LMFDB - Embedded newform 8007.2.a.i.1.11

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:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.02903 q^{2} +1.00000 q^{3} +2.11694 q^{4} +4.33739 q^{5} -2.02903 q^{6} -3.04221 q^{7} -0.237280 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.02903 q^{2} +1.00000 q^{3} +2.11694 q^{4} +4.33739 q^{5} -2.02903 q^{6} -3.04221 q^{7} -0.237280 q^{8} +1.00000 q^{9} -8.80067 q^{10} -2.48095 q^{11} +2.11694 q^{12} -2.83592 q^{13} +6.17272 q^{14} +4.33739 q^{15} -3.75244 q^{16} +1.00000 q^{17} -2.02903 q^{18} -1.71391 q^{19} +9.18200 q^{20} -3.04221 q^{21} +5.03392 q^{22} -2.49567 q^{23} -0.237280 q^{24} +13.8129 q^{25} +5.75416 q^{26} +1.00000 q^{27} -6.44018 q^{28} -2.97228 q^{29} -8.80067 q^{30} -0.206606 q^{31} +8.08835 q^{32} -2.48095 q^{33} -2.02903 q^{34} -13.1952 q^{35} +2.11694 q^{36} +10.5877 q^{37} +3.47757 q^{38} -2.83592 q^{39} -1.02918 q^{40} +4.56632 q^{41} +6.17272 q^{42} +10.7284 q^{43} -5.25204 q^{44} +4.33739 q^{45} +5.06378 q^{46} -1.56364 q^{47} -3.75244 q^{48} +2.25503 q^{49} -28.0268 q^{50} +1.00000 q^{51} -6.00349 q^{52} -3.33236 q^{53} -2.02903 q^{54} -10.7609 q^{55} +0.721856 q^{56} -1.71391 q^{57} +6.03084 q^{58} -11.5571 q^{59} +9.18200 q^{60} +13.3272 q^{61} +0.419209 q^{62} -3.04221 q^{63} -8.90659 q^{64} -12.3005 q^{65} +5.03392 q^{66} -3.95247 q^{67} +2.11694 q^{68} -2.49567 q^{69} +26.7735 q^{70} +7.14457 q^{71} -0.237280 q^{72} -10.4608 q^{73} -21.4828 q^{74} +13.8129 q^{75} -3.62825 q^{76} +7.54758 q^{77} +5.75416 q^{78} -3.69072 q^{79} -16.2758 q^{80} +1.00000 q^{81} -9.26519 q^{82} -1.81049 q^{83} -6.44018 q^{84} +4.33739 q^{85} -21.7682 q^{86} -2.97228 q^{87} +0.588681 q^{88} +16.6642 q^{89} -8.80067 q^{90} +8.62747 q^{91} -5.28320 q^{92} -0.206606 q^{93} +3.17267 q^{94} -7.43390 q^{95} +8.08835 q^{96} +9.74805 q^{97} -4.57551 q^{98} -2.48095 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * 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 $

$2$	−2.02903	−1.43474	−0.717369	−	0.696694i	$-0.754654\pi$
$2$	−2.02903	−1.43474	−0.717369	+	0.696694i	$0.754654\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.11694	1.05847
$5$	4.33739	1.93974	0.969870	−	0.243625i	$-0.0783366\pi$
$5$	4.33739	1.93974	0.969870	+	0.243625i	$0.0783366\pi$
$6$	−2.02903	−0.828346
$7$	−3.04221	−1.14985	−0.574923	−	0.818207i	$-0.694968\pi$
$7$	−3.04221	−1.14985	−0.574923	+	0.818207i	$0.694968\pi$
$8$	−0.237280	−0.0838912
$9$	1.00000	0.333333
$10$	−8.80067	−2.78302
$11$	−2.48095	−0.748036	−0.374018	−	0.927422i	$-0.622020\pi$
$11$	−2.48095	−0.748036	−0.374018	+	0.927422i	$0.622020\pi$
$12$	2.11694	0.611109
$13$	−2.83592	−0.786544	−0.393272	−	0.919422i	$-0.628657\pi$
$13$	−2.83592	−0.786544	−0.393272	+	0.919422i	$0.628657\pi$
$14$	6.17272	1.64973
$15$	4.33739	1.11991
$16$	−3.75244	−0.938110
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.02903	−0.478246
$19$	−1.71391	−0.393198	−0.196599	−	0.980484i	$-0.562990\pi$
$19$	−1.71391	−0.393198	−0.196599	+	0.980484i	$0.562990\pi$
$20$	9.18200	2.05316
$21$	−3.04221	−0.663864
$22$	5.03392	1.07323
$23$	−2.49567	−0.520384	−0.260192	−	0.965557i	$-0.583786\pi$
$23$	−2.49567	−0.520384	−0.260192	+	0.965557i	$0.583786\pi$
$24$	−0.237280	−0.0484346
$25$	13.8129	2.76259
$26$	5.75416	1.12848
$27$	1.00000	0.192450
$28$	−6.44018	−1.21708
$29$	−2.97228	−0.551939	−0.275970	−	0.961166i	$-0.588999\pi$
$29$	−2.97228	−0.551939	−0.275970	+	0.961166i	$0.588999\pi$
$30$	−8.80067	−1.60678
$31$	−0.206606	−0.0371076	−0.0185538	−	0.999828i	$-0.505906\pi$
$31$	−0.206606	−0.0371076	−0.0185538	+	0.999828i	$0.505906\pi$
$32$	8.08835	1.42983
$33$	−2.48095	−0.431879
$34$	−2.02903	−0.347975
$35$	−13.1952	−2.23040
$36$	2.11694	0.352824
$37$	10.5877	1.74061	0.870305	−	0.492512i	$-0.163921\pi$
$37$	10.5877	1.74061	0.870305	+	0.492512i	$0.163921\pi$
$38$	3.47757	0.564136
$39$	−2.83592	−0.454111
$40$	−1.02918	−0.162727
$41$	4.56632	0.713140	0.356570	−	0.934269i	$-0.383946\pi$
$41$	4.56632	0.713140	0.356570	+	0.934269i	$0.383946\pi$
$42$	6.17272	0.952471
$43$	10.7284	1.63607	0.818033	−	0.575171i	$-0.195065\pi$
$43$	10.7284	1.63607	0.818033	+	0.575171i	$0.195065\pi$
$44$	−5.25204	−0.791774
$45$	4.33739	0.646580
$46$	5.06378	0.746614
$47$	−1.56364	−0.228081	−0.114040	−	0.993476i	$-0.536379\pi$
$47$	−1.56364	−0.228081	−0.114040	+	0.993476i	$0.536379\pi$
$48$	−3.75244	−0.541618
$49$	2.25503	0.322147
$50$	−28.0268	−3.96359
$51$	1.00000	0.140028
$52$	−6.00349	−0.832534
$53$	−3.33236	−0.457735	−0.228867	−	0.973458i	$-0.573502\pi$
$53$	−3.33236	−0.457735	−0.228867	+	0.973458i	$0.573502\pi$
$54$	−2.02903	−0.276115
$55$	−10.7609	−1.45099
$56$	0.721856	0.0964620
$57$	−1.71391	−0.227013
$58$	6.03084	0.791888
$59$	−11.5571	−1.50461	−0.752304	−	0.658816i	$-0.771057\pi$
$59$	−11.5571	−1.50461	−0.752304	+	0.658816i	$0.771057\pi$
$60$	9.18200	1.18539
$61$	13.3272	1.70637	0.853187	−	0.521605i	$-0.174666\pi$
$61$	13.3272	1.70637	0.853187	+	0.521605i	$0.174666\pi$
$62$	0.419209	0.0532396
$63$	−3.04221	−0.383282
$64$	−8.90659	−1.11332
$65$	−12.3005	−1.52569
$66$	5.03392	0.619632
$67$	−3.95247	−0.482871	−0.241435	−	0.970417i	$-0.577618\pi$
$67$	−3.95247	−0.482871	−0.241435	+	0.970417i	$0.577618\pi$
$68$	2.11694	0.256717
$69$	−2.49567	−0.300444
$70$	26.7735	3.20004
$71$	7.14457	0.847905	0.423952	−	0.905684i	$-0.360642\pi$
$71$	7.14457	0.847905	0.423952	+	0.905684i	$0.360642\pi$
$72$	−0.237280	−0.0279637
$73$	−10.4608	−1.22434	−0.612172	−	0.790724i	$-0.709704\pi$
$73$	−10.4608	−1.22434	−0.612172	+	0.790724i	$0.709704\pi$
$74$	−21.4828	−2.49732
$75$	13.8129	1.59498
$76$	−3.62825	−0.416189
$77$	7.54758	0.860126
$78$	5.75416	0.651530
$79$	−3.69072	−0.415238	−0.207619	−	0.978210i	$-0.566571\pi$
$79$	−3.69072	−0.415238	−0.207619	+	0.978210i	$0.566571\pi$
$80$	−16.2758	−1.81969
$81$	1.00000	0.111111
$82$	−9.26519	−1.02317
$83$	−1.81049	−0.198727	−0.0993636	−	0.995051i	$-0.531681\pi$
$83$	−1.81049	−0.198727	−0.0993636	+	0.995051i	$0.531681\pi$
$84$	−6.44018	−0.702681
$85$	4.33739	0.470456
$86$	−21.7682	−2.34733
$87$	−2.97228	−0.318662
$88$	0.588681	0.0627536
$89$	16.6642	1.76640	0.883200	−	0.468997i	$-0.155384\pi$
$89$	16.6642	1.76640	0.883200	+	0.468997i	$0.155384\pi$
$90$	−8.80067	−0.927672
$91$	8.62747	0.904404
$92$	−5.28320	−0.550811
$93$	−0.206606	−0.0214241
$94$	3.17267	0.327236
$95$	−7.43390	−0.762702
$96$	8.08835	0.825514
$97$	9.74805	0.989764	0.494882	−	0.868960i	$-0.335211\pi$
$97$	9.74805	0.989764	0.494882	+	0.868960i	$0.335211\pi$
$98$	−4.57551	−0.462196
$99$	−2.48095	−0.249345
$100$	29.2412	2.92412
$101$	−7.84278	−0.780386	−0.390193	−	0.920733i	$-0.627592\pi$
$101$	−7.84278	−0.780386	−0.390193	+	0.920733i	$0.627592\pi$
$102$	−2.02903	−0.200903
$103$	−4.23429	−0.417217	−0.208608	−	0.977999i	$-0.566893\pi$
$103$	−4.23429	−0.417217	−0.208608	+	0.977999i	$0.566893\pi$
$104$	0.672908	0.0659841
$105$	−13.1952	−1.28772
$106$	6.76144	0.656729
$107$	−1.84744	−0.178599	−0.0892996	−	0.996005i	$-0.528463\pi$
$107$	−1.84744	−0.178599	−0.0892996	+	0.996005i	$0.528463\pi$
$108$	2.11694	0.203703
$109$	17.9716	1.72137	0.860683	−	0.509141i	$-0.170037\pi$
$109$	17.9716	1.72137	0.860683	+	0.509141i	$0.170037\pi$
$110$	21.8341	2.08180
$111$	10.5877	1.00494
$112$	11.4157	1.07868
$113$	10.4247	0.980674	0.490337	−	0.871533i	$-0.336874\pi$
$113$	10.4247	0.980674	0.490337	+	0.871533i	$0.336874\pi$
$114$	3.47757	0.325704
$115$	−10.8247	−1.00941
$116$	−6.29216	−0.584212
$117$	−2.83592	−0.262181
$118$	23.4497	2.15872
$119$	−3.04221	−0.278879
$120$	−1.02918	−0.0939505
$121$	−4.84487	−0.440443
$122$	−27.0412	−2.44820
$123$	4.56632	0.411732
$124$	−0.437373	−0.0392773
$125$	38.2251	3.41896
$126$	6.17272	0.549909
$127$	−17.0834	−1.51591	−0.757953	−	0.652309i	$-0.773800\pi$
$127$	−17.0834	−1.51591	−0.757953	+	0.652309i	$0.773800\pi$
$128$	1.89500	0.167496
$129$	10.7284	0.944583
$130$	24.9580	2.18896
$131$	14.6619	1.28101	0.640507	−	0.767952i	$-0.278724\pi$
$131$	14.6619	1.28101	0.640507	+	0.767952i	$0.278724\pi$
$132$	−5.25204	−0.457131
$133$	5.21407	0.452117
$134$	8.01965	0.692793
$135$	4.33739	0.373303
$136$	−0.237280	−0.0203466
$137$	−17.4703	−1.49259	−0.746295	−	0.665615i	$-0.768169\pi$
$137$	−17.4703	−1.49259	−0.746295	+	0.665615i	$0.768169\pi$
$138$	5.06378	0.431058
$139$	−12.3183	−1.04482	−0.522412	−	0.852693i	$-0.674968\pi$
$139$	−12.3183	−1.04482	−0.522412	+	0.852693i	$0.674968\pi$
$140$	−27.9336	−2.36082
$141$	−1.56364	−0.131682
$142$	−14.4965	−1.21652
$143$	7.03579	0.588363
$144$	−3.75244	−0.312703
$145$	−12.8919	−1.07062
$146$	21.2252	1.75661
$147$	2.25503	0.185992
$148$	22.4136	1.84239
$149$	0.702898	0.0575837	0.0287918	−	0.999585i	$-0.490834\pi$
$149$	0.702898	0.0575837	0.0287918	+	0.999585i	$0.490834\pi$
$150$	−28.0268	−2.28838
$151$	−23.4715	−1.91008	−0.955041	−	0.296475i	$-0.904189\pi$
$151$	−23.4715	−1.91008	−0.955041	+	0.296475i	$0.904189\pi$
$152$	0.406677	0.0329859
$153$	1.00000	0.0808452
$154$	−15.3142	−1.23406
$155$	−0.896131	−0.0719790
$156$	−6.00349	−0.480664
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	7.48856	0.595758
$159$	−3.33236	−0.264273
$160$	35.0823	2.77350
$161$	7.59236	0.598361
$162$	−2.02903	−0.159415
$163$	13.5041	1.05772	0.528861	−	0.848708i	$-0.322619\pi$
$163$	13.5041	1.05772	0.528861	+	0.848708i	$0.322619\pi$
$164$	9.66665	0.754838
$165$	−10.7609	−0.837732
$166$	3.67353	0.285121
$167$	24.3642	1.88536	0.942679	−	0.333701i	$-0.108298\pi$
$167$	24.3642	1.88536	0.942679	+	0.333701i	$0.108298\pi$
$168$	0.721856	0.0556924
$169$	−4.95754	−0.381349
$170$	−8.80067	−0.674981
$171$	−1.71391	−0.131066
$172$	22.7114	1.73173
$173$	2.75723	0.209628	0.104814	−	0.994492i	$-0.466575\pi$
$173$	2.75723	0.209628	0.104814	+	0.994492i	$0.466575\pi$
$174$	6.03084	0.457197
$175$	−42.0218	−3.17655
$176$	9.30963	0.701739
$177$	−11.5571	−0.868686
$178$	−33.8120	−2.53432
$179$	21.1616	1.58169	0.790845	−	0.612016i	$-0.209641\pi$
$179$	21.1616	1.58169	0.790845	+	0.612016i	$0.209641\pi$
$180$	9.18200	0.684386
$181$	24.0748	1.78947	0.894735	−	0.446598i	$-0.147365\pi$
$181$	24.0748	1.78947	0.894735	+	0.446598i	$0.147365\pi$
$182$	−17.5053	−1.29758
$183$	13.3272	0.985176
$184$	0.592174	0.0436556
$185$	45.9231	3.37633
$186$	0.419209	0.0307379
$187$	−2.48095	−0.181425
$188$	−3.31014	−0.241417
$189$	−3.04221	−0.221288
$190$	15.0836	1.09428
$191$	12.0618	0.872762	0.436381	−	0.899762i	$-0.356260\pi$
$191$	12.0618	0.872762	0.436381	+	0.899762i	$0.356260\pi$
$192$	−8.90659	−0.642778
$193$	−18.3096	−1.31796	−0.658978	−	0.752163i	$-0.729011\pi$
$193$	−18.3096	−1.31796	−0.658978	+	0.752163i	$0.729011\pi$
$194$	−19.7790	−1.42005
$195$	−12.3005	−0.880857
$196$	4.77377	0.340983
$197$	0.950036	0.0676873	0.0338436	−	0.999427i	$-0.489225\pi$
$197$	0.950036	0.0676873	0.0338436	+	0.999427i	$0.489225\pi$
$198$	5.03392	0.357745
$199$	11.6263	0.824164	0.412082	−	0.911147i	$-0.364802\pi$
$199$	11.6263	0.824164	0.412082	+	0.911147i	$0.364802\pi$
$200$	−3.27754	−0.231757
$201$	−3.95247	−0.278786
$202$	15.9132	1.11965
$203$	9.04231	0.634645
$204$	2.11694	0.148216
$205$	19.8059	1.38331
$206$	8.59148	0.598596
$207$	−2.49567	−0.173461
$208$	10.6416	0.737864
$209$	4.25213	0.294126
$210$	26.7735	1.84754
$211$	26.4117	1.81825	0.909127	−	0.416519i	$-0.136750\pi$
$211$	26.4117	1.81825	0.909127	+	0.416519i	$0.136750\pi$
$212$	−7.05441	−0.484499
$213$	7.14457	0.489538
$214$	3.74851	0.256243
$215$	46.5332	3.17354
$216$	−0.237280	−0.0161449
$217$	0.628539	0.0426680
$218$	−36.4648	−2.46971
$219$	−10.4608	−0.706876
$220$	−22.7801	−1.53584
$221$	−2.83592	−0.190765
$222$	−21.4828	−1.44183
$223$	24.8083	1.66129	0.830643	−	0.556805i	$-0.187973\pi$
$223$	24.8083	1.66129	0.830643	+	0.556805i	$0.187973\pi$
$224$	−24.6064	−1.64409
$225$	13.8129	0.920863
$226$	−21.1520	−1.40701
$227$	3.66507	0.243259	0.121630	−	0.992576i	$-0.461188\pi$
$227$	3.66507	0.243259	0.121630	+	0.992576i	$0.461188\pi$
$228$	−3.62825	−0.240287
$229$	18.0273	1.19128	0.595640	−	0.803252i	$-0.296899\pi$
$229$	18.0273	1.19128	0.595640	+	0.803252i	$0.296899\pi$
$230$	21.9636	1.44824
$231$	7.54758	0.496594
$232$	0.705264	0.0463029
$233$	4.05523	0.265667	0.132834	−	0.991138i	$-0.457592\pi$
$233$	4.05523	0.265667	0.132834	+	0.991138i	$0.457592\pi$
$234$	5.75416	0.376161
$235$	−6.78212	−0.442417
$236$	−24.4657	−1.59258
$237$	−3.69072	−0.239738
$238$	6.17272	0.400118
$239$	−19.7857	−1.27983	−0.639916	−	0.768445i	$-0.721031\pi$
$239$	−19.7857	−1.27983	−0.639916	+	0.768445i	$0.721031\pi$
$240$	−16.2758	−1.05060
$241$	17.9625	1.15707	0.578533	−	0.815659i	$-0.303626\pi$
$241$	17.9625	1.15707	0.578533	+	0.815659i	$0.303626\pi$
$242$	9.83036	0.631919
$243$	1.00000	0.0641500
$244$	28.2129	1.80615
$245$	9.78093	0.624881
$246$	−9.26519	−0.590727
$247$	4.86052	0.309267
$248$	0.0490235	0.00311300
$249$	−1.81049	−0.114735
$250$	−77.5598	−4.90531
$251$	7.45092	0.470298	0.235149	−	0.971959i	$-0.424442\pi$
$251$	7.45092	0.470298	0.235149	+	0.971959i	$0.424442\pi$
$252$	−6.44018	−0.405693
$253$	6.19165	0.389266
$254$	34.6626	2.17493
$255$	4.33739	0.271618
$256$	13.9682	0.873012
$257$	21.8356	1.36207	0.681033	−	0.732253i	$-0.261531\pi$
$257$	21.8356	1.36207	0.681033	+	0.732253i	$0.261531\pi$
$258$	−21.7682	−1.35523
$259$	−32.2101	−2.00144
$260$	−26.0395	−1.61490
$261$	−2.97228	−0.183980
$262$	−29.7493	−1.83792
$263$	−9.79833	−0.604191	−0.302095	−	0.953278i	$-0.597686\pi$
$263$	−9.79833	−0.604191	−0.302095	+	0.953278i	$0.597686\pi$
$264$	0.588681	0.0362308
$265$	−14.4537	−0.887886
$266$	−10.5795	−0.648670
$267$	16.6642	1.01983
$268$	−8.36715	−0.511105
$269$	29.0279	1.76986	0.884930	−	0.465724i	$-0.154206\pi$
$269$	29.0279	1.76986	0.884930	+	0.465724i	$0.154206\pi$
$270$	−8.80067	−0.535592
$271$	−13.3293	−0.809697	−0.404849	−	0.914384i	$-0.632676\pi$
$271$	−13.3293	−0.809697	−0.404849	+	0.914384i	$0.632676\pi$
$272$	−3.75244	−0.227525
$273$	8.62747	0.522158
$274$	35.4477	2.14148
$275$	−34.2693	−2.06651
$276$	−5.28320	−0.318011
$277$	25.2409	1.51658	0.758288	−	0.651919i	$-0.226036\pi$
$277$	25.2409	1.51658	0.758288	+	0.651919i	$0.226036\pi$
$278$	24.9941	1.49905
$279$	−0.206606	−0.0123692
$280$	3.13097	0.187111
$281$	−24.6239	−1.46894	−0.734470	−	0.678641i	$-0.762569\pi$
$281$	−24.6239	−1.46894	−0.734470	+	0.678641i	$0.762569\pi$
$282$	3.17267	0.188930
$283$	−6.67364	−0.396707	−0.198353	−	0.980131i	$-0.563559\pi$
$283$	−6.67364	−0.396707	−0.198353	+	0.980131i	$0.563559\pi$
$284$	15.1247	0.897483
$285$	−7.43390	−0.440346
$286$	−14.2758	−0.844146
$287$	−13.8917	−0.820002
$288$	8.08835	0.476611
$289$	1.00000	0.0588235
$290$	26.1581	1.53606
$291$	9.74805	0.571441
$292$	−22.1449	−1.29593
$293$	6.40980	0.374464	0.187232	−	0.982316i	$-0.440048\pi$
$293$	6.40980	0.374464	0.187232	+	0.982316i	$0.440048\pi$
$294$	−4.57551	−0.266849
$295$	−50.1277	−2.91855
$296$	−2.51226	−0.146022
$297$	−2.48095	−0.143960
$298$	−1.42620	−0.0826174
$299$	7.07754	0.409305
$300$	29.2412	1.68824
$301$	−32.6380	−1.88122
$302$	47.6242	2.74046
$303$	−7.84278	−0.450556
$304$	6.43134	0.368863
$305$	57.8053	3.30992
$306$	−2.02903	−0.115992
$307$	−5.50105	−0.313961	−0.156981	−	0.987602i	$-0.550176\pi$
$307$	−5.50105	−0.313961	−0.156981	+	0.987602i	$0.550176\pi$
$308$	15.9778	0.910419
$309$	−4.23429	−0.240880
$310$	1.81827	0.103271
$311$	−19.5463	−1.10837	−0.554186	−	0.832393i	$-0.686970\pi$
$311$	−19.5463	−1.10837	−0.554186	+	0.832393i	$0.686970\pi$
$312$	0.672908	0.0380959
$313$	16.6493	0.941076	0.470538	−	0.882380i	$-0.344060\pi$
$313$	16.6493	0.941076	0.470538	+	0.882380i	$0.344060\pi$
$314$	−2.02903	−0.114505
$315$	−13.1952	−0.743467
$316$	−7.81304	−0.439518
$317$	−1.84809	−0.103799	−0.0518994	−	0.998652i	$-0.516528\pi$
$317$	−1.84809	−0.103799	−0.0518994	+	0.998652i	$0.516528\pi$
$318$	6.76144	0.379163
$319$	7.37410	0.412870
$320$	−38.6314	−2.15956
$321$	−1.84744	−0.103114
$322$	−15.4051	−0.858492
$323$	−1.71391	−0.0953645
$324$	2.11694	0.117608
$325$	−39.1724	−2.17290
$326$	−27.4001	−1.51755
$327$	17.9716	0.993831
$328$	−1.08350	−0.0598262
$329$	4.75692	0.262258
$330$	21.8341	1.20193
$331$	−2.38003	−0.130819	−0.0654093	−	0.997859i	$-0.520835\pi$
$331$	−2.38003	−0.130819	−0.0654093	+	0.997859i	$0.520835\pi$
$332$	−3.83271	−0.210347
$333$	10.5877	0.580204
$334$	−49.4356	−2.70499
$335$	−17.1434	−0.936643
$336$	11.4157	0.622777
$337$	−17.6299	−0.960362	−0.480181	−	0.877170i	$-0.659429\pi$
$337$	−17.6299	−0.960362	−0.480181	+	0.877170i	$0.659429\pi$
$338$	10.0590	0.547136
$339$	10.4247	0.566193
$340$	9.18200	0.497964
$341$	0.512580	0.0277578
$342$	3.47757	0.188045
$343$	14.4352	0.779427
$344$	−2.54564	−0.137252
$345$	−10.8247	−0.582782
$346$	−5.59449	−0.300761
$347$	20.9777	1.12614	0.563072	−	0.826408i	$-0.309619\pi$
$347$	20.9777	1.12614	0.563072	+	0.826408i	$0.309619\pi$
$348$	−6.29216	−0.337295
$349$	11.2771	0.603647	0.301824	−	0.953364i	$-0.402405\pi$
$349$	11.2771	0.603647	0.301824	+	0.953364i	$0.402405\pi$
$350$	85.2633	4.55752
$351$	−2.83592	−0.151370
$352$	−20.0668	−1.06957
$353$	2.69501	0.143441	0.0717204	−	0.997425i	$-0.477151\pi$
$353$	2.69501	0.143441	0.0717204	+	0.997425i	$0.477151\pi$
$354$	23.4497	1.24634
$355$	30.9888	1.64471
$356$	35.2771	1.86968
$357$	−3.04221	−0.161011
$358$	−42.9374	−2.26931
$359$	−2.50405	−0.132159	−0.0660793	−	0.997814i	$-0.521049\pi$
$359$	−2.50405	−0.132159	−0.0660793	+	0.997814i	$0.521049\pi$
$360$	−1.02918	−0.0542424
$361$	−16.0625	−0.845395
$362$	−48.8485	−2.56742
$363$	−4.84487	−0.254290
$364$	18.2639	0.957286
$365$	−45.3726	−2.37491
$366$	−27.0412	−1.41347
$367$	−12.9267	−0.674770	−0.337385	−	0.941367i	$-0.609542\pi$
$367$	−12.9267	−0.674770	−0.337385	+	0.941367i	$0.609542\pi$
$368$	9.36486	0.488177
$369$	4.56632	0.237713
$370$	−93.1790	−4.84415
$371$	10.1377	0.526325
$372$	−0.437373	−0.0226768
$373$	−18.1284	−0.938655	−0.469327	−	0.883024i	$-0.655504\pi$
$373$	−18.1284	−0.938655	−0.469327	+	0.883024i	$0.655504\pi$
$374$	5.03392	0.260298
$375$	38.2251	1.97394
$376$	0.371021	0.0191340
$377$	8.42917	0.434124
$378$	6.17272	0.317490
$379$	28.8584	1.48236	0.741179	−	0.671308i	$-0.234267\pi$
$379$	28.8584	1.48236	0.741179	+	0.671308i	$0.234267\pi$
$380$	−15.7371	−0.807298
$381$	−17.0834	−0.875209
$382$	−24.4737	−1.25218
$383$	16.3185	0.833835	0.416917	−	0.908944i	$-0.363110\pi$
$383$	16.3185	0.833835	0.416917	+	0.908944i	$0.363110\pi$
$384$	1.89500	0.0967036
$385$	32.7368	1.66842
$386$	37.1507	1.89092
$387$	10.7284	0.545355
$388$	20.6361	1.04764
$389$	−16.9161	−0.857678	−0.428839	−	0.903381i	$-0.641077\pi$
$389$	−16.9161	−0.857678	−0.428839	+	0.903381i	$0.641077\pi$
$390$	24.9580	1.26380
$391$	−2.49567	−0.126212
$392$	−0.535074	−0.0270253
$393$	14.6619	0.739594
$394$	−1.92765	−0.0971135
$395$	−16.0081	−0.805454
$396$	−5.25204	−0.263925
$397$	31.6534	1.58864	0.794320	−	0.607499i	$-0.207827\pi$
$397$	31.6534	1.58864	0.794320	+	0.607499i	$0.207827\pi$
$398$	−23.5900	−1.18246
$399$	5.21407	0.261030
$400$	−51.8322	−2.59161
$401$	−2.83679	−0.141663	−0.0708313	−	0.997488i	$-0.522565\pi$
$401$	−2.83679	−0.141663	−0.0708313	+	0.997488i	$0.522565\pi$
$402$	8.01965	0.399984
$403$	0.585919	0.0291867
$404$	−16.6027	−0.826016
$405$	4.33739	0.215527
$406$	−18.3471	−0.910549
$407$	−26.2676	−1.30204
$408$	−0.237280	−0.0117471
$409$	6.77076	0.334793	0.167396	−	0.985890i	$-0.446464\pi$
$409$	6.77076	0.334793	0.167396	+	0.985890i	$0.446464\pi$
$410$	−40.1867	−1.98468
$411$	−17.4703	−0.861748
$412$	−8.96374	−0.441612
$413$	35.1591	1.73007
$414$	5.06378	0.248871
$415$	−7.85280	−0.385479
$416$	−22.9379	−1.12463
$417$	−12.3183	−0.603230
$418$	−8.62769	−0.421994
$419$	17.6732	0.863392	0.431696	−	0.902019i	$-0.357915\pi$
$419$	17.6732	0.863392	0.431696	+	0.902019i	$0.357915\pi$
$420$	−27.9336	−1.36302
$421$	−34.4675	−1.67984	−0.839922	−	0.542707i	$-0.817400\pi$
$421$	−34.4675	−1.67984	−0.839922	+	0.542707i	$0.817400\pi$
$422$	−53.5899	−2.60872
$423$	−1.56364	−0.0760269
$424$	0.790703	0.0383999
$425$	13.8129	0.670026
$426$	−14.4965	−0.702359
$427$	−40.5441	−1.96207
$428$	−3.91094	−0.189042
$429$	7.03579	0.339691
$430$	−94.4171	−4.55320
$431$	−0.390666	−0.0188177	−0.00940886	−	0.999956i	$-0.502995\pi$
$431$	−0.390666	−0.0188177	−0.00940886	+	0.999956i	$0.502995\pi$
$432$	−3.75244	−0.180539
$433$	−38.0307	−1.82764	−0.913820	−	0.406120i	$-0.866881\pi$
$433$	−38.0307	−1.82764	−0.913820	+	0.406120i	$0.866881\pi$
$434$	−1.27532	−0.0612174
$435$	−12.8919	−0.618122
$436$	38.0448	1.82202
$437$	4.27736	0.204614
$438$	21.2252	1.01418
$439$	−5.60904	−0.267705	−0.133852	−	0.991001i	$-0.542735\pi$
$439$	−5.60904	−0.267705	−0.133852	+	0.991001i	$0.542735\pi$
$440$	2.55334	0.121726
$441$	2.25503	0.107382
$442$	5.75416	0.273697
$443$	−0.359747	−0.0170921	−0.00854604	−	0.999963i	$-0.502720\pi$
$443$	−0.359747	−0.0170921	−0.00854604	+	0.999963i	$0.502720\pi$
$444$	22.4136	1.06370
$445$	72.2790	3.42635
$446$	−50.3367	−2.38351
$447$	0.702898	0.0332459
$448$	27.0957	1.28015
$449$	−15.5512	−0.733908	−0.366954	−	0.930239i	$-0.619599\pi$
$449$	−15.5512	−0.733908	−0.366954	+	0.930239i	$0.619599\pi$
$450$	−28.0268	−1.32120
$451$	−11.3288	−0.533454
$452$	22.0685	1.03802
$453$	−23.4715	−1.10279
$454$	−7.43652	−0.349013
$455$	37.4207	1.75431
$456$	0.406677	0.0190444
$457$	−19.4379	−0.909265	−0.454632	−	0.890679i	$-0.650229\pi$
$457$	−19.4379	−0.909265	−0.454632	+	0.890679i	$0.650229\pi$
$458$	−36.5779	−1.70917
$459$	1.00000	0.0466760
$460$	−22.9153	−1.06843
$461$	15.9970	0.745054	0.372527	−	0.928021i	$-0.378491\pi$
$461$	15.9970	0.745054	0.372527	+	0.928021i	$0.378491\pi$
$462$	−15.3142	−0.712482
$463$	−27.4791	−1.27706	−0.638530	−	0.769597i	$-0.720457\pi$
$463$	−27.4791	−1.27706	−0.638530	+	0.769597i	$0.720457\pi$
$464$	11.1533	0.517780
$465$	−0.896131	−0.0415571
$466$	−8.22817	−0.381162
$467$	−34.1414	−1.57987	−0.789937	−	0.613188i	$-0.789887\pi$
$467$	−34.1414	−1.57987	−0.789937	+	0.613188i	$0.789887\pi$
$468$	−6.00349	−0.277511
$469$	12.0242	0.555227
$470$	13.7611	0.634752
$471$	1.00000	0.0460776
$472$	2.74227	0.126223
$473$	−26.6167	−1.22384
$474$	7.48856	0.343961
$475$	−23.6741	−1.08624
$476$	−6.44018	−0.295185
$477$	−3.33236	−0.152578
$478$	40.1457	1.83622
$479$	25.4012	1.16061	0.580306	−	0.814398i	$-0.302933\pi$
$479$	25.4012	1.16061	0.580306	+	0.814398i	$0.302933\pi$
$480$	35.0823	1.60128
$481$	−30.0260	−1.36907
$482$	−36.4463	−1.66008
$483$	7.59236	0.345464
$484$	−10.2563	−0.466196
$485$	42.2811	1.91988
$486$	−2.02903	−0.0920384
$487$	36.4125	1.65001	0.825004	−	0.565127i	$-0.191173\pi$
$487$	36.4125	1.65001	0.825004	+	0.565127i	$0.191173\pi$
$488$	−3.16228	−0.143150
$489$	13.5041	0.610676
$490$	−19.8458	−0.896540
$491$	22.0393	0.994620	0.497310	−	0.867573i	$-0.334321\pi$
$491$	22.0393	0.994620	0.497310	+	0.867573i	$0.334321\pi$
$492$	9.66665	0.435806
$493$	−2.97228	−0.133865
$494$	−9.86212	−0.443718
$495$	−10.7609	−0.483665
$496$	0.775277	0.0348109
$497$	−21.7353	−0.974960
$498$	3.67353	0.164615
$499$	30.7360	1.37593	0.687965	−	0.725743i	$-0.258504\pi$
$499$	30.7360	1.37593	0.687965	+	0.725743i	$0.258504\pi$
$500$	80.9204	3.61887
$501$	24.3642	1.08851
$502$	−15.1181	−0.674754
$503$	1.36067	0.0606694	0.0303347	−	0.999540i	$-0.490343\pi$
$503$	1.36067	0.0606694	0.0303347	+	0.999540i	$0.490343\pi$
$504$	0.721856	0.0321540
$505$	−34.0172	−1.51374
$506$	−12.5630	−0.558494
$507$	−4.95754	−0.220172
$508$	−36.1646	−1.60454
$509$	4.91757	0.217967	0.108984	−	0.994044i	$-0.465240\pi$
$509$	4.91757	0.217967	0.108984	+	0.994044i	$0.465240\pi$
$510$	−8.80067	−0.389700
$511$	31.8239	1.40781
$512$	−32.1318	−1.42004
$513$	−1.71391	−0.0756710
$514$	−44.3049	−1.95421
$515$	−18.3657	−0.809292
$516$	22.7114	0.999814
$517$	3.87932	0.170612
$518$	65.3550	2.87153
$519$	2.75723	0.121029
$520$	2.91867	0.127992
$521$	−36.7653	−1.61072	−0.805359	−	0.592787i	$-0.798028\pi$
$521$	−36.7653	−1.61072	−0.805359	+	0.592787i	$0.798028\pi$
$522$	6.03084	0.263963
$523$	22.1738	0.969592	0.484796	−	0.874627i	$-0.338894\pi$
$523$	22.1738	0.969592	0.484796	+	0.874627i	$0.338894\pi$
$524$	31.0383	1.35592
$525$	−42.0218	−1.83398
$526$	19.8811	0.866855
$527$	−0.206606	−0.00899990
$528$	9.30963	0.405149
$529$	−16.7716	−0.729201
$530$	29.3270	1.27388
$531$	−11.5571	−0.501536
$532$	11.0379	0.478553
$533$	−12.9497	−0.560916
$534$	−33.8120	−1.46319
$535$	−8.01309	−0.346436
$536$	0.937842	0.0405086
$537$	21.1616	0.913190
$538$	−58.8983	−2.53928
$539$	−5.59462	−0.240977
$540$	9.18200	0.395131
$541$	−12.4314	−0.534466	−0.267233	−	0.963632i	$-0.586109\pi$
$541$	−12.4314	−0.534466	−0.267233	+	0.963632i	$0.586109\pi$
$542$	27.0455	1.16170
$543$	24.0748	1.03315
$544$	8.08835	0.346785
$545$	77.9497	3.33900
$546$	−17.5053	−0.749160
$547$	9.83134	0.420358	0.210179	−	0.977663i	$-0.432595\pi$
$547$	9.83134	0.420358	0.210179	+	0.977663i	$0.432595\pi$
$548$	−36.9837	−1.57986
$549$	13.3272	0.568792
$550$	69.5332	2.96491
$551$	5.09423	0.217021
$552$	0.592174	0.0252046
$553$	11.2279	0.477460
$554$	−51.2144	−2.17589
$555$	45.9231	1.94933
$556$	−26.0771	−1.10592
$557$	−24.1835	−1.02469	−0.512343	−	0.858781i	$-0.671222\pi$
$557$	−24.1835	−1.02469	−0.512343	+	0.858781i	$0.671222\pi$
$558$	0.419209	0.0177465
$559$	−30.4249	−1.28684
$560$	49.5143	2.09236
$561$	−2.48095	−0.104746
$562$	49.9626	2.10754
$563$	12.1098	0.510368	0.255184	−	0.966893i	$-0.417864\pi$
$563$	12.1098	0.510368	0.255184	+	0.966893i	$0.417864\pi$
$564$	−3.31014	−0.139382
$565$	45.2160	1.90225
$566$	13.5410	0.569170
$567$	−3.04221	−0.127761
$568$	−1.69527	−0.0711318
$569$	−14.3539	−0.601749	−0.300874	−	0.953664i	$-0.597278\pi$
$569$	−14.3539	−0.601749	−0.300874	+	0.953664i	$0.597278\pi$
$570$	15.0836	0.631781
$571$	30.3527	1.27022	0.635111	−	0.772421i	$-0.280954\pi$
$571$	30.3527	1.27022	0.635111	+	0.772421i	$0.280954\pi$
$572$	14.8944	0.622765
$573$	12.0618	0.503889
$574$	28.1866	1.17649
$575$	−34.4726	−1.43761
$576$	−8.90659	−0.371108
$577$	34.4598	1.43458	0.717290	−	0.696775i	$-0.245382\pi$
$577$	34.4598	1.43458	0.717290	+	0.696775i	$0.245382\pi$
$578$	−2.02903	−0.0843963
$579$	−18.3096	−0.760922
$580$	−27.2915	−1.13322
$581$	5.50789	0.228506
$582$	−19.7790	−0.819867
$583$	8.26743	0.342402
$584$	2.48214	0.102712
$585$	−12.3005	−0.508563
$586$	−13.0056	−0.537258
$587$	28.4278	1.17334	0.586670	−	0.809826i	$-0.300439\pi$
$587$	28.4278	1.17334	0.586670	+	0.809826i	$0.300439\pi$
$588$	4.77377	0.196867
$589$	0.354104	0.0145906
$590$	101.710	4.18735
$591$	0.950036	0.0390793
$592$	−39.7298	−1.63288
$593$	32.8256	1.34799	0.673993	−	0.738737i	$-0.264578\pi$
$593$	32.8256	1.34799	0.673993	+	0.738737i	$0.264578\pi$
$594$	5.03392	0.206544
$595$	−13.1952	−0.540952
$596$	1.48800	0.0609507
$597$	11.6263	0.475831
$598$	−14.3605	−0.587245
$599$	−12.1815	−0.497723	−0.248862	−	0.968539i	$-0.580056\pi$
$599$	−12.1815	−0.497723	−0.248862	+	0.968539i	$0.580056\pi$
$600$	−3.27754	−0.133805
$601$	−25.9996	−1.06055	−0.530273	−	0.847827i	$-0.677911\pi$
$601$	−25.9996	−1.06055	−0.530273	+	0.847827i	$0.677911\pi$
$602$	66.2234	2.69906
$603$	−3.95247	−0.160957
$604$	−49.6878	−2.02177
$605$	−21.0141	−0.854344
$606$	15.9132	0.646429
$607$	−35.1807	−1.42794	−0.713971	−	0.700175i	$-0.753105\pi$
$607$	−35.1807	−1.42794	−0.713971	+	0.700175i	$0.753105\pi$
$608$	−13.8627	−0.562207
$609$	9.04231	0.366413
$610$	−117.288	−4.74887
$611$	4.43437	0.179395
$612$	2.11694	0.0855723
$613$	12.5541	0.507057	0.253529	−	0.967328i	$-0.418409\pi$
$613$	12.5541	0.507057	0.253529	+	0.967328i	$0.418409\pi$
$614$	11.1618	0.450452
$615$	19.8059	0.798652
$616$	−1.79089	−0.0721570
$617$	46.1072	1.85621	0.928103	−	0.372323i	$-0.121439\pi$
$617$	46.1072	1.85621	0.928103	+	0.372323i	$0.121439\pi$
$618$	8.59148	0.345600
$619$	−28.4276	−1.14260	−0.571300	−	0.820741i	$-0.693561\pi$
$619$	−28.4276	−1.14260	−0.571300	+	0.820741i	$0.693561\pi$
$620$	−1.89706	−0.0761877
$621$	−2.49567	−0.100148
$622$	39.6600	1.59022
$623$	−50.6959	−2.03109
$624$	10.6416	0.426006
$625$	96.7326	3.86930
$626$	−33.7819	−1.35020
$627$	4.25213	0.169814
$628$	2.11694	0.0844752
$629$	10.5877	0.422160
$630$	26.7735	1.06668
$631$	−7.69323	−0.306263	−0.153131	−	0.988206i	$-0.548936\pi$
$631$	−7.69323	−0.306263	−0.153131	+	0.988206i	$0.548936\pi$
$632$	0.875734	0.0348348
$633$	26.4117	1.04977
$634$	3.74981	0.148924
$635$	−74.0973	−2.94046
$636$	−7.05441	−0.279726
$637$	−6.39509	−0.253383
$638$	−14.9622	−0.592360
$639$	7.14457	0.282635
$640$	8.21934	0.324898
$641$	−10.8466	−0.428417	−0.214208	−	0.976788i	$-0.568717\pi$
$641$	−10.8466	−0.428417	−0.214208	+	0.976788i	$0.568717\pi$
$642$	3.74851	0.147942
$643$	21.5341	0.849224	0.424612	−	0.905376i	$-0.360411\pi$
$643$	21.5341	0.849224	0.424612	+	0.905376i	$0.360411\pi$
$644$	16.0726	0.633349
$645$	46.5332	1.83224
$646$	3.47757	0.136823
$647$	27.6790	1.08817	0.544086	−	0.839029i	$-0.316876\pi$
$647$	27.6790	1.08817	0.544086	+	0.839029i	$0.316876\pi$
$648$	−0.237280	−0.00932125
$649$	28.6727	1.12550
$650$	79.4818	3.11753
$651$	0.628539	0.0246344
$652$	28.5874	1.11957
$653$	5.57383	0.218121	0.109060	−	0.994035i	$-0.465216\pi$
$653$	5.57383	0.218121	0.109060	+	0.994035i	$0.465216\pi$
$654$	−36.4648	−1.42589
$655$	63.5942	2.48483
$656$	−17.1349	−0.669004
$657$	−10.4608	−0.408115
$658$	−9.65192	−0.376271
$659$	24.5583	0.956654	0.478327	−	0.878182i	$-0.341243\pi$
$659$	24.5583	0.956654	0.478327	+	0.878182i	$0.341243\pi$
$660$	−22.7801	−0.886715
$661$	−13.1731	−0.512374	−0.256187	−	0.966627i	$-0.582466\pi$
$661$	−13.1731	−0.512374	−0.256187	+	0.966627i	$0.582466\pi$
$662$	4.82915	0.187690
$663$	−2.83592	−0.110138
$664$	0.429594	0.0166715
$665$	22.6155	0.876990
$666$	−21.4828	−0.832440
$667$	7.41785	0.287220
$668$	51.5776	1.99560
$669$	24.8083	0.959144
$670$	34.7844	1.34384
$671$	−33.0642	−1.27643
$672$	−24.6064	−0.949214
$673$	39.0564	1.50551	0.752756	−	0.658300i	$-0.228724\pi$
$673$	39.0564	1.50551	0.752756	+	0.658300i	$0.228724\pi$
$674$	35.7715	1.37787
$675$	13.8129	0.531660
$676$	−10.4948	−0.403647
$677$	3.55016	0.136444	0.0682220	−	0.997670i	$-0.478267\pi$
$677$	3.55016	0.136444	0.0682220	+	0.997670i	$0.478267\pi$
$678$	−21.1520	−0.812338
$679$	−29.6556	−1.13808
$680$	−1.02918	−0.0394671
$681$	3.66507	0.140446
$682$	−1.04004	−0.0398251
$683$	−19.8106	−0.758032	−0.379016	−	0.925390i	$-0.623737\pi$
$683$	−19.8106	−0.758032	−0.379016	+	0.925390i	$0.623737\pi$
$684$	−3.62825	−0.138730
$685$	−75.7756	−2.89524
$686$	−29.2894	−1.11827
$687$	18.0273	0.687786
$688$	−40.2577	−1.53481
$689$	9.45031	0.360028
$690$	21.9636	0.836140
$691$	−7.72246	−0.293776	−0.146888	−	0.989153i	$-0.546926\pi$
$691$	−7.72246	−0.293776	−0.146888	+	0.989153i	$0.546926\pi$
$692$	5.83690	0.221886
$693$	7.54758	0.286709
$694$	−42.5644	−1.61572
$695$	−53.4293	−2.02669
$696$	0.705264	0.0267330
$697$	4.56632	0.172962
$698$	−22.8814	−0.866075
$699$	4.05523	0.153383
$700$	−88.9578	−3.36229
$701$	−39.3642	−1.48677	−0.743383	−	0.668866i	$-0.766780\pi$
$701$	−39.3642	−1.48677	−0.743383	+	0.668866i	$0.766780\pi$
$702$	5.75416	0.217177
$703$	−18.1464	−0.684405
$704$	22.0968	0.832806
$705$	−6.78212	−0.255430
$706$	−5.46824	−0.205800
$707$	23.8594	0.897324
$708$	−24.4657	−0.919479
$709$	−36.6393	−1.37602	−0.688009	−	0.725702i	$-0.741515\pi$
$709$	−36.6393	−1.37602	−0.688009	+	0.725702i	$0.741515\pi$
$710$	−62.8770	−2.35973
$711$	−3.69072	−0.138413
$712$	−3.95408	−0.148185
$713$	0.515621	0.0193102
$714$	6.17272	0.231008
$715$	30.5170	1.14127
$716$	44.7979	1.67417
$717$	−19.7857	−0.738912
$718$	5.08077	0.189613
$719$	11.3012	0.421464	0.210732	−	0.977544i	$-0.432415\pi$
$719$	11.3012	0.421464	0.210732	+	0.977544i	$0.432415\pi$
$720$	−16.2758	−0.606563
$721$	12.8816	0.479735
$722$	32.5912	1.21292
$723$	17.9625	0.668032
$724$	50.9651	1.89410
$725$	−41.0560	−1.52478
$726$	9.83036	0.364839
$727$	15.1101	0.560403	0.280202	−	0.959941i	$-0.409599\pi$
$727$	15.1101	0.560403	0.280202	+	0.959941i	$0.409599\pi$
$728$	−2.04713	−0.0758716
$729$	1.00000	0.0370370
$730$	92.0621	3.40737
$731$	10.7284	0.396804
$732$	28.2129	1.04278
$733$	15.5737	0.575228	0.287614	−	0.957746i	$-0.407138\pi$
$733$	15.5737	0.575228	0.287614	+	0.957746i	$0.407138\pi$
$734$	26.2287	0.968117
$735$	9.78093	0.360775
$736$	−20.1859	−0.744061
$737$	9.80589	0.361205
$738$	−9.26519	−0.341056
$739$	−10.7846	−0.396717	−0.198358	−	0.980130i	$-0.563561\pi$
$739$	−10.7846	−0.396717	−0.198358	+	0.980130i	$0.563561\pi$
$740$	97.2165	3.57375
$741$	4.86052	0.178556
$742$	−20.5697	−0.755138
$743$	8.16216	0.299440	0.149720	−	0.988728i	$-0.452163\pi$
$743$	8.16216	0.299440	0.149720	+	0.988728i	$0.452163\pi$
$744$	0.0490235	0.00179729
$745$	3.04874	0.111697
$746$	36.7830	1.34672
$747$	−1.81049	−0.0662424
$748$	−5.25204	−0.192034
$749$	5.62031	0.205362
$750$	−77.5598	−2.83208
$751$	−24.4452	−0.892016	−0.446008	−	0.895029i	$-0.647155\pi$
$751$	−24.4452	−0.892016	−0.446008	+	0.895029i	$0.647155\pi$
$752$	5.86747	0.213965
$753$	7.45092	0.271527
$754$	−17.1030	−0.622854
$755$	−101.805	−3.70506
$756$	−6.44018	−0.234227
$757$	5.15457	0.187346	0.0936731	−	0.995603i	$-0.470139\pi$
$757$	5.15457	0.187346	0.0936731	+	0.995603i	$0.470139\pi$
$758$	−58.5545	−2.12679
$759$	6.19165	0.224743
$760$	1.76392	0.0639840
$761$	5.60100	0.203036	0.101518	−	0.994834i	$-0.467630\pi$
$761$	5.60100	0.203036	0.101518	+	0.994834i	$0.467630\pi$
$762$	34.6626	1.25569
$763$	−54.6733	−1.97931
$764$	25.5342	0.923793
$765$	4.33739	0.156819
$766$	−33.1106	−1.19633
$767$	32.7751	1.18344
$768$	13.9682	0.504034
$769$	−34.1015	−1.22973	−0.614866	−	0.788631i	$-0.710790\pi$
$769$	−34.1015	−1.22973	−0.614866	+	0.788631i	$0.710790\pi$
$770$	−66.4237	−2.39375
$771$	21.8356	0.786389
$772$	−38.7604	−1.39502
$773$	38.1150	1.37090	0.685451	−	0.728118i	$-0.259605\pi$
$773$	38.1150	1.37090	0.685451	+	0.728118i	$0.259605\pi$
$774$	−21.7682	−0.782442
$775$	−2.85384	−0.102513
$776$	−2.31302	−0.0830325
$777$	−32.2101	−1.15553
$778$	34.3231	1.23054
$779$	−7.82627	−0.280405
$780$	−26.0395	−0.932362
$781$	−17.7254	−0.634263
$782$	5.06378	0.181081
$783$	−2.97228	−0.106221
$784$	−8.46186	−0.302209
$785$	4.33739	0.154808
$786$	−29.7493	−1.06112
$787$	14.1501	0.504396	0.252198	−	0.967676i	$-0.418847\pi$
$787$	14.1501	0.504396	0.252198	+	0.967676i	$0.418847\pi$
$788$	2.01117	0.0716451
$789$	−9.79833	−0.348830
$790$	32.4808	1.15561
$791$	−31.7141	−1.12762
$792$	0.588681	0.0209179
$793$	−37.7950	−1.34214
$794$	−64.2256	−2.27928
$795$	−14.4537	−0.512621
$796$	24.6121	0.872354
$797$	37.0314	1.31172	0.655860	−	0.754882i	$-0.272306\pi$
$797$	37.0314	1.31172	0.655860	+	0.754882i	$0.272306\pi$
$798$	−10.5795	−0.374510
$799$	−1.56364	−0.0553177
$800$	111.724	3.95004
$801$	16.6642	0.588800
$802$	5.75592	0.203249
$803$	25.9528	0.915854
$804$	−8.36715	−0.295087
$805$	32.9310	1.16067
$806$	−1.18884	−0.0418753
$807$	29.0279	1.02183
$808$	1.86094	0.0654675
$809$	−18.3228	−0.644195	−0.322097	−	0.946707i	$-0.604388\pi$
$809$	−18.3228	−0.644195	−0.322097	+	0.946707i	$0.604388\pi$
$810$	−8.80067	−0.309224
$811$	−19.6896	−0.691397	−0.345698	−	0.938346i	$-0.612358\pi$
$811$	−19.6896	−0.691397	−0.345698	+	0.938346i	$0.612358\pi$
$812$	19.1420	0.671754
$813$	−13.3293	−0.467479
$814$	53.2977	1.86808
$815$	58.5725	2.05170
$816$	−3.75244	−0.131362
$817$	−18.3875	−0.643298
$818$	−13.7380	−0.480340
$819$	8.62747	0.301468
$820$	41.9280	1.46419
$821$	−10.4932	−0.366216	−0.183108	−	0.983093i	$-0.558616\pi$
$821$	−10.4932	−0.366216	−0.183108	+	0.983093i	$0.558616\pi$
$822$	35.4477	1.23638
$823$	−5.17633	−0.180436	−0.0902178	−	0.995922i	$-0.528756\pi$
$823$	−5.17633	−0.180436	−0.0902178	+	0.995922i	$0.528756\pi$
$824$	1.00471	0.0350008
$825$	−34.2693	−1.19310
$826$	−71.3388	−2.48219
$827$	33.2105	1.15484	0.577421	−	0.816447i	$-0.304059\pi$
$827$	33.2105	1.15484	0.577421	+	0.816447i	$0.304059\pi$
$828$	−5.28320	−0.183604
$829$	−19.1621	−0.665528	−0.332764	−	0.943010i	$-0.607981\pi$
$829$	−19.1621	−0.665528	−0.332764	+	0.943010i	$0.607981\pi$
$830$	15.9335	0.553061
$831$	25.2409	0.875596
$832$	25.2584	0.875678
$833$	2.25503	0.0781321
$834$	24.9941	0.865477
$835$	105.677	3.65710
$836$	9.00152	0.311324
$837$	−0.206606	−0.00714135
$838$	−35.8594	−1.23874
$839$	22.2975	0.769794	0.384897	−	0.922960i	$-0.374237\pi$
$839$	22.2975	0.769794	0.384897	+	0.922960i	$0.374237\pi$
$840$	3.13097	0.108029
$841$	−20.1655	−0.695363
$842$	69.9355	2.41014
$843$	−24.6239	−0.848093
$844$	55.9120	1.92457
$845$	−21.5028	−0.739718
$846$	3.17267	0.109079
$847$	14.7391	0.506441
$848$	12.5045	0.429405
$849$	−6.67364	−0.229039
$850$	−28.0268	−0.961311
$851$	−26.4235	−0.905786
$852$	15.1247	0.518162
$853$	24.8370	0.850402	0.425201	−	0.905099i	$-0.360203\pi$
$853$	24.8370	0.850402	0.425201	+	0.905099i	$0.360203\pi$
$854$	82.2651	2.81505
$855$	−7.43390	−0.254234
$856$	0.438362	0.0149829
$857$	22.1234	0.755721	0.377861	−	0.925863i	$-0.376660\pi$
$857$	22.1234	0.755721	0.377861	+	0.925863i	$0.376660\pi$
$858$	−14.2758	−0.487368
$859$	−27.7242	−0.945936	−0.472968	−	0.881080i	$-0.656817\pi$
$859$	−27.7242	−0.945936	−0.472968	+	0.881080i	$0.656817\pi$
$860$	98.5082	3.35910
$861$	−13.8917	−0.473428
$862$	0.792671	0.0269985
$863$	−27.5512	−0.937852	−0.468926	−	0.883237i	$-0.655359\pi$
$863$	−27.5512	−0.937852	−0.468926	+	0.883237i	$0.655359\pi$
$864$	8.08835	0.275171
$865$	11.9592	0.406624
$866$	77.1653	2.62218
$867$	1.00000	0.0339618
$868$	1.33058	0.0451628
$869$	9.15650	0.310613
$870$	26.1581	0.886842
$871$	11.2089	0.379799
$872$	−4.26430	−0.144407
$873$	9.74805	0.329921
$874$	−8.67887	−0.293567
$875$	−116.289	−3.93128
$876$	−22.1449	−0.748208
$877$	6.48081	0.218842	0.109421	−	0.993996i	$-0.465100\pi$
$877$	6.48081	0.218842	0.109421	+	0.993996i	$0.465100\pi$
$878$	11.3809	0.384086
$879$	6.40980	0.216197
$880$	40.3795	1.36119
$881$	21.9520	0.739581	0.369791	−	0.929115i	$-0.379429\pi$
$881$	21.9520	0.739581	0.369791	+	0.929115i	$0.379429\pi$
$882$	−4.57551	−0.154065
$883$	2.27900	0.0766944	0.0383472	−	0.999264i	$-0.487791\pi$
$883$	2.27900	0.0766944	0.0383472	+	0.999264i	$0.487791\pi$
$884$	−6.00349	−0.201919
$885$	−50.1277	−1.68502
$886$	0.729935	0.0245227
$887$	30.2297	1.01502	0.507508	−	0.861647i	$-0.330567\pi$
$887$	30.2297	1.01502	0.507508	+	0.861647i	$0.330567\pi$
$888$	−2.51226	−0.0843058
$889$	51.9712	1.74306
$890$	−146.656	−4.91592
$891$	−2.48095	−0.0831151
$892$	52.5178	1.75842
$893$	2.67994	0.0896809
$894$	−1.42620	−0.0476992
$895$	91.7860	3.06807
$896$	−5.76497	−0.192594
$897$	7.07754	0.236312
$898$	31.5538	1.05297
$899$	0.614092	0.0204811
$900$	29.2412	0.974707
$901$	−3.33236	−0.111017
$902$	22.9865	0.765367
$903$	−32.6380	−1.08613
$904$	−2.47358	−0.0822700
$905$	104.422	3.47110
$906$	47.6242	1.58221
$907$	36.3444	1.20680	0.603398	−	0.797440i	$-0.293813\pi$
$907$	36.3444	1.20680	0.603398	+	0.797440i	$0.293813\pi$
$908$	7.75874	0.257483
$909$	−7.84278	−0.260129
$910$	−75.9275	−2.51697
$911$	55.9184	1.85266	0.926329	−	0.376716i	$-0.122947\pi$
$911$	55.9184	1.85266	0.926329	+	0.376716i	$0.122947\pi$
$912$	6.43134	0.212963
$913$	4.49174	0.148655
$914$	39.4399	1.30456
$915$	57.8053	1.91098
$916$	38.1628	1.26094
$917$	−44.6045	−1.47297
$918$	−2.02903	−0.0669678
$919$	−14.7142	−0.485376	−0.242688	−	0.970104i	$-0.578029\pi$
$919$	−14.7142	−0.485376	−0.242688	+	0.970104i	$0.578029\pi$
$920$	2.56849	0.0846805
$921$	−5.50105	−0.181266
$922$	−32.4583	−1.06896
$923$	−20.2615	−0.666914
$924$	15.9778	0.525631
$925$	146.248	4.80859
$926$	55.7557	1.83225
$927$	−4.23429	−0.139072
$928$	−24.0409	−0.789180
$929$	29.2848	0.960804	0.480402	−	0.877048i	$-0.340491\pi$
$929$	29.2848	0.960804	0.480402	+	0.877048i	$0.340491\pi$
$930$	1.81827	0.0596235
$931$	−3.86492	−0.126668
$932$	8.58469	0.281201
$933$	−19.5463	−0.639918
$934$	69.2737	2.26670
$935$	−10.7609	−0.351918
$936$	0.672908	0.0219947
$937$	50.2976	1.64315	0.821576	−	0.570099i	$-0.193095\pi$
$937$	50.2976	1.64315	0.821576	+	0.570099i	$0.193095\pi$
$938$	−24.3975	−0.796605
$939$	16.6493	0.543330
$940$	−14.3574	−0.468286
$941$	−54.1344	−1.76473	−0.882365	−	0.470566i	$-0.844050\pi$
$941$	−54.1344	−1.76473	−0.882365	+	0.470566i	$0.844050\pi$
$942$	−2.02903	−0.0661092
$943$	−11.3961	−0.371107
$944$	43.3673	1.41149
$945$	−13.1952	−0.429241
$946$	54.0059	1.75588
$947$	−38.6745	−1.25675	−0.628377	−	0.777909i	$-0.716280\pi$
$947$	−38.6745	−1.25675	−0.628377	+	0.777909i	$0.716280\pi$
$948$	−7.81304	−0.253756
$949$	29.6660	0.963001
$950$	48.0354	1.55848
$951$	−1.84809	−0.0599283
$952$	0.721856	0.0233955
$953$	20.8108	0.674128	0.337064	−	0.941482i	$-0.390566\pi$
$953$	20.8108	0.674128	0.337064	+	0.941482i	$0.390566\pi$
$954$	6.76144	0.218910
$955$	52.3167	1.69293
$956$	−41.8853	−1.35467
$957$	7.37410	0.238371
$958$	−51.5398	−1.66517
$959$	53.1484	1.71625
$960$	−38.6314	−1.24682
$961$	−30.9573	−0.998623
$962$	60.9234	1.96425
$963$	−1.84744	−0.0595331
$964$	38.0256	1.22472
$965$	−79.4159	−2.55649
$966$	−15.4051	−0.495650
$967$	22.1259	0.711520	0.355760	−	0.934577i	$-0.384222\pi$
$967$	22.1259	0.711520	0.355760	+	0.934577i	$0.384222\pi$
$968$	1.14959	0.0369493
$969$	−1.71391	−0.0550587
$970$	−85.7893	−2.75453
$971$	36.4603	1.17007	0.585033	−	0.811009i	$-0.301081\pi$
$971$	36.4603	1.17007	0.585033	+	0.811009i	$0.301081\pi$
$972$	2.11694	0.0679010
$973$	37.4748	1.20139
$974$	−73.8819	−2.36733
$975$	−39.1724	−1.25452
$976$	−50.0095	−1.60077
$977$	31.2840	1.00086	0.500432	−	0.865776i	$-0.333175\pi$
$977$	31.2840	1.00086	0.500432	+	0.865776i	$0.333175\pi$
$978$	−27.4001	−0.876160
$979$	−41.3431	−1.32133
$980$	20.7057	0.661419
$981$	17.9716	0.573789
$982$	−44.7183	−1.42702
$983$	−35.9301	−1.14599	−0.572996	−	0.819558i	$-0.694219\pi$
$983$	−35.9301	−1.14599	−0.572996	+	0.819558i	$0.694219\pi$
$984$	−1.08350	−0.0345407
$985$	4.12068	0.131296
$986$	6.03084	0.192061
$987$	4.75692	0.151415
$988$	10.2894	0.327351
$989$	−26.7746	−0.851382
$990$	21.8341	0.693932
$991$	−8.39164	−0.266569	−0.133285	−	0.991078i	$-0.542552\pi$
$991$	−8.39164	−0.266569	−0.133285	+	0.991078i	$0.542552\pi$
$992$	−1.67110	−0.0530576
$993$	−2.38003	−0.0755281
$994$	44.1014	1.39881
$995$	50.4276	1.59866
$996$	−3.83271	−0.121444
$997$	25.7281	0.814818	0.407409	−	0.913246i	$-0.366432\pi$
$997$	25.7281	0.814818	0.407409	+	0.913246i	$0.366432\pi$
$998$	−62.3640	−1.97410
$999$	10.5877	0.334981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.11	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.11	✓	63	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)

\(f(q)\)	\(=\)	\(q-2.02903 q^{2} +1.00000 q^{3} +2.11694 q^{4} +4.33739 q^{5} -2.02903 q^{6} -3.04221 q^{7} -0.237280 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.02903 q^{2} +1.00000 q^{3} +2.11694 q^{4} +4.33739 q^{5} -2.02903 q^{6} -3.04221 q^{7} -0.237280 q^{8} +1.00000 q^{9} -8.80067 q^{10} -2.48095 q^{11} +2.11694 q^{12} -2.83592 q^{13} +6.17272 q^{14} +4.33739 q^{15} -3.75244 q^{16} +1.00000 q^{17} -2.02903 q^{18} -1.71391 q^{19} +9.18200 q^{20} -3.04221 q^{21} +5.03392 q^{22} -2.49567 q^{23} -0.237280 q^{24} +13.8129 q^{25} +5.75416 q^{26} +1.00000 q^{27} -6.44018 q^{28} -2.97228 q^{29} -8.80067 q^{30} -0.206606 q^{31} +8.08835 q^{32} -2.48095 q^{33} -2.02903 q^{34} -13.1952 q^{35} +2.11694 q^{36} +10.5877 q^{37} +3.47757 q^{38} -2.83592 q^{39} -1.02918 q^{40} +4.56632 q^{41} +6.17272 q^{42} +10.7284 q^{43} -5.25204 q^{44} +4.33739 q^{45} +5.06378 q^{46} -1.56364 q^{47} -3.75244 q^{48} +2.25503 q^{49} -28.0268 q^{50} +1.00000 q^{51} -6.00349 q^{52} -3.33236 q^{53} -2.02903 q^{54} -10.7609 q^{55} +0.721856 q^{56} -1.71391 q^{57} +6.03084 q^{58} -11.5571 q^{59} +9.18200 q^{60} +13.3272 q^{61} +0.419209 q^{62} -3.04221 q^{63} -8.90659 q^{64} -12.3005 q^{65} +5.03392 q^{66} -3.95247 q^{67} +2.11694 q^{68} -2.49567 q^{69} +26.7735 q^{70} +7.14457 q^{71} -0.237280 q^{72} -10.4608 q^{73} -21.4828 q^{74} +13.8129 q^{75} -3.62825 q^{76} +7.54758 q^{77} +5.75416 q^{78} -3.69072 q^{79} -16.2758 q^{80} +1.00000 q^{81} -9.26519 q^{82} -1.81049 q^{83} -6.44018 q^{84} +4.33739 q^{85} -21.7682 q^{86} -2.97228 q^{87} +0.588681 q^{88} +16.6642 q^{89} -8.80067 q^{90} +8.62747 q^{91} -5.28320 q^{92} -0.206606 q^{93} +3.17267 q^{94} -7.43390 q^{95} +8.08835 q^{96} +9.74805 q^{97} -4.57551 q^{98} -2.48095 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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