LMFDB - Embedded newform 6031.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05386 q^{2} -1.85254 q^{3} +2.21834 q^{4} -0.958510 q^{5} +3.80486 q^{6} +0.0563033 q^{7} -0.448438 q^{8} +0.431918 q^{9} +O(q^{10})$	\(q-2.05386 q^{2} -1.85254 q^{3} +2.21834 q^{4} -0.958510 q^{5} +3.80486 q^{6} +0.0563033 q^{7} -0.448438 q^{8} +0.431918 q^{9} +1.96864 q^{10} +3.83257 q^{11} -4.10957 q^{12} -2.53430 q^{13} -0.115639 q^{14} +1.77568 q^{15} -3.51565 q^{16} +3.80932 q^{17} -0.887100 q^{18} -6.70558 q^{19} -2.12630 q^{20} -0.104304 q^{21} -7.87157 q^{22} -0.340043 q^{23} +0.830751 q^{24} -4.08126 q^{25} +5.20510 q^{26} +4.75748 q^{27} +0.124900 q^{28} +4.99000 q^{29} -3.64700 q^{30} +7.03132 q^{31} +8.11753 q^{32} -7.10001 q^{33} -7.82382 q^{34} -0.0539672 q^{35} +0.958141 q^{36} +1.00000 q^{37} +13.7723 q^{38} +4.69491 q^{39} +0.429832 q^{40} +2.40185 q^{41} +0.214226 q^{42} -0.985503 q^{43} +8.50195 q^{44} -0.413998 q^{45} +0.698400 q^{46} -0.377730 q^{47} +6.51289 q^{48} -6.99683 q^{49} +8.38233 q^{50} -7.05694 q^{51} -5.62194 q^{52} -5.64693 q^{53} -9.77120 q^{54} -3.67356 q^{55} -0.0252485 q^{56} +12.4224 q^{57} -10.2488 q^{58} -9.01439 q^{59} +3.93906 q^{60} -3.77455 q^{61} -14.4413 q^{62} +0.0243184 q^{63} -9.64096 q^{64} +2.42915 q^{65} +14.5824 q^{66} +2.76583 q^{67} +8.45037 q^{68} +0.629944 q^{69} +0.110841 q^{70} -13.4217 q^{71} -0.193689 q^{72} +8.50848 q^{73} -2.05386 q^{74} +7.56071 q^{75} -14.8753 q^{76} +0.215787 q^{77} -9.64268 q^{78} +5.69589 q^{79} +3.36978 q^{80} -10.1092 q^{81} -4.93307 q^{82} -4.06456 q^{83} -0.231382 q^{84} -3.65127 q^{85} +2.02409 q^{86} -9.24419 q^{87} -1.71867 q^{88} +7.77938 q^{89} +0.850293 q^{90} -0.142690 q^{91} -0.754330 q^{92} -13.0258 q^{93} +0.775805 q^{94} +6.42736 q^{95} -15.0381 q^{96} -0.109519 q^{97} +14.3705 q^{98} +1.65536 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) $ 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * 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 $

$2$	−2.05386	−1.45230	−0.726149	−	0.687537i	$-0.758692\pi$
$2$	−2.05386	−1.45230	−0.726149	+	0.687537i	$0.758692\pi$
$3$	−1.85254	−1.06957	−0.534783	−	0.844989i	$-0.679607\pi$
$3$	−1.85254	−1.06957	−0.534783	+	0.844989i	$0.679607\pi$
$4$	2.21834	1.10917
$5$	−0.958510	−0.428659	−0.214329	−	0.976761i	$-0.568757\pi$
$5$	−0.958510	−0.428659	−0.214329	+	0.976761i	$0.568757\pi$
$6$	3.80486	1.55333
$7$	0.0563033	0.0212806	0.0106403	−	0.999943i	$-0.496613\pi$
$7$	0.0563033	0.0212806	0.0106403	+	0.999943i	$0.496613\pi$
$8$	−0.448438	−0.158547
$9$	0.431918	0.143973
$10$	1.96864	0.622540
$11$	3.83257	1.15556	0.577782	−	0.816191i	$-0.303918\pi$
$11$	3.83257	1.15556	0.577782	+	0.816191i	$0.303918\pi$
$12$	−4.10957	−1.18633
$13$	−2.53430	−0.702889	−0.351445	−	0.936209i	$-0.614309\pi$
$13$	−2.53430	−0.702889	−0.351445	+	0.936209i	$0.614309\pi$
$14$	−0.115639	−0.0309058
$15$	1.77568	0.458479
$16$	−3.51565	−0.878912
$17$	3.80932	0.923897	0.461948	−	0.886907i	$-0.347151\pi$
$17$	3.80932	0.923897	0.461948	+	0.886907i	$0.347151\pi$
$18$	−0.887100	−0.209091
$19$	−6.70558	−1.53837	−0.769183	−	0.639029i	$-0.779336\pi$
$19$	−6.70558	−1.53837	−0.769183	+	0.639029i	$0.779336\pi$
$20$	−2.12630	−0.475455
$21$	−0.104304	−0.0227611
$22$	−7.87157	−1.67822
$23$	−0.340043	−0.0709038	−0.0354519	−	0.999371i	$-0.511287\pi$
$23$	−0.340043	−0.0709038	−0.0354519	+	0.999371i	$0.511287\pi$
$24$	0.830751	0.169576
$25$	−4.08126	−0.816252
$26$	5.20510	1.02080
$27$	4.75748	0.915578
$28$	0.124900	0.0236038
$29$	4.99000	0.926619	0.463310	−	0.886196i	$-0.346662\pi$
$29$	4.99000	0.926619	0.463310	+	0.886196i	$0.346662\pi$
$30$	−3.64700	−0.665848
$31$	7.03132	1.26286	0.631431	−	0.775432i	$-0.282468\pi$
$31$	7.03132	1.26286	0.631431	+	0.775432i	$0.282468\pi$
$32$	8.11753	1.43499
$33$	−7.10001	−1.23595
$34$	−7.82382	−1.34177
$35$	−0.0539672	−0.00912213
$36$	0.958141	0.159690
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	13.7723	2.23417
$39$	4.69491	0.751787
$40$	0.429832	0.0679624
$41$	2.40185	0.375107	0.187553	−	0.982254i	$-0.439944\pi$
$41$	2.40185	0.375107	0.187553	+	0.982254i	$0.439944\pi$
$42$	0.214226	0.0330559
$43$	−0.985503	−0.150288	−0.0751439	−	0.997173i	$-0.523942\pi$
$43$	−0.985503	−0.150288	−0.0751439	+	0.997173i	$0.523942\pi$
$44$	8.50195	1.28172
$45$	−0.413998	−0.0617152
$46$	0.698400	0.102973
$47$	−0.377730	−0.0550976	−0.0275488	−	0.999620i	$-0.508770\pi$
$47$	−0.377730	−0.0550976	−0.0275488	+	0.999620i	$0.508770\pi$
$48$	6.51289	0.940055
$49$	−6.99683	−0.999547
$50$	8.38233	1.18544
$51$	−7.05694	−0.988169
$52$	−5.62194	−0.779623
$53$	−5.64693	−0.775665	−0.387833	−	0.921730i	$-0.626776\pi$
$53$	−5.64693	−0.775665	−0.387833	+	0.921730i	$0.626776\pi$
$54$	−9.77120	−1.32969
$55$	−3.67356	−0.495343
$56$	−0.0252485	−0.00337398
$57$	12.4224	1.64538
$58$	−10.2488	−1.34573
$59$	−9.01439	−1.17357	−0.586787	−	0.809742i	$-0.699607\pi$
$59$	−9.01439	−1.17357	−0.586787	+	0.809742i	$0.699607\pi$
$60$	3.93906	0.508531
$61$	−3.77455	−0.483281	−0.241641	−	0.970366i	$-0.577686\pi$
$61$	−3.77455	−0.483281	−0.241641	+	0.970366i	$0.577686\pi$
$62$	−14.4413	−1.83405
$63$	0.0243184	0.00306383
$64$	−9.64096	−1.20512
$65$	2.42915	0.301300
$66$	14.5824	1.79497
$67$	2.76583	0.337900	0.168950	−	0.985625i	$-0.445962\pi$
$67$	2.76583	0.337900	0.168950	+	0.985625i	$0.445962\pi$
$68$	8.45037	1.02476
$69$	0.629944	0.0758364
$70$	0.110841	0.0132481
$71$	−13.4217	−1.59286	−0.796429	−	0.604732i	$-0.793280\pi$
$71$	−13.4217	−1.59286	−0.796429	+	0.604732i	$0.793280\pi$
$72$	−0.193689	−0.0228264
$73$	8.50848	0.995842	0.497921	−	0.867222i	$-0.334097\pi$
$73$	8.50848	0.995842	0.497921	+	0.867222i	$0.334097\pi$
$74$	−2.05386	−0.238756
$75$	7.56071	0.873036
$76$	−14.8753	−1.70631
$77$	0.215787	0.0245912
$78$	−9.64268	−1.09182
$79$	5.69589	0.640838	0.320419	−	0.947276i	$-0.396176\pi$
$79$	5.69589	0.640838	0.320419	+	0.947276i	$0.396176\pi$
$80$	3.36978	0.376753
$81$	−10.1092	−1.12324
$82$	−4.93307	−0.544766
$83$	−4.06456	−0.446143	−0.223071	−	0.974802i	$-0.571608\pi$
$83$	−4.06456	−0.446143	−0.223071	+	0.974802i	$0.571608\pi$
$84$	−0.231382	−0.0252459
$85$	−3.65127	−0.396036
$86$	2.02409	0.218263
$87$	−9.24419	−0.991081
$88$	−1.71867	−0.183211
$89$	7.77938	0.824612	0.412306	−	0.911045i	$-0.364723\pi$
$89$	7.77938	0.824612	0.412306	+	0.911045i	$0.364723\pi$
$90$	0.850293	0.0896288
$91$	−0.142690	−0.0149579
$92$	−0.754330	−0.0786444
$93$	−13.0258	−1.35071
$94$	0.775805	0.0800182
$95$	6.42736	0.659434
$96$	−15.0381	−1.53482
$97$	−0.109519	−0.0111200	−0.00555999	−	0.999985i	$-0.501770\pi$
$97$	−0.109519	−0.0111200	−0.00555999	+	0.999985i	$0.501770\pi$
$98$	14.3705	1.45164
$99$	1.65536	0.166370
$100$	−9.05362	−0.905362
$101$	9.30723	0.926104	0.463052	−	0.886331i	$-0.346754\pi$
$101$	9.30723	0.926104	0.463052	+	0.886331i	$0.346754\pi$
$102$	14.4940	1.43512
$103$	−13.5145	−1.33162	−0.665812	−	0.746120i	$-0.731915\pi$
$103$	−13.5145	−1.33162	−0.665812	+	0.746120i	$0.731915\pi$
$104$	1.13648	0.111441
$105$	0.0999767	0.00975673
$106$	11.5980	1.12650
$107$	−5.84344	−0.564907	−0.282453	−	0.959281i	$-0.591148\pi$
$107$	−5.84344	−0.564907	−0.282453	+	0.959281i	$0.591148\pi$
$108$	10.5537	1.01553
$109$	−4.35881	−0.417498	−0.208749	−	0.977969i	$-0.566939\pi$
$109$	−4.35881	−0.417498	−0.208749	+	0.977969i	$0.566939\pi$
$110$	7.54497	0.719385
$111$	−1.85254	−0.175836
$112$	−0.197943	−0.0187038
$113$	−7.50002	−0.705542	−0.352771	−	0.935710i	$-0.614761\pi$
$113$	−7.50002	−0.705542	−0.352771	+	0.935710i	$0.614761\pi$
$114$	−25.5138	−2.38959
$115$	0.325934	0.0303935
$116$	11.0695	1.02778
$117$	−1.09461	−0.101197
$118$	18.5143	1.70438
$119$	0.214477	0.0196611
$120$	−0.796283	−0.0726904
$121$	3.68862	0.335329
$122$	7.75239	0.701869
$123$	−4.44954	−0.401201
$124$	15.5978	1.40073
$125$	8.70447	0.778552
$126$	−0.0499466	−0.00444960
$127$	8.71271	0.773128	0.386564	−	0.922263i	$-0.373662\pi$
$127$	8.71271	0.773128	0.386564	+	0.922263i	$0.373662\pi$
$128$	3.56613	0.315204
$129$	1.82569	0.160743
$130$	−4.98914	−0.437577
$131$	15.2478	1.33221	0.666103	−	0.745860i	$-0.267961\pi$
$131$	15.2478	1.33221	0.666103	+	0.745860i	$0.267961\pi$
$132$	−15.7502	−1.37088
$133$	−0.377546	−0.0327374
$134$	−5.68063	−0.490732
$135$	−4.56009	−0.392470
$136$	−1.70825	−0.146481
$137$	0.852102	0.0728000	0.0364000	−	0.999337i	$-0.488411\pi$
$137$	0.852102	0.0728000	0.0364000	+	0.999337i	$0.488411\pi$
$138$	−1.29382	−0.110137
$139$	21.4579	1.82003	0.910016	−	0.414573i	$-0.136069\pi$
$139$	21.4579	1.82003	0.910016	+	0.414573i	$0.136069\pi$
$140$	−0.119718	−0.0101180
$141$	0.699762	0.0589306
$142$	27.5662	2.31331
$143$	−9.71291	−0.812234
$144$	−1.51847	−0.126539
$145$	−4.78296	−0.397203
$146$	−17.4752	−1.44626
$147$	12.9619	1.06908
$148$	2.21834	0.182346
$149$	20.9928	1.71980	0.859898	−	0.510465i	$-0.170527\pi$
$149$	20.9928	1.71980	0.859898	+	0.510465i	$0.170527\pi$
$150$	−15.5286	−1.26791
$151$	18.7916	1.52924	0.764619	−	0.644482i	$-0.222927\pi$
$151$	18.7916	1.52924	0.764619	+	0.644482i	$0.222927\pi$
$152$	3.00704	0.243903
$153$	1.64532	0.133016
$154$	−0.443195	−0.0357137
$155$	−6.73959	−0.541337
$156$	10.4149	0.833859
$157$	12.2168	0.975008	0.487504	−	0.873121i	$-0.337907\pi$
$157$	12.2168	0.975008	0.487504	+	0.873121i	$0.337907\pi$
$158$	−11.6986	−0.930687
$159$	10.4612	0.829625
$160$	−7.78073	−0.615121
$161$	−0.0191455	−0.00150888
$162$	20.7629	1.63129
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	5.32813	0.416057
$165$	6.80543	0.529802
$166$	8.34803	0.647933
$167$	0.941954	0.0728906	0.0364453	−	0.999336i	$-0.488397\pi$
$167$	0.941954	0.0728906	0.0364453	+	0.999336i	$0.488397\pi$
$168$	0.0467740	0.00360869
$169$	−6.57731	−0.505947
$170$	7.49920	0.575163
$171$	−2.89626	−0.221483
$172$	−2.18618	−0.166695
$173$	11.4985	0.874218	0.437109	−	0.899409i	$-0.356002\pi$
$173$	11.4985	0.874218	0.437109	+	0.899409i	$0.356002\pi$
$174$	18.9863	1.43935
$175$	−0.229788	−0.0173704
$176$	−13.4740	−1.01564
$177$	16.6995	1.25521
$178$	−15.9777	−1.19758
$179$	12.1970	0.911647	0.455823	−	0.890070i	$-0.349345\pi$
$179$	12.1970	0.911647	0.455823	+	0.890070i	$0.349345\pi$
$180$	−0.918388	−0.0684526
$181$	−20.2170	−1.50272	−0.751361	−	0.659892i	$-0.770602\pi$
$181$	−20.2170	−1.50272	−0.751361	+	0.659892i	$0.770602\pi$
$182$	0.293064	0.0217234
$183$	6.99252	0.516902
$184$	0.152488	0.0112416
$185$	−0.958510	−0.0704710
$186$	26.7532	1.96164
$187$	14.5995	1.06762
$188$	−0.837934	−0.0611126
$189$	0.267862	0.0194841
$190$	−13.2009	−0.957694
$191$	−9.77549	−0.707329	−0.353665	−	0.935372i	$-0.615065\pi$
$191$	−9.77549	−0.707329	−0.353665	+	0.935372i	$0.615065\pi$
$192$	17.8603	1.28896
$193$	−1.00629	−0.0724342	−0.0362171	−	0.999344i	$-0.511531\pi$
$193$	−1.00629	−0.0724342	−0.0362171	+	0.999344i	$0.511531\pi$
$194$	0.224937	0.0161495
$195$	−4.50011	−0.322260
$196$	−15.5213	−1.10867
$197$	13.9173	0.991570	0.495785	−	0.868445i	$-0.334880\pi$
$197$	13.9173	0.991570	0.495785	+	0.868445i	$0.334880\pi$
$198$	−3.39987	−0.241619
$199$	−4.69309	−0.332684	−0.166342	−	0.986068i	$-0.553196\pi$
$199$	−4.69309	−0.332684	−0.166342	+	0.986068i	$0.553196\pi$
$200$	1.83019	0.129414
$201$	−5.12383	−0.361407
$202$	−19.1158	−1.34498
$203$	0.280953	0.0197191
$204$	−15.6547	−1.09605
$205$	−2.30220	−0.160793
$206$	27.7569	1.93391
$207$	−0.146871	−0.0102082
$208$	8.90972	0.617778
$209$	−25.6996	−1.77768
$210$	−0.205338	−0.0141697
$211$	−2.03273	−0.139939	−0.0699696	−	0.997549i	$-0.522290\pi$
$211$	−2.03273	−0.139939	−0.0699696	+	0.997549i	$0.522290\pi$
$212$	−12.5268	−0.860344
$213$	24.8642	1.70367
$214$	12.0016	0.820413
$215$	0.944615	0.0644222
$216$	−2.13344	−0.145162
$217$	0.395886	0.0268745
$218$	8.95238	0.606331
$219$	−15.7623	−1.06512
$220$	−8.14920	−0.549419
$221$	−9.65398	−0.649397
$222$	3.80486	0.255366
$223$	18.4323	1.23432	0.617159	−	0.786838i	$-0.288283\pi$
$223$	18.4323	1.23432	0.617159	+	0.786838i	$0.288283\pi$
$224$	0.457043	0.0305375
$225$	−1.76277	−0.117518
$226$	15.4040	1.02466
$227$	−4.13819	−0.274661	−0.137331	−	0.990525i	$-0.543852\pi$
$227$	−4.13819	−0.274661	−0.137331	+	0.990525i	$0.543852\pi$
$228$	27.5571	1.82501
$229$	−18.8481	−1.24552	−0.622760	−	0.782413i	$-0.713989\pi$
$229$	−18.8481	−1.24552	−0.622760	+	0.782413i	$0.713989\pi$
$230$	−0.669423	−0.0441405
$231$	−0.399754	−0.0263019
$232$	−2.23770	−0.146913
$233$	5.05162	0.330943	0.165471	−	0.986215i	$-0.447085\pi$
$233$	5.05162	0.330943	0.165471	+	0.986215i	$0.447085\pi$
$234$	2.24818	0.146968
$235$	0.362058	0.0236181
$236$	−19.9970	−1.30169
$237$	−10.5519	−0.685419
$238$	−0.440507	−0.0285538
$239$	−17.3176	−1.12018	−0.560090	−	0.828432i	$-0.689233\pi$
$239$	−17.3176	−1.12018	−0.560090	+	0.828432i	$0.689233\pi$
$240$	−6.24267	−0.402963
$241$	−6.88953	−0.443794	−0.221897	−	0.975070i	$-0.571225\pi$
$241$	−6.88953	−0.443794	−0.221897	+	0.975070i	$0.571225\pi$
$242$	−7.57591	−0.486998
$243$	4.45529	0.285807
$244$	−8.37323	−0.536041
$245$	6.70653	0.428464
$246$	9.13873	0.582664
$247$	16.9940	1.08130
$248$	−3.15311	−0.200223
$249$	7.52977	0.477180
$250$	−17.8778	−1.13069
$251$	−30.4901	−1.92452	−0.962260	−	0.272133i	$-0.912271\pi$
$251$	−30.4901	−1.92452	−0.962260	+	0.272133i	$0.912271\pi$
$252$	0.0539465	0.00339831
$253$	−1.30324	−0.0819339
$254$	−17.8947	−1.12281
$255$	6.76414	0.423587
$256$	11.9576	0.747350
$257$	8.16392	0.509252	0.254626	−	0.967040i	$-0.418048\pi$
$257$	8.16392	0.509252	0.254626	+	0.967040i	$0.418048\pi$
$258$	−3.74971	−0.233447
$259$	0.0563033	0.00349852
$260$	5.38869	0.334192
$261$	2.15527	0.133408
$262$	−31.3168	−1.93476
$263$	−30.9868	−1.91073	−0.955363	−	0.295433i	$-0.904536\pi$
$263$	−30.9868	−1.91073	−0.955363	+	0.295433i	$0.904536\pi$
$264$	3.18392	0.195956
$265$	5.41263	0.332495
$266$	0.775427	0.0475445
$267$	−14.4116	−0.881978
$268$	6.13556	0.374789
$269$	0.506775	0.0308986	0.0154493	−	0.999881i	$-0.495082\pi$
$269$	0.506775	0.0308986	0.0154493	+	0.999881i	$0.495082\pi$
$270$	9.36579	0.569984
$271$	−1.54990	−0.0941500	−0.0470750	−	0.998891i	$-0.514990\pi$
$271$	−1.54990	−0.0941500	−0.0470750	+	0.998891i	$0.514990\pi$
$272$	−13.3922	−0.812024
$273$	0.264339	0.0159985
$274$	−1.75010	−0.105727
$275$	−15.6417	−0.943232
$276$	1.39743	0.0841154
$277$	26.8991	1.61621	0.808104	−	0.589040i	$-0.200494\pi$
$277$	26.8991	1.61621	0.808104	+	0.589040i	$0.200494\pi$
$278$	−44.0714	−2.64323
$279$	3.03695	0.181818
$280$	0.0242010	0.00144628
$281$	3.77180	0.225007	0.112503	−	0.993651i	$-0.464113\pi$
$281$	3.77180	0.225007	0.112503	+	0.993651i	$0.464113\pi$
$282$	−1.43721	−0.0855848
$283$	31.1252	1.85020	0.925101	−	0.379720i	$-0.123980\pi$
$283$	31.1252	1.85020	0.925101	+	0.379720i	$0.123980\pi$
$284$	−29.7738	−1.76675
$285$	−11.9070	−0.705308
$286$	19.9489	1.17961
$287$	0.135232	0.00798251
$288$	3.50611	0.206599
$289$	−2.48905	−0.146415
$290$	9.82353	0.576858
$291$	0.202889	0.0118936
$292$	18.8747	1.10456
$293$	−18.0105	−1.05219	−0.526093	−	0.850427i	$-0.676344\pi$
$293$	−18.0105	−1.05219	−0.526093	+	0.850427i	$0.676344\pi$
$294$	−26.6220	−1.55263
$295$	8.64038	0.503062
$296$	−0.448438	−0.0260649
$297$	18.2334	1.05801
$298$	−43.1163	−2.49766
$299$	0.861772	0.0498375
$300$	16.7722	0.968345
$301$	−0.0554871	−0.00319822
$302$	−38.5953	−2.22091
$303$	−17.2421	−0.990530
$304$	23.5745	1.35209
$305$	3.61794	0.207163
$306$	−3.37925	−0.193179
$307$	14.4907	0.827028	0.413514	−	0.910498i	$-0.364301\pi$
$307$	14.4907	0.827028	0.413514	+	0.910498i	$0.364301\pi$
$308$	0.478688	0.0272758
$309$	25.0362	1.42426
$310$	13.8422	0.786182
$311$	−4.14032	−0.234776	−0.117388	−	0.993086i	$-0.537452\pi$
$311$	−4.14032	−0.234776	−0.117388	+	0.993086i	$0.537452\pi$
$312$	−2.10538	−0.119193
$313$	24.3406	1.37581	0.687905	−	0.725801i	$-0.258531\pi$
$313$	24.3406	1.37581	0.687905	+	0.725801i	$0.258531\pi$
$314$	−25.0916	−1.41600
$315$	−0.0233094	−0.00131334
$316$	12.6354	0.710798
$317$	16.7292	0.939606	0.469803	−	0.882771i	$-0.344325\pi$
$317$	16.7292	0.939606	0.469803	+	0.882771i	$0.344325\pi$
$318$	−21.4858	−1.20486
$319$	19.1245	1.07077
$320$	9.24095	0.516585
$321$	10.8252	0.604205
$322$	0.0393222	0.00219134
$323$	−25.5437	−1.42129
$324$	−22.4256	−1.24587
$325$	10.3431	0.573735
$326$	−2.05386	−0.113753
$327$	8.07488	0.446542
$328$	−1.07708	−0.0594719
$329$	−0.0212675	−0.00117251
$330$	−13.9774	−0.769430
$331$	−13.7376	−0.755084	−0.377542	−	0.925992i	$-0.623231\pi$
$331$	−13.7376	−0.755084	−0.377542	+	0.925992i	$0.623231\pi$
$332$	−9.01656	−0.494848
$333$	0.431918	0.0236690
$334$	−1.93464	−0.105859
$335$	−2.65108	−0.144844
$336$	0.366697	0.0200050
$337$	21.2041	1.15506	0.577529	−	0.816370i	$-0.304017\pi$
$337$	21.2041	1.15506	0.577529	+	0.816370i	$0.304017\pi$
$338$	13.5089	0.734785
$339$	13.8941	0.754624
$340$	−8.09976	−0.439271
$341$	26.9480	1.45932
$342$	5.94852	0.321659
$343$	−0.788068	−0.0425516
$344$	0.441937	0.0238277
$345$	−0.603807	−0.0325079
$346$	−23.6164	−1.26963
$347$	32.7467	1.75793	0.878966	−	0.476884i	$-0.158234\pi$
$347$	32.7467	1.75793	0.878966	+	0.476884i	$0.158234\pi$
$348$	−20.5067	−1.09928
$349$	−21.9300	−1.17389	−0.586943	−	0.809628i	$-0.699669\pi$
$349$	−21.9300	−1.17389	−0.586943	+	0.809628i	$0.699669\pi$
$350$	0.471953	0.0252269
$351$	−12.0569	−0.643550
$352$	31.1110	1.65822
$353$	−27.2823	−1.45209	−0.726046	−	0.687646i	$-0.758644\pi$
$353$	−27.2823	−1.45209	−0.726046	+	0.687646i	$0.758644\pi$
$354$	−34.2985	−1.82295
$355$	12.8648	0.682793
$356$	17.2573	0.914635
$357$	−0.397329	−0.0210289
$358$	−25.0509	−1.32398
$359$	−14.0569	−0.741894	−0.370947	−	0.928654i	$-0.620967\pi$
$359$	−14.0569	−0.741894	−0.370947	+	0.928654i	$0.620967\pi$
$360$	0.185652	0.00978474
$361$	25.9648	1.36657
$362$	41.5230	2.18240
$363$	−6.83334	−0.358657
$364$	−0.316534	−0.0165909
$365$	−8.15546	−0.426876
$366$	−14.3616	−0.750695
$367$	18.6970	0.975974	0.487987	−	0.872851i	$-0.337731\pi$
$367$	18.6970	0.975974	0.487987	+	0.872851i	$0.337731\pi$
$368$	1.19547	0.0623182
$369$	1.03740	0.0540051
$370$	1.96864	0.102345
$371$	−0.317941	−0.0165067
$372$	−28.8957	−1.49817
$373$	−24.5199	−1.26959	−0.634797	−	0.772679i	$-0.718916\pi$
$373$	−24.5199	−1.26959	−0.634797	+	0.772679i	$0.718916\pi$
$374$	−29.9854	−1.55051
$375$	−16.1254	−0.832713
$376$	0.169389	0.00873555
$377$	−12.6462	−0.651311
$378$	−0.550151	−0.0282967
$379$	−18.6504	−0.958007	−0.479003	−	0.877813i	$-0.659002\pi$
$379$	−18.6504	−0.958007	−0.479003	+	0.877813i	$0.659002\pi$
$380$	14.2581	0.731424
$381$	−16.1407	−0.826912
$382$	20.0775	1.02725
$383$	11.3134	0.578090	0.289045	−	0.957316i	$-0.406662\pi$
$383$	11.3134	0.578090	0.289045	+	0.957316i	$0.406662\pi$
$384$	−6.60641	−0.337132
$385$	−0.206833	−0.0105412
$386$	2.06677	0.105196
$387$	−0.425657	−0.0216374
$388$	−0.242951	−0.0123340
$389$	23.7954	1.20647	0.603237	−	0.797562i	$-0.293878\pi$
$389$	23.7954	1.20647	0.603237	+	0.797562i	$0.293878\pi$
$390$	9.24260	0.468017
$391$	−1.29533	−0.0655078
$392$	3.13765	0.158475
$393$	−28.2472	−1.42488
$394$	−28.5843	−1.44005
$395$	−5.45956	−0.274701
$396$	3.67215	0.184532
$397$	−14.0753	−0.706417	−0.353208	−	0.935545i	$-0.614909\pi$
$397$	−14.0753	−0.706417	−0.353208	+	0.935545i	$0.614909\pi$
$398$	9.63895	0.483157
$399$	0.699421	0.0350148
$400$	14.3483	0.717414
$401$	−30.3567	−1.51594	−0.757971	−	0.652288i	$-0.773809\pi$
$401$	−30.3567	−1.51594	−0.757971	+	0.652288i	$0.773809\pi$
$402$	10.5236	0.524871
$403$	−17.8195	−0.887652
$404$	20.6466	1.02721
$405$	9.68977	0.481488
$406$	−0.577039	−0.0286379
$407$	3.83257	0.189974
$408$	3.16460	0.156671
$409$	7.58009	0.374811	0.187406	−	0.982283i	$-0.439992\pi$
$409$	7.58009	0.374811	0.187406	+	0.982283i	$0.439992\pi$
$410$	4.72840	0.233519
$411$	−1.57856	−0.0778644
$412$	−29.9797	−1.47700
$413$	−0.507540	−0.0249744
$414$	0.301652	0.0148254
$415$	3.89592	0.191243
$416$	−20.5723	−1.00864
$417$	−39.7516	−1.94665
$418$	52.7834	2.58172
$419$	−19.8612	−0.970281	−0.485141	−	0.874436i	$-0.661232\pi$
$419$	−19.8612	−0.970281	−0.485141	+	0.874436i	$0.661232\pi$
$420$	0.221782	0.0108219
$421$	−32.0566	−1.56234	−0.781172	−	0.624315i	$-0.785378\pi$
$421$	−32.0566	−1.56234	−0.781172	+	0.624315i	$0.785378\pi$
$422$	4.17495	0.203233
$423$	−0.163149	−0.00793256
$424$	2.53230	0.122979
$425$	−15.5468	−0.754132
$426$	−51.0676	−2.47423
$427$	−0.212519	−0.0102845
$428$	−12.9627	−0.626577
$429$	17.9936	0.868738
$430$	−1.94011	−0.0935602
$431$	40.3574	1.94395	0.971973	−	0.235092i	$-0.0755390\pi$
$431$	40.3574	1.94395	0.971973	+	0.235092i	$0.0755390\pi$
$432$	−16.7256	−0.804713
$433$	35.9150	1.72596	0.862982	−	0.505234i	$-0.168594\pi$
$433$	35.9150	1.72596	0.862982	+	0.505234i	$0.168594\pi$
$434$	−0.813095	−0.0390298
$435$	8.86064	0.424835
$436$	−9.66931	−0.463076
$437$	2.28018	0.109076
$438$	32.3736	1.54687
$439$	−30.5617	−1.45863	−0.729315	−	0.684178i	$-0.760161\pi$
$439$	−30.5617	−1.45863	−0.729315	+	0.684178i	$0.760161\pi$
$440$	1.64736	0.0785350
$441$	−3.02206	−0.143908
$442$	19.8279	0.943118
$443$	−2.71698	−0.129087	−0.0645437	−	0.997915i	$-0.520559\pi$
$443$	−2.71698	−0.129087	−0.0645437	+	0.997915i	$0.520559\pi$
$444$	−4.10957	−0.195032
$445$	−7.45661	−0.353477
$446$	−37.8574	−1.79260
$447$	−38.8901	−1.83944
$448$	−0.542818	−0.0256457
$449$	13.4967	0.636950	0.318475	−	0.947931i	$-0.396829\pi$
$449$	13.4967	0.636950	0.318475	+	0.947931i	$0.396829\pi$
$450$	3.62048	0.170671
$451$	9.20528	0.433460
$452$	−16.6376	−0.782566
$453$	−34.8123	−1.63562
$454$	8.49926	0.398890
$455$	0.136769	0.00641185
$456$	−5.57067	−0.260870
$457$	−21.3425	−0.998360	−0.499180	−	0.866498i	$-0.666365\pi$
$457$	−21.3425	−0.998360	−0.499180	+	0.866498i	$0.666365\pi$
$458$	38.7114	1.80887
$459$	18.1228	0.845900
$460$	0.723033	0.0337116
$461$	−21.1165	−0.983494	−0.491747	−	0.870738i	$-0.663642\pi$
$461$	−21.1165	−0.983494	−0.491747	+	0.870738i	$0.663642\pi$
$462$	0.821039	0.0381982
$463$	15.8408	0.736183	0.368091	−	0.929790i	$-0.380011\pi$
$463$	15.8408	0.736183	0.368091	+	0.929790i	$0.380011\pi$
$464$	−17.5431	−0.814417
$465$	12.4854	0.578995
$466$	−10.3753	−0.480628
$467$	−33.3353	−1.54257	−0.771286	−	0.636489i	$-0.780386\pi$
$467$	−33.3353	−1.54257	−0.771286	+	0.636489i	$0.780386\pi$
$468$	−2.42822	−0.112245
$469$	0.155726	0.00719074
$470$	−0.743617	−0.0343005
$471$	−22.6322	−1.04284
$472$	4.04240	0.186066
$473$	−3.77701	−0.173667
$474$	21.6721	0.995432
$475$	27.3672	1.25569
$476$	0.475784	0.0218075
$477$	−2.43901	−0.111675
$478$	35.5678	1.62683
$479$	−21.0463	−0.961628	−0.480814	−	0.876823i	$-0.659659\pi$
$479$	−21.0463	−0.961628	−0.480814	+	0.876823i	$0.659659\pi$
$480$	14.4141	0.657912
$481$	−2.53430	−0.115554
$482$	14.1501	0.644520
$483$	0.0354679	0.00161385
$484$	8.18262	0.371937
$485$	0.104975	0.00476668
$486$	−9.15053	−0.415077
$487$	−31.8625	−1.44383	−0.721914	−	0.691983i	$-0.756737\pi$
$487$	−31.8625	−1.44383	−0.721914	+	0.691983i	$0.756737\pi$
$488$	1.69265	0.0766227
$489$	−1.85254	−0.0837749
$490$	−13.7743	−0.622258
$491$	−28.5135	−1.28680	−0.643399	−	0.765531i	$-0.722476\pi$
$491$	−28.5135	−1.28680	−0.643399	+	0.765531i	$0.722476\pi$
$492$	−9.87059	−0.445000
$493$	19.0085	0.856100
$494$	−34.9032	−1.57037
$495$	−1.58668	−0.0713158
$496$	−24.7196	−1.10994
$497$	−0.755684	−0.0338971
$498$	−15.4651	−0.693007
$499$	34.8206	1.55878	0.779392	−	0.626537i	$-0.215528\pi$
$499$	34.8206	1.55878	0.779392	+	0.626537i	$0.215528\pi$
$500$	19.3095	0.863546
$501$	−1.74501	−0.0779614
$502$	62.6224	2.79498
$503$	−28.6418	−1.27707	−0.638536	−	0.769592i	$-0.720460\pi$
$503$	−28.6418	−1.27707	−0.638536	+	0.769592i	$0.720460\pi$
$504$	−0.0109053	−0.000485761 0
$505$	−8.92107	−0.396983
$506$	2.67667	0.118992
$507$	12.1847	0.541144
$508$	19.3277	0.857530
$509$	−4.20427	−0.186351	−0.0931755	−	0.995650i	$-0.529702\pi$
$509$	−4.20427	−0.186351	−0.0931755	+	0.995650i	$0.529702\pi$
$510$	−13.8926	−0.615175
$511$	0.479056	0.0211922
$512$	−31.6915	−1.40058
$513$	−31.9017	−1.40849
$514$	−16.7676	−0.739585
$515$	12.9538	0.570812
$516$	4.05000	0.178291
$517$	−1.44768	−0.0636689
$518$	−0.115639	−0.00508089
$519$	−21.3016	−0.935035
$520$	−1.08933	−0.0477701
$521$	−36.1845	−1.58527	−0.792637	−	0.609694i	$-0.791292\pi$
$521$	−36.1845	−1.58527	−0.792637	+	0.609694i	$0.791292\pi$
$522$	−4.42662	−0.193748
$523$	11.8257	0.517100	0.258550	−	0.965998i	$-0.416755\pi$
$523$	11.8257	0.517100	0.258550	+	0.965998i	$0.416755\pi$
$524$	33.8248	1.47764
$525$	0.425693	0.0185788
$526$	63.6425	2.77494
$527$	26.7846	1.16675
$528$	24.9611	1.08629
$529$	−22.8844	−0.994973
$530$	−11.1168	−0.482882
$531$	−3.89348	−0.168963
$532$	−0.837526	−0.0363113
$533$	−6.08703	−0.263658
$534$	29.5995	1.28089
$535$	5.60099	0.242152
$536$	−1.24031	−0.0535730
$537$	−22.5955	−0.975067
$538$	−1.04084	−0.0448740
$539$	−26.8159	−1.15504
$540$	−10.1158	−0.435316
$541$	42.5447	1.82914	0.914571	−	0.404426i	$-0.132529\pi$
$541$	42.5447	1.82914	0.914571	+	0.404426i	$0.132529\pi$
$542$	3.18329	0.136734
$543$	37.4530	1.60726
$544$	30.9223	1.32578
$545$	4.17796	0.178964
$546$	−0.542915	−0.0232346
$547$	27.2665	1.16583	0.582915	−	0.812533i	$-0.301912\pi$
$547$	27.2665	1.16583	0.582915	+	0.812533i	$0.301912\pi$
$548$	1.89025	0.0807475
$549$	−1.63030	−0.0695794
$550$	32.1259	1.36985
$551$	−33.4608	−1.42548
$552$	−0.282491	−0.0120236
$553$	0.320697	0.0136374
$554$	−55.2469	−2.34722
$555$	1.77568	0.0753735
$556$	47.6008	2.01872
$557$	−24.4021	−1.03395	−0.516976	−	0.856000i	$-0.672942\pi$
$557$	−24.4021	−1.03395	−0.516976	+	0.856000i	$0.672942\pi$
$558$	−6.23748	−0.264054
$559$	2.49756	0.105636
$560$	0.189730	0.00801755
$561$	−27.0462	−1.14189
$562$	−7.74674	−0.326777
$563$	9.58770	0.404073	0.202037	−	0.979378i	$-0.435244\pi$
$563$	9.58770	0.404073	0.202037	+	0.979378i	$0.435244\pi$
$564$	1.55231	0.0653640
$565$	7.18884	0.302437
$566$	−63.9268	−2.68705
$567$	−0.569181	−0.0239034
$568$	6.01879	0.252543
$569$	−23.7459	−0.995481	−0.497741	−	0.867326i	$-0.665837\pi$
$569$	−23.7459	−0.995481	−0.497741	+	0.867326i	$0.665837\pi$
$570$	24.4552	1.02432
$571$	−26.8817	−1.12496	−0.562482	−	0.826810i	$-0.690153\pi$
$571$	−26.8817	−1.12496	−0.562482	+	0.826810i	$0.690153\pi$
$572$	−21.5465	−0.900905
$573$	18.1095	0.756536
$574$	−0.277748	−0.0115930
$575$	1.38780	0.0578754
$576$	−4.16411	−0.173504
$577$	6.86305	0.285712	0.142856	−	0.989743i	$-0.454371\pi$
$577$	6.86305	0.285712	0.142856	+	0.989743i	$0.454371\pi$
$578$	5.11217	0.212638
$579$	1.86419	0.0774732
$580$	−10.6102	−0.440566
$581$	−0.228848	−0.00949421
$582$	−0.416706	−0.0172730
$583$	−21.6423	−0.896331
$584$	−3.81553	−0.157888
$585$	1.04920	0.0433789
$586$	36.9911	1.52809
$587$	43.0689	1.77764	0.888821	−	0.458254i	$-0.151525\pi$
$587$	43.0689	1.77764	0.888821	+	0.458254i	$0.151525\pi$
$588$	28.7540	1.18579
$589$	−47.1491	−1.94274
$590$	−17.7461	−0.730596
$591$	−25.7825	−1.06055
$592$	−3.51565	−0.144492
$593$	−0.585805	−0.0240561	−0.0120281	−	0.999928i	$-0.503829\pi$
$593$	−0.585805	−0.0240561	−0.0120281	+	0.999928i	$0.503829\pi$
$594$	−37.4489	−1.53655
$595$	−0.205579	−0.00842791
$596$	46.5691	1.90755
$597$	8.69415	0.355828
$598$	−1.76996	−0.0723790
$599$	−11.0842	−0.452887	−0.226443	−	0.974024i	$-0.572710\pi$
$599$	−11.0842	−0.452887	−0.226443	+	0.974024i	$0.572710\pi$
$600$	−3.39051	−0.138417
$601$	−46.7263	−1.90600	−0.953002	−	0.302965i	$-0.902024\pi$
$601$	−46.7263	−1.90600	−0.953002	+	0.302965i	$0.902024\pi$
$602$	0.113963	0.00464477
$603$	1.19461	0.0486485
$604$	41.6861	1.69619
$605$	−3.53558	−0.143742
$606$	35.4128	1.43855
$607$	−0.0151401	−0.000614518 0	−0.000307259	−	1.00000i	$-0.500098\pi$
$607$	−0.0151401	−0.000614518 0	−0.000307259		1.00000i	$0.500098\pi$
$608$	−54.4327	−2.20754
$609$	−0.520478	−0.0210908
$610$	−7.43074	−0.300862
$611$	0.957283	0.0387275
$612$	3.64987	0.147537
$613$	16.2083	0.654647	0.327323	−	0.944912i	$-0.393853\pi$
$613$	16.2083	0.654647	0.327323	+	0.944912i	$0.393853\pi$
$614$	−29.7618	−1.20109
$615$	4.26493	0.171978
$616$	−0.0967669	−0.00389885
$617$	−33.3267	−1.34168	−0.670841	−	0.741601i	$-0.734067\pi$
$617$	−33.3267	−1.34168	−0.670841	+	0.741601i	$0.734067\pi$
$618$	−51.4208	−2.06845
$619$	−42.3955	−1.70402	−0.852011	−	0.523525i	$-0.824617\pi$
$619$	−42.3955	−1.70402	−0.852011	+	0.523525i	$0.824617\pi$
$620$	−14.9507	−0.600434
$621$	−1.61775	−0.0649180
$622$	8.50364	0.340965
$623$	0.438005	0.0175483
$624$	−16.5057	−0.660755
$625$	12.0630	0.482519
$626$	−49.9921	−1.99809
$627$	47.6097	1.90135
$628$	27.1010	1.08145
$629$	3.80932	0.151888
$630$	0.0478743	0.00190736
$631$	−2.35799	−0.0938701	−0.0469351	−	0.998898i	$-0.514945\pi$
$631$	−2.35799	−0.0938701	−0.0469351	+	0.998898i	$0.514945\pi$
$632$	−2.55425	−0.101603
$633$	3.76573	0.149674
$634$	−34.3594	−1.36459
$635$	−8.35122	−0.331408
$636$	23.2064	0.920195
$637$	17.7321	0.702571
$638$	−39.2791	−1.55507
$639$	−5.79706	−0.229328
$640$	−3.41817	−0.135115
$641$	−3.93575	−0.155453	−0.0777263	−	0.996975i	$-0.524766\pi$
$641$	−3.93575	−0.155453	−0.0777263	+	0.996975i	$0.524766\pi$
$642$	−22.2335	−0.877486
$643$	−19.6361	−0.774371	−0.387186	−	0.922002i	$-0.626553\pi$
$643$	−19.6361	−0.774371	−0.387186	+	0.922002i	$0.626553\pi$
$644$	−0.0424713	−0.00167360
$645$	−1.74994	−0.0689038
$646$	52.4632	2.06414
$647$	4.54425	0.178653	0.0893265	−	0.996002i	$-0.471529\pi$
$647$	4.54425	0.178653	0.0893265	+	0.996002i	$0.471529\pi$
$648$	4.53335	0.178087
$649$	−34.5483	−1.35614
$650$	−21.2434	−0.833234
$651$	−0.733397	−0.0287441
$652$	2.21834	0.0868769
$653$	−24.5445	−0.960501	−0.480250	−	0.877131i	$-0.659454\pi$
$653$	−24.5445	−0.960501	−0.480250	+	0.877131i	$0.659454\pi$
$654$	−16.5847	−0.648512
$655$	−14.6152	−0.571062
$656$	−8.44408	−0.329686
$657$	3.67497	0.143374
$658$	0.0436804	0.00170284
$659$	42.6076	1.65976	0.829879	−	0.557943i	$-0.188409\pi$
$659$	42.6076	1.65976	0.829879	+	0.557943i	$0.188409\pi$
$660$	15.0967	0.587640
$661$	−16.4090	−0.638235	−0.319117	−	0.947715i	$-0.603386\pi$
$661$	−16.4090	−0.638235	−0.319117	+	0.947715i	$0.603386\pi$
$662$	28.2150	1.09661
$663$	17.8844	0.694573
$664$	1.82270	0.0707345
$665$	0.361882	0.0140332
$666$	−0.887100	−0.0343744
$667$	−1.69681	−0.0657008
$668$	2.08957	0.0808481
$669$	−34.1467	−1.32019
$670$	5.44494	0.210356
$671$	−14.4662	−0.558463
$672$	−0.846693	−0.0326619
$673$	−14.6717	−0.565553	−0.282776	−	0.959186i	$-0.591255\pi$
$673$	−14.6717	−0.565553	−0.282776	+	0.959186i	$0.591255\pi$
$674$	−43.5502	−1.67749
$675$	−19.4165	−0.747342
$676$	−14.5907	−0.561181
$677$	−25.8030	−0.991690	−0.495845	−	0.868411i	$-0.665142\pi$
$677$	−25.8030	−0.991690	−0.495845	+	0.868411i	$0.665142\pi$
$678$	−28.5365	−1.09594
$679$	−0.00616629	−0.000236640 0
$680$	1.63737	0.0627903
$681$	7.66617	0.293768
$682$	−55.3475	−2.11937
$683$	7.03626	0.269235	0.134618	−	0.990898i	$-0.457019\pi$
$683$	7.03626	0.269235	0.134618	+	0.990898i	$0.457019\pi$
$684$	−6.42489	−0.245662
$685$	−0.816748	−0.0312063
$686$	1.61858	0.0617977
$687$	34.9170	1.33217
$688$	3.46468	0.132090
$689$	14.3110	0.545207
$690$	1.24014	0.0472112
$691$	−25.7042	−0.977832	−0.488916	−	0.872331i	$-0.662608\pi$
$691$	−25.7042	−0.977832	−0.488916	+	0.872331i	$0.662608\pi$
$692$	25.5077	0.969656
$693$	0.0932021	0.00354046
$694$	−67.2570	−2.55304
$695$	−20.5676	−0.780172
$696$	4.14545	0.157133
$697$	9.14944	0.346560
$698$	45.0412	1.70483
$699$	−9.35836	−0.353966
$700$	−0.509748	−0.0192667
$701$	26.0313	0.983187	0.491593	−	0.870825i	$-0.336415\pi$
$701$	26.0313	0.983187	0.491593	+	0.870825i	$0.336415\pi$
$702$	24.7632	0.934627
$703$	−6.70558	−0.252906
$704$	−36.9497	−1.39259
$705$	−0.670729	−0.0252611
$706$	56.0341	2.10887
$707$	0.524028	0.0197081
$708$	37.0453	1.39225
$709$	−32.4586	−1.21901	−0.609505	−	0.792782i	$-0.708632\pi$
$709$	−32.4586	−1.21901	−0.609505	+	0.792782i	$0.708632\pi$
$710$	−26.4225	−0.991618
$711$	2.46016	0.0922632
$712$	−3.48857	−0.130740
$713$	−2.39095	−0.0895417
$714$	0.816058	0.0305402
$715$	9.30991	0.348171
$716$	27.0571	1.01117
$717$	32.0815	1.19811
$718$	28.8709	1.07745
$719$	−23.0618	−0.860061	−0.430030	−	0.902814i	$-0.641497\pi$
$719$	−23.0618	−0.860061	−0.430030	+	0.902814i	$0.641497\pi$
$720$	1.45547	0.0542422
$721$	−0.760911	−0.0283378
$722$	−53.3281	−1.98466
$723$	12.7632	0.474667
$724$	−44.8483	−1.66677
$725$	−20.3655	−0.756355
$726$	14.0347	0.520877
$727$	−6.73471	−0.249777	−0.124888	−	0.992171i	$-0.539857\pi$
$727$	−6.73471	−0.249777	−0.124888	+	0.992171i	$0.539857\pi$
$728$	0.0639875	0.00237153
$729$	22.0740	0.817555
$730$	16.7502	0.619952
$731$	−3.75410	−0.138850
$732$	15.5118	0.573332
$733$	−16.5693	−0.612002	−0.306001	−	0.952031i	$-0.598991\pi$
$733$	−16.5693	−0.612002	−0.306001	+	0.952031i	$0.598991\pi$
$734$	−38.4010	−1.41741
$735$	−12.4241	−0.458271
$736$	−2.76031	−0.101746
$737$	10.6003	0.390466
$738$	−2.13068	−0.0784315
$739$	7.36184	0.270810	0.135405	−	0.990790i	$-0.456766\pi$
$739$	7.36184	0.270810	0.135405	+	0.990790i	$0.456766\pi$
$740$	−2.12630	−0.0781643
$741$	−31.4821	−1.15652
$742$	0.653005	0.0239726
$743$	−0.397775	−0.0145930	−0.00729648	−	0.999973i	$-0.502323\pi$
$743$	−0.397775	−0.0145930	−0.00729648	+	0.999973i	$0.502323\pi$
$744$	5.84128	0.214152
$745$	−20.1218	−0.737206
$746$	50.3605	1.84383
$747$	−1.75556	−0.0642324
$748$	32.3867	1.18417
$749$	−0.329005	−0.0120216
$750$	33.1193	1.20935
$751$	−13.9193	−0.507921	−0.253961	−	0.967215i	$-0.581733\pi$
$751$	−13.9193	−0.507921	−0.253961	+	0.967215i	$0.581733\pi$
$752$	1.32797	0.0484260
$753$	56.4843	2.05840
$754$	25.9735	0.945897
$755$	−18.0119	−0.655521
$756$	0.594209	0.0216112
$757$	31.4329	1.14245	0.571224	−	0.820794i	$-0.306469\pi$
$757$	31.4329	1.14245	0.571224	+	0.820794i	$0.306469\pi$
$758$	38.3053	1.39131
$759$	2.41431	0.0876338
$760$	−2.88227	−0.104551
$761$	−13.3332	−0.483327	−0.241663	−	0.970360i	$-0.577693\pi$
$761$	−13.3332	−0.483327	−0.241663	+	0.970360i	$0.577693\pi$
$762$	33.1507	1.20092
$763$	−0.245415	−0.00888462
$764$	−21.6853	−0.784548
$765$	−1.57705	−0.0570184
$766$	−23.2362	−0.839559
$767$	22.8452	0.824892
$768$	−22.1520	−0.799340
$769$	−31.3330	−1.12990	−0.564948	−	0.825127i	$-0.691104\pi$
$769$	−31.3330	−1.12990	−0.564948	+	0.825127i	$0.691104\pi$
$770$	0.424807	0.0153090
$771$	−15.1240	−0.544679
$772$	−2.23229	−0.0803418
$773$	12.9743	0.466653	0.233327	−	0.972398i	$-0.425039\pi$
$773$	12.9743	0.466653	0.233327	+	0.972398i	$0.425039\pi$
$774$	0.874240	0.0314239
$775$	−28.6966	−1.03081
$776$	0.0491126	0.00176304
$777$	−0.104304	−0.00374190
$778$	−48.8723	−1.75216
$779$	−16.1058	−0.577051
$780$	−9.98278	−0.357441
$781$	−51.4395	−1.84065
$782$	2.66043	0.0951368
$783$	23.7398	0.848392
$784$	24.5984	0.878514
$785$	−11.7099	−0.417946
$786$	58.0158	2.06936
$787$	25.7833	0.919075	0.459538	−	0.888158i	$-0.348015\pi$
$787$	25.7833	0.919075	0.459538	+	0.888158i	$0.348015\pi$
$788$	30.8734	1.09982
$789$	57.4044	2.04365
$790$	11.2132	0.398947
$791$	−0.422276	−0.0150144
$792$	−0.742326	−0.0263774
$793$	9.56585	0.339693
$794$	28.9086	1.02593
$795$	−10.0271	−0.355626
$796$	−10.4109	−0.369003
$797$	−10.0199	−0.354924	−0.177462	−	0.984128i	$-0.556789\pi$
$797$	−10.0199	−0.354924	−0.177462	+	0.984128i	$0.556789\pi$
$798$	−1.43651	−0.0508520
$799$	−1.43890	−0.0509045
$800$	−33.1297	−1.17131
$801$	3.36006	0.118722
$802$	62.3484	2.20160
$803$	32.6094	1.15076
$804$	−11.3664	−0.400862
$805$	0.0183512	0.000646794 0
$806$	36.5987	1.28914
$807$	−0.938822	−0.0330481
$808$	−4.17372	−0.146831
$809$	46.1402	1.62220	0.811101	−	0.584906i	$-0.198869\pi$
$809$	46.1402	1.62220	0.811101	+	0.584906i	$0.198869\pi$
$810$	−19.9014	−0.699265
$811$	9.40500	0.330254	0.165127	−	0.986272i	$-0.447197\pi$
$811$	9.40500	0.330254	0.165127	+	0.986272i	$0.447197\pi$
$812$	0.623250	0.0218718
$813$	2.87126	0.100700
$814$	−7.87157	−0.275898
$815$	−0.958510	−0.0335751
$816$	24.8097	0.868514
$817$	6.60837	0.231198
$818$	−15.5684	−0.544338
$819$	−0.0616303	−0.00215354
$820$	−5.10706	−0.178346
$821$	−18.1631	−0.633898	−0.316949	−	0.948443i	$-0.602658\pi$
$821$	−18.1631	−0.633898	−0.316949	+	0.948443i	$0.602658\pi$
$822$	3.24213	0.113082
$823$	4.05041	0.141189	0.0705943	−	0.997505i	$-0.477510\pi$
$823$	4.05041	0.141189	0.0705943	+	0.997505i	$0.477510\pi$
$824$	6.06042	0.211125
$825$	28.9770	1.00885
$826$	1.04242	0.0362703
$827$	44.3747	1.54306	0.771529	−	0.636194i	$-0.219492\pi$
$827$	44.3747	1.54306	0.771529	+	0.636194i	$0.219492\pi$
$828$	−0.325809	−0.0113226
$829$	−28.0699	−0.974906	−0.487453	−	0.873149i	$-0.662074\pi$
$829$	−28.0699	−0.974906	−0.487453	+	0.873149i	$0.662074\pi$
$830$	−8.00166	−0.277742
$831$	−49.8317	−1.72864
$832$	24.4331	0.847066
$833$	−26.6532	−0.923478
$834$	81.6443	2.82711
$835$	−0.902872	−0.0312452
$836$	−57.0105	−1.97175
$837$	33.4514	1.15625
$838$	40.7920	1.40914
$839$	−23.3457	−0.805982	−0.402991	−	0.915204i	$-0.632029\pi$
$839$	−23.3457	−0.805982	−0.402991	+	0.915204i	$0.632029\pi$
$840$	−0.0448334	−0.00154690
$841$	−4.09993	−0.141377
$842$	65.8398	2.26899
$843$	−6.98742	−0.240660
$844$	−4.50929	−0.155216
$845$	6.30441	0.216878
$846$	0.335084	0.0115204
$847$	0.207682	0.00713602
$848$	19.8526	0.681742
$849$	−57.6608	−1.97891
$850$	31.9310	1.09522
$851$	−0.340043	−0.0116565
$852$	55.1573	1.88966
$853$	−19.1047	−0.654131	−0.327066	−	0.945002i	$-0.606060\pi$
$853$	−19.1047	−0.654131	−0.327066	+	0.945002i	$0.606060\pi$
$854$	0.436485	0.0149362
$855$	2.77610	0.0949405
$856$	2.62042	0.0895642
$857$	−47.0141	−1.60597	−0.802985	−	0.595999i	$-0.796756\pi$
$857$	−47.0141	−1.60597	−0.802985	+	0.595999i	$0.796756\pi$
$858$	−36.9563	−1.26167
$859$	23.6627	0.807361	0.403681	−	0.914900i	$-0.367731\pi$
$859$	23.6627	0.807361	0.403681	+	0.914900i	$0.367731\pi$
$860$	2.09548	0.0714551
$861$	−0.250524	−0.00853782
$862$	−82.8884	−2.82319
$863$	23.9208	0.814273	0.407136	−	0.913367i	$-0.366527\pi$
$863$	23.9208	0.814273	0.407136	+	0.913367i	$0.366527\pi$
$864$	38.6190	1.31385
$865$	−11.0215	−0.374741
$866$	−73.7644	−2.50662
$867$	4.61108	0.156601
$868$	0.878210	0.0298084
$869$	21.8299	0.740529
$870$	−18.1985	−0.616988
$871$	−7.00946	−0.237507
$872$	1.95465	0.0661930
$873$	−0.0473033	−0.00160098
$874$	−4.68318	−0.158411
$875$	0.490091	0.0165681
$876$	−34.9662	−1.18140
$877$	1.24176	0.0419312	0.0209656	−	0.999780i	$-0.493326\pi$
$877$	1.24176	0.0419312	0.0209656	+	0.999780i	$0.493326\pi$
$878$	62.7694	2.11836
$879$	33.3653	1.12538
$880$	12.9149	0.435363
$881$	−13.2922	−0.447827	−0.223913	−	0.974609i	$-0.571883\pi$
$881$	−13.2922	−0.447827	−0.223913	+	0.974609i	$0.571883\pi$
$882$	6.20688	0.208997
$883$	23.3807	0.786823	0.393411	−	0.919362i	$-0.371295\pi$
$883$	23.3807	0.786823	0.393411	+	0.919362i	$0.371295\pi$
$884$	−21.4158	−0.720292
$885$	−16.0067	−0.538059
$886$	5.58029	0.187473
$887$	−23.8031	−0.799229	−0.399614	−	0.916683i	$-0.630856\pi$
$887$	−23.8031	−0.799229	−0.399614	+	0.916683i	$0.630856\pi$
$888$	0.830751	0.0278782
$889$	0.490554	0.0164527
$890$	15.3148	0.513354
$891$	−38.7443	−1.29798
$892$	40.8891	1.36907
$893$	2.53290	0.0847603
$894$	79.8747	2.67141
$895$	−11.6909	−0.390785
$896$	0.200785	0.00670775
$897$	−1.59647	−0.0533046
$898$	−27.7204	−0.925041
$899$	35.0863	1.17019
$900$	−3.91042	−0.130347
$901$	−21.5110	−0.716634
$902$	−18.9064	−0.629513
$903$	0.102792	0.00342071
$904$	3.36329	0.111861
$905$	19.3782	0.644154
$906$	71.4995	2.37541
$907$	−42.2449	−1.40272	−0.701359	−	0.712809i	$-0.747423\pi$
$907$	−42.2449	−1.40272	−0.701359	+	0.712809i	$0.747423\pi$
$908$	−9.17990	−0.304646
$909$	4.01996	0.133334
$910$	−0.280905	−0.00931191
$911$	−13.9966	−0.463728	−0.231864	−	0.972748i	$-0.574483\pi$
$911$	−13.9966	−0.463728	−0.231864	+	0.972748i	$0.574483\pi$
$912$	−43.6727	−1.44615
$913$	−15.5777	−0.515547
$914$	43.8345	1.44992
$915$	−6.70239	−0.221574
$916$	−41.8116	−1.38149
$917$	0.858501	0.0283502
$918$	−37.2217	−1.22850
$919$	47.8002	1.57678	0.788392	−	0.615173i	$-0.210914\pi$
$919$	47.8002	1.57678	0.788392	+	0.615173i	$0.210914\pi$
$920$	−0.146161	−0.00481880
$921$	−26.8446	−0.884561
$922$	43.3703	1.42833
$923$	34.0146	1.11960
$924$	−0.886790	−0.0291732
$925$	−4.08126	−0.134191
$926$	−32.5347	−1.06916
$927$	−5.83716	−0.191717
$928$	40.5064	1.32969
$929$	−4.10494	−0.134679	−0.0673394	−	0.997730i	$-0.521451\pi$
$929$	−4.10494	−0.134679	−0.0673394	+	0.997730i	$0.521451\pi$
$930$	−25.6432	−0.840874
$931$	46.9178	1.53767
$932$	11.2062	0.367072
$933$	7.67012	0.251109
$934$	68.4659	2.24027
$935$	−13.9938	−0.457645
$936$	0.490866	0.0160444
$937$	34.4731	1.12619	0.563094	−	0.826393i	$-0.309611\pi$
$937$	34.4731	1.12619	0.563094	+	0.826393i	$0.309611\pi$
$938$	−0.319838	−0.0104431
$939$	−45.0920	−1.47152
$940$	0.803168	0.0261964
$941$	3.84126	0.125222	0.0626108	−	0.998038i	$-0.480057\pi$
$941$	3.84126	0.125222	0.0626108	+	0.998038i	$0.480057\pi$
$942$	46.4833	1.51451
$943$	−0.816733	−0.0265965
$944$	31.6914	1.03147
$945$	−0.256748	−0.00835202
$946$	7.75746	0.252217
$947$	18.5936	0.604211	0.302106	−	0.953274i	$-0.402310\pi$
$947$	18.5936	0.604211	0.302106	+	0.953274i	$0.402310\pi$
$948$	−23.4077	−0.760245
$949$	−21.5631	−0.699967
$950$	−56.2084	−1.82364
$951$	−30.9916	−1.00497
$952$	−0.0961799	−0.00311721
$953$	−55.7455	−1.80577	−0.902887	−	0.429878i	$-0.858557\pi$
$953$	−55.7455	−1.80577	−0.902887	+	0.429878i	$0.858557\pi$
$954$	5.00939	0.162185
$955$	9.36990	0.303203
$956$	−38.4162	−1.24247
$957$	−35.4290	−1.14526
$958$	43.2261	1.39657
$959$	0.0479762	0.00154923
$960$	−17.1193	−0.552522
$961$	18.4394	0.594820
$962$	5.20510	0.167819
$963$	−2.52389	−0.0813312
$964$	−15.2833	−0.492242
$965$	0.964537	0.0310495
$966$	−0.0728461	−0.00234379
$967$	−21.1291	−0.679468	−0.339734	−	0.940522i	$-0.610337\pi$
$967$	−21.1291	−0.679468	−0.339734	+	0.940522i	$0.610337\pi$
$968$	−1.65412	−0.0531654
$969$	47.3209	1.52017
$970$	−0.215604	−0.00692264
$971$	48.9789	1.57181	0.785903	−	0.618349i	$-0.212198\pi$
$971$	48.9789	1.57181	0.785903	+	0.618349i	$0.212198\pi$
$972$	9.88334	0.317008
$973$	1.20815	0.0387315
$974$	65.4411	2.09687
$975$	−19.1611	−0.613648
$976$	13.2700	0.424762
$977$	−39.0304	−1.24869	−0.624346	−	0.781148i	$-0.714634\pi$
$977$	−39.0304	−1.24869	−0.624346	+	0.781148i	$0.714634\pi$
$978$	3.80486	0.121666
$979$	29.8150	0.952893
$980$	14.8774	0.475240
$981$	−1.88265	−0.0601083
$982$	58.5628	1.86881
$983$	36.7464	1.17203	0.586013	−	0.810301i	$-0.300697\pi$
$983$	36.7464	1.17203	0.586013	+	0.810301i	$0.300697\pi$
$984$	1.99534	0.0636092
$985$	−13.3399	−0.425045
$986$	−39.0408	−1.24331
$987$	0.0393989	0.00125408
$988$	37.6984	1.19935
$989$	0.335113	0.0106560
$990$	3.25881	0.103572
$991$	−18.3602	−0.583231	−0.291615	−	0.956536i	$-0.594193\pi$
$991$	−18.3602	−0.583231	−0.291615	+	0.956536i	$0.594193\pi$
$992$	57.0769	1.81219
$993$	25.4494	0.807613
$994$	1.55207	0.0492286
$995$	4.49837	0.142608
$996$	16.7036	0.529273
$997$	−49.9808	−1.58291	−0.791455	−	0.611228i	$-0.790676\pi$
$997$	−49.9808	−1.58291	−0.791455	+	0.611228i	$0.790676\pi$
$998$	−71.5166	−2.26382
$999$	4.75748	0.150520

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.b.1.20	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.b.1.20	✓	109	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05386 q^{2} -1.85254 q^{3} +2.21834 q^{4} -0.958510 q^{5} +3.80486 q^{6} +0.0563033 q^{7} -0.448438 q^{8} +0.431918 q^{9} +O(q^{10})\)	\(q-2.05386 q^{2} -1.85254 q^{3} +2.21834 q^{4} -0.958510 q^{5} +3.80486 q^{6} +0.0563033 q^{7} -0.448438 q^{8} +0.431918 q^{9} +1.96864 q^{10} +3.83257 q^{11} -4.10957 q^{12} -2.53430 q^{13} -0.115639 q^{14} +1.77568 q^{15} -3.51565 q^{16} +3.80932 q^{17} -0.887100 q^{18} -6.70558 q^{19} -2.12630 q^{20} -0.104304 q^{21} -7.87157 q^{22} -0.340043 q^{23} +0.830751 q^{24} -4.08126 q^{25} +5.20510 q^{26} +4.75748 q^{27} +0.124900 q^{28} +4.99000 q^{29} -3.64700 q^{30} +7.03132 q^{31} +8.11753 q^{32} -7.10001 q^{33} -7.82382 q^{34} -0.0539672 q^{35} +0.958141 q^{36} +1.00000 q^{37} +13.7723 q^{38} +4.69491 q^{39} +0.429832 q^{40} +2.40185 q^{41} +0.214226 q^{42} -0.985503 q^{43} +8.50195 q^{44} -0.413998 q^{45} +0.698400 q^{46} -0.377730 q^{47} +6.51289 q^{48} -6.99683 q^{49} +8.38233 q^{50} -7.05694 q^{51} -5.62194 q^{52} -5.64693 q^{53} -9.77120 q^{54} -3.67356 q^{55} -0.0252485 q^{56} +12.4224 q^{57} -10.2488 q^{58} -9.01439 q^{59} +3.93906 q^{60} -3.77455 q^{61} -14.4413 q^{62} +0.0243184 q^{63} -9.64096 q^{64} +2.42915 q^{65} +14.5824 q^{66} +2.76583 q^{67} +8.45037 q^{68} +0.629944 q^{69} +0.110841 q^{70} -13.4217 q^{71} -0.193689 q^{72} +8.50848 q^{73} -2.05386 q^{74} +7.56071 q^{75} -14.8753 q^{76} +0.215787 q^{77} -9.64268 q^{78} +5.69589 q^{79} +3.36978 q^{80} -10.1092 q^{81} -4.93307 q^{82} -4.06456 q^{83} -0.231382 q^{84} -3.65127 q^{85} +2.02409 q^{86} -9.24419 q^{87} -1.71867 q^{88} +7.77938 q^{89} +0.850293 q^{90} -0.142690 q^{91} -0.754330 q^{92} -13.0258 q^{93} +0.775805 q^{94} +6.42736 q^{95} -15.0381 q^{96} -0.109519 q^{97} +14.3705 q^{98} +1.65536 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * q^99

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