LMFDB - Embedded newform 6001.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68420 q^{2} +3.02151 q^{3} +5.20492 q^{4} +3.70816 q^{5} -8.11034 q^{6} +3.11131 q^{7} -8.60266 q^{8} +6.12953 q^{9} +O(q^{10})$	\(q-2.68420 q^{2} +3.02151 q^{3} +5.20492 q^{4} +3.70816 q^{5} -8.11034 q^{6} +3.11131 q^{7} -8.60266 q^{8} +6.12953 q^{9} -9.95344 q^{10} -1.64808 q^{11} +15.7267 q^{12} -1.87062 q^{13} -8.35137 q^{14} +11.2043 q^{15} +12.6814 q^{16} +1.00000 q^{17} -16.4529 q^{18} +0.371867 q^{19} +19.3007 q^{20} +9.40085 q^{21} +4.42378 q^{22} -3.54142 q^{23} -25.9930 q^{24} +8.75046 q^{25} +5.02113 q^{26} +9.45592 q^{27} +16.1941 q^{28} +4.60164 q^{29} -30.0744 q^{30} -5.90888 q^{31} -16.8341 q^{32} -4.97970 q^{33} -2.68420 q^{34} +11.5372 q^{35} +31.9038 q^{36} +8.96623 q^{37} -0.998166 q^{38} -5.65211 q^{39} -31.9000 q^{40} +7.61923 q^{41} -25.2338 q^{42} -0.00667754 q^{43} -8.57815 q^{44} +22.7293 q^{45} +9.50589 q^{46} +7.50028 q^{47} +38.3170 q^{48} +2.68024 q^{49} -23.4880 q^{50} +3.02151 q^{51} -9.73646 q^{52} +8.09685 q^{53} -25.3816 q^{54} -6.11136 q^{55} -26.7655 q^{56} +1.12360 q^{57} -12.3517 q^{58} +7.34375 q^{59} +58.3173 q^{60} -11.8938 q^{61} +15.8606 q^{62} +19.0709 q^{63} +19.8232 q^{64} -6.93658 q^{65} +13.3665 q^{66} -7.36310 q^{67} +5.20492 q^{68} -10.7005 q^{69} -30.9682 q^{70} -2.28537 q^{71} -52.7303 q^{72} -9.54108 q^{73} -24.0671 q^{74} +26.4396 q^{75} +1.93554 q^{76} -5.12770 q^{77} +15.1714 q^{78} -14.7441 q^{79} +47.0246 q^{80} +10.1826 q^{81} -20.4515 q^{82} +5.64336 q^{83} +48.9307 q^{84} +3.70816 q^{85} +0.0179239 q^{86} +13.9039 q^{87} +14.1779 q^{88} -10.0130 q^{89} -61.0100 q^{90} -5.82009 q^{91} -18.4328 q^{92} -17.8538 q^{93} -20.1323 q^{94} +1.37894 q^{95} -50.8643 q^{96} +6.08057 q^{97} -7.19429 q^{98} -10.1020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.68420	−1.89802	−0.949008	−	0.315253i	$-0.897911\pi$
$2$	−2.68420	−1.89802	−0.949008	+	0.315253i	$0.897911\pi$
$3$	3.02151	1.74447	0.872235	−	0.489086i	$-0.162670\pi$
$3$	3.02151	1.74447	0.872235	+	0.489086i	$0.162670\pi$
$4$	5.20492	2.60246
$5$	3.70816	1.65834	0.829170	−	0.558996i	$-0.188813\pi$
$5$	3.70816	1.65834	0.829170	+	0.558996i	$0.188813\pi$
$6$	−8.11034	−3.31103
$7$	3.11131	1.17596	0.587982	−	0.808874i	$-0.299923\pi$
$7$	3.11131	1.17596	0.587982	+	0.808874i	$0.299923\pi$
$8$	−8.60266	−3.04150
$9$	6.12953	2.04318
$10$	−9.95344	−3.14756
$11$	−1.64808	−0.496916	−0.248458	−	0.968643i	$-0.579924\pi$
$11$	−1.64808	−0.496916	−0.248458	+	0.968643i	$0.579924\pi$
$12$	15.7267	4.53992
$13$	−1.87062	−0.518818	−0.259409	−	0.965768i	$-0.583528\pi$
$13$	−1.87062	−0.518818	−0.259409	+	0.965768i	$0.583528\pi$
$14$	−8.35137	−2.23200
$15$	11.2043	2.89293
$16$	12.6814	3.17035
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−16.4529	−3.87798
$19$	0.371867	0.0853122	0.0426561	−	0.999090i	$-0.486418\pi$
$19$	0.371867	0.0853122	0.0426561	+	0.999090i	$0.486418\pi$
$20$	19.3007	4.31577
$21$	9.40085	2.05143
$22$	4.42378	0.943154
$23$	−3.54142	−0.738438	−0.369219	−	0.929342i	$-0.620375\pi$
$23$	−3.54142	−0.738438	−0.369219	+	0.929342i	$0.620375\pi$
$24$	−25.9930	−5.30580
$25$	8.75046	1.75009
$26$	5.02113	0.984724
$27$	9.45592	1.81979
$28$	16.1941	3.06040
$29$	4.60164	0.854503	0.427251	−	0.904133i	$-0.359482\pi$
$29$	4.60164	0.854503	0.427251	+	0.904133i	$0.359482\pi$
$30$	−30.0744	−5.49082
$31$	−5.90888	−1.06127	−0.530633	−	0.847601i	$-0.678046\pi$
$31$	−5.90888	−1.06127	−0.530633	+	0.847601i	$0.678046\pi$
$32$	−16.8341	−2.97587
$33$	−4.97970	−0.866855
$34$	−2.68420	−0.460336
$35$	11.5372	1.95015
$36$	31.9038	5.31729
$37$	8.96623	1.47404	0.737019	−	0.675872i	$-0.236233\pi$
$37$	8.96623	1.47404	0.737019	+	0.675872i	$0.236233\pi$
$38$	−0.998166	−0.161924
$39$	−5.65211	−0.905063
$40$	−31.9000	−5.04384
$41$	7.61923	1.18992	0.594962	−	0.803754i	$-0.297167\pi$
$41$	7.61923	1.18992	0.594962	+	0.803754i	$0.297167\pi$
$42$	−25.2338	−3.89365
$43$	−0.00667754	−0.00101832	−0.000509158	−	1.00000i	$-0.500162\pi$
$43$	−0.00667754	−0.00101832	−0.000509158		1.00000i	$0.500162\pi$
$44$	−8.57815	−1.29320
$45$	22.7293	3.38828
$46$	9.50589	1.40157
$47$	7.50028	1.09403	0.547014	−	0.837123i	$-0.315764\pi$
$47$	7.50028	1.09403	0.547014	+	0.837123i	$0.315764\pi$
$48$	38.3170	5.53058
$49$	2.68024	0.382891
$50$	−23.4880	−3.32170
$51$	3.02151	0.423096
$52$	−9.73646	−1.35020
$53$	8.09685	1.11219	0.556094	−	0.831119i	$-0.312299\pi$
$53$	8.09685	1.11219	0.556094	+	0.831119i	$0.312299\pi$
$54$	−25.3816	−3.45399
$55$	−6.11136	−0.824056
$56$	−26.7655	−3.57669
$57$	1.12360	0.148825
$58$	−12.3517	−1.62186
$59$	7.34375	0.956074	0.478037	−	0.878340i	$-0.341348\pi$
$59$	7.34375	0.956074	0.478037	+	0.878340i	$0.341348\pi$
$60$	58.3173	7.52873
$61$	−11.8938	−1.52285	−0.761424	−	0.648254i	$-0.775500\pi$
$61$	−11.8938	−1.52285	−0.761424	+	0.648254i	$0.775500\pi$
$62$	15.8606	2.01430
$63$	19.0709	2.40270
$64$	19.8232	2.47790
$65$	−6.93658	−0.860377
$66$	13.3665	1.64530
$67$	−7.36310	−0.899546	−0.449773	−	0.893143i	$-0.648495\pi$
$67$	−7.36310	−0.899546	−0.449773	+	0.893143i	$0.648495\pi$
$68$	5.20492	0.631190
$69$	−10.7005	−1.28818
$70$	−30.9682	−3.70141
$71$	−2.28537	−0.271223	−0.135612	−	0.990762i	$-0.543300\pi$
$71$	−2.28537	−0.271223	−0.135612	+	0.990762i	$0.543300\pi$
$72$	−52.7303	−6.21432
$73$	−9.54108	−1.11670	−0.558350	−	0.829606i	$-0.688565\pi$
$73$	−9.54108	−1.11670	−0.558350	+	0.829606i	$0.688565\pi$
$74$	−24.0671	−2.79775
$75$	26.4396	3.05298
$76$	1.93554	0.222022
$77$	−5.12770	−0.584355
$78$	15.1714	1.71782
$79$	−14.7441	−1.65884	−0.829421	−	0.558624i	$-0.811329\pi$
$79$	−14.7441	−1.65884	−0.829421	+	0.558624i	$0.811329\pi$
$80$	47.0246	5.25752
$81$	10.1826	1.13140
$82$	−20.4515	−2.25849
$83$	5.64336	0.619439	0.309720	−	0.950828i	$-0.399765\pi$
$83$	5.64336	0.619439	0.309720	+	0.950828i	$0.399765\pi$
$84$	48.9307	5.33878
$85$	3.70816	0.402207
$86$	0.0179239	0.00193278
$87$	13.9039	1.49066
$88$	14.1779	1.51137
$89$	−10.0130	−1.06138	−0.530689	−	0.847567i	$-0.678067\pi$
$89$	−10.0130	−1.06138	−0.530689	+	0.847567i	$0.678067\pi$
$90$	−61.0100	−6.43101
$91$	−5.82009	−0.610111
$92$	−18.4328	−1.92176
$93$	−17.8538	−1.85135
$94$	−20.1323	−2.07648
$95$	1.37894	0.141477
$96$	−50.8643	−5.19132
$97$	6.08057	0.617389	0.308694	−	0.951161i	$-0.400108\pi$
$97$	6.08057	0.617389	0.308694	+	0.951161i	$0.400108\pi$
$98$	−7.19429	−0.726733
$99$	−10.1020	−1.01529
$100$	45.5455	4.55455
$101$	13.4937	1.34268	0.671338	−	0.741151i	$-0.265720\pi$
$101$	13.4937	1.34268	0.671338	+	0.741151i	$0.265720\pi$
$102$	−8.11034	−0.803043
$103$	2.48200	0.244558	0.122279	−	0.992496i	$-0.460980\pi$
$103$	2.48200	0.244558	0.122279	+	0.992496i	$0.460980\pi$
$104$	16.0923	1.57798
$105$	34.8599	3.40198
$106$	−21.7336	−2.11095
$107$	−14.9251	−1.44287	−0.721434	−	0.692483i	$-0.756517\pi$
$107$	−14.9251	−1.44287	−0.721434	+	0.692483i	$0.756517\pi$
$108$	49.2173	4.73594
$109$	−16.5365	−1.58391	−0.791954	−	0.610580i	$-0.790936\pi$
$109$	−16.5365	−1.58391	−0.791954	+	0.610580i	$0.790936\pi$
$110$	16.4041	1.56407
$111$	27.0916	2.57142
$112$	39.4557	3.72821
$113$	12.3092	1.15795	0.578975	−	0.815345i	$-0.303453\pi$
$113$	12.3092	1.15795	0.578975	+	0.815345i	$0.303453\pi$
$114$	−3.01597	−0.282471
$115$	−13.1322	−1.22458
$116$	23.9512	2.22381
$117$	−11.4661	−1.06004
$118$	−19.7121	−1.81464
$119$	3.11131	0.285213
$120$	−96.3863	−8.79883
$121$	−8.28382	−0.753075
$122$	31.9254	2.89039
$123$	23.0216	2.07579
$124$	−30.7553	−2.76191
$125$	13.9073	1.24391
$126$	−51.1900	−4.56037
$127$	−2.50938	−0.222672	−0.111336	−	0.993783i	$-0.535513\pi$
$127$	−2.50938	−0.222672	−0.111336	+	0.993783i	$0.535513\pi$
$128$	−19.5413	−1.72722
$129$	−0.0201763	−0.00177642
$130$	18.6192	1.63301
$131$	−3.97789	−0.347549	−0.173775	−	0.984785i	$-0.555596\pi$
$131$	−3.97789	−0.347549	−0.173775	+	0.984785i	$0.555596\pi$
$132$	−25.9190	−2.25596
$133$	1.15699	0.100324
$134$	19.7640	1.70735
$135$	35.0641	3.01784
$136$	−8.60266	−0.737672
$137$	−18.5319	−1.58329	−0.791643	−	0.610983i	$-0.790774\pi$
$137$	−18.5319	−1.58329	−0.791643	+	0.610983i	$0.790774\pi$
$138$	28.7221	2.44499
$139$	18.8375	1.59778	0.798889	−	0.601478i	$-0.205421\pi$
$139$	18.8375	1.59778	0.798889	+	0.601478i	$0.205421\pi$
$140$	60.0504	5.07519
$141$	22.6622	1.90850
$142$	6.13438	0.514786
$143$	3.08295	0.257809
$144$	77.7310	6.47758
$145$	17.0636	1.41706
$146$	25.6102	2.11951
$147$	8.09836	0.667942
$148$	46.6685	3.83613
$149$	−8.93968	−0.732367	−0.366184	−	0.930543i	$-0.619336\pi$
$149$	−8.93968	−0.732367	−0.366184	+	0.930543i	$0.619336\pi$
$150$	−70.9692	−5.79461
$151$	9.97931	0.812105	0.406053	−	0.913850i	$-0.366905\pi$
$151$	9.97931	0.812105	0.406053	+	0.913850i	$0.366905\pi$
$152$	−3.19905	−0.259477
$153$	6.12953	0.495543
$154$	13.7638	1.10911
$155$	−21.9111	−1.75994
$156$	−29.4188	−2.35539
$157$	−8.35960	−0.667168	−0.333584	−	0.942720i	$-0.608258\pi$
$157$	−8.35960	−0.667168	−0.333584	+	0.942720i	$0.608258\pi$
$158$	39.5761	3.14851
$159$	24.4647	1.94018
$160$	−62.4234	−4.93501
$161$	−11.0185	−0.868376
$162$	−27.3321	−2.14741
$163$	−6.16902	−0.483195	−0.241597	−	0.970377i	$-0.577671\pi$
$163$	−6.16902	−0.483195	−0.241597	+	0.970377i	$0.577671\pi$
$164$	39.6575	3.09673
$165$	−18.4655	−1.43754
$166$	−15.1479	−1.17571
$167$	1.83808	0.142235	0.0711175	−	0.997468i	$-0.477343\pi$
$167$	1.83808	0.142235	0.0711175	+	0.997468i	$0.477343\pi$
$168$	−80.8723	−6.23943
$169$	−9.50076	−0.730828
$170$	−9.95344	−0.763394
$171$	2.27937	0.174308
$172$	−0.0347561	−0.00265013
$173$	−21.8584	−1.66186	−0.830931	−	0.556375i	$-0.812192\pi$
$173$	−21.8584	−1.66186	−0.830931	+	0.556375i	$0.812192\pi$
$174$	−37.3209	−2.82929
$175$	27.2254	2.05805
$176$	−20.9000	−1.57540
$177$	22.1892	1.66784
$178$	26.8769	2.01451
$179$	25.6413	1.91652	0.958259	−	0.285900i	$-0.0922926\pi$
$179$	25.6413	1.91652	0.958259	+	0.285900i	$0.0922926\pi$
$180$	118.304	8.81788
$181$	12.8452	0.954778	0.477389	−	0.878692i	$-0.341583\pi$
$181$	12.8452	0.954778	0.477389	+	0.878692i	$0.341583\pi$
$182$	15.6223	1.15800
$183$	−35.9373	−2.65657
$184$	30.4657	2.24596
$185$	33.2482	2.44446
$186$	47.9231	3.51389
$187$	−1.64808	−0.120520
$188$	39.0384	2.84717
$189$	29.4203	2.14001
$190$	−3.70136	−0.268525
$191$	9.37729	0.678517	0.339259	−	0.940693i	$-0.389824\pi$
$191$	9.37729	0.678517	0.339259	+	0.940693i	$0.389824\pi$
$192$	59.8960	4.32262
$193$	16.2998	1.17328	0.586641	−	0.809847i	$-0.300450\pi$
$193$	16.2998	1.17328	0.586641	+	0.809847i	$0.300450\pi$
$194$	−16.3215	−1.17181
$195$	−20.9589	−1.50090
$196$	13.9504	0.996459
$197$	−20.9350	−1.49156	−0.745779	−	0.666193i	$-0.767923\pi$
$197$	−20.9350	−1.49156	−0.745779	+	0.666193i	$0.767923\pi$
$198$	27.1157	1.92703
$199$	−2.90921	−0.206228	−0.103114	−	0.994670i	$-0.532881\pi$
$199$	−2.90921	−0.206228	−0.103114	+	0.994670i	$0.532881\pi$
$200$	−75.2772	−5.32290
$201$	−22.2477	−1.56923
$202$	−36.2198	−2.54842
$203$	14.3171	1.00486
$204$	15.7267	1.10109
$205$	28.2533	1.97330
$206$	−6.66217	−0.464175
$207$	−21.7073	−1.50876
$208$	−23.7221	−1.64483
$209$	−0.612868	−0.0423930
$210$	−93.5709	−6.45700
$211$	5.01017	0.344915	0.172457	−	0.985017i	$-0.444829\pi$
$211$	5.01017	0.344915	0.172457	+	0.985017i	$0.444829\pi$
$212$	42.1435	2.89443
$213$	−6.90526	−0.473141
$214$	40.0621	2.73859
$215$	−0.0247614	−0.00168871
$216$	−81.3460	−5.53490
$217$	−18.3844	−1.24801
$218$	44.3872	3.00628
$219$	−28.8285	−1.94805
$220$	−31.8092	−2.14457
$221$	−1.87062	−0.125832
$222$	−72.7191	−4.88059
$223$	13.9340	0.933089	0.466545	−	0.884498i	$-0.345499\pi$
$223$	13.9340	0.933089	0.466545	+	0.884498i	$0.345499\pi$
$224$	−52.3760	−3.49952
$225$	53.6362	3.57575
$226$	−33.0403	−2.19781
$227$	6.34284	0.420989	0.210494	−	0.977595i	$-0.432493\pi$
$227$	6.34284	0.420989	0.210494	+	0.977595i	$0.432493\pi$
$228$	5.84826	0.387310
$229$	0.656388	0.0433753	0.0216877	−	0.999765i	$-0.493096\pi$
$229$	0.656388	0.0433753	0.0216877	+	0.999765i	$0.493096\pi$
$230$	35.2494	2.32427
$231$	−15.4934	−1.01939
$232$	−39.5863	−2.59897
$233$	−7.16149	−0.469165	−0.234582	−	0.972096i	$-0.575372\pi$
$233$	−7.16149	−0.469165	−0.234582	+	0.972096i	$0.575372\pi$
$234$	30.7772	2.01197
$235$	27.8123	1.81427
$236$	38.2236	2.48815
$237$	−44.5495	−2.89380
$238$	−8.35137	−0.541339
$239$	24.2149	1.56633	0.783165	−	0.621814i	$-0.213604\pi$
$239$	24.2149	1.56633	0.783165	+	0.621814i	$0.213604\pi$
$240$	142.086	9.17158
$241$	−12.8752	−0.829364	−0.414682	−	0.909966i	$-0.636107\pi$
$241$	−12.8752	−0.829364	−0.414682	+	0.909966i	$0.636107\pi$
$242$	22.2354	1.42935
$243$	2.39901	0.153896
$244$	−61.9065	−3.96316
$245$	9.93875	0.634963
$246$	−61.7945	−3.93987
$247$	−0.695624	−0.0442615
$248$	50.8321	3.22784
$249$	17.0515	1.08059
$250$	−37.3300	−2.36096
$251$	5.74953	0.362907	0.181454	−	0.983400i	$-0.441920\pi$
$251$	5.74953	0.362907	0.181454	+	0.983400i	$0.441920\pi$
$252$	99.2624	6.25294
$253$	5.83656	0.366942
$254$	6.73568	0.422634
$255$	11.2043	0.701638
$256$	12.8063	0.800394
$257$	−8.98615	−0.560541	−0.280270	−	0.959921i	$-0.590424\pi$
$257$	−8.98615	−0.560541	−0.280270	+	0.959921i	$0.590424\pi$
$258$	0.0541571	0.00337168
$259$	27.8967	1.73342
$260$	−36.1044	−2.23910
$261$	28.2059	1.74590
$262$	10.6774	0.659654
$263$	25.5346	1.57453	0.787264	−	0.616615i	$-0.211497\pi$
$263$	25.5346	1.57453	0.787264	+	0.616615i	$0.211497\pi$
$264$	42.8387	2.63654
$265$	30.0244	1.84439
$266$	−3.10560	−0.190417
$267$	−30.2545	−1.85154
$268$	−38.3244	−2.34103
$269$	−1.68909	−0.102986	−0.0514928	−	0.998673i	$-0.516398\pi$
$269$	−1.68909	−0.102986	−0.0514928	+	0.998673i	$0.516398\pi$
$270$	−94.1190	−5.72790
$271$	25.9017	1.57342	0.786709	−	0.617324i	$-0.211783\pi$
$271$	25.9017	1.57342	0.786709	+	0.617324i	$0.211783\pi$
$272$	12.6814	0.768922
$273$	−17.5855	−1.06432
$274$	49.7433	3.00510
$275$	−14.4215	−0.869649
$276$	−55.6951	−3.35245
$277$	−14.1112	−0.847857	−0.423928	−	0.905696i	$-0.639349\pi$
$277$	−14.1112	−0.847857	−0.423928	+	0.905696i	$0.639349\pi$
$278$	−50.5637	−3.03261
$279$	−36.2187	−2.16836
$280$	−99.2508	−5.93137
$281$	−26.6444	−1.58947	−0.794735	−	0.606956i	$-0.792390\pi$
$281$	−26.6444	−1.58947	−0.794735	+	0.606956i	$0.792390\pi$
$282$	−60.8298	−3.62236
$283$	−13.5396	−0.804843	−0.402422	−	0.915454i	$-0.631831\pi$
$283$	−13.5396	−0.804843	−0.402422	+	0.915454i	$0.631831\pi$
$284$	−11.8952	−0.705848
$285$	4.16649	0.246802
$286$	−8.27524	−0.489325
$287$	23.7058	1.39931
$288$	−103.185	−6.08023
$289$	1.00000	0.0588235
$290$	−45.8022	−2.68960
$291$	18.3725	1.07702
$292$	−49.6606	−2.90617
$293$	−10.1549	−0.593253	−0.296626	−	0.954994i	$-0.595862\pi$
$293$	−10.1549	−0.593253	−0.296626	+	0.954994i	$0.595862\pi$
$294$	−21.7376	−1.26776
$295$	27.2318	1.58550
$296$	−77.1334	−4.48329
$297$	−15.5841	−0.904284
$298$	23.9959	1.39004
$299$	6.62467	0.383115
$300$	137.616	7.94528
$301$	−0.0207759	−0.00119750
$302$	−26.7865	−1.54139
$303$	40.7714	2.34226
$304$	4.71579	0.270469
$305$	−44.1042	−2.52540
$306$	−16.4529	−0.940549
$307$	−4.98549	−0.284537	−0.142268	−	0.989828i	$-0.545440\pi$
$307$	−4.98549	−0.284537	−0.142268	+	0.989828i	$0.545440\pi$
$308$	−26.6893	−1.52076
$309$	7.49938	0.426625
$310$	58.8137	3.34040
$311$	1.97230	0.111839	0.0559195	−	0.998435i	$-0.482191\pi$
$311$	1.97230	0.111839	0.0559195	+	0.998435i	$0.482191\pi$
$312$	48.6232	2.75275
$313$	−3.17802	−0.179632	−0.0898162	−	0.995958i	$-0.528628\pi$
$313$	−3.17802	−0.179632	−0.0898162	+	0.995958i	$0.528628\pi$
$314$	22.4388	1.26630
$315$	70.7178	3.98450
$316$	−76.7420	−4.31707
$317$	30.9799	1.74000	0.870002	−	0.493048i	$-0.164117\pi$
$317$	30.9799	1.74000	0.870002	+	0.493048i	$0.164117\pi$
$318$	−65.6682	−3.68249
$319$	−7.58389	−0.424616
$320$	73.5076	4.10920
$321$	−45.0965	−2.51704
$322$	29.5757	1.64819
$323$	0.371867	0.0206912
$324$	52.9995	2.94442
$325$	−16.3688	−0.907979
$326$	16.5589	0.917112
$327$	−49.9652	−2.76308
$328$	−65.5456	−3.61915
$329$	23.3357	1.28654
$330$	49.5652	2.72847
$331$	21.2520	1.16812	0.584058	−	0.811712i	$-0.301464\pi$
$331$	21.2520	1.16812	0.584058	+	0.811712i	$0.301464\pi$
$332$	29.3733	1.61207
$333$	54.9588	3.01172
$334$	−4.93378	−0.269964
$335$	−27.3036	−1.49175
$336$	119.216	6.50376
$337$	24.2334	1.32008	0.660038	−	0.751232i	$-0.270540\pi$
$337$	24.2334	1.32008	0.660038	+	0.751232i	$0.270540\pi$
$338$	25.5019	1.38712
$339$	37.1923	2.02001
$340$	19.3007	1.04673
$341$	9.73834	0.527360
$342$	−6.11829	−0.330839
$343$	−13.4401	−0.725698
$344$	0.0574446	0.00309721
$345$	−39.6790	−2.13625
$346$	58.6723	3.15424
$347$	−10.5249	−0.565005	−0.282503	−	0.959267i	$-0.591165\pi$
$347$	−10.5249	−0.565005	−0.282503	+	0.959267i	$0.591165\pi$
$348$	72.3688	3.87937
$349$	−5.75712	−0.308172	−0.154086	−	0.988057i	$-0.549243\pi$
$349$	−5.75712	−0.308172	−0.154086	+	0.988057i	$0.549243\pi$
$350$	−73.0783	−3.90620
$351$	−17.6885	−0.944141
$352$	27.7439	1.47876
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−59.5603	−3.16559
$355$	−8.47451	−0.449780
$356$	−52.1170	−2.76220
$357$	9.40085	0.497546
$358$	−68.8263	−3.63758
$359$	−14.7855	−0.780347	−0.390173	−	0.920741i	$-0.627585\pi$
$359$	−14.7855	−0.780347	−0.390173	+	0.920741i	$0.627585\pi$
$360$	−195.532	−10.3055
$361$	−18.8617	−0.992722
$362$	−34.4791	−1.81218
$363$	−25.0297	−1.31372
$364$	−30.2931	−1.58779
$365$	−35.3799	−1.85187
$366$	96.4630	5.04220
$367$	−29.7685	−1.55390	−0.776952	−	0.629560i	$-0.783235\pi$
$367$	−29.7685	−1.55390	−0.776952	+	0.629560i	$0.783235\pi$
$368$	−44.9102	−2.34111
$369$	46.7023	2.43122
$370$	−89.2448	−4.63962
$371$	25.1918	1.30789
$372$	−92.9275	−4.81807
$373$	−3.09367	−0.160184	−0.0800920	−	0.996787i	$-0.525521\pi$
$373$	−3.09367	−0.160184	−0.0800920	+	0.996787i	$0.525521\pi$
$374$	4.42378	0.228748
$375$	42.0211	2.16996
$376$	−64.5224	−3.32749
$377$	−8.60794	−0.443331
$378$	−78.9699	−4.06177
$379$	−16.0250	−0.823147	−0.411574	−	0.911376i	$-0.635021\pi$
$379$	−16.0250	−0.823147	−0.411574	+	0.911376i	$0.635021\pi$
$380$	7.17730	0.368188
$381$	−7.58212	−0.388444
$382$	−25.1705	−1.28784
$383$	5.62865	0.287611	0.143805	−	0.989606i	$-0.454066\pi$
$383$	5.62865	0.287611	0.143805	+	0.989606i	$0.454066\pi$
$384$	−59.0442	−3.01309
$385$	−19.0143	−0.969060
$386$	−43.7518	−2.22691
$387$	−0.0409302	−0.00208060
$388$	31.6489	1.60673
$389$	−19.9548	−1.01175	−0.505874	−	0.862607i	$-0.668830\pi$
$389$	−19.9548	−1.01175	−0.505874	+	0.862607i	$0.668830\pi$
$390$	56.2580	2.84873
$391$	−3.54142	−0.179098
$392$	−23.0571	−1.16456
$393$	−12.0192	−0.606290
$394$	56.1938	2.83100
$395$	−54.6735	−2.75092
$396$	−52.5801	−2.64225
$397$	4.78728	0.240267	0.120133	−	0.992758i	$-0.461668\pi$
$397$	4.78728	0.240267	0.120133	+	0.992758i	$0.461668\pi$
$398$	7.80890	0.391425
$399$	3.49587	0.175012
$400$	110.968	5.54840
$401$	−8.69119	−0.434017	−0.217009	−	0.976170i	$-0.569630\pi$
$401$	−8.69119	−0.434017	−0.217009	+	0.976170i	$0.569630\pi$
$402$	59.7172	2.97842
$403$	11.0533	0.550604
$404$	70.2338	3.49426
$405$	37.7586	1.87624
$406$	−38.4300	−1.90725
$407$	−14.7771	−0.732473
$408$	−25.9930	−1.28685
$409$	−14.2551	−0.704868	−0.352434	−	0.935837i	$-0.614646\pi$
$409$	−14.2551	−0.704868	−0.352434	+	0.935837i	$0.614646\pi$
$410$	−75.8376	−3.74535
$411$	−55.9943	−2.76200
$412$	12.9186	0.636454
$413$	22.8487	1.12431
$414$	58.2666	2.86365
$415$	20.9265	1.02724
$416$	31.4902	1.54393
$417$	56.9178	2.78728
$418$	1.64506	0.0804625
$419$	28.5231	1.39344	0.696721	−	0.717342i	$-0.254642\pi$
$419$	28.5231	1.39344	0.696721	+	0.717342i	$0.254642\pi$
$420$	181.443	8.85351
$421$	37.4554	1.82546	0.912732	−	0.408558i	$-0.133968\pi$
$421$	37.4554	1.82546	0.912732	+	0.408558i	$0.133968\pi$
$422$	−13.4483	−0.654653
$423$	45.9732	2.23529
$424$	−69.6544	−3.38272
$425$	8.75046	0.424460
$426$	18.5351	0.898028
$427$	−37.0054	−1.79082
$428$	−77.6843	−3.75501
$429$	9.31516	0.449740
$430$	0.0664645	0.00320520
$431$	−19.1605	−0.922931	−0.461466	−	0.887158i	$-0.652676\pi$
$431$	−19.1605	−0.922931	−0.461466	+	0.887158i	$0.652676\pi$
$432$	119.914	5.76938
$433$	4.67257	0.224549	0.112275	−	0.993677i	$-0.464186\pi$
$433$	4.67257	0.224549	0.112275	+	0.993677i	$0.464186\pi$
$434$	49.3473	2.36874
$435$	51.5579	2.47201
$436$	−86.0712	−4.12206
$437$	−1.31694	−0.0629978
$438$	77.3814	3.69743
$439$	−34.6823	−1.65530	−0.827648	−	0.561248i	$-0.810321\pi$
$439$	−34.6823	−1.65530	−0.827648	+	0.561248i	$0.810321\pi$
$440$	52.5739	2.50636
$441$	16.4286	0.782314
$442$	5.02113	0.238831
$443$	25.3938	1.20650	0.603249	−	0.797553i	$-0.293873\pi$
$443$	25.3938	1.20650	0.603249	+	0.797553i	$0.293873\pi$
$444$	141.010	6.69202
$445$	−37.1299	−1.76013
$446$	−37.4016	−1.77102
$447$	−27.0114	−1.27759
$448$	61.6761	2.91392
$449$	−26.5489	−1.25292	−0.626460	−	0.779453i	$-0.715497\pi$
$449$	−26.5489	−1.25292	−0.626460	+	0.779453i	$0.715497\pi$
$450$	−143.970	−6.78683
$451$	−12.5571	−0.591292
$452$	64.0684	3.01352
$453$	30.1526	1.41669
$454$	−17.0254	−0.799043
$455$	−21.5818	−1.01177
$456$	−9.66595	−0.452650
$457$	−9.45111	−0.442104	−0.221052	−	0.975262i	$-0.570949\pi$
$457$	−9.45111	−0.442104	−0.221052	+	0.975262i	$0.570949\pi$
$458$	−1.76188	−0.0823271
$459$	9.45592	0.441365
$460$	−68.3520	−3.18693
$461$	20.5211	0.955762	0.477881	−	0.878424i	$-0.341405\pi$
$461$	20.5211	0.955762	0.477881	+	0.878424i	$0.341405\pi$
$462$	41.5873	1.93482
$463$	−25.5302	−1.18649	−0.593245	−	0.805022i	$-0.702154\pi$
$463$	−25.5302	−1.18649	−0.593245	+	0.805022i	$0.702154\pi$
$464$	58.3552	2.70907
$465$	−66.2046	−3.07017
$466$	19.2229	0.890482
$467$	12.4253	0.574972	0.287486	−	0.957785i	$-0.407181\pi$
$467$	12.4253	0.574972	0.287486	+	0.957785i	$0.407181\pi$
$468$	−59.6799	−2.75871
$469$	−22.9089	−1.05783
$470$	−74.6536	−3.44352
$471$	−25.2586	−1.16386
$472$	−63.1757	−2.90790
$473$	0.0110051	0.000506017 0
$474$	119.580	5.49248
$475$	3.25401	0.149304
$476$	16.1941	0.742256
$477$	49.6299	2.27240
$478$	−64.9975	−2.97292
$479$	12.3004	0.562018	0.281009	−	0.959705i	$-0.409331\pi$
$479$	12.3004	0.562018	0.281009	+	0.959705i	$0.409331\pi$
$480$	−188.613	−8.60897
$481$	−16.7724	−0.764758
$482$	34.5596	1.57414
$483$	−33.2924	−1.51486
$484$	−43.1167	−1.95985
$485$	22.5478	1.02384
$486$	−6.43941	−0.292097
$487$	31.9193	1.44640	0.723201	−	0.690637i	$-0.242670\pi$
$487$	31.9193	1.44640	0.723201	+	0.690637i	$0.242670\pi$
$488$	102.319	4.63174
$489$	−18.6398	−0.842919
$490$	−26.6776	−1.20517
$491$	−34.2764	−1.54687	−0.773436	−	0.633874i	$-0.781464\pi$
$491$	−34.2764	−1.54687	−0.773436	+	0.633874i	$0.781464\pi$
$492$	119.826	5.40216
$493$	4.60164	0.207247
$494$	1.86719	0.0840090
$495$	−37.4598	−1.68369
$496$	−74.9329	−3.36459
$497$	−7.11048	−0.318949
$498$	−45.7696	−2.05098
$499$	37.9362	1.69826	0.849130	−	0.528185i	$-0.177127\pi$
$499$	37.9362	1.69826	0.849130	+	0.528185i	$0.177127\pi$
$500$	72.3865	3.23722
$501$	5.55378	0.248125
$502$	−15.4329	−0.688804
$503$	−10.1644	−0.453209	−0.226605	−	0.973987i	$-0.572763\pi$
$503$	−10.1644	−0.453209	−0.226605	+	0.973987i	$0.572763\pi$
$504$	−164.060	−7.30782
$505$	50.0369	2.22661
$506$	−15.6665	−0.696461
$507$	−28.7067	−1.27491
$508$	−13.0611	−0.579494
$509$	−4.03941	−0.179044	−0.0895218	−	0.995985i	$-0.528534\pi$
$509$	−4.03941	−0.179044	−0.0895218	+	0.995985i	$0.528534\pi$
$510$	−30.0744	−1.33172
$511$	−29.6852	−1.31320
$512$	4.70790	0.208062
$513$	3.51635	0.155250
$514$	24.1206	1.06392
$515$	9.20364	0.405561
$516$	−0.105016	−0.00462307
$517$	−12.3611	−0.543640
$518$	−74.8803	−3.29005
$519$	−66.0454	−2.89907
$520$	59.6730	2.61683
$521$	2.72800	0.119516	0.0597579	−	0.998213i	$-0.480967\pi$
$521$	2.72800	0.119516	0.0597579	+	0.998213i	$0.480967\pi$
$522$	−75.7102	−3.31375
$523$	−32.9903	−1.44256	−0.721282	−	0.692642i	$-0.756447\pi$
$523$	−32.9903	−1.44256	−0.721282	+	0.692642i	$0.756447\pi$
$524$	−20.7046	−0.904484
$525$	82.2618	3.59020
$526$	−68.5399	−2.98848
$527$	−5.90888	−0.257395
$528$	−63.1496	−2.74823
$529$	−10.4583	−0.454709
$530$	−80.5916	−3.50067
$531$	45.0137	1.95343
$532$	6.02206	0.261090
$533$	−14.2527	−0.617354
$534$	81.2090	3.51426
$535$	−55.3449	−2.39277
$536$	63.3422	2.73597
$537$	77.4754	3.34331
$538$	4.53385	0.195468
$539$	−4.41725	−0.190265
$540$	182.506	7.85380
$541$	19.0700	0.819884	0.409942	−	0.912112i	$-0.365549\pi$
$541$	19.0700	0.819884	0.409942	+	0.912112i	$0.365549\pi$
$542$	−69.5254	−2.98637
$543$	38.8120	1.66558
$544$	−16.8341	−0.721755
$545$	−61.3200	−2.62666
$546$	47.2029	2.02010
$547$	26.2078	1.12057	0.560283	−	0.828301i	$-0.310692\pi$
$547$	26.2078	1.12057	0.560283	+	0.828301i	$0.310692\pi$
$548$	−96.4571	−4.12044
$549$	−72.9036	−3.11145
$550$	38.7102	1.65061
$551$	1.71120	0.0728995
$552$	92.0523	3.91801
$553$	−45.8735	−1.95074
$554$	37.8771	1.60925
$555$	100.460	4.26428
$556$	98.0479	4.15816
$557$	−35.3867	−1.49938	−0.749691	−	0.661788i	$-0.769798\pi$
$557$	−35.3867	−1.49938	−0.749691	+	0.661788i	$0.769798\pi$
$558$	97.2182	4.11557
$559$	0.0124912	0.000528320 0
$560$	146.308	6.18265
$561$	−4.97970	−0.210243
$562$	71.5188	3.01684
$563$	−33.1986	−1.39916	−0.699578	−	0.714556i	$-0.746629\pi$
$563$	−33.1986	−1.39916	−0.699578	+	0.714556i	$0.746629\pi$
$564$	117.955	4.96680
$565$	45.6444	1.92028
$566$	36.3429	1.52760
$567$	31.6811	1.33048
$568$	19.6602	0.824924
$569$	25.1574	1.05465	0.527326	−	0.849663i	$-0.323195\pi$
$569$	25.1574	1.05465	0.527326	+	0.849663i	$0.323195\pi$
$570$	−11.1837	−0.468434
$571$	−31.5603	−1.32076	−0.660378	−	0.750934i	$-0.729604\pi$
$571$	−31.5603	−1.32076	−0.660378	+	0.750934i	$0.729604\pi$
$572$	16.0465	0.670938
$573$	28.3336	1.18365
$574$	−63.6310	−2.65591
$575$	−30.9891	−1.29233
$576$	121.507	5.06279
$577$	−39.9664	−1.66382	−0.831911	−	0.554909i	$-0.812753\pi$
$577$	−39.9664	−1.66382	−0.831911	+	0.554909i	$0.812753\pi$
$578$	−2.68420	−0.111648
$579$	49.2499	2.04676
$580$	88.8149	3.68784
$581$	17.5582	0.728438
$582$	−49.3155	−2.04419
$583$	−13.3443	−0.552664
$584$	82.0787	3.39644
$585$	−42.5180	−1.75790
$586$	27.2576	1.12600
$587$	33.1709	1.36911	0.684554	−	0.728962i	$-0.259997\pi$
$587$	33.1709	1.36911	0.684554	+	0.728962i	$0.259997\pi$
$588$	42.1514	1.73829
$589$	−2.19732	−0.0905390
$590$	−73.0956	−3.00930
$591$	−63.2554	−2.60198
$592$	113.704	4.67322
$593$	30.6357	1.25806	0.629028	−	0.777382i	$-0.283453\pi$
$593$	30.6357	1.25806	0.629028	+	0.777382i	$0.283453\pi$
$594$	41.8309	1.71634
$595$	11.5372	0.472980
$596$	−46.5304	−1.90596
$597$	−8.79021	−0.359760
$598$	−17.7819	−0.727158
$599$	17.1439	0.700479	0.350240	−	0.936660i	$-0.386100\pi$
$599$	17.1439	0.700479	0.350240	+	0.936660i	$0.386100\pi$
$600$	−227.451	−9.28565
$601$	−19.4135	−0.791892	−0.395946	−	0.918274i	$-0.629583\pi$
$601$	−19.4135	−0.791892	−0.395946	+	0.918274i	$0.629583\pi$
$602$	0.0557666	0.00227288
$603$	−45.1323	−1.83793
$604$	51.9416	2.11347
$605$	−30.7177	−1.24885
$606$	−109.439	−4.44564
$607$	14.3442	0.582212	0.291106	−	0.956691i	$-0.405977\pi$
$607$	14.3442	0.582212	0.291106	+	0.956691i	$0.405977\pi$
$608$	−6.26004	−0.253878
$609$	43.2593	1.75296
$610$	118.385	4.79325
$611$	−14.0302	−0.567602
$612$	31.9038	1.28963
$613$	14.0729	0.568399	0.284199	−	0.958765i	$-0.408272\pi$
$613$	14.0729	0.568399	0.284199	+	0.958765i	$0.408272\pi$
$614$	13.3820	0.540055
$615$	85.3678	3.44236
$616$	44.1118	1.77731
$617$	24.1024	0.970326	0.485163	−	0.874424i	$-0.338760\pi$
$617$	24.1024	0.970326	0.485163	+	0.874424i	$0.338760\pi$
$618$	−20.1298	−0.809740
$619$	28.3433	1.13921	0.569607	−	0.821917i	$-0.307096\pi$
$619$	28.3433	1.13921	0.569607	+	0.821917i	$0.307096\pi$
$620$	−114.046	−4.58018
$621$	−33.4874	−1.34380
$622$	−5.29405	−0.212272
$623$	−31.1536	−1.24814
$624$	−71.6767	−2.86936
$625$	7.81827	0.312731
$626$	8.53044	0.340945
$627$	−1.85179	−0.0739533
$628$	−43.5111	−1.73628
$629$	8.96623	0.357507
$630$	−189.821	−7.56264
$631$	−32.8168	−1.30642	−0.653208	−	0.757179i	$-0.726577\pi$
$631$	−32.8168	−1.30642	−0.653208	+	0.757179i	$0.726577\pi$
$632$	126.838	5.04536
$633$	15.1383	0.601693
$634$	−83.1562	−3.30256
$635$	−9.30519	−0.369265
$636$	127.337	5.04925
$637$	−5.01371	−0.198651
$638$	20.3567	0.805928
$639$	−14.0082	−0.554157
$640$	−72.4623	−2.86432
$641$	24.0570	0.950195	0.475097	−	0.879933i	$-0.342413\pi$
$641$	24.0570	0.950195	0.475097	+	0.879933i	$0.342413\pi$
$642$	121.048	4.77738
$643$	6.97952	0.275246	0.137623	−	0.990485i	$-0.456054\pi$
$643$	6.97952	0.275246	0.137623	+	0.990485i	$0.456054\pi$
$644$	−57.3503	−2.25992
$645$	−0.0748169	−0.00294591
$646$	−0.998166	−0.0392723
$647$	−16.2808	−0.640064	−0.320032	−	0.947407i	$-0.603694\pi$
$647$	−16.2808	−0.640064	−0.320032	+	0.947407i	$0.603694\pi$
$648$	−87.5972	−3.44114
$649$	−12.1031	−0.475088
$650$	43.9372	1.72336
$651$	−55.5485	−2.17712
$652$	−32.1093	−1.25750
$653$	−4.02928	−0.157678	−0.0788390	−	0.996887i	$-0.525121\pi$
$653$	−4.02928	−0.157678	−0.0788390	+	0.996887i	$0.525121\pi$
$654$	134.117	5.24437
$655$	−14.7506	−0.576355
$656$	96.6224	3.77247
$657$	−58.4824	−2.28162
$658$	−62.6376	−2.44187
$659$	17.9645	0.699797	0.349898	−	0.936788i	$-0.386216\pi$
$659$	17.9645	0.699797	0.349898	+	0.936788i	$0.386216\pi$
$660$	−96.1118	−3.74115
$661$	6.51947	0.253578	0.126789	−	0.991930i	$-0.459533\pi$
$661$	6.51947	0.253578	0.126789	+	0.991930i	$0.459533\pi$
$662$	−57.0446	−2.21710
$663$	−5.65211	−0.219510
$664$	−48.5479	−1.88402
$665$	4.29032	0.166371
$666$	−147.520	−5.71630
$667$	−16.2964	−0.630997
$668$	9.56707	0.370161
$669$	42.1017	1.62775
$670$	73.2882	2.83137
$671$	19.6020	0.756728
$672$	−158.255	−6.10480
$673$	28.8887	1.11358	0.556790	−	0.830654i	$-0.312033\pi$
$673$	28.8887	1.11358	0.556790	+	0.830654i	$0.312033\pi$
$674$	−65.0472	−2.50553
$675$	82.7437	3.18480
$676$	−49.4508	−1.90195
$677$	38.2752	1.47104	0.735518	−	0.677505i	$-0.236939\pi$
$677$	38.2752	1.47104	0.735518	+	0.677505i	$0.236939\pi$
$678$	−99.8316	−3.83401
$679$	18.9185	0.726027
$680$	−31.9000	−1.22331
$681$	19.1650	0.734403
$682$	−26.1396	−1.00094
$683$	11.5294	0.441160	0.220580	−	0.975369i	$-0.429205\pi$
$683$	11.5294	0.441160	0.220580	+	0.975369i	$0.429205\pi$
$684$	11.8640	0.453630
$685$	−68.7193	−2.62563
$686$	36.0759	1.37739
$687$	1.98328	0.0756670
$688$	−0.0846805	−0.00322841
$689$	−15.1462	−0.577023
$690$	106.506	4.05463
$691$	−0.603541	−0.0229598	−0.0114799	−	0.999934i	$-0.503654\pi$
$691$	−0.603541	−0.0229598	−0.0114799	+	0.999934i	$0.503654\pi$
$692$	−113.771	−4.32493
$693$	−31.4304	−1.19394
$694$	28.2509	1.07239
$695$	69.8526	2.64966
$696$	−119.611	−4.53383
$697$	7.61923	0.288599
$698$	15.4533	0.584914
$699$	−21.6385	−0.818444
$700$	141.706	5.35598
$701$	15.8672	0.599297	0.299649	−	0.954050i	$-0.403131\pi$
$701$	15.8672	0.599297	0.299649	+	0.954050i	$0.403131\pi$
$702$	47.4794	1.79199
$703$	3.33425	0.125753
$704$	−32.6703	−1.23131
$705$	84.0351	3.16494
$706$	2.68420	0.101021
$707$	41.9831	1.57894
$708$	115.493	4.34050
$709$	−47.1152	−1.76945	−0.884724	−	0.466115i	$-0.845653\pi$
$709$	−47.1152	−1.76945	−0.884724	+	0.466115i	$0.845653\pi$
$710$	22.7473	0.853690
$711$	−90.3745	−3.38931
$712$	86.1386	3.22818
$713$	20.9259	0.783680
$714$	−25.2338	−0.944350
$715$	11.4321	0.427535
$716$	133.461	4.98767
$717$	73.1655	2.73242
$718$	39.6871	1.48111
$719$	15.2172	0.567506	0.283753	−	0.958897i	$-0.408420\pi$
$719$	15.2172	0.567506	0.283753	+	0.958897i	$0.408420\pi$
$720$	288.239	10.7420
$721$	7.72225	0.287592
$722$	50.6286	1.88420
$723$	−38.9025	−1.44680
$724$	66.8584	2.48477
$725$	40.2665	1.49546
$726$	67.1846	2.49345
$727$	−10.5678	−0.391937	−0.195968	−	0.980610i	$-0.562785\pi$
$727$	−10.5678	−0.391937	−0.195968	+	0.980610i	$0.562785\pi$
$728$	50.0682	1.85565
$729$	−23.2991	−0.862930
$730$	94.9666	3.51487
$731$	−0.00667754	−0.000246978 0
$732$	−187.051	−6.91361
$733$	−26.5998	−0.982486	−0.491243	−	0.871022i	$-0.663457\pi$
$733$	−26.5998	−0.982486	−0.491243	+	0.871022i	$0.663457\pi$
$734$	79.9047	2.94933
$735$	30.0300	1.10767
$736$	59.6166	2.19750
$737$	12.1350	0.446998
$738$	−125.358	−4.61450
$739$	50.2600	1.84885	0.924423	−	0.381370i	$-0.124547\pi$
$739$	50.2600	1.84885	0.924423	+	0.381370i	$0.124547\pi$
$740$	173.054	6.36161
$741$	−2.10184	−0.0772129
$742$	−67.6198	−2.48240
$743$	43.0226	1.57835	0.789174	−	0.614170i	$-0.210509\pi$
$743$	43.0226	1.57835	0.789174	+	0.614170i	$0.210509\pi$
$744$	153.590	5.63087
$745$	−33.1498	−1.21451
$746$	8.30401	0.304032
$747$	34.5912	1.26562
$748$	−8.57815	−0.313648
$749$	−46.4367	−1.69676
$750$	−112.793	−4.11862
$751$	−37.1291	−1.35486	−0.677430	−	0.735588i	$-0.736906\pi$
$751$	−37.1291	−1.35486	−0.677430	+	0.735588i	$0.736906\pi$
$752$	95.1140	3.46845
$753$	17.3723	0.633081
$754$	23.1054	0.841450
$755$	37.0049	1.34675
$756$	153.130	5.56930
$757$	−25.1831	−0.915296	−0.457648	−	0.889133i	$-0.651308\pi$
$757$	−25.1831	−0.915296	−0.457648	+	0.889133i	$0.651308\pi$
$758$	43.0142	1.56235
$759$	17.6352	0.640119
$760$	−11.8626	−0.430301
$761$	14.1581	0.513229	0.256615	−	0.966514i	$-0.417393\pi$
$761$	14.1581	0.513229	0.256615	+	0.966514i	$0.417393\pi$
$762$	20.3519	0.737272
$763$	−51.4501	−1.86262
$764$	48.8081	1.76582
$765$	22.7293	0.821779
$766$	−15.1084	−0.545889
$767$	−13.7374	−0.496028
$768$	38.6944	1.39626
$769$	43.4316	1.56618	0.783092	−	0.621906i	$-0.213641\pi$
$769$	43.4316	1.56618	0.783092	+	0.621906i	$0.213641\pi$
$770$	51.0382	1.83929
$771$	−27.1518	−0.977847
$772$	84.8390	3.05342
$773$	−14.1772	−0.509920	−0.254960	−	0.966952i	$-0.582062\pi$
$773$	−14.1772	−0.509920	−0.254960	+	0.966952i	$0.582062\pi$
$774$	0.109865	0.00394901
$775$	−51.7055	−1.85732
$776$	−52.3091	−1.87779
$777$	84.2902	3.02389
$778$	53.5627	1.92031
$779$	2.83334	0.101515
$780$	−109.090	−3.90604
$781$	3.76647	0.134775
$782$	9.50589	0.339930
$783$	43.5127	1.55502
$784$	33.9891	1.21390
$785$	−30.9987	−1.10639
$786$	32.2620	1.15075
$787$	40.9071	1.45818	0.729090	−	0.684418i	$-0.239944\pi$
$787$	40.9071	1.45818	0.729090	+	0.684418i	$0.239944\pi$
$788$	−108.965	−3.88173
$789$	77.1530	2.74672
$790$	146.755	5.22130
$791$	38.2977	1.36171
$792$	86.9039	3.08799
$793$	22.2489	0.790081
$794$	−12.8500	−0.456030
$795$	90.7192	3.21748
$796$	−15.1422	−0.536702
$797$	−38.9090	−1.37823	−0.689114	−	0.724653i	$-0.742000\pi$
$797$	−38.9090	−1.37823	−0.689114	+	0.724653i	$0.742000\pi$
$798$	−9.38361	−0.332176
$799$	7.50028	0.265341
$800$	−147.306	−5.20805
$801$	−61.3751	−2.16858
$802$	23.3289	0.823771
$803$	15.7245	0.554906
$804$	−115.798	−4.08386
$805$	−40.8582	−1.44006
$806$	−29.6693	−1.04506
$807$	−5.10360	−0.179655
$808$	−116.082	−4.08375
$809$	−8.46908	−0.297757	−0.148878	−	0.988856i	$-0.547566\pi$
$809$	−8.46908	−0.297757	−0.148878	+	0.988856i	$0.547566\pi$
$810$	−101.352	−3.56113
$811$	23.2594	0.816747	0.408373	−	0.912815i	$-0.366096\pi$
$811$	23.2594	0.816747	0.408373	+	0.912815i	$0.366096\pi$
$812$	74.5195	2.61512
$813$	78.2623	2.74478
$814$	39.6647	1.39025
$815$	−22.8757	−0.801302
$816$	38.3170	1.34136
$817$	−0.00248316	−8.68747e−5 0
$818$	38.2635	1.33785
$819$	−35.6744	−1.24657
$820$	147.056	5.13543
$821$	−19.6131	−0.684502	−0.342251	−	0.939609i	$-0.611189\pi$
$821$	−19.6131	−0.684502	−0.342251	+	0.939609i	$0.611189\pi$
$822$	150.300	5.24231
$823$	42.5853	1.48443	0.742215	−	0.670162i	$-0.233775\pi$
$823$	42.5853	1.48443	0.742215	+	0.670162i	$0.233775\pi$
$824$	−21.3517	−0.743823
$825$	−43.5747	−1.51708
$826$	−61.3303	−2.13396
$827$	−22.2434	−0.773480	−0.386740	−	0.922189i	$-0.626399\pi$
$827$	−22.2434	−0.773480	−0.386740	+	0.922189i	$0.626399\pi$
$828$	−112.985	−3.92649
$829$	21.2110	0.736690	0.368345	−	0.929689i	$-0.379925\pi$
$829$	21.2110	0.736690	0.368345	+	0.929689i	$0.379925\pi$
$830$	−56.1709	−1.94972
$831$	−42.6370	−1.47906
$832$	−37.0818	−1.28558
$833$	2.68024	0.0928647
$834$	−152.779	−5.29029
$835$	6.81590	0.235874
$836$	−3.18993	−0.110326
$837$	−55.8739	−1.93129
$838$	−76.5615	−2.64477
$839$	34.6808	1.19731	0.598657	−	0.801006i	$-0.295701\pi$
$839$	34.6808	1.19731	0.598657	+	0.801006i	$0.295701\pi$
$840$	−299.888	−10.3471
$841$	−7.82492	−0.269825
$842$	−100.538	−3.46476
$843$	−80.5063	−2.77278
$844$	26.0776	0.897627
$845$	−35.2304	−1.21196
$846$	−123.401	−4.24262
$847$	−25.7735	−0.885588
$848$	102.679	3.52602
$849$	−40.9099	−1.40403
$850$	−23.4880	−0.805631
$851$	−31.7532	−1.08849
$852$	−35.9414	−1.23133
$853$	25.8866	0.886340	0.443170	−	0.896438i	$-0.353854\pi$
$853$	25.8866	0.886340	0.443170	+	0.896438i	$0.353854\pi$
$854$	99.3298	3.39899
$855$	8.45228	0.289062
$856$	128.396	4.38848
$857$	−17.4038	−0.594504	−0.297252	−	0.954799i	$-0.596070\pi$
$857$	−17.4038	−0.594504	−0.297252	+	0.954799i	$0.596070\pi$
$858$	−25.0037	−0.853613
$859$	−40.2236	−1.37241	−0.686206	−	0.727407i	$-0.740725\pi$
$859$	−40.2236	−1.37241	−0.686206	+	0.727407i	$0.740725\pi$
$860$	−0.128881	−0.00439481
$861$	71.6272	2.44105
$862$	51.4307	1.75174
$863$	20.0518	0.682571	0.341286	−	0.939960i	$-0.389138\pi$
$863$	20.0518	0.682571	0.341286	+	0.939960i	$0.389138\pi$
$864$	−159.182	−5.41547
$865$	−81.0544	−2.75593
$866$	−12.5421	−0.426198
$867$	3.02151	0.102616
$868$	−95.6892	−3.24790
$869$	24.2995	0.824305
$870$	−138.392	−4.69192
$871$	13.7736	0.466700
$872$	142.258	4.81746
$873$	37.2711	1.26143
$874$	3.53493	0.119571
$875$	43.2699	1.46279
$876$	−150.050	−5.06972
$877$	53.2554	1.79831	0.899154	−	0.437633i	$-0.144183\pi$
$877$	53.2554	1.79831	0.899154	+	0.437633i	$0.144183\pi$
$878$	93.0942	3.14178
$879$	−30.6830	−1.03491
$880$	−77.5005	−2.61254
$881$	−12.8344	−0.432403	−0.216202	−	0.976349i	$-0.569367\pi$
$881$	−12.8344	−0.432403	−0.216202	+	0.976349i	$0.569367\pi$
$882$	−44.0976	−1.48484
$883$	−23.2349	−0.781918	−0.390959	−	0.920408i	$-0.627857\pi$
$883$	−23.2349	−0.781918	−0.390959	+	0.920408i	$0.627857\pi$
$884$	−9.73646	−0.327473
$885$	82.2812	2.76585
$886$	−68.1621	−2.28995
$887$	12.7948	0.429606	0.214803	−	0.976657i	$-0.431089\pi$
$887$	12.7948	0.429606	0.214803	+	0.976657i	$0.431089\pi$
$888$	−233.059	−7.82096
$889$	−7.80745	−0.261854
$890$	99.6640	3.34075
$891$	−16.7817	−0.562209
$892$	72.5254	2.42833
$893$	2.78911	0.0933340
$894$	72.5039	2.42489
$895$	95.0820	3.17824
$896$	−60.7990	−2.03115
$897$	20.0165	0.668333
$898$	71.2626	2.37806
$899$	−27.1906	−0.906856
$900$	279.173	9.30575
$901$	8.09685	0.269745
$902$	33.7058	1.12228
$903$	−0.0627746	−0.00208901
$904$	−105.892	−3.52190
$905$	47.6321	1.58335
$906$	−80.9356	−2.68891
$907$	−26.0610	−0.865343	−0.432671	−	0.901552i	$-0.642429\pi$
$907$	−26.0610	−0.865343	−0.432671	+	0.901552i	$0.642429\pi$
$908$	33.0140	1.09561
$909$	82.7102	2.74332
$910$	57.9299	1.92036
$911$	−16.3767	−0.542585	−0.271293	−	0.962497i	$-0.587451\pi$
$911$	−16.3767	−0.542585	−0.271293	+	0.962497i	$0.587451\pi$
$912$	14.2488	0.471826
$913$	−9.30073	−0.307809
$914$	25.3687	0.839120
$915$	−133.261	−4.40549
$916$	3.41645	0.112883
$917$	−12.3764	−0.408706
$918$	−25.3816	−0.837717
$919$	−24.1308	−0.796003	−0.398002	−	0.917385i	$-0.630296\pi$
$919$	−24.1308	−0.796003	−0.398002	+	0.917385i	$0.630296\pi$
$920$	112.972	3.72456
$921$	−15.0637	−0.496366
$922$	−55.0827	−1.81405
$923$	4.27506	0.140715
$924$	−80.6419	−2.65292
$925$	78.4586	2.57970
$926$	68.5282	2.25198
$927$	15.2135	0.499676
$928$	−77.4643	−2.54289
$929$	−41.1594	−1.35040	−0.675198	−	0.737637i	$-0.735942\pi$
$929$	−41.1594	−1.35040	−0.675198	+	0.737637i	$0.735942\pi$
$930$	177.706	5.82722
$931$	0.996692	0.0326652
$932$	−37.2750	−1.22098
$933$	5.95934	0.195100
$934$	−33.3519	−1.09131
$935$	−6.11136	−0.199863
$936$	98.6385	3.22410
$937$	−16.5009	−0.539059	−0.269530	−	0.962992i	$-0.586868\pi$
$937$	−16.5009	−0.539059	−0.269530	+	0.962992i	$0.586868\pi$
$938$	61.4919	2.00778
$939$	−9.60243	−0.313363
$940$	144.761	4.72157
$941$	−28.5609	−0.931058	−0.465529	−	0.885033i	$-0.654136\pi$
$941$	−28.5609	−0.931058	−0.465529	+	0.885033i	$0.654136\pi$
$942$	67.7992	2.20902
$943$	−26.9829	−0.878685
$944$	93.1289	3.03109
$945$	109.095	3.54886
$946$	−0.0295400	−0.000960428 0
$947$	6.39709	0.207877	0.103939	−	0.994584i	$-0.466855\pi$
$947$	6.39709	0.207877	0.103939	+	0.994584i	$0.466855\pi$
$948$	−231.877	−7.53101
$949$	17.8478	0.579364
$950$	−8.73441	−0.283382
$951$	93.6061	3.03539
$952$	−26.7655	−0.867475
$953$	−33.0208	−1.06965	−0.534825	−	0.844963i	$-0.679622\pi$
$953$	−33.0208	−1.06965	−0.534825	+	0.844963i	$0.679622\pi$
$954$	−133.217	−4.31305
$955$	34.7725	1.12521
$956$	126.037	4.07631
$957$	−22.9148	−0.740730
$958$	−33.0166	−1.06672
$959$	−57.6584	−1.86189
$960$	222.104	7.16838
$961$	3.91491	0.126288
$962$	45.0206	1.45152
$963$	−91.4842	−2.94804
$964$	−67.0144	−2.15839
$965$	60.4421	1.94570
$966$	89.3634	2.87522
$967$	−24.5064	−0.788072	−0.394036	−	0.919095i	$-0.628922\pi$
$967$	−24.5064	−0.788072	−0.394036	+	0.919095i	$0.628922\pi$
$968$	71.2629	2.29047
$969$	1.12360	0.0360953
$970$	−60.5227	−1.94327
$971$	34.4658	1.10606	0.553031	−	0.833161i	$-0.313471\pi$
$971$	34.4658	1.10606	0.553031	+	0.833161i	$0.313471\pi$
$972$	12.4866	0.400509
$973$	58.6093	1.87893
$974$	−85.6778	−2.74529
$975$	−49.4586	−1.58394
$976$	−150.830	−4.82796
$977$	20.1405	0.644353	0.322177	−	0.946680i	$-0.395586\pi$
$977$	20.1405	0.644353	0.322177	+	0.946680i	$0.395586\pi$
$978$	50.0328	1.59987
$979$	16.5023	0.527416
$980$	51.7304	1.65247
$981$	−101.361	−3.23621
$982$	92.0047	2.93599
$983$	−39.9313	−1.27361	−0.636805	−	0.771025i	$-0.719745\pi$
$983$	−39.9313	−1.27361	−0.636805	+	0.771025i	$0.719745\pi$
$984$	−198.047	−6.31350
$985$	−77.6304	−2.47351
$986$	−12.3517	−0.393359
$987$	70.5091	2.24433
$988$	−3.62067	−0.115189
$989$	0.0236480	0.000751963 0
$990$	100.550	3.19567
$991$	−9.77166	−0.310407	−0.155203	−	0.987883i	$-0.549603\pi$
$991$	−9.77166	−0.310407	−0.155203	+	0.987883i	$0.549603\pi$
$992$	99.4706	3.15819
$993$	64.2132	2.03774
$994$	19.0859	0.605369
$995$	−10.7878	−0.341997
$996$	88.7517	2.81220
$997$	−31.0234	−0.982522	−0.491261	−	0.871012i	$-0.663464\pi$
$997$	−31.0234	−0.982522	−0.491261	+	0.871012i	$0.663464\pi$
$998$	−101.828	−3.22332
$999$	84.7839	2.68244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.3	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.3	✓	121	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68420 q^{2} +3.02151 q^{3} +5.20492 q^{4} +3.70816 q^{5} -8.11034 q^{6} +3.11131 q^{7} -8.60266 q^{8} +6.12953 q^{9} +O(q^{10})\)	\(q-2.68420 q^{2} +3.02151 q^{3} +5.20492 q^{4} +3.70816 q^{5} -8.11034 q^{6} +3.11131 q^{7} -8.60266 q^{8} +6.12953 q^{9} -9.95344 q^{10} -1.64808 q^{11} +15.7267 q^{12} -1.87062 q^{13} -8.35137 q^{14} +11.2043 q^{15} +12.6814 q^{16} +1.00000 q^{17} -16.4529 q^{18} +0.371867 q^{19} +19.3007 q^{20} +9.40085 q^{21} +4.42378 q^{22} -3.54142 q^{23} -25.9930 q^{24} +8.75046 q^{25} +5.02113 q^{26} +9.45592 q^{27} +16.1941 q^{28} +4.60164 q^{29} -30.0744 q^{30} -5.90888 q^{31} -16.8341 q^{32} -4.97970 q^{33} -2.68420 q^{34} +11.5372 q^{35} +31.9038 q^{36} +8.96623 q^{37} -0.998166 q^{38} -5.65211 q^{39} -31.9000 q^{40} +7.61923 q^{41} -25.2338 q^{42} -0.00667754 q^{43} -8.57815 q^{44} +22.7293 q^{45} +9.50589 q^{46} +7.50028 q^{47} +38.3170 q^{48} +2.68024 q^{49} -23.4880 q^{50} +3.02151 q^{51} -9.73646 q^{52} +8.09685 q^{53} -25.3816 q^{54} -6.11136 q^{55} -26.7655 q^{56} +1.12360 q^{57} -12.3517 q^{58} +7.34375 q^{59} +58.3173 q^{60} -11.8938 q^{61} +15.8606 q^{62} +19.0709 q^{63} +19.8232 q^{64} -6.93658 q^{65} +13.3665 q^{66} -7.36310 q^{67} +5.20492 q^{68} -10.7005 q^{69} -30.9682 q^{70} -2.28537 q^{71} -52.7303 q^{72} -9.54108 q^{73} -24.0671 q^{74} +26.4396 q^{75} +1.93554 q^{76} -5.12770 q^{77} +15.1714 q^{78} -14.7441 q^{79} +47.0246 q^{80} +10.1826 q^{81} -20.4515 q^{82} +5.64336 q^{83} +48.9307 q^{84} +3.70816 q^{85} +0.0179239 q^{86} +13.9039 q^{87} +14.1779 q^{88} -10.0130 q^{89} -61.0100 q^{90} -5.82009 q^{91} -18.4328 q^{92} -17.8538 q^{93} -20.1323 q^{94} +1.37894 q^{95} -50.8643 q^{96} +6.08057 q^{97} -7.19429 q^{98} -10.1020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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