LMFDB - Embedded newform 8002.2.a.e.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.54939 q^{3} +1.00000 q^{4} +1.18464 q^{5} +1.54939 q^{6} -2.23562 q^{7} -1.00000 q^{8} -0.599398 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.54939 q^{3} +1.00000 q^{4} +1.18464 q^{5} +1.54939 q^{6} -2.23562 q^{7} -1.00000 q^{8} -0.599398 q^{9} -1.18464 q^{10} +2.08413 q^{11} -1.54939 q^{12} +0.616183 q^{13} +2.23562 q^{14} -1.83546 q^{15} +1.00000 q^{16} +0.0853455 q^{17} +0.599398 q^{18} -2.09858 q^{19} +1.18464 q^{20} +3.46384 q^{21} -2.08413 q^{22} +2.46108 q^{23} +1.54939 q^{24} -3.59663 q^{25} -0.616183 q^{26} +5.57686 q^{27} -2.23562 q^{28} -2.80207 q^{29} +1.83546 q^{30} +5.52768 q^{31} -1.00000 q^{32} -3.22913 q^{33} -0.0853455 q^{34} -2.64840 q^{35} -0.599398 q^{36} -1.40539 q^{37} +2.09858 q^{38} -0.954706 q^{39} -1.18464 q^{40} +3.99564 q^{41} -3.46384 q^{42} -3.91535 q^{43} +2.08413 q^{44} -0.710070 q^{45} -2.46108 q^{46} -3.08120 q^{47} -1.54939 q^{48} -2.00200 q^{49} +3.59663 q^{50} -0.132233 q^{51} +0.616183 q^{52} +5.22685 q^{53} -5.57686 q^{54} +2.46895 q^{55} +2.23562 q^{56} +3.25151 q^{57} +2.80207 q^{58} -1.78135 q^{59} -1.83546 q^{60} +0.736094 q^{61} -5.52768 q^{62} +1.34003 q^{63} +1.00000 q^{64} +0.729954 q^{65} +3.22913 q^{66} +8.21469 q^{67} +0.0853455 q^{68} -3.81317 q^{69} +2.64840 q^{70} -8.70683 q^{71} +0.599398 q^{72} +7.19753 q^{73} +1.40539 q^{74} +5.57258 q^{75} -2.09858 q^{76} -4.65933 q^{77} +0.954706 q^{78} -4.43576 q^{79} +1.18464 q^{80} -6.84253 q^{81} -3.99564 q^{82} -14.4941 q^{83} +3.46384 q^{84} +0.101104 q^{85} +3.91535 q^{86} +4.34150 q^{87} -2.08413 q^{88} +3.29596 q^{89} +0.710070 q^{90} -1.37755 q^{91} +2.46108 q^{92} -8.56451 q^{93} +3.08120 q^{94} -2.48606 q^{95} +1.54939 q^{96} +3.18740 q^{97} +2.00200 q^{98} -1.24923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.54939	−0.894539	−0.447270	−	0.894399i	$-0.647604\pi$
$3$	−1.54939	−0.894539	−0.447270	+	0.894399i	$0.647604\pi$
$4$	1.00000	0.500000
$5$	1.18464	0.529786	0.264893	−	0.964278i	$-0.414663\pi$
$5$	1.18464	0.529786	0.264893	+	0.964278i	$0.414663\pi$
$6$	1.54939	0.632535
$7$	−2.23562	−0.844985	−0.422493	−	0.906366i	$-0.638845\pi$
$7$	−2.23562	−0.844985	−0.422493	+	0.906366i	$0.638845\pi$
$8$	−1.00000	−0.353553
$9$	−0.599398	−0.199799
$10$	−1.18464	−0.374615
$11$	2.08413	0.628390	0.314195	−	0.949358i	$-0.398265\pi$
$11$	2.08413	0.628390	0.314195	+	0.949358i	$0.398265\pi$
$12$	−1.54939	−0.447270
$13$	0.616183	0.170898	0.0854492	−	0.996343i	$-0.472767\pi$
$13$	0.616183	0.170898	0.0854492	+	0.996343i	$0.472767\pi$
$14$	2.23562	0.597495
$15$	−1.83546	−0.473915
$16$	1.00000	0.250000
$17$	0.0853455	0.0206993	0.0103497	−	0.999946i	$-0.496706\pi$
$17$	0.0853455	0.0206993	0.0103497	+	0.999946i	$0.496706\pi$
$18$	0.599398	0.141279
$19$	−2.09858	−0.481447	−0.240723	−	0.970594i	$-0.577385\pi$
$19$	−2.09858	−0.481447	−0.240723	+	0.970594i	$0.577385\pi$
$20$	1.18464	0.264893
$21$	3.46384	0.755873
$22$	−2.08413	−0.444339
$23$	2.46108	0.513171	0.256586	−	0.966521i	$-0.417402\pi$
$23$	2.46108	0.513171	0.256586	+	0.966521i	$0.417402\pi$
$24$	1.54939	0.316267
$25$	−3.59663	−0.719326
$26$	−0.616183	−0.120843
$27$	5.57686	1.07327
$28$	−2.23562	−0.422493
$29$	−2.80207	−0.520332	−0.260166	−	0.965564i	$-0.583777\pi$
$29$	−2.80207	−0.520332	−0.260166	+	0.965564i	$0.583777\pi$
$30$	1.83546	0.335108
$31$	5.52768	0.992800	0.496400	−	0.868094i	$-0.334655\pi$
$31$	5.52768	0.992800	0.496400	+	0.868094i	$0.334655\pi$
$32$	−1.00000	−0.176777
$33$	−3.22913	−0.562120
$34$	−0.0853455	−0.0146366
$35$	−2.64840	−0.447662
$36$	−0.599398	−0.0998997
$37$	−1.40539	−0.231044	−0.115522	−	0.993305i	$-0.536854\pi$
$37$	−1.40539	−0.231044	−0.115522	+	0.993305i	$0.536854\pi$
$38$	2.09858	0.340434
$39$	−0.954706	−0.152875
$40$	−1.18464	−0.187308
$41$	3.99564	0.624015	0.312007	−	0.950080i	$-0.398999\pi$
$41$	3.99564	0.624015	0.312007	+	0.950080i	$0.398999\pi$
$42$	−3.46384	−0.534483
$43$	−3.91535	−0.597085	−0.298542	−	0.954396i	$-0.596500\pi$
$43$	−3.91535	−0.597085	−0.298542	+	0.954396i	$0.596500\pi$
$44$	2.08413	0.314195
$45$	−0.710070	−0.105851
$46$	−2.46108	−0.362867
$47$	−3.08120	−0.449439	−0.224720	−	0.974423i	$-0.572147\pi$
$47$	−3.08120	−0.449439	−0.224720	+	0.974423i	$0.572147\pi$
$48$	−1.54939	−0.223635
$49$	−2.00200	−0.286000
$50$	3.59663	0.508641
$51$	−0.132233	−0.0185164
$52$	0.616183	0.0854492
$53$	5.22685	0.717963	0.358981	−	0.933345i	$-0.383124\pi$
$53$	5.22685	0.717963	0.358981	+	0.933345i	$0.383124\pi$
$54$	−5.57686	−0.758915
$55$	2.46895	0.332912
$56$	2.23562	0.298747
$57$	3.25151	0.430673
$58$	2.80207	0.367930
$59$	−1.78135	−0.231912	−0.115956	−	0.993254i	$-0.536993\pi$
$59$	−1.78135	−0.231912	−0.115956	+	0.993254i	$0.536993\pi$
$60$	−1.83546	−0.236957
$61$	0.736094	0.0942472	0.0471236	−	0.998889i	$-0.484995\pi$
$61$	0.736094	0.0942472	0.0471236	+	0.998889i	$0.484995\pi$
$62$	−5.52768	−0.702016
$63$	1.34003	0.168828
$64$	1.00000	0.125000
$65$	0.729954	0.0905396
$66$	3.22913	0.397479
$67$	8.21469	1.00358	0.501792	−	0.864988i	$-0.332674\pi$
$67$	8.21469	1.00358	0.501792	+	0.864988i	$0.332674\pi$
$68$	0.0853455	0.0103497
$69$	−3.81317	−0.459052
$70$	2.64840	0.316545
$71$	−8.70683	−1.03331	−0.516655	−	0.856194i	$-0.672823\pi$
$71$	−8.70683	−1.03331	−0.516655	+	0.856194i	$0.672823\pi$
$72$	0.599398	0.0706397
$73$	7.19753	0.842407	0.421203	−	0.906966i	$-0.361608\pi$
$73$	7.19753	0.842407	0.421203	+	0.906966i	$0.361608\pi$
$74$	1.40539	0.163373
$75$	5.57258	0.643466
$76$	−2.09858	−0.240723
$77$	−4.65933	−0.530980
$78$	0.954706	0.108099
$79$	−4.43576	−0.499062	−0.249531	−	0.968367i	$-0.580276\pi$
$79$	−4.43576	−0.499062	−0.249531	+	0.968367i	$0.580276\pi$
$80$	1.18464	0.132447
$81$	−6.84253	−0.760281
$82$	−3.99564	−0.441245
$83$	−14.4941	−1.59094	−0.795470	−	0.605993i	$-0.792776\pi$
$83$	−14.4941	−1.59094	−0.795470	+	0.605993i	$0.792776\pi$
$84$	3.46384	0.377936
$85$	0.101104	0.0109662
$86$	3.91535	0.422203
$87$	4.34150	0.465457
$88$	−2.08413	−0.222169
$89$	3.29596	0.349371	0.174686	−	0.984624i	$-0.444109\pi$
$89$	3.29596	0.349371	0.174686	+	0.984624i	$0.444109\pi$
$90$	0.710070	0.0748479
$91$	−1.37755	−0.144407
$92$	2.46108	0.256586
$93$	−8.56451	−0.888099
$94$	3.08120	0.317801
$95$	−2.48606	−0.255064
$96$	1.54939	0.158134
$97$	3.18740	0.323632	0.161816	−	0.986821i	$-0.448265\pi$
$97$	3.18740	0.323632	0.161816	+	0.986821i	$0.448265\pi$
$98$	2.00200	0.202232
$99$	−1.24923	−0.125552
$100$	−3.59663	−0.359663
$101$	−16.7232	−1.66402	−0.832012	−	0.554757i	$-0.812811\pi$
$101$	−16.7232	−1.66402	−0.832012	+	0.554757i	$0.812811\pi$
$102$	0.132233	0.0130930
$103$	12.2582	1.20783	0.603917	−	0.797047i	$-0.293606\pi$
$103$	12.2582	1.20783	0.603917	+	0.797047i	$0.293606\pi$
$104$	−0.616183	−0.0604217
$105$	4.10340	0.400451
$106$	−5.22685	−0.507676
$107$	4.70273	0.454630	0.227315	−	0.973821i	$-0.427005\pi$
$107$	4.70273	0.454630	0.227315	+	0.973821i	$0.427005\pi$
$108$	5.57686	0.536634
$109$	9.20986	0.882145	0.441072	−	0.897471i	$-0.354598\pi$
$109$	9.20986	0.882145	0.441072	+	0.897471i	$0.354598\pi$
$110$	−2.46895	−0.235405
$111$	2.17749	0.206678
$112$	−2.23562	−0.211246
$113$	−4.26029	−0.400775	−0.200387	−	0.979717i	$-0.564220\pi$
$113$	−4.26029	−0.400775	−0.200387	+	0.979717i	$0.564220\pi$
$114$	−3.25151	−0.304532
$115$	2.91549	0.271871
$116$	−2.80207	−0.260166
$117$	−0.369339	−0.0341454
$118$	1.78135	0.163986
$119$	−0.190800	−0.0174906
$120$	1.83546	0.167554
$121$	−6.65638	−0.605126
$122$	−0.736094	−0.0666428
$123$	−6.19080	−0.558206
$124$	5.52768	0.496400
$125$	−10.1839	−0.910876
$126$	−1.34003	−0.119379
$127$	−1.86165	−0.165194	−0.0825972	−	0.996583i	$-0.526321\pi$
$127$	−1.86165	−0.165194	−0.0825972	+	0.996583i	$0.526321\pi$
$128$	−1.00000	−0.0883883
$129$	6.06639	0.534116
$130$	−0.729954	−0.0640212
$131$	−6.56815	−0.573862	−0.286931	−	0.957951i	$-0.592635\pi$
$131$	−6.56815	−0.573862	−0.286931	+	0.957951i	$0.592635\pi$
$132$	−3.22913	−0.281060
$133$	4.69162	0.406815
$134$	−8.21469	−0.709641
$135$	6.60656	0.568603
$136$	−0.0853455	−0.00731832
$137$	−3.37838	−0.288635	−0.144317	−	0.989531i	$-0.546099\pi$
$137$	−3.37838	−0.288635	−0.144317	+	0.989531i	$0.546099\pi$
$138$	3.81317	0.324599
$139$	4.48479	0.380395	0.190197	−	0.981746i	$-0.439087\pi$
$139$	4.48479	0.380395	0.190197	+	0.981746i	$0.439087\pi$
$140$	−2.64840	−0.223831
$141$	4.77397	0.402041
$142$	8.70683	0.730661
$143$	1.28421	0.107391
$144$	−0.599398	−0.0499498
$145$	−3.31944	−0.275665
$146$	−7.19753	−0.595672
$147$	3.10187	0.255838
$148$	−1.40539	−0.115522
$149$	6.24348	0.511486	0.255743	−	0.966745i	$-0.417680\pi$
$149$	6.24348	0.511486	0.255743	+	0.966745i	$0.417680\pi$
$150$	−5.57258	−0.454999
$151$	13.2055	1.07465	0.537323	−	0.843377i	$-0.319436\pi$
$151$	13.2055	1.07465	0.537323	+	0.843377i	$0.319436\pi$
$152$	2.09858	0.170217
$153$	−0.0511559	−0.00413571
$154$	4.65933	0.375460
$155$	6.54830	0.525972
$156$	−0.954706	−0.0764377
$157$	−4.66822	−0.372565	−0.186282	−	0.982496i	$-0.559644\pi$
$157$	−4.66822	−0.372565	−0.186282	+	0.982496i	$0.559644\pi$
$158$	4.43576	0.352890
$159$	−8.09842	−0.642246
$160$	−1.18464	−0.0936539
$161$	−5.50205	−0.433622
$162$	6.84253	0.537600
$163$	−2.89494	−0.226749	−0.113375	−	0.993552i	$-0.536166\pi$
$163$	−2.89494	−0.226749	−0.113375	+	0.993552i	$0.536166\pi$
$164$	3.99564	0.312007
$165$	−3.82535	−0.297803
$166$	14.4941	1.12496
$167$	−0.302117	−0.0233785	−0.0116893	−	0.999932i	$-0.503721\pi$
$167$	−0.302117	−0.0233785	−0.0116893	+	0.999932i	$0.503721\pi$
$168$	−3.46384	−0.267241
$169$	−12.6203	−0.970794
$170$	−0.101104	−0.00775429
$171$	1.25788	0.0961927
$172$	−3.91535	−0.298542
$173$	17.9027	1.36111	0.680557	−	0.732695i	$-0.261738\pi$
$173$	17.9027	1.36111	0.680557	+	0.732695i	$0.261738\pi$
$174$	−4.34150	−0.329128
$175$	8.04071	0.607820
$176$	2.08413	0.157098
$177$	2.76000	0.207454
$178$	−3.29596	−0.247043
$179$	8.45060	0.631628	0.315814	−	0.948821i	$-0.397722\pi$
$179$	8.45060	0.631628	0.315814	+	0.948821i	$0.397722\pi$
$180$	−0.710070	−0.0529255
$181$	6.27324	0.466286	0.233143	−	0.972442i	$-0.425099\pi$
$181$	6.27324	0.466286	0.233143	+	0.972442i	$0.425099\pi$
$182$	1.37755	0.102111
$183$	−1.14050	−0.0843078
$184$	−2.46108	−0.181433
$185$	−1.66488	−0.122404
$186$	8.56451	0.627981
$187$	0.177871	0.0130073
$188$	−3.08120	−0.224720
$189$	−12.4678	−0.906896
$190$	2.48606	0.180357
$191$	6.42003	0.464537	0.232268	−	0.972652i	$-0.425385\pi$
$191$	6.42003	0.464537	0.232268	+	0.972652i	$0.425385\pi$
$192$	−1.54939	−0.111817
$193$	17.3140	1.24629	0.623145	−	0.782106i	$-0.285855\pi$
$193$	17.3140	1.24629	0.623145	+	0.782106i	$0.285855\pi$
$194$	−3.18740	−0.228842
$195$	−1.13098	−0.0809913
$196$	−2.00200	−0.143000
$197$	11.1575	0.794939	0.397470	−	0.917615i	$-0.369888\pi$
$197$	11.1575	0.794939	0.397470	+	0.917615i	$0.369888\pi$
$198$	1.24923	0.0887786
$199$	−17.7646	−1.25930	−0.629651	−	0.776878i	$-0.716802\pi$
$199$	−17.7646	−1.25930	−0.629651	+	0.776878i	$0.716802\pi$
$200$	3.59663	0.254320
$201$	−12.7277	−0.897745
$202$	16.7232	1.17664
$203$	6.26437	0.439673
$204$	−0.132233	−0.00925818
$205$	4.73339	0.330594
$206$	−12.2582	−0.854067
$207$	−1.47517	−0.102531
$208$	0.616183	0.0427246
$209$	−4.37372	−0.302536
$210$	−4.10340	−0.283162
$211$	23.0967	1.59005	0.795023	−	0.606580i	$-0.207459\pi$
$211$	23.0967	1.59005	0.795023	+	0.606580i	$0.207459\pi$
$212$	5.22685	0.358981
$213$	13.4903	0.924337
$214$	−4.70273	−0.321472
$215$	−4.63827	−0.316327
$216$	−5.57686	−0.379457
$217$	−12.3578	−0.838902
$218$	−9.20986	−0.623771
$219$	−11.1518	−0.753566
$220$	2.46895	0.166456
$221$	0.0525885	0.00353748
$222$	−2.17749	−0.146144
$223$	−4.39676	−0.294429	−0.147214	−	0.989105i	$-0.547031\pi$
$223$	−4.39676	−0.294429	−0.147214	+	0.989105i	$0.547031\pi$
$224$	2.23562	0.149374
$225$	2.15581	0.143721
$226$	4.26029	0.283391
$227$	8.34531	0.553898	0.276949	−	0.960885i	$-0.410677\pi$
$227$	8.34531	0.553898	0.276949	+	0.960885i	$0.410677\pi$
$228$	3.25151	0.215337
$229$	−4.18222	−0.276369	−0.138184	−	0.990407i	$-0.544127\pi$
$229$	−4.18222	−0.276369	−0.138184	+	0.990407i	$0.544127\pi$
$230$	−2.91549	−0.192242
$231$	7.21912	0.474983
$232$	2.80207	0.183965
$233$	−12.4407	−0.815020	−0.407510	−	0.913201i	$-0.633603\pi$
$233$	−12.4407	−0.815020	−0.407510	+	0.913201i	$0.633603\pi$
$234$	0.369339	0.0241444
$235$	−3.65011	−0.238107
$236$	−1.78135	−0.115956
$237$	6.87271	0.446431
$238$	0.190800	0.0123677
$239$	−3.45695	−0.223612	−0.111806	−	0.993730i	$-0.535663\pi$
$239$	−3.45695	−0.223612	−0.111806	+	0.993730i	$0.535663\pi$
$240$	−1.83546	−0.118479
$241$	20.4983	1.32041	0.660206	−	0.751085i	$-0.270469\pi$
$241$	20.4983	1.32041	0.660206	+	0.751085i	$0.270469\pi$
$242$	6.65638	0.427889
$243$	−6.12886	−0.393167
$244$	0.736094	0.0471236
$245$	−2.37164	−0.151519
$246$	6.19080	0.394711
$247$	−1.29311	−0.0822785
$248$	−5.52768	−0.351008
$249$	22.4571	1.42316
$250$	10.1839	0.644086
$251$	23.5592	1.48704	0.743522	−	0.668712i	$-0.233154\pi$
$251$	23.5592	1.48704	0.743522	+	0.668712i	$0.233154\pi$
$252$	1.34003	0.0844138
$253$	5.12923	0.322472
$254$	1.86165	0.116810
$255$	−0.156649	−0.00980971
$256$	1.00000	0.0625000
$257$	7.83129	0.488503	0.244251	−	0.969712i	$-0.421458\pi$
$257$	7.83129	0.488503	0.244251	+	0.969712i	$0.421458\pi$
$258$	−6.06639	−0.377677
$259$	3.14192	0.195229
$260$	0.729954	0.0452698
$261$	1.67956	0.103962
$262$	6.56815	0.405782
$263$	9.97057	0.614812	0.307406	−	0.951578i	$-0.400539\pi$
$263$	9.97057	0.614812	0.307406	+	0.951578i	$0.400539\pi$
$264$	3.22913	0.198739
$265$	6.19193	0.380367
$266$	−4.69162	−0.287662
$267$	−5.10672	−0.312526
$268$	8.21469	0.501792
$269$	−18.2496	−1.11270	−0.556349	−	0.830949i	$-0.687798\pi$
$269$	−18.2496	−1.11270	−0.556349	+	0.830949i	$0.687798\pi$
$270$	−6.60656	−0.402063
$271$	−20.8667	−1.26756	−0.633782	−	0.773511i	$-0.718499\pi$
$271$	−20.8667	−1.26756	−0.633782	+	0.773511i	$0.718499\pi$
$272$	0.0853455	0.00517483
$273$	2.13436	0.129177
$274$	3.37838	0.204096
$275$	−7.49586	−0.452018
$276$	−3.81317	−0.229526
$277$	−31.6857	−1.90381	−0.951904	−	0.306395i	$-0.900877\pi$
$277$	−31.6857	−1.90381	−0.951904	+	0.306395i	$0.900877\pi$
$278$	−4.48479	−0.268980
$279$	−3.31328	−0.198361
$280$	2.64840	0.158272
$281$	−16.0612	−0.958128	−0.479064	−	0.877780i	$-0.659024\pi$
$281$	−16.0612	−0.958128	−0.479064	+	0.877780i	$0.659024\pi$
$282$	−4.77397	−0.284286
$283$	−24.6154	−1.46323	−0.731616	−	0.681717i	$-0.761233\pi$
$283$	−24.6154	−1.46323	−0.731616	+	0.681717i	$0.761233\pi$
$284$	−8.70683	−0.516655
$285$	3.85186	0.228165
$286$	−1.28421	−0.0759368
$287$	−8.93274	−0.527283
$288$	0.599398	0.0353199
$289$	−16.9927	−0.999572
$290$	3.31944	0.194924
$291$	−4.93853	−0.289501
$292$	7.19753	0.421203
$293$	−24.9600	−1.45818	−0.729089	−	0.684419i	$-0.760056\pi$
$293$	−24.9600	−1.45818	−0.729089	+	0.684419i	$0.760056\pi$
$294$	−3.10187	−0.180905
$295$	−2.11025	−0.122864
$296$	1.40539	0.0816865
$297$	11.6229	0.674431
$298$	−6.24348	−0.361675
$299$	1.51648	0.0877002
$300$	5.57258	0.321733
$301$	8.75323	0.504528
$302$	−13.2055	−0.759889
$303$	25.9108	1.48854
$304$	−2.09858	−0.120362
$305$	0.872005	0.0499309
$306$	0.0511559	0.00292439
$307$	25.6563	1.46428	0.732142	−	0.681152i	$-0.238521\pi$
$307$	25.6563	1.46428	0.732142	+	0.681152i	$0.238521\pi$
$308$	−4.65933	−0.265490
$309$	−18.9927	−1.08045
$310$	−6.54830	−0.371918
$311$	13.6939	0.776512	0.388256	−	0.921551i	$-0.373078\pi$
$311$	13.6939	0.776512	0.388256	+	0.921551i	$0.373078\pi$
$312$	0.954706	0.0540496
$313$	14.1322	0.798802	0.399401	−	0.916776i	$-0.369218\pi$
$313$	14.1322	0.798802	0.399401	+	0.916776i	$0.369218\pi$
$314$	4.66822	0.263443
$315$	1.58745	0.0894425
$316$	−4.43576	−0.249531
$317$	21.0108	1.18009	0.590043	−	0.807372i	$-0.299111\pi$
$317$	21.0108	1.18009	0.590043	+	0.807372i	$0.299111\pi$
$318$	8.09842	0.454137
$319$	−5.83989	−0.326971
$320$	1.18464	0.0662233
$321$	−7.28636	−0.406685
$322$	5.50205	0.306617
$323$	−0.179104	−0.00996562
$324$	−6.84253	−0.380140
$325$	−2.21618	−0.122932
$326$	2.89494	0.160336
$327$	−14.2696	−0.789113
$328$	−3.99564	−0.220622
$329$	6.88839	0.379769
$330$	3.82535	0.210579
$331$	−2.17808	−0.119718	−0.0598591	−	0.998207i	$-0.519065\pi$
$331$	−2.17808	−0.119718	−0.0598591	+	0.998207i	$0.519065\pi$
$332$	−14.4941	−0.795470
$333$	0.842387	0.0461625
$334$	0.302117	0.0165311
$335$	9.73143	0.531685
$336$	3.46384	0.188968
$337$	8.57052	0.466866	0.233433	−	0.972373i	$-0.425004\pi$
$337$	8.57052	0.466866	0.233433	+	0.972373i	$0.425004\pi$
$338$	12.6203	0.686455
$339$	6.60085	0.358509
$340$	0.101104	0.00548311
$341$	11.5204	0.623866
$342$	−1.25788	−0.0680185
$343$	20.1251	1.08665
$344$	3.91535	0.211101
$345$	−4.51723	−0.243199
$346$	−17.9027	−0.962453
$347$	15.3170	0.822261	0.411131	−	0.911576i	$-0.365134\pi$
$347$	15.3170	0.822261	0.411131	+	0.911576i	$0.365134\pi$
$348$	4.34150	0.232729
$349$	−6.21125	−0.332480	−0.166240	−	0.986085i	$-0.553163\pi$
$349$	−6.21125	−0.332480	−0.166240	+	0.986085i	$0.553163\pi$
$350$	−8.04071	−0.429794
$351$	3.43637	0.183420
$352$	−2.08413	−0.111085
$353$	−27.5688	−1.46734	−0.733669	−	0.679507i	$-0.762194\pi$
$353$	−27.5688	−1.46734	−0.733669	+	0.679507i	$0.762194\pi$
$354$	−2.76000	−0.146692
$355$	−10.3144	−0.547434
$356$	3.29596	0.174686
$357$	0.295623	0.0156461
$358$	−8.45060	−0.446628
$359$	18.9020	0.997610	0.498805	−	0.866714i	$-0.333772\pi$
$359$	18.9020	0.997610	0.498805	+	0.866714i	$0.333772\pi$
$360$	0.710070	0.0374240
$361$	−14.5960	−0.768209
$362$	−6.27324	−0.329714
$363$	10.3133	0.541309
$364$	−1.37755	−0.0722033
$365$	8.52647	0.446296
$366$	1.14050	0.0596146
$367$	25.5971	1.33616	0.668080	−	0.744089i	$-0.267116\pi$
$367$	25.5971	1.33616	0.668080	+	0.744089i	$0.267116\pi$
$368$	2.46108	0.128293
$369$	−2.39498	−0.124678
$370$	1.66488	0.0865528
$371$	−11.6853	−0.606668
$372$	−8.56451	−0.444049
$373$	8.94235	0.463018	0.231509	−	0.972833i	$-0.425634\pi$
$373$	8.94235	0.463018	0.231509	+	0.972833i	$0.425634\pi$
$374$	−0.177871	−0.00919752
$375$	15.7788	0.814814
$376$	3.08120	0.158901
$377$	−1.72659	−0.0889239
$378$	12.4678	0.641272
$379$	−36.9425	−1.89761	−0.948804	−	0.315866i	$-0.897705\pi$
$379$	−36.9425	−1.89761	−0.948804	+	0.315866i	$0.897705\pi$
$380$	−2.48606	−0.127532
$381$	2.88441	0.147773
$382$	−6.42003	−0.328477
$383$	38.3775	1.96100	0.980498	−	0.196529i	$-0.0629669\pi$
$383$	38.3775	1.96100	0.980498	+	0.196529i	$0.0629669\pi$
$384$	1.54939	0.0790669
$385$	−5.51963	−0.281306
$386$	−17.3140	−0.881260
$387$	2.34685	0.119297
$388$	3.18740	0.161816
$389$	36.1897	1.83489	0.917445	−	0.397864i	$-0.130248\pi$
$389$	36.1897	1.83489	0.917445	+	0.397864i	$0.130248\pi$
$390$	1.13098	0.0572695
$391$	0.210042	0.0106223
$392$	2.00200	0.101116
$393$	10.1766	0.513342
$394$	−11.1575	−0.562107
$395$	−5.25477	−0.264396
$396$	−1.24923	−0.0627760
$397$	−20.9953	−1.05372	−0.526862	−	0.849951i	$-0.676631\pi$
$397$	−20.9953	−1.05372	−0.526862	+	0.849951i	$0.676631\pi$
$398$	17.7646	0.890461
$399$	−7.26914	−0.363912
$400$	−3.59663	−0.179832
$401$	20.1314	1.00531	0.502656	−	0.864487i	$-0.332356\pi$
$401$	20.1314	1.00531	0.502656	+	0.864487i	$0.332356\pi$
$402$	12.7277	0.634802
$403$	3.40606	0.169668
$404$	−16.7232	−0.832012
$405$	−8.10592	−0.402786
$406$	−6.26437	−0.310896
$407$	−2.92902	−0.145186
$408$	0.132233	0.00654652
$409$	−14.3918	−0.711629	−0.355814	−	0.934557i	$-0.615797\pi$
$409$	−14.3918	−0.711629	−0.355814	+	0.934557i	$0.615797\pi$
$410$	−4.73339	−0.233766
$411$	5.23443	0.258195
$412$	12.2582	0.603917
$413$	3.98242	0.195962
$414$	1.47517	0.0725006
$415$	−17.1703	−0.842858
$416$	−0.616183	−0.0302109
$417$	−6.94867	−0.340278
$418$	4.37372	0.213926
$419$	3.67054	0.179318	0.0896588	−	0.995973i	$-0.471422\pi$
$419$	3.67054	0.179318	0.0896588	+	0.995973i	$0.471422\pi$
$420$	4.10340	0.200225
$421$	−16.7506	−0.816377	−0.408188	−	0.912898i	$-0.633839\pi$
$421$	−16.7506	−0.816377	−0.408188	+	0.912898i	$0.633839\pi$
$422$	−23.0967	−1.12433
$423$	1.84686	0.0897976
$424$	−5.22685	−0.253838
$425$	−0.306956	−0.0148896
$426$	−13.4903	−0.653605
$427$	−1.64563	−0.0796375
$428$	4.70273	0.227315
$429$	−1.98974	−0.0960654
$430$	4.63827	0.223677
$431$	31.9911	1.54096	0.770480	−	0.637465i	$-0.220017\pi$
$431$	31.9911	1.54096	0.770480	+	0.637465i	$0.220017\pi$
$432$	5.57686	0.268317
$433$	22.1535	1.06463	0.532315	−	0.846547i	$-0.321322\pi$
$433$	22.1535	1.06463	0.532315	+	0.846547i	$0.321322\pi$
$434$	12.3578	0.593193
$435$	5.14310	0.246593
$436$	9.20986	0.441072
$437$	−5.16477	−0.247065
$438$	11.1518	0.532852
$439$	11.9672	0.571163	0.285581	−	0.958354i	$-0.407813\pi$
$439$	11.9672	0.571163	0.285581	+	0.958354i	$0.407813\pi$
$440$	−2.46895	−0.117702
$441$	1.19999	0.0571426
$442$	−0.0525885	−0.00250138
$443$	27.8304	1.32226	0.661132	−	0.750270i	$-0.270076\pi$
$443$	27.8304	1.32226	0.661132	+	0.750270i	$0.270076\pi$
$444$	2.17749	0.103339
$445$	3.90452	0.185092
$446$	4.39676	0.208193
$447$	−9.67357	−0.457544
$448$	−2.23562	−0.105623
$449$	−18.8760	−0.890814	−0.445407	−	0.895328i	$-0.646941\pi$
$449$	−18.8760	−0.890814	−0.445407	+	0.895328i	$0.646941\pi$
$450$	−2.15581	−0.101626
$451$	8.32746	0.392125
$452$	−4.26029	−0.200387
$453$	−20.4604	−0.961312
$454$	−8.34531	−0.391665
$455$	−1.63190	−0.0765047
$456$	−3.25151	−0.152266
$457$	31.0685	1.45332	0.726661	−	0.686996i	$-0.241071\pi$
$457$	31.0685	1.45332	0.726661	+	0.686996i	$0.241071\pi$
$458$	4.18222	0.195422
$459$	0.475960	0.0222159
$460$	2.91549	0.135936
$461$	−5.78443	−0.269408	−0.134704	−	0.990886i	$-0.543008\pi$
$461$	−5.78443	−0.269408	−0.134704	+	0.990886i	$0.543008\pi$
$462$	−7.21912	−0.335864
$463$	5.55388	0.258111	0.129055	−	0.991637i	$-0.458806\pi$
$463$	5.55388	0.258111	0.129055	+	0.991637i	$0.458806\pi$
$464$	−2.80207	−0.130083
$465$	−10.1458	−0.470503
$466$	12.4407	0.576306
$467$	28.9515	1.33971	0.669857	−	0.742490i	$-0.266355\pi$
$467$	28.9515	1.33971	0.669857	+	0.742490i	$0.266355\pi$
$468$	−0.369339	−0.0170727
$469$	−18.3649	−0.848013
$470$	3.65011	0.168367
$471$	7.23289	0.333274
$472$	1.78135	0.0819932
$473$	−8.16011	−0.375202
$474$	−6.87271	−0.315674
$475$	7.54781	0.346317
$476$	−0.190800	−0.00874531
$477$	−3.13296	−0.143449
$478$	3.45695	0.158117
$479$	−13.6257	−0.622572	−0.311286	−	0.950316i	$-0.600760\pi$
$479$	−13.6257	−0.622572	−0.311286	+	0.950316i	$0.600760\pi$
$480$	1.83546	0.0837771
$481$	−0.865976	−0.0394851
$482$	−20.4983	−0.933672
$483$	8.52481	0.387892
$484$	−6.65638	−0.302563
$485$	3.77592	0.171456
$486$	6.12886	0.278011
$487$	13.2519	0.600500	0.300250	−	0.953861i	$-0.402930\pi$
$487$	13.2519	0.600500	0.300250	+	0.953861i	$0.402930\pi$
$488$	−0.736094	−0.0333214
$489$	4.48539	0.202836
$490$	2.37164	0.107140
$491$	32.5756	1.47012	0.735059	−	0.678003i	$-0.237155\pi$
$491$	32.5756	1.47012	0.735059	+	0.678003i	$0.237155\pi$
$492$	−6.19080	−0.279103
$493$	−0.239144	−0.0107705
$494$	1.29311	0.0581797
$495$	−1.47988	−0.0665157
$496$	5.52768	0.248200
$497$	19.4652	0.873132
$498$	−22.4571	−1.00632
$499$	−16.4762	−0.737578	−0.368789	−	0.929513i	$-0.620227\pi$
$499$	−16.4762	−0.737578	−0.368789	+	0.929513i	$0.620227\pi$
$500$	−10.1839	−0.455438
$501$	0.468097	0.0209130
$502$	−23.5592	−1.05150
$503$	−17.5764	−0.783692	−0.391846	−	0.920031i	$-0.628163\pi$
$503$	−17.5764	−0.783692	−0.391846	+	0.920031i	$0.628163\pi$
$504$	−1.34003	−0.0596895
$505$	−19.8110	−0.881578
$506$	−5.12923	−0.228022
$507$	19.5538	0.868413
$508$	−1.86165	−0.0825972
$509$	−41.3926	−1.83470	−0.917348	−	0.398086i	$-0.869675\pi$
$509$	−41.3926	−1.83470	−0.917348	+	0.398086i	$0.869675\pi$
$510$	0.156649	0.00693652
$511$	−16.0909	−0.711821
$512$	−1.00000	−0.0441942
$513$	−11.7035	−0.516721
$514$	−7.83129	−0.345423
$515$	14.5215	0.639894
$516$	6.06639	0.267058
$517$	−6.42163	−0.282423
$518$	−3.14192	−0.138048
$519$	−27.7382	−1.21757
$520$	−0.729954	−0.0320106
$521$	−2.04085	−0.0894114	−0.0447057	−	0.999000i	$-0.514235\pi$
$521$	−2.04085	−0.0894114	−0.0447057	+	0.999000i	$0.514235\pi$
$522$	−1.67956	−0.0735122
$523$	30.2047	1.32076	0.660379	−	0.750933i	$-0.270396\pi$
$523$	30.2047	1.32076	0.660379	+	0.750933i	$0.270396\pi$
$524$	−6.56815	−0.286931
$525$	−12.4582	−0.543719
$526$	−9.97057	−0.434738
$527$	0.471762	0.0205503
$528$	−3.22913	−0.140530
$529$	−16.9431	−0.736655
$530$	−6.19193	−0.268960
$531$	1.06774	0.0463358
$532$	4.69162	0.203408
$533$	2.46205	0.106643
$534$	5.10672	0.220989
$535$	5.57104	0.240857
$536$	−8.21469	−0.354820
$537$	−13.0933	−0.565016
$538$	18.2496	0.786796
$539$	−4.17243	−0.179719
$540$	6.60656	0.284301
$541$	3.86461	0.166153	0.0830763	−	0.996543i	$-0.473525\pi$
$541$	3.86461	0.166153	0.0830763	+	0.996543i	$0.473525\pi$
$542$	20.8667	0.896304
$543$	−9.71967	−0.417111
$544$	−0.0853455	−0.00365916
$545$	10.9104	0.467348
$546$	−2.13436	−0.0913423
$547$	34.1464	1.45999	0.729997	−	0.683451i	$-0.239522\pi$
$547$	34.1464	1.45999	0.729997	+	0.683451i	$0.239522\pi$
$548$	−3.37838	−0.144317
$549$	−0.441213	−0.0188305
$550$	7.49586	0.319625
$551$	5.88037	0.250512
$552$	3.81317	0.162299
$553$	9.91668	0.421700
$554$	31.6857	1.34620
$555$	2.57954	0.109495
$556$	4.48479	0.190197
$557$	17.8487	0.756272	0.378136	−	0.925750i	$-0.376565\pi$
$557$	17.8487	0.756272	0.378136	+	0.925750i	$0.376565\pi$
$558$	3.31328	0.140262
$559$	−2.41257	−0.102041
$560$	−2.64840	−0.111915
$561$	−0.275592	−0.0116355
$562$	16.0612	0.677499
$563$	40.3652	1.70119	0.850595	−	0.525822i	$-0.176242\pi$
$563$	40.3652	1.70119	0.850595	+	0.525822i	$0.176242\pi$
$564$	4.77397	0.201020
$565$	−5.04691	−0.212325
$566$	24.6154	1.03466
$567$	15.2973	0.642426
$568$	8.70683	0.365330
$569$	36.6768	1.53757	0.768786	−	0.639506i	$-0.220861\pi$
$569$	36.6768	1.53757	0.768786	+	0.639506i	$0.220861\pi$
$570$	−3.85186	−0.161337
$571$	14.0893	0.589620	0.294810	−	0.955556i	$-0.404744\pi$
$571$	14.0893	0.589620	0.294810	+	0.955556i	$0.404744\pi$
$572$	1.28421	0.0536954
$573$	−9.94711	−0.415546
$574$	8.93274	0.372846
$575$	−8.85161	−0.369138
$576$	−0.599398	−0.0249749
$577$	−16.5259	−0.687983	−0.343991	−	0.938973i	$-0.611779\pi$
$577$	−16.5259	−0.687983	−0.343991	+	0.938973i	$0.611779\pi$
$578$	16.9927	0.706804
$579$	−26.8261	−1.11486
$580$	−3.31944	−0.137832
$581$	32.4034	1.34432
$582$	4.93853	0.204708
$583$	10.8935	0.451161
$584$	−7.19753	−0.297836
$585$	−0.437533	−0.0180898
$586$	24.9600	1.03109
$587$	−4.17748	−0.172423	−0.0862116	−	0.996277i	$-0.527476\pi$
$587$	−4.17748	−0.172423	−0.0862116	+	0.996277i	$0.527476\pi$
$588$	3.10187	0.127919
$589$	−11.6003	−0.477980
$590$	2.11025	0.0868777
$591$	−17.2873	−0.711104
$592$	−1.40539	−0.0577611
$593$	−10.3311	−0.424248	−0.212124	−	0.977243i	$-0.568038\pi$
$593$	−10.3311	−0.424248	−0.212124	+	0.977243i	$0.568038\pi$
$594$	−11.6229	−0.476895
$595$	−0.226029	−0.00926629
$596$	6.24348	0.255743
$597$	27.5243	1.12649
$598$	−1.51648	−0.0620134
$599$	−0.916716	−0.0374560	−0.0187280	−	0.999825i	$-0.505962\pi$
$599$	−0.916716	−0.0374560	−0.0187280	+	0.999825i	$0.505962\pi$
$600$	−5.57258	−0.227500
$601$	20.2716	0.826894	0.413447	−	0.910528i	$-0.364325\pi$
$601$	20.2716	0.826894	0.413447	+	0.910528i	$0.364325\pi$
$602$	−8.75323	−0.356755
$603$	−4.92387	−0.200515
$604$	13.2055	0.537323
$605$	−7.88541	−0.320587
$606$	−25.9108	−1.05255
$607$	−11.0198	−0.447280	−0.223640	−	0.974672i	$-0.571794\pi$
$607$	−11.0198	−0.447280	−0.223640	+	0.974672i	$0.571794\pi$
$608$	2.09858	0.0851086
$609$	−9.70594	−0.393305
$610$	−0.872005	−0.0353065
$611$	−1.89858	−0.0768084
$612$	−0.0511559	−0.00206786
$613$	26.2104	1.05863	0.529314	−	0.848426i	$-0.322450\pi$
$613$	26.2104	1.05863	0.529314	+	0.848426i	$0.322450\pi$
$614$	−25.6563	−1.03540
$615$	−7.33386	−0.295730
$616$	4.65933	0.187730
$617$	−48.3128	−1.94500	−0.972501	−	0.232900i	$-0.925179\pi$
$617$	−48.3128	−1.94500	−0.972501	+	0.232900i	$0.925179\pi$
$618$	18.9927	0.763997
$619$	−15.3177	−0.615671	−0.307836	−	0.951440i	$-0.599605\pi$
$619$	−15.3177	−0.615671	−0.307836	+	0.951440i	$0.599605\pi$
$620$	6.54830	0.262986
$621$	13.7251	0.550770
$622$	−13.6939	−0.549077
$623$	−7.36852	−0.295213
$624$	−0.954706	−0.0382188
$625$	5.91893	0.236757
$626$	−14.1322	−0.564838
$627$	6.77658	0.270631
$628$	−4.66822	−0.186282
$629$	−0.119944	−0.00478246
$630$	−1.58745	−0.0632454
$631$	26.5314	1.05620	0.528099	−	0.849183i	$-0.322905\pi$
$631$	26.5314	1.05620	0.528099	+	0.849183i	$0.322905\pi$
$632$	4.43576	0.176445
$633$	−35.7858	−1.42236
$634$	−21.0108	−0.834447
$635$	−2.20538	−0.0875177
$636$	−8.09842	−0.321123
$637$	−1.23360	−0.0488769
$638$	5.83989	0.231204
$639$	5.21886	0.206455
$640$	−1.18464	−0.0468269
$641$	−42.8302	−1.69169	−0.845845	−	0.533429i	$-0.820903\pi$
$641$	−42.8302	−1.69169	−0.845845	+	0.533429i	$0.820903\pi$
$642$	7.28636	0.287570
$643$	37.0297	1.46031	0.730154	−	0.683283i	$-0.239448\pi$
$643$	37.0297	1.46031	0.730154	+	0.683283i	$0.239448\pi$
$644$	−5.50205	−0.216811
$645$	7.18648	0.282967
$646$	0.179104	0.00704676
$647$	26.3476	1.03583	0.517916	−	0.855431i	$-0.326708\pi$
$647$	26.3476	1.03583	0.517916	+	0.855431i	$0.326708\pi$
$648$	6.84253	0.268800
$649$	−3.71257	−0.145731
$650$	2.21618	0.0869259
$651$	19.1470	0.750430
$652$	−2.89494	−0.113375
$653$	33.2456	1.30100	0.650500	−	0.759506i	$-0.274559\pi$
$653$	33.2456	1.30100	0.650500	+	0.759506i	$0.274559\pi$
$654$	14.2696	0.557987
$655$	−7.78088	−0.304024
$656$	3.99564	0.156004
$657$	−4.31418	−0.168312
$658$	−6.88839	−0.268538
$659$	44.2476	1.72364	0.861822	−	0.507212i	$-0.169324\pi$
$659$	44.2476	1.72364	0.861822	+	0.507212i	$0.169324\pi$
$660$	−3.82535	−0.148902
$661$	30.7252	1.19507	0.597536	−	0.801842i	$-0.296147\pi$
$661$	30.7252	1.19507	0.597536	+	0.801842i	$0.296147\pi$
$662$	2.17808	0.0846535
$663$	−0.0814799	−0.00316442
$664$	14.4941	0.562482
$665$	5.55788	0.215525
$666$	−0.842387	−0.0326418
$667$	−6.89613	−0.267019
$668$	−0.302117	−0.0116893
$669$	6.81228	0.263378
$670$	−9.73143	−0.375958
$671$	1.53412	0.0592240
$672$	−3.46384	−0.133621
$673$	−27.1464	−1.04642	−0.523209	−	0.852204i	$-0.675265\pi$
$673$	−27.1464	−1.04642	−0.523209	+	0.852204i	$0.675265\pi$
$674$	−8.57052	−0.330124
$675$	−20.0579	−0.772030
$676$	−12.6203	−0.485397
$677$	−32.1746	−1.23657	−0.618284	−	0.785954i	$-0.712172\pi$
$677$	−32.1746	−1.23657	−0.618284	+	0.785954i	$0.712172\pi$
$678$	−6.60085	−0.253504
$679$	−7.12583	−0.273464
$680$	−0.101104	−0.00387714
$681$	−12.9301	−0.495483
$682$	−11.5204	−0.441140
$683$	13.7038	0.524360	0.262180	−	0.965019i	$-0.415559\pi$
$683$	13.7038	0.524360	0.262180	+	0.965019i	$0.415559\pi$
$684$	1.25788	0.0480964
$685$	−4.00216	−0.152915
$686$	−20.1251	−0.768378
$687$	6.47988	0.247223
$688$	−3.91535	−0.149271
$689$	3.22070	0.122699
$690$	4.51723	0.171968
$691$	3.51426	0.133689	0.0668445	−	0.997763i	$-0.478707\pi$
$691$	3.51426	0.133689	0.0668445	+	0.997763i	$0.478707\pi$
$692$	17.9027	0.680557
$693$	2.79280	0.106090
$694$	−15.3170	−0.581426
$695$	5.31285	0.201528
$696$	−4.34150	−0.164564
$697$	0.341010	0.0129167
$698$	6.21125	0.235099
$699$	19.2755	0.729067
$700$	8.04071	0.303910
$701$	8.31720	0.314136	0.157068	−	0.987588i	$-0.449796\pi$
$701$	8.31720	0.314136	0.157068	+	0.987588i	$0.449796\pi$
$702$	−3.43637	−0.129697
$703$	2.94932	0.111236
$704$	2.08413	0.0785488
$705$	5.65543	0.212996
$706$	27.5688	1.03757
$707$	37.3868	1.40608
$708$	2.76000	0.103727
$709$	46.3478	1.74063	0.870314	−	0.492497i	$-0.163916\pi$
$709$	46.3478	1.74063	0.870314	+	0.492497i	$0.163916\pi$
$710$	10.3144	0.387094
$711$	2.65879	0.0997123
$712$	−3.29596	−0.123521
$713$	13.6041	0.509476
$714$	−0.295623	−0.0110634
$715$	1.52132	0.0568942
$716$	8.45060	0.315814
$717$	5.35616	0.200029
$718$	−18.9020	−0.705417
$719$	−30.3126	−1.13047	−0.565235	−	0.824930i	$-0.691215\pi$
$719$	−30.3126	−1.13047	−0.565235	+	0.824930i	$0.691215\pi$
$720$	−0.710070	−0.0264627
$721$	−27.4046	−1.02060
$722$	14.5960	0.543206
$723$	−31.7598	−1.18116
$724$	6.27324	0.233143
$725$	10.0780	0.374288
$726$	−10.3133	−0.382763
$727$	21.5438	0.799015	0.399508	−	0.916730i	$-0.369181\pi$
$727$	21.5438	0.799015	0.399508	+	0.916730i	$0.369181\pi$
$728$	1.37755	0.0510555
$729$	30.0236	1.11198
$730$	−8.52647	−0.315579
$731$	−0.334157	−0.0123593
$732$	−1.14050	−0.0421539
$733$	33.5105	1.23774	0.618870	−	0.785493i	$-0.287591\pi$
$733$	33.5105	1.23774	0.618870	+	0.785493i	$0.287591\pi$
$734$	−25.5971	−0.944808
$735$	3.67459	0.135539
$736$	−2.46108	−0.0907167
$737$	17.1205	0.630642
$738$	2.39498	0.0881605
$739$	27.5671	1.01407	0.507036	−	0.861925i	$-0.330741\pi$
$739$	27.5671	1.01407	0.507036	+	0.861925i	$0.330741\pi$
$740$	−1.66488	−0.0612021
$741$	2.00353	0.0736013
$742$	11.6853	0.428979
$743$	53.7865	1.97323	0.986617	−	0.163052i	$-0.0521339\pi$
$743$	53.7865	1.97323	0.986617	+	0.163052i	$0.0521339\pi$
$744$	8.56451	0.313990
$745$	7.39627	0.270978
$746$	−8.94235	−0.327403
$747$	8.68776	0.317869
$748$	0.177871	0.00650363
$749$	−10.5135	−0.384156
$750$	−15.7788	−0.576161
$751$	35.7743	1.30542	0.652711	−	0.757607i	$-0.273632\pi$
$751$	35.7743	1.30542	0.652711	+	0.757607i	$0.273632\pi$
$752$	−3.08120	−0.112360
$753$	−36.5023	−1.33022
$754$	1.72659	0.0628787
$755$	15.6437	0.569332
$756$	−12.4678	−0.453448
$757$	21.6522	0.786961	0.393481	−	0.919333i	$-0.371271\pi$
$757$	21.6522	0.786961	0.393481	+	0.919333i	$0.371271\pi$
$758$	36.9425	1.34181
$759$	−7.94716	−0.288464
$760$	2.48606	0.0901787
$761$	32.3912	1.17418	0.587090	−	0.809522i	$-0.300274\pi$
$761$	32.3912	1.17418	0.587090	+	0.809522i	$0.300274\pi$
$762$	−2.88441	−0.104491
$763$	−20.5898	−0.745400
$764$	6.42003	0.232268
$765$	−0.0606013	−0.00219104
$766$	−38.3775	−1.38663
$767$	−1.09764	−0.0396333
$768$	−1.54939	−0.0559087
$769$	−13.8100	−0.498002	−0.249001	−	0.968503i	$-0.580102\pi$
$769$	−13.8100	−0.498002	−0.249001	+	0.968503i	$0.580102\pi$
$770$	5.51963	0.198914
$771$	−12.1337	−0.436985
$772$	17.3140	0.623145
$773$	−32.3956	−1.16519	−0.582594	−	0.812763i	$-0.697962\pi$
$773$	−32.3956	−1.16519	−0.582594	+	0.812763i	$0.697962\pi$
$774$	−2.34685	−0.0843558
$775$	−19.8810	−0.714147
$776$	−3.18740	−0.114421
$777$	−4.86804	−0.174640
$778$	−36.1897	−1.29746
$779$	−8.38517	−0.300430
$780$	−1.13098	−0.0404956
$781$	−18.1462	−0.649322
$782$	−0.210042	−0.00751110
$783$	−15.6268	−0.558455
$784$	−2.00200	−0.0714999
$785$	−5.53016	−0.197380
$786$	−10.1766	−0.362988
$787$	6.98886	0.249126	0.124563	−	0.992212i	$-0.460247\pi$
$787$	6.98886	0.249126	0.124563	+	0.992212i	$0.460247\pi$
$788$	11.1575	0.397470
$789$	−15.4483	−0.549973
$790$	5.25477	0.186956
$791$	9.52440	0.338649
$792$	1.24923	0.0443893
$793$	0.453569	0.0161067
$794$	20.9953	0.745095
$795$	−9.59369	−0.340253
$796$	−17.7646	−0.629651
$797$	41.9641	1.48644	0.743222	−	0.669045i	$-0.233297\pi$
$797$	41.9641	1.48644	0.743222	+	0.669045i	$0.233297\pi$
$798$	7.26914	0.257325
$799$	−0.262966	−0.00930309
$800$	3.59663	0.127160
$801$	−1.97559	−0.0698041
$802$	−20.1314	−0.710863
$803$	15.0006	0.529360
$804$	−12.7277	−0.448873
$805$	−6.51794	−0.229727
$806$	−3.40606	−0.119973
$807$	28.2757	0.995352
$808$	16.7232	0.588322
$809$	7.93893	0.279118	0.139559	−	0.990214i	$-0.455432\pi$
$809$	7.93893	0.279118	0.139559	+	0.990214i	$0.455432\pi$
$810$	8.10592	0.284813
$811$	45.6182	1.60187	0.800936	−	0.598751i	$-0.204336\pi$
$811$	45.6182	1.60187	0.800936	+	0.598751i	$0.204336\pi$
$812$	6.26437	0.219836
$813$	32.3307	1.13389
$814$	2.92902	0.102662
$815$	−3.42946	−0.120129
$816$	−0.132233	−0.00462909
$817$	8.21666	0.287464
$818$	14.3918	0.503198
$819$	0.825702	0.0288524
$820$	4.73339	0.165297
$821$	−47.1851	−1.64677	−0.823386	−	0.567482i	$-0.807918\pi$
$821$	−47.1851	−1.64677	−0.823386	+	0.567482i	$0.807918\pi$
$822$	−5.23443	−0.182572
$823$	−45.8349	−1.59770	−0.798852	−	0.601528i	$-0.794559\pi$
$823$	−45.8349	−1.59770	−0.798852	+	0.601528i	$0.794559\pi$
$824$	−12.2582	−0.427034
$825$	11.6140	0.404348
$826$	−3.98242	−0.138566
$827$	11.1175	0.386593	0.193297	−	0.981140i	$-0.438082\pi$
$827$	11.1175	0.386593	0.193297	+	0.981140i	$0.438082\pi$
$828$	−1.47517	−0.0512656
$829$	−22.3646	−0.776753	−0.388377	−	0.921501i	$-0.626964\pi$
$829$	−22.3646	−0.776753	−0.388377	+	0.921501i	$0.626964\pi$
$830$	17.1703	0.595990
$831$	49.0934	1.70303
$832$	0.616183	0.0213623
$833$	−0.170862	−0.00592000
$834$	6.94867	0.240613
$835$	−0.357900	−0.0123856
$836$	−4.37372	−0.151268
$837$	30.8271	1.06554
$838$	−3.67054	−0.126797
$839$	25.3237	0.874270	0.437135	−	0.899396i	$-0.355993\pi$
$839$	25.3237	0.874270	0.437135	+	0.899396i	$0.355993\pi$
$840$	−4.10340	−0.141581
$841$	−21.1484	−0.729255
$842$	16.7506	0.577265
$843$	24.8850	0.857083
$844$	23.0967	0.795023
$845$	−14.9505	−0.514313
$846$	−1.84686	−0.0634965
$847$	14.8812	0.511322
$848$	5.22685	0.179491
$849$	38.1387	1.30892
$850$	0.306956	0.0105285
$851$	−3.45878	−0.118565
$852$	13.4903	0.462168
$853$	−14.4782	−0.495723	−0.247861	−	0.968796i	$-0.579728\pi$
$853$	−14.4782	−0.495723	−0.247861	+	0.968796i	$0.579728\pi$
$854$	1.64563	0.0563122
$855$	1.49014	0.0509616
$856$	−4.70273	−0.160736
$857$	39.3597	1.34450	0.672251	−	0.740324i	$-0.265328\pi$
$857$	39.3597	1.34450	0.672251	+	0.740324i	$0.265328\pi$
$858$	1.98974	0.0679285
$859$	31.4140	1.07183	0.535915	−	0.844272i	$-0.319967\pi$
$859$	31.4140	1.07183	0.535915	+	0.844272i	$0.319967\pi$
$860$	−4.63827	−0.158164
$861$	13.8403	0.471676
$862$	−31.9911	−1.08962
$863$	−24.3105	−0.827539	−0.413769	−	0.910382i	$-0.635788\pi$
$863$	−24.3105	−0.827539	−0.413769	+	0.910382i	$0.635788\pi$
$864$	−5.57686	−0.189729
$865$	21.2082	0.721100
$866$	−22.1535	−0.752806
$867$	26.3283	0.894156
$868$	−12.3578	−0.419451
$869$	−9.24472	−0.313606
$870$	−5.14310	−0.174367
$871$	5.06175	0.171511
$872$	−9.20986	−0.311885
$873$	−1.91052	−0.0646614
$874$	5.16477	0.174701
$875$	22.7673	0.769677
$876$	−11.1518	−0.376783
$877$	−27.8307	−0.939776	−0.469888	−	0.882726i	$-0.655706\pi$
$877$	−27.8307	−0.939776	−0.469888	+	0.882726i	$0.655706\pi$
$878$	−11.9672	−0.403873
$879$	38.6727	1.30440
$880$	2.46895	0.0832281
$881$	2.65167	0.0893372	0.0446686	−	0.999002i	$-0.485777\pi$
$881$	2.65167	0.0893372	0.0446686	+	0.999002i	$0.485777\pi$
$882$	−1.19999	−0.0404059
$883$	4.85943	0.163533	0.0817664	−	0.996652i	$-0.473944\pi$
$883$	4.85943	0.163533	0.0817664	+	0.996652i	$0.473944\pi$
$884$	0.0525885	0.00176874
$885$	3.26960	0.109906
$886$	−27.8304	−0.934982
$887$	−1.07381	−0.0360551	−0.0180276	−	0.999837i	$-0.505739\pi$
$887$	−1.07381	−0.0360551	−0.0180276	+	0.999837i	$0.505739\pi$
$888$	−2.17749	−0.0730718
$889$	4.16194	0.139587
$890$	−3.90452	−0.130880
$891$	−14.2607	−0.477753
$892$	−4.39676	−0.147214
$893$	6.46614	0.216381
$894$	9.67357	0.323533
$895$	10.0109	0.334628
$896$	2.23562	0.0746869
$897$	−2.34961	−0.0784512
$898$	18.8760	0.629901
$899$	−15.4889	−0.516585
$900$	2.15581	0.0718605
$901$	0.446088	0.0148613
$902$	−8.32746	−0.277274
$903$	−13.5621	−0.451320
$904$	4.26029	0.141695
$905$	7.43151	0.247032
$906$	20.4604	0.679751
$907$	−22.2026	−0.737224	−0.368612	−	0.929583i	$-0.620167\pi$
$907$	−22.2026	−0.737224	−0.368612	+	0.929583i	$0.620167\pi$
$908$	8.34531	0.276949
$909$	10.0239	0.332471
$910$	1.63190	0.0540970
$911$	−23.1745	−0.767807	−0.383903	−	0.923373i	$-0.625420\pi$
$911$	−23.1745	−0.767807	−0.383903	+	0.923373i	$0.625420\pi$
$912$	3.25151	0.107668
$913$	−30.2077	−0.999730
$914$	−31.0685	−1.02765
$915$	−1.35107	−0.0446651
$916$	−4.18222	−0.138184
$917$	14.6839	0.484905
$918$	−0.475960	−0.0157090
$919$	0.655689	0.0216292	0.0108146	−	0.999942i	$-0.496558\pi$
$919$	0.655689	0.0216292	0.0108146	+	0.999942i	$0.496558\pi$
$920$	−2.91549	−0.0961210
$921$	−39.7516	−1.30986
$922$	5.78443	0.190500
$923$	−5.36500	−0.176591
$924$	7.21912	0.237491
$925$	5.05466	0.166196
$926$	−5.55388	−0.182512
$927$	−7.34753	−0.241324
$928$	2.80207	0.0919825
$929$	25.9128	0.850170	0.425085	−	0.905153i	$-0.360244\pi$
$929$	25.9128	0.850170	0.425085	+	0.905153i	$0.360244\pi$
$930$	10.1458	0.332696
$931$	4.20135	0.137694
$932$	−12.4407	−0.407510
$933$	−21.2172	−0.694621
$934$	−28.9515	−0.947321
$935$	0.210713	0.00689106
$936$	0.369339	0.0120722
$937$	45.5253	1.48725	0.743624	−	0.668598i	$-0.233105\pi$
$937$	45.5253	1.48725	0.743624	+	0.668598i	$0.233105\pi$
$938$	18.3649	0.599636
$939$	−21.8963	−0.714559
$940$	−3.65011	−0.119053
$941$	16.0068	0.521807	0.260904	−	0.965365i	$-0.415980\pi$
$941$	16.0068	0.521807	0.260904	+	0.965365i	$0.415980\pi$
$942$	−7.23289	−0.235660
$943$	9.83361	0.320226
$944$	−1.78135	−0.0579779
$945$	−14.7698	−0.480461
$946$	8.16011	0.265308
$947$	42.5454	1.38254	0.691271	−	0.722596i	$-0.257051\pi$
$947$	42.5454	1.38254	0.691271	+	0.722596i	$0.257051\pi$
$948$	6.87271	0.223215
$949$	4.43499	0.143966
$950$	−7.54781	−0.244883
$951$	−32.5539	−1.05563
$952$	0.190800	0.00618387
$953$	−1.44915	−0.0469426	−0.0234713	−	0.999725i	$-0.507472\pi$
$953$	−1.44915	−0.0469426	−0.0234713	+	0.999725i	$0.507472\pi$
$954$	3.13296	0.101433
$955$	7.60541	0.246105
$956$	−3.45695	−0.111806
$957$	9.04826	0.292489
$958$	13.6257	0.440225
$959$	7.55279	0.243892
$960$	−1.83546	−0.0592393
$961$	−0.444791	−0.0143481
$962$	0.865976	0.0279202
$963$	−2.81881	−0.0908349
$964$	20.4983	0.660206
$965$	20.5108	0.660268
$966$	−8.52481	−0.274281
$967$	42.8692	1.37858	0.689289	−	0.724486i	$-0.257923\pi$
$967$	42.8692	1.37858	0.689289	+	0.724486i	$0.257923\pi$
$968$	6.65638	0.213944
$969$	0.277502	0.00891464
$970$	−3.77592	−0.121238
$971$	23.4143	0.751402	0.375701	−	0.926741i	$-0.377402\pi$
$971$	23.4143	0.751402	0.375701	+	0.926741i	$0.377402\pi$
$972$	−6.12886	−0.196583
$973$	−10.0263	−0.321428
$974$	−13.2519	−0.424618
$975$	3.43373	0.109967
$976$	0.736094	0.0235618
$977$	51.5662	1.64975	0.824875	−	0.565316i	$-0.191246\pi$
$977$	51.5662	1.64975	0.824875	+	0.565316i	$0.191246\pi$
$978$	−4.48539	−0.143427
$979$	6.86922	0.219541
$980$	−2.37164	−0.0757594
$981$	−5.52037	−0.176252
$982$	−32.5756	−1.03953
$983$	−21.5589	−0.687621	−0.343811	−	0.939039i	$-0.611718\pi$
$983$	−21.5589	−0.687621	−0.343811	+	0.939039i	$0.611718\pi$
$984$	6.19080	0.197355
$985$	13.2176	0.421148
$986$	0.239144	0.00761591
$987$	−10.6728	−0.339719
$988$	−1.29311	−0.0411392
$989$	−9.63599	−0.306407
$990$	1.47988	0.0470337
$991$	−51.0819	−1.62267	−0.811335	−	0.584582i	$-0.801259\pi$
$991$	−51.0819	−1.62267	−0.811335	+	0.584582i	$0.801259\pi$
$992$	−5.52768	−0.175504
$993$	3.37469	0.107093
$994$	−19.4652	−0.617398
$995$	−21.0447	−0.667161
$996$	22.4571	0.711579
$997$	−22.8124	−0.722474	−0.361237	−	0.932474i	$-0.617646\pi$
$997$	−22.8124	−0.722474	−0.361237	+	0.932474i	$0.617646\pi$
$998$	16.4762	0.521546
$999$	−7.83766	−0.247972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.22	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.22	✓	77	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.54939 q^{3} +1.00000 q^{4} +1.18464 q^{5} +1.54939 q^{6} -2.23562 q^{7} -1.00000 q^{8} -0.599398 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.54939 q^{3} +1.00000 q^{4} +1.18464 q^{5} +1.54939 q^{6} -2.23562 q^{7} -1.00000 q^{8} -0.599398 q^{9} -1.18464 q^{10} +2.08413 q^{11} -1.54939 q^{12} +0.616183 q^{13} +2.23562 q^{14} -1.83546 q^{15} +1.00000 q^{16} +0.0853455 q^{17} +0.599398 q^{18} -2.09858 q^{19} +1.18464 q^{20} +3.46384 q^{21} -2.08413 q^{22} +2.46108 q^{23} +1.54939 q^{24} -3.59663 q^{25} -0.616183 q^{26} +5.57686 q^{27} -2.23562 q^{28} -2.80207 q^{29} +1.83546 q^{30} +5.52768 q^{31} -1.00000 q^{32} -3.22913 q^{33} -0.0853455 q^{34} -2.64840 q^{35} -0.599398 q^{36} -1.40539 q^{37} +2.09858 q^{38} -0.954706 q^{39} -1.18464 q^{40} +3.99564 q^{41} -3.46384 q^{42} -3.91535 q^{43} +2.08413 q^{44} -0.710070 q^{45} -2.46108 q^{46} -3.08120 q^{47} -1.54939 q^{48} -2.00200 q^{49} +3.59663 q^{50} -0.132233 q^{51} +0.616183 q^{52} +5.22685 q^{53} -5.57686 q^{54} +2.46895 q^{55} +2.23562 q^{56} +3.25151 q^{57} +2.80207 q^{58} -1.78135 q^{59} -1.83546 q^{60} +0.736094 q^{61} -5.52768 q^{62} +1.34003 q^{63} +1.00000 q^{64} +0.729954 q^{65} +3.22913 q^{66} +8.21469 q^{67} +0.0853455 q^{68} -3.81317 q^{69} +2.64840 q^{70} -8.70683 q^{71} +0.599398 q^{72} +7.19753 q^{73} +1.40539 q^{74} +5.57258 q^{75} -2.09858 q^{76} -4.65933 q^{77} +0.954706 q^{78} -4.43576 q^{79} +1.18464 q^{80} -6.84253 q^{81} -3.99564 q^{82} -14.4941 q^{83} +3.46384 q^{84} +0.101104 q^{85} +3.91535 q^{86} +4.34150 q^{87} -2.08413 q^{88} +3.29596 q^{89} +0.710070 q^{90} -1.37755 q^{91} +2.46108 q^{92} -8.56451 q^{93} +3.08120 q^{94} -2.48606 q^{95} +1.54939 q^{96} +3.18740 q^{97} +2.00200 q^{98} -1.24923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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