LMFDB - Embedded newform 2678.2.a.s.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2678,2,Mod(1,2678)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2678, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2678.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2678 = 2 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2678.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:	$21.3839376613$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 8x^{8} + 37x^{7} + 20x^{6} - 106x^{5} - 17x^{4} + 90x^{3} + 2x^{2} - 17x - 2 $ x^10 - 4x^9 - 8x^8 + 37x^7 + 20x^6 - 106x^5 - 17x^4 + 90x^3 + 2x^2 - 17*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.639130$ of defining polynomial
Character	$\chi$	$=$	2678.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.360870 q^{3} +1.00000 q^{4} +4.09092 q^{5} -0.360870 q^{6} -3.96412 q^{7} +1.00000 q^{8} -2.86977 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.360870 q^{3} +1.00000 q^{4} +4.09092 q^{5} -0.360870 q^{6} -3.96412 q^{7} +1.00000 q^{8} -2.86977 q^{9} +4.09092 q^{10} -6.50067 q^{11} -0.360870 q^{12} -1.00000 q^{13} -3.96412 q^{14} -1.47629 q^{15} +1.00000 q^{16} +1.07719 q^{17} -2.86977 q^{18} -1.75604 q^{19} +4.09092 q^{20} +1.43053 q^{21} -6.50067 q^{22} +5.71795 q^{23} -0.360870 q^{24} +11.7356 q^{25} -1.00000 q^{26} +2.11822 q^{27} -3.96412 q^{28} -5.58981 q^{29} -1.47629 q^{30} -8.57913 q^{31} +1.00000 q^{32} +2.34590 q^{33} +1.07719 q^{34} -16.2169 q^{35} -2.86977 q^{36} +4.73810 q^{37} -1.75604 q^{38} +0.360870 q^{39} +4.09092 q^{40} -5.00260 q^{41} +1.43053 q^{42} -10.6964 q^{43} -6.50067 q^{44} -11.7400 q^{45} +5.71795 q^{46} -0.493365 q^{47} -0.360870 q^{48} +8.71423 q^{49} +11.7356 q^{50} -0.388727 q^{51} -1.00000 q^{52} +2.16173 q^{53} +2.11822 q^{54} -26.5937 q^{55} -3.96412 q^{56} +0.633702 q^{57} -5.58981 q^{58} -10.0453 q^{59} -1.47629 q^{60} -6.29473 q^{61} -8.57913 q^{62} +11.3761 q^{63} +1.00000 q^{64} -4.09092 q^{65} +2.34590 q^{66} +3.45091 q^{67} +1.07719 q^{68} -2.06344 q^{69} -16.2169 q^{70} -3.56940 q^{71} -2.86977 q^{72} -10.1158 q^{73} +4.73810 q^{74} -4.23503 q^{75} -1.75604 q^{76} +25.7694 q^{77} +0.360870 q^{78} -6.57382 q^{79} +4.09092 q^{80} +7.84491 q^{81} -5.00260 q^{82} +14.7080 q^{83} +1.43053 q^{84} +4.40671 q^{85} -10.6964 q^{86} +2.01720 q^{87} -6.50067 q^{88} -11.4903 q^{89} -11.7400 q^{90} +3.96412 q^{91} +5.71795 q^{92} +3.09595 q^{93} -0.493365 q^{94} -7.18381 q^{95} -0.360870 q^{96} -15.8171 q^{97} +8.71423 q^{98} +18.6555 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 6 q^{3} + 10 q^{4} - 3 q^{5} - 6 q^{6} - 10 q^{7} + 10 q^{8} + 4 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 6 * q^3 + 10 * q^4 - 3 * q^5 - 6 * q^6 - 10 * q^7 + 10 * q^8 + 4 * q^9	\( 10 q + 10 q^{2} - 6 q^{3} + 10 q^{4} - 3 q^{5} - 6 q^{6} - 10 q^{7} + 10 q^{8} + 4 q^{9} - 3 q^{10} - 5 q^{11} - 6 q^{12} - 10 q^{13} - 10 q^{14} - 13 q^{15} + 10 q^{16} - 13 q^{17} + 4 q^{18} - 21 q^{19} - 3 q^{20} + 5 q^{21} - 5 q^{22} - 5 q^{23} - 6 q^{24} + 13 q^{25} - 10 q^{26} - 9 q^{27} - 10 q^{28} + 6 q^{29} - 13 q^{30} - 33 q^{31} + 10 q^{32} - 22 q^{33} - 13 q^{34} - 9 q^{35} + 4 q^{36} - 7 q^{37} - 21 q^{38} + 6 q^{39} - 3 q^{40} - 20 q^{41} + 5 q^{42} - 22 q^{43} - 5 q^{44} - 14 q^{45} - 5 q^{46} - 31 q^{47} - 6 q^{48} + 8 q^{49} + 13 q^{50} - 8 q^{51} - 10 q^{52} + q^{53} - 9 q^{54} - 30 q^{55} - 10 q^{56} + 33 q^{57} + 6 q^{58} - 51 q^{59} - 13 q^{60} - 6 q^{61} - 33 q^{62} - 25 q^{63} + 10 q^{64} + 3 q^{65} - 22 q^{66} - 19 q^{67} - 13 q^{68} + 6 q^{69} - 9 q^{70} - 14 q^{71} + 4 q^{72} - 16 q^{73} - 7 q^{74} + 5 q^{75} - 21 q^{76} - 5 q^{77} + 6 q^{78} + 11 q^{79} - 3 q^{80} - 2 q^{81} - 20 q^{82} + q^{83} + 5 q^{84} - 27 q^{85} - 22 q^{86} - 5 q^{88} - 47 q^{89} - 14 q^{90} + 10 q^{91} - 5 q^{92} + 12 q^{93} - 31 q^{94} - 14 q^{95} - 6 q^{96} - 44 q^{97} + 8 q^{98} + 23 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 6 * q^3 + 10 * q^4 - 3 * q^5 - 6 * q^6 - 10 * q^7 + 10 * q^8 + 4 * q^9 - 3 * q^10 - 5 * q^11 - 6 * q^12 - 10 * q^13 - 10 * q^14 - 13 * q^15 + 10 * q^16 - 13 * q^17 + 4 * q^18 - 21 * q^19 - 3 * q^20 + 5 * q^21 - 5 * q^22 - 5 * q^23 - 6 * q^24 + 13 * q^25 - 10 * q^26 - 9 * q^27 - 10 * q^28 + 6 * q^29 - 13 * q^30 - 33 * q^31 + 10 * q^32 - 22 * q^33 - 13 * q^34 - 9 * q^35 + 4 * q^36 - 7 * q^37 - 21 * q^38 + 6 * q^39 - 3 * q^40 - 20 * q^41 + 5 * q^42 - 22 * q^43 - 5 * q^44 - 14 * q^45 - 5 * q^46 - 31 * q^47 - 6 * q^48 + 8 * q^49 + 13 * q^50 - 8 * q^51 - 10 * q^52 + q^53 - 9 * q^54 - 30 * q^55 - 10 * q^56 + 33 * q^57 + 6 * q^58 - 51 * q^59 - 13 * q^60 - 6 * q^61 - 33 * q^62 - 25 * q^63 + 10 * q^64 + 3 * q^65 - 22 * q^66 - 19 * q^67 - 13 * q^68 + 6 * q^69 - 9 * q^70 - 14 * q^71 + 4 * q^72 - 16 * q^73 - 7 * q^74 + 5 * q^75 - 21 * q^76 - 5 * q^77 + 6 * q^78 + 11 * q^79 - 3 * q^80 - 2 * q^81 - 20 * q^82 + q^83 + 5 * q^84 - 27 * q^85 - 22 * q^86 - 5 * q^88 - 47 * q^89 - 14 * q^90 + 10 * q^91 - 5 * q^92 + 12 * q^93 - 31 * q^94 - 14 * q^95 - 6 * q^96 - 44 * q^97 + 8 * q^98 + 23 * 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
$3$	−0.360870	−0.208348	−0.104174	−	0.994559i	$-0.533220\pi$
$3$	−0.360870	−0.208348	−0.104174	+	0.994559i	$0.533220\pi$
$4$	1.00000	0.500000
$5$	4.09092	1.82951	0.914757	−	0.404005i	$-0.132382\pi$
$5$	4.09092	1.82951	0.914757	+	0.404005i	$0.132382\pi$
$6$	−0.360870	−0.147325
$7$	−3.96412	−1.49830	−0.749148	−	0.662403i	$-0.769537\pi$
$7$	−3.96412	−1.49830	−0.749148	+	0.662403i	$0.769537\pi$
$8$	1.00000	0.353553
$9$	−2.86977	−0.956591
$10$	4.09092	1.29366
$11$	−6.50067	−1.96003	−0.980013	−	0.198932i	$-0.936253\pi$
$11$	−6.50067	−1.96003	−0.980013	+	0.198932i	$0.936253\pi$
$12$	−0.360870	−0.104174
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.96412	−1.05945
$15$	−1.47629	−0.381176
$16$	1.00000	0.250000
$17$	1.07719	0.261258	0.130629	−	0.991431i	$-0.458300\pi$
$17$	1.07719	0.261258	0.130629	+	0.991431i	$0.458300\pi$
$18$	−2.86977	−0.676412
$19$	−1.75604	−0.402863	−0.201431	−	0.979503i	$-0.564559\pi$
$19$	−1.75604	−0.402863	−0.201431	+	0.979503i	$0.564559\pi$
$20$	4.09092	0.914757
$21$	1.43053	0.312167
$22$	−6.50067	−1.38595
$23$	5.71795	1.19227	0.596137	−	0.802883i	$-0.296701\pi$
$23$	5.71795	1.19227	0.596137	+	0.802883i	$0.296701\pi$
$24$	−0.360870	−0.0736623
$25$	11.7356	2.34712
$26$	−1.00000	−0.196116
$27$	2.11822	0.407653
$28$	−3.96412	−0.749148
$29$	−5.58981	−1.03800	−0.519001	−	0.854774i	$-0.673696\pi$
$29$	−5.58981	−1.03800	−0.519001	+	0.854774i	$0.673696\pi$
$30$	−1.47629	−0.269532
$31$	−8.57913	−1.54086	−0.770429	−	0.637526i	$-0.779958\pi$
$31$	−8.57913	−1.54086	−0.770429	+	0.637526i	$0.779958\pi$
$32$	1.00000	0.176777
$33$	2.34590	0.408368
$34$	1.07719	0.184737
$35$	−16.2169	−2.74115
$36$	−2.86977	−0.478295
$37$	4.73810	0.778939	0.389470	−	0.921039i	$-0.372658\pi$
$37$	4.73810	0.778939	0.389470	+	0.921039i	$0.372658\pi$
$38$	−1.75604	−0.284867
$39$	0.360870	0.0577854
$40$	4.09092	0.646831
$41$	−5.00260	−0.781275	−0.390638	−	0.920545i	$-0.627745\pi$
$41$	−5.00260	−0.781275	−0.390638	+	0.920545i	$0.627745\pi$
$42$	1.43053	0.220736
$43$	−10.6964	−1.63119	−0.815595	−	0.578623i	$-0.803590\pi$
$43$	−10.6964	−1.63119	−0.815595	+	0.578623i	$0.803590\pi$
$44$	−6.50067	−0.980013
$45$	−11.7400	−1.75010
$46$	5.71795	0.843065
$47$	−0.493365	−0.0719647	−0.0359824	−	0.999352i	$-0.511456\pi$
$47$	−0.493365	−0.0719647	−0.0359824	+	0.999352i	$0.511456\pi$
$48$	−0.360870	−0.0520871
$49$	8.71423	1.24489
$50$	11.7356	1.65966
$51$	−0.388727	−0.0544326
$52$	−1.00000	−0.138675
$53$	2.16173	0.296936	0.148468	−	0.988917i	$-0.452566\pi$
$53$	2.16173	0.296936	0.148468	+	0.988917i	$0.452566\pi$
$54$	2.11822	0.288254
$55$	−26.5937	−3.58590
$56$	−3.96412	−0.529727
$57$	0.633702	0.0839358
$58$	−5.58981	−0.733978
$59$	−10.0453	−1.30779	−0.653893	−	0.756587i	$-0.726865\pi$
$59$	−10.0453	−1.30779	−0.653893	+	0.756587i	$0.726865\pi$
$60$	−1.47629	−0.190588
$61$	−6.29473	−0.805957	−0.402979	−	0.915209i	$-0.632025\pi$
$61$	−6.29473	−0.805957	−0.402979	+	0.915209i	$0.632025\pi$
$62$	−8.57913	−1.08955
$63$	11.3761	1.43326
$64$	1.00000	0.125000
$65$	−4.09092	−0.507416
$66$	2.34590	0.288760
$67$	3.45091	0.421595	0.210798	−	0.977530i	$-0.432394\pi$
$67$	3.45091	0.421595	0.210798	+	0.977530i	$0.432394\pi$
$68$	1.07719	0.130629
$69$	−2.06344	−0.248408
$70$	−16.2169	−1.93829
$71$	−3.56940	−0.423610	−0.211805	−	0.977312i	$-0.567934\pi$
$71$	−3.56940	−0.423610	−0.211805	+	0.977312i	$0.567934\pi$
$72$	−2.86977	−0.338206
$73$	−10.1158	−1.18397	−0.591983	−	0.805951i	$-0.701655\pi$
$73$	−10.1158	−1.18397	−0.591983	+	0.805951i	$0.701655\pi$
$74$	4.73810	0.550793
$75$	−4.23503	−0.489019
$76$	−1.75604	−0.201431
$77$	25.7694	2.93670
$78$	0.360870	0.0408605
$79$	−6.57382	−0.739613	−0.369806	−	0.929109i	$-0.620576\pi$
$79$	−6.57382	−0.739613	−0.369806	+	0.929109i	$0.620576\pi$
$80$	4.09092	0.457378
$81$	7.84491	0.871657
$82$	−5.00260	−0.552445
$83$	14.7080	1.61441	0.807207	−	0.590268i	$-0.200978\pi$
$83$	14.7080	1.61441	0.807207	+	0.590268i	$0.200978\pi$
$84$	1.43053	0.156084
$85$	4.40671	0.477975
$86$	−10.6964	−1.15343
$87$	2.01720	0.216266
$88$	−6.50067	−0.692974
$89$	−11.4903	−1.21797	−0.608986	−	0.793181i	$-0.708423\pi$
$89$	−11.4903	−1.21797	−0.608986	+	0.793181i	$0.708423\pi$
$90$	−11.7400	−1.23750
$91$	3.96412	0.415552
$92$	5.71795	0.596137
$93$	3.09595	0.321035
$94$	−0.493365	−0.0508868
$95$	−7.18381	−0.737043
$96$	−0.360870	−0.0368311
$97$	−15.8171	−1.60598	−0.802991	−	0.595992i	$-0.796759\pi$
$97$	−15.8171	−1.60598	−0.802991	+	0.595992i	$0.796759\pi$
$98$	8.71423	0.880270
$99$	18.6555	1.87494
$100$	11.7356	1.17356
$101$	5.41239	0.538553	0.269277	−	0.963063i	$-0.413215\pi$
$101$	5.41239	0.538553	0.269277	+	0.963063i	$0.413215\pi$
$102$	−0.388727	−0.0384897
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	5.85218	0.571115
$106$	2.16173	0.209966
$107$	−4.65825	−0.450330	−0.225165	−	0.974321i	$-0.572292\pi$
$107$	−4.65825	−0.450330	−0.225165	+	0.974321i	$0.572292\pi$
$108$	2.11822	0.203826
$109$	−2.23019	−0.213613	−0.106807	−	0.994280i	$-0.534063\pi$
$109$	−2.23019	−0.213613	−0.106807	+	0.994280i	$0.534063\pi$
$110$	−26.5937	−2.53561
$111$	−1.70984	−0.162291
$112$	−3.96412	−0.374574
$113$	11.9639	1.12547	0.562733	−	0.826638i	$-0.309750\pi$
$113$	11.9639	1.12547	0.562733	+	0.826638i	$0.309750\pi$
$114$	0.633702	0.0593516
$115$	23.3916	2.18128
$116$	−5.58981	−0.519001
$117$	2.86977	0.265311
$118$	−10.0453	−0.924745
$119$	−4.27012	−0.391441
$120$	−1.47629	−0.134766
$121$	31.2587	2.84170
$122$	−6.29473	−0.569898
$123$	1.80529	0.162777
$124$	−8.57913	−0.770429
$125$	27.5548	2.46458
$126$	11.3761	1.01347
$127$	18.3997	1.63271	0.816354	−	0.577551i	$-0.195992\pi$
$127$	18.3997	1.63271	0.816354	+	0.577551i	$0.195992\pi$
$128$	1.00000	0.0883883
$129$	3.86002	0.339856
$130$	−4.09092	−0.358797
$131$	−3.62334	−0.316573	−0.158286	−	0.987393i	$-0.550597\pi$
$131$	−3.62334	−0.316573	−0.158286	+	0.987393i	$0.550597\pi$
$132$	2.34590	0.204184
$133$	6.96114	0.603608
$134$	3.45091	0.298113
$135$	8.66548	0.745806
$136$	1.07719	0.0923686
$137$	−0.556476	−0.0475430	−0.0237715	−	0.999717i	$-0.507567\pi$
$137$	−0.556476	−0.0475430	−0.0237715	+	0.999717i	$0.507567\pi$
$138$	−2.06344	−0.175651
$139$	22.5163	1.90981	0.954905	−	0.296911i	$-0.0959566\pi$
$139$	22.5163	1.90981	0.954905	+	0.296911i	$0.0959566\pi$
$140$	−16.2169	−1.37058
$141$	0.178041	0.0149937
$142$	−3.56940	−0.299538
$143$	6.50067	0.543614
$144$	−2.86977	−0.239148
$145$	−22.8675	−1.89904
$146$	−10.1158	−0.837190
$147$	−3.14470	−0.259371
$148$	4.73810	0.389470
$149$	−12.4696	−1.02155	−0.510775	−	0.859714i	$-0.670642\pi$
$149$	−12.4696	−1.02155	−0.510775	+	0.859714i	$0.670642\pi$
$150$	−4.23503	−0.345788
$151$	−21.3319	−1.73597	−0.867984	−	0.496593i	$-0.834584\pi$
$151$	−21.3319	−1.73597	−0.867984	+	0.496593i	$0.834584\pi$
$152$	−1.75604	−0.142434
$153$	−3.09130	−0.249917
$154$	25.7694	2.07656
$155$	−35.0965	−2.81902
$156$	0.360870	0.0288927
$157$	11.0967	0.885612	0.442806	−	0.896617i	$-0.353983\pi$
$157$	11.0967	0.885612	0.442806	+	0.896617i	$0.353983\pi$
$158$	−6.57382	−0.522985
$159$	−0.780103	−0.0618662
$160$	4.09092	0.323415
$161$	−22.6666	−1.78638
$162$	7.84491	0.616355
$163$	3.33891	0.261523	0.130762	−	0.991414i	$-0.458258\pi$
$163$	3.33891	0.261523	0.130762	+	0.991414i	$0.458258\pi$
$164$	−5.00260	−0.390638
$165$	9.59687	0.747115
$166$	14.7080	1.14156
$167$	6.64557	0.514250	0.257125	−	0.966378i	$-0.417225\pi$
$167$	6.64557	0.514250	0.257125	+	0.966378i	$0.417225\pi$
$168$	1.43053	0.110368
$169$	1.00000	0.0769231
$170$	4.40671	0.337979
$171$	5.03943	0.385375
$172$	−10.6964	−0.815595
$173$	−5.97455	−0.454237	−0.227118	−	0.973867i	$-0.572930\pi$
$173$	−5.97455	−0.454237	−0.227118	+	0.973867i	$0.572930\pi$
$174$	2.01720	0.152923
$175$	−46.5213	−3.51668
$176$	−6.50067	−0.490007
$177$	3.62505	0.272475
$178$	−11.4903	−0.861236
$179$	−17.6181	−1.31684	−0.658418	−	0.752652i	$-0.728774\pi$
$179$	−17.6181	−1.31684	−0.658418	+	0.752652i	$0.728774\pi$
$180$	−11.7400	−0.875048
$181$	14.9512	1.11131	0.555656	−	0.831412i	$-0.312467\pi$
$181$	14.9512	1.11131	0.555656	+	0.831412i	$0.312467\pi$
$182$	3.96412	0.293840
$183$	2.27158	0.167920
$184$	5.71795	0.421533
$185$	19.3832	1.42508
$186$	3.09595	0.227006
$187$	−7.00248	−0.512072
$188$	−0.493365	−0.0359824
$189$	−8.39689	−0.610784
$190$	−7.18381	−0.521168
$191$	−15.5024	−1.12172	−0.560858	−	0.827912i	$-0.689529\pi$
$191$	−15.5024	−1.12172	−0.560858	+	0.827912i	$0.689529\pi$
$192$	−0.360870	−0.0260435
$193$	0.318902	0.0229551	0.0114776	−	0.999934i	$-0.496347\pi$
$193$	0.318902	0.0229551	0.0114776	+	0.999934i	$0.496347\pi$
$194$	−15.8171	−1.13560
$195$	1.47629	0.105719
$196$	8.71423	0.622445
$197$	7.17598	0.511268	0.255634	−	0.966774i	$-0.417716\pi$
$197$	7.17598	0.511268	0.255634	+	0.966774i	$0.417716\pi$
$198$	18.6555	1.32579
$199$	19.4697	1.38017	0.690085	−	0.723729i	$-0.257573\pi$
$199$	19.4697	1.38017	0.690085	+	0.723729i	$0.257573\pi$
$200$	11.7356	0.829832
$201$	−1.24533	−0.0878387
$202$	5.41239	0.380815
$203$	22.1587	1.55523
$204$	−0.388727	−0.0272163
$205$	−20.4652	−1.42935
$206$	1.00000	0.0696733
$207$	−16.4092	−1.14052
$208$	−1.00000	−0.0693375
$209$	11.4154	0.789622
$210$	5.85218	0.403839
$211$	22.1678	1.52609	0.763046	−	0.646345i	$-0.223703\pi$
$211$	22.1678	1.52609	0.763046	+	0.646345i	$0.223703\pi$
$212$	2.16173	0.148468
$213$	1.28809	0.0882585
$214$	−4.65825	−0.318431
$215$	−43.7582	−2.98429
$216$	2.11822	0.144127
$217$	34.0087	2.30866
$218$	−2.23019	−0.151047
$219$	3.65049	0.246677
$220$	−26.5937	−1.79295
$221$	−1.07719	−0.0724599
$222$	−1.70984	−0.114757
$223$	19.4824	1.30464	0.652318	−	0.757946i	$-0.273797\pi$
$223$	19.4824	1.30464	0.652318	+	0.757946i	$0.273797\pi$
$224$	−3.96412	−0.264864
$225$	−33.6785	−2.24523
$226$	11.9639	0.795825
$227$	8.49923	0.564114	0.282057	−	0.959398i	$-0.408983\pi$
$227$	8.49923	0.564114	0.282057	+	0.959398i	$0.408983\pi$
$228$	0.633702	0.0419679
$229$	−1.17814	−0.0778539	−0.0389270	−	0.999242i	$-0.512394\pi$
$229$	−1.17814	−0.0778539	−0.0389270	+	0.999242i	$0.512394\pi$
$230$	23.3916	1.54240
$231$	−9.29941	−0.611856
$232$	−5.58981	−0.366989
$233$	−15.8784	−1.04023	−0.520115	−	0.854096i	$-0.674111\pi$
$233$	−15.8784	−1.04023	−0.520115	+	0.854096i	$0.674111\pi$
$234$	2.86977	0.187603
$235$	−2.01832	−0.131660
$236$	−10.0453	−0.653893
$237$	2.37229	0.154097
$238$	−4.27012	−0.276791
$239$	−7.52640	−0.486843	−0.243421	−	0.969921i	$-0.578270\pi$
$239$	−7.52640	−0.486843	−0.243421	+	0.969921i	$0.578270\pi$
$240$	−1.47629	−0.0952941
$241$	19.8024	1.27559	0.637793	−	0.770207i	$-0.279847\pi$
$241$	19.8024	1.27559	0.637793	+	0.770207i	$0.279847\pi$
$242$	31.2587	2.00939
$243$	−9.18567	−0.589261
$244$	−6.29473	−0.402979
$245$	35.6492	2.27754
$246$	1.80529	0.115101
$247$	1.75604	0.111734
$248$	−8.57913	−0.544775
$249$	−5.30768	−0.336361
$250$	27.5548	1.74272
$251$	−20.6708	−1.30473	−0.652365	−	0.757905i	$-0.726223\pi$
$251$	−20.6708	−1.30473	−0.652365	+	0.757905i	$0.726223\pi$
$252$	11.3761	0.716628
$253$	−37.1705	−2.33689
$254$	18.3997	1.15450
$255$	−1.59025	−0.0995853
$256$	1.00000	0.0625000
$257$	5.46497	0.340896	0.170448	−	0.985367i	$-0.445479\pi$
$257$	5.46497	0.340896	0.170448	+	0.985367i	$0.445479\pi$
$258$	3.86002	0.240314
$259$	−18.7824	−1.16708
$260$	−4.09092	−0.253708
$261$	16.0415	0.992943
$262$	−3.62334	−0.223851
$263$	0.392303	0.0241905	0.0120952	−	0.999927i	$-0.496150\pi$
$263$	0.392303	0.0241905	0.0120952	+	0.999927i	$0.496150\pi$
$264$	2.34590	0.144380
$265$	8.84346	0.543249
$266$	6.96114	0.426815
$267$	4.14651	0.253762
$268$	3.45091	0.210798
$269$	7.39684	0.450993	0.225497	−	0.974244i	$-0.427600\pi$
$269$	7.39684	0.450993	0.225497	+	0.974244i	$0.427600\pi$
$270$	8.66548	0.527364
$271$	−24.1462	−1.46678	−0.733389	−	0.679809i	$-0.762063\pi$
$271$	−24.1462	−1.46678	−0.733389	+	0.679809i	$0.762063\pi$
$272$	1.07719	0.0653144
$273$	−1.43053	−0.0865797
$274$	−0.556476	−0.0336180
$275$	−76.2893	−4.60042
$276$	−2.06344	−0.124204
$277$	−16.8694	−1.01359	−0.506793	−	0.862068i	$-0.669169\pi$
$277$	−16.8694	−1.01359	−0.506793	+	0.862068i	$0.669169\pi$
$278$	22.5163	1.35044
$279$	24.6202	1.47397
$280$	−16.2169	−0.969144
$281$	14.2121	0.847822	0.423911	−	0.905704i	$-0.360657\pi$
$281$	14.2121	0.847822	0.423911	+	0.905704i	$0.360657\pi$
$282$	0.178041	0.0106022
$283$	−0.861073	−0.0511855	−0.0255927	−	0.999672i	$-0.508147\pi$
$283$	−0.861073	−0.0511855	−0.0255927	+	0.999672i	$0.508147\pi$
$284$	−3.56940	−0.211805
$285$	2.59242	0.153562
$286$	6.50067	0.384393
$287$	19.8309	1.17058
$288$	−2.86977	−0.169103
$289$	−15.8397	−0.931744
$290$	−22.8675	−1.34282
$291$	5.70791	0.334604
$292$	−10.1158	−0.591983
$293$	10.5662	0.617283	0.308641	−	0.951179i	$-0.400126\pi$
$293$	10.5662	0.617283	0.308641	+	0.951179i	$0.400126\pi$
$294$	−3.14470	−0.183403
$295$	−41.0945	−2.39261
$296$	4.73810	0.275397
$297$	−13.7699	−0.799010
$298$	−12.4696	−0.722345
$299$	−5.71795	−0.330677
$300$	−4.23503	−0.244509
$301$	42.4019	2.44401
$302$	−21.3319	−1.22751
$303$	−1.95317	−0.112207
$304$	−1.75604	−0.100716
$305$	−25.7512	−1.47451
$306$	−3.09130	−0.176718
$307$	12.3046	0.702261	0.351131	−	0.936327i	$-0.385797\pi$
$307$	12.3046	0.702261	0.351131	+	0.936327i	$0.385797\pi$
$308$	25.7694	1.46835
$309$	−0.360870	−0.0205292
$310$	−35.0965	−1.99335
$311$	27.1270	1.53823	0.769117	−	0.639108i	$-0.220697\pi$
$311$	27.1270	1.53823	0.769117	+	0.639108i	$0.220697\pi$
$312$	0.360870	0.0204302
$313$	4.23415	0.239328	0.119664	−	0.992814i	$-0.461818\pi$
$313$	4.23415	0.239328	0.119664	+	0.992814i	$0.461818\pi$
$314$	11.0967	0.626222
$315$	46.5387	2.62216
$316$	−6.57382	−0.369806
$317$	−18.3972	−1.03329	−0.516645	−	0.856200i	$-0.672819\pi$
$317$	−18.3972	−1.03329	−0.516645	+	0.856200i	$0.672819\pi$
$318$	−0.780103	−0.0437460
$319$	36.3375	2.03451
$320$	4.09092	0.228689
$321$	1.68102	0.0938255
$322$	−22.6666	−1.26316
$323$	−1.89159	−0.105251
$324$	7.84491	0.435829
$325$	−11.7356	−0.650974
$326$	3.33891	0.184925
$327$	0.804808	0.0445060
$328$	−5.00260	−0.276223
$329$	1.95576	0.107824
$330$	9.59687	0.528290
$331$	−8.96200	−0.492596	−0.246298	−	0.969194i	$-0.579214\pi$
$331$	−8.96200	−0.492596	−0.246298	+	0.969194i	$0.579214\pi$
$332$	14.7080	0.807207
$333$	−13.5973	−0.745126
$334$	6.64557	0.363630
$335$	14.1174	0.771315
$336$	1.43053	0.0780419
$337$	27.3704	1.49096	0.745479	−	0.666529i	$-0.232221\pi$
$337$	27.3704	1.49096	0.745479	+	0.666529i	$0.232221\pi$
$338$	1.00000	0.0543928
$339$	−4.31740	−0.234489
$340$	4.40671	0.238987
$341$	55.7701	3.02012
$342$	5.03943	0.272501
$343$	−6.79540	−0.366917
$344$	−10.6964	−0.576713
$345$	−8.44134	−0.454467
$346$	−5.97455	−0.321194
$347$	4.50346	0.241758	0.120879	−	0.992667i	$-0.461429\pi$
$347$	4.50346	0.241758	0.120879	+	0.992667i	$0.461429\pi$
$348$	2.01720	0.108133
$349$	−29.2702	−1.56680	−0.783399	−	0.621519i	$-0.786516\pi$
$349$	−29.2702	−1.56680	−0.783399	+	0.621519i	$0.786516\pi$
$350$	−46.5213	−2.48667
$351$	−2.11822	−0.113062
$352$	−6.50067	−0.346487
$353$	24.6452	1.31173	0.655866	−	0.754877i	$-0.272304\pi$
$353$	24.6452	1.31173	0.655866	+	0.754877i	$0.272304\pi$
$354$	3.62505	0.192669
$355$	−14.6021	−0.775000
$356$	−11.4903	−0.608986
$357$	1.54096	0.0815562
$358$	−17.6181	−0.931144
$359$	−7.16361	−0.378081	−0.189040	−	0.981969i	$-0.560538\pi$
$359$	−7.16361	−0.378081	−0.189040	+	0.981969i	$0.560538\pi$
$360$	−11.7400	−0.618752
$361$	−15.9163	−0.837701
$362$	14.9512	0.785816
$363$	−11.2803	−0.592064
$364$	3.96412	0.207776
$365$	−41.3829	−2.16608
$366$	2.27158	0.118737
$367$	−17.7245	−0.925210	−0.462605	−	0.886564i	$-0.653085\pi$
$367$	−17.7245	−0.925210	−0.462605	+	0.886564i	$0.653085\pi$
$368$	5.71795	0.298069
$369$	14.3563	0.747361
$370$	19.3832	1.00768
$371$	−8.56935	−0.444899
$372$	3.09595	0.160518
$373$	−35.2383	−1.82457	−0.912284	−	0.409557i	$-0.865683\pi$
$373$	−35.2383	−1.82457	−0.912284	+	0.409557i	$0.865683\pi$
$374$	−7.00248	−0.362090
$375$	−9.94370	−0.513490
$376$	−0.493365	−0.0254434
$377$	5.58981	0.287890
$378$	−8.39689	−0.431890
$379$	21.9728	1.12867	0.564333	−	0.825547i	$-0.309133\pi$
$379$	21.9728	1.12867	0.564333	+	0.825547i	$0.309133\pi$
$380$	−7.18381	−0.368522
$381$	−6.63990	−0.340172
$382$	−15.5024	−0.793173
$383$	−28.0022	−1.43085	−0.715423	−	0.698692i	$-0.753766\pi$
$383$	−28.0022	−1.43085	−0.715423	+	0.698692i	$0.753766\pi$
$384$	−0.360870	−0.0184156
$385$	105.421	5.37273
$386$	0.318902	0.0162317
$387$	30.6963	1.56038
$388$	−15.8171	−0.802991
$389$	−32.8877	−1.66747	−0.833736	−	0.552164i	$-0.813802\pi$
$389$	−32.8877	−1.66747	−0.833736	+	0.552164i	$0.813802\pi$
$390$	1.47629	0.0747548
$391$	6.15934	0.311491
$392$	8.71423	0.440135
$393$	1.30755	0.0659574
$394$	7.17598	0.361521
$395$	−26.8930	−1.35313
$396$	18.6555	0.937472
$397$	21.1875	1.06337	0.531685	−	0.846942i	$-0.321559\pi$
$397$	21.1875	1.06337	0.531685	+	0.846942i	$0.321559\pi$
$398$	19.4697	0.975927
$399$	−2.51207	−0.125761
$400$	11.7356	0.586780
$401$	−18.4713	−0.922410	−0.461205	−	0.887294i	$-0.652583\pi$
$401$	−18.4713	−0.922410	−0.461205	+	0.887294i	$0.652583\pi$
$402$	−1.24533	−0.0621114
$403$	8.57913	0.427357
$404$	5.41239	0.269277
$405$	32.0929	1.59471
$406$	22.1587	1.09972
$407$	−30.8009	−1.52674
$408$	−0.388727	−0.0192448
$409$	−14.5704	−0.720461	−0.360230	−	0.932863i	$-0.617302\pi$
$409$	−14.5704	−0.720461	−0.360230	+	0.932863i	$0.617302\pi$
$410$	−20.4652	−1.01071
$411$	0.200816	0.00990551
$412$	1.00000	0.0492665
$413$	39.8207	1.95945
$414$	−16.4092	−0.806469
$415$	60.1693	2.95359
$416$	−1.00000	−0.0490290
$417$	−8.12547	−0.397906
$418$	11.4154	0.558347
$419$	−27.4941	−1.34317	−0.671586	−	0.740926i	$-0.734387\pi$
$419$	−27.4941	−1.34317	−0.671586	+	0.740926i	$0.734387\pi$
$420$	5.85218	0.285557
$421$	16.5966	0.808869	0.404434	−	0.914567i	$-0.367468\pi$
$421$	16.5966	0.808869	0.404434	+	0.914567i	$0.367468\pi$
$422$	22.1678	1.07911
$423$	1.41585	0.0688408
$424$	2.16173	0.104983
$425$	12.6415	0.613203
$426$	1.28809	0.0624082
$427$	24.9530	1.20756
$428$	−4.65825	−0.225165
$429$	−2.34590	−0.113261
$430$	−43.7582	−2.11021
$431$	23.7582	1.14439	0.572195	−	0.820118i	$-0.306092\pi$
$431$	23.7582	1.14439	0.572195	+	0.820118i	$0.306092\pi$
$432$	2.11822	0.101913
$433$	17.9047	0.860447	0.430224	−	0.902722i	$-0.358435\pi$
$433$	17.9047	0.860447	0.430224	+	0.902722i	$0.358435\pi$
$434$	34.0087	1.63247
$435$	8.25218	0.395662
$436$	−2.23019	−0.106807
$437$	−10.0409	−0.480323
$438$	3.65049	0.174427
$439$	−35.4022	−1.68966	−0.844828	−	0.535038i	$-0.820297\pi$
$439$	−35.4022	−1.68966	−0.844828	+	0.535038i	$0.820297\pi$
$440$	−26.5937	−1.26781
$441$	−25.0079	−1.19085
$442$	−1.07719	−0.0512369
$443$	−3.19591	−0.151842	−0.0759211	−	0.997114i	$-0.524190\pi$
$443$	−3.19591	−0.151842	−0.0759211	+	0.997114i	$0.524190\pi$
$444$	−1.70984	−0.0811454
$445$	−47.0059	−2.22829
$446$	19.4824	0.922516
$447$	4.49991	0.212838
$448$	−3.96412	−0.187287
$449$	38.6889	1.82584	0.912922	−	0.408134i	$-0.133820\pi$
$449$	38.6889	1.82584	0.912922	+	0.408134i	$0.133820\pi$
$450$	−33.6785	−1.58762
$451$	32.5203	1.53132
$452$	11.9639	0.562733
$453$	7.69805	0.361686
$454$	8.49923	0.398889
$455$	16.2169	0.760259
$456$	0.633702	0.0296758
$457$	−8.09619	−0.378724	−0.189362	−	0.981907i	$-0.560642\pi$
$457$	−8.09619	−0.378724	−0.189362	+	0.981907i	$0.560642\pi$
$458$	−1.17814	−0.0550510
$459$	2.28174	0.106502
$460$	23.3916	1.09064
$461$	−22.1299	−1.03069	−0.515345	−	0.856983i	$-0.672336\pi$
$461$	−22.1299	−1.03069	−0.515345	+	0.856983i	$0.672336\pi$
$462$	−9.29941	−0.432648
$463$	23.9541	1.11324	0.556622	−	0.830766i	$-0.312097\pi$
$463$	23.9541	1.11324	0.556622	+	0.830766i	$0.312097\pi$
$464$	−5.58981	−0.259501
$465$	12.6653	0.587338
$466$	−15.8784	−0.735554
$467$	22.9059	1.05996	0.529978	−	0.848011i	$-0.322200\pi$
$467$	22.9059	1.05996	0.529978	+	0.848011i	$0.322200\pi$
$468$	2.86977	0.132655
$469$	−13.6798	−0.631675
$470$	−2.01832	−0.0930980
$471$	−4.00446	−0.184516
$472$	−10.0453	−0.462372
$473$	69.5340	3.19718
$474$	2.37229	0.108963
$475$	−20.6082	−0.945568
$476$	−4.27012	−0.195721
$477$	−6.20367	−0.284047
$478$	−7.52640	−0.344250
$479$	10.1931	0.465735	0.232867	−	0.972508i	$-0.425189\pi$
$479$	10.1931	0.465735	0.232867	+	0.972508i	$0.425189\pi$
$480$	−1.47629	−0.0673831
$481$	−4.73810	−0.216039
$482$	19.8024	0.901976
$483$	8.17970	0.372189
$484$	31.2587	1.42085
$485$	−64.7064	−2.93816
$486$	−9.18567	−0.416670
$487$	2.15068	0.0974566	0.0487283	−	0.998812i	$-0.484483\pi$
$487$	2.15068	0.0974566	0.0487283	+	0.998812i	$0.484483\pi$
$488$	−6.29473	−0.284949
$489$	−1.20491	−0.0544880
$490$	35.6492	1.61047
$491$	−11.3889	−0.513972	−0.256986	−	0.966415i	$-0.582729\pi$
$491$	−11.3889	−0.513972	−0.256986	+	0.966415i	$0.582729\pi$
$492$	1.80529	0.0813887
$493$	−6.02131	−0.271186
$494$	1.75604	0.0790079
$495$	76.3179	3.43023
$496$	−8.57913	−0.385214
$497$	14.1495	0.634693
$498$	−5.30768	−0.237843
$499$	16.7236	0.748650	0.374325	−	0.927298i	$-0.377874\pi$
$499$	16.7236	0.748650	0.374325	+	0.927298i	$0.377874\pi$
$500$	27.5548	1.23229
$501$	−2.39819	−0.107143
$502$	−20.6708	−0.922583
$503$	−26.0565	−1.16180	−0.580900	−	0.813975i	$-0.697299\pi$
$503$	−26.0565	−1.16180	−0.580900	+	0.813975i	$0.697299\pi$
$504$	11.3761	0.506733
$505$	22.1417	0.985291
$506$	−37.1705	−1.65243
$507$	−0.360870	−0.0160268
$508$	18.3997	0.816354
$509$	−3.85947	−0.171068	−0.0855340	−	0.996335i	$-0.527260\pi$
$509$	−3.85947	−0.171068	−0.0855340	+	0.996335i	$0.527260\pi$
$510$	−1.59025	−0.0704174
$511$	40.1003	1.77393
$512$	1.00000	0.0441942
$513$	−3.71969	−0.164228
$514$	5.46497	0.241050
$515$	4.09092	0.180267
$516$	3.86002	0.169928
$517$	3.20721	0.141053
$518$	−18.7824	−0.825251
$519$	2.15604	0.0946395
$520$	−4.09092	−0.179399
$521$	−0.492946	−0.0215963	−0.0107982	−	0.999942i	$-0.503437\pi$
$521$	−0.492946	−0.0215963	−0.0107982	+	0.999942i	$0.503437\pi$
$522$	16.0415	0.702117
$523$	6.96186	0.304421	0.152210	−	0.988348i	$-0.451361\pi$
$523$	6.96186	0.304421	0.152210	+	0.988348i	$0.451361\pi$
$524$	−3.62334	−0.158286
$525$	16.7881	0.732695
$526$	0.392303	0.0171052
$527$	−9.24138	−0.402561
$528$	2.34590	0.102092
$529$	9.69492	0.421518
$530$	8.84346	0.384135
$531$	28.8277	1.25102
$532$	6.96114	0.301804
$533$	5.00260	0.216687
$534$	4.14651	0.179437
$535$	−19.0565	−0.823885
$536$	3.45091	0.149056
$537$	6.35783	0.274361
$538$	7.39684	0.318900
$539$	−56.6483	−2.44002
$540$	8.66548	0.372903
$541$	0.849710	0.0365319	0.0182659	−	0.999833i	$-0.494185\pi$
$541$	0.849710	0.0365319	0.0182659	+	0.999833i	$0.494185\pi$
$542$	−24.1462	−1.03717
$543$	−5.39543	−0.231540
$544$	1.07719	0.0461843
$545$	−9.12351	−0.390808
$546$	−1.43053	−0.0612211
$547$	−10.8455	−0.463721	−0.231861	−	0.972749i	$-0.574481\pi$
$547$	−10.8455	−0.463721	−0.231861	+	0.972749i	$0.574481\pi$
$548$	−0.556476	−0.0237715
$549$	18.0644	0.770972
$550$	−76.2893	−3.25299
$551$	9.81593	0.418173
$552$	−2.06344	−0.0878257
$553$	26.0594	1.10816
$554$	−16.8694	−0.716713
$555$	−6.99481	−0.296913
$556$	22.5163	0.954905
$557$	−10.7034	−0.453517	−0.226758	−	0.973951i	$-0.572813\pi$
$557$	−10.7034	−0.453517	−0.226758	+	0.973951i	$0.572813\pi$
$558$	24.6202	1.04225
$559$	10.6964	0.452411
$560$	−16.2169	−0.685288
$561$	2.52699	0.106689
$562$	14.2121	0.599501
$563$	−36.5886	−1.54202	−0.771012	−	0.636820i	$-0.780249\pi$
$563$	−36.5886	−1.54202	−0.771012	+	0.636820i	$0.780249\pi$
$564$	0.178041	0.00749687
$565$	48.9432	2.05906
$566$	−0.861073	−0.0361936
$567$	−31.0982	−1.30600
$568$	−3.56940	−0.149769
$569$	31.2438	1.30981	0.654903	−	0.755713i	$-0.272709\pi$
$569$	31.2438	1.30981	0.654903	+	0.755713i	$0.272709\pi$
$570$	2.59242	0.108585
$571$	24.2943	1.01669	0.508343	−	0.861155i	$-0.330258\pi$
$571$	24.2943	1.01669	0.508343	+	0.861155i	$0.330258\pi$
$572$	6.50067	0.271807
$573$	5.59436	0.233708
$574$	19.8309	0.827726
$575$	67.1036	2.79841
$576$	−2.86977	−0.119574
$577$	−38.0076	−1.58228	−0.791139	−	0.611637i	$-0.790511\pi$
$577$	−38.0076	−1.58228	−0.791139	+	0.611637i	$0.790511\pi$
$578$	−15.8397	−0.658843
$579$	−0.115082	−0.00478266
$580$	−22.8675	−0.949520
$581$	−58.3043	−2.41887
$582$	5.70791	0.236600
$583$	−14.0527	−0.582003
$584$	−10.1158	−0.418595
$585$	11.7400	0.485389
$586$	10.5662	0.436485
$587$	−1.50989	−0.0623198	−0.0311599	−	0.999514i	$-0.509920\pi$
$587$	−1.50989	−0.0623198	−0.0311599	+	0.999514i	$0.509920\pi$
$588$	−3.14470	−0.129685
$589$	15.0653	0.620754
$590$	−41.0945	−1.69183
$591$	−2.58960	−0.106522
$592$	4.73810	0.194735
$593$	−29.3620	−1.20575	−0.602877	−	0.797834i	$-0.705979\pi$
$593$	−29.3620	−1.20575	−0.602877	+	0.797834i	$0.705979\pi$
$594$	−13.7699	−0.564985
$595$	−17.4687	−0.716147
$596$	−12.4696	−0.510775
$597$	−7.02602	−0.287556
$598$	−5.71795	−0.233824
$599$	18.2869	0.747184	0.373592	−	0.927593i	$-0.378126\pi$
$599$	18.2869	0.747184	0.373592	+	0.927593i	$0.378126\pi$
$600$	−4.23503	−0.172894
$601$	−14.8965	−0.607641	−0.303821	−	0.952729i	$-0.598262\pi$
$601$	−14.8965	−0.607641	−0.303821	+	0.952729i	$0.598262\pi$
$602$	42.4019	1.72817
$603$	−9.90332	−0.403294
$604$	−21.3319	−0.867984
$605$	127.877	5.19894
$606$	−1.95317	−0.0793421
$607$	17.4930	0.710018	0.355009	−	0.934863i	$-0.384478\pi$
$607$	17.4930	0.710018	0.355009	+	0.934863i	$0.384478\pi$
$608$	−1.75604	−0.0712168
$609$	−7.99640	−0.324030
$610$	−25.7512	−1.04264
$611$	0.493365	0.0199594
$612$	−3.09130	−0.124958
$613$	−8.20919	−0.331566	−0.165783	−	0.986162i	$-0.553015\pi$
$613$	−8.20919	−0.331566	−0.165783	+	0.986162i	$0.553015\pi$
$614$	12.3046	0.496574
$615$	7.38529	0.297804
$616$	25.7694	1.03828
$617$	−15.1607	−0.610345	−0.305172	−	0.952297i	$-0.598714\pi$
$617$	−15.1607	−0.610345	−0.305172	+	0.952297i	$0.598714\pi$
$618$	−0.360870	−0.0145163
$619$	−34.1768	−1.37368	−0.686841	−	0.726807i	$-0.741003\pi$
$619$	−34.1768	−1.37368	−0.686841	+	0.726807i	$0.741003\pi$
$620$	−35.0965	−1.40951
$621$	12.1119	0.486034
$622$	27.1270	1.08770
$623$	45.5490	1.82488
$624$	0.360870	0.0144464
$625$	54.0463	2.16185
$626$	4.23415	0.169231
$627$	−4.11949	−0.164516
$628$	11.0967	0.442806
$629$	5.10385	0.203504
$630$	46.5387	1.85415
$631$	−29.6036	−1.17850	−0.589250	−	0.807950i	$-0.700577\pi$
$631$	−29.6036	−1.17850	−0.589250	+	0.807950i	$0.700577\pi$
$632$	−6.57382	−0.261493
$633$	−7.99968	−0.317959
$634$	−18.3972	−0.730647
$635$	75.2716	2.98706
$636$	−0.780103	−0.0309331
$637$	−8.71423	−0.345270
$638$	36.3375	1.43862
$639$	10.2434	0.405222
$640$	4.09092	0.161708
$641$	12.2963	0.485673	0.242837	−	0.970067i	$-0.421922\pi$
$641$	12.2963	0.485673	0.242837	+	0.970067i	$0.421922\pi$
$642$	1.68102	0.0663446
$643$	4.36858	0.172280	0.0861399	−	0.996283i	$-0.472547\pi$
$643$	4.36858	0.172280	0.0861399	+	0.996283i	$0.472547\pi$
$644$	−22.6666	−0.893190
$645$	15.7910	0.621771
$646$	−1.89159	−0.0744238
$647$	16.1328	0.634248	0.317124	−	0.948384i	$-0.397283\pi$
$647$	16.1328	0.634248	0.317124	+	0.948384i	$0.397283\pi$
$648$	7.84491	0.308177
$649$	65.3012	2.56330
$650$	−11.7356	−0.460308
$651$	−12.2727	−0.481006
$652$	3.33891	0.130762
$653$	−11.1126	−0.434870	−0.217435	−	0.976075i	$-0.569769\pi$
$653$	−11.1126	−0.434870	−0.217435	+	0.976075i	$0.569769\pi$
$654$	0.804808	0.0314705
$655$	−14.8228	−0.579174
$656$	−5.00260	−0.195319
$657$	29.0301	1.13257
$658$	1.95576	0.0762434
$659$	33.3001	1.29719	0.648594	−	0.761135i	$-0.275357\pi$
$659$	33.3001	1.29719	0.648594	+	0.761135i	$0.275357\pi$
$660$	9.59687	0.373558
$661$	−13.0796	−0.508737	−0.254368	−	0.967107i	$-0.581868\pi$
$661$	−13.0796	−0.508737	−0.254368	+	0.967107i	$0.581868\pi$
$662$	−8.96200	−0.348318
$663$	0.388727	0.0150969
$664$	14.7080	0.570782
$665$	28.4775	1.10431
$666$	−13.5973	−0.526884
$667$	−31.9623	−1.23758
$668$	6.64557	0.257125
$669$	−7.03060	−0.271819
$670$	14.1174	0.545402
$671$	40.9200	1.57970
$672$	1.43053	0.0551839
$673$	18.9754	0.731448	0.365724	−	0.930723i	$-0.380821\pi$
$673$	18.9754	0.731448	0.365724	+	0.930723i	$0.380821\pi$
$674$	27.3704	1.05427
$675$	24.8586	0.956810
$676$	1.00000	0.0384615
$677$	−34.8924	−1.34102	−0.670511	−	0.741899i	$-0.733925\pi$
$677$	−34.8924	−1.34102	−0.670511	+	0.741899i	$0.733925\pi$
$678$	−4.31740	−0.165809
$679$	62.7008	2.40623
$680$	4.40671	0.168990
$681$	−3.06712	−0.117532
$682$	55.7701	2.13555
$683$	−5.69397	−0.217874	−0.108937	−	0.994049i	$-0.534745\pi$
$683$	−5.69397	−0.217874	−0.108937	+	0.994049i	$0.534745\pi$
$684$	5.03943	0.192688
$685$	−2.27650	−0.0869806
$686$	−6.79540	−0.259450
$687$	0.425157	0.0162207
$688$	−10.6964	−0.407798
$689$	−2.16173	−0.0823553
$690$	−8.44134	−0.321356
$691$	17.8359	0.678508	0.339254	−	0.940695i	$-0.389825\pi$
$691$	17.8359	0.678508	0.339254	+	0.940695i	$0.389825\pi$
$692$	−5.97455	−0.227118
$693$	−73.9524	−2.80922
$694$	4.50346	0.170949
$695$	92.1124	3.49402
$696$	2.01720	0.0764616
$697$	−5.38877	−0.204114
$698$	−29.2702	−1.10789
$699$	5.73005	0.216730
$700$	−46.5213	−1.75834
$701$	−7.32994	−0.276848	−0.138424	−	0.990373i	$-0.544204\pi$
$701$	−7.32994	−0.276848	−0.138424	+	0.990373i	$0.544204\pi$
$702$	−2.11822	−0.0799472
$703$	−8.32029	−0.313806
$704$	−6.50067	−0.245003
$705$	0.728350	0.0274313
$706$	24.6452	0.927535
$707$	−21.4554	−0.806912
$708$	3.62505	0.136238
$709$	−21.2185	−0.796877	−0.398439	−	0.917195i	$-0.630448\pi$
$709$	−21.2185	−0.796877	−0.398439	+	0.917195i	$0.630448\pi$
$710$	−14.6021	−0.548008
$711$	18.8654	0.707507
$712$	−11.4903	−0.430618
$713$	−49.0550	−1.83713
$714$	1.54096	0.0576689
$715$	26.5937	0.994548
$716$	−17.6181	−0.658418
$717$	2.71605	0.101433
$718$	−7.16361	−0.267343
$719$	−21.4383	−0.799513	−0.399757	−	0.916621i	$-0.630905\pi$
$719$	−21.4383	−0.799513	−0.399757	+	0.916621i	$0.630905\pi$
$720$	−11.7400	−0.437524
$721$	−3.96412	−0.147631
$722$	−15.9163	−0.592344
$723$	−7.14610	−0.265766
$724$	14.9512	0.555656
$725$	−65.5998	−2.43632
$726$	−11.2803	−0.418653
$727$	−53.0116	−1.96609	−0.983045	−	0.183362i	$-0.941302\pi$
$727$	−53.0116	−1.96609	−0.983045	+	0.183362i	$0.941302\pi$
$728$	3.96412	0.146920
$729$	−20.2199	−0.748886
$730$	−41.3829	−1.53165
$731$	−11.5221	−0.426161
$732$	2.27158	0.0839600
$733$	−13.5828	−0.501692	−0.250846	−	0.968027i	$-0.580709\pi$
$733$	−13.5828	−0.501692	−0.250846	+	0.968027i	$0.580709\pi$
$734$	−17.7245	−0.654223
$735$	−12.8647	−0.474522
$736$	5.71795	0.210766
$737$	−22.4332	−0.826338
$738$	14.3563	0.528464
$739$	−14.2622	−0.524645	−0.262323	−	0.964980i	$-0.584488\pi$
$739$	−14.2622	−0.524645	−0.262323	+	0.964980i	$0.584488\pi$
$740$	19.3832	0.712540
$741$	−0.633702	−0.0232796
$742$	−8.56935	−0.314591
$743$	−34.9306	−1.28148	−0.640740	−	0.767758i	$-0.721372\pi$
$743$	−34.9306	−1.28148	−0.640740	+	0.767758i	$0.721372\pi$
$744$	3.09595	0.113503
$745$	−51.0122	−1.86894
$746$	−35.2383	−1.29016
$747$	−42.2087	−1.54433
$748$	−7.00248	−0.256036
$749$	18.4658	0.674727
$750$	−9.94370	−0.363092
$751$	−14.0172	−0.511494	−0.255747	−	0.966744i	$-0.582321\pi$
$751$	−14.0172	−0.511494	−0.255747	+	0.966744i	$0.582321\pi$
$752$	−0.493365	−0.0179912
$753$	7.45947	0.271838
$754$	5.58981	0.203569
$755$	−87.2671	−3.17598
$756$	−8.39689	−0.305392
$757$	−9.85676	−0.358250	−0.179125	−	0.983826i	$-0.557327\pi$
$757$	−9.85676	−0.358250	−0.179125	+	0.983826i	$0.557327\pi$
$758$	21.9728	0.798087
$759$	13.4137	0.486887
$760$	−7.18381	−0.260584
$761$	−11.9038	−0.431512	−0.215756	−	0.976447i	$-0.569222\pi$
$761$	−11.9038	−0.431512	−0.215756	+	0.976447i	$0.569222\pi$
$762$	−6.63990	−0.240538
$763$	8.84073	0.320056
$764$	−15.5024	−0.560858
$765$	−12.6463	−0.457226
$766$	−28.0022	−1.01176
$767$	10.0453	0.362715
$768$	−0.360870	−0.0130218
$769$	−49.1535	−1.77252	−0.886259	−	0.463189i	$-0.846705\pi$
$769$	−49.1535	−1.77252	−0.886259	+	0.463189i	$0.846705\pi$
$770$	105.421	3.79909
$771$	−1.97215	−0.0710251
$772$	0.318902	0.0114776
$773$	19.4135	0.698255	0.349128	−	0.937075i	$-0.386478\pi$
$773$	19.4135	0.698255	0.349128	+	0.937075i	$0.386478\pi$
$774$	30.6963	1.10336
$775$	−100.681	−3.61658
$776$	−15.8171	−0.567800
$777$	6.77800	0.243160
$778$	−32.8877	−1.17908
$779$	8.78477	0.314747
$780$	1.47629	0.0528596
$781$	23.2035	0.830287
$782$	6.15934	0.220257
$783$	−11.8405	−0.423144
$784$	8.71423	0.311222
$785$	45.3956	1.62024
$786$	1.30755	0.0466389
$787$	21.3907	0.762496	0.381248	−	0.924473i	$-0.375494\pi$
$787$	21.3907	0.762496	0.381248	+	0.924473i	$0.375494\pi$
$788$	7.17598	0.255634
$789$	−0.141571	−0.00504004
$790$	−26.8930	−0.956808
$791$	−47.4262	−1.68628
$792$	18.6555	0.662893
$793$	6.29473	0.223532
$794$	21.1875	0.751916
$795$	−3.19134	−0.113185
$796$	19.4697	0.690085
$797$	−25.7214	−0.911100	−0.455550	−	0.890210i	$-0.650557\pi$
$797$	−25.7214	−0.911100	−0.455550	+	0.890210i	$0.650557\pi$
$798$	−2.51207	−0.0889262
$799$	−0.531450	−0.0188014
$800$	11.7356	0.414916
$801$	32.9746	1.16510
$802$	−18.4713	−0.652243
$803$	65.7596	2.32060
$804$	−1.24533	−0.0439194
$805$	−92.7272	−3.26821
$806$	8.57913	0.302187
$807$	−2.66930	−0.0939637
$808$	5.41239	0.190407
$809$	−34.6807	−1.21931	−0.609654	−	0.792668i	$-0.708691\pi$
$809$	−34.6807	−1.21931	−0.609654	+	0.792668i	$0.708691\pi$
$810$	32.0929	1.12763
$811$	−38.2847	−1.34436	−0.672180	−	0.740388i	$-0.734642\pi$
$811$	−38.2847	−1.34436	−0.672180	+	0.740388i	$0.734642\pi$
$812$	22.1587	0.777617
$813$	8.71364	0.305601
$814$	−30.8009	−1.07957
$815$	13.6592	0.478461
$816$	−0.388727	−0.0136082
$817$	18.7834	0.657146
$818$	−14.5704	−0.509443
$819$	−11.3761	−0.397514
$820$	−20.4652	−0.714677
$821$	−22.3853	−0.781254	−0.390627	−	0.920549i	$-0.627742\pi$
$821$	−22.3853	−0.781254	−0.390627	+	0.920549i	$0.627742\pi$
$822$	0.200816	0.00700425
$823$	33.5619	1.16990	0.584948	−	0.811071i	$-0.301115\pi$
$823$	33.5619	1.16990	0.584948	+	0.811071i	$0.301115\pi$
$824$	1.00000	0.0348367
$825$	27.5305	0.958490
$826$	39.8207	1.38554
$827$	9.97575	0.346891	0.173445	−	0.984843i	$-0.444510\pi$
$827$	9.97575	0.346891	0.173445	+	0.984843i	$0.444510\pi$
$828$	−16.4092	−0.570259
$829$	17.2480	0.599046	0.299523	−	0.954089i	$-0.403172\pi$
$829$	17.2480	0.599046	0.299523	+	0.954089i	$0.403172\pi$
$830$	60.1693	2.08851
$831$	6.08767	0.211179
$832$	−1.00000	−0.0346688
$833$	9.38691	0.325237
$834$	−8.12547	−0.281362
$835$	27.1865	0.940827
$836$	11.4154	0.394811
$837$	−18.1725	−0.628135
$838$	−27.4941	−0.949767
$839$	3.33170	0.115023	0.0575115	−	0.998345i	$-0.481683\pi$
$839$	3.33170	0.115023	0.0575115	+	0.998345i	$0.481683\pi$
$840$	5.85218	0.201920
$841$	2.24600	0.0774484
$842$	16.5966	0.571957
$843$	−5.12872	−0.176642
$844$	22.1678	0.763046
$845$	4.09092	0.140732
$846$	1.41585	0.0486778
$847$	−123.913	−4.25771
$848$	2.16173	0.0742341
$849$	0.310736	0.0106644
$850$	12.6415	0.433600
$851$	27.0922	0.928710
$852$	1.28809	0.0441292
$853$	4.88431	0.167235	0.0836177	−	0.996498i	$-0.473353\pi$
$853$	4.88431	0.167235	0.0836177	+	0.996498i	$0.473353\pi$
$854$	24.9530	0.853876
$855$	20.6159	0.705049
$856$	−4.65825	−0.159216
$857$	−18.4522	−0.630314	−0.315157	−	0.949040i	$-0.602057\pi$
$857$	−18.4522	−0.630314	−0.315157	+	0.949040i	$0.602057\pi$
$858$	−2.34590	−0.0800876
$859$	−34.7102	−1.18430	−0.592148	−	0.805829i	$-0.701720\pi$
$859$	−34.7102	−1.18430	−0.592148	+	0.805829i	$0.701720\pi$
$860$	−43.7582	−1.49214
$861$	−7.15638	−0.243889
$862$	23.7582	0.809206
$863$	27.6453	0.941056	0.470528	−	0.882385i	$-0.344064\pi$
$863$	27.6453	0.941056	0.470528	+	0.882385i	$0.344064\pi$
$864$	2.11822	0.0720635
$865$	−24.4414	−0.831033
$866$	17.9047	0.608428
$867$	5.71606	0.194127
$868$	34.0087	1.15433
$869$	42.7343	1.44966
$870$	8.25218	0.279775
$871$	−3.45091	−0.116930
$872$	−2.23019	−0.0755237
$873$	45.3914	1.53627
$874$	−10.0409	−0.339640
$875$	−109.230	−3.69266
$876$	3.65049	0.123339
$877$	−10.4316	−0.352250	−0.176125	−	0.984368i	$-0.556356\pi$
$877$	−10.4316	−0.352250	−0.176125	+	0.984368i	$0.556356\pi$
$878$	−35.4022	−1.19477
$879$	−3.81302	−0.128610
$880$	−26.5937	−0.896474
$881$	19.7479	0.665325	0.332662	−	0.943046i	$-0.392053\pi$
$881$	19.7479	0.665325	0.332662	+	0.943046i	$0.392053\pi$
$882$	−25.0079	−0.842058
$883$	42.0926	1.41653	0.708265	−	0.705947i	$-0.249478\pi$
$883$	42.0926	1.41653	0.708265	+	0.705947i	$0.249478\pi$
$884$	−1.07719	−0.0362299
$885$	14.8298	0.498497
$886$	−3.19591	−0.107369
$887$	−32.5038	−1.09137	−0.545685	−	0.837990i	$-0.683730\pi$
$887$	−32.5038	−1.09137	−0.545685	+	0.837990i	$0.683730\pi$
$888$	−1.70984	−0.0573784
$889$	−72.9385	−2.44628
$890$	−47.0059	−1.57564
$891$	−50.9972	−1.70847
$892$	19.4824	0.652318
$893$	0.866369	0.0289919
$894$	4.49991	0.150499
$895$	−72.0741	−2.40917
$896$	−3.96412	−0.132432
$897$	2.06344	0.0688961
$898$	38.6889	1.29107
$899$	47.9557	1.59941
$900$	−33.6785	−1.12262
$901$	2.32860	0.0775770
$902$	32.5203	1.08281
$903$	−15.3016	−0.509205
$904$	11.9639	0.397913
$905$	61.1640	2.03316
$906$	7.69805	0.255751
$907$	22.2006	0.737158	0.368579	−	0.929596i	$-0.379844\pi$
$907$	22.2006	0.737158	0.368579	+	0.929596i	$0.379844\pi$
$908$	8.49923	0.282057
$909$	−15.5323	−0.515175
$910$	16.2169	0.537584
$911$	−36.2076	−1.19961	−0.599806	−	0.800145i	$-0.704756\pi$
$911$	−36.2076	−1.19961	−0.599806	+	0.800145i	$0.704756\pi$
$912$	0.633702	0.0209840
$913$	−95.6120	−3.16430
$914$	−8.09619	−0.267798
$915$	9.29284	0.307212
$916$	−1.17814	−0.0389270
$917$	14.3633	0.474319
$918$	2.28174	0.0753086
$919$	−36.3854	−1.20024	−0.600122	−	0.799908i	$-0.704881\pi$
$919$	−36.3854	−1.20024	−0.600122	+	0.799908i	$0.704881\pi$
$920$	23.3916	0.771200
$921$	−4.44036	−0.146315
$922$	−22.1299	−0.728809
$923$	3.56940	0.117488
$924$	−9.29941	−0.305928
$925$	55.6045	1.82826
$926$	23.9541	0.787182
$927$	−2.86977	−0.0942557
$928$	−5.58981	−0.183495
$929$	18.9639	0.622186	0.311093	−	0.950380i	$-0.399305\pi$
$929$	18.9639	0.622186	0.311093	+	0.950380i	$0.399305\pi$
$930$	12.6653	0.415311
$931$	−15.3025	−0.501520
$932$	−15.8784	−0.520115
$933$	−9.78933	−0.320488
$934$	22.9059	0.749503
$935$	−28.6466	−0.936843
$936$	2.86977	0.0938015
$937$	4.81166	0.157190	0.0785950	−	0.996907i	$-0.474957\pi$
$937$	4.81166	0.157190	0.0785950	+	0.996907i	$0.474957\pi$
$938$	−13.6798	−0.446661
$939$	−1.52798	−0.0498637
$940$	−2.01832	−0.0658302
$941$	18.0145	0.587257	0.293629	−	0.955920i	$-0.405137\pi$
$941$	18.0145	0.587257	0.293629	+	0.955920i	$0.405137\pi$
$942$	−4.00446	−0.130472
$943$	−28.6046	−0.931495
$944$	−10.0453	−0.326947
$945$	−34.3510	−1.11744
$946$	69.5340	2.26075
$947$	−19.3957	−0.630275	−0.315137	−	0.949046i	$-0.602051\pi$
$947$	−19.3957	−0.630275	−0.315137	+	0.949046i	$0.602051\pi$
$948$	2.37229	0.0770486
$949$	10.1158	0.328373
$950$	−20.6082	−0.668617
$951$	6.63900	0.215284
$952$	−4.27012	−0.138395
$953$	−24.5981	−0.796812	−0.398406	−	0.917209i	$-0.630437\pi$
$953$	−24.5981	−0.796812	−0.398406	+	0.917209i	$0.630437\pi$
$954$	−6.20367	−0.200851
$955$	−63.4191	−2.05219
$956$	−7.52640	−0.243421
$957$	−13.1131	−0.423887
$958$	10.1931	0.329324
$959$	2.20594	0.0712335
$960$	−1.47629	−0.0476470
$961$	42.6015	1.37424
$962$	−4.73810	−0.152763
$963$	13.3681	0.430781
$964$	19.8024	0.637793
$965$	1.30460	0.0419967
$966$	8.17970	0.263178
$967$	0.252006	0.00810398	0.00405199	−	0.999992i	$-0.498710\pi$
$967$	0.252006	0.00810398	0.00405199	+	0.999992i	$0.498710\pi$
$968$	31.2587	1.00469
$969$	0.682619	0.0219289
$970$	−64.7064	−2.07760
$971$	−1.70853	−0.0548294	−0.0274147	−	0.999624i	$-0.508727\pi$
$971$	−1.70853	−0.0548294	−0.0274147	+	0.999624i	$0.508727\pi$
$972$	−9.18567	−0.294630
$973$	−89.2574	−2.86146
$974$	2.15068	0.0689122
$975$	4.23503	0.135629
$976$	−6.29473	−0.201489
$977$	−31.7128	−1.01458	−0.507291	−	0.861775i	$-0.669353\pi$
$977$	−31.7128	−1.01458	−0.507291	+	0.861775i	$0.669353\pi$
$978$	−1.20491	−0.0385288
$979$	74.6948	2.38726
$980$	35.6492	1.13877
$981$	6.40013	0.204340
$982$	−11.3889	−0.363433
$983$	9.31698	0.297165	0.148583	−	0.988900i	$-0.452529\pi$
$983$	9.31698	0.297165	0.148583	+	0.988900i	$0.452529\pi$
$984$	1.80529	0.0575505
$985$	29.3563	0.935371
$986$	−6.02131	−0.191758
$987$	−0.705775	−0.0224651
$988$	1.75604	0.0558670
$989$	−61.1616	−1.94483
$990$	76.3179	2.42554
$991$	−15.3276	−0.486897	−0.243448	−	0.969914i	$-0.578279\pi$
$991$	−15.3276	−0.486897	−0.243448	+	0.969914i	$0.578279\pi$
$992$	−8.57913	−0.272388
$993$	3.23412	0.102632
$994$	14.1495	0.448796
$995$	79.6489	2.52504
$996$	−5.30768	−0.168180
$997$	−47.7041	−1.51080	−0.755402	−	0.655261i	$-0.772559\pi$
$997$	−47.7041	−1.51080	−0.755402	+	0.655261i	$0.772559\pi$
$998$	16.7236	0.529376
$999$	10.0364	0.317537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2678.2.a.s.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2678.2.a.s.1.6	✓	10	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:	\( N \)	\(=\)	\( 2678 = 2 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2678.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.360870 q^{3} +1.00000 q^{4} +4.09092 q^{5} -0.360870 q^{6} -3.96412 q^{7} +1.00000 q^{8} -2.86977 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.360870 q^{3} +1.00000 q^{4} +4.09092 q^{5} -0.360870 q^{6} -3.96412 q^{7} +1.00000 q^{8} -2.86977 q^{9} +4.09092 q^{10} -6.50067 q^{11} -0.360870 q^{12} -1.00000 q^{13} -3.96412 q^{14} -1.47629 q^{15} +1.00000 q^{16} +1.07719 q^{17} -2.86977 q^{18} -1.75604 q^{19} +4.09092 q^{20} +1.43053 q^{21} -6.50067 q^{22} +5.71795 q^{23} -0.360870 q^{24} +11.7356 q^{25} -1.00000 q^{26} +2.11822 q^{27} -3.96412 q^{28} -5.58981 q^{29} -1.47629 q^{30} -8.57913 q^{31} +1.00000 q^{32} +2.34590 q^{33} +1.07719 q^{34} -16.2169 q^{35} -2.86977 q^{36} +4.73810 q^{37} -1.75604 q^{38} +0.360870 q^{39} +4.09092 q^{40} -5.00260 q^{41} +1.43053 q^{42} -10.6964 q^{43} -6.50067 q^{44} -11.7400 q^{45} +5.71795 q^{46} -0.493365 q^{47} -0.360870 q^{48} +8.71423 q^{49} +11.7356 q^{50} -0.388727 q^{51} -1.00000 q^{52} +2.16173 q^{53} +2.11822 q^{54} -26.5937 q^{55} -3.96412 q^{56} +0.633702 q^{57} -5.58981 q^{58} -10.0453 q^{59} -1.47629 q^{60} -6.29473 q^{61} -8.57913 q^{62} +11.3761 q^{63} +1.00000 q^{64} -4.09092 q^{65} +2.34590 q^{66} +3.45091 q^{67} +1.07719 q^{68} -2.06344 q^{69} -16.2169 q^{70} -3.56940 q^{71} -2.86977 q^{72} -10.1158 q^{73} +4.73810 q^{74} -4.23503 q^{75} -1.75604 q^{76} +25.7694 q^{77} +0.360870 q^{78} -6.57382 q^{79} +4.09092 q^{80} +7.84491 q^{81} -5.00260 q^{82} +14.7080 q^{83} +1.43053 q^{84} +4.40671 q^{85} -10.6964 q^{86} +2.01720 q^{87} -6.50067 q^{88} -11.4903 q^{89} -11.7400 q^{90} +3.96412 q^{91} +5.71795 q^{92} +3.09595 q^{93} -0.493365 q^{94} -7.18381 q^{95} -0.360870 q^{96} -15.8171 q^{97} +8.71423 q^{98} +18.6555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 6 q^{3} + 10 q^{4} - 3 q^{5} - 6 q^{6} - 10 q^{7} + 10 q^{8} + 4 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 6 * q^3 + 10 * q^4 - 3 * q^5 - 6 * q^6 - 10 * q^7 + 10 * q^8 + 4 * q^9	\( 10 q + 10 q^{2} - 6 q^{3} + 10 q^{4} - 3 q^{5} - 6 q^{6} - 10 q^{7} + 10 q^{8} + 4 q^{9} - 3 q^{10} - 5 q^{11} - 6 q^{12} - 10 q^{13} - 10 q^{14} - 13 q^{15} + 10 q^{16} - 13 q^{17} + 4 q^{18} - 21 q^{19} - 3 q^{20} + 5 q^{21} - 5 q^{22} - 5 q^{23} - 6 q^{24} + 13 q^{25} - 10 q^{26} - 9 q^{27} - 10 q^{28} + 6 q^{29} - 13 q^{30} - 33 q^{31} + 10 q^{32} - 22 q^{33} - 13 q^{34} - 9 q^{35} + 4 q^{36} - 7 q^{37} - 21 q^{38} + 6 q^{39} - 3 q^{40} - 20 q^{41} + 5 q^{42} - 22 q^{43} - 5 q^{44} - 14 q^{45} - 5 q^{46} - 31 q^{47} - 6 q^{48} + 8 q^{49} + 13 q^{50} - 8 q^{51} - 10 q^{52} + q^{53} - 9 q^{54} - 30 q^{55} - 10 q^{56} + 33 q^{57} + 6 q^{58} - 51 q^{59} - 13 q^{60} - 6 q^{61} - 33 q^{62} - 25 q^{63} + 10 q^{64} + 3 q^{65} - 22 q^{66} - 19 q^{67} - 13 q^{68} + 6 q^{69} - 9 q^{70} - 14 q^{71} + 4 q^{72} - 16 q^{73} - 7 q^{74} + 5 q^{75} - 21 q^{76} - 5 q^{77} + 6 q^{78} + 11 q^{79} - 3 q^{80} - 2 q^{81} - 20 q^{82} + q^{83} + 5 q^{84} - 27 q^{85} - 22 q^{86} - 5 q^{88} - 47 q^{89} - 14 q^{90} + 10 q^{91} - 5 q^{92} + 12 q^{93} - 31 q^{94} - 14 q^{95} - 6 q^{96} - 44 q^{97} + 8 q^{98} + 23 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 6 * q^3 + 10 * q^4 - 3 * q^5 - 6 * q^6 - 10 * q^7 + 10 * q^8 + 4 * q^9 - 3 * q^10 - 5 * q^11 - 6 * q^12 - 10 * q^13 - 10 * q^14 - 13 * q^15 + 10 * q^16 - 13 * q^17 + 4 * q^18 - 21 * q^19 - 3 * q^20 + 5 * q^21 - 5 * q^22 - 5 * q^23 - 6 * q^24 + 13 * q^25 - 10 * q^26 - 9 * q^27 - 10 * q^28 + 6 * q^29 - 13 * q^30 - 33 * q^31 + 10 * q^32 - 22 * q^33 - 13 * q^34 - 9 * q^35 + 4 * q^36 - 7 * q^37 - 21 * q^38 + 6 * q^39 - 3 * q^40 - 20 * q^41 + 5 * q^42 - 22 * q^43 - 5 * q^44 - 14 * q^45 - 5 * q^46 - 31 * q^47 - 6 * q^48 + 8 * q^49 + 13 * q^50 - 8 * q^51 - 10 * q^52 + q^53 - 9 * q^54 - 30 * q^55 - 10 * q^56 + 33 * q^57 + 6 * q^58 - 51 * q^59 - 13 * q^60 - 6 * q^61 - 33 * q^62 - 25 * q^63 + 10 * q^64 + 3 * q^65 - 22 * q^66 - 19 * q^67 - 13 * q^68 + 6 * q^69 - 9 * q^70 - 14 * q^71 + 4 * q^72 - 16 * q^73 - 7 * q^74 + 5 * q^75 - 21 * q^76 - 5 * q^77 + 6 * q^78 + 11 * q^79 - 3 * q^80 - 2 * q^81 - 20 * q^82 + q^83 + 5 * q^84 - 27 * q^85 - 22 * q^86 - 5 * q^88 - 47 * q^89 - 14 * q^90 + 10 * q^91 - 5 * q^92 + 12 * q^93 - 31 * q^94 - 14 * q^95 - 6 * q^96 - 44 * q^97 + 8 * q^98 + 23 * q^99

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