LMFDB - Embedded newform 671.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.08860 q^{2} +3.36235 q^{3} +2.36225 q^{4} -0.0546248 q^{5} +7.02260 q^{6} -2.53368 q^{7} +0.756597 q^{8} +8.30537 q^{9} +O(q^{10})$	\(q+2.08860 q^{2} +3.36235 q^{3} +2.36225 q^{4} -0.0546248 q^{5} +7.02260 q^{6} -2.53368 q^{7} +0.756597 q^{8} +8.30537 q^{9} -0.114089 q^{10} -1.00000 q^{11} +7.94270 q^{12} -5.23032 q^{13} -5.29184 q^{14} -0.183667 q^{15} -3.14427 q^{16} -1.86520 q^{17} +17.3466 q^{18} +5.90415 q^{19} -0.129037 q^{20} -8.51909 q^{21} -2.08860 q^{22} -3.02455 q^{23} +2.54394 q^{24} -4.99702 q^{25} -10.9241 q^{26} +17.8385 q^{27} -5.98518 q^{28} -5.01122 q^{29} -0.383608 q^{30} +10.9903 q^{31} -8.08032 q^{32} -3.36235 q^{33} -3.89566 q^{34} +0.138402 q^{35} +19.6194 q^{36} -6.62481 q^{37} +12.3314 q^{38} -17.5862 q^{39} -0.0413289 q^{40} +6.90471 q^{41} -17.7930 q^{42} +8.34046 q^{43} -2.36225 q^{44} -0.453679 q^{45} -6.31708 q^{46} +7.83501 q^{47} -10.5721 q^{48} -0.580488 q^{49} -10.4368 q^{50} -6.27145 q^{51} -12.3553 q^{52} +13.1653 q^{53} +37.2575 q^{54} +0.0546248 q^{55} -1.91697 q^{56} +19.8518 q^{57} -10.4664 q^{58} -7.54879 q^{59} -0.433869 q^{60} +1.00000 q^{61} +22.9543 q^{62} -21.0431 q^{63} -10.5880 q^{64} +0.285705 q^{65} -7.02260 q^{66} +1.62570 q^{67} -4.40607 q^{68} -10.1696 q^{69} +0.289065 q^{70} -7.43556 q^{71} +6.28382 q^{72} -11.4445 q^{73} -13.8366 q^{74} -16.8017 q^{75} +13.9471 q^{76} +2.53368 q^{77} -36.7305 q^{78} -8.45057 q^{79} +0.171755 q^{80} +35.0631 q^{81} +14.4212 q^{82} +0.244004 q^{83} -20.1242 q^{84} +0.101886 q^{85} +17.4199 q^{86} -16.8495 q^{87} -0.756597 q^{88} +5.48780 q^{89} -0.947555 q^{90} +13.2519 q^{91} -7.14475 q^{92} +36.9530 q^{93} +16.3642 q^{94} -0.322513 q^{95} -27.1688 q^{96} -1.77860 q^{97} -1.21241 q^{98} -8.30537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * 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 $

$2$	2.08860	1.47686	0.738432	−	0.674328i	$-0.235567\pi$
$2$	2.08860	1.47686	0.738432	+	0.674328i	$0.235567\pi$
$3$	3.36235	1.94125	0.970626	−	0.240595i	$-0.0773424\pi$
$3$	3.36235	1.94125	0.970626	+	0.240595i	$0.0773424\pi$
$4$	2.36225	1.18113
$5$	−0.0546248	−0.0244290	−0.0122145	−	0.999925i	$-0.503888\pi$
$5$	−0.0546248	−0.0244290	−0.0122145	+	0.999925i	$0.503888\pi$
$6$	7.02260	2.86696
$7$	−2.53368	−0.957639	−0.478820	−	0.877913i	$-0.658935\pi$
$7$	−2.53368	−0.957639	−0.478820	+	0.877913i	$0.658935\pi$
$8$	0.756597	0.267497
$9$	8.30537	2.76846
$10$	−0.114089	−0.0360782
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	7.94270	2.29286
$13$	−5.23032	−1.45063	−0.725315	−	0.688417i	$-0.758306\pi$
$13$	−5.23032	−1.45063	−0.725315	+	0.688417i	$0.758306\pi$
$14$	−5.29184	−1.41430
$15$	−0.183667	−0.0474227
$16$	−3.14427	−0.786068
$17$	−1.86520	−0.452377	−0.226189	−	0.974084i	$-0.572627\pi$
$17$	−1.86520	−0.452377	−0.226189	+	0.974084i	$0.572627\pi$
$18$	17.3466	4.08863
$19$	5.90415	1.35450	0.677252	−	0.735751i	$-0.263171\pi$
$19$	5.90415	1.35450	0.677252	+	0.735751i	$0.263171\pi$
$20$	−0.129037	−0.0288537
$21$	−8.51909	−1.85902
$22$	−2.08860	−0.445291
$23$	−3.02455	−0.630663	−0.315331	−	0.948982i	$-0.602116\pi$
$23$	−3.02455	−0.630663	−0.315331	+	0.948982i	$0.602116\pi$
$24$	2.54394	0.519280
$25$	−4.99702	−0.999403
$26$	−10.9241	−2.14238
$27$	17.8385	3.43302
$28$	−5.98518	−1.13109
$29$	−5.01122	−0.930560	−0.465280	−	0.885163i	$-0.654046\pi$
$29$	−5.01122	−0.930560	−0.465280	+	0.885163i	$0.654046\pi$
$30$	−0.383608	−0.0700369
$31$	10.9903	1.97391	0.986954	−	0.161001i	$-0.0514722\pi$
$31$	10.9903	1.97391	0.986954	+	0.161001i	$0.0514722\pi$
$32$	−8.08032	−1.42841
$33$	−3.36235	−0.585309
$34$	−3.89566	−0.668100
$35$	0.138402	0.0233941
$36$	19.6194	3.26989
$37$	−6.62481	−1.08911	−0.544556	−	0.838725i	$-0.683302\pi$
$37$	−6.62481	−1.08911	−0.544556	+	0.838725i	$0.683302\pi$
$38$	12.3314	2.00042
$39$	−17.5862	−2.81604
$40$	−0.0413289	−0.00653468
$41$	6.90471	1.07833	0.539167	−	0.842199i	$-0.318739\pi$
$41$	6.90471	1.07833	0.539167	+	0.842199i	$0.318739\pi$
$42$	−17.7930	−2.74552
$43$	8.34046	1.27191	0.635954	−	0.771727i	$-0.280607\pi$
$43$	8.34046	1.27191	0.635954	+	0.771727i	$0.280607\pi$
$44$	−2.36225	−0.356123
$45$	−0.453679	−0.0676305
$46$	−6.31708	−0.931403
$47$	7.83501	1.14285	0.571427	−	0.820653i	$-0.306390\pi$
$47$	7.83501	1.14285	0.571427	+	0.820653i	$0.306390\pi$
$48$	−10.5721	−1.52596
$49$	−0.580488	−0.0829269
$50$	−10.4368	−1.47598
$51$	−6.27145	−0.878178
$52$	−12.3553	−1.71338
$53$	13.1653	1.80840	0.904199	−	0.427112i	$-0.140469\pi$
$53$	13.1653	1.80840	0.904199	+	0.427112i	$0.140469\pi$
$54$	37.2575	5.07010
$55$	0.0546248	0.00736561
$56$	−1.91697	−0.256166
$57$	19.8518	2.62943
$58$	−10.4664	−1.37431
$59$	−7.54879	−0.982768	−0.491384	−	0.870943i	$-0.663509\pi$
$59$	−7.54879	−0.982768	−0.491384	+	0.870943i	$0.663509\pi$
$60$	−0.433869	−0.0560122
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	22.9543	2.91519
$63$	−21.0431	−2.65118
$64$	−10.5880	−1.32350
$65$	0.285705	0.0354374
$66$	−7.02260	−0.864422
$67$	1.62570	0.198611	0.0993053	−	0.995057i	$-0.468338\pi$
$67$	1.62570	0.198611	0.0993053	+	0.995057i	$0.468338\pi$
$68$	−4.40607	−0.534314
$69$	−10.1696	−1.22427
$70$	0.289065	0.0345499
$71$	−7.43556	−0.882439	−0.441220	−	0.897399i	$-0.645454\pi$
$71$	−7.43556	−0.882439	−0.441220	+	0.897399i	$0.645454\pi$
$72$	6.28382	0.740555
$73$	−11.4445	−1.33948	−0.669738	−	0.742598i	$-0.733594\pi$
$73$	−11.4445	−1.33948	−0.669738	+	0.742598i	$0.733594\pi$
$74$	−13.8366	−1.60847
$75$	−16.8017	−1.94009
$76$	13.9471	1.59984
$77$	2.53368	0.288739
$78$	−36.7305	−4.15891
$79$	−8.45057	−0.950764	−0.475382	−	0.879780i	$-0.657690\pi$
$79$	−8.45057	−0.950764	−0.475382	+	0.879780i	$0.657690\pi$
$80$	0.171755	0.0192028
$81$	35.0631	3.89590
$82$	14.4212	1.59255
$83$	0.244004	0.0267829	0.0133914	−	0.999910i	$-0.495737\pi$
$83$	0.244004	0.0267829	0.0133914	+	0.999910i	$0.495737\pi$
$84$	−20.1242	−2.19573
$85$	0.101886	0.0110511
$86$	17.4199	1.87844
$87$	−16.8495	−1.80645
$88$	−0.756597	−0.0806535
$89$	5.48780	0.581705	0.290853	−	0.956768i	$-0.406061\pi$
$89$	5.48780	0.581705	0.290853	+	0.956768i	$0.406061\pi$
$90$	−0.947555	−0.0998810
$91$	13.2519	1.38918
$92$	−7.14475	−0.744892
$93$	36.9530	3.83185
$94$	16.3642	1.68784
$95$	−0.322513	−0.0330891
$96$	−27.1688	−2.77291
$97$	−1.77860	−0.180589	−0.0902946	−	0.995915i	$-0.528781\pi$
$97$	−1.77860	−0.180589	−0.0902946	+	0.995915i	$0.528781\pi$
$98$	−1.21241	−0.122472
$99$	−8.30537	−0.834721
$100$	−11.8042	−1.18042
$101$	−5.10624	−0.508090	−0.254045	−	0.967192i	$-0.581761\pi$
$101$	−5.10624	−0.508090	−0.254045	+	0.967192i	$0.581761\pi$
$102$	−13.0985	−1.29695
$103$	15.1942	1.49713	0.748566	−	0.663060i	$-0.230743\pi$
$103$	15.1942	1.49713	0.748566	+	0.663060i	$0.230743\pi$
$104$	−3.95725	−0.388040
$105$	0.465354	0.0454139
$106$	27.4971	2.67076
$107$	3.18945	0.308336	0.154168	−	0.988045i	$-0.450730\pi$
$107$	3.18945	0.308336	0.154168	+	0.988045i	$0.450730\pi$
$108$	42.1390	4.05483
$109$	2.09373	0.200543	0.100272	−	0.994960i	$-0.468029\pi$
$109$	2.09373	0.200543	0.100272	+	0.994960i	$0.468029\pi$
$110$	0.114089	0.0108780
$111$	−22.2749	−2.11424
$112$	7.96657	0.752770
$113$	4.46037	0.419596	0.209798	−	0.977745i	$-0.432719\pi$
$113$	4.46037	0.419596	0.209798	+	0.977745i	$0.432719\pi$
$114$	41.4625	3.88332
$115$	0.165216	0.0154064
$116$	−11.8378	−1.09911
$117$	−43.4398	−4.01601
$118$	−15.7664	−1.45141
$119$	4.72581	0.433214
$120$	−0.138962	−0.0126855
$121$	1.00000	0.0909091
$122$	2.08860	0.189093
$123$	23.2160	2.09332
$124$	25.9617	2.33143
$125$	0.546085	0.0488433
$126$	−43.9507	−3.91544
$127$	−4.90153	−0.434941	−0.217470	−	0.976067i	$-0.569781\pi$
$127$	−4.90153	−0.434941	−0.217470	+	0.976067i	$0.569781\pi$
$128$	−5.95349	−0.526219
$129$	28.0435	2.46909
$130$	0.596724	0.0523362
$131$	−5.39573	−0.471427	−0.235714	−	0.971823i	$-0.575743\pi$
$131$	−5.39573	−0.471427	−0.235714	+	0.971823i	$0.575743\pi$
$132$	−7.94270	−0.691324
$133$	−14.9592	−1.29713
$134$	3.39543	0.293321
$135$	−0.974424	−0.0838651
$136$	−1.41120	−0.121010
$137$	4.95504	0.423337	0.211669	−	0.977341i	$-0.432110\pi$
$137$	4.95504	0.423337	0.211669	+	0.977341i	$0.432110\pi$
$138$	−21.2402	−1.80809
$139$	10.7376	0.910749	0.455374	−	0.890300i	$-0.349505\pi$
$139$	10.7376	0.910749	0.455374	+	0.890300i	$0.349505\pi$
$140$	0.326939	0.0276314
$141$	26.3440	2.21857
$142$	−15.5299	−1.30324
$143$	5.23032	0.437382
$144$	−26.1144	−2.17620
$145$	0.273737	0.0227326
$146$	−23.9030	−1.97822
$147$	−1.95180	−0.160982
$148$	−15.6495	−1.28638
$149$	4.46537	0.365817	0.182909	−	0.983130i	$-0.441449\pi$
$149$	4.46537	0.365817	0.182909	+	0.983130i	$0.441449\pi$
$150$	−35.0920	−2.86525
$151$	−3.16784	−0.257795	−0.128898	−	0.991658i	$-0.541144\pi$
$151$	−3.16784	−0.257795	−0.128898	+	0.991658i	$0.541144\pi$
$152$	4.46706	0.362326
$153$	−15.4912	−1.25239
$154$	5.29184	0.426428
$155$	−0.600341	−0.0482205
$156$	−41.5429	−3.32610
$157$	−8.29886	−0.662321	−0.331160	−	0.943574i	$-0.607440\pi$
$157$	−8.29886	−0.662321	−0.331160	+	0.943574i	$0.607440\pi$
$158$	−17.6499	−1.40415
$159$	44.2664	3.51055
$160$	0.441386	0.0348946
$161$	7.66323	0.603947
$162$	73.2327	5.75371
$163$	−10.4955	−0.822075	−0.411037	−	0.911618i	$-0.634833\pi$
$163$	−10.4955	−0.822075	−0.411037	+	0.911618i	$0.634833\pi$
$164$	16.3107	1.27365
$165$	0.183667	0.0142985
$166$	0.509626	0.0395547
$167$	−14.8113	−1.14613	−0.573066	−	0.819509i	$-0.694246\pi$
$167$	−14.8113	−1.14613	−0.573066	+	0.819509i	$0.694246\pi$
$168$	−6.44552	−0.497282
$169$	14.3563	1.10433
$170$	0.212799	0.0163210
$171$	49.0362	3.74989
$172$	19.7023	1.50228
$173$	−18.7388	−1.42469	−0.712343	−	0.701832i	$-0.752366\pi$
$173$	−18.7388	−1.42469	−0.712343	+	0.701832i	$0.752366\pi$
$174$	−35.1918	−2.66788
$175$	12.6608	0.957068
$176$	3.14427	0.237009
$177$	−25.3816	−1.90780
$178$	11.4618	0.859099
$179$	5.36434	0.400950	0.200475	−	0.979699i	$-0.435751\pi$
$179$	5.36434	0.400950	0.200475	+	0.979699i	$0.435751\pi$
$180$	−1.07170	−0.0798801
$181$	−12.9516	−0.962685	−0.481343	−	0.876533i	$-0.659851\pi$
$181$	−12.9516	−0.962685	−0.481343	+	0.876533i	$0.659851\pi$
$182$	27.6780	2.05163
$183$	3.36235	0.248552
$184$	−2.28837	−0.168701
$185$	0.361879	0.0266059
$186$	77.1801	5.65912
$187$	1.86520	0.136397
$188$	18.5083	1.34985
$189$	−45.1970	−3.28759
$190$	−0.673601	−0.0488681
$191$	−8.27195	−0.598537	−0.299269	−	0.954169i	$-0.596743\pi$
$191$	−8.27195	−0.598537	−0.299269	+	0.954169i	$0.596743\pi$
$192$	−35.6006	−2.56925
$193$	24.7486	1.78144	0.890721	−	0.454551i	$-0.150200\pi$
$193$	24.7486	1.78144	0.890721	+	0.454551i	$0.150200\pi$
$194$	−3.71478	−0.266706
$195$	0.960641	0.0687929
$196$	−1.37126	−0.0979470
$197$	−0.0247262	−0.00176167	−0.000880834	−	1.00000i	$-0.500280\pi$
$197$	−0.0247262	−0.00176167	−0.000880834		1.00000i	$0.500280\pi$
$198$	−17.3466	−1.23277
$199$	8.90683	0.631389	0.315694	−	0.948861i	$-0.397763\pi$
$199$	8.90683	0.631389	0.315694	+	0.948861i	$0.397763\pi$
$200$	−3.78073	−0.267338
$201$	5.46616	0.385553
$202$	−10.6649	−0.750379
$203$	12.6968	0.891141
$204$	−14.8147	−1.03724
$205$	−0.377168	−0.0263426
$206$	31.7347	2.21106
$207$	−25.1200	−1.74596
$208$	16.4456	1.14030
$209$	−5.90415	−0.408399
$210$	0.971938	0.0670701
$211$	−0.531492	−0.0365894	−0.0182947	−	0.999833i	$-0.505824\pi$
$211$	−0.531492	−0.0365894	−0.0182947	+	0.999833i	$0.505824\pi$
$212$	31.0998	2.13594
$213$	−25.0009	−1.71304
$214$	6.66149	0.455370
$215$	−0.455596	−0.0310714
$216$	13.4965	0.918323
$217$	−27.8457	−1.89029
$218$	4.37297	0.296175
$219$	−38.4803	−2.60026
$220$	0.129037	0.00869970
$221$	9.75560	0.656233
$222$	−46.5234	−3.12244
$223$	−21.8811	−1.46527	−0.732633	−	0.680624i	$-0.761709\pi$
$223$	−21.8811	−1.46527	−0.732633	+	0.680624i	$0.761709\pi$
$224$	20.4729	1.36790
$225$	−41.5021	−2.76680
$226$	9.31593	0.619686
$227$	−13.6230	−0.904189	−0.452095	−	0.891970i	$-0.649323\pi$
$227$	−13.6230	−0.904189	−0.452095	+	0.891970i	$0.649323\pi$
$228$	46.8949	3.10569
$229$	8.45925	0.559003	0.279501	−	0.960145i	$-0.409831\pi$
$229$	8.45925	0.559003	0.279501	+	0.960145i	$0.409831\pi$
$230$	0.345069	0.0227532
$231$	8.51909	0.560515
$232$	−3.79147	−0.248922
$233$	−23.0355	−1.50910	−0.754552	−	0.656240i	$-0.772146\pi$
$233$	−23.0355	−1.50910	−0.754552	+	0.656240i	$0.772146\pi$
$234$	−90.7283	−5.93110
$235$	−0.427986	−0.0279187
$236$	−17.8321	−1.16077
$237$	−28.4137	−1.84567
$238$	9.87033	0.639798
$239$	2.20539	0.142655	0.0713276	−	0.997453i	$-0.477276\pi$
$239$	2.20539	0.142655	0.0713276	+	0.997453i	$0.477276\pi$
$240$	0.577501	0.0372775
$241$	21.7875	1.40345	0.701727	−	0.712446i	$-0.252413\pi$
$241$	21.7875	1.40345	0.701727	+	0.712446i	$0.252413\pi$
$242$	2.08860	0.134260
$243$	64.3787	4.12990
$244$	2.36225	0.151228
$245$	0.0317090	0.00202582
$246$	48.4890	3.09155
$247$	−30.8806	−1.96489
$248$	8.31519	0.528015
$249$	0.820425	0.0519923
$250$	1.14055	0.0721349
$251$	−25.2079	−1.59111	−0.795555	−	0.605881i	$-0.792821\pi$
$251$	−25.2079	−1.59111	−0.795555	+	0.605881i	$0.792821\pi$
$252$	−49.7091	−3.13138
$253$	3.02455	0.190152
$254$	−10.2373	−0.642348
$255$	0.342577	0.0214530
$256$	8.74158	0.546349
$257$	−8.00087	−0.499081	−0.249540	−	0.968364i	$-0.580280\pi$
$257$	−8.00087	−0.499081	−0.249540	+	0.968364i	$0.580280\pi$
$258$	58.5717	3.64652
$259$	16.7851	1.04298
$260$	0.674908	0.0418560
$261$	−41.6200	−2.57622
$262$	−11.2695	−0.696234
$263$	11.9903	0.739351	0.369676	−	0.929161i	$-0.379469\pi$
$263$	11.9903	0.739351	0.369676	+	0.929161i	$0.379469\pi$
$264$	−2.54394	−0.156569
$265$	−0.719154	−0.0441773
$266$	−31.2438	−1.91568
$267$	18.4519	1.12924
$268$	3.84030	0.234584
$269$	26.1874	1.59667	0.798337	−	0.602211i	$-0.205714\pi$
$269$	26.1874	1.59667	0.798337	+	0.602211i	$0.205714\pi$
$270$	−2.03518	−0.123857
$271$	3.76377	0.228633	0.114316	−	0.993444i	$-0.463532\pi$
$271$	3.76377	0.228633	0.114316	+	0.993444i	$0.463532\pi$
$272$	5.86470	0.355600
$273$	44.5576	2.69675
$274$	10.3491	0.625211
$275$	4.99702	0.301331
$276$	−24.0231	−1.44602
$277$	2.45926	0.147762	0.0738812	−	0.997267i	$-0.476461\pi$
$277$	2.45926	0.147762	0.0738812	+	0.997267i	$0.476461\pi$
$278$	22.4265	1.34505
$279$	91.2782	5.46468
$280$	0.104714	0.00625787
$281$	15.2626	0.910490	0.455245	−	0.890366i	$-0.349552\pi$
$281$	15.2626	0.910490	0.455245	+	0.890366i	$0.349552\pi$
$282$	55.0221	3.27652
$283$	−2.86670	−0.170408	−0.0852038	−	0.996364i	$-0.527154\pi$
$283$	−2.86670	−0.170408	−0.0852038	+	0.996364i	$0.527154\pi$
$284$	−17.5647	−1.04227
$285$	−1.08440	−0.0642343
$286$	10.9241	0.645953
$287$	−17.4943	−1.03266
$288$	−67.1101	−3.95450
$289$	−13.5210	−0.795355
$290$	0.571727	0.0335730
$291$	−5.98026	−0.350569
$292$	−27.0347	−1.58209
$293$	−9.90006	−0.578367	−0.289184	−	0.957274i	$-0.593384\pi$
$293$	−9.90006	−0.578367	−0.289184	+	0.957274i	$0.593384\pi$
$294$	−4.07653	−0.237748
$295$	0.412351	0.0240080
$296$	−5.01231	−0.291334
$297$	−17.8385	−1.03509
$298$	9.32637	0.540262
$299$	15.8194	0.914859
$300$	−39.6898	−2.29149
$301$	−21.1320	−1.21803
$302$	−6.61636	−0.380729
$303$	−17.1689	−0.986330
$304$	−18.5643	−1.06473
$305$	−0.0546248	−0.00312781
$306$	−32.3549	−1.84961
$307$	−0.444317	−0.0253585	−0.0126793	−	0.999920i	$-0.504036\pi$
$307$	−0.444317	−0.0253585	−0.0126793	+	0.999920i	$0.504036\pi$
$308$	5.98518	0.341037
$309$	51.0883	2.90631
$310$	−1.25387	−0.0712151
$311$	11.3854	0.645605	0.322803	−	0.946466i	$-0.395375\pi$
$311$	11.3854	0.645605	0.322803	+	0.946466i	$0.395375\pi$
$312$	−13.3056	−0.753283
$313$	−1.13437	−0.0641185	−0.0320592	−	0.999486i	$-0.510207\pi$
$313$	−1.13437	−0.0641185	−0.0320592	+	0.999486i	$0.510207\pi$
$314$	−17.3330	−0.978158
$315$	1.14948	0.0647656
$316$	−19.9624	−1.12297
$317$	−5.78668	−0.325013	−0.162506	−	0.986708i	$-0.551958\pi$
$317$	−5.78668	−0.325013	−0.162506	+	0.986708i	$0.551958\pi$
$318$	92.4548	5.18461
$319$	5.01122	0.280575
$320$	0.578368	0.0323318
$321$	10.7240	0.598557
$322$	16.0054	0.891948
$323$	−11.0124	−0.612747
$324$	82.8278	4.60154
$325$	26.1360	1.44977
$326$	−21.9210	−1.21409
$327$	7.03986	0.389305
$328$	5.22408	0.288452
$329$	−19.8514	−1.09444
$330$	0.383608	0.0211169
$331$	−17.4742	−0.960467	−0.480234	−	0.877141i	$-0.659448\pi$
$331$	−17.4742	−0.960467	−0.480234	+	0.877141i	$0.659448\pi$
$332$	0.576398	0.0316339
$333$	−55.0215	−3.01516
$334$	−30.9349	−1.69268
$335$	−0.0888034	−0.00485185
$336$	26.7864	1.46132
$337$	4.76655	0.259651	0.129825	−	0.991537i	$-0.458558\pi$
$337$	4.76655	0.259651	0.129825	+	0.991537i	$0.458558\pi$
$338$	29.9846	1.63094
$339$	14.9973	0.814542
$340$	0.240681	0.0130527
$341$	−10.9903	−0.595156
$342$	102.417	5.53807
$343$	19.2065	1.03705
$344$	6.31037	0.340232
$345$	0.555512	0.0299078
$346$	−39.1379	−2.10407
$347$	−15.2910	−0.820863	−0.410432	−	0.911891i	$-0.634622\pi$
$347$	−15.2910	−0.820863	−0.410432	+	0.911891i	$0.634622\pi$
$348$	−39.8026	−2.13365
$349$	12.6745	0.678451	0.339225	−	0.940705i	$-0.389835\pi$
$349$	12.6745	0.678451	0.339225	+	0.940705i	$0.389835\pi$
$350$	26.4434	1.41346
$351$	−93.3011	−4.98004
$352$	8.08032	0.430683
$353$	5.01209	0.266767	0.133383	−	0.991065i	$-0.457416\pi$
$353$	5.01209	0.266767	0.133383	+	0.991065i	$0.457416\pi$
$354$	−53.0121	−2.81756
$355$	0.406166	0.0215571
$356$	12.9636	0.687067
$357$	15.8898	0.840978
$358$	11.2040	0.592148
$359$	3.32119	0.175286	0.0876428	−	0.996152i	$-0.472067\pi$
$359$	3.32119	0.175286	0.0876428	+	0.996152i	$0.472067\pi$
$360$	−0.343252	−0.0180910
$361$	15.8590	0.834683
$362$	−27.0507	−1.42175
$363$	3.36235	0.176477
$364$	31.3044	1.64080
$365$	0.625153	0.0327220
$366$	7.02260	0.367077
$367$	−22.2924	−1.16366	−0.581828	−	0.813312i	$-0.697662\pi$
$367$	−22.2924	−1.16366	−0.581828	+	0.813312i	$0.697662\pi$
$368$	9.51002	0.495744
$369$	57.3462	2.98532
$370$	0.755820	0.0392932
$371$	−33.3567	−1.73179
$372$	87.2924	4.52590
$373$	35.5737	1.84194	0.920968	−	0.389638i	$-0.127400\pi$
$373$	35.5737	1.84194	0.920968	+	0.389638i	$0.127400\pi$
$374$	3.89566	0.201440
$375$	1.83613	0.0948172
$376$	5.92794	0.305710
$377$	26.2103	1.34990
$378$	−94.3984	−4.85533
$379$	28.3631	1.45692	0.728458	−	0.685091i	$-0.240237\pi$
$379$	28.3631	1.45692	0.728458	+	0.685091i	$0.240237\pi$
$380$	−0.761857	−0.0390824
$381$	−16.4806	−0.844329
$382$	−17.2768	−0.883958
$383$	5.91089	0.302033	0.151016	−	0.988531i	$-0.451745\pi$
$383$	5.91089	0.302033	0.151016	+	0.988531i	$0.451745\pi$
$384$	−20.0177	−1.02152
$385$	−0.138402	−0.00705360
$386$	51.6899	2.63095
$387$	69.2706	3.52122
$388$	−4.20149	−0.213299
$389$	−14.8685	−0.753862	−0.376931	−	0.926241i	$-0.623021\pi$
$389$	−14.8685	−0.753862	−0.376931	+	0.926241i	$0.623021\pi$
$390$	2.00639	0.101598
$391$	5.64139	0.285298
$392$	−0.439195	−0.0221827
$393$	−18.1423	−0.915159
$394$	−0.0516431	−0.00260174
$395$	0.461611	0.0232262
$396$	−19.6194	−0.985910
$397$	36.2467	1.81917	0.909584	−	0.415521i	$-0.136401\pi$
$397$	36.2467	1.81917	0.909584	+	0.415521i	$0.136401\pi$
$398$	18.6028	0.932475
$399$	−50.2980	−2.51805
$400$	15.7120	0.785599
$401$	15.8574	0.791881	0.395941	−	0.918276i	$-0.370419\pi$
$401$	15.8574	0.791881	0.395941	+	0.918276i	$0.370419\pi$
$402$	11.4166	0.569409
$403$	−57.4826	−2.86341
$404$	−12.0622	−0.600118
$405$	−1.91531	−0.0951727
$406$	26.5186	1.31609
$407$	6.62481	0.328380
$408$	−4.74496	−0.234910
$409$	13.3784	0.661521	0.330761	−	0.943715i	$-0.392695\pi$
$409$	13.3784	0.661521	0.330761	+	0.943715i	$0.392695\pi$
$410$	−0.787754	−0.0389044
$411$	16.6605	0.821804
$412$	35.8926	1.76830
$413$	19.1262	0.941138
$414$	−52.4657	−2.57855
$415$	−0.0133287	−0.000654278 0
$416$	42.2627	2.07210
$417$	36.1034	1.76799
$418$	−12.3314	−0.603149
$419$	−26.9440	−1.31630	−0.658150	−	0.752887i	$-0.728661\pi$
$419$	−26.9440	−1.31630	−0.658150	+	0.752887i	$0.728661\pi$
$420$	1.09928	0.0536395
$421$	−21.4553	−1.04567	−0.522834	−	0.852434i	$-0.675125\pi$
$421$	−21.4553	−1.04567	−0.522834	+	0.852434i	$0.675125\pi$
$422$	−1.11007	−0.0540376
$423$	65.0727	3.16394
$424$	9.96085	0.483741
$425$	9.32043	0.452107
$426$	−52.2170	−2.52992
$427$	−2.53368	−0.122613
$428$	7.53428	0.364183
$429$	17.5862	0.849068
$430$	−0.951558	−0.0458882
$431$	13.1240	0.632159	0.316079	−	0.948733i	$-0.397633\pi$
$431$	13.1240	0.632159	0.316079	+	0.948733i	$0.397633\pi$
$432$	−56.0891	−2.69859
$433$	−16.1807	−0.777593	−0.388796	−	0.921324i	$-0.627109\pi$
$433$	−16.1807	−0.777593	−0.388796	+	0.921324i	$0.627109\pi$
$434$	−58.1586	−2.79170
$435$	0.920398	0.0441297
$436$	4.94592	0.236867
$437$	−17.8574	−0.854236
$438$	−80.3700	−3.84023
$439$	5.84007	0.278732	0.139366	−	0.990241i	$-0.455494\pi$
$439$	5.84007	0.278732	0.139366	+	0.990241i	$0.455494\pi$
$440$	0.0413289	0.00197028
$441$	−4.82117	−0.229579
$442$	20.3755	0.969166
$443$	8.30013	0.394351	0.197176	−	0.980368i	$-0.436823\pi$
$443$	8.30013	0.394351	0.197176	+	0.980368i	$0.436823\pi$
$444$	−52.6189	−2.49718
$445$	−0.299770	−0.0142105
$446$	−45.7008	−2.16400
$447$	15.0141	0.710143
$448$	26.8266	1.26744
$449$	−23.4866	−1.10840	−0.554200	−	0.832384i	$-0.686976\pi$
$449$	−23.4866	−1.10840	−0.554200	+	0.832384i	$0.686976\pi$
$450$	−86.6812	−4.08619
$451$	−6.90471	−0.325130
$452$	10.5365	0.495596
$453$	−10.6514	−0.500446
$454$	−28.4530	−1.33536
$455$	−0.723885	−0.0339362
$456$	15.0198	0.703367
$457$	−14.0256	−0.656092	−0.328046	−	0.944662i	$-0.606390\pi$
$457$	−14.0256	−0.656092	−0.328046	+	0.944662i	$0.606390\pi$
$458$	17.6680	0.825571
$459$	−33.2724	−1.55302
$460$	0.390281	0.0181969
$461$	−17.1938	−0.800796	−0.400398	−	0.916341i	$-0.631128\pi$
$461$	−17.1938	−0.800796	−0.400398	+	0.916341i	$0.631128\pi$
$462$	17.7930	0.827804
$463$	27.6210	1.28366	0.641829	−	0.766847i	$-0.278176\pi$
$463$	27.6210	1.28366	0.641829	+	0.766847i	$0.278176\pi$
$464$	15.7566	0.731484
$465$	−2.01855	−0.0936082
$466$	−48.1119	−2.22874
$467$	15.0201	0.695048	0.347524	−	0.937671i	$-0.387022\pi$
$467$	15.0201	0.695048	0.347524	+	0.937671i	$0.387022\pi$
$468$	−102.616	−4.74341
$469$	−4.11899	−0.190197
$470$	−0.893891	−0.0412321
$471$	−27.9036	−1.28573
$472$	−5.71139	−0.262888
$473$	−8.34046	−0.383495
$474$	−59.3450	−2.72580
$475$	−29.5031	−1.35370
$476$	11.1636	0.511680
$477$	109.343	5.00647
$478$	4.60619	0.210682
$479$	39.7319	1.81540	0.907698	−	0.419624i	$-0.137838\pi$
$479$	39.7319	1.81540	0.907698	+	0.419624i	$0.137838\pi$
$480$	1.48409	0.0677393
$481$	34.6499	1.57990
$482$	45.5053	2.07271
$483$	25.7664	1.17241
$484$	2.36225	0.107375
$485$	0.0971556	0.00441161
$486$	134.461	6.09929
$487$	23.0014	1.04229	0.521146	−	0.853468i	$-0.325505\pi$
$487$	23.0014	1.04229	0.521146	+	0.853468i	$0.325505\pi$
$488$	0.756597	0.0342495
$489$	−35.2897	−1.59585
$490$	0.0662275	0.00299185
$491$	−11.8174	−0.533310	−0.266655	−	0.963792i	$-0.585918\pi$
$491$	−11.8174	−0.533310	−0.266655	+	0.963792i	$0.585918\pi$
$492$	54.8421	2.47247
$493$	9.34693	0.420964
$494$	−64.4973	−2.90187
$495$	0.453679	0.0203914
$496$	−34.5564	−1.55163
$497$	18.8393	0.845059
$498$	1.71354	0.0767855
$499$	18.5206	0.829094	0.414547	−	0.910028i	$-0.363940\pi$
$499$	18.5206	0.829094	0.414547	+	0.910028i	$0.363940\pi$
$500$	1.28999	0.0576901
$501$	−49.8007	−2.22493
$502$	−52.6493	−2.34985
$503$	−21.1614	−0.943541	−0.471770	−	0.881721i	$-0.656385\pi$
$503$	−21.1614	−0.943541	−0.471770	+	0.881721i	$0.656385\pi$
$504$	−15.9212	−0.709184
$505$	0.278927	0.0124121
$506$	6.31708	0.280828
$507$	48.2708	2.14378
$508$	−11.5786	−0.513719
$509$	6.80161	0.301476	0.150738	−	0.988574i	$-0.451835\pi$
$509$	6.80161	0.301476	0.150738	+	0.988574i	$0.451835\pi$
$510$	0.715505	0.0316831
$511$	28.9966	1.28273
$512$	30.1646	1.33310
$513$	105.321	4.65004
$514$	−16.7106	−0.737074
$515$	−0.829982	−0.0365734
$516$	66.2458	2.91631
$517$	−7.83501	−0.344583
$518$	35.0574	1.54033
$519$	−63.0064	−2.76567
$520$	0.216164	0.00947941
$521$	−35.4533	−1.55324	−0.776618	−	0.629972i	$-0.783066\pi$
$521$	−35.4533	−1.55324	−0.776618	+	0.629972i	$0.783066\pi$
$522$	−86.9276	−3.80472
$523$	14.7539	0.645145	0.322572	−	0.946545i	$-0.395452\pi$
$523$	14.7539	0.645145	0.322572	+	0.946545i	$0.395452\pi$
$524$	−12.7461	−0.556815
$525$	42.5701	1.85791
$526$	25.0429	1.09192
$527$	−20.4990	−0.892952
$528$	10.5721	0.460093
$529$	−13.8521	−0.602265
$530$	−1.50202	−0.0652438
$531$	−62.6955	−2.72075
$532$	−35.3374	−1.53207
$533$	−36.1139	−1.56427
$534$	38.5386	1.66773
$535$	−0.174223	−0.00753232
$536$	1.23000	0.0531278
$537$	18.0368	0.778345
$538$	54.6950	2.35807
$539$	0.580488	0.0250034
$540$	−2.30183	−0.0990552
$541$	18.1801	0.781623	0.390811	−	0.920471i	$-0.372194\pi$
$541$	18.1801	0.781623	0.390811	+	0.920471i	$0.372194\pi$
$542$	7.86102	0.337660
$543$	−43.5478	−1.86881
$544$	15.0714	0.646182
$545$	−0.114370	−0.00489906
$546$	93.0631	3.98273
$547$	−29.2289	−1.24974	−0.624868	−	0.780730i	$-0.714847\pi$
$547$	−29.2289	−1.24974	−0.624868	+	0.780730i	$0.714847\pi$
$548$	11.7050	0.500015
$549$	8.30537	0.354465
$550$	10.4368	0.445025
$551$	−29.5870	−1.26045
$552$	−7.69428	−0.327490
$553$	21.4110	0.910489
$554$	5.13640	0.218225
$555$	1.21676	0.0516487
$556$	25.3648	1.07571
$557$	8.04926	0.341058	0.170529	−	0.985353i	$-0.445452\pi$
$557$	8.04926	0.341058	0.170529	+	0.985353i	$0.445452\pi$
$558$	190.644	8.07059
$559$	−43.6233	−1.84507
$560$	−0.435172	−0.0183894
$561$	6.27145	0.264781
$562$	31.8775	1.34467
$563$	−31.6260	−1.33288	−0.666439	−	0.745560i	$-0.732182\pi$
$563$	−31.6260	−1.33288	−0.666439	+	0.745560i	$0.732182\pi$
$564$	62.2312	2.62040
$565$	−0.243647	−0.0102503
$566$	−5.98739	−0.251669
$567$	−88.8385	−3.73086
$568$	−5.62572	−0.236050
$569$	11.5788	0.485409	0.242704	−	0.970100i	$-0.421965\pi$
$569$	11.5788	0.485409	0.242704	+	0.970100i	$0.421965\pi$
$570$	−2.26488	−0.0948653
$571$	37.3352	1.56243	0.781214	−	0.624263i	$-0.214601\pi$
$571$	37.3352	1.56243	0.781214	+	0.624263i	$0.214601\pi$
$572$	12.3553	0.516603
$573$	−27.8132	−1.16191
$574$	−36.5386	−1.52509
$575$	15.1137	0.630286
$576$	−87.9374	−3.66406
$577$	−34.5570	−1.43863	−0.719313	−	0.694686i	$-0.755543\pi$
$577$	−34.5570	−1.43863	−0.719313	+	0.694686i	$0.755543\pi$
$578$	−28.2400	−1.17463
$579$	83.2133	3.45823
$580$	0.646635	0.0268501
$581$	−0.618226	−0.0256483
$582$	−12.4904	−0.517743
$583$	−13.1653	−0.545252
$584$	−8.65886	−0.358306
$585$	2.37289	0.0981069
$586$	−20.6773	−0.854170
$587$	3.45220	0.142487	0.0712437	−	0.997459i	$-0.477303\pi$
$587$	3.45220	0.142487	0.0712437	+	0.997459i	$0.477303\pi$
$588$	−4.61065	−0.190140
$589$	64.8881	2.67367
$590$	0.861236	0.0354565
$591$	−0.0831380	−0.00341984
$592$	20.8302	0.856116
$593$	−26.9166	−1.10533	−0.552665	−	0.833403i	$-0.686389\pi$
$593$	−26.9166	−1.10533	−0.552665	+	0.833403i	$0.686389\pi$
$594$	−37.2575	−1.52869
$595$	−0.258147	−0.0105830
$596$	10.5483	0.432076
$597$	29.9479	1.22568
$598$	33.0404	1.35112
$599$	3.52190	0.143901	0.0719505	−	0.997408i	$-0.477078\pi$
$599$	3.52190	0.143901	0.0719505	+	0.997408i	$0.477078\pi$
$600$	−12.7121	−0.518970
$601$	39.0312	1.59211	0.796057	−	0.605222i	$-0.206915\pi$
$601$	39.0312	1.59211	0.796057	+	0.605222i	$0.206915\pi$
$602$	−44.1364	−1.79886
$603$	13.5020	0.549845
$604$	−7.48324	−0.304489
$605$	−0.0546248	−0.00222081
$606$	−35.8591	−1.45668
$607$	−40.6168	−1.64858	−0.824292	−	0.566165i	$-0.808427\pi$
$607$	−40.6168	−1.64858	−0.824292	+	0.566165i	$0.808427\pi$
$608$	−47.7074	−1.93479
$609$	42.6911	1.72993
$610$	−0.114089	−0.00461934
$611$	−40.9796	−1.65786
$612$	−36.5940	−1.47923
$613$	4.97412	0.200903	0.100451	−	0.994942i	$-0.467971\pi$
$613$	4.97412	0.200903	0.100451	+	0.994942i	$0.467971\pi$
$614$	−0.928001	−0.0374511
$615$	−1.26817	−0.0511376
$616$	1.91697	0.0772369
$617$	−30.5207	−1.22872	−0.614359	−	0.789027i	$-0.710585\pi$
$617$	−30.5207	−1.22872	−0.614359	+	0.789027i	$0.710585\pi$
$618$	106.703	4.29222
$619$	28.2162	1.13411	0.567053	−	0.823682i	$-0.308084\pi$
$619$	28.2162	1.13411	0.567053	+	0.823682i	$0.308084\pi$
$620$	−1.41816	−0.0569545
$621$	−53.9535	−2.16508
$622$	23.7795	0.953471
$623$	−13.9043	−0.557064
$624$	55.2957	2.21360
$625$	24.9553	0.998210
$626$	−2.36925	−0.0946942
$627$	−19.8518	−0.792804
$628$	−19.6040	−0.782284
$629$	12.3566	0.492690
$630$	2.40080	0.0956500
$631$	−8.36165	−0.332872	−0.166436	−	0.986052i	$-0.553226\pi$
$631$	−8.36165	−0.332872	−0.166436	+	0.986052i	$0.553226\pi$
$632$	−6.39367	−0.254327
$633$	−1.78706	−0.0710293
$634$	−12.0861	−0.479999
$635$	0.267745	0.0106251
$636$	104.568	4.14640
$637$	3.03614	0.120296
$638$	10.4664	0.414370
$639$	−61.7551	−2.44299
$640$	0.325208	0.0128550
$641$	−12.3242	−0.486778	−0.243389	−	0.969929i	$-0.578259\pi$
$641$	−12.3242	−0.486778	−0.243389	+	0.969929i	$0.578259\pi$
$642$	22.3982	0.883988
$643$	18.0223	0.710729	0.355364	−	0.934728i	$-0.384357\pi$
$643$	18.0223	0.710729	0.355364	+	0.934728i	$0.384357\pi$
$644$	18.1025	0.713338
$645$	−1.53187	−0.0603174
$646$	−23.0005	−0.904944
$647$	−43.9768	−1.72891	−0.864453	−	0.502714i	$-0.832335\pi$
$647$	−43.9768	−1.72891	−0.864453	+	0.502714i	$0.832335\pi$
$648$	26.5286	1.04214
$649$	7.54879	0.296316
$650$	54.5877	2.14111
$651$	−93.6270	−3.66953
$652$	−24.7931	−0.970973
$653$	−34.9267	−1.36679	−0.683393	−	0.730051i	$-0.739496\pi$
$653$	−34.9267	−1.36679	−0.683393	+	0.730051i	$0.739496\pi$
$654$	14.7034	0.574950
$655$	0.294741	0.0115165
$656$	−21.7103	−0.847645
$657$	−95.0507	−3.70828
$658$	−41.4616	−1.61634
$659$	−14.6263	−0.569761	−0.284880	−	0.958563i	$-0.591954\pi$
$659$	−14.6263	−0.569761	−0.284880	+	0.958563i	$0.591954\pi$
$660$	0.433869	0.0168883
$661$	17.8775	0.695353	0.347677	−	0.937614i	$-0.386971\pi$
$661$	17.8775	0.695353	0.347677	+	0.937614i	$0.386971\pi$
$662$	−36.4966	−1.41848
$663$	32.8017	1.27391
$664$	0.184612	0.00716435
$665$	0.817143	0.0316875
$666$	−114.918	−4.45298
$667$	15.1567	0.586870
$668$	−34.9880	−1.35373
$669$	−73.5718	−2.84445
$670$	−0.185475	−0.00716552
$671$	−1.00000	−0.0386046
$672$	68.8370	2.65545
$673$	22.9005	0.882748	0.441374	−	0.897323i	$-0.354491\pi$
$673$	22.9005	0.882748	0.441374	+	0.897323i	$0.354491\pi$
$674$	9.95542	0.383468
$675$	−89.1392	−3.43097
$676$	33.9132	1.30435
$677$	23.9875	0.921915	0.460957	−	0.887422i	$-0.347506\pi$
$677$	23.9875	0.921915	0.460957	+	0.887422i	$0.347506\pi$
$678$	31.3234	1.20297
$679$	4.50639	0.172939
$680$	0.0770867	0.00295614
$681$	−45.8052	−1.75526
$682$	−22.9543	−0.878964
$683$	−4.48000	−0.171422	−0.0857112	−	0.996320i	$-0.527316\pi$
$683$	−4.48000	−0.171422	−0.0857112	+	0.996320i	$0.527316\pi$
$684$	115.836	4.42909
$685$	−0.270668	−0.0103417
$686$	40.1147	1.53159
$687$	28.4429	1.08517
$688$	−26.2247	−0.999807
$689$	−68.8590	−2.62332
$690$	1.16024	0.0441697
$691$	−34.3696	−1.30748	−0.653741	−	0.756719i	$-0.726801\pi$
$691$	−34.3696	−1.30748	−0.653741	+	0.756719i	$0.726801\pi$
$692$	−44.2658	−1.68273
$693$	21.0431	0.799362
$694$	−31.9368	−1.21230
$695$	−0.586538	−0.0222486
$696$	−12.7482	−0.483221
$697$	−12.8787	−0.487814
$698$	26.4720	1.00198
$699$	−77.4532	−2.92955
$700$	29.9080	1.13042
$701$	4.09075	0.154505	0.0772527	−	0.997012i	$-0.475385\pi$
$701$	4.09075	0.154505	0.0772527	+	0.997012i	$0.475385\pi$
$702$	−194.869	−7.35484
$703$	−39.1139	−1.47521
$704$	10.5880	0.399051
$705$	−1.43904	−0.0541972
$706$	10.4683	0.393978
$707$	12.9376	0.486567
$708$	−59.9578	−2.25335
$709$	12.8748	0.483522	0.241761	−	0.970336i	$-0.422275\pi$
$709$	12.8748	0.483522	0.241761	+	0.970336i	$0.422275\pi$
$710$	0.848319	0.0318368
$711$	−70.1851	−2.63215
$712$	4.15205	0.155605
$713$	−33.2406	−1.24487
$714$	33.1875	1.24201
$715$	−0.285705	−0.0106848
$716$	12.6719	0.473572
$717$	7.41530	0.276929
$718$	6.93664	0.258873
$719$	−31.8648	−1.18836	−0.594178	−	0.804334i	$-0.702522\pi$
$719$	−31.8648	−1.18836	−0.594178	+	0.804334i	$0.702522\pi$
$720$	1.42649	0.0531622
$721$	−38.4973	−1.43371
$722$	33.1231	1.23271
$723$	73.2570	2.72446
$724$	−30.5949	−1.13705
$725$	25.0412	0.930005
$726$	7.02260	0.260633
$727$	−0.979480	−0.0363269	−0.0181634	−	0.999835i	$-0.505782\pi$
$727$	−0.979480	−0.0363269	−0.0181634	+	0.999835i	$0.505782\pi$
$728$	10.0264	0.371602
$729$	111.274	4.12127
$730$	1.30569	0.0483259
$731$	−15.5566	−0.575383
$732$	7.94270	0.293571
$733$	−6.93572	−0.256177	−0.128088	−	0.991763i	$-0.540884\pi$
$733$	−6.93572	−0.256177	−0.128088	+	0.991763i	$0.540884\pi$
$734$	−46.5600	−1.71856
$735$	0.106617	0.00393262
$736$	24.4394	0.900847
$737$	−1.62570	−0.0598833
$738$	119.773	4.40891
$739$	−8.67021	−0.318939	−0.159469	−	0.987203i	$-0.550978\pi$
$739$	−8.67021	−0.318939	−0.159469	+	0.987203i	$0.550978\pi$
$740$	0.854849	0.0314249
$741$	−103.831	−3.81434
$742$	−69.6688	−2.55762
$743$	−21.3488	−0.783213	−0.391606	−	0.920133i	$-0.628080\pi$
$743$	−21.3488	−0.783213	−0.391606	+	0.920133i	$0.628080\pi$
$744$	27.9586	1.02501
$745$	−0.243920	−0.00893653
$746$	74.2992	2.72029
$747$	2.02654	0.0741473
$748$	4.40607	0.161102
$749$	−8.08103	−0.295275
$750$	3.83493	0.140032
$751$	−24.9844	−0.911695	−0.455848	−	0.890058i	$-0.650664\pi$
$751$	−24.9844	−0.911695	−0.455848	+	0.890058i	$0.650664\pi$
$752$	−24.6354	−0.898361
$753$	−84.7578	−3.08875
$754$	54.7429	1.99362
$755$	0.173043	0.00629767
$756$	−106.767	−3.88306
$757$	42.6252	1.54924	0.774620	−	0.632427i	$-0.217941\pi$
$757$	42.6252	1.54924	0.774620	+	0.632427i	$0.217941\pi$
$758$	59.2392	2.15167
$759$	10.1696	0.369133
$760$	−0.244012	−0.00885125
$761$	8.19697	0.297140	0.148570	−	0.988902i	$-0.452533\pi$
$761$	8.19697	0.297140	0.148570	+	0.988902i	$0.452533\pi$
$762$	−34.4215	−1.24696
$763$	−5.30484	−0.192048
$764$	−19.5404	−0.706948
$765$	0.846202	0.0305945
$766$	12.3455	0.446061
$767$	39.4826	1.42563
$768$	29.3922	1.06060
$769$	41.8162	1.50793	0.753965	−	0.656915i	$-0.228139\pi$
$769$	41.8162	1.50793	0.753965	+	0.656915i	$0.228139\pi$
$770$	−0.289065	−0.0104172
$771$	−26.9017	−0.968841
$772$	58.4623	2.10411
$773$	1.69058	0.0608058	0.0304029	−	0.999538i	$-0.490321\pi$
$773$	1.69058	0.0608058	0.0304029	+	0.999538i	$0.490321\pi$
$774$	144.679	5.20037
$775$	−54.9185	−1.97273
$776$	−1.34568	−0.0483072
$777$	56.4374	2.02468
$778$	−31.0543	−1.11335
$779$	40.7664	1.46061
$780$	2.26927	0.0812530
$781$	7.43556	0.266065
$782$	11.7826	0.421346
$783$	−89.3926	−3.19463
$784$	1.82521	0.0651862
$785$	0.453323	0.0161798
$786$	−37.8921	−1.35157
$787$	−37.0461	−1.32055	−0.660275	−	0.751024i	$-0.729560\pi$
$787$	−37.0461	−1.32055	−0.660275	+	0.751024i	$0.729560\pi$
$788$	−0.0584095	−0.00208075
$789$	40.3154	1.43527
$790$	0.964120	0.0343019
$791$	−11.3011	−0.401822
$792$	−6.28382	−0.223286
$793$	−5.23032	−0.185734
$794$	75.7048	2.68666
$795$	−2.41804	−0.0857592
$796$	21.0402	0.745749
$797$	22.5259	0.797907	0.398953	−	0.916971i	$-0.369374\pi$
$797$	22.5259	0.797907	0.398953	+	0.916971i	$0.369374\pi$
$798$	−105.052	−3.71882
$799$	−14.6139	−0.517001
$800$	40.3775	1.42756
$801$	45.5782	1.61043
$802$	33.1198	1.16950
$803$	11.4445	0.403867
$804$	12.9124	0.455386
$805$	−0.418603	−0.0147538
$806$	−120.058	−4.22887
$807$	88.0511	3.09954
$808$	−3.86336	−0.135913
$809$	−6.11443	−0.214972	−0.107486	−	0.994207i	$-0.534280\pi$
$809$	−6.11443	−0.214972	−0.107486	+	0.994207i	$0.534280\pi$
$810$	−4.00032	−0.140557
$811$	17.1180	0.601093	0.300547	−	0.953767i	$-0.402831\pi$
$811$	17.1180	0.601093	0.300547	+	0.953767i	$0.402831\pi$
$812$	29.9930	1.05255
$813$	12.6551	0.443834
$814$	13.8366	0.484972
$815$	0.573317	0.0200824
$816$	19.7191	0.690308
$817$	49.2433	1.72281
$818$	27.9422	0.976977
$819$	110.062	3.84589
$820$	−0.890966	−0.0311139
$821$	−1.13393	−0.0395746	−0.0197873	−	0.999804i	$-0.506299\pi$
$821$	−1.13393	−0.0395746	−0.0197873	+	0.999804i	$0.506299\pi$
$822$	34.7972	1.21369
$823$	19.9980	0.697085	0.348543	−	0.937293i	$-0.386677\pi$
$823$	19.9980	0.697085	0.348543	+	0.937293i	$0.386677\pi$
$824$	11.4959	0.400479
$825$	16.8017	0.584960
$826$	39.9469	1.38993
$827$	−42.4296	−1.47542	−0.737710	−	0.675117i	$-0.764093\pi$
$827$	−42.4296	−1.47542	−0.737710	+	0.675117i	$0.764093\pi$
$828$	−59.3398	−2.06220
$829$	−27.8808	−0.968339	−0.484169	−	0.874974i	$-0.660878\pi$
$829$	−27.8808	−0.968339	−0.484169	+	0.874974i	$0.660878\pi$
$830$	−0.0278382	−0.000966279 0
$831$	8.26887	0.286844
$832$	55.3788	1.91991
$833$	1.08273	0.0375142
$834$	75.4056	2.61108
$835$	0.809064	0.0279988
$836$	−13.9471	−0.482370
$837$	196.050	6.77647
$838$	−56.2752	−1.94399
$839$	−54.1518	−1.86953	−0.934765	−	0.355267i	$-0.884390\pi$
$839$	−54.1518	−1.86953	−0.934765	+	0.355267i	$0.884390\pi$
$840$	0.352085	0.0121481
$841$	−3.88766	−0.134057
$842$	−44.8116	−1.54431
$843$	51.3181	1.76749
$844$	−1.25552	−0.0432167
$845$	−0.784210	−0.0269776
$846$	135.911	4.67271
$847$	−2.53368	−0.0870581
$848$	−41.3954	−1.42152
$849$	−9.63884	−0.330804
$850$	19.4667	0.667701
$851$	20.0371	0.686862
$852$	−59.0585	−2.02331
$853$	12.5283	0.428962	0.214481	−	0.976728i	$-0.431194\pi$
$853$	12.5283	0.428962	0.214481	+	0.976728i	$0.431194\pi$
$854$	−5.29184	−0.181083
$855$	−2.67859	−0.0916059
$856$	2.41313	0.0824790
$857$	−19.5208	−0.666818	−0.333409	−	0.942782i	$-0.608199\pi$
$857$	−19.5208	−0.666818	−0.333409	+	0.942782i	$0.608199\pi$
$858$	36.7305	1.25396
$859$	31.3290	1.06893	0.534465	−	0.845190i	$-0.320513\pi$
$859$	31.3290	1.06893	0.534465	+	0.845190i	$0.320513\pi$
$860$	−1.07623	−0.0366992
$861$	−58.8219	−2.00464
$862$	27.4107	0.933612
$863$	4.59414	0.156386	0.0781931	−	0.996938i	$-0.475085\pi$
$863$	4.59414	0.156386	0.0781931	+	0.996938i	$0.475085\pi$
$864$	−144.141	−4.90377
$865$	1.02360	0.0348036
$866$	−33.7949	−1.14840
$867$	−45.4624	−1.54398
$868$	−65.7786	−2.23267
$869$	8.45057	0.286666
$870$	1.92234	0.0651736
$871$	−8.50292	−0.288111
$872$	1.58411	0.0536448
$873$	−14.7719	−0.499954
$874$	−37.2970	−1.26159
$875$	−1.38360	−0.0467743
$876$	−90.9002	−3.07123
$877$	−6.75510	−0.228103	−0.114052	−	0.993475i	$-0.536383\pi$
$877$	−6.75510	−0.228103	−0.114052	+	0.993475i	$0.536383\pi$
$878$	12.1976	0.411648
$879$	−33.2874	−1.12276
$880$	−0.171755	−0.00578987
$881$	12.3007	0.414420	0.207210	−	0.978296i	$-0.433562\pi$
$881$	12.3007	0.414420	0.207210	+	0.978296i	$0.433562\pi$
$882$	−10.0695	−0.339058
$883$	−6.57113	−0.221136	−0.110568	−	0.993869i	$-0.535267\pi$
$883$	−6.57113	−0.221136	−0.110568	+	0.993869i	$0.535267\pi$
$884$	23.0452	0.775093
$885$	1.38647	0.0466056
$886$	17.3357	0.582403
$887$	−40.9550	−1.37513	−0.687567	−	0.726121i	$-0.741321\pi$
$887$	−40.9550	−1.37513	−0.687567	+	0.726121i	$0.741321\pi$
$888$	−16.8531	−0.565553
$889$	12.4189	0.416516
$890$	−0.626099	−0.0209869
$891$	−35.0631	−1.17466
$892$	−51.6886	−1.73066
$893$	46.2591	1.54800
$894$	31.3585	1.04878
$895$	−0.293026	−0.00979479
$896$	15.0842	0.503928
$897$	53.1903	1.77597
$898$	−49.0541	−1.63695
$899$	−55.0746	−1.83684
$900$	−98.0383	−3.26794
$901$	−24.5560	−0.818078
$902$	−14.4212	−0.480173
$903$	−71.0532	−2.36450
$904$	3.37470	0.112241
$905$	0.707479	0.0235174
$906$	−22.2465	−0.739090
$907$	17.5819	0.583799	0.291899	−	0.956449i	$-0.405713\pi$
$907$	17.5819	0.583799	0.291899	+	0.956449i	$0.405713\pi$
$908$	−32.1809	−1.06796
$909$	−42.4092	−1.40663
$910$	−1.51191	−0.0501192
$911$	−9.78913	−0.324328	−0.162164	−	0.986764i	$-0.551847\pi$
$911$	−9.78913	−0.324328	−0.162164	+	0.986764i	$0.551847\pi$
$912$	−62.4195	−2.06692
$913$	−0.244004	−0.00807534
$914$	−29.2940	−0.968959
$915$	−0.183667	−0.00607186
$916$	19.9829	0.660252
$917$	13.6710	0.451458
$918$	−69.4926	−2.29360
$919$	−6.50515	−0.214585	−0.107293	−	0.994227i	$-0.534218\pi$
$919$	−6.50515	−0.214585	−0.107293	+	0.994227i	$0.534218\pi$
$920$	0.125002	0.00412118
$921$	−1.49395	−0.0492273
$922$	−35.9110	−1.18267
$923$	38.8904	1.28009
$924$	20.1242	0.662039
$925$	33.1043	1.08846
$926$	57.6893	1.89579
$927$	126.194	4.14475
$928$	40.4923	1.32922
$929$	16.0748	0.527397	0.263698	−	0.964605i	$-0.415058\pi$
$929$	16.0748	0.527397	0.263698	+	0.964605i	$0.415058\pi$
$930$	−4.21595	−0.138246
$931$	−3.42729	−0.112325
$932$	−54.4155	−1.78244
$933$	38.2816	1.25328
$934$	31.3710	1.02649
$935$	−0.101886	−0.00333203
$936$	−32.8664	−1.07427
$937$	−42.1089	−1.37564	−0.687819	−	0.725883i	$-0.741432\pi$
$937$	−42.1089	−1.37564	−0.687819	+	0.725883i	$0.741432\pi$
$938$	−8.60292	−0.280895
$939$	−3.81415	−0.124470
$940$	−1.01101	−0.0329755
$941$	0.723386	0.0235817	0.0117908	−	0.999930i	$-0.496247\pi$
$941$	0.723386	0.0235817	0.0117908	+	0.999930i	$0.496247\pi$
$942$	−58.2795	−1.89885
$943$	−20.8837	−0.680065
$944$	23.7355	0.772523
$945$	2.46887	0.0803125
$946$	−17.4199	−0.566370
$947$	16.3324	0.530733	0.265366	−	0.964148i	$-0.414507\pi$
$947$	16.3324	0.530733	0.265366	+	0.964148i	$0.414507\pi$
$948$	−67.1204	−2.17997
$949$	59.8584	1.94308
$950$	−61.6202	−1.99922
$951$	−19.4568	−0.630931
$952$	3.57553	0.115884
$953$	−23.2780	−0.754048	−0.377024	−	0.926203i	$-0.623053\pi$
$953$	−23.2780	−0.754048	−0.377024	+	0.926203i	$0.623053\pi$
$954$	228.374	7.39387
$955$	0.451854	0.0146216
$956$	5.20969	0.168494
$957$	16.8495	0.544666
$958$	82.9840	2.68109
$959$	−12.5545	−0.405405
$960$	1.94467	0.0627641
$961$	89.7858	2.89631
$962$	72.3698	2.33330
$963$	26.4896	0.853615
$964$	51.4675	1.65766
$965$	−1.35189	−0.0435187
$966$	53.8158	1.73149
$967$	5.72052	0.183959	0.0919797	−	0.995761i	$-0.470680\pi$
$967$	5.72052	0.183959	0.0919797	+	0.995761i	$0.470680\pi$
$968$	0.756597	0.0243179
$969$	−37.0276	−1.18950
$970$	0.202919	0.00651534
$971$	28.8927	0.927211	0.463606	−	0.886042i	$-0.346555\pi$
$971$	28.8927	0.927211	0.463606	+	0.886042i	$0.346555\pi$
$972$	152.079	4.87792
$973$	−27.2055	−0.872169
$974$	48.0407	1.53932
$975$	87.8783	2.81436
$976$	−3.14427	−0.100646
$977$	−18.8314	−0.602469	−0.301235	−	0.953550i	$-0.597399\pi$
$977$	−18.8314	−0.602469	−0.301235	+	0.953550i	$0.597399\pi$
$978$	−73.7060	−2.35686
$979$	−5.48780	−0.175391
$980$	0.0749047	0.00239274
$981$	17.3892	0.555195
$982$	−24.6817	−0.787626
$983$	−7.65201	−0.244061	−0.122031	−	0.992526i	$-0.538941\pi$
$983$	−7.65201	−0.244061	−0.122031	+	0.992526i	$0.538941\pi$
$984$	17.5652	0.559957
$985$	0.00135066	4.30357e−5 0
$986$	19.5220	0.621707
$987$	−66.7472	−2.12459
$988$	−72.9478	−2.32078
$989$	−25.2262	−0.802145
$990$	0.947555	0.0301153
$991$	−19.4093	−0.616558	−0.308279	−	0.951296i	$-0.599753\pi$
$991$	−19.4093	−0.616558	−0.308279	+	0.951296i	$0.599753\pi$
$992$	−88.8048	−2.81956
$993$	−58.7542	−1.86451
$994$	39.3478	1.24804
$995$	−0.486534	−0.0154242
$996$	1.93805	0.0614094
$997$	−9.83103	−0.311352	−0.155676	−	0.987808i	$-0.549756\pi$
$997$	−9.83103	−0.311352	−0.155676	+	0.987808i	$0.549756\pi$
$998$	38.6820	1.22446
$999$	−118.177	−3.73894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.17	✓	21
3.2	odd	2		6039.2.a.l.1.5		21
11.10	odd	2		7381.2.a.j.1.5		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.17	✓	21	1.1	even	1	trivial
6039.2.a.l.1.5		21	3.2	odd	2
7381.2.a.j.1.5		21	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+2.08860 q^{2} +3.36235 q^{3} +2.36225 q^{4} -0.0546248 q^{5} +7.02260 q^{6} -2.53368 q^{7} +0.756597 q^{8} +8.30537 q^{9} +O(q^{10})\)	\(q+2.08860 q^{2} +3.36235 q^{3} +2.36225 q^{4} -0.0546248 q^{5} +7.02260 q^{6} -2.53368 q^{7} +0.756597 q^{8} +8.30537 q^{9} -0.114089 q^{10} -1.00000 q^{11} +7.94270 q^{12} -5.23032 q^{13} -5.29184 q^{14} -0.183667 q^{15} -3.14427 q^{16} -1.86520 q^{17} +17.3466 q^{18} +5.90415 q^{19} -0.129037 q^{20} -8.51909 q^{21} -2.08860 q^{22} -3.02455 q^{23} +2.54394 q^{24} -4.99702 q^{25} -10.9241 q^{26} +17.8385 q^{27} -5.98518 q^{28} -5.01122 q^{29} -0.383608 q^{30} +10.9903 q^{31} -8.08032 q^{32} -3.36235 q^{33} -3.89566 q^{34} +0.138402 q^{35} +19.6194 q^{36} -6.62481 q^{37} +12.3314 q^{38} -17.5862 q^{39} -0.0413289 q^{40} +6.90471 q^{41} -17.7930 q^{42} +8.34046 q^{43} -2.36225 q^{44} -0.453679 q^{45} -6.31708 q^{46} +7.83501 q^{47} -10.5721 q^{48} -0.580488 q^{49} -10.4368 q^{50} -6.27145 q^{51} -12.3553 q^{52} +13.1653 q^{53} +37.2575 q^{54} +0.0546248 q^{55} -1.91697 q^{56} +19.8518 q^{57} -10.4664 q^{58} -7.54879 q^{59} -0.433869 q^{60} +1.00000 q^{61} +22.9543 q^{62} -21.0431 q^{63} -10.5880 q^{64} +0.285705 q^{65} -7.02260 q^{66} +1.62570 q^{67} -4.40607 q^{68} -10.1696 q^{69} +0.289065 q^{70} -7.43556 q^{71} +6.28382 q^{72} -11.4445 q^{73} -13.8366 q^{74} -16.8017 q^{75} +13.9471 q^{76} +2.53368 q^{77} -36.7305 q^{78} -8.45057 q^{79} +0.171755 q^{80} +35.0631 q^{81} +14.4212 q^{82} +0.244004 q^{83} -20.1242 q^{84} +0.101886 q^{85} +17.4199 q^{86} -16.8495 q^{87} -0.756597 q^{88} +5.48780 q^{89} -0.947555 q^{90} +13.2519 q^{91} -7.14475 q^{92} +36.9530 q^{93} +16.3642 q^{94} -0.322513 q^{95} -27.1688 q^{96} -1.77860 q^{97} -1.21241 q^{98} -8.30537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * q^99

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