LMFDB - Embedded newform 8002.2.a.d.1.19

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:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.96903 q^{3} +1.00000 q^{4} +3.30115 q^{5} -1.96903 q^{6} +1.85739 q^{7} +1.00000 q^{8} +0.877064 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.96903 q^{3} +1.00000 q^{4} +3.30115 q^{5} -1.96903 q^{6} +1.85739 q^{7} +1.00000 q^{8} +0.877064 q^{9} +3.30115 q^{10} -3.08990 q^{11} -1.96903 q^{12} +2.43216 q^{13} +1.85739 q^{14} -6.50006 q^{15} +1.00000 q^{16} -4.43573 q^{17} +0.877064 q^{18} +1.86336 q^{19} +3.30115 q^{20} -3.65725 q^{21} -3.08990 q^{22} -7.06371 q^{23} -1.96903 q^{24} +5.89761 q^{25} +2.43216 q^{26} +4.18012 q^{27} +1.85739 q^{28} +1.65879 q^{29} -6.50006 q^{30} -9.92897 q^{31} +1.00000 q^{32} +6.08410 q^{33} -4.43573 q^{34} +6.13153 q^{35} +0.877064 q^{36} -9.20402 q^{37} +1.86336 q^{38} -4.78898 q^{39} +3.30115 q^{40} -9.80139 q^{41} -3.65725 q^{42} +1.14766 q^{43} -3.08990 q^{44} +2.89532 q^{45} -7.06371 q^{46} +1.76021 q^{47} -1.96903 q^{48} -3.55010 q^{49} +5.89761 q^{50} +8.73408 q^{51} +2.43216 q^{52} -3.91707 q^{53} +4.18012 q^{54} -10.2002 q^{55} +1.85739 q^{56} -3.66900 q^{57} +1.65879 q^{58} +11.0174 q^{59} -6.50006 q^{60} -11.4546 q^{61} -9.92897 q^{62} +1.62905 q^{63} +1.00000 q^{64} +8.02891 q^{65} +6.08410 q^{66} -3.36449 q^{67} -4.43573 q^{68} +13.9086 q^{69} +6.13153 q^{70} +1.81745 q^{71} +0.877064 q^{72} +3.70540 q^{73} -9.20402 q^{74} -11.6125 q^{75} +1.86336 q^{76} -5.73916 q^{77} -4.78898 q^{78} -8.92708 q^{79} +3.30115 q^{80} -10.8620 q^{81} -9.80139 q^{82} +7.98237 q^{83} -3.65725 q^{84} -14.6430 q^{85} +1.14766 q^{86} -3.26619 q^{87} -3.08990 q^{88} -9.55337 q^{89} +2.89532 q^{90} +4.51746 q^{91} -7.06371 q^{92} +19.5504 q^{93} +1.76021 q^{94} +6.15122 q^{95} -1.96903 q^{96} -18.5452 q^{97} -3.55010 q^{98} -2.71004 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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
$3$	−1.96903	−1.13682	−0.568409	−	0.822746i	$-0.692441\pi$
$3$	−1.96903	−1.13682	−0.568409	+	0.822746i	$0.692441\pi$
$4$	1.00000	0.500000
$5$	3.30115	1.47632	0.738160	−	0.674626i	$-0.235695\pi$
$5$	3.30115	1.47632	0.738160	+	0.674626i	$0.235695\pi$
$6$	−1.96903	−0.803852
$7$	1.85739	0.702028	0.351014	−	0.936370i	$-0.385837\pi$
$7$	1.85739	0.702028	0.351014	+	0.936370i	$0.385837\pi$
$8$	1.00000	0.353553
$9$	0.877064	0.292355
$10$	3.30115	1.04392
$11$	−3.08990	−0.931641	−0.465820	−	0.884879i	$-0.654241\pi$
$11$	−3.08990	−0.931641	−0.465820	+	0.884879i	$0.654241\pi$
$12$	−1.96903	−0.568409
$13$	2.43216	0.674558	0.337279	−	0.941405i	$-0.390493\pi$
$13$	2.43216	0.674558	0.337279	+	0.941405i	$0.390493\pi$
$14$	1.85739	0.496409
$15$	−6.50006	−1.67831
$16$	1.00000	0.250000
$17$	−4.43573	−1.07582	−0.537912	−	0.843001i	$-0.680787\pi$
$17$	−4.43573	−1.07582	−0.537912	+	0.843001i	$0.680787\pi$
$18$	0.877064	0.206726
$19$	1.86336	0.427483	0.213742	−	0.976890i	$-0.431435\pi$
$19$	1.86336	0.427483	0.213742	+	0.976890i	$0.431435\pi$
$20$	3.30115	0.738160
$21$	−3.65725	−0.798078
$22$	−3.08990	−0.658769
$23$	−7.06371	−1.47288	−0.736442	−	0.676500i	$-0.763496\pi$
$23$	−7.06371	−1.47288	−0.736442	+	0.676500i	$0.763496\pi$
$24$	−1.96903	−0.401926
$25$	5.89761	1.17952
$26$	2.43216	0.476985
$27$	4.18012	0.804464
$28$	1.85739	0.351014
$29$	1.65879	0.308029	0.154014	−	0.988069i	$-0.450780\pi$
$29$	1.65879	0.308029	0.154014	+	0.988069i	$0.450780\pi$
$30$	−6.50006	−1.18674
$31$	−9.92897	−1.78330	−0.891648	−	0.452729i	$-0.850451\pi$
$31$	−9.92897	−1.78330	−0.891648	+	0.452729i	$0.850451\pi$
$32$	1.00000	0.176777
$33$	6.08410	1.05911
$34$	−4.43573	−0.760722
$35$	6.13153	1.03642
$36$	0.877064	0.146177
$37$	−9.20402	−1.51313	−0.756566	−	0.653918i	$-0.773124\pi$
$37$	−9.20402	−1.51313	−0.756566	+	0.653918i	$0.773124\pi$
$38$	1.86336	0.302276
$39$	−4.78898	−0.766850
$40$	3.30115	0.521958
$41$	−9.80139	−1.53072	−0.765360	−	0.643602i	$-0.777439\pi$
$41$	−9.80139	−1.53072	−0.765360	+	0.643602i	$0.777439\pi$
$42$	−3.65725	−0.564326
$43$	1.14766	0.175017	0.0875085	−	0.996164i	$-0.472110\pi$
$43$	1.14766	0.175017	0.0875085	+	0.996164i	$0.472110\pi$
$44$	−3.08990	−0.465820
$45$	2.89532	0.431609
$46$	−7.06371	−1.04149
$47$	1.76021	0.256753	0.128376	−	0.991726i	$-0.459023\pi$
$47$	1.76021	0.256753	0.128376	+	0.991726i	$0.459023\pi$
$48$	−1.96903	−0.284204
$49$	−3.55010	−0.507157
$50$	5.89761	0.834048
$51$	8.73408	1.22302
$52$	2.43216	0.337279
$53$	−3.91707	−0.538051	−0.269025	−	0.963133i	$-0.586702\pi$
$53$	−3.91707	−0.538051	−0.269025	+	0.963133i	$0.586702\pi$
$54$	4.18012	0.568842
$55$	−10.2002	−1.37540
$56$	1.85739	0.248204
$57$	−3.66900	−0.485971
$58$	1.65879	0.217809
$59$	11.0174	1.43434	0.717169	−	0.696900i	$-0.245438\pi$
$59$	11.0174	1.43434	0.717169	+	0.696900i	$0.245438\pi$
$60$	−6.50006	−0.839153
$61$	−11.4546	−1.46661	−0.733306	−	0.679899i	$-0.762024\pi$
$61$	−11.4546	−1.46661	−0.733306	+	0.679899i	$0.762024\pi$
$62$	−9.92897	−1.26098
$63$	1.62905	0.205241
$64$	1.00000	0.125000
$65$	8.02891	0.995864
$66$	6.08410	0.748901
$67$	−3.36449	−0.411038	−0.205519	−	0.978653i	$-0.565888\pi$
$67$	−3.36449	−0.411038	−0.205519	+	0.978653i	$0.565888\pi$
$68$	−4.43573	−0.537912
$69$	13.9086	1.67440
$70$	6.13153	0.732858
$71$	1.81745	0.215692	0.107846	−	0.994168i	$-0.465605\pi$
$71$	1.81745	0.215692	0.107846	+	0.994168i	$0.465605\pi$
$72$	0.877064	0.103363
$73$	3.70540	0.433684	0.216842	−	0.976207i	$-0.430424\pi$
$73$	3.70540	0.433684	0.216842	+	0.976207i	$0.430424\pi$
$74$	−9.20402	−1.06995
$75$	−11.6125	−1.34090
$76$	1.86336	0.213742
$77$	−5.73916	−0.654038
$78$	−4.78898	−0.542245
$79$	−8.92708	−1.00438	−0.502188	−	0.864759i	$-0.667471\pi$
$79$	−8.92708	−1.00438	−0.502188	+	0.864759i	$0.667471\pi$
$80$	3.30115	0.369080
$81$	−10.8620	−1.20688
$82$	−9.80139	−1.08238
$83$	7.98237	0.876179	0.438090	−	0.898931i	$-0.355655\pi$
$83$	7.98237	0.876179	0.438090	+	0.898931i	$0.355655\pi$
$84$	−3.65725	−0.399039
$85$	−14.6430	−1.58826
$86$	1.14766	0.123756
$87$	−3.26619	−0.350173
$88$	−3.08990	−0.329385
$89$	−9.55337	−1.01266	−0.506328	−	0.862341i	$-0.668997\pi$
$89$	−9.55337	−1.01266	−0.506328	+	0.862341i	$0.668997\pi$
$90$	2.89532	0.305194
$91$	4.51746	0.473559
$92$	−7.06371	−0.736442
$93$	19.5504	2.02728
$94$	1.76021	0.181551
$95$	6.15122	0.631102
$96$	−1.96903	−0.200963
$97$	−18.5452	−1.88298	−0.941490	−	0.337040i	$-0.890574\pi$
$97$	−18.5452	−1.88298	−0.941490	+	0.337040i	$0.890574\pi$
$98$	−3.55010	−0.358614
$99$	−2.71004	−0.272369
$100$	5.89761	0.589761
$101$	−17.4314	−1.73448	−0.867242	−	0.497887i	$-0.834110\pi$
$101$	−17.4314	−1.73448	−0.867242	+	0.497887i	$0.834110\pi$
$102$	8.73408	0.864802
$103$	8.97142	0.883981	0.441990	−	0.897020i	$-0.354273\pi$
$103$	8.97142	0.883981	0.441990	+	0.897020i	$0.354273\pi$
$104$	2.43216	0.238492
$105$	−12.0731	−1.17822
$106$	−3.91707	−0.380459
$107$	10.4022	1.00562	0.502812	−	0.864396i	$-0.332299\pi$
$107$	10.4022	1.00562	0.502812	+	0.864396i	$0.332299\pi$
$108$	4.18012	0.402232
$109$	1.43512	0.137459	0.0687296	−	0.997635i	$-0.478105\pi$
$109$	1.43512	0.137459	0.0687296	+	0.997635i	$0.478105\pi$
$110$	−10.2002	−0.972555
$111$	18.1230	1.72015
$112$	1.85739	0.175507
$113$	−11.6128	−1.09244	−0.546222	−	0.837640i	$-0.683935\pi$
$113$	−11.6128	−1.09244	−0.546222	+	0.837640i	$0.683935\pi$
$114$	−3.66900	−0.343633
$115$	−23.3184	−2.17445
$116$	1.65879	0.154014
$117$	2.13315	0.197210
$118$	11.0174	1.01423
$119$	−8.23889	−0.755258
$120$	−6.50006	−0.593371
$121$	−1.45250	−0.132046
$122$	−11.4546	−1.03705
$123$	19.2992	1.74015
$124$	−9.92897	−0.891648
$125$	2.96314	0.265031
$126$	1.62905	0.145127
$127$	3.51605	0.311999	0.155999	−	0.987757i	$-0.450140\pi$
$127$	3.51605	0.311999	0.155999	+	0.987757i	$0.450140\pi$
$128$	1.00000	0.0883883
$129$	−2.25978	−0.198962
$130$	8.02891	0.704182
$131$	19.4772	1.70173	0.850864	−	0.525386i	$-0.176079\pi$
$131$	19.4772	1.70173	0.850864	+	0.525386i	$0.176079\pi$
$132$	6.08410	0.529553
$133$	3.46098	0.300105
$134$	−3.36449	−0.290648
$135$	13.7992	1.18765
$136$	−4.43573	−0.380361
$137$	5.15592	0.440500	0.220250	−	0.975443i	$-0.429313\pi$
$137$	5.15592	0.440500	0.220250	+	0.975443i	$0.429313\pi$
$138$	13.9086	1.18398
$139$	10.7889	0.915099	0.457550	−	0.889184i	$-0.348727\pi$
$139$	10.7889	0.915099	0.457550	+	0.889184i	$0.348727\pi$
$140$	6.13153	0.518209
$141$	−3.46589	−0.291881
$142$	1.81745	0.152517
$143$	−7.51512	−0.628446
$144$	0.877064	0.0730886
$145$	5.47591	0.454749
$146$	3.70540	0.306661
$147$	6.99024	0.576545
$148$	−9.20402	−0.756566
$149$	20.4133	1.67232	0.836161	−	0.548485i	$-0.184795\pi$
$149$	20.4133	1.67232	0.836161	+	0.548485i	$0.184795\pi$
$150$	−11.6125	−0.948160
$151$	−6.13396	−0.499174	−0.249587	−	0.968352i	$-0.580295\pi$
$151$	−6.13396	−0.499174	−0.249587	+	0.968352i	$0.580295\pi$
$152$	1.86336	0.151138
$153$	−3.89042	−0.314522
$154$	−5.73916	−0.462474
$155$	−32.7771	−2.63272
$156$	−4.78898	−0.383425
$157$	−3.51678	−0.280670	−0.140335	−	0.990104i	$-0.544818\pi$
$157$	−3.51678	−0.280670	−0.140335	+	0.990104i	$0.544818\pi$
$158$	−8.92708	−0.710201
$159$	7.71281	0.611666
$160$	3.30115	0.260979
$161$	−13.1201	−1.03401
$162$	−10.8620	−0.853395
$163$	−0.253671	−0.0198690	−0.00993451	−	0.999951i	$-0.503162\pi$
$163$	−0.253671	−0.0198690	−0.00993451	+	0.999951i	$0.503162\pi$
$164$	−9.80139	−0.765360
$165$	20.0845	1.56358
$166$	7.98237	0.619552
$167$	−16.2070	−1.25413	−0.627066	−	0.778966i	$-0.715744\pi$
$167$	−16.2070	−1.25413	−0.627066	+	0.778966i	$0.715744\pi$
$168$	−3.65725	−0.282163
$169$	−7.08462	−0.544971
$170$	−14.6430	−1.12307
$171$	1.63428	0.124977
$172$	1.14766	0.0875085
$173$	9.63707	0.732693	0.366346	−	0.930479i	$-0.380609\pi$
$173$	9.63707	0.732693	0.366346	+	0.930479i	$0.380609\pi$
$174$	−3.26619	−0.247609
$175$	10.9542	0.828057
$176$	−3.08990	−0.232910
$177$	−21.6935	−1.63058
$178$	−9.55337	−0.716055
$179$	−3.01116	−0.225065	−0.112532	−	0.993648i	$-0.535896\pi$
$179$	−3.01116	−0.225065	−0.112532	+	0.993648i	$0.535896\pi$
$180$	2.89532	0.215804
$181$	−0.836448	−0.0621727	−0.0310864	−	0.999517i	$-0.509897\pi$
$181$	−0.836448	−0.0621727	−0.0310864	+	0.999517i	$0.509897\pi$
$182$	4.51746	0.334857
$183$	22.5544	1.66727
$184$	−7.06371	−0.520743
$185$	−30.3839	−2.23387
$186$	19.5504	1.43351
$187$	13.7060	1.00228
$188$	1.76021	0.128376
$189$	7.76411	0.564756
$190$	6.15122	0.446257
$191$	1.65960	0.120085	0.0600423	−	0.998196i	$-0.480876\pi$
$191$	1.65960	0.120085	0.0600423	+	0.998196i	$0.480876\pi$
$192$	−1.96903	−0.142102
$193$	15.6955	1.12979	0.564893	−	0.825164i	$-0.308917\pi$
$193$	15.6955	1.12979	0.564893	+	0.825164i	$0.308917\pi$
$194$	−18.5452	−1.33147
$195$	−15.8091	−1.13212
$196$	−3.55010	−0.253579
$197$	4.17827	0.297689	0.148845	−	0.988861i	$-0.452445\pi$
$197$	4.17827	0.297689	0.148845	+	0.988861i	$0.452445\pi$
$198$	−2.71004	−0.192594
$199$	12.3731	0.877107	0.438553	−	0.898705i	$-0.355491\pi$
$199$	12.3731	0.877107	0.438553	+	0.898705i	$0.355491\pi$
$200$	5.89761	0.417024
$201$	6.62477	0.467275
$202$	−17.4314	−1.22647
$203$	3.08101	0.216245
$204$	8.73408	0.611508
$205$	−32.3559	−2.25983
$206$	8.97142	0.625069
$207$	−6.19532	−0.430605
$208$	2.43216	0.168640
$209$	−5.75759	−0.398261
$210$	−12.0731	−0.833126
$211$	8.69248	0.598415	0.299207	−	0.954188i	$-0.403278\pi$
$211$	8.69248	0.598415	0.299207	+	0.954188i	$0.403278\pi$
$212$	−3.91707	−0.269025
$213$	−3.57861	−0.245202
$214$	10.4022	0.711083
$215$	3.78861	0.258381
$216$	4.18012	0.284421
$217$	−18.4420	−1.25192
$218$	1.43512	0.0971983
$219$	−7.29603	−0.493020
$220$	−10.2002	−0.687700
$221$	−10.7884	−0.725706
$222$	18.1230	1.21633
$223$	24.9148	1.66842	0.834210	−	0.551447i	$-0.185924\pi$
$223$	24.9148	1.66842	0.834210	+	0.551447i	$0.185924\pi$
$224$	1.85739	0.124102
$225$	5.17258	0.344838
$226$	−11.6128	−0.772475
$227$	5.98015	0.396916	0.198458	−	0.980109i	$-0.436407\pi$
$227$	5.98015	0.396916	0.198458	+	0.980109i	$0.436407\pi$
$228$	−3.66900	−0.242985
$229$	16.3355	1.07948	0.539739	−	0.841833i	$-0.318523\pi$
$229$	16.3355	1.07948	0.539739	+	0.841833i	$0.318523\pi$
$230$	−23.3184	−1.53757
$231$	11.3005	0.743522
$232$	1.65879	0.108905
$233$	−16.5570	−1.08468	−0.542342	−	0.840158i	$-0.682462\pi$
$233$	−16.5570	−1.08468	−0.542342	+	0.840158i	$0.682462\pi$
$234$	2.13315	0.139449
$235$	5.81071	0.379049
$236$	11.0174	0.717169
$237$	17.5777	1.14179
$238$	−8.23889	−0.534048
$239$	6.85890	0.443665	0.221833	−	0.975085i	$-0.428796\pi$
$239$	6.85890	0.443665	0.221833	+	0.975085i	$0.428796\pi$
$240$	−6.50006	−0.419577
$241$	1.98551	0.127898	0.0639489	−	0.997953i	$-0.479631\pi$
$241$	1.98551	0.127898	0.0639489	+	0.997953i	$0.479631\pi$
$242$	−1.45250	−0.0933703
$243$	8.84711	0.567542
$244$	−11.4546	−0.733306
$245$	−11.7194	−0.748726
$246$	19.2992	1.23047
$247$	4.53197	0.288362
$248$	−9.92897	−0.630491
$249$	−15.7175	−0.996056
$250$	2.96314	0.187405
$251$	2.62668	0.165795	0.0828974	−	0.996558i	$-0.473583\pi$
$251$	2.62668	0.165795	0.0828974	+	0.996558i	$0.473583\pi$
$252$	1.62905	0.102620
$253$	21.8262	1.37220
$254$	3.51605	0.220617
$255$	28.8325	1.80556
$256$	1.00000	0.0625000
$257$	15.5398	0.969345	0.484672	−	0.874696i	$-0.338939\pi$
$257$	15.5398	0.969345	0.484672	+	0.874696i	$0.338939\pi$
$258$	−2.25978	−0.140688
$259$	−17.0955	−1.06226
$260$	8.02891	0.497932
$261$	1.45486	0.0900536
$262$	19.4772	1.20330
$263$	−18.0404	−1.11242	−0.556208	−	0.831043i	$-0.687744\pi$
$263$	−18.0404	−1.11242	−0.556208	+	0.831043i	$0.687744\pi$
$264$	6.08410	0.374450
$265$	−12.9308	−0.794335
$266$	3.46098	0.212206
$267$	18.8108	1.15120
$268$	−3.36449	−0.205519
$269$	2.55414	0.155729	0.0778644	−	0.996964i	$-0.475190\pi$
$269$	2.55414	0.155729	0.0778644	+	0.996964i	$0.475190\pi$
$270$	13.7992	0.839793
$271$	15.7943	0.959435	0.479718	−	0.877423i	$-0.340739\pi$
$271$	15.7943	0.959435	0.479718	+	0.877423i	$0.340739\pi$
$272$	−4.43573	−0.268956
$273$	−8.89500	−0.538350
$274$	5.15592	0.311480
$275$	−18.2230	−1.09889
$276$	13.9086	0.837201
$277$	−17.2823	−1.03839	−0.519196	−	0.854655i	$-0.673768\pi$
$277$	−17.2823	−1.03839	−0.519196	+	0.854655i	$0.673768\pi$
$278$	10.7889	0.647073
$279$	−8.70834	−0.521355
$280$	6.13153	0.366429
$281$	−2.70883	−0.161595	−0.0807977	−	0.996731i	$-0.525747\pi$
$281$	−2.70883	−0.161595	−0.0807977	+	0.996731i	$0.525747\pi$
$282$	−3.46589	−0.206391
$283$	−18.6728	−1.10998	−0.554992	−	0.831855i	$-0.687279\pi$
$283$	−18.6728	−1.10998	−0.554992	+	0.831855i	$0.687279\pi$
$284$	1.81745	0.107846
$285$	−12.1119	−0.717448
$286$	−7.51512	−0.444379
$287$	−18.2050	−1.07461
$288$	0.877064	0.0516815
$289$	2.67574	0.157397
$290$	5.47591	0.321556
$291$	36.5160	2.14061
$292$	3.70540	0.216842
$293$	14.7638	0.862513	0.431256	−	0.902229i	$-0.358070\pi$
$293$	14.7638	0.862513	0.431256	+	0.902229i	$0.358070\pi$
$294$	6.99024	0.407679
$295$	36.3700	2.11754
$296$	−9.20402	−0.534973
$297$	−12.9162	−0.749471
$298$	20.4133	1.18251
$299$	−17.1800	−0.993547
$300$	−11.6125	−0.670450
$301$	2.13166	0.122867
$302$	−6.13396	−0.352969
$303$	34.3228	1.97179
$304$	1.86336	0.106871
$305$	−37.8134	−2.16519
$306$	−3.89042	−0.222401
$307$	22.9778	1.31141	0.655705	−	0.755017i	$-0.272371\pi$
$307$	22.9778	1.31141	0.655705	+	0.755017i	$0.272371\pi$
$308$	−5.73916	−0.327019
$309$	−17.6650	−1.00492
$310$	−32.7771	−1.86161
$311$	−23.7259	−1.34537	−0.672686	−	0.739928i	$-0.734860\pi$
$311$	−23.7259	−1.34537	−0.672686	+	0.739928i	$0.734860\pi$
$312$	−4.78898	−0.271122
$313$	22.8174	1.28972	0.644858	−	0.764302i	$-0.276916\pi$
$313$	22.8174	1.28972	0.644858	+	0.764302i	$0.276916\pi$
$314$	−3.51678	−0.198463
$315$	5.37774	0.303001
$316$	−8.92708	−0.502188
$317$	−3.37029	−0.189294	−0.0946471	−	0.995511i	$-0.530172\pi$
$317$	−3.37029	−0.189294	−0.0946471	+	0.995511i	$0.530172\pi$
$318$	7.71281	0.432513
$319$	−5.12549	−0.286972
$320$	3.30115	0.184540
$321$	−20.4823	−1.14321
$322$	−13.1201	−0.731153
$323$	−8.26535	−0.459897
$324$	−10.8620	−0.603442
$325$	14.3439	0.795656
$326$	−0.253671	−0.0140495
$327$	−2.82578	−0.156266
$328$	−9.80139	−0.541191
$329$	3.26939	0.180247
$330$	20.0845	1.10562
$331$	−17.7755	−0.977029	−0.488515	−	0.872556i	$-0.662461\pi$
$331$	−17.7755	−0.977029	−0.488515	+	0.872556i	$0.662461\pi$
$332$	7.98237	0.438090
$333$	−8.07251	−0.442371
$334$	−16.2070	−0.886805
$335$	−11.1067	−0.606823
$336$	−3.65725	−0.199519
$337$	2.85351	0.155441	0.0777204	−	0.996975i	$-0.475236\pi$
$337$	2.85351	0.155441	0.0777204	+	0.996975i	$0.475236\pi$
$338$	−7.08462	−0.385353
$339$	22.8660	1.24191
$340$	−14.6430	−0.794130
$341$	30.6796	1.66139
$342$	1.63428	0.0883718
$343$	−19.5957	−1.05807
$344$	1.14766	0.0618778
$345$	45.9145	2.47195
$346$	9.63707	0.518092
$347$	10.0494	0.539478	0.269739	−	0.962933i	$-0.413063\pi$
$347$	10.0494	0.539478	0.269739	+	0.962933i	$0.413063\pi$
$348$	−3.26619	−0.175086
$349$	26.6497	1.42652	0.713262	−	0.700897i	$-0.247217\pi$
$349$	26.6497	1.42652	0.713262	+	0.700897i	$0.247217\pi$
$350$	10.9542	0.585525
$351$	10.1667	0.542658
$352$	−3.08990	−0.164692
$353$	2.24877	0.119690	0.0598450	−	0.998208i	$-0.480939\pi$
$353$	2.24877	0.119690	0.0598450	+	0.998208i	$0.480939\pi$
$354$	−21.6935	−1.15299
$355$	5.99968	0.318430
$356$	−9.55337	−0.506328
$357$	16.2226	0.858591
$358$	−3.01116	−0.159145
$359$	−21.4690	−1.13309	−0.566544	−	0.824031i	$-0.691720\pi$
$359$	−21.4690	−1.13309	−0.566544	+	0.824031i	$0.691720\pi$
$360$	2.89532	0.152597
$361$	−15.5279	−0.817258
$362$	−0.836448	−0.0439627
$363$	2.86001	0.150112
$364$	4.51746	0.236779
$365$	12.2321	0.640257
$366$	22.5544	1.17894
$367$	−17.9391	−0.936412	−0.468206	−	0.883619i	$-0.655099\pi$
$367$	−17.9391	−0.936412	−0.468206	+	0.883619i	$0.655099\pi$
$368$	−7.06371	−0.368221
$369$	−8.59644	−0.447513
$370$	−30.3839	−1.57958
$371$	−7.27553	−0.377727
$372$	19.5504	1.01364
$373$	24.2363	1.25491	0.627455	−	0.778653i	$-0.284097\pi$
$373$	24.2363	1.25491	0.627455	+	0.778653i	$0.284097\pi$
$374$	13.7060	0.708720
$375$	−5.83450	−0.301292
$376$	1.76021	0.0907757
$377$	4.03442	0.207783
$378$	7.76411	0.399343
$379$	9.25112	0.475198	0.237599	−	0.971363i	$-0.423640\pi$
$379$	9.25112	0.475198	0.237599	+	0.971363i	$0.423640\pi$
$380$	6.15122	0.315551
$381$	−6.92319	−0.354686
$382$	1.65960	0.0849126
$383$	−2.97151	−0.151837	−0.0759185	−	0.997114i	$-0.524189\pi$
$383$	−2.97151	−0.151837	−0.0759185	+	0.997114i	$0.524189\pi$
$384$	−1.96903	−0.100481
$385$	−18.9458	−0.965569
$386$	15.6955	0.798879
$387$	1.00657	0.0511670
$388$	−18.5452	−0.941490
$389$	−12.6105	−0.639379	−0.319690	−	0.947522i	$-0.603579\pi$
$389$	−12.6105	−0.639379	−0.319690	+	0.947522i	$0.603579\pi$
$390$	−15.8091	−0.800527
$391$	31.3327	1.58456
$392$	−3.55010	−0.179307
$393$	−38.3510	−1.93455
$394$	4.17827	0.210498
$395$	−29.4697	−1.48278
$396$	−2.71004	−0.136185
$397$	−25.7601	−1.29286	−0.646432	−	0.762972i	$-0.723739\pi$
$397$	−25.7601	−1.29286	−0.646432	+	0.762972i	$0.723739\pi$
$398$	12.3731	0.620208
$399$	−6.81476	−0.341165
$400$	5.89761	0.294880
$401$	−29.4609	−1.47121	−0.735603	−	0.677412i	$-0.763101\pi$
$401$	−29.4609	−1.47121	−0.735603	+	0.677412i	$0.763101\pi$
$402$	6.62477	0.330413
$403$	−24.1488	−1.20294
$404$	−17.4314	−0.867242
$405$	−35.8570	−1.78175
$406$	3.08101	0.152908
$407$	28.4395	1.40969
$408$	8.73408	0.432401
$409$	9.91199	0.490116	0.245058	−	0.969508i	$-0.421193\pi$
$409$	9.91199	0.490116	0.245058	+	0.969508i	$0.421193\pi$
$410$	−32.3559	−1.59794
$411$	−10.1521	−0.500768
$412$	8.97142	0.441990
$413$	20.4635	1.00694
$414$	−6.19532	−0.304483
$415$	26.3510	1.29352
$416$	2.43216	0.119246
$417$	−21.2435	−1.04030
$418$	−5.75759	−0.281613
$419$	−15.2195	−0.743521	−0.371760	−	0.928329i	$-0.621246\pi$
$419$	−15.2195	−0.743521	−0.371760	+	0.928329i	$0.621246\pi$
$420$	−12.0731	−0.589109
$421$	27.9218	1.36082	0.680412	−	0.732830i	$-0.261801\pi$
$421$	27.9218	1.36082	0.680412	+	0.732830i	$0.261801\pi$
$422$	8.69248	0.423143
$423$	1.54381	0.0750628
$424$	−3.91707	−0.190230
$425$	−26.1602	−1.26896
$426$	−3.57861	−0.173384
$427$	−21.2757	−1.02960
$428$	10.4022	0.502812
$429$	14.7975	0.714429
$430$	3.78861	0.182703
$431$	−21.4912	−1.03520	−0.517598	−	0.855624i	$-0.673174\pi$
$431$	−21.4912	−1.03520	−0.517598	+	0.855624i	$0.673174\pi$
$432$	4.18012	0.201116
$433$	−15.6415	−0.751681	−0.375840	−	0.926684i	$-0.622646\pi$
$433$	−15.6415	−0.751681	−0.375840	+	0.926684i	$0.622646\pi$
$434$	−18.4420	−0.885244
$435$	−10.7822	−0.516967
$436$	1.43512	0.0687296
$437$	−13.1622	−0.629634
$438$	−7.29603	−0.348618
$439$	−0.372896	−0.0177974	−0.00889869	−	0.999960i	$-0.502833\pi$
$439$	−0.372896	−0.0177974	−0.00889869	+	0.999960i	$0.502833\pi$
$440$	−10.2002	−0.486277
$441$	−3.11366	−0.148270
$442$	−10.7884	−0.513152
$443$	−23.0059	−1.09305	−0.546523	−	0.837444i	$-0.684049\pi$
$443$	−23.0059	−1.09305	−0.546523	+	0.837444i	$0.684049\pi$
$444$	18.1230	0.860077
$445$	−31.5371	−1.49500
$446$	24.9148	1.17975
$447$	−40.1943	−1.90112
$448$	1.85739	0.0877535
$449$	0.341228	0.0161036	0.00805178	−	0.999968i	$-0.497437\pi$
$449$	0.341228	0.0161036	0.00805178	+	0.999968i	$0.497437\pi$
$450$	5.17258	0.243838
$451$	30.2853	1.42608
$452$	−11.6128	−0.546222
$453$	12.0779	0.567470
$454$	5.98015	0.280662
$455$	14.9128	0.699124
$456$	−3.66900	−0.171817
$457$	−15.9510	−0.746156	−0.373078	−	0.927800i	$-0.621698\pi$
$457$	−15.9510	−0.746156	−0.373078	+	0.927800i	$0.621698\pi$
$458$	16.3355	0.763306
$459$	−18.5419	−0.865461
$460$	−23.3184	−1.08722
$461$	−10.0048	−0.465970	−0.232985	−	0.972480i	$-0.574849\pi$
$461$	−10.0048	−0.465970	−0.232985	+	0.972480i	$0.574849\pi$
$462$	11.3005	0.525749
$463$	10.9141	0.507221	0.253610	−	0.967306i	$-0.418382\pi$
$463$	10.9141	0.507221	0.253610	+	0.967306i	$0.418382\pi$
$464$	1.65879	0.0770072
$465$	64.5389	2.99292
$466$	−16.5570	−0.766987
$467$	12.8464	0.594460	0.297230	−	0.954806i	$-0.403937\pi$
$467$	12.8464	0.594460	0.297230	+	0.954806i	$0.403937\pi$
$468$	2.13315	0.0986051
$469$	−6.24917	−0.288560
$470$	5.81071	0.268028
$471$	6.92463	0.319070
$472$	11.0174	0.507115
$473$	−3.54617	−0.163053
$474$	17.5777	0.807369
$475$	10.9893	0.504226
$476$	−8.23889	−0.377629
$477$	−3.43552	−0.157302
$478$	6.85890	0.313719
$479$	−19.9150	−0.909938	−0.454969	−	0.890507i	$-0.650350\pi$
$479$	−19.9150	−0.909938	−0.454969	+	0.890507i	$0.650350\pi$
$480$	−6.50006	−0.296686
$481$	−22.3856	−1.02070
$482$	1.98551	0.0904374
$483$	25.8337	1.17548
$484$	−1.45250	−0.0660228
$485$	−61.2206	−2.77988
$486$	8.84711	0.401313
$487$	4.82401	0.218597	0.109298	−	0.994009i	$-0.465140\pi$
$487$	4.82401	0.218597	0.109298	+	0.994009i	$0.465140\pi$
$488$	−11.4546	−0.518526
$489$	0.499484	0.0225875
$490$	−11.7194	−0.529429
$491$	−42.5241	−1.91908	−0.959542	−	0.281565i	$-0.909147\pi$
$491$	−42.5241	−1.91908	−0.959542	+	0.281565i	$0.909147\pi$
$492$	19.2992	0.870075
$493$	−7.35793	−0.331385
$494$	4.53197	0.203903
$495$	−8.94626	−0.402104
$496$	−9.92897	−0.445824
$497$	3.37572	0.151422
$498$	−15.7175	−0.704318
$499$	−8.65225	−0.387328	−0.193664	−	0.981068i	$-0.562037\pi$
$499$	−8.65225	−0.387328	−0.193664	+	0.981068i	$0.562037\pi$
$500$	2.96314	0.132516
$501$	31.9119	1.42572
$502$	2.62668	0.117235
$503$	1.89418	0.0844575	0.0422288	−	0.999108i	$-0.486554\pi$
$503$	1.89418	0.0844575	0.0422288	+	0.999108i	$0.486554\pi$
$504$	1.62905	0.0725636
$505$	−57.5435	−2.56065
$506$	21.8262	0.970292
$507$	13.9498	0.619533
$508$	3.51605	0.155999
$509$	11.1608	0.494692	0.247346	−	0.968927i	$-0.420442\pi$
$509$	11.1608	0.494692	0.247346	+	0.968927i	$0.420442\pi$
$510$	28.8325	1.27673
$511$	6.88237	0.304458
$512$	1.00000	0.0441942
$513$	7.78905	0.343895
$514$	15.5398	0.685430
$515$	29.6160	1.30504
$516$	−2.25978	−0.0994812
$517$	−5.43887	−0.239201
$518$	−17.0955	−0.751131
$519$	−18.9756	−0.832938
$520$	8.02891	0.352091
$521$	−1.45362	−0.0636841	−0.0318420	−	0.999493i	$-0.510137\pi$
$521$	−1.45362	−0.0636841	−0.0318420	+	0.999493i	$0.510137\pi$
$522$	1.45486	0.0636775
$523$	−14.4576	−0.632185	−0.316092	−	0.948728i	$-0.602371\pi$
$523$	−14.4576	−0.632185	−0.316092	+	0.948728i	$0.602371\pi$
$524$	19.4772	0.850864
$525$	−21.5690	−0.941350
$526$	−18.0404	−0.786597
$527$	44.0423	1.91851
$528$	6.08410	0.264776
$529$	26.8960	1.16939
$530$	−12.9308	−0.561680
$531$	9.66292	0.419335
$532$	3.46098	0.150053
$533$	−23.8385	−1.03256
$534$	18.8108	0.814024
$535$	34.3394	1.48462
$536$	−3.36449	−0.145324
$537$	5.92905	0.255857
$538$	2.55414	0.110117
$539$	10.9695	0.472488
$540$	13.7992	0.593823
$541$	43.6182	1.87529	0.937647	−	0.347588i	$-0.112999\pi$
$541$	43.6182	1.87529	0.937647	+	0.347588i	$0.112999\pi$
$542$	15.7943	0.678423
$543$	1.64699	0.0706790
$544$	−4.43573	−0.190181
$545$	4.73754	0.202934
$546$	−8.89500	−0.380671
$547$	−26.5465	−1.13505	−0.567523	−	0.823357i	$-0.692098\pi$
$547$	−26.5465	−1.13505	−0.567523	+	0.823357i	$0.692098\pi$
$548$	5.15592	0.220250
$549$	−10.0464	−0.428771
$550$	−18.2230	−0.777033
$551$	3.09091	0.131677
$552$	13.9086	0.591990
$553$	−16.5811	−0.705099
$554$	−17.2823	−0.734253
$555$	59.8266	2.53950
$556$	10.7889	0.457550
$557$	3.49412	0.148051	0.0740254	−	0.997256i	$-0.476415\pi$
$557$	3.49412	0.148051	0.0740254	+	0.997256i	$0.476415\pi$
$558$	−8.70834	−0.368653
$559$	2.79129	0.118059
$560$	6.13153	0.259104
$561$	−26.9874	−1.13941
$562$	−2.70883	−0.114265
$563$	−24.0819	−1.01493	−0.507466	−	0.861672i	$-0.669418\pi$
$563$	−24.0819	−1.01493	−0.507466	+	0.861672i	$0.669418\pi$
$564$	−3.46589	−0.145940
$565$	−38.3358	−1.61280
$566$	−18.6728	−0.784878
$567$	−20.1749	−0.847266
$568$	1.81745	0.0762585
$569$	−19.0014	−0.796581	−0.398291	−	0.917259i	$-0.630396\pi$
$569$	−19.0014	−0.796581	−0.398291	+	0.917259i	$0.630396\pi$
$570$	−12.1119	−0.507312
$571$	−0.168188	−0.00703846	−0.00351923	−	0.999994i	$-0.501120\pi$
$571$	−0.168188	−0.00703846	−0.00351923	+	0.999994i	$0.501120\pi$
$572$	−7.51512	−0.314223
$573$	−3.26780	−0.136514
$574$	−18.2050	−0.759863
$575$	−41.6590	−1.73730
$576$	0.877064	0.0365443
$577$	−11.3984	−0.474523	−0.237261	−	0.971446i	$-0.576250\pi$
$577$	−11.3984	−0.474523	−0.237261	+	0.971446i	$0.576250\pi$
$578$	2.67574	0.111296
$579$	−30.9048	−1.28436
$580$	5.47591	0.227375
$581$	14.8264	0.615102
$582$	36.5160	1.51364
$583$	12.1034	0.501270
$584$	3.70540	0.153330
$585$	7.04187	0.291145
$586$	14.7638	0.609889
$587$	−38.3179	−1.58155	−0.790774	−	0.612109i	$-0.790322\pi$
$587$	−38.3179	−1.58155	−0.790774	+	0.612109i	$0.790322\pi$
$588$	6.99024	0.288273
$589$	−18.5012	−0.762329
$590$	36.3700	1.49733
$591$	−8.22711	−0.338418
$592$	−9.20402	−0.378283
$593$	−5.71708	−0.234772	−0.117386	−	0.993086i	$-0.537452\pi$
$593$	−5.71708	−0.234772	−0.117386	+	0.993086i	$0.537452\pi$
$594$	−12.9162	−0.529956
$595$	−27.1978	−1.11500
$596$	20.4133	0.836161
$597$	−24.3630	−0.997111
$598$	−17.1800	−0.702544
$599$	−39.3916	−1.60950	−0.804749	−	0.593615i	$-0.797700\pi$
$599$	−39.3916	−1.60950	−0.804749	+	0.593615i	$0.797700\pi$
$600$	−11.6125	−0.474080
$601$	2.40324	0.0980301	0.0490150	−	0.998798i	$-0.484392\pi$
$601$	2.40324	0.0980301	0.0490150	+	0.998798i	$0.484392\pi$
$602$	2.13166	0.0868799
$603$	−2.95087	−0.120169
$604$	−6.13396	−0.249587
$605$	−4.79493	−0.194942
$606$	34.3228	1.39427
$607$	4.40536	0.178808	0.0894040	−	0.995995i	$-0.471504\pi$
$607$	4.40536	0.178808	0.0894040	+	0.995995i	$0.471504\pi$
$608$	1.86336	0.0755691
$609$	−6.06660	−0.245831
$610$	−37.8134	−1.53102
$611$	4.28110	0.173195
$612$	−3.89042	−0.157261
$613$	20.4673	0.826668	0.413334	−	0.910580i	$-0.364364\pi$
$613$	20.4673	0.826668	0.413334	+	0.910580i	$0.364364\pi$
$614$	22.9778	0.927307
$615$	63.7096	2.56902
$616$	−5.73916	−0.231237
$617$	−19.6640	−0.791643	−0.395821	−	0.918328i	$-0.629540\pi$
$617$	−19.6640	−0.791643	−0.395821	+	0.918328i	$0.629540\pi$
$618$	−17.6650	−0.710589
$619$	11.7181	0.470989	0.235495	−	0.971876i	$-0.424329\pi$
$619$	11.7181	0.470989	0.235495	+	0.971876i	$0.424329\pi$
$620$	−32.7771	−1.31636
$621$	−29.5271	−1.18488
$622$	−23.7259	−0.951322
$623$	−17.7443	−0.710912
$624$	−4.78898	−0.191713
$625$	−19.7063	−0.788251
$626$	22.8174	0.911967
$627$	11.3368	0.452750
$628$	−3.51678	−0.140335
$629$	40.8266	1.62786
$630$	5.37774	0.214254
$631$	−12.7538	−0.507722	−0.253861	−	0.967241i	$-0.581701\pi$
$631$	−12.7538	−0.507722	−0.253861	+	0.967241i	$0.581701\pi$
$632$	−8.92708	−0.355100
$633$	−17.1157	−0.680289
$634$	−3.37029	−0.133851
$635$	11.6070	0.460610
$636$	7.71281	0.305833
$637$	−8.63439	−0.342107
$638$	−5.12549	−0.202920
$639$	1.59402	0.0630584
$640$	3.30115	0.130490
$641$	−26.6301	−1.05183	−0.525914	−	0.850538i	$-0.676276\pi$
$641$	−26.6301	−1.05183	−0.525914	+	0.850538i	$0.676276\pi$
$642$	−20.4823	−0.808372
$643$	−6.55098	−0.258345	−0.129173	−	0.991622i	$-0.541232\pi$
$643$	−6.55098	−0.258345	−0.129173	+	0.991622i	$0.541232\pi$
$644$	−13.1201	−0.517003
$645$	−7.45987	−0.293732
$646$	−8.26535	−0.325196
$647$	35.0038	1.37614	0.688071	−	0.725643i	$-0.258458\pi$
$647$	35.0038	1.37614	0.688071	+	0.725643i	$0.258458\pi$
$648$	−10.8620	−0.426698
$649$	−34.0426	−1.33629
$650$	14.3439	0.562614
$651$	36.3127	1.42321
$652$	−0.253671	−0.00993451
$653$	−0.218475	−0.00854957	−0.00427478	−	0.999991i	$-0.501361\pi$
$653$	−0.218475	−0.00854957	−0.00427478	+	0.999991i	$0.501361\pi$
$654$	−2.82578	−0.110497
$655$	64.2971	2.51230
$656$	−9.80139	−0.382680
$657$	3.24987	0.126789
$658$	3.26939	0.127454
$659$	46.1873	1.79920	0.899601	−	0.436713i	$-0.143857\pi$
$659$	46.1873	1.79920	0.899601	+	0.436713i	$0.143857\pi$
$660$	20.0845	0.781790
$661$	−3.13371	−0.121887	−0.0609435	−	0.998141i	$-0.519411\pi$
$661$	−3.13371	−0.121887	−0.0609435	+	0.998141i	$0.519411\pi$
$662$	−17.7755	−0.690864
$663$	21.2426	0.824995
$664$	7.98237	0.309776
$665$	11.4252	0.443051
$666$	−8.07251	−0.312803
$667$	−11.7172	−0.453691
$668$	−16.2070	−0.627066
$669$	−49.0579	−1.89669
$670$	−11.1067	−0.429089
$671$	35.3936	1.36636
$672$	−3.65725	−0.141082
$673$	35.9208	1.38465	0.692323	−	0.721588i	$-0.256587\pi$
$673$	35.9208	1.38465	0.692323	+	0.721588i	$0.256587\pi$
$674$	2.85351	0.109913
$675$	24.6527	0.948882
$676$	−7.08462	−0.272485
$677$	2.06627	0.0794131	0.0397065	−	0.999211i	$-0.487358\pi$
$677$	2.06627	0.0794131	0.0397065	+	0.999211i	$0.487358\pi$
$678$	22.8660	0.878164
$679$	−34.4457	−1.32190
$680$	−14.6430	−0.561535
$681$	−11.7751	−0.451222
$682$	30.6796	1.17478
$683$	1.28584	0.0492013	0.0246007	−	0.999697i	$-0.492169\pi$
$683$	1.28584	0.0492013	0.0246007	+	0.999697i	$0.492169\pi$
$684$	1.63428	0.0624883
$685$	17.0205	0.650319
$686$	−19.5957	−0.748166
$687$	−32.1649	−1.22717
$688$	1.14766	0.0437542
$689$	−9.52692	−0.362947
$690$	45.9145	1.74793
$691$	15.2029	0.578344	0.289172	−	0.957277i	$-0.406620\pi$
$691$	15.2029	0.578344	0.289172	+	0.957277i	$0.406620\pi$
$692$	9.63707	0.366346
$693$	−5.03361	−0.191211
$694$	10.0494	0.381469
$695$	35.6157	1.35098
$696$	−3.26619	−0.123805
$697$	43.4764	1.64678
$698$	26.6497	1.00871
$699$	32.6011	1.23309
$700$	10.9542	0.414028
$701$	46.1050	1.74136	0.870680	−	0.491849i	$-0.163679\pi$
$701$	46.1050	1.74136	0.870680	+	0.491849i	$0.163679\pi$
$702$	10.1667	0.383717
$703$	−17.1504	−0.646838
$704$	−3.08990	−0.116455
$705$	−11.4414	−0.430910
$706$	2.24877	0.0846336
$707$	−32.3768	−1.21766
$708$	−21.6935	−0.815290
$709$	−33.4378	−1.25578	−0.627891	−	0.778302i	$-0.716081\pi$
$709$	−33.4378	−1.25578	−0.627891	+	0.778302i	$0.716081\pi$
$710$	5.99968	0.225164
$711$	−7.82962	−0.293634
$712$	−9.55337	−0.358028
$713$	70.1354	2.62659
$714$	16.2226	0.607115
$715$	−24.8086	−0.927788
$716$	−3.01116	−0.112532
$717$	−13.5053	−0.504366
$718$	−21.4690	−0.801214
$719$	−48.3873	−1.80454	−0.902271	−	0.431168i	$-0.858101\pi$
$719$	−48.3873	−1.80454	−0.902271	+	0.431168i	$0.858101\pi$
$720$	2.89532	0.107902
$721$	16.6634	0.620579
$722$	−15.5279	−0.577889
$723$	−3.90952	−0.145397
$724$	−0.836448	−0.0310864
$725$	9.78287	0.363327
$726$	2.86001	0.106145
$727$	−13.4339	−0.498236	−0.249118	−	0.968473i	$-0.580141\pi$
$727$	−13.4339	−0.498236	−0.249118	+	0.968473i	$0.580141\pi$
$728$	4.51746	0.167428
$729$	15.1657	0.561691
$730$	12.2321	0.452730
$731$	−5.09073	−0.188287
$732$	22.5544	0.833635
$733$	19.9571	0.737133	0.368566	−	0.929601i	$-0.379849\pi$
$733$	19.9571	0.737133	0.368566	+	0.929601i	$0.379849\pi$
$734$	−17.9391	−0.662143
$735$	23.0758	0.851165
$736$	−7.06371	−0.260372
$737$	10.3959	0.382940
$738$	−8.59644	−0.316439
$739$	33.8681	1.24586	0.622928	−	0.782279i	$-0.285943\pi$
$739$	33.8681	1.24586	0.622928	+	0.782279i	$0.285943\pi$
$740$	−30.3839	−1.11693
$741$	−8.92357	−0.327816
$742$	−7.27553	−0.267093
$743$	−48.0257	−1.76189	−0.880946	−	0.473217i	$-0.843093\pi$
$743$	−48.0257	−1.76189	−0.880946	+	0.473217i	$0.843093\pi$
$744$	19.5504	0.716753
$745$	67.3873	2.46888
$746$	24.2363	0.887355
$747$	7.00105	0.256155
$748$	13.7060	0.501141
$749$	19.3210	0.705975
$750$	−5.83450	−0.213046
$751$	−32.5747	−1.18867	−0.594333	−	0.804219i	$-0.702584\pi$
$751$	−32.5747	−1.18867	−0.594333	+	0.804219i	$0.702584\pi$
$752$	1.76021	0.0641881
$753$	−5.17201	−0.188478
$754$	4.03442	0.146925
$755$	−20.2491	−0.736941
$756$	7.76411	0.282378
$757$	8.56134	0.311167	0.155584	−	0.987823i	$-0.450274\pi$
$757$	8.56134	0.311167	0.155584	+	0.987823i	$0.450274\pi$
$758$	9.25112	0.336016
$759$	−42.9763	−1.55994
$760$	6.15122	0.223128
$761$	−43.7731	−1.58677	−0.793387	−	0.608718i	$-0.791684\pi$
$761$	−43.7731	−1.58677	−0.793387	+	0.608718i	$0.791684\pi$
$762$	−6.92319	−0.250801
$763$	2.66557	0.0965002
$764$	1.65960	0.0600423
$765$	−12.8429	−0.464335
$766$	−2.97151	−0.107365
$767$	26.7959	0.967544
$768$	−1.96903	−0.0710511
$769$	30.0122	1.08227	0.541134	−	0.840936i	$-0.317995\pi$
$769$	30.0122	1.08227	0.541134	+	0.840936i	$0.317995\pi$
$770$	−18.9458	−0.682760
$771$	−30.5982	−1.10197
$772$	15.6955	0.564893
$773$	30.6254	1.10152	0.550759	−	0.834665i	$-0.314338\pi$
$773$	30.6254	1.10152	0.550759	+	0.834665i	$0.314338\pi$
$774$	1.00657	0.0361805
$775$	−58.5572	−2.10344
$776$	−18.5452	−0.665734
$777$	33.6614	1.20760
$778$	−12.6105	−0.452109
$779$	−18.2635	−0.654357
$780$	−15.8091	−0.566058
$781$	−5.61574	−0.200947
$782$	31.3327	1.12046
$783$	6.93392	0.247798
$784$	−3.55010	−0.126789
$785$	−11.6094	−0.414358
$786$	−38.3510	−1.36794
$787$	19.3665	0.690341	0.345171	−	0.938540i	$-0.387821\pi$
$787$	19.3665	0.690341	0.345171	+	0.938540i	$0.387821\pi$
$788$	4.17827	0.148845
$789$	35.5219	1.26461
$790$	−29.4697	−1.04848
$791$	−21.5696	−0.766927
$792$	−2.71004	−0.0962971
$793$	−27.8594	−0.989315
$794$	−25.7601	−0.914192
$795$	25.4612	0.903015
$796$	12.3731	0.438553
$797$	−33.2779	−1.17876	−0.589382	−	0.807855i	$-0.700629\pi$
$797$	−33.2779	−1.17876	−0.589382	+	0.807855i	$0.700629\pi$
$798$	−6.81476	−0.241240
$799$	−7.80781	−0.276220
$800$	5.89761	0.208512
$801$	−8.37891	−0.296054
$802$	−29.4609	−1.04030
$803$	−11.4493	−0.404038
$804$	6.62477	0.233638
$805$	−43.3113	−1.52652
$806$	−24.1488	−0.850605
$807$	−5.02917	−0.177035
$808$	−17.4314	−0.613233
$809$	−5.16129	−0.181461	−0.0907307	−	0.995875i	$-0.528920\pi$
$809$	−5.16129	−0.181461	−0.0907307	+	0.995875i	$0.528920\pi$
$810$	−35.8570	−1.25988
$811$	30.1396	1.05835	0.529173	−	0.848514i	$-0.322502\pi$
$811$	30.1396	1.05835	0.529173	+	0.848514i	$0.322502\pi$
$812$	3.08101	0.108122
$813$	−31.0994	−1.09070
$814$	28.4395	0.996805
$815$	−0.837406	−0.0293331
$816$	8.73408	0.305754
$817$	2.13851	0.0748168
$818$	9.91199	0.346565
$819$	3.96210	0.138447
$820$	−32.3559	−1.12992
$821$	19.5959	0.683903	0.341951	−	0.939718i	$-0.388912\pi$
$821$	19.5959	0.683903	0.341951	+	0.939718i	$0.388912\pi$
$822$	−10.1521	−0.354096
$823$	38.4553	1.34047	0.670234	−	0.742150i	$-0.266194\pi$
$823$	38.4553	1.34047	0.670234	+	0.742150i	$0.266194\pi$
$824$	8.97142	0.312534
$825$	35.8816	1.24924
$826$	20.4635	0.712017
$827$	47.8490	1.66387	0.831937	−	0.554870i	$-0.187232\pi$
$827$	47.8490	1.66387	0.831937	+	0.554870i	$0.187232\pi$
$828$	−6.19532	−0.215302
$829$	−51.4777	−1.78790	−0.893948	−	0.448171i	$-0.852076\pi$
$829$	−51.4777	−1.78790	−0.893948	+	0.448171i	$0.852076\pi$
$830$	26.3510	0.914657
$831$	34.0292	1.18046
$832$	2.43216	0.0843198
$833$	15.7473	0.545612
$834$	−21.2435	−0.735604
$835$	−53.5016	−1.85150
$836$	−5.75759	−0.199130
$837$	−41.5043	−1.43460
$838$	−15.2195	−0.525749
$839$	29.8656	1.03107	0.515537	−	0.856868i	$-0.327593\pi$
$839$	29.8656	1.03107	0.515537	+	0.856868i	$0.327593\pi$
$840$	−12.0731	−0.416563
$841$	−26.2484	−0.905118
$842$	27.9218	0.962247
$843$	5.33376	0.183705
$844$	8.69248	0.299207
$845$	−23.3874	−0.804552
$846$	1.54381	0.0530774
$847$	−2.69786	−0.0926996
$848$	−3.91707	−0.134513
$849$	36.7673	1.26185
$850$	−26.1602	−0.897288
$851$	65.0145	2.22867
$852$	−3.57861	−0.122601
$853$	43.5825	1.49224	0.746118	−	0.665814i	$-0.231915\pi$
$853$	43.5825	1.49224	0.746118	+	0.665814i	$0.231915\pi$
$854$	−21.2757	−0.728039
$855$	5.39501	0.184506
$856$	10.4022	0.355541
$857$	6.03342	0.206098	0.103049	−	0.994676i	$-0.467140\pi$
$857$	6.03342	0.206098	0.103049	+	0.994676i	$0.467140\pi$
$858$	14.7975	0.505177
$859$	−39.0553	−1.33255	−0.666274	−	0.745707i	$-0.732112\pi$
$859$	−39.0553	−1.33255	−0.666274	+	0.745707i	$0.732112\pi$
$860$	3.78861	0.129191
$861$	35.8461	1.22163
$862$	−21.4912	−0.731993
$863$	−20.1470	−0.685813	−0.342906	−	0.939370i	$-0.611411\pi$
$863$	−20.1470	−0.685813	−0.342906	+	0.939370i	$0.611411\pi$
$864$	4.18012	0.142210
$865$	31.8134	1.08169
$866$	−15.6415	−0.531519
$867$	−5.26861	−0.178931
$868$	−18.4420	−0.625962
$869$	27.5838	0.935717
$870$	−10.7822	−0.365551
$871$	−8.18296	−0.277269
$872$	1.43512	0.0485992
$873$	−16.2653	−0.550498
$874$	−13.1622	−0.445218
$875$	5.50371	0.186059
$876$	−7.29603	−0.246510
$877$	−8.94746	−0.302134	−0.151067	−	0.988523i	$-0.548271\pi$
$877$	−8.94746	−0.302134	−0.151067	+	0.988523i	$0.548271\pi$
$878$	−0.372896	−0.0125846
$879$	−29.0704	−0.980520
$880$	−10.2002	−0.343850
$881$	−1.80227	−0.0607201	−0.0303601	−	0.999539i	$-0.509665\pi$
$881$	−1.80227	−0.0607201	−0.0303601	+	0.999539i	$0.509665\pi$
$882$	−3.11366	−0.104842
$883$	−31.8607	−1.07220	−0.536099	−	0.844155i	$-0.680103\pi$
$883$	−31.8607	−1.07220	−0.536099	+	0.844155i	$0.680103\pi$
$884$	−10.7884	−0.362853
$885$	−71.6134	−2.40726
$886$	−23.0059	−0.772900
$887$	7.16627	0.240620	0.120310	−	0.992736i	$-0.461611\pi$
$887$	7.16627	0.240620	0.120310	+	0.992736i	$0.461611\pi$
$888$	18.1230	0.608167
$889$	6.53068	0.219032
$890$	−31.5371	−1.05713
$891$	33.5624	1.12438
$892$	24.9148	0.834210
$893$	3.27989	0.109757
$894$	−40.1943	−1.34430
$895$	−9.94030	−0.332267
$896$	1.85739	0.0620511
$897$	33.8279	1.12948
$898$	0.341228	0.0113869
$899$	−16.4700	−0.549307
$900$	5.17258	0.172419
$901$	17.3751	0.578848
$902$	30.2853	1.00839
$903$	−4.19729	−0.139677
$904$	−11.6128	−0.386238
$905$	−2.76124	−0.0917868
$906$	12.0779	0.401262
$907$	4.75130	0.157764	0.0788822	−	0.996884i	$-0.474865\pi$
$907$	4.75130	0.157764	0.0788822	+	0.996884i	$0.474865\pi$
$908$	5.98015	0.198458
$909$	−15.2884	−0.507084
$910$	14.9128	0.494356
$911$	−39.1743	−1.29790	−0.648951	−	0.760830i	$-0.724792\pi$
$911$	−39.1743	−1.29790	−0.648951	+	0.760830i	$0.724792\pi$
$912$	−3.66900	−0.121493
$913$	−24.6647	−0.816284
$914$	−15.9510	−0.527612
$915$	74.4556	2.46143
$916$	16.3355	0.539739
$917$	36.1767	1.19466
$918$	−18.5419	−0.611974
$919$	46.7454	1.54199	0.770995	−	0.636841i	$-0.219759\pi$
$919$	46.7454	1.54199	0.770995	+	0.636841i	$0.219759\pi$
$920$	−23.3184	−0.768784
$921$	−45.2438	−1.49083
$922$	−10.0048	−0.329491
$923$	4.42032	0.145497
$924$	11.3005	0.371761
$925$	−54.2817	−1.78477
$926$	10.9141	0.358659
$927$	7.86851	0.258436
$928$	1.65879	0.0544523
$929$	42.1050	1.38142	0.690711	−	0.723131i	$-0.257298\pi$
$929$	42.1050	1.38142	0.690711	+	0.723131i	$0.257298\pi$
$930$	64.5389	2.11631
$931$	−6.61510	−0.216801
$932$	−16.5570	−0.542342
$933$	46.7169	1.52944
$934$	12.8464	0.420347
$935$	45.2456	1.47969
$936$	2.13315	0.0697243
$937$	−27.4100	−0.895444	−0.447722	−	0.894173i	$-0.647765\pi$
$937$	−27.4100	−0.895444	−0.447722	+	0.894173i	$0.647765\pi$
$938$	−6.24917	−0.204043
$939$	−44.9281	−1.46617
$940$	5.81071	0.189524
$941$	−20.1827	−0.657937	−0.328969	−	0.944341i	$-0.606701\pi$
$941$	−20.1827	−0.657937	−0.328969	+	0.944341i	$0.606701\pi$
$942$	6.92463	0.225617
$943$	69.2342	2.25457
$944$	11.0174	0.358584
$945$	25.6305	0.833761
$946$	−3.54617	−0.115296
$947$	−0.716471	−0.0232822	−0.0116411	−	0.999932i	$-0.503706\pi$
$947$	−0.716471	−0.0232822	−0.0116411	+	0.999932i	$0.503706\pi$
$948$	17.5777	0.570896
$949$	9.01210	0.292545
$950$	10.9893	0.356541
$951$	6.63619	0.215193
$952$	−8.23889	−0.267024
$953$	12.7870	0.414212	0.207106	−	0.978318i	$-0.433595\pi$
$953$	12.7870	0.414212	0.207106	+	0.978318i	$0.433595\pi$
$954$	−3.43552	−0.111229
$955$	5.47860	0.177283
$956$	6.85890	0.221833
$957$	10.0922	0.326235
$958$	−19.9150	−0.643423
$959$	9.57655	0.309243
$960$	−6.50006	−0.209788
$961$	67.5845	2.18015
$962$	−22.3856	−0.721741
$963$	9.12343	0.293998
$964$	1.98551	0.0639489
$965$	51.8132	1.66793
$966$	25.8337	0.831187
$967$	17.3260	0.557167	0.278583	−	0.960412i	$-0.410135\pi$
$967$	17.3260	0.557167	0.278583	+	0.960412i	$0.410135\pi$
$968$	−1.45250	−0.0466851
$969$	16.2747	0.522819
$970$	−61.2206	−1.96567
$971$	23.9207	0.767650	0.383825	−	0.923406i	$-0.374607\pi$
$971$	23.9207	0.767650	0.383825	+	0.923406i	$0.374607\pi$
$972$	8.84711	0.283771
$973$	20.0391	0.642425
$974$	4.82401	0.154571
$975$	−28.2435	−0.904516
$976$	−11.4546	−0.366653
$977$	41.0508	1.31333	0.656666	−	0.754182i	$-0.271966\pi$
$977$	41.0508	1.31333	0.656666	+	0.754182i	$0.271966\pi$
$978$	0.499484	0.0159717
$979$	29.5190	0.943431
$980$	−11.7194	−0.374363
$981$	1.25869	0.0401868
$982$	−42.5241	−1.35700
$983$	49.5424	1.58016	0.790079	−	0.613005i	$-0.210040\pi$
$983$	49.5424	1.58016	0.790079	+	0.613005i	$0.210040\pi$
$984$	19.2992	0.615236
$985$	13.7931	0.439484
$986$	−7.35793	−0.234324
$987$	−6.43752	−0.204908
$988$	4.53197	0.144181
$989$	−8.10676	−0.257780
$990$	−8.94626	−0.284331
$991$	−13.5708	−0.431092	−0.215546	−	0.976494i	$-0.569153\pi$
$991$	−13.5708	−0.431092	−0.215546	+	0.976494i	$0.569153\pi$
$992$	−9.92897	−0.315245
$993$	35.0004	1.11070
$994$	3.37572	0.107071
$995$	40.8455	1.29489
$996$	−15.7175	−0.498028
$997$	−38.8697	−1.23102	−0.615508	−	0.788131i	$-0.711049\pi$
$997$	−38.8697	−1.23102	−0.615508	+	0.788131i	$0.711049\pi$
$998$	−8.65225	−0.273882
$999$	−38.4739	−1.21726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.19	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.19	✓	69	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.96903 q^{3} +1.00000 q^{4} +3.30115 q^{5} -1.96903 q^{6} +1.85739 q^{7} +1.00000 q^{8} +0.877064 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.96903 q^{3} +1.00000 q^{4} +3.30115 q^{5} -1.96903 q^{6} +1.85739 q^{7} +1.00000 q^{8} +0.877064 q^{9} +3.30115 q^{10} -3.08990 q^{11} -1.96903 q^{12} +2.43216 q^{13} +1.85739 q^{14} -6.50006 q^{15} +1.00000 q^{16} -4.43573 q^{17} +0.877064 q^{18} +1.86336 q^{19} +3.30115 q^{20} -3.65725 q^{21} -3.08990 q^{22} -7.06371 q^{23} -1.96903 q^{24} +5.89761 q^{25} +2.43216 q^{26} +4.18012 q^{27} +1.85739 q^{28} +1.65879 q^{29} -6.50006 q^{30} -9.92897 q^{31} +1.00000 q^{32} +6.08410 q^{33} -4.43573 q^{34} +6.13153 q^{35} +0.877064 q^{36} -9.20402 q^{37} +1.86336 q^{38} -4.78898 q^{39} +3.30115 q^{40} -9.80139 q^{41} -3.65725 q^{42} +1.14766 q^{43} -3.08990 q^{44} +2.89532 q^{45} -7.06371 q^{46} +1.76021 q^{47} -1.96903 q^{48} -3.55010 q^{49} +5.89761 q^{50} +8.73408 q^{51} +2.43216 q^{52} -3.91707 q^{53} +4.18012 q^{54} -10.2002 q^{55} +1.85739 q^{56} -3.66900 q^{57} +1.65879 q^{58} +11.0174 q^{59} -6.50006 q^{60} -11.4546 q^{61} -9.92897 q^{62} +1.62905 q^{63} +1.00000 q^{64} +8.02891 q^{65} +6.08410 q^{66} -3.36449 q^{67} -4.43573 q^{68} +13.9086 q^{69} +6.13153 q^{70} +1.81745 q^{71} +0.877064 q^{72} +3.70540 q^{73} -9.20402 q^{74} -11.6125 q^{75} +1.86336 q^{76} -5.73916 q^{77} -4.78898 q^{78} -8.92708 q^{79} +3.30115 q^{80} -10.8620 q^{81} -9.80139 q^{82} +7.98237 q^{83} -3.65725 q^{84} -14.6430 q^{85} +1.14766 q^{86} -3.26619 q^{87} -3.08990 q^{88} -9.55337 q^{89} +2.89532 q^{90} +4.51746 q^{91} -7.06371 q^{92} +19.5504 q^{93} +1.76021 q^{94} +6.15122 q^{95} -1.96903 q^{96} -18.5452 q^{97} -3.55010 q^{98} -2.71004 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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