LMFDB - Embedded newform 2670.2.a.t.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2670,2,Mod(1,2670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2670, 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("2670.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2670 = 2 \cdot 3 \cdot 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2670.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:	$21.3200573397$
Analytic rank:	$0$
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} - 24x^{5} + 34x^{4} + 111x^{3} - 127x^{2} - 20x + 16 $ x^7 - 3x^6 - 24x^5 + 34x^4 + 111x^3 - 127x^2 - 20x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.69745$ of defining polynomial
Character	$\chi$	$=$	2670.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.15694 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.15694 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -6.34399 q^{11} -1.00000 q^{12} -5.23358 q^{13} -1.15694 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.50216 q^{17} -1.00000 q^{18} +1.05092 q^{19} -1.00000 q^{20} -1.15694 q^{21} +6.34399 q^{22} +0.797994 q^{23} +1.00000 q^{24} +1.00000 q^{25} +5.23358 q^{26} -1.00000 q^{27} +1.15694 q^{28} -7.76739 q^{29} -1.00000 q^{30} +9.54746 q^{31} -1.00000 q^{32} +6.34399 q^{33} +6.50216 q^{34} -1.15694 q^{35} +1.00000 q^{36} +0.264192 q^{37} -1.05092 q^{38} +5.23358 q^{39} +1.00000 q^{40} +0.200768 q^{41} +1.15694 q^{42} -3.28211 q^{43} -6.34399 q^{44} -1.00000 q^{45} -0.797994 q^{46} +5.08250 q^{47} -1.00000 q^{48} -5.66149 q^{49} -1.00000 q^{50} +6.50216 q^{51} -5.23358 q^{52} +14.2876 q^{53} +1.00000 q^{54} +6.34399 q^{55} -1.15694 q^{56} -1.05092 q^{57} +7.76739 q^{58} +11.5381 q^{59} +1.00000 q^{60} +11.4084 q^{61} -9.54746 q^{62} +1.15694 q^{63} +1.00000 q^{64} +5.23358 q^{65} -6.34399 q^{66} -11.7854 q^{67} -6.50216 q^{68} -0.797994 q^{69} +1.15694 q^{70} -8.25150 q^{71} -1.00000 q^{72} -8.45709 q^{73} -0.264192 q^{74} -1.00000 q^{75} +1.05092 q^{76} -7.33960 q^{77} -5.23358 q^{78} +5.32834 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.200768 q^{82} -0.830997 q^{83} -1.15694 q^{84} +6.50216 q^{85} +3.28211 q^{86} +7.76739 q^{87} +6.34399 q^{88} +1.00000 q^{89} +1.00000 q^{90} -6.05493 q^{91} +0.797994 q^{92} -9.54746 q^{93} -5.08250 q^{94} -1.05092 q^{95} +1.00000 q^{96} +0.404012 q^{97} +5.66149 q^{98} -6.34399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 7 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 7 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 7 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 7 q^{10} + q^{11} - 7 q^{12} - q^{14} + 7 q^{15} + 7 q^{16} - 9 q^{17} - 7 q^{18} + 9 q^{19} - 7 q^{20} - q^{21} - q^{22} - 8 q^{23} + 7 q^{24} + 7 q^{25} - 7 q^{27} + q^{28} - 4 q^{29} - 7 q^{30} + 16 q^{31} - 7 q^{32} - q^{33} + 9 q^{34} - q^{35} + 7 q^{36} + 2 q^{37} - 9 q^{38} + 7 q^{40} - q^{41} + q^{42} - 10 q^{43} + q^{44} - 7 q^{45} + 8 q^{46} - 13 q^{47} - 7 q^{48} + 26 q^{49} - 7 q^{50} + 9 q^{51} - 24 q^{53} + 7 q^{54} - q^{55} - q^{56} - 9 q^{57} + 4 q^{58} - 6 q^{59} + 7 q^{60} + 23 q^{61} - 16 q^{62} + q^{63} + 7 q^{64} + q^{66} + 5 q^{67} - 9 q^{68} + 8 q^{69} + q^{70} - 8 q^{71} - 7 q^{72} - 2 q^{73} - 2 q^{74} - 7 q^{75} + 9 q^{76} - 6 q^{77} + 7 q^{79} - 7 q^{80} + 7 q^{81} + q^{82} - 7 q^{83} - q^{84} + 9 q^{85} + 10 q^{86} + 4 q^{87} - q^{88} + 7 q^{89} + 7 q^{90} + 48 q^{91} - 8 q^{92} - 16 q^{93} + 13 q^{94} - 9 q^{95} + 7 q^{96} + 30 q^{97} - 26 q^{98} + q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 7 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 7 * q^10 + q^11 - 7 * q^12 - q^14 + 7 * q^15 + 7 * q^16 - 9 * q^17 - 7 * q^18 + 9 * q^19 - 7 * q^20 - q^21 - q^22 - 8 * q^23 + 7 * q^24 + 7 * q^25 - 7 * q^27 + q^28 - 4 * q^29 - 7 * q^30 + 16 * q^31 - 7 * q^32 - q^33 + 9 * q^34 - q^35 + 7 * q^36 + 2 * q^37 - 9 * q^38 + 7 * q^40 - q^41 + q^42 - 10 * q^43 + q^44 - 7 * q^45 + 8 * q^46 - 13 * q^47 - 7 * q^48 + 26 * q^49 - 7 * q^50 + 9 * q^51 - 24 * q^53 + 7 * q^54 - q^55 - q^56 - 9 * q^57 + 4 * q^58 - 6 * q^59 + 7 * q^60 + 23 * q^61 - 16 * q^62 + q^63 + 7 * q^64 + q^66 + 5 * q^67 - 9 * q^68 + 8 * q^69 + q^70 - 8 * q^71 - 7 * q^72 - 2 * q^73 - 2 * q^74 - 7 * q^75 + 9 * q^76 - 6 * q^77 + 7 * q^79 - 7 * q^80 + 7 * q^81 + q^82 - 7 * q^83 - q^84 + 9 * q^85 + 10 * q^86 + 4 * q^87 - q^88 + 7 * q^89 + 7 * q^90 + 48 * q^91 - 8 * q^92 - 16 * q^93 + 13 * q^94 - 9 * q^95 + 7 * q^96 + 30 * q^97 - 26 * q^98 + 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
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	1.15694	0.437282	0.218641	−	0.975805i	$-0.429838\pi$
$7$	1.15694	0.437282	0.218641	+	0.975805i	$0.429838\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−6.34399	−1.91278	−0.956392	−	0.292087i	$-0.905650\pi$
$11$	−6.34399	−1.91278	−0.956392	+	0.292087i	$0.905650\pi$
$12$	−1.00000	−0.288675
$13$	−5.23358	−1.45153	−0.725767	−	0.687940i	$-0.758515\pi$
$13$	−5.23358	−1.45153	−0.725767	+	0.687940i	$0.758515\pi$
$14$	−1.15694	−0.309205
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−6.50216	−1.57701	−0.788503	−	0.615031i	$-0.789143\pi$
$17$	−6.50216	−1.57701	−0.788503	+	0.615031i	$0.789143\pi$
$18$	−1.00000	−0.235702
$19$	1.05092	0.241098	0.120549	−	0.992707i	$-0.461535\pi$
$19$	1.05092	0.241098	0.120549	+	0.992707i	$0.461535\pi$
$20$	−1.00000	−0.223607
$21$	−1.15694	−0.252465
$22$	6.34399	1.35254
$23$	0.797994	0.166393	0.0831966	−	0.996533i	$-0.473487\pi$
$23$	0.797994	0.166393	0.0831966	+	0.996533i	$0.473487\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	5.23358	1.02639
$27$	−1.00000	−0.192450
$28$	1.15694	0.218641
$29$	−7.76739	−1.44237	−0.721184	−	0.692744i	$-0.756402\pi$
$29$	−7.76739	−1.44237	−0.721184	+	0.692744i	$0.756402\pi$
$30$	−1.00000	−0.182574
$31$	9.54746	1.71477	0.857387	−	0.514672i	$-0.172086\pi$
$31$	9.54746	1.71477	0.857387	+	0.514672i	$0.172086\pi$
$32$	−1.00000	−0.176777
$33$	6.34399	1.10435
$34$	6.50216	1.11511
$35$	−1.15694	−0.195558
$36$	1.00000	0.166667
$37$	0.264192	0.0434329	0.0217165	−	0.999764i	$-0.493087\pi$
$37$	0.264192	0.0434329	0.0217165	+	0.999764i	$0.493087\pi$
$38$	−1.05092	−0.170482
$39$	5.23358	0.838044
$40$	1.00000	0.158114
$41$	0.200768	0.0313547	0.0156774	−	0.999877i	$-0.495010\pi$
$41$	0.200768	0.0313547	0.0156774	+	0.999877i	$0.495010\pi$
$42$	1.15694	0.178519
$43$	−3.28211	−0.500517	−0.250259	−	0.968179i	$-0.580516\pi$
$43$	−3.28211	−0.500517	−0.250259	+	0.968179i	$0.580516\pi$
$44$	−6.34399	−0.956392
$45$	−1.00000	−0.149071
$46$	−0.797994	−0.117658
$47$	5.08250	0.741359	0.370679	−	0.928761i	$-0.379125\pi$
$47$	5.08250	0.741359	0.370679	+	0.928761i	$0.379125\pi$
$48$	−1.00000	−0.144338
$49$	−5.66149	−0.808785
$50$	−1.00000	−0.141421
$51$	6.50216	0.910485
$52$	−5.23358	−0.725767
$53$	14.2876	1.96255	0.981276	−	0.192608i	$-0.0616945\pi$
$53$	14.2876	1.96255	0.981276	+	0.192608i	$0.0616945\pi$
$54$	1.00000	0.136083
$55$	6.34399	0.855423
$56$	−1.15694	−0.154602
$57$	−1.05092	−0.139198
$58$	7.76739	1.01991
$59$	11.5381	1.50214	0.751068	−	0.660225i	$-0.229539\pi$
$59$	11.5381	1.50214	0.751068	+	0.660225i	$0.229539\pi$
$60$	1.00000	0.129099
$61$	11.4084	1.46070	0.730351	−	0.683072i	$-0.239357\pi$
$61$	11.4084	1.46070	0.730351	+	0.683072i	$0.239357\pi$
$62$	−9.54746	−1.21253
$63$	1.15694	0.145761
$64$	1.00000	0.125000
$65$	5.23358	0.649146
$66$	−6.34399	−0.780891
$67$	−11.7854	−1.43982	−0.719910	−	0.694068i	$-0.755817\pi$
$67$	−11.7854	−1.43982	−0.719910	+	0.694068i	$0.755817\pi$
$68$	−6.50216	−0.788503
$69$	−0.797994	−0.0960672
$70$	1.15694	0.138281
$71$	−8.25150	−0.979273	−0.489637	−	0.871927i	$-0.662871\pi$
$71$	−8.25150	−0.979273	−0.489637	+	0.871927i	$0.662871\pi$
$72$	−1.00000	−0.117851
$73$	−8.45709	−0.989828	−0.494914	−	0.868942i	$-0.664800\pi$
$73$	−8.45709	−0.989828	−0.494914	+	0.868942i	$0.664800\pi$
$74$	−0.264192	−0.0307117
$75$	−1.00000	−0.115470
$76$	1.05092	0.120549
$77$	−7.33960	−0.836425
$78$	−5.23358	−0.592587
$79$	5.32834	0.599485	0.299742	−	0.954020i	$-0.403099\pi$
$79$	5.32834	0.599485	0.299742	+	0.954020i	$0.403099\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−0.200768	−0.0221711
$83$	−0.830997	−0.0912137	−0.0456069	−	0.998959i	$-0.514522\pi$
$83$	−0.830997	−0.0912137	−0.0456069	+	0.998959i	$0.514522\pi$
$84$	−1.15694	−0.126232
$85$	6.50216	0.705258
$86$	3.28211	0.353919
$87$	7.76739	0.832751
$88$	6.34399	0.676271
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	1.00000	0.105409
$91$	−6.05493	−0.634729
$92$	0.797994	0.0831966
$93$	−9.54746	−0.990025
$94$	−5.08250	−0.524220
$95$	−1.05092	−0.107822
$96$	1.00000	0.102062
$97$	0.404012	0.0410212	0.0205106	−	0.999790i	$-0.493471\pi$
$97$	0.404012	0.0410212	0.0205106	+	0.999790i	$0.493471\pi$
$98$	5.66149	0.571897
$99$	−6.34399	−0.637595
$100$	1.00000	0.100000
$101$	7.02243	0.698758	0.349379	−	0.936982i	$-0.386393\pi$
$101$	7.02243	0.698758	0.349379	+	0.936982i	$0.386393\pi$
$102$	−6.50216	−0.643810
$103$	−0.684886	−0.0674838	−0.0337419	−	0.999431i	$-0.510742\pi$
$103$	−0.684886	−0.0674838	−0.0337419	+	0.999431i	$0.510742\pi$
$104$	5.23358	0.513195
$105$	1.15694	0.112906
$106$	−14.2876	−1.38773
$107$	−18.2840	−1.76758	−0.883789	−	0.467887i	$-0.845016\pi$
$107$	−18.2840	−1.76758	−0.883789	+	0.467887i	$0.845016\pi$
$108$	−1.00000	−0.0962250
$109$	−4.56538	−0.437284	−0.218642	−	0.975805i	$-0.570163\pi$
$109$	−4.56538	−0.437284	−0.218642	+	0.975805i	$0.570163\pi$
$110$	−6.34399	−0.604875
$111$	−0.264192	−0.0250760
$112$	1.15694	0.109320
$113$	−0.850154	−0.0799757	−0.0399879	−	0.999200i	$-0.512732\pi$
$113$	−0.850154	−0.0799757	−0.0399879	+	0.999200i	$0.512732\pi$
$114$	1.05092	0.0984279
$115$	−0.797994	−0.0744133
$116$	−7.76739	−0.721184
$117$	−5.23358	−0.483845
$118$	−11.5381	−1.06217
$119$	−7.52260	−0.689596
$120$	−1.00000	−0.0912871
$121$	29.2462	2.65874
$122$	−11.4084	−1.03287
$123$	−0.200768	−0.0181027
$124$	9.54746	0.857387
$125$	−1.00000	−0.0894427
$126$	−1.15694	−0.103068
$127$	5.53078	0.490777	0.245389	−	0.969425i	$-0.421084\pi$
$127$	5.53078	0.490777	0.245389	+	0.969425i	$0.421084\pi$
$128$	−1.00000	−0.0883883
$129$	3.28211	0.288974
$130$	−5.23358	−0.459016
$131$	−13.0712	−1.14203	−0.571017	−	0.820938i	$-0.693451\pi$
$131$	−13.0712	−1.14203	−0.571017	+	0.820938i	$0.693451\pi$
$132$	6.34399	0.552173
$133$	1.21585	0.105428
$134$	11.7854	1.01811
$135$	1.00000	0.0860663
$136$	6.50216	0.557556
$137$	17.5381	1.49838	0.749192	−	0.662353i	$-0.230442\pi$
$137$	17.5381	1.49838	0.749192	+	0.662353i	$0.230442\pi$
$138$	0.797994	0.0679298
$139$	14.3741	1.21919	0.609597	−	0.792711i	$-0.291331\pi$
$139$	14.3741	1.21919	0.609597	+	0.792711i	$0.291331\pi$
$140$	−1.15694	−0.0977791
$141$	−5.08250	−0.428024
$142$	8.25150	0.692451
$143$	33.2018	2.77647
$144$	1.00000	0.0833333
$145$	7.76739	0.645046
$146$	8.45709	0.699914
$147$	5.66149	0.466952
$148$	0.264192	0.0217165
$149$	9.98305	0.817843	0.408922	−	0.912569i	$-0.365905\pi$
$149$	9.98305	0.817843	0.408922	+	0.912569i	$0.365905\pi$
$150$	1.00000	0.0816497
$151$	13.4544	1.09490	0.547451	−	0.836838i	$-0.315598\pi$
$151$	13.4544	1.09490	0.547451	+	0.836838i	$0.315598\pi$
$152$	−1.05092	−0.0852410
$153$	−6.50216	−0.525669
$154$	7.33960	0.591442
$155$	−9.54746	−0.766870
$156$	5.23358	0.419022
$157$	18.5890	1.48357	0.741784	−	0.670639i	$-0.233980\pi$
$157$	18.5890	1.48357	0.741784	+	0.670639i	$0.233980\pi$
$158$	−5.32834	−0.423900
$159$	−14.2876	−1.13308
$160$	1.00000	0.0790569
$161$	0.923230	0.0727607
$162$	−1.00000	−0.0785674
$163$	−14.5861	−1.14247	−0.571237	−	0.820785i	$-0.693536\pi$
$163$	−14.5861	−1.14247	−0.571237	+	0.820785i	$0.693536\pi$
$164$	0.200768	0.0156774
$165$	−6.34399	−0.493879
$166$	0.830997	0.0644979
$167$	−14.3327	−1.10909	−0.554547	−	0.832152i	$-0.687109\pi$
$167$	−14.3327	−1.10909	−0.554547	+	0.832152i	$0.687109\pi$
$168$	1.15694	0.0892597
$169$	14.3904	1.10695
$170$	−6.50216	−0.498693
$171$	1.05092	0.0803660
$172$	−3.28211	−0.250259
$173$	−11.1025	−0.844110	−0.422055	−	0.906570i	$-0.638691\pi$
$173$	−11.1025	−0.844110	−0.422055	+	0.906570i	$0.638691\pi$
$174$	−7.76739	−0.588844
$175$	1.15694	0.0874563
$176$	−6.34399	−0.478196
$177$	−11.5381	−0.867259
$178$	−1.00000	−0.0749532
$179$	1.20998	0.0904379	0.0452190	−	0.998977i	$-0.485601\pi$
$179$	1.20998	0.0904379	0.0452190	+	0.998977i	$0.485601\pi$
$180$	−1.00000	−0.0745356
$181$	5.97667	0.444242	0.222121	−	0.975019i	$-0.428702\pi$
$181$	5.97667	0.444242	0.222121	+	0.975019i	$0.428702\pi$
$182$	6.05493	0.448822
$183$	−11.4084	−0.843336
$184$	−0.797994	−0.0588289
$185$	−0.264192	−0.0194238
$186$	9.54746	0.700054
$187$	41.2496	3.01647
$188$	5.08250	0.370679
$189$	−1.15694	−0.0841549
$190$	1.05092	0.0762419
$191$	11.8046	0.854148	0.427074	−	0.904217i	$-0.359544\pi$
$191$	11.8046	0.854148	0.427074	+	0.904217i	$0.359544\pi$
$192$	−1.00000	−0.0721688
$193$	−2.84768	−0.204980	−0.102490	−	0.994734i	$-0.532681\pi$
$193$	−2.84768	−0.204980	−0.102490	+	0.994734i	$0.532681\pi$
$194$	−0.404012	−0.0290064
$195$	−5.23358	−0.374785
$196$	−5.66149	−0.404392
$197$	22.0561	1.57143	0.785715	−	0.618589i	$-0.212295\pi$
$197$	22.0561	1.57143	0.785715	+	0.618589i	$0.212295\pi$
$198$	6.34399	0.450847
$199$	−9.06110	−0.642324	−0.321162	−	0.947024i	$-0.604073\pi$
$199$	−9.06110	−0.642324	−0.321162	+	0.947024i	$0.604073\pi$
$200$	−1.00000	−0.0707107
$201$	11.7854	0.831280
$202$	−7.02243	−0.494096
$203$	−8.98639	−0.630721
$204$	6.50216	0.455242
$205$	−0.200768	−0.0140223
$206$	0.684886	0.0477182
$207$	0.797994	0.0554644
$208$	−5.23358	−0.362884
$209$	−6.66703	−0.461168
$210$	−1.15694	−0.0798363
$211$	−9.07734	−0.624910	−0.312455	−	0.949933i	$-0.601151\pi$
$211$	−9.07734	−0.624910	−0.312455	+	0.949933i	$0.601151\pi$
$212$	14.2876	0.981276
$213$	8.25150	0.565384
$214$	18.2840	1.24987
$215$	3.28211	0.223838
$216$	1.00000	0.0680414
$217$	11.0458	0.749839
$218$	4.56538	0.309207
$219$	8.45709	0.571477
$220$	6.34399	0.427711
$221$	34.0296	2.28908
$222$	0.264192	0.0177314
$223$	6.78866	0.454602	0.227301	−	0.973825i	$-0.427010\pi$
$223$	6.78866	0.454602	0.227301	+	0.973825i	$0.427010\pi$
$224$	−1.15694	−0.0773012
$225$	1.00000	0.0666667
$226$	0.850154	0.0565514
$227$	−3.49414	−0.231915	−0.115957	−	0.993254i	$-0.536994\pi$
$227$	−3.49414	−0.231915	−0.115957	+	0.993254i	$0.536994\pi$
$228$	−1.05092	−0.0695990
$229$	−20.1681	−1.33274	−0.666372	−	0.745619i	$-0.732154\pi$
$229$	−20.1681	−1.33274	−0.666372	+	0.745619i	$0.732154\pi$
$230$	0.797994	0.0526182
$231$	7.33960	0.482910
$232$	7.76739	0.509954
$233$	−3.59903	−0.235780	−0.117890	−	0.993027i	$-0.537613\pi$
$233$	−3.59903	−0.235780	−0.117890	+	0.993027i	$0.537613\pi$
$234$	5.23358	0.342130
$235$	−5.08250	−0.331546
$236$	11.5381	0.751068
$237$	−5.32834	−0.346113
$238$	7.52260	0.487618
$239$	16.9984	1.09953	0.549767	−	0.835318i	$-0.314716\pi$
$239$	16.9984	1.09953	0.549767	+	0.835318i	$0.314716\pi$
$240$	1.00000	0.0645497
$241$	23.4059	1.50770	0.753852	−	0.657044i	$-0.228194\pi$
$241$	23.4059	1.50770	0.753852	+	0.657044i	$0.228194\pi$
$242$	−29.2462	−1.88001
$243$	−1.00000	−0.0641500
$244$	11.4084	0.730351
$245$	5.66149	0.361700
$246$	0.200768	0.0128005
$247$	−5.50009	−0.349962
$248$	−9.54746	−0.606264
$249$	0.830997	0.0526623
$250$	1.00000	0.0632456
$251$	8.52642	0.538183	0.269091	−	0.963115i	$-0.413277\pi$
$251$	8.52642	0.538183	0.269091	+	0.963115i	$0.413277\pi$
$252$	1.15694	0.0728803
$253$	−5.06246	−0.318274
$254$	−5.53078	−0.347032
$255$	−6.50216	−0.407181
$256$	1.00000	0.0625000
$257$	30.0031	1.87154	0.935772	−	0.352606i	$-0.114704\pi$
$257$	30.0031	1.87154	0.935772	+	0.352606i	$0.114704\pi$
$258$	−3.28211	−0.204335
$259$	0.305654	0.0189924
$260$	5.23358	0.324573
$261$	−7.76739	−0.480789
$262$	13.0712	0.807540
$263$	−11.0156	−0.679250	−0.339625	−	0.940561i	$-0.610300\pi$
$263$	−11.0156	−0.679250	−0.339625	+	0.940561i	$0.610300\pi$
$264$	−6.34399	−0.390445
$265$	−14.2876	−0.877680
$266$	−1.21585	−0.0745487
$267$	−1.00000	−0.0611990
$268$	−11.7854	−0.719910
$269$	17.9259	1.09296	0.546481	−	0.837471i	$-0.315967\pi$
$269$	17.9259	1.09296	0.546481	+	0.837471i	$0.315967\pi$
$270$	−1.00000	−0.0608581
$271$	−5.04757	−0.306618	−0.153309	−	0.988178i	$-0.548993\pi$
$271$	−5.04757	−0.306618	−0.153309	+	0.988178i	$0.548993\pi$
$272$	−6.50216	−0.394251
$273$	6.05493	0.366461
$274$	−17.5381	−1.05952
$275$	−6.34399	−0.382557
$276$	−0.797994	−0.0480336
$277$	−9.34349	−0.561396	−0.280698	−	0.959796i	$-0.590566\pi$
$277$	−9.34349	−0.561396	−0.280698	+	0.959796i	$0.590566\pi$
$278$	−14.3741	−0.862101
$279$	9.54746	0.571591
$280$	1.15694	0.0691403
$281$	−4.26392	−0.254364	−0.127182	−	0.991879i	$-0.540593\pi$
$281$	−4.26392	−0.254364	−0.127182	+	0.991879i	$0.540593\pi$
$282$	5.08250	0.302658
$283$	−22.0993	−1.31367	−0.656834	−	0.754035i	$-0.728105\pi$
$283$	−22.0993	−1.31367	−0.656834	+	0.754035i	$0.728105\pi$
$284$	−8.25150	−0.489637
$285$	1.05092	0.0622512
$286$	−33.2018	−1.96326
$287$	0.232276	0.0137108
$288$	−1.00000	−0.0589256
$289$	25.2781	1.48695
$290$	−7.76739	−0.456117
$291$	−0.404012	−0.0236836
$292$	−8.45709	−0.494914
$293$	−17.5011	−1.02243	−0.511214	−	0.859454i	$-0.670804\pi$
$293$	−17.5011	−1.02243	−0.511214	+	0.859454i	$0.670804\pi$
$294$	−5.66149	−0.330185
$295$	−11.5381	−0.671776
$296$	−0.264192	−0.0153559
$297$	6.34399	0.368115
$298$	−9.98305	−0.578303
$299$	−4.17637	−0.241526
$300$	−1.00000	−0.0577350
$301$	−3.79720	−0.218867
$302$	−13.4544	−0.774213
$303$	−7.02243	−0.403428
$304$	1.05092	0.0602745
$305$	−11.4084	−0.653245
$306$	6.50216	0.371704
$307$	−8.36765	−0.477567	−0.238784	−	0.971073i	$-0.576749\pi$
$307$	−8.36765	−0.477567	−0.238784	+	0.971073i	$0.576749\pi$
$308$	−7.33960	−0.418213
$309$	0.684886	0.0389618
$310$	9.54746	0.542259
$311$	5.19383	0.294515	0.147257	−	0.989098i	$-0.452955\pi$
$311$	5.19383	0.294515	0.147257	+	0.989098i	$0.452955\pi$
$312$	−5.23358	−0.296293
$313$	8.24724	0.466162	0.233081	−	0.972457i	$-0.425119\pi$
$313$	8.24724	0.466162	0.233081	+	0.972457i	$0.425119\pi$
$314$	−18.5890	−1.04904
$315$	−1.15694	−0.0651861
$316$	5.32834	0.299742
$317$	7.49484	0.420952	0.210476	−	0.977599i	$-0.432499\pi$
$317$	7.49484	0.420952	0.210476	+	0.977599i	$0.432499\pi$
$318$	14.2876	0.801208
$319$	49.2762	2.75894
$320$	−1.00000	−0.0559017
$321$	18.2840	1.02051
$322$	−0.923230	−0.0514496
$323$	−6.83326	−0.380213
$324$	1.00000	0.0555556
$325$	−5.23358	−0.290307
$326$	14.5861	0.807851
$327$	4.56538	0.252466
$328$	−0.200768	−0.0110856
$329$	5.88014	0.324183
$330$	6.34399	0.349225
$331$	15.1551	0.833002	0.416501	−	0.909135i	$-0.363256\pi$
$331$	15.1551	0.833002	0.416501	+	0.909135i	$0.363256\pi$
$332$	−0.830997	−0.0456069
$333$	0.264192	0.0144776
$334$	14.3327	0.784248
$335$	11.7854	0.643907
$336$	−1.15694	−0.0631162
$337$	26.3691	1.43642	0.718209	−	0.695828i	$-0.244962\pi$
$337$	26.3691	1.43642	0.718209	+	0.695828i	$0.244962\pi$
$338$	−14.3904	−0.782734
$339$	0.850154	0.0461740
$340$	6.50216	0.352629
$341$	−60.5690	−3.27999
$342$	−1.05092	−0.0568274
$343$	−14.6486	−0.790948
$344$	3.28211	0.176960
$345$	0.797994	0.0429626
$346$	11.1025	0.596876
$347$	−20.1580	−1.08214	−0.541069	−	0.840978i	$-0.681980\pi$
$347$	−20.1580	−1.08214	−0.541069	+	0.840978i	$0.681980\pi$
$348$	7.76739	0.416376
$349$	−1.80005	−0.0963544	−0.0481772	−	0.998839i	$-0.515341\pi$
$349$	−1.80005	−0.0963544	−0.0481772	+	0.998839i	$0.515341\pi$
$350$	−1.15694	−0.0618410
$351$	5.23358	0.279348
$352$	6.34399	0.338136
$353$	−5.02841	−0.267635	−0.133818	−	0.991006i	$-0.542724\pi$
$353$	−5.02841	−0.267635	−0.133818	+	0.991006i	$0.542724\pi$
$354$	11.5381	0.613244
$355$	8.25150	0.437944
$356$	1.00000	0.0529999
$357$	7.52260	0.398138
$358$	−1.20998	−0.0639493
$359$	−12.4533	−0.657261	−0.328631	−	0.944459i	$-0.606587\pi$
$359$	−12.4533	−0.657261	−0.328631	+	0.944459i	$0.606587\pi$
$360$	1.00000	0.0527046
$361$	−17.8956	−0.941872
$362$	−5.97667	−0.314127
$363$	−29.2462	−1.53503
$364$	−6.05493	−0.317365
$365$	8.45709	0.442665
$366$	11.4084	0.596329
$367$	17.2175	0.898747	0.449373	−	0.893344i	$-0.351647\pi$
$367$	17.2175	0.898747	0.449373	+	0.893344i	$0.351647\pi$
$368$	0.797994	0.0415983
$369$	0.200768	0.0104516
$370$	0.264192	0.0137347
$371$	16.5299	0.858188
$372$	−9.54746	−0.495013
$373$	−6.98439	−0.361638	−0.180819	−	0.983516i	$-0.557875\pi$
$373$	−6.98439	−0.361638	−0.180819	+	0.983516i	$0.557875\pi$
$374$	−41.2496	−2.13297
$375$	1.00000	0.0516398
$376$	−5.08250	−0.262110
$377$	40.6513	2.09365
$378$	1.15694	0.0595065
$379$	25.1405	1.29138	0.645690	−	0.763599i	$-0.276570\pi$
$379$	25.1405	1.29138	0.645690	+	0.763599i	$0.276570\pi$
$380$	−1.05092	−0.0539112
$381$	−5.53078	−0.283350
$382$	−11.8046	−0.603974
$383$	−2.67425	−0.136648	−0.0683238	−	0.997663i	$-0.521765\pi$
$383$	−2.67425	−0.136648	−0.0683238	+	0.997663i	$0.521765\pi$
$384$	1.00000	0.0510310
$385$	7.33960	0.374061
$386$	2.84768	0.144943
$387$	−3.28211	−0.166839
$388$	0.404012	0.0205106
$389$	11.8593	0.601290	0.300645	−	0.953736i	$-0.402798\pi$
$389$	11.8593	0.601290	0.300645	+	0.953736i	$0.402798\pi$
$390$	5.23358	0.265013
$391$	−5.18869	−0.262403
$392$	5.66149	0.285949
$393$	13.0712	0.659353
$394$	−22.0561	−1.11117
$395$	−5.32834	−0.268098
$396$	−6.34399	−0.318797
$397$	−18.8058	−0.943834	−0.471917	−	0.881643i	$-0.656438\pi$
$397$	−18.8058	−0.943834	−0.471917	+	0.881643i	$0.656438\pi$
$398$	9.06110	0.454192
$399$	−1.21585	−0.0608687
$400$	1.00000	0.0500000
$401$	−11.6112	−0.579836	−0.289918	−	0.957052i	$-0.593628\pi$
$401$	−11.6112	−0.579836	−0.289918	+	0.957052i	$0.593628\pi$
$402$	−11.7854	−0.587804
$403$	−49.9674	−2.48906
$404$	7.02243	0.349379
$405$	−1.00000	−0.0496904
$406$	8.98639	0.445987
$407$	−1.67603	−0.0830778
$408$	−6.50216	−0.321905
$409$	21.7125	1.07361	0.536807	−	0.843705i	$-0.319630\pi$
$409$	21.7125	1.07361	0.536807	+	0.843705i	$0.319630\pi$
$410$	0.200768	0.00991523
$411$	−17.5381	−0.865092
$412$	−0.684886	−0.0337419
$413$	13.3489	0.656856
$414$	−0.797994	−0.0392193
$415$	0.830997	0.0407920
$416$	5.23358	0.256598
$417$	−14.3741	−0.703902
$418$	6.66703	0.326095
$419$	1.88192	0.0919377	0.0459689	−	0.998943i	$-0.485362\pi$
$419$	1.88192	0.0919377	0.0459689	+	0.998943i	$0.485362\pi$
$420$	1.15694	0.0564528
$421$	10.3674	0.505275	0.252638	−	0.967561i	$-0.418702\pi$
$421$	10.3674	0.505275	0.252638	+	0.967561i	$0.418702\pi$
$422$	9.07734	0.441878
$423$	5.08250	0.247120
$424$	−14.2876	−0.693867
$425$	−6.50216	−0.315401
$426$	−8.25150	−0.399787
$427$	13.1989	0.638738
$428$	−18.2840	−0.883789
$429$	−33.2018	−1.60300
$430$	−3.28211	−0.158277
$431$	26.2335	1.26362	0.631811	−	0.775123i	$-0.282312\pi$
$431$	26.2335	1.26362	0.631811	+	0.775123i	$0.282312\pi$
$432$	−1.00000	−0.0481125
$433$	−13.3883	−0.643400	−0.321700	−	0.946842i	$-0.604254\pi$
$433$	−13.3883	−0.643400	−0.321700	+	0.946842i	$0.604254\pi$
$434$	−11.0458	−0.530216
$435$	−7.76739	−0.372418
$436$	−4.56538	−0.218642
$437$	0.838630	0.0401171
$438$	−8.45709	−0.404096
$439$	24.9135	1.18906	0.594528	−	0.804075i	$-0.297339\pi$
$439$	24.9135	1.18906	0.594528	+	0.804075i	$0.297339\pi$
$440$	−6.34399	−0.302438
$441$	−5.66149	−0.269595
$442$	−34.0296	−1.61862
$443$	−15.6385	−0.743008	−0.371504	−	0.928431i	$-0.621158\pi$
$443$	−15.6385	−0.743008	−0.371504	+	0.928431i	$0.621158\pi$
$444$	−0.264192	−0.0125380
$445$	−1.00000	−0.0474045
$446$	−6.78866	−0.321452
$447$	−9.98305	−0.472182
$448$	1.15694	0.0546602
$449$	0.672509	0.0317377	0.0158688	−	0.999874i	$-0.494949\pi$
$449$	0.672509	0.0317377	0.0158688	+	0.999874i	$0.494949\pi$
$450$	−1.00000	−0.0471405
$451$	−1.27367	−0.0599748
$452$	−0.850154	−0.0399879
$453$	−13.4544	−0.632142
$454$	3.49414	0.163988
$455$	6.05493	0.283860
$456$	1.05092	0.0492139
$457$	18.3894	0.860218	0.430109	−	0.902777i	$-0.358475\pi$
$457$	18.3894	0.860218	0.430109	+	0.902777i	$0.358475\pi$
$458$	20.1681	0.942393
$459$	6.50216	0.303495
$460$	−0.797994	−0.0372067
$461$	−13.2258	−0.615989	−0.307994	−	0.951388i	$-0.599658\pi$
$461$	−13.2258	−0.615989	−0.307994	+	0.951388i	$0.599658\pi$
$462$	−7.33960	−0.341469
$463$	19.9137	0.925466	0.462733	−	0.886498i	$-0.346869\pi$
$463$	19.9137	0.925466	0.462733	+	0.886498i	$0.346869\pi$
$464$	−7.76739	−0.360592
$465$	9.54746	0.442753
$466$	3.59903	0.166722
$467$	26.9449	1.24686	0.623430	−	0.781879i	$-0.285739\pi$
$467$	26.9449	1.24686	0.623430	+	0.781879i	$0.285739\pi$
$468$	−5.23358	−0.241922
$469$	−13.6350	−0.629606
$470$	5.08250	0.234438
$471$	−18.5890	−0.856538
$472$	−11.5381	−0.531085
$473$	20.8217	0.957381
$474$	5.32834	0.244739
$475$	1.05092	0.0482196
$476$	−7.52260	−0.344798
$477$	14.2876	0.654184
$478$	−16.9984	−0.777488
$479$	−43.5500	−1.98985	−0.994925	−	0.100621i	$-0.967917\pi$
$479$	−43.5500	−1.98985	−0.994925	+	0.100621i	$0.967917\pi$
$480$	−1.00000	−0.0456435
$481$	−1.38267	−0.0630444
$482$	−23.4059	−1.06611
$483$	−0.923230	−0.0420084
$484$	29.2462	1.32937
$485$	−0.404012	−0.0183452
$486$	1.00000	0.0453609
$487$	17.3139	0.784570	0.392285	−	0.919844i	$-0.371685\pi$
$487$	17.3139	0.784570	0.392285	+	0.919844i	$0.371685\pi$
$488$	−11.4084	−0.516436
$489$	14.5861	0.659607
$490$	−5.66149	−0.255760
$491$	15.0081	0.677308	0.338654	−	0.940911i	$-0.390028\pi$
$491$	15.0081	0.677308	0.338654	+	0.940911i	$0.390028\pi$
$492$	−0.200768	−0.00905133
$493$	50.5048	2.27462
$494$	5.50009	0.247461
$495$	6.34399	0.285141
$496$	9.54746	0.428694
$497$	−9.54648	−0.428218
$498$	−0.830997	−0.0372379
$499$	−27.7202	−1.24093	−0.620464	−	0.784235i	$-0.713056\pi$
$499$	−27.7202	−1.24093	−0.620464	+	0.784235i	$0.713056\pi$
$500$	−1.00000	−0.0447214
$501$	14.3327	0.640336
$502$	−8.52642	−0.380553
$503$	6.83045	0.304555	0.152277	−	0.988338i	$-0.451339\pi$
$503$	6.83045	0.304555	0.152277	+	0.988338i	$0.451339\pi$
$504$	−1.15694	−0.0515341
$505$	−7.02243	−0.312494
$506$	5.06246	0.225054
$507$	−14.3904	−0.639100
$508$	5.53078	0.245389
$509$	−25.1436	−1.11447	−0.557236	−	0.830354i	$-0.688138\pi$
$509$	−25.1436	−1.11447	−0.557236	+	0.830354i	$0.688138\pi$
$510$	6.50216	0.287921
$511$	−9.78434	−0.432834
$512$	−1.00000	−0.0441942
$513$	−1.05092	−0.0463993
$514$	−30.0031	−1.32338
$515$	0.684886	0.0301797
$516$	3.28211	0.144487
$517$	−32.2433	−1.41806
$518$	−0.305654	−0.0134297
$519$	11.1025	0.487347
$520$	−5.23358	−0.229508
$521$	−1.58630	−0.0694970	−0.0347485	−	0.999396i	$-0.511063\pi$
$521$	−1.58630	−0.0694970	−0.0347485	+	0.999396i	$0.511063\pi$
$522$	7.76739	0.339969
$523$	0.945454	0.0413418	0.0206709	−	0.999786i	$-0.493420\pi$
$523$	0.945454	0.0413418	0.0206709	+	0.999786i	$0.493420\pi$
$524$	−13.0712	−0.571017
$525$	−1.15694	−0.0504929
$526$	11.0156	0.480302
$527$	−62.0791	−2.70421
$528$	6.34399	0.276087
$529$	−22.3632	−0.972313
$530$	14.2876	0.620613
$531$	11.5381	0.500712
$532$	1.21585	0.0527139
$533$	−1.05074	−0.0455125
$534$	1.00000	0.0432742
$535$	18.2840	0.790485
$536$	11.7854	0.509053
$537$	−1.20998	−0.0522144
$538$	−17.9259	−0.772841
$539$	35.9164	1.54703
$540$	1.00000	0.0430331
$541$	15.4324	0.663489	0.331745	−	0.943369i	$-0.392363\pi$
$541$	15.4324	0.663489	0.331745	+	0.943369i	$0.392363\pi$
$542$	5.04757	0.216812
$543$	−5.97667	−0.256483
$544$	6.50216	0.278778
$545$	4.56538	0.195559
$546$	−6.05493	−0.259127
$547$	−34.3808	−1.47002	−0.735009	−	0.678057i	$-0.762822\pi$
$547$	−34.3808	−1.47002	−0.735009	+	0.678057i	$0.762822\pi$
$548$	17.5381	0.749192
$549$	11.4084	0.486900
$550$	6.34399	0.270508
$551$	−8.16292	−0.347752
$552$	0.797994	0.0339649
$553$	6.16456	0.262144
$554$	9.34349	0.396967
$555$	0.264192	0.0112143
$556$	14.3741	0.609597
$557$	7.52918	0.319022	0.159511	−	0.987196i	$-0.449008\pi$
$557$	7.52918	0.319022	0.159511	+	0.987196i	$0.449008\pi$
$558$	−9.54746	−0.404176
$559$	17.1772	0.726518
$560$	−1.15694	−0.0488896
$561$	−41.2496	−1.74156
$562$	4.26392	0.179863
$563$	−42.7985	−1.80374	−0.901871	−	0.432005i	$-0.857806\pi$
$563$	−42.7985	−1.80374	−0.901871	+	0.432005i	$0.857806\pi$
$564$	−5.08250	−0.214012
$565$	0.850154	0.0357662
$566$	22.0993	0.928903
$567$	1.15694	0.0485868
$568$	8.25150	0.346225
$569$	36.0110	1.50966	0.754829	−	0.655922i	$-0.227720\pi$
$569$	36.0110	1.50966	0.754829	+	0.655922i	$0.227720\pi$
$570$	−1.05092	−0.0440183
$571$	−4.78702	−0.200330	−0.100165	−	0.994971i	$-0.531937\pi$
$571$	−4.78702	−0.200330	−0.100165	+	0.994971i	$0.531937\pi$
$572$	33.2018	1.38824
$573$	−11.8046	−0.493143
$574$	−0.232276	−0.00969503
$575$	0.797994	0.0332787
$576$	1.00000	0.0416667
$577$	−8.05913	−0.335506	−0.167753	−	0.985829i	$-0.553651\pi$
$577$	−8.05913	−0.335506	−0.167753	+	0.985829i	$0.553651\pi$
$578$	−25.2781	−1.05143
$579$	2.84768	0.118345
$580$	7.76739	0.322523
$581$	−0.961412	−0.0398861
$582$	0.404012	0.0167468
$583$	−90.6403	−3.75394
$584$	8.45709	0.349957
$585$	5.23358	0.216382
$586$	17.5011	0.722965
$587$	5.29582	0.218582	0.109291	−	0.994010i	$-0.465142\pi$
$587$	5.29582	0.218582	0.109291	+	0.994010i	$0.465142\pi$
$588$	5.66149	0.233476
$589$	10.0336	0.413429
$590$	11.5381	0.475017
$591$	−22.0561	−0.907265
$592$	0.264192	0.0108582
$593$	−43.9422	−1.80449	−0.902245	−	0.431223i	$-0.858082\pi$
$593$	−43.9422	−1.80449	−0.902245	+	0.431223i	$0.858082\pi$
$594$	−6.34399	−0.260297
$595$	7.52260	0.308397
$596$	9.98305	0.408922
$597$	9.06110	0.370846
$598$	4.17637	0.170784
$599$	41.6932	1.70354	0.851769	−	0.523918i	$-0.175530\pi$
$599$	41.6932	1.70354	0.851769	+	0.523918i	$0.175530\pi$
$600$	1.00000	0.0408248
$601$	−27.8348	−1.13540	−0.567702	−	0.823234i	$-0.692168\pi$
$601$	−27.8348	−1.13540	−0.567702	+	0.823234i	$0.692168\pi$
$602$	3.79720	0.154762
$603$	−11.7854	−0.479940
$604$	13.4544	0.547451
$605$	−29.2462	−1.18903
$606$	7.02243	0.285267
$607$	−20.6503	−0.838169	−0.419085	−	0.907947i	$-0.637649\pi$
$607$	−20.6503	−0.838169	−0.419085	+	0.907947i	$0.637649\pi$
$608$	−1.05092	−0.0426205
$609$	8.98639	0.364147
$610$	11.4084	0.461914
$611$	−26.5997	−1.07611
$612$	−6.50216	−0.262834
$613$	46.9888	1.89786	0.948929	−	0.315489i	$-0.102169\pi$
$613$	46.9888	1.89786	0.948929	+	0.315489i	$0.102169\pi$
$614$	8.36765	0.337691
$615$	0.200768	0.00809575
$616$	7.33960	0.295721
$617$	−13.7101	−0.551947	−0.275974	−	0.961165i	$-0.589000\pi$
$617$	−13.7101	−0.551947	−0.275974	+	0.961165i	$0.589000\pi$
$618$	−0.684886	−0.0275501
$619$	−17.4661	−0.702021	−0.351010	−	0.936372i	$-0.614162\pi$
$619$	−17.4661	−0.702021	−0.351010	+	0.936372i	$0.614162\pi$
$620$	−9.54746	−0.383435
$621$	−0.797994	−0.0320224
$622$	−5.19383	−0.208253
$623$	1.15694	0.0463518
$624$	5.23358	0.209511
$625$	1.00000	0.0400000
$626$	−8.24724	−0.329626
$627$	6.66703	0.266256
$628$	18.5890	0.741784
$629$	−1.71782	−0.0684940
$630$	1.15694	0.0460935
$631$	28.7311	1.14377	0.571883	−	0.820335i	$-0.306213\pi$
$631$	28.7311	1.14377	0.571883	+	0.820335i	$0.306213\pi$
$632$	−5.32834	−0.211950
$633$	9.07734	0.360792
$634$	−7.49484	−0.297658
$635$	−5.53078	−0.219482
$636$	−14.2876	−0.566540
$637$	29.6299	1.17398
$638$	−49.2762	−1.95086
$639$	−8.25150	−0.326424
$640$	1.00000	0.0395285
$641$	−6.25163	−0.246925	−0.123462	−	0.992349i	$-0.539400\pi$
$641$	−6.25163	−0.246925	−0.123462	+	0.992349i	$0.539400\pi$
$642$	−18.2840	−0.721610
$643$	8.48465	0.334602	0.167301	−	0.985906i	$-0.446495\pi$
$643$	8.48465	0.334602	0.167301	+	0.985906i	$0.446495\pi$
$644$	0.923230	0.0363804
$645$	−3.28211	−0.129233
$646$	6.83326	0.268851
$647$	15.6273	0.614372	0.307186	−	0.951650i	$-0.400613\pi$
$647$	15.6273	0.614372	0.307186	+	0.951650i	$0.400613\pi$
$648$	−1.00000	−0.0392837
$649$	−73.1977	−2.87326
$650$	5.23358	0.205278
$651$	−11.0458	−0.432920
$652$	−14.5861	−0.571237
$653$	24.4506	0.956827	0.478414	−	0.878135i	$-0.341212\pi$
$653$	24.4506	0.956827	0.478414	+	0.878135i	$0.341212\pi$
$654$	−4.56538	−0.178520
$655$	13.0712	0.510733
$656$	0.200768	0.00783868
$657$	−8.45709	−0.329943
$658$	−5.88014	−0.229232
$659$	41.2531	1.60699	0.803496	−	0.595310i	$-0.202971\pi$
$659$	41.2531	1.60699	0.803496	+	0.595310i	$0.202971\pi$
$660$	−6.34399	−0.246939
$661$	−39.5552	−1.53852	−0.769260	−	0.638936i	$-0.779375\pi$
$661$	−39.5552	−1.53852	−0.769260	+	0.638936i	$0.779375\pi$
$662$	−15.1551	−0.589021
$663$	−34.0296	−1.32160
$664$	0.830997	0.0322489
$665$	−1.21585	−0.0471487
$666$	−0.264192	−0.0102372
$667$	−6.19833	−0.240000
$668$	−14.3327	−0.554547
$669$	−6.78866	−0.262465
$670$	−11.7854	−0.455311
$671$	−72.3750	−2.79401
$672$	1.15694	0.0446299
$673$	9.42310	0.363234	0.181617	−	0.983369i	$-0.441867\pi$
$673$	9.42310	0.363234	0.181617	+	0.983369i	$0.441867\pi$
$674$	−26.3691	−1.01570
$675$	−1.00000	−0.0384900
$676$	14.3904	0.553477
$677$	4.17878	0.160604	0.0803018	−	0.996771i	$-0.474412\pi$
$677$	4.17878	0.160604	0.0803018	+	0.996771i	$0.474412\pi$
$678$	−0.850154	−0.0326500
$679$	0.467417	0.0179378
$680$	−6.50216	−0.249347
$681$	3.49414	0.133896
$682$	60.5690	2.31931
$683$	2.45500	0.0939380	0.0469690	−	0.998896i	$-0.485044\pi$
$683$	2.45500	0.0939380	0.0469690	+	0.998896i	$0.485044\pi$
$684$	1.05092	0.0401830
$685$	−17.5381	−0.670097
$686$	14.6486	0.559285
$687$	20.1681	0.769460
$688$	−3.28211	−0.125129
$689$	−74.7753	−2.84871
$690$	−0.797994	−0.0303791
$691$	−21.6124	−0.822173	−0.411086	−	0.911596i	$-0.634851\pi$
$691$	−21.6124	−0.822173	−0.411086	+	0.911596i	$0.634851\pi$
$692$	−11.1025	−0.422055
$693$	−7.33960	−0.278808
$694$	20.1580	0.765187
$695$	−14.3741	−0.545241
$696$	−7.76739	−0.294422
$697$	−1.30543	−0.0494466
$698$	1.80005	0.0681329
$699$	3.59903	0.136128
$700$	1.15694	0.0437282
$701$	−50.2850	−1.89924	−0.949619	−	0.313408i	$-0.898529\pi$
$701$	−50.2850	−1.89924	−0.949619	+	0.313408i	$0.898529\pi$
$702$	−5.23358	−0.197529
$703$	0.277646	0.0104716
$704$	−6.34399	−0.239098
$705$	5.08250	0.191418
$706$	5.02841	0.189247
$707$	8.12452	0.305554
$708$	−11.5381	−0.433629
$709$	−9.84854	−0.369870	−0.184935	−	0.982751i	$-0.559207\pi$
$709$	−9.84854	−0.369870	−0.184935	+	0.982751i	$0.559207\pi$
$710$	−8.25150	−0.309673
$711$	5.32834	0.199828
$712$	−1.00000	−0.0374766
$713$	7.61882	0.285327
$714$	−7.52260	−0.281526
$715$	−33.2018	−1.24168
$716$	1.20998	0.0452190
$717$	−16.9984	−0.634816
$718$	12.4533	0.464754
$719$	11.1493	0.415801	0.207900	−	0.978150i	$-0.433337\pi$
$719$	11.1493	0.415801	0.207900	+	0.978150i	$0.433337\pi$
$720$	−1.00000	−0.0372678
$721$	−0.792370	−0.0295094
$722$	17.8956	0.666004
$723$	−23.4059	−0.870473
$724$	5.97667	0.222121
$725$	−7.76739	−0.288473
$726$	29.2462	1.08543
$727$	27.5465	1.02164	0.510821	−	0.859687i	$-0.329342\pi$
$727$	27.5465	1.02164	0.510821	+	0.859687i	$0.329342\pi$
$728$	6.05493	0.224411
$729$	1.00000	0.0370370
$730$	−8.45709	−0.313011
$731$	21.3408	0.789319
$732$	−11.4084	−0.421668
$733$	26.6775	0.985356	0.492678	−	0.870212i	$-0.336018\pi$
$733$	26.6775	0.985356	0.492678	+	0.870212i	$0.336018\pi$
$734$	−17.2175	−0.635510
$735$	−5.66149	−0.208827
$736$	−0.797994	−0.0294145
$737$	74.7666	2.75406
$738$	−0.200768	−0.00739038
$739$	−6.93806	−0.255221	−0.127610	−	0.991824i	$-0.540731\pi$
$739$	−6.93806	−0.255221	−0.127610	+	0.991824i	$0.540731\pi$
$740$	−0.264192	−0.00971190
$741$	5.50009	0.202051
$742$	−16.5299	−0.606830
$743$	−1.88236	−0.0690572	−0.0345286	−	0.999404i	$-0.510993\pi$
$743$	−1.88236	−0.0690572	−0.0345286	+	0.999404i	$0.510993\pi$
$744$	9.54746	0.350027
$745$	−9.98305	−0.365751
$746$	6.98439	0.255717
$747$	−0.830997	−0.0304046
$748$	41.2496	1.50824
$749$	−21.1534	−0.772929
$750$	−1.00000	−0.0365148
$751$	−37.9470	−1.38470	−0.692352	−	0.721560i	$-0.743426\pi$
$751$	−37.9470	−1.38470	−0.692352	+	0.721560i	$0.743426\pi$
$752$	5.08250	0.185340
$753$	−8.52642	−0.310720
$754$	−40.6513	−1.48043
$755$	−13.4544	−0.489655
$756$	−1.15694	−0.0420774
$757$	3.41535	0.124133	0.0620665	−	0.998072i	$-0.480231\pi$
$757$	3.41535	0.124133	0.0620665	+	0.998072i	$0.480231\pi$
$758$	−25.1405	−0.913144
$759$	5.06246	0.183756
$760$	1.05092	0.0381209
$761$	9.66792	0.350462	0.175231	−	0.984527i	$-0.443933\pi$
$761$	9.66792	0.350462	0.175231	+	0.984527i	$0.443933\pi$
$762$	5.53078	0.200359
$763$	−5.28186	−0.191216
$764$	11.8046	0.427074
$765$	6.50216	0.235086
$766$	2.67425	0.0966244
$767$	−60.3857	−2.18040
$768$	−1.00000	−0.0360844
$769$	−51.9267	−1.87252	−0.936262	−	0.351302i	$-0.885739\pi$
$769$	−51.9267	−1.87252	−0.936262	+	0.351302i	$0.885739\pi$
$770$	−7.33960	−0.264501
$771$	−30.0031	−1.08054
$772$	−2.84768	−0.102490
$773$	−16.2763	−0.585417	−0.292708	−	0.956202i	$-0.594556\pi$
$773$	−16.2763	−0.585417	−0.292708	+	0.956202i	$0.594556\pi$
$774$	3.28211	0.117973
$775$	9.54746	0.342955
$776$	−0.404012	−0.0145032
$777$	−0.305654	−0.0109653
$778$	−11.8593	−0.425177
$779$	0.210992	0.00755956
$780$	−5.23358	−0.187392
$781$	52.3474	1.87314
$782$	5.18869	0.185547
$783$	7.76739	0.277584
$784$	−5.66149	−0.202196
$785$	−18.5890	−0.663472
$786$	−13.0712	−0.466233
$787$	34.5652	1.23212	0.616059	−	0.787700i	$-0.288728\pi$
$787$	34.5652	1.23212	0.616059	+	0.787700i	$0.288728\pi$
$788$	22.0561	0.785715
$789$	11.0156	0.392165
$790$	5.32834	0.189574
$791$	−0.983576	−0.0349719
$792$	6.34399	0.225424
$793$	−59.7070	−2.12026
$794$	18.8058	0.667392
$795$	14.2876	0.506729
$796$	−9.06110	−0.321162
$797$	30.8359	1.09226	0.546131	−	0.837700i	$-0.316100\pi$
$797$	30.8359	1.09226	0.546131	+	0.837700i	$0.316100\pi$
$798$	1.21585	0.0430407
$799$	−33.0472	−1.16913
$800$	−1.00000	−0.0353553
$801$	1.00000	0.0353333
$802$	11.6112	0.410006
$803$	53.6517	1.89333
$804$	11.7854	0.415640
$805$	−0.923230	−0.0325396
$806$	49.9674	1.76003
$807$	−17.9259	−0.631022
$808$	−7.02243	−0.247048
$809$	−19.8073	−0.696387	−0.348193	−	0.937423i	$-0.613205\pi$
$809$	−19.8073	−0.696387	−0.348193	+	0.937423i	$0.613205\pi$
$810$	1.00000	0.0351364
$811$	−40.9023	−1.43627	−0.718137	−	0.695901i	$-0.755005\pi$
$811$	−40.9023	−1.43627	−0.718137	+	0.695901i	$0.755005\pi$
$812$	−8.98639	−0.315360
$813$	5.04757	0.177026
$814$	1.67603	0.0587449
$815$	14.5861	0.510930
$816$	6.50216	0.227621
$817$	−3.44924	−0.120674
$818$	−21.7125	−0.759160
$819$	−6.05493	−0.211576
$820$	−0.200768	−0.00701113
$821$	47.7676	1.66710	0.833551	−	0.552443i	$-0.186304\pi$
$821$	47.7676	1.66710	0.833551	+	0.552443i	$0.186304\pi$
$822$	17.5381	0.611712
$823$	−49.4308	−1.72305	−0.861524	−	0.507717i	$-0.830490\pi$
$823$	−49.4308	−1.72305	−0.861524	+	0.507717i	$0.830490\pi$
$824$	0.684886	0.0238591
$825$	6.34399	0.220869
$826$	−13.3489	−0.464468
$827$	42.6789	1.48409	0.742045	−	0.670350i	$-0.233856\pi$
$827$	42.6789	1.48409	0.742045	+	0.670350i	$0.233856\pi$
$828$	0.797994	0.0277322
$829$	18.6192	0.646672	0.323336	−	0.946284i	$-0.395196\pi$
$829$	18.6192	0.646672	0.323336	+	0.946284i	$0.395196\pi$
$830$	−0.830997	−0.0288443
$831$	9.34349	0.324122
$832$	−5.23358	−0.181442
$833$	36.8119	1.27546
$834$	14.3741	0.497734
$835$	14.3327	0.496002
$836$	−6.66703	−0.230584
$837$	−9.54746	−0.330008
$838$	−1.88192	−0.0650098
$839$	3.40953	0.117710	0.0588550	−	0.998267i	$-0.481255\pi$
$839$	3.40953	0.117710	0.0588550	+	0.998267i	$0.481255\pi$
$840$	−1.15694	−0.0399182
$841$	31.3323	1.08042
$842$	−10.3674	−0.357283
$843$	4.26392	0.146857
$844$	−9.07734	−0.312455
$845$	−14.3904	−0.495045
$846$	−5.08250	−0.174740
$847$	33.8360	1.16262
$848$	14.2876	0.490638
$849$	22.0993	0.758446
$850$	6.50216	0.223022
$851$	0.210824	0.00722695
$852$	8.25150	0.282692
$853$	−3.48932	−0.119472	−0.0597360	−	0.998214i	$-0.519026\pi$
$853$	−3.48932	−0.119472	−0.0597360	+	0.998214i	$0.519026\pi$
$854$	−13.1989	−0.451656
$855$	−1.05092	−0.0359408
$856$	18.2840	0.624933
$857$	46.2751	1.58073	0.790363	−	0.612639i	$-0.209892\pi$
$857$	46.2751	1.58073	0.790363	+	0.612639i	$0.209892\pi$
$858$	33.2018	1.13349
$859$	−28.8050	−0.982813	−0.491406	−	0.870930i	$-0.663517\pi$
$859$	−28.8050	−0.982813	−0.491406	+	0.870930i	$0.663517\pi$
$860$	3.28211	0.111919
$861$	−0.232276	−0.00791596
$862$	−26.2335	−0.893515
$863$	49.8079	1.69548	0.847740	−	0.530412i	$-0.177963\pi$
$863$	49.8079	1.69548	0.847740	+	0.530412i	$0.177963\pi$
$864$	1.00000	0.0340207
$865$	11.1025	0.377498
$866$	13.3883	0.454952
$867$	−25.2781	−0.858490
$868$	11.0458	0.374920
$869$	−33.8029	−1.14668
$870$	7.76739	0.263339
$871$	61.6800	2.08995
$872$	4.56538	0.154603
$873$	0.404012	0.0136737
$874$	−0.838630	−0.0283671
$875$	−1.15694	−0.0391117
$876$	8.45709	0.285739
$877$	12.8829	0.435025	0.217512	−	0.976058i	$-0.430206\pi$
$877$	12.8829	0.435025	0.217512	+	0.976058i	$0.430206\pi$
$878$	−24.9135	−0.840789
$879$	17.5011	0.590299
$880$	6.34399	0.213856
$881$	2.87516	0.0968667	0.0484334	−	0.998826i	$-0.484577\pi$
$881$	2.87516	0.0968667	0.0484334	+	0.998826i	$0.484577\pi$
$882$	5.66149	0.190632
$883$	12.5127	0.421084	0.210542	−	0.977585i	$-0.432477\pi$
$883$	12.5127	0.421084	0.210542	+	0.977585i	$0.432477\pi$
$884$	34.0296	1.14454
$885$	11.5381	0.387850
$886$	15.6385	0.525386
$887$	−56.2689	−1.88933	−0.944663	−	0.328042i	$-0.893611\pi$
$887$	−56.2689	−1.88933	−0.944663	+	0.328042i	$0.893611\pi$
$888$	0.264192	0.00886571
$889$	6.39877	0.214608
$890$	1.00000	0.0335201
$891$	−6.34399	−0.212532
$892$	6.78866	0.227301
$893$	5.34131	0.178740
$894$	9.98305	0.333883
$895$	−1.20998	−0.0404451
$896$	−1.15694	−0.0386506
$897$	4.17637	0.139445
$898$	−0.672509	−0.0224419
$899$	−74.1588	−2.47333
$900$	1.00000	0.0333333
$901$	−92.9002	−3.09496
$902$	1.27367	0.0424086
$903$	3.79720	0.126363
$904$	0.850154	0.0282757
$905$	−5.97667	−0.198671
$906$	13.4544	0.446992
$907$	−19.5219	−0.648214	−0.324107	−	0.946020i	$-0.605064\pi$
$907$	−19.5219	−0.648214	−0.324107	+	0.946020i	$0.605064\pi$
$908$	−3.49414	−0.115957
$909$	7.02243	0.232919
$910$	−6.05493	−0.200719
$911$	53.6591	1.77780	0.888902	−	0.458098i	$-0.151469\pi$
$911$	53.6591	1.77780	0.888902	+	0.458098i	$0.151469\pi$
$912$	−1.05092	−0.0347995
$913$	5.27183	0.174472
$914$	−18.3894	−0.608266
$915$	11.4084	0.377151
$916$	−20.1681	−0.666372
$917$	−15.1225	−0.499390
$918$	−6.50216	−0.214603
$919$	−47.0818	−1.55309	−0.776543	−	0.630064i	$-0.783029\pi$
$919$	−47.0818	−1.55309	−0.776543	+	0.630064i	$0.783029\pi$
$920$	0.797994	0.0263091
$921$	8.36765	0.275724
$922$	13.2258	0.435570
$923$	43.1849	1.42145
$924$	7.33960	0.241455
$925$	0.264192	0.00868659
$926$	−19.9137	−0.654403
$927$	−0.684886	−0.0224946
$928$	7.76739	0.254977
$929$	29.2380	0.959268	0.479634	−	0.877469i	$-0.340769\pi$
$929$	29.2380	0.959268	0.479634	+	0.877469i	$0.340769\pi$
$930$	−9.54746	−0.313074
$931$	−5.94979	−0.194996
$932$	−3.59903	−0.117890
$933$	−5.19383	−0.170038
$934$	−26.9449	−0.881663
$935$	−41.2496	−1.34901
$936$	5.23358	0.171065
$937$	21.1311	0.690324	0.345162	−	0.938543i	$-0.387824\pi$
$937$	21.1311	0.690324	0.345162	+	0.938543i	$0.387824\pi$
$938$	13.6350	0.445199
$939$	−8.24724	−0.269139
$940$	−5.08250	−0.165773
$941$	42.9525	1.40021	0.700106	−	0.714039i	$-0.253136\pi$
$941$	42.9525	1.40021	0.700106	+	0.714039i	$0.253136\pi$
$942$	18.5890	0.605664
$943$	0.160212	0.00521721
$944$	11.5381	0.375534
$945$	1.15694	0.0376352
$946$	−20.8217	−0.676971
$947$	42.0424	1.36619	0.683097	−	0.730327i	$-0.260632\pi$
$947$	42.0424	1.36619	0.683097	+	0.730327i	$0.260632\pi$
$948$	−5.32834	−0.173056
$949$	44.2609	1.43677
$950$	−1.05092	−0.0340964
$951$	−7.49484	−0.243037
$952$	7.52260	0.243809
$953$	43.7077	1.41583	0.707915	−	0.706298i	$-0.249636\pi$
$953$	43.7077	1.41583	0.707915	+	0.706298i	$0.249636\pi$
$954$	−14.2876	−0.462578
$955$	−11.8046	−0.381987
$956$	16.9984	0.549767
$957$	−49.2762	−1.59287
$958$	43.5500	1.40704
$959$	20.2905	0.655215
$960$	1.00000	0.0322749
$961$	60.1540	1.94045
$962$	1.38267	0.0445792
$963$	−18.2840	−0.589192
$964$	23.4059	0.753852
$965$	2.84768	0.0916700
$966$	0.923230	0.0297044
$967$	−19.4995	−0.627063	−0.313532	−	0.949578i	$-0.601512\pi$
$967$	−19.4995	−0.627063	−0.313532	+	0.949578i	$0.601512\pi$
$968$	−29.2462	−0.940007
$969$	6.83326	0.219516
$970$	0.404012	0.0129720
$971$	−45.8348	−1.47091	−0.735454	−	0.677575i	$-0.763031\pi$
$971$	−45.8348	−1.47091	−0.735454	+	0.677575i	$0.763031\pi$
$972$	−1.00000	−0.0320750
$973$	16.6299	0.533131
$974$	−17.3139	−0.554775
$975$	5.23358	0.167609
$976$	11.4084	0.365175
$977$	44.6445	1.42830	0.714152	−	0.699990i	$-0.246812\pi$
$977$	44.6445	1.42830	0.714152	+	0.699990i	$0.246812\pi$
$978$	−14.5861	−0.466413
$979$	−6.34399	−0.202755
$980$	5.66149	0.180850
$981$	−4.56538	−0.145761
$982$	−15.0081	−0.478929
$983$	−54.2941	−1.73171	−0.865856	−	0.500293i	$-0.833226\pi$
$983$	−54.2941	−1.73171	−0.865856	+	0.500293i	$0.833226\pi$
$984$	0.200768	0.00640025
$985$	−22.0561	−0.702765
$986$	−50.5048	−1.60840
$987$	−5.88014	−0.187167
$988$	−5.50009	−0.174981
$989$	−2.61911	−0.0832827
$990$	−6.34399	−0.201625
$991$	−7.35886	−0.233762	−0.116881	−	0.993146i	$-0.537290\pi$
$991$	−7.35886	−0.233762	−0.116881	+	0.993146i	$0.537290\pi$
$992$	−9.54746	−0.303132
$993$	−15.1551	−0.480934
$994$	9.54648	0.302796
$995$	9.06110	0.287256
$996$	0.830997	0.0263311
$997$	60.1173	1.90393	0.951967	−	0.306199i	$-0.0990573\pi$
$997$	60.1173	1.90393	0.951967	+	0.306199i	$0.0990573\pi$
$998$	27.7202	0.877469
$999$	−0.264192	−0.00835867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2670.2.a.t.1.4	✓	7
3.2	odd	2		8010.2.a.bn.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2670.2.a.t.1.4	✓	7	1.1	even	1	trivial
8010.2.a.bn.1.4		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 2670 = 2 \cdot 3 \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2670.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.15694 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.15694 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -6.34399 q^{11} -1.00000 q^{12} -5.23358 q^{13} -1.15694 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.50216 q^{17} -1.00000 q^{18} +1.05092 q^{19} -1.00000 q^{20} -1.15694 q^{21} +6.34399 q^{22} +0.797994 q^{23} +1.00000 q^{24} +1.00000 q^{25} +5.23358 q^{26} -1.00000 q^{27} +1.15694 q^{28} -7.76739 q^{29} -1.00000 q^{30} +9.54746 q^{31} -1.00000 q^{32} +6.34399 q^{33} +6.50216 q^{34} -1.15694 q^{35} +1.00000 q^{36} +0.264192 q^{37} -1.05092 q^{38} +5.23358 q^{39} +1.00000 q^{40} +0.200768 q^{41} +1.15694 q^{42} -3.28211 q^{43} -6.34399 q^{44} -1.00000 q^{45} -0.797994 q^{46} +5.08250 q^{47} -1.00000 q^{48} -5.66149 q^{49} -1.00000 q^{50} +6.50216 q^{51} -5.23358 q^{52} +14.2876 q^{53} +1.00000 q^{54} +6.34399 q^{55} -1.15694 q^{56} -1.05092 q^{57} +7.76739 q^{58} +11.5381 q^{59} +1.00000 q^{60} +11.4084 q^{61} -9.54746 q^{62} +1.15694 q^{63} +1.00000 q^{64} +5.23358 q^{65} -6.34399 q^{66} -11.7854 q^{67} -6.50216 q^{68} -0.797994 q^{69} +1.15694 q^{70} -8.25150 q^{71} -1.00000 q^{72} -8.45709 q^{73} -0.264192 q^{74} -1.00000 q^{75} +1.05092 q^{76} -7.33960 q^{77} -5.23358 q^{78} +5.32834 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.200768 q^{82} -0.830997 q^{83} -1.15694 q^{84} +6.50216 q^{85} +3.28211 q^{86} +7.76739 q^{87} +6.34399 q^{88} +1.00000 q^{89} +1.00000 q^{90} -6.05493 q^{91} +0.797994 q^{92} -9.54746 q^{93} -5.08250 q^{94} -1.05092 q^{95} +1.00000 q^{96} +0.404012 q^{97} +5.66149 q^{98} -6.34399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 7 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 7 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 7 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 7 q^{10} + q^{11} - 7 q^{12} - q^{14} + 7 q^{15} + 7 q^{16} - 9 q^{17} - 7 q^{18} + 9 q^{19} - 7 q^{20} - q^{21} - q^{22} - 8 q^{23} + 7 q^{24} + 7 q^{25} - 7 q^{27} + q^{28} - 4 q^{29} - 7 q^{30} + 16 q^{31} - 7 q^{32} - q^{33} + 9 q^{34} - q^{35} + 7 q^{36} + 2 q^{37} - 9 q^{38} + 7 q^{40} - q^{41} + q^{42} - 10 q^{43} + q^{44} - 7 q^{45} + 8 q^{46} - 13 q^{47} - 7 q^{48} + 26 q^{49} - 7 q^{50} + 9 q^{51} - 24 q^{53} + 7 q^{54} - q^{55} - q^{56} - 9 q^{57} + 4 q^{58} - 6 q^{59} + 7 q^{60} + 23 q^{61} - 16 q^{62} + q^{63} + 7 q^{64} + q^{66} + 5 q^{67} - 9 q^{68} + 8 q^{69} + q^{70} - 8 q^{71} - 7 q^{72} - 2 q^{73} - 2 q^{74} - 7 q^{75} + 9 q^{76} - 6 q^{77} + 7 q^{79} - 7 q^{80} + 7 q^{81} + q^{82} - 7 q^{83} - q^{84} + 9 q^{85} + 10 q^{86} + 4 q^{87} - q^{88} + 7 q^{89} + 7 q^{90} + 48 q^{91} - 8 q^{92} - 16 q^{93} + 13 q^{94} - 9 q^{95} + 7 q^{96} + 30 q^{97} - 26 q^{98} + q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 7 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 7 * q^10 + q^11 - 7 * q^12 - q^14 + 7 * q^15 + 7 * q^16 - 9 * q^17 - 7 * q^18 + 9 * q^19 - 7 * q^20 - q^21 - q^22 - 8 * q^23 + 7 * q^24 + 7 * q^25 - 7 * q^27 + q^28 - 4 * q^29 - 7 * q^30 + 16 * q^31 - 7 * q^32 - q^33 + 9 * q^34 - q^35 + 7 * q^36 + 2 * q^37 - 9 * q^38 + 7 * q^40 - q^41 + q^42 - 10 * q^43 + q^44 - 7 * q^45 + 8 * q^46 - 13 * q^47 - 7 * q^48 + 26 * q^49 - 7 * q^50 + 9 * q^51 - 24 * q^53 + 7 * q^54 - q^55 - q^56 - 9 * q^57 + 4 * q^58 - 6 * q^59 + 7 * q^60 + 23 * q^61 - 16 * q^62 + q^63 + 7 * q^64 + q^66 + 5 * q^67 - 9 * q^68 + 8 * q^69 + q^70 - 8 * q^71 - 7 * q^72 - 2 * q^73 - 2 * q^74 - 7 * q^75 + 9 * q^76 - 6 * q^77 + 7 * q^79 - 7 * q^80 + 7 * q^81 + q^82 - 7 * q^83 - q^84 + 9 * q^85 + 10 * q^86 + 4 * q^87 - q^88 + 7 * q^89 + 7 * q^90 + 48 * q^91 - 8 * q^92 - 16 * q^93 + 13 * q^94 - 9 * q^95 + 7 * q^96 + 30 * q^97 - 26 * q^98 + q^99

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