LMFDB - Embedded newform 855.2.c.d.514.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(514,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("855.514");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.c (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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.16516096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 13x^{2} + 1 $ x^6 + 9x^4 + 13x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			514.2
Root			$-2.68667i$ of defining polynomial
Character	$\chi$	$=$	855.514
Dual form			855.2.c.d.514.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82254i q^{2} -1.32164 q^{4} +(-1.94827 + 1.09737i) q^{5} +1.45033i q^{7} -1.23634i q^{8} +O(q^{10})$	\(q-1.82254i q^{2} -1.32164 q^{4} +(-1.94827 + 1.09737i) q^{5} +1.45033i q^{7} -1.23634i q^{8} +(2.00000 + 3.55080i) q^{10} +3.89655 q^{11} -3.05888i q^{13} +2.64327 q^{14} -4.89655 q^{16} -3.92301i q^{17} +1.00000 q^{19} +(2.57491 - 1.45033i) q^{20} -7.10160i q^{22} -5.37334i q^{23} +(2.59155 - 4.27596i) q^{25} -5.57491 q^{26} -1.91681i q^{28} +6.00000 q^{29} -8.43637 q^{31} +6.45146i q^{32} -7.14982 q^{34} +(-1.59155 - 2.82564i) q^{35} -5.95953i q^{37} -1.82254i q^{38} +(1.35673 + 2.40873i) q^{40} -10.4364 q^{41} +1.45033i q^{43} -5.14982 q^{44} -9.79310 q^{46} -4.90686i q^{47} +4.89655 q^{49} +(-7.79310 - 4.72319i) q^{50} +4.04272i q^{52} -4.23127i q^{53} +(-7.59155 + 4.27596i) q^{55} +1.79310 q^{56} -10.9352i q^{58} +3.35673 q^{59} +10.3329 q^{61} +15.3756i q^{62} +1.96491 q^{64} +(3.35673 + 5.95953i) q^{65} -9.84404i q^{67} +5.18479i q^{68} +(-5.14982 + 2.90066i) q^{70} -8.64327 q^{71} +2.43418i q^{73} -10.8615 q^{74} -1.32164 q^{76} +5.65127i q^{77} +12.4364 q^{79} +(9.53982 - 5.37334i) q^{80} +19.0207i q^{82} +12.6635i q^{83} +(4.30500 + 7.64310i) q^{85} +2.64327 q^{86} -4.81746i q^{88} +12.3662 q^{89} +4.43637 q^{91} +7.10160i q^{92} -8.94292 q^{94} +(-1.94827 + 1.09737i) q^{95} +3.05888i q^{97} -8.92414i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 8 q^{4} + q^{5}+O(q^{10}) $ 6 * q - 8 * q^4 + q^5	$ 6 q - 8 q^{4} + q^{5} + 12 q^{10} - 2 q^{11} + 16 q^{14} - 4 q^{16} + 6 q^{19} - 10 q^{20} + 3 q^{25} - 8 q^{26} + 36 q^{29} + 8 q^{34} + 3 q^{35} + 8 q^{40} - 12 q^{41} + 20 q^{44} - 8 q^{46} + 4 q^{49} + 4 q^{50} - 33 q^{55} - 40 q^{56} + 20 q^{59} - 14 q^{61} + 12 q^{64} + 20 q^{65} + 20 q^{70} - 52 q^{71} - 40 q^{74} - 8 q^{76} + 24 q^{79} + 32 q^{80} + 13 q^{85} + 16 q^{86} + 24 q^{89} - 24 q^{91} + 48 q^{94} + q^{95}+O(q^{100}) $ 6 * q - 8 * q^4 + q^5 + 12 * q^10 - 2 * q^11 + 16 * q^14 - 4 * q^16 + 6 * q^19 - 10 * q^20 + 3 * q^25 - 8 * q^26 + 36 * q^29 + 8 * q^34 + 3 * q^35 + 8 * q^40 - 12 * q^41 + 20 * q^44 - 8 * q^46 + 4 * q^49 + 4 * q^50 - 33 * q^55 - 40 * q^56 + 20 * q^59 - 14 * q^61 + 12 * q^64 + 20 * q^65 + 20 * q^70 - 52 * q^71 - 40 * q^74 - 8 * q^76 + 24 * q^79 + 32 * q^80 + 13 * q^85 + 16 * q^86 + 24 * q^89 - 24 * q^91 + 48 * q^94 + q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.82254i		−	1.28873i	−0.764719	−	0.644364i	$-0.777122\pi$
$2$		−	1.82254i		−	1.28873i	0.764719	−	0.644364i	$-0.222878\pi$
$3$		0			0
$3$		0			0
$4$	−1.32164			−0.660819
$5$	−1.94827	+	1.09737i	−0.871295	+	0.490760i
$5$	−1.94827	+	1.09737i	−0.871295	+	0.490760i
$6$		0			0
$7$			1.45033i			0.548172i	0.961705	+	0.274086i	$0.0883754\pi$
$7$			1.45033i			0.548172i	−0.961705	+	0.274086i	$0.911625\pi$
$8$		−	1.23634i		−	0.437112i
$9$		0			0
$10$	2.00000	+	3.55080i	0.632456	+	1.12286i
$11$	3.89655			1.17485			0.587427	−	0.809277i	$-0.300141\pi$
$11$	3.89655			1.17485			0.587427	+	0.809277i	$0.300141\pi$
$12$		0			0
$13$		−	3.05888i		−	0.848380i	−0.905573	−	0.424190i	$-0.860559\pi$
$13$		−	3.05888i		−	0.848380i	0.905573	−	0.424190i	$-0.139441\pi$
$14$	2.64327			0.706445
$15$		0			0
$16$	−4.89655			−1.22414
$17$		−	3.92301i		−	0.951469i	−0.879589	−	0.475735i	$-0.842182\pi$
$17$		−	3.92301i		−	0.951469i	0.879589	−	0.475735i	$-0.157818\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	2.57491	−	1.45033i	0.575768	−	0.324303i
$21$		0			0
$22$		−	7.10160i		−	1.51407i
$23$		−	5.37334i		−	1.12042i	−0.828351	−	0.560209i	$-0.810721\pi$
$23$		−	5.37334i		−	1.12042i	0.828351	−	0.560209i	$-0.189279\pi$
$24$		0			0
$25$	2.59155	−	4.27596i	0.518310	−	0.855193i
$26$	−5.57491			−1.09333
$27$		0			0
$28$		−	1.91681i		−	0.362242i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−8.43637			−1.51522			−0.757609	−	0.652709i	$-0.773632\pi$
$31$	−8.43637			−1.51522			−0.757609	+	0.652709i	$0.773632\pi$
$32$			6.45146i			1.14047i
$33$		0			0
$34$	−7.14982			−1.22618
$35$	−1.59155	−	2.82564i	−0.269021	−	0.477620i
$36$		0			0
$37$		−	5.95953i		−	0.979741i	−0.871795	−	0.489871i	$-0.837044\pi$
$37$		−	5.95953i		−	0.979741i	0.871795	−	0.489871i	$-0.162956\pi$
$38$		−	1.82254i		−	0.295654i
$39$		0			0
$40$	1.35673	+	2.40873i	0.214517	+	0.380854i
$41$	−10.4364			−1.62989			−0.814944	−	0.579540i	$-0.803232\pi$
$41$	−10.4364			−1.62989			−0.814944	+	0.579540i	$0.803232\pi$
$42$		0			0
$43$			1.45033i			0.221173i	0.993867	+	0.110586i	$0.0352729\pi$
$43$			1.45033i			0.221173i	−0.993867	+	0.110586i	$0.964727\pi$
$44$	−5.14982			−0.776365
$45$		0			0
$46$	−9.79310			−1.44391
$47$		−	4.90686i		−	0.715739i	−0.933772	−	0.357869i	$-0.883503\pi$
$47$		−	4.90686i		−	0.715739i	0.933772	−	0.357869i	$-0.116497\pi$
$48$		0			0
$49$	4.89655			0.699507
$50$	−7.79310	−	4.72319i	−1.10211	−	0.667960i
$51$		0			0
$52$			4.04272i			0.560625i
$53$		−	4.23127i		−	0.581209i	−0.956843	−	0.290605i	$-0.906144\pi$
$53$		−	4.23127i		−	0.581209i	0.956843	−	0.290605i	$-0.0938564\pi$
$54$		0			0
$55$	−7.59155	+	4.27596i	−1.02364	+	0.576571i
$56$	1.79310			0.239613
$57$		0			0
$58$		−	10.9352i		−	1.43586i
$59$	3.35673			0.437008			0.218504	−	0.975836i	$-0.429882\pi$
$59$	3.35673			0.437008			0.218504	+	0.975836i	$0.429882\pi$
$60$		0			0
$61$	10.3329			1.32300			0.661498	−	0.749947i	$-0.269921\pi$
$61$	10.3329			1.32300			0.661498	+	0.749947i	$0.269921\pi$
$62$			15.3756i			1.95270i
$63$		0			0
$64$	1.96491			0.245614
$65$	3.35673	+	5.95953i	0.416351	+	0.739189i
$66$		0			0
$67$		−	9.84404i		−	1.20264i	−0.799008	−	0.601320i	$-0.794642\pi$
$67$		−	9.84404i		−	1.20264i	0.799008	−	0.601320i	$-0.205358\pi$
$68$			5.18479i			0.628749i
$69$		0			0
$70$	−5.14982	+	2.90066i	−0.615522	+	0.346695i
$71$	−8.64327			−1.02577			−0.512884	−	0.858458i	$-0.671423\pi$
$71$	−8.64327			−1.02577			−0.512884	+	0.858458i	$0.671423\pi$
$72$		0			0
$73$			2.43418i			0.284899i	0.989802	+	0.142449i	$0.0454978\pi$
$73$			2.43418i			0.284899i	−0.989802	+	0.142449i	$0.954502\pi$
$74$	−10.8615			−1.26262
$75$		0			0
$76$	−1.32164			−0.151602
$77$			5.65127i			0.644022i
$78$		0			0
$79$	12.4364			1.39920			0.699601	−	0.714534i	$-0.253361\pi$
$79$	12.4364			1.39920			0.699601	+	0.714534i	$0.253361\pi$
$80$	9.53982	−	5.37334i	1.06658	−	0.600757i
$81$		0			0
$82$			19.0207i			2.10048i
$83$			12.6635i			1.39000i	0.719011	+	0.694999i	$0.244595\pi$
$83$			12.6635i			1.39000i	−0.719011	+	0.694999i	$0.755405\pi$
$84$		0			0
$85$	4.30500	+	7.64310i	0.466943	+	0.829011i
$86$	2.64327			0.285032
$87$		0			0
$88$		−	4.81746i		−	0.513543i
$89$	12.3662			1.31081			0.655407	−	0.755276i	$-0.272497\pi$
$89$	12.3662			1.31081			0.655407	+	0.755276i	$0.272497\pi$
$90$		0			0
$91$	4.43637			0.465058
$92$			7.10160i			0.740393i
$93$		0			0
$94$	−8.94292			−0.922392
$95$	−1.94827	+	1.09737i	−0.199889	+	0.112588i
$96$		0			0
$97$			3.05888i			0.310582i	0.987869	+	0.155291i	$0.0496315\pi$
$97$			3.05888i			0.310582i	−0.987869	+	0.155291i	$0.950369\pi$
$98$		−	8.92414i		−	0.901474i
$99$		0			0
$100$	−3.42509	+	5.65127i	−0.342509	+	0.565127i
$101$	−3.35673			−0.334007			−0.167003	−	0.985956i	$-0.553409\pi$
$101$	−3.35673			−0.334007			−0.167003	+	0.985956i	$0.553409\pi$
$102$		0			0
$103$		−	13.0611i		−	1.28695i	−0.765466	−	0.643476i	$-0.777492\pi$
$103$		−	13.0611i		−	1.28695i	0.765466	−	0.643476i	$-0.222508\pi$
$104$	−3.78181			−0.370837
$105$		0			0
$106$	−7.71164			−0.749020
$107$			5.77099i			0.557903i	0.960305	+	0.278951i	$0.0899868\pi$
$107$			5.77099i			0.557903i	−0.960305	+	0.278951i	$0.910013\pi$
$108$		0			0
$109$	−6.64327			−0.636310			−0.318155	−	0.948039i	$-0.603063\pi$
$109$	−6.64327			−0.636310			−0.318155	+	0.948039i	$0.603063\pi$
$110$	7.79310	+	13.8359i	0.743043	+	1.31920i
$111$		0			0
$112$		−	7.10160i		−	0.671038i
$113$		−	9.41606i		−	0.885789i	−0.896574	−	0.442894i	$-0.853952\pi$
$113$		−	9.41606i		−	0.885789i	0.896574	−	0.442894i	$-0.146048\pi$
$114$		0			0
$115$	5.89655	+	10.4687i	0.549856	+	0.976215i
$116$	−7.92982			−0.736266
$117$		0			0
$118$		−	6.11775i		−	0.563185i
$119$	5.68965			0.521569
$120$		0			0
$121$	4.18310			0.380282
$122$		−	18.8321i		−	1.70498i
$123$		0			0
$124$	11.1498			1.00128
$125$	−0.356726	+	11.1746i	−0.0319065	+	0.999491i
$126$		0			0
$127$			11.0934i			0.984383i	0.870487	+	0.492192i	$0.163804\pi$
$127$			11.0934i			0.984383i	−0.870487	+	0.492192i	$0.836196\pi$
$128$			9.32179i			0.823938i
$129$		0			0
$130$	10.8615	−	6.11775i	0.952613	−	0.536562i
$131$	−4.61000			−0.402778			−0.201389	−	0.979511i	$-0.564545\pi$
$131$	−4.61000			−0.402778			−0.201389	+	0.979511i	$0.564545\pi$
$132$		0			0
$133$			1.45033i			0.125759i
$134$	−17.9411			−1.54988
$135$		0			0
$136$	−4.85018			−0.415899
$137$			13.1808i			1.12612i	0.826417	+	0.563058i	$0.190375\pi$
$137$			13.1808i			1.12612i	−0.826417	+	0.563058i	$0.809625\pi$
$138$		0			0
$139$	−1.18310			−0.100349			−0.0501745	−	0.998740i	$-0.515978\pi$
$139$	−1.18310			−0.100349			−0.0501745	+	0.998740i	$0.515978\pi$
$140$	2.10345	+	3.73447i	0.177774	+	0.315620i
$141$		0			0
$142$			15.7527i			1.32194i
$143$		−	11.9191i		−	0.996722i
$144$		0			0
$145$	−11.6896	+	6.58423i	−0.970772	+	0.546791i
$146$	4.43637			0.367157
$147$		0			0
$148$			7.87634i			0.647431i
$149$	5.46018			0.447315			0.223658	−	0.974668i	$-0.428200\pi$
$149$	5.46018			0.447315			0.223658	+	0.974668i	$0.428200\pi$
$150$		0			0
$151$	−5.07965			−0.413376			−0.206688	−	0.978407i	$-0.566268\pi$
$151$	−5.07965			−0.413376			−0.206688	+	0.978407i	$0.566268\pi$
$152$		−	1.23634i		−	0.100280i
$153$		0			0
$154$	10.2996			0.829969
$155$	16.4364	−	9.25784i	1.32020	−	0.743608i
$156$		0			0
$157$			6.11775i			0.488250i	0.969744	+	0.244125i	$0.0785007\pi$
$157$			6.11775i			0.488250i	−0.969744	+	0.244125i	$0.921499\pi$
$158$		−	22.6657i		−	1.80319i
$159$		0			0
$160$	−7.07965	−	12.5692i	−0.559695	−	0.993683i
$161$	7.79310			0.614182
$162$		0			0
$163$			16.4365i			1.28740i	0.765277	+	0.643701i	$0.222602\pi$
$163$			16.4365i			1.28740i	−0.765277	+	0.643701i	$0.777398\pi$
$164$	13.7931			1.07706
$165$		0			0
$166$	23.0796			1.79133
$167$			3.80329i			0.294308i	0.989114	+	0.147154i	$0.0470112\pi$
$167$			3.80329i			0.294308i	−0.989114	+	0.147154i	$0.952989\pi$
$168$		0			0
$169$	3.64327			0.280252
$170$	13.9298	−	7.84602i	1.06837	−	0.601762i
$171$		0			0
$172$		−	1.91681i		−	0.146155i
$173$		−	11.3838i		−	0.865491i	−0.901516	−	0.432746i	$-0.857545\pi$
$173$		−	11.3838i		−	0.865491i	0.901516	−	0.432746i	$-0.142455\pi$
$174$		0			0
$175$	6.20155	+	3.75860i	0.468793	+	0.284123i
$176$	−19.0796			−1.43818
$177$		0			0
$178$		−	22.5378i		−	1.68928i
$179$	10.0702			0.752680			0.376340	−	0.926482i	$-0.377182\pi$
$179$	10.0702			0.752680			0.376340	+	0.926482i	$0.377182\pi$
$180$		0			0
$181$	0.573097			0.0425980			0.0212990	−	0.999773i	$-0.493220\pi$
$181$	0.573097			0.0425980			0.0212990	+	0.999773i	$0.493220\pi$
$182$		−	8.08545i		−	0.599333i
$183$		0			0
$184$	−6.64327			−0.489749
$185$	6.53982	+	11.6108i	0.480817	+	0.853643i
$186$		0			0
$187$		−	15.2862i		−	1.11784i
$188$			6.48509i			0.472973i
$189$		0			0
$190$	2.00000	+	3.55080i	0.145095	+	0.257602i
$191$	3.18310			0.230321			0.115160	−	0.993347i	$-0.463262\pi$
$191$	3.18310			0.230321			0.115160	+	0.993347i	$0.463262\pi$
$192$		0			0
$193$		−	3.05888i		−	0.220183i	−0.993921	−	0.110091i	$-0.964886\pi$
$193$		−	3.05888i		−	0.220183i	0.993921	−	0.110091i	$-0.0351143\pi$
$194$	5.57491			0.400255
$195$		0			0
$196$	−6.47146			−0.462247
$197$		−	21.4933i		−	1.53134i	−0.643235	−	0.765669i	$-0.722408\pi$
$197$		−	21.4933i		−	1.53134i	0.643235	−	0.765669i	$-0.277592\pi$
$198$		0			0
$199$	4.81690			0.341461			0.170731	−	0.985318i	$-0.445387\pi$
$199$	4.81690			0.341461			0.170731	+	0.985318i	$0.445387\pi$
$200$	−5.28655	−	3.20404i	−0.373815	−	0.226560i
$201$		0			0
$202$			6.11775i			0.430444i
$203$			8.70197i			0.610758i
$204$		0			0
$205$	20.3329	−	11.4526i	1.42011	−	0.799883i
$206$	−23.8044			−1.65853
$207$		0			0
$208$			14.9779i			1.03853i
$209$	3.89655			0.269530
$210$		0			0
$211$	10.5066			0.723301			0.361650	−	0.932314i	$-0.382213\pi$
$211$	10.5066			0.723301			0.361650	+	0.932314i	$0.382213\pi$
$212$			5.59220i			0.384074i
$213$		0			0
$214$	10.5178			0.718984
$215$	−1.59155	−	2.82564i	−0.108543	−	0.192707i
$216$		0			0
$217$		−	12.2355i		−	0.830600i
$218$			12.1076i			0.820031i
$219$		0			0
$220$	10.0333	−	5.65127i	0.676443	−	0.381009i
$221$	−12.0000			−0.807207
$222$		0			0
$223$			16.8947i			1.13136i	0.824626	+	0.565678i	$0.191385\pi$
$223$			16.8947i			1.13136i	−0.824626	+	0.565678i	$0.808615\pi$
$224$	−9.35673			−0.625173
$225$		0			0
$226$	−17.1611			−1.14154
$227$		−	17.1342i		−	1.13724i	−0.822602	−	0.568618i	$-0.807478\pi$
$227$		−	17.1342i		−	1.13724i	0.822602	−	0.568618i	$-0.192522\pi$
$228$		0			0
$229$	−25.0464			−1.65511			−0.827555	−	0.561384i	$-0.810269\pi$
$229$	−25.0464			−1.65511			−0.827555	+	0.561384i	$0.810269\pi$
$230$	19.0796	−	10.7467i	1.25807	−	0.708615i
$231$		0			0
$232$		−	7.41804i		−	0.487018i
$233$			19.2986i			1.26429i	0.774849	+	0.632147i	$0.217826\pi$
$233$			19.2986i			1.26429i	−0.774849	+	0.632147i	$0.782174\pi$
$234$		0			0
$235$	5.38465	+	9.55991i	0.351256	+	0.623620i
$236$	−4.43637			−0.288783
$237$		0			0
$238$		−	10.3696i		−	0.672161i
$239$	18.7693			1.21408			0.607042	−	0.794669i	$-0.292356\pi$
$239$	18.7693			1.21408			0.607042	+	0.794669i	$0.292356\pi$
$240$		0			0
$241$	−14.4364			−0.929929			−0.464964	−	0.885329i	$-0.653933\pi$
$241$	−14.4364			−0.929929			−0.464964	+	0.885329i	$0.653933\pi$
$242$		−	7.62385i		−	0.490079i
$243$		0			0
$244$	−13.6564			−0.874260
$245$	−9.53982	+	5.37334i	−0.609477	+	0.343290i
$246$		0			0
$247$		−	3.05888i		−	0.194632i
$248$			10.4302i			0.662320i
$249$		0			0
$250$	20.3662	+	0.650145i	1.28807	+	0.0411188i
$251$	10.9762			0.692811			0.346406	−	0.938085i	$-0.387402\pi$
$251$	10.9762			0.692811			0.346406	+	0.938085i	$0.387402\pi$
$252$		0			0
$253$		−	20.9375i		−	1.31633i
$254$	20.2182			1.26860
$255$		0			0
$256$	20.9191			1.30745
$257$			17.6392i			1.10030i	0.835066	+	0.550150i	$0.185430\pi$
$257$			17.6392i			1.10030i	−0.835066	+	0.550150i	$0.814570\pi$
$258$		0			0
$259$	8.64327			0.537067
$260$	−4.43637	−	7.87634i	−0.275132	−	0.488470i
$261$		0			0
$262$			8.40189i			0.519071i
$263$		−	1.68976i		−	0.104195i	−0.998642	−	0.0520975i	$-0.983409\pi$
$263$		−	1.68976i		−	0.104195i	0.998642	−	0.0520975i	$-0.0165907\pi$
$264$		0			0
$265$	4.64327	+	8.24367i	0.285234	+	0.506405i
$266$	2.64327			0.162070
$267$		0			0
$268$			13.0102i			0.794727i
$269$	−27.1022			−1.65245			−0.826226	−	0.563339i	$-0.809516\pi$
$269$	−27.1022			−1.65245			−0.826226	+	0.563339i	$0.809516\pi$
$270$		0			0
$271$	23.9524			1.45500			0.727502	−	0.686105i	$-0.240681\pi$
$271$	23.9524			1.45500			0.727502	+	0.686105i	$0.240681\pi$
$272$			19.2092i			1.16473i
$273$		0			0
$274$	24.0226			1.45126
$275$	10.0981	−	16.6615i	0.608938	−	1.00473i
$276$		0			0
$277$			8.23549i			0.494822i	0.968911	+	0.247411i	$0.0795799\pi$
$277$			8.23549i			0.494822i	−0.968911	+	0.247411i	$0.920420\pi$
$278$			2.15624i			0.129323i
$279$		0			0
$280$	−3.49345	+	1.96770i	−0.208774	+	0.117592i
$281$	10.4364			0.622582			0.311291	−	0.950315i	$-0.399239\pi$
$281$	10.4364			0.622582			0.311291	+	0.950315i	$0.399239\pi$
$282$		0			0
$283$			10.4687i			0.622302i	0.950361	+	0.311151i	$0.100714\pi$
$283$			10.4687i			0.622302i	−0.950361	+	0.311151i	$0.899286\pi$
$284$	11.4233			0.677847
$285$		0			0
$286$	−21.7229			−1.28450
$287$		−	15.1362i		−	0.893459i
$288$		0			0
$289$	1.61000			0.0947059
$290$	12.0000	+	21.3048i	0.704664	+	1.25106i
$291$		0			0
$292$		−	3.21710i		−	0.188266i
$293$		−	16.4668i		−	0.961999i	−0.876721	−	0.481000i	$-0.840274\pi$
$293$		−	16.4668i		−	0.961999i	0.876721	−	0.481000i	$-0.159726\pi$
$294$		0			0
$295$	−6.53982	+	3.68358i	−0.380763	+	0.214466i
$296$	−7.36801			−0.428257
$297$		0			0
$298$		−	9.95137i		−	0.576467i
$299$	−16.4364			−0.950540
$300$		0			0
$301$	−2.10345			−0.121241
$302$			9.25784i			0.532729i
$303$		0			0
$304$	−4.89655			−0.280836
$305$	−20.1314	+	11.3391i	−1.15272	+	0.649273i
$306$		0			0
$307$			7.87634i			0.449526i	0.974413	+	0.224763i	$0.0721609\pi$
$307$			7.87634i			0.449526i	−0.974413	+	0.224763i	$0.927839\pi$
$308$		−	7.46893i		−	0.425582i
$309$		0			0
$310$	−16.8727	−	29.9559i	−0.958308	−	1.70138i
$311$	−3.89655			−0.220953			−0.110477	−	0.993879i	$-0.535238\pi$
$311$	−3.89655			−0.220953			−0.110477	+	0.993879i	$0.535238\pi$
$312$		0			0
$313$		−	7.76901i		−	0.439130i	−0.975598	−	0.219565i	$-0.929536\pi$
$313$		−	7.76901i		−	0.439130i	0.975598	−	0.219565i	$-0.0704638\pi$
$314$	11.1498			0.629221
$315$		0			0
$316$	−16.4364			−0.924618
$317$		−	19.0510i		−	1.07001i	−0.844849	−	0.535005i	$-0.820310\pi$
$317$		−	19.0510i		−	1.07001i	0.844849	−	0.535005i	$-0.179690\pi$
$318$		0			0
$319$	23.3793			1.30899
$320$	−3.82819	+	2.15624i	−0.214002	+	0.120537i
$321$		0			0
$322$		−	14.2032i		−	0.791514i
$323$		−	3.92301i		−	0.218282i
$324$		0			0
$325$	−13.0796	−	7.92723i	−0.725528	−	0.439724i
$326$	29.9560			1.65911
$327$		0			0
$328$			12.9029i			0.712444i
$329$	7.11655			0.392348
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		−	16.7365i		−	0.918536i
$333$		0			0
$334$	6.93164			0.379282
$335$	10.8026	+	19.1789i	0.590207	+	1.04785i
$336$		0			0
$337$		−	6.89249i		−	0.375458i	−0.982221	−	0.187729i	$-0.939887\pi$
$337$		−	6.89249i		−	0.375458i	0.982221	−	0.187729i	$-0.0601127\pi$
$338$		−	6.64000i		−	0.361168i
$339$		0			0
$340$	−5.68965	−	10.1014i	−0.308565	−	0.547826i
$341$	−32.8727			−1.78016
$342$		0			0
$343$			17.2539i			0.931623i
$344$	1.79310			0.0966774
$345$		0			0
$346$	−20.7473			−1.11538
$347$			30.5503i			1.64002i	0.572346	+	0.820012i	$0.306033\pi$
$347$			30.5503i			1.64002i	−0.572346	+	0.820012i	$0.693967\pi$
$348$		0			0
$349$	−16.7693			−0.897640			−0.448820	−	0.893622i	$-0.648156\pi$
$349$	−16.7693			−0.897640			−0.448820	+	0.893622i	$0.648156\pi$
$350$	6.85018	−	11.3025i	0.366157	−	0.604147i
$351$		0			0
$352$			25.1384i			1.33988i
$353$			29.0999i			1.54883i	0.632676	+	0.774417i	$0.281956\pi$
$353$			29.0999i			1.54883i	−0.632676	+	0.774417i	$0.718044\pi$
$354$		0			0
$355$	16.8395	−	9.48489i	0.893746	−	0.503406i
$356$	−16.3436			−0.866210
$357$		0			0
$358$		−	18.3533i		−	0.970000i
$359$	−11.6896			−0.616956			−0.308478	−	0.951231i	$-0.599820\pi$
$359$	−11.6896			−0.616956			−0.308478	+	0.951231i	$0.599820\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	1.04449i		−	0.0548972i
$363$		0			0
$364$	−5.86328			−0.307319
$365$	−2.67120	−	4.74244i	−0.139817	−	0.248231i
$366$		0			0
$367$		−	4.20095i		−	0.219288i	−0.993971	−	0.109644i	$-0.965029\pi$
$367$		−	4.20095i		−	0.219288i	0.993971	−	0.109644i	$-0.0349710\pi$
$368$			26.3108i			1.37155i
$369$		0			0
$370$	21.1611	−	11.9191i	1.10011	−	0.619643i
$371$	6.13672			0.318603
$372$		0			0
$373$			16.9456i			0.877412i	0.898631	+	0.438706i	$0.144563\pi$
$373$			16.9456i			0.877412i	−0.898631	+	0.438706i	$0.855437\pi$
$374$	−27.8596			−1.44059
$375$		0			0
$376$	−6.06655			−0.312858
$377$		−	18.3533i		−	0.945241i
$378$		0			0
$379$	−10.3662			−0.532476			−0.266238	−	0.963907i	$-0.585781\pi$
$379$	−10.3662			−0.532476			−0.266238	+	0.963907i	$0.585781\pi$
$380$	2.57491	−	1.45033i	0.132090	−	0.0744002i
$381$		0			0
$382$		−	5.80131i		−	0.296821i
$383$			20.5907i			1.05214i	0.850442	+	0.526068i	$0.176334\pi$
$383$			20.5907i			1.05214i	−0.850442	+	0.526068i	$0.823666\pi$
$384$		0			0
$385$	−6.20155	−	11.0102i	−0.316060	−	0.561133i
$386$	−5.57491			−0.283756
$387$		0			0
$388$		−	4.04272i		−	0.205238i
$389$	8.10345			0.410861			0.205431	−	0.978672i	$-0.434141\pi$
$389$	8.10345			0.410861			0.205431	+	0.978672i	$0.434141\pi$
$390$		0			0
$391$	−21.0796			−1.06604
$392$		−	6.05380i		−	0.305763i
$393$		0			0
$394$	−39.1724			−1.97348
$395$	−24.2295	+	13.6473i	−1.21912	+	0.686672i
$396$		0			0
$397$			3.46891i			0.174100i	0.996204	+	0.0870499i	$0.0277440\pi$
$397$			3.46891i			0.174100i	−0.996204	+	0.0870499i	$0.972256\pi$
$398$		−	8.77898i		−	0.440050i
$399$		0			0
$400$	−12.6896	+	20.9375i	−0.634482	+	1.04687i
$401$	15.9524			0.796625			0.398312	−	0.917250i	$-0.369596\pi$
$401$	15.9524			0.796625			0.398312	+	0.917250i	$0.369596\pi$
$402$		0			0
$403$			25.8058i			1.28548i
$404$	4.43637			0.220718
$405$		0			0
$406$	15.8596			0.787101
$407$		−	23.2216i		−	1.15105i
$408$		0			0
$409$	3.92982			0.194317			0.0971586	−	0.995269i	$-0.469025\pi$
$409$	3.92982			0.194317			0.0971586	+	0.995269i	$0.469025\pi$
$410$	−20.8727	−	37.0575i	−1.03083	−	1.83014i
$411$		0			0
$412$			17.2621i			0.850442i
$413$			4.86835i			0.239556i
$414$		0			0
$415$	−13.8965	−	24.6719i	−0.682155	−	1.21110i
$416$	19.7342			0.967549
$417$		0			0
$418$		−	7.10160i		−	0.347351i
$419$	−34.2996			−1.67565			−0.837824	−	0.545941i	$-0.816172\pi$
$419$	−34.2996			−1.67565			−0.837824	+	0.545941i	$0.816172\pi$
$420$		0			0
$421$	−26.0891			−1.27151			−0.635753	−	0.771893i	$-0.719310\pi$
$421$	−26.0891			−1.27151			−0.635753	+	0.771893i	$0.719310\pi$
$422$		−	19.1486i		−	0.932138i
$423$		0			0
$424$	−5.23129			−0.254054
$425$	−16.7746	−	10.1667i	−0.813690	−	0.493156i
$426$		0			0
$427$			14.9861i			0.725229i
$428$		−	7.62715i		−	0.368672i
$429$		0			0
$430$	−5.14982	+	2.90066i	−0.248347	+	0.139882i
$431$	−10.2996			−0.496117			−0.248058	−	0.968745i	$-0.579792\pi$
$431$	−10.2996			−0.496117			−0.248058	+	0.968745i	$0.579792\pi$
$432$		0			0
$433$			36.2319i			1.74119i	0.491999	+	0.870596i	$0.336266\pi$
$433$			36.2319i			1.74119i	−0.491999	+	0.870596i	$0.663734\pi$
$434$	−22.2996			−1.07042
$435$		0			0
$436$	8.78000			0.420486
$437$		−	5.37334i		−	0.257042i
$438$		0			0
$439$	24.0891			1.14971			0.574855	−	0.818255i	$-0.305058\pi$
$439$	24.0891			1.14971			0.574855	+	0.818255i	$0.305058\pi$
$440$	5.28655	+	9.38574i	0.252026	+	0.447448i
$441$		0			0
$442$			21.8704i			1.04027i
$443$		−	5.52337i		−	0.262423i	−0.991354	−	0.131212i	$-0.958113\pi$
$443$		−	5.52337i		−	0.262423i	0.991354	−	0.131212i	$-0.0418868\pi$
$444$		0			0
$445$	−24.0927	+	13.5703i	−1.14211	+	0.643295i
$446$	30.7913			1.45801
$447$		0			0
$448$			2.84977i			0.134639i
$449$	7.92982			0.374231			0.187116	−	0.982338i	$-0.440086\pi$
$449$	7.92982			0.374231			0.187116	+	0.982338i	$0.440086\pi$
$450$		0			0
$451$	−40.6658			−1.91488
$452$			12.4446i			0.585346i
$453$		0			0
$454$	−31.2277			−1.46559
$455$	−8.64327	+	4.86835i	−0.405203	+	0.228232i
$456$		0			0
$457$		−	22.6534i		−	1.05968i	−0.848098	−	0.529840i	$-0.822252\pi$
$457$		−	22.6534i		−	1.05968i	0.848098	−	0.529840i	$-0.177748\pi$
$458$			45.6479i			2.13299i
$459$		0			0
$460$	−7.79310	−	13.8359i	−0.363355	−	0.645101i
$461$	−13.3900			−0.623634			−0.311817	−	0.950142i	$-0.600938\pi$
$461$	−13.3900			−0.623634			−0.311817	+	0.950142i	$0.600938\pi$
$462$		0			0
$463$			16.9029i			0.785546i	0.919635	+	0.392773i	$0.128484\pi$
$463$			16.9029i			0.785546i	−0.919635	+	0.392773i	$0.871516\pi$
$464$	−29.3793			−1.36390
$465$		0			0
$466$	35.1724			1.62933
$467$			22.2501i			1.02961i	0.857306	+	0.514807i	$0.172136\pi$
$467$			22.2501i			1.02961i	−0.857306	+	0.514807i	$0.827864\pi$
$468$		0			0
$469$	14.2771			0.659254
$470$	17.4233	−	9.81371i	0.803676	−	0.452673i
$471$		0			0
$472$		−	4.15006i		−	0.191022i
$473$			5.65127i			0.259846i
$474$		0			0
$475$	2.59155	−	4.27596i	0.118908	−	0.196195i
$476$	−7.51965			−0.344663
$477$		0			0
$478$		−	34.2077i		−	1.56462i
$479$	0.366196			0.0167319			0.00836597	−	0.999965i	$-0.497337\pi$
$479$	0.366196			0.0167319			0.00836597	+	0.999965i	$0.497337\pi$
$480$		0			0
$481$	−18.2295			−0.831192
$482$			26.3108i			1.19842i
$483$		0			0
$484$	−5.52854			−0.251297
$485$	−3.35673	−	5.95953i	−0.152421	−	0.270608i
$486$		0			0
$487$		−	26.8461i		−	1.21651i	−0.793740	−	0.608257i	$-0.791869\pi$
$487$		−	26.8461i		−	1.21651i	0.793740	−	0.608257i	$-0.208131\pi$
$488$		−	12.7750i		−	0.578298i
$489$		0			0
$490$	9.79310	+	17.3867i	0.442407	+	0.785450i
$491$	23.7266			1.07076			0.535382	−	0.844610i	$-0.320168\pi$
$491$	23.7266			1.07076			0.535382	+	0.844610i	$0.320168\pi$
$492$		0			0
$493$		−	23.5381i		−	1.06010i
$494$	−5.57491			−0.250827
$495$		0			0
$496$	41.3091			1.85483
$497$		−	12.5356i		−	0.562298i
$498$		0			0
$499$	−6.81690			−0.305166			−0.152583	−	0.988291i	$-0.548759\pi$
$499$	−6.81690			−0.305166			−0.152583	+	0.988291i	$0.548759\pi$
$500$	0.471462	−	14.7688i	0.0210844	−	0.660482i
$501$		0			0
$502$		−	20.0045i		−	0.892845i
$503$		−	23.4102i		−	1.04381i	−0.853004	−	0.521904i	$-0.825222\pi$
$503$		−	23.4102i		−	1.04381i	0.853004	−	0.521904i	$-0.174778\pi$
$504$		0			0
$505$	6.53982	−	3.68358i	0.291018	−	0.163917i
$506$	−38.1593			−1.69639
$507$		0			0
$508$		−	14.6615i		−	0.650499i
$509$	16.9204			0.749981			0.374991	−	0.927029i	$-0.377646\pi$
$509$	16.9204			0.749981			0.374991	+	0.927029i	$0.377646\pi$
$510$		0			0
$511$	−3.53035			−0.156174
$512$		−	19.4823i		−	0.861003i
$513$		0			0
$514$	32.1480			1.41799
$515$	14.3329	+	25.4467i	0.631584	+	1.12131i
$516$		0			0
$517$		−	19.1198i		−	0.840888i
$518$		−	15.7527i		−	0.692133i
$519$		0			0
$520$	7.36801	−	4.15006i	0.323109	−	0.181992i
$521$	3.49345			0.153051			0.0765254	−	0.997068i	$-0.475617\pi$
$521$	3.49345			0.153051			0.0765254	+	0.997068i	$0.475617\pi$
$522$		0			0
$523$			14.9271i			0.652714i	0.945247	+	0.326357i	$0.105821\pi$
$523$			14.9271i			0.652714i	−0.945247	+	0.326357i	$0.894179\pi$
$524$	6.09275			0.266163
$525$		0			0
$526$	−3.07965			−0.134279
$527$			33.0960i			1.44168i
$528$		0			0
$529$	−5.87275			−0.255337
$530$	15.0244	−	8.46253i	0.652618	−	0.367589i
$531$		0			0
$532$		−	1.91681i		−	0.0831041i
$533$			31.9236i			1.38276i
$534$		0			0
$535$	−6.33292	−	11.2435i	−0.273796	−	0.486098i
$536$	−12.1706			−0.525689
$537$		0			0
$538$			49.3948i			2.12956i
$539$	19.0796			0.821819
$540$		0			0
$541$	−12.6991			−0.545978			−0.272989	−	0.962017i	$-0.588012\pi$
$541$	−12.6991			−0.545978			−0.272989	+	0.962017i	$0.588012\pi$
$542$		−	43.6541i		−	1.87510i
$543$		0			0
$544$	25.3091			1.08512
$545$	12.9429	−	7.29014i	0.554414	−	0.312275i
$546$		0			0
$547$		−	31.8162i		−	1.36036i	−0.733043	−	0.680182i	$-0.761901\pi$
$547$		−	31.8162i		−	1.36036i	0.733043	−	0.680182i	$-0.238099\pi$
$548$		−	17.4203i		−	0.744158i
$549$		0			0
$550$	−30.3662	−	18.4041i	−1.29482	−	0.784756i
$551$	6.00000			0.255609
$552$		0			0
$553$			18.0368i			0.767003i
$554$	15.0095			0.637691
$555$		0			0
$556$	1.56363			0.0663125
$557$			9.64731i			0.408770i	0.978891	+	0.204385i	$0.0655194\pi$
$557$			9.64731i			0.408770i	−0.978891	+	0.204385i	$0.934481\pi$
$558$		0			0
$559$	4.43637			0.187639
$560$	7.79310	+	13.8359i	0.329319	+	0.584672i
$561$		0			0
$562$		−	19.0207i		−	0.802338i
$563$		−	4.28216i		−	0.180471i	−0.995920	−	0.0902357i	$-0.971238\pi$
$563$		−	4.28216i		−	0.180471i	0.995920	−	0.0902357i	$-0.0287620\pi$
$564$		0			0
$565$	10.3329	+	18.3451i	0.434709	+	0.771783i
$566$	19.0796			0.801977
$567$		0			0
$568$			10.6860i			0.448376i
$569$	42.2295			1.77035			0.885176	−	0.465257i	$-0.154038\pi$
$569$	42.2295			1.77035			0.885176	+	0.465257i	$0.154038\pi$
$570$		0			0
$571$	−19.2200			−0.804332			−0.402166	−	0.915567i	$-0.631743\pi$
$571$	−19.2200			−0.804332			−0.402166	+	0.915567i	$0.631743\pi$
$572$			15.7527i			0.658653i
$573$		0			0
$574$	−27.5862			−1.15143
$575$	−22.9762	−	13.9253i	−0.958174	−	0.580724i
$576$		0			0
$577$		−	40.7919i		−	1.69819i	−0.528239	−	0.849096i	$-0.677148\pi$
$577$		−	40.7919i		−	1.69819i	0.528239	−	0.849096i	$-0.322852\pi$
$578$		−	2.93428i		−	0.122050i
$579$		0			0
$580$	15.4495	−	8.70197i	0.641504	−	0.361329i
$581$	−18.3662			−0.761958
$582$		0			0
$583$		−	16.4873i		−	0.682836i
$584$	3.00947			0.124533
$585$		0			0
$586$	−30.0113			−1.23975
$587$			31.8851i			1.31604i	0.753001	+	0.658019i	$0.228605\pi$
$587$			31.8851i			1.31604i	−0.753001	+	0.658019i	$0.771395\pi$
$588$		0			0
$589$	−8.43637			−0.347615
$590$	6.71345	+	11.9191i	0.276388	+	0.490700i
$591$		0			0
$592$			29.1811i			1.19934i
$593$		−	38.8973i		−	1.59732i	−0.601783	−	0.798660i	$-0.705543\pi$
$593$		−	38.8973i		−	1.59732i	0.601783	−	0.798660i	$-0.294457\pi$
$594$		0			0
$595$	−11.0850	+	6.24366i	−0.454441	+	0.255965i
$596$	−7.21637			−0.295594
$597$		0			0
$598$			29.9559i			1.22499i
$599$	28.1629			1.15071			0.575353	−	0.817905i	$-0.304865\pi$
$599$	28.1629			1.15071			0.575353	+	0.817905i	$0.304865\pi$
$600$		0			0
$601$	−5.56363			−0.226945			−0.113473	−	0.993541i	$-0.536197\pi$
$601$	−5.56363			−0.226945			−0.113473	+	0.993541i	$0.536197\pi$
$602$			3.83361i			0.156246i
$603$		0			0
$604$	6.71345			0.273166
$605$	−8.14982	+	4.59042i	−0.331337	+	0.186627i
$606$		0			0
$607$			33.9986i			1.37996i	0.723828	+	0.689980i	$0.242381\pi$
$607$			33.9986i			1.37996i	−0.723828	+	0.689980i	$0.757619\pi$
$608$			6.45146i			0.261641i
$609$		0			0
$610$	20.6658	+	36.6902i	0.836736	+	1.48554i
$611$	−15.0095			−0.607218
$612$		0			0
$613$		−	17.5703i		−	0.709659i	−0.934931	−	0.354830i	$-0.884539\pi$
$613$		−	17.5703i		−	0.709659i	0.934931	−	0.354830i	$-0.115461\pi$
$614$	14.3549			0.579317
$615$		0			0
$616$	6.98690			0.281510
$617$			13.0791i			0.526544i	0.964722	+	0.263272i	$0.0848016\pi$
$617$			13.0791i			0.526544i	−0.964722	+	0.263272i	$0.915198\pi$
$618$		0			0
$619$	18.9393			0.761234			0.380617	−	0.924733i	$-0.375712\pi$
$619$	18.9393			0.761234			0.380617	+	0.924733i	$0.375712\pi$
$620$	−21.7229	+	12.2355i	−0.872414	+	0.491390i
$621$		0			0
$622$			7.10160i			0.284748i
$623$			17.9350i			0.718552i
$624$		0			0
$625$	−11.5677	−	22.1627i	−0.462710	−	0.886510i
$626$	−14.1593			−0.565919
$627$		0			0
$628$		−	8.08545i		−	0.322645i
$629$	−23.3793			−0.932194
$630$		0			0
$631$	31.6896			1.26154			0.630772	−	0.775968i	$-0.282738\pi$
$631$	31.6896			1.26154			0.630772	+	0.775968i	$0.282738\pi$
$632$		−	15.3756i		−	0.611608i
$633$		0			0
$634$	−34.7211			−1.37895
$635$	−12.1736	−	21.6131i	−0.483096	−	0.857688i
$636$		0			0
$637$		−	14.9779i		−	0.593448i
$638$		−	42.6096i		−	1.68693i
$639$		0			0
$640$	−10.2295	−	18.1614i	−0.404355	−	0.717893i
$641$	−47.9750			−1.89490			−0.947449	−	0.319908i	$-0.896348\pi$
$641$	−47.9750			−1.89490			−0.947449	+	0.319908i	$0.896348\pi$
$642$		0			0
$643$			0.200927i			0.00792378i	0.999992	+	0.00396189i	$0.00126111\pi$
$643$			0.200927i			0.00792378i	−0.999992	+	0.00396189i	$0.998739\pi$
$644$	−10.2996			−0.405863
$645$		0			0
$646$	−7.14982			−0.281306
$647$		−	1.58798i		−	0.0624299i	−0.999513	−	0.0312150i	$-0.990062\pi$
$647$		−	1.58798i		−	0.0624299i	0.999513	−	0.0312150i	$-0.00993765\pi$
$648$		0			0
$649$	13.0796			0.513421
$650$	−14.4477	+	23.8381i	−0.566684	+	0.935008i
$651$		0			0
$652$		−	21.7230i		−	0.850739i
$653$		−	33.5624i		−	1.31340i	−0.754152	−	0.656700i	$-0.771952\pi$
$653$		−	33.5624i		−	1.31340i	0.754152	−	0.656700i	$-0.228048\pi$
$654$		0			0
$655$	8.98155	−	5.05889i	0.350938	−	0.197667i
$656$	51.1022			1.99521
$657$		0			0
$658$		−	12.9702i		−	0.505630i
$659$	15.3567			0.598213			0.299107	−	0.954220i	$-0.403311\pi$
$659$	15.3567			0.598213			0.299107	+	0.954220i	$0.403311\pi$
$660$		0			0
$661$	12.8026			0.497962			0.248981	−	0.968508i	$-0.419904\pi$
$661$	12.8026			0.497962			0.248981	+	0.968508i	$0.419904\pi$
$662$		−	14.5803i		−	0.566679i
$663$		0			0
$664$	15.6564			0.607585
$665$	−1.59155	−	2.82564i	−0.0617176	−	0.109573i
$666$		0			0
$667$		−	32.2400i		−	1.24834i
$668$		−	5.02657i		−	0.194484i
$669$		0			0
$670$	34.9542	−	19.6881i	1.35040	−	0.760617i
$671$	40.2627			1.55433
$672$		0			0
$673$		−	7.82545i		−	0.301649i	−0.988561	−	0.150824i	$-0.951807\pi$
$673$		−	7.82545i		−	0.301649i	0.988561	−	0.150824i	$-0.0481928\pi$
$674$	−12.5618			−0.483863
$675$		0			0
$676$	−4.81509			−0.185196
$677$		−	21.6516i		−	0.832137i	−0.909333	−	0.416069i	$-0.863408\pi$
$677$		−	21.6516i		−	0.832137i	0.909333	−	0.416069i	$-0.136592\pi$
$678$		0			0
$679$	−4.43637			−0.170252
$680$	9.44947	−	5.32245i	0.362371	−	0.204107i
$681$		0			0
$682$			59.9118i			2.29414i
$683$			6.38751i			0.244411i	0.992505	+	0.122206i	$0.0389967\pi$
$683$			6.38751i			0.244411i	−0.992505	+	0.122206i	$0.961003\pi$
$684$		0			0
$685$	−14.4643	−	25.6799i	−0.552652	−	0.981179i
$686$	31.4458			1.20061
$687$		0			0
$688$		−	7.10160i		−	0.270746i
$689$	−12.9429			−0.493086
$690$		0			0
$691$	44.4958			1.69270			0.846351	−	0.532626i	$-0.178795\pi$
$691$	44.4958			1.69270			0.846351	+	0.532626i	$0.178795\pi$
$692$			15.0452i			0.571933i
$693$		0			0
$694$	55.6789			2.11354
$695$	2.30500	−	1.29830i	0.0874336	−	0.0492473i
$696$		0			0
$697$			40.9420i			1.55079i
$698$			30.5626i			1.15681i
$699$		0			0
$700$	−8.19620	−	4.96750i	−0.309787	−	0.187754i
$701$	−17.5160			−0.661571			−0.330785	−	0.943706i	$-0.607314\pi$
$701$	−17.5160			−0.661571			−0.330785	+	0.943706i	$0.607314\pi$
$702$		0			0
$703$		−	5.95953i		−	0.224768i
$704$	7.65638			0.288560
$705$		0			0
$706$	53.0357			1.99602
$707$		−	4.86835i		−	0.183093i
$708$		0			0
$709$	−11.4269			−0.429146			−0.214573	−	0.976708i	$-0.568836\pi$
$709$	−11.4269			−0.429146			−0.214573	+	0.976708i	$0.568836\pi$
$710$	−17.2865	−	30.6905i	−0.648753	−	1.15180i
$711$		0			0
$712$		−	15.2888i		−	0.572973i
$713$			45.3315i			1.69768i
$714$		0			0
$715$	13.0796	+	23.2216i	0.489151	+	0.868439i
$716$	−13.3091			−0.497385
$717$		0			0
$718$			21.3048i			0.795088i
$719$	15.8965			0.592841			0.296421	−	0.955057i	$-0.404207\pi$
$719$	15.8965			0.592841			0.296421	+	0.955057i	$0.404207\pi$
$720$		0			0
$721$	18.9429			0.705471
$722$		−	1.82254i		−	0.0678278i
$723$		0			0
$724$	−0.757427			−0.0281495
$725$	15.5493	−	25.6558i	0.577486	−	0.952832i
$726$		0			0
$727$			41.9905i			1.55734i	0.627434	+	0.778670i	$0.284105\pi$
$727$			41.9905i			1.55734i	−0.627434	+	0.778670i	$0.715895\pi$
$728$		−	5.48487i		−	0.203283i
$729$		0			0
$730$	−8.64327	+	4.86835i	−0.319902	+	0.180186i
$731$	5.68965			0.210439
$732$		0			0
$733$			0.632884i			0.0233761i	0.999932	+	0.0116881i	$0.00372051\pi$
$733$			0.632884i			0.0233761i	−0.999932	+	0.0116881i	$0.996279\pi$
$734$	−7.65638			−0.282602
$735$		0			0
$736$	34.6658			1.27780
$737$		−	38.3578i		−	1.41293i
$738$		0			0
$739$	29.5493			1.08699			0.543494	−	0.839413i	$-0.317101\pi$
$739$	29.5493			1.08699			0.543494	+	0.839413i	$0.317101\pi$
$740$	−8.64327	−	15.3453i	−0.317733	−	0.564103i
$741$		0			0
$742$		−	11.1844i		−	0.410592i
$743$		−	31.3374i		−	1.14966i	−0.818274	−	0.574829i	$-0.805069\pi$
$743$		−	31.3374i		−	1.14966i	0.818274	−	0.574829i	$-0.194931\pi$
$744$		0			0
$745$	−10.6379	+	5.99184i	−0.389743	+	0.219524i
$746$	30.8840			1.13074
$747$		0			0
$748$			20.2028i			0.738688i
$749$	−8.36983			−0.305827
$750$		0			0
$751$	25.0131			0.912741			0.456371	−	0.889790i	$-0.349149\pi$
$751$	25.0131			0.912741			0.456371	+	0.889790i	$0.349149\pi$
$752$			24.0267i			0.876163i
$753$		0			0
$754$	−33.4495			−1.21816
$755$	9.89655	−	5.57426i	0.360172	−	0.202868i
$756$		0			0
$757$		−	32.0900i		−	1.16633i	−0.812354	−	0.583165i	$-0.801814\pi$
$757$		−	32.0900i		−	1.16633i	0.812354	−	0.583165i	$-0.198186\pi$
$758$			18.8928i			0.686216i
$759$		0			0
$760$	1.35673	+	2.40873i	0.0492136	+	0.0873739i
$761$	40.4922			1.46784			0.733921	−	0.679235i	$-0.237688\pi$
$761$	40.4922			1.46784			0.733921	+	0.679235i	$0.237688\pi$
$762$		0			0
$763$		−	9.63492i		−	0.348808i
$764$	−4.20690			−0.152200
$765$		0			0
$766$	37.5273			1.35592
$767$		−	10.2678i		−	0.370749i
$768$		0			0
$769$	−3.09398			−0.111572			−0.0557859	−	0.998443i	$-0.517766\pi$
$769$	−3.09398			−0.111572			−0.0557859	+	0.998443i	$0.517766\pi$
$770$	−20.0665	+	11.3025i	−0.723148	+	0.407316i
$771$		0			0
$772$			4.04272i			0.145501i
$773$		−	1.96350i		−	0.0706220i	−0.999376	−	0.0353110i	$-0.988758\pi$
$773$		−	1.96350i		−	0.0706220i	0.999376	−	0.0353110i	$-0.0112422\pi$
$774$		0			0
$775$	−21.8633	+	36.0736i	−0.785352	+	1.29580i
$776$	3.78181			0.135759
$777$		0			0
$778$		−	14.7688i		−	0.529488i
$779$	−10.4364			−0.373922
$780$		0			0
$781$	−33.6789			−1.20513
$782$			38.4184i			1.37384i
$783$		0			0
$784$	−23.9762			−0.856293
$785$	−6.71345	−	11.9191i	−0.239613	−	0.425410i
$786$		0			0
$787$		−	0.107331i		−	0.00382595i	−0.999998	−	0.00191297i	$-0.999391\pi$
$787$		−	0.107331i		−	0.00382595i	0.999998	−	0.00191297i	$-0.000608919\pi$
$788$			28.4064i			1.01194i
$789$		0			0
$790$	24.8727	+	44.1591i	0.884933	+	1.57111i
$791$	13.6564			0.485565
$792$		0			0
$793$		−	31.6071i		−	1.12240i
$794$	6.32222			0.224367
$795$		0			0
$796$	−6.36620			−0.225644
$797$			8.32068i			0.294734i	0.989082	+	0.147367i	$0.0470798\pi$
$797$			8.32068i			0.294734i	−0.989082	+	0.147367i	$0.952920\pi$
$798$		0			0
$799$	−19.2496			−0.681003
$800$	27.5862	+	16.7193i	0.975319	+	0.591115i
$801$		0			0
$802$		−	29.0738i		−	1.02663i
$803$			9.48489i			0.334714i
$804$		0			0
$805$	−15.1831	+	8.55193i	−0.535134	+	0.301416i
$806$	47.0320			1.65663
$807$		0			0
$808$			4.15006i			0.145998i
$809$	−27.6231			−0.971177			−0.485588	−	0.874188i	$-0.661395\pi$
$809$	−27.6231			−0.971177			−0.485588	+	0.874188i	$0.661395\pi$
$810$		0			0
$811$	23.0095			0.807972			0.403986	−	0.914765i	$-0.367624\pi$
$811$	23.0095			0.807972			0.403986	+	0.914765i	$0.367624\pi$
$812$		−	11.5008i		−	0.403600i
$813$		0			0
$814$	−42.3222			−1.48339
$815$	−18.0369	−	32.0227i	−0.631805	−	1.12171i
$816$		0			0
$817$			1.45033i			0.0507405i
$818$		−	7.16224i		−	0.250422i
$819$		0			0
$820$	−26.8727	+	15.1362i	−0.938437	+	0.528578i
$821$	−31.1355			−1.08664			−0.543318	−	0.839527i	$-0.682832\pi$
$821$	−31.1355			−1.08664			−0.543318	+	0.839527i	$0.682832\pi$
$822$		0			0
$823$		−	20.4201i		−	0.711800i	−0.934524	−	0.355900i	$-0.884174\pi$
$823$		−	20.4201i		−	0.711800i	0.934524	−	0.355900i	$-0.115826\pi$
$824$	−16.1480			−0.562543
$825$		0			0
$826$	8.87275			0.308722
$827$			0.902638i			0.0313878i	0.999877	+	0.0156939i	$0.00499573\pi$
$827$			0.902638i			0.0313878i	−0.999877	+	0.0156939i	$0.995004\pi$
$828$		0			0
$829$	13.4971			0.468773			0.234386	−	0.972143i	$-0.424692\pi$
$829$	13.4971			0.468773			0.234386	+	0.972143i	$0.424692\pi$
$830$	−44.9655	+	25.3270i	−1.56078	+	0.879112i
$831$		0			0
$832$		−	6.01042i		−	0.208374i
$833$		−	19.2092i		−	0.665560i
$834$		0			0
$835$	−4.17363	−	7.40986i	−0.144434	−	0.256429i
$836$	−5.14982			−0.178110
$837$		0			0
$838$			62.5123i			2.15945i
$839$	33.1022			1.14282			0.571408	−	0.820666i	$-0.306397\pi$
$839$	33.1022			1.14282			0.571408	+	0.820666i	$0.306397\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$			47.5484i			1.63862i
$843$		0			0
$844$	−13.8858			−0.477971
$845$	−7.09810	+	3.99803i	−0.244182	+	0.137536i
$846$		0			0
$847$			6.06686i			0.208460i
$848$			20.7186i			0.711480i
$849$		0			0
$850$	−18.5291	+	30.5724i	−0.635544	+	1.04862i
$851$	−32.0226			−1.09772
$852$		0			0
$853$		−	50.9097i		−	1.74312i	−0.490293	−	0.871558i	$-0.663110\pi$
$853$		−	50.9097i		−	1.74312i	0.490293	−	0.871558i	$-0.336890\pi$
$854$	27.3128			0.934623
$855$		0			0
$856$	7.13491			0.243866
$857$		−	21.2333i		−	0.725317i	−0.931922	−	0.362659i	$-0.881869\pi$
$857$		−	21.2333i		−	0.725317i	0.931922	−	0.362659i	$-0.118131\pi$
$858$		0			0
$859$	−29.4827			−1.00594			−0.502969	−	0.864304i	$-0.667759\pi$
$859$	−29.4827			−1.00594			−0.502969	+	0.864304i	$0.667759\pi$
$860$	2.10345	+	3.73447i	0.0717271	+	0.127344i
$861$		0			0
$862$			18.7715i			0.639359i
$863$			25.7755i			0.877408i	0.898632	+	0.438704i	$0.144562\pi$
$863$			25.7755i			0.877408i	−0.898632	+	0.438704i	$0.855438\pi$
$864$		0			0
$865$	12.4922	+	22.1787i	0.424748	+	0.754098i
$866$	66.0339			2.24392
$867$		0			0
$868$			16.1709i			0.548876i
$869$	48.4589			1.64386
$870$		0			0
$871$	−30.1117			−1.02030
$872$			8.21335i			0.278139i
$873$		0			0
$874$	−9.79310			−0.331257
$875$	−16.2069	−	0.517369i	−0.547893	−	0.0174903i
$876$		0			0
$877$			54.2687i			1.83252i	0.400581	+	0.916261i	$0.368808\pi$
$877$			54.2687i			1.83252i	−0.400581	+	0.916261i	$0.631192\pi$
$878$		−	43.9033i		−	1.48166i
$879$		0			0
$880$	37.1724	−	20.9375i	1.25308	−	0.705802i
$881$	28.4922			0.959927			0.479964	−	0.877288i	$-0.340650\pi$
$881$	28.4922			0.959927			0.479964	+	0.877288i	$0.340650\pi$
$882$		0			0
$883$		−	40.5264i		−	1.36382i	−0.731435	−	0.681911i	$-0.761149\pi$
$883$		−	40.5264i		−	1.36382i	0.731435	−	0.681911i	$-0.238851\pi$
$884$	15.8596			0.533418
$885$		0			0
$886$	−10.0665			−0.338192
$887$			11.4705i			0.385142i	0.981283	+	0.192571i	$0.0616826\pi$
$887$			11.4705i			0.385142i	−0.981283	+	0.192571i	$0.938317\pi$
$888$		0			0
$889$	−16.0891			−0.539612
$890$	24.7324	+	43.9099i	0.829032	+	1.47186i
$891$		0			0
$892$		−	22.3287i		−	0.747621i
$893$		−	4.90686i		−	0.164202i
$894$		0			0
$895$	−19.6195	+	11.0507i	−0.655807	+	0.369385i
$896$	−13.5197			−0.451660
$897$		0			0
$898$		−	14.4524i		−	0.482282i
$899$	−50.6182			−1.68821
$900$		0			0
$901$	−16.5993			−0.553003
$902$			74.1150i			2.46776i
$903$		0			0
$904$	−11.6415			−0.387189
$905$	−1.11655	+	0.628901i	−0.0371154	+	0.0209054i
$906$		0			0
$907$		−	48.1000i		−	1.59714i	−0.601905	−	0.798568i	$-0.705591\pi$
$907$		−	48.1000i		−	1.59714i	0.601905	−	0.798568i	$-0.294409\pi$
$908$			22.6452i			0.751506i
$909$		0			0
$910$	8.87275	+	15.7527i	0.294129	+	0.522196i
$911$	12.8062			0.424288			0.212144	−	0.977238i	$-0.431955\pi$
$911$	12.8062			0.424288			0.212144	+	0.977238i	$0.431955\pi$
$912$		0			0
$913$			49.3439i			1.63304i
$914$	−41.2865			−1.36564
$915$		0			0
$916$	33.1022			1.09373
$917$		−	6.68601i		−	0.220792i
$918$		0			0
$919$	38.7135			1.27704			0.638519	−	0.769606i	$-0.279547\pi$
$919$	38.7135			1.27704			0.638519	+	0.769606i	$0.279547\pi$
$920$	12.9429	−	7.29014i	0.426716	−	0.240349i
$921$		0			0
$922$			24.4038i			0.803695i
$923$			26.4387i			0.870241i
$924$		0			0
$925$	−25.4827	−	15.4444i	−0.837868	−	0.507809i
$926$	30.8062			1.01235
$927$		0			0
$928$			38.7087i			1.27068i
$929$	−36.0189			−1.18174			−0.590872	−	0.806766i	$-0.701216\pi$
$929$	−36.0189			−1.18174			−0.590872	+	0.806766i	$0.701216\pi$
$930$		0			0
$931$	4.89655			0.160478
$932$		−	25.5058i		−	0.835469i
$933$		0			0
$934$	40.5517			1.32689
$935$	16.7746	+	29.7817i	0.548590	+	0.973966i
$936$		0			0
$937$			45.2421i			1.47799i	0.673709	+	0.738997i	$0.264700\pi$
$937$			45.2421i			1.47799i	−0.673709	+	0.738997i	$0.735300\pi$
$938$		−	26.0205i		−	0.849599i
$939$		0			0
$940$	−7.11655	−	12.6347i	−0.232116	−	0.412099i
$941$	11.7455			0.382892			0.191446	−	0.981503i	$-0.438682\pi$
$941$	11.7455			0.382892			0.191446	+	0.981503i	$0.438682\pi$
$942$		0			0
$943$			56.0781i			1.82616i
$944$	−16.4364			−0.534958
$945$		0			0
$946$	10.2996			0.334870
$947$		−	13.7752i		−	0.447635i	−0.974631	−	0.223817i	$-0.928148\pi$
$947$		−	13.7752i		−	0.447635i	0.974631	−	0.223817i	$-0.0718519\pi$
$948$		0			0
$949$	7.44584			0.241702
$950$	−7.79310	−	4.72319i	−0.252842	−	0.153241i
$951$		0			0
$952$		−	7.03434i		−	0.227984i
$953$		−	9.01421i		−	0.291999i	−0.989285	−	0.145999i	$-0.953360\pi$
$953$		−	9.01421i		−	0.291999i	0.989285	−	0.145999i	$-0.0466398\pi$
$954$		0			0
$955$	−6.20155	+	3.49304i	−0.200677	+	0.113032i
$956$	−24.8062			−0.802290
$957$		0			0
$958$		−	0.667406i		−	0.0215629i
$959$	−19.1166			−0.617306
$960$		0			0
$961$	40.1724			1.29588
$962$			33.2239i			1.07118i
$963$		0			0
$964$	19.0796			0.614514
$965$	3.35673	+	5.95953i	0.108057	+	0.191844i
$966$		0			0
$967$		−	30.3232i		−	0.975129i	−0.873087	−	0.487564i	$-0.837885\pi$
$967$		−	30.3232i		−	0.975129i	0.873087	−	0.487564i	$-0.162115\pi$
$968$		−	5.17173i		−	0.166226i
$969$		0			0
$970$	−10.8615	+	6.11775i	−0.348740	+	0.196429i
$971$	31.5636			1.01292			0.506462	−	0.862262i	$-0.330953\pi$
$971$	31.5636			1.01292			0.506462	+	0.862262i	$0.330953\pi$
$972$		0			0
$973$		−	1.71588i		−	0.0550086i
$974$	−48.9280			−1.56775
$975$		0			0
$976$	−50.5957			−1.61953
$977$			43.1285i			1.37980i	0.723903	+	0.689902i	$0.242346\pi$
$977$			43.1285i			1.37980i	−0.723903	+	0.689902i	$0.757654\pi$
$978$		0			0
$979$	48.1855			1.54002
$980$	12.6082	−	7.10160i	0.402754	−	0.226852i
$981$		0			0
$982$		−	43.2425i		−	1.37992i
$983$		−	7.81570i		−	0.249282i	−0.992202	−	0.124641i	$-0.960222\pi$
$983$		−	7.81570i		−	0.249282i	0.992202	−	0.124641i	$-0.0397779\pi$
$984$		0			0
$985$	23.5862	+	41.8749i	0.751519	+	1.33425i
$986$	−42.8989			−1.36618
$987$		0			0
$988$			4.04272i			0.128616i
$989$	7.79310			0.247806
$990$		0			0
$991$	−23.5197			−0.747126			−0.373563	−	0.927605i	$-0.621864\pi$
$991$	−23.5197			−0.747126			−0.373563	+	0.927605i	$0.621864\pi$
$992$		−	54.4269i		−	1.72806i
$993$		0			0
$994$	−22.8465			−0.724648
$995$	−9.38465	+	5.28593i	−0.297513	+	0.167575i
$996$		0			0
$997$			33.6395i			1.06537i	0.846313	+	0.532686i	$0.178817\pi$
$997$			33.6395i			1.06537i	−0.846313	+	0.532686i	$0.821183\pi$
$998$			12.4240i			0.393276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.c.d.514.2		6
3.2	odd	2		95.2.b.b.39.5	yes	6
5.2	odd	4		4275.2.a.br.1.5		6
5.3	odd	4		4275.2.a.br.1.2		6
5.4	even	2	inner	855.2.c.d.514.5		6
12.11	even	2		1520.2.d.h.609.5		6
15.2	even	4		475.2.a.j.1.2		6
15.8	even	4		475.2.a.j.1.5		6
15.14	odd	2		95.2.b.b.39.2	✓	6
57.56	even	2		1805.2.b.e.1084.2		6
60.23	odd	4		7600.2.a.ck.1.2		6
60.47	odd	4		7600.2.a.ck.1.5		6
60.59	even	2		1520.2.d.h.609.2		6
285.113	odd	4		9025.2.a.bx.1.2		6
285.227	odd	4		9025.2.a.bx.1.5		6
285.284	even	2		1805.2.b.e.1084.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.b.b.39.2	✓	6	15.14	odd	2
95.2.b.b.39.5	yes	6	3.2	odd	2
475.2.a.j.1.2		6	15.2	even	4
475.2.a.j.1.5		6	15.8	even	4
855.2.c.d.514.2		6	1.1	even	1	trivial
855.2.c.d.514.5		6	5.4	even	2	inner
1520.2.d.h.609.2		6	60.59	even	2
1520.2.d.h.609.5		6	12.11	even	2
1805.2.b.e.1084.2		6	57.56	even	2
1805.2.b.e.1084.5		6	285.284	even	2
4275.2.a.br.1.2		6	5.3	odd	4
4275.2.a.br.1.5		6	5.2	odd	4
7600.2.a.ck.1.2		6	60.23	odd	4
7600.2.a.ck.1.5		6	60.47	odd	4
9025.2.a.bx.1.2		6	285.113	odd	4
9025.2.a.bx.1.5		6	285.227	odd	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.82254i q^{2} -1.32164 q^{4} +(-1.94827 + 1.09737i) q^{5} +1.45033i q^{7} -1.23634i q^{8} +O(q^{10})\)	\(q-1.82254i q^{2} -1.32164 q^{4} +(-1.94827 + 1.09737i) q^{5} +1.45033i q^{7} -1.23634i q^{8} +(2.00000 + 3.55080i) q^{10} +3.89655 q^{11} -3.05888i q^{13} +2.64327 q^{14} -4.89655 q^{16} -3.92301i q^{17} +1.00000 q^{19} +(2.57491 - 1.45033i) q^{20} -7.10160i q^{22} -5.37334i q^{23} +(2.59155 - 4.27596i) q^{25} -5.57491 q^{26} -1.91681i q^{28} +6.00000 q^{29} -8.43637 q^{31} +6.45146i q^{32} -7.14982 q^{34} +(-1.59155 - 2.82564i) q^{35} -5.95953i q^{37} -1.82254i q^{38} +(1.35673 + 2.40873i) q^{40} -10.4364 q^{41} +1.45033i q^{43} -5.14982 q^{44} -9.79310 q^{46} -4.90686i q^{47} +4.89655 q^{49} +(-7.79310 - 4.72319i) q^{50} +4.04272i q^{52} -4.23127i q^{53} +(-7.59155 + 4.27596i) q^{55} +1.79310 q^{56} -10.9352i q^{58} +3.35673 q^{59} +10.3329 q^{61} +15.3756i q^{62} +1.96491 q^{64} +(3.35673 + 5.95953i) q^{65} -9.84404i q^{67} +5.18479i q^{68} +(-5.14982 + 2.90066i) q^{70} -8.64327 q^{71} +2.43418i q^{73} -10.8615 q^{74} -1.32164 q^{76} +5.65127i q^{77} +12.4364 q^{79} +(9.53982 - 5.37334i) q^{80} +19.0207i q^{82} +12.6635i q^{83} +(4.30500 + 7.64310i) q^{85} +2.64327 q^{86} -4.81746i q^{88} +12.3662 q^{89} +4.43637 q^{91} +7.10160i q^{92} -8.94292 q^{94} +(-1.94827 + 1.09737i) q^{95} +3.05888i q^{97} -8.92414i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 8 q^{4} + q^{5}+O(q^{10}) \) 6 * q - 8 * q^4 + q^5	\( 6 q - 8 q^{4} + q^{5} + 12 q^{10} - 2 q^{11} + 16 q^{14} - 4 q^{16} + 6 q^{19} - 10 q^{20} + 3 q^{25} - 8 q^{26} + 36 q^{29} + 8 q^{34} + 3 q^{35} + 8 q^{40} - 12 q^{41} + 20 q^{44} - 8 q^{46} + 4 q^{49} + 4 q^{50} - 33 q^{55} - 40 q^{56} + 20 q^{59} - 14 q^{61} + 12 q^{64} + 20 q^{65} + 20 q^{70} - 52 q^{71} - 40 q^{74} - 8 q^{76} + 24 q^{79} + 32 q^{80} + 13 q^{85} + 16 q^{86} + 24 q^{89} - 24 q^{91} + 48 q^{94} + q^{95}+O(q^{100}) \) 6 * q - 8 * q^4 + q^5 + 12 * q^10 - 2 * q^11 + 16 * q^14 - 4 * q^16 + 6 * q^19 - 10 * q^20 + 3 * q^25 - 8 * q^26 + 36 * q^29 + 8 * q^34 + 3 * q^35 + 8 * q^40 - 12 * q^41 + 20 * q^44 - 8 * q^46 + 4 * q^49 + 4 * q^50 - 33 * q^55 - 40 * q^56 + 20 * q^59 - 14 * q^61 + 12 * q^64 + 20 * q^65 + 20 * q^70 - 52 * q^71 - 40 * q^74 - 8 * q^76 + 24 * q^79 + 32 * q^80 + 13 * q^85 + 16 * q^86 + 24 * q^89 - 24 * q^91 + 48 * q^94 + q^95

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