LMFDB - Embedded newform 810.3.b.b.809.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(809,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.809");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.b (of order $2$, degree $1$, 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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 230x^{12} - 96x^{10} + 25551x^{8} - 7776x^{6} - 1509030x^{4} + 1062882x^{2} + 43046721 $ x^16 + 2x^14 - 230x^12 - 96x^10 + 25551x^8 - 7776x^6 - 1509030x^4 + 1062882*x^2 + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			809.13
Root			$-0.633522 - 2.93235i$ of defining polynomial
Character	$\chi$	$=$	810.809
Dual form			810.3.b.b.809.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +2.00000 q^{4} +(0.882096 - 4.92158i) q^{5} +8.76643i q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+1.41421 q^{2} +2.00000 q^{4} +(0.882096 - 4.92158i) q^{5} +8.76643i q^{7} +2.82843 q^{8} +(1.24747 - 6.96016i) q^{10} -13.4435i q^{11} +17.2428i q^{13} +12.3976i q^{14} +4.00000 q^{16} +0.183062 q^{17} +34.7310 q^{19} +(1.76419 - 9.84315i) q^{20} -19.0120i q^{22} +34.4211 q^{23} +(-23.4438 - 8.68261i) q^{25} +24.3850i q^{26} +17.5329i q^{28} -10.3748i q^{29} +20.6516 q^{31} +5.65685 q^{32} +0.258889 q^{34} +(43.1447 + 7.73284i) q^{35} -8.75453i q^{37} +49.1171 q^{38} +(2.49495 - 13.9203i) q^{40} -1.57758i q^{41} -40.5709i q^{43} -26.8871i q^{44} +48.6787 q^{46} -30.9907 q^{47} -27.8503 q^{49} +(-33.1546 - 12.2791i) q^{50} +34.4856i q^{52} +21.1989 q^{53} +(-66.1634 - 11.8585i) q^{55} +24.7952i q^{56} -14.6722i q^{58} +30.2162i q^{59} +72.6660 q^{61} +29.2057 q^{62} +8.00000 q^{64} +(84.8617 + 15.2098i) q^{65} +6.55995i q^{67} +0.366125 q^{68} +(61.0158 + 10.9359i) q^{70} +1.02858i q^{71} -16.8284i q^{73} -12.3808i q^{74} +69.4620 q^{76} +117.852 q^{77} -83.1641 q^{79} +(3.52839 - 19.6863i) q^{80} -2.23103i q^{82} -2.31619 q^{83} +(0.161479 - 0.900955i) q^{85} -57.3759i q^{86} -38.0241i q^{88} -137.546i q^{89} -151.158 q^{91} +68.8421 q^{92} -43.8275 q^{94} +(30.6361 - 170.931i) q^{95} +54.0828i q^{97} -39.3863 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} - 16 q^{10} + 64 q^{16} + 144 q^{19} - 12 q^{25} - 56 q^{31} + 272 q^{34} - 32 q^{40} - 56 q^{46} - 24 q^{49} + 20 q^{55} - 136 q^{61} + 128 q^{64} + 224 q^{70} + 288 q^{76} - 840 q^{79} + 272 q^{85} - 168 q^{91} + 328 q^{94}+O(q^{100}) $ 16 * q + 32 * q^4 - 16 * q^10 + 64 * q^16 + 144 * q^19 - 12 * q^25 - 56 * q^31 + 272 * q^34 - 32 * q^40 - 56 * q^46 - 24 * q^49 + 20 * q^55 - 136 * q^61 + 128 * q^64 + 224 * q^70 + 288 * q^76 - 840 * q^79 + 272 * q^85 - 168 * q^91 + 328 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$		0			0
$3$		0			0
$4$	2.00000			0.500000
$5$	0.882096	−	4.92158i	0.176419	−	0.984315i
$5$	0.882096	−	4.92158i	0.176419	−	0.984315i
$6$		0			0
$7$			8.76643i			1.25235i	0.779684	+	0.626174i	$0.215380\pi$
$7$			8.76643i			1.25235i	−0.779684	+	0.626174i	$0.784620\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	1.24747	−	6.96016i	0.124747	−	0.696016i
$11$		−	13.4435i		−	1.22214i	−0.791577	−	0.611070i	$-0.790739\pi$
$11$		−	13.4435i		−	1.22214i	0.791577	−	0.611070i	$-0.209261\pi$
$12$		0			0
$13$			17.2428i			1.32637i	0.748456	+	0.663185i	$0.230796\pi$
$13$			17.2428i			1.32637i	−0.748456	+	0.663185i	$0.769204\pi$
$14$			12.3976i			0.885543i
$15$		0			0
$16$	4.00000			0.250000
$17$	0.183062			0.0107684			0.00538419	−	0.999986i	$-0.498286\pi$
$17$	0.183062			0.0107684			0.00538419	+	0.999986i	$0.498286\pi$
$18$		0			0
$19$	34.7310			1.82795			0.913974	−	0.405773i	$-0.132998\pi$
$19$	34.7310			1.82795			0.913974	+	0.405773i	$0.132998\pi$
$20$	1.76419	−	9.84315i	0.0882096	−	0.492158i
$21$		0			0
$22$		−	19.0120i		−	0.864183i
$23$	34.4211			1.49657			0.748284	−	0.663378i	$-0.230878\pi$
$23$	34.4211			1.49657			0.748284	+	0.663378i	$0.230878\pi$
$24$		0			0
$25$	−23.4438	−	8.68261i	−0.937752	−	0.347304i
$26$			24.3850i			0.937885i
$27$		0			0
$28$			17.5329i			0.626174i
$29$		−	10.3748i		−	0.357752i	−0.983872	−	0.178876i	$-0.942754\pi$
$29$		−	10.3748i		−	0.357752i	0.983872	−	0.178876i	$-0.0572460\pi$
$30$		0			0
$31$	20.6516			0.666180			0.333090	−	0.942895i	$-0.391909\pi$
$31$	20.6516			0.666180			0.333090	+	0.942895i	$0.391909\pi$
$32$	5.65685			0.176777
$33$		0			0
$34$	0.258889			0.00761439
$35$	43.1447	+	7.73284i	1.23270	+	0.220938i
$36$		0			0
$37$		−	8.75453i		−	0.236609i	−0.992977	−	0.118304i	$-0.962254\pi$
$37$		−	8.75453i		−	0.236609i	0.992977	−	0.118304i	$-0.0377459\pi$
$38$	49.1171			1.29255
$39$		0			0
$40$	2.49495	−	13.9203i	0.0623736	−	0.348008i
$41$		−	1.57758i		−	0.0384774i	−0.999815	−	0.0192387i	$-0.993876\pi$
$41$		−	1.57758i		−	0.0384774i	0.999815	−	0.0192387i	$-0.00612425\pi$
$42$		0			0
$43$		−	40.5709i		−	0.943509i	−0.881730	−	0.471755i	$-0.843621\pi$
$43$		−	40.5709i		−	0.943509i	0.881730	−	0.471755i	$-0.156379\pi$
$44$		−	26.8871i		−	0.611070i
$45$		0			0
$46$	48.6787			1.05823
$47$	−30.9907			−0.659377			−0.329689	−	0.944090i	$-0.606944\pi$
$47$	−30.9907			−0.659377			−0.329689	+	0.944090i	$0.606944\pi$
$48$		0			0
$49$	−27.8503			−0.568374
$50$	−33.1546	−	12.2791i	−0.663091	−	0.245581i
$51$		0			0
$52$			34.4856i			0.663185i
$53$	21.1989			0.399979			0.199990	−	0.979798i	$-0.435909\pi$
$53$	21.1989			0.399979			0.199990	+	0.979798i	$0.435909\pi$
$54$		0			0
$55$	−66.1634	−	11.8585i	−1.20297	−	0.215609i
$56$			24.7952i			0.442772i
$57$		0			0
$58$		−	14.6722i		−	0.252969i
$59$			30.2162i			0.512139i	0.966658	+	0.256069i	$0.0824276\pi$
$59$			30.2162i			0.512139i	−0.966658	+	0.256069i	$0.917572\pi$
$60$		0			0
$61$	72.6660			1.19125			0.595623	−	0.803264i	$-0.296905\pi$
$61$	72.6660			1.19125			0.595623	+	0.803264i	$0.296905\pi$
$62$	29.2057			0.471060
$63$		0			0
$64$	8.00000			0.125000
$65$	84.8617	+	15.2098i	1.30557	+	0.233997i
$66$		0			0
$67$			6.55995i			0.0979096i	0.998801	+	0.0489548i	$0.0155890\pi$
$67$			6.55995i			0.0979096i	−0.998801	+	0.0489548i	$0.984411\pi$
$68$	0.366125			0.00538419
$69$		0			0
$70$	61.0158	+	10.9359i	0.871654	+	0.156227i
$71$			1.02858i			0.0144870i	0.999974	+	0.00724351i	$0.00230570\pi$
$71$			1.02858i			0.0144870i	−0.999974	+	0.00724351i	$0.997694\pi$
$72$		0			0
$73$		−	16.8284i		−	0.230526i	−0.993335	−	0.115263i	$-0.963229\pi$
$73$		−	16.8284i		−	0.230526i	0.993335	−	0.115263i	$-0.0367711\pi$
$74$		−	12.3808i		−	0.167308i
$75$		0			0
$76$	69.4620			0.913974
$77$	117.852			1.53054
$78$		0			0
$79$	−83.1641			−1.05271			−0.526355	−	0.850265i	$-0.676442\pi$
$79$	−83.1641			−1.05271			−0.526355	+	0.850265i	$0.676442\pi$
$80$	3.52839	−	19.6863i	0.0441048	−	0.246079i
$81$		0			0
$82$		−	2.23103i		−	0.0272077i
$83$	−2.31619			−0.0279059			−0.0139529	−	0.999903i	$-0.504442\pi$
$83$	−2.31619			−0.0279059			−0.0139529	+	0.999903i	$0.504442\pi$
$84$		0			0
$85$	0.161479	−	0.900955i	0.00189975	−	0.0105995i
$86$		−	57.3759i		−	0.667162i
$87$		0			0
$88$		−	38.0241i		−	0.432092i
$89$		−	137.546i		−	1.54546i	−0.634733	−	0.772732i	$-0.718890\pi$
$89$		−	137.546i		−	1.54546i	0.634733	−	0.772732i	$-0.281110\pi$
$90$		0			0
$91$	−151.158			−1.66107
$92$	68.8421			0.748284
$93$		0			0
$94$	−43.8275			−0.466250
$95$	30.6361	−	170.931i	0.322485	−	1.79928i
$96$		0			0
$97$			54.0828i			0.557555i	0.960356	+	0.278777i	$0.0899291\pi$
$97$			54.0828i			0.557555i	−0.960356	+	0.278777i	$0.910071\pi$
$98$	−39.3863			−0.401901
$99$		0			0
$100$	−46.8876	−	17.3652i	−0.468876	−	0.173652i
$101$			122.064i			1.20855i	0.796774	+	0.604277i	$0.206538\pi$
$101$			122.064i			1.20855i	−0.796774	+	0.604277i	$0.793462\pi$
$102$		0			0
$103$			55.2183i			0.536100i	0.963405	+	0.268050i	$0.0863792\pi$
$103$			55.2183i			0.536100i	−0.963405	+	0.268050i	$0.913621\pi$
$104$			48.7700i			0.468942i
$105$		0			0
$106$	29.9798			0.282828
$107$	23.9215			0.223565			0.111783	−	0.993733i	$-0.464344\pi$
$107$	23.9215			0.223565			0.111783	+	0.993733i	$0.464344\pi$
$108$		0			0
$109$	32.4094			0.297334			0.148667	−	0.988887i	$-0.452502\pi$
$109$	32.4094			0.297334			0.148667	+	0.988887i	$0.452502\pi$
$110$	−93.5692	−	16.7704i	−0.850629	−	0.152459i
$111$		0			0
$112$			35.0657i			0.313087i
$113$	−14.2209			−0.125848			−0.0629241	−	0.998018i	$-0.520043\pi$
$113$	−14.2209			−0.125848			−0.0629241	+	0.998018i	$0.520043\pi$
$114$		0			0
$115$	30.3627	−	169.406i	0.264023	−	1.47309i
$116$		−	20.7496i		−	0.178876i
$117$		0			0
$118$			42.7321i			0.362137i
$119$			1.60480i			0.0134857i
$120$		0			0
$121$	−59.7288			−0.493626
$122$	102.765			0.842338
$123$		0			0
$124$	41.3031			0.333090
$125$	−63.4118	+	107.722i	−0.507294	+	0.861773i
$126$		0			0
$127$			185.926i			1.46398i	0.681315	+	0.731991i	$0.261409\pi$
$127$			185.926i			1.46398i	−0.681315	+	0.731991i	$0.738591\pi$
$128$	11.3137			0.0883883
$129$		0			0
$130$	120.013	+	21.5099i	0.923174	+	0.165461i
$131$			120.385i			0.918969i	0.888186	+	0.459485i	$0.151966\pi$
$131$			120.385i			0.918969i	−0.888186	+	0.459485i	$0.848034\pi$
$132$		0			0
$133$			304.467i			2.28923i
$134$			9.27716i			0.0692326i
$135$		0			0
$136$	0.517778			0.00380719
$137$	204.223			1.49068			0.745340	−	0.666685i	$-0.232287\pi$
$137$	204.223			1.49068			0.745340	+	0.666685i	$0.232287\pi$
$138$		0			0
$139$	−241.635			−1.73838			−0.869191	−	0.494476i	$-0.835360\pi$
$139$	−241.635			−1.73838			−0.869191	+	0.494476i	$0.835360\pi$
$140$	86.2893	+	15.4657i	0.616352	+	0.110469i
$141$		0			0
$142$			1.45463i			0.0102439i
$143$	231.804			1.62101
$144$		0			0
$145$	−51.0603	−	9.15157i	−0.352140	−	0.0631143i
$146$		−	23.7989i		−	0.163006i
$147$		0			0
$148$		−	17.5091i		−	0.118304i
$149$			126.267i			0.847427i	0.905796	+	0.423713i	$0.139274\pi$
$149$			126.267i			0.847427i	−0.905796	+	0.423713i	$0.860726\pi$
$150$		0			0
$151$	−267.744			−1.77314			−0.886569	−	0.462596i	$-0.846918\pi$
$151$	−267.744			−1.77314			−0.886569	+	0.462596i	$0.846918\pi$
$152$	98.2341			0.646277
$153$		0			0
$154$	166.668			1.08226
$155$	18.2167	−	101.638i	0.117527	−	0.655731i
$156$		0			0
$157$			54.5272i			0.347307i	0.984807	+	0.173654i	$0.0555573\pi$
$157$			54.5272i			0.347307i	−0.984807	+	0.173654i	$0.944443\pi$
$158$	−117.612			−0.744379
$159$		0			0
$160$	4.98989	−	27.8406i	0.0311868	−	0.174004i
$161$			301.750i			1.87422i
$162$		0			0
$163$		−	112.166i		−	0.688134i	−0.938945	−	0.344067i	$-0.888195\pi$
$163$		−	112.166i		−	0.688134i	0.938945	−	0.344067i	$-0.111805\pi$
$164$		−	3.15515i		−	0.0192387i
$165$		0			0
$166$	−3.27559			−0.0197324
$167$	−317.602			−1.90181			−0.950906	−	0.309481i	$-0.899845\pi$
$167$	−317.602			−1.90181			−0.950906	+	0.309481i	$0.899845\pi$
$168$		0			0
$169$	−128.314			−0.759255
$170$	0.228365	−	1.27414i	0.00134332	−	0.00749496i
$171$		0			0
$172$		−	81.1418i		−	0.471755i
$173$	−89.4131			−0.516839			−0.258419	−	0.966033i	$-0.583202\pi$
$173$	−89.4131			−0.516839			−0.258419	+	0.966033i	$0.583202\pi$
$174$		0			0
$175$	76.1155	−	205.519i	0.434946	−	1.17439i
$176$		−	53.7742i		−	0.305535i
$177$		0			0
$178$		−	194.520i		−	1.09281i
$179$		−	258.659i		−	1.44502i	−0.691360	−	0.722510i	$-0.742988\pi$
$179$		−	258.659i		−	1.44502i	0.691360	−	0.722510i	$-0.257012\pi$
$180$		0			0
$181$	−35.1427			−0.194159			−0.0970793	−	0.995277i	$-0.530950\pi$
$181$	−35.1427			−0.194159			−0.0970793	+	0.995277i	$0.530950\pi$
$182$	−213.769			−1.17456
$183$		0			0
$184$	97.3575			0.529117
$185$	−43.0861	−	7.72234i	−0.232898	−	0.0417424i
$186$		0			0
$187$		−	2.46101i		−	0.0131605i
$188$	−61.9814			−0.329689
$189$		0			0
$190$	43.3260	−	241.733i	0.228031	−	1.27228i
$191$		−	43.2055i		−	0.226207i	−0.993583	−	0.113103i	$-0.963921\pi$
$191$		−	43.2055i		−	0.226207i	0.993583	−	0.113103i	$-0.0360791\pi$
$192$		0			0
$193$		−	268.087i		−	1.38905i	−0.719468	−	0.694526i	$-0.755614\pi$
$193$		−	268.087i		−	1.38905i	0.719468	−	0.694526i	$-0.244386\pi$
$194$			76.4846i			0.394251i
$195$		0			0
$196$	−55.7007			−0.284187
$197$	−244.575			−1.24150			−0.620748	−	0.784010i	$-0.713171\pi$
$197$	−244.575			−1.24150			−0.620748	+	0.784010i	$0.713171\pi$
$198$		0			0
$199$	207.471			1.04257			0.521283	−	0.853384i	$-0.325454\pi$
$199$	207.471			1.04257			0.521283	+	0.853384i	$0.325454\pi$
$200$	−66.3091	−	24.5581i	−0.331546	−	0.122791i
$201$		0			0
$202$			172.624i			0.854577i
$203$	90.9499			0.448029
$204$		0			0
$205$	−7.76416	−	1.39157i	−0.0378739	−	0.00678816i
$206$			78.0905i			0.379080i
$207$		0			0
$208$			68.9712i			0.331592i
$209$		−	466.908i		−	2.23401i
$210$		0			0
$211$	−187.198			−0.887196			−0.443598	−	0.896226i	$-0.646298\pi$
$211$	−187.198			−0.887196			−0.443598	+	0.896226i	$0.646298\pi$
$212$	42.3978			0.199990
$213$		0			0
$214$	33.8301			0.158085
$215$	−199.673	−	35.7874i	−0.928710	−	0.166453i
$216$		0			0
$217$			181.041i			0.834288i
$218$	45.8338			0.210247
$219$		0			0
$220$	−132.327	−	23.7170i	−0.601485	−	0.107805i
$221$			3.15651i			0.0142828i
$222$		0			0
$223$		−	69.0382i		−	0.309588i	−0.987947	−	0.154794i	$-0.950529\pi$
$223$		−	69.0382i		−	0.309588i	0.987947	−	0.154794i	$-0.0494714\pi$
$224$			49.5904i			0.221386i
$225$		0			0
$226$	−20.1113			−0.0889882
$227$	−295.539			−1.30194			−0.650968	−	0.759105i	$-0.725637\pi$
$227$	−295.539			−1.30194			−0.650968	+	0.759105i	$0.725637\pi$
$228$		0			0
$229$	172.185			0.751898			0.375949	−	0.926640i	$-0.377317\pi$
$229$	172.185			0.751898			0.375949	+	0.926640i	$0.377317\pi$
$230$	42.9393	−	239.576i	0.186693	−	1.04164i
$231$		0			0
$232$		−	29.3443i		−	0.126484i
$233$	−225.911			−0.969575			−0.484788	−	0.874632i	$-0.661103\pi$
$233$	−225.911			−0.969575			−0.484788	+	0.874632i	$0.661103\pi$
$234$		0			0
$235$	−27.3368	+	152.523i	−0.116327	+	0.649035i
$236$			60.4324i			0.256069i
$237$		0			0
$238$			2.26953i			0.00953586i
$239$		−	185.265i		−	0.775166i	−0.921835	−	0.387583i	$-0.873310\pi$
$239$		−	185.265i		−	0.775166i	0.921835	−	0.387583i	$-0.126690\pi$
$240$		0			0
$241$	189.814			0.787609			0.393804	−	0.919194i	$-0.371159\pi$
$241$	189.814			0.787609			0.393804	+	0.919194i	$0.371159\pi$
$242$	−84.4692			−0.349046
$243$		0			0
$244$	145.332			0.595623
$245$	−24.5667	+	137.068i	−0.100272	+	0.559459i
$246$		0			0
$247$			598.860i			2.42453i
$248$	58.4115			0.235530
$249$		0			0
$250$	−89.6778	+	152.341i	−0.358711	+	0.609365i
$251$			17.6615i			0.0703644i	0.999381	+	0.0351822i	$0.0112011\pi$
$251$			17.6615i			0.0703644i	−0.999381	+	0.0351822i	$0.988799\pi$
$252$		0			0
$253$		−	462.741i		−	1.82902i
$254$			262.939i			1.03519i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−245.102			−0.953703			−0.476852	−	0.878984i	$-0.658222\pi$
$257$	−245.102			−0.953703			−0.476852	+	0.878984i	$0.658222\pi$
$258$		0			0
$259$	76.7460			0.296317
$260$	169.723	+	30.4196i	0.652783	+	0.116999i
$261$		0			0
$262$			170.250i			0.649809i
$263$	−267.401			−1.01674			−0.508368	−	0.861140i	$-0.669751\pi$
$263$	−267.401			−1.01674			−0.508368	+	0.861140i	$0.669751\pi$
$264$		0			0
$265$	18.6995	−	104.332i	0.0705641	−	0.393706i
$266$			430.581i			1.61873i
$267$		0			0
$268$			13.1199i			0.0489548i
$269$			243.457i			0.905044i	0.891753	+	0.452522i	$0.149476\pi$
$269$			243.457i			0.905044i	−0.891753	+	0.452522i	$0.850524\pi$
$270$		0			0
$271$	−91.5943			−0.337987			−0.168993	−	0.985617i	$-0.554052\pi$
$271$	−91.5943			−0.337987			−0.168993	+	0.985617i	$0.554052\pi$
$272$	0.732249			0.00269209
$273$		0			0
$274$	288.815			1.05407
$275$	−116.725	+	315.168i	−0.424454	+	1.14606i
$276$		0			0
$277$			268.152i			0.968059i	0.875052	+	0.484030i	$0.160827\pi$
$277$			268.152i			0.968059i	−0.875052	+	0.484030i	$0.839173\pi$
$278$	−341.724			−1.22922
$279$		0			0
$280$	122.032	+	21.8718i	0.435827	+	0.0781135i
$281$			279.033i			0.993002i	0.868036	+	0.496501i	$0.165382\pi$
$281$			279.033i			0.993002i	−0.868036	+	0.496501i	$0.834618\pi$
$282$		0			0
$283$		−	131.398i		−	0.464306i	−0.972679	−	0.232153i	$-0.925423\pi$
$283$		−	131.398i		−	0.464306i	0.972679	−	0.232153i	$-0.0745769\pi$
$284$			2.05716i			0.00724351i
$285$		0			0
$286$	327.821			1.14623
$287$	13.8297			0.0481871
$288$		0			0
$289$	−288.966			−0.999884
$290$	−72.2102	−	12.9423i	−0.249001	−	0.0446285i
$291$		0			0
$292$		−	33.6568i		−	0.115263i
$293$	−99.5943			−0.339912			−0.169956	−	0.985452i	$-0.554363\pi$
$293$	−99.5943			−0.339912			−0.169956	+	0.985452i	$0.554363\pi$
$294$		0			0
$295$	148.711	+	26.6536i	0.504106	+	0.0903511i
$296$		−	24.7615i		−	0.0836539i
$297$		0			0
$298$			178.568i			0.599221i
$299$			593.516i			1.98500i
$300$		0			0
$301$	355.662			1.18160
$302$	−378.647			−1.25380
$303$		0			0
$304$	138.924			0.456987
$305$	64.0984	−	357.631i	0.210159	−	1.17256i
$306$		0			0
$307$			256.585i			0.835781i	0.908497	+	0.417890i	$0.137230\pi$
$307$			256.585i			0.835781i	−0.908497	+	0.417890i	$0.862770\pi$
$308$	235.704			0.765272
$309$		0			0
$310$	25.7623	−	143.738i	0.0831041	−	0.463672i
$311$		−	151.027i		−	0.485616i	−0.970074	−	0.242808i	$-0.921931\pi$
$311$		−	151.027i		−	0.485616i	0.970074	−	0.242808i	$-0.0780685\pi$
$312$		0			0
$313$		−	543.294i		−	1.73576i	−0.496772	−	0.867881i	$-0.665481\pi$
$313$		−	543.294i		−	1.73576i	0.496772	−	0.867881i	$-0.334519\pi$
$314$			77.1131i			0.245583i
$315$		0			0
$316$	−166.328			−0.526355
$317$	321.111			1.01297			0.506485	−	0.862249i	$-0.330945\pi$
$317$	321.111			1.01297			0.506485	+	0.862249i	$0.330945\pi$
$318$		0			0
$319$	−139.474			−0.437222
$320$	7.05677	−	39.3726i	0.0220524	−	0.123039i
$321$		0			0
$322$			426.739i			1.32528i
$323$	6.35794			0.0196840
$324$		0			0
$325$	149.712	−	404.237i	0.460654	−	1.24381i
$326$		−	158.626i		−	0.486584i
$327$		0			0
$328$		−	4.46206i		−	0.0136038i
$329$		−	271.678i		−	0.825769i
$330$		0			0
$331$	−107.383			−0.324419			−0.162209	−	0.986756i	$-0.551862\pi$
$331$	−107.383			−0.324419			−0.162209	+	0.986756i	$0.551862\pi$
$332$	−4.63238			−0.0139529
$333$		0			0
$334$	−449.158			−1.34478
$335$	32.2853	+	5.78650i	0.0963739	+	0.0172731i
$336$		0			0
$337$		−	381.174i		−	1.13108i	−0.824721	−	0.565540i	$-0.808668\pi$
$337$		−	381.174i		−	1.13108i	0.824721	−	0.565540i	$-0.191332\pi$
$338$	−181.463			−0.536874
$339$		0			0
$340$	0.322957	−	1.80191i	0.000949874	−	0.00529974i
$341$		−	277.630i		−	0.814165i
$342$		0			0
$343$			185.407i			0.540545i
$344$		−	114.752i		−	0.333581i
$345$		0			0
$346$	−126.449			−0.365460
$347$	132.705			0.382434			0.191217	−	0.981548i	$-0.438757\pi$
$347$	132.705			0.382434			0.191217	+	0.981548i	$0.438757\pi$
$348$		0			0
$349$	404.732			1.15969			0.579845	−	0.814727i	$-0.303113\pi$
$349$	404.732			1.15969			0.579845	+	0.814727i	$0.303113\pi$
$350$	107.644	−	290.647i	0.307553	−	0.830421i
$351$		0			0
$352$		−	76.0481i		−	0.216046i
$353$	−537.501			−1.52267			−0.761333	−	0.648362i	$-0.775455\pi$
$353$	−537.501			−1.52267			−0.761333	+	0.648362i	$0.775455\pi$
$354$		0			0
$355$	5.06223	+	0.907305i	0.0142598	+	0.00255579i
$356$		−	275.093i		−	0.772732i
$357$		0			0
$358$		−	365.799i		−	1.02178i
$359$			104.348i			0.290662i	0.989383	+	0.145331i	$0.0464247\pi$
$359$			104.348i			0.290662i	−0.989383	+	0.145331i	$0.953575\pi$
$360$		0			0
$361$	845.242			2.34139
$362$	−49.6993			−0.137291
$363$		0			0
$364$	−302.316			−0.830537
$365$	−82.8222	−	14.8443i	−0.226910	−	0.0406692i
$366$		0			0
$367$			60.4157i			0.164621i	0.996607	+	0.0823103i	$0.0262299\pi$
$367$			60.4157i			0.164621i	−0.996607	+	0.0823103i	$0.973770\pi$
$368$	137.684			0.374142
$369$		0			0
$370$	−60.9329	−	10.9210i	−0.164684	−	0.0295163i
$371$			185.839i			0.500913i
$372$		0			0
$373$			601.750i			1.61327i	0.591049	+	0.806636i	$0.298714\pi$
$373$			601.750i			1.61327i	−0.591049	+	0.806636i	$0.701286\pi$
$374$		−	3.48039i		−	0.00930585i
$375$		0			0
$376$	−87.6550			−0.233125
$377$	178.890			0.474511
$378$		0			0
$379$	−703.470			−1.85612			−0.928061	−	0.372428i	$-0.878525\pi$
$379$	−703.470			−1.85612			−0.928061	+	0.372428i	$0.878525\pi$
$380$	61.2722	−	341.862i	0.161243	−	0.899638i
$381$		0			0
$382$		−	61.1018i		−	0.159952i
$383$	340.041			0.887835			0.443918	−	0.896068i	$-0.353588\pi$
$383$	340.041			0.887835			0.443918	+	0.896068i	$0.353588\pi$
$384$		0			0
$385$	103.957	−	580.017i	0.270017	−	1.50654i
$386$		−	379.132i		−	0.982208i
$387$		0			0
$388$			108.166i			0.278777i
$389$		−	239.923i		−	0.616770i	−0.951262	−	0.308385i	$-0.900212\pi$
$389$		−	239.923i		−	0.616770i	0.951262	−	0.308385i	$-0.0997885\pi$
$390$		0			0
$391$	6.30120			0.0161156
$392$	−78.7726			−0.200951
$393$		0			0
$394$	−345.881			−0.877871
$395$	−73.3588	+	409.298i	−0.185718	+	1.03620i
$396$		0			0
$397$			531.985i			1.34001i	0.742355	+	0.670006i	$0.233709\pi$
$397$			531.985i			1.34001i	−0.742355	+	0.670006i	$0.766291\pi$
$398$	293.408			0.737206
$399$		0			0
$400$	−93.7752	−	34.7304i	−0.234438	−	0.0868261i
$401$			260.285i			0.649091i	0.945870	+	0.324545i	$0.105211\pi$
$401$			260.285i			0.649091i	−0.945870	+	0.324545i	$0.894789\pi$
$402$		0			0
$403$			356.091i			0.883600i
$404$			244.128i			0.604277i
$405$		0			0
$406$	128.623			0.316804
$407$	−117.692			−0.289169
$408$		0			0
$409$	484.545			1.18471			0.592353	−	0.805679i	$-0.298199\pi$
$409$	484.545			1.18471			0.592353	+	0.805679i	$0.298199\pi$
$410$	−10.9802	−	1.96798i	−0.0267809	−	0.00479996i
$411$		0			0
$412$			110.437i			0.268050i
$413$	−264.888			−0.641376
$414$		0			0
$415$	−2.04310	+	11.3993i	−0.00492314	+	0.0274682i
$416$			97.5400i			0.234471i
$417$		0			0
$418$		−	660.307i		−	1.57968i
$419$		−	307.106i		−	0.732950i	−0.930428	−	0.366475i	$-0.880565\pi$
$419$		−	307.106i		−	0.732950i	0.930428	−	0.366475i	$-0.119435\pi$
$420$		0			0
$421$	−2.92204			−0.00694071			−0.00347035	−	0.999994i	$-0.501105\pi$
$421$	−2.92204			−0.00694071			−0.00347035	+	0.999994i	$0.501105\pi$
$422$	−264.738			−0.627342
$423$		0			0
$424$	59.9596			0.141414
$425$	−4.29168	−	1.58946i	−0.0100981	−	0.00373990i
$426$		0			0
$427$			637.022i			1.49185i
$428$	47.8430			0.111783
$429$		0			0
$430$	−282.380	−	50.6111i	−0.656697	−	0.117700i
$431$			305.204i			0.708129i	0.935221	+	0.354064i	$0.115201\pi$
$431$			305.204i			0.708129i	−0.935221	+	0.354064i	$0.884799\pi$
$432$		0			0
$433$		−	565.472i		−	1.30594i	−0.757383	−	0.652971i	$-0.773523\pi$
$433$		−	565.472i		−	1.30594i	0.757383	−	0.652971i	$-0.226477\pi$
$434$			256.030i			0.589931i
$435$		0			0
$436$	64.8188			0.148667
$437$	1195.48			2.73565
$438$		0			0
$439$	−342.535			−0.780263			−0.390132	−	0.920759i	$-0.627570\pi$
$439$	−342.535			−0.780263			−0.390132	+	0.920759i	$0.627570\pi$
$440$	−187.138	−	33.5409i	−0.425314	−	0.0762293i
$441$		0			0
$442$			4.46397i			0.0100995i
$443$	333.269			0.752301			0.376150	−	0.926559i	$-0.377248\pi$
$443$	333.269			0.752301			0.376150	+	0.926559i	$0.377248\pi$
$444$		0			0
$445$	−676.944	−	121.329i	−1.52122	−	0.272650i
$446$		−	97.6347i		−	0.218912i
$447$		0			0
$448$			70.1315i			0.156543i
$449$		−	223.412i		−	0.497576i	−0.968558	−	0.248788i	$-0.919968\pi$
$449$		−	223.412i		−	0.497576i	0.968558	−	0.248788i	$-0.0800323\pi$
$450$		0			0
$451$	−21.2082			−0.0470248
$452$	−28.4417			−0.0629241
$453$		0			0
$454$	−417.956			−0.920608
$455$	−133.336	+	743.935i	−0.293046	+	1.63502i
$456$		0			0
$457$			563.639i			1.23335i	0.787219	+	0.616673i	$0.211520\pi$
$457$			563.639i			1.23335i	−0.787219	+	0.616673i	$0.788480\pi$
$458$	243.506			0.531672
$459$		0			0
$460$	60.7254	−	338.812i	0.132012	−	0.736547i
$461$		−	389.635i		−	0.845195i	−0.906318	−	0.422597i	$-0.861118\pi$
$461$		−	389.635i		−	0.845195i	0.906318	−	0.422597i	$-0.138882\pi$
$462$		0			0
$463$		−	400.392i		−	0.864777i	−0.901687	−	0.432389i	$-0.857671\pi$
$463$		−	400.392i		−	0.864777i	0.901687	−	0.432389i	$-0.142329\pi$
$464$		−	41.4992i		−	0.0894379i
$465$		0			0
$466$	−319.486			−0.685593
$467$	505.244			1.08189			0.540946	−	0.841057i	$-0.318066\pi$
$467$	505.244			1.08189			0.540946	+	0.841057i	$0.318066\pi$
$468$		0			0
$469$	−57.5073			−0.122617
$470$	−38.6601	+	215.700i	−0.0822555	+	0.458937i
$471$		0			0
$472$			85.4643i			0.181068i
$473$	−545.416			−1.15310
$474$		0			0
$475$	−814.227	−	301.556i	−1.71416	−	0.634854i
$476$			3.20961i			0.00674287i
$477$		0			0
$478$		−	262.004i		−	0.548125i
$479$		−	827.559i		−	1.72768i	−0.503766	−	0.863840i	$-0.668053\pi$
$479$		−	827.559i		−	1.72768i	0.503766	−	0.863840i	$-0.331947\pi$
$480$		0			0
$481$	150.953			0.313831
$482$	268.437			0.556923
$483$		0			0
$484$	−119.458			−0.246813
$485$	266.173	+	47.7062i	0.548809	+	0.0983634i
$486$		0			0
$487$		−	640.978i		−	1.31618i	−0.752941	−	0.658089i	$-0.771365\pi$
$487$		−	640.978i		−	1.31618i	0.752941	−	0.658089i	$-0.228635\pi$
$488$	205.531			0.421169
$489$		0			0
$490$	−34.7425	+	193.843i	−0.0709031	+	0.395597i
$491$			457.821i			0.932427i	0.884672	+	0.466213i	$0.154382\pi$
$491$			457.821i			0.932427i	−0.884672	+	0.466213i	$0.845618\pi$
$492$		0			0
$493$		−	1.89923i		−	0.00385240i
$494$			846.915i			1.71440i
$495$		0			0
$496$	82.6063			0.166545
$497$	−9.01696			−0.0181428
$498$		0			0
$499$	407.703			0.817040			0.408520	−	0.912749i	$-0.366045\pi$
$499$	407.703			0.817040			0.408520	+	0.912749i	$0.366045\pi$
$500$	−126.824	+	215.443i	−0.253647	+	0.430886i
$501$		0			0
$502$			24.9771i			0.0497551i
$503$	500.538			0.995106			0.497553	−	0.867434i	$-0.334232\pi$
$503$	500.538			0.995106			0.497553	+	0.867434i	$0.334232\pi$
$504$		0			0
$505$	600.747	+	107.672i	1.18960	+	0.213212i
$506$		−	654.415i		−	1.29331i
$507$		0			0
$508$			371.851i			0.731991i
$509$		−	686.976i		−	1.34966i	−0.737975	−	0.674829i	$-0.764218\pi$
$509$		−	686.976i		−	1.34966i	0.737975	−	0.674829i	$-0.235782\pi$
$510$		0			0
$511$	147.525			0.288699
$512$	22.6274			0.0441942
$513$		0			0
$514$	−346.626			−0.674370
$515$	271.761	+	48.7079i	0.527691	+	0.0945784i
$516$		0			0
$517$			416.625i			0.805851i
$518$	108.535			0.209527
$519$		0			0
$520$	240.025	+	43.0198i	0.461587	+	0.0827304i
$521$		−	205.758i		−	0.394930i	−0.980310	−	0.197465i	$-0.936729\pi$
$521$		−	205.758i		−	0.394930i	0.980310	−	0.197465i	$-0.0632708\pi$
$522$		0			0
$523$		−	156.769i		−	0.299749i	−0.988705	−	0.149875i	$-0.952113\pi$
$523$		−	156.769i		−	0.299749i	0.988705	−	0.149875i	$-0.0478870\pi$
$524$			240.770i			0.459485i
$525$		0			0
$526$	−378.163			−0.718941
$527$	3.78052			0.00717367
$528$		0			0
$529$	655.810			1.23972
$530$	26.4451	−	147.548i	0.0498963	−	0.278392i
$531$		0			0
$532$			608.934i			1.14461i
$533$	27.2018			0.0510353
$534$		0			0
$535$	21.1011	−	117.731i	0.0394413	−	0.220059i
$536$			18.5543i			0.0346163i
$537$		0			0
$538$			344.300i			0.639962i
$539$			374.407i			0.694633i
$540$		0			0
$541$	218.865			0.404556			0.202278	−	0.979328i	$-0.435166\pi$
$541$	218.865			0.404556			0.202278	+	0.979328i	$0.435166\pi$
$542$	−129.534			−0.238993
$543$		0			0
$544$	1.03556			0.00190360
$545$	28.5882	−	159.505i	0.0524554	−	0.292670i
$546$		0			0
$547$			343.838i			0.628589i	0.949326	+	0.314294i	$0.101768\pi$
$547$			343.838i			0.628589i	−0.949326	+	0.314294i	$0.898232\pi$
$548$	408.446			0.745340
$549$		0			0
$550$	−165.074	+	445.715i	−0.300135	+	0.810390i
$551$		−	360.327i		−	0.653951i
$552$		0			0
$553$		−	729.053i		−	1.31836i
$554$			379.225i			0.684521i
$555$		0			0
$556$	−483.270			−0.869191
$557$	−510.208			−0.915992			−0.457996	−	0.888954i	$-0.651433\pi$
$557$	−510.208			−0.915992			−0.457996	+	0.888954i	$0.651433\pi$
$558$		0			0
$559$	699.556			1.25144
$560$	172.579	+	30.9314i	0.308176	+	0.0552346i
$561$		0			0
$562$			394.613i			0.702158i
$563$	19.9165			0.0353756			0.0176878	−	0.999844i	$-0.494370\pi$
$563$	19.9165			0.0353756			0.0176878	+	0.999844i	$0.494370\pi$
$564$		0			0
$565$	−12.5442	+	69.9890i	−0.0222021	+	0.123874i
$566$		−	185.826i		−	0.328314i
$567$		0			0
$568$			2.90926i			0.00512193i
$569$			535.633i			0.941358i	0.882304	+	0.470679i	$0.155991\pi$
$569$			535.633i			0.941358i	−0.882304	+	0.470679i	$0.844009\pi$
$570$		0			0
$571$	−795.875			−1.39383			−0.696914	−	0.717155i	$-0.745444\pi$
$571$	−795.875			−1.39383			−0.696914	+	0.717155i	$0.745444\pi$
$572$	463.608			0.810504
$573$		0			0
$574$	19.5582			0.0340734
$575$	−806.961	−	298.865i	−1.40341	−	0.519765i
$576$		0			0
$577$			961.892i			1.66706i	0.552477	+	0.833528i	$0.313683\pi$
$577$			961.892i			1.66706i	−0.552477	+	0.833528i	$0.686317\pi$
$578$	−408.660			−0.707025
$579$		0			0
$580$	−102.121	−	18.3031i	−0.176070	−	0.0315571i
$581$		−	20.3047i		−	0.0349479i
$582$		0			0
$583$		−	284.988i		−	0.488831i
$584$		−	47.5979i		−	0.0815032i
$585$		0			0
$586$	−140.848			−0.240354
$587$	718.007			1.22318			0.611590	−	0.791175i	$-0.290530\pi$
$587$	718.007			1.22318			0.611590	+	0.791175i	$0.290530\pi$
$588$		0			0
$589$	717.250			1.21774
$590$	210.309	+	37.6939i	0.356457	+	0.0638879i
$591$		0			0
$592$		−	35.0181i		−	0.0591522i
$593$	1159.26			1.95490			0.977452	−	0.211160i	$-0.0677241\pi$
$593$	1159.26			1.95490			0.977452	+	0.211160i	$0.0677241\pi$
$594$		0			0
$595$	7.89816	+	1.41559i	0.0132742	+	0.00237914i
$596$			252.533i			0.423713i
$597$		0			0
$598$			839.358i			1.40361i
$599$		−	554.025i		−	0.924916i	−0.886641	−	0.462458i	$-0.846968\pi$
$599$		−	554.025i		−	0.924916i	0.886641	−	0.462458i	$-0.153032\pi$
$600$		0			0
$601$	295.049			0.490931			0.245465	−	0.969405i	$-0.421059\pi$
$601$	295.049			0.490931			0.245465	+	0.969405i	$0.421059\pi$
$602$	502.982			0.835518
$603$		0			0
$604$	−535.488			−0.886569
$605$	−52.6865	+	293.960i	−0.0870852	+	0.485884i
$606$		0			0
$607$		−	1004.37i		−	1.65465i	−0.561721	−	0.827327i	$-0.689861\pi$
$607$		−	1004.37i		−	1.65465i	0.561721	−	0.827327i	$-0.310139\pi$
$608$	196.468			0.323139
$609$		0			0
$610$	90.6489	−	505.767i	0.148605	−	0.829126i
$611$		−	534.367i		−	0.874577i
$612$		0			0
$613$			922.012i			1.50410i	0.659107	+	0.752049i	$0.270934\pi$
$613$			922.012i			1.50410i	−0.659107	+	0.752049i	$0.729066\pi$
$614$			362.865i			0.590986i
$615$		0			0
$616$	333.335			0.541129
$617$	−570.605			−0.924805			−0.462403	−	0.886670i	$-0.653013\pi$
$617$	−570.605			−0.924805			−0.462403	+	0.886670i	$0.653013\pi$
$618$		0			0
$619$	6.52049			0.0105339			0.00526695	−	0.999986i	$-0.498323\pi$
$619$	6.52049			0.0105339			0.00526695	+	0.999986i	$0.498323\pi$
$620$	36.4333	−	203.277i	0.0587635	−	0.327865i
$621$		0			0
$622$		−	213.584i		−	0.343383i
$623$	1205.79			1.93546
$624$		0			0
$625$	474.225	+	407.107i	0.758759	+	0.651371i
$626$		−	768.333i		−	1.22737i
$627$		0			0
$628$			109.054i			0.173654i
$629$		−	1.60262i		−	0.00254789i
$630$		0			0
$631$	−948.440			−1.50307			−0.751537	−	0.659691i	$-0.770687\pi$
$631$	−948.440			−1.50307			−0.751537	+	0.659691i	$0.770687\pi$
$632$	−235.224			−0.372189
$633$		0			0
$634$	454.120			0.716278
$635$	915.047	+	164.004i	1.44102	+	0.258274i
$636$		0			0
$637$		−	480.218i		−	0.753874i
$638$	−197.246			−0.309163
$639$		0			0
$640$	9.97978	−	55.6813i	0.0155934	−	0.0870020i
$641$			56.0811i			0.0874900i	0.999043	+	0.0437450i	$0.0139289\pi$
$641$			56.0811i			0.0874900i	−0.999043	+	0.0437450i	$0.986071\pi$
$642$		0			0
$643$		−	189.437i		−	0.294615i	−0.989091	−	0.147308i	$-0.952939\pi$
$643$		−	189.437i		−	0.294615i	0.989091	−	0.147308i	$-0.0470607\pi$
$644$			603.500i			0.937112i
$645$		0			0
$646$	8.99148			0.0139187
$647$	−70.1526			−0.108427			−0.0542137	−	0.998529i	$-0.517265\pi$
$647$	−70.1526			−0.108427			−0.0542137	+	0.998529i	$0.517265\pi$
$648$		0			0
$649$	406.213			0.625905
$650$	211.725	−	571.677i	0.325731	−	0.879504i
$651$		0			0
$652$		−	224.332i		−	0.344067i
$653$	196.295			0.300604			0.150302	−	0.988640i	$-0.451975\pi$
$653$	196.295			0.300604			0.150302	+	0.988640i	$0.451975\pi$
$654$		0			0
$655$	592.484	+	106.191i	0.904555	+	0.162124i
$656$		−	6.31030i		−	0.00961936i
$657$		0			0
$658$		−	384.211i		−	0.583907i
$659$		−	419.796i		−	0.637020i	−0.947920	−	0.318510i	$-0.896818\pi$
$659$		−	419.796i		−	0.637020i	0.947920	−	0.318510i	$-0.103182\pi$
$660$		0			0
$661$	139.280			0.210711			0.105356	−	0.994435i	$-0.466402\pi$
$661$	139.280			0.210711			0.105356	+	0.994435i	$0.466402\pi$
$662$	−151.862			−0.229399
$663$		0			0
$664$	−6.55117			−0.00986622
$665$	1498.46	+	268.569i	2.25332	+	0.403863i
$666$		0			0
$667$		−	357.112i		−	0.535400i
$668$	−635.205			−0.950906
$669$		0			0
$670$	45.6583	+	8.18335i	0.0681467	+	0.0122140i
$671$		−	976.889i		−	1.45587i
$672$		0			0
$673$		−	30.0015i		−	0.0445787i	−0.999752	−	0.0222894i	$-0.992904\pi$
$673$		−	30.0015i		−	0.0445787i	0.999752	−	0.0222894i	$-0.00709551\pi$
$674$		−	539.061i		−	0.799794i
$675$		0			0
$676$	−256.628			−0.379627
$677$	−241.807			−0.357175			−0.178587	−	0.983924i	$-0.557153\pi$
$677$	−241.807			−0.357175			−0.178587	+	0.983924i	$0.557153\pi$
$678$		0			0
$679$	−474.113			−0.698252
$680$	0.456730	−	2.54829i	0.000671662	−	0.00374748i
$681$		0			0
$682$		−	392.628i		−	0.575701i
$683$	−1055.81			−1.54585			−0.772924	−	0.634498i	$-0.781207\pi$
$683$	−1055.81			−1.54585			−0.772924	+	0.634498i	$0.781207\pi$
$684$		0			0
$685$	180.144	−	1005.10i	0.262985	−	1.46730i
$686$			262.205i			0.382223i
$687$		0			0
$688$		−	162.284i		−	0.235877i
$689$			365.528i			0.530520i
$690$		0			0
$691$	248.192			0.359179			0.179589	−	0.983742i	$-0.442523\pi$
$691$	248.192			0.359179			0.179589	+	0.983742i	$0.442523\pi$
$692$	−178.826			−0.258419
$693$		0			0
$694$	187.673			0.270422
$695$	−213.145	+	1189.23i	−0.306684	+	1.71112i
$696$		0			0
$697$		−	0.288795i		−	0.000414339i
$698$	572.377			0.820025
$699$		0			0
$700$	152.231	−	411.037i	0.217473	−	0.587196i
$701$		−	402.671i		−	0.574423i	−0.957867	−	0.287212i	$-0.907272\pi$
$701$		−	402.671i		−	0.574423i	0.957867	−	0.287212i	$-0.0927283\pi$
$702$		0			0
$703$		−	304.054i		−	0.432509i
$704$		−	107.548i		−	0.152767i
$705$		0			0
$706$	−760.141			−1.07669
$707$	−1070.07			−1.51353
$708$		0			0
$709$	376.768			0.531408			0.265704	−	0.964055i	$-0.414396\pi$
$709$	376.768			0.531408			0.265704	+	0.964055i	$0.414396\pi$
$710$	7.15907	+	1.28312i	0.0100832	+	0.00180722i
$711$		0			0
$712$		−	389.040i		−	0.546404i
$713$	710.849			0.996983
$714$		0			0
$715$	204.474	−	1140.84i	0.285977	−	1.59558i
$716$		−	517.317i		−	0.722510i
$717$		0			0
$718$			147.570i			0.205529i
$719$		−	1256.87i		−	1.74808i	−0.485856	−	0.874039i	$-0.661492\pi$
$719$		−	1256.87i		−	1.74808i	0.485856	−	0.874039i	$-0.338508\pi$
$720$		0			0
$721$	−484.067			−0.671383
$722$	1195.35			1.65561
$723$		0			0
$724$	−70.2854			−0.0970793
$725$	−90.0803	+	243.225i	−0.124249	+	0.335482i
$726$		0			0
$727$			718.195i			0.987888i	0.869494	+	0.493944i	$0.164445\pi$
$727$			718.195i			0.987888i	−0.869494	+	0.493944i	$0.835555\pi$
$728$	−427.539			−0.587279
$729$		0			0
$730$	−117.128	−	20.9930i	−0.160450	−	0.0287575i
$731$		−	7.42700i		−	0.0101601i
$732$		0			0
$733$			780.822i			1.06524i	0.846354	+	0.532621i	$0.178793\pi$
$733$			780.822i			1.06524i	−0.846354	+	0.532621i	$0.821207\pi$
$734$			85.4408i			0.116404i
$735$		0			0
$736$	194.715			0.264558
$737$	88.1889			0.119659
$738$		0			0
$739$	−574.801			−0.777809			−0.388905	−	0.921278i	$-0.627146\pi$
$739$	−574.801			−0.777809			−0.388905	+	0.921278i	$0.627146\pi$
$740$	−86.1722	−	15.4447i	−0.116449	−	0.0208712i
$741$		0			0
$742$			262.816i			0.354199i
$743$	472.436			0.635850			0.317925	−	0.948116i	$-0.397014\pi$
$743$	472.436			0.635850			0.317925	+	0.948116i	$0.397014\pi$
$744$		0			0
$745$	621.431	+	111.379i	0.834135	+	0.149502i
$746$			851.003i			1.14076i
$747$		0			0
$748$		−	4.92201i		−	0.00658023i
$749$			209.706i			0.279982i
$750$		0			0
$751$	770.718			1.02626			0.513128	−	0.858312i	$-0.328487\pi$
$751$	770.718			1.02626			0.513128	+	0.858312i	$0.328487\pi$
$752$	−123.963			−0.164844
$753$		0			0
$754$	252.989			0.335530
$755$	−236.176	+	1317.72i	−0.312816	+	1.74533i
$756$		0			0
$757$		−	485.944i		−	0.641934i	−0.947090	−	0.320967i	$-0.895992\pi$
$757$		−	485.944i		−	0.641934i	0.947090	−	0.320967i	$-0.104008\pi$
$758$	−994.857			−1.31248
$759$		0			0
$760$	86.6519	−	483.467i	0.114016	−	0.636140i
$761$			982.528i			1.29110i	0.763718	+	0.645550i	$0.223372\pi$
$761$			982.528i			1.29110i	−0.763718	+	0.645550i	$0.776628\pi$
$762$		0			0
$763$			284.115i			0.372365i
$764$		−	86.4110i		−	0.113103i
$765$		0			0
$766$	480.890			0.627794
$767$	−521.012			−0.679285
$768$		0			0
$769$	−763.509			−0.992859			−0.496430	−	0.868077i	$-0.665356\pi$
$769$	−763.509			−0.992859			−0.496430	+	0.868077i	$0.665356\pi$
$770$	147.017	−	820.268i	0.190931	−	1.06528i
$771$		0			0
$772$		−	536.174i		−	0.694526i
$773$	−631.822			−0.817363			−0.408682	−	0.912677i	$-0.634011\pi$
$773$	−631.822			−0.817363			−0.408682	+	0.912677i	$0.634011\pi$
$774$		0			0
$775$	−484.151	−	179.309i	−0.624712	−	0.231367i
$776$			152.969i			0.197125i
$777$		0			0
$778$		−	339.303i		−	0.436122i
$779$		−	54.7908i		−	0.0703347i
$780$		0			0
$781$	13.8277			0.0177052
$782$	8.91124			0.0113955
$783$		0			0
$784$	−111.401			−0.142094
$785$	268.360	+	48.0983i	0.341860	+	0.0612717i
$786$		0			0
$787$			967.596i			1.22947i	0.788732	+	0.614737i	$0.210738\pi$
$787$			967.596i			1.22947i	−0.788732	+	0.614737i	$0.789262\pi$
$788$	−489.150			−0.620748
$789$		0			0
$790$	−103.745	+	578.835i	−0.131323	+	0.732703i
$791$		−	124.666i		−	0.157606i
$792$		0			0
$793$			1252.97i			1.58003i
$794$			752.341i			0.947532i
$795$		0			0
$796$	414.941			0.521283
$797$	378.648			0.475092			0.237546	−	0.971376i	$-0.423657\pi$
$797$	378.648			0.475092			0.237546	+	0.971376i	$0.423657\pi$
$798$		0			0
$799$	−5.67323			−0.00710042
$800$	−132.618	−	49.1162i	−0.165773	−	0.0613953i
$801$		0			0
$802$			368.099i			0.458976i
$803$	−226.233			−0.281735
$804$		0			0
$805$	1485.09	+	266.173i	1.84483	+	0.330649i
$806$			503.588i			0.624800i
$807$		0			0
$808$			345.249i			0.427288i
$809$			141.580i			0.175006i	0.996164	+	0.0875029i	$0.0278887\pi$
$809$			141.580i			0.175006i	−0.996164	+	0.0875029i	$0.972111\pi$
$810$		0			0
$811$	550.861			0.679237			0.339618	−	0.940563i	$-0.389702\pi$
$811$	550.861			0.679237			0.339618	+	0.940563i	$0.389702\pi$
$812$	181.900			0.224015
$813$		0			0
$814$	−166.441			−0.204474
$815$	−552.033	−	98.9411i	−0.677341	−	0.121400i
$816$		0			0
$817$		−	1409.07i		−	1.72468i
$818$	685.250			0.837714
$819$		0			0
$820$	−15.5283	−	2.78315i	−0.0189370	−	0.00339408i
$821$		−	230.115i		−	0.280286i	−0.990131	−	0.140143i	$-0.955244\pi$
$821$		−	230.115i		−	0.280286i	0.990131	−	0.140143i	$-0.0447562\pi$
$822$		0			0
$823$			398.690i			0.484435i	0.970222	+	0.242218i	$0.0778748\pi$
$823$			398.690i			0.484435i	−0.970222	+	0.242218i	$0.922125\pi$
$824$			156.181i			0.189540i
$825$		0			0
$826$	−374.608			−0.453521
$827$	755.037			0.912983			0.456491	−	0.889728i	$-0.349106\pi$
$827$	755.037			0.912983			0.456491	+	0.889728i	$0.349106\pi$
$828$		0			0
$829$	1507.17			1.81806			0.909032	−	0.416727i	$-0.136823\pi$
$829$	1507.17			1.81806			0.909032	+	0.416727i	$0.136823\pi$
$830$	−2.88938	+	16.1210i	−0.00348118	+	0.0194229i
$831$		0			0
$832$			137.942i			0.165796i
$833$	−5.09835			−0.00612046
$834$		0			0
$835$	−280.156	+	1563.10i	−0.335516	+	1.87198i
$836$		−	933.815i		−	1.11700i
$837$		0			0
$838$		−	434.313i		−	0.518274i
$839$		−	139.204i		−	0.165916i	−0.996553	−	0.0829581i	$-0.973563\pi$
$839$		−	139.204i		−	0.165916i	0.996553	−	0.0829581i	$-0.0264368\pi$
$840$		0			0
$841$	733.364			0.872014
$842$	−4.13238			−0.00490782
$843$		0			0
$844$	−374.397			−0.443598
$845$	−113.185	+	631.507i	−0.133947	+	0.747346i
$846$		0			0
$847$		−	523.608i		−	0.618191i
$848$	84.7956			0.0999948
$849$		0			0
$850$	−6.06935	−	2.24783i	−0.00714041	−	0.00264451i
$851$		−	301.340i		−	0.354101i
$852$		0			0
$853$		−	1143.30i		−	1.34032i	−0.742215	−	0.670162i	$-0.766225\pi$
$853$		−	1143.30i		−	1.34032i	0.742215	−	0.670162i	$-0.233775\pi$
$854$			900.885i			1.05490i
$855$		0			0
$856$	67.6602			0.0790423
$857$	−1134.36			−1.32364			−0.661819	−	0.749664i	$-0.730215\pi$
$857$	−1134.36			−1.32364			−0.661819	+	0.749664i	$0.730215\pi$
$858$		0			0
$859$	−1242.61			−1.44658			−0.723291	−	0.690543i	$-0.757372\pi$
$859$	−1242.61			−1.44658			−0.723291	+	0.690543i	$0.757372\pi$
$860$	−399.345	−	71.5749i	−0.464355	−	0.0832266i
$861$		0			0
$862$			431.623i			0.500723i
$863$	−1572.04			−1.82160			−0.910800	−	0.412847i	$-0.864534\pi$
$863$	−1572.04			−1.82160			−0.910800	+	0.412847i	$0.864534\pi$
$864$		0			0
$865$	−78.8710	+	440.054i	−0.0911803	+	0.508732i
$866$		−	799.699i		−	0.923440i
$867$		0			0
$868$			362.081i			0.417144i
$869$			1118.02i			1.28656i
$870$		0			0
$871$	−113.112			−0.129864
$872$	91.6676			0.105123
$873$		0			0
$874$	1690.66			1.93440
$875$	−944.334	−	555.895i	−1.07924	−	0.635309i
$876$		0			0
$877$		−	1054.12i		−	1.20196i	−0.799263	−	0.600982i	$-0.794777\pi$
$877$		−	1054.12i		−	1.20196i	0.799263	−	0.600982i	$-0.205223\pi$
$878$	−484.418			−0.551729
$879$		0			0
$880$	−264.654	−	47.4340i	−0.300743	−	0.0539023i
$881$			1421.43i			1.61342i	0.590946	+	0.806711i	$0.298755\pi$
$881$			1421.43i			1.61342i	−0.590946	+	0.806711i	$0.701245\pi$
$882$		0			0
$883$			1353.15i			1.53244i	0.642576	+	0.766222i	$0.277866\pi$
$883$			1353.15i			1.53244i	−0.642576	+	0.766222i	$0.722134\pi$
$884$			6.31301i			0.00714142i
$885$		0			0
$886$	471.314			0.531957
$887$	−66.3012			−0.0747477			−0.0373739	−	0.999301i	$-0.511899\pi$
$887$	−66.3012			−0.0747477			−0.0373739	+	0.999301i	$0.511899\pi$
$888$		0			0
$889$	−1629.90			−1.83341
$890$	−957.344	−	171.585i	−1.07567	−	0.192792i
$891$		0			0
$892$		−	138.076i		−	0.154794i
$893$	−1076.34			−1.20531
$894$		0			0
$895$	−1273.01	−	228.162i	−1.42236	−	0.254929i
$896$			99.1809i			0.110693i
$897$		0			0
$898$		−	315.952i		−	0.351839i
$899$		−	214.256i		−	0.238327i
$900$		0			0
$901$	3.88072			0.00430713
$902$	−29.9929			−0.0332516
$903$		0			0
$904$	−40.2227			−0.0444941
$905$	−30.9992	+	172.957i	−0.0342533	+	0.191113i
$906$		0			0
$907$		−	227.817i		−	0.251177i	−0.992082	−	0.125588i	$-0.959918\pi$
$907$		−	227.817i		−	0.251177i	0.992082	−	0.125588i	$-0.0400819\pi$
$908$	−591.079			−0.650968
$909$		0			0
$910$	−188.565	+	1052.08i	−0.207215	+	1.15613i
$911$		−	369.957i		−	0.406100i	−0.979168	−	0.203050i	$-0.934915\pi$
$911$		−	369.957i		−	0.406100i	0.979168	−	0.203050i	$-0.0650853\pi$
$912$		0			0
$913$			31.1378i			0.0341049i
$914$			797.106i			0.872107i
$915$		0			0
$916$	344.369			0.375949
$917$	−1055.35			−1.15087
$918$		0			0
$919$	−406.648			−0.442490			−0.221245	−	0.975218i	$-0.571012\pi$
$919$	−406.648			−0.442490			−0.221245	+	0.975218i	$0.571012\pi$
$920$	85.8787	−	479.152i	0.0933464	−	0.520818i
$921$		0			0
$922$		−	551.027i		−	0.597643i
$923$	−17.7356			−0.0192151
$924$		0			0
$925$	−76.0121	+	205.240i	−0.0821753	+	0.221881i
$926$		−	566.240i		−	0.611490i
$927$		0			0
$928$		−	58.6887i		−	0.0632421i
$929$		−	1442.09i		−	1.55231i	−0.630545	−	0.776153i	$-0.717169\pi$
$929$		−	1442.09i		−	1.55231i	0.630545	−	0.776153i	$-0.282831\pi$
$930$		0			0
$931$	−967.270			−1.03896
$932$	−451.822			−0.484788
$933$		0			0
$934$	714.523			0.765014
$935$	−12.1120	−	2.17084i	−0.0129540	−	0.00232176i
$936$		0			0
$937$			468.717i			0.500231i	0.968216	+	0.250116i	$0.0804686\pi$
$937$			468.717i			0.500231i	−0.968216	+	0.250116i	$0.919531\pi$
$938$	−81.3276			−0.0867032
$939$		0			0
$940$	−54.6736	+	305.046i	−0.0581634	+	0.324517i
$941$		−	1654.14i		−	1.75786i	−0.476952	−	0.878929i	$-0.658259\pi$
$941$		−	1654.14i		−	1.75786i	0.476952	−	0.878929i	$-0.341741\pi$
$942$		0			0
$943$		−	54.3018i		−	0.0575841i
$944$			120.865i			0.128035i
$945$		0			0
$946$	−771.335			−0.815365
$947$	35.3996			0.0373807			0.0186904	−	0.999825i	$-0.494050\pi$
$947$	35.3996			0.0373807			0.0186904	+	0.999825i	$0.494050\pi$
$948$		0			0
$949$	290.169			0.305763
$950$	−1151.49	−	426.464i	−1.21210	−	0.448910i
$951$		0			0
$952$			4.53907i			0.00476793i
$953$	1248.30			1.30986			0.654929	−	0.755690i	$-0.272698\pi$
$953$	1248.30			1.30986			0.654929	+	0.755690i	$0.272698\pi$
$954$		0			0
$955$	−212.639	−	38.1114i	−0.222659	−	0.0399072i
$956$		−	370.529i		−	0.387583i
$957$		0			0
$958$		−	1170.35i		−	1.22165i
$959$			1790.31i			1.86685i
$960$		0			0
$961$	−534.513			−0.556205
$962$	213.479			0.221912
$963$		0			0
$964$	379.627			0.393804
$965$	−1319.41	−	236.479i	−1.36727	−	0.245056i
$966$		0			0
$967$			1872.90i			1.93682i	0.249372	+	0.968408i	$0.419776\pi$
$967$			1872.90i			1.93682i	−0.249372	+	0.968408i	$0.580224\pi$
$968$	−168.938			−0.174523
$969$		0			0
$970$	376.425	+	67.4668i	0.388067	+	0.0695534i
$971$		−	254.758i		−	0.262366i	−0.991358	−	0.131183i	$-0.958122\pi$
$971$		−	254.758i		−	0.262366i	0.991358	−	0.131183i	$-0.0418776\pi$
$972$		0			0
$973$		−	2118.28i		−	2.17706i
$974$		−	906.480i		−	0.930678i
$975$		0			0
$976$	290.664			0.297812
$977$	−1267.06			−1.29689			−0.648444	−	0.761263i	$-0.724580\pi$
$977$	−1267.06			−1.29689			−0.648444	+	0.761263i	$0.724580\pi$
$978$		0			0
$979$	−1849.11			−1.88877
$980$	−49.1334	+	274.135i	−0.0501361	+	0.279730i
$981$		0			0
$982$			647.457i			0.659325i
$983$	627.538			0.638391			0.319195	−	0.947689i	$-0.396587\pi$
$983$	627.538			0.638391			0.319195	+	0.947689i	$0.396587\pi$
$984$		0			0
$985$	−215.739	+	1203.69i	−0.219024	+	1.22202i
$986$		−	2.68592i		−	0.00272406i
$987$		0			0
$988$			1197.72i			1.21227i
$989$		−	1396.49i		−	1.41203i
$990$		0			0
$991$	1140.06			1.15042			0.575209	−	0.818007i	$-0.304921\pi$
$991$	1140.06			1.15042			0.575209	+	0.818007i	$0.304921\pi$
$992$	116.823			0.117765
$993$		0			0
$994$	−12.7519			−0.0128289
$995$	183.009	−	1021.08i	0.183929	−	1.02621i
$996$		0			0
$997$			727.662i			0.729851i	0.931037	+	0.364926i	$0.118906\pi$
$997$			727.662i			0.729851i	−0.931037	+	0.364926i	$0.881094\pi$
$998$	576.579			0.577735
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.b.b.809.13		16
3.2	odd	2	inner	810.3.b.b.809.4		16
5.4	even	2	inner	810.3.b.b.809.3		16
9.2	odd	6		270.3.j.b.179.6		16
9.4	even	3		270.3.j.b.89.1		16
9.5	odd	6		90.3.j.b.29.5	yes	16
9.7	even	3		90.3.j.b.59.4	yes	16
15.14	odd	2	inner	810.3.b.b.809.14		16
45.2	even	12		1350.3.i.e.1151.4		16
45.4	even	6		270.3.j.b.89.6		16
45.7	odd	12		450.3.i.e.401.6		16
45.13	odd	12		1350.3.i.e.251.5		16
45.14	odd	6		90.3.j.b.29.4	✓	16
45.22	odd	12		1350.3.i.e.251.4		16
45.23	even	12		450.3.i.e.101.3		16
45.29	odd	6		270.3.j.b.179.1		16
45.32	even	12		450.3.i.e.101.6		16
45.34	even	6		90.3.j.b.59.5	yes	16
45.38	even	12		1350.3.i.e.1151.5		16
45.43	odd	12		450.3.i.e.401.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.j.b.29.4	✓	16	45.14	odd	6
90.3.j.b.29.5	yes	16	9.5	odd	6
90.3.j.b.59.4	yes	16	9.7	even	3
90.3.j.b.59.5	yes	16	45.34	even	6
270.3.j.b.89.1		16	9.4	even	3
270.3.j.b.89.6		16	45.4	even	6
270.3.j.b.179.1		16	45.29	odd	6
270.3.j.b.179.6		16	9.2	odd	6
450.3.i.e.101.3		16	45.23	even	12
450.3.i.e.101.6		16	45.32	even	12
450.3.i.e.401.3		16	45.43	odd	12
450.3.i.e.401.6		16	45.7	odd	12
810.3.b.b.809.3		16	5.4	even	2	inner
810.3.b.b.809.4		16	3.2	odd	2	inner
810.3.b.b.809.13		16	1.1	even	1	trivial
810.3.b.b.809.14		16	15.14	odd	2	inner
1350.3.i.e.251.4		16	45.22	odd	12
1350.3.i.e.251.5		16	45.13	odd	12
1350.3.i.e.1151.4		16	45.2	even	12
1350.3.i.e.1151.5		16	45.38	even	12

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +2.00000 q^{4} +(0.882096 - 4.92158i) q^{5} +8.76643i q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+1.41421 q^{2} +2.00000 q^{4} +(0.882096 - 4.92158i) q^{5} +8.76643i q^{7} +2.82843 q^{8} +(1.24747 - 6.96016i) q^{10} -13.4435i q^{11} +17.2428i q^{13} +12.3976i q^{14} +4.00000 q^{16} +0.183062 q^{17} +34.7310 q^{19} +(1.76419 - 9.84315i) q^{20} -19.0120i q^{22} +34.4211 q^{23} +(-23.4438 - 8.68261i) q^{25} +24.3850i q^{26} +17.5329i q^{28} -10.3748i q^{29} +20.6516 q^{31} +5.65685 q^{32} +0.258889 q^{34} +(43.1447 + 7.73284i) q^{35} -8.75453i q^{37} +49.1171 q^{38} +(2.49495 - 13.9203i) q^{40} -1.57758i q^{41} -40.5709i q^{43} -26.8871i q^{44} +48.6787 q^{46} -30.9907 q^{47} -27.8503 q^{49} +(-33.1546 - 12.2791i) q^{50} +34.4856i q^{52} +21.1989 q^{53} +(-66.1634 - 11.8585i) q^{55} +24.7952i q^{56} -14.6722i q^{58} +30.2162i q^{59} +72.6660 q^{61} +29.2057 q^{62} +8.00000 q^{64} +(84.8617 + 15.2098i) q^{65} +6.55995i q^{67} +0.366125 q^{68} +(61.0158 + 10.9359i) q^{70} +1.02858i q^{71} -16.8284i q^{73} -12.3808i q^{74} +69.4620 q^{76} +117.852 q^{77} -83.1641 q^{79} +(3.52839 - 19.6863i) q^{80} -2.23103i q^{82} -2.31619 q^{83} +(0.161479 - 0.900955i) q^{85} -57.3759i q^{86} -38.0241i q^{88} -137.546i q^{89} -151.158 q^{91} +68.8421 q^{92} -43.8275 q^{94} +(30.6361 - 170.931i) q^{95} +54.0828i q^{97} -39.3863 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} - 16 q^{10} + 64 q^{16} + 144 q^{19} - 12 q^{25} - 56 q^{31} + 272 q^{34} - 32 q^{40} - 56 q^{46} - 24 q^{49} + 20 q^{55} - 136 q^{61} + 128 q^{64} + 224 q^{70} + 288 q^{76} - 840 q^{79} + 272 q^{85} - 168 q^{91} + 328 q^{94}+O(q^{100}) \) 16 * q + 32 * q^4 - 16 * q^10 + 64 * q^16 + 144 * q^19 - 12 * q^25 - 56 * q^31 + 272 * q^34 - 32 * q^40 - 56 * q^46 - 24 * q^49 + 20 * q^55 - 136 * q^61 + 128 * q^64 + 224 * q^70 + 288 * q^76 - 840 * q^79 + 272 * q^85 - 168 * q^91 + 328 * q^94

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