LMFDB - Embedded newform 6015.2.a.f.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.659715 q^{2} -1.00000 q^{3} -1.56478 q^{4} -1.00000 q^{5} -0.659715 q^{6} -0.736249 q^{7} -2.35174 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.659715 q^{2} -1.00000 q^{3} -1.56478 q^{4} -1.00000 q^{5} -0.659715 q^{6} -0.736249 q^{7} -2.35174 q^{8} +1.00000 q^{9} -0.659715 q^{10} -6.01678 q^{11} +1.56478 q^{12} +2.15232 q^{13} -0.485715 q^{14} +1.00000 q^{15} +1.57807 q^{16} +2.53953 q^{17} +0.659715 q^{18} +2.06285 q^{19} +1.56478 q^{20} +0.736249 q^{21} -3.96936 q^{22} +4.57814 q^{23} +2.35174 q^{24} +1.00000 q^{25} +1.41992 q^{26} -1.00000 q^{27} +1.15206 q^{28} -6.14918 q^{29} +0.659715 q^{30} +0.341475 q^{31} +5.74455 q^{32} +6.01678 q^{33} +1.67536 q^{34} +0.736249 q^{35} -1.56478 q^{36} +6.50619 q^{37} +1.36089 q^{38} -2.15232 q^{39} +2.35174 q^{40} -4.61104 q^{41} +0.485715 q^{42} +7.89193 q^{43} +9.41491 q^{44} -1.00000 q^{45} +3.02027 q^{46} +9.07538 q^{47} -1.57807 q^{48} -6.45794 q^{49} +0.659715 q^{50} -2.53953 q^{51} -3.36790 q^{52} -5.97806 q^{53} -0.659715 q^{54} +6.01678 q^{55} +1.73146 q^{56} -2.06285 q^{57} -4.05671 q^{58} +5.43452 q^{59} -1.56478 q^{60} +1.79844 q^{61} +0.225276 q^{62} -0.736249 q^{63} +0.633622 q^{64} -2.15232 q^{65} +3.96936 q^{66} +6.44734 q^{67} -3.97379 q^{68} -4.57814 q^{69} +0.485715 q^{70} -12.9278 q^{71} -2.35174 q^{72} +14.4026 q^{73} +4.29224 q^{74} -1.00000 q^{75} -3.22790 q^{76} +4.42984 q^{77} -1.41992 q^{78} -1.91430 q^{79} -1.57807 q^{80} +1.00000 q^{81} -3.04197 q^{82} -7.27560 q^{83} -1.15206 q^{84} -2.53953 q^{85} +5.20643 q^{86} +6.14918 q^{87} +14.1499 q^{88} +5.29895 q^{89} -0.659715 q^{90} -1.58465 q^{91} -7.16376 q^{92} -0.341475 q^{93} +5.98716 q^{94} -2.06285 q^{95} -5.74455 q^{96} -16.5616 q^{97} -4.26040 q^{98} -6.01678 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.659715	0.466489	0.233245	−	0.972418i	$-0.425066\pi$
$2$	0.659715	0.466489	0.233245	+	0.972418i	$0.425066\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.56478	−0.782388
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.659715	−0.269328
$7$	−0.736249	−0.278276	−0.139138	−	0.990273i	$-0.544433\pi$
$7$	−0.736249	−0.278276	−0.139138	+	0.990273i	$0.544433\pi$
$8$	−2.35174	−0.831465
$9$	1.00000	0.333333
$10$	−0.659715	−0.208620
$11$	−6.01678	−1.81413	−0.907063	−	0.420994i	$-0.861681\pi$
$11$	−6.01678	−1.81413	−0.907063	+	0.420994i	$0.861681\pi$
$12$	1.56478	0.451712
$13$	2.15232	0.596947	0.298474	−	0.954418i	$-0.403523\pi$
$13$	2.15232	0.596947	0.298474	+	0.954418i	$0.403523\pi$
$14$	−0.485715	−0.129813
$15$	1.00000	0.258199
$16$	1.57807	0.394519
$17$	2.53953	0.615925	0.307963	−	0.951398i	$-0.400353\pi$
$17$	2.53953	0.615925	0.307963	+	0.951398i	$0.400353\pi$
$18$	0.659715	0.155496
$19$	2.06285	0.473250	0.236625	−	0.971601i	$-0.423959\pi$
$19$	2.06285	0.473250	0.236625	+	0.971601i	$0.423959\pi$
$20$	1.56478	0.349894
$21$	0.736249	0.160663
$22$	−3.96936	−0.846270
$23$	4.57814	0.954608	0.477304	−	0.878738i	$-0.341614\pi$
$23$	4.57814	0.954608	0.477304	+	0.878738i	$0.341614\pi$
$24$	2.35174	0.480046
$25$	1.00000	0.200000
$26$	1.41992	0.278469
$27$	−1.00000	−0.192450
$28$	1.15206	0.217720
$29$	−6.14918	−1.14187	−0.570937	−	0.820994i	$-0.693420\pi$
$29$	−6.14918	−1.14187	−0.570937	+	0.820994i	$0.693420\pi$
$30$	0.659715	0.120447
$31$	0.341475	0.0613306	0.0306653	−	0.999530i	$-0.490237\pi$
$31$	0.341475	0.0613306	0.0306653	+	0.999530i	$0.490237\pi$
$32$	5.74455	1.01550
$33$	6.01678	1.04739
$34$	1.67536	0.287323
$35$	0.736249	0.124449
$36$	−1.56478	−0.260796
$37$	6.50619	1.06961	0.534806	−	0.844975i	$-0.320385\pi$
$37$	6.50619	1.06961	0.534806	+	0.844975i	$0.320385\pi$
$38$	1.36089	0.220766
$39$	−2.15232	−0.344648
$40$	2.35174	0.371842
$41$	−4.61104	−0.720123	−0.360062	−	0.932929i	$-0.617244\pi$
$41$	−4.61104	−0.720123	−0.360062	+	0.932929i	$0.617244\pi$
$42$	0.485715	0.0749474
$43$	7.89193	1.20351	0.601754	−	0.798681i	$-0.294469\pi$
$43$	7.89193	1.20351	0.601754	+	0.798681i	$0.294469\pi$
$44$	9.41491	1.41935
$45$	−1.00000	−0.149071
$46$	3.02027	0.445314
$47$	9.07538	1.32378	0.661890	−	0.749601i	$-0.269755\pi$
$47$	9.07538	1.32378	0.661890	+	0.749601i	$0.269755\pi$
$48$	−1.57807	−0.227775
$49$	−6.45794	−0.922563
$50$	0.659715	0.0932978
$51$	−2.53953	−0.355605
$52$	−3.36790	−0.467044
$53$	−5.97806	−0.821150	−0.410575	−	0.911827i	$-0.634672\pi$
$53$	−5.97806	−0.821150	−0.410575	+	0.911827i	$0.634672\pi$
$54$	−0.659715	−0.0897759
$55$	6.01678	0.811302
$56$	1.73146	0.231377
$57$	−2.06285	−0.273231
$58$	−4.05671	−0.532672
$59$	5.43452	0.707514	0.353757	−	0.935337i	$-0.384904\pi$
$59$	5.43452	0.707514	0.353757	+	0.935337i	$0.384904\pi$
$60$	−1.56478	−0.202012
$61$	1.79844	0.230267	0.115133	−	0.993350i	$-0.463270\pi$
$61$	1.79844	0.230267	0.115133	+	0.993350i	$0.463270\pi$
$62$	0.225276	0.0286101
$63$	−0.736249	−0.0927586
$64$	0.633622	0.0792028
$65$	−2.15232	−0.266963
$66$	3.96936	0.488594
$67$	6.44734	0.787668	0.393834	−	0.919182i	$-0.371148\pi$
$67$	6.44734	0.787668	0.393834	+	0.919182i	$0.371148\pi$
$68$	−3.97379	−0.481893
$69$	−4.57814	−0.551143
$70$	0.485715	0.0580540
$71$	−12.9278	−1.53425	−0.767123	−	0.641500i	$-0.778312\pi$
$71$	−12.9278	−1.53425	−0.767123	+	0.641500i	$0.778312\pi$
$72$	−2.35174	−0.277155
$73$	14.4026	1.68570	0.842849	−	0.538151i	$-0.180877\pi$
$73$	14.4026	1.68570	0.842849	+	0.538151i	$0.180877\pi$
$74$	4.29224	0.498962
$75$	−1.00000	−0.115470
$76$	−3.22790	−0.370265
$77$	4.42984	0.504828
$78$	−1.41992	−0.160774
$79$	−1.91430	−0.215375	−0.107688	−	0.994185i	$-0.534345\pi$
$79$	−1.91430	−0.215375	−0.107688	+	0.994185i	$0.534345\pi$
$80$	−1.57807	−0.176434
$81$	1.00000	0.111111
$82$	−3.04197	−0.335930
$83$	−7.27560	−0.798600	−0.399300	−	0.916820i	$-0.630747\pi$
$83$	−7.27560	−0.798600	−0.399300	+	0.916820i	$0.630747\pi$
$84$	−1.15206	−0.125700
$85$	−2.53953	−0.275450
$86$	5.20643	0.561424
$87$	6.14918	0.659261
$88$	14.1499	1.50838
$89$	5.29895	0.561688	0.280844	−	0.959753i	$-0.409386\pi$
$89$	5.29895	0.561688	0.280844	+	0.959753i	$0.409386\pi$
$90$	−0.659715	−0.0695401
$91$	−1.58465	−0.166116
$92$	−7.16376	−0.746873
$93$	−0.341475	−0.0354093
$94$	5.98716	0.617529
$95$	−2.06285	−0.211644
$96$	−5.74455	−0.586301
$97$	−16.5616	−1.68158	−0.840789	−	0.541363i	$-0.817909\pi$
$97$	−16.5616	−1.68158	−0.840789	+	0.541363i	$0.817909\pi$
$98$	−4.26040	−0.430365
$99$	−6.01678	−0.604709
$100$	−1.56478	−0.156478
$101$	3.26792	0.325170	0.162585	−	0.986695i	$-0.448017\pi$
$101$	3.26792	0.325170	0.162585	+	0.986695i	$0.448017\pi$
$102$	−1.67536	−0.165886
$103$	−5.71539	−0.563154	−0.281577	−	0.959539i	$-0.590857\pi$
$103$	−5.71539	−0.563154	−0.281577	+	0.959539i	$0.590857\pi$
$104$	−5.06170	−0.496340
$105$	−0.736249	−0.0718505
$106$	−3.94382	−0.383058
$107$	−0.0350723	−0.00339057	−0.00169528	−	0.999999i	$-0.500540\pi$
$107$	−0.0350723	−0.00339057	−0.00169528	+	0.999999i	$0.500540\pi$
$108$	1.56478	0.150571
$109$	−7.28146	−0.697438	−0.348719	−	0.937227i	$-0.613383\pi$
$109$	−7.28146	−0.697438	−0.348719	+	0.937227i	$0.613383\pi$
$110$	3.96936	0.378464
$111$	−6.50619	−0.617541
$112$	−1.16186	−0.109785
$113$	−7.03586	−0.661878	−0.330939	−	0.943652i	$-0.607365\pi$
$113$	−7.03586	−0.661878	−0.330939	+	0.943652i	$0.607365\pi$
$114$	−1.36089	−0.127459
$115$	−4.57814	−0.426914
$116$	9.62209	0.893389
$117$	2.15232	0.198982
$118$	3.58524	0.330048
$119$	−1.86972	−0.171397
$120$	−2.35174	−0.214683
$121$	25.2016	2.29105
$122$	1.18646	0.107417
$123$	4.61104	0.415763
$124$	−0.534331	−0.0479843
$125$	−1.00000	−0.0894427
$126$	−0.485715	−0.0432709
$127$	13.4065	1.18964	0.594818	−	0.803860i	$-0.297224\pi$
$127$	13.4065	1.18964	0.594818	+	0.803860i	$0.297224\pi$
$128$	−11.0711	−0.978556
$129$	−7.89193	−0.694846
$130$	−1.41992	−0.124535
$131$	−15.5603	−1.35951	−0.679756	−	0.733439i	$-0.737914\pi$
$131$	−15.5603	−1.35951	−0.679756	+	0.733439i	$0.737914\pi$
$132$	−9.41491	−0.819462
$133$	−1.51877	−0.131694
$134$	4.25341	0.367439
$135$	1.00000	0.0860663
$136$	−5.97230	−0.512120
$137$	−0.248932	−0.0212677	−0.0106338	−	0.999943i	$-0.503385\pi$
$137$	−0.248932	−0.0212677	−0.0106338	+	0.999943i	$0.503385\pi$
$138$	−3.02027	−0.257102
$139$	0.565959	0.0480041	0.0240020	−	0.999712i	$-0.492359\pi$
$139$	0.565959	0.0480041	0.0240020	+	0.999712i	$0.492359\pi$
$140$	−1.15206	−0.0973672
$141$	−9.07538	−0.764284
$142$	−8.52866	−0.715709
$143$	−12.9500	−1.08294
$144$	1.57807	0.131506
$145$	6.14918	0.510662
$146$	9.50162	0.786360
$147$	6.45794	0.532642
$148$	−10.1807	−0.836851
$149$	−7.00441	−0.573823	−0.286912	−	0.957957i	$-0.592629\pi$
$149$	−7.00441	−0.573823	−0.286912	+	0.957957i	$0.592629\pi$
$150$	−0.659715	−0.0538655
$151$	−18.8089	−1.53065	−0.765325	−	0.643644i	$-0.777422\pi$
$151$	−18.8089	−1.53065	−0.765325	+	0.643644i	$0.777422\pi$
$152$	−4.85128	−0.393491
$153$	2.53953	0.205308
$154$	2.92244	0.235497
$155$	−0.341475	−0.0274279
$156$	3.36790	0.269648
$157$	5.90708	0.471436	0.235718	−	0.971821i	$-0.424256\pi$
$157$	5.90708	0.471436	0.235718	+	0.971821i	$0.424256\pi$
$158$	−1.26289	−0.100470
$159$	5.97806	0.474091
$160$	−5.74455	−0.454147
$161$	−3.37065	−0.265644
$162$	0.659715	0.0518321
$163$	24.1257	1.88967	0.944834	−	0.327549i	$-0.106223\pi$
$163$	24.1257	1.88967	0.944834	+	0.327549i	$0.106223\pi$
$164$	7.21524	0.563416
$165$	−6.01678	−0.468405
$166$	−4.79982	−0.372538
$167$	−24.4414	−1.89133	−0.945667	−	0.325135i	$-0.894590\pi$
$167$	−24.4414	−1.89133	−0.945667	+	0.325135i	$0.894590\pi$
$168$	−1.73146	−0.133585
$169$	−8.36750	−0.643654
$170$	−1.67536	−0.128495
$171$	2.06285	0.157750
$172$	−12.3491	−0.941611
$173$	16.8160	1.27849	0.639247	−	0.769001i	$-0.279246\pi$
$173$	16.8160	1.27849	0.639247	+	0.769001i	$0.279246\pi$
$174$	4.05671	0.307538
$175$	−0.736249	−0.0556552
$176$	−9.49492	−0.715707
$177$	−5.43452	−0.408483
$178$	3.49580	0.262021
$179$	24.2686	1.81392	0.906959	−	0.421219i	$-0.138398\pi$
$179$	24.2686	1.81392	0.906959	+	0.421219i	$0.138398\pi$
$180$	1.56478	0.116631
$181$	6.21152	0.461698	0.230849	−	0.972990i	$-0.425850\pi$
$181$	6.21152	0.461698	0.230849	+	0.972990i	$0.425850\pi$
$182$	−1.04541	−0.0774913
$183$	−1.79844	−0.132944
$184$	−10.7666	−0.793723
$185$	−6.50619	−0.478345
$186$	−0.225276	−0.0165180
$187$	−15.2798	−1.11737
$188$	−14.2009	−1.03571
$189$	0.736249	0.0535542
$190$	−1.36089	−0.0987297
$191$	19.1418	1.38505	0.692526	−	0.721393i	$-0.256498\pi$
$191$	19.1418	1.38505	0.692526	+	0.721393i	$0.256498\pi$
$192$	−0.633622	−0.0457277
$193$	−25.9517	−1.86804	−0.934021	−	0.357218i	$-0.883725\pi$
$193$	−25.9517	−1.86804	−0.934021	+	0.357218i	$0.883725\pi$
$194$	−10.9260	−0.784438
$195$	2.15232	0.154131
$196$	10.1052	0.721802
$197$	−24.5585	−1.74972	−0.874859	−	0.484378i	$-0.839046\pi$
$197$	−24.5585	−1.74972	−0.874859	+	0.484378i	$0.839046\pi$
$198$	−3.96936	−0.282090
$199$	−12.8264	−0.909237	−0.454619	−	0.890686i	$-0.650224\pi$
$199$	−12.8264	−0.909237	−0.454619	+	0.890686i	$0.650224\pi$
$200$	−2.35174	−0.166293
$201$	−6.44734	−0.454760
$202$	2.15590	0.151688
$203$	4.52733	0.317756
$204$	3.97379	0.278221
$205$	4.61104	0.322049
$206$	−3.77053	−0.262705
$207$	4.57814	0.318203
$208$	3.39653	0.235507
$209$	−12.4117	−0.858536
$210$	−0.485715	−0.0335175
$211$	−27.5681	−1.89787	−0.948933	−	0.315478i	$-0.897835\pi$
$211$	−27.5681	−1.89787	−0.948933	+	0.315478i	$0.897835\pi$
$212$	9.35433	0.642458
$213$	12.9278	0.885797
$214$	−0.0231377	−0.00158166
$215$	−7.89193	−0.538225
$216$	2.35174	0.160015
$217$	−0.251410	−0.0170668
$218$	−4.80369	−0.325347
$219$	−14.4026	−0.973238
$220$	−9.41491	−0.634753
$221$	5.46588	0.367675
$222$	−4.29224	−0.288076
$223$	14.6293	0.979651	0.489826	−	0.871820i	$-0.337060\pi$
$223$	14.6293	0.979651	0.489826	+	0.871820i	$0.337060\pi$
$224$	−4.22942	−0.282590
$225$	1.00000	0.0666667
$226$	−4.64166	−0.308759
$227$	−15.3896	−1.02145	−0.510723	−	0.859745i	$-0.670622\pi$
$227$	−15.3896	−1.02145	−0.510723	+	0.859745i	$0.670622\pi$
$228$	3.22790	0.213773
$229$	21.9637	1.45140	0.725702	−	0.688009i	$-0.241515\pi$
$229$	21.9637	1.45140	0.725702	+	0.688009i	$0.241515\pi$
$230$	−3.02027	−0.199151
$231$	−4.42984	−0.291462
$232$	14.4613	0.949428
$233$	−17.6105	−1.15370	−0.576850	−	0.816850i	$-0.695718\pi$
$233$	−17.6105	−1.15370	−0.576850	+	0.816850i	$0.695718\pi$
$234$	1.41992	0.0928231
$235$	−9.07538	−0.592012
$236$	−8.50380	−0.553550
$237$	1.91430	0.124347
$238$	−1.23348	−0.0799549
$239$	−11.1883	−0.723713	−0.361857	−	0.932234i	$-0.617857\pi$
$239$	−11.1883	−0.723713	−0.361857	+	0.932234i	$0.617857\pi$
$240$	1.57807	0.101864
$241$	−14.4887	−0.933297	−0.466648	−	0.884443i	$-0.654539\pi$
$241$	−14.4887	−0.933297	−0.466648	+	0.884443i	$0.654539\pi$
$242$	16.6259	1.06875
$243$	−1.00000	−0.0641500
$244$	−2.81415	−0.180158
$245$	6.45794	0.412583
$246$	3.04197	0.193949
$247$	4.43992	0.282506
$248$	−0.803058	−0.0509943
$249$	7.27560	0.461072
$250$	−0.659715	−0.0417241
$251$	−10.0606	−0.635022	−0.317511	−	0.948255i	$-0.602847\pi$
$251$	−10.0606	−0.635022	−0.317511	+	0.948255i	$0.602847\pi$
$252$	1.15206	0.0725732
$253$	−27.5456	−1.73178
$254$	8.84449	0.554953
$255$	2.53953	0.159031
$256$	−8.57102	−0.535689
$257$	−22.6084	−1.41027	−0.705135	−	0.709073i	$-0.749114\pi$
$257$	−22.6084	−1.41027	−0.705135	+	0.709073i	$0.749114\pi$
$258$	−5.20643	−0.324138
$259$	−4.79018	−0.297647
$260$	3.36790	0.208868
$261$	−6.14918	−0.380625
$262$	−10.2654	−0.634197
$263$	8.06125	0.497078	0.248539	−	0.968622i	$-0.420050\pi$
$263$	8.06125	0.497078	0.248539	+	0.968622i	$0.420050\pi$
$264$	−14.1499	−0.870865
$265$	5.97806	0.367230
$266$	−1.00196	−0.0614339
$267$	−5.29895	−0.324291
$268$	−10.0886	−0.616262
$269$	4.48640	0.273541	0.136770	−	0.990603i	$-0.456328\pi$
$269$	4.48640	0.273541	0.136770	+	0.990603i	$0.456328\pi$
$270$	0.659715	0.0401490
$271$	10.0845	0.612588	0.306294	−	0.951937i	$-0.400911\pi$
$271$	10.0845	0.612588	0.306294	+	0.951937i	$0.400911\pi$
$272$	4.00756	0.242994
$273$	1.58465	0.0959071
$274$	−0.164224	−0.00992114
$275$	−6.01678	−0.362825
$276$	7.16376	0.431208
$277$	−31.2172	−1.87566	−0.937830	−	0.347095i	$-0.887168\pi$
$277$	−31.2172	−1.87566	−0.937830	+	0.347095i	$0.887168\pi$
$278$	0.373372	0.0223934
$279$	0.341475	0.0204435
$280$	−1.73146	−0.103475
$281$	23.9734	1.43013	0.715067	−	0.699056i	$-0.246396\pi$
$281$	23.9734	1.43013	0.715067	+	0.699056i	$0.246396\pi$
$282$	−5.98716	−0.356530
$283$	23.6262	1.40443	0.702216	−	0.711964i	$-0.252194\pi$
$283$	23.6262	1.40443	0.702216	+	0.711964i	$0.252194\pi$
$284$	20.2291	1.20038
$285$	2.06285	0.122193
$286$	−8.54335	−0.505179
$287$	3.39487	0.200393
$288$	5.74455	0.338501
$289$	−10.5508	−0.620636
$290$	4.05671	0.238218
$291$	16.5616	0.970860
$292$	−22.5368	−1.31887
$293$	15.0550	0.879525	0.439762	−	0.898114i	$-0.355063\pi$
$293$	15.0550	0.879525	0.439762	+	0.898114i	$0.355063\pi$
$294$	4.26040	0.248472
$295$	−5.43452	−0.316410
$296$	−15.3009	−0.889344
$297$	6.01678	0.349129
$298$	−4.62091	−0.267682
$299$	9.85363	0.569850
$300$	1.56478	0.0903424
$301$	−5.81043	−0.334907
$302$	−12.4085	−0.714032
$303$	−3.26792	−0.187737
$304$	3.25533	0.186706
$305$	−1.79844	−0.102978
$306$	1.67536	0.0957742
$307$	28.1580	1.60706	0.803530	−	0.595264i	$-0.202952\pi$
$307$	28.1580	1.60706	0.803530	+	0.595264i	$0.202952\pi$
$308$	−6.93171	−0.394971
$309$	5.71539	0.325137
$310$	−0.225276	−0.0127948
$311$	11.6336	0.659680	0.329840	−	0.944037i	$-0.393005\pi$
$311$	11.6336	0.659680	0.329840	+	0.944037i	$0.393005\pi$
$312$	5.06170	0.286562
$313$	18.7983	1.06254	0.531272	−	0.847201i	$-0.321714\pi$
$313$	18.7983	1.06254	0.531272	+	0.847201i	$0.321714\pi$
$314$	3.89699	0.219920
$315$	0.736249	0.0414829
$316$	2.99544	0.168507
$317$	−8.99643	−0.505290	−0.252645	−	0.967559i	$-0.581300\pi$
$317$	−8.99643	−0.505290	−0.252645	+	0.967559i	$0.581300\pi$
$318$	3.94382	0.221158
$319$	36.9983	2.07150
$320$	−0.633622	−0.0354205
$321$	0.0350723	0.00195754
$322$	−2.22367	−0.123920
$323$	5.23866	0.291487
$324$	−1.56478	−0.0869320
$325$	2.15232	0.119389
$326$	15.9161	0.881510
$327$	7.28146	0.402666
$328$	10.8439	0.598757
$329$	−6.68173	−0.368376
$330$	−3.96936	−0.218506
$331$	−7.02051	−0.385882	−0.192941	−	0.981210i	$-0.561803\pi$
$331$	−7.02051	−0.385882	−0.192941	+	0.981210i	$0.561803\pi$
$332$	11.3847	0.624815
$333$	6.50619	0.356537
$334$	−16.1244	−0.882287
$335$	−6.44734	−0.352256
$336$	1.16186	0.0633844
$337$	−25.0462	−1.36436	−0.682178	−	0.731186i	$-0.738967\pi$
$337$	−25.0462	−1.36436	−0.682178	+	0.731186i	$0.738967\pi$
$338$	−5.52017	−0.300258
$339$	7.03586	0.382135
$340$	3.97379	0.215509
$341$	−2.05458	−0.111262
$342$	1.36089	0.0735887
$343$	9.90839	0.535003
$344$	−18.5598	−1.00068
$345$	4.57814	0.246479
$346$	11.0938	0.596404
$347$	−12.4265	−0.667089	−0.333544	−	0.942734i	$-0.608245\pi$
$347$	−12.4265	−0.667089	−0.333544	+	0.942734i	$0.608245\pi$
$348$	−9.62209	−0.515798
$349$	−28.6543	−1.53383	−0.766914	−	0.641750i	$-0.778209\pi$
$349$	−28.6543	−1.53383	−0.766914	+	0.641750i	$0.778209\pi$
$350$	−0.485715	−0.0259625
$351$	−2.15232	−0.114883
$352$	−34.5637	−1.84225
$353$	9.10431	0.484574	0.242287	−	0.970205i	$-0.422103\pi$
$353$	9.10431	0.484574	0.242287	+	0.970205i	$0.422103\pi$
$354$	−3.58524	−0.190553
$355$	12.9278	0.686136
$356$	−8.29167	−0.439458
$357$	1.86972	0.0989562
$358$	16.0103	0.846173
$359$	25.9689	1.37058	0.685292	−	0.728268i	$-0.259674\pi$
$359$	25.9689	1.37058	0.685292	+	0.728268i	$0.259674\pi$
$360$	2.35174	0.123947
$361$	−14.7446	−0.776034
$362$	4.09783	0.215377
$363$	−25.2016	−1.32274
$364$	2.47961	0.129967
$365$	−14.4026	−0.753867
$366$	−1.18646	−0.0620171
$367$	−26.2352	−1.36947	−0.684733	−	0.728794i	$-0.740081\pi$
$367$	−26.2352	−1.36947	−0.684733	+	0.728794i	$0.740081\pi$
$368$	7.22464	0.376610
$369$	−4.61104	−0.240041
$370$	−4.29224	−0.223143
$371$	4.40134	0.228506
$372$	0.534331	0.0277038
$373$	9.99310	0.517423	0.258712	−	0.965955i	$-0.416702\pi$
$373$	9.99310	0.517423	0.258712	+	0.965955i	$0.416702\pi$
$374$	−10.0803	−0.521240
$375$	1.00000	0.0516398
$376$	−21.3429	−1.10068
$377$	−13.2350	−0.681639
$378$	0.485715	0.0249825
$379$	−2.98936	−0.153553	−0.0767765	−	0.997048i	$-0.524463\pi$
$379$	−2.98936	−0.153553	−0.0767765	+	0.997048i	$0.524463\pi$
$380$	3.22790	0.165588
$381$	−13.4065	−0.686837
$382$	12.6281	0.646111
$383$	25.4263	1.29922	0.649612	−	0.760266i	$-0.274931\pi$
$383$	25.4263	1.29922	0.649612	+	0.760266i	$0.274931\pi$
$384$	11.0711	0.564970
$385$	−4.42984	−0.225766
$386$	−17.1207	−0.871421
$387$	7.89193	0.401170
$388$	25.9152	1.31565
$389$	−27.0360	−1.37078	−0.685389	−	0.728177i	$-0.740368\pi$
$389$	−27.0360	−1.37078	−0.685389	+	0.728177i	$0.740368\pi$
$390$	1.41992	0.0719005
$391$	11.6263	0.587967
$392$	15.1874	0.767078
$393$	15.5603	0.784914
$394$	−16.2016	−0.816224
$395$	1.91430	0.0963187
$396$	9.41491	0.473117
$397$	5.44224	0.273138	0.136569	−	0.990631i	$-0.456392\pi$
$397$	5.44224	0.273138	0.136569	+	0.990631i	$0.456392\pi$
$398$	−8.46175	−0.424149
$399$	1.51877	0.0760337
$400$	1.57807	0.0789037
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−4.25341	−0.212141
$403$	0.734964	0.0366111
$404$	−5.11356	−0.254409
$405$	−1.00000	−0.0496904
$406$	2.98675	0.148230
$407$	−39.1463	−1.94041
$408$	5.97230	0.295673
$409$	−36.8843	−1.82381	−0.911905	−	0.410401i	$-0.865389\pi$
$409$	−36.8843	−1.82381	−0.911905	+	0.410401i	$0.865389\pi$
$410$	3.04197	0.150232
$411$	0.248932	0.0122789
$412$	8.94330	0.440605
$413$	−4.00116	−0.196884
$414$	3.02027	0.148438
$415$	7.27560	0.357145
$416$	12.3641	0.606202
$417$	−0.565959	−0.0277152
$418$	−8.18820	−0.400498
$419$	9.03503	0.441390	0.220695	−	0.975343i	$-0.429167\pi$
$419$	9.03503	0.441390	0.220695	+	0.975343i	$0.429167\pi$
$420$	1.15206	0.0562150
$421$	19.9685	0.973204	0.486602	−	0.873624i	$-0.338236\pi$
$421$	19.9685	0.973204	0.486602	+	0.873624i	$0.338236\pi$
$422$	−18.1871	−0.885334
$423$	9.07538	0.441260
$424$	14.0588	0.682757
$425$	2.53953	0.123185
$426$	8.52866	0.413215
$427$	−1.32410	−0.0640776
$428$	0.0548803	0.00265274
$429$	12.9500	0.625234
$430$	−5.20643	−0.251076
$431$	−12.8386	−0.618411	−0.309206	−	0.950995i	$-0.600063\pi$
$431$	−12.8386	−0.618411	−0.309206	+	0.950995i	$0.600063\pi$
$432$	−1.57807	−0.0759251
$433$	4.77843	0.229637	0.114818	−	0.993387i	$-0.463371\pi$
$433$	4.77843	0.229637	0.114818	+	0.993387i	$0.463371\pi$
$434$	−0.165859	−0.00796149
$435$	−6.14918	−0.294831
$436$	11.3939	0.545667
$437$	9.44402	0.451769
$438$	−9.50162	−0.454005
$439$	−16.1648	−0.771505	−0.385752	−	0.922602i	$-0.626058\pi$
$439$	−16.1648	−0.771505	−0.385752	+	0.922602i	$0.626058\pi$
$440$	−14.1499	−0.674569
$441$	−6.45794	−0.307521
$442$	3.60593	0.171516
$443$	−14.1469	−0.672139	−0.336069	−	0.941837i	$-0.609098\pi$
$443$	−14.1469	−0.672139	−0.336069	+	0.941837i	$0.609098\pi$
$444$	10.1807	0.483156
$445$	−5.29895	−0.251194
$446$	9.65118	0.456997
$447$	7.00441	0.331297
$448$	−0.466503	−0.0220402
$449$	−14.5404	−0.686206	−0.343103	−	0.939298i	$-0.611478\pi$
$449$	−14.5404	−0.686206	−0.343103	+	0.939298i	$0.611478\pi$
$450$	0.659715	0.0310993
$451$	27.7436	1.30639
$452$	11.0095	0.517845
$453$	18.8089	0.883721
$454$	−10.1528	−0.476493
$455$	1.58465	0.0742893
$456$	4.85128	0.227182
$457$	−0.642868	−0.0300721	−0.0150361	−	0.999887i	$-0.504786\pi$
$457$	−0.642868	−0.0300721	−0.0150361	+	0.999887i	$0.504786\pi$
$458$	14.4898	0.677064
$459$	−2.53953	−0.118535
$460$	7.16376	0.334012
$461$	19.0066	0.885225	0.442612	−	0.896713i	$-0.354052\pi$
$461$	19.0066	0.885225	0.442612	+	0.896713i	$0.354052\pi$
$462$	−2.92244	−0.135964
$463$	−20.4971	−0.952581	−0.476291	−	0.879288i	$-0.658019\pi$
$463$	−20.4971	−0.952581	−0.476291	+	0.879288i	$0.658019\pi$
$464$	−9.70386	−0.450491
$465$	0.341475	0.0158355
$466$	−11.6179	−0.538189
$467$	25.4042	1.17557	0.587784	−	0.809018i	$-0.300001\pi$
$467$	25.4042	1.17557	0.587784	+	0.809018i	$0.300001\pi$
$468$	−3.36790	−0.155681
$469$	−4.74685	−0.219189
$470$	−5.98716	−0.276167
$471$	−5.90708	−0.272184
$472$	−12.7806	−0.588273
$473$	−47.4840	−2.18332
$474$	1.26289	0.0580065
$475$	2.06285	0.0946501
$476$	2.92570	0.134099
$477$	−5.97806	−0.273717
$478$	−7.38112	−0.337605
$479$	15.6661	0.715801	0.357900	−	0.933760i	$-0.383493\pi$
$479$	15.6661	0.715801	0.357900	+	0.933760i	$0.383493\pi$
$480$	5.74455	0.262202
$481$	14.0034	0.638502
$482$	−9.55839	−0.435373
$483$	3.37065	0.153370
$484$	−39.4349	−1.79249
$485$	16.5616	0.752025
$486$	−0.659715	−0.0299253
$487$	−25.1474	−1.13954	−0.569768	−	0.821805i	$-0.692967\pi$
$487$	−25.1474	−1.13954	−0.569768	+	0.821805i	$0.692967\pi$
$488$	−4.22946	−0.191458
$489$	−24.1257	−1.09100
$490$	4.26040	0.192465
$491$	28.0493	1.26585	0.632924	−	0.774214i	$-0.281854\pi$
$491$	28.0493	1.26585	0.632924	+	0.774214i	$0.281854\pi$
$492$	−7.21524	−0.325288
$493$	−15.6160	−0.703309
$494$	2.92909	0.131786
$495$	6.01678	0.270434
$496$	0.538872	0.0241961
$497$	9.51807	0.426944
$498$	4.79982	0.215085
$499$	−29.2917	−1.31128	−0.655638	−	0.755075i	$-0.727600\pi$
$499$	−29.2917	−1.31128	−0.655638	+	0.755075i	$0.727600\pi$
$500$	1.56478	0.0699789
$501$	24.4414	1.09196
$502$	−6.63716	−0.296231
$503$	20.1470	0.898311	0.449155	−	0.893454i	$-0.351725\pi$
$503$	20.1470	0.898311	0.449155	+	0.893454i	$0.351725\pi$
$504$	1.73146	0.0771255
$505$	−3.26792	−0.145421
$506$	−18.1723	−0.807856
$507$	8.36750	0.371614
$508$	−20.9782	−0.930757
$509$	−14.0665	−0.623487	−0.311744	−	0.950166i	$-0.600913\pi$
$509$	−14.0665	−0.623487	−0.311744	+	0.950166i	$0.600913\pi$
$510$	1.67536	0.0741864
$511$	−10.6039	−0.469089
$512$	16.4878	0.728663
$513$	−2.06285	−0.0910771
$514$	−14.9151	−0.657876
$515$	5.71539	0.251850
$516$	12.3491	0.543639
$517$	−54.6045	−2.40150
$518$	−3.16015	−0.138849
$519$	−16.8160	−0.738139
$520$	5.06170	0.221970
$521$	−13.4838	−0.590736	−0.295368	−	0.955384i	$-0.595442\pi$
$521$	−13.4838	−0.590736	−0.295368	+	0.955384i	$0.595442\pi$
$522$	−4.05671	−0.177557
$523$	−32.9607	−1.44127	−0.720635	−	0.693315i	$-0.756149\pi$
$523$	−32.9607	−1.44127	−0.720635	+	0.693315i	$0.756149\pi$
$524$	24.3484	1.06366
$525$	0.736249	0.0321325
$526$	5.31813	0.231881
$527$	0.867183	0.0377751
$528$	9.49492	0.413213
$529$	−2.04066	−0.0887242
$530$	3.94382	0.171309
$531$	5.43452	0.235838
$532$	2.37654	0.103036
$533$	−9.92445	−0.429875
$534$	−3.49580	−0.151278
$535$	0.0350723	0.00151631
$536$	−15.1624	−0.654918
$537$	−24.2686	−1.04727
$538$	2.95975	0.127604
$539$	38.8560	1.67365
$540$	−1.56478	−0.0673372
$541$	−13.2669	−0.570391	−0.285195	−	0.958469i	$-0.592058\pi$
$541$	−13.2669	−0.570391	−0.285195	+	0.958469i	$0.592058\pi$
$542$	6.65288	0.285766
$543$	−6.21152	−0.266562
$544$	14.5884	0.625474
$545$	7.28146	0.311904
$546$	1.04541	0.0447396
$547$	36.8682	1.57637	0.788186	−	0.615437i	$-0.211021\pi$
$547$	36.8682	1.57637	0.788186	+	0.615437i	$0.211021\pi$
$548$	0.389522	0.0166396
$549$	1.79844	0.0767555
$550$	−3.96936	−0.169254
$551$	−12.6848	−0.540393
$552$	10.7666	0.458256
$553$	1.40940	0.0599337
$554$	−20.5945	−0.874975
$555$	6.50619	0.276173
$556$	−0.885600	−0.0375578
$557$	−13.1188	−0.555863	−0.277932	−	0.960601i	$-0.589649\pi$
$557$	−13.1188	−0.555863	−0.277932	+	0.960601i	$0.589649\pi$
$558$	0.225276	0.00953669
$559$	16.9860	0.718431
$560$	1.16186	0.0490973
$561$	15.2798	0.645112
$562$	15.8156	0.667142
$563$	−19.4308	−0.818912	−0.409456	−	0.912330i	$-0.634281\pi$
$563$	−19.4308	−0.818912	−0.409456	+	0.912330i	$0.634281\pi$
$564$	14.2009	0.597967
$565$	7.03586	0.296001
$566$	15.5866	0.655153
$567$	−0.736249	−0.0309195
$568$	30.4028	1.27567
$569$	−34.0749	−1.42850	−0.714248	−	0.699893i	$-0.753231\pi$
$569$	−34.0749	−1.42850	−0.714248	+	0.699893i	$0.753231\pi$
$570$	1.36089	0.0570016
$571$	5.08662	0.212868	0.106434	−	0.994320i	$-0.466057\pi$
$571$	5.08662	0.212868	0.106434	+	0.994320i	$0.466057\pi$
$572$	20.2639	0.847277
$573$	−19.1418	−0.799660
$574$	2.23965	0.0934811
$575$	4.57814	0.190922
$576$	0.633622	0.0264009
$577$	−0.681504	−0.0283714	−0.0141857	−	0.999899i	$-0.504516\pi$
$577$	−0.681504	−0.0283714	−0.0141857	+	0.999899i	$0.504516\pi$
$578$	−6.96053	−0.289520
$579$	25.9517	1.07851
$580$	−9.62209	−0.399535
$581$	5.35665	0.222231
$582$	10.9260	0.452896
$583$	35.9687	1.48967
$584$	−33.8711	−1.40160
$585$	−2.15232	−0.0889876
$586$	9.93204	0.410289
$587$	−6.49631	−0.268131	−0.134066	−	0.990972i	$-0.542803\pi$
$587$	−6.49631	−0.268131	−0.134066	+	0.990972i	$0.542803\pi$
$588$	−10.1052	−0.416732
$589$	0.704411	0.0290248
$590$	−3.58524	−0.147602
$591$	24.5585	1.01020
$592$	10.2673	0.421982
$593$	−33.4387	−1.37316	−0.686581	−	0.727053i	$-0.740889\pi$
$593$	−33.4387	−1.37316	−0.686581	+	0.727053i	$0.740889\pi$
$594$	3.96936	0.162865
$595$	1.86972	0.0766511
$596$	10.9603	0.448952
$597$	12.8264	0.524948
$598$	6.50059	0.265829
$599$	−39.0186	−1.59426	−0.797129	−	0.603809i	$-0.793649\pi$
$599$	−39.0186	−1.59426	−0.797129	+	0.603809i	$0.793649\pi$
$600$	2.35174	0.0960093
$601$	−15.5310	−0.633524	−0.316762	−	0.948505i	$-0.602596\pi$
$601$	−15.5310	−0.633524	−0.316762	+	0.948505i	$0.602596\pi$
$602$	−3.83323	−0.156231
$603$	6.44734	0.262556
$604$	29.4318	1.19756
$605$	−25.2016	−1.02459
$606$	−2.15590	−0.0875773
$607$	−18.1975	−0.738612	−0.369306	−	0.929308i	$-0.620405\pi$
$607$	−18.1975	−0.738612	−0.369306	+	0.929308i	$0.620405\pi$
$608$	11.8502	0.480587
$609$	−4.52733	−0.183457
$610$	−1.18646	−0.0480383
$611$	19.5331	0.790226
$612$	−3.97379	−0.160631
$613$	23.4670	0.947822	0.473911	−	0.880573i	$-0.342842\pi$
$613$	23.4670	0.947822	0.473911	+	0.880573i	$0.342842\pi$
$614$	18.5763	0.749676
$615$	−4.61104	−0.185935
$616$	−10.4178	−0.419746
$617$	33.0052	1.32874	0.664371	−	0.747403i	$-0.268700\pi$
$617$	33.0052	1.32874	0.664371	+	0.747403i	$0.268700\pi$
$618$	3.77053	0.151673
$619$	23.2956	0.936329	0.468164	−	0.883641i	$-0.344915\pi$
$619$	23.2956	0.936329	0.468164	+	0.883641i	$0.344915\pi$
$620$	0.534331	0.0214593
$621$	−4.57814	−0.183714
$622$	7.67485	0.307734
$623$	−3.90135	−0.156304
$624$	−3.39653	−0.135970
$625$	1.00000	0.0400000
$626$	12.4015	0.495666
$627$	12.4117	0.495676
$628$	−9.24326	−0.368846
$629$	16.5226	0.658801
$630$	0.485715	0.0193513
$631$	−15.7838	−0.628342	−0.314171	−	0.949366i	$-0.601726\pi$
$631$	−15.7838	−0.628342	−0.314171	+	0.949366i	$0.601726\pi$
$632$	4.50192	0.179077
$633$	27.5681	1.09573
$634$	−5.93508	−0.235712
$635$	−13.4065	−0.532022
$636$	−9.35433	−0.370923
$637$	−13.8996	−0.550721
$638$	24.4083	0.966334
$639$	−12.9278	−0.511415
$640$	11.0711	0.437624
$641$	−14.9462	−0.590341	−0.295171	−	0.955445i	$-0.595377\pi$
$641$	−14.9462	−0.590341	−0.295171	+	0.955445i	$0.595377\pi$
$642$	0.0231377	0.000913174 0
$643$	34.8508	1.37438	0.687190	−	0.726477i	$-0.258844\pi$
$643$	34.8508	1.37438	0.687190	+	0.726477i	$0.258844\pi$
$644$	5.27431	0.207837
$645$	7.89193	0.310745
$646$	3.45603	0.135976
$647$	4.01643	0.157902	0.0789512	−	0.996878i	$-0.474843\pi$
$647$	4.01643	0.157902	0.0789512	+	0.996878i	$0.474843\pi$
$648$	−2.35174	−0.0923850
$649$	−32.6983	−1.28352
$650$	1.41992	0.0556939
$651$	0.251410	0.00985354
$652$	−37.7513	−1.47845
$653$	−19.1046	−0.747621	−0.373810	−	0.927505i	$-0.621949\pi$
$653$	−19.1046	−0.747621	−0.373810	+	0.927505i	$0.621949\pi$
$654$	4.80369	0.187839
$655$	15.5603	0.607992
$656$	−7.27656	−0.284102
$657$	14.4026	0.561899
$658$	−4.40804	−0.171843
$659$	2.30189	0.0896688	0.0448344	−	0.998994i	$-0.485724\pi$
$659$	2.30189	0.0896688	0.0448344	+	0.998994i	$0.485724\pi$
$660$	9.41491	0.366475
$661$	32.5842	1.26738	0.633689	−	0.773588i	$-0.281540\pi$
$661$	32.5842	1.26738	0.633689	+	0.773588i	$0.281540\pi$
$662$	−4.63154	−0.180010
$663$	−5.46588	−0.212277
$664$	17.1103	0.664008
$665$	1.51877	0.0588954
$666$	4.29224	0.166321
$667$	−28.1518	−1.09004
$668$	38.2454	1.47976
$669$	−14.6293	−0.565602
$670$	−4.25341	−0.164324
$671$	−10.8208	−0.417733
$672$	4.22942	0.163153
$673$	1.18365	0.0456262	0.0228131	−	0.999740i	$-0.492738\pi$
$673$	1.18365	0.0456262	0.0228131	+	0.999740i	$0.492738\pi$
$674$	−16.5234	−0.636457
$675$	−1.00000	−0.0384900
$676$	13.0933	0.503587
$677$	−42.3637	−1.62817	−0.814084	−	0.580747i	$-0.802761\pi$
$677$	−42.3637	−1.62817	−0.814084	+	0.580747i	$0.802761\pi$
$678$	4.64166	0.178262
$679$	12.1935	0.467943
$680$	5.97230	0.229027
$681$	15.3896	0.589732
$682$	−1.35544	−0.0519023
$683$	−18.9658	−0.725705	−0.362852	−	0.931847i	$-0.618197\pi$
$683$	−18.9658	−0.725705	−0.362852	+	0.931847i	$0.618197\pi$
$684$	−3.22790	−0.123422
$685$	0.248932	0.00951119
$686$	6.53672	0.249573
$687$	−21.9637	−0.837969
$688$	12.4541	0.474807
$689$	−12.8667	−0.490183
$690$	3.02027	0.114980
$691$	42.9619	1.63435	0.817174	−	0.576391i	$-0.195539\pi$
$691$	42.9619	1.63435	0.817174	+	0.576391i	$0.195539\pi$
$692$	−26.3132	−1.00028
$693$	4.42984	0.168276
$694$	−8.19794	−0.311190
$695$	−0.565959	−0.0214681
$696$	−14.4613	−0.548153
$697$	−11.7099	−0.443542
$698$	−18.9037	−0.715514
$699$	17.6105	0.666089
$700$	1.15206	0.0435439
$701$	7.30544	0.275923	0.137961	−	0.990438i	$-0.455945\pi$
$701$	7.30544	0.275923	0.137961	+	0.990438i	$0.455945\pi$
$702$	−1.41992	−0.0535915
$703$	13.4213	0.506194
$704$	−3.81236	−0.143684
$705$	9.07538	0.341798
$706$	6.00625	0.226048
$707$	−2.40600	−0.0904870
$708$	8.50380	0.319592
$709$	15.9347	0.598441	0.299220	−	0.954184i	$-0.403273\pi$
$709$	15.9347	0.598441	0.299220	+	0.954184i	$0.403273\pi$
$710$	8.52866	0.320075
$711$	−1.91430	−0.0717917
$712$	−12.4617	−0.467023
$713$	1.56332	0.0585467
$714$	1.23348	0.0461620
$715$	12.9500	0.484304
$716$	−37.9749	−1.41919
$717$	11.1883	0.417836
$718$	17.1321	0.639363
$719$	−47.1152	−1.75710	−0.878551	−	0.477649i	$-0.841489\pi$
$719$	−47.1152	−1.75710	−0.878551	+	0.477649i	$0.841489\pi$
$720$	−1.57807	−0.0588114
$721$	4.20795	0.156712
$722$	−9.72727	−0.362011
$723$	14.4887	0.538839
$724$	−9.71963	−0.361227
$725$	−6.14918	−0.228375
$726$	−16.6259	−0.617044
$727$	−18.4200	−0.683160	−0.341580	−	0.939853i	$-0.610962\pi$
$727$	−18.4200	−0.683160	−0.341580	+	0.939853i	$0.610962\pi$
$728$	3.72667	0.138120
$729$	1.00000	0.0370370
$730$	−9.50162	−0.351671
$731$	20.0418	0.741272
$732$	2.81415	0.104014
$733$	−45.0175	−1.66276	−0.831380	−	0.555704i	$-0.812449\pi$
$733$	−45.0175	−1.66276	−0.831380	+	0.555704i	$0.812449\pi$
$734$	−17.3078	−0.638841
$735$	−6.45794	−0.238205
$736$	26.2994	0.969407
$737$	−38.7922	−1.42893
$738$	−3.04197	−0.111977
$739$	35.6292	1.31064	0.655321	−	0.755350i	$-0.272533\pi$
$739$	35.6292	1.31064	0.655321	+	0.755350i	$0.272533\pi$
$740$	10.1807	0.374251
$741$	−4.43992	−0.163105
$742$	2.90363	0.106596
$743$	−26.5332	−0.973408	−0.486704	−	0.873567i	$-0.661801\pi$
$743$	−26.5332	−0.973408	−0.486704	+	0.873567i	$0.661801\pi$
$744$	0.803058	0.0294415
$745$	7.00441	0.256622
$746$	6.59260	0.241372
$747$	−7.27560	−0.266200
$748$	23.9094	0.874214
$749$	0.0258219	0.000943513 0
$750$	0.659715	0.0240894
$751$	43.7649	1.59700	0.798501	−	0.601993i	$-0.205627\pi$
$751$	43.7649	1.59700	0.798501	+	0.601993i	$0.205627\pi$
$752$	14.3216	0.522256
$753$	10.0606	0.366630
$754$	−8.73135	−0.317977
$755$	18.8089	0.684527
$756$	−1.15206	−0.0419002
$757$	−18.3736	−0.667800	−0.333900	−	0.942609i	$-0.608365\pi$
$757$	−18.3736	−0.667800	−0.333900	+	0.942609i	$0.608365\pi$
$758$	−1.97212	−0.0716308
$759$	27.5456	0.999843
$760$	4.85128	0.175975
$761$	−9.85743	−0.357332	−0.178666	−	0.983910i	$-0.557178\pi$
$761$	−9.85743	−0.357332	−0.178666	+	0.983910i	$0.557178\pi$
$762$	−8.84449	−0.320402
$763$	5.36097	0.194080
$764$	−29.9526	−1.08365
$765$	−2.53953	−0.0918168
$766$	16.7741	0.606074
$767$	11.6968	0.422348
$768$	8.57102	0.309280
$769$	29.1539	1.05132	0.525659	−	0.850695i	$-0.323819\pi$
$769$	29.1539	1.05132	0.525659	+	0.850695i	$0.323819\pi$
$770$	−2.92244	−0.105317
$771$	22.6084	0.814220
$772$	40.6085	1.46153
$773$	24.1330	0.868002	0.434001	−	0.900912i	$-0.357101\pi$
$773$	24.1330	0.868002	0.434001	+	0.900912i	$0.357101\pi$
$774$	5.20643	0.187141
$775$	0.341475	0.0122661
$776$	38.9486	1.39817
$777$	4.79018	0.171847
$778$	−17.8360	−0.639453
$779$	−9.51189	−0.340799
$780$	−3.36790	−0.120590
$781$	77.7836	2.78332
$782$	7.67005	0.274280
$783$	6.14918	0.219754
$784$	−10.1911	−0.363968
$785$	−5.90708	−0.210833
$786$	10.2654	0.366154
$787$	−27.5006	−0.980289	−0.490145	−	0.871641i	$-0.663056\pi$
$787$	−27.5006	−0.980289	−0.490145	+	0.871641i	$0.663056\pi$
$788$	38.4285	1.36896
$789$	−8.06125	−0.286988
$790$	1.26289	0.0449316
$791$	5.18014	0.184185
$792$	14.1499	0.502794
$793$	3.87082	0.137457
$794$	3.59033	0.127416
$795$	−5.97806	−0.212020
$796$	20.0704	0.711376
$797$	17.6308	0.624516	0.312258	−	0.949997i	$-0.398915\pi$
$797$	17.6308	0.624516	0.312258	+	0.949997i	$0.398915\pi$
$798$	1.00196	0.0354689
$799$	23.0472	0.815350
$800$	5.74455	0.203101
$801$	5.29895	0.187229
$802$	−0.659715	−0.0232954
$803$	−86.6573	−3.05807
$804$	10.0886	0.355799
$805$	3.37065	0.118800
$806$	0.484867	0.0170787
$807$	−4.48640	−0.157929
$808$	−7.68529	−0.270368
$809$	29.4275	1.03461	0.517307	−	0.855800i	$-0.326934\pi$
$809$	29.4275	1.03461	0.517307	+	0.855800i	$0.326934\pi$
$810$	−0.659715	−0.0231800
$811$	28.8591	1.01338	0.506690	−	0.862129i	$-0.330869\pi$
$811$	28.8591	1.01338	0.506690	+	0.862129i	$0.330869\pi$
$812$	−7.08425	−0.248608
$813$	−10.0845	−0.353678
$814$	−25.8254	−0.905181
$815$	−24.1257	−0.845085
$816$	−4.00756	−0.140293
$817$	16.2799	0.569561
$818$	−24.3331	−0.850788
$819$	−1.58465	−0.0553720
$820$	−7.21524	−0.251967
$821$	−31.3571	−1.09437	−0.547184	−	0.837012i	$-0.684300\pi$
$821$	−31.3571	−1.09437	−0.547184	+	0.837012i	$0.684300\pi$
$822$	0.164224	0.00572797
$823$	49.5080	1.72574	0.862870	−	0.505426i	$-0.168665\pi$
$823$	49.5080	1.72574	0.862870	+	0.505426i	$0.168665\pi$
$824$	13.4411	0.468243
$825$	6.01678	0.209477
$826$	−2.63962	−0.0918443
$827$	−9.91708	−0.344851	−0.172425	−	0.985023i	$-0.555160\pi$
$827$	−9.91708	−0.344851	−0.172425	+	0.985023i	$0.555160\pi$
$828$	−7.16376	−0.248958
$829$	16.9706	0.589413	0.294706	−	0.955588i	$-0.404778\pi$
$829$	16.9706	0.589413	0.294706	+	0.955588i	$0.404778\pi$
$830$	4.79982	0.166604
$831$	31.2172	1.08291
$832$	1.36376	0.0472799
$833$	−16.4001	−0.568230
$834$	−0.373372	−0.0129288
$835$	24.4414	0.845831
$836$	19.4215	0.671708
$837$	−0.341475	−0.0118031
$838$	5.96055	0.205904
$839$	−30.0963	−1.03904	−0.519520	−	0.854458i	$-0.673889\pi$
$839$	−30.0963	−1.03904	−0.519520	+	0.854458i	$0.673889\pi$
$840$	1.73146	0.0597412
$841$	8.81243	0.303877
$842$	13.1735	0.453989
$843$	−23.9734	−0.825688
$844$	43.1379	1.48487
$845$	8.36750	0.287851
$846$	5.98716	0.205843
$847$	−18.5546	−0.637545
$848$	−9.43383	−0.323959
$849$	−23.6262	−0.810850
$850$	1.67536	0.0574645
$851$	29.7862	1.02106
$852$	−20.2291	−0.693037
$853$	49.4068	1.69166	0.845829	−	0.533455i	$-0.179107\pi$
$853$	49.4068	1.69166	0.845829	+	0.533455i	$0.179107\pi$
$854$	−0.873528	−0.0298915
$855$	−2.06285	−0.0705480
$856$	0.0824808	0.00281914
$857$	47.4108	1.61952	0.809762	−	0.586759i	$-0.199596\pi$
$857$	47.4108	1.61952	0.809762	+	0.586759i	$0.199596\pi$
$858$	8.54335	0.291665
$859$	31.7475	1.08321	0.541605	−	0.840633i	$-0.317817\pi$
$859$	31.7475	1.08321	0.541605	+	0.840633i	$0.317817\pi$
$860$	12.3491	0.421101
$861$	−3.39487	−0.115697
$862$	−8.46979	−0.288482
$863$	−32.0155	−1.08982	−0.544910	−	0.838495i	$-0.683436\pi$
$863$	−32.0155	−1.08982	−0.544910	+	0.838495i	$0.683436\pi$
$864$	−5.74455	−0.195434
$865$	−16.8160	−0.571760
$866$	3.15240	0.107123
$867$	10.5508	0.358324
$868$	0.393401	0.0133529
$869$	11.5179	0.390718
$870$	−4.05671	−0.137535
$871$	13.8768	0.470196
$872$	17.1241	0.579895
$873$	−16.5616	−0.560526
$874$	6.23036	0.210745
$875$	0.736249	0.0248897
$876$	22.5368	0.761449
$877$	−16.2874	−0.549986	−0.274993	−	0.961446i	$-0.588675\pi$
$877$	−16.2874	−0.549986	−0.274993	+	0.961446i	$0.588675\pi$
$878$	−10.6642	−0.359899
$879$	−15.0550	−0.507794
$880$	9.49492	0.320074
$881$	30.4633	1.02633	0.513167	−	0.858289i	$-0.328472\pi$
$881$	30.4633	1.02633	0.513167	+	0.858289i	$0.328472\pi$
$882$	−4.26040	−0.143455
$883$	30.7316	1.03420	0.517101	−	0.855924i	$-0.327011\pi$
$883$	30.7316	1.03420	0.517101	+	0.855924i	$0.327011\pi$
$884$	−8.55288	−0.287664
$885$	5.43452	0.182679
$886$	−9.33292	−0.313545
$887$	−44.1990	−1.48406	−0.742029	−	0.670368i	$-0.766136\pi$
$887$	−44.1990	−1.48406	−0.742029	+	0.670368i	$0.766136\pi$
$888$	15.3009	0.513463
$889$	−9.87053	−0.331047
$890$	−3.49580	−0.117179
$891$	−6.01678	−0.201570
$892$	−22.8916	−0.766467
$893$	18.7211	0.626479
$894$	4.62091	0.154546
$895$	−24.2686	−0.811209
$896$	8.15108	0.272309
$897$	−9.85363	−0.329003
$898$	−9.59255	−0.320108
$899$	−2.09979	−0.0700319
$900$	−1.56478	−0.0521592
$901$	−15.1814	−0.505767
$902$	18.3029	0.609419
$903$	5.81043	0.193359
$904$	16.5465	0.550328
$905$	−6.21152	−0.206478
$906$	12.4085	0.412246
$907$	−19.3366	−0.642060	−0.321030	−	0.947069i	$-0.604029\pi$
$907$	−19.3366	−0.642060	−0.321030	+	0.947069i	$0.604029\pi$
$908$	24.0813	0.799167
$909$	3.26792	0.108390
$910$	1.04541	0.0346552
$911$	−27.6230	−0.915189	−0.457595	−	0.889161i	$-0.651289\pi$
$911$	−27.6230	−0.915189	−0.457595	+	0.889161i	$0.651289\pi$
$912$	−3.25533	−0.107795
$913$	43.7756	1.44876
$914$	−0.424110	−0.0140283
$915$	1.79844	0.0594546
$916$	−34.3683	−1.13556
$917$	11.4563	0.378319
$918$	−1.67536	−0.0552953
$919$	−11.5703	−0.381671	−0.190835	−	0.981622i	$-0.561120\pi$
$919$	−11.5703	−0.381671	−0.190835	+	0.981622i	$0.561120\pi$
$920$	10.7666	0.354964
$921$	−28.1580	−0.927837
$922$	12.5389	0.412948
$923$	−27.8248	−0.915864
$924$	6.93171	0.228037
$925$	6.50619	0.213922
$926$	−13.5223	−0.444369
$927$	−5.71539	−0.187718
$928$	−35.3243	−1.15958
$929$	3.99658	0.131124	0.0655618	−	0.997849i	$-0.479116\pi$
$929$	3.99658	0.131124	0.0655618	+	0.997849i	$0.479116\pi$
$930$	0.225276	0.00738709
$931$	−13.3218	−0.436603
$932$	27.5564	0.902641
$933$	−11.6336	−0.380866
$934$	16.7596	0.548390
$935$	15.2798	0.499702
$936$	−5.06170	−0.165447
$937$	32.8731	1.07392	0.536959	−	0.843608i	$-0.319573\pi$
$937$	32.8731	1.07392	0.536959	+	0.843608i	$0.319573\pi$
$938$	−3.13157	−0.102249
$939$	−18.7983	−0.613460
$940$	14.2009	0.463183
$941$	41.7455	1.36086	0.680431	−	0.732812i	$-0.261792\pi$
$941$	41.7455	1.36086	0.680431	+	0.732812i	$0.261792\pi$
$942$	−3.89699	−0.126971
$943$	−21.1100	−0.687435
$944$	8.57607	0.279127
$945$	−0.736249	−0.0239502
$946$	−31.3259	−1.01849
$947$	30.7893	1.00052	0.500258	−	0.865876i	$-0.333238\pi$
$947$	30.7893	1.00052	0.500258	+	0.865876i	$0.333238\pi$
$948$	−2.99544	−0.0972875
$949$	30.9991	1.00627
$950$	1.36089	0.0441532
$951$	8.99643	0.291729
$952$	4.39710	0.142511
$953$	12.2328	0.396260	0.198130	−	0.980176i	$-0.436513\pi$
$953$	12.2328	0.396260	0.198130	+	0.980176i	$0.436513\pi$
$954$	−3.94382	−0.127686
$955$	−19.1418	−0.619414
$956$	17.5072	0.566225
$957$	−36.9983	−1.19598
$958$	10.3351	0.333913
$959$	0.183276	0.00591828
$960$	0.633622	0.0204501
$961$	−30.8834	−0.996239
$962$	9.23828	0.297854
$963$	−0.0350723	−0.00113019
$964$	22.6715	0.730200
$965$	25.9517	0.835414
$966$	2.22367	0.0715453
$967$	1.32450	0.0425931	0.0212965	−	0.999773i	$-0.493221\pi$
$967$	1.32450	0.0425931	0.0212965	+	0.999773i	$0.493221\pi$
$968$	−59.2676	−1.90493
$969$	−5.23866	−0.168290
$970$	10.9260	0.350811
$971$	−27.5867	−0.885299	−0.442649	−	0.896695i	$-0.645961\pi$
$971$	−27.5867	−0.885299	−0.442649	+	0.896695i	$0.645961\pi$
$972$	1.56478	0.0501902
$973$	−0.416687	−0.0133584
$974$	−16.5901	−0.531581
$975$	−2.15232	−0.0689295
$976$	2.83807	0.0908444
$977$	−44.8062	−1.43348	−0.716739	−	0.697342i	$-0.754366\pi$
$977$	−44.8062	−1.43348	−0.716739	+	0.697342i	$0.754366\pi$
$978$	−15.9161	−0.508940
$979$	−31.8826	−1.01897
$980$	−10.1052	−0.322800
$981$	−7.28146	−0.232479
$982$	18.5046	0.590505
$983$	50.8512	1.62190	0.810951	−	0.585114i	$-0.198950\pi$
$983$	50.8512	1.62190	0.810951	+	0.585114i	$0.198950\pi$
$984$	−10.8439	−0.345692
$985$	24.5585	0.782497
$986$	−10.3021	−0.328086
$987$	6.68173	0.212682
$988$	−6.94748	−0.221029
$989$	36.1304	1.14888
$990$	3.96936	0.126155
$991$	23.5385	0.747725	0.373862	−	0.927484i	$-0.378033\pi$
$991$	23.5385	0.747725	0.373862	+	0.927484i	$0.378033\pi$
$992$	1.96162	0.0622815
$993$	7.02051	0.222789
$994$	6.27921	0.199165
$995$	12.8264	0.406623
$996$	−11.3847	−0.360737
$997$	−44.5180	−1.40990	−0.704949	−	0.709258i	$-0.749030\pi$
$997$	−44.5180	−1.40990	−0.704949	+	0.709258i	$0.749030\pi$
$998$	−19.3242	−0.611696
$999$	−6.50619	−0.205847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.23	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.23	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.659715 q^{2} -1.00000 q^{3} -1.56478 q^{4} -1.00000 q^{5} -0.659715 q^{6} -0.736249 q^{7} -2.35174 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.659715 q^{2} -1.00000 q^{3} -1.56478 q^{4} -1.00000 q^{5} -0.659715 q^{6} -0.736249 q^{7} -2.35174 q^{8} +1.00000 q^{9} -0.659715 q^{10} -6.01678 q^{11} +1.56478 q^{12} +2.15232 q^{13} -0.485715 q^{14} +1.00000 q^{15} +1.57807 q^{16} +2.53953 q^{17} +0.659715 q^{18} +2.06285 q^{19} +1.56478 q^{20} +0.736249 q^{21} -3.96936 q^{22} +4.57814 q^{23} +2.35174 q^{24} +1.00000 q^{25} +1.41992 q^{26} -1.00000 q^{27} +1.15206 q^{28} -6.14918 q^{29} +0.659715 q^{30} +0.341475 q^{31} +5.74455 q^{32} +6.01678 q^{33} +1.67536 q^{34} +0.736249 q^{35} -1.56478 q^{36} +6.50619 q^{37} +1.36089 q^{38} -2.15232 q^{39} +2.35174 q^{40} -4.61104 q^{41} +0.485715 q^{42} +7.89193 q^{43} +9.41491 q^{44} -1.00000 q^{45} +3.02027 q^{46} +9.07538 q^{47} -1.57807 q^{48} -6.45794 q^{49} +0.659715 q^{50} -2.53953 q^{51} -3.36790 q^{52} -5.97806 q^{53} -0.659715 q^{54} +6.01678 q^{55} +1.73146 q^{56} -2.06285 q^{57} -4.05671 q^{58} +5.43452 q^{59} -1.56478 q^{60} +1.79844 q^{61} +0.225276 q^{62} -0.736249 q^{63} +0.633622 q^{64} -2.15232 q^{65} +3.96936 q^{66} +6.44734 q^{67} -3.97379 q^{68} -4.57814 q^{69} +0.485715 q^{70} -12.9278 q^{71} -2.35174 q^{72} +14.4026 q^{73} +4.29224 q^{74} -1.00000 q^{75} -3.22790 q^{76} +4.42984 q^{77} -1.41992 q^{78} -1.91430 q^{79} -1.57807 q^{80} +1.00000 q^{81} -3.04197 q^{82} -7.27560 q^{83} -1.15206 q^{84} -2.53953 q^{85} +5.20643 q^{86} +6.14918 q^{87} +14.1499 q^{88} +5.29895 q^{89} -0.659715 q^{90} -1.58465 q^{91} -7.16376 q^{92} -0.341475 q^{93} +5.98716 q^{94} -2.06285 q^{95} -5.74455 q^{96} -16.5616 q^{97} -4.26040 q^{98} -6.01678 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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