LMFDB - Embedded newform 6422.2.a.bn.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} + \cdots + 358 $ x^14 - 4x^13 - 22x^12 + 98x^11 + 164x^10 - 912x^9 - 374x^8 + 3996x^7 - 817x^6 - 8194x^5 + 4418x^4 + 6430x^3 - 4327x^2 - 922*x + 358
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.231327$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.231327 q^{3} +1.00000 q^{4} -2.62395 q^{5} +0.231327 q^{6} -2.76976 q^{7} +1.00000 q^{8} -2.94649 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.231327 q^{3} +1.00000 q^{4} -2.62395 q^{5} +0.231327 q^{6} -2.76976 q^{7} +1.00000 q^{8} -2.94649 q^{9} -2.62395 q^{10} +5.25802 q^{11} +0.231327 q^{12} -2.76976 q^{14} -0.606990 q^{15} +1.00000 q^{16} +4.16913 q^{17} -2.94649 q^{18} +1.00000 q^{19} -2.62395 q^{20} -0.640721 q^{21} +5.25802 q^{22} +1.84399 q^{23} +0.231327 q^{24} +1.88509 q^{25} -1.37558 q^{27} -2.76976 q^{28} -5.48476 q^{29} -0.606990 q^{30} -9.97993 q^{31} +1.00000 q^{32} +1.21632 q^{33} +4.16913 q^{34} +7.26771 q^{35} -2.94649 q^{36} -10.9258 q^{37} +1.00000 q^{38} -2.62395 q^{40} +9.70557 q^{41} -0.640721 q^{42} +4.14997 q^{43} +5.25802 q^{44} +7.73142 q^{45} +1.84399 q^{46} +2.12223 q^{47} +0.231327 q^{48} +0.671595 q^{49} +1.88509 q^{50} +0.964432 q^{51} -2.38244 q^{53} -1.37558 q^{54} -13.7968 q^{55} -2.76976 q^{56} +0.231327 q^{57} -5.48476 q^{58} -1.31845 q^{59} -0.606990 q^{60} +11.6271 q^{61} -9.97993 q^{62} +8.16108 q^{63} +1.00000 q^{64} +1.21632 q^{66} -0.0187119 q^{67} +4.16913 q^{68} +0.426564 q^{69} +7.26771 q^{70} -2.03293 q^{71} -2.94649 q^{72} -3.46314 q^{73} -10.9258 q^{74} +0.436072 q^{75} +1.00000 q^{76} -14.5635 q^{77} +14.7983 q^{79} -2.62395 q^{80} +8.52125 q^{81} +9.70557 q^{82} +9.18902 q^{83} -0.640721 q^{84} -10.9396 q^{85} +4.14997 q^{86} -1.26877 q^{87} +5.25802 q^{88} +1.80113 q^{89} +7.73142 q^{90} +1.84399 q^{92} -2.30863 q^{93} +2.12223 q^{94} -2.62395 q^{95} +0.231327 q^{96} +10.0259 q^{97} +0.671595 q^{98} -15.4927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9} - 2 q^{10} + 10 q^{11} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 14 q^{16} + 2 q^{17} + 18 q^{18} + 14 q^{19} - 2 q^{20} - 18 q^{21} + 10 q^{22} + 12 q^{23} + 4 q^{24} + 44 q^{25} + 10 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} + 4 q^{31} + 14 q^{32} + 12 q^{33} + 2 q^{34} + 14 q^{35} + 18 q^{36} + 18 q^{37} + 14 q^{38} - 2 q^{40} + 6 q^{41} - 18 q^{42} + 28 q^{43} + 10 q^{44} + 8 q^{45} + 12 q^{46} - 20 q^{47} + 4 q^{48} + 28 q^{49} + 44 q^{50} + 10 q^{51} + 12 q^{53} + 10 q^{54} - 2 q^{55} + 2 q^{56} + 4 q^{57} + 4 q^{58} + 16 q^{59} - 4 q^{60} + 30 q^{61} + 4 q^{62} + 28 q^{63} + 14 q^{64} + 12 q^{66} + 2 q^{67} + 2 q^{68} - 42 q^{69} + 14 q^{70} + 44 q^{71} + 18 q^{72} - 36 q^{73} + 18 q^{74} + 46 q^{75} + 14 q^{76} + 68 q^{77} + 34 q^{79} - 2 q^{80} - 6 q^{81} + 6 q^{82} + 2 q^{83} - 18 q^{84} - 30 q^{85} + 28 q^{86} + 52 q^{87} + 10 q^{88} + 42 q^{89} + 8 q^{90} + 12 q^{92} - 12 q^{93} - 20 q^{94} - 2 q^{95} + 4 q^{96} + 40 q^{97} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9 - 2 * q^10 + 10 * q^11 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 14 * q^16 + 2 * q^17 + 18 * q^18 + 14 * q^19 - 2 * q^20 - 18 * q^21 + 10 * q^22 + 12 * q^23 + 4 * q^24 + 44 * q^25 + 10 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 + 4 * q^31 + 14 * q^32 + 12 * q^33 + 2 * q^34 + 14 * q^35 + 18 * q^36 + 18 * q^37 + 14 * q^38 - 2 * q^40 + 6 * q^41 - 18 * q^42 + 28 * q^43 + 10 * q^44 + 8 * q^45 + 12 * q^46 - 20 * q^47 + 4 * q^48 + 28 * q^49 + 44 * q^50 + 10 * q^51 + 12 * q^53 + 10 * q^54 - 2 * q^55 + 2 * q^56 + 4 * q^57 + 4 * q^58 + 16 * q^59 - 4 * q^60 + 30 * q^61 + 4 * q^62 + 28 * q^63 + 14 * q^64 + 12 * q^66 + 2 * q^67 + 2 * q^68 - 42 * q^69 + 14 * q^70 + 44 * q^71 + 18 * q^72 - 36 * q^73 + 18 * q^74 + 46 * q^75 + 14 * q^76 + 68 * q^77 + 34 * q^79 - 2 * q^80 - 6 * q^81 + 6 * q^82 + 2 * q^83 - 18 * q^84 - 30 * q^85 + 28 * q^86 + 52 * q^87 + 10 * q^88 + 42 * q^89 + 8 * q^90 + 12 * q^92 - 12 * q^93 - 20 * q^94 - 2 * q^95 + 4 * q^96 + 40 * q^97 + 28 * q^98 + 12 * 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
$3$	0.231327	0.133557	0.0667784	−	0.997768i	$-0.478728\pi$
$3$	0.231327	0.133557	0.0667784	+	0.997768i	$0.478728\pi$
$4$	1.00000	0.500000
$5$	−2.62395	−1.17346	−0.586732	−	0.809781i	$-0.699586\pi$
$5$	−2.62395	−1.17346	−0.586732	+	0.809781i	$0.699586\pi$
$6$	0.231327	0.0944389
$7$	−2.76976	−1.04687	−0.523436	−	0.852065i	$-0.675350\pi$
$7$	−2.76976	−1.04687	−0.523436	+	0.852065i	$0.675350\pi$
$8$	1.00000	0.353553
$9$	−2.94649	−0.982163
$10$	−2.62395	−0.829764
$11$	5.25802	1.58535	0.792676	−	0.609643i	$-0.208687\pi$
$11$	5.25802	1.58535	0.792676	+	0.609643i	$0.208687\pi$
$12$	0.231327	0.0667784
$13$	0	0
$13$	0	0
$14$	−2.76976	−0.740251
$15$	−0.606990	−0.156724
$16$	1.00000	0.250000
$17$	4.16913	1.01116	0.505581	−	0.862779i	$-0.331278\pi$
$17$	4.16913	1.01116	0.505581	+	0.862779i	$0.331278\pi$
$18$	−2.94649	−0.694494
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.62395	−0.586732
$21$	−0.640721	−0.139817
$22$	5.25802	1.12101
$23$	1.84399	0.384498	0.192249	−	0.981346i	$-0.438422\pi$
$23$	1.84399	0.384498	0.192249	+	0.981346i	$0.438422\pi$
$24$	0.231327	0.0472194
$25$	1.88509	0.377018
$26$	0	0
$27$	−1.37558	−0.264731
$28$	−2.76976	−0.523436
$29$	−5.48476	−1.01849	−0.509247	−	0.860620i	$-0.670076\pi$
$29$	−5.48476	−1.01849	−0.509247	+	0.860620i	$0.670076\pi$
$30$	−0.606990	−0.110821
$31$	−9.97993	−1.79245	−0.896225	−	0.443601i	$-0.853701\pi$
$31$	−9.97993	−1.79245	−0.896225	+	0.443601i	$0.853701\pi$
$32$	1.00000	0.176777
$33$	1.21632	0.211735
$34$	4.16913	0.715000
$35$	7.26771	1.22847
$36$	−2.94649	−0.491081
$37$	−10.9258	−1.79619	−0.898094	−	0.439803i	$-0.855048\pi$
$37$	−10.9258	−1.79619	−0.898094	+	0.439803i	$0.855048\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−2.62395	−0.414882
$41$	9.70557	1.51575	0.757877	−	0.652397i	$-0.226236\pi$
$41$	9.70557	1.51575	0.757877	+	0.652397i	$0.226236\pi$
$42$	−0.640721	−0.0988655
$43$	4.14997	0.632864	0.316432	−	0.948615i	$-0.397515\pi$
$43$	4.14997	0.632864	0.316432	+	0.948615i	$0.397515\pi$
$44$	5.25802	0.792676
$45$	7.73142	1.15253
$46$	1.84399	0.271881
$47$	2.12223	0.309559	0.154780	−	0.987949i	$-0.450533\pi$
$47$	2.12223	0.309559	0.154780	+	0.987949i	$0.450533\pi$
$48$	0.231327	0.0333892
$49$	0.671595	0.0959421
$50$	1.88509	0.266592
$51$	0.964432	0.135048
$52$	0	0
$53$	−2.38244	−0.327253	−0.163627	−	0.986522i	$-0.552319\pi$
$53$	−2.38244	−0.327253	−0.163627	+	0.986522i	$0.552319\pi$
$54$	−1.37558	−0.187193
$55$	−13.7968	−1.86035
$56$	−2.76976	−0.370125
$57$	0.231327	0.0306400
$58$	−5.48476	−0.720185
$59$	−1.31845	−0.171648	−0.0858240	−	0.996310i	$-0.527352\pi$
$59$	−1.31845	−0.171648	−0.0858240	+	0.996310i	$0.527352\pi$
$60$	−0.606990	−0.0783620
$61$	11.6271	1.48869	0.744347	−	0.667793i	$-0.232761\pi$
$61$	11.6271	1.48869	0.744347	+	0.667793i	$0.232761\pi$
$62$	−9.97993	−1.26745
$63$	8.16108	1.02820
$64$	1.00000	0.125000
$65$	0	0
$66$	1.21632	0.149719
$67$	−0.0187119	−0.00228602	−0.00114301	−	0.999999i	$-0.500364\pi$
$67$	−0.0187119	−0.00228602	−0.00114301	+	0.999999i	$0.500364\pi$
$68$	4.16913	0.505581
$69$	0.426564	0.0513523
$70$	7.26771	0.868658
$71$	−2.03293	−0.241264	−0.120632	−	0.992697i	$-0.538492\pi$
$71$	−2.03293	−0.241264	−0.120632	+	0.992697i	$0.538492\pi$
$72$	−2.94649	−0.347247
$73$	−3.46314	−0.405330	−0.202665	−	0.979248i	$-0.564960\pi$
$73$	−3.46314	−0.405330	−0.202665	+	0.979248i	$0.564960\pi$
$74$	−10.9258	−1.27010
$75$	0.436072	0.0503533
$76$	1.00000	0.114708
$77$	−14.5635	−1.65966
$78$	0	0
$79$	14.7983	1.66494	0.832469	−	0.554071i	$-0.186926\pi$
$79$	14.7983	1.66494	0.832469	+	0.554071i	$0.186926\pi$
$80$	−2.62395	−0.293366
$81$	8.52125	0.946806
$82$	9.70557	1.07180
$83$	9.18902	1.00863	0.504313	−	0.863521i	$-0.331746\pi$
$83$	9.18902	1.00863	0.504313	+	0.863521i	$0.331746\pi$
$84$	−0.640721	−0.0699084
$85$	−10.9396	−1.18656
$86$	4.14997	0.447503
$87$	−1.26877	−0.136027
$88$	5.25802	0.560507
$89$	1.80113	0.190920	0.0954598	−	0.995433i	$-0.469568\pi$
$89$	1.80113	0.190920	0.0954598	+	0.995433i	$0.469568\pi$
$90$	7.73142	0.814964
$91$	0	0
$92$	1.84399	0.192249
$93$	−2.30863	−0.239394
$94$	2.12223	0.218891
$95$	−2.62395	−0.269211
$96$	0.231327	0.0236097
$97$	10.0259	1.01798	0.508988	−	0.860773i	$-0.330020\pi$
$97$	10.0259	1.01798	0.508988	+	0.860773i	$0.330020\pi$
$98$	0.671595	0.0678413
$99$	−15.4927	−1.55707
$100$	1.88509	0.188509
$101$	15.8375	1.57589	0.787947	−	0.615743i	$-0.211144\pi$
$101$	15.8375	1.57589	0.787947	+	0.615743i	$0.211144\pi$
$102$	0.964432	0.0954930
$103$	−1.39849	−0.137797	−0.0688985	−	0.997624i	$-0.521948\pi$
$103$	−1.39849	−0.137797	−0.0688985	+	0.997624i	$0.521948\pi$
$104$	0	0
$105$	1.68122	0.164070
$106$	−2.38244	−0.231403
$107$	4.48619	0.433696	0.216848	−	0.976205i	$-0.430422\pi$
$107$	4.48619	0.433696	0.216848	+	0.976205i	$0.430422\pi$
$108$	−1.37558	−0.132366
$109$	2.01319	0.192829	0.0964144	−	0.995341i	$-0.469263\pi$
$109$	2.01319	0.192829	0.0964144	+	0.995341i	$0.469263\pi$
$110$	−13.7968	−1.31547
$111$	−2.52743	−0.239893
$112$	−2.76976	−0.261718
$113$	19.5277	1.83701	0.918506	−	0.395406i	$-0.129396\pi$
$113$	19.5277	1.83701	0.918506	+	0.395406i	$0.129396\pi$
$114$	0.231327	0.0216658
$115$	−4.83852	−0.451194
$116$	−5.48476	−0.509247
$117$	0	0
$118$	−1.31845	−0.121373
$119$	−11.5475	−1.05856
$120$	−0.606990	−0.0554103
$121$	16.6468	1.51334
$122$	11.6271	1.05267
$123$	2.24516	0.202439
$124$	−9.97993	−0.896225
$125$	8.17335	0.731047
$126$	8.16108	0.727047
$127$	0.0631019	0.00559939	0.00279970	−	0.999996i	$-0.499109\pi$
$127$	0.0631019	0.00559939	0.00279970	+	0.999996i	$0.499109\pi$
$128$	1.00000	0.0883883
$129$	0.960000	0.0845233
$130$	0	0
$131$	11.9829	1.04695	0.523474	−	0.852042i	$-0.324636\pi$
$131$	11.9829	1.04695	0.523474	+	0.852042i	$0.324636\pi$
$132$	1.21632	0.105867
$133$	−2.76976	−0.240169
$134$	−0.0187119	−0.00161646
$135$	3.60946	0.310653
$136$	4.16913	0.357500
$137$	−8.85725	−0.756726	−0.378363	−	0.925657i	$-0.623513\pi$
$137$	−8.85725	−0.756726	−0.378363	+	0.925657i	$0.623513\pi$
$138$	0.426564	0.0363115
$139$	−13.3000	−1.12809	−0.564044	−	0.825745i	$-0.690755\pi$
$139$	−13.3000	−1.12809	−0.564044	+	0.825745i	$0.690755\pi$
$140$	7.26771	0.614234
$141$	0.490929	0.0413437
$142$	−2.03293	−0.170599
$143$	0	0
$144$	−2.94649	−0.245541
$145$	14.3917	1.19517
$146$	−3.46314	−0.286611
$147$	0.155358	0.0128137
$148$	−10.9258	−0.898094
$149$	−4.39913	−0.360391	−0.180196	−	0.983631i	$-0.557673\pi$
$149$	−4.39913	−0.360391	−0.180196	+	0.983631i	$0.557673\pi$
$150$	0.436072	0.0356052
$151$	−17.0109	−1.38433	−0.692163	−	0.721741i	$-0.743342\pi$
$151$	−17.0109	−1.38433	−0.692163	+	0.721741i	$0.743342\pi$
$152$	1.00000	0.0811107
$153$	−12.2843	−0.993126
$154$	−14.5635	−1.17356
$155$	26.1868	2.10337
$156$	0	0
$157$	16.3327	1.30349	0.651746	−	0.758437i	$-0.274037\pi$
$157$	16.3327	1.30349	0.651746	+	0.758437i	$0.274037\pi$
$158$	14.7983	1.17729
$159$	−0.551123	−0.0437069
$160$	−2.62395	−0.207441
$161$	−5.10741	−0.402520
$162$	8.52125	0.669493
$163$	−6.96605	−0.545623	−0.272812	−	0.962067i	$-0.587954\pi$
$163$	−6.96605	−0.545623	−0.272812	+	0.962067i	$0.587954\pi$
$164$	9.70557	0.757877
$165$	−3.19156	−0.248463
$166$	9.18902	0.713206
$167$	14.4951	1.12167	0.560833	−	0.827929i	$-0.310481\pi$
$167$	14.4951	1.12167	0.560833	+	0.827929i	$0.310481\pi$
$168$	−0.640721	−0.0494327
$169$	0	0
$170$	−10.9396	−0.839026
$171$	−2.94649	−0.225324
$172$	4.14997	0.316432
$173$	15.5430	1.18172	0.590858	−	0.806776i	$-0.298789\pi$
$173$	15.5430	1.18172	0.590858	+	0.806776i	$0.298789\pi$
$174$	−1.26877	−0.0961855
$175$	−5.22126	−0.394690
$176$	5.25802	0.396338
$177$	−0.304994	−0.0229247
$178$	1.80113	0.135000
$179$	15.5096	1.15925	0.579623	−	0.814885i	$-0.303200\pi$
$179$	15.5096	1.15925	0.579623	+	0.814885i	$0.303200\pi$
$180$	7.73142	0.576266
$181$	−9.43915	−0.701607	−0.350803	−	0.936449i	$-0.614091\pi$
$181$	−9.43915	−0.701607	−0.350803	+	0.936449i	$0.614091\pi$
$182$	0	0
$183$	2.68966	0.198825
$184$	1.84399	0.135941
$185$	28.6687	2.10776
$186$	−2.30863	−0.169277
$187$	21.9214	1.60305
$188$	2.12223	0.154780
$189$	3.81004	0.277140
$190$	−2.62395	−0.190361
$191$	25.2656	1.82815	0.914077	−	0.405540i	$-0.132916\pi$
$191$	25.2656	1.82815	0.914077	+	0.405540i	$0.132916\pi$
$192$	0.231327	0.0166946
$193$	3.71677	0.267539	0.133769	−	0.991012i	$-0.457292\pi$
$193$	3.71677	0.267539	0.133769	+	0.991012i	$0.457292\pi$
$194$	10.0259	0.719818
$195$	0	0
$196$	0.671595	0.0479710
$197$	−7.33682	−0.522727	−0.261363	−	0.965240i	$-0.584172\pi$
$197$	−7.33682	−0.522727	−0.261363	+	0.965240i	$0.584172\pi$
$198$	−15.4927	−1.10102
$199$	−3.91252	−0.277351	−0.138676	−	0.990338i	$-0.544285\pi$
$199$	−3.91252	−0.277351	−0.138676	+	0.990338i	$0.544285\pi$
$200$	1.88509	0.133296
$201$	−0.00432857	−0.000305314 0
$202$	15.8375	1.11433
$203$	15.1915	1.06623
$204$	0.964432	0.0675238
$205$	−25.4669	−1.77868
$206$	−1.39849	−0.0974373
$207$	−5.43328	−0.377639
$208$	0	0
$209$	5.25802	0.363705
$210$	1.68122	0.116015
$211$	9.52598	0.655796	0.327898	−	0.944713i	$-0.393660\pi$
$211$	9.52598	0.655796	0.327898	+	0.944713i	$0.393660\pi$
$212$	−2.38244	−0.163627
$213$	−0.470271	−0.0322224
$214$	4.48619	0.306669
$215$	−10.8893	−0.742644
$216$	−1.37558	−0.0935966
$217$	27.6421	1.87647
$218$	2.01319	0.136351
$219$	−0.801118	−0.0541345
$220$	−13.7968	−0.930177
$221$	0	0
$222$	−2.52743	−0.169630
$223$	19.1965	1.28549	0.642745	−	0.766080i	$-0.277796\pi$
$223$	19.1965	1.28549	0.642745	+	0.766080i	$0.277796\pi$
$224$	−2.76976	−0.185063
$225$	−5.55440	−0.370293
$226$	19.5277	1.29896
$227$	18.8685	1.25235	0.626174	−	0.779683i	$-0.284620\pi$
$227$	18.8685	1.25235	0.626174	+	0.779683i	$0.284620\pi$
$228$	0.231327	0.0153200
$229$	1.02603	0.0678018	0.0339009	−	0.999425i	$-0.489207\pi$
$229$	1.02603	0.0678018	0.0339009	+	0.999425i	$0.489207\pi$
$230$	−4.83852	−0.319043
$231$	−3.36893	−0.221659
$232$	−5.48476	−0.360092
$233$	23.1615	1.51736	0.758680	−	0.651463i	$-0.225845\pi$
$233$	23.1615	1.51736	0.758680	+	0.651463i	$0.225845\pi$
$234$	0	0
$235$	−5.56862	−0.363257
$236$	−1.31845	−0.0858240
$237$	3.42325	0.222364
$238$	−11.5475	−0.748514
$239$	4.69804	0.303891	0.151946	−	0.988389i	$-0.451446\pi$
$239$	4.69804	0.303891	0.151946	+	0.988389i	$0.451446\pi$
$240$	−0.606990	−0.0391810
$241$	7.07187	0.455539	0.227770	−	0.973715i	$-0.426857\pi$
$241$	7.07187	0.455539	0.227770	+	0.973715i	$0.426857\pi$
$242$	16.6468	1.07010
$243$	6.09795	0.391184
$244$	11.6271	0.744347
$245$	−1.76223	−0.112585
$246$	2.24516	0.143146
$247$	0	0
$248$	−9.97993	−0.633726
$249$	2.12567	0.134709
$250$	8.17335	0.516928
$251$	−15.0248	−0.948356	−0.474178	−	0.880429i	$-0.657255\pi$
$251$	−15.0248	−0.948356	−0.474178	+	0.880429i	$0.657255\pi$
$252$	8.16108	0.514100
$253$	9.69572	0.609565
$254$	0.0631019	0.00395937
$255$	−2.53062	−0.158473
$256$	1.00000	0.0625000
$257$	−9.53616	−0.594849	−0.297425	−	0.954745i	$-0.596128\pi$
$257$	−9.53616	−0.594849	−0.297425	+	0.954745i	$0.596128\pi$
$258$	0.960000	0.0597670
$259$	30.2619	1.88038
$260$	0	0
$261$	16.1608	1.00033
$262$	11.9829	0.740304
$263$	−16.1412	−0.995307	−0.497654	−	0.867376i	$-0.665805\pi$
$263$	−16.1412	−0.995307	−0.497654	+	0.867376i	$0.665805\pi$
$264$	1.21632	0.0748595
$265$	6.25139	0.384020
$266$	−2.76976	−0.169825
$267$	0.416650	0.0254986
$268$	−0.0187119	−0.00114301
$269$	−17.7516	−1.08233	−0.541166	−	0.840916i	$-0.682017\pi$
$269$	−17.7516	−1.08233	−0.541166	+	0.840916i	$0.682017\pi$
$270$	3.60946	0.219665
$271$	−22.7371	−1.38118	−0.690589	−	0.723248i	$-0.742649\pi$
$271$	−22.7371	−1.38118	−0.690589	+	0.723248i	$0.742649\pi$
$272$	4.16913	0.252791
$273$	0	0
$274$	−8.85725	−0.535086
$275$	9.91185	0.597707
$276$	0.426564	0.0256761
$277$	17.6200	1.05868	0.529340	−	0.848409i	$-0.322439\pi$
$277$	17.6200	1.05868	0.529340	+	0.848409i	$0.322439\pi$
$278$	−13.3000	−0.797679
$279$	29.4058	1.76048
$280$	7.26771	0.434329
$281$	10.5581	0.629842	0.314921	−	0.949118i	$-0.398022\pi$
$281$	10.5581	0.629842	0.314921	+	0.949118i	$0.398022\pi$
$282$	0.490929	0.0292344
$283$	−19.8729	−1.18132	−0.590661	−	0.806919i	$-0.701133\pi$
$283$	−19.8729	−1.18132	−0.590661	+	0.806919i	$0.701133\pi$
$284$	−2.03293	−0.120632
$285$	−0.606990	−0.0359550
$286$	0	0
$287$	−26.8821	−1.58680
$288$	−2.94649	−0.173623
$289$	0.381633	0.0224490
$290$	14.3917	0.845111
$291$	2.31926	0.135958
$292$	−3.46314	−0.202665
$293$	−17.6933	−1.03365	−0.516826	−	0.856090i	$-0.672887\pi$
$293$	−17.6933	−1.03365	−0.516826	+	0.856090i	$0.672887\pi$
$294$	0.155358	0.00906066
$295$	3.45955	0.201423
$296$	−10.9258	−0.635049
$297$	−7.23285	−0.419692
$298$	−4.39913	−0.254835
$299$	0	0
$300$	0.436072	0.0251767
$301$	−11.4944	−0.662528
$302$	−17.0109	−0.978866
$303$	3.66365	0.210471
$304$	1.00000	0.0573539
$305$	−30.5088	−1.74693
$306$	−12.2843	−0.702246
$307$	−7.36105	−0.420118	−0.210059	−	0.977689i	$-0.567366\pi$
$307$	−7.36105	−0.420118	−0.210059	+	0.977689i	$0.567366\pi$
$308$	−14.5635	−0.829831
$309$	−0.323508	−0.0184037
$310$	26.1868	1.48731
$311$	−9.32425	−0.528730	−0.264365	−	0.964423i	$-0.585162\pi$
$311$	−9.32425	−0.528730	−0.264365	+	0.964423i	$0.585162\pi$
$312$	0	0
$313$	−4.14064	−0.234043	−0.117022	−	0.993129i	$-0.537335\pi$
$313$	−4.14064	−0.234043	−0.117022	+	0.993129i	$0.537335\pi$
$314$	16.3327	0.921708
$315$	−21.4142	−1.20655
$316$	14.7983	0.832469
$317$	27.5465	1.54717	0.773584	−	0.633694i	$-0.218462\pi$
$317$	27.5465	1.54717	0.773584	+	0.633694i	$0.218462\pi$
$318$	−0.551123	−0.0309054
$319$	−28.8390	−1.61467
$320$	−2.62395	−0.146683
$321$	1.03778	0.0579230
$322$	−5.10741	−0.284625
$323$	4.16913	0.231977
$324$	8.52125	0.473403
$325$	0	0
$326$	−6.96605	−0.385814
$327$	0.465706	0.0257536
$328$	9.70557	0.535900
$329$	−5.87808	−0.324069
$330$	−3.19156	−0.175690
$331$	−15.9830	−0.878508	−0.439254	−	0.898363i	$-0.644757\pi$
$331$	−15.9830	−0.878508	−0.439254	+	0.898363i	$0.644757\pi$
$332$	9.18902	0.504313
$333$	32.1927	1.76415
$334$	14.4951	0.793138
$335$	0.0490990	0.00268256
$336$	−0.640721	−0.0349542
$337$	−15.7428	−0.857564	−0.428782	−	0.903408i	$-0.641057\pi$
$337$	−15.7428	−0.857564	−0.428782	+	0.903408i	$0.641057\pi$
$338$	0	0
$339$	4.51729	0.245345
$340$	−10.9396	−0.593281
$341$	−52.4747	−2.84166
$342$	−2.94649	−0.159328
$343$	17.5282	0.946433
$344$	4.14997	0.223751
$345$	−1.11928	−0.0602601
$346$	15.5430	0.835599
$347$	−18.2097	−0.977550	−0.488775	−	0.872410i	$-0.662556\pi$
$347$	−18.2097	−0.977550	−0.488775	+	0.872410i	$0.662556\pi$
$348$	−1.26877	−0.0680134
$349$	−36.7759	−1.96857	−0.984285	−	0.176587i	$-0.943494\pi$
$349$	−36.7759	−1.96857	−0.984285	+	0.176587i	$0.943494\pi$
$350$	−5.22126	−0.279088
$351$	0	0
$352$	5.25802	0.280253
$353$	−19.5686	−1.04153	−0.520764	−	0.853700i	$-0.674353\pi$
$353$	−19.5686	−1.04153	−0.520764	+	0.853700i	$0.674353\pi$
$354$	−0.304994	−0.0162102
$355$	5.33429	0.283114
$356$	1.80113	0.0954598
$357$	−2.67125	−0.141378
$358$	15.5096	0.819710
$359$	9.71547	0.512763	0.256381	−	0.966576i	$-0.417470\pi$
$359$	9.71547	0.512763	0.256381	+	0.966576i	$0.417470\pi$
$360$	7.73142	0.407482
$361$	1.00000	0.0526316
$362$	−9.43915	−0.496111
$363$	3.85085	0.202117
$364$	0	0
$365$	9.08709	0.475640
$366$	2.68966	0.140591
$367$	−29.6577	−1.54812	−0.774061	−	0.633111i	$-0.781777\pi$
$367$	−29.6577	−1.54812	−0.774061	+	0.633111i	$0.781777\pi$
$368$	1.84399	0.0961245
$369$	−28.5973	−1.48872
$370$	28.6687	1.49041
$371$	6.59879	0.342592
$372$	−2.30863	−0.119697
$373$	31.2898	1.62013	0.810063	−	0.586343i	$-0.199433\pi$
$373$	31.2898	1.62013	0.810063	+	0.586343i	$0.199433\pi$
$374$	21.9214	1.13353
$375$	1.89072	0.0976363
$376$	2.12223	0.109446
$377$	0	0
$378$	3.81004	0.195967
$379$	21.7549	1.11747	0.558737	−	0.829345i	$-0.311286\pi$
$379$	21.7549	1.11747	0.558737	+	0.829345i	$0.311286\pi$
$380$	−2.62395	−0.134606
$381$	0.0145972	0.000747836 0
$382$	25.2656	1.29270
$383$	25.4924	1.30260	0.651302	−	0.758819i	$-0.274223\pi$
$383$	25.4924	1.30260	0.651302	+	0.758819i	$0.274223\pi$
$384$	0.231327	0.0118049
$385$	38.2138	1.94755
$386$	3.71677	0.189179
$387$	−12.2278	−0.621576
$388$	10.0259	0.508988
$389$	34.7782	1.76332	0.881662	−	0.471882i	$-0.156425\pi$
$389$	34.7782	1.76332	0.881662	+	0.471882i	$0.156425\pi$
$390$	0	0
$391$	7.68782	0.388790
$392$	0.671595	0.0339207
$393$	2.77196	0.139827
$394$	−7.33682	−0.369624
$395$	−38.8299	−1.95375
$396$	−15.4927	−0.778537
$397$	−3.75293	−0.188354	−0.0941771	−	0.995555i	$-0.530022\pi$
$397$	−3.75293	−0.188354	−0.0941771	+	0.995555i	$0.530022\pi$
$398$	−3.91252	−0.196117
$399$	−0.640721	−0.0320762
$400$	1.88509	0.0942545
$401$	−10.0861	−0.503677	−0.251839	−	0.967769i	$-0.581035\pi$
$401$	−10.0861	−0.503677	−0.251839	+	0.967769i	$0.581035\pi$
$402$	−0.00432857	−0.000215889 0
$403$	0	0
$404$	15.8375	0.787947
$405$	−22.3593	−1.11104
$406$	15.1915	0.753942
$407$	−57.4480	−2.84759
$408$	0.964432	0.0477465
$409$	12.1675	0.601642	0.300821	−	0.953681i	$-0.402739\pi$
$409$	12.1675	0.601642	0.300821	+	0.953681i	$0.402739\pi$
$410$	−25.4669	−1.25772
$411$	−2.04892	−0.101066
$412$	−1.39849	−0.0688985
$413$	3.65180	0.179694
$414$	−5.43328	−0.267031
$415$	−24.1115	−1.18359
$416$	0	0
$417$	−3.07664	−0.150664
$418$	5.25802	0.257178
$419$	−1.68120	−0.0821320	−0.0410660	−	0.999156i	$-0.513075\pi$
$419$	−1.68120	−0.0821320	−0.0410660	+	0.999156i	$0.513075\pi$
$420$	1.68122	0.0820351
$421$	20.0552	0.977429	0.488714	−	0.872444i	$-0.337466\pi$
$421$	20.0552	0.977429	0.488714	+	0.872444i	$0.337466\pi$
$422$	9.52598	0.463718
$423$	−6.25313	−0.304037
$424$	−2.38244	−0.115701
$425$	7.85918	0.381226
$426$	−0.470271	−0.0227847
$427$	−32.2043	−1.55847
$428$	4.48619	0.216848
$429$	0	0
$430$	−10.8893	−0.525128
$431$	3.10014	0.149328	0.0746642	−	0.997209i	$-0.476212\pi$
$431$	3.10014	0.149328	0.0746642	+	0.997209i	$0.476212\pi$
$432$	−1.37558	−0.0661828
$433$	27.9700	1.34415	0.672076	−	0.740482i	$-0.265403\pi$
$433$	27.9700	1.34415	0.672076	+	0.740482i	$0.265403\pi$
$434$	27.6421	1.32686
$435$	3.32919	0.159623
$436$	2.01319	0.0964144
$437$	1.84399	0.0882098
$438$	−0.801118	−0.0382789
$439$	−32.8257	−1.56669	−0.783343	−	0.621590i	$-0.786487\pi$
$439$	−32.8257	−1.56669	−0.783343	+	0.621590i	$0.786487\pi$
$440$	−13.7968	−0.657735
$441$	−1.97885	−0.0942307
$442$	0	0
$443$	25.9529	1.23306	0.616531	−	0.787331i	$-0.288538\pi$
$443$	25.9529	1.23306	0.616531	+	0.787331i	$0.288538\pi$
$444$	−2.52743	−0.119947
$445$	−4.72607	−0.224037
$446$	19.1965	0.908978
$447$	−1.01764	−0.0481327
$448$	−2.76976	−0.130859
$449$	7.57195	0.357342	0.178671	−	0.983909i	$-0.442820\pi$
$449$	7.57195	0.357342	0.178671	+	0.983909i	$0.442820\pi$
$450$	−5.55440	−0.261837
$451$	51.0321	2.40301
$452$	19.5277	0.918506
$453$	−3.93508	−0.184886
$454$	18.8685	0.885544
$455$	0	0
$456$	0.231327	0.0108329
$457$	8.92915	0.417688	0.208844	−	0.977949i	$-0.433030\pi$
$457$	8.92915	0.417688	0.208844	+	0.977949i	$0.433030\pi$
$458$	1.02603	0.0479431
$459$	−5.73499	−0.267686
$460$	−4.83852	−0.225597
$461$	−25.4738	−1.18643	−0.593217	−	0.805043i	$-0.702142\pi$
$461$	−25.4738	−1.18643	−0.593217	+	0.805043i	$0.702142\pi$
$462$	−3.36893	−0.156737
$463$	−32.7337	−1.52126	−0.760632	−	0.649183i	$-0.775111\pi$
$463$	−32.7337	−1.52126	−0.760632	+	0.649183i	$0.775111\pi$
$464$	−5.48476	−0.254624
$465$	6.05772	0.280920
$466$	23.1615	1.07294
$467$	−38.0221	−1.75945	−0.879726	−	0.475480i	$-0.842274\pi$
$467$	−38.0221	−1.75945	−0.879726	+	0.475480i	$0.842274\pi$
$468$	0	0
$469$	0.0518275	0.00239317
$470$	−5.56862	−0.256861
$471$	3.77820	0.174090
$472$	−1.31845	−0.0606867
$473$	21.8206	1.00331
$474$	3.42325	0.157235
$475$	1.88509	0.0864939
$476$	−11.5475	−0.529279
$477$	7.01983	0.321416
$478$	4.69804	0.214883
$479$	−18.4210	−0.841677	−0.420838	−	0.907136i	$-0.638264\pi$
$479$	−18.4210	−0.841677	−0.420838	+	0.907136i	$0.638264\pi$
$480$	−0.606990	−0.0277052
$481$	0	0
$482$	7.07187	0.322115
$483$	−1.18148	−0.0537593
$484$	16.6468	0.756672
$485$	−26.3074	−1.19456
$486$	6.09795	0.276609
$487$	−5.57081	−0.252438	−0.126219	−	0.992002i	$-0.540284\pi$
$487$	−5.57081	−0.252438	−0.126219	+	0.992002i	$0.540284\pi$
$488$	11.6271	0.526333
$489$	−1.61144	−0.0728717
$490$	−1.76223	−0.0796093
$491$	26.1718	1.18112	0.590559	−	0.806995i	$-0.298907\pi$
$491$	26.1718	1.18112	0.590559	+	0.806995i	$0.298907\pi$
$492$	2.24516	0.101220
$493$	−22.8667	−1.02986
$494$	0	0
$495$	40.6520	1.82717
$496$	−9.97993	−0.448112
$497$	5.63072	0.252572
$498$	2.12567	0.0952535
$499$	−16.4627	−0.736973	−0.368487	−	0.929633i	$-0.620124\pi$
$499$	−16.4627	−0.736973	−0.368487	+	0.929633i	$0.620124\pi$
$500$	8.17335	0.365523
$501$	3.35311	0.149806
$502$	−15.0248	−0.670589
$503$	−17.3127	−0.771935	−0.385968	−	0.922512i	$-0.626132\pi$
$503$	−17.3127	−0.771935	−0.385968	+	0.922512i	$0.626132\pi$
$504$	8.16108	0.363523
$505$	−41.5569	−1.84926
$506$	9.69572	0.431027
$507$	0	0
$508$	0.0631019	0.00279970
$509$	−13.0192	−0.577065	−0.288532	−	0.957470i	$-0.593167\pi$
$509$	−13.0192	−0.577065	−0.288532	+	0.957470i	$0.593167\pi$
$510$	−2.53062	−0.112058
$511$	9.59208	0.424329
$512$	1.00000	0.0441942
$513$	−1.37558	−0.0607335
$514$	−9.53616	−0.420622
$515$	3.66956	0.161700
$516$	0.960000	0.0422616
$517$	11.1587	0.490761
$518$	30.2619	1.32963
$519$	3.59553	0.157826
$520$	0	0
$521$	17.1816	0.752742	0.376371	−	0.926469i	$-0.377172\pi$
$521$	17.1816	0.752742	0.376371	+	0.926469i	$0.377172\pi$
$522$	16.1608	0.707338
$523$	2.80717	0.122749	0.0613744	−	0.998115i	$-0.480452\pi$
$523$	2.80717	0.122749	0.0613744	+	0.998115i	$0.480452\pi$
$524$	11.9829	0.523474
$525$	−1.20782	−0.0527135
$526$	−16.1412	−0.703789
$527$	−41.6076	−1.81246
$528$	1.21632	0.0529336
$529$	−19.5997	−0.852161
$530$	6.25139	0.271543
$531$	3.88481	0.168586
$532$	−2.76976	−0.120085
$533$	0	0
$534$	0.416650	0.0180302
$535$	−11.7715	−0.508927
$536$	−0.0187119	−0.000808231 0
$537$	3.58780	0.154825
$538$	−17.7516	−0.765324
$539$	3.53126	0.152102
$540$	3.60946	0.155326
$541$	−29.8907	−1.28510	−0.642550	−	0.766243i	$-0.722124\pi$
$541$	−29.8907	−1.28510	−0.642550	+	0.766243i	$0.722124\pi$
$542$	−22.7371	−0.976640
$543$	−2.18353	−0.0937043
$544$	4.16913	0.178750
$545$	−5.28251	−0.226278
$546$	0	0
$547$	32.1922	1.37644	0.688219	−	0.725503i	$-0.258393\pi$
$547$	32.1922	1.37644	0.688219	+	0.725503i	$0.258393\pi$
$548$	−8.85725	−0.378363
$549$	−34.2590	−1.46214
$550$	9.91185	0.422643
$551$	−5.48476	−0.233659
$552$	0.426564	0.0181558
$553$	−40.9878	−1.74298
$554$	17.6200	0.748600
$555$	6.63184	0.281506
$556$	−13.3000	−0.564044
$557$	23.2022	0.983108	0.491554	−	0.870847i	$-0.336429\pi$
$557$	23.2022	0.983108	0.491554	+	0.870847i	$0.336429\pi$
$558$	29.4058	1.24484
$559$	0	0
$560$	7.26771	0.307117
$561$	5.07101	0.214098
$562$	10.5581	0.445365
$563$	7.19169	0.303093	0.151547	−	0.988450i	$-0.451575\pi$
$563$	7.19169	0.303093	0.151547	+	0.988450i	$0.451575\pi$
$564$	0.490929	0.0206719
$565$	−51.2397	−2.15567
$566$	−19.8729	−0.835321
$567$	−23.6019	−0.991185
$568$	−2.03293	−0.0852996
$569$	27.8405	1.16714	0.583568	−	0.812064i	$-0.301656\pi$
$569$	27.8405	1.16714	0.583568	+	0.812064i	$0.301656\pi$
$570$	−0.606990	−0.0254240
$571$	35.6544	1.49209	0.746045	−	0.665896i	$-0.231951\pi$
$571$	35.6544	1.49209	0.746045	+	0.665896i	$0.231951\pi$
$572$	0	0
$573$	5.84462	0.244162
$574$	−26.8821	−1.12204
$575$	3.47608	0.144963
$576$	−2.94649	−0.122770
$577$	−16.2869	−0.678035	−0.339017	−	0.940780i	$-0.610095\pi$
$577$	−16.2869	−0.678035	−0.339017	+	0.940780i	$0.610095\pi$
$578$	0.381633	0.0158739
$579$	0.859789	0.0357316
$580$	14.3917	0.597584
$581$	−25.4514	−1.05590
$582$	2.31926	0.0961366
$583$	−12.5269	−0.518812
$584$	−3.46314	−0.143306
$585$	0	0
$586$	−17.6933	−0.730902
$587$	−24.7782	−1.02270	−0.511352	−	0.859371i	$-0.670855\pi$
$587$	−24.7782	−1.02270	−0.511352	+	0.859371i	$0.670855\pi$
$588$	0.155358	0.00640686
$589$	−9.97993	−0.411216
$590$	3.45955	0.142427
$591$	−1.69721	−0.0698137
$592$	−10.9258	−0.449047
$593$	−33.2723	−1.36633	−0.683165	−	0.730264i	$-0.739397\pi$
$593$	−33.2723	−1.36633	−0.683165	+	0.730264i	$0.739397\pi$
$594$	−7.23285	−0.296767
$595$	30.3000	1.24218
$596$	−4.39913	−0.180196
$597$	−0.905072	−0.0370421
$598$	0	0
$599$	−27.7252	−1.13282	−0.566410	−	0.824124i	$-0.691668\pi$
$599$	−27.7252	−1.13282	−0.566410	+	0.824124i	$0.691668\pi$
$600$	0.436072	0.0178026
$601$	12.8848	0.525582	0.262791	−	0.964853i	$-0.415357\pi$
$601$	12.8848	0.525582	0.262791	+	0.964853i	$0.415357\pi$
$602$	−11.4944	−0.468478
$603$	0.0551344	0.00224524
$604$	−17.0109	−0.692163
$605$	−43.6803	−1.77585
$606$	3.66365	0.148826
$607$	−35.7657	−1.45168	−0.725842	−	0.687862i	$-0.758550\pi$
$607$	−35.7657	−1.45168	−0.725842	+	0.687862i	$0.758550\pi$
$608$	1.00000	0.0405554
$609$	3.51421	0.142403
$610$	−30.5088	−1.23527
$611$	0	0
$612$	−12.2843	−0.496563
$613$	−40.4250	−1.63275	−0.816375	−	0.577522i	$-0.804020\pi$
$613$	−40.4250	−1.63275	−0.816375	+	0.577522i	$0.804020\pi$
$614$	−7.36105	−0.297068
$615$	−5.89118	−0.237555
$616$	−14.5635	−0.586779
$617$	25.9123	1.04319	0.521595	−	0.853193i	$-0.325337\pi$
$617$	25.9123	1.04319	0.521595	+	0.853193i	$0.325337\pi$
$618$	−0.323508	−0.0130134
$619$	9.04414	0.363515	0.181757	−	0.983343i	$-0.441821\pi$
$619$	9.04414	0.363515	0.181757	+	0.983343i	$0.441821\pi$
$620$	26.1868	1.05169
$621$	−2.53656	−0.101789
$622$	−9.32425	−0.373868
$623$	−4.98871	−0.199868
$624$	0	0
$625$	−30.8719	−1.23488
$626$	−4.14064	−0.165493
$627$	1.21632	0.0485752
$628$	16.3327	0.651746
$629$	−45.5510	−1.81624
$630$	−21.4142	−0.853163
$631$	42.9877	1.71131	0.855656	−	0.517545i	$-0.173154\pi$
$631$	42.9877	1.71131	0.855656	+	0.517545i	$0.173154\pi$
$632$	14.7983	0.588645
$633$	2.20362	0.0875860
$634$	27.5465	1.09401
$635$	−0.165576	−0.00657068
$636$	−0.551123	−0.0218534
$637$	0	0
$638$	−28.8390	−1.14175
$639$	5.98999	0.236960
$640$	−2.62395	−0.103721
$641$	−1.16242	−0.0459127	−0.0229564	−	0.999736i	$-0.507308\pi$
$641$	−1.16242	−0.0459127	−0.0229564	+	0.999736i	$0.507308\pi$
$642$	1.03778	0.0409578
$643$	30.2178	1.19167	0.595836	−	0.803106i	$-0.296821\pi$
$643$	30.2178	1.19167	0.595836	+	0.803106i	$0.296821\pi$
$644$	−5.10741	−0.201260
$645$	−2.51899	−0.0991851
$646$	4.16913	0.164032
$647$	33.3468	1.31100	0.655499	−	0.755196i	$-0.272458\pi$
$647$	33.3468	1.31100	0.655499	+	0.755196i	$0.272458\pi$
$648$	8.52125	0.334746
$649$	−6.93245	−0.272123
$650$	0	0
$651$	6.39436	0.250615
$652$	−6.96605	−0.272812
$653$	7.48762	0.293013	0.146507	−	0.989210i	$-0.453197\pi$
$653$	7.48762	0.293013	0.146507	+	0.989210i	$0.453197\pi$
$654$	0.465706	0.0182105
$655$	−31.4424	−1.22856
$656$	9.70557	0.378939
$657$	10.2041	0.398100
$658$	−5.87808	−0.229151
$659$	31.3926	1.22288	0.611441	−	0.791290i	$-0.290590\pi$
$659$	31.3926	1.22288	0.611441	+	0.791290i	$0.290590\pi$
$660$	−3.19156	−0.124231
$661$	44.1808	1.71843	0.859217	−	0.511611i	$-0.170951\pi$
$661$	44.1808	1.71843	0.859217	+	0.511611i	$0.170951\pi$
$662$	−15.9830	−0.621199
$663$	0	0
$664$	9.18902	0.356603
$665$	7.26771	0.281830
$666$	32.1927	1.24744
$667$	−10.1138	−0.391609
$668$	14.4951	0.560833
$669$	4.44066	0.171686
$670$	0.0490990	0.00189686
$671$	61.1354	2.36011
$672$	−0.640721	−0.0247164
$673$	−21.6539	−0.834696	−0.417348	−	0.908747i	$-0.637040\pi$
$673$	−21.6539	−0.834696	−0.417348	+	0.908747i	$0.637040\pi$
$674$	−15.7428	−0.606389
$675$	−2.59310	−0.0998085
$676$	0	0
$677$	−46.8716	−1.80142	−0.900712	−	0.434417i	$-0.856954\pi$
$677$	−46.8716	−1.80142	−0.900712	+	0.434417i	$0.856954\pi$
$678$	4.51729	0.173485
$679$	−27.7694	−1.06569
$680$	−10.9396	−0.419513
$681$	4.36480	0.167260
$682$	−52.4747	−2.00936
$683$	−12.4591	−0.476735	−0.238367	−	0.971175i	$-0.576612\pi$
$683$	−12.4591	−0.476735	−0.238367	+	0.971175i	$0.576612\pi$
$684$	−2.94649	−0.112662
$685$	23.2409	0.887990
$686$	17.5282	0.669229
$687$	0.237348	0.00905538
$688$	4.14997	0.158216
$689$	0	0
$690$	−1.11928	−0.0426103
$691$	0.527046	0.0200498	0.0100249	−	0.999950i	$-0.496809\pi$
$691$	0.527046	0.0200498	0.0100249	+	0.999950i	$0.496809\pi$
$692$	15.5430	0.590858
$693$	42.9111	1.63006
$694$	−18.2097	−0.691232
$695$	34.8984	1.32377
$696$	−1.26877	−0.0480928
$697$	40.4638	1.53267
$698$	−36.7759	−1.39199
$699$	5.35788	0.202654
$700$	−5.22126	−0.197345
$701$	−17.6680	−0.667312	−0.333656	−	0.942695i	$-0.608282\pi$
$701$	−17.6680	−0.667312	−0.333656	+	0.942695i	$0.608282\pi$
$702$	0	0
$703$	−10.9258	−0.412074
$704$	5.25802	0.198169
$705$	−1.28817	−0.0485154
$706$	−19.5686	−0.736472
$707$	−43.8663	−1.64976
$708$	−0.304994	−0.0114624
$709$	8.45957	0.317706	0.158853	−	0.987302i	$-0.449220\pi$
$709$	8.45957	0.317706	0.158853	+	0.987302i	$0.449220\pi$
$710$	5.33429	0.200192
$711$	−43.6030	−1.63524
$712$	1.80113	0.0675002
$713$	−18.4029	−0.689193
$714$	−2.67125	−0.0999690
$715$	0	0
$716$	15.5096	0.579623
$717$	1.08678	0.0405867
$718$	9.71547	0.362578
$719$	14.5139	0.541277	0.270639	−	0.962681i	$-0.412765\pi$
$719$	14.5139	0.541277	0.270639	+	0.962681i	$0.412765\pi$
$720$	7.73142	0.288133
$721$	3.87348	0.144256
$722$	1.00000	0.0372161
$723$	1.63592	0.0608403
$724$	−9.43915	−0.350803
$725$	−10.3393	−0.383991
$726$	3.85085	0.142919
$727$	27.0801	1.00435	0.502173	−	0.864767i	$-0.332534\pi$
$727$	27.0801	1.00435	0.502173	+	0.864767i	$0.332534\pi$
$728$	0	0
$729$	−24.1531	−0.894561
$730$	9.08709	0.336328
$731$	17.3018	0.639928
$732$	2.68966	0.0994126
$733$	24.5633	0.907266	0.453633	−	0.891189i	$-0.350128\pi$
$733$	24.5633	0.907266	0.453633	+	0.891189i	$0.350128\pi$
$734$	−29.6577	−1.09469
$735$	−0.407651	−0.0150364
$736$	1.84399	0.0679703
$737$	−0.0983875	−0.00362415
$738$	−28.5973	−1.05268
$739$	17.3964	0.639936	0.319968	−	0.947428i	$-0.396328\pi$
$739$	17.3964	0.639936	0.319968	+	0.947428i	$0.396328\pi$
$740$	28.6687	1.05388
$741$	0	0
$742$	6.59879	0.242249
$743$	37.7707	1.38567	0.692837	−	0.721094i	$-0.256361\pi$
$743$	37.7707	1.38567	0.692837	+	0.721094i	$0.256361\pi$
$744$	−2.30863	−0.0846385
$745$	11.5431	0.422906
$746$	31.2898	1.14560
$747$	−27.0753	−0.990634
$748$	21.9214	0.801525
$749$	−12.4257	−0.454024
$750$	1.89072	0.0690393
$751$	−14.5166	−0.529717	−0.264858	−	0.964287i	$-0.585325\pi$
$751$	−14.5166	−0.529717	−0.264858	+	0.964287i	$0.585325\pi$
$752$	2.12223	0.0773898
$753$	−3.47564	−0.126659
$754$	0	0
$755$	44.6356	1.62446
$756$	3.81004	0.138570
$757$	35.9465	1.30650	0.653249	−	0.757143i	$-0.273405\pi$
$757$	35.9465	1.30650	0.653249	+	0.757143i	$0.273405\pi$
$758$	21.7549	0.790173
$759$	2.24288	0.0814115
$760$	−2.62395	−0.0951805
$761$	18.0139	0.653003	0.326502	−	0.945197i	$-0.394130\pi$
$761$	18.0139	0.653003	0.326502	+	0.945197i	$0.394130\pi$
$762$	0.0145972	0.000528800 0
$763$	−5.57607	−0.201867
$764$	25.2656	0.914077
$765$	32.2333	1.16540
$766$	25.4924	0.921080
$767$	0	0
$768$	0.231327	0.00834730
$769$	16.3810	0.590713	0.295356	−	0.955387i	$-0.404562\pi$
$769$	16.3810	0.590713	0.295356	+	0.955387i	$0.404562\pi$
$770$	38.2138	1.37713
$771$	−2.20597	−0.0794461
$772$	3.71677	0.133769
$773$	21.2717	0.765090	0.382545	−	0.923937i	$-0.375048\pi$
$773$	21.2717	0.765090	0.382545	+	0.923937i	$0.375048\pi$
$774$	−12.2278	−0.439520
$775$	−18.8131	−0.675786
$776$	10.0259	0.359909
$777$	7.00039	0.251137
$778$	34.7782	1.24686
$779$	9.70557	0.347738
$780$	0	0
$781$	−10.6892	−0.382488
$782$	7.68782	0.274916
$783$	7.54475	0.269627
$784$	0.671595	0.0239855
$785$	−42.8562	−1.52960
$786$	2.77196	0.0988726
$787$	12.1733	0.433932	0.216966	−	0.976179i	$-0.430384\pi$
$787$	12.1733	0.433932	0.216966	+	0.976179i	$0.430384\pi$
$788$	−7.33682	−0.261363
$789$	−3.73389	−0.132930
$790$	−38.8299	−1.38151
$791$	−54.0872	−1.92312
$792$	−15.4927	−0.550509
$793$	0	0
$794$	−3.75293	−0.133186
$795$	1.44612	0.0512884
$796$	−3.91252	−0.138676
$797$	−15.3633	−0.544197	−0.272098	−	0.962269i	$-0.587718\pi$
$797$	−15.3633	−0.544197	−0.272098	+	0.962269i	$0.587718\pi$
$798$	−0.640721	−0.0226813
$799$	8.84785	0.313015
$800$	1.88509	0.0666480
$801$	−5.30701	−0.187514
$802$	−10.0861	−0.356154
$803$	−18.2093	−0.642591
$804$	−0.00432857	−0.000152657 0
$805$	13.4016	0.472343
$806$	0	0
$807$	−4.10642	−0.144553
$808$	15.8375	0.557163
$809$	−38.4275	−1.35104	−0.675519	−	0.737342i	$-0.736081\pi$
$809$	−38.4275	−1.35104	−0.675519	+	0.737342i	$0.736081\pi$
$810$	−22.3593	−0.785626
$811$	−17.0180	−0.597581	−0.298791	−	0.954319i	$-0.596583\pi$
$811$	−17.0180	−0.597581	−0.298791	+	0.954319i	$0.596583\pi$
$812$	15.1915	0.533117
$813$	−5.25970	−0.184466
$814$	−57.4480	−2.01355
$815$	18.2785	0.640270
$816$	0.964432	0.0337619
$817$	4.14997	0.145189
$818$	12.1675	0.425425
$819$	0	0
$820$	−25.4669	−0.889342
$821$	11.7873	0.411380	0.205690	−	0.978617i	$-0.434056\pi$
$821$	11.7873	0.411380	0.205690	+	0.978617i	$0.434056\pi$
$822$	−2.04892	−0.0714643
$823$	13.5598	0.472664	0.236332	−	0.971672i	$-0.424055\pi$
$823$	13.5598	0.472664	0.236332	+	0.971672i	$0.424055\pi$
$824$	−1.39849	−0.0487186
$825$	2.29288	0.0798278
$826$	3.65180	0.127063
$827$	−11.2630	−0.391654	−0.195827	−	0.980638i	$-0.562739\pi$
$827$	−11.2630	−0.391654	−0.195827	+	0.980638i	$0.562739\pi$
$828$	−5.43328	−0.188820
$829$	13.8998	0.482762	0.241381	−	0.970430i	$-0.422400\pi$
$829$	13.8998	0.482762	0.241381	+	0.970430i	$0.422400\pi$
$830$	−24.1115	−0.836922
$831$	4.07597	0.141394
$832$	0	0
$833$	2.79996	0.0970130
$834$	−3.07664	−0.106535
$835$	−38.0344	−1.31624
$836$	5.25802	0.181852
$837$	13.7282	0.474517
$838$	−1.68120	−0.0580761
$839$	32.6007	1.12550	0.562750	−	0.826627i	$-0.309743\pi$
$839$	32.6007	1.12550	0.562750	+	0.826627i	$0.309743\pi$
$840$	1.68122	0.0580075
$841$	1.08262	0.0373318
$842$	20.0552	0.691146
$843$	2.44237	0.0841196
$844$	9.52598	0.327898
$845$	0	0
$846$	−6.25313	−0.214987
$847$	−46.1077	−1.58428
$848$	−2.38244	−0.0818133
$849$	−4.59715	−0.157774
$850$	7.85918	0.269568
$851$	−20.1470	−0.690631
$852$	−0.470271	−0.0161112
$853$	−7.06760	−0.241990	−0.120995	−	0.992653i	$-0.538609\pi$
$853$	−7.06760	−0.241990	−0.120995	+	0.992653i	$0.538609\pi$
$854$	−32.2043	−1.10201
$855$	7.73142	0.264409
$856$	4.48619	0.153335
$857$	−12.9237	−0.441466	−0.220733	−	0.975334i	$-0.570845\pi$
$857$	−12.9237	−0.441466	−0.220733	+	0.975334i	$0.570845\pi$
$858$	0	0
$859$	−40.7951	−1.39191	−0.695955	−	0.718085i	$-0.745019\pi$
$859$	−40.7951	−1.39191	−0.695955	+	0.718085i	$0.745019\pi$
$860$	−10.8893	−0.371322
$861$	−6.21857	−0.211928
$862$	3.10014	0.105591
$863$	7.60862	0.259001	0.129500	−	0.991579i	$-0.458663\pi$
$863$	7.60862	0.259001	0.129500	+	0.991579i	$0.458663\pi$
$864$	−1.37558	−0.0467983
$865$	−40.7841	−1.38670
$866$	27.9700	0.950459
$867$	0.0882821	0.00299822
$868$	27.6421	0.938233
$869$	77.8098	2.63952
$870$	3.32919	0.112870
$871$	0	0
$872$	2.01319	0.0681753
$873$	−29.5412	−0.999818
$874$	1.84399	0.0623738
$875$	−22.6383	−0.765313
$876$	−0.801118	−0.0270673
$877$	21.1342	0.713650	0.356825	−	0.934171i	$-0.383859\pi$
$877$	21.1342	0.713650	0.356825	+	0.934171i	$0.383859\pi$
$878$	−32.8257	−1.10781
$879$	−4.09293	−0.138051
$880$	−13.7968	−0.465089
$881$	−16.3312	−0.550212	−0.275106	−	0.961414i	$-0.588713\pi$
$881$	−16.3312	−0.550212	−0.275106	+	0.961414i	$0.588713\pi$
$882$	−1.97885	−0.0666312
$883$	46.7394	1.57291	0.786453	−	0.617650i	$-0.211915\pi$
$883$	46.7394	1.57291	0.786453	+	0.617650i	$0.211915\pi$
$884$	0	0
$885$	0.800287	0.0269014
$886$	25.9529	0.871906
$887$	15.4212	0.517794	0.258897	−	0.965905i	$-0.416641\pi$
$887$	15.4212	0.517794	0.258897	+	0.965905i	$0.416641\pi$
$888$	−2.52743	−0.0848150
$889$	−0.174777	−0.00586185
$890$	−4.72607	−0.158418
$891$	44.8049	1.50102
$892$	19.1965	0.642745
$893$	2.12223	0.0710178
$894$	−1.01764	−0.0340349
$895$	−40.6965	−1.36033
$896$	−2.76976	−0.0925313
$897$	0	0
$898$	7.57195	0.252679
$899$	54.7376	1.82560
$900$	−5.55440	−0.185147
$901$	−9.93269	−0.330906
$902$	51.0321	1.69918
$903$	−2.65897	−0.0884851
$904$	19.5277	0.649482
$905$	24.7678	0.823310
$906$	−3.93508	−0.130734
$907$	−18.7271	−0.621823	−0.310912	−	0.950439i	$-0.600634\pi$
$907$	−18.7271	−0.621823	−0.310912	+	0.950439i	$0.600634\pi$
$908$	18.8685	0.626174
$909$	−46.6651	−1.54778
$910$	0	0
$911$	10.7408	0.355859	0.177929	−	0.984043i	$-0.443060\pi$
$911$	10.7408	0.355859	0.177929	+	0.984043i	$0.443060\pi$
$912$	0.231327	0.00766000
$913$	48.3160	1.59903
$914$	8.92915	0.295350
$915$	−7.05751	−0.233314
$916$	1.02603	0.0339009
$917$	−33.1897	−1.09602
$918$	−5.73499	−0.189283
$919$	19.9251	0.657268	0.328634	−	0.944457i	$-0.393412\pi$
$919$	19.9251	0.657268	0.328634	+	0.944457i	$0.393412\pi$
$920$	−4.83852	−0.159521
$921$	−1.70281	−0.0561095
$922$	−25.4738	−0.838936
$923$	0	0
$924$	−3.36893	−0.110830
$925$	−20.5961	−0.677196
$926$	−32.7337	−1.07570
$927$	4.12063	0.135339
$928$	−5.48476	−0.180046
$929$	−29.3873	−0.964164	−0.482082	−	0.876126i	$-0.660119\pi$
$929$	−29.3873	−0.964164	−0.482082	+	0.876126i	$0.660119\pi$
$930$	6.05772	0.198640
$931$	0.671595	0.0220106
$932$	23.1615	0.758680
$933$	−2.15695	−0.0706154
$934$	−38.0221	−1.24412
$935$	−57.5205	−1.88112
$936$	0	0
$937$	−16.5361	−0.540212	−0.270106	−	0.962831i	$-0.587059\pi$
$937$	−16.5361	−0.540212	−0.270106	+	0.962831i	$0.587059\pi$
$938$	0.0518275	0.00169223
$939$	−0.957843	−0.0312580
$940$	−5.56862	−0.181628
$941$	−44.6652	−1.45604	−0.728022	−	0.685553i	$-0.759560\pi$
$941$	−44.6652	−1.45604	−0.728022	+	0.685553i	$0.759560\pi$
$942$	3.77820	0.123100
$943$	17.8969	0.582804
$944$	−1.31845	−0.0429120
$945$	−9.99734	−0.325214
$946$	21.8206	0.709450
$947$	−25.4077	−0.825638	−0.412819	−	0.910813i	$-0.635456\pi$
$947$	−25.4077	−0.825638	−0.412819	+	0.910813i	$0.635456\pi$
$948$	3.42325	0.111182
$949$	0	0
$950$	1.88509	0.0611604
$951$	6.37226	0.206635
$952$	−11.5475	−0.374257
$953$	12.2990	0.398405	0.199203	−	0.979958i	$-0.436165\pi$
$953$	12.2990	0.398405	0.199203	+	0.979958i	$0.436165\pi$
$954$	7.01983	0.227275
$955$	−66.2956	−2.14527
$956$	4.69804	0.151946
$957$	−6.67124	−0.215651
$958$	−18.4210	−0.595155
$959$	24.5325	0.792195
$960$	−0.606990	−0.0195905
$961$	68.5991	2.21287
$962$	0	0
$963$	−13.2185	−0.425960
$964$	7.07187	0.227770
$965$	−9.75260	−0.313947
$966$	−1.18148	−0.0380136
$967$	25.8356	0.830816	0.415408	−	0.909635i	$-0.363639\pi$
$967$	25.8356	0.830816	0.415408	+	0.909635i	$0.363639\pi$
$968$	16.6468	0.535048
$969$	0.964432	0.0309820
$970$	−26.3074	−0.844681
$971$	2.54867	0.0817908	0.0408954	−	0.999163i	$-0.486979\pi$
$971$	2.54867	0.0817908	0.0408954	+	0.999163i	$0.486979\pi$
$972$	6.09795	0.195592
$973$	36.8378	1.18096
$974$	−5.57081	−0.178500
$975$	0	0
$976$	11.6271	0.372174
$977$	−4.37934	−0.140108	−0.0700538	−	0.997543i	$-0.522317\pi$
$977$	−4.37934	−0.140108	−0.0700538	+	0.997543i	$0.522317\pi$
$978$	−1.61144	−0.0515281
$979$	9.47039	0.302675
$980$	−1.76223	−0.0562923
$981$	−5.93185	−0.189389
$982$	26.1718	0.835176
$983$	20.0863	0.640652	0.320326	−	0.947307i	$-0.396207\pi$
$983$	20.0863	0.640652	0.320326	+	0.947307i	$0.396207\pi$
$984$	2.24516	0.0715731
$985$	19.2514	0.613401
$986$	−22.8667	−0.728223
$987$	−1.35976	−0.0432816
$988$	0	0
$989$	7.65249	0.243335
$990$	40.6520	1.29200
$991$	16.7889	0.533319	0.266659	−	0.963791i	$-0.414080\pi$
$991$	16.7889	0.533319	0.266659	+	0.963791i	$0.414080\pi$
$992$	−9.97993	−0.316863
$993$	−3.69731	−0.117331
$994$	5.63072	0.178596
$995$	10.2662	0.325462
$996$	2.12567	0.0673544
$997$	−19.0585	−0.603589	−0.301794	−	0.953373i	$-0.597586\pi$
$997$	−19.0585	−0.603589	−0.301794	+	0.953373i	$0.597586\pi$
$998$	−16.4627	−0.521119
$999$	15.0293	0.475507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bn.1.7		14
13.2	odd	12		494.2.m.b.381.11	yes	28
13.7	odd	12		494.2.m.b.153.11	✓	28
13.12	even	2		6422.2.a.bm.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.11	✓	28	13.7	odd	12
494.2.m.b.381.11	yes	28	13.2	odd	12
6422.2.a.bm.1.7		14	13.12	even	2
6422.2.a.bn.1.7		14	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:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.231327 q^{3} +1.00000 q^{4} -2.62395 q^{5} +0.231327 q^{6} -2.76976 q^{7} +1.00000 q^{8} -2.94649 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.231327 q^{3} +1.00000 q^{4} -2.62395 q^{5} +0.231327 q^{6} -2.76976 q^{7} +1.00000 q^{8} -2.94649 q^{9} -2.62395 q^{10} +5.25802 q^{11} +0.231327 q^{12} -2.76976 q^{14} -0.606990 q^{15} +1.00000 q^{16} +4.16913 q^{17} -2.94649 q^{18} +1.00000 q^{19} -2.62395 q^{20} -0.640721 q^{21} +5.25802 q^{22} +1.84399 q^{23} +0.231327 q^{24} +1.88509 q^{25} -1.37558 q^{27} -2.76976 q^{28} -5.48476 q^{29} -0.606990 q^{30} -9.97993 q^{31} +1.00000 q^{32} +1.21632 q^{33} +4.16913 q^{34} +7.26771 q^{35} -2.94649 q^{36} -10.9258 q^{37} +1.00000 q^{38} -2.62395 q^{40} +9.70557 q^{41} -0.640721 q^{42} +4.14997 q^{43} +5.25802 q^{44} +7.73142 q^{45} +1.84399 q^{46} +2.12223 q^{47} +0.231327 q^{48} +0.671595 q^{49} +1.88509 q^{50} +0.964432 q^{51} -2.38244 q^{53} -1.37558 q^{54} -13.7968 q^{55} -2.76976 q^{56} +0.231327 q^{57} -5.48476 q^{58} -1.31845 q^{59} -0.606990 q^{60} +11.6271 q^{61} -9.97993 q^{62} +8.16108 q^{63} +1.00000 q^{64} +1.21632 q^{66} -0.0187119 q^{67} +4.16913 q^{68} +0.426564 q^{69} +7.26771 q^{70} -2.03293 q^{71} -2.94649 q^{72} -3.46314 q^{73} -10.9258 q^{74} +0.436072 q^{75} +1.00000 q^{76} -14.5635 q^{77} +14.7983 q^{79} -2.62395 q^{80} +8.52125 q^{81} +9.70557 q^{82} +9.18902 q^{83} -0.640721 q^{84} -10.9396 q^{85} +4.14997 q^{86} -1.26877 q^{87} +5.25802 q^{88} +1.80113 q^{89} +7.73142 q^{90} +1.84399 q^{92} -2.30863 q^{93} +2.12223 q^{94} -2.62395 q^{95} +0.231327 q^{96} +10.0259 q^{97} +0.671595 q^{98} -15.4927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9	\( 14 q + 14 q^{2} + 4 q^{3} + 14 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{7} + 14 q^{8} + 18 q^{9} - 2 q^{10} + 10 q^{11} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 14 q^{16} + 2 q^{17} + 18 q^{18} + 14 q^{19} - 2 q^{20} - 18 q^{21} + 10 q^{22} + 12 q^{23} + 4 q^{24} + 44 q^{25} + 10 q^{27} + 2 q^{28} + 4 q^{29} - 4 q^{30} + 4 q^{31} + 14 q^{32} + 12 q^{33} + 2 q^{34} + 14 q^{35} + 18 q^{36} + 18 q^{37} + 14 q^{38} - 2 q^{40} + 6 q^{41} - 18 q^{42} + 28 q^{43} + 10 q^{44} + 8 q^{45} + 12 q^{46} - 20 q^{47} + 4 q^{48} + 28 q^{49} + 44 q^{50} + 10 q^{51} + 12 q^{53} + 10 q^{54} - 2 q^{55} + 2 q^{56} + 4 q^{57} + 4 q^{58} + 16 q^{59} - 4 q^{60} + 30 q^{61} + 4 q^{62} + 28 q^{63} + 14 q^{64} + 12 q^{66} + 2 q^{67} + 2 q^{68} - 42 q^{69} + 14 q^{70} + 44 q^{71} + 18 q^{72} - 36 q^{73} + 18 q^{74} + 46 q^{75} + 14 q^{76} + 68 q^{77} + 34 q^{79} - 2 q^{80} - 6 q^{81} + 6 q^{82} + 2 q^{83} - 18 q^{84} - 30 q^{85} + 28 q^{86} + 52 q^{87} + 10 q^{88} + 42 q^{89} + 8 q^{90} + 12 q^{92} - 12 q^{93} - 20 q^{94} - 2 q^{95} + 4 q^{96} + 40 q^{97} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 4 * q^3 + 14 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^7 + 14 * q^8 + 18 * q^9 - 2 * q^10 + 10 * q^11 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 14 * q^16 + 2 * q^17 + 18 * q^18 + 14 * q^19 - 2 * q^20 - 18 * q^21 + 10 * q^22 + 12 * q^23 + 4 * q^24 + 44 * q^25 + 10 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 + 4 * q^31 + 14 * q^32 + 12 * q^33 + 2 * q^34 + 14 * q^35 + 18 * q^36 + 18 * q^37 + 14 * q^38 - 2 * q^40 + 6 * q^41 - 18 * q^42 + 28 * q^43 + 10 * q^44 + 8 * q^45 + 12 * q^46 - 20 * q^47 + 4 * q^48 + 28 * q^49 + 44 * q^50 + 10 * q^51 + 12 * q^53 + 10 * q^54 - 2 * q^55 + 2 * q^56 + 4 * q^57 + 4 * q^58 + 16 * q^59 - 4 * q^60 + 30 * q^61 + 4 * q^62 + 28 * q^63 + 14 * q^64 + 12 * q^66 + 2 * q^67 + 2 * q^68 - 42 * q^69 + 14 * q^70 + 44 * q^71 + 18 * q^72 - 36 * q^73 + 18 * q^74 + 46 * q^75 + 14 * q^76 + 68 * q^77 + 34 * q^79 - 2 * q^80 - 6 * q^81 + 6 * q^82 + 2 * q^83 - 18 * q^84 - 30 * q^85 + 28 * q^86 + 52 * q^87 + 10 * q^88 + 42 * q^89 + 8 * q^90 + 12 * q^92 - 12 * q^93 - 20 * q^94 - 2 * q^95 + 4 * q^96 + 40 * q^97 + 28 * q^98 + 12 * q^99

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