LMFDB - Embedded newform 983.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.120414 q^{2} -1.94834 q^{3} -1.98550 q^{4} +0.840169 q^{5} +0.234608 q^{6} -0.0546560 q^{7} +0.479911 q^{8} +0.796025 q^{9} +O(q^{10})$	\(q-0.120414 q^{2} -1.94834 q^{3} -1.98550 q^{4} +0.840169 q^{5} +0.234608 q^{6} -0.0546560 q^{7} +0.479911 q^{8} +0.796025 q^{9} -0.101168 q^{10} +0.589353 q^{11} +3.86843 q^{12} +4.51501 q^{13} +0.00658136 q^{14} -1.63693 q^{15} +3.91321 q^{16} -2.29274 q^{17} -0.0958528 q^{18} -4.24034 q^{19} -1.66816 q^{20} +0.106488 q^{21} -0.0709664 q^{22} +3.68884 q^{23} -0.935029 q^{24} -4.29412 q^{25} -0.543671 q^{26} +4.29409 q^{27} +0.108520 q^{28} +2.07092 q^{29} +0.197110 q^{30} +6.16491 q^{31} -1.43103 q^{32} -1.14826 q^{33} +0.276079 q^{34} -0.0459203 q^{35} -1.58051 q^{36} -10.8035 q^{37} +0.510597 q^{38} -8.79676 q^{39} +0.403206 q^{40} -7.43886 q^{41} -0.0128227 q^{42} -0.730770 q^{43} -1.17016 q^{44} +0.668796 q^{45} -0.444188 q^{46} -3.38643 q^{47} -7.62427 q^{48} -6.99701 q^{49} +0.517073 q^{50} +4.46704 q^{51} -8.96455 q^{52} -7.23861 q^{53} -0.517070 q^{54} +0.495156 q^{55} -0.0262300 q^{56} +8.26161 q^{57} -0.249369 q^{58} -7.42398 q^{59} +3.25013 q^{60} -7.21626 q^{61} -0.742343 q^{62} -0.0435076 q^{63} -7.65411 q^{64} +3.79337 q^{65} +0.138267 q^{66} -3.13815 q^{67} +4.55224 q^{68} -7.18710 q^{69} +0.00552946 q^{70} +0.156801 q^{71} +0.382021 q^{72} +3.32512 q^{73} +1.30090 q^{74} +8.36639 q^{75} +8.41919 q^{76} -0.0322117 q^{77} +1.05926 q^{78} +15.0145 q^{79} +3.28776 q^{80} -10.7544 q^{81} +0.895744 q^{82} +4.97774 q^{83} -0.211433 q^{84} -1.92629 q^{85} +0.0879951 q^{86} -4.03486 q^{87} +0.282837 q^{88} -15.9566 q^{89} -0.0805325 q^{90} -0.246772 q^{91} -7.32418 q^{92} -12.0113 q^{93} +0.407774 q^{94} -3.56260 q^{95} +2.78813 q^{96} +5.96849 q^{97} +0.842540 q^{98} +0.469140 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * 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 $

$2$	−0.120414	−0.0851457	−0.0425729	−	0.999093i	$-0.513555\pi$
$2$	−0.120414	−0.0851457	−0.0425729	+	0.999093i	$0.513555\pi$
$3$	−1.94834	−1.12487	−0.562437	−	0.826840i	$-0.690136\pi$
$3$	−1.94834	−1.12487	−0.562437	+	0.826840i	$0.690136\pi$
$4$	−1.98550	−0.992750
$5$	0.840169	0.375735	0.187868	−	0.982194i	$-0.439842\pi$
$5$	0.840169	0.375735	0.187868	+	0.982194i	$0.439842\pi$
$6$	0.234608	0.0957782
$7$	−0.0546560	−0.0206580	−0.0103290	−	0.999947i	$-0.503288\pi$
$7$	−0.0546560	−0.0206580	−0.0103290	+	0.999947i	$0.503288\pi$
$8$	0.479911	0.169674
$9$	0.796025	0.265342
$10$	−0.101168	−0.0319922
$11$	0.589353	0.177697	0.0888483	−	0.996045i	$-0.471681\pi$
$11$	0.589353	0.177697	0.0888483	+	0.996045i	$0.471681\pi$
$12$	3.86843	1.11672
$13$	4.51501	1.25224	0.626119	−	0.779728i	$-0.284642\pi$
$13$	4.51501	1.25224	0.626119	+	0.779728i	$0.284642\pi$
$14$	0.00658136	0.00175894
$15$	−1.63693	−0.422655
$16$	3.91321	0.978303
$17$	−2.29274	−0.556072	−0.278036	−	0.960571i	$-0.589683\pi$
$17$	−2.29274	−0.556072	−0.278036	+	0.960571i	$0.589683\pi$
$18$	−0.0958528	−0.0225927
$19$	−4.24034	−0.972800	−0.486400	−	0.873736i	$-0.661690\pi$
$19$	−4.24034	−0.972800	−0.486400	+	0.873736i	$0.661690\pi$
$20$	−1.66816	−0.373011
$21$	0.106488	0.0232377
$22$	−0.0709664	−0.0151301
$23$	3.68884	0.769175	0.384588	−	0.923088i	$-0.374344\pi$
$23$	3.68884	0.769175	0.384588	+	0.923088i	$0.374344\pi$
$24$	−0.935029	−0.190862
$25$	−4.29412	−0.858823
$26$	−0.543671	−0.106623
$27$	4.29409	0.826398
$28$	0.108520	0.0205083
$29$	2.07092	0.384561	0.192280	−	0.981340i	$-0.438412\pi$
$29$	2.07092	0.384561	0.192280	+	0.981340i	$0.438412\pi$
$30$	0.197110	0.0359872
$31$	6.16491	1.10725	0.553626	−	0.832766i	$-0.313244\pi$
$31$	6.16491	1.10725	0.553626	+	0.832766i	$0.313244\pi$
$32$	−1.43103	−0.252972
$33$	−1.14826	−0.199886
$34$	0.276079	0.0473471
$35$	−0.0459203	−0.00776195
$36$	−1.58051	−0.263418
$37$	−10.8035	−1.77609	−0.888043	−	0.459761i	$-0.847935\pi$
$37$	−10.8035	−1.77609	−0.888043	+	0.459761i	$0.847935\pi$
$38$	0.510597	0.0828297
$39$	−8.79676	−1.40861
$40$	0.403206	0.0637525
$41$	−7.43886	−1.16175	−0.580877	−	0.813991i	$-0.697290\pi$
$41$	−7.43886	−1.16175	−0.580877	+	0.813991i	$0.697290\pi$
$42$	−0.0128227	−0.00197859
$43$	−0.730770	−0.111441	−0.0557207	−	0.998446i	$-0.517746\pi$
$43$	−0.730770	−0.111441	−0.0557207	+	0.998446i	$0.517746\pi$
$44$	−1.17016	−0.176408
$45$	0.668796	0.0996982
$46$	−0.444188	−0.0654920
$47$	−3.38643	−0.493961	−0.246981	−	0.969020i	$-0.579438\pi$
$47$	−3.38643	−0.493961	−0.246981	+	0.969020i	$0.579438\pi$
$48$	−7.62427	−1.10047
$49$	−6.99701	−0.999573
$50$	0.517073	0.0731251
$51$	4.46704	0.625511
$52$	−8.96455	−1.24316
$53$	−7.23861	−0.994299	−0.497150	−	0.867665i	$-0.665620\pi$
$53$	−7.23861	−0.994299	−0.497150	+	0.867665i	$0.665620\pi$
$54$	−0.517070	−0.0703643
$55$	0.495156	0.0667668
$56$	−0.0262300	−0.00350513
$57$	8.26161	1.09428
$58$	−0.249369	−0.0327437
$59$	−7.42398	−0.966520	−0.483260	−	0.875477i	$-0.660547\pi$
$59$	−7.42398	−0.966520	−0.483260	+	0.875477i	$0.660547\pi$
$60$	3.25013	0.419591
$61$	−7.21626	−0.923948	−0.461974	−	0.886894i	$-0.652859\pi$
$61$	−7.21626	−0.923948	−0.461974	+	0.886894i	$0.652859\pi$
$62$	−0.742343	−0.0942777
$63$	−0.0435076	−0.00548144
$64$	−7.65411	−0.956764
$65$	3.79337	0.470510
$66$	0.138267	0.0170195
$67$	−3.13815	−0.383386	−0.191693	−	0.981455i	$-0.561398\pi$
$67$	−3.13815	−0.383386	−0.191693	+	0.981455i	$0.561398\pi$
$68$	4.55224	0.552040
$69$	−7.18710	−0.865225
$70$	0.00552946	0.000660897 0
$71$	0.156801	0.0186088	0.00930442	−	0.999957i	$-0.497038\pi$
$71$	0.156801	0.0186088	0.00930442	+	0.999957i	$0.497038\pi$
$72$	0.382021	0.0450216
$73$	3.32512	0.389175	0.194588	−	0.980885i	$-0.437663\pi$
$73$	3.32512	0.389175	0.194588	+	0.980885i	$0.437663\pi$
$74$	1.30090	0.151226
$75$	8.36639	0.966068
$76$	8.41919	0.965747
$77$	−0.0322117	−0.00367086
$78$	1.05926	0.119937
$79$	15.0145	1.68927	0.844634	−	0.535345i	$-0.179818\pi$
$79$	15.0145	1.68927	0.844634	+	0.535345i	$0.179818\pi$
$80$	3.28776	0.367583
$81$	−10.7544	−1.19494
$82$	0.895744	0.0989184
$83$	4.97774	0.546378	0.273189	−	0.961960i	$-0.411922\pi$
$83$	4.97774	0.546378	0.273189	+	0.961960i	$0.411922\pi$
$84$	−0.211433	−0.0230692
$85$	−1.92629	−0.208936
$86$	0.0879951	0.00948875
$87$	−4.03486	−0.432583
$88$	0.282837	0.0301505
$89$	−15.9566	−1.69140	−0.845700	−	0.533658i	$-0.820817\pi$
$89$	−15.9566	−1.69140	−0.845700	+	0.533658i	$0.820817\pi$
$90$	−0.0805325	−0.00848888
$91$	−0.246772	−0.0258688
$92$	−7.32418	−0.763599
$93$	−12.0113	−1.24552
$94$	0.407774	0.0420587
$95$	−3.56260	−0.365515
$96$	2.78813	0.284562
$97$	5.96849	0.606009	0.303004	−	0.952989i	$-0.402010\pi$
$97$	5.96849	0.606009	0.303004	+	0.952989i	$0.402010\pi$
$98$	0.842540	0.0851094
$99$	0.469140	0.0471503
$100$	8.52597	0.852597
$101$	−13.6245	−1.35569	−0.677843	−	0.735207i	$-0.737085\pi$
$101$	−13.6245	−1.35569	−0.677843	+	0.735207i	$0.737085\pi$
$102$	−0.537895	−0.0532595
$103$	−16.9851	−1.67359	−0.836796	−	0.547515i	$-0.815574\pi$
$103$	−16.9851	−1.67359	−0.836796	+	0.547515i	$0.815574\pi$
$104$	2.16680	0.212472
$105$	0.0894683	0.00873121
$106$	0.871631	0.0846603
$107$	−4.79836	−0.463875	−0.231938	−	0.972731i	$-0.574507\pi$
$107$	−4.79836	−0.463875	−0.231938	+	0.972731i	$0.574507\pi$
$108$	−8.52592	−0.820407
$109$	10.7037	1.02523	0.512613	−	0.858620i	$-0.328678\pi$
$109$	10.7037	1.02523	0.512613	+	0.858620i	$0.328678\pi$
$110$	−0.0596238	−0.00568491
$111$	21.0489	1.99787
$112$	−0.213881	−0.0202098
$113$	14.5569	1.36939	0.684697	−	0.728827i	$-0.259934\pi$
$113$	14.5569	1.36939	0.684697	+	0.728827i	$0.259934\pi$
$114$	−0.994816	−0.0931730
$115$	3.09925	0.289006
$116$	−4.11182	−0.381773
$117$	3.59406	0.332271
$118$	0.893953	0.0822950
$119$	0.125312	0.0114873
$120$	−0.785583	−0.0717136
$121$	−10.6527	−0.968424
$122$	0.868941	0.0786702
$123$	14.4934	1.30683
$124$	−12.2404	−1.09922
$125$	−7.80863	−0.698425
$126$	0.00523893	0.000466721 0
$127$	−12.1869	−1.08142	−0.540708	−	0.841210i	$-0.681844\pi$
$127$	−12.1869	−1.08142	−0.540708	+	0.841210i	$0.681844\pi$
$128$	3.78372	0.334437
$129$	1.42379	0.125357
$130$	−0.456776	−0.0400619
$131$	18.0655	1.57839	0.789194	−	0.614144i	$-0.210499\pi$
$131$	18.0655	1.57839	0.789194	+	0.614144i	$0.210499\pi$
$132$	2.27987	0.198437
$133$	0.231760	0.0200961
$134$	0.377878	0.0326437
$135$	3.60776	0.310507
$136$	−1.10031	−0.0943510
$137$	4.15678	0.355137	0.177569	−	0.984108i	$-0.443177\pi$
$137$	4.15678	0.355137	0.177569	+	0.984108i	$0.443177\pi$
$138$	0.865429	0.0736702
$139$	18.4723	1.56680	0.783400	−	0.621517i	$-0.213483\pi$
$139$	18.4723	1.56680	0.783400	+	0.621517i	$0.213483\pi$
$140$	0.0911748	0.00770567
$141$	6.59791	0.555644
$142$	−0.0188811	−0.00158446
$143$	2.66093	0.222518
$144$	3.11502	0.259585
$145$	1.73993	0.144493
$146$	−0.400391	−0.0331366
$147$	13.6326	1.12439
$148$	21.4504	1.76321
$149$	−11.4922	−0.941480	−0.470740	−	0.882272i	$-0.656013\pi$
$149$	−11.4922	−0.941480	−0.470740	+	0.882272i	$0.656013\pi$
$150$	−1.00743	−0.0822565
$151$	−3.55870	−0.289603	−0.144802	−	0.989461i	$-0.546254\pi$
$151$	−3.55870	−0.289603	−0.144802	+	0.989461i	$0.546254\pi$
$152$	−2.03498	−0.165059
$153$	−1.82508	−0.147549
$154$	0.00387874	0.000312558 0
$155$	5.17957	0.416033
$156$	17.4660	1.39840
$157$	−11.8873	−0.948707	−0.474353	−	0.880335i	$-0.657318\pi$
$157$	−11.8873	−0.948707	−0.474353	+	0.880335i	$0.657318\pi$
$158$	−1.80796	−0.143834
$159$	14.1033	1.11846
$160$	−1.20231	−0.0950506
$161$	−0.201617	−0.0158896
$162$	1.29499	0.101744
$163$	−1.94053	−0.151994	−0.0759972	−	0.997108i	$-0.524214\pi$
$163$	−1.94053	−0.151994	−0.0759972	+	0.997108i	$0.524214\pi$
$164$	14.7699	1.15333
$165$	−0.964732	−0.0751043
$166$	−0.599391	−0.0465218
$167$	−13.6577	−1.05686	−0.528431	−	0.848976i	$-0.677219\pi$
$167$	−13.6577	−1.05686	−0.528431	+	0.848976i	$0.677219\pi$
$168$	0.0511050	0.00394283
$169$	7.38529	0.568099
$170$	0.231953	0.0177900
$171$	−3.37541	−0.258124
$172$	1.45094	0.110633
$173$	24.0139	1.82575	0.912873	−	0.408243i	$-0.133858\pi$
$173$	24.0139	1.82575	0.912873	+	0.408243i	$0.133858\pi$
$174$	0.485855	0.0368326
$175$	0.234699	0.0177416
$176$	2.30626	0.173841
$177$	14.4644	1.08721
$178$	1.92141	0.144015
$179$	−10.5723	−0.790209	−0.395104	−	0.918636i	$-0.629292\pi$
$179$	−10.5723	−0.790209	−0.395104	+	0.918636i	$0.629292\pi$
$180$	−1.32789	−0.0989754
$181$	−14.1573	−1.05230	−0.526152	−	0.850390i	$-0.676366\pi$
$181$	−14.1573	−1.05230	−0.526152	+	0.850390i	$0.676366\pi$
$182$	0.0297149	0.00220261
$183$	14.0597	1.03932
$184$	1.77031	0.130509
$185$	−9.07677	−0.667338
$186$	1.44634	0.106051
$187$	−1.35123	−0.0988120
$188$	6.72375	0.490380
$189$	−0.234698	−0.0170718
$190$	0.428988	0.0311220
$191$	8.84540	0.640031	0.320015	−	0.947412i	$-0.396312\pi$
$191$	8.84540	0.640031	0.320015	+	0.947412i	$0.396312\pi$
$192$	14.9128	1.07624
$193$	−2.42371	−0.174462	−0.0872311	−	0.996188i	$-0.527802\pi$
$193$	−2.42371	−0.174462	−0.0872311	+	0.996188i	$0.527802\pi$
$194$	−0.718692	−0.0515991
$195$	−7.39077	−0.529264
$196$	13.8926	0.992327
$197$	−2.65995	−0.189514	−0.0947569	−	0.995500i	$-0.530207\pi$
$197$	−2.65995	−0.189514	−0.0947569	+	0.995500i	$0.530207\pi$
$198$	−0.0564911	−0.00401465
$199$	11.2780	0.799473	0.399737	−	0.916630i	$-0.369102\pi$
$199$	11.2780	0.799473	0.399737	+	0.916630i	$0.369102\pi$
$200$	−2.06079	−0.145720
$201$	6.11418	0.431261
$202$	1.64058	0.115431
$203$	−0.113188	−0.00794427
$204$	−8.86931	−0.620976
$205$	−6.24990	−0.436512
$206$	2.04525	0.142499
$207$	2.93641	0.204094
$208$	17.6682	1.22507
$209$	−2.49905	−0.172863
$210$	−0.0107733	−0.000743425 0
$211$	2.10056	0.144608	0.0723042	−	0.997383i	$-0.476965\pi$
$211$	2.10056	0.144608	0.0723042	+	0.997383i	$0.476965\pi$
$212$	14.3723	0.987091
$213$	−0.305501	−0.0209326
$214$	0.577791	0.0394970
$215$	−0.613970	−0.0418724
$216$	2.06078	0.140218
$217$	−0.336950	−0.0228736
$218$	−1.28887	−0.0872935
$219$	−6.47846	−0.437773
$220$	−0.983133	−0.0662828
$221$	−10.3517	−0.696334
$222$	−2.53459	−0.170110
$223$	−12.0244	−0.805212	−0.402606	−	0.915373i	$-0.631896\pi$
$223$	−12.0244	−0.805212	−0.402606	+	0.915373i	$0.631896\pi$
$224$	0.0782143	0.00522591
$225$	−3.41822	−0.227882
$226$	−1.75285	−0.116598
$227$	−25.1252	−1.66762	−0.833810	−	0.552052i	$-0.813845\pi$
$227$	−25.1252	−1.66762	−0.833810	+	0.552052i	$0.813845\pi$
$228$	−16.4034	−1.08634
$229$	1.39527	0.0922018	0.0461009	−	0.998937i	$-0.485320\pi$
$229$	1.39527	0.0922018	0.0461009	+	0.998937i	$0.485320\pi$
$230$	−0.373193	−0.0246076
$231$	0.0627592	0.00412925
$232$	0.993859	0.0652501
$233$	0.0560675	0.00367310	0.00183655	−	0.999998i	$-0.499415\pi$
$233$	0.0560675	0.00367310	0.00183655	+	0.999998i	$0.499415\pi$
$234$	−0.432776	−0.0282914
$235$	−2.84517	−0.185599
$236$	14.7403	0.959513
$237$	−29.2534	−1.90021
$238$	−0.0150894	−0.000978098 0
$239$	−5.38711	−0.348463	−0.174232	−	0.984705i	$-0.555744\pi$
$239$	−5.38711	−0.348463	−0.174232	+	0.984705i	$0.555744\pi$
$240$	−6.40567	−0.413484
$241$	−11.7181	−0.754829	−0.377415	−	0.926044i	$-0.623187\pi$
$241$	−11.7181	−0.754829	−0.377415	+	0.926044i	$0.623187\pi$
$242$	1.28273	0.0824571
$243$	8.07098	0.517754
$244$	14.3279	0.917249
$245$	−5.87868	−0.375575
$246$	−1.74521	−0.111271
$247$	−19.1452	−1.21818
$248$	2.95861	0.187872
$249$	−9.69833	−0.614607
$250$	0.940270	0.0594679
$251$	23.7148	1.49686	0.748432	−	0.663211i	$-0.230807\pi$
$251$	23.7148	1.49686	0.748432	+	0.663211i	$0.230807\pi$
$252$	0.0863843	0.00544170
$253$	2.17403	0.136680
$254$	1.46748	0.0920780
$255$	3.75307	0.235026
$256$	14.8526	0.928288
$257$	29.8049	1.85918	0.929590	−	0.368594i	$-0.120161\pi$
$257$	29.8049	1.85918	0.929590	+	0.368594i	$0.120161\pi$
$258$	−0.171444	−0.0106737
$259$	0.590476	0.0366904
$260$	−7.53174	−0.467099
$261$	1.64851	0.102040
$262$	−2.17534	−0.134393
$263$	−4.91043	−0.302790	−0.151395	−	0.988473i	$-0.548377\pi$
$263$	−4.91043	−0.302790	−0.151395	+	0.988473i	$0.548377\pi$
$264$	−0.551062	−0.0339155
$265$	−6.08166	−0.373593
$266$	−0.0279072	−0.00171110
$267$	31.0889	1.90261
$268$	6.23080	0.380606
$269$	13.6728	0.833648	0.416824	−	0.908987i	$-0.363143\pi$
$269$	13.6728	0.833648	0.416824	+	0.908987i	$0.363143\pi$
$270$	−0.434426	−0.0264383
$271$	−27.8024	−1.68887	−0.844437	−	0.535655i	$-0.820065\pi$
$271$	−27.8024	−1.68887	−0.844437	+	0.535655i	$0.820065\pi$
$272$	−8.97199	−0.544007
$273$	0.480796	0.0290991
$274$	−0.500535	−0.0302384
$275$	−2.53075	−0.152610
$276$	14.2700	0.858953
$277$	−15.7068	−0.943730	−0.471865	−	0.881671i	$-0.656419\pi$
$277$	−15.7068	−0.943730	−0.471865	+	0.881671i	$0.656419\pi$
$278$	−2.22433	−0.133406
$279$	4.90743	0.293800
$280$	−0.0220377	−0.00131700
$281$	25.8031	1.53928	0.769642	−	0.638475i	$-0.220435\pi$
$281$	25.8031	1.53928	0.769642	+	0.638475i	$0.220435\pi$
$282$	−0.794482	−0.0473107
$283$	−22.7835	−1.35434	−0.677171	−	0.735826i	$-0.736794\pi$
$283$	−22.7835	−1.35434	−0.677171	+	0.735826i	$0.736794\pi$
$284$	−0.311328	−0.0184739
$285$	6.94115	0.411159
$286$	−0.320414	−0.0189465
$287$	0.406578	0.0239996
$288$	−1.13913	−0.0671241
$289$	−11.7433	−0.690784
$290$	−0.209512	−0.0123030
$291$	−11.6287	−0.681684
$292$	−6.60202	−0.386354
$293$	19.3304	1.12929	0.564647	−	0.825333i	$-0.309012\pi$
$293$	19.3304	1.12929	0.564647	+	0.825333i	$0.309012\pi$
$294$	−1.64155	−0.0957373
$295$	−6.23740	−0.363155
$296$	−5.18472	−0.301356
$297$	2.53073	0.146848
$298$	1.38383	0.0801630
$299$	16.6551	0.963190
$300$	−16.6115	−0.959064
$301$	0.0399409	0.00230216
$302$	0.428519	0.0246585
$303$	26.5451	1.52498
$304$	−16.5933	−0.951693
$305$	−6.06288	−0.347160
$306$	0.219766	0.0125632
$307$	−19.8168	−1.13100	−0.565501	−	0.824748i	$-0.691317\pi$
$307$	−19.8168	−1.13100	−0.565501	+	0.824748i	$0.691317\pi$
$308$	0.0639563	0.00364425
$309$	33.0927	1.88258
$310$	−0.623694	−0.0354234
$311$	26.9323	1.52719	0.763594	−	0.645696i	$-0.223433\pi$
$311$	26.9323	1.52719	0.763594	+	0.645696i	$0.223433\pi$
$312$	−4.22166	−0.239005
$313$	−6.60523	−0.373349	−0.186675	−	0.982422i	$-0.559771\pi$
$313$	−6.60523	−0.373349	−0.186675	+	0.982422i	$0.559771\pi$
$314$	1.43140	0.0807783
$315$	−0.0365537	−0.00205957
$316$	−29.8114	−1.67702
$317$	−24.7298	−1.38896	−0.694481	−	0.719511i	$-0.744366\pi$
$317$	−24.7298	−1.38896	−0.694481	+	0.719511i	$0.744366\pi$
$318$	−1.69823	−0.0952322
$319$	1.22050	0.0683351
$320$	−6.43075	−0.359490
$321$	9.34884	0.521801
$322$	0.0242776	0.00135294
$323$	9.72200	0.540946
$324$	21.3529	1.18627
$325$	−19.3880	−1.07545
$326$	0.233668	0.0129417
$327$	−20.8544	−1.15325
$328$	−3.56999	−0.197120
$329$	0.185089	0.0102043
$330$	0.116167	0.00639481
$331$	10.0936	0.554792	0.277396	−	0.960756i	$-0.410529\pi$
$331$	10.0936	0.554792	0.277396	+	0.960756i	$0.410529\pi$
$332$	−9.88331	−0.542417
$333$	−8.59986	−0.471270
$334$	1.64458	0.0899872
$335$	−2.63658	−0.144052
$336$	0.416712	0.0227335
$337$	4.06860	0.221631	0.110815	−	0.993841i	$-0.464654\pi$
$337$	4.06860	0.221631	0.110815	+	0.993841i	$0.464654\pi$
$338$	−0.889294	−0.0483712
$339$	−28.3617	−1.54040
$340$	3.82465	0.207421
$341$	3.63331	0.196755
$342$	0.406448	0.0219782
$343$	0.765021	0.0413072
$344$	−0.350704	−0.0189087
$345$	−6.03838	−0.325096
$346$	−2.89162	−0.155454
$347$	−14.8985	−0.799794	−0.399897	−	0.916560i	$-0.630954\pi$
$347$	−14.8985	−0.799794	−0.399897	+	0.916560i	$0.630954\pi$
$348$	8.01122	0.429447
$349$	15.8702	0.849515	0.424757	−	0.905307i	$-0.360359\pi$
$349$	15.8702	0.849515	0.424757	+	0.905307i	$0.360359\pi$
$350$	−0.0282611	−0.00151062
$351$	19.3878	1.03485
$352$	−0.843380	−0.0449523
$353$	−7.82470	−0.416467	−0.208233	−	0.978079i	$-0.566771\pi$
$353$	−7.82470	−0.416467	−0.208233	+	0.978079i	$0.566771\pi$
$354$	−1.74172	−0.0925715
$355$	0.131739	0.00699200
$356$	31.6819	1.67914
$357$	−0.244151	−0.0129218
$358$	1.27305	0.0672829
$359$	−6.32783	−0.333970	−0.166985	−	0.985959i	$-0.553403\pi$
$359$	−6.32783	−0.333970	−0.166985	+	0.985959i	$0.553403\pi$
$360$	0.320962	0.0169162
$361$	−1.01954	−0.0536602
$362$	1.70474	0.0895992
$363$	20.7550	1.08936
$364$	0.489966	0.0256812
$365$	2.79366	0.146227
$366$	−1.69299	−0.0884941
$367$	−17.2065	−0.898170	−0.449085	−	0.893489i	$-0.648250\pi$
$367$	−17.2065	−0.898170	−0.449085	+	0.893489i	$0.648250\pi$
$368$	14.4352	0.752487
$369$	−5.92152	−0.308262
$370$	1.09297	0.0568209
$371$	0.395633	0.0205403
$372$	23.8485	1.23649
$373$	−25.4949	−1.32008	−0.660039	−	0.751232i	$-0.729460\pi$
$373$	−25.4949	−1.32008	−0.660039	+	0.751232i	$0.729460\pi$
$374$	0.162708	0.00841342
$375$	15.2139	0.785640
$376$	−1.62518	−0.0838124
$377$	9.35024	0.481562
$378$	0.0282610	0.00145359
$379$	−7.92683	−0.407174	−0.203587	−	0.979057i	$-0.565260\pi$
$379$	−7.92683	−0.407174	−0.203587	+	0.979057i	$0.565260\pi$
$380$	7.07355	0.362865
$381$	23.7443	1.21646
$382$	−1.06511	−0.0544959
$383$	−22.0221	−1.12528	−0.562639	−	0.826703i	$-0.690214\pi$
$383$	−22.0221	−1.12528	−0.562639	+	0.826703i	$0.690214\pi$
$384$	−7.37197	−0.376199
$385$	−0.0270632	−0.00137927
$386$	0.291849	0.0148547
$387$	−0.581711	−0.0295700
$388$	−11.8504	−0.601615
$389$	−6.61993	−0.335644	−0.167822	−	0.985817i	$-0.553673\pi$
$389$	−6.61993	−0.335644	−0.167822	+	0.985817i	$0.553673\pi$
$390$	0.889954	0.0450646
$391$	−8.45755	−0.427717
$392$	−3.35794	−0.169602
$393$	−35.1977	−1.77549
$394$	0.320296	0.0161363
$395$	12.6148	0.634717
$396$	−0.931477	−0.0468085
$397$	−12.0159	−0.603061	−0.301531	−	0.953456i	$-0.597498\pi$
$397$	−12.0159	−0.603061	−0.301531	+	0.953456i	$0.597498\pi$
$398$	−1.35803	−0.0680717
$399$	−0.451547	−0.0226056
$400$	−16.8038	−0.840189
$401$	−37.1908	−1.85722	−0.928609	−	0.371059i	$-0.878995\pi$
$401$	−37.1908	−1.85722	−0.928609	+	0.371059i	$0.878995\pi$
$402$	−0.736234	−0.0367200
$403$	27.8346	1.38654
$404$	27.0514	1.34586
$405$	−9.03553	−0.448979
$406$	0.0136295	0.000676421 0
$407$	−6.36707	−0.315604
$408$	2.14378	0.106133
$409$	26.0336	1.28728	0.643639	−	0.765329i	$-0.277424\pi$
$409$	26.0336	1.28728	0.643639	+	0.765329i	$0.277424\pi$
$410$	0.752577	0.0371671
$411$	−8.09881	−0.399485
$412$	33.7239	1.66146
$413$	0.405765	0.0199664
$414$	−0.353585	−0.0173778
$415$	4.18215	0.205294
$416$	−6.46110	−0.316782
$417$	−35.9903	−1.76245
$418$	0.300922	0.0147186
$419$	31.5532	1.54147	0.770736	−	0.637154i	$-0.219889\pi$
$419$	31.5532	1.54147	0.770736	+	0.637154i	$0.219889\pi$
$420$	−0.177639	−0.00866791
$421$	−17.0191	−0.829461	−0.414730	−	0.909944i	$-0.636124\pi$
$421$	−17.0191	−0.829461	−0.414730	+	0.909944i	$0.636124\pi$
$422$	−0.252937	−0.0123128
$423$	−2.69568	−0.131069
$424$	−3.47389	−0.168707
$425$	9.84530	0.477567
$426$	0.0367867	0.00178232
$427$	0.394412	0.0190869
$428$	9.52715	0.460512
$429$	−5.18440	−0.250305
$430$	0.0739307	0.00356526
$431$	34.1225	1.64362	0.821812	−	0.569759i	$-0.192963\pi$
$431$	34.1225	1.64362	0.821812	+	0.569759i	$0.192963\pi$
$432$	16.8037	0.808468
$433$	−12.1851	−0.585580	−0.292790	−	0.956177i	$-0.594584\pi$
$433$	−12.1851	−0.585580	−0.292790	+	0.956177i	$0.594584\pi$
$434$	0.0405735	0.00194759
$435$	−3.38997	−0.162537
$436$	−21.2521	−1.01779
$437$	−15.6419	−0.748254
$438$	0.780098	0.0372745
$439$	14.8210	0.707369	0.353684	−	0.935365i	$-0.384929\pi$
$439$	14.8210	0.707369	0.353684	+	0.935365i	$0.384929\pi$
$440$	0.237631	0.0113286
$441$	−5.56980	−0.265228
$442$	1.24650	0.0592898
$443$	24.4053	1.15953	0.579765	−	0.814784i	$-0.303144\pi$
$443$	24.4053	1.15953	0.579765	+	0.814784i	$0.303144\pi$
$444$	−41.7926	−1.98339
$445$	−13.4063	−0.635519
$446$	1.44791	0.0685604
$447$	22.3908	1.05905
$448$	0.418343	0.0197648
$449$	−0.0830312	−0.00391848	−0.00195924	−	0.999998i	$-0.500624\pi$
$449$	−0.0830312	−0.00391848	−0.00195924	+	0.999998i	$0.500624\pi$
$450$	0.411603	0.0194031
$451$	−4.38411	−0.206440
$452$	−28.9027	−1.35947
$453$	6.93356	0.325767
$454$	3.02543	0.141991
$455$	−0.207330	−0.00971980
$456$	3.96484	0.185671
$457$	−4.76513	−0.222903	−0.111452	−	0.993770i	$-0.535550\pi$
$457$	−4.76513	−0.222903	−0.111452	+	0.993770i	$0.535550\pi$
$458$	−0.168010	−0.00785059
$459$	−9.84524	−0.459537
$460$	−6.15356	−0.286911
$461$	27.3458	1.27362	0.636809	−	0.771021i	$-0.280254\pi$
$461$	27.3458	1.27362	0.636809	+	0.771021i	$0.280254\pi$
$462$	−0.00755710	−0.000351588 0
$463$	−27.8276	−1.29326	−0.646629	−	0.762805i	$-0.723822\pi$
$463$	−27.8276	−1.29326	−0.646629	+	0.762805i	$0.723822\pi$
$464$	8.10397	0.376217
$465$	−10.0916	−0.467985
$466$	−0.00675132	−0.000312749 0
$467$	24.5453	1.13582	0.567911	−	0.823090i	$-0.307752\pi$
$467$	24.5453	1.13582	0.567911	+	0.823090i	$0.307752\pi$
$468$	−7.13601	−0.329862
$469$	0.171519	0.00792000
$470$	0.342599	0.0158029
$471$	23.1604	1.06718
$472$	−3.56285	−0.163993
$473$	−0.430681	−0.0198027
$474$	3.52253	0.161795
$475$	18.2085	0.835463
$476$	−0.248807	−0.0114041
$477$	−5.76211	−0.263829
$478$	0.648685	0.0296701
$479$	−39.5325	−1.80628	−0.903142	−	0.429342i	$-0.858746\pi$
$479$	−39.5325	−1.80628	−0.903142	+	0.429342i	$0.858746\pi$
$480$	2.34250	0.106920
$481$	−48.7779	−2.22408
$482$	1.41103	0.0642705
$483$	0.392818	0.0178739
$484$	21.1509	0.961403
$485$	5.01455	0.227699
$486$	−0.971861	−0.0440845
$487$	−22.8302	−1.03453	−0.517267	−	0.855824i	$-0.673050\pi$
$487$	−22.8302	−1.03453	−0.517267	+	0.855824i	$0.673050\pi$
$488$	−3.46316	−0.156770
$489$	3.78082	0.170975
$490$	0.707876	0.0319786
$491$	3.09060	0.139477	0.0697385	−	0.997565i	$-0.477784\pi$
$491$	3.09060	0.139477	0.0697385	+	0.997565i	$0.477784\pi$
$492$	−28.7767	−1.29735
$493$	−4.74810	−0.213843
$494$	2.30535	0.103723
$495$	0.394157	0.0177160
$496$	24.1246	1.08323
$497$	−0.00857011	−0.000384422 0
$498$	1.16782	0.0523311
$499$	30.1632	1.35029	0.675146	−	0.737684i	$-0.264081\pi$
$499$	30.1632	1.35029	0.675146	+	0.737684i	$0.264081\pi$
$500$	15.5040	0.693362
$501$	26.6098	1.18884
$502$	−2.85560	−0.127452
$503$	10.2118	0.455321	0.227661	−	0.973741i	$-0.426892\pi$
$503$	10.2118	0.455321	0.227661	+	0.973741i	$0.426892\pi$
$504$	−0.0208798	−0.000930058 0
$505$	−11.4469	−0.509379
$506$	−0.261784	−0.0116377
$507$	−14.3890	−0.639040
$508$	24.1972	1.07358
$509$	4.56787	0.202467	0.101234	−	0.994863i	$-0.467721\pi$
$509$	4.56787	0.202467	0.101234	+	0.994863i	$0.467721\pi$
$510$	−0.451923	−0.0200115
$511$	−0.181738	−0.00803960
$512$	−9.35591	−0.413477
$513$	−18.2084	−0.803920
$514$	−3.58894	−0.158301
$515$	−14.2704	−0.628827
$516$	−2.82693	−0.124449
$517$	−1.99580	−0.0877752
$518$	−0.0711018	−0.00312403
$519$	−46.7873	−2.05373
$520$	1.82048	0.0798333
$521$	39.5518	1.73280	0.866398	−	0.499354i	$-0.166429\pi$
$521$	39.5518	1.73280	0.866398	+	0.499354i	$0.166429\pi$
$522$	−0.198504	−0.00868828
$523$	25.4730	1.11386	0.556929	−	0.830560i	$-0.311979\pi$
$523$	25.4730	1.11386	0.556929	+	0.830560i	$0.311979\pi$
$524$	−35.8690	−1.56694
$525$	−0.457274	−0.0199571
$526$	0.591286	0.0257813
$527$	−14.1346	−0.615711
$528$	−4.49338	−0.195549
$529$	−9.39249	−0.408369
$530$	0.732318	0.0318099
$531$	−5.90968	−0.256458
$532$	−0.460159	−0.0199504
$533$	−33.5865	−1.45479
$534$	−3.74355	−0.161999
$535$	−4.03144	−0.174294
$536$	−1.50603	−0.0650507
$537$	20.5984	0.888886
$538$	−1.64640	−0.0709815
$539$	−4.12371	−0.177621
$540$	−7.16321	−0.308256
$541$	26.8402	1.15395	0.576974	−	0.816762i	$-0.304233\pi$
$541$	26.8402	1.15395	0.576974	+	0.816762i	$0.304233\pi$
$542$	3.34780	0.143800
$543$	27.5832	1.18371
$544$	3.28098	0.140671
$545$	8.99289	0.385213
$546$	−0.0578947	−0.00247766
$547$	26.8046	1.14608	0.573042	−	0.819526i	$-0.305763\pi$
$547$	26.8046	1.14608	0.573042	+	0.819526i	$0.305763\pi$
$548$	−8.25328	−0.352563
$549$	−5.74433	−0.245162
$550$	0.304738	0.0129941
$551$	−8.78142	−0.374101
$552$	−3.44917	−0.146806
$553$	−0.820635	−0.0348969
$554$	1.89132	0.0803545
$555$	17.6846	0.750671
$556$	−36.6768	−1.55544
$557$	40.8521	1.73096	0.865479	−	0.500945i	$-0.167014\pi$
$557$	40.8521	1.73096	0.865479	+	0.500945i	$0.167014\pi$
$558$	−0.590924	−0.0250158
$559$	−3.29943	−0.139551
$560$	−0.179696	−0.00759354
$561$	2.63266	0.111151
$562$	−3.10706	−0.131063
$563$	−31.4955	−1.32738	−0.663688	−	0.748009i	$-0.731010\pi$
$563$	−31.4955	−1.32738	−0.663688	+	0.748009i	$0.731010\pi$
$564$	−13.1002	−0.551616
$565$	12.2302	0.514530
$566$	2.74346	0.115316
$567$	0.587794	0.0246850
$568$	0.0752505	0.00315744
$569$	−7.67533	−0.321766	−0.160883	−	0.986973i	$-0.551434\pi$
$569$	−7.67533	−0.321766	−0.160883	+	0.986973i	$0.551434\pi$
$570$	−0.835814	−0.0350084
$571$	21.0512	0.880964	0.440482	−	0.897761i	$-0.354808\pi$
$571$	21.0512	0.880964	0.440482	+	0.897761i	$0.354808\pi$
$572$	−5.28328	−0.220905
$573$	−17.2338	−0.719954
$574$	−0.0489578	−0.00204346
$575$	−15.8403	−0.660586
$576$	−6.09286	−0.253869
$577$	−37.1539	−1.54674	−0.773369	−	0.633956i	$-0.781430\pi$
$577$	−37.1539	−1.54674	−0.773369	+	0.633956i	$0.781430\pi$
$578$	1.41406	0.0588173
$579$	4.72220	0.196248
$580$	−3.45463	−0.143446
$581$	−0.272064	−0.0112871
$582$	1.40025	0.0580424
$583$	−4.26609	−0.176684
$584$	1.59576	0.0660330
$585$	3.01962	0.124846
$586$	−2.32765	−0.0961545
$587$	−27.0838	−1.11787	−0.558935	−	0.829212i	$-0.688790\pi$
$587$	−27.0838	−1.11787	−0.558935	+	0.829212i	$0.688790\pi$
$588$	−27.0674	−1.11624
$589$	−26.1413	−1.07713
$590$	0.751072	0.0309211
$591$	5.18249	0.213179
$592$	−42.2764	−1.73755
$593$	5.83245	0.239510	0.119755	−	0.992803i	$-0.461789\pi$
$593$	5.83245	0.239510	0.119755	+	0.992803i	$0.461789\pi$
$594$	−0.304736	−0.0125035
$595$	0.105283	0.00431620
$596$	22.8178	0.934655
$597$	−21.9733	−0.899307
$598$	−2.00551	−0.0820115
$599$	−7.11032	−0.290520	−0.145260	−	0.989394i	$-0.546402\pi$
$599$	−7.11032	−0.290520	−0.145260	+	0.989394i	$0.546402\pi$
$600$	4.01512	0.163917
$601$	−45.2759	−1.84684	−0.923422	−	0.383787i	$-0.874620\pi$
$601$	−45.2759	−1.84684	−0.923422	+	0.383787i	$0.874620\pi$
$602$	−0.00480946	−0.000196019 0
$603$	−2.49805	−0.101728
$604$	7.06581	0.287504
$605$	−8.95004	−0.363871
$606$	−3.19641	−0.129845
$607$	4.55321	0.184809	0.0924045	−	0.995722i	$-0.470545\pi$
$607$	4.55321	0.184809	0.0924045	+	0.995722i	$0.470545\pi$
$608$	6.06804	0.246092
$609$	0.220529	0.00893631
$610$	0.730057	0.0295592
$611$	−15.2897	−0.618557
$612$	3.62370	0.146479
$613$	46.3970	1.87396	0.936978	−	0.349389i	$-0.113611\pi$
$613$	46.3970	1.87396	0.936978	+	0.349389i	$0.113611\pi$
$614$	2.38622	0.0963000
$615$	12.1769	0.491021
$616$	−0.0154587	−0.000622850 0
$617$	−19.7618	−0.795582	−0.397791	−	0.917476i	$-0.630223\pi$
$617$	−19.7618	−0.795582	−0.397791	+	0.917476i	$0.630223\pi$
$618$	−3.98484	−0.160294
$619$	−39.0741	−1.57052	−0.785260	−	0.619166i	$-0.787471\pi$
$619$	−39.0741	−1.57052	−0.785260	+	0.619166i	$0.787471\pi$
$620$	−10.2840	−0.413017
$621$	15.8402	0.635645
$622$	−3.24303	−0.130034
$623$	0.872126	0.0349410
$624$	−34.4236	−1.37805
$625$	14.9100	0.596400
$626$	0.795363	0.0317891
$627$	4.86900	0.194449
$628$	23.6022	0.941829
$629$	24.7697	0.987631
$630$	0.00440159	0.000175363 0
$631$	20.2311	0.805387	0.402694	−	0.915335i	$-0.368074\pi$
$631$	20.2311	0.805387	0.402694	+	0.915335i	$0.368074\pi$
$632$	7.20564	0.286625
$633$	−4.09260	−0.162666
$634$	2.97782	0.118264
$635$	−10.2391	−0.406326
$636$	−28.0020	−1.11035
$637$	−31.5916	−1.25170
$638$	−0.146966	−0.00581845
$639$	0.124817	0.00493770
$640$	3.17897	0.125660
$641$	−12.2556	−0.484066	−0.242033	−	0.970268i	$-0.577814\pi$
$641$	−12.2556	−0.484066	−0.242033	+	0.970268i	$0.577814\pi$
$642$	−1.12573	−0.0444292
$643$	8.97224	0.353831	0.176915	−	0.984226i	$-0.443388\pi$
$643$	8.97224	0.353831	0.176915	+	0.984226i	$0.443388\pi$
$644$	0.400311	0.0157744
$645$	1.19622	0.0471012
$646$	−1.17067	−0.0460593
$647$	23.6836	0.931098	0.465549	−	0.885022i	$-0.345857\pi$
$647$	23.6836	0.931098	0.465549	+	0.885022i	$0.345857\pi$
$648$	−5.16116	−0.202750
$649$	−4.37534	−0.171747
$650$	2.33459	0.0915700
$651$	0.656492	0.0257299
$652$	3.85293	0.150892
$653$	−1.65246	−0.0646656	−0.0323328	−	0.999477i	$-0.510294\pi$
$653$	−1.65246	−0.0646656	−0.0323328	+	0.999477i	$0.510294\pi$
$654$	2.51116	0.0981942
$655$	15.1781	0.593056
$656$	−29.1098	−1.13655
$657$	2.64688	0.103264
$658$	−0.0222873	−0.000868849 0
$659$	−10.3144	−0.401793	−0.200896	−	0.979613i	$-0.564385\pi$
$659$	−10.3144	−0.401793	−0.200896	+	0.979613i	$0.564385\pi$
$660$	1.91548	0.0745598
$661$	3.56452	0.138644	0.0693218	−	0.997594i	$-0.477916\pi$
$661$	3.56452	0.138644	0.0693218	+	0.997594i	$0.477916\pi$
$662$	−1.21541	−0.0472382
$663$	20.1687	0.783288
$664$	2.38887	0.0927063
$665$	0.194718	0.00755082
$666$	1.03555	0.0401266
$667$	7.63930	0.295795
$668$	27.1173	1.04920
$669$	23.4276	0.905763
$670$	0.317481	0.0122654
$671$	−4.25292	−0.164182
$672$	−0.152388	−0.00587849
$673$	−30.0717	−1.15918	−0.579589	−	0.814909i	$-0.696787\pi$
$673$	−30.0717	−1.15918	−0.579589	+	0.814909i	$0.696787\pi$
$674$	−0.489918	−0.0188709
$675$	−18.4393	−0.709730
$676$	−14.6635	−0.563981
$677$	−12.3134	−0.473242	−0.236621	−	0.971602i	$-0.576040\pi$
$677$	−12.3134	−0.473242	−0.236621	+	0.971602i	$0.576040\pi$
$678$	3.41515	0.131158
$679$	−0.326214	−0.0125189
$680$	−0.924448	−0.0354510
$681$	48.9525	1.87586
$682$	−0.437502	−0.0167528
$683$	25.5988	0.979512	0.489756	−	0.871859i	$-0.337086\pi$
$683$	25.5988	0.979512	0.489756	+	0.871859i	$0.337086\pi$
$684$	6.70189	0.256253
$685$	3.49240	0.133438
$686$	−0.0921194	−0.00351713
$687$	−2.71845	−0.103715
$688$	−2.85966	−0.109023
$689$	−32.6824	−1.24510
$690$	0.727107	0.0276805
$691$	36.9047	1.40392	0.701961	−	0.712215i	$-0.252308\pi$
$691$	36.9047	1.40392	0.701961	+	0.712215i	$0.252308\pi$
$692$	−47.6797	−1.81251
$693$	−0.0256413	−0.000974032 0
$694$	1.79399	0.0680991
$695$	15.5199	0.588702
$696$	−1.93637	−0.0733981
$697$	17.0554	0.646019
$698$	−1.91100	−0.0723325
$699$	−0.109239	−0.00413178
$700$	−0.465995	−0.0176130
$701$	39.8211	1.50402	0.752010	−	0.659151i	$-0.229084\pi$
$701$	39.8211	1.50402	0.752010	+	0.659151i	$0.229084\pi$
$702$	−2.33457	−0.0881128
$703$	45.8105	1.72778
$704$	−4.51097	−0.170014
$705$	5.54336	0.208775
$706$	0.942205	0.0354604
$707$	0.744659	0.0280058
$708$	−28.7191	−1.07933
$709$	−2.24795	−0.0844235	−0.0422118	−	0.999109i	$-0.513440\pi$
$709$	−2.24795	−0.0844235	−0.0422118	+	0.999109i	$0.513440\pi$
$710$	−0.0158633	−0.000595338 0
$711$	11.9520	0.448233
$712$	−7.65777	−0.286987
$713$	22.7414	0.851670
$714$	0.0293992	0.00110024
$715$	2.23563	0.0836079
$716$	20.9913	0.784480
$717$	10.4959	0.391977
$718$	0.761960	0.0284361
$719$	43.6084	1.62632	0.813159	−	0.582041i	$-0.197746\pi$
$719$	43.6084	1.62632	0.813159	+	0.582041i	$0.197746\pi$
$720$	2.61714	0.0975351
$721$	0.928338	0.0345731
$722$	0.122768	0.00456894
$723$	22.8308	0.849088
$724$	28.1093	1.04468
$725$	−8.89279	−0.330270
$726$	−2.49920	−0.0927539
$727$	7.00243	0.259706	0.129853	−	0.991533i	$-0.458550\pi$
$727$	7.00243	0.259706	0.129853	+	0.991533i	$0.458550\pi$
$728$	−0.118429	−0.00438926
$729$	16.5382	0.612528
$730$	−0.336397	−0.0124506
$731$	1.67547	0.0619694
$732$	−27.9156	−1.03179
$733$	−27.7271	−1.02412	−0.512062	−	0.858949i	$-0.671118\pi$
$733$	−27.7271	−1.02412	−0.512062	+	0.858949i	$0.671118\pi$
$734$	2.07190	0.0764753
$735$	11.4537	0.422474
$736$	−5.27883	−0.194580
$737$	−1.84948	−0.0681263
$738$	0.713035	0.0262472
$739$	−6.02316	−0.221565	−0.110783	−	0.993845i	$-0.535336\pi$
$739$	−6.02316	−0.221565	−0.110783	+	0.993845i	$0.535336\pi$
$740$	18.0219	0.662500
$741$	37.3012	1.37030
$742$	−0.0476399	−0.00174892
$743$	20.4659	0.750820	0.375410	−	0.926859i	$-0.377502\pi$
$743$	20.4659	0.750820	0.375410	+	0.926859i	$0.377502\pi$
$744$	−5.76437	−0.211332
$745$	−9.65542	−0.353747
$746$	3.06995	0.112399
$747$	3.96241	0.144977
$748$	2.68288	0.0980956
$749$	0.262259	0.00958275
$750$	−1.83197	−0.0668939
$751$	41.4100	1.51107	0.755537	−	0.655106i	$-0.227376\pi$
$751$	41.4100	1.51107	0.755537	+	0.655106i	$0.227376\pi$
$752$	−13.2518	−0.483244
$753$	−46.2045	−1.68378
$754$	−1.12590	−0.0410029
$755$	−2.98991	−0.108814
$756$	0.465993	0.0169480
$757$	3.45982	0.125749	0.0628746	−	0.998021i	$-0.479973\pi$
$757$	3.45982	0.125749	0.0628746	+	0.998021i	$0.479973\pi$
$758$	0.954503	0.0346691
$759$	−4.23574	−0.153748
$760$	−1.70973	−0.0620185
$761$	3.84565	0.139405	0.0697023	−	0.997568i	$-0.477795\pi$
$761$	3.84565	0.139405	0.0697023	+	0.997568i	$0.477795\pi$
$762$	−2.85915	−0.103576
$763$	−0.585019	−0.0211791
$764$	−17.5625	−0.635391
$765$	−1.53338	−0.0554393
$766$	2.65178	0.0958125
$767$	−33.5193	−1.21031
$768$	−28.9379	−1.04421
$769$	26.3384	0.949788	0.474894	−	0.880043i	$-0.342486\pi$
$769$	26.3384	0.949788	0.474894	+	0.880043i	$0.342486\pi$
$770$	0.00325880	0.000117439 0
$771$	−58.0701	−2.09134
$772$	4.81227	0.173197
$773$	−30.6672	−1.10302	−0.551511	−	0.834168i	$-0.685948\pi$
$773$	−30.6672	−1.10302	−0.551511	+	0.834168i	$0.685948\pi$
$774$	0.0700463	0.00251776
$775$	−26.4729	−0.950933
$776$	2.86435	0.102824
$777$	−1.15045	−0.0412721
$778$	0.797134	0.0285786
$779$	31.5433	1.13015
$780$	14.6744	0.525427
$781$	0.0924110	0.00330673
$782$	1.01841	0.0364182
$783$	8.89274	0.317800
$784$	−27.3808	−0.977886
$785$	−9.98731	−0.356462
$786$	4.23830	0.151175
$787$	28.9590	1.03228	0.516138	−	0.856505i	$-0.327369\pi$
$787$	28.9590	1.03228	0.516138	+	0.856505i	$0.327369\pi$
$788$	5.28134	0.188140
$789$	9.56719	0.340601
$790$	−1.51900	−0.0540434
$791$	−0.795620	−0.0282890
$792$	0.225145	0.00800019
$793$	−32.5815	−1.15700
$794$	1.44689	0.0513481
$795$	11.8491	0.420245
$796$	−22.3924	−0.793677
$797$	13.8538	0.490726	0.245363	−	0.969431i	$-0.421093\pi$
$797$	13.8538	0.490726	0.245363	+	0.969431i	$0.421093\pi$
$798$	0.0543727	0.00192477
$799$	7.76421	0.274678
$800$	6.14500	0.217259
$801$	−12.7019	−0.448799
$802$	4.47830	0.158134
$803$	1.95967	0.0691551
$804$	−12.1397	−0.428134
$805$	−0.169392	−0.00597030
$806$	−3.35169	−0.118058
$807$	−26.6393	−0.937749
$808$	−6.53853	−0.230025
$809$	4.45170	0.156513	0.0782567	−	0.996933i	$-0.475065\pi$
$809$	4.45170	0.156513	0.0782567	+	0.996933i	$0.475065\pi$
$810$	1.08801	0.0382287
$811$	29.5055	1.03608	0.518039	−	0.855357i	$-0.326662\pi$
$811$	29.5055	1.03608	0.518039	+	0.855357i	$0.326662\pi$
$812$	0.224736	0.00788668
$813$	54.1684	1.89977
$814$	0.766686	0.0268723
$815$	−1.63038	−0.0571096
$816$	17.4805	0.611939
$817$	3.09871	0.108410
$818$	−3.13482	−0.109606
$819$	−0.196437	−0.00686406
$820$	12.4092	0.433347
$821$	50.2150	1.75252	0.876258	−	0.481842i	$-0.160032\pi$
$821$	50.2150	1.75252	0.876258	+	0.481842i	$0.160032\pi$
$822$	0.975212	0.0340144
$823$	−6.17290	−0.215174	−0.107587	−	0.994196i	$-0.534312\pi$
$823$	−6.17290	−0.215174	−0.107587	+	0.994196i	$0.534312\pi$
$824$	−8.15134	−0.283965
$825$	4.93076	0.171667
$826$	−0.0488599	−0.00170005
$827$	−11.0194	−0.383182	−0.191591	−	0.981475i	$-0.561365\pi$
$827$	−11.0194	−0.383182	−0.191591	+	0.981475i	$0.561365\pi$
$828$	−5.83024	−0.202615
$829$	−25.1800	−0.874538	−0.437269	−	0.899331i	$-0.644054\pi$
$829$	−25.1800	−0.874538	−0.437269	+	0.899331i	$0.644054\pi$
$830$	−0.503590	−0.0174799
$831$	30.6022	1.06158
$832$	−34.5584	−1.19810
$833$	16.0423	0.555834
$834$	4.33375	0.150065
$835$	−11.4747	−0.397100
$836$	4.96187	0.171610
$837$	26.4727	0.915030
$838$	−3.79945	−0.131250
$839$	30.2986	1.04602	0.523012	−	0.852326i	$-0.324808\pi$
$839$	30.2986	1.04602	0.523012	+	0.852326i	$0.324808\pi$
$840$	0.0429368	0.00148146
$841$	−24.7113	−0.852113
$842$	2.04934	0.0706250
$843$	−50.2732	−1.73150
$844$	−4.17066	−0.143560
$845$	6.20489	0.213455
$846$	0.324598	0.0111599
$847$	0.582232	0.0200057
$848$	−28.3262	−0.972726
$849$	44.3901	1.52346
$850$	−1.18551	−0.0406628
$851$	−39.8524	−1.36612
$852$	0.606573	0.0207808
$853$	−30.1975	−1.03394	−0.516971	−	0.856003i	$-0.672941\pi$
$853$	−30.1975	−1.03394	−0.516971	+	0.856003i	$0.672941\pi$
$854$	−0.0474928	−0.00162517
$855$	−2.83592	−0.0969864
$856$	−2.30279	−0.0787077
$857$	14.3740	0.491005	0.245503	−	0.969396i	$-0.421047\pi$
$857$	14.3740	0.491005	0.245503	+	0.969396i	$0.421047\pi$
$858$	0.624275	0.0213124
$859$	−22.1502	−0.755756	−0.377878	−	0.925855i	$-0.623346\pi$
$859$	−22.1502	−0.755756	−0.377878	+	0.925855i	$0.623346\pi$
$860$	1.21904	0.0415689
$861$	−0.792152	−0.0269965
$862$	−4.10884	−0.139948
$863$	39.5575	1.34655	0.673276	−	0.739391i	$-0.264887\pi$
$863$	39.5575	1.34655	0.673276	+	0.739391i	$0.264887\pi$
$864$	−6.14496	−0.209056
$865$	20.1758	0.685997
$866$	1.46726	0.0498597
$867$	22.8800	0.777045
$868$	0.669013	0.0227078
$869$	8.84886	0.300177
$870$	0.408200	0.0138393
$871$	−14.1688	−0.480090
$872$	5.13681	0.173954
$873$	4.75107	0.160799
$874$	1.88351	0.0637106
$875$	0.426789	0.0144281
$876$	12.8630	0.434600
$877$	17.4737	0.590046	0.295023	−	0.955490i	$-0.404673\pi$
$877$	17.4737	0.590046	0.295023	+	0.955490i	$0.404673\pi$
$878$	−1.78466	−0.0602294
$879$	−37.6621	−1.27031
$880$	1.93765	0.0653182
$881$	44.6426	1.50405	0.752023	−	0.659136i	$-0.229078\pi$
$881$	44.6426	1.50405	0.752023	+	0.659136i	$0.229078\pi$
$882$	0.670683	0.0225831
$883$	−9.35907	−0.314958	−0.157479	−	0.987522i	$-0.550337\pi$
$883$	−9.35907	−0.314958	−0.157479	+	0.987522i	$0.550337\pi$
$884$	20.5534	0.691286
$885$	12.1526	0.408504
$886$	−2.93874	−0.0987290
$887$	−30.8615	−1.03623	−0.518114	−	0.855312i	$-0.673366\pi$
$887$	−30.8615	−1.03623	−0.518114	+	0.855312i	$0.673366\pi$
$888$	10.1016	0.338987
$889$	0.666090	0.0223399
$890$	1.61431	0.0541117
$891$	−6.33815	−0.212336
$892$	23.8744	0.799375
$893$	14.3596	0.480525
$894$	−2.69617	−0.0901733
$895$	−8.88250	−0.296909
$896$	−0.206803	−0.00690880
$897$	−32.4498	−1.08347
$898$	0.00999814	0.000333642 0
$899$	12.7671	0.425806
$900$	6.78689	0.226230
$901$	16.5963	0.552902
$902$	0.527909	0.0175775
$903$	−0.0778185	−0.00258964
$904$	6.98600	0.232351
$905$	−11.8945	−0.395388
$906$	−0.834899	−0.0277377
$907$	34.1043	1.13241	0.566207	−	0.824263i	$-0.308410\pi$
$907$	34.1043	1.13241	0.566207	+	0.824263i	$0.308410\pi$
$908$	49.8861	1.65553
$909$	−10.8454	−0.359720
$910$	0.0249655	0.000827599 0
$911$	−55.6955	−1.84527	−0.922637	−	0.385670i	$-0.873970\pi$
$911$	−55.6955	−1.84527	−0.922637	+	0.385670i	$0.873970\pi$
$912$	32.3295	1.07054
$913$	2.93365	0.0970895
$914$	0.573789	0.0189793
$915$	11.8126	0.390511
$916$	−2.77030	−0.0915333
$917$	−0.987387	−0.0326064
$918$	1.18551	0.0391276
$919$	−15.0276	−0.495713	−0.247857	−	0.968797i	$-0.579726\pi$
$919$	−15.0276	−0.495713	−0.247857	+	0.968797i	$0.579726\pi$
$920$	1.48736	0.0490369
$921$	38.6098	1.27223
$922$	−3.29282	−0.108443
$923$	0.707957	0.0233027
$924$	−0.124608	−0.00409932
$925$	46.3915	1.52534
$926$	3.35084	0.110115
$927$	−13.5206	−0.444074
$928$	−2.96355	−0.0972833
$929$	−32.7054	−1.07303	−0.536514	−	0.843891i	$-0.680259\pi$
$929$	−32.7054	−1.07303	−0.536514	+	0.843891i	$0.680259\pi$
$930$	1.21517	0.0398469
$931$	29.6697	0.972385
$932$	−0.111322	−0.00364648
$933$	−52.4732	−1.71790
$934$	−2.95560	−0.0967103
$935$	−1.13527	−0.0371271
$936$	1.72483	0.0563778
$937$	33.6986	1.10089	0.550443	−	0.834873i	$-0.314459\pi$
$937$	33.6986	1.10089	0.550443	+	0.834873i	$0.314459\pi$
$938$	−0.0206533	−0.000674354 0
$939$	12.8692	0.419971
$940$	5.64909	0.184253
$941$	−4.62358	−0.150724	−0.0753622	−	0.997156i	$-0.524011\pi$
$941$	−4.62358	−0.150724	−0.0753622	+	0.997156i	$0.524011\pi$
$942$	−2.78884	−0.0908654
$943$	−27.4407	−0.893593
$944$	−29.0516	−0.945549
$945$	−0.197186	−0.00641446
$946$	0.0518601	0.00168612
$947$	5.57063	0.181021	0.0905106	−	0.995895i	$-0.471150\pi$
$947$	5.57063	0.181021	0.0905106	+	0.995895i	$0.471150\pi$
$948$	58.0827	1.88644
$949$	15.0129	0.487340
$950$	−2.19256	−0.0711361
$951$	48.1820	1.56241
$952$	0.0601387	0.00194911
$953$	5.10823	0.165472	0.0827360	−	0.996572i	$-0.473634\pi$
$953$	5.10823	0.165472	0.0827360	+	0.996572i	$0.473634\pi$
$954$	0.693840	0.0224639
$955$	7.43163	0.240482
$956$	10.6961	0.345937
$957$	−2.37796	−0.0768684
$958$	4.76027	0.153797
$959$	−0.227193	−0.00733644
$960$	12.5293	0.404381
$961$	7.00616	0.226005
$962$	5.87355	0.189371
$963$	−3.81962	−0.123085
$964$	23.2663	0.749357
$965$	−2.03632	−0.0655516
$966$	−0.0473009	−0.00152188
$967$	−28.6123	−0.920109	−0.460055	−	0.887891i	$-0.652170\pi$
$967$	−28.6123	−0.920109	−0.460055	+	0.887891i	$0.652170\pi$
$968$	−5.11233	−0.164316
$969$	−18.9418	−0.608497
$970$	−0.603823	−0.0193876
$971$	39.1682	1.25697	0.628483	−	0.777823i	$-0.283676\pi$
$971$	39.1682	1.25697	0.628483	+	0.777823i	$0.283676\pi$
$972$	−16.0249	−0.514000
$973$	−1.00962	−0.0323670
$974$	2.74908	0.0880861
$975$	37.7743	1.20975
$976$	−28.2388	−0.903901
$977$	−21.2118	−0.678624	−0.339312	−	0.940674i	$-0.610194\pi$
$977$	−21.2118	−0.678624	−0.339312	+	0.940674i	$0.610194\pi$
$978$	−0.455264	−0.0145578
$979$	−9.40409	−0.300556
$980$	11.6721	0.372852
$981$	8.52039	0.272035
$982$	−0.372153	−0.0118759
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	6.95555	0.221735
$985$	−2.23481	−0.0712070
$986$	0.571738	0.0182079
$987$	−0.360615	−0.0114785
$988$	38.0127	1.20935
$989$	−2.69569	−0.0857179
$990$	−0.0474621	−0.00150844
$991$	−37.7577	−1.19941	−0.599707	−	0.800220i	$-0.704716\pi$
$991$	−37.7577	−1.19941	−0.599707	+	0.800220i	$0.704716\pi$
$992$	−8.82217	−0.280104
$993$	−19.6657	−0.624071
$994$	0.00103196	3.27319e−5 0
$995$	9.47539	0.300390
$996$	19.2560	0.610151
$997$	48.1175	1.52390	0.761948	−	0.647638i	$-0.224243\pi$
$997$	48.1175	1.52390	0.761948	+	0.647638i	$0.224243\pi$
$998$	−3.63208	−0.114972
$999$	−46.3912	−1.46775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.a.1.16	✓	28
3.2	odd	2		8847.2.a.b.1.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.a.1.16	✓	28	1.1	even	1	trivial
8847.2.a.b.1.13		28	3.2	odd	2

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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-0.120414 q^{2} -1.94834 q^{3} -1.98550 q^{4} +0.840169 q^{5} +0.234608 q^{6} -0.0546560 q^{7} +0.479911 q^{8} +0.796025 q^{9} +O(q^{10})\)	\(q-0.120414 q^{2} -1.94834 q^{3} -1.98550 q^{4} +0.840169 q^{5} +0.234608 q^{6} -0.0546560 q^{7} +0.479911 q^{8} +0.796025 q^{9} -0.101168 q^{10} +0.589353 q^{11} +3.86843 q^{12} +4.51501 q^{13} +0.00658136 q^{14} -1.63693 q^{15} +3.91321 q^{16} -2.29274 q^{17} -0.0958528 q^{18} -4.24034 q^{19} -1.66816 q^{20} +0.106488 q^{21} -0.0709664 q^{22} +3.68884 q^{23} -0.935029 q^{24} -4.29412 q^{25} -0.543671 q^{26} +4.29409 q^{27} +0.108520 q^{28} +2.07092 q^{29} +0.197110 q^{30} +6.16491 q^{31} -1.43103 q^{32} -1.14826 q^{33} +0.276079 q^{34} -0.0459203 q^{35} -1.58051 q^{36} -10.8035 q^{37} +0.510597 q^{38} -8.79676 q^{39} +0.403206 q^{40} -7.43886 q^{41} -0.0128227 q^{42} -0.730770 q^{43} -1.17016 q^{44} +0.668796 q^{45} -0.444188 q^{46} -3.38643 q^{47} -7.62427 q^{48} -6.99701 q^{49} +0.517073 q^{50} +4.46704 q^{51} -8.96455 q^{52} -7.23861 q^{53} -0.517070 q^{54} +0.495156 q^{55} -0.0262300 q^{56} +8.26161 q^{57} -0.249369 q^{58} -7.42398 q^{59} +3.25013 q^{60} -7.21626 q^{61} -0.742343 q^{62} -0.0435076 q^{63} -7.65411 q^{64} +3.79337 q^{65} +0.138267 q^{66} -3.13815 q^{67} +4.55224 q^{68} -7.18710 q^{69} +0.00552946 q^{70} +0.156801 q^{71} +0.382021 q^{72} +3.32512 q^{73} +1.30090 q^{74} +8.36639 q^{75} +8.41919 q^{76} -0.0322117 q^{77} +1.05926 q^{78} +15.0145 q^{79} +3.28776 q^{80} -10.7544 q^{81} +0.895744 q^{82} +4.97774 q^{83} -0.211433 q^{84} -1.92629 q^{85} +0.0879951 q^{86} -4.03486 q^{87} +0.282837 q^{88} -15.9566 q^{89} -0.0805325 q^{90} -0.246772 q^{91} -7.32418 q^{92} -12.0113 q^{93} +0.407774 q^{94} -3.56260 q^{95} +2.78813 q^{96} +5.96849 q^{97} +0.842540 q^{98} +0.469140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

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