LMFDB - Embedded newform 6010.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.30184 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.30184 q^{6} +0.511613 q^{7} +1.00000 q^{8} -1.30521 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.30184 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.30184 q^{6} +0.511613 q^{7} +1.00000 q^{8} -1.30521 q^{9} -1.00000 q^{10} -2.76717 q^{11} -1.30184 q^{12} +1.86691 q^{13} +0.511613 q^{14} +1.30184 q^{15} +1.00000 q^{16} +2.86112 q^{17} -1.30521 q^{18} -5.33416 q^{19} -1.00000 q^{20} -0.666038 q^{21} -2.76717 q^{22} +6.87494 q^{23} -1.30184 q^{24} +1.00000 q^{25} +1.86691 q^{26} +5.60470 q^{27} +0.511613 q^{28} -0.778586 q^{29} +1.30184 q^{30} -4.45016 q^{31} +1.00000 q^{32} +3.60241 q^{33} +2.86112 q^{34} -0.511613 q^{35} -1.30521 q^{36} +9.31124 q^{37} -5.33416 q^{38} -2.43042 q^{39} -1.00000 q^{40} -6.78500 q^{41} -0.666038 q^{42} +7.76292 q^{43} -2.76717 q^{44} +1.30521 q^{45} +6.87494 q^{46} -3.86374 q^{47} -1.30184 q^{48} -6.73825 q^{49} +1.00000 q^{50} -3.72473 q^{51} +1.86691 q^{52} -13.5175 q^{53} +5.60470 q^{54} +2.76717 q^{55} +0.511613 q^{56} +6.94423 q^{57} -0.778586 q^{58} +5.31563 q^{59} +1.30184 q^{60} +9.06356 q^{61} -4.45016 q^{62} -0.667762 q^{63} +1.00000 q^{64} -1.86691 q^{65} +3.60241 q^{66} +0.425747 q^{67} +2.86112 q^{68} -8.95008 q^{69} -0.511613 q^{70} -5.77829 q^{71} -1.30521 q^{72} -5.03635 q^{73} +9.31124 q^{74} -1.30184 q^{75} -5.33416 q^{76} -1.41572 q^{77} -2.43042 q^{78} -8.28529 q^{79} -1.00000 q^{80} -3.38080 q^{81} -6.78500 q^{82} -1.66411 q^{83} -0.666038 q^{84} -2.86112 q^{85} +7.76292 q^{86} +1.01360 q^{87} -2.76717 q^{88} -3.59998 q^{89} +1.30521 q^{90} +0.955136 q^{91} +6.87494 q^{92} +5.79339 q^{93} -3.86374 q^{94} +5.33416 q^{95} -1.30184 q^{96} -4.07748 q^{97} -6.73825 q^{98} +3.61173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * 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
$3$	−1.30184	−0.751618	−0.375809	−	0.926697i	$-0.622635\pi$
$3$	−1.30184	−0.751618	−0.375809	+	0.926697i	$0.622635\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.30184	−0.531474
$7$	0.511613	0.193371	0.0966857	−	0.995315i	$-0.469176\pi$
$7$	0.511613	0.193371	0.0966857	+	0.995315i	$0.469176\pi$
$8$	1.00000	0.353553
$9$	−1.30521	−0.435070
$10$	−1.00000	−0.316228
$11$	−2.76717	−0.834332	−0.417166	−	0.908830i	$-0.636977\pi$
$11$	−2.76717	−0.834332	−0.417166	+	0.908830i	$0.636977\pi$
$12$	−1.30184	−0.375809
$13$	1.86691	0.517788	0.258894	−	0.965906i	$-0.416642\pi$
$13$	1.86691	0.517788	0.258894	+	0.965906i	$0.416642\pi$
$14$	0.511613	0.136734
$15$	1.30184	0.336134
$16$	1.00000	0.250000
$17$	2.86112	0.693924	0.346962	−	0.937879i	$-0.387213\pi$
$17$	2.86112	0.693924	0.346962	+	0.937879i	$0.387213\pi$
$18$	−1.30521	−0.307641
$19$	−5.33416	−1.22374	−0.611870	−	0.790958i	$-0.709582\pi$
$19$	−5.33416	−1.22374	−0.611870	+	0.790958i	$0.709582\pi$
$20$	−1.00000	−0.223607
$21$	−0.666038	−0.145341
$22$	−2.76717	−0.589962
$23$	6.87494	1.43352	0.716762	−	0.697317i	$-0.245623\pi$
$23$	6.87494	1.43352	0.716762	+	0.697317i	$0.245623\pi$
$24$	−1.30184	−0.265737
$25$	1.00000	0.200000
$26$	1.86691	0.366132
$27$	5.60470	1.07862
$28$	0.511613	0.0966857
$29$	−0.778586	−0.144580	−0.0722899	−	0.997384i	$-0.523031\pi$
$29$	−0.778586	−0.144580	−0.0722899	+	0.997384i	$0.523031\pi$
$30$	1.30184	0.237683
$31$	−4.45016	−0.799272	−0.399636	−	0.916674i	$-0.630863\pi$
$31$	−4.45016	−0.799272	−0.399636	+	0.916674i	$0.630863\pi$
$32$	1.00000	0.176777
$33$	3.60241	0.627099
$34$	2.86112	0.490679
$35$	−0.511613	−0.0864783
$36$	−1.30521	−0.217535
$37$	9.31124	1.53076	0.765379	−	0.643579i	$-0.222551\pi$
$37$	9.31124	1.53076	0.765379	+	0.643579i	$0.222551\pi$
$38$	−5.33416	−0.865315
$39$	−2.43042	−0.389179
$40$	−1.00000	−0.158114
$41$	−6.78500	−1.05964	−0.529819	−	0.848111i	$-0.677740\pi$
$41$	−6.78500	−1.05964	−0.529819	+	0.848111i	$0.677740\pi$
$42$	−0.666038	−0.102772
$43$	7.76292	1.18383	0.591917	−	0.805999i	$-0.298371\pi$
$43$	7.76292	1.18383	0.591917	+	0.805999i	$0.298371\pi$
$44$	−2.76717	−0.417166
$45$	1.30521	0.194569
$46$	6.87494	1.01366
$47$	−3.86374	−0.563584	−0.281792	−	0.959476i	$-0.590929\pi$
$47$	−3.86374	−0.563584	−0.281792	+	0.959476i	$0.590929\pi$
$48$	−1.30184	−0.187905
$49$	−6.73825	−0.962608
$50$	1.00000	0.141421
$51$	−3.72473	−0.521566
$52$	1.86691	0.258894
$53$	−13.5175	−1.85677	−0.928386	−	0.371617i	$-0.878803\pi$
$53$	−13.5175	−1.85677	−0.928386	+	0.371617i	$0.878803\pi$
$54$	5.60470	0.762703
$55$	2.76717	0.373125
$56$	0.511613	0.0683671
$57$	6.94423	0.919785
$58$	−0.778586	−0.102233
$59$	5.31563	0.692036	0.346018	−	0.938228i	$-0.387534\pi$
$59$	5.31563	0.692036	0.346018	+	0.938228i	$0.387534\pi$
$60$	1.30184	0.168067
$61$	9.06356	1.16047	0.580235	−	0.814449i	$-0.302961\pi$
$61$	9.06356	1.16047	0.580235	+	0.814449i	$0.302961\pi$
$62$	−4.45016	−0.565170
$63$	−0.667762	−0.0841301
$64$	1.00000	0.125000
$65$	−1.86691	−0.231562
$66$	3.60241	0.443426
$67$	0.425747	0.0520133	0.0260066	−	0.999662i	$-0.491721\pi$
$67$	0.425747	0.0520133	0.0260066	+	0.999662i	$0.491721\pi$
$68$	2.86112	0.346962
$69$	−8.95008	−1.07746
$70$	−0.511613	−0.0611494
$71$	−5.77829	−0.685757	−0.342879	−	0.939380i	$-0.611402\pi$
$71$	−5.77829	−0.685757	−0.342879	+	0.939380i	$0.611402\pi$
$72$	−1.30521	−0.153820
$73$	−5.03635	−0.589460	−0.294730	−	0.955581i	$-0.595230\pi$
$73$	−5.03635	−0.589460	−0.294730	+	0.955581i	$0.595230\pi$
$74$	9.31124	1.08241
$75$	−1.30184	−0.150324
$76$	−5.33416	−0.611870
$77$	−1.41572	−0.161336
$78$	−2.43042	−0.275191
$79$	−8.28529	−0.932168	−0.466084	−	0.884740i	$-0.654336\pi$
$79$	−8.28529	−0.932168	−0.466084	+	0.884740i	$0.654336\pi$
$80$	−1.00000	−0.111803
$81$	−3.38080	−0.375644
$82$	−6.78500	−0.749278
$83$	−1.66411	−0.182660	−0.0913301	−	0.995821i	$-0.529112\pi$
$83$	−1.66411	−0.182660	−0.0913301	+	0.995821i	$0.529112\pi$
$84$	−0.666038	−0.0726707
$85$	−2.86112	−0.310332
$86$	7.76292	0.837097
$87$	1.01360	0.108669
$88$	−2.76717	−0.294981
$89$	−3.59998	−0.381597	−0.190799	−	0.981629i	$-0.561108\pi$
$89$	−3.59998	−0.381597	−0.190799	+	0.981629i	$0.561108\pi$
$90$	1.30521	0.137581
$91$	0.955136	0.100125
$92$	6.87494	0.716762
$93$	5.79339	0.600747
$94$	−3.86374	−0.398514
$95$	5.33416	0.547273
$96$	−1.30184	−0.132869
$97$	−4.07748	−0.414005	−0.207003	−	0.978340i	$-0.566371\pi$
$97$	−4.07748	−0.414005	−0.207003	+	0.978340i	$0.566371\pi$
$98$	−6.73825	−0.680666
$99$	3.61173	0.362993
$100$	1.00000	0.100000
$101$	−12.0161	−1.19564	−0.597822	−	0.801629i	$-0.703967\pi$
$101$	−12.0161	−1.19564	−0.597822	+	0.801629i	$0.703967\pi$
$102$	−3.72473	−0.368803
$103$	12.3606	1.21793	0.608964	−	0.793198i	$-0.291585\pi$
$103$	12.3606	1.21793	0.608964	+	0.793198i	$0.291585\pi$
$104$	1.86691	0.183066
$105$	0.666038	0.0649987
$106$	−13.5175	−1.31294
$107$	−11.2350	−1.08612	−0.543062	−	0.839693i	$-0.682735\pi$
$107$	−11.2350	−1.08612	−0.543062	+	0.839693i	$0.682735\pi$
$108$	5.60470	0.539312
$109$	−11.0248	−1.05599	−0.527994	−	0.849248i	$-0.677056\pi$
$109$	−11.0248	−1.05599	−0.527994	+	0.849248i	$0.677056\pi$
$110$	2.76717	0.263839
$111$	−12.1218	−1.15055
$112$	0.511613	0.0483428
$113$	6.90198	0.649283	0.324642	−	0.945837i	$-0.394756\pi$
$113$	6.90198	0.649283	0.324642	+	0.945837i	$0.394756\pi$
$114$	6.94423	0.650386
$115$	−6.87494	−0.641092
$116$	−0.778586	−0.0722899
$117$	−2.43671	−0.225274
$118$	5.31563	0.489344
$119$	1.46379	0.134185
$120$	1.30184	0.118841
$121$	−3.34279	−0.303890
$122$	9.06356	0.820577
$123$	8.83299	0.796444
$124$	−4.45016	−0.399636
$125$	−1.00000	−0.0894427
$126$	−0.667762	−0.0594890
$127$	11.1340	0.987980	0.493990	−	0.869467i	$-0.335538\pi$
$127$	11.1340	0.987980	0.493990	+	0.869467i	$0.335538\pi$
$128$	1.00000	0.0883883
$129$	−10.1061	−0.889791
$130$	−1.86691	−0.163739
$131$	−15.3600	−1.34201	−0.671007	−	0.741451i	$-0.734138\pi$
$131$	−15.3600	−1.34201	−0.671007	+	0.741451i	$0.734138\pi$
$132$	3.60241	0.313549
$133$	−2.72902	−0.236636
$134$	0.425747	0.0367789
$135$	−5.60470	−0.482376
$136$	2.86112	0.245339
$137$	−10.4562	−0.893332	−0.446666	−	0.894701i	$-0.647389\pi$
$137$	−10.4562	−0.893332	−0.446666	+	0.894701i	$0.647389\pi$
$138$	−8.95008	−0.761882
$139$	−23.0323	−1.95357	−0.976787	−	0.214213i	$-0.931281\pi$
$139$	−23.0323	−1.95357	−0.976787	+	0.214213i	$0.931281\pi$
$140$	−0.511613	−0.0432391
$141$	5.02997	0.423600
$142$	−5.77829	−0.484903
$143$	−5.16606	−0.432007
$144$	−1.30521	−0.108768
$145$	0.778586	0.0646581
$146$	−5.03635	−0.416811
$147$	8.77213	0.723513
$148$	9.31124	0.765379
$149$	−7.72970	−0.633242	−0.316621	−	0.948552i	$-0.602548\pi$
$149$	−7.72970	−0.633242	−0.316621	+	0.948552i	$0.602548\pi$
$150$	−1.30184	−0.106295
$151$	16.2204	1.32000	0.660000	−	0.751266i	$-0.270556\pi$
$151$	16.2204	1.32000	0.660000	+	0.751266i	$0.270556\pi$
$152$	−5.33416	−0.432657
$153$	−3.73437	−0.301906
$154$	−1.41572	−0.114082
$155$	4.45016	0.357445
$156$	−2.43042	−0.194590
$157$	−3.96919	−0.316776	−0.158388	−	0.987377i	$-0.550630\pi$
$157$	−3.96919	−0.316776	−0.158388	+	0.987377i	$0.550630\pi$
$158$	−8.28529	−0.659142
$159$	17.5976	1.39558
$160$	−1.00000	−0.0790569
$161$	3.51731	0.277203
$162$	−3.38080	−0.265620
$163$	−7.56172	−0.592280	−0.296140	−	0.955145i	$-0.595699\pi$
$163$	−7.56172	−0.592280	−0.296140	+	0.955145i	$0.595699\pi$
$164$	−6.78500	−0.529819
$165$	−3.60241	−0.280447
$166$	−1.66411	−0.129160
$167$	−9.44054	−0.730531	−0.365265	−	0.930903i	$-0.619022\pi$
$167$	−9.44054	−0.730531	−0.365265	+	0.930903i	$0.619022\pi$
$168$	−0.666038	−0.0513860
$169$	−9.51464	−0.731895
$170$	−2.86112	−0.219438
$171$	6.96220	0.532413
$172$	7.76292	0.591917
$173$	6.75561	0.513620	0.256810	−	0.966462i	$-0.417329\pi$
$173$	6.75561	0.513620	0.256810	+	0.966462i	$0.417329\pi$
$174$	1.01360	0.0768405
$175$	0.511613	0.0386743
$176$	−2.76717	−0.208583
$177$	−6.92011	−0.520147
$178$	−3.59998	−0.269830
$179$	4.60124	0.343913	0.171957	−	0.985105i	$-0.444991\pi$
$179$	4.60124	0.343913	0.171957	+	0.985105i	$0.444991\pi$
$180$	1.30521	0.0972846
$181$	5.52301	0.410522	0.205261	−	0.978707i	$-0.434196\pi$
$181$	5.52301	0.410522	0.205261	+	0.978707i	$0.434196\pi$
$182$	0.955136	0.0707994
$183$	−11.7993	−0.872231
$184$	6.87494	0.506828
$185$	−9.31124	−0.684576
$186$	5.79339	0.424792
$187$	−7.91720	−0.578963
$188$	−3.86374	−0.281792
$189$	2.86743	0.208575
$190$	5.33416	0.386981
$191$	−8.39085	−0.607141	−0.303570	−	0.952809i	$-0.598179\pi$
$191$	−8.39085	−0.607141	−0.303570	+	0.952809i	$0.598179\pi$
$192$	−1.30184	−0.0939523
$193$	−6.83295	−0.491847	−0.245923	−	0.969289i	$-0.579091\pi$
$193$	−6.83295	−0.491847	−0.245923	+	0.969289i	$0.579091\pi$
$194$	−4.07748	−0.292746
$195$	2.43042	0.174046
$196$	−6.73825	−0.481304
$197$	7.96232	0.567292	0.283646	−	0.958929i	$-0.408456\pi$
$197$	7.96232	0.567292	0.283646	+	0.958929i	$0.408456\pi$
$198$	3.61173	0.256675
$199$	10.7652	0.763124	0.381562	−	0.924343i	$-0.375386\pi$
$199$	10.7652	0.763124	0.381562	+	0.924343i	$0.375386\pi$
$200$	1.00000	0.0707107
$201$	−0.554255	−0.0390941
$202$	−12.0161	−0.845448
$203$	−0.398335	−0.0279576
$204$	−3.72473	−0.260783
$205$	6.78500	0.473885
$206$	12.3606	0.861205
$207$	−8.97325	−0.623684
$208$	1.86691	0.129447
$209$	14.7605	1.02101
$210$	0.666038	0.0459610
$211$	19.3981	1.33542	0.667710	−	0.744421i	$-0.267275\pi$
$211$	19.3981	1.33542	0.667710	+	0.744421i	$0.267275\pi$
$212$	−13.5175	−0.928386
$213$	7.52242	0.515428
$214$	−11.2350	−0.768006
$215$	−7.76292	−0.529427
$216$	5.60470	0.381351
$217$	−2.27676	−0.154556
$218$	−11.0248	−0.746696
$219$	6.55652	0.443049
$220$	2.76717	0.186562
$221$	5.34147	0.359306
$222$	−12.1218	−0.813559
$223$	−22.2725	−1.49148	−0.745738	−	0.666239i	$-0.767903\pi$
$223$	−22.2725	−1.49148	−0.745738	+	0.666239i	$0.767903\pi$
$224$	0.511613	0.0341835
$225$	−1.30521	−0.0870140
$226$	6.90198	0.459113
$227$	22.4936	1.49295	0.746476	−	0.665412i	$-0.231744\pi$
$227$	22.4936	1.49295	0.746476	+	0.665412i	$0.231744\pi$
$228$	6.94423	0.459893
$229$	−18.5908	−1.22851	−0.614257	−	0.789106i	$-0.710544\pi$
$229$	−18.5908	−1.22851	−0.614257	+	0.789106i	$0.710544\pi$
$230$	−6.87494	−0.453320
$231$	1.84304	0.121263
$232$	−0.778586	−0.0511167
$233$	−3.85904	−0.252814	−0.126407	−	0.991978i	$-0.540345\pi$
$233$	−3.85904	−0.252814	−0.126407	+	0.991978i	$0.540345\pi$
$234$	−2.43671	−0.159293
$235$	3.86374	0.252042
$236$	5.31563	0.346018
$237$	10.7861	0.700635
$238$	1.46379	0.0948832
$239$	25.1783	1.62865	0.814324	−	0.580411i	$-0.197108\pi$
$239$	25.1783	1.62865	0.814324	+	0.580411i	$0.197108\pi$
$240$	1.30184	0.0840335
$241$	−17.9583	−1.15680	−0.578399	−	0.815754i	$-0.696322\pi$
$241$	−17.9583	−1.15680	−0.578399	+	0.815754i	$0.696322\pi$
$242$	−3.34279	−0.214883
$243$	−12.4128	−0.796284
$244$	9.06356	0.580235
$245$	6.73825	0.430491
$246$	8.83299	0.563171
$247$	−9.95841	−0.633638
$248$	−4.45016	−0.282585
$249$	2.16641	0.137291
$250$	−1.00000	−0.0632456
$251$	−1.20387	−0.0759873	−0.0379937	−	0.999278i	$-0.512097\pi$
$251$	−1.20387	−0.0759873	−0.0379937	+	0.999278i	$0.512097\pi$
$252$	−0.667762	−0.0420650
$253$	−19.0241	−1.19604
$254$	11.1340	0.698608
$255$	3.72473	0.233252
$256$	1.00000	0.0625000
$257$	8.26683	0.515671	0.257835	−	0.966189i	$-0.416991\pi$
$257$	8.26683	0.515671	0.257835	+	0.966189i	$0.416991\pi$
$258$	−10.1061	−0.629178
$259$	4.76375	0.296005
$260$	−1.86691	−0.115781
$261$	1.01622	0.0629024
$262$	−15.3600	−0.948947
$263$	−22.3622	−1.37891	−0.689455	−	0.724329i	$-0.742150\pi$
$263$	−22.3622	−1.37891	−0.689455	+	0.724329i	$0.742150\pi$
$264$	3.60241	0.221713
$265$	13.5175	0.830374
$266$	−2.72902	−0.167327
$267$	4.68661	0.286816
$268$	0.425747	0.0260066
$269$	−22.6589	−1.38154	−0.690769	−	0.723075i	$-0.742728\pi$
$269$	−22.6589	−1.38154	−0.690769	+	0.723075i	$0.742728\pi$
$270$	−5.60470	−0.341091
$271$	−17.7653	−1.07916	−0.539582	−	0.841933i	$-0.681418\pi$
$271$	−17.7653	−1.07916	−0.539582	+	0.841933i	$0.681418\pi$
$272$	2.86112	0.173481
$273$	−1.24344	−0.0752561
$274$	−10.4562	−0.631681
$275$	−2.76717	−0.166866
$276$	−8.95008	−0.538732
$277$	−6.47119	−0.388816	−0.194408	−	0.980921i	$-0.562279\pi$
$277$	−6.47119	−0.388816	−0.194408	+	0.980921i	$0.562279\pi$
$278$	−23.0323	−1.38139
$279$	5.80839	0.347739
$280$	−0.511613	−0.0305747
$281$	21.5317	1.28447	0.642236	−	0.766507i	$-0.278007\pi$
$281$	21.5317	1.28447	0.642236	+	0.766507i	$0.278007\pi$
$282$	5.02997	0.299530
$283$	−18.2524	−1.08500	−0.542498	−	0.840057i	$-0.682521\pi$
$283$	−18.2524	−1.08500	−0.542498	+	0.840057i	$0.682521\pi$
$284$	−5.77829	−0.342879
$285$	−6.94423	−0.411340
$286$	−5.16606	−0.305475
$287$	−3.47129	−0.204904
$288$	−1.30521	−0.0769102
$289$	−8.81397	−0.518469
$290$	0.778586	0.0457202
$291$	5.30823	0.311174
$292$	−5.03635	−0.294730
$293$	12.6182	0.737161	0.368580	−	0.929596i	$-0.379844\pi$
$293$	12.6182	0.737161	0.368580	+	0.929596i	$0.379844\pi$
$294$	8.77213	0.511601
$295$	−5.31563	−0.309488
$296$	9.31124	0.541205
$297$	−15.5091	−0.899931
$298$	−7.72970	−0.447769
$299$	12.8349	0.742263
$300$	−1.30184	−0.0751618
$301$	3.97161	0.228920
$302$	16.2204	0.933381
$303$	15.6430	0.898668
$304$	−5.33416	−0.305935
$305$	−9.06356	−0.518978
$306$	−3.73437	−0.213480
$307$	13.5012	0.770552	0.385276	−	0.922801i	$-0.374106\pi$
$307$	13.5012	0.770552	0.385276	+	0.922801i	$0.374106\pi$
$308$	−1.41572	−0.0806679
$309$	−16.0916	−0.915417
$310$	4.45016	0.252752
$311$	−2.05211	−0.116364	−0.0581822	−	0.998306i	$-0.518530\pi$
$311$	−2.05211	−0.116364	−0.0581822	+	0.998306i	$0.518530\pi$
$312$	−2.43042	−0.137596
$313$	−29.7025	−1.67888	−0.839442	−	0.543450i	$-0.817118\pi$
$313$	−29.7025	−1.67888	−0.839442	+	0.543450i	$0.817118\pi$
$314$	−3.96919	−0.223994
$315$	0.667762	0.0376241
$316$	−8.28529	−0.466084
$317$	10.3940	0.583784	0.291892	−	0.956451i	$-0.405715\pi$
$317$	10.3940	0.583784	0.291892	+	0.956451i	$0.405715\pi$
$318$	17.5976	0.986827
$319$	2.15448	0.120628
$320$	−1.00000	−0.0559017
$321$	14.6261	0.816351
$322$	3.51731	0.196012
$323$	−15.2617	−0.849183
$324$	−3.38080	−0.187822
$325$	1.86691	0.103558
$326$	−7.56172	−0.418805
$327$	14.3526	0.793700
$328$	−6.78500	−0.374639
$329$	−1.97674	−0.108981
$330$	−3.60241	−0.198306
$331$	−1.80093	−0.0989880	−0.0494940	−	0.998774i	$-0.515761\pi$
$331$	−1.80093	−0.0989880	−0.0494940	+	0.998774i	$0.515761\pi$
$332$	−1.66411	−0.0913301
$333$	−12.1531	−0.665987
$334$	−9.44054	−0.516563
$335$	−0.425747	−0.0232610
$336$	−0.666038	−0.0363354
$337$	−11.6109	−0.632485	−0.316242	−	0.948678i	$-0.602421\pi$
$337$	−11.6109	−0.632485	−0.316242	+	0.948678i	$0.602421\pi$
$338$	−9.51464	−0.517528
$339$	−8.98528	−0.488013
$340$	−2.86112	−0.155166
$341$	12.3143	0.666858
$342$	6.96220	0.376473
$343$	−7.02866	−0.379512
$344$	7.76292	0.418549
$345$	8.95008	0.481856
$346$	6.75561	0.363184
$347$	−10.6748	−0.573054	−0.286527	−	0.958072i	$-0.592501\pi$
$347$	−10.6748	−0.573054	−0.286527	+	0.958072i	$0.592501\pi$
$348$	1.01360	0.0543344
$349$	−1.56401	−0.0837195	−0.0418598	−	0.999123i	$-0.513328\pi$
$349$	−1.56401	−0.0837195	−0.0418598	+	0.999123i	$0.513328\pi$
$350$	0.511613	0.0273468
$351$	10.4635	0.558499
$352$	−2.76717	−0.147490
$353$	−2.47014	−0.131472	−0.0657360	−	0.997837i	$-0.520940\pi$
$353$	−2.47014	−0.131472	−0.0657360	+	0.997837i	$0.520940\pi$
$354$	−6.92011	−0.367800
$355$	5.77829	0.306680
$356$	−3.59998	−0.190799
$357$	−1.90562	−0.100856
$358$	4.60124	0.243183
$359$	−25.1351	−1.32658	−0.663291	−	0.748362i	$-0.730841\pi$
$359$	−25.1351	−1.32658	−0.663291	+	0.748362i	$0.730841\pi$
$360$	1.30521	0.0687906
$361$	9.45325	0.497539
$362$	5.52301	0.290283
$363$	4.35179	0.228410
$364$	0.955136	0.0500627
$365$	5.03635	0.263614
$366$	−11.7993	−0.616760
$367$	25.2607	1.31860	0.659298	−	0.751882i	$-0.270853\pi$
$367$	25.2607	1.31860	0.659298	+	0.751882i	$0.270853\pi$
$368$	6.87494	0.358381
$369$	8.85585	0.461017
$370$	−9.31124	−0.484068
$371$	−6.91573	−0.359047
$372$	5.79339	0.300374
$373$	−2.45720	−0.127229	−0.0636146	−	0.997975i	$-0.520263\pi$
$373$	−2.45720	−0.127229	−0.0636146	+	0.997975i	$0.520263\pi$
$374$	−7.91720	−0.409389
$375$	1.30184	0.0672268
$376$	−3.86374	−0.199257
$377$	−1.45355	−0.0748618
$378$	2.86743	0.147485
$379$	4.37297	0.224624	0.112312	−	0.993673i	$-0.464174\pi$
$379$	4.37297	0.224624	0.112312	+	0.993673i	$0.464174\pi$
$380$	5.33416	0.273637
$381$	−14.4947	−0.742584
$382$	−8.39085	−0.429313
$383$	19.9828	1.02107	0.510537	−	0.859856i	$-0.329447\pi$
$383$	19.9828	1.02107	0.510537	+	0.859856i	$0.329447\pi$
$384$	−1.30184	−0.0664343
$385$	1.41572	0.0721516
$386$	−6.83295	−0.347788
$387$	−10.1322	−0.515051
$388$	−4.07748	−0.207003
$389$	15.2304	0.772213	0.386107	−	0.922454i	$-0.373820\pi$
$389$	15.2304	0.772213	0.386107	+	0.922454i	$0.373820\pi$
$390$	2.43042	0.123069
$391$	19.6701	0.994758
$392$	−6.73825	−0.340333
$393$	19.9963	1.00868
$394$	7.96232	0.401136
$395$	8.28529	0.416878
$396$	3.61173	0.181496
$397$	17.4686	0.876726	0.438363	−	0.898798i	$-0.355558\pi$
$397$	17.4686	0.876726	0.438363	+	0.898798i	$0.355558\pi$
$398$	10.7652	0.539610
$399$	3.55275	0.177860
$400$	1.00000	0.0500000
$401$	−5.81171	−0.290223	−0.145112	−	0.989415i	$-0.546354\pi$
$401$	−5.81171	−0.290223	−0.145112	+	0.989415i	$0.546354\pi$
$402$	−0.554255	−0.0276437
$403$	−8.30805	−0.413854
$404$	−12.0161	−0.597822
$405$	3.38080	0.167993
$406$	−0.398335	−0.0197690
$407$	−25.7657	−1.27716
$408$	−3.72473	−0.184402
$409$	−12.9038	−0.638051	−0.319025	−	0.947746i	$-0.603356\pi$
$409$	−12.9038	−0.638051	−0.319025	+	0.947746i	$0.603356\pi$
$410$	6.78500	0.335087
$411$	13.6123	0.671444
$412$	12.3606	0.608964
$413$	2.71954	0.133820
$414$	−8.97325	−0.441011
$415$	1.66411	0.0816881
$416$	1.86691	0.0915329
$417$	29.9844	1.46834
$418$	14.7605	0.721960
$419$	−24.4309	−1.19353	−0.596763	−	0.802417i	$-0.703547\pi$
$419$	−24.4309	−1.19353	−0.596763	+	0.802417i	$0.703547\pi$
$420$	0.666038	0.0324993
$421$	−10.1115	−0.492805	−0.246402	−	0.969168i	$-0.579248\pi$
$421$	−10.1115	−0.492805	−0.246402	+	0.969168i	$0.579248\pi$
$422$	19.3981	0.944285
$423$	5.04299	0.245198
$424$	−13.5175	−0.656468
$425$	2.86112	0.138785
$426$	7.52242	0.364462
$427$	4.63703	0.224402
$428$	−11.2350	−0.543062
$429$	6.72538	0.324705
$430$	−7.76292	−0.374361
$431$	8.88491	0.427971	0.213985	−	0.976837i	$-0.431355\pi$
$431$	8.88491	0.427971	0.213985	+	0.976837i	$0.431355\pi$
$432$	5.60470	0.269656
$433$	6.83796	0.328611	0.164306	−	0.986409i	$-0.447462\pi$
$433$	6.83796	0.328611	0.164306	+	0.986409i	$0.447462\pi$
$434$	−2.27676	−0.109288
$435$	−1.01360	−0.0485982
$436$	−11.0248	−0.527994
$437$	−36.6720	−1.75426
$438$	6.55652	0.313283
$439$	24.7300	1.18030	0.590149	−	0.807295i	$-0.299069\pi$
$439$	24.7300	1.18030	0.590149	+	0.807295i	$0.299069\pi$
$440$	2.76717	0.131919
$441$	8.79484	0.418802
$442$	5.34147	0.254068
$443$	6.18029	0.293634	0.146817	−	0.989164i	$-0.453097\pi$
$443$	6.18029	0.293634	0.146817	+	0.989164i	$0.453097\pi$
$444$	−12.1218	−0.575273
$445$	3.59998	0.170656
$446$	−22.2725	−1.05463
$447$	10.0628	0.475956
$448$	0.511613	0.0241714
$449$	−16.4506	−0.776351	−0.388175	−	0.921585i	$-0.626895\pi$
$449$	−16.4506	−0.776351	−0.388175	+	0.921585i	$0.626895\pi$
$450$	−1.30521	−0.0615282
$451$	18.7752	0.884090
$452$	6.90198	0.324642
$453$	−21.1164	−0.992136
$454$	22.4936	1.05568
$455$	−0.955136	−0.0447775
$456$	6.94423	0.325193
$457$	−25.2094	−1.17925	−0.589623	−	0.807679i	$-0.700724\pi$
$457$	−25.2094	−1.17925	−0.589623	+	0.807679i	$0.700724\pi$
$458$	−18.5908	−0.868690
$459$	16.0357	0.748484
$460$	−6.87494	−0.320546
$461$	5.48340	0.255388	0.127694	−	0.991814i	$-0.459243\pi$
$461$	5.48340	0.255388	0.127694	+	0.991814i	$0.459243\pi$
$462$	1.84304	0.0857459
$463$	4.81067	0.223571	0.111785	−	0.993732i	$-0.464343\pi$
$463$	4.81067	0.223571	0.111785	+	0.993732i	$0.464343\pi$
$464$	−0.778586	−0.0361450
$465$	−5.79339	−0.268662
$466$	−3.85904	−0.178767
$467$	−18.3643	−0.849800	−0.424900	−	0.905240i	$-0.639691\pi$
$467$	−18.3643	−0.849800	−0.424900	+	0.905240i	$0.639691\pi$
$468$	−2.43671	−0.112637
$469$	0.217818	0.0100579
$470$	3.86374	0.178221
$471$	5.16725	0.238094
$472$	5.31563	0.244672
$473$	−21.4813	−0.987711
$474$	10.7861	0.495423
$475$	−5.33416	−0.244748
$476$	1.46379	0.0670926
$477$	17.6432	0.807826
$478$	25.1783	1.15163
$479$	−19.2009	−0.877309	−0.438655	−	0.898656i	$-0.644545\pi$
$479$	−19.2009	−0.877309	−0.438655	+	0.898656i	$0.644545\pi$
$480$	1.30184	0.0594206
$481$	17.3833	0.792609
$482$	−17.9583	−0.817980
$483$	−4.57897	−0.208351
$484$	−3.34279	−0.151945
$485$	4.07748	0.185149
$486$	−12.4128	−0.563058
$487$	−12.1262	−0.549489	−0.274745	−	0.961517i	$-0.588593\pi$
$487$	−12.1262	−0.549489	−0.274745	+	0.961517i	$0.588593\pi$
$488$	9.06356	0.410288
$489$	9.84416	0.445168
$490$	6.73825	0.304403
$491$	3.87065	0.174680	0.0873401	−	0.996179i	$-0.472163\pi$
$491$	3.87065	0.174680	0.0873401	+	0.996179i	$0.472163\pi$
$492$	8.83299	0.398222
$493$	−2.22763	−0.100328
$494$	−9.95841	−0.448050
$495$	−3.61173	−0.162335
$496$	−4.45016	−0.199818
$497$	−2.95625	−0.132606
$498$	2.16641	0.0970792
$499$	−11.8944	−0.532468	−0.266234	−	0.963908i	$-0.585779\pi$
$499$	−11.8944	−0.532468	−0.266234	+	0.963908i	$0.585779\pi$
$500$	−1.00000	−0.0447214
$501$	12.2901	0.549080
$502$	−1.20387	−0.0537312
$503$	−31.7051	−1.41366	−0.706830	−	0.707383i	$-0.749876\pi$
$503$	−31.7051	−1.41366	−0.706830	+	0.707383i	$0.749876\pi$
$504$	−0.667762	−0.0297445
$505$	12.0161	0.534708
$506$	−19.0241	−0.845725
$507$	12.3865	0.550106
$508$	11.1340	0.493990
$509$	2.96721	0.131519	0.0657596	−	0.997835i	$-0.479053\pi$
$509$	2.96721	0.131519	0.0657596	+	0.997835i	$0.479053\pi$
$510$	3.72473	0.164934
$511$	−2.57666	−0.113985
$512$	1.00000	0.0441942
$513$	−29.8964	−1.31996
$514$	8.26683	0.364634
$515$	−12.3606	−0.544674
$516$	−10.1061	−0.444896
$517$	10.6916	0.470216
$518$	4.76375	0.209307
$519$	−8.79474	−0.386046
$520$	−1.86691	−0.0818695
$521$	−24.4037	−1.06915	−0.534573	−	0.845122i	$-0.679527\pi$
$521$	−24.4037	−1.06915	−0.534573	+	0.845122i	$0.679527\pi$
$522$	1.01622	0.0444787
$523$	−0.963832	−0.0421454	−0.0210727	−	0.999778i	$-0.506708\pi$
$523$	−0.963832	−0.0421454	−0.0210727	+	0.999778i	$0.506708\pi$
$524$	−15.3600	−0.671007
$525$	−0.666038	−0.0290683
$526$	−22.3622	−0.975036
$527$	−12.7324	−0.554634
$528$	3.60241	0.156775
$529$	24.2649	1.05499
$530$	13.5175	0.587163
$531$	−6.93802	−0.301084
$532$	−2.72902	−0.118318
$533$	−12.6670	−0.548669
$534$	4.68661	0.202809
$535$	11.2350	0.485729
$536$	0.425747	0.0183895
$537$	−5.99009	−0.258491
$538$	−22.6589	−0.976896
$539$	18.6459	0.803134
$540$	−5.60470	−0.241188
$541$	33.8791	1.45657	0.728287	−	0.685272i	$-0.240317\pi$
$541$	33.8791	1.45657	0.728287	+	0.685272i	$0.240317\pi$
$542$	−17.7653	−0.763084
$543$	−7.19008	−0.308556
$544$	2.86112	0.122670
$545$	11.0248	0.472252
$546$	−1.24344	−0.0532141
$547$	−8.19444	−0.350369	−0.175184	−	0.984536i	$-0.556052\pi$
$547$	−8.19444	−0.350369	−0.175184	+	0.984536i	$0.556052\pi$
$548$	−10.4562	−0.446666
$549$	−11.8299	−0.504886
$550$	−2.76717	−0.117992
$551$	4.15310	0.176928
$552$	−8.95008	−0.380941
$553$	−4.23886	−0.180255
$554$	−6.47119	−0.274935
$555$	12.1218	0.514540
$556$	−23.0323	−0.976787
$557$	25.9853	1.10103	0.550516	−	0.834825i	$-0.314431\pi$
$557$	25.9853	1.10103	0.550516	+	0.834825i	$0.314431\pi$
$558$	5.80839	0.245889
$559$	14.4927	0.612976
$560$	−0.511613	−0.0216196
$561$	10.3069	0.435159
$562$	21.5317	0.908259
$563$	−35.7510	−1.50672	−0.753362	−	0.657606i	$-0.771569\pi$
$563$	−35.7510	−1.50672	−0.753362	+	0.657606i	$0.771569\pi$
$564$	5.02997	0.211800
$565$	−6.90198	−0.290368
$566$	−18.2524	−0.767208
$567$	−1.72966	−0.0726388
$568$	−5.77829	−0.242452
$569$	−22.2468	−0.932636	−0.466318	−	0.884617i	$-0.654420\pi$
$569$	−22.2468	−0.932636	−0.466318	+	0.884617i	$0.654420\pi$
$570$	−6.94423	−0.290862
$571$	46.6655	1.95289	0.976445	−	0.215766i	$-0.0692250\pi$
$571$	46.6655	1.95289	0.976445	+	0.215766i	$0.0692250\pi$
$572$	−5.16606	−0.216004
$573$	10.9236	0.456338
$574$	−3.47129	−0.144889
$575$	6.87494	0.286705
$576$	−1.30521	−0.0543838
$577$	0.930996	0.0387579	0.0193789	−	0.999812i	$-0.493831\pi$
$577$	0.930996	0.0387579	0.0193789	+	0.999812i	$0.493831\pi$
$578$	−8.81397	−0.366613
$579$	8.89542	0.369681
$580$	0.778586	0.0323290
$581$	−0.851381	−0.0353212
$582$	5.30823	0.220033
$583$	37.4052	1.54916
$584$	−5.03635	−0.208405
$585$	2.43671	0.100746
$586$	12.6182	0.521251
$587$	42.5477	1.75613	0.878066	−	0.478540i	$-0.158834\pi$
$587$	42.5477	1.75613	0.878066	+	0.478540i	$0.158834\pi$
$588$	8.77213	0.361757
$589$	23.7378	0.978100
$590$	−5.31563	−0.218841
$591$	−10.3657	−0.426387
$592$	9.31124	0.382690
$593$	17.0955	0.702029	0.351014	−	0.936370i	$-0.385837\pi$
$593$	17.0955	0.702029	0.351014	+	0.936370i	$0.385837\pi$
$594$	−15.5091	−0.636347
$595$	−1.46379	−0.0600094
$596$	−7.72970	−0.316621
$597$	−14.0146	−0.573578
$598$	12.8349	0.524859
$599$	3.59940	0.147068	0.0735338	−	0.997293i	$-0.476572\pi$
$599$	3.59940	0.147068	0.0735338	+	0.997293i	$0.476572\pi$
$600$	−1.30184	−0.0531474
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	3.97161	0.161871
$603$	−0.555689	−0.0226294
$604$	16.2204	0.660000
$605$	3.34279	0.135904
$606$	15.6430	0.635454
$607$	45.2967	1.83853	0.919267	−	0.393634i	$-0.128782\pi$
$607$	45.2967	1.83853	0.919267	+	0.393634i	$0.128782\pi$
$608$	−5.33416	−0.216329
$609$	0.518568	0.0210134
$610$	−9.06356	−0.366973
$611$	−7.21326	−0.291817
$612$	−3.73437	−0.150953
$613$	−38.2982	−1.54685	−0.773426	−	0.633887i	$-0.781458\pi$
$613$	−38.2982	−1.54685	−0.773426	+	0.633887i	$0.781458\pi$
$614$	13.5012	0.544863
$615$	−8.83299	−0.356180
$616$	−1.41572	−0.0570408
$617$	23.1717	0.932859	0.466429	−	0.884559i	$-0.345540\pi$
$617$	23.1717	0.932859	0.466429	+	0.884559i	$0.345540\pi$
$618$	−16.0916	−0.647298
$619$	23.6047	0.948751	0.474376	−	0.880322i	$-0.342674\pi$
$619$	23.6047	0.948751	0.474376	+	0.880322i	$0.342674\pi$
$620$	4.45016	0.178723
$621$	38.5320	1.54624
$622$	−2.05211	−0.0822821
$623$	−1.84180	−0.0737900
$624$	−2.43042	−0.0972948
$625$	1.00000	0.0400000
$626$	−29.7025	−1.18715
$627$	−19.2158	−0.767406
$628$	−3.96919	−0.158388
$629$	26.6406	1.06223
$630$	0.667762	0.0266043
$631$	29.2626	1.16493	0.582463	−	0.812857i	$-0.302089\pi$
$631$	29.2626	1.16493	0.582463	+	0.812857i	$0.302089\pi$
$632$	−8.28529	−0.329571
$633$	−25.2532	−1.00373
$634$	10.3940	0.412798
$635$	−11.1340	−0.441838
$636$	17.5976	0.697792
$637$	−12.5797	−0.498427
$638$	2.15448	0.0852966
$639$	7.54189	0.298352
$640$	−1.00000	−0.0395285
$641$	−22.9929	−0.908166	−0.454083	−	0.890959i	$-0.650033\pi$
$641$	−22.9929	−0.908166	−0.454083	+	0.890959i	$0.650033\pi$
$642$	14.6261	0.577247
$643$	−17.3593	−0.684584	−0.342292	−	0.939594i	$-0.611203\pi$
$643$	−17.3593	−0.684584	−0.342292	+	0.939594i	$0.611203\pi$
$644$	3.51731	0.138601
$645$	10.1061	0.397927
$646$	−15.2617	−0.600463
$647$	−42.0535	−1.65329	−0.826647	−	0.562720i	$-0.809755\pi$
$647$	−42.0535	−1.65329	−0.826647	+	0.562720i	$0.809755\pi$
$648$	−3.38080	−0.132810
$649$	−14.7092	−0.577388
$650$	1.86691	0.0732263
$651$	2.96397	0.116167
$652$	−7.56172	−0.296140
$653$	−12.4136	−0.485783	−0.242891	−	0.970053i	$-0.578096\pi$
$653$	−12.4136	−0.485783	−0.242891	+	0.970053i	$0.578096\pi$
$654$	14.3526	0.561230
$655$	15.3600	0.600167
$656$	−6.78500	−0.264910
$657$	6.57349	0.256456
$658$	−1.97674	−0.0770612
$659$	−19.3043	−0.751990	−0.375995	−	0.926622i	$-0.622699\pi$
$659$	−19.3043	−0.751990	−0.375995	+	0.926622i	$0.622699\pi$
$660$	−3.60241	−0.140224
$661$	10.7828	0.419404	0.209702	−	0.977765i	$-0.432751\pi$
$661$	10.7828	0.419404	0.209702	+	0.977765i	$0.432751\pi$
$662$	−1.80093	−0.0699951
$663$	−6.95374	−0.270061
$664$	−1.66411	−0.0645801
$665$	2.72902	0.105827
$666$	−12.1531	−0.470924
$667$	−5.35274	−0.207259
$668$	−9.44054	−0.365265
$669$	28.9952	1.12102
$670$	−0.425747	−0.0164480
$671$	−25.0804	−0.968217
$672$	−0.666038	−0.0256930
$673$	−43.0462	−1.65931	−0.829654	−	0.558278i	$-0.811462\pi$
$673$	−43.0462	−1.65931	−0.829654	+	0.558278i	$0.811462\pi$
$674$	−11.6109	−0.447234
$675$	5.60470	0.215725
$676$	−9.51464	−0.365948
$677$	1.19214	0.0458177	0.0229088	−	0.999738i	$-0.492707\pi$
$677$	1.19214	0.0458177	0.0229088	+	0.999738i	$0.492707\pi$
$678$	−8.98528	−0.345077
$679$	−2.08609	−0.0800567
$680$	−2.86112	−0.109719
$681$	−29.2831	−1.12213
$682$	12.3143	0.471540
$683$	19.0843	0.730242	0.365121	−	0.930960i	$-0.381028\pi$
$683$	19.0843	0.730242	0.365121	+	0.930960i	$0.381028\pi$
$684$	6.96220	0.266206
$685$	10.4562	0.399510
$686$	−7.02866	−0.268356
$687$	24.2022	0.923373
$688$	7.76292	0.295959
$689$	−25.2360	−0.961415
$690$	8.95008	0.340724
$691$	−6.10107	−0.232096	−0.116048	−	0.993244i	$-0.537023\pi$
$691$	−6.10107	−0.232096	−0.116048	+	0.993244i	$0.537023\pi$
$692$	6.75561	0.256810
$693$	1.84781	0.0701924
$694$	−10.6748	−0.405210
$695$	23.0323	0.873665
$696$	1.01360	0.0384202
$697$	−19.4127	−0.735309
$698$	−1.56401	−0.0591987
$699$	5.02386	0.190020
$700$	0.511613	0.0193371
$701$	−45.4995	−1.71849	−0.859247	−	0.511561i	$-0.829067\pi$
$701$	−45.4995	−1.71849	−0.859247	+	0.511561i	$0.829067\pi$
$702$	10.4635	0.394919
$703$	−49.6676	−1.87325
$704$	−2.76717	−0.104291
$705$	−5.02997	−0.189440
$706$	−2.47014	−0.0929648
$707$	−6.14757	−0.231203
$708$	−6.92011	−0.260074
$709$	38.2818	1.43770	0.718852	−	0.695163i	$-0.244668\pi$
$709$	38.2818	1.43770	0.718852	+	0.695163i	$0.244668\pi$
$710$	5.77829	0.216855
$711$	10.8140	0.405558
$712$	−3.59998	−0.134915
$713$	−30.5946	−1.14578
$714$	−1.90562	−0.0713159
$715$	5.16606	0.193200
$716$	4.60124	0.171957
$717$	−32.7781	−1.22412
$718$	−25.1351	−0.938035
$719$	−27.3302	−1.01924	−0.509622	−	0.860398i	$-0.670215\pi$
$719$	−27.3302	−1.01924	−0.509622	+	0.860398i	$0.670215\pi$
$720$	1.30521	0.0486423
$721$	6.32385	0.235512
$722$	9.45325	0.351813
$723$	23.3789	0.869471
$724$	5.52301	0.205261
$725$	−0.778586	−0.0289160
$726$	4.35179	0.161510
$727$	29.3214	1.08747	0.543736	−	0.839256i	$-0.317009\pi$
$727$	29.3214	1.08747	0.543736	+	0.839256i	$0.317009\pi$
$728$	0.955136	0.0353997
$729$	26.3019	0.974145
$730$	5.03635	0.186404
$731$	22.2107	0.821492
$732$	−11.7993	−0.436115
$733$	41.1760	1.52087	0.760435	−	0.649414i	$-0.224986\pi$
$733$	41.1760	1.52087	0.760435	+	0.649414i	$0.224986\pi$
$734$	25.2607	0.932388
$735$	−8.77213	−0.323565
$736$	6.87494	0.253414
$737$	−1.17811	−0.0433963
$738$	8.85585	0.325988
$739$	2.58316	0.0950231	0.0475116	−	0.998871i	$-0.484871\pi$
$739$	2.58316	0.0950231	0.0475116	+	0.998871i	$0.484871\pi$
$740$	−9.31124	−0.342288
$741$	12.9643	0.476254
$742$	−6.91573	−0.253884
$743$	32.6369	1.19733	0.598666	−	0.800999i	$-0.295698\pi$
$743$	32.6369	1.19733	0.598666	+	0.800999i	$0.295698\pi$
$744$	5.79339	0.212396
$745$	7.72970	0.283194
$746$	−2.45720	−0.0899646
$747$	2.17202	0.0794700
$748$	−7.91720	−0.289482
$749$	−5.74794	−0.210025
$750$	1.30184	0.0475365
$751$	−35.7215	−1.30350	−0.651748	−	0.758435i	$-0.725964\pi$
$751$	−35.7215	−1.30350	−0.651748	+	0.758435i	$0.725964\pi$
$752$	−3.86374	−0.140896
$753$	1.56724	0.0571135
$754$	−1.45355	−0.0529353
$755$	−16.2204	−0.590322
$756$	2.86743	0.104288
$757$	46.8214	1.70175	0.850876	−	0.525366i	$-0.176072\pi$
$757$	46.8214	1.70175	0.850876	+	0.525366i	$0.176072\pi$
$758$	4.37297	0.158834
$759$	24.7664	0.898962
$760$	5.33416	0.193490
$761$	−39.1569	−1.41944	−0.709718	−	0.704485i	$-0.751178\pi$
$761$	−39.1569	−1.41944	−0.709718	+	0.704485i	$0.751178\pi$
$762$	−14.4947	−0.525086
$763$	−5.64044	−0.204198
$764$	−8.39085	−0.303570
$765$	3.73437	0.135016
$766$	19.9828	0.722008
$767$	9.92382	0.358328
$768$	−1.30184	−0.0469761
$769$	−29.3287	−1.05762	−0.528810	−	0.848740i	$-0.677361\pi$
$769$	−29.3287	−1.05762	−0.528810	+	0.848740i	$0.677361\pi$
$770$	1.41572	0.0510189
$771$	−10.7621	−0.387588
$772$	−6.83295	−0.245923
$773$	1.01225	0.0364082	0.0182041	−	0.999834i	$-0.494205\pi$
$773$	1.01225	0.0364082	0.0182041	+	0.999834i	$0.494205\pi$
$774$	−10.1322	−0.364196
$775$	−4.45016	−0.159854
$776$	−4.07748	−0.146373
$777$	−6.20164	−0.222483
$778$	15.2304	0.546037
$779$	36.1923	1.29672
$780$	2.43042	0.0870231
$781$	15.9895	0.572149
$782$	19.6701	0.703400
$783$	−4.36374	−0.155947
$784$	−6.73825	−0.240652
$785$	3.96919	0.141666
$786$	19.9963	0.713246
$787$	−12.5828	−0.448528	−0.224264	−	0.974528i	$-0.571998\pi$
$787$	−12.5828	−0.448528	−0.224264	+	0.974528i	$0.571998\pi$
$788$	7.96232	0.283646
$789$	29.1120	1.03641
$790$	8.28529	0.294777
$791$	3.53114	0.125553
$792$	3.61173	0.128337
$793$	16.9209	0.600878
$794$	17.4686	0.619939
$795$	−17.5976	−0.624124
$796$	10.7652	0.381562
$797$	41.9050	1.48435	0.742175	−	0.670206i	$-0.233794\pi$
$797$	41.9050	1.48435	0.742175	+	0.670206i	$0.233794\pi$
$798$	3.55275	0.125766
$799$	−11.0546	−0.391085
$800$	1.00000	0.0353553
$801$	4.69873	0.166022
$802$	−5.81171	−0.205219
$803$	13.9364	0.491805
$804$	−0.554255	−0.0195471
$805$	−3.51731	−0.123969
$806$	−8.30805	−0.292639
$807$	29.4983	1.03839
$808$	−12.0161	−0.422724
$809$	11.3141	0.397782	0.198891	−	0.980022i	$-0.436266\pi$
$809$	11.3141	0.397782	0.198891	+	0.980022i	$0.436266\pi$
$810$	3.38080	0.118789
$811$	51.5954	1.81176	0.905879	−	0.423536i	$-0.139211\pi$
$811$	51.5954	1.81176	0.905879	+	0.423536i	$0.139211\pi$
$812$	−0.398335	−0.0139788
$813$	23.1276	0.811120
$814$	−25.7657	−0.903089
$815$	7.56172	0.264876
$816$	−3.72473	−0.130392
$817$	−41.4087	−1.44871
$818$	−12.9038	−0.451170
$819$	−1.24665	−0.0435616
$820$	6.78500	0.236942
$821$	28.0341	0.978397	0.489199	−	0.872172i	$-0.337289\pi$
$821$	28.0341	0.978397	0.489199	+	0.872172i	$0.337289\pi$
$822$	13.6123	0.474783
$823$	55.5949	1.93792	0.968958	−	0.247225i	$-0.0795188\pi$
$823$	55.5949	1.93792	0.968958	+	0.247225i	$0.0795188\pi$
$824$	12.3606	0.430603
$825$	3.60241	0.125420
$826$	2.71954	0.0946250
$827$	−30.7466	−1.06916	−0.534581	−	0.845117i	$-0.679531\pi$
$827$	−30.7466	−1.06916	−0.534581	+	0.845117i	$0.679531\pi$
$828$	−8.97325	−0.311842
$829$	32.6198	1.13293	0.566466	−	0.824085i	$-0.308310\pi$
$829$	32.6198	1.13293	0.566466	+	0.824085i	$0.308310\pi$
$830$	1.66411	0.0577622
$831$	8.42447	0.292242
$832$	1.86691	0.0647236
$833$	−19.2790	−0.667977
$834$	29.9844	1.03827
$835$	9.44054	0.326703
$836$	14.7605	0.510503
$837$	−24.9418	−0.862114
$838$	−24.4309	−0.843951
$839$	−36.2825	−1.25261	−0.626306	−	0.779578i	$-0.715434\pi$
$839$	−36.2825	−1.25261	−0.626306	+	0.779578i	$0.715434\pi$
$840$	0.666038	0.0229805
$841$	−28.3938	−0.979097
$842$	−10.1115	−0.348466
$843$	−28.0308	−0.965433
$844$	19.3981	0.667710
$845$	9.51464	0.327313
$846$	5.04299	0.173382
$847$	−1.71022	−0.0587637
$848$	−13.5175	−0.464193
$849$	23.7618	0.815502
$850$	2.86112	0.0981357
$851$	64.0143	2.19438
$852$	7.52242	0.257714
$853$	11.5458	0.395320	0.197660	−	0.980271i	$-0.436666\pi$
$853$	11.5458	0.395320	0.197660	+	0.980271i	$0.436666\pi$
$854$	4.63703	0.158676
$855$	−6.96220	−0.238102
$856$	−11.2350	−0.384003
$857$	24.5155	0.837433	0.418716	−	0.908117i	$-0.362480\pi$
$857$	24.5155	0.837433	0.418716	+	0.908117i	$0.362480\pi$
$858$	6.72538	0.229601
$859$	48.1631	1.64330	0.821652	−	0.569990i	$-0.193053\pi$
$859$	48.1631	1.64330	0.821652	+	0.569990i	$0.193053\pi$
$860$	−7.76292	−0.264713
$861$	4.51907	0.154009
$862$	8.88491	0.302621
$863$	−16.4880	−0.561259	−0.280629	−	0.959816i	$-0.590543\pi$
$863$	−16.4880	−0.561259	−0.280629	+	0.959816i	$0.590543\pi$
$864$	5.60470	0.190676
$865$	−6.75561	−0.229698
$866$	6.83796	0.232363
$867$	11.4744	0.389691
$868$	−2.27676	−0.0772781
$869$	22.9268	0.777737
$870$	−1.01360	−0.0343641
$871$	0.794833	0.0269319
$872$	−11.0248	−0.373348
$873$	5.32196	0.180121
$874$	−36.6720	−1.24045
$875$	−0.511613	−0.0172957
$876$	6.55652	0.221524
$877$	30.0238	1.01383	0.506915	−	0.861996i	$-0.330786\pi$
$877$	30.0238	1.01383	0.506915	+	0.861996i	$0.330786\pi$
$878$	24.7300	0.834596
$879$	−16.4268	−0.554064
$880$	2.76717	0.0932811
$881$	−16.0114	−0.539437	−0.269718	−	0.962939i	$-0.586931\pi$
$881$	−16.0114	−0.539437	−0.269718	+	0.962939i	$0.586931\pi$
$882$	8.79484	0.296138
$883$	−21.0566	−0.708610	−0.354305	−	0.935130i	$-0.615282\pi$
$883$	−21.0566	−0.708610	−0.354305	+	0.935130i	$0.615282\pi$
$884$	5.34147	0.179653
$885$	6.92011	0.232617
$886$	6.18029	0.207631
$887$	−12.7956	−0.429635	−0.214818	−	0.976654i	$-0.568916\pi$
$887$	−12.7956	−0.429635	−0.214818	+	0.976654i	$0.568916\pi$
$888$	−12.1218	−0.406779
$889$	5.69628	0.191047
$890$	3.59998	0.120672
$891$	9.35522	0.313412
$892$	−22.2725	−0.745738
$893$	20.6098	0.689680
$894$	10.0628	0.336552
$895$	−4.60124	−0.153803
$896$	0.511613	0.0170918
$897$	−16.7090	−0.557898
$898$	−16.4506	−0.548963
$899$	3.46483	0.115559
$900$	−1.30521	−0.0435070
$901$	−38.6753	−1.28846
$902$	18.7752	0.625146
$903$	−5.17040	−0.172060
$904$	6.90198	0.229556
$905$	−5.52301	−0.183591
$906$	−21.1164	−0.701546
$907$	41.8066	1.38817	0.694083	−	0.719895i	$-0.255810\pi$
$907$	41.8066	1.38817	0.694083	+	0.719895i	$0.255810\pi$
$908$	22.4936	0.746476
$909$	15.6835	0.520189
$910$	−0.955136	−0.0316625
$911$	11.5161	0.381546	0.190773	−	0.981634i	$-0.438901\pi$
$911$	11.5161	0.381546	0.190773	+	0.981634i	$0.438901\pi$
$912$	6.94423	0.229946
$913$	4.60488	0.152399
$914$	−25.2094	−0.833852
$915$	11.7993	0.390073
$916$	−18.5908	−0.614257
$917$	−7.85839	−0.259507
$918$	16.0357	0.529258
$919$	46.5723	1.53628	0.768140	−	0.640282i	$-0.221183\pi$
$919$	46.5723	1.53628	0.768140	+	0.640282i	$0.221183\pi$
$920$	−6.87494	−0.226660
$921$	−17.5764	−0.579161
$922$	5.48340	0.180586
$923$	−10.7876	−0.355077
$924$	1.84304	0.0606315
$925$	9.31124	0.306152
$926$	4.81067	0.158088
$927$	−16.1332	−0.529884
$928$	−0.778586	−0.0255584
$929$	3.89391	0.127755	0.0638775	−	0.997958i	$-0.479653\pi$
$929$	3.89391	0.127755	0.0638775	+	0.997958i	$0.479653\pi$
$930$	−5.79339	−0.189973
$931$	35.9429	1.17798
$932$	−3.85904	−0.126407
$933$	2.67152	0.0874617
$934$	−18.3643	−0.600900
$935$	7.91720	0.258920
$936$	−2.43671	−0.0796465
$937$	13.0330	0.425769	0.212885	−	0.977077i	$-0.431714\pi$
$937$	13.0330	0.425769	0.212885	+	0.977077i	$0.431714\pi$
$938$	0.217818	0.00711199
$939$	38.6679	1.26188
$940$	3.86374	0.126021
$941$	18.9654	0.618254	0.309127	−	0.951021i	$-0.399963\pi$
$941$	18.9654	0.618254	0.309127	+	0.951021i	$0.399963\pi$
$942$	5.16725	0.168358
$943$	−46.6465	−1.51902
$944$	5.31563	0.173009
$945$	−2.86743	−0.0932776
$946$	−21.4813	−0.698417
$947$	10.1848	0.330960	0.165480	−	0.986213i	$-0.447083\pi$
$947$	10.1848	0.330960	0.165480	+	0.986213i	$0.447083\pi$
$948$	10.7861	0.350317
$949$	−9.40242	−0.305215
$950$	−5.33416	−0.173063
$951$	−13.5313	−0.438783
$952$	1.46379	0.0474416
$953$	−47.1948	−1.52879	−0.764395	−	0.644748i	$-0.776962\pi$
$953$	−47.1948	−1.52879	−0.764395	+	0.644748i	$0.776962\pi$
$954$	17.6432	0.571219
$955$	8.39085	0.271522
$956$	25.1783	0.814324
$957$	−2.80479	−0.0906659
$958$	−19.2009	−0.620351
$959$	−5.34951	−0.172745
$960$	1.30184	0.0420167
$961$	−11.1961	−0.361165
$962$	17.3833	0.560459
$963$	14.6640	0.472540
$964$	−17.9583	−0.578399
$965$	6.83295	0.219961
$966$	−4.57897	−0.147326
$967$	18.1184	0.582648	0.291324	−	0.956624i	$-0.405904\pi$
$967$	18.1184	0.582648	0.291324	+	0.956624i	$0.405904\pi$
$968$	−3.34279	−0.107441
$969$	19.8683	0.638261
$970$	4.07748	0.130920
$971$	−2.61144	−0.0838051	−0.0419025	−	0.999122i	$-0.513342\pi$
$971$	−2.61144	−0.0838051	−0.0419025	+	0.999122i	$0.513342\pi$
$972$	−12.4128	−0.398142
$973$	−11.7836	−0.377765
$974$	−12.1262	−0.388548
$975$	−2.43042	−0.0778359
$976$	9.06356	0.290118
$977$	54.8133	1.75363	0.876816	−	0.480826i	$-0.159663\pi$
$977$	54.8133	1.75363	0.876816	+	0.480826i	$0.159663\pi$
$978$	9.84416	0.314781
$979$	9.96175	0.318379
$980$	6.73825	0.215246
$981$	14.3897	0.459429
$982$	3.87065	0.123518
$983$	−4.86789	−0.155262	−0.0776308	−	0.996982i	$-0.524736\pi$
$983$	−4.86789	−0.155262	−0.0776308	+	0.996982i	$0.524736\pi$
$984$	8.83299	0.281585
$985$	−7.96232	−0.253701
$986$	−2.22763	−0.0709423
$987$	2.57340	0.0819121
$988$	−9.95841	−0.316819
$989$	53.3697	1.69706
$990$	−3.61173	−0.114788
$991$	49.0536	1.55824	0.779119	−	0.626876i	$-0.215667\pi$
$991$	49.0536	1.55824	0.779119	+	0.626876i	$0.215667\pi$
$992$	−4.45016	−0.141293
$993$	2.34452	0.0744012
$994$	−2.95625	−0.0937664
$995$	−10.7652	−0.341279
$996$	2.16641	0.0686453
$997$	−30.9890	−0.981432	−0.490716	−	0.871320i	$-0.663265\pi$
$997$	−30.9890	−0.981432	−0.490716	+	0.871320i	$0.663265\pi$
$998$	−11.8944	−0.376512
$999$	52.1867	1.65111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.10	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.30184 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.30184 q^{6} +0.511613 q^{7} +1.00000 q^{8} -1.30521 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.30184 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.30184 q^{6} +0.511613 q^{7} +1.00000 q^{8} -1.30521 q^{9} -1.00000 q^{10} -2.76717 q^{11} -1.30184 q^{12} +1.86691 q^{13} +0.511613 q^{14} +1.30184 q^{15} +1.00000 q^{16} +2.86112 q^{17} -1.30521 q^{18} -5.33416 q^{19} -1.00000 q^{20} -0.666038 q^{21} -2.76717 q^{22} +6.87494 q^{23} -1.30184 q^{24} +1.00000 q^{25} +1.86691 q^{26} +5.60470 q^{27} +0.511613 q^{28} -0.778586 q^{29} +1.30184 q^{30} -4.45016 q^{31} +1.00000 q^{32} +3.60241 q^{33} +2.86112 q^{34} -0.511613 q^{35} -1.30521 q^{36} +9.31124 q^{37} -5.33416 q^{38} -2.43042 q^{39} -1.00000 q^{40} -6.78500 q^{41} -0.666038 q^{42} +7.76292 q^{43} -2.76717 q^{44} +1.30521 q^{45} +6.87494 q^{46} -3.86374 q^{47} -1.30184 q^{48} -6.73825 q^{49} +1.00000 q^{50} -3.72473 q^{51} +1.86691 q^{52} -13.5175 q^{53} +5.60470 q^{54} +2.76717 q^{55} +0.511613 q^{56} +6.94423 q^{57} -0.778586 q^{58} +5.31563 q^{59} +1.30184 q^{60} +9.06356 q^{61} -4.45016 q^{62} -0.667762 q^{63} +1.00000 q^{64} -1.86691 q^{65} +3.60241 q^{66} +0.425747 q^{67} +2.86112 q^{68} -8.95008 q^{69} -0.511613 q^{70} -5.77829 q^{71} -1.30521 q^{72} -5.03635 q^{73} +9.31124 q^{74} -1.30184 q^{75} -5.33416 q^{76} -1.41572 q^{77} -2.43042 q^{78} -8.28529 q^{79} -1.00000 q^{80} -3.38080 q^{81} -6.78500 q^{82} -1.66411 q^{83} -0.666038 q^{84} -2.86112 q^{85} +7.76292 q^{86} +1.01360 q^{87} -2.76717 q^{88} -3.59998 q^{89} +1.30521 q^{90} +0.955136 q^{91} +6.87494 q^{92} +5.79339 q^{93} -3.86374 q^{94} +5.33416 q^{95} -1.30184 q^{96} -4.07748 q^{97} -6.73825 q^{98} +3.61173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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