LMFDB - Embedded newform 2738.2.a.w.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 8 x^{17} - 8 x^{16} + 209 x^{15} - 253 x^{14} - 1996 x^{13} + 4196 x^{12} + 8667 x^{11} + \cdots + 113 $ x^18 - 8x^17 - 8x^16 + 209x^15 - 253x^14 - 1996x^13 + 4196x^12 + 8667x^11 - 24522x^10 - 18284x^9 + 68697x^8 + 20865x^7 - 97011x^6 - 20844x^5 + 64568x^4 + 17499x^3 - 13387x^2 - 3713*x + 113
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$3.21182$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.320182 q^{3} +1.00000 q^{4} -3.73221 q^{5} +0.320182 q^{6} +2.93372 q^{7} -1.00000 q^{8} -2.89748 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.320182 q^{3} +1.00000 q^{4} -3.73221 q^{5} +0.320182 q^{6} +2.93372 q^{7} -1.00000 q^{8} -2.89748 q^{9} +3.73221 q^{10} +4.47132 q^{11} -0.320182 q^{12} +5.74629 q^{13} -2.93372 q^{14} +1.19499 q^{15} +1.00000 q^{16} -2.67759 q^{17} +2.89748 q^{18} +5.14247 q^{19} -3.73221 q^{20} -0.939325 q^{21} -4.47132 q^{22} -0.733776 q^{23} +0.320182 q^{24} +8.92938 q^{25} -5.74629 q^{26} +1.88827 q^{27} +2.93372 q^{28} -3.89230 q^{29} -1.19499 q^{30} -7.74468 q^{31} -1.00000 q^{32} -1.43163 q^{33} +2.67759 q^{34} -10.9493 q^{35} -2.89748 q^{36} -5.14247 q^{38} -1.83986 q^{39} +3.73221 q^{40} -1.26590 q^{41} +0.939325 q^{42} -5.70174 q^{43} +4.47132 q^{44} +10.8140 q^{45} +0.733776 q^{46} +3.65985 q^{47} -0.320182 q^{48} +1.60673 q^{49} -8.92938 q^{50} +0.857316 q^{51} +5.74629 q^{52} -2.28501 q^{53} -1.88827 q^{54} -16.6879 q^{55} -2.93372 q^{56} -1.64653 q^{57} +3.89230 q^{58} +4.77466 q^{59} +1.19499 q^{60} +3.67128 q^{61} +7.74468 q^{62} -8.50041 q^{63} +1.00000 q^{64} -21.4463 q^{65} +1.43163 q^{66} -5.10474 q^{67} -2.67759 q^{68} +0.234942 q^{69} +10.9493 q^{70} +0.0947712 q^{71} +2.89748 q^{72} -0.442146 q^{73} -2.85902 q^{75} +5.14247 q^{76} +13.1176 q^{77} +1.83986 q^{78} +14.4805 q^{79} -3.73221 q^{80} +8.08786 q^{81} +1.26590 q^{82} +0.0724002 q^{83} -0.939325 q^{84} +9.99333 q^{85} +5.70174 q^{86} +1.24624 q^{87} -4.47132 q^{88} -5.63322 q^{89} -10.8140 q^{90} +16.8580 q^{91} -0.733776 q^{92} +2.47970 q^{93} -3.65985 q^{94} -19.1928 q^{95} +0.320182 q^{96} +19.0908 q^{97} -1.60673 q^{98} -12.9556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9} + 9 q^{10} + 10 q^{11} + 8 q^{12} - 9 q^{13} - 18 q^{14} + 4 q^{15} + 18 q^{16} - 13 q^{17} - 26 q^{18} - 2 q^{19} - 9 q^{20} + 24 q^{21} - 10 q^{22} + 11 q^{23} - 8 q^{24} + 49 q^{25} + 9 q^{26} + 29 q^{27} + 18 q^{28} - 30 q^{29} - 4 q^{30} + 8 q^{31} - 18 q^{32} + 42 q^{33} + 13 q^{34} - 25 q^{35} + 26 q^{36} + 2 q^{38} + 45 q^{39} + 9 q^{40} + 5 q^{41} - 24 q^{42} + 3 q^{43} + 10 q^{44} + 30 q^{45} - 11 q^{46} + 37 q^{47} + 8 q^{48} + 50 q^{49} - 49 q^{50} - 10 q^{51} - 9 q^{52} + 25 q^{53} - 29 q^{54} + 44 q^{55} - 18 q^{56} - 22 q^{57} + 30 q^{58} - 26 q^{59} + 4 q^{60} - 27 q^{61} - 8 q^{62} + 74 q^{63} + 18 q^{64} - 16 q^{65} - 42 q^{66} + 23 q^{67} - 13 q^{68} + 2 q^{69} + 25 q^{70} - 25 q^{71} - 26 q^{72} + 77 q^{73} - q^{75} - 2 q^{76} - 6 q^{77} - 45 q^{78} + 13 q^{79} - 9 q^{80} + 38 q^{81} - 5 q^{82} - 10 q^{83} + 24 q^{84} + 16 q^{85} - 3 q^{86} + 55 q^{87} - 10 q^{88} - 55 q^{89} - 30 q^{90} - 12 q^{91} + 11 q^{92} + 58 q^{93} - 37 q^{94} - 18 q^{95} - 8 q^{96} + 59 q^{97} - 50 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9 + 9 * q^10 + 10 * q^11 + 8 * q^12 - 9 * q^13 - 18 * q^14 + 4 * q^15 + 18 * q^16 - 13 * q^17 - 26 * q^18 - 2 * q^19 - 9 * q^20 + 24 * q^21 - 10 * q^22 + 11 * q^23 - 8 * q^24 + 49 * q^25 + 9 * q^26 + 29 * q^27 + 18 * q^28 - 30 * q^29 - 4 * q^30 + 8 * q^31 - 18 * q^32 + 42 * q^33 + 13 * q^34 - 25 * q^35 + 26 * q^36 + 2 * q^38 + 45 * q^39 + 9 * q^40 + 5 * q^41 - 24 * q^42 + 3 * q^43 + 10 * q^44 + 30 * q^45 - 11 * q^46 + 37 * q^47 + 8 * q^48 + 50 * q^49 - 49 * q^50 - 10 * q^51 - 9 * q^52 + 25 * q^53 - 29 * q^54 + 44 * q^55 - 18 * q^56 - 22 * q^57 + 30 * q^58 - 26 * q^59 + 4 * q^60 - 27 * q^61 - 8 * q^62 + 74 * q^63 + 18 * q^64 - 16 * q^65 - 42 * q^66 + 23 * q^67 - 13 * q^68 + 2 * q^69 + 25 * q^70 - 25 * q^71 - 26 * q^72 + 77 * q^73 - q^75 - 2 * q^76 - 6 * q^77 - 45 * q^78 + 13 * q^79 - 9 * q^80 + 38 * q^81 - 5 * q^82 - 10 * q^83 + 24 * q^84 + 16 * q^85 - 3 * q^86 + 55 * q^87 - 10 * q^88 - 55 * q^89 - 30 * q^90 - 12 * q^91 + 11 * q^92 + 58 * q^93 - 37 * q^94 - 18 * q^95 - 8 * q^96 + 59 * q^97 - 50 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.320182	−0.184857	−0.0924285	−	0.995719i	$-0.529463\pi$
$3$	−0.320182	−0.184857	−0.0924285	+	0.995719i	$0.529463\pi$
$4$	1.00000	0.500000
$5$	−3.73221	−1.66909	−0.834547	−	0.550937i	$-0.814271\pi$
$5$	−3.73221	−1.66909	−0.834547	+	0.550937i	$0.814271\pi$
$6$	0.320182	0.130714
$7$	2.93372	1.10884	0.554421	−	0.832236i	$-0.312940\pi$
$7$	2.93372	1.10884	0.554421	+	0.832236i	$0.312940\pi$
$8$	−1.00000	−0.353553
$9$	−2.89748	−0.965828
$10$	3.73221	1.18023
$11$	4.47132	1.34815	0.674076	−	0.738662i	$-0.264542\pi$
$11$	4.47132	1.34815	0.674076	+	0.738662i	$0.264542\pi$
$12$	−0.320182	−0.0924285
$13$	5.74629	1.59373	0.796867	−	0.604155i	$-0.206489\pi$
$13$	5.74629	1.59373	0.796867	+	0.604155i	$0.206489\pi$
$14$	−2.93372	−0.784070
$15$	1.19499	0.308544
$16$	1.00000	0.250000
$17$	−2.67759	−0.649411	−0.324706	−	0.945815i	$-0.605265\pi$
$17$	−2.67759	−0.649411	−0.324706	+	0.945815i	$0.605265\pi$
$18$	2.89748	0.682943
$19$	5.14247	1.17976	0.589882	−	0.807490i	$-0.299174\pi$
$19$	5.14247	1.17976	0.589882	+	0.807490i	$0.299174\pi$
$20$	−3.73221	−0.834547
$21$	−0.939325	−0.204977
$22$	−4.47132	−0.953288
$23$	−0.733776	−0.153003	−0.0765014	−	0.997069i	$-0.524375\pi$
$23$	−0.733776	−0.153003	−0.0765014	+	0.997069i	$0.524375\pi$
$24$	0.320182	0.0653568
$25$	8.92938	1.78588
$26$	−5.74629	−1.12694
$27$	1.88827	0.363397
$28$	2.93372	0.554421
$29$	−3.89230	−0.722782	−0.361391	−	0.932414i	$-0.617698\pi$
$29$	−3.89230	−0.722782	−0.361391	+	0.932414i	$0.617698\pi$
$30$	−1.19499	−0.218173
$31$	−7.74468	−1.39098	−0.695492	−	0.718533i	$-0.744814\pi$
$31$	−7.74468	−1.39098	−0.695492	+	0.718533i	$0.744814\pi$
$32$	−1.00000	−0.176777
$33$	−1.43163	−0.249216
$34$	2.67759	0.459203
$35$	−10.9493	−1.85076
$36$	−2.89748	−0.482914
$37$	0	0
$37$	0	0
$38$	−5.14247	−0.834219
$39$	−1.83986	−0.294613
$40$	3.73221	0.590114
$41$	−1.26590	−0.197700	−0.0988501	−	0.995102i	$-0.531516\pi$
$41$	−1.26590	−0.197700	−0.0988501	+	0.995102i	$0.531516\pi$
$42$	0.939325	0.144941
$43$	−5.70174	−0.869507	−0.434753	−	0.900550i	$-0.643164\pi$
$43$	−5.70174	−0.869507	−0.434753	+	0.900550i	$0.643164\pi$
$44$	4.47132	0.674076
$45$	10.8140	1.61206
$46$	0.733776	0.108189
$47$	3.65985	0.533844	0.266922	−	0.963718i	$-0.413993\pi$
$47$	3.65985	0.533844	0.266922	+	0.963718i	$0.413993\pi$
$48$	−0.320182	−0.0462143
$49$	1.60673	0.229532
$50$	−8.92938	−1.26280
$51$	0.857316	0.120048
$52$	5.74629	0.796867
$53$	−2.28501	−0.313871	−0.156935	−	0.987609i	$-0.550161\pi$
$53$	−2.28501	−0.313871	−0.156935	+	0.987609i	$0.550161\pi$
$54$	−1.88827	−0.256961
$55$	−16.6879	−2.25019
$56$	−2.93372	−0.392035
$57$	−1.64653	−0.218088
$58$	3.89230	0.511084
$59$	4.77466	0.621608	0.310804	−	0.950474i	$-0.399402\pi$
$59$	4.77466	0.621608	0.310804	+	0.950474i	$0.399402\pi$
$60$	1.19499	0.154272
$61$	3.67128	0.470059	0.235030	−	0.971988i	$-0.424481\pi$
$61$	3.67128	0.470059	0.235030	+	0.971988i	$0.424481\pi$
$62$	7.74468	0.983575
$63$	−8.50041	−1.07095
$64$	1.00000	0.125000
$65$	−21.4463	−2.66009
$66$	1.43163	0.176222
$67$	−5.10474	−0.623643	−0.311822	−	0.950141i	$-0.600939\pi$
$67$	−5.10474	−0.623643	−0.311822	+	0.950141i	$0.600939\pi$
$68$	−2.67759	−0.324706
$69$	0.234942	0.0282837
$70$	10.9493	1.30869
$71$	0.0947712	0.0112473	0.00562364	−	0.999984i	$-0.498210\pi$
$71$	0.0947712	0.0112473	0.00562364	+	0.999984i	$0.498210\pi$
$72$	2.89748	0.341472
$73$	−0.442146	−0.0517493	−0.0258746	−	0.999665i	$-0.508237\pi$
$73$	−0.442146	−0.0517493	−0.0258746	+	0.999665i	$0.508237\pi$
$74$	0	0
$75$	−2.85902	−0.330132
$76$	5.14247	0.589882
$77$	13.1176	1.49489
$78$	1.83986	0.208323
$79$	14.4805	1.62918	0.814592	−	0.580035i	$-0.196961\pi$
$79$	14.4805	1.62918	0.814592	+	0.580035i	$0.196961\pi$
$80$	−3.73221	−0.417274
$81$	8.08786	0.898651
$82$	1.26590	0.139795
$83$	0.0724002	0.00794696	0.00397348	−	0.999992i	$-0.498735\pi$
$83$	0.0724002	0.00794696	0.00397348	+	0.999992i	$0.498735\pi$
$84$	−0.939325	−0.102489
$85$	9.99333	1.08393
$86$	5.70174	0.614834
$87$	1.24624	0.133611
$88$	−4.47132	−0.476644
$89$	−5.63322	−0.597120	−0.298560	−	0.954391i	$-0.596506\pi$
$89$	−5.63322	−0.597120	−0.298560	+	0.954391i	$0.596506\pi$
$90$	−10.8140	−1.13990
$91$	16.8580	1.76720
$92$	−0.733776	−0.0765014
$93$	2.47970	0.257133
$94$	−3.65985	−0.377485
$95$	−19.1928	−1.96914
$96$	0.320182	0.0326784
$97$	19.0908	1.93838	0.969190	−	0.246313i	$-0.0792191\pi$
$97$	19.0908	1.93838	0.969190	+	0.246313i	$0.0792191\pi$
$98$	−1.60673	−0.162304
$99$	−12.9556	−1.30208
$100$	8.92938	0.892938
$101$	14.4410	1.43694	0.718468	−	0.695560i	$-0.244843\pi$
$101$	14.4410	1.43694	0.718468	+	0.695560i	$0.244843\pi$
$102$	−0.857316	−0.0848869
$103$	4.35741	0.429348	0.214674	−	0.976686i	$-0.431131\pi$
$103$	4.35741	0.429348	0.214674	+	0.976686i	$0.431131\pi$
$104$	−5.74629	−0.563470
$105$	3.50575	0.342127
$106$	2.28501	0.221940
$107$	12.1421	1.17382	0.586911	−	0.809652i	$-0.300344\pi$
$107$	12.1421	1.17382	0.586911	+	0.809652i	$0.300344\pi$
$108$	1.88827	0.181699
$109$	15.0753	1.44396	0.721978	−	0.691916i	$-0.243233\pi$
$109$	15.0753	1.44396	0.721978	+	0.691916i	$0.243233\pi$
$110$	16.6879	1.59113
$111$	0	0
$112$	2.93372	0.277211
$113$	−0.406240	−0.0382159	−0.0191079	−	0.999817i	$-0.506083\pi$
$113$	−0.406240	−0.0382159	−0.0191079	+	0.999817i	$0.506083\pi$
$114$	1.64653	0.154211
$115$	2.73860	0.255376
$116$	−3.89230	−0.361391
$117$	−16.6498	−1.53927
$118$	−4.77466	−0.439543
$119$	−7.85531	−0.720095
$120$	−1.19499	−0.109087
$121$	8.99267	0.817516
$122$	−3.67128	−0.332382
$123$	0.405318	0.0365463
$124$	−7.74468	−0.695492
$125$	−14.6653	−1.31170
$126$	8.50041	0.757277
$127$	−11.1969	−0.993568	−0.496784	−	0.867874i	$-0.665486\pi$
$127$	−11.1969	−0.993568	−0.496784	+	0.867874i	$0.665486\pi$
$128$	−1.00000	−0.0883883
$129$	1.82559	0.160734
$130$	21.4463	1.88097
$131$	−17.0888	−1.49306	−0.746528	−	0.665354i	$-0.768280\pi$
$131$	−17.0888	−1.49306	−0.746528	+	0.665354i	$0.768280\pi$
$132$	−1.43163	−0.124608
$133$	15.0866	1.30817
$134$	5.10474	0.440982
$135$	−7.04741	−0.606544
$136$	2.67759	0.229601
$137$	0.00968616	0.000827545 0	0.000413772	−	1.00000i	$-0.499868\pi$
$137$	0.00968616	0.000827545 0	0.000413772		1.00000i	$0.499868\pi$
$138$	−0.234942	−0.0199996
$139$	−2.38206	−0.202044	−0.101022	−	0.994884i	$-0.532211\pi$
$139$	−2.38206	−0.202044	−0.101022	+	0.994884i	$0.532211\pi$
$140$	−10.9493	−0.925382
$141$	−1.17182	−0.0986848
$142$	−0.0947712	−0.00795302
$143$	25.6935	2.14860
$144$	−2.89748	−0.241457
$145$	14.5269	1.20639
$146$	0.442146	0.0365923
$147$	−0.514445	−0.0424307
$148$	0	0
$149$	16.7900	1.37549	0.687747	−	0.725950i	$-0.258600\pi$
$149$	16.7900	1.37549	0.687747	+	0.725950i	$0.258600\pi$
$150$	2.85902	0.233438
$151$	−10.1575	−0.826604	−0.413302	−	0.910594i	$-0.635625\pi$
$151$	−10.1575	−0.826604	−0.413302	+	0.910594i	$0.635625\pi$
$152$	−5.14247	−0.417109
$153$	7.75827	0.627219
$154$	−13.1176	−1.05705
$155$	28.9047	2.32168
$156$	−1.83986	−0.147306
$157$	2.28147	0.182081	0.0910404	−	0.995847i	$-0.470981\pi$
$157$	2.28147	0.182081	0.0910404	+	0.995847i	$0.470981\pi$
$158$	−14.4805	−1.15201
$159$	0.731620	0.0580212
$160$	3.73221	0.295057
$161$	−2.15270	−0.169656
$162$	−8.08786	−0.635442
$163$	3.99005	0.312525	0.156263	−	0.987716i	$-0.450055\pi$
$163$	3.99005	0.312525	0.156263	+	0.987716i	$0.450055\pi$
$164$	−1.26590	−0.0988501
$165$	5.34316	0.415964
$166$	−0.0724002	−0.00561935
$167$	−12.4588	−0.964091	−0.482046	−	0.876146i	$-0.660106\pi$
$167$	−12.4588	−0.964091	−0.482046	+	0.876146i	$0.660106\pi$
$168$	0.939325	0.0724705
$169$	20.0198	1.53998
$170$	−9.99333	−0.766453
$171$	−14.9002	−1.13945
$172$	−5.70174	−0.434753
$173$	18.3709	1.39671	0.698357	−	0.715750i	$-0.253915\pi$
$173$	18.3709	1.39671	0.698357	+	0.715750i	$0.253915\pi$
$174$	−1.24624	−0.0944775
$175$	26.1963	1.98026
$176$	4.47132	0.337038
$177$	−1.52876	−0.114909
$178$	5.63322	0.422228
$179$	20.6620	1.54435	0.772175	−	0.635410i	$-0.219169\pi$
$179$	20.6620	1.54435	0.772175	+	0.635410i	$0.219169\pi$
$180$	10.8140	0.806029
$181$	3.77241	0.280401	0.140201	−	0.990123i	$-0.455225\pi$
$181$	3.77241	0.280401	0.140201	+	0.990123i	$0.455225\pi$
$182$	−16.8580	−1.24960
$183$	−1.17548	−0.0868937
$184$	0.733776	0.0540947
$185$	0	0
$186$	−2.47970	−0.181821
$187$	−11.9724	−0.875505
$188$	3.65985	0.266922
$189$	5.53965	0.402950
$190$	19.1928	1.39239
$191$	15.2024	1.10001	0.550005	−	0.835161i	$-0.314626\pi$
$191$	15.2024	1.10001	0.550005	+	0.835161i	$0.314626\pi$
$192$	−0.320182	−0.0231071
$193$	21.6678	1.55969	0.779843	−	0.625976i	$-0.215299\pi$
$193$	21.6678	1.55969	0.779843	+	0.625976i	$0.215299\pi$
$194$	−19.0908	−1.37064
$195$	6.86673	0.491737
$196$	1.60673	0.114766
$197$	−13.7395	−0.978898	−0.489449	−	0.872032i	$-0.662802\pi$
$197$	−13.7395	−0.978898	−0.489449	+	0.872032i	$0.662802\pi$
$198$	12.9556	0.920712
$199$	5.63105	0.399174	0.199587	−	0.979880i	$-0.436040\pi$
$199$	5.63105	0.399174	0.199587	+	0.979880i	$0.436040\pi$
$200$	−8.92938	−0.631402
$201$	1.63444	0.115285
$202$	−14.4410	−1.01607
$203$	−11.4189	−0.801452
$204$	0.857316	0.0600241
$205$	4.72460	0.329980
$206$	−4.35741	−0.303595
$207$	2.12610	0.147774
$208$	5.74629	0.398433
$209$	22.9936	1.59050
$210$	−3.50575	−0.241920
$211$	−23.0510	−1.58689	−0.793447	−	0.608639i	$-0.791716\pi$
$211$	−23.0510	−1.58689	−0.793447	+	0.608639i	$0.791716\pi$
$212$	−2.28501	−0.156935
$213$	−0.0303440	−0.00207914
$214$	−12.1421	−0.830017
$215$	21.2801	1.45129
$216$	−1.88827	−0.128480
$217$	−22.7207	−1.54238
$218$	−15.0753	−1.02103
$219$	0.141567	0.00956622
$220$	−16.6879	−1.12510
$221$	−15.3862	−1.03499
$222$	0	0
$223$	−15.2412	−1.02062	−0.510312	−	0.859989i	$-0.670470\pi$
$223$	−15.2412	−1.02062	−0.510312	+	0.859989i	$0.670470\pi$
$224$	−2.93372	−0.196018
$225$	−25.8727	−1.72485
$226$	0.406240	0.0270227
$227$	−12.8314	−0.851648	−0.425824	−	0.904806i	$-0.640016\pi$
$227$	−12.8314	−0.851648	−0.425824	+	0.904806i	$0.640016\pi$
$228$	−1.64653	−0.109044
$229$	−20.2815	−1.34024	−0.670120	−	0.742253i	$-0.733757\pi$
$229$	−20.2815	−1.34024	−0.670120	+	0.742253i	$0.733757\pi$
$230$	−2.73860	−0.180578
$231$	−4.20002	−0.276341
$232$	3.89230	0.255542
$233$	20.2108	1.32405	0.662027	−	0.749480i	$-0.269696\pi$
$233$	20.2108	1.32405	0.662027	+	0.749480i	$0.269696\pi$
$234$	16.6498	1.08843
$235$	−13.6593	−0.891036
$236$	4.77466	0.310804
$237$	−4.63639	−0.301166
$238$	7.85531	0.509184
$239$	6.87306	0.444582	0.222291	−	0.974980i	$-0.428647\pi$
$239$	6.87306	0.444582	0.222291	+	0.974980i	$0.428647\pi$
$240$	1.19499	0.0771360
$241$	−14.1313	−0.910279	−0.455140	−	0.890420i	$-0.650411\pi$
$241$	−14.1313	−0.910279	−0.455140	+	0.890420i	$0.650411\pi$
$242$	−8.99267	−0.578071
$243$	−8.25439	−0.529519
$244$	3.67128	0.235030
$245$	−5.99664	−0.383111
$246$	−0.405318	−0.0258421
$247$	29.5501	1.88023
$248$	7.74468	0.491787
$249$	−0.0231812	−0.00146905
$250$	14.6653	0.927512
$251$	−21.4139	−1.35163	−0.675816	−	0.737070i	$-0.736209\pi$
$251$	−21.4139	−1.35163	−0.675816	+	0.737070i	$0.736209\pi$
$252$	−8.50041	−0.535476
$253$	−3.28095	−0.206271
$254$	11.1969	0.702559
$255$	−3.19968	−0.200372
$256$	1.00000	0.0625000
$257$	−0.281256	−0.0175443	−0.00877214	−	0.999962i	$-0.502792\pi$
$257$	−0.281256	−0.0175443	−0.00877214	+	0.999962i	$0.502792\pi$
$258$	−1.82559	−0.113656
$259$	0	0
$260$	−21.4463	−1.33005
$261$	11.2779	0.698083
$262$	17.0888	1.05575
$263$	12.8063	0.789669	0.394834	−	0.918752i	$-0.370802\pi$
$263$	12.8063	0.789669	0.394834	+	0.918752i	$0.370802\pi$
$264$	1.43163	0.0881110
$265$	8.52814	0.523880
$266$	−15.0866	−0.925018
$267$	1.80366	0.110382
$268$	−5.10474	−0.311822
$269$	11.7216	0.714677	0.357338	−	0.933975i	$-0.383684\pi$
$269$	11.7216	0.714677	0.357338	+	0.933975i	$0.383684\pi$
$270$	7.04741	0.428891
$271$	5.46425	0.331930	0.165965	−	0.986132i	$-0.446926\pi$
$271$	5.46425	0.331930	0.165965	+	0.986132i	$0.446926\pi$
$272$	−2.67759	−0.162353
$273$	−5.39763	−0.326679
$274$	−0.00968616	−0.000585162 0
$275$	39.9261	2.40763
$276$	0.234942	0.0141418
$277$	6.34878	0.381461	0.190731	−	0.981642i	$-0.438914\pi$
$277$	6.34878	0.381461	0.190731	+	0.981642i	$0.438914\pi$
$278$	2.38206	0.142867
$279$	22.4401	1.34345
$280$	10.9493	0.654344
$281$	7.35463	0.438741	0.219370	−	0.975642i	$-0.429600\pi$
$281$	7.35463	0.438741	0.219370	+	0.975642i	$0.429600\pi$
$282$	1.17182	0.0697807
$283$	26.3239	1.56479	0.782395	−	0.622782i	$-0.213998\pi$
$283$	26.3239	1.56479	0.782395	+	0.622782i	$0.213998\pi$
$284$	0.0947712	0.00562364
$285$	6.14518	0.364009
$286$	−25.6935	−1.51929
$287$	−3.71380	−0.219218
$288$	2.89748	0.170736
$289$	−9.83051	−0.578265
$290$	−14.5269	−0.853048
$291$	−6.11254	−0.358323
$292$	−0.442146	−0.0258746
$293$	−20.7874	−1.21441	−0.607207	−	0.794543i	$-0.707710\pi$
$293$	−20.7874	−1.21441	−0.607207	+	0.794543i	$0.707710\pi$
$294$	0.514445	0.0300030
$295$	−17.8200	−1.03752
$296$	0	0
$297$	8.44304	0.489915
$298$	−16.7900	−0.972621
$299$	−4.21649	−0.243846
$300$	−2.85902	−0.165066
$301$	−16.7273	−0.964146
$302$	10.1575	0.584497
$303$	−4.62376	−0.265628
$304$	5.14247	0.294941
$305$	−13.7020	−0.784573
$306$	−7.75827	−0.443511
$307$	7.73062	0.441210	0.220605	−	0.975363i	$-0.429197\pi$
$307$	7.73062	0.441210	0.220605	+	0.975363i	$0.429197\pi$
$308$	13.1176	0.747445
$309$	−1.39516	−0.0793680
$310$	−28.9047	−1.64168
$311$	27.6312	1.56682	0.783411	−	0.621504i	$-0.213478\pi$
$311$	27.6312	1.56682	0.783411	+	0.621504i	$0.213478\pi$
$312$	1.83986	0.104161
$313$	−12.3333	−0.697119	−0.348559	−	0.937287i	$-0.613329\pi$
$313$	−12.3333	−0.697119	−0.348559	+	0.937287i	$0.613329\pi$
$314$	−2.28147	−0.128751
$315$	31.7253	1.78752
$316$	14.4805	0.814592
$317$	−0.315766	−0.0177352	−0.00886760	−	0.999961i	$-0.502823\pi$
$317$	−0.315766	−0.0177352	−0.00886760	+	0.999961i	$0.502823\pi$
$318$	−0.731620	−0.0410272
$319$	−17.4037	−0.974421
$320$	−3.73221	−0.208637
$321$	−3.88768	−0.216989
$322$	2.15270	0.119965
$323$	−13.7694	−0.766152
$324$	8.08786	0.449326
$325$	51.3108	2.84621
$326$	−3.99005	−0.220989
$327$	−4.82685	−0.266926
$328$	1.26590	0.0698976
$329$	10.7370	0.591949
$330$	−5.34316	−0.294131
$331$	16.9231	0.930179	0.465089	−	0.885264i	$-0.346022\pi$
$331$	16.9231	0.930179	0.465089	+	0.885264i	$0.346022\pi$
$332$	0.0724002	0.00397348
$333$	0	0
$334$	12.4588	0.681715
$335$	19.0519	1.04092
$336$	−0.939325	−0.0512444
$337$	15.5319	0.846075	0.423037	−	0.906112i	$-0.360964\pi$
$337$	15.5319	0.846075	0.423037	+	0.906112i	$0.360964\pi$
$338$	−20.0198	−1.08893
$339$	0.130071	0.00706447
$340$	9.99333	0.541964
$341$	−34.6289	−1.87526
$342$	14.9002	0.805712
$343$	−15.8224	−0.854327
$344$	5.70174	0.307417
$345$	−0.876851	−0.0472081
$346$	−18.3709	−0.987625
$347$	23.8773	1.28180	0.640900	−	0.767624i	$-0.278561\pi$
$347$	23.8773	1.28180	0.640900	+	0.767624i	$0.278561\pi$
$348$	1.24624	0.0668057
$349$	18.8292	1.00790	0.503951	−	0.863732i	$-0.331879\pi$
$349$	18.8292	1.00790	0.503951	+	0.863732i	$0.331879\pi$
$350$	−26.1963	−1.40025
$351$	10.8505	0.579158
$352$	−4.47132	−0.238322
$353$	−2.49614	−0.132856	−0.0664280	−	0.997791i	$-0.521160\pi$
$353$	−2.49614	−0.132856	−0.0664280	+	0.997791i	$0.521160\pi$
$354$	1.52876	0.0812527
$355$	−0.353706	−0.0187728
$356$	−5.63322	−0.298560
$357$	2.51513	0.133115
$358$	−20.6620	−1.09202
$359$	12.0536	0.636164	0.318082	−	0.948063i	$-0.396961\pi$
$359$	12.0536	0.636164	0.318082	+	0.948063i	$0.396961\pi$
$360$	−10.8140	−0.569948
$361$	7.44500	0.391842
$362$	−3.77241	−0.198274
$363$	−2.87929	−0.151124
$364$	16.8580	0.883600
$365$	1.65018	0.0863744
$366$	1.17548	0.0614431
$367$	37.0543	1.93422	0.967111	−	0.254356i	$-0.0818636\pi$
$367$	37.0543	1.93422	0.967111	+	0.254356i	$0.0818636\pi$
$368$	−0.733776	−0.0382507
$369$	3.66792	0.190944
$370$	0	0
$371$	−6.70359	−0.348033
$372$	2.47970	0.128567
$373$	−5.38668	−0.278912	−0.139456	−	0.990228i	$-0.544535\pi$
$373$	−5.38668	−0.278912	−0.139456	+	0.990228i	$0.544535\pi$
$374$	11.9724	0.619076
$375$	4.69555	0.242477
$376$	−3.65985	−0.188742
$377$	−22.3663	−1.15192
$378$	−5.53965	−0.284929
$379$	21.6224	1.11067	0.555335	−	0.831627i	$-0.312590\pi$
$379$	21.6224	1.11067	0.555335	+	0.831627i	$0.312590\pi$
$380$	−19.1928	−0.984568
$381$	3.58506	0.183668
$382$	−15.2024	−0.777825
$383$	37.0449	1.89290	0.946452	−	0.322845i	$-0.104639\pi$
$383$	37.0449	1.89290	0.946452	+	0.322845i	$0.104639\pi$
$384$	0.320182	0.0163392
$385$	−48.9576	−2.49511
$386$	−21.6678	−1.10286
$387$	16.5207	0.839794
$388$	19.0908	0.969190
$389$	−22.5262	−1.14212	−0.571062	−	0.820907i	$-0.693468\pi$
$389$	−22.5262	−1.14212	−0.571062	+	0.820907i	$0.693468\pi$
$390$	−6.86673	−0.347710
$391$	1.96475	0.0993618
$392$	−1.60673	−0.0811520
$393$	5.47152	0.276002
$394$	13.7395	0.692185
$395$	−54.0442	−2.71926
$396$	−12.9556	−0.651042
$397$	17.0296	0.854689	0.427344	−	0.904089i	$-0.359449\pi$
$397$	17.0296	0.854689	0.427344	+	0.904089i	$0.359449\pi$
$398$	−5.63105	−0.282259
$399$	−4.83045	−0.241825
$400$	8.92938	0.446469
$401$	−20.7727	−1.03734	−0.518671	−	0.854974i	$-0.673573\pi$
$401$	−20.7727	−1.03734	−0.518671	+	0.854974i	$0.673573\pi$
$402$	−1.63444	−0.0815187
$403$	−44.5031	−2.21686
$404$	14.4410	0.718468
$405$	−30.1856	−1.49993
$406$	11.4189	0.566712
$407$	0	0
$408$	−0.857316	−0.0424435
$409$	0.949968	0.0469729	0.0234865	−	0.999724i	$-0.492523\pi$
$409$	0.949968	0.0469729	0.0234865	+	0.999724i	$0.492523\pi$
$410$	−4.72460	−0.233331
$411$	−0.00310133	−0.000152977 0
$412$	4.35741	0.214674
$413$	14.0075	0.689266
$414$	−2.12610	−0.104492
$415$	−0.270213	−0.0132642
$416$	−5.74629	−0.281735
$417$	0.762694	0.0373493
$418$	−22.9936	−1.12465
$419$	−30.2920	−1.47986	−0.739930	−	0.672684i	$-0.765141\pi$
$419$	−30.2920	−1.47986	−0.739930	+	0.672684i	$0.765141\pi$
$420$	3.50575	0.171063
$421$	−19.7724	−0.963649	−0.481824	−	0.876268i	$-0.660026\pi$
$421$	−19.7724	−0.963649	−0.481824	+	0.876268i	$0.660026\pi$
$422$	23.0510	1.12210
$423$	−10.6044	−0.515601
$424$	2.28501	0.110970
$425$	−23.9092	−1.15977
$426$	0.0303440	0.00147017
$427$	10.7705	0.521222
$428$	12.1421	0.586911
$429$	−8.22658	−0.397183
$430$	−21.2801	−1.02622
$431$	−5.15897	−0.248499	−0.124249	−	0.992251i	$-0.539652\pi$
$431$	−5.15897	−0.248499	−0.124249	+	0.992251i	$0.539652\pi$
$432$	1.88827	0.0908493
$433$	16.4459	0.790339	0.395170	−	0.918608i	$-0.370686\pi$
$433$	16.4459	0.790339	0.395170	+	0.918608i	$0.370686\pi$
$434$	22.7207	1.09063
$435$	−4.65124	−0.223010
$436$	15.0753	0.721978
$437$	−3.77342	−0.180507
$438$	−0.141567	−0.00676434
$439$	8.72749	0.416540	0.208270	−	0.978071i	$-0.433217\pi$
$439$	8.72749	0.416540	0.208270	+	0.978071i	$0.433217\pi$
$440$	16.6879	0.795564
$441$	−4.65547	−0.221689
$442$	15.3862	0.731847
$443$	20.5472	0.976225	0.488112	−	0.872781i	$-0.337686\pi$
$443$	20.5472	0.976225	0.488112	+	0.872781i	$0.337686\pi$
$444$	0	0
$445$	21.0244	0.996650
$446$	15.2412	0.721690
$447$	−5.37587	−0.254270
$448$	2.93372	0.138605
$449$	4.84047	0.228436	0.114218	−	0.993456i	$-0.463564\pi$
$449$	4.84047	0.228436	0.114218	+	0.993456i	$0.463564\pi$
$450$	25.8727	1.21965
$451$	−5.66023	−0.266530
$452$	−0.406240	−0.0191079
$453$	3.25224	0.152804
$454$	12.8314	0.602206
$455$	−62.9176	−2.94962
$456$	1.64653	0.0771056
$457$	28.5767	1.33676	0.668380	−	0.743820i	$-0.266988\pi$
$457$	28.5767	1.33676	0.668380	+	0.743820i	$0.266988\pi$
$458$	20.2815	0.947692
$459$	−5.05601	−0.235994
$460$	2.73860	0.127688
$461$	41.8146	1.94750	0.973749	−	0.227625i	$-0.0730960\pi$
$461$	41.8146	1.94750	0.973749	+	0.227625i	$0.0730960\pi$
$462$	4.20002	0.195403
$463$	−24.6079	−1.14363	−0.571814	−	0.820383i	$-0.693760\pi$
$463$	−24.6079	−1.14363	−0.571814	+	0.820383i	$0.693760\pi$
$464$	−3.89230	−0.180696
$465$	−9.25477	−0.429180
$466$	−20.2108	−0.936248
$467$	8.21176	0.379995	0.189998	−	0.981785i	$-0.439152\pi$
$467$	8.21176	0.379995	0.189998	+	0.981785i	$0.439152\pi$
$468$	−16.6498	−0.769636
$469$	−14.9759	−0.691522
$470$	13.6593	0.630058
$471$	−0.730484	−0.0336589
$472$	−4.77466	−0.219772
$473$	−25.4943	−1.17223
$474$	4.63639	0.212957
$475$	45.9191	2.10691
$476$	−7.85531	−0.360047
$477$	6.62079	0.303145
$478$	−6.87306	−0.314367
$479$	1.46099	0.0667546	0.0333773	−	0.999443i	$-0.489374\pi$
$479$	1.46099	0.0667546	0.0333773	+	0.999443i	$0.489374\pi$
$480$	−1.19499	−0.0545434
$481$	0	0
$482$	14.1313	0.643665
$483$	0.689254	0.0313621
$484$	8.99267	0.408758
$485$	−71.2510	−3.23534
$486$	8.25439	0.374427
$487$	−3.63728	−0.164821	−0.0824103	−	0.996598i	$-0.526262\pi$
$487$	−3.63728	−0.164821	−0.0824103	+	0.996598i	$0.526262\pi$
$488$	−3.67128	−0.166191
$489$	−1.27754	−0.0577725
$490$	5.99664	0.270901
$491$	−22.2913	−1.00599	−0.502996	−	0.864289i	$-0.667769\pi$
$491$	−22.2913	−1.00599	−0.502996	+	0.864289i	$0.667769\pi$
$492$	0.405318	0.0182731
$493$	10.4220	0.469383
$494$	−29.5501	−1.32952
$495$	48.3529	2.17330
$496$	−7.74468	−0.347746
$497$	0.278032	0.0124715
$498$	0.0231812	0.00103878
$499$	26.3887	1.18132	0.590660	−	0.806921i	$-0.298867\pi$
$499$	26.3887	1.18132	0.590660	+	0.806921i	$0.298867\pi$
$500$	−14.6653	−0.655850
$501$	3.98908	0.178219
$502$	21.4139	0.955748
$503$	27.9428	1.24591	0.622954	−	0.782258i	$-0.285932\pi$
$503$	27.9428	1.24591	0.622954	+	0.782258i	$0.285932\pi$
$504$	8.50041	0.378638
$505$	−53.8970	−2.39838
$506$	3.28095	0.145856
$507$	−6.40998	−0.284677
$508$	−11.1969	−0.496784
$509$	18.5327	0.821449	0.410724	−	0.911760i	$-0.365276\pi$
$509$	18.5327	0.821449	0.410724	+	0.911760i	$0.365276\pi$
$510$	3.19968	0.141684
$511$	−1.29713	−0.0573818
$512$	−1.00000	−0.0441942
$513$	9.71036	0.428723
$514$	0.281256	0.0124057
$515$	−16.2628	−0.716623
$516$	1.82559	0.0803672
$517$	16.3643	0.719703
$518$	0	0
$519$	−5.88203	−0.258192
$520$	21.4463	0.940484
$521$	5.19140	0.227439	0.113720	−	0.993513i	$-0.463723\pi$
$521$	5.19140	0.227439	0.113720	+	0.993513i	$0.463723\pi$
$522$	−11.2779	−0.493619
$523$	−1.80007	−0.0787117	−0.0393558	−	0.999225i	$-0.512531\pi$
$523$	−1.80007	−0.0787117	−0.0393558	+	0.999225i	$0.512531\pi$
$524$	−17.0888	−0.746528
$525$	−8.38758	−0.366064
$526$	−12.8063	−0.558380
$527$	20.7371	0.903321
$528$	−1.43163	−0.0623039
$529$	−22.4616	−0.976590
$530$	−8.52814	−0.370439
$531$	−13.8345	−0.600367
$532$	15.0866	0.654086
$533$	−7.27422	−0.315081
$534$	−1.80366	−0.0780518
$535$	−45.3169	−1.95922
$536$	5.10474	0.220491
$537$	−6.61560	−0.285484
$538$	−11.7216	−0.505353
$539$	7.18419	0.309445
$540$	−7.04741	−0.303272
$541$	−9.30927	−0.400237	−0.200118	−	0.979772i	$-0.564133\pi$
$541$	−9.30927	−0.400237	−0.200118	+	0.979772i	$0.564133\pi$
$542$	−5.46425	−0.234710
$543$	−1.20786	−0.0518342
$544$	2.67759	0.114801
$545$	−56.2643	−2.41010
$546$	5.39763	0.230997
$547$	34.3737	1.46971	0.734857	−	0.678222i	$-0.237249\pi$
$547$	34.3737	1.46971	0.734857	+	0.678222i	$0.237249\pi$
$548$	0.00968616	0.000413772 0
$549$	−10.6375	−0.453996
$550$	−39.9261	−1.70245
$551$	−20.0160	−0.852712
$552$	−0.234942	−0.00999978
$553$	42.4818	1.80651
$554$	−6.34878	−0.269734
$555$	0	0
$556$	−2.38206	−0.101022
$557$	−24.6868	−1.04601	−0.523007	−	0.852328i	$-0.675190\pi$
$557$	−24.6868	−1.04601	−0.523007	+	0.852328i	$0.675190\pi$
$558$	−22.4401	−0.949964
$559$	−32.7638	−1.38576
$560$	−10.9493	−0.462691
$561$	3.83333	0.161843
$562$	−7.35463	−0.310236
$563$	32.7573	1.38056	0.690279	−	0.723544i	$-0.257488\pi$
$563$	32.7573	1.38056	0.690279	+	0.723544i	$0.257488\pi$
$564$	−1.17182	−0.0493424
$565$	1.51617	0.0637859
$566$	−26.3239	−1.10647
$567$	23.7275	0.996463
$568$	−0.0947712	−0.00397651
$569$	34.7114	1.45518	0.727589	−	0.686013i	$-0.240641\pi$
$569$	34.7114	1.45518	0.727589	+	0.686013i	$0.240641\pi$
$570$	−6.14518	−0.257393
$571$	−45.0052	−1.88341	−0.941704	−	0.336442i	$-0.890777\pi$
$571$	−45.0052	−1.88341	−0.941704	+	0.336442i	$0.890777\pi$
$572$	25.6935	1.07430
$573$	−4.86755	−0.203345
$574$	3.71380	0.155011
$575$	−6.55216	−0.273244
$576$	−2.89748	−0.120728
$577$	−18.2468	−0.759625	−0.379813	−	0.925063i	$-0.624012\pi$
$577$	−18.2468	−0.759625	−0.379813	+	0.925063i	$0.624012\pi$
$578$	9.83051	0.408895
$579$	−6.93765	−0.288319
$580$	14.5269	0.603196
$581$	0.212402	0.00881193
$582$	6.11254	0.253373
$583$	−10.2170	−0.423146
$584$	0.442146	0.0182961
$585$	62.1404	2.56919
$586$	20.7874	0.858721
$587$	−29.7791	−1.22911	−0.614557	−	0.788872i	$-0.710665\pi$
$587$	−29.7791	−1.22911	−0.614557	+	0.788872i	$0.710665\pi$
$588$	−0.514445	−0.0212153
$589$	−39.8268	−1.64103
$590$	17.8200	0.733639
$591$	4.39913	0.180956
$592$	0	0
$593$	21.5120	0.883392	0.441696	−	0.897165i	$-0.354377\pi$
$593$	21.5120	0.883392	0.441696	+	0.897165i	$0.354377\pi$
$594$	−8.44304	−0.346422
$595$	29.3176	1.20191
$596$	16.7900	0.687747
$597$	−1.80296	−0.0737902
$598$	4.21649	0.172425
$599$	−1.94068	−0.0792940	−0.0396470	−	0.999214i	$-0.512623\pi$
$599$	−1.94068	−0.0792940	−0.0396470	+	0.999214i	$0.512623\pi$
$600$	2.85902	0.116719
$601$	−4.10385	−0.167400	−0.0836998	−	0.996491i	$-0.526674\pi$
$601$	−4.10385	−0.167400	−0.0836998	+	0.996491i	$0.526674\pi$
$602$	16.7273	0.681754
$603$	14.7909	0.602332
$604$	−10.1575	−0.413302
$605$	−33.5625	−1.36451
$606$	4.62376	0.187827
$607$	−5.19962	−0.211046	−0.105523	−	0.994417i	$-0.533652\pi$
$607$	−5.19962	−0.211046	−0.105523	+	0.994417i	$0.533652\pi$
$608$	−5.14247	−0.208555
$609$	3.65613	0.148154
$610$	13.7020	0.554777
$611$	21.0305	0.850805
$612$	7.75827	0.313610
$613$	−18.0439	−0.728787	−0.364394	−	0.931245i	$-0.618724\pi$
$613$	−18.0439	−0.728787	−0.364394	+	0.931245i	$0.618724\pi$
$614$	−7.73062	−0.311982
$615$	−1.51273	−0.0609992
$616$	−13.1176	−0.528523
$617$	−49.2054	−1.98093	−0.990467	−	0.137751i	$-0.956013\pi$
$617$	−49.2054	−1.98093	−0.990467	+	0.137751i	$0.956013\pi$
$618$	1.39516	0.0561217
$619$	−25.8553	−1.03921	−0.519606	−	0.854406i	$-0.673921\pi$
$619$	−25.8553	−1.03921	−0.519606	+	0.854406i	$0.673921\pi$
$620$	28.9047	1.16084
$621$	−1.38557	−0.0556008
$622$	−27.6312	−1.10791
$623$	−16.5263	−0.662113
$624$	−1.83986	−0.0736532
$625$	10.0869	0.403476
$626$	12.3333	0.492937
$627$	−7.36214	−0.294015
$628$	2.28147	0.0910404
$629$	0	0
$630$	−31.7253	−1.26397
$631$	−31.1715	−1.24092	−0.620460	−	0.784238i	$-0.713054\pi$
$631$	−31.1715	−1.24092	−0.620460	+	0.784238i	$0.713054\pi$
$632$	−14.4805	−0.576003
$633$	7.38050	0.293349
$634$	0.315766	0.0125407
$635$	41.7893	1.65836
$636$	0.731620	0.0290106
$637$	9.23271	0.365813
$638$	17.4037	0.689019
$639$	−0.274598	−0.0108629
$640$	3.73221	0.147528
$641$	13.0685	0.516175	0.258088	−	0.966121i	$-0.416908\pi$
$641$	13.0685	0.516175	0.258088	+	0.966121i	$0.416908\pi$
$642$	3.88768	0.153435
$643$	9.93462	0.391783	0.195892	−	0.980626i	$-0.437240\pi$
$643$	9.93462	0.391783	0.195892	+	0.980626i	$0.437240\pi$
$644$	−2.15270	−0.0848281
$645$	−6.81349	−0.268281
$646$	13.7694	0.541751
$647$	15.3932	0.605168	0.302584	−	0.953123i	$-0.402151\pi$
$647$	15.3932	0.605168	0.302584	+	0.953123i	$0.402151\pi$
$648$	−8.08786	−0.317721
$649$	21.3490	0.838023
$650$	−51.3108	−2.01257
$651$	7.27476	0.285120
$652$	3.99005	0.156263
$653$	−36.4160	−1.42507	−0.712534	−	0.701638i	$-0.752452\pi$
$653$	−36.4160	−1.42507	−0.712534	+	0.701638i	$0.752452\pi$
$654$	4.82685	0.188745
$655$	63.7790	2.49205
$656$	−1.26590	−0.0494250
$657$	1.28111	0.0499809
$658$	−10.7370	−0.418571
$659$	−27.5451	−1.07300	−0.536502	−	0.843899i	$-0.680255\pi$
$659$	−27.5451	−1.07300	−0.536502	+	0.843899i	$0.680255\pi$
$660$	5.34316	0.207982
$661$	−46.4292	−1.80589	−0.902943	−	0.429759i	$-0.858598\pi$
$661$	−46.4292	−1.80589	−0.902943	+	0.429759i	$0.858598\pi$
$662$	−16.9231	−0.657736
$663$	4.92638	0.191325
$664$	−0.0724002	−0.00280967
$665$	−56.3063	−2.18346
$666$	0	0
$667$	2.85608	0.110588
$668$	−12.4588	−0.482046
$669$	4.87994	0.188670
$670$	−19.0519	−0.736041
$671$	16.4154	0.633711
$672$	0.939325	0.0362352
$673$	19.1950	0.739914	0.369957	−	0.929049i	$-0.379372\pi$
$673$	19.1950	0.739914	0.369957	+	0.929049i	$0.379372\pi$
$674$	−15.5319	−0.598265
$675$	16.8610	0.648982
$676$	20.0198	0.769992
$677$	21.8139	0.838376	0.419188	−	0.907899i	$-0.362315\pi$
$677$	21.8139	0.838376	0.419188	+	0.907899i	$0.362315\pi$
$678$	−0.130071	−0.00499534
$679$	56.0072	2.14936
$680$	−9.99333	−0.383227
$681$	4.10837	0.157433
$682$	34.6289	1.32601
$683$	−21.1418	−0.808968	−0.404484	−	0.914545i	$-0.632549\pi$
$683$	−21.1418	−0.808968	−0.404484	+	0.914545i	$0.632549\pi$
$684$	−14.9002	−0.569724
$685$	−0.0361508	−0.00138125
$686$	15.8224	0.604101
$687$	6.49377	0.247753
$688$	−5.70174	−0.217377
$689$	−13.1303	−0.500226
$690$	0.876851	0.0333812
$691$	42.4308	1.61414	0.807072	−	0.590453i	$-0.201051\pi$
$691$	42.4308	1.61414	0.807072	+	0.590453i	$0.201051\pi$
$692$	18.3709	0.698357
$693$	−38.0080	−1.44381
$694$	−23.8773	−0.906370
$695$	8.89036	0.337231
$696$	−1.24624	−0.0472388
$697$	3.38956	0.128389
$698$	−18.8292	−0.712695
$699$	−6.47114	−0.244761
$700$	26.1963	0.990128
$701$	−2.56487	−0.0968738	−0.0484369	−	0.998826i	$-0.515424\pi$
$701$	−2.56487	−0.0968738	−0.0484369	+	0.998826i	$0.515424\pi$
$702$	−10.8505	−0.409527
$703$	0	0
$704$	4.47132	0.168519
$705$	4.37347	0.164714
$706$	2.49614	0.0939434
$707$	42.3660	1.59334
$708$	−1.52876	−0.0574543
$709$	−11.5917	−0.435334	−0.217667	−	0.976023i	$-0.569845\pi$
$709$	−11.5917	−0.435334	−0.217667	+	0.976023i	$0.569845\pi$
$710$	0.353706	0.0132743
$711$	−41.9570	−1.57351
$712$	5.63322	0.211114
$713$	5.68286	0.212825
$714$	−2.51513	−0.0941262
$715$	−95.8934	−3.58621
$716$	20.6620	0.772175
$717$	−2.20063	−0.0821840
$718$	−12.0536	−0.449836
$719$	−2.58903	−0.0965546	−0.0482773	−	0.998834i	$-0.515373\pi$
$719$	−2.58903	−0.0965546	−0.0482773	+	0.998834i	$0.515373\pi$
$720$	10.8140	0.403014
$721$	12.7834	0.476080
$722$	−7.44500	−0.277074
$723$	4.52460	0.168272
$724$	3.77241	0.140201
$725$	−34.7558	−1.29080
$726$	2.87929	0.106861
$727$	24.2191	0.898235	0.449117	−	0.893473i	$-0.351738\pi$
$727$	24.2191	0.898235	0.449117	+	0.893473i	$0.351738\pi$
$728$	−16.8580	−0.624799
$729$	−21.6207	−0.800766
$730$	−1.65018	−0.0610759
$731$	15.2669	0.564667
$732$	−1.17548	−0.0434469
$733$	7.45122	0.275217	0.137609	−	0.990487i	$-0.456058\pi$
$733$	7.45122	0.275217	0.137609	+	0.990487i	$0.456058\pi$
$734$	−37.0543	−1.36770
$735$	1.92002	0.0708208
$736$	0.733776	0.0270473
$737$	−22.8249	−0.840766
$738$	−3.66792	−0.135018
$739$	16.4721	0.605937	0.302968	−	0.953001i	$-0.402022\pi$
$739$	16.4721	0.605937	0.302968	+	0.953001i	$0.402022\pi$
$740$	0	0
$741$	−9.46141	−0.347573
$742$	6.70359	0.246097
$743$	17.0926	0.627068	0.313534	−	0.949577i	$-0.398487\pi$
$743$	17.0926	0.627068	0.313534	+	0.949577i	$0.398487\pi$
$744$	−2.47970	−0.0909104
$745$	−62.6640	−2.29583
$746$	5.38668	0.197220
$747$	−0.209779	−0.00767540
$748$	−11.9724	−0.437753
$749$	35.6216	1.30158
$750$	−4.69555	−0.171457
$751$	−48.2150	−1.75939	−0.879695	−	0.475539i	$-0.842253\pi$
$751$	−48.2150	−1.75939	−0.879695	+	0.475539i	$0.842253\pi$
$752$	3.65985	0.133461
$753$	6.85633	0.249859
$754$	22.3663	0.814532
$755$	37.9098	1.37968
$756$	5.53965	0.201475
$757$	−47.1168	−1.71249	−0.856244	−	0.516572i	$-0.827208\pi$
$757$	−47.1168	−1.71249	−0.856244	+	0.516572i	$0.827208\pi$
$758$	−21.6224	−0.785363
$759$	1.05050	0.0381307
$760$	19.1928	0.696195
$761$	14.4394	0.523427	0.261713	−	0.965146i	$-0.415712\pi$
$761$	14.4394	0.523427	0.261713	+	0.965146i	$0.415712\pi$
$762$	−3.58506	−0.129873
$763$	44.2269	1.60112
$764$	15.2024	0.550005
$765$	−28.9555	−1.04689
$766$	−37.0449	−1.33849
$767$	27.4366	0.990678
$768$	−0.320182	−0.0115536
$769$	0.332592	0.0119936	0.00599678	−	0.999982i	$-0.498091\pi$
$769$	0.332592	0.0119936	0.00599678	+	0.999982i	$0.498091\pi$
$770$	48.9576	1.76431
$771$	0.0900531	0.00324318
$772$	21.6678	0.779843
$773$	−9.73329	−0.350082	−0.175041	−	0.984561i	$-0.556006\pi$
$773$	−9.73329	−0.350082	−0.175041	+	0.984561i	$0.556006\pi$
$774$	−16.5207	−0.593824
$775$	−69.1551	−2.48413
$776$	−19.0908	−0.685321
$777$	0	0
$778$	22.5262	0.807604
$779$	−6.50985	−0.233239
$780$	6.86673	0.245868
$781$	0.423752	0.0151630
$782$	−1.96475	−0.0702594
$783$	−7.34970	−0.262657
$784$	1.60673	0.0573831
$785$	−8.51491	−0.303910
$786$	−5.47152	−0.195163
$787$	−43.8694	−1.56377	−0.781887	−	0.623420i	$-0.785743\pi$
$787$	−43.8694	−1.56377	−0.781887	+	0.623420i	$0.785743\pi$
$788$	−13.7395	−0.489449
$789$	−4.10034	−0.145976
$790$	54.0442	1.92281
$791$	−1.19180	−0.0423754
$792$	12.9556	0.460356
$793$	21.0962	0.749149
$794$	−17.0296	−0.604356
$795$	−2.73056	−0.0968429
$796$	5.63105	0.199587
$797$	45.6572	1.61726	0.808630	−	0.588317i	$-0.200209\pi$
$797$	45.6572	1.61726	0.808630	+	0.588317i	$0.200209\pi$
$798$	4.83045	0.170996
$799$	−9.79958	−0.346684
$800$	−8.92938	−0.315701
$801$	16.3222	0.576715
$802$	20.7727	0.733511
$803$	−1.97697	−0.0697659
$804$	1.63444	0.0576424
$805$	8.03431	0.283172
$806$	44.5031	1.56756
$807$	−3.75303	−0.132113
$808$	−14.4410	−0.508034
$809$	6.66702	0.234400	0.117200	−	0.993108i	$-0.462608\pi$
$809$	6.66702	0.234400	0.117200	+	0.993108i	$0.462608\pi$
$810$	30.1856	1.06061
$811$	24.9303	0.875421	0.437711	−	0.899116i	$-0.355789\pi$
$811$	24.9303	0.875421	0.437711	+	0.899116i	$0.355789\pi$
$812$	−11.4189	−0.400726
$813$	−1.74955	−0.0613596
$814$	0	0
$815$	−14.8917	−0.521634
$816$	0.857316	0.0300121
$817$	−29.3210	−1.02581
$818$	−0.949968	−0.0332149
$819$	−48.8458	−1.70681
$820$	4.72460	0.164990
$821$	36.1645	1.26215	0.631074	−	0.775722i	$-0.282614\pi$
$821$	36.1645	1.26215	0.631074	+	0.775722i	$0.282614\pi$
$822$	0.00310133	0.000108171 0
$823$	−23.7373	−0.827430	−0.413715	−	0.910406i	$-0.635769\pi$
$823$	−23.7373	−0.827430	−0.413715	+	0.910406i	$0.635769\pi$
$824$	−4.35741	−0.151797
$825$	−12.7836	−0.445068
$826$	−14.0075	−0.487385
$827$	−37.0497	−1.28834	−0.644172	−	0.764881i	$-0.722798\pi$
$827$	−37.0497	−1.28834	−0.644172	+	0.764881i	$0.722798\pi$
$828$	2.12610	0.0738872
$829$	−22.0397	−0.765469	−0.382735	−	0.923858i	$-0.625018\pi$
$829$	−22.0397	−0.765469	−0.382735	+	0.923858i	$0.625018\pi$
$830$	0.270213	0.00937922
$831$	−2.03276	−0.0705158
$832$	5.74629	0.199217
$833$	−4.30216	−0.149061
$834$	−0.762694	−0.0264099
$835$	46.4988	1.60916
$836$	22.9936	0.795251
$837$	−14.6240	−0.505480
$838$	30.2920	1.04642
$839$	40.4379	1.39607	0.698035	−	0.716063i	$-0.254058\pi$
$839$	40.4379	1.39607	0.698035	+	0.716063i	$0.254058\pi$
$840$	−3.50575	−0.120960
$841$	−13.8500	−0.477586
$842$	19.7724	0.681403
$843$	−2.35482	−0.0811043
$844$	−23.0510	−0.793447
$845$	−74.7181	−2.57038
$846$	10.6044	0.364585
$847$	26.3820	0.906497
$848$	−2.28501	−0.0784677
$849$	−8.42842	−0.289263
$850$	23.9092	0.820079
$851$	0	0
$852$	−0.0303440	−0.00103957
$853$	32.5765	1.11540	0.557699	−	0.830043i	$-0.311684\pi$
$853$	32.5765	1.11540	0.557699	+	0.830043i	$0.311684\pi$
$854$	−10.7705	−0.368559
$855$	55.6107	1.90185
$856$	−12.1421	−0.415009
$857$	−19.1790	−0.655143	−0.327572	−	0.944826i	$-0.606230\pi$
$857$	−19.1790	−0.655143	−0.327572	+	0.944826i	$0.606230\pi$
$858$	8.22658	0.280851
$859$	0.252055	0.00859999	0.00429999	−	0.999991i	$-0.498631\pi$
$859$	0.252055	0.00859999	0.00429999	+	0.999991i	$0.498631\pi$
$860$	21.2801	0.725644
$861$	1.18909	0.0405241
$862$	5.15897	0.175715
$863$	7.81387	0.265987	0.132994	−	0.991117i	$-0.457541\pi$
$863$	7.81387	0.265987	0.132994	+	0.991117i	$0.457541\pi$
$864$	−1.88827	−0.0642401
$865$	−68.5640	−2.33125
$866$	−16.4459	−0.558854
$867$	3.14755	0.106896
$868$	−22.7207	−0.771192
$869$	64.7469	2.19639
$870$	4.65124	0.157692
$871$	−29.3333	−0.993921
$872$	−15.0753	−0.510516
$873$	−55.3154	−1.87214
$874$	3.77342	0.127638
$875$	−43.0238	−1.45447
$876$	0.141567	0.00478311
$877$	−30.9298	−1.04443	−0.522213	−	0.852815i	$-0.674893\pi$
$877$	−30.9298	−1.04443	−0.522213	+	0.852815i	$0.674893\pi$
$878$	−8.72749	−0.294538
$879$	6.65576	0.224493
$880$	−16.6879	−0.562548
$881$	−40.7550	−1.37307	−0.686535	−	0.727096i	$-0.740869\pi$
$881$	−40.7550	−1.37307	−0.686535	+	0.727096i	$0.740869\pi$
$882$	4.65547	0.156758
$883$	−19.9199	−0.670359	−0.335180	−	0.942154i	$-0.608797\pi$
$883$	−19.9199	−0.670359	−0.335180	+	0.942154i	$0.608797\pi$
$884$	−15.3862	−0.517494
$885$	5.70565	0.191793
$886$	−20.5472	−0.690295
$887$	16.2717	0.546350	0.273175	−	0.961964i	$-0.411926\pi$
$887$	16.2717	0.546350	0.273175	+	0.961964i	$0.411926\pi$
$888$	0	0
$889$	−32.8487	−1.10171
$890$	−21.0244	−0.704738
$891$	36.1634	1.21152
$892$	−15.2412	−0.510312
$893$	18.8207	0.629810
$894$	5.37587	0.179796
$895$	−77.1149	−2.57767
$896$	−2.93372	−0.0980088
$897$	1.35004	0.0450766
$898$	−4.84047	−0.161529
$899$	30.1446	1.00538
$900$	−25.8727	−0.862424
$901$	6.11833	0.203831
$902$	5.66023	0.188465
$903$	5.35578	0.178229
$904$	0.406240	0.0135114
$905$	−14.0794	−0.468016
$906$	−3.25224	−0.108048
$907$	−21.9857	−0.730025	−0.365012	−	0.931003i	$-0.618935\pi$
$907$	−21.9857	−0.730025	−0.365012	+	0.931003i	$0.618935\pi$
$908$	−12.8314	−0.425824
$909$	−41.8427	−1.38783
$910$	62.9176	2.08570
$911$	−56.0393	−1.85667	−0.928333	−	0.371750i	$-0.878758\pi$
$911$	−56.0393	−1.85667	−0.928333	+	0.371750i	$0.878758\pi$
$912$	−1.64653	−0.0545219
$913$	0.323724	0.0107137
$914$	−28.5767	−0.945233
$915$	4.38712	0.145034
$916$	−20.2815	−0.670120
$917$	−50.1338	−1.65556
$918$	5.05601	0.166873
$919$	9.19098	0.303183	0.151591	−	0.988443i	$-0.451560\pi$
$919$	9.19098	0.303183	0.151591	+	0.988443i	$0.451560\pi$
$920$	−2.73860	−0.0902891
$921$	−2.47520	−0.0815608
$922$	−41.8146	−1.37709
$923$	0.544583	0.0179252
$924$	−4.20002	−0.138170
$925$	0	0
$926$	24.6079	0.808667
$927$	−12.6255	−0.414676
$928$	3.89230	0.127771
$929$	−16.7411	−0.549257	−0.274629	−	0.961550i	$-0.588555\pi$
$929$	−16.7411	−0.549257	−0.274629	+	0.961550i	$0.588555\pi$
$930$	9.25477	0.303476
$931$	8.26255	0.270794
$932$	20.2108	0.662027
$933$	−8.84701	−0.289638
$934$	−8.21176	−0.268697
$935$	44.6833	1.46130
$936$	16.6498	0.544215
$937$	52.7728	1.72401	0.862006	−	0.506898i	$-0.169208\pi$
$937$	52.7728	1.72401	0.862006	+	0.506898i	$0.169208\pi$
$938$	14.9759	0.488980
$939$	3.94890	0.128867
$940$	−13.6593	−0.445518
$941$	−6.39927	−0.208610	−0.104305	−	0.994545i	$-0.533262\pi$
$941$	−6.39927	−0.208610	−0.104305	+	0.994545i	$0.533262\pi$
$942$	0.730484	0.0238005
$943$	0.928886	0.0302487
$944$	4.77466	0.155402
$945$	−20.6751	−0.672562
$946$	25.4943	0.828890
$947$	−12.8938	−0.418992	−0.209496	−	0.977810i	$-0.567182\pi$
$947$	−12.8938	−0.418992	−0.209496	+	0.977810i	$0.567182\pi$
$948$	−4.63639	−0.150583
$949$	−2.54070	−0.0824745
$950$	−45.9191	−1.48981
$951$	0.101103	0.00327848
$952$	7.85531	0.254592
$953$	−32.6387	−1.05727	−0.528635	−	0.848849i	$-0.677296\pi$
$953$	−32.6387	−1.05727	−0.528635	+	0.848849i	$0.677296\pi$
$954$	−6.62079	−0.214356
$955$	−56.7387	−1.83602
$956$	6.87306	0.222291
$957$	5.57235	0.180129
$958$	−1.46099	−0.0472026
$959$	0.0284165	0.000917617 0
$960$	1.19499	0.0385680
$961$	28.9800	0.934839
$962$	0	0
$963$	−35.1816	−1.13371
$964$	−14.1313	−0.455140
$965$	−80.8689	−2.60326
$966$	−0.689254	−0.0221764
$967$	58.4647	1.88010	0.940050	−	0.341038i	$-0.110778\pi$
$967$	58.4647	1.88010	0.940050	+	0.341038i	$0.110778\pi$
$968$	−8.99267	−0.289035
$969$	4.40872	0.141629
$970$	71.2510	2.28773
$971$	−4.47224	−0.143521	−0.0717606	−	0.997422i	$-0.522862\pi$
$971$	−4.47224	−0.143521	−0.0717606	+	0.997422i	$0.522862\pi$
$972$	−8.25439	−0.264760
$973$	−6.98832	−0.224035
$974$	3.63728	0.116546
$975$	−16.4288	−0.526142
$976$	3.67128	0.117515
$977$	42.1220	1.34760	0.673802	−	0.738912i	$-0.264660\pi$
$977$	42.1220	1.34760	0.673802	+	0.738912i	$0.264660\pi$
$978$	1.27754	0.0408513
$979$	−25.1879	−0.805009
$980$	−5.99664	−0.191556
$981$	−43.6806	−1.39461
$982$	22.2913	0.711343
$983$	15.0374	0.479618	0.239809	−	0.970820i	$-0.422915\pi$
$983$	15.0374	0.479618	0.239809	+	0.970820i	$0.422915\pi$
$984$	−0.405318	−0.0129211
$985$	51.2786	1.63387
$986$	−10.4220	−0.331904
$987$	−3.43779	−0.109426
$988$	29.5501	0.940114
$989$	4.18380	0.133037
$990$	−48.3529	−1.53676
$991$	36.1371	1.14793	0.573966	−	0.818879i	$-0.305404\pi$
$991$	36.1371	1.14793	0.573966	+	0.818879i	$0.305404\pi$
$992$	7.74468	0.245894
$993$	−5.41847	−0.171950
$994$	−0.278032	−0.00881865
$995$	−21.0162	−0.666260
$996$	−0.0231812	−0.000734526 0
$997$	31.5891	1.00044	0.500218	−	0.865899i	$-0.333253\pi$
$997$	31.5891	1.00044	0.500218	+	0.865899i	$0.333253\pi$
$998$	−26.3887	−0.835319
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.w.1.8	✓	18
37.36	even	2		2738.2.a.x.1.8	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.w.1.8	✓	18	1.1	even	1	trivial
2738.2.a.x.1.8	yes	18	37.36	even	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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.320182 q^{3} +1.00000 q^{4} -3.73221 q^{5} +0.320182 q^{6} +2.93372 q^{7} -1.00000 q^{8} -2.89748 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.320182 q^{3} +1.00000 q^{4} -3.73221 q^{5} +0.320182 q^{6} +2.93372 q^{7} -1.00000 q^{8} -2.89748 q^{9} +3.73221 q^{10} +4.47132 q^{11} -0.320182 q^{12} +5.74629 q^{13} -2.93372 q^{14} +1.19499 q^{15} +1.00000 q^{16} -2.67759 q^{17} +2.89748 q^{18} +5.14247 q^{19} -3.73221 q^{20} -0.939325 q^{21} -4.47132 q^{22} -0.733776 q^{23} +0.320182 q^{24} +8.92938 q^{25} -5.74629 q^{26} +1.88827 q^{27} +2.93372 q^{28} -3.89230 q^{29} -1.19499 q^{30} -7.74468 q^{31} -1.00000 q^{32} -1.43163 q^{33} +2.67759 q^{34} -10.9493 q^{35} -2.89748 q^{36} -5.14247 q^{38} -1.83986 q^{39} +3.73221 q^{40} -1.26590 q^{41} +0.939325 q^{42} -5.70174 q^{43} +4.47132 q^{44} +10.8140 q^{45} +0.733776 q^{46} +3.65985 q^{47} -0.320182 q^{48} +1.60673 q^{49} -8.92938 q^{50} +0.857316 q^{51} +5.74629 q^{52} -2.28501 q^{53} -1.88827 q^{54} -16.6879 q^{55} -2.93372 q^{56} -1.64653 q^{57} +3.89230 q^{58} +4.77466 q^{59} +1.19499 q^{60} +3.67128 q^{61} +7.74468 q^{62} -8.50041 q^{63} +1.00000 q^{64} -21.4463 q^{65} +1.43163 q^{66} -5.10474 q^{67} -2.67759 q^{68} +0.234942 q^{69} +10.9493 q^{70} +0.0947712 q^{71} +2.89748 q^{72} -0.442146 q^{73} -2.85902 q^{75} +5.14247 q^{76} +13.1176 q^{77} +1.83986 q^{78} +14.4805 q^{79} -3.73221 q^{80} +8.08786 q^{81} +1.26590 q^{82} +0.0724002 q^{83} -0.939325 q^{84} +9.99333 q^{85} +5.70174 q^{86} +1.24624 q^{87} -4.47132 q^{88} -5.63322 q^{89} -10.8140 q^{90} +16.8580 q^{91} -0.733776 q^{92} +2.47970 q^{93} -3.65985 q^{94} -19.1928 q^{95} +0.320182 q^{96} +19.0908 q^{97} -1.60673 q^{98} -12.9556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9} + 9 q^{10} + 10 q^{11} + 8 q^{12} - 9 q^{13} - 18 q^{14} + 4 q^{15} + 18 q^{16} - 13 q^{17} - 26 q^{18} - 2 q^{19} - 9 q^{20} + 24 q^{21} - 10 q^{22} + 11 q^{23} - 8 q^{24} + 49 q^{25} + 9 q^{26} + 29 q^{27} + 18 q^{28} - 30 q^{29} - 4 q^{30} + 8 q^{31} - 18 q^{32} + 42 q^{33} + 13 q^{34} - 25 q^{35} + 26 q^{36} + 2 q^{38} + 45 q^{39} + 9 q^{40} + 5 q^{41} - 24 q^{42} + 3 q^{43} + 10 q^{44} + 30 q^{45} - 11 q^{46} + 37 q^{47} + 8 q^{48} + 50 q^{49} - 49 q^{50} - 10 q^{51} - 9 q^{52} + 25 q^{53} - 29 q^{54} + 44 q^{55} - 18 q^{56} - 22 q^{57} + 30 q^{58} - 26 q^{59} + 4 q^{60} - 27 q^{61} - 8 q^{62} + 74 q^{63} + 18 q^{64} - 16 q^{65} - 42 q^{66} + 23 q^{67} - 13 q^{68} + 2 q^{69} + 25 q^{70} - 25 q^{71} - 26 q^{72} + 77 q^{73} - q^{75} - 2 q^{76} - 6 q^{77} - 45 q^{78} + 13 q^{79} - 9 q^{80} + 38 q^{81} - 5 q^{82} - 10 q^{83} + 24 q^{84} + 16 q^{85} - 3 q^{86} + 55 q^{87} - 10 q^{88} - 55 q^{89} - 30 q^{90} - 12 q^{91} + 11 q^{92} + 58 q^{93} - 37 q^{94} - 18 q^{95} - 8 q^{96} + 59 q^{97} - 50 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9 + 9 * q^10 + 10 * q^11 + 8 * q^12 - 9 * q^13 - 18 * q^14 + 4 * q^15 + 18 * q^16 - 13 * q^17 - 26 * q^18 - 2 * q^19 - 9 * q^20 + 24 * q^21 - 10 * q^22 + 11 * q^23 - 8 * q^24 + 49 * q^25 + 9 * q^26 + 29 * q^27 + 18 * q^28 - 30 * q^29 - 4 * q^30 + 8 * q^31 - 18 * q^32 + 42 * q^33 + 13 * q^34 - 25 * q^35 + 26 * q^36 + 2 * q^38 + 45 * q^39 + 9 * q^40 + 5 * q^41 - 24 * q^42 + 3 * q^43 + 10 * q^44 + 30 * q^45 - 11 * q^46 + 37 * q^47 + 8 * q^48 + 50 * q^49 - 49 * q^50 - 10 * q^51 - 9 * q^52 + 25 * q^53 - 29 * q^54 + 44 * q^55 - 18 * q^56 - 22 * q^57 + 30 * q^58 - 26 * q^59 + 4 * q^60 - 27 * q^61 - 8 * q^62 + 74 * q^63 + 18 * q^64 - 16 * q^65 - 42 * q^66 + 23 * q^67 - 13 * q^68 + 2 * q^69 + 25 * q^70 - 25 * q^71 - 26 * q^72 + 77 * q^73 - q^75 - 2 * q^76 - 6 * q^77 - 45 * q^78 + 13 * q^79 - 9 * q^80 + 38 * q^81 - 5 * q^82 - 10 * q^83 + 24 * q^84 + 16 * q^85 - 3 * q^86 + 55 * q^87 - 10 * q^88 - 55 * q^89 - 30 * q^90 - 12 * q^91 + 11 * q^92 + 58 * q^93 - 37 * q^94 - 18 * q^95 - 8 * q^96 + 59 * q^97 - 50 * q^98 + 11 * q^99

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