LMFDB - Embedded newform 6041.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75252 q^{2} -2.26942 q^{3} +5.57639 q^{4} +4.03697 q^{5} +6.24664 q^{6} +1.00000 q^{7} -9.84409 q^{8} +2.15028 q^{9} +O(q^{10})$	\(q-2.75252 q^{2} -2.26942 q^{3} +5.57639 q^{4} +4.03697 q^{5} +6.24664 q^{6} +1.00000 q^{7} -9.84409 q^{8} +2.15028 q^{9} -11.1119 q^{10} +5.59978 q^{11} -12.6552 q^{12} -6.36706 q^{13} -2.75252 q^{14} -9.16159 q^{15} +15.9433 q^{16} +3.68559 q^{17} -5.91869 q^{18} +0.306021 q^{19} +22.5117 q^{20} -2.26942 q^{21} -15.4135 q^{22} +4.37544 q^{23} +22.3404 q^{24} +11.2971 q^{25} +17.5255 q^{26} +1.92838 q^{27} +5.57639 q^{28} +3.33467 q^{29} +25.2175 q^{30} -5.49463 q^{31} -24.1962 q^{32} -12.7083 q^{33} -10.1447 q^{34} +4.03697 q^{35} +11.9908 q^{36} +0.873713 q^{37} -0.842329 q^{38} +14.4496 q^{39} -39.7403 q^{40} -6.95623 q^{41} +6.24664 q^{42} -8.46973 q^{43} +31.2265 q^{44} +8.68061 q^{45} -12.0435 q^{46} -13.4609 q^{47} -36.1821 q^{48} +1.00000 q^{49} -31.0956 q^{50} -8.36416 q^{51} -35.5052 q^{52} +12.2196 q^{53} -5.30791 q^{54} +22.6061 q^{55} -9.84409 q^{56} -0.694490 q^{57} -9.17876 q^{58} +9.57366 q^{59} -51.0886 q^{60} -7.33583 q^{61} +15.1241 q^{62} +2.15028 q^{63} +34.7140 q^{64} -25.7036 q^{65} +34.9798 q^{66} +12.9283 q^{67} +20.5523 q^{68} -9.92971 q^{69} -11.1119 q^{70} -1.49753 q^{71} -21.1675 q^{72} +5.95771 q^{73} -2.40492 q^{74} -25.6380 q^{75} +1.70649 q^{76} +5.59978 q^{77} -39.7727 q^{78} +5.78081 q^{79} +64.3628 q^{80} -10.8271 q^{81} +19.1472 q^{82} +0.537141 q^{83} -12.6552 q^{84} +14.8786 q^{85} +23.3131 q^{86} -7.56778 q^{87} -55.1247 q^{88} +3.53672 q^{89} -23.8936 q^{90} -6.36706 q^{91} +24.3991 q^{92} +12.4696 q^{93} +37.0514 q^{94} +1.23540 q^{95} +54.9114 q^{96} -9.25815 q^{97} -2.75252 q^{98} +12.0411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.75252	−1.94633	−0.973164	−	0.230112i	$-0.926091\pi$
$2$	−2.75252	−1.94633	−0.973164	+	0.230112i	$0.926091\pi$
$3$	−2.26942	−1.31025	−0.655126	−	0.755520i	$-0.727384\pi$
$3$	−2.26942	−1.31025	−0.655126	+	0.755520i	$0.727384\pi$
$4$	5.57639	2.78819
$5$	4.03697	1.80539	0.902694	−	0.430283i	$-0.141586\pi$
$5$	4.03697	1.80539	0.902694	+	0.430283i	$0.141586\pi$
$6$	6.24664	2.55018
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−9.84409	−3.48041
$9$	2.15028	0.716759
$10$	−11.1119	−3.51388
$11$	5.59978	1.68840	0.844198	−	0.536031i	$-0.180077\pi$
$11$	5.59978	1.68840	0.844198	+	0.536031i	$0.180077\pi$
$12$	−12.6552	−3.65324
$13$	−6.36706	−1.76591	−0.882953	−	0.469462i	$-0.844448\pi$
$13$	−6.36706	−1.76591	−0.882953	+	0.469462i	$0.844448\pi$
$14$	−2.75252	−0.735643
$15$	−9.16159	−2.36551
$16$	15.9433	3.98583
$17$	3.68559	0.893887	0.446943	−	0.894562i	$-0.352513\pi$
$17$	3.68559	0.893887	0.446943	+	0.894562i	$0.352513\pi$
$18$	−5.91869	−1.39505
$19$	0.306021	0.0702059	0.0351030	−	0.999384i	$-0.488824\pi$
$19$	0.306021	0.0702059	0.0351030	+	0.999384i	$0.488824\pi$
$20$	22.5117	5.03377
$21$	−2.26942	−0.495229
$22$	−15.4135	−3.28617
$23$	4.37544	0.912342	0.456171	−	0.889892i	$-0.349221\pi$
$23$	4.37544	0.912342	0.456171	+	0.889892i	$0.349221\pi$
$24$	22.3404	4.56022
$25$	11.2971	2.25943
$26$	17.5255	3.43703
$27$	1.92838	0.371117
$28$	5.57639	1.05384
$29$	3.33467	0.619233	0.309617	−	0.950862i	$-0.399799\pi$
$29$	3.33467	0.619233	0.309617	+	0.950862i	$0.399799\pi$
$30$	25.2175	4.60406
$31$	−5.49463	−0.986864	−0.493432	−	0.869784i	$-0.664258\pi$
$31$	−5.49463	−0.986864	−0.493432	+	0.869784i	$0.664258\pi$
$32$	−24.1962	−4.27733
$33$	−12.7083	−2.21222
$34$	−10.1447	−1.73980
$35$	4.03697	0.682373
$36$	11.9908	1.99846
$37$	0.873713	0.143638	0.0718188	−	0.997418i	$-0.477120\pi$
$37$	0.873713	0.143638	0.0718188	+	0.997418i	$0.477120\pi$
$38$	−0.842329	−0.136644
$39$	14.4496	2.31378
$40$	−39.7403	−6.28350
$41$	−6.95623	−1.08638	−0.543190	−	0.839610i	$-0.682784\pi$
$41$	−6.95623	−1.08638	−0.543190	+	0.839610i	$0.682784\pi$
$42$	6.24664	0.963877
$43$	−8.46973	−1.29162	−0.645811	−	0.763498i	$-0.723480\pi$
$43$	−8.46973	−1.29162	−0.645811	+	0.763498i	$0.723480\pi$
$44$	31.2265	4.70758
$45$	8.68061	1.29403
$46$	−12.0435	−1.77572
$47$	−13.4609	−1.96347	−0.981737	−	0.190245i	$-0.939072\pi$
$47$	−13.4609	−1.96347	−0.981737	+	0.190245i	$0.939072\pi$
$48$	−36.1821	−5.22244
$49$	1.00000	0.142857
$50$	−31.0956	−4.39759
$51$	−8.36416	−1.17122
$52$	−35.5052	−4.92369
$53$	12.2196	1.67849	0.839244	−	0.543755i	$-0.182998\pi$
$53$	12.2196	1.67849	0.839244	+	0.543755i	$0.182998\pi$
$54$	−5.30791	−0.722315
$55$	22.6061	3.04821
$56$	−9.84409	−1.31547
$57$	−0.694490	−0.0919874
$58$	−9.17876	−1.20523
$59$	9.57366	1.24638	0.623192	−	0.782069i	$-0.285835\pi$
$59$	9.57366	1.24638	0.623192	+	0.782069i	$0.285835\pi$
$60$	−51.0886	−6.59551
$61$	−7.33583	−0.939256	−0.469628	−	0.882864i	$-0.655612\pi$
$61$	−7.33583	−0.939256	−0.469628	+	0.882864i	$0.655612\pi$
$62$	15.1241	1.92076
$63$	2.15028	0.270910
$64$	34.7140	4.33925
$65$	−25.7036	−3.18814
$66$	34.9798	4.30571
$67$	12.9283	1.57944	0.789720	−	0.613467i	$-0.210226\pi$
$67$	12.9283	1.57944	0.789720	+	0.613467i	$0.210226\pi$
$68$	20.5523	2.49233
$69$	−9.92971	−1.19540
$70$	−11.1119	−1.32812
$71$	−1.49753	−0.177724	−0.0888621	−	0.996044i	$-0.528323\pi$
$71$	−1.49753	−0.177724	−0.0888621	+	0.996044i	$0.528323\pi$
$72$	−21.1675	−2.49462
$73$	5.95771	0.697297	0.348649	−	0.937253i	$-0.386641\pi$
$73$	5.95771	0.697297	0.348649	+	0.937253i	$0.386641\pi$
$74$	−2.40492	−0.279566
$75$	−25.6380	−2.96042
$76$	1.70649	0.195748
$77$	5.59978	0.638154
$78$	−39.7727	−4.50338
$79$	5.78081	0.650392	0.325196	−	0.945647i	$-0.394570\pi$
$79$	5.78081	0.650392	0.325196	+	0.945647i	$0.394570\pi$
$80$	64.3628	7.19597
$81$	−10.8271	−1.20302
$82$	19.1472	2.11445
$83$	0.537141	0.0589589	0.0294794	−	0.999565i	$-0.490615\pi$
$83$	0.537141	0.0589589	0.0294794	+	0.999565i	$0.490615\pi$
$84$	−12.6552	−1.38079
$85$	14.8786	1.61381
$86$	23.3131	2.51392
$87$	−7.56778	−0.811351
$88$	−55.1247	−5.87632
$89$	3.53672	0.374891	0.187446	−	0.982275i	$-0.439979\pi$
$89$	3.53672	0.374891	0.187446	+	0.982275i	$0.439979\pi$
$90$	−23.8936	−2.51861
$91$	−6.36706	−0.667449
$92$	24.3991	2.54379
$93$	12.4696	1.29304
$94$	37.0514	3.82156
$95$	1.23540	0.126749
$96$	54.9114	5.60437
$97$	−9.25815	−0.940022	−0.470011	−	0.882660i	$-0.655750\pi$
$97$	−9.25815	−0.940022	−0.470011	+	0.882660i	$0.655750\pi$
$98$	−2.75252	−0.278047
$99$	12.0411	1.21017
$100$	62.9972	6.29972
$101$	6.53574	0.650330	0.325165	−	0.945657i	$-0.394580\pi$
$101$	6.53574	0.650330	0.325165	+	0.945657i	$0.394580\pi$
$102$	23.0225	2.27957
$103$	−3.41180	−0.336174	−0.168087	−	0.985772i	$-0.553759\pi$
$103$	−3.41180	−0.336174	−0.168087	+	0.985772i	$0.553759\pi$
$104$	62.6780	6.14608
$105$	−9.16159	−0.894080
$106$	−33.6347	−3.26689
$107$	9.31172	0.900197	0.450099	−	0.892979i	$-0.351389\pi$
$107$	9.31172	0.900197	0.450099	+	0.892979i	$0.351389\pi$
$108$	10.7534	1.03475
$109$	11.3959	1.09153	0.545766	−	0.837938i	$-0.316239\pi$
$109$	11.3959	1.09153	0.545766	+	0.837938i	$0.316239\pi$
$110$	−62.2239	−5.93282
$111$	−1.98282	−0.188201
$112$	15.9433	1.50650
$113$	−15.4706	−1.45535	−0.727673	−	0.685924i	$-0.759398\pi$
$113$	−15.4706	−1.45535	−0.727673	+	0.685924i	$0.759398\pi$
$114$	1.91160	0.179038
$115$	17.6635	1.64713
$116$	18.5954	1.72654
$117$	−13.6910	−1.26573
$118$	−26.3517	−2.42587
$119$	3.68559	0.337857
$120$	90.1876	8.23296
$121$	20.3575	1.85068
$122$	20.1920	1.82810
$123$	15.7866	1.42343
$124$	−30.6402	−2.75157
$125$	25.4213	2.27375
$126$	−5.91869	−0.527279
$127$	15.9098	1.41176	0.705882	−	0.708330i	$-0.250551\pi$
$127$	15.9098	1.41176	0.705882	+	0.708330i	$0.250551\pi$
$128$	−47.1587	−4.16828
$129$	19.2214	1.69235
$130$	70.7499	6.20518
$131$	−2.26496	−0.197891	−0.0989454	−	0.995093i	$-0.531547\pi$
$131$	−2.26496	−0.197891	−0.0989454	+	0.995093i	$0.531547\pi$
$132$	−70.8662	−6.16811
$133$	0.306021	0.0265353
$134$	−35.5854	−3.07411
$135$	7.78481	0.670009
$136$	−36.2813	−3.11110
$137$	−0.336057	−0.0287113	−0.0143557	−	0.999897i	$-0.504570\pi$
$137$	−0.336057	−0.0287113	−0.0143557	+	0.999897i	$0.504570\pi$
$138$	27.3318	2.32663
$139$	−0.0807869	−0.00685226	−0.00342613	−	0.999994i	$-0.501091\pi$
$139$	−0.0807869	−0.00685226	−0.00342613	+	0.999994i	$0.501091\pi$
$140$	22.5117	1.90259
$141$	30.5485	2.57264
$142$	4.12199	0.345910
$143$	−35.6541	−2.98155
$144$	34.2826	2.85688
$145$	13.4620	1.11796
$146$	−16.3987	−1.35717
$147$	−2.26942	−0.187179
$148$	4.87216	0.400489
$149$	13.8693	1.13622	0.568109	−	0.822954i	$-0.307675\pi$
$149$	13.8693	1.13622	0.568109	+	0.822954i	$0.307675\pi$
$150$	70.5691	5.76194
$151$	4.05473	0.329969	0.164984	−	0.986296i	$-0.447243\pi$
$151$	4.05473	0.329969	0.164984	+	0.986296i	$0.447243\pi$
$152$	−3.01249	−0.244346
$153$	7.92504	0.640702
$154$	−15.4135	−1.24206
$155$	−22.1817	−1.78167
$156$	80.5763	6.45127
$157$	−13.9466	−1.11306	−0.556531	−	0.830827i	$-0.687868\pi$
$157$	−13.9466	−1.11306	−0.556531	+	0.830827i	$0.687868\pi$
$158$	−15.9118	−1.26588
$159$	−27.7314	−2.19924
$160$	−97.6794	−7.72223
$161$	4.37544	0.344833
$162$	29.8020	2.34146
$163$	6.82129	0.534284	0.267142	−	0.963657i	$-0.413921\pi$
$163$	6.82129	0.534284	0.267142	+	0.963657i	$0.413921\pi$
$164$	−38.7906	−3.02904
$165$	−51.3029	−3.99392
$166$	−1.47849	−0.114753
$167$	−10.8806	−0.841967	−0.420983	−	0.907068i	$-0.638315\pi$
$167$	−10.8806	−0.841967	−0.420983	+	0.907068i	$0.638315\pi$
$168$	22.3404	1.72360
$169$	27.5395	2.11842
$170$	−40.9538	−3.14101
$171$	0.658029	0.0503208
$172$	−47.2305	−3.60129
$173$	12.7630	0.970353	0.485176	−	0.874416i	$-0.338755\pi$
$173$	12.7630	0.970353	0.485176	+	0.874416i	$0.338755\pi$
$174$	20.8305	1.57916
$175$	11.2971	0.853983
$176$	89.2791	6.72966
$177$	−21.7267	−1.63308
$178$	−9.73490	−0.729662
$179$	8.17347	0.610914	0.305457	−	0.952206i	$-0.401191\pi$
$179$	8.17347	0.610914	0.305457	+	0.952206i	$0.401191\pi$
$180$	48.4064	3.60800
$181$	14.5821	1.08388	0.541940	−	0.840417i	$-0.317690\pi$
$181$	14.5821	1.08388	0.541940	+	0.840417i	$0.317690\pi$
$182$	17.5255	1.29908
$183$	16.6481	1.23066
$184$	−43.0722	−3.17533
$185$	3.52715	0.259322
$186$	−34.3230	−2.51668
$187$	20.6385	1.50923
$188$	−75.0632	−5.47454
$189$	1.92838	0.140269
$190$	−3.40046	−0.246695
$191$	13.9763	1.01129	0.505644	−	0.862742i	$-0.331255\pi$
$191$	13.9763	1.01129	0.505644	+	0.862742i	$0.331255\pi$
$192$	−78.7807	−5.68551
$193$	−1.91960	−0.138176	−0.0690878	−	0.997611i	$-0.522009\pi$
$193$	−1.91960	−0.138176	−0.0690878	+	0.997611i	$0.522009\pi$
$194$	25.4833	1.82959
$195$	58.3324	4.17727
$196$	5.57639	0.398313
$197$	−26.2985	−1.87369	−0.936846	−	0.349742i	$-0.886269\pi$
$197$	−26.2985	−1.87369	−0.936846	+	0.349742i	$0.886269\pi$
$198$	−33.1433	−2.35540
$199$	7.44641	0.527862	0.263931	−	0.964542i	$-0.414981\pi$
$199$	7.44641	0.527862	0.263931	+	0.964542i	$0.414981\pi$
$200$	−111.210	−7.86374
$201$	−29.3397	−2.06946
$202$	−17.9898	−1.26576
$203$	3.33467	0.234048
$204$	−46.6418	−3.26558
$205$	−28.0821	−1.96134
$206$	9.39105	0.654305
$207$	9.40840	0.653929
$208$	−101.512	−7.03860
$209$	1.71365	0.118535
$210$	25.2175	1.74017
$211$	22.8447	1.57269	0.786346	−	0.617786i	$-0.211970\pi$
$211$	22.8447	1.57269	0.786346	+	0.617786i	$0.211970\pi$
$212$	68.1411	4.67995
$213$	3.39853	0.232863
$214$	−25.6307	−1.75208
$215$	−34.1920	−2.33188
$216$	−18.9831	−1.29164
$217$	−5.49463	−0.373000
$218$	−31.3676	−2.12448
$219$	−13.5206	−0.913635
$220$	126.061	8.49900
$221$	−23.4664	−1.57852
$222$	5.45777	0.366302
$223$	−17.9074	−1.19916	−0.599582	−	0.800313i	$-0.704667\pi$
$223$	−17.9074	−1.19916	−0.599582	+	0.800313i	$0.704667\pi$
$224$	−24.1962	−1.61668
$225$	24.2920	1.61947
$226$	42.5831	2.83258
$227$	−6.64621	−0.441124	−0.220562	−	0.975373i	$-0.570789\pi$
$227$	−6.64621	−0.441124	−0.220562	+	0.975373i	$0.570789\pi$
$228$	−3.87274	−0.256479
$229$	3.04788	0.201409	0.100705	−	0.994916i	$-0.467890\pi$
$229$	3.04788	0.201409	0.100705	+	0.994916i	$0.467890\pi$
$230$	−48.6192	−3.20586
$231$	−12.7083	−0.836142
$232$	−32.8268	−2.15519
$233$	−11.3683	−0.744760	−0.372380	−	0.928080i	$-0.621458\pi$
$233$	−11.3683	−0.744760	−0.372380	+	0.928080i	$0.621458\pi$
$234$	37.6847	2.46352
$235$	−54.3412	−3.54483
$236$	53.3864	3.47516
$237$	−13.1191	−0.852177
$238$	−10.1447	−0.657582
$239$	−10.8856	−0.704131	−0.352065	−	0.935975i	$-0.614521\pi$
$239$	−10.8856	−0.704131	−0.352065	+	0.935975i	$0.614521\pi$
$240$	−146.066	−9.42854
$241$	−3.12332	−0.201190	−0.100595	−	0.994927i	$-0.532075\pi$
$241$	−3.12332	−0.201190	−0.100595	+	0.994927i	$0.532075\pi$
$242$	−56.0345	−3.60203
$243$	18.7862	1.20514
$244$	−40.9074	−2.61883
$245$	4.03697	0.257913
$246$	−43.4531	−2.77047
$247$	−1.94845	−0.123977
$248$	54.0896	3.43470
$249$	−1.21900	−0.0772510
$250$	−69.9729	−4.42547
$251$	21.6662	1.36756	0.683780	−	0.729688i	$-0.260335\pi$
$251$	21.6662	1.36756	0.683780	+	0.729688i	$0.260335\pi$
$252$	11.9908	0.755348
$253$	24.5015	1.54039
$254$	−43.7920	−2.74776
$255$	−33.7659	−2.11450
$256$	60.3774	3.77358
$257$	0.981209	0.0612061	0.0306031	−	0.999532i	$-0.490257\pi$
$257$	0.981209	0.0612061	0.0306031	+	0.999532i	$0.490257\pi$
$258$	−52.9073	−3.29387
$259$	0.873713	0.0542899
$260$	−143.333	−8.88917
$261$	7.17047	0.443841
$262$	6.23437	0.385161
$263$	28.4589	1.75485	0.877427	−	0.479711i	$-0.159259\pi$
$263$	28.4589	1.75485	0.877427	+	0.479711i	$0.159259\pi$
$264$	125.101	7.69945
$265$	49.3301	3.03032
$266$	−0.842329	−0.0516465
$267$	−8.02631	−0.491202
$268$	72.0931	4.40379
$269$	14.2842	0.870924	0.435462	−	0.900207i	$-0.356585\pi$
$269$	14.2842	0.870924	0.435462	+	0.900207i	$0.356585\pi$
$270$	−21.4279	−1.30406
$271$	5.59980	0.340163	0.170082	−	0.985430i	$-0.445597\pi$
$271$	5.59980	0.340163	0.170082	+	0.985430i	$0.445597\pi$
$272$	58.7606	3.56288
$273$	14.4496	0.874527
$274$	0.925006	0.0558816
$275$	63.2614	3.81481
$276$	−55.3719	−3.33300
$277$	14.9843	0.900318	0.450159	−	0.892948i	$-0.351367\pi$
$277$	14.9843	0.900318	0.450159	+	0.892948i	$0.351367\pi$
$278$	0.222368	0.0133367
$279$	−11.8150	−0.707344
$280$	−39.7403	−2.37494
$281$	−10.5310	−0.628229	−0.314115	−	0.949385i	$-0.601708\pi$
$281$	−10.5310	−0.628229	−0.314115	+	0.949385i	$0.601708\pi$
$282$	−84.0854	−5.00721
$283$	−20.0101	−1.18947	−0.594737	−	0.803920i	$-0.702744\pi$
$283$	−20.0101	−1.18947	−0.594737	+	0.803920i	$0.702744\pi$
$284$	−8.35081	−0.495530
$285$	−2.80364	−0.166073
$286$	98.1388	5.80307
$287$	−6.95623	−0.410613
$288$	−52.0286	−3.06581
$289$	−3.41643	−0.200966
$290$	−37.0544	−2.17591
$291$	21.0106	1.23167
$292$	33.2225	1.94420
$293$	−15.1033	−0.882347	−0.441173	−	0.897422i	$-0.645438\pi$
$293$	−15.1033	−0.882347	−0.441173	+	0.897422i	$0.645438\pi$
$294$	6.24664	0.364311
$295$	38.6486	2.25021
$296$	−8.60092	−0.499918
$297$	10.7985	0.626592
$298$	−38.1756	−2.21145
$299$	−27.8587	−1.61111
$300$	−142.967	−8.25422
$301$	−8.46973	−0.488187
$302$	−11.1607	−0.642228
$303$	−14.8323	−0.852096
$304$	4.87899	0.279829
$305$	−29.6145	−1.69572
$306$	−21.8139	−1.24702
$307$	14.4431	0.824312	0.412156	−	0.911113i	$-0.364776\pi$
$307$	14.4431	0.824312	0.412156	+	0.911113i	$0.364776\pi$
$308$	31.2265	1.77930
$309$	7.74280	0.440473
$310$	61.0555	3.46772
$311$	−0.259509	−0.0147154	−0.00735771	−	0.999973i	$-0.502342\pi$
$311$	−0.259509	−0.0147154	−0.00735771	+	0.999973i	$0.502342\pi$
$312$	−142.243	−8.05291
$313$	21.0940	1.19230	0.596151	−	0.802872i	$-0.296696\pi$
$313$	21.0940	1.19230	0.596151	+	0.802872i	$0.296696\pi$
$314$	38.3884	2.16638
$315$	8.68061	0.489097
$316$	32.2360	1.81342
$317$	−19.5633	−1.09878	−0.549392	−	0.835565i	$-0.685141\pi$
$317$	−19.5633	−1.09878	−0.549392	+	0.835565i	$0.685141\pi$
$318$	76.3313	4.28045
$319$	18.6734	1.04551
$320$	140.139	7.83403
$321$	−21.1322	−1.17949
$322$	−12.0435	−0.671158
$323$	1.12787	0.0627561
$324$	−60.3763	−3.35424
$325$	−71.9295	−3.98993
$326$	−18.7758	−1.03989
$327$	−25.8622	−1.43018
$328$	68.4778	3.78105
$329$	−13.4609	−0.742123
$330$	141.212	7.77348
$331$	−5.71041	−0.313872	−0.156936	−	0.987609i	$-0.550162\pi$
$331$	−5.71041	−0.313872	−0.156936	+	0.987609i	$0.550162\pi$
$332$	2.99531	0.164389
$333$	1.87873	0.102954
$334$	29.9491	1.63874
$335$	52.1911	2.85150
$336$	−36.1821	−1.97390
$337$	24.0421	1.30965	0.654827	−	0.755779i	$-0.272741\pi$
$337$	24.0421	1.30965	0.654827	+	0.755779i	$0.272741\pi$
$338$	−75.8031	−4.12314
$339$	35.1092	1.90687
$340$	82.9689	4.49962
$341$	−30.7687	−1.66622
$342$	−1.81124	−0.0979407
$343$	1.00000	0.0539949
$344$	83.3768	4.49537
$345$	−40.0860	−2.15816
$346$	−35.1305	−1.88862
$347$	−0.329970	−0.0177137	−0.00885687	−	0.999961i	$-0.502819\pi$
$347$	−0.329970	−0.0177137	−0.00885687	+	0.999961i	$0.502819\pi$
$348$	−42.2009	−2.26220
$349$	6.67993	0.357569	0.178784	−	0.983888i	$-0.442784\pi$
$349$	6.67993	0.357569	0.178784	+	0.983888i	$0.442784\pi$
$350$	−31.0956	−1.66213
$351$	−12.2781	−0.655357
$352$	−135.493	−7.22182
$353$	−12.2971	−0.654510	−0.327255	−	0.944936i	$-0.606124\pi$
$353$	−12.2971	−0.654510	−0.327255	+	0.944936i	$0.606124\pi$
$354$	59.8032	3.17850
$355$	−6.04549	−0.320861
$356$	19.7221	1.04527
$357$	−8.36416	−0.442678
$358$	−22.4977	−1.18904
$359$	−19.4540	−1.02674	−0.513371	−	0.858167i	$-0.671604\pi$
$359$	−19.4540	−1.02674	−0.513371	+	0.858167i	$0.671604\pi$
$360$	−85.4527	−4.50375
$361$	−18.9064	−0.995071
$362$	−40.1376	−2.10959
$363$	−46.1998	−2.42486
$364$	−35.5052	−1.86098
$365$	24.0511	1.25889
$366$	−45.8243	−2.39527
$367$	15.5108	0.809657	0.404828	−	0.914393i	$-0.367331\pi$
$367$	15.5108	0.809657	0.404828	+	0.914393i	$0.367331\pi$
$368$	69.7590	3.63644
$369$	−14.9578	−0.778673
$370$	−9.70858	−0.504725
$371$	12.2196	0.634409
$372$	69.5355	3.60525
$373$	−7.78323	−0.403000	−0.201500	−	0.979488i	$-0.564582\pi$
$373$	−7.78323	−0.403000	−0.201500	+	0.979488i	$0.564582\pi$
$374$	−56.8079	−2.93747
$375$	−57.6918	−2.97919
$376$	132.510	6.83370
$377$	−21.2321	−1.09351
$378$	−5.30791	−0.273009
$379$	29.3733	1.50881	0.754404	−	0.656411i	$-0.227926\pi$
$379$	29.3733	1.50881	0.754404	+	0.656411i	$0.227926\pi$
$380$	6.88905	0.353401
$381$	−36.1060	−1.84977
$382$	−38.4700	−1.96830
$383$	18.0431	0.921960	0.460980	−	0.887410i	$-0.347498\pi$
$383$	18.0431	0.921960	0.460980	+	0.887410i	$0.347498\pi$
$384$	107.023	5.46149
$385$	22.6061	1.15212
$386$	5.28374	0.268935
$387$	−18.2123	−0.925781
$388$	−51.6270	−2.62097
$389$	−16.9277	−0.858269	−0.429134	−	0.903241i	$-0.641181\pi$
$389$	−16.9277	−0.858269	−0.429134	+	0.903241i	$0.641181\pi$
$390$	−160.561	−8.13034
$391$	16.1261	0.815530
$392$	−9.84409	−0.497202
$393$	5.14016	0.259287
$394$	72.3873	3.64682
$395$	23.3370	1.17421
$396$	67.1457	3.37420
$397$	−14.7989	−0.742734	−0.371367	−	0.928486i	$-0.621111\pi$
$397$	−14.7989	−0.742734	−0.371367	+	0.928486i	$0.621111\pi$
$398$	−20.4964	−1.02739
$399$	−0.694490	−0.0347680
$400$	180.114	9.00570
$401$	−11.3183	−0.565210	−0.282605	−	0.959236i	$-0.591199\pi$
$401$	−11.3183	−0.565210	−0.282605	+	0.959236i	$0.591199\pi$
$402$	80.7583	4.02786
$403$	34.9846	1.74271
$404$	36.4458	1.81325
$405$	−43.7088	−2.17191
$406$	−9.17876	−0.455534
$407$	4.89260	0.242517
$408$	82.3376	4.07632
$409$	−30.8220	−1.52405	−0.762026	−	0.647547i	$-0.775795\pi$
$409$	−30.8220	−1.52405	−0.762026	+	0.647547i	$0.775795\pi$
$410$	77.2966	3.81741
$411$	0.762656	0.0376190
$412$	−19.0255	−0.937319
$413$	9.57366	0.471089
$414$	−25.8969	−1.27276
$415$	2.16842	0.106444
$416$	154.059	7.55335
$417$	0.183340	0.00897818
$418$	−4.71685	−0.230709
$419$	15.6141	0.762799	0.381400	−	0.924410i	$-0.375442\pi$
$419$	15.6141	0.762799	0.381400	+	0.924410i	$0.375442\pi$
$420$	−51.0886	−2.49287
$421$	−38.1872	−1.86113	−0.930564	−	0.366130i	$-0.880683\pi$
$421$	−38.1872	−1.86113	−0.930564	+	0.366130i	$0.880683\pi$
$422$	−62.8805	−3.06098
$423$	−28.9447	−1.40734
$424$	−120.291	−5.84183
$425$	41.6366	2.01967
$426$	−9.35453	−0.453229
$427$	−7.33583	−0.355006
$428$	51.9257	2.50993
$429$	80.9143	3.90658
$430$	94.1144	4.53860
$431$	−3.59797	−0.173308	−0.0866541	−	0.996238i	$-0.527617\pi$
$431$	−3.59797	−0.173308	−0.0866541	+	0.996238i	$0.527617\pi$
$432$	30.7448	1.47921
$433$	3.57470	0.171789	0.0858945	−	0.996304i	$-0.472625\pi$
$433$	3.57470	0.171789	0.0858945	+	0.996304i	$0.472625\pi$
$434$	15.1241	0.725980
$435$	−30.5509	−1.46480
$436$	63.5481	3.04340
$437$	1.33897	0.0640518
$438$	37.2157	1.77823
$439$	−6.60211	−0.315101	−0.157551	−	0.987511i	$-0.550360\pi$
$439$	−6.60211	−0.315101	−0.157551	+	0.987511i	$0.550360\pi$
$440$	−222.537	−10.6090
$441$	2.15028	0.102394
$442$	64.5918	3.07232
$443$	39.2262	1.86369	0.931847	−	0.362852i	$-0.118197\pi$
$443$	39.2262	1.86369	0.931847	+	0.362852i	$0.118197\pi$
$444$	−11.0570	−0.524742
$445$	14.2776	0.676824
$446$	49.2904	2.33397
$447$	−31.4753	−1.48873
$448$	34.7140	1.64008
$449$	24.2865	1.14615	0.573076	−	0.819502i	$-0.305750\pi$
$449$	24.2865	1.14615	0.573076	+	0.819502i	$0.305750\pi$
$450$	−66.8642	−3.15201
$451$	−38.9533	−1.83424
$452$	−86.2698	−4.05779
$453$	−9.20189	−0.432342
$454$	18.2938	0.858573
$455$	−25.7036	−1.20501
$456$	6.83662	0.320154
$457$	−16.7421	−0.783163	−0.391581	−	0.920143i	$-0.628072\pi$
$457$	−16.7421	−0.783163	−0.391581	+	0.920143i	$0.628072\pi$
$458$	−8.38935	−0.392009
$459$	7.10721	0.331736
$460$	98.4986	4.59252
$461$	−18.6385	−0.868083	−0.434042	−	0.900893i	$-0.642913\pi$
$461$	−18.6385	−0.868083	−0.434042	+	0.900893i	$0.642913\pi$
$462$	34.9798	1.62741
$463$	0.884971	0.0411281	0.0205640	−	0.999789i	$-0.493454\pi$
$463$	0.884971	0.0411281	0.0205640	+	0.999789i	$0.493454\pi$
$464$	53.1658	2.46816
$465$	50.3395	2.33444
$466$	31.2914	1.44955
$467$	21.5353	0.996534	0.498267	−	0.867024i	$-0.333970\pi$
$467$	21.5353	0.996534	0.498267	+	0.867024i	$0.333970\pi$
$468$	−76.3461	−3.52910
$469$	12.9283	0.596972
$470$	149.576	6.89941
$471$	31.6508	1.45839
$472$	−94.2440	−4.33793
$473$	−47.4286	−2.18077
$474$	36.1106	1.65862
$475$	3.45715	0.158625
$476$	20.5523	0.942012
$477$	26.2755	1.20307
$478$	29.9629	1.37047
$479$	−41.0404	−1.87518	−0.937592	−	0.347738i	$-0.886950\pi$
$479$	−41.0404	−1.87518	−0.937592	+	0.347738i	$0.886950\pi$
$480$	221.676	10.1181
$481$	−5.56299	−0.253650
$482$	8.59700	0.391583
$483$	−9.92971	−0.451818
$484$	113.521	5.16006
$485$	−37.3749	−1.69711
$486$	−51.7095	−2.34559
$487$	7.54063	0.341699	0.170849	−	0.985297i	$-0.445349\pi$
$487$	7.54063	0.341699	0.170849	+	0.985297i	$0.445349\pi$
$488$	72.2146	3.26900
$489$	−15.4804	−0.700047
$490$	−11.1119	−0.501983
$491$	−8.90635	−0.401938	−0.200969	−	0.979598i	$-0.564409\pi$
$491$	−8.90635	−0.401938	−0.200969	+	0.979598i	$0.564409\pi$
$492$	88.0323	3.96880
$493$	12.2902	0.553524
$494$	5.36316	0.241300
$495$	48.6095	2.18483
$496$	−87.6027	−3.93348
$497$	−1.49753	−0.0671734
$498$	3.35533	0.150356
$499$	20.9496	0.937835	0.468917	−	0.883242i	$-0.344644\pi$
$499$	20.9496	0.937835	0.468917	+	0.883242i	$0.344644\pi$
$500$	141.759	6.33967
$501$	24.6927	1.10319
$502$	−59.6368	−2.66172
$503$	5.42274	0.241788	0.120894	−	0.992665i	$-0.461424\pi$
$503$	5.42274	0.241788	0.120894	+	0.992665i	$0.461424\pi$
$504$	−21.1675	−0.942877
$505$	26.3846	1.17410
$506$	−67.4409	−2.99811
$507$	−62.4987	−2.77566
$508$	88.7191	3.93627
$509$	−16.5523	−0.733666	−0.366833	−	0.930287i	$-0.619558\pi$
$509$	−16.5523	−0.733666	−0.366833	+	0.930287i	$0.619558\pi$
$510$	92.9414	4.11551
$511$	5.95771	0.263554
$512$	−71.8728	−3.17636
$513$	0.590123	0.0260546
$514$	−2.70080	−0.119127
$515$	−13.7733	−0.606925
$516$	107.186	4.71860
$517$	−75.3780	−3.31512
$518$	−2.40492	−0.105666
$519$	−28.9646	−1.27141
$520$	253.029	11.0961
$521$	7.19428	0.315187	0.157594	−	0.987504i	$-0.449626\pi$
$521$	7.19428	0.315187	0.157594	+	0.987504i	$0.449626\pi$
$522$	−19.7369	−0.863860
$523$	2.17422	0.0950720	0.0475360	−	0.998870i	$-0.484863\pi$
$523$	2.17422	0.0950720	0.0475360	+	0.998870i	$0.484863\pi$
$524$	−12.6303	−0.551758
$525$	−25.6380	−1.11893
$526$	−78.3339	−3.41552
$527$	−20.2509	−0.882145
$528$	−202.612	−8.81755
$529$	−3.85556	−0.167633
$530$	−135.782	−5.89800
$531$	20.5860	0.893358
$532$	1.70649	0.0739857
$533$	44.2907	1.91844
$534$	22.0926	0.956040
$535$	37.5911	1.62521
$536$	−127.267	−5.49710
$537$	−18.5491	−0.800451
$538$	−39.3177	−1.69510
$539$	5.59978	0.241199
$540$	43.4111	1.86812
$541$	−19.1835	−0.824763	−0.412382	−	0.911011i	$-0.635303\pi$
$541$	−19.1835	−0.824763	−0.412382	+	0.911011i	$0.635303\pi$
$542$	−15.4136	−0.662070
$543$	−33.0930	−1.42015
$544$	−89.1773	−3.82344
$545$	46.0050	1.97064
$546$	−39.7727	−1.70212
$547$	−35.6979	−1.52633	−0.763166	−	0.646202i	$-0.776356\pi$
$547$	−35.6979	−1.52633	−0.763166	+	0.646202i	$0.776356\pi$
$548$	−1.87399	−0.0800527
$549$	−15.7741	−0.673221
$550$	−174.129	−7.42487
$551$	1.02048	0.0434738
$552$	97.7490	4.16047
$553$	5.78081	0.245825
$554$	−41.2446	−1.75231
$555$	−8.00460	−0.339777
$556$	−0.450499	−0.0191054
$557$	−18.8724	−0.799651	−0.399826	−	0.916591i	$-0.630929\pi$
$557$	−18.8724	−0.799651	−0.399826	+	0.916591i	$0.630929\pi$
$558$	32.5210	1.37672
$559$	53.9273	2.28088
$560$	64.3628	2.71982
$561$	−46.8374	−1.97748
$562$	28.9870	1.22274
$563$	−34.9320	−1.47221	−0.736105	−	0.676867i	$-0.763337\pi$
$563$	−34.9320	−1.47221	−0.736105	+	0.676867i	$0.763337\pi$
$564$	170.350	7.17303
$565$	−62.4542	−2.62747
$566$	55.0782	2.31511
$567$	−10.8271	−0.454697
$568$	14.7418	0.618554
$569$	−9.90202	−0.415114	−0.207557	−	0.978223i	$-0.566551\pi$
$569$	−9.90202	−0.415114	−0.207557	+	0.978223i	$0.566551\pi$
$570$	7.71707	0.323233
$571$	−26.8154	−1.12219	−0.561095	−	0.827752i	$-0.689620\pi$
$571$	−26.8154	−1.12219	−0.561095	+	0.827752i	$0.689620\pi$
$572$	−198.821	−8.31313
$573$	−31.7181	−1.32504
$574$	19.1472	0.799188
$575$	49.4299	2.06137
$576$	74.6447	3.11020
$577$	4.66582	0.194240	0.0971202	−	0.995273i	$-0.469037\pi$
$577$	4.66582	0.194240	0.0971202	+	0.995273i	$0.469037\pi$
$578$	9.40380	0.391147
$579$	4.35638	0.181045
$580$	75.0692	3.11708
$581$	0.537141	0.0222844
$582$	−57.8323	−2.39723
$583$	68.4269	2.83395
$584$	−58.6483	−2.42688
$585$	−55.2700	−2.28513
$586$	41.5723	1.71734
$587$	−24.6937	−1.01922	−0.509608	−	0.860407i	$-0.670210\pi$
$587$	−24.6937	−1.01922	−0.509608	+	0.860407i	$0.670210\pi$
$588$	−12.6552	−0.521891
$589$	−1.68147	−0.0692837
$590$	−106.381	−4.37964
$591$	59.6825	2.45501
$592$	13.9299	0.572515
$593$	15.4558	0.634696	0.317348	−	0.948309i	$-0.397208\pi$
$593$	15.4558	0.634696	0.317348	+	0.948309i	$0.397208\pi$
$594$	−29.7231	−1.21955
$595$	14.8786	0.609964
$596$	77.3406	3.16799
$597$	−16.8991	−0.691632
$598$	76.6817	3.13575
$599$	−34.4534	−1.40773	−0.703864	−	0.710335i	$-0.748543\pi$
$599$	−34.4534	−1.40773	−0.703864	+	0.710335i	$0.748543\pi$
$600$	252.383	10.3035
$601$	20.9532	0.854697	0.427348	−	0.904087i	$-0.359448\pi$
$601$	20.9532	0.854697	0.427348	+	0.904087i	$0.359448\pi$
$602$	23.3131	0.950172
$603$	27.7994	1.13208
$604$	22.6107	0.920017
$605$	82.1826	3.34120
$606$	40.8264	1.65846
$607$	35.1636	1.42725	0.713623	−	0.700530i	$-0.247053\pi$
$607$	35.1636	1.42725	0.713623	+	0.700530i	$0.247053\pi$
$608$	−7.40454	−0.300294
$609$	−7.56778	−0.306662
$610$	81.5147	3.30043
$611$	85.7063	3.46731
$612$	44.1931	1.78640
$613$	46.8476	1.89216	0.946079	−	0.323937i	$-0.105007\pi$
$613$	46.8476	1.89216	0.946079	+	0.323937i	$0.105007\pi$
$614$	−39.7550	−1.60438
$615$	63.7301	2.56985
$616$	−55.1247	−2.22104
$617$	−20.3129	−0.817768	−0.408884	−	0.912586i	$-0.634082\pi$
$617$	−20.3129	−0.817768	−0.408884	+	0.912586i	$0.634082\pi$
$618$	−21.3123	−0.857305
$619$	−0.422058	−0.0169640	−0.00848198	−	0.999964i	$-0.502700\pi$
$619$	−0.422058	−0.0169640	−0.00848198	+	0.999964i	$0.502700\pi$
$620$	−123.694	−4.96765
$621$	8.43750	0.338585
$622$	0.714305	0.0286410
$623$	3.53672	0.141696
$624$	230.374	9.22234
$625$	46.1396	1.84558
$626$	−58.0617	−2.32061
$627$	−3.88899	−0.155311
$628$	−77.7718	−3.10343
$629$	3.22015	0.128396
$630$	−23.8936	−0.951943
$631$	19.0673	0.759057	0.379528	−	0.925180i	$-0.376086\pi$
$631$	19.0673	0.759057	0.379528	+	0.925180i	$0.376086\pi$
$632$	−56.9068	−2.26363
$633$	−51.8442	−2.06062
$634$	53.8484	2.13859
$635$	64.2273	2.54878
$636$	−154.641	−6.13191
$637$	−6.36706	−0.252272
$638$	−51.3990	−2.03491
$639$	−3.22011	−0.127385
$640$	−190.378	−7.52536
$641$	−4.16979	−0.164697	−0.0823484	−	0.996604i	$-0.526242\pi$
$641$	−4.16979	−0.164697	−0.0823484	+	0.996604i	$0.526242\pi$
$642$	58.1669	2.29567
$643$	17.8953	0.705723	0.352861	−	0.935676i	$-0.385209\pi$
$643$	17.8953	0.705723	0.352861	+	0.935676i	$0.385209\pi$
$644$	24.3991	0.961460
$645$	77.5962	3.05535
$646$	−3.10448	−0.122144
$647$	30.7522	1.20899	0.604496	−	0.796608i	$-0.293374\pi$
$647$	30.7522	1.20899	0.604496	+	0.796608i	$0.293374\pi$
$648$	106.583	4.18699
$649$	53.6104	2.10439
$650$	197.988	7.76572
$651$	12.4696	0.488723
$652$	38.0381	1.48969
$653$	13.9743	0.546857	0.273428	−	0.961892i	$-0.411842\pi$
$653$	13.9743	0.546857	0.273428	+	0.961892i	$0.411842\pi$
$654$	71.1863	2.78360
$655$	−9.14359	−0.357270
$656$	−110.905	−4.33013
$657$	12.8107	0.499794
$658$	37.0514	1.44442
$659$	−13.2136	−0.514729	−0.257365	−	0.966314i	$-0.582854\pi$
$659$	−13.2136	−0.514729	−0.257365	+	0.966314i	$0.582854\pi$
$660$	−286.085	−11.1358
$661$	39.8009	1.54807	0.774037	−	0.633140i	$-0.218234\pi$
$661$	39.8009	1.54807	0.774037	+	0.633140i	$0.218234\pi$
$662$	15.7180	0.610899
$663$	53.2551	2.06826
$664$	−5.28767	−0.205201
$665$	1.23540	0.0479066
$666$	−5.17124	−0.200381
$667$	14.5906	0.564952
$668$	−60.6745	−2.34757
$669$	40.6393	1.57121
$670$	−143.657	−5.54996
$671$	−41.0790	−1.58584
$672$	54.9114	2.11825
$673$	10.1016	0.389388	0.194694	−	0.980864i	$-0.437629\pi$
$673$	10.1016	0.389388	0.194694	+	0.980864i	$0.437629\pi$
$674$	−66.1763	−2.54902
$675$	21.7851	0.838511
$676$	153.571	5.90657
$677$	1.71973	0.0660944	0.0330472	−	0.999454i	$-0.489479\pi$
$677$	1.71973	0.0660944	0.0330472	+	0.999454i	$0.489479\pi$
$678$	−96.6389	−3.71140
$679$	−9.25815	−0.355295
$680$	−146.467	−5.61673
$681$	15.0831	0.577984
$682$	84.6916	3.24301
$683$	7.50469	0.287159	0.143580	−	0.989639i	$-0.454139\pi$
$683$	7.50469	0.287159	0.143580	+	0.989639i	$0.454139\pi$
$684$	3.66943	0.140304
$685$	−1.35665	−0.0518351
$686$	−2.75252	−0.105092
$687$	−6.91692	−0.263897
$688$	−135.036	−5.14818
$689$	−77.8028	−2.96405
$690$	110.338	4.20048
$691$	2.26007	0.0859772	0.0429886	−	0.999076i	$-0.486312\pi$
$691$	2.26007	0.0859772	0.0429886	+	0.999076i	$0.486312\pi$
$692$	71.1714	2.70553
$693$	12.0411	0.457403
$694$	0.908251	0.0344767
$695$	−0.326135	−0.0123710
$696$	74.4979	2.82384
$697$	−25.6378	−0.971101
$698$	−18.3867	−0.695946
$699$	25.7994	0.975822
$700$	62.9972	2.38107
$701$	−21.7335	−0.820862	−0.410431	−	0.911892i	$-0.634622\pi$
$701$	−21.7335	−0.820862	−0.410431	+	0.911892i	$0.634622\pi$
$702$	33.7958	1.27554
$703$	0.267374	0.0100842
$704$	194.391	7.32637
$705$	123.323	4.64462
$706$	33.8481	1.27389
$707$	6.53574	0.245802
$708$	−121.156	−4.55334
$709$	5.55232	0.208522	0.104261	−	0.994550i	$-0.466752\pi$
$709$	5.55232	0.208522	0.104261	+	0.994550i	$0.466752\pi$
$710$	16.6403	0.624501
$711$	12.4303	0.466174
$712$	−34.8158	−1.30478
$713$	−24.0414	−0.900357
$714$	23.0225	0.861597
$715$	−143.935	−5.38285
$716$	45.5784	1.70335
$717$	24.7040	0.922588
$718$	53.5476	1.99838
$719$	38.0539	1.41917	0.709585	−	0.704620i	$-0.248883\pi$
$719$	38.0539	1.41917	0.709585	+	0.704620i	$0.248883\pi$
$720$	138.398	5.15778
$721$	−3.41180	−0.127062
$722$	52.0402	1.93674
$723$	7.08812	0.263610
$724$	81.3155	3.02207
$725$	37.6722	1.39911
$726$	127.166	4.71957
$727$	43.9899	1.63149	0.815747	−	0.578409i	$-0.196326\pi$
$727$	43.9899	1.63149	0.815747	+	0.578409i	$0.196326\pi$
$728$	62.6780	2.32300
$729$	−10.1524	−0.376016
$730$	−66.2013	−2.45022
$731$	−31.2159	−1.15456
$732$	92.8362	3.43132
$733$	34.9919	1.29246	0.646228	−	0.763145i	$-0.276346\pi$
$733$	34.9919	1.29246	0.646228	+	0.763145i	$0.276346\pi$
$734$	−42.6938	−1.57586
$735$	−9.16159	−0.337930
$736$	−105.869	−3.90238
$737$	72.3954	2.66672
$738$	41.1718	1.51555
$739$	−11.6467	−0.428432	−0.214216	−	0.976786i	$-0.568720\pi$
$739$	−11.6467	−0.428432	−0.214216	+	0.976786i	$0.568720\pi$
$740$	19.6688	0.723039
$741$	4.42186	0.162441
$742$	−33.6347	−1.23477
$743$	4.80862	0.176411	0.0882056	−	0.996102i	$-0.471887\pi$
$743$	4.80862	0.176411	0.0882056	+	0.996102i	$0.471887\pi$
$744$	−122.752	−4.50032
$745$	55.9899	2.05131
$746$	21.4235	0.784371
$747$	1.15500	0.0422593
$748$	115.088	4.20804
$749$	9.31172	0.340243
$750$	158.798	5.79848
$751$	43.8853	1.60140	0.800698	−	0.599068i	$-0.204462\pi$
$751$	43.8853	1.60140	0.800698	+	0.599068i	$0.204462\pi$
$752$	−214.611	−7.82607
$753$	−49.1698	−1.79185
$754$	58.4418	2.12832
$755$	16.3688	0.595722
$756$	10.7534	0.391097
$757$	−42.6501	−1.55014	−0.775072	−	0.631872i	$-0.782287\pi$
$757$	−42.6501	−1.55014	−0.775072	+	0.631872i	$0.782287\pi$
$758$	−80.8508	−2.93663
$759$	−55.6042	−2.01830
$760$	−12.1614	−0.441139
$761$	−1.24666	−0.0451912	−0.0225956	−	0.999745i	$-0.507193\pi$
$761$	−1.24666	−0.0451912	−0.0225956	+	0.999745i	$0.507193\pi$
$762$	99.3826	3.60025
$763$	11.3959	0.412560
$764$	77.9371	2.81967
$765$	31.9932	1.15672
$766$	−49.6641	−1.79444
$767$	−60.9561	−2.20100
$768$	−137.022	−4.94435
$769$	−25.8256	−0.931294	−0.465647	−	0.884971i	$-0.654178\pi$
$769$	−25.8256	−0.931294	−0.465647	+	0.884971i	$0.654178\pi$
$770$	−62.2239	−2.24239
$771$	−2.22678	−0.0801954
$772$	−10.7044	−0.385260
$773$	33.0297	1.18799	0.593997	−	0.804467i	$-0.297549\pi$
$773$	33.0297	1.18799	0.593997	+	0.804467i	$0.297549\pi$
$774$	50.1297	1.80187
$775$	−62.0736	−2.22975
$776$	91.1381	3.27167
$777$	−1.98282	−0.0711334
$778$	46.5939	1.67047
$779$	−2.12875	−0.0762703
$780$	325.284	11.6470
$781$	−8.38584	−0.300069
$782$	−44.3874	−1.58729
$783$	6.43051	0.229808
$784$	15.9433	0.569405
$785$	−56.3021	−2.00951
$786$	−14.1484	−0.504657
$787$	17.3694	0.619152	0.309576	−	0.950875i	$-0.399813\pi$
$787$	17.3694	0.619152	0.309576	+	0.950875i	$0.399813\pi$
$788$	−146.651	−5.22422
$789$	−64.5853	−2.29930
$790$	−64.2355	−2.28540
$791$	−15.4706	−0.550069
$792$	−118.533	−4.21190
$793$	46.7077	1.65864
$794$	40.7343	1.44561
$795$	−111.951	−3.97049
$796$	41.5241	1.47178
$797$	30.5718	1.08291	0.541454	−	0.840730i	$-0.317874\pi$
$797$	30.5718	1.08291	0.541454	+	0.840730i	$0.317874\pi$
$798$	1.91160	0.0676699
$799$	−49.6113	−1.75512
$800$	−273.348	−9.66430
$801$	7.60493	0.268707
$802$	31.1539	1.10008
$803$	33.3619	1.17731
$804$	−163.610	−5.77007
$805$	17.6635	0.622557
$806$	−96.2961	−3.39188
$807$	−32.4169	−1.14113
$808$	−64.3384	−2.26342
$809$	−36.4530	−1.28162	−0.640809	−	0.767700i	$-0.721401\pi$
$809$	−36.4530	−1.28162	−0.640809	+	0.767700i	$0.721401\pi$
$810$	120.310	4.22725
$811$	3.31899	0.116546	0.0582728	−	0.998301i	$-0.481441\pi$
$811$	3.31899	0.116546	0.0582728	+	0.998301i	$0.481441\pi$
$812$	18.5954	0.652571
$813$	−12.7083	−0.445700
$814$	−13.4670	−0.472018
$815$	27.5373	0.964591
$816$	−133.353	−4.66827
$817$	−2.59191	−0.0906795
$818$	84.8384	2.96630
$819$	−13.6910	−0.478401
$820$	−156.597	−5.46859
$821$	−29.4861	−1.02907	−0.514536	−	0.857468i	$-0.672036\pi$
$821$	−29.4861	−1.02907	−0.514536	+	0.857468i	$0.672036\pi$
$822$	−2.09923	−0.0732190
$823$	25.9180	0.903446	0.451723	−	0.892158i	$-0.350810\pi$
$823$	25.9180	0.903446	0.451723	+	0.892158i	$0.350810\pi$
$824$	33.5860	1.17002
$825$	−143.567	−4.99836
$826$	−26.3517	−0.916894
$827$	48.0656	1.67140	0.835702	−	0.549183i	$-0.185061\pi$
$827$	48.0656	1.67140	0.835702	+	0.549183i	$0.185061\pi$
$828$	52.4649	1.82328
$829$	−20.2709	−0.704037	−0.352019	−	0.935993i	$-0.614505\pi$
$829$	−20.2709	−0.704037	−0.352019	+	0.935993i	$0.614505\pi$
$830$	−5.96863	−0.207174
$831$	−34.0056	−1.17964
$832$	−221.026	−7.66270
$833$	3.68559	0.127698
$834$	−0.504647	−0.0174745
$835$	−43.9247	−1.52008
$836$	9.55596	0.330500
$837$	−10.5957	−0.366242
$838$	−42.9782	−1.48466
$839$	15.8256	0.546359	0.273180	−	0.961963i	$-0.411925\pi$
$839$	15.8256	0.546359	0.273180	+	0.961963i	$0.411925\pi$
$840$	90.1876	3.11177
$841$	−17.8800	−0.616550
$842$	105.111	3.62237
$843$	23.8994	0.823139
$844$	127.391	4.38497
$845$	111.176	3.82457
$846$	79.6709	2.73914
$847$	20.3575	0.699492
$848$	194.821	6.69017
$849$	45.4113	1.55851
$850$	−114.606	−3.93094
$851$	3.82288	0.131047
$852$	18.9515	0.649268
$853$	16.3067	0.558330	0.279165	−	0.960243i	$-0.409942\pi$
$853$	16.3067	0.558330	0.279165	+	0.960243i	$0.409942\pi$
$854$	20.1920	0.690957
$855$	2.65644	0.0908485
$856$	−91.6654	−3.13306
$857$	−7.58254	−0.259015	−0.129507	−	0.991578i	$-0.541340\pi$
$857$	−7.58254	−0.259015	−0.129507	+	0.991578i	$0.541340\pi$
$858$	−222.718	−7.60348
$859$	−21.6731	−0.739477	−0.369739	−	0.929136i	$-0.620553\pi$
$859$	−21.6731	−0.739477	−0.369739	+	0.929136i	$0.620553\pi$
$860$	−190.668	−6.50173
$861$	15.7866	0.538007
$862$	9.90350	0.337315
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−46.6594	−1.58739
$865$	51.5238	1.75186
$866$	−9.83944	−0.334358
$867$	7.75332	0.263317
$868$	−30.6402	−1.04000
$869$	32.3712	1.09812
$870$	84.0921	2.85099
$871$	−82.3151	−2.78914
$872$	−112.183	−3.79898
$873$	−19.9076	−0.673770
$874$	−3.68556	−0.124666
$875$	25.4213	0.859398
$876$	−75.3959	−2.54739
$877$	40.3619	1.36293	0.681463	−	0.731853i	$-0.261344\pi$
$877$	40.3619	1.36293	0.681463	+	0.731853i	$0.261344\pi$
$878$	18.1725	0.613291
$879$	34.2759	1.15610
$880$	360.417	12.1497
$881$	38.5069	1.29733	0.648666	−	0.761073i	$-0.275327\pi$
$881$	38.5069	1.29733	0.648666	+	0.761073i	$0.275327\pi$
$882$	−5.91869	−0.199293
$883$	−38.9146	−1.30958	−0.654791	−	0.755810i	$-0.727243\pi$
$883$	−38.9146	−1.30958	−0.654791	+	0.755810i	$0.727243\pi$
$884$	−130.858	−4.40122
$885$	−87.7100	−2.94834
$886$	−107.971	−3.62736
$887$	−19.3811	−0.650755	−0.325377	−	0.945584i	$-0.605491\pi$
$887$	−19.3811	−0.650755	−0.325377	+	0.945584i	$0.605491\pi$
$888$	19.5191	0.655018
$889$	15.9098	0.533597
$890$	−39.2995	−1.31732
$891$	−60.6296	−2.03117
$892$	−99.8583	−3.34350
$893$	−4.11931	−0.137847
$894$	86.6365	2.89756
$895$	32.9961	1.10294
$896$	−47.1587	−1.57546
$897$	63.2231	2.11096
$898$	−66.8492	−2.23079
$899$	−18.3228	−0.611099
$900$	135.461	4.51538
$901$	45.0364	1.50038
$902$	107.220	3.57003
$903$	19.2214	0.639648
$904$	152.294	5.06521
$905$	58.8675	1.95682
$906$	25.3284	0.841480
$907$	−12.1399	−0.403098	−0.201549	−	0.979478i	$-0.564598\pi$
$907$	−12.1399	−0.403098	−0.201549	+	0.979478i	$0.564598\pi$
$908$	−37.0618	−1.22994
$909$	14.0537	0.466130
$910$	70.7499	2.34534
$911$	24.1882	0.801392	0.400696	−	0.916211i	$-0.368768\pi$
$911$	24.1882	0.801392	0.400696	+	0.916211i	$0.368768\pi$
$912$	−11.0725	−0.366646
$913$	3.00787	0.0995459
$914$	46.0831	1.52429
$915$	67.2078	2.22182
$916$	16.9961	0.561568
$917$	−2.26496	−0.0747957
$918$	−19.5628	−0.645668
$919$	15.3900	0.507669	0.253835	−	0.967248i	$-0.418308\pi$
$919$	15.3900	0.507669	0.253835	+	0.967248i	$0.418308\pi$
$920$	−173.881	−5.73269
$921$	−32.7775	−1.08006
$922$	51.3030	1.68957
$923$	9.53487	0.313844
$924$	−70.8662	−2.33133
$925$	9.87046	0.324539
$926$	−2.43590	−0.0800487
$927$	−7.33631	−0.240956
$928$	−80.6864	−2.64866
$929$	9.34089	0.306465	0.153232	−	0.988190i	$-0.451032\pi$
$929$	9.34089	0.306465	0.153232	+	0.988190i	$0.451032\pi$
$930$	−138.561	−4.54359
$931$	0.306021	0.0100294
$932$	−63.3938	−2.07653
$933$	0.588936	0.0192809
$934$	−59.2764	−1.93958
$935$	83.3169	2.72475
$936$	134.775	4.40526
$937$	−57.6677	−1.88392	−0.941961	−	0.335721i	$-0.891020\pi$
$937$	−57.6677	−1.88392	−0.941961	+	0.335721i	$0.891020\pi$
$938$	−35.5854	−1.16190
$939$	−47.8712	−1.56222
$940$	−303.028	−9.88368
$941$	−30.2752	−0.986944	−0.493472	−	0.869762i	$-0.664272\pi$
$941$	−30.2752	−0.986944	−0.493472	+	0.869762i	$0.664272\pi$
$942$	−87.1196	−2.83851
$943$	−30.4365	−0.991150
$944$	152.636	4.96788
$945$	7.78481	0.253240
$946$	130.548	4.24449
$947$	−0.954310	−0.0310109	−0.0155055	−	0.999880i	$-0.504936\pi$
$947$	−0.954310	−0.0310109	−0.0155055	+	0.999880i	$0.504936\pi$
$948$	−73.1572	−2.37603
$949$	−37.9331	−1.23136
$950$	−9.51590	−0.308737
$951$	44.3974	1.43968
$952$	−36.2813	−1.17588
$953$	51.7656	1.67685	0.838427	−	0.545014i	$-0.183476\pi$
$953$	51.7656	1.67685	0.838427	+	0.545014i	$0.183476\pi$
$954$	−72.3239	−2.34157
$955$	56.4218	1.82577
$956$	−60.7023	−1.96325
$957$	−42.3779	−1.36988
$958$	112.965	3.64972
$959$	−0.336057	−0.0108519
$960$	−318.035	−10.2645
$961$	−0.809057	−0.0260986
$962$	15.3123	0.493687
$963$	20.0228	0.645225
$964$	−17.4168	−0.560958
$965$	−7.74936	−0.249461
$966$	27.3318	0.879385
$967$	−9.01813	−0.290004	−0.145002	−	0.989431i	$-0.546319\pi$
$967$	−9.01813	−0.290004	−0.145002	+	0.989431i	$0.546319\pi$
$968$	−200.401	−6.44113
$969$	−2.55960	−0.0822263
$970$	102.875	3.30312
$971$	7.96092	0.255478	0.127739	−	0.991808i	$-0.459228\pi$
$971$	7.96092	0.255478	0.127739	+	0.991808i	$0.459228\pi$
$972$	104.759	3.36015
$973$	−0.0807869	−0.00258991
$974$	−20.7558	−0.665058
$975$	163.239	5.22782
$976$	−116.957	−3.74372
$977$	11.9982	0.383856	0.191928	−	0.981409i	$-0.438526\pi$
$977$	11.9982	0.383856	0.191928	+	0.981409i	$0.438526\pi$
$978$	42.6101	1.36252
$979$	19.8048	0.632965
$980$	22.5117	0.719110
$981$	24.5044	0.782366
$982$	24.5150	0.782304
$983$	40.8538	1.30303	0.651517	−	0.758634i	$-0.274133\pi$
$983$	40.8538	1.30303	0.651517	+	0.758634i	$0.274133\pi$
$984$	−155.405	−4.95413
$985$	−106.166	−3.38274
$986$	−33.8292	−1.07734
$987$	30.5485	0.972368
$988$	−10.8653	−0.345672
$989$	−37.0587	−1.17840
$990$	−133.799	−4.25240
$991$	50.6979	1.61047	0.805235	−	0.592955i	$-0.202039\pi$
$991$	50.6979	1.61047	0.805235	+	0.592955i	$0.202039\pi$
$992$	132.949	4.22114
$993$	12.9593	0.411252
$994$	4.12199	0.130742
$995$	30.0609	0.952996
$996$	−6.79761	−0.215391
$997$	53.0875	1.68130	0.840650	−	0.541579i	$-0.182173\pi$
$997$	53.0875	1.68130	0.840650	+	0.541579i	$0.182173\pi$
$998$	−57.6644	−1.82533
$999$	1.68485	0.0533063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.4	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.4	✓	132	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75252 q^{2} -2.26942 q^{3} +5.57639 q^{4} +4.03697 q^{5} +6.24664 q^{6} +1.00000 q^{7} -9.84409 q^{8} +2.15028 q^{9} +O(q^{10})\)	\(q-2.75252 q^{2} -2.26942 q^{3} +5.57639 q^{4} +4.03697 q^{5} +6.24664 q^{6} +1.00000 q^{7} -9.84409 q^{8} +2.15028 q^{9} -11.1119 q^{10} +5.59978 q^{11} -12.6552 q^{12} -6.36706 q^{13} -2.75252 q^{14} -9.16159 q^{15} +15.9433 q^{16} +3.68559 q^{17} -5.91869 q^{18} +0.306021 q^{19} +22.5117 q^{20} -2.26942 q^{21} -15.4135 q^{22} +4.37544 q^{23} +22.3404 q^{24} +11.2971 q^{25} +17.5255 q^{26} +1.92838 q^{27} +5.57639 q^{28} +3.33467 q^{29} +25.2175 q^{30} -5.49463 q^{31} -24.1962 q^{32} -12.7083 q^{33} -10.1447 q^{34} +4.03697 q^{35} +11.9908 q^{36} +0.873713 q^{37} -0.842329 q^{38} +14.4496 q^{39} -39.7403 q^{40} -6.95623 q^{41} +6.24664 q^{42} -8.46973 q^{43} +31.2265 q^{44} +8.68061 q^{45} -12.0435 q^{46} -13.4609 q^{47} -36.1821 q^{48} +1.00000 q^{49} -31.0956 q^{50} -8.36416 q^{51} -35.5052 q^{52} +12.2196 q^{53} -5.30791 q^{54} +22.6061 q^{55} -9.84409 q^{56} -0.694490 q^{57} -9.17876 q^{58} +9.57366 q^{59} -51.0886 q^{60} -7.33583 q^{61} +15.1241 q^{62} +2.15028 q^{63} +34.7140 q^{64} -25.7036 q^{65} +34.9798 q^{66} +12.9283 q^{67} +20.5523 q^{68} -9.92971 q^{69} -11.1119 q^{70} -1.49753 q^{71} -21.1675 q^{72} +5.95771 q^{73} -2.40492 q^{74} -25.6380 q^{75} +1.70649 q^{76} +5.59978 q^{77} -39.7727 q^{78} +5.78081 q^{79} +64.3628 q^{80} -10.8271 q^{81} +19.1472 q^{82} +0.537141 q^{83} -12.6552 q^{84} +14.8786 q^{85} +23.3131 q^{86} -7.56778 q^{87} -55.1247 q^{88} +3.53672 q^{89} -23.8936 q^{90} -6.36706 q^{91} +24.3991 q^{92} +12.4696 q^{93} +37.0514 q^{94} +1.23540 q^{95} +54.9114 q^{96} -9.25815 q^{97} -2.75252 q^{98} +12.0411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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