LMFDB - Embedded newform 1502.2.a.g.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, 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("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + \cdots + 864 $ x^16 - 3x^15 - 25x^14 + 59x^13 + 273x^12 - 443x^11 - 1620x^10 + 1595x^9 + 5490x^8 - 2787x^7 - 10540x^6 + 1919x^5 + 10822x^4 + 132x^3 - 5202x^2 - 408*x + 864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.11488$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.11488 q^{3} +1.00000 q^{4} -1.27093 q^{5} +2.11488 q^{6} +2.13923 q^{7} +1.00000 q^{8} +1.47271 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.11488 q^{3} +1.00000 q^{4} -1.27093 q^{5} +2.11488 q^{6} +2.13923 q^{7} +1.00000 q^{8} +1.47271 q^{9} -1.27093 q^{10} +4.19810 q^{11} +2.11488 q^{12} -4.74654 q^{13} +2.13923 q^{14} -2.68787 q^{15} +1.00000 q^{16} +0.786096 q^{17} +1.47271 q^{18} +2.45197 q^{19} -1.27093 q^{20} +4.52421 q^{21} +4.19810 q^{22} +3.93297 q^{23} +2.11488 q^{24} -3.38473 q^{25} -4.74654 q^{26} -3.23003 q^{27} +2.13923 q^{28} +9.32923 q^{29} -2.68787 q^{30} +8.02354 q^{31} +1.00000 q^{32} +8.87847 q^{33} +0.786096 q^{34} -2.71882 q^{35} +1.47271 q^{36} +2.00613 q^{37} +2.45197 q^{38} -10.0384 q^{39} -1.27093 q^{40} +3.68588 q^{41} +4.52421 q^{42} -9.71318 q^{43} +4.19810 q^{44} -1.87172 q^{45} +3.93297 q^{46} -9.05334 q^{47} +2.11488 q^{48} -2.42369 q^{49} -3.38473 q^{50} +1.66250 q^{51} -4.74654 q^{52} -1.37283 q^{53} -3.23003 q^{54} -5.33550 q^{55} +2.13923 q^{56} +5.18562 q^{57} +9.32923 q^{58} -4.83043 q^{59} -2.68787 q^{60} +0.763317 q^{61} +8.02354 q^{62} +3.15047 q^{63} +1.00000 q^{64} +6.03254 q^{65} +8.87847 q^{66} -5.66687 q^{67} +0.786096 q^{68} +8.31774 q^{69} -2.71882 q^{70} -15.5110 q^{71} +1.47271 q^{72} +12.4729 q^{73} +2.00613 q^{74} -7.15829 q^{75} +2.45197 q^{76} +8.98070 q^{77} -10.0384 q^{78} -3.24441 q^{79} -1.27093 q^{80} -11.2493 q^{81} +3.68588 q^{82} +10.1043 q^{83} +4.52421 q^{84} -0.999075 q^{85} -9.71318 q^{86} +19.7302 q^{87} +4.19810 q^{88} -10.3286 q^{89} -1.87172 q^{90} -10.1540 q^{91} +3.93297 q^{92} +16.9688 q^{93} -9.05334 q^{94} -3.11629 q^{95} +2.11488 q^{96} -7.89685 q^{97} -2.42369 q^{98} +6.18258 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * 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
$3$	2.11488	1.22103	0.610513	−	0.792006i	$-0.290963\pi$
$3$	2.11488	1.22103	0.610513	+	0.792006i	$0.290963\pi$
$4$	1.00000	0.500000
$5$	−1.27093	−0.568378	−0.284189	−	0.958768i	$-0.591724\pi$
$5$	−1.27093	−0.568378	−0.284189	+	0.958768i	$0.591724\pi$
$6$	2.11488	0.863396
$7$	2.13923	0.808553	0.404277	−	0.914637i	$-0.367523\pi$
$7$	2.13923	0.808553	0.404277	+	0.914637i	$0.367523\pi$
$8$	1.00000	0.353553
$9$	1.47271	0.490904
$10$	−1.27093	−0.401904
$11$	4.19810	1.26577	0.632887	−	0.774244i	$-0.281870\pi$
$11$	4.19810	1.26577	0.632887	+	0.774244i	$0.281870\pi$
$12$	2.11488	0.610513
$13$	−4.74654	−1.31645	−0.658227	−	0.752819i	$-0.728693\pi$
$13$	−4.74654	−1.31645	−0.658227	+	0.752819i	$0.728693\pi$
$14$	2.13923	0.571733
$15$	−2.68787	−0.694005
$16$	1.00000	0.250000
$17$	0.786096	0.190656	0.0953281	−	0.995446i	$-0.469610\pi$
$17$	0.786096	0.190656	0.0953281	+	0.995446i	$0.469610\pi$
$18$	1.47271	0.347121
$19$	2.45197	0.562521	0.281261	−	0.959631i	$-0.409247\pi$
$19$	2.45197	0.562521	0.281261	+	0.959631i	$0.409247\pi$
$20$	−1.27093	−0.284189
$21$	4.52421	0.987264
$22$	4.19810	0.895037
$23$	3.93297	0.820080	0.410040	−	0.912068i	$-0.365515\pi$
$23$	3.93297	0.820080	0.410040	+	0.912068i	$0.365515\pi$
$24$	2.11488	0.431698
$25$	−3.38473	−0.676946
$26$	−4.74654	−0.930874
$27$	−3.23003	−0.621620
$28$	2.13923	0.404277
$29$	9.32923	1.73239	0.866197	−	0.499702i	$-0.166557\pi$
$29$	9.32923	1.73239	0.866197	+	0.499702i	$0.166557\pi$
$30$	−2.68787	−0.490735
$31$	8.02354	1.44107	0.720535	−	0.693418i	$-0.243896\pi$
$31$	8.02354	1.44107	0.720535	+	0.693418i	$0.243896\pi$
$32$	1.00000	0.176777
$33$	8.87847	1.54554
$34$	0.786096	0.134814
$35$	−2.71882	−0.459564
$36$	1.47271	0.245452
$37$	2.00613	0.329806	0.164903	−	0.986310i	$-0.447269\pi$
$37$	2.00613	0.329806	0.164903	+	0.986310i	$0.447269\pi$
$38$	2.45197	0.397762
$39$	−10.0384	−1.60742
$40$	−1.27093	−0.200952
$41$	3.68588	0.575638	0.287819	−	0.957685i	$-0.407070\pi$
$41$	3.68588	0.575638	0.287819	+	0.957685i	$0.407070\pi$
$42$	4.52421	0.698101
$43$	−9.71318	−1.48125	−0.740623	−	0.671921i	$-0.765469\pi$
$43$	−9.71318	−1.48125	−0.740623	+	0.671921i	$0.765469\pi$
$44$	4.19810	0.632887
$45$	−1.87172	−0.279019
$46$	3.93297	0.579884
$47$	−9.05334	−1.32057	−0.660283	−	0.751017i	$-0.729564\pi$
$47$	−9.05334	−1.32057	−0.660283	+	0.751017i	$0.729564\pi$
$48$	2.11488	0.305256
$49$	−2.42369	−0.346242
$50$	−3.38473	−0.478673
$51$	1.66250	0.232796
$52$	−4.74654	−0.658227
$53$	−1.37283	−0.188573	−0.0942865	−	0.995545i	$-0.530057\pi$
$53$	−1.37283	−0.188573	−0.0942865	+	0.995545i	$0.530057\pi$
$54$	−3.23003	−0.439551
$55$	−5.33550	−0.719439
$56$	2.13923	0.285867
$57$	5.18562	0.686853
$58$	9.32923	1.22499
$59$	−4.83043	−0.628868	−0.314434	−	0.949279i	$-0.601815\pi$
$59$	−4.83043	−0.628868	−0.314434	+	0.949279i	$0.601815\pi$
$60$	−2.68787	−0.347002
$61$	0.763317	0.0977327	0.0488664	−	0.998805i	$-0.484439\pi$
$61$	0.763317	0.0977327	0.0488664	+	0.998805i	$0.484439\pi$
$62$	8.02354	1.01899
$63$	3.15047	0.396922
$64$	1.00000	0.125000
$65$	6.03254	0.748244
$66$	8.87847	1.09286
$67$	−5.66687	−0.692318	−0.346159	−	0.938176i	$-0.612514\pi$
$67$	−5.66687	−0.692318	−0.346159	+	0.938176i	$0.612514\pi$
$68$	0.786096	0.0953281
$69$	8.31774	1.00134
$70$	−2.71882	−0.324961
$71$	−15.5110	−1.84082	−0.920411	−	0.390952i	$-0.872146\pi$
$71$	−15.5110	−1.84082	−0.920411	+	0.390952i	$0.872146\pi$
$72$	1.47271	0.173561
$73$	12.4729	1.45984	0.729922	−	0.683530i	$-0.239556\pi$
$73$	12.4729	1.45984	0.729922	+	0.683530i	$0.239556\pi$
$74$	2.00613	0.233208
$75$	−7.15829	−0.826568
$76$	2.45197	0.281261
$77$	8.98070	1.02345
$78$	−10.0384	−1.13662
$79$	−3.24441	−0.365024	−0.182512	−	0.983204i	$-0.558423\pi$
$79$	−3.24441	−0.365024	−0.182512	+	0.983204i	$0.558423\pi$
$80$	−1.27093	−0.142095
$81$	−11.2493	−1.24992
$82$	3.68588	0.407038
$83$	10.1043	1.10909	0.554544	−	0.832155i	$-0.312893\pi$
$83$	10.1043	1.10909	0.554544	+	0.832155i	$0.312893\pi$
$84$	4.52421	0.493632
$85$	−0.999075	−0.108365
$86$	−9.71318	−1.04740
$87$	19.7302	2.11530
$88$	4.19810	0.447519
$89$	−10.3286	−1.09483	−0.547415	−	0.836861i	$-0.684388\pi$
$89$	−10.3286	−1.09483	−0.547415	+	0.836861i	$0.684388\pi$
$90$	−1.87172	−0.197296
$91$	−10.1540	−1.06442
$92$	3.93297	0.410040
$93$	16.9688	1.75958
$94$	−9.05334	−0.933781
$95$	−3.11629	−0.319725
$96$	2.11488	0.215849
$97$	−7.89685	−0.801804	−0.400902	−	0.916121i	$-0.631303\pi$
$97$	−7.89685	−0.801804	−0.400902	+	0.916121i	$0.631303\pi$
$98$	−2.42369	−0.244830
$99$	6.18258	0.621373
$100$	−3.38473	−0.338473
$101$	−4.01048	−0.399058	−0.199529	−	0.979892i	$-0.563941\pi$
$101$	−4.01048	−0.399058	−0.199529	+	0.979892i	$0.563941\pi$
$102$	1.66250	0.164612
$103$	11.1968	1.10325	0.551626	−	0.834092i	$-0.314008\pi$
$103$	11.1968	1.10325	0.551626	+	0.834092i	$0.314008\pi$
$104$	−4.74654	−0.465437
$105$	−5.74997	−0.561140
$106$	−1.37283	−0.133341
$107$	0.144693	0.0139880	0.00699402	−	0.999976i	$-0.497774\pi$
$107$	0.144693	0.0139880	0.00699402	+	0.999976i	$0.497774\pi$
$108$	−3.23003	−0.310810
$109$	−3.06972	−0.294026	−0.147013	−	0.989135i	$-0.546966\pi$
$109$	−3.06972	−0.294026	−0.147013	+	0.989135i	$0.546966\pi$
$110$	−5.33550	−0.508720
$111$	4.24273	0.402702
$112$	2.13923	0.202138
$113$	−2.15869	−0.203072	−0.101536	−	0.994832i	$-0.532376\pi$
$113$	−2.15869	−0.203072	−0.101536	+	0.994832i	$0.532376\pi$
$114$	5.18562	0.485678
$115$	−4.99853	−0.466116
$116$	9.32923	0.866197
$117$	−6.99029	−0.646252
$118$	−4.83043	−0.444677
$119$	1.68164	0.154156
$120$	−2.68787	−0.245368
$121$	6.62402	0.602183
$122$	0.763317	0.0691075
$123$	7.79520	0.702869
$124$	8.02354	0.720535
$125$	10.6564	0.953140
$126$	3.15047	0.280666
$127$	19.2496	1.70812	0.854061	−	0.520172i	$-0.174132\pi$
$127$	19.2496	1.70812	0.854061	+	0.520172i	$0.174132\pi$
$128$	1.00000	0.0883883
$129$	−20.5422	−1.80864
$130$	6.03254	0.529089
$131$	1.79303	0.156658	0.0783289	−	0.996928i	$-0.475042\pi$
$131$	1.79303	0.156658	0.0783289	+	0.996928i	$0.475042\pi$
$132$	8.87847	0.772771
$133$	5.24533	0.454828
$134$	−5.66687	−0.489543
$135$	4.10515	0.353315
$136$	0.786096	0.0674071
$137$	−15.7401	−1.34477	−0.672385	−	0.740202i	$-0.734730\pi$
$137$	−15.7401	−1.34477	−0.672385	+	0.740202i	$0.734730\pi$
$138$	8.31774	0.708053
$139$	−15.0711	−1.27831	−0.639157	−	0.769076i	$-0.720717\pi$
$139$	−15.0711	−1.27831	−0.639157	+	0.769076i	$0.720717\pi$
$140$	−2.71882	−0.229782
$141$	−19.1467	−1.61244
$142$	−15.5110	−1.30166
$143$	−19.9265	−1.66633
$144$	1.47271	0.122726
$145$	−11.8568	−0.984656
$146$	12.4729	1.03227
$147$	−5.12582	−0.422770
$148$	2.00613	0.164903
$149$	3.17614	0.260199	0.130100	−	0.991501i	$-0.458470\pi$
$149$	3.17614	0.260199	0.130100	+	0.991501i	$0.458470\pi$
$150$	−7.15829	−0.584472
$151$	−7.51244	−0.611354	−0.305677	−	0.952135i	$-0.598883\pi$
$151$	−7.51244	−0.611354	−0.305677	+	0.952135i	$0.598883\pi$
$152$	2.45197	0.198881
$153$	1.15769	0.0935938
$154$	8.98070	0.723685
$155$	−10.1974	−0.819073
$156$	−10.0384	−0.803712
$157$	18.1005	1.44457	0.722287	−	0.691593i	$-0.243091\pi$
$157$	18.1005	1.44457	0.722287	+	0.691593i	$0.243091\pi$
$158$	−3.24441	−0.258111
$159$	−2.90337	−0.230253
$160$	−1.27093	−0.100476
$161$	8.41352	0.663078
$162$	−11.2493	−0.883825
$163$	−12.9063	−1.01090	−0.505450	−	0.862856i	$-0.668674\pi$
$163$	−12.9063	−1.01090	−0.505450	+	0.862856i	$0.668674\pi$
$164$	3.68588	0.287819
$165$	−11.2839	−0.878453
$166$	10.1043	0.784243
$167$	−17.0474	−1.31917	−0.659584	−	0.751631i	$-0.729267\pi$
$167$	−17.0474	−1.31917	−0.659584	+	0.751631i	$0.729267\pi$
$168$	4.52421	0.349051
$169$	9.52968	0.733052
$170$	−0.999075	−0.0766255
$171$	3.61105	0.276144
$172$	−9.71318	−0.740623
$173$	20.1624	1.53292	0.766461	−	0.642291i	$-0.222016\pi$
$173$	20.1624	1.53292	0.766461	+	0.642291i	$0.222016\pi$
$174$	19.7302	1.49574
$175$	−7.24072	−0.547347
$176$	4.19810	0.316443
$177$	−10.2158	−0.767865
$178$	−10.3286	−0.774162
$179$	−22.1302	−1.65409	−0.827043	−	0.562139i	$-0.809979\pi$
$179$	−22.1302	−1.65409	−0.827043	+	0.562139i	$0.809979\pi$
$180$	−1.87172	−0.139510
$181$	−6.67057	−0.495819	−0.247910	−	0.968783i	$-0.579744\pi$
$181$	−6.67057	−0.495819	−0.247910	+	0.968783i	$0.579744\pi$
$182$	−10.1540	−0.752661
$183$	1.61432	0.119334
$184$	3.93297	0.289942
$185$	−2.54966	−0.187455
$186$	16.9688	1.24421
$187$	3.30011	0.241328
$188$	−9.05334	−0.660283
$189$	−6.90978	−0.502612
$190$	−3.11629	−0.226080
$191$	−18.1251	−1.31148	−0.655742	−	0.754985i	$-0.727644\pi$
$191$	−18.1251	−1.31148	−0.655742	+	0.754985i	$0.727644\pi$
$192$	2.11488	0.152628
$193$	5.28190	0.380200	0.190100	−	0.981765i	$-0.439119\pi$
$193$	5.28190	0.380200	0.190100	+	0.981765i	$0.439119\pi$
$194$	−7.89685	−0.566961
$195$	12.7581	0.913626
$196$	−2.42369	−0.173121
$197$	−23.0555	−1.64264	−0.821319	−	0.570469i	$-0.806761\pi$
$197$	−23.0555	−1.64264	−0.821319	+	0.570469i	$0.806761\pi$
$198$	6.18258	0.439377
$199$	25.6445	1.81789	0.908946	−	0.416915i	$-0.136889\pi$
$199$	25.6445	1.81789	0.908946	+	0.416915i	$0.136889\pi$
$200$	−3.38473	−0.239337
$201$	−11.9847	−0.845338
$202$	−4.01048	−0.282177
$203$	19.9574	1.40073
$204$	1.66250	0.116398
$205$	−4.68451	−0.327180
$206$	11.1968	0.780117
$207$	5.79212	0.402580
$208$	−4.74654	−0.329114
$209$	10.2936	0.712025
$210$	−5.74997	−0.396786
$211$	−5.09872	−0.351010	−0.175505	−	0.984479i	$-0.556156\pi$
$211$	−5.09872	−0.351010	−0.175505	+	0.984479i	$0.556156\pi$
$212$	−1.37283	−0.0942865
$213$	−32.8040	−2.24769
$214$	0.144693	0.00989103
$215$	12.3448	0.841908
$216$	−3.23003	−0.219776
$217$	17.1642	1.16518
$218$	−3.06972	−0.207908
$219$	26.3787	1.78251
$220$	−5.33550	−0.359719
$221$	−3.73124	−0.250990
$222$	4.24273	0.284753
$223$	26.8551	1.79835	0.899174	−	0.437591i	$-0.144168\pi$
$223$	26.8551	1.79835	0.899174	+	0.437591i	$0.144168\pi$
$224$	2.13923	0.142933
$225$	−4.98473	−0.332315
$226$	−2.15869	−0.143594
$227$	−0.269108	−0.0178613	−0.00893067	−	0.999960i	$-0.502843\pi$
$227$	−0.269108	−0.0178613	−0.00893067	+	0.999960i	$0.502843\pi$
$228$	5.18562	0.343426
$229$	8.53224	0.563826	0.281913	−	0.959440i	$-0.409031\pi$
$229$	8.53224	0.563826	0.281913	+	0.959440i	$0.409031\pi$
$230$	−4.99853	−0.329594
$231$	18.9931	1.24965
$232$	9.32923	0.612494
$233$	1.70821	0.111909	0.0559543	−	0.998433i	$-0.482180\pi$
$233$	1.70821	0.111909	0.0559543	+	0.998433i	$0.482180\pi$
$234$	−6.99029	−0.456969
$235$	11.5062	0.750581
$236$	−4.83043	−0.314434
$237$	−6.86153	−0.445704
$238$	1.68164	0.109004
$239$	−28.1154	−1.81864	−0.909318	−	0.416101i	$-0.863396\pi$
$239$	−28.1154	−1.81864	−0.909318	+	0.416101i	$0.863396\pi$
$240$	−2.68787	−0.173501
$241$	−20.7039	−1.33365	−0.666827	−	0.745212i	$-0.732348\pi$
$241$	−20.7039	−1.33365	−0.666827	+	0.745212i	$0.732348\pi$
$242$	6.62402	0.425808
$243$	−14.1007	−0.904561
$244$	0.763317	0.0488664
$245$	3.08035	0.196796
$246$	7.79520	0.497004
$247$	−11.6384	−0.740533
$248$	8.02354	0.509495
$249$	21.3693	1.35422
$250$	10.6564	0.673972
$251$	14.2233	0.897766	0.448883	−	0.893590i	$-0.351822\pi$
$251$	14.2233	0.897766	0.448883	+	0.893590i	$0.351822\pi$
$252$	3.15047	0.198461
$253$	16.5110	1.03804
$254$	19.2496	1.20782
$255$	−2.11292	−0.132316
$256$	1.00000	0.0625000
$257$	−6.63428	−0.413835	−0.206917	−	0.978358i	$-0.566343\pi$
$257$	−6.63428	−0.413835	−0.206917	+	0.978358i	$0.566343\pi$
$258$	−20.5422	−1.27890
$259$	4.29158	0.266666
$260$	6.03254	0.374122
$261$	13.7393	0.850439
$262$	1.79303	0.110774
$263$	−17.5473	−1.08201	−0.541005	−	0.841019i	$-0.681956\pi$
$263$	−17.5473	−1.08201	−0.541005	+	0.841019i	$0.681956\pi$
$264$	8.87847	0.546432
$265$	1.74478	0.107181
$266$	5.24533	0.321612
$267$	−21.8438	−1.33682
$268$	−5.66687	−0.346159
$269$	−18.5881	−1.13334	−0.566669	−	0.823946i	$-0.691768\pi$
$269$	−18.5881	−1.13334	−0.566669	+	0.823946i	$0.691768\pi$
$270$	4.10515	0.249832
$271$	26.3525	1.60080	0.800399	−	0.599468i	$-0.204621\pi$
$271$	26.3525	1.60080	0.800399	+	0.599468i	$0.204621\pi$
$272$	0.786096	0.0476640
$273$	−21.4744	−1.29969
$274$	−15.7401	−0.950896
$275$	−14.2094	−0.856860
$276$	8.31774	0.500669
$277$	8.48577	0.509861	0.254930	−	0.966959i	$-0.417947\pi$
$277$	8.48577	0.509861	0.254930	+	0.966959i	$0.417947\pi$
$278$	−15.0711	−0.903905
$279$	11.8164	0.707427
$280$	−2.71882	−0.162480
$281$	2.61324	0.155893	0.0779466	−	0.996958i	$-0.475164\pi$
$281$	2.61324	0.155893	0.0779466	+	0.996958i	$0.475164\pi$
$282$	−19.1467	−1.14017
$283$	9.03258	0.536931	0.268466	−	0.963289i	$-0.413483\pi$
$283$	9.03258	0.536931	0.268466	+	0.963289i	$0.413483\pi$
$284$	−15.5110	−0.920411
$285$	−6.59058	−0.390392
$286$	−19.9265	−1.17828
$287$	7.88495	0.465434
$288$	1.47271	0.0867803
$289$	−16.3821	−0.963650
$290$	−11.8568	−0.696257
$291$	−16.7009	−0.979023
$292$	12.4729	0.729922
$293$	21.8948	1.27911	0.639553	−	0.768747i	$-0.279119\pi$
$293$	21.8948	1.27911	0.639553	+	0.768747i	$0.279119\pi$
$294$	−5.12582	−0.298944
$295$	6.13915	0.357435
$296$	2.00613	0.116604
$297$	−13.5600	−0.786830
$298$	3.17614	0.183989
$299$	−18.6680	−1.07960
$300$	−7.15829	−0.413284
$301$	−20.7787	−1.19767
$302$	−7.51244	−0.432293
$303$	−8.48168	−0.487260
$304$	2.45197	0.140630
$305$	−0.970125	−0.0555492
$306$	1.15769	0.0661808
$307$	1.96217	0.111987	0.0559935	−	0.998431i	$-0.482167\pi$
$307$	1.96217	0.111987	0.0559935	+	0.998431i	$0.482167\pi$
$308$	8.98070	0.511723
$309$	23.6798	1.34710
$310$	−10.1974	−0.579172
$311$	−10.5492	−0.598191	−0.299095	−	0.954223i	$-0.596685\pi$
$311$	−10.5492	−0.598191	−0.299095	+	0.954223i	$0.596685\pi$
$312$	−10.0384	−0.568310
$313$	25.8604	1.46172	0.730858	−	0.682529i	$-0.239120\pi$
$313$	25.8604	1.46172	0.730858	+	0.682529i	$0.239120\pi$
$314$	18.1005	1.02147
$315$	−4.00403	−0.225602
$316$	−3.24441	−0.182512
$317$	11.4450	0.642817	0.321408	−	0.946941i	$-0.395844\pi$
$317$	11.4450	0.642817	0.321408	+	0.946941i	$0.395844\pi$
$318$	−2.90337	−0.162813
$319$	39.1650	2.19282
$320$	−1.27093	−0.0710473
$321$	0.306009	0.0170797
$322$	8.41352	0.468867
$323$	1.92748	0.107248
$324$	−11.2493	−0.624959
$325$	16.0658	0.891168
$326$	−12.9063	−0.714815
$327$	−6.49208	−0.359013
$328$	3.68588	0.203519
$329$	−19.3672	−1.06775
$330$	−11.2839	−0.621160
$331$	1.43248	0.0787362	0.0393681	−	0.999225i	$-0.487466\pi$
$331$	1.43248	0.0787362	0.0393681	+	0.999225i	$0.487466\pi$
$332$	10.1043	0.554544
$333$	2.95445	0.161903
$334$	−17.0474	−0.932792
$335$	7.20221	0.393499
$336$	4.52421	0.246816
$337$	18.1296	0.987582	0.493791	−	0.869581i	$-0.335611\pi$
$337$	18.1296	0.987582	0.493791	+	0.869581i	$0.335611\pi$
$338$	9.52968	0.518346
$339$	−4.56536	−0.247957
$340$	−0.999075	−0.0541824
$341$	33.6836	1.82407
$342$	3.61105	0.195263
$343$	−20.1595	−1.08851
$344$	−9.71318	−0.523699
$345$	−10.5713	−0.569139
$346$	20.1624	1.08394
$347$	22.6298	1.21483	0.607417	−	0.794384i	$-0.292206\pi$
$347$	22.6298	1.21483	0.607417	+	0.794384i	$0.292206\pi$
$348$	19.7302	1.05765
$349$	5.47597	0.293122	0.146561	−	0.989202i	$-0.453180\pi$
$349$	5.47597	0.293122	0.146561	+	0.989202i	$0.453180\pi$
$350$	−7.24072	−0.387033
$351$	15.3315	0.818334
$352$	4.19810	0.223759
$353$	−23.1167	−1.23038	−0.615189	−	0.788380i	$-0.710920\pi$
$353$	−23.1167	−1.23038	−0.615189	+	0.788380i	$0.710920\pi$
$354$	−10.2158	−0.542962
$355$	19.7135	1.04628
$356$	−10.3286	−0.547415
$357$	3.55646	0.188228
$358$	−22.1302	−1.16962
$359$	10.5594	0.557304	0.278652	−	0.960392i	$-0.410112\pi$
$359$	10.5594	0.557304	0.278652	+	0.960392i	$0.410112\pi$
$360$	−1.87172	−0.0986482
$361$	−12.9878	−0.683570
$362$	−6.67057	−0.350597
$363$	14.0090	0.735281
$364$	−10.1540	−0.532212
$365$	−15.8522	−0.829744
$366$	1.61432	0.0843820
$367$	10.9262	0.570343	0.285171	−	0.958477i	$-0.407950\pi$
$367$	10.9262	0.570343	0.285171	+	0.958477i	$0.407950\pi$
$368$	3.93297	0.205020
$369$	5.42824	0.282583
$370$	−2.54966	−0.132550
$371$	−2.93681	−0.152471
$372$	16.9688	0.879792
$373$	8.91405	0.461552	0.230776	−	0.973007i	$-0.425874\pi$
$373$	8.91405	0.461552	0.230776	+	0.973007i	$0.425874\pi$
$374$	3.30011	0.170644
$375$	22.5371	1.16381
$376$	−9.05334	−0.466890
$377$	−44.2816	−2.28062
$378$	−6.90978	−0.355401
$379$	−1.41748	−0.0728110	−0.0364055	−	0.999337i	$-0.511591\pi$
$379$	−1.41748	−0.0728110	−0.0364055	+	0.999337i	$0.511591\pi$
$380$	−3.11629	−0.159862
$381$	40.7105	2.08566
$382$	−18.1251	−0.927359
$383$	29.2482	1.49451	0.747256	−	0.664537i	$-0.231371\pi$
$383$	29.2482	1.49451	0.747256	+	0.664537i	$0.231371\pi$
$384$	2.11488	0.107924
$385$	−11.4139	−0.581704
$386$	5.28190	0.268842
$387$	−14.3047	−0.727149
$388$	−7.89685	−0.400902
$389$	−32.9653	−1.67141	−0.835704	−	0.549181i	$-0.814940\pi$
$389$	−32.9653	−1.67141	−0.835704	+	0.549181i	$0.814940\pi$
$390$	12.7581	0.646031
$391$	3.09169	0.156353
$392$	−2.42369	−0.122415
$393$	3.79204	0.191283
$394$	−23.0555	−1.16152
$395$	4.12342	0.207472
$396$	6.18258	0.310687
$397$	9.67467	0.485558	0.242779	−	0.970082i	$-0.421941\pi$
$397$	9.67467	0.485558	0.242779	+	0.970082i	$0.421941\pi$
$398$	25.6445	1.28544
$399$	11.0932	0.555357
$400$	−3.38473	−0.169236
$401$	27.8668	1.39160	0.695802	−	0.718234i	$-0.255049\pi$
$401$	27.8668	1.39160	0.695802	+	0.718234i	$0.255049\pi$
$402$	−11.9847	−0.597745
$403$	−38.0841	−1.89710
$404$	−4.01048	−0.199529
$405$	14.2970	0.710426
$406$	19.9574	0.990468
$407$	8.42194	0.417460
$408$	1.66250	0.0823058
$409$	−31.6511	−1.56505	−0.782524	−	0.622621i	$-0.786068\pi$
$409$	−31.6511	−1.56505	−0.782524	+	0.622621i	$0.786068\pi$
$410$	−4.68451	−0.231352
$411$	−33.2885	−1.64200
$412$	11.1968	0.551626
$413$	−10.3334	−0.508474
$414$	5.79212	0.284667
$415$	−12.8418	−0.630382
$416$	−4.74654	−0.232718
$417$	−31.8736	−1.56086
$418$	10.2936	0.503477
$419$	−29.3740	−1.43502	−0.717508	−	0.696550i	$-0.754717\pi$
$419$	−29.3740	−1.43502	−0.717508	+	0.696550i	$0.754717\pi$
$420$	−5.74997	−0.280570
$421$	−11.7752	−0.573886	−0.286943	−	0.957948i	$-0.592639\pi$
$421$	−11.7752	−0.573886	−0.286943	+	0.957948i	$0.592639\pi$
$422$	−5.09872	−0.248202
$423$	−13.3330	−0.648271
$424$	−1.37283	−0.0666706
$425$	−2.66072	−0.129064
$426$	−32.8040	−1.58936
$427$	1.63291	0.0790221
$428$	0.144693	0.00699402
$429$	−42.1420	−2.03464
$430$	12.3448	0.595319
$431$	−18.2362	−0.878405	−0.439203	−	0.898388i	$-0.644739\pi$
$431$	−18.2362	−0.878405	−0.439203	+	0.898388i	$0.644739\pi$
$432$	−3.23003	−0.155405
$433$	35.5400	1.70794	0.853972	−	0.520319i	$-0.174187\pi$
$433$	35.5400	1.70794	0.853972	+	0.520319i	$0.174187\pi$
$434$	17.1642	0.823908
$435$	−25.0757	−1.20229
$436$	−3.06972	−0.147013
$437$	9.64352	0.461312
$438$	26.3787	1.26042
$439$	−38.7866	−1.85118	−0.925591	−	0.378526i	$-0.876431\pi$
$439$	−38.7866	−1.85118	−0.925591	+	0.378526i	$0.876431\pi$
$440$	−5.33550	−0.254360
$441$	−3.56940	−0.169971
$442$	−3.73124	−0.177477
$443$	3.23745	0.153816	0.0769079	−	0.997038i	$-0.475495\pi$
$443$	3.23745	0.153816	0.0769079	+	0.997038i	$0.475495\pi$
$444$	4.24273	0.201351
$445$	13.1270	0.622278
$446$	26.8551	1.27162
$447$	6.71715	0.317710
$448$	2.13923	0.101069
$449$	7.86531	0.371187	0.185594	−	0.982627i	$-0.440579\pi$
$449$	7.86531	0.371187	0.185594	+	0.982627i	$0.440579\pi$
$450$	−4.98473	−0.234982
$451$	15.4737	0.728628
$452$	−2.15869	−0.101536
$453$	−15.8879	−0.746479
$454$	−0.269108	−0.0126299
$455$	12.9050	0.604995
$456$	5.18562	0.242839
$457$	−6.13742	−0.287096	−0.143548	−	0.989643i	$-0.545851\pi$
$457$	−6.13742	−0.287096	−0.143548	+	0.989643i	$0.545851\pi$
$458$	8.53224	0.398685
$459$	−2.53911	−0.118516
$460$	−4.99853	−0.233058
$461$	18.3659	0.855387	0.427694	−	0.903924i	$-0.359326\pi$
$461$	18.3659	0.855387	0.427694	+	0.903924i	$0.359326\pi$
$462$	18.9931	0.883638
$463$	−19.6269	−0.912140	−0.456070	−	0.889944i	$-0.650743\pi$
$463$	−19.6269	−0.912140	−0.456070	+	0.889944i	$0.650743\pi$
$464$	9.32923	0.433099
$465$	−21.5662	−1.00011
$466$	1.70821	0.0791313
$467$	1.29014	0.0597003	0.0298502	−	0.999554i	$-0.490497\pi$
$467$	1.29014	0.0597003	0.0298502	+	0.999554i	$0.490497\pi$
$468$	−6.99029	−0.323126
$469$	−12.1227	−0.559776
$470$	11.5062	0.530741
$471$	38.2803	1.76386
$472$	−4.83043	−0.222339
$473$	−40.7769	−1.87492
$474$	−6.86153	−0.315160
$475$	−8.29926	−0.380796
$476$	1.68164	0.0770778
$477$	−2.02179	−0.0925712
$478$	−28.1154	−1.28597
$479$	−7.56142	−0.345490	−0.172745	−	0.984967i	$-0.555264\pi$
$479$	−7.56142	−0.345490	−0.172745	+	0.984967i	$0.555264\pi$
$480$	−2.68787	−0.122684
$481$	−9.52219	−0.434175
$482$	−20.7039	−0.943036
$483$	17.7936	0.809635
$484$	6.62402	0.301092
$485$	10.0364	0.455728
$486$	−14.1007	−0.639622
$487$	−17.4374	−0.790165	−0.395083	−	0.918646i	$-0.629284\pi$
$487$	−17.4374	−0.790165	−0.395083	+	0.918646i	$0.629284\pi$
$488$	0.763317	0.0345537
$489$	−27.2953	−1.23434
$490$	3.08035	0.139156
$491$	29.0399	1.31055	0.655277	−	0.755389i	$-0.272552\pi$
$491$	29.0399	1.31055	0.655277	+	0.755389i	$0.272552\pi$
$492$	7.79520	0.351435
$493$	7.33367	0.330292
$494$	−11.6384	−0.523636
$495$	−7.85765	−0.353175
$496$	8.02354	0.360268
$497$	−33.1817	−1.48840
$498$	21.3693	0.957581
$499$	14.9748	0.670365	0.335183	−	0.942153i	$-0.391202\pi$
$499$	14.9748	0.670365	0.335183	+	0.942153i	$0.391202\pi$
$500$	10.6564	0.476570
$501$	−36.0532	−1.61074
$502$	14.2233	0.634817
$503$	20.4872	0.913478	0.456739	−	0.889601i	$-0.349017\pi$
$503$	20.4872	0.913478	0.456739	+	0.889601i	$0.349017\pi$
$504$	3.15047	0.140333
$505$	5.09705	0.226816
$506$	16.5110	0.734002
$507$	20.1541	0.895076
$508$	19.2496	0.854061
$509$	12.4720	0.552812	0.276406	−	0.961041i	$-0.410857\pi$
$509$	12.4720	0.552812	0.276406	+	0.961041i	$0.410857\pi$
$510$	−2.11292	−0.0935617
$511$	26.6825	1.18036
$512$	1.00000	0.0441942
$513$	−7.91995	−0.349674
$514$	−6.63428	−0.292625
$515$	−14.2304	−0.627065
$516$	−20.5422	−0.904320
$517$	−38.0068	−1.67154
$518$	4.29158	0.188561
$519$	42.6411	1.87174
$520$	6.03254	0.264544
$521$	9.83035	0.430676	0.215338	−	0.976540i	$-0.430915\pi$
$521$	9.83035	0.430676	0.215338	+	0.976540i	$0.430915\pi$
$522$	13.7393	0.601351
$523$	−13.1909	−0.576800	−0.288400	−	0.957510i	$-0.593123\pi$
$523$	−13.1909	−0.576800	−0.288400	+	0.957510i	$0.593123\pi$
$524$	1.79303	0.0783289
$525$	−15.3132	−0.668324
$526$	−17.5473	−0.765097
$527$	6.30727	0.274749
$528$	8.87847	0.386386
$529$	−7.53178	−0.327469
$530$	1.74478	0.0757883
$531$	−7.11383	−0.308714
$532$	5.24533	0.227414
$533$	−17.4952	−0.757802
$534$	−21.8438	−0.945272
$535$	−0.183896	−0.00795050
$536$	−5.66687	−0.244771
$537$	−46.8026	−2.01968
$538$	−18.5881	−0.801390
$539$	−10.1749	−0.438264
$540$	4.10515	0.176658
$541$	14.6067	0.627992	0.313996	−	0.949424i	$-0.398332\pi$
$541$	14.6067	0.627992	0.313996	+	0.949424i	$0.398332\pi$
$542$	26.3525	1.13193
$543$	−14.1074	−0.605408
$544$	0.786096	0.0337036
$545$	3.90141	0.167118
$546$	−21.4744	−0.919018
$547$	38.9766	1.66652	0.833259	−	0.552882i	$-0.186472\pi$
$547$	38.9766	1.66652	0.833259	+	0.552882i	$0.186472\pi$
$548$	−15.7401	−0.672385
$549$	1.12415	0.0479774
$550$	−14.2094	−0.605892
$551$	22.8750	0.974509
$552$	8.31774	0.354027
$553$	−6.94054	−0.295142
$554$	8.48577	0.360526
$555$	−5.39222	−0.228887
$556$	−15.0711	−0.639157
$557$	29.1595	1.23553	0.617763	−	0.786364i	$-0.288039\pi$
$557$	29.1595	1.23553	0.617763	+	0.786364i	$0.288039\pi$
$558$	11.8164	0.500226
$559$	46.1040	1.94999
$560$	−2.71882	−0.114891
$561$	6.97932	0.294667
$562$	2.61324	0.110233
$563$	−2.63199	−0.110925	−0.0554625	−	0.998461i	$-0.517663\pi$
$563$	−2.63199	−0.110925	−0.0554625	+	0.998461i	$0.517663\pi$
$564$	−19.1467	−0.806222
$565$	2.74355	0.115422
$566$	9.03258	0.379668
$567$	−24.0647	−1.01062
$568$	−15.5110	−0.650829
$569$	−6.59533	−0.276491	−0.138245	−	0.990398i	$-0.544146\pi$
$569$	−6.59533	−0.276491	−0.138245	+	0.990398i	$0.544146\pi$
$570$	−6.59058	−0.276049
$571$	−7.83090	−0.327713	−0.163856	−	0.986484i	$-0.552393\pi$
$571$	−7.83090	−0.327713	−0.163856	+	0.986484i	$0.552393\pi$
$572$	−19.9265	−0.833167
$573$	−38.3323	−1.60136
$574$	7.88495	0.329112
$575$	−13.3120	−0.555150
$576$	1.47271	0.0613630
$577$	20.9517	0.872230	0.436115	−	0.899891i	$-0.356354\pi$
$577$	20.9517	0.872230	0.436115	+	0.899891i	$0.356354\pi$
$578$	−16.3821	−0.681404
$579$	11.1706	0.464234
$580$	−11.8568	−0.492328
$581$	21.6154	0.896756
$582$	−16.7009	−0.692274
$583$	−5.76328	−0.238691
$584$	12.4729	0.516133
$585$	8.88419	0.367316
$586$	21.8948	0.904465
$587$	12.2812	0.506897	0.253449	−	0.967349i	$-0.418435\pi$
$587$	12.2812	0.506897	0.253449	+	0.967349i	$0.418435\pi$
$588$	−5.12582	−0.211385
$589$	19.6735	0.810632
$590$	6.13915	0.252745
$591$	−48.7596	−2.00570
$592$	2.00613	0.0824515
$593$	22.5190	0.924746	0.462373	−	0.886686i	$-0.346998\pi$
$593$	22.5190	0.924746	0.462373	+	0.886686i	$0.346998\pi$
$594$	−13.5600	−0.556373
$595$	−2.13725	−0.0876187
$596$	3.17614	0.130100
$597$	54.2350	2.21969
$598$	−18.6680	−0.763391
$599$	34.6526	1.41587	0.707934	−	0.706278i	$-0.249627\pi$
$599$	34.6526	1.41587	0.707934	+	0.706278i	$0.249627\pi$
$600$	−7.15829	−0.292236
$601$	−2.83712	−0.115729	−0.0578643	−	0.998324i	$-0.518429\pi$
$601$	−2.83712	−0.115729	−0.0578643	+	0.998324i	$0.518429\pi$
$602$	−20.7787	−0.846878
$603$	−8.34566	−0.339862
$604$	−7.51244	−0.305677
$605$	−8.41868	−0.342268
$606$	−8.48168	−0.344545
$607$	−18.5474	−0.752816	−0.376408	−	0.926454i	$-0.622841\pi$
$607$	−18.5474	−0.752816	−0.376408	+	0.926454i	$0.622841\pi$
$608$	2.45197	0.0994406
$609$	42.2074	1.71033
$610$	−0.970125	−0.0392792
$611$	42.9721	1.73846
$612$	1.15769	0.0467969
$613$	−18.8221	−0.760216	−0.380108	−	0.924942i	$-0.624113\pi$
$613$	−18.8221	−0.760216	−0.380108	+	0.924942i	$0.624113\pi$
$614$	1.96217	0.0791868
$615$	−9.90717	−0.399496
$616$	8.98070	0.361843
$617$	−0.729772	−0.0293795	−0.0146897	−	0.999892i	$-0.504676\pi$
$617$	−0.729772	−0.0293795	−0.0146897	+	0.999892i	$0.504676\pi$
$618$	23.6798	0.952543
$619$	−16.2267	−0.652208	−0.326104	−	0.945334i	$-0.605736\pi$
$619$	−16.2267	−0.652208	−0.326104	+	0.945334i	$0.605736\pi$
$620$	−10.1974	−0.409537
$621$	−12.7036	−0.509778
$622$	−10.5492	−0.422985
$623$	−22.0953	−0.885229
$624$	−10.0384	−0.401856
$625$	3.38004	0.135202
$626$	25.8604	1.03359
$627$	21.7698	0.869400
$628$	18.1005	0.722287
$629$	1.57701	0.0628796
$630$	−4.00403	−0.159525
$631$	29.5561	1.17661	0.588305	−	0.808639i	$-0.299796\pi$
$631$	29.5561	1.17661	0.588305	+	0.808639i	$0.299796\pi$
$632$	−3.24441	−0.129056
$633$	−10.7832	−0.428593
$634$	11.4450	0.454540
$635$	−24.4649	−0.970860
$636$	−2.90337	−0.115126
$637$	11.5042	0.455812
$638$	39.1650	1.55056
$639$	−22.8433	−0.903667
$640$	−1.27093	−0.0502380
$641$	−14.1243	−0.557875	−0.278938	−	0.960309i	$-0.589982\pi$
$641$	−14.1243	−0.557875	−0.278938	+	0.960309i	$0.589982\pi$
$642$	0.306009	0.0120772
$643$	−19.3530	−0.763209	−0.381605	−	0.924326i	$-0.624628\pi$
$643$	−19.3530	−0.763209	−0.381605	+	0.924326i	$0.624628\pi$
$644$	8.41352	0.331539
$645$	26.1077	1.02799
$646$	1.92748	0.0758359
$647$	44.3317	1.74286	0.871430	−	0.490519i	$-0.163193\pi$
$647$	44.3317	1.74286	0.871430	+	0.490519i	$0.163193\pi$
$648$	−11.2493	−0.441912
$649$	−20.2786	−0.796005
$650$	16.0658	0.630151
$651$	36.3002	1.42272
$652$	−12.9063	−0.505450
$653$	19.6220	0.767867	0.383933	−	0.923361i	$-0.374569\pi$
$653$	19.6220	0.767867	0.383933	+	0.923361i	$0.374569\pi$
$654$	−6.49208	−0.253861
$655$	−2.27882	−0.0890410
$656$	3.68588	0.143910
$657$	18.3690	0.716643
$658$	−19.3672	−0.755012
$659$	10.1842	0.396718	0.198359	−	0.980129i	$-0.436439\pi$
$659$	10.1842	0.396718	0.198359	+	0.980129i	$0.436439\pi$
$660$	−11.2839	−0.439227
$661$	49.2996	1.91753	0.958766	−	0.284196i	$-0.0917266\pi$
$661$	49.2996	1.91753	0.958766	+	0.284196i	$0.0917266\pi$
$662$	1.43248	0.0556749
$663$	−7.89111	−0.306465
$664$	10.1043	0.392122
$665$	−6.66647	−0.258515
$666$	2.95445	0.114483
$667$	36.6915	1.42070
$668$	−17.0474	−0.659584
$669$	56.7952	2.19583
$670$	7.20221	0.278246
$671$	3.20448	0.123708
$672$	4.52421	0.174525
$673$	−3.25303	−0.125395	−0.0626976	−	0.998033i	$-0.519970\pi$
$673$	−3.25303	−0.125395	−0.0626976	+	0.998033i	$0.519970\pi$
$674$	18.1296	0.698326
$675$	10.9328	0.420803
$676$	9.52968	0.366526
$677$	−38.9778	−1.49804	−0.749019	−	0.662549i	$-0.769475\pi$
$677$	−38.9778	−1.49804	−0.749019	+	0.662549i	$0.769475\pi$
$678$	−4.56536	−0.175332
$679$	−16.8932	−0.648301
$680$	−0.999075	−0.0383128
$681$	−0.569131	−0.0218092
$682$	33.6836	1.28981
$683$	23.7164	0.907482	0.453741	−	0.891134i	$-0.350089\pi$
$683$	23.7164	0.907482	0.453741	+	0.891134i	$0.350089\pi$
$684$	3.61105	0.138072
$685$	20.0046	0.764338
$686$	−20.1595	−0.769691
$687$	18.0446	0.688446
$688$	−9.71318	−0.370311
$689$	6.51621	0.248248
$690$	−10.5713	−0.402442
$691$	−24.8753	−0.946303	−0.473151	−	0.880981i	$-0.656884\pi$
$691$	−24.8753	−0.946303	−0.473151	+	0.880981i	$0.656884\pi$
$692$	20.1624	0.766461
$693$	13.2260	0.502413
$694$	22.6298	0.859017
$695$	19.1544	0.726567
$696$	19.7302	0.747871
$697$	2.89746	0.109749
$698$	5.47597	0.207268
$699$	3.61266	0.136643
$700$	−7.24072	−0.273673
$701$	23.9703	0.905347	0.452674	−	0.891676i	$-0.350470\pi$
$701$	23.9703	0.905347	0.452674	+	0.891676i	$0.350470\pi$
$702$	15.3315	0.578649
$703$	4.91898	0.185523
$704$	4.19810	0.158222
$705$	24.3342	0.916479
$706$	−23.1167	−0.870008
$707$	−8.57935	−0.322659
$708$	−10.2158	−0.383932
$709$	−3.39277	−0.127418	−0.0637091	−	0.997969i	$-0.520293\pi$
$709$	−3.39277	−0.127418	−0.0637091	+	0.997969i	$0.520293\pi$
$710$	19.7135	0.739834
$711$	−4.77808	−0.179192
$712$	−10.3286	−0.387081
$713$	31.5563	1.18179
$714$	3.55646	0.133097
$715$	25.3252	0.947108
$716$	−22.1302	−0.827043
$717$	−59.4607	−2.22060
$718$	10.5594	0.394074
$719$	31.5154	1.17533	0.587664	−	0.809105i	$-0.300048\pi$
$719$	31.5154	1.17533	0.587664	+	0.809105i	$0.300048\pi$
$720$	−1.87172	−0.0697548
$721$	23.9525	0.892038
$722$	−12.9878	−0.483357
$723$	−43.7862	−1.62843
$724$	−6.67057	−0.247910
$725$	−31.5769	−1.17274
$726$	14.0090	0.519923
$727$	6.57600	0.243890	0.121945	−	0.992537i	$-0.461087\pi$
$727$	6.57600	0.243890	0.121945	+	0.992537i	$0.461087\pi$
$728$	−10.1540	−0.376330
$729$	3.92646	0.145425
$730$	−15.8522	−0.586718
$731$	−7.63549	−0.282409
$732$	1.61432	0.0596671
$733$	0.917979	0.0339063	0.0169532	−	0.999856i	$-0.494603\pi$
$733$	0.917979	0.0339063	0.0169532	+	0.999856i	$0.494603\pi$
$734$	10.9262	0.403293
$735$	6.51457	0.240294
$736$	3.93297	0.144971
$737$	−23.7901	−0.876318
$738$	5.42824	0.199816
$739$	38.0579	1.39998	0.699992	−	0.714151i	$-0.253187\pi$
$739$	38.0579	1.39998	0.699992	+	0.714151i	$0.253187\pi$
$740$	−2.54966	−0.0937273
$741$	−24.6138	−0.904210
$742$	−2.93681	−0.107814
$743$	−42.7894	−1.56979	−0.784895	−	0.619628i	$-0.787283\pi$
$743$	−42.7894	−1.56979	−0.784895	+	0.619628i	$0.787283\pi$
$744$	16.9688	0.622107
$745$	−4.03666	−0.147892
$746$	8.91405	0.326366
$747$	14.8807	0.544455
$748$	3.30011	0.120664
$749$	0.309532	0.0113101
$750$	22.5371	0.822937
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	−9.05334	−0.330141
$753$	30.0805	1.09620
$754$	−44.2816	−1.61264
$755$	9.54781	0.347480
$756$	−6.90978	−0.251306
$757$	49.8891	1.81325	0.906624	−	0.421939i	$-0.138650\pi$
$757$	49.8891	1.81325	0.906624	+	0.421939i	$0.138650\pi$
$758$	−1.41748	−0.0514852
$759$	34.9187	1.26747
$760$	−3.11629	−0.113040
$761$	12.7241	0.461249	0.230625	−	0.973043i	$-0.425923\pi$
$761$	12.7241	0.461249	0.230625	+	0.973043i	$0.425923\pi$
$762$	40.7105	1.47479
$763$	−6.56684	−0.237736
$764$	−18.1251	−0.655742
$765$	−1.47135	−0.0531967
$766$	29.2482	1.05678
$767$	22.9278	0.827877
$768$	2.11488	0.0763141
$769$	4.57505	0.164981	0.0824903	−	0.996592i	$-0.473713\pi$
$769$	4.57505	0.164981	0.0824903	+	0.996592i	$0.473713\pi$
$770$	−11.4139	−0.411327
$771$	−14.0307	−0.505303
$772$	5.28190	0.190100
$773$	29.4698	1.05995	0.529977	−	0.848012i	$-0.322201\pi$
$773$	29.4698	1.05995	0.529977	+	0.848012i	$0.322201\pi$
$774$	−14.3047	−0.514172
$775$	−27.1575	−0.975527
$776$	−7.89685	−0.283481
$777$	9.07617	0.325606
$778$	−32.9653	−1.18186
$779$	9.03769	0.323809
$780$	12.7581	0.456813
$781$	−65.1169	−2.33006
$782$	3.09169	0.110558
$783$	−30.1337	−1.07689
$784$	−2.42369	−0.0865605
$785$	−23.0045	−0.821065
$786$	3.79204	0.135258
$787$	−9.71642	−0.346353	−0.173177	−	0.984891i	$-0.555403\pi$
$787$	−9.71642	−0.346353	−0.173177	+	0.984891i	$0.555403\pi$
$788$	−23.0555	−0.821319
$789$	−37.1103	−1.32116
$790$	4.12342	0.146705
$791$	−4.61793	−0.164195
$792$	6.18258	0.219689
$793$	−3.62312	−0.128661
$794$	9.67467	0.343341
$795$	3.68999	0.130871
$796$	25.6445	0.908946
$797$	−43.7992	−1.55145	−0.775724	−	0.631073i	$-0.782615\pi$
$797$	−43.7992	−1.55145	−0.775724	+	0.631073i	$0.782615\pi$
$798$	11.0932	0.392697
$799$	−7.11679	−0.251774
$800$	−3.38473	−0.119668
$801$	−15.2111	−0.537456
$802$	27.8668	0.984013
$803$	52.3625	1.84783
$804$	−11.9847	−0.422669
$805$	−10.6930	−0.376879
$806$	−38.0841	−1.34145
$807$	−39.3116	−1.38383
$808$	−4.01048	−0.141088
$809$	−39.1365	−1.37597	−0.687983	−	0.725727i	$-0.741503\pi$
$809$	−39.1365	−1.37597	−0.687983	+	0.725727i	$0.741503\pi$
$810$	14.2970	0.502347
$811$	45.4537	1.59610	0.798048	−	0.602594i	$-0.205866\pi$
$811$	45.4537	1.59610	0.798048	+	0.602594i	$0.205866\pi$
$812$	19.9574	0.700367
$813$	55.7322	1.95462
$814$	8.42194	0.295189
$815$	16.4031	0.574574
$816$	1.66250	0.0581990
$817$	−23.8164	−0.833232
$818$	−31.6511	−1.10666
$819$	−14.9538	−0.522529
$820$	−4.68451	−0.163590
$821$	−44.0860	−1.53861	−0.769306	−	0.638881i	$-0.779398\pi$
$821$	−44.0860	−1.53861	−0.769306	+	0.638881i	$0.779398\pi$
$822$	−33.2885	−1.16107
$823$	22.9023	0.798323	0.399161	−	0.916881i	$-0.369301\pi$
$823$	22.9023	0.798323	0.399161	+	0.916881i	$0.369301\pi$
$824$	11.1968	0.390058
$825$	−30.0512	−1.04625
$826$	−10.3334	−0.359545
$827$	32.3006	1.12320	0.561601	−	0.827408i	$-0.310186\pi$
$827$	32.3006	1.12320	0.561601	+	0.827408i	$0.310186\pi$
$828$	5.79212	0.201290
$829$	17.6156	0.611814	0.305907	−	0.952061i	$-0.401040\pi$
$829$	17.6156	0.611814	0.305907	+	0.952061i	$0.401040\pi$
$830$	−12.8418	−0.445747
$831$	17.9464	0.622553
$832$	−4.74654	−0.164557
$833$	−1.90525	−0.0660132
$834$	−31.8736	−1.10369
$835$	21.6661	0.749786
$836$	10.2936	0.356012
$837$	−25.9163	−0.895798
$838$	−29.3740	−1.01471
$839$	52.3356	1.80683	0.903413	−	0.428771i	$-0.141053\pi$
$839$	52.3356	1.80683	0.903413	+	0.428771i	$0.141053\pi$
$840$	−5.74997	−0.198393
$841$	58.0345	2.00119
$842$	−11.7752	−0.405799
$843$	5.52670	0.190349
$844$	−5.09872	−0.175505
$845$	−12.1116	−0.416651
$846$	−13.3330	−0.458397
$847$	14.1703	0.486897
$848$	−1.37283	−0.0471433
$849$	19.1028	0.655607
$850$	−2.66072	−0.0912620
$851$	7.89005	0.270467
$852$	−32.8040	−1.12385
$853$	−8.38608	−0.287134	−0.143567	−	0.989641i	$-0.545857\pi$
$853$	−8.38608	−0.287134	−0.143567	+	0.989641i	$0.545857\pi$
$854$	1.63291	0.0558771
$855$	−4.58940	−0.156954
$856$	0.144693	0.00494552
$857$	2.68336	0.0916618	0.0458309	−	0.998949i	$-0.485406\pi$
$857$	2.68336	0.0916618	0.0458309	+	0.998949i	$0.485406\pi$
$858$	−42.1420	−1.43870
$859$	−34.4319	−1.17480	−0.587400	−	0.809297i	$-0.699848\pi$
$859$	−34.4319	−1.17480	−0.587400	+	0.809297i	$0.699848\pi$
$860$	12.3448	0.420954
$861$	16.6757	0.568307
$862$	−18.2362	−0.621126
$863$	−30.2315	−1.02909	−0.514546	−	0.857463i	$-0.672040\pi$
$863$	−30.2315	−1.02909	−0.514546	+	0.857463i	$0.672040\pi$
$864$	−3.23003	−0.109888
$865$	−25.6251	−0.871279
$866$	35.5400	1.20770
$867$	−34.6461	−1.17664
$868$	17.1642	0.582591
$869$	−13.6203	−0.462038
$870$	−25.0757	−0.850147
$871$	26.8980	0.911405
$872$	−3.06972	−0.103954
$873$	−11.6298	−0.393609
$874$	9.64352	0.326197
$875$	22.7966	0.770664
$876$	26.3787	0.891254
$877$	8.49605	0.286891	0.143446	−	0.989658i	$-0.454182\pi$
$877$	8.49605	0.286891	0.143446	+	0.989658i	$0.454182\pi$
$878$	−38.7866	−1.30898
$879$	46.3048	1.56182
$880$	−5.33550	−0.179860
$881$	−2.87805	−0.0969639	−0.0484819	−	0.998824i	$-0.515438\pi$
$881$	−2.87805	−0.0969639	−0.0484819	+	0.998824i	$0.515438\pi$
$882$	−3.56940	−0.120188
$883$	3.52833	0.118738	0.0593690	−	0.998236i	$-0.481091\pi$
$883$	3.52833	0.118738	0.0593690	+	0.998236i	$0.481091\pi$
$884$	−3.73124	−0.125495
$885$	12.9836	0.436438
$886$	3.23745	0.108764
$887$	9.37322	0.314722	0.157361	−	0.987541i	$-0.449701\pi$
$887$	9.37322	0.314722	0.157361	+	0.987541i	$0.449701\pi$
$888$	4.24273	0.142377
$889$	41.1792	1.38111
$890$	13.1270	0.440017
$891$	−47.2255	−1.58211
$892$	26.8551	0.899174
$893$	−22.1985	−0.742846
$894$	6.71715	0.224655
$895$	28.1259	0.940147
$896$	2.13923	0.0714667
$897$	−39.4805	−1.31822
$898$	7.86531	0.262469
$899$	74.8535	2.49650
$900$	−4.98473	−0.166158
$901$	−1.07918	−0.0359526
$902$	15.4737	0.515218
$903$	−43.9445	−1.46238
$904$	−2.15869	−0.0717969
$905$	8.47784	0.281813
$906$	−15.8879	−0.527840
$907$	55.6775	1.84874	0.924370	−	0.381496i	$-0.124591\pi$
$907$	55.6775	1.84874	0.924370	+	0.381496i	$0.124591\pi$
$908$	−0.269108	−0.00893067
$909$	−5.90628	−0.195899
$910$	12.9050	0.427796
$911$	−46.7581	−1.54917	−0.774583	−	0.632473i	$-0.782040\pi$
$911$	−46.7581	−1.54917	−0.774583	+	0.632473i	$0.782040\pi$
$912$	5.18562	0.171713
$913$	42.4187	1.40385
$914$	−6.13742	−0.203008
$915$	−2.05170	−0.0678270
$916$	8.53224	0.281913
$917$	3.83571	0.126666
$918$	−2.53911	−0.0838032
$919$	−13.1358	−0.433310	−0.216655	−	0.976248i	$-0.569515\pi$
$919$	−13.1358	−0.433310	−0.216655	+	0.976248i	$0.569515\pi$
$920$	−4.99853	−0.164797
$921$	4.14975	0.136739
$922$	18.3659	0.604850
$923$	73.6239	2.42336
$924$	18.9931	0.624827
$925$	−6.79021	−0.223261
$926$	−19.6269	−0.644981
$927$	16.4896	0.541590
$928$	9.32923	0.306247
$929$	7.24104	0.237571	0.118785	−	0.992920i	$-0.462100\pi$
$929$	7.24104	0.237571	0.118785	+	0.992920i	$0.462100\pi$
$930$	−21.5662	−0.707184
$931$	−5.94283	−0.194768
$932$	1.70821	0.0559543
$933$	−22.3103	−0.730406
$934$	1.29014	0.0422145
$935$	−4.19421	−0.137165
$936$	−6.99029	−0.228485
$937$	−26.1168	−0.853197	−0.426599	−	0.904441i	$-0.640288\pi$
$937$	−26.1168	−0.853197	−0.426599	+	0.904441i	$0.640288\pi$
$938$	−12.1227	−0.395821
$939$	54.6916	1.78479
$940$	11.5062	0.375291
$941$	−22.1921	−0.723443	−0.361722	−	0.932286i	$-0.617811\pi$
$941$	−22.1921	−0.723443	−0.361722	+	0.932286i	$0.617811\pi$
$942$	38.2803	1.24724
$943$	14.4965	0.472069
$944$	−4.83043	−0.157217
$945$	8.78187	0.285674
$946$	−40.7769	−1.32577
$947$	−9.19313	−0.298737	−0.149368	−	0.988782i	$-0.547724\pi$
$947$	−9.19313	−0.298737	−0.149368	+	0.988782i	$0.547724\pi$
$948$	−6.86153	−0.222852
$949$	−59.2033	−1.92182
$950$	−8.29926	−0.269264
$951$	24.2048	0.784896
$952$	1.68164	0.0545022
$953$	49.4080	1.60048	0.800241	−	0.599679i	$-0.204705\pi$
$953$	49.4080	1.60048	0.800241	+	0.599679i	$0.204705\pi$
$954$	−2.02179	−0.0654577
$955$	23.0357	0.745419
$956$	−28.1154	−0.909318
$957$	82.8292	2.67749
$958$	−7.56142	−0.244299
$959$	−33.6718	−1.08732
$960$	−2.68787	−0.0867506
$961$	33.3772	1.07668
$962$	−9.52219	−0.307008
$963$	0.213091	0.00686678
$964$	−20.7039	−0.666827
$965$	−6.71294	−0.216097
$966$	17.7936	0.572499
$967$	−37.8915	−1.21851	−0.609254	−	0.792975i	$-0.708531\pi$
$967$	−37.8915	−1.21851	−0.609254	+	0.792975i	$0.708531\pi$
$968$	6.62402	0.212904
$969$	4.07640	0.130953
$970$	10.0364	0.322248
$971$	−15.8497	−0.508641	−0.254321	−	0.967120i	$-0.581852\pi$
$971$	−15.8497	−0.508641	−0.254321	+	0.967120i	$0.581852\pi$
$972$	−14.1007	−0.452281
$973$	−32.2406	−1.03359
$974$	−17.4374	−0.558731
$975$	33.9771	1.08814
$976$	0.763317	0.0244332
$977$	13.0912	0.418825	0.209413	−	0.977827i	$-0.432845\pi$
$977$	13.0912	0.418825	0.209413	+	0.977827i	$0.432845\pi$
$978$	−27.2953	−0.872807
$979$	−43.3605	−1.38581
$980$	3.08035	0.0983982
$981$	−4.52081	−0.144338
$982$	29.0399	0.926701
$983$	−16.5172	−0.526817	−0.263409	−	0.964684i	$-0.584847\pi$
$983$	−16.5172	−0.526817	−0.263409	+	0.964684i	$0.584847\pi$
$984$	7.79520	0.248502
$985$	29.3020	0.933640
$986$	7.33367	0.233552
$987$	−40.9592	−1.30375
$988$	−11.6384	−0.370267
$989$	−38.2016	−1.21474
$990$	−7.85765	−0.249732
$991$	50.7439	1.61193	0.805967	−	0.591960i	$-0.201646\pi$
$991$	50.7439	1.61193	0.805967	+	0.591960i	$0.201646\pi$
$992$	8.02354	0.254748
$993$	3.02952	0.0961389
$994$	−33.1817	−1.05246
$995$	−32.5925	−1.03325
$996$	21.3693	0.677112
$997$	43.5625	1.37964	0.689818	−	0.723982i	$-0.257690\pi$
$997$	43.5625	1.37964	0.689818	+	0.723982i	$0.257690\pi$
$998$	14.9748	0.474020
$999$	−6.47987	−0.205014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.g.1.11	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.g.1.11	✓	16	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.11488 q^{3} +1.00000 q^{4} -1.27093 q^{5} +2.11488 q^{6} +2.13923 q^{7} +1.00000 q^{8} +1.47271 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.11488 q^{3} +1.00000 q^{4} -1.27093 q^{5} +2.11488 q^{6} +2.13923 q^{7} +1.00000 q^{8} +1.47271 q^{9} -1.27093 q^{10} +4.19810 q^{11} +2.11488 q^{12} -4.74654 q^{13} +2.13923 q^{14} -2.68787 q^{15} +1.00000 q^{16} +0.786096 q^{17} +1.47271 q^{18} +2.45197 q^{19} -1.27093 q^{20} +4.52421 q^{21} +4.19810 q^{22} +3.93297 q^{23} +2.11488 q^{24} -3.38473 q^{25} -4.74654 q^{26} -3.23003 q^{27} +2.13923 q^{28} +9.32923 q^{29} -2.68787 q^{30} +8.02354 q^{31} +1.00000 q^{32} +8.87847 q^{33} +0.786096 q^{34} -2.71882 q^{35} +1.47271 q^{36} +2.00613 q^{37} +2.45197 q^{38} -10.0384 q^{39} -1.27093 q^{40} +3.68588 q^{41} +4.52421 q^{42} -9.71318 q^{43} +4.19810 q^{44} -1.87172 q^{45} +3.93297 q^{46} -9.05334 q^{47} +2.11488 q^{48} -2.42369 q^{49} -3.38473 q^{50} +1.66250 q^{51} -4.74654 q^{52} -1.37283 q^{53} -3.23003 q^{54} -5.33550 q^{55} +2.13923 q^{56} +5.18562 q^{57} +9.32923 q^{58} -4.83043 q^{59} -2.68787 q^{60} +0.763317 q^{61} +8.02354 q^{62} +3.15047 q^{63} +1.00000 q^{64} +6.03254 q^{65} +8.87847 q^{66} -5.66687 q^{67} +0.786096 q^{68} +8.31774 q^{69} -2.71882 q^{70} -15.5110 q^{71} +1.47271 q^{72} +12.4729 q^{73} +2.00613 q^{74} -7.15829 q^{75} +2.45197 q^{76} +8.98070 q^{77} -10.0384 q^{78} -3.24441 q^{79} -1.27093 q^{80} -11.2493 q^{81} +3.68588 q^{82} +10.1043 q^{83} +4.52421 q^{84} -0.999075 q^{85} -9.71318 q^{86} +19.7302 q^{87} +4.19810 q^{88} -10.3286 q^{89} -1.87172 q^{90} -10.1540 q^{91} +3.93297 q^{92} +16.9688 q^{93} -9.05334 q^{94} -3.11629 q^{95} +2.11488 q^{96} -7.89685 q^{97} -2.42369 q^{98} +6.18258 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * q^99

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