	−	0.388156i	0.287694	−	0.957722i	$-0.407111\pi$
$941$	−16.3885	−	11.9070i	−0.534251	−	0.388156i	−0.821945	+	0.569566i	$0.807111\pi$
$942$		0			0
$943$	−25.7302	−	25.7302i	−0.837890	−	0.837890i
$944$	−25.7155	+	7.51318i	−0.836968	+	0.244533i
$945$		0			0
$946$	8.26537	−	0.588356i	0.268730	−	0.0191291i
$947$	−8.14549	−	15.9864i	−0.264693	−	0.519489i	0.719960	−	0.694016i	$-0.244160\pi$
$947$	−8.14549	−	15.9864i	−0.264693	−	0.519489i	−0.984652	+	0.174527i	$0.944160\pi$
$948$		0			0
$949$		−	12.6440i		−	0.410440i
$950$	4.77721	+	20.3469i	0.154993	+	0.660141i
$951$		0			0
$952$	−4.90509	+	7.61556i	−0.158975	+	0.246822i
$953$	−3.40557	−	6.68381i	−0.110317	−	0.216510i	0.829247	−	0.558882i	$-0.188770\pi$
$953$	−3.40557	−	6.68381i	−0.110317	−	0.216510i	−0.939564	+	0.342372i	$0.888770\pi$
$954$		0			0
$955$	−39.3868	+	0.0485992i	−1.27453	+	0.00157263i
$956$	26.9316	−	50.9580i	0.871030	−	1.64810i
$957$		0			0
$958$	−4.55444	−	0.392725i	−0.147147	−	0.0126884i
$959$	−33.0635	−	24.0220i	−1.06768	−	0.775711i
$960$		0			0
$961$	23.8814	−	17.3508i	0.770367	−	0.559704i
$962$	−10.3611	+	6.24323i	−0.334056	+	0.201290i
$963$		0			0
$964$	−37.0554	−	6.43837i	−1.19347	−	0.207366i
$965$	−17.4040	−	2.73452i	−0.560256	−	0.0880273i
$966$		0			0
$967$	−6.58765	−	3.35657i	−0.211844	−	0.107940i	0.344849	−	0.938658i	$-0.387930\pi$
$967$	−6.58765	−	3.35657i	−0.211844	−	0.107940i	−0.556693	+	0.830718i	$0.687930\pi$
$968$	27.9494	−	10.8492i	0.898328	−	0.348707i
$969$		0			0
$970$	12.2508	−	49.6603i	0.393348	−	1.59450i
$971$	−33.1625	−	10.7751i	−1.06424	−	0.345791i	−0.275995	−	0.961159i	$-0.589007\pi$
$971$	−33.1625	−	10.7751i	−1.06424	−	0.345791i	−0.788240	+	0.615368i	$0.789007\pi$
$972$		0			0
$973$	−4.06974	+	25.6953i	−0.130470	+	0.823754i
$974$	−4.63430	−	11.4291i	−0.148492	−	0.366213i
$975$		0			0
$976$	1.52392	−	50.9425i	0.0487795	−	1.63063i
$977$	−61.5368	−	9.74647i	−1.96874	−	0.311817i	−0.997184	−	0.0749929i	$-0.976107\pi$
$977$	−61.5368	−	9.74647i	−1.96874	−	0.311817i	−0.971552	−	0.236824i	$-0.923893\pi$
$978$		0			0
$979$	−3.18496	+	9.80228i	−0.101792	+	0.313282i
$980$	0.453011	−	0.859719i	0.0144709	−	0.0274627i
$981$		0			0
$982$	20.2584	+	8.56933i	0.646473	+	0.273458i
$983$	−17.3594	+	34.0698i	−0.553679	+	1.08666i	0.429338	+	0.903144i	$0.358747\pi$
$983$	−17.3594	+	34.0698i	−0.553679	+	1.08666i	−0.983017	+	0.183513i	$0.941253\pi$
$984$		0			0
$985$	14.8430	+	7.53985i	0.472939	+	0.240240i
$986$	−7.86652	−	4.90188i	−0.250521	−	0.156108i
$987$		0			0
$988$	8.02252	+	6.01401i	0.255230	+	0.191331i
$989$	23.1207	+	31.8229i	0.735194	+	1.01191i
$990$		0			0
$991$	−16.5933	+	22.8387i	−0.527103	+	0.725495i	−0.986686	−	0.162640i	$-0.947999\pi$
$991$	−16.5933	+	22.8387i	−0.527103	+	0.725495i	0.459582	+	0.888135i	$0.347999\pi$
$992$	−43.7116	−	5.08994i	−1.38784	−	0.161606i
$993$		0			0
$994$	27.3777	+	32.5448i	0.868369	+	1.03226i
$995$	14.7923	+	20.3071i	0.468946	+	0.643777i
$996$		0			0
$997$	23.7517	−	12.1021i	0.752224	−	0.383277i	−0.0354484	−	0.999372i	$-0.511286\pi$
$997$	23.7517	−	12.1021i	0.752224	−	0.383277i	0.787672	+	0.616094i	$0.211286\pi$
$998$	5.70635	+	24.5767i	0.180631	+	0.777962i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.13		240
3.2	odd	2		300.2.w.a.127.18	✓	240
4.3	odd	2	inner	900.2.bj.f.127.10		240
12.11	even	2		300.2.w.a.127.21	yes	240
25.13	odd	20	inner	900.2.bj.f.163.10		240
75.38	even	20		300.2.w.a.163.21	yes	240
100.63	even	20	inner	900.2.bj.f.163.13		240
300.263	odd	20		300.2.w.a.163.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.18	✓	240	3.2	odd	2
300.2.w.a.127.21	yes	240	12.11	even	2
300.2.w.a.163.18	yes	240	300.263	odd	20
300.2.w.a.163.21	yes	240	75.38	even	20
900.2.bj.f.127.10		240	4.3	odd	2	inner
900.2.bj.f.127.13		240	1.1	even	1	trivial
900.2.bj.f.163.10		240	25.13	odd	20	inner
900.2.bj.f.163.13		240	100.63	even	20	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.319851 - 1.37757i) q^{2} +(-1.79539 + 0.881234i) q^{4} +(-1.31656 - 1.80739i) q^{5} +(-1.89964 + 1.89964i) q^{7} +(1.78822 + 2.19141i) q^{8} +O(q^{10})\)	\(q+(-0.319851 - 1.37757i) q^{2} +(-1.79539 + 0.881234i) q^{4} +(-1.31656 - 1.80739i) q^{5} +(-1.89964 + 1.89964i) q^{7} +(1.78822 + 2.19141i) q^{8} +(-2.06871 + 2.39175i) q^{10} +(0.371763 + 0.511688i) q^{11} +(-1.67521 + 0.265328i) q^{13} +(3.22449 + 2.00929i) q^{14} +(2.44685 - 3.16432i) q^{16} +(0.541217 - 1.06220i) q^{17} +(0.913372 + 2.81107i) q^{19} +(3.95647 + 2.08478i) q^{20} +(0.585977 - 0.675794i) q^{22} +(4.19377 + 0.664227i) q^{23} +(-1.53335 + 4.75908i) q^{25} +(0.901327 + 2.22286i) q^{26} +(1.73657 - 5.08463i) q^{28} +(5.22865 + 1.69889i) q^{29} +(7.39865 - 2.40397i) q^{31} +(-5.14170 - 2.35859i) q^{32} +(-1.63636 - 0.405818i) q^{34} +(5.93440 + 0.932412i) q^{35} +(0.788923 + 4.98106i) q^{37} +(3.58030 - 2.15736i) q^{38} +(1.60644 - 6.11713i) q^{40} +(-6.93315 - 5.03723i) q^{41} +(6.55061 + 6.55061i) q^{43} +(-1.11838 - 0.591069i) q^{44} +(-0.426363 - 5.98966i) q^{46} +(3.03945 + 5.96526i) q^{47} -0.217294i q^{49} +(7.04640 + 0.590090i) q^{50} +(2.77385 - 1.95262i) q^{52} +(-4.62574 - 9.07852i) q^{53} +(0.435374 - 1.34559i) q^{55} +(-7.55988 - 0.765918i) q^{56} +(0.667949 - 7.74622i) q^{58} +(-5.41851 - 3.93677i) q^{59} +(10.3079 - 7.48916i) q^{61} +(-5.67809 - 9.42323i) q^{62} +(-1.60455 + 7.83744i) q^{64} +(2.68507 + 2.67845i) q^{65} +(4.48471 + 2.28507i) q^{67} +(-0.0356501 + 2.38400i) q^{68} +(-0.613664 - 8.47327i) q^{70} +(10.6460 + 3.45911i) q^{71} +(-1.16618 + 7.36296i) q^{73} +(6.60942 - 2.68000i) q^{74} +(-4.11707 - 4.24207i) q^{76} +(-1.67824 - 0.265808i) q^{77} +(-2.84085 + 8.74324i) q^{79} +(-8.94060 - 0.256412i) q^{80} +(-4.72155 + 11.1621i) q^{82} +(1.18719 - 2.32999i) q^{83} +(-2.63235 + 0.420254i) q^{85} +(6.92870 - 11.1191i) q^{86} +(-0.456524 + 1.72970i) q^{88} +(9.57838 + 13.1835i) q^{89} +(2.67828 - 3.68634i) q^{91} +(-8.11479 + 2.50314i) q^{92} +(7.24538 - 6.09505i) q^{94} +(3.87820 - 5.35176i) q^{95} +(-14.4118 + 7.34318i) q^{97} +(-0.299338 + 0.0695018i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

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