LMFDB - Embedded newform 855.2.k.h.676.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (of order $3$, degree $2$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.4
Root			$-0.245959 + 0.426014i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.h.406.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37901 - 2.38851i) q^{2} +(-2.80333 - 4.85550i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.84864 q^{7} -9.94721 q^{8} +O(q^{10})$	\(q+(1.37901 - 2.38851i) q^{2} +(-2.80333 - 4.85550i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.84864 q^{7} -9.94721 q^{8} +(-1.37901 - 2.38851i) q^{10} +0.864801 q^{11} +(-0.321640 - 0.557098i) q^{13} +(-3.92829 + 6.80401i) q^{14} +(-8.11063 + 14.0480i) q^{16} +(1.87093 - 3.24054i) q^{17} +(-3.36069 + 2.77592i) q^{19} -5.60665 q^{20} +(1.19257 - 2.06559i) q^{22} +(0.208730 + 0.361531i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.77418 q^{26} +(7.98566 + 13.8316i) q^{28} +(-4.85261 - 8.40497i) q^{29} +4.93349 q^{31} +(12.4220 + 21.5156i) q^{32} +(-5.16005 - 8.93746i) q^{34} +(-1.42432 + 2.46699i) q^{35} +6.36467 q^{37} +(1.99589 + 11.8551i) q^{38} +(-4.97360 + 8.61454i) q^{40} +(-2.00686 + 3.47598i) q^{41} +(1.02915 - 1.78254i) q^{43} +(-2.42432 - 4.19904i) q^{44} +1.15136 q^{46} +(-1.97698 - 3.42423i) q^{47} +1.11474 q^{49} -2.75802 q^{50} +(-1.80333 + 3.12345i) q^{52} +(-5.49374 - 9.51544i) q^{53} +(0.432400 - 0.748939i) q^{55} +28.3360 q^{56} -26.7672 q^{58} +(1.22980 - 2.13007i) q^{59} +(-3.16740 - 5.48609i) q^{61} +(6.80333 - 11.7837i) q^{62} +36.0778 q^{64} -0.643281 q^{65} +(1.26610 + 2.19295i) q^{67} -20.9793 q^{68} +(3.92829 + 6.80401i) q^{70} +(-0.891065 + 1.54337i) q^{71} +(3.56545 - 6.17554i) q^{73} +(8.77693 - 15.2021i) q^{74} +(22.8996 + 8.53606i) q^{76} -2.46350 q^{77} +(-0.912262 + 1.58008i) q^{79} +(8.11063 + 14.0480i) q^{80} +(5.53495 + 9.58681i) q^{82} +7.43913 q^{83} +(-1.87093 - 3.24054i) q^{85} +(-2.83841 - 4.91626i) q^{86} -8.60235 q^{88} +(2.22294 + 3.85024i) q^{89} +(0.916237 + 1.58697i) q^{91} +(1.17028 - 2.02698i) q^{92} -10.9051 q^{94} +(0.723670 + 4.29841i) q^{95} +(5.42707 - 9.39996i) q^{97} +(1.53723 - 2.66256i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10}) $ 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8	$ 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8} - q^{10} + 4 q^{11} - 7 q^{13} - q^{14} - 7 q^{16} - q^{17} + 5 q^{19} - 10 q^{20} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 6 q^{26} + 19 q^{28} - q^{29} + 30 q^{32} - 15 q^{34} - 4 q^{35} - 4 q^{37} - 13 q^{38} - 12 q^{40} - 8 q^{41} - q^{43} - 12 q^{44} + 24 q^{46} - 12 q^{47} - 20 q^{49} - 2 q^{50} + 3 q^{52} - 5 q^{53} + 2 q^{55} + 82 q^{56} - 54 q^{58} - 5 q^{59} + 37 q^{62} + 112 q^{64} - 14 q^{65} - 4 q^{67} - 32 q^{68} + q^{70} + 20 q^{71} + 20 q^{73} + 25 q^{74} + 63 q^{76} - 28 q^{77} - 17 q^{79} + 7 q^{80} - 21 q^{82} - 2 q^{83} + q^{85} + 8 q^{86} - 14 q^{88} + 11 q^{89} - 6 q^{91} - q^{92} - 62 q^{94} + 4 q^{95} - q^{97} + 9 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8 - q^10 + 4 * q^11 - 7 * q^13 - q^14 - 7 * q^16 - q^17 + 5 * q^19 - 10 * q^20 - 2 * q^22 + 2 * q^23 - 4 * q^25 - 6 * q^26 + 19 * q^28 - q^29 + 30 * q^32 - 15 * q^34 - 4 * q^35 - 4 * q^37 - 13 * q^38 - 12 * q^40 - 8 * q^41 - q^43 - 12 * q^44 + 24 * q^46 - 12 * q^47 - 20 * q^49 - 2 * q^50 + 3 * q^52 - 5 * q^53 + 2 * q^55 + 82 * q^56 - 54 * q^58 - 5 * q^59 + 37 * q^62 + 112 * q^64 - 14 * q^65 - 4 * q^67 - 32 * q^68 + q^70 + 20 * q^71 + 20 * q^73 + 25 * q^74 + 63 * q^76 - 28 * q^77 - 17 * q^79 + 7 * q^80 - 21 * q^82 - 2 * q^83 + q^85 + 8 * q^86 - 14 * q^88 + 11 * q^89 - 6 * q^91 - q^92 - 62 * q^94 + 4 * q^95 - q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.37901	−	2.38851i	0.975106	−	1.68893i	0.295521	−	0.955336i	$-0.404507\pi$
$2$	1.37901	−	2.38851i	0.975106	−	1.68893i	0.679585	−	0.733597i	$-0.262160\pi$
$3$		0			0
$3$		0			0
$4$	−2.80333	−	4.85550i	−1.40166	−	2.42775i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−2.84864			−1.07668			−0.538342	−	0.842727i	$-0.680949\pi$
$7$	−2.84864			−1.07668			−0.538342	+	0.842727i	$0.680949\pi$
$8$	−9.94721			−3.51687
$9$		0			0
$10$	−1.37901	−	2.38851i	−0.436081	−	0.755314i
$11$	0.864801			0.260747			0.130374	−	0.991465i	$-0.458382\pi$
$11$	0.864801			0.260747			0.130374	+	0.991465i	$0.458382\pi$
$12$		0			0
$13$	−0.321640	−	0.557098i	−0.0892070	−	0.154511i	0.817969	−	0.575262i	$-0.195100\pi$
$13$	−0.321640	−	0.557098i	−0.0892070	−	0.154511i	−0.907176	+	0.420751i	$0.861767\pi$
$14$	−3.92829	+	6.80401i	−1.04988	+	1.81845i
$15$		0			0
$16$	−8.11063	+	14.0480i	−2.02766	+	3.51201i
$17$	1.87093	−	3.24054i	0.453766	−	0.785946i	−0.544850	−	0.838534i	$-0.683413\pi$
$17$	1.87093	−	3.24054i	0.453766	−	0.785946i	0.998616	+	0.0525872i	$0.0167467\pi$
$18$		0			0
$19$	−3.36069	+	2.77592i	−0.770996	+	0.636840i
$19$	−3.36069	+	2.77592i	−0.770996	+	0.636840i
$20$	−5.60665			−1.25369
$21$		0			0
$22$	1.19257	−	2.06559i	0.254256	−	0.440385i
$23$	0.208730	+	0.361531i	0.0435233	+	0.0753845i	0.886966	−	0.461834i	$-0.152808\pi$
$23$	0.208730	+	0.361531i	0.0435233	+	0.0753845i	−0.843443	+	0.537218i	$0.819475\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.77418			−0.347945
$27$		0			0
$28$	7.98566	+	13.8316i	1.50915	+	2.61392i
$29$	−4.85261	−	8.40497i	−0.901108	−	1.56076i	−0.826059	−	0.563584i	$-0.809422\pi$
$29$	−4.85261	−	8.40497i	−0.901108	−	1.56076i	−0.0750490	−	0.997180i	$-0.523911\pi$
$30$		0			0
$31$	4.93349			0.886081			0.443041	−	0.896501i	$-0.353900\pi$
$31$	4.93349			0.886081			0.443041	+	0.896501i	$0.353900\pi$
$32$	12.4220	+	21.5156i	2.19593	+	3.80346i
$33$		0			0
$34$	−5.16005	−	8.93746i	−0.884941	−	1.53276i
$35$	−1.42432	+	2.46699i	−0.240754	+	0.416998i
$36$		0			0
$37$	6.36467			1.04635			0.523173	−	0.852227i	$-0.324748\pi$
$37$	6.36467			1.04635			0.523173	+	0.852227i	$0.324748\pi$
$38$	1.99589	+	11.8551i	0.323777	+	1.92315i
$39$		0			0
$40$	−4.97360	+	8.61454i	−0.786396	+	1.36208i
$41$	−2.00686	+	3.47598i	−0.313419	+	0.542857i	−0.979100	−	0.203379i	$-0.934808\pi$
$41$	−2.00686	+	3.47598i	−0.313419	+	0.542857i	0.665681	+	0.746236i	$0.268141\pi$
$42$		0			0
$43$	1.02915	−	1.78254i	0.156944	−	0.271834i	−0.776821	−	0.629721i	$-0.783169\pi$
$43$	1.02915	−	1.78254i	0.156944	−	0.271834i	0.933765	+	0.357887i	$0.116503\pi$
$44$	−2.42432	−	4.19904i	−0.365480	−	0.633030i
$45$		0			0
$46$	1.15136			0.169759
$47$	−1.97698	−	3.42423i	−0.288372	−	0.499475i	0.685049	−	0.728497i	$-0.259781\pi$
$47$	−1.97698	−	3.42423i	−0.288372	−	0.499475i	−0.973421	+	0.229022i	$0.926447\pi$
$48$		0			0
$49$	1.11474			0.159248
$50$	−2.75802			−0.390042
$51$		0			0
$52$	−1.80333	+	3.12345i	−0.250076	+	0.433145i
$53$	−5.49374	−	9.51544i	−0.754624	−	1.30705i	−0.945561	−	0.325444i	$-0.894486\pi$
$53$	−5.49374	−	9.51544i	−0.754624	−	1.30705i	0.190937	−	0.981602i	$-0.438847\pi$
$54$		0			0
$55$	0.432400	−	0.748939i	0.0583048	−	0.100987i
$56$	28.3360			3.78656
$57$		0			0
$58$	−26.7672			−3.51470
$59$	1.22980	−	2.13007i	0.160106	−	0.277311i	−0.774801	−	0.632206i	$-0.782150\pi$
$59$	1.22980	−	2.13007i	0.160106	−	0.277311i	0.934906	+	0.354894i	$0.115483\pi$
$60$		0			0
$61$	−3.16740	−	5.48609i	−0.405543	−	0.702422i	0.588841	−	0.808249i	$-0.299584\pi$
$61$	−3.16740	−	5.48609i	−0.405543	−	0.702422i	−0.994385	+	0.105827i	$0.966251\pi$
$62$	6.80333	−	11.7837i	0.864023	−	1.49653i
$63$		0			0
$64$	36.0778			4.50973
$65$	−0.643281			−0.0797892
$66$		0			0
$67$	1.26610	+	2.19295i	0.154678	+	0.267911i	0.932942	−	0.360027i	$-0.117233\pi$
$67$	1.26610	+	2.19295i	0.154678	+	0.267911i	−0.778263	+	0.627938i	$0.783899\pi$
$68$	−20.9793			−2.54411
$69$		0			0
$70$	3.92829	+	6.80401i	0.469521	+	0.813234i
$71$	−0.891065	+	1.54337i	−0.105750	+	0.183164i	−0.914044	−	0.405614i	$-0.867058\pi$
$71$	−0.891065	+	1.54337i	−0.105750	+	0.183164i	0.808294	+	0.588779i	$0.200391\pi$
$72$		0			0
$73$	3.56545	−	6.17554i	0.417304	−	0.722792i	−0.578363	−	0.815780i	$-0.696308\pi$
$73$	3.56545	−	6.17554i	0.417304	−	0.722792i	0.995667	+	0.0929873i	$0.0296416\pi$
$74$	8.77693	−	15.2021i	1.02030	−	1.76721i
$75$		0			0
$76$	22.8996	+	8.53606i	2.62677	+	0.979153i
$77$	−2.46350			−0.280742
$78$		0			0
$79$	−0.912262	+	1.58008i	−0.102637	+	0.177773i	−0.912771	−	0.408473i	$-0.866061\pi$
$79$	−0.912262	+	1.58008i	−0.102637	+	0.177773i	0.810133	+	0.586246i	$0.199395\pi$
$80$	8.11063	+	14.0480i	0.906796	+	1.57062i
$81$		0			0
$82$	5.53495	+	9.58681i	0.611233	+	1.05869i
$83$	7.43913			0.816550			0.408275	−	0.912859i	$-0.366130\pi$
$83$	7.43913			0.816550			0.408275	+	0.912859i	$0.366130\pi$
$84$		0			0
$85$	−1.87093	−	3.24054i	−0.202930	−	0.351486i
$86$	−2.83841	−	4.91626i	−0.306073	−	0.530134i
$87$		0			0
$88$	−8.60235			−0.917014
$89$	2.22294	+	3.85024i	0.235631	+	0.408125i	0.959456	−	0.281859i	$-0.0909510\pi$
$89$	2.22294	+	3.85024i	0.235631	+	0.408125i	−0.723825	+	0.689984i	$0.757618\pi$
$90$		0			0
$91$	0.916237	+	1.58697i	0.0960478	+	0.166360i
$92$	1.17028	−	2.02698i	0.122010	−	0.211327i
$93$		0			0
$94$	−10.9051			−1.12477
$95$	0.723670	+	4.29841i	0.0742470	+	0.441007i
$96$		0			0
$97$	5.42707	−	9.39996i	0.551036	−	0.954422i	−0.447165	−	0.894452i	$-0.647566\pi$
$97$	5.42707	−	9.39996i	0.551036	−	0.954422i	0.998200	−	0.0599699i	$-0.0191005\pi$
$98$	1.53723	−	2.66256i	0.155284	−	0.268959i
$99$		0			0
$100$	−2.80333	+	4.85550i	−0.280333	+	0.485550i
$101$	−2.64799	−	4.58645i	−0.263485	−	0.456369i	0.703681	−	0.710516i	$-0.251539\pi$
$101$	−2.64799	−	4.58645i	−0.263485	−	0.456369i	−0.967166	+	0.254147i	$0.918205\pi$
$102$		0			0
$103$	−0.385134			−0.0379484			−0.0189742	−	0.999820i	$-0.506040\pi$
$103$	−0.385134			−0.0379484			−0.0189742	+	0.999820i	$0.506040\pi$
$104$	3.19943	+	5.54157i	0.313729	+	0.543395i
$105$		0			0
$106$	−30.3037			−2.94335
$107$	6.43336			0.621937			0.310968	−	0.950420i	$-0.399347\pi$
$107$	6.43336			0.621937			0.310968	+	0.950420i	$0.399347\pi$
$108$		0			0
$109$	−3.28441	+	5.68877i	−0.314590	+	0.544885i	−0.979350	−	0.202171i	$-0.935200\pi$
$109$	−3.28441	+	5.68877i	−0.314590	+	0.544885i	0.664761	+	0.747056i	$0.268534\pi$
$110$	−1.19257	−	2.06559i	−0.113707	−	0.196946i
$111$		0			0
$112$	23.1042	−	40.0177i	2.18315	−	3.78132i
$113$	−0.294513			−0.0277054			−0.0138527	−	0.999904i	$-0.504410\pi$
$113$	−0.294513			−0.0277054			−0.0138527	+	0.999904i	$0.504410\pi$
$114$		0			0
$115$	0.417460			0.0389284
$116$	−27.2069	+	47.1238i	−2.52610	+	4.37533i
$117$		0			0
$118$	−3.39180	−	5.87477i	−0.312240	−	0.540816i
$119$	−5.32959	+	9.23112i	−0.488563	+	0.846216i
$120$		0			0
$121$	−10.2521			−0.932011
$122$	−17.4715			−1.58179
$123$		0			0
$124$	−13.8302	−	23.9546i	−1.24199	−	2.15119i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−4.41746	−	7.65127i	−0.391986	−	0.678940i	0.600725	−	0.799456i	$-0.294879\pi$
$127$	−4.41746	−	7.65127i	−0.391986	−	0.678940i	−0.992711	+	0.120516i	$0.961545\pi$
$128$	24.9076	−	43.1412i	2.20154	−	3.81318i
$129$		0			0
$130$	−0.887090	+	1.53648i	−0.0778029	+	0.134759i
$131$	10.4564	−	18.1110i	0.913578	−	1.58236i	0.104609	−	0.994513i	$-0.466641\pi$
$131$	10.4564	−	18.1110i	0.913578	−	1.58236i	0.808969	−	0.587851i	$-0.200026\pi$
$132$		0			0
$133$	9.57340	−	7.90759i	0.830119	−	0.685675i
$134$	6.98384			0.603312
$135$		0			0
$136$	−18.6105	+	32.2343i	−1.59584	+	2.76407i
$137$	2.60739	+	4.51613i	0.222764	+	0.385839i	0.955646	−	0.294517i	$-0.0951587\pi$
$137$	2.60739	+	4.51613i	0.222764	+	0.385839i	−0.732882	+	0.680356i	$0.761825\pi$
$138$		0			0
$139$	5.36192	+	9.28711i	0.454792	+	0.787723i	0.998676	−	0.0514375i	$-0.0163803\pi$
$139$	5.36192	+	9.28711i	0.454792	+	0.787723i	−0.543884	+	0.839160i	$0.683047\pi$
$140$	15.9713			1.34982
$141$		0			0
$142$	2.45757	+	4.25664i	0.206235	+	0.357209i
$143$	−0.278155	−	0.481778i	−0.0232605	−	0.0402883i
$144$		0			0
$145$	−9.70523			−0.805975
$146$	−9.83357	−	17.0322i	−0.813832	−	1.40960i
$147$		0			0
$148$	−17.8423	−	30.9037i	−1.46662	−	2.54027i
$149$	−7.45578	+	12.9138i	−0.610801	+	1.05794i	0.380304	+	0.924861i	$0.375819\pi$
$149$	−7.45578	+	12.9138i	−0.610801	+	1.05794i	−0.991106	+	0.133078i	$0.957514\pi$
$150$		0			0
$151$	21.4589			1.74630			0.873152	−	0.487448i	$-0.162072\pi$
$151$	21.4589			1.74630			0.873152	+	0.487448i	$0.162072\pi$
$152$	33.4295	−	27.6127i	2.71149	−	2.23968i
$153$		0			0
$154$	−3.39719	+	5.88411i	−0.273753	+	0.474155i
$155$	2.46675	−	4.27253i	0.198134	−	0.343178i
$156$		0			0
$157$	1.21559	−	2.10546i	0.0970145	−	0.168034i	−0.813433	−	0.581659i	$-0.802404\pi$
$157$	1.21559	−	2.10546i	0.0970145	−	0.168034i	0.910448	+	0.413624i	$0.135737\pi$
$158$	2.51603	+	4.35790i	0.200165	+	0.346696i
$159$		0			0
$160$	24.8441			1.96410
$161$	−0.594597	−	1.02987i	−0.0468608	−	0.0811653i
$162$		0			0
$163$	17.8175			1.39558			0.697788	−	0.716305i	$-0.254168\pi$
$163$	17.8175			1.39558			0.697788	+	0.716305i	$0.254168\pi$
$164$	22.5035			1.75723
$165$		0			0
$166$	10.2586	−	17.7684i	0.796223	−	1.37910i
$167$	−0.202799	−	0.351258i	−0.0156931	−	0.0271812i	0.858072	−	0.513529i	$-0.171662\pi$
$167$	−0.202799	−	0.351258i	−0.0156931	−	0.0271812i	−0.873765	+	0.486348i	$0.838329\pi$
$168$		0			0
$169$	6.29309	−	10.9000i	0.484084	−	0.838458i
$170$	−10.3201			−0.791515
$171$		0			0
$172$	−11.5401			−0.879928
$173$	9.01051	−	15.6067i	0.685056	−	1.18655i	−0.288363	−	0.957521i	$-0.593111\pi$
$173$	9.01051	−	15.6067i	0.685056	−	1.18655i	0.973419	−	0.229031i	$-0.0735557\pi$
$174$		0			0
$175$	1.42432	+	2.46699i	0.107668	+	0.186487i
$176$	−7.01408	+	12.1487i	−0.528706	+	0.915746i
$177$		0			0
$178$	12.2618			0.919061
$179$	−20.1523			−1.50625			−0.753127	−	0.657875i	$-0.771455\pi$
$179$	−20.1523			−1.50625			−0.753127	+	0.657875i	$0.771455\pi$
$180$		0			0
$181$	8.55541	+	14.8184i	0.635919	+	1.10144i	0.986320	+	0.164844i	$0.0527120\pi$
$181$	8.55541	+	14.8184i	0.635919	+	1.10144i	−0.350401	+	0.936600i	$0.613955\pi$
$182$	5.05399			0.374627
$183$		0			0
$184$	−2.07628	−	3.59623i	−0.153066	−	0.265117i
$185$	3.18233	−	5.51197i	0.233970	−	0.405248i
$186$		0			0
$187$	1.61798	−	2.80242i	0.118318	−	0.204933i
$188$	−11.0842	+	19.1985i	−0.808401	+	1.40019i
$189$		0			0
$190$	11.2647	+	4.19904i	0.817230	+	0.304631i
$191$	−5.28080			−0.382105			−0.191053	−	0.981580i	$-0.561190\pi$
$191$	−5.28080			−0.382105			−0.191053	+	0.981580i	$0.561190\pi$
$192$		0			0
$193$	−9.00182	+	15.5916i	−0.647966	+	1.12231i	0.335642	+	0.941989i	$0.391047\pi$
$193$	−9.00182	+	15.5916i	−0.647966	+	1.12231i	−0.983608	+	0.180320i	$0.942287\pi$
$194$	−14.9679	−	25.9252i	−1.07464	−	1.86132i
$195$		0			0
$196$	−3.12497	−	5.41260i	−0.223212	−	0.386614i
$197$	−8.07785			−0.575523			−0.287761	−	0.957702i	$-0.592911\pi$
$197$	−8.07785			−0.575523			−0.287761	+	0.957702i	$0.592911\pi$
$198$		0			0
$199$	−0.701872	−	1.21568i	−0.0497544	−	0.0861771i	0.840076	−	0.542469i	$-0.182511\pi$
$199$	−0.701872	−	1.21568i	−0.0497544	−	0.0861771i	−0.889830	+	0.456292i	$0.849177\pi$
$200$	4.97360	+	8.61454i	0.351687	+	0.609140i
$201$		0			0
$202$	−14.6064			−1.02770
$203$	13.8233	+	23.9427i	0.970208	+	1.68045i
$204$		0			0
$205$	2.00686	+	3.47598i	0.140165	+	0.242773i
$206$	−0.531103	+	0.919897i	−0.0370037	+	0.0640923i
$207$		0			0
$208$	10.4348			0.723525
$209$	−2.90633	+	2.40062i	−0.201035	+	0.166054i
$210$		0			0
$211$	−9.45817	+	16.3820i	−0.651128	+	1.12779i	0.331722	+	0.943377i	$0.392370\pi$
$211$	−9.45817	+	16.3820i	−0.651128	+	1.12779i	−0.982850	+	0.184409i	$0.940963\pi$
$212$	−30.8015	+	53.3498i	−2.11546	+	3.66408i
$213$		0			0
$214$	8.87166	−	15.3662i	0.606454	−	1.05041i
$215$	−1.02915	−	1.78254i	−0.0701873	−	0.121568i
$216$		0			0
$217$	−14.0537			−0.954030
$218$	9.05846	+	15.6897i	0.613516	+	1.06264i
$219$		0			0
$220$	−4.84864			−0.326895
$221$	−2.40706			−0.161917
$222$		0			0
$223$	8.07400	−	13.9846i	0.540675	−	0.936477i	−0.458190	−	0.888854i	$-0.651502\pi$
$223$	8.07400	−	13.9846i	0.540675	−	0.936477i	0.998865	−	0.0476227i	$-0.0151645\pi$
$224$	−35.3859	−	61.2901i	−2.36432	−	4.09512i
$225$		0			0
$226$	−0.406136	+	0.703448i	−0.0270157	+	0.0467926i
$227$	−26.3186			−1.74683			−0.873414	−	0.486978i	$-0.838099\pi$
$227$	−26.3186			−1.74683			−0.873414	+	0.486978i	$0.838099\pi$
$228$		0			0
$229$	−13.3323			−0.881026			−0.440513	−	0.897746i	$-0.645203\pi$
$229$	−13.3323			−0.881026			−0.440513	+	0.897746i	$0.645203\pi$
$230$	0.575681	−	0.997109i	0.0379593	−	0.0657474i
$231$		0			0
$232$	48.2700	+	83.6060i	3.16908	+	5.48900i
$233$	12.6547	−	21.9186i	0.829038	−	1.43594i	−0.0697556	−	0.997564i	$-0.522222\pi$
$233$	12.6547	−	21.9186i	0.829038	−	1.43594i	0.898794	−	0.438372i	$-0.144445\pi$
$234$		0			0
$235$	−3.95396			−0.257928
$236$	−13.7901			−0.897658
$237$		0			0
$238$	14.6991	+	25.4596i	0.952801	+	1.65030i
$239$	23.5500			1.52332			0.761660	−	0.647977i	$-0.224385\pi$
$239$	23.5500			1.52332			0.761660	+	0.647977i	$0.224385\pi$
$240$		0			0
$241$	−4.19208	−	7.26089i	−0.270035	−	0.467715i	0.698835	−	0.715283i	$-0.253702\pi$
$241$	−4.19208	−	7.26089i	−0.270035	−	0.467715i	−0.968871	+	0.247568i	$0.920369\pi$
$242$	−14.1378	+	24.4873i	−0.908809	+	1.57410i
$243$		0			0
$244$	−17.7585	+	30.7586i	−1.13687	+	1.96912i
$245$	0.557368	−	0.965389i	0.0356089	−	0.0616764i
$246$		0			0
$247$	2.62739	+	0.979387i	0.167177	+	0.0623169i
$248$	−49.0745			−3.11623
$249$		0			0
$250$	−1.37901	+	2.38851i	−0.0872161	+	0.151063i
$251$	9.12391	+	15.8031i	0.575896	+	0.997481i	0.995944	+	0.0899792i	$0.0286800\pi$
$251$	9.12391	+	15.8031i	0.575896	+	0.997481i	−0.420048	+	0.907502i	$0.637987\pi$
$252$		0			0
$253$	0.180510	+	0.312652i	0.0113486	+	0.0196563i
$254$	−24.3669			−1.52891
$255$		0			0
$256$	−32.6176	−	56.4954i	−2.03860	−	3.53096i
$257$	7.04989	+	12.2108i	0.439760	+	0.761687i	0.997671	−	0.0682144i	$-0.0217302\pi$
$257$	7.04989	+	12.2108i	0.439760	+	0.761687i	−0.557911	+	0.829901i	$0.688397\pi$
$258$		0			0
$259$	−18.1306			−1.12658
$260$	1.80333	+	3.12345i	0.111838	+	0.193708i
$261$		0			0
$262$	−28.8389	−	49.9504i	−1.78167	−	3.08595i
$263$	−3.20536	+	5.55184i	−0.197651	+	0.342341i	−0.947766	−	0.318966i	$-0.896665\pi$
$263$	−3.20536	+	5.55184i	−0.197651	+	0.342341i	0.750116	+	0.661307i	$0.229998\pi$
$264$		0			0
$265$	−10.9875			−0.674956
$266$	−5.68558	−	33.7708i	−0.348605	−	2.07062i
$267$		0			0
$268$	7.09857	−	12.2951i	0.433614	−	0.751042i
$269$	8.99557	−	15.5808i	0.548469	−	0.949977i	−0.449910	−	0.893074i	$-0.648544\pi$
$269$	8.99557	−	15.5808i	0.548469	−	0.949977i	0.998380	−	0.0569032i	$-0.0181226\pi$
$270$		0			0
$271$	−5.94095	+	10.2900i	−0.360887	+	0.625075i	−0.988107	−	0.153767i	$-0.950859\pi$
$271$	−5.94095	+	10.2900i	−0.360887	+	0.625075i	0.627220	+	0.778842i	$0.284193\pi$
$272$	30.3488	+	52.5656i	1.84017	+	3.18726i
$273$		0			0
$274$	14.3824			0.868874
$275$	−0.432400	−	0.748939i	−0.0260747	−	0.0451627i
$276$		0			0
$277$	23.6240			1.41943			0.709715	−	0.704489i	$-0.248824\pi$
$277$	23.6240			1.41943			0.709715	+	0.704489i	$0.248824\pi$
$278$	29.5765			1.77388
$279$		0			0
$280$	14.1680	−	24.5397i	0.846700	−	1.46653i
$281$	6.90465	+	11.9592i	0.411897	+	0.713426i	0.995097	−	0.0989020i	$-0.0315330\pi$
$281$	6.90465	+	11.9592i	0.411897	+	0.713426i	−0.583200	+	0.812328i	$0.698200\pi$
$282$		0			0
$283$	5.87868	−	10.1822i	0.349451	−	0.605268i	−0.636701	−	0.771111i	$-0.719701\pi$
$283$	5.87868	−	10.1822i	0.349451	−	0.605268i	0.986152	+	0.165843i	$0.0530346\pi$
$284$	9.99179			0.592904
$285$		0			0
$286$	−1.53431			−0.0907257
$287$	5.71681	−	9.90181i	0.337453	−	0.584485i
$288$		0			0
$289$	1.49927	+	2.59681i	0.0881922	+	0.152753i
$290$	−13.3836	+	23.1810i	−0.785911	+	1.36124i
$291$		0			0
$292$	−39.9805			−2.33968
$293$	27.0576			1.58072			0.790362	−	0.612640i	$-0.209892\pi$
$293$	27.0576			1.58072			0.790362	+	0.612640i	$0.209892\pi$
$294$		0			0
$295$	−1.22980	−	2.13007i	−0.0716015	−	0.124017i
$296$	−63.3107			−3.67986
$297$		0			0
$298$	20.5632	+	35.6165i	1.19119	+	2.06321i
$299$	0.134272	−	0.232566i	0.00776516	−	0.0134497i
$300$		0			0
$301$	−2.93167	+	5.07780i	−0.168979	+	0.292679i
$302$	29.5921	−	51.2549i	1.70283	−	2.94939i
$303$		0			0
$304$	−11.7388	−	69.7256i	−0.673269	−	3.99904i
$305$	−6.33479			−0.362729
$306$		0			0
$307$	−4.41912	+	7.65414i	−0.252212	+	0.436845i	−0.964135	−	0.265414i	$-0.914492\pi$
$307$	−4.41912	+	7.65414i	−0.252212	+	0.436845i	0.711922	+	0.702258i	$0.247825\pi$
$308$	6.90601	+	11.9616i	0.393506	+	0.681573i
$309$		0			0
$310$	−6.80333	−	11.7837i	−0.386403	−	0.669270i
$311$	0.651493			0.0369428			0.0184714	−	0.999829i	$-0.494120\pi$
$311$	0.651493			0.0369428			0.0184714	+	0.999829i	$0.494120\pi$
$312$		0			0
$313$	1.48278	+	2.56825i	0.0838116	+	0.145166i	0.904884	−	0.425658i	$-0.139957\pi$
$313$	1.48278	+	2.56825i	0.0838116	+	0.145166i	−0.821073	+	0.570824i	$0.806624\pi$
$314$	−3.35261	−	5.80690i	−0.189199	−	0.327702i
$315$		0			0
$316$	10.2295			0.575453
$317$	−5.18993	−	8.98921i	−0.291495	−	0.504885i	0.682668	−	0.730728i	$-0.260819\pi$
$317$	−5.18993	−	8.98921i	−0.291495	−	0.504885i	−0.974164	+	0.225844i	$0.927486\pi$
$318$		0			0
$319$	−4.19654	−	7.26862i	−0.234961	−	0.406965i
$320$	18.0389	−	31.2443i	1.00841	−	1.74661i
$321$		0			0
$322$	−3.27981			−0.182777
$323$	2.70787	+	16.0840i	0.150670	+	0.894938i
$324$		0			0
$325$	−0.321640	+	0.557098i	−0.0178414	+	0.0309022i
$326$	24.5705	−	42.5574i	1.36083	−	2.35703i
$327$		0			0
$328$	19.9626	−	34.5763i	1.10225	−	1.90916i
$329$	5.63170	+	9.75438i	0.310485	+	0.537776i
$330$		0			0
$331$	15.0922			0.829543			0.414772	−	0.909926i	$-0.363861\pi$
$331$	15.0922			0.829543			0.414772	+	0.909926i	$0.363861\pi$
$332$	−20.8543	−	36.1207i	−1.14453	−	1.98238i
$333$		0			0
$334$	−1.11865			−0.0612096
$335$	2.53220			0.138349
$336$		0			0
$337$	−7.89872	+	13.6810i	−0.430271	+	0.745251i	−0.996896	−	0.0787246i	$-0.974915\pi$
$337$	−7.89872	+	13.6810i	−0.430271	+	0.745251i	0.566626	+	0.823975i	$0.308249\pi$
$338$	−17.3565	−	30.0623i	−0.944067	−	1.63517i
$339$		0			0
$340$	−10.4896	+	18.1686i	−0.568880	+	0.985330i
$341$	4.26649			0.231043
$342$		0			0
$343$	16.7650			0.905224
$344$	−10.2371	+	17.7313i	−0.551950	+	0.956005i
$345$		0			0
$346$	−24.8511	−	43.0434i	−1.33600	−	2.31403i
$347$	−10.6761	+	18.4915i	−0.573122	+	0.992676i	0.423121	+	0.906073i	$0.360935\pi$
$347$	−10.6761	+	18.4915i	−0.573122	+	0.992676i	−0.996243	+	0.0866031i	$0.972399\pi$
$348$		0			0
$349$	−32.3897			−1.73378			−0.866891	−	0.498497i	$-0.833885\pi$
$349$	−32.3897			−1.73378			−0.866891	+	0.498497i	$0.833885\pi$
$350$	7.85659			0.419952
$351$		0			0
$352$	10.7426	+	18.6067i	0.572582	+	0.991741i
$353$	−0.730583			−0.0388850			−0.0194425	−	0.999811i	$-0.506189\pi$
$353$	−0.730583			−0.0388850			−0.0194425	+	0.999811i	$0.506189\pi$
$354$		0			0
$355$	0.891065	+	1.54337i	0.0472928	+	0.0819136i
$356$	12.4632	−	21.5870i	0.660551	−	1.14411i
$357$		0			0
$358$	−27.7902	+	48.1340i	−1.46876	+	2.54396i
$359$	−13.4248	+	23.2524i	−0.708533	+	1.22722i	0.256868	+	0.966447i	$0.417309\pi$
$359$	−13.4248	+	23.2524i	−0.708533	+	1.22722i	−0.965401	+	0.260769i	$0.916024\pi$
$360$		0			0
$361$	3.58853	−	18.6580i	0.188870	−	0.982002i
$362$	47.1919			2.48035
$363$		0			0
$364$	5.13702	−	8.89759i	0.269253	−	0.466360i
$365$	−3.56545	−	6.17554i	−0.186624	−	0.323242i
$366$		0			0
$367$	11.4822	+	19.8877i	0.599364	+	1.03813i	0.992915	+	0.118826i	$0.0379130\pi$
$367$	11.4822	+	19.8877i	0.599364	+	1.03813i	−0.393551	+	0.919303i	$0.628754\pi$
$368$	−6.77173			−0.353001
$369$		0			0
$370$	−8.77693	−	15.2021i	−0.456291	−	0.790319i
$371$	15.6497	+	27.1060i	0.812491	+	1.40728i
$372$		0			0
$373$	29.5305			1.52903			0.764515	−	0.644606i	$-0.222979\pi$
$373$	29.5305			1.52903			0.764515	+	0.644606i	$0.222979\pi$
$374$	−4.46241	−	7.72912i	−0.230746	−	0.399663i
$375$		0			0
$376$	19.6654	+	34.0615i	1.01417	+	1.75659i
$377$	−3.12159	+	5.40676i	−0.160770	+	0.278462i
$378$		0			0
$379$	17.5117			0.899517			0.449759	−	0.893150i	$-0.351510\pi$
$379$	17.5117			0.899517			0.449759	+	0.893150i	$0.351510\pi$
$380$	18.8423	−	15.5636i	0.966587	−	0.798397i
$381$		0			0
$382$	−7.28226	+	12.6132i	−0.372593	+	0.645350i
$383$	4.05326	−	7.02045i	0.207112	−	0.358728i	−0.743692	−	0.668523i	$-0.766927\pi$
$383$	4.05326	−	7.02045i	0.207112	−	0.358728i	0.950804	+	0.309794i	$0.100260\pi$
$384$		0			0
$385$	−1.23175	+	2.13346i	−0.0627759	+	0.108731i
$386$	24.8272	+	43.0019i	1.26367	+	2.18874i
$387$		0			0
$388$	−60.8554			−3.08947
$389$	8.65392	+	14.9890i	0.438771	+	0.759974i	0.997595	−	0.0693125i	$-0.0220805\pi$
$389$	8.65392	+	14.9890i	0.438771	+	0.759974i	−0.558824	+	0.829286i	$0.688747\pi$
$390$		0			0
$391$	1.56208			0.0789976
$392$	−11.0885			−0.560054
$393$		0			0
$394$	−11.1394	+	19.2940i	−0.561196	+	0.972019i
$395$	0.912262	+	1.58008i	0.0459009	+	0.0795026i
$396$		0			0
$397$	5.69472	−	9.86354i	0.285810	−	0.495037i	−0.686996	−	0.726662i	$-0.741071\pi$
$397$	5.69472	−	9.86354i	0.285810	−	0.495037i	0.972805	+	0.231625i	$0.0744041\pi$
$398$	−3.87155			−0.194063
$399$		0			0
$400$	16.2213			0.811063
$401$	−4.46930	+	7.74106i	−0.223186	+	0.386570i	−0.955774	−	0.294103i	$-0.904979\pi$
$401$	−4.46930	+	7.74106i	−0.223186	+	0.386570i	0.732587	+	0.680673i	$0.238313\pi$
$402$		0			0
$403$	−1.58681	−	2.74844i	−0.0790447	−	0.136909i
$404$	−14.8464	+	25.7146i	−0.738634	+	1.27935i
$405$		0			0
$406$	76.2500			3.78422
$407$	5.50417			0.272832
$408$		0			0
$409$	3.27235	+	5.66788i	0.161808	+	0.280259i	0.935517	−	0.353282i	$-0.114934\pi$
$409$	3.27235	+	5.66788i	0.161808	+	0.280259i	−0.773709	+	0.633541i	$0.781601\pi$
$410$	11.0699			0.546703
$411$		0			0
$412$	1.07966	+	1.87002i	0.0531909	+	0.0921293i
$413$	−3.50324	+	6.06780i	−0.172383	+	0.298577i
$414$		0			0
$415$	3.71956	−	6.44247i	0.182586	−	0.316249i
$416$	7.99086	−	13.8406i	0.391784	−	0.678590i
$417$		0			0
$418$	1.72605	+	10.2523i	0.0844239	+	0.501455i
$419$	−21.8441			−1.06715			−0.533576	−	0.845752i	$-0.679152\pi$
$419$	−21.8441			−1.06715			−0.533576	+	0.845752i	$0.679152\pi$
$420$		0			0
$421$	14.6717	−	25.4121i	0.715054	−	1.23851i	−0.247885	−	0.968789i	$-0.579736\pi$
$421$	14.6717	−	25.4121i	0.715054	−	1.23851i	0.962939	−	0.269720i	$-0.0869311\pi$
$422$	26.0858	+	45.1819i	1.26984	+	2.19942i
$423$		0			0
$424$	54.6474	+	94.6521i	2.65391	+	4.59671i
$425$	−3.74185			−0.181507
$426$		0			0
$427$	9.02276	+	15.6279i	0.436642	+	0.756286i
$428$	−18.0348	−	31.2372i	−0.871746	−	1.50991i
$429$		0			0
$430$	−5.67681			−0.273760
$431$	−6.44336	−	11.1602i	−0.310366	−	0.537570i	0.668076	−	0.744093i	$-0.267118\pi$
$431$	−6.44336	−	11.1602i	−0.310366	−	0.537570i	−0.978442	+	0.206524i	$0.933785\pi$
$432$		0			0
$433$	6.92144	+	11.9883i	0.332623	+	0.576120i	0.983025	−	0.183470i	$-0.0587330\pi$
$433$	6.92144	+	11.9883i	0.332623	+	0.576120i	−0.650402	+	0.759590i	$0.725400\pi$
$434$	−19.3802	+	33.5675i	−0.930280	+	1.61129i
$435$		0			0
$436$	36.8291			1.76379
$437$	−1.70506	−	0.635578i	−0.0815641	−	0.0304038i
$438$		0			0
$439$	0.0354040	−	0.0613216i	0.00168974	−	0.00292672i	−0.865179	−	0.501463i	$-0.832795\pi$
$439$	0.0354040	−	0.0613216i	0.00168974	−	0.00292672i	0.866869	+	0.498536i	$0.166129\pi$
$440$	−4.30118	+	7.44986i	−0.205051	+	0.355158i
$441$		0			0
$442$	−3.31936	+	5.74930i	−0.157886	+	0.273466i
$443$	−1.89457	−	3.28149i	−0.0900137	−	0.155908i	0.817503	−	0.575924i	$-0.195358\pi$
$443$	−1.89457	−	3.28149i	−0.0900137	−	0.155908i	−0.907517	+	0.420016i	$0.862024\pi$
$444$		0			0
$445$	4.44588			0.210755
$446$	−22.2682	−	38.5697i	−1.05443	−	1.82633i
$447$		0			0
$448$	−102.773			−4.85555
$449$	26.5765			1.25422			0.627112	−	0.778929i	$-0.284237\pi$
$449$	26.5765			1.25422			0.627112	+	0.778929i	$0.284237\pi$
$450$		0			0
$451$	−1.73553	+	3.00603i	−0.0817230	+	0.141548i
$452$	0.825616	+	1.43001i	0.0388337	+	0.0672620i
$453$		0			0
$454$	−36.2936	+	62.8624i	−1.70334	+	2.95028i
$455$	1.83247			0.0859077
$456$		0			0
$457$	−33.1523			−1.55080			−0.775400	−	0.631471i	$-0.782452\pi$
$457$	−33.1523			−1.55080			−0.775400	+	0.631471i	$0.782452\pi$
$458$	−18.3854	+	31.8445i	−0.859094	+	1.48799i
$459$		0			0
$460$	−1.17028	−	2.02698i	−0.0545645	−	0.0945085i
$461$	−9.62679	+	16.6741i	−0.448364	+	0.776590i	−0.998280	−	0.0586304i	$-0.981327\pi$
$461$	−9.62679	+	16.6741i	−0.448364	+	0.776590i	0.549915	+	0.835220i	$0.314660\pi$
$462$		0			0
$463$	39.1713			1.82044			0.910222	−	0.414120i	$-0.135911\pi$
$463$	39.1713			1.82044			0.910222	+	0.414120i	$0.135911\pi$
$464$	157.431			7.30855
$465$		0			0
$466$	−34.9019	−	60.4519i	−1.61680	−	2.80038i
$467$	39.0650			1.80771			0.903856	−	0.427836i	$-0.140724\pi$
$467$	39.0650			1.80771			0.903856	+	0.427836i	$0.140724\pi$
$468$		0			0
$469$	−3.60665	−	6.24691i	−0.166540	−	0.288455i
$470$	−5.45254	+	9.44407i	−0.251507	+	0.435623i
$471$		0			0
$472$	−12.2330	+	21.1882i	−0.563071	+	0.975268i
$473$	0.890007	−	1.54154i	0.0409226	−	0.0708800i
$474$		0			0
$475$	4.08436	+	1.52249i	0.187404	+	0.0698565i
$476$	59.7623			2.73920
$477$		0			0
$478$	32.4756	−	56.2493i	1.48540	−	2.57279i
$479$	−12.3775	−	21.4385i	−0.565543	−	0.979550i	−0.996999	−	0.0774158i	$-0.975333\pi$
$479$	−12.3775	−	21.4385i	−0.565543	−	0.979550i	0.431455	−	0.902134i	$-0.358000\pi$
$480$		0			0
$481$	−2.04714	−	3.54574i	−0.0933413	−	0.161672i
$482$	−23.1236			−1.05325
$483$		0			0
$484$	28.7400	+	49.7792i	1.30637	+	2.26269i
$485$	−5.42707	−	9.39996i	−0.246431	−	0.426830i
$486$		0			0
$487$	21.8871			0.991797			0.495899	−	0.868380i	$-0.334839\pi$
$487$	21.8871			0.991797			0.495899	+	0.868380i	$0.334839\pi$
$488$	31.5067	+	54.5713i	1.42624	+	2.47033i
$489$		0			0
$490$	−1.53723	−	2.66256i	−0.0694449	−	0.120282i
$491$	4.69777	−	8.13677i	0.212007	−	0.367207i	−0.740335	−	0.672238i	$-0.765333\pi$
$491$	4.69777	−	8.13677i	0.212007	−	0.367207i	0.952343	+	0.305030i	$0.0986666\pi$
$492$		0			0
$493$	−36.3155			−1.63557
$494$	5.96247	−	4.92498i	0.268264	−	0.221585i
$495$		0			0
$496$	−40.0137	+	69.3058i	−1.79667	+	3.11192i
$497$	2.53832	−	4.39650i	0.113859	−	0.197210i
$498$		0			0
$499$	−12.4558	+	21.5740i	−0.557596	+	0.965785i	0.440100	+	0.897949i	$0.354943\pi$
$499$	−12.4558	+	21.5740i	−0.557596	+	0.965785i	−0.997696	+	0.0678367i	$0.978390\pi$
$500$	2.80333	+	4.85550i	0.125369	+	0.217145i
$501$		0			0
$502$	50.3278			2.24624
$503$	−15.6590	−	27.1222i	−0.698200	−	1.20932i	−0.969090	−	0.246707i	$-0.920651\pi$
$503$	−15.6590	−	27.1222i	−0.698200	−	1.20932i	0.270890	−	0.962610i	$-0.412682\pi$
$504$		0			0
$505$	−5.29598			−0.235668
$506$	0.995699			0.0442642
$507$		0			0
$508$	−24.7672	+	42.8980i	−1.09887	+	1.90329i
$509$	−4.83310	−	8.37117i	−0.214223	−	0.371045i	0.738809	−	0.673915i	$-0.235389\pi$
$509$	−4.83310	−	8.37117i	−0.214223	−	0.371045i	−0.953032	+	0.302870i	$0.902055\pi$
$510$		0			0
$511$	−10.1567	+	17.5919i	−0.449305	+	0.778219i
$512$	−80.2896			−3.54833
$513$		0			0
$514$	38.8874			1.71525
$515$	−0.192567	+	0.333536i	−0.00848552	+	0.0146973i
$516$		0			0
$517$	−1.70969	−	2.96127i	−0.0751922	−	0.130237i
$518$	−25.0023	+	43.3052i	−1.09854	+	1.90272i
$519$		0			0
$520$	6.39885			0.280608
$521$	0.982633			0.0430499			0.0215250	−	0.999768i	$-0.493148\pi$
$521$	0.982633			0.0430499			0.0215250	+	0.999768i	$0.493148\pi$
$522$		0			0
$523$	−19.8604	−	34.3993i	−0.868436	−	1.50418i	−0.863594	−	0.504187i	$-0.831792\pi$
$523$	−19.8604	−	34.3993i	−0.868436	−	1.50418i	−0.00484172	−	0.999988i	$-0.501541\pi$
$524$	−117.251			−5.12212
$525$		0			0
$526$	8.84043	+	15.3121i	0.385461	+	0.667638i
$527$	9.23020	−	15.9872i	0.402074	−	0.696413i
$528$		0			0
$529$	11.4129	−	19.7677i	0.496211	−	0.859463i
$530$	−15.1518	+	26.2437i	−0.658154	+	1.13996i
$531$		0			0
$532$	−65.2327	−	24.3161i	−2.82820	−	1.05424i
$533$	2.58195			0.111837
$534$		0			0
$535$	3.21668	−	5.57146i	0.139069	−	0.240875i
$536$	−12.5941	−	21.8137i	−0.543984	−	0.942208i
$537$		0			0
$538$	−24.8099	−	42.9720i	−1.06963	−	1.85266i
$539$	0.964024			0.0415234
$540$		0			0
$541$	−15.3887	−	26.6541i	−0.661614	−	1.14595i	−0.980191	−	0.198052i	$-0.936538\pi$
$541$	−15.3887	−	26.6541i	−0.661614	−	1.14595i	0.318577	−	0.947897i	$-0.396795\pi$
$542$	16.3852	+	28.3801i	0.703807	+	1.21903i
$543$		0			0
$544$	92.9629			3.98575
$545$	3.28441	+	5.68877i	0.140689	+	0.243680i
$546$		0			0
$547$	8.93287	+	15.4722i	0.381942	+	0.661543i	0.991340	−	0.131322i	$-0.0419221\pi$
$547$	8.93287	+	15.4722i	0.381942	+	0.661543i	−0.609398	+	0.792865i	$0.708589\pi$
$548$	14.6187	−	25.3203i	0.624480	−	1.08163i
$549$		0			0
$550$	−2.38513			−0.101702
$551$	39.6397	+	14.7761i	1.68871	+	0.629482i
$552$		0			0
$553$	2.59870	−	4.50109i	0.110508	−	0.191406i
$554$	32.5777	−	56.4263i	1.38409	−	2.39732i
$555$		0			0
$556$	30.0624	−	52.0696i	1.27493	−	2.20824i
$557$	−5.32878	−	9.22971i	−0.225787	−	0.391075i	0.730768	−	0.682626i	$-0.239162\pi$
$557$	−5.32878	−	9.22971i	−0.225787	−	0.391075i	−0.956555	+	0.291551i	$0.905829\pi$
$558$		0			0
$559$	−1.32406			−0.0560019
$560$	−23.1042	−	40.0177i	−0.976332	−	1.69106i
$561$		0			0
$562$	38.0863			1.60657
$563$	−7.75961			−0.327029			−0.163514	−	0.986541i	$-0.552283\pi$
$563$	−7.75961			−0.327029			−0.163514	+	0.986541i	$0.552283\pi$
$564$		0			0
$565$	−0.147256	+	0.255056i	−0.00619513	+	0.0107303i
$566$	−16.2135	−	28.0826i	−0.681504	−	1.18040i
$567$		0			0
$568$	8.86361	−	15.3522i	0.371909	−	0.644165i
$569$	−5.72754			−0.240111			−0.120056	−	0.992767i	$-0.538307\pi$
$569$	−5.72754			−0.240111			−0.120056	+	0.992767i	$0.538307\pi$
$570$		0			0
$571$	−20.8347			−0.871903			−0.435952	−	0.899970i	$-0.643588\pi$
$571$	−20.8347			−0.871903			−0.435952	+	0.899970i	$0.643588\pi$
$572$	−1.55952	+	2.70116i	−0.0652067	+	0.112941i
$573$		0			0
$574$	−15.7671	−	27.3093i	−0.658104	−	1.13987i
$575$	0.208730	−	0.361531i	0.00870465	−	0.0150769i
$576$		0			0
$577$	−5.11190			−0.212811			−0.106406	−	0.994323i	$-0.533934\pi$
$577$	−5.11190			−0.212811			−0.106406	+	0.994323i	$0.533934\pi$
$578$	8.27001			0.343987
$579$		0			0
$580$	27.2069	+	47.1238i	1.12971	+	1.95671i
$581$	−21.1914			−0.879167
$582$		0			0
$583$	−4.75099	−	8.22896i	−0.196766	−	0.340809i
$584$	−35.4663	+	61.4294i	−1.46760	+	2.54197i
$585$		0			0
$586$	37.3127	−	64.6275i	1.54137	−	2.66974i
$587$	−5.33462	+	9.23984i	−0.220184	+	0.381369i	−0.954864	−	0.297045i	$-0.903999\pi$
$587$	−5.33462	+	9.23984i	−0.220184	+	0.381369i	0.734680	+	0.678414i	$0.237332\pi$
$588$		0			0
$589$	−16.5800	+	13.6950i	−0.683165	+	0.564292i
$590$	−6.78360			−0.279276
$591$		0			0
$592$	−51.6215	+	89.4110i	−2.12163	+	3.67477i
$593$	−8.50133	−	14.7247i	−0.349108	−	0.604673i	0.636983	−	0.770878i	$-0.280182\pi$
$593$	−8.50133	−	14.7247i	−0.349108	−	0.604673i	−0.986091	+	0.166205i	$0.946849\pi$
$594$		0			0
$595$	5.32959	+	9.23112i	0.218492	+	0.378439i
$596$	83.6040			3.42455
$597$		0			0
$598$	−0.370325	−	0.641421i	−0.0151437	−	0.0262297i
$599$	14.3375	+	24.8334i	0.585816	+	1.01466i	0.994773	+	0.102110i	$0.0325592\pi$
$599$	14.3375	+	24.8334i	0.585816	+	1.01466i	−0.408957	+	0.912554i	$0.634107\pi$
$600$		0			0
$601$	27.4370			1.11918			0.559590	−	0.828770i	$-0.310959\pi$
$601$	27.4370			1.11918			0.559590	+	0.828770i	$0.310959\pi$
$602$	8.08559	+	14.0046i	0.329544	+	0.570787i
$603$		0			0
$604$	−60.1564	−	104.194i	−2.44773	−	4.23959i
$605$	−5.12606	+	8.87860i	−0.208404	+	0.360966i
$606$		0			0
$607$	−17.7547			−0.720639			−0.360320	−	0.932829i	$-0.617332\pi$
$607$	−17.7547			−0.720639			−0.360320	+	0.932829i	$0.617332\pi$
$608$	−101.472	−	37.8248i	−4.11524	−	1.53400i
$609$		0			0
$610$	−8.73573	+	15.1307i	−0.353699	+	0.612625i
$611$	−1.27175	+	2.20274i	−0.0514496	+	0.0891133i
$612$		0			0
$613$	−17.3196	+	29.9983i	−0.699530	+	1.21162i	0.269099	+	0.963112i	$0.413274\pi$
$613$	−17.3196	+	29.9983i	−0.699530	+	1.21162i	−0.968629	+	0.248509i	$0.920059\pi$
$614$	12.1880	+	21.1102i	0.491868	+	0.851940i
$615$		0			0
$616$	24.5050			0.987334
$617$	2.23284	+	3.86740i	0.0898909	+	0.155696i	0.907465	−	0.420128i	$-0.138015\pi$
$617$	2.23284	+	3.86740i	0.0898909	+	0.155696i	−0.817574	+	0.575824i	$0.804681\pi$
$618$		0			0
$619$	−17.9112			−0.719913			−0.359957	−	0.932969i	$-0.617209\pi$
$619$	−17.9112			−0.719913			−0.359957	+	0.932969i	$0.617209\pi$
$620$	−27.6604			−1.11087
$621$		0			0
$622$	0.898414	−	1.55610i	0.0360231	−	0.0623939i
$623$	−6.33234	−	10.9679i	−0.253700	−	0.439421i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	8.17906			0.326901
$627$		0			0
$628$	−13.6308			−0.543927
$629$	11.9078	−	20.6250i	0.474796	−	0.822371i
$630$		0			0
$631$	−2.48440	−	4.30311i	−0.0989026	−	0.171304i	0.812328	−	0.583201i	$-0.198200\pi$
$631$	−2.48440	−	4.30311i	−0.0989026	−	0.171304i	−0.911231	+	0.411896i	$0.864867\pi$
$632$	9.07446	−	15.7174i	0.360963	−	0.625205i
$633$		0			0
$634$	−28.6278			−1.13696
$635$	−8.83492			−0.350603
$636$		0			0
$637$	−0.358544	−	0.621016i	−0.0142060	−	0.0246056i
$638$	−23.1483			−0.916449
$639$		0			0
$640$	−24.9076	−	43.1412i	−0.984558	−	1.70530i
$641$	−18.9760	+	32.8675i	−0.749508	+	1.29819i	0.198550	+	0.980091i	$0.436377\pi$
$641$	−18.9760	+	32.8675i	−0.749508	+	1.29819i	−0.948059	+	0.318096i	$0.896957\pi$
$642$		0			0
$643$	−17.6251	+	30.5276i	−0.695067	+	1.20389i	0.275092	+	0.961418i	$0.411292\pi$
$643$	−17.6251	+	30.5276i	−0.695067	+	1.20389i	−0.970158	+	0.242473i	$0.922042\pi$
$644$	−3.33370	+	5.77413i	−0.131366	+	0.227533i
$645$		0			0
$646$	42.1510	+	15.7122i	1.65841	+	0.618188i
$647$	−35.5219			−1.39651			−0.698254	−	0.715850i	$-0.746040\pi$
$647$	−35.5219			−1.39651			−0.698254	+	0.715850i	$0.746040\pi$
$648$		0			0
$649$	1.06353	−	1.84209i	0.0417471	−	0.0723082i
$650$	0.887090	+	1.53648i	0.0347945	+	0.0602659i
$651$		0			0
$652$	−49.9483	−	86.5130i	−1.95613	−	3.38811i
$653$	−8.02411			−0.314008			−0.157004	−	0.987598i	$-0.550184\pi$
$653$	−8.02411			−0.314008			−0.157004	+	0.987598i	$0.550184\pi$
$654$		0			0
$655$	−10.4564	−	18.1110i	−0.408565	−	0.707655i
$656$	−32.5538	−	56.3848i	−1.27101	−	2.20146i
$657$		0			0
$658$	31.0646			1.21102
$659$	−23.6098	−	40.8933i	−0.919706	−	1.59298i	−0.799861	−	0.600185i	$-0.795094\pi$
$659$	−23.6098	−	40.8933i	−0.919706	−	1.59298i	−0.119844	−	0.992793i	$-0.538240\pi$
$660$		0			0
$661$	13.0580	+	22.6171i	0.507896	+	0.879702i	0.999958	+	0.00914181i	$0.00290997\pi$
$661$	13.0580	+	22.6171i	0.507896	+	0.879702i	−0.492062	+	0.870560i	$0.663757\pi$
$662$	20.8123	−	36.0479i	0.808892	−	1.40104i
$663$		0			0
$664$	−73.9986			−2.87170
$665$	−2.06147	−	12.2446i	−0.0799405	−	0.474825i
$666$		0			0
$667$	2.02577	−	3.50874i	0.0784383	−	0.135859i
$668$	−1.13702	+	1.96938i	−0.0439928	+	0.0761978i
$669$		0			0
$670$	3.49192	−	6.04818i	0.134905	−	0.233662i
$671$	−2.73917	−	4.74437i	−0.105744	−	0.183154i
$672$		0			0
$673$	15.3820			0.592931			0.296466	−	0.955044i	$-0.404192\pi$
$673$	15.3820			0.592931			0.296466	+	0.955044i	$0.404192\pi$
$674$	21.7848	+	37.7324i	0.839119	+	1.45340i
$675$		0			0
$676$	−70.5664			−2.71409
$677$	−24.4763			−0.940701			−0.470350	−	0.882480i	$-0.655872\pi$
$677$	−24.4763			−0.940701			−0.470350	+	0.882480i	$0.655872\pi$
$678$		0			0
$679$	−15.4598	+	26.7771i	−0.593291	+	1.02761i
$680$	18.6105	+	32.2343i	0.713680	+	1.23613i
$681$		0			0
$682$	5.88352	−	10.1906i	0.225292	−	0.390217i
$683$	17.8502			0.683018			0.341509	−	0.939879i	$-0.389062\pi$
$683$	17.8502			0.683018			0.341509	+	0.939879i	$0.389062\pi$
$684$		0			0
$685$	5.21477			0.199246
$686$	23.1191	−	40.0434i	0.882689	−	1.52886i
$687$		0			0
$688$	16.6941	+	28.9150i	0.636455	+	1.10237i
$689$	−3.53402	+	6.12110i	−0.134635	+	0.233195i
$690$		0			0
$691$	−9.27242			−0.352739			−0.176370	−	0.984324i	$-0.556435\pi$
$691$	−9.27242			−0.352739			−0.176370	+	0.984324i	$0.556435\pi$
$692$	−101.038			−3.84087
$693$		0			0
$694$	29.4448	+	50.9999i	1.11771	+	1.93593i
$695$	10.7238			0.406778
$696$		0			0
$697$	7.50937	+	13.0066i	0.284438	+	0.492660i
$698$	−44.6657	+	77.3633i	−1.69062	+	2.92824i
$699$		0			0
$700$	7.98566	−	13.8316i	0.301830	−	0.522784i
$701$	−3.84453	+	6.65892i	−0.145206	+	0.251504i	−0.929450	−	0.368949i	$-0.879718\pi$
$701$	−3.84453	+	6.65892i	−0.145206	+	0.251504i	0.784244	+	0.620453i	$0.213051\pi$
$702$		0			0
$703$	−21.3897	+	17.6678i	−0.806728	+	0.666354i
$704$	31.2001			1.17590
$705$		0			0
$706$	−1.00748	+	1.74501i	−0.0379170	+	0.0656742i
$707$	7.54316	+	13.0651i	0.283690	+	0.491365i
$708$		0			0
$709$	−12.2187	−	21.1635i	−0.458885	−	0.794812i	0.540018	−	0.841654i	$-0.318418\pi$
$709$	−12.2187	−	21.1635i	−0.458885	−	0.794812i	−0.998902	+	0.0468421i	$0.985084\pi$
$710$	4.91514			0.184462
$711$		0			0
$712$	−22.1120	−	38.2992i	−0.828683	−	1.43532i
$713$	1.02977	+	1.78361i	0.0385652	+	0.0667968i
$714$		0			0
$715$	−0.556310			−0.0208048
$716$	56.4935	+	97.8496i	2.11126	+	3.65681i
$717$		0			0
$718$	37.0258	+	64.1305i	1.38179	+	2.39333i
$719$	−11.0563	+	19.1501i	−0.412331	+	0.714178i	−0.995144	−	0.0984282i	$-0.968619\pi$
$719$	−11.0563	+	19.1501i	−0.412331	+	0.714178i	0.582813	+	0.812606i	$0.301952\pi$
$720$		0			0
$721$	1.09711			0.0408584
$722$	−39.6163	−	34.3008i	−1.47437	−	1.27655i
$723$		0			0
$724$	47.9672	−	83.0817i	1.78269	−	3.08771i
$725$	−4.85261	+	8.40497i	−0.180222	+	0.312153i
$726$		0			0
$727$	14.5247	−	25.1575i	0.538692	−	0.933042i	−0.460283	−	0.887772i	$-0.652252\pi$
$727$	14.5247	−	25.1575i	0.538692	−	0.933042i	0.998975	−	0.0452694i	$-0.0144146\pi$
$728$	−9.11400	−	15.7859i	−0.337787	−	0.585065i
$729$		0			0
$730$	−19.6671			−0.727913
$731$	−3.85092	−	6.66999i	−0.142431	−	0.246698i
$732$		0			0
$733$	14.5428			0.537151			0.268576	−	0.963259i	$-0.413447\pi$
$733$	14.5428			0.537151			0.268576	+	0.963259i	$0.413447\pi$
$734$	63.3360			2.33777
$735$		0			0
$736$	−5.18571	+	8.98191i	−0.191148	+	0.331078i
$737$	1.09492	+	1.89646i	0.0403320	+	0.0698570i
$738$		0			0
$739$	2.37798	−	4.11878i	0.0874754	−	0.151512i	−0.818968	−	0.573839i	$-0.805453\pi$
$739$	2.37798	−	4.11878i	0.0874754	−	0.151512i	0.906443	+	0.422327i	$0.138787\pi$
$740$	−35.6845			−1.31179
$741$		0			0
$742$	86.3242			3.16906
$743$	2.93853	−	5.08968i	0.107804	−	0.186722i	−0.807076	−	0.590447i	$-0.798951\pi$
$743$	2.93853	−	5.08968i	0.107804	−	0.186722i	0.914880	+	0.403725i	$0.132285\pi$
$744$		0			0
$745$	7.45578	+	12.9138i	0.273159	+	0.473125i
$746$	40.7228	−	70.5339i	1.49097	−	2.58243i
$747$		0			0
$748$	−18.1429			−0.663370
$749$	−18.3263			−0.669629
$750$		0			0
$751$	−0.810481	−	1.40379i	−0.0295749	−	0.0512252i	0.850859	−	0.525394i	$-0.176082\pi$
$751$	−0.810481	−	1.40379i	−0.0295749	−	0.0512252i	−0.880434	+	0.474169i	$0.842749\pi$
$752$	64.1382			2.33888
$753$		0			0
$754$	8.60941	+	14.9119i	0.313536	+	0.543060i
$755$	10.7295	−	18.5840i	0.390485	−	0.676341i
$756$		0			0
$757$	14.0567	−	24.3470i	0.510901	−	0.884907i	−0.489019	−	0.872273i	$-0.662645\pi$
$757$	14.0567	−	24.3470i	0.510901	−	0.884907i	0.999920	−	0.0126336i	$-0.00402151\pi$
$758$	24.1488	−	41.8270i	0.877125	−	1.51922i
$759$		0			0
$760$	−7.19850	−	42.7572i	−0.261117	−	1.55096i
$761$	−20.1663			−0.731027			−0.365514	−	0.930806i	$-0.619107\pi$
$761$	−20.1663			−0.731027			−0.365514	+	0.930806i	$0.619107\pi$
$762$		0			0
$763$	9.35610	−	16.2052i	0.338713	−	0.586669i
$764$	14.8038	+	25.6409i	0.535583	+	0.927656i
$765$		0			0
$766$	−11.1790	−	19.3625i	−0.403912	−	0.699597i
$767$	−1.58221			−0.0571303
$768$		0			0
$769$	−22.6524	−	39.2350i	−0.816865	−	1.41485i	−0.907981	−	0.419011i	$-0.862377\pi$
$769$	−22.6524	−	39.2350i	−0.816865	−	1.41485i	0.0911160	−	0.995840i	$-0.470957\pi$
$770$	3.39719	+	5.88411i	0.122426	+	0.212049i
$771$		0			0
$772$	100.940			3.63292
$773$	−10.0881	−	17.4731i	−0.362843	−	0.628462i	0.625585	−	0.780156i	$-0.284861\pi$
$773$	−10.0881	−	17.4731i	−0.362843	−	0.628462i	−0.988428	+	0.151694i	$0.951527\pi$
$774$		0			0
$775$	−2.46675	−	4.27253i	−0.0886081	−	0.153474i
$776$	−53.9842	+	93.5034i	−1.93792	+	3.35658i
$777$		0			0
$778$	47.7353			1.71139
$779$	−2.90461	−	17.2526i	−0.104068	−	0.618138i
$780$		0			0
$781$	−0.770594	+	1.33471i	−0.0275740	+	0.0477596i
$782$	2.15411	−	3.73104i	0.0770310	−	0.133422i
$783$		0

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37901 - 2.38851i) q^{2} +(-2.80333 - 4.85550i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.84864 q^{7} -9.94721 q^{8} +O(q^{10})\)	\(q+(1.37901 - 2.38851i) q^{2} +(-2.80333 - 4.85550i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.84864 q^{7} -9.94721 q^{8} +(-1.37901 - 2.38851i) q^{10} +0.864801 q^{11} +(-0.321640 - 0.557098i) q^{13} +(-3.92829 + 6.80401i) q^{14} +(-8.11063 + 14.0480i) q^{16} +(1.87093 - 3.24054i) q^{17} +(-3.36069 + 2.77592i) q^{19} -5.60665 q^{20} +(1.19257 - 2.06559i) q^{22} +(0.208730 + 0.361531i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.77418 q^{26} +(7.98566 + 13.8316i) q^{28} +(-4.85261 - 8.40497i) q^{29} +4.93349 q^{31} +(12.4220 + 21.5156i) q^{32} +(-5.16005 - 8.93746i) q^{34} +(-1.42432 + 2.46699i) q^{35} +6.36467 q^{37} +(1.99589 + 11.8551i) q^{38} +(-4.97360 + 8.61454i) q^{40} +(-2.00686 + 3.47598i) q^{41} +(1.02915 - 1.78254i) q^{43} +(-2.42432 - 4.19904i) q^{44} +1.15136 q^{46} +(-1.97698 - 3.42423i) q^{47} +1.11474 q^{49} -2.75802 q^{50} +(-1.80333 + 3.12345i) q^{52} +(-5.49374 - 9.51544i) q^{53} +(0.432400 - 0.748939i) q^{55} +28.3360 q^{56} -26.7672 q^{58} +(1.22980 - 2.13007i) q^{59} +(-3.16740 - 5.48609i) q^{61} +(6.80333 - 11.7837i) q^{62} +36.0778 q^{64} -0.643281 q^{65} +(1.26610 + 2.19295i) q^{67} -20.9793 q^{68} +(3.92829 + 6.80401i) q^{70} +(-0.891065 + 1.54337i) q^{71} +(3.56545 - 6.17554i) q^{73} +(8.77693 - 15.2021i) q^{74} +(22.8996 + 8.53606i) q^{76} -2.46350 q^{77} +(-0.912262 + 1.58008i) q^{79} +(8.11063 + 14.0480i) q^{80} +(5.53495 + 9.58681i) q^{82} +7.43913 q^{83} +(-1.87093 - 3.24054i) q^{85} +(-2.83841 - 4.91626i) q^{86} -8.60235 q^{88} +(2.22294 + 3.85024i) q^{89} +(0.916237 + 1.58697i) q^{91} +(1.17028 - 2.02698i) q^{92} -10.9051 q^{94} +(0.723670 + 4.29841i) q^{95} +(5.42707 - 9.39996i) q^{97} +(1.53723 - 2.66256i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8	\( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8} - q^{10} + 4 q^{11} - 7 q^{13} - q^{14} - 7 q^{16} - q^{17} + 5 q^{19} - 10 q^{20} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 6 q^{26} + 19 q^{28} - q^{29} + 30 q^{32} - 15 q^{34} - 4 q^{35} - 4 q^{37} - 13 q^{38} - 12 q^{40} - 8 q^{41} - q^{43} - 12 q^{44} + 24 q^{46} - 12 q^{47} - 20 q^{49} - 2 q^{50} + 3 q^{52} - 5 q^{53} + 2 q^{55} + 82 q^{56} - 54 q^{58} - 5 q^{59} + 37 q^{62} + 112 q^{64} - 14 q^{65} - 4 q^{67} - 32 q^{68} + q^{70} + 20 q^{71} + 20 q^{73} + 25 q^{74} + 63 q^{76} - 28 q^{77} - 17 q^{79} + 7 q^{80} - 21 q^{82} - 2 q^{83} + q^{85} + 8 q^{86} - 14 q^{88} + 11 q^{89} - 6 q^{91} - q^{92} - 62 q^{94} + 4 q^{95} - q^{97} + 9 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8 - q^10 + 4 * q^11 - 7 * q^13 - q^14 - 7 * q^16 - q^17 + 5 * q^19 - 10 * q^20 - 2 * q^22 + 2 * q^23 - 4 * q^25 - 6 * q^26 + 19 * q^28 - q^29 + 30 * q^32 - 15 * q^34 - 4 * q^35 - 4 * q^37 - 13 * q^38 - 12 * q^40 - 8 * q^41 - q^43 - 12 * q^44 + 24 * q^46 - 12 * q^47 - 20 * q^49 - 2 * q^50 + 3 * q^52 - 5 * q^53 + 2 * q^55 + 82 * q^56 - 54 * q^58 - 5 * q^59 + 37 * q^62 + 112 * q^64 - 14 * q^65 - 4 * q^67 - 32 * q^68 + q^70 + 20 * q^71 + 20 * q^73 + 25 * q^74 + 63 * q^76 - 28 * q^77 - 17 * q^79 + 7 * q^80 - 21 * q^82 - 2 * q^83 + q^85 + 8 * q^86 - 14 * q^88 + 11 * q^89 - 6 * q^91 - q^92 - 62 * q^94 + 4 * q^95 - q^97 + 9 * q^98

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