LMFDB - Embedded newform 671.2.a.d.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.60374 q^{2} +2.97894 q^{3} +4.77947 q^{4} +0.851432 q^{5} -7.75638 q^{6} +3.04314 q^{7} -7.23702 q^{8} +5.87407 q^{9} +O(q^{10})$	\(q-2.60374 q^{2} +2.97894 q^{3} +4.77947 q^{4} +0.851432 q^{5} -7.75638 q^{6} +3.04314 q^{7} -7.23702 q^{8} +5.87407 q^{9} -2.21691 q^{10} -1.00000 q^{11} +14.2377 q^{12} +1.25630 q^{13} -7.92356 q^{14} +2.53636 q^{15} +9.28438 q^{16} -7.73575 q^{17} -15.2946 q^{18} +6.82604 q^{19} +4.06939 q^{20} +9.06534 q^{21} +2.60374 q^{22} +8.40462 q^{23} -21.5586 q^{24} -4.27506 q^{25} -3.27109 q^{26} +8.56167 q^{27} +14.5446 q^{28} +1.09847 q^{29} -6.60403 q^{30} -2.03738 q^{31} -9.70010 q^{32} -2.97894 q^{33} +20.1419 q^{34} +2.59103 q^{35} +28.0749 q^{36} -6.32030 q^{37} -17.7732 q^{38} +3.74245 q^{39} -6.16183 q^{40} -9.82455 q^{41} -23.6038 q^{42} -8.23734 q^{43} -4.77947 q^{44} +5.00137 q^{45} -21.8835 q^{46} +1.11751 q^{47} +27.6576 q^{48} +2.26073 q^{49} +11.1312 q^{50} -23.0443 q^{51} +6.00447 q^{52} -4.72415 q^{53} -22.2924 q^{54} -0.851432 q^{55} -22.0233 q^{56} +20.3343 q^{57} -2.86013 q^{58} +11.0384 q^{59} +12.1225 q^{60} +1.00000 q^{61} +5.30480 q^{62} +17.8756 q^{63} +6.68778 q^{64} +1.06966 q^{65} +7.75638 q^{66} +6.91010 q^{67} -36.9728 q^{68} +25.0368 q^{69} -6.74637 q^{70} -7.00240 q^{71} -42.5107 q^{72} +1.27134 q^{73} +16.4564 q^{74} -12.7351 q^{75} +32.6248 q^{76} -3.04314 q^{77} -9.74438 q^{78} -3.71107 q^{79} +7.90502 q^{80} +7.88248 q^{81} +25.5806 q^{82} +11.2940 q^{83} +43.3275 q^{84} -6.58646 q^{85} +21.4479 q^{86} +3.27227 q^{87} +7.23702 q^{88} -3.62680 q^{89} -13.0223 q^{90} +3.82312 q^{91} +40.1696 q^{92} -6.06922 q^{93} -2.90971 q^{94} +5.81191 q^{95} -28.8960 q^{96} -0.113236 q^{97} -5.88635 q^{98} -5.87407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60374	−1.84112	−0.920562	−	0.390598i	$-0.872268\pi$
$2$	−2.60374	−1.84112	−0.920562	+	0.390598i	$0.872268\pi$
$3$	2.97894	1.71989	0.859945	−	0.510386i	$-0.170498\pi$
$3$	2.97894	1.71989	0.859945	+	0.510386i	$0.170498\pi$
$4$	4.77947	2.38973
$5$	0.851432	0.380772	0.190386	−	0.981709i	$-0.439026\pi$
$5$	0.851432	0.380772	0.190386	+	0.981709i	$0.439026\pi$
$6$	−7.75638	−3.16653
$7$	3.04314	1.15020	0.575100	−	0.818083i	$-0.304963\pi$
$7$	3.04314	1.15020	0.575100	+	0.818083i	$0.304963\pi$
$8$	−7.23702	−2.55867
$9$	5.87407	1.95802
$10$	−2.21691	−0.701048
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	14.2377	4.11008
$13$	1.25630	0.348436	0.174218	−	0.984707i	$-0.444260\pi$
$13$	1.25630	0.348436	0.174218	+	0.984707i	$0.444260\pi$
$14$	−7.92356	−2.11766
$15$	2.53636	0.654886
$16$	9.28438	2.32110
$17$	−7.73575	−1.87619	−0.938097	−	0.346373i	$-0.887413\pi$
$17$	−7.73575	−1.87619	−0.938097	+	0.346373i	$0.887413\pi$
$18$	−15.2946	−3.60496
$19$	6.82604	1.56600	0.783000	−	0.622021i	$-0.213688\pi$
$19$	6.82604	1.56600	0.783000	+	0.622021i	$0.213688\pi$
$20$	4.06939	0.909944
$21$	9.06534	1.97822
$22$	2.60374	0.555120
$23$	8.40462	1.75248	0.876242	−	0.481871i	$-0.160042\pi$
$23$	8.40462	1.75248	0.876242	+	0.481871i	$0.160042\pi$
$24$	−21.5586	−4.40064
$25$	−4.27506	−0.855013
$26$	−3.27109	−0.641514
$27$	8.56167	1.64769
$28$	14.5446	2.74867
$29$	1.09847	0.203980	0.101990	−	0.994785i	$-0.467479\pi$
$29$	1.09847	0.203980	0.101990	+	0.994785i	$0.467479\pi$
$30$	−6.60403	−1.20573
$31$	−2.03738	−0.365924	−0.182962	−	0.983120i	$-0.558568\pi$
$31$	−2.03738	−0.365924	−0.182962	+	0.983120i	$0.558568\pi$
$32$	−9.70010	−1.71475
$33$	−2.97894	−0.518566
$34$	20.1419	3.45430
$35$	2.59103	0.437964
$36$	28.0749	4.67916
$37$	−6.32030	−1.03905	−0.519525	−	0.854455i	$-0.673891\pi$
$37$	−6.32030	−1.03905	−0.519525	+	0.854455i	$0.673891\pi$
$38$	−17.7732	−2.88320
$39$	3.74245	0.599272
$40$	−6.16183	−0.974271
$41$	−9.82455	−1.53434	−0.767168	−	0.641446i	$-0.778335\pi$
$41$	−9.82455	−1.53434	−0.767168	+	0.641446i	$0.778335\pi$
$42$	−23.6038	−3.64214
$43$	−8.23734	−1.25618	−0.628091	−	0.778140i	$-0.716163\pi$
$43$	−8.23734	−1.25618	−0.628091	+	0.778140i	$0.716163\pi$
$44$	−4.77947	−0.720532
$45$	5.00137	0.745560
$46$	−21.8835	−3.22654
$47$	1.11751	0.163006	0.0815029	−	0.996673i	$-0.474028\pi$
$47$	1.11751	0.163006	0.0815029	+	0.996673i	$0.474028\pi$
$48$	27.6576	3.99203
$49$	2.26073	0.322961
$50$	11.1312	1.57418
$51$	−23.0443	−3.22685
$52$	6.00447	0.832670
$53$	−4.72415	−0.648912	−0.324456	−	0.945901i	$-0.605181\pi$
$53$	−4.72415	−0.648912	−0.324456	+	0.945901i	$0.605181\pi$
$54$	−22.2924	−3.03361
$55$	−0.851432	−0.114807
$56$	−22.0233	−2.94299
$57$	20.3343	2.69335
$58$	−2.86013	−0.375553
$59$	11.0384	1.43708	0.718540	−	0.695485i	$-0.244811\pi$
$59$	11.0384	1.43708	0.718540	+	0.695485i	$0.244811\pi$
$60$	12.1225	1.56500
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	5.30480	0.673711
$63$	17.8756	2.25212
$64$	6.68778	0.835972
$65$	1.06966	0.132675
$66$	7.75638	0.954745
$67$	6.91010	0.844203	0.422102	−	0.906549i	$-0.361293\pi$
$67$	6.91010	0.844203	0.422102	+	0.906549i	$0.361293\pi$
$68$	−36.9728	−4.48361
$69$	25.0368	3.01408
$70$	−6.74637	−0.806346
$71$	−7.00240	−0.831032	−0.415516	−	0.909586i	$-0.636399\pi$
$71$	−7.00240	−0.831032	−0.415516	+	0.909586i	$0.636399\pi$
$72$	−42.5107	−5.00994
$73$	1.27134	0.148799	0.0743995	−	0.997229i	$-0.476296\pi$
$73$	1.27134	0.148799	0.0743995	+	0.997229i	$0.476296\pi$
$74$	16.4564	1.91302
$75$	−12.7351	−1.47053
$76$	32.6248	3.74233
$77$	−3.04314	−0.346798
$78$	−9.74438	−1.10333
$79$	−3.71107	−0.417529	−0.208764	−	0.977966i	$-0.566944\pi$
$79$	−3.71107	−0.417529	−0.208764	+	0.977966i	$0.566944\pi$
$80$	7.90502	0.883808
$81$	7.88248	0.875832
$82$	25.5806	2.82490
$83$	11.2940	1.23967	0.619837	−	0.784731i	$-0.287199\pi$
$83$	11.2940	1.23967	0.619837	+	0.784731i	$0.287199\pi$
$84$	43.3275	4.72742
$85$	−6.58646	−0.714402
$86$	21.4479	2.31279
$87$	3.27227	0.350824
$88$	7.23702	0.771469
$89$	−3.62680	−0.384440	−0.192220	−	0.981352i	$-0.561569\pi$
$89$	−3.62680	−0.384440	−0.192220	+	0.981352i	$0.561569\pi$
$90$	−13.0223	−1.37267
$91$	3.82312	0.400771
$92$	40.1696	4.18797
$93$	−6.06922	−0.629349
$94$	−2.90971	−0.300114
$95$	5.81191	0.596289
$96$	−28.8960	−2.94918
$97$	−0.113236	−0.0114974	−0.00574869	−	0.999983i	$-0.501830\pi$
$97$	−0.113236	−0.0114974	−0.00574869	+	0.999983i	$0.501830\pi$
$98$	−5.88635	−0.594611
$99$	−5.87407	−0.590366
$100$	−20.4325	−2.04325
$101$	−3.13269	−0.311714	−0.155857	−	0.987780i	$-0.549814\pi$
$101$	−3.13269	−0.311714	−0.155857	+	0.987780i	$0.549814\pi$
$102$	60.0014	5.94102
$103$	−0.612788	−0.0603798	−0.0301899	−	0.999544i	$-0.509611\pi$
$103$	−0.612788	−0.0603798	−0.0301899	+	0.999544i	$0.509611\pi$
$104$	−9.09190	−0.891534
$105$	7.71852	0.753250
$106$	12.3005	1.19473
$107$	1.37535	0.132960	0.0664801	−	0.997788i	$-0.478823\pi$
$107$	1.37535	0.132960	0.0664801	+	0.997788i	$0.478823\pi$
$108$	40.9203	3.93755
$109$	20.5325	1.96665	0.983327	−	0.181845i	$-0.0582068\pi$
$109$	20.5325	1.96665	0.983327	+	0.181845i	$0.0582068\pi$
$110$	2.21691	0.211374
$111$	−18.8278	−1.78705
$112$	28.2537	2.66973
$113$	−0.112340	−0.0105681	−0.00528404	−	0.999986i	$-0.501682\pi$
$113$	−0.112340	−0.0105681	−0.00528404	+	0.999986i	$0.501682\pi$
$114$	−52.9454	−4.95879
$115$	7.15596	0.667297
$116$	5.25010	0.487459
$117$	7.37962	0.682246
$118$	−28.7412	−2.64584
$119$	−23.5410	−2.15800
$120$	−18.3557	−1.67564
$121$	1.00000	0.0909091
$122$	−2.60374	−0.235732
$123$	−29.2667	−2.63889
$124$	−9.73758	−0.874461
$125$	−7.89709	−0.706337
$126$	−46.5435	−4.14643
$127$	−12.5972	−1.11782	−0.558912	−	0.829227i	$-0.688781\pi$
$127$	−12.5972	−1.11782	−0.558912	+	0.829227i	$0.688781\pi$
$128$	1.98695	0.175624
$129$	−24.5385	−2.16050
$130$	−2.78511	−0.244271
$131$	6.91322	0.604011	0.302006	−	0.953306i	$-0.402344\pi$
$131$	6.91322	0.604011	0.302006	+	0.953306i	$0.402344\pi$
$132$	−14.2377	−1.23924
$133$	20.7726	1.80121
$134$	−17.9921	−1.55428
$135$	7.28968	0.627396
$136$	55.9837	4.80056
$137$	−8.75852	−0.748291	−0.374146	−	0.927370i	$-0.622064\pi$
$137$	−8.75852	−0.748291	−0.374146	+	0.927370i	$0.622064\pi$
$138$	−65.1895	−5.54930
$139$	13.2977	1.12790	0.563949	−	0.825809i	$-0.309281\pi$
$139$	13.2977	1.12790	0.563949	+	0.825809i	$0.309281\pi$
$140$	12.3837	1.04662
$141$	3.32900	0.280352
$142$	18.2324	1.53003
$143$	−1.25630	−0.105057
$144$	54.5371	4.54476
$145$	0.935271	0.0776700
$146$	−3.31024	−0.273957
$147$	6.73457	0.555458
$148$	−30.2077	−2.48305
$149$	2.50057	0.204855	0.102428	−	0.994740i	$-0.467339\pi$
$149$	2.50057	0.204855	0.102428	+	0.994740i	$0.467339\pi$
$150$	33.1590	2.70742
$151$	17.4446	1.41962	0.709811	−	0.704392i	$-0.248780\pi$
$151$	17.4446	1.41962	0.709811	+	0.704392i	$0.248780\pi$
$152$	−49.4002	−4.00688
$153$	−45.4403	−3.67363
$154$	7.92356	0.638499
$155$	−1.73469	−0.139334
$156$	17.8869	1.43210
$157$	−21.3392	−1.70305	−0.851526	−	0.524312i	$-0.824323\pi$
$157$	−21.3392	−1.70305	−0.851526	+	0.524312i	$0.824323\pi$
$158$	9.66268	0.768721
$159$	−14.0730	−1.11606
$160$	−8.25897	−0.652929
$161$	25.5765	2.01571
$162$	−20.5239	−1.61251
$163$	−13.4618	−1.05441	−0.527205	−	0.849738i	$-0.676760\pi$
$163$	−13.4618	−1.05441	−0.527205	+	0.849738i	$0.676760\pi$
$164$	−46.9561	−3.66666
$165$	−2.53636	−0.197456
$166$	−29.4065	−2.28239
$167$	24.1963	1.87237	0.936184	−	0.351510i	$-0.114332\pi$
$167$	24.1963	1.87237	0.936184	+	0.351510i	$0.114332\pi$
$168$	−65.6060	−5.06161
$169$	−11.4217	−0.878592
$170$	17.1494	1.31530
$171$	40.0966	3.06627
$172$	−39.3701	−3.00194
$173$	−6.87500	−0.522697	−0.261348	−	0.965245i	$-0.584167\pi$
$173$	−6.87500	−0.522697	−0.261348	+	0.965245i	$0.584167\pi$
$174$	−8.52014	−0.645910
$175$	−13.0096	−0.983436
$176$	−9.28438	−0.699837
$177$	32.8828	2.47162
$178$	9.44324	0.707801
$179$	−7.18760	−0.537227	−0.268613	−	0.963248i	$-0.586565\pi$
$179$	−7.18760	−0.537227	−0.268613	+	0.963248i	$0.586565\pi$
$180$	23.9039	1.78169
$181$	−3.28618	−0.244260	−0.122130	−	0.992514i	$-0.538972\pi$
$181$	−3.28618	−0.244260	−0.122130	+	0.992514i	$0.538972\pi$
$182$	−9.95441	−0.737870
$183$	2.97894	0.220209
$184$	−60.8244	−4.48403
$185$	−5.38130	−0.395641
$186$	15.8027	1.15871
$187$	7.73575	0.565694
$188$	5.34111	0.389541
$189$	26.0544	1.89518
$190$	−15.1327	−1.09784
$191$	−15.9729	−1.15576	−0.577878	−	0.816123i	$-0.696119\pi$
$191$	−15.9729	−1.15576	−0.577878	+	0.816123i	$0.696119\pi$
$192$	19.9225	1.43778
$193$	−5.16456	−0.371753	−0.185876	−	0.982573i	$-0.559512\pi$
$193$	−5.16456	−0.371753	−0.185876	+	0.982573i	$0.559512\pi$
$194$	0.294837	0.0211681
$195$	3.18644	0.228186
$196$	10.8051	0.771791
$197$	−19.1277	−1.36280	−0.681398	−	0.731914i	$-0.738627\pi$
$197$	−19.1277	−1.36280	−0.681398	+	0.731914i	$0.738627\pi$
$198$	15.2946	1.08694
$199$	0.0471165	0.00334000	0.00167000	−	0.999999i	$-0.499468\pi$
$199$	0.0471165	0.00334000	0.00167000	+	0.999999i	$0.499468\pi$
$200$	30.9387	2.18770
$201$	20.5848	1.45194
$202$	8.15672	0.573905
$203$	3.34280	0.234618
$204$	−110.140	−7.71131
$205$	−8.36493	−0.584232
$206$	1.59554	0.111167
$207$	49.3693	3.43141
$208$	11.6640	0.808754
$209$	−6.82604	−0.472167
$210$	−20.0970	−1.38683
$211$	20.7627	1.42936	0.714681	−	0.699451i	$-0.246572\pi$
$211$	20.7627	1.42936	0.714681	+	0.699451i	$0.246572\pi$
$212$	−22.5789	−1.55073
$213$	−20.8597	−1.42928
$214$	−3.58106	−0.244796
$215$	−7.01353	−0.478319
$216$	−61.9610	−4.21591
$217$	−6.20003	−0.420886
$218$	−53.4613	−3.62085
$219$	3.78724	0.255918
$220$	−4.06939	−0.274358
$221$	−9.71845	−0.653734
$222$	49.0226	3.29018
$223$	10.9949	0.736273	0.368137	−	0.929772i	$-0.379996\pi$
$223$	10.9949	0.736273	0.368137	+	0.929772i	$0.379996\pi$
$224$	−29.5188	−1.97231
$225$	−25.1120	−1.67413
$226$	0.292505	0.0194572
$227$	9.54696	0.633654	0.316827	−	0.948483i	$-0.397383\pi$
$227$	9.54696	0.633654	0.316827	+	0.948483i	$0.397383\pi$
$228$	97.1874	6.43639
$229$	9.08724	0.600502	0.300251	−	0.953860i	$-0.402930\pi$
$229$	9.08724	0.600502	0.300251	+	0.953860i	$0.402930\pi$
$230$	−18.6323	−1.22858
$231$	−9.06534	−0.596455
$232$	−7.94963	−0.521919
$233$	−9.22388	−0.604277	−0.302138	−	0.953264i	$-0.597700\pi$
$233$	−9.22388	−0.604277	−0.302138	+	0.953264i	$0.597700\pi$
$234$	−19.2146	−1.25610
$235$	0.951486	0.0620681
$236$	52.7578	3.43424
$237$	−11.0551	−0.718103
$238$	61.2947	3.97314
$239$	−14.5862	−0.943501	−0.471751	−	0.881732i	$-0.656378\pi$
$239$	−14.5862	−0.943501	−0.471751	+	0.881732i	$0.656378\pi$
$240$	23.5486	1.52005
$241$	−10.7788	−0.694325	−0.347163	−	0.937805i	$-0.612855\pi$
$241$	−10.7788	−0.694325	−0.347163	+	0.937805i	$0.612855\pi$
$242$	−2.60374	−0.167375
$243$	−2.20359	−0.141361
$244$	4.77947	0.305974
$245$	1.92486	0.122975
$246$	76.2029	4.85852
$247$	8.57558	0.545651
$248$	14.7445	0.936279
$249$	33.6440	2.13210
$250$	20.5620	1.30045
$251$	15.2761	0.964220	0.482110	−	0.876111i	$-0.339871\pi$
$251$	15.2761	0.964220	0.482110	+	0.876111i	$0.339871\pi$
$252$	85.4361	5.38197
$253$	−8.40462	−0.528394
$254$	32.7999	2.05805
$255$	−19.6207	−1.22869
$256$	−18.5491	−1.15932
$257$	−4.08000	−0.254503	−0.127252	−	0.991870i	$-0.540616\pi$
$257$	−4.08000	−0.254503	−0.127252	+	0.991870i	$0.540616\pi$
$258$	63.8919	3.97774
$259$	−19.2336	−1.19512
$260$	5.11240	0.317057
$261$	6.45248	0.399398
$262$	−18.0002	−1.11206
$263$	1.06475	0.0656553	0.0328276	−	0.999461i	$-0.489549\pi$
$263$	1.06475	0.0656553	0.0328276	+	0.999461i	$0.489549\pi$
$264$	21.5586	1.32684
$265$	−4.02230	−0.247088
$266$	−54.0865	−3.31626
$267$	−10.8040	−0.661194
$268$	33.0266	2.01742
$269$	−7.89164	−0.481162	−0.240581	−	0.970629i	$-0.577338\pi$
$269$	−7.89164	−0.481162	−0.240581	+	0.970629i	$0.577338\pi$
$270$	−18.9804	−1.15511
$271$	−21.7155	−1.31912	−0.659560	−	0.751652i	$-0.729257\pi$
$271$	−21.7155	−1.31912	−0.659560	+	0.751652i	$0.729257\pi$
$272$	−71.8216	−4.35483
$273$	11.3888	0.689283
$274$	22.8049	1.37770
$275$	4.27506	0.257796
$276$	119.663	7.20285
$277$	−17.6944	−1.06316	−0.531578	−	0.847009i	$-0.678401\pi$
$277$	−17.6944	−1.06316	−0.531578	+	0.847009i	$0.678401\pi$
$278$	−34.6238	−2.07660
$279$	−11.9677	−0.716487
$280$	−18.7513	−1.12061
$281$	30.9826	1.84827	0.924133	−	0.382072i	$-0.124789\pi$
$281$	30.9826	1.84827	0.924133	+	0.382072i	$0.124789\pi$
$282$	−8.66785	−0.516163
$283$	−9.38441	−0.557846	−0.278923	−	0.960314i	$-0.589977\pi$
$283$	−9.38441	−0.557846	−0.278923	+	0.960314i	$0.589977\pi$
$284$	−33.4677	−1.98594
$285$	17.3133	1.02555
$286$	3.27109	0.193424
$287$	−29.8975	−1.76479
$288$	−56.9790	−3.35752
$289$	42.8418	2.52010
$290$	−2.43520	−0.143000
$291$	−0.337323	−0.0197742
$292$	6.07633	0.355590
$293$	−1.25100	−0.0730845	−0.0365422	−	0.999332i	$-0.511634\pi$
$293$	−1.25100	−0.0730845	−0.0365422	+	0.999332i	$0.511634\pi$
$294$	−17.5351	−1.02267
$295$	9.39847	0.547200
$296$	45.7401	2.65859
$297$	−8.56167	−0.496799
$298$	−6.51085	−0.377163
$299$	10.5588	0.610629
$300$	−60.8672	−3.51417
$301$	−25.0674	−1.44486
$302$	−45.4212	−2.61370
$303$	−9.33209	−0.536115
$304$	63.3756	3.63484
$305$	0.851432	0.0487529
$306$	118.315	6.76361
$307$	−28.7361	−1.64005	−0.820027	−	0.572325i	$-0.806041\pi$
$307$	−28.7361	−1.64005	−0.820027	+	0.572325i	$0.806041\pi$
$308$	−14.5446	−0.828756
$309$	−1.82546	−0.103847
$310$	4.51668	0.256530
$311$	15.3899	0.872679	0.436339	−	0.899782i	$-0.356275\pi$
$311$	15.3899	0.872679	0.436339	+	0.899782i	$0.356275\pi$
$312$	−27.0842	−1.53334
$313$	14.0136	0.792096	0.396048	−	0.918230i	$-0.370381\pi$
$313$	14.0136	0.792096	0.396048	+	0.918230i	$0.370381\pi$
$314$	55.5617	3.13553
$315$	15.2199	0.857544
$316$	−17.7370	−0.997782
$317$	18.4283	1.03504	0.517519	−	0.855672i	$-0.326856\pi$
$317$	18.4283	1.03504	0.517519	+	0.855672i	$0.326856\pi$
$318$	36.6423	2.05480
$319$	−1.09847	−0.0615024
$320$	5.69419	0.318315
$321$	4.09709	0.228677
$322$	−66.5945	−3.71117
$323$	−52.8045	−2.93812
$324$	37.6741	2.09300
$325$	−5.37078	−0.297917
$326$	35.0511	1.94130
$327$	61.1650	3.38243
$328$	71.1004	3.92586
$329$	3.40075	0.187489
$330$	6.60403	0.363540
$331$	32.9871	1.81313	0.906567	−	0.422062i	$-0.138694\pi$
$331$	32.9871	1.81313	0.906567	+	0.422062i	$0.138694\pi$
$332$	53.9791	2.96249
$333$	−37.1259	−2.03449
$334$	−63.0010	−3.44726
$335$	5.88348	0.321449
$336$	84.1661	4.59164
$337$	−26.8517	−1.46271	−0.731354	−	0.681998i	$-0.761111\pi$
$337$	−26.8517	−1.46271	−0.731354	+	0.681998i	$0.761111\pi$
$338$	29.7391	1.61760
$339$	−0.334655	−0.0181760
$340$	−31.4798	−1.70723
$341$	2.03738	0.110330
$342$	−104.401	−5.64537
$343$	−14.4223	−0.778731
$344$	59.6138	3.21416
$345$	21.3172	1.14768
$346$	17.9007	0.962349
$347$	−1.44142	−0.0773795	−0.0386897	−	0.999251i	$-0.512318\pi$
$347$	−1.44142	−0.0773795	−0.0386897	+	0.999251i	$0.512318\pi$
$348$	15.6397	0.838376
$349$	−10.1255	−0.542004	−0.271002	−	0.962579i	$-0.587355\pi$
$349$	−10.1255	−0.542004	−0.271002	+	0.962579i	$0.587355\pi$
$350$	33.8737	1.81063
$351$	10.7561	0.574117
$352$	9.70010	0.517017
$353$	6.94974	0.369897	0.184949	−	0.982748i	$-0.440788\pi$
$353$	6.94974	0.369897	0.184949	+	0.982748i	$0.440788\pi$
$354$	−85.6183	−4.55056
$355$	−5.96206	−0.316434
$356$	−17.3342	−0.918708
$357$	−70.1271	−3.71152
$358$	18.7147	0.989100
$359$	16.5539	0.873681	0.436840	−	0.899539i	$-0.356097\pi$
$359$	16.5539	0.873681	0.436840	+	0.899539i	$0.356097\pi$
$360$	−36.1950	−1.90764
$361$	27.5948	1.45236
$362$	8.55637	0.449713
$363$	2.97894	0.156354
$364$	18.2725	0.957737
$365$	1.08246	0.0566585
$366$	−7.75638	−0.405433
$367$	−17.4739	−0.912132	−0.456066	−	0.889946i	$-0.650742\pi$
$367$	−17.4739	−0.912132	−0.456066	+	0.889946i	$0.650742\pi$
$368$	78.0317	4.06768
$369$	−57.7101	−3.00427
$370$	14.0115	0.728424
$371$	−14.3763	−0.746379
$372$	−29.0076	−1.50398
$373$	−32.0776	−1.66092	−0.830458	−	0.557082i	$-0.811921\pi$
$373$	−32.0776	−1.66092	−0.830458	+	0.557082i	$0.811921\pi$
$374$	−20.1419	−1.04151
$375$	−23.5249	−1.21482
$376$	−8.08745	−0.417079
$377$	1.38001	0.0710742
$378$	−67.8389	−3.48926
$379$	−5.75540	−0.295635	−0.147817	−	0.989015i	$-0.547225\pi$
$379$	−5.75540	−0.295635	−0.147817	+	0.989015i	$0.547225\pi$
$380$	27.7778	1.42497
$381$	−37.5264	−1.92253
$382$	41.5892	2.12789
$383$	−25.7524	−1.31589	−0.657944	−	0.753067i	$-0.728574\pi$
$383$	−25.7524	−1.31589	−0.657944	+	0.753067i	$0.728574\pi$
$384$	5.91901	0.302053
$385$	−2.59103	−0.132051
$386$	13.4472	0.684443
$387$	−48.3867	−2.45963
$388$	−0.541208	−0.0274757
$389$	19.6307	0.995314	0.497657	−	0.867374i	$-0.334194\pi$
$389$	19.6307	0.995314	0.497657	+	0.867374i	$0.334194\pi$
$390$	−8.29668	−0.420119
$391$	−65.0160	−3.28800
$392$	−16.3609	−0.826351
$393$	20.5941	1.03883
$394$	49.8037	2.50907
$395$	−3.15973	−0.158983
$396$	−28.0749	−1.41082
$397$	−16.9311	−0.849747	−0.424873	−	0.905253i	$-0.639681\pi$
$397$	−16.9311	−0.849747	−0.424873	+	0.905253i	$0.639681\pi$
$398$	−0.122679	−0.00614935
$399$	61.8803	3.09789
$400$	−39.6913	−1.98457
$401$	−8.13681	−0.406333	−0.203167	−	0.979144i	$-0.565123\pi$
$401$	−8.13681	−0.406333	−0.203167	+	0.979144i	$0.565123\pi$
$402$	−53.5974	−2.67320
$403$	−2.55957	−0.127501
$404$	−14.9726	−0.744914
$405$	6.71140	0.333492
$406$	−8.70378	−0.431961
$407$	6.32030	0.313286
$408$	166.772	8.25645
$409$	16.5019	0.815966	0.407983	−	0.912990i	$-0.366232\pi$
$409$	16.5019	0.815966	0.407983	+	0.912990i	$0.366232\pi$
$410$	21.7801	1.07564
$411$	−26.0911	−1.28698
$412$	−2.92880	−0.144292
$413$	33.5915	1.65293
$414$	−128.545	−6.31764
$415$	9.61604	0.472033
$416$	−12.1863	−0.597481
$417$	39.6131	1.93986
$418$	17.7732	0.869318
$419$	4.06852	0.198760	0.0993802	−	0.995050i	$-0.468314\pi$
$419$	4.06852	0.198760	0.0993802	+	0.995050i	$0.468314\pi$
$420$	36.8904	1.80007
$421$	−22.4972	−1.09645	−0.548223	−	0.836332i	$-0.684696\pi$
$421$	−22.4972	−1.09645	−0.548223	+	0.836332i	$0.684696\pi$
$422$	−54.0606	−2.63163
$423$	6.56434	0.319169
$424$	34.1888	1.66035
$425$	33.0708	1.60417
$426$	54.3133	2.63149
$427$	3.04314	0.147268
$428$	6.57345	0.317740
$429$	−3.74245	−0.180687
$430$	18.2614	0.880644
$431$	14.8069	0.713225	0.356613	−	0.934252i	$-0.383932\pi$
$431$	14.8069	0.713225	0.356613	+	0.934252i	$0.383932\pi$
$432$	79.4899	3.82446
$433$	13.8033	0.663343	0.331671	−	0.943395i	$-0.392387\pi$
$433$	13.8033	0.663343	0.331671	+	0.943395i	$0.392387\pi$
$434$	16.1433	0.774902
$435$	2.78611	0.133584
$436$	98.1343	4.69978
$437$	57.3703	2.74439
$438$	−9.86099	−0.471177
$439$	−19.4862	−0.930027	−0.465013	−	0.885304i	$-0.653950\pi$
$439$	−19.4862	−0.930027	−0.465013	+	0.885304i	$0.653950\pi$
$440$	6.16183	0.293754
$441$	13.2797	0.632365
$442$	25.3043	1.20360
$443$	24.5693	1.16732	0.583661	−	0.811997i	$-0.301620\pi$
$443$	24.5693	1.16732	0.583661	+	0.811997i	$0.301620\pi$
$444$	−89.9867	−4.27058
$445$	−3.08797	−0.146384
$446$	−28.6279	−1.35557
$447$	7.44906	0.352328
$448$	20.3519	0.961535
$449$	20.1319	0.950081	0.475041	−	0.879964i	$-0.342433\pi$
$449$	20.1319	0.950081	0.475041	+	0.879964i	$0.342433\pi$
$450$	65.3852	3.08229
$451$	9.82455	0.462620
$452$	−0.536927	−0.0252549
$453$	51.9664	2.44159
$454$	−24.8578	−1.16664
$455$	3.25512	0.152603
$456$	−147.160	−6.89140
$457$	−14.6515	−0.685366	−0.342683	−	0.939451i	$-0.611336\pi$
$457$	−14.6515	−0.685366	−0.342683	+	0.939451i	$0.611336\pi$
$458$	−23.6608	−1.10560
$459$	−66.2309	−3.09140
$460$	34.2017	1.59466
$461$	−8.90582	−0.414785	−0.207393	−	0.978258i	$-0.566498\pi$
$461$	−8.90582	−0.414785	−0.207393	+	0.978258i	$0.566498\pi$
$462$	23.6038	1.09815
$463$	−32.9705	−1.53227	−0.766133	−	0.642681i	$-0.777822\pi$
$463$	−32.9705	−1.53227	−0.766133	+	0.642681i	$0.777822\pi$
$464$	10.1986	0.473458
$465$	−5.16753	−0.239638
$466$	24.0166	1.11255
$467$	21.5869	0.998921	0.499461	−	0.866337i	$-0.333532\pi$
$467$	21.5869	0.998921	0.499461	+	0.866337i	$0.333532\pi$
$468$	35.2707	1.63039
$469$	21.0284	0.971003
$470$	−2.47742	−0.114275
$471$	−63.5681	−2.92906
$472$	−79.8853	−3.67702
$473$	8.23734	0.378753
$474$	28.7845	1.32212
$475$	−29.1818	−1.33895
$476$	−112.513	−5.15704
$477$	−27.7500	−1.27059
$478$	37.9786	1.73710
$479$	−13.8271	−0.631774	−0.315887	−	0.948797i	$-0.602302\pi$
$479$	−13.8271	−0.631774	−0.315887	+	0.948797i	$0.602302\pi$
$480$	−24.6030	−1.12297
$481$	−7.94022	−0.362043
$482$	28.0653	1.27834
$483$	76.1907	3.46680
$484$	4.77947	0.217249
$485$	−0.0964127	−0.00437788
$486$	5.73759	0.260262
$487$	35.7656	1.62069	0.810347	−	0.585950i	$-0.199279\pi$
$487$	35.7656	1.62069	0.810347	+	0.585950i	$0.199279\pi$
$488$	−7.23702	−0.327604
$489$	−40.1019	−1.81347
$490$	−5.01183	−0.226411
$491$	−30.4054	−1.37217	−0.686087	−	0.727519i	$-0.740673\pi$
$491$	−30.4054	−1.37217	−0.686087	+	0.727519i	$0.740673\pi$
$492$	−139.879	−6.30625
$493$	−8.49747	−0.382707
$494$	−22.3286	−1.00461
$495$	−5.00137	−0.224795
$496$	−18.9158	−0.849344
$497$	−21.3093	−0.955853
$498$	−87.6003	−3.92546
$499$	4.63293	0.207398	0.103699	−	0.994609i	$-0.466932\pi$
$499$	4.63293	0.207398	0.103699	+	0.994609i	$0.466932\pi$
$500$	−37.7439	−1.68796
$501$	72.0794	3.22027
$502$	−39.7751	−1.77525
$503$	13.7105	0.611319	0.305660	−	0.952141i	$-0.401123\pi$
$503$	13.7105	0.611319	0.305660	+	0.952141i	$0.401123\pi$
$504$	−129.366	−5.76243
$505$	−2.66727	−0.118692
$506$	21.8835	0.972838
$507$	−34.0245	−1.51108
$508$	−60.2081	−2.67130
$509$	−11.0272	−0.488771	−0.244386	−	0.969678i	$-0.578586\pi$
$509$	−11.0272	−0.488771	−0.244386	+	0.969678i	$0.578586\pi$
$510$	51.0871	2.26218
$511$	3.86887	0.171149
$512$	44.3231	1.95882
$513$	58.4423	2.58029
$514$	10.6233	0.468572
$515$	−0.521748	−0.0229909
$516$	−117.281	−5.16301
$517$	−1.11751	−0.0491481
$518$	50.0793	2.20036
$519$	−20.4802	−0.898981
$520$	−7.74113	−0.339471
$521$	5.84854	0.256229	0.128115	−	0.991759i	$-0.459107\pi$
$521$	5.84854	0.256229	0.128115	+	0.991759i	$0.459107\pi$
$522$	−16.8006	−0.735342
$523$	26.2499	1.14783	0.573914	−	0.818915i	$-0.305424\pi$
$523$	26.2499	1.14783	0.573914	+	0.818915i	$0.305424\pi$
$524$	33.0415	1.44343
$525$	−38.7549	−1.69140
$526$	−2.77233	−0.120879
$527$	15.7606	0.686544
$528$	−27.6576	−1.20364
$529$	47.6377	2.07120
$530$	10.4730	0.454919
$531$	64.8405	2.81384
$532$	99.2821	4.30442
$533$	−12.3426	−0.534618
$534$	28.1308	1.21734
$535$	1.17102	0.0506275
$536$	−50.0085	−2.16004
$537$	−21.4114	−0.923971
$538$	20.5478	0.885878
$539$	−2.26073	−0.0973764
$540$	34.8408	1.49931
$541$	21.5728	0.927487	0.463743	−	0.885970i	$-0.346506\pi$
$541$	21.5728	0.927487	0.463743	+	0.885970i	$0.346506\pi$
$542$	56.5414	2.42866
$543$	−9.78933	−0.420100
$544$	75.0375	3.21721
$545$	17.4820	0.748847
$546$	−29.6536	−1.26905
$547$	−13.2689	−0.567339	−0.283669	−	0.958922i	$-0.591552\pi$
$547$	−13.2689	−0.567339	−0.283669	+	0.958922i	$0.591552\pi$
$548$	−41.8611	−1.78822
$549$	5.87407	0.250699
$550$	−11.1312	−0.474634
$551$	7.49819	0.319434
$552$	−181.192	−7.71205
$553$	−11.2933	−0.480241
$554$	46.0717	1.95740
$555$	−16.0306	−0.680460
$556$	63.5561	2.69538
$557$	−19.7663	−0.837525	−0.418762	−	0.908096i	$-0.637536\pi$
$557$	−19.7663	−0.837525	−0.418762	+	0.908096i	$0.637536\pi$
$558$	31.1608	1.31914
$559$	−10.3486	−0.437699
$560$	24.0561	1.01656
$561$	23.0443	0.972931
$562$	−80.6706	−3.40288
$563$	−21.9105	−0.923418	−0.461709	−	0.887032i	$-0.652763\pi$
$563$	−21.9105	−0.923418	−0.461709	+	0.887032i	$0.652763\pi$
$564$	15.9108	0.669967
$565$	−0.0956501	−0.00402403
$566$	24.4346	1.02706
$567$	23.9875	1.00738
$568$	50.6765	2.12634
$569$	−33.2783	−1.39510	−0.697550	−	0.716536i	$-0.745727\pi$
$569$	−33.2783	−1.39510	−0.697550	+	0.716536i	$0.745727\pi$
$570$	−45.0794	−1.88817
$571$	4.34024	0.181633	0.0908166	−	0.995868i	$-0.471052\pi$
$571$	4.34024	0.181633	0.0908166	+	0.995868i	$0.471052\pi$
$572$	−6.00447	−0.251059
$573$	−47.5822	−1.98778
$574$	77.8454	3.24920
$575$	−35.9303	−1.49840
$576$	39.2845	1.63685
$577$	25.8729	1.07710	0.538552	−	0.842592i	$-0.318971\pi$
$577$	25.8729	1.07710	0.538552	+	0.842592i	$0.318971\pi$
$578$	−111.549	−4.63982
$579$	−15.3849	−0.639374
$580$	4.47010	0.185611
$581$	34.3691	1.42587
$582$	0.878302	0.0364068
$583$	4.72415	0.195654
$584$	−9.20070	−0.380728
$585$	6.28324	0.259780
$586$	3.25729	0.134558
$587$	−13.9531	−0.575908	−0.287954	−	0.957644i	$-0.592975\pi$
$587$	−13.9531	−0.575908	−0.287954	+	0.957644i	$0.592975\pi$
$588$	32.1876	1.32740
$589$	−13.9072	−0.573037
$590$	−24.4712	−1.00746
$591$	−56.9803	−2.34386
$592$	−58.6801	−2.41174
$593$	−41.4876	−1.70369	−0.851846	−	0.523792i	$-0.824517\pi$
$593$	−41.4876	−1.70369	−0.851846	+	0.523792i	$0.824517\pi$
$594$	22.2924	0.914668
$595$	−20.0436	−0.821706
$596$	11.9514	0.489549
$597$	0.140357	0.00574444
$598$	−27.4923	−1.12424
$599$	1.63508	0.0668077	0.0334038	−	0.999442i	$-0.489365\pi$
$599$	1.63508	0.0668077	0.0334038	+	0.999442i	$0.489365\pi$
$600$	92.1645	3.76260
$601$	37.8743	1.54492	0.772462	−	0.635062i	$-0.219025\pi$
$601$	37.8743	1.54492	0.772462	+	0.635062i	$0.219025\pi$
$602$	65.2690	2.66017
$603$	40.5904	1.65297
$604$	83.3759	3.39252
$605$	0.851432	0.0346156
$606$	24.2983	0.987053
$607$	1.25664	0.0510055	0.0255027	−	0.999675i	$-0.491881\pi$
$607$	1.25664	0.0510055	0.0255027	+	0.999675i	$0.491881\pi$
$608$	−66.2132	−2.68530
$609$	9.95799	0.403518
$610$	−2.21691	−0.0897600
$611$	1.40394	0.0567972
$612$	−217.181	−8.77900
$613$	22.7888	0.920430	0.460215	−	0.887807i	$-0.347772\pi$
$613$	22.7888	0.920430	0.460215	+	0.887807i	$0.347772\pi$
$614$	74.8212	3.01954
$615$	−24.9186	−1.00482
$616$	22.0233	0.887344
$617$	−9.66482	−0.389091	−0.194545	−	0.980894i	$-0.562323\pi$
$617$	−9.66482	−0.389091	−0.194545	+	0.980894i	$0.562323\pi$
$618$	4.75302	0.191195
$619$	12.2722	0.493263	0.246632	−	0.969109i	$-0.420676\pi$
$619$	12.2722	0.493263	0.246632	+	0.969109i	$0.420676\pi$
$620$	−8.29089	−0.332970
$621$	71.9576	2.88756
$622$	−40.0712	−1.60671
$623$	−11.0369	−0.442183
$624$	34.7464	1.39097
$625$	14.6515	0.586059
$626$	−36.4878	−1.45835
$627$	−20.3343	−0.812076
$628$	−101.990	−4.06984
$629$	48.8922	1.94946
$630$	−39.6287	−1.57884
$631$	32.5982	1.29772	0.648858	−	0.760910i	$-0.275247\pi$
$631$	32.5982	1.29772	0.648858	+	0.760910i	$0.275247\pi$
$632$	26.8571	1.06832
$633$	61.8507	2.45834
$634$	−47.9826	−1.90563
$635$	−10.7257	−0.425636
$636$	−67.2613	−2.66708
$637$	2.84016	0.112531
$638$	2.86013	0.113234
$639$	−41.1326	−1.62718
$640$	1.69176	0.0668725
$641$	39.4363	1.55764	0.778820	−	0.627248i	$-0.215819\pi$
$641$	39.4363	1.55764	0.778820	+	0.627248i	$0.215819\pi$
$642$	−10.6678	−0.421023
$643$	35.4044	1.39621	0.698107	−	0.715993i	$-0.254026\pi$
$643$	35.4044	1.39621	0.698107	+	0.715993i	$0.254026\pi$
$644$	122.242	4.81701
$645$	−20.8929	−0.822656
$646$	137.489	5.40944
$647$	−25.6571	−1.00869	−0.504343	−	0.863504i	$-0.668265\pi$
$647$	−25.6571	−1.00869	−0.504343	+	0.863504i	$0.668265\pi$
$648$	−57.0457	−2.24097
$649$	−11.0384	−0.433296
$650$	13.9841	0.548503
$651$	−18.4695	−0.723877
$652$	−64.3403	−2.51976
$653$	−3.64441	−0.142617	−0.0713085	−	0.997454i	$-0.522717\pi$
$653$	−3.64441	−0.142617	−0.0713085	+	0.997454i	$0.522717\pi$
$654$	−159.258	−6.22747
$655$	5.88614	0.229991
$656$	−91.2149	−3.56134
$657$	7.46794	0.291352
$658$	−8.85467	−0.345191
$659$	−3.49371	−0.136095	−0.0680477	−	0.997682i	$-0.521677\pi$
$659$	−3.49371	−0.136095	−0.0680477	+	0.997682i	$0.521677\pi$
$660$	−12.1225	−0.471866
$661$	−49.5134	−1.92585	−0.962923	−	0.269775i	$-0.913051\pi$
$661$	−49.5134	−1.92585	−0.962923	+	0.269775i	$0.913051\pi$
$662$	−85.8898	−3.33820
$663$	−28.9507	−1.12435
$664$	−81.7346	−3.17192
$665$	17.6865	0.685852
$666$	96.6662	3.74574
$667$	9.23221	0.357473
$668$	115.646	4.47446
$669$	32.7531	1.26631
$670$	−15.3191	−0.591827
$671$	−1.00000	−0.0386046
$672$	−87.9346	−3.39215
$673$	−17.3434	−0.668538	−0.334269	−	0.942478i	$-0.608489\pi$
$673$	−17.3434	−0.668538	−0.334269	+	0.942478i	$0.608489\pi$
$674$	69.9150	2.69302
$675$	−36.6017	−1.40880
$676$	−54.5897	−2.09960
$677$	23.0773	0.886931	0.443466	−	0.896291i	$-0.353749\pi$
$677$	23.0773	0.886931	0.443466	+	0.896291i	$0.353749\pi$
$678$	0.871354	0.0334642
$679$	−0.344593	−0.0132243
$680$	47.6663	1.82792
$681$	28.4398	1.08982
$682$	−5.30480	−0.203131
$683$	41.1141	1.57319	0.786593	−	0.617471i	$-0.211843\pi$
$683$	41.1141	1.57319	0.786593	+	0.617471i	$0.211843\pi$
$684$	191.641	7.32756
$685$	−7.45729	−0.284928
$686$	37.5519	1.43374
$687$	27.0703	1.03280
$688$	−76.4786	−2.91572
$689$	−5.93498	−0.226105
$690$	−55.5044	−2.11302
$691$	0.00796003	0.000302814 0	0.000151407	−	1.00000i	$-0.499952\pi$
$691$	0.00796003	0.000302814 0	0.000151407		1.00000i	$0.499952\pi$
$692$	−32.8589	−1.24911
$693$	−17.8756	−0.679039
$694$	3.75308	0.142465
$695$	11.3221	0.429472
$696$	−23.6815	−0.897644
$697$	76.0002	2.87871
$698$	26.3641	0.997896
$699$	−27.4774	−1.03929
$700$	−62.1791	−2.35015
$701$	15.6416	0.590774	0.295387	−	0.955378i	$-0.404551\pi$
$701$	15.6416	0.590774	0.295387	+	0.955378i	$0.404551\pi$
$702$	−28.0060	−1.05702
$703$	−43.1426	−1.62715
$704$	−6.68778	−0.252055
$705$	2.83442	0.106750
$706$	−18.0953	−0.681026
$707$	−9.53323	−0.358534
$708$	157.162	5.90652
$709$	16.5953	0.623250	0.311625	−	0.950205i	$-0.399127\pi$
$709$	16.5953	0.623250	0.311625	+	0.950205i	$0.399127\pi$
$710$	15.5237	0.582593
$711$	−21.7991	−0.817530
$712$	26.2472	0.983655
$713$	−17.1234	−0.641276
$714$	182.593	6.83337
$715$	−1.06966	−0.0400029
$716$	−34.3529	−1.28383
$717$	−43.4513	−1.62272
$718$	−43.1020	−1.60855
$719$	−25.8212	−0.962967	−0.481484	−	0.876455i	$-0.659902\pi$
$719$	−25.8212	−0.962967	−0.481484	+	0.876455i	$0.659902\pi$
$720$	46.4346	1.73052
$721$	−1.86480	−0.0694489
$722$	−71.8497	−2.67397
$723$	−32.1095	−1.19416
$724$	−15.7062	−0.583716
$725$	−4.69602	−0.174406
$726$	−7.75638	−0.287866
$727$	−20.5085	−0.760619	−0.380310	−	0.924859i	$-0.624183\pi$
$727$	−20.5085	−0.760619	−0.380310	+	0.924859i	$0.624183\pi$
$728$	−27.6680	−1.02544
$729$	−30.2118	−1.11896
$730$	−2.81844	−0.104315
$731$	63.7220	2.35684
$732$	14.2377	0.526242
$733$	46.0269	1.70004	0.850021	−	0.526749i	$-0.176589\pi$
$733$	46.0269	1.70004	0.850021	+	0.526749i	$0.176589\pi$
$734$	45.4976	1.67935
$735$	5.73402	0.211503
$736$	−81.5256	−3.00508
$737$	−6.91010	−0.254537
$738$	150.262	5.53122
$739$	33.7128	1.24015	0.620073	−	0.784544i	$-0.287103\pi$
$739$	33.7128	1.24015	0.620073	+	0.784544i	$0.287103\pi$
$740$	−25.7198	−0.945478
$741$	25.5461	0.938461
$742$	37.4321	1.37418
$743$	−1.80937	−0.0663793	−0.0331896	−	0.999449i	$-0.510567\pi$
$743$	−1.80937	−0.0663793	−0.0331896	+	0.999449i	$0.510567\pi$
$744$	43.9231	1.61030
$745$	2.12907	0.0780031
$746$	83.5218	3.05795
$747$	66.3415	2.42731
$748$	36.9728	1.35186
$749$	4.18539	0.152931
$750$	61.2528	2.23664
$751$	−17.2718	−0.630256	−0.315128	−	0.949049i	$-0.602047\pi$
$751$	−17.2718	−0.630256	−0.315128	+	0.949049i	$0.602047\pi$
$752$	10.3754	0.378352
$753$	45.5066	1.65835
$754$	−3.59319	−0.130856
$755$	14.8529	0.540552
$756$	124.526	4.52898
$757$	−0.988737	−0.0359363	−0.0179681	−	0.999839i	$-0.505720\pi$
$757$	−0.988737	−0.0359363	−0.0179681	+	0.999839i	$0.505720\pi$
$758$	14.9856	0.544300
$759$	−25.0368	−0.908780
$760$	−42.0609	−1.52571
$761$	47.0722	1.70636	0.853182	−	0.521613i	$-0.174670\pi$
$761$	47.0722	1.70636	0.853182	+	0.521613i	$0.174670\pi$
$762$	97.7090	3.53962
$763$	62.4833	2.26205
$764$	−76.3419	−2.76195
$765$	−38.6893	−1.39882
$766$	67.0527	2.42271
$767$	13.8676	0.500731
$768$	−55.2565	−1.99390
$769$	26.8992	0.970009	0.485004	−	0.874512i	$-0.338818\pi$
$769$	26.8992	0.970009	0.485004	+	0.874512i	$0.338818\pi$
$770$	6.74637	0.243122
$771$	−12.1541	−0.437718
$772$	−24.6838	−0.888391
$773$	12.9507	0.465804	0.232902	−	0.972500i	$-0.425178\pi$
$773$	12.9507	0.465804	0.232902	+	0.972500i	$0.425178\pi$
$774$	125.986	4.52849
$775$	8.70992	0.312869
$776$	0.819491	0.0294180
$777$	−57.2956	−2.05547
$778$	−51.1132	−1.83250
$779$	−67.0627	−2.40277
$780$	15.2295	0.545304
$781$	7.00240	0.250565
$782$	169.285	6.05362
$783$	9.40473	0.336098
$784$	20.9895	0.749623
$785$	−18.1689	−0.648475
$786$	−53.6216	−1.91262
$787$	−36.5969	−1.30454	−0.652270	−	0.757987i	$-0.726183\pi$
$787$	−36.5969	−1.30454	−0.652270	+	0.757987i	$0.726183\pi$
$788$	−91.4204	−3.25672
$789$	3.17182	0.112920
$790$	8.22711	0.292708
$791$	−0.341868	−0.0121554
$792$	42.5107	1.51055
$793$	1.25630	0.0446127
$794$	44.0842	1.56449
$795$	−11.9822	−0.424964
$796$	0.225192	0.00798172
$797$	27.8407	0.986167	0.493083	−	0.869982i	$-0.335870\pi$
$797$	27.8407	0.986167	0.493083	+	0.869982i	$0.335870\pi$
$798$	−161.120	−5.70360
$799$	−8.64479	−0.305831
$800$	41.4685	1.46613
$801$	−21.3041	−0.752742
$802$	21.1862	0.748109
$803$	−1.27134	−0.0448646
$804$	98.3842	3.46974
$805$	21.7766	0.767525
$806$	6.66445	0.234745
$807$	−23.5087	−0.827545
$808$	22.6713	0.797575
$809$	−1.23289	−0.0433461	−0.0216730	−	0.999765i	$-0.506899\pi$
$809$	−1.23289	−0.0433461	−0.0216730	+	0.999765i	$0.506899\pi$
$810$	−17.4747	−0.614000
$811$	−30.2942	−1.06377	−0.531886	−	0.846816i	$-0.678516\pi$
$811$	−30.2942	−1.06377	−0.531886	+	0.846816i	$0.678516\pi$
$812$	15.9768	0.560676
$813$	−64.6890	−2.26874
$814$	−16.4564	−0.576797
$815$	−11.4618	−0.401490
$816$	−213.952	−7.48982
$817$	−56.2284	−1.96718
$818$	−42.9666	−1.50229
$819$	22.4572	0.784720
$820$	−39.9799	−1.39616
$821$	37.4922	1.30849	0.654244	−	0.756283i	$-0.272987\pi$
$821$	37.4922	1.30849	0.654244	+	0.756283i	$0.272987\pi$
$822$	67.9345	2.36949
$823$	23.5323	0.820285	0.410142	−	0.912022i	$-0.365479\pi$
$823$	23.5323	0.820285	0.410142	+	0.912022i	$0.365479\pi$
$824$	4.43476	0.154492
$825$	12.7351	0.443381
$826$	−87.4636	−3.04325
$827$	26.7937	0.931707	0.465854	−	0.884862i	$-0.345747\pi$
$827$	26.7937	0.931707	0.465854	+	0.884862i	$0.345747\pi$
$828$	235.959	8.20015
$829$	−9.76779	−0.339249	−0.169625	−	0.985509i	$-0.554256\pi$
$829$	−9.76779	−0.339249	−0.169625	+	0.985509i	$0.554256\pi$
$830$	−25.0377	−0.869070
$831$	−52.7106	−1.82851
$832$	8.40188	0.291283
$833$	−17.4884	−0.605938
$834$	−103.142	−3.57152
$835$	20.6015	0.712945
$836$	−32.6248	−1.12835
$837$	−17.4434	−0.602931
$838$	−10.5934	−0.365942
$839$	−2.24302	−0.0774376	−0.0387188	−	0.999250i	$-0.512328\pi$
$839$	−2.24302	−0.0774376	−0.0387188	+	0.999250i	$0.512328\pi$
$840$	−55.8590	−1.92732
$841$	−27.7934	−0.958392
$842$	58.5769	2.01869
$843$	92.2951	3.17881
$844$	99.2345	3.41579
$845$	−9.72480	−0.334543
$846$	−17.0919	−0.587630
$847$	3.04314	0.104564
$848$	−43.8609	−1.50619
$849$	−27.9556	−0.959433
$850$	−86.1078	−2.95347
$851$	−53.1197	−1.82092
$852$	−99.6983	−3.41561
$853$	−44.3477	−1.51843	−0.759217	−	0.650837i	$-0.774418\pi$
$853$	−44.3477	−1.51843	−0.759217	+	0.650837i	$0.774418\pi$
$854$	−7.92356	−0.271139
$855$	34.1396	1.16755
$856$	−9.95345	−0.340202
$857$	19.5439	0.667608	0.333804	−	0.942642i	$-0.391668\pi$
$857$	19.5439	0.667608	0.333804	+	0.942642i	$0.391668\pi$
$858$	9.74438	0.332668
$859$	21.0704	0.718913	0.359456	−	0.933162i	$-0.382962\pi$
$859$	21.0704	0.718913	0.359456	+	0.933162i	$0.382962\pi$
$860$	−33.5210	−1.14306
$861$	−89.0628	−3.03525
$862$	−38.5534	−1.31314
$863$	−55.0745	−1.87476	−0.937380	−	0.348309i	$-0.886756\pi$
$863$	−55.0745	−1.87476	−0.937380	+	0.348309i	$0.886756\pi$
$864$	−83.0491	−2.82539
$865$	−5.85360	−0.199028
$866$	−35.9401	−1.22130
$867$	127.623	4.33430
$868$	−29.6329	−1.00580
$869$	3.71107	0.125890
$870$	−7.25432	−0.245945
$871$	8.68119	0.294151
$872$	−148.594	−5.03202
$873$	−0.665156	−0.0225121
$874$	−149.377	−5.05276
$875$	−24.0320	−0.812429
$876$	18.1010	0.611576
$877$	−14.0361	−0.473965	−0.236983	−	0.971514i	$-0.576158\pi$
$877$	−14.0361	−0.473965	−0.236983	+	0.971514i	$0.576158\pi$
$878$	50.7371	1.71229
$879$	−3.72667	−0.125697
$880$	−7.90502	−0.266478
$881$	−23.7847	−0.801326	−0.400663	−	0.916226i	$-0.631220\pi$
$881$	−23.7847	−0.801326	−0.400663	+	0.916226i	$0.631220\pi$
$882$	−34.5768	−1.16426
$883$	−13.7523	−0.462801	−0.231401	−	0.972859i	$-0.574331\pi$
$883$	−13.7523	−0.462801	−0.231401	+	0.972859i	$0.574331\pi$
$884$	−46.4490	−1.56225
$885$	27.9975	0.941124
$886$	−63.9721	−2.14918
$887$	30.3096	1.01770	0.508849	−	0.860856i	$-0.330071\pi$
$887$	30.3096	1.01770	0.508849	+	0.860856i	$0.330071\pi$
$888$	136.257	4.57248
$889$	−38.3352	−1.28572
$890$	8.04027	0.269511
$891$	−7.88248	−0.264073
$892$	52.5498	1.75950
$893$	7.62818	0.255267
$894$	−19.3954	−0.648680
$895$	−6.11975	−0.204561
$896$	6.04659	0.202002
$897$	31.4539	1.05022
$898$	−52.4182	−1.74922
$899$	−2.23799	−0.0746413
$900$	−120.022	−4.00074
$901$	36.5449	1.21749
$902$	−25.5806	−0.851740
$903$	−74.6742	−2.48500
$904$	0.813009	0.0270403
$905$	−2.79796	−0.0930073
$906$	−135.307	−4.49527
$907$	−36.6102	−1.21562	−0.607812	−	0.794081i	$-0.707952\pi$
$907$	−36.6102	−1.21562	−0.607812	+	0.794081i	$0.707952\pi$
$908$	45.6294	1.51426
$909$	−18.4016	−0.610344
$910$	−8.47550	−0.280960
$911$	34.9673	1.15852	0.579258	−	0.815144i	$-0.303342\pi$
$911$	34.9673	1.15852	0.579258	+	0.815144i	$0.303342\pi$
$912$	188.792	6.25152
$913$	−11.2940	−0.373776
$914$	38.1486	1.26184
$915$	2.53636	0.0838496
$916$	43.4322	1.43504
$917$	21.0379	0.694734
$918$	172.448	5.69164
$919$	6.04826	0.199514	0.0997568	−	0.995012i	$-0.468194\pi$
$919$	6.04826	0.199514	0.0997568	+	0.995012i	$0.468194\pi$
$920$	−51.7878	−1.70739
$921$	−85.6029	−2.82071
$922$	23.1884	0.763671
$923$	−8.79714	−0.289562
$924$	−43.3275	−1.42537
$925$	27.0197	0.888401
$926$	85.8465	2.82109
$927$	−3.59956	−0.118225
$928$	−10.6552	−0.349776
$929$	−50.8532	−1.66844	−0.834219	−	0.551433i	$-0.814081\pi$
$929$	−50.8532	−1.66844	−0.834219	+	0.551433i	$0.814081\pi$
$930$	13.4549	0.441204
$931$	15.4318	0.505757
$932$	−44.0853	−1.44406
$933$	45.8454	1.50091
$934$	−56.2066	−1.83914
$935$	6.58646	0.215400
$936$	−53.4064	−1.74564
$937$	27.2266	0.889453	0.444726	−	0.895666i	$-0.353301\pi$
$937$	27.2266	0.889453	0.444726	+	0.895666i	$0.353301\pi$
$938$	−54.7526	−1.78774
$939$	41.7457	1.36232
$940$	4.54760	0.148326
$941$	18.7448	0.611064	0.305532	−	0.952182i	$-0.401166\pi$
$941$	18.7448	0.611064	0.305532	+	0.952182i	$0.401166\pi$
$942$	165.515	5.39277
$943$	−82.5716	−2.68890
$944$	102.485	3.33560
$945$	22.1836	0.721631
$946$	−21.4479	−0.697331
$947$	51.2919	1.66676	0.833381	−	0.552698i	$-0.186402\pi$
$947$	51.2919	1.66676	0.833381	+	0.552698i	$0.186402\pi$
$948$	−52.8373	−1.71608
$949$	1.59719	0.0518470
$950$	75.9817	2.46517
$951$	54.8969	1.78015
$952$	170.367	5.52161
$953$	12.0797	0.391301	0.195651	−	0.980674i	$-0.437318\pi$
$953$	12.0797	0.391301	0.195651	+	0.980674i	$0.437318\pi$
$954$	72.2538	2.33930
$955$	−13.5998	−0.440080
$956$	−69.7142	−2.25472
$957$	−3.27227	−0.105777
$958$	36.0021	1.16317
$959$	−26.6535	−0.860685
$960$	16.9626	0.547466
$961$	−26.8491	−0.866100
$962$	20.6743	0.666565
$963$	8.07891	0.260339
$964$	−51.5171	−1.65925
$965$	−4.39727	−0.141553
$966$	−198.381	−6.38280
$967$	29.1060	0.935985	0.467992	−	0.883732i	$-0.344977\pi$
$967$	29.1060	0.935985	0.467992	+	0.883732i	$0.344977\pi$
$968$	−7.23702	−0.232607
$969$	−157.301	−5.05325
$970$	0.251034	0.00806021
$971$	6.38454	0.204890	0.102445	−	0.994739i	$-0.467334\pi$
$971$	6.38454	0.204890	0.102445	+	0.994739i	$0.467334\pi$
$972$	−10.5320	−0.337814
$973$	40.4669	1.29731
$974$	−93.1244	−2.98390
$975$	−15.9992	−0.512385
$976$	9.28438	0.297186
$977$	−33.0182	−1.05634	−0.528172	−	0.849137i	$-0.677122\pi$
$977$	−33.0182	−1.05634	−0.528172	+	0.849137i	$0.677122\pi$
$978$	104.415	3.33882
$979$	3.62680	0.115913
$980$	9.19979	0.293876
$981$	120.609	3.85076
$982$	79.1677	2.52634
$983$	48.1934	1.53713	0.768566	−	0.639770i	$-0.220971\pi$
$983$	48.1934	1.53713	0.768566	+	0.639770i	$0.220971\pi$
$984$	211.804	6.75206
$985$	−16.2860	−0.518914
$986$	22.1252	0.704611
$987$	10.1306	0.322461
$988$	40.9867	1.30396
$989$	−69.2317	−2.20144
$990$	13.0223	0.413875
$991$	42.8697	1.36180	0.680900	−	0.732376i	$-0.261589\pi$
$991$	42.8697	1.36180	0.680900	+	0.732376i	$0.261589\pi$
$992$	19.7628	0.627468
$993$	98.2665	3.11839
$994$	55.4839	1.75984
$995$	0.0401165	0.00127178
$996$	160.800	5.09516
$997$	14.1040	0.446679	0.223340	−	0.974741i	$-0.428304\pi$
$997$	14.1040	0.446679	0.223340	+	0.974741i	$0.428304\pi$
$998$	−12.0629	−0.381846
$999$	−54.1123	−1.71204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.2	✓	21
3.2	odd	2		6039.2.a.l.1.20		21
11.10	odd	2		7381.2.a.j.1.20		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.2	✓	21	1.1	even	1	trivial
6039.2.a.l.1.20		21	3.2	odd	2
7381.2.a.j.1.20		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)

\(f(q)\)	\(=\)	\(q-2.60374 q^{2} +2.97894 q^{3} +4.77947 q^{4} +0.851432 q^{5} -7.75638 q^{6} +3.04314 q^{7} -7.23702 q^{8} +5.87407 q^{9} +O(q^{10})\)	\(q-2.60374 q^{2} +2.97894 q^{3} +4.77947 q^{4} +0.851432 q^{5} -7.75638 q^{6} +3.04314 q^{7} -7.23702 q^{8} +5.87407 q^{9} -2.21691 q^{10} -1.00000 q^{11} +14.2377 q^{12} +1.25630 q^{13} -7.92356 q^{14} +2.53636 q^{15} +9.28438 q^{16} -7.73575 q^{17} -15.2946 q^{18} +6.82604 q^{19} +4.06939 q^{20} +9.06534 q^{21} +2.60374 q^{22} +8.40462 q^{23} -21.5586 q^{24} -4.27506 q^{25} -3.27109 q^{26} +8.56167 q^{27} +14.5446 q^{28} +1.09847 q^{29} -6.60403 q^{30} -2.03738 q^{31} -9.70010 q^{32} -2.97894 q^{33} +20.1419 q^{34} +2.59103 q^{35} +28.0749 q^{36} -6.32030 q^{37} -17.7732 q^{38} +3.74245 q^{39} -6.16183 q^{40} -9.82455 q^{41} -23.6038 q^{42} -8.23734 q^{43} -4.77947 q^{44} +5.00137 q^{45} -21.8835 q^{46} +1.11751 q^{47} +27.6576 q^{48} +2.26073 q^{49} +11.1312 q^{50} -23.0443 q^{51} +6.00447 q^{52} -4.72415 q^{53} -22.2924 q^{54} -0.851432 q^{55} -22.0233 q^{56} +20.3343 q^{57} -2.86013 q^{58} +11.0384 q^{59} +12.1225 q^{60} +1.00000 q^{61} +5.30480 q^{62} +17.8756 q^{63} +6.68778 q^{64} +1.06966 q^{65} +7.75638 q^{66} +6.91010 q^{67} -36.9728 q^{68} +25.0368 q^{69} -6.74637 q^{70} -7.00240 q^{71} -42.5107 q^{72} +1.27134 q^{73} +16.4564 q^{74} -12.7351 q^{75} +32.6248 q^{76} -3.04314 q^{77} -9.74438 q^{78} -3.71107 q^{79} +7.90502 q^{80} +7.88248 q^{81} +25.5806 q^{82} +11.2940 q^{83} +43.3275 q^{84} -6.58646 q^{85} +21.4479 q^{86} +3.27227 q^{87} +7.23702 q^{88} -3.62680 q^{89} -13.0223 q^{90} +3.82312 q^{91} +40.1696 q^{92} -6.06922 q^{93} -2.90971 q^{94} +5.81191 q^{95} -28.8960 q^{96} -0.113236 q^{97} -5.88635 q^{98} -5.87407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 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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