LMFDB - Embedded newform 1710.2.d.e.1369.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1369,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, 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("1710.1369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.d (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.5
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.e.1369.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-0.311108 + 2.21432i) q^{5} +4.42864i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.311108 + 2.21432i) q^{5} +4.42864i q^{7} -1.00000i q^{8} +(-2.21432 - 0.311108i) q^{10} +5.80642 q^{11} +6.42864i q^{13} -4.42864 q^{14} +1.00000 q^{16} +3.37778i q^{17} +1.00000 q^{19} +(0.311108 - 2.21432i) q^{20} +5.80642i q^{22} -6.42864i q^{23} +(-4.80642 - 1.37778i) q^{25} -6.42864 q^{26} -4.42864i q^{28} +7.80642 q^{29} +9.05086 q^{31} +1.00000i q^{32} -3.37778 q^{34} +(-9.80642 - 1.37778i) q^{35} +3.67307i q^{37} +1.00000i q^{38} +(2.21432 + 0.311108i) q^{40} -4.42864 q^{41} +1.05086i q^{43} -5.80642 q^{44} +6.42864 q^{46} -5.18421i q^{47} -12.6128 q^{49} +(1.37778 - 4.80642i) q^{50} -6.42864i q^{52} -4.75557i q^{53} +(-1.80642 + 12.8573i) q^{55} +4.42864 q^{56} +7.80642i q^{58} +4.62222 q^{59} +2.00000 q^{61} +9.05086i q^{62} -1.00000 q^{64} +(-14.2351 - 2.00000i) q^{65} +2.75557i q^{67} -3.37778i q^{68} +(1.37778 - 9.80642i) q^{70} -7.61285 q^{71} -11.6128i q^{73} -3.67307 q^{74} -1.00000 q^{76} +25.7146i q^{77} -2.94914 q^{79} +(-0.311108 + 2.21432i) q^{80} -4.42864i q^{82} -0.133353i q^{83} +(-7.47949 - 1.05086i) q^{85} -1.05086 q^{86} -5.80642i q^{88} -3.18421 q^{89} -28.4701 q^{91} +6.42864i q^{92} +5.18421 q^{94} +(-0.311108 + 2.21432i) q^{95} -11.4193i q^{97} -12.6128i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^5	$ 6 q - 6 q^{4} - 2 q^{5} + 8 q^{11} + 6 q^{16} + 6 q^{19} + 2 q^{20} - 2 q^{25} - 12 q^{26} + 20 q^{29} + 28 q^{31} - 20 q^{34} - 32 q^{35} - 8 q^{44} + 12 q^{46} - 22 q^{49} + 8 q^{50} + 16 q^{55} + 28 q^{59} + 12 q^{61} - 6 q^{64} - 32 q^{65} + 8 q^{70} + 8 q^{71} + 4 q^{74} - 6 q^{76} - 44 q^{79} - 2 q^{80} + 8 q^{85} + 20 q^{86} + 8 q^{89} - 64 q^{91} + 4 q^{94} - 2 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^11 + 6 * q^16 + 6 * q^19 + 2 * q^20 - 2 * q^25 - 12 * q^26 + 20 * q^29 + 28 * q^31 - 20 * q^34 - 32 * q^35 - 8 * q^44 + 12 * q^46 - 22 * q^49 + 8 * q^50 + 16 * q^55 + 28 * q^59 + 12 * q^61 - 6 * q^64 - 32 * q^65 + 8 * q^70 + 8 * q^71 + 4 * q^74 - 6 * q^76 - 44 * q^79 - 2 * q^80 + 8 * q^85 + 20 * q^86 + 8 * q^89 - 64 * q^91 + 4 * q^94 - 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.311108	+	2.21432i	−0.139132	+	0.990274i
$5$	−0.311108	+	2.21432i	−0.139132	+	0.990274i
$6$		0			0
$7$			4.42864i			1.67387i	0.547304	+	0.836934i	$0.315654\pi$
$7$			4.42864i			1.67387i	−0.547304	+	0.836934i	$0.684346\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−2.21432	−	0.311108i	−0.700229	−	0.0983809i
$11$	5.80642			1.75070			0.875351	−	0.483487i	$-0.160630\pi$
$11$	5.80642			1.75070			0.875351	+	0.483487i	$0.160630\pi$
$12$		0			0
$13$			6.42864i			1.78298i	0.453037	+	0.891492i	$0.350341\pi$
$13$			6.42864i			1.78298i	−0.453037	+	0.891492i	$0.649659\pi$
$14$	−4.42864			−1.18360
$15$		0			0
$16$	1.00000			0.250000
$17$			3.37778i			0.819233i	0.912258	+	0.409617i	$0.134337\pi$
$17$			3.37778i			0.819233i	−0.912258	+	0.409617i	$0.865663\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	0.311108	−	2.21432i	0.0695658	−	0.495137i
$21$		0			0
$22$			5.80642i			1.23793i
$23$		−	6.42864i		−	1.34046i	−0.742152	−	0.670232i	$-0.766195\pi$
$23$		−	6.42864i		−	1.34046i	0.742152	−	0.670232i	$-0.233805\pi$
$24$		0			0
$25$	−4.80642	−	1.37778i	−0.961285	−	0.275557i
$26$	−6.42864			−1.26076
$27$		0			0
$28$		−	4.42864i		−	0.836934i
$29$	7.80642			1.44962			0.724808	−	0.688951i	$-0.241928\pi$
$29$	7.80642			1.44962			0.724808	+	0.688951i	$0.241928\pi$
$30$		0			0
$31$	9.05086			1.62558			0.812791	−	0.582556i	$-0.197947\pi$
$31$	9.05086			1.62558			0.812791	+	0.582556i	$0.197947\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−3.37778			−0.579285
$35$	−9.80642	−	1.37778i	−1.65759	−	0.232888i
$36$		0			0
$37$			3.67307i			0.603849i	0.953332	+	0.301925i	$0.0976291\pi$
$37$			3.67307i			0.603849i	−0.953332	+	0.301925i	$0.902371\pi$
$38$			1.00000i			0.162221i
$39$		0			0
$40$	2.21432	+	0.311108i	0.350115	+	0.0491905i
$41$	−4.42864			−0.691637			−0.345819	−	0.938301i	$-0.612399\pi$
$41$	−4.42864			−0.691637			−0.345819	+	0.938301i	$0.612399\pi$
$42$		0			0
$43$			1.05086i			0.160254i	0.996785	+	0.0801270i	$0.0255326\pi$
$43$			1.05086i			0.160254i	−0.996785	+	0.0801270i	$0.974467\pi$
$44$	−5.80642			−0.875351
$45$		0			0
$46$	6.42864			0.947851
$47$		−	5.18421i		−	0.756194i	−0.925766	−	0.378097i	$-0.876578\pi$
$47$		−	5.18421i		−	0.756194i	0.925766	−	0.378097i	$-0.123422\pi$
$48$		0			0
$49$	−12.6128			−1.80184
$50$	1.37778	−	4.80642i	0.194848	−	0.679731i
$51$		0			0
$52$		−	6.42864i		−	0.891492i
$53$		−	4.75557i		−	0.653228i	−0.945158	−	0.326614i	$-0.894092\pi$
$53$		−	4.75557i		−	0.653228i	0.945158	−	0.326614i	$-0.105908\pi$
$54$		0			0
$55$	−1.80642	+	12.8573i	−0.243578	+	1.73368i
$56$	4.42864			0.591802
$57$		0			0
$58$			7.80642i			1.02503i
$59$	4.62222			0.601761			0.300881	−	0.953662i	$-0.402719\pi$
$59$	4.62222			0.601761			0.300881	+	0.953662i	$0.402719\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$			9.05086i			1.14946i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−14.2351	−	2.00000i	−1.76564	−	0.248069i
$66$		0			0
$67$			2.75557i			0.336646i	0.985732	+	0.168323i	$0.0538352\pi$
$67$			2.75557i			0.336646i	−0.985732	+	0.168323i	$0.946165\pi$
$68$		−	3.37778i		−	0.409617i
$69$		0			0
$70$	1.37778	−	9.80642i	0.164677	−	1.17209i
$71$	−7.61285			−0.903479			−0.451739	−	0.892150i	$-0.649196\pi$
$71$	−7.61285			−0.903479			−0.451739	+	0.892150i	$0.649196\pi$
$72$		0			0
$73$		−	11.6128i		−	1.35918i	−0.733592	−	0.679591i	$-0.762157\pi$
$73$		−	11.6128i		−	1.35918i	0.733592	−	0.679591i	$-0.237843\pi$
$74$	−3.67307			−0.426986
$75$		0			0
$76$	−1.00000			−0.114708
$77$			25.7146i			2.93045i
$78$		0			0
$79$	−2.94914			−0.331805			−0.165902	−	0.986142i	$-0.553054\pi$
$79$	−2.94914			−0.331805			−0.165902	+	0.986142i	$0.553054\pi$
$80$	−0.311108	+	2.21432i	−0.0347829	+	0.247568i
$81$		0			0
$82$		−	4.42864i		−	0.489061i
$83$		−	0.133353i		−	0.0146374i	−0.999973	−	0.00731870i	$-0.997670\pi$
$83$		−	0.133353i		−	0.0146374i	0.999973	−	0.00731870i	$-0.00232964\pi$
$84$		0			0
$85$	−7.47949	−	1.05086i	−0.811265	−	0.113981i
$86$	−1.05086			−0.113317
$87$		0			0
$88$		−	5.80642i		−	0.618967i
$89$	−3.18421			−0.337525			−0.168763	−	0.985657i	$-0.553977\pi$
$89$	−3.18421			−0.337525			−0.168763	+	0.985657i	$0.553977\pi$
$90$		0			0
$91$	−28.4701			−2.98448
$92$			6.42864i			0.670232i
$93$		0			0
$94$	5.18421			0.534710
$95$	−0.311108	+	2.21432i	−0.0319190	+	0.227184i
$96$		0			0
$97$		−	11.4193i		−	1.15945i	−0.814812	−	0.579726i	$-0.803160\pi$
$97$		−	11.4193i		−	1.15945i	0.814812	−	0.579726i	$-0.196840\pi$
$98$		−	12.6128i		−	1.27409i
$99$		0			0
$100$	4.80642	+	1.37778i	0.480642	+	0.137778i
$101$	1.86665			0.185738			0.0928692	−	0.995678i	$-0.470396\pi$
$101$	1.86665			0.185738			0.0928692	+	0.995678i	$0.470396\pi$
$102$		0			0
$103$		−	10.6222i		−	1.04664i	−0.852137	−	0.523319i	$-0.824694\pi$
$103$		−	10.6222i		−	1.04664i	0.852137	−	0.523319i	$-0.175306\pi$
$104$	6.42864			0.630380
$105$		0			0
$106$	4.75557			0.461902
$107$		−	7.61285i		−	0.735962i	−0.929833	−	0.367981i	$-0.880049\pi$
$107$		−	7.61285i		−	0.735962i	0.929833	−	0.367981i	$-0.119951\pi$
$108$		0			0
$109$	−5.53972			−0.530609			−0.265304	−	0.964165i	$-0.585472\pi$
$109$	−5.53972			−0.530609			−0.265304	+	0.964165i	$0.585472\pi$
$110$	−12.8573	−	1.80642i	−1.22589	−	0.172236i
$111$		0			0
$112$			4.42864i			0.418467i
$113$			12.3684i			1.16352i	0.813360	+	0.581761i	$0.197636\pi$
$113$			12.3684i			1.16352i	−0.813360	+	0.581761i	$0.802364\pi$
$114$		0			0
$115$	14.2351	+	2.00000i	1.32743	+	0.186501i
$116$	−7.80642			−0.724808
$117$		0			0
$118$			4.62222i			0.425509i
$119$	−14.9590			−1.37129
$120$		0			0
$121$	22.7146			2.06496
$122$			2.00000i			0.181071i
$123$		0			0
$124$	−9.05086			−0.812791
$125$	4.54617	−	10.2143i	0.406622	−	0.913597i
$126$		0			0
$127$			1.76494i			0.156613i	0.996929	+	0.0783064i	$0.0249512\pi$
$127$			1.76494i			0.156613i	−0.996929	+	0.0783064i	$0.975049\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	2.00000	−	14.2351i	0.175412	−	1.24850i
$131$	−9.80642			−0.856791			−0.428396	−	0.903591i	$-0.640921\pi$
$131$	−9.80642			−0.856791			−0.428396	+	0.903591i	$0.640921\pi$
$132$		0			0
$133$			4.42864i			0.384012i
$134$	−2.75557			−0.238045
$135$		0			0
$136$	3.37778			0.289643
$137$		−	1.47949i		−	0.126402i	−0.998001	−	0.0632009i	$-0.979869\pi$
$137$		−	1.47949i		−	0.126402i	0.998001	−	0.0632009i	$-0.0201309\pi$
$138$		0			0
$139$	4.85728			0.411989			0.205995	−	0.978553i	$-0.433957\pi$
$139$	4.85728			0.411989			0.205995	+	0.978553i	$0.433957\pi$
$140$	9.80642	+	1.37778i	0.828794	+	0.116444i
$141$		0			0
$142$		−	7.61285i		−	0.638856i
$143$			37.3274i			3.12147i
$144$		0			0
$145$	−2.42864	+	17.2859i	−0.201688	+	1.43552i
$146$	11.6128			0.961086
$147$		0			0
$148$		−	3.67307i		−	0.301925i
$149$	4.62222			0.378667			0.189333	−	0.981913i	$-0.439367\pi$
$149$	4.62222			0.378667			0.189333	+	0.981913i	$0.439367\pi$
$150$		0			0
$151$	−11.4193			−0.929287			−0.464644	−	0.885498i	$-0.653818\pi$
$151$	−11.4193			−0.929287			−0.464644	+	0.885498i	$0.653818\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		0			0
$154$	−25.7146			−2.07214
$155$	−2.81579	+	20.0415i	−0.226170	+	1.60977i
$156$		0			0
$157$			7.37778i			0.588811i	0.955681	+	0.294406i	$0.0951217\pi$
$157$			7.37778i			0.588811i	−0.955681	+	0.294406i	$0.904878\pi$
$158$		−	2.94914i		−	0.234621i
$159$		0			0
$160$	−2.21432	−	0.311108i	−0.175057	−	0.0245952i
$161$	28.4701			2.24376
$162$		0			0
$163$			5.90813i			0.462761i	0.972863	+	0.231380i	$0.0743242\pi$
$163$			5.90813i			0.462761i	−0.972863	+	0.231380i	$0.925676\pi$
$164$	4.42864			0.345819
$165$		0			0
$166$	0.133353			0.0103502
$167$		−	2.75557i		−	0.213232i	−0.994300	−	0.106616i	$-0.965998\pi$
$167$		−	2.75557i		−	0.213232i	0.994300	−	0.106616i	$-0.0340016\pi$
$168$		0			0
$169$	−28.3274			−2.17903
$170$	1.05086	−	7.47949i	0.0805969	−	0.573651i
$171$		0			0
$172$		−	1.05086i		−	0.0801270i
$173$		−	8.10171i		−	0.615962i	−0.951393	−	0.307981i	$-0.900347\pi$
$173$		−	8.10171i		−	0.615962i	0.951393	−	0.307981i	$-0.0996533\pi$
$174$		0			0
$175$	6.10171	−	21.2859i	0.461246	−	1.60906i
$176$	5.80642			0.437676
$177$		0			0
$178$		−	3.18421i		−	0.238666i
$179$	−0.235063			−0.0175695			−0.00878473	−	0.999961i	$-0.502796\pi$
$179$	−0.235063			−0.0175695			−0.00878473	+	0.999961i	$0.502796\pi$
$180$		0			0
$181$	11.3176			0.841228			0.420614	−	0.907240i	$-0.361815\pi$
$181$	11.3176			0.841228			0.420614	+	0.907240i	$0.361815\pi$
$182$		−	28.4701i		−	2.11035i
$183$		0			0
$184$	−6.42864			−0.473926
$185$	−8.13335	−	1.14272i	−0.597976	−	0.0840145i
$186$		0			0
$187$			19.6128i			1.43423i
$188$			5.18421i			0.378097i
$189$		0			0
$190$	−2.21432	−	0.311108i	−0.160644	−	0.0225701i
$191$	6.32693			0.457801			0.228900	−	0.973450i	$-0.426487\pi$
$191$	6.32693			0.457801			0.228900	+	0.973450i	$0.426487\pi$
$192$		0			0
$193$		−	11.5397i		−	0.830647i	−0.909674	−	0.415324i	$-0.863668\pi$
$193$		−	11.5397i		−	0.830647i	0.909674	−	0.415324i	$-0.136332\pi$
$194$	11.4193			0.819856
$195$		0			0
$196$	12.6128			0.900918
$197$		−	20.0415i		−	1.42790i	−0.700198	−	0.713948i	$-0.746905\pi$
$197$		−	20.0415i		−	1.42790i	0.700198	−	0.713948i	$-0.253095\pi$
$198$		0			0
$199$	20.4701			1.45109			0.725544	−	0.688175i	$-0.241588\pi$
$199$	20.4701			1.45109			0.725544	+	0.688175i	$0.241588\pi$
$200$	−1.37778	+	4.80642i	−0.0974241	+	0.339865i
$201$		0			0
$202$			1.86665i			0.131337i
$203$			34.5718i			2.42647i
$204$		0			0
$205$	1.37778	−	9.80642i	0.0962286	−	0.684910i
$206$	10.6222			0.740085
$207$		0			0
$208$			6.42864i			0.445746i
$209$	5.80642			0.401639
$210$		0			0
$211$	2.75557			0.189701			0.0948506	−	0.995492i	$-0.469763\pi$
$211$	2.75557			0.189701			0.0948506	+	0.995492i	$0.469763\pi$
$212$			4.75557i			0.326614i
$213$		0			0
$214$	7.61285			0.520404
$215$	−2.32693	−	0.326929i	−0.158695	−	0.0222964i
$216$		0			0
$217$			40.0830i			2.72101i
$218$		−	5.53972i		−	0.375197i
$219$		0			0
$220$	1.80642	−	12.8573i	0.121789	−	0.866838i
$221$	−21.7146			−1.46068
$222$		0			0
$223$		−	10.6222i		−	0.711316i	−0.934616	−	0.355658i	$-0.884257\pi$
$223$		−	10.6222i		−	0.711316i	0.934616	−	0.355658i	$-0.115743\pi$
$224$	−4.42864			−0.295901
$225$		0			0
$226$	−12.3684			−0.822735
$227$		−	15.3461i		−	1.01856i	−0.860601	−	0.509280i	$-0.829912\pi$
$227$		−	15.3461i		−	1.01856i	0.860601	−	0.509280i	$-0.170088\pi$
$228$		0			0
$229$	19.7146			1.30277			0.651387	−	0.758745i	$-0.274187\pi$
$229$	19.7146			1.30277			0.651387	+	0.758745i	$0.274187\pi$
$230$	−2.00000	+	14.2351i	−0.131876	+	0.938632i
$231$		0			0
$232$		−	7.80642i		−	0.512517i
$233$		−	29.5625i		−	1.93670i	−0.249593	−	0.968351i	$-0.580297\pi$
$233$		−	29.5625i		−	1.93670i	0.249593	−	0.968351i	$-0.419703\pi$
$234$		0			0
$235$	11.4795	+	1.61285i	0.748840	+	0.105211i
$236$	−4.62222			−0.300881
$237$		0			0
$238$		−	14.9590i		−	0.969647i
$239$	1.67307			0.108222			0.0541110	−	0.998535i	$-0.482768\pi$
$239$	1.67307			0.108222			0.0541110	+	0.998535i	$0.482768\pi$
$240$		0			0
$241$	−16.9590			−1.09242			−0.546212	−	0.837647i	$-0.683931\pi$
$241$	−16.9590			−1.09242			−0.546212	+	0.837647i	$0.683931\pi$
$242$			22.7146i			1.46015i
$243$		0			0
$244$	−2.00000			−0.128037
$245$	3.92396	−	27.9289i	0.250692	−	1.78431i
$246$		0			0
$247$			6.42864i			0.409045i
$248$		−	9.05086i		−	0.574730i
$249$		0			0
$250$	10.2143	+	4.54617i	0.646010	+	0.287525i
$251$	−4.94914			−0.312387			−0.156194	−	0.987726i	$-0.549922\pi$
$251$	−4.94914			−0.312387			−0.156194	+	0.987726i	$0.549922\pi$
$252$		0			0
$253$		−	37.3274i		−	2.34675i
$254$	−1.76494			−0.110742
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	5.34614i		−	0.333483i	−0.986001	−	0.166742i	$-0.946675\pi$
$257$		−	5.34614i		−	0.333483i	0.986001	−	0.166742i	$-0.0533246\pi$
$258$		0			0
$259$	−16.2667			−1.01076
$260$	14.2351	+	2.00000i	0.882821	+	0.124035i
$261$		0			0
$262$		−	9.80642i		−	0.605843i
$263$		−	9.45091i		−	0.582768i	−0.956606	−	0.291384i	$-0.905884\pi$
$263$		−	9.45091i		−	0.582768i	0.956606	−	0.291384i	$-0.0941158\pi$
$264$		0			0
$265$	10.5303	+	1.47949i	0.646874	+	0.0908846i
$266$	−4.42864			−0.271537
$267$		0			0
$268$		−	2.75557i		−	0.168323i
$269$	2.94914			0.179813			0.0899063	−	0.995950i	$-0.471343\pi$
$269$	2.94914			0.179813			0.0899063	+	0.995950i	$0.471343\pi$
$270$		0			0
$271$	30.9590			1.88062			0.940312	−	0.340313i	$-0.110533\pi$
$271$	30.9590			1.88062			0.940312	+	0.340313i	$0.110533\pi$
$272$			3.37778i			0.204808i
$273$		0			0
$274$	1.47949			0.0893795
$275$	−27.9081	−	8.00000i	−1.68292	−	0.482418i
$276$		0			0
$277$		−	13.0923i		−	0.786643i	−0.919401	−	0.393321i	$-0.871326\pi$
$277$		−	13.0923i		−	0.786643i	0.919401	−	0.393321i	$-0.128674\pi$
$278$			4.85728i			0.291320i
$279$		0			0
$280$	−1.37778	+	9.80642i	−0.0823384	+	0.586046i
$281$	−18.5303			−1.10543			−0.552714	−	0.833371i	$-0.686408\pi$
$281$	−18.5303			−1.10543			−0.552714	+	0.833371i	$0.686408\pi$
$282$		0			0
$283$			26.3783i			1.56802i	0.620745	+	0.784012i	$0.286830\pi$
$283$			26.3783i			1.56802i	−0.620745	+	0.784012i	$0.713170\pi$
$284$	7.61285			0.451739
$285$		0			0
$286$	−37.3274			−2.20722
$287$		−	19.6128i		−	1.15771i
$288$		0			0
$289$	5.59057			0.328857
$290$	−17.2859	−	2.42864i	−1.01506	−	0.142615i
$291$		0			0
$292$			11.6128i			0.679591i
$293$		−	28.5718i		−	1.66918i	−0.550868	−	0.834592i	$-0.685703\pi$
$293$		−	28.5718i		−	1.66918i	0.550868	−	0.834592i	$-0.314297\pi$
$294$		0			0
$295$	−1.43801	+	10.2351i	−0.0837240	+	0.595908i
$296$	3.67307			0.213493
$297$		0			0
$298$			4.62222i			0.267758i
$299$	41.3274			2.39003
$300$		0			0
$301$	−4.65386			−0.268244
$302$		−	11.4193i		−	0.657105i
$303$		0			0
$304$	1.00000			0.0573539
$305$	−0.622216	+	4.42864i	−0.0356280	+	0.253583i
$306$		0			0
$307$			22.7556i			1.29873i	0.760477	+	0.649364i	$0.224965\pi$
$307$			22.7556i			1.29873i	−0.760477	+	0.649364i	$0.775035\pi$
$308$		−	25.7146i		−	1.46522i
$309$		0			0
$310$	−20.0415	−	2.81579i	−1.13828	−	0.159926i
$311$	6.32693			0.358767			0.179384	−	0.983779i	$-0.442590\pi$
$311$	6.32693			0.358767			0.179384	+	0.983779i	$0.442590\pi$
$312$		0			0
$313$			13.7146i			0.775193i	0.921829	+	0.387596i	$0.126695\pi$
$313$			13.7146i			0.775193i	−0.921829	+	0.387596i	$0.873305\pi$
$314$	−7.37778			−0.416352
$315$		0			0
$316$	2.94914			0.165902
$317$			32.5718i			1.82942i	0.404115	+	0.914708i	$0.367580\pi$
$317$			32.5718i			1.82942i	−0.404115	+	0.914708i	$0.632420\pi$
$318$		0			0
$319$	45.3274			2.53785
$320$	0.311108	−	2.21432i	0.0173915	−	0.123784i
$321$		0			0
$322$			28.4701i			1.58658i
$323$			3.37778i			0.187945i
$324$		0			0
$325$	8.85728	−	30.8988i	0.491313	−	1.71396i
$326$	−5.90813			−0.327221
$327$		0			0
$328$			4.42864i			0.244531i
$329$	22.9590			1.26577
$330$		0			0
$331$	5.63158			0.309540			0.154770	−	0.987951i	$-0.450536\pi$
$331$	5.63158			0.309540			0.154770	+	0.987951i	$0.450536\pi$
$332$			0.133353i			0.00731870i
$333$		0			0
$334$	2.75557			0.150778
$335$	−6.10171	−	0.857279i	−0.333372	−	0.0468382i
$336$		0			0
$337$			5.70471i			0.310756i	0.987855	+	0.155378i	$0.0496595\pi$
$337$			5.70471i			0.310756i	−0.987855	+	0.155378i	$0.950341\pi$
$338$		−	28.3274i		−	1.54081i
$339$		0			0
$340$	7.47949	+	1.05086i	0.405633	+	0.0569906i
$341$	52.5531			2.84591
$342$		0			0
$343$		−	24.8573i		−	1.34217i
$344$	1.05086			0.0566583
$345$		0			0
$346$	8.10171			0.435551
$347$			2.62222i			0.140768i	0.997520	+	0.0703840i	$0.0224224\pi$
$347$			2.62222i			0.140768i	−0.997520	+	0.0703840i	$0.977578\pi$
$348$		0			0
$349$	24.1017			1.29013			0.645067	−	0.764126i	$-0.276829\pi$
$349$	24.1017			1.29013			0.645067	+	0.764126i	$0.276829\pi$
$350$	21.2859	+	6.10171i	1.13778	+	0.326150i
$351$		0			0
$352$			5.80642i			0.309483i
$353$			3.64449i			0.193977i	0.995286	+	0.0969883i	$0.0309210\pi$
$353$			3.64449i			0.193977i	−0.995286	+	0.0969883i	$0.969079\pi$
$354$		0			0
$355$	2.36842	−	16.8573i	0.125702	−	0.894691i
$356$	3.18421			0.168763
$357$		0			0
$358$		−	0.235063i		−	0.0124235i
$359$	9.08250			0.479356			0.239678	−	0.970852i	$-0.422958\pi$
$359$	9.08250			0.479356			0.239678	+	0.970852i	$0.422958\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$			11.3176i			0.594838i
$363$		0			0
$364$	28.4701			1.49224
$365$	25.7146	+	3.61285i	1.34596	+	0.189105i
$366$		0			0
$367$			3.95851i			0.206633i	0.994649	+	0.103316i	$0.0329454\pi$
$367$			3.95851i			0.206633i	−0.994649	+	0.103316i	$0.967055\pi$
$368$		−	6.42864i		−	0.335116i
$369$		0			0
$370$	1.14272	−	8.13335i	0.0594072	−	0.422833i
$371$	21.0607			1.09342
$372$		0			0
$373$		−	12.5303i		−	0.648797i	−0.945921	−	0.324398i	$-0.894838\pi$
$373$		−	12.5303i		−	0.648797i	0.945921	−	0.324398i	$-0.105162\pi$
$374$	−19.6128			−1.01416
$375$		0			0
$376$	−5.18421			−0.267355
$377$			50.1847i			2.58464i
$378$		0			0
$379$	−26.8385			−1.37860			−0.689302	−	0.724474i	$-0.742083\pi$
$379$	−26.8385			−1.37860			−0.689302	+	0.724474i	$0.742083\pi$
$380$	0.311108	−	2.21432i	0.0159595	−	0.113592i
$381$		0			0
$382$			6.32693i			0.323714i
$383$			17.5111i			0.894777i	0.894340	+	0.447389i	$0.147646\pi$
$383$			17.5111i			0.894777i	−0.894340	+	0.447389i	$0.852354\pi$
$384$		0			0
$385$	−56.9403	−	8.00000i	−2.90194	−	0.407718i
$386$	11.5397			0.587356
$387$		0			0
$388$			11.4193i			0.579726i
$389$	−29.4795			−1.49467			−0.747335	−	0.664448i	$-0.768667\pi$
$389$	−29.4795			−1.49467			−0.747335	+	0.664448i	$0.768667\pi$
$390$		0			0
$391$	21.7146			1.09815
$392$			12.6128i			0.637045i
$393$		0			0
$394$	20.0415			1.00968
$395$	0.917502	−	6.53035i	0.0461645	−	0.328578i
$396$		0			0
$397$			9.21279i			0.462377i	0.972909	+	0.231188i	$0.0742613\pi$
$397$			9.21279i			0.462377i	−0.972909	+	0.231188i	$0.925739\pi$
$398$			20.4701i			1.02607i
$399$		0			0
$400$	−4.80642	−	1.37778i	−0.240321	−	0.0688892i
$401$	−29.2859			−1.46247			−0.731234	−	0.682126i	$-0.761055\pi$
$401$	−29.2859			−1.46247			−0.731234	+	0.682126i	$0.761055\pi$
$402$		0			0
$403$			58.1847i			2.89839i
$404$	−1.86665			−0.0928692
$405$		0			0
$406$	−34.5718			−1.71577
$407$			21.3274i			1.05716i
$408$		0			0
$409$	17.8796			0.884087			0.442044	−	0.896994i	$-0.354254\pi$
$409$	17.8796			0.884087			0.442044	+	0.896994i	$0.354254\pi$
$410$	9.80642	+	1.37778i	0.484305	+	0.0680439i
$411$		0			0
$412$			10.6222i			0.523319i
$413$			20.4701i			1.00727i
$414$		0			0
$415$	0.295286	+	0.0414872i	0.0144950	+	0.00203653i
$416$	−6.42864			−0.315190
$417$		0			0
$418$			5.80642i			0.284001i
$419$	30.8671			1.50796			0.753979	−	0.656899i	$-0.228132\pi$
$419$	30.8671			1.50796			0.753979	+	0.656899i	$0.228132\pi$
$420$		0			0
$421$	−18.3970			−0.896615			−0.448307	−	0.893879i	$-0.647973\pi$
$421$	−18.3970			−0.896615			−0.448307	+	0.893879i	$0.647973\pi$
$422$			2.75557i			0.134139i
$423$		0			0
$424$	−4.75557			−0.230951
$425$	4.65386	−	16.2351i	0.225745	−	0.787516i
$426$		0			0
$427$			8.85728i			0.428634i
$428$			7.61285i			0.367981i
$429$		0			0
$430$	0.326929	−	2.32693i	0.0157659	−	0.112214i
$431$	−29.5941			−1.42550			−0.712749	−	0.701419i	$-0.752550\pi$
$431$	−29.5941			−1.42550			−0.712749	+	0.701419i	$0.752550\pi$
$432$		0			0
$433$		−	27.2988i		−	1.31190i	−0.754805	−	0.655949i	$-0.772269\pi$
$433$		−	27.2988i		−	1.31190i	0.754805	−	0.655949i	$-0.227731\pi$
$434$	−40.0830			−1.92404
$435$		0			0
$436$	5.53972			0.265304
$437$		−	6.42864i		−	0.307524i
$438$		0			0
$439$	−9.64143			−0.460160			−0.230080	−	0.973172i	$-0.573899\pi$
$439$	−9.64143			−0.460160			−0.230080	+	0.973172i	$0.573899\pi$
$440$	12.8573	+	1.80642i	0.612947	+	0.0861179i
$441$		0			0
$442$		−	21.7146i		−	1.03286i
$443$			6.70519i			0.318573i	0.987232	+	0.159287i	$0.0509194\pi$
$443$			6.70519i			0.318573i	−0.987232	+	0.159287i	$0.949081\pi$
$444$		0			0
$445$	0.990632	−	7.05086i	0.0469605	−	0.334243i
$446$	10.6222			0.502976
$447$		0			0
$448$		−	4.42864i		−	0.209234i
$449$	−13.9398			−0.657859			−0.328929	−	0.944355i	$-0.606688\pi$
$449$	−13.9398			−0.657859			−0.328929	+	0.944355i	$0.606688\pi$
$450$		0			0
$451$	−25.7146			−1.21085
$452$		−	12.3684i		−	0.581761i
$453$		0			0
$454$	15.3461			0.720230
$455$	8.85728	−	63.0420i	0.415236	−	2.95545i
$456$		0			0
$457$			23.2257i			1.08645i	0.839586	+	0.543226i	$0.182797\pi$
$457$			23.2257i			1.08645i	−0.839586	+	0.543226i	$0.817203\pi$
$458$			19.7146i			0.921201i
$459$		0			0
$460$	−14.2351	−	2.00000i	−0.663713	−	0.0932505i
$461$	−19.9684			−0.930019			−0.465010	−	0.885306i	$-0.653949\pi$
$461$	−19.9684			−0.930019			−0.465010	+	0.885306i	$0.653949\pi$
$462$		0			0
$463$			2.79706i			0.129990i	0.997886	+	0.0649951i	$0.0207032\pi$
$463$			2.79706i			0.129990i	−0.997886	+	0.0649951i	$0.979297\pi$
$464$	7.80642			0.362404
$465$		0			0
$466$	29.5625			1.36945
$467$			30.9719i			1.43321i	0.697480	+	0.716604i	$0.254305\pi$
$467$			30.9719i			1.43321i	−0.697480	+	0.716604i	$0.745695\pi$
$468$		0			0
$469$	−12.2034			−0.563502
$470$	−1.61285	+	11.4795i	−0.0743951	+	0.529510i
$471$		0			0
$472$		−	4.62222i		−	0.212755i
$473$			6.10171i			0.280557i
$474$		0			0
$475$	−4.80642	−	1.37778i	−0.220534	−	0.0632171i
$476$	14.9590			0.685644
$477$		0			0
$478$			1.67307i			0.0765245i
$479$	29.8765			1.36509			0.682546	−	0.730843i	$-0.260873\pi$
$479$	29.8765			1.36509			0.682546	+	0.730843i	$0.260873\pi$
$480$		0			0
$481$	−23.6128			−1.07665
$482$		−	16.9590i		−	0.772461i
$483$		0			0
$484$	−22.7146			−1.03248
$485$	25.2859	+	3.55262i	1.14817	+	0.161316i
$486$		0			0
$487$			17.8479i			0.808766i	0.914590	+	0.404383i	$0.132514\pi$
$487$			17.8479i			0.808766i	−0.914590	+	0.404383i	$0.867486\pi$
$488$		−	2.00000i		−	0.0905357i
$489$		0			0
$490$	27.9289	+	3.92396i	1.26170	+	0.177266i
$491$	8.68244			0.391833			0.195916	−	0.980621i	$-0.437232\pi$
$491$	8.68244			0.391833			0.195916	+	0.980621i	$0.437232\pi$
$492$		0			0
$493$			26.3684i			1.18757i
$494$	−6.42864			−0.289238
$495$		0			0
$496$	9.05086			0.406395
$497$		−	33.7146i		−	1.51230i
$498$		0			0
$499$	−11.2257			−0.502531			−0.251266	−	0.967918i	$-0.580847\pi$
$499$	−11.2257			−0.502531			−0.251266	+	0.967918i	$0.580847\pi$
$500$	−4.54617	+	10.2143i	−0.203311	+	0.456798i
$501$		0			0
$502$		−	4.94914i		−	0.220891i
$503$		−	17.6543i		−	0.787168i	−0.919289	−	0.393584i	$-0.871235\pi$
$503$		−	17.6543i		−	0.787168i	0.919289	−	0.393584i	$-0.128765\pi$
$504$		0			0
$505$	−0.580728	+	4.13335i	−0.0258421	+	0.183932i
$506$	37.3274			1.65941
$507$		0			0
$508$		−	1.76494i		−	0.0783064i
$509$	14.1748			0.628289			0.314144	−	0.949375i	$-0.398282\pi$
$509$	14.1748			0.628289			0.314144	+	0.949375i	$0.398282\pi$
$510$		0			0
$511$	51.4291			2.27509
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	5.34614			0.235808
$515$	23.5210	+	3.30465i	1.03646	+	0.145620i
$516$		0			0
$517$		−	30.1017i		−	1.32387i
$518$		−	16.2667i		−	0.714718i
$519$		0			0
$520$	−2.00000	+	14.2351i	−0.0877058	+	0.624249i
$521$	15.0005			0.657183			0.328591	−	0.944472i	$-0.393426\pi$
$521$	15.0005			0.657183			0.328591	+	0.944472i	$0.393426\pi$
$522$		0			0
$523$		−	40.2864i		−	1.76160i	−0.473488	−	0.880801i	$-0.657005\pi$
$523$		−	40.2864i		−	1.76160i	0.473488	−	0.880801i	$-0.342995\pi$
$524$	9.80642			0.428396
$525$		0			0
$526$	9.45091			0.412079
$527$			30.5718i			1.33173i
$528$		0			0
$529$	−18.3274			−0.796844
$530$	−1.47949	+	10.5303i	−0.0642651	+	0.457409i
$531$		0			0
$532$		−	4.42864i		−	0.192006i
$533$		−	28.4701i		−	1.23318i
$534$		0			0
$535$	16.8573	+	2.36842i	0.728804	+	0.102396i
$536$	2.75557			0.119022
$537$		0			0
$538$			2.94914i			0.127147i
$539$	−73.2355			−3.15448
$540$		0			0
$541$	−22.3872			−0.962499			−0.481249	−	0.876584i	$-0.659817\pi$
$541$	−22.3872			−0.962499			−0.481249	+	0.876584i	$0.659817\pi$
$542$			30.9590i			1.32980i
$543$		0			0
$544$	−3.37778			−0.144821
$545$	1.72345	−	12.2667i	0.0738245	−	0.525448i
$546$		0			0
$547$			19.7333i			0.843735i	0.906658	+	0.421867i	$0.138625\pi$
$547$			19.7333i			0.843735i	−0.906658	+	0.421867i	$0.861375\pi$
$548$			1.47949i			0.0632009i
$549$		0			0
$550$	8.00000	−	27.9081i	0.341121	−	1.19001i
$551$	7.80642			0.332565
$552$		0			0
$553$		−	13.0607i		−	0.555397i
$554$	13.0923			0.556240
$555$		0			0
$556$	−4.85728			−0.205995
$557$		−	15.6543i		−	0.663295i	−0.943403	−	0.331648i	$-0.892395\pi$
$557$		−	15.6543i		−	0.663295i	0.943403	−	0.331648i	$-0.107605\pi$
$558$		0			0
$559$	−6.75557			−0.285730
$560$	−9.80642	−	1.37778i	−0.414397	−	0.0582220i
$561$		0			0
$562$		−	18.5303i		−	0.781656i
$563$			36.9403i			1.55685i	0.627740	+	0.778423i	$0.283980\pi$
$563$			36.9403i			1.55685i	−0.627740	+	0.778423i	$0.716020\pi$
$564$		0			0
$565$	−27.3876	−	3.84791i	−1.15221	−	0.161883i
$566$	−26.3783			−1.10876
$567$		0			0
$568$			7.61285i			0.319428i
$569$	−1.20294			−0.0504300			−0.0252150	−	0.999682i	$-0.508027\pi$
$569$	−1.20294			−0.0504300			−0.0252150	+	0.999682i	$0.508027\pi$
$570$		0			0
$571$	37.7975			1.58178			0.790889	−	0.611960i	$-0.209619\pi$
$571$	37.7975			1.58178			0.790889	+	0.611960i	$0.209619\pi$
$572$		−	37.3274i		−	1.56074i
$573$		0			0
$574$	19.6128			0.818624
$575$	−8.85728	+	30.8988i	−0.369374	+	1.28857i
$576$		0			0
$577$			23.2257i			0.966898i	0.875372	+	0.483449i	$0.160616\pi$
$577$			23.2257i			0.966898i	−0.875372	+	0.483449i	$0.839384\pi$
$578$			5.59057i			0.232537i
$579$		0			0
$580$	2.42864	−	17.2859i	0.100844	−	0.717759i
$581$	0.590573			0.0245011
$582$		0			0
$583$		−	27.6128i		−	1.14361i
$584$	−11.6128			−0.480543
$585$		0			0
$586$	28.5718			1.18029
$587$		−	16.8069i		−	0.693695i	−0.937922	−	0.346848i	$-0.887252\pi$
$587$		−	16.8069i		−	0.693695i	0.937922	−	0.346848i	$-0.112748\pi$
$588$		0			0
$589$	9.05086			0.372934
$590$	−10.2351	−	1.43801i	−0.421371	−	0.0592018i
$591$		0			0
$592$			3.67307i			0.150962i
$593$		−	16.3555i		−	0.671640i	−0.941926	−	0.335820i	$-0.890987\pi$
$593$		−	16.3555i		−	0.671640i	0.941926	−	0.335820i	$-0.109013\pi$
$594$		0			0
$595$	4.65386	−	33.1240i	0.190790	−	1.35795i
$596$	−4.62222			−0.189333
$597$		0			0
$598$			41.3274i			1.69000i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	7.89829			0.322178			0.161089	−	0.986940i	$-0.448499\pi$
$601$	7.89829			0.322178			0.161089	+	0.986940i	$0.448499\pi$
$602$		−	4.65386i		−	0.189677i
$603$		0			0
$604$	11.4193			0.464644
$605$	−7.06668	+	50.2973i	−0.287301	+	2.04488i
$606$		0			0
$607$			17.8479i			0.724424i	0.932096	+	0.362212i	$0.117978\pi$
$607$			17.8479i			0.724424i	−0.932096	+	0.362212i	$0.882022\pi$
$608$			1.00000i			0.0405554i
$609$		0			0
$610$	−4.42864	−	0.622216i	−0.179310	−	0.0251928i
$611$	33.3274			1.34828
$612$		0			0
$613$		−	0.622216i		−	0.0251311i	−0.999921	−	0.0125655i	$-0.996000\pi$
$613$		−	0.622216i		−	0.0251311i	0.999921	−	0.0125655i	$-0.00399984\pi$
$614$	−22.7556			−0.918340
$615$		0			0
$616$	25.7146			1.03607
$617$			37.4795i			1.50887i	0.656376	+	0.754434i	$0.272088\pi$
$617$			37.4795i			1.50887i	−0.656376	+	0.754434i	$0.727912\pi$
$618$		0			0
$619$	−28.6735			−1.15249			−0.576244	−	0.817278i	$-0.695482\pi$
$619$	−28.6735			−1.15249			−0.576244	+	0.817278i	$0.695482\pi$
$620$	2.81579	−	20.0415i	0.113085	−	0.804885i
$621$		0			0
$622$			6.32693i			0.253687i
$623$		−	14.1017i		−	0.564973i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	−13.7146			−0.548144
$627$		0			0
$628$		−	7.37778i		−	0.294406i
$629$	−12.4068			−0.494693
$630$		0			0
$631$	1.24443			0.0495400			0.0247700	−	0.999693i	$-0.492115\pi$
$631$	1.24443			0.0495400			0.0247700	+	0.999693i	$0.492115\pi$
$632$			2.94914i			0.117311i
$633$		0			0
$634$	−32.5718			−1.29359
$635$	−3.90813	−	0.549086i	−0.155090	−	0.0217898i
$636$		0			0
$637$		−	81.0835i		−	3.21264i
$638$			45.3274i			1.79453i
$639$		0			0
$640$	2.21432	+	0.311108i	0.0875287	+	0.0122976i
$641$	17.4064			0.687510			0.343755	−	0.939059i	$-0.388301\pi$
$641$	17.4064			0.687510			0.343755	+	0.939059i	$0.388301\pi$
$642$		0			0
$643$			35.1526i			1.38628i	0.720802	+	0.693141i	$0.243774\pi$
$643$			35.1526i			1.38628i	−0.720802	+	0.693141i	$0.756226\pi$
$644$	−28.4701			−1.12188
$645$		0			0
$646$	−3.37778			−0.132897
$647$		−	34.4286i		−	1.35353i	−0.736199	−	0.676765i	$-0.763381\pi$
$647$		−	34.4286i		−	1.35353i	0.736199	−	0.676765i	$-0.236619\pi$
$648$		0			0
$649$	26.8385			1.05350
$650$	30.8988	+	8.85728i	1.21195	+	0.347411i
$651$		0			0
$652$		−	5.90813i		−	0.231380i
$653$		−	4.30819i		−	0.168593i	−0.996441	−	0.0842963i	$-0.973136\pi$
$653$		−	4.30819i		−	0.168593i	0.996441	−	0.0842963i	$-0.0268642\pi$
$654$		0			0
$655$	3.05086	−	21.7146i	0.119207	−	0.848458i
$656$	−4.42864			−0.172909
$657$		0			0
$658$			22.9590i			0.895035i
$659$	−27.0736			−1.05464			−0.527319	−	0.849667i	$-0.676803\pi$
$659$	−27.0736			−1.05464			−0.527319	+	0.849667i	$0.676803\pi$
$660$		0			0
$661$	−43.2543			−1.68240			−0.841198	−	0.540727i	$-0.818149\pi$
$661$	−43.2543			−1.68240			−0.841198	+	0.540727i	$0.818149\pi$
$662$			5.63158i			0.218878i
$663$		0			0
$664$	−0.133353			−0.00517510
$665$	−9.80642	−	1.37778i	−0.380277	−	0.0534282i
$666$		0			0
$667$		−	50.1847i		−	1.94316i
$668$			2.75557i			0.106616i
$669$		0			0
$670$	0.857279	−	6.10171i	0.0331196	−	0.235730i
$671$	11.6128			0.448309
$672$		0			0
$673$		−	15.0321i		−	0.579446i	−0.957111	−	0.289723i	$-0.906437\pi$
$673$		−	15.0321i		−	0.579446i	0.957111	−	0.289723i	$-0.0935631\pi$
$674$	−5.70471			−0.219737
$675$		0			0
$676$	28.3274			1.08952
$677$		−	22.9403i		−	0.881666i	−0.897589	−	0.440833i	$-0.854683\pi$
$677$		−	22.9403i		−	0.881666i	0.897589	−	0.440833i	$-0.145317\pi$
$678$		0			0
$679$	50.5718			1.94077
$680$	−1.05086	+	7.47949i	−0.0402985	+	0.286826i
$681$		0			0
$682$			52.5531i			2.01236i
$683$			9.77784i			0.374139i	0.982347	+	0.187069i	$0.0598989\pi$
$683$			9.77784i			0.374139i	−0.982347	+	0.187069i	$0.940101\pi$
$684$		0			0
$685$	3.27607	+	0.460282i	0.125172	+	0.0175865i
$686$	24.8573			0.949055
$687$		0			0
$688$			1.05086i			0.0400635i
$689$	30.5718			1.16469
$690$		0			0
$691$	−44.0830			−1.67700			−0.838498	−	0.544905i	$-0.816566\pi$
$691$	−44.0830			−1.67700			−0.838498	+	0.544905i	$0.816566\pi$
$692$			8.10171i			0.307981i
$693$		0			0
$694$	−2.62222			−0.0995379
$695$	−1.51114	+	10.7556i	−0.0573207	+	0.407982i
$696$		0			0
$697$		−	14.9590i		−	0.566612i
$698$			24.1017i			0.912263i
$699$		0			0
$700$	−6.10171	+	21.2859i	−0.230623	+	0.804532i
$701$	12.7685			0.482259			0.241129	−	0.970493i	$-0.422482\pi$
$701$	12.7685			0.482259			0.241129	+	0.970493i	$0.422482\pi$
$702$		0			0
$703$			3.67307i			0.138532i
$704$	−5.80642			−0.218838
$705$		0			0
$706$	−3.64449			−0.137162
$707$			8.26671i			0.310901i
$708$		0			0
$709$	47.5941			1.78743			0.893717	−	0.448631i	$-0.148088\pi$
$709$	47.5941			1.78743			0.893717	+	0.448631i	$0.148088\pi$
$710$	16.8573	+	2.36842i	0.632642	+	0.0888851i
$711$		0			0
$712$			3.18421i			0.119333i
$713$		−	58.1847i		−	2.17903i
$714$		0			0
$715$	−82.6548	−	11.6128i	−3.09111	−	0.434296i
$716$	0.235063			0.00878473
$717$		0			0
$718$			9.08250i			0.338956i
$719$	−47.0005			−1.75282			−0.876411	−	0.481564i	$-0.840069\pi$
$719$	−47.0005			−1.75282			−0.876411	+	0.481564i	$0.840069\pi$
$720$		0			0
$721$	47.0420			1.75193
$722$			1.00000i			0.0372161i
$723$		0			0
$724$	−11.3176			−0.420614
$725$	−37.5210	−	10.7556i	−1.39349	−	0.399452i
$726$		0			0
$727$			52.6321i			1.95202i	0.217737	+	0.976008i	$0.430133\pi$
$727$			52.6321i			1.95202i	−0.217737	+	0.976008i	$0.569867\pi$
$728$			28.4701i			1.05517i
$729$		0			0
$730$	−3.61285	+	25.7146i	−0.133717	+	0.951738i
$731$	−3.54956			−0.131285
$732$		0			0
$733$		−	27.3145i		−	1.00888i	−0.863446	−	0.504442i	$-0.831698\pi$
$733$		−	27.3145i		−	1.00888i	0.863446	−	0.504442i	$-0.168302\pi$
$734$	−3.95851			−0.146111
$735$		0			0
$736$	6.42864			0.236963
$737$			16.0000i			0.589368i
$738$		0			0
$739$	−25.3274			−0.931684			−0.465842	−	0.884868i	$-0.654248\pi$
$739$	−25.3274			−0.931684			−0.465842	+	0.884868i	$0.654248\pi$
$740$	8.13335	+	1.14272i	0.298988	+	0.0420073i
$741$		0			0
$742$			21.0607i			0.773163i
$743$		−	11.8796i		−	0.435819i	−0.975969	−	0.217909i	$-0.930076\pi$
$743$		−	11.8796i		−	0.435819i	0.975969	−	0.217909i	$-0.0699237\pi$
$744$		0			0
$745$	−1.43801	+	10.2351i	−0.0526845	+	0.374984i
$746$	12.5303			0.458769
$747$		0			0
$748$		−	19.6128i		−	0.717117i
$749$	33.7146			1.23190
$750$		0			0
$751$	−45.5210			−1.66108			−0.830542	−	0.556956i	$-0.811969\pi$
$751$	−45.5210			−1.66108			−0.830542	+	0.556956i	$0.811969\pi$
$752$		−	5.18421i		−	0.189049i
$753$		0			0
$754$	−50.1847			−1.82762
$755$	3.55262	−	25.2859i	0.129293	−	0.920249i
$756$		0			0
$757$		−	51.7275i		−	1.88007i	−0.341083	−	0.940033i	$-0.610794\pi$
$757$		−	51.7275i		−	1.88007i	0.341083	−	0.940033i	$-0.389206\pi$
$758$		−	26.8385i		−	0.974820i
$759$		0			0
$760$	2.21432	+	0.311108i	0.0803218	+	0.0112851i
$761$	−28.3684			−1.02835			−0.514177	−	0.857684i	$-0.671903\pi$
$761$	−28.3684			−1.02835			−0.514177	+	0.857684i	$0.671903\pi$
$762$		0			0
$763$		−	24.5334i		−	0.888169i
$764$	−6.32693			−0.228900
$765$		0			0
$766$	−17.5111			−0.632703
$767$			29.7146i			1.07293i
$768$		0			0
$769$	0.285442			0.0102933			0.00514665	−	0.999987i	$-0.498362\pi$
$769$	0.285442			0.0102933			0.00514665	+	0.999987i	$0.498362\pi$
$770$	8.00000	−	56.9403i	0.288300	−	2.05198i
$771$		0			0
$772$			11.5397i			0.415324i
$773$			49.8163i			1.79177i	0.444289	+	0.895883i	$0.353456\pi$
$773$			49.8163i			1.79177i	−0.444289	+	0.895883i	$0.646544\pi$
$774$		0			0
$775$	−43.5022	−	12.4701i	−1.56265	−	0.447940i
$776$	−11.4193			−0.409928
$777$		0			0
$778$		−	29.4795i		−	1.05689i
$779$	−4.42864			−0.158672
$780$		0			0
$781$	−44.2034			−1.58172
$782$			21.7146i			0.776511i
$783$		0			0
$784$	−12.6128			−0.450459
$785$	−16.3368	−	2.29529i	−0.583084	−	0.0819223i
$786$		0			0
$787$		−	20.7368i		−	0.739188i	−0.929193	−	0.369594i	$-0.879497\pi$
$787$		−	20.7368i		−	0.739188i	0.929193	−	0.369594i	$-0.120503\pi$
$788$			20.0415i			0.713948i
$789$		0			0
$790$	6.53035	+	0.917502i	0.232339	+	0.0326433i
$791$	−54.7753			−1.94758
$792$		0			0
$793$			12.8573i			0.456575i
$794$	−9.21279			−0.326950
$795$		0			0
$796$	−20.4701			−0.725544
$797$			21.3461i			0.756119i	0.925781	+	0.378060i	$0.123409\pi$
$797$			21.3461i			0.756119i	−0.925781	+	0.378060i	$0.876591\pi$
$798$		0			0
$799$	17.5111			0.619500
$800$	1.37778	−	4.80642i	0.0487120	−	0.169933i
$801$		0			0
$802$		−	29.2859i		−	1.03412i
$803$		−	67.4291i		−	2.37952i
$804$		0			0
$805$	−8.85728	+	63.0420i	−0.312178	+	2.22194i
$806$	−58.1847			−2.04947
$807$		0			0
$808$		−	1.86665i		−	0.0656684i
$809$	−18.6735			−0.656527			−0.328263	−	0.944586i	$-0.606463\pi$
$809$	−18.6735			−0.656527			−0.328263	+	0.944586i	$0.606463\pi$
$810$		0			0
$811$	−14.8385			−0.521052			−0.260526	−	0.965467i	$-0.583896\pi$
$811$	−14.8385			−0.521052			−0.260526	+	0.965467i	$0.583896\pi$
$812$		−	34.5718i		−	1.21323i
$813$		0			0
$814$	−21.3274			−0.747525
$815$	−13.0825	−	1.83807i	−0.458260	−	0.0643847i
$816$		0			0
$817$			1.05086i			0.0367648i
$818$			17.8796i			0.625144i
$819$		0			0
$820$	−1.37778	+	9.80642i	−0.0481143	+	0.342455i
$821$	−16.1521			−0.563712			−0.281856	−	0.959457i	$-0.590950\pi$
$821$	−16.1521			−0.563712			−0.281856	+	0.959457i	$0.590950\pi$
$822$		0			0
$823$			47.6543i			1.66113i	0.556925	+	0.830563i	$0.311981\pi$
$823$			47.6543i			1.66113i	−0.556925	+	0.830563i	$0.688019\pi$
$824$	−10.6222			−0.370042
$825$		0			0
$826$	−20.4701			−0.712247
$827$		−	26.1017i		−	0.907645i	−0.891092	−	0.453823i	$-0.850060\pi$
$827$		−	26.1017i		−	0.907645i	0.891092	−	0.453823i	$-0.149940\pi$
$828$		0			0
$829$	13.8894			0.482399			0.241199	−	0.970476i	$-0.422459\pi$
$829$	13.8894			0.482399			0.241199	+	0.970476i	$0.422459\pi$
$830$	−0.0414872	+	0.295286i	−0.00144004	+	0.0102495i
$831$		0			0
$832$		−	6.42864i		−	0.222873i
$833$		−	42.6035i		−	1.47612i
$834$		0			0
$835$	6.10171	+	0.857279i	0.211158	+	0.0296674i
$836$	−5.80642			−0.200819
$837$		0			0
$838$			30.8671i			1.06629i
$839$	31.6958			1.09426			0.547131	−	0.837047i	$-0.315720\pi$
$839$	31.6958			1.09426			0.547131	+	0.837047i	$0.315720\pi$
$840$		0			0
$841$	31.9403			1.10139
$842$		−	18.3970i		−	0.634002i
$843$		0			0
$844$	−2.75557			−0.0948506
$845$	8.81288	−	62.7259i	0.303172	−	2.15784i
$846$		0			0
$847$			100.595i			3.45647i
$848$		−	4.75557i		−	0.163307i
$849$		0			0
$850$	16.2351	+	4.65386i	0.556858	+	0.159626i
$851$	23.6128			0.809438
$852$		0			0
$853$		−	34.8702i		−	1.19393i	−0.802266	−	0.596966i	$-0.796373\pi$
$853$		−	34.8702i		−	1.19393i	0.802266	−	0.596966i	$-0.203627\pi$
$854$	−8.85728			−0.303090
$855$		0			0
$856$	−7.61285			−0.260202
$857$			33.9367i			1.15926i	0.814881	+	0.579628i	$0.196802\pi$
$857$			33.9367i			1.15926i	−0.814881	+	0.579628i	$0.803198\pi$
$858$		0			0
$859$	37.4479			1.27770			0.638852	−	0.769330i	$-0.279410\pi$
$859$	37.4479			1.27770			0.638852	+	0.769330i	$0.279410\pi$
$860$	2.32693	+	0.326929i	0.0793476	+	0.0111482i
$861$		0			0
$862$		−	29.5941i		−	1.00798i
$863$			15.5299i			0.528643i	0.964435	+	0.264322i	$0.0851480\pi$
$863$			15.5299i			0.528643i	−0.964435	+	0.264322i	$0.914852\pi$
$864$		0			0
$865$	17.9398	+	2.52051i	0.609971	+	0.0856998i
$866$	27.2988			0.927652
$867$		0			0
$868$		−	40.0830i		−	1.36050i
$869$	−17.1240			−0.580891
$870$		0			0
$871$	−17.7146			−0.600235
$872$			5.53972i			0.187599i
$873$		0			0
$874$	6.42864			0.217452
$875$	45.2355	+	20.1334i	1.52924	+	0.680632i
$876$		0			0
$877$		−	7.87649i		−	0.265970i	−0.991118	−	0.132985i	$-0.957544\pi$
$877$		−	7.87649i		−	0.265970i	0.991118	−	0.132985i	$-0.0424562\pi$
$878$		−	9.64143i		−	0.325382i
$879$		0			0
$880$	−1.80642	+	12.8573i	−0.0608945	+	0.433419i
$881$	−33.5496			−1.13031			−0.565157	−	0.824984i	$-0.691184\pi$
$881$	−33.5496			−1.13031			−0.565157	+	0.824984i	$0.691184\pi$
$882$		0			0
$883$		−	50.9688i		−	1.71524i	−0.514286	−	0.857619i	$-0.671943\pi$
$883$		−	50.9688i		−	1.71524i	0.514286	−	0.857619i	$-0.328057\pi$
$884$	21.7146			0.730340
$885$		0			0
$886$	−6.70519			−0.225265
$887$		−	17.0035i		−	0.570923i	−0.958390	−	0.285461i	$-0.907853\pi$
$887$		−	17.0035i		−	0.570923i	0.958390	−	0.285461i	$-0.0921469\pi$
$888$		0			0
$889$	−7.81627			−0.262149
$890$	7.05086	+	0.990632i	0.236345	+	0.0332061i
$891$		0			0
$892$			10.6222i			0.355658i
$893$		−	5.18421i		−	0.173483i
$894$		0			0
$895$	0.0731300	−	0.520505i	0.00244447	−	0.0173986i
$896$	4.42864			0.147950
$897$		0			0
$898$		−	13.9398i		−	0.465176i
$899$	70.6548			2.35647
$900$		0			0
$901$	16.0633			0.535146
$902$		−	25.7146i		−	0.856201i
$903$		0			0
$904$	12.3684			0.411367
$905$	−3.52098	+	25.0607i	−0.117041	+	0.833046i
$906$		0			0
$907$		−	21.7778i		−	0.723121i	−0.932349	−	0.361561i	$-0.882244\pi$
$907$		−	21.7778i		−	0.723121i	0.932349	−	0.361561i	$-0.117756\pi$
$908$			15.3461i			0.509280i
$909$		0			0
$910$	63.0420	+	8.85728i	2.08982	+	0.293616i
$911$	−10.6351			−0.352357			−0.176179	−	0.984358i	$-0.556374\pi$
$911$	−10.6351			−0.352357			−0.176179	+	0.984358i	$0.556374\pi$
$912$		0			0
$913$		−	0.774305i		−	0.0256257i
$914$	−23.2257			−0.768238
$915$		0			0
$916$	−19.7146			−0.651387
$917$		−	43.4291i		−	1.43416i
$918$		0			0
$919$	−12.2667			−0.404641			−0.202321	−	0.979319i	$-0.564848\pi$
$919$	−12.2667			−0.404641			−0.202321	+	0.979319i	$0.564848\pi$
$920$	2.00000	−	14.2351i	0.0659380	−	0.469316i
$921$		0			0
$922$		−	19.9684i		−	0.657623i
$923$		−	48.9403i		−	1.61089i
$924$		0			0
$925$	5.06070	−	17.6543i	0.166395	−	0.580471i
$926$	−2.79706			−0.0919170
$927$		0			0
$928$			7.80642i			0.256258i
$929$	−27.9180			−0.915959			−0.457980	−	0.888963i	$-0.651427\pi$
$929$	−27.9180			−0.915959			−0.457980	+	0.888963i	$0.651427\pi$
$930$		0			0
$931$	−12.6128			−0.413369
$932$			29.5625i			0.968351i
$933$		0			0
$934$	−30.9719			−1.01343
$935$	−43.4291	−	6.10171i	−1.42028	−	0.199547i
$936$		0			0
$937$		−	3.14272i		−	0.102668i	−0.998682	−	0.0513341i	$-0.983653\pi$
$937$		−	3.14272i		−	0.102668i	0.998682	−	0.0513341i	$-0.0163473\pi$
$938$		−	12.2034i		−	0.398456i
$939$		0			0
$940$	−11.4795	−	1.61285i	−0.374420	−	0.0526053i
$941$	19.6227			0.639681			0.319841	−	0.947471i	$-0.396371\pi$
$941$	19.6227			0.639681			0.319841	+	0.947471i	$0.396371\pi$
$942$		0			0
$943$			28.4701i			0.927115i
$944$	4.62222			0.150440
$945$		0			0
$946$	−6.10171			−0.198384
$947$		−	34.5018i		−	1.12116i	−0.828101	−	0.560578i	$-0.810579\pi$
$947$		−	34.5018i		−	1.12116i	0.828101	−	0.560578i	$-0.189421\pi$
$948$		0			0
$949$	74.6548			2.42340
$950$	1.37778	−	4.80642i	0.0447012	−	0.155941i
$951$		0			0
$952$			14.9590i			0.484824i
$953$		−	19.0035i		−	0.615585i	−0.951454	−	0.307793i	$-0.900410\pi$
$953$		−	19.0035i		−	0.615585i	0.951454	−	0.307793i	$-0.0995903\pi$
$954$		0			0
$955$	−1.96836	+	14.0098i	−0.0636945	+	0.453348i
$956$	−1.67307			−0.0541110
$957$		0			0
$958$			29.8765i			0.965266i
$959$	6.55215			0.211580
$960$		0			0
$961$	50.9180			1.64252
$962$		−	23.6128i		−	0.761309i
$963$		0			0
$964$	16.9590			0.546212
$965$	25.5526	+	3.59010i	0.822568	+	0.115569i
$966$		0			0
$967$		−	17.8765i		−	0.574869i	−0.957800	−	0.287435i	$-0.907198\pi$
$967$		−	17.8765i		−	0.574869i	0.957800	−	0.287435i	$-0.0928024\pi$
$968$		−	22.7146i		−	0.730074i
$969$		0			0
$970$	−3.55262	+	25.2859i	−0.114068	+	0.811882i
$971$	−34.0701			−1.09336			−0.546680	−	0.837341i	$-0.684109\pi$
$971$	−34.0701			−1.09336			−0.546680	+	0.837341i	$0.684109\pi$
$972$		0			0
$973$			21.5111i			0.689615i
$974$	−17.8479			−0.571884
$975$		0			0
$976$	2.00000			0.0640184
$977$			54.0830i			1.73027i	0.501541	+	0.865134i	$0.332767\pi$
$977$			54.0830i			1.73027i	−0.501541	+	0.865134i	$0.667233\pi$
$978$		0			0
$979$	−18.4889			−0.590907
$980$	−3.92396	+	27.9289i	−0.125346	+	0.892155i
$981$		0			0
$982$			8.68244i			0.277068i
$983$			56.9403i			1.81611i	0.418849	+	0.908056i	$0.362434\pi$
$983$			56.9403i			1.81611i	−0.418849	+	0.908056i	$0.637566\pi$
$984$		0			0
$985$	44.3783	+	6.23506i	1.41401	+	0.198666i
$986$	−26.3684			−0.839741
$987$		0			0
$988$		−	6.42864i		−	0.204522i
$989$	6.75557			0.214815
$990$		0			0
$991$	−47.0321			−1.49402			−0.747012	−	0.664810i	$-0.768512\pi$
$991$	−47.0321			−1.49402			−0.747012	+	0.664810i	$0.768512\pi$
$992$			9.05086i			0.287365i
$993$		0			0
$994$	33.7146			1.06936
$995$	−6.36842	+	45.3274i	−0.201892	+	1.43698i
$996$		0			0
$997$		−	20.8256i		−	0.659555i	−0.944059	−	0.329777i	$-0.893026\pi$
$997$		−	20.8256i		−	0.659555i	0.944059	−	0.329777i	$-0.106974\pi$
$998$		−	11.2257i		−	0.355343i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.e.1369.5		6
3.2	odd	2		570.2.d.d.229.2	✓	6
5.2	odd	4		8550.2.a.cf.1.1		3
5.3	odd	4		8550.2.a.cr.1.3		3
5.4	even	2	inner	1710.2.d.e.1369.2		6
15.2	even	4		2850.2.a.bn.1.1		3
15.8	even	4		2850.2.a.bk.1.3		3
15.14	odd	2		570.2.d.d.229.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.d.229.2	✓	6	3.2	odd	2
570.2.d.d.229.5	yes	6	15.14	odd	2
1710.2.d.e.1369.2		6	5.4	even	2	inner
1710.2.d.e.1369.5		6	1.1	even	1	trivial
2850.2.a.bk.1.3		3	15.8	even	4
2850.2.a.bn.1.1		3	15.2	even	4
8550.2.a.cf.1.1		3	5.2	odd	4
8550.2.a.cr.1.3		3	5.3	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.311108 + 2.21432i) q^{5} +4.42864i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.311108 + 2.21432i) q^{5} +4.42864i q^{7} -1.00000i q^{8} +(-2.21432 - 0.311108i) q^{10} +5.80642 q^{11} +6.42864i q^{13} -4.42864 q^{14} +1.00000 q^{16} +3.37778i q^{17} +1.00000 q^{19} +(0.311108 - 2.21432i) q^{20} +5.80642i q^{22} -6.42864i q^{23} +(-4.80642 - 1.37778i) q^{25} -6.42864 q^{26} -4.42864i q^{28} +7.80642 q^{29} +9.05086 q^{31} +1.00000i q^{32} -3.37778 q^{34} +(-9.80642 - 1.37778i) q^{35} +3.67307i q^{37} +1.00000i q^{38} +(2.21432 + 0.311108i) q^{40} -4.42864 q^{41} +1.05086i q^{43} -5.80642 q^{44} +6.42864 q^{46} -5.18421i q^{47} -12.6128 q^{49} +(1.37778 - 4.80642i) q^{50} -6.42864i q^{52} -4.75557i q^{53} +(-1.80642 + 12.8573i) q^{55} +4.42864 q^{56} +7.80642i q^{58} +4.62222 q^{59} +2.00000 q^{61} +9.05086i q^{62} -1.00000 q^{64} +(-14.2351 - 2.00000i) q^{65} +2.75557i q^{67} -3.37778i q^{68} +(1.37778 - 9.80642i) q^{70} -7.61285 q^{71} -11.6128i q^{73} -3.67307 q^{74} -1.00000 q^{76} +25.7146i q^{77} -2.94914 q^{79} +(-0.311108 + 2.21432i) q^{80} -4.42864i q^{82} -0.133353i q^{83} +(-7.47949 - 1.05086i) q^{85} -1.05086 q^{86} -5.80642i q^{88} -3.18421 q^{89} -28.4701 q^{91} +6.42864i q^{92} +5.18421 q^{94} +(-0.311108 + 2.21432i) q^{95} -11.4193i q^{97} -12.6128i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^5	\( 6 q - 6 q^{4} - 2 q^{5} + 8 q^{11} + 6 q^{16} + 6 q^{19} + 2 q^{20} - 2 q^{25} - 12 q^{26} + 20 q^{29} + 28 q^{31} - 20 q^{34} - 32 q^{35} - 8 q^{44} + 12 q^{46} - 22 q^{49} + 8 q^{50} + 16 q^{55} + 28 q^{59} + 12 q^{61} - 6 q^{64} - 32 q^{65} + 8 q^{70} + 8 q^{71} + 4 q^{74} - 6 q^{76} - 44 q^{79} - 2 q^{80} + 8 q^{85} + 20 q^{86} + 8 q^{89} - 64 q^{91} + 4 q^{94} - 2 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^11 + 6 * q^16 + 6 * q^19 + 2 * q^20 - 2 * q^25 - 12 * q^26 + 20 * q^29 + 28 * q^31 - 20 * q^34 - 32 * q^35 - 8 * q^44 + 12 * q^46 - 22 * q^49 + 8 * q^50 + 16 * q^55 + 28 * q^59 + 12 * q^61 - 6 * q^64 - 32 * q^65 + 8 * q^70 + 8 * q^71 + 4 * q^74 - 6 * q^76 - 44 * q^79 - 2 * q^80 + 8 * q^85 + 20 * q^86 + 8 * q^89 - 64 * q^91 + 4 * q^94 - 2 * q^95

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