LMFDB - Embedded newform 1183.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 $ x^12 - 3x^11 - 15x^10 + 46x^9 + 80x^8 - 246x^7 - 199x^6 + 562x^5 + 262x^4 - 542x^3 - 157x^2 + 183*x + 29
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.35819$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.35819 q^{2} +3.39737 q^{3} -0.155322 q^{4} -0.772491 q^{5} -4.61428 q^{6} +1.00000 q^{7} +2.92733 q^{8} +8.54215 q^{9} +O(q^{10})$	\(q-1.35819 q^{2} +3.39737 q^{3} -0.155322 q^{4} -0.772491 q^{5} -4.61428 q^{6} +1.00000 q^{7} +2.92733 q^{8} +8.54215 q^{9} +1.04919 q^{10} -2.11612 q^{11} -0.527686 q^{12} -1.35819 q^{14} -2.62444 q^{15} -3.66523 q^{16} +5.63627 q^{17} -11.6019 q^{18} +2.99988 q^{19} +0.119985 q^{20} +3.39737 q^{21} +2.87409 q^{22} +1.24177 q^{23} +9.94525 q^{24} -4.40326 q^{25} +18.8288 q^{27} -0.155322 q^{28} -7.96564 q^{29} +3.56449 q^{30} +1.26728 q^{31} -0.876591 q^{32} -7.18925 q^{33} -7.65512 q^{34} -0.772491 q^{35} -1.32678 q^{36} -4.54251 q^{37} -4.07440 q^{38} -2.26134 q^{40} +9.82390 q^{41} -4.61428 q^{42} +2.64573 q^{43} +0.328679 q^{44} -6.59873 q^{45} -1.68656 q^{46} +7.68703 q^{47} -12.4522 q^{48} +1.00000 q^{49} +5.98046 q^{50} +19.1485 q^{51} -0.350895 q^{53} -25.5730 q^{54} +1.63468 q^{55} +2.92733 q^{56} +10.1917 q^{57} +10.8188 q^{58} -5.00519 q^{59} +0.407633 q^{60} +4.24504 q^{61} -1.72120 q^{62} +8.54215 q^{63} +8.52104 q^{64} +9.76437 q^{66} -11.3053 q^{67} -0.875435 q^{68} +4.21876 q^{69} +1.04919 q^{70} +11.8975 q^{71} +25.0057 q^{72} +8.99347 q^{73} +6.16959 q^{74} -14.9595 q^{75} -0.465946 q^{76} -2.11612 q^{77} -6.30010 q^{79} +2.83136 q^{80} +38.3419 q^{81} -13.3427 q^{82} +2.92778 q^{83} -0.527686 q^{84} -4.35397 q^{85} -3.59340 q^{86} -27.0622 q^{87} -6.19459 q^{88} -1.97181 q^{89} +8.96233 q^{90} -0.192874 q^{92} +4.30541 q^{93} -10.4404 q^{94} -2.31738 q^{95} -2.97811 q^{96} +7.88255 q^{97} -1.35819 q^{98} -18.0762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * 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 $

$2$	−1.35819	−0.960385	−0.480192	−	0.877163i	$-0.659433\pi$
$2$	−1.35819	−0.960385	−0.480192	+	0.877163i	$0.659433\pi$
$3$	3.39737	1.96147	0.980737	−	0.195331i	$-0.0625782\pi$
$3$	3.39737	1.96147	0.980737	+	0.195331i	$0.0625782\pi$
$4$	−0.155322	−0.0776609
$5$	−0.772491	−0.345468	−0.172734	−	0.984968i	$-0.555260\pi$
$5$	−0.772491	−0.345468	−0.172734	+	0.984968i	$0.555260\pi$
$6$	−4.61428	−1.88377
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.92733	1.03497
$9$	8.54215	2.84738
$10$	1.04919	0.331783
$11$	−2.11612	−0.638034	−0.319017	−	0.947749i	$-0.603353\pi$
$11$	−2.11612	−0.638034	−0.319017	+	0.947749i	$0.603353\pi$
$12$	−0.527686	−0.152330
$13$	0	0
$13$	0	0
$14$	−1.35819	−0.362991
$15$	−2.62444	−0.677627
$16$	−3.66523	−0.916308
$17$	5.63627	1.36700	0.683498	−	0.729952i	$-0.260458\pi$
$17$	5.63627	1.36700	0.683498	+	0.729952i	$0.260458\pi$
$18$	−11.6019	−2.73458
$19$	2.99988	0.688219	0.344110	−	0.938930i	$-0.388181\pi$
$19$	2.99988	0.688219	0.344110	+	0.938930i	$0.388181\pi$
$20$	0.119985	0.0268294
$21$	3.39737	0.741368
$22$	2.87409	0.612759
$23$	1.24177	0.258927	0.129464	−	0.991584i	$-0.458674\pi$
$23$	1.24177	0.258927	0.129464	+	0.991584i	$0.458674\pi$
$24$	9.94525	2.03007
$25$	−4.40326	−0.880652
$26$	0	0
$27$	18.8288	3.62359
$28$	−0.155322	−0.0293530
$29$	−7.96564	−1.47918	−0.739591	−	0.673057i	$-0.764981\pi$
$29$	−7.96564	−1.47918	−0.739591	+	0.673057i	$0.764981\pi$
$30$	3.56449	0.650783
$31$	1.26728	0.227609	0.113805	−	0.993503i	$-0.463696\pi$
$31$	1.26728	0.227609	0.113805	+	0.993503i	$0.463696\pi$
$32$	−0.876591	−0.154961
$33$	−7.18925	−1.25149
$34$	−7.65512	−1.31284
$35$	−0.772491	−0.130575
$36$	−1.32678	−0.221130
$37$	−4.54251	−0.746784	−0.373392	−	0.927674i	$-0.621805\pi$
$37$	−4.54251	−0.746784	−0.373392	+	0.927674i	$0.621805\pi$
$38$	−4.07440	−0.660955
$39$	0	0
$40$	−2.26134	−0.357549
$41$	9.82390	1.53424	0.767118	−	0.641506i	$-0.221690\pi$
$41$	9.82390	1.53424	0.767118	+	0.641506i	$0.221690\pi$
$42$	−4.61428	−0.711998
$43$	2.64573	0.403470	0.201735	−	0.979440i	$-0.435342\pi$
$43$	2.64573	0.403470	0.201735	+	0.979440i	$0.435342\pi$
$44$	0.328679	0.0495503
$45$	−6.59873	−0.983681
$46$	−1.68656	−0.248670
$47$	7.68703	1.12127	0.560634	−	0.828064i	$-0.310557\pi$
$47$	7.68703	1.12127	0.560634	+	0.828064i	$0.310557\pi$
$48$	−12.4522	−1.79731
$49$	1.00000	0.142857
$50$	5.98046	0.845764
$51$	19.1485	2.68133
$52$	0	0
$53$	−0.350895	−0.0481991	−0.0240995	−	0.999710i	$-0.507672\pi$
$53$	−0.350895	−0.0481991	−0.0240995	+	0.999710i	$0.507672\pi$
$54$	−25.5730	−3.48005
$55$	1.63468	0.220421
$56$	2.92733	0.391182
$57$	10.1917	1.34992
$58$	10.8188	1.42058
$59$	−5.00519	−0.651621	−0.325810	−	0.945435i	$-0.605637\pi$
$59$	−5.00519	−0.651621	−0.325810	+	0.945435i	$0.605637\pi$
$60$	0.407633	0.0526251
$61$	4.24504	0.543522	0.271761	−	0.962365i	$-0.412394\pi$
$61$	4.24504	0.543522	0.271761	+	0.962365i	$0.412394\pi$
$62$	−1.72120	−0.218593
$63$	8.54215	1.07621
$64$	8.52104	1.06513
$65$	0	0
$66$	9.76437	1.20191
$67$	−11.3053	−1.38117	−0.690583	−	0.723253i	$-0.742646\pi$
$67$	−11.3053	−1.38117	−0.690583	+	0.723253i	$0.742646\pi$
$68$	−0.875435	−0.106162
$69$	4.21876	0.507879
$70$	1.04919	0.125402
$71$	11.8975	1.41198	0.705989	−	0.708223i	$-0.250503\pi$
$71$	11.8975	1.41198	0.705989	+	0.708223i	$0.250503\pi$
$72$	25.0057	2.94695
$73$	8.99347	1.05261	0.526303	−	0.850297i	$-0.323578\pi$
$73$	8.99347	1.05261	0.526303	+	0.850297i	$0.323578\pi$
$74$	6.16959	0.717200
$75$	−14.9595	−1.72738
$76$	−0.465946	−0.0534477
$77$	−2.11612	−0.241154
$78$	0	0
$79$	−6.30010	−0.708817	−0.354408	−	0.935091i	$-0.615318\pi$
$79$	−6.30010	−0.708817	−0.354408	+	0.935091i	$0.615318\pi$
$80$	2.83136	0.316555
$81$	38.3419	4.26021
$82$	−13.3427	−1.47346
$83$	2.92778	0.321366	0.160683	−	0.987006i	$-0.448630\pi$
$83$	2.92778	0.321366	0.160683	+	0.987006i	$0.448630\pi$
$84$	−0.527686	−0.0575753
$85$	−4.35397	−0.472254
$86$	−3.59340	−0.387487
$87$	−27.0622	−2.90138
$88$	−6.19459	−0.660346
$89$	−1.97181	−0.209012	−0.104506	−	0.994524i	$-0.533326\pi$
$89$	−1.97181	−0.209012	−0.104506	+	0.994524i	$0.533326\pi$
$90$	8.96233	0.944712
$91$	0	0
$92$	−0.192874	−0.0201085
$93$	4.30541	0.446450
$94$	−10.4404	−1.07685
$95$	−2.31738	−0.237758
$96$	−2.97811	−0.303952
$97$	7.88255	0.800352	0.400176	−	0.916438i	$-0.368949\pi$
$97$	7.88255	0.800352	0.400176	+	0.916438i	$0.368949\pi$
$98$	−1.35819	−0.137198
$99$	−18.0762	−1.81673
$100$	0.683922	0.0683922
$101$	1.76856	0.175978	0.0879890	−	0.996121i	$-0.471956\pi$
$101$	1.76856	0.175978	0.0879890	+	0.996121i	$0.471956\pi$
$102$	−26.0073	−2.57511
$103$	−11.4598	−1.12917	−0.564586	−	0.825375i	$-0.690964\pi$
$103$	−11.4598	−1.12917	−0.564586	+	0.825375i	$0.690964\pi$
$104$	0	0
$105$	−2.62444	−0.256119
$106$	0.476581	0.0462897
$107$	−3.29566	−0.318603	−0.159302	−	0.987230i	$-0.550924\pi$
$107$	−3.29566	−0.318603	−0.159302	+	0.987230i	$0.550924\pi$
$108$	−2.92451	−0.281412
$109$	−13.1559	−1.26011	−0.630055	−	0.776551i	$-0.716968\pi$
$109$	−13.1559	−1.26011	−0.630055	+	0.776551i	$0.716968\pi$
$110$	−2.22021	−0.211689
$111$	−15.4326	−1.46480
$112$	−3.66523	−0.346332
$113$	1.44552	0.135984	0.0679918	−	0.997686i	$-0.478341\pi$
$113$	1.44552	0.135984	0.0679918	+	0.997686i	$0.478341\pi$
$114$	−13.8423	−1.29645
$115$	−0.959257	−0.0894512
$116$	1.23724	0.114875
$117$	0	0
$118$	6.79800	0.625807
$119$	5.63627	0.516676
$120$	−7.68261	−0.701324
$121$	−6.52203	−0.592912
$122$	−5.76557	−0.521990
$123$	33.3755	3.00936
$124$	−0.196835	−0.0176763
$125$	7.26393	0.649706
$126$	−11.6019	−1.03358
$127$	−10.9224	−0.969209	−0.484605	−	0.874733i	$-0.661037\pi$
$127$	−10.9224	−0.969209	−0.484605	+	0.874733i	$0.661037\pi$
$128$	−9.82000	−0.867974
$129$	8.98854	0.791397
$130$	0	0
$131$	−2.24077	−0.195777	−0.0978886	−	0.995197i	$-0.531209\pi$
$131$	−2.24077	−0.195777	−0.0978886	+	0.995197i	$0.531209\pi$
$132$	1.11665	0.0971917
$133$	2.99988	0.260122
$134$	15.3548	1.32645
$135$	−14.5450	−1.25184
$136$	16.4993	1.41480
$137$	7.48827	0.639766	0.319883	−	0.947457i	$-0.396356\pi$
$137$	7.48827	0.639766	0.319883	+	0.947457i	$0.396356\pi$
$138$	−5.72988	−0.487759
$139$	3.17757	0.269518	0.134759	−	0.990878i	$-0.456974\pi$
$139$	3.17757	0.269518	0.134759	+	0.990878i	$0.456974\pi$
$140$	0.119985	0.0101405
$141$	26.1157	2.19934
$142$	−16.1591	−1.35604
$143$	0	0
$144$	−31.3090	−2.60908
$145$	6.15338	0.511010
$146$	−12.2148	−1.01091
$147$	3.39737	0.280211
$148$	0.705550	0.0579959
$149$	−15.6423	−1.28147	−0.640735	−	0.767762i	$-0.721370\pi$
$149$	−15.6423	−1.28147	−0.640735	+	0.767762i	$0.721370\pi$
$150$	20.3179	1.65895
$151$	15.2282	1.23925	0.619626	−	0.784897i	$-0.287284\pi$
$151$	15.2282	1.23925	0.619626	+	0.784897i	$0.287284\pi$
$152$	8.78165	0.712286
$153$	48.1459	3.89236
$154$	2.87409	0.231601
$155$	−0.978959	−0.0786318
$156$	0	0
$157$	−14.4128	−1.15027	−0.575134	−	0.818059i	$-0.695050\pi$
$157$	−14.4128	−1.15027	−0.575134	+	0.818059i	$0.695050\pi$
$158$	8.55673	0.680737
$159$	−1.19212	−0.0945413
$160$	0.677159	0.0535341
$161$	1.24177	0.0978653
$162$	−52.0755	−4.09144
$163$	−10.6875	−0.837113	−0.418556	−	0.908191i	$-0.637464\pi$
$163$	−10.6875	−0.837113	−0.418556	+	0.908191i	$0.637464\pi$
$164$	−1.52587	−0.119150
$165$	5.55363	0.432350
$166$	−3.97648	−0.308635
$167$	5.89574	0.456226	0.228113	−	0.973635i	$-0.426744\pi$
$167$	5.89574	0.456226	0.228113	+	0.973635i	$0.426744\pi$
$168$	9.94525	0.767293
$169$	0	0
$170$	5.91351	0.453546
$171$	25.6254	1.95962
$172$	−0.410940	−0.0313338
$173$	5.63112	0.428126	0.214063	−	0.976820i	$-0.431330\pi$
$173$	5.63112	0.428126	0.214063	+	0.976820i	$0.431330\pi$
$174$	36.7557	2.78644
$175$	−4.40326	−0.332855
$176$	7.75607	0.584636
$177$	−17.0045	−1.27814
$178$	2.67810	0.200732
$179$	7.18084	0.536721	0.268361	−	0.963318i	$-0.413518\pi$
$179$	7.18084	0.536721	0.268361	+	0.963318i	$0.413518\pi$
$180$	1.02493	0.0763935
$181$	−0.567427	−0.0421765	−0.0210883	−	0.999778i	$-0.506713\pi$
$181$	−0.567427	−0.0421765	−0.0210883	+	0.999778i	$0.506713\pi$
$182$	0	0
$183$	14.4220	1.06611
$184$	3.63508	0.267982
$185$	3.50905	0.257990
$186$	−5.84756	−0.428764
$187$	−11.9270	−0.872191
$188$	−1.19396	−0.0870787
$189$	18.8288	1.36959
$190$	3.14744	0.228339
$191$	−7.95163	−0.575360	−0.287680	−	0.957727i	$-0.592884\pi$
$191$	−7.95163	−0.575360	−0.287680	+	0.957727i	$0.592884\pi$
$192$	28.9492	2.08923
$193$	−20.5748	−1.48100	−0.740502	−	0.672054i	$-0.765412\pi$
$193$	−20.5748	−1.48100	−0.740502	+	0.672054i	$0.765412\pi$
$194$	−10.7060	−0.768646
$195$	0	0
$196$	−0.155322	−0.0110944
$197$	1.52219	0.108451	0.0542256	−	0.998529i	$-0.482731\pi$
$197$	1.52219	0.108451	0.0542256	+	0.998529i	$0.482731\pi$
$198$	24.5509	1.74476
$199$	25.3123	1.79434	0.897172	−	0.441681i	$-0.145618\pi$
$199$	25.3123	1.79434	0.897172	+	0.441681i	$0.145618\pi$
$200$	−12.8898	−0.911447
$201$	−38.4084	−2.70912
$202$	−2.40204	−0.169007
$203$	−7.96564	−0.559078
$204$	−2.97418	−0.208234
$205$	−7.58887	−0.530030
$206$	15.5646	1.08444
$207$	10.6074	0.737265
$208$	0	0
$209$	−6.34810	−0.439107
$210$	3.56449	0.245973
$211$	5.54406	0.381669	0.190834	−	0.981622i	$-0.438881\pi$
$211$	5.54406	0.381669	0.190834	+	0.981622i	$0.438881\pi$
$212$	0.0545016	0.00374318
$213$	40.4204	2.76956
$214$	4.47612	0.305982
$215$	−2.04380	−0.139386
$216$	55.1181	3.75031
$217$	1.26728	0.0860283
$218$	17.8682	1.21019
$219$	30.5542	2.06466
$220$	−0.253902	−0.0171181
$221$	0	0
$222$	20.9604	1.40677
$223$	−6.89711	−0.461865	−0.230932	−	0.972970i	$-0.574178\pi$
$223$	−6.89711	−0.461865	−0.230932	+	0.972970i	$0.574178\pi$
$224$	−0.876591	−0.0585697
$225$	−37.6133	−2.50755
$226$	−1.96330	−0.130597
$227$	−3.16626	−0.210152	−0.105076	−	0.994464i	$-0.533509\pi$
$227$	−3.16626	−0.210152	−0.105076	+	0.994464i	$0.533509\pi$
$228$	−1.58299	−0.104836
$229$	−23.3695	−1.54430	−0.772148	−	0.635442i	$-0.780818\pi$
$229$	−23.3695	−1.54430	−0.772148	+	0.635442i	$0.780818\pi$
$230$	1.30285	0.0859075
$231$	−7.18925	−0.473018
$232$	−23.3181	−1.53091
$233$	−9.65245	−0.632353	−0.316177	−	0.948700i	$-0.602399\pi$
$233$	−9.65245	−0.632353	−0.316177	+	0.948700i	$0.602399\pi$
$234$	0	0
$235$	−5.93816	−0.387363
$236$	0.777415	0.0506054
$237$	−21.4038	−1.39033
$238$	−7.65512	−0.496208
$239$	−6.98215	−0.451638	−0.225819	−	0.974169i	$-0.572506\pi$
$239$	−6.98215	−0.451638	−0.225819	+	0.974169i	$0.572506\pi$
$240$	9.61918	0.620915
$241$	−18.5592	−1.19550	−0.597751	−	0.801681i	$-0.703939\pi$
$241$	−18.5592	−1.19550	−0.597751	+	0.801681i	$0.703939\pi$
$242$	8.85816	0.569424
$243$	73.7754	4.73269
$244$	−0.659348	−0.0422104
$245$	−0.772491	−0.0493526
$246$	−45.3302	−2.89015
$247$	0	0
$248$	3.70974	0.235569
$249$	9.94677	0.630351
$250$	−9.86579	−0.623967
$251$	16.6573	1.05140	0.525699	−	0.850671i	$-0.323804\pi$
$251$	16.6573	1.05140	0.525699	+	0.850671i	$0.323804\pi$
$252$	−1.32678	−0.0835794
$253$	−2.62774	−0.165204
$254$	14.8347	0.930814
$255$	−14.7921	−0.926314
$256$	−3.70466	−0.231541
$257$	7.63652	0.476353	0.238177	−	0.971222i	$-0.423450\pi$
$257$	7.63652	0.476353	0.238177	+	0.971222i	$0.423450\pi$
$258$	−12.2081	−0.760045
$259$	−4.54251	−0.282258
$260$	0	0
$261$	−68.0436	−4.21180
$262$	3.04339	0.188022
$263$	−18.6358	−1.14913	−0.574567	−	0.818458i	$-0.694830\pi$
$263$	−18.6358	−1.14913	−0.574567	+	0.818458i	$0.694830\pi$
$264$	−21.0453	−1.29525
$265$	0.271063	0.0166513
$266$	−4.07440	−0.249818
$267$	−6.69899	−0.409971
$268$	1.75596	0.107263
$269$	24.8582	1.51563	0.757817	−	0.652467i	$-0.226266\pi$
$269$	24.8582	1.51563	0.757817	+	0.652467i	$0.226266\pi$
$270$	19.7549	1.20225
$271$	−22.0518	−1.33955	−0.669777	−	0.742562i	$-0.733610\pi$
$271$	−22.0518	−1.33955	−0.669777	+	0.742562i	$0.733610\pi$
$272$	−20.6582	−1.25259
$273$	0	0
$274$	−10.1705	−0.614421
$275$	9.31782	0.561886
$276$	−0.655265	−0.0394423
$277$	−19.7139	−1.18449	−0.592245	−	0.805758i	$-0.701758\pi$
$277$	−19.7139	−1.18449	−0.592245	+	0.805758i	$0.701758\pi$
$278$	−4.31574	−0.258841
$279$	10.8253	0.648091
$280$	−2.26134	−0.135141
$281$	4.42005	0.263678	0.131839	−	0.991271i	$-0.457912\pi$
$281$	4.42005	0.263678	0.131839	+	0.991271i	$0.457912\pi$
$282$	−35.4701	−2.11221
$283$	−31.9312	−1.89811	−0.949057	−	0.315106i	$-0.897960\pi$
$283$	−31.9312	−1.89811	−0.949057	+	0.315106i	$0.897960\pi$
$284$	−1.84795	−0.109655
$285$	−7.87300	−0.466356
$286$	0	0
$287$	9.82390	0.579887
$288$	−7.48797	−0.441233
$289$	14.7675	0.868679
$290$	−8.35746	−0.490767
$291$	26.7800	1.56987
$292$	−1.39688	−0.0817463
$293$	−16.2471	−0.949169	−0.474584	−	0.880210i	$-0.657402\pi$
$293$	−16.2471	−0.949169	−0.474584	+	0.880210i	$0.657402\pi$
$294$	−4.61428	−0.269110
$295$	3.86647	0.225114
$296$	−13.2974	−0.772898
$297$	−39.8439	−2.31198
$298$	21.2453	1.23071
$299$	0	0
$300$	2.32354	0.134150
$301$	2.64573	0.152497
$302$	−20.6828	−1.19016
$303$	6.00845	0.345176
$304$	−10.9952	−0.630621
$305$	−3.27926	−0.187770
$306$	−65.3912	−3.73817
$307$	−13.5052	−0.770782	−0.385391	−	0.922753i	$-0.625933\pi$
$307$	−13.5052	−0.770782	−0.385391	+	0.922753i	$0.625933\pi$
$308$	0.328679	0.0187283
$309$	−38.9333	−2.21484
$310$	1.32961	0.0755168
$311$	2.26442	0.128404	0.0642018	−	0.997937i	$-0.479550\pi$
$311$	2.26442	0.128404	0.0642018	+	0.997937i	$0.479550\pi$
$312$	0	0
$313$	20.1386	1.13830	0.569151	−	0.822233i	$-0.307272\pi$
$313$	20.1386	1.13830	0.569151	+	0.822233i	$0.307272\pi$
$314$	19.5753	1.10470
$315$	−6.59873	−0.371796
$316$	0.978543	0.0550473
$317$	−31.3079	−1.75843	−0.879213	−	0.476429i	$-0.841931\pi$
$317$	−31.3079	−1.75843	−0.879213	+	0.476429i	$0.841931\pi$
$318$	1.61913	0.0907960
$319$	16.8562	0.943769
$320$	−6.58243	−0.367969
$321$	−11.1966	−0.624932
$322$	−1.68656	−0.0939883
$323$	16.9081	0.940793
$324$	−5.95532	−0.330851
$325$	0	0
$326$	14.5157	0.803950
$327$	−44.6956	−2.47167
$328$	28.7578	1.58789
$329$	7.68703	0.423800
$330$	−7.54288	−0.415222
$331$	−5.86072	−0.322134	−0.161067	−	0.986943i	$-0.551494\pi$
$331$	−5.86072	−0.322134	−0.161067	+	0.986943i	$0.551494\pi$
$332$	−0.454748	−0.0249576
$333$	−38.8028	−2.12638
$334$	−8.00753	−0.438152
$335$	8.73327	0.477149
$336$	−12.4522	−0.679321
$337$	14.0167	0.763539	0.381769	−	0.924258i	$-0.375315\pi$
$337$	14.0167	0.763539	0.381769	+	0.924258i	$0.375315\pi$
$338$	0	0
$339$	4.91099	0.266728
$340$	0.676266	0.0366757
$341$	−2.68171	−0.145223
$342$	−34.8041	−1.88199
$343$	1.00000	0.0539949
$344$	7.74494	0.417579
$345$	−3.25895	−0.175456
$346$	−7.64813	−0.411166
$347$	−18.4346	−0.989622	−0.494811	−	0.869001i	$-0.664763\pi$
$347$	−18.4346	−0.989622	−0.494811	+	0.869001i	$0.664763\pi$
$348$	4.20335	0.225323
$349$	0.841480	0.0450434	0.0225217	−	0.999746i	$-0.492831\pi$
$349$	0.841480	0.0450434	0.0225217	+	0.999746i	$0.492831\pi$
$350$	5.98046	0.319669
$351$	0	0
$352$	1.85497	0.0988704
$353$	−4.32366	−0.230125	−0.115063	−	0.993358i	$-0.536707\pi$
$353$	−4.32366	−0.230125	−0.115063	+	0.993358i	$0.536707\pi$
$354$	23.0953	1.22750
$355$	−9.19074	−0.487794
$356$	0.306265	0.0162320
$357$	19.1485	1.01345
$358$	−9.75295	−0.515459
$359$	12.0924	0.638213	0.319107	−	0.947719i	$-0.396617\pi$
$359$	12.0924	0.638213	0.319107	+	0.947719i	$0.396617\pi$
$360$	−19.3167	−1.01808
$361$	−10.0007	−0.526355
$362$	0.770673	0.0405057
$363$	−22.1578	−1.16298
$364$	0	0
$365$	−6.94737	−0.363642
$366$	−19.5878	−1.02387
$367$	−9.05715	−0.472779	−0.236390	−	0.971658i	$-0.575964\pi$
$367$	−9.05715	−0.472779	−0.236390	+	0.971658i	$0.575964\pi$
$368$	−4.55138	−0.237257
$369$	83.9172	4.36856
$370$	−4.76595	−0.247770
$371$	−0.350895	−0.0182175
$372$	−0.668724	−0.0346717
$373$	−23.0254	−1.19221	−0.596104	−	0.802907i	$-0.703285\pi$
$373$	−23.0254	−1.19221	−0.596104	+	0.802907i	$0.703285\pi$
$374$	16.1992	0.837639
$375$	24.6783	1.27438
$376$	22.5025	1.16048
$377$	0	0
$378$	−25.5730	−1.31533
$379$	−29.5778	−1.51931	−0.759655	−	0.650326i	$-0.774632\pi$
$379$	−29.5778	−1.51931	−0.759655	+	0.650326i	$0.774632\pi$
$380$	0.359939	0.0184645
$381$	−37.1076	−1.90108
$382$	10.7998	0.552567
$383$	−19.0793	−0.974906	−0.487453	−	0.873149i	$-0.662074\pi$
$383$	−19.0793	−0.974906	−0.487453	+	0.873149i	$0.662074\pi$
$384$	−33.3622	−1.70251
$385$	1.63468	0.0833112
$386$	27.9444	1.42233
$387$	22.6002	1.14883
$388$	−1.22433	−0.0621560
$389$	−11.3977	−0.577885	−0.288942	−	0.957347i	$-0.593304\pi$
$389$	−11.3977	−0.577885	−0.288942	+	0.957347i	$0.593304\pi$
$390$	0	0
$391$	6.99896	0.353953
$392$	2.92733	0.147853
$393$	−7.61274	−0.384012
$394$	−2.06742	−0.104155
$395$	4.86677	0.244874
$396$	2.80763	0.141089
$397$	29.1687	1.46394	0.731968	−	0.681339i	$-0.238602\pi$
$397$	29.1687	1.46394	0.731968	+	0.681339i	$0.238602\pi$
$398$	−34.3790	−1.72326
$399$	10.1917	0.510223
$400$	16.1390	0.806948
$401$	17.0352	0.850697	0.425349	−	0.905030i	$-0.360151\pi$
$401$	17.0352	0.850697	0.425349	+	0.905030i	$0.360151\pi$
$402$	52.1659	2.60180
$403$	0	0
$404$	−0.274695	−0.0136666
$405$	−29.6187	−1.47177
$406$	10.8188	0.536930
$407$	9.61250	0.476474
$408$	56.0541	2.77509
$409$	7.21000	0.356511	0.178256	−	0.983984i	$-0.442955\pi$
$409$	7.21000	0.356511	0.178256	+	0.983984i	$0.442955\pi$
$410$	10.3071	0.509033
$411$	25.4404	1.25488
$412$	1.77996	0.0876924
$413$	−5.00519	−0.246289
$414$	−14.4069	−0.708058
$415$	−2.26169	−0.111022
$416$	0	0
$417$	10.7954	0.528653
$418$	8.62192	0.421712
$419$	34.1903	1.67030	0.835152	−	0.550019i	$-0.185379\pi$
$419$	34.1903	1.67030	0.835152	+	0.550019i	$0.185379\pi$
$420$	0.407633	0.0198904
$421$	33.3533	1.62554	0.812770	−	0.582585i	$-0.197959\pi$
$421$	33.3533	1.62554	0.812770	+	0.582585i	$0.197959\pi$
$422$	−7.52989	−0.366549
$423$	65.6638	3.19268
$424$	−1.02719	−0.0498846
$425$	−24.8180	−1.20385
$426$	−54.8985	−2.65984
$427$	4.24504	0.205432
$428$	0.511887	0.0247430
$429$	0	0
$430$	2.77587	0.133864
$431$	31.8622	1.53475	0.767374	−	0.641200i	$-0.221563\pi$
$431$	31.8622	1.53475	0.767374	+	0.641200i	$0.221563\pi$
$432$	−69.0117	−3.32033
$433$	2.69773	0.129645	0.0648223	−	0.997897i	$-0.479352\pi$
$433$	2.69773	0.129645	0.0648223	+	0.997897i	$0.479352\pi$
$434$	−1.72120	−0.0826202
$435$	20.9053	1.00233
$436$	2.04340	0.0978612
$437$	3.72516	0.178199
$438$	−41.4983	−1.98287
$439$	−21.5226	−1.02722	−0.513609	−	0.858024i	$-0.671692\pi$
$439$	−21.5226	−1.02722	−0.513609	+	0.858024i	$0.671692\pi$
$440$	4.78527	0.228129
$441$	8.54215	0.406769
$442$	0	0
$443$	6.74835	0.320624	0.160312	−	0.987066i	$-0.448750\pi$
$443$	6.74835	0.320624	0.160312	+	0.987066i	$0.448750\pi$
$444$	2.39702	0.113757
$445$	1.52321	0.0722069
$446$	9.36759	0.443568
$447$	−53.1429	−2.51357
$448$	8.52104	0.402581
$449$	−32.3984	−1.52898	−0.764488	−	0.644638i	$-0.777008\pi$
$449$	−32.3984	−1.52898	−0.764488	+	0.644638i	$0.777008\pi$
$450$	51.0860	2.40822
$451$	−20.7886	−0.978895
$452$	−0.224521	−0.0105606
$453$	51.7359	2.43076
$454$	4.30038	0.201827
$455$	0	0
$456$	29.8345	1.39713
$457$	5.27900	0.246941	0.123471	−	0.992348i	$-0.460598\pi$
$457$	5.27900	0.246941	0.123471	+	0.992348i	$0.460598\pi$
$458$	31.7401	1.48312
$459$	106.124	4.95344
$460$	0.148993	0.00694685
$461$	−39.9387	−1.86013	−0.930065	−	0.367396i	$-0.880250\pi$
$461$	−39.9387	−1.86013	−0.930065	+	0.367396i	$0.880250\pi$
$462$	9.76437	0.454279
$463$	7.02805	0.326621	0.163311	−	0.986575i	$-0.447783\pi$
$463$	7.02805	0.326621	0.163311	+	0.986575i	$0.447783\pi$
$464$	29.1959	1.35539
$465$	−3.32589	−0.154234
$466$	13.1099	0.607302
$467$	−12.7122	−0.588252	−0.294126	−	0.955767i	$-0.595029\pi$
$467$	−12.7122	−0.588252	−0.294126	+	0.955767i	$0.595029\pi$
$468$	0	0
$469$	−11.3053	−0.522032
$470$	8.06515	0.372017
$471$	−48.9657	−2.25622
$472$	−14.6519	−0.674407
$473$	−5.59869	−0.257428
$474$	29.0704	1.33525
$475$	−13.2092	−0.606081
$476$	−0.875435	−0.0401255
$477$	−2.99739	−0.137241
$478$	9.48309	0.433746
$479$	−23.9405	−1.09387	−0.546935	−	0.837175i	$-0.684206\pi$
$479$	−23.9405	−1.09387	−0.546935	+	0.837175i	$0.684206\pi$
$480$	2.30056	0.105006
$481$	0	0
$482$	25.2069	1.14814
$483$	4.21876	0.191960
$484$	1.01301	0.0460461
$485$	−6.08920	−0.276496
$486$	−100.201	−4.54521
$487$	−10.6960	−0.484683	−0.242342	−	0.970191i	$-0.577916\pi$
$487$	−10.6960	−0.484683	−0.242342	+	0.970191i	$0.577916\pi$
$488$	12.4267	0.562529
$489$	−36.3096	−1.64198
$490$	1.04919	0.0473975
$491$	13.8352	0.624373	0.312187	−	0.950021i	$-0.398939\pi$
$491$	13.8352	0.624373	0.312187	+	0.950021i	$0.398939\pi$
$492$	−5.18393	−0.233710
$493$	−44.8965	−2.02204
$494$	0	0
$495$	13.9637	0.627622
$496$	−4.64486	−0.208560
$497$	11.8975	0.533677
$498$	−13.5096	−0.605380
$499$	−14.6054	−0.653827	−0.326913	−	0.945054i	$-0.606009\pi$
$499$	−14.6054	−0.653827	−0.326913	+	0.945054i	$0.606009\pi$
$500$	−1.12825	−0.0504567
$501$	20.0300	0.894875
$502$	−22.6237	−1.00975
$503$	9.63765	0.429721	0.214861	−	0.976645i	$-0.431070\pi$
$503$	9.63765	0.429721	0.214861	+	0.976645i	$0.431070\pi$
$504$	25.0057	1.11384
$505$	−1.36619	−0.0607948
$506$	3.56897	0.158660
$507$	0	0
$508$	1.69649	0.0752696
$509$	6.16582	0.273295	0.136648	−	0.990620i	$-0.456367\pi$
$509$	6.16582	0.273295	0.136648	+	0.990620i	$0.456367\pi$
$510$	20.0904	0.889618
$511$	8.99347	0.397848
$512$	24.6716	1.09034
$513$	56.4839	2.49383
$514$	−10.3718	−0.457482
$515$	8.85262	0.390093
$516$	−1.39612	−0.0614606
$517$	−16.2667	−0.715408
$518$	6.16959	0.271076
$519$	19.1310	0.839759
$520$	0	0
$521$	−30.1162	−1.31942	−0.659708	−	0.751522i	$-0.729320\pi$
$521$	−30.1162	−1.31942	−0.659708	+	0.751522i	$0.729320\pi$
$522$	92.4162	4.04495
$523$	6.30225	0.275578	0.137789	−	0.990462i	$-0.456000\pi$
$523$	6.30225	0.275578	0.137789	+	0.990462i	$0.456000\pi$
$524$	0.348041	0.0152042
$525$	−14.9595	−0.652887
$526$	25.3110	1.10361
$527$	7.14271	0.311141
$528$	26.3503	1.14675
$529$	−21.4580	−0.932957
$530$	−0.368155	−0.0159916
$531$	−42.7551	−1.85541
$532$	−0.465946	−0.0202013
$533$	0	0
$534$	9.09849	0.393730
$535$	2.54586	0.110067
$536$	−33.0945	−1.42946
$537$	24.3960	1.05277
$538$	−33.7622	−1.45559
$539$	−2.11612	−0.0911478
$540$	2.25916	0.0972188
$541$	−1.95419	−0.0840171	−0.0420086	−	0.999117i	$-0.513376\pi$
$541$	−1.95419	−0.0840171	−0.0420086	+	0.999117i	$0.513376\pi$
$542$	29.9506	1.28649
$543$	−1.92776	−0.0827282
$544$	−4.94071	−0.211831
$545$	10.1628	0.435328
$546$	0	0
$547$	−45.2888	−1.93641	−0.968204	−	0.250162i	$-0.919516\pi$
$547$	−45.2888	−1.93641	−0.968204	+	0.250162i	$0.919516\pi$
$548$	−1.16309	−0.0496848
$549$	36.2618	1.54762
$550$	−12.6554	−0.539627
$551$	−23.8959	−1.01800
$552$	12.3497	0.525639
$553$	−6.30010	−0.267908
$554$	26.7751	1.13757
$555$	11.9215	0.506041
$556$	−0.493546	−0.0209310
$557$	4.02083	0.170368	0.0851841	−	0.996365i	$-0.472852\pi$
$557$	4.02083	0.170368	0.0851841	+	0.996365i	$0.472852\pi$
$558$	−14.7027	−0.622417
$559$	0	0
$560$	2.83136	0.119647
$561$	−40.5206	−1.71078
$562$	−6.00326	−0.253232
$563$	14.4667	0.609700	0.304850	−	0.952400i	$-0.401394\pi$
$563$	14.4667	0.609700	0.304850	+	0.952400i	$0.401394\pi$
$564$	−4.05634	−0.170803
$565$	−1.11665	−0.0469780
$566$	43.3686	1.82292
$567$	38.3419	1.61021
$568$	34.8281	1.46135
$569$	39.0095	1.63536	0.817682	−	0.575670i	$-0.195259\pi$
$569$	39.0095	1.63536	0.817682	+	0.575670i	$0.195259\pi$
$570$	10.6930	0.447881
$571$	−13.5719	−0.567966	−0.283983	−	0.958829i	$-0.591656\pi$
$571$	−13.5719	−0.567966	−0.283983	+	0.958829i	$0.591656\pi$
$572$	0	0
$573$	−27.0147	−1.12855
$574$	−13.3427	−0.556914
$575$	−5.46784	−0.228025
$576$	72.7880	3.03283
$577$	8.39100	0.349322	0.174661	−	0.984629i	$-0.444117\pi$
$577$	8.39100	0.349322	0.174661	+	0.984629i	$0.444117\pi$
$578$	−20.0571	−0.834266
$579$	−69.9002	−2.90495
$580$	−0.955754	−0.0396855
$581$	2.92778	0.121465
$582$	−36.3723	−1.50768
$583$	0.742535	0.0307527
$584$	26.3269	1.08941
$585$	0	0
$586$	22.0667	0.911567
$587$	−22.1640	−0.914808	−0.457404	−	0.889259i	$-0.651221\pi$
$587$	−22.1640	−0.914808	−0.457404	+	0.889259i	$0.651221\pi$
$588$	−0.527686	−0.0217614
$589$	3.80167	0.156645
$590$	−5.25139	−0.216196
$591$	5.17143	0.212724
$592$	16.6494	0.684284
$593$	39.0195	1.60234	0.801170	−	0.598437i	$-0.204211\pi$
$593$	39.0195	1.60234	0.801170	+	0.598437i	$0.204211\pi$
$594$	54.1156	2.22039
$595$	−4.35397	−0.178495
$596$	2.42960	0.0995201
$597$	85.9955	3.51956
$598$	0	0
$599$	31.3114	1.27935	0.639674	−	0.768646i	$-0.279069\pi$
$599$	31.3114	1.27935	0.639674	+	0.768646i	$0.279069\pi$
$600$	−43.7915	−1.78778
$601$	24.7669	1.01026	0.505132	−	0.863042i	$-0.331444\pi$
$601$	24.7669	1.01026	0.505132	+	0.863042i	$0.331444\pi$
$602$	−3.59340	−0.146456
$603$	−96.5718	−3.93271
$604$	−2.36527	−0.0962415
$605$	5.03821	0.204832
$606$	−8.16061	−0.331502
$607$	4.33301	0.175871	0.0879357	−	0.996126i	$-0.471973\pi$
$607$	4.33301	0.175871	0.0879357	+	0.996126i	$0.471973\pi$
$608$	−2.62967	−0.106647
$609$	−27.0622	−1.09662
$610$	4.45385	0.180331
$611$	0	0
$612$	−7.47810	−0.302284
$613$	−45.9015	−1.85394	−0.926972	−	0.375131i	$-0.877598\pi$
$613$	−45.9015	−1.85394	−0.926972	+	0.375131i	$0.877598\pi$
$614$	18.3426	0.740247
$615$	−25.7822	−1.03964
$616$	−6.19459	−0.249587
$617$	−29.0145	−1.16808	−0.584040	−	0.811725i	$-0.698529\pi$
$617$	−29.0145	−1.16808	−0.584040	+	0.811725i	$0.698529\pi$
$618$	52.8789	2.12710
$619$	−8.57642	−0.344715	−0.172358	−	0.985034i	$-0.555139\pi$
$619$	−8.57642	−0.344715	−0.172358	+	0.985034i	$0.555139\pi$
$620$	0.152054	0.00610662
$621$	23.3810	0.938247
$622$	−3.07551	−0.123317
$623$	−1.97181	−0.0789990
$624$	0	0
$625$	16.4050	0.656199
$626$	−27.3521	−1.09321
$627$	−21.5669	−0.861298
$628$	2.23862	0.0893308
$629$	−25.6028	−1.02085
$630$	8.96233	0.357068
$631$	31.4081	1.25034	0.625168	−	0.780490i	$-0.285030\pi$
$631$	31.4081	1.25034	0.625168	+	0.780490i	$0.285030\pi$
$632$	−18.4425	−0.733604
$633$	18.8353	0.748634
$634$	42.5220	1.68877
$635$	8.43748	0.334831
$636$	0.185162	0.00734216
$637$	0	0
$638$	−22.8940	−0.906381
$639$	101.631	4.02044
$640$	7.58586	0.299858
$641$	7.67208	0.303029	0.151514	−	0.988455i	$-0.451585\pi$
$641$	7.67208	0.303029	0.151514	+	0.988455i	$0.451585\pi$
$642$	15.2071	0.600175
$643$	7.48239	0.295076	0.147538	−	0.989056i	$-0.452865\pi$
$643$	7.48239	0.295076	0.147538	+	0.989056i	$0.452865\pi$
$644$	−0.192874	−0.00760030
$645$	−6.94356	−0.273403
$646$	−22.9644	−0.903523
$647$	23.9406	0.941201	0.470600	−	0.882346i	$-0.344037\pi$
$647$	23.9406	0.941201	0.470600	+	0.882346i	$0.344037\pi$
$648$	112.239	4.40918
$649$	10.5916	0.415756
$650$	0	0
$651$	4.30541	0.168742
$652$	1.66001	0.0650109
$653$	34.2885	1.34181	0.670907	−	0.741541i	$-0.265905\pi$
$653$	34.2885	1.34181	0.670907	+	0.741541i	$0.265905\pi$
$654$	60.7051	2.37376
$655$	1.73098	0.0676349
$656$	−36.0069	−1.40583
$657$	76.8235	2.99717
$658$	−10.4404	−0.407011
$659$	−8.82716	−0.343857	−0.171929	−	0.985109i	$-0.555000\pi$
$659$	−8.82716	−0.343857	−0.171929	+	0.985109i	$0.555000\pi$
$660$	−0.862600	−0.0335766
$661$	33.3881	1.29865	0.649324	−	0.760512i	$-0.275052\pi$
$661$	33.3881	1.29865	0.649324	+	0.760512i	$0.275052\pi$
$662$	7.95997	0.309373
$663$	0	0
$664$	8.57060	0.332604
$665$	−2.31738	−0.0898640
$666$	52.7015	2.04214
$667$	−9.89150	−0.383000
$668$	−0.915736	−0.0354309
$669$	−23.4321	−0.905936
$670$	−11.8614	−0.458247
$671$	−8.98302	−0.346786
$672$	−2.97811	−0.114883
$673$	33.1395	1.27743	0.638717	−	0.769442i	$-0.279466\pi$
$673$	33.1395	1.27743	0.638717	+	0.769442i	$0.279466\pi$
$674$	−19.0373	−0.733291
$675$	−82.9079	−3.19112
$676$	0	0
$677$	28.8217	1.10771	0.553854	−	0.832614i	$-0.313157\pi$
$677$	28.8217	1.10771	0.553854	+	0.832614i	$0.313157\pi$
$678$	−6.67005	−0.256162
$679$	7.88255	0.302505
$680$	−12.7455	−0.488768
$681$	−10.7570	−0.412207
$682$	3.64227	0.139470
$683$	17.0467	0.652274	0.326137	−	0.945323i	$-0.394253\pi$
$683$	17.0467	0.652274	0.326137	+	0.945323i	$0.394253\pi$
$684$	−3.98018	−0.152186
$685$	−5.78462	−0.221019
$686$	−1.35819	−0.0518559
$687$	−79.3948	−3.02910
$688$	−9.69722	−0.369703
$689$	0	0
$690$	4.42628	0.168505
$691$	3.56418	0.135588	0.0677939	−	0.997699i	$-0.478404\pi$
$691$	3.56418	0.135588	0.0677939	+	0.997699i	$0.478404\pi$
$692$	−0.874636	−0.0332487
$693$	−18.0762	−0.686659
$694$	25.0377	0.950418
$695$	−2.45464	−0.0931099
$696$	−79.2203	−3.00284
$697$	55.3702	2.09729
$698$	−1.14289	−0.0432590
$699$	−32.7930	−1.24034
$700$	0.683922	0.0258498
$701$	5.75672	0.217428	0.108714	−	0.994073i	$-0.465327\pi$
$701$	5.75672	0.217428	0.108714	+	0.994073i	$0.465327\pi$
$702$	0	0
$703$	−13.6270	−0.513951
$704$	−18.0315	−0.679590
$705$	−20.1741	−0.759802
$706$	5.87235	0.221009
$707$	1.76856	0.0665134
$708$	2.64117	0.0992613
$709$	−5.47541	−0.205633	−0.102817	−	0.994700i	$-0.532786\pi$
$709$	−5.47541	−0.205633	−0.102817	+	0.994700i	$0.532786\pi$
$710$	12.4828	0.468470
$711$	−53.8164	−2.01827
$712$	−5.77216	−0.216321
$713$	1.57367	0.0589343
$714$	−26.0073	−0.973299
$715$	0	0
$716$	−1.11534	−0.0416823
$717$	−23.7210	−0.885876
$718$	−16.4238	−0.612930
$719$	−45.1042	−1.68210	−0.841051	−	0.540955i	$-0.818063\pi$
$719$	−45.1042	−1.68210	−0.841051	+	0.540955i	$0.818063\pi$
$720$	24.1859	0.901354
$721$	−11.4598	−0.426787
$722$	13.5829	0.505503
$723$	−63.0525	−2.34495
$724$	0.0881337	0.00327546
$725$	35.0748	1.30264
$726$	30.0945	1.11691
$727$	35.7464	1.32576	0.662880	−	0.748725i	$-0.269334\pi$
$727$	35.7464	1.32576	0.662880	+	0.748725i	$0.269334\pi$
$728$	0	0
$729$	135.617	5.02285
$730$	9.43584	0.349236
$731$	14.9121	0.551542
$732$	−2.24005	−0.0827946
$733$	30.7972	1.13752	0.568761	−	0.822503i	$-0.307423\pi$
$733$	30.7972	1.13752	0.568761	+	0.822503i	$0.307423\pi$
$734$	12.3013	0.454050
$735$	−2.62444	−0.0968039
$736$	−1.08853	−0.0401236
$737$	23.9234	0.881231
$738$	−113.975	−4.19550
$739$	38.1399	1.40300	0.701499	−	0.712670i	$-0.252514\pi$
$739$	38.1399	1.40300	0.701499	+	0.712670i	$0.252514\pi$
$740$	−0.545031	−0.0200357
$741$	0	0
$742$	0.476581	0.0174959
$743$	19.8187	0.727079	0.363539	−	0.931579i	$-0.381568\pi$
$743$	19.8187	0.727079	0.363539	+	0.931579i	$0.381568\pi$
$744$	12.6034	0.462062
$745$	12.0836	0.442708
$746$	31.2728	1.14498
$747$	25.0096	0.915052
$748$	1.85253	0.0677351
$749$	−3.29566	−0.120421
$750$	−33.5178	−1.22390
$751$	11.0353	0.402683	0.201341	−	0.979521i	$-0.435470\pi$
$751$	11.0353	0.402683	0.201341	+	0.979521i	$0.435470\pi$
$752$	−28.1747	−1.02743
$753$	56.5910	2.06229
$754$	0	0
$755$	−11.7636	−0.428123
$756$	−2.92451	−0.106364
$757$	−5.63273	−0.204725	−0.102363	−	0.994747i	$-0.532640\pi$
$757$	−5.63273	−0.204725	−0.102363	+	0.994747i	$0.532640\pi$
$758$	40.1723	1.45912
$759$	−8.92741	−0.324044
$760$	−6.78374	−0.246072
$761$	−6.45648	−0.234047	−0.117024	−	0.993129i	$-0.537335\pi$
$761$	−6.45648	−0.234047	−0.117024	+	0.993129i	$0.537335\pi$
$762$	50.3991	1.82577
$763$	−13.1559	−0.476277
$764$	1.23506	0.0446830
$765$	−37.1922	−1.34469
$766$	25.9133	0.936285
$767$	0	0
$768$	−12.5861	−0.454162
$769$	−8.81720	−0.317956	−0.158978	−	0.987282i	$-0.550820\pi$
$769$	−8.81720	−0.317956	−0.158978	+	0.987282i	$0.550820\pi$
$770$	−2.22021	−0.0800108
$771$	25.9441	0.934355
$772$	3.19571	0.115016
$773$	46.0758	1.65723	0.828616	−	0.559818i	$-0.189129\pi$
$773$	46.0758	1.65723	0.828616	+	0.559818i	$0.189129\pi$
$774$	−30.6954	−1.10332
$775$	−5.58014	−0.200445
$776$	23.0749	0.828340
$777$	−15.4326	−0.553642
$778$	15.4802	0.554992
$779$	29.4705	1.05589
$780$	0	0
$781$	−25.1766	−0.900890
$782$	−9.50591	−0.339931
$783$	−149.983	−5.35995
$784$	−3.66523	−0.130901
$785$	11.1338	0.397381
$786$	10.3395	0.368799
$787$	2.92457	0.104250	0.0521248	−	0.998641i	$-0.483401\pi$
$787$	2.92457	0.104250	0.0521248	+	0.998641i	$0.483401\pi$
$788$	−0.236429	−0.00842242
$789$	−63.3129	−2.25400
$790$	−6.61000	−0.235173
$791$	1.44552	0.0513970
$792$	−52.9151	−1.88026
$793$	0	0
$794$	−39.6166	−1.40594
$795$	0.920902	0.0326610
$796$	−3.93156	−0.139350
$797$	34.7197	1.22984	0.614918	−	0.788591i	$-0.289189\pi$
$797$	34.7197	1.22984	0.614918	+	0.788591i	$0.289189\pi$
$798$	−13.8423	−0.490011
$799$	43.3262	1.53277
$800$	3.85986	0.136467
$801$	−16.8435	−0.595136
$802$	−23.1370	−0.816997
$803$	−19.0313	−0.671599
$804$	5.96567	0.210393
$805$	−0.959257	−0.0338094
$806$	0	0
$807$	84.4528	2.97288
$808$	5.17716	0.182132
$809$	−36.7435	−1.29183	−0.645917	−	0.763407i	$-0.723525\pi$
$809$	−36.7435	−1.29183	−0.645917	+	0.763407i	$0.723525\pi$
$810$	40.2278	1.41346
$811$	49.5717	1.74070	0.870348	−	0.492437i	$-0.163894\pi$
$811$	49.5717	1.74070	0.870348	+	0.492437i	$0.163894\pi$
$812$	1.23724	0.0434185
$813$	−74.9183	−2.62750
$814$	−13.0556	−0.457598
$815$	8.25603	0.289196
$816$	−70.1838	−2.45692
$817$	7.93687	0.277676
$818$	−9.79254	−0.342388
$819$	0	0
$820$	1.17872	0.0411626
$821$	−31.7074	−1.10660	−0.553299	−	0.832983i	$-0.686631\pi$
$821$	−31.7074	−1.10660	−0.553299	+	0.832983i	$0.686631\pi$
$822$	−34.5529	−1.20517
$823$	−28.7128	−1.00086	−0.500432	−	0.865776i	$-0.666826\pi$
$823$	−28.7128	−1.00086	−0.500432	+	0.865776i	$0.666826\pi$
$824$	−33.5468	−1.16866
$825$	31.6561	1.10213
$826$	6.79800	0.236533
$827$	30.8034	1.07114	0.535569	−	0.844491i	$-0.320097\pi$
$827$	30.8034	1.07114	0.535569	+	0.844491i	$0.320097\pi$
$828$	−1.64756	−0.0572566
$829$	30.9789	1.07594	0.537970	−	0.842964i	$-0.319191\pi$
$829$	30.9789	1.07594	0.537970	+	0.842964i	$0.319191\pi$
$830$	3.07180	0.106624
$831$	−66.9753	−2.32335
$832$	0	0
$833$	5.63627	0.195285
$834$	−14.6622	−0.507710
$835$	−4.55440	−0.157612
$836$	0.985998	0.0341015
$837$	23.8612	0.824764
$838$	−46.4369	−1.60414
$839$	−48.0432	−1.65863	−0.829317	−	0.558778i	$-0.811270\pi$
$839$	−48.0432	−1.65863	−0.829317	+	0.558778i	$0.811270\pi$
$840$	−7.68261	−0.265075
$841$	34.4514	1.18798
$842$	−45.3001	−1.56114
$843$	15.0166	0.517198
$844$	−0.861113	−0.0296407
$845$	0	0
$846$	−89.1838	−3.06620
$847$	−6.52203	−0.224100
$848$	1.28611	0.0441652
$849$	−108.482	−3.72310
$850$	33.7075	1.15616
$851$	−5.64076	−0.193363
$852$	−6.27816	−0.215086
$853$	−10.1693	−0.348189	−0.174095	−	0.984729i	$-0.555700\pi$
$853$	−10.1693	−0.348189	−0.174095	+	0.984729i	$0.555700\pi$
$854$	−5.76557	−0.197294
$855$	−19.7954	−0.676988
$856$	−9.64749	−0.329744
$857$	−4.52581	−0.154599	−0.0772993	−	0.997008i	$-0.524630\pi$
$857$	−4.52581	−0.154599	−0.0772993	+	0.997008i	$0.524630\pi$
$858$	0	0
$859$	29.8293	1.01776	0.508881	−	0.860837i	$-0.330059\pi$
$859$	29.8293	1.01776	0.508881	+	0.860837i	$0.330059\pi$
$860$	0.317447	0.0108249
$861$	33.3755	1.13743
$862$	−43.2749	−1.47395
$863$	34.3352	1.16879	0.584393	−	0.811471i	$-0.301333\pi$
$863$	34.3352	1.16879	0.584393	+	0.811471i	$0.301333\pi$
$864$	−16.5051	−0.561516
$865$	−4.34999	−0.147904
$866$	−3.66403	−0.124509
$867$	50.1709	1.70389
$868$	−0.196835	−0.00668103
$869$	13.3318	0.452249
$870$	−28.3934	−0.962626
$871$	0	0
$872$	−38.5118	−1.30417
$873$	67.3340	2.27891
$874$	−5.05947	−0.171139
$875$	7.26393	0.245566
$876$	−4.74573	−0.160343
$877$	−29.0504	−0.980963	−0.490481	−	0.871452i	$-0.663179\pi$
$877$	−29.0504	−0.980963	−0.490481	+	0.871452i	$0.663179\pi$
$878$	29.2318	0.986524
$879$	−55.1976	−1.86177
$880$	−5.99149	−0.201973
$881$	18.4225	0.620669	0.310335	−	0.950627i	$-0.399559\pi$
$881$	18.4225	0.620669	0.310335	+	0.950627i	$0.399559\pi$
$882$	−11.6019	−0.390655
$883$	33.6175	1.13132	0.565659	−	0.824639i	$-0.308622\pi$
$883$	33.6175	1.13132	0.565659	+	0.824639i	$0.308622\pi$
$884$	0	0
$885$	13.1358	0.441556
$886$	−9.16554	−0.307922
$887$	35.9829	1.20819	0.604094	−	0.796913i	$-0.293535\pi$
$887$	35.9829	1.20819	0.604094	+	0.796913i	$0.293535\pi$
$888$	−45.1764	−1.51602
$889$	−10.9224	−0.366327
$890$	−2.06880	−0.0693465
$891$	−81.1360	−2.71816
$892$	1.07127	0.0358688
$893$	23.0601	0.771678
$894$	72.1781	2.41400
$895$	−5.54714	−0.185420
$896$	−9.82000	−0.328063
$897$	0	0
$898$	44.0032	1.46841
$899$	−10.0947	−0.336676
$900$	5.84216	0.194739
$901$	−1.97774	−0.0658880
$902$	28.2348	0.940116
$903$	8.98854	0.299120
$904$	4.23154	0.140739
$905$	0.438332	0.0145706
$906$	−70.2671	−2.33447
$907$	−26.2877	−0.872868	−0.436434	−	0.899736i	$-0.643759\pi$
$907$	−26.2877	−0.872868	−0.436434	+	0.899736i	$0.643759\pi$
$908$	0.491788	0.0163206
$909$	15.1073	0.501077
$910$	0	0
$911$	−39.8689	−1.32092	−0.660458	−	0.750863i	$-0.729638\pi$
$911$	−39.8689	−1.32092	−0.660458	+	0.750863i	$0.729638\pi$
$912$	−37.3550	−1.23695
$913$	−6.19554	−0.205043
$914$	−7.16989	−0.237159
$915$	−11.1409	−0.368306
$916$	3.62978	0.119931
$917$	−2.24077	−0.0739969
$918$	−144.136	−4.75721
$919$	−27.5349	−0.908292	−0.454146	−	0.890927i	$-0.650056\pi$
$919$	−27.5349	−0.908292	−0.454146	+	0.890927i	$0.650056\pi$
$920$	−2.80807	−0.0925792
$921$	−45.8822	−1.51187
$922$	54.2443	1.78644
$923$	0	0
$924$	1.11665	0.0367350
$925$	20.0018	0.657657
$926$	−9.54542	−0.313682
$927$	−97.8916	−3.21518
$928$	6.98261	0.229215
$929$	14.5572	0.477607	0.238804	−	0.971068i	$-0.423245\pi$
$929$	14.5572	0.477607	0.238804	+	0.971068i	$0.423245\pi$
$930$	4.51719	0.148124
$931$	2.99988	0.0983170
$932$	1.49924	0.0491091
$933$	7.69308	0.251860
$934$	17.2656	0.564949
$935$	9.21352	0.301314
$936$	0	0
$937$	−1.11811	−0.0365270	−0.0182635	−	0.999833i	$-0.505814\pi$
$937$	−1.11811	−0.0365270	−0.0182635	+	0.999833i	$0.505814\pi$
$938$	15.3548	0.501351
$939$	68.4184	2.23275
$940$	0.922325	0.0300829
$941$	−30.8810	−1.00669	−0.503346	−	0.864085i	$-0.667898\pi$
$941$	−30.8810	−1.00669	−0.503346	+	0.864085i	$0.667898\pi$
$942$	66.5047	2.16684
$943$	12.1990	0.397255
$944$	18.3452	0.597085
$945$	−14.5450	−0.473150
$946$	7.60408	0.247230
$947$	−20.2675	−0.658604	−0.329302	−	0.944225i	$-0.606813\pi$
$947$	−20.2675	−0.658604	−0.329302	+	0.944225i	$0.606813\pi$
$948$	3.32448	0.107974
$949$	0	0
$950$	17.9406	0.582071
$951$	−106.365	−3.44911
$952$	16.4993	0.534744
$953$	30.7177	0.995043	0.497522	−	0.867452i	$-0.334243\pi$
$953$	30.7177	0.995043	0.497522	+	0.867452i	$0.334243\pi$
$954$	4.07103	0.131804
$955$	6.14256	0.198769
$956$	1.08448	0.0350746
$957$	57.2670	1.85118
$958$	32.5158	1.05054
$959$	7.48827	0.241809
$960$	−22.3630	−0.721761
$961$	−29.3940	−0.948194
$962$	0	0
$963$	−28.1520	−0.907185
$964$	2.88265	0.0928438
$965$	15.8938	0.511640
$966$	−5.72988	−0.184356
$967$	20.0281	0.644060	0.322030	−	0.946729i	$-0.395635\pi$
$967$	20.0281	0.644060	0.322030	+	0.946729i	$0.395635\pi$
$968$	−19.0922	−0.613646
$969$	57.4432	1.84534
$970$	8.27029	0.265543
$971$	−9.01006	−0.289146	−0.144573	−	0.989494i	$-0.546181\pi$
$971$	−9.01006	−0.289146	−0.144573	+	0.989494i	$0.546181\pi$
$972$	−11.4589	−0.367545
$973$	3.17757	0.101868
$974$	14.5272	0.465483
$975$	0	0
$976$	−15.5591	−0.498034
$977$	−15.4962	−0.495766	−0.247883	−	0.968790i	$-0.579735\pi$
$977$	−15.4962	−0.495766	−0.247883	+	0.968790i	$0.579735\pi$
$978$	49.3153	1.57693
$979$	4.17259	0.133357
$980$	0.119985	0.00383277
$981$	−112.380	−3.58801
$982$	−18.7908	−0.599639
$983$	45.8307	1.46177	0.730886	−	0.682499i	$-0.239107\pi$
$983$	45.8307	1.46177	0.730886	+	0.682499i	$0.239107\pi$
$984$	97.7012	3.11460
$985$	−1.17587	−0.0374665
$986$	60.9779	1.94193
$987$	26.1157	0.831272
$988$	0	0
$989$	3.28539	0.104469
$990$	−18.9654	−0.602759
$991$	5.91658	0.187946	0.0939731	−	0.995575i	$-0.470043\pi$
$991$	5.91658	0.187946	0.0939731	+	0.995575i	$0.470043\pi$
$992$	−1.11088	−0.0352706
$993$	−19.9111	−0.631858
$994$	−16.1591	−0.512536
$995$	−19.5536	−0.619889
$996$	−1.54495	−0.0489536
$997$	27.0852	0.857798	0.428899	−	0.903352i	$-0.358902\pi$
$997$	27.0852	0.857798	0.428899	+	0.903352i	$0.358902\pi$
$998$	19.8369	0.627925
$999$	−85.5298	−2.70604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.r.1.3	yes	12
7.6	odd	2		8281.2.a.cq.1.3		12
13.5	odd	4		1183.2.c.j.337.18		24
13.8	odd	4		1183.2.c.j.337.7		24
13.12	even	2		1183.2.a.q.1.10	✓	12
91.90	odd	2		8281.2.a.cn.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.10	✓	12	13.12	even	2
1183.2.a.r.1.3	yes	12	1.1	even	1	trivial
1183.2.c.j.337.7		24	13.8	odd	4
1183.2.c.j.337.18		24	13.5	odd	4
8281.2.a.cn.1.10		12	91.90	odd	2
8281.2.a.cq.1.3		12	7.6	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-1.35819 q^{2} +3.39737 q^{3} -0.155322 q^{4} -0.772491 q^{5} -4.61428 q^{6} +1.00000 q^{7} +2.92733 q^{8} +8.54215 q^{9} +O(q^{10})\)	\(q-1.35819 q^{2} +3.39737 q^{3} -0.155322 q^{4} -0.772491 q^{5} -4.61428 q^{6} +1.00000 q^{7} +2.92733 q^{8} +8.54215 q^{9} +1.04919 q^{10} -2.11612 q^{11} -0.527686 q^{12} -1.35819 q^{14} -2.62444 q^{15} -3.66523 q^{16} +5.63627 q^{17} -11.6019 q^{18} +2.99988 q^{19} +0.119985 q^{20} +3.39737 q^{21} +2.87409 q^{22} +1.24177 q^{23} +9.94525 q^{24} -4.40326 q^{25} +18.8288 q^{27} -0.155322 q^{28} -7.96564 q^{29} +3.56449 q^{30} +1.26728 q^{31} -0.876591 q^{32} -7.18925 q^{33} -7.65512 q^{34} -0.772491 q^{35} -1.32678 q^{36} -4.54251 q^{37} -4.07440 q^{38} -2.26134 q^{40} +9.82390 q^{41} -4.61428 q^{42} +2.64573 q^{43} +0.328679 q^{44} -6.59873 q^{45} -1.68656 q^{46} +7.68703 q^{47} -12.4522 q^{48} +1.00000 q^{49} +5.98046 q^{50} +19.1485 q^{51} -0.350895 q^{53} -25.5730 q^{54} +1.63468 q^{55} +2.92733 q^{56} +10.1917 q^{57} +10.8188 q^{58} -5.00519 q^{59} +0.407633 q^{60} +4.24504 q^{61} -1.72120 q^{62} +8.54215 q^{63} +8.52104 q^{64} +9.76437 q^{66} -11.3053 q^{67} -0.875435 q^{68} +4.21876 q^{69} +1.04919 q^{70} +11.8975 q^{71} +25.0057 q^{72} +8.99347 q^{73} +6.16959 q^{74} -14.9595 q^{75} -0.465946 q^{76} -2.11612 q^{77} -6.30010 q^{79} +2.83136 q^{80} +38.3419 q^{81} -13.3427 q^{82} +2.92778 q^{83} -0.527686 q^{84} -4.35397 q^{85} -3.59340 q^{86} -27.0622 q^{87} -6.19459 q^{88} -1.97181 q^{89} +8.96233 q^{90} -0.192874 q^{92} +4.30541 q^{93} -10.4404 q^{94} -2.31738 q^{95} -2.97811 q^{96} +7.88255 q^{97} -1.35819 q^{98} -18.0762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * q^99

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