LMFDB - Embedded newform 1002.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1002,2,Mod(1,1002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1002, 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("1002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1002 = 2 \cdot 3 \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1002.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:	$8.00101028253$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	1002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.675131 q^{5} -1.00000 q^{6} -5.15633 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.675131 q^{5} -1.00000 q^{6} -5.15633 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.675131 q^{10} +3.76845 q^{11} -1.00000 q^{12} -6.15633 q^{13} -5.15633 q^{14} -0.675131 q^{15} +1.00000 q^{16} -5.19394 q^{17} +1.00000 q^{18} +2.54420 q^{19} +0.675131 q^{20} +5.15633 q^{21} +3.76845 q^{22} +2.15633 q^{23} -1.00000 q^{24} -4.54420 q^{25} -6.15633 q^{26} -1.00000 q^{27} -5.15633 q^{28} -3.76845 q^{29} -0.675131 q^{30} -10.5369 q^{31} +1.00000 q^{32} -3.76845 q^{33} -5.19394 q^{34} -3.48119 q^{35} +1.00000 q^{36} -3.06300 q^{37} +2.54420 q^{38} +6.15633 q^{39} +0.675131 q^{40} +2.31265 q^{41} +5.15633 q^{42} -7.50659 q^{43} +3.76845 q^{44} +0.675131 q^{45} +2.15633 q^{46} +9.46898 q^{47} -1.00000 q^{48} +19.5877 q^{49} -4.54420 q^{50} +5.19394 q^{51} -6.15633 q^{52} -3.74306 q^{53} -1.00000 q^{54} +2.54420 q^{55} -5.15633 q^{56} -2.54420 q^{57} -3.76845 q^{58} -10.5999 q^{59} -0.675131 q^{60} -0.775746 q^{61} -10.5369 q^{62} -5.15633 q^{63} +1.00000 q^{64} -4.15633 q^{65} -3.76845 q^{66} +6.86177 q^{67} -5.19394 q^{68} -2.15633 q^{69} -3.48119 q^{70} +5.50659 q^{71} +1.00000 q^{72} -11.8192 q^{73} -3.06300 q^{74} +4.54420 q^{75} +2.54420 q^{76} -19.4314 q^{77} +6.15633 q^{78} +10.3879 q^{79} +0.675131 q^{80} +1.00000 q^{81} +2.31265 q^{82} +6.44358 q^{83} +5.15633 q^{84} -3.50659 q^{85} -7.50659 q^{86} +3.76845 q^{87} +3.76845 q^{88} -11.9321 q^{89} +0.675131 q^{90} +31.7440 q^{91} +2.15633 q^{92} +10.5369 q^{93} +9.46898 q^{94} +1.71767 q^{95} -1.00000 q^{96} +8.50659 q^{97} +19.5877 q^{98} +3.76845 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{12} - 8 q^{13} - 5 q^{14} + 3 q^{15} + 3 q^{16} - 16 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 5 q^{21} - 4 q^{23} - 3 q^{24} - 4 q^{25} - 8 q^{26} - 3 q^{27} - 5 q^{28} + 3 q^{30} - 9 q^{31} + 3 q^{32} - 16 q^{34} - 5 q^{35} + 3 q^{36} - 5 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} - 14 q^{41} + 5 q^{42} - 2 q^{43} - 3 q^{45} - 4 q^{46} - 3 q^{47} - 3 q^{48} + 6 q^{49} - 4 q^{50} + 16 q^{51} - 8 q^{52} - 15 q^{53} - 3 q^{54} - 2 q^{55} - 5 q^{56} + 2 q^{57} - 5 q^{59} + 3 q^{60} - 4 q^{61} - 9 q^{62} - 5 q^{63} + 3 q^{64} - 2 q^{65} + 3 q^{67} - 16 q^{68} + 4 q^{69} - 5 q^{70} - 4 q^{71} + 3 q^{72} + 6 q^{73} - 5 q^{74} + 4 q^{75} - 2 q^{76} - 16 q^{77} + 8 q^{78} + 32 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 3 q^{83} + 5 q^{84} + 10 q^{85} - 2 q^{86} - 27 q^{89} - 3 q^{90} + 32 q^{91} - 4 q^{92} + 9 q^{93} - 3 q^{94} + 24 q^{95} - 3 q^{96} + 5 q^{97} + 6 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^12 - 8 * q^13 - 5 * q^14 + 3 * q^15 + 3 * q^16 - 16 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 5 * q^21 - 4 * q^23 - 3 * q^24 - 4 * q^25 - 8 * q^26 - 3 * q^27 - 5 * q^28 + 3 * q^30 - 9 * q^31 + 3 * q^32 - 16 * q^34 - 5 * q^35 + 3 * q^36 - 5 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 - 14 * q^41 + 5 * q^42 - 2 * q^43 - 3 * q^45 - 4 * q^46 - 3 * q^47 - 3 * q^48 + 6 * q^49 - 4 * q^50 + 16 * q^51 - 8 * q^52 - 15 * q^53 - 3 * q^54 - 2 * q^55 - 5 * q^56 + 2 * q^57 - 5 * q^59 + 3 * q^60 - 4 * q^61 - 9 * q^62 - 5 * q^63 + 3 * q^64 - 2 * q^65 + 3 * q^67 - 16 * q^68 + 4 * q^69 - 5 * q^70 - 4 * q^71 + 3 * q^72 + 6 * q^73 - 5 * q^74 + 4 * q^75 - 2 * q^76 - 16 * q^77 + 8 * q^78 + 32 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 3 * q^83 + 5 * q^84 + 10 * q^85 - 2 * q^86 - 27 * q^89 - 3 * q^90 + 32 * q^91 - 4 * q^92 + 9 * q^93 - 3 * q^94 + 24 * q^95 - 3 * q^96 + 5 * q^97 + 6 * q^98

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
$5$	0.675131	0.301928	0.150964	−	0.988539i	$-0.451762\pi$
$5$	0.675131	0.301928	0.150964	+	0.988539i	$0.451762\pi$
$6$	−1.00000	−0.408248
$7$	−5.15633	−1.94891	−0.974454	−	0.224588i	$-0.927896\pi$
$7$	−5.15633	−1.94891	−0.974454	+	0.224588i	$0.927896\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.675131	0.213495
$11$	3.76845	1.13623	0.568116	−	0.822949i	$-0.307673\pi$
$11$	3.76845	1.13623	0.568116	+	0.822949i	$0.307673\pi$
$12$	−1.00000	−0.288675
$13$	−6.15633	−1.70746	−0.853729	−	0.520718i	$-0.825664\pi$
$13$	−6.15633	−1.70746	−0.853729	+	0.520718i	$0.825664\pi$
$14$	−5.15633	−1.37809
$15$	−0.675131	−0.174318
$16$	1.00000	0.250000
$17$	−5.19394	−1.25971	−0.629857	−	0.776711i	$-0.716887\pi$
$17$	−5.19394	−1.25971	−0.629857	+	0.776711i	$0.716887\pi$
$18$	1.00000	0.235702
$19$	2.54420	0.583679	0.291840	−	0.956467i	$-0.405733\pi$
$19$	2.54420	0.583679	0.291840	+	0.956467i	$0.405733\pi$
$20$	0.675131	0.150964
$21$	5.15633	1.12520
$22$	3.76845	0.803437
$23$	2.15633	0.449625	0.224812	−	0.974402i	$-0.427823\pi$
$23$	2.15633	0.449625	0.224812	+	0.974402i	$0.427823\pi$
$24$	−1.00000	−0.204124
$25$	−4.54420	−0.908840
$26$	−6.15633	−1.20735
$27$	−1.00000	−0.192450
$28$	−5.15633	−0.974454
$29$	−3.76845	−0.699784	−0.349892	−	0.936790i	$-0.613782\pi$
$29$	−3.76845	−0.699784	−0.349892	+	0.936790i	$0.613782\pi$
$30$	−0.675131	−0.123261
$31$	−10.5369	−1.89248	−0.946242	−	0.323460i	$-0.895154\pi$
$31$	−10.5369	−1.89248	−0.946242	+	0.323460i	$0.895154\pi$
$32$	1.00000	0.176777
$33$	−3.76845	−0.656003
$34$	−5.19394	−0.890753
$35$	−3.48119	−0.588429
$36$	1.00000	0.166667
$37$	−3.06300	−0.503555	−0.251777	−	0.967785i	$-0.581015\pi$
$37$	−3.06300	−0.503555	−0.251777	+	0.967785i	$0.581015\pi$
$38$	2.54420	0.412723
$39$	6.15633	0.985801
$40$	0.675131	0.106748
$41$	2.31265	0.361175	0.180588	−	0.983559i	$-0.442200\pi$
$41$	2.31265	0.361175	0.180588	+	0.983559i	$0.442200\pi$
$42$	5.15633	0.795638
$43$	−7.50659	−1.14474	−0.572372	−	0.819994i	$-0.693977\pi$
$43$	−7.50659	−1.14474	−0.572372	+	0.819994i	$0.693977\pi$
$44$	3.76845	0.568116
$45$	0.675131	0.100643
$46$	2.15633	0.317933
$47$	9.46898	1.38119	0.690596	−	0.723241i	$-0.257348\pi$
$47$	9.46898	1.38119	0.690596	+	0.723241i	$0.257348\pi$
$48$	−1.00000	−0.144338
$49$	19.5877	2.79824
$50$	−4.54420	−0.642647
$51$	5.19394	0.727297
$52$	−6.15633	−0.853729
$53$	−3.74306	−0.514149	−0.257074	−	0.966392i	$-0.582759\pi$
$53$	−3.74306	−0.514149	−0.257074	+	0.966392i	$0.582759\pi$
$54$	−1.00000	−0.136083
$55$	2.54420	0.343060
$56$	−5.15633	−0.689043
$57$	−2.54420	−0.336987
$58$	−3.76845	−0.494822
$59$	−10.5999	−1.37999	−0.689995	−	0.723814i	$-0.742387\pi$
$59$	−10.5999	−1.37999	−0.689995	+	0.723814i	$0.742387\pi$
$60$	−0.675131	−0.0871590
$61$	−0.775746	−0.0993241	−0.0496621	−	0.998766i	$-0.515814\pi$
$61$	−0.775746	−0.0993241	−0.0496621	+	0.998766i	$0.515814\pi$
$62$	−10.5369	−1.33819
$63$	−5.15633	−0.649636
$64$	1.00000	0.125000
$65$	−4.15633	−0.515529
$66$	−3.76845	−0.463864
$67$	6.86177	0.838299	0.419150	−	0.907917i	$-0.362328\pi$
$67$	6.86177	0.838299	0.419150	+	0.907917i	$0.362328\pi$
$68$	−5.19394	−0.629857
$69$	−2.15633	−0.259591
$70$	−3.48119	−0.416082
$71$	5.50659	0.653512	0.326756	−	0.945109i	$-0.394045\pi$
$71$	5.50659	0.653512	0.326756	+	0.945109i	$0.394045\pi$
$72$	1.00000	0.117851
$73$	−11.8192	−1.38334	−0.691669	−	0.722215i	$-0.743124\pi$
$73$	−11.8192	−1.38334	−0.691669	+	0.722215i	$0.743124\pi$
$74$	−3.06300	−0.356067
$75$	4.54420	0.524719
$76$	2.54420	0.291840
$77$	−19.4314	−2.21441
$78$	6.15633	0.697067
$79$	10.3879	1.16873	0.584364	−	0.811492i	$-0.301344\pi$
$79$	10.3879	1.16873	0.584364	+	0.811492i	$0.301344\pi$
$80$	0.675131	0.0754819
$81$	1.00000	0.111111
$82$	2.31265	0.255390
$83$	6.44358	0.707275	0.353638	−	0.935383i	$-0.384945\pi$
$83$	6.44358	0.707275	0.353638	+	0.935383i	$0.384945\pi$
$84$	5.15633	0.562601
$85$	−3.50659	−0.380343
$86$	−7.50659	−0.809456
$87$	3.76845	0.404020
$88$	3.76845	0.401718
$89$	−11.9321	−1.26480	−0.632399	−	0.774643i	$-0.717929\pi$
$89$	−11.9321	−1.26480	−0.632399	+	0.774643i	$0.717929\pi$
$90$	0.675131	0.0711650
$91$	31.7440	3.32768
$92$	2.15633	0.224812
$93$	10.5369	1.09263
$94$	9.46898	0.976650
$95$	1.71767	0.176229
$96$	−1.00000	−0.102062
$97$	8.50659	0.863713	0.431857	−	0.901942i	$-0.357859\pi$
$97$	8.50659	0.863713	0.431857	+	0.901942i	$0.357859\pi$
$98$	19.5877	1.97866
$99$	3.76845	0.378744
$100$	−4.54420	−0.454420
$101$	−16.4944	−1.64125	−0.820625	−	0.571466i	$-0.806375\pi$
$101$	−16.4944	−1.64125	−0.820625	+	0.571466i	$0.806375\pi$
$102$	5.19394	0.514276
$103$	6.12601	0.603614	0.301807	−	0.953369i	$-0.402410\pi$
$103$	6.12601	0.603614	0.301807	+	0.953369i	$0.402410\pi$
$104$	−6.15633	−0.603677
$105$	3.48119	0.339730
$106$	−3.74306	−0.363558
$107$	−6.49929	−0.628310	−0.314155	−	0.949372i	$-0.601721\pi$
$107$	−6.49929	−0.628310	−0.314155	+	0.949372i	$0.601721\pi$
$108$	−1.00000	−0.0962250
$109$	−0.0811024	−0.00776820	−0.00388410	−	0.999992i	$-0.501236\pi$
$109$	−0.0811024	−0.00776820	−0.00388410	+	0.999992i	$0.501236\pi$
$110$	2.54420	0.242580
$111$	3.06300	0.290727
$112$	−5.15633	−0.487227
$113$	16.9380	1.59339	0.796694	−	0.604383i	$-0.206580\pi$
$113$	16.9380	1.59339	0.796694	+	0.604383i	$0.206580\pi$
$114$	−2.54420	−0.238286
$115$	1.45580	0.135754
$116$	−3.76845	−0.349892
$117$	−6.15633	−0.569152
$118$	−10.5999	−0.975801
$119$	26.7816	2.45507
$120$	−0.675131	−0.0616307
$121$	3.20123	0.291021
$122$	−0.775746	−0.0702328
$123$	−2.31265	−0.208525
$124$	−10.5369	−0.946242
$125$	−6.44358	−0.576332
$126$	−5.15633	−0.459362
$127$	−0.425485	−0.0377556	−0.0188778	−	0.999822i	$-0.506009\pi$
$127$	−0.425485	−0.0377556	−0.0188778	+	0.999822i	$0.506009\pi$
$128$	1.00000	0.0883883
$129$	7.50659	0.660918
$130$	−4.15633	−0.364534
$131$	4.49341	0.392591	0.196296	−	0.980545i	$-0.437109\pi$
$131$	4.49341	0.392591	0.196296	+	0.980545i	$0.437109\pi$
$132$	−3.76845	−0.328002
$133$	−13.1187	−1.13754
$134$	6.86177	0.592767
$135$	−0.675131	−0.0581060
$136$	−5.19394	−0.445376
$137$	−6.50659	−0.555895	−0.277948	−	0.960596i	$-0.589654\pi$
$137$	−6.50659	−0.555895	−0.277948	+	0.960596i	$0.589654\pi$
$138$	−2.15633	−0.183559
$139$	14.2120	1.20545	0.602725	−	0.797949i	$-0.294082\pi$
$139$	14.2120	1.20545	0.602725	+	0.797949i	$0.294082\pi$
$140$	−3.48119	−0.294215
$141$	−9.46898	−0.797432
$142$	5.50659	0.462103
$143$	−23.1998	−1.94007
$144$	1.00000	0.0833333
$145$	−2.54420	−0.211284
$146$	−11.8192	−0.978167
$147$	−19.5877	−1.61557
$148$	−3.06300	−0.251777
$149$	15.9199	1.30421	0.652103	−	0.758131i	$-0.273887\pi$
$149$	15.9199	1.30421	0.652103	+	0.758131i	$0.273887\pi$
$150$	4.54420	0.371032
$151$	−18.3634	−1.49440	−0.747198	−	0.664602i	$-0.768601\pi$
$151$	−18.3634	−1.49440	−0.747198	+	0.664602i	$0.768601\pi$
$152$	2.54420	0.206362
$153$	−5.19394	−0.419905
$154$	−19.4314	−1.56582
$155$	−7.11379	−0.571393
$156$	6.15633	0.492900
$157$	4.05079	0.323288	0.161644	−	0.986849i	$-0.448320\pi$
$157$	4.05079	0.323288	0.161644	+	0.986849i	$0.448320\pi$
$158$	10.3879	0.826415
$159$	3.74306	0.296844
$160$	0.675131	0.0533738
$161$	−11.1187	−0.876277
$162$	1.00000	0.0785674
$163$	12.5696	0.984526	0.492263	−	0.870446i	$-0.336170\pi$
$163$	12.5696	0.984526	0.492263	+	0.870446i	$0.336170\pi$
$164$	2.31265	0.180588
$165$	−2.54420	−0.198066
$166$	6.44358	0.500119
$167$	1.00000	0.0773823
$167$	1.00000	0.0773823
$168$	5.15633	0.397819
$169$	24.9003	1.91541
$170$	−3.50659	−0.268943
$171$	2.54420	0.194560
$172$	−7.50659	−0.572372
$173$	−10.5139	−0.799356	−0.399678	−	0.916656i	$-0.630878\pi$
$173$	−10.5139	−0.799356	−0.399678	+	0.916656i	$0.630878\pi$
$174$	3.76845	0.285686
$175$	23.4314	1.77124
$176$	3.76845	0.284058
$177$	10.5999	0.796738
$178$	−11.9321	−0.894347
$179$	11.3054	0.845002	0.422501	−	0.906362i	$-0.361152\pi$
$179$	11.3054	0.845002	0.422501	+	0.906362i	$0.361152\pi$
$180$	0.675131	0.0503213
$181$	−4.03032	−0.299571	−0.149786	−	0.988719i	$-0.547858\pi$
$181$	−4.03032	−0.299571	−0.149786	+	0.988719i	$0.547858\pi$
$182$	31.7440	2.35302
$183$	0.775746	0.0573448
$184$	2.15633	0.158966
$185$	−2.06793	−0.152037
$186$	10.5369	0.772603
$187$	−19.5731	−1.43133
$188$	9.46898	0.690596
$189$	5.15633	0.375067
$190$	1.71767	0.124613
$191$	12.0884	0.874686	0.437343	−	0.899295i	$-0.355920\pi$
$191$	12.0884	0.874686	0.437343	+	0.899295i	$0.355920\pi$
$192$	−1.00000	−0.0721688
$193$	8.67021	0.624095	0.312048	−	0.950066i	$-0.398985\pi$
$193$	8.67021	0.624095	0.312048	+	0.950066i	$0.398985\pi$
$194$	8.50659	0.610737
$195$	4.15633	0.297641
$196$	19.5877	1.39912
$197$	−18.5296	−1.32018	−0.660090	−	0.751187i	$-0.729482\pi$
$197$	−18.5296	−1.32018	−0.660090	+	0.751187i	$0.729482\pi$
$198$	3.76845	0.267812
$199$	8.18664	0.580336	0.290168	−	0.956976i	$-0.406289\pi$
$199$	8.18664	0.580336	0.290168	+	0.956976i	$0.406289\pi$
$200$	−4.54420	−0.321323
$201$	−6.86177	−0.483992
$202$	−16.4944	−1.16054
$203$	19.4314	1.36381
$204$	5.19394	0.363648
$205$	1.56134	0.109049
$206$	6.12601	0.426819
$207$	2.15633	0.149875
$208$	−6.15633	−0.426864
$209$	9.58769	0.663194
$210$	3.48119	0.240225
$211$	2.52373	0.173741	0.0868704	−	0.996220i	$-0.472313\pi$
$211$	2.52373	0.173741	0.0868704	+	0.996220i	$0.472313\pi$
$212$	−3.74306	−0.257074
$213$	−5.50659	−0.377305
$214$	−6.49929	−0.444283
$215$	−5.06793	−0.345630
$216$	−1.00000	−0.0680414
$217$	54.3317	3.68828
$218$	−0.0811024	−0.00549295
$219$	11.8192	0.798670
$220$	2.54420	0.171530
$221$	31.9756	2.15091
$222$	3.06300	0.205575
$223$	−20.8945	−1.39920	−0.699598	−	0.714536i	$-0.746638\pi$
$223$	−20.8945	−1.39920	−0.699598	+	0.714536i	$0.746638\pi$
$224$	−5.15633	−0.344521
$225$	−4.54420	−0.302947
$226$	16.9380	1.12670
$227$	2.16125	0.143447	0.0717236	−	0.997425i	$-0.477150\pi$
$227$	2.16125	0.143447	0.0717236	+	0.997425i	$0.477150\pi$
$228$	−2.54420	−0.168494
$229$	−17.7743	−1.17456	−0.587280	−	0.809384i	$-0.699801\pi$
$229$	−17.7743	−1.17456	−0.587280	+	0.809384i	$0.699801\pi$
$230$	1.45580	0.0959927
$231$	19.4314	1.27849
$232$	−3.76845	−0.247411
$233$	−25.8872	−1.69592	−0.847962	−	0.530057i	$-0.822171\pi$
$233$	−25.8872	−1.69592	−0.847962	+	0.530057i	$0.822171\pi$
$234$	−6.15633	−0.402452
$235$	6.39280	0.417020
$236$	−10.5999	−0.689995
$237$	−10.3879	−0.674765
$238$	26.7816	1.73599
$239$	−16.4387	−1.06333	−0.531664	−	0.846955i	$-0.678433\pi$
$239$	−16.4387	−1.06333	−0.531664	+	0.846955i	$0.678433\pi$
$240$	−0.675131	−0.0435795
$241$	19.3054	1.24357	0.621784	−	0.783189i	$-0.286408\pi$
$241$	19.3054	1.24357	0.621784	+	0.783189i	$0.286408\pi$
$242$	3.20123	0.205783
$243$	−1.00000	−0.0641500
$244$	−0.775746	−0.0496621
$245$	13.2243	0.844867
$246$	−2.31265	−0.147449
$247$	−15.6629	−0.996607
$248$	−10.5369	−0.669094
$249$	−6.44358	−0.408345
$250$	−6.44358	−0.407528
$251$	26.5804	1.67774	0.838870	−	0.544332i	$-0.183217\pi$
$251$	26.5804	1.67774	0.838870	+	0.544332i	$0.183217\pi$
$252$	−5.15633	−0.324818
$253$	8.12601	0.510878
$254$	−0.425485	−0.0266973
$255$	3.50659	0.219591
$256$	1.00000	0.0625000
$257$	4.68006	0.291934	0.145967	−	0.989289i	$-0.453371\pi$
$257$	4.68006	0.291934	0.145967	+	0.989289i	$0.453371\pi$
$258$	7.50659	0.467340
$259$	15.7938	0.981382
$260$	−4.15633	−0.257764
$261$	−3.76845	−0.233261
$262$	4.49341	0.277604
$263$	−25.9175	−1.59814	−0.799070	−	0.601238i	$-0.794674\pi$
$263$	−25.9175	−1.59814	−0.799070	+	0.601238i	$0.794674\pi$
$264$	−3.76845	−0.231932
$265$	−2.52705	−0.155236
$266$	−13.1187	−0.804360
$267$	11.9321	0.730231
$268$	6.86177	0.419150
$269$	−0.750354	−0.0457499	−0.0228749	−	0.999738i	$-0.507282\pi$
$269$	−0.750354	−0.0457499	−0.0228749	+	0.999738i	$0.507282\pi$
$270$	−0.675131	−0.0410872
$271$	13.9551	0.847712	0.423856	−	0.905730i	$-0.360676\pi$
$271$	13.9551	0.847712	0.423856	+	0.905730i	$0.360676\pi$
$272$	−5.19394	−0.314929
$273$	−31.7440	−1.92124
$274$	−6.50659	−0.393077
$275$	−17.1246	−1.03265
$276$	−2.15633	−0.129796
$277$	−10.2569	−0.616280	−0.308140	−	0.951341i	$-0.599706\pi$
$277$	−10.2569	−0.616280	−0.308140	+	0.951341i	$0.599706\pi$
$278$	14.2120	0.852381
$279$	−10.5369	−0.630828
$280$	−3.48119	−0.208041
$281$	9.49929	0.566680	0.283340	−	0.959019i	$-0.408557\pi$
$281$	9.49929	0.566680	0.283340	+	0.959019i	$0.408557\pi$
$282$	−9.46898	−0.563869
$283$	−25.6483	−1.52463	−0.762317	−	0.647203i	$-0.775938\pi$
$283$	−25.6483	−1.52463	−0.762317	+	0.647203i	$0.775938\pi$
$284$	5.50659	0.326756
$285$	−1.71767	−0.101746
$286$	−23.1998	−1.37183
$287$	−11.9248	−0.703897
$288$	1.00000	0.0589256
$289$	9.97698	0.586881
$290$	−2.54420	−0.149400
$291$	−8.50659	−0.498665
$292$	−11.8192	−0.691669
$293$	24.1622	1.41157	0.705786	−	0.708426i	$-0.250594\pi$
$293$	24.1622	1.41157	0.705786	+	0.708426i	$0.250594\pi$
$294$	−19.5877	−1.14238
$295$	−7.15633	−0.416657
$296$	−3.06300	−0.178033
$297$	−3.76845	−0.218668
$298$	15.9199	0.922212
$299$	−13.2750	−0.767715
$300$	4.54420	0.262359
$301$	38.7064	2.23100
$302$	−18.3634	−1.05670
$303$	16.4944	0.947577
$304$	2.54420	0.145920
$305$	−0.523730	−0.0299887
$306$	−5.19394	−0.296918
$307$	3.48119	0.198682	0.0993411	−	0.995053i	$-0.468326\pi$
$307$	3.48119	0.198682	0.0993411	+	0.995053i	$0.468326\pi$
$308$	−19.4314	−1.10720
$309$	−6.12601	−0.348496
$310$	−7.11379	−0.404036
$311$	−12.2750	−0.696054	−0.348027	−	0.937485i	$-0.613148\pi$
$311$	−12.2750	−0.696054	−0.348027	+	0.937485i	$0.613148\pi$
$312$	6.15633	0.348533
$313$	−8.49341	−0.480076	−0.240038	−	0.970763i	$-0.577160\pi$
$313$	−8.49341	−0.480076	−0.240038	+	0.970763i	$0.577160\pi$
$314$	4.05079	0.228599
$315$	−3.48119	−0.196143
$316$	10.3879	0.584364
$317$	23.5574	1.32311	0.661557	−	0.749895i	$-0.269896\pi$
$317$	23.5574	1.32311	0.661557	+	0.749895i	$0.269896\pi$
$318$	3.74306	0.209900
$319$	−14.2012	−0.795116
$320$	0.675131	0.0377410
$321$	6.49929	0.362755
$322$	−11.1187	−0.619622
$323$	−13.2144	−0.735269
$324$	1.00000	0.0555556
$325$	27.9756	1.55180
$326$	12.5696	0.696165
$327$	0.0811024	0.00448497
$328$	2.31265	0.127695
$329$	−48.8251	−2.69182
$330$	−2.54420	−0.140054
$331$	−28.5052	−1.56679	−0.783393	−	0.621527i	$-0.786513\pi$
$331$	−28.5052	−1.56679	−0.783393	+	0.621527i	$0.786513\pi$
$332$	6.44358	0.353638
$333$	−3.06300	−0.167852
$334$	1.00000	0.0547176
$335$	4.63259	0.253106
$336$	5.15633	0.281301
$337$	16.5369	0.900823	0.450411	−	0.892821i	$-0.351277\pi$
$337$	16.5369	0.900823	0.450411	+	0.892821i	$0.351277\pi$
$338$	24.9003	1.35440
$339$	−16.9380	−0.919943
$340$	−3.50659	−0.190171
$341$	−39.7078	−2.15030
$342$	2.54420	0.137574
$343$	−64.9062	−3.50461
$344$	−7.50659	−0.404728
$345$	−1.45580	−0.0783777
$346$	−10.5139	−0.565230
$347$	20.1006	1.07906	0.539529	−	0.841967i	$-0.318602\pi$
$347$	20.1006	1.07906	0.539529	+	0.841967i	$0.318602\pi$
$348$	3.76845	0.202010
$349$	−7.01222	−0.375355	−0.187678	−	0.982231i	$-0.560096\pi$
$349$	−7.01222	−0.375355	−0.187678	+	0.982231i	$0.560096\pi$
$350$	23.4314	1.25246
$351$	6.15633	0.328600
$352$	3.76845	0.200859
$353$	−21.7005	−1.15500	−0.577501	−	0.816390i	$-0.695972\pi$
$353$	−21.7005	−1.15500	−0.577501	+	0.816390i	$0.695972\pi$
$354$	10.5999	0.563379
$355$	3.71767	0.197313
$356$	−11.9321	−0.632399
$357$	−26.7816	−1.41743
$358$	11.3054	0.597507
$359$	11.5125	0.607605	0.303802	−	0.952735i	$-0.401744\pi$
$359$	11.5125	0.607605	0.303802	+	0.952735i	$0.401744\pi$
$360$	0.675131	0.0355825
$361$	−12.5271	−0.659319
$362$	−4.03032	−0.211829
$363$	−3.20123	−0.168021
$364$	31.7440	1.66384
$365$	−7.97953	−0.417668
$366$	0.775746	0.0405489
$367$	−16.4387	−0.858091	−0.429045	−	0.903283i	$-0.641150\pi$
$367$	−16.4387	−0.858091	−0.429045	+	0.903283i	$0.641150\pi$
$368$	2.15633	0.112406
$369$	2.31265	0.120392
$370$	−2.06793	−0.107506
$371$	19.3004	1.00203
$372$	10.5369	0.546313
$373$	2.50422	0.129663	0.0648317	−	0.997896i	$-0.479349\pi$
$373$	2.50422	0.129663	0.0648317	+	0.997896i	$0.479349\pi$
$374$	−19.5731	−1.01210
$375$	6.44358	0.332745
$376$	9.46898	0.488325
$377$	23.1998	1.19485
$378$	5.15633	0.265213
$379$	28.2325	1.45021	0.725103	−	0.688640i	$-0.241792\pi$
$379$	28.2325	1.45021	0.725103	+	0.688640i	$0.241792\pi$
$380$	1.71767	0.0881144
$381$	0.425485	0.0217982
$382$	12.0884	0.618496
$383$	0.649738	0.0332001	0.0166000	−	0.999862i	$-0.494716\pi$
$383$	0.649738	0.0332001	0.0166000	+	0.999862i	$0.494716\pi$
$384$	−1.00000	−0.0510310
$385$	−13.1187	−0.668592
$386$	8.67021	0.441302
$387$	−7.50659	−0.381581
$388$	8.50659	0.431857
$389$	−37.4168	−1.89711	−0.948553	−	0.316619i	$-0.897452\pi$
$389$	−37.4168	−1.89711	−0.948553	+	0.316619i	$0.897452\pi$
$390$	4.15633	0.210464
$391$	−11.1998	−0.566399
$392$	19.5877	0.989328
$393$	−4.49341	−0.226663
$394$	−18.5296	−0.933508
$395$	7.01317	0.352871
$396$	3.76845	0.189372
$397$	8.67021	0.435145	0.217573	−	0.976044i	$-0.430186\pi$
$397$	8.67021	0.435145	0.217573	+	0.976044i	$0.430186\pi$
$398$	8.18664	0.410359
$399$	13.1187	0.656757
$400$	−4.54420	−0.227210
$401$	−9.67750	−0.483271	−0.241636	−	0.970367i	$-0.577684\pi$
$401$	−9.67750	−0.483271	−0.241636	+	0.970367i	$0.577684\pi$
$402$	−6.86177	−0.342234
$403$	64.8686	3.23134
$404$	−16.4944	−0.820625
$405$	0.675131	0.0335475
$406$	19.4314	0.964362
$407$	−11.5428	−0.572155
$408$	5.19394	0.257138
$409$	−18.1016	−0.895065	−0.447533	−	0.894268i	$-0.647697\pi$
$409$	−18.1016	−0.895065	−0.447533	+	0.894268i	$0.647697\pi$
$410$	1.56134	0.0771092
$411$	6.50659	0.320946
$412$	6.12601	0.301807
$413$	54.6566	2.68947
$414$	2.15633	0.105978
$415$	4.35026	0.213546
$416$	−6.15633	−0.301839
$417$	−14.2120	−0.695966
$418$	9.58769	0.468949
$419$	−15.4763	−0.756065	−0.378033	−	0.925792i	$-0.623399\pi$
$419$	−15.4763	−0.756065	−0.378033	+	0.925792i	$0.623399\pi$
$420$	3.48119	0.169865
$421$	−22.8061	−1.11150	−0.555750	−	0.831350i	$-0.687569\pi$
$421$	−22.8061	−1.11150	−0.555750	+	0.831350i	$0.687569\pi$
$422$	2.52373	0.122853
$423$	9.46898	0.460397
$424$	−3.74306	−0.181779
$425$	23.6023	1.14488
$426$	−5.50659	−0.266795
$427$	4.00000	0.193574
$428$	−6.49929	−0.314155
$429$	23.1998	1.12010
$430$	−5.06793	−0.244397
$431$	−29.0263	−1.39815	−0.699075	−	0.715048i	$-0.746405\pi$
$431$	−29.0263	−1.39815	−0.699075	+	0.715048i	$0.746405\pi$
$432$	−1.00000	−0.0481125
$433$	−36.5877	−1.75829	−0.879146	−	0.476552i	$-0.841886\pi$
$433$	−36.5877	−1.75829	−0.879146	+	0.476552i	$0.841886\pi$
$434$	54.3317	2.60801
$435$	2.54420	0.121985
$436$	−0.0811024	−0.00388410
$437$	5.48612	0.262437
$438$	11.8192	0.564745
$439$	−8.18664	−0.390727	−0.195364	−	0.980731i	$-0.562589\pi$
$439$	−8.18664	−0.390727	−0.195364	+	0.980731i	$0.562589\pi$
$440$	2.54420	0.121290
$441$	19.5877	0.932747
$442$	31.9756	1.52092
$443$	−13.8749	−0.659219	−0.329609	−	0.944117i	$-0.606917\pi$
$443$	−13.8749	−0.659219	−0.329609	+	0.944117i	$0.606917\pi$
$444$	3.06300	0.145364
$445$	−8.05571	−0.381877
$446$	−20.8945	−0.989381
$447$	−15.9199	−0.752983
$448$	−5.15633	−0.243613
$449$	−30.1695	−1.42379	−0.711893	−	0.702288i	$-0.752162\pi$
$449$	−30.1695	−1.42379	−0.711893	+	0.702288i	$0.752162\pi$
$450$	−4.54420	−0.214216
$451$	8.71511	0.410379
$452$	16.9380	0.796694
$453$	18.3634	0.862789
$454$	2.16125	0.101432
$455$	21.4314	1.00472
$456$	−2.54420	−0.119143
$457$	−1.53690	−0.0718933	−0.0359467	−	0.999354i	$-0.511445\pi$
$457$	−1.53690	−0.0718933	−0.0359467	+	0.999354i	$0.511445\pi$
$458$	−17.7743	−0.830540
$459$	5.19394	0.242432
$460$	1.45580	0.0678771
$461$	−31.4314	−1.46390	−0.731952	−	0.681356i	$-0.761391\pi$
$461$	−31.4314	−1.46390	−0.731952	+	0.681356i	$0.761391\pi$
$462$	19.4314	0.904029
$463$	−10.3733	−0.482087	−0.241044	−	0.970514i	$-0.577490\pi$
$463$	−10.3733	−0.482087	−0.241044	+	0.970514i	$0.577490\pi$
$464$	−3.76845	−0.174946
$465$	7.11379	0.329894
$466$	−25.8872	−1.19920
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	−6.15633	−0.284576
$469$	−35.3815	−1.63377
$470$	6.39280	0.294878
$471$	−4.05079	−0.186650
$472$	−10.5999	−0.487900
$473$	−28.2882	−1.30069
$474$	−10.3879	−0.477131
$475$	−11.5613	−0.530471
$476$	26.7816	1.22753
$477$	−3.74306	−0.171383
$478$	−16.4387	−0.751887
$479$	−42.0625	−1.92189	−0.960943	−	0.276745i	$-0.910744\pi$
$479$	−42.0625	−1.92189	−0.960943	+	0.276745i	$0.910744\pi$
$480$	−0.675131	−0.0308154
$481$	18.8568	0.859798
$482$	19.3054	0.879335
$483$	11.1187	0.505919
$484$	3.20123	0.145510
$485$	5.74306	0.260779
$486$	−1.00000	−0.0453609
$487$	−14.0957	−0.638737	−0.319368	−	0.947631i	$-0.603471\pi$
$487$	−14.0957	−0.638737	−0.319368	+	0.947631i	$0.603471\pi$
$488$	−0.775746	−0.0351164
$489$	−12.5696	−0.568417
$490$	13.2243	0.597411
$491$	−9.98541	−0.450635	−0.225318	−	0.974285i	$-0.572342\pi$
$491$	−9.98541	−0.450635	−0.225318	+	0.974285i	$0.572342\pi$
$492$	−2.31265	−0.104262
$493$	19.5731	0.881528
$494$	−15.6629	−0.704708
$495$	2.54420	0.114353
$496$	−10.5369	−0.473121
$497$	−28.3938	−1.27363
$498$	−6.44358	−0.288744
$499$	22.9829	1.02885	0.514427	−	0.857534i	$-0.328005\pi$
$499$	22.9829	1.02885	0.514427	+	0.857534i	$0.328005\pi$
$500$	−6.44358	−0.288166
$501$	−1.00000	−0.0446767
$502$	26.5804	1.18634
$503$	−0.800184	−0.0356784	−0.0178392	−	0.999841i	$-0.505679\pi$
$503$	−0.800184	−0.0356784	−0.0178392	+	0.999841i	$0.505679\pi$
$504$	−5.15633	−0.229681
$505$	−11.1359	−0.495539
$506$	8.12601	0.361245
$507$	−24.9003	−1.10586
$508$	−0.425485	−0.0188778
$509$	11.8740	0.526305	0.263153	−	0.964754i	$-0.415238\pi$
$509$	11.8740	0.526305	0.263153	+	0.964754i	$0.415238\pi$
$510$	3.50659	0.155274
$511$	60.9438	2.69600
$512$	1.00000	0.0441942
$513$	−2.54420	−0.112329
$514$	4.68006	0.206428
$515$	4.13586	0.182248
$516$	7.50659	0.330459
$517$	35.6834	1.56935
$518$	15.7938	0.693942
$519$	10.5139	0.461508
$520$	−4.15633	−0.182267
$521$	25.9307	1.13604	0.568021	−	0.823014i	$-0.307709\pi$
$521$	25.9307	1.13604	0.568021	+	0.823014i	$0.307709\pi$
$522$	−3.76845	−0.164941
$523$	−23.8945	−1.04483	−0.522416	−	0.852691i	$-0.674969\pi$
$523$	−23.8945	−1.04483	−0.522416	+	0.852691i	$0.674969\pi$
$524$	4.49341	0.196296
$525$	−23.4314	−1.02263
$526$	−25.9175	−1.13006
$527$	54.7280	2.38399
$528$	−3.76845	−0.164001
$529$	−18.3503	−0.797837
$530$	−2.52705	−0.109768
$531$	−10.5999	−0.459997
$532$	−13.1187	−0.568768
$533$	−14.2374	−0.616691
$534$	11.9321	0.516351
$535$	−4.38787	−0.189704
$536$	6.86177	0.296383
$537$	−11.3054	−0.487862
$538$	−0.750354	−0.0323500
$539$	73.8153	3.17945
$540$	−0.675131	−0.0290530
$541$	0.332163	0.0142808	0.00714041	−	0.999975i	$-0.497727\pi$
$541$	0.332163	0.0142808	0.00714041	+	0.999975i	$0.497727\pi$
$542$	13.9551	0.599423
$543$	4.03032	0.172957
$544$	−5.19394	−0.222688
$545$	−0.0547547	−0.00234543
$546$	−31.7440	−1.35852
$547$	−2.17584	−0.0930321	−0.0465161	−	0.998918i	$-0.514812\pi$
$547$	−2.17584	−0.0930321	−0.0465161	+	0.998918i	$0.514812\pi$
$548$	−6.50659	−0.277948
$549$	−0.775746	−0.0331080
$550$	−17.1246	−0.730195
$551$	−9.58769	−0.408449
$552$	−2.15633	−0.0917793
$553$	−53.5633	−2.27774
$554$	−10.2569	−0.435776
$555$	2.06793	0.0877787
$556$	14.2120	0.602725
$557$	39.5936	1.67763	0.838817	−	0.544414i	$-0.183248\pi$
$557$	39.5936	1.67763	0.838817	+	0.544414i	$0.183248\pi$
$558$	−10.5369	−0.446063
$559$	46.2130	1.95460
$560$	−3.48119	−0.147107
$561$	19.5731	0.826377
$562$	9.49929	0.400703
$563$	−19.6326	−0.827415	−0.413708	−	0.910410i	$-0.635766\pi$
$563$	−19.6326	−0.827415	−0.413708	+	0.910410i	$0.635766\pi$
$564$	−9.46898	−0.398716
$565$	11.4353	0.481088
$566$	−25.6483	−1.07808
$567$	−5.15633	−0.216545
$568$	5.50659	0.231051
$569$	−13.1939	−0.553119	−0.276559	−	0.960997i	$-0.589194\pi$
$569$	−13.1939	−0.553119	−0.276559	+	0.960997i	$0.589194\pi$
$570$	−1.71767	−0.0719451
$571$	−22.0459	−0.922591	−0.461295	−	0.887247i	$-0.652615\pi$
$571$	−22.0459	−0.922591	−0.461295	+	0.887247i	$0.652615\pi$
$572$	−23.1998	−0.970033
$573$	−12.0884	−0.505000
$574$	−11.9248	−0.497731
$575$	−9.79877	−0.408637
$576$	1.00000	0.0416667
$577$	23.7670	0.989435	0.494717	−	0.869054i	$-0.335272\pi$
$577$	23.7670	0.989435	0.494717	+	0.869054i	$0.335272\pi$
$578$	9.97698	0.414988
$579$	−8.67021	−0.360321
$580$	−2.54420	−0.105642
$581$	−33.2252	−1.37841
$582$	−8.50659	−0.352609
$583$	−14.1055	−0.584192
$584$	−11.8192	−0.489084
$585$	−4.15633	−0.171843
$586$	24.1622	0.998131
$587$	23.8183	0.983086	0.491543	−	0.870853i	$-0.336433\pi$
$587$	23.8183	0.983086	0.491543	+	0.870853i	$0.336433\pi$
$588$	−19.5877	−0.807783
$589$	−26.8080	−1.10460
$590$	−7.15633	−0.294621
$591$	18.5296	0.762206
$592$	−3.06300	−0.125889
$593$	17.0943	0.701978	0.350989	−	0.936380i	$-0.385845\pi$
$593$	17.0943	0.701978	0.350989	+	0.936380i	$0.385845\pi$
$594$	−3.76845	−0.154621
$595$	18.0811	0.741253
$596$	15.9199	0.652103
$597$	−8.18664	−0.335057
$598$	−13.2750	−0.542857
$599$	18.3101	0.748130	0.374065	−	0.927402i	$-0.377964\pi$
$599$	18.3101	0.748130	0.374065	+	0.927402i	$0.377964\pi$
$600$	4.54420	0.185516
$601$	34.8094	1.41990	0.709952	−	0.704250i	$-0.248716\pi$
$601$	34.8094	1.41990	0.709952	+	0.704250i	$0.248716\pi$
$602$	38.7064	1.57756
$603$	6.86177	0.279433
$604$	−18.3634	−0.747198
$605$	2.16125	0.0878673
$606$	16.4944	0.670038
$607$	37.1509	1.50791	0.753955	−	0.656926i	$-0.228144\pi$
$607$	37.1509	1.50791	0.753955	+	0.656926i	$0.228144\pi$
$608$	2.54420	0.103181
$609$	−19.4314	−0.787399
$610$	−0.523730	−0.0212052
$611$	−58.2941	−2.35833
$612$	−5.19394	−0.209952
$613$	−25.2692	−1.02061	−0.510306	−	0.859993i	$-0.670468\pi$
$613$	−25.2692	−1.02061	−0.510306	+	0.859993i	$0.670468\pi$
$614$	3.48119	0.140490
$615$	−1.56134	−0.0629594
$616$	−19.4314	−0.782912
$617$	−21.8251	−0.878646	−0.439323	−	0.898329i	$-0.644782\pi$
$617$	−21.8251	−0.878646	−0.439323	+	0.898329i	$0.644782\pi$
$618$	−6.12601	−0.246424
$619$	−21.1841	−0.851460	−0.425730	−	0.904850i	$-0.639983\pi$
$619$	−21.1841	−0.851460	−0.425730	+	0.904850i	$0.639983\pi$
$620$	−7.11379	−0.285697
$621$	−2.15633	−0.0865303
$622$	−12.2750	−0.492184
$623$	61.5256	2.46497
$624$	6.15633	0.246450
$625$	18.3707	0.734829
$626$	−8.49341	−0.339465
$627$	−9.58769	−0.382895
$628$	4.05079	0.161644
$629$	15.9090	0.634335
$630$	−3.48119	−0.138694
$631$	−16.2896	−0.648480	−0.324240	−	0.945975i	$-0.605109\pi$
$631$	−16.2896	−0.648480	−0.324240	+	0.945975i	$0.605109\pi$
$632$	10.3879	0.413207
$633$	−2.52373	−0.100309
$634$	23.5574	0.935583
$635$	−0.287258	−0.0113995
$636$	3.74306	0.148422
$637$	−120.588	−4.77788
$638$	−14.2012	−0.562232
$639$	5.50659	0.217837
$640$	0.675131	0.0266869
$641$	30.2520	1.19488	0.597441	−	0.801913i	$-0.296184\pi$
$641$	30.2520	1.19488	0.597441	+	0.801913i	$0.296184\pi$
$642$	6.49929	0.256507
$643$	−0.493413	−0.0194583	−0.00972916	−	0.999953i	$-0.503097\pi$
$643$	−0.493413	−0.0194583	−0.00972916	+	0.999953i	$0.503097\pi$
$644$	−11.1187	−0.438139
$645$	5.06793	0.199549
$646$	−13.2144	−0.519914
$647$	6.05079	0.237881	0.118940	−	0.992901i	$-0.462050\pi$
$647$	6.05079	0.237881	0.118940	+	0.992901i	$0.462050\pi$
$648$	1.00000	0.0392837
$649$	−39.9452	−1.56799
$650$	27.9756	1.09729
$651$	−54.3317	−2.12943
$652$	12.5696	0.492263
$653$	7.41564	0.290196	0.145098	−	0.989417i	$-0.453650\pi$
$653$	7.41564	0.290196	0.145098	+	0.989417i	$0.453650\pi$
$654$	0.0811024	0.00317135
$655$	3.03364	0.118534
$656$	2.31265	0.0902938
$657$	−11.8192	−0.461112
$658$	−48.8251	−1.90340
$659$	29.4568	1.14747	0.573736	−	0.819040i	$-0.305493\pi$
$659$	29.4568	1.14747	0.573736	+	0.819040i	$0.305493\pi$
$660$	−2.54420	−0.0990328
$661$	28.9584	1.12635	0.563176	−	0.826337i	$-0.309579\pi$
$661$	28.9584	1.12635	0.563176	+	0.826337i	$0.309579\pi$
$662$	−28.5052	−1.10788
$663$	−31.9756	−1.24183
$664$	6.44358	0.250060
$665$	−8.85685	−0.343454
$666$	−3.06300	−0.118689
$667$	−8.12601	−0.314640
$668$	1.00000	0.0386912
$669$	20.8945	0.807826
$670$	4.63259	0.178973
$671$	−2.92336	−0.112855
$672$	5.15633	0.198910
$673$	35.9307	1.38503	0.692513	−	0.721406i	$-0.256504\pi$
$673$	35.9307	1.38503	0.692513	+	0.721406i	$0.256504\pi$
$674$	16.5369	0.636978
$675$	4.54420	0.174906
$676$	24.9003	0.957705
$677$	−8.20711	−0.315425	−0.157712	−	0.987485i	$-0.550412\pi$
$677$	−8.20711	−0.315425	−0.157712	+	0.987485i	$0.550412\pi$
$678$	−16.9380	−0.650498
$679$	−43.8627	−1.68330
$680$	−3.50659	−0.134471
$681$	−2.16125	−0.0828193
$682$	−39.7078	−1.52049
$683$	−15.7830	−0.603921	−0.301961	−	0.953320i	$-0.597641\pi$
$683$	−15.7830	−0.603921	−0.301961	+	0.953320i	$0.597641\pi$
$684$	2.54420	0.0972799
$685$	−4.39280	−0.167840
$686$	−64.9062	−2.47813
$687$	17.7743	0.678133
$688$	−7.50659	−0.286186
$689$	23.0435	0.877887
$690$	−1.45580	−0.0554214
$691$	−12.3430	−0.469549	−0.234774	−	0.972050i	$-0.575435\pi$
$691$	−12.3430	−0.469549	−0.234774	+	0.972050i	$0.575435\pi$
$692$	−10.5139	−0.399678
$693$	−19.4314	−0.738136
$694$	20.1006	0.763009
$695$	9.59498	0.363958
$696$	3.76845	0.142843
$697$	−12.0118	−0.454978
$698$	−7.01222	−0.265416
$699$	25.8872	0.979143
$700$	23.4314	0.885622
$701$	14.2981	0.540030	0.270015	−	0.962856i	$-0.412971\pi$
$701$	14.2981	0.540030	0.270015	+	0.962856i	$0.412971\pi$
$702$	6.15633	0.232356
$703$	−7.79289	−0.293914
$704$	3.76845	0.142029
$705$	−6.39280	−0.240767
$706$	−21.7005	−0.816710
$707$	85.0503	3.19865
$708$	10.5999	0.398369
$709$	−25.0835	−0.942030	−0.471015	−	0.882125i	$-0.656112\pi$
$709$	−25.0835	−0.942030	−0.471015	+	0.882125i	$0.656112\pi$
$710$	3.71767	0.139522
$711$	10.3879	0.389576
$712$	−11.9321	−0.447173
$713$	−22.7210	−0.850908
$714$	−26.7816	−1.00228
$715$	−15.6629	−0.585760
$716$	11.3054	0.422501
$717$	16.4387	0.613913
$718$	11.5125	0.429641
$719$	29.1490	1.08708	0.543538	−	0.839385i	$-0.317084\pi$
$719$	29.1490	1.08708	0.543538	+	0.839385i	$0.317084\pi$
$720$	0.675131	0.0251606
$721$	−31.5877	−1.17639
$722$	−12.5271	−0.466209
$723$	−19.3054	−0.717974
$724$	−4.03032	−0.149786
$725$	17.1246	0.635991
$726$	−3.20123	−0.118809
$727$	−21.7177	−0.805464	−0.402732	−	0.915318i	$-0.631939\pi$
$727$	−21.7177	−0.805464	−0.402732	+	0.915318i	$0.631939\pi$
$728$	31.7440	1.17651
$729$	1.00000	0.0370370
$730$	−7.97953	−0.295336
$731$	38.9887	1.44205
$732$	0.775746	0.0286724
$733$	−11.1187	−0.410679	−0.205340	−	0.978691i	$-0.565830\pi$
$733$	−11.1187	−0.410679	−0.205340	+	0.978691i	$0.565830\pi$
$734$	−16.4387	−0.606762
$735$	−13.2243	−0.487784
$736$	2.15633	0.0794832
$737$	25.8583	0.952501
$738$	2.31265	0.0851298
$739$	−39.7694	−1.46294	−0.731471	−	0.681873i	$-0.761166\pi$
$739$	−39.7694	−1.46294	−0.731471	+	0.681873i	$0.761166\pi$
$740$	−2.06793	−0.0760186
$741$	15.6629	0.575391
$742$	19.3004	0.708541
$743$	34.8554	1.27872	0.639361	−	0.768907i	$-0.279199\pi$
$743$	34.8554	1.27872	0.639361	+	0.768907i	$0.279199\pi$
$744$	10.5369	0.386302
$745$	10.7480	0.393776
$746$	2.50422	0.0916859
$747$	6.44358	0.235758
$748$	−19.5731	−0.715663
$749$	33.5125	1.22452
$750$	6.44358	0.235286
$751$	−6.72099	−0.245252	−0.122626	−	0.992453i	$-0.539132\pi$
$751$	−6.72099	−0.245252	−0.122626	+	0.992453i	$0.539132\pi$
$752$	9.46898	0.345298
$753$	−26.5804	−0.968643
$754$	23.1998	0.844887
$755$	−12.3977	−0.451199
$756$	5.15633	0.187534
$757$	38.6556	1.40496	0.702481	−	0.711702i	$-0.252076\pi$
$757$	38.6556	1.40496	0.702481	+	0.711702i	$0.252076\pi$
$758$	28.2325	1.02545
$759$	−8.12601	−0.294955
$760$	1.71767	0.0623063
$761$	−27.3127	−0.990083	−0.495041	−	0.868869i	$-0.664847\pi$
$761$	−27.3127	−0.990083	−0.495041	+	0.868869i	$0.664847\pi$
$762$	0.425485	0.0154137
$763$	0.418190	0.0151395
$764$	12.0884	0.437343
$765$	−3.50659	−0.126781
$766$	0.649738	0.0234760
$767$	65.2565	2.35627
$768$	−1.00000	−0.0360844
$769$	−29.1549	−1.05135	−0.525676	−	0.850685i	$-0.676188\pi$
$769$	−29.1549	−1.05135	−0.525676	+	0.850685i	$0.676188\pi$
$770$	−13.1187	−0.472766
$771$	−4.68006	−0.168548
$772$	8.67021	0.312048
$773$	6.69560	0.240824	0.120412	−	0.992724i	$-0.461578\pi$
$773$	6.69560	0.240824	0.120412	+	0.992724i	$0.461578\pi$
$774$	−7.50659	−0.269819
$775$	47.8818	1.71996
$776$	8.50659	0.305369
$777$	−15.7938	−0.566601
$778$	−37.4168	−1.34146
$779$	5.88384	0.210810
$780$	4.15633	0.148820
$781$	20.7513	0.742540
$782$	−11.1998	−0.400505
$783$	3.76845	0.134673
$784$	19.5877	0.699560
$785$	2.73481	0.0976096
$786$	−4.49341	−0.160275
$787$	27.7586	0.989487	0.494744	−	0.869039i	$-0.335262\pi$
$787$	27.7586	0.989487	0.494744	+	0.869039i	$0.335262\pi$
$788$	−18.5296	−0.660090
$789$	25.9175	0.922687
$790$	7.01317	0.249518
$791$	−87.3376	−3.10537
$792$	3.76845	0.133906
$793$	4.77575	0.169592
$794$	8.67021	0.307694
$795$	2.52705	0.0896254
$796$	8.18664	0.290168
$797$	45.1206	1.59825	0.799127	−	0.601162i	$-0.205295\pi$
$797$	45.1206	1.59825	0.799127	+	0.601162i	$0.205295\pi$
$798$	13.1187	0.464397
$799$	−49.1813	−1.73991
$800$	−4.54420	−0.160662
$801$	−11.9321	−0.421599
$802$	−9.67750	−0.341724
$803$	−44.5402	−1.57179
$804$	−6.86177	−0.241996
$805$	−7.50659	−0.264572
$806$	64.8686	2.28490
$807$	0.750354	0.0264137
$808$	−16.4944	−0.580270
$809$	36.5672	1.28564	0.642818	−	0.766019i	$-0.277765\pi$
$809$	36.5672	1.28564	0.642818	+	0.766019i	$0.277765\pi$
$810$	0.675131	0.0237217
$811$	−11.7880	−0.413931	−0.206966	−	0.978348i	$-0.566359\pi$
$811$	−11.7880	−0.413931	−0.206966	+	0.978348i	$0.566359\pi$
$812$	19.4314	0.681907
$813$	−13.9551	−0.489427
$814$	−11.5428	−0.404574
$815$	8.48612	0.297256
$816$	5.19394	0.181824
$817$	−19.0982	−0.668163
$818$	−18.1016	−0.632907
$819$	31.7440	1.10923
$820$	1.56134	0.0545244
$821$	−30.9438	−1.07995	−0.539974	−	0.841682i	$-0.681566\pi$
$821$	−30.9438	−1.07995	−0.539974	+	0.841682i	$0.681566\pi$
$822$	6.50659	0.226943
$823$	42.1417	1.46897	0.734484	−	0.678626i	$-0.237424\pi$
$823$	42.1417	1.46897	0.734484	+	0.678626i	$0.237424\pi$
$824$	6.12601	0.213410
$825$	17.1246	0.596202
$826$	54.6566	1.90175
$827$	−39.3073	−1.36685	−0.683424	−	0.730022i	$-0.739510\pi$
$827$	−39.3073	−1.36685	−0.683424	+	0.730022i	$0.739510\pi$
$828$	2.15633	0.0749375
$829$	−9.19489	−0.319352	−0.159676	−	0.987169i	$-0.551045\pi$
$829$	−9.19489	−0.319352	−0.159676	+	0.987169i	$0.551045\pi$
$830$	4.35026	0.151000
$831$	10.2569	0.355809
$832$	−6.15633	−0.213432
$833$	−101.737	−3.52499
$834$	−14.2120	−0.492123
$835$	0.675131	0.0233639
$836$	9.58769	0.331597
$837$	10.5369	0.364209
$838$	−15.4763	−0.534619
$839$	−39.4603	−1.36232	−0.681160	−	0.732135i	$-0.738524\pi$
$839$	−39.4603	−1.36232	−0.681160	+	0.732135i	$0.738524\pi$
$840$	3.48119	0.120113
$841$	−14.7988	−0.510302
$842$	−22.8061	−0.785949
$843$	−9.49929	−0.327173
$844$	2.52373	0.0868704
$845$	16.8110	0.578316
$846$	9.46898	0.325550
$847$	−16.5066	−0.567173
$848$	−3.74306	−0.128537
$849$	25.6483	0.880248
$850$	23.6023	0.809551
$851$	−6.60483	−0.226411
$852$	−5.50659	−0.188653
$853$	29.5223	1.01082	0.505412	−	0.862878i	$-0.331340\pi$
$853$	29.5223	1.01082	0.505412	+	0.862878i	$0.331340\pi$
$854$	4.00000	0.136877
$855$	1.71767	0.0587430
$856$	−6.49929	−0.222141
$857$	24.3258	0.830954	0.415477	−	0.909604i	$-0.363615\pi$
$857$	24.3258	0.830954	0.415477	+	0.909604i	$0.363615\pi$
$858$	23.1998	0.792029
$859$	51.0943	1.74331	0.871657	−	0.490116i	$-0.163046\pi$
$859$	51.0943	1.74331	0.871657	+	0.490116i	$0.163046\pi$
$860$	−5.06793	−0.172815
$861$	11.9248	0.406395
$862$	−29.0263	−0.988641
$863$	−37.9248	−1.29097	−0.645487	−	0.763771i	$-0.723346\pi$
$863$	−37.9248	−1.29097	−0.645487	+	0.763771i	$0.723346\pi$
$864$	−1.00000	−0.0340207
$865$	−7.09825	−0.241348
$866$	−36.5877	−1.24330
$867$	−9.97698	−0.338836
$868$	54.3317	1.84414
$869$	39.1462	1.32794
$870$	2.54420	0.0862564
$871$	−42.2433	−1.43136
$872$	−0.0811024	−0.00274647
$873$	8.50659	0.287904
$874$	5.48612	0.185571
$875$	33.2252	1.12322
$876$	11.8192	0.399335
$877$	33.1695	1.12005	0.560027	−	0.828474i	$-0.310791\pi$
$877$	33.1695	1.12005	0.560027	+	0.828474i	$0.310791\pi$
$878$	−8.18664	−0.276286
$879$	−24.1622	−0.814971
$880$	2.54420	0.0857649
$881$	−28.1866	−0.949632	−0.474816	−	0.880085i	$-0.657485\pi$
$881$	−28.1866	−0.949632	−0.474816	+	0.880085i	$0.657485\pi$
$882$	19.5877	0.659552
$883$	−24.9419	−0.839362	−0.419681	−	0.907672i	$-0.637858\pi$
$883$	−24.9419	−0.839362	−0.419681	+	0.907672i	$0.637858\pi$
$884$	31.9756	1.07545
$885$	7.15633	0.240557
$886$	−13.8749	−0.466138
$887$	0.826531	0.0277522	0.0138761	−	0.999904i	$-0.495583\pi$
$887$	0.826531	0.0277522	0.0138761	+	0.999904i	$0.495583\pi$
$888$	3.06300	0.102788
$889$	2.19394	0.0735823
$890$	−8.05571	−0.270028
$891$	3.76845	0.126248
$892$	−20.8945	−0.699598
$893$	24.0910	0.806173
$894$	−15.9199	−0.532440
$895$	7.63259	0.255130
$896$	−5.15633	−0.172261
$897$	13.2750	0.443241
$898$	−30.1695	−1.00677
$899$	39.7078	1.32433
$900$	−4.54420	−0.151473
$901$	19.4412	0.647681
$902$	8.71511	0.290181
$903$	−38.7064	−1.28807
$904$	16.9380	0.563348
$905$	−2.72099	−0.0904488
$906$	18.3634	0.610084
$907$	−23.8291	−0.791232	−0.395616	−	0.918416i	$-0.629469\pi$
$907$	−23.8291	−0.791232	−0.395616	+	0.918416i	$0.629469\pi$
$908$	2.16125	0.0717236
$909$	−16.4944	−0.547084
$910$	21.4314	0.710443
$911$	−19.5091	−0.646367	−0.323183	−	0.946336i	$-0.604753\pi$
$911$	−19.5091	−0.646367	−0.323183	+	0.946336i	$0.604753\pi$
$912$	−2.54420	−0.0842468
$913$	24.2823	0.803628
$914$	−1.53690	−0.0508363
$915$	0.523730	0.0173140
$916$	−17.7743	−0.587280
$917$	−23.1695	−0.765124
$918$	5.19394	0.171425
$919$	5.07125	0.167285	0.0836426	−	0.996496i	$-0.473345\pi$
$919$	5.07125	0.167285	0.0836426	+	0.996496i	$0.473345\pi$
$920$	1.45580	0.0479964
$921$	−3.48119	−0.114709
$922$	−31.4314	−1.03514
$923$	−33.9003	−1.11584
$924$	19.4314	0.639245
$925$	13.9189	0.457651
$926$	−10.3733	−0.340887
$927$	6.12601	0.201205
$928$	−3.76845	−0.123705
$929$	−20.2262	−0.663599	−0.331799	−	0.943350i	$-0.607656\pi$
$929$	−20.2262	−0.663599	−0.331799	+	0.943350i	$0.607656\pi$
$930$	7.11379	0.233270
$931$	49.8350	1.63328
$932$	−25.8872	−0.847962
$933$	12.2750	0.401867
$934$	−6.00000	−0.196326
$935$	−13.2144	−0.432157
$936$	−6.15633	−0.201226
$937$	−33.0092	−1.07836	−0.539182	−	0.842189i	$-0.681266\pi$
$937$	−33.0092	−1.07836	−0.539182	+	0.842189i	$0.681266\pi$
$938$	−35.3815	−1.15525
$939$	8.49341	0.277172
$940$	6.39280	0.208510
$941$	17.0191	0.554805	0.277403	−	0.960754i	$-0.410526\pi$
$941$	17.0191	0.554805	0.277403	+	0.960754i	$0.410526\pi$
$942$	−4.05079	−0.131982
$943$	4.98683	0.162393
$944$	−10.5999	−0.344998
$945$	3.48119	0.113243
$946$	−28.2882	−0.919729
$947$	41.2360	1.33999	0.669995	−	0.742365i	$-0.266296\pi$
$947$	41.2360	1.33999	0.669995	+	0.742365i	$0.266296\pi$
$948$	−10.3879	−0.337382
$949$	72.7631	2.36199
$950$	−11.5613	−0.375099
$951$	−23.5574	−0.763900
$952$	26.7816	0.867997
$953$	−61.0698	−1.97825	−0.989123	−	0.147090i	$-0.953009\pi$
$953$	−61.0698	−1.97825	−0.989123	+	0.147090i	$0.953009\pi$
$954$	−3.74306	−0.121186
$955$	8.16125	0.264092
$956$	−16.4387	−0.531664
$957$	14.2012	0.459061
$958$	−42.0625	−1.35898
$959$	33.5501	1.08339
$960$	−0.675131	−0.0217898
$961$	80.0263	2.58150
$962$	18.8568	0.607969
$963$	−6.49929	−0.209437
$964$	19.3054	0.621784
$965$	5.85352	0.188432
$966$	11.1187	0.357739
$967$	−1.55149	−0.0498926	−0.0249463	−	0.999689i	$-0.507941\pi$
$967$	−1.55149	−0.0498926	−0.0249463	+	0.999689i	$0.507941\pi$
$968$	3.20123	0.102891
$969$	13.2144	0.424508
$970$	5.74306	0.184399
$971$	25.4812	0.817730	0.408865	−	0.912595i	$-0.365925\pi$
$971$	25.4812	0.817730	0.408865	+	0.912595i	$0.365925\pi$
$972$	−1.00000	−0.0320750
$973$	−73.2819	−2.34931
$974$	−14.0957	−0.451655
$975$	−27.9756	−0.895935
$976$	−0.775746	−0.0248310
$977$	15.1432	0.484472	0.242236	−	0.970217i	$-0.422119\pi$
$977$	15.1432	0.484472	0.242236	+	0.970217i	$0.422119\pi$
$978$	−12.5696	−0.401931
$979$	−44.9654	−1.43710
$980$	13.2243	0.422433
$981$	−0.0811024	−0.00258940
$982$	−9.98541	−0.318647
$983$	27.0376	0.862366	0.431183	−	0.902265i	$-0.358096\pi$
$983$	27.0376	0.862366	0.431183	+	0.902265i	$0.358096\pi$
$984$	−2.31265	−0.0737246
$985$	−12.5099	−0.398599
$986$	19.5731	0.623335
$987$	48.8251	1.55412
$988$	−15.6629	−0.498304
$989$	−16.1866	−0.514705
$990$	2.54420	0.0808599
$991$	24.1055	0.765738	0.382869	−	0.923803i	$-0.374936\pi$
$991$	24.1055	0.765738	0.382869	+	0.923803i	$0.374936\pi$
$992$	−10.5369	−0.334547
$993$	28.5052	0.904584
$994$	−28.3938	−0.900595
$995$	5.52705	0.175219
$996$	−6.44358	−0.204173
$997$	−2.54420	−0.0805756	−0.0402878	−	0.999188i	$-0.512827\pi$
$997$	−2.54420	−0.0805756	−0.0402878	+	0.999188i	$0.512827\pi$
$998$	22.9829	0.727510
$999$	3.06300	0.0969092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1002.2.a.h.1.3	✓	3
3.2	odd	2		3006.2.a.o.1.1		3
4.3	odd	2		8016.2.a.l.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1002.2.a.h.1.3	✓	3	1.1	even	1	trivial
3006.2.a.o.1.1		3	3.2	odd	2
8016.2.a.l.1.3		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 1002 = 2 \cdot 3 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.675131 q^{5} -1.00000 q^{6} -5.15633 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.675131 q^{5} -1.00000 q^{6} -5.15633 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.675131 q^{10} +3.76845 q^{11} -1.00000 q^{12} -6.15633 q^{13} -5.15633 q^{14} -0.675131 q^{15} +1.00000 q^{16} -5.19394 q^{17} +1.00000 q^{18} +2.54420 q^{19} +0.675131 q^{20} +5.15633 q^{21} +3.76845 q^{22} +2.15633 q^{23} -1.00000 q^{24} -4.54420 q^{25} -6.15633 q^{26} -1.00000 q^{27} -5.15633 q^{28} -3.76845 q^{29} -0.675131 q^{30} -10.5369 q^{31} +1.00000 q^{32} -3.76845 q^{33} -5.19394 q^{34} -3.48119 q^{35} +1.00000 q^{36} -3.06300 q^{37} +2.54420 q^{38} +6.15633 q^{39} +0.675131 q^{40} +2.31265 q^{41} +5.15633 q^{42} -7.50659 q^{43} +3.76845 q^{44} +0.675131 q^{45} +2.15633 q^{46} +9.46898 q^{47} -1.00000 q^{48} +19.5877 q^{49} -4.54420 q^{50} +5.19394 q^{51} -6.15633 q^{52} -3.74306 q^{53} -1.00000 q^{54} +2.54420 q^{55} -5.15633 q^{56} -2.54420 q^{57} -3.76845 q^{58} -10.5999 q^{59} -0.675131 q^{60} -0.775746 q^{61} -10.5369 q^{62} -5.15633 q^{63} +1.00000 q^{64} -4.15633 q^{65} -3.76845 q^{66} +6.86177 q^{67} -5.19394 q^{68} -2.15633 q^{69} -3.48119 q^{70} +5.50659 q^{71} +1.00000 q^{72} -11.8192 q^{73} -3.06300 q^{74} +4.54420 q^{75} +2.54420 q^{76} -19.4314 q^{77} +6.15633 q^{78} +10.3879 q^{79} +0.675131 q^{80} +1.00000 q^{81} +2.31265 q^{82} +6.44358 q^{83} +5.15633 q^{84} -3.50659 q^{85} -7.50659 q^{86} +3.76845 q^{87} +3.76845 q^{88} -11.9321 q^{89} +0.675131 q^{90} +31.7440 q^{91} +2.15633 q^{92} +10.5369 q^{93} +9.46898 q^{94} +1.71767 q^{95} -1.00000 q^{96} +8.50659 q^{97} +19.5877 q^{98} +3.76845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{12} - 8 q^{13} - 5 q^{14} + 3 q^{15} + 3 q^{16} - 16 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 5 q^{21} - 4 q^{23} - 3 q^{24} - 4 q^{25} - 8 q^{26} - 3 q^{27} - 5 q^{28} + 3 q^{30} - 9 q^{31} + 3 q^{32} - 16 q^{34} - 5 q^{35} + 3 q^{36} - 5 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} - 14 q^{41} + 5 q^{42} - 2 q^{43} - 3 q^{45} - 4 q^{46} - 3 q^{47} - 3 q^{48} + 6 q^{49} - 4 q^{50} + 16 q^{51} - 8 q^{52} - 15 q^{53} - 3 q^{54} - 2 q^{55} - 5 q^{56} + 2 q^{57} - 5 q^{59} + 3 q^{60} - 4 q^{61} - 9 q^{62} - 5 q^{63} + 3 q^{64} - 2 q^{65} + 3 q^{67} - 16 q^{68} + 4 q^{69} - 5 q^{70} - 4 q^{71} + 3 q^{72} + 6 q^{73} - 5 q^{74} + 4 q^{75} - 2 q^{76} - 16 q^{77} + 8 q^{78} + 32 q^{79} - 3 q^{80} + 3 q^{81} - 14 q^{82} + 3 q^{83} + 5 q^{84} + 10 q^{85} - 2 q^{86} - 27 q^{89} - 3 q^{90} + 32 q^{91} - 4 q^{92} + 9 q^{93} - 3 q^{94} + 24 q^{95} - 3 q^{96} + 5 q^{97} + 6 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^12 - 8 * q^13 - 5 * q^14 + 3 * q^15 + 3 * q^16 - 16 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 5 * q^21 - 4 * q^23 - 3 * q^24 - 4 * q^25 - 8 * q^26 - 3 * q^27 - 5 * q^28 + 3 * q^30 - 9 * q^31 + 3 * q^32 - 16 * q^34 - 5 * q^35 + 3 * q^36 - 5 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 - 14 * q^41 + 5 * q^42 - 2 * q^43 - 3 * q^45 - 4 * q^46 - 3 * q^47 - 3 * q^48 + 6 * q^49 - 4 * q^50 + 16 * q^51 - 8 * q^52 - 15 * q^53 - 3 * q^54 - 2 * q^55 - 5 * q^56 + 2 * q^57 - 5 * q^59 + 3 * q^60 - 4 * q^61 - 9 * q^62 - 5 * q^63 + 3 * q^64 - 2 * q^65 + 3 * q^67 - 16 * q^68 + 4 * q^69 - 5 * q^70 - 4 * q^71 + 3 * q^72 + 6 * q^73 - 5 * q^74 + 4 * q^75 - 2 * q^76 - 16 * q^77 + 8 * q^78 + 32 * q^79 - 3 * q^80 + 3 * q^81 - 14 * q^82 + 3 * q^83 + 5 * q^84 + 10 * q^85 - 2 * q^86 - 27 * q^89 - 3 * q^90 + 32 * q^91 - 4 * q^92 + 9 * q^93 - 3 * q^94 + 24 * q^95 - 3 * q^96 + 5 * q^97 + 6 * q^98

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