LMFDB - Embedded newform 1205.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 11x^{9} + 15x^{8} + 43x^{7} - 28x^{6} - 62x^{5} + 14x^{4} + 31x^{3} + x^{2} - 5x - 1 $ x^11 - 2x^10 - 11x^9 + 15x^8 + 43x^7 - 28x^6 - 62x^5 + 14x^4 + 31x^3 + x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.27000$ of defining polynomial
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.517395 q^{2} +0.462298 q^{3} -1.73230 q^{4} +1.00000 q^{5} -0.239191 q^{6} -3.59765 q^{7} +1.93107 q^{8} -2.78628 q^{9} +O(q^{10})$	\(q-0.517395 q^{2} +0.462298 q^{3} -1.73230 q^{4} +1.00000 q^{5} -0.239191 q^{6} -3.59765 q^{7} +1.93107 q^{8} -2.78628 q^{9} -0.517395 q^{10} +1.28534 q^{11} -0.800841 q^{12} +6.76028 q^{13} +1.86141 q^{14} +0.462298 q^{15} +2.46548 q^{16} +4.45514 q^{17} +1.44161 q^{18} -5.41949 q^{19} -1.73230 q^{20} -1.66319 q^{21} -0.665029 q^{22} -1.01188 q^{23} +0.892733 q^{24} +1.00000 q^{25} -3.49773 q^{26} -2.67499 q^{27} +6.23222 q^{28} -4.93749 q^{29} -0.239191 q^{30} -0.848965 q^{31} -5.13777 q^{32} +0.594211 q^{33} -2.30506 q^{34} -3.59765 q^{35} +4.82668 q^{36} -7.27577 q^{37} +2.80401 q^{38} +3.12527 q^{39} +1.93107 q^{40} -10.2535 q^{41} +0.860526 q^{42} -7.94388 q^{43} -2.22660 q^{44} -2.78628 q^{45} +0.523543 q^{46} -6.13542 q^{47} +1.13979 q^{48} +5.94311 q^{49} -0.517395 q^{50} +2.05960 q^{51} -11.7109 q^{52} -11.1495 q^{53} +1.38403 q^{54} +1.28534 q^{55} -6.94734 q^{56} -2.50542 q^{57} +2.55463 q^{58} -7.04462 q^{59} -0.800841 q^{60} +9.82532 q^{61} +0.439250 q^{62} +10.0241 q^{63} -2.27270 q^{64} +6.76028 q^{65} -0.307442 q^{66} +0.463226 q^{67} -7.71765 q^{68} -0.467792 q^{69} +1.86141 q^{70} +8.18132 q^{71} -5.38051 q^{72} +11.2666 q^{73} +3.76445 q^{74} +0.462298 q^{75} +9.38819 q^{76} -4.62421 q^{77} -1.61700 q^{78} -10.4509 q^{79} +2.46548 q^{80} +7.12220 q^{81} +5.30509 q^{82} -12.6471 q^{83} +2.88115 q^{84} +4.45514 q^{85} +4.11012 q^{86} -2.28259 q^{87} +2.48209 q^{88} +13.0208 q^{89} +1.44161 q^{90} -24.3211 q^{91} +1.75289 q^{92} -0.392475 q^{93} +3.17443 q^{94} -5.41949 q^{95} -2.37518 q^{96} +4.26849 q^{97} -3.07494 q^{98} -3.58132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 4 q^{2} - 8 q^{3} + 6 q^{4} + 11 q^{5} + 7 q^{6} - 9 q^{7} - 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q - 4 * q^2 - 8 * q^3 + 6 * q^4 + 11 * q^5 + 7 * q^6 - 9 * q^7 - 12 * q^8 + 9 * q^9	\( 11 q - 4 q^{2} - 8 q^{3} + 6 q^{4} + 11 q^{5} + 7 q^{6} - 9 q^{7} - 12 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 28 q^{12} - 9 q^{13} + 2 q^{14} - 8 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} - 33 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{22} - 31 q^{23} + 32 q^{24} + 11 q^{25} - 20 q^{26} - 32 q^{27} - q^{28} + q^{29} + 7 q^{30} + 6 q^{31} + 7 q^{32} - 35 q^{33} + 9 q^{34} - 9 q^{35} + 33 q^{36} - 23 q^{37} + 20 q^{38} + 14 q^{39} - 12 q^{40} + 8 q^{41} - 26 q^{42} - 19 q^{43} + 9 q^{45} + 6 q^{46} - 35 q^{47} + 16 q^{48} + 4 q^{49} - 4 q^{50} - 3 q^{51} - 3 q^{52} + 14 q^{53} + 9 q^{54} - 3 q^{55} + 33 q^{56} + q^{57} - 11 q^{58} - 6 q^{59} - 28 q^{60} + 9 q^{61} - 23 q^{62} - 31 q^{63} + 18 q^{64} - 9 q^{65} - 36 q^{66} - 54 q^{67} + q^{68} + 17 q^{69} + 2 q^{70} - 5 q^{71} - 64 q^{72} + 17 q^{73} + 8 q^{74} - 8 q^{75} - 31 q^{76} - 18 q^{77} + 15 q^{78} - 16 q^{79} - 16 q^{80} + 43 q^{81} - 61 q^{82} - 29 q^{83} + 69 q^{84} - 4 q^{85} + 5 q^{86} + 5 q^{87} - 14 q^{88} - 5 q^{89} - 6 q^{90} - 54 q^{91} - 6 q^{92} - 25 q^{93} - 19 q^{94} - 33 q^{95} + 9 q^{96} + 6 q^{97} - 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 - 8 * q^3 + 6 * q^4 + 11 * q^5 + 7 * q^6 - 9 * q^7 - 12 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 28 * q^12 - 9 * q^13 + 2 * q^14 - 8 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 - 33 * q^19 + 6 * q^20 + 2 * q^21 + 6 * q^22 - 31 * q^23 + 32 * q^24 + 11 * q^25 - 20 * q^26 - 32 * q^27 - q^28 + q^29 + 7 * q^30 + 6 * q^31 + 7 * q^32 - 35 * q^33 + 9 * q^34 - 9 * q^35 + 33 * q^36 - 23 * q^37 + 20 * q^38 + 14 * q^39 - 12 * q^40 + 8 * q^41 - 26 * q^42 - 19 * q^43 + 9 * q^45 + 6 * q^46 - 35 * q^47 + 16 * q^48 + 4 * q^49 - 4 * q^50 - 3 * q^51 - 3 * q^52 + 14 * q^53 + 9 * q^54 - 3 * q^55 + 33 * q^56 + q^57 - 11 * q^58 - 6 * q^59 - 28 * q^60 + 9 * q^61 - 23 * q^62 - 31 * q^63 + 18 * q^64 - 9 * q^65 - 36 * q^66 - 54 * q^67 + q^68 + 17 * q^69 + 2 * q^70 - 5 * q^71 - 64 * q^72 + 17 * q^73 + 8 * q^74 - 8 * q^75 - 31 * q^76 - 18 * q^77 + 15 * q^78 - 16 * q^79 - 16 * q^80 + 43 * q^81 - 61 * q^82 - 29 * q^83 + 69 * q^84 - 4 * q^85 + 5 * q^86 + 5 * q^87 - 14 * q^88 - 5 * q^89 - 6 * q^90 - 54 * q^91 - 6 * q^92 - 25 * q^93 - 19 * q^94 - 33 * q^95 + 9 * q^96 + 6 * q^97 - 29 * q^98 + 60 * 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 $

$2$	−0.517395	−0.365853	−0.182927	−	0.983127i	$-0.558557\pi$
$2$	−0.517395	−0.365853	−0.182927	+	0.983127i	$0.558557\pi$
$3$	0.462298	0.266908	0.133454	−	0.991055i	$-0.457393\pi$
$3$	0.462298	0.266908	0.133454	+	0.991055i	$0.457393\pi$
$4$	−1.73230	−0.866151
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.239191	−0.0976492
$7$	−3.59765	−1.35979	−0.679893	−	0.733312i	$-0.737974\pi$
$7$	−3.59765	−1.35979	−0.679893	+	0.733312i	$0.737974\pi$
$8$	1.93107	0.682738
$9$	−2.78628	−0.928760
$10$	−0.517395	−0.163615
$11$	1.28534	0.387545	0.193773	−	0.981046i	$-0.437928\pi$
$11$	1.28534	0.387545	0.193773	+	0.981046i	$0.437928\pi$
$12$	−0.800841	−0.231183
$13$	6.76028	1.87496	0.937482	−	0.348033i	$-0.113150\pi$
$13$	6.76028	1.87496	0.937482	+	0.348033i	$0.113150\pi$
$14$	1.86141	0.497482
$15$	0.462298	0.119365
$16$	2.46548	0.616369
$17$	4.45514	1.08053	0.540265	−	0.841495i	$-0.318324\pi$
$17$	4.45514	1.08053	0.540265	+	0.841495i	$0.318324\pi$
$18$	1.44161	0.339790
$19$	−5.41949	−1.24332	−0.621658	−	0.783289i	$-0.713541\pi$
$19$	−5.41949	−1.24332	−0.621658	+	0.783289i	$0.713541\pi$
$20$	−1.73230	−0.387355
$21$	−1.66319	−0.362938
$22$	−0.665029	−0.141785
$23$	−1.01188	−0.210992	−0.105496	−	0.994420i	$-0.533643\pi$
$23$	−1.01188	−0.210992	−0.105496	+	0.994420i	$0.533643\pi$
$24$	0.892733	0.182228
$25$	1.00000	0.200000
$26$	−3.49773	−0.685962
$27$	−2.67499	−0.514802
$28$	6.23222	1.17778
$29$	−4.93749	−0.916869	−0.458434	−	0.888728i	$-0.651590\pi$
$29$	−4.93749	−0.916869	−0.458434	+	0.888728i	$0.651590\pi$
$30$	−0.239191	−0.0436701
$31$	−0.848965	−0.152479	−0.0762393	−	0.997090i	$-0.524291\pi$
$31$	−0.848965	−0.152479	−0.0762393	+	0.997090i	$0.524291\pi$
$32$	−5.13777	−0.908239
$33$	0.594211	0.103439
$34$	−2.30506	−0.395315
$35$	−3.59765	−0.608114
$36$	4.82668	0.804447
$37$	−7.27577	−1.19613	−0.598065	−	0.801448i	$-0.704063\pi$
$37$	−7.27577	−1.19613	−0.598065	+	0.801448i	$0.704063\pi$
$38$	2.80401	0.454871
$39$	3.12527	0.500443
$40$	1.93107	0.305330
$41$	−10.2535	−1.60132	−0.800660	−	0.599118i	$-0.795518\pi$
$41$	−10.2535	−1.60132	−0.800660	+	0.599118i	$0.795518\pi$
$42$	0.860526	0.132782
$43$	−7.94388	−1.21143	−0.605715	−	0.795682i	$-0.707113\pi$
$43$	−7.94388	−1.21143	−0.605715	+	0.795682i	$0.707113\pi$
$44$	−2.22660	−0.335673
$45$	−2.78628	−0.415354
$46$	0.523543	0.0771922
$47$	−6.13542	−0.894943	−0.447471	−	0.894298i	$-0.647675\pi$
$47$	−6.13542	−0.894943	−0.447471	+	0.894298i	$0.647675\pi$
$48$	1.13979	0.164514
$49$	5.94311	0.849016
$50$	−0.517395	−0.0731707
$51$	2.05960	0.288402
$52$	−11.7109	−1.62400
$53$	−11.1495	−1.53150	−0.765751	−	0.643137i	$-0.777632\pi$
$53$	−11.1495	−1.53150	−0.765751	+	0.643137i	$0.777632\pi$
$54$	1.38403	0.188342
$55$	1.28534	0.173315
$56$	−6.94734	−0.928377
$57$	−2.50542	−0.331851
$58$	2.55463	0.335440
$59$	−7.04462	−0.917132	−0.458566	−	0.888660i	$-0.651637\pi$
$59$	−7.04462	−0.917132	−0.458566	+	0.888660i	$0.651637\pi$
$60$	−0.800841	−0.103388
$61$	9.82532	1.25800	0.629002	−	0.777404i	$-0.283464\pi$
$61$	9.82532	1.25800	0.629002	+	0.777404i	$0.283464\pi$
$62$	0.439250	0.0557848
$63$	10.0241	1.26291
$64$	−2.27270	−0.284087
$65$	6.76028	0.838510
$66$	−0.307442	−0.0378435
$67$	0.463226	0.0565920	0.0282960	−	0.999600i	$-0.490992\pi$
$67$	0.463226	0.0565920	0.0282960	+	0.999600i	$0.490992\pi$
$68$	−7.71765	−0.935902
$69$	−0.467792	−0.0563155
$70$	1.86141	0.222481
$71$	8.18132	0.970944	0.485472	−	0.874252i	$-0.338648\pi$
$71$	8.18132	0.970944	0.485472	+	0.874252i	$0.338648\pi$
$72$	−5.38051	−0.634100
$73$	11.2666	1.31865	0.659327	−	0.751857i	$-0.270841\pi$
$73$	11.2666	1.31865	0.659327	+	0.751857i	$0.270841\pi$
$74$	3.76445	0.437608
$75$	0.462298	0.0533816
$76$	9.38819	1.07690
$77$	−4.62421	−0.526978
$78$	−1.61700	−0.183089
$79$	−10.4509	−1.17581	−0.587907	−	0.808928i	$-0.700048\pi$
$79$	−10.4509	−1.17581	−0.587907	+	0.808928i	$0.700048\pi$
$80$	2.46548	0.275649
$81$	7.12220	0.791355
$82$	5.30509	0.585849
$83$	−12.6471	−1.38820	−0.694102	−	0.719876i	$-0.744199\pi$
$83$	−12.6471	−1.38820	−0.694102	+	0.719876i	$0.744199\pi$
$84$	2.88115	0.314359
$85$	4.45514	0.483227
$86$	4.11012	0.443206
$87$	−2.28259	−0.244720
$88$	2.48209	0.264592
$89$	13.0208	1.38020	0.690101	−	0.723713i	$-0.257566\pi$
$89$	13.0208	1.38020	0.690101	+	0.723713i	$0.257566\pi$
$90$	1.44161	0.151959
$91$	−24.3211	−2.54955
$92$	1.75289	0.182751
$93$	−0.392475	−0.0406978
$94$	3.17443	0.327418
$95$	−5.41949	−0.556028
$96$	−2.37518	−0.242416
$97$	4.26849	0.433400	0.216700	−	0.976238i	$-0.430471\pi$
$97$	4.26849	0.433400	0.216700	+	0.976238i	$0.430471\pi$
$98$	−3.07494	−0.310615
$99$	−3.58132	−0.359936
$100$	−1.73230	−0.173230
$101$	−1.82738	−0.181831	−0.0909155	−	0.995859i	$-0.528979\pi$
$101$	−1.82738	−0.181831	−0.0909155	+	0.995859i	$0.528979\pi$
$102$	−1.06563	−0.105513
$103$	−3.37538	−0.332586	−0.166293	−	0.986076i	$-0.553180\pi$
$103$	−3.37538	−0.332586	−0.166293	+	0.986076i	$0.553180\pi$
$104$	13.0546	1.28011
$105$	−1.66319	−0.162311
$106$	5.76869	0.560305
$107$	17.2402	1.66667	0.833336	−	0.552767i	$-0.186428\pi$
$107$	17.2402	1.66667	0.833336	+	0.552767i	$0.186428\pi$
$108$	4.63389	0.445896
$109$	3.20852	0.307321	0.153660	−	0.988124i	$-0.450894\pi$
$109$	3.20852	0.307321	0.153660	+	0.988124i	$0.450894\pi$
$110$	−0.665029	−0.0634080
$111$	−3.36358	−0.319257
$112$	−8.86993	−0.838130
$113$	−10.9326	−1.02845	−0.514227	−	0.857654i	$-0.671921\pi$
$113$	−10.9326	−1.02845	−0.514227	+	0.857654i	$0.671921\pi$
$114$	1.29629	0.121409
$115$	−1.01188	−0.0943586
$116$	8.55323	0.794147
$117$	−18.8360	−1.74139
$118$	3.64485	0.335536
$119$	−16.0280	−1.46929
$120$	0.892733	0.0814950
$121$	−9.34790	−0.849809
$122$	−5.08357	−0.460245
$123$	−4.74016	−0.427406
$124$	1.47066	0.132070
$125$	1.00000	0.0894427
$126$	−5.18640	−0.462042
$127$	−14.1660	−1.25703	−0.628515	−	0.777798i	$-0.716337\pi$
$127$	−14.1660	−1.25703	−0.628515	+	0.777798i	$0.716337\pi$
$128$	11.4514	1.01217
$129$	−3.67244	−0.323340
$130$	−3.49773	−0.306772
$131$	−12.1022	−1.05738	−0.528688	−	0.848816i	$-0.677316\pi$
$131$	−12.1022	−1.05738	−0.528688	+	0.848816i	$0.677316\pi$
$132$	−1.02935	−0.0895938
$133$	19.4974	1.69064
$134$	−0.239671	−0.0207044
$135$	−2.67499	−0.230226
$136$	8.60320	0.737718
$137$	−0.883492	−0.0754819	−0.0377409	−	0.999288i	$-0.512016\pi$
$137$	−0.883492	−0.0754819	−0.0377409	+	0.999288i	$0.512016\pi$
$138$	0.242033	0.0206032
$139$	6.07115	0.514948	0.257474	−	0.966285i	$-0.417110\pi$
$139$	6.07115	0.514948	0.257474	+	0.966285i	$0.417110\pi$
$140$	6.23222	0.526719
$141$	−2.83639	−0.238868
$142$	−4.23297	−0.355223
$143$	8.68927	0.726633
$144$	−6.86951	−0.572459
$145$	−4.93749	−0.410036
$146$	−5.82927	−0.482434
$147$	2.74749	0.226609
$148$	12.6038	1.03603
$149$	−1.37565	−0.112698	−0.0563488	−	0.998411i	$-0.517946\pi$
$149$	−1.37565	−0.112698	−0.0563488	+	0.998411i	$0.517946\pi$
$150$	−0.239191	−0.0195298
$151$	−11.2724	−0.917336	−0.458668	−	0.888608i	$-0.651673\pi$
$151$	−11.2724	−0.917336	−0.458668	+	0.888608i	$0.651673\pi$
$152$	−10.4654	−0.848859
$153$	−12.4133	−1.00355
$154$	2.39254	0.192797
$155$	−0.848965	−0.0681905
$156$	−5.41391	−0.433460
$157$	12.6557	1.01003	0.505017	−	0.863110i	$-0.331486\pi$
$157$	12.6557	1.01003	0.505017	+	0.863110i	$0.331486\pi$
$158$	5.40722	0.430176
$159$	−5.15440	−0.408770
$160$	−5.13777	−0.406177
$161$	3.64040	0.286904
$162$	−3.68499	−0.289520
$163$	−20.1764	−1.58034	−0.790170	−	0.612887i	$-0.790008\pi$
$163$	−20.1764	−1.58034	−0.790170	+	0.612887i	$0.790008\pi$
$164$	17.7621	1.38699
$165$	0.594211	0.0462593
$166$	6.54357	0.507880
$167$	15.5533	1.20355	0.601774	−	0.798667i	$-0.294461\pi$
$167$	15.5533	1.20355	0.601774	+	0.798667i	$0.294461\pi$
$168$	−3.21174	−0.247791
$169$	32.7014	2.51549
$170$	−2.30506	−0.176790
$171$	15.1002	1.15474
$172$	13.7612	1.04928
$173$	−16.5345	−1.25710	−0.628549	−	0.777770i	$-0.716351\pi$
$173$	−16.5345	−1.25710	−0.628549	+	0.777770i	$0.716351\pi$
$174$	1.18100	0.0895316
$175$	−3.59765	−0.271957
$176$	3.16898	0.238871
$177$	−3.25672	−0.244790
$178$	−6.73689	−0.504951
$179$	22.3811	1.67284	0.836421	−	0.548087i	$-0.184644\pi$
$179$	22.3811	1.67284	0.836421	+	0.548087i	$0.184644\pi$
$180$	4.82668	0.359760
$181$	6.54597	0.486558	0.243279	−	0.969956i	$-0.421777\pi$
$181$	6.54597	0.486558	0.243279	+	0.969956i	$0.421777\pi$
$182$	12.5836	0.932761
$183$	4.54223	0.335771
$184$	−1.95402	−0.144052
$185$	−7.27577	−0.534925
$186$	0.203065	0.0148894
$187$	5.72637	0.418754
$188$	10.6284	0.775156
$189$	9.62368	0.700020
$190$	2.80401	0.203425
$191$	−10.6695	−0.772020	−0.386010	−	0.922495i	$-0.626147\pi$
$191$	−10.6695	−0.772020	−0.386010	+	0.922495i	$0.626147\pi$
$192$	−1.05066	−0.0758252
$193$	−23.1527	−1.66657	−0.833283	−	0.552846i	$-0.813542\pi$
$193$	−23.1527	−1.66657	−0.833283	+	0.552846i	$0.813542\pi$
$194$	−2.20850	−0.158561
$195$	3.12527	0.223805
$196$	−10.2953	−0.735376
$197$	−12.0191	−0.856328	−0.428164	−	0.903701i	$-0.640839\pi$
$197$	−12.0191	−0.856328	−0.428164	+	0.903701i	$0.640839\pi$
$198$	1.85296	0.131684
$199$	9.46822	0.671184	0.335592	−	0.942007i	$-0.391064\pi$
$199$	9.46822	0.671184	0.335592	+	0.942007i	$0.391064\pi$
$200$	1.93107	0.136548
$201$	0.214148	0.0151049
$202$	0.945477	0.0665235
$203$	17.7634	1.24674
$204$	−3.56786	−0.249800
$205$	−10.2535	−0.716132
$206$	1.74641	0.121678
$207$	2.81939	0.195961
$208$	16.6673	1.15567
$209$	−6.96589	−0.481841
$210$	0.860526	0.0593819
$211$	0.300504	0.0206876	0.0103438	−	0.999947i	$-0.496707\pi$
$211$	0.300504	0.0206876	0.0103438	+	0.999947i	$0.496707\pi$
$212$	19.3143	1.32651
$213$	3.78221	0.259153
$214$	−8.91998	−0.609757
$215$	−7.94388	−0.541768
$216$	−5.16560	−0.351475
$217$	3.05428	0.207338
$218$	−1.66007	−0.112434
$219$	5.20852	0.351959
$220$	−2.22660	−0.150117
$221$	30.1180	2.02595
$222$	1.74030	0.116801
$223$	4.72726	0.316561	0.158280	−	0.987394i	$-0.449405\pi$
$223$	4.72726	0.316561	0.158280	+	0.987394i	$0.449405\pi$
$224$	18.4839	1.23501
$225$	−2.78628	−0.185752
$226$	5.65648	0.376263
$227$	−12.1363	−0.805516	−0.402758	−	0.915307i	$-0.631948\pi$
$227$	−12.1363	−0.805516	−0.402758	+	0.915307i	$0.631948\pi$
$228$	4.34015	0.287433
$229$	−21.8762	−1.44562	−0.722812	−	0.691045i	$-0.757151\pi$
$229$	−21.8762	−1.44562	−0.722812	+	0.691045i	$0.757151\pi$
$230$	0.523543	0.0345214
$231$	−2.13777	−0.140655
$232$	−9.53466	−0.625981
$233$	−8.84614	−0.579530	−0.289765	−	0.957098i	$-0.593577\pi$
$233$	−8.84614	−0.579530	−0.289765	+	0.957098i	$0.593577\pi$
$234$	9.74567	0.637094
$235$	−6.13542	−0.400231
$236$	12.2034	0.794375
$237$	−4.83142	−0.313834
$238$	8.29283	0.537544
$239$	7.30844	0.472744	0.236372	−	0.971663i	$-0.424042\pi$
$239$	7.30844	0.472744	0.236372	+	0.971663i	$0.424042\pi$
$240$	1.13979	0.0735729
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	4.83655	0.310905
$243$	11.3175	0.726021
$244$	−17.0204	−1.08962
$245$	5.94311	0.379692
$246$	2.45253	0.156368
$247$	−36.6373	−2.33117
$248$	−1.63941	−0.104103
$249$	−5.84676	−0.370523
$250$	−0.517395	−0.0327229
$251$	−5.43028	−0.342756	−0.171378	−	0.985205i	$-0.554822\pi$
$251$	−5.43028	−0.342756	−0.171378	+	0.985205i	$0.554822\pi$
$252$	−17.3647	−1.09387
$253$	−1.30062	−0.0817690
$254$	7.32941	0.459888
$255$	2.05960	0.128977
$256$	−1.37952	−0.0862198
$257$	−13.7606	−0.858364	−0.429182	−	0.903218i	$-0.641198\pi$
$257$	−13.7606	−0.858364	−0.429182	+	0.903218i	$0.641198\pi$
$258$	1.90010	0.118295
$259$	26.1757	1.62648
$260$	−11.7109	−0.726276
$261$	13.7572	0.851551
$262$	6.26162	0.386844
$263$	3.39787	0.209521	0.104761	−	0.994497i	$-0.466592\pi$
$263$	3.39787	0.209521	0.104761	+	0.994497i	$0.466592\pi$
$264$	1.14747	0.0706217
$265$	−11.1495	−0.684908
$266$	−10.0879	−0.618527
$267$	6.01949	0.368387
$268$	−0.802447	−0.0490173
$269$	24.6024	1.50004	0.750019	−	0.661417i	$-0.230044\pi$
$269$	24.6024	1.50004	0.750019	+	0.661417i	$0.230044\pi$
$270$	1.38403	0.0842291
$271$	10.2069	0.620025	0.310012	−	0.950733i	$-0.399667\pi$
$271$	10.2069	0.620025	0.310012	+	0.950733i	$0.399667\pi$
$272$	10.9840	0.666005
$273$	−11.2436	−0.680495
$274$	0.457114	0.0276153
$275$	1.28534	0.0775090
$276$	0.810357	0.0487778
$277$	−25.0274	−1.50375	−0.751875	−	0.659306i	$-0.770850\pi$
$277$	−25.0274	−1.50375	−0.751875	+	0.659306i	$0.770850\pi$
$278$	−3.14118	−0.188395
$279$	2.36546	0.141616
$280$	−6.94734	−0.415183
$281$	12.4788	0.744420	0.372210	−	0.928149i	$-0.378600\pi$
$281$	12.4788	0.744420	0.372210	+	0.928149i	$0.378600\pi$
$282$	1.46754	0.0873905
$283$	33.1554	1.97088	0.985441	−	0.170017i	$-0.0543821\pi$
$283$	33.1554	1.97088	0.985441	+	0.170017i	$0.0543821\pi$
$284$	−14.1725	−0.840985
$285$	−2.50542	−0.148408
$286$	−4.49578	−0.265841
$287$	36.8884	2.17745
$288$	14.3153	0.843536
$289$	2.84825	0.167544
$290$	2.55463	0.150013
$291$	1.97332	0.115678
$292$	−19.5171	−1.14215
$293$	28.2666	1.65135	0.825676	−	0.564145i	$-0.190794\pi$
$293$	28.2666	1.65135	0.825676	+	0.564145i	$0.190794\pi$
$294$	−1.42154	−0.0829058
$295$	−7.04462	−0.410154
$296$	−14.0501	−0.816643
$297$	−3.43827	−0.199509
$298$	0.711754	0.0412308
$299$	−6.84061	−0.395603
$300$	−0.800841	−0.0462366
$301$	28.5793	1.64728
$302$	5.83229	0.335610
$303$	−0.844795	−0.0485322
$304$	−13.3616	−0.766342
$305$	9.82532	0.562596
$306$	6.42256	0.367153
$307$	1.32541	0.0756450	0.0378225	−	0.999284i	$-0.487958\pi$
$307$	1.32541	0.0756450	0.0378225	+	0.999284i	$0.487958\pi$
$308$	8.01054	0.456443
$309$	−1.56043	−0.0887700
$310$	0.439250	0.0249477
$311$	−18.5927	−1.05429	−0.527147	−	0.849774i	$-0.676738\pi$
$311$	−18.5927	−1.05429	−0.527147	+	0.849774i	$0.676738\pi$
$312$	6.03512	0.341672
$313$	−18.9288	−1.06992	−0.534959	−	0.844878i	$-0.679673\pi$
$313$	−18.9288	−1.06992	−0.534959	+	0.844878i	$0.679673\pi$
$314$	−6.54799	−0.369524
$315$	10.0241	0.564792
$316$	18.1041	1.01843
$317$	9.31123	0.522971	0.261485	−	0.965207i	$-0.415788\pi$
$317$	9.31123	0.522971	0.261485	+	0.965207i	$0.415788\pi$
$318$	2.66686	0.149550
$319$	−6.34636	−0.355328
$320$	−2.27270	−0.127048
$321$	7.97011	0.444848
$322$	−1.88353	−0.104965
$323$	−24.1446	−1.34344
$324$	−12.3378	−0.685433
$325$	6.76028	0.374993
$326$	10.4392	0.578173
$327$	1.48329	0.0820264
$328$	−19.8002	−1.09328
$329$	22.0731	1.21693
$330$	−0.307442	−0.0169241
$331$	19.3008	1.06087	0.530435	−	0.847726i	$-0.322029\pi$
$331$	19.3008	1.06087	0.530435	+	0.847726i	$0.322029\pi$
$332$	21.9087	1.20240
$333$	20.2723	1.11092
$334$	−8.04718	−0.440322
$335$	0.463226	0.0253087
$336$	−4.10056	−0.223704
$337$	−20.0329	−1.09126	−0.545632	−	0.838025i	$-0.683710\pi$
$337$	−20.0329	−1.09126	−0.545632	+	0.838025i	$0.683710\pi$
$338$	−16.9195	−0.920301
$339$	−5.05413	−0.274503
$340$	−7.71765	−0.418548
$341$	−1.09121	−0.0590924
$342$	−7.81277	−0.422466
$343$	3.80231	0.205306
$344$	−15.3402	−0.827089
$345$	−0.467792	−0.0251851
$346$	8.55489	0.459914
$347$	−10.1261	−0.543597	−0.271799	−	0.962354i	$-0.587618\pi$
$347$	−10.1261	−0.543597	−0.271799	+	0.962354i	$0.587618\pi$
$348$	3.95414	0.211964
$349$	8.30709	0.444668	0.222334	−	0.974971i	$-0.428632\pi$
$349$	8.30709	0.444668	0.222334	+	0.974971i	$0.428632\pi$
$350$	1.86141	0.0994964
$351$	−18.0837	−0.965235
$352$	−6.60379	−0.351983
$353$	12.7305	0.677577	0.338788	−	0.940863i	$-0.389983\pi$
$353$	12.7305	0.677577	0.338788	+	0.940863i	$0.389983\pi$
$354$	1.68501	0.0895572
$355$	8.18132	0.434220
$356$	−22.5560	−1.19546
$357$	−7.40974	−0.392165
$358$	−11.5799	−0.612015
$359$	−3.11995	−0.164665	−0.0823324	−	0.996605i	$-0.526237\pi$
$359$	−3.11995	−0.164665	−0.0823324	+	0.996605i	$0.526237\pi$
$360$	−5.38051	−0.283578
$361$	10.3708	0.545834
$362$	−3.38685	−0.178009
$363$	−4.32152	−0.226821
$364$	42.1316	2.20830
$365$	11.2666	0.589720
$366$	−2.35013	−0.122843
$367$	−31.6451	−1.65186	−0.825931	−	0.563771i	$-0.809350\pi$
$367$	−31.6451	−1.65186	−0.825931	+	0.563771i	$0.809350\pi$
$368$	−2.49477	−0.130049
$369$	28.5690	1.48724
$370$	3.76445	0.195704
$371$	40.1120	2.08251
$372$	0.679886	0.0352504
$373$	−25.7053	−1.33097	−0.665486	−	0.746411i	$-0.731776\pi$
$373$	−25.7053	−1.33097	−0.665486	+	0.746411i	$0.731776\pi$
$374$	−2.96280	−0.153203
$375$	0.462298	0.0238730
$376$	−11.8480	−0.611011
$377$	−33.3788	−1.71910
$378$	−4.97924	−0.256105
$379$	−22.4807	−1.15475	−0.577377	−	0.816478i	$-0.695924\pi$
$379$	−22.4807	−1.15475	−0.577377	+	0.816478i	$0.695924\pi$
$380$	9.38819	0.481604
$381$	−6.54892	−0.335511
$382$	5.52036	0.282446
$383$	16.7960	0.858233	0.429117	−	0.903249i	$-0.358825\pi$
$383$	16.7960	0.858233	0.429117	+	0.903249i	$0.358825\pi$
$384$	5.29398	0.270157
$385$	−4.62421	−0.235672
$386$	11.9791	0.609719
$387$	22.1339	1.12513
$388$	−7.39432	−0.375390
$389$	0.583508	0.0295850	0.0147925	−	0.999891i	$-0.495291\pi$
$389$	0.583508	0.0295850	0.0147925	+	0.999891i	$0.495291\pi$
$390$	−1.61700	−0.0818798
$391$	−4.50808	−0.227983
$392$	11.4766	0.579655
$393$	−5.59483	−0.282222
$394$	6.21864	0.313290
$395$	−10.4509	−0.525840
$396$	6.20393	0.311759
$397$	27.5641	1.38340	0.691701	−	0.722184i	$-0.256861\pi$
$397$	27.5641	1.38340	0.691701	+	0.722184i	$0.256861\pi$
$398$	−4.89881	−0.245555
$399$	9.01364	0.451246
$400$	2.46548	0.123274
$401$	24.6066	1.22880	0.614398	−	0.788996i	$-0.289399\pi$
$401$	24.6066	1.22880	0.614398	+	0.788996i	$0.289399\pi$
$402$	−0.110799	−0.00552617
$403$	−5.73924	−0.285892
$404$	3.16557	0.157493
$405$	7.12220	0.353905
$406$	−9.19068	−0.456126
$407$	−9.35185	−0.463554
$408$	3.97725	0.196903
$409$	30.7476	1.52037	0.760186	−	0.649705i	$-0.225108\pi$
$409$	30.7476	1.52037	0.760186	+	0.649705i	$0.225108\pi$
$410$	5.30509	0.262000
$411$	−0.408437	−0.0201467
$412$	5.84718	0.288070
$413$	25.3441	1.24710
$414$	−1.45874	−0.0716930
$415$	−12.6471	−0.620824
$416$	−34.7328	−1.70292
$417$	2.80668	0.137444
$418$	3.60412	0.176283
$419$	27.7938	1.35782	0.678909	−	0.734223i	$-0.262453\pi$
$419$	27.7938	1.35782	0.678909	+	0.734223i	$0.262453\pi$
$420$	2.88115	0.140586
$421$	−24.6794	−1.20280	−0.601400	−	0.798948i	$-0.705390\pi$
$421$	−24.6794	−1.20280	−0.601400	+	0.798948i	$0.705390\pi$
$422$	−0.155479	−0.00756861
$423$	17.0950	0.831187
$424$	−21.5305	−1.04561
$425$	4.45514	0.216106
$426$	−1.95690	−0.0948120
$427$	−35.3481	−1.71061
$428$	−29.8652	−1.44359
$429$	4.01704	0.193944
$430$	4.11012	0.198208
$431$	19.2361	0.926571	0.463285	−	0.886209i	$-0.346670\pi$
$431$	19.2361	0.926571	0.463285	+	0.886209i	$0.346670\pi$
$432$	−6.59512	−0.317308
$433$	−3.49592	−0.168003	−0.0840016	−	0.996466i	$-0.526770\pi$
$433$	−3.49592	−0.168003	−0.0840016	+	0.996466i	$0.526770\pi$
$434$	−1.58027	−0.0758554
$435$	−2.28259	−0.109442
$436$	−5.55813	−0.266186
$437$	5.48389	0.262330
$438$	−2.69486	−0.128766
$439$	−22.1239	−1.05592	−0.527958	−	0.849270i	$-0.677042\pi$
$439$	−22.1239	−1.05592	−0.527958	+	0.849270i	$0.677042\pi$
$440$	2.48209	0.118329
$441$	−16.5592	−0.788532
$442$	−15.5829	−0.741202
$443$	−14.8329	−0.704732	−0.352366	−	0.935862i	$-0.614623\pi$
$443$	−14.8329	−0.704732	−0.352366	+	0.935862i	$0.614623\pi$
$444$	5.82673	0.276525
$445$	13.0208	0.617245
$446$	−2.44586	−0.115815
$447$	−0.635960	−0.0300799
$448$	8.17638	0.386297
$449$	−31.8110	−1.50125	−0.750626	−	0.660727i	$-0.770248\pi$
$449$	−31.8110	−1.50125	−0.750626	+	0.660727i	$0.770248\pi$
$450$	1.44161	0.0679580
$451$	−13.1792	−0.620584
$452$	18.9386	0.890797
$453$	−5.21122	−0.244844
$454$	6.27927	0.294701
$455$	−24.3211	−1.14019
$456$	−4.83815	−0.226567
$457$	11.1322	0.520743	0.260371	−	0.965509i	$-0.416155\pi$
$457$	11.1322	0.520743	0.260371	+	0.965509i	$0.416155\pi$
$458$	11.3187	0.528886
$459$	−11.9174	−0.556258
$460$	1.75289	0.0817288
$461$	30.5173	1.42133	0.710666	−	0.703530i	$-0.248394\pi$
$461$	30.5173	1.42133	0.710666	+	0.703530i	$0.248394\pi$
$462$	1.10607	0.0514590
$463$	−18.0675	−0.839669	−0.419834	−	0.907601i	$-0.637912\pi$
$463$	−18.0675	−0.839669	−0.419834	+	0.907601i	$0.637912\pi$
$464$	−12.1733	−0.565130
$465$	−0.392475	−0.0182006
$466$	4.57695	0.212023
$467$	8.19719	0.379321	0.189660	−	0.981850i	$-0.439261\pi$
$467$	8.19719	0.379321	0.189660	+	0.981850i	$0.439261\pi$
$468$	32.6297	1.50831
$469$	−1.66653	−0.0769530
$470$	3.17443	0.146426
$471$	5.85070	0.269586
$472$	−13.6037	−0.626160
$473$	−10.2106	−0.469484
$474$	2.49975	0.114817
$475$	−5.41949	−0.248663
$476$	27.7654	1.27263
$477$	31.0656	1.42240
$478$	−3.78135	−0.172955
$479$	24.6542	1.12648	0.563239	−	0.826294i	$-0.309555\pi$
$479$	24.6542	1.12648	0.563239	+	0.826294i	$0.309555\pi$
$480$	−2.37518	−0.108412
$481$	−49.1862	−2.24270
$482$	−0.517395	−0.0235667
$483$	1.68295	0.0765770
$484$	16.1934	0.736063
$485$	4.26849	0.193822
$486$	−5.85564	−0.265617
$487$	17.1733	0.778196	0.389098	−	0.921196i	$-0.372787\pi$
$487$	17.1733	0.778196	0.389098	+	0.921196i	$0.372787\pi$
$488$	18.9734	0.858886
$489$	−9.32754	−0.421806
$490$	−3.07494	−0.138911
$491$	6.59277	0.297527	0.148764	−	0.988873i	$-0.452471\pi$
$491$	6.59277	0.297527	0.148764	+	0.988873i	$0.452471\pi$
$492$	8.21139	0.370198
$493$	−21.9972	−0.990704
$494$	18.9559	0.852867
$495$	−3.58132	−0.160968
$496$	−2.09310	−0.0939832
$497$	−29.4336	−1.32028
$498$	3.02508	0.135557
$499$	18.3678	0.822256	0.411128	−	0.911578i	$-0.365135\pi$
$499$	18.3678	0.822256	0.411128	+	0.911578i	$0.365135\pi$
$500$	−1.73230	−0.0774709
$501$	7.19025	0.321237
$502$	2.80960	0.125399
$503$	−4.71369	−0.210173	−0.105087	−	0.994463i	$-0.533512\pi$
$503$	−4.71369	−0.210173	−0.105087	+	0.994463i	$0.533512\pi$
$504$	19.3572	0.862239
$505$	−1.82738	−0.0813173
$506$	0.672932	0.0299155
$507$	15.1178	0.671405
$508$	24.5398	1.08878
$509$	−13.3517	−0.591804	−0.295902	−	0.955218i	$-0.595620\pi$
$509$	−13.3517	−0.591804	−0.295902	+	0.955218i	$0.595620\pi$
$510$	−1.06563	−0.0471868
$511$	−40.5333	−1.79309
$512$	−22.1891	−0.980629
$513$	14.4971	0.640061
$514$	7.11967	0.314035
$515$	−3.37538	−0.148737
$516$	6.36178	0.280062
$517$	−7.88611	−0.346831
$518$	−13.5432	−0.595053
$519$	−7.64389	−0.335530
$520$	13.0546	0.572482
$521$	−21.9104	−0.959912	−0.479956	−	0.877292i	$-0.659347\pi$
$521$	−21.9104	−0.959912	−0.479956	+	0.877292i	$0.659347\pi$
$522$	−7.11792	−0.311543
$523$	−1.32237	−0.0578230	−0.0289115	−	0.999582i	$-0.509204\pi$
$523$	−1.32237	−0.0578230	−0.0289115	+	0.999582i	$0.509204\pi$
$524$	20.9647	0.915847
$525$	−1.66319	−0.0725875
$526$	−1.75804	−0.0766541
$527$	−3.78226	−0.164758
$528$	1.46501	0.0637566
$529$	−21.9761	−0.955482
$530$	5.76869	0.250576
$531$	19.6283	0.851795
$532$	−33.7755	−1.46435
$533$	−69.3162	−3.00242
$534$	−3.11446	−0.134776
$535$	17.2402	0.745358
$536$	0.894523	0.0386375
$537$	10.3467	0.446495
$538$	−12.7292	−0.548794
$539$	7.63893	0.329032
$540$	4.63389	0.199411
$541$	−1.30652	−0.0561716	−0.0280858	−	0.999606i	$-0.508941\pi$
$541$	−1.30652	−0.0561716	−0.0280858	+	0.999606i	$0.508941\pi$
$542$	−5.28099	−0.226838
$543$	3.02619	0.129866
$544$	−22.8895	−0.981379
$545$	3.20852	0.137438
$546$	5.81740	0.248962
$547$	−40.5520	−1.73388	−0.866940	−	0.498412i	$-0.833917\pi$
$547$	−40.5520	−1.73388	−0.866940	+	0.498412i	$0.833917\pi$
$548$	1.53048	0.0653787
$549$	−27.3761	−1.16838
$550$	−0.665029	−0.0283569
$551$	26.7587	1.13996
$552$	−0.903341	−0.0384487
$553$	37.5986	1.59886
$554$	12.9490	0.550152
$555$	−3.36358	−0.142776
$556$	−10.5171	−0.446023
$557$	12.2922	0.520839	0.260420	−	0.965496i	$-0.416139\pi$
$557$	12.2922	0.520839	0.260420	+	0.965496i	$0.416139\pi$
$558$	−1.22387	−0.0518107
$559$	−53.7028	−2.27139
$560$	−8.86993	−0.374823
$561$	2.64729	0.111769
$562$	−6.45644	−0.272349
$563$	28.4326	1.19829	0.599146	−	0.800640i	$-0.295507\pi$
$563$	28.4326	1.19829	0.599146	+	0.800640i	$0.295507\pi$
$564$	4.91349	0.206895
$565$	−10.9326	−0.459939
$566$	−17.1544	−0.721054
$567$	−25.6232	−1.07607
$568$	15.7987	0.662900
$569$	35.8760	1.50400	0.752000	−	0.659164i	$-0.229090\pi$
$569$	35.8760	1.50400	0.752000	+	0.659164i	$0.229090\pi$
$570$	1.29629	0.0542957
$571$	−38.7951	−1.62352	−0.811762	−	0.583989i	$-0.801491\pi$
$571$	−38.7951	−1.62352	−0.811762	+	0.583989i	$0.801491\pi$
$572$	−15.0524	−0.629374
$573$	−4.93251	−0.206058
$574$	−19.0859	−0.796629
$575$	−1.01188	−0.0421984
$576$	6.33237	0.263849
$577$	40.3003	1.67772	0.838861	−	0.544346i	$-0.183222\pi$
$577$	40.3003	1.67772	0.838861	+	0.544346i	$0.183222\pi$
$578$	−1.47367	−0.0612965
$579$	−10.7034	−0.444820
$580$	8.55323	0.355153
$581$	45.5001	1.88766
$582$	−1.02098	−0.0423212
$583$	−14.3309	−0.593526
$584$	21.7566	0.900295
$585$	−18.8360	−0.778774
$586$	−14.6250	−0.604153
$587$	−9.50572	−0.392343	−0.196172	−	0.980570i	$-0.562851\pi$
$587$	−9.50572	−0.392343	−0.196172	+	0.980570i	$0.562851\pi$
$588$	−4.75949	−0.196278
$589$	4.60096	0.189579
$590$	3.64485	0.150056
$591$	−5.55642	−0.228561
$592$	−17.9382	−0.737257
$593$	−7.37542	−0.302872	−0.151436	−	0.988467i	$-0.548390\pi$
$593$	−7.37542	−0.302872	−0.151436	+	0.988467i	$0.548390\pi$
$594$	1.77895	0.0729910
$595$	−16.0280	−0.657086
$596$	2.38304	0.0976131
$597$	4.37714	0.179145
$598$	3.53930	0.144733
$599$	47.2442	1.93035	0.965173	−	0.261614i	$-0.0842548\pi$
$599$	47.2442	1.93035	0.965173	+	0.261614i	$0.0842548\pi$
$600$	0.892733	0.0364457
$601$	19.6960	0.803418	0.401709	−	0.915767i	$-0.368416\pi$
$601$	19.6960	0.803418	0.401709	+	0.915767i	$0.368416\pi$
$602$	−14.7868	−0.602665
$603$	−1.29068	−0.0525604
$604$	19.5272	0.794551
$605$	−9.34790	−0.380046
$606$	0.437092	0.0177557
$607$	9.15246	0.371487	0.185744	−	0.982598i	$-0.440531\pi$
$607$	9.15246	0.371487	0.185744	+	0.982598i	$0.440531\pi$
$608$	27.8441	1.12923
$609$	8.21198	0.332766
$610$	−5.08357	−0.205828
$611$	−41.4772	−1.67799
$612$	21.5035	0.869228
$613$	−6.97258	−0.281620	−0.140810	−	0.990037i	$-0.544971\pi$
$613$	−6.97258	−0.281620	−0.140810	+	0.990037i	$0.544971\pi$
$614$	−0.685759	−0.0276750
$615$	−4.74016	−0.191142
$616$	−8.92970	−0.359788
$617$	−13.3135	−0.535980	−0.267990	−	0.963422i	$-0.586359\pi$
$617$	−13.3135	−0.535980	−0.267990	+	0.963422i	$0.586359\pi$
$618$	0.807361	0.0324768
$619$	−3.13603	−0.126048	−0.0630239	−	0.998012i	$-0.520074\pi$
$619$	−3.13603	−0.126048	−0.0630239	+	0.998012i	$0.520074\pi$
$620$	1.47066	0.0590633
$621$	2.70677	0.108619
$622$	9.61976	0.385717
$623$	−46.8443	−1.87678
$624$	7.70527	0.308458
$625$	1.00000	0.0400000
$626$	9.79365	0.391433
$627$	−3.22032	−0.128607
$628$	−21.9235	−0.874842
$629$	−32.4146	−1.29245
$630$	−5.18640	−0.206631
$631$	−24.6989	−0.983249	−0.491625	−	0.870807i	$-0.663597\pi$
$631$	−24.6989	−0.983249	−0.491625	+	0.870807i	$0.663597\pi$
$632$	−20.1814	−0.802773
$633$	0.138923	0.00552168
$634$	−4.81758	−0.191331
$635$	−14.1660	−0.562161
$636$	8.92897	0.354057
$637$	40.1771	1.59188
$638$	3.28357	0.129998
$639$	−22.7955	−0.901774
$640$	11.4514	0.452657
$641$	44.9841	1.77676	0.888382	−	0.459104i	$-0.151830\pi$
$641$	44.9841	1.77676	0.888382	+	0.459104i	$0.151830\pi$
$642$	−4.12369	−0.162749
$643$	−19.2598	−0.759531	−0.379765	−	0.925083i	$-0.623995\pi$
$643$	−19.2598	−0.759531	−0.379765	+	0.925083i	$0.623995\pi$
$644$	−6.30628	−0.248502
$645$	−3.67244	−0.144602
$646$	12.4923	0.491502
$647$	18.2715	0.718325	0.359163	−	0.933275i	$-0.383062\pi$
$647$	18.2715	0.718325	0.359163	+	0.933275i	$0.383062\pi$
$648$	13.7535	0.540288
$649$	−9.05475	−0.355430
$650$	−3.49773	−0.137192
$651$	1.41199	0.0553403
$652$	34.9517	1.36881
$653$	32.1861	1.25954	0.629770	−	0.776781i	$-0.283149\pi$
$653$	32.1861	1.25954	0.629770	+	0.776781i	$0.283149\pi$
$654$	−0.767449	−0.0300096
$655$	−12.1022	−0.472873
$656$	−25.2797	−0.987005
$657$	−31.3918	−1.22471
$658$	−11.4205	−0.445218
$659$	−45.5191	−1.77317	−0.886586	−	0.462564i	$-0.846929\pi$
$659$	−45.5191	−1.77317	−0.886586	+	0.462564i	$0.846929\pi$
$660$	−1.02935	−0.0400675
$661$	15.1872	0.590715	0.295358	−	0.955387i	$-0.404561\pi$
$661$	15.1872	0.590715	0.295358	+	0.955387i	$0.404561\pi$
$662$	−9.98616	−0.388123
$663$	13.9235	0.540744
$664$	−24.4226	−0.947780
$665$	19.4974	0.756078
$666$	−10.4888	−0.406433
$667$	4.99616	0.193452
$668$	−26.9430	−1.04245
$669$	2.18540	0.0844926
$670$	−0.239671	−0.00925928
$671$	12.6289	0.487533
$672$	8.54509	0.329634
$673$	−28.3153	−1.09148	−0.545738	−	0.837956i	$-0.683751\pi$
$673$	−28.3153	−1.09148	−0.545738	+	0.837956i	$0.683751\pi$
$674$	10.3649	0.399242
$675$	−2.67499	−0.102960
$676$	−56.6487	−2.17880
$677$	32.8443	1.26231	0.631155	−	0.775656i	$-0.282581\pi$
$677$	32.8443	1.26231	0.631155	+	0.775656i	$0.282581\pi$
$678$	2.61498	0.100428
$679$	−15.3566	−0.589331
$680$	8.60320	0.329918
$681$	−5.61060	−0.214999
$682$	0.564587	0.0216191
$683$	−19.0599	−0.729308	−0.364654	−	0.931143i	$-0.618813\pi$
$683$	−19.0599	−0.729308	−0.364654	+	0.931143i	$0.618813\pi$
$684$	−26.1581	−1.00018
$685$	−0.883492	−0.0337565
$686$	−1.96730	−0.0751118
$687$	−10.1134	−0.385849
$688$	−19.5854	−0.746688
$689$	−75.3738	−2.87151
$690$	0.242033	0.00921404
$691$	−23.9110	−0.909617	−0.454809	−	0.890589i	$-0.650292\pi$
$691$	−23.9110	−0.909617	−0.454809	+	0.890589i	$0.650292\pi$
$692$	28.6428	1.08884
$693$	12.8844	0.489436
$694$	5.23919	0.198877
$695$	6.07115	0.230292
$696$	−4.40786	−0.167079
$697$	−45.6806	−1.73027
$698$	−4.29804	−0.162683
$699$	−4.08956	−0.154681
$700$	6.23222	0.235556
$701$	−18.8422	−0.711661	−0.355831	−	0.934550i	$-0.615802\pi$
$701$	−18.8422	−0.711661	−0.355831	+	0.934550i	$0.615802\pi$
$702$	9.35640	0.353134
$703$	39.4309	1.48717
$704$	−2.92119	−0.110097
$705$	−2.83639	−0.106825
$706$	−6.58670	−0.247894
$707$	6.57428	0.247251
$708$	5.64162	0.212025
$709$	36.1574	1.35792	0.678960	−	0.734175i	$-0.262431\pi$
$709$	36.1574	1.35792	0.678960	+	0.734175i	$0.262431\pi$
$710$	−4.23297	−0.158861
$711$	29.1190	1.09205
$712$	25.1441	0.942316
$713$	0.859053	0.0321718
$714$	3.83376	0.143475
$715$	8.68927	0.324960
$716$	−38.7708	−1.44893
$717$	3.37868	0.126179
$718$	1.61425	0.0602432
$719$	10.3086	0.384446	0.192223	−	0.981351i	$-0.438430\pi$
$719$	10.3086	0.384446	0.192223	+	0.981351i	$0.438430\pi$
$720$	−6.86951	−0.256012
$721$	12.1435	0.452246
$722$	−5.36582	−0.199695
$723$	0.462298	0.0171931
$724$	−11.3396	−0.421433
$725$	−4.93749	−0.183374
$726$	2.23593	0.0829832
$727$	−19.4367	−0.720866	−0.360433	−	0.932785i	$-0.617371\pi$
$727$	−19.4367	−0.720866	−0.360433	+	0.932785i	$0.617371\pi$
$728$	−46.9659	−1.74067
$729$	−16.1345	−0.597574
$730$	−5.82927	−0.215751
$731$	−35.3911	−1.30899
$732$	−7.86852	−0.290829
$733$	−15.4107	−0.569207	−0.284604	−	0.958645i	$-0.591862\pi$
$733$	−15.4107	−0.569207	−0.284604	+	0.958645i	$0.591862\pi$
$734$	16.3730	0.604339
$735$	2.74749	0.101343
$736$	5.19882	0.191631
$737$	0.595403	0.0219320
$738$	−14.7815	−0.544113
$739$	7.81949	0.287645	0.143822	−	0.989604i	$-0.454061\pi$
$739$	7.81949	0.287645	0.143822	+	0.989604i	$0.454061\pi$
$740$	12.6038	0.463326
$741$	−16.9373	−0.622209
$742$	−20.7538	−0.761895
$743$	−28.5857	−1.04871	−0.524353	−	0.851501i	$-0.675693\pi$
$743$	−28.5857	−1.04871	−0.524353	+	0.851501i	$0.675693\pi$
$744$	−0.757899	−0.0277859
$745$	−1.37565	−0.0503999
$746$	13.2998	0.486940
$747$	35.2385	1.28931
$748$	−9.91981	−0.362704
$749$	−62.0242	−2.26632
$750$	−0.239191	−0.00873401
$751$	−11.8666	−0.433019	−0.216510	−	0.976280i	$-0.569467\pi$
$751$	−11.8666	−0.433019	−0.216510	+	0.976280i	$0.569467\pi$
$752$	−15.1267	−0.551615
$753$	−2.51041	−0.0914844
$754$	17.2700	0.628937
$755$	−11.2724	−0.410245
$756$	−16.6711	−0.606323
$757$	19.4160	0.705685	0.352843	−	0.935683i	$-0.385215\pi$
$757$	19.4160	0.705685	0.352843	+	0.935683i	$0.385215\pi$
$758$	11.6314	0.422471
$759$	−0.601272	−0.0218248
$760$	−10.4654	−0.379621
$761$	−3.61309	−0.130975	−0.0654873	−	0.997853i	$-0.520860\pi$
$761$	−3.61309	−0.130975	−0.0654873	+	0.997853i	$0.520860\pi$
$762$	3.38838	0.122748
$763$	−11.5431	−0.417890
$764$	18.4829	0.668686
$765$	−12.4133	−0.448802
$766$	−8.69014	−0.313988
$767$	−47.6236	−1.71959
$768$	−0.637748	−0.0230128
$769$	23.3498	0.842016	0.421008	−	0.907057i	$-0.361676\pi$
$769$	23.3498	0.842016	0.421008	+	0.907057i	$0.361676\pi$
$770$	2.39254	0.0862213
$771$	−6.36151	−0.229104
$772$	40.1074	1.44350
$773$	16.4650	0.592204	0.296102	−	0.955156i	$-0.404313\pi$
$773$	16.4650	0.592204	0.296102	+	0.955156i	$0.404313\pi$
$774$	−11.4519	−0.411632
$775$	−0.848965	−0.0304957
$776$	8.24278	0.295898
$777$	12.1010	0.434120
$778$	−0.301904	−0.0108238
$779$	55.5685	1.99095
$780$	−5.41391	−0.193849
$781$	10.5158	0.376285
$782$	2.33246	0.0834084
$783$	13.2077	0.472006
$784$	14.6526	0.523308
$785$	12.6557	0.451701
$786$	2.89474	0.103252
$787$	31.7545	1.13193	0.565963	−	0.824431i	$-0.308504\pi$
$787$	31.7545	1.13193	0.565963	+	0.824431i	$0.308504\pi$
$788$	20.8208	0.741709
$789$	1.57083	0.0559230
$790$	5.40722	0.192380
$791$	39.3318	1.39848
$792$	−6.91580	−0.245742
$793$	66.4219	2.35871
$794$	−14.2615	−0.506123
$795$	−5.15440	−0.182808
$796$	−16.4018	−0.581347
$797$	−1.56344	−0.0553800	−0.0276900	−	0.999617i	$-0.508815\pi$
$797$	−1.56344	−0.0553800	−0.0276900	+	0.999617i	$0.508815\pi$
$798$	−4.66361	−0.165090
$799$	−27.3341	−0.967012
$800$	−5.13777	−0.181648
$801$	−36.2796	−1.28188
$802$	−12.7313	−0.449559
$803$	14.4814	0.511038
$804$	−0.370970	−0.0130831
$805$	3.64040	0.128307
$806$	2.96945	0.104595
$807$	11.3737	0.400372
$808$	−3.52880	−0.124143
$809$	−26.4294	−0.929208	−0.464604	−	0.885519i	$-0.653803\pi$
$809$	−26.4294	−0.929208	−0.464604	+	0.885519i	$0.653803\pi$
$810$	−3.68499	−0.129477
$811$	36.2275	1.27212	0.636059	−	0.771640i	$-0.280563\pi$
$811$	36.2275	1.27212	0.636059	+	0.771640i	$0.280563\pi$
$812$	−30.7716	−1.07987
$813$	4.71863	0.165490
$814$	4.83860	0.169593
$815$	−20.1764	−0.706750
$816$	5.07790	0.177762
$817$	43.0517	1.50619
$818$	−15.9087	−0.556234
$819$	67.7655	2.36792
$820$	17.7621	0.620279
$821$	−11.0713	−0.386392	−0.193196	−	0.981160i	$-0.561885\pi$
$821$	−11.0713	−0.386392	−0.193196	+	0.981160i	$0.561885\pi$
$822$	0.211323	0.00737075
$823$	33.3273	1.16172	0.580858	−	0.814005i	$-0.302717\pi$
$823$	33.3273	1.16172	0.580858	+	0.814005i	$0.302717\pi$
$824$	−6.51812	−0.227069
$825$	0.594211	0.0206878
$826$	−13.1129	−0.456257
$827$	−4.82069	−0.167632	−0.0838158	−	0.996481i	$-0.526711\pi$
$827$	−4.82069	−0.167632	−0.0838158	+	0.996481i	$0.526711\pi$
$828$	−4.88403	−0.169732
$829$	6.97354	0.242201	0.121101	−	0.992640i	$-0.461358\pi$
$829$	6.97354	0.242201	0.121101	+	0.992640i	$0.461358\pi$
$830$	6.54357	0.227131
$831$	−11.5701	−0.401363
$832$	−15.3641	−0.532653
$833$	26.4774	0.917387
$834$	−1.45216	−0.0502843
$835$	15.5533	0.538243
$836$	12.0670	0.417347
$837$	2.27097	0.0784963
$838$	−14.3804	−0.496762
$839$	−27.3701	−0.944921	−0.472460	−	0.881352i	$-0.656634\pi$
$839$	−27.3701	−0.944921	−0.472460	+	0.881352i	$0.656634\pi$
$840$	−3.21174	−0.110816
$841$	−4.62119	−0.159351
$842$	12.7690	0.440049
$843$	5.76891	0.198692
$844$	−0.520564	−0.0179186
$845$	32.7014	1.12496
$846$	−8.84486	−0.304093
$847$	33.6305	1.15556
$848$	−27.4888	−0.943971
$849$	15.3277	0.526045
$850$	−2.30506	−0.0790631
$851$	7.36223	0.252374
$852$	−6.55194	−0.224466
$853$	21.2407	0.727267	0.363634	−	0.931542i	$-0.381536\pi$
$853$	21.2407	0.727267	0.363634	+	0.931542i	$0.381536\pi$
$854$	18.2889	0.625834
$855$	15.1002	0.516416
$856$	33.2921	1.13790
$857$	−28.0058	−0.956661	−0.478330	−	0.878180i	$-0.658758\pi$
$857$	−28.0058	−0.956661	−0.478330	+	0.878180i	$0.658758\pi$
$858$	−2.07839	−0.0709552
$859$	32.4432	1.10695	0.553474	−	0.832866i	$-0.313302\pi$
$859$	32.4432	1.10695	0.553474	+	0.832866i	$0.313302\pi$
$860$	13.7612	0.469253
$861$	17.0534	0.581180
$862$	−9.95266	−0.338989
$863$	−44.6876	−1.52118	−0.760592	−	0.649230i	$-0.775091\pi$
$863$	−44.6876	−1.52118	−0.760592	+	0.649230i	$0.775091\pi$
$864$	13.7435	0.467563
$865$	−16.5345	−0.562191
$866$	1.80877	0.0614646
$867$	1.31674	0.0447188
$868$	−5.29094	−0.179586
$869$	−13.4329	−0.455681
$870$	1.18100	0.0400397
$871$	3.13154	0.106108
$872$	6.19589	0.209819
$873$	−11.8932	−0.402524
$874$	−2.83733	−0.0959743
$875$	−3.59765	−0.121623
$876$	−9.02274	−0.304850
$877$	24.8385	0.838738	0.419369	−	0.907816i	$-0.362251\pi$
$877$	24.8385	0.838738	0.419369	+	0.907816i	$0.362251\pi$
$878$	11.4468	0.386310
$879$	13.0676	0.440759
$880$	3.16898	0.106826
$881$	50.4201	1.69870	0.849348	−	0.527834i	$-0.176996\pi$
$881$	50.4201	1.69870	0.849348	+	0.527834i	$0.176996\pi$
$882$	8.56763	0.288487
$883$	46.4343	1.56264	0.781318	−	0.624133i	$-0.214547\pi$
$883$	46.4343	1.56264	0.781318	+	0.624133i	$0.214547\pi$
$884$	−52.1734	−1.75478
$885$	−3.25672	−0.109473
$886$	7.67446	0.257829
$887$	11.4253	0.383625	0.191812	−	0.981432i	$-0.438563\pi$
$887$	11.4253	0.383625	0.191812	+	0.981432i	$0.438563\pi$
$888$	−6.49532	−0.217969
$889$	50.9644	1.70929
$890$	−6.73689	−0.225821
$891$	9.15446	0.306686
$892$	−8.18904	−0.274189
$893$	33.2508	1.11270
$894$	0.329043	0.0110048
$895$	22.3811	0.748118
$896$	−41.1983	−1.37634
$897$	−3.16240	−0.105590
$898$	16.4588	0.549238
$899$	4.19176	0.139803
$900$	4.82668	0.160889
$901$	−49.6726	−1.65483
$902$	6.81885	0.227043
$903$	13.2122	0.439674
$904$	−21.1117	−0.702165
$905$	6.54597	0.217595
$906$	2.69626	0.0895771
$907$	51.6187	1.71397	0.856985	−	0.515341i	$-0.172335\pi$
$907$	51.6187	1.71397	0.856985	+	0.515341i	$0.172335\pi$
$908$	21.0238	0.697699
$909$	5.09159	0.168877
$910$	12.5836	0.417144
$911$	2.51190	0.0832230	0.0416115	−	0.999134i	$-0.486751\pi$
$911$	2.51190	0.0832230	0.0416115	+	0.999134i	$0.486751\pi$
$912$	−6.17706	−0.204543
$913$	−16.2559	−0.537992
$914$	−5.75975	−0.190516
$915$	4.54223	0.150161
$916$	37.8963	1.25213
$917$	43.5396	1.43780
$918$	6.16602	0.203509
$919$	11.7201	0.386611	0.193305	−	0.981139i	$-0.438079\pi$
$919$	11.7201	0.386611	0.193305	+	0.981139i	$0.438079\pi$
$920$	−1.95402	−0.0644222
$921$	0.612734	0.0201903
$922$	−15.7895	−0.519999
$923$	55.3080	1.82049
$924$	3.70326	0.121828
$925$	−7.27577	−0.239226
$926$	9.34804	0.307196
$927$	9.40476	0.308893
$928$	25.3677	0.832736
$929$	−18.2262	−0.597982	−0.298991	−	0.954256i	$-0.596650\pi$
$929$	−18.2262	−0.597982	−0.298991	+	0.954256i	$0.596650\pi$
$930$	0.203065	0.00665875
$931$	−32.2086	−1.05560
$932$	15.3242	0.501960
$933$	−8.59537	−0.281400
$934$	−4.24119	−0.138776
$935$	5.72637	0.187272
$936$	−36.3738	−1.18891
$937$	−36.2363	−1.18379	−0.591894	−	0.806016i	$-0.701620\pi$
$937$	−36.2363	−1.18379	−0.591894	+	0.806016i	$0.701620\pi$
$938$	0.862252	0.0281535
$939$	−8.75074	−0.285570
$940$	10.6284	0.346660
$941$	27.9802	0.912130	0.456065	−	0.889946i	$-0.349258\pi$
$941$	27.9802	0.912130	0.456065	+	0.889946i	$0.349258\pi$
$942$	−3.02712	−0.0986290
$943$	10.3753	0.337866
$944$	−17.3684	−0.565292
$945$	9.62368	0.313058
$946$	5.28291	0.171762
$947$	−8.47417	−0.275374	−0.137687	−	0.990476i	$-0.543967\pi$
$947$	−8.47417	−0.275374	−0.137687	+	0.990476i	$0.543967\pi$
$948$	8.36948	0.271828
$949$	76.1652	2.47243
$950$	2.80401	0.0909743
$951$	4.30457	0.139585
$952$	−30.9513	−1.00314
$953$	16.5568	0.536328	0.268164	−	0.963373i	$-0.413583\pi$
$953$	16.5568	0.536328	0.268164	+	0.963373i	$0.413583\pi$
$954$	−16.0732	−0.520389
$955$	−10.6695	−0.345258
$956$	−12.6604	−0.409468
$957$	−2.93391	−0.0948399
$958$	−12.7559	−0.412126
$959$	3.17850	0.102639
$960$	−1.05066	−0.0339100
$961$	−30.2793	−0.976750
$962$	25.4487	0.820499
$963$	−48.0360	−1.54794
$964$	−1.73230	−0.0557937
$965$	−23.1527	−0.745311
$966$	−0.870751	−0.0280160
$967$	10.9162	0.351043	0.175521	−	0.984476i	$-0.443839\pi$
$967$	10.9162	0.351043	0.175521	+	0.984476i	$0.443839\pi$
$968$	−18.0515	−0.580197
$969$	−11.1620	−0.358575
$970$	−2.20850	−0.0709106
$971$	−47.8005	−1.53399	−0.766996	−	0.641652i	$-0.778249\pi$
$971$	−47.8005	−1.53399	−0.766996	+	0.641652i	$0.778249\pi$
$972$	−19.6054	−0.628844
$973$	−21.8419	−0.700219
$974$	−8.88538	−0.284706
$975$	3.12527	0.100089
$976$	24.2241	0.775395
$977$	−27.7877	−0.889008	−0.444504	−	0.895777i	$-0.646620\pi$
$977$	−27.7877	−0.889008	−0.444504	+	0.895777i	$0.646620\pi$
$978$	4.82602	0.154319
$979$	16.7362	0.534890
$980$	−10.2953	−0.328870
$981$	−8.93984	−0.285427
$982$	−3.41106	−0.108851
$983$	10.8079	0.344717	0.172359	−	0.985034i	$-0.444861\pi$
$983$	10.8079	0.344717	0.172359	+	0.985034i	$0.444861\pi$
$984$	−9.15359	−0.291806
$985$	−12.0191	−0.382961
$986$	11.3812	0.362452
$987$	10.2044	0.324809
$988$	63.4668	2.01915
$989$	8.03827	0.255602
$990$	1.85296	0.0588909
$991$	−41.2802	−1.31131	−0.655654	−	0.755061i	$-0.727607\pi$
$991$	−41.2802	−1.31131	−0.655654	+	0.755061i	$0.727607\pi$
$992$	4.36179	0.138487
$993$	8.92275	0.283155
$994$	15.2288	0.483027
$995$	9.46822	0.300163
$996$	10.1284	0.320929
$997$	40.5133	1.28307	0.641534	−	0.767095i	$-0.278298\pi$
$997$	40.5133	1.28307	0.641534	+	0.767095i	$0.278298\pi$
$998$	−9.50341	−0.300825
$999$	19.4626	0.615769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.b.1.6	✓	11
5.4	even	2		6025.2.a.g.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.6	✓	11	1.1	even	1	trivial
6025.2.a.g.1.6		11	5.4	even	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q-0.517395 q^{2} +0.462298 q^{3} -1.73230 q^{4} +1.00000 q^{5} -0.239191 q^{6} -3.59765 q^{7} +1.93107 q^{8} -2.78628 q^{9} +O(q^{10})\)	\(q-0.517395 q^{2} +0.462298 q^{3} -1.73230 q^{4} +1.00000 q^{5} -0.239191 q^{6} -3.59765 q^{7} +1.93107 q^{8} -2.78628 q^{9} -0.517395 q^{10} +1.28534 q^{11} -0.800841 q^{12} +6.76028 q^{13} +1.86141 q^{14} +0.462298 q^{15} +2.46548 q^{16} +4.45514 q^{17} +1.44161 q^{18} -5.41949 q^{19} -1.73230 q^{20} -1.66319 q^{21} -0.665029 q^{22} -1.01188 q^{23} +0.892733 q^{24} +1.00000 q^{25} -3.49773 q^{26} -2.67499 q^{27} +6.23222 q^{28} -4.93749 q^{29} -0.239191 q^{30} -0.848965 q^{31} -5.13777 q^{32} +0.594211 q^{33} -2.30506 q^{34} -3.59765 q^{35} +4.82668 q^{36} -7.27577 q^{37} +2.80401 q^{38} +3.12527 q^{39} +1.93107 q^{40} -10.2535 q^{41} +0.860526 q^{42} -7.94388 q^{43} -2.22660 q^{44} -2.78628 q^{45} +0.523543 q^{46} -6.13542 q^{47} +1.13979 q^{48} +5.94311 q^{49} -0.517395 q^{50} +2.05960 q^{51} -11.7109 q^{52} -11.1495 q^{53} +1.38403 q^{54} +1.28534 q^{55} -6.94734 q^{56} -2.50542 q^{57} +2.55463 q^{58} -7.04462 q^{59} -0.800841 q^{60} +9.82532 q^{61} +0.439250 q^{62} +10.0241 q^{63} -2.27270 q^{64} +6.76028 q^{65} -0.307442 q^{66} +0.463226 q^{67} -7.71765 q^{68} -0.467792 q^{69} +1.86141 q^{70} +8.18132 q^{71} -5.38051 q^{72} +11.2666 q^{73} +3.76445 q^{74} +0.462298 q^{75} +9.38819 q^{76} -4.62421 q^{77} -1.61700 q^{78} -10.4509 q^{79} +2.46548 q^{80} +7.12220 q^{81} +5.30509 q^{82} -12.6471 q^{83} +2.88115 q^{84} +4.45514 q^{85} +4.11012 q^{86} -2.28259 q^{87} +2.48209 q^{88} +13.0208 q^{89} +1.44161 q^{90} -24.3211 q^{91} +1.75289 q^{92} -0.392475 q^{93} +3.17443 q^{94} -5.41949 q^{95} -2.37518 q^{96} +4.26849 q^{97} -3.07494 q^{98} -3.58132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 4 q^{2} - 8 q^{3} + 6 q^{4} + 11 q^{5} + 7 q^{6} - 9 q^{7} - 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q - 4 * q^2 - 8 * q^3 + 6 * q^4 + 11 * q^5 + 7 * q^6 - 9 * q^7 - 12 * q^8 + 9 * q^9	\( 11 q - 4 q^{2} - 8 q^{3} + 6 q^{4} + 11 q^{5} + 7 q^{6} - 9 q^{7} - 12 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 28 q^{12} - 9 q^{13} + 2 q^{14} - 8 q^{15} - 16 q^{16} - 4 q^{17} - 6 q^{18} - 33 q^{19} + 6 q^{20} + 2 q^{21} + 6 q^{22} - 31 q^{23} + 32 q^{24} + 11 q^{25} - 20 q^{26} - 32 q^{27} - q^{28} + q^{29} + 7 q^{30} + 6 q^{31} + 7 q^{32} - 35 q^{33} + 9 q^{34} - 9 q^{35} + 33 q^{36} - 23 q^{37} + 20 q^{38} + 14 q^{39} - 12 q^{40} + 8 q^{41} - 26 q^{42} - 19 q^{43} + 9 q^{45} + 6 q^{46} - 35 q^{47} + 16 q^{48} + 4 q^{49} - 4 q^{50} - 3 q^{51} - 3 q^{52} + 14 q^{53} + 9 q^{54} - 3 q^{55} + 33 q^{56} + q^{57} - 11 q^{58} - 6 q^{59} - 28 q^{60} + 9 q^{61} - 23 q^{62} - 31 q^{63} + 18 q^{64} - 9 q^{65} - 36 q^{66} - 54 q^{67} + q^{68} + 17 q^{69} + 2 q^{70} - 5 q^{71} - 64 q^{72} + 17 q^{73} + 8 q^{74} - 8 q^{75} - 31 q^{76} - 18 q^{77} + 15 q^{78} - 16 q^{79} - 16 q^{80} + 43 q^{81} - 61 q^{82} - 29 q^{83} + 69 q^{84} - 4 q^{85} + 5 q^{86} + 5 q^{87} - 14 q^{88} - 5 q^{89} - 6 q^{90} - 54 q^{91} - 6 q^{92} - 25 q^{93} - 19 q^{94} - 33 q^{95} + 9 q^{96} + 6 q^{97} - 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q - 4 * q^2 - 8 * q^3 + 6 * q^4 + 11 * q^5 + 7 * q^6 - 9 * q^7 - 12 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 28 * q^12 - 9 * q^13 + 2 * q^14 - 8 * q^15 - 16 * q^16 - 4 * q^17 - 6 * q^18 - 33 * q^19 + 6 * q^20 + 2 * q^21 + 6 * q^22 - 31 * q^23 + 32 * q^24 + 11 * q^25 - 20 * q^26 - 32 * q^27 - q^28 + q^29 + 7 * q^30 + 6 * q^31 + 7 * q^32 - 35 * q^33 + 9 * q^34 - 9 * q^35 + 33 * q^36 - 23 * q^37 + 20 * q^38 + 14 * q^39 - 12 * q^40 + 8 * q^41 - 26 * q^42 - 19 * q^43 + 9 * q^45 + 6 * q^46 - 35 * q^47 + 16 * q^48 + 4 * q^49 - 4 * q^50 - 3 * q^51 - 3 * q^52 + 14 * q^53 + 9 * q^54 - 3 * q^55 + 33 * q^56 + q^57 - 11 * q^58 - 6 * q^59 - 28 * q^60 + 9 * q^61 - 23 * q^62 - 31 * q^63 + 18 * q^64 - 9 * q^65 - 36 * q^66 - 54 * q^67 + q^68 + 17 * q^69 + 2 * q^70 - 5 * q^71 - 64 * q^72 + 17 * q^73 + 8 * q^74 - 8 * q^75 - 31 * q^76 - 18 * q^77 + 15 * q^78 - 16 * q^79 - 16 * q^80 + 43 * q^81 - 61 * q^82 - 29 * q^83 + 69 * q^84 - 4 * q^85 + 5 * q^86 + 5 * q^87 - 14 * q^88 - 5 * q^89 - 6 * q^90 - 54 * q^91 - 6 * q^92 - 25 * q^93 - 19 * q^94 - 33 * q^95 + 9 * q^96 + 6 * q^97 - 29 * q^98 + 60 * q^99

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