LMFDB - Embedded newform 2520.2.bi.q.1801.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2520,2,Mod(361,2520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))

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

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

chi := DirichletCharacter("2520.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2520.bi (of order $3$, degree $2$, 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:	$20.1223013094$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11337408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 12 $ x^6 + 18x^4 + 81x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1801.1
Root			$-0.391571i$ of defining polynomial
Character	$\chi$	$=$	2520.1801
Dual form			2520.2.bi.q.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(-0.292113 - 2.62958i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(-0.292113 - 2.62958i) q^{7} +(0.839111 + 1.45338i) q^{11} -4.84667 q^{13} +(1.00000 + 1.73205i) q^{17} +(-3.42334 + 5.92939i) q^{19} +(-1.13122 + 1.95934i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.32178 q^{29} +(-4.58423 - 7.94011i) q^{31} +(-2.42334 - 1.06181i) q^{35} +(1.42334 - 2.46529i) q^{37} -9.52489 q^{41} +6.58423 q^{43} +(-6.10156 + 10.5682i) q^{47} +(-6.82934 + 1.53627i) q^{49} +(3.74511 + 6.48673i) q^{53} +1.67822 q^{55} +(4.00000 + 6.92820i) q^{59} +(3.24511 - 5.62070i) q^{61} +(-2.42334 + 4.19734i) q^{65} +(2.87634 + 4.98196i) q^{67} +(5.84667 + 10.1267i) q^{73} +(3.57666 - 2.63106i) q^{77} +(-2.84667 + 4.93058i) q^{79} +12.5842 q^{83} +2.00000 q^{85} +(-2.92334 + 5.06337i) q^{89} +(1.41577 + 12.7447i) q^{91} +(3.42334 + 5.92939i) q^{95} -2.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 6 q^{7}+O(q^{10}) $ 6 * q + 3 * q^5 + 6 * q^7	$ 6 q + 3 q^{5} + 6 q^{7} + 3 q^{11} + 6 q^{13} + 6 q^{17} - 3 q^{19} + 3 q^{23} - 3 q^{25} - 24 q^{29} - 12 q^{31} + 3 q^{35} - 9 q^{37} - 18 q^{41} + 24 q^{43} - 15 q^{47} - 12 q^{49} + 9 q^{53} + 6 q^{55} + 24 q^{59} + 6 q^{61} + 3 q^{65} - 6 q^{67} + 39 q^{77} + 18 q^{79} + 60 q^{83} + 12 q^{85} + 24 q^{91} + 3 q^{95} - 12 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 + 6 * q^7 + 3 * q^11 + 6 * q^13 + 6 * q^17 - 3 * q^19 + 3 * q^23 - 3 * q^25 - 24 * q^29 - 12 * q^31 + 3 * q^35 - 9 * q^37 - 18 * q^41 + 24 * q^43 - 15 * q^47 - 12 * q^49 + 9 * q^53 + 6 * q^55 + 24 * q^59 + 6 * q^61 + 3 * q^65 - 6 * q^67 + 39 * q^77 + 18 * q^79 + 60 * q^83 + 12 * q^85 + 24 * q^91 + 3 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−0.292113	−	2.62958i	−0.110408	−	0.993886i
$7$	−0.292113	−	2.62958i	−0.110408	−	0.993886i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.839111	+	1.45338i	0.253001	+	0.438211i	0.964351	−	0.264627i	$-0.0852490\pi$
$11$	0.839111	+	1.45338i	0.253001	+	0.438211i	−0.711349	+	0.702839i	$0.751916\pi$
$12$		0			0
$13$	−4.84667			−1.34422			−0.672112	−	0.740449i	$-0.734613\pi$
$13$	−4.84667			−1.34422			−0.672112	+	0.740449i	$0.734613\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	−3.42334	+	5.92939i	−0.785367	+	1.36030i	0.143412	+	0.989663i	$0.454192\pi$
$19$	−3.42334	+	5.92939i	−0.785367	+	1.36030i	−0.928779	+	0.370633i	$0.879141\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.13122	+	1.95934i	−0.235876	+	0.408550i	−0.959527	−	0.281617i	$-0.909129\pi$
$23$	−1.13122	+	1.95934i	−0.235876	+	0.408550i	0.723651	+	0.690166i	$0.242463\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.32178			−0.616839			−0.308419	−	0.951250i	$-0.599800\pi$
$29$	−3.32178			−0.616839			−0.308419	+	0.951250i	$0.599800\pi$
$30$		0			0
$31$	−4.58423	−	7.94011i	−0.823351	−	1.42609i	−0.903173	−	0.429277i	$-0.858768\pi$
$31$	−4.58423	−	7.94011i	−0.823351	−	1.42609i	0.0798217	−	0.996809i	$-0.474565\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.42334	−	1.06181i	−0.409619	−	0.179479i
$36$		0			0
$37$	1.42334	−	2.46529i	0.233995	−	0.405291i	−0.724985	−	0.688765i	$-0.758153\pi$
$37$	1.42334	−	2.46529i	0.233995	−	0.405291i	0.958980	+	0.283473i	$0.0914867\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.52489			−1.48754			−0.743769	−	0.668437i	$-0.766964\pi$
$41$	−9.52489			−1.48754			−0.743769	+	0.668437i	$0.766964\pi$
$42$		0			0
$43$	6.58423			1.00408			0.502042	−	0.864843i	$-0.332582\pi$
$43$	6.58423			1.00408			0.502042	+	0.864843i	$0.332582\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.10156	+	10.5682i	−0.890004	+	1.54153i	−0.0501344	+	0.998742i	$0.515965\pi$
$47$	−6.10156	+	10.5682i	−0.890004	+	1.54153i	−0.839869	+	0.542789i	$0.817368\pi$
$48$		0			0
$49$	−6.82934	+	1.53627i	−0.975620	+	0.219466i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.74511	+	6.48673i	0.514431	+	0.891021i	0.999860	+	0.0167445i	$0.00533020\pi$
$53$	3.74511	+	6.48673i	0.514431	+	0.891021i	−0.485429	+	0.874276i	$0.661336\pi$
$54$		0			0
$55$	1.67822			0.226291
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	3.24511	−	5.62070i	0.415494	−	0.719657i	−0.579986	−	0.814627i	$-0.696942\pi$
$61$	3.24511	−	5.62070i	0.415494	−	0.719657i	0.995480	+	0.0949692i	$0.0302753\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.42334	+	4.19734i	−0.300578	+	0.520616i
$66$		0			0
$67$	2.87634	+	4.98196i	0.351401	+	0.608644i	0.986495	−	0.163791i	$-0.0523722\pi$
$67$	2.87634	+	4.98196i	0.351401	+	0.608644i	−0.635094	+	0.772434i	$0.719039\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	5.84667	+	10.1267i	0.684301	+	1.18524i	0.973656	+	0.228022i	$0.0732260\pi$
$73$	5.84667	+	10.1267i	0.684301	+	1.18524i	−0.289355	+	0.957222i	$0.593441\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.57666	−	2.63106i	0.407599	−	0.299837i
$78$		0			0
$79$	−2.84667	+	4.93058i	−0.320276	+	0.554734i	−0.980545	−	0.196295i	$-0.937109\pi$
$79$	−2.84667	+	4.93058i	−0.320276	+	0.554734i	0.660269	+	0.751029i	$0.270442\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	12.5842			1.38130			0.690649	−	0.723190i	$-0.257325\pi$
$83$	12.5842			1.38130			0.690649	+	0.723190i	$0.257325\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.92334	+	5.06337i	−0.309873	+	0.536716i	−0.978334	−	0.207031i	$-0.933620\pi$
$89$	−2.92334	+	5.06337i	−0.309873	+	0.536716i	0.668461	+	0.743747i	$0.266953\pi$
$90$		0			0
$91$	1.41577	+	12.7447i	0.148414	+	1.33601i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.42334	+	5.92939i	0.351227	+	0.608343i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.50756	−	14.7355i	−0.846534	−	1.46624i	−0.884282	−	0.466953i	$-0.845352\pi$
$101$	−8.50756	−	14.7355i	−0.846534	−	1.46624i	0.0377483	−	0.999287i	$-0.487981\pi$
$102$		0			0
$103$	−3.55456	+	6.15668i	−0.350241	+	0.606635i	−0.986292	−	0.165012i	$-0.947234\pi$
$103$	−3.55456	+	6.15668i	−0.350241	+	0.606635i	0.636050	+	0.771648i	$0.280567\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.876338	+	1.51786i	−0.0847188	+	0.146737i	−0.905271	−	0.424834i	$-0.860333\pi$
$107$	−0.876338	+	1.51786i	−0.0847188	+	0.146737i	0.820553	+	0.571571i	$0.193666\pi$
$108$		0			0
$109$	−9.77001	−	16.9222i	−0.935797	−	1.62085i	−0.773206	−	0.634154i	$-0.781348\pi$
$109$	−9.77001	−	16.9222i	−0.935797	−	1.62085i	−0.162591	−	0.986694i	$-0.551985\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−10.3369			−0.972414			−0.486207	−	0.873844i	$-0.661620\pi$
$113$	−10.3369			−0.972414			−0.486207	+	0.873844i	$0.661620\pi$
$114$		0			0
$115$	1.13122	+	1.95934i	0.105487	+	0.182709i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.26245	−	3.13553i	0.390738	−	0.287434i
$120$		0			0
$121$	4.09179	−	7.08718i	0.371981	−	0.644289i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−19.1836			−1.70227			−0.851133	−	0.524949i	$-0.824084\pi$
$127$	−19.1836			−1.70227			−0.851133	+	0.524949i	$0.824084\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.91357	+	15.4387i	−0.778782	+	1.34889i	0.153862	+	0.988092i	$0.450829\pi$
$131$	−8.91357	+	15.4387i	−0.778782	+	1.34889i	−0.932644	+	0.360797i	$0.882505\pi$
$132$		0			0
$133$	16.5918	+	7.26987i	1.43869	+	0.630378i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	0.938725	−	0.344668i	$-0.112008\pi$
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	−0.767853	+	0.640626i	$0.778675\pi$
$138$		0			0
$139$	−5.16845			−0.438382			−0.219191	−	0.975682i	$-0.570342\pi$
$139$	−5.16845			−0.438382			−0.219191	+	0.975682i	$0.570342\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.06689	−	7.04407i	−0.340091	−	0.589054i
$144$		0			0
$145$	−1.66089	+	2.87674i	−0.137929	+	0.238901i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.398443	−	0.690123i	0.0326417	−	0.0565371i	−0.849243	−	0.528002i	$-0.822941\pi$
$149$	0.398443	−	0.690123i	0.0326417	−	0.0565371i	0.881885	+	0.471465i	$0.156275\pi$
$150$		0			0
$151$	8.26245	+	14.3110i	0.672388	+	1.16461i	0.977225	+	0.212206i	$0.0680648\pi$
$151$	8.26245	+	14.3110i	0.672388	+	1.16461i	−0.304837	+	0.952405i	$0.598602\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.16845			−0.736428
$156$		0			0
$157$	−4.10156	−	7.10411i	−0.327340	−	0.566969i	0.654643	−	0.755938i	$-0.272819\pi$
$157$	−4.10156	−	7.10411i	−0.327340	−	0.566969i	−0.981983	+	0.188969i	$0.939486\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.48267	+	2.40229i	0.432095	+	0.189327i
$162$		0			0
$163$	−1.84667	+	3.19853i	−0.144643	+	0.250528i	−0.929240	−	0.369478i	$-0.879537\pi$
$163$	−1.84667	+	3.19853i	−0.144643	+	0.250528i	0.784597	+	0.620006i	$0.212870\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.262447			0.0203087			0.0101544	−	0.999948i	$-0.496768\pi$
$167$	0.262447			0.0203087			0.0101544	+	0.999948i	$0.496768\pi$
$168$		0			0
$169$	10.4902			0.806941
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.42334	+	16.3217i	−0.716443	+	1.24092i	0.245957	+	0.969281i	$0.420898\pi$
$173$	−9.42334	+	16.3217i	−0.716443	+	1.24092i	−0.962400	+	0.271635i	$0.912436\pi$
$174$		0			0
$175$	−2.13122	+	1.56777i	−0.161105	+	0.118512i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.00756	−	10.4054i	−0.449026	−	0.777736i	0.549297	−	0.835627i	$-0.314896\pi$
$179$	−6.00756	−	10.4054i	−0.449026	−	0.777736i	−0.998323	+	0.0578912i	$0.981562\pi$
$180$		0			0
$181$	−6.03466			−0.448553			−0.224276	−	0.974526i	$-0.572002\pi$
$181$	−6.03466			−0.448553			−0.224276	+	0.974526i	$0.572002\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.42334	−	2.46529i	−0.104646	−	0.181252i
$186$		0			0
$187$	−1.67822	+	2.90676i	−0.122724	+	0.212564i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.41577	−	2.45219i	0.102442	−	0.177434i	−0.810248	−	0.586087i	$-0.800668\pi$
$191$	1.41577	−	2.45219i	0.102442	−	0.177434i	0.912690	+	0.408652i	$0.134001\pi$
$192$		0			0
$193$	−6.49023	−	11.2414i	−0.467177	−	0.809174i	0.532120	−	0.846669i	$-0.321396\pi$
$193$	−6.49023	−	11.2414i	−0.467177	−	0.809174i	−0.999297	+	0.0374948i	$0.988062\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.84667			0.345311			0.172656	−	0.984982i	$-0.444765\pi$
$197$	4.84667			0.345311			0.172656	+	0.984982i	$0.444765\pi$
$198$		0			0
$199$	7.69334	+	13.3253i	0.545367	+	0.944603i	0.998584	+	0.0532026i	$0.0169429\pi$
$199$	7.69334	+	13.3253i	0.545367	+	0.944603i	−0.453217	+	0.891400i	$0.649724\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.970334	+	8.73487i	0.0681041	+	0.613068i
$204$		0			0
$205$	−4.76245	+	8.24880i	−0.332624	+	0.576121i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.4902			−0.794796
$210$		0			0
$211$	9.18357			0.632223			0.316112	−	0.948722i	$-0.397623\pi$
$211$	9.18357			0.632223			0.316112	+	0.948722i	$0.397623\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.29211	−	5.70211i	0.224520	−	0.388880i
$216$		0			0
$217$	−19.5400	+	14.3740i	−1.32646	+	0.975769i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.84667	−	8.39468i	−0.326022	−	0.564687i
$222$		0			0
$223$	−12.9805			−0.869236			−0.434618	−	0.900615i	$-0.643117\pi$
$223$	−12.9805			−0.869236			−0.434618	+	0.900615i	$0.643117\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.0151	−	19.0788i	−0.731099	−	1.26630i	−0.956414	−	0.292015i	$-0.905674\pi$
$227$	−11.0151	−	19.0788i	−0.731099	−	1.26630i	0.225314	−	0.974286i	$-0.427659\pi$
$228$		0			0
$229$	−2.15333	+	3.72967i	−0.142296	+	0.246464i	−0.928361	−	0.371680i	$-0.878782\pi$
$229$	−2.15333	+	3.72967i	−0.142296	+	0.246464i	0.786065	+	0.618144i	$0.212115\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$		0			0
$235$	6.10156	+	10.5682i	0.398022	+	0.689394i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.8618			−0.702591			−0.351296	−	0.936265i	$-0.614259\pi$
$239$	−10.8618			−0.702591			−0.351296	+	0.936265i	$0.614259\pi$
$240$		0			0
$241$	−0.101557	−	0.175902i	−0.00654187	−	0.0113309i	0.862736	−	0.505655i	$-0.168749\pi$
$241$	−0.101557	−	0.175902i	−0.00654187	−	0.0113309i	−0.869278	+	0.494324i	$0.835416\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.08423	+	6.68251i	−0.133156	+	0.426930i
$246$		0			0
$247$	16.5918	−	28.7378i	1.05571	−	1.82854i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.03466			−0.317785			−0.158893	−	0.987296i	$-0.550792\pi$
$251$	−5.03466			−0.317785			−0.158893	+	0.987296i	$0.550792\pi$
$252$		0			0
$253$	−3.79689			−0.238708
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.6933	−	20.2535i	0.729411	−	1.26338i	−0.227722	−	0.973726i	$-0.573128\pi$
$257$	11.6933	−	20.2535i	0.729411	−	1.26338i	0.957133	−	0.289650i	$-0.0935390\pi$
$258$		0			0
$259$	−6.89844	−	3.02263i	−0.428648	−	0.187817i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13.5546	+	23.4772i	0.835810	+	1.44767i	0.893369	+	0.449323i	$0.148335\pi$
$263$	13.5546	+	23.4772i	0.835810	+	1.44767i	−0.0575594	+	0.998342i	$0.518332\pi$
$264$		0			0
$265$	7.49023			0.460121
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.24511	+	5.62070i	0.197858	+	0.342700i	0.947834	−	0.318765i	$-0.103268\pi$
$269$	3.24511	+	5.62070i	0.197858	+	0.342700i	−0.749976	+	0.661466i	$0.769935\pi$
$270$		0			0
$271$	11.6933	−	20.2535i	0.710320	−	1.23031i	−0.254417	−	0.967095i	$-0.581884\pi$
$271$	11.6933	−	20.2535i	0.710320	−	1.23031i	0.964737	−	0.263216i	$-0.0847831\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.839111	−	1.45338i	0.0506003	−	0.0876422i
$276$		0			0
$277$	−1.83155	−	3.17234i	−0.110047	−	0.190607i	0.805742	−	0.592267i	$-0.201767\pi$
$277$	−1.83155	−	3.17234i	−0.110047	−	0.190607i	−0.915789	+	0.401660i	$0.868434\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.8965			−0.828993			−0.414497	−	0.910051i	$-0.636042\pi$
$281$	−13.8965			−0.828993			−0.414497	+	0.910051i	$0.636042\pi$
$282$		0			0
$283$	10.1685	+	17.6123i	0.604452	+	1.04694i	0.992138	+	0.125150i	$0.0399411\pi$
$283$	10.1685	+	17.6123i	0.604452	+	1.04694i	−0.387686	+	0.921791i	$0.626726\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.78234	+	25.0464i	0.164236	+	1.47844i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−18.8467			−1.10103			−0.550517	−	0.834824i	$-0.685569\pi$
$293$	−18.8467			−1.10103			−0.550517	+	0.834824i	$0.685569\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.48267	−	9.49626i	0.317071	−	0.549183i
$300$		0			0
$301$	−1.92334	−	17.3137i	−0.110859	−	0.997946i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.24511	−	5.62070i	−0.185815	−	0.321841i
$306$		0			0
$307$	−2.39623			−0.136760			−0.0683802	−	0.997659i	$-0.521783\pi$
$307$	−2.39623			−0.136760			−0.0683802	+	0.997659i	$0.521783\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.83155	−	4.90439i	−0.160562	−	0.278102i	0.774508	−	0.632564i	$-0.217997\pi$
$311$	−2.83155	−	4.90439i	−0.160562	−	0.278102i	−0.935071	+	0.354462i	$0.884664\pi$
$312$		0			0
$313$	−14.8618	+	25.7414i	−0.840038	+	1.45499i	0.0498231	+	0.998758i	$0.484134\pi$
$313$	−14.8618	+	25.7414i	−0.840038	+	1.45499i	−0.889861	+	0.456231i	$0.849199\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.52489	−	16.4976i	0.534971	−	0.926597i	−0.464193	−	0.885734i	$-0.653656\pi$
$317$	9.52489	−	16.4976i	0.534971	−	0.926597i	0.999165	−	0.0408636i	$-0.0130109\pi$
$318$		0			0
$319$	−2.78734	−	4.82781i	−0.156061	−	0.270306i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.6933			−0.761918
$324$		0			0
$325$	2.42334	+	4.19734i	0.134422	+	0.232827i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	29.5722	+	12.9574i	1.63037	+	0.714365i
$330$		0			0
$331$	−1.16089	+	2.01072i	−0.0638083	+	0.110519i	−0.896165	−	0.443722i	$-0.853658\pi$
$331$	−1.16089	+	2.01072i	−0.0638083	+	0.110519i	0.832356	+	0.554241i	$0.186991\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.75268			0.314302
$336$		0			0
$337$	−16.4062			−0.893704			−0.446852	−	0.894608i	$-0.647455\pi$
$337$	−16.4062			−0.893704			−0.446852	+	0.894608i	$0.647455\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	7.69334	−	13.3253i	0.416618	−	0.721603i
$342$		0			0
$343$	6.03466	+	17.5095i	0.325841	+	0.945425i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.29211	+	3.97006i	0.123047	+	0.213124i	0.920968	−	0.389639i	$-0.127400\pi$
$347$	2.29211	+	3.97006i	0.123047	+	0.213124i	−0.797921	+	0.602762i	$0.794067\pi$
$348$		0			0
$349$	12.3716			0.662235			0.331117	−	0.943590i	$-0.392574\pi$
$349$	12.3716			0.662235			0.331117	+	0.943590i	$0.392574\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.69334	+	16.7894i	0.515925	+	0.893608i	0.999829	+	0.0184869i	$0.00588489\pi$
$353$	9.69334	+	16.7894i	0.515925	+	0.893608i	−0.483904	+	0.875121i	$0.660782\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.90600	+	8.49745i	−0.258929	+	0.448478i	−0.965955	−	0.258709i	$-0.916703\pi$
$359$	−4.90600	+	8.49745i	−0.258929	+	0.448478i	0.707026	+	0.707187i	$0.250036\pi$
$360$		0			0
$361$	−13.9385	−	24.1421i	−0.733603	−	1.27064i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.6933			0.612058
$366$		0			0
$367$	6.35901	+	11.0141i	0.331937	+	0.574933i	0.982892	−	0.184184i	$-0.0589644\pi$
$367$	6.35901	+	11.0141i	0.331937	+	0.574933i	−0.650954	+	0.759117i	$0.725631\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	15.9634	−	11.7429i	0.828776	−	0.609662i
$372$		0			0
$373$	8.20311	−	14.2082i	0.424741	−	0.735673i	−0.571655	−	0.820494i	$-0.693698\pi$
$373$	8.20311	−	14.2082i	0.424741	−	0.735673i	0.996396	+	0.0848208i	$0.0270318\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	16.0996			0.829170
$378$		0			0
$379$	14.4707			0.743309			0.371655	−	0.928371i	$-0.378791\pi$
$379$	14.4707			0.743309			0.371655	+	0.928371i	$0.378791\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.77478	+	3.07401i	−0.0906871	+	0.157075i	−0.907800	−	0.419402i	$-0.862240\pi$
$383$	−1.77478	+	3.07401i	−0.0906871	+	0.157075i	0.817113	+	0.576477i	$0.195573\pi$
$384$		0			0
$385$	−0.490230	−	4.41301i	−0.0249844	−	0.224908i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.49023	+	7.77731i	0.227664	+	0.394325i	0.957115	−	0.289707i	$-0.0935580\pi$
$389$	4.49023	+	7.77731i	0.227664	+	0.394325i	−0.729452	+	0.684032i	$0.760225\pi$
$390$		0			0
$391$	−4.52489			−0.228834
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.84667	+	4.93058i	0.143232	+	0.248084i
$396$		0			0
$397$	14.0498	−	24.3349i	0.705139	−	1.22134i	−0.261503	−	0.965203i	$-0.584218\pi$
$397$	14.0498	−	24.3349i	0.705139	−	1.22134i	0.966642	−	0.256133i	$-0.0824486\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.3467	+	23.1171i	−0.666501	+	1.15441i	0.312375	+	0.949959i	$0.398875\pi$
$401$	−13.3467	+	23.1171i	−0.666501	+	1.15441i	−0.978876	+	0.204455i	$0.934458\pi$
$402$		0			0
$403$	22.2182	+	38.4831i	1.10677	+	1.91698i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.77735			0.236804
$408$		0			0
$409$	−14.0325	−	24.3049i	−0.693860	−	1.20180i	−0.970563	−	0.240846i	$-0.922575\pi$
$409$	−14.0325	−	24.3049i	−0.693860	−	1.20180i	0.276703	−	0.960955i	$-0.410758\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	17.0498	−	12.5421i	0.838965	−	0.617157i
$414$		0			0
$415$	6.29211	−	10.8983i	0.308868	−	0.534974i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.8769			0.922198			0.461099	−	0.887349i	$-0.347455\pi$
$419$	18.8769			0.922198			0.461099	+	0.887349i	$0.347455\pi$
$420$		0			0
$421$	−28.1836			−1.37358			−0.686792	−	0.726854i	$-0.740982\pi$
$421$	−28.1836			−1.37358			−0.686792	+	0.726854i	$0.740982\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	−15.7280	−	6.89140i	−0.761132	−	0.333498i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.41577	+	2.45219i	0.0681955	+	0.118118i	0.898107	−	0.439777i	$-0.144943\pi$
$431$	1.41577	+	2.45219i	0.0681955	+	0.118118i	−0.829912	+	0.557895i	$0.811609\pi$
$432$		0			0
$433$	−2.33690			−0.112304			−0.0561522	−	0.998422i	$-0.517883\pi$
$433$	−2.33690			−0.112304			−0.0561522	+	0.998422i	$0.517883\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.74511	−	13.4149i	−0.370499	−	0.641723i
$438$		0			0
$439$	3.03466	−	5.25619i	0.144837	−	0.250864i	−0.784475	−	0.620160i	$-0.787068\pi$
$439$	3.03466	−	5.25619i	0.144837	−	0.250864i	0.929312	+	0.369296i	$0.120401\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.80188	−	10.0492i	0.275656	−	0.477450i	−0.694645	−	0.719353i	$-0.744438\pi$
$443$	5.80188	−	10.0492i	0.275656	−	0.477450i	0.970300	+	0.241903i	$0.0777717\pi$
$444$		0			0
$445$	2.92334	+	5.06337i	0.138579	+	0.240027i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−4.13821			−0.195294			−0.0976470	−	0.995221i	$-0.531132\pi$
$449$	−4.13821			−0.195294			−0.0976470	+	0.995221i	$0.531132\pi$
$450$		0			0
$451$	−7.99244	−	13.8433i	−0.376349	−	0.651856i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	11.7451	+	5.14625i	0.550619	+	0.241260i
$456$		0			0
$457$	6.32178	−	10.9496i	0.295720	−	0.512203i	−0.679432	−	0.733739i	$-0.737774\pi$
$457$	6.32178	−	10.9496i	0.295720	−	0.512203i	0.975152	+	0.221536i	$0.0711070\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−20.7129			−0.964695			−0.482348	−	0.875980i	$-0.660216\pi$
$461$	−20.7129			−0.964695			−0.482348	+	0.875980i	$0.660216\pi$
$462$		0			0
$463$	−16.3811			−0.761295			−0.380647	−	0.924720i	$-0.624299\pi$
$463$	−16.3811			−0.761295			−0.380647	+	0.924720i	$0.624299\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.861215	+	1.49167i	−0.0398523	+	0.0690262i	−0.885264	−	0.465090i	$-0.846022\pi$
$467$	−0.861215	+	1.49167i	−0.0398523	+	0.0690262i	0.845411	+	0.534116i	$0.179355\pi$
$468$		0			0
$469$	12.2602	−	9.01884i	0.566125	−	0.416452i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.52489	+	9.56940i	0.254035	+	0.440001i
$474$		0			0
$475$	6.84667			0.314147
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.890881	−	1.54305i	−0.0407054	−	0.0705038i	0.844955	−	0.534838i	$-0.179627\pi$
$479$	−0.890881	−	1.54305i	−0.0407054	−	0.0705038i	−0.885660	+	0.464334i	$0.846294\pi$
$480$		0			0
$481$	−6.89844	+	11.9485i	−0.314542	+	0.544803i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$		0			0
$487$	5.50977	+	9.54320i	0.249672	+	0.432444i	0.963435	−	0.267943i	$-0.0863440\pi$
$487$	5.50977	+	9.54320i	0.249672	+	0.432444i	−0.713763	+	0.700387i	$0.753011\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.9311			0.944608			0.472304	−	0.881436i	$-0.343422\pi$
$491$	20.9311			0.944608			0.472304	+	0.881436i	$0.343422\pi$
$492$		0			0
$493$	−3.32178	−	5.75349i	−0.149605	−	0.259124i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	3.75268	−	6.49983i	0.167993	−	0.290972i	−0.769721	−	0.638380i	$-0.779605\pi$
$499$	3.75268	−	6.49983i	0.167993	−	0.290972i	0.937714	+	0.347408i	$0.112938\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−20.5842			−0.917805			−0.458903	−	0.888487i	$-0.651757\pi$
$503$	−20.5842			−0.917805			−0.458903	+	0.888487i	$0.651757\pi$
$504$		0			0
$505$	−17.0151			−0.757163
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.82934	−	11.8288i	0.302705	−	0.524301i	−0.674043	−	0.738693i	$-0.735444\pi$
$509$	6.82934	−	11.8288i	0.302705	−	0.524301i	0.976748	+	0.214392i	$0.0687769\pi$
$510$		0			0
$511$	24.9211	−	18.3324i	1.10245	−	0.810978i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.55456	+	6.15668i	0.156633	+	0.271296i
$516$		0			0
$517$	−20.4795			−0.900688
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−21.0820	−	36.5151i	−0.923620	−	1.59976i	−0.793766	−	0.608224i	$-0.791882\pi$
$521$	−21.0820	−	36.5151i	−0.923620	−	1.59976i	−0.129854	−	0.991533i	$-0.541451\pi$
$522$		0			0
$523$	15.3218	−	26.5381i	0.669975	−	1.16043i	−0.307936	−	0.951407i	$-0.599638\pi$
$523$	15.3218	−	26.5381i	0.669975	−	1.16043i	0.977911	−	0.209023i	$-0.0670284\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.16845	−	15.8802i	0.399384	−	0.691753i
$528$		0			0
$529$	8.94067	+	15.4857i	0.388725	+	0.673291i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	46.1640			1.99959
$534$		0			0
$535$	0.876338	+	1.51786i	0.0378874	+	0.0656229i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.96335	−	8.63654i	−0.343006	−	0.372002i
$540$		0			0
$541$	16.8445	−	29.1755i	0.724200	−	1.25435i	−0.235102	−	0.971971i	$-0.575543\pi$
$541$	16.8445	−	29.1755i	0.724200	−	1.25435i	0.959302	−	0.282381i	$-0.0911241\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−19.5400			−0.837002
$546$		0			0
$547$	−3.03979			−0.129972			−0.0649861	−	0.997886i	$-0.520700\pi$
$547$	−3.03979			−0.129972			−0.0649861	+	0.997886i	$0.520700\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	11.3716	−	19.6961i	0.484445	−	0.839083i
$552$		0			0
$553$	13.7969	+	6.04526i	0.586703	+	0.257070i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.08202	+	15.7305i	0.384817	+	0.666523i	0.991744	−	0.128235i	$-0.0409311\pi$
$557$	9.08202	+	15.7305i	0.384817	+	0.666523i	−0.606926	+	0.794758i	$0.707598\pi$
$558$		0			0
$559$	−31.9116			−1.34972
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−18.4952	−	32.0347i	−0.779481	−	1.35010i	−0.932241	−	0.361837i	$-0.882150\pi$
$563$	−18.4952	−	32.0347i	−0.779481	−	1.35010i	0.152760	−	0.988263i	$-0.451184\pi$
$564$		0			0
$565$	−5.16845	+	8.95202i	−0.217438	+	0.376614i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.3047	−	28.2405i	0.683527	−	1.18390i	−0.290370	−	0.956915i	$-0.593778\pi$
$569$	16.3047	−	28.2405i	0.683527	−	1.18390i	0.973897	−	0.226990i	$-0.0728884\pi$
$570$		0			0
$571$	−20.2182	−	35.0190i	−0.846107	−	1.46550i	−0.884656	−	0.466243i	$-0.845607\pi$
$571$	−20.2182	−	35.0190i	−0.846107	−	1.46550i	0.0385496	−	0.999257i	$-0.487726\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.26245			0.0943505
$576$		0			0
$577$	19.0151	+	32.9352i	0.791610	+	1.37111i	0.924970	+	0.380041i	$0.124090\pi$
$577$	19.0151	+	32.9352i	0.791610	+	1.37111i	−0.133360	+	0.991068i	$0.542577\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.67601	−	33.0912i	−0.152507	−	1.37285i
$582$		0			0
$583$	−6.28513	+	10.8862i	−0.260304	+	0.450859i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−34.0302			−1.40458			−0.702289	−	0.711892i	$-0.747839\pi$
$587$	−34.0302			−1.40458			−0.702289	+	0.711892i	$0.747839\pi$
$588$		0			0
$589$	62.7734			2.58653
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.8618	+	29.2055i	−0.692431	+	1.19933i	0.278608	+	0.960405i	$0.410127\pi$
$593$	−16.8618	+	29.2055i	−0.692431	+	1.19933i	−0.971039	+	0.238921i	$0.923206\pi$
$594$		0			0
$595$	−0.584225	−	5.25915i	−0.0239509	−	0.215604i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.15333	+	5.46172i	0.128841	+	0.223160i	0.923228	−	0.384253i	$-0.125541\pi$
$599$	3.15333	+	5.46172i	0.128841	+	0.223160i	−0.794387	+	0.607413i	$0.792207\pi$
$600$		0			0
$601$	−11.2871			−0.460411			−0.230206	−	0.973142i	$-0.573940\pi$
$601$	−11.2871			−0.460411			−0.230206	+	0.973142i	$0.573940\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.09179	−	7.08718i	−0.166355	−	0.288135i
$606$		0			0
$607$	7.73057	−	13.3897i	0.313774	−	0.543473i	−0.665402	−	0.746485i	$-0.731740\pi$
$607$	7.73057	−	13.3897i	0.313774	−	0.543473i	0.979176	+	0.203012i	$0.0650732\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	29.5722	−	51.2206i	1.19637	−	2.07217i
$612$		0			0
$613$	11.0820	+	19.1946i	0.447598	+	0.775263i	0.998229	−	0.0594857i	$-0.0189461\pi$
$613$	11.0820	+	19.1946i	0.447598	+	0.775263i	−0.550631	+	0.834749i	$0.685613\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.9805			0.603091			0.301545	−	0.953452i	$-0.402498\pi$
$617$	14.9805			0.603091			0.301545	+	0.953452i	$0.402498\pi$
$618$		0			0
$619$	−11.8196	−	20.4721i	−0.475069	−	0.822843i	0.524524	−	0.851396i	$-0.324243\pi$
$619$	−11.8196	−	20.4721i	−0.475069	−	0.822843i	−0.999592	+	0.0285529i	$0.990910\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14.1685	+	6.20806i	0.567647	+	0.248721i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.69334			0.227008
$630$		0			0
$631$	−13.7818			−0.548643			−0.274322	−	0.961638i	$-0.588453\pi$
$631$	−13.7818			−0.548643			−0.274322	+	0.961638i	$0.588453\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−9.59179	+	16.6135i	−0.380638	+	0.659285i
$636$		0			0
$637$	33.0996	−	7.44577i	1.31145	−	0.295012i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	21.9309	+	37.9854i	0.866218	+	1.50033i	0.865832	+	0.500334i	$0.166790\pi$
$641$	21.9309	+	37.9854i	0.866218	+	1.50033i	0.000386062		1.00000i	$0.499877\pi$
$642$		0			0
$643$	7.04979			0.278016			0.139008	−	0.990291i	$-0.455609\pi$
$643$	7.04979			0.278016			0.139008	+	0.990291i	$0.455609\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.2403	−	21.2009i	−0.481217	−	0.833493i	0.518550	−	0.855047i	$-0.326472\pi$
$647$	−12.2403	−	21.2009i	−0.481217	−	0.833493i	−0.999768	+	0.0215540i	$0.993139\pi$
$648$		0			0
$649$	−6.71288	+	11.6271i	−0.263504	+	0.456402i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.408213	−	0.707046i	0.0159746	−	0.0276688i	−0.857928	−	0.513771i	$-0.828248\pi$
$653$	0.408213	−	0.707046i	0.0159746	−	0.0276688i	0.873902	+	0.486102i	$0.161582\pi$
$654$		0			0
$655$	8.91357	+	15.4387i	0.348282	+	0.603242i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−21.2871			−0.829228			−0.414614	−	0.909997i	$-0.636083\pi$
$659$	−21.2871			−0.829228			−0.414614	+	0.909997i	$0.636083\pi$
$660$		0			0
$661$	−12.9731	−	22.4701i	−0.504596	−	0.873986i	−0.999986	−	0.00531513i	$-0.998308\pi$
$661$	−12.9731	−	22.4701i	−0.504596	−	0.873986i	0.495390	−	0.868671i	$-0.335025\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	14.5918	−	10.7340i	0.565845	−	0.416246i
$666$		0			0
$667$	3.75767	−	6.50848i	0.145498	−	0.252009i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	10.8920			0.420483
$672$		0			0
$673$	22.0693			0.850710			0.425355	−	0.905027i	$-0.360149\pi$
$673$	22.0693			0.850710			0.425355	+	0.905027i	$0.360149\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.74511	−	4.75468i	0.105503	−	0.182737i	−0.808440	−	0.588578i	$-0.799688\pi$
$677$	2.74511	−	4.75468i	0.105503	−	0.182737i	0.913944	+	0.405841i	$0.133021\pi$
$678$		0			0
$679$	0.584225	+	5.25915i	0.0224205	+	0.201828i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.61389	+	16.6517i	0.367865	+	0.637161i	0.989232	−	0.146359i	$-0.0467554\pi$
$683$	9.61389	+	16.6517i	0.367865	+	0.637161i	−0.621366	+	0.783520i	$0.713422\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−18.1513	−	31.4390i	−0.691511	−	1.19773i
$690$		0			0
$691$	−7.10912	+	12.3134i	−0.270444	+	0.468422i	−0.968975	−	0.247157i	$-0.920504\pi$
$691$	−7.10912	+	12.3134i	−0.270444	+	0.468422i	0.698532	+	0.715579i	$0.253837\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.58423	+	4.47601i	−0.0980253	+	0.169785i
$696$		0			0
$697$	−9.52489	−	16.4976i	−0.360781	−	0.624891i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.1533			−0.534564			−0.267282	−	0.963618i	$-0.586125\pi$
$701$	−14.1533			−0.534564			−0.267282	+	0.963618i	$0.586125\pi$
$702$		0			0
$703$	9.74511	+	16.8790i	0.367544	+	0.636605i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−36.2630	+	26.6757i	−1.36381	+	1.00324i
$708$		0			0
$709$	−8.52268	+	14.7617i	−0.320076	+	0.554388i	−0.980503	−	0.196502i	$-0.937042\pi$
$709$	−8.52268	+	14.7617i	−0.320076	+	0.554388i	0.660427	+	0.750890i	$0.270375\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	20.7431			0.776836
$714$		0			0
$715$	−8.13379			−0.304186
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.75268	+	9.96393i	−0.214539	+	0.371592i	−0.953130	−	0.302562i	$-0.902158\pi$
$719$	−5.75268	+	9.96393i	−0.214539	+	0.371592i	0.738591	+	0.674154i	$0.235491\pi$
$720$		0			0
$721$	17.2278	+	7.54854i	0.641596	+	0.281122i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.66089	+	2.87674i	0.0616839	+	0.106840i
$726$		0			0
$727$	16.4114			0.608664			0.304332	−	0.952566i	$-0.401567\pi$
$727$	16.4114			0.608664			0.304332	+	0.952566i	$0.401567\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.58423	+	11.4042i	0.243526	+	0.421800i
$732$		0			0
$733$	4.55712	−	7.89317i	0.168321	−	0.291541i	−0.769509	−	0.638637i	$-0.779499\pi$
$733$	4.55712	−	7.89317i	0.168321	−	0.291541i	0.937830	+	0.347096i	$0.112832\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.82713	+	8.36084i	−0.177810	+	0.307975i
$738$		0			0
$739$	17.4978	+	30.3071i	0.643667	+	1.11486i	0.984608	+	0.174779i	$0.0559210\pi$
$739$	17.4978	+	30.3071i	0.643667	+	1.11486i	−0.340941	+	0.940085i	$0.610746\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	43.5305			1.59698			0.798489	−	0.602009i	$-0.205633\pi$
$743$	43.5305			1.59698			0.798489	+	0.602009i	$0.205633\pi$
$744$		0			0
$745$	−0.398443	−	0.690123i	−0.0145978	−	0.0252842i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.24732	+	1.86101i	0.155194	+	0.0679999i
$750$		0			0
$751$	−3.15333	+	5.46172i	−0.115067	+	0.199301i	−0.917806	−	0.397028i	$-0.870041\pi$
$751$	−3.15333	+	5.46172i	−0.115067	+	0.199301i	0.802740	+	0.596329i	$0.203375\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.5249			0.601402
$756$		0			0
$757$	24.3369			0.884540			0.442270	−	0.896882i	$-0.354173\pi$
$757$	24.3369			0.884540			0.442270	+	0.896882i	$0.354173\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.1016	+	24.4246i	−0.511181	+	0.885392i	0.488735	+	0.872432i	$0.337459\pi$
$761$	−14.1016	+	24.4246i	−0.511181	+	0.885392i	−0.999916	+	0.0129592i	$0.995875\pi$
$762$		0			0
$763$	−41.6441	+	30.6342i	−1.50762	+	1.10903i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−19.3867	−	33.5787i	−0.700013	−	1.21246i
$768$		0			0
$769$	−41.8965			−1.51082			−0.755412	−	0.655250i	$-0.772563\pi$
$769$	−41.8965			−1.51082			−0.755412	+	0.655250i	$0.772563\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	19.9287	+	34.5175i	0.716785	+	1.24151i	0.962267	+	0.272107i	$0.0877205\pi$
$773$	19.9287	+	34.5175i	0.716785	+	1.24151i	−0.245482	+	0.969401i	$0.578946\pi$
$774$		0			0
$775$	−4.58423	+	7.94011i	−0.164670	+	0.285217i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	32.6069	−	56.4768i	1.16826	−	2.02349i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.20311			−0.292782
$786$		0			0
$787$	−17.6637	−	30.5944i	−0.629642	−	1.09057i	−0.987623	−	0.156843i	$-0.949868\pi$
$787$	−17.6637	−	30.5944i	−0.629642	−	1.09057i	0.357981	−	0.933729i	$-0.383465\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.01954	+	27.1817i	0.107363	+	0.966469i
$792$		0			0
$793$	−15.7280	+	27.2417i	−0.558518	+	0.967381i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−29.6933			−1.05179			−0.525896	−	0.850549i	$-0.676270\pi$
$797$	−29.6933			−1.05179			−0.525896	+	0.850549i	$0.676270\pi$
$798$		0			0
$799$	−24.4062			−0.863430
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.81201	+	16.9949i	−0.346258	+	0.599737i
$804$		0			0
$805$	4.82178	−	3.54698i	0.169945	−	0.125015i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.82178	−	17.0118i	−0.345315	−	0.598104i	0.640096	−	0.768295i	$-0.278895\pi$
$809$	−9.82178	−	17.0118i	−0.345315	−	0.598104i	−0.985411	+	0.170191i	$0.945561\pi$
$810$		0			0
$811$	0.252452			0.00886479			0.00443239	−	0.999990i	$-0.498589\pi$
$811$	0.252452			0.00886479			0.00443239	+	0.999990i	$0.498589\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.84667	+	3.19853i	0.0646861	+	0.112040i
$816$		0			0
$817$	−22.5400	+	39.0405i	−0.788575	+	1.36585i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.3867	−	38.7749i	0.781301	−	1.35325i	−0.149883	−	0.988704i	$-0.547890\pi$
$821$	22.3867	−	38.7749i	0.781301	−	1.35325i	0.931184	−	0.364549i	$-0.118777\pi$
$822$		0			0
$823$	−1.64856	−	2.85538i	−0.0574650	−	0.0995323i	0.835862	−	0.548940i	$-0.184968\pi$
$823$	−1.64856	−	2.85538i	−0.0574650	−	0.0995323i	−0.893327	+	0.449408i	$0.851635\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.41577			−0.327419			−0.163709	−	0.986509i	$-0.552346\pi$
$827$	−9.41577			−0.327419			−0.163709	+	0.986509i	$0.552346\pi$
$828$		0			0
$829$	2.35644	+	4.08148i	0.0818426	+	0.141756i	0.904041	−	0.427445i	$-0.140586\pi$
$829$	2.35644	+	4.08148i	0.0818426	+	0.141756i	−0.822199	+	0.569200i	$0.807253\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−9.49023	−	10.2925i	−0.328817	−	0.356614i
$834$		0			0
$835$	0.131223	−	0.227285i	0.00454117	−	0.00786554i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−22.1880			−0.766015			−0.383007	−	0.923745i	$-0.625112\pi$
$839$	−22.1880			−0.766015			−0.383007	+	0.923745i	$0.625112\pi$
$840$		0			0
$841$	−17.9658			−0.619510
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.24511	−	9.08481i	0.180437	−	0.312527i
$846$		0			0
$847$	−19.8315	−	8.68941i	−0.681420	−	0.298572i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.22022	+	5.57759i	0.110388	+	0.191197i
$852$		0			0
$853$	39.9267			1.36706			0.683532	−	0.729920i	$-0.260443\pi$
$853$	39.9267			1.36706			0.683532	+	0.729920i	$0.260443\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.812009	−	1.40644i	−0.0277377	−	0.0480431i	0.851823	−	0.523829i	$-0.175497\pi$
$857$	−0.812009	−	1.40644i	−0.0277377	−	0.0480431i	−0.879561	+	0.475786i	$0.842164\pi$
$858$		0			0
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	−0.926161	−	0.377128i	$-0.876912\pi$
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	0.789683	+	0.613515i	$0.210245\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.11168	−	15.7819i	0.310165	−	0.537222i	−0.668233	−	0.743952i	$-0.732949\pi$
$863$	9.11168	−	15.7819i	0.310165	−	0.537222i	0.978398	+	0.206730i	$0.0662823\pi$
$864$		0			0
$865$	9.42334	+	16.3217i	0.320403	+	0.554954i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.55469			−0.324121
$870$		0			0
$871$	−13.9407	−	24.1459i	−0.472362	−	0.818154i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.292113	+	2.62958i	0.00987521	+	0.0888959i
$876$		0			0
$877$	25.4385	−	44.0607i	0.858996	−	1.48782i	−0.0138922	−	0.999903i	$-0.504422\pi$
$877$	25.4385	−	44.0607i	0.858996	−	1.48782i	0.872888	−	0.487921i	$-0.162244\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	19.1187			0.644124			0.322062	−	0.946719i	$-0.395624\pi$
$881$	19.1187			0.644124			0.322062	+	0.946719i	$0.395624\pi$
$882$		0			0
$883$	39.3174			1.32313			0.661567	−	0.749886i	$-0.269892\pi$
$883$	39.3174			1.32313			0.661567	+	0.749886i	$0.269892\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.5199	−	23.4171i	0.453954	−	0.786271i	−0.544674	−	0.838648i	$-0.683346\pi$
$887$	13.5199	−	23.4171i	0.453954	−	0.786271i	0.998627	+	0.0523772i	$0.0166798\pi$
$888$		0			0
$889$	5.60377	+	50.4447i	0.187944	+	1.69186i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−41.7754	−	72.3570i	−1.39796	−	2.42134i
$894$		0			0
$895$	−12.0151			−0.401621
$896$		0			0
$897$		0			0
$898$		0			0
$899$	15.2278	+	26.3753i	0.507875	+	0.879665i
$900$		0			0
$901$	−7.49023	+	12.9735i	−0.249536	+	0.432209i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.01733	+	5.22617i	−0.100299	+	0.173724i
$906$		0			0
$907$	−16.4012	−	28.4078i	−0.544594	−	0.943264i	−0.998632	−	0.0522823i	$-0.983350\pi$
$907$	−16.4012	−	28.4078i	−0.544594	−	0.943264i	0.454038	−	0.890982i	$-0.349983\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.18799			−0.205017			−0.102509	−	0.994732i	$-0.532687\pi$
$911$	−6.18799			−0.205017			−0.102509	+	0.994732i	$0.532687\pi$
$912$		0			0
$913$	10.5596	+	18.2897i	0.349470	+	0.605300i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	43.2011	+	18.9290i	1.42663	+	0.625092i
$918$		0			0
$919$	23.8965	−	41.3899i	0.788271	−	1.36533i	−0.138754	−	0.990327i	$-0.544310\pi$
$919$	23.8965	−	41.3899i	0.788271	−	1.36533i	0.927025	−	0.374999i	$-0.122357\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−2.84667			−0.0935980
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.9309	+	34.5213i	−0.653912	+	1.13261i	0.328254	+	0.944590i	$0.393540\pi$
$929$	−19.9309	+	34.5213i	−0.653912	+	1.13261i	−0.982165	+	0.188018i	$0.939794\pi$
$930$		0			0
$931$	14.2700	−	45.7530i	0.467681	−	1.49949i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.67822	+	2.90676i	0.0548837	+	0.0950614i
$936$		0			0
$937$	0.406229			0.0132709			0.00663546	−	0.999978i	$-0.497888\pi$
$937$	0.406229			0.0132709			0.00663546	+	0.999978i	$0.497888\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	16.8271	+	29.1454i	0.548549	+	0.950114i	0.998374	+	0.0569979i	$0.0181528\pi$
$941$	16.8271	+	29.1454i	0.548549	+	0.950114i	−0.449825	+	0.893116i	$0.648514\pi$
$942$		0			0
$943$	10.7748	−	18.6625i	0.350875	−	0.607734i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.92055	−	5.05854i	0.0949050	−	0.164380i	−0.814664	−	0.579933i	$-0.803079\pi$
$947$	2.92055	−	5.05854i	0.0949050	−	0.164380i	0.909569	+	0.415553i	$0.136412\pi$
$948$		0			0
$949$	−28.3369	−	49.0810i	−0.919855	−	1.59324i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−32.0605			−1.03854			−0.519271	−	0.854610i	$-0.673796\pi$
$953$	−32.0605			−1.03854			−0.519271	+	0.854610i	$0.673796\pi$
$954$		0			0
$955$	−1.41577	−	2.45219i	−0.0458134	−	0.0793511i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	8.52489	−	6.27106i	0.275283	−	0.202503i
$960$		0			0
$961$	−26.5302	+	45.9517i	−0.855814	+	1.48231i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.9805			−0.417856
$966$		0			0
$967$	24.0896			0.774669			0.387334	−	0.921939i	$-0.373396\pi$
$967$	24.0896			0.774669			0.387334	+	0.921939i	$0.373396\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.23534	−	15.9961i	0.296376	−	0.513339i	−0.678928	−	0.734205i	$-0.737555\pi$
$971$	9.23534	−	15.9961i	0.296376	−	0.513339i	0.975304	+	0.220866i	$0.0708884\pi$
$972$		0			0
$973$	1.50977	+	13.5908i	0.0484010	+	0.435702i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.1685	+	21.0764i	0.389303	+	0.674293i	0.992356	−	0.123408i	$-0.0393825\pi$
$977$	12.1685	+	21.0764i	0.389303	+	0.674293i	−0.603053	+	0.797701i	$0.706049\pi$
$978$		0			0
$979$	−9.81201			−0.313593
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.33434	+	7.50729i	0.138244	+	0.239445i	0.926832	−	0.375476i	$-0.122521\pi$
$983$	4.33434	+	7.50729i	0.138244	+	0.239445i	−0.788588	+	0.614922i	$0.789188\pi$
$984$		0			0
$985$	2.42334	−	4.19734i	0.0772139	−	0.133738i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.44823	+	12.9007i	−0.236840	+	0.410219i
$990$		0			0
$991$	27.7527	+	48.0690i	0.881593	+	1.52696i	0.849570	+	0.527476i	$0.176862\pi$
$991$	27.7527	+	48.0690i	0.881593	+	1.52696i	0.0320231	+	0.999487i	$0.489805\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	15.3867			0.487791
$996$		0			0
$997$	17.5596	+	30.4140i	0.556117	+	0.963222i	0.997816	+	0.0660591i	$0.0210426\pi$
$997$	17.5596	+	30.4140i	0.556117	+	0.963222i	−0.441699	+	0.897163i	$0.645624\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2520.2.bi.q.1801.1		6
3.2	odd	2		280.2.q.e.121.1	yes	6
7.4	even	3	inner	2520.2.bi.q.361.1		6
12.11	even	2		560.2.q.l.401.3		6
15.2	even	4		1400.2.bh.i.849.2		12
15.8	even	4		1400.2.bh.i.849.5		12
15.14	odd	2		1400.2.q.j.401.3		6
21.2	odd	6		1960.2.a.w.1.3		3
21.5	even	6		1960.2.a.v.1.1		3
21.11	odd	6		280.2.q.e.81.1	✓	6
21.17	even	6		1960.2.q.w.361.3		6
21.20	even	2		1960.2.q.w.961.3		6
84.11	even	6		560.2.q.l.81.3		6
84.23	even	6		3920.2.a.cc.1.1		3
84.47	odd	6		3920.2.a.cb.1.3		3
105.32	even	12		1400.2.bh.i.249.5		12
105.44	odd	6		9800.2.a.ce.1.1		3
105.53	even	12		1400.2.bh.i.249.2		12
105.74	odd	6		1400.2.q.j.1201.3		6
105.89	even	6		9800.2.a.cf.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.1	✓	6	21.11	odd	6
280.2.q.e.121.1	yes	6	3.2	odd	2
560.2.q.l.81.3		6	84.11	even	6
560.2.q.l.401.3		6	12.11	even	2
1400.2.q.j.401.3		6	15.14	odd	2
1400.2.q.j.1201.3		6	105.74	odd	6
1400.2.bh.i.249.2		12	105.53	even	12
1400.2.bh.i.249.5		12	105.32	even	12
1400.2.bh.i.849.2		12	15.2	even	4
1400.2.bh.i.849.5		12	15.8	even	4
1960.2.a.v.1.1		3	21.5	even	6
1960.2.a.w.1.3		3	21.2	odd	6
1960.2.q.w.361.3		6	21.17	even	6
1960.2.q.w.961.3		6	21.20	even	2
2520.2.bi.q.361.1		6	7.4	even	3	inner
2520.2.bi.q.1801.1		6	1.1	even	1	trivial
3920.2.a.cb.1.3		3	84.47	odd	6
3920.2.a.cc.1.1		3	84.23	even	6
9800.2.a.ce.1.1		3	105.44	odd	6
9800.2.a.cf.1.3		3	105.89	even	6

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:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.bi (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(-0.292113 - 2.62958i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(-0.292113 - 2.62958i) q^{7} +(0.839111 + 1.45338i) q^{11} -4.84667 q^{13} +(1.00000 + 1.73205i) q^{17} +(-3.42334 + 5.92939i) q^{19} +(-1.13122 + 1.95934i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.32178 q^{29} +(-4.58423 - 7.94011i) q^{31} +(-2.42334 - 1.06181i) q^{35} +(1.42334 - 2.46529i) q^{37} -9.52489 q^{41} +6.58423 q^{43} +(-6.10156 + 10.5682i) q^{47} +(-6.82934 + 1.53627i) q^{49} +(3.74511 + 6.48673i) q^{53} +1.67822 q^{55} +(4.00000 + 6.92820i) q^{59} +(3.24511 - 5.62070i) q^{61} +(-2.42334 + 4.19734i) q^{65} +(2.87634 + 4.98196i) q^{67} +(5.84667 + 10.1267i) q^{73} +(3.57666 - 2.63106i) q^{77} +(-2.84667 + 4.93058i) q^{79} +12.5842 q^{83} +2.00000 q^{85} +(-2.92334 + 5.06337i) q^{89} +(1.41577 + 12.7447i) q^{91} +(3.42334 + 5.92939i) q^{95} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 6 q^{7}+O(q^{10}) \) 6 * q + 3 * q^5 + 6 * q^7	\( 6 q + 3 q^{5} + 6 q^{7} + 3 q^{11} + 6 q^{13} + 6 q^{17} - 3 q^{19} + 3 q^{23} - 3 q^{25} - 24 q^{29} - 12 q^{31} + 3 q^{35} - 9 q^{37} - 18 q^{41} + 24 q^{43} - 15 q^{47} - 12 q^{49} + 9 q^{53} + 6 q^{55} + 24 q^{59} + 6 q^{61} + 3 q^{65} - 6 q^{67} + 39 q^{77} + 18 q^{79} + 60 q^{83} + 12 q^{85} + 24 q^{91} + 3 q^{95} - 12 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 + 6 * q^7 + 3 * q^11 + 6 * q^13 + 6 * q^17 - 3 * q^19 + 3 * q^23 - 3 * q^25 - 24 * q^29 - 12 * q^31 + 3 * q^35 - 9 * q^37 - 18 * q^41 + 24 * q^43 - 15 * q^47 - 12 * q^49 + 9 * q^53 + 6 * q^55 + 24 * q^59 + 6 * q^61 + 3 * q^65 - 6 * q^67 + 39 * q^77 + 18 * q^79 + 60 * q^83 + 12 * q^85 + 24 * q^91 + 3 * q^95 - 12 * q^97

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