LMFDB - Embedded newform 6042.2.a.y.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.a (trivial)

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:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 14x^{5} + 29x^{4} + 48x^{3} - 14x^{2} - 35x - 10 $ x^7 - 3x^6 - 14x^5 + 29x^4 + 48x^3 - 14x^2 - 35x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.456607$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.45661 q^{5} -1.00000 q^{6} +1.71471 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.45661 q^{5} -1.00000 q^{6} +1.71471 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.45661 q^{10} -2.01576 q^{11} +1.00000 q^{12} -3.15556 q^{13} -1.71471 q^{14} +1.45661 q^{15} +1.00000 q^{16} -8.17609 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.45661 q^{20} +1.71471 q^{21} +2.01576 q^{22} +7.84057 q^{23} -1.00000 q^{24} -2.87830 q^{25} +3.15556 q^{26} +1.00000 q^{27} +1.71471 q^{28} -5.97560 q^{29} -1.45661 q^{30} -0.954711 q^{31} -1.00000 q^{32} -2.01576 q^{33} +8.17609 q^{34} +2.49766 q^{35} +1.00000 q^{36} -4.94735 q^{37} +1.00000 q^{38} -3.15556 q^{39} -1.45661 q^{40} +7.49523 q^{41} -1.71471 q^{42} +4.28208 q^{43} -2.01576 q^{44} +1.45661 q^{45} -7.84057 q^{46} +12.9986 q^{47} +1.00000 q^{48} -4.05977 q^{49} +2.87830 q^{50} -8.17609 q^{51} -3.15556 q^{52} +1.00000 q^{53} -1.00000 q^{54} -2.93616 q^{55} -1.71471 q^{56} -1.00000 q^{57} +5.97560 q^{58} -5.14783 q^{59} +1.45661 q^{60} -15.3930 q^{61} +0.954711 q^{62} +1.71471 q^{63} +1.00000 q^{64} -4.59641 q^{65} +2.01576 q^{66} +1.93335 q^{67} -8.17609 q^{68} +7.84057 q^{69} -2.49766 q^{70} +0.646595 q^{71} -1.00000 q^{72} -0.474324 q^{73} +4.94735 q^{74} -2.87830 q^{75} -1.00000 q^{76} -3.45644 q^{77} +3.15556 q^{78} -5.19669 q^{79} +1.45661 q^{80} +1.00000 q^{81} -7.49523 q^{82} -8.68077 q^{83} +1.71471 q^{84} -11.9093 q^{85} -4.28208 q^{86} -5.97560 q^{87} +2.01576 q^{88} -0.797217 q^{89} -1.45661 q^{90} -5.41087 q^{91} +7.84057 q^{92} -0.954711 q^{93} -12.9986 q^{94} -1.45661 q^{95} -1.00000 q^{96} -12.5863 q^{97} +4.05977 q^{98} -2.01576 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 4 q^{10} - 2 q^{11} + 7 q^{12} - 7 q^{13} + 9 q^{14} + 4 q^{15} + 7 q^{16} - 10 q^{17} - 7 q^{18} - 7 q^{19} + 4 q^{20} - 9 q^{21} + 2 q^{22} + 2 q^{23} - 7 q^{24} + 3 q^{25} + 7 q^{26} + 7 q^{27} - 9 q^{28} - 6 q^{29} - 4 q^{30} + 3 q^{31} - 7 q^{32} - 2 q^{33} + 10 q^{34} + 7 q^{36} - 3 q^{37} + 7 q^{38} - 7 q^{39} - 4 q^{40} - 12 q^{41} + 9 q^{42} - 26 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{46} + 17 q^{47} + 7 q^{48} - 3 q^{50} - 10 q^{51} - 7 q^{52} + 7 q^{53} - 7 q^{54} - 23 q^{55} + 9 q^{56} - 7 q^{57} + 6 q^{58} + 7 q^{59} + 4 q^{60} - 18 q^{61} - 3 q^{62} - 9 q^{63} + 7 q^{64} - 23 q^{65} + 2 q^{66} - 3 q^{67} - 10 q^{68} + 2 q^{69} + 2 q^{71} - 7 q^{72} + q^{73} + 3 q^{74} + 3 q^{75} - 7 q^{76} - 23 q^{77} + 7 q^{78} - 18 q^{79} + 4 q^{80} + 7 q^{81} + 12 q^{82} - 17 q^{83} - 9 q^{84} - 3 q^{85} + 26 q^{86} - 6 q^{87} + 2 q^{88} - 13 q^{89} - 4 q^{90} - 8 q^{91} + 2 q^{92} + 3 q^{93} - 17 q^{94} - 4 q^{95} - 7 q^{96} - 20 q^{97} - 2 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 4 * q^10 - 2 * q^11 + 7 * q^12 - 7 * q^13 + 9 * q^14 + 4 * q^15 + 7 * q^16 - 10 * q^17 - 7 * q^18 - 7 * q^19 + 4 * q^20 - 9 * q^21 + 2 * q^22 + 2 * q^23 - 7 * q^24 + 3 * q^25 + 7 * q^26 + 7 * q^27 - 9 * q^28 - 6 * q^29 - 4 * q^30 + 3 * q^31 - 7 * q^32 - 2 * q^33 + 10 * q^34 + 7 * q^36 - 3 * q^37 + 7 * q^38 - 7 * q^39 - 4 * q^40 - 12 * q^41 + 9 * q^42 - 26 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^46 + 17 * q^47 + 7 * q^48 - 3 * q^50 - 10 * q^51 - 7 * q^52 + 7 * q^53 - 7 * q^54 - 23 * q^55 + 9 * q^56 - 7 * q^57 + 6 * q^58 + 7 * q^59 + 4 * q^60 - 18 * q^61 - 3 * q^62 - 9 * q^63 + 7 * q^64 - 23 * q^65 + 2 * q^66 - 3 * q^67 - 10 * q^68 + 2 * q^69 + 2 * q^71 - 7 * q^72 + q^73 + 3 * q^74 + 3 * q^75 - 7 * q^76 - 23 * q^77 + 7 * q^78 - 18 * q^79 + 4 * q^80 + 7 * q^81 + 12 * q^82 - 17 * q^83 - 9 * q^84 - 3 * q^85 + 26 * q^86 - 6 * q^87 + 2 * q^88 - 13 * q^89 - 4 * q^90 - 8 * q^91 + 2 * q^92 + 3 * q^93 - 17 * q^94 - 4 * q^95 - 7 * q^96 - 20 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.45661	0.651414	0.325707	−	0.945471i	$-0.394398\pi$
$5$	1.45661	0.651414	0.325707	+	0.945471i	$0.394398\pi$
$6$	−1.00000	−0.408248
$7$	1.71471	0.648099	0.324050	−	0.946040i	$-0.394955\pi$
$7$	1.71471	0.648099	0.324050	+	0.946040i	$0.394955\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.45661	−0.460620
$11$	−2.01576	−0.607773	−0.303887	−	0.952708i	$-0.598284\pi$
$11$	−2.01576	−0.607773	−0.303887	+	0.952708i	$0.598284\pi$
$12$	1.00000	0.288675
$13$	−3.15556	−0.875195	−0.437598	−	0.899171i	$-0.644171\pi$
$13$	−3.15556	−0.875195	−0.437598	+	0.899171i	$0.644171\pi$
$14$	−1.71471	−0.458276
$15$	1.45661	0.376094
$16$	1.00000	0.250000
$17$	−8.17609	−1.98299	−0.991496	−	0.130137i	$-0.958458\pi$
$17$	−8.17609	−1.98299	−0.991496	+	0.130137i	$0.958458\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.45661	0.325707
$21$	1.71471	0.374180
$22$	2.01576	0.429761
$23$	7.84057	1.63487	0.817436	−	0.576020i	$-0.195395\pi$
$23$	7.84057	1.63487	0.817436	+	0.576020i	$0.195395\pi$
$24$	−1.00000	−0.204124
$25$	−2.87830	−0.575659
$26$	3.15556	0.618856
$27$	1.00000	0.192450
$28$	1.71471	0.324050
$29$	−5.97560	−1.10964	−0.554821	−	0.831970i	$-0.687213\pi$
$29$	−5.97560	−1.10964	−0.554821	+	0.831970i	$0.687213\pi$
$30$	−1.45661	−0.265939
$31$	−0.954711	−0.171471	−0.0857356	−	0.996318i	$-0.527324\pi$
$31$	−0.954711	−0.171471	−0.0857356	+	0.996318i	$0.527324\pi$
$32$	−1.00000	−0.176777
$33$	−2.01576	−0.350898
$34$	8.17609	1.40219
$35$	2.49766	0.422181
$36$	1.00000	0.166667
$37$	−4.94735	−0.813339	−0.406669	−	0.913575i	$-0.633310\pi$
$37$	−4.94735	−0.813339	−0.406669	+	0.913575i	$0.633310\pi$
$38$	1.00000	0.162221
$39$	−3.15556	−0.505294
$40$	−1.45661	−0.230310
$41$	7.49523	1.17056	0.585279	−	0.810832i	$-0.300985\pi$
$41$	7.49523	1.17056	0.585279	+	0.810832i	$0.300985\pi$
$42$	−1.71471	−0.264585
$43$	4.28208	0.653011	0.326505	−	0.945195i	$-0.394129\pi$
$43$	4.28208	0.653011	0.326505	+	0.945195i	$0.394129\pi$
$44$	−2.01576	−0.303887
$45$	1.45661	0.217138
$46$	−7.84057	−1.15603
$47$	12.9986	1.89603	0.948017	−	0.318220i	$-0.103085\pi$
$47$	12.9986	1.89603	0.948017	+	0.318220i	$0.103085\pi$
$48$	1.00000	0.144338
$49$	−4.05977	−0.579967
$50$	2.87830	0.407053
$51$	−8.17609	−1.14488
$52$	−3.15556	−0.437598
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	−2.93616	−0.395912
$56$	−1.71471	−0.229138
$57$	−1.00000	−0.132453
$58$	5.97560	0.784635
$59$	−5.14783	−0.670190	−0.335095	−	0.942184i	$-0.608768\pi$
$59$	−5.14783	−0.670190	−0.335095	+	0.942184i	$0.608768\pi$
$60$	1.45661	0.188047
$61$	−15.3930	−1.97087	−0.985437	−	0.170043i	$-0.945609\pi$
$61$	−15.3930	−1.97087	−0.985437	+	0.170043i	$0.945609\pi$
$62$	0.954711	0.121248
$63$	1.71471	0.216033
$64$	1.00000	0.125000
$65$	−4.59641	−0.570115
$66$	2.01576	0.248122
$67$	1.93335	0.236197	0.118098	−	0.993002i	$-0.462320\pi$
$67$	1.93335	0.236197	0.118098	+	0.993002i	$0.462320\pi$
$68$	−8.17609	−0.991496
$69$	7.84057	0.943893
$70$	−2.49766	−0.298527
$71$	0.646595	0.0767367	0.0383684	−	0.999264i	$-0.487784\pi$
$71$	0.646595	0.0767367	0.0383684	+	0.999264i	$0.487784\pi$
$72$	−1.00000	−0.117851
$73$	−0.474324	−0.0555154	−0.0277577	−	0.999615i	$-0.508837\pi$
$73$	−0.474324	−0.0555154	−0.0277577	+	0.999615i	$0.508837\pi$
$74$	4.94735	0.575117
$75$	−2.87830	−0.332357
$76$	−1.00000	−0.114708
$77$	−3.45644	−0.393898
$78$	3.15556	0.357297
$79$	−5.19669	−0.584673	−0.292337	−	0.956315i	$-0.594433\pi$
$79$	−5.19669	−0.584673	−0.292337	+	0.956315i	$0.594433\pi$
$80$	1.45661	0.162854
$81$	1.00000	0.111111
$82$	−7.49523	−0.827710
$83$	−8.68077	−0.952839	−0.476419	−	0.879218i	$-0.658066\pi$
$83$	−8.68077	−0.952839	−0.476419	+	0.879218i	$0.658066\pi$
$84$	1.71471	0.187090
$85$	−11.9093	−1.29175
$86$	−4.28208	−0.461749
$87$	−5.97560	−0.640652
$88$	2.01576	0.214880
$89$	−0.797217	−0.0845049	−0.0422524	−	0.999107i	$-0.513453\pi$
$89$	−0.797217	−0.0845049	−0.0422524	+	0.999107i	$0.513453\pi$
$90$	−1.45661	−0.153540
$91$	−5.41087	−0.567214
$92$	7.84057	0.817436
$93$	−0.954711	−0.0989990
$94$	−12.9986	−1.34070
$95$	−1.45661	−0.149445
$96$	−1.00000	−0.102062
$97$	−12.5863	−1.27794	−0.638972	−	0.769230i	$-0.720640\pi$
$97$	−12.5863	−1.27794	−0.638972	+	0.769230i	$0.720640\pi$
$98$	4.05977	0.410099
$99$	−2.01576	−0.202591
$100$	−2.87830	−0.287830
$101$	−15.6789	−1.56010	−0.780052	−	0.625715i	$-0.784807\pi$
$101$	−15.6789	−1.56010	−0.780052	+	0.625715i	$0.784807\pi$
$102$	8.17609	0.809553
$103$	−0.386210	−0.0380544	−0.0190272	−	0.999819i	$-0.506057\pi$
$103$	−0.386210	−0.0380544	−0.0190272	+	0.999819i	$0.506057\pi$
$104$	3.15556	0.309428
$105$	2.49766	0.243747
$106$	−1.00000	−0.0971286
$107$	13.0879	1.26525	0.632625	−	0.774458i	$-0.281977\pi$
$107$	13.0879	1.26525	0.632625	+	0.774458i	$0.281977\pi$
$108$	1.00000	0.0962250
$109$	1.91654	0.183571	0.0917855	−	0.995779i	$-0.470743\pi$
$109$	1.91654	0.183571	0.0917855	+	0.995779i	$0.470743\pi$
$110$	2.93616	0.279952
$111$	−4.94735	−0.469581
$112$	1.71471	0.162025
$113$	8.84681	0.832238	0.416119	−	0.909310i	$-0.363390\pi$
$113$	8.84681	0.832238	0.416119	+	0.909310i	$0.363390\pi$
$114$	1.00000	0.0936586
$115$	11.4206	1.06498
$116$	−5.97560	−0.554821
$117$	−3.15556	−0.291732
$118$	5.14783	0.473896
$119$	−14.0196	−1.28518
$120$	−1.45661	−0.132969
$121$	−6.93673	−0.630612
$122$	15.3930	1.39362
$123$	7.49523	0.675822
$124$	−0.954711	−0.0857356
$125$	−11.4756	−1.02641
$126$	−1.71471	−0.152759
$127$	2.37117	0.210407	0.105204	−	0.994451i	$-0.466451\pi$
$127$	2.37117	0.210407	0.105204	+	0.994451i	$0.466451\pi$
$128$	−1.00000	−0.0883883
$129$	4.28208	0.377016
$130$	4.59641	0.403132
$131$	0.186795	0.0163204	0.00816019	−	0.999967i	$-0.497403\pi$
$131$	0.186795	0.0163204	0.00816019	+	0.999967i	$0.497403\pi$
$132$	−2.01576	−0.175449
$133$	−1.71471	−0.148684
$134$	−1.93335	−0.167016
$135$	1.45661	0.125365
$136$	8.17609	0.701094
$137$	−12.9713	−1.10821	−0.554107	−	0.832445i	$-0.686940\pi$
$137$	−12.9713	−1.10821	−0.554107	+	0.832445i	$0.686940\pi$
$138$	−7.84057	−0.667433
$139$	−17.2046	−1.45928	−0.729640	−	0.683832i	$-0.760312\pi$
$139$	−17.2046	−1.45928	−0.729640	+	0.683832i	$0.760312\pi$
$140$	2.49766	0.211091
$141$	12.9986	1.09468
$142$	−0.646595	−0.0542611
$143$	6.36084	0.531920
$144$	1.00000	0.0833333
$145$	−8.70411	−0.722837
$146$	0.474324	0.0392553
$147$	−4.05977	−0.334844
$148$	−4.94735	−0.406669
$149$	−14.7907	−1.21170	−0.605850	−	0.795579i	$-0.707167\pi$
$149$	−14.7907	−1.21170	−0.605850	+	0.795579i	$0.707167\pi$
$150$	2.87830	0.235012
$151$	0.539968	0.0439420	0.0219710	−	0.999759i	$-0.493006\pi$
$151$	0.539968	0.0439420	0.0219710	+	0.999759i	$0.493006\pi$
$152$	1.00000	0.0811107
$153$	−8.17609	−0.660997
$154$	3.45644	0.278528
$155$	−1.39064	−0.111699
$156$	−3.15556	−0.252647
$157$	−23.7162	−1.89276	−0.946381	−	0.323052i	$-0.895291\pi$
$157$	−23.7162	−1.89276	−0.946381	+	0.323052i	$0.895291\pi$
$158$	5.19669	0.413426
$159$	1.00000	0.0793052
$160$	−1.45661	−0.115155
$161$	13.4443	1.05956
$162$	−1.00000	−0.0785674
$163$	−11.5853	−0.907427	−0.453714	−	0.891148i	$-0.649901\pi$
$163$	−11.5853	−0.907427	−0.453714	+	0.891148i	$0.649901\pi$
$164$	7.49523	0.585279
$165$	−2.93616	−0.228580
$166$	8.68077	0.673759
$167$	−14.3376	−1.10948	−0.554738	−	0.832025i	$-0.687182\pi$
$167$	−14.3376	−1.10948	−0.554738	+	0.832025i	$0.687182\pi$
$168$	−1.71471	−0.132293
$169$	−3.04243	−0.234033
$170$	11.9093	0.913405
$171$	−1.00000	−0.0764719
$172$	4.28208	0.326505
$173$	−1.50648	−0.114536	−0.0572678	−	0.998359i	$-0.518239\pi$
$173$	−1.50648	−0.114536	−0.0572678	+	0.998359i	$0.518239\pi$
$174$	5.97560	0.453009
$175$	−4.93544	−0.373084
$176$	−2.01576	−0.151943
$177$	−5.14783	−0.386934
$178$	0.797217	0.0597540
$179$	12.9663	0.969145	0.484572	−	0.874751i	$-0.338975\pi$
$179$	12.9663	0.969145	0.484572	+	0.874751i	$0.338975\pi$
$180$	1.45661	0.108569
$181$	24.4025	1.81383	0.906913	−	0.421318i	$-0.138432\pi$
$181$	24.4025	1.81383	0.906913	+	0.421318i	$0.138432\pi$
$182$	5.41087	0.401081
$183$	−15.3930	−1.13788
$184$	−7.84057	−0.578014
$185$	−7.20634	−0.529821
$186$	0.954711	0.0700028
$187$	16.4810	1.20521
$188$	12.9986	0.948017
$189$	1.71471	0.124727
$190$	1.45661	0.105673
$191$	3.99785	0.289274	0.144637	−	0.989485i	$-0.453799\pi$
$191$	3.99785	0.289274	0.144637	+	0.989485i	$0.453799\pi$
$192$	1.00000	0.0721688
$193$	19.9714	1.43757	0.718785	−	0.695233i	$-0.244699\pi$
$193$	19.9714	1.43757	0.718785	+	0.695233i	$0.244699\pi$
$194$	12.5863	0.903644
$195$	−4.59641	−0.329156
$196$	−4.05977	−0.289984
$197$	−14.1989	−1.01163	−0.505816	−	0.862641i	$-0.668809\pi$
$197$	−14.1989	−1.01163	−0.505816	+	0.862641i	$0.668809\pi$
$198$	2.01576	0.143254
$199$	22.3504	1.58438	0.792189	−	0.610276i	$-0.208941\pi$
$199$	22.3504	1.58438	0.792189	+	0.610276i	$0.208941\pi$
$200$	2.87830	0.203526
$201$	1.93335	0.136368
$202$	15.6789	1.10316
$203$	−10.2464	−0.719158
$204$	−8.17609	−0.572440
$205$	10.9176	0.762519
$206$	0.386210	0.0269085
$207$	7.84057	0.544957
$208$	−3.15556	−0.218799
$209$	2.01576	0.139433
$210$	−2.49766	−0.172355
$211$	−27.6260	−1.90185	−0.950927	−	0.309415i	$-0.899867\pi$
$211$	−27.6260	−1.90185	−0.950927	+	0.309415i	$0.899867\pi$
$212$	1.00000	0.0686803
$213$	0.646595	0.0443040
$214$	−13.0879	−0.894667
$215$	6.23731	0.425381
$216$	−1.00000	−0.0680414
$217$	−1.63705	−0.111130
$218$	−1.91654	−0.129804
$219$	−0.474324	−0.0320518
$220$	−2.93616	−0.197956
$221$	25.8001	1.73551
$222$	4.94735	0.332044
$223$	5.46249	0.365795	0.182898	−	0.983132i	$-0.441452\pi$
$223$	5.46249	0.365795	0.182898	+	0.983132i	$0.441452\pi$
$224$	−1.71471	−0.114569
$225$	−2.87830	−0.191886
$226$	−8.84681	−0.588481
$227$	14.5887	0.968284	0.484142	−	0.874989i	$-0.339132\pi$
$227$	14.5887	0.968284	0.484142	+	0.874989i	$0.339132\pi$
$228$	−1.00000	−0.0662266
$229$	−7.53089	−0.497655	−0.248828	−	0.968548i	$-0.580045\pi$
$229$	−7.53089	−0.497655	−0.248828	+	0.968548i	$0.580045\pi$
$230$	−11.4206	−0.753054
$231$	−3.45644	−0.227417
$232$	5.97560	0.392318
$233$	9.34308	0.612086	0.306043	−	0.952018i	$-0.400995\pi$
$233$	9.34308	0.612086	0.306043	+	0.952018i	$0.400995\pi$
$234$	3.15556	0.206285
$235$	18.9338	1.23510
$236$	−5.14783	−0.335095
$237$	−5.19669	−0.337561
$238$	14.0196	0.908757
$239$	−2.42411	−0.156803	−0.0784014	−	0.996922i	$-0.524982\pi$
$239$	−2.42411	−0.156803	−0.0784014	+	0.996922i	$0.524982\pi$
$240$	1.45661	0.0940236
$241$	−1.11015	−0.0715111	−0.0357555	−	0.999361i	$-0.511384\pi$
$241$	−1.11015	−0.0715111	−0.0357555	+	0.999361i	$0.511384\pi$
$242$	6.93673	0.445910
$243$	1.00000	0.0641500
$244$	−15.3930	−0.985437
$245$	−5.91349	−0.377799
$246$	−7.49523	−0.477879
$247$	3.15556	0.200784
$248$	0.954711	0.0606242
$249$	−8.68077	−0.550122
$250$	11.4756	0.725779
$251$	−9.27273	−0.585290	−0.292645	−	0.956221i	$-0.594535\pi$
$251$	−9.27273	−0.585290	−0.292645	+	0.956221i	$0.594535\pi$
$252$	1.71471	0.108017
$253$	−15.8047	−0.993631
$254$	−2.37117	−0.148780
$255$	−11.9093	−0.745792
$256$	1.00000	0.0625000
$257$	−15.1544	−0.945303	−0.472651	−	0.881249i	$-0.656703\pi$
$257$	−15.1544	−0.945303	−0.472651	+	0.881249i	$0.656703\pi$
$258$	−4.28208	−0.266591
$259$	−8.48327	−0.527124
$260$	−4.59641	−0.285057
$261$	−5.97560	−0.369881
$262$	−0.186795	−0.0115403
$263$	17.2069	1.06102	0.530511	−	0.847678i	$-0.322000\pi$
$263$	17.2069	1.06102	0.530511	+	0.847678i	$0.322000\pi$
$264$	2.01576	0.124061
$265$	1.45661	0.0894787
$266$	1.71471	0.105136
$267$	−0.797217	−0.0487889
$268$	1.93335	0.118098
$269$	18.3261	1.11736	0.558682	−	0.829382i	$-0.311307\pi$
$269$	18.3261	1.11736	0.558682	+	0.829382i	$0.311307\pi$
$270$	−1.45661	−0.0886463
$271$	−8.08715	−0.491259	−0.245630	−	0.969364i	$-0.578995\pi$
$271$	−8.08715	−0.491259	−0.245630	+	0.969364i	$0.578995\pi$
$272$	−8.17609	−0.495748
$273$	−5.41087	−0.327481
$274$	12.9713	0.783626
$275$	5.80194	0.349870
$276$	7.84057	0.471947
$277$	−17.9579	−1.07899	−0.539493	−	0.841990i	$-0.681384\pi$
$277$	−17.9579	−1.07899	−0.539493	+	0.841990i	$0.681384\pi$
$278$	17.2046	1.03187
$279$	−0.954711	−0.0571571
$280$	−2.49766	−0.149264
$281$	16.8409	1.00464	0.502322	−	0.864681i	$-0.332479\pi$
$281$	16.8409	1.00464	0.502322	+	0.864681i	$0.332479\pi$
$282$	−12.9986	−0.774052
$283$	14.1051	0.838464	0.419232	−	0.907879i	$-0.362299\pi$
$283$	14.1051	0.838464	0.419232	+	0.907879i	$0.362299\pi$
$284$	0.646595	0.0383684
$285$	−1.45661	−0.0862819
$286$	−6.36084	−0.376124
$287$	12.8522	0.758638
$288$	−1.00000	−0.0589256
$289$	49.8484	2.93226
$290$	8.70411	0.511123
$291$	−12.5863	−0.737822
$292$	−0.474324	−0.0277577
$293$	15.3313	0.895663	0.447832	−	0.894118i	$-0.352196\pi$
$293$	15.3313	0.895663	0.447832	+	0.894118i	$0.352196\pi$
$294$	4.05977	0.236771
$295$	−7.49836	−0.436571
$296$	4.94735	0.287559
$297$	−2.01576	−0.116966
$298$	14.7907	0.856802
$299$	−24.7414	−1.43083
$300$	−2.87830	−0.166179
$301$	7.34252	0.423216
$302$	−0.539968	−0.0310717
$303$	−15.6789	−0.900727
$304$	−1.00000	−0.0573539
$305$	−22.4216	−1.28386
$306$	8.17609	0.467396
$307$	−25.1603	−1.43597	−0.717986	−	0.696057i	$-0.754936\pi$
$307$	−25.1603	−1.43597	−0.717986	+	0.696057i	$0.754936\pi$
$308$	−3.45644	−0.196949
$309$	−0.386210	−0.0219707
$310$	1.39064	0.0789830
$311$	−8.32956	−0.472326	−0.236163	−	0.971713i	$-0.575890\pi$
$311$	−8.32956	−0.472326	−0.236163	+	0.971713i	$0.575890\pi$
$312$	3.15556	0.178648
$313$	8.66237	0.489626	0.244813	−	0.969570i	$-0.421273\pi$
$313$	8.66237	0.489626	0.244813	+	0.969570i	$0.421273\pi$
$314$	23.7162	1.33839
$315$	2.49766	0.140727
$316$	−5.19669	−0.292337
$317$	−19.4340	−1.09152	−0.545761	−	0.837941i	$-0.683760\pi$
$317$	−19.4340	−1.09152	−0.545761	+	0.837941i	$0.683760\pi$
$318$	−1.00000	−0.0560772
$319$	12.0454	0.674411
$320$	1.45661	0.0814268
$321$	13.0879	0.730493
$322$	−13.4443	−0.749222
$323$	8.17609	0.454930
$324$	1.00000	0.0555556
$325$	9.08264	0.503814
$326$	11.5853	0.641648
$327$	1.91654	0.105985
$328$	−7.49523	−0.413855
$329$	22.2887	1.22882
$330$	2.93616	0.161630
$331$	−1.16487	−0.0640272	−0.0320136	−	0.999487i	$-0.510192\pi$
$331$	−1.16487	−0.0640272	−0.0320136	+	0.999487i	$0.510192\pi$
$332$	−8.68077	−0.476419
$333$	−4.94735	−0.271113
$334$	14.3376	0.784518
$335$	2.81614	0.153862
$336$	1.71471	0.0935451
$337$	8.67736	0.472686	0.236343	−	0.971670i	$-0.424051\pi$
$337$	8.67736	0.472686	0.236343	+	0.971670i	$0.424051\pi$
$338$	3.04243	0.165487
$339$	8.84681	0.480493
$340$	−11.9093	−0.645875
$341$	1.92446	0.104216
$342$	1.00000	0.0540738
$343$	−18.9643	−1.02398
$344$	−4.28208	−0.230874
$345$	11.4206	0.614866
$346$	1.50648	0.0809889
$347$	5.80054	0.311389	0.155695	−	0.987805i	$-0.450238\pi$
$347$	5.80054	0.311389	0.155695	+	0.987805i	$0.450238\pi$
$348$	−5.97560	−0.320326
$349$	−23.2831	−1.24631	−0.623157	−	0.782097i	$-0.714150\pi$
$349$	−23.2831	−1.24631	−0.623157	+	0.782097i	$0.714150\pi$
$350$	4.93544	0.263811
$351$	−3.15556	−0.168431
$352$	2.01576	0.107440
$353$	−7.09757	−0.377765	−0.188883	−	0.982000i	$-0.560487\pi$
$353$	−7.09757	−0.377765	−0.188883	+	0.982000i	$0.560487\pi$
$354$	5.14783	0.273604
$355$	0.941835	0.0499874
$356$	−0.797217	−0.0422524
$357$	−14.0196	−0.741997
$358$	−12.9663	−0.685289
$359$	6.89814	0.364070	0.182035	−	0.983292i	$-0.441732\pi$
$359$	6.89814	0.364070	0.182035	+	0.983292i	$0.441732\pi$
$360$	−1.45661	−0.0767699
$361$	1.00000	0.0526316
$362$	−24.4025	−1.28257
$363$	−6.93673	−0.364084
$364$	−5.41087	−0.283607
$365$	−0.690903	−0.0361635
$366$	15.3930	0.804606
$367$	13.0904	0.683311	0.341655	−	0.939825i	$-0.389012\pi$
$367$	13.0904	0.683311	0.341655	+	0.939825i	$0.389012\pi$
$368$	7.84057	0.408718
$369$	7.49523	0.390186
$370$	7.20634	0.374640
$371$	1.71471	0.0890233
$372$	−0.954711	−0.0494995
$373$	−17.5715	−0.909818	−0.454909	−	0.890538i	$-0.650328\pi$
$373$	−17.5715	−0.909818	−0.454909	+	0.890538i	$0.650328\pi$
$374$	−16.4810	−0.852212
$375$	−11.4756	−0.592596
$376$	−12.9986	−0.670349
$377$	18.8564	0.971153
$378$	−1.71471	−0.0881952
$379$	0.382274	0.0196361	0.00981804	−	0.999952i	$-0.496875\pi$
$379$	0.382274	0.0196361	0.00981804	+	0.999952i	$0.496875\pi$
$380$	−1.45661	−0.0747224
$381$	2.37117	0.121479
$382$	−3.99785	−0.204548
$383$	−23.6877	−1.21039	−0.605193	−	0.796079i	$-0.706904\pi$
$383$	−23.6877	−1.21039	−0.605193	+	0.796079i	$0.706904\pi$
$384$	−1.00000	−0.0510310
$385$	−5.03467	−0.256591
$386$	−19.9714	−1.01651
$387$	4.28208	0.217670
$388$	−12.5863	−0.638972
$389$	7.23425	0.366791	0.183395	−	0.983039i	$-0.441291\pi$
$389$	7.23425	0.366791	0.183395	+	0.983039i	$0.441291\pi$
$390$	4.59641	0.232748
$391$	−64.1052	−3.24194
$392$	4.05977	0.205049
$393$	0.186795	0.00942258
$394$	14.1989	0.715332
$395$	−7.56953	−0.380865
$396$	−2.01576	−0.101296
$397$	8.54971	0.429098	0.214549	−	0.976713i	$-0.431172\pi$
$397$	8.54971	0.429098	0.214549	+	0.976713i	$0.431172\pi$
$398$	−22.3504	−1.12032
$399$	−1.71471	−0.0858429
$400$	−2.87830	−0.143915
$401$	22.0123	1.09924	0.549622	−	0.835414i	$-0.314772\pi$
$401$	22.0123	1.09924	0.549622	+	0.835414i	$0.314772\pi$
$402$	−1.93335	−0.0964269
$403$	3.01265	0.150071
$404$	−15.6789	−0.780052
$405$	1.45661	0.0723794
$406$	10.2464	0.508522
$407$	9.97264	0.494326
$408$	8.17609	0.404777
$409$	−19.6391	−0.971092	−0.485546	−	0.874211i	$-0.661379\pi$
$409$	−19.6391	−0.971092	−0.485546	+	0.874211i	$0.661379\pi$
$410$	−10.9176	−0.539182
$411$	−12.9713	−0.639828
$412$	−0.386210	−0.0190272
$413$	−8.82703	−0.434350
$414$	−7.84057	−0.385343
$415$	−12.6445	−0.620693
$416$	3.15556	0.154714
$417$	−17.2046	−0.842515
$418$	−2.01576	−0.0985938
$419$	2.42298	0.118370	0.0591852	−	0.998247i	$-0.481150\pi$
$419$	2.42298	0.118370	0.0591852	+	0.998247i	$0.481150\pi$
$420$	2.49766	0.121873
$421$	2.38557	0.116266	0.0581329	−	0.998309i	$-0.481485\pi$
$421$	2.38557	0.116266	0.0581329	+	0.998309i	$0.481485\pi$
$422$	27.6260	1.34481
$423$	12.9986	0.632011
$424$	−1.00000	−0.0485643
$425$	23.5332	1.14153
$426$	−0.646595	−0.0313276
$427$	−26.3946	−1.27732
$428$	13.0879	0.632625
$429$	6.36084	0.307104
$430$	−6.23731	−0.300790
$431$	20.9378	1.00854	0.504269	−	0.863546i	$-0.331762\pi$
$431$	20.9378	1.00854	0.504269	+	0.863546i	$0.331762\pi$
$432$	1.00000	0.0481125
$433$	−23.0577	−1.10808	−0.554040	−	0.832490i	$-0.686915\pi$
$433$	−23.0577	−1.10808	−0.554040	+	0.832490i	$0.686915\pi$
$434$	1.63705	0.0785811
$435$	−8.70411	−0.417330
$436$	1.91654	0.0917855
$437$	−7.84057	−0.375065
$438$	0.474324	0.0226641
$439$	8.48716	0.405070	0.202535	−	0.979275i	$-0.435082\pi$
$439$	8.48716	0.405070	0.202535	+	0.979275i	$0.435082\pi$
$440$	2.93616	0.139976
$441$	−4.05977	−0.193322
$442$	−25.8001	−1.22719
$443$	−32.2670	−1.53305	−0.766527	−	0.642213i	$-0.778017\pi$
$443$	−32.2670	−1.53305	−0.766527	+	0.642213i	$0.778017\pi$
$444$	−4.94735	−0.234791
$445$	−1.16123	−0.0550477
$446$	−5.46249	−0.258656
$447$	−14.7907	−0.699576
$448$	1.71471	0.0810124
$449$	9.73554	0.459448	0.229724	−	0.973256i	$-0.426218\pi$
$449$	9.73554	0.459448	0.229724	+	0.973256i	$0.426218\pi$
$450$	2.87830	0.135684
$451$	−15.1086	−0.711434
$452$	8.84681	0.416119
$453$	0.539968	0.0253699
$454$	−14.5887	−0.684680
$455$	−7.88151	−0.369491
$456$	1.00000	0.0468293
$457$	23.7425	1.11063	0.555314	−	0.831641i	$-0.312598\pi$
$457$	23.7425	1.11063	0.555314	+	0.831641i	$0.312598\pi$
$458$	7.53089	0.351895
$459$	−8.17609	−0.381627
$460$	11.4206	0.532489
$461$	11.5229	0.536673	0.268337	−	0.963325i	$-0.413526\pi$
$461$	11.5229	0.536673	0.268337	+	0.963325i	$0.413526\pi$
$462$	3.45644	0.160808
$463$	−31.7796	−1.47692	−0.738461	−	0.674296i	$-0.764447\pi$
$463$	−31.7796	−1.47692	−0.738461	+	0.674296i	$0.764447\pi$
$464$	−5.97560	−0.277410
$465$	−1.39064	−0.0644894
$466$	−9.34308	−0.432810
$467$	31.9271	1.47741	0.738706	−	0.674028i	$-0.235437\pi$
$467$	31.9271	1.47741	0.738706	+	0.674028i	$0.235437\pi$
$468$	−3.15556	−0.145866
$469$	3.31514	0.153079
$470$	−18.9338	−0.873350
$471$	−23.7162	−1.09279
$472$	5.14783	0.236948
$473$	−8.63163	−0.396883
$474$	5.19669	0.238692
$475$	2.87830	0.132065
$476$	−14.0196	−0.642588
$477$	1.00000	0.0457869
$478$	2.42411	0.110876
$479$	20.5802	0.940335	0.470168	−	0.882577i	$-0.344193\pi$
$479$	20.5802	0.940335	0.470168	+	0.882577i	$0.344193\pi$
$480$	−1.45661	−0.0664847
$481$	15.6117	0.711830
$482$	1.11015	0.0505660
$483$	13.4443	0.611737
$484$	−6.93673	−0.315306
$485$	−18.3333	−0.832472
$486$	−1.00000	−0.0453609
$487$	−41.3601	−1.87420	−0.937102	−	0.349057i	$-0.886502\pi$
$487$	−41.3601	−1.87420	−0.937102	+	0.349057i	$0.886502\pi$
$488$	15.3930	0.696809
$489$	−11.5853	−0.523903
$490$	5.91349	0.267144
$491$	17.7674	0.801830	0.400915	−	0.916115i	$-0.368692\pi$
$491$	17.7674	0.801830	0.400915	+	0.916115i	$0.368692\pi$
$492$	7.49523	0.337911
$493$	48.8571	2.20041
$494$	−3.15556	−0.141975
$495$	−2.93616	−0.131971
$496$	−0.954711	−0.0428678
$497$	1.10872	0.0497330
$498$	8.68077	0.388995
$499$	21.3206	0.954439	0.477220	−	0.878784i	$-0.341645\pi$
$499$	21.3206	0.954439	0.477220	+	0.878784i	$0.341645\pi$
$500$	−11.4756	−0.513204
$501$	−14.3376	−0.640556
$502$	9.27273	0.413862
$503$	−7.83637	−0.349407	−0.174703	−	0.984621i	$-0.555897\pi$
$503$	−7.83637	−0.349407	−0.174703	+	0.984621i	$0.555897\pi$
$504$	−1.71471	−0.0763793
$505$	−22.8379	−1.01627
$506$	15.8047	0.702603
$507$	−3.04243	−0.135119
$508$	2.37117	0.105204
$509$	−7.16815	−0.317723	−0.158861	−	0.987301i	$-0.550782\pi$
$509$	−7.16815	−0.317723	−0.158861	+	0.987301i	$0.550782\pi$
$510$	11.9093	0.527355
$511$	−0.813328	−0.0359795
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	15.1544	0.668430
$515$	−0.562556	−0.0247892
$516$	4.28208	0.188508
$517$	−26.2019	−1.15236
$518$	8.48327	0.372733
$519$	−1.50648	−0.0661271
$520$	4.59641	0.201566
$521$	37.8920	1.66008	0.830040	−	0.557704i	$-0.188318\pi$
$521$	37.8920	1.66008	0.830040	+	0.557704i	$0.188318\pi$
$522$	5.97560	0.261545
$523$	30.3782	1.32835	0.664174	−	0.747578i	$-0.268783\pi$
$523$	30.3782	1.32835	0.664174	+	0.747578i	$0.268783\pi$
$524$	0.186795	0.00816019
$525$	−4.93544	−0.215400
$526$	−17.2069	−0.750257
$527$	7.80580	0.340026
$528$	−2.01576	−0.0877245
$529$	38.4745	1.67280
$530$	−1.45661	−0.0632710
$531$	−5.14783	−0.223397
$532$	−1.71471	−0.0743421
$533$	−23.6517	−1.02447
$534$	0.797217	0.0344990
$535$	19.0639	0.824203
$536$	−1.93335	−0.0835081
$537$	12.9663	0.559536
$538$	−18.3261	−0.790096
$539$	8.18350	0.352488
$540$	1.45661	0.0626824
$541$	8.58232	0.368983	0.184491	−	0.982834i	$-0.440936\pi$
$541$	8.58232	0.368983	0.184491	+	0.982834i	$0.440936\pi$
$542$	8.08715	0.347373
$543$	24.4025	1.04721
$544$	8.17609	0.350547
$545$	2.79164	0.119581
$546$	5.41087	0.231564
$547$	34.0427	1.45556	0.727781	−	0.685810i	$-0.240552\pi$
$547$	34.0427	1.45556	0.727781	+	0.685810i	$0.240552\pi$
$548$	−12.9713	−0.554107
$549$	−15.3930	−0.656958
$550$	−5.80194	−0.247396
$551$	5.97560	0.254569
$552$	−7.84057	−0.333717
$553$	−8.91082	−0.378926
$554$	17.9579	0.762958
$555$	−7.20634	−0.305892
$556$	−17.2046	−0.729640
$557$	22.9265	0.971427	0.485713	−	0.874118i	$-0.338560\pi$
$557$	22.9265	0.971427	0.485713	+	0.874118i	$0.338560\pi$
$558$	0.954711	0.0404162
$559$	−13.5124	−0.571512
$560$	2.49766	0.105545
$561$	16.4810	0.695828
$562$	−16.8409	−0.710391
$563$	−42.1077	−1.77463	−0.887313	−	0.461167i	$-0.847431\pi$
$563$	−42.1077	−1.77463	−0.887313	+	0.461167i	$0.847431\pi$
$564$	12.9986	0.547338
$565$	12.8863	0.542132
$566$	−14.1051	−0.592883
$567$	1.71471	0.0720111
$568$	−0.646595	−0.0271305
$569$	−35.7142	−1.49722	−0.748608	−	0.663013i	$-0.769277\pi$
$569$	−35.7142	−1.49722	−0.748608	+	0.663013i	$0.769277\pi$
$570$	1.45661	0.0610106
$571$	18.3752	0.768979	0.384490	−	0.923129i	$-0.374377\pi$
$571$	18.3752	0.768979	0.384490	+	0.923129i	$0.374377\pi$
$572$	6.36084	0.265960
$573$	3.99785	0.167013
$574$	−12.8522	−0.536438
$575$	−22.5675	−0.941129
$576$	1.00000	0.0416667
$577$	3.71272	0.154563	0.0772813	−	0.997009i	$-0.475376\pi$
$577$	3.71272	0.154563	0.0772813	+	0.997009i	$0.475376\pi$
$578$	−49.8484	−2.07342
$579$	19.9714	0.829981
$580$	−8.70411	−0.361418
$581$	−14.8850	−0.617534
$582$	12.5863	0.521719
$583$	−2.01576	−0.0834841
$584$	0.474324	0.0196277
$585$	−4.59641	−0.190038
$586$	−15.3313	−0.633329
$587$	−14.7618	−0.609284	−0.304642	−	0.952467i	$-0.598537\pi$
$587$	−14.7618	−0.609284	−0.304642	+	0.952467i	$0.598537\pi$
$588$	−4.05977	−0.167422
$589$	0.954711	0.0393382
$590$	7.49836	0.308703
$591$	−14.1989	−0.584066
$592$	−4.94735	−0.203335
$593$	−9.73242	−0.399663	−0.199831	−	0.979830i	$-0.564039\pi$
$593$	−9.73242	−0.399663	−0.199831	+	0.979830i	$0.564039\pi$
$594$	2.01576	0.0827075
$595$	−20.4211	−0.837182
$596$	−14.7907	−0.605850
$597$	22.3504	0.914741
$598$	24.7414	1.01175
$599$	14.3650	0.586939	0.293470	−	0.955968i	$-0.405190\pi$
$599$	14.3650	0.586939	0.293470	+	0.955968i	$0.405190\pi$
$600$	2.87830	0.117506
$601$	9.30521	0.379567	0.189784	−	0.981826i	$-0.439221\pi$
$601$	9.30521	0.379567	0.189784	+	0.981826i	$0.439221\pi$
$602$	−7.34252	−0.299259
$603$	1.93335	0.0787322
$604$	0.539968	0.0219710
$605$	−10.1041	−0.410790
$606$	15.6789	0.636910
$607$	−22.9576	−0.931820	−0.465910	−	0.884832i	$-0.654273\pi$
$607$	−22.9576	−0.931820	−0.465910	+	0.884832i	$0.654273\pi$
$608$	1.00000	0.0405554
$609$	−10.2464	−0.415206
$610$	22.4216	0.907823
$611$	−41.0177	−1.65940
$612$	−8.17609	−0.330499
$613$	−4.88814	−0.197430	−0.0987150	−	0.995116i	$-0.531473\pi$
$613$	−4.88814	−0.197430	−0.0987150	+	0.995116i	$0.531473\pi$
$614$	25.1603	1.01539
$615$	10.9176	0.440240
$616$	3.45644	0.139264
$617$	19.9091	0.801510	0.400755	−	0.916185i	$-0.368748\pi$
$617$	19.9091	0.801510	0.400755	+	0.916185i	$0.368748\pi$
$618$	0.386210	0.0155356
$619$	26.4602	1.06353	0.531763	−	0.846893i	$-0.321530\pi$
$619$	26.4602	1.06353	0.531763	+	0.846893i	$0.321530\pi$
$620$	−1.39064	−0.0558494
$621$	7.84057	0.314631
$622$	8.32956	0.333985
$623$	−1.36700	−0.0547676
$624$	−3.15556	−0.126324
$625$	−2.32393	−0.0929572
$626$	−8.66237	−0.346218
$627$	2.01576	0.0805015
$628$	−23.7162	−0.946381
$629$	40.4499	1.61284
$630$	−2.49766	−0.0995091
$631$	−29.8638	−1.18886	−0.594429	−	0.804148i	$-0.702622\pi$
$631$	−29.8638	−1.18886	−0.594429	+	0.804148i	$0.702622\pi$
$632$	5.19669	0.206713
$633$	−27.6260	−1.09804
$634$	19.4340	0.771823
$635$	3.45386	0.137062
$636$	1.00000	0.0396526
$637$	12.8109	0.507584
$638$	−12.0454	−0.476880
$639$	0.646595	0.0255789
$640$	−1.45661	−0.0575774
$641$	2.54367	0.100469	0.0502344	−	0.998737i	$-0.484003\pi$
$641$	2.54367	0.100469	0.0502344	+	0.998737i	$0.484003\pi$
$642$	−13.0879	−0.516536
$643$	20.8730	0.823151	0.411575	−	0.911376i	$-0.364979\pi$
$643$	20.8730	0.823151	0.411575	+	0.911376i	$0.364979\pi$
$644$	13.4443	0.529780
$645$	6.23731	0.245594
$646$	−8.17609	−0.321684
$647$	18.6441	0.732974	0.366487	−	0.930423i	$-0.380561\pi$
$647$	18.6441	0.732974	0.366487	+	0.930423i	$0.380561\pi$
$648$	−1.00000	−0.0392837
$649$	10.3768	0.407324
$650$	−9.08264	−0.356250
$651$	−1.63705	−0.0641612
$652$	−11.5853	−0.453714
$653$	25.8128	1.01013	0.505066	−	0.863081i	$-0.331468\pi$
$653$	25.8128	1.01013	0.505066	+	0.863081i	$0.331468\pi$
$654$	−1.91654	−0.0749425
$655$	0.272087	0.0106313
$656$	7.49523	0.292640
$657$	−0.474324	−0.0185051
$658$	−22.2887	−0.868906
$659$	13.5376	0.527352	0.263676	−	0.964611i	$-0.415065\pi$
$659$	13.5376	0.527352	0.263676	+	0.964611i	$0.415065\pi$
$660$	−2.93616	−0.114290
$661$	1.39401	0.0542206	0.0271103	−	0.999632i	$-0.491369\pi$
$661$	1.39401	0.0542206	0.0271103	+	0.999632i	$0.491369\pi$
$662$	1.16487	0.0452741
$663$	25.8001	1.00199
$664$	8.68077	0.336879
$665$	−2.49766	−0.0968550
$666$	4.94735	0.191706
$667$	−46.8521	−1.81412
$668$	−14.3376	−0.554738
$669$	5.46249	0.211192
$670$	−2.81614	−0.108797
$671$	31.0286	1.19784
$672$	−1.71471	−0.0661464
$673$	−27.4040	−1.05635	−0.528174	−	0.849136i	$-0.677123\pi$
$673$	−27.4040	−1.05635	−0.528174	+	0.849136i	$0.677123\pi$
$674$	−8.67736	−0.334240
$675$	−2.87830	−0.110786
$676$	−3.04243	−0.117017
$677$	−35.2320	−1.35408	−0.677038	−	0.735948i	$-0.736737\pi$
$677$	−35.2320	−1.35408	−0.677038	+	0.735948i	$0.736737\pi$
$678$	−8.84681	−0.339760
$679$	−21.5819	−0.828235
$680$	11.9093	0.456702
$681$	14.5887	0.559039
$682$	−1.92446	−0.0736916
$683$	35.8519	1.37184	0.685918	−	0.727679i	$-0.259401\pi$
$683$	35.8519	1.37184	0.685918	+	0.727679i	$0.259401\pi$
$684$	−1.00000	−0.0382360
$685$	−18.8941	−0.721907
$686$	18.9643	0.724060
$687$	−7.53089	−0.287321
$688$	4.28208	0.163253
$689$	−3.15556	−0.120217
$690$	−11.4206	−0.434776
$691$	28.9582	1.10162	0.550810	−	0.834631i	$-0.314319\pi$
$691$	28.9582	1.10162	0.550810	+	0.834631i	$0.314319\pi$
$692$	−1.50648	−0.0572678
$693$	−3.45644	−0.131299
$694$	−5.80054	−0.220186
$695$	−25.0604	−0.950595
$696$	5.97560	0.226505
$697$	−61.2817	−2.32121
$698$	23.2831	0.881277
$699$	9.34308	0.353388
$700$	−4.93544	−0.186542
$701$	20.0903	0.758799	0.379400	−	0.925233i	$-0.376131\pi$
$701$	20.0903	0.758799	0.379400	+	0.925233i	$0.376131\pi$
$702$	3.15556	0.119099
$703$	4.94735	0.186593
$704$	−2.01576	−0.0759717
$705$	18.9338	0.713087
$706$	7.09757	0.267120
$707$	−26.8847	−1.01110
$708$	−5.14783	−0.193467
$709$	−50.8058	−1.90805	−0.954025	−	0.299727i	$-0.903104\pi$
$709$	−50.8058	−1.90805	−0.954025	+	0.299727i	$0.903104\pi$
$710$	−0.941835	−0.0353464
$711$	−5.19669	−0.194891
$712$	0.797217	0.0298770
$713$	−7.48548	−0.280333
$714$	14.0196	0.524671
$715$	9.26524	0.346501
$716$	12.9663	0.484572
$717$	−2.42411	−0.0905301
$718$	−6.89814	−0.257436
$719$	−17.2812	−0.644479	−0.322239	−	0.946658i	$-0.604436\pi$
$719$	−17.2812	−0.644479	−0.322239	+	0.946658i	$0.604436\pi$
$720$	1.45661	0.0542845
$721$	−0.662238	−0.0246630
$722$	−1.00000	−0.0372161
$723$	−1.11015	−0.0412869
$724$	24.4025	0.906913
$725$	17.1996	0.638776
$726$	6.93673	0.257446
$727$	−4.19226	−0.155482	−0.0777412	−	0.996974i	$-0.524771\pi$
$727$	−4.19226	−0.155482	−0.0777412	+	0.996974i	$0.524771\pi$
$728$	5.41087	0.200540
$729$	1.00000	0.0370370
$730$	0.690903	0.0255715
$731$	−35.0106	−1.29492
$732$	−15.3930	−0.568942
$733$	−23.8746	−0.881830	−0.440915	−	0.897549i	$-0.645346\pi$
$733$	−23.8746	−0.881830	−0.440915	+	0.897549i	$0.645346\pi$
$734$	−13.0904	−0.483174
$735$	−5.91349	−0.218122
$736$	−7.84057	−0.289007
$737$	−3.89717	−0.143554
$738$	−7.49523	−0.275903
$739$	−42.8373	−1.57580	−0.787898	−	0.615806i	$-0.788831\pi$
$739$	−42.8373	−1.57580	−0.787898	+	0.615806i	$0.788831\pi$
$740$	−7.20634	−0.264910
$741$	3.15556	0.115922
$742$	−1.71471	−0.0629490
$743$	9.60881	0.352513	0.176256	−	0.984344i	$-0.443601\pi$
$743$	9.60881	0.352513	0.176256	+	0.984344i	$0.443601\pi$
$744$	0.954711	0.0350014
$745$	−21.5442	−0.789319
$746$	17.5715	0.643339
$747$	−8.68077	−0.317613
$748$	16.4810	0.602605
$749$	22.4419	0.820008
$750$	11.4756	0.419029
$751$	20.8143	0.759525	0.379762	−	0.925084i	$-0.376006\pi$
$751$	20.8143	0.759525	0.379762	+	0.925084i	$0.376006\pi$
$752$	12.9986	0.474008
$753$	−9.27273	−0.337917
$754$	−18.8564	−0.686709
$755$	0.786521	0.0286244
$756$	1.71471	0.0623634
$757$	−41.4758	−1.50746	−0.753732	−	0.657182i	$-0.771748\pi$
$757$	−41.4758	−1.50746	−0.753732	+	0.657182i	$0.771748\pi$
$758$	−0.382274	−0.0138848
$759$	−15.8047	−0.573673
$760$	1.45661	0.0528367
$761$	16.6677	0.604203	0.302101	−	0.953276i	$-0.402312\pi$
$761$	16.6677	0.604203	0.302101	+	0.953276i	$0.402312\pi$
$762$	−2.37117	−0.0858983
$763$	3.28631	0.118972
$764$	3.99785	0.144637
$765$	−11.9093	−0.430583
$766$	23.6877	0.855873
$767$	16.2443	0.586547
$768$	1.00000	0.0360844
$769$	17.8578	0.643970	0.321985	−	0.946745i	$-0.395650\pi$
$769$	17.8578	0.643970	0.321985	+	0.946745i	$0.395650\pi$
$770$	5.03467	0.181437
$771$	−15.1544	−0.545771
$772$	19.9714	0.718785
$773$	24.0274	0.864206	0.432103	−	0.901824i	$-0.357772\pi$
$773$	24.0274	0.864206	0.432103	+	0.901824i	$0.357772\pi$
$774$	−4.28208	−0.153916
$775$	2.74794	0.0987090
$776$	12.5863	0.451822
$777$	−8.48327	−0.304335
$778$	−7.23425	−0.259360
$779$	−7.49523	−0.268545
$780$	−4.59641	−0.164578
$781$	−1.30338	−0.0466385
$782$	64.1052	2.29240
$783$	−5.97560	−0.213551
$784$	−4.05977	−0.144992
$785$	−34.5453	−1.23297
$786$	−0.186795	−0.00666277
$787$	−47.2675	−1.68490	−0.842452	−	0.538772i	$-0.818888\pi$
$787$	−47.2675	−1.68490	−0.842452	+	0.538772i	$0.818888\pi$
$788$	−14.1989	−0.505816
$789$	17.2069	0.612582
$790$	7.56953	0.269312
$791$	15.1697	0.539373
$792$	2.01576	0.0716268
$793$	48.5736	1.72490
$794$	−8.54971	−0.303418
$795$	1.45661	0.0516605
$796$	22.3504	0.792189
$797$	27.7822	0.984097	0.492049	−	0.870568i	$-0.336248\pi$
$797$	27.7822	0.984097	0.492049	+	0.870568i	$0.336248\pi$
$798$	1.71471	0.0607001
$799$	−106.277	−3.75982
$800$	2.87830	0.101763
$801$	−0.797217	−0.0281683
$802$	−22.0123	−0.777282
$803$	0.956121	0.0337408
$804$	1.93335	0.0681841
$805$	19.5831	0.690212
$806$	−3.01265	−0.106116
$807$	18.3261	0.645110
$808$	15.6789	0.551580
$809$	−28.6512	−1.00732	−0.503662	−	0.863901i	$-0.668014\pi$
$809$	−28.6512	−1.00732	−0.503662	+	0.863901i	$0.668014\pi$
$810$	−1.45661	−0.0511800
$811$	6.66553	0.234058	0.117029	−	0.993128i	$-0.462663\pi$
$811$	6.66553	0.234058	0.117029	+	0.993128i	$0.462663\pi$
$812$	−10.2464	−0.359579
$813$	−8.08715	−0.283629
$814$	−9.97264	−0.349541
$815$	−16.8752	−0.591111
$816$	−8.17609	−0.286220
$817$	−4.28208	−0.149811
$818$	19.6391	0.686666
$819$	−5.41087	−0.189071
$820$	10.9176	0.381259
$821$	−22.1499	−0.773036	−0.386518	−	0.922282i	$-0.626322\pi$
$821$	−22.1499	−0.773036	−0.386518	+	0.922282i	$0.626322\pi$
$822$	12.9713	0.452427
$823$	−4.72359	−0.164654	−0.0823271	−	0.996605i	$-0.526235\pi$
$823$	−4.72359	−0.164654	−0.0823271	+	0.996605i	$0.526235\pi$
$824$	0.386210	0.0134543
$825$	5.80194	0.201998
$826$	8.82703	0.307132
$827$	−24.2493	−0.843231	−0.421615	−	0.906775i	$-0.638537\pi$
$827$	−24.2493	−0.843231	−0.421615	+	0.906775i	$0.638537\pi$
$828$	7.84057	0.272479
$829$	−43.8674	−1.52358	−0.761789	−	0.647825i	$-0.775679\pi$
$829$	−43.8674	−1.52358	−0.761789	+	0.647825i	$0.775679\pi$
$830$	12.6445	0.438896
$831$	−17.9579	−0.622953
$832$	−3.15556	−0.109399
$833$	33.1930	1.15007
$834$	17.2046	0.595748
$835$	−20.8842	−0.722729
$836$	2.01576	0.0697164
$837$	−0.954711	−0.0329997
$838$	−2.42298	−0.0837005
$839$	−46.8889	−1.61878	−0.809392	−	0.587269i	$-0.800203\pi$
$839$	−46.8889	−1.61878	−0.809392	+	0.587269i	$0.800203\pi$
$840$	−2.49766	−0.0861774
$841$	6.70785	0.231305
$842$	−2.38557	−0.0822123
$843$	16.8409	0.580032
$844$	−27.6260	−0.950927
$845$	−4.43163	−0.152453
$846$	−12.9986	−0.446899
$847$	−11.8945	−0.408699
$848$	1.00000	0.0343401
$849$	14.1051	0.484087
$850$	−23.5332	−0.807182
$851$	−38.7900	−1.32970
$852$	0.646595	0.0221520
$853$	2.70537	0.0926300	0.0463150	−	0.998927i	$-0.485252\pi$
$853$	2.70537	0.0926300	0.0463150	+	0.998927i	$0.485252\pi$
$854$	26.3946	0.903203
$855$	−1.45661	−0.0498149
$856$	−13.0879	−0.447334
$857$	0.939179	0.0320817	0.0160409	−	0.999871i	$-0.494894\pi$
$857$	0.939179	0.0320817	0.0160409	+	0.999871i	$0.494894\pi$
$858$	−6.36084	−0.217156
$859$	−42.3309	−1.44431	−0.722156	−	0.691731i	$-0.756849\pi$
$859$	−42.3309	−1.44431	−0.722156	+	0.691731i	$0.756849\pi$
$860$	6.23731	0.212690
$861$	12.8522	0.438000
$862$	−20.9378	−0.713144
$863$	−29.1571	−0.992519	−0.496259	−	0.868174i	$-0.665293\pi$
$863$	−29.1571	−0.992519	−0.496259	+	0.868174i	$0.665293\pi$
$864$	−1.00000	−0.0340207
$865$	−2.19435	−0.0746101
$866$	23.0577	0.783531
$867$	49.8484	1.69294
$868$	−1.63705	−0.0555652
$869$	10.4753	0.355349
$870$	8.70411	0.295097
$871$	−6.10082	−0.206718
$872$	−1.91654	−0.0649021
$873$	−12.5863	−0.425982
$874$	7.84057	0.265211
$875$	−19.6773	−0.665214
$876$	−0.474324	−0.0160259
$877$	40.6185	1.37159	0.685795	−	0.727794i	$-0.259454\pi$
$877$	40.6185	1.37159	0.685795	+	0.727794i	$0.259454\pi$
$878$	−8.48716	−0.286428
$879$	15.3313	0.517111
$880$	−2.93616	−0.0989781
$881$	−42.6280	−1.43617	−0.718087	−	0.695953i	$-0.754982\pi$
$881$	−42.6280	−1.43617	−0.718087	+	0.695953i	$0.754982\pi$
$882$	4.05977	0.136700
$883$	12.6480	0.425641	0.212820	−	0.977091i	$-0.431735\pi$
$883$	12.6480	0.425641	0.212820	+	0.977091i	$0.431735\pi$
$884$	25.8001	0.867753
$885$	−7.49836	−0.252055
$886$	32.2670	1.08403
$887$	21.1126	0.708892	0.354446	−	0.935076i	$-0.384669\pi$
$887$	21.1126	0.708892	0.354446	+	0.935076i	$0.384669\pi$
$888$	4.94735	0.166022
$889$	4.06586	0.136365
$890$	1.16123	0.0389246
$891$	−2.01576	−0.0675304
$892$	5.46249	0.182898
$893$	−12.9986	−0.434980
$894$	14.7907	0.494675
$895$	18.8868	0.631315
$896$	−1.71471	−0.0572844
$897$	−24.7414	−0.826091
$898$	−9.73554	−0.324879
$899$	5.70498	0.190272
$900$	−2.87830	−0.0959432
$901$	−8.17609	−0.272385
$902$	15.1086	0.503060
$903$	7.34252	0.244344
$904$	−8.84681	−0.294241
$905$	35.5449	1.18155
$906$	−0.539968	−0.0179392
$907$	48.7525	1.61880	0.809400	−	0.587258i	$-0.199793\pi$
$907$	48.7525	1.61880	0.809400	+	0.587258i	$0.199793\pi$
$908$	14.5887	0.484142
$909$	−15.6789	−0.520035
$910$	7.88151	0.261270
$911$	37.4082	1.23939	0.619694	−	0.784844i	$-0.287257\pi$
$911$	37.4082	1.23939	0.619694	+	0.784844i	$0.287257\pi$
$912$	−1.00000	−0.0331133
$913$	17.4983	0.579110
$914$	−23.7425	−0.785332
$915$	−22.4216	−0.741234
$916$	−7.53089	−0.248828
$917$	0.320300	0.0105772
$918$	8.17609	0.269851
$919$	45.0838	1.48718	0.743588	−	0.668638i	$-0.233122\pi$
$919$	45.0838	1.48718	0.743588	+	0.668638i	$0.233122\pi$
$920$	−11.4206	−0.376527
$921$	−25.1603	−0.829059
$922$	−11.5229	−0.379485
$923$	−2.04037	−0.0671596
$924$	−3.45644	−0.113708
$925$	14.2399	0.468206
$926$	31.7796	1.04434
$927$	−0.386210	−0.0126848
$928$	5.97560	0.196159
$929$	−24.0194	−0.788052	−0.394026	−	0.919099i	$-0.628918\pi$
$929$	−24.0194	−0.788052	−0.394026	+	0.919099i	$0.628918\pi$
$930$	1.39064	0.0456009
$931$	4.05977	0.133054
$932$	9.34308	0.306043
$933$	−8.32956	−0.272698
$934$	−31.9271	−1.04469
$935$	24.0063	0.785091
$936$	3.15556	0.103143
$937$	9.62733	0.314511	0.157256	−	0.987558i	$-0.449735\pi$
$937$	9.62733	0.314511	0.157256	+	0.987558i	$0.449735\pi$
$938$	−3.31514	−0.108243
$939$	8.66237	0.282686
$940$	18.9338	0.617552
$941$	−31.9153	−1.04041	−0.520205	−	0.854041i	$-0.674144\pi$
$941$	−31.9153	−1.04041	−0.520205	+	0.854041i	$0.674144\pi$
$942$	23.7162	0.772717
$943$	58.7669	1.91371
$944$	−5.14783	−0.167548
$945$	2.49766	0.0812488
$946$	8.63163	0.280638
$947$	−31.7414	−1.03146	−0.515728	−	0.856752i	$-0.672479\pi$
$947$	−31.7414	−1.03146	−0.515728	+	0.856752i	$0.672479\pi$
$948$	−5.19669	−0.168781
$949$	1.49676	0.0485868
$950$	−2.87830	−0.0933843
$951$	−19.4340	−0.630191
$952$	14.0196	0.454378
$953$	−23.7273	−0.768603	−0.384302	−	0.923208i	$-0.625558\pi$
$953$	−23.7273	−0.768603	−0.384302	+	0.923208i	$0.625558\pi$
$954$	−1.00000	−0.0323762
$955$	5.82330	0.188437
$956$	−2.42411	−0.0784014
$957$	12.0454	0.389371
$958$	−20.5802	−0.664917
$959$	−22.2421	−0.718234
$960$	1.45661	0.0470118
$961$	−30.0885	−0.970598
$962$	−15.6117	−0.503340
$963$	13.0879	0.421750
$964$	−1.11015	−0.0357555
$965$	29.0904	0.936453
$966$	−13.4443	−0.432563
$967$	−27.9388	−0.898451	−0.449226	−	0.893418i	$-0.648300\pi$
$967$	−27.9388	−0.898451	−0.449226	+	0.893418i	$0.648300\pi$
$968$	6.93673	0.222955
$969$	8.17609	0.262654
$970$	18.3333	0.588646
$971$	−10.3523	−0.332222	−0.166111	−	0.986107i	$-0.553121\pi$
$971$	−10.3523	−0.332222	−0.166111	+	0.986107i	$0.553121\pi$
$972$	1.00000	0.0320750
$973$	−29.5010	−0.945758
$974$	41.3601	1.32526
$975$	9.08264	0.290877
$976$	−15.3930	−0.492718
$977$	−4.54767	−0.145493	−0.0727464	−	0.997350i	$-0.523176\pi$
$977$	−4.54767	−0.145493	−0.0727464	+	0.997350i	$0.523176\pi$
$978$	11.5853	0.370456
$979$	1.60700	0.0513598
$980$	−5.91349	−0.188899
$981$	1.91654	0.0611903
$982$	−17.7674	−0.566979
$983$	20.9923	0.669550	0.334775	−	0.942298i	$-0.391340\pi$
$983$	20.9923	0.669550	0.334775	+	0.942298i	$0.391340\pi$
$984$	−7.49523	−0.238939
$985$	−20.6823	−0.658992
$986$	−48.8571	−1.55593
$987$	22.2887	0.709459
$988$	3.15556	0.100392
$989$	33.5739	1.06759
$990$	2.93616	0.0933174
$991$	6.87924	0.218526	0.109263	−	0.994013i	$-0.465151\pi$
$991$	6.87924	0.218526	0.109263	+	0.994013i	$0.465151\pi$
$992$	0.954711	0.0303121
$993$	−1.16487	−0.0369661
$994$	−1.10872	−0.0351666
$995$	32.5558	1.03209
$996$	−8.68077	−0.275061
$997$	−50.9983	−1.61513	−0.807566	−	0.589778i	$-0.799215\pi$
$997$	−50.9983	−1.61513	−0.807566	+	0.589778i	$0.799215\pi$
$998$	−21.3206	−0.674890
$999$	−4.94735	−0.156527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.y.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.y.1.4	✓	7	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.45661 q^{5} -1.00000 q^{6} +1.71471 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.45661 q^{5} -1.00000 q^{6} +1.71471 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.45661 q^{10} -2.01576 q^{11} +1.00000 q^{12} -3.15556 q^{13} -1.71471 q^{14} +1.45661 q^{15} +1.00000 q^{16} -8.17609 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.45661 q^{20} +1.71471 q^{21} +2.01576 q^{22} +7.84057 q^{23} -1.00000 q^{24} -2.87830 q^{25} +3.15556 q^{26} +1.00000 q^{27} +1.71471 q^{28} -5.97560 q^{29} -1.45661 q^{30} -0.954711 q^{31} -1.00000 q^{32} -2.01576 q^{33} +8.17609 q^{34} +2.49766 q^{35} +1.00000 q^{36} -4.94735 q^{37} +1.00000 q^{38} -3.15556 q^{39} -1.45661 q^{40} +7.49523 q^{41} -1.71471 q^{42} +4.28208 q^{43} -2.01576 q^{44} +1.45661 q^{45} -7.84057 q^{46} +12.9986 q^{47} +1.00000 q^{48} -4.05977 q^{49} +2.87830 q^{50} -8.17609 q^{51} -3.15556 q^{52} +1.00000 q^{53} -1.00000 q^{54} -2.93616 q^{55} -1.71471 q^{56} -1.00000 q^{57} +5.97560 q^{58} -5.14783 q^{59} +1.45661 q^{60} -15.3930 q^{61} +0.954711 q^{62} +1.71471 q^{63} +1.00000 q^{64} -4.59641 q^{65} +2.01576 q^{66} +1.93335 q^{67} -8.17609 q^{68} +7.84057 q^{69} -2.49766 q^{70} +0.646595 q^{71} -1.00000 q^{72} -0.474324 q^{73} +4.94735 q^{74} -2.87830 q^{75} -1.00000 q^{76} -3.45644 q^{77} +3.15556 q^{78} -5.19669 q^{79} +1.45661 q^{80} +1.00000 q^{81} -7.49523 q^{82} -8.68077 q^{83} +1.71471 q^{84} -11.9093 q^{85} -4.28208 q^{86} -5.97560 q^{87} +2.01576 q^{88} -0.797217 q^{89} -1.45661 q^{90} -5.41087 q^{91} +7.84057 q^{92} -0.954711 q^{93} -12.9986 q^{94} -1.45661 q^{95} -1.00000 q^{96} -12.5863 q^{97} +4.05977 q^{98} -2.01576 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} + 7 q^{3} + 7 q^{4} + 4 q^{5} - 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 4 q^{10} - 2 q^{11} + 7 q^{12} - 7 q^{13} + 9 q^{14} + 4 q^{15} + 7 q^{16} - 10 q^{17} - 7 q^{18} - 7 q^{19} + 4 q^{20} - 9 q^{21} + 2 q^{22} + 2 q^{23} - 7 q^{24} + 3 q^{25} + 7 q^{26} + 7 q^{27} - 9 q^{28} - 6 q^{29} - 4 q^{30} + 3 q^{31} - 7 q^{32} - 2 q^{33} + 10 q^{34} + 7 q^{36} - 3 q^{37} + 7 q^{38} - 7 q^{39} - 4 q^{40} - 12 q^{41} + 9 q^{42} - 26 q^{43} - 2 q^{44} + 4 q^{45} - 2 q^{46} + 17 q^{47} + 7 q^{48} - 3 q^{50} - 10 q^{51} - 7 q^{52} + 7 q^{53} - 7 q^{54} - 23 q^{55} + 9 q^{56} - 7 q^{57} + 6 q^{58} + 7 q^{59} + 4 q^{60} - 18 q^{61} - 3 q^{62} - 9 q^{63} + 7 q^{64} - 23 q^{65} + 2 q^{66} - 3 q^{67} - 10 q^{68} + 2 q^{69} + 2 q^{71} - 7 q^{72} + q^{73} + 3 q^{74} + 3 q^{75} - 7 q^{76} - 23 q^{77} + 7 q^{78} - 18 q^{79} + 4 q^{80} + 7 q^{81} + 12 q^{82} - 17 q^{83} - 9 q^{84} - 3 q^{85} + 26 q^{86} - 6 q^{87} + 2 q^{88} - 13 q^{89} - 4 q^{90} - 8 q^{91} + 2 q^{92} + 3 q^{93} - 17 q^{94} - 4 q^{95} - 7 q^{96} - 20 q^{97} - 2 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 7 * q^3 + 7 * q^4 + 4 * q^5 - 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 4 * q^10 - 2 * q^11 + 7 * q^12 - 7 * q^13 + 9 * q^14 + 4 * q^15 + 7 * q^16 - 10 * q^17 - 7 * q^18 - 7 * q^19 + 4 * q^20 - 9 * q^21 + 2 * q^22 + 2 * q^23 - 7 * q^24 + 3 * q^25 + 7 * q^26 + 7 * q^27 - 9 * q^28 - 6 * q^29 - 4 * q^30 + 3 * q^31 - 7 * q^32 - 2 * q^33 + 10 * q^34 + 7 * q^36 - 3 * q^37 + 7 * q^38 - 7 * q^39 - 4 * q^40 - 12 * q^41 + 9 * q^42 - 26 * q^43 - 2 * q^44 + 4 * q^45 - 2 * q^46 + 17 * q^47 + 7 * q^48 - 3 * q^50 - 10 * q^51 - 7 * q^52 + 7 * q^53 - 7 * q^54 - 23 * q^55 + 9 * q^56 - 7 * q^57 + 6 * q^58 + 7 * q^59 + 4 * q^60 - 18 * q^61 - 3 * q^62 - 9 * q^63 + 7 * q^64 - 23 * q^65 + 2 * q^66 - 3 * q^67 - 10 * q^68 + 2 * q^69 + 2 * q^71 - 7 * q^72 + q^73 + 3 * q^74 + 3 * q^75 - 7 * q^76 - 23 * q^77 + 7 * q^78 - 18 * q^79 + 4 * q^80 + 7 * q^81 + 12 * q^82 - 17 * q^83 - 9 * q^84 - 3 * q^85 + 26 * q^86 - 6 * q^87 + 2 * q^88 - 13 * q^89 - 4 * q^90 - 8 * q^91 + 2 * q^92 + 3 * q^93 - 17 * q^94 - 4 * q^95 - 7 * q^96 - 20 * q^97 - 2 * q^99

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