LMFDB - Embedded newform 4029.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.53461$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53461 q^{2} +1.00000 q^{3} +4.42426 q^{4} -2.65587 q^{5} -2.53461 q^{6} +1.73204 q^{7} -6.14455 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.53461 q^{2} +1.00000 q^{3} +4.42426 q^{4} -2.65587 q^{5} -2.53461 q^{6} +1.73204 q^{7} -6.14455 q^{8} +1.00000 q^{9} +6.73160 q^{10} -1.76946 q^{11} +4.42426 q^{12} -2.94944 q^{13} -4.39004 q^{14} -2.65587 q^{15} +6.72553 q^{16} +1.00000 q^{17} -2.53461 q^{18} +1.53421 q^{19} -11.7503 q^{20} +1.73204 q^{21} +4.48488 q^{22} -1.28569 q^{23} -6.14455 q^{24} +2.05365 q^{25} +7.47567 q^{26} +1.00000 q^{27} +7.66297 q^{28} -3.07519 q^{29} +6.73160 q^{30} +7.59686 q^{31} -4.75750 q^{32} -1.76946 q^{33} -2.53461 q^{34} -4.60006 q^{35} +4.42426 q^{36} +3.88559 q^{37} -3.88863 q^{38} -2.94944 q^{39} +16.3191 q^{40} +5.59169 q^{41} -4.39004 q^{42} +1.32749 q^{43} -7.82853 q^{44} -2.65587 q^{45} +3.25873 q^{46} -9.39913 q^{47} +6.72553 q^{48} -4.00005 q^{49} -5.20522 q^{50} +1.00000 q^{51} -13.0491 q^{52} +12.5140 q^{53} -2.53461 q^{54} +4.69945 q^{55} -10.6426 q^{56} +1.53421 q^{57} +7.79441 q^{58} -11.8669 q^{59} -11.7503 q^{60} -3.88080 q^{61} -19.2551 q^{62} +1.73204 q^{63} -1.39263 q^{64} +7.83332 q^{65} +4.48488 q^{66} +7.32608 q^{67} +4.42426 q^{68} -1.28569 q^{69} +11.6594 q^{70} +14.7183 q^{71} -6.14455 q^{72} -7.38852 q^{73} -9.84846 q^{74} +2.05365 q^{75} +6.78774 q^{76} -3.06476 q^{77} +7.47567 q^{78} -1.00000 q^{79} -17.8621 q^{80} +1.00000 q^{81} -14.1728 q^{82} -13.1683 q^{83} +7.66297 q^{84} -2.65587 q^{85} -3.36468 q^{86} -3.07519 q^{87} +10.8725 q^{88} -1.23162 q^{89} +6.73160 q^{90} -5.10853 q^{91} -5.68823 q^{92} +7.59686 q^{93} +23.8231 q^{94} -4.07467 q^{95} -4.75750 q^{96} +15.8945 q^{97} +10.1386 q^{98} -1.76946 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	−2.53461	−1.79224	−0.896120	−	0.443811i	$-0.853626\pi$
$2$	−2.53461	−1.79224	−0.896120	+	0.443811i	$0.853626\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.42426	2.21213
$5$	−2.65587	−1.18774	−0.593871	−	0.804560i	$-0.702401\pi$
$5$	−2.65587	−1.18774	−0.593871	+	0.804560i	$0.702401\pi$
$6$	−2.53461	−1.03475
$7$	1.73204	0.654648	0.327324	−	0.944912i	$-0.393853\pi$
$7$	1.73204	0.654648	0.327324	+	0.944912i	$0.393853\pi$
$8$	−6.14455	−2.17242
$9$	1.00000	0.333333
$10$	6.73160	2.12872
$11$	−1.76946	−0.533511	−0.266756	−	0.963764i	$-0.585952\pi$
$11$	−1.76946	−0.533511	−0.266756	+	0.963764i	$0.585952\pi$
$12$	4.42426	1.27717
$13$	−2.94944	−0.818026	−0.409013	−	0.912528i	$-0.634127\pi$
$13$	−2.94944	−0.818026	−0.409013	+	0.912528i	$0.634127\pi$
$14$	−4.39004	−1.17329
$15$	−2.65587	−0.685743
$16$	6.72553	1.68138
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.53461	−0.597414
$19$	1.53421	0.351972	0.175986	−	0.984393i	$-0.443689\pi$
$19$	1.53421	0.351972	0.175986	+	0.984393i	$0.443689\pi$
$20$	−11.7503	−2.62744
$21$	1.73204	0.377961
$22$	4.48488	0.956180
$23$	−1.28569	−0.268085	−0.134043	−	0.990976i	$-0.542796\pi$
$23$	−1.28569	−0.268085	−0.134043	+	0.990976i	$0.542796\pi$
$24$	−6.14455	−1.25425
$25$	2.05365	0.410731
$26$	7.47567	1.46610
$27$	1.00000	0.192450
$28$	7.66297	1.44816
$29$	−3.07519	−0.571048	−0.285524	−	0.958372i	$-0.592168\pi$
$29$	−3.07519	−0.571048	−0.285524	+	0.958372i	$0.592168\pi$
$30$	6.73160	1.22902
$31$	7.59686	1.36444	0.682218	−	0.731149i	$-0.261015\pi$
$31$	7.59686	1.36444	0.682218	+	0.731149i	$0.261015\pi$
$32$	−4.75750	−0.841015
$33$	−1.76946	−0.308023
$34$	−2.53461	−0.434682
$35$	−4.60006	−0.777553
$36$	4.42426	0.737376
$37$	3.88559	0.638787	0.319394	−	0.947622i	$-0.396521\pi$
$37$	3.88559	0.638787	0.319394	+	0.947622i	$0.396521\pi$
$38$	−3.88863	−0.630819
$39$	−2.94944	−0.472288
$40$	16.3191	2.58028
$41$	5.59169	0.873275	0.436638	−	0.899637i	$-0.356169\pi$
$41$	5.59169	0.873275	0.436638	+	0.899637i	$0.356169\pi$
$42$	−4.39004	−0.677398
$43$	1.32749	0.202441	0.101220	−	0.994864i	$-0.467725\pi$
$43$	1.32749	0.202441	0.101220	+	0.994864i	$0.467725\pi$
$44$	−7.82853	−1.18019
$45$	−2.65587	−0.395914
$46$	3.25873	0.480473
$47$	−9.39913	−1.37100	−0.685502	−	0.728071i	$-0.740417\pi$
$47$	−9.39913	−1.37100	−0.685502	+	0.728071i	$0.740417\pi$
$48$	6.72553	0.970746
$49$	−4.00005	−0.571436
$50$	−5.20522	−0.736129
$51$	1.00000	0.140028
$52$	−13.0491	−1.80958
$53$	12.5140	1.71894	0.859468	−	0.511190i	$-0.170795\pi$
$53$	12.5140	1.71894	0.859468	+	0.511190i	$0.170795\pi$
$54$	−2.53461	−0.344917
$55$	4.69945	0.633673
$56$	−10.6426	−1.42217
$57$	1.53421	0.203211
$58$	7.79441	1.02346
$59$	−11.8669	−1.54494	−0.772472	−	0.635049i	$-0.780980\pi$
$59$	−11.8669	−1.54494	−0.772472	+	0.635049i	$0.780980\pi$
$60$	−11.7503	−1.51695
$61$	−3.88080	−0.496885	−0.248443	−	0.968647i	$-0.579919\pi$
$61$	−3.88080	−0.496885	−0.248443	+	0.968647i	$0.579919\pi$
$62$	−19.2551	−2.44540
$63$	1.73204	0.218216
$64$	−1.39263	−0.174079
$65$	7.83332	0.971604
$66$	4.48488	0.552051
$67$	7.32608	0.895023	0.447511	−	0.894278i	$-0.352310\pi$
$67$	7.32608	0.895023	0.447511	+	0.894278i	$0.352310\pi$
$68$	4.42426	0.536520
$69$	−1.28569	−0.154779
$70$	11.6594	1.39356
$71$	14.7183	1.74674	0.873371	−	0.487056i	$-0.161929\pi$
$71$	14.7183	1.74674	0.873371	+	0.487056i	$0.161929\pi$
$72$	−6.14455	−0.724142
$73$	−7.38852	−0.864761	−0.432381	−	0.901691i	$-0.642326\pi$
$73$	−7.38852	−0.864761	−0.432381	+	0.901691i	$0.642326\pi$
$74$	−9.84846	−1.14486
$75$	2.05365	0.237136
$76$	6.78774	0.778607
$77$	−3.06476	−0.349262
$78$	7.47567	0.846453
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−17.8621	−1.99705
$81$	1.00000	0.111111
$82$	−14.1728	−1.56512
$83$	−13.1683	−1.44541	−0.722707	−	0.691155i	$-0.757102\pi$
$83$	−13.1683	−1.44541	−0.722707	+	0.691155i	$0.757102\pi$
$84$	7.66297	0.836098
$85$	−2.65587	−0.288070
$86$	−3.36468	−0.362823
$87$	−3.07519	−0.329695
$88$	10.8725	1.15901
$89$	−1.23162	−0.130552	−0.0652758	−	0.997867i	$-0.520793\pi$
$89$	−1.23162	−0.130552	−0.0652758	+	0.997867i	$0.520793\pi$
$90$	6.73160	0.709573
$91$	−5.10853	−0.535519
$92$	−5.68823	−0.593039
$93$	7.59686	0.787758
$94$	23.8231	2.45717
$95$	−4.07467	−0.418052
$96$	−4.75750	−0.485561
$97$	15.8945	1.61384	0.806922	−	0.590659i	$-0.201132\pi$
$97$	15.8945	1.61384	0.806922	+	0.590659i	$0.201132\pi$
$98$	10.1386	1.02415
$99$	−1.76946	−0.177837
$100$	9.08589	0.908589
$101$	−13.7983	−1.37298	−0.686489	−	0.727140i	$-0.740849\pi$
$101$	−13.7983	−1.37298	−0.686489	+	0.727140i	$0.740849\pi$
$102$	−2.53461	−0.250964
$103$	−3.30727	−0.325875	−0.162938	−	0.986636i	$-0.552097\pi$
$103$	−3.30727	−0.325875	−0.162938	+	0.986636i	$0.552097\pi$
$104$	18.1229	1.77710
$105$	−4.60006	−0.448920
$106$	−31.7182	−3.08075
$107$	−11.8546	−1.14603	−0.573016	−	0.819544i	$-0.694227\pi$
$107$	−11.8546	−1.14603	−0.573016	+	0.819544i	$0.694227\pi$
$108$	4.42426	0.425724
$109$	−16.1120	−1.54325	−0.771623	−	0.636080i	$-0.780555\pi$
$109$	−16.1120	−1.54325	−0.771623	+	0.636080i	$0.780555\pi$
$110$	−11.9113	−1.13570
$111$	3.88559	0.368804
$112$	11.6489	1.10071
$113$	17.1600	1.61428	0.807139	−	0.590362i	$-0.201015\pi$
$113$	17.1600	1.61428	0.807139	+	0.590362i	$0.201015\pi$
$114$	−3.88863	−0.364204
$115$	3.41463	0.318416
$116$	−13.6054	−1.26323
$117$	−2.94944	−0.272675
$118$	30.0781	2.76891
$119$	1.73204	0.158775
$120$	16.3191	1.48973
$121$	−7.86903	−0.715366
$122$	9.83631	0.890538
$123$	5.59169	0.504186
$124$	33.6104	3.01831
$125$	7.82512	0.699900
$126$	−4.39004	−0.391096
$127$	12.1073	1.07435	0.537174	−	0.843471i	$-0.319492\pi$
$127$	12.1073	1.07435	0.537174	+	0.843471i	$0.319492\pi$
$128$	13.0448	1.15301
$129$	1.32749	0.116879
$130$	−19.8544	−1.74135
$131$	−2.63988	−0.230647	−0.115324	−	0.993328i	$-0.536791\pi$
$131$	−2.63988	−0.230647	−0.115324	+	0.993328i	$0.536791\pi$
$132$	−7.82853	−0.681386
$133$	2.65731	0.230418
$134$	−18.5688	−1.60410
$135$	−2.65587	−0.228581
$136$	−6.14455	−0.526890
$137$	−14.7407	−1.25938	−0.629692	−	0.776845i	$-0.716819\pi$
$137$	−14.7407	−1.25938	−0.629692	+	0.776845i	$0.716819\pi$
$138$	3.25873	0.277401
$139$	14.9508	1.26811	0.634054	−	0.773289i	$-0.281390\pi$
$139$	14.9508	1.26811	0.634054	+	0.773289i	$0.281390\pi$
$140$	−20.3519	−1.72005
$141$	−9.39913	−0.791549
$142$	−37.3052	−3.13058
$143$	5.21890	0.436426
$144$	6.72553	0.560460
$145$	8.16730	0.678258
$146$	18.7270	1.54986
$147$	−4.00005	−0.329919
$148$	17.1908	1.41308
$149$	−1.18508	−0.0970853	−0.0485426	−	0.998821i	$-0.515458\pi$
$149$	−1.18508	−0.0970853	−0.0485426	+	0.998821i	$0.515458\pi$
$150$	−5.20522	−0.425004
$151$	−7.39519	−0.601812	−0.300906	−	0.953654i	$-0.597289\pi$
$151$	−7.39519	−0.601812	−0.300906	+	0.953654i	$0.597289\pi$
$152$	−9.42703	−0.764633
$153$	1.00000	0.0808452
$154$	7.76798	0.625962
$155$	−20.1763	−1.62060
$156$	−13.0491	−1.04476
$157$	−18.2595	−1.45727	−0.728633	−	0.684904i	$-0.759844\pi$
$157$	−18.2595	−1.45727	−0.728633	+	0.684904i	$0.759844\pi$
$158$	2.53461	0.201643
$159$	12.5140	0.992428
$160$	12.6353	0.998909
$161$	−2.22686	−0.175502
$162$	−2.53461	−0.199138
$163$	−12.4560	−0.975631	−0.487815	−	0.872947i	$-0.662206\pi$
$163$	−12.4560	−0.975631	−0.487815	+	0.872947i	$0.662206\pi$
$164$	24.7391	1.93180
$165$	4.69945	0.365852
$166$	33.3766	2.59053
$167$	−1.05353	−0.0815250	−0.0407625	−	0.999169i	$-0.512979\pi$
$167$	−1.05353	−0.0815250	−0.0407625	+	0.999169i	$0.512979\pi$
$168$	−10.6426	−0.821092
$169$	−4.30083	−0.330833
$170$	6.73160	0.516290
$171$	1.53421	0.117324
$172$	5.87317	0.447825
$173$	−4.04676	−0.307670	−0.153835	−	0.988097i	$-0.549162\pi$
$173$	−4.04676	−0.307670	−0.153835	+	0.988097i	$0.549162\pi$
$174$	7.79441	0.590892
$175$	3.55700	0.268884
$176$	−11.9005	−0.897035
$177$	−11.8669	−0.891974
$178$	3.12168	0.233980
$179$	−15.3923	−1.15048	−0.575239	−	0.817986i	$-0.695091\pi$
$179$	−15.3923	−1.15048	−0.575239	+	0.817986i	$0.695091\pi$
$180$	−11.7503	−0.875812
$181$	−24.7819	−1.84203	−0.921013	−	0.389532i	$-0.872637\pi$
$181$	−24.7819	−1.84203	−0.921013	+	0.389532i	$0.872637\pi$
$182$	12.9481	0.959780
$183$	−3.88080	−0.286877
$184$	7.89999	0.582395
$185$	−10.3196	−0.758714
$186$	−19.2551	−1.41185
$187$	−1.76946	−0.129395
$188$	−41.5841	−3.03283
$189$	1.73204	0.125987
$190$	10.3277	0.749250
$191$	−2.49954	−0.180860	−0.0904302	−	0.995903i	$-0.528824\pi$
$191$	−2.49954	−0.180860	−0.0904302	+	0.995903i	$0.528824\pi$
$192$	−1.39263	−0.100504
$193$	−0.191184	−0.0137617	−0.00688086	−	0.999976i	$-0.502190\pi$
$193$	−0.191184	−0.0137617	−0.00688086	+	0.999976i	$0.502190\pi$
$194$	−40.2864	−2.89240
$195$	7.83332	0.560956
$196$	−17.6973	−1.26409
$197$	5.88901	0.419575	0.209787	−	0.977747i	$-0.432723\pi$
$197$	5.88901	0.419575	0.209787	+	0.977747i	$0.432723\pi$
$198$	4.48488	0.318727
$199$	−5.96688	−0.422981	−0.211490	−	0.977380i	$-0.567832\pi$
$199$	−5.96688	−0.422981	−0.211490	+	0.977380i	$0.567832\pi$
$200$	−12.6188	−0.892282
$201$	7.32608	0.516742
$202$	34.9732	2.46071
$203$	−5.32633	−0.373835
$204$	4.42426	0.309760
$205$	−14.8508	−1.03723
$206$	8.38265	0.584047
$207$	−1.28569	−0.0893618
$208$	−19.8365	−1.37541
$209$	−2.71472	−0.187781
$210$	11.6594	0.804573
$211$	−3.40241	−0.234231	−0.117116	−	0.993118i	$-0.537365\pi$
$211$	−3.40241	−0.234231	−0.117116	+	0.993118i	$0.537365\pi$
$212$	55.3653	3.80250
$213$	14.7183	1.00848
$214$	30.0469	2.05396
$215$	−3.52565	−0.240447
$216$	−6.14455	−0.418083
$217$	13.1580	0.893225
$218$	40.8376	2.76587
$219$	−7.38852	−0.499270
$220$	20.7916	1.40177
$221$	−2.94944	−0.198401
$222$	−9.84846	−0.660985
$223$	2.96321	0.198431	0.0992157	−	0.995066i	$-0.468367\pi$
$223$	2.96321	0.198431	0.0992157	+	0.995066i	$0.468367\pi$
$224$	−8.24016	−0.550569
$225$	2.05365	0.136910
$226$	−43.4939	−2.89317
$227$	7.47831	0.496353	0.248177	−	0.968715i	$-0.420169\pi$
$227$	7.47831	0.496353	0.248177	+	0.968715i	$0.420169\pi$
$228$	6.78774	0.449529
$229$	7.82620	0.517170	0.258585	−	0.965989i	$-0.416744\pi$
$229$	7.82620	0.517170	0.258585	+	0.965989i	$0.416744\pi$
$230$	−8.65477	−0.570678
$231$	−3.06476	−0.201646
$232$	18.8956	1.24056
$233$	−0.254471	−0.0166710	−0.00833549	−	0.999965i	$-0.502653\pi$
$233$	−0.254471	−0.0166710	−0.00833549	+	0.999965i	$0.502653\pi$
$234$	7.47567	0.488700
$235$	24.9629	1.62840
$236$	−52.5024	−3.41761
$237$	−1.00000	−0.0649570
$238$	−4.39004	−0.284564
$239$	12.4953	0.808256	0.404128	−	0.914702i	$-0.367575\pi$
$239$	12.4953	0.808256	0.404128	+	0.914702i	$0.367575\pi$
$240$	−17.8621	−1.15300
$241$	27.4477	1.76806	0.884029	−	0.467431i	$-0.154821\pi$
$241$	27.4477	1.76806	0.884029	+	0.467431i	$0.154821\pi$
$242$	19.9449	1.28211
$243$	1.00000	0.0641500
$244$	−17.1696	−1.09917
$245$	10.6236	0.678718
$246$	−14.1728	−0.903622
$247$	−4.52506	−0.287923
$248$	−46.6792	−2.96414
$249$	−13.1683	−0.834510
$250$	−19.8336	−1.25439
$251$	5.35021	0.337702	0.168851	−	0.985642i	$-0.445994\pi$
$251$	5.35021	0.337702	0.168851	+	0.985642i	$0.445994\pi$
$252$	7.66297	0.482722
$253$	2.27498	0.143026
$254$	−30.6873	−1.92549
$255$	−2.65587	−0.166317
$256$	−30.2782	−1.89239
$257$	−6.13154	−0.382475	−0.191238	−	0.981544i	$-0.561250\pi$
$257$	−6.13154	−0.382475	−0.191238	+	0.981544i	$0.561250\pi$
$258$	−3.36468	−0.209476
$259$	6.72998	0.418181
$260$	34.6566	2.14931
$261$	−3.07519	−0.190349
$262$	6.69107	0.413376
$263$	18.2723	1.12672	0.563359	−	0.826212i	$-0.309509\pi$
$263$	18.2723	1.12672	0.563359	+	0.826212i	$0.309509\pi$
$264$	10.8725	0.669156
$265$	−33.2357	−2.04165
$266$	−6.73525	−0.412964
$267$	−1.23162	−0.0753740
$268$	32.4124	1.97990
$269$	13.6823	0.834227	0.417113	−	0.908854i	$-0.363042\pi$
$269$	13.6823	0.834227	0.417113	+	0.908854i	$0.363042\pi$
$270$	6.73160	0.409672
$271$	−11.1909	−0.679798	−0.339899	−	0.940462i	$-0.610393\pi$
$271$	−11.1909	−0.679798	−0.339899	+	0.940462i	$0.610393\pi$
$272$	6.72553	0.407795
$273$	−5.10853	−0.309182
$274$	37.3620	2.25712
$275$	−3.63385	−0.219129
$276$	−5.68823	−0.342391
$277$	−12.6761	−0.761636	−0.380818	−	0.924650i	$-0.624358\pi$
$277$	−12.6761	−0.761636	−0.380818	+	0.924650i	$0.624358\pi$
$278$	−37.8944	−2.27276
$279$	7.59686	0.454812
$280$	28.2653	1.68918
$281$	−0.666526	−0.0397616	−0.0198808	−	0.999802i	$-0.506329\pi$
$281$	−0.666526	−0.0397616	−0.0198808	+	0.999802i	$0.506329\pi$
$282$	23.8231	1.41865
$283$	−3.73803	−0.222203	−0.111101	−	0.993809i	$-0.535438\pi$
$283$	−3.73803	−0.222203	−0.111101	+	0.993809i	$0.535438\pi$
$284$	65.1175	3.86402
$285$	−4.07467	−0.241363
$286$	−13.2279	−0.782181
$287$	9.68501	0.571688
$288$	−4.75750	−0.280338
$289$	1.00000	0.0588235
$290$	−20.7009	−1.21560
$291$	15.8945	0.931753
$292$	−32.6887	−1.91296
$293$	17.6521	1.03125	0.515623	−	0.856816i	$-0.327561\pi$
$293$	17.6521	1.03125	0.515623	+	0.856816i	$0.327561\pi$
$294$	10.1386	0.591294
$295$	31.5171	1.83499
$296$	−23.8752	−1.38772
$297$	−1.76946	−0.102674
$298$	3.00371	0.174000
$299$	3.79207	0.219301
$300$	9.08589	0.524574
$301$	2.29927	0.132527
$302$	18.7439	1.07859
$303$	−13.7983	−0.792689
$304$	10.3184	0.591799
$305$	10.3069	0.590171
$306$	−2.53461	−0.144894
$307$	−13.5479	−0.773219	−0.386610	−	0.922243i	$-0.626354\pi$
$307$	−13.5479	−0.773219	−0.386610	+	0.922243i	$0.626354\pi$
$308$	−13.5593	−0.772612
$309$	−3.30727	−0.188144
$310$	51.1390	2.90450
$311$	6.30376	0.357453	0.178727	−	0.983899i	$-0.442802\pi$
$311$	6.30376	0.357453	0.178727	+	0.983899i	$0.442802\pi$
$312$	18.1229	1.02601
$313$	−30.8972	−1.74642	−0.873208	−	0.487348i	$-0.837964\pi$
$313$	−30.8972	−1.74642	−0.873208	+	0.487348i	$0.837964\pi$
$314$	46.2807	2.61177
$315$	−4.60006	−0.259184
$316$	−4.42426	−0.248884
$317$	−17.0755	−0.959057	−0.479529	−	0.877526i	$-0.659192\pi$
$317$	−17.0755	−0.959057	−0.479529	+	0.877526i	$0.659192\pi$
$318$	−31.7182	−1.77867
$319$	5.44141	0.304660
$320$	3.69865	0.206761
$321$	−11.8546	−0.661662
$322$	5.64424	0.314541
$323$	1.53421	0.0853658
$324$	4.42426	0.245792
$325$	−6.05712	−0.335989
$326$	31.5712	1.74857
$327$	−16.1120	−0.890994
$328$	−34.3584	−1.89713
$329$	−16.2796	−0.897525
$330$	−11.9113	−0.655694
$331$	31.6489	1.73958	0.869790	−	0.493421i	$-0.164254\pi$
$331$	31.6489	1.73958	0.869790	+	0.493421i	$0.164254\pi$
$332$	−58.2601	−3.19744
$333$	3.88559	0.212929
$334$	2.67030	0.146112
$335$	−19.4571	−1.06306
$336$	11.6489	0.635497
$337$	26.0034	1.41650	0.708248	−	0.705964i	$-0.249486\pi$
$337$	26.0034	1.41650	0.708248	+	0.705964i	$0.249486\pi$
$338$	10.9009	0.592932
$339$	17.1600	0.932003
$340$	−11.7503	−0.637247
$341$	−13.4423	−0.727942
$342$	−3.88863	−0.210273
$343$	−19.0525	−1.02874
$344$	−8.15684	−0.439787
$345$	3.41463	0.183838
$346$	10.2570	0.551418
$347$	−24.9628	−1.34007	−0.670037	−	0.742328i	$-0.733722\pi$
$347$	−24.9628	−1.34007	−0.670037	+	0.742328i	$0.733722\pi$
$348$	−13.6054	−0.729327
$349$	−32.8160	−1.75660	−0.878300	−	0.478110i	$-0.841322\pi$
$349$	−32.8160	−1.75660	−0.878300	+	0.478110i	$0.841322\pi$
$350$	−9.01562	−0.481905
$351$	−2.94944	−0.157429
$352$	8.41819	0.448691
$353$	0.269351	0.0143361	0.00716804	−	0.999974i	$-0.497718\pi$
$353$	0.269351	0.0143361	0.00716804	+	0.999974i	$0.497718\pi$
$354$	30.0781	1.59863
$355$	−39.0899	−2.07468
$356$	−5.44901	−0.288797
$357$	1.73204	0.0916691
$358$	39.0136	2.06193
$359$	7.95504	0.419851	0.209925	−	0.977717i	$-0.432678\pi$
$359$	7.95504	0.419851	0.209925	+	0.977717i	$0.432678\pi$
$360$	16.3191	0.860093
$361$	−16.6462	−0.876116
$362$	62.8125	3.30135
$363$	−7.86903	−0.413017
$364$	−22.6014	−1.18464
$365$	19.6230	1.02711
$366$	9.83631	0.514152
$367$	−31.9083	−1.66560	−0.832801	−	0.553572i	$-0.813264\pi$
$367$	−31.9083	−1.66560	−0.832801	+	0.553572i	$0.813264\pi$
$368$	−8.64695	−0.450754
$369$	5.59169	0.291092
$370$	26.1563	1.35980
$371$	21.6748	1.12530
$372$	33.6104	1.74262
$373$	−8.45529	−0.437798	−0.218899	−	0.975748i	$-0.570247\pi$
$373$	−8.45529	−0.437798	−0.218899	+	0.975748i	$0.570247\pi$
$374$	4.48488	0.231908
$375$	7.82512	0.404087
$376$	57.7534	2.97840
$377$	9.07007	0.467132
$378$	−4.39004	−0.225799
$379$	−13.7643	−0.707023	−0.353511	−	0.935430i	$-0.615012\pi$
$379$	−13.7643	−0.707023	−0.353511	+	0.935430i	$0.615012\pi$
$380$	−18.0274	−0.924785
$381$	12.1073	0.620275
$382$	6.33536	0.324145
$383$	36.4233	1.86114	0.930571	−	0.366111i	$-0.119311\pi$
$383$	36.4233	1.86114	0.930571	+	0.366111i	$0.119311\pi$
$384$	13.0448	0.665689
$385$	8.13961	0.414833
$386$	0.484577	0.0246643
$387$	1.32749	0.0674803
$388$	70.3214	3.57003
$389$	−30.1025	−1.52626	−0.763128	−	0.646247i	$-0.776338\pi$
$389$	−30.1025	−1.52626	−0.763128	+	0.646247i	$0.776338\pi$
$390$	−19.8544	−1.00537
$391$	−1.28569	−0.0650202
$392$	24.5785	1.24140
$393$	−2.63988	−0.133164
$394$	−14.9264	−0.751979
$395$	2.65587	0.133631
$396$	−7.82853	−0.393398
$397$	−8.74283	−0.438790	−0.219395	−	0.975636i	$-0.570408\pi$
$397$	−8.74283	−0.438790	−0.219395	+	0.975636i	$0.570408\pi$
$398$	15.1237	0.758083
$399$	2.65731	0.133032
$400$	13.8119	0.690595
$401$	−28.6329	−1.42986	−0.714928	−	0.699198i	$-0.753541\pi$
$401$	−28.6329	−1.42986	−0.714928	+	0.699198i	$0.753541\pi$
$402$	−18.5688	−0.926125
$403$	−22.4064	−1.11614
$404$	−61.0470	−3.03720
$405$	−2.65587	−0.131971
$406$	13.5002	0.670003
$407$	−6.87538	−0.340800
$408$	−6.14455	−0.304200
$409$	−23.0298	−1.13875	−0.569374	−	0.822078i	$-0.692815\pi$
$409$	−23.0298	−1.13875	−0.569374	+	0.822078i	$0.692815\pi$
$410$	37.6410	1.85896
$411$	−14.7407	−0.727105
$412$	−14.6322	−0.720878
$413$	−20.5540	−1.01139
$414$	3.25873	0.160158
$415$	34.9734	1.71678
$416$	14.0319	0.687973
$417$	14.9508	0.732143
$418$	6.88076	0.336549
$419$	−33.3525	−1.62938	−0.814689	−	0.579899i	$-0.803092\pi$
$419$	−33.3525	−1.62938	−0.814689	+	0.579899i	$0.803092\pi$
$420$	−20.3519	−0.993069
$421$	17.4571	0.850808	0.425404	−	0.905004i	$-0.360132\pi$
$421$	17.4571	0.850808	0.425404	+	0.905004i	$0.360132\pi$
$422$	8.62378	0.419799
$423$	−9.39913	−0.457001
$424$	−76.8931	−3.73426
$425$	2.05365	0.0996169
$426$	−37.3052	−1.80744
$427$	−6.72168	−0.325285
$428$	−52.4480	−2.53517
$429$	5.21890	0.251971
$430$	8.93616	0.430940
$431$	−25.3938	−1.22318	−0.611589	−	0.791176i	$-0.709469\pi$
$431$	−25.3938	−1.22318	−0.611589	+	0.791176i	$0.709469\pi$
$432$	6.72553	0.323582
$433$	−24.1731	−1.16168	−0.580842	−	0.814016i	$-0.697277\pi$
$433$	−24.1731	−1.16168	−0.580842	+	0.814016i	$0.697277\pi$
$434$	−33.3505	−1.60088
$435$	8.16730	0.391592
$436$	−71.2834	−3.41386
$437$	−1.97252	−0.0943586
$438$	18.7270	0.894812
$439$	−30.9996	−1.47953	−0.739766	−	0.672864i	$-0.765064\pi$
$439$	−30.9996	−1.47953	−0.739766	+	0.672864i	$0.765064\pi$
$440$	−28.8760	−1.37661
$441$	−4.00005	−0.190479
$442$	7.47567	0.355582
$443$	9.38453	0.445873	0.222936	−	0.974833i	$-0.428436\pi$
$443$	9.38453	0.445873	0.222936	+	0.974833i	$0.428436\pi$
$444$	17.1908	0.815841
$445$	3.27103	0.155062
$446$	−7.51059	−0.355637
$447$	−1.18508	−0.0560522
$448$	−2.41209	−0.113960
$449$	6.65154	0.313906	0.156953	−	0.987606i	$-0.449833\pi$
$449$	6.65154	0.313906	0.156953	+	0.987606i	$0.449833\pi$
$450$	−5.20522	−0.245376
$451$	−9.89425	−0.465902
$452$	75.9202	3.57099
$453$	−7.39519	−0.347456
$454$	−18.9546	−0.889584
$455$	13.5676	0.636059
$456$	−9.42703	−0.441461
$457$	−16.1895	−0.757313	−0.378657	−	0.925537i	$-0.623614\pi$
$457$	−16.1895	−0.757313	−0.378657	+	0.925537i	$0.623614\pi$
$458$	−19.8364	−0.926893
$459$	1.00000	0.0466760
$460$	15.1072	0.704377
$461$	11.8678	0.552737	0.276368	−	0.961052i	$-0.410869\pi$
$461$	11.8678	0.552737	0.276368	+	0.961052i	$0.410869\pi$
$462$	7.76798	0.361399
$463$	−24.7846	−1.15184	−0.575919	−	0.817507i	$-0.695356\pi$
$463$	−24.7846	−1.15184	−0.575919	+	0.817507i	$0.695356\pi$
$464$	−20.6823	−0.960149
$465$	−20.1763	−0.935653
$466$	0.644986	0.0298784
$467$	−19.1805	−0.887566	−0.443783	−	0.896134i	$-0.646364\pi$
$467$	−19.1805	−0.887566	−0.443783	+	0.896134i	$0.646364\pi$
$468$	−13.0491	−0.603193
$469$	12.6890	0.585925
$470$	−63.2712	−2.91848
$471$	−18.2595	−0.841353
$472$	72.9169	3.35627
$473$	−2.34894	−0.108004
$474$	2.53461	0.116419
$475$	3.15074	0.144566
$476$	7.66297	0.351232
$477$	12.5140	0.572978
$478$	−31.6708	−1.44859
$479$	−14.5699	−0.665717	−0.332859	−	0.942977i	$-0.608013\pi$
$479$	−14.5699	−0.665717	−0.332859	+	0.942977i	$0.608013\pi$
$480$	12.6353	0.576721
$481$	−11.4603	−0.522545
$482$	−69.5691	−3.16879
$483$	−2.22686	−0.101326
$484$	−34.8146	−1.58248
$485$	−42.2138	−1.91683
$486$	−2.53461	−0.114972
$487$	17.9051	0.811357	0.405679	−	0.914016i	$-0.367035\pi$
$487$	17.9051	0.811357	0.405679	+	0.914016i	$0.367035\pi$
$488$	23.8457	1.07945
$489$	−12.4560	−0.563281
$490$	−26.9268	−1.21643
$491$	−10.7628	−0.485719	−0.242859	−	0.970061i	$-0.578085\pi$
$491$	−10.7628	−0.485719	−0.242859	+	0.970061i	$0.578085\pi$
$492$	24.7391	1.11532
$493$	−3.07519	−0.138499
$494$	11.4693	0.516027
$495$	4.69945	0.211224
$496$	51.0929	2.29414
$497$	25.4926	1.14350
$498$	33.3766	1.49564
$499$	−3.22876	−0.144539	−0.0722695	−	0.997385i	$-0.523024\pi$
$499$	−3.22876	−0.144539	−0.0722695	+	0.997385i	$0.523024\pi$
$500$	34.6203	1.54827
$501$	−1.05353	−0.0470685
$502$	−13.5607	−0.605244
$503$	2.33814	0.104253	0.0521263	−	0.998640i	$-0.483400\pi$
$503$	2.33814	0.104253	0.0521263	+	0.998640i	$0.483400\pi$
$504$	−10.6426	−0.474058
$505$	36.6464	1.63074
$506$	−5.76618	−0.256338
$507$	−4.30083	−0.191007
$508$	53.5657	2.37660
$509$	12.9402	0.573564	0.286782	−	0.957996i	$-0.407414\pi$
$509$	12.9402	0.573564	0.286782	+	0.957996i	$0.407414\pi$
$510$	6.73160	0.298080
$511$	−12.7972	−0.566114
$512$	50.6539	2.23861
$513$	1.53421	0.0677371
$514$	15.5411	0.685488
$515$	8.78369	0.387056
$516$	5.87317	0.258552
$517$	16.6313	0.731446
$518$	−17.0579	−0.749481
$519$	−4.04676	−0.177633
$520$	−48.1322	−2.11074
$521$	−30.7519	−1.34727	−0.673633	−	0.739066i	$-0.735267\pi$
$521$	−30.7519	−1.34727	−0.673633	+	0.739066i	$0.735267\pi$
$522$	7.79441	0.341152
$523$	−7.30153	−0.319274	−0.159637	−	0.987176i	$-0.551032\pi$
$523$	−7.30153	−0.319274	−0.159637	+	0.987176i	$0.551032\pi$
$524$	−11.6795	−0.510222
$525$	3.55700	0.155240
$526$	−46.3132	−2.01935
$527$	7.59686	0.330924
$528$	−11.9005	−0.517904
$529$	−21.3470	−0.928130
$530$	84.2395	3.65913
$531$	−11.8669	−0.514981
$532$	11.7566	0.509714
$533$	−16.4923	−0.714362
$534$	3.12168	0.135088
$535$	31.4844	1.36119
$536$	−45.0154	−1.94437
$537$	−15.3923	−0.664228
$538$	−34.6794	−1.49514
$539$	7.07792	0.304867
$540$	−11.7503	−0.505650
$541$	−2.59205	−0.111441	−0.0557205	−	0.998446i	$-0.517746\pi$
$541$	−2.59205	−0.111441	−0.0557205	+	0.998446i	$0.517746\pi$
$542$	28.3646	1.21836
$543$	−24.7819	−1.06349
$544$	−4.75750	−0.203976
$545$	42.7913	1.83298
$546$	12.9481	0.554129
$547$	43.5004	1.85994	0.929971	−	0.367634i	$-0.119832\pi$
$547$	43.5004	1.85994	0.929971	+	0.367634i	$0.119832\pi$
$548$	−65.2167	−2.78592
$549$	−3.88080	−0.165628
$550$	9.21040	0.392733
$551$	−4.71799	−0.200993
$552$	7.89999	0.336246
$553$	−1.73204	−0.0736537
$554$	32.1291	1.36503
$555$	−10.3196	−0.438044
$556$	66.1461	2.80522
$557$	7.12969	0.302095	0.151047	−	0.988527i	$-0.451735\pi$
$557$	7.12969	0.302095	0.151047	+	0.988527i	$0.451735\pi$
$558$	−19.2551	−0.815133
$559$	−3.91536	−0.165602
$560$	−30.9379	−1.30736
$561$	−1.76946	−0.0747065
$562$	1.68938	0.0712624
$563$	−2.16562	−0.0912699	−0.0456349	−	0.998958i	$-0.514531\pi$
$563$	−2.16562	−0.0912699	−0.0456349	+	0.998958i	$0.514531\pi$
$564$	−41.5841	−1.75101
$565$	−45.5748	−1.91734
$566$	9.47445	0.398241
$567$	1.73204	0.0727387
$568$	−90.4373	−3.79466
$569$	−11.5121	−0.482613	−0.241307	−	0.970449i	$-0.577576\pi$
$569$	−11.5121	−0.482613	−0.241307	+	0.970449i	$0.577576\pi$
$570$	10.3277	0.432580
$571$	21.4527	0.897766	0.448883	−	0.893591i	$-0.351822\pi$
$571$	21.4527	0.897766	0.448883	+	0.893591i	$0.351822\pi$
$572$	23.0897	0.965430
$573$	−2.49954	−0.104420
$574$	−24.5477	−1.02460
$575$	−2.64037	−0.110111
$576$	−1.39263	−0.0580263
$577$	9.23844	0.384601	0.192301	−	0.981336i	$-0.438405\pi$
$577$	9.23844	0.384601	0.192301	+	0.981336i	$0.438405\pi$
$578$	−2.53461	−0.105426
$579$	−0.191184	−0.00794534
$580$	36.1342	1.50039
$581$	−22.8080	−0.946237
$582$	−40.2864	−1.66993
$583$	−22.1430	−0.917071
$584$	45.3991	1.87863
$585$	7.83332	0.323868
$586$	−44.7412	−1.84824
$587$	8.29711	0.342459	0.171229	−	0.985231i	$-0.445226\pi$
$587$	8.29711	0.342459	0.171229	+	0.985231i	$0.445226\pi$
$588$	−17.6973	−0.729822
$589$	11.6552	0.480244
$590$	−79.8835	−3.28875
$591$	5.88901	0.242242
$592$	26.1326	1.07404
$593$	−31.3954	−1.28926	−0.644628	−	0.764497i	$-0.722988\pi$
$593$	−31.3954	−1.28926	−0.644628	+	0.764497i	$0.722988\pi$
$594$	4.48488	0.184017
$595$	−4.60006	−0.188584
$596$	−5.24308	−0.214765
$597$	−5.96688	−0.244208
$598$	−9.61141	−0.393040
$599$	−29.4983	−1.20527	−0.602634	−	0.798018i	$-0.705882\pi$
$599$	−29.4983	−1.20527	−0.602634	+	0.798018i	$0.705882\pi$
$600$	−12.6188	−0.515159
$601$	−41.1982	−1.68051	−0.840255	−	0.542191i	$-0.817595\pi$
$601$	−41.1982	−1.68051	−0.840255	+	0.542191i	$0.817595\pi$
$602$	−5.82774	−0.237521
$603$	7.32608	0.298341
$604$	−32.7182	−1.33128
$605$	20.8991	0.849670
$606$	34.9732	1.42069
$607$	−10.9413	−0.444096	−0.222048	−	0.975036i	$-0.571274\pi$
$607$	−10.9413	−0.444096	−0.222048	+	0.975036i	$0.571274\pi$
$608$	−7.29901	−0.296014
$609$	−5.32633	−0.215834
$610$	−26.1240	−1.05773
$611$	27.7221	1.12152
$612$	4.42426	0.178840
$613$	0.670510	0.0270817	0.0135408	−	0.999908i	$-0.495690\pi$
$613$	0.670510	0.0270817	0.0135408	+	0.999908i	$0.495690\pi$
$614$	34.3387	1.38580
$615$	−14.8508	−0.598843
$616$	18.8316	0.758745
$617$	7.22151	0.290727	0.145364	−	0.989378i	$-0.453565\pi$
$617$	7.22151	0.290727	0.145364	+	0.989378i	$0.453565\pi$
$618$	8.38265	0.337200
$619$	4.64196	0.186576	0.0932880	−	0.995639i	$-0.470262\pi$
$619$	4.64196	0.186576	0.0932880	+	0.995639i	$0.470262\pi$
$620$	−89.2650	−3.58497
$621$	−1.28569	−0.0515930
$622$	−15.9776	−0.640642
$623$	−2.13321	−0.0854654
$624$	−19.8365	−0.794096
$625$	−31.0508	−1.24203
$626$	78.3125	3.13000
$627$	−2.71472	−0.108415
$628$	−80.7846	−3.22366
$629$	3.88559	0.154929
$630$	11.6594	0.464521
$631$	1.14355	0.0455241	0.0227620	−	0.999741i	$-0.492754\pi$
$631$	1.14355	0.0455241	0.0227620	+	0.999741i	$0.492754\pi$
$632$	6.14455	0.244417
$633$	−3.40241	−0.135234
$634$	43.2798	1.71886
$635$	−32.1554	−1.27605
$636$	55.3653	2.19538
$637$	11.7979	0.467450
$638$	−13.7919	−0.546025
$639$	14.7183	0.582247
$640$	−34.6453	−1.36947
$641$	−4.40393	−0.173945	−0.0869724	−	0.996211i	$-0.527719\pi$
$641$	−4.40393	−0.173945	−0.0869724	+	0.996211i	$0.527719\pi$
$642$	30.0469	1.18586
$643$	−5.68366	−0.224142	−0.112071	−	0.993700i	$-0.535748\pi$
$643$	−5.68366	−0.224142	−0.112071	+	0.993700i	$0.535748\pi$
$644$	−9.85222	−0.388232
$645$	−3.52565	−0.138822
$646$	−3.88863	−0.152996
$647$	41.9030	1.64738	0.823689	−	0.567042i	$-0.191912\pi$
$647$	41.9030	1.64738	0.823689	+	0.567042i	$0.191912\pi$
$648$	−6.14455	−0.241381
$649$	20.9980	0.824245
$650$	15.3524	0.602173
$651$	13.1580	0.515704
$652$	−55.1086	−2.15822
$653$	1.96570	0.0769239	0.0384620	−	0.999260i	$-0.487754\pi$
$653$	1.96570	0.0769239	0.0384620	+	0.999260i	$0.487754\pi$
$654$	40.8376	1.59688
$655$	7.01118	0.273950
$656$	37.6071	1.46831
$657$	−7.38852	−0.288254
$658$	41.2625	1.60858
$659$	5.17940	0.201761	0.100880	−	0.994899i	$-0.467834\pi$
$659$	5.17940	0.201761	0.100880	+	0.994899i	$0.467834\pi$
$660$	20.7916	0.809310
$661$	11.4109	0.443834	0.221917	−	0.975066i	$-0.428769\pi$
$661$	11.4109	0.443834	0.221917	+	0.975066i	$0.428769\pi$
$662$	−80.2177	−3.11775
$663$	−2.94944	−0.114547
$664$	80.9135	3.14005
$665$	−7.05747	−0.273677
$666$	−9.84846	−0.381620
$667$	3.95374	0.153090
$668$	−4.66111	−0.180344
$669$	2.96321	0.114564
$670$	49.3162	1.90525
$671$	6.86690	0.265094
$672$	−8.24016	−0.317871
$673$	−4.63259	−0.178573	−0.0892866	−	0.996006i	$-0.528459\pi$
$673$	−4.63259	−0.178573	−0.0892866	+	0.996006i	$0.528459\pi$
$674$	−65.9085	−2.53870
$675$	2.05365	0.0790452
$676$	−19.0280	−0.731845
$677$	−37.4061	−1.43763	−0.718817	−	0.695200i	$-0.755316\pi$
$677$	−37.4061	−1.43763	−0.718817	+	0.695200i	$0.755316\pi$
$678$	−43.4939	−1.67037
$679$	27.5299	1.05650
$680$	16.3191	0.625810
$681$	7.47831	0.286570
$682$	34.0710	1.30465
$683$	−12.0347	−0.460496	−0.230248	−	0.973132i	$-0.573954\pi$
$683$	−12.0347	−0.460496	−0.230248	+	0.973132i	$0.573954\pi$
$684$	6.78774	0.259536
$685$	39.1494	1.49582
$686$	48.2906	1.84375
$687$	7.82620	0.298588
$688$	8.92809	0.340380
$689$	−36.9093	−1.40613
$690$	−8.65477	−0.329481
$691$	−28.7599	−1.09408	−0.547039	−	0.837107i	$-0.684245\pi$
$691$	−28.7599	−1.09408	−0.547039	+	0.837107i	$0.684245\pi$
$692$	−17.9039	−0.680605
$693$	−3.06476	−0.116421
$694$	63.2710	2.40174
$695$	−39.7074	−1.50619
$696$	18.8956	0.716237
$697$	5.59169	0.211800
$698$	83.1758	3.14825
$699$	−0.254471	−0.00962499
$700$	15.7371	0.594806
$701$	−13.3318	−0.503536	−0.251768	−	0.967788i	$-0.581012\pi$
$701$	−13.3318	−0.503536	−0.251768	+	0.967788i	$0.581012\pi$
$702$	7.47567	0.282151
$703$	5.96132	0.224835
$704$	2.46420	0.0928730
$705$	24.9629	0.940156
$706$	−0.682699	−0.0256937
$707$	−23.8991	−0.898817
$708$	−52.5024	−1.97316
$709$	32.4949	1.22037	0.610186	−	0.792258i	$-0.291095\pi$
$709$	32.4949	1.22037	0.610186	+	0.792258i	$0.291095\pi$
$710$	99.0778	3.71832
$711$	−1.00000	−0.0375029
$712$	7.56775	0.283614
$713$	−9.76722	−0.365785
$714$	−4.39004	−0.164293
$715$	−13.8607	−0.518362
$716$	−68.0996	−2.54500
$717$	12.4953	0.466647
$718$	−20.1629	−0.752474
$719$	12.2266	0.455975	0.227988	−	0.973664i	$-0.426785\pi$
$719$	12.2266	0.455975	0.227988	+	0.973664i	$0.426785\pi$
$720$	−17.8621	−0.665682
$721$	−5.72832	−0.213334
$722$	42.1916	1.57021
$723$	27.4477	1.02079
$724$	−109.642	−4.07480
$725$	−6.31537	−0.234547
$726$	19.9449	0.740226
$727$	36.9353	1.36986	0.684928	−	0.728611i	$-0.259834\pi$
$727$	36.9353	1.36986	0.684928	+	0.728611i	$0.259834\pi$
$728$	31.3896	1.16338
$729$	1.00000	0.0370370
$730$	−49.7366	−1.84083
$731$	1.32749	0.0490991
$732$	−17.1696	−0.634608
$733$	−1.32672	−0.0490035	−0.0245018	−	0.999700i	$-0.507800\pi$
$733$	−1.32672	−0.0490035	−0.0245018	+	0.999700i	$0.507800\pi$
$734$	80.8753	2.98516
$735$	10.6236	0.391858
$736$	6.11668	0.225464
$737$	−12.9632	−0.477504
$738$	−14.1728	−0.521707
$739$	−41.5368	−1.52796	−0.763978	−	0.645242i	$-0.776756\pi$
$739$	−41.5368	−1.52796	−0.763978	+	0.645242i	$0.776756\pi$
$740$	−45.6567	−1.67837
$741$	−4.52506	−0.166232
$742$	−54.9371	−2.01680
$743$	−5.53511	−0.203064	−0.101532	−	0.994832i	$-0.532374\pi$
$743$	−5.53511	−0.203064	−0.101532	+	0.994832i	$0.532374\pi$
$744$	−46.6792	−1.71134
$745$	3.14741	0.115312
$746$	21.4309	0.784640
$747$	−13.1683	−0.481805
$748$	−7.82853	−0.286239
$749$	−20.5327	−0.750247
$750$	−19.8336	−0.724222
$751$	−6.65536	−0.242857	−0.121429	−	0.992600i	$-0.538748\pi$
$751$	−6.65536	−0.242857	−0.121429	+	0.992600i	$0.538748\pi$
$752$	−63.2141	−2.30518
$753$	5.35021	0.194973
$754$	−22.9891	−0.837214
$755$	19.6407	0.714797
$756$	7.66297	0.278699
$757$	40.1089	1.45778	0.728892	−	0.684628i	$-0.240036\pi$
$757$	40.1089	1.45778	0.728892	+	0.684628i	$0.240036\pi$
$758$	34.8871	1.26716
$759$	2.27498	0.0825764
$760$	25.0370	0.908187
$761$	−22.4899	−0.815257	−0.407628	−	0.913148i	$-0.633644\pi$
$761$	−22.4899	−0.815257	−0.407628	+	0.913148i	$0.633644\pi$
$762$	−30.6873	−1.11168
$763$	−27.9065	−1.01028
$764$	−11.0586	−0.400086
$765$	−2.65587	−0.0960232
$766$	−92.3188	−3.33562
$767$	35.0008	1.26380
$768$	−30.2782	−1.09257
$769$	7.52172	0.271240	0.135620	−	0.990761i	$-0.456697\pi$
$769$	7.52172	0.271240	0.135620	+	0.990761i	$0.456697\pi$
$770$	−20.6308	−0.743481
$771$	−6.13154	−0.220822
$772$	−0.845847	−0.0304427
$773$	4.44493	0.159873	0.0799366	−	0.996800i	$-0.474528\pi$
$773$	4.44493	0.159873	0.0799366	+	0.996800i	$0.474528\pi$
$774$	−3.36468	−0.120941
$775$	15.6013	0.560416
$776$	−97.6646	−3.50595
$777$	6.72998	0.241437
$778$	76.2981	2.73542
$779$	8.57883	0.307369
$780$	34.6566	1.24091
$781$	−26.0434	−0.931906
$782$	3.25873	0.116532
$783$	−3.07519	−0.109898
$784$	−26.9025	−0.960802
$785$	48.4949	1.73086
$786$	6.69107	0.238663
$787$	−38.3304	−1.36633	−0.683166	−	0.730263i	$-0.739397\pi$
$787$	−38.3304	−1.36633	−0.683166	+	0.730263i	$0.739397\pi$
$788$	26.0545	0.928153
$789$	18.2723	0.650511
$790$	−6.73160	−0.239500
$791$	29.7217	1.05678
$792$	10.8725	0.386338
$793$	11.4462	0.406465
$794$	22.1597	0.786418
$795$	−33.2357	−1.17875
$796$	−26.3990	−0.935687
$797$	12.4873	0.442323	0.221161	−	0.975237i	$-0.429015\pi$
$797$	12.4873	0.442323	0.221161	+	0.975237i	$0.429015\pi$
$798$	−6.73525	−0.238425
$799$	−9.39913	−0.332517
$800$	−9.77026	−0.345431
$801$	−1.23162	−0.0435172
$802$	72.5732	2.56265
$803$	13.0737	0.461360
$804$	32.4124	1.14310
$805$	5.91427	0.208450
$806$	56.7916	2.00040
$807$	13.6823	0.481641
$808$	84.7840	2.98269
$809$	−9.90831	−0.348358	−0.174179	−	0.984714i	$-0.555727\pi$
$809$	−9.90831	−0.348358	−0.174179	+	0.984714i	$0.555727\pi$
$810$	6.73160	0.236524
$811$	39.7874	1.39712	0.698562	−	0.715549i	$-0.253824\pi$
$811$	39.7874	1.39712	0.698562	+	0.715549i	$0.253824\pi$
$812$	−23.5651	−0.826972
$813$	−11.1909	−0.392482
$814$	17.4264	0.610796
$815$	33.0816	1.15880
$816$	6.72553	0.235440
$817$	2.03665	0.0712535
$818$	58.3715	2.04091
$819$	−5.10853	−0.178506
$820$	−65.7038	−2.29448
$821$	−33.6515	−1.17445	−0.587223	−	0.809425i	$-0.699779\pi$
$821$	−33.6515	−1.17445	−0.587223	+	0.809425i	$0.699779\pi$
$822$	37.3620	1.30315
$823$	32.9641	1.14906	0.574528	−	0.818485i	$-0.305186\pi$
$823$	32.9641	1.14906	0.574528	+	0.818485i	$0.305186\pi$
$824$	20.3217	0.707940
$825$	−3.63385	−0.126514
$826$	52.0963	1.81266
$827$	51.5785	1.79356	0.896780	−	0.442477i	$-0.145900\pi$
$827$	51.5785	1.79356	0.896780	+	0.442477i	$0.145900\pi$
$828$	−5.68823	−0.197680
$829$	11.6076	0.403148	0.201574	−	0.979473i	$-0.435394\pi$
$829$	11.6076	0.403148	0.201574	+	0.979473i	$0.435394\pi$
$830$	−88.6441	−3.07688
$831$	−12.6761	−0.439731
$832$	4.10748	0.142401
$833$	−4.00005	−0.138594
$834$	−37.8944	−1.31218
$835$	2.79805	0.0968306
$836$	−12.0106	−0.415396
$837$	7.59686	0.262586
$838$	84.5357	2.92024
$839$	35.6712	1.23151	0.615754	−	0.787938i	$-0.288851\pi$
$839$	35.6712	1.23151	0.615754	+	0.787938i	$0.288851\pi$
$840$	28.2653	0.975246
$841$	−19.5432	−0.673904
$842$	−44.2470	−1.52485
$843$	−0.666526	−0.0229564
$844$	−15.0531	−0.518150
$845$	11.4224	0.392944
$846$	23.8231	0.819056
$847$	−13.6294	−0.468313
$848$	84.1635	2.89019
$849$	−3.73803	−0.128289
$850$	−5.20522	−0.178537
$851$	−4.99567	−0.171249
$852$	65.1175	2.23089
$853$	19.5490	0.669344	0.334672	−	0.942335i	$-0.391375\pi$
$853$	19.5490	0.669344	0.334672	+	0.942335i	$0.391375\pi$
$854$	17.0368	0.582989
$855$	−4.07467	−0.139351
$856$	72.8414	2.48967
$857$	15.3961	0.525921	0.262960	−	0.964807i	$-0.415301\pi$
$857$	15.3961	0.525921	0.262960	+	0.964807i	$0.415301\pi$
$858$	−13.2279	−0.451592
$859$	−35.6522	−1.21644	−0.608218	−	0.793770i	$-0.708115\pi$
$859$	−35.6522	−1.21644	−0.608218	+	0.793770i	$0.708115\pi$
$860$	−15.5984	−0.531900
$861$	9.68501	0.330064
$862$	64.3635	2.19223
$863$	−16.0596	−0.546675	−0.273337	−	0.961918i	$-0.588128\pi$
$863$	−16.0596	−0.546675	−0.273337	+	0.961918i	$0.588128\pi$
$864$	−4.75750	−0.161854
$865$	10.7477	0.365432
$866$	61.2694	2.08202
$867$	1.00000	0.0339618
$868$	58.2145	1.97593
$869$	1.76946	0.0600247
$870$	−20.7009	−0.701828
$871$	−21.6078	−0.732152
$872$	99.0007	3.35259
$873$	15.8945	0.537948
$874$	4.99958	0.169113
$875$	13.5534	0.458188
$876$	−32.6887	−1.10445
$877$	0.122091	0.00412273	0.00206136	−	0.999998i	$-0.499344\pi$
$877$	0.122091	0.00412273	0.00206136	+	0.999998i	$0.499344\pi$
$878$	78.5720	2.65168
$879$	17.6521	0.595390
$880$	31.6063	1.06545
$881$	−0.501261	−0.0168879	−0.00844395	−	0.999964i	$-0.502688\pi$
$881$	−0.501261	−0.0168879	−0.00844395	+	0.999964i	$0.502688\pi$
$882$	10.1386	0.341384
$883$	33.8480	1.13908	0.569538	−	0.821965i	$-0.307122\pi$
$883$	33.8480	1.13908	0.569538	+	0.821965i	$0.307122\pi$
$884$	−13.0491	−0.438887
$885$	31.5171	1.05943
$886$	−23.7861	−0.799111
$887$	−34.2477	−1.14993	−0.574963	−	0.818180i	$-0.694983\pi$
$887$	−34.2477	−1.14993	−0.574963	+	0.818180i	$0.694983\pi$
$888$	−23.8752	−0.801199
$889$	20.9703	0.703320
$890$	−8.29079	−0.277908
$891$	−1.76946	−0.0592790
$892$	13.1100	0.438956
$893$	−14.4202	−0.482555
$894$	3.00371	0.100459
$895$	40.8801	1.36647
$896$	22.5940	0.754814
$897$	3.79207	0.126613
$898$	−16.8591	−0.562594
$899$	−23.3618	−0.779159
$900$	9.08589	0.302863
$901$	12.5140	0.416903
$902$	25.0781	0.835009
$903$	2.29927	0.0765148
$904$	−105.440	−3.50690
$905$	65.8176	2.18785
$906$	18.7439	0.622725
$907$	44.7409	1.48560	0.742799	−	0.669515i	$-0.233498\pi$
$907$	44.7409	1.48560	0.742799	+	0.669515i	$0.233498\pi$
$908$	33.0860	1.09800
$909$	−13.7983	−0.457659
$910$	−34.3886	−1.13997
$911$	−32.4252	−1.07429	−0.537147	−	0.843488i	$-0.680498\pi$
$911$	−32.4252	−1.07429	−0.537147	+	0.843488i	$0.680498\pi$
$912$	10.3184	0.341676
$913$	23.3008	0.771144
$914$	41.0341	1.35729
$915$	10.3069	0.340735
$916$	34.6251	1.14405
$917$	−4.57237	−0.150993
$918$	−2.53461	−0.0836546
$919$	11.5478	0.380926	0.190463	−	0.981694i	$-0.439001\pi$
$919$	11.5478	0.380926	0.190463	+	0.981694i	$0.439001\pi$
$920$	−20.9814	−0.691735
$921$	−13.5479	−0.446418
$922$	−30.0802	−0.990637
$923$	−43.4107	−1.42888
$924$	−13.5593	−0.446068
$925$	7.97966	0.262370
$926$	62.8193	2.06437
$927$	−3.30727	−0.108625
$928$	14.6302	0.480260
$929$	−17.8848	−0.586782	−0.293391	−	0.955993i	$-0.594784\pi$
$929$	−17.8848	−0.586782	−0.293391	+	0.955993i	$0.594784\pi$
$930$	51.1390	1.67692
$931$	−6.13692	−0.201130
$932$	−1.12585	−0.0368783
$933$	6.30376	0.206376
$934$	48.6150	1.59073
$935$	4.69945	0.153688
$936$	18.1229	0.592367
$937$	10.0604	0.328658	0.164329	−	0.986406i	$-0.447454\pi$
$937$	10.0604	0.328658	0.164329	+	0.986406i	$0.447454\pi$
$938$	−32.1617	−1.05012
$939$	−30.8972	−1.00829
$940$	110.442	3.60223
$941$	−8.42249	−0.274565	−0.137283	−	0.990532i	$-0.543837\pi$
$941$	−8.42249	−0.274565	−0.137283	+	0.990532i	$0.543837\pi$
$942$	46.2807	1.50791
$943$	−7.18919	−0.234112
$944$	−79.8114	−2.59764
$945$	−4.60006	−0.149640
$946$	5.95365	0.193570
$947$	−36.4027	−1.18293	−0.591464	−	0.806331i	$-0.701450\pi$
$947$	−36.4027	−1.18293	−0.591464	+	0.806331i	$0.701450\pi$
$948$	−4.42426	−0.143693
$949$	21.7920	0.707397
$950$	−7.98590	−0.259097
$951$	−17.0755	−0.553712
$952$	−10.6426	−0.344928
$953$	5.79103	0.187590	0.0937950	−	0.995592i	$-0.470100\pi$
$953$	5.79103	0.187590	0.0937950	+	0.995592i	$0.470100\pi$
$954$	−31.7182	−1.02692
$955$	6.63846	0.214815
$956$	55.2826	1.78797
$957$	5.44141	0.175896
$958$	36.9291	1.19313
$959$	−25.5314	−0.824453
$960$	3.69865	0.119373
$961$	26.7123	0.861686
$962$	29.0474	0.936526
$963$	−11.8546	−0.382010
$964$	121.435	3.91117
$965$	0.507760	0.0163454
$966$	5.64424	0.181600
$967$	24.5880	0.790698	0.395349	−	0.918531i	$-0.370624\pi$
$967$	24.5880	0.790698	0.395349	+	0.918531i	$0.370624\pi$
$968$	48.3516	1.55408
$969$	1.53421	0.0492860
$970$	106.996	3.43542
$971$	53.4729	1.71603	0.858013	−	0.513628i	$-0.171699\pi$
$971$	53.4729	1.71603	0.858013	+	0.513628i	$0.171699\pi$
$972$	4.42426	0.141908
$973$	25.8953	0.830165
$974$	−45.3824	−1.45415
$975$	−6.05712	−0.193983
$976$	−26.1004	−0.835453
$977$	46.2432	1.47945	0.739725	−	0.672909i	$-0.234956\pi$
$977$	46.2432	1.47945	0.739725	+	0.672909i	$0.234956\pi$
$978$	31.5712	1.00953
$979$	2.17930	0.0696507
$980$	47.0016	1.50141
$981$	−16.1120	−0.514415
$982$	27.2795	0.870525
$983$	29.7258	0.948104	0.474052	−	0.880497i	$-0.342791\pi$
$983$	29.7258	0.948104	0.474052	+	0.880497i	$0.342791\pi$
$984$	−34.3584	−1.09531
$985$	−15.6405	−0.498347
$986$	7.79441	0.248224
$987$	−16.2796	−0.518186
$988$	−20.0200	−0.636921
$989$	−1.70675	−0.0542714
$990$	−11.9113	−0.378565
$991$	34.3379	1.09078	0.545390	−	0.838182i	$-0.316381\pi$
$991$	34.3379	1.09078	0.545390	+	0.838182i	$0.316381\pi$
$992$	−36.1421	−1.14751
$993$	31.6489	1.00435
$994$	−64.6139	−2.04943
$995$	15.8473	0.502392
$996$	−58.2601	−1.84604
$997$	3.29123	0.104234	0.0521171	−	0.998641i	$-0.483403\pi$
$997$	3.29123	0.104234	0.0521171	+	0.998641i	$0.483403\pi$
$998$	8.18364	0.259049
$999$	3.88559	0.122935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.3	✓	18	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53461 q^{2} +1.00000 q^{3} +4.42426 q^{4} -2.65587 q^{5} -2.53461 q^{6} +1.73204 q^{7} -6.14455 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.53461 q^{2} +1.00000 q^{3} +4.42426 q^{4} -2.65587 q^{5} -2.53461 q^{6} +1.73204 q^{7} -6.14455 q^{8} +1.00000 q^{9} +6.73160 q^{10} -1.76946 q^{11} +4.42426 q^{12} -2.94944 q^{13} -4.39004 q^{14} -2.65587 q^{15} +6.72553 q^{16} +1.00000 q^{17} -2.53461 q^{18} +1.53421 q^{19} -11.7503 q^{20} +1.73204 q^{21} +4.48488 q^{22} -1.28569 q^{23} -6.14455 q^{24} +2.05365 q^{25} +7.47567 q^{26} +1.00000 q^{27} +7.66297 q^{28} -3.07519 q^{29} +6.73160 q^{30} +7.59686 q^{31} -4.75750 q^{32} -1.76946 q^{33} -2.53461 q^{34} -4.60006 q^{35} +4.42426 q^{36} +3.88559 q^{37} -3.88863 q^{38} -2.94944 q^{39} +16.3191 q^{40} +5.59169 q^{41} -4.39004 q^{42} +1.32749 q^{43} -7.82853 q^{44} -2.65587 q^{45} +3.25873 q^{46} -9.39913 q^{47} +6.72553 q^{48} -4.00005 q^{49} -5.20522 q^{50} +1.00000 q^{51} -13.0491 q^{52} +12.5140 q^{53} -2.53461 q^{54} +4.69945 q^{55} -10.6426 q^{56} +1.53421 q^{57} +7.79441 q^{58} -11.8669 q^{59} -11.7503 q^{60} -3.88080 q^{61} -19.2551 q^{62} +1.73204 q^{63} -1.39263 q^{64} +7.83332 q^{65} +4.48488 q^{66} +7.32608 q^{67} +4.42426 q^{68} -1.28569 q^{69} +11.6594 q^{70} +14.7183 q^{71} -6.14455 q^{72} -7.38852 q^{73} -9.84846 q^{74} +2.05365 q^{75} +6.78774 q^{76} -3.06476 q^{77} +7.47567 q^{78} -1.00000 q^{79} -17.8621 q^{80} +1.00000 q^{81} -14.1728 q^{82} -13.1683 q^{83} +7.66297 q^{84} -2.65587 q^{85} -3.36468 q^{86} -3.07519 q^{87} +10.8725 q^{88} -1.23162 q^{89} +6.73160 q^{90} -5.10853 q^{91} -5.68823 q^{92} +7.59686 q^{93} +23.8231 q^{94} -4.07467 q^{95} -4.75750 q^{96} +15.8945 q^{97} +10.1386 q^{98} -1.76946 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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