LMFDB - Embedded newform 8027.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54714 q^{2} -2.88541 q^{3} +4.48790 q^{4} -0.694174 q^{5} +7.34952 q^{6} -2.36870 q^{7} -6.33703 q^{8} +5.32557 q^{9} +O(q^{10})$	\(q-2.54714 q^{2} -2.88541 q^{3} +4.48790 q^{4} -0.694174 q^{5} +7.34952 q^{6} -2.36870 q^{7} -6.33703 q^{8} +5.32557 q^{9} +1.76816 q^{10} -0.794152 q^{11} -12.9494 q^{12} +0.522974 q^{13} +6.03339 q^{14} +2.00297 q^{15} +7.16547 q^{16} -6.07751 q^{17} -13.5649 q^{18} -3.32141 q^{19} -3.11538 q^{20} +6.83465 q^{21} +2.02281 q^{22} +1.00000 q^{23} +18.2849 q^{24} -4.51812 q^{25} -1.33209 q^{26} -6.71021 q^{27} -10.6305 q^{28} -0.799079 q^{29} -5.10185 q^{30} +1.65499 q^{31} -5.57738 q^{32} +2.29145 q^{33} +15.4803 q^{34} +1.64429 q^{35} +23.9006 q^{36} +4.52254 q^{37} +8.46009 q^{38} -1.50899 q^{39} +4.39900 q^{40} +10.2687 q^{41} -17.4088 q^{42} -6.15720 q^{43} -3.56408 q^{44} -3.69687 q^{45} -2.54714 q^{46} -1.18525 q^{47} -20.6753 q^{48} -1.38928 q^{49} +11.5083 q^{50} +17.5361 q^{51} +2.34706 q^{52} -4.39377 q^{53} +17.0918 q^{54} +0.551280 q^{55} +15.0105 q^{56} +9.58362 q^{57} +2.03536 q^{58} +6.08038 q^{59} +8.98915 q^{60} -3.94642 q^{61} -4.21549 q^{62} -12.6146 q^{63} -0.124608 q^{64} -0.363035 q^{65} -5.83664 q^{66} +2.22677 q^{67} -27.2753 q^{68} -2.88541 q^{69} -4.18822 q^{70} +3.92421 q^{71} -33.7483 q^{72} -10.7360 q^{73} -11.5195 q^{74} +13.0366 q^{75} -14.9062 q^{76} +1.88111 q^{77} +3.84361 q^{78} +7.28378 q^{79} -4.97408 q^{80} +3.38497 q^{81} -26.1559 q^{82} +8.99554 q^{83} +30.6732 q^{84} +4.21885 q^{85} +15.6832 q^{86} +2.30567 q^{87} +5.03257 q^{88} -0.433974 q^{89} +9.41643 q^{90} -1.23877 q^{91} +4.48790 q^{92} -4.77532 q^{93} +3.01899 q^{94} +2.30564 q^{95} +16.0930 q^{96} +8.99224 q^{97} +3.53869 q^{98} -4.22931 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.54714	−1.80110	−0.900549	−	0.434755i	$-0.856835\pi$
$2$	−2.54714	−1.80110	−0.900549	+	0.434755i	$0.856835\pi$
$3$	−2.88541	−1.66589	−0.832945	−	0.553356i	$-0.813347\pi$
$3$	−2.88541	−1.66589	−0.832945	+	0.553356i	$0.813347\pi$
$4$	4.48790	2.24395
$5$	−0.694174	−0.310444	−0.155222	−	0.987880i	$-0.549609\pi$
$5$	−0.694174	−0.310444	−0.155222	+	0.987880i	$0.549609\pi$
$6$	7.34952	3.00043
$7$	−2.36870	−0.895283	−0.447641	−	0.894213i	$-0.647736\pi$
$7$	−2.36870	−0.895283	−0.447641	+	0.894213i	$0.647736\pi$
$8$	−6.33703	−2.24048
$9$	5.32557	1.77519
$10$	1.76816	0.559140
$11$	−0.794152	−0.239446	−0.119723	−	0.992807i	$-0.538201\pi$
$11$	−0.794152	−0.239446	−0.119723	+	0.992807i	$0.538201\pi$
$12$	−12.9494	−3.73818
$13$	0.522974	0.145047	0.0725235	−	0.997367i	$-0.476895\pi$
$13$	0.522974	0.145047	0.0725235	+	0.997367i	$0.476895\pi$
$14$	6.03339	1.61249
$15$	2.00297	0.517165
$16$	7.16547	1.79137
$17$	−6.07751	−1.47401	−0.737007	−	0.675886i	$-0.763761\pi$
$17$	−6.07751	−1.47401	−0.737007	+	0.675886i	$0.763761\pi$
$18$	−13.5649	−3.19729
$19$	−3.32141	−0.761984	−0.380992	−	0.924578i	$-0.624418\pi$
$19$	−3.32141	−0.761984	−0.380992	+	0.924578i	$0.624418\pi$
$20$	−3.11538	−0.696621
$21$	6.83465	1.49144
$22$	2.02281	0.431266
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	18.2849	3.73239
$25$	−4.51812	−0.903625
$26$	−1.33209	−0.261244
$27$	−6.71021	−1.29138
$28$	−10.6305	−2.00897
$29$	−0.799079	−0.148385	−0.0741926	−	0.997244i	$-0.523638\pi$
$29$	−0.799079	−0.148385	−0.0741926	+	0.997244i	$0.523638\pi$
$30$	−5.10185	−0.931465
$31$	1.65499	0.297245	0.148623	−	0.988894i	$-0.452516\pi$
$31$	1.65499	0.297245	0.148623	+	0.988894i	$0.452516\pi$
$32$	−5.57738	−0.985950
$33$	2.29145	0.398891
$34$	15.4803	2.65484
$35$	1.64429	0.277935
$36$	23.9006	3.98344
$37$	4.52254	0.743501	0.371751	−	0.928333i	$-0.378758\pi$
$37$	4.52254	0.743501	0.371751	+	0.928333i	$0.378758\pi$
$38$	8.46009	1.37241
$39$	−1.50899	−0.241632
$40$	4.39900	0.695543
$41$	10.2687	1.60371	0.801854	−	0.597520i	$-0.203847\pi$
$41$	10.2687	1.60371	0.801854	+	0.597520i	$0.203847\pi$
$42$	−17.4088	−2.68623
$43$	−6.15720	−0.938963	−0.469482	−	0.882942i	$-0.655559\pi$
$43$	−6.15720	−0.938963	−0.469482	+	0.882942i	$0.655559\pi$
$44$	−3.56408	−0.537305
$45$	−3.69687	−0.551097
$46$	−2.54714	−0.375555
$47$	−1.18525	−0.172886	−0.0864431	−	0.996257i	$-0.527550\pi$
$47$	−1.18525	−0.172886	−0.0864431	+	0.996257i	$0.527550\pi$
$48$	−20.6753	−2.98422
$49$	−1.38928	−0.198469
$50$	11.5083	1.62752
$51$	17.5361	2.45554
$52$	2.34706	0.325478
$53$	−4.39377	−0.603530	−0.301765	−	0.953382i	$-0.597576\pi$
$53$	−4.39377	−0.603530	−0.301765	+	0.953382i	$0.597576\pi$
$54$	17.0918	2.32590
$55$	0.551280	0.0743345
$56$	15.0105	2.00586
$57$	9.58362	1.26938
$58$	2.03536	0.267256
$59$	6.08038	0.791599	0.395799	−	0.918337i	$-0.370468\pi$
$59$	6.08038	0.791599	0.395799	+	0.918337i	$0.370468\pi$
$60$	8.98915	1.16049
$61$	−3.94642	−0.505287	−0.252644	−	0.967559i	$-0.581300\pi$
$61$	−3.94642	−0.505287	−0.252644	+	0.967559i	$0.581300\pi$
$62$	−4.21549	−0.535367
$63$	−12.6146	−1.58930
$64$	−0.124608	−0.0155760
$65$	−0.363035	−0.0450289
$66$	−5.83664	−0.718441
$67$	2.22677	0.272043	0.136022	−	0.990706i	$-0.456568\pi$
$67$	2.22677	0.272043	0.136022	+	0.990706i	$0.456568\pi$
$68$	−27.2753	−3.30761
$69$	−2.88541	−0.347362
$70$	−4.18822	−0.500588
$71$	3.92421	0.465718	0.232859	−	0.972510i	$-0.425192\pi$
$71$	3.92421	0.465718	0.232859	+	0.972510i	$0.425192\pi$
$72$	−33.7483	−3.97727
$73$	−10.7360	−1.25656	−0.628280	−	0.777988i	$-0.716241\pi$
$73$	−10.7360	−1.25656	−0.628280	+	0.777988i	$0.716241\pi$
$74$	−11.5195	−1.33912
$75$	13.0366	1.50534
$76$	−14.9062	−1.70986
$77$	1.88111	0.214372
$78$	3.84361	0.435203
$79$	7.28378	0.819489	0.409745	−	0.912200i	$-0.365618\pi$
$79$	7.28378	0.819489	0.409745	+	0.912200i	$0.365618\pi$
$80$	−4.97408	−0.556119
$81$	3.38497	0.376108
$82$	−26.1559	−2.88843
$83$	8.99554	0.987389	0.493695	−	0.869635i	$-0.335646\pi$
$83$	8.99554	0.987389	0.493695	+	0.869635i	$0.335646\pi$
$84$	30.6732	3.34673
$85$	4.21885	0.457598
$86$	15.6832	1.69116
$87$	2.30567	0.247194
$88$	5.03257	0.536474
$89$	−0.433974	−0.0460011	−0.0230006	−	0.999735i	$-0.507322\pi$
$89$	−0.433974	−0.0460011	−0.0230006	+	0.999735i	$0.507322\pi$
$90$	9.41643	0.992579
$91$	−1.23877	−0.129858
$92$	4.48790	0.467896
$93$	−4.77532	−0.495177
$94$	3.01899	0.311385
$95$	2.30564	0.236553
$96$	16.0930	1.64248
$97$	8.99224	0.913024	0.456512	−	0.889717i	$-0.349099\pi$
$97$	8.99224	0.913024	0.456512	+	0.889717i	$0.349099\pi$
$98$	3.53869	0.357462
$99$	−4.22931	−0.425062
$100$	−20.2769	−2.02769
$101$	−2.35425	−0.234256	−0.117128	−	0.993117i	$-0.537369\pi$
$101$	−2.35425	−0.234256	−0.117128	+	0.993117i	$0.537369\pi$
$102$	−44.6668	−4.42267
$103$	−10.3906	−1.02382	−0.511908	−	0.859040i	$-0.671061\pi$
$103$	−10.3906	−1.02382	−0.511908	+	0.859040i	$0.671061\pi$
$104$	−3.31410	−0.324975
$105$	−4.74443	−0.463009
$106$	11.1915	1.08702
$107$	−6.05919	−0.585764	−0.292882	−	0.956149i	$-0.594614\pi$
$107$	−6.05919	−0.585764	−0.292882	+	0.956149i	$0.594614\pi$
$108$	−30.1148	−2.89780
$109$	−6.31753	−0.605110	−0.302555	−	0.953132i	$-0.597840\pi$
$109$	−6.31753	−0.605110	−0.302555	+	0.953132i	$0.597840\pi$
$110$	−1.40418	−0.133884
$111$	−13.0494	−1.23859
$112$	−16.9728	−1.60378
$113$	13.7127	1.28998	0.644992	−	0.764189i	$-0.276861\pi$
$113$	13.7127	1.28998	0.644992	+	0.764189i	$0.276861\pi$
$114$	−24.4108	−2.28628
$115$	−0.694174	−0.0647320
$116$	−3.58619	−0.332969
$117$	2.78513	0.257486
$118$	−15.4876	−1.42575
$119$	14.3958	1.31966
$120$	−12.6929	−1.15870
$121$	−10.3693	−0.942666
$122$	10.0521	0.910071
$123$	−29.6295	−2.67160
$124$	7.42744	0.667004
$125$	6.60723	0.590969
$126$	32.1312	2.86248
$127$	3.83557	0.340352	0.170176	−	0.985414i	$-0.445566\pi$
$127$	3.83557	0.340352	0.170176	+	0.985414i	$0.445566\pi$
$128$	11.4721	1.01400
$129$	17.7660	1.56421
$130$	0.924699	0.0811015
$131$	−4.38379	−0.383013	−0.191507	−	0.981491i	$-0.561337\pi$
$131$	−4.38379	−0.383013	−0.191507	+	0.981491i	$0.561337\pi$
$132$	10.2838	0.895091
$133$	7.86741	0.682191
$134$	−5.67188	−0.489976
$135$	4.65805	0.400901
$136$	38.5134	3.30249
$137$	−16.4694	−1.40708	−0.703538	−	0.710658i	$-0.748398\pi$
$137$	−16.4694	−1.40708	−0.703538	+	0.710658i	$0.748398\pi$
$138$	7.34952	0.625633
$139$	18.1794	1.54196	0.770979	−	0.636861i	$-0.219767\pi$
$139$	18.1794	1.54196	0.770979	+	0.636861i	$0.219767\pi$
$140$	7.37940	0.623673
$141$	3.41992	0.288009
$142$	−9.99550	−0.838804
$143$	−0.415321	−0.0347309
$144$	38.1602	3.18002
$145$	0.554700	0.0460653
$146$	27.3462	2.26319
$147$	4.00864	0.330627
$148$	20.2967	1.66838
$149$	14.1234	1.15704	0.578518	−	0.815670i	$-0.303631\pi$
$149$	14.1234	1.15704	0.578518	+	0.815670i	$0.303631\pi$
$150$	−33.2060	−2.71126
$151$	9.21476	0.749887	0.374943	−	0.927048i	$-0.377662\pi$
$151$	9.21476	0.749887	0.374943	+	0.927048i	$0.377662\pi$
$152$	21.0479	1.70721
$153$	−32.3662	−2.61665
$154$	−4.79143	−0.386105
$155$	−1.14885	−0.0922779
$156$	−6.77221	−0.542211
$157$	−22.0463	−1.75949	−0.879743	−	0.475449i	$-0.842285\pi$
$157$	−22.0463	−1.75949	−0.879743	+	0.475449i	$0.842285\pi$
$158$	−18.5528	−1.47598
$159$	12.6778	1.00541
$160$	3.87167	0.306082
$161$	−2.36870	−0.186679
$162$	−8.62198	−0.677407
$163$	6.76252	0.529682	0.264841	−	0.964292i	$-0.414681\pi$
$163$	6.76252	0.529682	0.264841	+	0.964292i	$0.414681\pi$
$164$	46.0851	3.59864
$165$	−1.59067	−0.123833
$166$	−22.9129	−1.77838
$167$	12.9626	1.00308	0.501538	−	0.865136i	$-0.332768\pi$
$167$	12.9626	1.00308	0.501538	+	0.865136i	$0.332768\pi$
$168$	−43.3114	−3.34154
$169$	−12.7265	−0.978961
$170$	−10.7460	−0.824179
$171$	−17.6884	−1.35267
$172$	−27.6329	−2.10699
$173$	−8.97654	−0.682473	−0.341237	−	0.939977i	$-0.610846\pi$
$173$	−8.97654	−0.682473	−0.341237	+	0.939977i	$0.610846\pi$
$174$	−5.87285	−0.445220
$175$	10.7021	0.808999
$176$	−5.69048	−0.428936
$177$	−17.5444	−1.31872
$178$	1.10539	0.0828525
$179$	0.882180	0.0659372	0.0329686	−	0.999456i	$-0.489504\pi$
$179$	0.882180	0.0659372	0.0329686	+	0.999456i	$0.489504\pi$
$180$	−16.5912	−1.23663
$181$	−4.83719	−0.359545	−0.179773	−	0.983708i	$-0.557536\pi$
$181$	−4.83719	−0.359545	−0.179773	+	0.983708i	$0.557536\pi$
$182$	3.15531	0.233887
$183$	11.3870	0.841753
$184$	−6.33703	−0.467172
$185$	−3.13943	−0.230815
$186$	12.1634	0.891863
$187$	4.82647	0.352946
$188$	−5.31928	−0.387948
$189$	15.8944	1.15615
$190$	−5.87277	−0.426056
$191$	7.98853	0.578030	0.289015	−	0.957325i	$-0.406672\pi$
$191$	7.98853	0.578030	0.289015	+	0.957325i	$0.406672\pi$
$192$	0.359544	0.0259479
$193$	−15.6239	−1.12463	−0.562317	−	0.826922i	$-0.690090\pi$
$193$	−15.6239	−1.12463	−0.562317	+	0.826922i	$0.690090\pi$
$194$	−22.9045	−1.64444
$195$	1.04750	0.0750133
$196$	−6.23497	−0.445355
$197$	−10.0004	−0.712503	−0.356251	−	0.934390i	$-0.615945\pi$
$197$	−10.0004	−0.712503	−0.356251	+	0.934390i	$0.615945\pi$
$198$	10.7726	0.765578
$199$	22.2594	1.57792	0.788962	−	0.614442i	$-0.210619\pi$
$199$	22.2594	1.57792	0.788962	+	0.614442i	$0.210619\pi$
$200$	28.6315	2.02455
$201$	−6.42513	−0.453194
$202$	5.99659	0.421918
$203$	1.89277	0.132847
$204$	78.7003	5.51012
$205$	−7.12829	−0.497861
$206$	26.4663	1.84399
$207$	5.32557	0.370153
$208$	3.74736	0.259832
$209$	2.63771	0.182454
$210$	12.0847	0.833925
$211$	4.34070	0.298826	0.149413	−	0.988775i	$-0.452262\pi$
$211$	4.34070	0.298826	0.149413	+	0.988775i	$0.452262\pi$
$212$	−19.7188	−1.35429
$213$	−11.3229	−0.775835
$214$	15.4336	1.05502
$215$	4.27416	0.291496
$216$	42.5228	2.89331
$217$	−3.92017	−0.266118
$218$	16.0916	1.08986
$219$	30.9779	2.09329
$220$	2.47409	0.166803
$221$	−3.17838	−0.213801
$222$	33.2385	2.23082
$223$	−4.99528	−0.334509	−0.167254	−	0.985914i	$-0.553490\pi$
$223$	−4.99528	−0.334509	−0.167254	+	0.985914i	$0.553490\pi$
$224$	13.2111	0.882704
$225$	−24.0616	−1.60410
$226$	−34.9282	−2.32339
$227$	28.9306	1.92019	0.960096	−	0.279672i	$-0.0902256\pi$
$227$	28.9306	1.92019	0.960096	+	0.279672i	$0.0902256\pi$
$228$	43.0104	2.84843
$229$	12.4665	0.823808	0.411904	−	0.911227i	$-0.364864\pi$
$229$	12.4665	0.823808	0.411904	+	0.911227i	$0.364864\pi$
$230$	1.76816	0.116589
$231$	−5.42775	−0.357120
$232$	5.06379	0.332454
$233$	27.6255	1.80981	0.904904	−	0.425615i	$-0.139942\pi$
$233$	27.6255	1.80981	0.904904	+	0.425615i	$0.139942\pi$
$234$	−7.09412	−0.463757
$235$	0.822768	0.0536715
$236$	27.2882	1.77631
$237$	−21.0167	−1.36518
$238$	−36.6680	−2.37683
$239$	−12.1757	−0.787583	−0.393792	−	0.919200i	$-0.628837\pi$
$239$	−12.1757	−0.787583	−0.393792	+	0.919200i	$0.628837\pi$
$240$	14.3522	0.926434
$241$	25.1792	1.62193	0.810966	−	0.585093i	$-0.198942\pi$
$241$	25.1792	1.62193	0.810966	+	0.585093i	$0.198942\pi$
$242$	26.4121	1.69783
$243$	10.3636	0.664826
$244$	−17.7111	−1.13384
$245$	0.964403	0.0616135
$246$	75.4703	4.81181
$247$	−1.73701	−0.110523
$248$	−10.4877	−0.665971
$249$	−25.9558	−1.64488
$250$	−16.8295	−1.06439
$251$	9.07553	0.572843	0.286421	−	0.958104i	$-0.407534\pi$
$251$	9.07553	0.572843	0.286421	+	0.958104i	$0.407534\pi$
$252$	−56.6133	−3.56630
$253$	−0.794152	−0.0499279
$254$	−9.76971	−0.613006
$255$	−12.1731	−0.762309
$256$	−28.9719	−1.81074
$257$	−20.7942	−1.29711	−0.648553	−	0.761169i	$-0.724626\pi$
$257$	−20.7942	−1.29711	−0.648553	+	0.761169i	$0.724626\pi$
$258$	−45.2524	−2.81729
$259$	−10.7125	−0.665644
$260$	−1.62927	−0.101043
$261$	−4.25555	−0.263412
$262$	11.1661	0.689844
$263$	14.3358	0.883983	0.441991	−	0.897019i	$-0.354272\pi$
$263$	14.3358	0.883983	0.441991	+	0.897019i	$0.354272\pi$
$264$	−14.5210	−0.893706
$265$	3.05004	0.187362
$266$	−20.0394	−1.22869
$267$	1.25219	0.0766328
$268$	9.99352	0.610452
$269$	1.61117	0.0982351	0.0491175	−	0.998793i	$-0.484359\pi$
$269$	1.61117	0.0982351	0.0491175	+	0.998793i	$0.484359\pi$
$270$	−11.8647	−0.722062
$271$	5.26602	0.319888	0.159944	−	0.987126i	$-0.448869\pi$
$271$	5.26602	0.319888	0.159944	+	0.987126i	$0.448869\pi$
$272$	−43.5482	−2.64050
$273$	3.57434	0.216329
$274$	41.9498	2.53428
$275$	3.58808	0.216369
$276$	−12.9494	−0.779464
$277$	3.36416	0.202133	0.101067	−	0.994880i	$-0.467775\pi$
$277$	3.36416	0.202133	0.101067	+	0.994880i	$0.467775\pi$
$278$	−46.3054	−2.77722
$279$	8.81376	0.527666
$280$	−10.4199	−0.622708
$281$	4.96381	0.296116	0.148058	−	0.988979i	$-0.452698\pi$
$281$	4.96381	0.296116	0.148058	+	0.988979i	$0.452698\pi$
$282$	−8.71101	−0.518733
$283$	−31.1497	−1.85166	−0.925828	−	0.377946i	$-0.876630\pi$
$283$	−31.1497	−1.85166	−0.925828	+	0.377946i	$0.876630\pi$
$284$	17.6115	1.04505
$285$	−6.65270	−0.394072
$286$	1.05788	0.0625537
$287$	−24.3235	−1.43577
$288$	−29.7027	−1.75025
$289$	19.9362	1.17271
$290$	−1.41290	−0.0829681
$291$	−25.9463	−1.52100
$292$	−48.1823	−2.81966
$293$	9.87381	0.576834	0.288417	−	0.957505i	$-0.406871\pi$
$293$	9.87381	0.576834	0.288417	+	0.957505i	$0.406871\pi$
$294$	−10.2106	−0.595492
$295$	−4.22084	−0.245747
$296$	−28.6595	−1.66580
$297$	5.32893	0.309216
$298$	−35.9743	−2.08393
$299$	0.522974	0.0302444
$300$	58.5071	3.37791
$301$	14.5845	0.840638
$302$	−23.4713	−1.35062
$303$	6.79296	0.390245
$304$	−23.7995	−1.36499
$305$	2.73950	0.156863
$306$	82.4411	4.71285
$307$	18.5329	1.05773	0.528863	−	0.848707i	$-0.322618\pi$
$307$	18.5329	1.05773	0.528863	+	0.848707i	$0.322618\pi$
$308$	8.44222	0.481040
$309$	29.9811	1.70556
$310$	2.92628	0.166202
$311$	14.5794	0.826723	0.413361	−	0.910567i	$-0.364355\pi$
$311$	14.5794	0.826723	0.413361	+	0.910567i	$0.364355\pi$
$312$	9.56253	0.541372
$313$	−10.5729	−0.597615	−0.298807	−	0.954313i	$-0.596589\pi$
$313$	−10.5729	−0.597615	−0.298807	+	0.954313i	$0.596589\pi$
$314$	56.1549	3.16901
$315$	8.75676	0.493387
$316$	32.6889	1.83889
$317$	16.4549	0.924199	0.462100	−	0.886828i	$-0.347096\pi$
$317$	16.4549	0.924199	0.462100	+	0.886828i	$0.347096\pi$
$318$	−32.2921	−1.81085
$319$	0.634591	0.0355303
$320$	0.0864995	0.00483547
$321$	17.4832	0.975818
$322$	6.03339	0.336228
$323$	20.1859	1.12317
$324$	15.1914	0.843968
$325$	−2.36286	−0.131068
$326$	−17.2251	−0.954008
$327$	18.2286	1.00805
$328$	−65.0733	−3.59307
$329$	2.80749	0.154782
$330$	4.05164	0.223036
$331$	−23.4495	−1.28890	−0.644449	−	0.764647i	$-0.722913\pi$
$331$	−23.4495	−1.28890	−0.644449	+	0.764647i	$0.722913\pi$
$332$	40.3711	2.21565
$333$	24.0851	1.31986
$334$	−33.0175	−1.80664
$335$	−1.54576	−0.0844541
$336$	48.9735	2.67172
$337$	4.85759	0.264610	0.132305	−	0.991209i	$-0.457762\pi$
$337$	4.85759	0.264610	0.132305	+	0.991209i	$0.457762\pi$
$338$	32.4161	1.76320
$339$	−39.5668	−2.14897
$340$	18.9338	1.02683
$341$	−1.31431	−0.0711741
$342$	45.0548	2.43628
$343$	19.8717	1.07297
$344$	39.0183	2.10373
$345$	2.00297	0.107836
$346$	22.8645	1.22920
$347$	−4.40639	−0.236547	−0.118274	−	0.992981i	$-0.537736\pi$
$347$	−4.40639	−0.236547	−0.118274	+	0.992981i	$0.537736\pi$
$348$	10.3476	0.554690
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−27.2596	−1.45709
$351$	−3.50927	−0.187311
$352$	4.42929	0.236082
$353$	28.5706	1.52066	0.760330	−	0.649536i	$-0.225037\pi$
$353$	28.5706	1.52066	0.760330	+	0.649536i	$0.225037\pi$
$354$	44.6879	2.37514
$355$	−2.72408	−0.144579
$356$	−1.94763	−0.103224
$357$	−41.5377	−2.19841
$358$	−2.24703	−0.118759
$359$	13.5407	0.714653	0.357326	−	0.933980i	$-0.383688\pi$
$359$	13.5407	0.714653	0.357326	+	0.933980i	$0.383688\pi$
$360$	23.4272	1.23472
$361$	−7.96822	−0.419380
$362$	12.3210	0.647576
$363$	29.9197	1.57038
$364$	−5.55946	−0.291395
$365$	7.45268	0.390091
$366$	−29.0043	−1.51608
$367$	28.6936	1.49779	0.748896	−	0.662687i	$-0.230584\pi$
$367$	28.6936	1.49779	0.748896	+	0.662687i	$0.230584\pi$
$368$	7.16547	0.373526
$369$	54.6869	2.84688
$370$	7.99656	0.415721
$371$	10.4075	0.540330
$372$	−21.4312	−1.11115
$373$	23.1724	1.19982	0.599912	−	0.800066i	$-0.295202\pi$
$373$	23.1724	1.19982	0.599912	+	0.800066i	$0.295202\pi$
$374$	−12.2937	−0.635691
$375$	−19.0645	−0.984489
$376$	7.51095	0.387348
$377$	−0.417898	−0.0215228
$378$	−40.4853	−2.08234
$379$	−1.47311	−0.0756688	−0.0378344	−	0.999284i	$-0.512046\pi$
$379$	−1.47311	−0.0756688	−0.0378344	+	0.999284i	$0.512046\pi$
$380$	10.3475	0.530814
$381$	−11.0672	−0.566988
$382$	−20.3479	−1.04109
$383$	−21.7035	−1.10899	−0.554497	−	0.832185i	$-0.687089\pi$
$383$	−21.7035	−1.10899	−0.554497	+	0.832185i	$0.687089\pi$
$384$	−33.1018	−1.68922
$385$	−1.30581	−0.0665504
$386$	39.7962	2.02557
$387$	−32.7906	−1.66684
$388$	40.3563	2.04878
$389$	33.3760	1.69223	0.846116	−	0.532999i	$-0.178935\pi$
$389$	33.3760	1.69223	0.846116	+	0.532999i	$0.178935\pi$
$390$	−2.66813	−0.135106
$391$	−6.07751	−0.307353
$392$	8.80393	0.444665
$393$	12.6490	0.638058
$394$	25.4725	1.28329
$395$	−5.05621	−0.254405
$396$	−18.9807	−0.953819
$397$	−7.98219	−0.400615	−0.200307	−	0.979733i	$-0.564194\pi$
$397$	−7.98219	−0.400615	−0.200307	+	0.979733i	$0.564194\pi$
$398$	−56.6976	−2.84200
$399$	−22.7007	−1.13646
$400$	−32.3745	−1.61872
$401$	−2.61344	−0.130509	−0.0652544	−	0.997869i	$-0.520786\pi$
$401$	−2.61344	−0.130509	−0.0652544	+	0.997869i	$0.520786\pi$
$402$	16.3657	0.816246
$403$	0.865517	0.0431145
$404$	−10.5656	−0.525660
$405$	−2.34976	−0.116760
$406$	−4.82116	−0.239270
$407$	−3.59159	−0.178028
$408$	−111.127	−5.50159
$409$	18.1535	0.897632	0.448816	−	0.893624i	$-0.351846\pi$
$409$	18.1535	0.897632	0.448816	+	0.893624i	$0.351846\pi$
$410$	18.1567	0.896697
$411$	47.5209	2.34403
$412$	−46.6320	−2.29739
$413$	−14.4026	−0.708705
$414$	−13.5649	−0.666681
$415$	−6.24447	−0.306529
$416$	−2.91682	−0.143009
$417$	−52.4550	−2.56873
$418$	−6.71860	−0.328618
$419$	−7.58081	−0.370347	−0.185173	−	0.982706i	$-0.559285\pi$
$419$	−7.58081	−0.370347	−0.185173	+	0.982706i	$0.559285\pi$
$420$	−21.2926	−1.03897
$421$	31.6502	1.54253	0.771267	−	0.636511i	$-0.219623\pi$
$421$	31.6502	1.54253	0.771267	+	0.636511i	$0.219623\pi$
$422$	−11.0564	−0.538215
$423$	−6.31212	−0.306906
$424$	27.8434	1.35220
$425$	27.4589	1.33195
$426$	28.8411	1.39736
$427$	9.34786	0.452375
$428$	−27.1931	−1.31443
$429$	1.19837	0.0578579
$430$	−10.8869	−0.525012
$431$	−9.21968	−0.444097	−0.222048	−	0.975036i	$-0.571274\pi$
$431$	−9.21968	−0.444097	−0.222048	+	0.975036i	$0.571274\pi$
$432$	−48.0818	−2.31334
$433$	1.24487	0.0598246	0.0299123	−	0.999553i	$-0.490477\pi$
$433$	1.24487	0.0598246	0.0299123	+	0.999553i	$0.490477\pi$
$434$	9.98520	0.479305
$435$	−1.60053	−0.0767397
$436$	−28.3525	−1.35784
$437$	−3.32141	−0.158885
$438$	−78.9048	−3.77022
$439$	6.96633	0.332485	0.166242	−	0.986085i	$-0.446837\pi$
$439$	6.96633	0.332485	0.166242	+	0.986085i	$0.446837\pi$
$440$	−3.49348	−0.166545
$441$	−7.39872	−0.352320
$442$	8.09577	0.385077
$443$	15.0226	0.713745	0.356872	−	0.934153i	$-0.383843\pi$
$443$	15.0226	0.713745	0.356872	+	0.934153i	$0.383843\pi$
$444$	−58.5643	−2.77934
$445$	0.301253	0.0142808
$446$	12.7237	0.602482
$447$	−40.7518	−1.92749
$448$	0.295158	0.0139449
$449$	−3.09371	−0.146001	−0.0730007	−	0.997332i	$-0.523258\pi$
$449$	−3.09371	−0.146001	−0.0730007	+	0.997332i	$0.523258\pi$
$450$	61.2881	2.88915
$451$	−8.15494	−0.384001
$452$	61.5414	2.89466
$453$	−26.5883	−1.24923
$454$	−73.6902	−3.45845
$455$	0.859919	0.0403136
$456$	−60.7317	−2.84402
$457$	2.36480	0.110621	0.0553103	−	0.998469i	$-0.482385\pi$
$457$	2.36480	0.110621	0.0553103	+	0.998469i	$0.482385\pi$
$458$	−31.7538	−1.48376
$459$	40.7814	1.90351
$460$	−3.11538	−0.145256
$461$	−17.3156	−0.806466	−0.403233	−	0.915097i	$-0.632114\pi$
$461$	−17.3156	−0.806466	−0.403233	+	0.915097i	$0.632114\pi$
$462$	13.8252	0.643208
$463$	−15.3467	−0.713223	−0.356612	−	0.934253i	$-0.616068\pi$
$463$	−15.3467	−0.713223	−0.356612	+	0.934253i	$0.616068\pi$
$464$	−5.72578	−0.265813
$465$	3.31490	0.153725
$466$	−70.3660	−3.25964
$467$	40.0437	1.85300	0.926501	−	0.376293i	$-0.122801\pi$
$467$	40.0437	1.85300	0.926501	+	0.376293i	$0.122801\pi$
$468$	12.4994	0.577786
$469$	−5.27454	−0.243555
$470$	−2.09570	−0.0966676
$471$	63.6125	2.93111
$472$	−38.5316	−1.77356
$473$	4.88975	0.224831
$474$	53.5323	2.45882
$475$	15.0065	0.688548
$476$	64.6068	2.96125
$477$	−23.3993	−1.07138
$478$	31.0133	1.41851
$479$	−1.41744	−0.0647643	−0.0323822	−	0.999476i	$-0.510309\pi$
$479$	−1.41744	−0.0647643	−0.0323822	+	0.999476i	$0.510309\pi$
$480$	−11.1713	−0.509899
$481$	2.36517	0.107843
$482$	−64.1348	−2.92126
$483$	6.83465	0.310987
$484$	−46.5365	−2.11530
$485$	−6.24218	−0.283443
$486$	−26.3975	−1.19742
$487$	26.0790	1.18175	0.590875	−	0.806763i	$-0.298783\pi$
$487$	26.0790	1.18175	0.590875	+	0.806763i	$0.298783\pi$
$488$	25.0086	1.13208
$489$	−19.5126	−0.882392
$490$	−2.45647	−0.110972
$491$	14.2551	0.643325	0.321662	−	0.946854i	$-0.395758\pi$
$491$	14.2551	0.643325	0.321662	+	0.946854i	$0.395758\pi$
$492$	−132.974	−5.99494
$493$	4.85641	0.218722
$494$	4.42441	0.199064
$495$	2.93588	0.131958
$496$	11.8588	0.532475
$497$	−9.29526	−0.416950
$498$	66.1130	2.96259
$499$	−9.37244	−0.419568	−0.209784	−	0.977748i	$-0.567276\pi$
$499$	−9.37244	−0.419568	−0.209784	+	0.977748i	$0.567276\pi$
$500$	29.6526	1.32611
$501$	−37.4023	−1.67101
$502$	−23.1166	−1.03175
$503$	5.14615	0.229455	0.114728	−	0.993397i	$-0.463400\pi$
$503$	5.14615	0.229455	0.114728	+	0.993397i	$0.463400\pi$
$504$	79.9394	3.56078
$505$	1.63426	0.0727234
$506$	2.02281	0.0899251
$507$	36.7211	1.63084
$508$	17.2137	0.763733
$509$	−28.2448	−1.25193	−0.625965	−	0.779851i	$-0.715295\pi$
$509$	−28.2448	−1.25193	−0.625965	+	0.779851i	$0.715295\pi$
$510$	31.0065	1.37299
$511$	25.4304	1.12498
$512$	50.8511	2.24732
$513$	22.2874	0.984011
$514$	52.9657	2.33621
$515$	7.21287	0.317837
$516$	79.7321	3.51001
$517$	0.941268	0.0413969
$518$	27.2863	1.19889
$519$	25.9009	1.13693
$520$	2.30056	0.100886
$521$	−5.59172	−0.244978	−0.122489	−	0.992470i	$-0.539088\pi$
$521$	−5.59172	−0.244978	−0.122489	+	0.992470i	$0.539088\pi$
$522$	10.8395	0.474431
$523$	3.83138	0.167534	0.0837672	−	0.996485i	$-0.473305\pi$
$523$	3.83138	0.167534	0.0837672	+	0.996485i	$0.473305\pi$
$524$	−19.6740	−0.859464
$525$	−30.8798	−1.34770
$526$	−36.5152	−1.59214
$527$	−10.0582	−0.438143
$528$	16.4193	0.714560
$529$	1.00000	0.0434783
$530$	−7.76886	−0.337458
$531$	32.3815	1.40524
$532$	35.3082	1.53080
$533$	5.37028	0.232613
$534$	−3.18950	−0.138023
$535$	4.20613	0.181847
$536$	−14.1111	−0.609507
$537$	−2.54545	−0.109844
$538$	−4.10388	−0.176931
$539$	1.10330	0.0475226
$540$	20.9049	0.899603
$541$	1.78611	0.0767910	0.0383955	−	0.999263i	$-0.487775\pi$
$541$	1.78611	0.0767910	0.0383955	+	0.999263i	$0.487775\pi$
$542$	−13.4133	−0.576150
$543$	13.9573	0.598963
$544$	33.8966	1.45330
$545$	4.38546	0.187853
$546$	−9.10434	−0.389630
$547$	−8.30835	−0.355240	−0.177620	−	0.984099i	$-0.556840\pi$
$547$	−8.30835	−0.355240	−0.177620	+	0.984099i	$0.556840\pi$
$548$	−73.9131	−3.15741
$549$	−21.0169	−0.896980
$550$	−9.13932	−0.389702
$551$	2.65407	0.113067
$552$	18.2849	0.778257
$553$	−17.2531	−0.733674
$554$	−8.56899	−0.364061
$555$	9.05853	0.384513
$556$	81.5874	3.46008
$557$	−15.7985	−0.669404	−0.334702	−	0.942324i	$-0.608636\pi$
$557$	−15.7985	−0.669404	−0.334702	+	0.942324i	$0.608636\pi$
$558$	−22.4499	−0.950378
$559$	−3.22005	−0.136194
$560$	11.7821	0.497884
$561$	−13.9263	−0.587970
$562$	−12.6435	−0.533334
$563$	2.88932	0.121770	0.0608851	−	0.998145i	$-0.480608\pi$
$563$	2.88932	0.121770	0.0608851	+	0.998145i	$0.480608\pi$
$564$	15.3483	0.646279
$565$	−9.51901	−0.400468
$566$	79.3424	3.33501
$567$	−8.01797	−0.336723
$568$	−24.8679	−1.04343
$569$	7.96269	0.333813	0.166907	−	0.985973i	$-0.446622\pi$
$569$	7.96269	0.333813	0.166907	+	0.985973i	$0.446622\pi$
$570$	16.9453	0.709762
$571$	−27.6931	−1.15892	−0.579460	−	0.815001i	$-0.696737\pi$
$571$	−27.6931	−1.15892	−0.579460	+	0.815001i	$0.696737\pi$
$572$	−1.86392	−0.0779345
$573$	−23.0502	−0.962934
$574$	61.9553	2.58596
$575$	−4.51812	−0.188419
$576$	−0.663608	−0.0276503
$577$	−39.1921	−1.63159	−0.815795	−	0.578341i	$-0.803700\pi$
$577$	−39.1921	−1.63159	−0.815795	+	0.578341i	$0.803700\pi$
$578$	−50.7801	−2.11217
$579$	45.0813	1.87352
$580$	2.48944	0.103368
$581$	−21.3077	−0.883992
$582$	66.0887	2.73946
$583$	3.48932	0.144513
$584$	68.0346	2.81529
$585$	−1.93337	−0.0799349
$586$	−25.1499	−1.03893
$587$	−9.67659	−0.399396	−0.199698	−	0.979858i	$-0.563996\pi$
$587$	−9.67659	−0.399396	−0.199698	+	0.979858i	$0.563996\pi$
$588$	17.9904	0.741912
$589$	−5.49691	−0.226496
$590$	10.7511	0.442614
$591$	28.8554	1.18695
$592$	32.4062	1.33188
$593$	21.2089	0.870946	0.435473	−	0.900202i	$-0.356581\pi$
$593$	21.2089	0.870946	0.435473	+	0.900202i	$0.356581\pi$
$594$	−13.5735	−0.556928
$595$	−9.99317	−0.409680
$596$	63.3845	2.59633
$597$	−64.2273	−2.62865
$598$	−1.33209	−0.0544731
$599$	−28.9480	−1.18278	−0.591391	−	0.806385i	$-0.701421\pi$
$599$	−28.9480	−1.18278	−0.591391	+	0.806385i	$0.701421\pi$
$600$	−82.6134	−3.37268
$601$	16.4352	0.670406	0.335203	−	0.942146i	$-0.391195\pi$
$601$	16.4352	0.670406	0.335203	+	0.942146i	$0.391195\pi$
$602$	−37.1488	−1.51407
$603$	11.8588	0.482928
$604$	41.3550	1.68271
$605$	7.19811	0.292645
$606$	−17.3026	−0.702870
$607$	−7.24888	−0.294223	−0.147111	−	0.989120i	$-0.546998\pi$
$607$	−7.24888	−0.294223	−0.147111	+	0.989120i	$0.546998\pi$
$608$	18.5248	0.751278
$609$	−5.46142	−0.221308
$610$	−6.97788	−0.282526
$611$	−0.619854	−0.0250766
$612$	−145.256	−5.87164
$613$	16.6218	0.671349	0.335674	−	0.941978i	$-0.391036\pi$
$613$	16.6218	0.671349	0.335674	+	0.941978i	$0.391036\pi$
$614$	−47.2058	−1.90507
$615$	20.5680	0.829382
$616$	−11.9206	−0.480295
$617$	−34.6313	−1.39420	−0.697102	−	0.716972i	$-0.745528\pi$
$617$	−34.6313	−1.39420	−0.697102	+	0.716972i	$0.745528\pi$
$618$	−76.3659	−3.07189
$619$	−36.2317	−1.45628	−0.728138	−	0.685430i	$-0.759614\pi$
$619$	−36.2317	−1.45628	−0.728138	+	0.685430i	$0.759614\pi$
$620$	−5.15593	−0.207067
$621$	−6.71021	−0.269271
$622$	−37.1358	−1.48901
$623$	1.02795	0.0411840
$624$	−10.8126	−0.432852
$625$	18.0040	0.720162
$626$	26.9306	1.07636
$627$	−7.61086	−0.303948
$628$	−98.9417	−3.94820
$629$	−27.4858	−1.09593
$630$	−22.3047	−0.888639
$631$	−47.8082	−1.90321	−0.951607	−	0.307317i	$-0.900569\pi$
$631$	−47.8082	−1.90321	−0.951607	+	0.307317i	$0.900569\pi$
$632$	−46.1575	−1.83605
$633$	−12.5247	−0.497811
$634$	−41.9129	−1.66457
$635$	−2.66255	−0.105660
$636$	56.8967	2.25610
$637$	−0.726559	−0.0287873
$638$	−1.61639	−0.0639934
$639$	20.8987	0.826738
$640$	−7.96366	−0.314791
$641$	29.8628	1.17951	0.589755	−	0.807582i	$-0.299224\pi$
$641$	29.8628	1.17951	0.589755	+	0.807582i	$0.299224\pi$
$642$	−44.5322	−1.75754
$643$	28.0081	1.10453	0.552265	−	0.833669i	$-0.313764\pi$
$643$	28.0081	1.10453	0.552265	+	0.833669i	$0.313764\pi$
$644$	−10.6305	−0.418899
$645$	−12.3327	−0.485599
$646$	−51.4163	−2.02295
$647$	−18.5019	−0.727386	−0.363693	−	0.931519i	$-0.618484\pi$
$647$	−18.5019	−0.727386	−0.363693	+	0.931519i	$0.618484\pi$
$648$	−21.4507	−0.842662
$649$	−4.82875	−0.189545
$650$	6.01853	0.236066
$651$	11.3113	0.443324
$652$	30.3496	1.18858
$653$	−10.6576	−0.417065	−0.208532	−	0.978015i	$-0.566869\pi$
$653$	−10.6576	−0.417065	−0.208532	+	0.978015i	$0.566869\pi$
$654$	−46.4308	−1.81559
$655$	3.04311	0.118904
$656$	73.5804	2.87283
$657$	−57.1755	−2.23063
$658$	−7.15106	−0.278778
$659$	22.9348	0.893413	0.446706	−	0.894681i	$-0.352597\pi$
$659$	22.9348	0.893413	0.446706	+	0.894681i	$0.352597\pi$
$660$	−7.13876	−0.277876
$661$	31.9539	1.24286	0.621432	−	0.783468i	$-0.286551\pi$
$661$	31.9539	1.24286	0.621432	+	0.783468i	$0.286551\pi$
$662$	59.7290	2.32143
$663$	9.17092	0.356169
$664$	−57.0050	−2.21222
$665$	−5.46135	−0.211782
$666$	−61.3481	−2.37719
$667$	−0.799079	−0.0309405
$668$	58.1749	2.25085
$669$	14.4134	0.557254
$670$	3.93727	0.152110
$671$	3.13406	0.120989
$672$	−38.1194	−1.47049
$673$	−19.8634	−0.765678	−0.382839	−	0.923815i	$-0.625054\pi$
$673$	−19.8634	−0.765678	−0.382839	+	0.923815i	$0.625054\pi$
$674$	−12.3729	−0.476588
$675$	30.3175	1.16692
$676$	−57.1153	−2.19674
$677$	−7.79237	−0.299485	−0.149743	−	0.988725i	$-0.547845\pi$
$677$	−7.79237	−0.299485	−0.149743	+	0.988725i	$0.547845\pi$
$678$	100.782	3.87051
$679$	−21.2999	−0.817414
$680$	−26.7350	−1.02524
$681$	−83.4765	−3.19883
$682$	3.34774	0.128192
$683$	−18.1594	−0.694849	−0.347425	−	0.937708i	$-0.612944\pi$
$683$	−18.1594	−0.694849	−0.347425	+	0.937708i	$0.612944\pi$
$684$	−79.3839	−3.03532
$685$	11.4326	0.436818
$686$	−50.6158	−1.93252
$687$	−35.9708	−1.37237
$688$	−44.1192	−1.68203
$689$	−2.29783	−0.0875402
$690$	−5.10185	−0.194224
$691$	−27.9878	−1.06471	−0.532353	−	0.846522i	$-0.678692\pi$
$691$	−27.9878	−1.06471	−0.532353	+	0.846522i	$0.678692\pi$
$692$	−40.2858	−1.53144
$693$	10.0180	0.380551
$694$	11.2237	0.426045
$695$	−12.6197	−0.478691
$696$	−14.6111	−0.553832
$697$	−62.4084	−2.36389
$698$	−2.54714	−0.0964105
$699$	−79.7109	−3.01494
$700$	48.0298	1.81536
$701$	−35.1052	−1.32591	−0.662953	−	0.748661i	$-0.730697\pi$
$701$	−35.1052	−1.32591	−0.662953	+	0.748661i	$0.730697\pi$
$702$	8.93858	0.337365
$703$	−15.0212	−0.566536
$704$	0.0989577	0.00372961
$705$	−2.37402	−0.0894108
$706$	−72.7733	−2.73886
$707$	5.57649	0.209726
$708$	−78.7375	−2.95914
$709$	−27.1112	−1.01818	−0.509092	−	0.860712i	$-0.670019\pi$
$709$	−27.1112	−1.01818	−0.509092	+	0.860712i	$0.670019\pi$
$710$	6.93862	0.260402
$711$	38.7903	1.45475
$712$	2.75011	0.103065
$713$	1.65499	0.0619799
$714$	105.802	3.95954
$715$	0.288305	0.0107820
$716$	3.95914	0.147960
$717$	35.1320	1.31203
$718$	−34.4901	−1.28716
$719$	−20.4963	−0.764382	−0.382191	−	0.924083i	$-0.624830\pi$
$719$	−20.4963	−0.764382	−0.382191	+	0.924083i	$0.624830\pi$
$720$	−26.4898	−0.987217
$721$	24.6121	0.916604
$722$	20.2961	0.755344
$723$	−72.6521	−2.70196
$724$	−21.7088	−0.806803
$725$	3.61034	0.134085
$726$	−76.2096	−2.82840
$727$	3.89427	0.144430	0.0722152	−	0.997389i	$-0.476993\pi$
$727$	3.89427	0.144430	0.0722152	+	0.997389i	$0.476993\pi$
$728$	7.85010	0.290944
$729$	−40.0581	−1.48363
$730$	−18.9830	−0.702592
$731$	37.4204	1.38404
$732$	51.1038	1.88885
$733$	−20.9025	−0.772050	−0.386025	−	0.922488i	$-0.626152\pi$
$733$	−20.9025	−0.772050	−0.386025	+	0.922488i	$0.626152\pi$
$734$	−73.0865	−2.69767
$735$	−2.78270	−0.102641
$736$	−5.57738	−0.205585
$737$	−1.76839	−0.0651396
$738$	−139.295	−5.12752
$739$	13.4748	0.495680	0.247840	−	0.968801i	$-0.420279\pi$
$739$	13.4748	0.495680	0.247840	+	0.968801i	$0.420279\pi$
$740$	−14.0895	−0.517939
$741$	5.01199	0.184120
$742$	−26.5093	−0.973187
$743$	48.6038	1.78310	0.891551	−	0.452920i	$-0.149618\pi$
$743$	48.6038	1.78310	0.891551	+	0.452920i	$0.149618\pi$
$744$	30.2613	1.10943
$745$	−9.80410	−0.359195
$746$	−59.0234	−2.16100
$747$	47.9064	1.75280
$748$	21.6607	0.791995
$749$	14.3524	0.524424
$750$	48.5600	1.77316
$751$	26.7118	0.974728	0.487364	−	0.873199i	$-0.337959\pi$
$751$	26.7118	0.974728	0.487364	+	0.873199i	$0.337959\pi$
$752$	−8.49286	−0.309703
$753$	−26.1866	−0.954293
$754$	1.06444	0.0387647
$755$	−6.39665	−0.232798
$756$	71.3327	2.59435
$757$	−18.5396	−0.673833	−0.336917	−	0.941534i	$-0.609384\pi$
$757$	−18.5396	−0.673833	−0.336917	+	0.941534i	$0.609384\pi$
$758$	3.75222	0.136287
$759$	2.29145	0.0831744
$760$	−14.6109	−0.529993
$761$	48.3369	1.75221	0.876106	−	0.482118i	$-0.160132\pi$
$761$	48.3369	1.75221	0.876106	+	0.482118i	$0.160132\pi$
$762$	28.1896	1.02120
$763$	14.9643	0.541744
$764$	35.8518	1.29707
$765$	22.4678	0.812324
$766$	55.2817	1.99741
$767$	3.17988	0.114819
$768$	83.5957	3.01650
$769$	38.8259	1.40010	0.700048	−	0.714096i	$-0.253162\pi$
$769$	38.8259	1.40010	0.700048	+	0.714096i	$0.253162\pi$
$770$	3.32609	0.119864
$771$	59.9997	2.16084
$772$	−70.1186	−2.52362
$773$	−9.08224	−0.326665	−0.163333	−	0.986571i	$-0.552224\pi$
$773$	−9.08224	−0.326665	−0.163333	+	0.986571i	$0.552224\pi$
$774$	83.5220	3.00214
$775$	−7.47745	−0.268598
$776$	−56.9841	−2.04561
$777$	30.9100	1.10889
$778$	−85.0133	−3.04787
$779$	−34.1067	−1.22200
$780$	4.70109	0.168326
$781$	−3.11642	−0.111514
$782$	15.4803	0.553573
$783$	5.36199	0.191622
$784$	−9.95487	−0.355531
$785$	15.3040	0.546222
$786$	−32.2188	−1.14920
$787$	1.36472	0.0486469	0.0243234	−	0.999704i	$-0.492257\pi$
$787$	1.36472	0.0486469	0.0243234	+	0.999704i	$0.492257\pi$
$788$	−44.8811	−1.59882
$789$	−41.3646	−1.47262
$790$	12.8788	0.458209
$791$	−32.4813	−1.15490
$792$	26.8013	0.952342
$793$	−2.06387	−0.0732903
$794$	20.3317	0.721546
$795$	−8.80060	−0.312125
$796$	99.8979	3.54079
$797$	12.7112	0.450252	0.225126	−	0.974330i	$-0.427721\pi$
$797$	12.7112	0.450252	0.225126	+	0.974330i	$0.427721\pi$
$798$	57.8217	2.04687
$799$	7.20336	0.254837
$800$	25.1993	0.890929
$801$	−2.31116	−0.0816607
$802$	6.65678	0.235059
$803$	8.52606	0.300878
$804$	−28.8354	−1.01695
$805$	1.64429	0.0579535
$806$	−2.20459	−0.0776534
$807$	−4.64889	−0.163649
$808$	14.9189	0.524846
$809$	−20.3719	−0.716239	−0.358120	−	0.933676i	$-0.616582\pi$
$809$	−20.3719	−0.716239	−0.358120	+	0.933676i	$0.616582\pi$
$810$	5.98515	0.210297
$811$	−24.8821	−0.873728	−0.436864	−	0.899528i	$-0.643911\pi$
$811$	−24.8821	−0.873728	−0.436864	+	0.899528i	$0.643911\pi$
$812$	8.49459	0.298102
$813$	−15.1946	−0.532898
$814$	9.14826	0.320647
$815$	−4.69437	−0.164436
$816$	125.654	4.39878
$817$	20.4506	0.715475
$818$	−46.2394	−1.61672
$819$	−6.59713	−0.230523
$820$	−31.9911	−1.11718
$821$	−11.7153	−0.408865	−0.204433	−	0.978881i	$-0.565535\pi$
$821$	−11.7153	−0.408865	−0.204433	+	0.978881i	$0.565535\pi$
$822$	−121.042	−4.22183
$823$	−44.2098	−1.54106	−0.770528	−	0.637406i	$-0.780007\pi$
$823$	−44.2098	−1.54106	−0.770528	+	0.637406i	$0.780007\pi$
$824$	65.8455	2.29384
$825$	−10.3531	−0.360447
$826$	36.6853	1.27645
$827$	−9.68017	−0.336612	−0.168306	−	0.985735i	$-0.553830\pi$
$827$	−9.68017	−0.336612	−0.168306	+	0.985735i	$0.553830\pi$
$828$	23.9006	0.830605
$829$	−29.4901	−1.02423	−0.512116	−	0.858916i	$-0.671138\pi$
$829$	−29.4901	−1.02423	−0.512116	+	0.858916i	$0.671138\pi$
$830$	15.9055	0.552089
$831$	−9.70698	−0.336731
$832$	−0.0651667	−0.00225925
$833$	8.44338	0.292546
$834$	133.610	4.62654
$835$	−8.99829	−0.311399
$836$	11.8378	0.409418
$837$	−11.1053	−0.383856
$838$	19.3093	0.667030
$839$	10.5428	0.363976	0.181988	−	0.983301i	$-0.441747\pi$
$839$	10.5428	0.363976	0.181988	+	0.983301i	$0.441747\pi$
$840$	30.0656	1.03736
$841$	−28.3615	−0.977982
$842$	−80.6173	−2.77826
$843$	−14.3226	−0.493297
$844$	19.4806	0.670551
$845$	8.83440	0.303913
$846$	16.0778	0.552767
$847$	24.5618	0.843952
$848$	−31.4834	−1.08114
$849$	89.8794	3.08465
$850$	−69.9417	−2.39898
$851$	4.52254	0.155031
$852$	−50.8163	−1.74094
$853$	4.56124	0.156174	0.0780869	−	0.996947i	$-0.475119\pi$
$853$	4.56124	0.156174	0.0780869	+	0.996947i	$0.475119\pi$
$854$	−23.8103	−0.814771
$855$	12.2788	0.419927
$856$	38.3973	1.31239
$857$	17.5347	0.598974	0.299487	−	0.954100i	$-0.403185\pi$
$857$	17.5347	0.598974	0.299487	+	0.954100i	$0.403185\pi$
$858$	−3.05241	−0.104208
$859$	5.57282	0.190142	0.0950711	−	0.995470i	$-0.469692\pi$
$859$	5.57282	0.190142	0.0950711	+	0.995470i	$0.469692\pi$
$860$	19.1820	0.654102
$861$	70.1832	2.39184
$862$	23.4838	0.799861
$863$	24.3099	0.827518	0.413759	−	0.910386i	$-0.364216\pi$
$863$	24.3099	0.827518	0.413759	+	0.910386i	$0.364216\pi$
$864$	37.4254	1.27324
$865$	6.23127	0.211870
$866$	−3.17085	−0.107750
$867$	−57.5239	−1.95361
$868$	−17.5933	−0.597157
$869$	−5.78443	−0.196223
$870$	4.07678	0.138216
$871$	1.16454	0.0394590
$872$	40.0344	1.35574
$873$	47.8888	1.62079
$874$	8.46009	0.286167
$875$	−15.6505	−0.529084
$876$	139.026	4.69724
$877$	−39.9081	−1.34760	−0.673800	−	0.738914i	$-0.735339\pi$
$877$	−39.9081	−1.34760	−0.673800	+	0.738914i	$0.735339\pi$
$878$	−17.7442	−0.598837
$879$	−28.4899	−0.960942
$880$	3.95018	0.133161
$881$	−9.50872	−0.320357	−0.160178	−	0.987088i	$-0.551207\pi$
$881$	−9.50872	−0.320357	−0.160178	+	0.987088i	$0.551207\pi$
$882$	18.8455	0.634563
$883$	−13.7605	−0.463078	−0.231539	−	0.972826i	$-0.574376\pi$
$883$	−13.7605	−0.463078	−0.231539	+	0.972826i	$0.574376\pi$
$884$	−14.2643	−0.479759
$885$	12.1788	0.409387
$886$	−38.2646	−1.28552
$887$	−1.48267	−0.0497831	−0.0248915	−	0.999690i	$-0.507924\pi$
$887$	−1.48267	−0.0497831	−0.0248915	+	0.999690i	$0.507924\pi$
$888$	82.6943	2.77504
$889$	−9.08529	−0.304711
$890$	−0.767333	−0.0257211
$891$	−2.68818	−0.0900575
$892$	−22.4183	−0.750621
$893$	3.93670	0.131737
$894$	103.800	3.47160
$895$	−0.612386	−0.0204698
$896$	−27.1740	−0.907820
$897$	−1.50899	−0.0503838
$898$	7.88011	0.262963
$899$	−1.32247	−0.0441068
$900$	−107.986	−3.59953
$901$	26.7032	0.889611
$902$	20.7718	0.691624
$903$	−42.0823	−1.40041
$904$	−86.8979	−2.89018
$905$	3.35785	0.111619
$906$	67.7241	2.24998
$907$	−22.3124	−0.740871	−0.370436	−	0.928858i	$-0.620792\pi$
$907$	−22.3124	−0.740871	−0.370436	+	0.928858i	$0.620792\pi$
$908$	129.838	4.30882
$909$	−12.5377	−0.415849
$910$	−2.19033	−0.0726088
$911$	−18.2642	−0.605120	−0.302560	−	0.953130i	$-0.597841\pi$
$911$	−18.2642	−0.605120	−0.302560	+	0.953130i	$0.597841\pi$
$912$	68.6712	2.27393
$913$	−7.14383	−0.236426
$914$	−6.02346	−0.199238
$915$	−7.90457	−0.261317
$916$	55.9483	1.84859
$917$	10.3839	0.342905
$918$	−103.876	−3.42841
$919$	−36.7482	−1.21221	−0.606106	−	0.795384i	$-0.707269\pi$
$919$	−36.7482	−1.21221	−0.606106	+	0.795384i	$0.707269\pi$
$920$	4.39900	0.145031
$921$	−53.4749	−1.76206
$922$	44.1051	1.45252
$923$	2.05226	0.0675510
$924$	−24.3592	−0.801360
$925$	−20.4334	−0.671846
$926$	39.0902	1.28458
$927$	−55.3358	−1.81747
$928$	4.45676	0.146300
$929$	6.18781	0.203015	0.101508	−	0.994835i	$-0.467633\pi$
$929$	6.18781	0.203015	0.101508	+	0.994835i	$0.467633\pi$
$930$	−8.44350	−0.276873
$931$	4.61438	0.151230
$932$	123.981	4.06112
$933$	−42.0675	−1.37723
$934$	−101.997	−3.33744
$935$	−3.35041	−0.109570
$936$	−17.6495	−0.576891
$937$	−14.3212	−0.467852	−0.233926	−	0.972254i	$-0.575157\pi$
$937$	−14.3212	−0.467852	−0.233926	+	0.972254i	$0.575157\pi$
$938$	13.4350	0.438667
$939$	30.5071	0.995560
$940$	3.69250	0.120436
$941$	2.74102	0.0893548	0.0446774	−	0.999001i	$-0.485774\pi$
$941$	2.74102	0.0893548	0.0446774	+	0.999001i	$0.485774\pi$
$942$	−162.030	−5.27922
$943$	10.2687	0.334396
$944$	43.5688	1.41804
$945$	−11.0335	−0.358920
$946$	−12.4549	−0.404943
$947$	−54.0519	−1.75645	−0.878226	−	0.478246i	$-0.841273\pi$
$947$	−54.0519	−1.75645	−0.878226	+	0.478246i	$0.841273\pi$
$948$	−94.3207	−3.06339
$949$	−5.61467	−0.182260
$950$	−38.2237	−1.24014
$951$	−47.4791	−1.53961
$952$	−91.2265	−2.95667
$953$	5.62294	0.182145	0.0910725	−	0.995844i	$-0.470971\pi$
$953$	5.62294	0.182145	0.0910725	+	0.995844i	$0.470971\pi$
$954$	59.6012	1.92966
$955$	−5.54543	−0.179446
$956$	−54.6436	−1.76730
$957$	−1.83105	−0.0591895
$958$	3.61040	0.116647
$959$	39.0110	1.25973
$960$	−0.249586	−0.00805536
$961$	−28.2610	−0.911645
$962$	−6.02442	−0.194235
$963$	−32.2686	−1.03984
$964$	113.002	3.63954
$965$	10.8457	0.349136
$966$	−17.4088	−0.560118
$967$	44.1437	1.41956	0.709782	−	0.704421i	$-0.248793\pi$
$967$	44.1437	1.41956	0.709782	+	0.704421i	$0.248793\pi$
$968$	65.7107	2.11202
$969$	−58.2446	−1.87109
$970$	15.8997	0.510508
$971$	−27.5113	−0.882878	−0.441439	−	0.897291i	$-0.645532\pi$
$971$	−27.5113	−0.882878	−0.441439	+	0.897291i	$0.645532\pi$
$972$	46.5109	1.49184
$973$	−43.0615	−1.38049
$974$	−66.4267	−2.12845
$975$	6.81781	0.218345
$976$	−28.2780	−0.905155
$977$	−23.9977	−0.767756	−0.383878	−	0.923384i	$-0.625412\pi$
$977$	−23.9977	−0.767756	−0.383878	+	0.923384i	$0.625412\pi$
$978$	49.7013	1.58927
$979$	0.344641	0.0110148
$980$	4.32815	0.138258
$981$	−33.6444	−1.07418
$982$	−36.3097	−1.15869
$983$	13.9370	0.444520	0.222260	−	0.974987i	$-0.428657\pi$
$983$	13.9370	0.444520	0.222260	+	0.974987i	$0.428657\pi$
$984$	187.763	5.98566
$985$	6.94205	0.221192
$986$	−12.3699	−0.393939
$987$	−8.10075	−0.257850
$988$	−7.79555	−0.248009
$989$	−6.15720	−0.195787
$990$	−7.47808	−0.237669
$991$	−23.8826	−0.758656	−0.379328	−	0.925262i	$-0.623845\pi$
$991$	−23.8826	−0.758656	−0.379328	+	0.925262i	$0.623845\pi$
$992$	−9.23050	−0.293069
$993$	67.6612	2.14716
$994$	23.6763	0.750967
$995$	−15.4519	−0.489857
$996$	−116.487	−3.69104
$997$	5.96965	0.189061	0.0945304	−	0.995522i	$-0.469865\pi$
$997$	5.96965	0.189061	0.0945304	+	0.995522i	$0.469865\pi$
$998$	23.8729	0.755683
$999$	−30.3472	−0.960143

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.10	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.10	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54714 q^{2} -2.88541 q^{3} +4.48790 q^{4} -0.694174 q^{5} +7.34952 q^{6} -2.36870 q^{7} -6.33703 q^{8} +5.32557 q^{9} +O(q^{10})\)	\(q-2.54714 q^{2} -2.88541 q^{3} +4.48790 q^{4} -0.694174 q^{5} +7.34952 q^{6} -2.36870 q^{7} -6.33703 q^{8} +5.32557 q^{9} +1.76816 q^{10} -0.794152 q^{11} -12.9494 q^{12} +0.522974 q^{13} +6.03339 q^{14} +2.00297 q^{15} +7.16547 q^{16} -6.07751 q^{17} -13.5649 q^{18} -3.32141 q^{19} -3.11538 q^{20} +6.83465 q^{21} +2.02281 q^{22} +1.00000 q^{23} +18.2849 q^{24} -4.51812 q^{25} -1.33209 q^{26} -6.71021 q^{27} -10.6305 q^{28} -0.799079 q^{29} -5.10185 q^{30} +1.65499 q^{31} -5.57738 q^{32} +2.29145 q^{33} +15.4803 q^{34} +1.64429 q^{35} +23.9006 q^{36} +4.52254 q^{37} +8.46009 q^{38} -1.50899 q^{39} +4.39900 q^{40} +10.2687 q^{41} -17.4088 q^{42} -6.15720 q^{43} -3.56408 q^{44} -3.69687 q^{45} -2.54714 q^{46} -1.18525 q^{47} -20.6753 q^{48} -1.38928 q^{49} +11.5083 q^{50} +17.5361 q^{51} +2.34706 q^{52} -4.39377 q^{53} +17.0918 q^{54} +0.551280 q^{55} +15.0105 q^{56} +9.58362 q^{57} +2.03536 q^{58} +6.08038 q^{59} +8.98915 q^{60} -3.94642 q^{61} -4.21549 q^{62} -12.6146 q^{63} -0.124608 q^{64} -0.363035 q^{65} -5.83664 q^{66} +2.22677 q^{67} -27.2753 q^{68} -2.88541 q^{69} -4.18822 q^{70} +3.92421 q^{71} -33.7483 q^{72} -10.7360 q^{73} -11.5195 q^{74} +13.0366 q^{75} -14.9062 q^{76} +1.88111 q^{77} +3.84361 q^{78} +7.28378 q^{79} -4.97408 q^{80} +3.38497 q^{81} -26.1559 q^{82} +8.99554 q^{83} +30.6732 q^{84} +4.21885 q^{85} +15.6832 q^{86} +2.30567 q^{87} +5.03257 q^{88} -0.433974 q^{89} +9.41643 q^{90} -1.23877 q^{91} +4.48790 q^{92} -4.77532 q^{93} +3.01899 q^{94} +2.30564 q^{95} +16.0930 q^{96} +8.99224 q^{97} +3.53869 q^{98} -4.22931 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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