LMFDB - Embedded newform 4017.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} + \cdots + 7 $ x^16 - 21x^14 - 3x^13 + 177x^12 + 45x^11 - 763x^10 - 251x^9 + 1771x^8 + 639x^7 - 2118x^6 - 710x^5 + 1113x^4 + 243x^3 - 183x^2 - 10x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.54124$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54124 q^{2} +1.00000 q^{3} +4.45789 q^{4} -0.349136 q^{5} -2.54124 q^{6} -1.96840 q^{7} -6.24610 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.54124 q^{2} +1.00000 q^{3} +4.45789 q^{4} -0.349136 q^{5} -2.54124 q^{6} -1.96840 q^{7} -6.24610 q^{8} +1.00000 q^{9} +0.887239 q^{10} +4.78997 q^{11} +4.45789 q^{12} -1.00000 q^{13} +5.00217 q^{14} -0.349136 q^{15} +6.95703 q^{16} +3.22212 q^{17} -2.54124 q^{18} +5.65511 q^{19} -1.55641 q^{20} -1.96840 q^{21} -12.1725 q^{22} -3.57828 q^{23} -6.24610 q^{24} -4.87810 q^{25} +2.54124 q^{26} +1.00000 q^{27} -8.77491 q^{28} -6.87628 q^{29} +0.887239 q^{30} -3.27348 q^{31} -5.18729 q^{32} +4.78997 q^{33} -8.18818 q^{34} +0.687239 q^{35} +4.45789 q^{36} -9.23399 q^{37} -14.3710 q^{38} -1.00000 q^{39} +2.18074 q^{40} -6.19045 q^{41} +5.00217 q^{42} -8.42056 q^{43} +21.3532 q^{44} -0.349136 q^{45} +9.09327 q^{46} +3.74930 q^{47} +6.95703 q^{48} -3.12541 q^{49} +12.3964 q^{50} +3.22212 q^{51} -4.45789 q^{52} -2.63140 q^{53} -2.54124 q^{54} -1.67235 q^{55} +12.2948 q^{56} +5.65511 q^{57} +17.4743 q^{58} +11.3408 q^{59} -1.55641 q^{60} -14.8520 q^{61} +8.31871 q^{62} -1.96840 q^{63} -0.731920 q^{64} +0.349136 q^{65} -12.1725 q^{66} +6.74113 q^{67} +14.3639 q^{68} -3.57828 q^{69} -1.74644 q^{70} +5.34073 q^{71} -6.24610 q^{72} +0.574825 q^{73} +23.4658 q^{74} -4.87810 q^{75} +25.2099 q^{76} -9.42857 q^{77} +2.54124 q^{78} +9.42438 q^{79} -2.42895 q^{80} +1.00000 q^{81} +15.7314 q^{82} +3.35694 q^{83} -8.77491 q^{84} -1.12496 q^{85} +21.3987 q^{86} -6.87628 q^{87} -29.9186 q^{88} +0.450399 q^{89} +0.887239 q^{90} +1.96840 q^{91} -15.9516 q^{92} -3.27348 q^{93} -9.52786 q^{94} -1.97441 q^{95} -5.18729 q^{96} -6.47649 q^{97} +7.94242 q^{98} +4.78997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * 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 $

$2$	−2.54124	−1.79693	−0.898464	−	0.439048i	$-0.855316\pi$
$2$	−2.54124	−1.79693	−0.898464	+	0.439048i	$0.855316\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.45789	2.22895
$5$	−0.349136	−0.156139	−0.0780693	−	0.996948i	$-0.524876\pi$
$5$	−0.349136	−0.156139	−0.0780693	+	0.996948i	$0.524876\pi$
$6$	−2.54124	−1.03746
$7$	−1.96840	−0.743984	−0.371992	−	0.928236i	$-0.621325\pi$
$7$	−1.96840	−0.743984	−0.371992	+	0.928236i	$0.621325\pi$
$8$	−6.24610	−2.20833
$9$	1.00000	0.333333
$10$	0.887239	0.280570
$11$	4.78997	1.44423	0.722116	−	0.691772i	$-0.243170\pi$
$11$	4.78997	1.44423	0.722116	+	0.691772i	$0.243170\pi$
$12$	4.45789	1.28688
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.00217	1.33689
$15$	−0.349136	−0.0901466
$16$	6.95703	1.73926
$17$	3.22212	0.781479	0.390740	−	0.920501i	$-0.372219\pi$
$17$	3.22212	0.781479	0.390740	+	0.920501i	$0.372219\pi$
$18$	−2.54124	−0.598976
$19$	5.65511	1.29737	0.648686	−	0.761056i	$-0.275319\pi$
$19$	5.65511	1.29737	0.648686	+	0.761056i	$0.275319\pi$
$20$	−1.55641	−0.348025
$21$	−1.96840	−0.429539
$22$	−12.1725	−2.59518
$23$	−3.57828	−0.746124	−0.373062	−	0.927806i	$-0.621692\pi$
$23$	−3.57828	−0.746124	−0.373062	+	0.927806i	$0.621692\pi$
$24$	−6.24610	−1.27498
$25$	−4.87810	−0.975621
$26$	2.54124	0.498378
$27$	1.00000	0.192450
$28$	−8.77491	−1.65830
$29$	−6.87628	−1.27689	−0.638447	−	0.769666i	$-0.720423\pi$
$29$	−6.87628	−1.27689	−0.638447	+	0.769666i	$0.720423\pi$
$30$	0.887239	0.161987
$31$	−3.27348	−0.587935	−0.293968	−	0.955815i	$-0.594976\pi$
$31$	−3.27348	−0.587935	−0.293968	+	0.955815i	$0.594976\pi$
$32$	−5.18729	−0.916993
$33$	4.78997	0.833828
$34$	−8.18818	−1.40426
$35$	0.687239	0.116165
$36$	4.45789	0.742982
$37$	−9.23399	−1.51806	−0.759029	−	0.651057i	$-0.774326\pi$
$37$	−9.23399	−1.51806	−0.759029	+	0.651057i	$0.774326\pi$
$38$	−14.3710	−2.33128
$39$	−1.00000	−0.160128
$40$	2.18074	0.344805
$41$	−6.19045	−0.966786	−0.483393	−	0.875403i	$-0.660596\pi$
$41$	−6.19045	−0.966786	−0.483393	+	0.875403i	$0.660596\pi$
$42$	5.00217	0.771851
$43$	−8.42056	−1.28412	−0.642062	−	0.766653i	$-0.721921\pi$
$43$	−8.42056	−1.28412	−0.642062	+	0.766653i	$0.721921\pi$
$44$	21.3532	3.21912
$45$	−0.349136	−0.0520462
$46$	9.09327	1.34073
$47$	3.74930	0.546891	0.273446	−	0.961887i	$-0.411837\pi$
$47$	3.74930	0.546891	0.273446	+	0.961887i	$0.411837\pi$
$48$	6.95703	1.00416
$49$	−3.12541	−0.446488
$50$	12.3964	1.75312
$51$	3.22212	0.451187
$52$	−4.45789	−0.618199
$53$	−2.63140	−0.361451	−0.180726	−	0.983534i	$-0.557845\pi$
$53$	−2.63140	−0.361451	−0.180726	+	0.983534i	$0.557845\pi$
$54$	−2.54124	−0.345819
$55$	−1.67235	−0.225500
$56$	12.2948	1.64296
$57$	5.65511	0.749038
$58$	17.4743	2.29449
$59$	11.3408	1.47645	0.738223	−	0.674557i	$-0.235665\pi$
$59$	11.3408	1.47645	0.738223	+	0.674557i	$0.235665\pi$
$60$	−1.55641	−0.200932
$61$	−14.8520	−1.90161	−0.950803	−	0.309796i	$-0.899739\pi$
$61$	−14.8520	−1.90161	−0.950803	+	0.309796i	$0.899739\pi$
$62$	8.31871	1.05648
$63$	−1.96840	−0.247995
$64$	−0.731920	−0.0914900
$65$	0.349136	0.0433050
$66$	−12.1725	−1.49833
$67$	6.74113	0.823560	0.411780	−	0.911283i	$-0.364907\pi$
$67$	6.74113	0.823560	0.411780	+	0.911283i	$0.364907\pi$
$68$	14.3639	1.74188
$69$	−3.57828	−0.430775
$70$	−1.74644	−0.208739
$71$	5.34073	0.633828	0.316914	−	0.948454i	$-0.397353\pi$
$71$	5.34073	0.633828	0.316914	+	0.948454i	$0.397353\pi$
$72$	−6.24610	−0.736110
$73$	0.574825	0.0672782	0.0336391	−	0.999434i	$-0.489290\pi$
$73$	0.574825	0.0672782	0.0336391	+	0.999434i	$0.489290\pi$
$74$	23.4658	2.72784
$75$	−4.87810	−0.563275
$76$	25.2099	2.89177
$77$	−9.42857	−1.07449
$78$	2.54124	0.287739
$79$	9.42438	1.06033	0.530163	−	0.847896i	$-0.322131\pi$
$79$	9.42438	1.06033	0.530163	+	0.847896i	$0.322131\pi$
$80$	−2.42895	−0.271565
$81$	1.00000	0.111111
$82$	15.7314	1.73724
$83$	3.35694	0.368472	0.184236	−	0.982882i	$-0.441019\pi$
$83$	3.35694	0.368472	0.184236	+	0.982882i	$0.441019\pi$
$84$	−8.77491	−0.957421
$85$	−1.12496	−0.122019
$86$	21.3987	2.30748
$87$	−6.87628	−0.737215
$88$	−29.9186	−3.18934
$89$	0.450399	0.0477422	0.0238711	−	0.999715i	$-0.492401\pi$
$89$	0.450399	0.0477422	0.0238711	+	0.999715i	$0.492401\pi$
$90$	0.887239	0.0935232
$91$	1.96840	0.206344
$92$	−15.9516	−1.66307
$93$	−3.27348	−0.339445
$94$	−9.52786	−0.982724
$95$	−1.97441	−0.202570
$96$	−5.18729	−0.529426
$97$	−6.47649	−0.657587	−0.328794	−	0.944402i	$-0.606642\pi$
$97$	−6.47649	−0.657587	−0.328794	+	0.944402i	$0.606642\pi$
$98$	7.94242	0.802306
$99$	4.78997	0.481411
$100$	−21.7461	−2.17461
$101$	0.803720	0.0799732	0.0399866	−	0.999200i	$-0.487268\pi$
$101$	0.803720	0.0799732	0.0399866	+	0.999200i	$0.487268\pi$
$102$	−8.18818	−0.810750
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	6.24610	0.612480
$105$	0.687239	0.0670677
$106$	6.68702	0.649501
$107$	10.8441	1.04834	0.524171	−	0.851613i	$-0.324375\pi$
$107$	10.8441	1.04834	0.524171	+	0.851613i	$0.324375\pi$
$108$	4.45789	0.428961
$109$	2.84604	0.272601	0.136301	−	0.990668i	$-0.456479\pi$
$109$	2.84604	0.272601	0.136301	+	0.990668i	$0.456479\pi$
$110$	4.24985	0.405208
$111$	−9.23399	−0.876451
$112$	−13.6942	−1.29398
$113$	−12.9515	−1.21837	−0.609186	−	0.793028i	$-0.708504\pi$
$113$	−12.9515	−1.21837	−0.609186	+	0.793028i	$0.708504\pi$
$114$	−14.3710	−1.34597
$115$	1.24931	0.116499
$116$	−30.6537	−2.84613
$117$	−1.00000	−0.0924500
$118$	−28.8197	−2.65306
$119$	−6.34241	−0.581408
$120$	2.18074	0.199073
$121$	11.9439	1.08581
$122$	37.7425	3.41705
$123$	−6.19045	−0.558174
$124$	−14.5928	−1.31048
$125$	3.44881	0.308471
$126$	5.00217	0.445628
$127$	−8.29190	−0.735787	−0.367893	−	0.929868i	$-0.619921\pi$
$127$	−8.29190	−0.735787	−0.367893	+	0.929868i	$0.619921\pi$
$128$	12.2346	1.08139
$129$	−8.42056	−0.741389
$130$	−0.887239	−0.0778160
$131$	−11.3548	−0.992071	−0.496035	−	0.868302i	$-0.665211\pi$
$131$	−11.3548	−0.992071	−0.496035	+	0.868302i	$0.665211\pi$
$132$	21.3532	1.85856
$133$	−11.1315	−0.965225
$134$	−17.1308	−1.47988
$135$	−0.349136	−0.0300489
$136$	−20.1257	−1.72576
$137$	−13.6405	−1.16538	−0.582692	−	0.812693i	$-0.698001\pi$
$137$	−13.6405	−1.16538	−0.582692	+	0.812693i	$0.698001\pi$
$138$	9.09327	0.774071
$139$	−10.5314	−0.893260	−0.446630	−	0.894719i	$-0.647376\pi$
$139$	−10.5314	−0.893260	−0.446630	+	0.894719i	$0.647376\pi$
$140$	3.06364	0.258925
$141$	3.74930	0.315748
$142$	−13.5721	−1.13894
$143$	−4.78997	−0.400558
$144$	6.95703	0.579753
$145$	2.40076	0.199372
$146$	−1.46077	−0.120894
$147$	−3.12541	−0.257780
$148$	−41.1642	−3.38367
$149$	17.3796	1.42379	0.711896	−	0.702285i	$-0.247837\pi$
$149$	17.3796	1.42379	0.711896	+	0.702285i	$0.247837\pi$
$150$	12.3964	1.01216
$151$	7.40260	0.602415	0.301208	−	0.953559i	$-0.402610\pi$
$151$	7.40260	0.602415	0.301208	+	0.953559i	$0.402610\pi$
$152$	−35.3224	−2.86502
$153$	3.22212	0.260493
$154$	23.9603	1.93077
$155$	1.14289	0.0917994
$156$	−4.45789	−0.356917
$157$	−1.77676	−0.141801	−0.0709004	−	0.997483i	$-0.522587\pi$
$157$	−1.77676	−0.141801	−0.0709004	+	0.997483i	$0.522587\pi$
$158$	−23.9496	−1.90533
$159$	−2.63140	−0.208684
$160$	1.81107	0.143178
$161$	7.04348	0.555104
$162$	−2.54124	−0.199659
$163$	−11.4311	−0.895355	−0.447677	−	0.894195i	$-0.647749\pi$
$163$	−11.4311	−0.895355	−0.447677	+	0.894195i	$0.647749\pi$
$164$	−27.5964	−2.15492
$165$	−1.67235	−0.130193
$166$	−8.53080	−0.662118
$167$	−17.4922	−1.35358	−0.676792	−	0.736175i	$-0.736630\pi$
$167$	−17.4922	−1.35358	−0.676792	+	0.736175i	$0.736630\pi$
$168$	12.2948	0.948564
$169$	1.00000	0.0769231
$170$	2.85879	0.219259
$171$	5.65511	0.432457
$172$	−37.5380	−2.86224
$173$	7.76121	0.590074	0.295037	−	0.955486i	$-0.404668\pi$
$173$	7.76121	0.590074	0.295037	+	0.955486i	$0.404668\pi$
$174$	17.4743	1.32472
$175$	9.60205	0.725846
$176$	33.3240	2.51189
$177$	11.3408	0.852426
$178$	−1.14457	−0.0857893
$179$	11.1975	0.836940	0.418470	−	0.908231i	$-0.362567\pi$
$179$	11.1975	0.836940	0.418470	+	0.908231i	$0.362567\pi$
$180$	−1.55641	−0.116008
$181$	−15.2855	−1.13616	−0.568081	−	0.822972i	$-0.692314\pi$
$181$	−15.2855	−1.13616	−0.568081	+	0.822972i	$0.692314\pi$
$182$	−5.00217	−0.370785
$183$	−14.8520	−1.09789
$184$	22.3503	1.64769
$185$	3.22392	0.237027
$186$	8.31871	0.609957
$187$	15.4339	1.12864
$188$	16.7140	1.21899
$189$	−1.96840	−0.143180
$190$	5.01744	0.364003
$191$	11.6765	0.844885	0.422442	−	0.906390i	$-0.361173\pi$
$191$	11.6765	0.844885	0.422442	+	0.906390i	$0.361173\pi$
$192$	−0.731920	−0.0528218
$193$	−9.42108	−0.678145	−0.339072	−	0.940760i	$-0.610113\pi$
$193$	−9.42108	−0.678145	−0.339072	+	0.940760i	$0.610113\pi$
$194$	16.4583	1.18164
$195$	0.349136	0.0250022
$196$	−13.9328	−0.995197
$197$	−1.16854	−0.0832553	−0.0416276	−	0.999133i	$-0.513254\pi$
$197$	−1.16854	−0.0832553	−0.0416276	+	0.999133i	$0.513254\pi$
$198$	−12.1725	−0.865060
$199$	16.9305	1.20017	0.600086	−	0.799935i	$-0.295133\pi$
$199$	16.9305	1.20017	0.600086	+	0.799935i	$0.295133\pi$
$200$	30.4691	2.15449
$201$	6.74113	0.475483
$202$	−2.04245	−0.143706
$203$	13.5353	0.949989
$204$	14.3639	1.00567
$205$	2.16131	0.150953
$206$	−2.54124	−0.177056
$207$	−3.57828	−0.248708
$208$	−6.95703	−0.482384
$209$	27.0879	1.87371
$210$	−1.74644	−0.120516
$211$	−10.3932	−0.715494	−0.357747	−	0.933818i	$-0.616455\pi$
$211$	−10.3932	−0.715494	−0.357747	+	0.933818i	$0.616455\pi$
$212$	−11.7305	−0.805655
$213$	5.34073	0.365941
$214$	−27.5575	−1.88380
$215$	2.93992	0.200501
$216$	−6.24610	−0.424993
$217$	6.44352	0.437414
$218$	−7.23246	−0.489844
$219$	0.574825	0.0388431
$220$	−7.45518	−0.502628
$221$	−3.22212	−0.216743
$222$	23.4658	1.57492
$223$	−29.2803	−1.96075	−0.980377	−	0.197133i	$-0.936837\pi$
$223$	−29.2803	−1.96075	−0.980377	+	0.197133i	$0.936837\pi$
$224$	10.2107	0.682228
$225$	−4.87810	−0.325207
$226$	32.9128	2.18932
$227$	−13.9002	−0.922589	−0.461295	−	0.887247i	$-0.652615\pi$
$227$	−13.9002	−0.922589	−0.461295	+	0.887247i	$0.652615\pi$
$228$	25.2099	1.66957
$229$	−23.9527	−1.58284	−0.791418	−	0.611275i	$-0.790657\pi$
$229$	−23.9527	−1.58284	−0.791418	+	0.611275i	$0.790657\pi$
$230$	−3.17479	−0.209340
$231$	−9.42857	−0.620355
$232$	42.9499	2.81980
$233$	9.77730	0.640532	0.320266	−	0.947328i	$-0.396228\pi$
$233$	9.77730	0.640532	0.320266	+	0.947328i	$0.396228\pi$
$234$	2.54124	0.166126
$235$	−1.30902	−0.0853908
$236$	50.5560	3.29092
$237$	9.42438	0.612179
$238$	16.1176	1.04475
$239$	3.42322	0.221430	0.110715	−	0.993852i	$-0.464686\pi$
$239$	3.42322	0.221430	0.110715	+	0.993852i	$0.464686\pi$
$240$	−2.42895	−0.156788
$241$	16.8430	1.08495	0.542476	−	0.840071i	$-0.317487\pi$
$241$	16.8430	1.08495	0.542476	+	0.840071i	$0.317487\pi$
$242$	−30.3522	−1.95111
$243$	1.00000	0.0641500
$244$	−66.2087	−4.23858
$245$	1.09120	0.0697139
$246$	15.7314	1.00300
$247$	−5.65511	−0.359826
$248$	20.4465	1.29835
$249$	3.35694	0.212738
$250$	−8.76424	−0.554299
$251$	−0.371977	−0.0234790	−0.0117395	−	0.999931i	$-0.503737\pi$
$251$	−0.371977	−0.0234790	−0.0117395	+	0.999931i	$0.503737\pi$
$252$	−8.77491	−0.552767
$253$	−17.1399	−1.07758
$254$	21.0717	1.32216
$255$	−1.12496	−0.0704477
$256$	−29.6271	−1.85170
$257$	−5.59594	−0.349065	−0.174533	−	0.984651i	$-0.555841\pi$
$257$	−5.59594	−0.349065	−0.174533	+	0.984651i	$0.555841\pi$
$258$	21.3987	1.33222
$259$	18.1762	1.12941
$260$	1.55641	0.0965247
$261$	−6.87628	−0.425631
$262$	28.8552	1.78268
$263$	−22.2643	−1.37287	−0.686436	−	0.727190i	$-0.740826\pi$
$263$	−22.2643	−1.37287	−0.686436	+	0.727190i	$0.740826\pi$
$264$	−29.9186	−1.84137
$265$	0.918719	0.0564364
$266$	28.2878	1.73444
$267$	0.450399	0.0275640
$268$	30.0512	1.83567
$269$	6.31839	0.385239	0.192620	−	0.981274i	$-0.438302\pi$
$269$	6.31839	0.385239	0.192620	+	0.981274i	$0.438302\pi$
$270$	0.887239	0.0539956
$271$	2.44165	0.148320	0.0741599	−	0.997246i	$-0.476372\pi$
$271$	2.44165	0.148320	0.0741599	+	0.997246i	$0.476372\pi$
$272$	22.4164	1.35919
$273$	1.96840	0.119133
$274$	34.6637	2.09411
$275$	−23.3660	−1.40902
$276$	−15.9516	−0.960174
$277$	5.76098	0.346144	0.173072	−	0.984909i	$-0.444631\pi$
$277$	5.76098	0.346144	0.173072	+	0.984909i	$0.444631\pi$
$278$	26.7627	1.60512
$279$	−3.27348	−0.195978
$280$	−4.29256	−0.256530
$281$	−14.5853	−0.870085	−0.435042	−	0.900410i	$-0.643267\pi$
$281$	−14.5853	−0.870085	−0.435042	+	0.900410i	$0.643267\pi$
$282$	−9.52786	−0.567376
$283$	20.5168	1.21960	0.609799	−	0.792556i	$-0.291250\pi$
$283$	20.5168	1.21960	0.609799	+	0.792556i	$0.291250\pi$
$284$	23.8084	1.41277
$285$	−1.97441	−0.116954
$286$	12.1725	0.719773
$287$	12.1853	0.719274
$288$	−5.18729	−0.305664
$289$	−6.61794	−0.389290
$290$	−6.10091	−0.358258
$291$	−6.47649	−0.379658
$292$	2.56251	0.149960
$293$	−2.85045	−0.166525	−0.0832626	−	0.996528i	$-0.526534\pi$
$293$	−2.85045	−0.166525	−0.0832626	+	0.996528i	$0.526534\pi$
$294$	7.94242	0.463211
$295$	−3.95948	−0.230530
$296$	57.6764	3.35237
$297$	4.78997	0.277943
$298$	−44.1657	−2.55845
$299$	3.57828	0.206937
$300$	−21.7461	−1.25551
$301$	16.5750	0.955367
$302$	−18.8118	−1.08250
$303$	0.803720	0.0461725
$304$	39.3428	2.25647
$305$	5.18538	0.296914
$306$	−8.18818	−0.468087
$307$	0.201856	0.0115205	0.00576026	−	0.999983i	$-0.498166\pi$
$307$	0.201856	0.0115205	0.00576026	+	0.999983i	$0.498166\pi$
$308$	−42.0316	−2.39497
$309$	1.00000	0.0568880
$310$	−2.90436	−0.164957
$311$	−8.84095	−0.501324	−0.250662	−	0.968075i	$-0.580648\pi$
$311$	−8.84095	−0.501324	−0.250662	+	0.968075i	$0.580648\pi$
$312$	6.24610	0.353616
$313$	14.2293	0.804287	0.402143	−	0.915577i	$-0.368265\pi$
$313$	14.2293	0.804287	0.402143	+	0.915577i	$0.368265\pi$
$314$	4.51517	0.254806
$315$	0.687239	0.0387215
$316$	42.0129	2.36341
$317$	−5.33700	−0.299756	−0.149878	−	0.988704i	$-0.547888\pi$
$317$	−5.33700	−0.299756	−0.149878	+	0.988704i	$0.547888\pi$
$318$	6.68702	0.374990
$319$	−32.9372	−1.84413
$320$	0.255540	0.0142851
$321$	10.8441	0.605261
$322$	−17.8992	−0.997482
$323$	18.2215	1.01387
$324$	4.45789	0.247661
$325$	4.87810	0.270589
$326$	29.0492	1.60889
$327$	2.84604	0.157386
$328$	38.6662	2.13498
$329$	−7.38010	−0.406878
$330$	4.24985	0.233947
$331$	10.4002	0.571649	0.285825	−	0.958282i	$-0.407732\pi$
$331$	10.4002	0.571649	0.285825	+	0.958282i	$0.407732\pi$
$332$	14.9649	0.821306
$333$	−9.23399	−0.506019
$334$	44.4517	2.43229
$335$	−2.35357	−0.128589
$336$	−13.6942	−0.747080
$337$	−17.4993	−0.953248	−0.476624	−	0.879107i	$-0.658140\pi$
$337$	−17.4993	−0.953248	−0.476624	+	0.879107i	$0.658140\pi$
$338$	−2.54124	−0.138225
$339$	−12.9515	−0.703427
$340$	−5.01495	−0.271974
$341$	−15.6799	−0.849115
$342$	−14.3710	−0.777095
$343$	19.9308	1.07616
$344$	52.5956	2.83577
$345$	1.24931	0.0672605
$346$	−19.7231	−1.06032
$347$	15.6775	0.841614	0.420807	−	0.907150i	$-0.361747\pi$
$347$	15.6775	0.841614	0.420807	+	0.907150i	$0.361747\pi$
$348$	−30.6537	−1.64321
$349$	23.0547	1.23409	0.617046	−	0.786927i	$-0.288329\pi$
$349$	23.0547	1.23409	0.617046	+	0.786927i	$0.288329\pi$
$350$	−24.4011	−1.30429
$351$	−1.00000	−0.0533761
$352$	−24.8470	−1.32435
$353$	−25.1330	−1.33770	−0.668848	−	0.743399i	$-0.733212\pi$
$353$	−25.1330	−1.33770	−0.668848	+	0.743399i	$0.733212\pi$
$354$	−28.8197	−1.53175
$355$	−1.86464	−0.0989650
$356$	2.00783	0.106415
$357$	−6.34241	−0.335676
$358$	−28.4555	−1.50392
$359$	−22.1772	−1.17047	−0.585235	−	0.810864i	$-0.698998\pi$
$359$	−22.1772	−1.17047	−0.585235	+	0.810864i	$0.698998\pi$
$360$	2.18074	0.114935
$361$	12.9803	0.683175
$362$	38.8441	2.04160
$363$	11.9439	0.626890
$364$	8.77491	0.459930
$365$	−0.200692	−0.0105047
$366$	37.7425	1.97283
$367$	−19.6430	−1.02536	−0.512678	−	0.858581i	$-0.671347\pi$
$367$	−19.6430	−1.02536	−0.512678	+	0.858581i	$0.671347\pi$
$368$	−24.8942	−1.29770
$369$	−6.19045	−0.322262
$370$	−8.19276	−0.425921
$371$	5.17965	0.268914
$372$	−14.5928	−0.756604
$373$	−15.9593	−0.826339	−0.413170	−	0.910654i	$-0.635578\pi$
$373$	−15.9593	−0.826339	−0.413170	+	0.910654i	$0.635578\pi$
$374$	−39.2212	−2.02808
$375$	3.44881	0.178096
$376$	−23.4185	−1.20772
$377$	6.87628	0.354147
$378$	5.00217	0.257284
$379$	−2.82104	−0.144907	−0.0724534	−	0.997372i	$-0.523083\pi$
$379$	−2.82104	−0.144907	−0.0724534	+	0.997372i	$0.523083\pi$
$380$	−8.80170	−0.451518
$381$	−8.29190	−0.424807
$382$	−29.6729	−1.51820
$383$	−28.7974	−1.47148	−0.735739	−	0.677265i	$-0.763165\pi$
$383$	−28.7974	−1.47148	−0.735739	+	0.677265i	$0.763165\pi$
$384$	12.2346	0.624343
$385$	3.29186	0.167769
$386$	23.9412	1.21858
$387$	−8.42056	−0.428041
$388$	−28.8715	−1.46573
$389$	−25.5347	−1.29466	−0.647330	−	0.762210i	$-0.724115\pi$
$389$	−25.5347	−1.29466	−0.647330	+	0.762210i	$0.724115\pi$
$390$	−0.887239	−0.0449271
$391$	−11.5297	−0.583080
$392$	19.5216	0.985991
$393$	−11.3548	−0.572772
$394$	2.96955	0.149604
$395$	−3.29039	−0.165558
$396$	21.3532	1.07304
$397$	−27.4763	−1.37900	−0.689499	−	0.724287i	$-0.742169\pi$
$397$	−27.4763	−1.37900	−0.689499	+	0.724287i	$0.742169\pi$
$398$	−43.0245	−2.15662
$399$	−11.1315	−0.557273
$400$	−33.9371	−1.69686
$401$	14.0155	0.699901	0.349951	−	0.936768i	$-0.386198\pi$
$401$	14.0155	0.699901	0.349951	+	0.936768i	$0.386198\pi$
$402$	−17.1308	−0.854408
$403$	3.27348	0.163064
$404$	3.58290	0.178256
$405$	−0.349136	−0.0173487
$406$	−34.3963	−1.70706
$407$	−44.2306	−2.19243
$408$	−20.1257	−0.996370
$409$	2.81056	0.138973	0.0694866	−	0.997583i	$-0.477864\pi$
$409$	2.81056	0.138973	0.0694866	+	0.997583i	$0.477864\pi$
$410$	−5.49241	−0.271251
$411$	−13.6405	−0.672835
$412$	4.45789	0.219625
$413$	−22.3232	−1.09845
$414$	9.09327	0.446910
$415$	−1.17203	−0.0575328
$416$	5.18729	0.254328
$417$	−10.5314	−0.515724
$418$	−68.8367	−3.36691
$419$	−17.3688	−0.848519	−0.424260	−	0.905541i	$-0.639466\pi$
$419$	−17.3688	−0.848519	−0.424260	+	0.905541i	$0.639466\pi$
$420$	3.06364	0.149490
$421$	−4.64050	−0.226164	−0.113082	−	0.993586i	$-0.536072\pi$
$421$	−4.64050	−0.226164	−0.113082	+	0.993586i	$0.536072\pi$
$422$	26.4115	1.28569
$423$	3.74930	0.182297
$424$	16.4360	0.798203
$425$	−15.7178	−0.762427
$426$	−13.5721	−0.657569
$427$	29.2347	1.41476
$428$	48.3420	2.33670
$429$	−4.78997	−0.231262
$430$	−7.47105	−0.360286
$431$	19.9184	0.959436	0.479718	−	0.877423i	$-0.340739\pi$
$431$	19.9184	0.959436	0.479718	+	0.877423i	$0.340739\pi$
$432$	6.95703	0.334721
$433$	−6.03960	−0.290244	−0.145122	−	0.989414i	$-0.546358\pi$
$433$	−6.03960	−0.290244	−0.145122	+	0.989414i	$0.546358\pi$
$434$	−16.3745	−0.786002
$435$	2.40076	0.115108
$436$	12.6873	0.607613
$437$	−20.2356	−0.968000
$438$	−1.46077	−0.0697982
$439$	27.5963	1.31710	0.658550	−	0.752537i	$-0.271170\pi$
$439$	27.5963	1.31710	0.658550	+	0.752537i	$0.271170\pi$
$440$	10.4457	0.497979
$441$	−3.12541	−0.148829
$442$	8.18818	0.389472
$443$	−38.9462	−1.85039	−0.925195	−	0.379493i	$-0.876099\pi$
$443$	−38.9462	−1.85039	−0.925195	+	0.379493i	$0.876099\pi$
$444$	−41.1642	−1.95356
$445$	−0.157251	−0.00745440
$446$	74.4082	3.52333
$447$	17.3796	0.822026
$448$	1.44071	0.0680671
$449$	−0.383962	−0.0181203	−0.00906015	−	0.999959i	$-0.502884\pi$
$449$	−0.383962	−0.0181203	−0.00906015	+	0.999959i	$0.502884\pi$
$450$	12.3964	0.584373
$451$	−29.6521	−1.39626
$452$	−57.7363	−2.71569
$453$	7.40260	0.347805
$454$	35.3237	1.65783
$455$	−0.687239	−0.0322183
$456$	−35.3224	−1.65412
$457$	37.5148	1.75487	0.877434	−	0.479698i	$-0.159254\pi$
$457$	37.5148	1.75487	0.877434	+	0.479698i	$0.159254\pi$
$458$	60.8694	2.84424
$459$	3.22212	0.150396
$460$	5.56929	0.259669
$461$	−3.57591	−0.166547	−0.0832734	−	0.996527i	$-0.526537\pi$
$461$	−3.57591	−0.166547	−0.0832734	+	0.996527i	$0.526537\pi$
$462$	23.9603	1.11473
$463$	−0.623948	−0.0289973	−0.0144987	−	0.999895i	$-0.504615\pi$
$463$	−0.623948	−0.0289973	−0.0144987	+	0.999895i	$0.504615\pi$
$464$	−47.8385	−2.22085
$465$	1.14289	0.0530004
$466$	−24.8465	−1.15099
$467$	−8.75136	−0.404965	−0.202482	−	0.979286i	$-0.564901\pi$
$467$	−8.75136	−0.404965	−0.202482	+	0.979286i	$0.564901\pi$
$468$	−4.45789	−0.206066
$469$	−13.2692	−0.612716
$470$	3.32652	0.153441
$471$	−1.77676	−0.0818687
$472$	−70.8357	−3.26048
$473$	−40.3343	−1.85457
$474$	−23.9496	−1.10004
$475$	−27.5862	−1.26574
$476$	−28.2738	−1.29593
$477$	−2.63140	−0.120484
$478$	−8.69922	−0.397893
$479$	−29.1139	−1.33025	−0.665123	−	0.746734i	$-0.731621\pi$
$479$	−29.1139	−1.33025	−0.665123	+	0.746734i	$0.731621\pi$
$480$	1.81107	0.0826638
$481$	9.23399	0.421034
$482$	−42.8021	−1.94958
$483$	7.04348	0.320490
$484$	53.2445	2.42020
$485$	2.26118	0.102675
$486$	−2.54124	−0.115273
$487$	−2.86223	−0.129700	−0.0648499	−	0.997895i	$-0.520657\pi$
$487$	−2.86223	−0.129700	−0.0648499	+	0.997895i	$0.520657\pi$
$488$	92.7672	4.19937
$489$	−11.4311	−0.516933
$490$	−2.77299	−0.125271
$491$	16.1890	0.730601	0.365300	−	0.930890i	$-0.380966\pi$
$491$	16.1890	0.730601	0.365300	+	0.930890i	$0.380966\pi$
$492$	−27.5964	−1.24414
$493$	−22.1562	−0.997866
$494$	14.3710	0.646582
$495$	−1.67235	−0.0751668
$496$	−22.7737	−1.02257
$497$	−10.5127	−0.471558
$498$	−8.53080	−0.382274
$499$	18.8705	0.844760	0.422380	−	0.906419i	$-0.361195\pi$
$499$	18.8705	0.844760	0.422380	+	0.906419i	$0.361195\pi$
$500$	15.3744	0.687565
$501$	−17.4922	−0.781492
$502$	0.945282	0.0421900
$503$	42.5487	1.89715	0.948576	−	0.316549i	$-0.102524\pi$
$503$	42.5487	1.89715	0.948576	+	0.316549i	$0.102524\pi$
$504$	12.2948	0.547654
$505$	−0.280608	−0.0124869
$506$	43.5566	1.93632
$507$	1.00000	0.0444116
$508$	−36.9644	−1.64003
$509$	−20.2156	−0.896039	−0.448020	−	0.894024i	$-0.647871\pi$
$509$	−20.2156	−0.896039	−0.448020	+	0.894024i	$0.647871\pi$
$510$	2.85879	0.126589
$511$	−1.13148	−0.0500539
$512$	50.8205	2.24597
$513$	5.65511	0.249679
$514$	14.2206	0.627245
$515$	−0.349136	−0.0153848
$516$	−37.5380	−1.65252
$517$	17.9590	0.789838
$518$	−46.1900	−2.02947
$519$	7.76121	0.340679
$520$	−2.18074	−0.0956318
$521$	25.9982	1.13900	0.569500	−	0.821991i	$-0.307137\pi$
$521$	25.9982	1.13900	0.569500	+	0.821991i	$0.307137\pi$
$522$	17.4743	0.764828
$523$	−15.5241	−0.678821	−0.339410	−	0.940638i	$-0.610228\pi$
$523$	−15.5241	−0.678821	−0.339410	+	0.940638i	$0.610228\pi$
$524$	−50.6184	−2.21127
$525$	9.60205	0.419068
$526$	56.5788	2.46695
$527$	−10.5476	−0.459459
$528$	33.3240	1.45024
$529$	−10.1959	−0.443299
$530$	−2.33468	−0.101412
$531$	11.3408	0.492148
$532$	−49.6231	−2.15143
$533$	6.19045	0.268138
$534$	−1.14457	−0.0495305
$535$	−3.78608	−0.163687
$536$	−42.1058	−1.81869
$537$	11.1975	0.483207
$538$	−16.0565	−0.692247
$539$	−14.9706	−0.644831
$540$	−1.55641	−0.0669774
$541$	−16.7457	−0.719954	−0.359977	−	0.932961i	$-0.617215\pi$
$541$	−16.7457	−0.719954	−0.359977	+	0.932961i	$0.617215\pi$
$542$	−6.20482	−0.266520
$543$	−15.2855	−0.655964
$544$	−16.7141	−0.716610
$545$	−0.993656	−0.0425635
$546$	−5.00217	−0.214073
$547$	−8.84543	−0.378203	−0.189102	−	0.981958i	$-0.560558\pi$
$547$	−8.84543	−0.378203	−0.189102	+	0.981958i	$0.560558\pi$
$548$	−60.8078	−2.59758
$549$	−14.8520	−0.633869
$550$	59.3786	2.53191
$551$	−38.8862	−1.65661
$552$	22.3503	0.951292
$553$	−18.5509	−0.788865
$554$	−14.6400	−0.621995
$555$	3.22392	0.136848
$556$	−46.9478	−1.99103
$557$	−26.5107	−1.12329	−0.561647	−	0.827377i	$-0.689832\pi$
$557$	−26.5107	−1.12329	−0.561647	+	0.827377i	$0.689832\pi$
$558$	8.31871	0.352159
$559$	8.42056	0.356152
$560$	4.78115	0.202040
$561$	15.4339	0.651619
$562$	37.0647	1.56348
$563$	32.6402	1.37562	0.687810	−	0.725890i	$-0.258572\pi$
$563$	32.6402	1.37562	0.687810	+	0.725890i	$0.258572\pi$
$564$	16.7140	0.703785
$565$	4.52183	0.190235
$566$	−52.1381	−2.19153
$567$	−1.96840	−0.0826649
$568$	−33.3587	−1.39970
$569$	−3.86589	−0.162067	−0.0810333	−	0.996711i	$-0.525822\pi$
$569$	−3.86589	−0.162067	−0.0810333	+	0.996711i	$0.525822\pi$
$570$	5.01744	0.210157
$571$	−30.0145	−1.25607	−0.628033	−	0.778187i	$-0.716140\pi$
$571$	−30.0145	−1.25607	−0.628033	+	0.778187i	$0.716140\pi$
$572$	−21.3532	−0.892822
$573$	11.6765	0.487794
$574$	−30.9657	−1.29248
$575$	17.4552	0.727934
$576$	−0.731920	−0.0304967
$577$	15.6647	0.652128	0.326064	−	0.945348i	$-0.394278\pi$
$577$	15.6647	0.652128	0.326064	+	0.945348i	$0.394278\pi$
$578$	16.8178	0.699527
$579$	−9.42108	−0.391527
$580$	10.7023	0.444390
$581$	−6.60780	−0.274138
$582$	16.4583	0.682218
$583$	−12.6044	−0.522019
$584$	−3.59041	−0.148572
$585$	0.349136	0.0144350
$586$	7.24368	0.299234
$587$	28.5845	1.17981	0.589904	−	0.807474i	$-0.299166\pi$
$587$	28.5845	1.17981	0.589904	+	0.807474i	$0.299166\pi$
$588$	−13.9328	−0.574577
$589$	−18.5119	−0.762771
$590$	10.0620	0.414246
$591$	−1.16854	−0.0480675
$592$	−64.2412	−2.64030
$593$	45.7417	1.87839	0.939193	−	0.343391i	$-0.111575\pi$
$593$	45.7417	1.87839	0.939193	+	0.343391i	$0.111575\pi$
$594$	−12.1725	−0.499442
$595$	2.21437	0.0907802
$596$	77.4764	3.17356
$597$	16.9305	0.692920
$598$	−9.09327	−0.371852
$599$	−31.5429	−1.28881	−0.644404	−	0.764685i	$-0.722895\pi$
$599$	−31.5429	−1.28881	−0.644404	+	0.764685i	$0.722895\pi$
$600$	30.4691	1.24390
$601$	15.4066	0.628450	0.314225	−	0.949348i	$-0.398255\pi$
$601$	15.4066	0.628450	0.314225	+	0.949348i	$0.398255\pi$
$602$	−42.1210	−1.71673
$603$	6.74113	0.274520
$604$	33.0000	1.34275
$605$	−4.17004	−0.169536
$606$	−2.04245	−0.0829687
$607$	−3.61636	−0.146784	−0.0733918	−	0.997303i	$-0.523382\pi$
$607$	−3.61636	−0.146784	−0.0733918	+	0.997303i	$0.523382\pi$
$608$	−29.3347	−1.18968
$609$	13.5353	0.548476
$610$	−13.1773	−0.533533
$611$	−3.74930	−0.151680
$612$	14.3639	0.580625
$613$	24.4427	0.987230	0.493615	−	0.869680i	$-0.335675\pi$
$613$	24.4427	0.987230	0.493615	+	0.869680i	$0.335675\pi$
$614$	−0.512964	−0.0207015
$615$	2.16131	0.0871525
$616$	58.8918	2.37282
$617$	−41.6532	−1.67689	−0.838447	−	0.544983i	$-0.816536\pi$
$617$	−41.6532	−1.67689	−0.838447	+	0.544983i	$0.816536\pi$
$618$	−2.54124	−0.102224
$619$	−7.30979	−0.293805	−0.146903	−	0.989151i	$-0.546930\pi$
$619$	−7.30979	−0.293805	−0.146903	+	0.989151i	$0.546930\pi$
$620$	5.09490	0.204616
$621$	−3.57828	−0.143592
$622$	22.4670	0.900843
$623$	−0.886564	−0.0355195
$624$	−6.95703	−0.278504
$625$	23.1864	0.927457
$626$	−36.1600	−1.44524
$627$	27.0879	1.08178
$628$	−7.92060	−0.316066
$629$	−29.7530	−1.18633
$630$	−1.74644	−0.0695798
$631$	13.0331	0.518841	0.259420	−	0.965764i	$-0.416468\pi$
$631$	13.0331	0.518841	0.259420	+	0.965764i	$0.416468\pi$
$632$	−58.8656	−2.34155
$633$	−10.3932	−0.413091
$634$	13.5626	0.538640
$635$	2.89500	0.114885
$636$	−11.7305	−0.465145
$637$	3.12541	0.123833
$638$	83.7013	3.31377
$639$	5.34073	0.211276
$640$	−4.27153	−0.168847
$641$	10.1465	0.400763	0.200382	−	0.979718i	$-0.435782\pi$
$641$	10.1465	0.400763	0.200382	+	0.979718i	$0.435782\pi$
$642$	−27.5575	−1.08761
$643$	45.0794	1.77776	0.888879	−	0.458143i	$-0.151485\pi$
$643$	45.0794	1.77776	0.888879	+	0.458143i	$0.151485\pi$
$644$	31.3991	1.23730
$645$	2.93992	0.115759
$646$	−46.3051	−1.82185
$647$	−25.6170	−1.00711	−0.503553	−	0.863964i	$-0.667974\pi$
$647$	−25.6170	−1.00711	−0.503553	+	0.863964i	$0.667974\pi$
$648$	−6.24610	−0.245370
$649$	54.3221	2.13233
$650$	−12.3964	−0.486228
$651$	6.44352	0.252541
$652$	−50.9587	−1.99570
$653$	12.8946	0.504604	0.252302	−	0.967649i	$-0.418812\pi$
$653$	12.8946	0.504604	0.252302	+	0.967649i	$0.418812\pi$
$654$	−7.23246	−0.282812
$655$	3.96436	0.154900
$656$	−43.0672	−1.68149
$657$	0.574825	0.0224261
$658$	18.7546	0.731131
$659$	19.1384	0.745528	0.372764	−	0.927926i	$-0.378410\pi$
$659$	19.1384	0.745528	0.372764	+	0.927926i	$0.378410\pi$
$660$	−7.45518	−0.290193
$661$	7.30735	0.284223	0.142112	−	0.989851i	$-0.454611\pi$
$661$	7.30735	0.284223	0.142112	+	0.989851i	$0.454611\pi$
$662$	−26.4295	−1.02721
$663$	−3.22212	−0.125137
$664$	−20.9678	−0.813708
$665$	3.88642	0.150709
$666$	23.4658	0.909280
$667$	24.6053	0.952721
$668$	−77.9782	−3.01707
$669$	−29.2803	−1.13204
$670$	5.98099	0.231066
$671$	−71.1408	−2.74636
$672$	10.2107	0.393884
$673$	−29.8955	−1.15239	−0.576194	−	0.817313i	$-0.695463\pi$
$673$	−29.8955	−1.15239	−0.576194	+	0.817313i	$0.695463\pi$
$674$	44.4699	1.71292
$675$	−4.87810	−0.187758
$676$	4.45789	0.171457
$677$	−13.0804	−0.502721	−0.251360	−	0.967894i	$-0.580878\pi$
$677$	−13.0804	−0.502721	−0.251360	+	0.967894i	$0.580878\pi$
$678$	32.9128	1.26401
$679$	12.7483	0.489235
$680$	7.02661	0.269458
$681$	−13.9002	−0.532657
$682$	39.8464	1.52580
$683$	−21.2860	−0.814487	−0.407244	−	0.913320i	$-0.633510\pi$
$683$	−21.2860	−0.814487	−0.407244	+	0.913320i	$0.633510\pi$
$684$	25.2099	0.963925
$685$	4.76239	0.181961
$686$	−50.6490	−1.93379
$687$	−23.9527	−0.913851
$688$	−58.5821	−2.23342
$689$	2.63140	0.100248
$690$	−3.17479	−0.120862
$691$	−9.07653	−0.345287	−0.172644	−	0.984984i	$-0.555231\pi$
$691$	−9.07653	−0.345287	−0.172644	+	0.984984i	$0.555231\pi$
$692$	34.5987	1.31524
$693$	−9.42857	−0.358162
$694$	−39.8404	−1.51232
$695$	3.67689	0.139472
$696$	42.9499	1.62801
$697$	−19.9464	−0.755523
$698$	−58.5876	−2.21757
$699$	9.77730	0.369811
$700$	42.8049	1.61787
$701$	−28.9554	−1.09363	−0.546814	−	0.837254i	$-0.684160\pi$
$701$	−28.9554	−1.09363	−0.546814	+	0.837254i	$0.684160\pi$
$702$	2.54124	0.0959129
$703$	−52.2193	−1.96949
$704$	−3.50588	−0.132133
$705$	−1.30902	−0.0493004
$706$	63.8690	2.40374
$707$	−1.58204	−0.0594988
$708$	50.5560	1.90001
$709$	17.4845	0.656645	0.328323	−	0.944566i	$-0.393517\pi$
$709$	17.4845	0.656645	0.328323	+	0.944566i	$0.393517\pi$
$710$	4.73851	0.177833
$711$	9.42438	0.353442
$712$	−2.81324	−0.105431
$713$	11.7135	0.438672
$714$	16.1176	0.603186
$715$	1.67235	0.0625425
$716$	49.9172	1.86549
$717$	3.42322	0.127843
$718$	56.3577	2.10325
$719$	−39.9455	−1.48972	−0.744858	−	0.667223i	$-0.767483\pi$
$719$	−39.9455	−1.48972	−0.744858	+	0.667223i	$0.767483\pi$
$720$	−2.42895	−0.0905218
$721$	−1.96840	−0.0733069
$722$	−32.9861	−1.22762
$723$	16.8430	0.626398
$724$	−68.1412	−2.53245
$725$	33.5432	1.24576
$726$	−30.3522	−1.12648
$727$	−25.9707	−0.963199	−0.481600	−	0.876391i	$-0.659944\pi$
$727$	−25.9707	−0.963199	−0.481600	+	0.876391i	$0.659944\pi$
$728$	−12.2948	−0.455676
$729$	1.00000	0.0370370
$730$	0.510007	0.0188762
$731$	−27.1321	−1.00352
$732$	−66.2087	−2.44715
$733$	−36.5548	−1.35018	−0.675091	−	0.737734i	$-0.735896\pi$
$733$	−36.5548	−1.35018	−0.675091	+	0.737734i	$0.735896\pi$
$734$	49.9175	1.84249
$735$	1.09120	0.0402494
$736$	18.5616	0.684190
$737$	32.2898	1.18941
$738$	15.7314	0.579081
$739$	−39.4344	−1.45062	−0.725310	−	0.688423i	$-0.758303\pi$
$739$	−39.4344	−1.45062	−0.725310	+	0.688423i	$0.758303\pi$
$740$	14.3719	0.528322
$741$	−5.65511	−0.207746
$742$	−13.1627	−0.483219
$743$	51.4925	1.88908	0.944538	−	0.328402i	$-0.106510\pi$
$743$	51.4925	1.88908	0.944538	+	0.328402i	$0.106510\pi$
$744$	20.4465	0.749605
$745$	−6.06785	−0.222309
$746$	40.5563	1.48487
$747$	3.35694	0.122824
$748$	68.8026	2.51567
$749$	−21.3456	−0.779950
$750$	−8.76424	−0.320025
$751$	17.4558	0.636971	0.318486	−	0.947928i	$-0.396826\pi$
$751$	17.4558	0.636971	0.318486	+	0.947928i	$0.396826\pi$
$752$	26.0840	0.951185
$753$	−0.371977	−0.0135556
$754$	−17.4743	−0.636376
$755$	−2.58452	−0.0940602
$756$	−8.77491	−0.319140
$757$	41.1778	1.49663	0.748316	−	0.663342i	$-0.230863\pi$
$757$	41.1778	1.49663	0.748316	+	0.663342i	$0.230863\pi$
$758$	7.16893	0.260387
$759$	−17.1399	−0.622139
$760$	12.3323	0.447341
$761$	33.9865	1.23201	0.616004	−	0.787743i	$-0.288750\pi$
$761$	33.9865	1.23201	0.616004	+	0.787743i	$0.288750\pi$
$762$	21.0717	0.763347
$763$	−5.60213	−0.202811
$764$	52.0528	1.88320
$765$	−1.12496	−0.0406730
$766$	73.1811	2.64414
$767$	−11.3408	−0.409492
$768$	−29.6271	−1.06908
$769$	−1.75414	−0.0632558	−0.0316279	−	0.999500i	$-0.510069\pi$
$769$	−1.75414	−0.0632558	−0.0316279	+	0.999500i	$0.510069\pi$
$770$	−8.36540	−0.301468
$771$	−5.59594	−0.201533
$772$	−41.9982	−1.51155
$773$	27.8112	1.00030	0.500149	−	0.865939i	$-0.333279\pi$
$773$	27.8112	1.00030	0.500149	+	0.865939i	$0.333279\pi$
$774$	21.3987	0.769159
$775$	15.9684	0.573602
$776$	40.4528	1.45217
$777$	18.1762	0.652066
$778$	64.8898	2.32641
$779$	−35.0077	−1.25428
$780$	1.55641	0.0557285
$781$	25.5820	0.915395
$782$	29.2996	1.04775
$783$	−6.87628	−0.245738
$784$	−21.7436	−0.776557
$785$	0.620331	0.0221406
$786$	28.8552	1.02923
$787$	−6.08813	−0.217018	−0.108509	−	0.994095i	$-0.534608\pi$
$787$	−6.08813	−0.217018	−0.108509	+	0.994095i	$0.534608\pi$
$788$	−5.20924	−0.185572
$789$	−22.2643	−0.792628
$790$	8.36167	0.297495
$791$	25.4936	0.906449
$792$	−29.9186	−1.06311
$793$	14.8520	0.527411
$794$	69.8239	2.47796
$795$	0.918719	0.0325836
$796$	75.4744	2.67512
$797$	−11.8355	−0.419235	−0.209618	−	0.977783i	$-0.567222\pi$
$797$	−11.8355	−0.419235	−0.209618	+	0.977783i	$0.567222\pi$
$798$	28.2878	1.00138
$799$	12.0807	0.427384
$800$	25.3042	0.894637
$801$	0.450399	0.0159141
$802$	−35.6168	−1.25767
$803$	2.75340	0.0971653
$804$	30.0512	1.05983
$805$	−2.45914	−0.0866732
$806$	−8.31871	−0.293014
$807$	6.31839	0.222418
$808$	−5.02012	−0.176607
$809$	41.9820	1.47601	0.738004	−	0.674797i	$-0.235769\pi$
$809$	41.9820	1.47601	0.738004	+	0.674797i	$0.235769\pi$
$810$	0.887239	0.0311744
$811$	−15.6800	−0.550601	−0.275300	−	0.961358i	$-0.588777\pi$
$811$	−15.6800	−0.550601	−0.275300	+	0.961358i	$0.588777\pi$
$812$	60.3387	2.11747
$813$	2.44165	0.0856325
$814$	112.400	3.93963
$815$	3.99102	0.139799
$816$	22.4164	0.784731
$817$	−47.6192	−1.66599
$818$	−7.14230	−0.249725
$819$	1.96840	0.0687814
$820$	9.63490	0.336465
$821$	41.4335	1.44604	0.723020	−	0.690827i	$-0.242753\pi$
$821$	41.4335	1.44604	0.723020	+	0.690827i	$0.242753\pi$
$822$	34.6637	1.20904
$823$	46.3615	1.61606	0.808030	−	0.589141i	$-0.200534\pi$
$823$	46.3615	1.61606	0.808030	+	0.589141i	$0.200534\pi$
$824$	−6.24610	−0.217593
$825$	−23.3660	−0.813499
$826$	56.7285	1.97384
$827$	−29.6243	−1.03014	−0.515068	−	0.857149i	$-0.672234\pi$
$827$	−29.6243	−1.03014	−0.515068	+	0.857149i	$0.672234\pi$
$828$	−15.9516	−0.554357
$829$	8.35708	0.290253	0.145127	−	0.989413i	$-0.453641\pi$
$829$	8.35708	0.290253	0.145127	+	0.989413i	$0.453641\pi$
$830$	2.97841	0.103382
$831$	5.76098	0.199846
$832$	0.731920	0.0253748
$833$	−10.0705	−0.348921
$834$	26.7627	0.926718
$835$	6.10715	0.211347
$836$	120.755	4.17639
$837$	−3.27348	−0.113148
$838$	44.1381	1.52473
$839$	26.9478	0.930340	0.465170	−	0.885221i	$-0.345993\pi$
$839$	26.9478	0.930340	0.465170	+	0.885221i	$0.345993\pi$
$840$	−4.29256	−0.148107
$841$	18.2833	0.630458
$842$	11.7926	0.406401
$843$	−14.5853	−0.502344
$844$	−46.3316	−1.59480
$845$	−0.349136	−0.0120107
$846$	−9.52786	−0.327575
$847$	−23.5103	−0.807822
$848$	−18.3068	−0.628657
$849$	20.5168	0.704135
$850$	39.9428	1.37003
$851$	33.0418	1.13266
$852$	23.8084	0.815663
$853$	−51.7075	−1.77043	−0.885216	−	0.465181i	$-0.845989\pi$
$853$	−51.7075	−1.77043	−0.885216	+	0.465181i	$0.845989\pi$
$854$	−74.2923	−2.54223
$855$	−1.97441	−0.0675233
$856$	−67.7336	−2.31509
$857$	−50.2663	−1.71706	−0.858532	−	0.512759i	$-0.828623\pi$
$857$	−50.2663	−1.71706	−0.858532	+	0.512759i	$0.828623\pi$
$858$	12.1725	0.415561
$859$	−48.6349	−1.65940	−0.829701	−	0.558208i	$-0.811489\pi$
$859$	−48.6349	−1.65940	−0.829701	+	0.558208i	$0.811489\pi$
$860$	13.1059	0.446907
$861$	12.1853	0.415273
$862$	−50.6174	−1.72404
$863$	42.2866	1.43945	0.719726	−	0.694258i	$-0.244267\pi$
$863$	42.2866	1.43945	0.719726	+	0.694258i	$0.244267\pi$
$864$	−5.18729	−0.176475
$865$	−2.70972	−0.0921333
$866$	15.3481	0.521548
$867$	−6.61794	−0.224757
$868$	28.7245	0.974974
$869$	45.1425	1.53136
$870$	−6.10091	−0.206840
$871$	−6.74113	−0.228414
$872$	−17.7766	−0.601993
$873$	−6.47649	−0.219196
$874$	51.4235	1.73943
$875$	−6.78862	−0.229497
$876$	2.56251	0.0865792
$877$	48.9040	1.65137	0.825686	−	0.564130i	$-0.190788\pi$
$877$	48.9040	1.65137	0.825686	+	0.564130i	$0.190788\pi$
$878$	−70.1288	−2.36673
$879$	−2.85045	−0.0961433
$880$	−11.6346	−0.392203
$881$	42.2313	1.42281	0.711404	−	0.702783i	$-0.248060\pi$
$881$	42.2313	1.42281	0.711404	+	0.702783i	$0.248060\pi$
$882$	7.94242	0.267435
$883$	54.9145	1.84802	0.924010	−	0.382368i	$-0.124891\pi$
$883$	54.9145	1.84802	0.924010	+	0.382368i	$0.124891\pi$
$884$	−14.3639	−0.483109
$885$	−3.95948	−0.133097
$886$	98.9716	3.32502
$887$	−21.1282	−0.709414	−0.354707	−	0.934977i	$-0.615419\pi$
$887$	−21.1282	−0.709414	−0.354707	+	0.934977i	$0.615419\pi$
$888$	57.6764	1.93549
$889$	16.3217	0.547414
$890$	0.399612	0.0133950
$891$	4.78997	0.160470
$892$	−130.528	−4.37042
$893$	21.2027	0.709521
$894$	−44.1657	−1.47712
$895$	−3.90945	−0.130679
$896$	−24.0825	−0.804540
$897$	3.57828	0.119475
$898$	0.975740	0.0325609
$899$	22.5094	0.750731
$900$	−21.7461	−0.724869
$901$	−8.47870	−0.282466
$902$	75.3531	2.50898
$903$	16.5750	0.551582
$904$	80.8961	2.69056
$905$	5.33673	0.177399
$906$	−18.8118	−0.624979
$907$	−12.6723	−0.420778	−0.210389	−	0.977618i	$-0.567473\pi$
$907$	−12.6723	−0.420778	−0.210389	+	0.977618i	$0.567473\pi$
$908$	−61.9656	−2.05640
$909$	0.803720	0.0266577
$910$	1.74644	0.0578939
$911$	−7.25022	−0.240210	−0.120105	−	0.992761i	$-0.538323\pi$
$911$	−7.25022	−0.240210	−0.120105	+	0.992761i	$0.538323\pi$
$912$	39.3428	1.30277
$913$	16.0797	0.532160
$914$	−95.3340	−3.15337
$915$	5.18538	0.171423
$916$	−106.778	−3.52806
$917$	22.3507	0.738085
$918$	−8.18818	−0.270250
$919$	−10.1058	−0.333361	−0.166680	−	0.986011i	$-0.553305\pi$
$919$	−10.1058	−0.333361	−0.166680	+	0.986011i	$0.553305\pi$
$920$	−7.80331	−0.257267
$921$	0.201856	0.00665138
$922$	9.08725	0.299273
$923$	−5.34073	−0.175792
$924$	−42.0316	−1.38274
$925$	45.0444	1.48105
$926$	1.58560	0.0521060
$927$	1.00000	0.0328443
$928$	35.6693	1.17090
$929$	−50.3357	−1.65146	−0.825730	−	0.564066i	$-0.809236\pi$
$929$	−50.3357	−1.65146	−0.825730	+	0.564066i	$0.809236\pi$
$930$	−2.90436	−0.0952378
$931$	−17.6746	−0.579261
$932$	43.5862	1.42771
$933$	−8.84095	−0.289440
$934$	22.2393	0.727692
$935$	−5.38853	−0.176224
$936$	6.24610	0.204160
$937$	16.5065	0.539245	0.269623	−	0.962966i	$-0.413101\pi$
$937$	16.5065	0.539245	0.269623	+	0.962966i	$0.413101\pi$
$938$	33.7203	1.10101
$939$	14.2293	0.464355
$940$	−5.83546	−0.190332
$941$	−2.15080	−0.0701142	−0.0350571	−	0.999385i	$-0.511161\pi$
$941$	−2.15080	−0.0701142	−0.0350571	+	0.999385i	$0.511161\pi$
$942$	4.51517	0.147112
$943$	22.1512	0.721342
$944$	78.8983	2.56792
$945$	0.687239	0.0223559
$946$	102.499	3.33253
$947$	−29.8192	−0.968995	−0.484497	−	0.874793i	$-0.660997\pi$
$947$	−29.8192	−0.968995	−0.484497	+	0.874793i	$0.660997\pi$
$948$	42.0129	1.36451
$949$	−0.574825	−0.0186596
$950$	70.1032	2.27445
$951$	−5.33700	−0.173064
$952$	39.6153	1.28394
$953$	22.9572	0.743656	0.371828	−	0.928302i	$-0.378731\pi$
$953$	22.9572	0.743656	0.371828	+	0.928302i	$0.378731\pi$
$954$	6.68702	0.216500
$955$	−4.07670	−0.131919
$956$	15.2604	0.493555
$957$	−32.9372	−1.06471
$958$	73.9853	2.39036
$959$	26.8499	0.867027
$960$	0.255540	0.00824751
$961$	−20.2843	−0.654332
$962$	−23.4658	−0.756567
$963$	10.8441	0.349448
$964$	75.0843	2.41830
$965$	3.28924	0.105885
$966$	−17.8992	−0.575896
$967$	44.5256	1.43185	0.715924	−	0.698179i	$-0.246006\pi$
$967$	44.5256	1.43185	0.715924	+	0.698179i	$0.246006\pi$
$968$	−74.6025	−2.39782
$969$	18.2215	0.585358
$970$	−5.74619	−0.184499
$971$	20.1443	0.646460	0.323230	−	0.946320i	$-0.395231\pi$
$971$	20.1443	0.646460	0.323230	+	0.946320i	$0.395231\pi$
$972$	4.45789	0.142987
$973$	20.7299	0.664571
$974$	7.27360	0.233061
$975$	4.87810	0.156224
$976$	−103.326	−3.30739
$977$	13.1474	0.420624	0.210312	−	0.977634i	$-0.432552\pi$
$977$	13.1474	0.420624	0.210312	+	0.977634i	$0.432552\pi$
$978$	29.0492	0.928891
$979$	2.15740	0.0689508
$980$	4.86443	0.155389
$981$	2.84604	0.0908670
$982$	−41.1402	−1.31284
$983$	−3.79026	−0.120890	−0.0604452	−	0.998172i	$-0.519252\pi$
$983$	−3.79026	−0.120890	−0.0604452	+	0.998172i	$0.519252\pi$
$984$	38.6662	1.23263
$985$	0.407981	0.0129994
$986$	56.3042	1.79309
$987$	−7.38010	−0.234911
$988$	−25.2099	−0.802034
$989$	30.1312	0.958115
$990$	4.24985	0.135069
$991$	46.7678	1.48563	0.742814	−	0.669497i	$-0.233490\pi$
$991$	46.7678	1.48563	0.742814	+	0.669497i	$0.233490\pi$
$992$	16.9805	0.539132
$993$	10.4002	0.330042
$994$	26.7152	0.847356
$995$	−5.91106	−0.187393
$996$	14.9649	0.474181
$997$	−0.765127	−0.0242318	−0.0121159	−	0.999927i	$-0.503857\pi$
$997$	−0.765127	−0.0242318	−0.0121159	+	0.999927i	$0.503857\pi$
$998$	−47.9545	−1.51797
$999$	−9.23399	−0.292150

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.e.1.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.e.1.1	✓	16	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54124 q^{2} +1.00000 q^{3} +4.45789 q^{4} -0.349136 q^{5} -2.54124 q^{6} -1.96840 q^{7} -6.24610 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.54124 q^{2} +1.00000 q^{3} +4.45789 q^{4} -0.349136 q^{5} -2.54124 q^{6} -1.96840 q^{7} -6.24610 q^{8} +1.00000 q^{9} +0.887239 q^{10} +4.78997 q^{11} +4.45789 q^{12} -1.00000 q^{13} +5.00217 q^{14} -0.349136 q^{15} +6.95703 q^{16} +3.22212 q^{17} -2.54124 q^{18} +5.65511 q^{19} -1.55641 q^{20} -1.96840 q^{21} -12.1725 q^{22} -3.57828 q^{23} -6.24610 q^{24} -4.87810 q^{25} +2.54124 q^{26} +1.00000 q^{27} -8.77491 q^{28} -6.87628 q^{29} +0.887239 q^{30} -3.27348 q^{31} -5.18729 q^{32} +4.78997 q^{33} -8.18818 q^{34} +0.687239 q^{35} +4.45789 q^{36} -9.23399 q^{37} -14.3710 q^{38} -1.00000 q^{39} +2.18074 q^{40} -6.19045 q^{41} +5.00217 q^{42} -8.42056 q^{43} +21.3532 q^{44} -0.349136 q^{45} +9.09327 q^{46} +3.74930 q^{47} +6.95703 q^{48} -3.12541 q^{49} +12.3964 q^{50} +3.22212 q^{51} -4.45789 q^{52} -2.63140 q^{53} -2.54124 q^{54} -1.67235 q^{55} +12.2948 q^{56} +5.65511 q^{57} +17.4743 q^{58} +11.3408 q^{59} -1.55641 q^{60} -14.8520 q^{61} +8.31871 q^{62} -1.96840 q^{63} -0.731920 q^{64} +0.349136 q^{65} -12.1725 q^{66} +6.74113 q^{67} +14.3639 q^{68} -3.57828 q^{69} -1.74644 q^{70} +5.34073 q^{71} -6.24610 q^{72} +0.574825 q^{73} +23.4658 q^{74} -4.87810 q^{75} +25.2099 q^{76} -9.42857 q^{77} +2.54124 q^{78} +9.42438 q^{79} -2.42895 q^{80} +1.00000 q^{81} +15.7314 q^{82} +3.35694 q^{83} -8.77491 q^{84} -1.12496 q^{85} +21.3987 q^{86} -6.87628 q^{87} -29.9186 q^{88} +0.450399 q^{89} +0.887239 q^{90} +1.96840 q^{91} -15.9516 q^{92} -3.27348 q^{93} -9.52786 q^{94} -1.97441 q^{95} -5.18729 q^{96} -6.47649 q^{97} +7.94242 q^{98} +4.78997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * q^99

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