LMFDB - Embedded newform 1003.2.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 $ x^16 - 6x^15 - 5x^14 + 90x^13 - 82x^12 - 456x^11 + 723x^10 + 951x^9 - 2105x^8 - 695x^7 + 2641x^6 - 151x^5 - 1323x^4 + 301x^3 + 179x^2 - 50*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-1.94258$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.94258 q^{2} -1.53769 q^{3} +1.77364 q^{4} +1.30751 q^{5} -2.98709 q^{6} -3.17249 q^{7} -0.439731 q^{8} -0.635509 q^{9} +O(q^{10})$	\(q+1.94258 q^{2} -1.53769 q^{3} +1.77364 q^{4} +1.30751 q^{5} -2.98709 q^{6} -3.17249 q^{7} -0.439731 q^{8} -0.635509 q^{9} +2.53995 q^{10} +2.42711 q^{11} -2.72730 q^{12} -5.43840 q^{13} -6.16284 q^{14} -2.01055 q^{15} -4.40149 q^{16} +1.00000 q^{17} -1.23453 q^{18} +2.44008 q^{19} +2.31905 q^{20} +4.87831 q^{21} +4.71487 q^{22} -8.76953 q^{23} +0.676170 q^{24} -3.29042 q^{25} -10.5646 q^{26} +5.59029 q^{27} -5.62685 q^{28} +2.08653 q^{29} -3.90566 q^{30} -3.49533 q^{31} -7.67080 q^{32} -3.73215 q^{33} +1.94258 q^{34} -4.14807 q^{35} -1.12716 q^{36} -8.01933 q^{37} +4.74007 q^{38} +8.36257 q^{39} -0.574953 q^{40} +0.176554 q^{41} +9.47654 q^{42} +9.91662 q^{43} +4.30482 q^{44} -0.830935 q^{45} -17.0356 q^{46} +0.618326 q^{47} +6.76812 q^{48} +3.06472 q^{49} -6.39191 q^{50} -1.53769 q^{51} -9.64574 q^{52} +8.02133 q^{53} +10.8596 q^{54} +3.17348 q^{55} +1.39504 q^{56} -3.75209 q^{57} +4.05327 q^{58} +1.00000 q^{59} -3.56598 q^{60} -11.5154 q^{61} -6.78998 q^{62} +2.01615 q^{63} -6.09821 q^{64} -7.11077 q^{65} -7.25001 q^{66} +2.62865 q^{67} +1.77364 q^{68} +13.4848 q^{69} -8.05798 q^{70} +5.17178 q^{71} +0.279453 q^{72} -12.2525 q^{73} -15.5782 q^{74} +5.05964 q^{75} +4.32782 q^{76} -7.70000 q^{77} +16.2450 q^{78} -10.0919 q^{79} -5.75499 q^{80} -6.68960 q^{81} +0.342972 q^{82} +6.17477 q^{83} +8.65235 q^{84} +1.30751 q^{85} +19.2639 q^{86} -3.20844 q^{87} -1.06728 q^{88} +16.0123 q^{89} -1.61416 q^{90} +17.2533 q^{91} -15.5540 q^{92} +5.37474 q^{93} +1.20115 q^{94} +3.19044 q^{95} +11.7953 q^{96} -11.3748 q^{97} +5.95347 q^{98} -1.54245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * 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 $

$2$	1.94258	1.37361	0.686807	−	0.726839i	$-0.259012\pi$
$2$	1.94258	1.37361	0.686807	+	0.726839i	$0.259012\pi$
$3$	−1.53769	−0.887786	−0.443893	−	0.896080i	$-0.646403\pi$
$3$	−1.53769	−0.887786	−0.443893	+	0.896080i	$0.646403\pi$
$4$	1.77364	0.886818
$5$	1.30751	0.584736	0.292368	−	0.956306i	$-0.405557\pi$
$5$	1.30751	0.584736	0.292368	+	0.956306i	$0.405557\pi$
$6$	−2.98709	−1.21948
$7$	−3.17249	−1.19909	−0.599545	−	0.800341i	$-0.704652\pi$
$7$	−3.17249	−1.19909	−0.599545	+	0.800341i	$0.704652\pi$
$8$	−0.439731	−0.155468
$9$	−0.635509	−0.211836
$10$	2.53995	0.803203
$11$	2.42711	0.731802	0.365901	−	0.930654i	$-0.380761\pi$
$11$	2.42711	0.731802	0.365901	+	0.930654i	$0.380761\pi$
$12$	−2.72730	−0.787304
$13$	−5.43840	−1.50834	−0.754170	−	0.656679i	$-0.771961\pi$
$13$	−5.43840	−1.50834	−0.754170	+	0.656679i	$0.771961\pi$
$14$	−6.16284	−1.64709
$15$	−2.01055	−0.519121
$16$	−4.40149	−1.10037
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.23453	−0.290982
$19$	2.44008	0.559794	0.279897	−	0.960030i	$-0.409700\pi$
$19$	2.44008	0.559794	0.279897	+	0.960030i	$0.409700\pi$
$20$	2.31905	0.518555
$21$	4.87831	1.06453
$22$	4.71487	1.00521
$23$	−8.76953	−1.82857	−0.914287	−	0.405068i	$-0.867248\pi$
$23$	−8.76953	−1.82857	−0.914287	+	0.405068i	$0.867248\pi$
$24$	0.676170	0.138023
$25$	−3.29042	−0.658083
$26$	−10.5646	−2.07188
$27$	5.59029	1.07585
$28$	−5.62685	−1.06337
$29$	2.08653	0.387460	0.193730	−	0.981055i	$-0.437941\pi$
$29$	2.08653	0.387460	0.193730	+	0.981055i	$0.437941\pi$
$30$	−3.90566	−0.713072
$31$	−3.49533	−0.627780	−0.313890	−	0.949459i	$-0.601632\pi$
$31$	−3.49533	−0.627780	−0.313890	+	0.949459i	$0.601632\pi$
$32$	−7.67080	−1.35602
$33$	−3.73215	−0.649684
$34$	1.94258	0.333151
$35$	−4.14807	−0.701152
$36$	−1.12716	−0.187860
$37$	−8.01933	−1.31837	−0.659185	−	0.751981i	$-0.729099\pi$
$37$	−8.01933	−1.31837	−0.659185	+	0.751981i	$0.729099\pi$
$38$	4.74007	0.768941
$39$	8.36257	1.33908
$40$	−0.574953	−0.0909080
$41$	0.176554	0.0275732	0.0137866	−	0.999905i	$-0.495611\pi$
$41$	0.176554	0.0275732	0.0137866	+	0.999905i	$0.495611\pi$
$42$	9.47654	1.46226
$43$	9.91662	1.51227	0.756135	−	0.654415i	$-0.227085\pi$
$43$	9.91662	1.51227	0.756135	+	0.654415i	$0.227085\pi$
$44$	4.30482	0.648975
$45$	−0.830935	−0.123868
$46$	−17.0356	−2.51176
$47$	0.618326	0.0901921	0.0450961	−	0.998983i	$-0.485641\pi$
$47$	0.618326	0.0901921	0.0450961	+	0.998983i	$0.485641\pi$
$48$	6.76812	0.976894
$49$	3.06472	0.437817
$50$	−6.39191	−0.903953
$51$	−1.53769	−0.215320
$52$	−9.64574	−1.33762
$53$	8.02133	1.10181	0.550907	−	0.834567i	$-0.314282\pi$
$53$	8.02133	1.10181	0.550907	+	0.834567i	$0.314282\pi$
$54$	10.8596	1.47781
$55$	3.17348	0.427911
$56$	1.39504	0.186421
$57$	−3.75209	−0.496977
$58$	4.05327	0.532220
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.56598	−0.460366
$61$	−11.5154	−1.47440	−0.737201	−	0.675674i	$-0.763853\pi$
$61$	−11.5154	−1.47440	−0.737201	+	0.675674i	$0.763853\pi$
$62$	−6.78998	−0.862328
$63$	2.01615	0.254011
$64$	−6.09821	−0.762276
$65$	−7.11077	−0.881982
$66$	−7.25001	−0.892415
$67$	2.62865	0.321141	0.160571	−	0.987024i	$-0.448667\pi$
$67$	2.62865	0.321141	0.160571	+	0.987024i	$0.448667\pi$
$68$	1.77364	0.215085
$69$	13.4848	1.62338
$70$	−8.05798	−0.963112
$71$	5.17178	0.613777	0.306888	−	0.951745i	$-0.400712\pi$
$71$	5.17178	0.613777	0.306888	+	0.951745i	$0.400712\pi$
$72$	0.279453	0.0329339
$73$	−12.2525	−1.43405	−0.717026	−	0.697046i	$-0.754497\pi$
$73$	−12.2525	−1.43405	−0.717026	+	0.697046i	$0.754497\pi$
$74$	−15.5782	−1.81093
$75$	5.05964	0.584237
$76$	4.32782	0.496435
$77$	−7.70000	−0.877497
$78$	16.2450	1.83939
$79$	−10.0919	−1.13543	−0.567714	−	0.823226i	$-0.692172\pi$
$79$	−10.0919	−1.13543	−0.567714	+	0.823226i	$0.692172\pi$
$80$	−5.75499	−0.643428
$81$	−6.68960	−0.743289
$82$	0.342972	0.0378749
$83$	6.17477	0.677769	0.338885	−	0.940828i	$-0.389950\pi$
$83$	6.17477	0.677769	0.338885	+	0.940828i	$0.389950\pi$
$84$	8.65235	0.944049
$85$	1.30751	0.141819
$86$	19.2639	2.07728
$87$	−3.20844	−0.343981
$88$	−1.06728	−0.113772
$89$	16.0123	1.69730	0.848650	−	0.528954i	$-0.177416\pi$
$89$	16.0123	1.69730	0.848650	+	0.528954i	$0.177416\pi$
$90$	−1.61416	−0.170148
$91$	17.2533	1.80864
$92$	−15.5540	−1.62161
$93$	5.37474	0.557334
$94$	1.20115	0.123889
$95$	3.19044	0.327332
$96$	11.7953	1.20385
$97$	−11.3748	−1.15493	−0.577466	−	0.816414i	$-0.695959\pi$
$97$	−11.3748	−1.15493	−0.577466	+	0.816414i	$0.695959\pi$
$98$	5.95347	0.601391
$99$	−1.54245	−0.155022
$100$	−5.83600	−0.583600
$101$	2.08320	0.207287	0.103643	−	0.994615i	$-0.466950\pi$
$101$	2.08320	0.207287	0.103643	+	0.994615i	$0.466950\pi$
$102$	−2.98709	−0.295766
$103$	−3.45428	−0.340360	−0.170180	−	0.985413i	$-0.554435\pi$
$103$	−3.45428	−0.340360	−0.170180	+	0.985413i	$0.554435\pi$
$104$	2.39143	0.234499
$105$	6.37844	0.622472
$106$	15.5821	1.51347
$107$	14.9639	1.44662	0.723310	−	0.690524i	$-0.242620\pi$
$107$	14.9639	1.44662	0.723310	+	0.690524i	$0.242620\pi$
$108$	9.91513	0.954084
$109$	10.0206	0.959803	0.479901	−	0.877322i	$-0.340672\pi$
$109$	10.0206	0.959803	0.479901	+	0.877322i	$0.340672\pi$
$110$	6.16475	0.587786
$111$	12.3313	1.17043
$112$	13.9637	1.31944
$113$	−0.833241	−0.0783847	−0.0391924	−	0.999232i	$-0.512479\pi$
$113$	−0.833241	−0.0783847	−0.0391924	+	0.999232i	$0.512479\pi$
$114$	−7.28876	−0.682655
$115$	−11.4663	−1.06923
$116$	3.70075	0.343606
$117$	3.45615	0.319521
$118$	1.94258	0.178829
$119$	−3.17249	−0.290822
$120$	0.884099	0.0807069
$121$	−5.10912	−0.464466
$122$	−22.3697	−2.02526
$123$	−0.271486	−0.0244791
$124$	−6.19945	−0.556727
$125$	−10.8398	−0.969542
$126$	3.91654	0.348913
$127$	−18.0207	−1.59907	−0.799537	−	0.600616i	$-0.794922\pi$
$127$	−18.0207	−1.59907	−0.799537	+	0.600616i	$0.794922\pi$
$128$	3.49532	0.308945
$129$	−15.2487	−1.34257
$130$	−13.8133	−1.21150
$131$	−2.38514	−0.208390	−0.104195	−	0.994557i	$-0.533227\pi$
$131$	−2.38514	−0.208390	−0.104195	+	0.994557i	$0.533227\pi$
$132$	−6.61947	−0.576151
$133$	−7.74115	−0.671243
$134$	5.10638	0.441124
$135$	7.30936	0.629089
$136$	−0.439731	−0.0377066
$137$	8.03896	0.686815	0.343407	−	0.939187i	$-0.388419\pi$
$137$	8.03896	0.686815	0.343407	+	0.939187i	$0.388419\pi$
$138$	26.1954	2.22990
$139$	13.3662	1.13370	0.566852	−	0.823819i	$-0.308161\pi$
$139$	13.3662	1.13370	0.566852	+	0.823819i	$0.308161\pi$
$140$	−7.35716	−0.621794
$141$	−0.950794	−0.0800713
$142$	10.0466	0.843093
$143$	−13.1996	−1.10381
$144$	2.79719	0.233099
$145$	2.72817	0.226562
$146$	−23.8016	−1.96984
$147$	−4.71258	−0.388687
$148$	−14.2234	−1.16915
$149$	3.38966	0.277692	0.138846	−	0.990314i	$-0.455661\pi$
$149$	3.38966	0.277692	0.138846	+	0.990314i	$0.455661\pi$
$150$	9.82878	0.802517
$151$	17.6395	1.43548	0.717739	−	0.696312i	$-0.245177\pi$
$151$	17.6395	1.43548	0.717739	+	0.696312i	$0.245177\pi$
$152$	−1.07298	−0.0870302
$153$	−0.635509	−0.0513779
$154$	−14.9579	−1.20534
$155$	−4.57018	−0.367086
$156$	14.8322	1.18752
$157$	−17.7271	−1.41478	−0.707388	−	0.706826i	$-0.750127\pi$
$157$	−17.7271	−1.41478	−0.707388	+	0.706826i	$0.750127\pi$
$158$	−19.6044	−1.55964
$159$	−12.3343	−0.978175
$160$	−10.0297	−0.792914
$161$	27.8213	2.19262
$162$	−12.9951	−1.02099
$163$	3.02185	0.236689	0.118345	−	0.992973i	$-0.462241\pi$
$163$	3.02185	0.236689	0.118345	+	0.992973i	$0.462241\pi$
$164$	0.313143	0.0244524
$165$	−4.87982	−0.379894
$166$	11.9950	0.930994
$167$	−16.8630	−1.30490	−0.652450	−	0.757832i	$-0.726259\pi$
$167$	−16.8630	−1.30490	−0.652450	+	0.757832i	$0.726259\pi$
$168$	−2.14515	−0.165502
$169$	16.5762	1.27509
$170$	2.53995	0.194805
$171$	−1.55070	−0.118585
$172$	17.5885	1.34111
$173$	−15.3736	−1.16883	−0.584416	−	0.811454i	$-0.698676\pi$
$173$	−15.3736	−1.16883	−0.584416	+	0.811454i	$0.698676\pi$
$174$	−6.23267	−0.472498
$175$	10.4388	0.789101
$176$	−10.6829	−0.805254
$177$	−1.53769	−0.115580
$178$	31.1053	2.33144
$179$	18.1129	1.35382	0.676909	−	0.736066i	$-0.263319\pi$
$179$	18.1129	1.35382	0.676909	+	0.736066i	$0.263319\pi$
$180$	−1.47378	−0.109849
$181$	−19.6120	−1.45775	−0.728874	−	0.684648i	$-0.759956\pi$
$181$	−19.6120	−1.45775	−0.728874	+	0.684648i	$0.759956\pi$
$182$	33.5160	2.48437
$183$	17.7072	1.30895
$184$	3.85623	0.284285
$185$	−10.4854	−0.770899
$186$	10.4409	0.765563
$187$	2.42711	0.177488
$188$	1.09669	0.0799840
$189$	−17.7351	−1.29004
$190$	6.19769	0.449628
$191$	4.26565	0.308651	0.154326	−	0.988020i	$-0.450679\pi$
$191$	4.26565	0.308651	0.154326	+	0.988020i	$0.450679\pi$
$192$	9.37715	0.676738
$193$	1.78305	0.128347	0.0641735	−	0.997939i	$-0.479559\pi$
$193$	1.78305	0.128347	0.0641735	+	0.997939i	$0.479559\pi$
$194$	−22.0965	−1.58643
$195$	10.9342	0.783011
$196$	5.43569	0.388264
$197$	20.7851	1.48088	0.740440	−	0.672123i	$-0.234617\pi$
$197$	20.7851	1.48088	0.740440	+	0.672123i	$0.234617\pi$
$198$	−2.99635	−0.212941
$199$	5.44205	0.385777	0.192888	−	0.981221i	$-0.438214\pi$
$199$	5.44205	0.385777	0.192888	+	0.981221i	$0.438214\pi$
$200$	1.44690	0.102311
$201$	−4.04205	−0.285104
$202$	4.04680	0.284732
$203$	−6.61952	−0.464599
$204$	−2.72730	−0.190949
$205$	0.230847	0.0161230
$206$	−6.71023	−0.467524
$207$	5.57312	0.387358
$208$	23.9370	1.65974
$209$	5.92236	0.409658
$210$	12.3907	0.855037
$211$	−6.38586	−0.439621	−0.219810	−	0.975543i	$-0.570544\pi$
$211$	−6.38586	−0.439621	−0.219810	+	0.975543i	$0.570544\pi$
$212$	14.2269	0.977108
$213$	−7.95259	−0.544902
$214$	29.0687	1.98710
$215$	12.9661	0.884280
$216$	−2.45822	−0.167261
$217$	11.0889	0.752765
$218$	19.4659	1.31840
$219$	18.8406	1.27313
$220$	5.62859	0.379480
$221$	−5.43840	−0.365826
$222$	23.9545	1.60772
$223$	2.09731	0.140446	0.0702231	−	0.997531i	$-0.477629\pi$
$223$	2.09731	0.140446	0.0702231	+	0.997531i	$0.477629\pi$
$224$	24.3356	1.62599
$225$	2.09109	0.139406
$226$	−1.61864	−0.107670
$227$	14.1602	0.939843	0.469921	−	0.882708i	$-0.344282\pi$
$227$	14.1602	0.939843	0.469921	+	0.882708i	$0.344282\pi$
$228$	−6.65485	−0.440728
$229$	9.03224	0.596867	0.298434	−	0.954430i	$-0.403536\pi$
$229$	9.03224	0.596867	0.298434	+	0.954430i	$0.403536\pi$
$230$	−22.2742	−1.46872
$231$	11.8402	0.779029
$232$	−0.917514	−0.0602377
$233$	2.18710	0.143282	0.0716408	−	0.997430i	$-0.477176\pi$
$233$	2.18710	0.143282	0.0716408	+	0.997430i	$0.477176\pi$
$234$	6.71387	0.438899
$235$	0.808468	0.0527386
$236$	1.77364	0.115454
$237$	15.5182	1.00802
$238$	−6.16284	−0.399477
$239$	−28.5031	−1.84371	−0.921857	−	0.387530i	$-0.873328\pi$
$239$	−28.5031	−1.84371	−0.921857	+	0.387530i	$0.873328\pi$
$240$	8.84939	0.571226
$241$	−25.7730	−1.66018	−0.830091	−	0.557627i	$-0.811712\pi$
$241$	−25.7730	−1.66018	−0.830091	+	0.557627i	$0.811712\pi$
$242$	−9.92490	−0.637997
$243$	−6.48433	−0.415970
$244$	−20.4242	−1.30753
$245$	4.00715	0.256007
$246$	−0.527385	−0.0336248
$247$	−13.2702	−0.844360
$248$	1.53701	0.0976000
$249$	−9.49488	−0.601714
$250$	−21.0572	−1.33178
$251$	−4.46444	−0.281793	−0.140896	−	0.990024i	$-0.544998\pi$
$251$	−4.46444	−0.281793	−0.140896	+	0.990024i	$0.544998\pi$
$252$	3.57591	0.225261
$253$	−21.2846	−1.33815
$254$	−35.0067	−2.19651
$255$	−2.01055	−0.125905
$256$	18.9864	1.18665
$257$	−9.33800	−0.582488	−0.291244	−	0.956649i	$-0.594069\pi$
$257$	−9.33800	−0.582488	−0.291244	+	0.956649i	$0.594069\pi$
$258$	−29.6219	−1.84418
$259$	25.4413	1.58084
$260$	−12.6119	−0.782158
$261$	−1.32601	−0.0820780
$262$	−4.63333	−0.286248
$263$	−10.8475	−0.668887	−0.334443	−	0.942416i	$-0.608548\pi$
$263$	−10.8475	−0.668887	−0.334443	+	0.942416i	$0.608548\pi$
$264$	1.64114	0.101005
$265$	10.4880	0.644271
$266$	−15.0378	−0.922030
$267$	−24.6220	−1.50684
$268$	4.66227	0.284794
$269$	7.39188	0.450691	0.225345	−	0.974279i	$-0.427649\pi$
$269$	7.39188	0.450691	0.225345	+	0.974279i	$0.427649\pi$
$270$	14.1990	0.864127
$271$	−10.9118	−0.662844	−0.331422	−	0.943483i	$-0.607528\pi$
$271$	−10.9118	−0.662844	−0.331422	+	0.943483i	$0.607528\pi$
$272$	−4.40149	−0.266879
$273$	−26.5302	−1.60568
$274$	15.6164	0.943419
$275$	−7.98621	−0.481587
$276$	23.9172	1.43964
$277$	−2.60483	−0.156509	−0.0782547	−	0.996933i	$-0.524935\pi$
$277$	−2.60483	−0.156509	−0.0782547	+	0.996933i	$0.524935\pi$
$278$	25.9649	1.55727
$279$	2.22132	0.132987
$280$	1.82403	0.109007
$281$	5.67931	0.338799	0.169400	−	0.985547i	$-0.445817\pi$
$281$	5.67931	0.338799	0.169400	+	0.985547i	$0.445817\pi$
$282$	−1.84700	−0.109987
$283$	−14.9387	−0.888015	−0.444007	−	0.896023i	$-0.646444\pi$
$283$	−14.9387	−0.888015	−0.444007	+	0.896023i	$0.646444\pi$
$284$	9.17285	0.544309
$285$	−4.90590	−0.290601
$286$	−25.6414	−1.51621
$287$	−0.560118	−0.0330627
$288$	4.87486	0.287254
$289$	1.00000	0.0588235
$290$	5.29969	0.311209
$291$	17.4909	1.02533
$292$	−21.7316	−1.27174
$293$	−31.8142	−1.85861	−0.929303	−	0.369318i	$-0.879591\pi$
$293$	−31.8142	−1.85861	−0.929303	+	0.369318i	$0.879591\pi$
$294$	−9.15459	−0.533907
$295$	1.30751	0.0761262
$296$	3.52635	0.204965
$297$	13.5683	0.787310
$298$	6.58471	0.381442
$299$	47.6922	2.75811
$300$	8.97396	0.518112
$301$	−31.4604	−1.81335
$302$	34.2661	1.97179
$303$	−3.20332	−0.184026
$304$	−10.7400	−0.615981
$305$	−15.0566	−0.862136
$306$	−1.23453	−0.0705734
$307$	4.04847	0.231058	0.115529	−	0.993304i	$-0.463144\pi$
$307$	4.04847	0.231058	0.115529	+	0.993304i	$0.463144\pi$
$308$	−13.6570	−0.778180
$309$	5.31161	0.302167
$310$	−8.87797	−0.504235
$311$	5.73967	0.325467	0.162733	−	0.986670i	$-0.447969\pi$
$311$	5.73967	0.325467	0.162733	+	0.986670i	$0.447969\pi$
$312$	−3.67728	−0.208185
$313$	−0.195203	−0.0110335	−0.00551677	−	0.999985i	$-0.501756\pi$
$313$	−0.195203	−0.0110335	−0.00551677	+	0.999985i	$0.501756\pi$
$314$	−34.4364	−1.94336
$315$	2.63614	0.148529
$316$	−17.8994	−1.00692
$317$	−34.7698	−1.95287	−0.976434	−	0.215818i	$-0.930758\pi$
$317$	−34.7698	−1.95287	−0.976434	+	0.215818i	$0.930758\pi$
$318$	−23.9605	−1.34364
$319$	5.06425	0.283544
$320$	−7.97347	−0.445731
$321$	−23.0099	−1.28429
$322$	54.0452	3.01182
$323$	2.44008	0.135770
$324$	−11.8649	−0.659162
$325$	17.8946	0.992614
$326$	5.87020	0.325120
$327$	−15.4086	−0.852099
$328$	−0.0776365	−0.00428676
$329$	−1.96164	−0.108148
$330$	−9.47947	−0.521828
$331$	−16.6240	−0.913736	−0.456868	−	0.889534i	$-0.651029\pi$
$331$	−16.6240	−0.913736	−0.456868	+	0.889534i	$0.651029\pi$
$332$	10.9518	0.601058
$333$	5.09636	0.279279
$334$	−32.7579	−1.79243
$335$	3.43699	0.187783
$336$	−21.4718	−1.17138
$337$	−28.1606	−1.53401	−0.767003	−	0.641644i	$-0.778253\pi$
$337$	−28.1606	−1.53401	−0.767003	+	0.641644i	$0.778253\pi$
$338$	32.2007	1.75149
$339$	1.28127	0.0695888
$340$	2.31905	0.125768
$341$	−8.48357	−0.459411
$342$	−3.01236	−0.162890
$343$	12.4847	0.674108
$344$	−4.36065	−0.235110
$345$	17.6315	0.949250
$346$	−29.8645	−1.60552
$347$	4.29462	0.230547	0.115274	−	0.993334i	$-0.463226\pi$
$347$	4.29462	0.230547	0.115274	+	0.993334i	$0.463226\pi$
$348$	−5.69061	−0.305049
$349$	15.0206	0.804034	0.402017	−	0.915632i	$-0.368309\pi$
$349$	15.0206	0.804034	0.402017	+	0.915632i	$0.368309\pi$
$350$	20.2783	1.08392
$351$	−30.4022	−1.62275
$352$	−18.6179	−0.992337
$353$	−28.3244	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$353$	−28.3244	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$354$	−2.98709	−0.158762
$355$	6.76215	0.358898
$356$	28.4000	1.50520
$357$	4.87831	0.258188
$358$	35.1858	1.85963
$359$	−9.49359	−0.501053	−0.250526	−	0.968110i	$-0.580604\pi$
$359$	−9.49359	−0.501053	−0.250526	+	0.968110i	$0.580604\pi$
$360$	0.365388	0.0192576
$361$	−13.0460	−0.686631
$362$	−38.0980	−2.00238
$363$	7.85625	0.412346
$364$	30.6011	1.60393
$365$	−16.0203	−0.838543
$366$	34.3977	1.79800
$367$	28.2943	1.47695	0.738476	−	0.674280i	$-0.235546\pi$
$367$	28.2943	1.47695	0.738476	+	0.674280i	$0.235546\pi$
$368$	38.5990	2.01211
$369$	−0.112202	−0.00584100
$370$	−20.3687	−1.05892
$371$	−25.4476	−1.32117
$372$	9.53283	0.494254
$373$	−24.0181	−1.24361	−0.621806	−	0.783172i	$-0.713601\pi$
$373$	−24.0181	−1.24361	−0.621806	+	0.783172i	$0.713601\pi$
$374$	4.71487	0.243800
$375$	16.6683	0.860745
$376$	−0.271897	−0.0140220
$377$	−11.3474	−0.584421
$378$	−34.4520	−1.77202
$379$	−8.48664	−0.435929	−0.217965	−	0.975957i	$-0.569942\pi$
$379$	−8.48664	−0.435929	−0.217965	+	0.975957i	$0.569942\pi$
$380$	5.65867	0.290284
$381$	27.7102	1.41964
$382$	8.28638	0.423968
$383$	−8.57046	−0.437930	−0.218965	−	0.975733i	$-0.570268\pi$
$383$	−8.57046	−0.437930	−0.218965	+	0.975733i	$0.570268\pi$
$384$	−5.37471	−0.274277
$385$	−10.0678	−0.513104
$386$	3.46373	0.176299
$387$	−6.30210	−0.320354
$388$	−20.1747	−1.02422
$389$	−0.289014	−0.0146536	−0.00732679	−	0.999973i	$-0.502332\pi$
$389$	−0.289014	−0.0146536	−0.00732679	+	0.999973i	$0.502332\pi$
$390$	21.2405	1.07556
$391$	−8.76953	−0.443494
$392$	−1.34765	−0.0680666
$393$	3.66760	0.185006
$394$	40.3769	2.03416
$395$	−13.1953	−0.663926
$396$	−2.73575	−0.137477
$397$	1.30822	0.0656579	0.0328290	−	0.999461i	$-0.489548\pi$
$397$	1.30822	0.0656579	0.0328290	+	0.999461i	$0.489548\pi$
$398$	10.5716	0.529909
$399$	11.9035	0.595920
$400$	14.4827	0.724136
$401$	35.5802	1.77679	0.888396	−	0.459078i	$-0.151820\pi$
$401$	35.5802	1.77679	0.888396	+	0.459078i	$0.151820\pi$
$402$	−7.85203	−0.391624
$403$	19.0090	0.946907
$404$	3.69485	0.183825
$405$	−8.74672	−0.434628
$406$	−12.8590	−0.638180
$407$	−19.4638	−0.964786
$408$	0.676170	0.0334754
$409$	−18.8222	−0.930699	−0.465350	−	0.885127i	$-0.654071\pi$
$409$	−18.8222	−0.930699	−0.465350	+	0.885127i	$0.654071\pi$
$410$	0.448439	0.0221468
$411$	−12.3614	−0.609744
$412$	−6.12664	−0.301838
$413$	−3.17249	−0.156108
$414$	10.8263	0.532081
$415$	8.07358	0.396316
$416$	41.7169	2.04534
$417$	−20.5530	−1.00649
$418$	11.5047	0.562713
$419$	−21.3178	−1.04144	−0.520722	−	0.853726i	$-0.674337\pi$
$419$	−21.3178	−1.04144	−0.520722	+	0.853726i	$0.674337\pi$
$420$	11.3130	0.552020
$421$	6.42371	0.313073	0.156536	−	0.987672i	$-0.449967\pi$
$421$	6.42371	0.313073	0.156536	+	0.987672i	$0.449967\pi$
$422$	−12.4051	−0.603870
$423$	−0.392952	−0.0191060
$424$	−3.52723	−0.171297
$425$	−3.29042	−0.159609
$426$	−15.4486	−0.748486
$427$	36.5327	1.76794
$428$	26.5406	1.28289
$429$	20.2969	0.979944
$430$	25.1877	1.21466
$431$	−29.7459	−1.43281	−0.716404	−	0.697686i	$-0.754213\pi$
$431$	−29.7459	−1.43281	−0.716404	+	0.697686i	$0.754213\pi$
$432$	−24.6056	−1.18384
$433$	−36.9876	−1.77751	−0.888756	−	0.458380i	$-0.848430\pi$
$433$	−36.9876	−1.77751	−0.888756	+	0.458380i	$0.848430\pi$
$434$	21.5412	1.03401
$435$	−4.19507	−0.201138
$436$	17.7730	0.851170
$437$	−21.3984	−1.02362
$438$	36.5995	1.74879
$439$	−25.4719	−1.21571	−0.607853	−	0.794050i	$-0.707969\pi$
$439$	−25.4719	−1.21571	−0.607853	+	0.794050i	$0.707969\pi$
$440$	−1.39548	−0.0665267
$441$	−1.94766	−0.0927455
$442$	−10.5646	−0.502505
$443$	34.5336	1.64074	0.820369	−	0.571834i	$-0.193768\pi$
$443$	34.5336	1.64074	0.820369	+	0.571834i	$0.193768\pi$
$444$	21.8712	1.03796
$445$	20.9363	0.992474
$446$	4.07420	0.192919
$447$	−5.21225	−0.246531
$448$	19.3465	0.914037
$449$	−9.67046	−0.456377	−0.228189	−	0.973617i	$-0.573280\pi$
$449$	−9.67046	−0.456377	−0.228189	+	0.973617i	$0.573280\pi$
$450$	4.06212	0.191490
$451$	0.428518	0.0201781
$452$	−1.47787	−0.0695130
$453$	−27.1240	−1.27440
$454$	27.5073	1.29098
$455$	22.5589	1.05758
$456$	1.64991	0.0772642
$457$	−37.1696	−1.73872	−0.869360	−	0.494179i	$-0.835469\pi$
$457$	−37.1696	−1.73872	−0.869360	+	0.494179i	$0.835469\pi$
$458$	17.5459	0.819866
$459$	5.59029	0.260932
$460$	−20.3370	−0.948216
$461$	−10.5649	−0.492057	−0.246029	−	0.969263i	$-0.579126\pi$
$461$	−10.5649	−0.492057	−0.246029	+	0.969263i	$0.579126\pi$
$462$	23.0006	1.07009
$463$	24.5093	1.13904	0.569521	−	0.821977i	$-0.307129\pi$
$463$	24.5093	1.13904	0.569521	+	0.821977i	$0.307129\pi$
$464$	−9.18385	−0.426350
$465$	7.02753	0.325894
$466$	4.24863	0.196814
$467$	−18.6796	−0.864390	−0.432195	−	0.901780i	$-0.642261\pi$
$467$	−18.6796	−0.864390	−0.432195	+	0.901780i	$0.642261\pi$
$468$	6.12996	0.283357
$469$	−8.33938	−0.385077
$470$	1.57052	0.0724426
$471$	27.2588	1.25602
$472$	−0.439731	−0.0202403
$473$	24.0688	1.10668
$474$	30.1454	1.38463
$475$	−8.02889	−0.368391
$476$	−5.62685	−0.257906
$477$	−5.09763	−0.233404
$478$	−55.3697	−2.53255
$479$	−0.308383	−0.0140904	−0.00704519	−	0.999975i	$-0.502243\pi$
$479$	−0.308383	−0.0140904	−0.00704519	+	0.999975i	$0.502243\pi$
$480$	15.4225	0.703937
$481$	43.6124	1.98855
$482$	−50.0662	−2.28045
$483$	−42.7805	−1.94658
$484$	−9.06172	−0.411897
$485$	−14.8726	−0.675331
$486$	−12.5964	−0.571382
$487$	10.5872	0.479750	0.239875	−	0.970804i	$-0.422894\pi$
$487$	10.5872	0.479750	0.239875	+	0.970804i	$0.422894\pi$
$488$	5.06370	0.229223
$489$	−4.64667	−0.210129
$490$	7.78423	0.351655
$491$	8.95979	0.404350	0.202175	−	0.979349i	$-0.435199\pi$
$491$	8.95979	0.404350	0.202175	+	0.979349i	$0.435199\pi$
$492$	−0.481517	−0.0217085
$493$	2.08653	0.0939728
$494$	−25.7784	−1.15983
$495$	−2.01677	−0.0906472
$496$	15.3847	0.690792
$497$	−16.4074	−0.735974
$498$	−18.4446	−0.826523
$499$	38.3304	1.71590	0.857951	−	0.513731i	$-0.171737\pi$
$499$	38.3304	1.71590	0.857951	+	0.513731i	$0.171737\pi$
$500$	−19.2259	−0.859807
$501$	25.9301	1.15847
$502$	−8.67255	−0.387075
$503$	4.32331	0.192767	0.0963835	−	0.995344i	$-0.469272\pi$
$503$	4.32331	0.192767	0.0963835	+	0.995344i	$0.469272\pi$
$504$	−0.886563	−0.0394907
$505$	2.72381	0.121208
$506$	−41.3472	−1.83811
$507$	−25.4891	−1.13201
$508$	−31.9621	−1.41809
$509$	32.6052	1.44520	0.722600	−	0.691266i	$-0.242947\pi$
$509$	32.6052	1.44520	0.722600	+	0.691266i	$0.242947\pi$
$510$	−3.90566	−0.172945
$511$	38.8711	1.71956
$512$	29.8920	1.32105
$513$	13.6408	0.602255
$514$	−18.1398	−0.800114
$515$	−4.51651	−0.199021
$516$	−27.0456	−1.19062
$517$	1.50075	0.0660028
$518$	49.4219	2.17147
$519$	23.6398	1.03767
$520$	3.12682	0.137120
$521$	9.92288	0.434729	0.217365	−	0.976090i	$-0.430254\pi$
$521$	9.92288	0.434729	0.217365	+	0.976090i	$0.430254\pi$
$522$	−2.57589	−0.112744
$523$	25.4334	1.11212	0.556062	−	0.831141i	$-0.312312\pi$
$523$	25.4334	1.11212	0.556062	+	0.831141i	$0.312312\pi$
$524$	−4.23037	−0.184804
$525$	−16.0517	−0.700553
$526$	−21.0722	−0.918793
$527$	−3.49533	−0.152259
$528$	16.4270	0.714893
$529$	53.9047	2.34368
$530$	20.3738	0.884980
$531$	−0.635509	−0.0275787
$532$	−13.7300	−0.595271
$533$	−0.960174	−0.0415897
$534$	−47.8303	−2.06982
$535$	19.5655	0.845891
$536$	−1.15590	−0.0499273
$537$	−27.8520	−1.20190
$538$	14.3594	0.619076
$539$	7.43841	0.320395
$540$	12.9641	0.557888
$541$	2.45027	0.105345	0.0526726	−	0.998612i	$-0.483226\pi$
$541$	2.45027	0.105345	0.0526726	+	0.998612i	$0.483226\pi$
$542$	−21.1971	−0.910493
$543$	30.1572	1.29417
$544$	−7.67080	−0.328883
$545$	13.1021	0.561232
$546$	−51.5372	−2.20559
$547$	−33.0609	−1.41358	−0.706791	−	0.707422i	$-0.749858\pi$
$547$	−33.0609	−1.41358	−0.706791	+	0.707422i	$0.749858\pi$
$548$	14.2582	0.609080
$549$	7.31817	0.312332
$550$	−15.5139	−0.661515
$551$	5.09132	0.216898
$552$	−5.92969	−0.252384
$553$	32.0165	1.36148
$554$	−5.06011	−0.214984
$555$	16.1232	0.684393
$556$	23.7067	1.00539
$557$	13.7776	0.583774	0.291887	−	0.956453i	$-0.405717\pi$
$557$	13.7776	0.583774	0.291887	+	0.956453i	$0.405717\pi$
$558$	4.31509	0.182673
$559$	−53.9305	−2.28102
$560$	18.2577	0.771527
$561$	−3.73215	−0.157571
$562$	11.0325	0.465380
$563$	15.6639	0.660153	0.330077	−	0.943954i	$-0.392925\pi$
$563$	15.6639	0.660153	0.330077	+	0.943954i	$0.392925\pi$
$564$	−1.68636	−0.0710087
$565$	−1.08947	−0.0458344
$566$	−29.0197	−1.21979
$567$	21.2227	0.891270
$568$	−2.27419	−0.0954229
$569$	16.8910	0.708108	0.354054	−	0.935225i	$-0.384803\pi$
$569$	16.8910	0.708108	0.354054	+	0.935225i	$0.384803\pi$
$570$	−9.53013	−0.399173
$571$	−36.0405	−1.50825	−0.754123	−	0.656733i	$-0.771938\pi$
$571$	−36.0405	−1.50825	−0.754123	+	0.656733i	$0.771938\pi$
$572$	−23.4113	−0.978876
$573$	−6.55924	−0.274016
$574$	−1.08808	−0.0454154
$575$	28.8554	1.20335
$576$	3.87547	0.161478
$577$	47.4216	1.97419	0.987094	−	0.160145i	$-0.0511961\pi$
$577$	47.4216	1.97419	0.987094	+	0.160145i	$0.0511961\pi$
$578$	1.94258	0.0808009
$579$	−2.74178	−0.113945
$580$	4.83877	0.200919
$581$	−19.5894	−0.812706
$582$	33.9775	1.40841
$583$	19.4687	0.806310
$584$	5.38782	0.222950
$585$	4.51896	0.186836
$586$	−61.8018	−2.55301
$587$	−24.5503	−1.01330	−0.506651	−	0.862151i	$-0.669117\pi$
$587$	−24.5503	−1.01330	−0.506651	+	0.862151i	$0.669117\pi$
$588$	−8.35841	−0.344695
$589$	−8.52891	−0.351428
$590$	2.53995	0.104568
$591$	−31.9611	−1.31470
$592$	35.2970	1.45070
$593$	−8.29655	−0.340699	−0.170349	−	0.985384i	$-0.554490\pi$
$593$	−8.29655	−0.340699	−0.170349	+	0.985384i	$0.554490\pi$
$594$	26.3575	1.08146
$595$	−4.14807	−0.170054
$596$	6.01203	0.246262
$597$	−8.36819	−0.342487
$598$	92.6462	3.78858
$599$	−2.22188	−0.0907835	−0.0453918	−	0.998969i	$-0.514454\pi$
$599$	−2.22188	−0.0907835	−0.0453918	+	0.998969i	$0.514454\pi$
$600$	−2.22488	−0.0908304
$601$	17.6371	0.719432	0.359716	−	0.933062i	$-0.382874\pi$
$601$	17.6371	0.719432	0.359716	+	0.933062i	$0.382874\pi$
$602$	−61.1145	−2.49084
$603$	−1.67053	−0.0680294
$604$	31.2860	1.27301
$605$	−6.68023	−0.271590
$606$	−6.22273	−0.252781
$607$	28.2574	1.14693	0.573467	−	0.819229i	$-0.305598\pi$
$607$	28.2574	1.14693	0.573467	+	0.819229i	$0.305598\pi$
$608$	−18.7174	−0.759091
$609$	10.1788	0.412464
$610$	−29.2486	−1.18424
$611$	−3.36271	−0.136040
$612$	−1.12716	−0.0455628
$613$	49.0945	1.98291	0.991454	−	0.130455i	$-0.0416440\pi$
$613$	49.0945	1.98291	0.991454	+	0.130455i	$0.0416440\pi$
$614$	7.86450	0.317385
$615$	−0.354971	−0.0143138
$616$	3.38593	0.136423
$617$	2.22950	0.0897563	0.0448782	−	0.998992i	$-0.485710\pi$
$617$	2.22950	0.0897563	0.0448782	+	0.998992i	$0.485710\pi$
$618$	10.3183	0.415061
$619$	−36.2913	−1.45867	−0.729336	−	0.684156i	$-0.760171\pi$
$619$	−36.2913	−1.45867	−0.729336	+	0.684156i	$0.760171\pi$
$620$	−8.10584	−0.325539
$621$	−49.0242	−1.96727
$622$	11.1498	0.447066
$623$	−50.7989	−2.03522
$624$	−36.8078	−1.47349
$625$	2.27892	0.0911568
$626$	−0.379199	−0.0151558
$627$	−9.10676	−0.363689
$628$	−31.4414	−1.25465
$629$	−8.01933	−0.319752
$630$	5.12092	0.204022
$631$	−32.8251	−1.30675	−0.653374	−	0.757035i	$-0.726647\pi$
$631$	−32.8251	−1.30675	−0.653374	+	0.757035i	$0.726647\pi$
$632$	4.43772	0.176523
$633$	9.81948	0.390289
$634$	−67.5433	−2.68249
$635$	−23.5622	−0.935037
$636$	−21.8766	−0.867463
$637$	−16.6672	−0.660377
$638$	9.83774	0.389480
$639$	−3.28671	−0.130020
$640$	4.57016	0.180652
$641$	28.5507	1.12769	0.563843	−	0.825882i	$-0.309322\pi$
$641$	28.5507	1.12769	0.563843	+	0.825882i	$0.309322\pi$
$642$	−44.6987	−1.76412
$643$	−6.84734	−0.270033	−0.135016	−	0.990843i	$-0.543109\pi$
$643$	−6.84734	−0.270033	−0.135016	+	0.990843i	$0.543109\pi$
$644$	49.3448	1.94446
$645$	−19.9378	−0.785051
$646$	4.74007	0.186496
$647$	7.35382	0.289109	0.144554	−	0.989497i	$-0.453825\pi$
$647$	7.35382	0.289109	0.144554	+	0.989497i	$0.453825\pi$
$648$	2.94162	0.115558
$649$	2.42711	0.0952725
$650$	34.7618	1.36347
$651$	−17.0513	−0.668294
$652$	5.35966	0.209900
$653$	20.3788	0.797485	0.398743	−	0.917063i	$-0.369447\pi$
$653$	20.3788	0.797485	0.398743	+	0.917063i	$0.369447\pi$
$654$	−29.9326	−1.17046
$655$	−3.11859	−0.121853
$656$	−0.777102	−0.0303407
$657$	7.78661	0.303784
$658$	−3.81064	−0.148554
$659$	24.8218	0.966919	0.483460	−	0.875367i	$-0.339380\pi$
$659$	24.8218	0.966919	0.483460	+	0.875367i	$0.339380\pi$
$660$	−8.65503	−0.336897
$661$	26.5217	1.03158	0.515788	−	0.856716i	$-0.327499\pi$
$661$	26.5217	1.03158	0.515788	+	0.856716i	$0.327499\pi$
$662$	−32.2935	−1.25512
$663$	8.36257	0.324775
$664$	−2.71524	−0.105372
$665$	−10.1216	−0.392500
$666$	9.90011	0.383622
$667$	−18.2979	−0.708498
$668$	−29.9089	−1.15721
$669$	−3.22501	−0.124686
$670$	6.67665	0.257941
$671$	−27.9493	−1.07897
$672$	−37.4206	−1.44353
$673$	10.5919	0.408286	0.204143	−	0.978941i	$-0.434559\pi$
$673$	10.5919	0.408286	0.204143	+	0.978941i	$0.434559\pi$
$674$	−54.7044	−2.10713
$675$	−18.3944	−0.708000
$676$	29.4001	1.13077
$677$	−34.5813	−1.32907	−0.664533	−	0.747259i	$-0.731370\pi$
$677$	−34.5813	−1.32907	−0.664533	+	0.747259i	$0.731370\pi$
$678$	2.48897	0.0955883
$679$	36.0864	1.38487
$680$	−0.574953	−0.0220484
$681$	−21.7739	−0.834379
$682$	−16.4801	−0.631054
$683$	−33.8178	−1.29400	−0.647001	−	0.762489i	$-0.723977\pi$
$683$	−33.8178	−1.29400	−0.647001	+	0.762489i	$0.723977\pi$
$684$	−2.75037	−0.105163
$685$	10.5110	0.401606
$686$	24.2525	0.925965
$687$	−13.8888	−0.529890
$688$	−43.6479	−1.66406
$689$	−43.6232	−1.66191
$690$	34.2508	1.30390
$691$	−13.2241	−0.503067	−0.251534	−	0.967849i	$-0.580935\pi$
$691$	−13.2241	−0.503067	−0.251534	+	0.967849i	$0.580935\pi$
$692$	−27.2671	−1.03654
$693$	4.89342	0.185886
$694$	8.34266	0.316683
$695$	17.4764	0.662919
$696$	1.41085	0.0534782
$697$	0.176554	0.00668748
$698$	29.1788	1.10443
$699$	−3.36308	−0.127203
$700$	18.5147	0.699789
$701$	34.8992	1.31813	0.659063	−	0.752088i	$-0.270953\pi$
$701$	34.8992	1.31813	0.659063	+	0.752088i	$0.270953\pi$
$702$	−59.0589	−2.22903
$703$	−19.5679	−0.738016
$704$	−14.8010	−0.557835
$705$	−1.24317	−0.0468206
$706$	−55.0226	−2.07080
$707$	−6.60895	−0.248555
$708$	−2.72730	−0.102498
$709$	−33.6050	−1.26206	−0.631030	−	0.775758i	$-0.717368\pi$
$709$	−33.6050	−1.26206	−0.631030	+	0.775758i	$0.717368\pi$
$710$	13.1361	0.492987
$711$	6.41349	0.240525
$712$	−7.04111	−0.263877
$713$	30.6524	1.14794
$714$	9.47654	0.354650
$715$	−17.2586	−0.645436
$716$	32.1256	1.20059
$717$	43.8290	1.63682
$718$	−18.4421	−0.688253
$719$	7.96711	0.297123	0.148562	−	0.988903i	$-0.452536\pi$
$719$	7.96711	0.297123	0.148562	+	0.988903i	$0.452536\pi$
$720$	3.65735	0.136301
$721$	10.9587	0.408123
$722$	−25.3429	−0.943166
$723$	39.6308	1.47389
$724$	−34.7845	−1.29276
$725$	−6.86557	−0.254981
$726$	15.2614	0.566405
$727$	21.8136	0.809021	0.404511	−	0.914533i	$-0.367442\pi$
$727$	21.8136	0.809021	0.404511	+	0.914533i	$0.367442\pi$
$728$	−7.58681	−0.281186
$729$	30.0397	1.11258
$730$	−31.1209	−1.15183
$731$	9.91662	0.366779
$732$	31.4061	1.16080
$733$	45.2043	1.66966	0.834830	−	0.550508i	$-0.185566\pi$
$733$	45.2043	1.66966	0.834830	+	0.550508i	$0.185566\pi$
$734$	54.9641	2.02876
$735$	−6.16175	−0.227280
$736$	67.2693	2.47958
$737$	6.38004	0.235012
$738$	−0.217962	−0.00802329
$739$	−1.32835	−0.0488642	−0.0244321	−	0.999701i	$-0.507778\pi$
$739$	−1.32835	−0.0488642	−0.0244321	+	0.999701i	$0.507778\pi$
$740$	−18.5972	−0.683647
$741$	20.4054	0.749611
$742$	−49.4341	−1.81478
$743$	−3.21958	−0.118115	−0.0590575	−	0.998255i	$-0.518810\pi$
$743$	−3.21958	−0.118115	−0.0590575	+	0.998255i	$0.518810\pi$
$744$	−2.36344	−0.0866479
$745$	4.43202	0.162377
$746$	−46.6572	−1.70824
$747$	−3.92412	−0.143576
$748$	4.30482	0.157400
$749$	−47.4730	−1.73463
$750$	32.3795	1.18233
$751$	−1.86537	−0.0680684	−0.0340342	−	0.999421i	$-0.510836\pi$
$751$	−1.86537	−0.0680684	−0.0340342	+	0.999421i	$0.510836\pi$
$752$	−2.72155	−0.0992449
$753$	6.86492	0.250172
$754$	−22.0433	−0.802770
$755$	23.0638	0.839376
$756$	−31.4557	−1.14403
$757$	20.5579	0.747188	0.373594	−	0.927592i	$-0.378125\pi$
$757$	20.5579	0.747188	0.373594	+	0.927592i	$0.378125\pi$
$758$	−16.4860	−0.598799
$759$	32.7292	1.18799
$760$	−1.40293	−0.0508898
$761$	−5.75989	−0.208796	−0.104398	−	0.994536i	$-0.533292\pi$
$761$	−5.75989	−0.208796	−0.104398	+	0.994536i	$0.533292\pi$
$762$	53.8294	1.95003
$763$	−31.7904	−1.15089
$764$	7.56571	0.273718
$765$	−0.830935	−0.0300425
$766$	−16.6488	−0.601547
$767$	−5.43840	−0.196369
$768$	−29.1951	−1.05349
$769$	−35.0604	−1.26431	−0.632156	−	0.774842i	$-0.717830\pi$
$769$	−35.0604	−1.26431	−0.632156	+	0.774842i	$0.717830\pi$
$770$	−19.5576	−0.704808
$771$	14.3589	0.517125
$772$	3.16249	0.113820
$773$	−47.6607	−1.71424	−0.857118	−	0.515120i	$-0.827747\pi$
$773$	−47.6607	−1.71424	−0.857118	+	0.515120i	$0.827747\pi$
$774$	−12.2424	−0.440043
$775$	11.5011	0.413132
$776$	5.00184	0.179556
$777$	−39.1208	−1.40345
$778$	−0.561434	−0.0201284
$779$	0.430808	0.0154353
$780$	19.3932	0.694388
$781$	12.5525	0.449163
$782$	−17.0356	−0.609190
$783$	11.6643	0.416849
$784$	−13.4893	−0.481761
$785$	−23.1784	−0.827271
$786$	7.12463	0.254127
$787$	−24.0447	−0.857100	−0.428550	−	0.903518i	$-0.640975\pi$
$787$	−24.0447	−0.857100	−0.428550	+	0.903518i	$0.640975\pi$
$788$	36.8653	1.31327
$789$	16.6801	0.593828
$790$	−25.6329	−0.911978
$791$	2.64345	0.0939903
$792$	0.678264	0.0241011
$793$	62.6256	2.22390
$794$	2.54134	0.0901887
$795$	−16.1272	−0.571974
$796$	9.65222	0.342114
$797$	−34.4399	−1.21993	−0.609963	−	0.792430i	$-0.708816\pi$
$797$	−34.4399	−1.21993	−0.609963	+	0.792430i	$0.708816\pi$
$798$	23.1235	0.818565
$799$	0.618326	0.0218748
$800$	25.2401	0.892373
$801$	−10.1760	−0.359550
$802$	69.1176	2.44063
$803$	−29.7383	−1.04944
$804$	−7.16913	−0.252836
$805$	36.3766	1.28211
$806$	36.9266	1.30069
$807$	−11.3664	−0.400117
$808$	−0.916050	−0.0322265
$809$	−26.0906	−0.917297	−0.458648	−	0.888618i	$-0.651666\pi$
$809$	−26.0906	−0.917297	−0.458648	+	0.888618i	$0.651666\pi$
$810$	−16.9913	−0.597012
$811$	13.4117	0.470947	0.235474	−	0.971881i	$-0.424336\pi$
$811$	13.4117	0.470947	0.235474	+	0.971881i	$0.424336\pi$
$812$	−11.7406	−0.412015
$813$	16.7790	0.588464
$814$	−37.8101	−1.32525
$815$	3.95110	0.138401
$816$	6.76812	0.236932
$817$	24.1974	0.846560
$818$	−36.5638	−1.27842
$819$	−10.9646	−0.383135
$820$	0.409438	0.0142982
$821$	34.9559	1.21997	0.609985	−	0.792413i	$-0.291175\pi$
$821$	34.9559	1.21997	0.609985	+	0.792413i	$0.291175\pi$
$822$	−24.0131	−0.837554
$823$	−1.50646	−0.0525119	−0.0262560	−	0.999655i	$-0.508358\pi$
$823$	−1.50646	−0.0525119	−0.0262560	+	0.999655i	$0.508358\pi$
$824$	1.51895	0.0529153
$825$	12.2803	0.427546
$826$	−6.16284	−0.214433
$827$	39.0029	1.35626	0.678132	−	0.734940i	$-0.262790\pi$
$827$	39.0029	1.35626	0.678132	+	0.734940i	$0.262790\pi$
$828$	9.88468	0.343516
$829$	−19.7492	−0.685917	−0.342958	−	0.939351i	$-0.611429\pi$
$829$	−19.7492	−0.685917	−0.342958	+	0.939351i	$0.611429\pi$
$830$	15.6836	0.544386
$831$	4.00543	0.138947
$832$	33.1645	1.14977
$833$	3.06472	0.106186
$834$	−39.9260	−1.38253
$835$	−22.0486	−0.763023
$836$	10.5041	0.363292
$837$	−19.5399	−0.675398
$838$	−41.4117	−1.43054
$839$	45.4294	1.56840	0.784198	−	0.620511i	$-0.213075\pi$
$839$	45.4294	1.56840	0.784198	+	0.620511i	$0.213075\pi$
$840$	−2.80480	−0.0967748
$841$	−24.6464	−0.849875
$842$	12.4786	0.430041
$843$	−8.73302	−0.300781
$844$	−11.3262	−0.389864
$845$	21.6736	0.745593
$846$	−0.763342	−0.0262443
$847$	16.2087	0.556936
$848$	−35.3058	−1.21240
$849$	22.9711	0.788367
$850$	−6.39191	−0.219241
$851$	70.3258	2.41074
$852$	−14.1050	−0.483229
$853$	47.8136	1.63711	0.818553	−	0.574431i	$-0.194777\pi$
$853$	47.8136	1.63711	0.818553	+	0.574431i	$0.194777\pi$
$854$	70.9678	2.42847
$855$	−2.02755	−0.0693408
$856$	−6.58011	−0.224904
$857$	34.7389	1.18666	0.593329	−	0.804960i	$-0.297813\pi$
$857$	34.7389	1.18666	0.593329	+	0.804960i	$0.297813\pi$
$858$	39.4285	1.34607
$859$	52.6213	1.79542	0.897709	−	0.440590i	$-0.145231\pi$
$859$	52.6213	1.79542	0.897709	+	0.440590i	$0.145231\pi$
$860$	22.9971	0.784195
$861$	0.861288	0.0293526
$862$	−57.7838	−1.96813
$863$	28.2181	0.960556	0.480278	−	0.877116i	$-0.340536\pi$
$863$	28.2181	0.960556	0.480278	+	0.877116i	$0.340536\pi$
$864$	−42.8820	−1.45887
$865$	−20.1011	−0.683458
$866$	−71.8516	−2.44162
$867$	−1.53769	−0.0522227
$868$	19.6677	0.667566
$869$	−24.4942	−0.830908
$870$	−8.14928	−0.276287
$871$	−14.2957	−0.484390
$872$	−4.40638	−0.149219
$873$	7.22877	0.244657
$874$	−41.5682	−1.40607
$875$	34.3892	1.16257
$876$	33.4164	1.12904
$877$	22.0107	0.743247	0.371624	−	0.928383i	$-0.378801\pi$
$877$	22.0107	0.743247	0.371624	+	0.928383i	$0.378801\pi$
$878$	−49.4812	−1.66991
$879$	48.9204	1.65004
$880$	−13.9680	−0.470862
$881$	−2.29845	−0.0774367	−0.0387184	−	0.999250i	$-0.512328\pi$
$881$	−2.29845	−0.0774367	−0.0387184	+	0.999250i	$0.512328\pi$
$882$	−3.78349	−0.127397
$883$	−7.82633	−0.263377	−0.131689	−	0.991291i	$-0.542040\pi$
$883$	−7.82633	−0.263377	−0.131689	+	0.991291i	$0.542040\pi$
$884$	−9.64574	−0.324421
$885$	−2.01055	−0.0675838
$886$	67.0844	2.25374
$887$	−24.8744	−0.835199	−0.417600	−	0.908631i	$-0.637129\pi$
$887$	−24.8744	−0.835199	−0.417600	+	0.908631i	$0.637129\pi$
$888$	−5.42243	−0.181965
$889$	57.1704	1.91743
$890$	40.6705	1.36328
$891$	−16.2364	−0.543940
$892$	3.71986	0.124550
$893$	1.50877	0.0504890
$894$	−10.1252	−0.338639
$895$	23.6828	0.791627
$896$	−11.0889	−0.370453
$897$	−73.3358	−2.44861
$898$	−18.7857	−0.626886
$899$	−7.29313	−0.243240
$900$	3.70883	0.123628
$901$	8.02133	0.267229
$902$	0.832432	0.0277169
$903$	48.3764	1.60986
$904$	0.366402	0.0121863
$905$	−25.6429	−0.852398
$906$	−52.6907	−1.75053
$907$	−48.6660	−1.61593	−0.807964	−	0.589231i	$-0.799431\pi$
$907$	−48.6660	−1.61593	−0.807964	+	0.589231i	$0.799431\pi$
$908$	25.1150	0.833470
$909$	−1.32390	−0.0439108
$910$	43.8225	1.45270
$911$	21.0492	0.697392	0.348696	−	0.937236i	$-0.386624\pi$
$911$	21.0492	0.697392	0.348696	+	0.937236i	$0.386624\pi$
$912$	16.5148	0.546859
$913$	14.9869	0.495993
$914$	−72.2051	−2.38833
$915$	23.1523	0.765392
$916$	16.0199	0.529313
$917$	7.56683	0.249879
$918$	10.8596	0.358420
$919$	13.7206	0.452602	0.226301	−	0.974057i	$-0.427337\pi$
$919$	13.7206	0.452602	0.226301	+	0.974057i	$0.427337\pi$
$920$	5.04207	0.166232
$921$	−6.22529	−0.205130
$922$	−20.5233	−0.675898
$923$	−28.1262	−0.925785
$924$	21.0002	0.690857
$925$	26.3870	0.867598
$926$	47.6113	1.56460
$927$	2.19523	0.0721007
$928$	−16.0054	−0.525403
$929$	−5.82082	−0.190975	−0.0954875	−	0.995431i	$-0.530441\pi$
$929$	−5.82082	−0.190975	−0.0954875	+	0.995431i	$0.530441\pi$
$930$	13.6516	0.447653
$931$	7.47817	0.245087
$932$	3.87912	0.127065
$933$	−8.82584	−0.288945
$934$	−36.2867	−1.18734
$935$	3.17348	0.103784
$936$	−1.51978	−0.0496755
$937$	24.3376	0.795074	0.397537	−	0.917586i	$-0.369865\pi$
$937$	24.3376	0.795074	0.397537	+	0.917586i	$0.369865\pi$
$938$	−16.2000	−0.528947
$939$	0.300162	0.00979541
$940$	1.43393	0.0467696
$941$	51.9819	1.69456	0.847281	−	0.531144i	$-0.178238\pi$
$941$	51.9819	1.69456	0.847281	+	0.531144i	$0.178238\pi$
$942$	52.9525	1.72528
$943$	−1.54830	−0.0504196
$944$	−4.40149	−0.143256
$945$	−23.1889	−0.754335
$946$	46.7556	1.52016
$947$	−44.4694	−1.44506	−0.722531	−	0.691338i	$-0.757021\pi$
$947$	−44.4694	−1.44506	−0.722531	+	0.691338i	$0.757021\pi$
$948$	27.5237	0.893927
$949$	66.6343	2.16304
$950$	−15.5968	−0.506027
$951$	53.4652	1.73373
$952$	1.39504	0.0452136
$953$	41.8380	1.35527	0.677633	−	0.735400i	$-0.263006\pi$
$953$	41.8380	1.35527	0.677633	+	0.735400i	$0.263006\pi$
$954$	−9.90257	−0.320608
$955$	5.57738	0.180480
$956$	−50.5542	−1.63504
$957$	−7.78725	−0.251726
$958$	−0.599060	−0.0193548
$959$	−25.5035	−0.823553
$960$	12.2607	0.395713
$961$	−18.7826	−0.605892
$962$	84.7207	2.73151
$963$	−9.50973	−0.306447
$964$	−45.7119	−1.47228
$965$	2.33136	0.0750492
$966$	−83.1048	−2.67385
$967$	26.6575	0.857248	0.428624	−	0.903483i	$-0.358999\pi$
$967$	26.6575	0.857248	0.428624	+	0.903483i	$0.358999\pi$
$968$	2.24664	0.0722097
$969$	−3.75209	−0.120535
$970$	−28.8913	−0.927645
$971$	−44.5436	−1.42947	−0.714736	−	0.699395i	$-0.753453\pi$
$971$	−44.5436	−1.42947	−0.714736	+	0.699395i	$0.753453\pi$
$972$	−11.5008	−0.368889
$973$	−42.4041	−1.35941
$974$	20.5665	0.658992
$975$	−27.5164	−0.881229
$976$	50.6851	1.62239
$977$	−10.4147	−0.333195	−0.166597	−	0.986025i	$-0.553278\pi$
$977$	−10.4147	−0.333195	−0.166597	+	0.986025i	$0.553278\pi$
$978$	−9.02654	−0.288637
$979$	38.8637	1.24209
$980$	7.10722	0.227032
$981$	−6.36821	−0.203321
$982$	17.4052	0.555421
$983$	35.2566	1.12451	0.562255	−	0.826964i	$-0.309934\pi$
$983$	35.2566	1.12451	0.562255	+	0.826964i	$0.309934\pi$
$984$	0.119381	0.00380572
$985$	27.1768	0.865924
$986$	4.05327	0.129082
$987$	3.01639	0.0960127
$988$	−23.5364	−0.748794
$989$	−86.9641	−2.76530
$990$	−3.91775	−0.124514
$991$	13.8327	0.439410	0.219705	−	0.975566i	$-0.429491\pi$
$991$	13.8327	0.439410	0.219705	+	0.975566i	$0.429491\pi$
$992$	26.8120	0.851282
$993$	25.5625	0.811202
$994$	−31.8728	−1.01094
$995$	7.11554	0.225578
$996$	−16.8405	−0.533611
$997$	−42.0020	−1.33022	−0.665109	−	0.746746i	$-0.731615\pi$
$997$	−42.0020	−1.33022	−0.665109	+	0.746746i	$0.731615\pi$
$998$	74.4600	2.35699
$999$	−44.8304	−1.41837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.15	✓	16
3.2	odd	2		9027.2.a.n.1.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.15	✓	16	1.1	even	1	trivial
9027.2.a.n.1.2		16	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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+1.94258 q^{2} -1.53769 q^{3} +1.77364 q^{4} +1.30751 q^{5} -2.98709 q^{6} -3.17249 q^{7} -0.439731 q^{8} -0.635509 q^{9} +O(q^{10})\)	\(q+1.94258 q^{2} -1.53769 q^{3} +1.77364 q^{4} +1.30751 q^{5} -2.98709 q^{6} -3.17249 q^{7} -0.439731 q^{8} -0.635509 q^{9} +2.53995 q^{10} +2.42711 q^{11} -2.72730 q^{12} -5.43840 q^{13} -6.16284 q^{14} -2.01055 q^{15} -4.40149 q^{16} +1.00000 q^{17} -1.23453 q^{18} +2.44008 q^{19} +2.31905 q^{20} +4.87831 q^{21} +4.71487 q^{22} -8.76953 q^{23} +0.676170 q^{24} -3.29042 q^{25} -10.5646 q^{26} +5.59029 q^{27} -5.62685 q^{28} +2.08653 q^{29} -3.90566 q^{30} -3.49533 q^{31} -7.67080 q^{32} -3.73215 q^{33} +1.94258 q^{34} -4.14807 q^{35} -1.12716 q^{36} -8.01933 q^{37} +4.74007 q^{38} +8.36257 q^{39} -0.574953 q^{40} +0.176554 q^{41} +9.47654 q^{42} +9.91662 q^{43} +4.30482 q^{44} -0.830935 q^{45} -17.0356 q^{46} +0.618326 q^{47} +6.76812 q^{48} +3.06472 q^{49} -6.39191 q^{50} -1.53769 q^{51} -9.64574 q^{52} +8.02133 q^{53} +10.8596 q^{54} +3.17348 q^{55} +1.39504 q^{56} -3.75209 q^{57} +4.05327 q^{58} +1.00000 q^{59} -3.56598 q^{60} -11.5154 q^{61} -6.78998 q^{62} +2.01615 q^{63} -6.09821 q^{64} -7.11077 q^{65} -7.25001 q^{66} +2.62865 q^{67} +1.77364 q^{68} +13.4848 q^{69} -8.05798 q^{70} +5.17178 q^{71} +0.279453 q^{72} -12.2525 q^{73} -15.5782 q^{74} +5.05964 q^{75} +4.32782 q^{76} -7.70000 q^{77} +16.2450 q^{78} -10.0919 q^{79} -5.75499 q^{80} -6.68960 q^{81} +0.342972 q^{82} +6.17477 q^{83} +8.65235 q^{84} +1.30751 q^{85} +19.2639 q^{86} -3.20844 q^{87} -1.06728 q^{88} +16.0123 q^{89} -1.61416 q^{90} +17.2533 q^{91} -15.5540 q^{92} +5.37474 q^{93} +1.20115 q^{94} +3.19044 q^{95} +11.7953 q^{96} -11.3748 q^{97} +5.95347 q^{98} -1.54245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

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