LMFDB - Embedded newform 6014.2.a.j.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.64406 q^{3} +1.00000 q^{4} -4.02843 q^{5} +1.64406 q^{6} +2.75493 q^{7} -1.00000 q^{8} -0.297060 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.64406 q^{3} +1.00000 q^{4} -4.02843 q^{5} +1.64406 q^{6} +2.75493 q^{7} -1.00000 q^{8} -0.297060 q^{9} +4.02843 q^{10} -1.24768 q^{11} -1.64406 q^{12} -0.823687 q^{13} -2.75493 q^{14} +6.62298 q^{15} +1.00000 q^{16} -6.05361 q^{17} +0.297060 q^{18} +0.349648 q^{19} -4.02843 q^{20} -4.52927 q^{21} +1.24768 q^{22} -2.04479 q^{23} +1.64406 q^{24} +11.2282 q^{25} +0.823687 q^{26} +5.42057 q^{27} +2.75493 q^{28} -0.869541 q^{29} -6.62298 q^{30} -1.00000 q^{31} -1.00000 q^{32} +2.05127 q^{33} +6.05361 q^{34} -11.0980 q^{35} -0.297060 q^{36} -1.12847 q^{37} -0.349648 q^{38} +1.35419 q^{39} +4.02843 q^{40} -8.19832 q^{41} +4.52927 q^{42} -4.72683 q^{43} -1.24768 q^{44} +1.19668 q^{45} +2.04479 q^{46} +6.48541 q^{47} -1.64406 q^{48} +0.589616 q^{49} -11.2282 q^{50} +9.95250 q^{51} -0.823687 q^{52} -7.47244 q^{53} -5.42057 q^{54} +5.02620 q^{55} -2.75493 q^{56} -0.574843 q^{57} +0.869541 q^{58} -11.9135 q^{59} +6.62298 q^{60} -4.85011 q^{61} +1.00000 q^{62} -0.818378 q^{63} +1.00000 q^{64} +3.31816 q^{65} -2.05127 q^{66} -3.84084 q^{67} -6.05361 q^{68} +3.36176 q^{69} +11.0980 q^{70} +6.93765 q^{71} +0.297060 q^{72} -15.3495 q^{73} +1.12847 q^{74} -18.4599 q^{75} +0.349648 q^{76} -3.43728 q^{77} -1.35419 q^{78} -1.71341 q^{79} -4.02843 q^{80} -8.02058 q^{81} +8.19832 q^{82} +11.4256 q^{83} -4.52927 q^{84} +24.3865 q^{85} +4.72683 q^{86} +1.42958 q^{87} +1.24768 q^{88} +4.29886 q^{89} -1.19668 q^{90} -2.26920 q^{91} -2.04479 q^{92} +1.64406 q^{93} -6.48541 q^{94} -1.40853 q^{95} +1.64406 q^{96} +1.00000 q^{97} -0.589616 q^{98} +0.370637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * 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
$3$	−1.64406	−0.949200	−0.474600	−	0.880202i	$-0.657407\pi$
$3$	−1.64406	−0.949200	−0.474600	+	0.880202i	$0.657407\pi$
$4$	1.00000	0.500000
$5$	−4.02843	−1.80157	−0.900783	−	0.434269i	$-0.857007\pi$
$5$	−4.02843	−1.80157	−0.900783	+	0.434269i	$0.857007\pi$
$6$	1.64406	0.671186
$7$	2.75493	1.04126	0.520632	−	0.853781i	$-0.325696\pi$
$7$	2.75493	1.04126	0.520632	+	0.853781i	$0.325696\pi$
$8$	−1.00000	−0.353553
$9$	−0.297060	−0.0990200
$10$	4.02843	1.27390
$11$	−1.24768	−0.376191	−0.188095	−	0.982151i	$-0.560231\pi$
$11$	−1.24768	−0.376191	−0.188095	+	0.982151i	$0.560231\pi$
$12$	−1.64406	−0.474600
$13$	−0.823687	−0.228450	−0.114225	−	0.993455i	$-0.536438\pi$
$13$	−0.823687	−0.228450	−0.114225	+	0.993455i	$0.536438\pi$
$14$	−2.75493	−0.736285
$15$	6.62298	1.71005
$16$	1.00000	0.250000
$17$	−6.05361	−1.46822	−0.734108	−	0.679033i	$-0.762399\pi$
$17$	−6.05361	−1.46822	−0.734108	+	0.679033i	$0.762399\pi$
$18$	0.297060	0.0700177
$19$	0.349648	0.0802148	0.0401074	−	0.999195i	$-0.487230\pi$
$19$	0.349648	0.0802148	0.0401074	+	0.999195i	$0.487230\pi$
$20$	−4.02843	−0.900783
$21$	−4.52927	−0.988368
$22$	1.24768	0.266007
$23$	−2.04479	−0.426369	−0.213184	−	0.977012i	$-0.568383\pi$
$23$	−2.04479	−0.426369	−0.213184	+	0.977012i	$0.568383\pi$
$24$	1.64406	0.335593
$25$	11.2282	2.24564
$26$	0.823687	0.161538
$27$	5.42057	1.04319
$28$	2.75493	0.520632
$29$	−0.869541	−0.161470	−0.0807348	−	0.996736i	$-0.525727\pi$
$29$	−0.869541	−0.161470	−0.0807348	+	0.996736i	$0.525727\pi$
$30$	−6.62298	−1.20919
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	2.05127	0.357080
$34$	6.05361	1.03818
$35$	−11.0980	−1.87591
$36$	−0.297060	−0.0495100
$37$	−1.12847	−0.185520	−0.0927599	−	0.995689i	$-0.529569\pi$
$37$	−1.12847	−0.185520	−0.0927599	+	0.995689i	$0.529569\pi$
$38$	−0.349648	−0.0567204
$39$	1.35419	0.216844
$40$	4.02843	0.636950
$41$	−8.19832	−1.28036	−0.640181	−	0.768224i	$-0.721141\pi$
$41$	−8.19832	−1.28036	−0.640181	+	0.768224i	$0.721141\pi$
$42$	4.52927	0.698881
$43$	−4.72683	−0.720834	−0.360417	−	0.932791i	$-0.617366\pi$
$43$	−4.72683	−0.720834	−0.360417	+	0.932791i	$0.617366\pi$
$44$	−1.24768	−0.188095
$45$	1.19668	0.178391
$46$	2.04479	0.301488
$47$	6.48541	0.945994	0.472997	−	0.881064i	$-0.343172\pi$
$47$	6.48541	0.945994	0.472997	+	0.881064i	$0.343172\pi$
$48$	−1.64406	−0.237300
$49$	0.589616	0.0842309
$50$	−11.2282	−1.58791
$51$	9.95250	1.39363
$52$	−0.823687	−0.114225
$53$	−7.47244	−1.02642	−0.513209	−	0.858263i	$-0.671544\pi$
$53$	−7.47244	−1.02642	−0.513209	+	0.858263i	$0.671544\pi$
$54$	−5.42057	−0.737646
$55$	5.02620	0.677733
$56$	−2.75493	−0.368142
$57$	−0.574843	−0.0761399
$58$	0.869541	0.114176
$59$	−11.9135	−1.55100	−0.775501	−	0.631346i	$-0.782503\pi$
$59$	−11.9135	−1.55100	−0.775501	+	0.631346i	$0.782503\pi$
$60$	6.62298	0.855023
$61$	−4.85011	−0.620992	−0.310496	−	0.950575i	$-0.600495\pi$
$61$	−4.85011	−0.620992	−0.310496	+	0.950575i	$0.600495\pi$
$62$	1.00000	0.127000
$63$	−0.818378	−0.103106
$64$	1.00000	0.125000
$65$	3.31816	0.411567
$66$	−2.05127	−0.252494
$67$	−3.84084	−0.469233	−0.234616	−	0.972088i	$-0.575383\pi$
$67$	−3.84084	−0.469233	−0.234616	+	0.972088i	$0.575383\pi$
$68$	−6.05361	−0.734108
$69$	3.36176	0.404709
$70$	11.0980	1.32647
$71$	6.93765	0.823347	0.411673	−	0.911331i	$-0.364944\pi$
$71$	6.93765	0.823347	0.411673	+	0.911331i	$0.364944\pi$
$72$	0.297060	0.0350089
$73$	−15.3495	−1.79652	−0.898260	−	0.439465i	$-0.855168\pi$
$73$	−15.3495	−1.79652	−0.898260	+	0.439465i	$0.855168\pi$
$74$	1.12847	0.131182
$75$	−18.4599	−2.13156
$76$	0.349648	0.0401074
$77$	−3.43728	−0.391714
$78$	−1.35419	−0.153332
$79$	−1.71341	−0.192773	−0.0963866	−	0.995344i	$-0.530729\pi$
$79$	−1.71341	−0.192773	−0.0963866	+	0.995344i	$0.530729\pi$
$80$	−4.02843	−0.450392
$81$	−8.02058	−0.891175
$82$	8.19832	0.905353
$83$	11.4256	1.25412	0.627061	−	0.778970i	$-0.284258\pi$
$83$	11.4256	1.25412	0.627061	+	0.778970i	$0.284258\pi$
$84$	−4.52927	−0.494184
$85$	24.3865	2.64509
$86$	4.72683	0.509707
$87$	1.42958	0.153267
$88$	1.24768	0.133004
$89$	4.29886	0.455679	0.227839	−	0.973699i	$-0.426834\pi$
$89$	4.29886	0.455679	0.227839	+	0.973699i	$0.426834\pi$
$90$	−1.19668	−0.126142
$91$	−2.26920	−0.237876
$92$	−2.04479	−0.213184
$93$	1.64406	0.170481
$94$	−6.48541	−0.668919
$95$	−1.40853	−0.144512
$96$	1.64406	0.167796
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−0.589616	−0.0595602
$99$	0.370637	0.0372504
$100$	11.2282	1.12282
$101$	9.17387	0.912834	0.456417	−	0.889766i	$-0.349132\pi$
$101$	9.17387	0.912834	0.456417	+	0.889766i	$0.349132\pi$
$102$	−9.95250	−0.985445
$103$	9.81128	0.966734	0.483367	−	0.875418i	$-0.339414\pi$
$103$	9.81128	0.966734	0.483367	+	0.875418i	$0.339414\pi$
$104$	0.823687	0.0807691
$105$	18.2458	1.78061
$106$	7.47244	0.725788
$107$	−17.5359	−1.69526	−0.847629	−	0.530590i	$-0.821971\pi$
$107$	−17.5359	−1.69526	−0.847629	+	0.530590i	$0.821971\pi$
$108$	5.42057	0.521595
$109$	−11.0380	−1.05725	−0.528624	−	0.848856i	$-0.677292\pi$
$109$	−11.0380	−1.05725	−0.528624	+	0.848856i	$0.677292\pi$
$110$	−5.02620	−0.479230
$111$	1.85528	0.176095
$112$	2.75493	0.260316
$113$	−16.9705	−1.59645	−0.798225	−	0.602360i	$-0.794227\pi$
$113$	−16.9705	−1.59645	−0.798225	+	0.602360i	$0.794227\pi$
$114$	0.574843	0.0538390
$115$	8.23729	0.768131
$116$	−0.869541	−0.0807348
$117$	0.244684	0.0226211
$118$	11.9135	1.09672
$119$	−16.6772	−1.52880
$120$	−6.62298	−0.604593
$121$	−9.44328	−0.858480
$122$	4.85011	0.439108
$123$	13.4786	1.21532
$124$	−1.00000	−0.0898027
$125$	−25.0899	−2.24411
$126$	0.818378	0.0729069
$127$	17.8732	1.58599	0.792997	−	0.609225i	$-0.208520\pi$
$127$	17.8732	1.58599	0.792997	+	0.609225i	$0.208520\pi$
$128$	−1.00000	−0.0883883
$129$	7.77120	0.684216
$130$	−3.31816	−0.291022
$131$	2.87105	0.250845	0.125422	−	0.992103i	$-0.459971\pi$
$131$	2.87105	0.250845	0.125422	+	0.992103i	$0.459971\pi$
$132$	2.05127	0.178540
$133$	0.963255	0.0835248
$134$	3.84084	0.331798
$135$	−21.8364	−1.87938
$136$	6.05361	0.519092
$137$	−19.8345	−1.69458	−0.847288	−	0.531134i	$-0.821766\pi$
$137$	−19.8345	−1.69458	−0.847288	+	0.531134i	$0.821766\pi$
$138$	−3.36176	−0.286172
$139$	−1.10501	−0.0937258	−0.0468629	−	0.998901i	$-0.514922\pi$
$139$	−1.10501	−0.0937258	−0.0468629	+	0.998901i	$0.514922\pi$
$140$	−11.0980	−0.937953
$141$	−10.6624	−0.897937
$142$	−6.93765	−0.582194
$143$	1.02770	0.0859407
$144$	−0.297060	−0.0247550
$145$	3.50288	0.290898
$146$	15.3495	1.27033
$147$	−0.969366	−0.0799519
$148$	−1.12847	−0.0927599
$149$	−9.66663	−0.791922	−0.395961	−	0.918267i	$-0.629588\pi$
$149$	−9.66663	−0.791922	−0.395961	+	0.918267i	$0.629588\pi$
$150$	18.4599	1.50724
$151$	9.60209	0.781407	0.390704	−	0.920516i	$-0.372232\pi$
$151$	9.60209	0.781407	0.390704	+	0.920516i	$0.372232\pi$
$152$	−0.349648	−0.0283602
$153$	1.79828	0.145383
$154$	3.43728	0.276984
$155$	4.02843	0.323571
$156$	1.35419	0.108422
$157$	−15.2346	−1.21586	−0.607928	−	0.793992i	$-0.707999\pi$
$157$	−15.2346	−1.21586	−0.607928	+	0.793992i	$0.707999\pi$
$158$	1.71341	0.136311
$159$	12.2852	0.974276
$160$	4.02843	0.318475
$161$	−5.63325	−0.443962
$162$	8.02058	0.630156
$163$	12.6682	0.992248	0.496124	−	0.868252i	$-0.334756\pi$
$163$	12.6682	0.992248	0.496124	+	0.868252i	$0.334756\pi$
$164$	−8.19832	−0.640181
$165$	−8.26339	−0.643304
$166$	−11.4256	−0.886798
$167$	−6.90987	−0.534702	−0.267351	−	0.963599i	$-0.586148\pi$
$167$	−6.90987	−0.534702	−0.267351	+	0.963599i	$0.586148\pi$
$168$	4.52927	0.349441
$169$	−12.3215	−0.947811
$170$	−24.3865	−1.87036
$171$	−0.103866	−0.00794287
$172$	−4.72683	−0.360417
$173$	−4.29773	−0.326750	−0.163375	−	0.986564i	$-0.552238\pi$
$173$	−4.29773	−0.326750	−0.163375	+	0.986564i	$0.552238\pi$
$174$	−1.42958	−0.108376
$175$	30.9329	2.33831
$176$	−1.24768	−0.0940477
$177$	19.5865	1.47221
$178$	−4.29886	−0.322214
$179$	−14.2515	−1.06521	−0.532604	−	0.846365i	$-0.678786\pi$
$179$	−14.2515	−1.06521	−0.532604	+	0.846365i	$0.678786\pi$
$180$	1.19668	0.0891956
$181$	4.33231	0.322018	0.161009	−	0.986953i	$-0.448525\pi$
$181$	4.33231	0.322018	0.161009	+	0.986953i	$0.448525\pi$
$182$	2.26920	0.168204
$183$	7.97387	0.589446
$184$	2.04479	0.150744
$185$	4.54597	0.334226
$186$	−1.64406	−0.120548
$187$	7.55299	0.552329
$188$	6.48541	0.472997
$189$	14.9333	1.08624
$190$	1.40853	0.102186
$191$	19.5249	1.41277	0.706387	−	0.707825i	$-0.250324\pi$
$191$	19.5249	1.41277	0.706387	+	0.707825i	$0.250324\pi$
$192$	−1.64406	−0.118650
$193$	−24.9606	−1.79670	−0.898350	−	0.439281i	$-0.855233\pi$
$193$	−24.9606	−1.79670	−0.898350	+	0.439281i	$0.855233\pi$
$194$	−1.00000	−0.0717958
$195$	−5.45526	−0.390659
$196$	0.589616	0.0421154
$197$	−21.2086	−1.51105	−0.755523	−	0.655122i	$-0.772617\pi$
$197$	−21.2086	−1.51105	−0.755523	+	0.655122i	$0.772617\pi$
$198$	−0.370637	−0.0263400
$199$	−0.661506	−0.0468929	−0.0234465	−	0.999725i	$-0.507464\pi$
$199$	−0.661506	−0.0468929	−0.0234465	+	0.999725i	$0.507464\pi$
$200$	−11.2282	−0.793955
$201$	6.31457	0.445396
$202$	−9.17387	−0.645471
$203$	−2.39552	−0.168133
$204$	9.95250	0.696815
$205$	33.0263	2.30666
$206$	−9.81128	−0.683584
$207$	0.607426	0.0422190
$208$	−0.823687	−0.0571124
$209$	−0.436251	−0.0301761
$210$	−18.2458	−1.25908
$211$	−16.7518	−1.15324	−0.576621	−	0.817012i	$-0.695629\pi$
$211$	−16.7518	−1.15324	−0.576621	+	0.817012i	$0.695629\pi$
$212$	−7.47244	−0.513209
$213$	−11.4059	−0.781521
$214$	17.5359	1.19873
$215$	19.0417	1.29863
$216$	−5.42057	−0.368823
$217$	−2.75493	−0.187017
$218$	11.0380	0.747588
$219$	25.2355	1.70526
$220$	5.02620	0.338867
$221$	4.98627	0.335413
$222$	−1.85528	−0.124518
$223$	−15.2116	−1.01864	−0.509321	−	0.860576i	$-0.670103\pi$
$223$	−15.2116	−1.01864	−0.509321	+	0.860576i	$0.670103\pi$
$224$	−2.75493	−0.184071
$225$	−3.33545	−0.222364
$226$	16.9705	1.12886
$227$	11.8873	0.788989	0.394495	−	0.918898i	$-0.370920\pi$
$227$	11.8873	0.788989	0.394495	+	0.918898i	$0.370920\pi$
$228$	−0.574843	−0.0380699
$229$	−24.4667	−1.61680	−0.808401	−	0.588631i	$-0.799667\pi$
$229$	−24.4667	−1.61680	−0.808401	+	0.588631i	$0.799667\pi$
$230$	−8.23729	−0.543151
$231$	5.65110	0.371815
$232$	0.869541	0.0570881
$233$	18.7217	1.22650	0.613251	−	0.789888i	$-0.289862\pi$
$233$	18.7217	1.22650	0.613251	+	0.789888i	$0.289862\pi$
$234$	−0.244684	−0.0159955
$235$	−26.1260	−1.70427
$236$	−11.9135	−0.775501
$237$	2.81695	0.182980
$238$	16.6772	1.08102
$239$	−7.62491	−0.493215	−0.246607	−	0.969115i	$-0.579316\pi$
$239$	−7.62491	−0.493215	−0.246607	+	0.969115i	$0.579316\pi$
$240$	6.62298	0.427512
$241$	15.8518	1.02110	0.510552	−	0.859847i	$-0.329441\pi$
$241$	15.8518	1.02110	0.510552	+	0.859847i	$0.329441\pi$
$242$	9.44328	0.607037
$243$	−3.07539	−0.197286
$244$	−4.85011	−0.310496
$245$	−2.37523	−0.151748
$246$	−13.4786	−0.859361
$247$	−0.288001	−0.0183250
$248$	1.00000	0.0635001
$249$	−18.7844	−1.19041
$250$	25.0899	1.58682
$251$	−11.5995	−0.732153	−0.366077	−	0.930585i	$-0.619299\pi$
$251$	−11.5995	−0.732153	−0.366077	+	0.930585i	$0.619299\pi$
$252$	−0.818378	−0.0515530
$253$	2.55125	0.160396
$254$	−17.8732	−1.12147
$255$	−40.0929	−2.51072
$256$	1.00000	0.0625000
$257$	−4.61018	−0.287575	−0.143787	−	0.989609i	$-0.545928\pi$
$257$	−4.61018	−0.287575	−0.143787	+	0.989609i	$0.545928\pi$
$258$	−7.77120	−0.483814
$259$	−3.10886	−0.193175
$260$	3.31816	0.205784
$261$	0.258306	0.0159887
$262$	−2.87105	−0.177374
$263$	−0.286855	−0.0176883	−0.00884413	−	0.999961i	$-0.502815\pi$
$263$	−0.286855	−0.0176883	−0.00884413	+	0.999961i	$0.502815\pi$
$264$	−2.05127	−0.126247
$265$	30.1022	1.84916
$266$	−0.963255	−0.0590609
$267$	−7.06760	−0.432530
$268$	−3.84084	−0.234616
$269$	13.0113	0.793315	0.396658	−	0.917967i	$-0.370170\pi$
$269$	13.0113	0.793315	0.396658	+	0.917967i	$0.370170\pi$
$270$	21.8364	1.32892
$271$	30.7233	1.86631	0.933154	−	0.359476i	$-0.117044\pi$
$271$	30.7233	1.86631	0.933154	+	0.359476i	$0.117044\pi$
$272$	−6.05361	−0.367054
$273$	3.73070	0.225792
$274$	19.8345	1.19825
$275$	−14.0093	−0.844791
$276$	3.36176	0.202354
$277$	24.2319	1.45595	0.727976	−	0.685602i	$-0.240461\pi$
$277$	24.2319	1.45595	0.727976	+	0.685602i	$0.240461\pi$
$278$	1.10501	0.0662742
$279$	0.297060	0.0177845
$280$	11.0980	0.663233
$281$	−5.63388	−0.336089	−0.168045	−	0.985779i	$-0.553745\pi$
$281$	−5.63388	−0.336089	−0.168045	+	0.985779i	$0.553745\pi$
$282$	10.6624	0.634937
$283$	16.4104	0.975497	0.487748	−	0.872984i	$-0.337818\pi$
$283$	16.4104	0.975497	0.487748	+	0.872984i	$0.337818\pi$
$284$	6.93765	0.411673
$285$	2.31571	0.137171
$286$	−1.02770	−0.0607692
$287$	−22.5858	−1.33320
$288$	0.297060	0.0175044
$289$	19.6462	1.15566
$290$	−3.50288	−0.205696
$291$	−1.64406	−0.0963766
$292$	−15.3495	−0.898260
$293$	12.3391	0.720860	0.360430	−	0.932786i	$-0.382630\pi$
$293$	12.3391	0.720860	0.360430	+	0.932786i	$0.382630\pi$
$294$	0.969366	0.0565346
$295$	47.9925	2.79423
$296$	1.12847	0.0655912
$297$	−6.76316	−0.392438
$298$	9.66663	0.559973
$299$	1.68427	0.0974037
$300$	−18.4599	−1.06578
$301$	−13.0221	−0.750579
$302$	−9.60209	−0.552538
$303$	−15.0824	−0.866462
$304$	0.349648	0.0200537
$305$	19.5383	1.11876
$306$	−1.79828	−0.102801
$307$	−1.63932	−0.0935611	−0.0467805	−	0.998905i	$-0.514896\pi$
$307$	−1.63932	−0.0935611	−0.0467805	+	0.998905i	$0.514896\pi$
$308$	−3.43728	−0.195857
$309$	−16.1304	−0.917624
$310$	−4.02843	−0.228799
$311$	31.0094	1.75838	0.879191	−	0.476470i	$-0.158084\pi$
$311$	31.0094	1.75838	0.879191	+	0.476470i	$0.158084\pi$
$312$	−1.35419	−0.0766660
$313$	28.5412	1.61324	0.806621	−	0.591068i	$-0.201294\pi$
$313$	28.5412	1.61324	0.806621	+	0.591068i	$0.201294\pi$
$314$	15.2346	0.859740
$315$	3.29678	0.185752
$316$	−1.71341	−0.0963866
$317$	1.08182	0.0607610	0.0303805	−	0.999538i	$-0.490328\pi$
$317$	1.08182	0.0607610	0.0303805	+	0.999538i	$0.490328\pi$
$318$	−12.2852	−0.688917
$319$	1.08491	0.0607434
$320$	−4.02843	−0.225196
$321$	28.8301	1.60914
$322$	5.63325	0.313929
$323$	−2.11663	−0.117773
$324$	−8.02058	−0.445588
$325$	−9.24853	−0.513016
$326$	−12.6682	−0.701625
$327$	18.1472	1.00354
$328$	8.19832	0.452677
$329$	17.8668	0.985029
$330$	8.26339	0.454885
$331$	34.5515	1.89912	0.949562	−	0.313579i	$-0.101528\pi$
$331$	34.5515	1.89912	0.949562	+	0.313579i	$0.101528\pi$
$332$	11.4256	0.627061
$333$	0.335224	0.0183702
$334$	6.90987	0.378091
$335$	15.4725	0.845354
$336$	−4.52927	−0.247092
$337$	−23.7918	−1.29602	−0.648011	−	0.761631i	$-0.724399\pi$
$337$	−23.7918	−1.29602	−0.648011	+	0.761631i	$0.724399\pi$
$338$	12.3215	0.670203
$339$	27.9005	1.51535
$340$	24.3865	1.32254
$341$	1.24768	0.0675659
$342$	0.103866	0.00561646
$343$	−17.6601	−0.953557
$344$	4.72683	0.254853
$345$	−13.5426	−0.729110
$346$	4.29773	0.231047
$347$	−17.0766	−0.916718	−0.458359	−	0.888767i	$-0.651563\pi$
$347$	−17.0766	−0.916718	−0.458359	+	0.888767i	$0.651563\pi$
$348$	1.42958	0.0766335
$349$	−5.65746	−0.302837	−0.151419	−	0.988470i	$-0.548384\pi$
$349$	−5.65746	−0.302837	−0.151419	+	0.988470i	$0.548384\pi$
$350$	−30.9329	−1.65343
$351$	−4.46485	−0.238316
$352$	1.24768	0.0665018
$353$	31.3927	1.67087	0.835433	−	0.549592i	$-0.185217\pi$
$353$	31.3927	1.67087	0.835433	+	0.549592i	$0.185217\pi$
$354$	−19.5865	−1.04101
$355$	−27.9478	−1.48331
$356$	4.29886	0.227839
$357$	27.4184	1.45114
$358$	14.2515	0.753215
$359$	23.1636	1.22253	0.611263	−	0.791428i	$-0.290662\pi$
$359$	23.1636	1.22253	0.611263	+	0.791428i	$0.290662\pi$
$360$	−1.19668	−0.0630708
$361$	−18.8777	−0.993566
$362$	−4.33231	−0.227701
$363$	15.5253	0.814869
$364$	−2.26920	−0.118938
$365$	61.8342	3.23655
$366$	−7.97387	−0.416801
$367$	15.2462	0.795847	0.397923	−	0.917419i	$-0.369731\pi$
$367$	15.2462	0.795847	0.397923	+	0.917419i	$0.369731\pi$
$368$	−2.04479	−0.106592
$369$	2.43539	0.126782
$370$	−4.54597	−0.236334
$371$	−20.5860	−1.06877
$372$	1.64406	0.0852406
$373$	−27.6931	−1.43390	−0.716948	−	0.697127i	$-0.754461\pi$
$373$	−27.6931	−1.43390	−0.716948	+	0.697127i	$0.754461\pi$
$374$	−7.55299	−0.390556
$375$	41.2494	2.13011
$376$	−6.48541	−0.334459
$377$	0.716229	0.0368877
$378$	−14.9333	−0.768085
$379$	−7.85267	−0.403364	−0.201682	−	0.979451i	$-0.564641\pi$
$379$	−7.85267	−0.403364	−0.201682	+	0.979451i	$0.564641\pi$
$380$	−1.40853	−0.0722562
$381$	−29.3847	−1.50543
$382$	−19.5249	−0.998983
$383$	32.7917	1.67558	0.837788	−	0.545996i	$-0.183849\pi$
$383$	32.7917	1.67558	0.837788	+	0.545996i	$0.183849\pi$
$384$	1.64406	0.0838982
$385$	13.8468	0.705699
$386$	24.9606	1.27046
$387$	1.40415	0.0713770
$388$	1.00000	0.0507673
$389$	−8.39238	−0.425511	−0.212755	−	0.977106i	$-0.568244\pi$
$389$	−8.39238	−0.425511	−0.212755	+	0.977106i	$0.568244\pi$
$390$	5.45526	0.276238
$391$	12.3784	0.626001
$392$	−0.589616	−0.0297801
$393$	−4.72018	−0.238102
$394$	21.2086	1.06847
$395$	6.90233	0.347294
$396$	0.370637	0.0186252
$397$	4.86978	0.244407	0.122204	−	0.992505i	$-0.461004\pi$
$397$	4.86978	0.244407	0.122204	+	0.992505i	$0.461004\pi$
$398$	0.661506	0.0331583
$399$	−1.58365	−0.0792817
$400$	11.2282	0.561411
$401$	30.9597	1.54605	0.773027	−	0.634373i	$-0.218742\pi$
$401$	30.9597	1.54605	0.773027	+	0.634373i	$0.218742\pi$
$402$	−6.31457	−0.314942
$403$	0.823687	0.0410307
$404$	9.17387	0.456417
$405$	32.3103	1.60551
$406$	2.39552	0.118888
$407$	1.40798	0.0697909
$408$	−9.95250	−0.492722
$409$	23.5701	1.16546	0.582732	−	0.812664i	$-0.301984\pi$
$409$	23.5701	1.16546	0.582732	+	0.812664i	$0.301984\pi$
$410$	−33.0263	−1.63105
$411$	32.6092	1.60849
$412$	9.81128	0.483367
$413$	−32.8207	−1.61500
$414$	−0.607426	−0.0298533
$415$	−46.0271	−2.25938
$416$	0.823687	0.0403846
$417$	1.81671	0.0889645
$418$	0.436251	0.0213377
$419$	12.4476	0.608106	0.304053	−	0.952655i	$-0.401660\pi$
$419$	12.4476	0.608106	0.304053	+	0.952655i	$0.401660\pi$
$420$	18.2458	0.890305
$421$	−17.4150	−0.848754	−0.424377	−	0.905486i	$-0.639507\pi$
$421$	−17.4150	−0.848754	−0.424377	+	0.905486i	$0.639507\pi$
$422$	16.7518	0.815465
$423$	−1.92655	−0.0936723
$424$	7.47244	0.362894
$425$	−67.9712	−3.29709
$426$	11.4059	0.552619
$427$	−13.3617	−0.646617
$428$	−17.5359	−0.847629
$429$	−1.68960	−0.0815748
$430$	−19.0417	−0.918271
$431$	12.3800	0.596322	0.298161	−	0.954516i	$-0.403627\pi$
$431$	12.3800	0.596322	0.298161	+	0.954516i	$0.403627\pi$
$432$	5.42057	0.260797
$433$	34.6528	1.66531	0.832655	−	0.553793i	$-0.186820\pi$
$433$	34.6528	1.66531	0.832655	+	0.553793i	$0.186820\pi$
$434$	2.75493	0.132241
$435$	−5.75895	−0.276121
$436$	−11.0380	−0.528624
$437$	−0.714958	−0.0342011
$438$	−25.2355	−1.20580
$439$	0.543294	0.0259300	0.0129650	−	0.999916i	$-0.495873\pi$
$439$	0.543294	0.0259300	0.0129650	+	0.999916i	$0.495873\pi$
$440$	−5.02620	−0.239615
$441$	−0.175151	−0.00834054
$442$	−4.98627	−0.237173
$443$	27.3877	1.30123	0.650614	−	0.759409i	$-0.274512\pi$
$443$	27.3877	1.30123	0.650614	+	0.759409i	$0.274512\pi$
$444$	1.85528	0.0880477
$445$	−17.3177	−0.820936
$446$	15.2116	0.720289
$447$	15.8925	0.751692
$448$	2.75493	0.130158
$449$	28.0397	1.32328	0.661639	−	0.749823i	$-0.269861\pi$
$449$	28.0397	1.32328	0.661639	+	0.749823i	$0.269861\pi$
$450$	3.33545	0.157235
$451$	10.2289	0.481661
$452$	−16.9705	−0.798225
$453$	−15.7864	−0.741712
$454$	−11.8873	−0.557900
$455$	9.14128	0.428550
$456$	0.574843	0.0269195
$457$	22.5285	1.05384	0.526920	−	0.849915i	$-0.323347\pi$
$457$	22.5285	1.05384	0.526920	+	0.849915i	$0.323347\pi$
$458$	24.4667	1.14325
$459$	−32.8140	−1.53163
$460$	8.23729	0.384066
$461$	−17.8075	−0.829376	−0.414688	−	0.909964i	$-0.636109\pi$
$461$	−17.8075	−0.829376	−0.414688	+	0.909964i	$0.636109\pi$
$462$	−5.65110	−0.262913
$463$	−8.40474	−0.390601	−0.195301	−	0.980743i	$-0.562568\pi$
$463$	−8.40474	−0.390601	−0.195301	+	0.980743i	$0.562568\pi$
$464$	−0.869541	−0.0403674
$465$	−6.62298	−0.307133
$466$	−18.7217	−0.867267
$467$	−3.80360	−0.176010	−0.0880048	−	0.996120i	$-0.528049\pi$
$467$	−3.80360	−0.176010	−0.0880048	+	0.996120i	$0.528049\pi$
$468$	0.244684	0.0113105
$469$	−10.5812	−0.488595
$470$	26.1260	1.20510
$471$	25.0467	1.15409
$472$	11.9135	0.548362
$473$	5.89759	0.271171
$474$	−2.81695	−0.129387
$475$	3.92592	0.180134
$476$	−16.6772	−0.764400
$477$	2.21976	0.101636
$478$	7.62491	0.348755
$479$	−0.549861	−0.0251238	−0.0125619	−	0.999921i	$-0.503999\pi$
$479$	−0.549861	−0.0251238	−0.0125619	+	0.999921i	$0.503999\pi$
$480$	−6.62298	−0.302296
$481$	0.929508	0.0423819
$482$	−15.8518	−0.722029
$483$	9.26141	0.421409
$484$	−9.44328	−0.429240
$485$	−4.02843	−0.182921
$486$	3.07539	0.139503
$487$	7.06504	0.320147	0.160074	−	0.987105i	$-0.448827\pi$
$487$	7.06504	0.320147	0.160074	+	0.987105i	$0.448827\pi$
$488$	4.85011	0.219554
$489$	−20.8273	−0.941841
$490$	2.37523	0.107302
$491$	20.7895	0.938219	0.469109	−	0.883140i	$-0.344575\pi$
$491$	20.7895	0.938219	0.469109	+	0.883140i	$0.344575\pi$
$492$	13.4786	0.607660
$493$	5.26386	0.237072
$494$	0.288001	0.0129578
$495$	−1.49308	−0.0671091
$496$	−1.00000	−0.0449013
$497$	19.1127	0.857322
$498$	18.7844	0.841748
$499$	24.1755	1.08225	0.541123	−	0.840943i	$-0.317999\pi$
$499$	24.1755	1.08225	0.541123	+	0.840943i	$0.317999\pi$
$500$	−25.0899	−1.12205
$501$	11.3603	0.507539
$502$	11.5995	0.517710
$503$	−43.3543	−1.93307	−0.966535	−	0.256533i	$-0.917420\pi$
$503$	−43.3543	−1.93307	−0.966535	+	0.256533i	$0.917420\pi$
$504$	0.818378	0.0364535
$505$	−36.9563	−1.64453
$506$	−2.55125	−0.113417
$507$	20.2574	0.899662
$508$	17.8732	0.792997
$509$	4.28939	0.190124	0.0950619	−	0.995471i	$-0.469695\pi$
$509$	4.28939	0.190124	0.0950619	+	0.995471i	$0.469695\pi$
$510$	40.0929	1.77534
$511$	−42.2867	−1.87065
$512$	−1.00000	−0.0441942
$513$	1.89529	0.0836792
$514$	4.61018	0.203346
$515$	−39.5240	−1.74164
$516$	7.77120	0.342108
$517$	−8.09174	−0.355874
$518$	3.10886	0.136595
$519$	7.06573	0.310151
$520$	−3.31816	−0.145511
$521$	−21.8967	−0.959314	−0.479657	−	0.877456i	$-0.659239\pi$
$521$	−21.8967	−0.959314	−0.479657	+	0.877456i	$0.659239\pi$
$522$	−0.258306	−0.0113057
$523$	5.64934	0.247029	0.123514	−	0.992343i	$-0.460584\pi$
$523$	5.64934	0.247029	0.123514	+	0.992343i	$0.460584\pi$
$524$	2.87105	0.125422
$525$	−50.8556	−2.21952
$526$	0.286855	0.0125075
$527$	6.05361	0.263699
$528$	2.05127	0.0892701
$529$	−18.8188	−0.818210
$530$	−30.1022	−1.30755
$531$	3.53902	0.153580
$532$	0.963255	0.0417624
$533$	6.75285	0.292498
$534$	7.06760	0.305845
$535$	70.6420	3.05412
$536$	3.84084	0.165899
$537$	23.4304	1.01109
$538$	−13.0113	−0.560959
$539$	−0.735655	−0.0316869
$540$	−21.8364	−0.939688
$541$	−32.5673	−1.40018	−0.700089	−	0.714056i	$-0.746856\pi$
$541$	−32.5673	−1.40018	−0.700089	+	0.714056i	$0.746856\pi$
$542$	−30.7233	−1.31968
$543$	−7.12258	−0.305659
$544$	6.05361	0.259546
$545$	44.4658	1.90470
$546$	−3.73070	−0.159659
$547$	−40.1222	−1.71550	−0.857751	−	0.514066i	$-0.828139\pi$
$547$	−40.1222	−1.71550	−0.857751	+	0.514066i	$0.828139\pi$
$548$	−19.8345	−0.847288
$549$	1.44077	0.0614907
$550$	14.0093	0.597357
$551$	−0.304033	−0.0129523
$552$	−3.36176	−0.143086
$553$	−4.72031	−0.200728
$554$	−24.2319	−1.02951
$555$	−7.47386	−0.317248
$556$	−1.10501	−0.0468629
$557$	33.0676	1.40112	0.700561	−	0.713593i	$-0.252933\pi$
$557$	33.0676	1.40112	0.700561	+	0.713593i	$0.252933\pi$
$558$	−0.297060	−0.0125756
$559$	3.89342	0.164674
$560$	−11.0980	−0.468977
$561$	−12.4176	−0.524271
$562$	5.63388	0.237651
$563$	−40.5382	−1.70848	−0.854241	−	0.519877i	$-0.825978\pi$
$563$	−40.5382	−1.70848	−0.854241	+	0.519877i	$0.825978\pi$
$564$	−10.6624	−0.448968
$565$	68.3644	2.87611
$566$	−16.4104	−0.689780
$567$	−22.0961	−0.927949
$568$	−6.93765	−0.291097
$569$	8.36441	0.350654	0.175327	−	0.984510i	$-0.443902\pi$
$569$	8.36441	0.350654	0.175327	+	0.984510i	$0.443902\pi$
$570$	−2.31571	−0.0969946
$571$	0.393677	0.0164749	0.00823744	−	0.999966i	$-0.497378\pi$
$571$	0.393677	0.0164749	0.00823744	+	0.999966i	$0.497378\pi$
$572$	1.02770	0.0429703
$573$	−32.1002	−1.34101
$574$	22.5858	0.942712
$575$	−22.9594	−0.957471
$576$	−0.297060	−0.0123775
$577$	19.9709	0.831400	0.415700	−	0.909502i	$-0.363537\pi$
$577$	19.9709	0.831400	0.415700	+	0.909502i	$0.363537\pi$
$578$	−19.6462	−0.817172
$579$	41.0367	1.70543
$580$	3.50288	0.145449
$581$	31.4767	1.30587
$582$	1.64406	0.0681486
$583$	9.32325	0.386129
$584$	15.3495	0.635166
$585$	−0.985693	−0.0407534
$586$	−12.3391	−0.509725
$587$	−17.2022	−0.710012	−0.355006	−	0.934864i	$-0.615521\pi$
$587$	−17.2022	−0.710012	−0.355006	+	0.934864i	$0.615521\pi$
$588$	−0.969366	−0.0399760
$589$	−0.349648	−0.0144070
$590$	−47.9925	−1.97582
$591$	34.8682	1.43429
$592$	−1.12847	−0.0463800
$593$	32.8817	1.35029	0.675146	−	0.737684i	$-0.264081\pi$
$593$	32.8817	1.35029	0.675146	+	0.737684i	$0.264081\pi$
$594$	6.76316	0.277496
$595$	67.1830	2.75423
$596$	−9.66663	−0.395961
$597$	1.08756	0.0445108
$598$	−1.68427	−0.0688748
$599$	−16.0623	−0.656288	−0.328144	−	0.944628i	$-0.606423\pi$
$599$	−16.0623	−0.656288	−0.328144	+	0.944628i	$0.606423\pi$
$600$	18.4599	0.753621
$601$	24.3937	0.995040	0.497520	−	0.867452i	$-0.334244\pi$
$601$	24.3937	0.995040	0.497520	+	0.867452i	$0.334244\pi$
$602$	13.0221	0.530739
$603$	1.14096	0.0464634
$604$	9.60209	0.390704
$605$	38.0416	1.54661
$606$	15.0824	0.612681
$607$	11.6553	0.473072	0.236536	−	0.971623i	$-0.423988\pi$
$607$	11.6553	0.473072	0.236536	+	0.971623i	$0.423988\pi$
$608$	−0.349648	−0.0141801
$609$	3.93838	0.159591
$610$	−19.5383	−0.791082
$611$	−5.34194	−0.216112
$612$	1.79828	0.0726913
$613$	−4.39243	−0.177408	−0.0887042	−	0.996058i	$-0.528273\pi$
$613$	−4.39243	−0.177408	−0.0887042	+	0.996058i	$0.528273\pi$
$614$	1.63932	0.0661577
$615$	−54.2973	−2.18948
$616$	3.43728	0.138492
$617$	−45.8590	−1.84621	−0.923107	−	0.384543i	$-0.874359\pi$
$617$	−45.8590	−1.84621	−0.923107	+	0.384543i	$0.874359\pi$
$618$	16.1304	0.648858
$619$	−9.95578	−0.400157	−0.200078	−	0.979780i	$-0.564120\pi$
$619$	−9.95578	−0.400157	−0.200078	+	0.979780i	$0.564120\pi$
$620$	4.02843	0.161785
$621$	−11.0839	−0.444783
$622$	−31.0094	−1.24336
$623$	11.8431	0.474482
$624$	1.35419	0.0542111
$625$	44.9317	1.79727
$626$	−28.5412	−1.14073
$627$	0.717223	0.0286431
$628$	−15.2346	−0.607928
$629$	6.83133	0.272383
$630$	−3.29678	−0.131347
$631$	15.7852	0.628399	0.314200	−	0.949357i	$-0.398264\pi$
$631$	15.7852	0.628399	0.314200	+	0.949357i	$0.398264\pi$
$632$	1.71341	0.0681557
$633$	27.5410	1.09466
$634$	−1.08182	−0.0429645
$635$	−72.0011	−2.85727
$636$	12.2852	0.487138
$637$	−0.485659	−0.0192425
$638$	−1.08491	−0.0429521
$639$	−2.06090	−0.0815278
$640$	4.02843	0.159238
$641$	32.6702	1.29039	0.645197	−	0.764016i	$-0.276775\pi$
$641$	32.6702	1.29039	0.645197	+	0.764016i	$0.276775\pi$
$642$	−28.8301	−1.13783
$643$	−24.5775	−0.969244	−0.484622	−	0.874724i	$-0.661043\pi$
$643$	−24.5775	−0.969244	−0.484622	+	0.874724i	$0.661043\pi$
$644$	−5.63325	−0.221981
$645$	−31.3057	−1.23266
$646$	2.11663	0.0832778
$647$	−3.63420	−0.142875	−0.0714376	−	0.997445i	$-0.522759\pi$
$647$	−3.63420	−0.142875	−0.0714376	+	0.997445i	$0.522759\pi$
$648$	8.02058	0.315078
$649$	14.8643	0.583473
$650$	9.24853	0.362757
$651$	4.52927	0.177516
$652$	12.6682	0.496124
$653$	25.6392	1.00334	0.501670	−	0.865059i	$-0.332719\pi$
$653$	25.6392	1.00334	0.501670	+	0.865059i	$0.332719\pi$
$654$	−18.1472	−0.709610
$655$	−11.5658	−0.451913
$656$	−8.19832	−0.320091
$657$	4.55971	0.177891
$658$	−17.8668	−0.696521
$659$	22.8664	0.890747	0.445373	−	0.895345i	$-0.353071\pi$
$659$	22.8664	0.890747	0.445373	+	0.895345i	$0.353071\pi$
$660$	−8.26339	−0.321652
$661$	20.6716	0.804032	0.402016	−	0.915633i	$-0.368310\pi$
$661$	20.6716	0.804032	0.402016	+	0.915633i	$0.368310\pi$
$662$	−34.5515	−1.34288
$663$	−8.19774	−0.318374
$664$	−11.4256	−0.443399
$665$	−3.88040	−0.150475
$666$	−0.335224	−0.0129897
$667$	1.77803	0.0688456
$668$	−6.90987	−0.267351
$669$	25.0088	0.966895
$670$	−15.4725	−0.597756
$671$	6.05140	0.233612
$672$	4.52927	0.174720
$673$	−15.8801	−0.612133	−0.306066	−	0.952010i	$-0.599013\pi$
$673$	−15.8801	−0.612133	−0.306066	+	0.952010i	$0.599013\pi$
$674$	23.7918	0.916426
$675$	60.8633	2.34263
$676$	−12.3215	−0.473905
$677$	−2.61715	−0.100585	−0.0502926	−	0.998735i	$-0.516015\pi$
$677$	−2.61715	−0.100585	−0.0502926	+	0.998735i	$0.516015\pi$
$678$	−27.9005	−1.07151
$679$	2.75493	0.105724
$680$	−24.3865	−0.935180
$681$	−19.5435	−0.748908
$682$	−1.24768	−0.0477763
$683$	9.37520	0.358732	0.179366	−	0.983782i	$-0.442595\pi$
$683$	9.37520	0.358732	0.179366	+	0.983782i	$0.442595\pi$
$684$	−0.103866	−0.00397143
$685$	79.9018	3.05289
$686$	17.6601	0.674267
$687$	40.2247	1.53467
$688$	−4.72683	−0.180209
$689$	6.15495	0.234485
$690$	13.5426	0.515559
$691$	25.3950	0.966070	0.483035	−	0.875601i	$-0.339534\pi$
$691$	25.3950	0.966070	0.483035	+	0.875601i	$0.339534\pi$
$692$	−4.29773	−0.163375
$693$	1.02108	0.0387875
$694$	17.0766	0.648218
$695$	4.45146	0.168853
$696$	−1.42958	−0.0541880
$697$	49.6294	1.87985
$698$	5.65746	0.214138
$699$	−30.7797	−1.16419
$700$	30.9329	1.16915
$701$	−45.5429	−1.72013	−0.860065	−	0.510184i	$-0.829577\pi$
$701$	−45.5429	−1.72013	−0.860065	+	0.510184i	$0.829577\pi$
$702$	4.46485	0.168515
$703$	−0.394569	−0.0148814
$704$	−1.24768	−0.0470239
$705$	42.9527	1.61769
$706$	−31.3927	−1.18148
$707$	25.2733	0.950502
$708$	19.5865	0.736105
$709$	−5.64651	−0.212059	−0.106030	−	0.994363i	$-0.533814\pi$
$709$	−5.64651	−0.212059	−0.106030	+	0.994363i	$0.533814\pi$
$710$	27.9478	1.04886
$711$	0.508984	0.0190884
$712$	−4.29886	−0.161107
$713$	2.04479	0.0765780
$714$	−27.4184	−1.02611
$715$	−4.14002	−0.154828
$716$	−14.2515	−0.532604
$717$	12.5358	0.468159
$718$	−23.1636	−0.864456
$719$	39.8465	1.48602	0.743011	−	0.669279i	$-0.233397\pi$
$719$	39.8465	1.48602	0.743011	+	0.669279i	$0.233397\pi$
$720$	1.19668	0.0445978
$721$	27.0294	1.00663
$722$	18.8777	0.702557
$723$	−26.0613	−0.969231
$724$	4.33231	0.161009
$725$	−9.76339	−0.362603
$726$	−15.5253	−0.576200
$727$	43.5290	1.61440	0.807201	−	0.590276i	$-0.200981\pi$
$727$	43.5290	1.61440	0.807201	+	0.590276i	$0.200981\pi$
$728$	2.26920	0.0841020
$729$	29.1179	1.07844
$730$	−61.8342	−2.28859
$731$	28.6143	1.05834
$732$	7.97387	0.294723
$733$	−23.6495	−0.873513	−0.436757	−	0.899580i	$-0.643873\pi$
$733$	−23.6495	−0.873513	−0.436757	+	0.899580i	$0.643873\pi$
$734$	−15.2462	−0.562749
$735$	3.90502	0.144039
$736$	2.04479	0.0753720
$737$	4.79215	0.176521
$738$	−2.43539	−0.0896481
$739$	9.53732	0.350836	0.175418	−	0.984494i	$-0.443872\pi$
$739$	9.53732	0.350836	0.175418	+	0.984494i	$0.443872\pi$
$740$	4.54597	0.167113
$741$	0.473491	0.0173941
$742$	20.5860	0.755737
$743$	−40.1069	−1.47138	−0.735689	−	0.677319i	$-0.763142\pi$
$743$	−40.1069	−1.47138	−0.735689	+	0.677319i	$0.763142\pi$
$744$	−1.64406	−0.0602742
$745$	38.9413	1.42670
$746$	27.6931	1.01392
$747$	−3.39409	−0.124183
$748$	7.55299	0.276165
$749$	−48.3101	−1.76521
$750$	−41.2494	−1.50621
$751$	−12.6042	−0.459935	−0.229968	−	0.973198i	$-0.573862\pi$
$751$	−12.6042	−0.459935	−0.229968	+	0.973198i	$0.573862\pi$
$752$	6.48541	0.236498
$753$	19.0703	0.694959
$754$	−0.716229	−0.0260835
$755$	−38.6813	−1.40776
$756$	14.9333	0.543118
$757$	−0.382911	−0.0139171	−0.00695857	−	0.999976i	$-0.502215\pi$
$757$	−0.382911	−0.0139171	−0.00695857	+	0.999976i	$0.502215\pi$
$758$	7.85267	0.285222
$759$	−4.19442	−0.152248
$760$	1.40853	0.0510928
$761$	−31.0400	−1.12520	−0.562600	−	0.826729i	$-0.690199\pi$
$761$	−31.0400	−1.12520	−0.562600	+	0.826729i	$0.690199\pi$
$762$	29.3847	1.06450
$763$	−30.4089	−1.10088
$764$	19.5249	0.706387
$765$	−7.24425	−0.261917
$766$	−32.7917	−1.18481
$767$	9.81297	0.354326
$768$	−1.64406	−0.0593250
$769$	−34.7341	−1.25254	−0.626271	−	0.779605i	$-0.715420\pi$
$769$	−34.7341	−1.25254	−0.626271	+	0.779605i	$0.715420\pi$
$770$	−13.8468	−0.499005
$771$	7.57942	0.272966
$772$	−24.9606	−0.898350
$773$	−13.2002	−0.474778	−0.237389	−	0.971415i	$-0.576292\pi$
$773$	−13.2002	−0.474778	−0.237389	+	0.971415i	$0.576292\pi$
$774$	−1.40415	−0.0504712
$775$	−11.2282	−0.403329
$776$	−1.00000	−0.0358979
$777$	5.11116	0.183362
$778$	8.39238	0.300881
$779$	−2.86653	−0.102704
$780$	−5.45526	−0.195330
$781$	−8.65599	−0.309736
$782$	−12.3784	−0.442649
$783$	−4.71341	−0.168443
$784$	0.589616	0.0210577
$785$	61.3716	2.19044
$786$	4.72018	0.168363
$787$	−43.9019	−1.56493	−0.782467	−	0.622693i	$-0.786039\pi$
$787$	−43.9019	−1.56493	−0.782467	+	0.622693i	$0.786039\pi$
$788$	−21.2086	−0.755523
$789$	0.471608	0.0167897
$790$	−6.90233	−0.245574
$791$	−46.7524	−1.66233
$792$	−0.370637	−0.0131700
$793$	3.99497	0.141865
$794$	−4.86978	−0.172822
$795$	−49.4898	−1.75522
$796$	−0.661506	−0.0234465
$797$	19.3045	0.683799	0.341899	−	0.939737i	$-0.388930\pi$
$797$	19.3045	0.683799	0.341899	+	0.939737i	$0.388930\pi$
$798$	1.58365	0.0560606
$799$	−39.2601	−1.38892
$800$	−11.2282	−0.396977
$801$	−1.27702	−0.0451213
$802$	−30.9597	−1.09323
$803$	19.1513	0.675834
$804$	6.31457	0.222698
$805$	22.6931	0.799828
$806$	−0.823687	−0.0290131
$807$	−21.3914	−0.753014
$808$	−9.17387	−0.322736
$809$	41.6685	1.46498	0.732492	−	0.680775i	$-0.238357\pi$
$809$	41.6685	1.46498	0.732492	+	0.680775i	$0.238357\pi$
$810$	−32.3103	−1.13527
$811$	8.19795	0.287869	0.143934	−	0.989587i	$-0.454025\pi$
$811$	8.19795	0.287869	0.143934	+	0.989587i	$0.454025\pi$
$812$	−2.39552	−0.0840663
$813$	−50.5110	−1.77150
$814$	−1.40798	−0.0493496
$815$	−51.0328	−1.78760
$816$	9.95250	0.348407
$817$	−1.65273	−0.0578216
$818$	−23.5701	−0.824108
$819$	0.674087	0.0235545
$820$	33.0263	1.15333
$821$	−22.9088	−0.799524	−0.399762	−	0.916619i	$-0.630907\pi$
$821$	−22.9088	−0.799524	−0.399762	+	0.916619i	$0.630907\pi$
$822$	−32.6092	−1.13737
$823$	−16.8701	−0.588054	−0.294027	−	0.955797i	$-0.594996\pi$
$823$	−16.8701	−0.588054	−0.294027	+	0.955797i	$0.594996\pi$
$824$	−9.81128	−0.341792
$825$	23.0321	0.801875
$826$	32.8207	1.14198
$827$	−35.9845	−1.25131	−0.625653	−	0.780102i	$-0.715167\pi$
$827$	−35.9845	−1.25131	−0.625653	+	0.780102i	$0.715167\pi$
$828$	0.607426	0.0211095
$829$	17.7568	0.616720	0.308360	−	0.951270i	$-0.400220\pi$
$829$	17.7568	0.616720	0.308360	+	0.951270i	$0.400220\pi$
$830$	46.0271	1.59763
$831$	−39.8387	−1.38199
$832$	−0.823687	−0.0285562
$833$	−3.56930	−0.123669
$834$	−1.81671	−0.0629074
$835$	27.8359	0.963301
$836$	−0.436251	−0.0150880
$837$	−5.42057	−0.187362
$838$	−12.4476	−0.429996
$839$	1.71621	0.0592502	0.0296251	−	0.999561i	$-0.490569\pi$
$839$	1.71621	0.0592502	0.0296251	+	0.999561i	$0.490569\pi$
$840$	−18.2458	−0.629541
$841$	−28.2439	−0.973928
$842$	17.4150	0.600159
$843$	9.26245	0.319016
$844$	−16.7518	−0.576621
$845$	49.6364	1.70754
$846$	1.92655	0.0662363
$847$	−26.0155	−0.893905
$848$	−7.47244	−0.256605
$849$	−26.9797	−0.925941
$850$	67.9712	2.33139
$851$	2.30749	0.0790998
$852$	−11.4059	−0.390760
$853$	−23.7254	−0.812343	−0.406171	−	0.913797i	$-0.633136\pi$
$853$	−23.7254	−0.812343	−0.406171	+	0.913797i	$0.633136\pi$
$854$	13.3617	0.457227
$855$	0.418418	0.0143096
$856$	17.5359	0.599364
$857$	22.5727	0.771069	0.385535	−	0.922693i	$-0.374017\pi$
$857$	22.5727	0.771069	0.385535	+	0.922693i	$0.374017\pi$
$858$	1.68960	0.0576821
$859$	−7.45020	−0.254197	−0.127099	−	0.991890i	$-0.540566\pi$
$859$	−7.45020	−0.254197	−0.127099	+	0.991890i	$0.540566\pi$
$860$	19.0417	0.649316
$861$	37.1324	1.26547
$862$	−12.3800	−0.421663
$863$	−16.7202	−0.569162	−0.284581	−	0.958652i	$-0.591855\pi$
$863$	−16.7202	−0.569162	−0.284581	+	0.958652i	$0.591855\pi$
$864$	−5.42057	−0.184412
$865$	17.3131	0.588662
$866$	−34.6528	−1.17755
$867$	−32.2995	−1.09695
$868$	−2.75493	−0.0935083
$869$	2.13779	0.0725196
$870$	5.75895	0.195247
$871$	3.16364	0.107196
$872$	11.0380	0.373794
$873$	−0.297060	−0.0100540
$874$	0.714958	0.0241838
$875$	−69.1208	−2.33671
$876$	25.2355	0.852628
$877$	−4.20631	−0.142037	−0.0710185	−	0.997475i	$-0.522625\pi$
$877$	−4.20631	−0.142037	−0.0710185	+	0.997475i	$0.522625\pi$
$878$	−0.543294	−0.0183353
$879$	−20.2863	−0.684240
$880$	5.02620	0.169433
$881$	−27.7485	−0.934870	−0.467435	−	0.884028i	$-0.654822\pi$
$881$	−27.7485	−0.934870	−0.467435	+	0.884028i	$0.654822\pi$
$882$	0.175151	0.00589765
$883$	−26.0335	−0.876097	−0.438048	−	0.898951i	$-0.644330\pi$
$883$	−26.0335	−0.876097	−0.438048	+	0.898951i	$0.644330\pi$
$884$	4.98627	0.167707
$885$	−78.9027	−2.65229
$886$	−27.3877	−0.920107
$887$	−20.6836	−0.694488	−0.347244	−	0.937775i	$-0.612882\pi$
$887$	−20.6836	−0.694488	−0.347244	+	0.937775i	$0.612882\pi$
$888$	−1.85528	−0.0622591
$889$	49.2395	1.65144
$890$	17.3177	0.580489
$891$	10.0071	0.335252
$892$	−15.2116	−0.509321
$893$	2.26761	0.0758827
$894$	−15.8925	−0.531526
$895$	57.4111	1.91904
$896$	−2.75493	−0.0920356
$897$	−2.76904	−0.0924555
$898$	−28.0397	−0.935699
$899$	0.869541	0.0290008
$900$	−3.33545	−0.111182
$901$	45.2352	1.50700
$902$	−10.2289	−0.340586
$903$	21.4091	0.712449
$904$	16.9705	0.564430
$905$	−17.4524	−0.580137
$906$	15.7864	0.524469
$907$	41.6359	1.38250	0.691248	−	0.722617i	$-0.257061\pi$
$907$	41.6359	1.38250	0.691248	+	0.722617i	$0.257061\pi$
$908$	11.8873	0.394495
$909$	−2.72519	−0.0903889
$910$	−9.14128	−0.303031
$911$	−2.12991	−0.0705672	−0.0352836	−	0.999377i	$-0.511233\pi$
$911$	−2.12991	−0.0705672	−0.0352836	+	0.999377i	$0.511233\pi$
$912$	−0.574843	−0.0190350
$913$	−14.2555	−0.471789
$914$	−22.5285	−0.745178
$915$	−32.1222	−1.06193
$916$	−24.4667	−0.808401
$917$	7.90952	0.261195
$918$	32.8140	1.08302
$919$	35.4426	1.16914	0.584572	−	0.811342i	$-0.301263\pi$
$919$	35.4426	1.16914	0.584572	+	0.811342i	$0.301263\pi$
$920$	−8.23729	−0.271575
$921$	2.69515	0.0888082
$922$	17.8075	0.586458
$923$	−5.71444	−0.188093
$924$	5.65110	0.185907
$925$	−12.6707	−0.416611
$926$	8.40474	0.276197
$927$	−2.91454	−0.0957260
$928$	0.869541	0.0285441
$929$	−23.9439	−0.785575	−0.392788	−	0.919629i	$-0.628489\pi$
$929$	−23.9439	−0.785575	−0.392788	+	0.919629i	$0.628489\pi$
$930$	6.62298	0.217176
$931$	0.206158	0.00675656
$932$	18.7217	0.613251
$933$	−50.9814	−1.66906
$934$	3.80360	0.124458
$935$	−30.4267	−0.995058
$936$	−0.244684	−0.00799776
$937$	−39.0695	−1.27635	−0.638173	−	0.769893i	$-0.720310\pi$
$937$	−39.0695	−1.27635	−0.638173	+	0.769893i	$0.720310\pi$
$938$	10.5812	0.345489
$939$	−46.9235	−1.53129
$940$	−26.1260	−0.852135
$941$	44.0586	1.43627	0.718135	−	0.695904i	$-0.244996\pi$
$941$	44.0586	1.43627	0.718135	+	0.695904i	$0.244996\pi$
$942$	−25.0467	−0.816065
$943$	16.7639	0.545906
$944$	−11.9135	−0.387750
$945$	−60.1576	−1.95693
$946$	−5.89759	−0.191747
$947$	−40.9011	−1.32911	−0.664554	−	0.747240i	$-0.731378\pi$
$947$	−40.9011	−1.32911	−0.664554	+	0.747240i	$0.731378\pi$
$948$	2.81695	0.0914902
$949$	12.6432	0.410414
$950$	−3.92592	−0.127374
$951$	−1.77858	−0.0576743
$952$	16.6772	0.540512
$953$	39.0588	1.26524	0.632619	−	0.774464i	$-0.281980\pi$
$953$	39.0588	1.26524	0.632619	+	0.774464i	$0.281980\pi$
$954$	−2.21976	−0.0718675
$955$	−78.6548	−2.54521
$956$	−7.62491	−0.246607
$957$	−1.78366	−0.0576576
$958$	0.549861	0.0177652
$959$	−54.6426	−1.76450
$960$	6.62298	0.213756
$961$	1.00000	0.0322581
$962$	−0.929508	−0.0299685
$963$	5.20921	0.167864
$964$	15.8518	0.510552
$965$	100.552	3.23687
$966$	−9.26141	−0.297981
$967$	7.09134	0.228042	0.114021	−	0.993478i	$-0.463627\pi$
$967$	7.09134	0.228042	0.114021	+	0.993478i	$0.463627\pi$
$968$	9.44328	0.303519
$969$	3.47988	0.111790
$970$	4.02843	0.129345
$971$	12.3392	0.395985	0.197992	−	0.980204i	$-0.436558\pi$
$971$	12.3392	0.395985	0.197992	+	0.980204i	$0.436558\pi$
$972$	−3.07539	−0.0986432
$973$	−3.04422	−0.0975934
$974$	−7.06504	−0.226378
$975$	15.2052	0.486955
$976$	−4.85011	−0.155248
$977$	5.51922	0.176575	0.0882877	−	0.996095i	$-0.471861\pi$
$977$	5.51922	0.176575	0.0882877	+	0.996095i	$0.471861\pi$
$978$	20.8273	0.665982
$979$	−5.36363	−0.171422
$980$	−2.37523	−0.0758738
$981$	3.27895	0.104689
$982$	−20.7895	−0.663421
$983$	−23.4845	−0.749038	−0.374519	−	0.927219i	$-0.622192\pi$
$983$	−23.4845	−0.749038	−0.374519	+	0.927219i	$0.622192\pi$
$984$	−13.4786	−0.429681
$985$	85.4371	2.72225
$986$	−5.26386	−0.167635
$987$	−29.3741	−0.934989
$988$	−0.288001	−0.00916252
$989$	9.66537	0.307341
$990$	1.49308	0.0474533
$991$	9.12090	0.289735	0.144867	−	0.989451i	$-0.453724\pi$
$991$	9.12090	0.289735	0.144867	+	0.989451i	$0.453724\pi$
$992$	1.00000	0.0317500
$993$	−56.8049	−1.80265
$994$	−19.1127	−0.606218
$995$	2.66483	0.0844807
$996$	−18.7844	−0.595206
$997$	12.8584	0.407230	0.203615	−	0.979051i	$-0.434731\pi$
$997$	12.8584	0.407230	0.203615	+	0.979051i	$0.434731\pi$
$998$	−24.1755	−0.765264
$999$	−6.11697	−0.193532

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.9	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.64406 q^{3} +1.00000 q^{4} -4.02843 q^{5} +1.64406 q^{6} +2.75493 q^{7} -1.00000 q^{8} -0.297060 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.64406 q^{3} +1.00000 q^{4} -4.02843 q^{5} +1.64406 q^{6} +2.75493 q^{7} -1.00000 q^{8} -0.297060 q^{9} +4.02843 q^{10} -1.24768 q^{11} -1.64406 q^{12} -0.823687 q^{13} -2.75493 q^{14} +6.62298 q^{15} +1.00000 q^{16} -6.05361 q^{17} +0.297060 q^{18} +0.349648 q^{19} -4.02843 q^{20} -4.52927 q^{21} +1.24768 q^{22} -2.04479 q^{23} +1.64406 q^{24} +11.2282 q^{25} +0.823687 q^{26} +5.42057 q^{27} +2.75493 q^{28} -0.869541 q^{29} -6.62298 q^{30} -1.00000 q^{31} -1.00000 q^{32} +2.05127 q^{33} +6.05361 q^{34} -11.0980 q^{35} -0.297060 q^{36} -1.12847 q^{37} -0.349648 q^{38} +1.35419 q^{39} +4.02843 q^{40} -8.19832 q^{41} +4.52927 q^{42} -4.72683 q^{43} -1.24768 q^{44} +1.19668 q^{45} +2.04479 q^{46} +6.48541 q^{47} -1.64406 q^{48} +0.589616 q^{49} -11.2282 q^{50} +9.95250 q^{51} -0.823687 q^{52} -7.47244 q^{53} -5.42057 q^{54} +5.02620 q^{55} -2.75493 q^{56} -0.574843 q^{57} +0.869541 q^{58} -11.9135 q^{59} +6.62298 q^{60} -4.85011 q^{61} +1.00000 q^{62} -0.818378 q^{63} +1.00000 q^{64} +3.31816 q^{65} -2.05127 q^{66} -3.84084 q^{67} -6.05361 q^{68} +3.36176 q^{69} +11.0980 q^{70} +6.93765 q^{71} +0.297060 q^{72} -15.3495 q^{73} +1.12847 q^{74} -18.4599 q^{75} +0.349648 q^{76} -3.43728 q^{77} -1.35419 q^{78} -1.71341 q^{79} -4.02843 q^{80} -8.02058 q^{81} +8.19832 q^{82} +11.4256 q^{83} -4.52927 q^{84} +24.3865 q^{85} +4.72683 q^{86} +1.42958 q^{87} +1.24768 q^{88} +4.29886 q^{89} -1.19668 q^{90} -2.26920 q^{91} -2.04479 q^{92} +1.64406 q^{93} -6.48541 q^{94} -1.40853 q^{95} +1.64406 q^{96} +1.00000 q^{97} -0.589616 q^{98} +0.370637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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