LMFDB - Embedded newform 2001.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 10x^{4} + 19x^{3} - 20x^{2} - 5x + 1 $ x^7 - x^6 - 9x^5 + 10x^4 + 19x^3 - 20x^2 - 5*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			1.7
Root			$-2.51747$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.35219 q^{2} +1.00000 q^{3} +3.53279 q^{4} -2.63525 q^{5} +2.35219 q^{6} -4.33765 q^{7} +3.60540 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.35219 q^{2} +1.00000 q^{3} +3.53279 q^{4} -2.63525 q^{5} +2.35219 q^{6} -4.33765 q^{7} +3.60540 q^{8} +1.00000 q^{9} -6.19860 q^{10} -3.30084 q^{11} +3.53279 q^{12} -1.48911 q^{13} -10.2030 q^{14} -2.63525 q^{15} +1.41501 q^{16} -3.34121 q^{17} +2.35219 q^{18} +3.79691 q^{19} -9.30978 q^{20} -4.33765 q^{21} -7.76420 q^{22} -1.00000 q^{23} +3.60540 q^{24} +1.94454 q^{25} -3.50266 q^{26} +1.00000 q^{27} -15.3240 q^{28} +1.00000 q^{29} -6.19860 q^{30} -4.86510 q^{31} -3.88244 q^{32} -3.30084 q^{33} -7.85914 q^{34} +11.4308 q^{35} +3.53279 q^{36} -5.99002 q^{37} +8.93105 q^{38} -1.48911 q^{39} -9.50113 q^{40} +6.66158 q^{41} -10.2030 q^{42} +0.770188 q^{43} -11.6612 q^{44} -2.63525 q^{45} -2.35219 q^{46} +11.2431 q^{47} +1.41501 q^{48} +11.8152 q^{49} +4.57393 q^{50} -3.34121 q^{51} -5.26070 q^{52} -1.22215 q^{53} +2.35219 q^{54} +8.69855 q^{55} -15.6390 q^{56} +3.79691 q^{57} +2.35219 q^{58} -2.22832 q^{59} -9.30978 q^{60} -7.57893 q^{61} -11.4436 q^{62} -4.33765 q^{63} -11.9622 q^{64} +3.92418 q^{65} -7.76420 q^{66} +2.09311 q^{67} -11.8038 q^{68} -1.00000 q^{69} +26.8874 q^{70} -6.50468 q^{71} +3.60540 q^{72} -3.22880 q^{73} -14.0897 q^{74} +1.94454 q^{75} +13.4137 q^{76} +14.3179 q^{77} -3.50266 q^{78} +3.80647 q^{79} -3.72889 q^{80} +1.00000 q^{81} +15.6693 q^{82} -4.75913 q^{83} -15.3240 q^{84} +8.80492 q^{85} +1.81163 q^{86} +1.00000 q^{87} -11.9009 q^{88} +4.46726 q^{89} -6.19860 q^{90} +6.45924 q^{91} -3.53279 q^{92} -4.86510 q^{93} +26.4459 q^{94} -10.0058 q^{95} -3.88244 q^{96} -10.8888 q^{97} +27.7917 q^{98} -3.30084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9} - 11 q^{10} - 12 q^{11} + 7 q^{12} - 13 q^{13} - 3 q^{14} - 5 q^{15} - 13 q^{16} - 12 q^{17} - q^{18} - 5 q^{19} - 8 q^{20} - 5 q^{21} - q^{22} - 7 q^{23} + 3 q^{24} - 4 q^{25} + 2 q^{26} + 7 q^{27} - 21 q^{28} + 7 q^{29} - 11 q^{30} - 8 q^{31} - 5 q^{32} - 12 q^{33} - 28 q^{34} + 5 q^{35} + 7 q^{36} - 24 q^{37} - 6 q^{38} - 13 q^{39} - 20 q^{40} + 9 q^{41} - 3 q^{42} - q^{43} - 23 q^{44} - 5 q^{45} + q^{46} + 27 q^{47} - 13 q^{48} - 14 q^{49} + 7 q^{50} - 12 q^{51} - 9 q^{52} - q^{53} - q^{54} - 11 q^{55} - 20 q^{56} - 5 q^{57} - q^{58} + 8 q^{59} - 8 q^{60} + q^{61} - 5 q^{63} + 3 q^{64} + 12 q^{65} - q^{66} - 16 q^{67} + 15 q^{68} - 7 q^{69} + 40 q^{70} - 13 q^{71} + 3 q^{72} - 23 q^{73} - 8 q^{74} - 4 q^{75} - 2 q^{76} + 13 q^{77} + 2 q^{78} - 44 q^{79} + 30 q^{80} + 7 q^{81} - 10 q^{82} + 21 q^{83} - 21 q^{84} + 6 q^{86} + 7 q^{87} + 21 q^{88} - 5 q^{89} - 11 q^{90} - 18 q^{91} - 7 q^{92} - 8 q^{93} + 28 q^{94} + 9 q^{95} - 5 q^{96} - 55 q^{97} + 36 q^{98} - 12 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9 - 11 * q^10 - 12 * q^11 + 7 * q^12 - 13 * q^13 - 3 * q^14 - 5 * q^15 - 13 * q^16 - 12 * q^17 - q^18 - 5 * q^19 - 8 * q^20 - 5 * q^21 - q^22 - 7 * q^23 + 3 * q^24 - 4 * q^25 + 2 * q^26 + 7 * q^27 - 21 * q^28 + 7 * q^29 - 11 * q^30 - 8 * q^31 - 5 * q^32 - 12 * q^33 - 28 * q^34 + 5 * q^35 + 7 * q^36 - 24 * q^37 - 6 * q^38 - 13 * q^39 - 20 * q^40 + 9 * q^41 - 3 * q^42 - q^43 - 23 * q^44 - 5 * q^45 + q^46 + 27 * q^47 - 13 * q^48 - 14 * q^49 + 7 * q^50 - 12 * q^51 - 9 * q^52 - q^53 - q^54 - 11 * q^55 - 20 * q^56 - 5 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + q^61 - 5 * q^63 + 3 * q^64 + 12 * q^65 - q^66 - 16 * q^67 + 15 * q^68 - 7 * q^69 + 40 * q^70 - 13 * q^71 + 3 * q^72 - 23 * q^73 - 8 * q^74 - 4 * q^75 - 2 * q^76 + 13 * q^77 + 2 * q^78 - 44 * q^79 + 30 * q^80 + 7 * q^81 - 10 * q^82 + 21 * q^83 - 21 * q^84 + 6 * q^86 + 7 * q^87 + 21 * q^88 - 5 * q^89 - 11 * q^90 - 18 * q^91 - 7 * q^92 - 8 * q^93 + 28 * q^94 + 9 * q^95 - 5 * q^96 - 55 * q^97 + 36 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.35219	1.66325	0.831624	−	0.555339i	$-0.187412\pi$
$2$	2.35219	1.66325	0.831624	+	0.555339i	$0.187412\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.53279	1.76639
$5$	−2.63525	−1.17852	−0.589260	−	0.807944i	$-0.700581\pi$
$5$	−2.63525	−1.17852	−0.589260	+	0.807944i	$0.700581\pi$
$6$	2.35219	0.960277
$7$	−4.33765	−1.63948	−0.819740	−	0.572736i	$-0.805882\pi$
$7$	−4.33765	−1.63948	−0.819740	+	0.572736i	$0.805882\pi$
$8$	3.60540	1.27470
$9$	1.00000	0.333333
$10$	−6.19860	−1.96017
$11$	−3.30084	−0.995242	−0.497621	−	0.867395i	$-0.665793\pi$
$11$	−3.30084	−0.995242	−0.497621	+	0.867395i	$0.665793\pi$
$12$	3.53279	1.01983
$13$	−1.48911	−0.413005	−0.206502	−	0.978446i	$-0.566208\pi$
$13$	−1.48911	−0.413005	−0.206502	+	0.978446i	$0.566208\pi$
$14$	−10.2030	−2.72686
$15$	−2.63525	−0.680419
$16$	1.41501	0.353751
$17$	−3.34121	−0.810362	−0.405181	−	0.914237i	$-0.632791\pi$
$17$	−3.34121	−0.810362	−0.405181	+	0.914237i	$0.632791\pi$
$18$	2.35219	0.554416
$19$	3.79691	0.871072	0.435536	−	0.900171i	$-0.356559\pi$
$19$	3.79691	0.871072	0.435536	+	0.900171i	$0.356559\pi$
$20$	−9.30978	−2.08173
$21$	−4.33765	−0.946554
$22$	−7.76420	−1.65533
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.60540	0.735949
$25$	1.94454	0.388909
$26$	−3.50266	−0.686929
$27$	1.00000	0.192450
$28$	−15.3240	−2.89596
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−6.19860	−1.13170
$31$	−4.86510	−0.873798	−0.436899	−	0.899511i	$-0.643923\pi$
$31$	−4.86510	−0.873798	−0.436899	+	0.899511i	$0.643923\pi$
$32$	−3.88244	−0.686325
$33$	−3.30084	−0.574603
$34$	−7.85914	−1.34783
$35$	11.4308	1.93216
$36$	3.53279	0.588798
$37$	−5.99002	−0.984754	−0.492377	−	0.870382i	$-0.663872\pi$
$37$	−5.99002	−0.984754	−0.492377	+	0.870382i	$0.663872\pi$
$38$	8.93105	1.44881
$39$	−1.48911	−0.238448
$40$	−9.50113	−1.50226
$41$	6.66158	1.04036	0.520182	−	0.854055i	$-0.325864\pi$
$41$	6.66158	1.04036	0.520182	+	0.854055i	$0.325864\pi$
$42$	−10.2030	−1.57435
$43$	0.770188	0.117453	0.0587263	−	0.998274i	$-0.481296\pi$
$43$	0.770188	0.117453	0.0587263	+	0.998274i	$0.481296\pi$
$44$	−11.6612	−1.75799
$45$	−2.63525	−0.392840
$46$	−2.35219	−0.346811
$47$	11.2431	1.63998	0.819988	−	0.572380i	$-0.193980\pi$
$47$	11.2431	1.63998	0.819988	+	0.572380i	$0.193980\pi$
$48$	1.41501	0.204238
$49$	11.8152	1.68789
$50$	4.57393	0.646852
$51$	−3.34121	−0.467863
$52$	−5.26070	−0.729528
$53$	−1.22215	−0.167875	−0.0839373	−	0.996471i	$-0.526750\pi$
$53$	−1.22215	−0.167875	−0.0839373	+	0.996471i	$0.526750\pi$
$54$	2.35219	0.320092
$55$	8.69855	1.17291
$56$	−15.6390	−2.08985
$57$	3.79691	0.502913
$58$	2.35219	0.308857
$59$	−2.22832	−0.290103	−0.145051	−	0.989424i	$-0.546335\pi$
$59$	−2.22832	−0.290103	−0.145051	+	0.989424i	$0.546335\pi$
$60$	−9.30978	−1.20189
$61$	−7.57893	−0.970382	−0.485191	−	0.874408i	$-0.661250\pi$
$61$	−7.57893	−0.970382	−0.485191	+	0.874408i	$0.661250\pi$
$62$	−11.4436	−1.45334
$63$	−4.33765	−0.546493
$64$	−11.9622	−1.49528
$65$	3.92418	0.486734
$66$	−7.76420	−0.955708
$67$	2.09311	0.255714	0.127857	−	0.991793i	$-0.459190\pi$
$67$	2.09311	0.255714	0.127857	+	0.991793i	$0.459190\pi$
$68$	−11.8038	−1.43142
$69$	−1.00000	−0.120386
$70$	26.8874	3.21366
$71$	−6.50468	−0.771964	−0.385982	−	0.922506i	$-0.626137\pi$
$71$	−6.50468	−0.771964	−0.385982	+	0.922506i	$0.626137\pi$
$72$	3.60540	0.424901
$73$	−3.22880	−0.377902	−0.188951	−	0.981987i	$-0.560509\pi$
$73$	−3.22880	−0.377902	−0.188951	+	0.981987i	$0.560509\pi$
$74$	−14.0897	−1.63789
$75$	1.94454	0.224537
$76$	13.4137	1.53866
$77$	14.3179	1.63168
$78$	−3.50266	−0.396599
$79$	3.80647	0.428261	0.214131	−	0.976805i	$-0.431308\pi$
$79$	3.80647	0.428261	0.214131	+	0.976805i	$0.431308\pi$
$80$	−3.72889	−0.416903
$81$	1.00000	0.111111
$82$	15.6693	1.73038
$83$	−4.75913	−0.522382	−0.261191	−	0.965287i	$-0.584115\pi$
$83$	−4.75913	−0.522382	−0.261191	+	0.965287i	$0.584115\pi$
$84$	−15.3240	−1.67199
$85$	8.80492	0.955027
$86$	1.81163	0.195353
$87$	1.00000	0.107211
$88$	−11.9009	−1.26864
$89$	4.46726	0.473529	0.236764	−	0.971567i	$-0.423913\pi$
$89$	4.46726	0.473529	0.236764	+	0.971567i	$0.423913\pi$
$90$	−6.19860	−0.653390
$91$	6.45924	0.677112
$92$	−3.53279	−0.368318
$93$	−4.86510	−0.504487
$94$	26.4459	2.72769
$95$	−10.0058	−1.02658
$96$	−3.88244	−0.396250
$97$	−10.8888	−1.10559	−0.552795	−	0.833317i	$-0.686439\pi$
$97$	−10.8888	−1.10559	−0.552795	+	0.833317i	$0.686439\pi$
$98$	27.7917	2.80738
$99$	−3.30084	−0.331747
$100$	6.86966	0.686966
$101$	−9.47066	−0.942366	−0.471183	−	0.882036i	$-0.656173\pi$
$101$	−9.47066	−0.942366	−0.471183	+	0.882036i	$0.656173\pi$
$102$	−7.85914	−0.778171
$103$	−2.80325	−0.276212	−0.138106	−	0.990417i	$-0.544102\pi$
$103$	−2.80325	−0.276212	−0.138106	+	0.990417i	$0.544102\pi$
$104$	−5.36883	−0.526458
$105$	11.4308	1.11553
$106$	−2.87472	−0.279217
$107$	16.8197	1.62602	0.813011	−	0.582248i	$-0.197827\pi$
$107$	16.8197	1.62602	0.813011	+	0.582248i	$0.197827\pi$
$108$	3.53279	0.339943
$109$	13.4063	1.28409	0.642045	−	0.766667i	$-0.278086\pi$
$109$	13.4063	1.28409	0.642045	+	0.766667i	$0.278086\pi$
$110$	20.4606	1.95084
$111$	−5.99002	−0.568548
$112$	−6.13781	−0.579968
$113$	−6.83233	−0.642731	−0.321366	−	0.946955i	$-0.604142\pi$
$113$	−6.83233	−0.642731	−0.321366	+	0.946955i	$0.604142\pi$
$114$	8.93105	0.836470
$115$	2.63525	0.245738
$116$	3.53279	0.328011
$117$	−1.48911	−0.137668
$118$	−5.24143	−0.482513
$119$	14.4930	1.32857
$120$	−9.50113	−0.867331
$121$	−0.104428	−0.00949342
$122$	−17.8271	−1.61399
$123$	6.66158	0.600655
$124$	−17.1874	−1.54347
$125$	8.05189	0.720183
$126$	−10.2030	−0.908953
$127$	0.580826	0.0515400	0.0257700	−	0.999668i	$-0.491796\pi$
$127$	0.580826	0.0515400	0.0257700	+	0.999668i	$0.491796\pi$
$128$	−20.3726	−1.80070
$129$	0.770188	0.0678113
$130$	9.23040	0.809559
$131$	−2.97498	−0.259925	−0.129963	−	0.991519i	$-0.541486\pi$
$131$	−2.97498	−0.259925	−0.129963	+	0.991519i	$0.541486\pi$
$132$	−11.6612	−1.01498
$133$	−16.4697	−1.42810
$134$	4.92339	0.425317
$135$	−2.63525	−0.226806
$136$	−12.0464	−1.03297
$137$	14.5896	1.24647	0.623237	−	0.782033i	$-0.285817\pi$
$137$	14.5896	1.24647	0.623237	+	0.782033i	$0.285817\pi$
$138$	−2.35219	−0.200231
$139$	−6.91813	−0.586788	−0.293394	−	0.955992i	$-0.594785\pi$
$139$	−6.91813	−0.586788	−0.293394	+	0.955992i	$0.594785\pi$
$140$	40.3826	3.41295
$141$	11.2431	0.946841
$142$	−15.3002	−1.28397
$143$	4.91532	0.411039
$144$	1.41501	0.117917
$145$	−2.63525	−0.218846
$146$	−7.59474	−0.628545
$147$	11.8152	0.974505
$148$	−21.1615	−1.73946
$149$	−8.66779	−0.710093	−0.355046	−	0.934849i	$-0.615535\pi$
$149$	−8.66779	−0.710093	−0.355046	+	0.934849i	$0.615535\pi$
$150$	4.57393	0.373460
$151$	−12.8099	−1.04245	−0.521227	−	0.853418i	$-0.674526\pi$
$151$	−12.8099	−1.04245	−0.521227	+	0.853418i	$0.674526\pi$
$152$	13.6894	1.11036
$153$	−3.34121	−0.270121
$154$	33.6784	2.71389
$155$	12.8208	1.02979
$156$	−5.26070	−0.421193
$157$	0.0182463	0.00145621	0.000728105	−	1.00000i	$-0.499768\pi$
$157$	0.0182463	0.00145621	0.000728105		1.00000i	$0.499768\pi$
$158$	8.95353	0.712304
$159$	−1.22215	−0.0969225
$160$	10.2312	0.808848
$161$	4.33765	0.341855
$162$	2.35219	0.184805
$163$	5.13185	0.401958	0.200979	−	0.979596i	$-0.435588\pi$
$163$	5.13185	0.401958	0.200979	+	0.979596i	$0.435588\pi$
$164$	23.5340	1.83769
$165$	8.69855	0.677181
$166$	−11.1944	−0.868850
$167$	−14.0363	−1.08616	−0.543081	−	0.839680i	$-0.682742\pi$
$167$	−14.0363	−1.08616	−0.543081	+	0.839680i	$0.682742\pi$
$168$	−15.6390	−1.20657
$169$	−10.7826	−0.829427
$170$	20.7108	1.58845
$171$	3.79691	0.290357
$172$	2.72091	0.207467
$173$	13.3038	1.01147	0.505734	−	0.862689i	$-0.331222\pi$
$173$	13.3038	1.01147	0.505734	+	0.862689i	$0.331222\pi$
$174$	2.35219	0.178319
$175$	−8.43476	−0.637608
$176$	−4.67071	−0.352068
$177$	−2.22832	−0.167491
$178$	10.5078	0.787596
$179$	−26.3319	−1.96814	−0.984069	−	0.177786i	$-0.943106\pi$
$179$	−26.3319	−1.96814	−0.984069	+	0.177786i	$0.943106\pi$
$180$	−9.30978	−0.693910
$181$	−6.13764	−0.456207	−0.228104	−	0.973637i	$-0.573252\pi$
$181$	−6.13764	−0.456207	−0.228104	+	0.973637i	$0.573252\pi$
$182$	15.1933	1.12621
$183$	−7.57893	−0.560250
$184$	−3.60540	−0.265794
$185$	15.7852	1.16055
$186$	−11.4436	−0.839087
$187$	11.0288	0.806506
$188$	39.7195	2.89684
$189$	−4.33765	−0.315518
$190$	−23.5356	−1.70745
$191$	−6.26651	−0.453429	−0.226714	−	0.973961i	$-0.572798\pi$
$191$	−6.26651	−0.453429	−0.226714	+	0.973961i	$0.572798\pi$
$192$	−11.9622	−0.863301
$193$	−0.583321	−0.0419884	−0.0209942	−	0.999780i	$-0.506683\pi$
$193$	−0.583321	−0.0419884	−0.0209942	+	0.999780i	$0.506683\pi$
$194$	−25.6125	−1.83887
$195$	3.92418	0.281016
$196$	41.7407	2.98148
$197$	15.4663	1.10193	0.550964	−	0.834529i	$-0.314260\pi$
$197$	15.4663	1.10193	0.550964	+	0.834529i	$0.314260\pi$
$198$	−7.76420	−0.551778
$199$	−17.0015	−1.20520	−0.602601	−	0.798043i	$-0.705869\pi$
$199$	−17.0015	−1.20520	−0.602601	+	0.798043i	$0.705869\pi$
$200$	7.01086	0.495743
$201$	2.09311	0.147637
$202$	−22.2768	−1.56739
$203$	−4.33765	−0.304444
$204$	−11.8038	−0.826429
$205$	−17.5549	−1.22609
$206$	−6.59377	−0.459410
$207$	−1.00000	−0.0695048
$208$	−2.10710	−0.146101
$209$	−12.5330	−0.866927
$210$	26.8874	1.85541
$211$	−9.71551	−0.668843	−0.334422	−	0.942424i	$-0.608541\pi$
$211$	−9.71551	−0.668843	−0.334422	+	0.942424i	$0.608541\pi$
$212$	−4.31758	−0.296533
$213$	−6.50468	−0.445694
$214$	39.5631	2.70448
$215$	−2.02964	−0.138420
$216$	3.60540	0.245316
$217$	21.1031	1.43257
$218$	31.5341	2.13576
$219$	−3.22880	−0.218182
$220$	30.7301	2.07182
$221$	4.97542	0.334683
$222$	−14.0897	−0.945636
$223$	18.8364	1.26138	0.630690	−	0.776035i	$-0.282772\pi$
$223$	18.8364	1.26138	0.630690	+	0.776035i	$0.282772\pi$
$224$	16.8407	1.12522
$225$	1.94454	0.129636
$226$	−16.0709	−1.06902
$227$	17.0966	1.13474	0.567371	−	0.823462i	$-0.307961\pi$
$227$	17.0966	1.13474	0.567371	+	0.823462i	$0.307961\pi$
$228$	13.4137	0.888343
$229$	14.7155	0.972426	0.486213	−	0.873840i	$-0.338378\pi$
$229$	14.7155	0.972426	0.486213	+	0.873840i	$0.338378\pi$
$230$	6.19860	0.408724
$231$	14.3179	0.942050
$232$	3.60540	0.236706
$233$	6.40746	0.419767	0.209883	−	0.977726i	$-0.432692\pi$
$233$	6.40746	0.419767	0.209883	+	0.977726i	$0.432692\pi$
$234$	−3.50266	−0.228976
$235$	−29.6284	−1.93275
$236$	−7.87219	−0.512436
$237$	3.80647	0.247257
$238$	34.0903	2.20974
$239$	−25.3225	−1.63798	−0.818988	−	0.573810i	$-0.805465\pi$
$239$	−25.3225	−1.63798	−0.818988	+	0.573810i	$0.805465\pi$
$240$	−3.72889	−0.240699
$241$	15.7651	1.01552	0.507758	−	0.861499i	$-0.330474\pi$
$241$	15.7651	1.01552	0.507758	+	0.861499i	$0.330474\pi$
$242$	−0.245633	−0.0157899
$243$	1.00000	0.0641500
$244$	−26.7747	−1.71408
$245$	−31.1361	−1.98921
$246$	15.6693	0.999038
$247$	−5.65402	−0.359757
$248$	−17.5406	−1.11383
$249$	−4.75913	−0.301597
$250$	18.9396	1.19784
$251$	13.4488	0.848883	0.424441	−	0.905455i	$-0.360470\pi$
$251$	13.4488	0.848883	0.424441	+	0.905455i	$0.360470\pi$
$252$	−15.3240	−0.965322
$253$	3.30084	0.207522
$254$	1.36621	0.0857237
$255$	8.80492	0.551385
$256$	−23.9956	−1.49972
$257$	30.5277	1.90427	0.952133	−	0.305685i	$-0.0988855\pi$
$257$	30.5277	1.90427	0.952133	+	0.305685i	$0.0988855\pi$
$258$	1.81163	0.112787
$259$	25.9827	1.61448
$260$	13.8633	0.859764
$261$	1.00000	0.0618984
$262$	−6.99771	−0.432320
$263$	−25.4247	−1.56775	−0.783877	−	0.620916i	$-0.786761\pi$
$263$	−25.4247	−1.56775	−0.783877	+	0.620916i	$0.786761\pi$
$264$	−11.9009	−0.732448
$265$	3.22066	0.197844
$266$	−38.7398	−2.37529
$267$	4.46726	0.273392
$268$	7.39452	0.451692
$269$	22.7382	1.38637	0.693186	−	0.720759i	$-0.256206\pi$
$269$	22.7382	1.38637	0.693186	+	0.720759i	$0.256206\pi$
$270$	−6.19860	−0.377235
$271$	−14.4841	−0.879849	−0.439925	−	0.898035i	$-0.644995\pi$
$271$	−14.4841	−0.879849	−0.439925	+	0.898035i	$0.644995\pi$
$272$	−4.72783	−0.286667
$273$	6.45924	0.390931
$274$	34.3175	2.07319
$275$	−6.41864	−0.387058
$276$	−3.53279	−0.212649
$277$	−26.4781	−1.59091	−0.795456	−	0.606011i	$-0.792769\pi$
$277$	−26.4781	−1.59091	−0.795456	+	0.606011i	$0.792769\pi$
$278$	−16.2727	−0.975974
$279$	−4.86510	−0.291266
$280$	41.2126	2.46293
$281$	−1.48590	−0.0886416	−0.0443208	−	0.999017i	$-0.514112\pi$
$281$	−1.48590	−0.0886416	−0.0443208	+	0.999017i	$0.514112\pi$
$282$	26.4459	1.57483
$283$	−14.6032	−0.868069	−0.434034	−	0.900896i	$-0.642910\pi$
$283$	−14.6032	−0.868069	−0.434034	+	0.900896i	$0.642910\pi$
$284$	−22.9797	−1.36359
$285$	−10.0058	−0.592693
$286$	11.5617	0.683661
$287$	−28.8956	−1.70566
$288$	−3.88244	−0.228775
$289$	−5.83634	−0.343314
$290$	−6.19860	−0.363994
$291$	−10.8888	−0.638313
$292$	−11.4066	−0.667524
$293$	−29.4449	−1.72019	−0.860094	−	0.510135i	$-0.829595\pi$
$293$	−29.4449	−1.72019	−0.860094	+	0.510135i	$0.829595\pi$
$294$	27.7917	1.62084
$295$	5.87219	0.341892
$296$	−21.5964	−1.25527
$297$	−3.30084	−0.191534
$298$	−20.3883	−1.18106
$299$	1.48911	0.0861174
$300$	6.86966	0.396620
$301$	−3.34081	−0.192561
$302$	−30.1313	−1.73386
$303$	−9.47066	−0.544075
$304$	5.37265	0.308143
$305$	19.9724	1.14361
$306$	−7.85914	−0.449277
$307$	21.5926	1.23235	0.616177	−	0.787608i	$-0.288681\pi$
$307$	21.5926	1.23235	0.616177	+	0.787608i	$0.288681\pi$
$308$	50.5822	2.88219
$309$	−2.80325	−0.159471
$310$	30.1568	1.71279
$311$	−3.75877	−0.213140	−0.106570	−	0.994305i	$-0.533987\pi$
$311$	−3.75877	−0.213140	−0.106570	+	0.994305i	$0.533987\pi$
$312$	−5.36883	−0.303950
$313$	−20.6658	−1.16810	−0.584051	−	0.811717i	$-0.698533\pi$
$313$	−20.6658	−1.16810	−0.584051	+	0.811717i	$0.698533\pi$
$314$	0.0429186	0.00242204
$315$	11.4308	0.644053
$316$	13.4474	0.756478
$317$	−12.5574	−0.705293	−0.352646	−	0.935757i	$-0.614718\pi$
$317$	−12.5574	−0.705293	−0.352646	+	0.935757i	$0.614718\pi$
$318$	−2.87472	−0.161206
$319$	−3.30084	−0.184812
$320$	31.5235	1.76222
$321$	16.8197	0.938784
$322$	10.2030	0.568590
$323$	−12.6863	−0.705883
$324$	3.53279	0.196266
$325$	−2.89564	−0.160621
$326$	12.0711	0.668555
$327$	13.4063	0.741370
$328$	24.0177	1.32615
$329$	−48.7687	−2.68871
$330$	20.4606	1.12632
$331$	17.3460	0.953422	0.476711	−	0.879060i	$-0.341829\pi$
$331$	17.3460	0.953422	0.476711	+	0.879060i	$0.341829\pi$
$332$	−16.8130	−0.922732
$333$	−5.99002	−0.328251
$334$	−33.0160	−1.80656
$335$	−5.51588	−0.301365
$336$	−6.13781	−0.334845
$337$	4.61396	0.251339	0.125669	−	0.992072i	$-0.459892\pi$
$337$	4.61396	0.251339	0.125669	+	0.992072i	$0.459892\pi$
$338$	−25.3626	−1.37954
$339$	−6.83233	−0.371081
$340$	31.1059	1.68695
$341$	16.0589	0.869640
$342$	8.93105	0.482936
$343$	−20.8869	−1.12778
$344$	2.77684	0.149717
$345$	2.63525	0.141877
$346$	31.2930	1.68232
$347$	−23.3874	−1.25550	−0.627750	−	0.778415i	$-0.716024\pi$
$347$	−23.3874	−1.25550	−0.627750	+	0.778415i	$0.716024\pi$
$348$	3.53279	0.189377
$349$	7.92735	0.424341	0.212171	−	0.977233i	$-0.431947\pi$
$349$	7.92735	0.424341	0.212171	+	0.977233i	$0.431947\pi$
$350$	−19.8401	−1.06050
$351$	−1.48911	−0.0794828
$352$	12.8153	0.683060
$353$	28.4601	1.51478	0.757390	−	0.652963i	$-0.226474\pi$
$353$	28.4601	1.51478	0.757390	+	0.652963i	$0.226474\pi$
$354$	−5.24143	−0.278579
$355$	17.1415	0.909775
$356$	15.7819	0.836438
$357$	14.4930	0.767051
$358$	−61.9376	−3.27350
$359$	25.0193	1.32047	0.660234	−	0.751060i	$-0.270457\pi$
$359$	25.0193	1.32047	0.660234	+	0.751060i	$0.270457\pi$
$360$	−9.50113	−0.500754
$361$	−4.58345	−0.241234
$362$	−14.4369	−0.758785
$363$	−0.104428	−0.00548103
$364$	22.8191	1.19605
$365$	8.50869	0.445365
$366$	−17.8271	−0.931835
$367$	−25.6815	−1.34057	−0.670283	−	0.742106i	$-0.733827\pi$
$367$	−25.6815	−1.34057	−0.670283	+	0.742106i	$0.733827\pi$
$368$	−1.41501	−0.0737623
$369$	6.66158	0.346788
$370$	37.1298	1.93029
$371$	5.30125	0.275227
$372$	−17.1874	−0.891123
$373$	−17.9042	−0.927044	−0.463522	−	0.886085i	$-0.653415\pi$
$373$	−17.9042	−0.927044	−0.463522	+	0.886085i	$0.653415\pi$
$374$	25.9418	1.34142
$375$	8.05189	0.415798
$376$	40.5359	2.09048
$377$	−1.48911	−0.0766930
$378$	−10.2030	−0.524784
$379$	−21.8065	−1.12012	−0.560062	−	0.828451i	$-0.689223\pi$
$379$	−21.8065	−1.12012	−0.560062	+	0.828451i	$0.689223\pi$
$380$	−35.3484	−1.81334
$381$	0.580826	0.0297566
$382$	−14.7400	−0.754164
$383$	28.7431	1.46871	0.734353	−	0.678768i	$-0.237486\pi$
$383$	28.7431	1.46871	0.734353	+	0.678768i	$0.237486\pi$
$384$	−20.3726	−1.03963
$385$	−37.7313	−1.92297
$386$	−1.37208	−0.0698371
$387$	0.770188	0.0391508
$388$	−38.4678	−1.95291
$389$	−9.66359	−0.489963	−0.244982	−	0.969528i	$-0.578782\pi$
$389$	−9.66359	−0.489963	−0.244982	+	0.969528i	$0.578782\pi$
$390$	9.23040	0.467399
$391$	3.34121	0.168972
$392$	42.5987	2.15156
$393$	−2.97498	−0.150068
$394$	36.3796	1.83278
$395$	−10.0310	−0.504714
$396$	−11.6612	−0.585996
$397$	−26.1540	−1.31263	−0.656316	−	0.754486i	$-0.727886\pi$
$397$	−26.1540	−1.31263	−0.656316	+	0.754486i	$0.727886\pi$
$398$	−39.9906	−2.00455
$399$	−16.4697	−0.824516
$400$	2.75154	0.137577
$401$	−27.1656	−1.35659	−0.678293	−	0.734792i	$-0.737280\pi$
$401$	−27.1656	−1.35659	−0.678293	+	0.734792i	$0.737280\pi$
$402$	4.92339	0.245557
$403$	7.24466	0.360882
$404$	−33.4578	−1.66459
$405$	−2.63525	−0.130947
$406$	−10.2030	−0.506365
$407$	19.7721	0.980069
$408$	−12.0464	−0.596385
$409$	25.0792	1.24008	0.620042	−	0.784568i	$-0.287115\pi$
$409$	25.0792	1.24008	0.620042	+	0.784568i	$0.287115\pi$
$410$	−41.2925	−2.03929
$411$	14.5896	0.719652
$412$	−9.90328	−0.487900
$413$	9.66569	0.475618
$414$	−2.35219	−0.115604
$415$	12.5415	0.615637
$416$	5.78138	0.283455
$417$	−6.91813	−0.338782
$418$	−29.4800	−1.44191
$419$	−31.9195	−1.55937	−0.779684	−	0.626173i	$-0.784620\pi$
$419$	−31.9195	−1.55937	−0.779684	+	0.626173i	$0.784620\pi$
$420$	40.3826	1.97047
$421$	−34.1487	−1.66430	−0.832152	−	0.554548i	$-0.812891\pi$
$421$	−34.1487	−1.66430	−0.832152	+	0.554548i	$0.812891\pi$
$422$	−22.8527	−1.11245
$423$	11.2431	0.546659
$424$	−4.40633	−0.213990
$425$	−6.49712	−0.315157
$426$	−15.3002	−0.741299
$427$	32.8748	1.59092
$428$	59.4204	2.87219
$429$	4.91532	0.237314
$430$	−4.77409	−0.230227
$431$	−14.7084	−0.708480	−0.354240	−	0.935155i	$-0.615260\pi$
$431$	−14.7084	−0.708480	−0.354240	+	0.935155i	$0.615260\pi$
$432$	1.41501	0.0680795
$433$	19.0069	0.913415	0.456707	−	0.889617i	$-0.349029\pi$
$433$	19.0069	0.913415	0.456707	+	0.889617i	$0.349029\pi$
$434$	49.6385	2.38272
$435$	−2.63525	−0.126351
$436$	47.3616	2.26821
$437$	−3.79691	−0.181631
$438$	−7.59474	−0.362891
$439$	−10.8299	−0.516882	−0.258441	−	0.966027i	$-0.583209\pi$
$439$	−10.8299	−0.516882	−0.258441	+	0.966027i	$0.583209\pi$
$440$	31.3618	1.49511
$441$	11.8152	0.562631
$442$	11.7031	0.556661
$443$	−29.9413	−1.42256	−0.711278	−	0.702911i	$-0.751883\pi$
$443$	−29.9413	−1.42256	−0.711278	+	0.702911i	$0.751883\pi$
$444$	−21.1615	−1.00428
$445$	−11.7724	−0.558063
$446$	44.3068	2.09799
$447$	−8.66779	−0.409972
$448$	51.8881	2.45148
$449$	−9.89186	−0.466826	−0.233413	−	0.972378i	$-0.574989\pi$
$449$	−9.89186	−0.466826	−0.233413	+	0.972378i	$0.574989\pi$
$450$	4.57393	0.215617
$451$	−21.9889	−1.03541
$452$	−24.1372	−1.13532
$453$	−12.8099	−0.601861
$454$	40.2144	1.88736
$455$	−17.0217	−0.797990
$456$	13.6894	0.641065
$457$	7.33786	0.343251	0.171625	−	0.985162i	$-0.445098\pi$
$457$	7.33786	0.343251	0.171625	+	0.985162i	$0.445098\pi$
$458$	34.6136	1.61739
$459$	−3.34121	−0.155954
$460$	9.30978	0.434071
$461$	−24.6493	−1.14803	−0.574016	−	0.818844i	$-0.694615\pi$
$461$	−24.6493	−1.14803	−0.574016	+	0.818844i	$0.694615\pi$
$462$	33.6784	1.56686
$463$	13.5749	0.630880	0.315440	−	0.948946i	$-0.397848\pi$
$463$	13.5749	0.630880	0.315440	+	0.948946i	$0.397848\pi$
$464$	1.41501	0.0656900
$465$	12.8208	0.594548
$466$	15.0716	0.698176
$467$	35.4903	1.64230	0.821148	−	0.570715i	$-0.193334\pi$
$467$	35.4903	1.64230	0.821148	+	0.570715i	$0.193334\pi$
$468$	−5.26070	−0.243176
$469$	−9.07920	−0.419239
$470$	−69.6916	−3.21463
$471$	0.0182463	0.000840743 0
$472$	−8.03400	−0.369795
$473$	−2.54227	−0.116894
$474$	8.95353	0.411249
$475$	7.38326	0.338767
$476$	51.2007	2.34678
$477$	−1.22215	−0.0559582
$478$	−59.5633	−2.72436
$479$	1.38379	0.0632268	0.0316134	−	0.999500i	$-0.489935\pi$
$479$	1.38379	0.0632268	0.0316134	+	0.999500i	$0.489935\pi$
$480$	10.2312	0.466989
$481$	8.91980	0.406708
$482$	37.0824	1.68906
$483$	4.33765	0.197370
$484$	−0.368920	−0.0167691
$485$	28.6947	1.30296
$486$	2.35219	0.106697
$487$	−21.5426	−0.976190	−0.488095	−	0.872790i	$-0.662308\pi$
$487$	−21.5426	−0.976190	−0.488095	+	0.872790i	$0.662308\pi$
$488$	−27.3251	−1.23695
$489$	5.13185	0.232070
$490$	−73.2380	−3.30856
$491$	−14.0257	−0.632972	−0.316486	−	0.948597i	$-0.602503\pi$
$491$	−14.0257	−0.632972	−0.316486	+	0.948597i	$0.602503\pi$
$492$	23.5340	1.06099
$493$	−3.34121	−0.150480
$494$	−13.2993	−0.598364
$495$	8.69855	0.390971
$496$	−6.88414	−0.309107
$497$	28.2151	1.26562
$498$	−11.1944	−0.501631
$499$	8.29366	0.371275	0.185638	−	0.982618i	$-0.440565\pi$
$499$	8.29366	0.371275	0.185638	+	0.982618i	$0.440565\pi$
$500$	28.4456	1.27213
$501$	−14.0363	−0.627096
$502$	31.6342	1.41190
$503$	35.6536	1.58972	0.794858	−	0.606796i	$-0.207545\pi$
$503$	35.6536	1.58972	0.794858	+	0.606796i	$0.207545\pi$
$504$	−15.6390	−0.696616
$505$	24.9576	1.11060
$506$	7.76420	0.345161
$507$	−10.7826	−0.478870
$508$	2.05193	0.0910398
$509$	29.4297	1.30445	0.652225	−	0.758025i	$-0.273836\pi$
$509$	29.4297	1.30445	0.652225	+	0.758025i	$0.273836\pi$
$510$	20.7108	0.917090
$511$	14.0054	0.619563
$512$	−15.6970	−0.693716
$513$	3.79691	0.167638
$514$	71.8069	3.16726
$515$	7.38726	0.325522
$516$	2.72091	0.119781
$517$	−37.1118	−1.63217
$518$	61.1161	2.68529
$519$	13.3038	0.583972
$520$	14.1482	0.620441
$521$	−2.75758	−0.120812	−0.0604058	−	0.998174i	$-0.519239\pi$
$521$	−2.75758	−0.120812	−0.0604058	+	0.998174i	$0.519239\pi$
$522$	2.35219	0.102952
$523$	15.9815	0.698824	0.349412	−	0.936969i	$-0.386381\pi$
$523$	15.9815	0.698824	0.349412	+	0.936969i	$0.386381\pi$
$524$	−10.5100	−0.459130
$525$	−8.43476	−0.368123
$526$	−59.8037	−2.60756
$527$	16.2553	0.708092
$528$	−4.67071	−0.203267
$529$	1.00000	0.0434783
$530$	7.57560	0.329063
$531$	−2.22832	−0.0967010
$532$	−58.1839	−2.52259
$533$	−9.91983	−0.429675
$534$	10.5078	0.454719
$535$	−44.3241	−1.91630
$536$	7.54651	0.325960
$537$	−26.3319	−1.13631
$538$	53.4845	2.30588
$539$	−39.0003	−1.67986
$540$	−9.30978	−0.400629
$541$	7.87672	0.338647	0.169323	−	0.985561i	$-0.445842\pi$
$541$	7.87672	0.338647	0.169323	+	0.985561i	$0.445842\pi$
$542$	−34.0694	−1.46341
$543$	−6.13764	−0.263391
$544$	12.9720	0.556172
$545$	−35.3289	−1.51333
$546$	15.1933	0.650215
$547$	−34.7795	−1.48706	−0.743532	−	0.668700i	$-0.766851\pi$
$547$	−34.7795	−1.48706	−0.743532	+	0.668700i	$0.766851\pi$
$548$	51.5419	2.20176
$549$	−7.57893	−0.323461
$550$	−15.0978	−0.643774
$551$	3.79691	0.161754
$552$	−3.60540	−0.153456
$553$	−16.5111	−0.702125
$554$	−62.2814	−2.64608
$555$	15.7852	0.670045
$556$	−24.4403	−1.03650
$557$	20.8713	0.884345	0.442172	−	0.896930i	$-0.354208\pi$
$557$	20.8713	0.884345	0.442172	+	0.896930i	$0.354208\pi$
$558$	−11.4436	−0.484447
$559$	−1.14689	−0.0485084
$560$	16.1747	0.683504
$561$	11.0288	0.465636
$562$	−3.49513	−0.147433
$563$	30.1599	1.27109	0.635543	−	0.772065i	$-0.280776\pi$
$563$	30.1599	1.27109	0.635543	+	0.772065i	$0.280776\pi$
$564$	39.7195	1.67249
$565$	18.0049	0.757471
$566$	−34.3494	−1.44381
$567$	−4.33765	−0.182164
$568$	−23.4520	−0.984024
$569$	17.2484	0.723092	0.361546	−	0.932354i	$-0.382249\pi$
$569$	17.2484	0.723092	0.361546	+	0.932354i	$0.382249\pi$
$570$	−23.5356	−0.985796
$571$	0.414430	0.0173434	0.00867168	−	0.999962i	$-0.497240\pi$
$571$	0.414430	0.0173434	0.00867168	+	0.999962i	$0.497240\pi$
$572$	17.3648	0.726057
$573$	−6.26651	−0.261787
$574$	−67.9680	−2.83693
$575$	−1.94454	−0.0810931
$576$	−11.9622	−0.498427
$577$	−12.9467	−0.538978	−0.269489	−	0.963003i	$-0.586855\pi$
$577$	−12.9467	−0.538978	−0.269489	+	0.963003i	$0.586855\pi$
$578$	−13.7282	−0.571016
$579$	−0.583321	−0.0242420
$580$	−9.30978	−0.386567
$581$	20.6434	0.856434
$582$	−25.6125	−1.06167
$583$	4.03411	0.167076
$584$	−11.6411	−0.481712
$585$	3.92418	0.162245
$586$	−69.2599	−2.86110
$587$	39.6687	1.63730	0.818651	−	0.574292i	$-0.194722\pi$
$587$	39.6687	1.63730	0.818651	+	0.574292i	$0.194722\pi$
$588$	41.7407	1.72136
$589$	−18.4724	−0.761140
$590$	13.8125	0.568651
$591$	15.4663	0.636198
$592$	−8.47592	−0.348358
$593$	36.4355	1.49623	0.748114	−	0.663571i	$-0.230960\pi$
$593$	36.4355	1.49623	0.748114	+	0.663571i	$0.230960\pi$
$594$	−7.76420	−0.318569
$595$	−38.1927	−1.56575
$596$	−30.6214	−1.25430
$597$	−17.0015	−0.695823
$598$	3.50266	0.143235
$599$	16.3619	0.668529	0.334264	−	0.942479i	$-0.391512\pi$
$599$	16.3619	0.668529	0.334264	+	0.942479i	$0.391512\pi$
$600$	7.01086	0.286217
$601$	14.0262	0.572139	0.286070	−	0.958209i	$-0.407651\pi$
$601$	14.0262	0.572139	0.286070	+	0.958209i	$0.407651\pi$
$602$	−7.85821	−0.320277
$603$	2.09311	0.0852382
$604$	−45.2546	−1.84138
$605$	0.275193	0.0111882
$606$	−22.2768	−0.904932
$607$	14.3585	0.582793	0.291397	−	0.956602i	$-0.405880\pi$
$607$	14.3585	0.582793	0.291397	+	0.956602i	$0.405880\pi$
$608$	−14.7413	−0.597839
$609$	−4.33765	−0.175771
$610$	46.9788	1.90211
$611$	−16.7422	−0.677318
$612$	−11.8038	−0.477139
$613$	8.15493	0.329375	0.164687	−	0.986346i	$-0.447338\pi$
$613$	8.15493	0.329375	0.164687	+	0.986346i	$0.447338\pi$
$614$	50.7898	2.04971
$615$	−17.5549	−0.707884
$616$	51.6218	2.07990
$617$	6.15222	0.247679	0.123839	−	0.992302i	$-0.460479\pi$
$617$	6.15222	0.247679	0.123839	+	0.992302i	$0.460479\pi$
$618$	−6.59377	−0.265240
$619$	1.55668	0.0625682	0.0312841	−	0.999511i	$-0.490040\pi$
$619$	1.55668	0.0625682	0.0312841	+	0.999511i	$0.490040\pi$
$620$	45.2930	1.81901
$621$	−1.00000	−0.0401286
$622$	−8.84132	−0.354505
$623$	−19.3774	−0.776341
$624$	−2.10710	−0.0843514
$625$	−30.9415	−1.23766
$626$	−48.6099	−1.94284
$627$	−12.5330	−0.500521
$628$	0.0644601	0.00257224
$629$	20.0139	0.798007
$630$	26.8874	1.07122
$631$	−21.8057	−0.868072	−0.434036	−	0.900896i	$-0.642911\pi$
$631$	−21.8057	−0.868072	−0.434036	+	0.900896i	$0.642911\pi$
$632$	13.7238	0.545905
$633$	−9.71551	−0.386157
$634$	−29.5373	−1.17308
$635$	−1.53062	−0.0607409
$636$	−4.31758	−0.171203
$637$	−17.5942	−0.697107
$638$	−7.76420	−0.307388
$639$	−6.50468	−0.257321
$640$	53.6868	2.12216
$641$	42.2310	1.66802	0.834012	−	0.551746i	$-0.186038\pi$
$641$	42.2310	1.66802	0.834012	+	0.551746i	$0.186038\pi$
$642$	39.5631	1.56143
$643$	23.7996	0.938566	0.469283	−	0.883048i	$-0.344512\pi$
$643$	23.7996	0.938566	0.469283	+	0.883048i	$0.344512\pi$
$644$	15.3240	0.603850
$645$	−2.02964	−0.0799169
$646$	−29.8405	−1.17406
$647$	39.9087	1.56897	0.784487	−	0.620145i	$-0.212926\pi$
$647$	39.9087	1.56897	0.784487	+	0.620145i	$0.212926\pi$
$648$	3.60540	0.141634
$649$	7.35535	0.288723
$650$	−6.81108	−0.267153
$651$	21.1031	0.827096
$652$	18.1297	0.710015
$653$	20.6215	0.806980	0.403490	−	0.914984i	$-0.367797\pi$
$653$	20.6215	0.806980	0.403490	+	0.914984i	$0.367797\pi$
$654$	31.5341	1.23308
$655$	7.83982	0.306327
$656$	9.42618	0.368030
$657$	−3.22880	−0.125967
$658$	−114.713	−4.47199
$659$	−2.95211	−0.114998	−0.0574989	−	0.998346i	$-0.518313\pi$
$659$	−2.95211	−0.114998	−0.0574989	+	0.998346i	$0.518313\pi$
$660$	30.7301	1.19617
$661$	−17.3457	−0.674669	−0.337334	−	0.941385i	$-0.609525\pi$
$661$	−17.3457	−0.674669	−0.337334	+	0.941385i	$0.609525\pi$
$662$	40.8010	1.58578
$663$	4.97542	0.193229
$664$	−17.1586	−0.665881
$665$	43.4018	1.68305
$666$	−14.0897	−0.545963
$667$	−1.00000	−0.0387202
$668$	−49.5873	−1.91859
$669$	18.8364	0.728258
$670$	−12.9744	−0.501244
$671$	25.0169	0.965765
$672$	16.8407	0.649644
$673$	−9.44837	−0.364208	−0.182104	−	0.983279i	$-0.558291\pi$
$673$	−9.44837	−0.364208	−0.182104	+	0.983279i	$0.558291\pi$
$674$	10.8529	0.418038
$675$	1.94454	0.0748455
$676$	−38.0925	−1.46509
$677$	−19.5489	−0.751324	−0.375662	−	0.926757i	$-0.622585\pi$
$677$	−19.5489	−0.751324	−0.375662	+	0.926757i	$0.622585\pi$
$678$	−16.0709	−0.617200
$679$	47.2318	1.81259
$680$	31.7452	1.21737
$681$	17.0966	0.655143
$682$	37.7736	1.44643
$683$	−10.1412	−0.388043	−0.194022	−	0.980997i	$-0.562153\pi$
$683$	−10.1412	−0.388043	−0.194022	+	0.980997i	$0.562153\pi$
$684$	13.4137	0.512885
$685$	−38.4472	−1.46899
$686$	−49.1298	−1.87578
$687$	14.7155	0.561431
$688$	1.08982	0.0415490
$689$	1.81991	0.0693330
$690$	6.19860	0.235977
$691$	−23.8104	−0.905791	−0.452895	−	0.891564i	$-0.649609\pi$
$691$	−23.8104	−0.905791	−0.452895	+	0.891564i	$0.649609\pi$
$692$	46.9995	1.78665
$693$	14.3179	0.543893
$694$	−55.0115	−2.08821
$695$	18.2310	0.691541
$696$	3.60540	0.136662
$697$	−22.2577	−0.843072
$698$	18.6466	0.705785
$699$	6.40746	0.242353
$700$	−29.7982	−1.12627
$701$	13.3408	0.503874	0.251937	−	0.967744i	$-0.418932\pi$
$701$	13.3408	0.503874	0.251937	+	0.967744i	$0.418932\pi$
$702$	−3.50266	−0.132200
$703$	−22.7436	−0.857791
$704$	39.4855	1.48817
$705$	−29.6284	−1.11587
$706$	66.9435	2.51945
$707$	41.0804	1.54499
$708$	−7.87219	−0.295855
$709$	38.0560	1.42922	0.714612	−	0.699521i	$-0.246603\pi$
$709$	38.0560	1.42922	0.714612	+	0.699521i	$0.246603\pi$
$710$	40.3200	1.51318
$711$	3.80647	0.142754
$712$	16.1063	0.603608
$713$	4.86510	0.182199
$714$	34.0903	1.27580
$715$	−12.9531	−0.484418
$716$	−93.0250	−3.47651
$717$	−25.3225	−0.945686
$718$	58.8501	2.19626
$719$	−42.6703	−1.59133	−0.795666	−	0.605735i	$-0.792879\pi$
$719$	−42.6703	−1.59133	−0.795666	+	0.605735i	$0.792879\pi$
$720$	−3.72889	−0.138968
$721$	12.1595	0.452844
$722$	−10.7811	−0.401232
$723$	15.7651	0.586309
$724$	−21.6830	−0.805841
$725$	1.94454	0.0722185
$726$	−0.245633	−0.00911631
$727$	−34.7980	−1.29059	−0.645293	−	0.763935i	$-0.723265\pi$
$727$	−34.7980	−1.29059	−0.645293	+	0.763935i	$0.723265\pi$
$728$	23.2881	0.863116
$729$	1.00000	0.0370370
$730$	20.0140	0.740752
$731$	−2.57336	−0.0951790
$732$	−26.7747	−0.989623
$733$	−34.2000	−1.26320	−0.631602	−	0.775293i	$-0.717602\pi$
$733$	−34.2000	−1.26320	−0.631602	+	0.775293i	$0.717602\pi$
$734$	−60.4078	−2.22969
$735$	−31.1361	−1.14847
$736$	3.88244	0.143109
$737$	−6.90904	−0.254498
$738$	15.6693	0.576795
$739$	1.50718	0.0554425	0.0277213	−	0.999616i	$-0.491175\pi$
$739$	1.50718	0.0554425	0.0277213	+	0.999616i	$0.491175\pi$
$740$	55.7658	2.04999
$741$	−5.65402	−0.207706
$742$	12.4695	0.457771
$743$	16.7465	0.614369	0.307184	−	0.951650i	$-0.400613\pi$
$743$	16.7465	0.614369	0.307184	+	0.951650i	$0.400613\pi$
$744$	−17.5406	−0.643071
$745$	22.8418	0.836858
$746$	−42.1140	−1.54190
$747$	−4.75913	−0.174127
$748$	38.9624	1.42461
$749$	−72.9581	−2.66583
$750$	18.9396	0.691575
$751$	−49.7688	−1.81609	−0.908045	−	0.418873i	$-0.862425\pi$
$751$	−49.7688	−1.81609	−0.908045	+	0.418873i	$0.862425\pi$
$752$	15.9091	0.580144
$753$	13.4488	0.490103
$754$	−3.50266	−0.127560
$755$	33.7573	1.22855
$756$	−15.3240	−0.557329
$757$	4.38037	0.159207	0.0796037	−	0.996827i	$-0.474635\pi$
$757$	4.38037	0.159207	0.0796037	+	0.996827i	$0.474635\pi$
$758$	−51.2929	−1.86304
$759$	3.30084	0.119813
$760$	−36.0750	−1.30858
$761$	24.2915	0.880566	0.440283	−	0.897859i	$-0.354878\pi$
$761$	24.2915	0.880566	0.440283	+	0.897859i	$0.354878\pi$
$762$	1.36621	0.0494926
$763$	−58.1518	−2.10524
$764$	−22.1382	−0.800933
$765$	8.80492	0.318342
$766$	67.6092	2.44282
$767$	3.31822	0.119814
$768$	−23.9956	−0.865866
$769$	−47.9124	−1.72777	−0.863883	−	0.503693i	$-0.831974\pi$
$769$	−47.9124	−1.72777	−0.863883	+	0.503693i	$0.831974\pi$
$770$	−88.7511	−3.19837
$771$	30.5277	1.09943
$772$	−2.06075	−0.0741680
$773$	20.7334	0.745728	0.372864	−	0.927886i	$-0.378376\pi$
$773$	20.7334	0.745728	0.372864	+	0.927886i	$0.378376\pi$
$774$	1.81163	0.0651176
$775$	−9.46040	−0.339828
$776$	−39.2585	−1.40930
$777$	25.9827	0.932123
$778$	−22.7306	−0.814930
$779$	25.2935	0.906232
$780$	13.8633	0.496385
$781$	21.4710	0.768291
$782$	7.85914	0.281042
$783$	1.00000	0.0357371
$784$	16.7186	0.597094
$785$	−0.0480835	−0.00171617
$786$	−6.99771	−0.249600
$787$	33.6730	1.20031	0.600157	−	0.799882i	$-0.295105\pi$
$787$	33.6730	1.20031	0.600157	+	0.799882i	$0.295105\pi$
$788$	54.6391	1.94644
$789$	−25.4247	−0.905143
$790$	−23.5948	−0.839465
$791$	29.6363	1.05374
$792$	−11.9009	−0.422879
$793$	11.2859	0.400772
$794$	−61.5192	−2.18323
$795$	3.22066	0.114225
$796$	−60.0625	−2.12886
$797$	−12.2851	−0.435159	−0.217579	−	0.976043i	$-0.569816\pi$
$797$	−12.2851	−0.435159	−0.217579	+	0.976043i	$0.569816\pi$
$798$	−38.7398	−1.37137
$799$	−37.5656	−1.32897
$800$	−7.54958	−0.266918
$801$	4.46726	0.157843
$802$	−63.8986	−2.25634
$803$	10.6578	0.376104
$804$	7.39452	0.260785
$805$	−11.4308	−0.402883
$806$	17.0408	0.600237
$807$	22.7382	0.800422
$808$	−34.1455	−1.20124
$809$	−52.5032	−1.84592	−0.922958	−	0.384901i	$-0.874235\pi$
$809$	−52.5032	−1.84592	−0.922958	+	0.384901i	$0.874235\pi$
$810$	−6.19860	−0.217797
$811$	−15.7319	−0.552422	−0.276211	−	0.961097i	$-0.589079\pi$
$811$	−15.7319	−0.552422	−0.276211	+	0.961097i	$0.589079\pi$
$812$	−15.3240	−0.537767
$813$	−14.4841	−0.507981
$814$	46.5078	1.63010
$815$	−13.5237	−0.473715
$816$	−4.72783	−0.165507
$817$	2.92434	0.102310
$818$	58.9909	2.06257
$819$	6.45924	0.225704
$820$	−62.0179	−2.16576
$821$	41.8102	1.45919	0.729594	−	0.683881i	$-0.239709\pi$
$821$	41.8102	1.45919	0.729594	+	0.683881i	$0.239709\pi$
$822$	34.3175	1.19696
$823$	30.6131	1.06710	0.533552	−	0.845767i	$-0.320857\pi$
$823$	30.6131	1.06710	0.533552	+	0.845767i	$0.320857\pi$
$824$	−10.1068	−0.352088
$825$	−6.41864	−0.223468
$826$	22.7355	0.791070
$827$	−29.0441	−1.00996	−0.504980	−	0.863131i	$-0.668500\pi$
$827$	−29.0441	−1.00996	−0.504980	+	0.863131i	$0.668500\pi$
$828$	−3.53279	−0.122773
$829$	−1.85467	−0.0644154	−0.0322077	−	0.999481i	$-0.510254\pi$
$829$	−1.85467	−0.0644154	−0.0322077	+	0.999481i	$0.510254\pi$
$830$	29.4999	1.02396
$831$	−26.4781	−0.918514
$832$	17.8131	0.617558
$833$	−39.4772	−1.36780
$834$	−16.2727	−0.563479
$835$	36.9892	1.28006
$836$	−44.2765	−1.53133
$837$	−4.86510	−0.168162
$838$	−75.0806	−2.59362
$839$	35.8589	1.23799	0.618994	−	0.785396i	$-0.287540\pi$
$839$	35.8589	1.23799	0.618994	+	0.785396i	$0.287540\pi$
$840$	41.2126	1.42197
$841$	1.00000	0.0344828
$842$	−80.3240	−2.76815
$843$	−1.48590	−0.0511773
$844$	−34.3228	−1.18144
$845$	28.4147	0.977496
$846$	26.4459	0.909229
$847$	0.452971	0.0155643
$848$	−1.72934	−0.0593859
$849$	−14.6032	−0.501180
$850$	−15.2825	−0.524184
$851$	5.99002	0.205335
$852$	−22.9797	−0.787270
$853$	−13.6852	−0.468574	−0.234287	−	0.972168i	$-0.575275\pi$
$853$	−13.6852	−0.468574	−0.234287	+	0.972168i	$0.575275\pi$
$854$	77.3276	2.64610
$855$	−10.0058	−0.342192
$856$	60.6418	2.07269
$857$	−21.7705	−0.743666	−0.371833	−	0.928300i	$-0.621271\pi$
$857$	−21.7705	−0.743666	−0.371833	+	0.928300i	$0.621271\pi$
$858$	11.5617	0.394712
$859$	−48.6404	−1.65959	−0.829794	−	0.558070i	$-0.811542\pi$
$859$	−48.6404	−1.65959	−0.829794	+	0.558070i	$0.811542\pi$
$860$	−7.17028	−0.244504
$861$	−28.8956	−0.984761
$862$	−34.5970	−1.17838
$863$	17.9482	0.610965	0.305482	−	0.952198i	$-0.401182\pi$
$863$	17.9482	0.610965	0.305482	+	0.952198i	$0.401182\pi$
$864$	−3.88244	−0.132083
$865$	−35.0588	−1.19204
$866$	44.7079	1.51924
$867$	−5.83634	−0.198212
$868$	74.5528	2.53049
$869$	−12.5646	−0.426223
$870$	−6.19860	−0.210152
$871$	−3.11687	−0.105611
$872$	48.3350	1.63683
$873$	−10.8888	−0.368530
$874$	−8.93105	−0.302097
$875$	−34.9263	−1.18073
$876$	−11.4066	−0.385395
$877$	38.2368	1.29116	0.645582	−	0.763691i	$-0.276615\pi$
$877$	38.2368	1.29116	0.645582	+	0.763691i	$0.276615\pi$
$878$	−25.4739	−0.859702
$879$	−29.4449	−0.993151
$880$	12.3085	0.414919
$881$	−6.64786	−0.223972	−0.111986	−	0.993710i	$-0.535721\pi$
$881$	−6.64786	−0.223972	−0.111986	+	0.993710i	$0.535721\pi$
$882$	27.7917	0.935794
$883$	41.1571	1.38505	0.692523	−	0.721396i	$-0.256499\pi$
$883$	41.1571	1.38505	0.692523	+	0.721396i	$0.256499\pi$
$884$	17.5771	0.591182
$885$	5.87219	0.197391
$886$	−70.4276	−2.36606
$887$	−48.4438	−1.62658	−0.813291	−	0.581857i	$-0.802326\pi$
$887$	−48.4438	−1.62658	−0.813291	+	0.581857i	$0.802326\pi$
$888$	−21.5964	−0.724729
$889$	−2.51942	−0.0844987
$890$	−27.6908	−0.928197
$891$	−3.30084	−0.110582
$892$	66.5450	2.22809
$893$	42.6891	1.42854
$894$	−20.3883	−0.681885
$895$	69.3911	2.31949
$896$	88.3691	2.95220
$897$	1.48911	0.0497199
$898$	−23.2675	−0.776447
$899$	−4.86510	−0.162260
$900$	6.86966	0.228989
$901$	4.08344	0.136039
$902$	−51.7219	−1.72215
$903$	−3.34081	−0.111175
$904$	−24.6333	−0.819291
$905$	16.1742	0.537649
$906$	−30.1313	−1.00104
$907$	35.8582	1.19065	0.595326	−	0.803485i	$-0.297023\pi$
$907$	35.8582	1.19065	0.595326	+	0.803485i	$0.297023\pi$
$908$	60.3986	2.00440
$909$	−9.47066	−0.314122
$910$	−40.0383	−1.32726
$911$	−46.9697	−1.55618	−0.778088	−	0.628155i	$-0.783810\pi$
$911$	−46.9697	−1.55618	−0.778088	+	0.628155i	$0.783810\pi$
$912$	5.37265	0.177906
$913$	15.7091	0.519896
$914$	17.2600	0.570911
$915$	19.9724	0.660266
$916$	51.9867	1.71769
$917$	12.9044	0.426142
$918$	−7.85914	−0.259390
$919$	−29.4796	−0.972443	−0.486222	−	0.873836i	$-0.661625\pi$
$919$	−29.4796	−0.972443	−0.486222	+	0.873836i	$0.661625\pi$
$920$	9.50113	0.313243
$921$	21.5926	0.711499
$922$	−57.9797	−1.90946
$923$	9.68619	0.318825
$924$	50.5822	1.66403
$925$	−11.6479	−0.382979
$926$	31.9308	1.04931
$927$	−2.80325	−0.0920708
$928$	−3.88244	−0.127447
$929$	−25.2644	−0.828897	−0.414448	−	0.910073i	$-0.636025\pi$
$929$	−25.2644	−0.828897	−0.414448	+	0.910073i	$0.636025\pi$
$930$	30.1568	0.988881
$931$	44.8615	1.47027
$932$	22.6362	0.741473
$933$	−3.75877	−0.123056
$934$	83.4799	2.73155
$935$	−29.0637	−0.950483
$936$	−5.36883	−0.175486
$937$	10.3783	0.339045	0.169522	−	0.985526i	$-0.445777\pi$
$937$	10.3783	0.339045	0.169522	+	0.985526i	$0.445777\pi$
$938$	−21.3560	−0.697298
$939$	−20.6658	−0.674404
$940$	−104.671	−3.41399
$941$	14.1433	0.461057	0.230529	−	0.973066i	$-0.425954\pi$
$941$	14.1433	0.461057	0.230529	+	0.973066i	$0.425954\pi$
$942$	0.0429186	0.00139836
$943$	−6.66158	−0.216931
$944$	−3.15309	−0.102624
$945$	11.4308	0.371844
$946$	−5.97990	−0.194423
$947$	−56.6221	−1.83997	−0.919985	−	0.391953i	$-0.871800\pi$
$947$	−56.6221	−1.83997	−0.919985	+	0.391953i	$0.871800\pi$
$948$	13.4474	0.436753
$949$	4.80803	0.156075
$950$	17.3668	0.563454
$951$	−12.5574	−0.407201
$952$	52.2531	1.69353
$953$	29.1600	0.944585	0.472293	−	0.881442i	$-0.343427\pi$
$953$	29.1600	0.944585	0.472293	+	0.881442i	$0.343427\pi$
$954$	−2.87472	−0.0930724
$955$	16.5138	0.534375
$956$	−89.4590	−2.89331
$957$	−3.30084	−0.106701
$958$	3.25492	0.105162
$959$	−63.2846	−2.04357
$960$	31.5235	1.01742
$961$	−7.33081	−0.236478
$962$	20.9810	0.676456
$963$	16.8197	0.542007
$964$	55.6946	1.79380
$965$	1.53720	0.0494841
$966$	10.2030	0.328275
$967$	1.63849	0.0526903	0.0263451	−	0.999653i	$-0.491613\pi$
$967$	1.63849	0.0526903	0.0263451	+	0.999653i	$0.491613\pi$
$968$	−0.376503	−0.0121013
$969$	−12.6863	−0.407542
$970$	67.4953	2.16714
$971$	−4.80383	−0.154162	−0.0770811	−	0.997025i	$-0.524560\pi$
$971$	−4.80383	−0.154162	−0.0770811	+	0.997025i	$0.524560\pi$
$972$	3.53279	0.113314
$973$	30.0084	0.962027
$974$	−50.6723	−1.62365
$975$	−2.89564	−0.0927346
$976$	−10.7242	−0.343274
$977$	30.3817	0.971997	0.485999	−	0.873960i	$-0.338456\pi$
$977$	30.3817	0.971997	0.485999	+	0.873960i	$0.338456\pi$
$978$	12.0711	0.385990
$979$	−14.7457	−0.471276
$980$	−109.997	−3.51373
$981$	13.4063	0.428030
$982$	−32.9911	−1.05279
$983$	39.0853	1.24663	0.623313	−	0.781972i	$-0.285786\pi$
$983$	39.0853	1.24663	0.623313	+	0.781972i	$0.285786\pi$
$984$	24.0177	0.765656
$985$	−40.7576	−1.29864
$986$	−7.85914	−0.250286
$987$	−48.7687	−1.55233
$988$	−19.9744	−0.635472
$989$	−0.770188	−0.0244905
$990$	20.4606	0.650281
$991$	52.1297	1.65595	0.827977	−	0.560763i	$-0.189492\pi$
$991$	52.1297	1.65595	0.827977	+	0.560763i	$0.189492\pi$
$992$	18.8885	0.599709
$993$	17.3460	0.550458
$994$	66.3671	2.10504
$995$	44.8031	1.42035
$996$	−16.8130	−0.532739
$997$	−38.1559	−1.20841	−0.604204	−	0.796829i	$-0.706509\pi$
$997$	−38.1559	−1.20841	−0.604204	+	0.796829i	$0.706509\pi$
$998$	19.5082	0.617522
$999$	−5.99002	−0.189516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.j.1.7	✓	7
3.2	odd	2		6003.2.a.i.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.j.1.7	✓	7	1.1	even	1	trivial
6003.2.a.i.1.1		7	3.2	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+2.35219 q^{2} +1.00000 q^{3} +3.53279 q^{4} -2.63525 q^{5} +2.35219 q^{6} -4.33765 q^{7} +3.60540 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.35219 q^{2} +1.00000 q^{3} +3.53279 q^{4} -2.63525 q^{5} +2.35219 q^{6} -4.33765 q^{7} +3.60540 q^{8} +1.00000 q^{9} -6.19860 q^{10} -3.30084 q^{11} +3.53279 q^{12} -1.48911 q^{13} -10.2030 q^{14} -2.63525 q^{15} +1.41501 q^{16} -3.34121 q^{17} +2.35219 q^{18} +3.79691 q^{19} -9.30978 q^{20} -4.33765 q^{21} -7.76420 q^{22} -1.00000 q^{23} +3.60540 q^{24} +1.94454 q^{25} -3.50266 q^{26} +1.00000 q^{27} -15.3240 q^{28} +1.00000 q^{29} -6.19860 q^{30} -4.86510 q^{31} -3.88244 q^{32} -3.30084 q^{33} -7.85914 q^{34} +11.4308 q^{35} +3.53279 q^{36} -5.99002 q^{37} +8.93105 q^{38} -1.48911 q^{39} -9.50113 q^{40} +6.66158 q^{41} -10.2030 q^{42} +0.770188 q^{43} -11.6612 q^{44} -2.63525 q^{45} -2.35219 q^{46} +11.2431 q^{47} +1.41501 q^{48} +11.8152 q^{49} +4.57393 q^{50} -3.34121 q^{51} -5.26070 q^{52} -1.22215 q^{53} +2.35219 q^{54} +8.69855 q^{55} -15.6390 q^{56} +3.79691 q^{57} +2.35219 q^{58} -2.22832 q^{59} -9.30978 q^{60} -7.57893 q^{61} -11.4436 q^{62} -4.33765 q^{63} -11.9622 q^{64} +3.92418 q^{65} -7.76420 q^{66} +2.09311 q^{67} -11.8038 q^{68} -1.00000 q^{69} +26.8874 q^{70} -6.50468 q^{71} +3.60540 q^{72} -3.22880 q^{73} -14.0897 q^{74} +1.94454 q^{75} +13.4137 q^{76} +14.3179 q^{77} -3.50266 q^{78} +3.80647 q^{79} -3.72889 q^{80} +1.00000 q^{81} +15.6693 q^{82} -4.75913 q^{83} -15.3240 q^{84} +8.80492 q^{85} +1.81163 q^{86} +1.00000 q^{87} -11.9009 q^{88} +4.46726 q^{89} -6.19860 q^{90} +6.45924 q^{91} -3.53279 q^{92} -4.86510 q^{93} +26.4459 q^{94} -10.0058 q^{95} -3.88244 q^{96} -10.8888 q^{97} +27.7917 q^{98} -3.30084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9} - 11 q^{10} - 12 q^{11} + 7 q^{12} - 13 q^{13} - 3 q^{14} - 5 q^{15} - 13 q^{16} - 12 q^{17} - q^{18} - 5 q^{19} - 8 q^{20} - 5 q^{21} - q^{22} - 7 q^{23} + 3 q^{24} - 4 q^{25} + 2 q^{26} + 7 q^{27} - 21 q^{28} + 7 q^{29} - 11 q^{30} - 8 q^{31} - 5 q^{32} - 12 q^{33} - 28 q^{34} + 5 q^{35} + 7 q^{36} - 24 q^{37} - 6 q^{38} - 13 q^{39} - 20 q^{40} + 9 q^{41} - 3 q^{42} - q^{43} - 23 q^{44} - 5 q^{45} + q^{46} + 27 q^{47} - 13 q^{48} - 14 q^{49} + 7 q^{50} - 12 q^{51} - 9 q^{52} - q^{53} - q^{54} - 11 q^{55} - 20 q^{56} - 5 q^{57} - q^{58} + 8 q^{59} - 8 q^{60} + q^{61} - 5 q^{63} + 3 q^{64} + 12 q^{65} - q^{66} - 16 q^{67} + 15 q^{68} - 7 q^{69} + 40 q^{70} - 13 q^{71} + 3 q^{72} - 23 q^{73} - 8 q^{74} - 4 q^{75} - 2 q^{76} + 13 q^{77} + 2 q^{78} - 44 q^{79} + 30 q^{80} + 7 q^{81} - 10 q^{82} + 21 q^{83} - 21 q^{84} + 6 q^{86} + 7 q^{87} + 21 q^{88} - 5 q^{89} - 11 q^{90} - 18 q^{91} - 7 q^{92} - 8 q^{93} + 28 q^{94} + 9 q^{95} - 5 q^{96} - 55 q^{97} + 36 q^{98} - 12 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9 - 11 * q^10 - 12 * q^11 + 7 * q^12 - 13 * q^13 - 3 * q^14 - 5 * q^15 - 13 * q^16 - 12 * q^17 - q^18 - 5 * q^19 - 8 * q^20 - 5 * q^21 - q^22 - 7 * q^23 + 3 * q^24 - 4 * q^25 + 2 * q^26 + 7 * q^27 - 21 * q^28 + 7 * q^29 - 11 * q^30 - 8 * q^31 - 5 * q^32 - 12 * q^33 - 28 * q^34 + 5 * q^35 + 7 * q^36 - 24 * q^37 - 6 * q^38 - 13 * q^39 - 20 * q^40 + 9 * q^41 - 3 * q^42 - q^43 - 23 * q^44 - 5 * q^45 + q^46 + 27 * q^47 - 13 * q^48 - 14 * q^49 + 7 * q^50 - 12 * q^51 - 9 * q^52 - q^53 - q^54 - 11 * q^55 - 20 * q^56 - 5 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + q^61 - 5 * q^63 + 3 * q^64 + 12 * q^65 - q^66 - 16 * q^67 + 15 * q^68 - 7 * q^69 + 40 * q^70 - 13 * q^71 + 3 * q^72 - 23 * q^73 - 8 * q^74 - 4 * q^75 - 2 * q^76 + 13 * q^77 + 2 * q^78 - 44 * q^79 + 30 * q^80 + 7 * q^81 - 10 * q^82 + 21 * q^83 - 21 * q^84 + 6 * q^86 + 7 * q^87 + 21 * q^88 - 5 * q^89 - 11 * q^90 - 18 * q^91 - 7 * q^92 - 8 * q^93 + 28 * q^94 + 9 * q^95 - 5 * q^96 - 55 * q^97 + 36 * q^98 - 12 * q^99

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