LMFDB - Embedded newform 4026.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.11492689.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 13x^{2} + 18x - 8 $ x^5 - 2x^4 - 9x^3 + 13x^2 + 18x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.34840$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.34840 q^{5} -1.00000 q^{6} +0.833399 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.34840 q^{5} -1.00000 q^{6} +0.833399 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.34840 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.47852 q^{13} +0.833399 q^{14} -3.34840 q^{15} +1.00000 q^{16} +5.78408 q^{17} +1.00000 q^{18} +2.48499 q^{19} +3.34840 q^{20} -0.833399 q^{21} +1.00000 q^{22} -8.08965 q^{23} -1.00000 q^{24} +6.21182 q^{25} +2.47852 q^{26} -1.00000 q^{27} +0.833399 q^{28} +7.61748 q^{29} -3.34840 q^{30} -4.82693 q^{31} +1.00000 q^{32} -1.00000 q^{33} +5.78408 q^{34} +2.79056 q^{35} +1.00000 q^{36} +1.55149 q^{37} +2.48499 q^{38} -2.47852 q^{39} +3.34840 q^{40} +5.40009 q^{41} -0.833399 q^{42} +2.31192 q^{43} +1.00000 q^{44} +3.34840 q^{45} -8.08965 q^{46} -12.7928 q^{47} -1.00000 q^{48} -6.30545 q^{49} +6.21182 q^{50} -5.78408 q^{51} +2.47852 q^{52} -6.62633 q^{53} -1.00000 q^{54} +3.34840 q^{55} +0.833399 q^{56} -2.48499 q^{57} +7.61748 q^{58} +4.56669 q^{59} -3.34840 q^{60} +1.00000 q^{61} -4.82693 q^{62} +0.833399 q^{63} +1.00000 q^{64} +8.29909 q^{65} -1.00000 q^{66} +2.65397 q^{67} +5.78408 q^{68} +8.08965 q^{69} +2.79056 q^{70} +5.22386 q^{71} +1.00000 q^{72} -3.14781 q^{73} +1.55149 q^{74} -6.21182 q^{75} +2.48499 q^{76} +0.833399 q^{77} -2.47852 q^{78} -6.92940 q^{79} +3.34840 q^{80} +1.00000 q^{81} +5.40009 q^{82} -0.942855 q^{83} -0.833399 q^{84} +19.3675 q^{85} +2.31192 q^{86} -7.61748 q^{87} +1.00000 q^{88} -10.3231 q^{89} +3.34840 q^{90} +2.06560 q^{91} -8.08965 q^{92} +4.82693 q^{93} -12.7928 q^{94} +8.32077 q^{95} -1.00000 q^{96} +15.4745 q^{97} -6.30545 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 5 q^{12} - 2 q^{13} - 7 q^{15} + 5 q^{16} + 2 q^{17} + 5 q^{18} + 18 q^{19} + 7 q^{20} + 5 q^{22} - q^{23} - 5 q^{24} + 6 q^{25} - 2 q^{26} - 5 q^{27} + 7 q^{29} - 7 q^{30} + 5 q^{32} - 5 q^{33} + 2 q^{34} + 7 q^{35} + 5 q^{36} + 11 q^{37} + 18 q^{38} + 2 q^{39} + 7 q^{40} + 8 q^{41} - 7 q^{43} + 5 q^{44} + 7 q^{45} - q^{46} + q^{47} - 5 q^{48} + 7 q^{49} + 6 q^{50} - 2 q^{51} - 2 q^{52} + 10 q^{53} - 5 q^{54} + 7 q^{55} - 18 q^{57} + 7 q^{58} + 8 q^{59} - 7 q^{60} + 5 q^{61} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} + 34 q^{71} + 5 q^{72} + 13 q^{73} + 11 q^{74} - 6 q^{75} + 18 q^{76} + 2 q^{78} + 15 q^{79} + 7 q^{80} + 5 q^{81} + 8 q^{82} - 27 q^{83} - 2 q^{85} - 7 q^{86} - 7 q^{87} + 5 q^{88} + 11 q^{89} + 7 q^{90} + q^{91} - q^{92} + q^{94} + 11 q^{95} - 5 q^{96} + 37 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9 + 7 * q^10 + 5 * q^11 - 5 * q^12 - 2 * q^13 - 7 * q^15 + 5 * q^16 + 2 * q^17 + 5 * q^18 + 18 * q^19 + 7 * q^20 + 5 * q^22 - q^23 - 5 * q^24 + 6 * q^25 - 2 * q^26 - 5 * q^27 + 7 * q^29 - 7 * q^30 + 5 * q^32 - 5 * q^33 + 2 * q^34 + 7 * q^35 + 5 * q^36 + 11 * q^37 + 18 * q^38 + 2 * q^39 + 7 * q^40 + 8 * q^41 - 7 * q^43 + 5 * q^44 + 7 * q^45 - q^46 + q^47 - 5 * q^48 + 7 * q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 + 10 * q^53 - 5 * q^54 + 7 * q^55 - 18 * q^57 + 7 * q^58 + 8 * q^59 - 7 * q^60 + 5 * q^61 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 + 2 * q^68 + q^69 + 7 * q^70 + 34 * q^71 + 5 * q^72 + 13 * q^73 + 11 * q^74 - 6 * q^75 + 18 * q^76 + 2 * q^78 + 15 * q^79 + 7 * q^80 + 5 * q^81 + 8 * q^82 - 27 * q^83 - 2 * q^85 - 7 * q^86 - 7 * q^87 + 5 * q^88 + 11 * q^89 + 7 * q^90 + q^91 - q^92 + q^94 + 11 * q^95 - 5 * q^96 + 37 * q^97 + 7 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.34840	1.49745	0.748726	−	0.662879i	$-0.230666\pi$
$5$	3.34840	1.49745	0.748726	+	0.662879i	$0.230666\pi$
$6$	−1.00000	−0.408248
$7$	0.833399	0.314995	0.157498	−	0.987519i	$-0.449657\pi$
$7$	0.833399	0.314995	0.157498	+	0.987519i	$0.449657\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.34840	1.05886
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	2.47852	0.687418	0.343709	−	0.939076i	$-0.388317\pi$
$13$	2.47852	0.687418	0.343709	+	0.939076i	$0.388317\pi$
$14$	0.833399	0.222735
$15$	−3.34840	−0.864554
$16$	1.00000	0.250000
$17$	5.78408	1.40285	0.701423	−	0.712745i	$-0.252548\pi$
$17$	5.78408	1.40285	0.701423	+	0.712745i	$0.252548\pi$
$18$	1.00000	0.235702
$19$	2.48499	0.570097	0.285048	−	0.958513i	$-0.407990\pi$
$19$	2.48499	0.570097	0.285048	+	0.958513i	$0.407990\pi$
$20$	3.34840	0.748726
$21$	−0.833399	−0.181863
$22$	1.00000	0.213201
$23$	−8.08965	−1.68681	−0.843404	−	0.537280i	$-0.819452\pi$
$23$	−8.08965	−1.68681	−0.843404	+	0.537280i	$0.819452\pi$
$24$	−1.00000	−0.204124
$25$	6.21182	1.24236
$26$	2.47852	0.486078
$27$	−1.00000	−0.192450
$28$	0.833399	0.157498
$29$	7.61748	1.41453	0.707266	−	0.706948i	$-0.249929\pi$
$29$	7.61748	1.41453	0.707266	+	0.706948i	$0.249929\pi$
$30$	−3.34840	−0.611332
$31$	−4.82693	−0.866941	−0.433471	−	0.901168i	$-0.642711\pi$
$31$	−4.82693	−0.866941	−0.433471	+	0.901168i	$0.642711\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	5.78408	0.991962
$35$	2.79056	0.471690
$36$	1.00000	0.166667
$37$	1.55149	0.255064	0.127532	−	0.991834i	$-0.459295\pi$
$37$	1.55149	0.255064	0.127532	+	0.991834i	$0.459295\pi$
$38$	2.48499	0.403119
$39$	−2.47852	−0.396881
$40$	3.34840	0.529429
$41$	5.40009	0.843353	0.421676	−	0.906746i	$-0.361442\pi$
$41$	5.40009	0.843353	0.421676	+	0.906746i	$0.361442\pi$
$42$	−0.833399	−0.128596
$43$	2.31192	0.352564	0.176282	−	0.984340i	$-0.443593\pi$
$43$	2.31192	0.352564	0.176282	+	0.984340i	$0.443593\pi$
$44$	1.00000	0.150756
$45$	3.34840	0.499151
$46$	−8.08965	−1.19275
$47$	−12.7928	−1.86602	−0.933012	−	0.359846i	$-0.882829\pi$
$47$	−12.7928	−1.86602	−0.933012	+	0.359846i	$0.882829\pi$
$48$	−1.00000	−0.144338
$49$	−6.30545	−0.900778
$50$	6.21182	0.878483
$51$	−5.78408	−0.809934
$52$	2.47852	0.343709
$53$	−6.62633	−0.910197	−0.455098	−	0.890441i	$-0.650396\pi$
$53$	−6.62633	−0.910197	−0.455098	+	0.890441i	$0.650396\pi$
$54$	−1.00000	−0.136083
$55$	3.34840	0.451499
$56$	0.833399	0.111368
$57$	−2.48499	−0.329146
$58$	7.61748	1.00022
$59$	4.56669	0.594533	0.297266	−	0.954795i	$-0.403925\pi$
$59$	4.56669	0.594533	0.297266	+	0.954795i	$0.403925\pi$
$60$	−3.34840	−0.432277
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−4.82693	−0.613020
$63$	0.833399	0.104998
$64$	1.00000	0.125000
$65$	8.29909	1.02938
$66$	−1.00000	−0.123091
$67$	2.65397	0.324234	0.162117	−	0.986772i	$-0.448168\pi$
$67$	2.65397	0.324234	0.162117	+	0.986772i	$0.448168\pi$
$68$	5.78408	0.701423
$69$	8.08965	0.973879
$70$	2.79056	0.333535
$71$	5.22386	0.619959	0.309979	−	0.950743i	$-0.399678\pi$
$71$	5.22386	0.619959	0.309979	+	0.950743i	$0.399678\pi$
$72$	1.00000	0.117851
$73$	−3.14781	−0.368423	−0.184212	−	0.982887i	$-0.558973\pi$
$73$	−3.14781	−0.368423	−0.184212	+	0.982887i	$0.558973\pi$
$74$	1.55149	0.180357
$75$	−6.21182	−0.717279
$76$	2.48499	0.285048
$77$	0.833399	0.0949747
$78$	−2.47852	−0.280637
$79$	−6.92940	−0.779619	−0.389809	−	0.920896i	$-0.627459\pi$
$79$	−6.92940	−0.779619	−0.389809	+	0.920896i	$0.627459\pi$
$80$	3.34840	0.374363
$81$	1.00000	0.111111
$82$	5.40009	0.596341
$83$	−0.942855	−0.103492	−0.0517459	−	0.998660i	$-0.516479\pi$
$83$	−0.942855	−0.103492	−0.0517459	+	0.998660i	$0.516479\pi$
$84$	−0.833399	−0.0909313
$85$	19.3675	2.10070
$86$	2.31192	0.249301
$87$	−7.61748	−0.816680
$88$	1.00000	0.106600
$89$	−10.3231	−1.09425	−0.547125	−	0.837051i	$-0.684278\pi$
$89$	−10.3231	−1.09425	−0.547125	+	0.837051i	$0.684278\pi$
$90$	3.34840	0.352953
$91$	2.06560	0.216533
$92$	−8.08965	−0.843404
$93$	4.82693	0.500529
$94$	−12.7928	−1.31948
$95$	8.32077	0.853693
$96$	−1.00000	−0.102062
$97$	15.4745	1.57120	0.785601	−	0.618734i	$-0.212354\pi$
$97$	15.4745	1.57120	0.785601	+	0.618734i	$0.212354\pi$
$98$	−6.30545	−0.636946
$99$	1.00000	0.100504
$100$	6.21182	0.621182
$101$	9.22624	0.918045	0.459022	−	0.888425i	$-0.348200\pi$
$101$	9.22624	0.918045	0.459022	+	0.888425i	$0.348200\pi$
$102$	−5.78408	−0.572710
$103$	−6.40567	−0.631169	−0.315585	−	0.948897i	$-0.602201\pi$
$103$	−6.40567	−0.631169	−0.315585	+	0.948897i	$0.602201\pi$
$104$	2.47852	0.243039
$105$	−2.79056	−0.272331
$106$	−6.62633	−0.643606
$107$	10.7200	1.03634	0.518169	−	0.855278i	$-0.326614\pi$
$107$	10.7200	1.03634	0.518169	+	0.855278i	$0.326614\pi$
$108$	−1.00000	−0.0962250
$109$	−1.88509	−0.180559	−0.0902793	−	0.995916i	$-0.528776\pi$
$109$	−1.88509	−0.180559	−0.0902793	+	0.995916i	$0.528776\pi$
$110$	3.34840	0.319258
$111$	−1.55149	−0.147261
$112$	0.833399	0.0787488
$113$	−20.9466	−1.97049	−0.985244	−	0.171153i	$-0.945251\pi$
$113$	−20.9466	−1.97049	−0.985244	+	0.171153i	$0.945251\pi$
$114$	−2.48499	−0.232741
$115$	−27.0874	−2.52591
$116$	7.61748	0.707266
$117$	2.47852	0.229139
$118$	4.56669	0.420398
$119$	4.82045	0.441890
$120$	−3.34840	−0.305666
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−5.40009	−0.486910
$124$	−4.82693	−0.433471
$125$	4.05765	0.362927
$126$	0.833399	0.0742451
$127$	2.75407	0.244384	0.122192	−	0.992506i	$-0.461008\pi$
$127$	2.75407	0.244384	0.122192	+	0.992506i	$0.461008\pi$
$128$	1.00000	0.0883883
$129$	−2.31192	−0.203553
$130$	8.29909	0.727878
$131$	−10.4039	−0.908997	−0.454498	−	0.890748i	$-0.650181\pi$
$131$	−10.4039	−0.908997	−0.454498	+	0.890748i	$0.650181\pi$
$132$	−1.00000	−0.0870388
$133$	2.07099	0.179578
$134$	2.65397	0.229268
$135$	−3.34840	−0.288185
$136$	5.78408	0.495981
$137$	−6.44441	−0.550583	−0.275291	−	0.961361i	$-0.588774\pi$
$137$	−6.44441	−0.550583	−0.275291	+	0.961361i	$0.588774\pi$
$138$	8.08965	0.688637
$139$	−9.74997	−0.826982	−0.413491	−	0.910508i	$-0.635691\pi$
$139$	−9.74997	−0.826982	−0.413491	+	0.910508i	$0.635691\pi$
$140$	2.79056	0.235845
$141$	12.7928	1.07735
$142$	5.22386	0.438377
$143$	2.47852	0.207264
$144$	1.00000	0.0833333
$145$	25.5064	2.11819
$146$	−3.14781	−0.260515
$147$	6.30545	0.520064
$148$	1.55149	0.127532
$149$	3.82057	0.312993	0.156497	−	0.987678i	$-0.449980\pi$
$149$	3.82057	0.312993	0.156497	+	0.987678i	$0.449980\pi$
$150$	−6.21182	−0.507193
$151$	−3.56817	−0.290373	−0.145187	−	0.989404i	$-0.546378\pi$
$151$	−3.56817	−0.290373	−0.145187	+	0.989404i	$0.546378\pi$
$152$	2.48499	0.201560
$153$	5.78408	0.467615
$154$	0.833399	0.0671572
$155$	−16.1625	−1.29820
$156$	−2.47852	−0.198440
$157$	5.95068	0.474916	0.237458	−	0.971398i	$-0.423686\pi$
$157$	5.95068	0.474916	0.237458	+	0.971398i	$0.423686\pi$
$158$	−6.92940	−0.551274
$159$	6.62633	0.525502
$160$	3.34840	0.264715
$161$	−6.74191	−0.531337
$162$	1.00000	0.0785674
$163$	13.6775	1.07130	0.535652	−	0.844439i	$-0.320066\pi$
$163$	13.6775	1.07130	0.535652	+	0.844439i	$0.320066\pi$
$164$	5.40009	0.421676
$165$	−3.34840	−0.260673
$166$	−0.942855	−0.0731797
$167$	1.92952	0.149311	0.0746554	−	0.997209i	$-0.476214\pi$
$167$	1.92952	0.149311	0.0746554	+	0.997209i	$0.476214\pi$
$168$	−0.833399	−0.0642981
$169$	−6.85694	−0.527457
$170$	19.3675	1.48542
$171$	2.48499	0.190032
$172$	2.31192	0.176282
$173$	−11.2843	−0.857928	−0.428964	−	0.903322i	$-0.641121\pi$
$173$	−11.2843	−0.857928	−0.428964	+	0.903322i	$0.641121\pi$
$174$	−7.61748	−0.577480
$175$	5.17692	0.391339
$176$	1.00000	0.0753778
$177$	−4.56669	−0.343254
$178$	−10.3231	−0.773752
$179$	3.35000	0.250391	0.125195	−	0.992132i	$-0.460044\pi$
$179$	3.35000	0.250391	0.125195	+	0.992132i	$0.460044\pi$
$180$	3.34840	0.249575
$181$	9.90177	0.735992	0.367996	−	0.929827i	$-0.380044\pi$
$181$	9.90177	0.735992	0.367996	+	0.929827i	$0.380044\pi$
$182$	2.06560	0.153112
$183$	−1.00000	−0.0739221
$184$	−8.08965	−0.596377
$185$	5.19502	0.381945
$186$	4.82693	0.353927
$187$	5.78408	0.422974
$188$	−12.7928	−0.933012
$189$	−0.833399	−0.0606209
$190$	8.32077	0.603652
$191$	14.3407	1.03766	0.518829	−	0.854878i	$-0.326368\pi$
$191$	14.3407	1.03766	0.518829	+	0.854878i	$0.326368\pi$
$192$	−1.00000	−0.0721688
$193$	−6.63966	−0.477934	−0.238967	−	0.971028i	$-0.576809\pi$
$193$	−6.63966	−0.477934	−0.238967	+	0.971028i	$0.576809\pi$
$194$	15.4745	1.11101
$195$	−8.29909	−0.594310
$196$	−6.30545	−0.450389
$197$	7.00795	0.499296	0.249648	−	0.968337i	$-0.419685\pi$
$197$	7.00795	0.499296	0.249648	+	0.968337i	$0.419685\pi$
$198$	1.00000	0.0710669
$199$	0.0364853	0.00258637	0.00129319	−	0.999999i	$-0.499588\pi$
$199$	0.0364853	0.00258637	0.00129319	+	0.999999i	$0.499588\pi$
$200$	6.21182	0.439242
$201$	−2.65397	−0.187197
$202$	9.22624	0.649156
$203$	6.34840	0.445571
$204$	−5.78408	−0.404967
$205$	18.0817	1.26288
$206$	−6.40567	−0.446304
$207$	−8.08965	−0.562269
$208$	2.47852	0.171854
$209$	2.48499	0.171891
$210$	−2.79056	−0.192567
$211$	18.1224	1.24760	0.623800	−	0.781584i	$-0.285588\pi$
$211$	18.1224	1.24760	0.623800	+	0.781584i	$0.285588\pi$
$212$	−6.62633	−0.455098
$213$	−5.22386	−0.357933
$214$	10.7200	0.732801
$215$	7.74124	0.527948
$216$	−1.00000	−0.0680414
$217$	−4.02276	−0.273082
$218$	−1.88509	−0.127674
$219$	3.14781	0.212709
$220$	3.34840	0.225749
$221$	14.3360	0.964342
$222$	−1.55149	−0.104129
$223$	−24.8313	−1.66283	−0.831413	−	0.555655i	$-0.812468\pi$
$223$	−24.8313	−1.66283	−0.831413	+	0.555655i	$0.812468\pi$
$224$	0.833399	0.0556838
$225$	6.21182	0.414121
$226$	−20.9466	−1.39335
$227$	−5.80814	−0.385499	−0.192750	−	0.981248i	$-0.561741\pi$
$227$	−5.80814	−0.385499	−0.192750	+	0.981248i	$0.561741\pi$
$228$	−2.48499	−0.164573
$229$	18.8052	1.24269	0.621343	−	0.783539i	$-0.286587\pi$
$229$	18.8052	1.24269	0.621343	+	0.783539i	$0.286587\pi$
$230$	−27.0874	−1.78609
$231$	−0.833399	−0.0548336
$232$	7.61748	0.500112
$233$	−5.68449	−0.372404	−0.186202	−	0.982512i	$-0.559618\pi$
$233$	−5.68449	−0.372404	−0.186202	+	0.982512i	$0.559618\pi$
$234$	2.47852	0.162026
$235$	−42.8355	−2.79428
$236$	4.56669	0.297266
$237$	6.92940	0.450113
$238$	4.82045	0.312463
$239$	12.7198	0.822778	0.411389	−	0.911460i	$-0.365044\pi$
$239$	12.7198	0.822778	0.411389	+	0.911460i	$0.365044\pi$
$240$	−3.34840	−0.216139
$241$	−21.0514	−1.35604	−0.678021	−	0.735042i	$-0.737162\pi$
$241$	−21.0514	−1.35604	−0.678021	+	0.735042i	$0.737162\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	−21.1132	−1.34887
$246$	−5.40009	−0.344297
$247$	6.15911	0.391895
$248$	−4.82693	−0.306510
$249$	0.942855	0.0597510
$250$	4.05765	0.256628
$251$	20.4177	1.28875	0.644376	−	0.764709i	$-0.277117\pi$
$251$	20.4177	1.28875	0.644376	+	0.764709i	$0.277117\pi$
$252$	0.833399	0.0524992
$253$	−8.08965	−0.508592
$254$	2.75407	0.172806
$255$	−19.3675	−1.21284
$256$	1.00000	0.0625000
$257$	−12.1492	−0.757844	−0.378922	−	0.925429i	$-0.623705\pi$
$257$	−12.1492	−0.757844	−0.378922	+	0.925429i	$0.623705\pi$
$258$	−2.31192	−0.143934
$259$	1.29301	0.0803438
$260$	8.29909	0.514688
$261$	7.61748	0.471510
$262$	−10.4039	−0.642758
$263$	12.8511	0.792432	0.396216	−	0.918157i	$-0.370323\pi$
$263$	12.8511	0.792432	0.396216	+	0.918157i	$0.370323\pi$
$264$	−1.00000	−0.0615457
$265$	−22.1876	−1.36298
$266$	2.07099	0.126981
$267$	10.3231	0.631766
$268$	2.65397	0.162117
$269$	−2.50128	−0.152506	−0.0762528	−	0.997089i	$-0.524296\pi$
$269$	−2.50128	−0.152506	−0.0762528	+	0.997089i	$0.524296\pi$
$270$	−3.34840	−0.203777
$271$	25.2101	1.53140	0.765702	−	0.643196i	$-0.222392\pi$
$271$	25.2101	1.53140	0.765702	+	0.643196i	$0.222392\pi$
$272$	5.78408	0.350712
$273$	−2.06560	−0.125016
$274$	−6.44441	−0.389321
$275$	6.21182	0.374587
$276$	8.08965	0.486940
$277$	15.2073	0.913720	0.456860	−	0.889539i	$-0.348974\pi$
$277$	15.2073	0.913720	0.456860	+	0.889539i	$0.348974\pi$
$278$	−9.74997	−0.584764
$279$	−4.82693	−0.288980
$280$	2.79056	0.166768
$281$	−5.80814	−0.346484	−0.173242	−	0.984879i	$-0.555424\pi$
$281$	−5.80814	−0.346484	−0.173242	+	0.984879i	$0.555424\pi$
$282$	12.7928	0.761801
$283$	2.78498	0.165550	0.0827751	−	0.996568i	$-0.473622\pi$
$283$	2.78498	0.165550	0.0827751	+	0.996568i	$0.473622\pi$
$284$	5.22386	0.309979
$285$	−8.32077	−0.492880
$286$	2.47852	0.146558
$287$	4.50043	0.265652
$288$	1.00000	0.0589256
$289$	16.4556	0.967978
$290$	25.5064	1.49779
$291$	−15.4745	−0.907133
$292$	−3.14781	−0.184212
$293$	6.12286	0.357701	0.178851	−	0.983876i	$-0.442762\pi$
$293$	6.12286	0.357701	0.178851	+	0.983876i	$0.442762\pi$
$294$	6.30545	0.367741
$295$	15.2911	0.890285
$296$	1.55149	0.0901786
$297$	−1.00000	−0.0580259
$298$	3.82057	0.221320
$299$	−20.0504	−1.15954
$300$	−6.21182	−0.358639
$301$	1.92675	0.111056
$302$	−3.56817	−0.205325
$303$	−9.22624	−0.530033
$304$	2.48499	0.142524
$305$	3.34840	0.191729
$306$	5.78408	0.330654
$307$	19.4976	1.11279	0.556393	−	0.830920i	$-0.312185\pi$
$307$	19.4976	1.11279	0.556393	+	0.830920i	$0.312185\pi$
$308$	0.833399	0.0474873
$309$	6.40567	0.364406
$310$	−16.1625	−0.917968
$311$	1.73291	0.0982643	0.0491321	−	0.998792i	$-0.484354\pi$
$311$	1.73291	0.0982643	0.0491321	+	0.998792i	$0.484354\pi$
$312$	−2.47852	−0.140319
$313$	17.6213	0.996017	0.498008	−	0.867172i	$-0.334065\pi$
$313$	17.6213	0.996017	0.498008	+	0.867172i	$0.334065\pi$
$314$	5.95068	0.335817
$315$	2.79056	0.157230
$316$	−6.92940	−0.389809
$317$	19.9692	1.12158	0.560790	−	0.827958i	$-0.310498\pi$
$317$	19.9692	1.12158	0.560790	+	0.827958i	$0.310498\pi$
$318$	6.62633	0.371586
$319$	7.61748	0.426497
$320$	3.34840	0.187182
$321$	−10.7200	−0.598330
$322$	−6.74191	−0.375712
$323$	14.3734	0.799758
$324$	1.00000	0.0555556
$325$	15.3961	0.854023
$326$	13.6775	0.757527
$327$	1.88509	0.104246
$328$	5.40009	0.298170
$329$	−10.6615	−0.587789
$330$	−3.34840	−0.184324
$331$	−14.1809	−0.779453	−0.389727	−	0.920931i	$-0.627430\pi$
$331$	−14.1809	−0.779453	−0.389727	+	0.920931i	$0.627430\pi$
$332$	−0.942855	−0.0517459
$333$	1.55149	0.0850212
$334$	1.92952	0.105579
$335$	8.88656	0.485525
$336$	−0.833399	−0.0454657
$337$	−11.9127	−0.648928	−0.324464	−	0.945898i	$-0.605184\pi$
$337$	−11.9127	−0.648928	−0.324464	+	0.945898i	$0.605184\pi$
$338$	−6.85694	−0.372968
$339$	20.9466	1.13766
$340$	19.3675	1.05035
$341$	−4.82693	−0.261393
$342$	2.48499	0.134373
$343$	−11.0887	−0.598736
$344$	2.31192	0.124650
$345$	27.0874	1.45834
$346$	−11.2843	−0.606647
$347$	−20.5281	−1.10201	−0.551003	−	0.834503i	$-0.685755\pi$
$347$	−20.5281	−1.10201	−0.551003	+	0.834503i	$0.685755\pi$
$348$	−7.61748	−0.408340
$349$	−6.19809	−0.331776	−0.165888	−	0.986145i	$-0.553049\pi$
$349$	−6.19809	−0.331776	−0.165888	+	0.986145i	$0.553049\pi$
$350$	5.17692	0.276718
$351$	−2.47852	−0.132294
$352$	1.00000	0.0533002
$353$	3.50538	0.186572	0.0932862	−	0.995639i	$-0.470263\pi$
$353$	3.50538	0.186572	0.0932862	+	0.995639i	$0.470263\pi$
$354$	−4.56669	−0.242717
$355$	17.4916	0.928358
$356$	−10.3231	−0.547125
$357$	−4.82045	−0.255125
$358$	3.35000	0.177053
$359$	−5.53816	−0.292293	−0.146146	−	0.989263i	$-0.546687\pi$
$359$	−5.53816	−0.292293	−0.146146	+	0.989263i	$0.546687\pi$
$360$	3.34840	0.176476
$361$	−12.8248	−0.674990
$362$	9.90177	0.520425
$363$	−1.00000	−0.0524864
$364$	2.06560	0.108267
$365$	−10.5401	−0.551696
$366$	−1.00000	−0.0522708
$367$	−15.6333	−0.816052	−0.408026	−	0.912970i	$-0.633783\pi$
$367$	−15.6333	−0.816052	−0.408026	+	0.912970i	$0.633783\pi$
$368$	−8.08965	−0.421702
$369$	5.40009	0.281118
$370$	5.19502	0.270076
$371$	−5.52238	−0.286708
$372$	4.82693	0.250264
$373$	−37.0618	−1.91899	−0.959493	−	0.281734i	$-0.909090\pi$
$373$	−37.0618	−1.91899	−0.959493	+	0.281734i	$0.909090\pi$
$374$	5.78408	0.299088
$375$	−4.05765	−0.209536
$376$	−12.7928	−0.659739
$377$	18.8801	0.972374
$378$	−0.833399	−0.0428654
$379$	−4.96531	−0.255051	−0.127526	−	0.991835i	$-0.540703\pi$
$379$	−4.96531	−0.255051	−0.127526	+	0.991835i	$0.540703\pi$
$380$	8.32077	0.426846
$381$	−2.75407	−0.141095
$382$	14.3407	0.733735
$383$	23.5937	1.20558	0.602791	−	0.797899i	$-0.294055\pi$
$383$	23.5937	1.20558	0.602791	+	0.797899i	$0.294055\pi$
$384$	−1.00000	−0.0510310
$385$	2.79056	0.142220
$386$	−6.63966	−0.337950
$387$	2.31192	0.117521
$388$	15.4745	0.785601
$389$	10.9950	0.557469	0.278734	−	0.960368i	$-0.410085\pi$
$389$	10.9950	0.557469	0.278734	+	0.960368i	$0.410085\pi$
$390$	−8.29909	−0.420241
$391$	−46.7912	−2.36633
$392$	−6.30545	−0.318473
$393$	10.4039	0.524809
$394$	7.00795	0.353055
$395$	−23.2024	−1.16744
$396$	1.00000	0.0502519
$397$	−4.57254	−0.229489	−0.114745	−	0.993395i	$-0.536605\pi$
$397$	−4.57254	−0.229489	−0.114745	+	0.993395i	$0.536605\pi$
$398$	0.0364853	0.00182884
$399$	−2.07099	−0.103679
$400$	6.21182	0.310591
$401$	−18.3591	−0.916811	−0.458405	−	0.888743i	$-0.651579\pi$
$401$	−18.3591	−0.916811	−0.458405	+	0.888743i	$0.651579\pi$
$402$	−2.65397	−0.132368
$403$	−11.9636	−0.595951
$404$	9.22624	0.459022
$405$	3.34840	0.166384
$406$	6.34840	0.315066
$407$	1.55149	0.0769046
$408$	−5.78408	−0.286355
$409$	−39.8953	−1.97269	−0.986347	−	0.164679i	$-0.947341\pi$
$409$	−39.8953	−1.97269	−0.986347	+	0.164679i	$0.947341\pi$
$410$	18.0817	0.892992
$411$	6.44441	0.317879
$412$	−6.40567	−0.315585
$413$	3.80588	0.187275
$414$	−8.08965	−0.397585
$415$	−3.15706	−0.154974
$416$	2.47852	0.121519
$417$	9.74997	0.477458
$418$	2.48499	0.121545
$419$	−10.0324	−0.490114	−0.245057	−	0.969509i	$-0.578807\pi$
$419$	−10.0324	−0.490114	−0.245057	+	0.969509i	$0.578807\pi$
$420$	−2.79056	−0.136165
$421$	26.7722	1.30479	0.652397	−	0.757877i	$-0.273763\pi$
$421$	26.7722	1.30479	0.652397	+	0.757877i	$0.273763\pi$
$422$	18.1224	0.882186
$423$	−12.7928	−0.622008
$424$	−6.62633	−0.321803
$425$	35.9297	1.74284
$426$	−5.22386	−0.253097
$427$	0.833399	0.0403310
$428$	10.7200	0.518169
$429$	−2.47852	−0.119664
$430$	7.74124	0.373316
$431$	32.5251	1.56668	0.783339	−	0.621595i	$-0.213515\pi$
$431$	32.5251	1.56668	0.783339	+	0.621595i	$0.213515\pi$
$432$	−1.00000	−0.0481125
$433$	−31.8074	−1.52857	−0.764283	−	0.644881i	$-0.776907\pi$
$433$	−31.8074	−1.52857	−0.764283	+	0.644881i	$0.776907\pi$
$434$	−4.02276	−0.193098
$435$	−25.5064	−1.22294
$436$	−1.88509	−0.0902793
$437$	−20.1027	−0.961644
$438$	3.14781	0.150408
$439$	23.4750	1.12040	0.560200	−	0.828357i	$-0.310724\pi$
$439$	23.4750	1.12040	0.560200	+	0.828357i	$0.310724\pi$
$440$	3.34840	0.159629
$441$	−6.30545	−0.300259
$442$	14.3360	0.681893
$443$	−15.5145	−0.737116	−0.368558	−	0.929605i	$-0.620148\pi$
$443$	−15.5145	−0.737116	−0.368558	+	0.929605i	$0.620148\pi$
$444$	−1.55149	−0.0736305
$445$	−34.5661	−1.63859
$446$	−24.8313	−1.17580
$447$	−3.82057	−0.180707
$448$	0.833399	0.0393744
$449$	29.4615	1.39037	0.695186	−	0.718829i	$-0.255322\pi$
$449$	29.4615	1.39037	0.695186	+	0.718829i	$0.255322\pi$
$450$	6.21182	0.292828
$451$	5.40009	0.254280
$452$	−20.9466	−0.985244
$453$	3.56817	0.167647
$454$	−5.80814	−0.272589
$455$	6.91646	0.324248
$456$	−2.48499	−0.116371
$457$	21.8078	1.02012	0.510062	−	0.860138i	$-0.329622\pi$
$457$	21.8078	1.02012	0.510062	+	0.860138i	$0.329622\pi$
$458$	18.8052	0.878712
$459$	−5.78408	−0.269978
$460$	−27.0874	−1.26296
$461$	−11.3148	−0.526983	−0.263492	−	0.964662i	$-0.584874\pi$
$461$	−11.3148	−0.526983	−0.263492	+	0.964662i	$0.584874\pi$
$462$	−0.833399	−0.0387732
$463$	4.44363	0.206513	0.103256	−	0.994655i	$-0.467074\pi$
$463$	4.44363	0.206513	0.103256	+	0.994655i	$0.467074\pi$
$464$	7.61748	0.353633
$465$	16.1625	0.749518
$466$	−5.68449	−0.263329
$467$	−18.6738	−0.864123	−0.432061	−	0.901844i	$-0.642214\pi$
$467$	−18.6738	−0.864123	−0.432061	+	0.901844i	$0.642214\pi$
$468$	2.47852	0.114570
$469$	2.21182	0.102132
$470$	−42.8355	−1.97586
$471$	−5.95068	−0.274193
$472$	4.56669	0.210199
$473$	2.31192	0.106302
$474$	6.92940	0.318278
$475$	15.4363	0.708267
$476$	4.82045	0.220945
$477$	−6.62633	−0.303399
$478$	12.7198	0.581792
$479$	−16.6084	−0.758857	−0.379429	−	0.925221i	$-0.623879\pi$
$479$	−16.6084	−0.758857	−0.379429	+	0.925221i	$0.623879\pi$
$480$	−3.34840	−0.152833
$481$	3.84540	0.175335
$482$	−21.0514	−0.958867
$483$	6.74191	0.306767
$484$	1.00000	0.0454545
$485$	51.8150	2.35280
$486$	−1.00000	−0.0453609
$487$	−21.9216	−0.993364	−0.496682	−	0.867933i	$-0.665448\pi$
$487$	−21.9216	−0.993364	−0.496682	+	0.867933i	$0.665448\pi$
$488$	1.00000	0.0452679
$489$	−13.6775	−0.618518
$490$	−21.1132	−0.953796
$491$	12.9170	0.582935	0.291467	−	0.956581i	$-0.405857\pi$
$491$	12.9170	0.582935	0.291467	+	0.956581i	$0.405857\pi$
$492$	−5.40009	−0.243455
$493$	44.0602	1.98437
$494$	6.15911	0.277111
$495$	3.34840	0.150500
$496$	−4.82693	−0.216735
$497$	4.35356	0.195284
$498$	0.942855	0.0422503
$499$	−12.2820	−0.549819	−0.274910	−	0.961470i	$-0.588648\pi$
$499$	−12.2820	−0.549819	−0.274910	+	0.961470i	$0.588648\pi$
$500$	4.05765	0.181464
$501$	−1.92952	−0.0862046
$502$	20.4177	0.911285
$503$	−16.1751	−0.721210	−0.360605	−	0.932719i	$-0.617430\pi$
$503$	−16.1751	−0.721210	−0.360605	+	0.932719i	$0.617430\pi$
$504$	0.833399	0.0371226
$505$	30.8932	1.37473
$506$	−8.08965	−0.359629
$507$	6.85694	0.304527
$508$	2.75407	0.122192
$509$	5.13845	0.227758	0.113879	−	0.993495i	$-0.463672\pi$
$509$	5.13845	0.227758	0.113879	+	0.993495i	$0.463672\pi$
$510$	−19.3675	−0.857605
$511$	−2.62338	−0.116052
$512$	1.00000	0.0441942
$513$	−2.48499	−0.109715
$514$	−12.1492	−0.535877
$515$	−21.4488	−0.945146
$516$	−2.31192	−0.101777
$517$	−12.7928	−0.562627
$518$	1.29301	0.0568117
$519$	11.2843	0.495325
$520$	8.29909	0.363939
$521$	−32.7699	−1.43568	−0.717838	−	0.696210i	$-0.754868\pi$
$521$	−32.7699	−1.43568	−0.717838	+	0.696210i	$0.754868\pi$
$522$	7.61748	0.333408
$523$	−22.4896	−0.983403	−0.491701	−	0.870764i	$-0.663625\pi$
$523$	−22.4896	−0.983403	−0.491701	+	0.870764i	$0.663625\pi$
$524$	−10.4039	−0.454498
$525$	−5.17692	−0.225939
$526$	12.8511	0.560334
$527$	−27.9193	−1.21619
$528$	−1.00000	−0.0435194
$529$	42.4424	1.84532
$530$	−22.1876	−0.963769
$531$	4.56669	0.198178
$532$	2.07099	0.0897889
$533$	13.3842	0.579736
$534$	10.3231	0.446726
$535$	35.8948	1.55187
$536$	2.65397	0.114634
$537$	−3.35000	−0.144563
$538$	−2.50128	−0.107838
$539$	−6.30545	−0.271595
$540$	−3.34840	−0.144092
$541$	−31.8393	−1.36888	−0.684440	−	0.729069i	$-0.739953\pi$
$541$	−31.8393	−1.36888	−0.684440	+	0.729069i	$0.739953\pi$
$542$	25.2101	1.08287
$543$	−9.90177	−0.424925
$544$	5.78408	0.247991
$545$	−6.31204	−0.270378
$546$	−2.06560	−0.0883994
$547$	−0.145555	−0.00622349	−0.00311174	−	0.999995i	$-0.500991\pi$
$547$	−0.145555	−0.00622349	−0.00311174	+	0.999995i	$0.500991\pi$
$548$	−6.44441	−0.275291
$549$	1.00000	0.0426790
$550$	6.21182	0.264873
$551$	18.9294	0.806420
$552$	8.08965	0.344318
$553$	−5.77496	−0.245576
$554$	15.2073	0.646098
$555$	−5.19502	−0.220516
$556$	−9.74997	−0.413491
$557$	33.7160	1.42859	0.714296	−	0.699844i	$-0.246747\pi$
$557$	33.7160	1.42859	0.714296	+	0.699844i	$0.246747\pi$
$558$	−4.82693	−0.204340
$559$	5.73014	0.242359
$560$	2.79056	0.117923
$561$	−5.78408	−0.244204
$562$	−5.80814	−0.245001
$563$	43.3086	1.82524	0.912620	−	0.408809i	$-0.134056\pi$
$563$	43.3086	1.82524	0.912620	+	0.408809i	$0.134056\pi$
$564$	12.7928	0.538675
$565$	−70.1376	−2.95071
$566$	2.78498	0.117062
$567$	0.833399	0.0349995
$568$	5.22386	0.219188
$569$	−17.7999	−0.746209	−0.373105	−	0.927789i	$-0.621707\pi$
$569$	−17.7999	−0.746209	−0.373105	+	0.927789i	$0.621707\pi$
$570$	−8.32077	−0.348519
$571$	−36.3184	−1.51988	−0.759939	−	0.649994i	$-0.774771\pi$
$571$	−36.3184	−1.51988	−0.759939	+	0.649994i	$0.774771\pi$
$572$	2.47852	0.103632
$573$	−14.3407	−0.599092
$574$	4.50043	0.187844
$575$	−50.2514	−2.09563
$576$	1.00000	0.0416667
$577$	−1.29158	−0.0537693	−0.0268846	−	0.999639i	$-0.508559\pi$
$577$	−1.29158	−0.0537693	−0.0268846	+	0.999639i	$0.508559\pi$
$578$	16.4556	0.684464
$579$	6.63966	0.275935
$580$	25.5064	1.05910
$581$	−0.785775	−0.0325994
$582$	−15.4745	−0.641440
$583$	−6.62633	−0.274435
$584$	−3.14781	−0.130257
$585$	8.29909	0.343125
$586$	6.12286	0.252933
$587$	−6.93030	−0.286044	−0.143022	−	0.989719i	$-0.545682\pi$
$587$	−6.93030	−0.286044	−0.143022	+	0.989719i	$0.545682\pi$
$588$	6.30545	0.260032
$589$	−11.9949	−0.494241
$590$	15.2911	0.629526
$591$	−7.00795	−0.288268
$592$	1.55149	0.0637659
$593$	12.3169	0.505795	0.252897	−	0.967493i	$-0.418617\pi$
$593$	12.3169	0.505795	0.252897	+	0.967493i	$0.418617\pi$
$594$	−1.00000	−0.0410305
$595$	16.1408	0.661709
$596$	3.82057	0.156497
$597$	−0.0364853	−0.00149324
$598$	−20.0504	−0.819920
$599$	−12.1075	−0.494698	−0.247349	−	0.968926i	$-0.579559\pi$
$599$	−12.1075	−0.494698	−0.247349	+	0.968926i	$0.579559\pi$
$600$	−6.21182	−0.253596
$601$	−8.23517	−0.335920	−0.167960	−	0.985794i	$-0.553718\pi$
$601$	−8.23517	−0.335920	−0.167960	+	0.985794i	$0.553718\pi$
$602$	1.92675	0.0785286
$603$	2.65397	0.108078
$604$	−3.56817	−0.145187
$605$	3.34840	0.136132
$606$	−9.22624	−0.374790
$607$	−16.7291	−0.679012	−0.339506	−	0.940604i	$-0.610260\pi$
$607$	−16.7291	−0.679012	−0.339506	+	0.940604i	$0.610260\pi$
$608$	2.48499	0.100780
$609$	−6.34840	−0.257250
$610$	3.34840	0.135573
$611$	−31.7072	−1.28274
$612$	5.78408	0.233808
$613$	−26.0989	−1.05412	−0.527062	−	0.849827i	$-0.676706\pi$
$613$	−26.0989	−1.05412	−0.527062	+	0.849827i	$0.676706\pi$
$614$	19.4976	0.786858
$615$	−18.0817	−0.729125
$616$	0.833399	0.0335786
$617$	35.0227	1.40996	0.704981	−	0.709226i	$-0.250956\pi$
$617$	35.0227	1.40996	0.704981	+	0.709226i	$0.250956\pi$
$618$	6.40567	0.257674
$619$	−8.50557	−0.341868	−0.170934	−	0.985283i	$-0.554678\pi$
$619$	−8.50557	−0.341868	−0.170934	+	0.985283i	$0.554678\pi$
$620$	−16.1625	−0.649102
$621$	8.08965	0.324626
$622$	1.73291	0.0694833
$623$	−8.60330	−0.344684
$624$	−2.47852	−0.0992202
$625$	−17.4724	−0.698897
$626$	17.6213	0.704290
$627$	−2.48499	−0.0992411
$628$	5.95068	0.237458
$629$	8.97395	0.357815
$630$	2.79056	0.111178
$631$	−25.6967	−1.02297	−0.511485	−	0.859292i	$-0.670904\pi$
$631$	−25.6967	−1.02297	−0.511485	+	0.859292i	$0.670904\pi$
$632$	−6.92940	−0.275637
$633$	−18.1224	−0.720302
$634$	19.9692	0.793077
$635$	9.22175	0.365954
$636$	6.62633	0.262751
$637$	−15.6282	−0.619211
$638$	7.61748	0.301579
$639$	5.22386	0.206653
$640$	3.34840	0.132357
$641$	46.6857	1.84397	0.921987	−	0.387220i	$-0.126565\pi$
$641$	46.6857	1.84397	0.921987	+	0.387220i	$0.126565\pi$
$642$	−10.7200	−0.423083
$643$	−26.0309	−1.02656	−0.513279	−	0.858222i	$-0.671570\pi$
$643$	−26.0309	−1.02656	−0.513279	+	0.858222i	$0.671570\pi$
$644$	−6.74191	−0.265668
$645$	−7.74124	−0.304811
$646$	14.3734	0.565515
$647$	24.5298	0.964367	0.482183	−	0.876070i	$-0.339844\pi$
$647$	24.5298	0.964367	0.482183	+	0.876070i	$0.339844\pi$
$648$	1.00000	0.0392837
$649$	4.56669	0.179258
$650$	15.3961	0.603885
$651$	4.02276	0.157664
$652$	13.6775	0.535652
$653$	15.7267	0.615433	0.307716	−	0.951478i	$-0.400435\pi$
$653$	15.7267	0.615433	0.307716	+	0.951478i	$0.400435\pi$
$654$	1.88509	0.0737128
$655$	−34.8366	−1.36118
$656$	5.40009	0.210838
$657$	−3.14781	−0.122808
$658$	−10.6615	−0.415629
$659$	−6.25675	−0.243728	−0.121864	−	0.992547i	$-0.538887\pi$
$659$	−6.25675	−0.243728	−0.121864	+	0.992547i	$0.538887\pi$
$660$	−3.34840	−0.130336
$661$	32.1875	1.25195	0.625975	−	0.779843i	$-0.284701\pi$
$661$	32.1875	1.25195	0.625975	+	0.779843i	$0.284701\pi$
$662$	−14.1809	−0.551157
$663$	−14.3360	−0.556763
$664$	−0.942855	−0.0365899
$665$	6.93452	0.268909
$666$	1.55149	0.0601191
$667$	−61.6228	−2.38604
$668$	1.92952	0.0746554
$669$	24.8313	0.960033
$670$	8.88656	0.343318
$671$	1.00000	0.0386046
$672$	−0.833399	−0.0321491
$673$	−27.8844	−1.07487	−0.537433	−	0.843306i	$-0.680606\pi$
$673$	−27.8844	−1.07487	−0.537433	+	0.843306i	$0.680606\pi$
$674$	−11.9127	−0.458861
$675$	−6.21182	−0.239093
$676$	−6.85694	−0.263728
$677$	−49.9307	−1.91899	−0.959497	−	0.281720i	$-0.909095\pi$
$677$	−49.9307	−1.91899	−0.959497	+	0.281720i	$0.909095\pi$
$678$	20.9466	0.804449
$679$	12.8965	0.494921
$680$	19.3675	0.742708
$681$	5.80814	0.222568
$682$	−4.82693	−0.184833
$683$	20.0571	0.767465	0.383732	−	0.923444i	$-0.374639\pi$
$683$	20.0571	0.767465	0.383732	+	0.923444i	$0.374639\pi$
$684$	2.48499	0.0950161
$685$	−21.5785	−0.824472
$686$	−11.0887	−0.423370
$687$	−18.8052	−0.717465
$688$	2.31192	0.0881411
$689$	−16.4235	−0.625685
$690$	27.0874	1.03120
$691$	−0.347783	−0.0132303	−0.00661514	−	0.999978i	$-0.502106\pi$
$691$	−0.347783	−0.0132303	−0.00661514	+	0.999978i	$0.502106\pi$
$692$	−11.2843	−0.428964
$693$	0.833399	0.0316582
$694$	−20.5281	−0.779236
$695$	−32.6469	−1.23837
$696$	−7.61748	−0.288740
$697$	31.2346	1.18309
$698$	−6.19809	−0.234601
$699$	5.68449	0.215007
$700$	5.17692	0.195669
$701$	2.23883	0.0845595	0.0422797	−	0.999106i	$-0.486538\pi$
$701$	2.23883	0.0845595	0.0422797	+	0.999106i	$0.486538\pi$
$702$	−2.47852	−0.0935457
$703$	3.85545	0.145411
$704$	1.00000	0.0376889
$705$	42.8355	1.61328
$706$	3.50538	0.131927
$707$	7.68914	0.289180
$708$	−4.56669	−0.171627
$709$	16.8999	0.634687	0.317344	−	0.948311i	$-0.397209\pi$
$709$	16.8999	0.634687	0.317344	+	0.948311i	$0.397209\pi$
$710$	17.4916	0.656448
$711$	−6.92940	−0.259873
$712$	−10.3231	−0.386876
$713$	39.0481	1.46236
$714$	−4.82045	−0.180401
$715$	8.29909	0.310368
$716$	3.35000	0.125195
$717$	−12.7198	−0.475031
$718$	−5.53816	−0.206682
$719$	−14.4040	−0.537177	−0.268588	−	0.963255i	$-0.586557\pi$
$719$	−14.4040	−0.537177	−0.268588	+	0.963255i	$0.586557\pi$
$720$	3.34840	0.124788
$721$	−5.33848	−0.198815
$722$	−12.8248	−0.477290
$723$	21.0514	0.782911
$724$	9.90177	0.367996
$725$	47.3184	1.75736
$726$	−1.00000	−0.0371135
$727$	−34.8555	−1.29272	−0.646359	−	0.763034i	$-0.723709\pi$
$727$	−34.8555	−1.29272	−0.646359	+	0.763034i	$0.723709\pi$
$728$	2.06560	0.0765561
$729$	1.00000	0.0370370
$730$	−10.5401	−0.390108
$731$	13.3723	0.494594
$732$	−1.00000	−0.0369611
$733$	−25.7953	−0.952772	−0.476386	−	0.879236i	$-0.658053\pi$
$733$	−25.7953	−0.952772	−0.476386	+	0.879236i	$0.658053\pi$
$734$	−15.6333	−0.577036
$735$	21.1132	0.778772
$736$	−8.08965	−0.298188
$737$	2.65397	0.0977602
$738$	5.40009	0.198780
$739$	−35.2925	−1.29825	−0.649127	−	0.760680i	$-0.724866\pi$
$739$	−35.2925	−1.29825	−0.649127	+	0.760680i	$0.724866\pi$
$740$	5.19502	0.190973
$741$	−6.15911	−0.226261
$742$	−5.52238	−0.202733
$743$	18.6331	0.683581	0.341791	−	0.939776i	$-0.388967\pi$
$743$	18.6331	0.683581	0.341791	+	0.939776i	$0.388967\pi$
$744$	4.82693	0.176964
$745$	12.7928	0.468692
$746$	−37.0618	−1.35693
$747$	−0.942855	−0.0344973
$748$	5.78408	0.211487
$749$	8.93401	0.326442
$750$	−4.05765	−0.148164
$751$	−42.0869	−1.53577	−0.767887	−	0.640585i	$-0.778692\pi$
$751$	−42.0869	−1.53577	−0.767887	+	0.640585i	$0.778692\pi$
$752$	−12.7928	−0.466506
$753$	−20.4177	−0.744061
$754$	18.8801	0.687572
$755$	−11.9477	−0.434820
$756$	−0.833399	−0.0303104
$757$	9.27293	0.337030	0.168515	−	0.985699i	$-0.446103\pi$
$757$	9.27293	0.337030	0.168515	+	0.985699i	$0.446103\pi$
$758$	−4.96531	−0.180348
$759$	8.08965	0.293636
$760$	8.32077	0.301826
$761$	1.08331	0.0392699	0.0196350	−	0.999807i	$-0.493750\pi$
$761$	1.08331	0.0392699	0.0196350	+	0.999807i	$0.493750\pi$
$762$	−2.75407	−0.0997695
$763$	−1.57103	−0.0568751
$764$	14.3407	0.518829
$765$	19.3675	0.700232
$766$	23.5937	0.852475
$767$	11.3186	0.408693
$768$	−1.00000	−0.0360844
$769$	−11.9056	−0.429328	−0.214664	−	0.976688i	$-0.568866\pi$
$769$	−11.9056	−0.429328	−0.214664	+	0.976688i	$0.568866\pi$
$770$	2.79056	0.100565
$771$	12.1492	0.437542
$772$	−6.63966	−0.238967
$773$	−30.5845	−1.10005	−0.550024	−	0.835149i	$-0.685382\pi$
$773$	−30.5845	−1.10005	−0.550024	+	0.835149i	$0.685382\pi$
$774$	2.31192	0.0831002
$775$	−29.9840	−1.07706
$776$	15.4745	0.555504
$777$	−1.29301	−0.0463865
$778$	10.9950	0.394190
$779$	13.4192	0.480793
$780$	−8.29909	−0.297155
$781$	5.22386	0.186925
$782$	−46.7912	−1.67325
$783$	−7.61748	−0.272227
$784$	−6.30545	−0.225194
$785$	19.9253	0.711165
$786$	10.4039	0.371096
$787$	34.0312	1.21308	0.606540	−	0.795053i	$-0.292557\pi$
$787$	34.0312	1.21308	0.606540	+	0.795053i	$0.292557\pi$
$788$	7.00795	0.249648
$789$	−12.8511	−0.457511
$790$	−23.2024	−0.825506
$791$	−17.4569	−0.620695
$792$	1.00000	0.0355335
$793$	2.47852	0.0880148
$794$	−4.57254	−0.162273
$795$	22.1876	0.786914
$796$	0.0364853	0.00129319
$797$	5.31148	0.188142	0.0940711	−	0.995565i	$-0.470012\pi$
$797$	5.31148	0.188142	0.0940711	+	0.995565i	$0.470012\pi$
$798$	−2.07099	−0.0733123
$799$	−73.9947	−2.61774
$800$	6.21182	0.219621
$801$	−10.3231	−0.364750
$802$	−18.3591	−0.648283
$803$	−3.14781	−0.111084
$804$	−2.65397	−0.0935983
$805$	−22.5746	−0.795651
$806$	−11.9636	−0.421401
$807$	2.50128	0.0880491
$808$	9.22624	0.324578
$809$	−37.7173	−1.32607	−0.663034	−	0.748589i	$-0.730732\pi$
$809$	−37.7173	−1.32607	−0.663034	+	0.748589i	$0.730732\pi$
$810$	3.34840	0.117651
$811$	11.2253	0.394173	0.197087	−	0.980386i	$-0.436852\pi$
$811$	11.2253	0.394173	0.197087	+	0.980386i	$0.436852\pi$
$812$	6.34840	0.222785
$813$	−25.2101	−0.884156
$814$	1.55149	0.0543797
$815$	45.7978	1.60423
$816$	−5.78408	−0.202483
$817$	5.74511	0.200996
$818$	−39.8953	−1.39491
$819$	2.06560	0.0721778
$820$	18.0817	0.631440
$821$	−13.8383	−0.482959	−0.241479	−	0.970406i	$-0.577633\pi$
$821$	−13.8383	−0.482959	−0.241479	+	0.970406i	$0.577633\pi$
$822$	6.44441	0.224775
$823$	−36.5810	−1.27513	−0.637567	−	0.770395i	$-0.720059\pi$
$823$	−36.5810	−1.27513	−0.637567	+	0.770395i	$0.720059\pi$
$824$	−6.40567	−0.223152
$825$	−6.21182	−0.216268
$826$	3.80588	0.132423
$827$	−20.0512	−0.697248	−0.348624	−	0.937263i	$-0.613351\pi$
$827$	−20.0512	−0.697248	−0.348624	+	0.937263i	$0.613351\pi$
$828$	−8.08965	−0.281135
$829$	−16.7379	−0.581330	−0.290665	−	0.956825i	$-0.593876\pi$
$829$	−16.7379	−0.581330	−0.290665	+	0.956825i	$0.593876\pi$
$830$	−3.15706	−0.109583
$831$	−15.2073	−0.527536
$832$	2.47852	0.0859272
$833$	−36.4712	−1.26365
$834$	9.74997	0.337614
$835$	6.46082	0.223586
$836$	2.48499	0.0859453
$837$	4.82693	0.166843
$838$	−10.0324	−0.346563
$839$	−16.4125	−0.566623	−0.283311	−	0.959028i	$-0.591433\pi$
$839$	−16.4125	−0.566623	−0.283311	+	0.959028i	$0.591433\pi$
$840$	−2.79056	−0.0962834
$841$	29.0261	1.00090
$842$	26.7722	0.922629
$843$	5.80814	0.200043
$844$	18.1224	0.623800
$845$	−22.9598	−0.789841
$846$	−12.7928	−0.439826
$847$	0.833399	0.0286359
$848$	−6.62633	−0.227549
$849$	−2.78498	−0.0955804
$850$	35.9297	1.23238
$851$	−12.5510	−0.430243
$852$	−5.22386	−0.178967
$853$	−20.3536	−0.696894	−0.348447	−	0.937329i	$-0.613291\pi$
$853$	−20.3536	−0.696894	−0.348447	+	0.937329i	$0.613291\pi$
$854$	0.833399	0.0285183
$855$	8.32077	0.284564
$856$	10.7200	0.366401
$857$	−26.3089	−0.898694	−0.449347	−	0.893357i	$-0.648343\pi$
$857$	−26.3089	−0.898694	−0.449347	+	0.893357i	$0.648343\pi$
$858$	−2.47852	−0.0846153
$859$	−30.6409	−1.04545	−0.522727	−	0.852500i	$-0.675085\pi$
$859$	−30.6409	−1.04545	−0.522727	+	0.852500i	$0.675085\pi$
$860$	7.74124	0.263974
$861$	−4.50043	−0.153374
$862$	32.5251	1.10781
$863$	36.2894	1.23530	0.617652	−	0.786451i	$-0.288084\pi$
$863$	36.2894	1.23530	0.617652	+	0.786451i	$0.288084\pi$
$864$	−1.00000	−0.0340207
$865$	−37.7843	−1.28471
$866$	−31.8074	−1.08086
$867$	−16.4556	−0.558862
$868$	−4.02276	−0.136541
$869$	−6.92940	−0.235064
$870$	−25.5064	−0.864749
$871$	6.57792	0.222884
$872$	−1.88509	−0.0638371
$873$	15.4745	0.523734
$874$	−20.1027	−0.679985
$875$	3.38164	0.114320
$876$	3.14781	0.106355
$877$	−3.63769	−0.122836	−0.0614180	−	0.998112i	$-0.519562\pi$
$877$	−3.63769	−0.122836	−0.0614180	+	0.998112i	$0.519562\pi$
$878$	23.4750	0.792243
$879$	−6.12286	−0.206519
$880$	3.34840	0.112875
$881$	−32.6148	−1.09882	−0.549410	−	0.835553i	$-0.685148\pi$
$881$	−32.6148	−1.09882	−0.549410	+	0.835553i	$0.685148\pi$
$882$	−6.30545	−0.212315
$883$	−33.0337	−1.11167	−0.555837	−	0.831291i	$-0.687602\pi$
$883$	−33.0337	−1.11167	−0.555837	+	0.831291i	$0.687602\pi$
$884$	14.3360	0.482171
$885$	−15.2911	−0.514006
$886$	−15.5145	−0.521220
$887$	16.6329	0.558479	0.279239	−	0.960222i	$-0.409918\pi$
$887$	16.6329	0.558479	0.279239	+	0.960222i	$0.409918\pi$
$888$	−1.55149	−0.0520646
$889$	2.29524	0.0769800
$890$	−34.5661	−1.15866
$891$	1.00000	0.0335013
$892$	−24.8313	−0.831413
$893$	−31.7901	−1.06381
$894$	−3.82057	−0.127779
$895$	11.2171	0.374948
$896$	0.833399	0.0278419
$897$	20.0504	0.669462
$898$	29.4615	0.983142
$899$	−36.7690	−1.22632
$900$	6.21182	0.207061
$901$	−38.3273	−1.27687
$902$	5.40009	0.179803
$903$	−1.92675	−0.0641183
$904$	−20.9466	−0.696673
$905$	33.1551	1.10211
$906$	3.56817	0.118544
$907$	16.8593	0.559804	0.279902	−	0.960029i	$-0.409698\pi$
$907$	16.8593	0.559804	0.279902	+	0.960029i	$0.409698\pi$
$908$	−5.80814	−0.192750
$909$	9.22624	0.306015
$910$	6.91646	0.229278
$911$	−31.1658	−1.03257	−0.516285	−	0.856417i	$-0.672686\pi$
$911$	−31.1658	−1.03257	−0.516285	+	0.856417i	$0.672686\pi$
$912$	−2.48499	−0.0822864
$913$	−0.942855	−0.0312039
$914$	21.8078	0.721337
$915$	−3.34840	−0.110695
$916$	18.8052	0.621343
$917$	−8.67064	−0.286330
$918$	−5.78408	−0.190903
$919$	4.51238	0.148850	0.0744248	−	0.997227i	$-0.476288\pi$
$919$	4.51238	0.148850	0.0744248	+	0.997227i	$0.476288\pi$
$920$	−27.0874	−0.893046
$921$	−19.4976	−0.642467
$922$	−11.3148	−0.372633
$923$	12.9475	0.426171
$924$	−0.833399	−0.0274168
$925$	9.63758	0.316882
$926$	4.44363	0.146027
$927$	−6.40567	−0.210390
$928$	7.61748	0.250056
$929$	−6.60781	−0.216795	−0.108398	−	0.994108i	$-0.534572\pi$
$929$	−6.60781	−0.216795	−0.108398	+	0.994108i	$0.534572\pi$
$930$	16.1625	0.529989
$931$	−15.6690	−0.513531
$932$	−5.68449	−0.186202
$933$	−1.73291	−0.0567329
$934$	−18.6738	−0.611027
$935$	19.3675	0.633384
$936$	2.47852	0.0810130
$937$	−14.5468	−0.475222	−0.237611	−	0.971360i	$-0.576364\pi$
$937$	−14.5468	−0.475222	−0.237611	+	0.971360i	$0.576364\pi$
$938$	2.21182	0.0722183
$939$	−17.6213	−0.575050
$940$	−42.8355	−1.39714
$941$	4.69532	0.153063	0.0765315	−	0.997067i	$-0.475615\pi$
$941$	4.69532	0.153063	0.0765315	+	0.997067i	$0.475615\pi$
$942$	−5.95068	−0.193884
$943$	−43.6849	−1.42257
$944$	4.56669	0.148633
$945$	−2.79056	−0.0907769
$946$	2.31192	0.0751670
$947$	34.3582	1.11649	0.558245	−	0.829676i	$-0.311475\pi$
$947$	34.3582	1.11649	0.558245	+	0.829676i	$0.311475\pi$
$948$	6.92940	0.225057
$949$	−7.80191	−0.253261
$950$	15.4363	0.500821
$951$	−19.9692	−0.647544
$952$	4.82045	0.156232
$953$	−0.386632	−0.0125242	−0.00626212	−	0.999980i	$-0.501993\pi$
$953$	−0.386632	−0.0125242	−0.00626212	+	0.999980i	$0.501993\pi$
$954$	−6.62633	−0.214535
$955$	48.0185	1.55384
$956$	12.7198	0.411389
$957$	−7.61748	−0.246238
$958$	−16.6084	−0.536593
$959$	−5.37077	−0.173431
$960$	−3.34840	−0.108069
$961$	−7.70079	−0.248413
$962$	3.84540	0.123981
$963$	10.7200	0.345446
$964$	−21.0514	−0.678021
$965$	−22.2323	−0.715683
$966$	6.74191	0.216917
$967$	−24.5702	−0.790126	−0.395063	−	0.918654i	$-0.629277\pi$
$967$	−24.5702	−0.790126	−0.395063	+	0.918654i	$0.629277\pi$
$968$	1.00000	0.0321412
$969$	−14.3734	−0.461741
$970$	51.8150	1.66368
$971$	−19.8218	−0.636112	−0.318056	−	0.948072i	$-0.603030\pi$
$971$	−19.8218	−0.636112	−0.318056	+	0.948072i	$0.603030\pi$
$972$	−1.00000	−0.0320750
$973$	−8.12562	−0.260495
$974$	−21.9216	−0.702414
$975$	−15.3961	−0.493070
$976$	1.00000	0.0320092
$977$	−40.1558	−1.28470	−0.642349	−	0.766412i	$-0.722040\pi$
$977$	−40.1558	−1.28470	−0.642349	+	0.766412i	$0.722040\pi$
$978$	−13.6775	−0.437358
$979$	−10.3231	−0.329929
$980$	−21.1132	−0.674436
$981$	−1.88509	−0.0601862
$982$	12.9170	0.412197
$983$	−7.03753	−0.224462	−0.112231	−	0.993682i	$-0.535800\pi$
$983$	−7.03753	−0.224462	−0.112231	+	0.993682i	$0.535800\pi$
$984$	−5.40009	−0.172149
$985$	23.4654	0.747671
$986$	44.0602	1.40316
$987$	10.6615	0.339360
$988$	6.15911	0.195947
$989$	−18.7026	−0.594709
$990$	3.34840	0.106419
$991$	50.8657	1.61580	0.807901	−	0.589318i	$-0.200604\pi$
$991$	50.8657	1.61580	0.807901	+	0.589318i	$0.200604\pi$
$992$	−4.82693	−0.153255
$993$	14.1809	0.450017
$994$	4.35356	0.138087
$995$	0.122168	0.00387297
$996$	0.942855	0.0298755
$997$	15.8831	0.503023	0.251511	−	0.967854i	$-0.419072\pi$
$997$	15.8831	0.503023	0.251511	+	0.967854i	$0.419072\pi$
$998$	−12.2820	−0.388781
$999$	−1.55149	−0.0490870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.v.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.v.1.4	✓	5	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.34840 q^{5} -1.00000 q^{6} +0.833399 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.34840 q^{5} -1.00000 q^{6} +0.833399 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.34840 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.47852 q^{13} +0.833399 q^{14} -3.34840 q^{15} +1.00000 q^{16} +5.78408 q^{17} +1.00000 q^{18} +2.48499 q^{19} +3.34840 q^{20} -0.833399 q^{21} +1.00000 q^{22} -8.08965 q^{23} -1.00000 q^{24} +6.21182 q^{25} +2.47852 q^{26} -1.00000 q^{27} +0.833399 q^{28} +7.61748 q^{29} -3.34840 q^{30} -4.82693 q^{31} +1.00000 q^{32} -1.00000 q^{33} +5.78408 q^{34} +2.79056 q^{35} +1.00000 q^{36} +1.55149 q^{37} +2.48499 q^{38} -2.47852 q^{39} +3.34840 q^{40} +5.40009 q^{41} -0.833399 q^{42} +2.31192 q^{43} +1.00000 q^{44} +3.34840 q^{45} -8.08965 q^{46} -12.7928 q^{47} -1.00000 q^{48} -6.30545 q^{49} +6.21182 q^{50} -5.78408 q^{51} +2.47852 q^{52} -6.62633 q^{53} -1.00000 q^{54} +3.34840 q^{55} +0.833399 q^{56} -2.48499 q^{57} +7.61748 q^{58} +4.56669 q^{59} -3.34840 q^{60} +1.00000 q^{61} -4.82693 q^{62} +0.833399 q^{63} +1.00000 q^{64} +8.29909 q^{65} -1.00000 q^{66} +2.65397 q^{67} +5.78408 q^{68} +8.08965 q^{69} +2.79056 q^{70} +5.22386 q^{71} +1.00000 q^{72} -3.14781 q^{73} +1.55149 q^{74} -6.21182 q^{75} +2.48499 q^{76} +0.833399 q^{77} -2.47852 q^{78} -6.92940 q^{79} +3.34840 q^{80} +1.00000 q^{81} +5.40009 q^{82} -0.942855 q^{83} -0.833399 q^{84} +19.3675 q^{85} +2.31192 q^{86} -7.61748 q^{87} +1.00000 q^{88} -10.3231 q^{89} +3.34840 q^{90} +2.06560 q^{91} -8.08965 q^{92} +4.82693 q^{93} -12.7928 q^{94} +8.32077 q^{95} -1.00000 q^{96} +15.4745 q^{97} -6.30545 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 5 q^{12} - 2 q^{13} - 7 q^{15} + 5 q^{16} + 2 q^{17} + 5 q^{18} + 18 q^{19} + 7 q^{20} + 5 q^{22} - q^{23} - 5 q^{24} + 6 q^{25} - 2 q^{26} - 5 q^{27} + 7 q^{29} - 7 q^{30} + 5 q^{32} - 5 q^{33} + 2 q^{34} + 7 q^{35} + 5 q^{36} + 11 q^{37} + 18 q^{38} + 2 q^{39} + 7 q^{40} + 8 q^{41} - 7 q^{43} + 5 q^{44} + 7 q^{45} - q^{46} + q^{47} - 5 q^{48} + 7 q^{49} + 6 q^{50} - 2 q^{51} - 2 q^{52} + 10 q^{53} - 5 q^{54} + 7 q^{55} - 18 q^{57} + 7 q^{58} + 8 q^{59} - 7 q^{60} + 5 q^{61} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} + 34 q^{71} + 5 q^{72} + 13 q^{73} + 11 q^{74} - 6 q^{75} + 18 q^{76} + 2 q^{78} + 15 q^{79} + 7 q^{80} + 5 q^{81} + 8 q^{82} - 27 q^{83} - 2 q^{85} - 7 q^{86} - 7 q^{87} + 5 q^{88} + 11 q^{89} + 7 q^{90} + q^{91} - q^{92} + q^{94} + 11 q^{95} - 5 q^{96} + 37 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9 + 7 * q^10 + 5 * q^11 - 5 * q^12 - 2 * q^13 - 7 * q^15 + 5 * q^16 + 2 * q^17 + 5 * q^18 + 18 * q^19 + 7 * q^20 + 5 * q^22 - q^23 - 5 * q^24 + 6 * q^25 - 2 * q^26 - 5 * q^27 + 7 * q^29 - 7 * q^30 + 5 * q^32 - 5 * q^33 + 2 * q^34 + 7 * q^35 + 5 * q^36 + 11 * q^37 + 18 * q^38 + 2 * q^39 + 7 * q^40 + 8 * q^41 - 7 * q^43 + 5 * q^44 + 7 * q^45 - q^46 + q^47 - 5 * q^48 + 7 * q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 + 10 * q^53 - 5 * q^54 + 7 * q^55 - 18 * q^57 + 7 * q^58 + 8 * q^59 - 7 * q^60 + 5 * q^61 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 + 2 * q^68 + q^69 + 7 * q^70 + 34 * q^71 + 5 * q^72 + 13 * q^73 + 11 * q^74 - 6 * q^75 + 18 * q^76 + 2 * q^78 + 15 * q^79 + 7 * q^80 + 5 * q^81 + 8 * q^82 - 27 * q^83 - 2 * q^85 - 7 * q^86 - 7 * q^87 + 5 * q^88 + 11 * q^89 + 7 * q^90 + q^91 - q^92 + q^94 + 11 * q^95 - 5 * q^96 + 37 * q^97 + 7 * q^98 + 5 * q^99

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