LMFDB - Embedded newform 5054.2.a.bl.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 $ x^12 - 3x^11 - 24x^10 + 68x^9 + 213x^8 - 555x^7 - 814x^6 + 1911x^5 + 1005x^4 - 2326x^3 + 570x^2 + 105*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.98161$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.98161 q^{3} +1.00000 q^{4} -4.31337 q^{5} +2.98161 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.89001 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.98161 q^{3} +1.00000 q^{4} -4.31337 q^{5} +2.98161 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.89001 q^{9} +4.31337 q^{10} +0.362266 q^{11} -2.98161 q^{12} -5.24373 q^{13} -1.00000 q^{14} +12.8608 q^{15} +1.00000 q^{16} -4.63000 q^{17} -5.89001 q^{18} -4.31337 q^{20} -2.98161 q^{21} -0.362266 q^{22} +1.78046 q^{23} +2.98161 q^{24} +13.6052 q^{25} +5.24373 q^{26} -8.61690 q^{27} +1.00000 q^{28} -2.08498 q^{29} -12.8608 q^{30} +2.02090 q^{31} -1.00000 q^{32} -1.08014 q^{33} +4.63000 q^{34} -4.31337 q^{35} +5.89001 q^{36} -7.44807 q^{37} +15.6348 q^{39} +4.31337 q^{40} +2.71367 q^{41} +2.98161 q^{42} +3.97133 q^{43} +0.362266 q^{44} -25.4058 q^{45} -1.78046 q^{46} -3.27349 q^{47} -2.98161 q^{48} +1.00000 q^{49} -13.6052 q^{50} +13.8049 q^{51} -5.24373 q^{52} -11.7483 q^{53} +8.61690 q^{54} -1.56259 q^{55} -1.00000 q^{56} +2.08498 q^{58} -0.777397 q^{59} +12.8608 q^{60} -10.7422 q^{61} -2.02090 q^{62} +5.89001 q^{63} +1.00000 q^{64} +22.6181 q^{65} +1.08014 q^{66} +2.61230 q^{67} -4.63000 q^{68} -5.30866 q^{69} +4.31337 q^{70} -14.5430 q^{71} -5.89001 q^{72} +2.61980 q^{73} +7.44807 q^{74} -40.5654 q^{75} +0.362266 q^{77} -15.6348 q^{78} -0.554543 q^{79} -4.31337 q^{80} +8.02223 q^{81} -2.71367 q^{82} -5.06311 q^{83} -2.98161 q^{84} +19.9709 q^{85} -3.97133 q^{86} +6.21661 q^{87} -0.362266 q^{88} -7.02669 q^{89} +25.4058 q^{90} -5.24373 q^{91} +1.78046 q^{92} -6.02554 q^{93} +3.27349 q^{94} +2.98161 q^{96} -1.38858 q^{97} -1.00000 q^{98} +2.13375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 6 q^{15} + 12 q^{16} + 3 q^{17} - 21 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} - 21 q^{27} + 12 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} - 12 q^{32} + 6 q^{33} - 3 q^{34} + 3 q^{35} + 21 q^{36} - 27 q^{37} + 27 q^{39} - 3 q^{40} + 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} - 12 q^{46} + 21 q^{47} - 3 q^{48} + 12 q^{49} - 33 q^{50} - 3 q^{51} + 6 q^{52} - 6 q^{53} + 21 q^{54} + 48 q^{55} - 12 q^{56} + 6 q^{58} + 27 q^{59} + 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} + 9 q^{65} - 6 q^{66} - 9 q^{67} + 3 q^{68} - 18 q^{69} - 3 q^{70} - 27 q^{71} - 21 q^{72} - 9 q^{73} + 27 q^{74} - 33 q^{75} + 3 q^{77} - 27 q^{78} + 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} - 3 q^{84} + 78 q^{85} - 30 q^{86} - 45 q^{87} - 3 q^{88} + 24 q^{89} - 30 q^{90} + 6 q^{91} + 12 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 18 q^{97} - 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 6 * q^15 + 12 * q^16 + 3 * q^17 - 21 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 - 21 * q^27 + 12 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 - 12 * q^32 + 6 * q^33 - 3 * q^34 + 3 * q^35 + 21 * q^36 - 27 * q^37 + 27 * q^39 - 3 * q^40 + 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 - 12 * q^46 + 21 * q^47 - 3 * q^48 + 12 * q^49 - 33 * q^50 - 3 * q^51 + 6 * q^52 - 6 * q^53 + 21 * q^54 + 48 * q^55 - 12 * q^56 + 6 * q^58 + 27 * q^59 + 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 - 9 * q^67 + 3 * q^68 - 18 * q^69 - 3 * q^70 - 27 * q^71 - 21 * q^72 - 9 * q^73 + 27 * q^74 - 33 * q^75 + 3 * q^77 - 27 * q^78 + 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 - 3 * q^84 + 78 * q^85 - 30 * q^86 - 45 * q^87 - 3 * q^88 + 24 * q^89 - 30 * q^90 + 6 * q^91 + 12 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 18 * q^97 - 12 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.98161	−1.72143	−0.860717	−	0.509083i	$-0.829985\pi$
$3$	−2.98161	−1.72143	−0.860717	+	0.509083i	$0.829985\pi$
$4$	1.00000	0.500000
$5$	−4.31337	−1.92900	−0.964499	−	0.264085i	$-0.914930\pi$
$5$	−4.31337	−1.92900	−0.964499	+	0.264085i	$0.914930\pi$
$6$	2.98161	1.21724
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	5.89001	1.96334
$10$	4.31337	1.36401
$11$	0.362266	0.109227	0.0546137	−	0.998508i	$-0.482607\pi$
$11$	0.362266	0.109227	0.0546137	+	0.998508i	$0.482607\pi$
$12$	−2.98161	−0.860717
$13$	−5.24373	−1.45435	−0.727174	−	0.686453i	$-0.759167\pi$
$13$	−5.24373	−1.45435	−0.727174	+	0.686453i	$0.759167\pi$
$14$	−1.00000	−0.267261
$15$	12.8608	3.32065
$16$	1.00000	0.250000
$17$	−4.63000	−1.12294	−0.561470	−	0.827497i	$-0.689764\pi$
$17$	−4.63000	−1.12294	−0.561470	+	0.827497i	$0.689764\pi$
$18$	−5.89001	−1.38829
$19$	0	0
$19$	0	0
$20$	−4.31337	−0.964499
$21$	−2.98161	−0.650641
$22$	−0.362266	−0.0772354
$23$	1.78046	0.371253	0.185626	−	0.982620i	$-0.440569\pi$
$23$	1.78046	0.371253	0.185626	+	0.982620i	$0.440569\pi$
$24$	2.98161	0.608619
$25$	13.6052	2.72104
$26$	5.24373	1.02838
$27$	−8.61690	−1.65832
$28$	1.00000	0.188982
$29$	−2.08498	−0.387171	−0.193586	−	0.981083i	$-0.562012\pi$
$29$	−2.08498	−0.387171	−0.193586	+	0.981083i	$0.562012\pi$
$30$	−12.8608	−2.34805
$31$	2.02090	0.362965	0.181482	−	0.983394i	$-0.441910\pi$
$31$	2.02090	0.362965	0.181482	+	0.983394i	$0.441910\pi$
$32$	−1.00000	−0.176777
$33$	−1.08014	−0.188028
$34$	4.63000	0.794038
$35$	−4.31337	−0.729093
$36$	5.89001	0.981669
$37$	−7.44807	−1.22446	−0.612228	−	0.790682i	$-0.709726\pi$
$37$	−7.44807	−1.22446	−0.612228	+	0.790682i	$0.709726\pi$
$38$	0	0
$39$	15.6348	2.50357
$40$	4.31337	0.682004
$41$	2.71367	0.423804	0.211902	−	0.977291i	$-0.432034\pi$
$41$	2.71367	0.423804	0.211902	+	0.977291i	$0.432034\pi$
$42$	2.98161	0.460073
$43$	3.97133	0.605623	0.302811	−	0.953051i	$-0.402075\pi$
$43$	3.97133	0.605623	0.302811	+	0.953051i	$0.402075\pi$
$44$	0.362266	0.0546137
$45$	−25.4058	−3.78728
$46$	−1.78046	−0.262515
$47$	−3.27349	−0.477487	−0.238744	−	0.971083i	$-0.576736\pi$
$47$	−3.27349	−0.477487	−0.238744	+	0.971083i	$0.576736\pi$
$48$	−2.98161	−0.430359
$49$	1.00000	0.142857
$50$	−13.6052	−1.92406
$51$	13.8049	1.93307
$52$	−5.24373	−0.727174
$53$	−11.7483	−1.61375	−0.806874	−	0.590724i	$-0.798842\pi$
$53$	−11.7483	−1.61375	−0.806874	+	0.590724i	$0.798842\pi$
$54$	8.61690	1.17261
$55$	−1.56259	−0.210699
$56$	−1.00000	−0.133631
$57$	0	0
$58$	2.08498	0.273772
$59$	−0.777397	−0.101208	−0.0506042	−	0.998719i	$-0.516115\pi$
$59$	−0.777397	−0.101208	−0.0506042	+	0.998719i	$0.516115\pi$
$60$	12.8608	1.66032
$61$	−10.7422	−1.37540	−0.687698	−	0.725997i	$-0.741379\pi$
$61$	−10.7422	−1.37540	−0.687698	+	0.725997i	$0.741379\pi$
$62$	−2.02090	−0.256655
$63$	5.89001	0.742072
$64$	1.00000	0.125000
$65$	22.6181	2.80544
$66$	1.08014	0.132956
$67$	2.61230	0.319143	0.159572	−	0.987186i	$-0.448989\pi$
$67$	2.61230	0.319143	0.159572	+	0.987186i	$0.448989\pi$
$68$	−4.63000	−0.561470
$69$	−5.30866	−0.639087
$70$	4.31337	0.515547
$71$	−14.5430	−1.72594	−0.862968	−	0.505258i	$-0.831397\pi$
$71$	−14.5430	−1.72594	−0.862968	+	0.505258i	$0.831397\pi$
$72$	−5.89001	−0.694145
$73$	2.61980	0.306624	0.153312	−	0.988178i	$-0.451006\pi$
$73$	2.61980	0.306624	0.153312	+	0.988178i	$0.451006\pi$
$74$	7.44807	0.865821
$75$	−40.5654	−4.68409
$76$	0	0
$77$	0.362266	0.0412841
$78$	−15.6348	−1.77029
$79$	−0.554543	−0.0623910	−0.0311955	−	0.999513i	$-0.509931\pi$
$79$	−0.554543	−0.0623910	−0.0311955	+	0.999513i	$0.509931\pi$
$80$	−4.31337	−0.482250
$81$	8.02223	0.891358
$82$	−2.71367	−0.299675
$83$	−5.06311	−0.555748	−0.277874	−	0.960617i	$-0.589630\pi$
$83$	−5.06311	−0.555748	−0.277874	+	0.960617i	$0.589630\pi$
$84$	−2.98161	−0.325321
$85$	19.9709	2.16615
$86$	−3.97133	−0.428240
$87$	6.21661	0.666490
$88$	−0.362266	−0.0386177
$89$	−7.02669	−0.744827	−0.372414	−	0.928067i	$-0.621470\pi$
$89$	−7.02669	−0.744827	−0.372414	+	0.928067i	$0.621470\pi$
$90$	25.4058	2.67801
$91$	−5.24373	−0.549692
$92$	1.78046	0.185626
$93$	−6.02554	−0.624820
$94$	3.27349	0.337634
$95$	0	0
$96$	2.98161	0.304310
$97$	−1.38858	−0.140989	−0.0704944	−	0.997512i	$-0.522458\pi$
$97$	−1.38858	−0.140989	−0.0704944	+	0.997512i	$0.522458\pi$
$98$	−1.00000	−0.101015
$99$	2.13375	0.214450
$100$	13.6052	1.36052
$101$	−0.278655	−0.0277272	−0.0138636	−	0.999904i	$-0.504413\pi$
$101$	−0.278655	−0.0277272	−0.0138636	+	0.999904i	$0.504413\pi$
$102$	−13.8049	−1.36688
$103$	−10.9855	−1.08244	−0.541218	−	0.840882i	$-0.682037\pi$
$103$	−10.9855	−1.08244	−0.541218	+	0.840882i	$0.682037\pi$
$104$	5.24373	0.514190
$105$	12.8608	1.25509
$106$	11.7483	1.14109
$107$	−3.59786	−0.347819	−0.173909	−	0.984762i	$-0.555640\pi$
$107$	−3.59786	−0.347819	−0.173909	+	0.984762i	$0.555640\pi$
$108$	−8.61690	−0.829162
$109$	−10.9045	−1.04446	−0.522231	−	0.852804i	$-0.674900\pi$
$109$	−10.9045	−1.04446	−0.522231	+	0.852804i	$0.674900\pi$
$110$	1.56259	0.148987
$111$	22.2073	2.10782
$112$	1.00000	0.0944911
$113$	−4.29382	−0.403928	−0.201964	−	0.979393i	$-0.564732\pi$
$113$	−4.29382	−0.403928	−0.201964	+	0.979393i	$0.564732\pi$
$114$	0	0
$115$	−7.67981	−0.716146
$116$	−2.08498	−0.193586
$117$	−30.8856	−2.85538
$118$	0.777397	0.0715652
$119$	−4.63000	−0.424431
$120$	−12.8608	−1.17403
$121$	−10.8688	−0.988069
$122$	10.7422	0.972552
$123$	−8.09111	−0.729551
$124$	2.02090	0.181482
$125$	−37.1173	−3.31988
$126$	−5.89001	−0.524724
$127$	−11.0424	−0.979851	−0.489926	−	0.871764i	$-0.662976\pi$
$127$	−11.0424	−0.979851	−0.489926	+	0.871764i	$0.662976\pi$
$128$	−1.00000	−0.0883883
$129$	−11.8410	−1.04254
$130$	−22.6181	−1.98374
$131$	3.90396	0.341091	0.170546	−	0.985350i	$-0.445447\pi$
$131$	3.90396	0.341091	0.170546	+	0.985350i	$0.445447\pi$
$132$	−1.08014	−0.0940139
$133$	0	0
$134$	−2.61230	−0.225668
$135$	37.1679	3.19890
$136$	4.63000	0.397019
$137$	−10.8789	−0.929448	−0.464724	−	0.885456i	$-0.653846\pi$
$137$	−10.8789	−0.929448	−0.464724	+	0.885456i	$0.653846\pi$
$138$	5.30866	0.451903
$139$	12.0869	1.02520	0.512601	−	0.858627i	$-0.328682\pi$
$139$	12.0869	1.02520	0.512601	+	0.858627i	$0.328682\pi$
$140$	−4.31337	−0.364546
$141$	9.76027	0.821963
$142$	14.5430	1.22042
$143$	−1.89962	−0.158855
$144$	5.89001	0.490835
$145$	8.99330	0.746853
$146$	−2.61980	−0.216816
$147$	−2.98161	−0.245919
$148$	−7.44807	−0.612228
$149$	−19.8129	−1.62313	−0.811566	−	0.584260i	$-0.801385\pi$
$149$	−19.8129	−1.62313	−0.811566	+	0.584260i	$0.801385\pi$
$150$	40.5654	3.31215
$151$	16.3282	1.32877	0.664386	−	0.747390i	$-0.268693\pi$
$151$	16.3282	1.32877	0.664386	+	0.747390i	$0.268693\pi$
$152$	0	0
$153$	−27.2708	−2.20471
$154$	−0.362266	−0.0291922
$155$	−8.71690	−0.700158
$156$	15.6348	1.25178
$157$	−5.37439	−0.428923	−0.214462	−	0.976732i	$-0.568800\pi$
$157$	−5.37439	−0.428923	−0.214462	+	0.976732i	$0.568800\pi$
$158$	0.554543	0.0441171
$159$	35.0288	2.77796
$160$	4.31337	0.341002
$161$	1.78046	0.140320
$162$	−8.02223	−0.630286
$163$	−4.35537	−0.341139	−0.170569	−	0.985346i	$-0.554561\pi$
$163$	−4.35537	−0.341139	−0.170569	+	0.985346i	$0.554561\pi$
$164$	2.71367	0.211902
$165$	4.65903	0.362705
$166$	5.06311	0.392973
$167$	−23.9411	−1.85262	−0.926309	−	0.376766i	$-0.877036\pi$
$167$	−23.9411	−1.85262	−0.926309	+	0.376766i	$0.877036\pi$
$168$	2.98161	0.230036
$169$	14.4967	1.11513
$170$	−19.9709	−1.53170
$171$	0	0
$172$	3.97133	0.302811
$173$	−5.35580	−0.407194	−0.203597	−	0.979055i	$-0.565263\pi$
$173$	−5.35580	−0.407194	−0.203597	+	0.979055i	$0.565263\pi$
$174$	−6.21661	−0.471280
$175$	13.6052	1.02845
$176$	0.362266	0.0273068
$177$	2.31790	0.174224
$178$	7.02669	0.526672
$179$	19.3211	1.44413	0.722064	−	0.691826i	$-0.243193\pi$
$179$	19.3211	1.44413	0.722064	+	0.691826i	$0.243193\pi$
$180$	−25.4058	−1.89364
$181$	−9.50541	−0.706531	−0.353266	−	0.935523i	$-0.614929\pi$
$181$	−9.50541	−0.706531	−0.353266	+	0.935523i	$0.614929\pi$
$182$	5.24373	0.388691
$183$	32.0290	2.36765
$184$	−1.78046	−0.131258
$185$	32.1263	2.36197
$186$	6.02554	0.441814
$187$	−1.67729	−0.122656
$188$	−3.27349	−0.238744
$189$	−8.61690	−0.626787
$190$	0	0
$191$	−16.3533	−1.18329	−0.591643	−	0.806200i	$-0.701521\pi$
$191$	−16.3533	−1.18329	−0.591643	+	0.806200i	$0.701521\pi$
$192$	−2.98161	−0.215179
$193$	0.911504	0.0656115	0.0328057	−	0.999462i	$-0.489556\pi$
$193$	0.911504	0.0656115	0.0328057	+	0.999462i	$0.489556\pi$
$194$	1.38858	0.0996941
$195$	−67.4385	−4.82937
$196$	1.00000	0.0714286
$197$	−27.7280	−1.97554	−0.987770	−	0.155920i	$-0.950166\pi$
$197$	−27.7280	−1.97554	−0.987770	+	0.155920i	$0.950166\pi$
$198$	−2.13375	−0.151639
$199$	−6.58815	−0.467022	−0.233511	−	0.972354i	$-0.575021\pi$
$199$	−6.58815	−0.467022	−0.233511	+	0.972354i	$0.575021\pi$
$200$	−13.6052	−0.962031
$201$	−7.78887	−0.549385
$202$	0.278655	0.0196061
$203$	−2.08498	−0.146337
$204$	13.8049	0.966534
$205$	−11.7051	−0.817518
$206$	10.9855	0.765398
$207$	10.4870	0.728894
$208$	−5.24373	−0.363587
$209$	0	0
$210$	−12.8608	−0.887480
$211$	3.92985	0.270542	0.135271	−	0.990809i	$-0.456810\pi$
$211$	3.92985	0.270542	0.135271	+	0.990809i	$0.456810\pi$
$212$	−11.7483	−0.806874
$213$	43.3616	2.97109
$214$	3.59786	0.245945
$215$	−17.1298	−1.16825
$216$	8.61690	0.586306
$217$	2.02090	0.137188
$218$	10.9045	0.738547
$219$	−7.81121	−0.527833
$220$	−1.56259	−0.105350
$221$	24.2784	1.63314
$222$	−22.2073	−1.49045
$223$	−15.3681	−1.02912	−0.514562	−	0.857453i	$-0.672046\pi$
$223$	−15.3681	−1.02912	−0.514562	+	0.857453i	$0.672046\pi$
$224$	−1.00000	−0.0668153
$225$	80.1347	5.34231
$226$	4.29382	0.285621
$227$	15.6050	1.03574	0.517870	−	0.855459i	$-0.326725\pi$
$227$	15.6050	1.03574	0.517870	+	0.855459i	$0.326725\pi$
$228$	0	0
$229$	8.96359	0.592331	0.296165	−	0.955137i	$-0.404292\pi$
$229$	8.96359	0.592331	0.296165	+	0.955137i	$0.404292\pi$
$230$	7.67981	0.506391
$231$	−1.08014	−0.0710678
$232$	2.08498	0.136886
$233$	15.2270	0.997553	0.498776	−	0.866731i	$-0.333783\pi$
$233$	15.2270	0.997553	0.498776	+	0.866731i	$0.333783\pi$
$234$	30.8856	2.01906
$235$	14.1198	0.921072
$236$	−0.777397	−0.0506042
$237$	1.65343	0.107402
$238$	4.63000	0.300118
$239$	18.9069	1.22298	0.611492	−	0.791250i	$-0.290570\pi$
$239$	18.9069	1.22298	0.611492	+	0.791250i	$0.290570\pi$
$240$	12.8608	0.830161
$241$	18.6898	1.20391	0.601957	−	0.798529i	$-0.294388\pi$
$241$	18.6898	1.20391	0.601957	+	0.798529i	$0.294388\pi$
$242$	10.8688	0.698671
$243$	1.93154	0.123908
$244$	−10.7422	−0.687698
$245$	−4.31337	−0.275571
$246$	8.09111	0.515871
$247$	0	0
$248$	−2.02090	−0.128327
$249$	15.0962	0.956685
$250$	37.1173	2.34751
$251$	−17.5364	−1.10689	−0.553445	−	0.832885i	$-0.686687\pi$
$251$	−17.5364	−1.10689	−0.553445	+	0.832885i	$0.686687\pi$
$252$	5.89001	0.371036
$253$	0.645002	0.0405509
$254$	11.0424	0.692860
$255$	−59.5455	−3.72888
$256$	1.00000	0.0625000
$257$	11.5288	0.719145	0.359572	−	0.933117i	$-0.382923\pi$
$257$	11.5288	0.719145	0.359572	+	0.933117i	$0.382923\pi$
$258$	11.8410	0.737187
$259$	−7.44807	−0.462801
$260$	22.6181	1.40272
$261$	−12.2806	−0.760148
$262$	−3.90396	−0.241188
$263$	−5.34136	−0.329362	−0.164681	−	0.986347i	$-0.552660\pi$
$263$	−5.34136	−0.329362	−0.164681	+	0.986347i	$0.552660\pi$
$264$	1.08014	0.0664779
$265$	50.6746	3.11292
$266$	0	0
$267$	20.9509	1.28217
$268$	2.61230	0.159572
$269$	26.1618	1.59511	0.797557	−	0.603244i	$-0.206125\pi$
$269$	26.1618	1.59511	0.797557	+	0.603244i	$0.206125\pi$
$270$	−37.1679	−2.26197
$271$	−20.2805	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$271$	−20.2805	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$272$	−4.63000	−0.280735
$273$	15.6348	0.946259
$274$	10.8789	0.657219
$275$	4.92870	0.297212
$276$	−5.30866	−0.319544
$277$	31.1729	1.87300	0.936500	−	0.350666i	$-0.114045\pi$
$277$	31.1729	1.87300	0.936500	+	0.350666i	$0.114045\pi$
$278$	−12.0869	−0.724927
$279$	11.9031	0.712622
$280$	4.31337	0.257773
$281$	−6.00910	−0.358473	−0.179236	−	0.983806i	$-0.557363\pi$
$281$	−6.00910	−0.358473	−0.179236	+	0.983806i	$0.557363\pi$
$282$	−9.76027	−0.581216
$283$	12.2967	0.730963	0.365481	−	0.930819i	$-0.380904\pi$
$283$	12.2967	0.730963	0.365481	+	0.930819i	$0.380904\pi$
$284$	−14.5430	−0.862968
$285$	0	0
$286$	1.89962	0.112327
$287$	2.71367	0.160183
$288$	−5.89001	−0.347072
$289$	4.43688	0.260993
$290$	−8.99330	−0.528105
$291$	4.14020	0.242703
$292$	2.61980	0.153312
$293$	4.02655	0.235234	0.117617	−	0.993059i	$-0.462475\pi$
$293$	4.02655	0.235234	0.117617	+	0.993059i	$0.462475\pi$
$294$	2.98161	0.173891
$295$	3.35320	0.195231
$296$	7.44807	0.432910
$297$	−3.12161	−0.181134
$298$	19.8129	1.14773
$299$	−9.33627	−0.539930
$300$	−40.5654	−2.34204
$301$	3.97133	0.228904
$302$	−16.3282	−0.939584
$303$	0.830842	0.0477306
$304$	0	0
$305$	46.3350	2.65314
$306$	27.2708	1.55897
$307$	−22.6810	−1.29447	−0.647237	−	0.762289i	$-0.724075\pi$
$307$	−22.6810	−1.29447	−0.647237	+	0.762289i	$0.724075\pi$
$308$	0.362266	0.0206420
$309$	32.7546	1.86334
$310$	8.71690	0.495087
$311$	16.9035	0.958512	0.479256	−	0.877675i	$-0.340906\pi$
$311$	16.9035	0.958512	0.479256	+	0.877675i	$0.340906\pi$
$312$	−15.6348	−0.885144
$313$	−1.39972	−0.0791169	−0.0395585	−	0.999217i	$-0.512595\pi$
$313$	−1.39972	−0.0791169	−0.0395585	+	0.999217i	$0.512595\pi$
$314$	5.37439	0.303295
$315$	−25.4058	−1.43146
$316$	−0.554543	−0.0311955
$317$	10.9472	0.614856	0.307428	−	0.951571i	$-0.400532\pi$
$317$	10.9472	0.614856	0.307428	+	0.951571i	$0.400532\pi$
$318$	−35.0288	−1.96432
$319$	−0.755318	−0.0422897
$320$	−4.31337	−0.241125
$321$	10.7274	0.598747
$322$	−1.78046	−0.0992214
$323$	0	0
$324$	8.02223	0.445679
$325$	−71.3418	−3.95733
$326$	4.35537	0.241222
$327$	32.5130	1.79797
$328$	−2.71367	−0.149837
$329$	−3.27349	−0.180473
$330$	−4.65903	−0.256471
$331$	3.12383	0.171701	0.0858506	−	0.996308i	$-0.472639\pi$
$331$	3.12383	0.171701	0.0858506	+	0.996308i	$0.472639\pi$
$332$	−5.06311	−0.277874
$333$	−43.8692	−2.40402
$334$	23.9411	1.31000
$335$	−11.2678	−0.615627
$336$	−2.98161	−0.162660
$337$	−3.66902	−0.199864	−0.0999322	−	0.994994i	$-0.531863\pi$
$337$	−3.66902	−0.199864	−0.0999322	+	0.994994i	$0.531863\pi$
$338$	−14.4967	−0.788515
$339$	12.8025	0.695337
$340$	19.9709	1.08307
$341$	0.732104	0.0396457
$342$	0	0
$343$	1.00000	0.0539949
$344$	−3.97133	−0.214120
$345$	22.8982	1.23280
$346$	5.35580	0.287930
$347$	−14.2657	−0.765825	−0.382913	−	0.923785i	$-0.625079\pi$
$347$	−14.2657	−0.765825	−0.382913	+	0.923785i	$0.625079\pi$
$348$	6.21661	0.333245
$349$	−3.19923	−0.171251	−0.0856254	−	0.996327i	$-0.527289\pi$
$349$	−3.19923	−0.171251	−0.0856254	+	0.996327i	$0.527289\pi$
$350$	−13.6052	−0.727227
$351$	45.1847	2.41178
$352$	−0.362266	−0.0193089
$353$	−2.96498	−0.157810	−0.0789051	−	0.996882i	$-0.525142\pi$
$353$	−2.96498	−0.157810	−0.0789051	+	0.996882i	$0.525142\pi$
$354$	−2.31790	−0.123195
$355$	62.7294	3.32933
$356$	−7.02669	−0.372414
$357$	13.8049	0.730631
$358$	−19.3211	−1.02115
$359$	−20.5387	−1.08399	−0.541996	−	0.840381i	$-0.682331\pi$
$359$	−20.5387	−1.08399	−0.541996	+	0.840381i	$0.682331\pi$
$360$	25.4058	1.33900
$361$	0	0
$362$	9.50541	0.499593
$363$	32.4064	1.70090
$364$	−5.24373	−0.274846
$365$	−11.3002	−0.591477
$366$	−32.0290	−1.67418
$367$	−9.22982	−0.481792	−0.240896	−	0.970551i	$-0.577441\pi$
$367$	−9.22982	−0.481792	−0.240896	+	0.970551i	$0.577441\pi$
$368$	1.78046	0.0928131
$369$	15.9836	0.832071
$370$	−32.1263	−1.67017
$371$	−11.7483	−0.609939
$372$	−6.02554	−0.312410
$373$	−18.5739	−0.961722	−0.480861	−	0.876797i	$-0.659676\pi$
$373$	−18.5739	−0.961722	−0.480861	+	0.876797i	$0.659676\pi$
$374$	1.67729	0.0867307
$375$	110.670	5.71495
$376$	3.27349	0.168817
$377$	10.9331	0.563082
$378$	8.61690	0.443206
$379$	7.87312	0.404415	0.202207	−	0.979343i	$-0.435188\pi$
$379$	7.87312	0.404415	0.202207	+	0.979343i	$0.435188\pi$
$380$	0	0
$381$	32.9241	1.68675
$382$	16.3533	0.836710
$383$	14.6552	0.748846	0.374423	−	0.927258i	$-0.377841\pi$
$383$	14.6552	0.748846	0.374423	+	0.927258i	$0.377841\pi$
$384$	2.98161	0.152155
$385$	−1.56259	−0.0796369
$386$	−0.911504	−0.0463943
$387$	23.3912	1.18904
$388$	−1.38858	−0.0704944
$389$	17.0207	0.862986	0.431493	−	0.902116i	$-0.357987\pi$
$389$	17.0207	0.862986	0.431493	+	0.902116i	$0.357987\pi$
$390$	67.4385	3.41488
$391$	−8.24355	−0.416894
$392$	−1.00000	−0.0505076
$393$	−11.6401	−0.587166
$394$	27.7280	1.39692
$395$	2.39195	0.120352
$396$	2.13375	0.107225
$397$	10.4213	0.523032	0.261516	−	0.965199i	$-0.415778\pi$
$397$	10.4213	0.523032	0.261516	+	0.965199i	$0.415778\pi$
$398$	6.58815	0.330234
$399$	0	0
$400$	13.6052	0.680259
$401$	30.0758	1.50191	0.750956	−	0.660353i	$-0.229593\pi$
$401$	30.0758	1.50191	0.750956	+	0.660353i	$0.229593\pi$
$402$	7.78887	0.388474
$403$	−10.5971	−0.527877
$404$	−0.278655	−0.0138636
$405$	−34.6028	−1.71943
$406$	2.08498	0.103476
$407$	−2.69818	−0.133744
$408$	−13.8049	−0.683442
$409$	−11.0533	−0.546553	−0.273276	−	0.961936i	$-0.588107\pi$
$409$	−11.0533	−0.546553	−0.273276	+	0.961936i	$0.588107\pi$
$410$	11.7051	0.578072
$411$	32.4367	1.59998
$412$	−10.9855	−0.541218
$413$	−0.777397	−0.0382532
$414$	−10.4870	−0.515406
$415$	21.8391	1.07204
$416$	5.24373	0.257095
$417$	−36.0386	−1.76482
$418$	0	0
$419$	−14.4315	−0.705023	−0.352511	−	0.935808i	$-0.614672\pi$
$419$	−14.4315	−0.705023	−0.352511	+	0.935808i	$0.614672\pi$
$420$	12.8608	0.627543
$421$	26.6057	1.29668	0.648341	−	0.761350i	$-0.275463\pi$
$421$	26.6057	1.29668	0.648341	+	0.761350i	$0.275463\pi$
$422$	−3.92985	−0.191302
$423$	−19.2809	−0.937469
$424$	11.7483	0.570546
$425$	−62.9919	−3.05556
$426$	−43.3616	−2.10088
$427$	−10.7422	−0.519851
$428$	−3.59786	−0.173909
$429$	5.66395	0.273458
$430$	17.1298	0.826074
$431$	−20.2109	−0.973524	−0.486762	−	0.873534i	$-0.661822\pi$
$431$	−20.2109	−0.973524	−0.486762	+	0.873534i	$0.661822\pi$
$432$	−8.61690	−0.414581
$433$	36.1393	1.73674	0.868372	−	0.495913i	$-0.165167\pi$
$433$	36.1393	1.73674	0.868372	+	0.495913i	$0.165167\pi$
$434$	−2.02090	−0.0970064
$435$	−26.8145	−1.28566
$436$	−10.9045	−0.522231
$437$	0	0
$438$	7.81121	0.373234
$439$	18.9829	0.906004	0.453002	−	0.891509i	$-0.350353\pi$
$439$	18.9829	0.906004	0.453002	+	0.891509i	$0.350353\pi$
$440$	1.56259	0.0744935
$441$	5.89001	0.280477
$442$	−24.2784	−1.15481
$443$	−32.2823	−1.53378	−0.766888	−	0.641781i	$-0.778196\pi$
$443$	−32.2823	−1.53378	−0.766888	+	0.641781i	$0.778196\pi$
$444$	22.2073	1.05391
$445$	30.3087	1.43677
$446$	15.3681	0.727701
$447$	59.0743	2.79412
$448$	1.00000	0.0472456
$449$	−11.0150	−0.519829	−0.259914	−	0.965632i	$-0.583694\pi$
$449$	−11.0150	−0.519829	−0.259914	+	0.965632i	$0.583694\pi$
$450$	−80.1347	−3.77759
$451$	0.983071	0.0462910
$452$	−4.29382	−0.201964
$453$	−48.6844	−2.28739
$454$	−15.6050	−0.732379
$455$	22.6181	1.06035
$456$	0	0
$457$	−1.92274	−0.0899421	−0.0449710	−	0.998988i	$-0.514320\pi$
$457$	−1.92274	−0.0899421	−0.0449710	+	0.998988i	$0.514320\pi$
$458$	−8.96359	−0.418841
$459$	39.8962	1.86220
$460$	−7.67981	−0.358073
$461$	−3.81073	−0.177483	−0.0887416	−	0.996055i	$-0.528285\pi$
$461$	−3.81073	−0.177483	−0.0887416	+	0.996055i	$0.528285\pi$
$462$	1.08014	0.0502525
$463$	−34.9106	−1.62243	−0.811217	−	0.584745i	$-0.801195\pi$
$463$	−34.9106	−1.62243	−0.811217	+	0.584745i	$0.801195\pi$
$464$	−2.08498	−0.0967929
$465$	25.9904	1.20528
$466$	−15.2270	−0.705376
$467$	−33.2523	−1.53874	−0.769368	−	0.638806i	$-0.779428\pi$
$467$	−33.2523	−1.53874	−0.769368	+	0.638806i	$0.779428\pi$
$468$	−30.8856	−1.42769
$469$	2.61230	0.120625
$470$	−14.1198	−0.651296
$471$	16.0244	0.738363
$472$	0.777397	0.0357826
$473$	1.43868	0.0661506
$474$	−1.65343	−0.0759447
$475$	0	0
$476$	−4.63000	−0.212216
$477$	−69.1974	−3.16833
$478$	−18.9069	−0.864780
$479$	3.31481	0.151458	0.0757288	−	0.997128i	$-0.475872\pi$
$479$	3.31481	0.151458	0.0757288	+	0.997128i	$0.475872\pi$
$480$	−12.8608	−0.587013
$481$	39.0556	1.78078
$482$	−18.6898	−0.851295
$483$	−5.30866	−0.241552
$484$	−10.8688	−0.494035
$485$	5.98945	0.271967
$486$	−1.93154	−0.0876165
$487$	22.3772	1.01401	0.507005	−	0.861943i	$-0.330753\pi$
$487$	22.3772	1.01401	0.507005	+	0.861943i	$0.330753\pi$
$488$	10.7422	0.486276
$489$	12.9860	0.587249
$490$	4.31337	0.194858
$491$	−4.94993	−0.223387	−0.111693	−	0.993743i	$-0.535627\pi$
$491$	−4.94993	−0.223387	−0.111693	+	0.993743i	$0.535627\pi$
$492$	−8.09111	−0.364776
$493$	9.65346	0.434770
$494$	0	0
$495$	−9.20367	−0.413674
$496$	2.02090	0.0907411
$497$	−14.5430	−0.652343
$498$	−15.0962	−0.676478
$499$	−20.2919	−0.908389	−0.454194	−	0.890903i	$-0.650073\pi$
$499$	−20.2919	−0.908389	−0.454194	+	0.890903i	$0.650073\pi$
$500$	−37.1173	−1.65994
$501$	71.3831	3.18916
$502$	17.5364	0.782690
$503$	23.3232	1.03993	0.519965	−	0.854187i	$-0.325945\pi$
$503$	23.3232	1.03993	0.519965	+	0.854187i	$0.325945\pi$
$504$	−5.89001	−0.262362
$505$	1.20194	0.0534858
$506$	−0.645002	−0.0286738
$507$	−43.2234	−1.91962
$508$	−11.0424	−0.489926
$509$	−27.1210	−1.20212	−0.601058	−	0.799205i	$-0.705254\pi$
$509$	−27.1210	−1.20212	−0.601058	+	0.799205i	$0.705254\pi$
$510$	59.5455	2.63672
$511$	2.61980	0.115893
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−11.5288	−0.508512
$515$	47.3847	2.08802
$516$	−11.8410	−0.521270
$517$	−1.18587	−0.0521547
$518$	7.44807	0.327249
$519$	15.9689	0.700958
$520$	−22.6181	−0.991871
$521$	16.1295	0.706648	0.353324	−	0.935501i	$-0.385051\pi$
$521$	16.1295	0.706648	0.353324	+	0.935501i	$0.385051\pi$
$522$	12.2806	0.537506
$523$	24.9933	1.09288	0.546440	−	0.837498i	$-0.315983\pi$
$523$	24.9933	1.09288	0.546440	+	0.837498i	$0.315983\pi$
$524$	3.90396	0.170546
$525$	−40.5654	−1.77042
$526$	5.34136	0.232894
$527$	−9.35677	−0.407587
$528$	−1.08014	−0.0470069
$529$	−19.8299	−0.862172
$530$	−50.6746	−2.20116
$531$	−4.57888	−0.198706
$532$	0	0
$533$	−14.2297	−0.616359
$534$	−20.9509	−0.906632
$535$	15.5189	0.670942
$536$	−2.61230	−0.112834
$537$	−57.6081	−2.48597
$538$	−26.1618	−1.12792
$539$	0.362266	0.0156039
$540$	37.1679	1.59945
$541$	−11.3911	−0.489741	−0.244871	−	0.969556i	$-0.578745\pi$
$541$	−11.3911	−0.489741	−0.244871	+	0.969556i	$0.578745\pi$
$542$	20.2805	0.871122
$543$	28.3414	1.21625
$544$	4.63000	0.198510
$545$	47.0352	2.01477
$546$	−15.6348	−0.669106
$547$	−24.8812	−1.06384	−0.531921	−	0.846794i	$-0.678530\pi$
$547$	−24.8812	−1.06384	−0.531921	+	0.846794i	$0.678530\pi$
$548$	−10.8789	−0.464724
$549$	−63.2716	−2.70037
$550$	−4.92870	−0.210160
$551$	0	0
$552$	5.30866	0.225951
$553$	−0.554543	−0.0235816
$554$	−31.1729	−1.32441
$555$	−95.7882	−4.06598
$556$	12.0869	0.512601
$557$	11.1581	0.472784	0.236392	−	0.971658i	$-0.424035\pi$
$557$	11.1581	0.472784	0.236392	+	0.971658i	$0.424035\pi$
$558$	−11.9031	−0.503900
$559$	−20.8246	−0.880786
$560$	−4.31337	−0.182273
$561$	5.00103	0.211144
$562$	6.00910	0.253479
$563$	−18.8504	−0.794449	−0.397224	−	0.917722i	$-0.630026\pi$
$563$	−18.8504	−0.794449	−0.397224	+	0.917722i	$0.630026\pi$
$564$	9.76027	0.410981
$565$	18.5208	0.779177
$566$	−12.2967	−0.516869
$567$	8.02223	0.336902
$568$	14.5430	0.610211
$569$	−37.7923	−1.58434	−0.792168	−	0.610303i	$-0.791048\pi$
$569$	−37.7923	−1.58434	−0.792168	+	0.610303i	$0.791048\pi$
$570$	0	0
$571$	−10.6904	−0.447380	−0.223690	−	0.974660i	$-0.571810\pi$
$571$	−10.6904	−0.447380	−0.223690	+	0.974660i	$0.571810\pi$
$572$	−1.89962	−0.0794273
$573$	48.7593	2.03695
$574$	−2.71367	−0.113266
$575$	24.2235	1.01019
$576$	5.89001	0.245417
$577$	20.6689	0.860459	0.430229	−	0.902720i	$-0.358433\pi$
$577$	20.6689	0.860459	0.430229	+	0.902720i	$0.358433\pi$
$578$	−4.43688	−0.184550
$579$	−2.71775	−0.112946
$580$	8.99330	0.373427
$581$	−5.06311	−0.210053
$582$	−4.14020	−0.171617
$583$	−4.25600	−0.176265
$584$	−2.61980	−0.108408
$585$	133.221	5.50802
$586$	−4.02655	−0.166335
$587$	9.31019	0.384273	0.192136	−	0.981368i	$-0.438458\pi$
$587$	9.31019	0.384273	0.192136	+	0.981368i	$0.438458\pi$
$588$	−2.98161	−0.122960
$589$	0	0
$590$	−3.35320	−0.138049
$591$	82.6742	3.40076
$592$	−7.44807	−0.306114
$593$	−42.1221	−1.72975	−0.864873	−	0.501990i	$-0.832601\pi$
$593$	−42.1221	−1.72975	−0.864873	+	0.501990i	$0.832601\pi$
$594$	3.12161	0.128081
$595$	19.9709	0.818727
$596$	−19.8129	−0.811566
$597$	19.6433	0.803948
$598$	9.33627	0.381788
$599$	−21.5720	−0.881406	−0.440703	−	0.897653i	$-0.645271\pi$
$599$	−21.5720	−0.881406	−0.440703	+	0.897653i	$0.645271\pi$
$600$	40.5654	1.65607
$601$	17.4784	0.712959	0.356479	−	0.934303i	$-0.383977\pi$
$601$	17.4784	0.712959	0.356479	+	0.934303i	$0.383977\pi$
$602$	−3.97133	−0.161859
$603$	15.3865	0.626586
$604$	16.3282	0.664386
$605$	46.8810	1.90598
$606$	−0.830842	−0.0337506
$607$	−13.8157	−0.560763	−0.280381	−	0.959889i	$-0.590461\pi$
$607$	−13.8157	−0.560763	−0.280381	+	0.959889i	$0.590461\pi$
$608$	0	0
$609$	6.21661	0.251910
$610$	−46.3350	−1.87605
$611$	17.1653	0.694432
$612$	−27.2708	−1.10235
$613$	35.7849	1.44534	0.722669	−	0.691194i	$-0.242915\pi$
$613$	35.7849	1.44534	0.722669	+	0.691194i	$0.242915\pi$
$614$	22.6810	0.915331
$615$	34.9000	1.40730
$616$	−0.362266	−0.0145961
$617$	−28.2075	−1.13559	−0.567795	−	0.823170i	$-0.692204\pi$
$617$	−28.2075	−1.13559	−0.567795	+	0.823170i	$0.692204\pi$
$618$	−32.7546	−1.31758
$619$	−35.4746	−1.42584	−0.712922	−	0.701243i	$-0.752629\pi$
$619$	−35.4746	−1.42584	−0.712922	+	0.701243i	$0.752629\pi$
$620$	−8.71690	−0.350079
$621$	−15.3421	−0.615657
$622$	−16.9035	−0.677771
$623$	−7.02669	−0.281518
$624$	15.6348	0.625891
$625$	92.0750	3.68300
$626$	1.39972	0.0559441
$627$	0	0
$628$	−5.37439	−0.214462
$629$	34.4845	1.37499
$630$	25.4058	1.01219
$631$	43.6368	1.73716	0.868578	−	0.495553i	$-0.165035\pi$
$631$	43.6368	1.73716	0.868578	+	0.495553i	$0.165035\pi$
$632$	0.554543	0.0220586
$633$	−11.7173	−0.465720
$634$	−10.9472	−0.434769
$635$	47.6298	1.89013
$636$	35.0288	1.38898
$637$	−5.24373	−0.207764
$638$	0.755318	0.0299033
$639$	−85.6585	−3.38860
$640$	4.31337	0.170501
$641$	−4.51479	−0.178323	−0.0891616	−	0.996017i	$-0.528419\pi$
$641$	−4.51479	−0.178323	−0.0891616	+	0.996017i	$0.528419\pi$
$642$	−10.7274	−0.423378
$643$	−4.32950	−0.170739	−0.0853693	−	0.996349i	$-0.527207\pi$
$643$	−4.32950	−0.170739	−0.0853693	+	0.996349i	$0.527207\pi$
$644$	1.78046	0.0701601
$645$	51.0745	2.01106
$646$	0	0
$647$	21.4445	0.843071	0.421535	−	0.906812i	$-0.361491\pi$
$647$	21.4445	0.843071	0.421535	+	0.906812i	$0.361491\pi$
$648$	−8.02223	−0.315143
$649$	−0.281625	−0.0110547
$650$	71.3418	2.79826
$651$	−6.02554	−0.236160
$652$	−4.35537	−0.170569
$653$	36.7156	1.43679	0.718397	−	0.695634i	$-0.244876\pi$
$653$	36.7156	1.43679	0.718397	+	0.695634i	$0.244876\pi$
$654$	−32.5130	−1.27136
$655$	−16.8393	−0.657964
$656$	2.71367	0.105951
$657$	15.4306	0.602006
$658$	3.27349	0.127614
$659$	20.9897	0.817641	0.408821	−	0.912615i	$-0.365940\pi$
$659$	20.9897	0.817641	0.408821	+	0.912615i	$0.365940\pi$
$660$	4.65903	0.181353
$661$	−1.01862	−0.0396198	−0.0198099	−	0.999804i	$-0.506306\pi$
$661$	−1.01862	−0.0396198	−0.0198099	+	0.999804i	$0.506306\pi$
$662$	−3.12383	−0.121411
$663$	−72.3889	−2.81135
$664$	5.06311	0.196487
$665$	0	0
$666$	43.8692	1.69990
$667$	−3.71224	−0.143738
$668$	−23.9411	−0.926309
$669$	45.8218	1.77157
$670$	11.2678	0.435314
$671$	−3.89153	−0.150231
$672$	2.98161	0.115018
$673$	−45.4641	−1.75251	−0.876256	−	0.481846i	$-0.839966\pi$
$673$	−45.4641	−1.75251	−0.876256	+	0.481846i	$0.839966\pi$
$674$	3.66902	0.141325
$675$	−117.235	−4.51236
$676$	14.4967	0.557564
$677$	33.9501	1.30481	0.652405	−	0.757871i	$-0.273760\pi$
$677$	33.9501	1.30481	0.652405	+	0.757871i	$0.273760\pi$
$678$	−12.8025	−0.491677
$679$	−1.38858	−0.0532887
$680$	−19.9709	−0.765849
$681$	−46.5281	−1.78296
$682$	−0.732104	−0.0280337
$683$	−1.09066	−0.0417330	−0.0208665	−	0.999782i	$-0.506643\pi$
$683$	−1.09066	−0.0417330	−0.0208665	+	0.999782i	$0.506643\pi$
$684$	0	0
$685$	46.9248	1.79290
$686$	−1.00000	−0.0381802
$687$	−26.7259	−1.01966
$688$	3.97133	0.151406
$689$	61.6047	2.34695
$690$	−22.8982	−0.871720
$691$	−28.6243	−1.08892	−0.544459	−	0.838787i	$-0.683265\pi$
$691$	−28.6243	−1.08892	−0.544459	+	0.838787i	$0.683265\pi$
$692$	−5.35580	−0.203597
$693$	2.13375	0.0810546
$694$	14.2657	0.541520
$695$	−52.1355	−1.97761
$696$	−6.21661	−0.235640
$697$	−12.5643	−0.475906
$698$	3.19923	0.121093
$699$	−45.4010	−1.71722
$700$	13.6052	0.514227
$701$	−31.4941	−1.18952	−0.594759	−	0.803904i	$-0.702752\pi$
$701$	−31.4941	−1.18952	−0.594759	+	0.803904i	$0.702752\pi$
$702$	−45.1847	−1.70539
$703$	0	0
$704$	0.362266	0.0136534
$705$	−42.0997	−1.58557
$706$	2.96498	0.111589
$707$	−0.278655	−0.0104799
$708$	2.31790	0.0871119
$709$	−2.98911	−0.112258	−0.0561292	−	0.998424i	$-0.517876\pi$
$709$	−2.98911	−0.112258	−0.0561292	+	0.998424i	$0.517876\pi$
$710$	−62.7294	−2.35419
$711$	−3.26627	−0.122495
$712$	7.02669	0.263336
$713$	3.59814	0.134752
$714$	−13.8049	−0.516634
$715$	8.19379	0.306430
$716$	19.3211	0.722064
$717$	−56.3730	−2.10529
$718$	20.5387	0.766498
$719$	−50.7556	−1.89286	−0.946431	−	0.322905i	$-0.895341\pi$
$719$	−50.7556	−1.89286	−0.946431	+	0.322905i	$0.895341\pi$
$720$	−25.4058	−0.946819
$721$	−10.9855	−0.409122
$722$	0	0
$723$	−55.7256	−2.07246
$724$	−9.50541	−0.353266
$725$	−28.3665	−1.05351
$726$	−32.4064	−1.20272
$727$	44.4894	1.65002	0.825011	−	0.565117i	$-0.191169\pi$
$727$	44.4894	1.65002	0.825011	+	0.565117i	$0.191169\pi$
$728$	5.24373	0.194345
$729$	−29.8258	−1.10466
$730$	11.3002	0.418237
$731$	−18.3873	−0.680077
$732$	32.0290	1.18383
$733$	−24.6274	−0.909635	−0.454818	−	0.890585i	$-0.650296\pi$
$733$	−24.6274	−0.909635	−0.454818	+	0.890585i	$0.650296\pi$
$734$	9.22982	0.340679
$735$	12.8608	0.474378
$736$	−1.78046	−0.0656288
$737$	0.946349	0.0348592
$738$	−15.9836	−0.588363
$739$	−29.9616	−1.10216	−0.551078	−	0.834453i	$-0.685784\pi$
$739$	−29.9616	−1.10216	−0.551078	+	0.834453i	$0.685784\pi$
$740$	32.1263	1.18099
$741$	0	0
$742$	11.7483	0.431292
$743$	9.44786	0.346608	0.173304	−	0.984868i	$-0.444556\pi$
$743$	9.44786	0.346608	0.173304	+	0.984868i	$0.444556\pi$
$744$	6.02554	0.220907
$745$	85.4602	3.13102
$746$	18.5739	0.680040
$747$	−29.8218	−1.09112
$748$	−1.67729	−0.0613279
$749$	−3.59786	−0.131463
$750$	−110.670	−4.04108
$751$	−8.84575	−0.322786	−0.161393	−	0.986890i	$-0.551599\pi$
$751$	−8.84575	−0.322786	−0.161393	+	0.986890i	$0.551599\pi$
$752$	−3.27349	−0.119372
$753$	52.2869	1.90544
$754$	−10.9331	−0.398159
$755$	−70.4297	−2.56320
$756$	−8.61690	−0.313394
$757$	22.9044	0.832475	0.416238	−	0.909256i	$-0.363348\pi$
$757$	22.9044	0.832475	0.416238	+	0.909256i	$0.363348\pi$
$758$	−7.87312	−0.285964
$759$	−1.92315	−0.0698058
$760$	0	0
$761$	20.6868	0.749894	0.374947	−	0.927046i	$-0.377661\pi$
$761$	20.6868	0.749894	0.374947	+	0.927046i	$0.377661\pi$
$762$	−32.9241	−1.19271
$763$	−10.9045	−0.394770
$764$	−16.3533	−0.591643
$765$	117.629	4.25288
$766$	−14.6552	−0.529514
$767$	4.07646	0.147192
$768$	−2.98161	−0.107590
$769$	3.55285	0.128119	0.0640596	−	0.997946i	$-0.479595\pi$
$769$	3.55285	0.128119	0.0640596	+	0.997946i	$0.479595\pi$
$770$	1.56259	0.0563118
$771$	−34.3743	−1.23796
$772$	0.911504	0.0328057
$773$	29.9640	1.07773	0.538865	−	0.842392i	$-0.318853\pi$
$773$	29.9640	1.07773	0.538865	+	0.842392i	$0.318853\pi$
$774$	−23.3912	−0.840780
$775$	27.4947	0.987639
$776$	1.38858	0.0498471
$777$	22.2073	0.796681
$778$	−17.0207	−0.610223
$779$	0	0
$780$	−67.4385	−2.41469
$781$	−5.26844	−0.188519
$782$	8.24355	0.294789
$783$	17.9661	0.642056
$784$	1.00000	0.0357143
$785$	23.1818	0.827392
$786$	11.6401	0.415189
$787$	35.8277	1.27712	0.638559	−	0.769573i	$-0.279531\pi$
$787$	35.8277	1.27712	0.638559	+	0.769573i	$0.279531\pi$
$788$	−27.7280	−0.987770
$789$	15.9259	0.566976
$790$	−2.39195	−0.0851018
$791$	−4.29382	−0.152671
$792$	−2.13375	−0.0758196
$793$	56.3291	2.00030
$794$	−10.4213	−0.369839
$795$	−151.092	−5.35868
$796$	−6.58815	−0.233511
$797$	−31.7865	−1.12594	−0.562968	−	0.826479i	$-0.690341\pi$
$797$	−31.7865	−1.12594	−0.562968	+	0.826479i	$0.690341\pi$
$798$	0	0
$799$	15.1562	0.536189
$800$	−13.6052	−0.481016
$801$	−41.3873	−1.46235
$802$	−30.0758	−1.06201
$803$	0.949063	0.0334917
$804$	−7.78887	−0.274692
$805$	−7.67981	−0.270678
$806$	10.5971	0.373265
$807$	−78.0044	−2.74588
$808$	0.278655	0.00980306
$809$	−12.2092	−0.429252	−0.214626	−	0.976696i	$-0.568853\pi$
$809$	−12.2092	−0.429252	−0.214626	+	0.976696i	$0.568853\pi$
$810$	34.6028	1.21582
$811$	47.0483	1.65209	0.826044	−	0.563606i	$-0.190586\pi$
$811$	47.0483	1.65209	0.826044	+	0.563606i	$0.190586\pi$
$812$	−2.08498	−0.0731685
$813$	60.4686	2.12072
$814$	2.69818	0.0945713
$815$	18.7863	0.658057
$816$	13.8049	0.483267
$817$	0	0
$818$	11.0533	0.386471
$819$	−30.8856	−1.07923
$820$	−11.7051	−0.408759
$821$	26.1942	0.914183	0.457092	−	0.889420i	$-0.348891\pi$
$821$	26.1942	0.914183	0.457092	+	0.889420i	$0.348891\pi$
$822$	−32.4367	−1.13136
$823$	36.6952	1.27911	0.639557	−	0.768744i	$-0.279118\pi$
$823$	36.6952	1.27911	0.639557	+	0.768744i	$0.279118\pi$
$824$	10.9855	0.382699
$825$	−14.6955	−0.511630
$826$	0.777397	0.0270491
$827$	36.9160	1.28369	0.641847	−	0.766832i	$-0.278168\pi$
$827$	36.9160	1.28369	0.641847	+	0.766832i	$0.278168\pi$
$828$	10.4870	0.364447
$829$	−38.1788	−1.32600	−0.663002	−	0.748618i	$-0.730718\pi$
$829$	−38.1788	−1.32600	−0.663002	+	0.748618i	$0.730718\pi$
$830$	−21.8391	−0.758045
$831$	−92.9457	−3.22425
$832$	−5.24373	−0.181794
$833$	−4.63000	−0.160420
$834$	36.0386	1.24791
$835$	103.267	3.57370
$836$	0	0
$837$	−17.4139	−0.601913
$838$	14.4315	0.498526
$839$	5.08377	0.175511	0.0877556	−	0.996142i	$-0.472031\pi$
$839$	5.08377	0.175511	0.0877556	+	0.996142i	$0.472031\pi$
$840$	−12.8608	−0.443740
$841$	−24.6529	−0.850098
$842$	−26.6057	−0.916893
$843$	17.9168	0.617088
$844$	3.92985	0.135271
$845$	−62.5295	−2.15108
$846$	19.2809	0.662890
$847$	−10.8688	−0.373455
$848$	−11.7483	−0.403437
$849$	−36.6640	−1.25830
$850$	62.9919	2.16061
$851$	−13.2610	−0.454582
$852$	43.3616	1.48554
$853$	−10.1943	−0.349046	−0.174523	−	0.984653i	$-0.555838\pi$
$853$	−10.1943	−0.349046	−0.174523	+	0.984653i	$0.555838\pi$
$854$	10.7422	0.367590
$855$	0	0
$856$	3.59786	0.122972
$857$	8.02856	0.274250	0.137125	−	0.990554i	$-0.456214\pi$
$857$	8.02856	0.274250	0.137125	+	0.990554i	$0.456214\pi$
$858$	−5.66395	−0.193364
$859$	41.2373	1.40700	0.703499	−	0.710696i	$-0.251620\pi$
$859$	41.2373	1.40700	0.703499	+	0.710696i	$0.251620\pi$
$860$	−17.1298	−0.584123
$861$	−8.09111	−0.275744
$862$	20.2109	0.688386
$863$	0.552239	0.0187985	0.00939923	−	0.999956i	$-0.497008\pi$
$863$	0.552239	0.0187985	0.00939923	+	0.999956i	$0.497008\pi$
$864$	8.61690	0.293153
$865$	23.1016	0.785477
$866$	−36.1393	−1.22806
$867$	−13.2291	−0.449282
$868$	2.02090	0.0685939
$869$	−0.200892	−0.00681481
$870$	26.8145	0.909098
$871$	−13.6982	−0.464146
$872$	10.9045	0.369273
$873$	−8.17875	−0.276809
$874$	0	0
$875$	−37.1173	−1.25479
$876$	−7.81121	−0.263916
$877$	40.4583	1.36618	0.683090	−	0.730334i	$-0.260636\pi$
$877$	40.4583	1.36618	0.683090	+	0.730334i	$0.260636\pi$
$878$	−18.9829	−0.640642
$879$	−12.0056	−0.404939
$880$	−1.56259	−0.0526749
$881$	25.8951	0.872427	0.436213	−	0.899843i	$-0.356319\pi$
$881$	25.8951	0.872427	0.436213	+	0.899843i	$0.356319\pi$
$882$	−5.89001	−0.198327
$883$	51.1233	1.72044	0.860218	−	0.509926i	$-0.170327\pi$
$883$	51.1233	1.72044	0.860218	+	0.509926i	$0.170327\pi$
$884$	24.2784	0.816572
$885$	−9.99795	−0.336077
$886$	32.2823	1.08454
$887$	−31.1733	−1.04670	−0.523349	−	0.852119i	$-0.675318\pi$
$887$	−31.1733	−1.04670	−0.523349	+	0.852119i	$0.675318\pi$
$888$	−22.2073	−0.745227
$889$	−11.0424	−0.370349
$890$	−30.3087	−1.01595
$891$	2.90618	0.0973607
$892$	−15.3681	−0.514562
$893$	0	0
$894$	−59.0743	−1.97574
$895$	−83.3392	−2.78572
$896$	−1.00000	−0.0334077
$897$	27.8371	0.929455
$898$	11.0150	0.367574
$899$	−4.21354	−0.140530
$900$	80.1347	2.67116
$901$	54.3944	1.81214
$902$	−0.983071	−0.0327327
$903$	−11.8410	−0.394043
$904$	4.29382	0.142810
$905$	41.0004	1.36290
$906$	48.6844	1.61743
$907$	−7.77664	−0.258219	−0.129110	−	0.991630i	$-0.541212\pi$
$907$	−7.77664	−0.258219	−0.129110	+	0.991630i	$0.541212\pi$
$908$	15.6050	0.517870
$909$	−1.64128	−0.0544379
$910$	−22.6181	−0.749784
$911$	−13.8287	−0.458166	−0.229083	−	0.973407i	$-0.573573\pi$
$911$	−13.8287	−0.458166	−0.229083	+	0.973407i	$0.573573\pi$
$912$	0	0
$913$	−1.83419	−0.0607029
$914$	1.92274	0.0635986
$915$	−138.153	−4.56720
$916$	8.96359	0.296165
$917$	3.90396	0.128920
$918$	−39.8962	−1.31677
$919$	−52.4671	−1.73073	−0.865365	−	0.501143i	$-0.832913\pi$
$919$	−52.4671	−1.73073	−0.865365	+	0.501143i	$0.832913\pi$
$920$	7.67981	0.253196
$921$	67.6260	2.22835
$922$	3.81073	0.125500
$923$	76.2595	2.51011
$924$	−1.08014	−0.0355339
$925$	−101.332	−3.33179
$926$	34.9106	1.14723
$927$	−64.7049	−2.12519
$928$	2.08498	0.0684429
$929$	44.7025	1.46664	0.733320	−	0.679883i	$-0.237970\pi$
$929$	44.7025	1.46664	0.733320	+	0.679883i	$0.237970\pi$
$930$	−25.9904	−0.852259
$931$	0	0
$932$	15.2270	0.498776
$933$	−50.3998	−1.65002
$934$	33.2523	1.08805
$935$	7.23478	0.236603
$936$	30.8856	1.00953
$937$	−33.9615	−1.10947	−0.554737	−	0.832026i	$-0.687181\pi$
$937$	−33.9615	−1.10947	−0.554737	+	0.832026i	$0.687181\pi$
$938$	−2.61230	−0.0852947
$939$	4.17343	0.136195
$940$	14.1198	0.460536
$941$	3.18819	0.103932	0.0519659	−	0.998649i	$-0.483451\pi$
$941$	3.18819	0.103932	0.0519659	+	0.998649i	$0.483451\pi$
$942$	−16.0244	−0.522102
$943$	4.83159	0.157338
$944$	−0.777397	−0.0253021
$945$	37.1679	1.20907
$946$	−1.43868	−0.0467755
$947$	−5.45182	−0.177160	−0.0885801	−	0.996069i	$-0.528233\pi$
$947$	−5.45182	−0.177160	−0.0885801	+	0.996069i	$0.528233\pi$
$948$	1.65343	0.0537010
$949$	−13.7375	−0.445938
$950$	0	0
$951$	−32.6403	−1.05843
$952$	4.63000	0.150059
$953$	−11.1272	−0.360446	−0.180223	−	0.983626i	$-0.557682\pi$
$953$	−11.1272	−0.360446	−0.180223	+	0.983626i	$0.557682\pi$
$954$	69.1974	2.24035
$955$	70.5381	2.28256
$956$	18.9069	0.611492
$957$	2.25207	0.0727990
$958$	−3.31481	−0.107097
$959$	−10.8789	−0.351298
$960$	12.8608	0.415081
$961$	−26.9160	−0.868257
$962$	−39.0556	−1.25920
$963$	−21.1915	−0.682886
$964$	18.6898	0.601957
$965$	−3.93166	−0.126564
$966$	5.30866	0.170803
$967$	−49.5193	−1.59243	−0.796217	−	0.605012i	$-0.793168\pi$
$967$	−49.5193	−1.59243	−0.796217	+	0.605012i	$0.793168\pi$
$968$	10.8688	0.349335
$969$	0	0
$970$	−5.98945	−0.192310
$971$	11.6443	0.373683	0.186842	−	0.982390i	$-0.440175\pi$
$971$	11.6443	0.373683	0.186842	+	0.982390i	$0.440175\pi$
$972$	1.93154	0.0619542
$973$	12.0869	0.387490
$974$	−22.3772	−0.717013
$975$	212.714	6.81229
$976$	−10.7422	−0.343849
$977$	36.1804	1.15751	0.578757	−	0.815500i	$-0.303538\pi$
$977$	36.1804	1.15751	0.578757	+	0.815500i	$0.303538\pi$
$978$	−12.9860	−0.415247
$979$	−2.54553	−0.0813555
$980$	−4.31337	−0.137786
$981$	−64.2277	−2.05063
$982$	4.94993	0.157958
$983$	−9.63945	−0.307451	−0.153725	−	0.988114i	$-0.549127\pi$
$983$	−9.63945	−0.307451	−0.153725	+	0.988114i	$0.549127\pi$
$984$	8.09111	0.257935
$985$	119.601	3.81081
$986$	−9.65346	−0.307429
$987$	9.76027	0.310673
$988$	0	0
$989$	7.07082	0.224839
$990$	9.20367	0.292512
$991$	50.0192	1.58891	0.794456	−	0.607321i	$-0.207756\pi$
$991$	50.0192	1.58891	0.794456	+	0.607321i	$0.207756\pi$
$992$	−2.02090	−0.0641637
$993$	−9.31405	−0.295572
$994$	14.5430	0.461276
$995$	28.4172	0.900884
$996$	15.0962	0.478342
$997$	27.5717	0.873203	0.436602	−	0.899655i	$-0.356182\pi$
$997$	27.5717	0.873203	0.436602	+	0.899655i	$0.356182\pi$
$998$	20.2919	0.642328
$999$	64.1793	2.03054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bl.1.2		12
19.4	even	9		266.2.u.d.225.4	✓	24
19.5	even	9		266.2.u.d.253.4	yes	24
19.18	odd	2		5054.2.a.bm.1.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.d.225.4	✓	24	19.4	even	9
266.2.u.d.253.4	yes	24	19.5	even	9
5054.2.a.bl.1.2		12	1.1	even	1	trivial
5054.2.a.bm.1.11		12	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.98161 q^{3} +1.00000 q^{4} -4.31337 q^{5} +2.98161 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.89001 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.98161 q^{3} +1.00000 q^{4} -4.31337 q^{5} +2.98161 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.89001 q^{9} +4.31337 q^{10} +0.362266 q^{11} -2.98161 q^{12} -5.24373 q^{13} -1.00000 q^{14} +12.8608 q^{15} +1.00000 q^{16} -4.63000 q^{17} -5.89001 q^{18} -4.31337 q^{20} -2.98161 q^{21} -0.362266 q^{22} +1.78046 q^{23} +2.98161 q^{24} +13.6052 q^{25} +5.24373 q^{26} -8.61690 q^{27} +1.00000 q^{28} -2.08498 q^{29} -12.8608 q^{30} +2.02090 q^{31} -1.00000 q^{32} -1.08014 q^{33} +4.63000 q^{34} -4.31337 q^{35} +5.89001 q^{36} -7.44807 q^{37} +15.6348 q^{39} +4.31337 q^{40} +2.71367 q^{41} +2.98161 q^{42} +3.97133 q^{43} +0.362266 q^{44} -25.4058 q^{45} -1.78046 q^{46} -3.27349 q^{47} -2.98161 q^{48} +1.00000 q^{49} -13.6052 q^{50} +13.8049 q^{51} -5.24373 q^{52} -11.7483 q^{53} +8.61690 q^{54} -1.56259 q^{55} -1.00000 q^{56} +2.08498 q^{58} -0.777397 q^{59} +12.8608 q^{60} -10.7422 q^{61} -2.02090 q^{62} +5.89001 q^{63} +1.00000 q^{64} +22.6181 q^{65} +1.08014 q^{66} +2.61230 q^{67} -4.63000 q^{68} -5.30866 q^{69} +4.31337 q^{70} -14.5430 q^{71} -5.89001 q^{72} +2.61980 q^{73} +7.44807 q^{74} -40.5654 q^{75} +0.362266 q^{77} -15.6348 q^{78} -0.554543 q^{79} -4.31337 q^{80} +8.02223 q^{81} -2.71367 q^{82} -5.06311 q^{83} -2.98161 q^{84} +19.9709 q^{85} -3.97133 q^{86} +6.21661 q^{87} -0.362266 q^{88} -7.02669 q^{89} +25.4058 q^{90} -5.24373 q^{91} +1.78046 q^{92} -6.02554 q^{93} +3.27349 q^{94} +2.98161 q^{96} -1.38858 q^{97} -1.00000 q^{98} +2.13375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9	\( 12 q - 12 q^{2} - 3 q^{3} + 12 q^{4} + 3 q^{5} + 3 q^{6} + 12 q^{7} - 12 q^{8} + 21 q^{9} - 3 q^{10} + 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 6 q^{15} + 12 q^{16} + 3 q^{17} - 21 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 12 q^{23} + 3 q^{24} + 33 q^{25} - 6 q^{26} - 21 q^{27} + 12 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} - 12 q^{32} + 6 q^{33} - 3 q^{34} + 3 q^{35} + 21 q^{36} - 27 q^{37} + 27 q^{39} - 3 q^{40} + 27 q^{41} + 3 q^{42} + 30 q^{43} + 3 q^{44} + 30 q^{45} - 12 q^{46} + 21 q^{47} - 3 q^{48} + 12 q^{49} - 33 q^{50} - 3 q^{51} + 6 q^{52} - 6 q^{53} + 21 q^{54} + 48 q^{55} - 12 q^{56} + 6 q^{58} + 27 q^{59} + 6 q^{60} + 18 q^{61} + 3 q^{62} + 21 q^{63} + 12 q^{64} + 9 q^{65} - 6 q^{66} - 9 q^{67} + 3 q^{68} - 18 q^{69} - 3 q^{70} - 27 q^{71} - 21 q^{72} - 9 q^{73} + 27 q^{74} - 33 q^{75} + 3 q^{77} - 27 q^{78} + 12 q^{79} + 3 q^{80} + 24 q^{81} - 27 q^{82} + 9 q^{83} - 3 q^{84} + 78 q^{85} - 30 q^{86} - 45 q^{87} - 3 q^{88} + 24 q^{89} - 30 q^{90} + 6 q^{91} + 12 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 18 q^{97} - 12 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 3 * q^3 + 12 * q^4 + 3 * q^5 + 3 * q^6 + 12 * q^7 - 12 * q^8 + 21 * q^9 - 3 * q^10 + 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 6 * q^15 + 12 * q^16 + 3 * q^17 - 21 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 12 * q^23 + 3 * q^24 + 33 * q^25 - 6 * q^26 - 21 * q^27 + 12 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 - 12 * q^32 + 6 * q^33 - 3 * q^34 + 3 * q^35 + 21 * q^36 - 27 * q^37 + 27 * q^39 - 3 * q^40 + 27 * q^41 + 3 * q^42 + 30 * q^43 + 3 * q^44 + 30 * q^45 - 12 * q^46 + 21 * q^47 - 3 * q^48 + 12 * q^49 - 33 * q^50 - 3 * q^51 + 6 * q^52 - 6 * q^53 + 21 * q^54 + 48 * q^55 - 12 * q^56 + 6 * q^58 + 27 * q^59 + 6 * q^60 + 18 * q^61 + 3 * q^62 + 21 * q^63 + 12 * q^64 + 9 * q^65 - 6 * q^66 - 9 * q^67 + 3 * q^68 - 18 * q^69 - 3 * q^70 - 27 * q^71 - 21 * q^72 - 9 * q^73 + 27 * q^74 - 33 * q^75 + 3 * q^77 - 27 * q^78 + 12 * q^79 + 3 * q^80 + 24 * q^81 - 27 * q^82 + 9 * q^83 - 3 * q^84 + 78 * q^85 - 30 * q^86 - 45 * q^87 - 3 * q^88 + 24 * q^89 - 30 * q^90 + 6 * q^91 + 12 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 18 * q^97 - 12 * q^98 + 48 * q^99

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