LMFDB - Embedded newform 1502.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, 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("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 20x^{9} - 7x^{8} + 134x^{7} + 70x^{6} - 354x^{5} - 193x^{4} + 341x^{3} + 163x^{2} - 72x - 16 $ x^11 - 20x^9 - 7x^8 + 134x^7 + 70x^6 - 354x^5 - 193x^4 + 341x^3 + 163x^2 - 72*x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.799353$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.79935 q^{3} +1.00000 q^{4} -0.966216 q^{5} -1.79935 q^{6} -0.438762 q^{7} +1.00000 q^{8} +0.237673 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.79935 q^{3} +1.00000 q^{4} -0.966216 q^{5} -1.79935 q^{6} -0.438762 q^{7} +1.00000 q^{8} +0.237673 q^{9} -0.966216 q^{10} +5.48410 q^{11} -1.79935 q^{12} -2.87300 q^{13} -0.438762 q^{14} +1.73856 q^{15} +1.00000 q^{16} -3.91004 q^{17} +0.237673 q^{18} -1.98321 q^{19} -0.966216 q^{20} +0.789487 q^{21} +5.48410 q^{22} -2.64520 q^{23} -1.79935 q^{24} -4.06643 q^{25} -2.87300 q^{26} +4.97040 q^{27} -0.438762 q^{28} -2.70516 q^{29} +1.73856 q^{30} +2.88289 q^{31} +1.00000 q^{32} -9.86783 q^{33} -3.91004 q^{34} +0.423938 q^{35} +0.237673 q^{36} +7.19073 q^{37} -1.98321 q^{38} +5.16954 q^{39} -0.966216 q^{40} +0.437244 q^{41} +0.789487 q^{42} -4.07884 q^{43} +5.48410 q^{44} -0.229643 q^{45} -2.64520 q^{46} -11.0988 q^{47} -1.79935 q^{48} -6.80749 q^{49} -4.06643 q^{50} +7.03555 q^{51} -2.87300 q^{52} -1.44502 q^{53} +4.97040 q^{54} -5.29882 q^{55} -0.438762 q^{56} +3.56849 q^{57} -2.70516 q^{58} -12.4460 q^{59} +1.73856 q^{60} -4.00802 q^{61} +2.88289 q^{62} -0.104282 q^{63} +1.00000 q^{64} +2.77593 q^{65} -9.86783 q^{66} -9.02014 q^{67} -3.91004 q^{68} +4.75965 q^{69} +0.423938 q^{70} -2.57768 q^{71} +0.237673 q^{72} -9.43455 q^{73} +7.19073 q^{74} +7.31694 q^{75} -1.98321 q^{76} -2.40621 q^{77} +5.16954 q^{78} -2.33924 q^{79} -0.966216 q^{80} -9.65653 q^{81} +0.437244 q^{82} -14.4127 q^{83} +0.789487 q^{84} +3.77794 q^{85} -4.07884 q^{86} +4.86753 q^{87} +5.48410 q^{88} +6.44761 q^{89} -0.229643 q^{90} +1.26056 q^{91} -2.64520 q^{92} -5.18734 q^{93} -11.0988 q^{94} +1.91620 q^{95} -1.79935 q^{96} +12.5447 q^{97} -6.80749 q^{98} +1.30342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9} - 12 q^{10} - 7 q^{11} - 11 q^{12} - 21 q^{13} - 9 q^{14} - 3 q^{15} + 11 q^{16} - 16 q^{17} + 18 q^{18} - 22 q^{19} - 12 q^{20} - q^{21} - 7 q^{22} - 2 q^{23} - 11 q^{24} + 19 q^{25} - 21 q^{26} - 44 q^{27} - 9 q^{28} + 4 q^{29} - 3 q^{30} - 28 q^{31} + 11 q^{32} - 13 q^{33} - 16 q^{34} - 11 q^{35} + 18 q^{36} - 22 q^{37} - 22 q^{38} + 9 q^{39} - 12 q^{40} - 5 q^{41} - q^{42} - 7 q^{43} - 7 q^{44} - 23 q^{45} - 2 q^{46} - 31 q^{47} - 11 q^{48} - 2 q^{49} + 19 q^{50} - 6 q^{51} - 21 q^{52} - 17 q^{53} - 44 q^{54} - 18 q^{55} - 9 q^{56} + 7 q^{57} + 4 q^{58} - 18 q^{59} - 3 q^{60} - 18 q^{61} - 28 q^{62} - 27 q^{63} + 11 q^{64} + 22 q^{65} - 13 q^{66} - 11 q^{67} - 16 q^{68} + 9 q^{69} - 11 q^{70} - 16 q^{71} + 18 q^{72} - 33 q^{73} - 22 q^{74} - 21 q^{75} - 22 q^{76} + 9 q^{78} + 9 q^{79} - 12 q^{80} + 71 q^{81} - 5 q^{82} - 18 q^{83} - q^{84} - 8 q^{85} - 7 q^{86} - 17 q^{87} - 7 q^{88} - 23 q^{90} - 22 q^{91} - 2 q^{92} + 8 q^{93} - 31 q^{94} - 23 q^{95} - 11 q^{96} - 66 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9 - 12 * q^10 - 7 * q^11 - 11 * q^12 - 21 * q^13 - 9 * q^14 - 3 * q^15 + 11 * q^16 - 16 * q^17 + 18 * q^18 - 22 * q^19 - 12 * q^20 - q^21 - 7 * q^22 - 2 * q^23 - 11 * q^24 + 19 * q^25 - 21 * q^26 - 44 * q^27 - 9 * q^28 + 4 * q^29 - 3 * q^30 - 28 * q^31 + 11 * q^32 - 13 * q^33 - 16 * q^34 - 11 * q^35 + 18 * q^36 - 22 * q^37 - 22 * q^38 + 9 * q^39 - 12 * q^40 - 5 * q^41 - q^42 - 7 * q^43 - 7 * q^44 - 23 * q^45 - 2 * q^46 - 31 * q^47 - 11 * q^48 - 2 * q^49 + 19 * q^50 - 6 * q^51 - 21 * q^52 - 17 * q^53 - 44 * q^54 - 18 * q^55 - 9 * q^56 + 7 * q^57 + 4 * q^58 - 18 * q^59 - 3 * q^60 - 18 * q^61 - 28 * q^62 - 27 * q^63 + 11 * q^64 + 22 * q^65 - 13 * q^66 - 11 * q^67 - 16 * q^68 + 9 * q^69 - 11 * q^70 - 16 * q^71 + 18 * q^72 - 33 * q^73 - 22 * q^74 - 21 * q^75 - 22 * q^76 + 9 * q^78 + 9 * q^79 - 12 * q^80 + 71 * q^81 - 5 * q^82 - 18 * q^83 - q^84 - 8 * q^85 - 7 * q^86 - 17 * q^87 - 7 * q^88 - 23 * q^90 - 22 * q^91 - 2 * q^92 + 8 * q^93 - 31 * q^94 - 23 * q^95 - 11 * q^96 - 66 * q^97 - 2 * q^98 - 5 * 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
$3$	−1.79935	−1.03886	−0.519429	−	0.854514i	$-0.673855\pi$
$3$	−1.79935	−1.03886	−0.519429	+	0.854514i	$0.673855\pi$
$4$	1.00000	0.500000
$5$	−0.966216	−0.432105	−0.216052	−	0.976382i	$-0.569318\pi$
$5$	−0.966216	−0.432105	−0.216052	+	0.976382i	$0.569318\pi$
$6$	−1.79935	−0.734583
$7$	−0.438762	−0.165836	−0.0829182	−	0.996556i	$-0.526424\pi$
$7$	−0.438762	−0.165836	−0.0829182	+	0.996556i	$0.526424\pi$
$8$	1.00000	0.353553
$9$	0.237673	0.0792243
$10$	−0.966216	−0.305544
$11$	5.48410	1.65352	0.826759	−	0.562557i	$-0.190182\pi$
$11$	5.48410	1.65352	0.826759	+	0.562557i	$0.190182\pi$
$12$	−1.79935	−0.519429
$13$	−2.87300	−0.796826	−0.398413	−	0.917206i	$-0.630439\pi$
$13$	−2.87300	−0.796826	−0.398413	+	0.917206i	$0.630439\pi$
$14$	−0.438762	−0.117264
$15$	1.73856	0.448895
$16$	1.00000	0.250000
$17$	−3.91004	−0.948324	−0.474162	−	0.880438i	$-0.657249\pi$
$17$	−3.91004	−0.948324	−0.474162	+	0.880438i	$0.657249\pi$
$18$	0.237673	0.0560200
$19$	−1.98321	−0.454978	−0.227489	−	0.973781i	$-0.573052\pi$
$19$	−1.98321	−0.454978	−0.227489	+	0.973781i	$0.573052\pi$
$20$	−0.966216	−0.216052
$21$	0.789487	0.172280
$22$	5.48410	1.16921
$23$	−2.64520	−0.551563	−0.275781	−	0.961220i	$-0.588937\pi$
$23$	−2.64520	−0.551563	−0.275781	+	0.961220i	$0.588937\pi$
$24$	−1.79935	−0.367291
$25$	−4.06643	−0.813286
$26$	−2.87300	−0.563441
$27$	4.97040	0.956554
$28$	−0.438762	−0.0829182
$29$	−2.70516	−0.502335	−0.251167	−	0.967944i	$-0.580814\pi$
$29$	−2.70516	−0.502335	−0.251167	+	0.967944i	$0.580814\pi$
$30$	1.73856	0.317417
$31$	2.88289	0.517782	0.258891	−	0.965907i	$-0.416643\pi$
$31$	2.88289	0.517782	0.258891	+	0.965907i	$0.416643\pi$
$32$	1.00000	0.176777
$33$	−9.86783	−1.71777
$34$	−3.91004	−0.670567
$35$	0.423938	0.0716587
$36$	0.237673	0.0396122
$37$	7.19073	1.18215	0.591074	−	0.806617i	$-0.298704\pi$
$37$	7.19073	1.18215	0.591074	+	0.806617i	$0.298704\pi$
$38$	−1.98321	−0.321718
$39$	5.16954	0.827788
$40$	−0.966216	−0.152772
$41$	0.437244	0.0682860	0.0341430	−	0.999417i	$-0.489130\pi$
$41$	0.437244	0.0682860	0.0341430	+	0.999417i	$0.489130\pi$
$42$	0.789487	0.121821
$43$	−4.07884	−0.622018	−0.311009	−	0.950407i	$-0.600667\pi$
$43$	−4.07884	−0.622018	−0.311009	+	0.950407i	$0.600667\pi$
$44$	5.48410	0.826759
$45$	−0.229643	−0.0342332
$46$	−2.64520	−0.390014
$47$	−11.0988	−1.61893	−0.809464	−	0.587169i	$-0.800242\pi$
$47$	−11.0988	−1.61893	−0.809464	+	0.587169i	$0.800242\pi$
$48$	−1.79935	−0.259714
$49$	−6.80749	−0.972498
$50$	−4.06643	−0.575080
$51$	7.03555	0.985174
$52$	−2.87300	−0.398413
$53$	−1.44502	−0.198489	−0.0992447	−	0.995063i	$-0.531643\pi$
$53$	−1.44502	−0.198489	−0.0992447	+	0.995063i	$0.531643\pi$
$54$	4.97040	0.676386
$55$	−5.29882	−0.714493
$56$	−0.438762	−0.0586320
$57$	3.56849	0.472658
$58$	−2.70516	−0.355204
$59$	−12.4460	−1.62033	−0.810164	−	0.586203i	$-0.800622\pi$
$59$	−12.4460	−1.62033	−0.810164	+	0.586203i	$0.800622\pi$
$60$	1.73856	0.224448
$61$	−4.00802	−0.513175	−0.256587	−	0.966521i	$-0.582598\pi$
$61$	−4.00802	−0.513175	−0.256587	+	0.966521i	$0.582598\pi$
$62$	2.88289	0.366127
$63$	−0.104282	−0.0131383
$64$	1.00000	0.125000
$65$	2.77593	0.344312
$66$	−9.86783	−1.21465
$67$	−9.02014	−1.10199	−0.550993	−	0.834510i	$-0.685751\pi$
$67$	−9.02014	−1.10199	−0.550993	+	0.834510i	$0.685751\pi$
$68$	−3.91004	−0.474162
$69$	4.75965	0.572995
$70$	0.423938	0.0506703
$71$	−2.57768	−0.305915	−0.152957	−	0.988233i	$-0.548880\pi$
$71$	−2.57768	−0.305915	−0.152957	+	0.988233i	$0.548880\pi$
$72$	0.237673	0.0280100
$73$	−9.43455	−1.10423	−0.552115	−	0.833768i	$-0.686179\pi$
$73$	−9.43455	−1.10423	−0.552115	+	0.833768i	$0.686179\pi$
$74$	7.19073	0.835905
$75$	7.31694	0.844888
$76$	−1.98321	−0.227489
$77$	−2.40621	−0.274213
$78$	5.16954	0.585335
$79$	−2.33924	−0.263185	−0.131593	−	0.991304i	$-0.542009\pi$
$79$	−2.33924	−0.263185	−0.131593	+	0.991304i	$0.542009\pi$
$80$	−0.966216	−0.108026
$81$	−9.65653	−1.07295
$82$	0.437244	0.0482855
$83$	−14.4127	−1.58200	−0.791002	−	0.611813i	$-0.790440\pi$
$83$	−14.4127	−1.58200	−0.791002	+	0.611813i	$0.790440\pi$
$84$	0.789487	0.0861401
$85$	3.77794	0.409775
$86$	−4.07884	−0.439833
$87$	4.86753	0.521854
$88$	5.48410	0.584607
$89$	6.44761	0.683446	0.341723	−	0.939801i	$-0.388990\pi$
$89$	6.44761	0.683446	0.341723	+	0.939801i	$0.388990\pi$
$90$	−0.229643	−0.0242065
$91$	1.26056	0.132143
$92$	−2.64520	−0.275781
$93$	−5.18734	−0.537902
$94$	−11.0988	−1.14476
$95$	1.91620	0.196598
$96$	−1.79935	−0.183646
$97$	12.5447	1.27373	0.636863	−	0.770977i	$-0.280232\pi$
$97$	12.5447	1.27373	0.636863	+	0.770977i	$0.280232\pi$
$98$	−6.80749	−0.687660
$99$	1.30342	0.130999
$100$	−4.06643	−0.406643
$101$	−6.52257	−0.649020	−0.324510	−	0.945882i	$-0.605199\pi$
$101$	−6.52257	−0.649020	−0.324510	+	0.945882i	$0.605199\pi$
$102$	7.03555	0.696623
$103$	3.92953	0.387188	0.193594	−	0.981082i	$-0.437986\pi$
$103$	3.92953	0.387188	0.193594	+	0.981082i	$0.437986\pi$
$104$	−2.87300	−0.281720
$105$	−0.762815	−0.0744431
$106$	−1.44502	−0.140353
$107$	−7.42727	−0.718021	−0.359011	−	0.933333i	$-0.616886\pi$
$107$	−7.42727	−0.718021	−0.359011	+	0.933333i	$0.616886\pi$
$108$	4.97040	0.478277
$109$	13.2168	1.26594	0.632972	−	0.774174i	$-0.281835\pi$
$109$	13.2168	1.26594	0.632972	+	0.774174i	$0.281835\pi$
$110$	−5.29882	−0.505223
$111$	−12.9387	−1.22808
$112$	−0.438762	−0.0414591
$113$	−0.412709	−0.0388244	−0.0194122	−	0.999812i	$-0.506179\pi$
$113$	−0.412709	−0.0388244	−0.0194122	+	0.999812i	$0.506179\pi$
$114$	3.56849	0.334219
$115$	2.55583	0.238333
$116$	−2.70516	−0.251167
$117$	−0.682833	−0.0631280
$118$	−12.4460	−1.14574
$119$	1.71558	0.157267
$120$	1.73856	0.158708
$121$	19.0753	1.73412
$122$	−4.00802	−0.362869
$123$	−0.786757	−0.0709395
$124$	2.88289	0.258891
$125$	8.76012	0.783529
$126$	−0.104282	−0.00929016
$127$	−15.8915	−1.41014	−0.705070	−	0.709137i	$-0.749085\pi$
$127$	−15.8915	−1.41014	−0.705070	+	0.709137i	$0.749085\pi$
$128$	1.00000	0.0883883
$129$	7.33928	0.646188
$130$	2.77593	0.243465
$131$	14.3563	1.25432	0.627158	−	0.778892i	$-0.284218\pi$
$131$	14.3563	1.25432	0.627158	+	0.778892i	$0.284218\pi$
$132$	−9.86783	−0.858884
$133$	0.870154	0.0754519
$134$	−9.02014	−0.779221
$135$	−4.80248	−0.413332
$136$	−3.91004	−0.335283
$137$	11.3827	0.972490	0.486245	−	0.873822i	$-0.338366\pi$
$137$	11.3827	0.972490	0.486245	+	0.873822i	$0.338366\pi$
$138$	4.75965	0.405169
$139$	2.80852	0.238215	0.119108	−	0.992881i	$-0.461997\pi$
$139$	2.80852	0.238215	0.119108	+	0.992881i	$0.461997\pi$
$140$	0.423938	0.0358293
$141$	19.9707	1.68184
$142$	−2.57768	−0.216314
$143$	−15.7558	−1.31757
$144$	0.237673	0.0198061
$145$	2.61376	0.217061
$146$	−9.43455	−0.780809
$147$	12.2491	1.01029
$148$	7.19073	0.591074
$149$	13.0171	1.06640	0.533201	−	0.845989i	$-0.320989\pi$
$149$	13.0171	1.06640	0.533201	+	0.845989i	$0.320989\pi$
$150$	7.31694	0.597426
$151$	9.08544	0.739362	0.369681	−	0.929159i	$-0.379467\pi$
$151$	9.08544	0.739362	0.369681	+	0.929159i	$0.379467\pi$
$152$	−1.98321	−0.160859
$153$	−0.929311	−0.0751303
$154$	−2.40621	−0.193898
$155$	−2.78549	−0.223736
$156$	5.16954	0.413894
$157$	3.13075	0.249861	0.124930	−	0.992165i	$-0.460129\pi$
$157$	3.13075	0.249861	0.124930	+	0.992165i	$0.460129\pi$
$158$	−2.33924	−0.186100
$159$	2.60011	0.206202
$160$	−0.966216	−0.0763860
$161$	1.16061	0.0914691
$162$	−9.65653	−0.758689
$163$	−1.53457	−0.120196	−0.0600982	−	0.998192i	$-0.519141\pi$
$163$	−1.53457	−0.120196	−0.0600982	+	0.998192i	$0.519141\pi$
$164$	0.437244	0.0341430
$165$	9.53445	0.742256
$166$	−14.4127	−1.11865
$167$	11.2813	0.872971	0.436485	−	0.899711i	$-0.356223\pi$
$167$	11.2813	0.872971	0.436485	+	0.899711i	$0.356223\pi$
$168$	0.789487	0.0609103
$169$	−4.74589	−0.365069
$170$	3.77794	0.289755
$171$	−0.471354	−0.0360454
$172$	−4.07884	−0.311009
$173$	−5.71490	−0.434496	−0.217248	−	0.976116i	$-0.569708\pi$
$173$	−5.71490	−0.434496	−0.217248	+	0.976116i	$0.569708\pi$
$174$	4.86753	0.369007
$175$	1.78419	0.134872
$176$	5.48410	0.413379
$177$	22.3947	1.68329
$178$	6.44761	0.483269
$179$	11.6749	0.872626	0.436313	−	0.899795i	$-0.356284\pi$
$179$	11.6749	0.872626	0.436313	+	0.899795i	$0.356284\pi$
$180$	−0.229643	−0.0171166
$181$	−19.0210	−1.41382	−0.706908	−	0.707305i	$-0.749911\pi$
$181$	−19.0210	−1.41382	−0.706908	+	0.707305i	$0.749911\pi$
$182$	1.26056	0.0934390
$183$	7.21185	0.533115
$184$	−2.64520	−0.195007
$185$	−6.94779	−0.510812
$186$	−5.18734	−0.380354
$187$	−21.4430	−1.56807
$188$	−11.0988	−0.809464
$189$	−2.18082	−0.158631
$190$	1.91620	0.139016
$191$	4.25112	0.307600	0.153800	−	0.988102i	$-0.450849\pi$
$191$	4.25112	0.307600	0.153800	+	0.988102i	$0.450849\pi$
$192$	−1.79935	−0.129857
$193$	8.96955	0.645643	0.322821	−	0.946460i	$-0.395369\pi$
$193$	8.96955	0.645643	0.322821	+	0.946460i	$0.395369\pi$
$194$	12.5447	0.900660
$195$	−4.99489	−0.357691
$196$	−6.80749	−0.486249
$197$	3.97130	0.282943	0.141472	−	0.989942i	$-0.454817\pi$
$197$	3.97130	0.282943	0.141472	+	0.989942i	$0.454817\pi$
$198$	1.30342	0.0926301
$199$	−21.7215	−1.53979	−0.769897	−	0.638168i	$-0.779693\pi$
$199$	−21.7215	−1.53979	−0.769897	+	0.638168i	$0.779693\pi$
$200$	−4.06643	−0.287540
$201$	16.2304	1.14481
$202$	−6.52257	−0.458926
$203$	1.18692	0.0833054
$204$	7.03555	0.492587
$205$	−0.422472	−0.0295067
$206$	3.92953	0.273783
$207$	−0.628693	−0.0436972
$208$	−2.87300	−0.199206
$209$	−10.8761	−0.752315
$210$	−0.762815	−0.0526392
$211$	17.1975	1.18393	0.591963	−	0.805965i	$-0.298353\pi$
$211$	17.1975	1.18393	0.591963	+	0.805965i	$0.298353\pi$
$212$	−1.44502	−0.0992447
$213$	4.63816	0.317802
$214$	−7.42727	−0.507718
$215$	3.94104	0.268777
$216$	4.97040	0.338193
$217$	−1.26490	−0.0858671
$218$	13.2168	0.895158
$219$	16.9761	1.14714
$220$	−5.29882	−0.357246
$221$	11.2335	0.755649
$222$	−12.9387	−0.868386
$223$	1.99607	0.133667	0.0668335	−	0.997764i	$-0.478710\pi$
$223$	1.99607	0.133667	0.0668335	+	0.997764i	$0.478710\pi$
$224$	−0.438762	−0.0293160
$225$	−0.966480	−0.0644320
$226$	−0.412709	−0.0274530
$227$	−18.5008	−1.22794	−0.613970	−	0.789329i	$-0.710429\pi$
$227$	−18.5008	−1.22794	−0.613970	+	0.789329i	$0.710429\pi$
$228$	3.56849	0.236329
$229$	−22.2589	−1.47091	−0.735453	−	0.677575i	$-0.763031\pi$
$229$	−22.2589	−1.47091	−0.735453	+	0.677575i	$0.763031\pi$
$230$	2.55583	0.168527
$231$	4.32962	0.284868
$232$	−2.70516	−0.177602
$233$	11.1692	0.731717	0.365859	−	0.930670i	$-0.380775\pi$
$233$	11.1692	0.731717	0.365859	+	0.930670i	$0.380775\pi$
$234$	−0.682833	−0.0446382
$235$	10.7238	0.699547
$236$	−12.4460	−0.810164
$237$	4.20912	0.273412
$238$	1.71558	0.111204
$239$	−1.49814	−0.0969065	−0.0484533	−	0.998825i	$-0.515429\pi$
$239$	−1.49814	−0.0969065	−0.0484533	+	0.998825i	$0.515429\pi$
$240$	1.73856	0.112224
$241$	12.3432	0.795099	0.397549	−	0.917581i	$-0.369861\pi$
$241$	12.3432	0.795099	0.397549	+	0.917581i	$0.369861\pi$
$242$	19.0753	1.22621
$243$	2.46430	0.158085
$244$	−4.00802	−0.256587
$245$	6.57750	0.420221
$246$	−0.786757	−0.0501618
$247$	5.69774	0.362539
$248$	2.88289	0.183064
$249$	25.9336	1.64348
$250$	8.76012	0.554039
$251$	2.25393	0.142267	0.0711335	−	0.997467i	$-0.477338\pi$
$251$	2.25393	0.142267	0.0711335	+	0.997467i	$0.477338\pi$
$252$	−0.104282	−0.00656913
$253$	−14.5065	−0.912018
$254$	−15.8915	−0.997120
$255$	−6.79785	−0.425698
$256$	1.00000	0.0625000
$257$	6.84867	0.427208	0.213604	−	0.976920i	$-0.431480\pi$
$257$	6.84867	0.427208	0.213604	+	0.976920i	$0.431480\pi$
$258$	7.33928	0.456924
$259$	−3.15502	−0.196043
$260$	2.77593	0.172156
$261$	−0.642942	−0.0397971
$262$	14.3563	0.886935
$263$	2.00958	0.123916	0.0619579	−	0.998079i	$-0.480266\pi$
$263$	2.00958	0.123916	0.0619579	+	0.998079i	$0.480266\pi$
$264$	−9.86783	−0.607323
$265$	1.39621	0.0857682
$266$	0.870154	0.0533526
$267$	−11.6015	−0.710003
$268$	−9.02014	−0.550993
$269$	29.4265	1.79417	0.897083	−	0.441863i	$-0.145682\pi$
$269$	29.4265	1.79417	0.897083	+	0.441863i	$0.145682\pi$
$270$	−4.80248	−0.292270
$271$	−14.9541	−0.908398	−0.454199	−	0.890900i	$-0.650075\pi$
$271$	−14.9541	−0.908398	−0.454199	+	0.890900i	$0.650075\pi$
$272$	−3.91004	−0.237081
$273$	−2.26819	−0.137277
$274$	11.3827	0.687654
$275$	−22.3007	−1.34478
$276$	4.75965	0.286497
$277$	−20.2599	−1.21730	−0.608649	−	0.793440i	$-0.708288\pi$
$277$	−20.2599	−1.21730	−0.608649	+	0.793440i	$0.708288\pi$
$278$	2.80852	0.168444
$279$	0.685185	0.0410209
$280$	0.423938	0.0253352
$281$	23.2390	1.38632	0.693162	−	0.720782i	$-0.256217\pi$
$281$	23.2390	1.38632	0.693162	+	0.720782i	$0.256217\pi$
$282$	19.9707	1.18924
$283$	−18.8115	−1.11823	−0.559115	−	0.829090i	$-0.688859\pi$
$283$	−18.8115	−1.11823	−0.559115	+	0.829090i	$0.688859\pi$
$284$	−2.57768	−0.152957
$285$	−3.44793	−0.204238
$286$	−15.7558	−0.931659
$287$	−0.191846	−0.0113243
$288$	0.237673	0.0140050
$289$	−1.71157	−0.100681
$290$	2.61376	0.153485
$291$	−22.5724	−1.32322
$292$	−9.43455	−0.552115
$293$	−12.1578	−0.710269	−0.355134	−	0.934815i	$-0.615565\pi$
$293$	−12.1578	−0.710269	−0.355134	+	0.934815i	$0.615565\pi$
$294$	12.2491	0.714381
$295$	12.0255	0.700151
$296$	7.19073	0.417953
$297$	27.2582	1.58168
$298$	13.0171	0.754060
$299$	7.59965	0.439499
$300$	7.31694	0.422444
$301$	1.78964	0.103153
$302$	9.08544	0.522808
$303$	11.7364	0.674239
$304$	−1.98321	−0.113745
$305$	3.87261	0.221745
$306$	−0.929311	−0.0531252
$307$	−5.36181	−0.306015	−0.153007	−	0.988225i	$-0.548896\pi$
$307$	−5.36181	−0.306015	−0.153007	+	0.988225i	$0.548896\pi$
$308$	−2.40621	−0.137107
$309$	−7.07061	−0.402233
$310$	−2.78549	−0.158205
$311$	17.3894	0.986063	0.493031	−	0.870012i	$-0.335889\pi$
$311$	17.3894	0.986063	0.493031	+	0.870012i	$0.335889\pi$
$312$	5.16954	0.292667
$313$	23.6219	1.33519	0.667594	−	0.744525i	$-0.267324\pi$
$313$	23.6219	1.33519	0.667594	+	0.744525i	$0.267324\pi$
$314$	3.13075	0.176678
$315$	0.100759	0.00567711
$316$	−2.33924	−0.131593
$317$	3.80988	0.213984	0.106992	−	0.994260i	$-0.465878\pi$
$317$	3.80988	0.213984	0.106992	+	0.994260i	$0.465878\pi$
$318$	2.60011	0.145807
$319$	−14.8353	−0.830619
$320$	−0.966216	−0.0540131
$321$	13.3643	0.745921
$322$	1.16061	0.0646784
$323$	7.75441	0.431467
$324$	−9.65653	−0.536474
$325$	11.6828	0.648047
$326$	−1.53457	−0.0849917
$327$	−23.7818	−1.31514
$328$	0.437244	0.0241428
$329$	4.86973	0.268477
$330$	9.53445	0.524854
$331$	31.5948	1.73661	0.868304	−	0.496033i	$-0.165211\pi$
$331$	31.5948	1.73661	0.868304	+	0.496033i	$0.165211\pi$
$332$	−14.4127	−0.791002
$333$	1.70904	0.0936549
$334$	11.2813	0.617284
$335$	8.71540	0.476173
$336$	0.789487	0.0430701
$337$	−11.2216	−0.611280	−0.305640	−	0.952147i	$-0.598870\pi$
$337$	−11.2216	−0.611280	−0.305640	+	0.952147i	$0.598870\pi$
$338$	−4.74589	−0.258143
$339$	0.742609	0.0403330
$340$	3.77794	0.204888
$341$	15.8100	0.856162
$342$	−0.471354	−0.0254879
$343$	6.05820	0.327112
$344$	−4.07884	−0.219917
$345$	−4.59885	−0.247594
$346$	−5.71490	−0.307235
$347$	−13.9371	−0.748182	−0.374091	−	0.927392i	$-0.622045\pi$
$347$	−13.9371	−0.748182	−0.374091	+	0.927392i	$0.622045\pi$
$348$	4.86753	0.260927
$349$	13.0632	0.699259	0.349629	−	0.936888i	$-0.386308\pi$
$349$	13.0632	0.699259	0.349629	+	0.936888i	$0.386308\pi$
$350$	1.78419	0.0953691
$351$	−14.2799	−0.762207
$352$	5.48410	0.292303
$353$	34.8483	1.85479	0.927393	−	0.374088i	$-0.122044\pi$
$353$	34.8483	1.85479	0.927393	+	0.374088i	$0.122044\pi$
$354$	22.3947	1.19027
$355$	2.49060	0.132187
$356$	6.44761	0.341723
$357$	−3.08693	−0.163378
$358$	11.6749	0.617040
$359$	17.4742	0.922252	0.461126	−	0.887335i	$-0.347446\pi$
$359$	17.4742	0.922252	0.461126	+	0.887335i	$0.347446\pi$
$360$	−0.229643	−0.0121033
$361$	−15.0669	−0.792995
$362$	−19.0210	−0.999720
$363$	−34.3232	−1.80150
$364$	1.26056	0.0660713
$365$	9.11581	0.477143
$366$	7.21185	0.376969
$367$	2.60600	0.136032	0.0680162	−	0.997684i	$-0.478333\pi$
$367$	2.60600	0.136032	0.0680162	+	0.997684i	$0.478333\pi$
$368$	−2.64520	−0.137891
$369$	0.103921	0.00540991
$370$	−6.94779	−0.361199
$371$	0.634021	0.0329167
$372$	−5.18734	−0.268951
$373$	−33.0283	−1.71014	−0.855071	−	0.518511i	$-0.826486\pi$
$373$	−33.0283	−1.71014	−0.855071	+	0.518511i	$0.826486\pi$
$374$	−21.4430	−1.10879
$375$	−15.7626	−0.813975
$376$	−11.0988	−0.572378
$377$	7.77190	0.400273
$378$	−2.18082	−0.112169
$379$	−0.0431064	−0.00221422	−0.00110711	−	0.999999i	$-0.500352\pi$
$379$	−0.0431064	−0.00221422	−0.00110711	+	0.999999i	$0.500352\pi$
$380$	1.91620	0.0982992
$381$	28.5944	1.46493
$382$	4.25112	0.217506
$383$	1.86505	0.0952994	0.0476497	−	0.998864i	$-0.484827\pi$
$383$	1.86505	0.0952994	0.0476497	+	0.998864i	$0.484827\pi$
$384$	−1.79935	−0.0918229
$385$	2.32492	0.118489
$386$	8.96955	0.456538
$387$	−0.969431	−0.0492789
$388$	12.5447	0.636863
$389$	−17.5371	−0.889166	−0.444583	−	0.895738i	$-0.646648\pi$
$389$	−17.5371	−0.889166	−0.444583	+	0.895738i	$0.646648\pi$
$390$	−4.99489	−0.252926
$391$	10.3428	0.523060
$392$	−6.80749	−0.343830
$393$	−25.8321	−1.30306
$394$	3.97130	0.200071
$395$	2.26021	0.113724
$396$	1.30342	0.0654994
$397$	−34.9958	−1.75639	−0.878195	−	0.478302i	$-0.841252\pi$
$397$	−34.9958	−1.75639	−0.878195	+	0.478302i	$0.841252\pi$
$398$	−21.7215	−1.08880
$399$	−1.56572	−0.0783838
$400$	−4.06643	−0.203321
$401$	12.5189	0.625164	0.312582	−	0.949891i	$-0.398806\pi$
$401$	12.5189	0.625164	0.312582	+	0.949891i	$0.398806\pi$
$402$	16.2304	0.809500
$403$	−8.28253	−0.412582
$404$	−6.52257	−0.324510
$405$	9.33029	0.463626
$406$	1.18692	0.0589058
$407$	39.4347	1.95470
$408$	7.03555	0.348311
$409$	−1.06462	−0.0526422	−0.0263211	−	0.999654i	$-0.508379\pi$
$409$	−1.06462	−0.0526422	−0.0263211	+	0.999654i	$0.508379\pi$
$410$	−0.422472	−0.0208644
$411$	−20.4815	−1.01028
$412$	3.92953	0.193594
$413$	5.46082	0.268709
$414$	−0.628693	−0.0308986
$415$	13.9258	0.683592
$416$	−2.87300	−0.140860
$417$	−5.05352	−0.247472
$418$	−10.8761	−0.531967
$419$	3.35966	0.164130	0.0820650	−	0.996627i	$-0.473848\pi$
$419$	3.35966	0.164130	0.0820650	+	0.996627i	$0.473848\pi$
$420$	−0.762815	−0.0372216
$421$	−30.2611	−1.47484	−0.737418	−	0.675437i	$-0.763955\pi$
$421$	−30.2611	−1.47484	−0.737418	+	0.675437i	$0.763955\pi$
$422$	17.1975	0.837162
$423$	−2.63789	−0.128259
$424$	−1.44502	−0.0701766
$425$	15.8999	0.771259
$426$	4.63816	0.224720
$427$	1.75857	0.0851030
$428$	−7.42727	−0.359011
$429$	28.3502	1.36876
$430$	3.94104	0.190054
$431$	6.62111	0.318928	0.159464	−	0.987204i	$-0.449023\pi$
$431$	6.62111	0.318928	0.159464	+	0.987204i	$0.449023\pi$
$432$	4.97040	0.239139
$433$	−22.5657	−1.08444	−0.542220	−	0.840237i	$-0.682416\pi$
$433$	−22.5657	−1.08444	−0.542220	+	0.840237i	$0.682416\pi$
$434$	−1.26490	−0.0607172
$435$	−4.70308	−0.225496
$436$	13.2168	0.632972
$437$	5.24598	0.250949
$438$	16.9761	0.811149
$439$	9.16289	0.437321	0.218660	−	0.975801i	$-0.429831\pi$
$439$	9.16289	0.437321	0.218660	+	0.975801i	$0.429831\pi$
$440$	−5.29882	−0.252611
$441$	−1.61796	−0.0770455
$442$	11.2335	0.534325
$443$	−2.89832	−0.137703	−0.0688516	−	0.997627i	$-0.521934\pi$
$443$	−2.89832	−0.137703	−0.0688516	+	0.997627i	$0.521934\pi$
$444$	−12.9387	−0.614042
$445$	−6.22979	−0.295320
$446$	1.99607	0.0945169
$447$	−23.4223	−1.10784
$448$	−0.438762	−0.0207295
$449$	7.49105	0.353524	0.176762	−	0.984254i	$-0.443438\pi$
$449$	7.49105	0.353524	0.176762	+	0.984254i	$0.443438\pi$
$450$	−0.966480	−0.0455603
$451$	2.39789	0.112912
$452$	−0.412709	−0.0194122
$453$	−16.3479	−0.768092
$454$	−18.5008	−0.868285
$455$	−1.21797	−0.0570995
$456$	3.56849	0.167110
$457$	37.2857	1.74415	0.872075	−	0.489373i	$-0.162774\pi$
$457$	37.2857	1.74415	0.872075	+	0.489373i	$0.162774\pi$
$458$	−22.2589	−1.04009
$459$	−19.4345	−0.907124
$460$	2.55583	0.119166
$461$	17.5626	0.817971	0.408986	−	0.912541i	$-0.365883\pi$
$461$	17.5626	0.817971	0.408986	+	0.912541i	$0.365883\pi$
$462$	4.32962	0.201432
$463$	−21.3434	−0.991911	−0.495956	−	0.868348i	$-0.665182\pi$
$463$	−21.3434	−0.991911	−0.495956	+	0.868348i	$0.665182\pi$
$464$	−2.70516	−0.125584
$465$	5.01208	0.232430
$466$	11.1692	0.517402
$467$	−6.41506	−0.296854	−0.148427	−	0.988923i	$-0.547421\pi$
$467$	−6.41506	−0.296854	−0.148427	+	0.988923i	$0.547421\pi$
$468$	−0.682833	−0.0315640
$469$	3.95769	0.182749
$470$	10.7238	0.494654
$471$	−5.63332	−0.259570
$472$	−12.4460	−0.572872
$473$	−22.3688	−1.02852
$474$	4.20912	0.193331
$475$	8.06456	0.370027
$476$	1.71558	0.0786333
$477$	−0.343443	−0.0157252
$478$	−1.49814	−0.0685233
$479$	−26.6221	−1.21640	−0.608198	−	0.793785i	$-0.708107\pi$
$479$	−26.6221	−1.21640	−0.608198	+	0.793785i	$0.708107\pi$
$480$	1.73856	0.0793542
$481$	−20.6589	−0.941966
$482$	12.3432	0.562220
$483$	−2.08835	−0.0950234
$484$	19.0753	0.867060
$485$	−12.1209	−0.550383
$486$	2.46430	0.111783
$487$	−29.6396	−1.34310	−0.671550	−	0.740959i	$-0.734371\pi$
$487$	−29.6396	−1.34310	−0.671550	+	0.740959i	$0.734371\pi$
$488$	−4.00802	−0.181435
$489$	2.76123	0.124867
$490$	6.57750	0.297141
$491$	1.27028	0.0573271	0.0286636	−	0.999589i	$-0.490875\pi$
$491$	1.27028	0.0573271	0.0286636	+	0.999589i	$0.490875\pi$
$492$	−0.786757	−0.0354697
$493$	10.5773	0.476376
$494$	5.69774	0.256353
$495$	−1.25939	−0.0566052
$496$	2.88289	0.129446
$497$	1.13099	0.0507318
$498$	25.9336	1.16211
$499$	34.6567	1.55145	0.775723	−	0.631074i	$-0.217386\pi$
$499$	34.6567	1.55145	0.775723	+	0.631074i	$0.217386\pi$
$500$	8.76012	0.391765
$501$	−20.2990	−0.906892
$502$	2.25393	0.100598
$503$	−34.4211	−1.53476	−0.767381	−	0.641191i	$-0.778440\pi$
$503$	−34.4211	−1.53476	−0.767381	+	0.641191i	$0.778440\pi$
$504$	−0.104282	−0.00464508
$505$	6.30221	0.280445
$506$	−14.5065	−0.644894
$507$	8.53954	0.379254
$508$	−15.8915	−0.705070
$509$	−35.6197	−1.57881	−0.789407	−	0.613870i	$-0.789612\pi$
$509$	−35.6197	−1.57881	−0.789407	+	0.613870i	$0.789612\pi$
$510$	−6.79785	−0.301014
$511$	4.13952	0.183121
$512$	1.00000	0.0441942
$513$	−9.85733	−0.435212
$514$	6.84867	0.302082
$515$	−3.79677	−0.167306
$516$	7.33928	0.323094
$517$	−60.8670	−2.67693
$518$	−3.15502	−0.138623
$519$	10.2831	0.451379
$520$	2.77593	0.121733
$521$	−21.4466	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$521$	−21.4466	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$522$	−0.642942	−0.0281408
$523$	17.9598	0.785326	0.392663	−	0.919682i	$-0.371554\pi$
$523$	17.9598	0.785326	0.392663	+	0.919682i	$0.371554\pi$
$524$	14.3563	0.627158
$525$	−3.21039	−0.140113
$526$	2.00958	0.0876217
$527$	−11.2722	−0.491025
$528$	−9.86783	−0.429442
$529$	−16.0029	−0.695779
$530$	1.39621	0.0606473
$531$	−2.95807	−0.128369
$532$	0.870154	0.0377260
$533$	−1.25620	−0.0544121
$534$	−11.6015	−0.502048
$535$	7.17634	0.310260
$536$	−9.02014	−0.389611
$537$	−21.0073	−0.906534
$538$	29.4265	1.26867
$539$	−37.3329	−1.60804
$540$	−4.80248	−0.206666
$541$	−31.0191	−1.33361	−0.666807	−	0.745230i	$-0.732340\pi$
$541$	−31.0191	−1.33361	−0.666807	+	0.745230i	$0.732340\pi$
$542$	−14.9541	−0.642335
$543$	34.2254	1.46875
$544$	−3.91004	−0.167642
$545$	−12.7703	−0.547021
$546$	−2.26819	−0.0970697
$547$	0.412652	0.0176437	0.00882185	−	0.999961i	$-0.497192\pi$
$547$	0.412652	0.0176437	0.00882185	+	0.999961i	$0.497192\pi$
$548$	11.3827	0.486245
$549$	−0.952599	−0.0406559
$550$	−22.3007	−0.950904
$551$	5.36488	0.228552
$552$	4.75965	0.202584
$553$	1.02637	0.0436457
$554$	−20.2599	−0.860759
$555$	12.5015	0.530661
$556$	2.80852	0.119108
$557$	40.6057	1.72052	0.860259	−	0.509857i	$-0.170302\pi$
$557$	40.6057	1.72052	0.860259	+	0.509857i	$0.170302\pi$
$558$	0.685185	0.0290062
$559$	11.7185	0.495640
$560$	0.423938	0.0179147
$561$	38.5836	1.62900
$562$	23.2390	0.980279
$563$	−41.9135	−1.76644	−0.883221	−	0.468957i	$-0.844630\pi$
$563$	−41.9135	−1.76644	−0.883221	+	0.468957i	$0.844630\pi$
$564$	19.9707	0.840918
$565$	0.398765	0.0167762
$566$	−18.8115	−0.790708
$567$	4.23692	0.177934
$568$	−2.57768	−0.108157
$569$	−17.2899	−0.724829	−0.362414	−	0.932017i	$-0.618048\pi$
$569$	−17.2899	−0.724829	−0.362414	+	0.932017i	$0.618048\pi$
$570$	−3.44793	−0.144418
$571$	−9.93136	−0.415615	−0.207807	−	0.978170i	$-0.566633\pi$
$571$	−9.93136	−0.415615	−0.207807	+	0.978170i	$0.566633\pi$
$572$	−15.7558	−0.658783
$573$	−7.64927	−0.319553
$574$	−0.191846	−0.00800749
$575$	10.7565	0.448578
$576$	0.237673	0.00990304
$577$	−3.62109	−0.150748	−0.0753740	−	0.997155i	$-0.524015\pi$
$577$	−3.62109	−0.150748	−0.0753740	+	0.997155i	$0.524015\pi$
$578$	−1.71157	−0.0711921
$579$	−16.1394	−0.670730
$580$	2.61376	0.108531
$581$	6.32376	0.262354
$582$	−22.5724	−0.935657
$583$	−7.92465	−0.328206
$584$	−9.43455	−0.390404
$585$	0.659764	0.0272779
$586$	−12.1578	−0.502236
$587$	32.1195	1.32571	0.662856	−	0.748747i	$-0.269344\pi$
$587$	32.1195	1.32571	0.662856	+	0.748747i	$0.269344\pi$
$588$	12.2491	0.505143
$589$	−5.71736	−0.235580
$590$	12.0255	0.495082
$591$	−7.14577	−0.293938
$592$	7.19073	0.295537
$593$	−20.5966	−0.845800	−0.422900	−	0.906176i	$-0.638988\pi$
$593$	−20.5966	−0.845800	−0.422900	+	0.906176i	$0.638988\pi$
$594$	27.2582	1.11842
$595$	−1.65762	−0.0679557
$596$	13.0171	0.533201
$597$	39.0846	1.59963
$598$	7.59965	0.310773
$599$	−9.06095	−0.370220	−0.185110	−	0.982718i	$-0.559264\pi$
$599$	−9.06095	−0.370220	−0.185110	+	0.982718i	$0.559264\pi$
$600$	7.31694	0.298713
$601$	41.7897	1.70464	0.852318	−	0.523023i	$-0.175196\pi$
$601$	41.7897	1.70464	0.852318	+	0.523023i	$0.175196\pi$
$602$	1.78964	0.0729403
$603$	−2.14384	−0.0873040
$604$	9.08544	0.369681
$605$	−18.4309	−0.749321
$606$	11.7364	0.476759
$607$	27.4505	1.11418	0.557090	−	0.830452i	$-0.311918\pi$
$607$	27.4505	1.11418	0.557090	+	0.830452i	$0.311918\pi$
$608$	−1.98321	−0.0804296
$609$	−2.13569	−0.0865424
$610$	3.87261	0.156798
$611$	31.8869	1.29000
$612$	−0.929311	−0.0375652
$613$	9.64845	0.389697	0.194849	−	0.980833i	$-0.437578\pi$
$613$	9.64845	0.389697	0.194849	+	0.980833i	$0.437578\pi$
$614$	−5.36181	−0.216385
$615$	0.760176	0.0306533
$616$	−2.40621	−0.0969490
$617$	35.0765	1.41213	0.706063	−	0.708149i	$-0.250470\pi$
$617$	35.0765	1.41213	0.706063	+	0.708149i	$0.250470\pi$
$618$	−7.07061	−0.284422
$619$	−42.7551	−1.71847	−0.859236	−	0.511579i	$-0.829061\pi$
$619$	−42.7551	−1.71847	−0.859236	+	0.511579i	$0.829061\pi$
$620$	−2.78549	−0.111868
$621$	−13.1477	−0.527600
$622$	17.3894	0.697252
$623$	−2.82897	−0.113340
$624$	5.16954	0.206947
$625$	11.8680	0.474719
$626$	23.6219	0.944121
$627$	19.5699	0.781548
$628$	3.13075	0.124930
$629$	−28.1161	−1.12106
$630$	0.100759	0.00401432
$631$	−25.2402	−1.00480	−0.502399	−	0.864636i	$-0.667549\pi$
$631$	−25.2402	−1.00480	−0.502399	+	0.864636i	$0.667549\pi$
$632$	−2.33924	−0.0930500
$633$	−30.9444	−1.22993
$634$	3.80988	0.151310
$635$	15.3546	0.609328
$636$	2.60011	0.103101
$637$	19.5579	0.774912
$638$	−14.8353	−0.587337
$639$	−0.612646	−0.0242359
$640$	−0.966216	−0.0381930
$641$	−8.10811	−0.320251	−0.160125	−	0.987097i	$-0.551190\pi$
$641$	−8.10811	−0.320251	−0.160125	+	0.987097i	$0.551190\pi$
$642$	13.3643	0.527446
$643$	0.425048	0.0167623	0.00838113	−	0.999965i	$-0.497332\pi$
$643$	0.425048	0.0167623	0.00838113	+	0.999965i	$0.497332\pi$
$644$	1.16061	0.0457346
$645$	−7.09133	−0.279221
$646$	7.75441	0.305093
$647$	4.13829	0.162693	0.0813465	−	0.996686i	$-0.474078\pi$
$647$	4.13829	0.162693	0.0813465	+	0.996686i	$0.474078\pi$
$648$	−9.65653	−0.379344
$649$	−68.2549	−2.67924
$650$	11.6828	0.458238
$651$	2.27600	0.0892036
$652$	−1.53457	−0.0600982
$653$	−29.3109	−1.14702	−0.573512	−	0.819197i	$-0.694419\pi$
$653$	−29.3109	−1.14702	−0.573512	+	0.819197i	$0.694419\pi$
$654$	−23.7818	−0.929941
$655$	−13.8713	−0.541996
$656$	0.437244	0.0170715
$657$	−2.24234	−0.0874819
$658$	4.86973	0.189842
$659$	−10.3898	−0.404731	−0.202365	−	0.979310i	$-0.564863\pi$
$659$	−10.3898	−0.404731	−0.202365	+	0.979310i	$0.564863\pi$
$660$	9.53445	0.371128
$661$	6.24595	0.242939	0.121470	−	0.992595i	$-0.461239\pi$
$661$	6.24595	0.242939	0.121470	+	0.992595i	$0.461239\pi$
$662$	31.5948	1.22797
$663$	−20.2131	−0.785012
$664$	−14.4127	−0.559323
$665$	−0.840757	−0.0326031
$666$	1.70904	0.0662240
$667$	7.15568	0.277069
$668$	11.2813	0.436485
$669$	−3.59164	−0.138861
$670$	8.71540	0.336705
$671$	−21.9804	−0.848543
$672$	0.789487	0.0304551
$673$	31.4104	1.21078	0.605392	−	0.795928i	$-0.293017\pi$
$673$	31.4104	1.21078	0.605392	+	0.795928i	$0.293017\pi$
$674$	−11.2216	−0.432240
$675$	−20.2118	−0.777952
$676$	−4.74589	−0.182534
$677$	13.0512	0.501598	0.250799	−	0.968039i	$-0.419307\pi$
$677$	13.0512	0.501598	0.250799	+	0.968039i	$0.419307\pi$
$678$	0.742609	0.0285197
$679$	−5.50415	−0.211230
$680$	3.77794	0.144877
$681$	33.2895	1.27566
$682$	15.8100	0.605398
$683$	−45.4895	−1.74061	−0.870305	−	0.492514i	$-0.836078\pi$
$683$	−45.4895	−1.74061	−0.870305	+	0.492514i	$0.836078\pi$
$684$	−0.471354	−0.0180227
$685$	−10.9981	−0.420218
$686$	6.05820	0.231303
$687$	40.0515	1.52806
$688$	−4.07884	−0.155504
$689$	4.15155	0.158161
$690$	−4.59885	−0.175075
$691$	22.8148	0.867917	0.433959	−	0.900933i	$-0.357116\pi$
$691$	22.8148	0.867917	0.433959	+	0.900933i	$0.357116\pi$
$692$	−5.71490	−0.217248
$693$	−0.571891	−0.0217244
$694$	−13.9371	−0.529044
$695$	−2.71363	−0.102934
$696$	4.86753	0.184503
$697$	−1.70964	−0.0647573
$698$	13.0632	0.494451
$699$	−20.0973	−0.760150
$700$	1.78419	0.0674361
$701$	−3.92993	−0.148432	−0.0742158	−	0.997242i	$-0.523645\pi$
$701$	−3.92993	−0.148432	−0.0742158	+	0.997242i	$0.523645\pi$
$702$	−14.2799	−0.538962
$703$	−14.2607	−0.537852
$704$	5.48410	0.206690
$705$	−19.2960	−0.726729
$706$	34.8483	1.31153
$707$	2.86185	0.107631
$708$	22.3947	0.841645
$709$	−44.1605	−1.65848	−0.829241	−	0.558891i	$-0.811227\pi$
$709$	−44.1605	−1.65848	−0.829241	+	0.558891i	$0.811227\pi$
$710$	2.49060	0.0934705
$711$	−0.555974	−0.0208507
$712$	6.44761	0.241635
$713$	−7.62582	−0.285589
$714$	−3.08693	−0.115525
$715$	15.2235	0.569326
$716$	11.6749	0.436313
$717$	2.69568	0.100672
$718$	17.4742	0.652130
$719$	31.7586	1.18440	0.592198	−	0.805792i	$-0.298260\pi$
$719$	31.7586	1.18440	0.592198	+	0.805792i	$0.298260\pi$
$720$	−0.229643	−0.00855830
$721$	−1.72413	−0.0642098
$722$	−15.0669	−0.560732
$723$	−22.2099	−0.825994
$724$	−19.0210	−0.706908
$725$	11.0003	0.408542
$726$	−34.3232	−1.27385
$727$	−1.91107	−0.0708775	−0.0354388	−	0.999372i	$-0.511283\pi$
$727$	−1.91107	−0.0708775	−0.0354388	+	0.999372i	$0.511283\pi$
$728$	1.26056	0.0467195
$729$	24.5354	0.908720
$730$	9.11581	0.337391
$731$	15.9484	0.589875
$732$	7.21185	0.266558
$733$	23.7790	0.878298	0.439149	−	0.898414i	$-0.355280\pi$
$733$	23.7790	0.878298	0.439149	+	0.898414i	$0.355280\pi$
$734$	2.60600	0.0961894
$735$	−11.8352	−0.436550
$736$	−2.64520	−0.0975034
$737$	−49.4673	−1.82215
$738$	0.103921	0.00382539
$739$	−20.1669	−0.741852	−0.370926	−	0.928662i	$-0.620960\pi$
$739$	−20.1669	−0.741852	−0.370926	+	0.928662i	$0.620960\pi$
$740$	−6.94779	−0.255406
$741$	−10.2522	−0.376626
$742$	0.634021	0.0232757
$743$	4.87331	0.178785	0.0893923	−	0.995996i	$-0.471508\pi$
$743$	4.87331	0.178785	0.0893923	+	0.995996i	$0.471508\pi$
$744$	−5.18734	−0.190177
$745$	−12.5773	−0.460797
$746$	−33.0283	−1.20925
$747$	−3.42552	−0.125333
$748$	−21.4430	−0.784035
$749$	3.25880	0.119074
$750$	−15.7626	−0.575567
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	−11.0988	−0.404732
$753$	−4.05562	−0.147795
$754$	7.77190	0.283036
$755$	−8.77849	−0.319482
$756$	−2.18082	−0.0793157
$757$	1.09472	0.0397883	0.0198941	−	0.999802i	$-0.493667\pi$
$757$	1.09472	0.0397883	0.0198941	+	0.999802i	$0.493667\pi$
$758$	−0.0431064	−0.00156569
$759$	26.1024	0.947457
$760$	1.91620	0.0695080
$761$	32.5051	1.17831	0.589154	−	0.808021i	$-0.299461\pi$
$761$	32.5051	1.17831	0.589154	+	0.808021i	$0.299461\pi$
$762$	28.5944	1.03587
$763$	−5.79905	−0.209940
$764$	4.25112	0.153800
$765$	0.897915	0.0324642
$766$	1.86505	0.0673868
$767$	35.7572	1.29112
$768$	−1.79935	−0.0649286
$769$	23.5009	0.847464	0.423732	−	0.905788i	$-0.360720\pi$
$769$	23.5009	0.847464	0.423732	+	0.905788i	$0.360720\pi$
$770$	2.32492	0.0837842
$771$	−12.3232	−0.443808
$772$	8.96955	0.322821
$773$	5.54733	0.199524	0.0997618	−	0.995011i	$-0.468192\pi$
$773$	5.54733	0.199524	0.0997618	+	0.995011i	$0.468192\pi$
$774$	−0.969431	−0.0348455
$775$	−11.7231	−0.421105
$776$	12.5447	0.450330
$777$	5.67699	0.203661
$778$	−17.5371	−0.628735
$779$	−0.867145	−0.0310687
$780$	−4.99489	−0.178846
$781$	−14.1363	−0.505835
$782$	10.3428	0.369860
$783$	−13.4457	−0.480511
$784$	−6.80749	−0.243125
$785$	−3.02498	−0.107966
$786$	−25.8321	−0.921399
$787$	30.5643	1.08950	0.544750	−	0.838599i	$-0.316625\pi$
$787$	30.5643	1.08950	0.544750	+	0.838599i	$0.316625\pi$
$788$	3.97130	0.141472
$789$	−3.61594	−0.128731
$790$	2.26021	0.0804147
$791$	0.181081	0.00643849
$792$	1.30342	0.0463151
$793$	11.5150	0.408911
$794$	−34.9958	−1.24196
$795$	−2.51227	−0.0891009
$796$	−21.7215	−0.769897
$797$	9.23428	0.327095	0.163548	−	0.986535i	$-0.447706\pi$
$797$	9.23428	0.327095	0.163548	+	0.986535i	$0.447706\pi$
$798$	−1.56572	−0.0554257
$799$	43.3968	1.53527
$800$	−4.06643	−0.143770
$801$	1.53242	0.0541455
$802$	12.5189	0.442058
$803$	−51.7400	−1.82586
$804$	16.2304	0.572403
$805$	−1.12140	−0.0395242
$806$	−8.28253	−0.291740
$807$	−52.9487	−1.86388
$808$	−6.52257	−0.229463
$809$	36.2062	1.27294	0.636470	−	0.771301i	$-0.280394\pi$
$809$	36.2062	1.27294	0.636470	+	0.771301i	$0.280394\pi$
$810$	9.33029	0.327833
$811$	12.4470	0.437073	0.218537	−	0.975829i	$-0.429872\pi$
$811$	12.4470	0.437073	0.218537	+	0.975829i	$0.429872\pi$
$812$	1.18692	0.0416527
$813$	26.9078	0.943696
$814$	39.4347	1.38218
$815$	1.48272	0.0519375
$816$	7.03555	0.246293
$817$	8.08918	0.283005
$818$	−1.06462	−0.0372237
$819$	0.299601	0.0104689
$820$	−0.422472	−0.0147534
$821$	42.4898	1.48290	0.741452	−	0.671006i	$-0.234138\pi$
$821$	42.4898	1.48290	0.741452	+	0.671006i	$0.234138\pi$
$822$	−20.4815	−0.714375
$823$	52.0601	1.81470	0.907351	−	0.420373i	$-0.138101\pi$
$823$	52.0601	1.81470	0.907351	+	0.420373i	$0.138101\pi$
$824$	3.92953	0.136892
$825$	40.1268	1.39704
$826$	5.46082	0.190006
$827$	47.3044	1.64493	0.822467	−	0.568812i	$-0.192597\pi$
$827$	47.3044	1.64493	0.822467	+	0.568812i	$0.192597\pi$
$828$	−0.628693	−0.0218486
$829$	35.3984	1.22944	0.614719	−	0.788746i	$-0.289269\pi$
$829$	35.3984	1.22944	0.614719	+	0.788746i	$0.289269\pi$
$830$	13.9258	0.483372
$831$	36.4547	1.26460
$832$	−2.87300	−0.0996032
$833$	26.6176	0.922244
$834$	−5.05352	−0.174989
$835$	−10.9001	−0.377215
$836$	−10.8761	−0.376157
$837$	14.3291	0.495287
$838$	3.35966	0.116057
$839$	37.7803	1.30432	0.652160	−	0.758081i	$-0.273863\pi$
$839$	37.7803	1.30432	0.652160	+	0.758081i	$0.273863\pi$
$840$	−0.762815	−0.0263196
$841$	−21.6821	−0.747660
$842$	−30.2611	−1.04287
$843$	−41.8152	−1.44019
$844$	17.1975	0.591963
$845$	4.58556	0.157748
$846$	−2.63789	−0.0906925
$847$	−8.36951	−0.287580
$848$	−1.44502	−0.0496223
$849$	33.8486	1.16168
$850$	15.8999	0.545362
$851$	−19.0209	−0.652029
$852$	4.63816	0.158901
$853$	−7.66979	−0.262609	−0.131304	−	0.991342i	$-0.541917\pi$
$853$	−7.66979	−0.262609	−0.131304	+	0.991342i	$0.541917\pi$
$854$	1.75857	0.0601769
$855$	0.455430	0.0155754
$856$	−7.42727	−0.253859
$857$	−0.0857453	−0.00292900	−0.00146450	−	0.999999i	$-0.500466\pi$
$857$	−0.0857453	−0.00292900	−0.00146450	+	0.999999i	$0.500466\pi$
$858$	28.3502	0.967861
$859$	−51.6913	−1.76369	−0.881843	−	0.471544i	$-0.843697\pi$
$859$	−51.6913	−1.76369	−0.881843	+	0.471544i	$0.843697\pi$
$860$	3.94104	0.134388
$861$	0.345199	0.0117643
$862$	6.62111	0.225516
$863$	27.3571	0.931246	0.465623	−	0.884983i	$-0.345830\pi$
$863$	27.3571	0.931246	0.465623	+	0.884983i	$0.345830\pi$
$864$	4.97040	0.169097
$865$	5.52183	0.187748
$866$	−22.5657	−0.766815
$867$	3.07973	0.104593
$868$	−1.26490	−0.0429335
$869$	−12.8286	−0.435181
$870$	−4.70308	−0.159449
$871$	25.9148	0.878090
$872$	13.2168	0.447579
$873$	2.98155	0.100910
$874$	5.24598	0.177448
$875$	−3.84361	−0.129938
$876$	16.9761	0.573569
$877$	39.2550	1.32555	0.662774	−	0.748819i	$-0.269379\pi$
$877$	39.2550	1.32555	0.662774	+	0.748819i	$0.269379\pi$
$878$	9.16289	0.309232
$879$	21.8763	0.737868
$880$	−5.29882	−0.178623
$881$	−24.0746	−0.811094	−0.405547	−	0.914074i	$-0.632919\pi$
$881$	−24.0746	−0.811094	−0.405547	+	0.914074i	$0.632919\pi$
$882$	−1.61796	−0.0544794
$883$	−29.6110	−0.996490	−0.498245	−	0.867036i	$-0.666022\pi$
$883$	−29.6110	−0.996490	−0.498245	+	0.867036i	$0.666022\pi$
$884$	11.2335	0.377825
$885$	−21.6381	−0.727357
$886$	−2.89832	−0.0973709
$887$	−32.9992	−1.10800	−0.554002	−	0.832515i	$-0.686900\pi$
$887$	−32.9992	−1.10800	−0.554002	+	0.832515i	$0.686900\pi$
$888$	−12.9387	−0.434193
$889$	6.97257	0.233853
$890$	−6.22979	−0.208823
$891$	−52.9573	−1.77414
$892$	1.99607	0.0668335
$893$	22.0112	0.736578
$894$	−23.4223	−0.783360
$895$	−11.2805	−0.377066
$896$	−0.438762	−0.0146580
$897$	−13.6745	−0.456577
$898$	7.49105	0.249979
$899$	−7.79866	−0.260100
$900$	−0.966480	−0.0322160
$901$	5.65011	0.188232
$902$	2.39789	0.0798409
$903$	−3.22020	−0.107161
$904$	−0.412709	−0.0137265
$905$	18.3783	0.610917
$906$	−16.3479	−0.543123
$907$	−38.7010	−1.28505	−0.642523	−	0.766266i	$-0.722112\pi$
$907$	−38.7010	−1.28505	−0.642523	+	0.766266i	$0.722112\pi$
$908$	−18.5008	−0.613970
$909$	−1.55024	−0.0514182
$910$	−1.21797	−0.0403754
$911$	25.4009	0.841571	0.420785	−	0.907160i	$-0.361755\pi$
$911$	25.4009	0.841571	0.420785	+	0.907160i	$0.361755\pi$
$912$	3.56849	0.118164
$913$	−79.0409	−2.61587
$914$	37.2857	1.23330
$915$	−6.96820	−0.230362
$916$	−22.2589	−0.735453
$917$	−6.29900	−0.208011
$918$	−19.4345	−0.641433
$919$	−32.1543	−1.06067	−0.530336	−	0.847788i	$-0.677934\pi$
$919$	−32.1543	−1.06067	−0.530336	+	0.847788i	$0.677934\pi$
$920$	2.55583	0.0842634
$921$	9.64779	0.317906
$922$	17.5626	0.578393
$923$	7.40567	0.243761
$924$	4.32962	0.142434
$925$	−29.2406	−0.961424
$926$	−21.3434	−0.701387
$927$	0.933943	0.0306747
$928$	−2.70516	−0.0888011
$929$	2.33889	0.0767365	0.0383683	−	0.999264i	$-0.487784\pi$
$929$	2.33889	0.0767365	0.0383683	+	0.999264i	$0.487784\pi$
$930$	5.01208	0.164353
$931$	13.5006	0.442466
$932$	11.1692	0.365859
$933$	−31.2897	−1.02438
$934$	−6.41506	−0.209907
$935$	20.7186	0.677571
$936$	−0.682833	−0.0223191
$937$	−6.31421	−0.206276	−0.103138	−	0.994667i	$-0.532888\pi$
$937$	−6.31421	−0.206276	−0.103138	+	0.994667i	$0.532888\pi$
$938$	3.95769	0.129223
$939$	−42.5041	−1.38707
$940$	10.7238	0.349773
$941$	−14.4807	−0.472058	−0.236029	−	0.971746i	$-0.575846\pi$
$941$	−14.4807	−0.472058	−0.236029	+	0.971746i	$0.575846\pi$
$942$	−5.63332	−0.183544
$943$	−1.15660	−0.0376640
$944$	−12.4460	−0.405082
$945$	2.10714	0.0685454
$946$	−22.3688	−0.727271
$947$	−55.4712	−1.80257	−0.901286	−	0.433226i	$-0.857375\pi$
$947$	−55.4712	−1.80257	−0.901286	+	0.433226i	$0.857375\pi$
$948$	4.20912	0.136706
$949$	27.1054	0.879879
$950$	8.06456	0.261649
$951$	−6.85533	−0.222299
$952$	1.71558	0.0556022
$953$	25.1852	0.815830	0.407915	−	0.913020i	$-0.366256\pi$
$953$	25.1852	0.815830	0.407915	+	0.913020i	$0.366256\pi$
$954$	−0.343443	−0.0111194
$955$	−4.10750	−0.132916
$956$	−1.49814	−0.0484533
$957$	26.6940	0.862895
$958$	−26.6221	−0.860122
$959$	−4.99430	−0.161274
$960$	1.73856	0.0561119
$961$	−22.6890	−0.731902
$962$	−20.6589	−0.666071
$963$	−1.76526	−0.0568847
$964$	12.3432	0.397549
$965$	−8.66652	−0.278985
$966$	−2.08835	−0.0671917
$967$	−35.3683	−1.13737	−0.568685	−	0.822556i	$-0.692547\pi$
$967$	−35.3683	−1.13737	−0.568685	+	0.822556i	$0.692547\pi$
$968$	19.0753	0.613104
$969$	−13.9529	−0.448233
$970$	−12.1209	−0.389179
$971$	−27.1420	−0.871030	−0.435515	−	0.900182i	$-0.643434\pi$
$971$	−27.1420	−0.871030	−0.435515	+	0.900182i	$0.643434\pi$
$972$	2.46430	0.0790426
$973$	−1.23227	−0.0395048
$974$	−29.6396	−0.949715
$975$	−21.0215	−0.673228
$976$	−4.00802	−0.128294
$977$	23.9846	0.767334	0.383667	−	0.923472i	$-0.374661\pi$
$977$	23.9846	0.767334	0.383667	+	0.923472i	$0.374661\pi$
$978$	2.76123	0.0882943
$979$	35.3593	1.13009
$980$	6.57750	0.210111
$981$	3.14129	0.100294
$982$	1.27028	0.0405364
$983$	15.0693	0.480635	0.240318	−	0.970694i	$-0.422748\pi$
$983$	15.0693	0.480635	0.240318	+	0.970694i	$0.422748\pi$
$984$	−0.786757	−0.0250809
$985$	−3.83713	−0.122261
$986$	10.5773	0.336849
$987$	−8.76237	−0.278909
$988$	5.69774	0.181269
$989$	10.7894	0.343082
$990$	−1.25939	−0.0400259
$991$	−60.8761	−1.93379	−0.966896	−	0.255169i	$-0.917869\pi$
$991$	−60.8761	−1.93379	−0.966896	+	0.255169i	$0.917869\pi$
$992$	2.88289	0.0915318
$993$	−56.8502	−1.80409
$994$	1.13099	0.0358728
$995$	20.9876	0.665353
$996$	25.9336	0.821738
$997$	−20.3861	−0.645634	−0.322817	−	0.946461i	$-0.604630\pi$
$997$	−20.3861	−0.645634	−0.322817	+	0.946461i	$0.604630\pi$
$998$	34.6567	1.09704
$999$	35.7408	1.13079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.f.1.5	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.f.1.5	✓	11	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.79935 q^{3} +1.00000 q^{4} -0.966216 q^{5} -1.79935 q^{6} -0.438762 q^{7} +1.00000 q^{8} +0.237673 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.79935 q^{3} +1.00000 q^{4} -0.966216 q^{5} -1.79935 q^{6} -0.438762 q^{7} +1.00000 q^{8} +0.237673 q^{9} -0.966216 q^{10} +5.48410 q^{11} -1.79935 q^{12} -2.87300 q^{13} -0.438762 q^{14} +1.73856 q^{15} +1.00000 q^{16} -3.91004 q^{17} +0.237673 q^{18} -1.98321 q^{19} -0.966216 q^{20} +0.789487 q^{21} +5.48410 q^{22} -2.64520 q^{23} -1.79935 q^{24} -4.06643 q^{25} -2.87300 q^{26} +4.97040 q^{27} -0.438762 q^{28} -2.70516 q^{29} +1.73856 q^{30} +2.88289 q^{31} +1.00000 q^{32} -9.86783 q^{33} -3.91004 q^{34} +0.423938 q^{35} +0.237673 q^{36} +7.19073 q^{37} -1.98321 q^{38} +5.16954 q^{39} -0.966216 q^{40} +0.437244 q^{41} +0.789487 q^{42} -4.07884 q^{43} +5.48410 q^{44} -0.229643 q^{45} -2.64520 q^{46} -11.0988 q^{47} -1.79935 q^{48} -6.80749 q^{49} -4.06643 q^{50} +7.03555 q^{51} -2.87300 q^{52} -1.44502 q^{53} +4.97040 q^{54} -5.29882 q^{55} -0.438762 q^{56} +3.56849 q^{57} -2.70516 q^{58} -12.4460 q^{59} +1.73856 q^{60} -4.00802 q^{61} +2.88289 q^{62} -0.104282 q^{63} +1.00000 q^{64} +2.77593 q^{65} -9.86783 q^{66} -9.02014 q^{67} -3.91004 q^{68} +4.75965 q^{69} +0.423938 q^{70} -2.57768 q^{71} +0.237673 q^{72} -9.43455 q^{73} +7.19073 q^{74} +7.31694 q^{75} -1.98321 q^{76} -2.40621 q^{77} +5.16954 q^{78} -2.33924 q^{79} -0.966216 q^{80} -9.65653 q^{81} +0.437244 q^{82} -14.4127 q^{83} +0.789487 q^{84} +3.77794 q^{85} -4.07884 q^{86} +4.86753 q^{87} +5.48410 q^{88} +6.44761 q^{89} -0.229643 q^{90} +1.26056 q^{91} -2.64520 q^{92} -5.18734 q^{93} -11.0988 q^{94} +1.91620 q^{95} -1.79935 q^{96} +12.5447 q^{97} -6.80749 q^{98} +1.30342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9} - 12 q^{10} - 7 q^{11} - 11 q^{12} - 21 q^{13} - 9 q^{14} - 3 q^{15} + 11 q^{16} - 16 q^{17} + 18 q^{18} - 22 q^{19} - 12 q^{20} - q^{21} - 7 q^{22} - 2 q^{23} - 11 q^{24} + 19 q^{25} - 21 q^{26} - 44 q^{27} - 9 q^{28} + 4 q^{29} - 3 q^{30} - 28 q^{31} + 11 q^{32} - 13 q^{33} - 16 q^{34} - 11 q^{35} + 18 q^{36} - 22 q^{37} - 22 q^{38} + 9 q^{39} - 12 q^{40} - 5 q^{41} - q^{42} - 7 q^{43} - 7 q^{44} - 23 q^{45} - 2 q^{46} - 31 q^{47} - 11 q^{48} - 2 q^{49} + 19 q^{50} - 6 q^{51} - 21 q^{52} - 17 q^{53} - 44 q^{54} - 18 q^{55} - 9 q^{56} + 7 q^{57} + 4 q^{58} - 18 q^{59} - 3 q^{60} - 18 q^{61} - 28 q^{62} - 27 q^{63} + 11 q^{64} + 22 q^{65} - 13 q^{66} - 11 q^{67} - 16 q^{68} + 9 q^{69} - 11 q^{70} - 16 q^{71} + 18 q^{72} - 33 q^{73} - 22 q^{74} - 21 q^{75} - 22 q^{76} + 9 q^{78} + 9 q^{79} - 12 q^{80} + 71 q^{81} - 5 q^{82} - 18 q^{83} - q^{84} - 8 q^{85} - 7 q^{86} - 17 q^{87} - 7 q^{88} - 23 q^{90} - 22 q^{91} - 2 q^{92} + 8 q^{93} - 31 q^{94} - 23 q^{95} - 11 q^{96} - 66 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9 - 12 * q^10 - 7 * q^11 - 11 * q^12 - 21 * q^13 - 9 * q^14 - 3 * q^15 + 11 * q^16 - 16 * q^17 + 18 * q^18 - 22 * q^19 - 12 * q^20 - q^21 - 7 * q^22 - 2 * q^23 - 11 * q^24 + 19 * q^25 - 21 * q^26 - 44 * q^27 - 9 * q^28 + 4 * q^29 - 3 * q^30 - 28 * q^31 + 11 * q^32 - 13 * q^33 - 16 * q^34 - 11 * q^35 + 18 * q^36 - 22 * q^37 - 22 * q^38 + 9 * q^39 - 12 * q^40 - 5 * q^41 - q^42 - 7 * q^43 - 7 * q^44 - 23 * q^45 - 2 * q^46 - 31 * q^47 - 11 * q^48 - 2 * q^49 + 19 * q^50 - 6 * q^51 - 21 * q^52 - 17 * q^53 - 44 * q^54 - 18 * q^55 - 9 * q^56 + 7 * q^57 + 4 * q^58 - 18 * q^59 - 3 * q^60 - 18 * q^61 - 28 * q^62 - 27 * q^63 + 11 * q^64 + 22 * q^65 - 13 * q^66 - 11 * q^67 - 16 * q^68 + 9 * q^69 - 11 * q^70 - 16 * q^71 + 18 * q^72 - 33 * q^73 - 22 * q^74 - 21 * q^75 - 22 * q^76 + 9 * q^78 + 9 * q^79 - 12 * q^80 + 71 * q^81 - 5 * q^82 - 18 * q^83 - q^84 - 8 * q^85 - 7 * q^86 - 17 * q^87 - 7 * q^88 - 23 * q^90 - 22 * q^91 - 2 * q^92 + 8 * q^93 - 31 * q^94 - 23 * q^95 - 11 * q^96 - 66 * q^97 - 2 * q^98 - 5 * q^99

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