LMFDB - Embedded newform 8007.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80793 q^{2} +1.00000 q^{3} +5.88448 q^{4} -2.90815 q^{5} -2.80793 q^{6} -1.28847 q^{7} -10.9074 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.80793 q^{2} +1.00000 q^{3} +5.88448 q^{4} -2.90815 q^{5} -2.80793 q^{6} -1.28847 q^{7} -10.9074 q^{8} +1.00000 q^{9} +8.16589 q^{10} +2.87128 q^{11} +5.88448 q^{12} +0.133268 q^{13} +3.61794 q^{14} -2.90815 q^{15} +18.8582 q^{16} -1.00000 q^{17} -2.80793 q^{18} -3.66040 q^{19} -17.1130 q^{20} -1.28847 q^{21} -8.06235 q^{22} -6.74225 q^{23} -10.9074 q^{24} +3.45734 q^{25} -0.374207 q^{26} +1.00000 q^{27} -7.58199 q^{28} -3.28889 q^{29} +8.16589 q^{30} +8.99391 q^{31} -31.1377 q^{32} +2.87128 q^{33} +2.80793 q^{34} +3.74707 q^{35} +5.88448 q^{36} +2.72071 q^{37} +10.2781 q^{38} +0.133268 q^{39} +31.7202 q^{40} +6.71660 q^{41} +3.61794 q^{42} +5.12031 q^{43} +16.8960 q^{44} -2.90815 q^{45} +18.9318 q^{46} +3.31884 q^{47} +18.8582 q^{48} -5.33984 q^{49} -9.70797 q^{50} -1.00000 q^{51} +0.784212 q^{52} -2.37198 q^{53} -2.80793 q^{54} -8.35010 q^{55} +14.0538 q^{56} -3.66040 q^{57} +9.23497 q^{58} -1.05177 q^{59} -17.1130 q^{60} +1.13321 q^{61} -25.2543 q^{62} -1.28847 q^{63} +49.7162 q^{64} -0.387563 q^{65} -8.06235 q^{66} -5.26093 q^{67} -5.88448 q^{68} -6.74225 q^{69} -10.5215 q^{70} +14.3177 q^{71} -10.9074 q^{72} +12.5369 q^{73} -7.63956 q^{74} +3.45734 q^{75} -21.5395 q^{76} -3.69956 q^{77} -0.374207 q^{78} -5.39575 q^{79} -54.8423 q^{80} +1.00000 q^{81} -18.8598 q^{82} -9.57756 q^{83} -7.58199 q^{84} +2.90815 q^{85} -14.3775 q^{86} -3.28889 q^{87} -31.3180 q^{88} -14.0550 q^{89} +8.16589 q^{90} -0.171712 q^{91} -39.6746 q^{92} +8.99391 q^{93} -9.31907 q^{94} +10.6450 q^{95} -31.1377 q^{96} -8.78638 q^{97} +14.9939 q^{98} +2.87128 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	−2.80793	−1.98551	−0.992754	−	0.120166i	$-0.961657\pi$
$2$	−2.80793	−1.98551	−0.992754	+	0.120166i	$0.961657\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.88448	2.94224
$5$	−2.90815	−1.30056	−0.650282	−	0.759693i	$-0.725349\pi$
$5$	−2.90815	−1.30056	−0.650282	+	0.759693i	$0.725349\pi$
$6$	−2.80793	−1.14633
$7$	−1.28847	−0.486996	−0.243498	−	0.969901i	$-0.578295\pi$
$7$	−1.28847	−0.486996	−0.243498	+	0.969901i	$0.578295\pi$
$8$	−10.9074	−3.85633
$9$	1.00000	0.333333
$10$	8.16589	2.58228
$11$	2.87128	0.865722	0.432861	−	0.901461i	$-0.357504\pi$
$11$	2.87128	0.865722	0.432861	+	0.901461i	$0.357504\pi$
$12$	5.88448	1.69870
$13$	0.133268	0.0369619	0.0184809	−	0.999829i	$-0.494117\pi$
$13$	0.133268	0.0369619	0.0184809	+	0.999829i	$0.494117\pi$
$14$	3.61794	0.966935
$15$	−2.90815	−0.750881
$16$	18.8582	4.71454
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.80793	−0.661836
$19$	−3.66040	−0.839752	−0.419876	−	0.907581i	$-0.637927\pi$
$19$	−3.66040	−0.839752	−0.419876	+	0.907581i	$0.637927\pi$
$20$	−17.1130	−3.82657
$21$	−1.28847	−0.281168
$22$	−8.06235	−1.71890
$23$	−6.74225	−1.40586	−0.702928	−	0.711261i	$-0.748124\pi$
$23$	−6.74225	−1.40586	−0.702928	+	0.711261i	$0.748124\pi$
$24$	−10.9074	−2.22645
$25$	3.45734	0.691468
$26$	−0.374207	−0.0733880
$27$	1.00000	0.192450
$28$	−7.58199	−1.43286
$29$	−3.28889	−0.610731	−0.305365	−	0.952235i	$-0.598779\pi$
$29$	−3.28889	−0.610731	−0.305365	+	0.952235i	$0.598779\pi$
$30$	8.16589	1.49088
$31$	8.99391	1.61535	0.807677	−	0.589625i	$-0.200725\pi$
$31$	8.99391	1.61535	0.807677	+	0.589625i	$0.200725\pi$
$32$	−31.1377	−5.50442
$33$	2.87128	0.499825
$34$	2.80793	0.481556
$35$	3.74707	0.633370
$36$	5.88448	0.980747
$37$	2.72071	0.447282	0.223641	−	0.974672i	$-0.428206\pi$
$37$	2.72071	0.447282	0.223641	+	0.974672i	$0.428206\pi$
$38$	10.2781	1.66733
$39$	0.133268	0.0213399
$40$	31.7202	5.01541
$41$	6.71660	1.04896	0.524479	−	0.851424i	$-0.324260\pi$
$41$	6.71660	1.04896	0.524479	+	0.851424i	$0.324260\pi$
$42$	3.61794	0.558260
$43$	5.12031	0.780840	0.390420	−	0.920637i	$-0.372330\pi$
$43$	5.12031	0.780840	0.390420	+	0.920637i	$0.372330\pi$
$44$	16.8960	2.54716
$45$	−2.90815	−0.433521
$46$	18.9318	2.79134
$47$	3.31884	0.484102	0.242051	−	0.970264i	$-0.422180\pi$
$47$	3.31884	0.484102	0.242051	+	0.970264i	$0.422180\pi$
$48$	18.8582	2.72194
$49$	−5.33984	−0.762834
$50$	−9.70797	−1.37291
$51$	−1.00000	−0.140028
$52$	0.784212	0.108751
$53$	−2.37198	−0.325816	−0.162908	−	0.986641i	$-0.552087\pi$
$53$	−2.37198	−0.325816	−0.162908	+	0.986641i	$0.552087\pi$
$54$	−2.80793	−0.382111
$55$	−8.35010	−1.12593
$56$	14.0538	1.87802
$57$	−3.66040	−0.484831
$58$	9.23497	1.21261
$59$	−1.05177	−0.136929	−0.0684647	−	0.997654i	$-0.521810\pi$
$59$	−1.05177	−0.136929	−0.0684647	+	0.997654i	$0.521810\pi$
$60$	−17.1130	−2.20927
$61$	1.13321	0.145092	0.0725462	−	0.997365i	$-0.476888\pi$
$61$	1.13321	0.145092	0.0725462	+	0.997365i	$0.476888\pi$
$62$	−25.2543	−3.20730
$63$	−1.28847	−0.162332
$64$	49.7162	6.21453
$65$	−0.387563	−0.0480713
$66$	−8.06235	−0.992407
$67$	−5.26093	−0.642725	−0.321362	−	0.946956i	$-0.604141\pi$
$67$	−5.26093	−0.642725	−0.321362	+	0.946956i	$0.604141\pi$
$68$	−5.88448	−0.713598
$69$	−6.74225	−0.811671
$70$	−10.5215	−1.25756
$71$	14.3177	1.69919	0.849597	−	0.527432i	$-0.176845\pi$
$71$	14.3177	1.69919	0.849597	+	0.527432i	$0.176845\pi$
$72$	−10.9074	−1.28544
$73$	12.5369	1.46733	0.733666	−	0.679510i	$-0.237808\pi$
$73$	12.5369	1.46733	0.733666	+	0.679510i	$0.237808\pi$
$74$	−7.63956	−0.888081
$75$	3.45734	0.399219
$76$	−21.5395	−2.47075
$77$	−3.69956	−0.421604
$78$	−0.374207	−0.0423706
$79$	−5.39575	−0.607069	−0.303534	−	0.952820i	$-0.598167\pi$
$79$	−5.39575	−0.607069	−0.303534	+	0.952820i	$0.598167\pi$
$80$	−54.8423	−6.13156
$81$	1.00000	0.111111
$82$	−18.8598	−2.08271
$83$	−9.57756	−1.05127	−0.525637	−	0.850709i	$-0.676173\pi$
$83$	−9.57756	−1.05127	−0.525637	+	0.850709i	$0.676173\pi$
$84$	−7.58199	−0.827262
$85$	2.90815	0.315433
$86$	−14.3775	−1.55036
$87$	−3.28889	−0.352606
$88$	−31.3180	−3.33851
$89$	−14.0550	−1.48982	−0.744912	−	0.667163i	$-0.767509\pi$
$89$	−14.0550	−1.48982	−0.744912	+	0.667163i	$0.767509\pi$
$90$	8.16589	0.860760
$91$	−0.171712	−0.0180003
$92$	−39.6746	−4.13636
$93$	8.99391	0.932625
$94$	−9.31907	−0.961189
$95$	10.6450	1.09215
$96$	−31.1377	−3.17798
$97$	−8.78638	−0.892122	−0.446061	−	0.895003i	$-0.647174\pi$
$97$	−8.78638	−0.892122	−0.446061	+	0.895003i	$0.647174\pi$
$98$	14.9939	1.51461
$99$	2.87128	0.288574
$100$	20.3447	2.03447
$101$	10.4587	1.04068	0.520340	−	0.853959i	$-0.325805\pi$
$101$	10.4587	1.04068	0.520340	+	0.853959i	$0.325805\pi$
$102$	2.80793	0.278027
$103$	7.12706	0.702250	0.351125	−	0.936329i	$-0.385799\pi$
$103$	7.12706	0.702250	0.351125	+	0.936329i	$0.385799\pi$
$104$	−1.45360	−0.142537
$105$	3.74707	0.365677
$106$	6.66035	0.646910
$107$	−1.75715	−0.169870	−0.0849351	−	0.996386i	$-0.527068\pi$
$107$	−1.75715	−0.169870	−0.0849351	+	0.996386i	$0.527068\pi$
$108$	5.88448	0.566234
$109$	9.86784	0.945168	0.472584	−	0.881286i	$-0.343321\pi$
$109$	9.86784	0.945168	0.472584	+	0.881286i	$0.343321\pi$
$110$	23.4465	2.23554
$111$	2.72071	0.258238
$112$	−24.2982	−2.29596
$113$	−5.14403	−0.483910	−0.241955	−	0.970287i	$-0.577789\pi$
$113$	−5.14403	−0.483910	−0.241955	+	0.970287i	$0.577789\pi$
$114$	10.2781	0.962636
$115$	19.6075	1.82841
$116$	−19.3534	−1.79692
$117$	0.133268	0.0123206
$118$	2.95331	0.271874
$119$	1.28847	0.118114
$120$	31.7202	2.89565
$121$	−2.75577	−0.250525
$122$	−3.18197	−0.288082
$123$	6.71660	0.605616
$124$	52.9245	4.75276
$125$	4.48629	0.401266
$126$	3.61794	0.322312
$127$	−13.5002	−1.19795	−0.598976	−	0.800767i	$-0.704425\pi$
$127$	−13.5002	−1.19795	−0.598976	+	0.800767i	$0.704425\pi$
$128$	−77.3243	−6.83457
$129$	5.12031	0.450818
$130$	1.08825	0.0954459
$131$	6.58930	0.575710	0.287855	−	0.957674i	$-0.407058\pi$
$131$	6.58930	0.575710	0.287855	+	0.957674i	$0.407058\pi$
$132$	16.8960	1.47061
$133$	4.71632	0.408956
$134$	14.7723	1.27614
$135$	−2.90815	−0.250294
$136$	10.9074	0.935298
$137$	−3.73503	−0.319105	−0.159553	−	0.987189i	$-0.551005\pi$
$137$	−3.73503	−0.319105	−0.159553	+	0.987189i	$0.551005\pi$
$138$	18.9318	1.61158
$139$	2.67454	0.226851	0.113426	−	0.993546i	$-0.463818\pi$
$139$	2.67454	0.226851	0.113426	+	0.993546i	$0.463818\pi$
$140$	22.0496	1.86353
$141$	3.31884	0.279497
$142$	−40.2030	−3.37376
$143$	0.382649	0.0319987
$144$	18.8582	1.57151
$145$	9.56457	0.794295
$146$	−35.2027	−2.91340
$147$	−5.33984	−0.440423
$148$	16.0100	1.31601
$149$	20.6313	1.69018	0.845090	−	0.534624i	$-0.179547\pi$
$149$	20.6313	1.69018	0.845090	+	0.534624i	$0.179547\pi$
$150$	−9.70797	−0.792653
$151$	4.11025	0.334488	0.167244	−	0.985916i	$-0.446513\pi$
$151$	4.11025	0.334488	0.167244	+	0.985916i	$0.446513\pi$
$152$	39.9252	3.23836
$153$	−1.00000	−0.0808452
$154$	10.3881	0.837097
$155$	−26.1556	−2.10087
$156$	0.784212	0.0627872
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	15.1509	1.20534
$159$	−2.37198	−0.188110
$160$	90.5531	7.15885
$161$	8.68719	0.684647
$162$	−2.80793	−0.220612
$163$	−5.21415	−0.408404	−0.204202	−	0.978929i	$-0.565460\pi$
$163$	−5.21415	−0.408404	−0.204202	+	0.978929i	$0.565460\pi$
$164$	39.5237	3.08628
$165$	−8.35010	−0.650055
$166$	26.8931	2.08731
$167$	−1.38489	−0.107166	−0.0535831	−	0.998563i	$-0.517064\pi$
$167$	−1.38489	−0.107166	−0.0535831	+	0.998563i	$0.517064\pi$
$168$	14.0538	1.08428
$169$	−12.9822	−0.998634
$170$	−8.16589	−0.626295
$171$	−3.66040	−0.279917
$172$	30.1304	2.29742
$173$	11.1036	0.844195	0.422097	−	0.906551i	$-0.361294\pi$
$173$	11.1036	0.844195	0.422097	+	0.906551i	$0.361294\pi$
$174$	9.23497	0.700101
$175$	−4.45468	−0.336742
$176$	54.1470	4.08148
$177$	−1.05177	−0.0790562
$178$	39.4654	2.95806
$179$	−7.57997	−0.566553	−0.283277	−	0.959038i	$-0.591421\pi$
$179$	−7.57997	−0.566553	−0.283277	+	0.959038i	$0.591421\pi$
$180$	−17.1130	−1.27552
$181$	−18.0235	−1.33968	−0.669840	−	0.742506i	$-0.733637\pi$
$181$	−18.0235	−1.33968	−0.669840	+	0.742506i	$0.733637\pi$
$182$	0.482155	0.0357397
$183$	1.13321	0.0837692
$184$	73.5401	5.42145
$185$	−7.91223	−0.581719
$186$	−25.2543	−1.85173
$187$	−2.87128	−0.209969
$188$	19.5296	1.42435
$189$	−1.28847	−0.0937225
$190$	−29.8904	−2.16848
$191$	−8.52767	−0.617041	−0.308520	−	0.951218i	$-0.599834\pi$
$191$	−8.52767	−0.617041	−0.308520	+	0.951218i	$0.599834\pi$
$192$	49.7162	3.58796
$193$	13.6048	0.979292	0.489646	−	0.871921i	$-0.337126\pi$
$193$	13.6048	0.979292	0.489646	+	0.871921i	$0.337126\pi$
$194$	24.6716	1.77131
$195$	−0.387563	−0.0277540
$196$	−31.4222	−2.24444
$197$	−2.40419	−0.171291	−0.0856456	−	0.996326i	$-0.527295\pi$
$197$	−2.40419	−0.171291	−0.0856456	+	0.996326i	$0.527295\pi$
$198$	−8.06235	−0.572966
$199$	−19.2211	−1.36255	−0.681275	−	0.732028i	$-0.738574\pi$
$199$	−19.2211	−1.36255	−0.681275	+	0.732028i	$0.738574\pi$
$200$	−37.7104	−2.66653
$201$	−5.26093	−0.371077
$202$	−29.3674	−2.06628
$203$	4.23764	0.297424
$204$	−5.88448	−0.411996
$205$	−19.5329	−1.36424
$206$	−20.0123	−1.39432
$207$	−6.74225	−0.468618
$208$	2.51319	0.174258
$209$	−10.5100	−0.726993
$210$	−10.5215	−0.726053
$211$	22.2081	1.52887	0.764435	−	0.644701i	$-0.223018\pi$
$211$	22.2081	1.52887	0.764435	+	0.644701i	$0.223018\pi$
$212$	−13.9579	−0.958629
$213$	14.3177	0.981030
$214$	4.93396	0.337279
$215$	−14.8906	−1.01553
$216$	−10.9074	−0.742152
$217$	−11.5884	−0.786672
$218$	−27.7082	−1.87664
$219$	12.5369	0.847164
$220$	−49.1360	−3.31275
$221$	−0.133268	−0.00896457
$222$	−7.63956	−0.512734
$223$	0.0941128	0.00630226	0.00315113	−	0.999995i	$-0.498997\pi$
$223$	0.0941128	0.00630226	0.00315113	+	0.999995i	$0.498997\pi$
$224$	40.1200	2.68063
$225$	3.45734	0.230489
$226$	14.4441	0.960807
$227$	−14.0971	−0.935661	−0.467830	−	0.883818i	$-0.654964\pi$
$227$	−14.0971	−0.935661	−0.467830	+	0.883818i	$0.654964\pi$
$228$	−21.5395	−1.42649
$229$	−5.50497	−0.363779	−0.181889	−	0.983319i	$-0.558221\pi$
$229$	−5.50497	−0.363779	−0.181889	+	0.983319i	$0.558221\pi$
$230$	−55.0564	−3.63031
$231$	−3.69956	−0.243413
$232$	35.8730	2.35518
$233$	16.5264	1.08268	0.541341	−	0.840803i	$-0.317917\pi$
$233$	16.5264	1.08268	0.541341	+	0.840803i	$0.317917\pi$
$234$	−0.374207	−0.0244627
$235$	−9.65168	−0.629606
$236$	−6.18914	−0.402879
$237$	−5.39575	−0.350491
$238$	−3.61794	−0.234516
$239$	−5.72835	−0.370536	−0.185268	−	0.982688i	$-0.559315\pi$
$239$	−5.72835	−0.370536	−0.185268	+	0.982688i	$0.559315\pi$
$240$	−54.8423	−3.54006
$241$	1.50515	0.0969555	0.0484777	−	0.998824i	$-0.484563\pi$
$241$	1.50515	0.0969555	0.0484777	+	0.998824i	$0.484563\pi$
$242$	7.73802	0.497418
$243$	1.00000	0.0641500
$244$	6.66834	0.426897
$245$	15.5291	0.992115
$246$	−18.8598	−1.20245
$247$	−0.487813	−0.0310388
$248$	−98.0998	−6.22934
$249$	−9.57756	−0.606953
$250$	−12.5972	−0.796716
$251$	−23.3651	−1.47479	−0.737395	−	0.675462i	$-0.763944\pi$
$251$	−23.3651	−1.47479	−0.737395	+	0.675462i	$0.763944\pi$
$252$	−7.58199	−0.477620
$253$	−19.3589	−1.21708
$254$	37.9077	2.37854
$255$	2.90815	0.182115
$256$	117.689	7.35556
$257$	1.70344	0.106257	0.0531287	−	0.998588i	$-0.483081\pi$
$257$	1.70344	0.106257	0.0531287	+	0.998588i	$0.483081\pi$
$258$	−14.3775	−0.895102
$259$	−3.50555	−0.217825
$260$	−2.28061	−0.141437
$261$	−3.28889	−0.203577
$262$	−18.5023	−1.14308
$263$	9.94962	0.613520	0.306760	−	0.951787i	$-0.400755\pi$
$263$	9.94962	0.613520	0.306760	+	0.951787i	$0.400755\pi$
$264$	−31.3180	−1.92749
$265$	6.89807	0.423745
$266$	−13.2431	−0.811986
$267$	−14.0550	−0.860150
$268$	−30.9578	−1.89105
$269$	−17.1490	−1.04559	−0.522797	−	0.852457i	$-0.675111\pi$
$269$	−17.1490	−1.04559	−0.522797	+	0.852457i	$0.675111\pi$
$270$	8.16589	0.496960
$271$	21.8207	1.32551	0.662757	−	0.748835i	$-0.269386\pi$
$271$	21.8207	1.32551	0.662757	+	0.748835i	$0.269386\pi$
$272$	−18.8582	−1.14344
$273$	−0.171712	−0.0103925
$274$	10.4877	0.633585
$275$	9.92698	0.598619
$276$	−39.6746	−2.38813
$277$	−3.05926	−0.183813	−0.0919065	−	0.995768i	$-0.529296\pi$
$277$	−3.05926	−0.183813	−0.0919065	+	0.995768i	$0.529296\pi$
$278$	−7.50992	−0.450415
$279$	8.99391	0.538451
$280$	−40.8706	−2.44249
$281$	9.29164	0.554293	0.277146	−	0.960828i	$-0.410611\pi$
$281$	9.29164	0.554293	0.277146	+	0.960828i	$0.410611\pi$
$282$	−9.31907	−0.554943
$283$	2.06289	0.122626	0.0613129	−	0.998119i	$-0.480471\pi$
$283$	2.06289	0.122626	0.0613129	+	0.998119i	$0.480471\pi$
$284$	84.2520	4.99944
$285$	10.6450	0.630554
$286$	−1.07445	−0.0635337
$287$	−8.65415	−0.510838
$288$	−31.1377	−1.83481
$289$	1.00000	0.0588235
$290$	−26.8567	−1.57708
$291$	−8.78638	−0.515067
$292$	73.7731	4.31724
$293$	−19.8767	−1.16121	−0.580603	−	0.814187i	$-0.697183\pi$
$293$	−19.8767	−1.16121	−0.580603	+	0.814187i	$0.697183\pi$
$294$	14.9939	0.874463
$295$	3.05872	0.178085
$296$	−29.6757	−1.72487
$297$	2.87128	0.166608
$298$	−57.9312	−3.35587
$299$	−0.898525	−0.0519630
$300$	20.3447	1.17460
$301$	−6.59737	−0.380266
$302$	−11.5413	−0.664128
$303$	10.4587	0.600837
$304$	−69.0283	−3.95904
$305$	−3.29554	−0.188702
$306$	2.80793	0.160519
$307$	23.8024	1.35848	0.679238	−	0.733918i	$-0.262311\pi$
$307$	23.8024	1.35848	0.679238	+	0.733918i	$0.262311\pi$
$308$	−21.7700	−1.24046
$309$	7.12706	0.405444
$310$	73.4433	4.17130
$311$	17.9061	1.01536	0.507680	−	0.861545i	$-0.330503\pi$
$311$	17.9061	1.01536	0.507680	+	0.861545i	$0.330503\pi$
$312$	−1.45360	−0.0822939
$313$	−1.01797	−0.0575393	−0.0287697	−	0.999586i	$-0.509159\pi$
$313$	−1.01797	−0.0575393	−0.0287697	+	0.999586i	$0.509159\pi$
$314$	−2.80793	−0.158461
$315$	3.74707	0.211123
$316$	−31.7512	−1.78614
$317$	12.3144	0.691645	0.345822	−	0.938300i	$-0.387600\pi$
$317$	12.3144	0.691645	0.345822	+	0.938300i	$0.387600\pi$
$318$	6.66035	0.373494
$319$	−9.44330	−0.528723
$320$	−144.582	−8.08239
$321$	−1.75715	−0.0980746
$322$	−24.3930	−1.35937
$323$	3.66040	0.203670
$324$	5.88448	0.326916
$325$	0.460752	0.0255579
$326$	14.6410	0.810889
$327$	9.86784	0.545693
$328$	−73.2604	−4.04513
$329$	−4.27623	−0.235756
$330$	23.4465	1.29069
$331$	−8.45256	−0.464595	−0.232297	−	0.972645i	$-0.574624\pi$
$331$	−8.45256	−0.464595	−0.232297	+	0.972645i	$0.574624\pi$
$332$	−56.3590	−3.09310
$333$	2.72071	0.149094
$334$	3.88868	0.212779
$335$	15.2996	0.835905
$336$	−24.2982	−1.32558
$337$	−11.6009	−0.631941	−0.315971	−	0.948769i	$-0.602330\pi$
$337$	−11.6009	−0.631941	−0.315971	+	0.948769i	$0.602330\pi$
$338$	36.4532	1.98280
$339$	−5.14403	−0.279385
$340$	17.1130	0.928080
$341$	25.8240	1.39845
$342$	10.2781	0.555778
$343$	15.8995	0.858494
$344$	−55.8490	−3.01118
$345$	19.6075	1.05563
$346$	−31.1783	−1.67616
$347$	−31.9027	−1.71262	−0.856312	−	0.516459i	$-0.827250\pi$
$347$	−31.9027	−1.71262	−0.856312	+	0.516459i	$0.827250\pi$
$348$	−19.3534	−1.03745
$349$	−26.8329	−1.43633	−0.718165	−	0.695872i	$-0.755018\pi$
$349$	−26.8329	−1.43633	−0.718165	+	0.695872i	$0.755018\pi$
$350$	12.5084	0.668605
$351$	0.133268	0.00711331
$352$	−89.4049	−4.76530
$353$	−8.87924	−0.472594	−0.236297	−	0.971681i	$-0.575934\pi$
$353$	−8.87924	−0.472594	−0.236297	+	0.971681i	$0.575934\pi$
$354$	2.95331	0.156967
$355$	−41.6379	−2.20991
$356$	−82.7062	−4.38342
$357$	1.28847	0.0681931
$358$	21.2840	1.12490
$359$	14.5187	0.766268	0.383134	−	0.923693i	$-0.374845\pi$
$359$	14.5187	0.766268	0.383134	+	0.923693i	$0.374845\pi$
$360$	31.7202	1.67180
$361$	−5.60150	−0.294816
$362$	50.6089	2.65994
$363$	−2.75577	−0.144640
$364$	−1.01043	−0.0529612
$365$	−36.4592	−1.90836
$366$	−3.18197	−0.166324
$367$	3.60734	0.188302	0.0941509	−	0.995558i	$-0.469986\pi$
$367$	3.60734	0.188302	0.0941509	+	0.995558i	$0.469986\pi$
$368$	−127.146	−6.62796
$369$	6.71660	0.349652
$370$	22.2170	1.15501
$371$	3.05622	0.158671
$372$	52.9245	2.74401
$373$	−8.52599	−0.441459	−0.220730	−	0.975335i	$-0.570844\pi$
$373$	−8.52599	−0.441459	−0.220730	+	0.975335i	$0.570844\pi$
$374$	8.06235	0.416894
$375$	4.48629	0.231671
$376$	−36.1997	−1.86686
$377$	−0.438303	−0.0225737
$378$	3.61794	0.186087
$379$	33.2349	1.70716	0.853580	−	0.520961i	$-0.174426\pi$
$379$	33.2349	1.70716	0.853580	+	0.520961i	$0.174426\pi$
$380$	62.6402	3.21337
$381$	−13.5002	−0.691637
$382$	23.9451	1.22514
$383$	−31.5693	−1.61312	−0.806558	−	0.591155i	$-0.798672\pi$
$383$	−31.5693	−1.61312	−0.806558	+	0.591155i	$0.798672\pi$
$384$	−77.3243	−3.94594
$385$	10.7589	0.548323
$386$	−38.2012	−1.94439
$387$	5.12031	0.260280
$388$	−51.7033	−2.62484
$389$	−17.2392	−0.874063	−0.437031	−	0.899446i	$-0.643970\pi$
$389$	−17.2392	−0.874063	−0.437031	+	0.899446i	$0.643970\pi$
$390$	1.08825	0.0551057
$391$	6.74225	0.340970
$392$	58.2436	2.94174
$393$	6.58930	0.332386
$394$	6.75079	0.340100
$395$	15.6916	0.789532
$396$	16.8960	0.849055
$397$	−16.4911	−0.827662	−0.413831	−	0.910354i	$-0.635810\pi$
$397$	−16.4911	−0.827662	−0.413831	+	0.910354i	$0.635810\pi$
$398$	53.9716	2.70535
$399$	4.71632	0.236111
$400$	65.1990	3.25995
$401$	6.24554	0.311888	0.155944	−	0.987766i	$-0.450158\pi$
$401$	6.24554	0.311888	0.155944	+	0.987766i	$0.450158\pi$
$402$	14.7723	0.736777
$403$	1.19860	0.0597065
$404$	61.5441	3.06193
$405$	−2.90815	−0.144507
$406$	−11.8990	−0.590537
$407$	7.81190	0.387222
$408$	10.9074	0.539995
$409$	−4.86304	−0.240462	−0.120231	−	0.992746i	$-0.538363\pi$
$409$	−4.86304	−0.240462	−0.120231	+	0.992746i	$0.538363\pi$
$410$	54.8470	2.70870
$411$	−3.73503	−0.184235
$412$	41.9390	2.06619
$413$	1.35518	0.0666841
$414$	18.9318	0.930446
$415$	27.8530	1.36725
$416$	−4.14965	−0.203453
$417$	2.67454	0.130973
$418$	29.5114	1.44345
$419$	−29.2476	−1.42884	−0.714421	−	0.699717i	$-0.753310\pi$
$419$	−29.2476	−1.42884	−0.714421	+	0.699717i	$0.753310\pi$
$420$	22.0496	1.07591
$421$	−20.5578	−1.00192	−0.500962	−	0.865469i	$-0.667021\pi$
$421$	−20.5578	−1.00192	−0.500962	+	0.865469i	$0.667021\pi$
$422$	−62.3588	−3.03558
$423$	3.31884	0.161367
$424$	25.8720	1.25646
$425$	−3.45734	−0.167706
$426$	−40.2030	−1.94784
$427$	−1.46011	−0.0706595
$428$	−10.3399	−0.499799
$429$	0.382649	0.0184745
$430$	41.8119	2.01635
$431$	35.8182	1.72530	0.862652	−	0.505798i	$-0.168802\pi$
$431$	35.8182	1.72530	0.862652	+	0.505798i	$0.168802\pi$
$432$	18.8582	0.907313
$433$	4.07089	0.195634	0.0978172	−	0.995204i	$-0.468814\pi$
$433$	4.07089	0.195634	0.0978172	+	0.995204i	$0.468814\pi$
$434$	32.5394	1.56194
$435$	9.56457	0.458586
$436$	58.0671	2.78091
$437$	24.6793	1.18057
$438$	−35.2027	−1.68205
$439$	14.1330	0.674531	0.337266	−	0.941409i	$-0.390498\pi$
$439$	14.1330	0.674531	0.337266	+	0.941409i	$0.390498\pi$
$440$	91.0776	4.34195
$441$	−5.33984	−0.254278
$442$	0.374207	0.0177992
$443$	−0.407127	−0.0193432	−0.00967160	−	0.999953i	$-0.503079\pi$
$443$	−0.407127	−0.0193432	−0.00967160	+	0.999953i	$0.503079\pi$
$444$	16.0100	0.759799
$445$	40.8740	1.93761
$446$	−0.264262	−0.0125132
$447$	20.6313	0.975826
$448$	−64.0579	−3.02645
$449$	−5.41251	−0.255432	−0.127716	−	0.991811i	$-0.540765\pi$
$449$	−5.41251	−0.255432	−0.127716	+	0.991811i	$0.540765\pi$
$450$	−9.70797	−0.457638
$451$	19.2852	0.908106
$452$	−30.2700	−1.42378
$453$	4.11025	0.193117
$454$	39.5838	1.85776
$455$	0.499364	0.0234105
$456$	39.9252	1.86967
$457$	−13.7435	−0.642893	−0.321446	−	0.946928i	$-0.604169\pi$
$457$	−13.7435	−0.642893	−0.321446	+	0.946928i	$0.604169\pi$
$458$	15.4576	0.722285
$459$	−1.00000	−0.0466760
$460$	115.380	5.37961
$461$	15.6747	0.730045	0.365023	−	0.930999i	$-0.381061\pi$
$461$	15.6747	0.730045	0.365023	+	0.930999i	$0.381061\pi$
$462$	10.3881	0.483298
$463$	−6.47091	−0.300729	−0.150364	−	0.988631i	$-0.548045\pi$
$463$	−6.47091	−0.300729	−0.150364	+	0.988631i	$0.548045\pi$
$464$	−62.0223	−2.87931
$465$	−26.1556	−1.21294
$466$	−46.4051	−2.14967
$467$	22.9284	1.06100	0.530499	−	0.847685i	$-0.322004\pi$
$467$	22.9284	1.06100	0.530499	+	0.847685i	$0.322004\pi$
$468$	0.784212	0.0362502
$469$	6.77856	0.313005
$470$	27.1013	1.25009
$471$	1.00000	0.0460776
$472$	11.4721	0.528045
$473$	14.7018	0.675990
$474$	15.1509	0.695903
$475$	−12.6552	−0.580662
$476$	7.58199	0.347520
$477$	−2.37198	−0.108605
$478$	16.0848	0.735702
$479$	−30.0813	−1.37445	−0.687224	−	0.726445i	$-0.741171\pi$
$479$	−30.0813	−1.37445	−0.687224	+	0.726445i	$0.741171\pi$
$480$	90.5531	4.13316
$481$	0.362583	0.0165324
$482$	−4.22637	−0.192506
$483$	8.68719	0.395281
$484$	−16.2163	−0.737104
$485$	25.5521	1.16026
$486$	−2.80793	−0.127370
$487$	−27.2449	−1.23459	−0.617293	−	0.786733i	$-0.711771\pi$
$487$	−27.2449	−1.23459	−0.617293	+	0.786733i	$0.711771\pi$
$488$	−12.3603	−0.559525
$489$	−5.21415	−0.235792
$490$	−43.6045	−1.96985
$491$	−10.8703	−0.490571	−0.245286	−	0.969451i	$-0.578882\pi$
$491$	−10.8703	−0.490571	−0.245286	+	0.969451i	$0.578882\pi$
$492$	39.5237	1.78187
$493$	3.28889	0.148124
$494$	1.36975	0.0616278
$495$	−8.35010	−0.375309
$496$	169.609	7.61565
$497$	−18.4479	−0.827502
$498$	26.8931	1.20511
$499$	41.3409	1.85067	0.925336	−	0.379149i	$-0.123783\pi$
$499$	41.3409	1.85067	0.925336	+	0.379149i	$0.123783\pi$
$500$	26.3995	1.18062
$501$	−1.38489	−0.0618724
$502$	65.6075	2.92821
$503$	−19.2099	−0.856529	−0.428264	−	0.903653i	$-0.640875\pi$
$503$	−19.2099	−0.856529	−0.428264	+	0.903653i	$0.640875\pi$
$504$	14.0538	0.626007
$505$	−30.4155	−1.35347
$506$	54.3583	2.41652
$507$	−12.9822	−0.576562
$508$	−79.4418	−3.52466
$509$	24.7924	1.09890	0.549451	−	0.835526i	$-0.314837\pi$
$509$	24.7924	1.09890	0.549451	+	0.835526i	$0.314837\pi$
$510$	−8.16589	−0.361592
$511$	−16.1534	−0.714585
$512$	−175.814	−7.76996
$513$	−3.66040	−0.161610
$514$	−4.78313	−0.210975
$515$	−20.7266	−0.913321
$516$	30.1304	1.32641
$517$	9.52930	0.419098
$518$	9.84336	0.432492
$519$	11.1036	0.487396
$520$	4.22729	0.185379
$521$	−29.1578	−1.27743	−0.638713	−	0.769445i	$-0.720533\pi$
$521$	−29.1578	−1.27743	−0.638713	+	0.769445i	$0.720533\pi$
$522$	9.23497	0.404203
$523$	−8.95983	−0.391786	−0.195893	−	0.980625i	$-0.562761\pi$
$523$	−8.95983	−0.391786	−0.195893	+	0.980625i	$0.562761\pi$
$524$	38.7746	1.69388
$525$	−4.45468	−0.194418
$526$	−27.9379	−1.21815
$527$	−8.99391	−0.391781
$528$	54.1470	2.35644
$529$	22.4579	0.976430
$530$	−19.3693	−0.841348
$531$	−1.05177	−0.0456431
$532$	27.7531	1.20325
$533$	0.895107	0.0387714
$534$	39.4654	1.70783
$535$	5.11006	0.220927
$536$	57.3828	2.47856
$537$	−7.57997	−0.327100
$538$	48.1532	2.07603
$539$	−15.3322	−0.660403
$540$	−17.1130	−0.736424
$541$	−36.5427	−1.57109	−0.785546	−	0.618804i	$-0.787618\pi$
$541$	−36.5427	−1.57109	−0.785546	+	0.618804i	$0.787618\pi$
$542$	−61.2711	−2.63182
$543$	−18.0235	−0.773464
$544$	31.1377	1.33502
$545$	−28.6972	−1.22925
$546$	0.482155	0.0206343
$547$	−27.0369	−1.15601	−0.578006	−	0.816032i	$-0.696169\pi$
$547$	−27.0369	−1.15601	−0.578006	+	0.816032i	$0.696169\pi$
$548$	−21.9787	−0.938884
$549$	1.13321	0.0483642
$550$	−27.8743	−1.18856
$551$	12.0386	0.512863
$552$	73.5401	3.13007
$553$	6.95226	0.295640
$554$	8.59019	0.364962
$555$	−7.91223	−0.335855
$556$	15.7383	0.667451
$557$	32.1479	1.36215	0.681076	−	0.732213i	$-0.261512\pi$
$557$	32.1479	1.36215	0.681076	+	0.732213i	$0.261512\pi$
$558$	−25.2543	−1.06910
$559$	0.682372	0.0288613
$560$	70.6628	2.98605
$561$	−2.87128	−0.121225
$562$	−26.0903	−1.10055
$563$	−30.9982	−1.30642	−0.653209	−	0.757177i	$-0.726578\pi$
$563$	−30.9982	−1.30642	−0.653209	+	0.757177i	$0.726578\pi$
$564$	19.5296	0.822346
$565$	14.9596	0.629356
$566$	−5.79244	−0.243475
$567$	−1.28847	−0.0541107
$568$	−156.168	−6.55266
$569$	44.3789	1.86046	0.930229	−	0.366978i	$-0.119608\pi$
$569$	44.3789	1.86046	0.930229	+	0.366978i	$0.119608\pi$
$570$	−29.8904	−1.25197
$571$	−38.8995	−1.62789	−0.813947	−	0.580939i	$-0.802685\pi$
$571$	−38.8995	−1.62789	−0.813947	+	0.580939i	$0.802685\pi$
$572$	2.25169	0.0941479
$573$	−8.52767	−0.356249
$574$	24.3003	1.01427
$575$	−23.3102	−0.972104
$576$	49.7162	2.07151
$577$	17.9961	0.749186	0.374593	−	0.927189i	$-0.377782\pi$
$577$	17.9961	0.749186	0.374593	+	0.927189i	$0.377782\pi$
$578$	−2.80793	−0.116795
$579$	13.6048	0.565395
$580$	56.2826	2.33701
$581$	12.3404	0.511967
$582$	24.6716	1.02267
$583$	−6.81060	−0.282066
$584$	−136.744	−5.65852
$585$	−0.387563	−0.0160238
$586$	55.8123	2.30559
$587$	29.2595	1.20767	0.603835	−	0.797109i	$-0.293639\pi$
$587$	29.2595	1.20767	0.603835	+	0.797109i	$0.293639\pi$
$588$	−31.4222	−1.29583
$589$	−32.9213	−1.35650
$590$	−8.58867	−0.353590
$591$	−2.40419	−0.0988950
$592$	51.3075	2.10873
$593$	26.7778	1.09963	0.549817	−	0.835285i	$-0.314698\pi$
$593$	26.7778	1.09963	0.549817	+	0.835285i	$0.314698\pi$
$594$	−8.06235	−0.330802
$595$	−3.74707	−0.153615
$596$	121.404	4.97292
$597$	−19.2211	−0.786668
$598$	2.52300	0.103173
$599$	−5.39440	−0.220409	−0.110205	−	0.993909i	$-0.535151\pi$
$599$	−5.39440	−0.220409	−0.110205	+	0.993909i	$0.535151\pi$
$600$	−37.7104	−1.53952
$601$	1.00618	0.0410430	0.0205215	−	0.999789i	$-0.493467\pi$
$601$	1.00618	0.0410430	0.0205215	+	0.999789i	$0.493467\pi$
$602$	18.5250	0.755021
$603$	−5.26093	−0.214242
$604$	24.1867	0.984143
$605$	8.01420	0.325823
$606$	−29.3674	−1.19297
$607$	−24.7351	−1.00397	−0.501984	−	0.864877i	$-0.667396\pi$
$607$	−24.7351	−1.00397	−0.501984	+	0.864877i	$0.667396\pi$
$608$	113.976	4.62235
$609$	4.23764	0.171718
$610$	9.25365	0.374669
$611$	0.442294	0.0178933
$612$	−5.88448	−0.237866
$613$	0.521629	0.0210684	0.0105342	−	0.999945i	$-0.496647\pi$
$613$	0.521629	0.0210684	0.0105342	+	0.999945i	$0.496647\pi$
$614$	−66.8356	−2.69726
$615$	−19.5329	−0.787642
$616$	40.3524	1.62584
$617$	−39.4737	−1.58915	−0.794575	−	0.607165i	$-0.792306\pi$
$617$	−39.4737	−1.58915	−0.794575	+	0.607165i	$0.792306\pi$
$618$	−20.0123	−0.805012
$619$	8.44707	0.339516	0.169758	−	0.985486i	$-0.445701\pi$
$619$	8.44707	0.339516	0.169758	+	0.985486i	$0.445701\pi$
$620$	−153.912	−6.18127
$621$	−6.74225	−0.270557
$622$	−50.2791	−2.01601
$623$	18.1094	0.725539
$624$	2.51319	0.100608
$625$	−30.3335	−1.21334
$626$	2.85840	0.114245
$627$	−10.5100	−0.419729
$628$	5.88448	0.234816
$629$	−2.72071	−0.108482
$630$	−10.5215	−0.419187
$631$	−30.4099	−1.21060	−0.605300	−	0.795998i	$-0.706947\pi$
$631$	−30.4099	−1.21060	−0.605300	+	0.795998i	$0.706947\pi$
$632$	58.8533	2.34106
$633$	22.2081	0.882693
$634$	−34.5779	−1.37327
$635$	39.2607	1.55801
$636$	−13.9579	−0.553465
$637$	−0.711629	−0.0281958
$638$	26.5161	1.04978
$639$	14.3177	0.566398
$640$	224.871	8.88880
$641$	−49.1630	−1.94182	−0.970912	−	0.239437i	$-0.923037\pi$
$641$	−49.1630	−1.94182	−0.970912	+	0.239437i	$0.923037\pi$
$642$	4.93396	0.194728
$643$	−12.5553	−0.495131	−0.247566	−	0.968871i	$-0.579631\pi$
$643$	−12.5553	−0.495131	−0.247566	+	0.968871i	$0.579631\pi$
$644$	51.1196	2.01439
$645$	−14.8906	−0.586318
$646$	−10.2781	−0.404388
$647$	−41.7319	−1.64065	−0.820325	−	0.571897i	$-0.806208\pi$
$647$	−41.7319	−1.64065	−0.820325	+	0.571897i	$0.806208\pi$
$648$	−10.9074	−0.428481
$649$	−3.01993	−0.118543
$650$	−1.29376	−0.0507455
$651$	−11.5884	−0.454185
$652$	−30.6826	−1.20162
$653$	−0.473896	−0.0185450	−0.00927249	−	0.999957i	$-0.502952\pi$
$653$	−0.473896	−0.0185450	−0.00927249	+	0.999957i	$0.502952\pi$
$654$	−27.7082	−1.08348
$655$	−19.1627	−0.748748
$656$	126.663	4.94535
$657$	12.5369	0.489111
$658$	12.0074	0.468095
$659$	43.7787	1.70538	0.852688	−	0.522420i	$-0.174971\pi$
$659$	43.7787	1.70538	0.852688	+	0.522420i	$0.174971\pi$
$660$	−49.1360	−1.91262
$661$	−33.8576	−1.31691	−0.658455	−	0.752620i	$-0.728790\pi$
$661$	−33.8576	−1.31691	−0.658455	+	0.752620i	$0.728790\pi$
$662$	23.7342	0.922456
$663$	−0.133268	−0.00517569
$664$	104.466	4.05406
$665$	−13.7158	−0.531874
$666$	−7.63956	−0.296027
$667$	22.1745	0.858599
$668$	−8.14937	−0.315309
$669$	0.0941128	0.00363861
$670$	−42.9602	−1.65970
$671$	3.25375	0.125610
$672$	40.1200	1.54766
$673$	−4.74172	−0.182780	−0.0913899	−	0.995815i	$-0.529131\pi$
$673$	−4.74172	−0.182780	−0.0913899	+	0.995815i	$0.529131\pi$
$674$	32.5745	1.25472
$675$	3.45734	0.133073
$676$	−76.3937	−2.93822
$677$	−21.6484	−0.832014	−0.416007	−	0.909361i	$-0.636571\pi$
$677$	−21.6484	−0.832014	−0.416007	+	0.909361i	$0.636571\pi$
$678$	14.4441	0.554722
$679$	11.3210	0.434460
$680$	−31.7202	−1.21642
$681$	−14.0971	−0.540204
$682$	−72.5120	−2.77663
$683$	1.35646	0.0519035	0.0259517	−	0.999663i	$-0.491738\pi$
$683$	1.35646	0.0519035	0.0259517	+	0.999663i	$0.491738\pi$
$684$	−21.5395	−0.823584
$685$	10.8620	0.415017
$686$	−44.6448	−1.70455
$687$	−5.50497	−0.210028
$688$	96.5595	3.68130
$689$	−0.316108	−0.0120428
$690$	−55.0564	−2.09596
$691$	−28.9862	−1.10269	−0.551343	−	0.834278i	$-0.685885\pi$
$691$	−28.9862	−1.10269	−0.551343	+	0.834278i	$0.685885\pi$
$692$	65.3392	2.48382
$693$	−3.69956	−0.140535
$694$	89.5805	3.40043
$695$	−7.77796	−0.295035
$696$	35.8730	1.35976
$697$	−6.71660	−0.254409
$698$	75.3449	2.85185
$699$	16.5264	0.625087
$700$	−26.2135	−0.990777
$701$	51.6003	1.94891	0.974457	−	0.224572i	$-0.0720984\pi$
$701$	51.6003	1.94891	0.974457	+	0.224572i	$0.0720984\pi$
$702$	−0.374207	−0.0141235
$703$	−9.95887	−0.375606
$704$	142.749	5.38005
$705$	−9.65168	−0.363503
$706$	24.9323	0.938339
$707$	−13.4758	−0.506808
$708$	−6.18914	−0.232602
$709$	−2.83202	−0.106359	−0.0531793	−	0.998585i	$-0.516935\pi$
$709$	−2.83202	−0.106359	−0.0531793	+	0.998585i	$0.516935\pi$
$710$	116.916	4.38780
$711$	−5.39575	−0.202356
$712$	153.303	5.74526
$713$	−60.6392	−2.27095
$714$	−3.61794	−0.135398
$715$	−1.11280	−0.0416164
$716$	−44.6042	−1.66694
$717$	−5.72835	−0.213929
$718$	−40.7675	−1.52143
$719$	−33.9380	−1.26568	−0.632838	−	0.774284i	$-0.718110\pi$
$719$	−33.9380	−1.26568	−0.632838	+	0.774284i	$0.718110\pi$
$720$	−54.8423	−2.04385
$721$	−9.18301	−0.341993
$722$	15.7286	0.585359
$723$	1.50515	0.0559773
$724$	−106.059	−3.94166
$725$	−11.3708	−0.422301
$726$	7.73802	0.287185
$727$	28.5940	1.06049	0.530247	−	0.847843i	$-0.322099\pi$
$727$	28.5940	1.06049	0.530247	+	0.847843i	$0.322099\pi$
$728$	1.87292	0.0694151
$729$	1.00000	0.0370370
$730$	102.375	3.78906
$731$	−5.12031	−0.189381
$732$	6.66834	0.246469
$733$	−26.2415	−0.969251	−0.484625	−	0.874722i	$-0.661044\pi$
$733$	−26.2415	−0.969251	−0.484625	+	0.874722i	$0.661044\pi$
$734$	−10.1292	−0.373875
$735$	15.5291	0.572798
$736$	209.938	7.73842
$737$	−15.1056	−0.556421
$738$	−18.8598	−0.694237
$739$	−40.4398	−1.48760	−0.743801	−	0.668401i	$-0.766979\pi$
$739$	−40.4398	−1.48760	−0.743801	+	0.668401i	$0.766979\pi$
$740$	−46.5594	−1.71156
$741$	−0.487813	−0.0179203
$742$	−8.58167	−0.315043
$743$	−2.74985	−0.100882	−0.0504412	−	0.998727i	$-0.516063\pi$
$743$	−2.74985	−0.100882	−0.0504412	+	0.998727i	$0.516063\pi$
$744$	−98.0998	−3.59651
$745$	−59.9989	−2.19819
$746$	23.9404	0.876520
$747$	−9.57756	−0.350425
$748$	−16.8960	−0.617778
$749$	2.26404	0.0827262
$750$	−12.5972	−0.459984
$751$	−15.4487	−0.563730	−0.281865	−	0.959454i	$-0.590953\pi$
$751$	−15.4487	−0.563730	−0.281865	+	0.959454i	$0.590953\pi$
$752$	62.5871	2.28232
$753$	−23.3651	−0.851470
$754$	1.23072	0.0448203
$755$	−11.9532	−0.435023
$756$	−7.58199	−0.275754
$757$	−26.1707	−0.951190	−0.475595	−	0.879664i	$-0.657767\pi$
$757$	−26.1707	−0.951190	−0.475595	+	0.879664i	$0.657767\pi$
$758$	−93.3213	−3.38958
$759$	−19.3589	−0.702682
$760$	−116.109	−4.21170
$761$	33.1131	1.20035	0.600175	−	0.799869i	$-0.295098\pi$
$761$	33.1131	1.20035	0.600175	+	0.799869i	$0.295098\pi$
$762$	37.9077	1.37325
$763$	−12.7144	−0.460293
$764$	−50.1809	−1.81548
$765$	2.90815	0.105144
$766$	88.6445	3.20285
$767$	−0.140168	−0.00506116
$768$	117.689	4.24674
$769$	−29.4567	−1.06224	−0.531118	−	0.847298i	$-0.678228\pi$
$769$	−29.4567	−1.06224	−0.531118	+	0.847298i	$0.678228\pi$
$770$	−30.2102	−1.08870
$771$	1.70344	0.0613478
$772$	80.0570	2.88131
$773$	44.1402	1.58761	0.793806	−	0.608171i	$-0.208097\pi$
$773$	44.1402	1.58761	0.793806	+	0.608171i	$0.208097\pi$
$774$	−14.3775	−0.516788
$775$	31.0950	1.11697
$776$	95.8362	3.44032
$777$	−3.50555	−0.125761
$778$	48.4065	1.73546
$779$	−24.5854	−0.880864
$780$	−2.28061	−0.0816588
$781$	41.1100	1.47103
$782$	−18.9318	−0.676999
$783$	−3.28889	−0.117535
$784$	−100.700	−3.59641
$785$	−2.90815	−0.103796
$786$	−18.5023	−0.659956
$787$	−39.6166	−1.41218	−0.706090	−	0.708123i	$-0.749542\pi$
$787$	−39.6166	−1.41218	−0.706090	+	0.708123i	$0.749542\pi$
$788$	−14.1474	−0.503980
$789$	9.94962	0.354216
$790$	−44.0611	−1.56762
$791$	6.62794	0.235662
$792$	−31.3180	−1.11284
$793$	0.151020	0.00536289
$794$	46.3058	1.64333
$795$	6.89807	0.244649
$796$	−113.106	−4.00895
$797$	22.3187	0.790570	0.395285	−	0.918559i	$-0.370646\pi$
$797$	22.3187	0.790570	0.395285	+	0.918559i	$0.370646\pi$
$798$	−13.2431	−0.468800
$799$	−3.31884	−0.117412
$800$	−107.654	−3.80613
$801$	−14.0550	−0.496608
$802$	−17.5371	−0.619255
$803$	35.9969	1.27030
$804$	−30.9578	−1.09180
$805$	−25.2637	−0.890427
$806$	−3.36558	−0.118548
$807$	−17.1490	−0.603674
$808$	−114.077	−4.01321
$809$	−16.5912	−0.583315	−0.291658	−	0.956523i	$-0.594207\pi$
$809$	−16.5912	−0.583315	−0.291658	+	0.956523i	$0.594207\pi$
$810$	8.16589	0.286920
$811$	−49.7074	−1.74546	−0.872731	−	0.488201i	$-0.837653\pi$
$811$	−49.7074	−1.74546	−0.872731	+	0.488201i	$0.837653\pi$
$812$	24.9363	0.875092
$813$	21.8207	0.765286
$814$	−21.9353	−0.768832
$815$	15.1635	0.531156
$816$	−18.8582	−0.660167
$817$	−18.7424	−0.655712
$818$	13.6551	0.477439
$819$	−0.171712	−0.00600010
$820$	−114.941	−4.01391
$821$	15.1023	0.527072	0.263536	−	0.964650i	$-0.415111\pi$
$821$	15.1023	0.527072	0.263536	+	0.964650i	$0.415111\pi$
$822$	10.4877	0.365801
$823$	−1.21422	−0.0423250	−0.0211625	−	0.999776i	$-0.506737\pi$
$823$	−1.21422	−0.0423250	−0.0211625	+	0.999776i	$0.506737\pi$
$824$	−77.7374	−2.70811
$825$	9.92698	0.345613
$826$	−3.80526	−0.132402
$827$	−0.423889	−0.0147401	−0.00737004	−	0.999973i	$-0.502346\pi$
$827$	−0.423889	−0.0147401	−0.00737004	+	0.999973i	$0.502346\pi$
$828$	−39.6746	−1.37879
$829$	5.23791	0.181920	0.0909601	−	0.995855i	$-0.471006\pi$
$829$	5.23791	0.181920	0.0909601	+	0.995855i	$0.471006\pi$
$830$	−78.2093	−2.71468
$831$	−3.05926	−0.106125
$832$	6.62557	0.229700
$833$	5.33984	0.185015
$834$	−7.50992	−0.260047
$835$	4.02747	0.139376
$836$	−61.8459	−2.13899
$837$	8.99391	0.310875
$838$	82.1254	2.83697
$839$	28.1603	0.972201	0.486100	−	0.873903i	$-0.338419\pi$
$839$	28.1603	0.972201	0.486100	+	0.873903i	$0.338419\pi$
$840$	−40.8706	−1.41017
$841$	−18.1832	−0.627008
$842$	57.7248	1.98933
$843$	9.29164	0.320021
$844$	130.683	4.49830
$845$	37.7543	1.29879
$846$	−9.31907	−0.320396
$847$	3.55073	0.122005
$848$	−44.7311	−1.53607
$849$	2.06289	0.0707981
$850$	9.70797	0.332981
$851$	−18.3437	−0.628813
$852$	84.2520	2.88643
$853$	27.7941	0.951652	0.475826	−	0.879540i	$-0.342149\pi$
$853$	27.7941	0.951652	0.475826	+	0.879540i	$0.342149\pi$
$854$	4.09988	0.140295
$855$	10.6450	0.364051
$856$	19.1659	0.655076
$857$	−7.29383	−0.249153	−0.124576	−	0.992210i	$-0.539757\pi$
$857$	−7.29383	−0.249153	−0.124576	+	0.992210i	$0.539757\pi$
$858$	−1.07445	−0.0366812
$859$	−46.1510	−1.57465	−0.787326	−	0.616537i	$-0.788535\pi$
$859$	−46.1510	−1.57465	−0.787326	+	0.616537i	$0.788535\pi$
$860$	−87.6236	−2.98794
$861$	−8.65415	−0.294933
$862$	−100.575	−3.42560
$863$	−14.3470	−0.488378	−0.244189	−	0.969728i	$-0.578522\pi$
$863$	−14.3470	−0.488378	−0.244189	+	0.969728i	$0.578522\pi$
$864$	−31.1377	−1.05933
$865$	−32.2911	−1.09793
$866$	−11.4308	−0.388434
$867$	1.00000	0.0339618
$868$	−68.1917	−2.31458
$869$	−15.4927	−0.525553
$870$	−26.8567	−0.910526
$871$	−0.701113	−0.0237563
$872$	−107.632	−3.64488
$873$	−8.78638	−0.297374
$874$	−69.2978	−2.34403
$875$	−5.78045	−0.195415
$876$	73.7731	2.49256
$877$	49.4979	1.67143	0.835713	−	0.549166i	$-0.185054\pi$
$877$	49.4979	1.67143	0.835713	+	0.549166i	$0.185054\pi$
$878$	−39.6845	−1.33929
$879$	−19.8767	−0.670423
$880$	−157.468	−5.30823
$881$	29.5729	0.996335	0.498168	−	0.867081i	$-0.334006\pi$
$881$	29.5729	0.996335	0.498168	+	0.867081i	$0.334006\pi$
$882$	14.9939	0.504871
$883$	−6.27119	−0.211042	−0.105521	−	0.994417i	$-0.533651\pi$
$883$	−6.27119	−0.211042	−0.105521	+	0.994417i	$0.533651\pi$
$884$	−0.784212	−0.0263759
$885$	3.05872	0.102818
$886$	1.14319	0.0384061
$887$	9.12356	0.306339	0.153170	−	0.988200i	$-0.451052\pi$
$887$	9.12356	0.306339	0.153170	+	0.988200i	$0.451052\pi$
$888$	−29.6757	−0.995852
$889$	17.3947	0.583398
$890$	−114.771	−3.84714
$891$	2.87128	0.0961914
$892$	0.553805	0.0185428
$893$	−12.1483	−0.406526
$894$	−57.9312	−1.93751
$895$	22.0437	0.736839
$896$	99.6302	3.32841
$897$	−0.898525	−0.0300009
$898$	15.1980	0.507162
$899$	−29.5799	−0.986546
$900$	20.3447	0.678155
$901$	2.37198	0.0790220
$902$	−54.1516	−1.80305
$903$	−6.59737	−0.219547
$904$	56.1078	1.86612
$905$	52.4152	1.74234
$906$	−11.5413	−0.383434
$907$	13.6771	0.454141	0.227071	−	0.973878i	$-0.427085\pi$
$907$	13.6771	0.454141	0.227071	+	0.973878i	$0.427085\pi$
$908$	−82.9544	−2.75294
$909$	10.4587	0.346894
$910$	−1.40218	−0.0464818
$911$	41.0779	1.36097	0.680486	−	0.732761i	$-0.261769\pi$
$911$	41.0779	1.36097	0.680486	+	0.732761i	$0.261769\pi$
$912$	−69.0283	−2.28576
$913$	−27.4998	−0.910111
$914$	38.5907	1.27647
$915$	−3.29554	−0.108947
$916$	−32.3939	−1.07032
$917$	−8.49013	−0.280369
$918$	2.80793	0.0926756
$919$	−54.4953	−1.79763	−0.898816	−	0.438325i	$-0.855572\pi$
$919$	−54.4953	−1.79763	−0.898816	+	0.438325i	$0.855572\pi$
$920$	−213.866	−7.05094
$921$	23.8024	0.784316
$922$	−44.0136	−1.44951
$923$	1.90808	0.0628054
$924$	−21.7700	−0.716180
$925$	9.40641	0.309281
$926$	18.1699	0.597099
$927$	7.12706	0.234083
$928$	102.408	3.36172
$929$	10.8939	0.357418	0.178709	−	0.983902i	$-0.442808\pi$
$929$	10.8939	0.357418	0.178709	+	0.983902i	$0.442808\pi$
$930$	73.4433	2.40830
$931$	19.5459	0.640592
$932$	97.2494	3.18551
$933$	17.9061	0.586219
$934$	−64.3813	−2.10662
$935$	8.35010	0.273078
$936$	−1.45360	−0.0475124
$937$	−35.1768	−1.14917	−0.574587	−	0.818443i	$-0.694837\pi$
$937$	−35.1768	−1.14917	−0.574587	+	0.818443i	$0.694837\pi$
$938$	−19.0337	−0.621473
$939$	−1.01797	−0.0332203
$940$	−56.7951	−1.85245
$941$	−5.99388	−0.195395	−0.0976974	−	0.995216i	$-0.531148\pi$
$941$	−5.99388	−0.195395	−0.0976974	+	0.995216i	$0.531148\pi$
$942$	−2.80793	−0.0914874
$943$	−45.2850	−1.47468
$944$	−19.8345	−0.645559
$945$	3.74707	0.121892
$946$	−41.2817	−1.34218
$947$	−23.6295	−0.767856	−0.383928	−	0.923363i	$-0.625429\pi$
$947$	−23.6295	−0.767856	−0.383928	+	0.923363i	$0.625429\pi$
$948$	−31.7512	−1.03123
$949$	1.67076	0.0542353
$950$	35.5350	1.15291
$951$	12.3144	0.399321
$952$	−14.0538	−0.455487
$953$	−45.1915	−1.46390	−0.731949	−	0.681360i	$-0.761389\pi$
$953$	−45.1915	−1.46390	−0.731949	+	0.681360i	$0.761389\pi$
$954$	6.66035	0.215637
$955$	24.7998	0.802501
$956$	−33.7083	−1.09021
$957$	−9.44330	−0.305259
$958$	84.4662	2.72898
$959$	4.81248	0.155403
$960$	−144.582	−4.66637
$961$	49.8904	1.60937
$962$	−1.01811	−0.0328251
$963$	−1.75715	−0.0566234
$964$	8.85705	0.285266
$965$	−39.5647	−1.27363
$966$	−24.3930	−0.784833
$967$	−44.5026	−1.43111	−0.715554	−	0.698558i	$-0.753826\pi$
$967$	−44.5026	−1.43111	−0.715554	+	0.698558i	$0.753826\pi$
$968$	30.0582	0.966106
$969$	3.66040	0.117589
$970$	−71.7486	−2.30371
$971$	42.2630	1.35629	0.678143	−	0.734930i	$-0.262785\pi$
$971$	42.2630	1.35629	0.678143	+	0.734930i	$0.262785\pi$
$972$	5.88448	0.188745
$973$	−3.44607	−0.110476
$974$	76.5019	2.45128
$975$	0.460752	0.0147559
$976$	21.3702	0.684044
$977$	30.4814	0.975187	0.487593	−	0.873071i	$-0.337875\pi$
$977$	30.4814	0.975187	0.487593	+	0.873071i	$0.337875\pi$
$978$	14.6410	0.468167
$979$	−40.3557	−1.28977
$980$	91.3805	2.91904
$981$	9.86784	0.315056
$982$	30.5231	0.974033
$983$	−42.9806	−1.37087	−0.685434	−	0.728134i	$-0.740388\pi$
$983$	−42.9806	−1.37087	−0.685434	+	0.728134i	$0.740388\pi$
$984$	−73.2604	−2.33546
$985$	6.99174	0.222775
$986$	−9.23497	−0.294101
$987$	−4.27623	−0.136114
$988$	−2.87053	−0.0913236
$989$	−34.5224	−1.09775
$990$	23.4465	0.745179
$991$	3.13287	0.0995189	0.0497594	−	0.998761i	$-0.484155\pi$
$991$	3.13287	0.0995189	0.0497594	+	0.998761i	$0.484155\pi$
$992$	−280.050	−8.89158
$993$	−8.45256	−0.268234
$994$	51.8005	1.64301
$995$	55.8979	1.77208
$996$	−56.3590	−1.78580
$997$	45.9326	1.45470	0.727349	−	0.686267i	$-0.240752\pi$
$997$	45.9326	1.45470	0.727349	+	0.686267i	$0.240752\pi$
$998$	−116.082	−3.67452
$999$	2.72071	0.0860794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.1	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.1	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80793 q^{2} +1.00000 q^{3} +5.88448 q^{4} -2.90815 q^{5} -2.80793 q^{6} -1.28847 q^{7} -10.9074 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.80793 q^{2} +1.00000 q^{3} +5.88448 q^{4} -2.90815 q^{5} -2.80793 q^{6} -1.28847 q^{7} -10.9074 q^{8} +1.00000 q^{9} +8.16589 q^{10} +2.87128 q^{11} +5.88448 q^{12} +0.133268 q^{13} +3.61794 q^{14} -2.90815 q^{15} +18.8582 q^{16} -1.00000 q^{17} -2.80793 q^{18} -3.66040 q^{19} -17.1130 q^{20} -1.28847 q^{21} -8.06235 q^{22} -6.74225 q^{23} -10.9074 q^{24} +3.45734 q^{25} -0.374207 q^{26} +1.00000 q^{27} -7.58199 q^{28} -3.28889 q^{29} +8.16589 q^{30} +8.99391 q^{31} -31.1377 q^{32} +2.87128 q^{33} +2.80793 q^{34} +3.74707 q^{35} +5.88448 q^{36} +2.72071 q^{37} +10.2781 q^{38} +0.133268 q^{39} +31.7202 q^{40} +6.71660 q^{41} +3.61794 q^{42} +5.12031 q^{43} +16.8960 q^{44} -2.90815 q^{45} +18.9318 q^{46} +3.31884 q^{47} +18.8582 q^{48} -5.33984 q^{49} -9.70797 q^{50} -1.00000 q^{51} +0.784212 q^{52} -2.37198 q^{53} -2.80793 q^{54} -8.35010 q^{55} +14.0538 q^{56} -3.66040 q^{57} +9.23497 q^{58} -1.05177 q^{59} -17.1130 q^{60} +1.13321 q^{61} -25.2543 q^{62} -1.28847 q^{63} +49.7162 q^{64} -0.387563 q^{65} -8.06235 q^{66} -5.26093 q^{67} -5.88448 q^{68} -6.74225 q^{69} -10.5215 q^{70} +14.3177 q^{71} -10.9074 q^{72} +12.5369 q^{73} -7.63956 q^{74} +3.45734 q^{75} -21.5395 q^{76} -3.69956 q^{77} -0.374207 q^{78} -5.39575 q^{79} -54.8423 q^{80} +1.00000 q^{81} -18.8598 q^{82} -9.57756 q^{83} -7.58199 q^{84} +2.90815 q^{85} -14.3775 q^{86} -3.28889 q^{87} -31.3180 q^{88} -14.0550 q^{89} +8.16589 q^{90} -0.171712 q^{91} -39.6746 q^{92} +8.99391 q^{93} -9.31907 q^{94} +10.6450 q^{95} -31.1377 q^{96} -8.78638 q^{97} +14.9939 q^{98} +2.87128 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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