LMFDB - Embedded newform 3330.2.d.p.1999.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3330,2,Mod(1999,3330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3330, 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("3330.1999");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3330.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:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 51x^6 - 124x^5 + 154x^4 - 46x^3 + x^2 + 4x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1999.8
Root			$-0.282359 + 0.282359i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.p.1999.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-1.70518 + 1.44650i) q^{5} +1.83227i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.70518 + 1.44650i) q^{5} +1.83227i q^{7} -1.00000i q^{8} +(-1.44650 - 1.70518i) q^{10} -4.19017 q^{11} -0.369454i q^{13} -1.83227 q^{14} +1.00000 q^{16} -5.08317i q^{17} -3.55963 q^{19} +(1.70518 - 1.44650i) q^{20} -4.19017i q^{22} -5.62036i q^{23} +(0.815273 - 4.93309i) q^{25} +0.369454 q^{26} -1.83227i q^{28} +1.20681 q^{29} +10.1030 q^{31} +1.00000i q^{32} +5.08317 q^{34} +(-2.65038 - 3.12434i) q^{35} -1.00000i q^{37} -3.55963i q^{38} +(1.44650 + 1.70518i) q^{40} +8.01447 q^{41} -2.27264i q^{43} +4.19017 q^{44} +5.62036 q^{46} +10.9154i q^{47} +3.64280 q^{49} +(4.93309 + 0.815273i) q^{50} +0.369454i q^{52} +9.94355i q^{53} +(7.14499 - 6.06108i) q^{55} +1.83227 q^{56} +1.20681i q^{58} -5.34563 q^{59} -9.79428 q^{61} +10.1030i q^{62} -1.00000 q^{64} +(0.534415 + 0.629985i) q^{65} -1.85073i q^{67} +5.08317i q^{68} +(3.12434 - 2.65038i) q^{70} -2.86038 q^{71} -8.09942i q^{73} +1.00000 q^{74} +3.55963 q^{76} -7.67751i q^{77} -6.06361 q^{79} +(-1.70518 + 1.44650i) q^{80} +8.01447i q^{82} +8.93200i q^{83} +(7.35281 + 8.66772i) q^{85} +2.27264 q^{86} +4.19017i q^{88} +11.4773 q^{89} +0.676938 q^{91} +5.62036i q^{92} -10.9154 q^{94} +(6.06980 - 5.14900i) q^{95} -6.05864i q^{97} +3.64280i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} - 6 q^{5}+O(q^{10}) $ 10 * q - 10 * q^4 - 6 * q^5	$ 10 q - 10 q^{4} - 6 q^{5} + 2 q^{10} - 6 q^{11} - 2 q^{14} + 10 q^{16} - 8 q^{19} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 22 q^{29} + 46 q^{31} - 18 q^{34} - 32 q^{35} - 2 q^{40} + 14 q^{41} + 6 q^{44} + 12 q^{46} - 60 q^{49} - 8 q^{50} + 42 q^{55} + 2 q^{56} + 40 q^{59} - 18 q^{61} - 10 q^{64} - 4 q^{65} - 6 q^{70} - 12 q^{71} + 10 q^{74} + 8 q^{76} - 40 q^{79} - 6 q^{80} + 36 q^{85} + 34 q^{86} + 24 q^{89} + 32 q^{91} - 24 q^{94} - 12 q^{95}+O(q^{100}) $ 10 * q - 10 * q^4 - 6 * q^5 + 2 * q^10 - 6 * q^11 - 2 * q^14 + 10 * q^16 - 8 * q^19 + 6 * q^20 + 4 * q^25 + 12 * q^26 + 22 * q^29 + 46 * q^31 - 18 * q^34 - 32 * q^35 - 2 * q^40 + 14 * q^41 + 6 * q^44 + 12 * q^46 - 60 * q^49 - 8 * q^50 + 42 * q^55 + 2 * q^56 + 40 * q^59 - 18 * q^61 - 10 * q^64 - 4 * q^65 - 6 * q^70 - 12 * q^71 + 10 * q^74 + 8 * q^76 - 40 * q^79 - 6 * q^80 + 36 * q^85 + 34 * q^86 + 24 * q^89 + 32 * q^91 - 24 * q^94 - 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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
$5$	−1.70518	+	1.44650i	−0.762579	+	0.646895i
$5$	−1.70518	+	1.44650i	−0.762579	+	0.646895i
$6$		0			0
$7$			1.83227i			0.692532i	0.938136	+	0.346266i	$0.112551\pi$
$7$			1.83227i			0.692532i	−0.938136	+	0.346266i	$0.887449\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.44650	−	1.70518i	−0.457424	−	0.539225i
$11$	−4.19017			−1.26338			−0.631692	−	0.775219i	$-0.717639\pi$
$11$	−4.19017			−1.26338			−0.631692	+	0.775219i	$0.717639\pi$
$12$		0			0
$13$		−	0.369454i		−	0.102468i	−0.998687	−	0.0512340i	$-0.983685\pi$
$13$		−	0.369454i		−	0.102468i	0.998687	−	0.0512340i	$-0.0163154\pi$
$14$	−1.83227			−0.489694
$15$		0			0
$16$	1.00000			0.250000
$17$		−	5.08317i		−	1.23285i	−0.787414	−	0.616425i	$-0.788580\pi$
$17$		−	5.08317i		−	1.23285i	0.787414	−	0.616425i	$-0.211420\pi$
$18$		0			0
$19$	−3.55963			−0.816634			−0.408317	−	0.912840i	$-0.633884\pi$
$19$	−3.55963			−0.816634			−0.408317	+	0.912840i	$0.633884\pi$
$20$	1.70518	−	1.44650i	0.381290	−	0.323447i
$21$		0			0
$22$		−	4.19017i		−	0.893348i
$23$		−	5.62036i		−	1.17193i	−0.810338	−	0.585963i	$-0.800716\pi$
$23$		−	5.62036i		−	1.17193i	0.810338	−	0.585963i	$-0.199284\pi$
$24$		0			0
$25$	0.815273	−	4.93309i	0.163055	−	0.986617i
$26$	0.369454			0.0724559
$27$		0			0
$28$		−	1.83227i		−	0.346266i
$29$	1.20681			0.224100			0.112050	−	0.993703i	$-0.464258\pi$
$29$	1.20681			0.224100			0.112050	+	0.993703i	$0.464258\pi$
$30$		0			0
$31$	10.1030			1.81455			0.907276	−	0.420535i	$-0.138158\pi$
$31$	10.1030			1.81455			0.907276	+	0.420535i	$0.138158\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	5.08317			0.871757
$35$	−2.65038	−	3.12434i	−0.447995	−	0.528111i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	3.55963i		−	0.577447i
$39$		0			0
$40$	1.44650	+	1.70518i	0.228712	+	0.269613i
$41$	8.01447			1.25165			0.625825	−	0.779964i	$-0.284762\pi$
$41$	8.01447			1.25165			0.625825	+	0.779964i	$0.284762\pi$
$42$		0			0
$43$		−	2.27264i		−	0.346575i	−0.984871	−	0.173287i	$-0.944561\pi$
$43$		−	2.27264i		−	0.346575i	0.984871	−	0.173287i	$-0.0554389\pi$
$44$	4.19017			0.631692
$45$		0			0
$46$	5.62036			0.828677
$47$			10.9154i			1.59218i	0.605178	+	0.796090i	$0.293102\pi$
$47$			10.9154i			1.59218i	−0.605178	+	0.796090i	$0.706898\pi$
$48$		0			0
$49$	3.64280			0.520400
$50$	4.93309	+	0.815273i	0.697644	+	0.115297i
$51$		0			0
$52$			0.369454i			0.0512340i
$53$			9.94355i			1.36585i	0.730488	+	0.682926i	$0.239293\pi$
$53$			9.94355i			1.36585i	−0.730488	+	0.682926i	$0.760707\pi$
$54$		0			0
$55$	7.14499	−	6.06108i	0.963431	−	0.817276i
$56$	1.83227			0.244847
$57$		0			0
$58$			1.20681i			0.158463i
$59$	−5.34563			−0.695941			−0.347971	−	0.937505i	$-0.613129\pi$
$59$	−5.34563			−0.695941			−0.347971	+	0.937505i	$0.613129\pi$
$60$		0			0
$61$	−9.79428			−1.25403			−0.627015	−	0.779008i	$-0.715723\pi$
$61$	−9.79428			−1.25403			−0.627015	+	0.779008i	$0.715723\pi$
$62$			10.1030i			1.28308i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.534415	+	0.629985i	0.0662861	+	0.0781401i
$66$		0			0
$67$		−	1.85073i		−	0.226103i	−0.993589	−	0.113052i	$-0.963937\pi$
$67$		−	1.85073i		−	0.226103i	0.993589	−	0.113052i	$-0.0360625\pi$
$68$			5.08317i			0.616425i
$69$		0			0
$70$	3.12434	−	2.65038i	0.373431	−	0.316780i
$71$	−2.86038			−0.339464			−0.169732	−	0.985490i	$-0.554290\pi$
$71$	−2.86038			−0.339464			−0.169732	+	0.985490i	$0.554290\pi$
$72$		0			0
$73$		−	8.09942i		−	0.947966i	−0.880534	−	0.473983i	$-0.842816\pi$
$73$		−	8.09942i		−	0.947966i	0.880534	−	0.473983i	$-0.157184\pi$
$74$	1.00000			0.116248
$75$		0			0
$76$	3.55963			0.408317
$77$		−	7.67751i		−	0.874934i
$78$		0			0
$79$	−6.06361			−0.682209			−0.341105	−	0.940025i	$-0.610801\pi$
$79$	−6.06361			−0.682209			−0.341105	+	0.940025i	$0.610801\pi$
$80$	−1.70518	+	1.44650i	−0.190645	+	0.161724i
$81$		0			0
$82$			8.01447i			0.885050i
$83$			8.93200i			0.980414i	0.871606	+	0.490207i	$0.163079\pi$
$83$			8.93200i			0.980414i	−0.871606	+	0.490207i	$0.836921\pi$
$84$		0			0
$85$	7.35281	+	8.66772i	0.797524	+	0.940146i
$86$	2.27264			0.245065
$87$		0			0
$88$			4.19017i			0.446674i
$89$	11.4773			1.21659			0.608295	−	0.793711i	$-0.291854\pi$
$89$	11.4773			1.21659			0.608295	+	0.793711i	$0.291854\pi$
$90$		0			0
$91$	0.676938			0.0709624
$92$			5.62036i			0.585963i
$93$		0			0
$94$	−10.9154			−1.12584
$95$	6.06980	−	5.14900i	0.622748	−	0.528276i
$96$		0			0
$97$		−	6.05864i		−	0.615162i	−0.951522	−	0.307581i	$-0.900480\pi$
$97$		−	6.05864i		−	0.615162i	0.951522	−	0.307581i	$-0.0995195\pi$
$98$			3.64280i			0.367978i
$99$		0			0
$100$	−0.815273	+	4.93309i	−0.0815273	+	0.493309i
$101$	−4.96528			−0.494064			−0.247032	−	0.969007i	$-0.579455\pi$
$101$	−4.96528			−0.494064			−0.247032	+	0.969007i	$0.579455\pi$
$102$		0			0
$103$		−	7.33338i		−	0.722579i	−0.932454	−	0.361289i	$-0.882337\pi$
$103$		−	7.33338i		−	0.722579i	0.932454	−	0.361289i	$-0.117663\pi$
$104$	−0.369454			−0.0362279
$105$		0			0
$106$	−9.94355			−0.965803
$107$		−	8.21182i		−	0.793867i	−0.917847	−	0.396933i	$-0.870074\pi$
$107$		−	8.21182i		−	0.793867i	0.917847	−	0.396933i	$-0.129926\pi$
$108$		0			0
$109$	20.5503			1.96836			0.984179	−	0.177175i	$-0.0566960\pi$
$109$	20.5503			1.96836			0.984179	+	0.177175i	$0.0566960\pi$
$110$	6.06108	+	7.14499i	0.577902	+	0.681248i
$111$		0			0
$112$			1.83227i			0.173133i
$113$			0.652984i			0.0614276i	0.999528	+	0.0307138i	$0.00977804\pi$
$113$			0.652984i			0.0614276i	−0.999528	+	0.0307138i	$0.990222\pi$
$114$		0			0
$115$	8.12985	+	9.58372i	0.758113	+	0.893686i
$116$	−1.20681			−0.112050
$117$		0			0
$118$		−	5.34563i		−	0.492105i
$119$	9.31373			0.853788
$120$		0			0
$121$	6.55754			0.596140
$122$		−	9.79428i		−	0.886733i
$123$		0			0
$124$	−10.1030			−0.907276
$125$	5.74552	+	9.59109i	0.513895	+	0.857853i
$126$		0			0
$127$			19.2856i			1.71132i	0.517539	+	0.855660i	$0.326848\pi$
$127$			19.2856i			1.71132i	−0.517539	+	0.855660i	$0.673152\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−0.629985	+	0.534415i	−0.0552534	+	0.0468713i
$131$	8.82072			0.770670			0.385335	−	0.922777i	$-0.374086\pi$
$131$	8.82072			0.770670			0.385335	+	0.922777i	$0.374086\pi$
$132$		0			0
$133$		−	6.52218i		−	0.565545i
$134$	1.85073			0.159879
$135$		0			0
$136$	−5.08317			−0.435878
$137$			4.66126i			0.398239i	0.979975	+	0.199119i	$0.0638081\pi$
$137$			4.66126i			0.398239i	−0.979975	+	0.199119i	$0.936192\pi$
$138$		0			0
$139$	−16.4050			−1.39145			−0.695727	−	0.718306i	$-0.744918\pi$
$139$	−16.4050			−1.39145			−0.695727	+	0.718306i	$0.744918\pi$
$140$	2.65038	+	3.12434i	0.223998	+	0.264055i
$141$		0			0
$142$		−	2.86038i		−	0.240037i
$143$			1.54808i			0.129457i
$144$		0			0
$145$	−2.05784	+	1.74566i	−0.170894	+	0.144969i
$146$	8.09942			0.670313
$147$		0			0
$148$			1.00000i			0.0821995i
$149$	−5.86259			−0.480282			−0.240141	−	0.970738i	$-0.577194\pi$
$149$	−5.86259			−0.480282			−0.240141	+	0.970738i	$0.577194\pi$
$150$		0			0
$151$	13.1460			1.06981			0.534903	−	0.844913i	$-0.320348\pi$
$151$	13.1460			1.06981			0.534903	+	0.844913i	$0.320348\pi$
$152$			3.55963i			0.288724i
$153$		0			0
$154$	7.67751			0.618672
$155$	−17.2274	+	14.6140i	−1.38374	+	1.17382i
$156$		0			0
$157$			7.33629i			0.585500i	0.956189	+	0.292750i	$0.0945704\pi$
$157$			7.33629i			0.585500i	−0.956189	+	0.292750i	$0.905430\pi$
$158$		−	6.06361i		−	0.482395i
$159$		0			0
$160$	−1.44650	−	1.70518i	−0.114356	−	0.134806i
$161$	10.2980			0.811596
$162$		0			0
$163$		−	18.7968i		−	1.47228i	−0.676831	−	0.736138i	$-0.736647\pi$
$163$		−	18.7968i		−	1.47228i	0.676831	−	0.736138i	$-0.263353\pi$
$164$	−8.01447			−0.625825
$165$		0			0
$166$	−8.93200			−0.693257
$167$		−	5.92772i		−	0.458700i	−0.973344	−	0.229350i	$-0.926340\pi$
$167$		−	5.92772i		−	0.458700i	0.973344	−	0.229350i	$-0.0736601\pi$
$168$		0			0
$169$	12.8635			0.989500
$170$	−8.66772	+	7.35281i	−0.664784	+	0.563935i
$171$		0			0
$172$			2.27264i			0.173287i
$173$		−	5.78242i		−	0.439629i	−0.975542	−	0.219815i	$-0.929455\pi$
$173$		−	5.78242i		−	0.439629i	0.975542	−	0.219815i	$-0.0705453\pi$
$174$		0			0
$175$	9.03873	+	1.49380i	0.683264	+	0.112921i
$176$	−4.19017			−0.315846
$177$		0			0
$178$			11.4773i			0.860259i
$179$	7.13581			0.533355			0.266678	−	0.963786i	$-0.414074\pi$
$179$	7.13581			0.533355			0.266678	+	0.963786i	$0.414074\pi$
$180$		0			0
$181$	11.5365			0.857503			0.428752	−	0.903422i	$-0.358954\pi$
$181$	11.5365			0.857503			0.428752	+	0.903422i	$0.358954\pi$
$182$			0.676938i			0.0501780i
$183$		0			0
$184$	−5.62036			−0.414338
$185$	1.44650	+	1.70518i	0.106349	+	0.125367i
$186$		0			0
$187$			21.2994i			1.55756i
$188$		−	10.9154i		−	0.796090i
$189$		0			0
$190$	5.14900	+	6.06980i	0.373548	+	0.440350i
$191$	20.6048			1.49091			0.745456	−	0.666555i	$-0.232232\pi$
$191$	20.6048			1.49091			0.745456	+	0.666555i	$0.232232\pi$
$192$		0			0
$193$		−	26.1663i		−	1.88349i	−0.336321	−	0.941747i	$-0.609183\pi$
$193$		−	26.1663i		−	1.88349i	0.336321	−	0.941747i	$-0.390817\pi$
$194$	6.05864			0.434985
$195$		0			0
$196$	−3.64280			−0.260200
$197$			14.6067i			1.04069i	0.853957	+	0.520343i	$0.174196\pi$
$197$			14.6067i			1.04069i	−0.853957	+	0.520343i	$0.825804\pi$
$198$		0			0
$199$	−5.81275			−0.412055			−0.206027	−	0.978546i	$-0.566054\pi$
$199$	−5.81275			−0.412055			−0.206027	+	0.978546i	$0.566054\pi$
$200$	−4.93309	−	0.815273i	−0.348822	−	0.0576485i
$201$		0			0
$202$		−	4.96528i		−	0.349356i
$203$			2.21121i			0.155196i
$204$		0			0
$205$	−13.6661	+	11.5929i	−0.954482	+	0.809685i
$206$	7.33338			0.510940
$207$		0			0
$208$		−	0.369454i		−	0.0256170i
$209$	14.9154			1.03172
$210$		0			0
$211$	16.0976			1.10821			0.554104	−	0.832448i	$-0.313061\pi$
$211$	16.0976			1.10821			0.554104	+	0.832448i	$0.313061\pi$
$212$		−	9.94355i		−	0.682926i
$213$		0			0
$214$	8.21182			0.561349
$215$	3.28738	+	3.87526i	0.224197	+	0.264291i
$216$		0			0
$217$			18.5114i			1.25664i
$218$			20.5503i			1.39184i
$219$		0			0
$220$	−7.14499	+	6.06108i	−0.481715	+	0.408638i
$221$	−1.87800			−0.126328
$222$		0			0
$223$			25.3608i			1.69828i	0.528164	+	0.849142i	$0.322881\pi$
$223$			25.3608i			1.69828i	−0.528164	+	0.849142i	$0.677119\pi$
$224$	−1.83227			−0.122423
$225$		0			0
$226$	−0.652984			−0.0434359
$227$		−	5.57339i		−	0.369919i	−0.982746	−	0.184960i	$-0.940785\pi$
$227$		−	5.57339i		−	0.369919i	0.982746	−	0.184960i	$-0.0592154\pi$
$228$		0			0
$229$	−9.02035			−0.596081			−0.298041	−	0.954553i	$-0.596333\pi$
$229$	−9.02035			−0.596081			−0.298041	+	0.954553i	$0.596333\pi$
$230$	−9.58372	+	8.12985i	−0.631932	+	0.536067i
$231$		0			0
$232$		−	1.20681i		−	0.0792313i
$233$		−	11.8100i		−	0.773696i	−0.922144	−	0.386848i	$-0.873564\pi$
$233$		−	11.8100i		−	0.773696i	0.922144	−	0.386848i	$-0.126436\pi$
$234$		0			0
$235$	−15.7892	−	18.6128i	−1.02997	−	1.21416i
$236$	5.34563			0.347971
$237$		0			0
$238$			9.31373i			0.603719i
$239$	0.907160			0.0586793			0.0293396	−	0.999569i	$-0.490660\pi$
$239$	0.907160			0.0586793			0.0293396	+	0.999569i	$0.490660\pi$
$240$		0			0
$241$	−4.15616			−0.267722			−0.133861	−	0.991000i	$-0.542738\pi$
$241$	−4.15616			−0.267722			−0.133861	+	0.991000i	$0.542738\pi$
$242$			6.55754i			0.421534i
$243$		0			0
$244$	9.79428			0.627015
$245$	−6.21162	+	5.26931i	−0.396846	+	0.336644i
$246$		0			0
$247$			1.31512i			0.0836789i
$248$		−	10.1030i		−	0.641541i
$249$		0			0
$250$	−9.59109	+	5.74552i	−0.606594	+	0.363379i
$251$	−9.31888			−0.588203			−0.294101	−	0.955774i	$-0.595020\pi$
$251$	−9.31888			−0.588203			−0.294101	+	0.955774i	$0.595020\pi$
$252$		0			0
$253$			23.5503i			1.48059i
$254$	−19.2856			−1.21009
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	13.6312i		−	0.850294i	−0.905124	−	0.425147i	$-0.860222\pi$
$257$		−	13.6312i		−	0.850294i	0.905124	−	0.425147i	$-0.139778\pi$
$258$		0			0
$259$	1.83227			0.113852
$260$	−0.534415	−	0.629985i	−0.0331430	−	0.0390700i
$261$		0			0
$262$			8.82072i			0.544946i
$263$		−	27.2170i		−	1.67827i	−0.543921	−	0.839137i	$-0.683061\pi$
$263$		−	27.2170i		−	1.67827i	0.543921	−	0.839137i	$-0.316939\pi$
$264$		0			0
$265$	−14.3833	−	16.9555i	−0.883562	−	1.04157i
$266$	6.52218			0.399901
$267$		0			0
$268$			1.85073i			0.113052i
$269$	23.0550			1.40569			0.702845	−	0.711343i	$-0.251913\pi$
$269$	23.0550			1.40569			0.702845	+	0.711343i	$0.251913\pi$
$270$		0			0
$271$	22.9320			1.39302			0.696510	−	0.717547i	$-0.254735\pi$
$271$	22.9320			1.39302			0.696510	+	0.717547i	$0.254735\pi$
$272$		−	5.08317i		−	0.308213i
$273$		0			0
$274$	−4.66126			−0.281597
$275$	−3.41613	+	20.6705i	−0.206001	+	1.24648i
$276$		0			0
$277$			11.7534i			0.706192i	0.935587	+	0.353096i	$0.114871\pi$
$277$			11.7534i			0.706192i	−0.935587	+	0.353096i	$0.885129\pi$
$278$		−	16.4050i		−	0.983906i
$279$		0			0
$280$	−3.12434	+	2.65038i	−0.186715	+	0.158390i
$281$	29.0962			1.73573			0.867865	−	0.496799i	$-0.165492\pi$
$281$	29.0962			1.73573			0.867865	+	0.496799i	$0.165492\pi$
$282$		0			0
$283$		−	10.1829i		−	0.605311i	−0.953100	−	0.302655i	$-0.902127\pi$
$283$		−	10.1829i		−	0.605311i	0.953100	−	0.302655i	$-0.0978731\pi$
$284$	2.86038			0.169732
$285$		0			0
$286$	−1.54808			−0.0915396
$287$			14.6846i			0.866807i
$288$		0			0
$289$	−8.83864			−0.519920
$290$	−1.74566	−	2.05784i	−0.102509	−	0.120840i
$291$		0			0
$292$			8.09942i			0.473983i
$293$		−	18.1243i		−	1.05883i	−0.848363	−	0.529415i	$-0.822411\pi$
$293$		−	18.1243i		−	1.05883i	0.848363	−	0.529415i	$-0.177589\pi$
$294$		0			0
$295$	9.11525	−	7.73245i	0.530711	−	0.450201i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$		−	5.86259i		−	0.339611i
$299$	−2.07646			−0.120085
$300$		0			0
$301$	4.16409			0.240014
$302$			13.1460i			0.756467i
$303$		0			0
$304$	−3.55963			−0.204159
$305$	16.7010	−	14.1674i	0.956297	−	0.811225i
$306$		0			0
$307$			6.15561i			0.351319i	0.984451	+	0.175660i	$0.0562058\pi$
$307$			6.15561i			0.351319i	−0.984451	+	0.175660i	$0.943794\pi$
$308$			7.67751i			0.437467i
$309$		0			0
$310$	−14.6140	−	17.2274i	−0.830019	−	0.978452i
$311$	29.4512			1.67002			0.835011	−	0.550234i	$-0.185461\pi$
$311$	29.4512			1.67002			0.835011	+	0.550234i	$0.185461\pi$
$312$		0			0
$313$			13.0102i			0.735378i	0.929949	+	0.367689i	$0.119851\pi$
$313$			13.0102i			0.735378i	−0.929949	+	0.367689i	$0.880149\pi$
$314$	−7.33629			−0.414011
$315$		0			0
$316$	6.06361			0.341105
$317$		−	7.39826i		−	0.415528i	−0.978179	−	0.207764i	$-0.933381\pi$
$317$		−	7.39826i		−	0.415528i	0.978179	−	0.207764i	$-0.0666186\pi$
$318$		0			0
$319$	−5.05676			−0.283124
$320$	1.70518	−	1.44650i	0.0953224	−	0.0808618i
$321$		0			0
$322$			10.2980i			0.573885i
$323$			18.0942i			1.00679i
$324$		0			0
$325$	−1.82255	−	0.301206i	−0.101097	−	0.0167079i
$326$	18.7968			1.04106
$327$		0			0
$328$		−	8.01447i		−	0.442525i
$329$	−20.0000			−1.10264
$330$		0			0
$331$	33.2545			1.82783			0.913916	−	0.405903i	$-0.133043\pi$
$331$	33.2545			1.82783			0.913916	+	0.405903i	$0.133043\pi$
$332$		−	8.93200i		−	0.490207i
$333$		0			0
$334$	5.92772			0.324350
$335$	2.67709	+	3.15583i	0.146265	+	0.172422i
$336$		0			0
$337$		−	22.6288i		−	1.23267i	−0.787485	−	0.616334i	$-0.788617\pi$
$337$		−	22.6288i		−	1.23267i	0.787485	−	0.616334i	$-0.211383\pi$
$338$			12.8635i			0.699682i
$339$		0			0
$340$	−7.35281	−	8.66772i	−0.398762	−	0.470073i
$341$	−42.3333			−2.29248
$342$		0			0
$343$			19.5004i			1.05293i
$344$	−2.27264			−0.122533
$345$		0			0
$346$	5.78242			0.310865
$347$		−	24.1396i		−	1.29588i	−0.761691	−	0.647941i	$-0.775630\pi$
$347$		−	24.1396i		−	1.29588i	0.761691	−	0.647941i	$-0.224370\pi$
$348$		0			0
$349$	10.3702			0.555102			0.277551	−	0.960711i	$-0.410477\pi$
$349$	10.3702			0.555102			0.277551	+	0.960711i	$0.410477\pi$
$350$	−1.49380	+	9.03873i	−0.0798469	+	0.483140i
$351$		0			0
$352$		−	4.19017i		−	0.223337i
$353$			3.92699i			0.209013i	0.994524	+	0.104506i	$0.0333262\pi$
$353$			3.92699i			0.209013i	−0.994524	+	0.104506i	$0.966674\pi$
$354$		0			0
$355$	4.87745	−	4.13753i	0.258868	−	0.219598i
$356$	−11.4773			−0.608295
$357$		0			0
$358$			7.13581i			0.377139i
$359$	−9.85179			−0.519957			−0.259979	−	0.965614i	$-0.583716\pi$
$359$	−9.85179			−0.519957			−0.259979	+	0.965614i	$0.583716\pi$
$360$		0			0
$361$	−6.32907			−0.333109
$362$			11.5365i			0.606346i
$363$		0			0
$364$	−0.676938			−0.0354812
$365$	11.7158	+	13.8110i	0.613234	+	0.722899i
$366$		0			0
$367$		−	33.2559i		−	1.73594i	−0.496614	−	0.867972i	$-0.665423\pi$
$367$		−	33.2559i		−	1.73594i	0.496614	−	0.867972i	$-0.334577\pi$
$368$		−	5.62036i		−	0.292981i
$369$		0			0
$370$	−1.70518	+	1.44650i	−0.0886481	+	0.0752000i
$371$	−18.2192			−0.945896
$372$		0			0
$373$		−	28.5387i		−	1.47768i	−0.673882	−	0.738839i	$-0.735375\pi$
$373$		−	28.5387i		−	1.47768i	0.673882	−	0.738839i	$-0.264625\pi$
$374$	−21.2994			−1.10136
$375$		0			0
$376$	10.9154			0.562921
$377$		−	0.445862i		−	0.0229631i
$378$		0			0
$379$	−0.476554			−0.0244789			−0.0122395	−	0.999925i	$-0.503896\pi$
$379$	−0.476554			−0.0244789			−0.0122395	+	0.999925i	$0.503896\pi$
$380$	−6.06980	+	5.14900i	−0.311374	+	0.264138i
$381$		0			0
$382$			20.6048i			1.05423i
$383$		−	7.13962i		−	0.364818i	−0.983223	−	0.182409i	$-0.941611\pi$
$383$		−	7.13962i		−	0.364818i	0.983223	−	0.182409i	$-0.0583895\pi$
$384$		0			0
$385$	11.1055	+	13.0915i	0.565990	+	0.667206i
$386$	26.1663			1.33183
$387$		0			0
$388$			6.05864i			0.307581i
$389$	−24.2060			−1.22729			−0.613646	−	0.789581i	$-0.710298\pi$
$389$	−24.2060			−1.22729			−0.613646	+	0.789581i	$0.710298\pi$
$390$		0			0
$391$	−28.5693			−1.44481
$392$		−	3.64280i		−	0.183989i
$393$		0			0
$394$	−14.6067			−0.735876
$395$	10.3395	−	8.77101i	0.520239	−	0.441318i
$396$		0			0
$397$		−	20.7491i		−	1.04137i	−0.853750	−	0.520684i	$-0.825677\pi$
$397$		−	20.7491i		−	1.04137i	0.853750	−	0.520684i	$-0.174323\pi$
$398$		−	5.81275i		−	0.291367i
$399$		0			0
$400$	0.815273	−	4.93309i	0.0407637	−	0.246654i
$401$	34.8410			1.73988			0.869939	−	0.493159i	$-0.164158\pi$
$401$	34.8410			1.73988			0.869939	+	0.493159i	$0.164158\pi$
$402$		0			0
$403$		−	3.73259i		−	0.185934i
$404$	4.96528			0.247032
$405$		0			0
$406$	−2.21121			−0.109740
$407$			4.19017i			0.207699i
$408$		0			0
$409$	−25.2132			−1.24671			−0.623356	−	0.781938i	$-0.714231\pi$
$409$	−25.2132			−1.24671			−0.623356	+	0.781938i	$0.714231\pi$
$410$	−11.5929	−	13.6661i	−0.572534	−	0.674921i
$411$		0			0
$412$			7.33338i			0.361289i
$413$		−	9.79462i		−	0.481962i
$414$		0			0
$415$	−12.9201	−	15.2307i	−0.634225	−	0.747644i
$416$	0.369454			0.0181140
$417$		0			0
$418$			14.9154i			0.729538i
$419$	5.69695			0.278314			0.139157	−	0.990270i	$-0.455561\pi$
$419$	5.69695			0.278314			0.139157	+	0.990270i	$0.455561\pi$
$420$		0			0
$421$	3.38092			0.164776			0.0823880	−	0.996600i	$-0.473745\pi$
$421$	3.38092			0.164776			0.0823880	+	0.996600i	$0.473745\pi$
$422$			16.0976i			0.783621i
$423$		0			0
$424$	9.94355			0.482901
$425$	−25.0757	−	4.14417i	−1.21635	−	0.201022i
$426$		0			0
$427$		−	17.9457i		−	0.868455i
$428$			8.21182i			0.396933i
$429$		0			0
$430$	−3.87526	+	3.28738i	−0.186882	+	0.158531i
$431$	0.381731			0.0183873			0.00919367	−	0.999958i	$-0.497074\pi$
$431$	0.381731			0.0183873			0.00919367	+	0.999958i	$0.497074\pi$
$432$		0			0
$433$		−	21.6393i		−	1.03992i	−0.854192	−	0.519958i	$-0.825948\pi$
$433$		−	21.6393i		−	1.03992i	0.854192	−	0.519958i	$-0.174052\pi$
$434$	−18.5114			−0.888575
$435$		0			0
$436$	−20.5503			−0.984179
$437$			20.0064i			0.957035i
$438$		0			0
$439$	−26.4663			−1.26317			−0.631583	−	0.775308i	$-0.717595\pi$
$439$	−26.4663			−1.26317			−0.631583	+	0.775308i	$0.717595\pi$
$440$	−6.06108	−	7.14499i	−0.288951	−	0.340624i
$441$		0			0
$442$		−	1.87800i		−	0.0893273i
$443$			4.65489i			0.221161i	0.993867	+	0.110580i	$0.0352709\pi$
$443$			4.65489i			0.221161i	−0.993867	+	0.110580i	$0.964729\pi$
$444$		0			0
$445$	−19.5708	+	16.6019i	−0.927746	+	0.787005i
$446$	−25.3608			−1.20087
$447$		0			0
$448$		−	1.83227i		−	0.0865665i
$449$	−26.5531			−1.25312			−0.626558	−	0.779375i	$-0.715537\pi$
$449$	−26.5531			−1.25312			−0.626558	+	0.779375i	$0.715537\pi$
$450$		0			0
$451$	−33.5820			−1.58131
$452$		−	0.652984i		−	0.0307138i
$453$		0			0
$454$	5.57339			0.261572
$455$	−1.15430	+	0.979192i	−0.0541145	+	0.0459052i
$456$		0			0
$457$		−	4.27264i		−	0.199866i	−0.994994	−	0.0999329i	$-0.968137\pi$
$457$		−	4.27264i		−	0.199866i	0.994994	−	0.0999329i	$-0.0318628\pi$
$458$		−	9.02035i		−	0.421493i
$459$		0			0
$460$	−8.12985	−	9.58372i	−0.379056	−	0.446843i
$461$	−32.1873			−1.49911			−0.749555	−	0.661942i	$-0.769733\pi$
$461$	−32.1873			−1.49911			−0.749555	+	0.661942i	$0.769733\pi$
$462$		0			0
$463$			18.4014i			0.855186i	0.903971	+	0.427593i	$0.140638\pi$
$463$			18.4014i			0.855186i	−0.903971	+	0.427593i	$0.859362\pi$
$464$	1.20681			0.0560250
$465$		0			0
$466$	11.8100			0.547086
$467$		−	3.06777i		−	0.141959i	−0.997478	−	0.0709797i	$-0.977387\pi$
$467$		−	3.06777i		−	0.141959i	0.997478	−	0.0709797i	$-0.0226125\pi$
$468$		0			0
$469$	3.39104			0.156584
$470$	18.6128	−	15.7892i	0.858544	−	0.728301i
$471$		0			0
$472$			5.34563i			0.246052i
$473$			9.52276i			0.437857i
$474$		0			0
$475$	−2.90207	+	17.5599i	−0.133156	+	0.805705i
$476$	−9.31373			−0.426894
$477$		0			0
$478$			0.907160i			0.0414925i
$479$	8.78798			0.401533			0.200767	−	0.979639i	$-0.435657\pi$
$479$	8.78798			0.401533			0.200767	+	0.979639i	$0.435657\pi$
$480$		0			0
$481$	−0.369454			−0.0168457
$482$		−	4.15616i		−	0.189308i
$483$		0			0
$484$	−6.55754			−0.298070
$485$	8.76383	+	10.3311i	0.397945	+	0.469110i
$486$		0			0
$487$			22.4814i			1.01873i	0.860550	+	0.509366i	$0.170120\pi$
$487$			22.4814i			1.01873i	−0.860550	+	0.509366i	$0.829880\pi$
$488$			9.79428i			0.443366i
$489$		0			0
$490$	−5.26931	−	6.21162i	−0.238043	−	0.280613i
$491$	0.0441752			0.00199360			0.000996799	−	1.00000i	$-0.499683\pi$
$491$	0.0441752			0.00199360			0.000996799		1.00000i	$0.499683\pi$
$492$		0			0
$493$		−	6.13445i		−	0.276282i
$494$	−1.31512			−0.0591699
$495$		0			0
$496$	10.1030			0.453638
$497$		−	5.24097i		−	0.235090i
$498$		0			0
$499$	−28.2445			−1.26440			−0.632199	−	0.774806i	$-0.717847\pi$
$499$	−28.2445			−1.26440			−0.632199	+	0.774806i	$0.717847\pi$
$500$	−5.74552	−	9.59109i	−0.256948	−	0.428926i
$501$		0			0
$502$		−	9.31888i		−	0.415922i
$503$			19.7713i			0.881560i	0.897615	+	0.440780i	$0.145298\pi$
$503$			19.7713i			0.881560i	−0.897615	+	0.440780i	$0.854702\pi$
$504$		0			0
$505$	8.46670	−	7.18229i	0.376763	−	0.319608i
$506$	−23.5503			−1.04694
$507$		0			0
$508$		−	19.2856i		−	0.855660i
$509$	43.4809			1.92726			0.963628	−	0.267247i	$-0.0861141\pi$
$509$	43.4809			1.92726			0.963628	+	0.267247i	$0.0861141\pi$
$510$		0			0
$511$	14.8403			0.656496
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	13.6312			0.601249
$515$	10.6077	+	12.5047i	0.467432	+	0.551024i
$516$		0			0
$517$		−	45.7376i		−	2.01154i
$518$			1.83227i			0.0805052i
$519$		0			0
$520$	0.629985	−	0.534415i	0.0276267	−	0.0234357i
$521$	18.0325			0.790019			0.395009	−	0.918677i	$-0.370741\pi$
$521$	18.0325			0.790019			0.395009	+	0.918677i	$0.370741\pi$
$522$		0			0
$523$			31.6788i			1.38522i	0.721313	+	0.692610i	$0.243539\pi$
$523$			31.6788i			1.38522i	−0.721313	+	0.692610i	$0.756461\pi$
$524$	−8.82072			−0.385335
$525$		0			0
$526$	27.2170			1.18672
$527$		−	51.3553i		−	2.23707i
$528$		0			0
$529$	−8.58844			−0.373410
$530$	16.9555	−	14.3833i	0.736501	−	0.624773i
$531$		0			0
$532$			6.52218i			0.282773i
$533$		−	2.96098i		−	0.128254i
$534$		0			0
$535$	11.8784	+	14.0026i	0.513548	+	0.605387i
$536$	−1.85073			−0.0799395
$537$		0			0
$538$			23.0550i			0.993973i
$539$	−15.2639			−0.657465
$540$		0			0
$541$	9.39442			0.403898			0.201949	−	0.979396i	$-0.435273\pi$
$541$	9.39442			0.403898			0.201949	+	0.979396i	$0.435273\pi$
$542$			22.9320i			0.985014i
$543$		0			0
$544$	5.08317			0.217939
$545$	−35.0419	+	29.7260i	−1.50103	+	1.27332i
$546$		0			0
$547$		−	24.7824i		−	1.05962i	−0.848117	−	0.529809i	$-0.822263\pi$
$547$		−	24.7824i		−	1.05962i	0.848117	−	0.529809i	$-0.177737\pi$
$548$		−	4.66126i		−	0.199119i
$549$		0			0
$550$	−20.6705	−	3.41613i	−0.881392	−	0.145664i
$551$	−4.29581			−0.183008
$552$		0			0
$553$		−	11.1102i		−	0.472452i
$554$	−11.7534			−0.499353
$555$		0			0
$556$	16.4050			0.695727
$557$		−	22.1627i		−	0.939062i	−0.882916	−	0.469531i	$-0.844423\pi$
$557$		−	22.1627i		−	0.939062i	0.882916	−	0.469531i	$-0.155577\pi$
$558$		0			0
$559$	−0.839637			−0.0355128
$560$	−2.65038	−	3.12434i	−0.111999	−	0.132028i
$561$		0			0
$562$			29.0962i			1.22735i
$563$		−	6.46846i		−	0.272613i	−0.990667	−	0.136306i	$-0.956477\pi$
$563$		−	6.46846i		−	0.272613i	0.990667	−	0.136306i	$-0.0435232\pi$
$564$		0			0
$565$	−0.944542	−	1.11346i	−0.0397372	−	0.0468434i
$566$	10.1829			0.428019
$567$		0			0
$568$			2.86038i			0.120019i
$569$	8.26550			0.346508			0.173254	−	0.984877i	$-0.444572\pi$
$569$	8.26550			0.346508			0.173254	+	0.984877i	$0.444572\pi$
$570$		0			0
$571$	34.5179			1.44453			0.722264	−	0.691618i	$-0.243102\pi$
$571$	34.5179			1.44453			0.722264	+	0.691618i	$0.243102\pi$
$572$		−	1.54808i		−	0.0647283i
$573$		0			0
$574$	−14.6846			−0.612925
$575$	−27.7257	−	4.58213i	−1.15624	−	0.191088i
$576$		0			0
$577$			3.05347i			0.127117i	0.997978	+	0.0635587i	$0.0202450\pi$
$577$			3.05347i			0.127117i	−0.997978	+	0.0635587i	$0.979755\pi$
$578$		−	8.83864i		−	0.367639i
$579$		0			0
$580$	2.05784	−	1.74566i	0.0854470	−	0.0724845i
$581$	−16.3658			−0.678968
$582$		0			0
$583$		−	41.6652i		−	1.72559i
$584$	−8.09942			−0.335156
$585$		0			0
$586$	18.1243			0.748706
$587$		−	35.1344i		−	1.45015i	−0.688668	−	0.725076i	$-0.741804\pi$
$587$		−	35.1344i		−	1.45015i	0.688668	−	0.725076i	$-0.258196\pi$
$588$		0			0
$589$	−35.9629			−1.48183
$590$	7.73245	+	9.11525i	0.318340	+	0.375269i
$591$		0			0
$592$		−	1.00000i		−	0.0410997i
$593$			12.0400i			0.494424i	0.968961	+	0.247212i	$0.0795144\pi$
$593$			12.0400i			0.494424i	−0.968961	+	0.247212i	$0.920486\pi$
$594$		0			0
$595$	−15.8816	+	13.4723i	−0.651081	+	0.552311i
$596$	5.86259			0.240141
$597$		0			0
$598$		−	2.07646i		−	0.0849129i
$599$	−17.4701			−0.713810			−0.356905	−	0.934141i	$-0.616168\pi$
$599$	−17.4701			−0.713810			−0.356905	+	0.934141i	$0.616168\pi$
$600$		0			0
$601$	38.7044			1.57878			0.789392	−	0.613890i	$-0.210396\pi$
$601$	38.7044			1.57878			0.789392	+	0.613890i	$0.210396\pi$
$602$			4.16409i			0.169716i
$603$		0			0
$604$	−13.1460			−0.534903
$605$	−11.1818	+	9.48548i	−0.454604	+	0.385639i
$606$		0			0
$607$			28.7903i			1.16856i	0.811551	+	0.584282i	$0.198624\pi$
$607$			28.7903i			1.16856i	−0.811551	+	0.584282i	$0.801376\pi$
$608$		−	3.55963i		−	0.144362i
$609$		0			0
$610$	14.1674	+	16.7010i	0.573623	+	0.676204i
$611$	4.03275			0.163148
$612$		0			0
$613$		−	7.66539i		−	0.309602i	−0.987946	−	0.154801i	$-0.950526\pi$
$613$		−	7.66539i		−	0.309602i	0.987946	−	0.154801i	$-0.0494737\pi$
$614$	−6.15561			−0.248420
$615$		0			0
$616$	−7.67751			−0.309336
$617$			36.5388i			1.47100i	0.677527	+	0.735498i	$0.263052\pi$
$617$			36.5388i			1.47100i	−0.677527	+	0.735498i	$0.736948\pi$
$618$		0			0
$619$	45.8085			1.84120			0.920599	−	0.390510i	$-0.127701\pi$
$619$	45.8085			1.84120			0.920599	+	0.390510i	$0.127701\pi$
$620$	17.2274	−	14.6140i	0.691870	−	0.586912i
$621$		0			0
$622$			29.4512i			1.18088i
$623$			21.0294i			0.842527i
$624$		0			0
$625$	−23.6707	−	8.04362i	−0.946826	−	0.321745i
$626$	−13.0102			−0.519991
$627$		0			0
$628$		−	7.33629i		−	0.292750i
$629$	−5.08317			−0.202679
$630$		0			0
$631$	3.42682			0.136420			0.0682098	−	0.997671i	$-0.478271\pi$
$631$	3.42682			0.136420			0.0682098	+	0.997671i	$0.478271\pi$
$632$			6.06361i			0.241197i
$633$		0			0
$634$	7.39826			0.293823
$635$	−27.8966	−	32.8854i	−1.10704	−	1.30502i
$636$		0			0
$637$		−	1.34585i		−	0.0533244i
$638$		−	5.05676i		−	0.200199i
$639$		0			0
$640$	1.44650	+	1.70518i	0.0571779	+	0.0674031i
$641$	−38.3241			−1.51371			−0.756855	−	0.653583i	$-0.773265\pi$
$641$	−38.3241			−1.51371			−0.756855	+	0.653583i	$0.773265\pi$
$642$		0			0
$643$			1.36660i			0.0538935i	0.999637	+	0.0269468i	$0.00857846\pi$
$643$			1.36660i			0.0538935i	−0.999637	+	0.0269468i	$0.991422\pi$
$644$	−10.2980			−0.405798
$645$		0			0
$646$	−18.0942			−0.711906
$647$			11.2690i			0.443028i	0.975157	+	0.221514i	$0.0710999\pi$
$647$			11.2690i			0.443028i	−0.975157	+	0.221514i	$0.928900\pi$
$648$		0			0
$649$	22.3991			0.879241
$650$	0.301206	−	1.82255i	0.0118143	−	0.0714862i
$651$		0			0
$652$			18.7968i			0.736138i
$653$			29.5439i			1.15614i	0.815987	+	0.578070i	$0.196194\pi$
$653$			29.5439i			1.15614i	−0.815987	+	0.578070i	$0.803806\pi$
$654$		0			0
$655$	−15.0409	+	12.7592i	−0.587697	+	0.498542i
$656$	8.01447			0.312912
$657$		0			0
$658$		−	20.0000i		−	0.779681i
$659$	−49.9126			−1.94432			−0.972159	−	0.234324i	$-0.924712\pi$
$659$	−49.9126			−1.94432			−0.972159	+	0.234324i	$0.924712\pi$
$660$		0			0
$661$	25.9950			1.01109			0.505545	−	0.862800i	$-0.331292\pi$
$661$	25.9950			1.01109			0.505545	+	0.862800i	$0.331292\pi$
$662$			33.2545i			1.29247i
$663$		0			0
$664$	8.93200			0.346629
$665$	9.43434	+	11.1215i	0.365848	+	0.431273i
$666$		0			0
$667$		−	6.78273i		−	0.262628i
$668$			5.92772i			0.229350i
$669$		0			0
$670$	−3.15583	+	2.67709i	−0.121920	+	0.103425i
$671$	41.0397			1.58432
$672$		0			0
$673$			6.91054i			0.266382i	0.991090	+	0.133191i	$0.0425223\pi$
$673$			6.91054i			0.266382i	−0.991090	+	0.133191i	$0.957478\pi$
$674$	22.6288			0.871627
$675$		0			0
$676$	−12.8635			−0.494750
$677$		−	15.6913i		−	0.603065i	−0.953456	−	0.301532i	$-0.902502\pi$
$677$		−	15.6913i		−	0.603065i	0.953456	−	0.301532i	$-0.0974982\pi$
$678$		0			0
$679$	11.1011			0.426019
$680$	8.66772	−	7.35281i	0.332392	−	0.281967i
$681$		0			0
$682$		−	42.3333i		−	1.62103i
$683$			18.2002i			0.696412i	0.937418	+	0.348206i	$0.113209\pi$
$683$			18.2002i			0.696412i	−0.937418	+	0.348206i	$0.886791\pi$
$684$		0			0
$685$	−6.74252	−	7.94829i	−0.257618	−	0.303689i
$686$	−19.5004			−0.744531
$687$		0			0
$688$		−	2.27264i		−	0.0866437i
$689$	3.67368			0.139956
$690$		0			0
$691$	−2.58658			−0.0983982			−0.0491991	−	0.998789i	$-0.515667\pi$
$691$	−2.58658			−0.0983982			−0.0491991	+	0.998789i	$0.515667\pi$
$692$			5.78242i			0.219815i
$693$		0			0
$694$	24.1396			0.916327
$695$	27.9735	−	23.7298i	1.06109	−	0.900124i
$696$		0			0
$697$		−	40.7389i		−	1.54310i
$698$			10.3702i			0.392516i
$699$		0			0
$700$	−9.03873	−	1.49380i	−0.341632	−	0.0564603i
$701$	26.5092			1.00124			0.500620	−	0.865667i	$-0.333105\pi$
$701$	26.5092			1.00124			0.500620	+	0.865667i	$0.333105\pi$
$702$		0			0
$703$			3.55963i			0.134254i
$704$	4.19017			0.157923
$705$		0			0
$706$	−3.92699			−0.147794
$707$		−	9.09773i		−	0.342155i
$708$		0			0
$709$	25.0474			0.940674			0.470337	−	0.882487i	$-0.344132\pi$
$709$	25.0474			0.940674			0.470337	+	0.882487i	$0.344132\pi$
$710$	4.13753	+	4.87745i	0.155279	+	0.183048i
$711$		0			0
$712$		−	11.4773i		−	0.430129i
$713$		−	56.7825i		−	2.12652i
$714$		0			0
$715$	−2.23929	−	2.63975i	−0.0837448	−	0.0987209i
$716$	−7.13581			−0.266678
$717$		0			0
$718$		−	9.85179i		−	0.367665i
$719$	24.9551			0.930668			0.465334	−	0.885135i	$-0.345934\pi$
$719$	24.9551			0.930668			0.465334	+	0.885135i	$0.345934\pi$
$720$		0			0
$721$	13.4367			0.500409
$722$		−	6.32907i		−	0.235544i
$723$		0			0
$724$	−11.5365			−0.428752
$725$	0.983883	−	5.95332i	0.0365405	−	0.221101i
$726$		0			0
$727$			21.6774i			0.803970i	0.915646	+	0.401985i	$0.131680\pi$
$727$			21.6774i			0.803970i	−0.915646	+	0.401985i	$0.868320\pi$
$728$		−	0.676938i		−	0.0250890i
$729$		0			0
$730$	−13.8110	+	11.7158i	−0.511167	+	0.433622i
$731$	−11.5522			−0.427275
$732$		0			0
$733$			6.33267i			0.233903i	0.993138	+	0.116951i	$0.0373122\pi$
$733$			6.33267i			0.233903i	−0.993138	+	0.116951i	$0.962688\pi$
$734$	33.2559			1.22750
$735$		0			0
$736$	5.62036			0.207169
$737$			7.75489i			0.285655i
$738$		0			0
$739$	−12.8076			−0.471136			−0.235568	−	0.971858i	$-0.575695\pi$
$739$	−12.8076			−0.471136			−0.235568	+	0.971858i	$0.575695\pi$
$740$	−1.44650	−	1.70518i	−0.0531744	−	0.0626836i
$741$		0			0
$742$		−	18.2192i		−	0.668849i
$743$		−	11.0694i		−	0.406097i	−0.979169	−	0.203048i	$-0.934915\pi$
$743$		−	11.0694i		−	0.406097i	0.979169	−	0.203048i	$-0.0650848\pi$
$744$		0			0
$745$	9.99677	−	8.48024i	0.366253	−	0.310692i
$746$	28.5387			1.04488
$747$		0			0
$748$		−	21.2994i		−	0.778782i
$749$	15.0463			0.549778
$750$		0			0
$751$	−46.5316			−1.69796			−0.848981	−	0.528423i	$-0.822784\pi$
$751$	−46.5316			−1.69796			−0.848981	+	0.528423i	$0.822784\pi$
$752$			10.9154i			0.398045i
$753$		0			0
$754$	0.445862			0.0162374
$755$	−22.4163	+	19.0157i	−0.815812	+	0.692052i
$756$		0			0
$757$		−	32.9872i		−	1.19894i	−0.800397	−	0.599470i	$-0.795378\pi$
$757$		−	32.9872i		−	1.19894i	0.800397	−	0.599470i	$-0.204622\pi$
$758$		−	0.476554i		−	0.0173092i
$759$		0			0
$760$	−5.14900	−	6.06980i	−0.186774	−	0.220175i
$761$	−28.7913			−1.04369			−0.521843	−	0.853042i	$-0.674755\pi$
$761$	−28.7913			−1.04369			−0.521843	+	0.853042i	$0.674755\pi$
$762$		0			0
$763$			37.6536i			1.36315i
$764$	−20.6048			−0.745456
$765$		0			0
$766$	7.13962			0.257965
$767$			1.97496i			0.0713118i
$768$		0			0
$769$	−41.9025			−1.51104			−0.755521	−	0.655124i	$-0.772616\pi$
$769$	−41.9025			−1.51104			−0.755521	+	0.655124i	$0.772616\pi$
$770$	−13.0915	+	11.1055i	−0.471786	+	0.400215i
$771$		0			0
$772$			26.1663i			0.941747i
$773$		−	31.0931i		−	1.11834i	−0.829052	−	0.559171i	$-0.811119\pi$
$773$		−	31.0931i		−	1.11834i	0.829052	−	0.559171i	$-0.188881\pi$
$774$		0			0
$775$	8.23670	−	49.8390i	0.295871	−	1.79027i
$776$	−6.05864			−0.217493
$777$		0			0
$778$		−	24.2060i		−	0.867827i
$779$	−28.5285			−1.02214
$780$		0			0
$781$	11.9855			0.428874
$782$		−	28.5693i		−	1.02163i
$783$		0			0
$784$	3.64280			0.130100
$785$	−10.6120	−	12.5097i	−0.378757	−	0.446490i
$786$		0			0
$787$			18.2842i			0.651760i	0.945411	+	0.325880i	$0.105661\pi$
$787$			18.2842i			0.651760i	−0.945411	+	0.325880i	$0.894339\pi$
$788$		−	14.6067i		−	0.520343i
$789$		0			0
$790$	8.77101	+	10.3395i	0.312059	+	0.367864i
$791$	−1.19644			−0.0425406
$792$		0			0
$793$			3.61854i			0.128498i
$794$	20.7491			0.736358
$795$		0			0
$796$	5.81275			0.206027
$797$		−	40.6025i		−	1.43821i	−0.694900	−	0.719106i	$-0.744551\pi$
$797$		−	40.6025i		−	1.43821i	0.694900	−	0.719106i	$-0.255449\pi$
$798$		0			0
$799$	55.4851			1.96292
$800$	4.93309	+	0.815273i	0.174411	+	0.0288243i
$801$		0			0
$802$			34.8410i			1.23028i
$803$			33.9380i			1.19764i
$804$		0			0
$805$	−17.5599	+	14.8961i	−0.618906	+	0.525017i
$806$	3.73259			0.131475
$807$		0			0
$808$			4.96528i			0.174678i
$809$	41.1512			1.44680			0.723400	−	0.690429i	$-0.242578\pi$
$809$	41.1512			1.44680			0.723400	+	0.690429i	$0.242578\pi$
$810$		0			0
$811$	−6.71866			−0.235924			−0.117962	−	0.993018i	$-0.537636\pi$
$811$	−6.71866			−0.235924			−0.117962	+	0.993018i	$0.537636\pi$
$812$		−	2.21121i		−	0.0775981i
$813$		0			0
$814$	−4.19017			−0.146865
$815$	27.1895	+	32.0519i	0.952408	+	1.12273i
$816$		0			0
$817$			8.08975i			0.283025i
$818$		−	25.2132i		−	0.881558i
$819$		0			0
$820$	13.6661	−	11.5929i	0.477241	−	0.404843i
$821$	11.5263			0.402272			0.201136	−	0.979563i	$-0.435537\pi$
$821$	11.5263			0.402272			0.201136	+	0.979563i	$0.435537\pi$
$822$		0			0
$823$		−	4.69569i		−	0.163681i	−0.996645	−	0.0818407i	$-0.973920\pi$
$823$		−	4.69569i		−	0.163681i	0.996645	−	0.0818407i	$-0.0260799\pi$
$824$	−7.33338			−0.255470
$825$		0			0
$826$	9.79462			0.340798
$827$		−	28.4859i		−	0.990550i	−0.868736	−	0.495275i	$-0.835067\pi$
$827$		−	28.4859i		−	0.990550i	0.868736	−	0.495275i	$-0.164933\pi$
$828$		0			0
$829$	40.2771			1.39888			0.699441	−	0.714691i	$-0.253433\pi$
$829$	40.2771			1.39888			0.699441	+	0.714691i	$0.253433\pi$
$830$	15.2307	−	12.9201i	0.528664	−	0.448465i
$831$		0			0
$832$			0.369454i			0.0128085i
$833$		−	18.5170i		−	0.641575i
$834$		0			0
$835$	8.57444	+	10.1078i	0.296731	+	0.349796i
$836$	−14.9154			−0.515861
$837$		0			0
$838$			5.69695i			0.196798i
$839$	−9.99007			−0.344895			−0.172448	−	0.985019i	$-0.555168\pi$
$839$	−9.99007			−0.344895			−0.172448	+	0.985019i	$0.555168\pi$
$840$		0			0
$841$	−27.5436			−0.949779
$842$			3.38092i			0.116514i
$843$		0			0
$844$	−16.0976			−0.554104
$845$	−21.9346	+	18.6071i	−0.754573	+	0.640102i
$846$		0			0
$847$			12.0152i			0.412846i
$848$			9.94355i			0.341463i
$849$		0			0
$850$	4.14417	−	25.0757i	0.142144	−	0.860090i
$851$	−5.62036			−0.192663
$852$		0			0
$853$		−	18.0500i		−	0.618019i	−0.951059	−	0.309010i	$-0.900002\pi$
$853$		−	18.0500i		−	0.618019i	0.951059	−	0.309010i	$-0.0999975\pi$
$854$	17.9457			0.614091
$855$		0			0
$856$	−8.21182			−0.280674
$857$			24.3118i			0.830474i	0.909713	+	0.415237i	$0.136301\pi$
$857$			24.3118i			0.830474i	−0.909713	+	0.415237i	$0.863699\pi$
$858$		0			0
$859$	−35.2112			−1.20139			−0.600696	−	0.799477i	$-0.705110\pi$
$859$	−35.2112			−1.20139			−0.600696	+	0.799477i	$0.705110\pi$
$860$	−3.28738	−	3.87526i	−0.112099	−	0.132145i
$861$		0			0
$862$			0.381731i			0.0130018i
$863$		−	23.2986i		−	0.793093i	−0.918015	−	0.396546i	$-0.870209\pi$
$863$		−	23.2986i		−	0.793093i	0.918015	−	0.396546i	$-0.129791\pi$
$864$		0			0
$865$	8.36428	+	9.86007i	0.284394	+	0.335252i
$866$	21.6393			0.735332
$867$		0			0
$868$		−	18.5114i		−	0.628318i
$869$	25.4076			0.861893
$870$		0			0
$871$	−0.683761			−0.0231684
$872$		−	20.5503i		−	0.695920i
$873$		0			0
$874$	−20.0064			−0.676726
$875$	−17.5734	+	10.5273i	−0.594091	+	0.355889i
$876$		0			0
$877$		−	47.8713i		−	1.61650i	−0.588839	−	0.808250i	$-0.700415\pi$
$877$		−	47.8713i		−	1.61650i	0.588839	−	0.808250i	$-0.299585\pi$
$878$		−	26.4663i		−	0.893194i
$879$		0			0
$880$	7.14499	−	6.06108i	0.240858	−	0.204319i
$881$	40.1274			1.35193			0.675963	−	0.736936i	$-0.263728\pi$
$881$	40.1274			1.35193			0.675963	+	0.736936i	$0.263728\pi$
$882$		0			0
$883$			45.6747i			1.53708i	0.639803	+	0.768539i	$0.279016\pi$
$883$			45.6747i			1.53708i	−0.639803	+	0.768539i	$0.720984\pi$
$884$	1.87800			0.0631639
$885$		0			0
$886$	−4.65489			−0.156384
$887$		−	17.5417i		−	0.588992i	−0.955653	−	0.294496i	$-0.904848\pi$
$887$		−	17.5417i		−	0.588992i	0.955653	−	0.294496i	$-0.0951517\pi$
$888$		0			0
$889$	−35.3364			−1.18514
$890$	−16.6019	−	19.5708i	−0.556497	−	0.656015i
$891$		0			0
$892$		−	25.3608i		−	0.849142i
$893$		−	38.8549i		−	1.30023i
$894$		0			0
$895$	−12.1678	+	10.3220i	−0.406726	+	0.345025i
$896$	1.83227			0.0612117
$897$		0			0
$898$		−	26.5531i		−	0.886087i
$899$	12.1924			0.406641
$900$		0			0
$901$	50.5448			1.68389
$902$		−	33.5820i		−	1.11816i
$903$		0			0
$904$	0.652984			0.0217179
$905$	−19.6718	+	16.6876i	−0.653914	+	0.554714i
$906$		0			0
$907$			2.04294i			0.0678347i	0.999425	+	0.0339173i	$0.0107983\pi$
$907$			2.04294i			0.0678347i	−0.999425	+	0.0339173i	$0.989202\pi$
$908$			5.57339i			0.184960i
$909$		0			0
$910$	−0.979192	−	1.15430i	−0.0324599	−	0.0382647i
$911$	−54.3145			−1.79952			−0.899760	−	0.436385i	$-0.856258\pi$
$911$	−54.3145			−1.79952			−0.899760	+	0.436385i	$0.856258\pi$
$912$		0			0
$913$		−	37.4266i		−	1.23864i
$914$	4.27264			0.141326
$915$		0			0
$916$	9.02035			0.298041
$917$			16.1619i			0.533713i
$918$		0			0
$919$	−40.9771			−1.35171			−0.675855	−	0.737034i	$-0.736226\pi$
$919$	−40.9771			−1.35171			−0.675855	+	0.737034i	$0.736226\pi$
$920$	9.58372	−	8.12985i	0.315966	−	0.268033i
$921$		0			0
$922$		−	32.1873i		−	1.06003i
$923$			1.05678i			0.0347842i
$924$		0			0
$925$	−4.93309	−	0.815273i	−0.162199	−	0.0268060i
$926$	−18.4014			−0.604708
$927$		0			0
$928$			1.20681i			0.0396156i
$929$	−22.2458			−0.729860			−0.364930	−	0.931035i	$-0.618907\pi$
$929$	−22.2458			−0.729860			−0.364930	+	0.931035i	$0.618907\pi$
$930$		0			0
$931$	−12.9670			−0.424976
$932$			11.8100i			0.386848i
$933$		0			0
$934$	3.06777			0.100380
$935$	−30.8095	−	36.3192i	−1.00758	−	1.18777i
$936$		0			0
$937$			0.989771i			0.0323344i	0.999869	+	0.0161672i	$0.00514640\pi$
$937$			0.989771i			0.0323344i	−0.999869	+	0.0161672i	$0.994854\pi$
$938$			3.39104i			0.110721i
$939$		0			0
$940$	15.7892	+	18.6128i	0.514987	+	0.607082i
$941$	−0.255111			−0.00831639			−0.00415820	−	0.999991i	$-0.501324\pi$
$941$	−0.255111			−0.00831639			−0.00415820	+	0.999991i	$0.501324\pi$
$942$		0			0
$943$		−	45.0442i		−	1.46684i
$944$	−5.34563			−0.173985
$945$		0			0
$946$	−9.52276			−0.309612
$947$			58.4983i			1.90094i	0.310819	+	0.950469i	$0.399397\pi$
$947$			58.4983i			1.90094i	−0.310819	+	0.950469i	$0.600603\pi$
$948$		0			0
$949$	−2.99236			−0.0971362
$950$	−17.5599	−	2.90207i	−0.569720	−	0.0941555i
$951$		0			0
$952$		−	9.31373i		−	0.301860i
$953$		−	34.4365i		−	1.11551i	−0.830006	−	0.557755i	$-0.811663\pi$
$953$		−	34.4365i		−	1.11551i	0.830006	−	0.557755i	$-0.188337\pi$
$954$		0			0
$955$	−35.1349	+	29.8049i	−1.13694	+	0.964463i
$956$	−0.907160			−0.0293396
$957$		0			0
$958$			8.78798i			0.283927i
$959$	−8.54068			−0.275793
$960$		0			0
$961$	71.0706			2.29260
$962$		−	0.369454i		−	0.0119117i
$963$		0			0
$964$	4.15616			0.133861
$965$	37.8496	+	44.6183i	1.21842	+	1.43631i
$966$		0			0
$967$		−	19.0310i		−	0.611997i	−0.952032	−	0.305998i	$-0.901010\pi$
$967$		−	19.0310i		−	0.611997i	0.952032	−	0.305998i	$-0.0989902\pi$
$968$		−	6.55754i		−	0.210767i
$969$		0			0
$970$	−10.3311	+	8.76383i	−0.331711	+	0.281390i
$971$	−50.9856			−1.63621			−0.818103	−	0.575071i	$-0.804974\pi$
$971$	−50.9856			−1.63621			−0.818103	+	0.575071i	$0.804974\pi$
$972$		0			0
$973$		−	30.0583i		−	0.963626i
$974$	−22.4814			−0.720352
$975$		0			0
$976$	−9.79428			−0.313507
$977$		−	26.8574i		−	0.859245i	−0.903009	−	0.429622i	$-0.858647\pi$
$977$		−	26.8574i		−	0.859245i	0.903009	−	0.429622i	$-0.141353\pi$
$978$		0			0
$979$	−48.0918			−1.53702
$980$	6.21162	−	5.26931i	0.198423	−	0.168322i
$981$		0			0
$982$			0.0441752i			0.00140969i
$983$			7.09389i			0.226260i	0.993580	+	0.113130i	$0.0360877\pi$
$983$			7.09389i			0.226260i	−0.993580	+	0.113130i	$0.963912\pi$
$984$		0			0
$985$	−21.1286	−	24.9071i	−0.673214	−	0.793605i
$986$	6.13445			0.195361
$987$		0			0
$988$		−	1.31512i		−	0.0418395i
$989$	−12.7731			−0.406160
$990$		0			0
$991$	−27.2573			−0.865856			−0.432928	−	0.901429i	$-0.642520\pi$
$991$	−27.2573			−0.865856			−0.432928	+	0.901429i	$0.642520\pi$
$992$			10.1030i			0.320771i
$993$		0			0
$994$	5.24097			0.166234
$995$	9.91178	−	8.40814i	0.314224	−	0.266556i
$996$		0			0
$997$			24.6984i			0.782207i	0.920347	+	0.391103i	$0.127906\pi$
$997$			24.6984i			0.782207i	−0.920347	+	0.391103i	$0.872094\pi$
$998$		−	28.2445i		−	0.894064i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.p.1999.8		10
3.2	odd	2		370.2.b.d.149.5	✓	10
5.4	even	2	inner	3330.2.d.p.1999.3		10
15.2	even	4		1850.2.a.be.1.5		5
15.8	even	4		1850.2.a.bd.1.1		5
15.14	odd	2		370.2.b.d.149.6	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.d.149.5	✓	10	3.2	odd	2
370.2.b.d.149.6	yes	10	15.14	odd	2
1850.2.a.bd.1.1		5	15.8	even	4
1850.2.a.be.1.5		5	15.2	even	4
3330.2.d.p.1999.3		10	5.4	even	2	inner
3330.2.d.p.1999.8		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.70518 + 1.44650i) q^{5} +1.83227i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.70518 + 1.44650i) q^{5} +1.83227i q^{7} -1.00000i q^{8} +(-1.44650 - 1.70518i) q^{10} -4.19017 q^{11} -0.369454i q^{13} -1.83227 q^{14} +1.00000 q^{16} -5.08317i q^{17} -3.55963 q^{19} +(1.70518 - 1.44650i) q^{20} -4.19017i q^{22} -5.62036i q^{23} +(0.815273 - 4.93309i) q^{25} +0.369454 q^{26} -1.83227i q^{28} +1.20681 q^{29} +10.1030 q^{31} +1.00000i q^{32} +5.08317 q^{34} +(-2.65038 - 3.12434i) q^{35} -1.00000i q^{37} -3.55963i q^{38} +(1.44650 + 1.70518i) q^{40} +8.01447 q^{41} -2.27264i q^{43} +4.19017 q^{44} +5.62036 q^{46} +10.9154i q^{47} +3.64280 q^{49} +(4.93309 + 0.815273i) q^{50} +0.369454i q^{52} +9.94355i q^{53} +(7.14499 - 6.06108i) q^{55} +1.83227 q^{56} +1.20681i q^{58} -5.34563 q^{59} -9.79428 q^{61} +10.1030i q^{62} -1.00000 q^{64} +(0.534415 + 0.629985i) q^{65} -1.85073i q^{67} +5.08317i q^{68} +(3.12434 - 2.65038i) q^{70} -2.86038 q^{71} -8.09942i q^{73} +1.00000 q^{74} +3.55963 q^{76} -7.67751i q^{77} -6.06361 q^{79} +(-1.70518 + 1.44650i) q^{80} +8.01447i q^{82} +8.93200i q^{83} +(7.35281 + 8.66772i) q^{85} +2.27264 q^{86} +4.19017i q^{88} +11.4773 q^{89} +0.676938 q^{91} +5.62036i q^{92} -10.9154 q^{94} +(6.06980 - 5.14900i) q^{95} -6.05864i q^{97} +3.64280i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} - 6 q^{5}+O(q^{10}) \) 10 * q - 10 * q^4 - 6 * q^5	\( 10 q - 10 q^{4} - 6 q^{5} + 2 q^{10} - 6 q^{11} - 2 q^{14} + 10 q^{16} - 8 q^{19} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 22 q^{29} + 46 q^{31} - 18 q^{34} - 32 q^{35} - 2 q^{40} + 14 q^{41} + 6 q^{44} + 12 q^{46} - 60 q^{49} - 8 q^{50} + 42 q^{55} + 2 q^{56} + 40 q^{59} - 18 q^{61} - 10 q^{64} - 4 q^{65} - 6 q^{70} - 12 q^{71} + 10 q^{74} + 8 q^{76} - 40 q^{79} - 6 q^{80} + 36 q^{85} + 34 q^{86} + 24 q^{89} + 32 q^{91} - 24 q^{94} - 12 q^{95}+O(q^{100}) \) 10 * q - 10 * q^4 - 6 * q^5 + 2 * q^10 - 6 * q^11 - 2 * q^14 + 10 * q^16 - 8 * q^19 + 6 * q^20 + 4 * q^25 + 12 * q^26 + 22 * q^29 + 46 * q^31 - 18 * q^34 - 32 * q^35 - 2 * q^40 + 14 * q^41 + 6 * q^44 + 12 * q^46 - 60 * q^49 - 8 * q^50 + 42 * q^55 + 2 * q^56 + 40 * q^59 - 18 * q^61 - 10 * q^64 - 4 * q^65 - 6 * q^70 - 12 * q^71 + 10 * q^74 + 8 * q^76 - 40 * q^79 - 6 * q^80 + 36 * q^85 + 34 * q^86 + 24 * q^89 + 32 * q^91 - 24 * q^94 - 12 * q^95

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