LMFDB - Embedded newform 4022.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.75046 q^{3} +1.00000 q^{4} +1.28935 q^{5} -1.75046 q^{6} -0.876800 q^{7} +1.00000 q^{8} +0.0641056 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.75046 q^{3} +1.00000 q^{4} +1.28935 q^{5} -1.75046 q^{6} -0.876800 q^{7} +1.00000 q^{8} +0.0641056 q^{9} +1.28935 q^{10} -1.28293 q^{11} -1.75046 q^{12} +0.225028 q^{13} -0.876800 q^{14} -2.25696 q^{15} +1.00000 q^{16} +5.98652 q^{17} +0.0641056 q^{18} -7.24448 q^{19} +1.28935 q^{20} +1.53480 q^{21} -1.28293 q^{22} +2.70981 q^{23} -1.75046 q^{24} -3.33757 q^{25} +0.225028 q^{26} +5.13916 q^{27} -0.876800 q^{28} -6.42309 q^{29} -2.25696 q^{30} +1.49008 q^{31} +1.00000 q^{32} +2.24571 q^{33} +5.98652 q^{34} -1.13051 q^{35} +0.0641056 q^{36} -2.10289 q^{37} -7.24448 q^{38} -0.393901 q^{39} +1.28935 q^{40} +4.13514 q^{41} +1.53480 q^{42} -4.91283 q^{43} -1.28293 q^{44} +0.0826548 q^{45} +2.70981 q^{46} -1.88312 q^{47} -1.75046 q^{48} -6.23122 q^{49} -3.33757 q^{50} -10.4792 q^{51} +0.225028 q^{52} +2.06927 q^{53} +5.13916 q^{54} -1.65415 q^{55} -0.876800 q^{56} +12.6812 q^{57} -6.42309 q^{58} -8.60286 q^{59} -2.25696 q^{60} +12.1418 q^{61} +1.49008 q^{62} -0.0562077 q^{63} +1.00000 q^{64} +0.290140 q^{65} +2.24571 q^{66} +5.48626 q^{67} +5.98652 q^{68} -4.74341 q^{69} -1.13051 q^{70} -16.2228 q^{71} +0.0641056 q^{72} +2.50459 q^{73} -2.10289 q^{74} +5.84227 q^{75} -7.24448 q^{76} +1.12487 q^{77} -0.393901 q^{78} -10.0611 q^{79} +1.28935 q^{80} -9.18821 q^{81} +4.13514 q^{82} -6.40976 q^{83} +1.53480 q^{84} +7.71874 q^{85} -4.91283 q^{86} +11.2433 q^{87} -1.28293 q^{88} -14.1815 q^{89} +0.0826548 q^{90} -0.197304 q^{91} +2.70981 q^{92} -2.60832 q^{93} -1.88312 q^{94} -9.34071 q^{95} -1.75046 q^{96} +8.26993 q^{97} -6.23122 q^{98} -0.0822429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - 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
$3$	−1.75046	−1.01063	−0.505314	−	0.862936i	$-0.668623\pi$
$3$	−1.75046	−1.01063	−0.505314	+	0.862936i	$0.668623\pi$
$4$	1.00000	0.500000
$5$	1.28935	0.576617	0.288308	−	0.957538i	$-0.406907\pi$
$5$	1.28935	0.576617	0.288308	+	0.957538i	$0.406907\pi$
$6$	−1.75046	−0.714622
$7$	−0.876800	−0.331399	−0.165700	−	0.986176i	$-0.552988\pi$
$7$	−0.876800	−0.331399	−0.165700	+	0.986176i	$0.552988\pi$
$8$	1.00000	0.353553
$9$	0.0641056	0.0213685
$10$	1.28935	0.407730
$11$	−1.28293	−0.386818	−0.193409	−	0.981118i	$-0.561954\pi$
$11$	−1.28293	−0.386818	−0.193409	+	0.981118i	$0.561954\pi$
$12$	−1.75046	−0.505314
$13$	0.225028	0.0624114	0.0312057	−	0.999513i	$-0.490065\pi$
$13$	0.225028	0.0624114	0.0312057	+	0.999513i	$0.490065\pi$
$14$	−0.876800	−0.234335
$15$	−2.25696	−0.582745
$16$	1.00000	0.250000
$17$	5.98652	1.45194	0.725972	−	0.687724i	$-0.241390\pi$
$17$	5.98652	1.45194	0.725972	+	0.687724i	$0.241390\pi$
$18$	0.0641056	0.0151098
$19$	−7.24448	−1.66200	−0.830999	−	0.556273i	$-0.812231\pi$
$19$	−7.24448	−1.66200	−0.830999	+	0.556273i	$0.812231\pi$
$20$	1.28935	0.288308
$21$	1.53480	0.334921
$22$	−1.28293	−0.273521
$23$	2.70981	0.565034	0.282517	−	0.959262i	$-0.408831\pi$
$23$	2.70981	0.565034	0.282517	+	0.959262i	$0.408831\pi$
$24$	−1.75046	−0.357311
$25$	−3.33757	−0.667513
$26$	0.225028	0.0441315
$27$	5.13916	0.989032
$28$	−0.876800	−0.165700
$29$	−6.42309	−1.19274	−0.596369	−	0.802711i	$-0.703390\pi$
$29$	−6.42309	−1.19274	−0.596369	+	0.802711i	$0.703390\pi$
$30$	−2.25696	−0.412063
$31$	1.49008	0.267626	0.133813	−	0.991007i	$-0.457278\pi$
$31$	1.49008	0.267626	0.133813	+	0.991007i	$0.457278\pi$
$32$	1.00000	0.176777
$33$	2.24571	0.390929
$34$	5.98652	1.02668
$35$	−1.13051	−0.191090
$36$	0.0641056	0.0106843
$37$	−2.10289	−0.345712	−0.172856	−	0.984947i	$-0.555300\pi$
$37$	−2.10289	−0.345712	−0.172856	+	0.984947i	$0.555300\pi$
$38$	−7.24448	−1.17521
$39$	−0.393901	−0.0630747
$40$	1.28935	0.203865
$41$	4.13514	0.645801	0.322901	−	0.946433i	$-0.395342\pi$
$41$	4.13514	0.645801	0.322901	+	0.946433i	$0.395342\pi$
$42$	1.53480	0.236825
$43$	−4.91283	−0.749200	−0.374600	−	0.927187i	$-0.622220\pi$
$43$	−4.91283	−0.749200	−0.374600	+	0.927187i	$0.622220\pi$
$44$	−1.28293	−0.193409
$45$	0.0826548	0.0123214
$46$	2.70981	0.399539
$47$	−1.88312	−0.274681	−0.137340	−	0.990524i	$-0.543855\pi$
$47$	−1.88312	−0.274681	−0.137340	+	0.990524i	$0.543855\pi$
$48$	−1.75046	−0.252657
$49$	−6.23122	−0.890175
$50$	−3.33757	−0.472003
$51$	−10.4792	−1.46738
$52$	0.225028	0.0312057
$53$	2.06927	0.284237	0.142118	−	0.989850i	$-0.454609\pi$
$53$	2.06927	0.284237	0.142118	+	0.989850i	$0.454609\pi$
$54$	5.13916	0.699351
$55$	−1.65415	−0.223045
$56$	−0.876800	−0.117167
$57$	12.6812	1.67966
$58$	−6.42309	−0.843393
$59$	−8.60286	−1.12000	−0.559999	−	0.828494i	$-0.689198\pi$
$59$	−8.60286	−1.12000	−0.559999	+	0.828494i	$0.689198\pi$
$60$	−2.25696	−0.291372
$61$	12.1418	1.55460	0.777301	−	0.629129i	$-0.216588\pi$
$61$	12.1418	1.55460	0.777301	+	0.629129i	$0.216588\pi$
$62$	1.49008	0.189240
$63$	−0.0562077	−0.00708151
$64$	1.00000	0.125000
$65$	0.290140	0.0359875
$66$	2.24571	0.276428
$67$	5.48626	0.670254	0.335127	−	0.942173i	$-0.391221\pi$
$67$	5.48626	0.670254	0.335127	+	0.942173i	$0.391221\pi$
$68$	5.98652	0.725972
$69$	−4.74341	−0.571039
$70$	−1.13051	−0.135121
$71$	−16.2228	−1.92530	−0.962648	−	0.270756i	$-0.912726\pi$
$71$	−16.2228	−1.92530	−0.962648	+	0.270756i	$0.912726\pi$
$72$	0.0641056	0.00755491
$73$	2.50459	0.293140	0.146570	−	0.989200i	$-0.453177\pi$
$73$	2.50459	0.293140	0.146570	+	0.989200i	$0.453177\pi$
$74$	−2.10289	−0.244456
$75$	5.84227	0.674607
$76$	−7.24448	−0.830999
$77$	1.12487	0.128191
$78$	−0.393901	−0.0446006
$79$	−10.0611	−1.13196	−0.565981	−	0.824418i	$-0.691502\pi$
$79$	−10.0611	−1.13196	−0.565981	+	0.824418i	$0.691502\pi$
$80$	1.28935	0.144154
$81$	−9.18821	−1.02091
$82$	4.13514	0.456650
$83$	−6.40976	−0.703562	−0.351781	−	0.936082i	$-0.614424\pi$
$83$	−6.40976	−0.703562	−0.351781	+	0.936082i	$0.614424\pi$
$84$	1.53480	0.167461
$85$	7.71874	0.837215
$86$	−4.91283	−0.529764
$87$	11.2433	1.20541
$88$	−1.28293	−0.136761
$89$	−14.1815	−1.50324	−0.751619	−	0.659597i	$-0.770727\pi$
$89$	−14.1815	−1.50324	−0.751619	+	0.659597i	$0.770727\pi$
$90$	0.0826548	0.00871258
$91$	−0.197304	−0.0206831
$92$	2.70981	0.282517
$93$	−2.60832	−0.270470
$94$	−1.88312	−0.194228
$95$	−9.34071	−0.958336
$96$	−1.75046	−0.178655
$97$	8.26993	0.839684	0.419842	−	0.907597i	$-0.362086\pi$
$97$	8.26993	0.839684	0.419842	+	0.907597i	$0.362086\pi$
$98$	−6.23122	−0.629449
$99$	−0.0822429	−0.00826572
$100$	−3.33757	−0.333757
$101$	−14.5779	−1.45055	−0.725277	−	0.688458i	$-0.758288\pi$
$101$	−14.5779	−1.45055	−0.725277	+	0.688458i	$0.758288\pi$
$102$	−10.4792	−1.03759
$103$	−0.271941	−0.0267952	−0.0133976	−	0.999910i	$-0.504265\pi$
$103$	−0.271941	−0.0267952	−0.0133976	+	0.999910i	$0.504265\pi$
$104$	0.225028	0.0220658
$105$	1.97890	0.193121
$106$	2.06927	0.200986
$107$	9.60580	0.928627	0.464314	−	0.885671i	$-0.346301\pi$
$107$	9.60580	0.928627	0.464314	+	0.885671i	$0.346301\pi$
$108$	5.13916	0.494516
$109$	15.7206	1.50576	0.752881	−	0.658157i	$-0.228664\pi$
$109$	15.7206	1.50576	0.752881	+	0.658157i	$0.228664\pi$
$110$	−1.65415	−0.157717
$111$	3.68102	0.349387
$112$	−0.876800	−0.0828498
$113$	−10.0760	−0.947866	−0.473933	−	0.880561i	$-0.657166\pi$
$113$	−10.0760	−0.947866	−0.473933	+	0.880561i	$0.657166\pi$
$114$	12.6812	1.18770
$115$	3.49390	0.325808
$116$	−6.42309	−0.596369
$117$	0.0144255	0.00133364
$118$	−8.60286	−0.791958
$119$	−5.24898	−0.481173
$120$	−2.25696	−0.206031
$121$	−9.35409	−0.850372
$122$	12.1418	1.09927
$123$	−7.23840	−0.652665
$124$	1.49008	0.133813
$125$	−10.7501	−0.961516
$126$	−0.0562077	−0.00500738
$127$	−9.12133	−0.809387	−0.404694	−	0.914452i	$-0.632622\pi$
$127$	−9.12133	−0.809387	−0.404694	+	0.914452i	$0.632622\pi$
$128$	1.00000	0.0883883
$129$	8.59971	0.757162
$130$	0.290140	0.0254470
$131$	−6.00235	−0.524428	−0.262214	−	0.965010i	$-0.584453\pi$
$131$	−6.00235	−0.524428	−0.262214	+	0.965010i	$0.584453\pi$
$132$	2.24571	0.195464
$133$	6.35196	0.550785
$134$	5.48626	0.473941
$135$	6.62620	0.570292
$136$	5.98652	0.513340
$137$	8.40096	0.717742	0.358871	−	0.933387i	$-0.383162\pi$
$137$	8.40096	0.717742	0.358871	+	0.933387i	$0.383162\pi$
$138$	−4.74341	−0.403786
$139$	0.768712	0.0652013	0.0326007	−	0.999468i	$-0.489621\pi$
$139$	0.768712	0.0652013	0.0326007	+	0.999468i	$0.489621\pi$
$140$	−1.13051	−0.0955451
$141$	3.29632	0.277600
$142$	−16.2228	−1.36139
$143$	−0.288694	−0.0241418
$144$	0.0641056	0.00534213
$145$	−8.28163	−0.687752
$146$	2.50459	0.207281
$147$	10.9075	0.899635
$148$	−2.10289	−0.172856
$149$	−11.1812	−0.916001	−0.458000	−	0.888952i	$-0.651434\pi$
$149$	−11.1812	−0.916001	−0.458000	+	0.888952i	$0.651434\pi$
$150$	5.84227	0.477019
$151$	2.38218	0.193859	0.0969296	−	0.995291i	$-0.469098\pi$
$151$	2.38218	0.193859	0.0969296	+	0.995291i	$0.469098\pi$
$152$	−7.24448	−0.587605
$153$	0.383769	0.0310259
$154$	1.12487	0.0906447
$155$	1.92124	0.154317
$156$	−0.393901	−0.0315374
$157$	−0.304865	−0.0243309	−0.0121654	−	0.999926i	$-0.503872\pi$
$157$	−0.304865	−0.0243309	−0.0121654	+	0.999926i	$0.503872\pi$
$158$	−10.0611	−0.800418
$159$	−3.62218	−0.287257
$160$	1.28935	0.101932
$161$	−2.37596	−0.187252
$162$	−9.18821	−0.721894
$163$	8.38198	0.656528	0.328264	−	0.944586i	$-0.393536\pi$
$163$	8.38198	0.656528	0.328264	+	0.944586i	$0.393536\pi$
$164$	4.13514	0.322901
$165$	2.89552	0.225416
$166$	−6.40976	−0.497494
$167$	−12.1234	−0.938139	−0.469069	−	0.883161i	$-0.655411\pi$
$167$	−12.1234	−0.938139	−0.469069	+	0.883161i	$0.655411\pi$
$168$	1.53480	0.118413
$169$	−12.9494	−0.996105
$170$	7.71874	0.592001
$171$	−0.464412	−0.0355145
$172$	−4.91283	−0.374600
$173$	24.9433	1.89641	0.948204	−	0.317663i	$-0.102898\pi$
$173$	24.9433	1.89641	0.948204	+	0.317663i	$0.102898\pi$
$174$	11.2433	0.852356
$175$	2.92638	0.221213
$176$	−1.28293	−0.0967044
$177$	15.0590	1.13190
$178$	−14.1815	−1.06295
$179$	−14.3700	−1.07406	−0.537031	−	0.843563i	$-0.680454\pi$
$179$	−14.3700	−1.07406	−0.537031	+	0.843563i	$0.680454\pi$
$180$	0.0826548	0.00616072
$181$	11.7556	0.873787	0.436893	−	0.899513i	$-0.356079\pi$
$181$	11.7556	0.873787	0.436893	+	0.899513i	$0.356079\pi$
$182$	−0.197304	−0.0146252
$183$	−21.2538	−1.57112
$184$	2.70981	0.199770
$185$	−2.71137	−0.199344
$186$	−2.60832	−0.191251
$187$	−7.68028	−0.561637
$188$	−1.88312	−0.137340
$189$	−4.50602	−0.327764
$190$	−9.34071	−0.677646
$191$	−17.9153	−1.29631	−0.648154	−	0.761509i	$-0.724459\pi$
$191$	−17.9153	−1.29631	−0.648154	+	0.761509i	$0.724459\pi$
$192$	−1.75046	−0.126328
$193$	−22.0973	−1.59060	−0.795300	−	0.606216i	$-0.792687\pi$
$193$	−22.0973	−1.59060	−0.795300	+	0.606216i	$0.792687\pi$
$194$	8.26993	0.593746
$195$	−0.507878	−0.0363699
$196$	−6.23122	−0.445087
$197$	−5.86785	−0.418067	−0.209034	−	0.977908i	$-0.567032\pi$
$197$	−5.86785	−0.418067	−0.209034	+	0.977908i	$0.567032\pi$
$198$	−0.0822429	−0.00584475
$199$	−3.73945	−0.265083	−0.132541	−	0.991177i	$-0.542314\pi$
$199$	−3.73945	−0.265083	−0.132541	+	0.991177i	$0.542314\pi$
$200$	−3.33757	−0.236002
$201$	−9.60347	−0.677377
$202$	−14.5779	−1.02570
$203$	5.63176	0.395272
$204$	−10.4792	−0.733688
$205$	5.33167	0.372380
$206$	−0.271941	−0.0189471
$207$	0.173714	0.0120739
$208$	0.225028	0.0156029
$209$	9.29416	0.642890
$210$	1.97890	0.136557
$211$	27.7812	1.91254	0.956268	−	0.292493i	$-0.0944849\pi$
$211$	27.7812	1.91254	0.956268	+	0.292493i	$0.0944849\pi$
$212$	2.06927	0.142118
$213$	28.3974	1.94576
$214$	9.60580	0.656639
$215$	−6.33438	−0.432001
$216$	5.13916	0.349676
$217$	−1.30650	−0.0886909
$218$	15.7206	1.06473
$219$	−4.38417	−0.296255
$220$	−1.65415	−0.111523
$221$	1.34713	0.0906179
$222$	3.68102	0.247054
$223$	−22.9164	−1.53460	−0.767299	−	0.641290i	$-0.778400\pi$
$223$	−22.9164	−1.53460	−0.767299	+	0.641290i	$0.778400\pi$
$224$	−0.876800	−0.0585836
$225$	−0.213957	−0.0142638
$226$	−10.0760	−0.670243
$227$	−2.08411	−0.138328	−0.0691638	−	0.997605i	$-0.522033\pi$
$227$	−2.08411	−0.138328	−0.0691638	+	0.997605i	$0.522033\pi$
$228$	12.6812	0.839831
$229$	15.3090	1.01165	0.505823	−	0.862637i	$-0.331189\pi$
$229$	15.3090	1.01165	0.505823	+	0.862637i	$0.331189\pi$
$230$	3.49390	0.230381
$231$	−1.96904	−0.129553
$232$	−6.42309	−0.421696
$233$	19.1212	1.25267	0.626337	−	0.779553i	$-0.284554\pi$
$233$	19.1212	1.25267	0.626337	+	0.779553i	$0.284554\pi$
$234$	0.0144255	0.000943026 0
$235$	−2.42800	−0.158385
$236$	−8.60286	−0.559999
$237$	17.6115	1.14399
$238$	−5.24898	−0.340241
$239$	−11.8207	−0.764615	−0.382307	−	0.924035i	$-0.624870\pi$
$239$	−11.8207	−0.764615	−0.382307	+	0.924035i	$0.624870\pi$
$240$	−2.25696	−0.145686
$241$	−9.30234	−0.599216	−0.299608	−	0.954062i	$-0.596856\pi$
$241$	−9.30234	−0.599216	−0.299608	+	0.954062i	$0.596856\pi$
$242$	−9.35409	−0.601304
$243$	0.666091	0.0427298
$244$	12.1418	0.777301
$245$	−8.03425	−0.513290
$246$	−7.23840	−0.461504
$247$	−1.63021	−0.103728
$248$	1.49008	0.0946200
$249$	11.2200	0.711039
$250$	−10.7501	−0.679894
$251$	−9.41531	−0.594289	−0.297145	−	0.954832i	$-0.596034\pi$
$251$	−9.41531	−0.594289	−0.297145	+	0.954832i	$0.596034\pi$
$252$	−0.0562077	−0.00354075
$253$	−3.47649	−0.218565
$254$	−9.12133	−0.572323
$255$	−13.5113	−0.846113
$256$	1.00000	0.0625000
$257$	9.59526	0.598536	0.299268	−	0.954169i	$-0.403258\pi$
$257$	9.59526	0.598536	0.299268	+	0.954169i	$0.403258\pi$
$258$	8.59971	0.535394
$259$	1.84381	0.114569
$260$	0.290140	0.0179937
$261$	−0.411756	−0.0254870
$262$	−6.00235	−0.370826
$263$	−10.3149	−0.636042	−0.318021	−	0.948084i	$-0.603018\pi$
$263$	−10.3149	−0.636042	−0.318021	+	0.948084i	$0.603018\pi$
$264$	2.24571	0.138214
$265$	2.66803	0.163896
$266$	6.35196	0.389464
$267$	24.8242	1.51921
$268$	5.48626	0.335127
$269$	−6.15327	−0.375171	−0.187586	−	0.982248i	$-0.560066\pi$
$269$	−6.15327	−0.375171	−0.187586	+	0.982248i	$0.560066\pi$
$270$	6.62620	0.403258
$271$	−14.6018	−0.886998	−0.443499	−	0.896275i	$-0.646263\pi$
$271$	−14.6018	−0.886998	−0.443499	+	0.896275i	$0.646263\pi$
$272$	5.98652	0.362986
$273$	0.345373	0.0209029
$274$	8.40096	0.507520
$275$	4.28186	0.258206
$276$	−4.74341	−0.285520
$277$	4.45111	0.267441	0.133721	−	0.991019i	$-0.457308\pi$
$277$	4.45111	0.267441	0.133721	+	0.991019i	$0.457308\pi$
$278$	0.768712	0.0461043
$279$	0.0955222	0.00571877
$280$	−1.13051	−0.0675606
$281$	11.8982	0.709785	0.354892	−	0.934907i	$-0.384517\pi$
$281$	11.8982	0.709785	0.354892	+	0.934907i	$0.384517\pi$
$282$	3.29632	0.196293
$283$	−26.8019	−1.59321	−0.796605	−	0.604500i	$-0.793373\pi$
$283$	−26.8019	−1.59321	−0.796605	+	0.604500i	$0.793373\pi$
$284$	−16.2228	−0.962648
$285$	16.3505	0.968521
$286$	−0.288694	−0.0170709
$287$	−3.62569	−0.214018
$288$	0.0641056	0.00377746
$289$	18.8384	1.10814
$290$	−8.28163	−0.486314
$291$	−14.4762	−0.848608
$292$	2.50459	0.146570
$293$	−18.9677	−1.10811	−0.554053	−	0.832481i	$-0.686920\pi$
$293$	−18.9677	−1.10811	−0.554053	+	0.832481i	$0.686920\pi$
$294$	10.9075	0.636138
$295$	−11.0921	−0.645809
$296$	−2.10289	−0.122228
$297$	−6.59318	−0.382575
$298$	−11.1812	−0.647711
$299$	0.609782	0.0352646
$300$	5.84227	0.337304
$301$	4.30757	0.248284
$302$	2.38218	0.137079
$303$	25.5180	1.46597
$304$	−7.24448	−0.415500
$305$	15.6551	0.896409
$306$	0.383769	0.0219386
$307$	−8.17486	−0.466564	−0.233282	−	0.972409i	$-0.574947\pi$
$307$	−8.17486	−0.466564	−0.233282	+	0.972409i	$0.574947\pi$
$308$	1.12487	0.0640955
$309$	0.476022	0.0270800
$310$	1.92124	0.109119
$311$	15.6131	0.885339	0.442669	−	0.896685i	$-0.354032\pi$
$311$	15.6131	0.885339	0.442669	+	0.896685i	$0.354032\pi$
$312$	−0.393901	−0.0223003
$313$	−15.4596	−0.873828	−0.436914	−	0.899503i	$-0.643929\pi$
$313$	−15.4596	−0.873828	−0.436914	+	0.899503i	$0.643929\pi$
$314$	−0.304865	−0.0172045
$315$	−0.0724717	−0.00408332
$316$	−10.0611	−0.565981
$317$	−3.65132	−0.205079	−0.102539	−	0.994729i	$-0.532697\pi$
$317$	−3.65132	−0.205079	−0.102539	+	0.994729i	$0.532697\pi$
$318$	−3.62218	−0.203122
$319$	8.24036	0.461372
$320$	1.28935	0.0720771
$321$	−16.8146	−0.938497
$322$	−2.37596	−0.132407
$323$	−43.3692	−2.41313
$324$	−9.18821	−0.510456
$325$	−0.751044	−0.0416604
$326$	8.38198	0.464235
$327$	−27.5183	−1.52177
$328$	4.13514	0.228325
$329$	1.65111	0.0910289
$330$	2.89552	0.159393
$331$	−7.54768	−0.414858	−0.207429	−	0.978250i	$-0.566510\pi$
$331$	−7.54768	−0.414858	−0.207429	+	0.978250i	$0.566510\pi$
$332$	−6.40976	−0.351781
$333$	−0.134807	−0.00738736
$334$	−12.1234	−0.663364
$335$	7.07373	0.386479
$336$	1.53480	0.0837303
$337$	−25.3131	−1.37889	−0.689447	−	0.724336i	$-0.742146\pi$
$337$	−25.3131	−1.37889	−0.689447	+	0.724336i	$0.742146\pi$
$338$	−12.9494	−0.704352
$339$	17.6375	0.957940
$340$	7.71874	0.418608
$341$	−1.91166	−0.103522
$342$	−0.464412	−0.0251125
$343$	11.6011	0.626402
$344$	−4.91283	−0.264882
$345$	−6.11593	−0.329271
$346$	24.9433	1.34096
$347$	−17.3694	−0.932441	−0.466220	−	0.884669i	$-0.654385\pi$
$347$	−17.3694	−0.932441	−0.466220	+	0.884669i	$0.654385\pi$
$348$	11.2433	0.602707
$349$	−0.264359	−0.0141508	−0.00707540	−	0.999975i	$-0.502252\pi$
$349$	−0.264359	−0.0141508	−0.00707540	+	0.999975i	$0.502252\pi$
$350$	2.92638	0.156421
$351$	1.15645	0.0617269
$352$	−1.28293	−0.0683803
$353$	11.7868	0.627348	0.313674	−	0.949531i	$-0.398440\pi$
$353$	11.7868	0.627348	0.313674	+	0.949531i	$0.398440\pi$
$354$	15.0590	0.800374
$355$	−20.9170	−1.11016
$356$	−14.1815	−0.751619
$357$	9.18812	0.486287
$358$	−14.3700	−0.759476
$359$	24.0748	1.27062	0.635309	−	0.772258i	$-0.280873\pi$
$359$	24.0748	1.27062	0.635309	+	0.772258i	$0.280873\pi$
$360$	0.0826548	0.00435629
$361$	33.4826	1.76224
$362$	11.7556	0.617861
$363$	16.3740	0.859410
$364$	−0.197304	−0.0103415
$365$	3.22930	0.169029
$366$	−21.2538	−1.11095
$367$	−20.4094	−1.06536	−0.532681	−	0.846316i	$-0.678816\pi$
$367$	−20.4094	−1.06536	−0.532681	+	0.846316i	$0.678816\pi$
$368$	2.70981	0.141259
$369$	0.265086	0.0137998
$370$	−2.71137	−0.140957
$371$	−1.81434	−0.0941958
$372$	−2.60832	−0.135235
$373$	5.72325	0.296339	0.148169	−	0.988962i	$-0.452662\pi$
$373$	5.72325	0.296339	0.148169	+	0.988962i	$0.452662\pi$
$374$	−7.68028	−0.397138
$375$	18.8176	0.971735
$376$	−1.88312	−0.0971142
$377$	−1.44537	−0.0744404
$378$	−4.50602	−0.231764
$379$	13.6464	0.700970	0.350485	−	0.936568i	$-0.386017\pi$
$379$	13.6464	0.700970	0.350485	+	0.936568i	$0.386017\pi$
$380$	−9.34071	−0.479168
$381$	15.9665	0.817989
$382$	−17.9153	−0.916629
$383$	26.0858	1.33292	0.666460	−	0.745541i	$-0.267809\pi$
$383$	26.0858	1.33292	0.666460	+	0.745541i	$0.267809\pi$
$384$	−1.75046	−0.0893277
$385$	1.45036	0.0739171
$386$	−22.0973	−1.12472
$387$	−0.314940	−0.0160093
$388$	8.26993	0.419842
$389$	1.01582	0.0515040	0.0257520	−	0.999668i	$-0.491802\pi$
$389$	1.01582	0.0515040	0.0257520	+	0.999668i	$0.491802\pi$
$390$	−0.507878	−0.0257174
$391$	16.2223	0.820398
$392$	−6.23122	−0.314724
$393$	10.5069	0.530001
$394$	−5.86785	−0.295618
$395$	−12.9723	−0.652708
$396$	−0.0822429	−0.00413286
$397$	34.9079	1.75198	0.875988	−	0.482333i	$-0.160210\pi$
$397$	34.9079	1.75198	0.875988	+	0.482333i	$0.160210\pi$
$398$	−3.73945	−0.187442
$399$	−11.1188	−0.556639
$400$	−3.33757	−0.166878
$401$	22.3295	1.11508	0.557542	−	0.830149i	$-0.311744\pi$
$401$	22.3295	1.11508	0.557542	+	0.830149i	$0.311744\pi$
$402$	−9.60347	−0.478978
$403$	0.335308	0.0167029
$404$	−14.5779	−0.725277
$405$	−11.8469	−0.588675
$406$	5.63176	0.279500
$407$	2.69785	0.133728
$408$	−10.4792	−0.518795
$409$	−21.9297	−1.08435	−0.542177	−	0.840264i	$-0.682400\pi$
$409$	−21.9297	−1.08435	−0.542177	+	0.840264i	$0.682400\pi$
$410$	5.33167	0.263312
$411$	−14.7055	−0.725370
$412$	−0.271941	−0.0133976
$413$	7.54299	0.371166
$414$	0.173714	0.00853757
$415$	−8.26445	−0.405686
$416$	0.225028	0.0110329
$417$	−1.34560	−0.0658943
$418$	9.29416	0.454592
$419$	26.0991	1.27502	0.637512	−	0.770440i	$-0.279964\pi$
$419$	26.0991	1.27502	0.637512	+	0.770440i	$0.279964\pi$
$420$	1.97890	0.0965606
$421$	−13.5905	−0.662360	−0.331180	−	0.943568i	$-0.607447\pi$
$421$	−13.5905	−0.662360	−0.331180	+	0.943568i	$0.607447\pi$
$422$	27.7812	1.35237
$423$	−0.120718	−0.00586952
$424$	2.06927	0.100493
$425$	−19.9804	−0.969192
$426$	28.3974	1.37586
$427$	−10.6459	−0.515194
$428$	9.60580	0.464314
$429$	0.505347	0.0243984
$430$	−6.33438	−0.305471
$431$	6.09508	0.293590	0.146795	−	0.989167i	$-0.453104\pi$
$431$	6.09508	0.293590	0.146795	+	0.989167i	$0.453104\pi$
$432$	5.13916	0.247258
$433$	8.05600	0.387147	0.193573	−	0.981086i	$-0.437992\pi$
$433$	8.05600	0.387147	0.193573	+	0.981086i	$0.437992\pi$
$434$	−1.30650	−0.0627140
$435$	14.4967	0.695062
$436$	15.7206	0.752881
$437$	−19.6312	−0.939086
$438$	−4.38417	−0.209484
$439$	−30.2636	−1.44440	−0.722202	−	0.691682i	$-0.756870\pi$
$439$	−30.2636	−1.44440	−0.722202	+	0.691682i	$0.756870\pi$
$440$	−1.65415	−0.0788585
$441$	−0.399456	−0.0190217
$442$	1.34713	0.0640765
$443$	3.80455	0.180760	0.0903799	−	0.995907i	$-0.471192\pi$
$443$	3.80455	0.180760	0.0903799	+	0.995907i	$0.471192\pi$
$444$	3.68102	0.174693
$445$	−18.2850	−0.866792
$446$	−22.9164	−1.08512
$447$	19.5723	0.925736
$448$	−0.876800	−0.0414249
$449$	27.3357	1.29005	0.645026	−	0.764161i	$-0.276847\pi$
$449$	27.3357	1.29005	0.645026	+	0.764161i	$0.276847\pi$
$450$	−0.213957	−0.0100860
$451$	−5.30510	−0.249807
$452$	−10.0760	−0.473933
$453$	−4.16991	−0.195919
$454$	−2.08411	−0.0978123
$455$	−0.254395	−0.0119262
$456$	12.6812	0.593850
$457$	−1.81388	−0.0848496	−0.0424248	−	0.999100i	$-0.513508\pi$
$457$	−1.81388	−0.0848496	−0.0424248	+	0.999100i	$0.513508\pi$
$458$	15.3090	0.715341
$459$	30.7657	1.43602
$460$	3.49390	0.162904
$461$	16.2086	0.754912	0.377456	−	0.926028i	$-0.376799\pi$
$461$	16.2086	0.754912	0.377456	+	0.926028i	$0.376799\pi$
$462$	−1.96904	−0.0916081
$463$	35.3990	1.64513	0.822567	−	0.568669i	$-0.192541\pi$
$463$	35.3990	1.64513	0.822567	+	0.568669i	$0.192541\pi$
$464$	−6.42309	−0.298184
$465$	−3.36305	−0.155958
$466$	19.1212	0.885774
$467$	29.3005	1.35586	0.677932	−	0.735125i	$-0.262877\pi$
$467$	29.3005	1.35586	0.677932	+	0.735125i	$0.262877\pi$
$468$	0.0144255	0.000666820 0
$469$	−4.81035	−0.222121
$470$	−2.42800	−0.111995
$471$	0.533653	0.0245894
$472$	−8.60286	−0.395979
$473$	6.30281	0.289804
$474$	17.6115	0.808924
$475$	24.1789	1.10941
$476$	−5.24898	−0.240587
$477$	0.132652	0.00607372
$478$	−11.8207	−0.540664
$479$	−13.4423	−0.614193	−0.307096	−	0.951678i	$-0.599357\pi$
$479$	−13.4423	−0.614193	−0.307096	+	0.951678i	$0.599357\pi$
$480$	−2.25696	−0.103016
$481$	−0.473207	−0.0215764
$482$	−9.30234	−0.423710
$483$	4.15902	0.189242
$484$	−9.35409	−0.425186
$485$	10.6629	0.484176
$486$	0.666091	0.0302145
$487$	−6.77727	−0.307107	−0.153554	−	0.988140i	$-0.549072\pi$
$487$	−6.77727	−0.307107	−0.153554	+	0.988140i	$0.549072\pi$
$488$	12.1418	0.549635
$489$	−14.6723	−0.663505
$490$	−8.03425	−0.362951
$491$	13.0202	0.587594	0.293797	−	0.955868i	$-0.405081\pi$
$491$	13.0202	0.587594	0.293797	+	0.955868i	$0.405081\pi$
$492$	−7.23840	−0.326332
$493$	−38.4519	−1.73179
$494$	−1.63021	−0.0733466
$495$	−0.106040	−0.00476615
$496$	1.49008	0.0669064
$497$	14.2242	0.638041
$498$	11.2200	0.502781
$499$	−31.9234	−1.42909	−0.714543	−	0.699591i	$-0.753365\pi$
$499$	−31.9234	−1.42909	−0.714543	+	0.699591i	$0.753365\pi$
$500$	−10.7501	−0.480758
$501$	21.2216	0.948109
$502$	−9.41531	−0.420226
$503$	−34.3361	−1.53097	−0.765484	−	0.643454i	$-0.777501\pi$
$503$	−34.3361	−1.53097	−0.765484	+	0.643454i	$0.777501\pi$
$504$	−0.0562077	−0.00250369
$505$	−18.7960	−0.836413
$506$	−3.47649	−0.154549
$507$	22.6673	1.00669
$508$	−9.12133	−0.404694
$509$	−12.2442	−0.542715	−0.271358	−	0.962479i	$-0.587473\pi$
$509$	−12.2442	−0.542715	−0.271358	+	0.962479i	$0.587473\pi$
$510$	−13.5113	−0.598292
$511$	−2.19602	−0.0971462
$512$	1.00000	0.0441942
$513$	−37.2306	−1.64377
$514$	9.59526	0.423229
$515$	−0.350629	−0.0154506
$516$	8.59971	0.378581
$517$	2.41590	0.106251
$518$	1.84381	0.0810124
$519$	−43.6623	−1.91656
$520$	0.290140	0.0127235
$521$	−5.21914	−0.228654	−0.114327	−	0.993443i	$-0.536471\pi$
$521$	−5.21914	−0.228654	−0.114327	+	0.993443i	$0.536471\pi$
$522$	−0.411756	−0.0180221
$523$	2.36493	0.103411	0.0517055	−	0.998662i	$-0.483534\pi$
$523$	2.36493	0.103411	0.0517055	+	0.998662i	$0.483534\pi$
$524$	−6.00235	−0.262214
$525$	−5.12250	−0.223564
$526$	−10.3149	−0.449749
$527$	8.92038	0.388578
$528$	2.24571	0.0977321
$529$	−15.6569	−0.680736
$530$	2.66803	0.115892
$531$	−0.551491	−0.0239327
$532$	6.35196	0.275392
$533$	0.930522	0.0403054
$534$	24.8242	1.07425
$535$	12.3853	0.535462
$536$	5.48626	0.236970
$537$	25.1540	1.08548
$538$	−6.15327	−0.265286
$539$	7.99421	0.344335
$540$	6.62620	0.285146
$541$	28.2125	1.21295	0.606474	−	0.795103i	$-0.292583\pi$
$541$	28.2125	1.21295	0.606474	+	0.795103i	$0.292583\pi$
$542$	−14.6018	−0.627202
$543$	−20.5777	−0.883073
$544$	5.98652	0.256670
$545$	20.2694	0.868248
$546$	0.345373	0.0147806
$547$	40.4922	1.73132	0.865660	−	0.500632i	$-0.166899\pi$
$547$	40.4922	1.73132	0.865660	+	0.500632i	$0.166899\pi$
$548$	8.40096	0.358871
$549$	0.778358	0.0332195
$550$	4.28186	0.182579
$551$	46.5320	1.98233
$552$	−4.74341	−0.201893
$553$	8.82156	0.375131
$554$	4.45111	0.189109
$555$	4.74613	0.201462
$556$	0.768712	0.0326007
$557$	2.23615	0.0947486	0.0473743	−	0.998877i	$-0.484915\pi$
$557$	2.23615	0.0947486	0.0473743	+	0.998877i	$0.484915\pi$
$558$	0.0955222	0.00404378
$559$	−1.10552	−0.0467586
$560$	−1.13051	−0.0477726
$561$	13.4440	0.567606
$562$	11.8982	0.501894
$563$	15.4818	0.652482	0.326241	−	0.945287i	$-0.394218\pi$
$563$	15.4818	0.652482	0.326241	+	0.945287i	$0.394218\pi$
$564$	3.29632	0.138800
$565$	−12.9915	−0.546555
$566$	−26.8019	−1.12657
$567$	8.05622	0.338329
$568$	−16.2228	−0.680695
$569$	−23.2083	−0.972942	−0.486471	−	0.873697i	$-0.661716\pi$
$569$	−23.2083	−0.972942	−0.486471	+	0.873697i	$0.661716\pi$
$570$	16.3505	0.684848
$571$	15.1595	0.634404	0.317202	−	0.948358i	$-0.397257\pi$
$571$	15.1595	0.634404	0.317202	+	0.948358i	$0.397257\pi$
$572$	−0.288694	−0.0120709
$573$	31.3601	1.31009
$574$	−3.62569	−0.151334
$575$	−9.04416	−0.377168
$576$	0.0641056	0.00267107
$577$	−4.70253	−0.195769	−0.0978845	−	0.995198i	$-0.531208\pi$
$577$	−4.70253	−0.195769	−0.0978845	+	0.995198i	$0.531208\pi$
$578$	18.8384	0.783575
$579$	38.6804	1.60750
$580$	−8.28163	−0.343876
$581$	5.62007	0.233160
$582$	−14.4762	−0.600056
$583$	−2.65473	−0.109948
$584$	2.50459	0.103640
$585$	0.0185996	0.000768999 0
$586$	−18.9677	−0.783550
$587$	41.2810	1.70385	0.851925	−	0.523664i	$-0.175435\pi$
$587$	41.2810	1.70385	0.851925	+	0.523664i	$0.175435\pi$
$588$	10.9075	0.449818
$589$	−10.7948	−0.444794
$590$	−11.0921	−0.456656
$591$	10.2714	0.422510
$592$	−2.10289	−0.0864281
$593$	20.3271	0.834735	0.417367	−	0.908738i	$-0.362953\pi$
$593$	20.3271	0.834735	0.417367	+	0.908738i	$0.362953\pi$
$594$	−6.59318	−0.270521
$595$	−6.76779	−0.277452
$596$	−11.1812	−0.458000
$597$	6.54575	0.267900
$598$	0.609782	0.0249358
$599$	−14.4756	−0.591458	−0.295729	−	0.955272i	$-0.595563\pi$
$599$	−14.4756	−0.591458	−0.295729	+	0.955272i	$0.595563\pi$
$600$	5.84227	0.238510
$601$	−1.33792	−0.0545748	−0.0272874	−	0.999628i	$-0.508687\pi$
$601$	−1.33792	−0.0545748	−0.0272874	+	0.999628i	$0.508687\pi$
$602$	4.30757	0.175563
$603$	0.351700	0.0143223
$604$	2.38218	0.0969296
$605$	−12.0607	−0.490339
$606$	25.5180	1.03660
$607$	29.3920	1.19298	0.596491	−	0.802620i	$-0.296561\pi$
$607$	29.3920	1.19298	0.596491	+	0.802620i	$0.296561\pi$
$608$	−7.24448	−0.293803
$609$	−9.85816	−0.399473
$610$	15.6551	0.633857
$611$	−0.423753	−0.0171432
$612$	0.383769	0.0155129
$613$	13.0862	0.528545	0.264272	−	0.964448i	$-0.414868\pi$
$613$	13.0862	0.528545	0.264272	+	0.964448i	$0.414868\pi$
$614$	−8.17486	−0.329911
$615$	−9.33286	−0.376337
$616$	1.12487	0.0453224
$617$	−5.00707	−0.201577	−0.100789	−	0.994908i	$-0.532137\pi$
$617$	−5.00707	−0.201577	−0.100789	+	0.994908i	$0.532137\pi$
$618$	0.476022	0.0191484
$619$	−26.7064	−1.07342	−0.536711	−	0.843766i	$-0.680334\pi$
$619$	−26.7064	−1.07342	−0.536711	+	0.843766i	$0.680334\pi$
$620$	1.92124	0.0771587
$621$	13.9261	0.558837
$622$	15.6131	0.626029
$623$	12.4344	0.498172
$624$	−0.393901	−0.0157687
$625$	2.82718	0.113087
$626$	−15.4596	−0.617890
$627$	−16.2690	−0.649723
$628$	−0.304865	−0.0121654
$629$	−12.5890	−0.501955
$630$	−0.0724717	−0.00288734
$631$	−15.1426	−0.602817	−0.301408	−	0.953495i	$-0.597457\pi$
$631$	−15.1426	−0.602817	−0.301408	+	0.953495i	$0.597457\pi$
$632$	−10.0611	−0.400209
$633$	−48.6298	−1.93286
$634$	−3.65132	−0.145012
$635$	−11.7606	−0.466706
$636$	−3.62218	−0.143629
$637$	−1.40220	−0.0555571
$638$	8.24036	0.326239
$639$	−1.03997	−0.0411407
$640$	1.28935	0.0509662
$641$	31.8157	1.25664	0.628322	−	0.777954i	$-0.283742\pi$
$641$	31.8157	1.25664	0.628322	+	0.777954i	$0.283742\pi$
$642$	−16.8146	−0.663617
$643$	−18.0477	−0.711732	−0.355866	−	0.934537i	$-0.615814\pi$
$643$	−18.0477	−0.711732	−0.355866	+	0.934537i	$0.615814\pi$
$644$	−2.37596	−0.0936259
$645$	11.0881	0.436592
$646$	−43.3692	−1.70634
$647$	36.5087	1.43531	0.717653	−	0.696400i	$-0.245216\pi$
$647$	36.5087	1.43531	0.717653	+	0.696400i	$0.245216\pi$
$648$	−9.18821	−0.360947
$649$	11.0369	0.433234
$650$	−0.751044	−0.0294584
$651$	2.28697	0.0896335
$652$	8.38198	0.328264
$653$	23.9062	0.935521	0.467761	−	0.883855i	$-0.345061\pi$
$653$	23.9062	0.935521	0.467761	+	0.883855i	$0.345061\pi$
$654$	−27.5183	−1.07605
$655$	−7.73915	−0.302394
$656$	4.13514	0.161450
$657$	0.160558	0.00626396
$658$	1.65111	0.0643672
$659$	4.05862	0.158101	0.0790507	−	0.996871i	$-0.474811\pi$
$659$	4.05862	0.158101	0.0790507	+	0.996871i	$0.474811\pi$
$660$	2.89552	0.112708
$661$	7.52174	0.292562	0.146281	−	0.989243i	$-0.453270\pi$
$661$	7.52174	0.292562	0.146281	+	0.989243i	$0.453270\pi$
$662$	−7.54768	−0.293349
$663$	−2.35810	−0.0915810
$664$	−6.40976	−0.248747
$665$	8.18993	0.317592
$666$	−0.134807	−0.00522365
$667$	−17.4053	−0.673937
$668$	−12.1234	−0.469069
$669$	40.1143	1.55091
$670$	7.07373	0.273282
$671$	−15.5771	−0.601347
$672$	1.53480	0.0592063
$673$	31.7023	1.22203	0.611017	−	0.791618i	$-0.290761\pi$
$673$	31.7023	1.22203	0.611017	+	0.791618i	$0.290761\pi$
$674$	−25.3131	−0.975026
$675$	−17.1523	−0.660192
$676$	−12.9494	−0.498052
$677$	−34.8319	−1.33870	−0.669350	−	0.742947i	$-0.733427\pi$
$677$	−34.8319	−1.33870	−0.669350	+	0.742947i	$0.733427\pi$
$678$	17.6375	0.677366
$679$	−7.25107	−0.278270
$680$	7.71874	0.296000
$681$	3.64816	0.139798
$682$	−1.91166	−0.0732013
$683$	35.7552	1.36814	0.684068	−	0.729418i	$-0.260209\pi$
$683$	35.7552	1.36814	0.684068	+	0.729418i	$0.260209\pi$
$684$	−0.464412	−0.0177572
$685$	10.8318	0.413862
$686$	11.6011	0.442933
$687$	−26.7977	−1.02240
$688$	−4.91283	−0.187300
$689$	0.465644	0.0177396
$690$	−6.11593	−0.232830
$691$	1.28873	0.0490258	0.0245129	−	0.999700i	$-0.492197\pi$
$691$	1.28873	0.0490258	0.0245129	+	0.999700i	$0.492197\pi$
$692$	24.9433	0.948204
$693$	0.0721105	0.00273925
$694$	−17.3694	−0.659335
$695$	0.991142	0.0375962
$696$	11.2433	0.426178
$697$	24.7551	0.937667
$698$	−0.264359	−0.0100061
$699$	−33.4709	−1.26599
$700$	2.92638	0.110607
$701$	−32.9992	−1.24636	−0.623181	−	0.782078i	$-0.714160\pi$
$701$	−32.9992	−1.24636	−0.623181	+	0.782078i	$0.714160\pi$
$702$	1.15645	0.0436475
$703$	15.2343	0.574574
$704$	−1.28293	−0.0483522
$705$	4.25012	0.160069
$706$	11.7868	0.443602
$707$	12.7819	0.480712
$708$	15.0590	0.565950
$709$	−15.3692	−0.577203	−0.288601	−	0.957449i	$-0.593190\pi$
$709$	−15.3692	−0.577203	−0.288601	+	0.957449i	$0.593190\pi$
$710$	−20.9170	−0.785000
$711$	−0.644972	−0.0241883
$712$	−14.1815	−0.531475
$713$	4.03782	0.151218
$714$	9.18812	0.343857
$715$	−0.372229	−0.0139206
$716$	−14.3700	−0.537031
$717$	20.6916	0.772741
$718$	24.0748	0.898463
$719$	33.2661	1.24061	0.620307	−	0.784359i	$-0.287008\pi$
$719$	33.2661	1.24061	0.620307	+	0.784359i	$0.287008\pi$
$720$	0.0826548	0.00308036
$721$	0.238438	0.00887990
$722$	33.4826	1.24609
$723$	16.2834	0.605585
$724$	11.7556	0.436893
$725$	21.4375	0.796168
$726$	16.3740	0.607694
$727$	6.03799	0.223937	0.111968	−	0.993712i	$-0.464284\pi$
$727$	6.03799	0.223937	0.111968	+	0.993712i	$0.464284\pi$
$728$	−0.197304	−0.00731258
$729$	26.3987	0.977728
$730$	3.22930	0.119522
$731$	−29.4108	−1.08780
$732$	−21.2538	−0.785562
$733$	−8.66873	−0.320187	−0.160093	−	0.987102i	$-0.551180\pi$
$733$	−8.66873	−0.320187	−0.160093	+	0.987102i	$0.551180\pi$
$734$	−20.4094	−0.753325
$735$	14.0636	0.518745
$736$	2.70981	0.0998849
$737$	−7.03848	−0.259266
$738$	0.265086	0.00975794
$739$	45.1675	1.66151	0.830757	−	0.556636i	$-0.187908\pi$
$739$	45.1675	1.66151	0.830757	+	0.556636i	$0.187908\pi$
$740$	−2.71137	−0.0996718
$741$	2.85361	0.104830
$742$	−1.81434	−0.0666065
$743$	13.1991	0.484227	0.242113	−	0.970248i	$-0.422159\pi$
$743$	13.1991	0.484227	0.242113	+	0.970248i	$0.422159\pi$
$744$	−2.60832	−0.0956256
$745$	−14.4165	−0.528181
$746$	5.72325	0.209543
$747$	−0.410901	−0.0150341
$748$	−7.68028	−0.280819
$749$	−8.42236	−0.307746
$750$	18.8176	0.687120
$751$	34.0223	1.24149	0.620745	−	0.784012i	$-0.286830\pi$
$751$	34.0223	1.24149	0.620745	+	0.784012i	$0.286830\pi$
$752$	−1.88312	−0.0686701
$753$	16.4811	0.600605
$754$	−1.44537	−0.0526373
$755$	3.07147	0.111782
$756$	−4.50602	−0.163882
$757$	−19.1666	−0.696622	−0.348311	−	0.937379i	$-0.613245\pi$
$757$	−19.1666	−0.696622	−0.348311	+	0.937379i	$0.613245\pi$
$758$	13.6464	0.495661
$759$	6.08545	0.220888
$760$	−9.34071	−0.338823
$761$	−23.3773	−0.847427	−0.423713	−	0.905796i	$-0.639274\pi$
$761$	−23.3773	−0.847427	−0.423713	+	0.905796i	$0.639274\pi$
$762$	15.9665	0.578406
$763$	−13.7838	−0.499008
$764$	−17.9153	−0.648154
$765$	0.494814	0.0178901
$766$	26.0858	0.942516
$767$	−1.93588	−0.0699006
$768$	−1.75046	−0.0631642
$769$	32.0206	1.15469	0.577346	−	0.816500i	$-0.304088\pi$
$769$	32.0206	1.15469	0.577346	+	0.816500i	$0.304088\pi$
$770$	1.45036	0.0522673
$771$	−16.7961	−0.604897
$772$	−22.0973	−0.795300
$773$	35.7581	1.28613	0.643065	−	0.765811i	$-0.277662\pi$
$773$	35.7581	1.28613	0.643065	+	0.765811i	$0.277662\pi$
$774$	−0.314940	−0.0113203
$775$	−4.97323	−0.178644
$776$	8.26993	0.296873
$777$	−3.22751	−0.115786
$778$	1.01582	0.0364188
$779$	−29.9570	−1.07332
$780$	−0.507878	−0.0181850
$781$	20.8127	0.744738
$782$	16.2223	0.580109
$783$	−33.0093	−1.17966
$784$	−6.23122	−0.222544
$785$	−0.393079	−0.0140296
$786$	10.5069	0.374767
$787$	−35.0827	−1.25056	−0.625282	−	0.780399i	$-0.715016\pi$
$787$	−35.0827	−1.25056	−0.625282	+	0.780399i	$0.715016\pi$
$788$	−5.86785	−0.209034
$789$	18.0557	0.642801
$790$	−12.9723	−0.461534
$791$	8.83459	0.314122
$792$	−0.0822429	−0.00292237
$793$	2.73225	0.0970249
$794$	34.9079	1.23883
$795$	−4.67027	−0.165637
$796$	−3.73945	−0.132541
$797$	0.567616	0.0201060	0.0100530	−	0.999949i	$-0.496800\pi$
$797$	0.567616	0.0201060	0.0100530	+	0.999949i	$0.496800\pi$
$798$	−11.1188	−0.393603
$799$	−11.2733	−0.398821
$800$	−3.33757	−0.118001
$801$	−0.909114	−0.0321220
$802$	22.3295	0.788484
$803$	−3.21320	−0.113392
$804$	−9.60347	−0.338688
$805$	−3.06345	−0.107973
$806$	0.335308	0.0118107
$807$	10.7710	0.379158
$808$	−14.5779	−0.512848
$809$	50.5102	1.77584	0.887922	−	0.459994i	$-0.152148\pi$
$809$	50.5102	1.77584	0.887922	+	0.459994i	$0.152148\pi$
$810$	−11.8469	−0.416256
$811$	1.99742	0.0701391	0.0350695	−	0.999385i	$-0.488835\pi$
$811$	1.99742	0.0701391	0.0350695	+	0.999385i	$0.488835\pi$
$812$	5.63176	0.197636
$813$	25.5599	0.896425
$814$	2.69785	0.0945597
$815$	10.8073	0.378565
$816$	−10.4792	−0.366844
$817$	35.5909	1.24517
$818$	−21.9297	−0.766754
$819$	−0.0126483	−0.000441967 0
$820$	5.33167	0.186190
$821$	−38.2673	−1.33554	−0.667768	−	0.744369i	$-0.732750\pi$
$821$	−38.2673	−1.33554	−0.667768	+	0.744369i	$0.732750\pi$
$822$	−14.7055	−0.512914
$823$	45.7897	1.59613	0.798065	−	0.602571i	$-0.205857\pi$
$823$	45.7897	1.59613	0.798065	+	0.602571i	$0.205857\pi$
$824$	−0.271941	−0.00947353
$825$	−7.49522	−0.260950
$826$	7.54299	0.262454
$827$	12.3187	0.428363	0.214181	−	0.976794i	$-0.431292\pi$
$827$	12.3187	0.428363	0.214181	+	0.976794i	$0.431292\pi$
$828$	0.173714	0.00603697
$829$	45.5199	1.58097	0.790485	−	0.612481i	$-0.209828\pi$
$829$	45.5199	1.58097	0.790485	+	0.612481i	$0.209828\pi$
$830$	−8.26445	−0.286863
$831$	−7.79148	−0.270283
$832$	0.225028	0.00780143
$833$	−37.3033	−1.29248
$834$	−1.34560	−0.0465943
$835$	−15.6314	−0.540946
$836$	9.29416	0.321445
$837$	7.65775	0.264690
$838$	26.0991	0.901578
$839$	−35.8346	−1.23715	−0.618575	−	0.785726i	$-0.712290\pi$
$839$	−35.8346	−1.23715	−0.618575	+	0.785726i	$0.712290\pi$
$840$	1.97890	0.0682786
$841$	12.2560	0.422622
$842$	−13.5905	−0.468359
$843$	−20.8272	−0.717328
$844$	27.7812	0.956268
$845$	−16.6963	−0.574371
$846$	−0.120718	−0.00415038
$847$	8.20167	0.281813
$848$	2.06927	0.0710592
$849$	46.9157	1.61014
$850$	−19.9804	−0.685322
$851$	−5.69842	−0.195339
$852$	28.3974	0.972879
$853$	31.3074	1.07195	0.535973	−	0.844235i	$-0.319945\pi$
$853$	31.3074	1.07195	0.535973	+	0.844235i	$0.319945\pi$
$854$	−10.6459	−0.364297
$855$	−0.598791	−0.0204782
$856$	9.60580	0.328319
$857$	−35.2234	−1.20321	−0.601604	−	0.798794i	$-0.705472\pi$
$857$	−35.2234	−1.20321	−0.601604	+	0.798794i	$0.705472\pi$
$858$	0.505347	0.0172523
$859$	−37.7463	−1.28789	−0.643943	−	0.765074i	$-0.722703\pi$
$859$	−37.7463	−1.28789	−0.643943	+	0.765074i	$0.722703\pi$
$860$	−6.33438	−0.216001
$861$	6.34663	0.216292
$862$	6.09508	0.207599
$863$	−8.56516	−0.291561	−0.145781	−	0.989317i	$-0.546569\pi$
$863$	−8.56516	−0.291561	−0.145781	+	0.989317i	$0.546569\pi$
$864$	5.13916	0.174838
$865$	32.1608	1.09350
$866$	8.05600	0.273754
$867$	−32.9759	−1.11992
$868$	−1.30650	−0.0443455
$869$	12.9077	0.437863
$870$	14.4967	0.491483
$871$	1.23456	0.0418315
$872$	15.7206	0.532367
$873$	0.530148	0.0179428
$874$	−19.6312	−0.664034
$875$	9.42566	0.318646
$876$	−4.38417	−0.148127
$877$	−1.10800	−0.0374146	−0.0187073	−	0.999825i	$-0.505955\pi$
$877$	−1.10800	−0.0374146	−0.0187073	+	0.999825i	$0.505955\pi$
$878$	−30.2636	−1.02135
$879$	33.2022	1.11988
$880$	−1.65415	−0.0557614
$881$	23.9405	0.806575	0.403288	−	0.915073i	$-0.367867\pi$
$881$	23.9405	0.806575	0.403288	+	0.915073i	$0.367867\pi$
$882$	−0.399456	−0.0134504
$883$	−42.1192	−1.41742	−0.708712	−	0.705497i	$-0.750724\pi$
$883$	−42.1192	−1.41742	−0.708712	+	0.705497i	$0.750724\pi$
$884$	1.34713	0.0453089
$885$	19.4163	0.652672
$886$	3.80455	0.127817
$887$	−14.0197	−0.470735	−0.235367	−	0.971906i	$-0.575629\pi$
$887$	−14.0197	−0.470735	−0.235367	+	0.971906i	$0.575629\pi$
$888$	3.68102	0.123527
$889$	7.99758	0.268230
$890$	−18.2850	−0.612915
$891$	11.7878	0.394907
$892$	−22.9164	−0.767299
$893$	13.6422	0.456519
$894$	19.5723	0.654594
$895$	−18.5280	−0.619321
$896$	−0.876800	−0.0292918
$897$	−1.06740	−0.0356394
$898$	27.3357	0.912204
$899$	−9.57089	−0.319207
$900$	−0.213957	−0.00713189
$901$	12.3877	0.412696
$902$	−5.30510	−0.176640
$903$	−7.54022	−0.250923
$904$	−10.0760	−0.335121
$905$	15.1571	0.503840
$906$	−4.16991	−0.138536
$907$	0.401987	0.0133478	0.00667388	−	0.999978i	$-0.497876\pi$
$907$	0.401987	0.0133478	0.00667388	+	0.999978i	$0.497876\pi$
$908$	−2.08411	−0.0691638
$909$	−0.934523	−0.0309962
$910$	−0.254395	−0.00843311
$911$	15.8456	0.524987	0.262494	−	0.964934i	$-0.415455\pi$
$911$	15.8456	0.524987	0.262494	+	0.964934i	$0.415455\pi$
$912$	12.6812	0.419916
$913$	8.22326	0.272150
$914$	−1.81388	−0.0599977
$915$	−27.4036	−0.905936
$916$	15.3090	0.505823
$917$	5.26286	0.173795
$918$	30.7657	1.01542
$919$	−35.3236	−1.16522	−0.582610	−	0.812752i	$-0.697968\pi$
$919$	−35.3236	−1.16522	−0.582610	+	0.812752i	$0.697968\pi$
$920$	3.49390	0.115191
$921$	14.3098	0.471523
$922$	16.2086	0.533803
$923$	−3.65058	−0.120160
$924$	−1.96904	−0.0647767
$925$	7.01852	0.230768
$926$	35.3990	1.16328
$927$	−0.0174330	−0.000572573 0
$928$	−6.42309	−0.210848
$929$	48.9587	1.60628	0.803141	−	0.595788i	$-0.203160\pi$
$929$	48.9587	1.60628	0.803141	+	0.595788i	$0.203160\pi$
$930$	−3.36305	−0.110279
$931$	45.1420	1.47947
$932$	19.1212	0.626337
$933$	−27.3301	−0.894748
$934$	29.3005	0.958740
$935$	−9.90260	−0.323850
$936$	0.0144255	0.000471513 0
$937$	31.6916	1.03532	0.517660	−	0.855586i	$-0.326803\pi$
$937$	31.6916	1.03532	0.517660	+	0.855586i	$0.326803\pi$
$938$	−4.81035	−0.157064
$939$	27.0614	0.883115
$940$	−2.42800	−0.0791927
$941$	40.5097	1.32058	0.660289	−	0.751011i	$-0.270434\pi$
$941$	40.5097	1.32058	0.660289	+	0.751011i	$0.270434\pi$
$942$	0.533653	0.0173874
$943$	11.2054	0.364900
$944$	−8.60286	−0.279999
$945$	−5.80985	−0.188994
$946$	6.30281	0.204922
$947$	2.08600	0.0677860	0.0338930	−	0.999425i	$-0.489209\pi$
$947$	2.08600	0.0677860	0.0338930	+	0.999425i	$0.489209\pi$
$948$	17.6115	0.571996
$949$	0.563601	0.0182953
$950$	24.1789	0.784469
$951$	6.39149	0.207258
$952$	−5.24898	−0.170120
$953$	−2.86376	−0.0927664	−0.0463832	−	0.998924i	$-0.514770\pi$
$953$	−2.86376	−0.0927664	−0.0463832	+	0.998924i	$0.514770\pi$
$954$	0.132652	0.00429477
$955$	−23.0992	−0.747473
$956$	−11.8207	−0.382307
$957$	−14.4244	−0.466275
$958$	−13.4423	−0.434300
$959$	−7.36596	−0.237859
$960$	−2.25696	−0.0728431
$961$	−28.7797	−0.928376
$962$	−0.473207	−0.0152568
$963$	0.615785	0.0198434
$964$	−9.30234	−0.299608
$965$	−28.4913	−0.917166
$966$	4.15902	0.133814
$967$	40.7329	1.30988	0.654941	−	0.755680i	$-0.272693\pi$
$967$	40.7329	1.30988	0.654941	+	0.755680i	$0.272693\pi$
$968$	−9.35409	−0.300652
$969$	75.9161	2.43878
$970$	10.6629	0.342364
$971$	58.1185	1.86511	0.932556	−	0.361024i	$-0.117573\pi$
$971$	58.1185	1.86511	0.932556	+	0.361024i	$0.117573\pi$
$972$	0.666091	0.0213649
$973$	−0.674007	−0.0216077
$974$	−6.77727	−0.217158
$975$	1.31467	0.0421032
$976$	12.1418	0.388650
$977$	−50.9658	−1.63054	−0.815270	−	0.579080i	$-0.803412\pi$
$977$	−50.9658	−1.63054	−0.815270	+	0.579080i	$0.803412\pi$
$978$	−14.6723	−0.469169
$979$	18.1939	0.581479
$980$	−8.03425	−0.256645
$981$	1.00778	0.0321759
$982$	13.0202	0.415492
$983$	−57.8220	−1.84423	−0.922117	−	0.386911i	$-0.873542\pi$
$983$	−57.8220	−1.84423	−0.922117	+	0.386911i	$0.873542\pi$
$984$	−7.23840	−0.230752
$985$	−7.56574	−0.241065
$986$	−38.4519	−1.22456
$987$	−2.89021	−0.0919963
$988$	−1.63021	−0.0518638
$989$	−13.3128	−0.423323
$990$	−0.106040	−0.00337018
$991$	−26.5421	−0.843138	−0.421569	−	0.906796i	$-0.638520\pi$
$991$	−26.5421	−0.843138	−0.421569	+	0.906796i	$0.638520\pi$
$992$	1.49008	0.0473100
$993$	13.2119	0.419267
$994$	14.2242	0.451163
$995$	−4.82147	−0.152851
$996$	11.2200	0.355520
$997$	−53.3927	−1.69097	−0.845483	−	0.534003i	$-0.820687\pi$
$997$	−53.3927	−1.69097	−0.845483	+	0.534003i	$0.820687\pi$
$998$	−31.9234	−1.01052
$999$	−10.8071	−0.341921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.c.1.11	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.c.1.11	✓	31	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.75046 q^{3} +1.00000 q^{4} +1.28935 q^{5} -1.75046 q^{6} -0.876800 q^{7} +1.00000 q^{8} +0.0641056 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.75046 q^{3} +1.00000 q^{4} +1.28935 q^{5} -1.75046 q^{6} -0.876800 q^{7} +1.00000 q^{8} +0.0641056 q^{9} +1.28935 q^{10} -1.28293 q^{11} -1.75046 q^{12} +0.225028 q^{13} -0.876800 q^{14} -2.25696 q^{15} +1.00000 q^{16} +5.98652 q^{17} +0.0641056 q^{18} -7.24448 q^{19} +1.28935 q^{20} +1.53480 q^{21} -1.28293 q^{22} +2.70981 q^{23} -1.75046 q^{24} -3.33757 q^{25} +0.225028 q^{26} +5.13916 q^{27} -0.876800 q^{28} -6.42309 q^{29} -2.25696 q^{30} +1.49008 q^{31} +1.00000 q^{32} +2.24571 q^{33} +5.98652 q^{34} -1.13051 q^{35} +0.0641056 q^{36} -2.10289 q^{37} -7.24448 q^{38} -0.393901 q^{39} +1.28935 q^{40} +4.13514 q^{41} +1.53480 q^{42} -4.91283 q^{43} -1.28293 q^{44} +0.0826548 q^{45} +2.70981 q^{46} -1.88312 q^{47} -1.75046 q^{48} -6.23122 q^{49} -3.33757 q^{50} -10.4792 q^{51} +0.225028 q^{52} +2.06927 q^{53} +5.13916 q^{54} -1.65415 q^{55} -0.876800 q^{56} +12.6812 q^{57} -6.42309 q^{58} -8.60286 q^{59} -2.25696 q^{60} +12.1418 q^{61} +1.49008 q^{62} -0.0562077 q^{63} +1.00000 q^{64} +0.290140 q^{65} +2.24571 q^{66} +5.48626 q^{67} +5.98652 q^{68} -4.74341 q^{69} -1.13051 q^{70} -16.2228 q^{71} +0.0641056 q^{72} +2.50459 q^{73} -2.10289 q^{74} +5.84227 q^{75} -7.24448 q^{76} +1.12487 q^{77} -0.393901 q^{78} -10.0611 q^{79} +1.28935 q^{80} -9.18821 q^{81} +4.13514 q^{82} -6.40976 q^{83} +1.53480 q^{84} +7.71874 q^{85} -4.91283 q^{86} +11.2433 q^{87} -1.28293 q^{88} -14.1815 q^{89} +0.0826548 q^{90} -0.197304 q^{91} +2.70981 q^{92} -2.60832 q^{93} -1.88312 q^{94} -9.34071 q^{95} -1.75046 q^{96} +8.26993 q^{97} -6.23122 q^{98} -0.0822429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - q^99

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