LMFDB - Embedded newform 3330.2.d.p.1999.9

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			1999.9
Root			$0.478560 - 0.478560i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.p.1999.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.10390 - 1.94458i) q^{5} -3.51336i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.10390 - 1.94458i) q^{5} -3.51336i q^{7} -1.00000i q^{8} +(1.94458 + 1.10390i) q^{10} +0.290044 q^{11} -7.12558i q^{13} +3.51336 q^{14} +1.00000 q^{16} +6.17921i q^{17} -5.83553 q^{19} +(-1.10390 + 1.94458i) q^{20} +0.290044i q^{22} -6.45973i q^{23} +(-2.56279 - 4.29326i) q^{25} +7.12558 q^{26} +3.51336i q^{28} -1.18043 q^{29} +9.77838 q^{31} +1.00000i q^{32} -6.17921 q^{34} +(-6.83201 - 3.87841i) q^{35} -1.00000i q^{37} -5.83553i q^{38} +(-1.94458 - 1.10390i) q^{40} -1.64077 q^{41} +5.34889i q^{43} -0.290044 q^{44} +6.45973 q^{46} -5.69256i q^{47} -5.34367 q^{49} +(4.29326 - 2.56279i) q^{50} +7.12558i q^{52} +9.32034i q^{53} +(0.320181 - 0.564014i) q^{55} -3.51336 q^{56} -1.18043i q^{58} +5.94279 q^{59} -1.27699 q^{61} +9.77838i q^{62} -1.00000 q^{64} +(-13.8563 - 7.86596i) q^{65} +6.04334i q^{67} -6.17921i q^{68} +(3.87841 - 6.83201i) q^{70} -13.4995 q^{71} -1.71348i q^{73} +1.00000 q^{74} +5.83553 q^{76} -1.01903i q^{77} -8.25422 q^{79} +(1.10390 - 1.94458i) q^{80} -1.64077i q^{82} +2.41807i q^{83} +(12.0160 + 6.82126i) q^{85} -5.34889 q^{86} -0.290044i q^{88} -10.2797 q^{89} -25.0347 q^{91} +6.45973i q^{92} +5.69256 q^{94} +(-6.44187 + 11.3477i) q^{95} +15.1272i q^{97} -5.34367i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.10390	−	1.94458i	0.493681	−	0.869643i
$5$	1.10390	−	1.94458i	0.493681	−	0.869643i
$6$		0			0
$7$		−	3.51336i		−	1.32792i	−0.747766	−	0.663962i	$-0.768874\pi$
$7$		−	3.51336i		−	1.32792i	0.747766	−	0.663962i	$-0.231126\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.94458	+	1.10390i	0.614930	+	0.349085i
$11$	0.290044			0.0874516			0.0437258	−	0.999044i	$-0.486077\pi$
$11$	0.290044			0.0874516			0.0437258	+	0.999044i	$0.486077\pi$
$12$		0			0
$13$		−	7.12558i		−	1.97628i	−0.153559	−	0.988140i	$-0.549073\pi$
$13$		−	7.12558i		−	1.97628i	0.153559	−	0.988140i	$-0.450927\pi$
$14$	3.51336			0.938984
$15$		0			0
$16$	1.00000			0.250000
$17$			6.17921i			1.49868i	0.662187	+	0.749339i	$0.269628\pi$
$17$			6.17921i			1.49868i	−0.662187	+	0.749339i	$0.730372\pi$
$18$		0			0
$19$	−5.83553			−1.33876			−0.669381	−	0.742919i	$-0.733441\pi$
$19$	−5.83553			−1.33876			−0.669381	+	0.742919i	$0.733441\pi$
$20$	−1.10390	+	1.94458i	−0.246841	+	0.434821i
$21$		0			0
$22$			0.290044i			0.0618376i
$23$		−	6.45973i		−	1.34695i	−0.739212	−	0.673473i	$-0.764802\pi$
$23$		−	6.45973i		−	1.34695i	0.739212	−	0.673473i	$-0.235198\pi$
$24$		0			0
$25$	−2.56279	−	4.29326i	−0.512558	−	0.858653i
$26$	7.12558			1.39744
$27$		0			0
$28$			3.51336i			0.663962i
$29$	−1.18043			−0.219201			−0.109600	−	0.993976i	$-0.534957\pi$
$29$	−1.18043			−0.219201			−0.109600	+	0.993976i	$0.534957\pi$
$30$		0			0
$31$	9.77838			1.75625			0.878124	−	0.478433i	$-0.158795\pi$
$31$	9.77838			1.75625			0.878124	+	0.478433i	$0.158795\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−6.17921			−1.05972
$35$	−6.83201	−	3.87841i	−1.15482	−	0.655571i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	5.83553i		−	0.946648i
$39$		0			0
$40$	−1.94458	−	1.10390i	−0.307465	−	0.174543i
$41$	−1.64077			−0.256245			−0.128123	−	0.991758i	$-0.540895\pi$
$41$	−1.64077			−0.256245			−0.128123	+	0.991758i	$0.540895\pi$
$42$		0			0
$43$			5.34889i			0.815698i	0.913049	+	0.407849i	$0.133721\pi$
$43$			5.34889i			0.815698i	−0.913049	+	0.407849i	$0.866279\pi$
$44$	−0.290044			−0.0437258
$45$		0			0
$46$	6.45973			0.952435
$47$		−	5.69256i		−	0.830346i	−0.909743	−	0.415173i	$-0.863721\pi$
$47$		−	5.69256i		−	0.830346i	0.909743	−	0.415173i	$-0.136279\pi$
$48$		0			0
$49$	−5.34367			−0.763382
$50$	4.29326	−	2.56279i	0.607159	−	0.362433i
$51$		0			0
$52$			7.12558i			0.988140i
$53$			9.32034i			1.28025i	0.768272	+	0.640123i	$0.221117\pi$
$53$			9.32034i			1.28025i	−0.768272	+	0.640123i	$0.778883\pi$
$54$		0			0
$55$	0.320181	−	0.564014i	0.0431732	−	0.0760517i
$56$	−3.51336			−0.469492
$57$		0			0
$58$		−	1.18043i		−	0.154998i
$59$	5.94279			0.773686			0.386843	−	0.922146i	$-0.373566\pi$
$59$	5.94279			0.773686			0.386843	+	0.922146i	$0.373566\pi$
$60$		0			0
$61$	−1.27699			−0.163502			−0.0817512	−	0.996653i	$-0.526051\pi$
$61$	−1.27699			−0.163502			−0.0817512	+	0.996653i	$0.526051\pi$
$62$			9.77838i			1.24185i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−13.8563	−	7.86596i	−1.71866	−	0.975652i
$66$		0			0
$67$			6.04334i			0.738312i	0.929368	+	0.369156i	$0.120353\pi$
$67$			6.04334i			0.738312i	−0.929368	+	0.369156i	$0.879647\pi$
$68$		−	6.17921i		−	0.749339i
$69$		0			0
$70$	3.87841	−	6.83201i	0.463559	−	0.816581i
$71$	−13.4995			−1.60210			−0.801050	−	0.598597i	$-0.795725\pi$
$71$	−13.4995			−1.60210			−0.801050	+	0.598597i	$0.795725\pi$
$72$		0			0
$73$		−	1.71348i		−	0.200548i	−0.994960	−	0.100274i	$-0.968028\pi$
$73$		−	1.71348i		−	0.200548i	0.994960	−	0.100274i	$-0.0319719\pi$
$74$	1.00000			0.116248
$75$		0			0
$76$	5.83553			0.669381
$77$		−	1.01903i		−	0.116129i
$78$		0			0
$79$	−8.25422			−0.928672			−0.464336	−	0.885659i	$-0.653707\pi$
$79$	−8.25422			−0.928672			−0.464336	+	0.885659i	$0.653707\pi$
$80$	1.10390	−	1.94458i	0.123420	−	0.217411i
$81$		0			0
$82$		−	1.64077i		−	0.181193i
$83$			2.41807i			0.265418i	0.991155	+	0.132709i	$0.0423676\pi$
$83$			2.41807i			0.265418i	−0.991155	+	0.132709i	$0.957632\pi$
$84$		0			0
$85$	12.0160	+	6.82126i	1.30331	+	0.739869i
$86$	−5.34889			−0.576785
$87$		0			0
$88$		−	0.290044i		−	0.0309188i
$89$	−10.2797			−1.08965			−0.544823	−	0.838551i	$-0.683403\pi$
$89$	−10.2797			−1.08965			−0.544823	+	0.838551i	$0.683403\pi$
$90$		0			0
$91$	−25.0347			−2.62435
$92$			6.45973i			0.673473i
$93$		0			0
$94$	5.69256			0.587143
$95$	−6.44187	+	11.3477i	−0.660922	+	1.16425i
$96$		0			0
$97$			15.1272i			1.53594i	0.640489	+	0.767968i	$0.278732\pi$
$97$			15.1272i			1.53594i	−0.640489	+	0.767968i	$0.721268\pi$
$98$		−	5.34367i		−	0.539793i
$99$		0			0
$100$	2.56279	+	4.29326i	0.256279	+	0.429326i
$101$	−2.63730			−0.262421			−0.131210	−	0.991355i	$-0.541886\pi$
$101$	−2.63730			−0.262421			−0.131210	+	0.991355i	$0.541886\pi$
$102$		0			0
$103$			1.72469i			0.169939i	0.996384	+	0.0849695i	$0.0270793\pi$
$103$			1.72469i			0.169939i	−0.996384	+	0.0849695i	$0.972921\pi$
$104$	−7.12558			−0.698720
$105$		0			0
$106$	−9.32034			−0.905271
$107$		−	10.0279i		−	0.969438i	−0.874670	−	0.484719i	$-0.838922\pi$
$107$		−	10.0279i		−	0.969438i	0.874670	−	0.484719i	$-0.161078\pi$
$108$		0			0
$109$	−4.87361			−0.466807			−0.233403	−	0.972380i	$-0.574986\pi$
$109$	−4.87361			−0.466807			−0.233403	+	0.972380i	$0.574986\pi$
$110$	0.564014	+	0.320181i	0.0537767	+	0.0305281i
$111$		0			0
$112$		−	3.51336i		−	0.331981i
$113$		−	15.9290i		−	1.49847i	−0.662303	−	0.749236i	$-0.730421\pi$
$113$		−	15.9290i		−	1.49847i	0.662303	−	0.749236i	$-0.269579\pi$
$114$		0			0
$115$	−12.5615	−	7.13092i	−1.17136	−	0.664962i
$116$	1.18043			0.109600
$117$		0			0
$118$			5.94279i			0.547078i
$119$	21.7098			1.99013
$120$		0			0
$121$	−10.9159			−0.992352
$122$		−	1.27699i		−	0.115614i
$123$		0			0
$124$	−9.77838			−0.878124
$125$	−11.1777	+	0.244192i	−0.999761	+	0.0218412i
$126$		0			0
$127$			1.31265i			0.116479i	0.998303	+	0.0582395i	$0.0185487\pi$
$127$			1.31265i			0.116479i	−0.998303	+	0.0582395i	$0.981451\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	7.86596	−	13.8563i	0.689890	−	1.21527i
$131$	−2.41562			−0.211054			−0.105527	−	0.994416i	$-0.533653\pi$
$131$	−2.41562			−0.211054			−0.105527	+	0.994416i	$0.533653\pi$
$132$		0			0
$133$			20.5023i			1.77778i
$134$	−6.04334			−0.522065
$135$		0			0
$136$	6.17921			0.529862
$137$		−	6.87366i		−	0.587256i	−0.955920	−	0.293628i	$-0.905137\pi$
$137$		−	6.87366i		−	0.587256i	0.955920	−	0.293628i	$-0.0948627\pi$
$138$		0			0
$139$	9.80616			0.831748			0.415874	−	0.909422i	$-0.363476\pi$
$139$	9.80616			0.831748			0.415874	+	0.909422i	$0.363476\pi$
$140$	6.83201	+	3.87841i	0.577410	+	0.327786i
$141$		0			0
$142$		−	13.4995i		−	1.13286i
$143$		−	2.06673i		−	0.172829i
$144$		0			0
$145$	−1.30308	+	2.29545i	−0.108215	+	0.190626i
$146$	1.71348			0.141809
$147$		0			0
$148$			1.00000i			0.0821995i
$149$	−9.07687			−0.743606			−0.371803	−	0.928312i	$-0.621260\pi$
$149$	−9.07687			−0.743606			−0.371803	+	0.928312i	$0.621260\pi$
$150$		0			0
$151$	20.1964			1.64356			0.821780	−	0.569805i	$-0.192981\pi$
$151$	20.1964			1.64356			0.821780	+	0.569805i	$0.192981\pi$
$152$			5.83553i			0.473324i
$153$		0			0
$154$	1.01903			0.0821157
$155$	10.7944	−	19.0148i	0.867027	−	1.52731i
$156$		0			0
$157$		−	17.2677i		−	1.37811i	−0.724707	−	0.689057i	$-0.758025\pi$
$157$		−	17.2677i		−	1.37811i	0.724707	−	0.689057i	$-0.241975\pi$
$158$		−	8.25422i		−	0.656670i
$159$		0			0
$160$	1.94458	+	1.10390i	0.153733	+	0.0872713i
$161$	−22.6953			−1.78864
$162$		0			0
$163$		−	16.6901i		−	1.30727i	−0.756810	−	0.653634i	$-0.773243\pi$
$163$		−	16.6901i		−	1.30727i	0.756810	−	0.653634i	$-0.226757\pi$
$164$	1.64077			0.128123
$165$		0			0
$166$	−2.41807			−0.187679
$167$		−	1.47354i		−	0.114026i	−0.998373	−	0.0570130i	$-0.981842\pi$
$167$		−	1.47354i		−	0.114026i	0.998373	−	0.0570130i	$-0.0181577\pi$
$168$		0			0
$169$	−37.7738			−2.90568
$170$	−6.82126	+	12.0160i	−0.523166	+	0.921582i
$171$		0			0
$172$		−	5.34889i		−	0.407849i
$173$			13.8432i			1.05248i	0.850336	+	0.526240i	$0.176399\pi$
$173$			13.8432i			1.05248i	−0.850336	+	0.526240i	$0.823601\pi$
$174$		0			0
$175$	−15.0838	+	9.00399i	−1.14023	+	0.680637i
$176$	0.290044			0.0218629
$177$		0			0
$178$		−	10.2797i		−	0.770496i
$179$	21.7817			1.62804			0.814020	−	0.580836i	$-0.197274\pi$
$179$	21.7817			1.62804			0.814020	+	0.580836i	$0.197274\pi$
$180$		0			0
$181$	2.03100			0.150963			0.0754817	−	0.997147i	$-0.475951\pi$
$181$	2.03100			0.150963			0.0754817	+	0.997147i	$0.475951\pi$
$182$		−	25.0347i		−	1.85569i
$183$		0			0
$184$	−6.45973			−0.476217
$185$	−1.94458	−	1.10390i	−0.142968	−	0.0811607i
$186$		0			0
$187$			1.79224i			0.131062i
$188$			5.69256i			0.415173i
$189$		0			0
$190$	−11.3477	−	6.44187i	−0.823246	−	0.467343i
$191$	8.44668			0.611180			0.305590	−	0.952163i	$-0.401146\pi$
$191$	8.44668			0.611180			0.305590	+	0.952163i	$0.401146\pi$
$192$		0			0
$193$		−	3.64159i		−	0.262127i	−0.991374	−	0.131064i	$-0.958161\pi$
$193$		−	3.64159i		−	0.262127i	0.991374	−	0.131064i	$-0.0418392\pi$
$194$	−15.1272			−1.08607
$195$		0			0
$196$	5.34367			0.381691
$197$		−	10.1939i		−	0.726288i	−0.931733	−	0.363144i	$-0.881703\pi$
$197$		−	10.1939i		−	0.726288i	0.931733	−	0.363144i	$-0.118297\pi$
$198$		0			0
$199$	5.25299			0.372375			0.186187	−	0.982514i	$-0.440387\pi$
$199$	5.25299			0.372375			0.186187	+	0.982514i	$0.440387\pi$
$200$	−4.29326	+	2.56279i	−0.303580	+	0.181216i
$201$		0			0
$202$		−	2.63730i		−	0.185560i
$203$			4.14728i			0.291082i
$204$		0			0
$205$	−1.81125	+	3.19061i	−0.126504	+	0.222842i
$206$	−1.72469			−0.120165
$207$		0			0
$208$		−	7.12558i		−	0.494070i
$209$	−1.69256			−0.117077
$210$		0			0
$211$	−4.81998			−0.331821			−0.165910	−	0.986141i	$-0.553056\pi$
$211$	−4.81998			−0.331821			−0.165910	+	0.986141i	$0.553056\pi$
$212$		−	9.32034i		−	0.640123i
$213$		0			0
$214$	10.0279			0.685496
$215$	10.4013	+	5.90466i	0.709366	+	0.402695i
$216$		0			0
$217$		−	34.3549i		−	2.33216i
$218$		−	4.87361i		−	0.330082i
$219$		0			0
$220$	−0.320181	+	0.564014i	−0.0215866	+	0.0380258i
$221$	44.0304			2.96180
$222$		0			0
$223$		−	3.70392i		−	0.248033i	−0.992280	−	0.124017i	$-0.960422\pi$
$223$		−	3.70392i		−	0.248033i	0.992280	−	0.124017i	$-0.0395776\pi$
$224$	3.51336			0.234746
$225$		0			0
$226$	15.9290			1.05958
$227$		−	6.31512i		−	0.419149i	−0.977793	−	0.209575i	$-0.932792\pi$
$227$		−	6.31512i		−	0.419149i	0.977793	−	0.209575i	$-0.0672079\pi$
$228$		0			0
$229$	20.5548			1.35830			0.679150	−	0.734000i	$-0.262349\pi$
$229$	20.5548			1.35830			0.679150	+	0.734000i	$0.262349\pi$
$230$	7.13092	−	12.5615i	0.470199	−	0.828278i
$231$		0			0
$232$			1.18043i			0.0774992i
$233$			21.4393i			1.40453i	0.711914	+	0.702267i	$0.247829\pi$
$233$			21.4393i			1.40453i	−0.711914	+	0.702267i	$0.752171\pi$
$234$		0			0
$235$	−11.0696	−	6.28405i	−0.722104	−	0.409926i
$236$	−5.94279			−0.386843
$237$		0			0
$238$			21.7098i			1.40723i
$239$	−20.7479			−1.34207			−0.671034	−	0.741426i	$-0.734150\pi$
$239$	−20.7479			−1.34207			−0.671034	+	0.741426i	$0.734150\pi$
$240$		0			0
$241$	10.7731			0.693957			0.346978	−	0.937873i	$-0.387208\pi$
$241$	10.7731			0.693957			0.346978	+	0.937873i	$0.387208\pi$
$242$		−	10.9159i		−	0.701699i
$243$		0			0
$244$	1.27699			0.0817512
$245$	−5.89891	+	10.3912i	−0.376867	+	0.663870i
$246$		0			0
$247$			41.5815i			2.64577i
$248$		−	9.77838i		−	0.620927i
$249$		0			0
$250$	−0.244192	−	11.1777i	−0.0154440	−	0.706938i
$251$	4.46812			0.282025			0.141013	−	0.990008i	$-0.454964\pi$
$251$	4.46812			0.282025			0.141013	+	0.990008i	$0.454964\pi$
$252$		0			0
$253$		−	1.87361i		−	0.117793i
$254$	−1.31265			−0.0823631
$255$		0			0
$256$	1.00000			0.0625000
$257$			1.24594i			0.0777194i	0.999245	+	0.0388597i	$0.0123725\pi$
$257$			1.24594i			0.0777194i	−0.999245	+	0.0388597i	$0.987627\pi$
$258$		0			0
$259$	−3.51336			−0.218309
$260$	13.8563	+	7.86596i	0.859329	+	0.487826i
$261$		0			0
$262$		−	2.41562i		−	0.149237i
$263$			16.3230i			1.00652i	0.864135	+	0.503259i	$0.167866\pi$
$263$			16.3230i			1.00652i	−0.864135	+	0.503259i	$0.832134\pi$
$264$		0			0
$265$	18.1241	+	10.2888i	1.11336	+	0.632034i
$266$	−20.5023			−1.25708
$267$		0			0
$268$		−	6.04334i		−	0.369156i
$269$	−18.5763			−1.13262			−0.566309	−	0.824193i	$-0.691629\pi$
$269$	−18.5763			−1.13262			−0.566309	+	0.824193i	$0.691629\pi$
$270$		0			0
$271$	16.4181			0.997327			0.498663	−	0.866796i	$-0.333824\pi$
$271$	16.4181			0.997327			0.498663	+	0.866796i	$0.333824\pi$
$272$			6.17921i			0.374669i
$273$		0			0
$274$	6.87366			0.415253
$275$	−0.743322	−	1.24524i	−0.0448240	−	0.0750906i
$276$		0			0
$277$			15.6104i			0.937937i	0.883215	+	0.468968i	$0.155374\pi$
$277$			15.6104i			0.937937i	−0.883215	+	0.468968i	$0.844626\pi$
$278$			9.80616i			0.588134i
$279$		0			0
$280$	−3.87841	+	6.83201i	−0.231779	+	0.408290i
$281$	21.8665			1.30445			0.652224	−	0.758026i	$-0.273836\pi$
$281$	21.8665			1.30445			0.652224	+	0.758026i	$0.273836\pi$
$282$		0			0
$283$			2.24778i			0.133616i	0.997766	+	0.0668082i	$0.0212816\pi$
$283$			2.24778i			0.133616i	−0.997766	+	0.0668082i	$0.978718\pi$
$284$	13.4995			0.801050
$285$		0			0
$286$	2.06673			0.122208
$287$			5.76461i			0.340274i
$288$		0			0
$289$	−21.1826			−1.24603
$290$	−2.29545	−	1.30308i	−0.134793	−	0.0765198i
$291$		0			0
$292$			1.71348i			0.100274i
$293$		−	26.8794i		−	1.57031i	−0.619297	−	0.785157i	$-0.712582\pi$
$293$		−	26.8794i		−	1.57031i	0.619297	−	0.785157i	$-0.287418\pi$
$294$		0			0
$295$	6.56028	−	11.5562i	0.381954	−	0.672830i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$		−	9.07687i		−	0.525809i
$299$	−46.0293			−2.66194
$300$		0			0
$301$	18.7926			1.08318
$302$			20.1964i			1.16217i
$303$		0			0
$304$	−5.83553			−0.334691
$305$	−1.40968	+	2.48322i	−0.0807181	+	0.142189i
$306$		0			0
$307$		−	23.9979i		−	1.36963i	−0.728717	−	0.684815i	$-0.759883\pi$
$307$		−	23.9979i		−	1.36963i	0.728717	−	0.684815i	$-0.240117\pi$
$308$			1.01903i			0.0580645i
$309$		0			0
$310$	19.0148	+	10.7944i	1.07997	+	0.613081i
$311$	5.07563			0.287812			0.143906	−	0.989591i	$-0.454034\pi$
$311$	5.07563			0.287812			0.143906	+	0.989591i	$0.454034\pi$
$312$		0			0
$313$		−	8.96950i		−	0.506986i	−0.967337	−	0.253493i	$-0.918420\pi$
$313$		−	8.96950i		−	0.506986i	0.967337	−	0.253493i	$-0.0815795\pi$
$314$	17.2677			0.974474
$315$		0			0
$316$	8.25422			0.464336
$317$		−	22.0181i		−	1.23666i	−0.785918	−	0.618330i	$-0.787809\pi$
$317$		−	22.0181i		−	1.23666i	0.785918	−	0.618330i	$-0.212191\pi$
$318$		0			0
$319$	−0.342377			−0.0191695
$320$	−1.10390	+	1.94458i	−0.0617102	+	0.108705i
$321$		0			0
$322$		−	22.6953i		−	1.26476i
$323$		−	36.0589i		−	2.00637i
$324$		0			0
$325$	−30.5920	+	18.2613i	−1.69694	+	1.01296i
$326$	16.6901			0.924379
$327$		0			0
$328$			1.64077i			0.0905964i
$329$	−20.0000			−1.10264
$330$		0			0
$331$	−10.7134			−0.588864			−0.294432	−	0.955672i	$-0.595130\pi$
$331$	−10.7134			−0.588864			−0.294432	+	0.955672i	$0.595130\pi$
$332$		−	2.41807i		−	0.132709i
$333$		0			0
$334$	1.47354			0.0806286
$335$	11.7518	+	6.67127i	0.642067	+	0.364491i
$336$		0			0
$337$		−	1.34097i		−	0.0730471i	−0.999333	−	0.0365235i	$-0.988372\pi$
$337$		−	1.34097i		−	0.0730471i	0.999333	−	0.0365235i	$-0.0116284\pi$
$338$		−	37.7738i		−	2.05463i
$339$		0			0
$340$	−12.0160	−	6.82126i	−0.651657	−	0.369935i
$341$	2.83616			0.153587
$342$		0			0
$343$		−	5.81926i		−	0.314211i
$344$	5.34889			0.288393
$345$		0			0
$346$	−13.8432			−0.744216
$347$			0.883744i			0.0474419i	0.999719	+	0.0237209i	$0.00755131\pi$
$347$			0.883744i			0.0474419i	−0.999719	+	0.0237209i	$0.992449\pi$
$348$		0			0
$349$	9.00521			0.482038			0.241019	−	0.970520i	$-0.422518\pi$
$349$	9.00521			0.482038			0.241019	+	0.970520i	$0.422518\pi$
$350$	−9.00399	−	15.0838i	−0.481283	−	0.806261i
$351$		0			0
$352$			0.290044i			0.0154594i
$353$		−	6.79030i		−	0.361411i	−0.983537	−	0.180706i	$-0.942162\pi$
$353$		−	6.79030i		−	0.361411i	0.983537	−	0.180706i	$-0.0578381\pi$
$354$		0			0
$355$	−14.9022	+	26.2509i	−0.790927	+	1.39326i
$356$	10.2797			0.544823
$357$		0			0
$358$			21.7817i			1.15120i
$359$	−10.2263			−0.539722			−0.269861	−	0.962899i	$-0.586978\pi$
$359$	−10.2263			−0.539722			−0.269861	+	0.962899i	$0.586978\pi$
$360$		0			0
$361$	15.0534			0.792286
$362$			2.03100i			0.106747i
$363$		0			0
$364$	25.0347			1.31217
$365$	−3.33200	−	1.89152i	−0.174405	−	0.0990067i
$366$		0			0
$367$		−	17.1583i		−	0.895657i	−0.894119	−	0.447829i	$-0.852198\pi$
$367$		−	17.1583i		−	0.895657i	0.894119	−	0.447829i	$-0.147802\pi$
$368$		−	6.45973i		−	0.336737i
$369$		0			0
$370$	1.10390	−	1.94458i	0.0573893	−	0.101094i
$371$	32.7457			1.70007
$372$		0			0
$373$			17.1601i			0.888515i	0.895899	+	0.444257i	$0.146532\pi$
$373$			17.1601i			0.888515i	−0.895899	+	0.444257i	$0.853468\pi$
$374$	−1.79224			−0.0926747
$375$		0			0
$376$	−5.69256			−0.293571
$377$			8.41126i			0.433202i
$378$		0			0
$379$	27.5435			1.41482			0.707408	−	0.706805i	$-0.249864\pi$
$379$	27.5435			1.41482			0.707408	+	0.706805i	$0.249864\pi$
$380$	6.44187	−	11.3477i	0.330461	−	0.582123i
$381$		0			0
$382$			8.44668i			0.432170i
$383$			3.49954i			0.178818i	0.995995	+	0.0894091i	$0.0284979\pi$
$383$			3.49954i			0.178818i	−0.995995	+	0.0894091i	$0.971502\pi$
$384$		0			0
$385$	−1.98158	−	1.12491i	−0.100991	−	0.0573308i
$386$	3.64159			0.185352
$387$		0			0
$388$		−	15.1272i		−	0.767968i
$389$	−13.0015			−0.659203			−0.329602	−	0.944120i	$-0.606914\pi$
$389$	−13.0015			−0.659203			−0.329602	+	0.944120i	$0.606914\pi$
$390$		0			0
$391$	39.9160			2.01864
$392$			5.34367i			0.269896i
$393$		0			0
$394$	10.1939			0.513563
$395$	−9.11187	+	16.0510i	−0.458468	+	0.807613i
$396$		0			0
$397$		−	26.6658i		−	1.33832i	−0.743118	−	0.669160i	$-0.766654\pi$
$397$		−	26.6658i		−	1.33832i	0.743118	−	0.669160i	$-0.233346\pi$
$398$			5.25299i			0.263309i
$399$		0			0
$400$	−2.56279	−	4.29326i	−0.128139	−	0.214663i
$401$	−20.3546			−1.01646			−0.508231	−	0.861221i	$-0.669700\pi$
$401$	−20.3546			−1.01646			−0.508231	+	0.861221i	$0.669700\pi$
$402$		0			0
$403$		−	69.6766i		−	3.47084i
$404$	2.63730			0.131210
$405$		0			0
$406$	−4.14728			−0.205826
$407$		−	0.290044i		−	0.0143770i
$408$		0			0
$409$	−29.9603			−1.48144			−0.740720	−	0.671814i	$-0.765515\pi$
$409$	−29.9603			−1.48144			−0.740720	+	0.671814i	$0.765515\pi$
$410$	−3.19061	−	1.81125i	−0.157573	−	0.0894515i
$411$		0			0
$412$		−	1.72469i		−	0.0849695i
$413$		−	20.8791i		−	1.02740i
$414$		0			0
$415$	4.70214	+	2.66932i	0.230819	+	0.131032i
$416$	7.12558			0.349360
$417$		0			0
$418$		−	1.69256i		−	0.0827859i
$419$	23.3149			1.13901			0.569504	−	0.821988i	$-0.307135\pi$
$419$	23.3149			1.13901			0.569504	+	0.821988i	$0.307135\pi$
$420$		0			0
$421$	24.0289			1.17110			0.585548	−	0.810638i	$-0.300880\pi$
$421$	24.0289			1.17110			0.585548	+	0.810638i	$0.300880\pi$
$422$		−	4.81998i		−	0.234633i
$423$		0			0
$424$	9.32034			0.452636
$425$	26.5290	−	15.8360i	1.28684	−	0.768158i
$426$		0			0
$427$			4.48654i			0.217119i
$428$			10.0279i			0.484719i
$429$		0			0
$430$	−5.90466	+	10.4013i	−0.284748	+	0.501597i
$431$	19.2917			0.929247			0.464624	−	0.885508i	$-0.346190\pi$
$431$	19.2917			0.929247			0.464624	+	0.885508i	$0.346190\pi$
$432$		0			0
$433$			12.5816i			0.604634i	0.953207	+	0.302317i	$0.0977601\pi$
$433$			12.5816i			0.604634i	−0.953207	+	0.302317i	$0.902240\pi$
$434$	34.3549			1.64909
$435$		0			0
$436$	4.87361			0.233403
$437$			37.6959i			1.80324i
$438$		0			0
$439$	−14.0428			−0.670225			−0.335113	−	0.942178i	$-0.608774\pi$
$439$	−14.0428			−0.670225			−0.335113	+	0.942178i	$0.608774\pi$
$440$	−0.564014	−	0.320181i	−0.0268883	−	0.0152640i
$441$		0			0
$442$			44.0304i			2.09431i
$443$		−	24.5696i		−	1.16734i	−0.811992	−	0.583668i	$-0.801617\pi$
$443$		−	24.5696i		−	1.16734i	0.811992	−	0.583668i	$-0.198383\pi$
$444$		0			0
$445$	−11.3478	+	19.9897i	−0.537938	+	0.947603i
$446$	3.70392			0.175386
$447$		0			0
$448$			3.51336i			0.165990i
$449$	−12.7574			−0.602061			−0.301030	−	0.953615i	$-0.597331\pi$
$449$	−12.7574			−0.602061			−0.301030	+	0.953615i	$0.597331\pi$
$450$		0			0
$451$	−0.475896			−0.0224091
$452$			15.9290i			0.749236i
$453$		0			0
$454$	6.31512			0.296383
$455$	−27.6359	+	48.6820i	−1.29559	+	2.28225i
$456$		0			0
$457$			3.34889i			0.156654i	0.996928	+	0.0783272i	$0.0249579\pi$
$457$			3.34889i			0.156654i	−0.996928	+	0.0783272i	$0.975042\pi$
$458$			20.5548i			0.960463i
$459$		0			0
$460$	12.5615	+	7.13092i	0.585681	+	0.332481i
$461$	0.859501			0.0400310			0.0200155	−	0.999800i	$-0.493628\pi$
$461$	0.859501			0.0400310			0.0200155	+	0.999800i	$0.493628\pi$
$462$		0			0
$463$		−	13.8711i		−	0.644643i	−0.946630	−	0.322321i	$-0.895537\pi$
$463$		−	13.8711i		−	0.644643i	0.946630	−	0.322321i	$-0.104463\pi$
$464$	−1.18043			−0.0548002
$465$		0			0
$466$	−21.4393			−0.993155
$467$		−	40.9281i		−	1.89392i	−0.321344	−	0.946962i	$-0.604135\pi$
$467$		−	40.9281i		−	1.89392i	0.321344	−	0.946962i	$-0.395865\pi$
$468$		0			0
$469$	21.2324			0.980422
$470$	6.28405	−	11.0696i	0.289861	−	0.510605i
$471$		0			0
$472$		−	5.94279i		−	0.273539i
$473$			1.55141i			0.0713341i
$474$		0			0
$475$	14.9552	+	25.0535i	0.686193	+	1.14953i
$476$	−21.7098			−0.995065
$477$		0			0
$478$		−	20.7479i		−	0.948986i
$479$	8.58990			0.392483			0.196241	−	0.980556i	$-0.437126\pi$
$479$	8.58990			0.392483			0.196241	+	0.980556i	$0.437126\pi$
$480$		0			0
$481$	−7.12558			−0.324898
$482$			10.7731i			0.490702i
$483$		0			0
$484$	10.9159			0.496176
$485$	29.4161	+	16.6990i	1.33572	+	0.758263i
$486$		0			0
$487$			25.8389i			1.17087i	0.810718	+	0.585436i	$0.199077\pi$
$487$			25.8389i			1.17087i	−0.810718	+	0.585436i	$0.800923\pi$
$488$			1.27699i			0.0578068i
$489$		0			0
$490$	−10.3912	−	5.89891i	−0.469427	−	0.266486i
$491$	−11.4864			−0.518376			−0.259188	−	0.965827i	$-0.583455\pi$
$491$	−11.4864			−0.518376			−0.259188	+	0.965827i	$0.583455\pi$
$492$		0			0
$493$		−	7.29413i		−	0.328511i
$494$	−41.5815			−1.87084
$495$		0			0
$496$	9.77838			0.439062
$497$			47.4287i			2.12747i
$498$		0			0
$499$	9.74599			0.436290			0.218145	−	0.975916i	$-0.429999\pi$
$499$	9.74599			0.436290			0.218145	+	0.975916i	$0.429999\pi$
$500$	11.1777	−	0.244192i	0.499881	−	0.0109206i
$501$		0			0
$502$			4.46812i			0.199422i
$503$			17.4803i			0.779408i	0.920940	+	0.389704i	$0.127423\pi$
$503$			17.4803i			0.779408i	−0.920940	+	0.389704i	$0.872577\pi$
$504$		0			0
$505$	−2.91133	+	5.12844i	−0.129552	+	0.228212i
$506$	1.87361			0.0832920
$507$		0			0
$508$		−	1.31265i		−	0.0582395i
$509$	−16.3273			−0.723695			−0.361847	−	0.932237i	$-0.617854\pi$
$509$	−16.3273			−0.723695			−0.361847	+	0.932237i	$0.617854\pi$
$510$		0			0
$511$	−6.02007			−0.266312
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−1.24594			−0.0549559
$515$	3.35380	+	1.90390i	0.147786	+	0.0838957i
$516$		0			0
$517$		−	1.65109i		−	0.0726151i
$518$		−	3.51336i		−	0.154368i
$519$		0			0
$520$	−7.86596	+	13.8563i	−0.344945	+	0.607637i
$521$	4.78335			0.209562			0.104781	−	0.994495i	$-0.466586\pi$
$521$	4.78335			0.209562			0.104781	+	0.994495i	$0.466586\pi$
$522$		0			0
$523$			24.1224i			1.05480i	0.849618	+	0.527399i	$0.176833\pi$
$523$			24.1224i			1.05480i	−0.849618	+	0.527399i	$0.823167\pi$
$524$	2.41562			0.105527
$525$		0			0
$526$	−16.3230			−0.711716
$527$			60.4226i			2.63205i
$528$		0			0
$529$	−18.7281			−0.814264
$530$	−10.2888	+	18.1241i	−0.446915	+	0.787263i
$531$		0			0
$532$		−	20.5023i		−	0.888888i
$533$			11.6914i			0.506412i
$534$		0			0
$535$	−19.5001	−	11.0699i	−0.843064	−	0.478593i
$536$	6.04334			0.261033
$537$		0			0
$538$		−	18.5763i		−	0.800881i
$539$	−1.54990			−0.0667590
$540$		0			0
$541$	4.11745			0.177023			0.0885115	−	0.996075i	$-0.471789\pi$
$541$	4.11745			0.177023			0.0885115	+	0.996075i	$0.471789\pi$
$542$			16.4181i			0.705217i
$543$		0			0
$544$	−6.17921			−0.264931
$545$	−5.38000	+	9.47712i	−0.230454	+	0.405955i
$546$		0			0
$547$			9.22742i			0.394536i	0.980350	+	0.197268i	$0.0632069\pi$
$547$			9.22742i			0.394536i	−0.980350	+	0.197268i	$0.936793\pi$
$548$			6.87366i			0.293628i
$549$		0			0
$550$	1.24524	−	0.743322i	0.0530971	−	0.0316953i
$551$	6.88845			0.293458
$552$		0			0
$553$			29.0000i			1.23321i
$554$	−15.6104			−0.663222
$555$		0			0
$556$	−9.80616			−0.415874
$557$			2.25125i			0.0953885i	0.998862	+	0.0476943i	$0.0151873\pi$
$557$			2.25125i			0.0953885i	−0.998862	+	0.0476943i	$0.984813\pi$
$558$		0			0
$559$	38.1139			1.61205
$560$	−6.83201	−	3.87841i	−0.288705	−	0.163893i
$561$		0			0
$562$			21.8665i			0.922384i
$563$		−	5.79316i		−	0.244153i	−0.992521	−	0.122076i	$-0.961045\pi$
$563$		−	5.79316i		−	0.244153i	0.992521	−	0.122076i	$-0.0389553\pi$
$564$		0			0
$565$	−30.9752	−	17.5841i	−1.30314	−	0.739768i
$566$	−2.24778			−0.0944811
$567$		0			0
$568$			13.4995i			0.566428i
$569$	−34.4807			−1.44551			−0.722753	−	0.691106i	$-0.757124\pi$
$569$	−34.4807			−1.44551			−0.722753	+	0.691106i	$0.757124\pi$
$570$		0			0
$571$	−19.2152			−0.804133			−0.402066	−	0.915611i	$-0.631708\pi$
$571$	−19.2152			−0.804133			−0.402066	+	0.915611i	$0.631708\pi$
$572$			2.06673i			0.0864144i
$573$		0			0
$574$	−5.76461			−0.240610
$575$	−27.7333	+	16.5549i	−1.15656	+	0.690387i
$576$		0			0
$577$		−	6.33354i		−	0.263669i	−0.991272	−	0.131834i	$-0.957913\pi$
$577$		−	6.33354i		−	0.263669i	0.991272	−	0.131834i	$-0.0420867\pi$
$578$		−	21.1826i		−	0.881079i
$579$		0			0
$580$	1.30308	−	2.29545i	0.0541077	−	0.0953132i
$581$	8.49555			0.352455
$582$		0			0
$583$			2.70331i			0.111960i
$584$	−1.71348			−0.0709044
$585$		0			0
$586$	26.8794			1.11038
$587$		−	21.9099i		−	0.904320i	−0.891937	−	0.452160i	$-0.850654\pi$
$587$		−	21.9099i		−	0.904320i	0.891937	−	0.452160i	$-0.149346\pi$
$588$		0			0
$589$	−57.0620			−2.35120
$590$	11.5562	+	6.56028i	0.475763	+	0.270082i
$591$		0			0
$592$		−	1.00000i		−	0.0410997i
$593$			9.40482i			0.386210i	0.981178	+	0.193105i	$0.0618557\pi$
$593$			9.40482i			0.386210i	−0.981178	+	0.193105i	$0.938144\pi$
$594$		0			0
$595$	23.9655	−	42.2164i	0.982490	−	1.73070i
$596$	9.07687			0.371803
$597$		0			0
$598$		−	46.0293i		−	1.88228i
$599$	16.4095			0.670474			0.335237	−	0.942134i	$-0.391184\pi$
$599$	16.4095			0.670474			0.335237	+	0.942134i	$0.391184\pi$
$600$		0			0
$601$	−7.01392			−0.286104			−0.143052	−	0.989715i	$-0.545692\pi$
$601$	−7.01392			−0.286104			−0.143052	+	0.989715i	$0.545692\pi$
$602$			18.7926i			0.765927i
$603$		0			0
$604$	−20.1964			−0.821780
$605$	−12.0501	+	21.2268i	−0.489906	+	0.862992i
$606$		0			0
$607$		−	16.5621i		−	0.672234i	−0.941820	−	0.336117i	$-0.890886\pi$
$607$		−	16.5621i		−	0.672234i	0.941820	−	0.336117i	$-0.109114\pi$
$608$		−	5.83553i		−	0.236662i
$609$		0			0
$610$	−2.48322	−	1.40968i	−0.100543	−	0.0570763i
$611$	−40.5628			−1.64099
$612$		0			0
$613$			23.9370i			0.966804i	0.875398	+	0.483402i	$0.160599\pi$
$613$			23.9370i			0.966804i	−0.875398	+	0.483402i	$0.839401\pi$
$614$	23.9979			0.968475
$615$		0			0
$616$	−1.01903			−0.0410578
$617$		−	13.9489i		−	0.561563i	−0.959772	−	0.280781i	$-0.909406\pi$
$617$		−	13.9489i		−	0.561563i	0.959772	−	0.280781i	$-0.0905936\pi$
$618$		0			0
$619$	−21.6942			−0.871964			−0.435982	−	0.899955i	$-0.643599\pi$
$619$	−21.6942			−0.871964			−0.435982	+	0.899955i	$0.643599\pi$
$620$	−10.7944	+	19.0148i	−0.433513	+	0.763654i
$621$		0			0
$622$			5.07563i			0.203514i
$623$			36.1163i			1.44697i
$624$		0			0
$625$	−11.8642	+	22.0055i	−0.474570	+	0.880218i
$626$	8.96950			0.358493
$627$		0			0
$628$			17.2677i			0.689057i
$629$	6.17921			0.246381
$630$		0			0
$631$	−32.4902			−1.29342			−0.646708	−	0.762738i	$-0.723855\pi$
$631$	−32.4902			−1.29342			−0.646708	+	0.762738i	$0.723855\pi$
$632$			8.25422i			0.328335i
$633$		0			0
$634$	22.0181			0.874451
$635$	2.55256	+	1.44904i	0.101295	+	0.0575035i
$636$		0			0
$637$			38.0768i			1.50866i
$638$		−	0.342377i		−	0.0135549i
$639$		0			0
$640$	−1.94458	−	1.10390i	−0.0768663	−	0.0436357i
$641$	28.1621			1.11234			0.556168	−	0.831070i	$-0.312271\pi$
$641$	28.1621			1.11234			0.556168	+	0.831070i	$0.312271\pi$
$642$		0			0
$643$			8.32452i			0.328287i	0.986436	+	0.164144i	$0.0524860\pi$
$643$			8.32452i			0.328287i	−0.986436	+	0.164144i	$0.947514\pi$
$644$	22.6953			0.894321
$645$		0			0
$646$	36.0589			1.41872
$647$			1.75827i			0.0691249i	0.999403	+	0.0345624i	$0.0110038\pi$
$647$			1.75827i			0.0691249i	−0.999403	+	0.0345624i	$0.988996\pi$
$648$		0			0
$649$	1.72367			0.0676600
$650$	−18.2613	−	30.5920i	−0.716269	−	1.19992i
$651$		0			0
$652$			16.6901i			0.653634i
$653$		−	24.7416i		−	0.968213i	−0.875009	−	0.484106i	$-0.839145\pi$
$653$		−	24.7416i		−	0.968213i	0.875009	−	0.484106i	$-0.160855\pi$
$654$		0			0
$655$	−2.66661	+	4.69737i	−0.104193	+	0.183541i
$656$	−1.64077			−0.0640613
$657$		0			0
$658$		−	20.0000i		−	0.779681i
$659$	18.2640			0.711466			0.355733	−	0.934588i	$-0.384231\pi$
$659$	18.2640			0.711466			0.355733	+	0.934588i	$0.384231\pi$
$660$		0			0
$661$	2.61857			0.101851			0.0509253	−	0.998702i	$-0.483783\pi$
$661$	2.61857			0.101851			0.0509253	+	0.998702i	$0.483783\pi$
$662$		−	10.7134i		−	0.416390i
$663$		0			0
$664$	2.41807			0.0938394
$665$	39.8684	+	22.6326i	1.54603	+	0.877654i
$666$		0			0
$667$			7.62527i			0.295252i
$668$			1.47354i			0.0570130i
$669$		0			0
$670$	−6.67127	+	11.7518i	−0.257734	+	0.454010i
$671$	−0.370385			−0.0142986
$672$		0			0
$673$		−	48.4181i		−	1.86638i	−0.359384	−	0.933190i	$-0.617013\pi$
$673$		−	48.4181i		−	1.86638i	0.359384	−	0.933190i	$-0.382987\pi$
$674$	1.34097			0.0516521
$675$		0			0
$676$	37.7738			1.45284
$677$		−	7.49862i		−	0.288195i	−0.989563	−	0.144098i	$-0.953972\pi$
$677$		−	7.49862i		−	0.288195i	0.989563	−	0.144098i	$-0.0460280\pi$
$678$		0			0
$679$	53.1473			2.03961
$680$	6.82126	−	12.0160i	0.261583	−	0.460791i
$681$		0			0
$682$			2.83616i			0.108602i
$683$			33.2987i			1.27414i	0.770806	+	0.637070i	$0.219854\pi$
$683$			33.2987i			1.27414i	−0.770806	+	0.637070i	$0.780146\pi$
$684$		0			0
$685$	−13.3664	−	7.58787i	−0.510703	−	0.289917i
$686$	5.81926			0.222181
$687$		0			0
$688$			5.34889i			0.203924i
$689$	66.4128			2.53012
$690$		0			0
$691$	38.3695			1.45964			0.729822	−	0.683638i	$-0.239603\pi$
$691$	38.3695			1.45964			0.729822	+	0.683638i	$0.239603\pi$
$692$		−	13.8432i		−	0.526240i
$693$		0			0
$694$	−0.883744			−0.0335465
$695$	10.8251	−	19.0689i	0.410618	−	0.723324i
$696$		0			0
$697$		−	10.1387i		−	0.384029i
$698$			9.00521i			0.340852i
$699$		0			0
$700$	15.0838	−	9.00399i	0.570113	−	0.340319i
$701$	40.6339			1.53472			0.767360	−	0.641217i	$-0.221570\pi$
$701$	40.6339			1.53472			0.767360	+	0.641217i	$0.221570\pi$
$702$		0			0
$703$			5.83553i			0.220091i
$704$	−0.290044			−0.0109315
$705$		0			0
$706$	6.79030			0.255556
$707$			9.26577i			0.348475i
$708$		0			0
$709$	−11.1957			−0.420464			−0.210232	−	0.977651i	$-0.567422\pi$
$709$	−11.1957			−0.420464			−0.210232	+	0.977651i	$0.567422\pi$
$710$	−26.2509	−	14.9022i	−0.985180	−	0.559270i
$711$		0			0
$712$			10.2797i			0.385248i
$713$		−	63.1656i		−	2.36557i
$714$		0			0
$715$	−4.01893	−	2.28148i	−0.150299	−	0.0853223i
$716$	−21.7817			−0.814020
$717$		0			0
$718$		−	10.2263i		−	0.381641i
$719$	30.2226			1.12711			0.563556	−	0.826078i	$-0.309433\pi$
$719$	30.2226			1.12711			0.563556	+	0.826078i	$0.309433\pi$
$720$		0			0
$721$	6.05946			0.225666
$722$			15.0534i			0.560231i
$723$		0			0
$724$	−2.03100			−0.0754817
$725$	3.02520	+	5.06791i	0.112353	+	0.188217i
$726$		0			0
$727$			19.1911i			0.711758i	0.934532	+	0.355879i	$0.115818\pi$
$727$			19.1911i			0.711758i	−0.934532	+	0.355879i	$0.884182\pi$
$728$			25.0347i			0.927847i
$729$		0			0
$730$	1.89152	−	3.33200i	0.0700083	−	0.123323i
$731$	−33.0519			−1.22247
$732$		0			0
$733$			5.39567i			0.199294i	0.995023	+	0.0996468i	$0.0317713\pi$
$733$			5.39567i			0.199294i	−0.995023	+	0.0996468i	$0.968229\pi$
$734$	17.1583			0.633325
$735$		0			0
$736$	6.45973			0.238109
$737$			1.75284i			0.0645665i
$738$		0			0
$739$	−24.7127			−0.909072			−0.454536	−	0.890728i	$-0.650195\pi$
$739$	−24.7127			−0.909072			−0.454536	+	0.890728i	$0.650195\pi$
$740$	1.94458	+	1.10390i	0.0714842	+	0.0405804i
$741$		0			0
$742$			32.7457i			1.20213i
$743$		−	45.4537i		−	1.66753i	−0.552116	−	0.833767i	$-0.686180\pi$
$743$		−	45.4537i		−	1.66753i	0.552116	−	0.833767i	$-0.313820\pi$
$744$		0			0
$745$	−10.0200	+	17.6507i	−0.367104	+	0.646672i
$746$	−17.1601			−0.628275
$747$		0			0
$748$		−	1.79224i		−	0.0655309i
$749$	−35.2317			−1.28734
$750$		0			0
$751$	49.6360			1.81124			0.905621	−	0.424088i	$-0.139405\pi$
$751$	49.6360			1.81124			0.905621	+	0.424088i	$0.139405\pi$
$752$		−	5.69256i		−	0.207586i
$753$		0			0
$754$	−8.41126			−0.306320
$755$	22.2949	−	39.2735i	0.811395	−	1.42931i
$756$		0			0
$757$			27.9481i			1.01579i	0.861419	+	0.507896i	$0.169576\pi$
$757$			27.9481i			1.01579i	−0.861419	+	0.507896i	$0.830424\pi$
$758$			27.5435i			1.00043i
$759$		0			0
$760$	11.3477	+	6.44187i	0.411623	+	0.233671i
$761$	53.4744			1.93844			0.969222	−	0.246188i	$-0.0791781\pi$
$761$	53.4744			1.93844			0.969222	+	0.246188i	$0.0791781\pi$
$762$		0			0
$763$			17.1227i			0.619884i
$764$	−8.44668			−0.305590
$765$		0			0
$766$	−3.49954			−0.126444
$767$		−	42.3458i		−	1.52902i
$768$		0			0
$769$	8.46659			0.305313			0.152657	−	0.988279i	$-0.451217\pi$
$769$	8.46659			0.305313			0.152657	+	0.988279i	$0.451217\pi$
$770$	1.12491	−	1.98158i	0.0405390	−	0.0714113i
$771$		0			0
$772$			3.64159i			0.131064i
$773$			0.530866i			0.0190939i	0.999954	+	0.00954697i	$0.00303894\pi$
$773$			0.530866i			0.0190939i	−0.999954	+	0.00954697i	$0.996961\pi$
$774$		0			0
$775$	−25.0599	−	41.9811i	−0.900178	−	1.50801i
$776$	15.1272			0.543035
$777$		0			0
$778$		−	13.0015i		−	0.466127i
$779$	9.57477			0.343052
$780$		0			0
$781$	−3.91546			−0.140106
$782$			39.9160i			1.42739i
$783$		0			0
$784$	−5.34367			−0.190846
$785$	−33.5785	−	19.0619i	−1.19847	−	0.680349i
$786$		0			0
$787$			2.16917i			0.0773227i	0.999252	+	0.0386613i	$0.0123094\pi$
$787$			2.16917i			0.0773227i	−0.999252	+	0.0386613i	$0.987691\pi$
$788$			10.1939i			0.363144i
$789$		0			0
$790$	−16.0510	−	9.11187i	−0.571069	−	0.324186i
$791$	−55.9642			−1.98986
$792$		0			0
$793$			9.09932i			0.323126i
$794$	26.6658			0.946336
$795$		0			0
$796$	−5.25299			−0.186187
$797$			26.2510i			0.929857i	0.885348	+	0.464928i	$0.153920\pi$
$797$			26.2510i			0.929857i	−0.885348	+	0.464928i	$0.846080\pi$
$798$		0			0
$799$	35.1755			1.24442
$800$	4.29326	−	2.56279i	0.151790	−	0.0906082i
$801$		0			0
$802$		−	20.3546i		−	0.718747i
$803$		−	0.496986i		−	0.0175382i
$804$		0			0
$805$	−25.0535	+	44.1329i	−0.883019	+	1.55548i
$806$	69.6766			2.45425
$807$		0			0
$808$			2.63730i			0.0927798i
$809$	6.67443			0.234661			0.117330	−	0.993093i	$-0.462566\pi$
$809$	6.67443			0.234661			0.117330	+	0.993093i	$0.462566\pi$
$810$		0			0
$811$	−8.24768			−0.289615			−0.144808	−	0.989460i	$-0.546256\pi$
$811$	−8.24768			−0.289615			−0.144808	+	0.989460i	$0.546256\pi$
$812$		−	4.14728i		−	0.145541i
$813$		0			0
$814$	0.290044			0.0101660
$815$	−32.4552	−	18.4243i	−1.13686	−	0.645374i
$816$		0			0
$817$		−	31.2136i		−	1.09203i
$818$		−	29.9603i		−	1.04754i
$819$		0			0
$820$	1.81125	−	3.19061i	0.0632518	−	0.111421i
$821$	9.61631			0.335611			0.167806	−	0.985820i	$-0.446332\pi$
$821$	9.61631			0.335611			0.167806	+	0.985820i	$0.446332\pi$
$822$		0			0
$823$			32.7309i			1.14093i	0.821322	+	0.570464i	$0.193237\pi$
$823$			32.7309i			1.14093i	−0.821322	+	0.570464i	$0.806763\pi$
$824$	1.72469			0.0600825
$825$		0			0
$826$	20.8791			0.726478
$827$		−	39.9956i		−	1.39078i	−0.718631	−	0.695391i	$-0.755231\pi$
$827$		−	39.9956i		−	1.39078i	0.718631	−	0.695391i	$-0.244769\pi$
$828$		0			0
$829$	−36.8620			−1.28027			−0.640134	−	0.768263i	$-0.721121\pi$
$829$	−36.8620			−1.28027			−0.640134	+	0.768263i	$0.721121\pi$
$830$	−2.66932	+	4.70214i	−0.0926535	+	0.163214i
$831$		0			0
$832$			7.12558i			0.247035i
$833$		−	33.0197i		−	1.14406i
$834$		0			0
$835$	−2.86542	−	1.62665i	−0.0991620	−	0.0562925i
$836$	1.69256			0.0585385
$837$		0			0
$838$			23.3149i			0.805400i
$839$	36.7629			1.26919			0.634597	−	0.772843i	$-0.281166\pi$
$839$	36.7629			1.26919			0.634597	+	0.772843i	$0.281166\pi$
$840$		0			0
$841$	−27.6066			−0.951951
$842$			24.0289i			0.828089i
$843$		0			0
$844$	4.81998			0.165910
$845$	−41.6987	+	73.4543i	−1.43448	+	2.52690i
$846$		0			0
$847$			38.3514i			1.31777i
$848$			9.32034i			0.320062i
$849$		0			0
$850$	15.8360	+	26.5290i	0.543170	+	0.909936i
$851$	−6.45973			−0.221437
$852$		0			0
$853$			15.9547i			0.546278i	0.961975	+	0.273139i	$0.0880619\pi$
$853$			15.9547i			0.546278i	−0.961975	+	0.273139i	$0.911938\pi$
$854$	−4.48654			−0.153526
$855$		0			0
$856$	−10.0279			−0.342748
$857$		−	10.2157i		−	0.348963i	−0.984660	−	0.174481i	$-0.944175\pi$
$857$		−	10.2157i		−	0.348963i	0.984660	−	0.174481i	$-0.0558249\pi$
$858$		0			0
$859$	−7.41899			−0.253133			−0.126566	−	0.991958i	$-0.540396\pi$
$859$	−7.41899			−0.253133			−0.126566	+	0.991958i	$0.540396\pi$
$860$	−10.4013	−	5.90466i	−0.354683	−	0.201347i
$861$		0			0
$862$			19.2917i			0.657077i
$863$		−	9.35839i		−	0.318563i	−0.987233	−	0.159282i	$-0.949082\pi$
$863$		−	9.35839i		−	0.318563i	0.987233	−	0.159282i	$-0.0509178\pi$
$864$		0			0
$865$	26.9192	+	15.2816i	0.915282	+	0.519590i
$866$	−12.5816			−0.427541
$867$		0			0
$868$			34.3549i			1.16608i
$869$	−2.39409			−0.0812139
$870$		0			0
$871$	43.0623			1.45911
$872$			4.87361i			0.165041i
$873$		0			0
$874$	−37.6959			−1.27508
$875$	0.857933	+	39.2711i	0.0290034	+	1.32761i
$876$		0			0
$877$			13.1486i			0.443997i	0.975047	+	0.221998i	$0.0712580\pi$
$877$			13.1486i			0.443997i	−0.975047	+	0.221998i	$0.928742\pi$
$878$		−	14.0428i		−	0.473921i
$879$		0			0
$880$	0.320181	−	0.564014i	0.0107933	−	0.0190129i
$881$	−26.7781			−0.902178			−0.451089	−	0.892479i	$-0.648964\pi$
$881$	−26.7781			−0.902178			−0.451089	+	0.892479i	$0.648964\pi$
$882$		0			0
$883$		−	16.7245i		−	0.562824i	−0.959587	−	0.281412i	$-0.909197\pi$
$883$		−	16.7245i		−	0.562824i	0.959587	−	0.281412i	$-0.0908028\pi$
$884$	−44.0304			−1.48090
$885$		0			0
$886$	24.5696			0.825432
$887$			18.1469i			0.609312i	0.952462	+	0.304656i	$0.0985415\pi$
$887$			18.1469i			0.609312i	−0.952462	+	0.304656i	$0.901458\pi$
$888$		0			0
$889$	4.61181			0.154675
$890$	−19.9897	−	11.3478i	−0.670057	−	0.380380i
$891$		0			0
$892$			3.70392i			0.124017i
$893$			33.2191i			1.11164i
$894$		0			0
$895$	24.0449	−	42.3563i	0.803733	−	1.41581i
$896$	−3.51336			−0.117373
$897$		0			0
$898$		−	12.7574i		−	0.425721i
$899$	−11.5427			−0.384971
$900$		0			0
$901$	−57.5923			−1.91868
$902$		−	0.475896i		−	0.0158456i
$903$		0			0
$904$	−15.9290			−0.529790
$905$	2.24204	−	3.94945i	0.0745278	−	0.131284i
$906$		0			0
$907$		−	50.1481i		−	1.66514i	−0.553920	−	0.832570i	$-0.686869\pi$
$907$		−	50.1481i		−	1.66514i	0.553920	−	0.832570i	$-0.313131\pi$
$908$			6.31512i			0.209575i
$909$		0			0
$910$	−48.6820	−	27.6359i	−1.61379	−	0.916122i
$911$	−2.64691			−0.0876960			−0.0438480	−	0.999038i	$-0.513962\pi$
$911$	−2.64691			−0.0876960			−0.0438480	+	0.999038i	$0.513962\pi$
$912$		0			0
$913$			0.701348i			0.0232112i
$914$	−3.34889			−0.110771
$915$		0			0
$916$	−20.5548			−0.679150
$917$			8.48693i			0.280263i
$918$		0			0
$919$	39.5369			1.30420			0.652101	−	0.758132i	$-0.273888\pi$
$919$	39.5369			1.30420			0.652101	+	0.758132i	$0.273888\pi$
$920$	−7.13092	+	12.5615i	−0.235100	+	0.414139i
$921$		0			0
$922$			0.859501i			0.0283062i
$923$			96.1920i			3.16620i
$924$		0			0
$925$	−4.29326	+	2.56279i	−0.141162	+	0.0842639i
$926$	13.8711			0.455831
$927$		0			0
$928$		−	1.18043i		−	0.0387496i
$929$	−39.2999			−1.28939			−0.644693	−	0.764441i	$-0.723015\pi$
$929$	−39.2999			−1.28939			−0.644693	+	0.764441i	$0.723015\pi$
$930$		0			0
$931$	31.1832			1.02199
$932$		−	21.4393i		−	0.702267i
$933$		0			0
$934$	40.9281			1.33921
$935$	3.48516	+	1.97847i	0.113977	+	0.0647027i
$936$		0			0
$937$			27.7584i			0.906826i	0.891301	+	0.453413i	$0.149794\pi$
$937$			27.7584i			0.906826i	−0.891301	+	0.453413i	$0.850206\pi$
$938$			21.2324i			0.693263i
$939$		0			0
$940$	11.0696	+	6.28405i	0.361052	+	0.204963i
$941$	−48.2212			−1.57197			−0.785983	−	0.618249i	$-0.787842\pi$
$941$	−48.2212			−1.57197			−0.785983	+	0.618249i	$0.787842\pi$
$942$		0			0
$943$			10.5989i			0.345149i
$944$	5.94279			0.193421
$945$		0			0
$946$	−1.55141			−0.0504408
$947$		−	26.5111i		−	0.861495i	−0.902472	−	0.430748i	$-0.858250\pi$
$947$		−	26.5111i		−	0.861495i	0.902472	−	0.430748i	$-0.141750\pi$
$948$		0			0
$949$	−12.2095			−0.396339
$950$	−25.0535	+	14.9552i	−0.812842	+	0.485212i
$951$		0			0
$952$		−	21.7098i		−	0.703617i
$953$			31.8487i			1.03168i	0.856685	+	0.515840i	$0.172520\pi$
$953$			31.8487i			1.03168i	−0.856685	+	0.515840i	$0.827480\pi$
$954$		0			0
$955$	9.32433	−	16.4252i	0.301728	−	0.531508i
$956$	20.7479			0.671034
$957$		0			0
$958$			8.58990i			0.277527i
$959$	−24.1496			−0.779832
$960$		0			0
$961$	64.6166			2.08441
$962$		−	7.12558i		−	0.229738i
$963$		0			0
$964$	−10.7731			−0.346978
$965$	−7.08136	−	4.01997i	−0.227957	−	0.129407i
$966$		0			0
$967$		−	19.4699i		−	0.626109i	−0.949735	−	0.313054i	$-0.898648\pi$
$967$		−	19.4699i		−	0.626109i	0.949735	−	0.313054i	$-0.101352\pi$
$968$			10.9159i			0.350849i
$969$		0			0
$970$	−16.6990	+	29.4161i	−0.536173	+	0.944493i
$971$	21.8178			0.700168			0.350084	−	0.936718i	$-0.386153\pi$
$971$	21.8178			0.700168			0.350084	+	0.936718i	$0.386153\pi$
$972$		0			0
$973$		−	34.4525i		−	1.10450i
$974$	−25.8389			−0.827932
$975$		0			0
$976$	−1.27699			−0.0408756
$977$		−	41.8705i		−	1.33956i	−0.742561	−	0.669779i	$-0.766389\pi$
$977$		−	41.8705i		−	1.33956i	0.742561	−	0.669779i	$-0.233611\pi$
$978$		0			0
$979$	−2.98157			−0.0952913
$980$	5.89891	−	10.3912i	0.188434	−	0.331935i
$981$		0			0
$982$		−	11.4864i		−	0.366547i
$983$			37.0175i			1.18067i	0.807157	+	0.590337i	$0.201005\pi$
$983$			37.0175i			1.18067i	−0.807157	+	0.590337i	$0.798995\pi$
$984$		0			0
$985$	−19.8229	−	11.2531i	−0.631611	−	0.358555i
$986$	7.29413			0.232292
$987$		0			0
$988$		−	41.5815i		−	1.32288i
$989$	34.5524			1.09870
$990$		0			0
$991$	−28.4749			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$991$	−28.4749			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$992$			9.77838i			0.310464i
$993$		0			0
$994$	−47.4287			−1.50435
$995$	5.79880	−	10.2149i	0.183834	−	0.323833i
$996$		0			0
$997$			14.2442i			0.451118i	0.974229	+	0.225559i	$0.0724209\pi$
$997$			14.2442i			0.451118i	−0.974229	+	0.225559i	$0.927579\pi$
$998$			9.74599i			0.308504i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.p.1999.9		10
3.2	odd	2		370.2.b.d.149.3	✓	10
5.4	even	2	inner	3330.2.d.p.1999.4		10
15.2	even	4		1850.2.a.be.1.3		5
15.8	even	4		1850.2.a.bd.1.3		5
15.14	odd	2		370.2.b.d.149.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.d.149.3	✓	10	3.2	odd	2
370.2.b.d.149.8	yes	10	15.14	odd	2
1850.2.a.bd.1.3		5	15.8	even	4
1850.2.a.be.1.3		5	15.2	even	4
3330.2.d.p.1999.4		10	5.4	even	2	inner
3330.2.d.p.1999.9		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.10390 - 1.94458i) q^{5} -3.51336i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.10390 - 1.94458i) q^{5} -3.51336i q^{7} -1.00000i q^{8} +(1.94458 + 1.10390i) q^{10} +0.290044 q^{11} -7.12558i q^{13} +3.51336 q^{14} +1.00000 q^{16} +6.17921i q^{17} -5.83553 q^{19} +(-1.10390 + 1.94458i) q^{20} +0.290044i q^{22} -6.45973i q^{23} +(-2.56279 - 4.29326i) q^{25} +7.12558 q^{26} +3.51336i q^{28} -1.18043 q^{29} +9.77838 q^{31} +1.00000i q^{32} -6.17921 q^{34} +(-6.83201 - 3.87841i) q^{35} -1.00000i q^{37} -5.83553i q^{38} +(-1.94458 - 1.10390i) q^{40} -1.64077 q^{41} +5.34889i q^{43} -0.290044 q^{44} +6.45973 q^{46} -5.69256i q^{47} -5.34367 q^{49} +(4.29326 - 2.56279i) q^{50} +7.12558i q^{52} +9.32034i q^{53} +(0.320181 - 0.564014i) q^{55} -3.51336 q^{56} -1.18043i q^{58} +5.94279 q^{59} -1.27699 q^{61} +9.77838i q^{62} -1.00000 q^{64} +(-13.8563 - 7.86596i) q^{65} +6.04334i q^{67} -6.17921i q^{68} +(3.87841 - 6.83201i) q^{70} -13.4995 q^{71} -1.71348i q^{73} +1.00000 q^{74} +5.83553 q^{76} -1.01903i q^{77} -8.25422 q^{79} +(1.10390 - 1.94458i) q^{80} -1.64077i q^{82} +2.41807i q^{83} +(12.0160 + 6.82126i) q^{85} -5.34889 q^{86} -0.290044i q^{88} -10.2797 q^{89} -25.0347 q^{91} +6.45973i q^{92} +5.69256 q^{94} +(-6.44187 + 11.3477i) q^{95} +15.1272i q^{97} -5.34367i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} - 6 q^{5}+O(q^{10}) \) 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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