LMFDB - Embedded newform 103.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [103,2,Mod(1,103)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(103, 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("103.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	103.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:	$0.822459140819$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.6999257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 7x^{3} + 11x^{2} + x - 1 $ x^6 - 2x^5 - 6x^4 + 7x^3 + 11x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.68129$ of defining polynomial
Character	$\chi$	$=$	103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.68129 q^{2} +1.73515 q^{3} +0.826745 q^{4} +1.52866 q^{5} -2.91730 q^{6} -0.782217 q^{7} +1.97258 q^{8} +0.0107559 q^{9} +O(q^{10})$	\(q-1.68129 q^{2} +1.73515 q^{3} +0.826745 q^{4} +1.52866 q^{5} -2.91730 q^{6} -0.782217 q^{7} +1.97258 q^{8} +0.0107559 q^{9} -2.57012 q^{10} +4.82317 q^{11} +1.43453 q^{12} +1.31087 q^{13} +1.31513 q^{14} +2.65245 q^{15} -4.96998 q^{16} +0.699883 q^{17} -0.0180838 q^{18} -3.13508 q^{19} +1.26381 q^{20} -1.35727 q^{21} -8.10917 q^{22} -3.56393 q^{23} +3.42274 q^{24} -2.66321 q^{25} -2.20396 q^{26} -5.18680 q^{27} -0.646694 q^{28} +0.647664 q^{29} -4.45955 q^{30} -9.09774 q^{31} +4.41083 q^{32} +8.36894 q^{33} -1.17671 q^{34} -1.19574 q^{35} +0.00889237 q^{36} -1.31603 q^{37} +5.27099 q^{38} +2.27457 q^{39} +3.01540 q^{40} +1.14403 q^{41} +2.28196 q^{42} +12.4917 q^{43} +3.98754 q^{44} +0.0164420 q^{45} +5.99200 q^{46} -5.79269 q^{47} -8.62368 q^{48} -6.38814 q^{49} +4.47763 q^{50} +1.21440 q^{51} +1.08376 q^{52} +10.2799 q^{53} +8.72052 q^{54} +7.37298 q^{55} -1.54299 q^{56} -5.43985 q^{57} -1.08891 q^{58} -4.01092 q^{59} +2.19290 q^{60} +0.673825 q^{61} +15.2960 q^{62} -0.00841342 q^{63} +2.52407 q^{64} +2.00387 q^{65} -14.0706 q^{66} +6.65710 q^{67} +0.578625 q^{68} -6.18396 q^{69} +2.01039 q^{70} -11.7036 q^{71} +0.0212169 q^{72} +3.39836 q^{73} +2.21263 q^{74} -4.62107 q^{75} -2.59192 q^{76} -3.77277 q^{77} -3.82421 q^{78} -14.5081 q^{79} -7.59740 q^{80} -9.03215 q^{81} -1.92345 q^{82} -4.30580 q^{83} -1.12211 q^{84} +1.06988 q^{85} -21.0022 q^{86} +1.12380 q^{87} +9.51412 q^{88} +17.1403 q^{89} -0.0276439 q^{90} -1.02539 q^{91} -2.94646 q^{92} -15.7860 q^{93} +9.73921 q^{94} -4.79247 q^{95} +7.65346 q^{96} +11.3630 q^{97} +10.7403 q^{98} +0.0518774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 6 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 9 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + 4 * q^2 + 6 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 9 * q^8 + 8 * q^9	\( 6 q + 4 q^{2} + 6 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 9 q^{8} + 8 q^{9} - 10 q^{10} - q^{11} - 13 q^{12} - q^{13} - 9 q^{14} - 9 q^{15} + 2 q^{16} + 21 q^{17} - 3 q^{18} - 7 q^{19} - 9 q^{20} - 14 q^{21} - 11 q^{22} + 12 q^{23} - 36 q^{24} + q^{25} - 5 q^{26} - 10 q^{28} + 12 q^{29} + 2 q^{30} - 16 q^{31} + 27 q^{32} + 15 q^{33} + 10 q^{34} + 5 q^{35} - 3 q^{36} - 8 q^{38} + 5 q^{39} - q^{40} + 14 q^{41} + 25 q^{42} - 6 q^{43} - 4 q^{44} + 8 q^{45} + 19 q^{46} + q^{47} - 41 q^{48} - 2 q^{49} + q^{50} - 5 q^{51} - 5 q^{52} + 19 q^{53} + 23 q^{54} - 10 q^{55} - 13 q^{56} + 23 q^{57} + 4 q^{58} + 3 q^{59} + 17 q^{60} + q^{61} + 23 q^{62} - 20 q^{63} + 61 q^{64} + 23 q^{65} + q^{66} - 12 q^{67} + 14 q^{68} - 22 q^{69} - 14 q^{70} - 27 q^{71} + 31 q^{72} - 7 q^{73} + 15 q^{74} - 17 q^{75} - 38 q^{76} + 27 q^{77} - 20 q^{78} - 21 q^{79} - 28 q^{80} - 2 q^{81} + 53 q^{82} - 9 q^{83} + 61 q^{84} - 9 q^{85} - 11 q^{86} - 12 q^{87} - 31 q^{88} - 14 q^{89} - 22 q^{90} - 33 q^{91} + 30 q^{92} - 32 q^{93} - 6 q^{95} - 33 q^{96} - 8 q^{97} + 2 q^{98} - 54 q^{99}+O(q^{100}) \) 6 * q + 4 * q^2 + 6 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 9 * q^8 + 8 * q^9 - 10 * q^10 - q^11 - 13 * q^12 - q^13 - 9 * q^14 - 9 * q^15 + 2 * q^16 + 21 * q^17 - 3 * q^18 - 7 * q^19 - 9 * q^20 - 14 * q^21 - 11 * q^22 + 12 * q^23 - 36 * q^24 + q^25 - 5 * q^26 - 10 * q^28 + 12 * q^29 + 2 * q^30 - 16 * q^31 + 27 * q^32 + 15 * q^33 + 10 * q^34 + 5 * q^35 - 3 * q^36 - 8 * q^38 + 5 * q^39 - q^40 + 14 * q^41 + 25 * q^42 - 6 * q^43 - 4 * q^44 + 8 * q^45 + 19 * q^46 + q^47 - 41 * q^48 - 2 * q^49 + q^50 - 5 * q^51 - 5 * q^52 + 19 * q^53 + 23 * q^54 - 10 * q^55 - 13 * q^56 + 23 * q^57 + 4 * q^58 + 3 * q^59 + 17 * q^60 + q^61 + 23 * q^62 - 20 * q^63 + 61 * q^64 + 23 * q^65 + q^66 - 12 * q^67 + 14 * q^68 - 22 * q^69 - 14 * q^70 - 27 * q^71 + 31 * q^72 - 7 * q^73 + 15 * q^74 - 17 * q^75 - 38 * q^76 + 27 * q^77 - 20 * q^78 - 21 * q^79 - 28 * q^80 - 2 * q^81 + 53 * q^82 - 9 * q^83 + 61 * q^84 - 9 * q^85 - 11 * q^86 - 12 * q^87 - 31 * q^88 - 14 * q^89 - 22 * q^90 - 33 * q^91 + 30 * q^92 - 32 * q^93 - 6 * q^95 - 33 * q^96 - 8 * q^97 + 2 * q^98 - 54 * 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 $

$2$	−1.68129	−1.18885	−0.594427	−	0.804150i	$-0.702621\pi$
$2$	−1.68129	−1.18885	−0.594427	+	0.804150i	$0.702621\pi$
$3$	1.73515	1.00179	0.500896	−	0.865508i	$-0.333004\pi$
$3$	1.73515	1.00179	0.500896	+	0.865508i	$0.333004\pi$
$4$	0.826745	0.413373
$5$	1.52866	0.683636	0.341818	−	0.939766i	$-0.388957\pi$
$5$	1.52866	0.683636	0.341818	+	0.939766i	$0.388957\pi$
$6$	−2.91730	−1.19098
$7$	−0.782217	−0.295650	−0.147825	−	0.989014i	$-0.547227\pi$
$7$	−0.782217	−0.295650	−0.147825	+	0.989014i	$0.547227\pi$
$8$	1.97258	0.697414
$9$	0.0107559	0.00358529
$10$	−2.57012	−0.812743
$11$	4.82317	1.45424	0.727121	−	0.686510i	$-0.240858\pi$
$11$	4.82317	1.45424	0.727121	+	0.686510i	$0.240858\pi$
$12$	1.43453	0.414113
$13$	1.31087	0.363571	0.181785	−	0.983338i	$-0.441812\pi$
$13$	1.31087	0.363571	0.181785	+	0.983338i	$0.441812\pi$
$14$	1.31513	0.351485
$15$	2.65245	0.684860
$16$	−4.96998	−1.24250
$17$	0.699883	0.169746	0.0848732	−	0.996392i	$-0.472951\pi$
$17$	0.699883	0.169746	0.0848732	+	0.996392i	$0.472951\pi$
$18$	−0.0180838	−0.00426239
$19$	−3.13508	−0.719237	−0.359619	−	0.933099i	$-0.617093\pi$
$19$	−3.13508	−0.719237	−0.359619	+	0.933099i	$0.617093\pi$
$20$	1.26381	0.282596
$21$	−1.35727	−0.296180
$22$	−8.10917	−1.72888
$23$	−3.56393	−0.743130	−0.371565	−	0.928407i	$-0.621179\pi$
$23$	−3.56393	−0.743130	−0.371565	+	0.928407i	$0.621179\pi$
$24$	3.42274	0.698663
$25$	−2.66321	−0.532642
$26$	−2.20396	−0.432232
$27$	−5.18680	−0.998199
$28$	−0.646694	−0.122214
$29$	0.647664	0.120268	0.0601341	−	0.998190i	$-0.480847\pi$
$29$	0.647664	0.120268	0.0601341	+	0.998190i	$0.480847\pi$
$30$	−4.45955	−0.814199
$31$	−9.09774	−1.63400	−0.817001	−	0.576636i	$-0.804365\pi$
$31$	−9.09774	−1.63400	−0.817001	+	0.576636i	$0.804365\pi$
$32$	4.41083	0.779731
$33$	8.36894	1.45685
$34$	−1.17671	−0.201804
$35$	−1.19574	−0.202117
$36$	0.00889237	0.00148206
$37$	−1.31603	−0.216354	−0.108177	−	0.994132i	$-0.534501\pi$
$37$	−1.31603	−0.216354	−0.108177	+	0.994132i	$0.534501\pi$
$38$	5.27099	0.855068
$39$	2.27457	0.364222
$40$	3.01540	0.476777
$41$	1.14403	0.178667	0.0893336	−	0.996002i	$-0.471526\pi$
$41$	1.14403	0.178667	0.0893336	+	0.996002i	$0.471526\pi$
$42$	2.28196	0.352114
$43$	12.4917	1.90497	0.952483	−	0.304591i	$-0.0985197\pi$
$43$	12.4917	1.90497	0.952483	+	0.304591i	$0.0985197\pi$
$44$	3.98754	0.601144
$45$	0.0164420	0.00245103
$46$	5.99200	0.883473
$47$	−5.79269	−0.844951	−0.422475	−	0.906374i	$-0.638839\pi$
$47$	−5.79269	−0.844951	−0.422475	+	0.906374i	$0.638839\pi$
$48$	−8.62368	−1.24472
$49$	−6.38814	−0.912591
$50$	4.47763	0.633233
$51$	1.21440	0.170051
$52$	1.08376	0.150290
$53$	10.2799	1.41205	0.706025	−	0.708186i	$-0.250486\pi$
$53$	10.2799	1.41205	0.706025	+	0.708186i	$0.250486\pi$
$54$	8.72052	1.18671
$55$	7.37298	0.994172
$56$	−1.54299	−0.206190
$57$	−5.43985	−0.720526
$58$	−1.08891	−0.142981
$59$	−4.01092	−0.522177	−0.261089	−	0.965315i	$-0.584082\pi$
$59$	−4.01092	−0.522177	−0.261089	+	0.965315i	$0.584082\pi$
$60$	2.19290	0.283103
$61$	0.673825	0.0862744	0.0431372	−	0.999069i	$-0.486265\pi$
$61$	0.673825	0.0862744	0.0431372	+	0.999069i	$0.486265\pi$
$62$	15.2960	1.94259
$63$	−0.00841342	−0.00105999
$64$	2.52407	0.315509
$65$	2.00387	0.248550
$66$	−14.0706	−1.73198
$67$	6.65710	0.813294	0.406647	−	0.913585i	$-0.366698\pi$
$67$	6.65710	0.813294	0.406647	+	0.913585i	$0.366698\pi$
$68$	0.578625	0.0701686
$69$	−6.18396	−0.744461
$70$	2.01039	0.240288
$71$	−11.7036	−1.38897	−0.694483	−	0.719509i	$-0.744367\pi$
$71$	−11.7036	−1.38897	−0.694483	+	0.719509i	$0.744367\pi$
$72$	0.0212169	0.00250043
$73$	3.39836	0.397748	0.198874	−	0.980025i	$-0.436272\pi$
$73$	3.39836	0.397748	0.198874	+	0.980025i	$0.436272\pi$
$74$	2.21263	0.257213
$75$	−4.62107	−0.533596
$76$	−2.59192	−0.297313
$77$	−3.77277	−0.429947
$78$	−3.82421	−0.433007
$79$	−14.5081	−1.63228	−0.816142	−	0.577851i	$-0.803891\pi$
$79$	−14.5081	−1.63228	−0.816142	+	0.577851i	$0.803891\pi$
$80$	−7.59740	−0.849415
$81$	−9.03215	−1.00357
$82$	−1.92345	−0.212409
$83$	−4.30580	−0.472623	−0.236312	−	0.971677i	$-0.575939\pi$
$83$	−4.30580	−0.472623	−0.236312	+	0.971677i	$0.575939\pi$
$84$	−1.12211	−0.122433
$85$	1.06988	0.116045
$86$	−21.0022	−2.26473
$87$	1.12380	0.120484
$88$	9.51412	1.01421
$89$	17.1403	1.81687	0.908433	−	0.418030i	$-0.137279\pi$
$89$	17.1403	1.81687	0.908433	+	0.418030i	$0.137279\pi$
$90$	−0.0276439	−0.00291392
$91$	−1.02539	−0.107490
$92$	−2.94646	−0.307190
$93$	−15.7860	−1.63693
$94$	9.73921	1.00452
$95$	−4.79247	−0.491697
$96$	7.65346	0.781128
$97$	11.3630	1.15374	0.576868	−	0.816838i	$-0.304275\pi$
$97$	11.3630	1.15374	0.576868	+	0.816838i	$0.304275\pi$
$98$	10.7403	1.08494
$99$	0.0518774	0.00521388
$100$	−2.20180	−0.220180
$101$	16.8118	1.67283	0.836416	−	0.548094i	$-0.184647\pi$
$101$	16.8118	1.67283	0.836416	+	0.548094i	$0.184647\pi$
$102$	−2.04177	−0.202165
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.58581	0.253559
$105$	−2.07479	−0.202479
$106$	−17.2835	−1.67872
$107$	13.7563	1.32987	0.664937	−	0.746899i	$-0.268458\pi$
$107$	13.7563	1.32987	0.664937	+	0.746899i	$0.268458\pi$
$108$	−4.28816	−0.412628
$109$	4.22700	0.404873	0.202436	−	0.979295i	$-0.435114\pi$
$109$	4.22700	0.404873	0.202436	+	0.979295i	$0.435114\pi$
$110$	−12.3961	−1.18192
$111$	−2.28351	−0.216741
$112$	3.88760	0.367344
$113$	−9.23761	−0.869001	−0.434501	−	0.900672i	$-0.643075\pi$
$113$	−9.23761	−0.869001	−0.434501	+	0.900672i	$0.643075\pi$
$114$	9.14598	0.856599
$115$	−5.44802	−0.508031
$116$	0.535453	0.0497156
$117$	0.0140996	0.00130351
$118$	6.74353	0.620792
$119$	−0.547460	−0.0501856
$120$	5.23219	0.477631
$121$	12.2630	1.11482
$122$	−1.13290	−0.102568
$123$	1.98506	0.178987
$124$	−7.52151	−0.675452
$125$	−11.7144	−1.04777
$126$	0.0141454	0.00126017
$127$	2.41197	0.214027	0.107014	−	0.994258i	$-0.465871\pi$
$127$	2.41197	0.214027	0.107014	+	0.994258i	$0.465871\pi$
$128$	−13.0654	−1.15483
$129$	21.6750	1.90838
$130$	−3.36910	−0.295490
$131$	−11.1137	−0.971006	−0.485503	−	0.874235i	$-0.661364\pi$
$131$	−11.1137	−0.971006	−0.485503	+	0.874235i	$0.661364\pi$
$132$	6.91898	0.602220
$133$	2.45231	0.212643
$134$	−11.1925	−0.966888
$135$	−7.92883	−0.682405
$136$	1.38058	0.118384
$137$	14.5883	1.24636	0.623180	−	0.782078i	$-0.285840\pi$
$137$	14.5883	1.24636	0.623180	+	0.782078i	$0.285840\pi$
$138$	10.3970	0.885055
$139$	−6.85000	−0.581010	−0.290505	−	0.956874i	$-0.593823\pi$
$139$	−6.85000	−0.581010	−0.290505	+	0.956874i	$0.593823\pi$
$140$	−0.988573	−0.0835496
$141$	−10.0512	−0.846464
$142$	19.6772	1.65128
$143$	6.32257	0.528720
$144$	−0.0534565	−0.00445471
$145$	0.990056	0.0822197
$146$	−5.71364	−0.472864
$147$	−11.0844	−0.914226
$148$	−1.08802	−0.0894347
$149$	−15.2751	−1.25138	−0.625691	−	0.780071i	$-0.715183\pi$
$149$	−15.2751	−1.25138	−0.625691	+	0.780071i	$0.715183\pi$
$150$	7.76938	0.634367
$151$	−20.5473	−1.67212	−0.836058	−	0.548641i	$-0.815145\pi$
$151$	−20.5473	−1.67212	−0.836058	+	0.548641i	$0.815145\pi$
$152$	−6.18422	−0.501606
$153$	0.00752785	0.000608591 0
$154$	6.34312	0.511143
$155$	−13.9073	−1.11706
$156$	1.88049	0.150559
$157$	13.6390	1.08851	0.544253	−	0.838921i	$-0.316813\pi$
$157$	13.6390	1.08851	0.544253	+	0.838921i	$0.316813\pi$
$158$	24.3923	1.94055
$159$	17.8372	1.41458
$160$	6.74264	0.533052
$161$	2.78776	0.219706
$162$	15.1857	1.19310
$163$	−7.89319	−0.618243	−0.309121	−	0.951023i	$-0.600035\pi$
$163$	−7.89319	−0.618243	−0.309121	+	0.951023i	$0.600035\pi$
$164$	0.945820	0.0738561
$165$	12.7932	0.995952
$166$	7.23932	0.561880
$167$	−6.69805	−0.518311	−0.259155	−	0.965836i	$-0.583444\pi$
$167$	−6.69805	−0.518311	−0.259155	+	0.965836i	$0.583444\pi$
$168$	−2.67732	−0.206560
$169$	−11.2816	−0.867816
$170$	−1.79878	−0.137960
$171$	−0.0337206	−0.00257868
$172$	10.3275	0.787461
$173$	15.1957	1.15531	0.577654	−	0.816282i	$-0.303968\pi$
$173$	15.1957	1.15531	0.577654	+	0.816282i	$0.303968\pi$
$174$	−1.88943	−0.143237
$175$	2.08321	0.157476
$176$	−23.9711	−1.80689
$177$	−6.95956	−0.523113
$178$	−28.8178	−2.15999
$179$	14.1215	1.05549	0.527743	−	0.849404i	$-0.323038\pi$
$179$	14.1215	1.05549	0.527743	+	0.849404i	$0.323038\pi$
$180$	0.0135934	0.00101319
$181$	−9.99328	−0.742794	−0.371397	−	0.928474i	$-0.621121\pi$
$181$	−9.99328	−0.742794	−0.371397	+	0.928474i	$0.621121\pi$
$182$	1.72398	0.127790
$183$	1.16919	0.0864289
$184$	−7.03015	−0.518269
$185$	−2.01176	−0.147907
$186$	26.5408	1.94607
$187$	3.37566	0.246852
$188$	−4.78908	−0.349280
$189$	4.05720	0.295118
$190$	8.05754	0.584555
$191$	13.9354	1.00833	0.504166	−	0.863607i	$-0.331800\pi$
$191$	13.9354	1.00833	0.504166	+	0.863607i	$0.331800\pi$
$192$	4.37966	0.316074
$193$	−1.40002	−0.100775	−0.0503877	−	0.998730i	$-0.516046\pi$
$193$	−1.40002	−0.100775	−0.0503877	+	0.998730i	$0.516046\pi$
$194$	−19.1045	−1.37162
$195$	3.47703	0.248995
$196$	−5.28136	−0.377240
$197$	−3.15391	−0.224707	−0.112353	−	0.993668i	$-0.535839\pi$
$197$	−3.15391	−0.224707	−0.112353	+	0.993668i	$0.535839\pi$
$198$	−0.0872212	−0.00619854
$199$	27.3865	1.94138	0.970690	−	0.240336i	$-0.0772575\pi$
$199$	27.3865	1.94138	0.970690	+	0.240336i	$0.0772575\pi$
$200$	−5.25341	−0.371472
$201$	11.5511	0.814751
$202$	−28.2655	−1.98875
$203$	−0.506614	−0.0355573
$204$	1.00400	0.0702942
$205$	1.74883	0.122143
$206$	−1.68129	−0.117141
$207$	−0.0383332	−0.00266434
$208$	−6.51502	−0.451735
$209$	−15.1211	−1.04594
$210$	3.48833	0.240718
$211$	27.0220	1.86027	0.930137	−	0.367214i	$-0.119688\pi$
$211$	27.0220	1.86027	0.930137	+	0.367214i	$0.119688\pi$
$212$	8.49885	0.583703
$213$	−20.3076	−1.39145
$214$	−23.1284	−1.58103
$215$	19.0955	1.30230
$216$	−10.2314	−0.696158
$217$	7.11640	0.483093
$218$	−7.10682	−0.481334
$219$	5.89668	0.398461
$220$	6.09557	0.410963
$221$	0.917457	0.0617149
$222$	3.83925	0.257674
$223$	−25.6590	−1.71826	−0.859128	−	0.511760i	$-0.828994\pi$
$223$	−25.6590	−1.71826	−0.859128	+	0.511760i	$0.828994\pi$
$224$	−3.45022	−0.230528
$225$	−0.0286451	−0.00190968
$226$	15.5311	1.03312
$227$	−25.0004	−1.65934	−0.829668	−	0.558258i	$-0.811470\pi$
$227$	−25.0004	−1.65934	−0.829668	+	0.558258i	$0.811470\pi$
$228$	−4.49737	−0.297846
$229$	−17.5023	−1.15659	−0.578293	−	0.815829i	$-0.696281\pi$
$229$	−17.5023	−1.15659	−0.578293	+	0.815829i	$0.696281\pi$
$230$	9.15972	0.603974
$231$	−6.54633	−0.430717
$232$	1.27757	0.0838767
$233$	21.8436	1.43102	0.715512	−	0.698600i	$-0.246193\pi$
$233$	21.8436	1.43102	0.715512	+	0.698600i	$0.246193\pi$
$234$	−0.0237055	−0.00154968
$235$	−8.85504	−0.577639
$236$	−3.31601	−0.215854
$237$	−25.1737	−1.63521
$238$	0.920440	0.0596633
$239$	4.98290	0.322317	0.161159	−	0.986929i	$-0.448477\pi$
$239$	4.98290	0.322317	0.161159	+	0.986929i	$0.448477\pi$
$240$	−13.1826	−0.850936
$241$	7.63342	0.491712	0.245856	−	0.969306i	$-0.420931\pi$
$241$	7.63342	0.491712	0.245856	+	0.969306i	$0.420931\pi$
$242$	−20.6177	−1.32536
$243$	−0.111778	−0.00717055
$244$	0.557081	0.0356635
$245$	−9.76527	−0.623880
$246$	−3.33747	−0.212790
$247$	−4.10970	−0.261494
$248$	−17.9461	−1.13958
$249$	−7.47123	−0.473470
$250$	19.6954	1.24564
$251$	25.7238	1.62367	0.811836	−	0.583886i	$-0.198468\pi$
$251$	25.7238	1.62367	0.811836	+	0.583886i	$0.198468\pi$
$252$	−0.00695576	−0.000438172 0
$253$	−17.1894	−1.08069
$254$	−4.05522	−0.254447
$255$	1.85641	0.116253
$256$	16.9185	1.05741
$257$	4.52811	0.282456	0.141228	−	0.989977i	$-0.454895\pi$
$257$	4.52811	0.282456	0.141228	+	0.989977i	$0.454895\pi$
$258$	−36.4420	−2.26878
$259$	1.02942	0.0639650
$260$	1.65669	0.102744
$261$	0.00696620	0.000431197 0
$262$	18.6853	1.15438
$263$	5.02323	0.309746	0.154873	−	0.987934i	$-0.450503\pi$
$263$	5.02323	0.309746	0.154873	+	0.987934i	$0.450503\pi$
$264$	16.5084	1.01602
$265$	15.7144	0.965329
$266$	−4.12306	−0.252801
$267$	29.7410	1.82012
$268$	5.50373	0.336194
$269$	−0.0105133	−0.000641005 0	−0.000320503	−	1.00000i	$-0.500102\pi$
$269$	−0.0105133	−0.000641005 0	−0.000320503		1.00000i	$0.500102\pi$
$270$	13.3307	0.811280
$271$	1.51236	0.0918690	0.0459345	−	0.998944i	$-0.485373\pi$
$271$	1.51236	0.0918690	0.0459345	+	0.998944i	$0.485373\pi$
$272$	−3.47841	−0.210909
$273$	−1.77920	−0.107682
$274$	−24.5272	−1.48174
$275$	−12.8451	−0.774590
$276$	−5.11256	−0.307740
$277$	−5.36713	−0.322480	−0.161240	−	0.986915i	$-0.551549\pi$
$277$	−5.36713	−0.322480	−0.161240	+	0.986915i	$0.551549\pi$
$278$	11.5169	0.690736
$279$	−0.0978541	−0.00585837
$280$	−2.35870	−0.140959
$281$	23.9569	1.42915	0.714576	−	0.699558i	$-0.246620\pi$
$281$	23.9569	1.42915	0.714576	+	0.699558i	$0.246620\pi$
$282$	16.8990	1.00632
$283$	5.70459	0.339103	0.169551	−	0.985521i	$-0.445768\pi$
$283$	5.70459	0.339103	0.169551	+	0.985521i	$0.445768\pi$
$284$	−9.67592	−0.574160
$285$	−8.31566	−0.492577
$286$	−10.6301	−0.628570
$287$	−0.894878	−0.0528230
$288$	0.0474423	0.00279556
$289$	−16.5102	−0.971186
$290$	−1.66457	−0.0977472
$291$	19.7165	1.15580
$292$	2.80958	0.164418
$293$	−0.460563	−0.0269063	−0.0134532	−	0.999910i	$-0.504282\pi$
$293$	−0.460563	−0.0269063	−0.0134532	+	0.999910i	$0.504282\pi$
$294$	18.6361	1.08688
$295$	−6.13132	−0.356979
$296$	−2.59598	−0.150888
$297$	−25.0168	−1.45162
$298$	25.6818	1.48771
$299$	−4.67186	−0.270180
$300$	−3.82045	−0.220574
$301$	−9.77122	−0.563204
$302$	34.5460	1.98790
$303$	29.1710	1.67583
$304$	15.5813	0.893649
$305$	1.03005	0.0589803
$306$	−0.0126565	−0.000723525 0
$307$	7.03185	0.401329	0.200664	−	0.979660i	$-0.435690\pi$
$307$	7.03185	0.401329	0.200664	+	0.979660i	$0.435690\pi$
$308$	−3.11912	−0.177728
$309$	1.73515	0.0987094
$310$	23.3823	1.32802
$311$	−5.19655	−0.294669	−0.147335	−	0.989087i	$-0.547069\pi$
$311$	−5.19655	−0.294669	−0.147335	+	0.989087i	$0.547069\pi$
$312$	4.48677	0.254014
$313$	−21.7448	−1.22909	−0.614544	−	0.788882i	$-0.710660\pi$
$313$	−21.7448	−1.22909	−0.614544	+	0.788882i	$0.710660\pi$
$314$	−22.9311	−1.29408
$315$	−0.0128612	−0.000724649 0
$316$	−11.9945	−0.674742
$317$	1.37498	0.0772264	0.0386132	−	0.999254i	$-0.487706\pi$
$317$	1.37498	0.0772264	0.0386132	+	0.999254i	$0.487706\pi$
$318$	−29.9895	−1.68173
$319$	3.12380	0.174899
$320$	3.85844	0.215694
$321$	23.8693	1.33226
$322$	−4.68704	−0.261199
$323$	−2.19419	−0.122088
$324$	−7.46729	−0.414849
$325$	−3.49113	−0.193653
$326$	13.2708	0.735000
$327$	7.33448	0.405598
$328$	2.25669	0.124605
$329$	4.53114	0.249810
$330$	−21.5092	−1.18404
$331$	21.9177	1.20471	0.602353	−	0.798230i	$-0.294230\pi$
$331$	21.9177	1.20471	0.602353	+	0.798230i	$0.294230\pi$
$332$	−3.55980	−0.195370
$333$	−0.0141550	−0.000775691 0
$334$	11.2614	0.616195
$335$	10.1764	0.555997
$336$	6.74559	0.368002
$337$	8.19930	0.446644	0.223322	−	0.974745i	$-0.428310\pi$
$337$	8.19930	0.446644	0.223322	+	0.974745i	$0.428310\pi$
$338$	18.9677	1.03171
$339$	−16.0287	−0.870558
$340$	0.884518	0.0479698
$341$	−43.8800	−2.37623
$342$	0.0566941	0.00306567
$343$	10.4724	0.565458
$344$	24.6409	1.32855
$345$	−9.45315	−0.508940
$346$	−25.5484	−1.37349
$347$	0.121754	0.00653609	0.00326804	−	0.999995i	$-0.498960\pi$
$347$	0.121754	0.00653609	0.00326804	+	0.999995i	$0.498960\pi$
$348$	0.929093	0.0498046
$349$	20.1933	1.08092	0.540461	−	0.841369i	$-0.318250\pi$
$349$	20.1933	1.08092	0.540461	+	0.841369i	$0.318250\pi$
$350$	−3.50248	−0.187215
$351$	−6.79923	−0.362916
$352$	21.2742	1.13392
$353$	24.6973	1.31450	0.657252	−	0.753671i	$-0.271719\pi$
$353$	24.6973	1.31450	0.657252	+	0.753671i	$0.271719\pi$
$354$	11.7011	0.621904
$355$	−17.8908	−0.949547
$356$	14.1706	0.751043
$357$	−0.949927	−0.0502754
$358$	−23.7423	−1.25482
$359$	31.3654	1.65540	0.827702	−	0.561169i	$-0.189648\pi$
$359$	31.3654	1.65540	0.827702	+	0.561169i	$0.189648\pi$
$360$	0.0324333	0.00170939
$361$	−9.17125	−0.482697
$362$	16.8016	0.883074
$363$	21.2782	1.11681
$364$	−0.847734	−0.0444333
$365$	5.19493	0.271915
$366$	−1.96575	−0.102751
$367$	−8.31477	−0.434028	−0.217014	−	0.976169i	$-0.569632\pi$
$367$	−8.31477	−0.434028	−0.217014	+	0.976169i	$0.569632\pi$
$368$	17.7127	0.923336
$369$	0.0123050	0.000640574 0
$370$	3.38235	0.175840
$371$	−8.04110	−0.417473
$372$	−13.0510	−0.676661
$373$	−21.5528	−1.11596	−0.557981	−	0.829854i	$-0.688424\pi$
$373$	−21.5528	−1.11596	−0.557981	+	0.829854i	$0.688424\pi$
$374$	−5.67546	−0.293471
$375$	−20.3263	−1.04965
$376$	−11.4266	−0.589281
$377$	0.849006	0.0437260
$378$	−6.82134	−0.350852
$379$	−16.1159	−0.827818	−0.413909	−	0.910318i	$-0.635837\pi$
$379$	−16.1159	−0.827818	−0.413909	+	0.910318i	$0.635837\pi$
$380$	−3.96215	−0.203254
$381$	4.18513	0.214411
$382$	−23.4295	−1.19876
$383$	−21.5891	−1.10315	−0.551575	−	0.834125i	$-0.685973\pi$
$383$	−21.5891	−1.10315	−0.551575	+	0.834125i	$0.685973\pi$
$384$	−22.6704	−1.15689
$385$	−5.76726	−0.293927
$386$	2.35384	0.119807
$387$	0.134359	0.00682986
$388$	9.39429	0.476923
$389$	−18.4229	−0.934078	−0.467039	−	0.884237i	$-0.654679\pi$
$389$	−18.4229	−0.934078	−0.467039	+	0.884237i	$0.654679\pi$
$390$	−5.84590	−0.296019
$391$	−2.49433	−0.126144
$392$	−12.6011	−0.636454
$393$	−19.2839	−0.972745
$394$	5.30265	0.267144
$395$	−22.1778	−1.11589
$396$	0.0428894	0.00215528
$397$	8.40423	0.421796	0.210898	−	0.977508i	$-0.432361\pi$
$397$	8.40423	0.421796	0.210898	+	0.977508i	$0.432361\pi$
$398$	−46.0448	−2.30802
$399$	4.25514	0.213023
$400$	13.2361	0.661805
$401$	−12.0243	−0.600465	−0.300232	−	0.953866i	$-0.597064\pi$
$401$	−12.0243	−0.600465	−0.300232	+	0.953866i	$0.597064\pi$
$402$	−19.4208	−0.968620
$403$	−11.9260	−0.594075
$404$	13.8990	0.691503
$405$	−13.8071	−0.686078
$406$	0.851766	0.0422724
$407$	−6.34743	−0.314630
$408$	2.39551	0.118596
$409$	1.67474	0.0828103	0.0414052	−	0.999142i	$-0.486817\pi$
$409$	1.67474	0.0828103	0.0414052	+	0.999142i	$0.486817\pi$
$410$	−2.94029	−0.145211
$411$	25.3129	1.24859
$412$	0.826745	0.0407308
$413$	3.13741	0.154382
$414$	0.0644492	0.00316751
$415$	−6.58209	−0.323102
$416$	5.78203	0.283488
$417$	−11.8858	−0.582050
$418$	25.4229	1.24348
$419$	5.44089	0.265805	0.132902	−	0.991129i	$-0.457570\pi$
$419$	5.44089	0.265805	0.132902	+	0.991129i	$0.457570\pi$
$420$	−1.71533	−0.0836993
$421$	4.59748	0.224068	0.112034	−	0.993704i	$-0.464264\pi$
$421$	4.59748	0.224068	0.112034	+	0.993704i	$0.464264\pi$
$422$	−45.4319	−2.21159
$423$	−0.0623055	−0.00302940
$424$	20.2779	0.984784
$425$	−1.86393	−0.0904141
$426$	34.1430	1.65423
$427$	−0.527077	−0.0255070
$428$	11.3730	0.549734
$429$	10.9706	0.529667
$430$	−32.1052	−1.54825
$431$	7.59803	0.365984	0.182992	−	0.983114i	$-0.441422\pi$
$431$	7.59803	0.365984	0.182992	+	0.983114i	$0.441422\pi$
$432$	25.7783	1.24026
$433$	−21.2044	−1.01902	−0.509510	−	0.860465i	$-0.670173\pi$
$433$	−21.2044	−1.01902	−0.509510	+	0.860465i	$0.670173\pi$
$434$	−11.9648	−0.574327
$435$	1.71790	0.0823669
$436$	3.49465	0.167363
$437$	11.1732	0.534487
$438$	−9.91404	−0.473711
$439$	0.114879	0.00548287	0.00274144	−	0.999996i	$-0.499127\pi$
$439$	0.114879	0.00548287	0.00274144	+	0.999996i	$0.499127\pi$
$440$	14.5438	0.693349
$441$	−0.0687100	−0.00327191
$442$	−1.54251	−0.0733699
$443$	13.9550	0.663021	0.331510	−	0.943452i	$-0.392442\pi$
$443$	13.9550	0.663021	0.331510	+	0.943452i	$0.392442\pi$
$444$	−1.88788	−0.0895949
$445$	26.2016	1.24208
$446$	43.1404	2.04276
$447$	−26.5046	−1.25362
$448$	−1.97437	−0.0932804
$449$	−5.48566	−0.258884	−0.129442	−	0.991587i	$-0.541319\pi$
$449$	−5.48566	−0.258884	−0.129442	+	0.991587i	$0.541319\pi$
$450$	0.0481609	0.00227033
$451$	5.51785	0.259825
$452$	−7.63715	−0.359221
$453$	−35.6527	−1.67511
$454$	42.0330	1.97271
$455$	−1.56746	−0.0734839
$456$	−10.7306	−0.502505
$457$	28.8288	1.34855	0.674277	−	0.738479i	$-0.264456\pi$
$457$	28.8288	1.34855	0.674277	+	0.738479i	$0.264456\pi$
$458$	29.4265	1.37501
$459$	−3.63015	−0.169441
$460$	−4.50412	−0.210006
$461$	−21.3303	−0.993453	−0.496726	−	0.867907i	$-0.665465\pi$
$461$	−21.3303	−0.993453	−0.496726	+	0.867907i	$0.665465\pi$
$462$	11.0063	0.512059
$463$	33.3821	1.55140	0.775699	−	0.631103i	$-0.217397\pi$
$463$	33.3821	1.55140	0.775699	+	0.631103i	$0.217397\pi$
$464$	−3.21888	−0.149433
$465$	−24.1313	−1.11906
$466$	−36.7256	−1.70128
$467$	−21.5884	−0.998990	−0.499495	−	0.866317i	$-0.666481\pi$
$467$	−21.5884	−0.998990	−0.499495	+	0.866317i	$0.666481\pi$
$468$	0.0116568	0.000538834 0
$469$	−5.20730	−0.240451
$470$	14.8879	0.686728
$471$	23.6657	1.09046
$472$	−7.91188	−0.364174
$473$	60.2496	2.77028
$474$	42.3244	1.94402
$475$	8.34938	0.383096
$476$	−0.452610	−0.0207453
$477$	0.110569	0.00506261
$478$	−8.37772	−0.383188
$479$	−23.1552	−1.05799	−0.528995	−	0.848625i	$-0.677431\pi$
$479$	−23.1552	−1.05799	−0.528995	+	0.848625i	$0.677431\pi$
$480$	11.6995	0.534007
$481$	−1.72515	−0.0786599
$482$	−12.8340	−0.584574
$483$	4.83719	0.220100
$484$	10.1384	0.460835
$485$	17.3701	0.788735
$486$	0.187931	0.00852473
$487$	−22.8855	−1.03704	−0.518520	−	0.855066i	$-0.673517\pi$
$487$	−22.8855	−1.03704	−0.518520	+	0.855066i	$0.673517\pi$
$488$	1.32918	0.0601690
$489$	−13.6959	−0.619350
$490$	16.4183	0.741702
$491$	6.09481	0.275055	0.137527	−	0.990498i	$-0.456084\pi$
$491$	6.09481	0.275055	0.137527	+	0.990498i	$0.456084\pi$
$492$	1.64114	0.0739884
$493$	0.453289	0.0204151
$494$	6.90960	0.310878
$495$	0.0793028	0.00356440
$496$	45.2156	2.03024
$497$	9.15478	0.410648
$498$	12.5613	0.562886
$499$	−22.4084	−1.00314	−0.501569	−	0.865117i	$-0.667244\pi$
$499$	−22.4084	−1.00314	−0.501569	+	0.865117i	$0.667244\pi$
$500$	−9.68484	−0.433119
$501$	−11.6221	−0.519239
$502$	−43.2492	−1.93031
$503$	32.6213	1.45451	0.727255	−	0.686368i	$-0.240796\pi$
$503$	32.6213	1.45451	0.727255	+	0.686368i	$0.240796\pi$
$504$	−0.0165962	−0.000739253 0
$505$	25.6994	1.14361
$506$	28.9005	1.28478
$507$	−19.5753	−0.869371
$508$	1.99408	0.0884731
$509$	−17.0744	−0.756811	−0.378406	−	0.925640i	$-0.623528\pi$
$509$	−17.0744	−0.756811	−0.378406	+	0.925640i	$0.623528\pi$
$510$	−3.12116	−0.138207
$511$	−2.65825	−0.117594
$512$	−2.31431	−0.102279
$513$	16.2610	0.717942
$514$	−7.61308	−0.335798
$515$	1.52866	0.0673607
$516$	17.9197	0.788871
$517$	−27.9392	−1.22876
$518$	−1.73075	−0.0760450
$519$	26.3669	1.15738
$520$	3.95281	0.173342
$521$	2.04666	0.0896659	0.0448329	−	0.998994i	$-0.485724\pi$
$521$	2.04666	0.0896659	0.0448329	+	0.998994i	$0.485724\pi$
$522$	−0.0117122	−0.000512630 0
$523$	0.485991	0.0212509	0.0106255	−	0.999944i	$-0.496618\pi$
$523$	0.485991	0.0212509	0.0106255	+	0.999944i	$0.496618\pi$
$524$	−9.18818	−0.401387
$525$	3.61468	0.157758
$526$	−8.44553	−0.368242
$527$	−6.36735	−0.277366
$528$	−41.5935	−1.81012
$529$	−10.2984	−0.447758
$530$	−26.4205	−1.14763
$531$	−0.0431410	−0.00187216
$532$	2.02744	0.0879006
$533$	1.49968	0.0649582
$534$	−50.0033	−2.16386
$535$	21.0287	0.909150
$536$	13.1317	0.567203
$537$	24.5029	1.05738
$538$	0.0176759	0.000762061 0
$539$	−30.8111	−1.32713
$540$	−6.55512	−0.282088
$541$	−11.5678	−0.497337	−0.248669	−	0.968589i	$-0.579993\pi$
$541$	−11.5678	−0.497337	−0.248669	+	0.968589i	$0.579993\pi$
$542$	−2.54271	−0.109219
$543$	−17.3399	−0.744125
$544$	3.08706	0.132357
$545$	6.46162	0.276786
$546$	2.99136	0.128018
$547$	−31.1434	−1.33160	−0.665798	−	0.746132i	$-0.731909\pi$
$547$	−31.1434	−1.33160	−0.665798	+	0.746132i	$0.731909\pi$
$548$	12.0608	0.515211
$549$	0.00724757	0.000309319 0
$550$	21.5964	0.920874
$551$	−2.03048	−0.0865014
$552$	−12.1984	−0.519198
$553$	11.3484	0.482585
$554$	9.02372	0.383381
$555$	−3.49070	−0.148172
$556$	−5.66321	−0.240174
$557$	14.6789	0.621964	0.310982	−	0.950416i	$-0.399342\pi$
$557$	14.6789	0.621964	0.310982	+	0.950416i	$0.399342\pi$
$558$	0.164521	0.00696475
$559$	16.3750	0.692590
$560$	5.94281	0.251130
$561$	5.85728	0.247294
$562$	−40.2786	−1.69905
$563$	−23.6976	−0.998736	−0.499368	−	0.866390i	$-0.666434\pi$
$563$	−23.6976	−0.998736	−0.499368	+	0.866390i	$0.666434\pi$
$564$	−8.30979	−0.349905
$565$	−14.1211	−0.594081
$566$	−9.59109	−0.403144
$567$	7.06510	0.296706
$568$	−23.0864	−0.968684
$569$	15.1020	0.633110	0.316555	−	0.948574i	$-0.397474\pi$
$569$	15.1020	0.633110	0.316555	+	0.948574i	$0.397474\pi$
$570$	13.9811	0.585602
$571$	8.00134	0.334846	0.167423	−	0.985885i	$-0.446455\pi$
$571$	8.00134	0.334846	0.167423	+	0.985885i	$0.446455\pi$
$572$	5.22715	0.218558
$573$	24.1801	1.01014
$574$	1.50455	0.0627988
$575$	9.49148	0.395822
$576$	0.0271486	0.00113119
$577$	−15.3934	−0.640836	−0.320418	−	0.947276i	$-0.603823\pi$
$577$	−15.3934	−0.640836	−0.320418	+	0.947276i	$0.603823\pi$
$578$	27.7584	1.15460
$579$	−2.42924	−0.100956
$580$	0.818524	0.0339874
$581$	3.36807	0.139731
$582$	−33.1492	−1.37408
$583$	49.5817	2.05346
$584$	6.70356	0.277395
$585$	0.0215534	0.000891125 0
$586$	0.774340	0.0319877
$587$	−18.7495	−0.773874	−0.386937	−	0.922106i	$-0.626467\pi$
$587$	−18.7495	−0.773874	−0.386937	+	0.922106i	$0.626467\pi$
$588$	−9.16397	−0.377916
$589$	28.5222	1.17524
$590$	10.3085	0.424396
$591$	−5.47252	−0.225109
$592$	6.54064	0.268819
$593$	−28.8421	−1.18440	−0.592201	−	0.805790i	$-0.701741\pi$
$593$	−28.8421	−1.18440	−0.592201	+	0.805790i	$0.701741\pi$
$594$	42.0606	1.72577
$595$	−0.836878	−0.0343087
$596$	−12.6286	−0.517287
$597$	47.5198	1.94486
$598$	7.85476	0.321205
$599$	−15.8416	−0.647271	−0.323635	−	0.946182i	$-0.604905\pi$
$599$	−15.8416	−0.647271	−0.323635	+	0.946182i	$0.604905\pi$
$600$	−9.11546	−0.372137
$601$	−21.7054	−0.885382	−0.442691	−	0.896674i	$-0.645976\pi$
$601$	−21.7054	−0.885382	−0.442691	+	0.896674i	$0.645976\pi$
$602$	16.4283	0.669566
$603$	0.0716030	0.00291590
$604$	−16.9874	−0.691207
$605$	18.7459	0.762130
$606$	−49.0450	−1.99232
$607$	17.6133	0.714901	0.357451	−	0.933932i	$-0.383646\pi$
$607$	17.6133	0.714901	0.357451	+	0.933932i	$0.383646\pi$
$608$	−13.8283	−0.560812
$609$	−0.879052	−0.0356210
$610$	−1.73181	−0.0701189
$611$	−7.59348	−0.307199
$612$	0.00622362	0.000251575 0
$613$	−23.2228	−0.937961	−0.468981	−	0.883208i	$-0.655379\pi$
$613$	−23.2228	−0.937961	−0.468981	+	0.883208i	$0.655379\pi$
$614$	−11.8226	−0.477121
$615$	3.03448	0.122362
$616$	−7.44210	−0.299851
$617$	30.3027	1.21994	0.609970	−	0.792425i	$-0.291182\pi$
$617$	30.3027	1.21994	0.609970	+	0.792425i	$0.291182\pi$
$618$	−2.91730	−0.117351
$619$	−3.81054	−0.153159	−0.0765793	−	0.997063i	$-0.524400\pi$
$619$	−3.81054	−0.153159	−0.0765793	+	0.997063i	$0.524400\pi$
$620$	−11.4978	−0.461763
$621$	18.4854	0.741792
$622$	8.73693	0.350319
$623$	−13.4074	−0.537157
$624$	−11.3046	−0.452544
$625$	−4.59127	−0.183651
$626$	36.5594	1.46121
$627$	−26.2373	−1.04782
$628$	11.2759	0.449959
$629$	−0.921065	−0.0367253
$630$	0.0216235	0.000861501 0
$631$	34.3888	1.36900	0.684499	−	0.729014i	$-0.260021\pi$
$631$	34.3888	1.36900	0.684499	+	0.729014i	$0.260021\pi$
$632$	−28.6184	−1.13838
$633$	46.8874	1.86361
$634$	−2.31174	−0.0918108
$635$	3.68707	0.146317
$636$	14.7468	0.584749
$637$	−8.37404	−0.331791
$638$	−5.25202	−0.207929
$639$	−0.125883	−0.00497985
$640$	−19.9725	−0.789480
$641$	1.60826	0.0635226	0.0317613	−	0.999495i	$-0.489888\pi$
$641$	1.60826	0.0635226	0.0317613	+	0.999495i	$0.489888\pi$
$642$	−40.1313	−1.58386
$643$	26.9444	1.06258	0.531292	−	0.847189i	$-0.321707\pi$
$643$	26.9444	1.06258	0.531292	+	0.847189i	$0.321707\pi$
$644$	2.30477	0.0908206
$645$	33.1337	1.30464
$646$	3.68908	0.145145
$647$	−20.9789	−0.824765	−0.412382	−	0.911011i	$-0.635303\pi$
$647$	−20.9789	−0.824765	−0.412382	+	0.911011i	$0.635303\pi$
$648$	−17.8167	−0.699905
$649$	−19.3454	−0.759372
$650$	5.86961	0.230225
$651$	12.3480	0.483958
$652$	−6.52566	−0.255565
$653$	43.3749	1.69739	0.848695	−	0.528882i	$-0.177389\pi$
$653$	43.3749	1.69739	0.848695	+	0.528882i	$0.177389\pi$
$654$	−12.3314	−0.482196
$655$	−16.9890	−0.663815
$656$	−5.68580	−0.221993
$657$	0.0365524	0.00142604
$658$	−7.61817	−0.296987
$659$	12.4503	0.484994	0.242497	−	0.970152i	$-0.422034\pi$
$659$	12.4503	0.484994	0.242497	+	0.970152i	$0.422034\pi$
$660$	10.5768	0.411699
$661$	2.18829	0.0851146	0.0425573	−	0.999094i	$-0.486449\pi$
$661$	2.18829	0.0851146	0.0425573	+	0.999094i	$0.486449\pi$
$662$	−36.8501	−1.43222
$663$	1.59193	0.0618254
$664$	−8.49356	−0.329614
$665$	3.74875	0.145370
$666$	0.0237988	0.000922183 0
$667$	−2.30823	−0.0893749
$668$	−5.53758	−0.214255
$669$	−44.5224	−1.72133
$670$	−17.1095	−0.660999
$671$	3.24997	0.125464
$672$	−5.98666	−0.230941
$673$	−42.9027	−1.65378	−0.826888	−	0.562366i	$-0.809891\pi$
$673$	−42.9027	−1.65378	−0.826888	+	0.562366i	$0.809891\pi$
$674$	−13.7854	−0.530995
$675$	13.8135	0.531683
$676$	−9.32702	−0.358731
$677$	−20.4543	−0.786124	−0.393062	−	0.919512i	$-0.628584\pi$
$677$	−20.4543	−0.786124	−0.393062	+	0.919512i	$0.628584\pi$
$678$	26.9489	1.03497
$679$	−8.88831	−0.341102
$680$	2.11043	0.0809313
$681$	−43.3795	−1.66231
$682$	73.7751	2.82499
$683$	4.87265	0.186447	0.0932233	−	0.995645i	$-0.470283\pi$
$683$	4.87265	0.186447	0.0932233	+	0.995645i	$0.470283\pi$
$684$	−0.0278783	−0.00106595
$685$	22.3005	0.852057
$686$	−17.6072	−0.672246
$687$	−30.3692	−1.15866
$688$	−62.0835	−2.36691
$689$	13.4756	0.513380
$690$	15.8935	0.605056
$691$	−3.22095	−0.122531	−0.0612654	−	0.998122i	$-0.519514\pi$
$691$	−3.22095	−0.122531	−0.0612654	+	0.998122i	$0.519514\pi$
$692$	12.5630	0.477573
$693$	−0.0405794	−0.00154148
$694$	−0.204704	−0.00777045
$695$	−10.4713	−0.397199
$696$	2.21678	0.0840270
$697$	0.800686	0.0303281
$698$	−33.9508	−1.28506
$699$	37.9021	1.43359
$700$	1.72228	0.0650961
$701$	16.7635	0.633147	0.316574	−	0.948568i	$-0.397468\pi$
$701$	16.7635	0.633147	0.316574	+	0.948568i	$0.397468\pi$
$702$	11.4315	0.431454
$703$	4.12586	0.155610
$704$	12.1740	0.458827
$705$	−15.3648	−0.578673
$706$	−41.5234	−1.56275
$707$	−13.1504	−0.494573
$708$	−5.75378	−0.216240
$709$	11.9057	0.447127	0.223563	−	0.974689i	$-0.428231\pi$
$709$	11.9057	0.447127	0.223563	+	0.974689i	$0.428231\pi$
$710$	30.0797	1.12887
$711$	−0.156047	−0.00585221
$712$	33.8107	1.26711
$713$	32.4237	1.21428
$714$	1.59710	0.0597701
$715$	9.66504	0.361452
$716$	11.6748	0.436309
$717$	8.64610	0.322895
$718$	−52.7344	−1.96803
$719$	12.2479	0.456768	0.228384	−	0.973571i	$-0.426656\pi$
$719$	12.2479	0.456768	0.228384	+	0.973571i	$0.426656\pi$
$720$	−0.0817167	−0.00304540
$721$	−0.782217	−0.0291313
$722$	15.4196	0.573857
$723$	13.2452	0.492593
$724$	−8.26189	−0.307051
$725$	−1.72487	−0.0640599
$726$	−35.7748	−1.32773
$727$	20.1823	0.748520	0.374260	−	0.927324i	$-0.377897\pi$
$727$	20.1823	0.748520	0.374260	+	0.927324i	$0.377897\pi$
$728$	−2.02266	−0.0749648
$729$	26.9025	0.996389
$730$	−8.73420	−0.323267
$731$	8.74273	0.323361
$732$	0.966621	0.0357274
$733$	−16.3107	−0.602451	−0.301225	−	0.953553i	$-0.597396\pi$
$733$	−16.3107	−0.602451	−0.301225	+	0.953553i	$0.597396\pi$
$734$	13.9796	0.515995
$735$	−16.9442	−0.624998
$736$	−15.7199	−0.579442
$737$	32.1084	1.18273
$738$	−0.0206883	−0.000761549 0
$739$	−38.7789	−1.42651	−0.713253	−	0.700907i	$-0.752779\pi$
$739$	−38.7789	−1.42651	−0.713253	+	0.700907i	$0.752779\pi$
$740$	−1.66321	−0.0611408
$741$	−7.13095	−0.261962
$742$	13.5194	0.496314
$743$	−2.30849	−0.0846903	−0.0423451	−	0.999103i	$-0.513483\pi$
$743$	−2.30849	−0.0846903	−0.0423451	+	0.999103i	$0.513483\pi$
$744$	−31.1392	−1.14162
$745$	−23.3503	−0.855490
$746$	36.2366	1.32671
$747$	−0.0463127	−0.00169449
$748$	2.79081	0.102042
$749$	−10.7604	−0.393177
$750$	34.1745	1.24787
$751$	17.2692	0.630161	0.315080	−	0.949065i	$-0.397969\pi$
$751$	17.2692	0.630161	0.315080	+	0.949065i	$0.397969\pi$
$752$	28.7896	1.04985
$753$	44.6347	1.62658
$754$	−1.42743	−0.0519838
$755$	−31.4098	−1.14312
$756$	3.35427	0.121994
$757$	34.3910	1.24996	0.624981	−	0.780640i	$-0.285107\pi$
$757$	34.3910	1.24996	0.624981	+	0.780640i	$0.285107\pi$
$758$	27.0955	0.984154
$759$	−29.8263	−1.08263
$760$	−9.45355	−0.342916
$761$	−50.8178	−1.84214	−0.921072	−	0.389393i	$-0.872685\pi$
$761$	−50.8178	−1.84214	−0.921072	+	0.389393i	$0.872685\pi$
$762$	−7.03643	−0.254903
$763$	−3.30643	−0.119701
$764$	11.5210	0.416816
$765$	0.0115075	0.000416055 0
$766$	36.2976	1.31148
$767$	−5.25781	−0.189848
$768$	29.3563	1.05930
$769$	−51.6513	−1.86259	−0.931297	−	0.364261i	$-0.881322\pi$
$769$	−51.6513	−1.86259	−0.931297	+	0.364261i	$0.881322\pi$
$770$	9.69646	0.349436
$771$	7.85696	0.282962
$772$	−1.15746	−0.0416578
$773$	−31.2270	−1.12316	−0.561579	−	0.827423i	$-0.689806\pi$
$773$	−31.2270	−1.12316	−0.561579	+	0.827423i	$0.689806\pi$
$774$	−0.225897	−0.00811970
$775$	24.2292	0.870338
$776$	22.4144	0.804631
$777$	1.78620	0.0640795
$778$	30.9743	1.11048
$779$	−3.58662	−0.128504
$780$	2.87462	0.102928
$781$	−56.4487	−2.01989
$782$	4.19370	0.149966
$783$	−3.35930	−0.120052
$784$	31.7489	1.13389
$785$	20.8493	0.744142
$786$	32.4219	1.15645
$787$	35.3181	1.25895	0.629477	−	0.777019i	$-0.283269\pi$
$787$	35.3181	1.25895	0.629477	+	0.777019i	$0.283269\pi$
$788$	−2.60748	−0.0928877
$789$	8.71608	0.310301
$790$	37.2874	1.32663
$791$	7.22581	0.256920
$792$	0.102333	0.00363623
$793$	0.883299	0.0313669
$794$	−14.1300	−0.501454
$795$	27.2669	0.967058
$796$	22.6417	0.802513
$797$	−44.9084	−1.59074	−0.795369	−	0.606126i	$-0.792723\pi$
$797$	−44.9084	−1.59074	−0.795369	+	0.606126i	$0.792723\pi$
$798$	−7.15414	−0.253254
$799$	−4.05420	−0.143427
$800$	−11.7470	−0.415318
$801$	0.184359	0.00651399
$802$	20.2164	0.713864
$803$	16.3909	0.578422
$804$	9.54981	0.336796
$805$	4.26153	0.150199
$806$	20.0511	0.706269
$807$	−0.0182421	−0.000642153 0
$808$	33.1626	1.16666
$809$	−36.7446	−1.29187	−0.645937	−	0.763391i	$-0.723533\pi$
$809$	−36.7446	−1.29187	−0.645937	+	0.763391i	$0.723533\pi$
$810$	23.2137	0.815647
$811$	−15.2204	−0.534462	−0.267231	−	0.963633i	$-0.586109\pi$
$811$	−15.2204	−0.534462	−0.267231	+	0.963633i	$0.586109\pi$
$812$	−0.418840	−0.0146984
$813$	2.62417	0.0920336
$814$	10.6719	0.374050
$815$	−12.0660	−0.422653
$816$	−6.03556	−0.211287
$817$	−39.1625	−1.37012
$818$	−2.81572	−0.0984493
$819$	−0.0110289	−0.000385382 0
$820$	1.44583	0.0504907
$821$	53.5982	1.87059	0.935295	−	0.353869i	$-0.115134\pi$
$821$	53.5982	1.87059	0.935295	+	0.353869i	$0.115134\pi$
$822$	−42.5584	−1.48439
$823$	10.3285	0.360029	0.180015	−	0.983664i	$-0.442386\pi$
$823$	10.3285	0.360029	0.180015	+	0.983664i	$0.442386\pi$
$824$	1.97258	0.0687182
$825$	−22.2882	−0.775977
$826$	−5.27490	−0.183537
$827$	−6.88941	−0.239568	−0.119784	−	0.992800i	$-0.538220\pi$
$827$	−6.88941	−0.239568	−0.119784	+	0.992800i	$0.538220\pi$
$828$	−0.0316918	−0.00110136
$829$	53.6978	1.86500	0.932500	−	0.361169i	$-0.117622\pi$
$829$	53.6978	1.86500	0.932500	+	0.361169i	$0.117622\pi$
$830$	11.0664	0.384121
$831$	−9.31279	−0.323057
$832$	3.30874	0.114710
$833$	−4.47095	−0.154909
$834$	19.9835	0.691973
$835$	−10.2390	−0.354336
$836$	−12.5013	−0.432365
$837$	47.1881	1.63106
$838$	−9.14772	−0.316003
$839$	−31.1592	−1.07574	−0.537868	−	0.843029i	$-0.680770\pi$
$839$	−31.1592	−1.07574	−0.537868	+	0.843029i	$0.680770\pi$
$840$	−4.09270	−0.141212
$841$	−28.5805	−0.985536
$842$	−7.72971	−0.266383
$843$	41.5690	1.43171
$844$	22.3403	0.768986
$845$	−17.2457	−0.593270
$846$	0.104754	0.00360151
$847$	−9.59232	−0.329596
$848$	−51.0909	−1.75447
$849$	9.89834	0.339710
$850$	3.13382	0.107489
$851$	4.69023	0.160779
$852$	−16.7892	−0.575189
$853$	52.4569	1.79609	0.898046	−	0.439902i	$-0.144987\pi$
$853$	52.4569	1.79609	0.898046	+	0.439902i	$0.144987\pi$
$854$	0.886170	0.0303241
$855$	−0.0515472	−0.00176288
$856$	27.1355	0.927473
$857$	−8.85221	−0.302386	−0.151193	−	0.988504i	$-0.548311\pi$
$857$	−8.85221	−0.302386	−0.151193	+	0.988504i	$0.548311\pi$
$858$	−18.4448	−0.629696
$859$	−42.5410	−1.45148	−0.725741	−	0.687968i	$-0.758503\pi$
$859$	−42.5410	−1.45148	−0.725741	+	0.687968i	$0.758503\pi$
$860$	15.7871	0.538337
$861$	−1.55275	−0.0529176
$862$	−12.7745	−0.435102
$863$	−31.6927	−1.07883	−0.539416	−	0.842039i	$-0.681355\pi$
$863$	−31.6927	−1.07883	−0.539416	+	0.842039i	$0.681355\pi$
$864$	−22.8781	−0.778327
$865$	23.2290	0.789810
$866$	35.6509	1.21147
$867$	−28.6477	−0.972926
$868$	5.88345	0.199697
$869$	−69.9749	−2.37374
$870$	−2.88829	−0.0979222
$871$	8.72662	0.295690
$872$	8.33811	0.282364
$873$	0.122219	0.00413648
$874$	−18.7854	−0.635427
$875$	9.16321	0.309773
$876$	4.87505	0.164713
$877$	14.5294	0.490622	0.245311	−	0.969444i	$-0.421110\pi$
$877$	14.5294	0.490622	0.245311	+	0.969444i	$0.421110\pi$
$878$	−0.193145	−0.00651833
$879$	−0.799146	−0.0269545
$880$	−36.6436	−1.23525
$881$	−42.5188	−1.43249	−0.716247	−	0.697847i	$-0.754142\pi$
$881$	−42.5188	−1.43249	−0.716247	+	0.697847i	$0.754142\pi$
$882$	0.115522	0.00388982
$883$	−29.3820	−0.988785	−0.494392	−	0.869239i	$-0.664609\pi$
$883$	−29.3820	−0.988785	−0.494392	+	0.869239i	$0.664609\pi$
$884$	0.758504	0.0255112
$885$	−10.6388	−0.357619
$886$	−23.4624	−0.788234
$887$	−32.1116	−1.07820	−0.539102	−	0.842241i	$-0.681236\pi$
$887$	−32.1116	−1.07820	−0.539102	+	0.842241i	$0.681236\pi$
$888$	−4.50442	−0.151158
$889$	−1.88668	−0.0632772
$890$	−44.0526	−1.47665
$891$	−43.5636	−1.45944
$892$	−21.2135	−0.710280
$893$	18.1606	0.607720
$894$	44.5619	1.49037
$895$	21.5869	0.721569
$896$	10.2199	0.341424
$897$	−8.10639	−0.270664
$898$	9.22299	0.307775
$899$	−5.89228	−0.196519
$900$	−0.0236822	−0.000789408 0
$901$	7.19471	0.239691
$902$	−9.27711	−0.308894
$903$	−16.9546	−0.564212
$904$	−18.2220	−0.606054
$905$	−15.2763	−0.507801
$906$	59.9427	1.99146
$907$	42.5862	1.41405	0.707026	−	0.707187i	$-0.250036\pi$
$907$	42.5862	1.41405	0.707026	+	0.707187i	$0.250036\pi$
$908$	−20.6690	−0.685924
$909$	0.180825	0.00599759
$910$	2.63537	0.0873615
$911$	−38.1513	−1.26401	−0.632004	−	0.774965i	$-0.717767\pi$
$911$	−38.1513	−1.26401	−0.632004	+	0.774965i	$0.717767\pi$
$912$	27.0360	0.895250
$913$	−20.7676	−0.687308
$914$	−48.4696	−1.60323
$915$	1.78729	0.0590859
$916$	−14.4700	−0.478101
$917$	8.69330	0.287078
$918$	6.10334	0.201440
$919$	−33.4526	−1.10350	−0.551749	−	0.834010i	$-0.686039\pi$
$919$	−33.4526	−1.10350	−0.551749	+	0.834010i	$0.686039\pi$
$920$	−10.7467	−0.354308
$921$	12.2013	0.402047
$922$	35.8625	1.18107
$923$	−15.3420	−0.504987
$924$	−5.41214	−0.178046
$925$	3.50486	0.115239
$926$	−56.1251	−1.84439
$927$	0.0107559	0.000353269 0
$928$	2.85673	0.0937769
$929$	35.9530	1.17958	0.589790	−	0.807556i	$-0.299210\pi$
$929$	35.9530	1.17958	0.589790	+	0.807556i	$0.299210\pi$
$930$	40.5718	1.33040
$931$	20.0273	0.656370
$932$	18.0591	0.591547
$933$	−9.01681	−0.295197
$934$	36.2964	1.18765
$935$	5.16022	0.168757
$936$	0.0278126	0.000909084 0
$937$	53.8212	1.75826	0.879131	−	0.476580i	$-0.158124\pi$
$937$	53.8212	1.75826	0.879131	+	0.476580i	$0.158124\pi$
$938$	8.75499	0.285860
$939$	−37.7306	−1.23129
$940$	−7.32086	−0.238780
$941$	−16.8357	−0.548829	−0.274414	−	0.961612i	$-0.588484\pi$
$941$	−16.8357	−0.548829	−0.274414	+	0.961612i	$0.588484\pi$
$942$	−39.7889	−1.29639
$943$	−4.07723	−0.132773
$944$	19.9342	0.648803
$945$	6.20206	0.201753
$946$	−101.297	−3.29346
$947$	−29.3206	−0.952792	−0.476396	−	0.879231i	$-0.658057\pi$
$947$	−29.3206	−0.952792	−0.476396	+	0.879231i	$0.658057\pi$
$948$	−20.8122	−0.675950
$949$	4.45482	0.144610
$950$	−14.0378	−0.455445
$951$	2.38579	0.0773647
$952$	−1.07991	−0.0350001
$953$	−17.7916	−0.576328	−0.288164	−	0.957581i	$-0.593045\pi$
$953$	−17.7916	−0.576328	−0.288164	+	0.957581i	$0.593045\pi$
$954$	−0.185899	−0.00601871
$955$	21.3025	0.689331
$956$	4.11959	0.133237
$957$	5.42026	0.175212
$958$	38.9307	1.25779
$959$	−11.4112	−0.368487
$960$	6.69499	0.216080
$961$	51.7688	1.66996
$962$	2.90048	0.0935151
$963$	0.147961	0.00476799
$964$	6.31090	0.203260
$965$	−2.14014	−0.0688937
$966$	−8.13274	−0.261667
$967$	15.9325	0.512354	0.256177	−	0.966630i	$-0.417537\pi$
$967$	15.9325	0.512354	0.256177	+	0.966630i	$0.417537\pi$
$968$	24.1898	0.777490
$969$	−3.80726	−0.122307
$970$	−29.2042	−0.937690
$971$	−24.5069	−0.786465	−0.393232	−	0.919439i	$-0.628643\pi$
$971$	−24.5069	−0.786465	−0.393232	+	0.919439i	$0.628643\pi$
$972$	−0.0924118	−0.00296411
$973$	5.35819	0.171776
$974$	38.4772	1.23289
$975$	−6.05764	−0.194000
$976$	−3.34890	−0.107196
$977$	36.6526	1.17262	0.586311	−	0.810086i	$-0.300580\pi$
$977$	36.6526	1.17262	0.586311	+	0.810086i	$0.300580\pi$
$978$	23.0268	0.736316
$979$	82.6705	2.64216
$980$	−8.07339	−0.257895
$981$	0.0454650	0.00145159
$982$	−10.2472	−0.327000
$983$	−51.6002	−1.64579	−0.822895	−	0.568194i	$-0.807642\pi$
$983$	−51.6002	−1.64579	−0.822895	+	0.568194i	$0.807642\pi$
$984$	3.91571	0.124828
$985$	−4.82125	−0.153618
$986$	−0.762111	−0.0242706
$987$	7.86222	0.250257
$988$	−3.39767	−0.108094
$989$	−44.5195	−1.41564
$990$	−0.133331	−0.00423754
$991$	21.7388	0.690556	0.345278	−	0.938501i	$-0.387785\pi$
$991$	21.7388	0.690556	0.345278	+	0.938501i	$0.387785\pi$
$992$	−40.1285	−1.27408
$993$	38.0306	1.20686
$994$	−15.3919	−0.488200
$995$	41.8646	1.32720
$996$	−6.17680	−0.195719
$997$	36.9295	1.16957	0.584785	−	0.811188i	$-0.301179\pi$
$997$	36.9295	1.16957	0.584785	+	0.811188i	$0.301179\pi$
$998$	37.6751	1.19258
$999$	6.82597	0.215964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	103.2.a.b.1.1	✓	6
3.2	odd	2		927.2.a.f.1.6		6
4.3	odd	2		1648.2.a.m.1.2		6
5.4	even	2		2575.2.a.k.1.6		6
7.6	odd	2		5047.2.a.d.1.1		6
8.3	odd	2		6592.2.a.be.1.5		6
8.5	even	2		6592.2.a.bd.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
103.2.a.b.1.1	✓	6	1.1	even	1	trivial
927.2.a.f.1.6		6	3.2	odd	2
1648.2.a.m.1.2		6	4.3	odd	2
2575.2.a.k.1.6		6	5.4	even	2
5047.2.a.d.1.1		6	7.6	odd	2
6592.2.a.bd.1.2		6	8.5	even	2
6592.2.a.be.1.5		6	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	103.a (trivial)

\(f(q)\)	\(=\)	\(q-1.68129 q^{2} +1.73515 q^{3} +0.826745 q^{4} +1.52866 q^{5} -2.91730 q^{6} -0.782217 q^{7} +1.97258 q^{8} +0.0107559 q^{9} +O(q^{10})\)	\(q-1.68129 q^{2} +1.73515 q^{3} +0.826745 q^{4} +1.52866 q^{5} -2.91730 q^{6} -0.782217 q^{7} +1.97258 q^{8} +0.0107559 q^{9} -2.57012 q^{10} +4.82317 q^{11} +1.43453 q^{12} +1.31087 q^{13} +1.31513 q^{14} +2.65245 q^{15} -4.96998 q^{16} +0.699883 q^{17} -0.0180838 q^{18} -3.13508 q^{19} +1.26381 q^{20} -1.35727 q^{21} -8.10917 q^{22} -3.56393 q^{23} +3.42274 q^{24} -2.66321 q^{25} -2.20396 q^{26} -5.18680 q^{27} -0.646694 q^{28} +0.647664 q^{29} -4.45955 q^{30} -9.09774 q^{31} +4.41083 q^{32} +8.36894 q^{33} -1.17671 q^{34} -1.19574 q^{35} +0.00889237 q^{36} -1.31603 q^{37} +5.27099 q^{38} +2.27457 q^{39} +3.01540 q^{40} +1.14403 q^{41} +2.28196 q^{42} +12.4917 q^{43} +3.98754 q^{44} +0.0164420 q^{45} +5.99200 q^{46} -5.79269 q^{47} -8.62368 q^{48} -6.38814 q^{49} +4.47763 q^{50} +1.21440 q^{51} +1.08376 q^{52} +10.2799 q^{53} +8.72052 q^{54} +7.37298 q^{55} -1.54299 q^{56} -5.43985 q^{57} -1.08891 q^{58} -4.01092 q^{59} +2.19290 q^{60} +0.673825 q^{61} +15.2960 q^{62} -0.00841342 q^{63} +2.52407 q^{64} +2.00387 q^{65} -14.0706 q^{66} +6.65710 q^{67} +0.578625 q^{68} -6.18396 q^{69} +2.01039 q^{70} -11.7036 q^{71} +0.0212169 q^{72} +3.39836 q^{73} +2.21263 q^{74} -4.62107 q^{75} -2.59192 q^{76} -3.77277 q^{77} -3.82421 q^{78} -14.5081 q^{79} -7.59740 q^{80} -9.03215 q^{81} -1.92345 q^{82} -4.30580 q^{83} -1.12211 q^{84} +1.06988 q^{85} -21.0022 q^{86} +1.12380 q^{87} +9.51412 q^{88} +17.1403 q^{89} -0.0276439 q^{90} -1.02539 q^{91} -2.94646 q^{92} -15.7860 q^{93} +9.73921 q^{94} -4.79247 q^{95} +7.65346 q^{96} +11.3630 q^{97} +10.7403 q^{98} +0.0518774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 6 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 9 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + 4 * q^2 + 6 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 9 * q^8 + 8 * q^9	\( 6 q + 4 q^{2} + 6 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 9 q^{8} + 8 q^{9} - 10 q^{10} - q^{11} - 13 q^{12} - q^{13} - 9 q^{14} - 9 q^{15} + 2 q^{16} + 21 q^{17} - 3 q^{18} - 7 q^{19} - 9 q^{20} - 14 q^{21} - 11 q^{22} + 12 q^{23} - 36 q^{24} + q^{25} - 5 q^{26} - 10 q^{28} + 12 q^{29} + 2 q^{30} - 16 q^{31} + 27 q^{32} + 15 q^{33} + 10 q^{34} + 5 q^{35} - 3 q^{36} - 8 q^{38} + 5 q^{39} - q^{40} + 14 q^{41} + 25 q^{42} - 6 q^{43} - 4 q^{44} + 8 q^{45} + 19 q^{46} + q^{47} - 41 q^{48} - 2 q^{49} + q^{50} - 5 q^{51} - 5 q^{52} + 19 q^{53} + 23 q^{54} - 10 q^{55} - 13 q^{56} + 23 q^{57} + 4 q^{58} + 3 q^{59} + 17 q^{60} + q^{61} + 23 q^{62} - 20 q^{63} + 61 q^{64} + 23 q^{65} + q^{66} - 12 q^{67} + 14 q^{68} - 22 q^{69} - 14 q^{70} - 27 q^{71} + 31 q^{72} - 7 q^{73} + 15 q^{74} - 17 q^{75} - 38 q^{76} + 27 q^{77} - 20 q^{78} - 21 q^{79} - 28 q^{80} - 2 q^{81} + 53 q^{82} - 9 q^{83} + 61 q^{84} - 9 q^{85} - 11 q^{86} - 12 q^{87} - 31 q^{88} - 14 q^{89} - 22 q^{90} - 33 q^{91} + 30 q^{92} - 32 q^{93} - 6 q^{95} - 33 q^{96} - 8 q^{97} + 2 q^{98} - 54 q^{99}+O(q^{100}) \) 6 * q + 4 * q^2 + 6 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 9 * q^8 + 8 * q^9 - 10 * q^10 - q^11 - 13 * q^12 - q^13 - 9 * q^14 - 9 * q^15 + 2 * q^16 + 21 * q^17 - 3 * q^18 - 7 * q^19 - 9 * q^20 - 14 * q^21 - 11 * q^22 + 12 * q^23 - 36 * q^24 + q^25 - 5 * q^26 - 10 * q^28 + 12 * q^29 + 2 * q^30 - 16 * q^31 + 27 * q^32 + 15 * q^33 + 10 * q^34 + 5 * q^35 - 3 * q^36 - 8 * q^38 + 5 * q^39 - q^40 + 14 * q^41 + 25 * q^42 - 6 * q^43 - 4 * q^44 + 8 * q^45 + 19 * q^46 + q^47 - 41 * q^48 - 2 * q^49 + q^50 - 5 * q^51 - 5 * q^52 + 19 * q^53 + 23 * q^54 - 10 * q^55 - 13 * q^56 + 23 * q^57 + 4 * q^58 + 3 * q^59 + 17 * q^60 + q^61 + 23 * q^62 - 20 * q^63 + 61 * q^64 + 23 * q^65 + q^66 - 12 * q^67 + 14 * q^68 - 22 * q^69 - 14 * q^70 - 27 * q^71 + 31 * q^72 - 7 * q^73 + 15 * q^74 - 17 * q^75 - 38 * q^76 + 27 * q^77 - 20 * q^78 - 21 * q^79 - 28 * q^80 - 2 * q^81 + 53 * q^82 - 9 * q^83 + 61 * q^84 - 9 * q^85 - 11 * q^86 - 12 * q^87 - 31 * q^88 - 14 * q^89 - 22 * q^90 - 33 * q^91 + 30 * q^92 - 32 * q^93 - 6 * q^95 - 33 * q^96 - 8 * q^97 + 2 * q^98 - 54 * q^99

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