LMFDB - Embedded newform 2366.2.d.p.337.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(337,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("2366.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.d (of order $2$, degree $1$, not 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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.153664.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} + 6x^{2} + 1 $ x^6 + 5x^4 + 6x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.4
Root			$-1.80194i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.p.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.801938 q^{3} -1.00000 q^{4} -3.04892i q^{5} -0.801938i q^{6} +1.00000i q^{7} -1.00000i q^{8} -2.35690 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.801938 q^{3} -1.00000 q^{4} -3.04892i q^{5} -0.801938i q^{6} +1.00000i q^{7} -1.00000i q^{8} -2.35690 q^{9} +3.04892 q^{10} +1.24698i q^{11} +0.801938 q^{12} -1.00000 q^{14} +2.44504i q^{15} +1.00000 q^{16} +1.13706 q^{17} -2.35690i q^{18} +6.69202i q^{19} +3.04892i q^{20} -0.801938i q^{21} -1.24698 q^{22} +2.93900 q^{23} +0.801938i q^{24} -4.29590 q^{25} +4.29590 q^{27} -1.00000i q^{28} -4.54288 q^{29} -2.44504 q^{30} -1.26875i q^{31} +1.00000i q^{32} -1.00000i q^{33} +1.13706i q^{34} +3.04892 q^{35} +2.35690 q^{36} -9.44504i q^{37} -6.69202 q^{38} -3.04892 q^{40} +10.5429i q^{41} +0.801938 q^{42} +7.89977 q^{43} -1.24698i q^{44} +7.18598i q^{45} +2.93900i q^{46} -6.18060i q^{47} -0.801938 q^{48} -1.00000 q^{49} -4.29590i q^{50} -0.911854 q^{51} +0.405813 q^{53} +4.29590i q^{54} +3.80194 q^{55} +1.00000 q^{56} -5.36658i q^{57} -4.54288i q^{58} -3.07069i q^{59} -2.44504i q^{60} +7.12498 q^{61} +1.26875 q^{62} -2.35690i q^{63} -1.00000 q^{64} +1.00000 q^{66} -9.00969i q^{67} -1.13706 q^{68} -2.35690 q^{69} +3.04892i q^{70} -2.02715i q^{71} +2.35690i q^{72} -16.8334i q^{73} +9.44504 q^{74} +3.44504 q^{75} -6.69202i q^{76} -1.24698 q^{77} +16.3817 q^{79} -3.04892i q^{80} +3.62565 q^{81} -10.5429 q^{82} -4.93900i q^{83} +0.801938i q^{84} -3.46681i q^{85} +7.89977i q^{86} +3.64310 q^{87} +1.24698 q^{88} -2.51142i q^{89} -7.18598 q^{90} -2.93900 q^{92} +1.01746i q^{93} +6.18060 q^{94} +20.4034 q^{95} -0.801938i q^{96} -8.04892i q^{97} -1.00000i q^{98} -2.93900i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} - 6 q^{4} - 6 q^{9}+O(q^{10}) $ 6 * q + 4 * q^3 - 6 * q^4 - 6 * q^9	$ 6 q + 4 q^{3} - 6 q^{4} - 6 q^{9} - 4 q^{12} - 6 q^{14} + 6 q^{16} - 4 q^{17} + 2 q^{22} - 2 q^{23} + 2 q^{25} - 2 q^{27} + 10 q^{29} - 14 q^{30} + 6 q^{36} - 30 q^{38} - 4 q^{42} + 2 q^{43} + 4 q^{48} - 6 q^{49} + 2 q^{51} - 24 q^{53} + 14 q^{55} + 6 q^{56} - 6 q^{61} - 8 q^{62} - 6 q^{64} + 6 q^{66} + 4 q^{68} - 6 q^{69} + 56 q^{74} + 20 q^{75} + 2 q^{77} - 4 q^{79} - 2 q^{81} - 26 q^{82} + 30 q^{87} - 2 q^{88} - 14 q^{90} + 2 q^{92} + 14 q^{94} + 14 q^{95}+O(q^{100}) $ 6 * q + 4 * q^3 - 6 * q^4 - 6 * q^9 - 4 * q^12 - 6 * q^14 + 6 * q^16 - 4 * q^17 + 2 * q^22 - 2 * q^23 + 2 * q^25 - 2 * q^27 + 10 * q^29 - 14 * q^30 + 6 * q^36 - 30 * q^38 - 4 * q^42 + 2 * q^43 + 4 * q^48 - 6 * q^49 + 2 * q^51 - 24 * q^53 + 14 * q^55 + 6 * q^56 - 6 * q^61 - 8 * q^62 - 6 * q^64 + 6 * q^66 + 4 * q^68 - 6 * q^69 + 56 * q^74 + 20 * q^75 + 2 * q^77 - 4 * q^79 - 2 * q^81 - 26 * q^82 + 30 * q^87 - 2 * q^88 - 14 * q^90 + 2 * q^92 + 14 * q^94 + 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2366\mathbb{Z}\right)^\times$.

$n$	$339$	$2199$
$\chi(n)$	$1$	$-1$

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
$3$	−0.801938	−0.462999	−0.231499	−	0.972835i	$-0.574363\pi$
$3$	−0.801938	−0.462999	−0.231499	+	0.972835i	$0.574363\pi$
$4$	−1.00000	−0.500000
$5$	− 3.04892i	− 1.36352i	−0.731577	−	0.681759i	$-0.761215\pi$
$5$	− 3.04892i	− 1.36352i	0.731577	−	0.681759i	$-0.238785\pi$
$6$	− 0.801938i	− 0.327390i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	−2.35690	−0.785632
$10$	3.04892	0.964152
$11$	1.24698i	0.375978i	0.982171	+	0.187989i	$0.0601970\pi$
$11$	1.24698i	0.375978i	−0.982171	+	0.187989i	$0.939803\pi$
$12$	0.801938	0.231499
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	2.44504i	0.631307i
$16$	1.00000	0.250000
$17$	1.13706	0.275778	0.137889	−	0.990448i	$-0.455968\pi$
$17$	1.13706	0.275778	0.137889	+	0.990448i	$0.455968\pi$
$18$	− 2.35690i	− 0.555526i
$19$	6.69202i	1.53526i	0.640896	+	0.767628i	$0.278563\pi$
$19$	6.69202i	1.53526i	−0.640896	+	0.767628i	$0.721437\pi$
$20$	3.04892i	0.681759i
$21$	− 0.801938i	− 0.174997i
$22$	−1.24698	−0.265857
$23$	2.93900	0.612824	0.306412	−	0.951899i	$-0.400871\pi$
$23$	2.93900	0.612824	0.306412	+	0.951899i	$0.400871\pi$
$24$	0.801938i	0.163695i
$25$	−4.29590	−0.859179
$26$	0	0
$27$	4.29590	0.826746
$28$	− 1.00000i	− 0.188982i
$29$	−4.54288	−0.843591	−0.421795	−	0.906691i	$-0.638600\pi$
$29$	−4.54288	−0.843591	−0.421795	+	0.906691i	$0.638600\pi$
$30$	−2.44504	−0.446402
$31$	− 1.26875i	− 0.227874i	−0.993488	−	0.113937i	$-0.963654\pi$
$31$	− 1.26875i	− 0.227874i	0.993488	−	0.113937i	$-0.0363462\pi$
$32$	1.00000i	0.176777i
$33$	− 1.00000i	− 0.174078i
$34$	1.13706i	0.195005i
$35$	3.04892	0.515361
$36$	2.35690	0.392816
$37$	− 9.44504i	− 1.55276i	−0.630268	−	0.776378i	$-0.717055\pi$
$37$	− 9.44504i	− 1.55276i	0.630268	−	0.776378i	$-0.282945\pi$
$38$	−6.69202	−1.08559
$39$	0	0
$40$	−3.04892	−0.482076
$41$	10.5429i	1.64652i	0.567664	+	0.823260i	$0.307847\pi$
$41$	10.5429i	1.64652i	−0.567664	+	0.823260i	$0.692153\pi$
$42$	0.801938	0.123742
$43$	7.89977	1.20470	0.602352	−	0.798231i	$-0.294230\pi$
$43$	7.89977	1.20470	0.602352	+	0.798231i	$0.294230\pi$
$44$	− 1.24698i	− 0.187989i
$45$	7.18598i	1.07122i
$46$	2.93900i	0.433332i
$47$	− 6.18060i	− 0.901534i	−0.892642	−	0.450767i	$-0.851151\pi$
$47$	− 6.18060i	− 0.901534i	0.892642	−	0.450767i	$-0.148849\pi$
$48$	−0.801938	−0.115750
$49$	−1.00000	−0.142857
$50$	− 4.29590i	− 0.607532i
$51$	−0.911854	−0.127685
$52$	0	0
$53$	0.405813	0.0557427	0.0278714	−	0.999612i	$-0.491127\pi$
$53$	0.405813	0.0557427	0.0278714	+	0.999612i	$0.491127\pi$
$54$	4.29590i	0.584598i
$55$	3.80194	0.512653
$56$	1.00000	0.133631
$57$	− 5.36658i	− 0.710821i
$58$	− 4.54288i	− 0.596509i
$59$	− 3.07069i	− 0.399769i	−0.979819	−	0.199885i	$-0.935943\pi$
$59$	− 3.07069i	− 0.399769i	0.979819	−	0.199885i	$-0.0640568\pi$
$60$	− 2.44504i	− 0.315654i
$61$	7.12498	0.912260	0.456130	−	0.889913i	$-0.349235\pi$
$61$	7.12498	0.912260	0.456130	+	0.889913i	$0.349235\pi$
$62$	1.26875	0.161131
$63$	− 2.35690i	− 0.296941i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	− 9.00969i	− 1.10071i	−0.834931	−	0.550354i	$-0.814493\pi$
$67$	− 9.00969i	− 1.10071i	0.834931	−	0.550354i	$-0.185507\pi$
$68$	−1.13706	−0.137889
$69$	−2.35690	−0.283737
$70$	3.04892i	0.364415i
$71$	− 2.02715i	− 0.240578i	−0.992739	−	0.120289i	$-0.961618\pi$
$71$	− 2.02715i	− 0.240578i	0.992739	−	0.120289i	$-0.0383821\pi$
$72$	2.35690i	0.277763i
$73$	− 16.8334i	− 1.97020i	−0.171982	−	0.985100i	$-0.555017\pi$
$73$	− 16.8334i	− 1.97020i	0.171982	−	0.985100i	$-0.444983\pi$
$74$	9.44504	1.09796
$75$	3.44504	0.397799
$76$	− 6.69202i	− 0.767628i
$77$	−1.24698	−0.142107
$78$	0	0
$79$	16.3817	1.84308	0.921540	−	0.388284i	$-0.126932\pi$
$79$	16.3817	1.84308	0.921540	+	0.388284i	$0.126932\pi$
$80$	− 3.04892i	− 0.340879i
$81$	3.62565	0.402850
$82$	−10.5429	−1.16427
$83$	− 4.93900i	− 0.542126i	−0.962562	−	0.271063i	$-0.912625\pi$
$83$	− 4.93900i	− 0.542126i	0.962562	−	0.271063i	$-0.0873751\pi$
$84$	0.801938i	0.0874986i
$85$	− 3.46681i	− 0.376029i
$86$	7.89977i	0.851854i
$87$	3.64310	0.390582
$88$	1.24698	0.132928
$89$	− 2.51142i	− 0.266210i	−0.991102	−	0.133105i	$-0.957505\pi$
$89$	− 2.51142i	− 0.266210i	0.991102	−	0.133105i	$-0.0424947\pi$
$90$	−7.18598	−0.757469
$91$	0	0
$92$	−2.93900	−0.306412
$93$	1.01746i	0.105506i
$94$	6.18060	0.637481
$95$	20.4034	2.09335
$96$	− 0.801938i	− 0.0818474i
$97$	− 8.04892i	− 0.817244i	−0.912704	−	0.408622i	$-0.866009\pi$
$97$	− 8.04892i	− 0.817244i	0.912704	−	0.408622i	$-0.133991\pi$
$98$	− 1.00000i	− 0.101015i
$99$	− 2.93900i	− 0.295381i
$100$	4.29590	0.429590
$101$	−0.0609989	−0.00606962	−0.00303481	−	0.999995i	$-0.500966\pi$
$101$	−0.0609989	−0.00606962	−0.00303481	+	0.999995i	$0.500966\pi$
$102$	− 0.911854i	− 0.0902870i
$103$	−11.3817	−1.12147	−0.560734	−	0.827996i	$-0.689481\pi$
$103$	−11.3817	−1.12147	−0.560734	+	0.827996i	$0.689481\pi$
$104$	0	0
$105$	−2.44504	−0.238612
$106$	0.405813i	0.0394161i
$107$	18.2784	1.76704	0.883522	−	0.468390i	$-0.155166\pi$
$107$	18.2784	1.76704	0.883522	+	0.468390i	$0.155166\pi$
$108$	−4.29590	−0.413373
$109$	13.7506i	1.31707i	0.752550	+	0.658536i	$0.228824\pi$
$109$	13.7506i	1.31707i	−0.752550	+	0.658536i	$0.771176\pi$
$110$	3.80194i	0.362501i
$111$	7.57434i	0.718924i
$112$	1.00000i	0.0944911i
$113$	−11.0925	−1.04349	−0.521745	−	0.853101i	$-0.674719\pi$
$113$	−11.0925	−1.04349	−0.521745	+	0.853101i	$0.674719\pi$
$114$	5.36658	0.502627
$115$	− 8.96077i	− 0.835596i
$116$	4.54288	0.421795
$117$	0	0
$118$	3.07069	0.282680
$119$	1.13706i	0.104234i
$120$	2.44504	0.223201
$121$	9.44504	0.858640
$122$	7.12498i	0.645066i
$123$	− 8.45473i	− 0.762337i
$124$	1.26875i	0.113937i
$125$	− 2.14675i	− 0.192011i
$126$	2.35690	0.209969
$127$	16.4722	1.46167	0.730835	−	0.682554i	$-0.239131\pi$
$127$	16.4722	1.46167	0.730835	+	0.682554i	$0.239131\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−6.33513	−0.557777
$130$	0	0
$131$	−10.0707	−0.879880	−0.439940	−	0.898027i	$-0.645000\pi$
$131$	−10.0707	−0.879880	−0.439940	+	0.898027i	$0.645000\pi$
$132$	1.00000i	0.0870388i
$133$	−6.69202	−0.580272
$134$	9.00969	0.778319
$135$	− 13.0978i	− 1.12728i
$136$	− 1.13706i	− 0.0975024i
$137$	11.3720i	0.971572i	0.874078	+	0.485786i	$0.161467\pi$
$137$	11.3720i	0.971572i	−0.874078	+	0.485786i	$0.838533\pi$
$138$	− 2.35690i	− 0.200632i
$139$	−5.78017	−0.490267	−0.245134	−	0.969489i	$-0.578832\pi$
$139$	−5.78017	−0.490267	−0.245134	+	0.969489i	$0.578832\pi$
$140$	−3.04892	−0.257681
$141$	4.95646i	0.417409i
$142$	2.02715	0.170114
$143$	0	0
$144$	−2.35690	−0.196408
$145$	13.8509i	1.15025i
$146$	16.8334	1.39314
$147$	0.801938	0.0661427
$148$	9.44504i	0.776378i
$149$	− 21.5211i	− 1.76308i	−0.472111	−	0.881539i	$-0.656508\pi$
$149$	− 21.5211i	− 1.76308i	0.472111	−	0.881539i	$-0.343492\pi$
$150$	3.44504i	0.281286i
$151$	− 19.2892i	− 1.56973i	−0.619665	−	0.784866i	$-0.712732\pi$
$151$	− 19.2892i	− 1.56973i	0.619665	−	0.784866i	$-0.287268\pi$
$152$	6.69202	0.542795
$153$	−2.67994	−0.216660
$154$	− 1.24698i	− 0.100484i
$155$	−3.86831	−0.310710
$156$	0	0
$157$	22.3424	1.78312	0.891560	−	0.452903i	$-0.149612\pi$
$157$	22.3424	1.78312	0.891560	+	0.452903i	$0.149612\pi$
$158$	16.3817i	1.30325i
$159$	−0.325437	−0.0258088
$160$	3.04892	0.241038
$161$	2.93900i	0.231626i
$162$	3.62565i	0.284858i
$163$	− 10.3351i	− 0.809510i	−0.914425	−	0.404755i	$-0.867357\pi$
$163$	− 10.3351i	− 0.809510i	0.914425	−	0.404755i	$-0.132643\pi$
$164$	− 10.5429i	− 0.823260i
$165$	−3.04892	−0.237358
$166$	4.93900	0.383341
$167$	17.3991i	1.34638i	0.739468	+	0.673192i	$0.235077\pi$
$167$	17.3991i	1.34638i	−0.739468	+	0.673192i	$0.764923\pi$
$168$	−0.801938	−0.0618708
$169$	0	0
$170$	3.46681	0.265892
$171$	− 15.7724i	− 1.20615i
$172$	−7.89977	−0.602352
$173$	1.41119	0.107291	0.0536454	−	0.998560i	$-0.482916\pi$
$173$	1.41119	0.107291	0.0536454	+	0.998560i	$0.482916\pi$
$174$	3.64310i	0.276183i
$175$	− 4.29590i	− 0.324739i
$176$	1.24698i	0.0939946i
$177$	2.46250i	0.185093i
$178$	2.51142	0.188239
$179$	−10.1293	−0.757099	−0.378549	−	0.925581i	$-0.623577\pi$
$179$	−10.1293	−0.757099	−0.378549	+	0.925581i	$0.623577\pi$
$180$	− 7.18598i	− 0.535611i
$181$	22.0194	1.63669	0.818344	−	0.574729i	$-0.194893\pi$
$181$	22.0194	1.63669	0.818344	+	0.574729i	$0.194893\pi$
$182$	0	0
$183$	−5.71379	−0.422376
$184$	− 2.93900i	− 0.216666i
$185$	−28.7972	−2.11721
$186$	−1.01746	−0.0746037
$187$	1.41789i	0.103687i
$188$	6.18060i	0.450767i
$189$	4.29590i	0.312481i
$190$	20.4034i	1.48022i
$191$	13.6093	0.984731	0.492365	−	0.870389i	$-0.336132\pi$
$191$	13.6093	0.984731	0.492365	+	0.870389i	$0.336132\pi$
$192$	0.801938	0.0578749
$193$	8.13706i	0.585719i	0.956156	+	0.292859i	$0.0946068\pi$
$193$	8.13706i	0.585719i	−0.956156	+	0.292859i	$0.905393\pi$
$194$	8.04892	0.577879
$195$	0	0
$196$	1.00000	0.0714286
$197$	25.0398i	1.78401i	0.452022	+	0.892007i	$0.350703\pi$
$197$	25.0398i	1.78401i	−0.452022	+	0.892007i	$0.649297\pi$
$198$	2.93900	0.208866
$199$	−4.68233	−0.331922	−0.165961	−	0.986132i	$-0.553073\pi$
$199$	−4.68233	−0.331922	−0.165961	+	0.986132i	$0.553073\pi$
$200$	4.29590i	0.303766i
$201$	7.22521i	0.509627i
$202$	− 0.0609989i	− 0.00429187i
$203$	− 4.54288i	− 0.318847i
$204$	0.911854	0.0638425
$205$	32.1444	2.24506
$206$	− 11.3817i	− 0.792997i
$207$	−6.92692	−0.481454
$208$	0	0
$209$	−8.34481	−0.577223
$210$	− 2.44504i	− 0.168724i
$211$	3.36765	0.231839	0.115919	−	0.993259i	$-0.463019\pi$
$211$	3.36765	0.231839	0.115919	+	0.993259i	$0.463019\pi$
$212$	−0.405813	−0.0278714
$213$	1.62565i	0.111387i
$214$	18.2784i	1.24949i
$215$	− 24.0858i	− 1.64263i
$216$	− 4.29590i	− 0.292299i
$217$	1.26875	0.0861284
$218$	−13.7506	−0.931310
$219$	13.4993i	0.912201i
$220$	−3.80194	−0.256327
$221$	0	0
$222$	−7.57434	−0.508356
$223$	13.1631i	0.881469i	0.897637	+	0.440735i	$0.145282\pi$
$223$	13.1631i	0.881469i	−0.897637	+	0.440735i	$0.854718\pi$
$224$	−1.00000	−0.0668153
$225$	10.1250	0.674999
$226$	− 11.0925i	− 0.737859i
$227$	16.6950i	1.10809i	0.832488	+	0.554043i	$0.186916\pi$
$227$	16.6950i	1.10809i	−0.832488	+	0.554043i	$0.813084\pi$
$228$	5.36658i	0.355411i
$229$	− 13.6256i	− 0.900408i	−0.892926	−	0.450204i	$-0.851351\pi$
$229$	− 13.6256i	− 0.900408i	0.892926	−	0.450204i	$-0.148649\pi$
$230$	8.96077	0.590856
$231$	1.00000	0.0657952
$232$	4.54288i	0.298254i
$233$	12.4112	0.813084	0.406542	−	0.913632i	$-0.366734\pi$
$233$	12.4112	0.813084	0.406542	+	0.913632i	$0.366734\pi$
$234$	0	0
$235$	−18.8442	−1.22926
$236$	3.07069i	0.199885i
$237$	−13.1371	−0.853344
$238$	−1.13706	−0.0737049
$239$	13.4843i	0.872225i	0.899892	+	0.436112i	$0.143645\pi$
$239$	13.4843i	0.872225i	−0.899892	+	0.436112i	$0.856355\pi$
$240$	2.44504i	0.157827i
$241$	11.6485i	0.750345i	0.926955	+	0.375172i	$0.122416\pi$
$241$	11.6485i	0.750345i	−0.926955	+	0.375172i	$0.877584\pi$
$242$	9.44504i	0.607150i
$243$	−15.7952	−1.01326
$244$	−7.12498	−0.456130
$245$	3.04892i	0.194788i
$246$	8.45473	0.539054
$247$	0	0
$248$	−1.26875	−0.0805657
$249$	3.96077i	0.251004i
$250$	2.14675	0.135773
$251$	7.60925	0.480292	0.240146	−	0.970737i	$-0.422805\pi$
$251$	7.60925	0.480292	0.240146	+	0.970737i	$0.422805\pi$
$252$	2.35690i	0.148470i
$253$	3.66487i	0.230409i
$254$	16.4722i	1.03356i
$255$	2.78017i	0.174101i
$256$	1.00000	0.0625000
$257$	−13.7385	−0.856987	−0.428493	−	0.903545i	$-0.640956\pi$
$257$	−13.7385	−0.856987	−0.428493	+	0.903545i	$0.640956\pi$
$258$	− 6.33513i	− 0.394408i
$259$	9.44504	0.586886
$260$	0	0
$261$	10.7071	0.662752
$262$	− 10.0707i	− 0.622169i
$263$	−1.70841	−0.105345	−0.0526727	−	0.998612i	$-0.516774\pi$
$263$	−1.70841	−0.105345	−0.0526727	+	0.998612i	$0.516774\pi$
$264$	−1.00000	−0.0615457
$265$	− 1.23729i	− 0.0760062i
$266$	− 6.69202i	− 0.410314i
$267$	2.01400i	0.123255i
$268$	9.00969i	0.550354i
$269$	−2.14138	−0.130562	−0.0652810	−	0.997867i	$-0.520794\pi$
$269$	−2.14138	−0.130562	−0.0652810	+	0.997867i	$0.520794\pi$
$270$	13.0978	0.797109
$271$	− 12.4354i	− 0.755394i	−0.925929	−	0.377697i	$-0.876716\pi$
$271$	− 12.4354i	− 0.755394i	0.925929	−	0.377697i	$-0.123284\pi$
$272$	1.13706	0.0689446
$273$	0	0
$274$	−11.3720	−0.687005
$275$	− 5.35690i	− 0.323033i
$276$	2.35690	0.141868
$277$	1.20477	0.0723874	0.0361937	−	0.999345i	$-0.488477\pi$
$277$	1.20477	0.0723874	0.0361937	+	0.999345i	$0.488477\pi$
$278$	− 5.78017i	− 0.346671i
$279$	2.99031i	0.179025i
$280$	− 3.04892i	− 0.182208i
$281$	12.9922i	0.775051i	0.921859	+	0.387526i	$0.126670\pi$
$281$	12.9922i	0.775051i	−0.921859	+	0.387526i	$0.873330\pi$
$282$	−4.95646	−0.295153
$283$	13.7047	0.814660	0.407330	−	0.913281i	$-0.366460\pi$
$283$	13.7047	0.814660	0.407330	+	0.913281i	$0.366460\pi$
$284$	2.02715i	0.120289i
$285$	−16.3623	−0.969217
$286$	0	0
$287$	−10.5429	−0.622326
$288$	− 2.35690i	− 0.138881i
$289$	−15.7071	−0.923946
$290$	−13.8509	−0.813350
$291$	6.45473i	0.378383i
$292$	16.8334i	0.985100i
$293$	− 18.7832i	− 1.09732i	−0.836044	−	0.548662i	$-0.815138\pi$
$293$	− 18.7832i	− 1.09732i	0.836044	−	0.548662i	$-0.184862\pi$
$294$	0.801938i	0.0467700i
$295$	−9.36227	−0.545093
$296$	−9.44504	−0.548982
$297$	5.35690i	0.310839i
$298$	21.5211	1.24668
$299$	0	0
$300$	−3.44504	−0.198900
$301$	7.89977i	0.455335i
$302$	19.2892	1.10997
$303$	0.0489173	0.00281023
$304$	6.69202i	0.383814i
$305$	− 21.7235i	− 1.24388i
$306$	− 2.67994i	− 0.153202i
$307$	14.7356i	0.841003i	0.907292	+	0.420501i	$0.138146\pi$
$307$	14.7356i	0.841003i	−0.907292	+	0.420501i	$0.861854\pi$
$308$	1.24698	0.0710533
$309$	9.12737	0.519238
$310$	− 3.86831i	− 0.219705i
$311$	−2.45175	−0.139026	−0.0695129	−	0.997581i	$-0.522145\pi$
$311$	−2.45175	−0.139026	−0.0695129	+	0.997581i	$0.522145\pi$
$312$	0	0
$313$	−2.25236	−0.127311	−0.0636554	−	0.997972i	$-0.520276\pi$
$313$	−2.25236	−0.127311	−0.0636554	+	0.997972i	$0.520276\pi$
$314$	22.3424i	1.26086i
$315$	−7.18598	−0.404884
$316$	−16.3817	−0.921540
$317$	− 9.17928i	− 0.515559i	−0.966204	−	0.257780i	$-0.917009\pi$
$317$	− 9.17928i	− 0.515559i	0.966204	−	0.257780i	$-0.0829909\pi$
$318$	− 0.325437i	− 0.0182496i
$319$	− 5.66487i	− 0.317172i
$320$	3.04892i	0.170440i
$321$	−14.6582	−0.818139
$322$	−2.93900	−0.163784
$323$	7.60925i	0.423390i
$324$	−3.62565	−0.201425
$325$	0	0
$326$	10.3351	0.572410
$327$	− 11.0271i	− 0.609803i
$328$	10.5429	0.582133
$329$	6.18060	0.340748
$330$	− 3.04892i	− 0.167837i
$331$	− 4.62565i	− 0.254248i	−0.991887	−	0.127124i	$-0.959425\pi$
$331$	− 4.62565i	− 0.254248i	0.991887	−	0.127124i	$-0.0405747\pi$
$332$	4.93900i	0.271063i
$333$	22.2610i	1.21989i
$334$	−17.3991	−0.952037
$335$	−27.4698	−1.50084
$336$	− 0.801938i	− 0.0437493i
$337$	9.90648	0.539640	0.269820	−	0.962911i	$-0.413036\pi$
$337$	9.90648	0.539640	0.269820	+	0.962911i	$0.413036\pi$
$338$	0	0
$339$	8.89546	0.483135
$340$	3.46681i	0.188014i
$341$	1.58211	0.0856758
$342$	15.7724	0.852874
$343$	− 1.00000i	− 0.0539949i
$344$	− 7.89977i	− 0.425927i
$345$	7.18598i	0.386880i
$346$	1.41119i	0.0758660i
$347$	24.0659	1.29193	0.645963	−	0.763369i	$-0.276456\pi$
$347$	24.0659	1.29193	0.645963	+	0.763369i	$0.276456\pi$
$348$	−3.64310	−0.195291
$349$	18.0140i	0.964267i	0.876098	+	0.482134i	$0.160138\pi$
$349$	18.0140i	0.964267i	−0.876098	+	0.482134i	$0.839862\pi$
$350$	4.29590	0.229625
$351$	0	0
$352$	−1.24698	−0.0664642
$353$	− 12.9734i	− 0.690507i	−0.938510	−	0.345253i	$-0.887793\pi$
$353$	− 12.9734i	− 0.690507i	0.938510	−	0.345253i	$-0.112207\pi$
$354$	−2.46250	−0.130880
$355$	−6.18060	−0.328032
$356$	2.51142i	0.133105i
$357$	− 0.911854i	− 0.0482604i
$358$	− 10.1293i	− 0.535350i
$359$	− 7.04892i	− 0.372028i	−0.982547	−	0.186014i	$-0.940443\pi$
$359$	− 7.04892i	− 0.372028i	0.982547	−	0.186014i	$-0.0595569\pi$
$360$	7.18598	0.378734
$361$	−25.7832	−1.35701
$362$	22.0194i	1.15731i
$363$	−7.57434	−0.397550
$364$	0	0
$365$	−51.3236	−2.68640
$366$	− 5.71379i	− 0.298665i
$367$	17.3623	0.906303	0.453152	−	0.891433i	$-0.350300\pi$
$367$	17.3623	0.906303	0.453152	+	0.891433i	$0.350300\pi$
$368$	2.93900	0.153206
$369$	− 24.8485i	− 1.29356i
$370$	− 28.7972i	− 1.49709i
$371$	0.405813i	0.0210688i
$372$	− 1.01746i	− 0.0527528i
$373$	−7.67456	−0.397374	−0.198687	−	0.980063i	$-0.563668\pi$
$373$	−7.67456	−0.397374	−0.198687	+	0.980063i	$0.563668\pi$
$374$	−1.41789	−0.0733176
$375$	1.72156i	0.0889011i
$376$	−6.18060	−0.318740
$377$	0	0
$378$	−4.29590	−0.220957
$379$	7.51035i	0.385781i	0.981220	+	0.192890i	$0.0617862\pi$
$379$	7.51035i	0.385781i	−0.981220	+	0.192890i	$0.938214\pi$
$380$	−20.4034	−1.04667
$381$	−13.2097	−0.676752
$382$	13.6093i	0.696310i
$383$	− 33.7808i	− 1.72612i	−0.505105	−	0.863058i	$-0.668546\pi$
$383$	− 33.7808i	− 1.72612i	0.505105	−	0.863058i	$-0.331454\pi$
$384$	0.801938i	0.0409237i
$385$	3.80194i	0.193765i
$386$	−8.13706	−0.414166
$387$	−18.6189	−0.946454
$388$	8.04892i	0.408622i
$389$	26.0019	1.31835	0.659175	−	0.751990i	$-0.270906\pi$
$389$	26.0019	1.31835	0.659175	+	0.751990i	$0.270906\pi$
$390$	0	0
$391$	3.34183	0.169004
$392$	1.00000i	0.0505076i
$393$	8.07606	0.407384
$394$	−25.0398	−1.26149
$395$	− 49.9463i	− 2.51307i
$396$	2.93900i	0.147690i
$397$	− 28.0277i	− 1.40667i	−0.710858	−	0.703336i	$-0.751693\pi$
$397$	− 28.0277i	− 1.40667i	0.710858	−	0.703336i	$-0.248307\pi$
$398$	− 4.68233i	− 0.234704i
$399$	5.36658	0.268665
$400$	−4.29590	−0.214795
$401$	− 29.5338i	− 1.47485i	−0.675431	−	0.737423i	$-0.736042\pi$
$401$	− 29.5338i	− 1.47485i	0.675431	−	0.737423i	$-0.263958\pi$
$402$	−7.22521	−0.360361
$403$	0	0
$404$	0.0609989	0.00303481
$405$	− 11.0543i	− 0.549292i
$406$	4.54288	0.225459
$407$	11.7778	0.583803
$408$	0.911854i	0.0451435i
$409$	31.1943i	1.54246i	0.636556	+	0.771230i	$0.280358\pi$
$409$	31.1943i	1.54246i	−0.636556	+	0.771230i	$0.719642\pi$
$410$	32.1444i	1.58750i
$411$	− 9.11960i	− 0.449837i
$412$	11.3817	0.560734
$413$	3.07069	0.151099
$414$	− 6.92692i	− 0.340440i
$415$	−15.0586	−0.739198
$416$	0	0
$417$	4.63533	0.226993
$418$	− 8.34481i	− 0.408158i
$419$	−8.83041	−0.431394	−0.215697	−	0.976460i	$-0.569202\pi$
$419$	−8.83041	−0.431394	−0.215697	+	0.976460i	$0.569202\pi$
$420$	2.44504	0.119306
$421$	33.7700i	1.64585i	0.568151	+	0.822925i	$0.307659\pi$
$421$	33.7700i	1.64585i	−0.568151	+	0.822925i	$0.692341\pi$
$422$	3.36765i	0.163935i
$423$	14.5670i	0.708274i
$424$	− 0.405813i	− 0.0197080i
$425$	−4.88471	−0.236943
$426$	−1.62565	−0.0787628
$427$	7.12498i	0.344802i
$428$	−18.2784	−0.883522
$429$	0	0
$430$	24.0858	1.16152
$431$	− 38.7875i	− 1.86833i	−0.356846	−	0.934163i	$-0.616148\pi$
$431$	− 38.7875i	− 1.86833i	0.356846	−	0.934163i	$-0.383852\pi$
$432$	4.29590	0.206686
$433$	−9.77777	−0.469890	−0.234945	−	0.972009i	$-0.575491\pi$
$433$	−9.77777	−0.469890	−0.234945	+	0.972009i	$0.575491\pi$
$434$	1.26875i	0.0609019i
$435$	− 11.1075i	− 0.532565i
$436$	− 13.7506i	− 0.658536i
$437$	19.6679i	0.940841i
$438$	−13.4993	−0.645023
$439$	−21.2591	−1.01464	−0.507320	−	0.861758i	$-0.669364\pi$
$439$	−21.2591	−1.01464	−0.507320	+	0.861758i	$0.669364\pi$
$440$	− 3.80194i	− 0.181250i
$441$	2.35690	0.112233
$442$	0	0
$443$	32.7047	1.55385	0.776923	−	0.629595i	$-0.216779\pi$
$443$	32.7047	1.55385	0.776923	+	0.629595i	$0.216779\pi$
$444$	− 7.57434i	− 0.359462i
$445$	−7.65710	−0.362982
$446$	−13.1631	−0.623293
$447$	17.2586i	0.816303i
$448$	− 1.00000i	− 0.0472456i
$449$	4.80300i	0.226668i	0.993557	+	0.113334i	$0.0361530\pi$
$449$	4.80300i	0.226668i	−0.993557	+	0.113334i	$0.963847\pi$
$450$	10.1250i	0.477296i
$451$	−13.1468	−0.619056
$452$	11.0925	0.521745
$453$	15.4687i	0.726784i
$454$	−16.6950	−0.783535
$455$	0	0
$456$	−5.36658	−0.251313
$457$	− 30.2693i	− 1.41594i	−0.706242	−	0.707970i	$-0.749611\pi$
$457$	− 30.2693i	− 1.41594i	0.706242	−	0.707970i	$-0.250389\pi$
$458$	13.6256	0.636685
$459$	4.88471	0.227999
$460$	8.96077i	0.417798i
$461$	13.8974i	0.647265i	0.946183	+	0.323633i	$0.104904\pi$
$461$	13.8974i	0.647265i	−0.946183	+	0.323633i	$0.895096\pi$
$462$	1.00000i	0.0465242i
$463$	0.610580i	0.0283761i	0.999899	+	0.0141880i	$0.00451634\pi$
$463$	0.610580i	0.0283761i	−0.999899	+	0.0141880i	$0.995484\pi$
$464$	−4.54288	−0.210898
$465$	3.10215	0.143859
$466$	12.4112i	0.574937i
$467$	−13.7530	−0.636414	−0.318207	−	0.948021i	$-0.603081\pi$
$467$	−13.7530	−0.636414	−0.318207	+	0.948021i	$0.603081\pi$
$468$	0	0
$469$	9.00969	0.416029
$470$	− 18.8442i	− 0.869216i
$471$	−17.9172	−0.825582
$472$	−3.07069	−0.141340
$473$	9.85086i	0.452943i
$474$	− 13.1371i	− 0.603405i
$475$	− 28.7482i	− 1.31906i
$476$	− 1.13706i	− 0.0521172i
$477$	−0.956459	−0.0437933
$478$	−13.4843	−0.616756
$479$	− 29.3043i	− 1.33895i	−0.742837	−	0.669473i	$-0.766520\pi$
$479$	− 29.3043i	− 1.33895i	0.742837	−	0.669473i	$-0.233480\pi$
$480$	−2.44504	−0.111600
$481$	0	0
$482$	−11.6485	−0.530574
$483$	− 2.35690i	− 0.107242i
$484$	−9.44504	−0.429320
$485$	−24.5405	−1.11433
$486$	− 15.7952i	− 0.716486i
$487$	− 12.5496i	− 0.568676i	−0.958724	−	0.284338i	$-0.908226\pi$
$487$	− 12.5496i	− 0.568676i	0.958724	−	0.284338i	$-0.0917738\pi$
$488$	− 7.12498i	− 0.322533i
$489$	8.28813i	0.374802i
$490$	−3.04892	−0.137736
$491$	−31.0267	−1.40021	−0.700107	−	0.714038i	$-0.746864\pi$
$491$	−31.0267	−1.40021	−0.700107	+	0.714038i	$0.746864\pi$
$492$	8.45473i	0.381169i
$493$	−5.16554	−0.232644
$494$	0	0
$495$	−8.96077	−0.402757
$496$	− 1.26875i	− 0.0569686i
$497$	2.02715	0.0909300
$498$	−3.96077	−0.177486
$499$	31.6728i	1.41787i	0.705275	+	0.708934i	$0.250823\pi$
$499$	31.6728i	1.41787i	−0.705275	+	0.708934i	$0.749177\pi$
$500$	2.14675i	0.0960057i
$501$	− 13.9530i	− 0.623374i
$502$	7.60925i	0.339618i
$503$	−16.3599	−0.729451	−0.364725	−	0.931115i	$-0.618837\pi$
$503$	−16.3599	−0.729451	−0.364725	+	0.931115i	$0.618837\pi$
$504$	−2.35690	−0.104984
$505$	0.185981i	0.00827603i
$506$	−3.66487	−0.162924
$507$	0	0
$508$	−16.4722	−0.730835
$509$	− 10.3230i	− 0.457561i	−0.973478	−	0.228780i	$-0.926526\pi$
$509$	− 10.3230i	− 0.457561i	0.973478	−	0.228780i	$-0.0734738\pi$
$510$	−2.78017	−0.123108
$511$	16.8334	0.744666
$512$	1.00000i	0.0441942i
$513$	28.7482i	1.26927i
$514$	− 13.7385i	− 0.605981i
$515$	34.7017i	1.52914i
$516$	6.33513	0.278888
$517$	7.70709	0.338957
$518$	9.44504i	0.414991i
$519$	−1.13169	−0.0496755
$520$	0	0
$521$	26.5512	1.16323	0.581615	−	0.813464i	$-0.302421\pi$
$521$	26.5512	1.16323	0.581615	+	0.813464i	$0.302421\pi$
$522$	10.7071i	0.468636i
$523$	34.9323	1.52748	0.763741	−	0.645522i	$-0.223360\pi$
$523$	34.9323	1.52748	0.763741	+	0.645522i	$0.223360\pi$
$524$	10.0707	0.439940
$525$	3.44504i	0.150354i
$526$	− 1.70841i	− 0.0744904i
$527$	− 1.44265i	− 0.0628428i
$528$	− 1.00000i	− 0.0435194i
$529$	−14.3623	−0.624447
$530$	1.23729	0.0537445
$531$	7.23729i	0.314072i
$532$	6.69202	0.290136
$533$	0	0
$534$	−2.01400	−0.0871543
$535$	− 55.7294i	− 2.40939i
$536$	−9.00969	−0.389159
$537$	8.12306	0.350536
$538$	− 2.14138i	− 0.0923212i
$539$	− 1.24698i	− 0.0537112i
$540$	13.0978i	0.563641i
$541$	− 44.0019i	− 1.89179i	−0.324473	−	0.945895i	$-0.605187\pi$
$541$	− 44.0019i	− 1.89179i	0.324473	−	0.945895i	$-0.394813\pi$
$542$	12.4354	0.534144
$543$	−17.6582	−0.757785
$544$	1.13706i	0.0487512i
$545$	41.9245	1.79585
$546$	0	0
$547$	10.3515	0.442599	0.221299	−	0.975206i	$-0.428970\pi$
$547$	10.3515	0.442599	0.221299	+	0.975206i	$0.428970\pi$
$548$	− 11.3720i	− 0.485786i
$549$	−16.7928	−0.716701
$550$	5.35690	0.228419
$551$	− 30.4010i	− 1.29513i
$552$	2.35690i	0.100316i
$553$	16.3817i	0.696619i
$554$	1.20477i	0.0511856i
$555$	23.0935	0.980265
$556$	5.78017	0.245134
$557$	16.7041i	0.707776i	0.935288	+	0.353888i	$0.115141\pi$
$557$	16.7041i	0.707776i	−0.935288	+	0.353888i	$0.884859\pi$
$558$	−2.99031	−0.126590
$559$	0	0
$560$	3.04892	0.128840
$561$	− 1.13706i	− 0.0480069i
$562$	−12.9922	−0.548044
$563$	−42.1933	−1.77823	−0.889117	−	0.457679i	$-0.848681\pi$
$563$	−42.1933	−1.77823	−0.889117	+	0.457679i	$0.848681\pi$
$564$	− 4.95646i	− 0.208705i
$565$	33.8200i	1.42282i
$566$	13.7047i	0.576051i
$567$	3.62565i	0.152263i
$568$	−2.02715	−0.0850572
$569$	−9.05993	−0.379812	−0.189906	−	0.981802i	$-0.560818\pi$
$569$	−9.05993	−0.379812	−0.189906	+	0.981802i	$0.560818\pi$
$570$	− 16.3623i	− 0.685340i
$571$	26.0355	1.08955	0.544776	−	0.838582i	$-0.316615\pi$
$571$	26.0355	1.08955	0.544776	+	0.838582i	$0.316615\pi$
$572$	0	0
$573$	−10.9138	−0.455929
$574$	− 10.5429i	− 0.440051i
$575$	−12.6256	−0.526526
$576$	2.35690	0.0982040
$577$	− 41.5623i	− 1.73026i	−0.501548	−	0.865130i	$-0.667236\pi$
$577$	− 41.5623i	− 1.73026i	0.501548	−	0.865130i	$-0.332764\pi$
$578$	− 15.7071i	− 0.653329i
$579$	− 6.52542i	− 0.271187i
$580$	− 13.8509i	− 0.575125i
$581$	4.93900	0.204904
$582$	−6.45473	−0.267557
$583$	0.506041i	0.0209581i
$584$	−16.8334	−0.696571
$585$	0	0
$586$	18.7832	0.775925
$587$	− 41.9530i	− 1.73159i	−0.500403	−	0.865793i	$-0.666815\pi$
$587$	− 41.9530i	− 1.73159i	0.500403	−	0.865793i	$-0.333185\pi$
$588$	−0.801938	−0.0330714
$589$	8.49050	0.349845
$590$	− 9.36227i	− 0.385439i
$591$	− 20.0804i	− 0.825996i
$592$	− 9.44504i	− 0.388189i
$593$	28.5991i	1.17442i	0.809433	+	0.587212i	$0.199774\pi$
$593$	28.5991i	1.17442i	−0.809433	+	0.587212i	$0.800226\pi$
$594$	−5.35690	−0.219796
$595$	3.46681	0.142125
$596$	21.5211i	0.881539i
$597$	3.75494	0.153679
$598$	0	0
$599$	6.05131	0.247250	0.123625	−	0.992329i	$-0.460548\pi$
$599$	6.05131	0.247250	0.123625	+	0.992329i	$0.460548\pi$
$600$	− 3.44504i	− 0.140643i
$601$	−3.94033	−0.160729	−0.0803647	−	0.996766i	$-0.525608\pi$
$601$	−3.94033	−0.160729	−0.0803647	+	0.996766i	$0.525608\pi$
$602$	−7.89977	−0.321971
$603$	21.2349i	0.864752i
$604$	19.2892i	0.784866i
$605$	− 28.7972i	− 1.17077i
$606$	0.0489173i	0.00198713i
$607$	−21.4601	−0.871039	−0.435519	−	0.900179i	$-0.643435\pi$
$607$	−21.4601	−0.871039	−0.435519	+	0.900179i	$0.643435\pi$
$608$	−6.69202	−0.271397
$609$	3.64310i	0.147626i
$610$	21.7235	0.879558
$611$	0	0
$612$	2.67994	0.108330
$613$	30.0073i	1.21198i	0.795471	+	0.605992i	$0.207224\pi$
$613$	30.0073i	1.21198i	−0.795471	+	0.605992i	$0.792776\pi$
$614$	−14.7356	−0.594679
$615$	−25.7778	−1.03946
$616$	1.24698i	0.0502422i
$617$	25.5937i	1.03036i	0.857081	+	0.515182i	$0.172276\pi$
$617$	25.5937i	1.03036i	−0.857081	+	0.515182i	$0.827724\pi$
$618$	9.12737i	0.367157i
$619$	0.861609i	0.0346310i	0.999850	+	0.0173155i	$0.00551197\pi$
$619$	0.861609i	0.0346310i	−0.999850	+	0.0173155i	$0.994488\pi$
$620$	3.86831	0.155355
$621$	12.6256	0.506650
$622$	− 2.45175i	− 0.0983061i
$623$	2.51142	0.100618
$624$	0	0
$625$	−28.0248	−1.12099
$626$	− 2.25236i	− 0.0900223i
$627$	6.69202	0.267254
$628$	−22.3424	−0.891560
$629$	− 10.7396i	− 0.428216i
$630$	− 7.18598i	− 0.286296i
$631$	− 16.2034i	− 0.645049i	−0.946561	−	0.322524i	$-0.895469\pi$
$631$	− 16.2034i	− 0.645049i	0.946561	−	0.322524i	$-0.104531\pi$
$632$	− 16.3817i	− 0.651627i
$633$	−2.70065	−0.107341
$634$	9.17928	0.364556
$635$	− 50.2223i	− 1.99301i
$636$	0.325437	0.0129044
$637$	0	0
$638$	5.66487	0.224275
$639$	4.77777i	0.189006i
$640$	−3.04892	−0.120519
$641$	7.74333	0.305843	0.152922	−	0.988238i	$-0.451132\pi$
$641$	7.74333	0.305843	0.152922	+	0.988238i	$0.451132\pi$
$642$	− 14.6582i	− 0.578512i
$643$	− 10.1371i	− 0.399767i	−0.979820	−	0.199883i	$-0.935944\pi$
$643$	− 10.1371i	− 0.399767i	0.979820	−	0.199883i	$-0.0640563\pi$
$644$	− 2.93900i	− 0.115813i
$645$	19.3153i	0.760538i
$646$	−7.60925	−0.299382
$647$	24.3726	0.958184	0.479092	−	0.877765i	$-0.340966\pi$
$647$	24.3726	0.958184	0.479092	+	0.877765i	$0.340966\pi$
$648$	− 3.62565i	− 0.142429i
$649$	3.82908	0.150305
$650$	0	0
$651$	−1.01746	−0.0398773
$652$	10.3351i	0.404755i
$653$	−22.3749	−0.875599	−0.437800	−	0.899073i	$-0.644242\pi$
$653$	−22.3749	−0.875599	−0.437800	+	0.899073i	$0.644242\pi$
$654$	11.0271	0.431196
$655$	30.7047i	1.19973i
$656$	10.5429i	0.411630i
$657$	39.6746i	1.54785i
$658$	6.18060i	0.240945i
$659$	28.7506	1.11997	0.559983	−	0.828504i	$-0.310808\pi$
$659$	28.7506	1.11997	0.559983	+	0.828504i	$0.310808\pi$
$660$	3.04892	0.118679
$661$	27.0629i	1.05263i	0.850291	+	0.526313i	$0.176426\pi$
$661$	27.0629i	1.05263i	−0.850291	+	0.526313i	$0.823574\pi$
$662$	4.62565	0.179781
$663$	0	0
$664$	−4.93900	−0.191670
$665$	20.4034i	0.791211i
$666$	−22.2610	−0.862595
$667$	−13.3515	−0.516973
$668$	− 17.3991i	− 0.673192i
$669$	− 10.5560i	− 0.408119i
$670$	− 27.4698i	− 1.06125i
$671$	8.88471i	0.342990i
$672$	0.801938	0.0309354
$673$	16.6571	0.642084	0.321042	−	0.947065i	$-0.395967\pi$
$673$	16.6571	0.642084	0.321042	+	0.947065i	$0.395967\pi$
$674$	9.90648i	0.381583i
$675$	−18.4547	−0.710323
$676$	0	0
$677$	26.2795	1.01000	0.505002	−	0.863118i	$-0.331492\pi$
$677$	26.2795	1.01000	0.505002	+	0.863118i	$0.331492\pi$
$678$	8.89546i	0.341628i
$679$	8.04892	0.308889
$680$	−3.46681	−0.132946
$681$	− 13.3884i	− 0.513043i
$682$	1.58211i	0.0605819i
$683$	27.7888i	1.06331i	0.846961	+	0.531654i	$0.178429\pi$
$683$	27.7888i	1.06331i	−0.846961	+	0.531654i	$0.821571\pi$
$684$	15.7724i	0.603073i
$685$	34.6722	1.32476
$686$	1.00000	0.0381802
$687$	10.9269i	0.416888i
$688$	7.89977	0.301176
$689$	0	0
$690$	−7.18598	−0.273566
$691$	35.8509i	1.36383i	0.731431	+	0.681915i	$0.238853\pi$
$691$	35.8509i	1.36383i	−0.731431	+	0.681915i	$0.761147\pi$
$692$	−1.41119	−0.0536454
$693$	2.93900	0.111643
$694$	24.0659i	0.913529i
$695$	17.6233i	0.668488i
$696$	− 3.64310i	− 0.138092i
$697$	11.9879i	0.454075i
$698$	−18.0140	−0.681840
$699$	−9.95300	−0.376457
$700$	4.29590i	0.162370i
$701$	38.7995	1.46544	0.732719	−	0.680531i	$-0.238251\pi$
$701$	38.7995	1.46544	0.732719	+	0.680531i	$0.238251\pi$
$702$	0	0
$703$	63.2064	2.38388
$704$	− 1.24698i	− 0.0469973i
$705$	15.1118	0.569145
$706$	12.9734	0.488262
$707$	− 0.0609989i	− 0.00229410i
$708$	− 2.46250i	− 0.0925464i
$709$	11.8683i	0.445724i	0.974850	+	0.222862i	$0.0715399\pi$
$709$	11.8683i	0.445724i	−0.974850	+	0.222862i	$0.928460\pi$
$710$	− 6.18060i	− 0.231954i
$711$	−38.6098	−1.44798
$712$	−2.51142	−0.0941194
$713$	− 3.72886i	− 0.139647i
$714$	0.911854	0.0341253
$715$	0	0
$716$	10.1293	0.378549
$717$	− 10.8135i	− 0.403839i
$718$	7.04892	0.263063
$719$	−41.5036	−1.54782	−0.773912	−	0.633293i	$-0.781703\pi$
$719$	−41.5036	−1.54782	−0.773912	+	0.633293i	$0.781703\pi$
$720$	7.18598i	0.267806i
$721$	− 11.3817i	− 0.423875i
$722$	− 25.7832i	− 0.959550i
$723$	− 9.34136i	− 0.347409i
$724$	−22.0194	−0.818344
$725$	19.5157	0.724796
$726$	− 7.57434i	− 0.281110i
$727$	17.6437	0.654368	0.327184	−	0.944961i	$-0.393900\pi$
$727$	17.6437	0.654368	0.327184	+	0.944961i	$0.393900\pi$
$728$	0	0
$729$	1.78986	0.0662910
$730$	− 51.3236i	− 1.89957i
$731$	8.98254	0.332231
$732$	5.71379	0.211188
$733$	14.5157i	0.536151i	0.963398	+	0.268075i	$0.0863876\pi$
$733$	14.5157i	0.536151i	−0.963398	+	0.268075i	$0.913612\pi$
$734$	17.3623i	0.640853i
$735$	− 2.44504i	− 0.0901867i
$736$	2.93900i	0.108333i
$737$	11.2349	0.413843
$738$	24.8485	0.914685
$739$	− 4.23862i	− 0.155920i	−0.996956	−	0.0779601i	$-0.975159\pi$
$739$	− 4.23862i	− 0.155920i	0.996956	−	0.0779601i	$-0.0248407\pi$
$740$	28.7972	1.05860
$741$	0	0
$742$	−0.405813	−0.0148979
$743$	22.0810i	0.810072i	0.914301	+	0.405036i	$0.132741\pi$
$743$	22.0810i	0.810072i	−0.914301	+	0.405036i	$0.867259\pi$
$744$	1.01746	0.0373018
$745$	−65.6161	−2.40399
$746$	− 7.67456i	− 0.280986i
$747$	11.6407i	0.425911i
$748$	− 1.41789i	− 0.0518434i
$749$	18.2784i	0.667880i
$750$	−1.72156	−0.0628625
$751$	23.6058	0.861388	0.430694	−	0.902498i	$-0.358269\pi$
$751$	23.6058	0.861388	0.430694	+	0.902498i	$0.358269\pi$
$752$	− 6.18060i	− 0.225383i
$753$	−6.10215	−0.222375
$754$	0	0
$755$	−58.8112	−2.14036
$756$	− 4.29590i	− 0.156240i
$757$	19.4024	0.705191	0.352595	−	0.935776i	$-0.385299\pi$
$757$	19.4024	0.705191	0.352595	+	0.935776i	$0.385299\pi$
$758$	−7.51035	−0.272788
$759$	− 2.93900i	− 0.106679i
$760$	− 20.4034i	− 0.740110i
$761$	50.4476i	1.82872i	0.404900	+	0.914361i	$0.367306\pi$
$761$	50.4476i	1.82872i	−0.404900	+	0.914361i	$0.632694\pi$
$762$	− 13.2097i	− 0.478536i
$763$	−13.7506	−0.497806
$764$	−13.6093	−0.492365
$765$	8.17092i	0.295420i
$766$	33.7808	1.22055
$767$	0	0
$768$	−0.801938	−0.0289374
$769$	− 6.40150i	− 0.230844i	−0.993317	−	0.115422i	$-0.963178\pi$
$769$	− 6.40150i	− 0.230844i	0.993317	−	0.115422i	$-0.0368220\pi$
$770$	−3.80194	−0.137012
$771$	11.0175	0.396784
$772$	− 8.13706i	− 0.292859i
$773$	10.9162i	0.392627i	0.980541	+	0.196314i	$0.0628971\pi$
$773$	10.9162i	0.392627i	−0.980541	+	0.196314i	$0.937103\pi$
$774$	− 18.6189i	− 0.669244i
$775$	5.45042i	0.195785i
$776$	−8.04892	−0.288939
$777$	−7.57434	−0.271728
$778$	26.0019i	0.932214i
$779$	−70.5532	−2.52783
$780$	0	0
$781$	2.52781	0.0904522
$782$	3.34183i	0.119504i
$783$	−19.5157	−0.697435
$784$	−1.00000	−0.0357143
$785$	− 68.1202i	− 2.43131i
$786$	8.07606i	0.288064i
$787$	1.94810i	0.0694422i	0.999397	+	0.0347211i	$0.0110543\pi$
$787$	1.94810i	0.0694422i	−0.999397	+	0.0347211i	$0.988946\pi$
$788$	− 25.0398i	− 0.892007i
$789$	1.37004	0.0487748
$790$	49.9463	1.77701
$791$	− 11.0925i	− 0.394402i
$792$	−2.93900	−0.104433
$793$	0	0
$794$	28.0277	0.994667
$795$	0.992230i	0.0351908i
$796$	4.68233	0.165961
$797$	−22.6708	−0.803042	−0.401521	−	0.915850i	$-0.631518\pi$
$797$	−22.6708	−0.803042	−0.401521	+	0.915850i	$0.631518\pi$
$798$	5.36658i	0.189975i
$799$	− 7.02774i	− 0.248624i
$800$	− 4.29590i	− 0.151883i
$801$	5.91915i	0.209143i
$802$	29.5338	1.04287
$803$	20.9909	0.740753
$804$	− 7.22521i	− 0.254813i
$805$	8.96077	0.315826
$806$	0	0
$807$	1.71725	0.0604500
$808$	0.0609989i	0.00214593i
$809$	−36.7162	−1.29087	−0.645436	−	0.763814i	$-0.723324\pi$
$809$	−36.7162	−1.29087	−0.645436	+	0.763814i	$0.723324\pi$
$810$	11.0543	0.388408
$811$	45.8049i	1.60843i	0.594340	+	0.804214i	$0.297414\pi$
$811$	45.8049i	1.60843i	−0.594340	+	0.804214i	$0.702586\pi$
$812$	4.54288i	0.159424i
$813$	9.97238i	0.349747i
$814$	11.7778i	0.412811i
$815$	−31.5109	−1.10378
$816$	−0.911854	−0.0319213
$817$	52.8654i	1.84953i
$818$	−31.1943	−1.09068
$819$	0	0
$820$	−32.1444	−1.12253
$821$	− 10.6910i	− 0.373117i	−0.982444	−	0.186558i	$-0.940267\pi$
$821$	− 10.6910i	− 0.373117i	0.982444	−	0.186558i	$-0.0597334\pi$
$822$	9.11960	0.318083
$823$	−11.3817	−0.396739	−0.198370	−	0.980127i	$-0.563565\pi$
$823$	−11.3817	−0.396739	−0.198370	+	0.980127i	$0.563565\pi$
$824$	11.3817i	0.396499i
$825$	4.29590i	0.149564i
$826$	3.07069i	0.106843i
$827$	− 41.3226i	− 1.43693i	−0.695565	−	0.718463i	$-0.744846\pi$
$827$	− 41.3226i	− 1.43693i	0.695565	−	0.718463i	$-0.255154\pi$
$828$	6.92692	0.240727
$829$	−4.52052	−0.157004	−0.0785020	−	0.996914i	$-0.525014\pi$
$829$	−4.52052	−0.157004	−0.0785020	+	0.996914i	$0.525014\pi$
$830$	− 15.0586i	− 0.522692i
$831$	−0.966148	−0.0335153
$832$	0	0
$833$	−1.13706	−0.0393969
$834$	4.63533i	0.160509i
$835$	53.0484	1.83582
$836$	8.34481	0.288611
$837$	− 5.45042i	− 0.188394i
$838$	− 8.83041i	− 0.305042i
$839$	− 48.3836i	− 1.67039i	−0.549957	−	0.835193i	$-0.685356\pi$
$839$	− 48.3836i	− 1.67039i	0.549957	−	0.835193i	$-0.314644\pi$
$840$	2.44504i	0.0843620i
$841$	−8.36227	−0.288354
$842$	−33.7700	−1.16379
$843$	− 10.4190i	− 0.358848i
$844$	−3.36765	−0.115919
$845$	0	0
$846$	−14.5670	−0.500825
$847$	9.44504i	0.324535i
$848$	0.405813	0.0139357
$849$	−10.9903	−0.377187
$850$	− 4.88471i	− 0.167544i
$851$	− 27.7590i	− 0.951566i
$852$	− 1.62565i	− 0.0556937i
$853$	19.8799i	0.680676i	0.940303	+	0.340338i	$0.110541\pi$
$853$	19.8799i	0.680676i	−0.940303	+	0.340338i	$0.889459\pi$
$854$	−7.12498	−0.243812
$855$	−48.0887	−1.64460
$856$	− 18.2784i	− 0.624744i
$857$	−53.5220	−1.82828	−0.914138	−	0.405404i	$-0.867131\pi$
$857$	−53.5220	−1.82828	−0.914138	+	0.405404i	$0.867131\pi$
$858$	0	0
$859$	27.4276	0.935817	0.467909	−	0.883777i	$-0.345008\pi$
$859$	27.4276	0.935817	0.467909	+	0.883777i	$0.345008\pi$
$860$	24.0858i	0.821317i
$861$	8.45473	0.288136
$862$	38.7875	1.32111
$863$	13.8888i	0.472779i	0.971658	+	0.236389i	$0.0759641\pi$
$863$	13.8888i	0.472779i	−0.971658	+	0.236389i	$0.924036\pi$
$864$	4.29590i	0.146149i
$865$	− 4.30260i	− 0.146293i
$866$	− 9.77777i	− 0.332262i
$867$	12.5961	0.427786
$868$	−1.26875	−0.0430642
$869$	20.4276i	0.692958i
$870$	11.1075	0.376580
$871$	0	0
$872$	13.7506	0.465655
$873$	18.9705i	0.642053i
$874$	−19.6679	−0.665275
$875$	2.14675	0.0725735
$876$	− 13.4993i	− 0.456100i
$877$	49.0297i	1.65561i	0.561013	+	0.827807i	$0.310412\pi$
$877$	49.0297i	1.65561i	−0.561013	+	0.827807i	$0.689588\pi$
$878$	− 21.2591i	− 0.717459i
$879$	15.0629i	0.508060i
$880$	3.80194	0.128163
$881$	−23.5846	−0.794586	−0.397293	−	0.917692i	$-0.630050\pi$
$881$	−23.5846	−0.794586	−0.397293	+	0.917692i	$0.630050\pi$
$882$	2.35690i	0.0793608i
$883$	−1.11828	−0.0376330	−0.0188165	−	0.999823i	$-0.505990\pi$
$883$	−1.11828	−0.0376330	−0.0188165	+	0.999823i	$0.505990\pi$
$884$	0	0
$885$	7.50796	0.252377
$886$	32.7047i	1.09874i
$887$	−3.13228	−0.105172	−0.0525858	−	0.998616i	$-0.516746\pi$
$887$	−3.13228	−0.105172	−0.0525858	+	0.998616i	$0.516746\pi$
$888$	7.57434	0.254178
$889$	16.4722i	0.552459i
$890$	− 7.65710i	− 0.256667i
$891$	4.52111i	0.151463i
$892$	− 13.1631i	− 0.440735i
$893$	41.3607	1.38408
$894$	−17.2586	−0.577214
$895$	30.8834i	1.03232i
$896$	1.00000	0.0334077
$897$	0	0
$898$	−4.80300	−0.160278
$899$	5.76377i	0.192233i
$900$	−10.1250	−0.337499
$901$	0.461435	0.0153726
$902$	− 13.1468i	− 0.437739i
$903$	− 6.33513i	− 0.210820i
$904$	11.0925i	0.368930i
$905$	− 67.1353i	− 2.23165i
$906$	−15.4687	−0.513914
$907$	−3.48725	−0.115792	−0.0578962	−	0.998323i	$-0.518439\pi$
$907$	−3.48725	−0.115792	−0.0578962	+	0.998323i	$0.518439\pi$
$908$	− 16.6950i	− 0.554043i
$909$	0.143768	0.00476849
$910$	0	0
$911$	−45.9288	−1.52169	−0.760845	−	0.648933i	$-0.775215\pi$
$911$	−45.9288	−1.52169	−0.760845	+	0.648933i	$0.775215\pi$
$912$	− 5.36658i	− 0.177705i
$913$	6.15883	0.203828
$914$	30.2693	1.00122
$915$	17.4209i	0.575916i
$916$	13.6256i	0.450204i
$917$	− 10.0707i	− 0.332563i
$918$	4.88471i	0.161219i
$919$	30.9705	1.02162	0.510811	−	0.859693i	$-0.329345\pi$
$919$	30.9705	1.02162	0.510811	+	0.859693i	$0.329345\pi$
$920$	−8.96077	−0.295428
$921$	− 11.8170i	− 0.389383i
$922$	−13.8974	−0.457686
$923$	0	0
$924$	−1.00000	−0.0328976
$925$	40.5749i	1.33410i
$926$	−0.610580	−0.0200649
$927$	26.8254	0.881061
$928$	− 4.54288i	− 0.149127i
$929$	2.55197i	0.0837276i	0.999123	+	0.0418638i	$0.0133296\pi$
$929$	2.55197i	0.0837276i	−0.999123	+	0.0418638i	$0.986670\pi$
$930$	3.10215i	0.101723i
$931$	− 6.69202i	− 0.219322i
$932$	−12.4112	−0.406542
$933$	1.96615	0.0643688
$934$	− 13.7530i	− 0.450013i
$935$	4.32304	0.141379
$936$	0	0
$937$	−52.9480	−1.72973	−0.864867	−	0.502001i	$-0.832597\pi$
$937$	−52.9480	−1.72973	−0.864867	+	0.502001i	$0.832597\pi$
$938$	9.00969i	0.294177i
$939$	1.80625	0.0589447
$940$	18.8442	0.614628
$941$	− 6.85623i	− 0.223507i	−0.993736	−	0.111753i	$-0.964353\pi$
$941$	− 6.85623i	− 0.223507i	0.993736	−	0.111753i	$-0.0356467\pi$
$942$	− 17.9172i	− 0.583775i
$943$	30.9855i	1.00903i
$944$	− 3.07069i	− 0.0999424i
$945$	13.0978	0.426073
$946$	−9.85086	−0.320279
$947$	− 2.83579i	− 0.0921508i	−0.998938	−	0.0460754i	$-0.985329\pi$
$947$	− 2.83579i	− 0.0921508i	0.998938	−	0.0460754i	$-0.0146714\pi$
$948$	13.1371	0.426672
$949$	0	0
$950$	28.7482	0.932716
$951$	7.36121i	0.238704i
$952$	1.13706	0.0368524
$953$	17.0968	0.553819	0.276909	−	0.960896i	$-0.410690\pi$
$953$	17.0968	0.553819	0.276909	+	0.960896i	$0.410690\pi$
$954$	− 0.956459i	− 0.0309665i
$955$	− 41.4935i	− 1.34270i
$956$	− 13.4843i	− 0.436112i
$957$	4.54288i	0.146850i
$958$	29.3043	0.946778
$959$	−11.3720	−0.367220
$960$	− 2.44504i	− 0.0789134i
$961$	29.3903	0.948073
$962$	0	0
$963$	−43.0804	−1.38825
$964$	− 11.6485i	− 0.375172i
$965$	24.8092	0.798637
$966$	2.35690	0.0758319
$967$	43.0694i	1.38502i	0.721410	+	0.692509i	$0.243495\pi$
$967$	43.0694i	1.38502i	−0.721410	+	0.692509i	$0.756505\pi$
$968$	− 9.44504i	− 0.303575i
$969$	− 6.10215i	− 0.196029i
$970$	− 24.5405i	− 0.787947i
$971$	−11.7549	−0.377234	−0.188617	−	0.982051i	$-0.560400\pi$
$971$	−11.7549	−0.377234	−0.188617	+	0.982051i	$0.560400\pi$
$972$	15.7952	0.506632
$973$	− 5.78017i	− 0.185304i
$974$	12.5496	0.402115
$975$	0	0
$976$	7.12498	0.228065
$977$	− 3.20046i	− 0.102392i	−0.998689	−	0.0511958i	$-0.983697\pi$
$977$	− 3.20046i	− 0.102392i	0.998689	−	0.0511958i	$-0.0163033\pi$
$978$	−8.28813	−0.265025
$979$	3.13169	0.100089
$980$	− 3.04892i	− 0.0973941i
$981$	− 32.4088i	− 1.03473i
$982$	− 31.0267i	− 0.990101i
$983$	− 16.4246i	− 0.523863i	−0.965086	−	0.261932i	$-0.915640\pi$
$983$	− 16.4246i	− 0.523863i	0.965086	−	0.261932i	$-0.0843595\pi$
$984$	−8.45473	−0.269527
$985$	76.3443	2.43253
$986$	− 5.16554i	− 0.164504i
$987$	−4.95646	−0.157766
$988$	0	0
$989$	23.2174	0.738272
$990$	− 8.96077i	− 0.284792i
$991$	45.7881	1.45451	0.727253	−	0.686370i	$-0.240797\pi$
$991$	45.7881	1.45451	0.727253	+	0.686370i	$0.240797\pi$
$992$	1.26875	0.0402828
$993$	3.70948i	0.117717i
$994$	2.02715i	0.0642972i
$995$	14.2760i	0.452581i
$996$	− 3.96077i	− 0.125502i
$997$	57.8074	1.83078	0.915390	−	0.402568i	$-0.131882\pi$
$997$	57.8074	1.83078	0.915390	+	0.402568i	$0.131882\pi$
$998$	−31.6728	−1.00258
$999$	− 40.5749i	− 1.28373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.p.337.4		6
13.5	odd	4		2366.2.a.bd.1.1	yes	3
13.8	odd	4		2366.2.a.y.1.1	✓	3
13.12	even	2	inner	2366.2.d.p.337.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.y.1.1	✓	3	13.8	odd	4
2366.2.a.bd.1.1	yes	3	13.5	odd	4
2366.2.d.p.337.1		6	13.12	even	2	inner
2366.2.d.p.337.4		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.801938 q^{3} -1.00000 q^{4} -3.04892i q^{5} -0.801938i q^{6} +1.00000i q^{7} -1.00000i q^{8} -2.35690 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.801938 q^{3} -1.00000 q^{4} -3.04892i q^{5} -0.801938i q^{6} +1.00000i q^{7} -1.00000i q^{8} -2.35690 q^{9} +3.04892 q^{10} +1.24698i q^{11} +0.801938 q^{12} -1.00000 q^{14} +2.44504i q^{15} +1.00000 q^{16} +1.13706 q^{17} -2.35690i q^{18} +6.69202i q^{19} +3.04892i q^{20} -0.801938i q^{21} -1.24698 q^{22} +2.93900 q^{23} +0.801938i q^{24} -4.29590 q^{25} +4.29590 q^{27} -1.00000i q^{28} -4.54288 q^{29} -2.44504 q^{30} -1.26875i q^{31} +1.00000i q^{32} -1.00000i q^{33} +1.13706i q^{34} +3.04892 q^{35} +2.35690 q^{36} -9.44504i q^{37} -6.69202 q^{38} -3.04892 q^{40} +10.5429i q^{41} +0.801938 q^{42} +7.89977 q^{43} -1.24698i q^{44} +7.18598i q^{45} +2.93900i q^{46} -6.18060i q^{47} -0.801938 q^{48} -1.00000 q^{49} -4.29590i q^{50} -0.911854 q^{51} +0.405813 q^{53} +4.29590i q^{54} +3.80194 q^{55} +1.00000 q^{56} -5.36658i q^{57} -4.54288i q^{58} -3.07069i q^{59} -2.44504i q^{60} +7.12498 q^{61} +1.26875 q^{62} -2.35690i q^{63} -1.00000 q^{64} +1.00000 q^{66} -9.00969i q^{67} -1.13706 q^{68} -2.35690 q^{69} +3.04892i q^{70} -2.02715i q^{71} +2.35690i q^{72} -16.8334i q^{73} +9.44504 q^{74} +3.44504 q^{75} -6.69202i q^{76} -1.24698 q^{77} +16.3817 q^{79} -3.04892i q^{80} +3.62565 q^{81} -10.5429 q^{82} -4.93900i q^{83} +0.801938i q^{84} -3.46681i q^{85} +7.89977i q^{86} +3.64310 q^{87} +1.24698 q^{88} -2.51142i q^{89} -7.18598 q^{90} -2.93900 q^{92} +1.01746i q^{93} +6.18060 q^{94} +20.4034 q^{95} -0.801938i q^{96} -8.04892i q^{97} -1.00000i q^{98} -2.93900i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} - 6 q^{4} - 6 q^{9}+O(q^{10}) \) 6 * q + 4 * q^3 - 6 * q^4 - 6 * q^9	\( 6 q + 4 q^{3} - 6 q^{4} - 6 q^{9} - 4 q^{12} - 6 q^{14} + 6 q^{16} - 4 q^{17} + 2 q^{22} - 2 q^{23} + 2 q^{25} - 2 q^{27} + 10 q^{29} - 14 q^{30} + 6 q^{36} - 30 q^{38} - 4 q^{42} + 2 q^{43} + 4 q^{48} - 6 q^{49} + 2 q^{51} - 24 q^{53} + 14 q^{55} + 6 q^{56} - 6 q^{61} - 8 q^{62} - 6 q^{64} + 6 q^{66} + 4 q^{68} - 6 q^{69} + 56 q^{74} + 20 q^{75} + 2 q^{77} - 4 q^{79} - 2 q^{81} - 26 q^{82} + 30 q^{87} - 2 q^{88} - 14 q^{90} + 2 q^{92} + 14 q^{94} + 14 q^{95}+O(q^{100}) \) 6 * q + 4 * q^3 - 6 * q^4 - 6 * q^9 - 4 * q^12 - 6 * q^14 + 6 * q^16 - 4 * q^17 + 2 * q^22 - 2 * q^23 + 2 * q^25 - 2 * q^27 + 10 * q^29 - 14 * q^30 + 6 * q^36 - 30 * q^38 - 4 * q^42 + 2 * q^43 + 4 * q^48 - 6 * q^49 + 2 * q^51 - 24 * q^53 + 14 * q^55 + 6 * q^56 - 6 * q^61 - 8 * q^62 - 6 * q^64 + 6 * q^66 + 4 * q^68 - 6 * q^69 + 56 * q^74 + 20 * q^75 + 2 * q^77 - 4 * q^79 - 2 * q^81 - 26 * q^82 + 30 * q^87 - 2 * q^88 - 14 * q^90 + 2 * q^92 + 14 * q^94 + 14 * q^95

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