LMFDB - Embedded newform 6014.2.a.l.1.8

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:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.25991 q^{3} +1.00000 q^{4} +3.07445 q^{5} +2.25991 q^{6} -1.73147 q^{7} -1.00000 q^{8} +2.10720 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.25991 q^{3} +1.00000 q^{4} +3.07445 q^{5} +2.25991 q^{6} -1.73147 q^{7} -1.00000 q^{8} +2.10720 q^{9} -3.07445 q^{10} -3.48187 q^{11} -2.25991 q^{12} +4.87641 q^{13} +1.73147 q^{14} -6.94799 q^{15} +1.00000 q^{16} +8.01399 q^{17} -2.10720 q^{18} -6.18727 q^{19} +3.07445 q^{20} +3.91296 q^{21} +3.48187 q^{22} +8.17418 q^{23} +2.25991 q^{24} +4.45225 q^{25} -4.87641 q^{26} +2.01765 q^{27} -1.73147 q^{28} +10.0276 q^{29} +6.94799 q^{30} +1.00000 q^{31} -1.00000 q^{32} +7.86872 q^{33} -8.01399 q^{34} -5.32332 q^{35} +2.10720 q^{36} -11.0913 q^{37} +6.18727 q^{38} -11.0203 q^{39} -3.07445 q^{40} -2.09358 q^{41} -3.91296 q^{42} +0.403640 q^{43} -3.48187 q^{44} +6.47848 q^{45} -8.17418 q^{46} +10.8185 q^{47} -2.25991 q^{48} -4.00202 q^{49} -4.45225 q^{50} -18.1109 q^{51} +4.87641 q^{52} -7.60002 q^{53} -2.01765 q^{54} -10.7048 q^{55} +1.73147 q^{56} +13.9827 q^{57} -10.0276 q^{58} +4.99435 q^{59} -6.94799 q^{60} -3.38807 q^{61} -1.00000 q^{62} -3.64855 q^{63} +1.00000 q^{64} +14.9923 q^{65} -7.86872 q^{66} -8.37261 q^{67} +8.01399 q^{68} -18.4729 q^{69} +5.32332 q^{70} +7.27302 q^{71} -2.10720 q^{72} +16.0937 q^{73} +11.0913 q^{74} -10.0617 q^{75} -6.18727 q^{76} +6.02875 q^{77} +11.0203 q^{78} -3.36263 q^{79} +3.07445 q^{80} -10.8813 q^{81} +2.09358 q^{82} -1.55538 q^{83} +3.91296 q^{84} +24.6386 q^{85} -0.403640 q^{86} -22.6616 q^{87} +3.48187 q^{88} +4.59023 q^{89} -6.47848 q^{90} -8.44336 q^{91} +8.17418 q^{92} -2.25991 q^{93} -10.8185 q^{94} -19.0224 q^{95} +2.25991 q^{96} -1.00000 q^{97} +4.00202 q^{98} -7.33699 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) $ 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * 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
$3$	−2.25991	−1.30476	−0.652380	−	0.757892i	$-0.726229\pi$
$3$	−2.25991	−1.30476	−0.652380	+	0.757892i	$0.726229\pi$
$4$	1.00000	0.500000
$5$	3.07445	1.37494	0.687468	−	0.726214i	$-0.258722\pi$
$5$	3.07445	1.37494	0.687468	+	0.726214i	$0.258722\pi$
$6$	2.25991	0.922605
$7$	−1.73147	−0.654434	−0.327217	−	0.944949i	$-0.606111\pi$
$7$	−1.73147	−0.654434	−0.327217	+	0.944949i	$0.606111\pi$
$8$	−1.00000	−0.353553
$9$	2.10720	0.702399
$10$	−3.07445	−0.972227
$11$	−3.48187	−1.04982	−0.524912	−	0.851157i	$-0.675902\pi$
$11$	−3.48187	−1.04982	−0.524912	+	0.851157i	$0.675902\pi$
$12$	−2.25991	−0.652380
$13$	4.87641	1.35247	0.676237	−	0.736684i	$-0.263610\pi$
$13$	4.87641	1.35247	0.676237	+	0.736684i	$0.263610\pi$
$14$	1.73147	0.462754
$15$	−6.94799	−1.79396
$16$	1.00000	0.250000
$17$	8.01399	1.94368	0.971839	−	0.235648i	$-0.0757211\pi$
$17$	8.01399	1.94368	0.971839	+	0.235648i	$0.0757211\pi$
$18$	−2.10720	−0.496671
$19$	−6.18727	−1.41946	−0.709728	−	0.704476i	$-0.751182\pi$
$19$	−6.18727	−1.41946	−0.709728	+	0.704476i	$0.751182\pi$
$20$	3.07445	0.687468
$21$	3.91296	0.853879
$22$	3.48187	0.742337
$23$	8.17418	1.70444	0.852218	−	0.523188i	$-0.175257\pi$
$23$	8.17418	1.70444	0.852218	+	0.523188i	$0.175257\pi$
$24$	2.25991	0.461302
$25$	4.45225	0.890450
$26$	−4.87641	−0.956344
$27$	2.01765	0.388298
$28$	−1.73147	−0.327217
$29$	10.0276	1.86208	0.931042	−	0.364911i	$-0.118901\pi$
$29$	10.0276	1.86208	0.931042	+	0.364911i	$0.118901\pi$
$30$	6.94799	1.26852
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	7.86872	1.36977
$34$	−8.01399	−1.37439
$35$	−5.32332	−0.899805
$36$	2.10720	0.351200
$37$	−11.0913	−1.82341	−0.911703	−	0.410850i	$-0.865232\pi$
$37$	−11.0913	−1.82341	−0.911703	+	0.410850i	$0.865232\pi$
$38$	6.18727	1.00371
$39$	−11.0203	−1.76465
$40$	−3.07445	−0.486113
$41$	−2.09358	−0.326962	−0.163481	−	0.986546i	$-0.552272\pi$
$41$	−2.09358	−0.326962	−0.163481	+	0.986546i	$0.552272\pi$
$42$	−3.91296	−0.603784
$43$	0.403640	0.0615545	0.0307772	−	0.999526i	$-0.490202\pi$
$43$	0.403640	0.0615545	0.0307772	+	0.999526i	$0.490202\pi$
$44$	−3.48187	−0.524912
$45$	6.47848	0.965754
$46$	−8.17418	−1.20522
$47$	10.8185	1.57805	0.789024	−	0.614363i	$-0.210587\pi$
$47$	10.8185	1.57805	0.789024	+	0.614363i	$0.210587\pi$
$48$	−2.25991	−0.326190
$49$	−4.00202	−0.571717
$50$	−4.45225	−0.629643
$51$	−18.1109	−2.53603
$52$	4.87641	0.676237
$53$	−7.60002	−1.04394	−0.521971	−	0.852963i	$-0.674803\pi$
$53$	−7.60002	−1.04394	−0.521971	+	0.852963i	$0.674803\pi$
$54$	−2.01765	−0.274568
$55$	−10.7048	−1.44344
$56$	1.73147	0.231377
$57$	13.9827	1.85205
$58$	−10.0276	−1.31669
$59$	4.99435	0.650209	0.325105	−	0.945678i	$-0.394600\pi$
$59$	4.99435	0.650209	0.325105	+	0.945678i	$0.394600\pi$
$60$	−6.94799	−0.896981
$61$	−3.38807	−0.433798	−0.216899	−	0.976194i	$-0.569594\pi$
$61$	−3.38807	−0.433798	−0.216899	+	0.976194i	$0.569594\pi$
$62$	−1.00000	−0.127000
$63$	−3.64855	−0.459674
$64$	1.00000	0.125000
$65$	14.9923	1.85957
$66$	−7.86872	−0.968572
$67$	−8.37261	−1.02288	−0.511439	−	0.859320i	$-0.670887\pi$
$67$	−8.37261	−1.02288	−0.511439	+	0.859320i	$0.670887\pi$
$68$	8.01399	0.971839
$69$	−18.4729	−2.22388
$70$	5.32332	0.636258
$71$	7.27302	0.863149	0.431574	−	0.902077i	$-0.357958\pi$
$71$	7.27302	0.863149	0.431574	+	0.902077i	$0.357958\pi$
$72$	−2.10720	−0.248336
$73$	16.0937	1.88362	0.941812	−	0.336141i	$-0.109122\pi$
$73$	16.0937	1.88362	0.941812	+	0.336141i	$0.109122\pi$
$74$	11.0913	1.28934
$75$	−10.0617	−1.16182
$76$	−6.18727	−0.709728
$77$	6.02875	0.687040
$78$	11.0203	1.24780
$79$	−3.36263	−0.378326	−0.189163	−	0.981946i	$-0.560577\pi$
$79$	−3.36263	−0.378326	−0.189163	+	0.981946i	$0.560577\pi$
$80$	3.07445	0.343734
$81$	−10.8813	−1.20903
$82$	2.09358	0.231197
$83$	−1.55538	−0.170725	−0.0853627	−	0.996350i	$-0.527205\pi$
$83$	−1.55538	−0.170725	−0.0853627	+	0.996350i	$0.527205\pi$
$84$	3.91296	0.426939
$85$	24.6386	2.67243
$86$	−0.403640	−0.0435256
$87$	−22.6616	−2.42957
$88$	3.48187	0.371169
$89$	4.59023	0.486564	0.243282	−	0.969956i	$-0.421776\pi$
$89$	4.59023	0.486564	0.243282	+	0.969956i	$0.421776\pi$
$90$	−6.47848	−0.682891
$91$	−8.44336	−0.885104
$92$	8.17418	0.852218
$93$	−2.25991	−0.234342
$94$	−10.8185	−1.11585
$95$	−19.0224	−1.95166
$96$	2.25991	0.230651
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	4.00202	0.404265
$99$	−7.33699	−0.737395
$100$	4.45225	0.445225
$101$	−2.64320	−0.263008	−0.131504	−	0.991316i	$-0.541981\pi$
$101$	−2.64320	−0.263008	−0.131504	+	0.991316i	$0.541981\pi$
$102$	18.1109	1.79325
$103$	−11.1786	−1.10146	−0.550731	−	0.834683i	$-0.685651\pi$
$103$	−11.1786	−1.10146	−0.550731	+	0.834683i	$0.685651\pi$
$104$	−4.87641	−0.478172
$105$	12.0302	1.17403
$106$	7.60002	0.738179
$107$	8.72054	0.843047	0.421523	−	0.906818i	$-0.361496\pi$
$107$	8.72054	0.843047	0.421523	+	0.906818i	$0.361496\pi$
$108$	2.01765	0.194149
$109$	5.28900	0.506594	0.253297	−	0.967389i	$-0.418485\pi$
$109$	5.28900	0.506594	0.253297	+	0.967389i	$0.418485\pi$
$110$	10.7048	1.02067
$111$	25.0654	2.37911
$112$	−1.73147	−0.163608
$113$	5.56140	0.523172	0.261586	−	0.965180i	$-0.415754\pi$
$113$	5.56140	0.523172	0.261586	+	0.965180i	$0.415754\pi$
$114$	−13.9827	−1.30960
$115$	25.1311	2.34349
$116$	10.0276	0.931042
$117$	10.2756	0.949977
$118$	−4.99435	−0.459767
$119$	−13.8760	−1.27201
$120$	6.94799	0.634261
$121$	1.12342	0.102129
$122$	3.38807	0.306741
$123$	4.73130	0.426607
$124$	1.00000	0.0898027
$125$	−1.68403	−0.150624
$126$	3.64855	0.325038
$127$	6.16786	0.547309	0.273655	−	0.961828i	$-0.411767\pi$
$127$	6.16786	0.547309	0.273655	+	0.961828i	$0.411767\pi$
$128$	−1.00000	−0.0883883
$129$	−0.912190	−0.0803138
$130$	−14.9923	−1.31491
$131$	−1.55102	−0.135513	−0.0677567	−	0.997702i	$-0.521584\pi$
$131$	−1.55102	−0.135513	−0.0677567	+	0.997702i	$0.521584\pi$
$132$	7.86872	0.684884
$133$	10.7131	0.928940
$134$	8.37261	0.723284
$135$	6.20318	0.533885
$136$	−8.01399	−0.687194
$137$	16.5680	1.41550	0.707751	−	0.706462i	$-0.249710\pi$
$137$	16.5680	1.41550	0.707751	+	0.706462i	$0.249710\pi$
$138$	18.4729	1.57252
$139$	−3.89870	−0.330683	−0.165342	−	0.986236i	$-0.552873\pi$
$139$	−3.89870	−0.330683	−0.165342	+	0.986236i	$0.552873\pi$
$140$	−5.32332	−0.449902
$141$	−24.4490	−2.05897
$142$	−7.27302	−0.610338
$143$	−16.9790	−1.41986
$144$	2.10720	0.175600
$145$	30.8295	2.56025
$146$	−16.0937	−1.33192
$147$	9.04420	0.745953
$148$	−11.0913	−0.911703
$149$	5.93094	0.485881	0.242941	−	0.970041i	$-0.421888\pi$
$149$	5.93094	0.485881	0.242941	+	0.970041i	$0.421888\pi$
$150$	10.0617	0.821534
$151$	1.34253	0.109253	0.0546266	−	0.998507i	$-0.482603\pi$
$151$	1.34253	0.109253	0.0546266	+	0.998507i	$0.482603\pi$
$152$	6.18727	0.501854
$153$	16.8871	1.36524
$154$	−6.02875	−0.485810
$155$	3.07445	0.246946
$156$	−11.0203	−0.882327
$157$	−10.7424	−0.857338	−0.428669	−	0.903462i	$-0.641017\pi$
$157$	−10.7424	−0.857338	−0.428669	+	0.903462i	$0.641017\pi$
$158$	3.36263	0.267517
$159$	17.1754	1.36209
$160$	−3.07445	−0.243057
$161$	−14.1533	−1.11544
$162$	10.8813	0.854917
$163$	3.60879	0.282663	0.141331	−	0.989962i	$-0.454862\pi$
$163$	3.60879	0.282663	0.141331	+	0.989962i	$0.454862\pi$
$164$	−2.09358	−0.163481
$165$	24.1920	1.88334
$166$	1.55538	0.120721
$167$	8.02327	0.620859	0.310430	−	0.950596i	$-0.399527\pi$
$167$	8.02327	0.620859	0.310430	+	0.950596i	$0.399527\pi$
$168$	−3.91296	−0.301892
$169$	10.7794	0.829186
$170$	−24.6386	−1.88970
$171$	−13.0378	−0.997025
$172$	0.403640	0.0307772
$173$	−9.37935	−0.713098	−0.356549	−	0.934277i	$-0.616047\pi$
$173$	−9.37935	−0.713098	−0.356549	+	0.934277i	$0.616047\pi$
$174$	22.6616	1.71797
$175$	−7.70893	−0.582741
$176$	−3.48187	−0.262456
$177$	−11.2868	−0.848367
$178$	−4.59023	−0.344053
$179$	−21.5266	−1.60897	−0.804486	−	0.593971i	$-0.797559\pi$
$179$	−21.5266	−1.60897	−0.804486	+	0.593971i	$0.797559\pi$
$180$	6.47848	0.482877
$181$	−19.0791	−1.41814	−0.709070	−	0.705138i	$-0.750885\pi$
$181$	−19.0791	−1.41814	−0.709070	+	0.705138i	$0.750885\pi$
$182$	8.44336	0.625863
$183$	7.65673	0.566002
$184$	−8.17418	−0.602609
$185$	−34.0998	−2.50707
$186$	2.25991	0.165705
$187$	−27.9037	−2.04052
$188$	10.8185	0.789024
$189$	−3.49350	−0.254115
$190$	19.0224	1.38003
$191$	−10.7148	−0.775296	−0.387648	−	0.921807i	$-0.626712\pi$
$191$	−10.7148	−0.775296	−0.387648	+	0.921807i	$0.626712\pi$
$192$	−2.25991	−0.163095
$193$	−0.396397	−0.0285333	−0.0142667	−	0.999898i	$-0.504541\pi$
$193$	−0.396397	−0.0285333	−0.0142667	+	0.999898i	$0.504541\pi$
$194$	1.00000	0.0717958
$195$	−33.8813	−2.42629
$196$	−4.00202	−0.285858
$197$	−21.2569	−1.51449	−0.757246	−	0.653129i	$-0.773456\pi$
$197$	−21.2569	−1.51449	−0.757246	+	0.653129i	$0.773456\pi$
$198$	7.33699	0.521417
$199$	7.73991	0.548667	0.274334	−	0.961635i	$-0.411543\pi$
$199$	7.73991	0.548667	0.274334	+	0.961635i	$0.411543\pi$
$200$	−4.45225	−0.314822
$201$	18.9214	1.33461
$202$	2.64320	0.185975
$203$	−17.3625	−1.21861
$204$	−18.1109	−1.26802
$205$	−6.43660	−0.449552
$206$	11.1786	0.778851
$207$	17.2246	1.19719
$208$	4.87641	0.338118
$209$	21.5433	1.49018
$210$	−12.0302	−0.830164
$211$	15.1125	1.04039	0.520193	−	0.854049i	$-0.325860\pi$
$211$	15.1125	1.04039	0.520193	+	0.854049i	$0.325860\pi$
$212$	−7.60002	−0.521971
$213$	−16.4364	−1.12620
$214$	−8.72054	−0.596124
$215$	1.24097	0.0846335
$216$	−2.01765	−0.137284
$217$	−1.73147	−0.117540
$218$	−5.28900	−0.358216
$219$	−36.3703	−2.45768
$220$	−10.7048	−0.721720
$221$	39.0795	2.62877
$222$	−25.0654	−1.68228
$223$	14.3405	0.960314	0.480157	−	0.877183i	$-0.340580\pi$
$223$	14.3405	0.960314	0.480157	+	0.877183i	$0.340580\pi$
$224$	1.73147	0.115689
$225$	9.38177	0.625451
$226$	−5.56140	−0.369939
$227$	−27.0464	−1.79513	−0.897567	−	0.440879i	$-0.854667\pi$
$227$	−27.0464	−1.79513	−0.897567	+	0.440879i	$0.854667\pi$
$228$	13.9827	0.926025
$229$	25.5356	1.68744	0.843720	−	0.536784i	$-0.180361\pi$
$229$	25.5356	1.68744	0.843720	+	0.536784i	$0.180361\pi$
$230$	−25.1311	−1.65710
$231$	−13.6244	−0.896422
$232$	−10.0276	−0.658346
$233$	14.0329	0.919324	0.459662	−	0.888094i	$-0.347971\pi$
$233$	14.0329	0.919324	0.459662	+	0.888094i	$0.347971\pi$
$234$	−10.2756	−0.671735
$235$	33.2611	2.16971
$236$	4.99435	0.325105
$237$	7.59925	0.493624
$238$	13.8760	0.899445
$239$	−9.62661	−0.622693	−0.311347	−	0.950296i	$-0.600780\pi$
$239$	−9.62661	−0.622693	−0.311347	+	0.950296i	$0.600780\pi$
$240$	−6.94799	−0.448491
$241$	14.9911	0.965662	0.482831	−	0.875713i	$-0.339608\pi$
$241$	14.9911	0.965662	0.482831	+	0.875713i	$0.339608\pi$
$242$	−1.12342	−0.0722159
$243$	18.5378	1.18920
$244$	−3.38807	−0.216899
$245$	−12.3040	−0.786074
$246$	−4.73130	−0.301657
$247$	−30.1717	−1.91978
$248$	−1.00000	−0.0635001
$249$	3.51503	0.222756
$250$	1.68403	0.106507
$251$	11.6157	0.733177	0.366588	−	0.930383i	$-0.380526\pi$
$251$	11.6157	0.733177	0.366588	+	0.930383i	$0.380526\pi$
$252$	−3.64855	−0.229837
$253$	−28.4614	−1.78936
$254$	−6.16786	−0.387006
$255$	−55.6811	−3.48688
$256$	1.00000	0.0625000
$257$	−9.86074	−0.615096	−0.307548	−	0.951533i	$-0.599508\pi$
$257$	−9.86074	−0.615096	−0.307548	+	0.951533i	$0.599508\pi$
$258$	0.912190	0.0567904
$259$	19.2043	1.19330
$260$	14.9923	0.929783
$261$	21.1302	1.30793
$262$	1.55102	0.0958224
$263$	−1.75801	−0.108403	−0.0542017	−	0.998530i	$-0.517261\pi$
$263$	−1.75801	−0.108403	−0.0542017	+	0.998530i	$0.517261\pi$
$264$	−7.86872	−0.484286
$265$	−23.3659	−1.43535
$266$	−10.7131	−0.656860
$267$	−10.3735	−0.634849
$268$	−8.37261	−0.511439
$269$	31.1196	1.89739	0.948697	−	0.316188i	$-0.102403\pi$
$269$	31.1196	1.89739	0.948697	+	0.316188i	$0.102403\pi$
$270$	−6.20318	−0.377513
$271$	29.1632	1.77154	0.885770	−	0.464125i	$-0.153631\pi$
$271$	29.1632	1.77154	0.885770	+	0.464125i	$0.153631\pi$
$272$	8.01399	0.485919
$273$	19.0812	1.15485
$274$	−16.5680	−1.00091
$275$	−15.5022	−0.934815
$276$	−18.4729	−1.11194
$277$	13.7569	0.826574	0.413287	−	0.910601i	$-0.364381\pi$
$277$	13.7569	0.826574	0.413287	+	0.910601i	$0.364381\pi$
$278$	3.89870	0.233828
$279$	2.10720	0.126155
$280$	5.32332	0.318129
$281$	10.9001	0.650248	0.325124	−	0.945671i	$-0.394594\pi$
$281$	10.9001	0.650248	0.325124	+	0.945671i	$0.394594\pi$
$282$	24.4490	1.45591
$283$	−20.7842	−1.23549	−0.617746	−	0.786377i	$-0.711954\pi$
$283$	−20.7842	−1.23549	−0.617746	+	0.786377i	$0.711954\pi$
$284$	7.27302	0.431574
$285$	42.9890	2.54645
$286$	16.9790	1.00399
$287$	3.62496	0.213975
$288$	−2.10720	−0.124168
$289$	47.2240	2.77788
$290$	−30.8295	−1.81037
$291$	2.25991	0.132478
$292$	16.0937	0.941812
$293$	0.726759	0.0424577	0.0212288	−	0.999775i	$-0.493242\pi$
$293$	0.726759	0.0424577	0.0212288	+	0.999775i	$0.493242\pi$
$294$	−9.04420	−0.527468
$295$	15.3549	0.893996
$296$	11.0913	0.644671
$297$	−7.02521	−0.407644
$298$	−5.93094	−0.343570
$299$	39.8607	2.30520
$300$	−10.0617	−0.580912
$301$	−0.698889	−0.0402833
$302$	−1.34253	−0.0772537
$303$	5.97339	0.343162
$304$	−6.18727	−0.354864
$305$	−10.4165	−0.596444
$306$	−16.8871	−0.965369
$307$	−25.0521	−1.42980	−0.714898	−	0.699229i	$-0.753527\pi$
$307$	−25.0521	−1.42980	−0.714898	+	0.699229i	$0.753527\pi$
$308$	6.02875	0.343520
$309$	25.2627	1.43714
$310$	−3.07445	−0.174617
$311$	−21.3784	−1.21226	−0.606130	−	0.795366i	$-0.707279\pi$
$311$	−21.3784	−1.21226	−0.606130	+	0.795366i	$0.707279\pi$
$312$	11.0203	0.623899
$313$	−33.0851	−1.87008	−0.935040	−	0.354543i	$-0.884636\pi$
$313$	−33.0851	−1.87008	−0.935040	+	0.354543i	$0.884636\pi$
$314$	10.7424	0.606229
$315$	−11.2173	−0.632022
$316$	−3.36263	−0.189163
$317$	32.3738	1.81829	0.909147	−	0.416476i	$-0.136735\pi$
$317$	32.3738	1.81829	0.909147	+	0.416476i	$0.136735\pi$
$318$	−17.1754	−0.963146
$319$	−34.9149	−1.95486
$320$	3.07445	0.171867
$321$	−19.7077	−1.09997
$322$	14.1533	0.788735
$323$	−49.5847	−2.75896
$324$	−10.8813	−0.604517
$325$	21.7110	1.20431
$326$	−3.60879	−0.199873
$327$	−11.9527	−0.660984
$328$	2.09358	0.115598
$329$	−18.7320	−1.03273
$330$	−24.1920	−1.33172
$331$	16.3363	0.897925	0.448963	−	0.893550i	$-0.351794\pi$
$331$	16.3363	0.897925	0.448963	+	0.893550i	$0.351794\pi$
$332$	−1.55538	−0.0853627
$333$	−23.3717	−1.28076
$334$	−8.02327	−0.439014
$335$	−25.7412	−1.40639
$336$	3.91296	0.213470
$337$	4.36911	0.238000	0.119000	−	0.992894i	$-0.462031\pi$
$337$	4.36911	0.238000	0.119000	+	0.992894i	$0.462031\pi$
$338$	−10.7794	−0.586323
$339$	−12.5683	−0.682614
$340$	24.6386	1.33622
$341$	−3.48187	−0.188554
$342$	13.0378	0.705003
$343$	19.0496	1.02858
$344$	−0.403640	−0.0217628
$345$	−56.7941	−3.05769
$346$	9.37935	0.504237
$347$	7.42394	0.398538	0.199269	−	0.979945i	$-0.436143\pi$
$347$	7.42394	0.398538	0.199269	+	0.979945i	$0.436143\pi$
$348$	−22.6616	−1.21479
$349$	8.45295	0.452476	0.226238	−	0.974072i	$-0.427357\pi$
$349$	8.45295	0.452476	0.226238	+	0.974072i	$0.427357\pi$
$350$	7.70893	0.412060
$351$	9.83892	0.525163
$352$	3.48187	0.185584
$353$	9.63410	0.512771	0.256386	−	0.966575i	$-0.417468\pi$
$353$	9.63410	0.512771	0.256386	+	0.966575i	$0.417468\pi$
$354$	11.2868	0.599886
$355$	22.3605	1.18677
$356$	4.59023	0.243282
$357$	31.3584	1.65967
$358$	21.5266	1.13772
$359$	31.9175	1.68454	0.842271	−	0.539055i	$-0.181218\pi$
$359$	31.9175	1.68454	0.842271	+	0.539055i	$0.181218\pi$
$360$	−6.47848	−0.341446
$361$	19.2823	1.01486
$362$	19.0791	1.00278
$363$	−2.53882	−0.133253
$364$	−8.44336	−0.442552
$365$	49.4793	2.58986
$366$	−7.65673	−0.400224
$367$	−8.22638	−0.429414	−0.214707	−	0.976679i	$-0.568880\pi$
$367$	−8.22638	−0.429414	−0.214707	+	0.976679i	$0.568880\pi$
$368$	8.17418	0.426109
$369$	−4.41158	−0.229658
$370$	34.0998	1.77276
$371$	13.1592	0.683191
$372$	−2.25991	−0.117171
$373$	−23.8347	−1.23411	−0.617056	−	0.786919i	$-0.711675\pi$
$373$	−23.8347	−1.23411	−0.617056	+	0.786919i	$0.711675\pi$
$374$	27.9037	1.44286
$375$	3.80575	0.196528
$376$	−10.8185	−0.557924
$377$	48.8989	2.51842
$378$	3.49350	0.179686
$379$	−4.22881	−0.217219	−0.108610	−	0.994084i	$-0.534640\pi$
$379$	−4.22881	−0.217219	−0.108610	+	0.994084i	$0.534640\pi$
$380$	−19.0224	−0.975831
$381$	−13.9388	−0.714108
$382$	10.7148	0.548217
$383$	−1.83796	−0.0939152	−0.0469576	−	0.998897i	$-0.514953\pi$
$383$	−1.83796	−0.0939152	−0.0469576	+	0.998897i	$0.514953\pi$
$384$	2.25991	0.115326
$385$	18.5351	0.944636
$386$	0.396397	0.0201761
$387$	0.850548	0.0432358
$388$	−1.00000	−0.0507673
$389$	−16.2884	−0.825857	−0.412928	−	0.910763i	$-0.635494\pi$
$389$	−16.2884	−0.825857	−0.412928	+	0.910763i	$0.635494\pi$
$390$	33.8813	1.71564
$391$	65.5078	3.31287
$392$	4.00202	0.202132
$393$	3.50517	0.176812
$394$	21.2569	1.07091
$395$	−10.3383	−0.520174
$396$	−7.33699	−0.368697
$397$	16.6183	0.834048	0.417024	−	0.908895i	$-0.363073\pi$
$397$	16.6183	0.834048	0.417024	+	0.908895i	$0.363073\pi$
$398$	−7.73991	−0.387966
$399$	−24.2106	−1.21204
$400$	4.45225	0.222613
$401$	−18.9732	−0.947476	−0.473738	−	0.880666i	$-0.657096\pi$
$401$	−18.9732	−0.947476	−0.473738	+	0.880666i	$0.657096\pi$
$402$	−18.9214	−0.943712
$403$	4.87641	0.242911
$404$	−2.64320	−0.131504
$405$	−33.4541	−1.66235
$406$	17.3625	0.861688
$407$	38.6186	1.91425
$408$	18.1109	0.896623
$409$	32.6587	1.61487	0.807435	−	0.589956i	$-0.200855\pi$
$409$	32.6587	1.61487	0.807435	+	0.589956i	$0.200855\pi$
$410$	6.43660	0.317881
$411$	−37.4423	−1.84689
$412$	−11.1786	−0.550731
$413$	−8.64756	−0.425519
$414$	−17.2246	−0.846544
$415$	−4.78195	−0.234737
$416$	−4.87641	−0.239086
$417$	8.81071	0.431462
$418$	−21.5433	−1.05371
$419$	25.8154	1.26117	0.630583	−	0.776122i	$-0.282816\pi$
$419$	25.8154	1.26117	0.630583	+	0.776122i	$0.282816\pi$
$420$	12.0302	0.587015
$421$	−19.8356	−0.966730	−0.483365	−	0.875419i	$-0.660586\pi$
$421$	−19.8356	−0.966730	−0.483365	+	0.875419i	$0.660586\pi$
$422$	−15.1125	−0.735663
$423$	22.7968	1.10842
$424$	7.60002	0.369089
$425$	35.6803	1.73075
$426$	16.4364	0.796345
$427$	5.86633	0.283892
$428$	8.72054	0.421523
$429$	38.3711	1.85257
$430$	−1.24097	−0.0598449
$431$	15.5720	0.750074	0.375037	−	0.927010i	$-0.377630\pi$
$431$	15.5720	0.750074	0.375037	+	0.927010i	$0.377630\pi$
$432$	2.01765	0.0970744
$433$	−26.1223	−1.25536	−0.627679	−	0.778472i	$-0.715995\pi$
$433$	−26.1223	−1.25536	−0.627679	+	0.778472i	$0.715995\pi$
$434$	1.73147	0.0831132
$435$	−69.6719	−3.34051
$436$	5.28900	0.253297
$437$	−50.5758	−2.41937
$438$	36.3703	1.73784
$439$	−6.62098	−0.316002	−0.158001	−	0.987439i	$-0.550505\pi$
$439$	−6.62098	−0.316002	−0.158001	+	0.987439i	$0.550505\pi$
$440$	10.7048	0.510333
$441$	−8.43304	−0.401573
$442$	−39.0795	−1.85882
$443$	−2.00774	−0.0953904	−0.0476952	−	0.998862i	$-0.515188\pi$
$443$	−2.00774	−0.0953904	−0.0476952	+	0.998862i	$0.515188\pi$
$444$	25.0654	1.18955
$445$	14.1125	0.668994
$446$	−14.3405	−0.679045
$447$	−13.4034	−0.633959
$448$	−1.73147	−0.0818042
$449$	32.9038	1.55283	0.776413	−	0.630225i	$-0.217037\pi$
$449$	32.9038	1.55283	0.776413	+	0.630225i	$0.217037\pi$
$450$	−9.38177	−0.442261
$451$	7.28956	0.343252
$452$	5.56140	0.261586
$453$	−3.03399	−0.142549
$454$	27.0464	1.26935
$455$	−25.9587	−1.21696
$456$	−13.9827	−0.654799
$457$	−37.1885	−1.73960	−0.869802	−	0.493401i	$-0.835753\pi$
$457$	−37.1885	−1.73960	−0.869802	+	0.493401i	$0.835753\pi$
$458$	−25.5356	−1.19320
$459$	16.1695	0.754725
$460$	25.1311	1.17174
$461$	22.7608	1.06008	0.530039	−	0.847973i	$-0.322177\pi$
$461$	22.7608	1.06008	0.530039	+	0.847973i	$0.322177\pi$
$462$	13.6244	0.633866
$463$	39.0721	1.81583	0.907917	−	0.419150i	$-0.137672\pi$
$463$	39.0721	1.81583	0.907917	+	0.419150i	$0.137672\pi$
$464$	10.0276	0.465521
$465$	−6.94799	−0.322205
$466$	−14.0329	−0.650060
$467$	26.4974	1.22615	0.613077	−	0.790023i	$-0.289932\pi$
$467$	26.4974	1.22615	0.613077	+	0.790023i	$0.289932\pi$
$468$	10.2756	0.474988
$469$	14.4969	0.669406
$470$	−33.2611	−1.53422
$471$	24.2769	1.11862
$472$	−4.99435	−0.229884
$473$	−1.40542	−0.0646213
$474$	−7.59925	−0.349045
$475$	−27.5473	−1.26395
$476$	−13.8760	−0.636004
$477$	−16.0147	−0.733264
$478$	9.62661	0.440311
$479$	10.0890	0.460976	0.230488	−	0.973075i	$-0.425968\pi$
$479$	10.0890	0.460976	0.230488	+	0.973075i	$0.425968\pi$
$480$	6.94799	0.317131
$481$	−54.0860	−2.46611
$482$	−14.9911	−0.682826
$483$	31.9853	1.45538
$484$	1.12342	0.0510643
$485$	−3.07445	−0.139604
$486$	−18.5378	−0.840893
$487$	5.69305	0.257977	0.128988	−	0.991646i	$-0.458827\pi$
$487$	5.69305	0.257977	0.128988	+	0.991646i	$0.458827\pi$
$488$	3.38807	0.153371
$489$	−8.15555	−0.368807
$490$	12.3040	0.555838
$491$	−5.36156	−0.241964	−0.120982	−	0.992655i	$-0.538604\pi$
$491$	−5.36156	−0.241964	−0.120982	+	0.992655i	$0.538604\pi$
$492$	4.73130	0.213303
$493$	80.3613	3.61929
$494$	30.1717	1.35749
$495$	−22.5572	−1.01387
$496$	1.00000	0.0449013
$497$	−12.5930	−0.564873
$498$	−3.51503	−0.157512
$499$	−29.6875	−1.32899	−0.664497	−	0.747291i	$-0.731354\pi$
$499$	−29.6875	−1.32899	−0.664497	+	0.747291i	$0.731354\pi$
$500$	−1.68403	−0.0753120
$501$	−18.1319	−0.810073
$502$	−11.6157	−0.518434
$503$	−7.80374	−0.347952	−0.173976	−	0.984750i	$-0.555661\pi$
$503$	−7.80374	−0.347952	−0.173976	+	0.984750i	$0.555661\pi$
$504$	3.64855	0.162519
$505$	−8.12638	−0.361619
$506$	28.4614	1.26527
$507$	−24.3605	−1.08189
$508$	6.16786	0.273655
$509$	−28.7929	−1.27622	−0.638111	−	0.769944i	$-0.720284\pi$
$509$	−28.7929	−1.27622	−0.638111	+	0.769944i	$0.720284\pi$
$510$	55.6811	2.46560
$511$	−27.8657	−1.23271
$512$	−1.00000	−0.0441942
$513$	−12.4838	−0.551172
$514$	9.86074	0.434938
$515$	−34.3681	−1.51444
$516$	−0.912190	−0.0401569
$517$	−37.6688	−1.65667
$518$	−19.2043	−0.843789
$519$	21.1965	0.930422
$520$	−14.9923	−0.657456
$521$	24.9279	1.09211	0.546056	−	0.837749i	$-0.316129\pi$
$521$	24.9279	1.09211	0.546056	+	0.837749i	$0.316129\pi$
$522$	−21.1302	−0.924844
$523$	−12.3195	−0.538695	−0.269347	−	0.963043i	$-0.586808\pi$
$523$	−12.3195	−0.538695	−0.269347	+	0.963043i	$0.586808\pi$
$524$	−1.55102	−0.0677567
$525$	17.4215	0.760337
$526$	1.75801	0.0766528
$527$	8.01399	0.349095
$528$	7.86872	0.342442
$529$	43.8173	1.90510
$530$	23.3659	1.01495
$531$	10.5241	0.456706
$532$	10.7131	0.464470
$533$	−10.2091	−0.442207
$534$	10.3735	0.448906
$535$	26.8109	1.15914
$536$	8.37261	0.361642
$537$	48.6482	2.09932
$538$	−31.1196	−1.34166
$539$	13.9345	0.600201
$540$	6.20318	0.266942
$541$	8.08912	0.347778	0.173889	−	0.984765i	$-0.444367\pi$
$541$	8.08912	0.347778	0.173889	+	0.984765i	$0.444367\pi$
$542$	−29.1632	−1.25267
$543$	43.1171	1.85033
$544$	−8.01399	−0.343597
$545$	16.2608	0.696535
$546$	−19.0812	−0.816602
$547$	43.1503	1.84497	0.922487	−	0.386029i	$-0.126154\pi$
$547$	43.1503	1.84497	0.922487	+	0.386029i	$0.126154\pi$
$548$	16.5680	0.707751
$549$	−7.13933	−0.304699
$550$	15.5022	0.661014
$551$	−62.0436	−2.64315
$552$	18.4729	0.786260
$553$	5.82229	0.247589
$554$	−13.7569	−0.584476
$555$	77.0625	3.27112
$556$	−3.89870	−0.165342
$557$	23.2767	0.986266	0.493133	−	0.869954i	$-0.335852\pi$
$557$	23.2767	0.986266	0.493133	+	0.869954i	$0.335852\pi$
$558$	−2.10720	−0.0892048
$559$	1.96831	0.0832508
$560$	−5.32332	−0.224951
$561$	63.0598	2.66239
$562$	−10.9001	−0.459795
$563$	26.9697	1.13664	0.568318	−	0.822809i	$-0.307594\pi$
$563$	26.9697	1.13664	0.568318	+	0.822809i	$0.307594\pi$
$564$	−24.4490	−1.02949
$565$	17.0982	0.719328
$566$	20.7842	0.873625
$567$	18.8406	0.791233
$568$	−7.27302	−0.305169
$569$	−34.7414	−1.45644	−0.728218	−	0.685346i	$-0.759651\pi$
$569$	−34.7414	−1.45644	−0.728218	+	0.685346i	$0.759651\pi$
$570$	−42.9890	−1.80061
$571$	26.8184	1.12232	0.561158	−	0.827709i	$-0.310356\pi$
$571$	26.8184	1.12232	0.561158	+	0.827709i	$0.310356\pi$
$572$	−16.9790	−0.709929
$573$	24.2145	1.01158
$574$	−3.62496	−0.151303
$575$	36.3935	1.51771
$576$	2.10720	0.0877999
$577$	−33.8599	−1.40961	−0.704803	−	0.709403i	$-0.748964\pi$
$577$	−33.8599	−1.40961	−0.704803	+	0.709403i	$0.748964\pi$
$578$	−47.2240	−1.96426
$579$	0.895823	0.0372291
$580$	30.8295	1.28012
$581$	2.69310	0.111728
$582$	−2.25991	−0.0936763
$583$	26.4623	1.09596
$584$	−16.0937	−0.665962
$585$	31.5917	1.30616
$586$	−0.726759	−0.0300221
$587$	7.61593	0.314343	0.157172	−	0.987571i	$-0.449762\pi$
$587$	7.61593	0.314343	0.157172	+	0.987571i	$0.449762\pi$
$588$	9.04420	0.372977
$589$	−6.18727	−0.254942
$590$	−15.3549	−0.632151
$591$	48.0387	1.97605
$592$	−11.0913	−0.455851
$593$	46.5937	1.91337	0.956687	−	0.291118i	$-0.0940271\pi$
$593$	46.5937	1.91337	0.956687	+	0.291118i	$0.0940271\pi$
$594$	7.02521	0.288248
$595$	−42.6610	−1.74893
$596$	5.93094	0.242941
$597$	−17.4915	−0.715879
$598$	−39.8607	−1.63003
$599$	27.3200	1.11626	0.558132	−	0.829752i	$-0.311518\pi$
$599$	27.3200	1.11626	0.558132	+	0.829752i	$0.311518\pi$
$600$	10.0617	0.410767
$601$	−15.1306	−0.617188	−0.308594	−	0.951194i	$-0.599859\pi$
$601$	−15.1306	−0.617188	−0.308594	+	0.951194i	$0.599859\pi$
$602$	0.698889	0.0284846
$603$	−17.6428	−0.718468
$604$	1.34253	0.0546266
$605$	3.45389	0.140420
$606$	−5.97339	−0.242652
$607$	−0.0453893	−0.00184229	−0.000921147	−	1.00000i	$-0.500293\pi$
$607$	−0.0453893	−0.00184229	−0.000921147		1.00000i	$0.500293\pi$
$608$	6.18727	0.250927
$609$	39.2378	1.58999
$610$	10.4165	0.421750
$611$	52.7557	2.13427
$612$	16.8871	0.682619
$613$	1.64275	0.0663502	0.0331751	−	0.999450i	$-0.489438\pi$
$613$	1.64275	0.0663502	0.0331751	+	0.999450i	$0.489438\pi$
$614$	25.0521	1.01102
$615$	14.5461	0.586557
$616$	−6.02875	−0.242905
$617$	4.34803	0.175045	0.0875226	−	0.996163i	$-0.472105\pi$
$617$	4.34803	0.175045	0.0875226	+	0.996163i	$0.472105\pi$
$618$	−25.2627	−1.01621
$619$	−9.76938	−0.392664	−0.196332	−	0.980537i	$-0.562903\pi$
$619$	−9.76938	−0.392664	−0.196332	+	0.980537i	$0.562903\pi$
$620$	3.07445	0.123473
$621$	16.4927	0.661828
$622$	21.3784	0.857197
$623$	−7.94785	−0.318424
$624$	−11.0203	−0.441164
$625$	−27.4387	−1.09755
$626$	33.0851	1.32235
$627$	−48.6858	−1.94432
$628$	−10.7424	−0.428669
$629$	−88.8859	−3.54411
$630$	11.2173	0.446907
$631$	2.94301	0.117159	0.0585796	−	0.998283i	$-0.481343\pi$
$631$	2.94301	0.117159	0.0585796	+	0.998283i	$0.481343\pi$
$632$	3.36263	0.133758
$633$	−34.1528	−1.35745
$634$	−32.3738	−1.28573
$635$	18.9628	0.752516
$636$	17.1754	0.681047
$637$	−19.5155	−0.773232
$638$	34.9149	1.38229
$639$	15.3257	0.606275
$640$	−3.07445	−0.121528
$641$	−18.5239	−0.731649	−0.365824	−	0.930684i	$-0.619213\pi$
$641$	−18.5239	−0.731649	−0.365824	+	0.930684i	$0.619213\pi$
$642$	19.7077	0.777799
$643$	−6.56352	−0.258840	−0.129420	−	0.991590i	$-0.541312\pi$
$643$	−6.56352	−0.258840	−0.129420	+	0.991590i	$0.541312\pi$
$644$	−14.1533	−0.557720
$645$	−2.80448	−0.110426
$646$	49.5847	1.95088
$647$	2.10202	0.0826391	0.0413196	−	0.999146i	$-0.486844\pi$
$647$	2.10202	0.0826391	0.0413196	+	0.999146i	$0.486844\pi$
$648$	10.8813	0.427458
$649$	−17.3897	−0.682605
$650$	−21.7110	−0.851576
$651$	3.91296	0.153361
$652$	3.60879	0.141331
$653$	−6.41524	−0.251048	−0.125524	−	0.992091i	$-0.540061\pi$
$653$	−6.41524	−0.251048	−0.125524	+	0.992091i	$0.540061\pi$
$654$	11.9527	0.467386
$655$	−4.76854	−0.186322
$656$	−2.09358	−0.0817405
$657$	33.9126	1.32306
$658$	18.7320	0.730248
$659$	7.09040	0.276203	0.138101	−	0.990418i	$-0.455900\pi$
$659$	7.09040	0.276203	0.138101	+	0.990418i	$0.455900\pi$
$660$	24.1920	0.941672
$661$	15.0268	0.584475	0.292237	−	0.956346i	$-0.405600\pi$
$661$	15.0268	0.584475	0.292237	+	0.956346i	$0.405600\pi$
$662$	−16.3363	−0.634929
$663$	−88.3162	−3.42992
$664$	1.55538	0.0603606
$665$	32.9368	1.27723
$666$	23.3717	0.905633
$667$	81.9677	3.17380
$668$	8.02327	0.310430
$669$	−32.4084	−1.25298
$670$	25.7412	0.994469
$671$	11.7968	0.455411
$672$	−3.91296	−0.150946
$673$	19.7707	0.762103	0.381051	−	0.924554i	$-0.375562\pi$
$673$	19.7707	0.762103	0.381051	+	0.924554i	$0.375562\pi$
$674$	−4.36911	−0.168292
$675$	8.98310	0.345760
$676$	10.7794	0.414593
$677$	17.1753	0.660099	0.330049	−	0.943964i	$-0.392935\pi$
$677$	17.1753	0.660099	0.330049	+	0.943964i	$0.392935\pi$
$678$	12.5683	0.482681
$679$	1.73147	0.0664477
$680$	−24.6386	−0.944848
$681$	61.1225	2.34222
$682$	3.48187	0.133328
$683$	22.7329	0.869851	0.434926	−	0.900466i	$-0.356775\pi$
$683$	22.7329	0.869851	0.434926	+	0.900466i	$0.356775\pi$
$684$	−13.0378	−0.498512
$685$	50.9376	1.94623
$686$	−19.0496	−0.727319
$687$	−57.7082	−2.20170
$688$	0.403640	0.0153886
$689$	−37.0608	−1.41191
$690$	56.7941	2.16211
$691$	−1.11753	−0.0425128	−0.0212564	−	0.999774i	$-0.506767\pi$
$691$	−1.11753	−0.0425128	−0.0212564	+	0.999774i	$0.506767\pi$
$692$	−9.37935	−0.356549
$693$	12.7038	0.482576
$694$	−7.42394	−0.281809
$695$	−11.9864	−0.454668
$696$	22.6616	0.858984
$697$	−16.7779	−0.635508
$698$	−8.45295	−0.319949
$699$	−31.7130	−1.19950
$700$	−7.70893	−0.291370
$701$	−14.9540	−0.564805	−0.282402	−	0.959296i	$-0.591131\pi$
$701$	−14.9540	−0.564805	−0.282402	+	0.959296i	$0.591131\pi$
$702$	−9.83892	−0.371346
$703$	68.6251	2.58824
$704$	−3.48187	−0.131228
$705$	−75.1671	−2.83096
$706$	−9.63410	−0.362584
$707$	4.57661	0.172121
$708$	−11.2868	−0.424184
$709$	24.5084	0.920433	0.460216	−	0.887807i	$-0.347772\pi$
$709$	24.5084	0.920433	0.460216	+	0.887807i	$0.347772\pi$
$710$	−22.3605	−0.839176
$711$	−7.08573	−0.265736
$712$	−4.59023	−0.172026
$713$	8.17418	0.306126
$714$	−31.3584	−1.17356
$715$	−52.2012	−1.95222
$716$	−21.5266	−0.804486
$717$	21.7553	0.812465
$718$	−31.9175	−1.19115
$719$	13.3197	0.496740	0.248370	−	0.968665i	$-0.420105\pi$
$719$	13.3197	0.496740	0.248370	+	0.968665i	$0.420105\pi$
$720$	6.47848	0.241439
$721$	19.3554	0.720833
$722$	−19.2823	−0.717611
$723$	−33.8786	−1.25996
$724$	−19.0791	−0.709070
$725$	44.6455	1.65809
$726$	2.53882	0.0942244
$727$	26.8999	0.997663	0.498832	−	0.866699i	$-0.333763\pi$
$727$	26.8999	0.997663	0.498832	+	0.866699i	$0.333763\pi$
$728$	8.44336	0.312932
$729$	−9.24992	−0.342590
$730$	−49.4793	−1.83131
$731$	3.23476	0.119642
$732$	7.65673	0.283001
$733$	30.0756	1.11087	0.555433	−	0.831561i	$-0.312553\pi$
$733$	30.0756	1.11087	0.555433	+	0.831561i	$0.312553\pi$
$734$	8.22638	0.303641
$735$	27.8060	1.02564
$736$	−8.17418	−0.301304
$737$	29.1524	1.07384
$738$	4.41158	0.162393
$739$	−45.1013	−1.65908	−0.829539	−	0.558449i	$-0.811397\pi$
$739$	−45.1013	−1.65908	−0.829539	+	0.558449i	$0.811397\pi$
$740$	−34.0998	−1.25353
$741$	68.1853	2.50485
$742$	−13.1592	−0.483089
$743$	5.07266	0.186098	0.0930490	−	0.995662i	$-0.470339\pi$
$743$	5.07266	0.186098	0.0930490	+	0.995662i	$0.470339\pi$
$744$	2.25991	0.0828524
$745$	18.2344	0.668056
$746$	23.8347	0.872649
$747$	−3.27750	−0.119917
$748$	−27.9037	−1.02026
$749$	−15.0993	−0.551718
$750$	−3.80575	−0.138966
$751$	−3.68999	−0.134650	−0.0673248	−	0.997731i	$-0.521446\pi$
$751$	−3.68999	−0.134650	−0.0673248	+	0.997731i	$0.521446\pi$
$752$	10.8185	0.394512
$753$	−26.2505	−0.956620
$754$	−48.8989	−1.78079
$755$	4.12753	0.150216
$756$	−3.49350	−0.127058
$757$	48.3916	1.75882	0.879411	−	0.476062i	$-0.157936\pi$
$757$	48.3916	1.75882	0.879411	+	0.476062i	$0.157936\pi$
$758$	4.22881	0.153597
$759$	64.3203	2.33468
$760$	19.0224	0.690017
$761$	−16.5706	−0.600684	−0.300342	−	0.953832i	$-0.597101\pi$
$761$	−16.5706	−0.600684	−0.300342	+	0.953832i	$0.597101\pi$
$762$	13.9388	0.504950
$763$	−9.15774	−0.331532
$764$	−10.7148	−0.387648
$765$	51.9184	1.87711
$766$	1.83796	0.0664081
$767$	24.3545	0.879391
$768$	−2.25991	−0.0815475
$769$	−2.07644	−0.0748784	−0.0374392	−	0.999299i	$-0.511920\pi$
$769$	−2.07644	−0.0748784	−0.0374392	+	0.999299i	$0.511920\pi$
$770$	−18.5351	−0.667958
$771$	22.2844	0.802553
$772$	−0.396397	−0.0142667
$773$	0.747919	0.0269008	0.0134504	−	0.999910i	$-0.495718\pi$
$773$	0.747919	0.0269008	0.0134504	+	0.999910i	$0.495718\pi$
$774$	−0.850548	−0.0305723
$775$	4.45225	0.159930
$776$	1.00000	0.0358979
$777$	−43.4000	−1.55697
$778$	16.2884	0.583969
$779$	12.9535	0.464108
$780$	−33.8813	−1.21314
$781$	−25.3237	−0.906153
$782$	−65.5078	−2.34255
$783$	20.2323	0.723043
$784$	−4.00202	−0.142929
$785$	−33.0270	−1.17878
$786$	−3.50517	−0.125025
$787$	−4.80134	−0.171149	−0.0855746	−	0.996332i	$-0.527273\pi$
$787$	−4.80134	−0.171149	−0.0855746	+	0.996332i	$0.527273\pi$
$788$	−21.2569	−0.757246
$789$	3.97294	0.141441
$790$	10.3383	0.367818
$791$	−9.62938	−0.342381
$792$	7.33699	0.260708
$793$	−16.5216	−0.586700
$794$	−16.6183	−0.589761
$795$	52.8048	1.87279
$796$	7.73991	0.274334
$797$	−35.2121	−1.24728	−0.623639	−	0.781713i	$-0.714346\pi$
$797$	−35.2121	−1.24728	−0.623639	+	0.781713i	$0.714346\pi$
$798$	24.2106	0.857044
$799$	86.6997	3.06721
$800$	−4.45225	−0.157411
$801$	9.67253	0.341762
$802$	18.9732	0.669967
$803$	−56.0361	−1.97747
$804$	18.9214	0.667305
$805$	−43.5138	−1.53366
$806$	−4.87641	−0.171764
$807$	−70.3274	−2.47564
$808$	2.64320	0.0929874
$809$	2.20434	0.0775003	0.0387502	−	0.999249i	$-0.487662\pi$
$809$	2.20434	0.0775003	0.0387502	+	0.999249i	$0.487662\pi$
$810$	33.4541	1.17546
$811$	17.5633	0.616731	0.308366	−	0.951268i	$-0.400218\pi$
$811$	17.5633	0.616731	0.308366	+	0.951268i	$0.400218\pi$
$812$	−17.3625	−0.609305
$813$	−65.9063	−2.31143
$814$	−38.6186	−1.35358
$815$	11.0951	0.388643
$816$	−18.1109	−0.634008
$817$	−2.49743	−0.0873739
$818$	−32.6587	−1.14189
$819$	−17.7918	−0.621697
$820$	−6.43660	−0.224776
$821$	33.7978	1.17955	0.589776	−	0.807567i	$-0.299216\pi$
$821$	33.7978	1.17955	0.589776	+	0.807567i	$0.299216\pi$
$822$	37.4423	1.30595
$823$	−27.5626	−0.960772	−0.480386	−	0.877057i	$-0.659503\pi$
$823$	−27.5626	−0.960772	−0.480386	+	0.877057i	$0.659503\pi$
$824$	11.1786	0.389425
$825$	35.0335	1.21971
$826$	8.64756	0.300887
$827$	36.3621	1.26443	0.632217	−	0.774792i	$-0.282145\pi$
$827$	36.3621	1.26443	0.632217	+	0.774792i	$0.282145\pi$
$828$	17.2246	0.598597
$829$	14.0761	0.488883	0.244441	−	0.969664i	$-0.421395\pi$
$829$	14.0761	0.488883	0.244441	+	0.969664i	$0.421395\pi$
$830$	4.78195	0.165984
$831$	−31.0895	−1.07848
$832$	4.87641	0.169059
$833$	−32.0721	−1.11123
$834$	−8.81071	−0.305090
$835$	24.6672	0.853642
$836$	21.5433	0.745089
$837$	2.01765	0.0697403
$838$	−25.8154	−0.891779
$839$	44.7809	1.54601	0.773004	−	0.634401i	$-0.218753\pi$
$839$	44.7809	1.54601	0.773004	+	0.634401i	$0.218753\pi$
$840$	−12.0302	−0.415082
$841$	71.5534	2.46736
$842$	19.8356	0.683581
$843$	−24.6334	−0.848418
$844$	15.1125	0.520193
$845$	33.1408	1.14008
$846$	−22.7968	−0.783771
$847$	−1.94516	−0.0668364
$848$	−7.60002	−0.260986
$849$	46.9705	1.61202
$850$	−35.6803	−1.22382
$851$	−90.6627	−3.10788
$852$	−16.4364	−0.563101
$853$	21.6110	0.739947	0.369973	−	0.929042i	$-0.379367\pi$
$853$	21.6110	0.739947	0.369973	+	0.929042i	$0.379367\pi$
$854$	−5.86633	−0.200742
$855$	−40.0841	−1.37085
$856$	−8.72054	−0.298062
$857$	−33.0145	−1.12775	−0.563877	−	0.825859i	$-0.690691\pi$
$857$	−33.0145	−1.12775	−0.563877	+	0.825859i	$0.690691\pi$
$858$	−38.3711	−1.30997
$859$	17.8306	0.608372	0.304186	−	0.952613i	$-0.401616\pi$
$859$	17.8306	0.608372	0.304186	+	0.952613i	$0.401616\pi$
$860$	1.24097	0.0423167
$861$	−8.19209	−0.279186
$862$	−15.5720	−0.530383
$863$	−7.53414	−0.256465	−0.128233	−	0.991744i	$-0.540930\pi$
$863$	−7.53414	−0.256465	−0.128233	+	0.991744i	$0.540930\pi$
$864$	−2.01765	−0.0686420
$865$	−28.8363	−0.980465
$866$	26.1223	0.887672
$867$	−106.722	−3.62447
$868$	−1.73147	−0.0587699
$869$	11.7082	0.397175
$870$	69.6719	2.36210
$871$	−40.8283	−1.38342
$872$	−5.28900	−0.179108
$873$	−2.10720	−0.0713178
$874$	50.5758	1.71075
$875$	2.91584	0.0985734
$876$	−36.3703	−1.22884
$877$	15.0917	0.509611	0.254805	−	0.966992i	$-0.417989\pi$
$877$	15.0917	0.509611	0.254805	+	0.966992i	$0.417989\pi$
$878$	6.62098	0.223447
$879$	−1.64241	−0.0553971
$880$	−10.7048	−0.360860
$881$	−5.08221	−0.171224	−0.0856121	−	0.996329i	$-0.527285\pi$
$881$	−5.08221	−0.171224	−0.0856121	+	0.996329i	$0.527285\pi$
$882$	8.43304	0.283955
$883$	28.6003	0.962476	0.481238	−	0.876590i	$-0.340187\pi$
$883$	28.6003	0.962476	0.481238	+	0.876590i	$0.340187\pi$
$884$	39.0795	1.31439
$885$	−34.7007	−1.16645
$886$	2.00774	0.0674512
$887$	−56.9258	−1.91138	−0.955691	−	0.294372i	$-0.904890\pi$
$887$	−56.9258	−1.91138	−0.955691	+	0.294372i	$0.904890\pi$
$888$	−25.0654	−0.841141
$889$	−10.6795	−0.358178
$890$	−14.1125	−0.473050
$891$	37.8873	1.26927
$892$	14.3405	0.480157
$893$	−66.9372	−2.23997
$894$	13.4034	0.448277
$895$	−66.1824	−2.21223
$896$	1.73147	0.0578443
$897$	−90.0816	−3.00774
$898$	−32.9038	−1.09801
$899$	10.0276	0.334440
$900$	9.38177	0.312726
$901$	−60.9064	−2.02909
$902$	−7.28956	−0.242716
$903$	1.57943	0.0525601
$904$	−5.56140	−0.184969
$905$	−58.6579	−1.94985
$906$	3.03399	0.100798
$907$	−15.3393	−0.509334	−0.254667	−	0.967029i	$-0.581966\pi$
$907$	−15.3393	−0.509334	−0.254667	+	0.967029i	$0.581966\pi$
$908$	−27.0464	−0.897567
$909$	−5.56974	−0.184737
$910$	25.9587	0.860522
$911$	4.18779	0.138748	0.0693739	−	0.997591i	$-0.477900\pi$
$911$	4.18779	0.138748	0.0693739	+	0.997591i	$0.477900\pi$
$912$	13.9827	0.463012
$913$	5.41564	0.179232
$914$	37.1885	1.23009
$915$	23.5403	0.778217
$916$	25.5356	0.843720
$917$	2.68555	0.0886845
$918$	−16.1695	−0.533671
$919$	24.8485	0.819677	0.409839	−	0.912158i	$-0.365585\pi$
$919$	24.8485	0.819677	0.409839	+	0.912158i	$0.365585\pi$
$920$	−25.1311	−0.828549
$921$	56.6154	1.86554
$922$	−22.7608	−0.749588
$923$	35.4663	1.16739
$924$	−13.6244	−0.448211
$925$	−49.3814	−1.62365
$926$	−39.0721	−1.28399
$927$	−23.5555	−0.773666
$928$	−10.0276	−0.329173
$929$	−26.5236	−0.870212	−0.435106	−	0.900379i	$-0.643289\pi$
$929$	−26.5236	−0.870212	−0.435106	+	0.900379i	$0.643289\pi$
$930$	6.94799	0.227833
$931$	24.7615	0.811527
$932$	14.0329	0.459662
$933$	48.3133	1.58171
$934$	−26.4974	−0.867022
$935$	−85.7884	−2.80558
$936$	−10.2756	−0.335867
$937$	−35.2960	−1.15307	−0.576535	−	0.817073i	$-0.695595\pi$
$937$	−35.2960	−1.15307	−0.576535	+	0.817073i	$0.695595\pi$
$938$	−14.4969	−0.473341
$939$	74.7693	2.44001
$940$	33.2611	1.08486
$941$	22.5901	0.736415	0.368207	−	0.929744i	$-0.379972\pi$
$941$	22.5901	0.736415	0.368207	+	0.929744i	$0.379972\pi$
$942$	−24.2769	−0.790984
$943$	−17.1133	−0.557285
$944$	4.99435	0.162552
$945$	−10.7406	−0.349392
$946$	1.40542	0.0456942
$947$	46.9814	1.52669	0.763346	−	0.645990i	$-0.223555\pi$
$947$	46.9814	1.52669	0.763346	+	0.645990i	$0.223555\pi$
$948$	7.59925	0.246812
$949$	78.4795	2.54755
$950$	27.5473	0.893751
$951$	−73.1619	−2.37244
$952$	13.8760	0.449723
$953$	5.23044	0.169431	0.0847154	−	0.996405i	$-0.473002\pi$
$953$	5.23044	0.169431	0.0847154	+	0.996405i	$0.473002\pi$
$954$	16.0147	0.518496
$955$	−32.9422	−1.06598
$956$	−9.62661	−0.311347
$957$	78.9046	2.55062
$958$	−10.0890	−0.325959
$959$	−28.6870	−0.926353
$960$	−6.94799	−0.224245
$961$	1.00000	0.0322581
$962$	54.0860	1.74380
$963$	18.3759	0.592155
$964$	14.9911	0.482831
$965$	−1.21870	−0.0392315
$966$	−31.9853	−1.02911
$967$	−36.5473	−1.17528	−0.587640	−	0.809122i	$-0.699943\pi$
$967$	−36.5473	−1.17528	−0.587640	+	0.809122i	$0.699943\pi$
$968$	−1.12342	−0.0361079
$969$	112.057	3.59979
$970$	3.07445	0.0987147
$971$	14.0294	0.450224	0.225112	−	0.974333i	$-0.427725\pi$
$971$	14.0294	0.450224	0.225112	+	0.974333i	$0.427725\pi$
$972$	18.5378	0.594601
$973$	6.75047	0.216410
$974$	−5.69305	−0.182417
$975$	−49.0650	−1.57134
$976$	−3.38807	−0.108449
$977$	−0.239874	−0.00767423	−0.00383712	−	0.999993i	$-0.501221\pi$
$977$	−0.239874	−0.00767423	−0.00383712	+	0.999993i	$0.501221\pi$
$978$	8.15555	0.260786
$979$	−15.9826	−0.510806
$980$	−12.3040	−0.393037
$981$	11.1450	0.355831
$982$	5.36156	0.171094
$983$	−59.7688	−1.90633	−0.953164	−	0.302454i	$-0.902194\pi$
$983$	−59.7688	−1.90633	−0.953164	+	0.302454i	$0.902194\pi$
$984$	−4.73130	−0.150828
$985$	−65.3534	−2.08233
$986$	−80.3613	−2.55923
$987$	42.3326	1.34746
$988$	−30.1717	−0.959889
$989$	3.29942	0.104916
$990$	22.5572	0.716915
$991$	−12.4483	−0.395435	−0.197717	−	0.980259i	$-0.563353\pi$
$991$	−12.4483	−0.395435	−0.197717	+	0.980259i	$0.563353\pi$
$992$	−1.00000	−0.0317500
$993$	−36.9186	−1.17158
$994$	12.5930	0.399426
$995$	23.7960	0.754383
$996$	3.51503	0.111378
$997$	12.5219	0.396574	0.198287	−	0.980144i	$-0.436462\pi$
$997$	12.5219	0.396574	0.198287	+	0.980144i	$0.436462\pi$
$998$	29.6875	0.939740
$999$	−22.3785	−0.708024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.l.1.8	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.l.1.8	✓	38	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.25991 q^{3} +1.00000 q^{4} +3.07445 q^{5} +2.25991 q^{6} -1.73147 q^{7} -1.00000 q^{8} +2.10720 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.25991 q^{3} +1.00000 q^{4} +3.07445 q^{5} +2.25991 q^{6} -1.73147 q^{7} -1.00000 q^{8} +2.10720 q^{9} -3.07445 q^{10} -3.48187 q^{11} -2.25991 q^{12} +4.87641 q^{13} +1.73147 q^{14} -6.94799 q^{15} +1.00000 q^{16} +8.01399 q^{17} -2.10720 q^{18} -6.18727 q^{19} +3.07445 q^{20} +3.91296 q^{21} +3.48187 q^{22} +8.17418 q^{23} +2.25991 q^{24} +4.45225 q^{25} -4.87641 q^{26} +2.01765 q^{27} -1.73147 q^{28} +10.0276 q^{29} +6.94799 q^{30} +1.00000 q^{31} -1.00000 q^{32} +7.86872 q^{33} -8.01399 q^{34} -5.32332 q^{35} +2.10720 q^{36} -11.0913 q^{37} +6.18727 q^{38} -11.0203 q^{39} -3.07445 q^{40} -2.09358 q^{41} -3.91296 q^{42} +0.403640 q^{43} -3.48187 q^{44} +6.47848 q^{45} -8.17418 q^{46} +10.8185 q^{47} -2.25991 q^{48} -4.00202 q^{49} -4.45225 q^{50} -18.1109 q^{51} +4.87641 q^{52} -7.60002 q^{53} -2.01765 q^{54} -10.7048 q^{55} +1.73147 q^{56} +13.9827 q^{57} -10.0276 q^{58} +4.99435 q^{59} -6.94799 q^{60} -3.38807 q^{61} -1.00000 q^{62} -3.64855 q^{63} +1.00000 q^{64} +14.9923 q^{65} -7.86872 q^{66} -8.37261 q^{67} +8.01399 q^{68} -18.4729 q^{69} +5.32332 q^{70} +7.27302 q^{71} -2.10720 q^{72} +16.0937 q^{73} +11.0913 q^{74} -10.0617 q^{75} -6.18727 q^{76} +6.02875 q^{77} +11.0203 q^{78} -3.36263 q^{79} +3.07445 q^{80} -10.8813 q^{81} +2.09358 q^{82} -1.55538 q^{83} +3.91296 q^{84} +24.6386 q^{85} -0.403640 q^{86} -22.6616 q^{87} +3.48187 q^{88} +4.59023 q^{89} -6.47848 q^{90} -8.44336 q^{91} +8.17418 q^{92} -2.25991 q^{93} -10.8185 q^{94} -19.0224 q^{95} +2.25991 q^{96} -1.00000 q^{97} +4.00202 q^{98} -7.33699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

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