LMFDB - Embedded newform 2006.2.a.w.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 9 x^{11} + 91 x^{10} + 14 x^{9} - 517 x^{8} + 70 x^{7} + 1296 x^{6} - 300 x^{5} + \cdots + 16 $ x^13 - 6x^12 - 9x^11 + 91x^10 + 14x^9 - 517x^8 + 70x^7 + 1296x^6 - 300x^5 - 1312x^4 + 472x^3 + 368x^2 - 176x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.714077$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.285923 q^{3} +1.00000 q^{4} -4.07831 q^{5} +0.285923 q^{6} +3.91932 q^{7} +1.00000 q^{8} -2.91825 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.285923 q^{3} +1.00000 q^{4} -4.07831 q^{5} +0.285923 q^{6} +3.91932 q^{7} +1.00000 q^{8} -2.91825 q^{9} -4.07831 q^{10} -4.78029 q^{11} +0.285923 q^{12} -1.31677 q^{13} +3.91932 q^{14} -1.16608 q^{15} +1.00000 q^{16} +1.00000 q^{17} -2.91825 q^{18} +6.42042 q^{19} -4.07831 q^{20} +1.12062 q^{21} -4.78029 q^{22} +9.01311 q^{23} +0.285923 q^{24} +11.6326 q^{25} -1.31677 q^{26} -1.69216 q^{27} +3.91932 q^{28} +2.41282 q^{29} -1.16608 q^{30} +6.04717 q^{31} +1.00000 q^{32} -1.36680 q^{33} +1.00000 q^{34} -15.9842 q^{35} -2.91825 q^{36} +11.7684 q^{37} +6.42042 q^{38} -0.376494 q^{39} -4.07831 q^{40} -3.60766 q^{41} +1.12062 q^{42} -7.85985 q^{43} -4.78029 q^{44} +11.9015 q^{45} +9.01311 q^{46} +11.5330 q^{47} +0.285923 q^{48} +8.36104 q^{49} +11.6326 q^{50} +0.285923 q^{51} -1.31677 q^{52} -3.92090 q^{53} -1.69216 q^{54} +19.4955 q^{55} +3.91932 q^{56} +1.83575 q^{57} +2.41282 q^{58} +1.00000 q^{59} -1.16608 q^{60} +5.01230 q^{61} +6.04717 q^{62} -11.4375 q^{63} +1.00000 q^{64} +5.37019 q^{65} -1.36680 q^{66} -4.12322 q^{67} +1.00000 q^{68} +2.57706 q^{69} -15.9842 q^{70} -3.58105 q^{71} -2.91825 q^{72} +0.330371 q^{73} +11.7684 q^{74} +3.32603 q^{75} +6.42042 q^{76} -18.7355 q^{77} -0.376494 q^{78} -11.9131 q^{79} -4.07831 q^{80} +8.27092 q^{81} -3.60766 q^{82} -13.6770 q^{83} +1.12062 q^{84} -4.07831 q^{85} -7.85985 q^{86} +0.689882 q^{87} -4.78029 q^{88} -10.0894 q^{89} +11.9015 q^{90} -5.16083 q^{91} +9.01311 q^{92} +1.72903 q^{93} +11.5330 q^{94} -26.1845 q^{95} +0.285923 q^{96} +3.82169 q^{97} +8.36104 q^{98} +13.9501 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.285923	0.165078	0.0825389	−	0.996588i	$-0.473697\pi$
$3$	0.285923	0.165078	0.0825389	+	0.996588i	$0.473697\pi$
$4$	1.00000	0.500000
$5$	−4.07831	−1.82388	−0.911938	−	0.410328i	$-0.865414\pi$
$5$	−4.07831	−1.82388	−0.911938	+	0.410328i	$0.865414\pi$
$6$	0.285923	0.116728
$7$	3.91932	1.48136	0.740681	−	0.671857i	$-0.234503\pi$
$7$	3.91932	1.48136	0.740681	+	0.671857i	$0.234503\pi$
$8$	1.00000	0.353553
$9$	−2.91825	−0.972749
$10$	−4.07831	−1.28967
$11$	−4.78029	−1.44131	−0.720656	−	0.693293i	$-0.756159\pi$
$11$	−4.78029	−1.44131	−0.720656	+	0.693293i	$0.756159\pi$
$12$	0.285923	0.0825389
$13$	−1.31677	−0.365206	−0.182603	−	0.983187i	$-0.558452\pi$
$13$	−1.31677	−0.365206	−0.182603	+	0.983187i	$0.558452\pi$
$14$	3.91932	1.04748
$15$	−1.16608	−0.301081
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.91825	−0.687838
$19$	6.42042	1.47295	0.736473	−	0.676467i	$-0.236490\pi$
$19$	6.42042	1.47295	0.736473	+	0.676467i	$0.236490\pi$
$20$	−4.07831	−0.911938
$21$	1.12062	0.244540
$22$	−4.78029	−1.01916
$23$	9.01311	1.87936	0.939682	−	0.342051i	$-0.111121\pi$
$23$	9.01311	1.87936	0.939682	+	0.342051i	$0.111121\pi$
$24$	0.285923	0.0583638
$25$	11.6326	2.32652
$26$	−1.31677	−0.258239
$27$	−1.69216	−0.325657
$28$	3.91932	0.740681
$29$	2.41282	0.448050	0.224025	−	0.974583i	$-0.428080\pi$
$29$	2.41282	0.448050	0.224025	+	0.974583i	$0.428080\pi$
$30$	−1.16608	−0.212897
$31$	6.04717	1.08610	0.543052	−	0.839699i	$-0.317269\pi$
$31$	6.04717	1.08610	0.543052	+	0.839699i	$0.317269\pi$
$32$	1.00000	0.176777
$33$	−1.36680	−0.237929
$34$	1.00000	0.171499
$35$	−15.9842	−2.70182
$36$	−2.91825	−0.486375
$37$	11.7684	1.93472	0.967360	−	0.253408i	$-0.0815515\pi$
$37$	11.7684	1.93472	0.967360	+	0.253408i	$0.0815515\pi$
$38$	6.42042	1.04153
$39$	−0.376494	−0.0602873
$40$	−4.07831	−0.644837
$41$	−3.60766	−0.563421	−0.281711	−	0.959499i	$-0.590902\pi$
$41$	−3.60766	−0.563421	−0.281711	+	0.959499i	$0.590902\pi$
$42$	1.12062	0.172916
$43$	−7.85985	−1.19862	−0.599308	−	0.800519i	$-0.704557\pi$
$43$	−7.85985	−1.19862	−0.599308	+	0.800519i	$0.704557\pi$
$44$	−4.78029	−0.720656
$45$	11.9015	1.77417
$46$	9.01311	1.32891
$47$	11.5330	1.68226	0.841132	−	0.540830i	$-0.181890\pi$
$47$	11.5330	1.68226	0.841132	+	0.540830i	$0.181890\pi$
$48$	0.285923	0.0412694
$49$	8.36104	1.19443
$50$	11.6326	1.64510
$51$	0.285923	0.0400372
$52$	−1.31677	−0.182603
$53$	−3.92090	−0.538577	−0.269289	−	0.963060i	$-0.586789\pi$
$53$	−3.92090	−0.538577	−0.269289	+	0.963060i	$0.586789\pi$
$54$	−1.69216	−0.230274
$55$	19.4955	2.62877
$56$	3.91932	0.523741
$57$	1.83575	0.243151
$58$	2.41282	0.316819
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−1.16608	−0.150541
$61$	5.01230	0.641759	0.320880	−	0.947120i	$-0.396022\pi$
$61$	5.01230	0.641759	0.320880	+	0.947120i	$0.396022\pi$
$62$	6.04717	0.767991
$63$	−11.4375	−1.44099
$64$	1.00000	0.125000
$65$	5.37019	0.666090
$66$	−1.36680	−0.168241
$67$	−4.12322	−0.503732	−0.251866	−	0.967762i	$-0.581044\pi$
$67$	−4.12322	−0.503732	−0.251866	+	0.967762i	$0.581044\pi$
$68$	1.00000	0.121268
$69$	2.57706	0.310241
$70$	−15.9842	−1.91048
$71$	−3.58105	−0.424992	−0.212496	−	0.977162i	$-0.568159\pi$
$71$	−3.58105	−0.424992	−0.212496	+	0.977162i	$0.568159\pi$
$72$	−2.91825	−0.343919
$73$	0.330371	0.0386670	0.0193335	−	0.999813i	$-0.493846\pi$
$73$	0.330371	0.0386670	0.0193335	+	0.999813i	$0.493846\pi$
$74$	11.7684	1.36805
$75$	3.32603	0.384057
$76$	6.42042	0.736473
$77$	−18.7355	−2.13511
$78$	−0.376494	−0.0426296
$79$	−11.9131	−1.34033	−0.670163	−	0.742214i	$-0.733776\pi$
$79$	−11.9131	−1.34033	−0.670163	+	0.742214i	$0.733776\pi$
$80$	−4.07831	−0.455969
$81$	8.27092	0.918991
$82$	−3.60766	−0.398399
$83$	−13.6770	−1.50125	−0.750624	−	0.660730i	$-0.770247\pi$
$83$	−13.6770	−1.50125	−0.750624	+	0.660730i	$0.770247\pi$
$84$	1.12062	0.122270
$85$	−4.07831	−0.442355
$86$	−7.85985	−0.847549
$87$	0.689882	0.0739631
$88$	−4.78029	−0.509581
$89$	−10.0894	−1.06948	−0.534739	−	0.845017i	$-0.679590\pi$
$89$	−10.0894	−1.06948	−0.534739	+	0.845017i	$0.679590\pi$
$90$	11.9015	1.25453
$91$	−5.16083	−0.541002
$92$	9.01311	0.939682
$93$	1.72903	0.179292
$94$	11.5330	1.18954
$95$	−26.1845	−2.68647
$96$	0.285923	0.0291819
$97$	3.82169	0.388033	0.194017	−	0.980998i	$-0.437848\pi$
$97$	3.82169	0.388033	0.194017	+	0.980998i	$0.437848\pi$
$98$	8.36104	0.844593
$99$	13.9501	1.40204
$100$	11.6326	1.16326
$101$	15.1764	1.51011	0.755053	−	0.655663i	$-0.227611\pi$
$101$	15.1764	1.51011	0.755053	+	0.655663i	$0.227611\pi$
$102$	0.285923	0.0283106
$103$	−0.575533	−0.0567090	−0.0283545	−	0.999598i	$-0.509027\pi$
$103$	−0.575533	−0.0567090	−0.0283545	+	0.999598i	$0.509027\pi$
$104$	−1.31677	−0.129120
$105$	−4.57025	−0.446011
$106$	−3.92090	−0.380832
$107$	7.53819	0.728744	0.364372	−	0.931253i	$-0.381284\pi$
$107$	7.53819	0.728744	0.364372	+	0.931253i	$0.381284\pi$
$108$	−1.69216	−0.162829
$109$	−6.35140	−0.608354	−0.304177	−	0.952615i	$-0.598381\pi$
$109$	−6.35140	−0.608354	−0.304177	+	0.952615i	$0.598381\pi$
$110$	19.4955	1.85882
$111$	3.36487	0.319379
$112$	3.91932	0.370341
$113$	14.6008	1.37352	0.686762	−	0.726883i	$-0.259032\pi$
$113$	14.6008	1.37352	0.686762	+	0.726883i	$0.259032\pi$
$114$	1.83575	0.171934
$115$	−36.7583	−3.42772
$116$	2.41282	0.224025
$117$	3.84265	0.355253
$118$	1.00000	0.0920575
$119$	3.91932	0.359283
$120$	−1.16608	−0.106448
$121$	11.8512	1.07738
$122$	5.01230	0.453792
$123$	−1.03151	−0.0930083
$124$	6.04717	0.543052
$125$	−27.0499	−2.41941
$126$	−11.4375	−1.01894
$127$	16.1567	1.43368	0.716838	−	0.697240i	$-0.245589\pi$
$127$	16.1567	1.43368	0.716838	+	0.697240i	$0.245589\pi$
$128$	1.00000	0.0883883
$129$	−2.24731	−0.197865
$130$	5.37019	0.470996
$131$	−10.3907	−0.907838	−0.453919	−	0.891043i	$-0.649974\pi$
$131$	−10.3907	−0.907838	−0.453919	+	0.891043i	$0.649974\pi$
$132$	−1.36680	−0.118964
$133$	25.1637	2.18197
$134$	−4.12322	−0.356192
$135$	6.90117	0.593958
$136$	1.00000	0.0857493
$137$	13.3930	1.14424	0.572119	−	0.820170i	$-0.306121\pi$
$137$	13.3930	1.14424	0.572119	+	0.820170i	$0.306121\pi$
$138$	2.57706	0.219374
$139$	5.48028	0.464831	0.232415	−	0.972617i	$-0.425337\pi$
$139$	5.48028	0.464831	0.232415	+	0.972617i	$0.425337\pi$
$140$	−15.9842	−1.35091
$141$	3.29756	0.277704
$142$	−3.58105	−0.300515
$143$	6.29453	0.526375
$144$	−2.91825	−0.243187
$145$	−9.84024	−0.817188
$146$	0.330371	0.0273417
$147$	2.39061	0.197175
$148$	11.7684	0.967360
$149$	−3.79352	−0.310778	−0.155389	−	0.987853i	$-0.549663\pi$
$149$	−3.79352	−0.310778	−0.155389	+	0.987853i	$0.549663\pi$
$150$	3.32603	0.271569
$151$	−15.3533	−1.24943	−0.624715	−	0.780852i	$-0.714785\pi$
$151$	−15.3533	−1.24943	−0.624715	+	0.780852i	$0.714785\pi$
$152$	6.42042	0.520765
$153$	−2.91825	−0.235926
$154$	−18.7355	−1.50975
$155$	−24.6622	−1.98092
$156$	−0.376494	−0.0301437
$157$	4.34405	0.346693	0.173346	−	0.984861i	$-0.444542\pi$
$157$	4.34405	0.346693	0.173346	+	0.984861i	$0.444542\pi$
$158$	−11.9131	−0.947753
$159$	−1.12108	−0.0889071
$160$	−4.07831	−0.322419
$161$	35.3252	2.78402
$162$	8.27092	0.649824
$163$	7.69125	0.602425	0.301213	−	0.953557i	$-0.402609\pi$
$163$	7.69125	0.602425	0.301213	+	0.953557i	$0.402609\pi$
$164$	−3.60766	−0.281711
$165$	5.57422	0.433952
$166$	−13.6770	−1.06154
$167$	16.9112	1.30863	0.654315	−	0.756222i	$-0.272957\pi$
$167$	16.9112	1.30863	0.654315	+	0.756222i	$0.272957\pi$
$168$	1.12062	0.0864580
$169$	−11.2661	−0.866625
$170$	−4.07831	−0.312792
$171$	−18.7364	−1.43281
$172$	−7.85985	−0.599308
$173$	−1.60169	−0.121774	−0.0608871	−	0.998145i	$-0.519393\pi$
$173$	−1.60169	−0.121774	−0.0608871	+	0.998145i	$0.519393\pi$
$174$	0.689882	0.0522998
$175$	45.5919	3.44642
$176$	−4.78029	−0.360328
$177$	0.285923	0.0214913
$178$	−10.0894	−0.756235
$179$	−6.18835	−0.462539	−0.231269	−	0.972890i	$-0.574288\pi$
$179$	−6.18835	−0.462539	−0.231269	+	0.972890i	$0.574288\pi$
$180$	11.9015	0.887087
$181$	−4.82804	−0.358865	−0.179433	−	0.983770i	$-0.557426\pi$
$181$	−4.82804	−0.358865	−0.179433	+	0.983770i	$0.557426\pi$
$182$	−5.16083	−0.382546
$183$	1.43313	0.105940
$184$	9.01311	0.664455
$185$	−47.9953	−3.52869
$186$	1.72903	0.126778
$187$	−4.78029	−0.349570
$188$	11.5330	0.841132
$189$	−6.63213	−0.482416
$190$	−26.1845	−1.89962
$191$	−7.32688	−0.530154	−0.265077	−	0.964227i	$-0.585397\pi$
$191$	−7.32688	−0.530154	−0.265077	+	0.964227i	$0.585397\pi$
$192$	0.285923	0.0206347
$193$	9.49196	0.683246	0.341623	−	0.939837i	$-0.389023\pi$
$193$	9.49196	0.683246	0.341623	+	0.939837i	$0.389023\pi$
$194$	3.82169	0.274381
$195$	1.53546	0.109957
$196$	8.36104	0.597217
$197$	26.2593	1.87089	0.935447	−	0.353466i	$-0.114997\pi$
$197$	26.2593	1.87089	0.935447	+	0.353466i	$0.114997\pi$
$198$	13.9501	0.991389
$199$	13.9431	0.988397	0.494199	−	0.869349i	$-0.335462\pi$
$199$	13.9431	0.988397	0.494199	+	0.869349i	$0.335462\pi$
$200$	11.6326	0.822550
$201$	−1.17892	−0.0831549
$202$	15.1764	1.06781
$203$	9.45662	0.663724
$204$	0.285923	0.0200186
$205$	14.7131	1.02761
$206$	−0.575533	−0.0400993
$207$	−26.3025	−1.82815
$208$	−1.31677	−0.0913014
$209$	−30.6915	−2.12298
$210$	−4.57025	−0.315377
$211$	8.60278	0.592240	0.296120	−	0.955151i	$-0.404307\pi$
$211$	8.60278	0.592240	0.296120	+	0.955151i	$0.404307\pi$
$212$	−3.92090	−0.269289
$213$	−1.02390	−0.0701567
$214$	7.53819	0.515300
$215$	32.0549	2.18613
$216$	−1.69216	−0.115137
$217$	23.7008	1.60891
$218$	−6.35140	−0.430171
$219$	0.0944608	0.00638307
$220$	19.4955	1.31439
$221$	−1.31677	−0.0885754
$222$	3.36487	0.225835
$223$	−14.7026	−0.984557	−0.492278	−	0.870438i	$-0.663836\pi$
$223$	−14.7026	−0.984557	−0.492278	+	0.870438i	$0.663836\pi$
$224$	3.91932	0.261870
$225$	−33.9469	−2.26312
$226$	14.6008	0.971228
$227$	8.64795	0.573985	0.286992	−	0.957933i	$-0.407345\pi$
$227$	8.64795	0.573985	0.286992	+	0.957933i	$0.407345\pi$
$228$	1.83575	0.121575
$229$	−18.3738	−1.21418	−0.607088	−	0.794635i	$-0.707662\pi$
$229$	−18.3738	−1.21418	−0.607088	+	0.794635i	$0.707662\pi$
$230$	−36.7583	−2.42377
$231$	−5.35691	−0.352459
$232$	2.41282	0.158410
$233$	−4.65656	−0.305061	−0.152531	−	0.988299i	$-0.548742\pi$
$233$	−4.65656	−0.305061	−0.152531	+	0.988299i	$0.548742\pi$
$234$	3.84265	0.251202
$235$	−47.0352	−3.06824
$236$	1.00000	0.0650945
$237$	−3.40622	−0.221258
$238$	3.91932	0.254052
$239$	−16.3798	−1.05952	−0.529760	−	0.848148i	$-0.677718\pi$
$239$	−16.3798	−1.05952	−0.529760	+	0.848148i	$0.677718\pi$
$240$	−1.16608	−0.0752703
$241$	22.0759	1.42204	0.711018	−	0.703173i	$-0.248234\pi$
$241$	22.0759	1.42204	0.711018	+	0.703173i	$0.248234\pi$
$242$	11.8512	0.761824
$243$	7.44134	0.477362
$244$	5.01230	0.320880
$245$	−34.0989	−2.17850
$246$	−1.03151	−0.0657668
$247$	−8.45421	−0.537928
$248$	6.04717	0.383996
$249$	−3.91057	−0.247823
$250$	−27.0499	−1.71078
$251$	−11.6741	−0.736866	−0.368433	−	0.929654i	$-0.620106\pi$
$251$	−11.6741	−0.736866	−0.368433	+	0.929654i	$0.620106\pi$
$252$	−11.4375	−0.720497
$253$	−43.0853	−2.70875
$254$	16.1567	1.01376
$255$	−1.16608	−0.0730230
$256$	1.00000	0.0625000
$257$	−1.32767	−0.0828179	−0.0414090	−	0.999142i	$-0.513185\pi$
$257$	−1.32767	−0.0828179	−0.0414090	+	0.999142i	$0.513185\pi$
$258$	−2.24731	−0.139912
$259$	46.1242	2.86602
$260$	5.37019	0.333045
$261$	−7.04122	−0.435840
$262$	−10.3907	−0.641938
$263$	−17.4168	−1.07396	−0.536982	−	0.843594i	$-0.680436\pi$
$263$	−17.4168	−1.07396	−0.536982	+	0.843594i	$0.680436\pi$
$264$	−1.36680	−0.0841205
$265$	15.9906	0.982298
$266$	25.1637	1.54288
$267$	−2.88480	−0.176547
$268$	−4.12322	−0.251866
$269$	−3.88471	−0.236855	−0.118427	−	0.992963i	$-0.537785\pi$
$269$	−3.88471	−0.236855	−0.118427	+	0.992963i	$0.537785\pi$
$270$	6.90117	0.419992
$271$	12.9137	0.784451	0.392225	−	0.919869i	$-0.371705\pi$
$271$	12.9137	0.784451	0.392225	+	0.919869i	$0.371705\pi$
$272$	1.00000	0.0606339
$273$	−1.47560	−0.0893074
$274$	13.3930	0.809099
$275$	−55.6073	−3.35325
$276$	2.57706	0.155121
$277$	−13.6686	−0.821265	−0.410633	−	0.911801i	$-0.634692\pi$
$277$	−13.6686	−0.821265	−0.410633	+	0.911801i	$0.634692\pi$
$278$	5.48028	0.328685
$279$	−17.6471	−1.05651
$280$	−15.9842	−0.955238
$281$	−10.3044	−0.614708	−0.307354	−	0.951595i	$-0.599444\pi$
$281$	−10.3044	−0.614708	−0.307354	+	0.951595i	$0.599444\pi$
$282$	3.29756	0.196367
$283$	12.3823	0.736053	0.368026	−	0.929815i	$-0.380034\pi$
$283$	12.3823	0.736053	0.368026	+	0.929815i	$0.380034\pi$
$284$	−3.58105	−0.212496
$285$	−7.48675	−0.443477
$286$	6.29453	0.372204
$287$	−14.1395	−0.834631
$288$	−2.91825	−0.171959
$289$	1.00000	0.0588235
$290$	−9.84024	−0.577839
$291$	1.09271	0.0640557
$292$	0.330371	0.0193335
$293$	−0.258834	−0.0151213	−0.00756064	−	0.999971i	$-0.502407\pi$
$293$	−0.258834	−0.0151213	−0.00756064	+	0.999971i	$0.502407\pi$
$294$	2.39061	0.139423
$295$	−4.07831	−0.237448
$296$	11.7684	0.684026
$297$	8.08904	0.469374
$298$	−3.79352	−0.219753
$299$	−11.8682	−0.686354
$300$	3.32603	0.192029
$301$	−30.8052	−1.77558
$302$	−15.3533	−0.883481
$303$	4.33928	0.249285
$304$	6.42042	0.368237
$305$	−20.4417	−1.17049
$306$	−2.91825	−0.166825
$307$	19.9342	1.13770	0.568852	−	0.822440i	$-0.307388\pi$
$307$	19.9342	1.13770	0.568852	+	0.822440i	$0.307388\pi$
$308$	−18.7355	−1.06755
$309$	−0.164558	−0.00936139
$310$	−24.6622	−1.40072
$311$	−14.0614	−0.797346	−0.398673	−	0.917093i	$-0.630529\pi$
$311$	−14.0614	−0.797346	−0.398673	+	0.917093i	$0.630529\pi$
$312$	−0.376494	−0.0213148
$313$	5.49437	0.310560	0.155280	−	0.987870i	$-0.450372\pi$
$313$	5.49437	0.310560	0.155280	+	0.987870i	$0.450372\pi$
$314$	4.34405	0.245149
$315$	46.6458	2.62819
$316$	−11.9131	−0.670163
$317$	−28.1515	−1.58114	−0.790572	−	0.612369i	$-0.790217\pi$
$317$	−28.1515	−1.58114	−0.790572	+	0.612369i	$0.790217\pi$
$318$	−1.12108	−0.0628668
$319$	−11.5340	−0.645780
$320$	−4.07831	−0.227984
$321$	2.15534	0.120299
$322$	35.3252	1.96860
$323$	6.42042	0.357242
$324$	8.27092	0.459495
$325$	−15.3174	−0.849659
$326$	7.69125	0.425979
$327$	−1.81601	−0.100426
$328$	−3.60766	−0.199200
$329$	45.2016	2.49204
$330$	5.57422	0.306851
$331$	−16.6197	−0.913499	−0.456749	−	0.889595i	$-0.650986\pi$
$331$	−16.6197	−0.913499	−0.456749	+	0.889595i	$0.650986\pi$
$332$	−13.6770	−0.750624
$333$	−34.3432	−1.88200
$334$	16.9112	0.925342
$335$	16.8158	0.918744
$336$	1.12062	0.0611350
$337$	0.466888	0.0254330	0.0127165	−	0.999919i	$-0.495952\pi$
$337$	0.466888	0.0254330	0.0127165	+	0.999919i	$0.495952\pi$
$338$	−11.2661	−0.612796
$339$	4.17469	0.226738
$340$	−4.07831	−0.221177
$341$	−28.9072	−1.56541
$342$	−18.7364	−1.01315
$343$	5.33435	0.288028
$344$	−7.85985	−0.423775
$345$	−10.5100	−0.565841
$346$	−1.60169	−0.0861074
$347$	14.5689	0.782097	0.391049	−	0.920370i	$-0.372112\pi$
$347$	14.5689	0.782097	0.391049	+	0.920370i	$0.372112\pi$
$348$	0.689882	0.0369816
$349$	26.9840	1.44442	0.722210	−	0.691674i	$-0.243126\pi$
$349$	26.9840	1.44442	0.722210	+	0.691674i	$0.243126\pi$
$350$	45.5919	2.43699
$351$	2.22819	0.118932
$352$	−4.78029	−0.254790
$353$	25.7758	1.37191	0.685955	−	0.727644i	$-0.259385\pi$
$353$	25.7758	1.37191	0.685955	+	0.727644i	$0.259385\pi$
$354$	0.285923	0.0151966
$355$	14.6046	0.775133
$356$	−10.0894	−0.534739
$357$	1.12062	0.0593097
$358$	−6.18835	−0.327064
$359$	−16.0162	−0.845303	−0.422651	−	0.906292i	$-0.638901\pi$
$359$	−16.0162	−0.845303	−0.422651	+	0.906292i	$0.638901\pi$
$360$	11.9015	0.627265
$361$	22.2219	1.16957
$362$	−4.82804	−0.253756
$363$	3.38853	0.177852
$364$	−5.16083	−0.270501
$365$	−1.34736	−0.0705238
$366$	1.43313	0.0749110
$367$	−14.8026	−0.772688	−0.386344	−	0.922355i	$-0.626262\pi$
$367$	−14.8026	−0.772688	−0.386344	+	0.922355i	$0.626262\pi$
$368$	9.01311	0.469841
$369$	10.5280	0.548068
$370$	−47.9953	−2.49516
$371$	−15.3672	−0.797828
$372$	1.72903	0.0896458
$373$	23.9462	1.23989	0.619943	−	0.784647i	$-0.287156\pi$
$373$	23.9462	1.23989	0.619943	+	0.784647i	$0.287156\pi$
$374$	−4.78029	−0.247183
$375$	−7.73418	−0.399391
$376$	11.5330	0.594770
$377$	−3.17713	−0.163630
$378$	−6.63213	−0.341120
$379$	−16.1971	−0.831991	−0.415996	−	0.909367i	$-0.636567\pi$
$379$	−16.1971	−0.831991	−0.415996	+	0.909367i	$0.636567\pi$
$380$	−26.1845	−1.34324
$381$	4.61957	0.236668
$382$	−7.32688	−0.374876
$383$	33.6348	1.71866	0.859328	−	0.511425i	$-0.170882\pi$
$383$	33.6348	1.71866	0.859328	+	0.511425i	$0.170882\pi$
$384$	0.285923	0.0145910
$385$	76.4091	3.89417
$386$	9.49196	0.483128
$387$	22.9370	1.16595
$388$	3.82169	0.194017
$389$	7.62197	0.386449	0.193224	−	0.981155i	$-0.438105\pi$
$389$	7.62197	0.386449	0.193224	+	0.981155i	$0.438105\pi$
$390$	1.53546	0.0777511
$391$	9.01311	0.455812
$392$	8.36104	0.422296
$393$	−2.97094	−0.149864
$394$	26.2593	1.32292
$395$	48.5852	2.44459
$396$	13.9501	0.701018
$397$	16.0194	0.803989	0.401994	−	0.915642i	$-0.368317\pi$
$397$	16.0194	0.803989	0.401994	+	0.915642i	$0.368317\pi$
$398$	13.9431	0.698902
$399$	7.19488	0.360194
$400$	11.6326	0.581631
$401$	−24.9142	−1.24416	−0.622078	−	0.782955i	$-0.713711\pi$
$401$	−24.9142	−1.24416	−0.622078	+	0.782955i	$0.713711\pi$
$402$	−1.17892	−0.0587994
$403$	−7.96271	−0.396651
$404$	15.1764	0.755053
$405$	−33.7314	−1.67612
$406$	9.45662	0.469324
$407$	−56.2566	−2.78853
$408$	0.285923	0.0141553
$409$	−29.5482	−1.46107	−0.730533	−	0.682877i	$-0.760728\pi$
$409$	−29.5482	−1.46107	−0.730533	+	0.682877i	$0.760728\pi$
$410$	14.7131	0.726630
$411$	3.82936	0.188888
$412$	−0.575533	−0.0283545
$413$	3.91932	0.192857
$414$	−26.3025	−1.29270
$415$	55.7791	2.73809
$416$	−1.31677	−0.0645598
$417$	1.56694	0.0767333
$418$	−30.6915	−1.50117
$419$	32.8870	1.60664	0.803318	−	0.595551i	$-0.203066\pi$
$419$	32.8870	1.60664	0.803318	+	0.595551i	$0.203066\pi$
$420$	−4.57025	−0.223005
$421$	−5.33348	−0.259938	−0.129969	−	0.991518i	$-0.541488\pi$
$421$	−5.33348	−0.259938	−0.129969	+	0.991518i	$0.541488\pi$
$422$	8.60278	0.418777
$423$	−33.6562	−1.63642
$424$	−3.92090	−0.190416
$425$	11.6326	0.564265
$426$	−1.02390	−0.0496083
$427$	19.6448	0.950678
$428$	7.53819	0.364372
$429$	1.79975	0.0868929
$430$	32.0549	1.54582
$431$	−27.2486	−1.31252	−0.656259	−	0.754536i	$-0.727862\pi$
$431$	−27.2486	−1.31252	−0.656259	+	0.754536i	$0.727862\pi$
$432$	−1.69216	−0.0814143
$433$	−13.1313	−0.631052	−0.315526	−	0.948917i	$-0.602181\pi$
$433$	−13.1313	−0.631052	−0.315526	+	0.948917i	$0.602181\pi$
$434$	23.7008	1.13767
$435$	−2.81355	−0.134900
$436$	−6.35140	−0.304177
$437$	57.8680	2.76820
$438$	0.0944608	0.00451351
$439$	−37.6702	−1.79790	−0.898951	−	0.438050i	$-0.855669\pi$
$439$	−37.6702	−1.79790	−0.898951	+	0.438050i	$0.855669\pi$
$440$	19.4955	0.929412
$441$	−24.3996	−1.16189
$442$	−1.31677	−0.0626322
$443$	4.00192	0.190137	0.0950685	−	0.995471i	$-0.469693\pi$
$443$	4.00192	0.190137	0.0950685	+	0.995471i	$0.469693\pi$
$444$	3.36487	0.159690
$445$	41.1479	1.95060
$446$	−14.7026	−0.696187
$447$	−1.08466	−0.0513025
$448$	3.91932	0.185170
$449$	37.1350	1.75251	0.876254	−	0.481850i	$-0.160035\pi$
$449$	37.1350	1.75251	0.876254	+	0.481850i	$0.160035\pi$
$450$	−33.9469	−1.60027
$451$	17.2457	0.812066
$452$	14.6008	0.686762
$453$	−4.38985	−0.206253
$454$	8.64795	0.405868
$455$	21.0475	0.986720
$456$	1.83575	0.0859668
$457$	−28.3711	−1.32715	−0.663573	−	0.748111i	$-0.730961\pi$
$457$	−28.3711	−1.32715	−0.663573	+	0.748111i	$0.730961\pi$
$458$	−18.3738	−0.858552
$459$	−1.69216	−0.0789834
$460$	−36.7583	−1.71386
$461$	−13.9578	−0.650079	−0.325039	−	0.945700i	$-0.605378\pi$
$461$	−13.9578	−0.650079	−0.325039	+	0.945700i	$0.605378\pi$
$462$	−5.35691	−0.249226
$463$	22.5179	1.04649	0.523247	−	0.852181i	$-0.324720\pi$
$463$	22.5179	1.04649	0.523247	+	0.852181i	$0.324720\pi$
$464$	2.41282	0.112013
$465$	−7.05150	−0.327006
$466$	−4.65656	−0.215711
$467$	6.23544	0.288542	0.144271	−	0.989538i	$-0.453916\pi$
$467$	6.23544	0.288542	0.144271	+	0.989538i	$0.453916\pi$
$468$	3.84265	0.177627
$469$	−16.1602	−0.746209
$470$	−47.0352	−2.16957
$471$	1.24206	0.0572313
$472$	1.00000	0.0460287
$473$	37.5724	1.72758
$474$	−3.40622	−0.156453
$475$	74.6863	3.42684
$476$	3.91932	0.179642
$477$	11.4422	0.523901
$478$	−16.3798	−0.749194
$479$	40.6366	1.85673	0.928367	−	0.371665i	$-0.121213\pi$
$479$	40.6366	1.85673	0.928367	+	0.371665i	$0.121213\pi$
$480$	−1.16608	−0.0532242
$481$	−15.4963	−0.706570
$482$	22.0759	1.00553
$483$	10.1003	0.459579
$484$	11.8512	0.538691
$485$	−15.5860	−0.707725
$486$	7.44134	0.337546
$487$	15.6653	0.709862	0.354931	−	0.934892i	$-0.384504\pi$
$487$	15.6653	0.709862	0.354931	+	0.934892i	$0.384504\pi$
$488$	5.01230	0.226896
$489$	2.19911	0.0994470
$490$	−34.0989	−1.54043
$491$	−39.7101	−1.79209	−0.896047	−	0.443960i	$-0.853573\pi$
$491$	−39.7101	−1.79209	−0.896047	+	0.443960i	$0.853573\pi$
$492$	−1.03151	−0.0465042
$493$	2.41282	0.108668
$494$	−8.45421	−0.380373
$495$	−56.8927	−2.55714
$496$	6.04717	0.271526
$497$	−14.0353	−0.629567
$498$	−3.91057	−0.175237
$499$	−28.6830	−1.28403	−0.642013	−	0.766694i	$-0.721900\pi$
$499$	−28.6830	−1.28403	−0.642013	+	0.766694i	$0.721900\pi$
$500$	−27.0499	−1.20971
$501$	4.83531	0.216026
$502$	−11.6741	−0.521043
$503$	24.6019	1.09695	0.548473	−	0.836168i	$-0.315209\pi$
$503$	24.6019	1.09695	0.548473	+	0.836168i	$0.315209\pi$
$504$	−11.4375	−0.509468
$505$	−61.8940	−2.75425
$506$	−43.0853	−1.91537
$507$	−3.22125	−0.143061
$508$	16.1567	0.716838
$509$	4.48227	0.198673	0.0993366	−	0.995054i	$-0.468328\pi$
$509$	4.48227	0.198673	0.0993366	+	0.995054i	$0.468328\pi$
$510$	−1.16608	−0.0516350
$511$	1.29483	0.0572799
$512$	1.00000	0.0441942
$513$	−10.8644	−0.479675
$514$	−1.32767	−0.0585611
$515$	2.34720	0.103430
$516$	−2.24731	−0.0989324
$517$	−55.1312	−2.42467
$518$	46.1242	2.02658
$519$	−0.457960	−0.0201022
$520$	5.37019	0.235498
$521$	−19.4774	−0.853322	−0.426661	−	0.904412i	$-0.640310\pi$
$521$	−19.4774	−0.853322	−0.426661	+	0.904412i	$0.640310\pi$
$522$	−7.04122	−0.308186
$523$	−8.86027	−0.387433	−0.193716	−	0.981058i	$-0.562054\pi$
$523$	−8.86027	−0.387433	−0.193716	+	0.981058i	$0.562054\pi$
$524$	−10.3907	−0.453919
$525$	13.0358	0.568928
$526$	−17.4168	−0.759408
$527$	6.04717	0.263419
$528$	−1.36680	−0.0594822
$529$	58.2361	2.53201
$530$	15.9906	0.694589
$531$	−2.91825	−0.126641
$532$	25.1637	1.09098
$533$	4.75044	0.205765
$534$	−2.88480	−0.124838
$535$	−30.7431	−1.32914
$536$	−4.12322	−0.178096
$537$	−1.76939	−0.0763549
$538$	−3.88471	−0.167482
$539$	−39.9682	−1.72155
$540$	6.90117	0.296979
$541$	−21.5681	−0.927286	−0.463643	−	0.886022i	$-0.653458\pi$
$541$	−21.5681	−0.927286	−0.463643	+	0.886022i	$0.653458\pi$
$542$	12.9137	0.554690
$543$	−1.38045	−0.0592407
$544$	1.00000	0.0428746
$545$	25.9030	1.10956
$546$	−1.47560	−0.0631498
$547$	3.76800	0.161108	0.0805541	−	0.996750i	$-0.474331\pi$
$547$	3.76800	0.161108	0.0805541	+	0.996750i	$0.474331\pi$
$548$	13.3930	0.572119
$549$	−14.6271	−0.624271
$550$	−55.6073	−2.37110
$551$	15.4913	0.659954
$552$	2.57706	0.109687
$553$	−46.6911	−1.98551
$554$	−13.6686	−0.580722
$555$	−13.7230	−0.582508
$556$	5.48028	0.232415
$557$	−7.21686	−0.305788	−0.152894	−	0.988243i	$-0.548859\pi$
$557$	−7.21686	−0.305788	−0.152894	+	0.988243i	$0.548859\pi$
$558$	−17.6471	−0.747063
$559$	10.3496	0.437741
$560$	−15.9842	−0.675455
$561$	−1.36680	−0.0577062
$562$	−10.3044	−0.434664
$563$	12.8289	0.540673	0.270337	−	0.962766i	$-0.412865\pi$
$563$	12.8289	0.540673	0.270337	+	0.962766i	$0.412865\pi$
$564$	3.29756	0.138852
$565$	−59.5464	−2.50514
$566$	12.3823	0.520468
$567$	32.4163	1.36136
$568$	−3.58105	−0.150257
$569$	−16.7703	−0.703048	−0.351524	−	0.936179i	$-0.614336\pi$
$569$	−16.7703	−0.703048	−0.351524	+	0.936179i	$0.614336\pi$
$570$	−7.48675	−0.313585
$571$	−4.42731	−0.185277	−0.0926385	−	0.995700i	$-0.529530\pi$
$571$	−4.42731	−0.185277	−0.0926385	+	0.995700i	$0.529530\pi$
$572$	6.29453	0.263188
$573$	−2.09492	−0.0875167
$574$	−14.1395	−0.590173
$575$	104.846	4.37238
$576$	−2.91825	−0.121594
$577$	7.04886	0.293448	0.146724	−	0.989177i	$-0.453127\pi$
$577$	7.04886	0.293448	0.146724	+	0.989177i	$0.453127\pi$
$578$	1.00000	0.0415945
$579$	2.71397	0.112789
$580$	−9.84024	−0.408594
$581$	−53.6045	−2.22389
$582$	1.09271	0.0452942
$583$	18.7431	0.776258
$584$	0.330371	0.0136709
$585$	−15.6715	−0.647938
$586$	−0.258834	−0.0106924
$587$	2.51459	0.103788	0.0518942	−	0.998653i	$-0.483474\pi$
$587$	2.51459	0.103788	0.0518942	+	0.998653i	$0.483474\pi$
$588$	2.39061	0.0985873
$589$	38.8254	1.59977
$590$	−4.07831	−0.167901
$591$	7.50813	0.308843
$592$	11.7684	0.483680
$593$	−1.31934	−0.0541787	−0.0270894	−	0.999633i	$-0.508624\pi$
$593$	−1.31934	−0.0541787	−0.0270894	+	0.999633i	$0.508624\pi$
$594$	8.08904	0.331897
$595$	−15.9842	−0.655288
$596$	−3.79352	−0.155389
$597$	3.98664	0.163162
$598$	−11.8682	−0.485325
$599$	14.7129	0.601154	0.300577	−	0.953758i	$-0.402821\pi$
$599$	14.7129	0.601154	0.300577	+	0.953758i	$0.402821\pi$
$600$	3.32603	0.135785
$601$	−2.64763	−0.107999	−0.0539995	−	0.998541i	$-0.517197\pi$
$601$	−2.64763	−0.107999	−0.0539995	+	0.998541i	$0.517197\pi$
$602$	−30.8052	−1.25553
$603$	12.0326	0.490005
$604$	−15.3533	−0.624715
$605$	−48.3328	−1.96501
$606$	4.33928	0.176271
$607$	0.827234	0.0335764	0.0167882	−	0.999859i	$-0.494656\pi$
$607$	0.827234	0.0335764	0.0167882	+	0.999859i	$0.494656\pi$
$608$	6.42042	0.260383
$609$	2.70387	0.109566
$610$	−20.4417	−0.827661
$611$	−15.1863	−0.614372
$612$	−2.91825	−0.117963
$613$	−26.9609	−1.08894	−0.544470	−	0.838780i	$-0.683269\pi$
$613$	−26.9609	−1.08894	−0.544470	+	0.838780i	$0.683269\pi$
$614$	19.9342	0.804478
$615$	4.20683	0.169636
$616$	−18.7355	−0.754874
$617$	3.13421	0.126179	0.0630894	−	0.998008i	$-0.479905\pi$
$617$	3.13421	0.126179	0.0630894	+	0.998008i	$0.479905\pi$
$618$	−0.164558	−0.00661950
$619$	24.7604	0.995205	0.497603	−	0.867405i	$-0.334214\pi$
$619$	24.7604	0.995205	0.497603	+	0.867405i	$0.334214\pi$
$620$	−24.6622	−0.990459
$621$	−15.2517	−0.612028
$622$	−14.0614	−0.563809
$623$	−39.5437	−1.58428
$624$	−0.376494	−0.0150718
$625$	52.1546	2.08619
$626$	5.49437	0.219599
$627$	−8.77541	−0.350456
$628$	4.34405	0.173346
$629$	11.7684	0.469238
$630$	46.6458	1.85841
$631$	24.2027	0.963495	0.481748	−	0.876310i	$-0.340002\pi$
$631$	24.2027	0.963495	0.481748	+	0.876310i	$0.340002\pi$
$632$	−11.9131	−0.473877
$633$	2.45973	0.0977657
$634$	−28.1515	−1.11804
$635$	−65.8920	−2.61485
$636$	−1.12108	−0.0444536
$637$	−11.0095	−0.436214
$638$	−11.5340	−0.456635
$639$	10.4504	0.413411
$640$	−4.07831	−0.161209
$641$	−43.0296	−1.69957	−0.849784	−	0.527131i	$-0.823268\pi$
$641$	−43.0296	−1.69957	−0.849784	+	0.527131i	$0.823268\pi$
$642$	2.15534	0.0850646
$643$	−19.0732	−0.752173	−0.376087	−	0.926585i	$-0.622730\pi$
$643$	−19.0732	−0.752173	−0.376087	+	0.926585i	$0.622730\pi$
$644$	35.3252	1.39201
$645$	9.16524	0.360881
$646$	6.42042	0.252608
$647$	−28.3976	−1.11642	−0.558212	−	0.829698i	$-0.688513\pi$
$647$	−28.3976	−1.11642	−0.558212	+	0.829698i	$0.688513\pi$
$648$	8.27092	0.324912
$649$	−4.78029	−0.187643
$650$	−15.3174	−0.600800
$651$	6.77660	0.265596
$652$	7.69125	0.301213
$653$	−12.6923	−0.496687	−0.248344	−	0.968672i	$-0.579886\pi$
$653$	−12.6923	−0.496687	−0.248344	+	0.968672i	$0.579886\pi$
$654$	−1.81601	−0.0710117
$655$	42.3764	1.65578
$656$	−3.60766	−0.140855
$657$	−0.964105	−0.0376133
$658$	45.2016	1.76214
$659$	42.9742	1.67404	0.837018	−	0.547175i	$-0.184297\pi$
$659$	42.9742	1.67404	0.837018	+	0.547175i	$0.184297\pi$
$660$	5.57422	0.216976
$661$	10.1703	0.395577	0.197789	−	0.980245i	$-0.436624\pi$
$661$	10.1703	0.395577	0.197789	+	0.980245i	$0.436624\pi$
$662$	−16.6197	−0.645941
$663$	−0.376494	−0.0146218
$664$	−13.6770	−0.530771
$665$	−102.625	−3.97964
$666$	−34.3432	−1.33077
$667$	21.7470	0.842049
$668$	16.9112	0.654315
$669$	−4.20380	−0.162528
$670$	16.8158	0.649650
$671$	−23.9603	−0.924975
$672$	1.12062	0.0432290
$673$	−17.2957	−0.666701	−0.333351	−	0.942803i	$-0.608179\pi$
$673$	−17.2957	−0.666701	−0.333351	+	0.942803i	$0.608179\pi$
$674$	0.466888	0.0179838
$675$	−19.6843	−0.757649
$676$	−11.2661	−0.433312
$677$	7.84403	0.301471	0.150735	−	0.988574i	$-0.451836\pi$
$677$	7.84403	0.301471	0.150735	+	0.988574i	$0.451836\pi$
$678$	4.17469	0.160328
$679$	14.9784	0.574818
$680$	−4.07831	−0.156396
$681$	2.47265	0.0947521
$682$	−28.9072	−1.10692
$683$	47.5044	1.81771	0.908853	−	0.417117i	$-0.136959\pi$
$683$	47.5044	1.81771	0.908853	+	0.417117i	$0.136959\pi$
$684$	−18.7364	−0.716404
$685$	−54.6207	−2.08695
$686$	5.33435	0.203666
$687$	−5.25350	−0.200433
$688$	−7.85985	−0.299654
$689$	5.16291	0.196691
$690$	−10.5100	−0.400110
$691$	−41.7085	−1.58667	−0.793333	−	0.608788i	$-0.791656\pi$
$691$	−41.7085	−1.58667	−0.793333	+	0.608788i	$0.791656\pi$
$692$	−1.60169	−0.0608871
$693$	54.6748	2.07692
$694$	14.5689	0.553026
$695$	−22.3503	−0.847794
$696$	0.689882	0.0261499
$697$	−3.60766	−0.136650
$698$	26.9840	1.02136
$699$	−1.33142	−0.0503589
$700$	45.5919	1.72321
$701$	−20.5485	−0.776105	−0.388052	−	0.921637i	$-0.626852\pi$
$701$	−20.5485	−0.776105	−0.388052	+	0.921637i	$0.626852\pi$
$702$	2.22819	0.0840975
$703$	75.5584	2.84974
$704$	−4.78029	−0.180164
$705$	−13.4485	−0.506498
$706$	25.7758	0.970087
$707$	59.4810	2.23701
$708$	0.285923	0.0107456
$709$	−47.6900	−1.79104	−0.895518	−	0.445024i	$-0.853195\pi$
$709$	−47.6900	−1.79104	−0.895518	+	0.445024i	$0.853195\pi$
$710$	14.6046	0.548101
$711$	34.7653	1.30380
$712$	−10.0894	−0.378118
$713$	54.5038	2.04118
$714$	1.12062	0.0419383
$715$	−25.6711	−0.960043
$716$	−6.18835	−0.231269
$717$	−4.68336	−0.174903
$718$	−16.0162	−0.597719
$719$	28.2735	1.05442	0.527212	−	0.849734i	$-0.323237\pi$
$719$	28.2735	1.05442	0.527212	+	0.849734i	$0.323237\pi$
$720$	11.9015	0.443543
$721$	−2.25570	−0.0840065
$722$	22.2219	0.827012
$723$	6.31202	0.234747
$724$	−4.82804	−0.179433
$725$	28.0674	1.04240
$726$	3.38853	0.125760
$727$	−5.62825	−0.208740	−0.104370	−	0.994539i	$-0.533283\pi$
$727$	−5.62825	−0.208740	−0.104370	+	0.994539i	$0.533283\pi$
$728$	−5.16083	−0.191273
$729$	−22.6851	−0.840189
$730$	−1.34736	−0.0498679
$731$	−7.85985	−0.290707
$732$	1.43313	0.0529701
$733$	−13.2762	−0.490367	−0.245183	−	0.969477i	$-0.578848\pi$
$733$	−13.2762	−0.490367	−0.245183	+	0.969477i	$0.578848\pi$
$734$	−14.8026	−0.546373
$735$	−9.74967	−0.359622
$736$	9.01311	0.332228
$737$	19.7102	0.726035
$738$	10.5280	0.387542
$739$	−34.6130	−1.27326	−0.636629	−	0.771170i	$-0.719672\pi$
$739$	−34.6130	−1.27326	−0.636629	+	0.771170i	$0.719672\pi$
$740$	−47.9953	−1.76434
$741$	−2.41725	−0.0888000
$742$	−15.3672	−0.564149
$743$	6.08926	0.223393	0.111697	−	0.993742i	$-0.464372\pi$
$743$	6.08926	0.223393	0.111697	+	0.993742i	$0.464372\pi$
$744$	1.72903	0.0633891
$745$	15.4712	0.566820
$746$	23.9462	0.876731
$747$	39.9129	1.46034
$748$	−4.78029	−0.174785
$749$	29.5445	1.07953
$750$	−7.73418	−0.282412
$751$	38.8137	1.41633	0.708166	−	0.706046i	$-0.249523\pi$
$751$	38.8137	1.41633	0.708166	+	0.706046i	$0.249523\pi$
$752$	11.5330	0.420566
$753$	−3.33791	−0.121640
$754$	−3.17713	−0.115704
$755$	62.6154	2.27881
$756$	−6.63213	−0.241208
$757$	5.72381	0.208036	0.104018	−	0.994575i	$-0.466830\pi$
$757$	5.72381	0.208036	0.104018	+	0.994575i	$0.466830\pi$
$758$	−16.1971	−0.588307
$759$	−12.3191	−0.447154
$760$	−26.1845	−0.949811
$761$	−4.82087	−0.174756	−0.0873782	−	0.996175i	$-0.527849\pi$
$761$	−4.82087	−0.174756	−0.0873782	+	0.996175i	$0.527849\pi$
$762$	4.61957	0.167350
$763$	−24.8932	−0.901193
$764$	−7.32688	−0.265077
$765$	11.9015	0.430300
$766$	33.6348	1.21527
$767$	−1.31677	−0.0475457
$768$	0.285923	0.0103174
$769$	15.3874	0.554882	0.277441	−	0.960743i	$-0.410514\pi$
$769$	15.3874	0.554882	0.277441	+	0.960743i	$0.410514\pi$
$770$	76.4091	2.75359
$771$	−0.379612	−0.0136714
$772$	9.49196	0.341623
$773$	−4.05167	−0.145728	−0.0728642	−	0.997342i	$-0.523214\pi$
$773$	−4.05167	−0.145728	−0.0728642	+	0.997342i	$0.523214\pi$
$774$	22.9370	0.824453
$775$	70.3444	2.52684
$776$	3.82169	0.137191
$777$	13.1880	0.473116
$778$	7.62197	0.273261
$779$	−23.1627	−0.829889
$780$	1.53546	0.0549783
$781$	17.1184	0.612546
$782$	9.01311	0.322308
$783$	−4.08289	−0.145911
$784$	8.36104	0.298609
$785$	−17.7164	−0.632325
$786$	−2.97094	−0.105970
$787$	29.3671	1.04682	0.523411	−	0.852080i	$-0.324659\pi$
$787$	29.3671	1.04682	0.523411	+	0.852080i	$0.324659\pi$
$788$	26.2593	0.935447
$789$	−4.97986	−0.177288
$790$	48.5852	1.72858
$791$	57.2250	2.03469
$792$	13.9501	0.495694
$793$	−6.60003	−0.234374
$794$	16.0194	0.568506
$795$	4.57210	0.162156
$796$	13.9431	0.494199
$797$	−21.4564	−0.760026	−0.380013	−	0.924981i	$-0.624080\pi$
$797$	−21.4564	−0.760026	−0.380013	+	0.924981i	$0.624080\pi$
$798$	7.19488	0.254696
$799$	11.5330	0.408009
$800$	11.6326	0.411275
$801$	29.4435	1.04033
$802$	−24.9142	−0.879751
$803$	−1.57927	−0.0557313
$804$	−1.17892	−0.0415775
$805$	−144.067	−5.07770
$806$	−7.96271	−0.280475
$807$	−1.11073	−0.0390995
$808$	15.1764	0.533903
$809$	−16.9585	−0.596227	−0.298114	−	0.954530i	$-0.596357\pi$
$809$	−16.9585	−0.596227	−0.298114	+	0.954530i	$0.596357\pi$
$810$	−33.7314	−1.18520
$811$	−15.8166	−0.555396	−0.277698	−	0.960668i	$-0.589571\pi$
$811$	−15.8166	−0.555396	−0.277698	+	0.960668i	$0.589571\pi$
$812$	9.45662	0.331862
$813$	3.69232	0.129495
$814$	−56.2566	−1.97179
$815$	−31.3673	−1.09875
$816$	0.285923	0.0100093
$817$	−50.4636	−1.76550
$818$	−29.5482	−1.03313
$819$	15.0606	0.526259
$820$	14.7131	0.513805
$821$	−1.08622	−0.0379093	−0.0189547	−	0.999820i	$-0.506034\pi$
$821$	−1.08622	−0.0379093	−0.0189547	+	0.999820i	$0.506034\pi$
$822$	3.82936	0.133564
$823$	−5.20503	−0.181436	−0.0907180	−	0.995877i	$-0.528916\pi$
$823$	−5.20503	−0.181436	−0.0907180	+	0.995877i	$0.528916\pi$
$824$	−0.575533	−0.0200496
$825$	−15.8994	−0.553546
$826$	3.91932	0.136370
$827$	34.1843	1.18870	0.594352	−	0.804205i	$-0.297409\pi$
$827$	34.1843	1.18870	0.594352	+	0.804205i	$0.297409\pi$
$828$	−26.3025	−0.914075
$829$	51.5959	1.79200	0.896000	−	0.444054i	$-0.146460\pi$
$829$	51.5959	1.79200	0.896000	+	0.444054i	$0.146460\pi$
$830$	55.7791	1.93612
$831$	−3.90816	−0.135573
$832$	−1.31677	−0.0456507
$833$	8.36104	0.289693
$834$	1.56694	0.0542586
$835$	−68.9693	−2.38678
$836$	−30.6915	−1.06149
$837$	−10.2328	−0.353697
$838$	32.8870	1.13606
$839$	1.00043	0.0345386	0.0172693	−	0.999851i	$-0.494503\pi$
$839$	1.00043	0.0345386	0.0172693	+	0.999851i	$0.494503\pi$
$840$	−4.57025	−0.157689
$841$	−23.1783	−0.799251
$842$	−5.33348	−0.183804
$843$	−2.94626	−0.101475
$844$	8.60278	0.296120
$845$	45.9467	1.58062
$846$	−33.6562	−1.15712
$847$	46.4486	1.59599
$848$	−3.92090	−0.134644
$849$	3.54039	0.121506
$850$	11.6326	0.398995
$851$	106.070	3.63604
$852$	−1.02390	−0.0350784
$853$	−6.19927	−0.212259	−0.106129	−	0.994352i	$-0.533846\pi$
$853$	−6.19927	−0.212259	−0.106129	+	0.994352i	$0.533846\pi$
$854$	19.6448	0.672231
$855$	76.4128	2.61326
$856$	7.53819	0.257650
$857$	19.2655	0.658097	0.329049	−	0.944313i	$-0.393272\pi$
$857$	19.2655	0.658097	0.329049	+	0.944313i	$0.393272\pi$
$858$	1.79975	0.0614425
$859$	−13.5764	−0.463222	−0.231611	−	0.972809i	$-0.574400\pi$
$859$	−13.5764	−0.463222	−0.231611	+	0.972809i	$0.574400\pi$
$860$	32.0549	1.09306
$861$	−4.04282	−0.137779
$862$	−27.2486	−0.928091
$863$	−30.3958	−1.03469	−0.517343	−	0.855778i	$-0.673079\pi$
$863$	−30.3958	−1.03469	−0.517343	+	0.855778i	$0.673079\pi$
$864$	−1.69216	−0.0575686
$865$	6.53219	0.222101
$866$	−13.1313	−0.446221
$867$	0.285923	0.00971046
$868$	23.7008	0.804456
$869$	56.9480	1.93183
$870$	−2.81355	−0.0953884
$871$	5.42933	0.183966
$872$	−6.35140	−0.215086
$873$	−11.1526	−0.377459
$874$	57.8680	1.95741
$875$	−106.017	−3.58403
$876$	0.0944608	0.00319153
$877$	−1.83888	−0.0620946	−0.0310473	−	0.999518i	$-0.509884\pi$
$877$	−1.83888	−0.0620946	−0.0310473	+	0.999518i	$0.509884\pi$
$878$	−37.6702	−1.27131
$879$	−0.0740068	−0.00249619
$880$	19.4955	0.657194
$881$	55.2016	1.85979	0.929894	−	0.367827i	$-0.119898\pi$
$881$	55.2016	1.85979	0.929894	+	0.367827i	$0.119898\pi$
$882$	−24.3996	−0.821577
$883$	−39.6808	−1.33537	−0.667683	−	0.744446i	$-0.732714\pi$
$883$	−39.6808	−1.33537	−0.667683	+	0.744446i	$0.732714\pi$
$884$	−1.31677	−0.0442877
$885$	−1.16608	−0.0391975
$886$	4.00192	0.134447
$887$	−49.5253	−1.66290	−0.831448	−	0.555603i	$-0.812488\pi$
$887$	−49.5253	−1.66290	−0.831448	+	0.555603i	$0.812488\pi$
$888$	3.36487	0.112918
$889$	63.3232	2.12379
$890$	41.1479	1.37928
$891$	−39.5374	−1.32455
$892$	−14.7026	−0.492278
$893$	74.0469	2.47789
$894$	−1.08466	−0.0362763
$895$	25.2380	0.843614
$896$	3.91932	0.130935
$897$	−3.39338	−0.113302
$898$	37.1350	1.23921
$899$	14.5907	0.486629
$900$	−33.9469	−1.13156
$901$	−3.92090	−0.130624
$902$	17.2457	0.574217
$903$	−8.80793	−0.293110
$904$	14.6008	0.485614
$905$	19.6902	0.654526
$906$	−4.38985	−0.145843
$907$	−27.6506	−0.918122	−0.459061	−	0.888405i	$-0.651814\pi$
$907$	−27.6506	−0.918122	−0.459061	+	0.888405i	$0.651814\pi$
$908$	8.64795	0.286992
$909$	−44.2884	−1.46896
$910$	21.0475	0.697716
$911$	−33.8927	−1.12291	−0.561457	−	0.827506i	$-0.689759\pi$
$911$	−33.8927	−1.12291	−0.561457	+	0.827506i	$0.689759\pi$
$912$	1.83575	0.0607877
$913$	65.3801	2.16377
$914$	−28.3711	−0.938434
$915$	−5.84476	−0.193222
$916$	−18.3738	−0.607088
$917$	−40.7244	−1.34484
$918$	−1.69216	−0.0558497
$919$	−46.9522	−1.54881	−0.774405	−	0.632690i	$-0.781951\pi$
$919$	−46.9522	−1.54881	−0.774405	+	0.632690i	$0.781951\pi$
$920$	−36.7583	−1.21188
$921$	5.69964	0.187809
$922$	−13.9578	−0.459675
$923$	4.71540	0.155209
$924$	−5.35691	−0.176229
$925$	136.898	4.50117
$926$	22.5179	0.739983
$927$	1.67955	0.0551636
$928$	2.41282	0.0792048
$929$	−21.6479	−0.710245	−0.355122	−	0.934820i	$-0.615561\pi$
$929$	−21.6479	−0.710245	−0.355122	+	0.934820i	$0.615561\pi$
$930$	−7.05150	−0.231228
$931$	53.6814	1.75934
$932$	−4.65656	−0.152531
$933$	−4.02047	−0.131624
$934$	6.23544	0.204030
$935$	19.4955	0.637572
$936$	3.84265	0.125601
$937$	−41.5811	−1.35839	−0.679197	−	0.733956i	$-0.737672\pi$
$937$	−41.5811	−1.35839	−0.679197	+	0.733956i	$0.737672\pi$
$938$	−16.1602	−0.527650
$939$	1.57097	0.0512666
$940$	−47.0352	−1.53412
$941$	1.18000	0.0384668	0.0192334	−	0.999815i	$-0.493877\pi$
$941$	1.18000	0.0384668	0.0192334	+	0.999815i	$0.493877\pi$
$942$	1.24206	0.0404686
$943$	−32.5162	−1.05887
$944$	1.00000	0.0325472
$945$	27.0479	0.879867
$946$	37.5724	1.22158
$947$	14.0903	0.457874	0.228937	−	0.973441i	$-0.426475\pi$
$947$	14.0903	0.457874	0.228937	+	0.973441i	$0.426475\pi$
$948$	−3.40622	−0.110629
$949$	−0.435022	−0.0141214
$950$	74.6863	2.42314
$951$	−8.04915	−0.261012
$952$	3.91932	0.127026
$953$	43.0548	1.39468	0.697341	−	0.716739i	$-0.254366\pi$
$953$	43.0548	1.39468	0.697341	+	0.716739i	$0.254366\pi$
$954$	11.4422	0.370454
$955$	29.8813	0.966935
$956$	−16.3798	−0.529760
$957$	−3.29784	−0.106604
$958$	40.6366	1.31291
$959$	52.4913	1.69503
$960$	−1.16608	−0.0376352
$961$	5.56825	0.179621
$962$	−15.4963	−0.499621
$963$	−21.9983	−0.708885
$964$	22.0759	0.711018
$965$	−38.7112	−1.24616
$966$	10.1003	0.324972
$967$	23.5152	0.756198	0.378099	−	0.925765i	$-0.376578\pi$
$967$	23.5152	0.756198	0.378099	+	0.925765i	$0.376578\pi$
$968$	11.8512	0.380912
$969$	1.83575	0.0589727
$970$	−15.5860	−0.500437
$971$	−3.20186	−0.102752	−0.0513762	−	0.998679i	$-0.516361\pi$
$971$	−3.20186	−0.102752	−0.0513762	+	0.998679i	$0.516361\pi$
$972$	7.44134	0.238681
$973$	21.4789	0.688583
$974$	15.6653	0.501948
$975$	−4.37961	−0.140260
$976$	5.01230	0.160440
$977$	−27.9312	−0.893598	−0.446799	−	0.894634i	$-0.647436\pi$
$977$	−27.9312	−0.893598	−0.446799	+	0.894634i	$0.647436\pi$
$978$	2.19911	0.0703197
$979$	48.2305	1.54145
$980$	−34.0989	−1.08925
$981$	18.5350	0.591776
$982$	−39.7101	−1.26720
$983$	13.0970	0.417731	0.208865	−	0.977944i	$-0.433023\pi$
$983$	13.0970	0.417731	0.208865	+	0.977944i	$0.433023\pi$
$984$	−1.03151	−0.0328834
$985$	−107.093	−3.41228
$986$	2.41282	0.0768399
$987$	12.9242	0.411381
$988$	−8.45421	−0.268964
$989$	−70.8417	−2.25263
$990$	−56.8927	−1.80817
$991$	24.8676	0.789944	0.394972	−	0.918693i	$-0.370754\pi$
$991$	24.8676	0.789944	0.394972	+	0.918693i	$0.370754\pi$
$992$	6.04717	0.191998
$993$	−4.75194	−0.150798
$994$	−14.0353	−0.445171
$995$	−56.8641	−1.80271
$996$	−3.91057	−0.123911
$997$	29.3761	0.930351	0.465176	−	0.885218i	$-0.345991\pi$
$997$	29.3761	0.930351	0.465176	+	0.885218i	$0.345991\pi$
$998$	−28.6830	−0.907943
$999$	−19.9141	−0.630055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.w.1.6	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.w.1.6	✓	13	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.285923 q^{3} +1.00000 q^{4} -4.07831 q^{5} +0.285923 q^{6} +3.91932 q^{7} +1.00000 q^{8} -2.91825 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.285923 q^{3} +1.00000 q^{4} -4.07831 q^{5} +0.285923 q^{6} +3.91932 q^{7} +1.00000 q^{8} -2.91825 q^{9} -4.07831 q^{10} -4.78029 q^{11} +0.285923 q^{12} -1.31677 q^{13} +3.91932 q^{14} -1.16608 q^{15} +1.00000 q^{16} +1.00000 q^{17} -2.91825 q^{18} +6.42042 q^{19} -4.07831 q^{20} +1.12062 q^{21} -4.78029 q^{22} +9.01311 q^{23} +0.285923 q^{24} +11.6326 q^{25} -1.31677 q^{26} -1.69216 q^{27} +3.91932 q^{28} +2.41282 q^{29} -1.16608 q^{30} +6.04717 q^{31} +1.00000 q^{32} -1.36680 q^{33} +1.00000 q^{34} -15.9842 q^{35} -2.91825 q^{36} +11.7684 q^{37} +6.42042 q^{38} -0.376494 q^{39} -4.07831 q^{40} -3.60766 q^{41} +1.12062 q^{42} -7.85985 q^{43} -4.78029 q^{44} +11.9015 q^{45} +9.01311 q^{46} +11.5330 q^{47} +0.285923 q^{48} +8.36104 q^{49} +11.6326 q^{50} +0.285923 q^{51} -1.31677 q^{52} -3.92090 q^{53} -1.69216 q^{54} +19.4955 q^{55} +3.91932 q^{56} +1.83575 q^{57} +2.41282 q^{58} +1.00000 q^{59} -1.16608 q^{60} +5.01230 q^{61} +6.04717 q^{62} -11.4375 q^{63} +1.00000 q^{64} +5.37019 q^{65} -1.36680 q^{66} -4.12322 q^{67} +1.00000 q^{68} +2.57706 q^{69} -15.9842 q^{70} -3.58105 q^{71} -2.91825 q^{72} +0.330371 q^{73} +11.7684 q^{74} +3.32603 q^{75} +6.42042 q^{76} -18.7355 q^{77} -0.376494 q^{78} -11.9131 q^{79} -4.07831 q^{80} +8.27092 q^{81} -3.60766 q^{82} -13.6770 q^{83} +1.12062 q^{84} -4.07831 q^{85} -7.85985 q^{86} +0.689882 q^{87} -4.78029 q^{88} -10.0894 q^{89} +11.9015 q^{90} -5.16083 q^{91} +9.01311 q^{92} +1.72903 q^{93} +11.5330 q^{94} -26.1845 q^{95} +0.285923 q^{96} +3.82169 q^{97} +8.36104 q^{98} +13.9501 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9	\( 13 q + 13 q^{2} + 7 q^{3} + 13 q^{4} + q^{5} + 7 q^{6} + 8 q^{7} + 13 q^{8} + 16 q^{9} + q^{10} + 13 q^{11} + 7 q^{12} + 9 q^{13} + 8 q^{14} - 9 q^{15} + 13 q^{16} + 13 q^{17} + 16 q^{18} + 16 q^{19} + q^{20} - 3 q^{21} + 13 q^{22} + 18 q^{23} + 7 q^{24} + 14 q^{25} + 9 q^{26} + 10 q^{27} + 8 q^{28} + 8 q^{29} - 9 q^{30} + 32 q^{31} + 13 q^{32} + 13 q^{33} + 13 q^{34} - q^{35} + 16 q^{36} - 3 q^{37} + 16 q^{38} + 20 q^{39} + q^{40} + 24 q^{41} - 3 q^{42} - 2 q^{43} + 13 q^{44} - 3 q^{45} + 18 q^{46} + 26 q^{47} + 7 q^{48} + 23 q^{49} + 14 q^{50} + 7 q^{51} + 9 q^{52} - 27 q^{53} + 10 q^{54} - 7 q^{55} + 8 q^{56} - 21 q^{57} + 8 q^{58} + 13 q^{59} - 9 q^{60} + 20 q^{61} + 32 q^{62} - 3 q^{63} + 13 q^{64} + 16 q^{65} + 13 q^{66} + 4 q^{67} + 13 q^{68} - 2 q^{69} - q^{70} - 8 q^{71} + 16 q^{72} + 10 q^{73} - 3 q^{74} + 39 q^{75} + 16 q^{76} - 15 q^{77} + 20 q^{78} + 35 q^{79} + q^{80} + 29 q^{81} + 24 q^{82} - q^{83} - 3 q^{84} + q^{85} - 2 q^{86} - 32 q^{87} + 13 q^{88} - 20 q^{89} - 3 q^{90} - 15 q^{91} + 18 q^{92} - 7 q^{93} + 26 q^{94} - 3 q^{95} + 7 q^{96} - 3 q^{97} + 23 q^{98} + 65 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 7 * q^3 + 13 * q^4 + q^5 + 7 * q^6 + 8 * q^7 + 13 * q^8 + 16 * q^9 + q^10 + 13 * q^11 + 7 * q^12 + 9 * q^13 + 8 * q^14 - 9 * q^15 + 13 * q^16 + 13 * q^17 + 16 * q^18 + 16 * q^19 + q^20 - 3 * q^21 + 13 * q^22 + 18 * q^23 + 7 * q^24 + 14 * q^25 + 9 * q^26 + 10 * q^27 + 8 * q^28 + 8 * q^29 - 9 * q^30 + 32 * q^31 + 13 * q^32 + 13 * q^33 + 13 * q^34 - q^35 + 16 * q^36 - 3 * q^37 + 16 * q^38 + 20 * q^39 + q^40 + 24 * q^41 - 3 * q^42 - 2 * q^43 + 13 * q^44 - 3 * q^45 + 18 * q^46 + 26 * q^47 + 7 * q^48 + 23 * q^49 + 14 * q^50 + 7 * q^51 + 9 * q^52 - 27 * q^53 + 10 * q^54 - 7 * q^55 + 8 * q^56 - 21 * q^57 + 8 * q^58 + 13 * q^59 - 9 * q^60 + 20 * q^61 + 32 * q^62 - 3 * q^63 + 13 * q^64 + 16 * q^65 + 13 * q^66 + 4 * q^67 + 13 * q^68 - 2 * q^69 - q^70 - 8 * q^71 + 16 * q^72 + 10 * q^73 - 3 * q^74 + 39 * q^75 + 16 * q^76 - 15 * q^77 + 20 * q^78 + 35 * q^79 + q^80 + 29 * q^81 + 24 * q^82 - q^83 - 3 * q^84 + q^85 - 2 * q^86 - 32 * q^87 + 13 * q^88 - 20 * q^89 - 3 * q^90 - 15 * q^91 + 18 * q^92 - 7 * q^93 + 26 * q^94 - 3 * q^95 + 7 * q^96 - 3 * q^97 + 23 * q^98 + 65 * q^99

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