LMFDB - Embedded newform 671.2.a.d.1.19

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			1.19
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)

$f(q)$	$=$	$q+2.54333 q^{2} +0.588033 q^{3} +4.46852 q^{4} -0.268217 q^{5} +1.49556 q^{6} +2.27426 q^{7} +6.27827 q^{8} -2.65422 q^{9} +O(q^{10})$	\(q+2.54333 q^{2} +0.588033 q^{3} +4.46852 q^{4} -0.268217 q^{5} +1.49556 q^{6} +2.27426 q^{7} +6.27827 q^{8} -2.65422 q^{9} -0.682163 q^{10} -1.00000 q^{11} +2.62764 q^{12} +2.39243 q^{13} +5.78420 q^{14} -0.157720 q^{15} +7.03066 q^{16} -6.76468 q^{17} -6.75055 q^{18} +3.70980 q^{19} -1.19853 q^{20} +1.33734 q^{21} -2.54333 q^{22} -8.19571 q^{23} +3.69183 q^{24} -4.92806 q^{25} +6.08473 q^{26} -3.32487 q^{27} +10.1626 q^{28} +6.34878 q^{29} -0.401135 q^{30} +8.61478 q^{31} +5.32474 q^{32} -0.588033 q^{33} -17.2048 q^{34} -0.609995 q^{35} -11.8604 q^{36} +7.70345 q^{37} +9.43525 q^{38} +1.40683 q^{39} -1.68394 q^{40} -2.20942 q^{41} +3.40130 q^{42} +5.10772 q^{43} -4.46852 q^{44} +0.711905 q^{45} -20.8444 q^{46} -10.5052 q^{47} +4.13426 q^{48} -1.82773 q^{49} -12.5337 q^{50} -3.97786 q^{51} +10.6906 q^{52} -10.6862 q^{53} -8.45623 q^{54} +0.268217 q^{55} +14.2784 q^{56} +2.18149 q^{57} +16.1470 q^{58} +7.23987 q^{59} -0.704777 q^{60} +1.00000 q^{61} +21.9102 q^{62} -6.03639 q^{63} -0.518756 q^{64} -0.641689 q^{65} -1.49556 q^{66} +0.912151 q^{67} -30.2281 q^{68} -4.81935 q^{69} -1.55142 q^{70} +9.89206 q^{71} -16.6639 q^{72} -14.2591 q^{73} +19.5924 q^{74} -2.89786 q^{75} +16.5773 q^{76} -2.27426 q^{77} +3.57802 q^{78} +7.24684 q^{79} -1.88574 q^{80} +6.00752 q^{81} -5.61928 q^{82} +5.85956 q^{83} +5.97594 q^{84} +1.81440 q^{85} +12.9906 q^{86} +3.73329 q^{87} -6.27827 q^{88} -11.9080 q^{89} +1.81061 q^{90} +5.44101 q^{91} -36.6227 q^{92} +5.06577 q^{93} -26.7182 q^{94} -0.995031 q^{95} +3.13112 q^{96} -14.3284 q^{97} -4.64851 q^{98} +2.65422 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.54333	1.79841	0.899203	−	0.437532i	$-0.144147\pi$
$2$	2.54333	1.79841	0.899203	+	0.437532i	$0.144147\pi$
$3$	0.588033	0.339501	0.169751	−	0.985487i	$-0.445704\pi$
$3$	0.588033	0.339501	0.169751	+	0.985487i	$0.445704\pi$
$4$	4.46852	2.23426
$5$	−0.268217	−0.119950	−0.0599751	−	0.998200i	$-0.519102\pi$
$5$	−0.268217	−0.119950	−0.0599751	+	0.998200i	$0.519102\pi$
$6$	1.49556	0.610561
$7$	2.27426	0.859591	0.429795	−	0.902926i	$-0.358586\pi$
$7$	2.27426	0.859591	0.429795	+	0.902926i	$0.358586\pi$
$8$	6.27827	2.21970
$9$	−2.65422	−0.884739
$10$	−0.682163	−0.215719
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.62764	0.758534
$13$	2.39243	0.663540	0.331770	−	0.943360i	$-0.392354\pi$
$13$	2.39243	0.663540	0.331770	+	0.943360i	$0.392354\pi$
$14$	5.78420	1.54589
$15$	−0.157720	−0.0407232
$16$	7.03066	1.75766
$17$	−6.76468	−1.64068	−0.820338	−	0.571879i	$-0.806215\pi$
$17$	−6.76468	−1.64068	−0.820338	+	0.571879i	$0.806215\pi$
$18$	−6.75055	−1.59112
$19$	3.70980	0.851087	0.425544	−	0.904938i	$-0.360083\pi$
$19$	3.70980	0.851087	0.425544	+	0.904938i	$0.360083\pi$
$20$	−1.19853	−0.268000
$21$	1.33734	0.291832
$22$	−2.54333	−0.542240
$23$	−8.19571	−1.70892	−0.854462	−	0.519513i	$-0.826113\pi$
$23$	−8.19571	−1.70892	−0.854462	+	0.519513i	$0.826113\pi$
$24$	3.69183	0.753592
$25$	−4.92806	−0.985612
$26$	6.08473	1.19331
$27$	−3.32487	−0.639871
$28$	10.1626	1.92055
$29$	6.34878	1.17894	0.589469	−	0.807791i	$-0.299337\pi$
$29$	6.34878	1.17894	0.589469	+	0.807791i	$0.299337\pi$
$30$	−0.401135	−0.0732368
$31$	8.61478	1.54726	0.773630	−	0.633638i	$-0.218439\pi$
$31$	8.61478	1.54726	0.773630	+	0.633638i	$0.218439\pi$
$32$	5.32474	0.941289
$33$	−0.588033	−0.102363
$34$	−17.2048	−2.95060
$35$	−0.609995	−0.103108
$36$	−11.8604	−1.97674
$37$	7.70345	1.26644	0.633220	−	0.773972i	$-0.281733\pi$
$37$	7.70345	1.26644	0.633220	+	0.773972i	$0.281733\pi$
$38$	9.43525	1.53060
$39$	1.40683	0.225272
$40$	−1.68394	−0.266254
$41$	−2.20942	−0.345053	−0.172527	−	0.985005i	$-0.555193\pi$
$41$	−2.20942	−0.345053	−0.172527	+	0.985005i	$0.555193\pi$
$42$	3.40130	0.524832
$43$	5.10772	0.778920	0.389460	−	0.921043i	$-0.372662\pi$
$43$	5.10772	0.778920	0.389460	+	0.921043i	$0.372662\pi$
$44$	−4.46852	−0.673655
$45$	0.711905	0.106125
$46$	−20.8444	−3.07334
$47$	−10.5052	−1.53234	−0.766170	−	0.642638i	$-0.777840\pi$
$47$	−10.5052	−1.53234	−0.766170	+	0.642638i	$0.777840\pi$
$48$	4.13426	0.596729
$49$	−1.82773	−0.261104
$50$	−12.5337	−1.77253
$51$	−3.97786	−0.557011
$52$	10.6906	1.48252
$53$	−10.6862	−1.46786	−0.733931	−	0.679224i	$-0.762317\pi$
$53$	−10.6862	−1.46786	−0.733931	+	0.679224i	$0.762317\pi$
$54$	−8.45623	−1.15075
$55$	0.268217	0.0361663
$56$	14.2784	1.90804
$57$	2.18149	0.288945
$58$	16.1470	2.12021
$59$	7.23987	0.942551	0.471275	−	0.881986i	$-0.343794\pi$
$59$	7.23987	0.942551	0.471275	+	0.881986i	$0.343794\pi$
$60$	−0.704777	−0.0909863
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	21.9102	2.78260
$63$	−6.03639	−0.760513
$64$	−0.518756	−0.0648445
$65$	−0.641689	−0.0795917
$66$	−1.49556	−0.184091
$67$	0.912151	0.111437	0.0557185	−	0.998447i	$-0.482255\pi$
$67$	0.912151	0.111437	0.0557185	+	0.998447i	$0.482255\pi$
$68$	−30.2281	−3.66570
$69$	−4.81935	−0.580182
$70$	−1.55142	−0.185430
$71$	9.89206	1.17397	0.586986	−	0.809597i	$-0.300315\pi$
$71$	9.89206	1.17397	0.586986	+	0.809597i	$0.300315\pi$
$72$	−16.6639	−1.96386
$73$	−14.2591	−1.66891	−0.834453	−	0.551079i	$-0.814216\pi$
$73$	−14.2591	−1.66891	−0.834453	+	0.551079i	$0.814216\pi$
$74$	19.5924	2.27757
$75$	−2.89786	−0.334616
$76$	16.5773	1.90155
$77$	−2.27426	−0.259176
$78$	3.57802	0.405131
$79$	7.24684	0.815333	0.407667	−	0.913131i	$-0.366343\pi$
$79$	7.24684	0.815333	0.407667	+	0.913131i	$0.366343\pi$
$80$	−1.88574	−0.210832
$81$	6.00752	0.667502
$82$	−5.61928	−0.620545
$83$	5.85956	0.643170	0.321585	−	0.946881i	$-0.395784\pi$
$83$	5.85956	0.643170	0.321585	+	0.946881i	$0.395784\pi$
$84$	5.97594	0.652029
$85$	1.81440	0.196799
$86$	12.9906	1.40081
$87$	3.73329	0.400251
$88$	−6.27827	−0.669266
$89$	−11.9080	−1.26225	−0.631123	−	0.775683i	$-0.717406\pi$
$89$	−11.9080	−1.26225	−0.631123	+	0.775683i	$0.717406\pi$
$90$	1.81061	0.190855
$91$	5.44101	0.570373
$92$	−36.6227	−3.81818
$93$	5.06577	0.525296
$94$	−26.7182	−2.75577
$95$	−0.995031	−0.102088
$96$	3.13112	0.319569
$97$	−14.3284	−1.45483	−0.727415	−	0.686198i	$-0.759278\pi$
$97$	−14.3284	−1.45483	−0.727415	+	0.686198i	$0.759278\pi$
$98$	−4.64851	−0.469570
$99$	2.65422	0.266759
$100$	−22.0212	−2.20212
$101$	10.7833	1.07298	0.536490	−	0.843907i	$-0.319750\pi$
$101$	10.7833	1.07298	0.536490	+	0.843907i	$0.319750\pi$
$102$	−10.1170	−1.00173
$103$	−11.0361	−1.08742	−0.543709	−	0.839273i	$-0.682981\pi$
$103$	−11.0361	−1.08742	−0.543709	+	0.839273i	$0.682981\pi$
$104$	15.0203	1.47286
$105$	−0.358697	−0.0350053
$106$	−27.1785	−2.63981
$107$	−8.48015	−0.819807	−0.409903	−	0.912129i	$-0.634438\pi$
$107$	−8.48015	−0.819807	−0.409903	+	0.912129i	$0.634438\pi$
$108$	−14.8572	−1.42964
$109$	18.4885	1.77087	0.885437	−	0.464759i	$-0.153859\pi$
$109$	18.4885	1.77087	0.885437	+	0.464759i	$0.153859\pi$
$110$	0.682163	0.0650417
$111$	4.52988	0.429957
$112$	15.9896	1.51087
$113$	14.8100	1.39321	0.696604	−	0.717456i	$-0.254693\pi$
$113$	14.8100	1.39321	0.696604	+	0.717456i	$0.254693\pi$
$114$	5.54824	0.519640
$115$	2.19823	0.204986
$116$	28.3697	2.63406
$117$	−6.35002	−0.587060
$118$	18.4134	1.69509
$119$	−15.3847	−1.41031
$120$	−0.990210	−0.0903934
$121$	1.00000	0.0909091
$122$	2.54333	0.230262
$123$	−1.29921	−0.117146
$124$	38.4953	3.45698
$125$	2.66287	0.238174
$126$	−15.3525	−1.36771
$127$	21.6108	1.91765	0.958824	−	0.284001i	$-0.0916618\pi$
$127$	21.6108	1.91765	0.958824	+	0.284001i	$0.0916618\pi$
$128$	−11.9688	−1.05791
$129$	3.00351	0.264444
$130$	−1.63203	−0.143138
$131$	−18.9627	−1.65678	−0.828391	−	0.560150i	$-0.810744\pi$
$131$	−18.9627	−1.65678	−0.828391	+	0.560150i	$0.810744\pi$
$132$	−2.62764	−0.228707
$133$	8.43707	0.731587
$134$	2.31990	0.200409
$135$	0.891785	0.0767526
$136$	−42.4705	−3.64181
$137$	9.47422	0.809437	0.404718	−	0.914441i	$-0.367370\pi$
$137$	9.47422	0.809437	0.404718	+	0.914441i	$0.367370\pi$
$138$	−12.2572	−1.04340
$139$	5.66742	0.480704	0.240352	−	0.970686i	$-0.422737\pi$
$139$	5.66742	0.480704	0.240352	+	0.970686i	$0.422737\pi$
$140$	−2.72578	−0.230370
$141$	−6.17740	−0.520231
$142$	25.1588	2.11128
$143$	−2.39243	−0.200065
$144$	−18.6609	−1.55507
$145$	−1.70285	−0.141414
$146$	−36.2657	−3.00137
$147$	−1.07476	−0.0886450
$148$	34.4230	2.82956
$149$	4.29297	0.351694	0.175847	−	0.984418i	$-0.443734\pi$
$149$	4.29297	0.351694	0.175847	+	0.984418i	$0.443734\pi$
$150$	−7.37022	−0.601776
$151$	0.261474	0.0212785	0.0106392	−	0.999943i	$-0.496613\pi$
$151$	0.261474	0.0212785	0.0106392	+	0.999943i	$0.496613\pi$
$152$	23.2911	1.88916
$153$	17.9549	1.45157
$154$	−5.78420	−0.466104
$155$	−2.31063	−0.185594
$156$	6.28644	0.503318
$157$	1.39628	0.111436	0.0557178	−	0.998447i	$-0.482255\pi$
$157$	1.39628	0.111436	0.0557178	+	0.998447i	$0.482255\pi$
$158$	18.4311	1.46630
$159$	−6.28384	−0.498341
$160$	−1.42818	−0.112908
$161$	−18.6392	−1.46898
$162$	15.2791	1.20044
$163$	−7.80501	−0.611336	−0.305668	−	0.952138i	$-0.598880\pi$
$163$	−7.80501	−0.611336	−0.305668	+	0.952138i	$0.598880\pi$
$164$	−9.87283	−0.770939
$165$	0.157720	0.0122785
$166$	14.9028	1.15668
$167$	−6.06695	−0.469475	−0.234737	−	0.972059i	$-0.575423\pi$
$167$	−6.06695	−0.469475	−0.234737	+	0.972059i	$0.575423\pi$
$168$	8.39619	0.647780
$169$	−7.27629	−0.559715
$170$	4.61462	0.353925
$171$	−9.84662	−0.752990
$172$	22.8240	1.74031
$173$	2.87182	0.218340	0.109170	−	0.994023i	$-0.465181\pi$
$173$	2.87182	0.218340	0.109170	+	0.994023i	$0.465181\pi$
$174$	9.49499	0.719813
$175$	−11.2077	−0.847223
$176$	−7.03066	−0.529956
$177$	4.25728	0.319997
$178$	−30.2860	−2.27003
$179$	9.36671	0.700101	0.350050	−	0.936731i	$-0.386164\pi$
$179$	9.36671	0.700101	0.350050	+	0.936731i	$0.386164\pi$
$180$	3.18117	0.237110
$181$	9.91202	0.736754	0.368377	−	0.929676i	$-0.379913\pi$
$181$	9.91202	0.736754	0.368377	+	0.929676i	$0.379913\pi$
$182$	13.8383	1.02576
$183$	0.588033	0.0434687
$184$	−51.4549	−3.79330
$185$	−2.06619	−0.151910
$186$	12.8839	0.944696
$187$	6.76468	0.494683
$188$	−46.9427	−3.42365
$189$	−7.56162	−0.550027
$190$	−2.53069	−0.183596
$191$	21.8887	1.58381	0.791906	−	0.610643i	$-0.209089\pi$
$191$	21.8887	1.58381	0.791906	+	0.610643i	$0.209089\pi$
$192$	−0.305046	−0.0220148
$193$	−13.0204	−0.937229	−0.468615	−	0.883403i	$-0.655247\pi$
$193$	−13.0204	−0.937229	−0.468615	+	0.883403i	$0.655247\pi$
$194$	−36.4419	−2.61637
$195$	−0.377334	−0.0270215
$196$	−8.16724	−0.583374
$197$	21.7701	1.55106	0.775528	−	0.631313i	$-0.217484\pi$
$197$	21.7701	1.55106	0.775528	+	0.631313i	$0.217484\pi$
$198$	6.75055	0.479741
$199$	0.850734	0.0603069	0.0301535	−	0.999545i	$-0.490400\pi$
$199$	0.850734	0.0603069	0.0301535	+	0.999545i	$0.490400\pi$
$200$	−30.9397	−2.18777
$201$	0.536375	0.0378330
$202$	27.4255	1.92965
$203$	14.4388	1.01340
$204$	−17.7751	−1.24451
$205$	0.592603	0.0413892
$206$	−28.0684	−1.95562
$207$	21.7532	1.51195
$208$	16.8203	1.16628
$209$	−3.70980	−0.256613
$210$	−0.912286	−0.0629537
$211$	−23.3364	−1.60654	−0.803272	−	0.595612i	$-0.796909\pi$
$211$	−23.3364	−1.60654	−0.803272	+	0.595612i	$0.796909\pi$
$212$	−47.7515	−3.27959
$213$	5.81686	0.398564
$214$	−21.5678	−1.47434
$215$	−1.36998	−0.0934315
$216$	−20.8744	−1.42032
$217$	19.5923	1.33001
$218$	47.0223	3.18475
$219$	−8.38485	−0.566596
$220$	1.19853	0.0808051
$221$	−16.1840	−1.08865
$222$	11.5210	0.773238
$223$	−2.86261	−0.191695	−0.0958473	−	0.995396i	$-0.530556\pi$
$223$	−2.86261	−0.191695	−0.0958473	+	0.995396i	$0.530556\pi$
$224$	12.1099	0.809123
$225$	13.0801	0.872009
$226$	37.6667	2.50555
$227$	5.34114	0.354504	0.177252	−	0.984166i	$-0.443279\pi$
$227$	5.34114	0.354504	0.177252	+	0.984166i	$0.443279\pi$
$228$	9.74803	0.645579
$229$	21.8569	1.44435	0.722174	−	0.691712i	$-0.243143\pi$
$229$	21.8569	1.44435	0.722174	+	0.691712i	$0.243143\pi$
$230$	5.59082	0.368647
$231$	−1.33734	−0.0879906
$232$	39.8593	2.61689
$233$	6.28612	0.411817	0.205909	−	0.978571i	$-0.433985\pi$
$233$	6.28612	0.411817	0.205909	+	0.978571i	$0.433985\pi$
$234$	−16.1502	−1.05577
$235$	2.81767	0.183804
$236$	32.3515	2.10591
$237$	4.26138	0.276806
$238$	−39.1283	−2.53631
$239$	3.64449	0.235742	0.117871	−	0.993029i	$-0.462393\pi$
$239$	3.64449	0.235742	0.117871	+	0.993029i	$0.462393\pi$
$240$	−1.10888	−0.0715777
$241$	−4.75672	−0.306408	−0.153204	−	0.988195i	$-0.548959\pi$
$241$	−4.75672	−0.306408	−0.153204	+	0.988195i	$0.548959\pi$
$242$	2.54333	0.163491
$243$	13.5072	0.866489
$244$	4.46852	0.286068
$245$	0.490227	0.0313194
$246$	−3.30432	−0.210676
$247$	8.87543	0.564730
$248$	54.0859	3.43446
$249$	3.44561	0.218357
$250$	6.77256	0.428334
$251$	9.89748	0.624723	0.312362	−	0.949963i	$-0.398880\pi$
$251$	9.89748	0.624723	0.312362	+	0.949963i	$0.398880\pi$
$252$	−26.9737	−1.69919
$253$	8.19571	0.515260
$254$	54.9634	3.44871
$255$	1.06693	0.0668136
$256$	−29.4032	−1.83770
$257$	25.9774	1.62043	0.810214	−	0.586134i	$-0.199351\pi$
$257$	25.9774	1.62043	0.810214	+	0.586134i	$0.199351\pi$
$258$	7.63891	0.475578
$259$	17.5197	1.08862
$260$	−2.86740	−0.177829
$261$	−16.8510	−1.04305
$262$	−48.2285	−2.97957
$263$	−12.4771	−0.769368	−0.384684	−	0.923048i	$-0.625690\pi$
$263$	−12.4771	−0.769368	−0.384684	+	0.923048i	$0.625690\pi$
$264$	−3.69183	−0.227216
$265$	2.86622	0.176070
$266$	21.4582	1.31569
$267$	−7.00230	−0.428534
$268$	4.07597	0.248980
$269$	−9.73847	−0.593765	−0.296882	−	0.954914i	$-0.595947\pi$
$269$	−9.73847	−0.593765	−0.296882	+	0.954914i	$0.595947\pi$
$270$	2.26810	0.138032
$271$	−1.85154	−0.112473	−0.0562364	−	0.998417i	$-0.517910\pi$
$271$	−1.85154	−0.112473	−0.0562364	+	0.998417i	$0.517910\pi$
$272$	−47.5601	−2.88376
$273$	3.19949	0.193642
$274$	24.0961	1.45570
$275$	4.92806	0.297173
$276$	−21.5354	−1.29628
$277$	−5.45610	−0.327825	−0.163913	−	0.986475i	$-0.552412\pi$
$277$	−5.45610	−0.327825	−0.163913	+	0.986475i	$0.552412\pi$
$278$	14.4141	0.864501
$279$	−22.8655	−1.36892
$280$	−3.82971	−0.228869
$281$	9.38435	0.559824	0.279912	−	0.960026i	$-0.409695\pi$
$281$	9.38435	0.559824	0.279912	+	0.960026i	$0.409695\pi$
$282$	−15.7112	−0.935586
$283$	−18.3303	−1.08962	−0.544812	−	0.838558i	$-0.683399\pi$
$283$	−18.3303	−1.08962	−0.544812	+	0.838558i	$0.683399\pi$
$284$	44.2029	2.62296
$285$	−0.585111	−0.0346590
$286$	−6.08473	−0.359798
$287$	−5.02480	−0.296604
$288$	−14.1330	−0.832795
$289$	28.7609	1.69182
$290$	−4.33090	−0.254319
$291$	−8.42558	−0.493916
$292$	−63.7173	−3.72877
$293$	6.93908	0.405386	0.202693	−	0.979242i	$-0.435031\pi$
$293$	6.93908	0.405386	0.202693	+	0.979242i	$0.435031\pi$
$294$	−2.73348	−0.159420
$295$	−1.94185	−0.113059
$296$	48.3643	2.81112
$297$	3.32487	0.192928
$298$	10.9184	0.632487
$299$	−19.6076	−1.13394
$300$	−12.9492	−0.747620
$301$	11.6163	0.669552
$302$	0.665015	0.0382673
$303$	6.34094	0.364278
$304$	26.0824	1.49593
$305$	−0.268217	−0.0153580
$306$	45.6653	2.61051
$307$	−2.56195	−0.146218	−0.0731092	−	0.997324i	$-0.523292\pi$
$307$	−2.56195	−0.146218	−0.0731092	+	0.997324i	$0.523292\pi$
$308$	−10.1626	−0.579068
$309$	−6.48959	−0.369180
$310$	−5.87668	−0.333773
$311$	−7.13396	−0.404530	−0.202265	−	0.979331i	$-0.564830\pi$
$311$	−7.13396	−0.404530	−0.202265	+	0.979331i	$0.564830\pi$
$312$	8.83243	0.500038
$313$	−31.6225	−1.78741	−0.893706	−	0.448653i	$-0.851904\pi$
$313$	−31.6225	−1.78741	−0.893706	+	0.448653i	$0.851904\pi$
$314$	3.55121	0.200406
$315$	1.61906	0.0912237
$316$	32.3827	1.82167
$317$	11.6075	0.651943	0.325972	−	0.945380i	$-0.394309\pi$
$317$	11.6075	0.651943	0.325972	+	0.945380i	$0.394309\pi$
$318$	−15.9819	−0.896219
$319$	−6.34878	−0.355463
$320$	0.139139	0.00777811
$321$	−4.98661	−0.278325
$322$	−47.4057	−2.64181
$323$	−25.0956	−1.39636
$324$	26.8447	1.49137
$325$	−11.7900	−0.653993
$326$	−19.8507	−1.09943
$327$	10.8718	0.601214
$328$	−13.8713	−0.765915
$329$	−23.8916	−1.31718
$330$	0.401135	0.0220817
$331$	−14.5420	−0.799301	−0.399650	−	0.916668i	$-0.630868\pi$
$331$	−14.5420	−0.799301	−0.399650	+	0.916668i	$0.630868\pi$
$332$	26.1836	1.43701
$333$	−20.4466	−1.12047
$334$	−15.4303	−0.844306
$335$	−0.244654	−0.0133669
$336$	9.40239	0.512943
$337$	15.0782	0.821364	0.410682	−	0.911779i	$-0.365291\pi$
$337$	15.0782	0.821364	0.410682	+	0.911779i	$0.365291\pi$
$338$	−18.5060	−1.00659
$339$	8.70878	0.472996
$340$	8.10769	0.439701
$341$	−8.61478	−0.466516
$342$	−25.0432	−1.35418
$343$	−20.0766	−1.08403
$344$	32.0676	1.72897
$345$	1.29263	0.0695929
$346$	7.30398	0.392665
$347$	15.0759	0.809317	0.404658	−	0.914468i	$-0.367390\pi$
$347$	15.0759	0.809317	0.404658	+	0.914468i	$0.367390\pi$
$348$	16.6823	0.894265
$349$	−9.78375	−0.523712	−0.261856	−	0.965107i	$-0.584335\pi$
$349$	−9.78375	−0.523712	−0.261856	+	0.965107i	$0.584335\pi$
$350$	−28.5049	−1.52365
$351$	−7.95450	−0.424580
$352$	−5.32474	−0.283809
$353$	30.7992	1.63928	0.819639	−	0.572880i	$-0.194174\pi$
$353$	30.7992	1.63928	0.819639	+	0.572880i	$0.194174\pi$
$354$	10.8277	0.575484
$355$	−2.65321	−0.140818
$356$	−53.2112	−2.82019
$357$	−9.04669	−0.478802
$358$	23.8226	1.25906
$359$	−10.9039	−0.575483	−0.287742	−	0.957708i	$-0.592904\pi$
$359$	−10.9039	−0.575483	−0.287742	+	0.957708i	$0.592904\pi$
$360$	4.46953	0.235565
$361$	−5.23735	−0.275650
$362$	25.2095	1.32498
$363$	0.588033	0.0308637
$364$	24.3133	1.27436
$365$	3.82454	0.200186
$366$	1.49556	0.0781743
$367$	15.8444	0.827069	0.413534	−	0.910489i	$-0.364294\pi$
$367$	15.8444	0.827069	0.413534	+	0.910489i	$0.364294\pi$
$368$	−57.6212	−3.00371
$369$	5.86427	0.305282
$370$	−5.25501	−0.273195
$371$	−24.3032	−1.26176
$372$	22.6365	1.17365
$373$	7.51469	0.389096	0.194548	−	0.980893i	$-0.437676\pi$
$373$	7.51469	0.389096	0.194548	+	0.980893i	$0.437676\pi$
$374$	17.2048	0.889640
$375$	1.56586	0.0808605
$376$	−65.9544	−3.40134
$377$	15.1890	0.782273
$378$	−19.2317	−0.989172
$379$	1.54178	0.0791958	0.0395979	−	0.999216i	$-0.487392\pi$
$379$	1.54178	0.0791958	0.0395979	+	0.999216i	$0.487392\pi$
$380$	−4.44632	−0.228091
$381$	12.7079	0.651044
$382$	55.6702	2.84834
$383$	−18.6775	−0.954378	−0.477189	−	0.878801i	$-0.658344\pi$
$383$	−18.6775	−0.954378	−0.477189	+	0.878801i	$0.658344\pi$
$384$	−7.03807	−0.359160
$385$	0.609995	0.0310882
$386$	−33.1152	−1.68552
$387$	−13.5570	−0.689141
$388$	−64.0268	−3.25047
$389$	12.0294	0.609913	0.304956	−	0.952366i	$-0.401358\pi$
$389$	12.0294	0.609913	0.304956	+	0.952366i	$0.401358\pi$
$390$	−0.959685	−0.0485956
$391$	55.4414	2.80379
$392$	−11.4750	−0.579573
$393$	−11.1507	−0.562479
$394$	55.3686	2.78943
$395$	−1.94372	−0.0977993
$396$	11.8604	0.596009
$397$	−27.6893	−1.38969	−0.694843	−	0.719162i	$-0.744526\pi$
$397$	−27.6893	−1.38969	−0.694843	+	0.719162i	$0.744526\pi$
$398$	2.16370	0.108456
$399$	4.96128	0.248375
$400$	−34.6475	−1.73237
$401$	5.63370	0.281334	0.140667	−	0.990057i	$-0.455075\pi$
$401$	5.63370	0.281334	0.140667	+	0.990057i	$0.455075\pi$
$402$	1.36418	0.0680391
$403$	20.6102	1.02667
$404$	48.1855	2.39732
$405$	−1.61132	−0.0800670
$406$	36.7226	1.82251
$407$	−7.70345	−0.381846
$408$	−24.9741	−1.23640
$409$	26.5983	1.31520	0.657601	−	0.753366i	$-0.271571\pi$
$409$	26.5983	1.31520	0.657601	+	0.753366i	$0.271571\pi$
$410$	1.50718	0.0744345
$411$	5.57115	0.274805
$412$	−49.3151	−2.42958
$413$	16.4654	0.810208
$414$	55.3256	2.71910
$415$	−1.57163	−0.0771484
$416$	12.7390	0.624583
$417$	3.33263	0.163200
$418$	−9.43525	−0.461493
$419$	20.0159	0.977842	0.488921	−	0.872328i	$-0.337391\pi$
$419$	20.0159	0.977842	0.488921	+	0.872328i	$0.337391\pi$
$420$	−1.60285	−0.0782110
$421$	−22.2461	−1.08421	−0.542105	−	0.840311i	$-0.682373\pi$
$421$	−22.2461	−1.08421	−0.542105	+	0.840311i	$0.682373\pi$
$422$	−59.3521	−2.88922
$423$	27.8831	1.35572
$424$	−67.0908	−3.25822
$425$	33.3368	1.61707
$426$	14.7942	0.716780
$427$	2.27426	0.110059
$428$	−37.8937	−1.83166
$429$	−1.40683	−0.0679222
$430$	−3.48430	−0.168028
$431$	−12.6240	−0.608076	−0.304038	−	0.952660i	$-0.598335\pi$
$431$	−12.6240	−0.608076	−0.304038	+	0.952660i	$0.598335\pi$
$432$	−23.3760	−1.12468
$433$	16.0435	0.771001	0.385501	−	0.922708i	$-0.374029\pi$
$433$	16.0435	0.771001	0.385501	+	0.922708i	$0.374029\pi$
$434$	49.8296	2.39190
$435$	−1.00133	−0.0480102
$436$	82.6162	3.95660
$437$	−30.4045	−1.45444
$438$	−21.3254	−1.01897
$439$	−4.25047	−0.202864	−0.101432	−	0.994842i	$-0.532342\pi$
$439$	−4.25047	−0.202864	−0.101432	+	0.994842i	$0.532342\pi$
$440$	1.68394	0.0802785
$441$	4.85118	0.231009
$442$	−41.1613	−1.95784
$443$	−2.38602	−0.113363	−0.0566816	−	0.998392i	$-0.518052\pi$
$443$	−2.38602	−0.113363	−0.0566816	+	0.998392i	$0.518052\pi$
$444$	20.2419	0.960637
$445$	3.19392	0.151407
$446$	−7.28056	−0.344744
$447$	2.52441	0.119400
$448$	−1.17979	−0.0557397
$449$	10.0708	0.475272	0.237636	−	0.971354i	$-0.423627\pi$
$449$	10.0708	0.475272	0.237636	+	0.971354i	$0.423627\pi$
$450$	33.2671	1.56823
$451$	2.20942	0.104037
$452$	66.1789	3.11279
$453$	0.153756	0.00722407
$454$	13.5843	0.637541
$455$	−1.45937	−0.0684163
$456$	13.6960	0.641372
$457$	33.4630	1.56533	0.782667	−	0.622440i	$-0.213859\pi$
$457$	33.4630	1.56533	0.782667	+	0.622440i	$0.213859\pi$
$458$	55.5894	2.59752
$459$	22.4917	1.04982
$460$	9.82283	0.457992
$461$	−29.1558	−1.35792	−0.678960	−	0.734175i	$-0.737569\pi$
$461$	−29.1558	−1.35792	−0.678960	+	0.734175i	$0.737569\pi$
$462$	−3.40130	−0.158243
$463$	−32.3657	−1.50416	−0.752080	−	0.659072i	$-0.770949\pi$
$463$	−32.3657	−1.50416	−0.752080	+	0.659072i	$0.770949\pi$
$464$	44.6361	2.07218
$465$	−1.35873	−0.0630094
$466$	15.9877	0.740615
$467$	14.8403	0.686726	0.343363	−	0.939203i	$-0.388434\pi$
$467$	14.8403	0.686726	0.343363	+	0.939203i	$0.388434\pi$
$468$	−28.3752	−1.31164
$469$	2.07447	0.0957902
$470$	7.16626	0.330555
$471$	0.821061	0.0378325
$472$	45.4539	2.09218
$473$	−5.10772	−0.234853
$474$	10.8381	0.497810
$475$	−18.2821	−0.838842
$476$	−68.7468	−3.15100
$477$	28.3635	1.29868
$478$	9.26914	0.423960
$479$	−7.63345	−0.348781	−0.174391	−	0.984677i	$-0.555796\pi$
$479$	−7.63345	−0.348781	−0.174391	+	0.984677i	$0.555796\pi$
$480$	−0.839819	−0.0383323
$481$	18.4299	0.840333
$482$	−12.0979	−0.551045
$483$	−10.9605	−0.498719
$484$	4.46852	0.203115
$485$	3.84312	0.174507
$486$	34.3533	1.55830
$487$	0.869772	0.0394131	0.0197066	−	0.999806i	$-0.493727\pi$
$487$	0.869772	0.0394131	0.0197066	+	0.999806i	$0.493727\pi$
$488$	6.27827	0.284204
$489$	−4.58961	−0.207549
$490$	1.24681	0.0563250
$491$	−30.4975	−1.37633	−0.688166	−	0.725554i	$-0.741584\pi$
$491$	−30.4975	−1.37633	−0.688166	+	0.725554i	$0.741584\pi$
$492$	−5.80555	−0.261735
$493$	−42.9475	−1.93426
$494$	22.5732	1.01561
$495$	−0.711905	−0.0319978
$496$	60.5675	2.71956
$497$	22.4971	1.00913
$498$	8.76333	0.392694
$499$	−29.8430	−1.33596	−0.667978	−	0.744181i	$-0.732840\pi$
$499$	−29.8430	−1.33596	−0.667978	+	0.744181i	$0.732840\pi$
$500$	11.8991	0.532144
$501$	−3.56757	−0.159387
$502$	25.1726	1.12351
$503$	−24.2068	−1.07933	−0.539664	−	0.841880i	$-0.681449\pi$
$503$	−24.2068	−1.07933	−0.539664	+	0.841880i	$0.681449\pi$
$504$	−37.8981	−1.68811
$505$	−2.89226	−0.128704
$506$	20.8444	0.926647
$507$	−4.27870	−0.190024
$508$	96.5684	4.28453
$509$	−22.5117	−0.997814	−0.498907	−	0.866656i	$-0.666265\pi$
$509$	−22.5117	−0.997814	−0.498907	+	0.866656i	$0.666265\pi$
$510$	2.71355	0.120158
$511$	−32.4291	−1.43458
$512$	−50.8443	−2.24702
$513$	−12.3346	−0.544586
$514$	66.0692	2.91419
$515$	2.96007	0.130436
$516$	13.4212	0.590837
$517$	10.5052	0.462018
$518$	44.5583	1.95778
$519$	1.68872	0.0741268
$520$	−4.02869	−0.176670
$521$	0.379741	0.0166368	0.00831838	−	0.999965i	$-0.497352\pi$
$521$	0.379741	0.0166368	0.00831838	+	0.999965i	$0.497352\pi$
$522$	−42.8577	−1.87583
$523$	−3.85823	−0.168708	−0.0843542	−	0.996436i	$-0.526883\pi$
$523$	−3.85823	−0.168708	−0.0843542	+	0.996436i	$0.526883\pi$
$524$	−84.7355	−3.70169
$525$	−6.59050	−0.287633
$526$	−31.7333	−1.38364
$527$	−58.2762	−2.53855
$528$	−4.13426	−0.179920
$529$	44.1697	1.92042
$530$	7.28974	0.316646
$531$	−19.2162	−0.833912
$532$	37.7012	1.63456
$533$	−5.28587	−0.228956
$534$	−17.8092	−0.770677
$535$	2.27452	0.0983359
$536$	5.72673	0.247357
$537$	5.50793	0.237685
$538$	−24.7681	−1.06783
$539$	1.82773	0.0787258
$540$	3.98496	0.171485
$541$	−6.04494	−0.259892	−0.129946	−	0.991521i	$-0.541480\pi$
$541$	−6.04494	−0.259892	−0.129946	+	0.991521i	$0.541480\pi$
$542$	−4.70907	−0.202272
$543$	5.82859	0.250129
$544$	−36.0201	−1.54435
$545$	−4.95892	−0.212417
$546$	8.13736	0.348247
$547$	−20.2616	−0.866324	−0.433162	−	0.901316i	$-0.642602\pi$
$547$	−20.2616	−0.866324	−0.433162	+	0.901316i	$0.642602\pi$
$548$	42.3358	1.80849
$549$	−2.65422	−0.113279
$550$	12.5337	0.534438
$551$	23.5527	1.00338
$552$	−30.2572	−1.28783
$553$	16.4812	0.700853
$554$	−13.8767	−0.589563
$555$	−1.21499	−0.0515735
$556$	25.3250	1.07402
$557$	−13.9691	−0.591888	−0.295944	−	0.955205i	$-0.595634\pi$
$557$	−13.9691	−0.591888	−0.295944	+	0.955205i	$0.595634\pi$
$558$	−58.1545	−2.46187
$559$	12.2198	0.516844
$560$	−4.28867	−0.181229
$561$	3.97786	0.167945
$562$	23.8675	1.00679
$563$	−8.07806	−0.340450	−0.170225	−	0.985405i	$-0.554449\pi$
$563$	−8.07806	−0.340450	−0.170225	+	0.985405i	$0.554449\pi$
$564$	−27.6039	−1.16233
$565$	−3.97229	−0.167116
$566$	−46.6200	−1.95958
$567$	13.6627	0.573779
$568$	62.1050	2.60587
$569$	−6.85160	−0.287234	−0.143617	−	0.989633i	$-0.545873\pi$
$569$	−6.85160	−0.287234	−0.143617	+	0.989633i	$0.545873\pi$
$570$	−1.48813	−0.0623309
$571$	−10.8342	−0.453396	−0.226698	−	0.973965i	$-0.572793\pi$
$571$	−10.8342	−0.453396	−0.226698	+	0.973965i	$0.572793\pi$
$572$	−10.6906	−0.446997
$573$	12.8713	0.537706
$574$	−12.7797	−0.533415
$575$	40.3890	1.68434
$576$	1.37689	0.0573704
$577$	−38.8492	−1.61731	−0.808656	−	0.588282i	$-0.799805\pi$
$577$	−38.8492	−1.61731	−0.808656	+	0.588282i	$0.799805\pi$
$578$	73.1485	3.04258
$579$	−7.65643	−0.318190
$580$	−7.60922	−0.315956
$581$	13.3262	0.552863
$582$	−21.4290	−0.888262
$583$	10.6862	0.442577
$584$	−89.5227	−3.70448
$585$	1.70318	0.0704179
$586$	17.6484	0.729048
$587$	37.1784	1.53452	0.767259	−	0.641337i	$-0.221620\pi$
$587$	37.1784	1.53452	0.767259	+	0.641337i	$0.221620\pi$
$588$	−4.80261	−0.198056
$589$	31.9591	1.31685
$590$	−4.93877	−0.203326
$591$	12.8016	0.526585
$592$	54.1603	2.22597
$593$	−23.5488	−0.967033	−0.483517	−	0.875335i	$-0.660641\pi$
$593$	−23.5488	−0.967033	−0.483517	+	0.875335i	$0.660641\pi$
$594$	8.45623	0.346963
$595$	4.12642	0.169167
$596$	19.1832	0.785775
$597$	0.500259	0.0204743
$598$	−49.8687	−2.03928
$599$	17.7941	0.727045	0.363523	−	0.931585i	$-0.381574\pi$
$599$	17.7941	0.727045	0.363523	+	0.931585i	$0.381574\pi$
$600$	−18.1936	−0.742749
$601$	−17.9014	−0.730215	−0.365107	−	0.930965i	$-0.618968\pi$
$601$	−17.9014	−0.730215	−0.365107	+	0.930965i	$0.618968\pi$
$602$	29.5441	1.20413
$603$	−2.42105	−0.0985927
$604$	1.16840	0.0475417
$605$	−0.268217	−0.0109046
$606$	16.1271	0.655119
$607$	−13.4478	−0.545830	−0.272915	−	0.962038i	$-0.587988\pi$
$607$	−13.4478	−0.545830	−0.272915	+	0.962038i	$0.587988\pi$
$608$	19.7537	0.801119
$609$	8.49049	0.344052
$610$	−0.682163	−0.0276200
$611$	−25.1329	−1.01677
$612$	80.2320	3.24319
$613$	5.45446	0.220304	0.110152	−	0.993915i	$-0.464866\pi$
$613$	5.45446	0.220304	0.110152	+	0.993915i	$0.464866\pi$
$614$	−6.51589	−0.262960
$615$	0.348470	0.0140517
$616$	−14.2784	−0.575295
$617$	−14.5796	−0.586951	−0.293476	−	0.955967i	$-0.594812\pi$
$617$	−14.5796	−0.586951	−0.293476	+	0.955967i	$0.594812\pi$
$618$	−16.5052	−0.663935
$619$	22.8964	0.920285	0.460142	−	0.887845i	$-0.347798\pi$
$619$	22.8964	0.920285	0.460142	+	0.887845i	$0.347798\pi$
$620$	−10.3251	−0.414666
$621$	27.2497	1.09349
$622$	−18.1440	−0.727508
$623$	−27.0819	−1.08501
$624$	9.89091	0.395953
$625$	23.9261	0.957043
$626$	−80.4265	−3.21449
$627$	−2.18149	−0.0871202
$628$	6.23933	0.248976
$629$	−52.1114	−2.07782
$630$	4.11780	0.164057
$631$	−3.50546	−0.139550	−0.0697751	−	0.997563i	$-0.522228\pi$
$631$	−3.50546	−0.139550	−0.0697751	+	0.997563i	$0.522228\pi$
$632$	45.4976	1.80980
$633$	−13.7226	−0.545423
$634$	29.5217	1.17246
$635$	−5.79638	−0.230022
$636$	−28.0795	−1.11342
$637$	−4.37270	−0.173253
$638$	−16.1470	−0.639267
$639$	−26.2557	−1.03866
$640$	3.21024	0.126896
$641$	−31.9564	−1.26220	−0.631100	−	0.775701i	$-0.717396\pi$
$641$	−31.9564	−1.26220	−0.631100	+	0.775701i	$0.717396\pi$
$642$	−12.6826	−0.500542
$643$	−34.4497	−1.35857	−0.679283	−	0.733877i	$-0.737709\pi$
$643$	−34.4497	−1.35857	−0.679283	+	0.733877i	$0.737709\pi$
$644$	−83.2898	−3.28208
$645$	−0.805591	−0.0317201
$646$	−63.8265	−2.51122
$647$	−23.0090	−0.904577	−0.452289	−	0.891872i	$-0.649392\pi$
$647$	−23.0090	−0.904577	−0.452289	+	0.891872i	$0.649392\pi$
$648$	37.7168	1.48166
$649$	−7.23987	−0.284190
$650$	−29.9859	−1.17614
$651$	11.5209	0.451540
$652$	−34.8769	−1.36588
$653$	23.4692	0.918423	0.459211	−	0.888327i	$-0.348132\pi$
$653$	23.4692	0.918423	0.459211	+	0.888327i	$0.348132\pi$
$654$	27.6507	1.08123
$655$	5.08612	0.198731
$656$	−15.5337	−0.606487
$657$	37.8469	1.47655
$658$	−60.7641	−2.36883
$659$	11.2283	0.437393	0.218697	−	0.975793i	$-0.429819\pi$
$659$	11.2283	0.437393	0.218697	+	0.975793i	$0.429819\pi$
$660$	0.704777	0.0274334
$661$	31.6939	1.23275	0.616375	−	0.787453i	$-0.288601\pi$
$661$	31.6939	1.23275	0.616375	+	0.787453i	$0.288601\pi$
$662$	−36.9851	−1.43747
$663$	−9.51673	−0.369599
$664$	36.7879	1.42765
$665$	−2.26296	−0.0877540
$666$	−52.0025	−2.01506
$667$	−52.0328	−2.01472
$668$	−27.1103	−1.04893
$669$	−1.68331	−0.0650805
$670$	−0.622236	−0.0240391
$671$	−1.00000	−0.0386046
$672$	7.12099	0.274698
$673$	46.4972	1.79233	0.896167	−	0.443716i	$-0.146340\pi$
$673$	46.4972	1.79233	0.896167	+	0.443716i	$0.146340\pi$
$674$	38.3489	1.47714
$675$	16.3851	0.630664
$676$	−32.5143	−1.25055
$677$	−3.18018	−0.122224	−0.0611120	−	0.998131i	$-0.519465\pi$
$677$	−3.18018	−0.122224	−0.0611120	+	0.998131i	$0.519465\pi$
$678$	22.1493	0.850638
$679$	−32.5866	−1.25056
$680$	11.3913	0.436836
$681$	3.14076	0.120354
$682$	−21.9102	−0.838985
$683$	−33.8501	−1.29524	−0.647619	−	0.761965i	$-0.724235\pi$
$683$	−33.8501	−1.29524	−0.647619	+	0.761965i	$0.724235\pi$
$684$	−43.9999	−1.68238
$685$	−2.54114	−0.0970921
$686$	−51.0613	−1.94953
$687$	12.8526	0.490358
$688$	35.9106	1.36908
$689$	−25.5660	−0.973985
$690$	3.28758	0.125156
$691$	11.3379	0.431314	0.215657	−	0.976469i	$-0.430811\pi$
$691$	11.3379	0.431314	0.215657	+	0.976469i	$0.430811\pi$
$692$	12.8328	0.487830
$693$	6.03639	0.229303
$694$	38.3430	1.45548
$695$	−1.52010	−0.0576606
$696$	23.4386	0.888438
$697$	14.9460	0.566120
$698$	−24.8833	−0.941846
$699$	3.69645	0.139812
$700$	−50.0819	−1.89292
$701$	−21.7692	−0.822212	−0.411106	−	0.911588i	$-0.634857\pi$
$701$	−21.7692	−0.822212	−0.411106	+	0.911588i	$0.634857\pi$
$702$	−20.2309	−0.763567
$703$	28.5783	1.07785
$704$	0.518756	0.0195513
$705$	1.65688	0.0624018
$706$	78.3326	2.94809
$707$	24.5241	0.922323
$708$	19.0238	0.714957
$709$	33.0900	1.24272	0.621361	−	0.783524i	$-0.286580\pi$
$709$	33.0900	1.24272	0.621361	+	0.783524i	$0.286580\pi$
$710$	−6.74800	−0.253248
$711$	−19.2347	−0.721357
$712$	−74.7616	−2.80181
$713$	−70.6042	−2.64415
$714$	−23.0087	−0.861080
$715$	0.641689	0.0239978
$716$	41.8554	1.56421
$717$	2.14308	0.0800348
$718$	−27.7321	−1.03495
$719$	−8.38146	−0.312576	−0.156288	−	0.987712i	$-0.549953\pi$
$719$	−8.38146	−0.312576	−0.156288	+	0.987712i	$0.549953\pi$
$720$	5.00516	0.186531
$721$	−25.0990	−0.934735
$722$	−13.3203	−0.495731
$723$	−2.79711	−0.104026
$724$	44.2921	1.64610
$725$	−31.2872	−1.16198
$726$	1.49556	0.0555055
$727$	4.65557	0.172666	0.0863328	−	0.996266i	$-0.472485\pi$
$727$	4.65557	0.172666	0.0863328	+	0.996266i	$0.472485\pi$
$728$	34.1601	1.26606
$729$	−10.0799	−0.373328
$730$	9.72707	0.360015
$731$	−34.5521	−1.27796
$732$	2.62764	0.0971204
$733$	−0.0796111	−0.00294050	−0.00147025	−	0.999999i	$-0.500468\pi$
$733$	−0.0796111	−0.00294050	−0.00147025	+	0.999999i	$0.500468\pi$
$734$	40.2974	1.48740
$735$	0.288270	0.0106330
$736$	−43.6400	−1.60859
$737$	−0.912151	−0.0335995
$738$	14.9148	0.549021
$739$	−17.0136	−0.625855	−0.312928	−	0.949777i	$-0.601310\pi$
$739$	−17.0136	−0.625855	−0.312928	+	0.949777i	$0.601310\pi$
$740$	−9.23283	−0.339406
$741$	5.21905	0.191727
$742$	−61.8111	−2.26916
$743$	−49.1035	−1.80143	−0.900717	−	0.434407i	$-0.856958\pi$
$743$	−49.1035	−1.80143	−0.900717	+	0.434407i	$0.856958\pi$
$744$	31.8043	1.16600
$745$	−1.15145	−0.0421857
$746$	19.1123	0.699752
$747$	−15.5525	−0.569038
$748$	30.2281	1.10525
$749$	−19.2861	−0.704698
$750$	3.98249	0.145420
$751$	5.83659	0.212980	0.106490	−	0.994314i	$-0.466039\pi$
$751$	5.83659	0.212980	0.106490	+	0.994314i	$0.466039\pi$
$752$	−73.8584	−2.69334
$753$	5.82005	0.212094
$754$	38.6306	1.40684
$755$	−0.0701318	−0.00255236
$756$	−33.7893	−1.22890
$757$	−10.5446	−0.383250	−0.191625	−	0.981468i	$-0.561376\pi$
$757$	−10.5446	−0.383250	−0.191625	+	0.981468i	$0.561376\pi$
$758$	3.92125	0.142426
$759$	4.81935	0.174931
$760$	−6.24707	−0.226605
$761$	−40.9921	−1.48596	−0.742981	−	0.669312i	$-0.766589\pi$
$761$	−40.9921	−1.48596	−0.742981	+	0.669312i	$0.766589\pi$
$762$	32.3203	1.17084
$763$	42.0477	1.52223
$764$	97.8103	3.53865
$765$	−4.81581	−0.174116
$766$	−47.5031	−1.71636
$767$	17.3209	0.625420
$768$	−17.2900	−0.623901
$769$	−13.9367	−0.502569	−0.251284	−	0.967913i	$-0.580853\pi$
$769$	−13.9367	−0.502569	−0.251284	+	0.967913i	$0.580853\pi$
$770$	1.55142	0.0559093
$771$	15.2756	0.550137
$772$	−58.1820	−2.09402
$773$	16.1258	0.580005	0.290002	−	0.957026i	$-0.406344\pi$
$773$	16.1258	0.580005	0.290002	+	0.957026i	$0.406344\pi$
$774$	−34.4799	−1.23935
$775$	−42.4541	−1.52500
$776$	−89.9576	−3.22929
$777$	10.3021	0.369587
$778$	30.5946	1.09687
$779$	−8.19651	−0.293670
$780$	−1.68613	−0.0603730
$781$	−9.89206	−0.353966
$782$	141.006	5.04235
$783$	−21.1088	−0.754369
$784$	−12.8501	−0.458933
$785$	−0.374507	−0.0133667
$786$	−28.3600	−1.01157
$787$	−8.69159	−0.309822	−0.154911	−	0.987928i	$-0.549509\pi$
$787$	−8.69159	−0.309822	−0.154911	+	0.987928i	$0.549509\pi$
$788$	97.2803	3.46547
$789$	−7.33692	−0.261201
$790$	−4.94353	−0.175883
$791$	33.6819	1.19759
$792$	16.6639	0.592125
$793$	2.39243	0.0849576
$794$	−70.4230	−2.49922
$795$	1.68543	0.0597761
$796$	3.80152	0.134741
$797$	−23.2545	−0.823715	−0.411858	−	0.911248i	$-0.635120\pi$
$797$	−23.2545	−0.823715	−0.411858	+	0.911248i	$0.635120\pi$
$798$	12.6182	0.446678
$799$	71.0643	2.51407
$800$	−26.2406	−0.927746
$801$	31.6064	1.11676
$802$	14.3284	0.505952
$803$	14.2591	0.503194
$804$	2.39681	0.0845288
$805$	4.99935	0.176204
$806$	52.4186	1.84637
$807$	−5.72654	−0.201584
$808$	67.7005	2.38170
$809$	−1.18724	−0.0417411	−0.0208705	−	0.999782i	$-0.506644\pi$
$809$	−1.18724	−0.0417411	−0.0208705	+	0.999782i	$0.506644\pi$
$810$	−4.09811	−0.143993
$811$	−34.5434	−1.21298	−0.606491	−	0.795091i	$-0.707423\pi$
$811$	−34.5434	−1.21298	−0.606491	+	0.795091i	$0.707423\pi$
$812$	64.5201	2.26421
$813$	−1.08876	−0.0381846
$814$	−19.5924	−0.686713
$815$	2.09344	0.0733298
$816$	−27.9669	−0.979039
$817$	18.9486	0.662929
$818$	67.6483	2.36527
$819$	−14.4416	−0.504631
$820$	2.64806	0.0924742
$821$	−7.42183	−0.259024	−0.129512	−	0.991578i	$-0.541341\pi$
$821$	−7.42183	−0.259024	−0.129512	+	0.991578i	$0.541341\pi$
$822$	14.1693	0.494210
$823$	−43.7096	−1.52362	−0.761811	−	0.647799i	$-0.775689\pi$
$823$	−43.7096	−1.52362	−0.761811	+	0.647799i	$0.775689\pi$
$824$	−69.2876	−2.41375
$825$	2.89786	0.100891
$826$	41.8769	1.45708
$827$	33.7632	1.17406	0.587030	−	0.809565i	$-0.300297\pi$
$827$	33.7632	1.17406	0.587030	+	0.809565i	$0.300297\pi$
$828$	97.2047	3.37810
$829$	6.39006	0.221936	0.110968	−	0.993824i	$-0.464605\pi$
$829$	6.39006	0.221936	0.110968	+	0.993824i	$0.464605\pi$
$830$	−3.99718	−0.138744
$831$	−3.20837	−0.111297
$832$	−1.24109	−0.0430269
$833$	12.3640	0.428387
$834$	8.47598	0.293499
$835$	1.62726	0.0563136
$836$	−16.5773	−0.573340
$837$	−28.6430	−0.990046
$838$	50.9071	1.75856
$839$	−24.6067	−0.849516	−0.424758	−	0.905307i	$-0.639641\pi$
$839$	−24.6067	−0.849516	−0.424758	+	0.905307i	$0.639641\pi$
$840$	−2.25200	−0.0777013
$841$	11.3070	0.389897
$842$	−56.5792	−1.94985
$843$	5.51831	0.190061
$844$	−104.279	−3.58944
$845$	1.95162	0.0671379
$846$	70.9158	2.43813
$847$	2.27426	0.0781446
$848$	−75.1310	−2.58001
$849$	−10.7788	−0.369928
$850$	84.7864	2.90815
$851$	−63.1353	−2.16425
$852$	25.9928	0.890497
$853$	−25.9968	−0.890114	−0.445057	−	0.895502i	$-0.646817\pi$
$853$	−25.9968	−0.890114	−0.445057	+	0.895502i	$0.646817\pi$
$854$	5.78420	0.197931
$855$	2.64103	0.0903213
$856$	−53.2406	−1.81973
$857$	−51.9940	−1.77608	−0.888041	−	0.459764i	$-0.847934\pi$
$857$	−51.9940	−1.77608	−0.888041	+	0.459764i	$0.847934\pi$
$858$	−3.57802	−0.122152
$859$	17.2351	0.588053	0.294026	−	0.955797i	$-0.405005\pi$
$859$	17.2351	0.588053	0.294026	+	0.955797i	$0.405005\pi$
$860$	−6.12177	−0.208751
$861$	−2.95475	−0.100698
$862$	−32.1070	−1.09357
$863$	32.5544	1.10816	0.554082	−	0.832462i	$-0.313070\pi$
$863$	32.5544	1.10816	0.554082	+	0.832462i	$0.313070\pi$
$864$	−17.7040	−0.602304
$865$	−0.770270	−0.0261900
$866$	40.8039	1.38657
$867$	16.9124	0.574374
$868$	87.5485	2.97159
$869$	−7.24684	−0.245832
$870$	−2.54672	−0.0863417
$871$	2.18226	0.0739429
$872$	116.076	3.93082
$873$	38.0307	1.28714
$874$	−77.3286	−2.61568
$875$	6.05607	0.204733
$876$	−37.4679	−1.26592
$877$	−23.6383	−0.798208	−0.399104	−	0.916906i	$-0.630679\pi$
$877$	−23.6383	−0.798208	−0.399104	+	0.916906i	$0.630679\pi$
$878$	−10.8104	−0.364832
$879$	4.08041	0.137629
$880$	1.88574	0.0635683
$881$	9.24859	0.311593	0.155797	−	0.987789i	$-0.450206\pi$
$881$	9.24859	0.311593	0.155797	+	0.987789i	$0.450206\pi$
$882$	12.3382	0.415447
$883$	31.1166	1.04716	0.523578	−	0.851977i	$-0.324597\pi$
$883$	31.1166	1.04716	0.523578	+	0.851977i	$0.324597\pi$
$884$	−72.3186	−2.43234
$885$	−1.14187	−0.0383837
$886$	−6.06843	−0.203873
$887$	−19.7859	−0.664346	−0.332173	−	0.943218i	$-0.607782\pi$
$887$	−19.7859	−0.664346	−0.332173	+	0.943218i	$0.607782\pi$
$888$	28.4398	0.954378
$889$	49.1486	1.64839
$890$	8.12320	0.272290
$891$	−6.00752	−0.201259
$892$	−12.7916	−0.428296
$893$	−38.9722	−1.30415
$894$	6.42040	0.214730
$895$	−2.51231	−0.0839772
$896$	−27.2203	−0.909366
$897$	−11.5299	−0.384974
$898$	25.6134	0.854731
$899$	54.6933	1.82412
$900$	58.4489	1.94830
$901$	72.2888	2.40829
$902$	5.61928	0.187101
$903$	6.83077	0.227314
$904$	92.9812	3.09251
$905$	−2.65857	−0.0883738
$906$	0.391051	0.0129918
$907$	13.8162	0.458760	0.229380	−	0.973337i	$-0.426330\pi$
$907$	13.8162	0.458760	0.229380	+	0.973337i	$0.426330\pi$
$908$	23.8670	0.792054
$909$	−28.6213	−0.949307
$910$	−3.71166	−0.123040
$911$	−14.3964	−0.476975	−0.238488	−	0.971146i	$-0.576652\pi$
$911$	−14.3964	−0.476975	−0.238488	+	0.971146i	$0.576652\pi$
$912$	15.3373	0.507868
$913$	−5.85956	−0.193923
$914$	85.1075	2.81511
$915$	−0.157720	−0.00521407
$916$	97.6683	3.22705
$917$	−43.1263	−1.42415
$918$	57.2037	1.88800
$919$	4.52709	0.149335	0.0746674	−	0.997208i	$-0.476210\pi$
$919$	4.52709	0.149335	0.0746674	+	0.997208i	$0.476210\pi$
$920$	13.8011	0.455008
$921$	−1.50651	−0.0496413
$922$	−74.1527	−2.44209
$923$	23.6660	0.778977
$924$	−5.97594	−0.196594
$925$	−37.9631	−1.24822
$926$	−82.3165	−2.70509
$927$	29.2922	0.962082
$928$	33.8056	1.10972
$929$	20.1862	0.662289	0.331145	−	0.943580i	$-0.392565\pi$
$929$	20.1862	0.662289	0.331145	+	0.943580i	$0.392565\pi$
$930$	−3.45569	−0.113316
$931$	−6.78051	−0.222222
$932$	28.0897	0.920108
$933$	−4.19500	−0.137338
$934$	37.7437	1.23501
$935$	−1.81440	−0.0593372
$936$	−39.8671	−1.30310
$937$	7.24032	0.236531	0.118266	−	0.992982i	$-0.462267\pi$
$937$	7.24032	0.236531	0.118266	+	0.992982i	$0.462267\pi$
$938$	5.27607	0.172270
$939$	−18.5951	−0.606828
$940$	12.5908	0.410667
$941$	45.9669	1.49848	0.749239	−	0.662300i	$-0.230420\pi$
$941$	45.9669	1.49848	0.749239	+	0.662300i	$0.230420\pi$
$942$	2.08823	0.0680382
$943$	18.1078	0.589670
$944$	50.9010	1.65669
$945$	2.02815	0.0659758
$946$	−12.9906	−0.422361
$947$	−8.65681	−0.281309	−0.140654	−	0.990059i	$-0.544921\pi$
$947$	−8.65681	−0.281309	−0.140654	+	0.990059i	$0.544921\pi$
$948$	19.0421	0.618458
$949$	−34.1140	−1.10739
$950$	−46.4975	−1.50858
$951$	6.82561	0.221335
$952$	−96.5891	−3.13047
$953$	32.4369	1.05074	0.525368	−	0.850875i	$-0.323928\pi$
$953$	32.4369	1.05074	0.525368	+	0.850875i	$0.323928\pi$
$954$	72.1377	2.33554
$955$	−5.87092	−0.189979
$956$	16.2855	0.526710
$957$	−3.73329	−0.120680
$958$	−19.4144	−0.627250
$959$	21.5469	0.695784
$960$	0.0818183	0.00264068
$961$	43.2144	1.39401
$962$	46.8734	1.51126
$963$	22.5082	0.725315
$964$	−21.2555	−0.684595
$965$	3.49229	0.112421
$966$	−27.8761	−0.896899
$967$	36.1243	1.16168	0.580839	−	0.814018i	$-0.302724\pi$
$967$	36.1243	1.16168	0.580839	+	0.814018i	$0.302724\pi$
$968$	6.27827	0.201791
$969$	−14.7571	−0.474065
$970$	9.77432	0.313834
$971$	2.71466	0.0871177	0.0435588	−	0.999051i	$-0.486130\pi$
$971$	2.71466	0.0871177	0.0435588	+	0.999051i	$0.486130\pi$
$972$	60.3573	1.93596
$973$	12.8892	0.413209
$974$	2.21212	0.0708808
$975$	−6.93292	−0.222031
$976$	7.03066	0.225046
$977$	−43.2797	−1.38464	−0.692320	−	0.721591i	$-0.743411\pi$
$977$	−43.2797	−1.38464	−0.692320	+	0.721591i	$0.743411\pi$
$978$	−11.6729	−0.373258
$979$	11.9080	0.380581
$980$	2.19059	0.0699758
$981$	−49.0724	−1.56676
$982$	−77.5651	−2.47520
$983$	−29.9885	−0.956485	−0.478243	−	0.878228i	$-0.658726\pi$
$983$	−29.9885	−0.956485	−0.478243	+	0.878228i	$0.658726\pi$
$984$	−8.15679	−0.260029
$985$	−5.83911	−0.186050
$986$	−109.230	−3.47858
$987$	−14.0490	−0.447186
$988$	39.6601	1.26176
$989$	−41.8614	−1.33112
$990$	−1.81061	−0.0575450
$991$	−7.20865	−0.228990	−0.114495	−	0.993424i	$-0.536525\pi$
$991$	−7.20865	−0.228990	−0.114495	+	0.993424i	$0.536525\pi$
$992$	45.8714	1.45642
$993$	−8.55118	−0.271363
$994$	57.2176	1.81483
$995$	−0.228181	−0.00723382
$996$	15.3968	0.487867
$997$	47.5918	1.50725	0.753624	−	0.657305i	$-0.228304\pi$
$997$	47.5918	1.50725	0.753624	+	0.657305i	$0.228304\pi$
$998$	−75.9005	−2.40259
$999$	−25.6129	−0.810358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.19	✓	21
3.2	odd	2		6039.2.a.l.1.3		21
11.10	odd	2		7381.2.a.j.1.3		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.19	✓	21	1.1	even	1	trivial
6039.2.a.l.1.3		21	3.2	odd	2
7381.2.a.j.1.3		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)

\(f(q)\)	\(=\)	\(q+2.54333 q^{2} +0.588033 q^{3} +4.46852 q^{4} -0.268217 q^{5} +1.49556 q^{6} +2.27426 q^{7} +6.27827 q^{8} -2.65422 q^{9} +O(q^{10})\)	\(q+2.54333 q^{2} +0.588033 q^{3} +4.46852 q^{4} -0.268217 q^{5} +1.49556 q^{6} +2.27426 q^{7} +6.27827 q^{8} -2.65422 q^{9} -0.682163 q^{10} -1.00000 q^{11} +2.62764 q^{12} +2.39243 q^{13} +5.78420 q^{14} -0.157720 q^{15} +7.03066 q^{16} -6.76468 q^{17} -6.75055 q^{18} +3.70980 q^{19} -1.19853 q^{20} +1.33734 q^{21} -2.54333 q^{22} -8.19571 q^{23} +3.69183 q^{24} -4.92806 q^{25} +6.08473 q^{26} -3.32487 q^{27} +10.1626 q^{28} +6.34878 q^{29} -0.401135 q^{30} +8.61478 q^{31} +5.32474 q^{32} -0.588033 q^{33} -17.2048 q^{34} -0.609995 q^{35} -11.8604 q^{36} +7.70345 q^{37} +9.43525 q^{38} +1.40683 q^{39} -1.68394 q^{40} -2.20942 q^{41} +3.40130 q^{42} +5.10772 q^{43} -4.46852 q^{44} +0.711905 q^{45} -20.8444 q^{46} -10.5052 q^{47} +4.13426 q^{48} -1.82773 q^{49} -12.5337 q^{50} -3.97786 q^{51} +10.6906 q^{52} -10.6862 q^{53} -8.45623 q^{54} +0.268217 q^{55} +14.2784 q^{56} +2.18149 q^{57} +16.1470 q^{58} +7.23987 q^{59} -0.704777 q^{60} +1.00000 q^{61} +21.9102 q^{62} -6.03639 q^{63} -0.518756 q^{64} -0.641689 q^{65} -1.49556 q^{66} +0.912151 q^{67} -30.2281 q^{68} -4.81935 q^{69} -1.55142 q^{70} +9.89206 q^{71} -16.6639 q^{72} -14.2591 q^{73} +19.5924 q^{74} -2.89786 q^{75} +16.5773 q^{76} -2.27426 q^{77} +3.57802 q^{78} +7.24684 q^{79} -1.88574 q^{80} +6.00752 q^{81} -5.61928 q^{82} +5.85956 q^{83} +5.97594 q^{84} +1.81440 q^{85} +12.9906 q^{86} +3.73329 q^{87} -6.27827 q^{88} -11.9080 q^{89} +1.81061 q^{90} +5.44101 q^{91} -36.6227 q^{92} +5.06577 q^{93} -26.7182 q^{94} -0.995031 q^{95} +3.13112 q^{96} -14.3284 q^{97} -4.64851 q^{98} +2.65422 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 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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