LMFDB - Embedded newform 3330.2.d.l.1999.1

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:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1999.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.l.1999.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -2.46410i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -2.46410i q^{7} +1.00000i q^{8} +(2.00000 - 1.00000i) q^{10} +1.73205 q^{11} +4.00000i q^{13} -2.46410 q^{14} +1.00000 q^{16} -0.464102i q^{17} -6.92820 q^{19} +(-1.00000 - 2.00000i) q^{20} -1.73205i q^{22} +5.46410i q^{23} +(-3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +2.46410i q^{28} -3.00000 q^{29} -5.73205 q^{31} -1.00000i q^{32} -0.464102 q^{34} +(4.92820 - 2.46410i) q^{35} -1.00000i q^{37} +6.92820i q^{38} +(-2.00000 + 1.00000i) q^{40} -9.19615 q^{41} +3.19615i q^{43} -1.73205 q^{44} +5.46410 q^{46} -11.4641i q^{47} +0.928203 q^{49} +(4.00000 + 3.00000i) q^{50} -4.00000i q^{52} -0.267949i q^{53} +(1.73205 + 3.46410i) q^{55} +2.46410 q^{56} +3.00000i q^{58} -9.46410 q^{59} -5.19615 q^{61} +5.73205i q^{62} -1.00000 q^{64} +(-8.00000 + 4.00000i) q^{65} -1.46410i q^{67} +0.464102i q^{68} +(-2.46410 - 4.92820i) q^{70} +12.9282 q^{71} -6.39230i q^{73} -1.00000 q^{74} +6.92820 q^{76} -4.26795i q^{77} +4.53590 q^{79} +(1.00000 + 2.00000i) q^{80} +9.19615i q^{82} -2.53590i q^{83} +(0.928203 - 0.464102i) q^{85} +3.19615 q^{86} +1.73205i q^{88} -9.46410 q^{89} +9.85641 q^{91} -5.46410i q^{92} -11.4641 q^{94} +(-6.92820 - 13.8564i) q^{95} +17.5885i q^{97} -0.928203i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^5	$ 4 q - 4 q^{4} + 4 q^{5} + 8 q^{10} + 4 q^{14} + 4 q^{16} - 4 q^{20} - 12 q^{25} + 16 q^{26} - 12 q^{29} - 16 q^{31} + 12 q^{34} - 8 q^{35} - 8 q^{40} - 16 q^{41} + 8 q^{46} - 24 q^{49} + 16 q^{50} - 4 q^{56} - 24 q^{59} - 4 q^{64} - 32 q^{65} + 4 q^{70} + 24 q^{71} - 4 q^{74} + 32 q^{79} + 4 q^{80} - 24 q^{85} - 8 q^{86} - 24 q^{89} - 16 q^{91} - 32 q^{94}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^5 + 8 * q^10 + 4 * q^14 + 4 * q^16 - 4 * q^20 - 12 * q^25 + 16 * q^26 - 12 * q^29 - 16 * q^31 + 12 * q^34 - 8 * q^35 - 8 * q^40 - 16 * q^41 + 8 * q^46 - 24 * q^49 + 16 * q^50 - 4 * q^56 - 24 * q^59 - 4 * q^64 - 32 * q^65 + 4 * q^70 + 24 * q^71 - 4 * q^74 + 32 * q^79 + 4 * q^80 - 24 * q^85 - 8 * q^86 - 24 * q^89 - 16 * q^91 - 32 * q^94

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
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$		−	2.46410i		−	0.931343i	−0.884958	−	0.465671i	$-0.845813\pi$
$7$		−	2.46410i		−	0.931343i	0.884958	−	0.465671i	$-0.154187\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$	1.73205			0.522233			0.261116	−	0.965307i	$-0.415909\pi$
$11$	1.73205			0.522233			0.261116	+	0.965307i	$0.415909\pi$
$12$		0			0
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−2.46410			−0.658559
$15$		0			0
$16$	1.00000			0.250000
$17$		−	0.464102i		−	0.112561i	−0.998415	−	0.0562806i	$-0.982076\pi$
$17$		−	0.464102i		−	0.112561i	0.998415	−	0.0562806i	$-0.0179241\pi$
$18$		0			0
$19$	−6.92820			−1.58944			−0.794719	−	0.606977i	$-0.792382\pi$
$19$	−6.92820			−1.58944			−0.794719	+	0.606977i	$0.792382\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$		−	1.73205i		−	0.369274i
$23$			5.46410i			1.13934i	0.821872	+	0.569672i	$0.192930\pi$
$23$			5.46410i			1.13934i	−0.821872	+	0.569672i	$0.807070\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	4.00000			0.784465
$27$		0			0
$28$			2.46410i			0.465671i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	−5.73205			−1.02951			−0.514753	−	0.857338i	$-0.672117\pi$
$31$	−5.73205			−1.02951			−0.514753	+	0.857338i	$0.672117\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−0.464102			−0.0795928
$35$	4.92820	−	2.46410i	0.833018	−	0.416509i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$			6.92820i			1.12390i
$39$		0			0
$40$	−2.00000	+	1.00000i	−0.316228	+	0.158114i
$41$	−9.19615			−1.43620			−0.718099	−	0.695941i	$-0.754987\pi$
$41$	−9.19615			−1.43620			−0.718099	+	0.695941i	$0.754987\pi$
$42$		0			0
$43$			3.19615i			0.487409i	0.969850	+	0.243704i	$0.0783627\pi$
$43$			3.19615i			0.487409i	−0.969850	+	0.243704i	$0.921637\pi$
$44$	−1.73205			−0.261116
$45$		0			0
$46$	5.46410			0.805638
$47$		−	11.4641i		−	1.67221i	−0.548569	−	0.836106i	$-0.684827\pi$
$47$		−	11.4641i		−	1.67221i	0.548569	−	0.836106i	$-0.315173\pi$
$48$		0			0
$49$	0.928203			0.132600
$50$	4.00000	+	3.00000i	0.565685	+	0.424264i
$51$		0			0
$52$		−	4.00000i		−	0.554700i
$53$		−	0.267949i		−	0.0368057i	−0.999831	−	0.0184028i	$-0.994142\pi$
$53$		−	0.267949i		−	0.0368057i	0.999831	−	0.0184028i	$-0.00585813\pi$
$54$		0			0
$55$	1.73205	+	3.46410i	0.233550	+	0.467099i
$56$	2.46410			0.329279
$57$		0			0
$58$			3.00000i			0.393919i
$59$	−9.46410			−1.23212			−0.616061	−	0.787699i	$-0.711272\pi$
$59$	−9.46410			−1.23212			−0.616061	+	0.787699i	$0.711272\pi$
$60$		0			0
$61$	−5.19615			−0.665299			−0.332650	−	0.943051i	$-0.607943\pi$
$61$	−5.19615			−0.665299			−0.332650	+	0.943051i	$0.607943\pi$
$62$			5.73205i			0.727971i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.00000	+	4.00000i	−0.992278	+	0.496139i
$66$		0			0
$67$		−	1.46410i		−	0.178868i	−0.995993	−	0.0894342i	$-0.971494\pi$
$67$		−	1.46410i		−	0.178868i	0.995993	−	0.0894342i	$-0.0285059\pi$
$68$			0.464102i			0.0562806i
$69$		0			0
$70$	−2.46410	−	4.92820i	−0.294516	−	0.589033i
$71$	12.9282			1.53430			0.767148	−	0.641470i	$-0.221675\pi$
$71$	12.9282			1.53430			0.767148	+	0.641470i	$0.221675\pi$
$72$		0			0
$73$		−	6.39230i		−	0.748163i	−0.927396	−	0.374081i	$-0.877958\pi$
$73$		−	6.39230i		−	0.748163i	0.927396	−	0.374081i	$-0.122042\pi$
$74$	−1.00000			−0.116248
$75$		0			0
$76$	6.92820			0.794719
$77$		−	4.26795i		−	0.486378i
$78$		0			0
$79$	4.53590			0.510328			0.255164	−	0.966898i	$-0.417870\pi$
$79$	4.53590			0.510328			0.255164	+	0.966898i	$0.417870\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$		0			0
$82$			9.19615i			1.01555i
$83$		−	2.53590i		−	0.278351i	−0.990268	−	0.139176i	$-0.955555\pi$
$83$		−	2.53590i		−	0.278351i	0.990268	−	0.139176i	$-0.0444452\pi$
$84$		0			0
$85$	0.928203	−	0.464102i	0.100678	−	0.0503389i
$86$	3.19615			0.344650
$87$		0			0
$88$			1.73205i			0.184637i
$89$	−9.46410			−1.00319			−0.501596	−	0.865102i	$-0.667254\pi$
$89$	−9.46410			−1.00319			−0.501596	+	0.865102i	$0.667254\pi$
$90$		0			0
$91$	9.85641			1.03323
$92$		−	5.46410i		−	0.569672i
$93$		0			0
$94$	−11.4641			−1.18243
$95$	−6.92820	−	13.8564i	−0.710819	−	1.42164i
$96$		0			0
$97$			17.5885i			1.78584i	0.450218	+	0.892919i	$0.351346\pi$
$97$			17.5885i			1.78584i	−0.450218	+	0.892919i	$0.648654\pi$
$98$		−	0.928203i		−	0.0937627i
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	−14.3923			−1.43209			−0.716044	−	0.698055i	$-0.754049\pi$
$101$	−14.3923			−1.43209			−0.716044	+	0.698055i	$0.754049\pi$
$102$		0			0
$103$			9.46410i			0.932526i	0.884646	+	0.466263i	$0.154400\pi$
$103$			9.46410i			0.932526i	−0.884646	+	0.466263i	$0.845600\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	−0.267949			−0.0260255
$107$		−	7.46410i		−	0.721582i	−0.932647	−	0.360791i	$-0.882507\pi$
$107$		−	7.46410i		−	0.721582i	0.932647	−	0.360791i	$-0.117493\pi$
$108$		0			0
$109$	4.66025			0.446371			0.223186	−	0.974776i	$-0.428354\pi$
$109$	4.66025			0.446371			0.223186	+	0.974776i	$0.428354\pi$
$110$	3.46410	−	1.73205i	0.330289	−	0.165145i
$111$		0			0
$112$		−	2.46410i		−	0.232836i
$113$		−	14.4641i		−	1.36067i	−0.732902	−	0.680334i	$-0.761835\pi$
$113$		−	14.4641i		−	1.36067i	0.732902	−	0.680334i	$-0.238165\pi$
$114$		0			0
$115$	−10.9282	+	5.46410i	−1.01906	+	0.509530i
$116$	3.00000			0.278543
$117$		0			0
$118$			9.46410i			0.871241i
$119$	−1.14359			−0.104833
$120$		0			0
$121$	−8.00000			−0.727273
$122$			5.19615i			0.470438i
$123$		0			0
$124$	5.73205			0.514753
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	4.00000	+	8.00000i	0.350823	+	0.701646i
$131$	11.4641			1.00162			0.500812	−	0.865556i	$-0.333035\pi$
$131$	11.4641			1.00162			0.500812	+	0.865556i	$0.333035\pi$
$132$		0			0
$133$			17.0718i			1.48031i
$134$	−1.46410			−0.126479
$135$		0			0
$136$	0.464102			0.0397964
$137$			7.85641i			0.671218i	0.942001	+	0.335609i	$0.108942\pi$
$137$			7.85641i			0.671218i	−0.942001	+	0.335609i	$0.891058\pi$
$138$		0			0
$139$	−7.92820			−0.672461			−0.336231	−	0.941780i	$-0.609152\pi$
$139$	−7.92820			−0.672461			−0.336231	+	0.941780i	$0.609152\pi$
$140$	−4.92820	+	2.46410i	−0.416509	+	0.208255i
$141$		0			0
$142$		−	12.9282i		−	1.08491i
$143$			6.92820i			0.579365i
$144$		0			0
$145$	−3.00000	−	6.00000i	−0.249136	−	0.498273i
$146$	−6.39230			−0.529031
$147$		0			0
$148$			1.00000i			0.0821995i
$149$	−8.00000			−0.655386			−0.327693	−	0.944784i	$-0.606271\pi$
$149$	−8.00000			−0.655386			−0.327693	+	0.944784i	$0.606271\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$		−	6.92820i		−	0.561951i
$153$		0			0
$154$	−4.26795			−0.343921
$155$	−5.73205	−	11.4641i	−0.460409	−	0.920819i
$156$		0			0
$157$			16.4641i			1.31398i	0.753900	+	0.656989i	$0.228170\pi$
$157$			16.4641i			1.31398i	−0.753900	+	0.656989i	$0.771830\pi$
$158$		−	4.53590i		−	0.360857i
$159$		0			0
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$	13.4641			1.06112
$162$		0			0
$163$			7.73205i			0.605621i	0.953051	+	0.302810i	$0.0979249\pi$
$163$			7.73205i			0.605621i	−0.953051	+	0.302810i	$0.902075\pi$
$164$	9.19615			0.718099
$165$		0			0
$166$	−2.53590			−0.196824
$167$		−	6.39230i		−	0.494651i	−0.968932	−	0.247326i	$-0.920448\pi$
$167$		−	6.39230i		−	0.494651i	0.968932	−	0.247326i	$-0.0795518\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	−0.464102	−	0.928203i	−0.0355950	−	0.0711899i
$171$		0			0
$172$		−	3.19615i		−	0.243704i
$173$			17.0526i			1.29648i	0.761435	+	0.648241i	$0.224495\pi$
$173$			17.0526i			1.29648i	−0.761435	+	0.648241i	$0.775505\pi$
$174$		0			0
$175$	9.85641	+	7.39230i	0.745074	+	0.558806i
$176$	1.73205			0.130558
$177$		0			0
$178$			9.46410i			0.709364i
$179$	−5.60770			−0.419139			−0.209569	−	0.977794i	$-0.567206\pi$
$179$	−5.60770			−0.419139			−0.209569	+	0.977794i	$0.567206\pi$
$180$		0			0
$181$	−8.39230			−0.623795			−0.311898	−	0.950116i	$-0.600965\pi$
$181$	−8.39230			−0.623795			−0.311898	+	0.950116i	$0.600965\pi$
$182$		−	9.85641i		−	0.730605i
$183$		0			0
$184$	−5.46410			−0.402819
$185$	2.00000	−	1.00000i	0.147043	−	0.0735215i
$186$		0			0
$187$		−	0.803848i		−	0.0587832i
$188$			11.4641i			0.836106i
$189$		0			0
$190$	−13.8564	+	6.92820i	−1.00525	+	0.502625i
$191$	−19.7846			−1.43156			−0.715782	−	0.698324i	$-0.753930\pi$
$191$	−19.7846			−1.43156			−0.715782	+	0.698324i	$0.753930\pi$
$192$		0			0
$193$			20.0000i			1.43963i	0.694165	+	0.719816i	$0.255774\pi$
$193$			20.0000i			1.43963i	−0.694165	+	0.719816i	$0.744226\pi$
$194$	17.5885			1.26278
$195$		0			0
$196$	−0.928203			−0.0663002
$197$			16.7846i			1.19585i	0.801551	+	0.597927i	$0.204009\pi$
$197$			16.7846i			1.19585i	−0.801551	+	0.597927i	$0.795991\pi$
$198$		0			0
$199$	25.3205			1.79492			0.897462	−	0.441093i	$-0.145409\pi$
$199$	25.3205			1.79492			0.897462	+	0.441093i	$0.145409\pi$
$200$	−4.00000	−	3.00000i	−0.282843	−	0.212132i
$201$		0			0
$202$			14.3923i			1.01264i
$203$			7.39230i			0.518838i
$204$		0			0
$205$	−9.19615	−	18.3923i	−0.642287	−	1.28457i
$206$	9.46410			0.659395
$207$		0			0
$208$			4.00000i			0.277350i
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−27.7846			−1.91277			−0.956386	−	0.292107i	$-0.905644\pi$
$211$	−27.7846			−1.91277			−0.956386	+	0.292107i	$0.905644\pi$
$212$			0.267949i			0.0184028i
$213$		0			0
$214$	−7.46410			−0.510235
$215$	−6.39230	+	3.19615i	−0.435952	+	0.217976i
$216$		0			0
$217$			14.1244i			0.958824i
$218$		−	4.66025i		−	0.315632i
$219$		0			0
$220$	−1.73205	−	3.46410i	−0.116775	−	0.233550i
$221$	1.85641			0.124875
$222$		0			0
$223$		−	10.3205i		−	0.691112i	−0.938398	−	0.345556i	$-0.887690\pi$
$223$		−	10.3205i		−	0.691112i	0.938398	−	0.345556i	$-0.112310\pi$
$224$	−2.46410			−0.164640
$225$		0			0
$226$	−14.4641			−0.962138
$227$			7.53590i			0.500175i	0.968223	+	0.250088i	$0.0804594\pi$
$227$			7.53590i			0.500175i	−0.968223	+	0.250088i	$0.919541\pi$
$228$		0			0
$229$	−24.3923			−1.61189			−0.805944	−	0.591991i	$-0.798342\pi$
$229$	−24.3923			−1.61189			−0.805944	+	0.591991i	$0.798342\pi$
$230$	5.46410	+	10.9282i	0.360292	+	0.720584i
$231$		0			0
$232$		−	3.00000i		−	0.196960i
$233$		−	17.3205i		−	1.13470i	−0.823475	−	0.567352i	$-0.807968\pi$
$233$		−	17.3205i		−	1.13470i	0.823475	−	0.567352i	$-0.192032\pi$
$234$		0			0
$235$	22.9282	−	11.4641i	1.49567	−	0.747836i
$236$	9.46410			0.616061
$237$		0			0
$238$			1.14359i			0.0741282i
$239$	5.00000			0.323423			0.161712	−	0.986838i	$-0.448299\pi$
$239$	5.00000			0.323423			0.161712	+	0.986838i	$0.448299\pi$
$240$		0			0
$241$	−20.9282			−1.34810			−0.674052	−	0.738684i	$-0.735448\pi$
$241$	−20.9282			−1.34810			−0.674052	+	0.738684i	$0.735448\pi$
$242$			8.00000i			0.514259i
$243$		0			0
$244$	5.19615			0.332650
$245$	0.928203	+	1.85641i	0.0593007	+	0.118601i
$246$		0			0
$247$		−	27.7128i		−	1.76332i
$248$		−	5.73205i		−	0.363986i
$249$		0			0
$250$	−2.00000	+	11.0000i	−0.126491	+	0.695701i
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$			9.46410i			0.595003i
$254$	16.0000			1.00393
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	7.85641i		−	0.490069i	−0.969514	−	0.245035i	$-0.921201\pi$
$257$		−	7.85641i		−	0.490069i	0.969514	−	0.245035i	$-0.0787993\pi$
$258$		0			0
$259$	−2.46410			−0.153112
$260$	8.00000	−	4.00000i	0.496139	−	0.248069i
$261$		0			0
$262$		−	11.4641i		−	0.708255i
$263$		−	10.1244i		−	0.624295i	−0.950034	−	0.312147i	$-0.898952\pi$
$263$		−	10.1244i		−	0.624295i	0.950034	−	0.312147i	$-0.101048\pi$
$264$		0			0
$265$	0.535898	−	0.267949i	0.0329200	−	0.0164600i
$266$	17.0718			1.04674
$267$		0			0
$268$			1.46410i			0.0894342i
$269$	16.0000			0.975537			0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000			0.975537			0.487769	+	0.872973i	$0.337811\pi$
$270$		0			0
$271$	−3.85641			−0.234260			−0.117130	−	0.993117i	$-0.537369\pi$
$271$	−3.85641			−0.234260			−0.117130	+	0.993117i	$0.537369\pi$
$272$		−	0.464102i		−	0.0281403i
$273$		0			0
$274$	7.85641			0.474623
$275$	−5.19615	+	6.92820i	−0.313340	+	0.417786i
$276$		0			0
$277$		−	27.7128i		−	1.66510i	−0.553949	−	0.832551i	$-0.686880\pi$
$277$		−	27.7128i		−	1.66510i	0.553949	−	0.832551i	$-0.313120\pi$
$278$			7.92820i			0.475502i
$279$		0			0
$280$	2.46410	+	4.92820i	0.147258	+	0.294516i
$281$	−0.928203			−0.0553720			−0.0276860	−	0.999617i	$-0.508814\pi$
$281$	−0.928203			−0.0553720			−0.0276860	+	0.999617i	$0.508814\pi$
$282$		0			0
$283$			4.53590i			0.269631i	0.990871	+	0.134816i	$0.0430442\pi$
$283$			4.53590i			0.269631i	−0.990871	+	0.134816i	$0.956956\pi$
$284$	−12.9282			−0.767148
$285$		0			0
$286$	6.92820			0.409673
$287$			22.6603i			1.33759i
$288$		0			0
$289$	16.7846			0.987330
$290$	−6.00000	+	3.00000i	−0.352332	+	0.176166i
$291$		0			0
$292$			6.39230i			0.374081i
$293$		−	5.87564i		−	0.343259i	−0.985162	−	0.171629i	$-0.945097\pi$
$293$		−	5.87564i		−	0.343259i	0.985162	−	0.171629i	$-0.0549032\pi$
$294$		0			0
$295$	−9.46410	−	18.9282i	−0.551021	−	1.10204i
$296$	1.00000			0.0581238
$297$		0			0
$298$			8.00000i			0.463428i
$299$	−21.8564			−1.26399
$300$		0			0
$301$	7.87564			0.453945
$302$			2.00000i			0.115087i
$303$		0			0
$304$	−6.92820			−0.397360
$305$	−5.19615	−	10.3923i	−0.297531	−	0.595062i
$306$		0			0
$307$			6.53590i			0.373023i	0.982453	+	0.186512i	$0.0597182\pi$
$307$			6.53590i			0.373023i	−0.982453	+	0.186512i	$0.940282\pi$
$308$			4.26795i			0.243189i
$309$		0			0
$310$	−11.4641	+	5.73205i	−0.651117	+	0.325559i
$311$	23.7846			1.34870			0.674351	−	0.738411i	$-0.264424\pi$
$311$	23.7846			1.34870			0.674351	+	0.738411i	$0.264424\pi$
$312$		0			0
$313$			9.85641i			0.557117i	0.960419	+	0.278559i	$0.0898566\pi$
$313$			9.85641i			0.557117i	−0.960419	+	0.278559i	$0.910143\pi$
$314$	16.4641			0.929123
$315$		0			0
$316$	−4.53590			−0.255164
$317$			11.1962i			0.628839i	0.949284	+	0.314419i	$0.101810\pi$
$317$			11.1962i			0.628839i	−0.949284	+	0.314419i	$0.898190\pi$
$318$		0			0
$319$	−5.19615			−0.290929
$320$	−1.00000	−	2.00000i	−0.0559017	−	0.111803i
$321$		0			0
$322$		−	13.4641i		−	0.750325i
$323$			3.21539i			0.178909i
$324$		0			0
$325$	−16.0000	−	12.0000i	−0.887520	−	0.665640i
$326$	7.73205			0.428239
$327$		0			0
$328$		−	9.19615i		−	0.507773i
$329$	−28.2487			−1.55740
$330$		0			0
$331$	20.9282			1.15032			0.575159	−	0.818042i	$-0.304940\pi$
$331$	20.9282			1.15032			0.575159	+	0.818042i	$0.304940\pi$
$332$			2.53590i			0.139176i
$333$		0			0
$334$	−6.39230			−0.349771
$335$	2.92820	−	1.46410i	0.159985	−	0.0799924i
$336$		0			0
$337$			31.3205i			1.70614i	0.521799	+	0.853068i	$0.325261\pi$
$337$			31.3205i			1.70614i	−0.521799	+	0.853068i	$0.674739\pi$
$338$			3.00000i			0.163178i
$339$		0			0
$340$	−0.928203	+	0.464102i	−0.0503389	+	0.0251694i
$341$	−9.92820			−0.537642
$342$		0			0
$343$		−	19.5359i		−	1.05484i
$344$	−3.19615			−0.172325
$345$		0			0
$346$	17.0526			0.916751
$347$			17.0718i			0.916462i	0.888833	+	0.458231i	$0.151517\pi$
$347$			17.0718i			0.916462i	−0.888833	+	0.458231i	$0.848483\pi$
$348$		0			0
$349$	8.53590			0.456916			0.228458	−	0.973554i	$-0.426632\pi$
$349$	8.53590			0.456916			0.228458	+	0.973554i	$0.426632\pi$
$350$	7.39230	−	9.85641i	0.395135	−	0.526847i
$351$		0			0
$352$		−	1.73205i		−	0.0923186i
$353$			4.60770i			0.245243i	0.992454	+	0.122621i	$0.0391301\pi$
$353$			4.60770i			0.245243i	−0.992454	+	0.122621i	$0.960870\pi$
$354$		0			0
$355$	12.9282	+	25.8564i	0.686158	+	1.37232i
$356$	9.46410			0.501596
$357$		0			0
$358$			5.60770i			0.296376i
$359$	0.143594			0.00757858			0.00378929	−	0.999993i	$-0.498794\pi$
$359$	0.143594			0.00757858			0.00378929	+	0.999993i	$0.498794\pi$
$360$		0			0
$361$	29.0000			1.52632
$362$			8.39230i			0.441090i
$363$		0			0
$364$	−9.85641			−0.516616
$365$	12.7846	−	6.39230i	0.669177	−	0.334589i
$366$		0			0
$367$		−	6.60770i		−	0.344919i	−0.985017	−	0.172459i	$-0.944829\pi$
$367$		−	6.60770i		−	0.344919i	0.985017	−	0.172459i	$-0.0551714\pi$
$368$			5.46410i			0.284836i
$369$		0			0
$370$	−1.00000	−	2.00000i	−0.0519875	−	0.103975i
$371$	−0.660254			−0.0342787
$372$		0			0
$373$			25.7128i			1.33136i	0.746238	+	0.665679i	$0.231858\pi$
$373$			25.7128i			1.33136i	−0.746238	+	0.665679i	$0.768142\pi$
$374$	−0.803848			−0.0415660
$375$		0			0
$376$	11.4641			0.591216
$377$		−	12.0000i		−	0.618031i
$378$		0			0
$379$	6.92820			0.355878			0.177939	−	0.984042i	$-0.443057\pi$
$379$	6.92820			0.355878			0.177939	+	0.984042i	$0.443057\pi$
$380$	6.92820	+	13.8564i	0.355409	+	0.710819i
$381$		0			0
$382$			19.7846i			1.01227i
$383$		−	24.3923i		−	1.24639i	−0.782067	−	0.623194i	$-0.785835\pi$
$383$		−	24.3923i		−	1.24639i	0.782067	−	0.623194i	$-0.214165\pi$
$384$		0			0
$385$	8.53590	−	4.26795i	0.435030	−	0.217515i
$386$	20.0000			1.01797
$387$		0			0
$388$		−	17.5885i		−	0.892919i
$389$	14.8564			0.753250			0.376625	−	0.926366i	$-0.377085\pi$
$389$	14.8564			0.753250			0.376625	+	0.926366i	$0.377085\pi$
$390$		0			0
$391$	2.53590			0.128246
$392$			0.928203i			0.0468813i
$393$		0			0
$394$	16.7846			0.845596
$395$	4.53590	+	9.07180i	0.228226	+	0.456452i
$396$		0			0
$397$		−	15.0718i		−	0.756432i	−0.925717	−	0.378216i	$-0.876538\pi$
$397$		−	15.0718i		−	0.756432i	0.925717	−	0.378216i	$-0.123462\pi$
$398$		−	25.3205i		−	1.26920i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	16.9282			0.845354			0.422677	−	0.906280i	$-0.361090\pi$
$401$	16.9282			0.845354			0.422677	+	0.906280i	$0.361090\pi$
$402$		0			0
$403$		−	22.9282i		−	1.14214i
$404$	14.3923			0.716044
$405$		0			0
$406$	7.39230			0.366874
$407$		−	1.73205i		−	0.0858546i
$408$		0			0
$409$	−3.60770			−0.178389			−0.0891945	−	0.996014i	$-0.528429\pi$
$409$	−3.60770			−0.178389			−0.0891945	+	0.996014i	$0.528429\pi$
$410$	−18.3923	+	9.19615i	−0.908331	+	0.454166i
$411$		0			0
$412$		−	9.46410i		−	0.466263i
$413$			23.3205i			1.14753i
$414$		0			0
$415$	5.07180	−	2.53590i	0.248965	−	0.124482i
$416$	4.00000			0.196116
$417$		0			0
$418$			12.0000i			0.586939i
$419$	9.32051			0.455337			0.227668	−	0.973739i	$-0.426890\pi$
$419$	9.32051			0.455337			0.227668	+	0.973739i	$0.426890\pi$
$420$		0			0
$421$	13.8564			0.675320			0.337660	−	0.941268i	$-0.390365\pi$
$421$	13.8564			0.675320			0.337660	+	0.941268i	$0.390365\pi$
$422$			27.7846i			1.35253i
$423$		0			0
$424$	0.267949			0.0130128
$425$	1.85641	+	1.39230i	0.0900489	+	0.0675367i
$426$		0			0
$427$			12.8038i			0.619622i
$428$			7.46410i			0.360791i
$429$		0			0
$430$	3.19615	+	6.39230i	0.154132	+	0.308264i
$431$	29.9282			1.44159			0.720795	−	0.693148i	$-0.243777\pi$
$431$	29.9282			1.44159			0.720795	+	0.693148i	$0.243777\pi$
$432$		0			0
$433$		−	3.60770i		−	0.173375i	−0.996236	−	0.0866874i	$-0.972372\pi$
$433$		−	3.60770i		−	0.173375i	0.996236	−	0.0866874i	$-0.0276281\pi$
$434$	14.1244			0.677991
$435$		0			0
$436$	−4.66025			−0.223186
$437$		−	37.8564i		−	1.81092i
$438$		0			0
$439$	13.1962			0.629818			0.314909	−	0.949122i	$-0.398026\pi$
$439$	13.1962			0.629818			0.314909	+	0.949122i	$0.398026\pi$
$440$	−3.46410	+	1.73205i	−0.165145	+	0.0825723i
$441$		0			0
$442$		−	1.85641i		−	0.0883003i
$443$			26.0000i			1.23530i	0.786454	+	0.617649i	$0.211915\pi$
$443$			26.0000i			1.23530i	−0.786454	+	0.617649i	$0.788085\pi$
$444$		0			0
$445$	−9.46410	−	18.9282i	−0.448641	−	0.897283i
$446$	−10.3205			−0.488690
$447$		0			0
$448$			2.46410i			0.116418i
$449$	−26.5359			−1.25231			−0.626153	−	0.779700i	$-0.715372\pi$
$449$	−26.5359			−1.25231			−0.626153	+	0.779700i	$0.715372\pi$
$450$		0			0
$451$	−15.9282			−0.750030
$452$			14.4641i			0.680334i
$453$		0			0
$454$	7.53590			0.353677
$455$	9.85641	+	19.7128i	0.462075	+	0.924151i
$456$		0			0
$457$			19.1962i			0.897958i	0.893542	+	0.448979i	$0.148212\pi$
$457$			19.1962i			0.897958i	−0.893542	+	0.448979i	$0.851788\pi$
$458$			24.3923i			1.13978i
$459$		0			0
$460$	10.9282	−	5.46410i	0.509530	−	0.254765i
$461$	15.9282			0.741850			0.370925	−	0.928663i	$-0.379041\pi$
$461$	15.9282			0.741850			0.370925	+	0.928663i	$0.379041\pi$
$462$		0			0
$463$			27.3205i			1.26969i	0.772639	+	0.634846i	$0.218936\pi$
$463$			27.3205i			1.26969i	−0.772639	+	0.634846i	$0.781064\pi$
$464$	−3.00000			−0.139272
$465$		0			0
$466$	−17.3205			−0.802357
$467$			1.39230i			0.0644282i	0.999481	+	0.0322141i	$0.0102558\pi$
$467$			1.39230i			0.0644282i	−0.999481	+	0.0322141i	$0.989744\pi$
$468$		0			0
$469$	−3.60770			−0.166588
$470$	−11.4641	−	22.9282i	−0.528800	−	1.05760i
$471$		0			0
$472$		−	9.46410i		−	0.435621i
$473$			5.53590i			0.254541i
$474$		0			0
$475$	20.7846	−	27.7128i	0.953663	−	1.27155i
$476$	1.14359			0.0524165
$477$		0			0
$478$		−	5.00000i		−	0.228695i
$479$	−25.8564			−1.18141			−0.590705	−	0.806888i	$-0.701150\pi$
$479$	−25.8564			−1.18141			−0.590705	+	0.806888i	$0.701150\pi$
$480$		0			0
$481$	4.00000			0.182384
$482$			20.9282i			0.953254i
$483$		0			0
$484$	8.00000			0.363636
$485$	−35.1769	+	17.5885i	−1.59730	+	0.798651i
$486$		0			0
$487$		−	40.3923i		−	1.83035i	−0.403057	−	0.915175i	$-0.632052\pi$
$487$		−	40.3923i		−	1.83035i	0.403057	−	0.915175i	$-0.367948\pi$
$488$		−	5.19615i		−	0.235219i
$489$		0			0
$490$	1.85641	−	0.928203i	0.0838639	−	0.0419319i
$491$	13.6077			0.614107			0.307053	−	0.951692i	$-0.400657\pi$
$491$	13.6077			0.614107			0.307053	+	0.951692i	$0.400657\pi$
$492$		0			0
$493$			1.39230i			0.0627063i
$494$	−27.7128			−1.24686
$495$		0			0
$496$	−5.73205			−0.257377
$497$		−	31.8564i		−	1.42896i
$498$		0			0
$499$	−6.00000			−0.268597			−0.134298	−	0.990941i	$-0.542878\pi$
$499$	−6.00000			−0.268597			−0.134298	+	0.990941i	$0.542878\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$		0			0
$502$		−	20.0000i		−	0.892644i
$503$		−	27.0718i		−	1.20707i	−0.797336	−	0.603536i	$-0.793758\pi$
$503$		−	27.0718i		−	1.20707i	0.797336	−	0.603536i	$-0.206242\pi$
$504$		0			0
$505$	−14.3923	−	28.7846i	−0.640449	−	1.28090i
$506$	9.46410			0.420731
$507$		0			0
$508$		−	16.0000i		−	0.709885i
$509$	−34.3923			−1.52441			−0.762206	−	0.647334i	$-0.775884\pi$
$509$	−34.3923			−1.52441			−0.762206	+	0.647334i	$0.775884\pi$
$510$		0			0
$511$	−15.7513			−0.696796
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−7.85641			−0.346531
$515$	−18.9282	+	9.46410i	−0.834076	+	0.417038i
$516$		0			0
$517$		−	19.8564i		−	0.873284i
$518$			2.46410i			0.108266i
$519$		0			0
$520$	−4.00000	−	8.00000i	−0.175412	−	0.350823i
$521$	25.4449			1.11476			0.557380	−	0.830258i	$-0.311807\pi$
$521$	25.4449			1.11476			0.557380	+	0.830258i	$0.311807\pi$
$522$		0			0
$523$			20.2487i			0.885414i	0.896666	+	0.442707i	$0.145982\pi$
$523$			20.2487i			0.885414i	−0.896666	+	0.442707i	$0.854018\pi$
$524$	−11.4641			−0.500812
$525$		0			0
$526$	−10.1244			−0.441443
$527$			2.66025i			0.115882i
$528$		0			0
$529$	−6.85641			−0.298105
$530$	−0.267949	−	0.535898i	−0.0116390	−	0.0232779i
$531$		0			0
$532$		−	17.0718i		−	0.740156i
$533$		−	36.7846i		−	1.59332i
$534$		0			0
$535$	14.9282	−	7.46410i	0.645403	−	0.322701i
$536$	1.46410			0.0632396
$537$		0			0
$538$		−	16.0000i		−	0.689809i
$539$	1.60770			0.0692483
$540$		0			0
$541$	−2.14359			−0.0921603			−0.0460801	−	0.998938i	$-0.514673\pi$
$541$	−2.14359			−0.0921603			−0.0460801	+	0.998938i	$0.514673\pi$
$542$			3.85641i			0.165647i
$543$		0			0
$544$	−0.464102			−0.0198982
$545$	4.66025	+	9.32051i	0.199623	+	0.399247i
$546$		0			0
$547$			29.5885i			1.26511i	0.774515	+	0.632556i	$0.217994\pi$
$547$			29.5885i			1.26511i	−0.774515	+	0.632556i	$0.782006\pi$
$548$		−	7.85641i		−	0.335609i
$549$		0			0
$550$	6.92820	+	5.19615i	0.295420	+	0.221565i
$551$	20.7846			0.885454
$552$		0			0
$553$		−	11.1769i		−	0.475291i
$554$	−27.7128			−1.17740
$555$		0			0
$556$	7.92820			0.336231
$557$			22.3923i			0.948792i	0.880311	+	0.474396i	$0.157334\pi$
$557$			22.3923i			0.948792i	−0.880311	+	0.474396i	$0.842666\pi$
$558$		0			0
$559$	−12.7846			−0.540731
$560$	4.92820	−	2.46410i	0.208255	−	0.104127i
$561$		0			0
$562$			0.928203i			0.0391539i
$563$		−	18.1769i		−	0.766066i	−0.923735	−	0.383033i	$-0.874880\pi$
$563$		−	18.1769i		−	0.766066i	0.923735	−	0.383033i	$-0.125120\pi$
$564$		0			0
$565$	28.9282	−	14.4641i	1.21702	−	0.608509i
$566$	4.53590			0.190658
$567$		0			0
$568$			12.9282i			0.542455i
$569$	−4.53590			−0.190155			−0.0950774	−	0.995470i	$-0.530310\pi$
$569$	−4.53590			−0.190155			−0.0950774	+	0.995470i	$0.530310\pi$
$570$		0			0
$571$	3.78461			0.158381			0.0791905	−	0.996860i	$-0.474766\pi$
$571$	3.78461			0.158381			0.0791905	+	0.996860i	$0.474766\pi$
$572$		−	6.92820i		−	0.289683i
$573$		0			0
$574$	22.6603			0.945821
$575$	−21.8564	−	16.3923i	−0.911475	−	0.683606i
$576$		0			0
$577$		−	4.78461i		−	0.199186i	−0.995028	−	0.0995930i	$-0.968246\pi$
$577$		−	4.78461i		−	0.199186i	0.995028	−	0.0995930i	$-0.0317541\pi$
$578$		−	16.7846i		−	0.698148i
$579$		0			0
$580$	3.00000	+	6.00000i	0.124568	+	0.249136i
$581$	−6.24871			−0.259240
$582$		0			0
$583$		−	0.464102i		−	0.0192211i
$584$	6.39230			0.264515
$585$		0			0
$586$	−5.87564			−0.242721
$587$		−	43.3923i		−	1.79099i	−0.445069	−	0.895496i	$-0.646821\pi$
$587$		−	43.3923i		−	1.79099i	0.445069	−	0.895496i	$-0.353179\pi$
$588$		0			0
$589$	39.7128			1.63634
$590$	−18.9282	+	9.46410i	−0.779262	+	0.389631i
$591$		0			0
$592$		−	1.00000i		−	0.0410997i
$593$		−	37.1769i		−	1.52667i	−0.646001	−	0.763336i	$-0.723560\pi$
$593$		−	37.1769i		−	1.52667i	0.646001	−	0.763336i	$-0.276440\pi$
$594$		0			0
$595$	−1.14359	−	2.28719i	−0.0468828	−	0.0937655i
$596$	8.00000			0.327693
$597$		0			0
$598$			21.8564i			0.893775i
$599$	26.2487			1.07249			0.536247	−	0.844061i	$-0.319842\pi$
$599$	26.2487			1.07249			0.536247	+	0.844061i	$0.319842\pi$
$600$		0			0
$601$	25.0000			1.01977			0.509886	−	0.860242i	$-0.329688\pi$
$601$	25.0000			1.01977			0.509886	+	0.860242i	$0.329688\pi$
$602$		−	7.87564i		−	0.320987i
$603$		0			0
$604$	2.00000			0.0813788
$605$	−8.00000	−	16.0000i	−0.325246	−	0.650493i
$606$		0			0
$607$		−	6.00000i		−	0.243532i	−0.992559	−	0.121766i	$-0.961144\pi$
$607$		−	6.00000i		−	0.243532i	0.992559	−	0.121766i	$-0.0388558\pi$
$608$			6.92820i			0.280976i
$609$		0			0
$610$	−10.3923	+	5.19615i	−0.420772	+	0.210386i
$611$	45.8564			1.85515
$612$		0			0
$613$		−	26.3205i		−	1.06308i	−0.847035	−	0.531538i	$-0.821614\pi$
$613$		−	26.3205i		−	1.06308i	0.847035	−	0.531538i	$-0.178386\pi$
$614$	6.53590			0.263767
$615$		0			0
$616$	4.26795			0.171961
$617$		−	33.7128i		−	1.35723i	−0.734496	−	0.678613i	$-0.762581\pi$
$617$		−	33.7128i		−	1.35723i	0.734496	−	0.678613i	$-0.237419\pi$
$618$		0			0
$619$	−47.6410			−1.91485			−0.957427	−	0.288675i	$-0.906785\pi$
$619$	−47.6410			−1.91485			−0.957427	+	0.288675i	$0.906785\pi$
$620$	5.73205	+	11.4641i	0.230205	+	0.460409i
$621$		0			0
$622$		−	23.7846i		−	0.953676i
$623$			23.3205i			0.934316i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	9.85641			0.393941
$627$		0			0
$628$		−	16.4641i		−	0.656989i
$629$	−0.464102			−0.0185049
$630$		0			0
$631$	−18.5167			−0.737137			−0.368568	−	0.929601i	$-0.620152\pi$
$631$	−18.5167			−0.737137			−0.368568	+	0.929601i	$0.620152\pi$
$632$			4.53590i			0.180428i
$633$		0			0
$634$	11.1962			0.444656
$635$	−32.0000	+	16.0000i	−1.26988	+	0.634941i
$636$		0			0
$637$			3.71281i			0.147107i
$638$			5.19615i			0.205718i
$639$		0			0
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$	−5.73205			−0.226402			−0.113201	−	0.993572i	$-0.536110\pi$
$641$	−5.73205			−0.226402			−0.113201	+	0.993572i	$0.536110\pi$
$642$		0			0
$643$			3.73205i			0.147178i	0.997289	+	0.0735889i	$0.0234453\pi$
$643$			3.73205i			0.147178i	−0.997289	+	0.0735889i	$0.976555\pi$
$644$	−13.4641			−0.530560
$645$		0			0
$646$	3.21539			0.126508
$647$			39.1769i			1.54020i	0.637921	+	0.770102i	$0.279795\pi$
$647$			39.1769i			1.54020i	−0.637921	+	0.770102i	$0.720205\pi$
$648$		0			0
$649$	−16.3923			−0.643454
$650$	−12.0000	+	16.0000i	−0.470679	+	0.627572i
$651$		0			0
$652$		−	7.73205i		−	0.302810i
$653$		−	15.1769i		−	0.593919i	−0.954890	−	0.296959i	$-0.904027\pi$
$653$		−	15.1769i		−	0.593919i	0.954890	−	0.296959i	$-0.0959726\pi$
$654$		0			0
$655$	11.4641	+	22.9282i	0.447940	+	0.895879i
$656$	−9.19615			−0.359049
$657$		0			0
$658$			28.2487i			1.10125i
$659$	27.4641			1.06985			0.534925	−	0.844900i	$-0.320340\pi$
$659$	27.4641			1.06985			0.534925	+	0.844900i	$0.320340\pi$
$660$		0			0
$661$	−43.8372			−1.70507			−0.852534	−	0.522672i	$-0.824935\pi$
$661$	−43.8372			−1.70507			−0.852534	+	0.522672i	$0.824935\pi$
$662$		−	20.9282i		−	0.813398i
$663$		0			0
$664$	2.53590			0.0984119
$665$	−34.1436	+	17.0718i	−1.32403	+	0.662016i
$666$		0			0
$667$		−	16.3923i		−	0.634713i
$668$			6.39230i			0.247326i
$669$		0			0
$670$	−1.46410	−	2.92820i	−0.0565632	−	0.113126i
$671$	−9.00000			−0.347441
$672$		0			0
$673$		−	49.1769i		−	1.89563i	−0.318820	−	0.947815i	$-0.603286\pi$
$673$		−	49.1769i		−	1.89563i	0.318820	−	0.947815i	$-0.396714\pi$
$674$	31.3205			1.20642
$675$		0			0
$676$	3.00000			0.115385
$677$			8.78461i			0.337620i	0.985649	+	0.168810i	$0.0539924\pi$
$677$			8.78461i			0.337620i	−0.985649	+	0.168810i	$0.946008\pi$
$678$		0			0
$679$	43.3397			1.66323
$680$	0.464102	+	0.928203i	0.0177975	+	0.0355950i
$681$		0			0
$682$			9.92820i			0.380171i
$683$			43.1051i			1.64937i	0.565591	+	0.824686i	$0.308648\pi$
$683$			43.1051i			1.64937i	−0.565591	+	0.824686i	$0.691352\pi$
$684$		0			0
$685$	−15.7128	+	7.85641i	−0.600356	+	0.300178i
$686$	−19.5359			−0.745884
$687$		0			0
$688$			3.19615i			0.121852i
$689$	1.07180			0.0408322
$690$		0			0
$691$	26.8564			1.02167			0.510833	−	0.859680i	$-0.329337\pi$
$691$	26.8564			1.02167			0.510833	+	0.859680i	$0.329337\pi$
$692$		−	17.0526i		−	0.648241i
$693$		0			0
$694$	17.0718			0.648037
$695$	−7.92820	−	15.8564i	−0.300734	−	0.601468i
$696$		0			0
$697$			4.26795i			0.161660i
$698$		−	8.53590i		−	0.323089i
$699$		0			0
$700$	−9.85641	−	7.39230i	−0.372537	−	0.279403i
$701$	−15.0718			−0.569254			−0.284627	−	0.958638i	$-0.591870\pi$
$701$	−15.0718			−0.569254			−0.284627	+	0.958638i	$0.591870\pi$
$702$		0			0
$703$			6.92820i			0.261302i
$704$	−1.73205			−0.0652791
$705$		0			0
$706$	4.60770			0.173413
$707$			35.4641i			1.33376i
$708$		0			0
$709$	−37.4449			−1.40627			−0.703136	−	0.711056i	$-0.748217\pi$
$709$	−37.4449			−1.40627			−0.703136	+	0.711056i	$0.748217\pi$
$710$	25.8564	−	12.9282i	0.970374	−	0.485187i
$711$		0			0
$712$		−	9.46410i		−	0.354682i
$713$		−	31.3205i		−	1.17296i
$714$		0			0
$715$	−13.8564	+	6.92820i	−0.518200	+	0.259100i
$716$	5.60770			0.209569
$717$		0			0
$718$		−	0.143594i		−	0.00535886i
$719$	−22.5359			−0.840447			−0.420224	−	0.907421i	$-0.638048\pi$
$719$	−22.5359			−0.840447			−0.420224	+	0.907421i	$0.638048\pi$
$720$		0			0
$721$	23.3205			0.868501
$722$		−	29.0000i		−	1.07927i
$723$		0			0
$724$	8.39230			0.311898
$725$	9.00000	−	12.0000i	0.334252	−	0.445669i
$726$		0			0
$727$			19.4641i			0.721884i	0.932588	+	0.360942i	$0.117545\pi$
$727$			19.4641i			0.721884i	−0.932588	+	0.360942i	$0.882455\pi$
$728$			9.85641i			0.365303i
$729$		0			0
$730$	−6.39230	−	12.7846i	−0.236590	−	0.473180i
$731$	1.48334			0.0548633
$732$		0			0
$733$		−	12.3205i		−	0.455068i	−0.973770	−	0.227534i	$-0.926934\pi$
$733$		−	12.3205i		−	0.455068i	0.973770	−	0.227534i	$-0.0730663\pi$
$734$	−6.60770			−0.243894
$735$		0			0
$736$	5.46410			0.201409
$737$		−	2.53590i		−	0.0934110i
$738$		0			0
$739$	−15.9282			−0.585928			−0.292964	−	0.956123i	$-0.594642\pi$
$739$	−15.9282			−0.585928			−0.292964	+	0.956123i	$0.594642\pi$
$740$	−2.00000	+	1.00000i	−0.0735215	+	0.0367607i
$741$		0			0
$742$			0.660254i			0.0242387i
$743$		−	0.267949i		−	0.00983010i	−0.999988	−	0.00491505i	$-0.998435\pi$
$743$		−	0.267949i		−	0.00983010i	0.999988	−	0.00491505i	$-0.00156452\pi$
$744$		0			0
$745$	−8.00000	−	16.0000i	−0.293097	−	0.586195i
$746$	25.7128			0.941413
$747$		0			0
$748$			0.803848i			0.0293916i
$749$	−18.3923			−0.672040
$750$		0			0
$751$	53.1769			1.94045			0.970227	−	0.242199i	$-0.0778687\pi$
$751$	53.1769			1.94045			0.970227	+	0.242199i	$0.0778687\pi$
$752$		−	11.4641i		−	0.418053i
$753$		0			0
$754$	−12.0000			−0.437014
$755$	−2.00000	−	4.00000i	−0.0727875	−	0.145575i
$756$		0			0
$757$			34.5359i			1.25523i	0.778524	+	0.627614i	$0.215968\pi$
$757$			34.5359i			1.25523i	−0.778524	+	0.627614i	$0.784032\pi$
$758$		−	6.92820i		−	0.251644i
$759$		0			0
$760$	13.8564	−	6.92820i	0.502625	−	0.251312i
$761$	−21.7321			−0.787786			−0.393893	−	0.919156i	$-0.628872\pi$
$761$	−21.7321			−0.787786			−0.393893	+	0.919156i	$0.628872\pi$
$762$		0			0
$763$		−	11.4833i		−	0.415725i
$764$	19.7846			0.715782
$765$		0			0
$766$	−24.3923			−0.881330
$767$		−	37.8564i		−	1.36692i
$768$		0			0
$769$	−6.53590			−0.235691			−0.117845	−	0.993032i	$-0.537599\pi$
$769$	−6.53590			−0.235691			−0.117845	+	0.993032i	$0.537599\pi$
$770$	−4.26795	−	8.53590i	−0.153806	−	0.307612i
$771$		0			0
$772$		−	20.0000i		−	0.719816i
$773$		−	19.9808i		−	0.718658i	−0.933211	−	0.359329i	$-0.883006\pi$
$773$		−	19.9808i		−	0.718658i	0.933211	−	0.359329i	$-0.116994\pi$
$774$		0			0
$775$	17.1962	−	22.9282i	0.617704	−	0.823605i
$776$	−17.5885			−0.631389
$777$		0			0
$778$		−	14.8564i		−	0.532628i
$779$	63.7128			2.28275
$780$		0			0
$781$	22.3923			0.801260
$782$		−	2.53590i		−	0.0906835i
$783$		0			0
$784$	0.928203			0.0331501
$785$	−32.9282	+	16.4641i	−1.17526	+	0.587629i
$786$		0			0
$787$			5.60770i			0.199893i	0.994993	+	0.0999464i	$0.0318671\pi$
$787$			5.60770i			0.199893i	−0.994993	+	0.0999464i	$0.968133\pi$
$788$		−	16.7846i		−	0.597927i
$789$		0			0
$790$	9.07180	−	4.53590i	0.322760	−	0.161380i
$791$	−35.6410			−1.26725
$792$		0			0
$793$		−	20.7846i		−	0.738083i
$794$	−15.0718			−0.534878
$795$		0			0
$796$	−25.3205			−0.897462
$797$			18.9282i			0.670471i	0.942134	+	0.335236i	$0.108816\pi$
$797$			18.9282i			0.670471i	−0.942134	+	0.335236i	$0.891184\pi$
$798$		0			0
$799$	−5.32051			−0.188226
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$		0			0
$802$		−	16.9282i		−	0.597756i
$803$		−	11.0718i		−	0.390715i
$804$		0			0
$805$	13.4641	+	26.9282i	0.474547	+	0.949094i
$806$	−22.9282			−0.807612
$807$		0			0
$808$		−	14.3923i		−	0.506320i
$809$	−26.5359			−0.932953			−0.466476	−	0.884534i	$-0.654477\pi$
$809$	−26.5359			−0.932953			−0.466476	+	0.884534i	$0.654477\pi$
$810$		0			0
$811$	10.1436			0.356190			0.178095	−	0.984013i	$-0.443007\pi$
$811$	10.1436			0.356190			0.178095	+	0.984013i	$0.443007\pi$
$812$		−	7.39230i		−	0.259419i
$813$		0			0
$814$	−1.73205			−0.0607083
$815$	−15.4641	+	7.73205i	−0.541684	+	0.270842i
$816$		0			0
$817$		−	22.1436i		−	0.774706i
$818$			3.60770i			0.126140i
$819$		0			0
$820$	9.19615	+	18.3923i	0.321144	+	0.642287i
$821$	−3.85641			−0.134590			−0.0672948	−	0.997733i	$-0.521437\pi$
$821$	−3.85641			−0.134590			−0.0672948	+	0.997733i	$0.521437\pi$
$822$		0			0
$823$		−	33.5692i		−	1.17015i	−0.810979	−	0.585075i	$-0.801065\pi$
$823$		−	33.5692i		−	1.17015i	0.810979	−	0.585075i	$-0.198935\pi$
$824$	−9.46410			−0.329698
$825$		0			0
$826$	23.3205			0.811424
$827$		−	2.75129i		−	0.0956717i	−0.998855	−	0.0478358i	$-0.984768\pi$
$827$		−	2.75129i		−	0.0956717i	0.998855	−	0.0478358i	$-0.0152324\pi$
$828$		0			0
$829$	23.3397			0.810623			0.405311	−	0.914179i	$-0.367163\pi$
$829$	23.3397			0.810623			0.405311	+	0.914179i	$0.367163\pi$
$830$	−2.53590	−	5.07180i	−0.0880223	−	0.176045i
$831$		0			0
$832$		−	4.00000i		−	0.138675i
$833$		−	0.430781i		−	0.0149257i
$834$		0			0
$835$	12.7846	−	6.39230i	0.442430	−	0.221215i
$836$	12.0000			0.415029
$837$		0			0
$838$		−	9.32051i		−	0.321972i
$839$	−10.1436			−0.350196			−0.175098	−	0.984551i	$-0.556024\pi$
$839$	−10.1436			−0.350196			−0.175098	+	0.984551i	$0.556024\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		−	13.8564i		−	0.477523i
$843$		0			0
$844$	27.7846			0.956386
$845$	−3.00000	−	6.00000i	−0.103203	−	0.206406i
$846$		0			0
$847$			19.7128i			0.677340i
$848$		−	0.267949i		−	0.00920141i
$849$		0			0
$850$	1.39230	−	1.85641i	0.0477557	−	0.0636742i
$851$	5.46410			0.187307
$852$		0			0
$853$			33.0333i			1.13104i	0.824735	+	0.565520i	$0.191324\pi$
$853$			33.0333i			1.13104i	−0.824735	+	0.565520i	$0.808676\pi$
$854$	12.8038			0.438139
$855$		0			0
$856$	7.46410			0.255118
$857$		−	10.3205i		−	0.352542i	−0.984342	−	0.176271i	$-0.943597\pi$
$857$		−	10.3205i		−	0.352542i	0.984342	−	0.176271i	$-0.0564035\pi$
$858$		0			0
$859$	−55.7128			−1.90090			−0.950448	−	0.310883i	$-0.899375\pi$
$859$	−55.7128			−1.90090			−0.950448	+	0.310883i	$0.899375\pi$
$860$	6.39230	−	3.19615i	0.217976	−	0.108988i
$861$		0			0
$862$		−	29.9282i		−	1.01936i
$863$		−	7.98076i		−	0.271668i	−0.990732	−	0.135834i	$-0.956629\pi$
$863$		−	7.98076i		−	0.271668i	0.990732	−	0.135834i	$-0.0433714\pi$
$864$		0			0
$865$	−34.1051	+	17.0526i	−1.15961	+	0.579804i
$866$	−3.60770			−0.122594
$867$		0			0
$868$		−	14.1244i		−	0.479412i
$869$	7.85641			0.266510
$870$		0			0
$871$	5.85641			0.198437
$872$			4.66025i			0.157816i
$873$		0			0
$874$	−37.8564			−1.28051
$875$	−4.92820	+	27.1051i	−0.166604	+	0.916320i
$876$		0			0
$877$		−	32.1769i		−	1.08654i	−0.839559	−	0.543269i	$-0.817187\pi$
$877$		−	32.1769i		−	1.08654i	0.839559	−	0.543269i	$-0.182813\pi$
$878$		−	13.1962i		−	0.445349i
$879$		0			0
$880$	1.73205	+	3.46410i	0.0583874	+	0.116775i
$881$	42.8038			1.44210			0.721049	−	0.692884i	$-0.243660\pi$
$881$	42.8038			1.44210			0.721049	+	0.692884i	$0.243660\pi$
$882$		0			0
$883$		−	19.1962i		−	0.646002i	−0.946399	−	0.323001i	$-0.895308\pi$
$883$		−	19.1962i		−	0.646002i	0.946399	−	0.323001i	$-0.104692\pi$
$884$	−1.85641			−0.0624377
$885$		0			0
$886$	26.0000			0.873487
$887$			15.1962i			0.510237i	0.966910	+	0.255118i	$0.0821145\pi$
$887$			15.1962i			0.510237i	−0.966910	+	0.255118i	$0.917886\pi$
$888$		0			0
$889$	39.4256			1.32229
$890$	−18.9282	+	9.46410i	−0.634475	+	0.317237i
$891$		0			0
$892$			10.3205i			0.345556i
$893$			79.4256i			2.65788i
$894$		0			0
$895$	−5.60770	−	11.2154i	−0.187445	−	0.374889i
$896$	2.46410			0.0823199
$897$		0			0
$898$			26.5359i			0.885514i
$899$	17.1962			0.573524
$900$		0			0
$901$	−0.124356			−0.00414289
$902$			15.9282i			0.530351i
$903$		0			0
$904$	14.4641			0.481069
$905$	−8.39230	−	16.7846i	−0.278970	−	0.557939i
$906$		0			0
$907$			16.2487i			0.539530i	0.962926	+	0.269765i	$0.0869460\pi$
$907$			16.2487i			0.539530i	−0.962926	+	0.269765i	$0.913054\pi$
$908$		−	7.53590i		−	0.250088i
$909$		0			0
$910$	19.7128	−	9.85641i	0.653473	−	0.326737i
$911$	15.7128			0.520589			0.260294	−	0.965529i	$-0.416180\pi$
$911$	15.7128			0.520589			0.260294	+	0.965529i	$0.416180\pi$
$912$		0			0
$913$		−	4.39230i		−	0.145364i
$914$	19.1962			0.634952
$915$		0			0
$916$	24.3923			0.805944
$917$		−	28.2487i		−	0.932855i
$918$		0			0
$919$	−11.4641			−0.378166			−0.189083	−	0.981961i	$-0.560551\pi$
$919$	−11.4641			−0.378166			−0.189083	+	0.981961i	$0.560551\pi$
$920$	−5.46410	−	10.9282i	−0.180146	−	0.360292i
$921$		0			0
$922$		−	15.9282i		−	0.524567i
$923$			51.7128i			1.70215i
$924$		0			0
$925$	4.00000	+	3.00000i	0.131519	+	0.0986394i
$926$	27.3205			0.897808
$927$		0			0
$928$			3.00000i			0.0984798i
$929$	−23.8756			−0.783334			−0.391667	−	0.920107i	$-0.628102\pi$
$929$	−23.8756			−0.783334			−0.391667	+	0.920107i	$0.628102\pi$
$930$		0			0
$931$	−6.43078			−0.210760
$932$			17.3205i			0.567352i
$933$		0			0
$934$	1.39230			0.0455576
$935$	1.60770	−	0.803848i	0.0525773	−	0.0262886i
$936$		0			0
$937$		−	28.7846i		−	0.940352i	−0.882573	−	0.470176i	$-0.844190\pi$
$937$		−	28.7846i		−	0.940352i	0.882573	−	0.470176i	$-0.155810\pi$
$938$			3.60770i			0.117795i
$939$		0			0
$940$	−22.9282	+	11.4641i	−0.747836	+	0.373918i
$941$	−58.4974			−1.90696			−0.953481	−	0.301454i	$-0.902528\pi$
$941$	−58.4974			−1.90696			−0.953481	+	0.301454i	$0.902528\pi$
$942$		0			0
$943$		−	50.2487i		−	1.63632i
$944$	−9.46410			−0.308030
$945$		0			0
$946$	5.53590			0.179988
$947$			8.60770i			0.279713i	0.990172	+	0.139856i	$0.0446640\pi$
$947$			8.60770i			0.279713i	−0.990172	+	0.139856i	$0.955336\pi$
$948$		0			0
$949$	25.5692			0.830012
$950$	−27.7128	−	20.7846i	−0.899122	−	0.674342i
$951$		0			0
$952$		−	1.14359i		−	0.0370641i
$953$			4.14359i			0.134224i	0.997745	+	0.0671121i	$0.0213785\pi$
$953$			4.14359i			0.134224i	−0.997745	+	0.0671121i	$0.978621\pi$
$954$		0			0
$955$	−19.7846	−	39.5692i	−0.640215	−	1.28043i
$956$	−5.00000			−0.161712
$957$		0			0
$958$			25.8564i			0.835383i
$959$	19.3590			0.625134
$960$		0			0
$961$	1.85641			0.0598841
$962$		−	4.00000i		−	0.128965i
$963$		0			0
$964$	20.9282			0.674052
$965$	−40.0000	+	20.0000i	−1.28765	+	0.643823i
$966$		0			0
$967$			60.6410i			1.95008i	0.222021	+	0.975042i	$0.428735\pi$
$967$			60.6410i			1.95008i	−0.222021	+	0.975042i	$0.571265\pi$
$968$		−	8.00000i		−	0.257130i
$969$		0			0
$970$	17.5885	+	35.1769i	0.564731	+	1.12946i
$971$	−19.8372			−0.636605			−0.318303	−	0.947989i	$-0.603113\pi$
$971$	−19.8372			−0.636605			−0.318303	+	0.947989i	$0.603113\pi$
$972$		0			0
$973$			19.5359i			0.626292i
$974$	−40.3923			−1.29425
$975$		0			0
$976$	−5.19615			−0.166325
$977$			12.4641i			0.398762i	0.979922	+	0.199381i	$0.0638931\pi$
$977$			12.4641i			0.398762i	−0.979922	+	0.199381i	$0.936107\pi$
$978$		0			0
$979$	−16.3923			−0.523900
$980$	−0.928203	−	1.85641i	−0.0296504	−	0.0593007i
$981$		0			0
$982$		−	13.6077i		−	0.434239i
$983$			33.3013i			1.06215i	0.847326	+	0.531073i	$0.178211\pi$
$983$			33.3013i			1.06215i	−0.847326	+	0.531073i	$0.821789\pi$
$984$		0			0
$985$	−33.5692	+	16.7846i	−1.06960	+	0.534802i
$986$	1.39230			0.0443400
$987$		0			0
$988$			27.7128i			0.881662i
$989$	−17.4641			−0.555326
$990$		0			0
$991$	27.3397			0.868476			0.434238	−	0.900798i	$-0.357018\pi$
$991$	27.3397			0.868476			0.434238	+	0.900798i	$0.357018\pi$
$992$			5.73205i			0.181993i
$993$		0			0
$994$	−31.8564			−1.01042
$995$	25.3205	+	50.6410i	0.802714	+	1.60543i
$996$		0			0
$997$			8.39230i			0.265787i	0.991130	+	0.132893i	$0.0424268\pi$
$997$			8.39230i			0.265787i	−0.991130	+	0.132893i	$0.957573\pi$
$998$			6.00000i			0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.l.1999.1	yes	4
3.2	odd	2		3330.2.d.i.1999.3	yes	4
5.4	even	2	inner	3330.2.d.l.1999.4	yes	4
15.14	odd	2		3330.2.d.i.1999.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3330.2.d.i.1999.2	✓	4	15.14	odd	2
3330.2.d.i.1999.3	yes	4	3.2	odd	2
3330.2.d.l.1999.1	yes	4	1.1	even	1	trivial
3330.2.d.l.1999.4	yes	4	5.4	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -2.46410i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -2.46410i q^{7} +1.00000i q^{8} +(2.00000 - 1.00000i) q^{10} +1.73205 q^{11} +4.00000i q^{13} -2.46410 q^{14} +1.00000 q^{16} -0.464102i q^{17} -6.92820 q^{19} +(-1.00000 - 2.00000i) q^{20} -1.73205i q^{22} +5.46410i q^{23} +(-3.00000 + 4.00000i) q^{25} +4.00000 q^{26} +2.46410i q^{28} -3.00000 q^{29} -5.73205 q^{31} -1.00000i q^{32} -0.464102 q^{34} +(4.92820 - 2.46410i) q^{35} -1.00000i q^{37} +6.92820i q^{38} +(-2.00000 + 1.00000i) q^{40} -9.19615 q^{41} +3.19615i q^{43} -1.73205 q^{44} +5.46410 q^{46} -11.4641i q^{47} +0.928203 q^{49} +(4.00000 + 3.00000i) q^{50} -4.00000i q^{52} -0.267949i q^{53} +(1.73205 + 3.46410i) q^{55} +2.46410 q^{56} +3.00000i q^{58} -9.46410 q^{59} -5.19615 q^{61} +5.73205i q^{62} -1.00000 q^{64} +(-8.00000 + 4.00000i) q^{65} -1.46410i q^{67} +0.464102i q^{68} +(-2.46410 - 4.92820i) q^{70} +12.9282 q^{71} -6.39230i q^{73} -1.00000 q^{74} +6.92820 q^{76} -4.26795i q^{77} +4.53590 q^{79} +(1.00000 + 2.00000i) q^{80} +9.19615i q^{82} -2.53590i q^{83} +(0.928203 - 0.464102i) q^{85} +3.19615 q^{86} +1.73205i q^{88} -9.46410 q^{89} +9.85641 q^{91} -5.46410i q^{92} -11.4641 q^{94} +(-6.92820 - 13.8564i) q^{95} +17.5885i q^{97} -0.928203i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^5	\( 4 q - 4 q^{4} + 4 q^{5} + 8 q^{10} + 4 q^{14} + 4 q^{16} - 4 q^{20} - 12 q^{25} + 16 q^{26} - 12 q^{29} - 16 q^{31} + 12 q^{34} - 8 q^{35} - 8 q^{40} - 16 q^{41} + 8 q^{46} - 24 q^{49} + 16 q^{50} - 4 q^{56} - 24 q^{59} - 4 q^{64} - 32 q^{65} + 4 q^{70} + 24 q^{71} - 4 q^{74} + 32 q^{79} + 4 q^{80} - 24 q^{85} - 8 q^{86} - 24 q^{89} - 16 q^{91} - 32 q^{94}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^5 + 8 * q^10 + 4 * q^14 + 4 * q^16 - 4 * q^20 - 12 * q^25 + 16 * q^26 - 12 * q^29 - 16 * q^31 + 12 * q^34 - 8 * q^35 - 8 * q^40 - 16 * q^41 + 8 * q^46 - 24 * q^49 + 16 * q^50 - 4 * q^56 - 24 * q^59 - 4 * q^64 - 32 * q^65 + 4 * q^70 + 24 * q^71 - 4 * q^74 + 32 * q^79 + 4 * q^80 - 24 * q^85 - 8 * q^86 - 24 * q^89 - 16 * q^91 - 32 * q^94

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