LMFDB - Embedded newform 900.2.bj.f.487.28

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			487.28
Character	$\chi$	$=$	900.487
Dual form			900.2.bj.f.523.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35338 + 0.410309i) q^{2} +(1.66329 + 1.11061i) q^{4} +(-2.17065 + 0.536923i) q^{5} +(0.403183 - 0.403183i) q^{7} +(1.79538 + 2.18554i) q^{8} +O(q^{10})$	\(q+(1.35338 + 0.410309i) q^{2} +(1.66329 + 1.11061i) q^{4} +(-2.17065 + 0.536923i) q^{5} +(0.403183 - 0.403183i) q^{7} +(1.79538 + 2.18554i) q^{8} +(-3.15802 - 0.163973i) q^{10} +(-2.68322 + 3.69314i) q^{11} +(-0.669605 + 4.22772i) q^{13} +(0.711090 - 0.380232i) q^{14} +(1.53309 + 3.69454i) q^{16} +(-1.13184 + 0.576699i) q^{17} +(0.214045 - 0.658762i) q^{19} +(-4.20674 - 1.51768i) q^{20} +(-5.14676 + 3.89729i) q^{22} +(-0.103651 - 0.654427i) q^{23} +(4.42343 - 2.33094i) q^{25} +(-2.64090 + 5.44698i) q^{26} +(1.11839 - 0.222833i) q^{28} +(-5.48448 + 1.78201i) q^{29} +(7.87705 + 2.55941i) q^{31} +(0.558959 + 5.62917i) q^{32} +(-1.76843 + 0.316093i) q^{34} +(-0.658690 + 1.09165i) q^{35} +(-0.551102 - 0.0872860i) q^{37} +(0.559981 - 0.803734i) q^{38} +(-5.07061 - 3.78007i) q^{40} +(3.58374 - 2.60374i) q^{41} +(2.72923 + 2.72923i) q^{43} +(-8.56463 + 3.16276i) q^{44} +(0.128237 - 0.928219i) q^{46} +(9.06571 + 4.61921i) q^{47} +6.67489i q^{49} +(6.94300 - 1.33969i) q^{50} +(-5.80910 + 6.28827i) q^{52} +(-7.66275 - 3.90436i) q^{53} +(3.84140 - 9.45719i) q^{55} +(1.60504 + 0.157307i) q^{56} +(-8.15378 + 0.161421i) q^{58} +(5.72938 - 4.16264i) q^{59} +(-10.7384 - 7.80192i) q^{61} +(9.61052 + 6.69588i) q^{62} +(-1.55321 + 7.84777i) q^{64} +(-0.816485 - 9.53642i) q^{65} +(-4.20759 - 8.25787i) q^{67} +(-2.52306 - 0.297808i) q^{68} +(-1.33937 + 1.20715i) q^{70} +(-1.71079 + 0.555870i) q^{71} +(-6.95389 + 1.10139i) q^{73} +(-0.710038 - 0.344253i) q^{74} +(1.08765 - 0.857995i) q^{76} +(0.407181 + 2.57084i) q^{77} +(2.36601 + 7.28182i) q^{79} +(-5.31149 - 7.19640i) q^{80} +(5.91851 - 2.05342i) q^{82} +(7.97834 - 4.06517i) q^{83} +(2.14717 - 1.85952i) q^{85} +(2.57387 + 4.81352i) q^{86} +(-12.8889 + 0.766290i) q^{88} +(-3.05003 + 4.19801i) q^{89} +(1.43457 + 1.97452i) q^{91} +(0.554411 - 1.20362i) q^{92} +(10.3741 + 9.97131i) q^{94} +(-0.110911 + 1.54487i) q^{95} +(5.74169 - 11.2687i) q^{97} +(-2.73876 + 9.03368i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	1.35338	+	0.410309i	0.956987	+	0.290132i
$2$	1.35338	+	0.410309i	0.956987	+	0.290132i
$3$		0			0
$3$		0			0
$4$	1.66329	+	1.11061i	0.831647	+	0.555305i
$5$	−2.17065	+	0.536923i	−0.970743	+	0.240119i
$5$	−2.17065	+	0.536923i	−0.970743	+	0.240119i
$6$		0			0
$7$	0.403183	−	0.403183i	0.152389	−	0.152389i	−0.626795	−	0.779184i	$-0.715634\pi$
$7$	0.403183	−	0.403183i	0.152389	−	0.152389i	0.779184	+	0.626795i	$0.215634\pi$
$8$	1.79538	+	2.18554i	0.634763	+	0.772707i
$9$		0			0
$10$	−3.15802	−	0.163973i	−0.998655	−	0.0518527i
$11$	−2.68322	+	3.69314i	−0.809022	+	1.11352i	0.182451	+	0.983215i	$0.441597\pi$
$11$	−2.68322	+	3.69314i	−0.809022	+	1.11352i	−0.991473	+	0.130309i	$0.958403\pi$
$12$		0			0
$13$	−0.669605	+	4.22772i	−0.185715	+	1.17256i	0.702004	+	0.712173i	$0.252289\pi$
$13$	−0.669605	+	4.22772i	−0.185715	+	1.17256i	−0.887719	+	0.460386i	$0.847711\pi$
$14$	0.711090	−	0.380232i	0.190047	−	0.101621i
$15$		0			0
$16$	1.53309	+	3.69454i	0.383273	+	0.923635i
$17$	−1.13184	+	0.576699i	−0.274511	+	0.139870i	−0.585827	−	0.810436i	$-0.699230\pi$
$17$	−1.13184	+	0.576699i	−0.274511	+	0.139870i	0.311316	+	0.950306i	$0.399230\pi$
$18$		0			0
$19$	0.214045	−	0.658762i	0.0491053	−	0.151130i	−0.923497	−	0.383605i	$-0.874682\pi$
$19$	0.214045	−	0.658762i	0.0491053	−	0.151130i	0.972602	+	0.232475i	$0.0746823\pi$
$20$	−4.20674	−	1.51768i	−0.940655	−	0.339364i
$21$		0			0
$22$	−5.14676	+	3.89729i	−1.09729	+	0.830904i
$23$	−0.103651	−	0.654427i	−0.0216127	−	0.136457i	0.974523	−	0.224289i	$-0.0720061\pi$
$23$	−0.103651	−	0.654427i	−0.0216127	−	0.136457i	−0.996135	+	0.0878321i	$0.972006\pi$
$24$		0			0
$25$	4.42343	−	2.33094i	0.884685	−	0.466189i
$26$	−2.64090	+	5.44698i	−0.517924	+	1.06824i
$27$		0			0
$28$	1.11839	−	0.222833i	0.211356	−	0.0421114i
$29$	−5.48448	+	1.78201i	−1.01844	+	0.330912i	−0.770211	−	0.637789i	$-0.779849\pi$
$29$	−5.48448	+	1.78201i	−1.01844	+	0.330912i	−0.248231	+	0.968701i	$0.579849\pi$
$30$		0			0
$31$	7.87705	+	2.55941i	1.41476	+	0.459683i	0.913933	−	0.405865i	$-0.133030\pi$
$31$	7.87705	+	2.55941i	1.41476	+	0.459683i	0.500826	+	0.865548i	$0.333030\pi$
$32$	0.558959	+	5.62917i	0.0988109	+	0.995106i
$33$		0			0
$34$	−1.76843	+	0.316093i	−0.303284	+	0.0542095i
$35$	−0.658690	+	1.09165i	−0.111339	+	0.184522i
$36$		0			0
$37$	−0.551102	−	0.0872860i	−0.0906006	−	0.0143497i	0.110970	−	0.993824i	$-0.464604\pi$
$37$	−0.551102	−	0.0872860i	−0.0906006	−	0.0143497i	−0.201570	+	0.979474i	$0.564604\pi$
$38$	0.559981	−	0.803734i	0.0908409	−	0.130383i
$39$		0			0
$40$	−5.07061	−	3.78007i	−0.801734	−	0.597681i
$41$	3.58374	−	2.60374i	0.559686	−	0.406636i	−0.271658	−	0.962394i	$-0.587572\pi$
$41$	3.58374	−	2.60374i	0.559686	−	0.406636i	0.831344	+	0.555758i	$0.187572\pi$
$42$		0			0
$43$	2.72923	+	2.72923i	0.416204	+	0.416204i	0.883893	−	0.467689i	$-0.154913\pi$
$43$	2.72923	+	2.72923i	0.416204	+	0.416204i	−0.467689	+	0.883893i	$0.654913\pi$
$44$	−8.56463	+	3.16276i	−1.29117	+	0.476804i
$45$		0			0
$46$	0.128237	−	0.928219i	0.0189076	−	0.136858i
$47$	9.06571	+	4.61921i	1.32237	+	0.673781i	0.965507	−	0.260375i	$-0.0838463\pi$
$47$	9.06571	+	4.61921i	1.32237	+	0.673781i	0.356863	+	0.934157i	$0.383846\pi$
$48$		0			0
$49$			6.67489i			0.953555i
$50$	6.94300	−	1.33969i	0.981888	−	0.189461i
$51$		0			0
$52$	−5.80910	+	6.28827i	−0.805577	+	0.872027i
$53$	−7.66275	−	3.90436i	−1.05256	−	0.536306i	−0.159944	−	0.987126i	$-0.551132\pi$
$53$	−7.66275	−	3.90436i	−1.05256	−	0.536306i	−0.892615	+	0.450820i	$0.851132\pi$
$54$		0			0
$55$	3.84140	−	9.45719i	0.517974	−	1.27521i
$56$	1.60504	+	0.157307i	0.214483	+	0.0210211i
$57$		0			0
$58$	−8.15378	+	0.161421i	−1.07064	+	0.0211956i
$59$	5.72938	−	4.16264i	0.745902	−	0.541929i	−0.148652	−	0.988890i	$-0.547493\pi$
$59$	5.72938	−	4.16264i	0.745902	−	0.541929i	0.894554	+	0.446960i	$0.147493\pi$
$60$		0			0
$61$	−10.7384	−	7.80192i	−1.37491	−	0.998934i	−0.997335	−	0.0729561i	$-0.976757\pi$
$61$	−10.7384	−	7.80192i	−1.37491	−	0.998934i	−0.377579	−	0.925977i	$-0.623243\pi$
$62$	9.61052	+	6.69588i	1.22054	+	0.850378i
$63$		0			0
$64$	−1.55321	+	7.84777i	−0.194151	+	0.980972i
$65$	−0.816485	−	9.53642i	−0.101272	−	1.18285i
$66$		0			0
$67$	−4.20759	−	8.25787i	−0.514039	−	1.00886i	−0.991488	−	0.130199i	$-0.958438\pi$
$67$	−4.20759	−	8.25787i	−0.514039	−	1.00886i	0.477448	−	0.878660i	$-0.341562\pi$
$68$	−2.52306	−	0.297808i	−0.305966	−	0.0361145i
$69$		0			0
$70$	−1.33937	+	1.20715i	−0.160086	+	0.144282i
$71$	−1.71079	+	0.555870i	−0.203034	+	0.0659696i	−0.408768	−	0.912638i	$-0.634042\pi$
$71$	−1.71079	+	0.555870i	−0.203034	+	0.0659696i	0.205735	+	0.978608i	$0.434042\pi$
$72$		0			0
$73$	−6.95389	+	1.10139i	−0.813892	+	0.128908i	−0.549485	−	0.835504i	$-0.685176\pi$
$73$	−6.95389	+	1.10139i	−0.813892	+	0.128908i	−0.264407	+	0.964411i	$0.585176\pi$
$74$	−0.710038	−	0.344253i	−0.0825402	−	0.0400186i
$75$		0			0
$76$	1.08765	−	0.857995i	0.124762	−	0.0984188i
$77$	0.407181	+	2.57084i	0.0464026	+	0.292974i
$78$		0			0
$79$	2.36601	+	7.28182i	0.266197	+	0.819269i	0.991415	+	0.130750i	$0.0417386\pi$
$79$	2.36601	+	7.28182i	0.266197	+	0.819269i	−0.725219	+	0.688518i	$0.758261\pi$
$80$	−5.31149	−	7.19640i	−0.593842	−	0.804581i
$81$		0			0
$82$	5.91851	−	2.05342i	0.653590	−	0.226762i
$83$	7.97834	−	4.06517i	0.875737	−	0.446210i	0.0424806	−	0.999097i	$-0.486474\pi$
$83$	7.97834	−	4.06517i	0.875737	−	0.446210i	0.833256	+	0.552887i	$0.186474\pi$
$84$		0			0
$85$	2.14717	−	1.85952i	0.232894	−	0.201693i
$86$	2.57387	+	4.81352i	0.277547	+	0.519055i
$87$		0			0
$88$	−12.8889	+	0.766290i	−1.37397	+	0.0816868i
$89$	−3.05003	+	4.19801i	−0.323303	+	0.444988i	−0.939472	−	0.342626i	$-0.888684\pi$
$89$	−3.05003	+	4.19801i	−0.323303	+	0.444988i	0.616169	+	0.787614i	$0.288684\pi$
$90$		0			0
$91$	1.43457	+	1.97452i	0.150384	+	0.206986i
$92$	0.554411	−	1.20362i	0.0578013	−	0.125486i
$93$		0			0
$94$	10.3741	+	9.97131i	1.07001	+	1.02846i
$95$	−0.110911	+	1.54487i	−0.0113793	+	0.158500i
$96$		0			0
$97$	5.74169	−	11.2687i	0.582981	−	1.14416i	−0.391602	−	0.920135i	$-0.628079\pi$
$97$	5.74169	−	11.2687i	0.582981	−	1.14416i	0.974582	−	0.224029i	$-0.0719210\pi$
$98$	−2.73876	+	9.03368i	−0.276657	+	0.912540i
$99$		0			0
$100$	9.94623	+	1.03566i	0.994623	+	0.103566i
$101$	18.5684			1.84763			0.923813	−	0.382845i	$-0.125055\pi$
$101$	18.5684			1.84763			0.923813	+	0.382845i	$0.125055\pi$
$102$		0			0
$103$	3.40490	−	6.68249i	0.335495	−	0.658445i	−0.660205	−	0.751085i	$-0.729531\pi$
$103$	3.40490	−	6.68249i	0.335495	−	0.658445i	0.995700	+	0.0926401i	$0.0295306\pi$
$104$	−10.4421	+	6.12692i	−1.02393	+	0.600794i
$105$		0			0
$106$	−8.76864	−	8.42819i	−0.851686	−	0.818618i
$107$	0.808322	−	0.808322i	0.0781434	−	0.0781434i	−0.666955	−	0.745098i	$-0.732403\pi$
$107$	0.808322	−	0.808322i	0.0781434	−	0.0781434i	0.745098	+	0.666955i	$0.232403\pi$
$108$		0			0
$109$	−10.5714	−	14.5503i	−1.01256	−	1.39367i	−0.917291	−	0.398218i	$-0.869629\pi$
$109$	−10.5714	−	14.5503i	−1.01256	−	1.39367i	−0.0952690	−	0.995452i	$-0.530371\pi$
$110$	9.07926	−	11.2231i	0.865673	−	1.07008i
$111$		0			0
$112$	2.10769	+	0.871459i	0.199158	+	0.0823451i
$113$	1.84765	−	11.6656i	0.173813	−	1.09741i	−0.734343	−	0.678778i	$-0.762510\pi$
$113$	1.84765	−	11.6656i	0.173813	−	1.09741i	0.908156	−	0.418632i	$-0.137490\pi$
$114$		0			0
$115$	0.576367	+	1.36488i	0.0537465	+	0.127276i
$116$	−11.1014	−	3.12710i	−1.03074	−	0.290344i
$117$		0			0
$118$	9.46201	−	3.28283i	0.871049	−	0.302209i
$119$	−0.223822	+	0.688852i	−0.0205177	+	0.0631469i
$120$		0			0
$121$	−3.04041	−	9.35742i	−0.276401	−	0.850675i
$122$	−11.3320	−	14.9651i	−1.02595	−	1.35487i
$123$		0			0
$124$	10.2593	+	13.0054i	0.921316	+	1.16792i
$125$	−8.35017	+	7.43470i	−0.746862	+	0.664980i
$126$		0			0
$127$	19.6106	−	3.10602i	1.74016	−	0.275614i	0.796047	−	0.605235i	$-0.206921\pi$
$127$	19.6106	−	3.10602i	1.74016	−	0.275614i	0.944113	+	0.329621i	$0.106921\pi$
$128$	−5.32210	+	9.98375i	−0.470412	+	0.882447i
$129$		0			0
$130$	2.80786	−	13.2415i	0.246266	−	1.16135i
$131$	21.6599	+	7.03773i	1.89243	+	0.614889i	0.977351	+	0.211625i	$0.0678755\pi$
$131$	21.6599	+	7.03773i	1.89243	+	0.614889i	0.915083	+	0.403264i	$0.132125\pi$
$132$		0			0
$133$	−0.179302	−	0.351901i	−0.0155475	−	0.0305137i
$134$	−2.30621	−	12.9025i	−0.199227	−	1.11460i
$135$		0			0
$136$	−3.29248	−	1.43828i	−0.282328	−	0.123332i
$137$	16.5163	+	2.61593i	1.41109	+	0.223494i	0.815016	−	0.579438i	$-0.196728\pi$
$137$	16.5163	+	2.61593i	1.41109	+	0.223494i	0.596070	+	0.802932i	$0.296728\pi$
$138$		0			0
$139$	−0.991605	−	0.720443i	−0.0841068	−	0.0611072i	0.544937	−	0.838477i	$-0.316553\pi$
$139$	−0.991605	−	0.720443i	−0.0841068	−	0.0611072i	−0.629044	+	0.777370i	$0.716553\pi$
$140$	−2.30799	+	1.08418i	−0.195061	+	0.0916300i
$141$		0			0
$142$	−2.54343	+	0.0503525i	−0.213440	+	0.00422549i
$143$	−13.8169	−	13.8169i	−1.15542	−	1.15542i
$144$		0			0
$145$	10.9481	−	6.81287i	0.909187	−	0.565778i
$146$	−9.86319	−	1.36264i	−0.816284	−	0.112773i
$147$		0			0
$148$	−0.819704	−	0.757241i	−0.0673792	−	0.0622449i
$149$			13.9644i			1.14401i	0.820251	+	0.572003i	$0.193834\pi$
$149$			13.9644i			1.14401i	−0.820251	+	0.572003i	$0.806166\pi$
$150$		0			0
$151$			19.3040i			1.57094i	0.618901	+	0.785469i	$0.287578\pi$
$151$			19.3040i			1.57094i	−0.618901	+	0.785469i	$0.712422\pi$
$152$	1.82405	−	0.714925i	0.147950	−	0.0579881i
$153$		0			0
$154$	−0.503766	+	3.64640i	−0.0405946	+	0.293836i
$155$	−18.4725	−	1.32620i	−1.48375	−	0.106523i
$156$		0			0
$157$	11.6248	+	11.6248i	0.927763	+	0.927763i	0.997561	−	0.0697978i	$-0.0222354\pi$
$157$	11.6248	+	11.6248i	0.927763	+	0.927763i	−0.0697978	+	0.997561i	$0.522235\pi$
$158$	0.214321	+	10.8259i	0.0170504	+	0.861261i
$159$		0			0
$160$	−4.23574	−	11.9188i	−0.334864	−	0.942266i
$161$	−0.305644	−	0.222063i	−0.0240881	−	0.0175010i
$162$		0			0
$163$	−17.3839	−	2.75333i	−1.36161	−	0.215658i	−0.567470	−	0.823394i	$-0.692078\pi$
$163$	−17.3839	−	2.75333i	−1.36161	−	0.215658i	−0.794139	+	0.607736i	$0.792078\pi$
$164$	8.85255	−	0.350646i	0.691268	−	0.0273809i
$165$		0			0
$166$	12.4657	−	2.22815i	0.967528	−	0.172938i
$167$	−3.04644	−	5.97897i	−0.235741	−	0.462667i	0.742582	−	0.669756i	$-0.233601\pi$
$167$	−3.04644	−	5.97897i	−0.235741	−	0.462667i	−0.978322	+	0.207089i	$0.933601\pi$
$168$		0			0
$169$	−5.06153	−	1.64459i	−0.389349	−	0.126507i
$170$	3.66893	−	1.63564i	0.281394	−	0.125448i
$171$		0			0
$172$	1.50840	+	7.57062i	0.115015	+	0.577254i
$173$	0.974029	−	0.154271i	0.0740540	−	0.0117290i	−0.119297	−	0.992859i	$-0.538064\pi$
$173$	0.974029	−	0.154271i	0.0740540	−	0.0117290i	0.193352	+	0.981130i	$0.438064\pi$
$174$		0			0
$175$	0.843653	−	2.72325i	0.0637742	−	0.205858i
$176$	−17.7581	−	4.25136i	−1.33857	−	0.320458i
$177$		0			0
$178$	−5.85034	+	4.43006i	−0.438502	+	0.332047i
$179$	−5.08238	−	15.6420i	−0.379875	−	1.16914i	−0.940130	−	0.340815i	$-0.889297\pi$
$179$	−5.08238	−	15.6420i	−0.379875	−	1.16914i	0.560255	−	0.828320i	$-0.310703\pi$
$180$		0			0
$181$	−7.05393	+	21.7098i	−0.524314	+	1.61367i	0.241353	+	0.970437i	$0.422409\pi$
$181$	−7.05393	+	21.7098i	−0.524314	+	1.61367i	−0.765668	+	0.643236i	$0.777591\pi$
$182$	1.13136	+	3.26090i	0.0838622	+	0.241714i
$183$		0			0
$184$	1.24419	−	1.40148i	0.0917226	−	0.103318i
$185$	1.24311	−	0.106432i	0.0913956	−	0.00782506i
$186$		0			0
$187$	0.907138	−	5.72744i	0.0663365	−	0.418832i
$188$	9.94880	+	17.7516i	0.725591	+	1.29467i
$189$		0			0
$190$	−0.783978	+	2.04529i	−0.0568757	+	0.148381i
$191$	−5.09993	−	7.01945i	−0.369018	−	0.507910i	0.583616	−	0.812030i	$-0.301638\pi$
$191$	−5.09993	−	7.01945i	−0.369018	−	0.507910i	−0.952634	+	0.304120i	$0.901638\pi$
$192$		0			0
$193$	3.60845	−	3.60845i	0.259742	−	0.259742i	−0.565207	−	0.824949i	$-0.691204\pi$
$193$	3.60845	−	3.60845i	0.259742	−	0.259742i	0.824949	+	0.565207i	$0.191204\pi$
$194$	12.3944	−	12.8950i	0.889863	−	0.925808i
$195$		0			0
$196$	−7.41320	+	11.1023i	−0.529514	+	0.793021i
$197$	−5.27204	+	10.3470i	−0.375617	+	0.737190i	−0.998999	−	0.0447274i	$-0.985758\pi$
$197$	−5.27204	+	10.3470i	−0.375617	+	0.737190i	0.623382	+	0.781917i	$0.285758\pi$
$198$		0			0
$199$	−1.27147			−0.0901321			−0.0450661	−	0.998984i	$-0.514350\pi$
$199$	−1.27147			−0.0901321			−0.0450661	+	0.998984i	$0.514350\pi$
$200$	13.0361	+	5.48267i	0.921793	+	0.387683i
$201$		0			0
$202$	25.1302	+	7.61878i	1.76815	+	0.536055i
$203$	−1.49277	+	2.92972i	−0.104772	+	0.205626i
$204$		0			0
$205$	−6.38103	+	7.57599i	−0.445670	+	0.529130i
$206$	7.35002	−	7.64691i	0.512100	−	0.532786i
$207$		0			0
$208$	−16.6461	+	4.00760i	−1.15420	+	0.277877i
$209$	1.85857	+	2.55811i	0.128560	+	0.176948i
$210$		0			0
$211$	−2.56831	+	3.53497i	−0.176810	+	0.243358i	−0.888219	−	0.459420i	$-0.848057\pi$
$211$	−2.56831	+	3.53497i	−0.176810	+	0.243358i	0.711409	+	0.702778i	$0.248057\pi$
$212$	−8.40917	−	15.0044i	−0.577544	−	1.03051i
$213$		0			0
$214$	1.42563	−	0.762308i	0.0974541	−	0.0521103i
$215$	−7.38958	−	4.45881i	−0.503965	−	0.304088i
$216$		0			0
$217$	4.20780	−	2.14398i	0.285644	−	0.145543i
$218$	−8.33708	−	24.0297i	−0.564658	−	1.62750i
$219$		0			0
$220$	16.8926	−	11.4638i	1.13890	−	0.772889i
$221$	−1.68024	−	5.17125i	−0.113025	−	0.347856i
$222$		0			0
$223$	−1.79466	−	11.3311i	−0.120180	−	0.758784i	−0.972005	−	0.234959i	$-0.924504\pi$
$223$	−1.79466	−	11.3311i	−0.120180	−	0.758784i	0.851826	−	0.523825i	$-0.175496\pi$
$224$	2.49495	+	2.04422i	0.166701	+	0.136585i
$225$		0			0
$226$	7.28709	−	15.0300i	0.484730	−	0.999778i
$227$	29.6086	−	4.68955i	1.96519	−	0.311256i	0.966733	−	0.255786i	$-0.0823344\pi$
$227$	29.6086	−	4.68955i	1.96519	−	0.311256i	0.998460	−	0.0554697i	$-0.0176656\pi$
$228$		0			0
$229$	0.824628	−	0.267938i	0.0544929	−	0.0177058i	−0.281644	−	0.959519i	$-0.590880\pi$
$229$	0.824628	−	0.267938i	0.0544929	−	0.0177058i	0.336137	+	0.941813i	$0.390880\pi$
$230$	0.220024	+	2.08369i	0.0145080	+	0.137395i
$231$		0			0
$232$	−13.7414	−	8.78718i	−0.902167	−	0.576906i
$233$	4.29817	+	8.43563i	0.281582	+	0.552637i	0.987869	−	0.155289i	$-0.0496310\pi$
$233$	4.29817	+	8.43563i	0.281582	+	0.552637i	−0.706287	+	0.707926i	$0.749631\pi$
$234$		0			0
$235$	−22.1586	−	5.15909i	−1.44547	−	0.336542i
$236$	14.1527	−	0.560584i	0.921263	−	0.0364909i
$237$		0			0
$238$	−0.585558	+	0.840445i	−0.0379561	+	0.0544779i
$239$	−8.95405	−	6.50550i	−0.579190	−	0.420806i	0.259242	−	0.965812i	$-0.416527\pi$
$239$	−8.95405	−	6.50550i	−0.579190	−	0.420806i	−0.838432	+	0.545006i	$0.816527\pi$
$240$		0			0
$241$	−0.593499	+	0.431202i	−0.0382306	+	0.0277762i	−0.606736	−	0.794903i	$-0.707522\pi$
$241$	−0.593499	+	0.431202i	−0.0382306	+	0.0277762i	0.568506	+	0.822679i	$0.307522\pi$
$242$	−0.275411	−	13.9117i	−0.0177041	−	0.894277i
$243$		0			0
$244$	−9.19626	−	24.9031i	−0.588730	−	1.59426i
$245$	−3.58390	−	14.4888i	−0.228967	−	0.925658i
$246$		0			0
$247$	2.64174	+	1.34603i	0.168090	+	0.0856461i
$248$	8.54860	+	21.8107i	0.542837	+	1.38498i
$249$		0			0
$250$	−14.3515	+	6.63585i	−0.907668	+	0.419688i
$251$			13.1418i			0.829505i	0.909934	+	0.414753i	$0.136132\pi$
$251$			13.1418i			0.829505i	−0.909934	+	0.414753i	$0.863868\pi$
$252$		0			0
$253$	2.69501	+	1.37318i	0.169434	+	0.0863308i
$254$	27.8151	+	3.84277i	1.74527	+	0.241117i
$255$		0			0
$256$	−11.2993	+	11.3281i	−0.706204	+	0.708009i
$257$	−11.0515	−	11.0515i	−0.689375	−	0.689375i	0.272719	−	0.962094i	$-0.412077\pi$
$257$	−11.0515	−	11.0515i	−0.689375	−	0.689375i	−0.962094	+	0.272719i	$0.912077\pi$
$258$		0			0
$259$	−0.257387	+	0.187003i	−0.0159932	+	0.0116198i
$260$	9.23319	−	16.7687i	0.572618	−	1.03995i
$261$		0			0
$262$	26.4265	+	18.4120i	1.63264	+	1.13750i
$263$	−13.8057	−	2.18660i	−0.851294	−	0.134832i	−0.284485	−	0.958681i	$-0.591822\pi$
$263$	−13.8057	−	2.18660i	−0.851294	−	0.134832i	−0.566810	+	0.823849i	$0.691822\pi$
$264$		0			0
$265$	18.7295	+	4.36069i	1.15054	+	0.267875i
$266$	−0.0982770	−	0.549826i	−0.00602575	−	0.0337120i
$267$		0			0
$268$	2.17281	−	18.4083i	0.132725	−	1.12446i
$269$	5.95656	+	1.93540i	0.363178	+	0.118004i	0.484921	−	0.874558i	$-0.338848\pi$
$269$	5.95656	+	1.93540i	0.363178	+	0.118004i	−0.121743	+	0.992562i	$0.538848\pi$
$270$		0			0
$271$	−19.0797	+	6.19936i	−1.15901	+	0.376584i	−0.824529	−	0.565820i	$-0.808560\pi$
$271$	−19.0797	+	6.19936i	−1.15901	+	0.376584i	−0.334478	+	0.942404i	$0.608560\pi$
$272$	−3.86585	−	3.29748i	−0.234401	−	0.199939i
$273$		0			0
$274$	21.2796	+	10.3172i	1.28555	+	0.623282i
$275$	−3.26054	+	22.5908i	−0.196618	+	1.36228i
$276$		0			0
$277$	1.56268	+	9.86635i	0.0938922	+	0.592812i	0.989109	+	0.147182i	$0.0470203\pi$
$277$	1.56268	+	9.86635i	0.0938922	+	0.592812i	−0.895217	+	0.445630i	$0.852980\pi$
$278$	−1.04642	−	1.38190i	−0.0627600	−	0.0828809i
$279$		0			0
$280$	−3.56844	+	0.520325i	−0.213255	+	0.0310954i
$281$	8.65459	−	26.6361i	0.516290	−	1.58898i	−0.264633	−	0.964349i	$-0.585251\pi$
$281$	8.65459	−	26.6361i	0.516290	−	1.58898i	0.780923	−	0.624627i	$-0.214749\pi$
$282$		0			0
$283$	8.54906	−	4.35596i	0.508189	−	0.258935i	−0.181044	−	0.983475i	$-0.557948\pi$
$283$	8.54906	−	4.35596i	0.508189	−	0.258935i	0.689233	+	0.724540i	$0.257948\pi$
$284$	−3.46290	−	0.975447i	−0.205485	−	0.0578821i
$285$		0			0
$286$	−13.0303	−	24.3687i	−0.770500	−	1.44095i
$287$	0.395119	−	2.49468i	0.0233232	−	0.147257i
$288$		0			0
$289$	−9.04388	+	12.4478i	−0.531993	+	0.732225i
$290$	17.6123	−	4.72834i	1.03423	−	0.277658i
$291$		0			0
$292$	−12.7896	−	5.89113i	−0.748454	−	0.344752i
$293$	0.365499	−	0.365499i	0.0213527	−	0.0213527i	−0.696350	−	0.717703i	$-0.745194\pi$
$293$	0.365499	−	0.365499i	0.0213527	−	0.0213527i	0.717703	+	0.696350i	$0.245194\pi$
$294$		0			0
$295$	−10.2014	+	12.1119i	−0.593951	+	0.705180i
$296$	−0.798671	−	1.36117i	−0.0464218	−	0.0791164i
$297$		0			0
$298$	−5.72970	+	18.8992i	−0.331913	+	1.09480i
$299$	2.83614			0.164018
$300$		0			0
$301$	2.20076			0.126850
$302$	−7.92060	+	26.1257i	−0.455780	+	1.50337i
$303$		0			0
$304$	2.76198	−	0.219146i	0.158410	−	0.0125689i
$305$	27.4984	+	11.1695i	1.57455	+	0.639565i
$306$		0			0
$307$	7.86266	−	7.86266i	0.448745	−	0.448745i	−0.446192	−	0.894937i	$-0.647220\pi$
$307$	7.86266	−	7.86266i	0.448745	−	0.448745i	0.894937	+	0.446192i	$0.147220\pi$
$308$	−2.17794	+	4.72828i	−0.124100	+	0.269419i
$309$		0			0
$310$	−24.4562	−	9.37429i	−1.38902	−	0.532424i
$311$	−11.2964	+	15.5482i	−0.640562	+	0.881658i	−0.998645	−	0.0520319i	$-0.983430\pi$
$311$	−11.2964	+	15.5482i	−0.640562	+	0.881658i	0.358084	+	0.933689i	$0.383430\pi$
$312$		0			0
$313$	1.18066	−	7.45438i	0.0667347	−	0.421346i	−0.931591	−	0.363508i	$-0.881579\pi$
$313$	1.18066	−	7.45438i	0.0667347	−	0.421346i	0.998326	−	0.0578387i	$-0.0184209\pi$
$314$	10.9631	+	20.5026i	0.618683	+	1.15703i
$315$		0			0
$316$	−4.15190	+	14.7395i	−0.233562	+	0.829162i
$317$	−10.8062	+	5.50604i	−0.606937	+	0.309250i	−0.730316	−	0.683110i	$-0.760627\pi$
$317$	−10.8062	+	5.50604i	−0.606937	+	0.309250i	0.123379	+	0.992360i	$0.460627\pi$
$318$		0			0
$319$	8.13485	−	25.0365i	0.455464	−	1.40177i
$320$	−0.842175	−	17.8687i	−0.0470790	−	0.998891i
$321$		0			0
$322$	−0.322539	−	0.425945i	−0.0179744	−	0.0237370i
$323$	0.137644	+	0.869050i	0.00765872	+	0.0483553i
$324$		0			0
$325$	6.89263	+	20.2618i	0.382334	+	1.12392i
$326$	−22.3973	−	10.8591i	−1.24047	−	0.601428i
$327$		0			0
$328$	12.1248	+	3.15772i	0.669478	+	0.174356i
$329$	5.51753	−	1.79275i	0.304191	−	0.0988377i
$330$		0			0
$331$	−1.45790	−	0.473702i	−0.0801336	−	0.0260370i	0.268676	−	0.963231i	$-0.413414\pi$
$331$	−1.45790	−	0.473702i	−0.0801336	−	0.0260370i	−0.348809	+	0.937194i	$0.613414\pi$
$332$	17.7851	+	2.09926i	0.976086	+	0.115212i
$333$		0			0
$334$	−1.66978	−	9.34182i	−0.0913661	−	0.511162i
$335$	13.5670	+	15.6658i	0.741247	+	0.855913i
$336$		0			0
$337$	1.08031	+	0.171104i	0.0588481	+	0.00932062i	0.185789	−	0.982590i	$-0.440516\pi$
$337$	1.08031	+	0.171104i	0.0588481	+	0.00932062i	−0.126941	+	0.991910i	$0.540516\pi$
$338$	−6.17540	−	4.30255i	−0.335898	−	0.234028i
$339$		0			0
$340$	5.63658	−	0.708255i	0.305687	−	0.0384105i
$341$	−30.5881	+	22.2236i	−1.65644	+	1.20347i
$342$		0			0
$343$	5.51348	+	5.51348i	0.297700	+	0.297700i
$344$	−1.06485	+	10.8649i	−0.0574126	+	0.585794i
$345$		0			0
$346$	1.38153	+	0.190865i	0.0742717	+	0.0102609i
$347$	20.4311	+	10.4102i	1.09680	+	0.558846i	0.906212	−	0.422824i	$-0.138961\pi$
$347$	20.4311	+	10.4102i	1.09680	+	0.558846i	0.190586	+	0.981670i	$0.438961\pi$
$348$		0			0
$349$			20.7955i			1.11316i	0.830795	+	0.556578i	$0.187886\pi$
$349$			20.7955i			1.11316i	−0.830795	+	0.556578i	$0.812114\pi$
$350$	2.25916	−	3.33944i	0.120757	−	0.178500i
$351$		0			0
$352$	−22.2891	−	13.0400i	−1.18801	−	0.695035i
$353$	−20.9677	−	10.6836i	−1.11600	−	0.568628i	−0.204059	−	0.978959i	$-0.565413\pi$
$353$	−20.9677	−	10.6836i	−1.11600	−	0.568628i	−0.911937	+	0.410330i	$0.865413\pi$
$354$		0			0
$355$	3.41507	−	2.12516i	0.181253	−	0.112792i
$356$	−9.73545	+	3.59513i	−0.515978	+	0.190541i
$357$		0			0
$358$	−0.460379	−	23.2549i	−0.0243318	−	1.22906i
$359$	−28.2460	+	20.5219i	−1.49077	+	1.08311i	−0.516885	+	0.856055i	$0.672908\pi$
$359$	−28.2460	+	20.5219i	−1.49077	+	1.08311i	−0.973883	+	0.227051i	$0.927092\pi$
$360$		0			0
$361$	14.9832	+	10.8859i	0.788588	+	0.572943i
$362$	−18.4544	+	26.4873i	−0.969940	+	1.39214i
$363$		0			0
$364$	0.193194	+	4.87745i	0.0101261	+	0.255648i
$365$	14.5031	−	6.12443i	0.759127	−	0.320568i
$366$		0			0
$367$	7.31720	+	14.3608i	0.381955	+	0.749628i	0.999313	−	0.0370536i	$-0.0117972\pi$
$367$	7.31720	+	14.3608i	0.381955	+	0.749628i	−0.617359	+	0.786682i	$0.711797\pi$
$368$	2.25890	−	1.38624i	0.117753	−	0.0722627i
$369$		0			0
$370$	1.72608	+	0.366017i	0.0897346	+	0.0190283i
$371$	−4.66366	+	1.51531i	−0.242125	+	0.0786712i
$372$		0			0
$373$	−11.3634	+	1.79978i	−0.588373	+	0.0931891i	−0.443520	−	0.896264i	$-0.646271\pi$
$373$	−11.3634	+	1.79978i	−0.588373	+	0.0931891i	−0.144852	+	0.989453i	$0.546271\pi$
$374$	3.57772	−	7.37922i	0.185000	−	0.381570i
$375$		0			0
$376$	6.18092	+	28.1068i	0.318757	+	1.44950i
$377$	−3.86143	−	24.3801i	−0.198874	−	1.25564i
$378$		0			0
$379$	3.02441	+	9.30816i	0.155353	+	0.478128i	0.998197	−	0.0600309i	$-0.0191199\pi$
$379$	3.02441	+	9.30816i	0.155353	+	0.478128i	−0.842843	+	0.538159i	$0.819120\pi$
$380$	−1.90022	+	2.44639i	−0.0974794	+	0.125497i
$381$		0			0
$382$	−4.02202	−	11.5926i	−0.205784	−	0.593127i
$383$	14.8289	−	7.55569i	0.757720	−	0.386078i	−0.0320454	−	0.999486i	$-0.510202\pi$
$383$	14.8289	−	7.55569i	0.757720	−	0.386078i	0.789766	+	0.613409i	$0.210202\pi$
$384$		0			0
$385$	−2.26419	−	5.36176i	−0.115394	−	0.273261i
$386$	6.36419	−	3.40304i	0.323929	−	0.173210i
$387$		0			0
$388$	22.0653	−	12.3664i	1.12019	−	0.627808i
$389$	−8.71062	+	11.9891i	−0.441646	+	0.607873i	−0.970577	−	0.240792i	$-0.922593\pi$
$389$	−8.71062	+	11.9891i	−0.441646	+	0.607873i	0.528931	+	0.848665i	$0.322593\pi$
$390$		0			0
$391$	0.494723	+	0.680928i	0.0250192	+	0.0344360i
$392$	−14.5883	+	11.9840i	−0.736819	+	0.605282i
$393$		0			0
$394$	−11.3805	+	11.8402i	−0.573343	+	0.596502i
$395$	−9.04555	−	14.5359i	−0.455131	−	0.731381i
$396$		0			0
$397$	16.9966	−	33.3577i	0.853034	−	1.67417i	0.121267	−	0.992620i	$-0.461304\pi$
$397$	16.9966	−	33.3577i	0.853034	−	1.67417i	0.731768	−	0.681554i	$-0.238696\pi$
$398$	−1.72079	−	0.521695i	−0.0862552	−	0.0261502i
$399$		0			0
$400$	15.3933	+	12.7690i	0.769664	+	0.638449i
$401$	−6.38092			−0.318648			−0.159324	−	0.987226i	$-0.550931\pi$
$401$	−6.38092			−0.318648			−0.159324	+	0.987226i	$0.550931\pi$
$402$		0			0
$403$	−16.0950	+	31.5882i	−0.801748	+	1.57352i
$404$	30.8847	+	20.6223i	1.53657	+	1.02600i
$405$		0			0
$406$	−3.22238	+	3.35254i	−0.159924	+	0.166384i
$407$	1.80109	−	1.80109i	0.0892767	−	0.0892767i
$408$		0			0
$409$	7.75145	+	10.6690i	0.383285	+	0.527546i	0.956451	−	0.291893i	$-0.0942851\pi$
$409$	7.75145	+	10.6690i	0.383285	+	0.527546i	−0.573166	+	0.819439i	$0.694285\pi$
$410$	−11.7445	+	7.63503i	−0.580018	+	0.377067i
$411$		0			0
$412$	13.0850	−	7.33343i	0.644651	−	0.361292i
$413$	0.631683	−	3.98829i	0.0310831	−	0.196251i
$414$		0			0
$415$	−15.1355	+	13.1078i	−0.742972	+	0.643437i
$416$	−24.1729	−	1.40620i	−1.18517	−	0.0689447i
$417$		0			0
$418$	1.46575	+	4.22469i	0.0716921	+	0.206636i
$419$	1.32767	−	4.08615i	0.0648610	−	0.199622i	−0.913374	−	0.407121i	$-0.866533\pi$
$419$	1.32767	−	4.08615i	0.0648610	−	0.199622i	0.978235	+	0.207500i	$0.0665326\pi$
$420$		0			0
$421$	−1.80550	−	5.55676i	−0.0879948	−	0.270820i	0.897370	−	0.441279i	$-0.145475\pi$
$421$	−1.80550	−	5.55676i	−0.0879948	−	0.270820i	−0.985365	+	0.170459i	$0.945475\pi$
$422$	−4.92634	+	3.73038i	−0.239810	+	0.181592i
$423$		0			0
$424$	−5.22439	−	23.7571i	−0.253719	−	1.15375i
$425$	−3.66234	+	5.18923i	−0.177650	+	0.251715i
$426$		0			0
$427$	−7.47515	+	1.18395i	−0.361748	+	0.0572952i
$428$	2.24221	−	0.446746i	0.108381	−	0.0215943i
$429$		0			0
$430$	−8.17145	−	9.06649i	−0.394062	−	0.437225i
$431$	2.92353	+	0.949912i	0.140821	+	0.0457556i	0.378580	−	0.925569i	$-0.376413\pi$
$431$	2.92353	+	0.949912i	0.140821	+	0.0457556i	−0.237758	+	0.971324i	$0.576413\pi$
$432$		0			0
$433$	−12.4138	−	24.3634i	−0.596568	−	1.17083i	−0.969984	−	0.243167i	$-0.921814\pi$
$433$	−12.4138	−	24.3634i	−0.596568	−	1.17083i	0.373416	−	0.927664i	$-0.378186\pi$
$434$	6.57446	−	1.17513i	0.315584	−	0.0564081i
$435$		0			0
$436$	−1.42366	−	35.9422i	−0.0681809	−	1.72132i
$437$	−0.453298	−	0.0717953i	−0.0216842	−	0.00343444i
$438$		0			0
$439$	−19.5015	−	14.1687i	−0.930757	−	0.676235i	0.0154210	−	0.999881i	$-0.495091\pi$
$439$	−19.5015	−	14.1687i	−0.930757	−	0.676235i	−0.946178	+	0.323646i	$0.895091\pi$
$440$	27.5659	−	8.58372i	1.31415	−	0.409213i
$441$		0			0
$442$	−0.152202	−	7.68810i	−0.00723950	−	0.365686i
$443$	−17.8280	−	17.8280i	−0.847032	−	0.847032i	0.142730	−	0.989762i	$-0.454412\pi$
$443$	−17.8280	−	17.8280i	−0.847032	−	0.847032i	−0.989762	+	0.142730i	$0.954412\pi$
$444$		0			0
$445$	4.36654	−	10.7500i	0.206994	−	0.509601i
$446$	2.22036	−	16.0716i	0.105137	−	0.761014i
$447$		0			0
$448$	2.53786	+	3.79031i	0.119903	+	0.179076i
$449$			10.8433i			0.511725i	0.966713	+	0.255862i	$0.0823594\pi$
$449$			10.8433i			0.511725i	−0.966713	+	0.255862i	$0.917641\pi$
$450$		0			0
$451$			20.2217i			0.952201i
$452$	16.0291	−	17.3513i	0.753948	−	0.816138i
$453$		0			0
$454$	41.9960	+	5.80192i	1.97097	+	0.272298i
$455$	−4.17411	−	3.51573i	−0.195686	−	0.164820i
$456$		0			0
$457$	−10.7529	−	10.7529i	−0.502999	−	0.502999i	0.409369	−	0.912369i	$-0.365749\pi$
$457$	−10.7529	−	10.7529i	−0.502999	−	0.502999i	−0.912369	+	0.409369i	$0.865749\pi$
$458$	1.22597	−	0.0242707i	0.0572860	−	0.00113410i
$459$		0			0
$460$	−0.557179	+	2.91031i	−0.0259786	+	0.135694i
$461$	6.99954	+	5.08547i	0.326001	+	0.236854i	0.738732	−	0.673999i	$-0.235425\pi$
$461$	6.99954	+	5.08547i	0.326001	+	0.236854i	−0.412731	+	0.910853i	$0.635425\pi$
$462$		0			0
$463$	−6.98414	−	1.10618i	−0.324581	−	0.0514085i	−0.00798209	−	0.999968i	$-0.502541\pi$
$463$	−6.98414	−	1.10618i	−0.324581	−	0.0514085i	−0.316599	+	0.948560i	$0.602541\pi$
$464$	−14.9919	−	17.5306i	−0.695983	−	0.813839i
$465$		0			0
$466$	2.35586	+	13.1802i	0.109133	+	0.610562i
$467$	−8.40547	−	16.4967i	−0.388959	−	0.763374i	0.610634	−	0.791913i	$-0.290915\pi$
$467$	−8.40547	−	16.4967i	−0.388959	−	0.763374i	−0.999593	+	0.0285385i	$0.990915\pi$
$468$		0			0
$469$	−5.02586	−	1.63300i	−0.232073	−	0.0754050i
$470$	−27.8723	−	16.0741i	−1.28565	−	0.741443i
$471$		0			0
$472$	19.3841	+	5.04829i	0.892223	+	0.232367i
$473$	−17.4026	+	2.75630i	−0.800171	+	0.126735i
$474$		0			0
$475$	−0.588726	−	3.41291i	−0.0270126	−	0.156595i
$476$	−1.13733	+	0.897185i	−0.0521293	+	0.0411224i
$477$		0			0
$478$	−9.44901	−	12.4784i	−0.432187	−	0.570747i
$479$	7.81425	+	24.0498i	0.357042	+	1.09886i	0.954816	+	0.297198i	$0.0960521\pi$
$479$	7.81425	+	24.0498i	0.357042	+	1.09886i	−0.597774	+	0.801665i	$0.703948\pi$
$480$		0			0
$481$	0.738042	−	2.27146i	0.0336518	−	0.103570i
$482$	−0.980158	+	0.340064i	−0.0446450	+	0.0154895i
$483$		0			0
$484$	5.33535	−	18.9409i	0.242516	−	0.860948i
$485$	−6.41276	+	27.5432i	−0.291189	+	1.25067i
$486$		0			0
$487$	−3.69540	+	23.3318i	−0.167455	+	1.05727i	0.750584	+	0.660775i	$0.229772\pi$
$487$	−3.69540	+	23.3318i	−0.167455	+	1.05727i	−0.918038	+	0.396491i	$0.870228\pi$
$488$	−2.22812	−	37.4767i	−0.100862	−	1.69649i
$489$		0			0
$490$	1.09450	−	21.0795i	0.0494444	−	0.952273i
$491$	14.0618	+	19.3544i	0.634599	+	0.873451i	0.998313	−	0.0580598i	$-0.0184914\pi$
$491$	14.0618	+	19.3544i	0.634599	+	0.873451i	−0.363714	+	0.931511i	$0.618491\pi$
$492$		0			0
$493$	5.17984	−	5.17984i	0.233288	−	0.233288i
$494$	3.02300	+	2.90563i	0.136011	+	0.130730i
$495$		0			0
$496$	2.62040	+	33.0259i	0.117659	+	1.48291i
$497$	−0.465644	+	0.913879i	−0.0208870	+	0.0409931i
$498$		0			0
$499$	−3.20194			−0.143339			−0.0716693	−	0.997428i	$-0.522833\pi$
$499$	−3.20194			−0.143339			−0.0716693	+	0.997428i	$0.522833\pi$
$500$	−22.1458	+	3.09231i	−0.990391	+	0.138292i
$501$		0			0
$502$	−5.39221	+	17.7859i	−0.240666	+	0.793825i
$503$	5.20750	−	10.2203i	0.232191	−	0.455701i	−0.745285	−	0.666746i	$-0.767687\pi$
$503$	5.20750	−	10.2203i	0.232191	−	0.455701i	0.977476	+	0.211045i	$0.0676867\pi$
$504$		0			0
$505$	−40.3055	+	9.96981i	−1.79357	+	0.443651i
$506$	3.08396	+	2.96422i	0.137099	+	0.131776i
$507$		0			0
$508$	36.0678	+	16.6135i	1.60025	+	0.737106i
$509$	−13.6267	−	18.7556i	−0.603994	−	0.831327i	0.392072	−	0.919934i	$-0.371758\pi$
$509$	−13.6267	−	18.7556i	−0.603994	−	0.831327i	−0.996067	+	0.0886075i	$0.971758\pi$
$510$		0			0
$511$	−2.35963	+	3.24775i	−0.104384	+	0.143672i
$512$	−19.9403	+	10.6951i	−0.881244	+	0.472662i
$513$		0			0
$514$	−10.4224	−	19.4915i	−0.459713	−	0.859732i
$515$	−3.80285	+	16.3335i	−0.167574	+	0.719740i
$516$		0			0
$517$	−41.3847	+	21.0866i	−1.82010	+	0.927387i
$518$	−0.425072	+	0.147478i	−0.0186766	+	0.00647982i
$519$		0			0
$520$	19.3764	−	18.9060i	0.849711	−	0.829082i
$521$	4.78400	+	14.7236i	0.209591	+	0.645054i	0.999494	+	0.0318218i	$0.0101309\pi$
$521$	4.78400	+	14.7236i	0.209591	+	0.645054i	−0.789903	+	0.613232i	$0.789869\pi$
$522$		0			0
$523$	−1.35911	−	8.58111i	−0.0594299	−	0.375226i	−0.999421	−	0.0340265i	$-0.989167\pi$
$523$	−1.35911	−	8.58111i	−0.0594299	−	0.375226i	0.939991	−	0.341199i	$-0.110833\pi$
$524$	28.2106	+	35.7615i	1.23239	+	1.56225i
$525$		0			0
$526$	−17.7872	−	8.62390i	−0.775558	−	0.376020i
$527$	−10.3915	+	1.64586i	−0.452662	+	0.0716946i
$528$		0			0
$529$	21.4568	−	6.97173i	0.932903	−	0.303119i
$530$	23.5589	+	13.5866i	1.02333	+	0.590162i
$531$		0			0
$532$	0.0925920	−	0.784450i	0.00401437	−	0.0340102i
$533$	8.60819	+	16.8945i	0.372862	+	0.731783i
$534$		0			0
$535$	−1.32058	+	2.18859i	−0.0570935	+	0.0946210i
$536$	10.4937	−	24.0219i	0.453259	−	1.03759i
$537$		0			0
$538$	7.26739	+	5.06337i	0.313319	+	0.218297i
$539$	−24.6513	−	17.9102i	−1.06181	−	0.771448i
$540$		0			0
$541$	30.7034	−	22.3073i	1.32004	−	0.959067i	0.320111	−	0.947380i	$-0.396280\pi$
$541$	30.7034	−	22.3073i	1.32004	−	0.959067i	0.999932	−	0.0116875i	$-0.00372033\pi$
$542$	−28.3657	+	0.561559i	−1.21841	+	0.0241210i
$543$		0			0
$544$	−3.87899	−	6.04895i	−0.166310	−	0.259346i
$545$	30.7593	+	25.9076i	1.31758	+	1.10976i
$546$		0			0
$547$	−12.8211	−	6.53267i	−0.548190	−	0.279317i	0.157881	−	0.987458i	$-0.449534\pi$
$547$	−12.8211	−	6.53267i	−0.548190	−	0.279317i	−0.706071	+	0.708141i	$0.749534\pi$
$548$	24.5662	+	22.6943i	1.04942	+	0.969451i
$549$		0			0
$550$	−13.6820	+	29.2362i	−0.583401	+	1.24663i
$551$			3.99440i			0.170167i
$552$		0			0
$553$	3.88984	+	1.98197i	0.165413	+	0.0842820i
$554$	−1.93335	+	13.9941i	−0.0821401	+	0.594554i
$555$		0			0
$556$	−0.849199	−	2.29960i	−0.0360141	−	0.0975246i
$557$	−22.6217	−	22.6217i	−0.958513	−	0.958513i	0.0406596	−	0.999173i	$-0.487054\pi$
$557$	−22.6217	−	22.6217i	−0.958513	−	0.958513i	−0.999173	+	0.0406596i	$0.987054\pi$
$558$		0			0
$559$	−13.3659	+	9.71092i	−0.565319	+	0.410728i
$560$	−5.04296	−	0.759962i	−0.213104	−	0.0321143i
$561$		0			0
$562$	22.6420	−	32.4978i	0.955095	−	1.37084i
$563$	33.9090	+	5.37066i	1.42909	+	0.226346i	0.822545	−	0.568700i	$-0.192553\pi$
$563$	33.9090	+	5.37066i	1.42909	+	0.226346i	0.606549	+	0.795046i	$0.292553\pi$
$564$		0			0
$565$	2.25294	+	26.3140i	0.0947819	+	1.10704i
$566$	13.3574	−	2.38754i	0.561455	−	0.100356i
$567$		0			0
$568$	−4.28640	−	2.74101i	−0.179853	−	0.115010i
$569$	13.8272	+	4.49274i	0.579667	+	0.188345i	0.584151	−	0.811645i	$-0.301427\pi$
$569$	13.8272	+	4.49274i	0.579667	+	0.188345i	−0.00448435	+	0.999990i	$0.501427\pi$
$570$		0			0
$571$	32.5728	−	10.5835i	1.36313	−	0.442908i	0.466043	−	0.884762i	$-0.345679\pi$
$571$	32.5728	−	10.5835i	1.36313	−	0.442908i	0.897087	+	0.441854i	$0.145679\pi$
$572$	−7.63636	−	38.3267i	−0.319292	−	1.60252i
$573$		0			0
$574$	1.55834	−	3.21414i	0.0650438	−	0.134156i
$575$	−1.98392	−	2.65320i	−0.0827354	−	0.110646i
$576$		0			0
$577$	4.65814	+	29.4103i	0.193921	+	1.22437i	0.872047	+	0.489422i	$0.162792\pi$
$577$	4.65814	+	29.4103i	0.193921	+	1.22437i	−0.678126	+	0.734945i	$0.737208\pi$
$578$	−17.3473	+	13.1359i	−0.721552	+	0.546382i
$579$		0			0
$580$	25.7763	+	0.827225i	1.07030	+	0.0343487i
$581$	1.57772	−	4.85574i	0.0654550	−	0.201450i
$582$		0			0
$583$	34.9802	−	17.8233i	1.44873	−	0.738166i
$584$	−14.8920	−	13.2206i	−0.616236	−	0.547074i
$585$		0			0
$586$	0.644627	−	0.344693i	0.0266293	−	0.0142391i
$587$	−0.417161	+	2.63385i	−0.0172181	+	0.108711i	−0.994801	−	0.101842i	$-0.967526\pi$
$587$	−0.417161	+	2.63385i	−0.0172181	+	0.108711i	0.977583	+	0.210553i	$0.0675264\pi$
$588$		0			0
$589$	3.37208	−	4.64127i	0.138944	−	0.191240i
$590$	−18.7761	+	12.2062i	−0.772999	+	0.502523i
$591$		0			0
$592$	−0.522408	−	2.16989i	−0.0214708	−	0.0891817i
$593$	4.29407	−	4.29407i	0.176336	−	0.176336i	−0.613420	−	0.789757i	$-0.710207\pi$
$593$	4.29407	−	4.29407i	0.176336	−	0.176336i	0.789757	+	0.613420i	$0.210207\pi$
$594$		0			0
$595$	0.115977	−	1.61543i	0.00475460	−	0.0662262i
$596$	−15.5090	+	23.2269i	−0.635272	+	0.951409i
$597$		0			0
$598$	3.83839	+	1.16369i	0.156963	+	0.0475869i
$599$	1.90922			0.0780086			0.0390043	−	0.999239i	$-0.487581\pi$
$599$	1.90922			0.0780086			0.0390043	+	0.999239i	$0.487581\pi$
$600$		0			0
$601$	−19.9000			−0.811739			−0.405869	−	0.913931i	$-0.633031\pi$
$601$	−19.9000			−0.811739			−0.405869	+	0.913931i	$0.633031\pi$
$602$	2.97847	+	0.902990i	0.121393	+	0.0368031i
$603$		0			0
$604$	−21.4392	+	32.1082i	−0.872350	+	1.30647i
$605$	11.6239	+	18.6792i	0.472578	+	0.759418i
$606$		0			0
$607$	6.68008	−	6.68008i	0.271136	−	0.271136i	−0.558421	−	0.829557i	$-0.688593\pi$
$607$	6.68008	−	6.68008i	0.271136	−	0.271136i	0.829557	+	0.558421i	$0.188593\pi$
$608$	3.82793	+	0.836674i	0.155243	+	0.0339316i
$609$		0			0
$610$	32.6329	+	26.3995i	1.32127	+	1.06888i
$611$	−25.5992	+	35.2343i	−1.03563	+	1.42543i
$612$		0			0
$613$	1.64882	−	10.4102i	0.0665950	−	0.420465i	−0.931757	−	0.363082i	$-0.881725\pi$
$613$	1.64882	−	10.4102i	0.0665950	−	0.420465i	0.998352	−	0.0573826i	$-0.0182755\pi$
$614$	13.8673	−	7.41507i	0.559639	−	0.299248i
$615$		0			0
$616$	−4.88764	+	5.50555i	−0.196929	+	0.221825i
$617$	33.5664	−	17.1029i	1.35133	−	0.688538i	0.379717	−	0.925103i	$-0.376021\pi$
$617$	33.5664	−	17.1029i	1.35133	−	0.688538i	0.971616	+	0.236564i	$0.0760214\pi$
$618$		0			0
$619$	−11.4354	+	35.1945i	−0.459627	+	1.41459i	0.405989	+	0.913878i	$0.366927\pi$
$619$	−11.4354	+	35.1945i	−0.459627	+	1.41459i	−0.865616	+	0.500708i	$0.833073\pi$
$620$	−29.2523	−	22.7216i	−1.17480	−	0.912522i
$621$		0			0
$622$	−21.6680	+	16.4077i	−0.868806	+	0.657887i
$623$	0.462845	+	2.92229i	0.0185435	+	0.117079i
$624$		0			0
$625$	14.1334	−	20.6215i	0.565336	−	0.824860i
$626$	4.65648	−	9.60420i	0.186110	−	0.383861i
$627$		0			0
$628$	6.42486	+	32.2462i	0.256380	+	1.28676i
$629$	0.674095	−	0.219027i	0.0268779	−	0.00873316i
$630$		0			0
$631$	11.9182	+	3.87246i	0.474456	+	0.154160i	0.536477	−	0.843915i	$-0.319755\pi$
$631$	11.9182	+	3.87246i	0.474456	+	0.154160i	−0.0620213	+	0.998075i	$0.519755\pi$
$632$	−11.6669	+	18.2447i	−0.464083	+	0.725733i
$633$		0			0
$634$	−16.8841	+	3.01790i	−0.670554	+	0.119856i
$635$	−40.9000	+	17.2715i	−1.62307	+	0.685397i
$636$		0			0
$637$	−28.2196	−	4.46954i	−1.11810	−	0.177090i
$638$	21.2823	−	30.5462i	0.842573	−	1.20933i
$639$		0			0
$640$	6.19190	−	24.5288i	0.244756	−	0.969585i
$641$	−12.9136	+	9.38230i	−0.510058	+	0.370579i	−0.812845	−	0.582479i	$-0.802083\pi$
$641$	−12.9136	+	9.38230i	−0.510058	+	0.370579i	0.302788	+	0.953058i	$0.402083\pi$
$642$		0			0
$643$	−18.8472	−	18.8472i	−0.743260	−	0.743260i	0.229944	−	0.973204i	$-0.426146\pi$
$643$	−18.8472	−	18.8472i	−0.743260	−	0.743260i	−0.973204	+	0.229944i	$0.926146\pi$
$644$	−0.261750	−	0.708808i	−0.0103144	−	0.0279309i
$645$		0			0
$646$	−0.170294	+	1.23264i	−0.00670012	+	0.0484974i
$647$	−9.13665	−	4.65536i	−0.359199	−	0.183021i	0.265073	−	0.964228i	$-0.414604\pi$
$647$	−9.13665	−	4.65536i	−0.359199	−	0.183021i	−0.624271	+	0.781207i	$0.714604\pi$
$648$		0			0
$649$			32.3287i			1.26901i
$650$	1.01477	+	30.2501i	0.0398024	+	1.18651i
$651$		0			0
$652$	−25.8566	−	23.8863i	−1.01262	−	0.935459i
$653$	16.6573	+	8.48730i	0.651849	+	0.332134i	0.748452	−	0.663189i	$-0.230798\pi$
$653$	16.6573	+	8.48730i	0.651849	+	0.332134i	−0.0966028	+	0.995323i	$0.530798\pi$
$654$		0			0
$655$	−50.7947	−	3.64673i	−1.98472	−	0.142489i
$656$	15.1138	+	9.24850i	0.590096	+	0.361093i
$657$		0			0
$658$	8.20291	−	0.162394i	0.319783	−	0.00633076i
$659$	−2.98224	+	2.16672i	−0.116171	+	0.0844035i	−0.644354	−	0.764727i	$-0.722874\pi$
$659$	−2.98224	+	2.16672i	−0.116171	+	0.0844035i	0.528183	+	0.849131i	$0.322874\pi$
$660$		0			0
$661$	19.7563	+	14.3538i	0.768432	+	0.558299i	0.901485	−	0.432810i	$-0.142478\pi$
$661$	19.7563	+	14.3538i	0.768432	+	0.558299i	−0.133053	+	0.991109i	$0.542478\pi$
$662$	−1.77874	−	1.23929i	−0.0691327	−	0.0481664i
$663$		0			0
$664$	23.2088	+	10.1385i	0.900675	+	0.393450i
$665$	0.578146	+	0.667581i	0.0224196	+	0.0258877i
$666$		0			0
$667$	1.73467	+	3.40448i	0.0671667	+	0.131822i
$668$	1.57318	−	13.3282i	0.0608683	−	0.515683i
$669$		0			0
$670$	11.9336	+	26.7685i	0.461036	+	1.03416i
$671$	57.6272	−	18.7242i	2.22467	−	0.722840i
$672$		0			0
$673$	−23.5644	+	3.73224i	−0.908342	+	0.143867i	−0.593086	−	0.805139i	$-0.702090\pi$
$673$	−23.5644	+	3.73224i	−0.908342	+	0.143867i	−0.315256	+	0.949007i	$0.602090\pi$
$674$	1.39186	+	0.674828i	0.0536126	+	0.0259934i
$675$		0			0
$676$	−6.59231	−	8.35682i	−0.253550	−	0.321416i
$677$	−1.26062	−	7.95924i	−0.0484495	−	0.305898i	0.951549	−	0.307497i	$-0.0994913\pi$
$677$	−1.26062	−	7.95924i	−0.0484495	−	0.305898i	−0.999999	+	0.00159823i	$0.999491\pi$
$678$		0			0
$679$	−2.22840	−	6.85830i	−0.0855180	−	0.263197i
$680$	7.91906	+	1.35420i	0.303682	+	0.0519311i
$681$		0			0
$682$	−50.5160	+	17.5264i	−1.93436	+	0.671122i
$683$	35.5849	−	18.1314i	1.36162	−	0.693780i	0.387937	−	0.921686i	$-0.373188\pi$
$683$	35.5849	−	18.1314i	1.36162	−	0.693780i	0.973683	+	0.227906i	$0.0731880\pi$
$684$		0			0
$685$	−37.2557	+	3.18974i	−1.42347	+	0.121874i
$686$	5.19962	+	9.72408i	0.198523	+	0.371267i
$687$		0			0
$688$	−5.89909	+	14.2674i	−0.224901	+	0.543940i
$689$	21.6376	−	29.7816i	0.824326	−	1.13459i
$690$		0			0
$691$	−28.5593	−	39.3084i	−1.08645	−	1.49536i	−0.852222	−	0.523181i	$-0.824745\pi$
$691$	−28.5593	−	39.3084i	−1.08645	−	1.49536i	−0.234223	−	0.972183i	$-0.575255\pi$
$692$	1.79143	+	0.825168i	0.0681000	+	0.0313682i
$693$		0			0
$694$	23.3797	+	22.4720i	0.887482	+	0.853025i
$695$	2.53925	+	1.03141i	0.0963192	+	0.0391237i
$696$		0			0
$697$	−2.55463	+	5.01374i	−0.0967635	+	0.189909i
$698$	−8.53257	+	28.1443i	−0.322962	+	1.06528i
$699$		0			0
$700$	4.42771	−	3.59259i	0.167352	−	0.135787i
$701$	0.239240			0.00903597			0.00451799	−	0.999990i	$-0.498562\pi$
$701$	0.239240			0.00903597			0.00451799	+	0.999990i	$0.498562\pi$
$702$		0			0
$703$	−0.175461	+	0.344362i	−0.00661765	+	0.0129879i
$704$	−24.8153	−	26.7936i	−0.935262	−	1.00982i
$705$		0			0
$706$	−23.9937	−	23.0622i	−0.903016	−	0.867956i
$707$	7.48646	−	7.48646i	0.281557	−	0.281557i
$708$		0			0
$709$	−8.43241	−	11.6062i	−0.316686	−	0.435881i	0.620766	−	0.783996i	$-0.286822\pi$
$709$	−8.43241	−	11.6062i	−0.316686	−	0.435881i	−0.937452	+	0.348115i	$0.886822\pi$
$710$	5.49387	−	1.47493i	0.206181	−	0.0553530i
$711$		0			0
$712$	−14.6509	+	0.871046i	−0.549066	+	0.0326438i
$713$	0.858481	−	5.42024i	0.0321504	−	0.202989i
$714$		0			0
$715$	37.4102	+	22.5730i	1.39906	+	0.844181i
$716$	8.91863	−	31.6617i	0.333305	−	1.18325i
$717$		0			0
$718$	−46.6480	+	16.1845i	−1.74089	+	0.603999i
$719$	9.40688	−	28.9514i	0.350818	−	1.07971i	−0.607578	−	0.794260i	$-0.707859\pi$
$719$	9.40688	−	28.9514i	0.350818	−	1.07971i	0.958395	−	0.285445i	$-0.0921414\pi$
$720$		0			0
$721$	−1.32147	−	4.06706i	−0.0492141	−	0.151465i
$722$	15.8114	+	20.8805i	0.588439	+	0.777093i
$723$		0			0
$724$	−35.8438	+	28.2755i	−1.33213	+	1.05085i
$725$	−20.1064	+	20.6666i	−0.746733	+	0.767539i
$726$		0			0
$727$	21.2294	−	3.36240i	0.787354	−	0.124705i	0.250206	−	0.968193i	$-0.419502\pi$
$727$	21.2294	−	3.36240i	0.787354	−	0.124705i	0.537148	+	0.843488i	$0.319502\pi$
$728$	−1.73980	+	6.68033i	−0.0644811	+	0.247590i
$729$		0			0
$730$	22.1412	−	2.33796i	0.819481	−	0.0865319i
$731$	−4.66298	−	1.51510i	−0.172467	−	0.0560378i
$732$		0			0
$733$	14.4461	+	28.3522i	0.533581	+	1.04721i	0.987713	+	0.156277i	$0.0499492\pi$
$733$	14.4461	+	28.3522i	0.533581	+	1.04721i	−0.454133	+	0.890934i	$0.650051\pi$
$734$	4.01061	+	22.4380i	0.148034	+	0.828201i
$735$		0			0
$736$	3.62594	−	0.949267i	0.133654	−	0.0349904i
$737$	41.7874	+	6.61847i	1.53926	+	0.243795i
$738$		0			0
$739$	9.06553	+	6.58650i	0.333481	+	0.242288i	0.741906	−	0.670504i	$-0.233922\pi$
$739$	9.06553	+	6.58650i	0.333481	+	0.242288i	−0.408425	+	0.912792i	$0.633922\pi$
$740$	2.18587	+	1.20359i	0.0803541	+	0.0442447i
$741$		0			0
$742$	−6.93347	+	0.137262i	−0.254536	+	0.00503906i
$743$	22.0818	+	22.0818i	0.810104	+	0.810104i	0.984649	−	0.174545i	$-0.0558455\pi$
$743$	22.0818	+	22.0818i	0.810104	+	0.810104i	−0.174545	+	0.984649i	$0.555846\pi$
$744$		0			0
$745$	−7.49780	−	30.3118i	−0.274698	−	1.11054i
$746$	−16.1175	−	2.22669i	−0.590102	−	0.0815250i
$747$		0			0
$748$	7.86979	−	8.51894i	0.287748	−	0.311483i
$749$		−	0.651803i		−	0.0238164i
$750$		0			0
$751$			3.26645i			0.119194i	0.998223	+	0.0595972i	$0.0189816\pi$
$751$			3.26645i			0.119194i	−0.998223	+	0.0595972i	$0.981018\pi$
$752$	−3.16730	+	40.5753i	−0.115499	+	1.47963i
$753$		0			0
$754$	4.77737	−	34.5800i	0.173982	−	1.25933i
$755$	−10.3648	−	41.9022i	−0.377213	−	1.52498i
$756$		0			0
$757$	−1.58095	−	1.58095i	−0.0574608	−	0.0574608i	0.677792	−	0.735253i	$-0.262937\pi$
$757$	−1.58095	−	1.58095i	−0.0574608	−	0.0574608i	−0.735253	+	0.677792i	$0.762937\pi$
$758$	0.273961	+	13.8385i	0.00995070	+	0.502635i
$759$		0			0
$760$	−3.57550	+	2.53122i	−0.129697	+	0.0918172i
$761$	0.114145	+	0.0829313i	0.00413776	+	0.00300626i	0.589852	−	0.807511i	$-0.299186\pi$
$761$	0.114145	+	0.0829313i	0.00413776	+	0.00300626i	−0.585714	+	0.810517i	$0.699186\pi$
$762$		0			0
$763$	−10.1287	−	1.60422i	−0.366682	−	0.0580768i
$764$	−0.686809	−	17.3394i	−0.0248479	−	0.627319i
$765$		0			0
$766$	23.1693	−	4.14133i	0.837142	−	0.149632i
$767$	13.7621	+	27.0096i	0.496919	+	0.975258i
$768$		0			0
$769$	30.9057	+	10.0419i	1.11449	+	0.362120i	0.807662	−	0.589645i	$-0.200733\pi$
$769$	30.9057	+	10.0419i	1.11449	+	0.362120i	0.306828	+	0.951765i	$0.400733\pi$
$770$	−0.864340	−	8.18554i	−0.0311487	−	0.294986i
$771$		0			0
$772$	10.0095	−	1.99433i	0.360249	−	0.0717776i
$773$	−35.2942	+	5.59005i	−1.26944	+	0.201060i	−0.754578	−	0.656210i	$-0.772158\pi$
$773$	−35.2942	+	5.59005i	−1.26944	+	0.201060i	−0.514866	+	0.857271i	$0.672158\pi$
$774$		0			0
$775$	40.8094	−	7.03959i	1.46592	−	0.252870i
$776$	34.9368	−	7.68290i	1.25416	−	0.275800i
$777$		0			0
$778$	−16.7080	+	12.6519i	−0.599013	+	0.453591i
$779$	−0.948164	−	2.91815i	−0.0339715	−	0.104554i
$780$		0			0
$781$	2.53753	−	7.80972i	0.0908000	−	0.279454i
$782$	0.390160	+	1.12455i	0.0139521	+	0.0402137i
$783$		0			0
$784$	−24.6606	+	10.2332i	−0.880737	+	0.365472i
$785$	−31.4751	−	18.9918i	−1.12339	−	0.677846i
$786$		0			0
$787$	−2.87851	+	18.1742i	−0.102608	+	0.647841i	0.881758	+	0.471703i	$0.156361\pi$
$787$	−2.87851	+	18.1742i	−0.102608	+	0.647841i	−0.984365	+	0.176138i	$0.943639\pi$
$788$	−20.2604	+	11.3548i	−0.721746	+	0.404500i
$789$		0			0
$790$	−6.27789	−	23.3841i	−0.223357	−	0.831970i
$791$	−3.95844	−	5.44832i	−0.140746	−	0.193720i
$792$		0			0
$793$	40.1749	−	40.1749i	1.42665	−	1.42665i
$794$	36.6898	−	38.1719i	1.30207	−	1.35467i
$795$		0			0
$796$	−2.11483	−	1.41211i	−0.0749581	−	0.0500508i
$797$	0.180269	−	0.353797i	0.00638545	−	0.0125322i	−0.887792	−	0.460245i	$-0.847761\pi$
$797$	0.180269	−	0.353797i	0.00638545	−	0.0125322i	0.894177	+	0.447713i	$0.147761\pi$
$798$		0			0
$799$	−12.9248			−0.457246
$800$	15.5938	+	23.5973i	0.551324	+	0.834291i
$801$		0			0
$802$	−8.63583	−	2.61815i	−0.304942	−	0.0924500i
$803$	14.5913	−	28.6370i	0.514915	−	1.01058i
$804$		0			0
$805$	0.782676	+	0.317914i	0.0275857	+	0.0112050i
$806$	−34.7436	+	36.1470i	−1.22379	+	1.27322i
$807$		0			0
$808$	33.3374	+	40.5821i	1.17280	+	1.42767i
$809$	−27.2343	−	37.4848i	−0.957506	−	1.31789i	−0.948111	−	0.317938i	$-0.897009\pi$
$809$	−27.2343	−	37.4848i	−0.957506	−	1.31789i	−0.00939488	−	0.999956i	$-0.502991\pi$
$810$		0			0
$811$	10.0855	−	13.8814i	0.354148	−	0.487443i	−0.594358	−	0.804200i	$-0.702594\pi$
$811$	10.0855	−	13.8814i	0.354148	−	0.487443i	0.948507	+	0.316757i	$0.102594\pi$
$812$	−5.73669	+	3.21511i	−0.201319	+	0.112828i
$813$		0			0
$814$	3.17657	−	1.69856i	0.111339	−	0.0595346i
$815$	39.2126	−	3.35728i	1.37356	−	0.117600i
$816$		0			0
$817$	2.38209	−	1.21374i	0.0833388	−	0.0424633i
$818$	6.11312	+	17.6197i	0.213740	+	0.616058i
$819$		0			0
$820$	−19.0275	+	5.51427i	−0.664469	+	0.192567i
$821$	7.99259	+	24.5987i	0.278943	+	0.858499i	0.988149	+	0.153498i	$0.0490537\pi$
$821$	7.99259	+	24.5987i	0.278943	+	0.858499i	−0.709206	+	0.705002i	$0.750946\pi$
$822$		0			0
$823$	−4.34747	−	27.4488i	−0.151543	−	0.956806i	−0.939866	−	0.341544i	$-0.889050\pi$
$823$	−4.34747	−	27.4488i	−0.151543	−	0.956806i	0.788323	−	0.615262i	$-0.210950\pi$
$824$	20.7180	−	4.55606i	0.721745	−	0.158718i
$825$		0			0
$826$	2.49134	−	5.13850i	0.0866848	−	0.178791i
$827$	−27.6226	+	4.37499i	−0.960533	+	0.152133i	−0.616962	−	0.786993i	$-0.711637\pi$
$827$	−27.6226	+	4.37499i	−0.960533	+	0.152133i	−0.343571	+	0.939127i	$0.611637\pi$
$828$		0			0
$829$	26.8128	−	8.71201i	0.931248	−	0.302581i	0.196175	−	0.980569i	$-0.437148\pi$
$829$	26.8128	−	8.71201i	0.931248	−	0.302581i	0.735073	+	0.677988i	$0.237148\pi$
$830$	−25.8624	+	11.5297i	−0.897696	+	0.400201i
$831$		0			0
$832$	−32.1382	−	11.8215i	−1.11419	−	0.409835i
$833$	−3.84940	−	7.55488i	−0.133374	−	0.261761i
$834$		0			0
$835$	9.82300	+	11.3425i	0.339939	+	0.392525i
$836$	0.250295	+	6.31903i	0.00865662	+	0.218548i
$837$		0			0
$838$	3.47343	−	4.98538i	0.119988	−	0.172217i
$839$	−26.1157	−	18.9742i	−0.901615	−	0.655062i	0.0372654	−	0.999305i	$-0.488135\pi$
$839$	−26.1157	−	18.9742i	−0.901615	−	0.655062i	−0.938880	+	0.344244i	$0.888135\pi$
$840$		0			0
$841$	3.44243	−	2.50107i	0.118704	−	0.0862438i
$842$	−0.163548	−	8.26125i	−0.00563625	−	0.284701i
$843$		0			0
$844$	−8.19783	+	3.02731i	−0.282181	+	0.104204i
$845$	11.8698	+	0.852175i	0.408334	+	0.0293157i
$846$		0			0
$847$	−4.99859	−	2.54691i	−0.171754	−	0.0875129i
$848$	2.67714	−	34.2961i	0.0919334	−	1.17773i
$849$		0			0
$850$	−7.08574	+	5.52033i	−0.243039	+	0.189346i
$851$			0.369703i			0.0126733i
$852$		0			0
$853$	11.7252	+	5.97427i	0.401462	+	0.204555i	0.643051	−	0.765824i	$-0.277668\pi$
$853$	11.7252	+	5.97427i	0.401462	+	0.204555i	−0.241589	+	0.970379i	$0.577668\pi$
$854$	−10.6025	−	1.46478i	−0.362811	−	0.0501238i
$855$		0			0
$856$	3.21787	+	0.315378i	0.109985	+	0.0107794i
$857$	−17.3368	−	17.3368i	−0.592213	−	0.592213i	0.346015	−	0.938229i	$-0.387534\pi$
$857$	−17.3368	−	17.3368i	−0.592213	−	0.592213i	−0.938229	+	0.346015i	$0.887534\pi$
$858$		0			0
$859$	26.4354	−	19.2065i	0.901966	−	0.655317i	−0.0370044	−	0.999315i	$-0.511782\pi$
$859$	26.4354	−	19.2065i	0.901966	−	0.655317i	0.938970	+	0.343999i	$0.111782\pi$
$860$	−7.33905	−	15.6233i	−0.250260	−	0.532749i
$861$		0			0
$862$	3.56690	+	2.48514i	0.121489	+	0.0846443i
$863$	−25.5766	−	4.05093i	−0.870637	−	0.137895i	−0.294898	−	0.955529i	$-0.595286\pi$
$863$	−25.5766	−	4.05093i	−0.870637	−	0.137895i	−0.575739	+	0.817634i	$0.695286\pi$
$864$		0			0
$865$	−2.03144	+	0.857847i	−0.0690711	+	0.0291677i
$866$	−6.80408	−	38.0665i	−0.231212	−	1.29355i
$867$		0			0
$868$	9.37993	+	1.10715i	0.318376	+	0.0375792i
$869$	−33.2413	−	10.8008i	−1.12763	−	0.366391i
$870$		0			0
$871$	37.7294	−	12.2590i	1.27841	−	0.415381i
$872$	12.8206	−	49.2277i	0.434162	−	1.66706i
$873$		0			0
$874$	−0.584028	−	0.283159i	−0.0197550	−	0.00957798i
$875$	−0.369101	+	6.36419i	−0.0124779	+	0.215149i
$876$		0			0
$877$	−2.40885	−	15.2089i	−0.0813410	−	0.513567i	−0.994395	−	0.105728i	$-0.966283\pi$
$877$	−2.40885	−	15.2089i	−0.0813410	−	0.513567i	0.913054	−	0.407839i	$-0.133717\pi$
$878$	−20.5795	−	27.1773i	−0.694525	−	0.917190i
$879$		0			0
$880$	40.8292	−	0.306531i	1.37635	−	0.0103331i
$881$	6.30400	−	19.4017i	0.212387	−	0.653660i	−0.786942	−	0.617027i	$-0.788337\pi$
$881$	6.30400	−	19.4017i	0.212387	−	0.653660i	0.999329	−	0.0366329i	$-0.0116632\pi$
$882$		0			0
$883$	42.2974	−	21.5516i	1.42342	−	0.725270i	0.438575	−	0.898694i	$-0.355483\pi$
$883$	42.2974	−	21.5516i	1.42342	−	0.725270i	0.984847	+	0.173424i	$0.0554833\pi$
$884$	2.94851	−	10.4674i	0.0991690	−	0.352057i
$885$		0			0
$886$	−16.8131	−	31.4430i	−0.564847	−	1.05635i
$887$	5.53478	−	34.9452i	0.185840	−	1.17335i	−0.701651	−	0.712521i	$-0.747553\pi$
$887$	5.53478	−	34.9452i	0.185840	−	1.17335i	0.887491	−	0.460825i	$-0.152447\pi$
$888$		0			0
$889$	6.65437	−	9.15895i	0.223180	−	0.307181i
$890$	10.3204	−	12.7573i	0.345942	−	0.427625i
$891$		0			0
$892$	9.59934	−	20.8401i	0.321410	−	0.697777i
$893$	4.98343	−	4.98343i	0.166764	−	0.166764i
$894$		0			0
$895$	19.4306	+	31.2244i	0.649493	+	1.04372i
$896$	1.87950	+	6.17105i	0.0627896	+	0.206160i
$897$		0			0
$898$	−4.44908	+	14.6751i	−0.148468	+	0.489714i
$899$	−47.7624			−1.59296
$900$		0			0
$901$	10.9246			0.363952
$902$	−8.29713	+	27.3677i	−0.276264	+	0.911244i
$903$		0			0
$904$	28.8130	−	16.9061i	0.958306	−	0.562289i
$905$	3.65512	−	50.9117i	0.121500	−	1.69236i
$906$		0			0
$907$	25.9955	−	25.9955i	0.863166	−	0.863166i	−0.128538	−	0.991705i	$-0.541029\pi$
$907$	25.9955	−	25.9955i	0.863166	−	0.863166i	0.991705	+	0.128538i	$0.0410286\pi$
$908$	54.4561	+	25.0835i	1.80719	+	0.832427i
$909$		0			0
$910$	−4.20664	−	6.47081i	−0.139449	−	0.214505i
$911$	4.91355	−	6.76292i	0.162793	−	0.224065i	−0.719826	−	0.694155i	$-0.755778\pi$
$911$	4.91355	−	6.76292i	0.162793	−	0.224065i	0.882619	+	0.470089i	$0.155778\pi$
$912$		0			0
$913$	−6.39444	+	40.3729i	−0.211625	+	1.33615i
$914$	−10.1408	−	18.9648i	−0.335427	−	0.627300i
$915$		0			0
$916$	1.66917	+	0.470180i	0.0551510	+	0.0155352i
$917$	11.5704	−	5.89541i	0.382088	−	0.194684i
$918$		0			0
$919$	12.4509	−	38.3200i	0.410718	−	1.26406i	−0.505307	−	0.862940i	$-0.668621\pi$
$919$	12.4509	−	38.3200i	0.410718	−	1.26406i	0.916025	−	0.401121i	$-0.131379\pi$
$920$	−1.94820	+	3.71015i	−0.0642304	+	0.122320i
$921$		0			0
$922$	7.38646	+	9.75456i	0.243260	+	0.321249i
$923$	−1.20451	−	7.60496i	−0.0396469	−	0.250320i
$924$		0			0
$925$	−2.64122	+	0.898484i	−0.0868427	+	0.0295420i
$926$	−8.99835	−	4.36274i	−0.295704	−	0.143369i
$927$		0			0
$928$	−13.0969	−	29.8770i	−0.429926	−	0.980760i
$929$	−15.1027	+	4.90715i	−0.495502	+	0.160998i	−0.546099	−	0.837721i	$-0.683888\pi$
$929$	−15.1027	+	4.90715i	−0.495502	+	0.160998i	0.0505966	+	0.998719i	$0.483888\pi$
$930$		0			0
$931$	4.39717	+	1.42873i	0.144111	+	0.0468246i
$932$	−2.21958	+	18.8045i	−0.0727047	+	0.615962i
$933$		0			0
$934$	−4.60710	−	25.7751i	−0.150749	−	0.843389i
$935$	1.10612	+	12.9193i	0.0361740	+	0.422507i
$936$		0			0
$937$	−2.53917	−	0.402165i	−0.0829512	−	0.0131382i	0.114821	−	0.993386i	$-0.463371\pi$
$937$	−2.53917	−	0.402165i	−0.0829512	−	0.0131382i	−0.197772	+	0.980248i	$0.563371\pi$
$938$	−6.13188	−	4.27223i	−0.200213	−	0.139493i
$939$		0			0
$940$	−31.1266	−	33.1907i	−1.01524	−	1.08256i
$941$	13.7615	−	9.99831i	0.448612	−	0.325935i	−0.340436	−	0.940268i	$-0.610575\pi$
$941$	13.7615	−	9.99831i	0.448612	−	0.325935i	0.789047	+	0.614332i	$0.210575\pi$
$942$		0			0
$943$	−2.07541	−	2.07541i	−0.0675848	−	0.0675848i
$944$	24.1627	+	14.7857i	0.786429	+	0.481234i
$945$		0			0
$946$	−24.6833	−	3.41010i	−0.802522	−	0.110872i
$947$	25.4121	+	12.9481i	0.825782	+	0.420757i	0.815195	−	0.579187i	$-0.196630\pi$
$947$	25.4121	+	12.9481i	0.825782	+	0.420757i	0.0105872	+	0.999944i	$0.496630\pi$
$948$		0			0
$949$		−	30.1366i		−	0.978276i
$950$	0.603576	−	4.86054i	0.0195826	−	0.157697i
$951$		0			0
$952$	−1.90736	+	0.747580i	−0.0618179	+	0.0242292i
$953$	13.9573	+	7.11160i	0.452121	+	0.230367i	0.665196	−	0.746669i	$-0.268348\pi$
$953$	13.9573	+	7.11160i	0.452121	+	0.230367i	−0.213075	+	0.977036i	$0.568348\pi$
$954$		0			0
$955$	14.8391	+	12.4985i	0.480181	+	0.404442i
$956$	−7.66815	−	20.7650i	−0.248006	−	0.671589i
$957$		0			0
$958$	0.707841	+	35.7548i	0.0228693	+	1.15519i
$959$	7.71380	−	5.60441i	0.249092	−	0.180976i
$960$		0			0
$961$	30.4178	+	22.0998i	0.981218	+	0.712897i
$962$	1.93085	−	2.77133i	0.0622532	−	0.0893513i
$963$		0			0
$964$	−1.46606	+	0.0580702i	−0.0472186	+	0.00187031i
$965$	−5.89521	+	9.77013i	−0.189774	+	0.314512i
$966$		0			0
$967$	1.53584	+	3.01425i	0.0493891	+	0.0969316i	0.914382	−	0.404853i	$-0.132677\pi$
$967$	1.53584	+	3.01425i	0.0493891	+	0.0969316i	−0.864993	+	0.501784i	$0.832677\pi$
$968$	14.9924	−	23.4451i	0.481873	−	0.753554i
$969$		0			0
$970$	−19.9802	+	34.6454i	−0.641524	+	1.11240i
$971$	−0.924449	+	0.300372i	−0.0296670	+	0.00963939i	−0.323813	−	0.946121i	$-0.604965\pi$
$971$	−0.924449	+	0.300372i	−0.0296670	+	0.00963939i	0.294146	+	0.955761i	$0.404965\pi$
$972$		0			0
$973$	−0.690268	+	0.109328i	−0.0221290	+	0.00350489i
$974$	−14.5746	+	30.0607i	−0.466999	+	0.963206i
$975$		0			0
$976$	12.3615	−	51.6346i	0.395683	−	1.65278i
$977$	1.61466	+	10.1946i	0.0516576	+	0.326153i	0.999961	+	0.00878920i	$0.00279773\pi$
$977$	1.61466	+	10.1946i	0.0516576	+	0.326153i	−0.948304	+	0.317364i	$0.897202\pi$
$978$		0			0
$979$	−7.31992	−	22.5284i	−0.233946	−	0.720011i
$980$	10.1304	−	28.0795i	0.323602	−	0.896967i
$981$		0			0
$982$	11.0897	+	31.9636i	0.353887	+	1.02000i
$983$	2.23630	−	1.13945i	0.0713268	−	0.0363428i	−0.417963	−	0.908464i	$-0.637256\pi$
$983$	2.23630	−	1.13945i	0.0713268	−	0.0363428i	0.489290	+	0.872121i	$0.337256\pi$
$984$		0			0
$985$	5.88821	−	25.2903i	0.187614	−	0.805815i
$986$	9.13565	−	4.88498i	0.290938	−	0.155569i
$987$		0			0
$988$	2.89907	+	5.17279i	0.0922317	+	0.164568i
$989$	1.50319	−	2.06897i	0.0477988	−	0.0657894i
$990$		0			0
$991$	−22.1826	−	30.5317i	−0.704653	−	0.969871i	−0.999896	−	0.0144492i	$-0.995401\pi$
$991$	−22.1826	−	30.5317i	−0.704653	−	0.969871i	0.295243	−	0.955422i	$-0.404599\pi$
$992$	−10.0044	+	45.7718i	−0.317640	+	1.45326i
$993$		0			0
$994$	−1.00517	+	1.04577i	−0.0318820	+	0.0331698i
$995$	2.75991	−	0.682682i	0.0874952	−	0.0216425i
$996$		0			0
$997$	3.03505	−	5.95663i	0.0961211	−	0.188648i	−0.837939	−	0.545764i	$-0.816240\pi$
$997$	3.03505	−	5.95663i	0.0961211	−	0.188648i	0.934060	+	0.357115i	$0.116240\pi$
$998$	−4.33345	−	1.31378i	−0.137173	−	0.0415871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.487.28		240
3.2	odd	2		300.2.w.a.187.3	✓	240
4.3	odd	2	inner	900.2.bj.f.487.6		240
12.11	even	2		300.2.w.a.187.25	yes	240
25.23	odd	20	inner	900.2.bj.f.523.6		240
75.23	even	20		300.2.w.a.223.25	yes	240
100.23	even	20	inner	900.2.bj.f.523.28		240
300.23	odd	20		300.2.w.a.223.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.3	✓	240	3.2	odd	2
300.2.w.a.187.25	yes	240	12.11	even	2
300.2.w.a.223.3	yes	240	300.23	odd	20
300.2.w.a.223.25	yes	240	75.23	even	20
900.2.bj.f.487.6		240	4.3	odd	2	inner
900.2.bj.f.487.28		240	1.1	even	1	trivial
900.2.bj.f.523.6		240	25.23	odd	20	inner
900.2.bj.f.523.28		240	100.23	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)

\(f(q)\)	\(=\)	\(q+(1.35338 + 0.410309i) q^{2} +(1.66329 + 1.11061i) q^{4} +(-2.17065 + 0.536923i) q^{5} +(0.403183 - 0.403183i) q^{7} +(1.79538 + 2.18554i) q^{8} +O(q^{10})\)	\(q+(1.35338 + 0.410309i) q^{2} +(1.66329 + 1.11061i) q^{4} +(-2.17065 + 0.536923i) q^{5} +(0.403183 - 0.403183i) q^{7} +(1.79538 + 2.18554i) q^{8} +(-3.15802 - 0.163973i) q^{10} +(-2.68322 + 3.69314i) q^{11} +(-0.669605 + 4.22772i) q^{13} +(0.711090 - 0.380232i) q^{14} +(1.53309 + 3.69454i) q^{16} +(-1.13184 + 0.576699i) q^{17} +(0.214045 - 0.658762i) q^{19} +(-4.20674 - 1.51768i) q^{20} +(-5.14676 + 3.89729i) q^{22} +(-0.103651 - 0.654427i) q^{23} +(4.42343 - 2.33094i) q^{25} +(-2.64090 + 5.44698i) q^{26} +(1.11839 - 0.222833i) q^{28} +(-5.48448 + 1.78201i) q^{29} +(7.87705 + 2.55941i) q^{31} +(0.558959 + 5.62917i) q^{32} +(-1.76843 + 0.316093i) q^{34} +(-0.658690 + 1.09165i) q^{35} +(-0.551102 - 0.0872860i) q^{37} +(0.559981 - 0.803734i) q^{38} +(-5.07061 - 3.78007i) q^{40} +(3.58374 - 2.60374i) q^{41} +(2.72923 + 2.72923i) q^{43} +(-8.56463 + 3.16276i) q^{44} +(0.128237 - 0.928219i) q^{46} +(9.06571 + 4.61921i) q^{47} +6.67489i q^{49} +(6.94300 - 1.33969i) q^{50} +(-5.80910 + 6.28827i) q^{52} +(-7.66275 - 3.90436i) q^{53} +(3.84140 - 9.45719i) q^{55} +(1.60504 + 0.157307i) q^{56} +(-8.15378 + 0.161421i) q^{58} +(5.72938 - 4.16264i) q^{59} +(-10.7384 - 7.80192i) q^{61} +(9.61052 + 6.69588i) q^{62} +(-1.55321 + 7.84777i) q^{64} +(-0.816485 - 9.53642i) q^{65} +(-4.20759 - 8.25787i) q^{67} +(-2.52306 - 0.297808i) q^{68} +(-1.33937 + 1.20715i) q^{70} +(-1.71079 + 0.555870i) q^{71} +(-6.95389 + 1.10139i) q^{73} +(-0.710038 - 0.344253i) q^{74} +(1.08765 - 0.857995i) q^{76} +(0.407181 + 2.57084i) q^{77} +(2.36601 + 7.28182i) q^{79} +(-5.31149 - 7.19640i) q^{80} +(5.91851 - 2.05342i) q^{82} +(7.97834 - 4.06517i) q^{83} +(2.14717 - 1.85952i) q^{85} +(2.57387 + 4.81352i) q^{86} +(-12.8889 + 0.766290i) q^{88} +(-3.05003 + 4.19801i) q^{89} +(1.43457 + 1.97452i) q^{91} +(0.554411 - 1.20362i) q^{92} +(10.3741 + 9.97131i) q^{94} +(-0.110911 + 1.54487i) q^{95} +(5.74169 - 11.2687i) q^{97} +(-2.73876 + 9.03368i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 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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