LMFDB - Embedded newform 1334.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 44x^{6} + 87x^{5} - 209x^{4} - 160x^{3} + 348x^{2} + 12x - 100 $ x^9 - 3x^8 - 16x^7 + 44x^6 + 87x^5 - 209x^4 - 160x^3 + 348x^2 + 12x - 100
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			1.7
Root			$-2.05766$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.05766 q^{3} +1.00000 q^{4} +3.66144 q^{5} -2.05766 q^{6} +4.21443 q^{7} -1.00000 q^{8} +1.23398 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.05766 q^{3} +1.00000 q^{4} +3.66144 q^{5} -2.05766 q^{6} +4.21443 q^{7} -1.00000 q^{8} +1.23398 q^{9} -3.66144 q^{10} -3.07114 q^{11} +2.05766 q^{12} +3.04852 q^{13} -4.21443 q^{14} +7.53401 q^{15} +1.00000 q^{16} -6.40651 q^{17} -1.23398 q^{18} +3.39989 q^{19} +3.66144 q^{20} +8.67188 q^{21} +3.07114 q^{22} -1.00000 q^{23} -2.05766 q^{24} +8.40614 q^{25} -3.04852 q^{26} -3.63387 q^{27} +4.21443 q^{28} +1.00000 q^{29} -7.53401 q^{30} -1.07114 q^{31} -1.00000 q^{32} -6.31937 q^{33} +6.40651 q^{34} +15.4309 q^{35} +1.23398 q^{36} -0.533936 q^{37} -3.39989 q^{38} +6.27282 q^{39} -3.66144 q^{40} -2.53394 q^{41} -8.67188 q^{42} +7.18646 q^{43} -3.07114 q^{44} +4.51814 q^{45} +1.00000 q^{46} -7.95918 q^{47} +2.05766 q^{48} +10.7614 q^{49} -8.40614 q^{50} -13.1824 q^{51} +3.04852 q^{52} -3.19348 q^{53} +3.63387 q^{54} -11.2448 q^{55} -4.21443 q^{56} +6.99584 q^{57} -1.00000 q^{58} -8.47686 q^{59} +7.53401 q^{60} -11.7310 q^{61} +1.07114 q^{62} +5.20053 q^{63} +1.00000 q^{64} +11.1620 q^{65} +6.31937 q^{66} -5.27790 q^{67} -6.40651 q^{68} -2.05766 q^{69} -15.4309 q^{70} +3.30120 q^{71} -1.23398 q^{72} -6.15868 q^{73} +0.533936 q^{74} +17.2970 q^{75} +3.39989 q^{76} -12.9431 q^{77} -6.27282 q^{78} -9.10993 q^{79} +3.66144 q^{80} -11.1792 q^{81} +2.53394 q^{82} +13.6365 q^{83} +8.67188 q^{84} -23.4570 q^{85} -7.18646 q^{86} +2.05766 q^{87} +3.07114 q^{88} +3.79632 q^{89} -4.51814 q^{90} +12.8478 q^{91} -1.00000 q^{92} -2.20404 q^{93} +7.95918 q^{94} +12.4485 q^{95} -2.05766 q^{96} +18.0174 q^{97} -10.7614 q^{98} -3.78972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * 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
$3$	2.05766	1.18799	0.593996	−	0.804468i	$-0.297549\pi$
$3$	2.05766	1.18799	0.593996	+	0.804468i	$0.297549\pi$
$4$	1.00000	0.500000
$5$	3.66144	1.63745	0.818723	−	0.574189i	$-0.194683\pi$
$5$	3.66144	1.63745	0.818723	+	0.574189i	$0.194683\pi$
$6$	−2.05766	−0.840038
$7$	4.21443	1.59291	0.796453	−	0.604701i	$-0.206707\pi$
$7$	4.21443	1.59291	0.796453	+	0.604701i	$0.206707\pi$
$8$	−1.00000	−0.353553
$9$	1.23398	0.411327
$10$	−3.66144	−1.15785
$11$	−3.07114	−0.925982	−0.462991	−	0.886363i	$-0.653224\pi$
$11$	−3.07114	−0.925982	−0.462991	+	0.886363i	$0.653224\pi$
$12$	2.05766	0.593996
$13$	3.04852	0.845507	0.422753	−	0.906245i	$-0.361064\pi$
$13$	3.04852	0.845507	0.422753	+	0.906245i	$0.361064\pi$
$14$	−4.21443	−1.12635
$15$	7.53401	1.94527
$16$	1.00000	0.250000
$17$	−6.40651	−1.55381	−0.776903	−	0.629620i	$-0.783211\pi$
$17$	−6.40651	−1.55381	−0.776903	+	0.629620i	$0.783211\pi$
$18$	−1.23398	−0.290852
$19$	3.39989	0.779989	0.389995	−	0.920817i	$-0.372477\pi$
$19$	3.39989	0.779989	0.389995	+	0.920817i	$0.372477\pi$
$20$	3.66144	0.818723
$21$	8.67188	1.89236
$22$	3.07114	0.654768
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.05766	−0.420019
$25$	8.40614	1.68123
$26$	−3.04852	−0.597863
$27$	−3.63387	−0.699339
$28$	4.21443	0.796453
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−7.53401	−1.37552
$31$	−1.07114	−0.192382	−0.0961909	−	0.995363i	$-0.530666\pi$
$31$	−1.07114	−0.192382	−0.0961909	+	0.995363i	$0.530666\pi$
$32$	−1.00000	−0.176777
$33$	−6.31937	−1.10006
$34$	6.40651	1.09871
$35$	15.4309	2.60830
$36$	1.23398	0.205663
$37$	−0.533936	−0.0877785	−0.0438892	−	0.999036i	$-0.513975\pi$
$37$	−0.533936	−0.0877785	−0.0438892	+	0.999036i	$0.513975\pi$
$38$	−3.39989	−0.551536
$39$	6.27282	1.00446
$40$	−3.66144	−0.578924
$41$	−2.53394	−0.395734	−0.197867	−	0.980229i	$-0.563401\pi$
$41$	−2.53394	−0.395734	−0.197867	+	0.980229i	$0.563401\pi$
$42$	−8.67188	−1.33810
$43$	7.18646	1.09593	0.547963	−	0.836503i	$-0.315404\pi$
$43$	7.18646	1.09593	0.547963	+	0.836503i	$0.315404\pi$
$44$	−3.07114	−0.462991
$45$	4.51814	0.673525
$46$	1.00000	0.147442
$47$	−7.95918	−1.16097	−0.580483	−	0.814272i	$-0.697136\pi$
$47$	−7.95918	−1.16097	−0.580483	+	0.814272i	$0.697136\pi$
$48$	2.05766	0.296998
$49$	10.7614	1.53735
$50$	−8.40614	−1.18881
$51$	−13.1824	−1.84591
$52$	3.04852	0.422753
$53$	−3.19348	−0.438658	−0.219329	−	0.975651i	$-0.570387\pi$
$53$	−3.19348	−0.438658	−0.219329	+	0.975651i	$0.570387\pi$
$54$	3.63387	0.494508
$55$	−11.2448	−1.51625
$56$	−4.21443	−0.563177
$57$	6.99584	0.926622
$58$	−1.00000	−0.131306
$59$	−8.47686	−1.10359	−0.551797	−	0.833979i	$-0.686058\pi$
$59$	−8.47686	−1.10359	−0.551797	+	0.833979i	$0.686058\pi$
$60$	7.53401	0.972637
$61$	−11.7310	−1.50200	−0.751001	−	0.660302i	$-0.770428\pi$
$61$	−11.7310	−1.50200	−0.751001	+	0.660302i	$0.770428\pi$
$62$	1.07114	0.136034
$63$	5.20053	0.655205
$64$	1.00000	0.125000
$65$	11.1620	1.38447
$66$	6.31937	0.777860
$67$	−5.27790	−0.644799	−0.322399	−	0.946604i	$-0.604489\pi$
$67$	−5.27790	−0.644799	−0.322399	+	0.946604i	$0.604489\pi$
$68$	−6.40651	−0.776903
$69$	−2.05766	−0.247714
$70$	−15.4309	−1.84434
$71$	3.30120	0.391781	0.195890	−	0.980626i	$-0.437240\pi$
$71$	3.30120	0.391781	0.195890	+	0.980626i	$0.437240\pi$
$72$	−1.23398	−0.145426
$73$	−6.15868	−0.720819	−0.360410	−	0.932794i	$-0.617363\pi$
$73$	−6.15868	−0.720819	−0.360410	+	0.932794i	$0.617363\pi$
$74$	0.533936	0.0620688
$75$	17.2970	1.99729
$76$	3.39989	0.389995
$77$	−12.9431	−1.47500
$78$	−6.27282	−0.710257
$79$	−9.10993	−1.02495	−0.512473	−	0.858703i	$-0.671271\pi$
$79$	−9.10993	−1.02495	−0.512473	+	0.858703i	$0.671271\pi$
$80$	3.66144	0.409361
$81$	−11.1792	−1.24214
$82$	2.53394	0.279826
$83$	13.6365	1.49680	0.748400	−	0.663248i	$-0.230823\pi$
$83$	13.6365	1.49680	0.748400	+	0.663248i	$0.230823\pi$
$84$	8.67188	0.946180
$85$	−23.4570	−2.54427
$86$	−7.18646	−0.774936
$87$	2.05766	0.220605
$88$	3.07114	0.327384
$89$	3.79632	0.402409	0.201204	−	0.979549i	$-0.435514\pi$
$89$	3.79632	0.402409	0.201204	+	0.979549i	$0.435514\pi$
$90$	−4.51814	−0.476254
$91$	12.8478	1.34681
$92$	−1.00000	−0.104257
$93$	−2.20404	−0.228548
$94$	7.95918	0.820927
$95$	12.4485	1.27719
$96$	−2.05766	−0.210009
$97$	18.0174	1.82939	0.914695	−	0.404144i	$-0.132430\pi$
$97$	18.0174	1.82939	0.914695	+	0.404144i	$0.132430\pi$
$98$	−10.7614	−1.08707
$99$	−3.78972	−0.380881
$100$	8.40614	0.840614
$101$	11.5122	1.14551	0.572755	−	0.819727i	$-0.305875\pi$
$101$	11.5122	1.14551	0.572755	+	0.819727i	$0.305875\pi$
$102$	13.1824	1.30526
$103$	2.49338	0.245680	0.122840	−	0.992426i	$-0.460800\pi$
$103$	2.49338	0.245680	0.122840	+	0.992426i	$0.460800\pi$
$104$	−3.04852	−0.298932
$105$	31.7516	3.09864
$106$	3.19348	0.310178
$107$	−17.7205	−1.71311	−0.856554	−	0.516058i	$-0.827399\pi$
$107$	−17.7205	−1.71311	−0.856554	+	0.516058i	$0.827399\pi$
$108$	−3.63387	−0.349670
$109$	−13.0276	−1.24782	−0.623908	−	0.781498i	$-0.714456\pi$
$109$	−13.0276	−1.24782	−0.623908	+	0.781498i	$0.714456\pi$
$110$	11.2448	1.07215
$111$	−1.09866	−0.104280
$112$	4.21443	0.398226
$113$	8.97667	0.844454	0.422227	−	0.906490i	$-0.361248\pi$
$113$	8.97667	0.844454	0.422227	+	0.906490i	$0.361248\pi$
$114$	−6.99584	−0.655220
$115$	−3.66144	−0.341431
$116$	1.00000	0.0928477
$117$	3.76181	0.347780
$118$	8.47686	0.780358
$119$	−26.9998	−2.47507
$120$	−7.53401	−0.687758
$121$	−1.56812	−0.142557
$122$	11.7310	1.06208
$123$	−5.21399	−0.470129
$124$	−1.07114	−0.0961909
$125$	12.4714	1.11547
$126$	−5.20053	−0.463300
$127$	−11.5872	−1.02820	−0.514098	−	0.857732i	$-0.671873\pi$
$127$	−11.5872	−1.02820	−0.514098	+	0.857732i	$0.671873\pi$
$128$	−1.00000	−0.0883883
$129$	14.7873	1.30195
$130$	−11.1620	−0.978969
$131$	4.25914	0.372123	0.186061	−	0.982538i	$-0.440428\pi$
$131$	4.25914	0.372123	0.186061	+	0.982538i	$0.440428\pi$
$132$	−6.31937	−0.550030
$133$	14.3286	1.24245
$134$	5.27790	0.455942
$135$	−13.3052	−1.14513
$136$	6.40651	0.549353
$137$	9.20087	0.786084	0.393042	−	0.919521i	$-0.371423\pi$
$137$	9.20087	0.786084	0.393042	+	0.919521i	$0.371423\pi$
$138$	2.05766	0.175160
$139$	0.939552	0.0796918	0.0398459	−	0.999206i	$-0.487313\pi$
$139$	0.939552	0.0796918	0.0398459	+	0.999206i	$0.487313\pi$
$140$	15.4309	1.30415
$141$	−16.3773	−1.37922
$142$	−3.30120	−0.277031
$143$	−9.36241	−0.782924
$144$	1.23398	0.102832
$145$	3.66144	0.304066
$146$	6.15868	0.509696
$147$	22.1434	1.82636
$148$	−0.533936	−0.0438892
$149$	−16.6712	−1.36576	−0.682878	−	0.730532i	$-0.739272\pi$
$149$	−16.6712	−1.36576	−0.682878	+	0.730532i	$0.739272\pi$
$150$	−17.2970	−1.41229
$151$	20.5725	1.67416	0.837081	−	0.547078i	$-0.184260\pi$
$151$	20.5725	1.67416	0.837081	+	0.547078i	$0.184260\pi$
$152$	−3.39989	−0.275768
$153$	−7.90550	−0.639122
$154$	12.9431	1.04298
$155$	−3.92190	−0.315015
$156$	6.27282	0.502228
$157$	11.3921	0.909188	0.454594	−	0.890699i	$-0.349784\pi$
$157$	11.3921	0.909188	0.454594	+	0.890699i	$0.349784\pi$
$158$	9.10993	0.724747
$159$	−6.57110	−0.521122
$160$	−3.66144	−0.289462
$161$	−4.21443	−0.332144
$162$	11.1792	0.878324
$163$	−12.1186	−0.949203	−0.474601	−	0.880201i	$-0.657408\pi$
$163$	−12.1186	−0.949203	−0.474601	+	0.880201i	$0.657408\pi$
$164$	−2.53394	−0.197867
$165$	−23.1380	−1.80129
$166$	−13.6365	−1.05840
$167$	12.7893	0.989669	0.494834	−	0.868987i	$-0.335229\pi$
$167$	12.7893	0.989669	0.494834	+	0.868987i	$0.335229\pi$
$168$	−8.67188	−0.669050
$169$	−3.70654	−0.285119
$170$	23.4570	1.79907
$171$	4.19540	0.320830
$172$	7.18646	0.547963
$173$	20.7121	1.57471	0.787356	−	0.616499i	$-0.211450\pi$
$173$	20.7121	1.57471	0.787356	+	0.616499i	$0.211450\pi$
$174$	−2.05766	−0.155991
$175$	35.4271	2.67804
$176$	−3.07114	−0.231496
$177$	−17.4425	−1.31106
$178$	−3.79632	−0.284546
$179$	22.1311	1.65415	0.827077	−	0.562089i	$-0.190002\pi$
$179$	22.1311	1.65415	0.827077	+	0.562089i	$0.190002\pi$
$180$	4.51814	0.336763
$181$	6.06155	0.450551	0.225276	−	0.974295i	$-0.427672\pi$
$181$	6.06155	0.450551	0.225276	+	0.974295i	$0.427672\pi$
$182$	−12.8478	−0.952340
$183$	−24.1385	−1.78437
$184$	1.00000	0.0737210
$185$	−1.95497	−0.143732
$186$	2.20404	0.161608
$187$	19.6753	1.43880
$188$	−7.95918	−0.580483
$189$	−15.3147	−1.11398
$190$	−12.4485	−0.903109
$191$	−11.7511	−0.850278	−0.425139	−	0.905128i	$-0.639775\pi$
$191$	−11.7511	−0.850278	−0.425139	+	0.905128i	$0.639775\pi$
$192$	2.05766	0.148499
$193$	22.3997	1.61236	0.806181	−	0.591669i	$-0.201531\pi$
$193$	22.3997	1.61236	0.806181	+	0.591669i	$0.201531\pi$
$194$	−18.0174	−1.29357
$195$	22.9676	1.64474
$196$	10.7614	0.768673
$197$	4.33273	0.308694	0.154347	−	0.988017i	$-0.450673\pi$
$197$	4.33273	0.308694	0.154347	+	0.988017i	$0.450673\pi$
$198$	3.78972	0.269324
$199$	11.9827	0.849434	0.424717	−	0.905326i	$-0.360374\pi$
$199$	11.9827	0.849434	0.424717	+	0.905326i	$0.360374\pi$
$200$	−8.40614	−0.594404
$201$	−10.8602	−0.766016
$202$	−11.5122	−0.809997
$203$	4.21443	0.295795
$204$	−13.1824	−0.922955
$205$	−9.27785	−0.647993
$206$	−2.49338	−0.173722
$207$	−1.23398	−0.0857676
$208$	3.04852	0.211377
$209$	−10.4415	−0.722256
$210$	−31.7516	−2.19107
$211$	8.08766	0.556777	0.278389	−	0.960469i	$-0.410200\pi$
$211$	8.08766	0.556777	0.278389	+	0.960469i	$0.410200\pi$
$212$	−3.19348	−0.219329
$213$	6.79276	0.465432
$214$	17.7205	1.21135
$215$	26.3128	1.79452
$216$	3.63387	0.247254
$217$	−4.51423	−0.306446
$218$	13.0276	0.882340
$219$	−12.6725	−0.856328
$220$	−11.2448	−0.758123
$221$	−19.5303	−1.31375
$222$	1.09866	0.0737372
$223$	−25.1121	−1.68163	−0.840815	−	0.541323i	$-0.817924\pi$
$223$	−25.1121	−1.68163	−0.840815	+	0.541323i	$0.817924\pi$
$224$	−4.21443	−0.281589
$225$	10.3730	0.691534
$226$	−8.97667	−0.597119
$227$	−2.67321	−0.177427	−0.0887135	−	0.996057i	$-0.528276\pi$
$227$	−2.67321	−0.177427	−0.0887135	+	0.996057i	$0.528276\pi$
$228$	6.99584	0.463311
$229$	−17.8685	−1.18079	−0.590393	−	0.807116i	$-0.701027\pi$
$229$	−17.8685	−1.18079	−0.590393	+	0.807116i	$0.701027\pi$
$230$	3.66144	0.241428
$231$	−26.6325	−1.75229
$232$	−1.00000	−0.0656532
$233$	22.0601	1.44521	0.722603	−	0.691263i	$-0.242946\pi$
$233$	22.0601	1.44521	0.722603	+	0.691263i	$0.242946\pi$
$234$	−3.76181	−0.245917
$235$	−29.1421	−1.90102
$236$	−8.47686	−0.551797
$237$	−18.7452	−1.21763
$238$	26.9998	1.75014
$239$	−1.49350	−0.0966062	−0.0483031	−	0.998833i	$-0.515381\pi$
$239$	−1.49350	−0.0966062	−0.0483031	+	0.998833i	$0.515381\pi$
$240$	7.53401	0.486318
$241$	−18.1496	−1.16912	−0.584559	−	0.811351i	$-0.698732\pi$
$241$	−18.1496	−1.16912	−0.584559	+	0.811351i	$0.698732\pi$
$242$	1.56812	0.100803
$243$	−12.1015	−0.776310
$244$	−11.7310	−0.751001
$245$	39.4023	2.51732
$246$	5.21399	0.332432
$247$	10.3646	0.659486
$248$	1.07114	0.0680172
$249$	28.0593	1.77819
$250$	−12.4714	−0.788758
$251$	−12.3539	−0.779774	−0.389887	−	0.920863i	$-0.627486\pi$
$251$	−12.3539	−0.779774	−0.389887	+	0.920863i	$0.627486\pi$
$252$	5.20053	0.327602
$253$	3.07114	0.193081
$254$	11.5872	0.727044
$255$	−48.2667	−3.02258
$256$	1.00000	0.0625000
$257$	−28.7017	−1.79036	−0.895181	−	0.445703i	$-0.852954\pi$
$257$	−28.7017	−1.79036	−0.895181	+	0.445703i	$0.852954\pi$
$258$	−14.7873	−0.920619
$259$	−2.25023	−0.139823
$260$	11.1620	0.692235
$261$	1.23398	0.0763815
$262$	−4.25914	−0.263130
$263$	0.570229	0.0351618	0.0175809	−	0.999845i	$-0.494404\pi$
$263$	0.570229	0.0351618	0.0175809	+	0.999845i	$0.494404\pi$
$264$	6.31937	0.388930
$265$	−11.6927	−0.718278
$266$	−14.3286	−0.878544
$267$	7.81154	0.478059
$268$	−5.27790	−0.322399
$269$	25.8197	1.57425	0.787126	−	0.616792i	$-0.211568\pi$
$269$	25.8197	1.57425	0.787126	+	0.616792i	$0.211568\pi$
$270$	13.3052	0.809729
$271$	7.02613	0.426807	0.213404	−	0.976964i	$-0.431545\pi$
$271$	7.02613	0.426807	0.213404	+	0.976964i	$0.431545\pi$
$272$	−6.40651	−0.388452
$273$	26.4364	1.60000
$274$	−9.20087	−0.555845
$275$	−25.8164	−1.55679
$276$	−2.05766	−0.123857
$277$	31.6374	1.90091	0.950453	−	0.310867i	$-0.100619\pi$
$277$	31.6374	1.90091	0.950453	+	0.310867i	$0.100619\pi$
$278$	−0.939552	−0.0563506
$279$	−1.32176	−0.0791318
$280$	−15.4309	−0.922172
$281$	8.33845	0.497431	0.248715	−	0.968577i	$-0.419992\pi$
$281$	8.33845	0.497431	0.248715	+	0.968577i	$0.419992\pi$
$282$	16.3773	0.975255
$283$	−20.7763	−1.23502	−0.617510	−	0.786563i	$-0.711859\pi$
$283$	−20.7763	−1.23502	−0.617510	+	0.786563i	$0.711859\pi$
$284$	3.30120	0.195890
$285$	25.6148	1.51729
$286$	9.36241	0.553611
$287$	−10.6791	−0.630367
$288$	−1.23398	−0.0727130
$289$	24.0433	1.41431
$290$	−3.66144	−0.215007
$291$	37.0738	2.17330
$292$	−6.15868	−0.360410
$293$	1.98886	0.116190	0.0580952	−	0.998311i	$-0.481497\pi$
$293$	1.98886	0.116190	0.0580952	+	0.998311i	$0.481497\pi$
$294$	−22.1434	−1.29143
$295$	−31.0375	−1.80707
$296$	0.533936	0.0310344
$297$	11.1601	0.647576
$298$	16.6712	0.965736
$299$	−3.04852	−0.176300
$300$	17.2970	0.998643
$301$	30.2869	1.74571
$302$	−20.5725	−1.18381
$303$	23.6883	1.36086
$304$	3.39989	0.194997
$305$	−42.9524	−2.45944
$306$	7.90550	0.451928
$307$	15.7537	0.899108	0.449554	−	0.893253i	$-0.351583\pi$
$307$	15.7537	0.899108	0.449554	+	0.893253i	$0.351583\pi$
$308$	−12.9431	−0.737501
$309$	5.13054	0.291866
$310$	3.92190	0.222749
$311$	−25.1822	−1.42795	−0.713977	−	0.700169i	$-0.753108\pi$
$311$	−25.1822	−1.42795	−0.713977	+	0.700169i	$0.753108\pi$
$312$	−6.27282	−0.355129
$313$	19.6650	1.11153	0.555766	−	0.831339i	$-0.312425\pi$
$313$	19.6650	1.11153	0.555766	+	0.831339i	$0.312425\pi$
$314$	−11.3921	−0.642893
$315$	19.0414	1.07286
$316$	−9.10993	−0.512473
$317$	−26.7597	−1.50298	−0.751488	−	0.659746i	$-0.770664\pi$
$317$	−26.7597	−1.50298	−0.751488	+	0.659746i	$0.770664\pi$
$318$	6.57110	0.368489
$319$	−3.07114	−0.171951
$320$	3.66144	0.204681
$321$	−36.4629	−2.03516
$322$	4.21443	0.234861
$323$	−21.7814	−1.21195
$324$	−11.1792	−0.621069
$325$	25.6263	1.42149
$326$	12.1186	0.671188
$327$	−26.8064	−1.48240
$328$	2.53394	0.139913
$329$	−33.5434	−1.84931
$330$	23.1380	1.27370
$331$	−29.1110	−1.60009	−0.800043	−	0.599942i	$-0.795190\pi$
$331$	−29.1110	−1.60009	−0.800043	+	0.599942i	$0.795190\pi$
$332$	13.6365	0.748400
$333$	−0.658866	−0.0361056
$334$	−12.7893	−0.699802
$335$	−19.3247	−1.05582
$336$	8.67188	0.473090
$337$	5.55188	0.302430	0.151215	−	0.988501i	$-0.451681\pi$
$337$	5.55188	0.302430	0.151215	+	0.988501i	$0.451681\pi$
$338$	3.70654	0.201609
$339$	18.4710	1.00321
$340$	−23.4570	−1.27214
$341$	3.28960	0.178142
$342$	−4.19540	−0.226861
$343$	15.8523	0.855943
$344$	−7.18646	−0.387468
$345$	−7.53401	−0.405618
$346$	−20.7121	−1.11349
$347$	0.0795825	0.00427221	0.00213611	−	0.999998i	$-0.499320\pi$
$347$	0.0795825	0.00427221	0.00213611	+	0.999998i	$0.499320\pi$
$348$	2.05766	0.110302
$349$	−23.6538	−1.26616	−0.633081	−	0.774086i	$-0.718210\pi$
$349$	−23.6538	−1.26616	−0.633081	+	0.774086i	$0.718210\pi$
$350$	−35.4271	−1.89366
$351$	−11.0779	−0.591296
$352$	3.07114	0.163692
$353$	−19.6686	−1.04685	−0.523426	−	0.852071i	$-0.675346\pi$
$353$	−19.6686	−1.04685	−0.523426	+	0.852071i	$0.675346\pi$
$354$	17.4425	0.927060
$355$	12.0871	0.641519
$356$	3.79632	0.201204
$357$	−55.5565	−2.94036
$358$	−22.1311	−1.16966
$359$	26.0150	1.37302	0.686510	−	0.727120i	$-0.259142\pi$
$359$	26.0150	1.37302	0.686510	+	0.727120i	$0.259142\pi$
$360$	−4.51814	−0.238127
$361$	−7.44072	−0.391617
$362$	−6.06155	−0.318588
$363$	−3.22667	−0.169356
$364$	12.8478	0.673406
$365$	−22.5496	−1.18030
$366$	24.1385	1.26174
$367$	4.31458	0.225219	0.112609	−	0.993639i	$-0.464079\pi$
$367$	4.31458	0.225219	0.112609	+	0.993639i	$0.464079\pi$
$368$	−1.00000	−0.0521286
$369$	−3.12683	−0.162776
$370$	1.95497	0.101634
$371$	−13.4587	−0.698741
$372$	−2.20404	−0.114274
$373$	5.84761	0.302778	0.151389	−	0.988474i	$-0.451625\pi$
$373$	5.84761	0.302778	0.151389	+	0.988474i	$0.451625\pi$
$374$	−19.6753	−1.01738
$375$	25.6619	1.32517
$376$	7.95918	0.410463
$377$	3.04852	0.157007
$378$	15.3147	0.787704
$379$	8.90788	0.457567	0.228783	−	0.973477i	$-0.426525\pi$
$379$	8.90788	0.457567	0.228783	+	0.973477i	$0.426525\pi$
$380$	12.4485	0.638595
$381$	−23.8425	−1.22149
$382$	11.7511	0.601237
$383$	−10.9621	−0.560136	−0.280068	−	0.959980i	$-0.590357\pi$
$383$	−10.9621	−0.560136	−0.280068	+	0.959980i	$0.590357\pi$
$384$	−2.05766	−0.105005
$385$	−47.3903	−2.41524
$386$	−22.3997	−1.14011
$387$	8.86796	0.450784
$388$	18.0174	0.914695
$389$	9.81544	0.497663	0.248831	−	0.968547i	$-0.419954\pi$
$389$	9.81544	0.497663	0.248831	+	0.968547i	$0.419954\pi$
$390$	−22.9676	−1.16301
$391$	6.40651	0.323991
$392$	−10.7614	−0.543534
$393$	8.76387	0.442079
$394$	−4.33273	−0.218280
$395$	−33.3554	−1.67829
$396$	−3.78972	−0.190441
$397$	15.3287	0.769325	0.384662	−	0.923057i	$-0.374318\pi$
$397$	15.3287	0.769325	0.384662	+	0.923057i	$0.374318\pi$
$398$	−11.9827	−0.600640
$399$	29.4835	1.47602
$400$	8.40614	0.420307
$401$	−17.0948	−0.853674	−0.426837	−	0.904329i	$-0.640372\pi$
$401$	−17.0948	−0.853674	−0.426837	+	0.904329i	$0.640372\pi$
$402$	10.8602	0.541655
$403$	−3.26538	−0.162660
$404$	11.5122	0.572755
$405$	−40.9321	−2.03393
$406$	−4.21443	−0.209159
$407$	1.63979	0.0812813
$408$	13.1824	0.652628
$409$	26.6218	1.31636	0.658182	−	0.752859i	$-0.271326\pi$
$409$	26.6218	1.31636	0.658182	+	0.752859i	$0.271326\pi$
$410$	9.27785	0.458200
$411$	18.9323	0.933862
$412$	2.49338	0.122840
$413$	−35.7251	−1.75792
$414$	1.23398	0.0606468
$415$	49.9292	2.45093
$416$	−3.04852	−0.149466
$417$	1.93328	0.0946733
$418$	10.4415	0.510712
$419$	16.1432	0.788647	0.394324	−	0.918972i	$-0.370979\pi$
$419$	16.1432	0.788647	0.394324	+	0.918972i	$0.370979\pi$
$420$	31.7516	1.54932
$421$	−28.3340	−1.38092	−0.690458	−	0.723372i	$-0.742591\pi$
$421$	−28.3340	−1.38092	−0.690458	+	0.723372i	$0.742591\pi$
$422$	−8.08766	−0.393701
$423$	−9.82147	−0.477536
$424$	3.19348	0.155089
$425$	−53.8540	−2.61230
$426$	−6.79276	−0.329110
$427$	−49.4395	−2.39255
$428$	−17.7205	−0.856554
$429$	−19.2647	−0.930108
$430$	−26.3128	−1.26892
$431$	−5.50963	−0.265390	−0.132695	−	0.991157i	$-0.542363\pi$
$431$	−5.50963	−0.265390	−0.132695	+	0.991157i	$0.542363\pi$
$432$	−3.63387	−0.174835
$433$	28.7766	1.38292	0.691458	−	0.722417i	$-0.256969\pi$
$433$	28.7766	1.38292	0.691458	+	0.722417i	$0.256969\pi$
$434$	4.51423	0.216690
$435$	7.53401	0.361228
$436$	−13.0276	−0.623908
$437$	−3.39989	−0.162639
$438$	12.6725	0.605515
$439$	−32.4587	−1.54917	−0.774586	−	0.632469i	$-0.782042\pi$
$439$	−32.4587	−1.54917	−0.774586	+	0.632469i	$0.782042\pi$
$440$	11.2448	0.536074
$441$	13.2794	0.632352
$442$	19.5303	0.928964
$443$	−34.2159	−1.62565	−0.812824	−	0.582510i	$-0.802071\pi$
$443$	−34.2159	−1.62565	−0.812824	+	0.582510i	$0.802071\pi$
$444$	−1.09866	−0.0521401
$445$	13.9000	0.658922
$446$	25.1121	1.18909
$447$	−34.3037	−1.62251
$448$	4.21443	0.199113
$449$	−3.41946	−0.161374	−0.0806872	−	0.996739i	$-0.525711\pi$
$449$	−3.41946	−0.161374	−0.0806872	+	0.996739i	$0.525711\pi$
$450$	−10.3730	−0.488988
$451$	7.78206	0.366443
$452$	8.97667	0.422227
$453$	42.3312	1.98889
$454$	2.67321	0.125460
$455$	47.0413	2.20533
$456$	−6.99584	−0.327610
$457$	28.3384	1.32562	0.662808	−	0.748790i	$-0.269365\pi$
$457$	28.3384	1.32562	0.662808	+	0.748790i	$0.269365\pi$
$458$	17.8685	0.834941
$459$	23.2804	1.08664
$460$	−3.66144	−0.170715
$461$	−2.30643	−0.107421	−0.0537106	−	0.998557i	$-0.517105\pi$
$461$	−2.30643	−0.107421	−0.0537106	+	0.998557i	$0.517105\pi$
$462$	26.6325	1.23906
$463$	−30.1156	−1.39959	−0.699794	−	0.714344i	$-0.746725\pi$
$463$	−30.1156	−1.39959	−0.699794	+	0.714344i	$0.746725\pi$
$464$	1.00000	0.0464238
$465$	−8.06995	−0.374235
$466$	−22.0601	−1.02191
$467$	−23.5775	−1.09104	−0.545518	−	0.838099i	$-0.683667\pi$
$467$	−23.5775	−1.09104	−0.545518	+	0.838099i	$0.683667\pi$
$468$	3.76181	0.173890
$469$	−22.2434	−1.02710
$470$	29.1421	1.34422
$471$	23.4411	1.08011
$472$	8.47686	0.390179
$473$	−22.0706	−1.01481
$474$	18.7452	0.860994
$475$	28.5800	1.31134
$476$	−26.9998	−1.23753
$477$	−3.94069	−0.180432
$478$	1.49350	0.0683109
$479$	37.9145	1.73236	0.866178	−	0.499735i	$-0.166569\pi$
$479$	37.9145	1.73236	0.866178	+	0.499735i	$0.166569\pi$
$480$	−7.53401	−0.343879
$481$	−1.62771	−0.0742173
$482$	18.1496	0.826691
$483$	−8.67188	−0.394584
$484$	−1.56812	−0.0712783
$485$	65.9697	2.99553
$486$	12.1015	0.548934
$487$	−8.85727	−0.401361	−0.200681	−	0.979657i	$-0.564315\pi$
$487$	−8.85727	−0.401361	−0.200681	+	0.979657i	$0.564315\pi$
$488$	11.7310	0.531038
$489$	−24.9360	−1.12765
$490$	−39.4023	−1.78002
$491$	−5.17434	−0.233515	−0.116757	−	0.993160i	$-0.537250\pi$
$491$	−5.17434	−0.233515	−0.116757	+	0.993160i	$0.537250\pi$
$492$	−5.21399	−0.235065
$493$	−6.40651	−0.288535
$494$	−10.3646	−0.466327
$495$	−13.8758	−0.623672
$496$	−1.07114	−0.0480954
$497$	13.9127	0.624069
$498$	−28.0593	−1.25737
$499$	29.1059	1.30296	0.651480	−	0.758666i	$-0.274148\pi$
$499$	29.1059	1.30296	0.651480	+	0.758666i	$0.274148\pi$
$500$	12.4714	0.557736
$501$	26.3162	1.17572
$502$	12.3539	0.551383
$503$	24.5844	1.09617	0.548083	−	0.836424i	$-0.315358\pi$
$503$	24.5844	1.09617	0.548083	+	0.836424i	$0.315358\pi$
$504$	−5.20053	−0.231650
$505$	42.1513	1.87571
$506$	−3.07114	−0.136529
$507$	−7.62682	−0.338719
$508$	−11.5872	−0.514098
$509$	−7.11033	−0.315160	−0.157580	−	0.987506i	$-0.550369\pi$
$509$	−7.11033	−0.315160	−0.157580	+	0.987506i	$0.550369\pi$
$510$	48.2667	2.13729
$511$	−25.9553	−1.14820
$512$	−1.00000	−0.0441942
$513$	−12.3548	−0.545477
$514$	28.7017	1.26598
$515$	9.12937	0.402288
$516$	14.7873	0.650976
$517$	24.4437	1.07503
$518$	2.25023	0.0988696
$519$	42.6185	1.87075
$520$	−11.1620	−0.489484
$521$	15.5674	0.682021	0.341010	−	0.940060i	$-0.389231\pi$
$521$	15.5674	0.682021	0.341010	+	0.940060i	$0.389231\pi$
$522$	−1.23398	−0.0540099
$523$	−2.18618	−0.0955950	−0.0477975	−	0.998857i	$-0.515220\pi$
$523$	−2.18618	−0.0955950	−0.0477975	+	0.998857i	$0.515220\pi$
$524$	4.25914	0.186061
$525$	72.8970	3.18149
$526$	−0.570229	−0.0248632
$527$	6.86224	0.298924
$528$	−6.31937	−0.275015
$529$	1.00000	0.0434783
$530$	11.6927	0.507900
$531$	−10.4603	−0.453938
$532$	14.3286	0.621224
$533$	−7.72475	−0.334596
$534$	−7.81154	−0.338039
$535$	−64.8826	−2.80512
$536$	5.27790	0.227971
$537$	45.5383	1.96512
$538$	−25.8197	−1.11316
$539$	−33.0498	−1.42356
$540$	−13.3052	−0.572565
$541$	19.8046	0.851465	0.425733	−	0.904849i	$-0.360016\pi$
$541$	19.8046	0.851465	0.425733	+	0.904849i	$0.360016\pi$
$542$	−7.02613	−0.301798
$543$	12.4726	0.535252
$544$	6.40651	0.274677
$545$	−47.6997	−2.04323
$546$	−26.4364	−1.13137
$547$	−8.93891	−0.382200	−0.191100	−	0.981571i	$-0.561206\pi$
$547$	−8.93891	−0.382200	−0.191100	+	0.981571i	$0.561206\pi$
$548$	9.20087	0.393042
$549$	−14.4758	−0.617813
$550$	25.8164	1.10081
$551$	3.39989	0.144840
$552$	2.05766	0.0875800
$553$	−38.3932	−1.63264
$554$	−31.6374	−1.34414
$555$	−4.02268	−0.170753
$556$	0.939552	0.0398459
$557$	18.1571	0.769342	0.384671	−	0.923054i	$-0.374315\pi$
$557$	18.1571	0.769342	0.384671	+	0.923054i	$0.374315\pi$
$558$	1.32176	0.0559546
$559$	21.9081	0.926612
$560$	15.4309	0.652074
$561$	40.4851	1.70928
$562$	−8.33845	−0.351736
$563$	−17.6536	−0.744011	−0.372005	−	0.928231i	$-0.621330\pi$
$563$	−17.6536	−0.744011	−0.372005	+	0.928231i	$0.621330\pi$
$564$	−16.3773	−0.689610
$565$	32.8675	1.38275
$566$	20.7763	0.873292
$567$	−47.1141	−1.97861
$568$	−3.30120	−0.138515
$569$	38.0884	1.59675	0.798374	−	0.602162i	$-0.205694\pi$
$569$	38.0884	1.59675	0.798374	+	0.602162i	$0.205694\pi$
$570$	−25.6148	−1.07289
$571$	4.00414	0.167568	0.0837841	−	0.996484i	$-0.473299\pi$
$571$	4.00414	0.167568	0.0837841	+	0.996484i	$0.473299\pi$
$572$	−9.36241	−0.391462
$573$	−24.1798	−1.01012
$574$	10.6791	0.445737
$575$	−8.40614	−0.350560
$576$	1.23398	0.0514159
$577$	−6.97263	−0.290274	−0.145137	−	0.989412i	$-0.546362\pi$
$577$	−6.97263	−0.290274	−0.145137	+	0.989412i	$0.546362\pi$
$578$	−24.0433	−1.00007
$579$	46.0909	1.91547
$580$	3.66144	0.152033
$581$	57.4701	2.38426
$582$	−37.0738	−1.53676
$583$	9.80761	0.406190
$584$	6.15868	0.254848
$585$	13.7736	0.569470
$586$	−1.98886	−0.0821590
$587$	3.94918	0.163000	0.0815000	−	0.996673i	$-0.474029\pi$
$587$	3.94918	0.163000	0.0815000	+	0.996673i	$0.474029\pi$
$588$	22.1434	0.913178
$589$	−3.64175	−0.150056
$590$	31.0375	1.27779
$591$	8.91530	0.366727
$592$	−0.533936	−0.0219446
$593$	−39.3581	−1.61624	−0.808122	−	0.589016i	$-0.799516\pi$
$593$	−39.3581	−1.61624	−0.808122	+	0.589016i	$0.799516\pi$
$594$	−11.1601	−0.457905
$595$	−98.8581	−4.05279
$596$	−16.6712	−0.682878
$597$	24.6564	1.00912
$598$	3.04852	0.124663
$599$	10.4965	0.428877	0.214439	−	0.976737i	$-0.431208\pi$
$599$	10.4965	0.428877	0.214439	+	0.976737i	$0.431208\pi$
$600$	−17.2970	−0.706147
$601$	48.2042	1.96629	0.983146	−	0.182821i	$-0.0585229\pi$
$601$	48.2042	1.96629	0.983146	+	0.182821i	$0.0585229\pi$
$602$	−30.2869	−1.23440
$603$	−6.51283	−0.265223
$604$	20.5725	0.837081
$605$	−5.74159	−0.233429
$606$	−23.6883	−0.962271
$607$	−9.19482	−0.373206	−0.186603	−	0.982435i	$-0.559748\pi$
$607$	−9.19482	−0.373206	−0.186603	+	0.982435i	$0.559748\pi$
$608$	−3.39989	−0.137884
$609$	8.67188	0.351402
$610$	42.9524	1.73909
$611$	−24.2637	−0.981604
$612$	−7.90550	−0.319561
$613$	−26.9992	−1.09049	−0.545243	−	0.838278i	$-0.683563\pi$
$613$	−26.9992	−1.09049	−0.545243	+	0.838278i	$0.683563\pi$
$614$	−15.7537	−0.635766
$615$	−19.0907	−0.769811
$616$	12.9431	0.521492
$617$	−41.5423	−1.67243	−0.836216	−	0.548400i	$-0.815237\pi$
$617$	−41.5423	−1.67243	−0.836216	+	0.548400i	$0.815237\pi$
$618$	−5.13054	−0.206381
$619$	−31.5957	−1.26994	−0.634970	−	0.772537i	$-0.718987\pi$
$619$	−31.5957	−1.26994	−0.634970	+	0.772537i	$0.718987\pi$
$620$	−3.92190	−0.157507
$621$	3.63387	0.145822
$622$	25.1822	1.00972
$623$	15.9993	0.640999
$624$	6.27282	0.251114
$625$	3.63245	0.145298
$626$	−19.6650	−0.785972
$627$	−21.4852	−0.858035
$628$	11.3921	0.454594
$629$	3.42066	0.136391
$630$	−19.0414	−0.758628
$631$	38.3067	1.52496	0.762482	−	0.647009i	$-0.223980\pi$
$631$	38.3067	1.52496	0.762482	+	0.647009i	$0.223980\pi$
$632$	9.10993	0.362373
$633$	16.6417	0.661447
$634$	26.7597	1.06277
$635$	−42.4257	−1.68361
$636$	−6.57110	−0.260561
$637$	32.8064	1.29984
$638$	3.07114	0.121587
$639$	4.07362	0.161150
$640$	−3.66144	−0.144731
$641$	31.0652	1.22700	0.613501	−	0.789694i	$-0.289761\pi$
$641$	31.0652	1.22700	0.613501	+	0.789694i	$0.289761\pi$
$642$	36.4629	1.43908
$643$	−18.0089	−0.710202	−0.355101	−	0.934828i	$-0.615553\pi$
$643$	−18.0089	−0.710202	−0.355101	+	0.934828i	$0.615553\pi$
$644$	−4.21443	−0.166072
$645$	54.1429	2.13187
$646$	21.7814	0.856980
$647$	−2.34685	−0.0922641	−0.0461321	−	0.998935i	$-0.514690\pi$
$647$	−2.34685	−0.0922641	−0.0461321	+	0.998935i	$0.514690\pi$
$648$	11.1792	0.439162
$649$	26.0336	1.02191
$650$	−25.6263	−1.00514
$651$	−9.28877	−0.364055
$652$	−12.1186	−0.474601
$653$	−2.98146	−0.116674	−0.0583368	−	0.998297i	$-0.518580\pi$
$653$	−2.98146	−0.116674	−0.0583368	+	0.998297i	$0.518580\pi$
$654$	26.8064	1.04821
$655$	15.5946	0.609330
$656$	−2.53394	−0.0989336
$657$	−7.59970	−0.296492
$658$	33.5434	1.30766
$659$	24.6873	0.961682	0.480841	−	0.876808i	$-0.340331\pi$
$659$	24.6873	0.961682	0.480841	+	0.876808i	$0.340331\pi$
$660$	−23.1380	−0.900644
$661$	23.9413	0.931209	0.465604	−	0.884993i	$-0.345837\pi$
$661$	23.9413	0.931209	0.465604	+	0.884993i	$0.345837\pi$
$662$	29.1110	1.13143
$663$	−40.1869	−1.56073
$664$	−13.6365	−0.529199
$665$	52.4634	2.03444
$666$	0.658866	0.0255305
$667$	−1.00000	−0.0387202
$668$	12.7893	0.494834
$669$	−51.6722	−1.99776
$670$	19.3247	0.746579
$671$	36.0275	1.39083
$672$	−8.67188	−0.334525
$673$	45.1082	1.73879	0.869396	−	0.494116i	$-0.164508\pi$
$673$	45.1082	1.73879	0.869396	+	0.494116i	$0.164508\pi$
$674$	−5.55188	−0.213851
$675$	−30.5468	−1.17575
$676$	−3.70654	−0.142559
$677$	19.5450	0.751175	0.375588	−	0.926787i	$-0.377441\pi$
$677$	19.5450	0.751175	0.375588	+	0.926787i	$0.377441\pi$
$678$	−18.4710	−0.709373
$679$	75.9331	2.91405
$680$	23.4570	0.899536
$681$	−5.50056	−0.210782
$682$	−3.28960	−0.125965
$683$	6.90721	0.264297	0.132149	−	0.991230i	$-0.457812\pi$
$683$	6.90721	0.264297	0.132149	+	0.991230i	$0.457812\pi$
$684$	4.19540	0.160415
$685$	33.6884	1.28717
$686$	−15.8523	−0.605243
$687$	−36.7674	−1.40276
$688$	7.18646	0.273981
$689$	−9.73537	−0.370888
$690$	7.53401	0.286815
$691$	−35.6782	−1.35726	−0.678632	−	0.734479i	$-0.737427\pi$
$691$	−35.6782	−1.35726	−0.678632	+	0.734479i	$0.737427\pi$
$692$	20.7121	0.787356
$693$	−15.9715	−0.606708
$694$	−0.0795825	−0.00302091
$695$	3.44011	0.130491
$696$	−2.05766	−0.0779955
$697$	16.2337	0.614894
$698$	23.6538	0.895311
$699$	45.3923	1.71689
$700$	35.4271	1.33902
$701$	−3.30613	−0.124871	−0.0624354	−	0.998049i	$-0.519887\pi$
$701$	−3.30613	−0.124871	−0.0624354	+	0.998049i	$0.519887\pi$
$702$	11.0779	0.418109
$703$	−1.81532	−0.0684663
$704$	−3.07114	−0.115748
$705$	−59.9646	−2.25840
$706$	19.6686	0.740236
$707$	48.5175	1.82469
$708$	−17.4425	−0.655530
$709$	−5.50854	−0.206878	−0.103439	−	0.994636i	$-0.532985\pi$
$709$	−5.50854	−0.206878	−0.103439	+	0.994636i	$0.532985\pi$
$710$	−12.0871	−0.453623
$711$	−11.2415	−0.421588
$712$	−3.79632	−0.142273
$713$	1.07114	0.0401144
$714$	55.5565	2.07915
$715$	−34.2799	−1.28200
$716$	22.1311	0.827077
$717$	−3.07311	−0.114768
$718$	−26.0150	−0.970872
$719$	−20.3250	−0.757994	−0.378997	−	0.925398i	$-0.623731\pi$
$719$	−20.3250	−0.757994	−0.378997	+	0.925398i	$0.623731\pi$
$720$	4.51814	0.168381
$721$	10.5082	0.391346
$722$	7.44072	0.276915
$723$	−37.3457	−1.38890
$724$	6.06155	0.225276
$725$	8.40614	0.312196
$726$	3.22667	0.119753
$727$	5.04732	0.187195	0.0935974	−	0.995610i	$-0.470163\pi$
$727$	5.04732	0.187195	0.0935974	+	0.995610i	$0.470163\pi$
$728$	−12.8478	−0.476170
$729$	8.63692	0.319886
$730$	22.5496	0.834600
$731$	−46.0401	−1.70286
$732$	−24.1385	−0.892183
$733$	2.99066	0.110463	0.0552313	−	0.998474i	$-0.482410\pi$
$733$	2.99066	0.110463	0.0552313	+	0.998474i	$0.482410\pi$
$734$	−4.31458	−0.159254
$735$	81.0767	2.99056
$736$	1.00000	0.0368605
$737$	16.2092	0.597072
$738$	3.12683	0.115100
$739$	−17.6674	−0.649906	−0.324953	−	0.945730i	$-0.605348\pi$
$739$	−17.6674	−0.649906	−0.324953	+	0.945730i	$0.605348\pi$
$740$	−1.95497	−0.0718662
$741$	21.3269	0.783465
$742$	13.4587	0.494084
$743$	−22.1833	−0.813826	−0.406913	−	0.913467i	$-0.633395\pi$
$743$	−22.1833	−0.813826	−0.406913	+	0.913467i	$0.633395\pi$
$744$	2.20404	0.0808040
$745$	−61.0405	−2.23635
$746$	−5.84761	−0.214096
$747$	16.8272	0.615674
$748$	19.6753	0.719399
$749$	−74.6819	−2.72882
$750$	−25.6619	−0.937039
$751$	−29.2016	−1.06558	−0.532790	−	0.846247i	$-0.678857\pi$
$751$	−29.2016	−1.06558	−0.532790	+	0.846247i	$0.678857\pi$
$752$	−7.95918	−0.290242
$753$	−25.4203	−0.926366
$754$	−3.04852	−0.111020
$755$	75.3248	2.74135
$756$	−15.3147	−0.556991
$757$	−2.77607	−0.100898	−0.0504490	−	0.998727i	$-0.516065\pi$
$757$	−2.77607	−0.100898	−0.0504490	+	0.998727i	$0.516065\pi$
$758$	−8.90788	−0.323549
$759$	6.31937	0.229378
$760$	−12.4485	−0.451555
$761$	5.17278	0.187513	0.0937566	−	0.995595i	$-0.470112\pi$
$761$	5.17278	0.187513	0.0937566	+	0.995595i	$0.470112\pi$
$762$	23.8425	0.863723
$763$	−54.9039	−1.98765
$764$	−11.7511	−0.425139
$765$	−28.9455	−1.04653
$766$	10.9621	0.396076
$767$	−25.8419	−0.933095
$768$	2.05766	0.0742495
$769$	46.2505	1.66784	0.833918	−	0.551889i	$-0.186093\pi$
$769$	46.2505	1.66784	0.833918	+	0.551889i	$0.186093\pi$
$770$	47.3903	1.70783
$771$	−59.0584	−2.12694
$772$	22.3997	0.806181
$773$	−0.585005	−0.0210412	−0.0105206	−	0.999945i	$-0.503349\pi$
$773$	−0.585005	−0.0210412	−0.0105206	+	0.999945i	$0.503349\pi$
$774$	−8.86796	−0.318752
$775$	−9.00412	−0.323437
$776$	−18.0174	−0.646787
$777$	−4.63023	−0.166108
$778$	−9.81544	−0.351901
$779$	−8.61511	−0.308668
$780$	22.9676	0.822371
$781$	−10.1384	−0.362782
$782$	−6.40651	−0.229096
$783$	−3.63387	−0.129864
$784$	10.7614	0.384337
$785$	41.7114	1.48874
$786$	−8.76387	−0.312597
$787$	39.0713	1.39274	0.696370	−	0.717683i	$-0.254797\pi$
$787$	39.0713	1.39274	0.696370	+	0.717683i	$0.254797\pi$
$788$	4.33273	0.154347
$789$	1.17334	0.0417720
$790$	33.3554	1.18673
$791$	37.8316	1.34514
$792$	3.78972	0.134662
$793$	−35.7622	−1.26995
$794$	−15.3287	−0.543995
$795$	−24.0597	−0.853310
$796$	11.9827	0.424717
$797$	51.8089	1.83517	0.917583	−	0.397544i	$-0.130137\pi$
$797$	51.8089	1.83517	0.917583	+	0.397544i	$0.130137\pi$
$798$	−29.4835	−1.04370
$799$	50.9906	1.80392
$800$	−8.40614	−0.297202
$801$	4.68458	0.165521
$802$	17.0948	0.603638
$803$	18.9142	0.667466
$804$	−10.8602	−0.383008
$805$	−15.4309	−0.543867
$806$	3.26538	0.115018
$807$	53.1282	1.87020
$808$	−11.5122	−0.404999
$809$	37.3671	1.31376	0.656878	−	0.753997i	$-0.271876\pi$
$809$	37.3671	1.31376	0.656878	+	0.753997i	$0.271876\pi$
$810$	40.9321	1.43821
$811$	−36.5518	−1.28351	−0.641754	−	0.766911i	$-0.721793\pi$
$811$	−36.5518	−1.28351	−0.641754	+	0.766911i	$0.721793\pi$
$812$	4.21443	0.147898
$813$	14.4574	0.507044
$814$	−1.63979	−0.0574746
$815$	−44.3715	−1.55427
$816$	−13.1824	−0.461478
$817$	24.4332	0.854810
$818$	−26.6218	−0.930810
$819$	15.8539	0.553980
$820$	−9.27785	−0.323997
$821$	11.6848	0.407803	0.203902	−	0.978991i	$-0.434638\pi$
$821$	11.6848	0.407803	0.203902	+	0.978991i	$0.434638\pi$
$822$	−18.9323	−0.660340
$823$	−2.84344	−0.0991162	−0.0495581	−	0.998771i	$-0.515781\pi$
$823$	−2.84344	−0.0991162	−0.0495581	+	0.998771i	$0.515781\pi$
$824$	−2.49338	−0.0868611
$825$	−53.1214	−1.84945
$826$	35.7251	1.24304
$827$	1.17399	0.0408237	0.0204118	−	0.999792i	$-0.493502\pi$
$827$	1.17399	0.0408237	0.0204118	+	0.999792i	$0.493502\pi$
$828$	−1.23398	−0.0428838
$829$	29.6476	1.02970	0.514851	−	0.857279i	$-0.327847\pi$
$829$	29.6476	1.02970	0.514851	+	0.857279i	$0.327847\pi$
$830$	−49.9292	−1.73307
$831$	65.0991	2.25826
$832$	3.04852	0.105688
$833$	−68.9432	−2.38874
$834$	−1.93328	−0.0669441
$835$	46.8274	1.62053
$836$	−10.4415	−0.361128
$837$	3.89237	0.134540
$838$	−16.1432	−0.557658
$839$	−22.6882	−0.783283	−0.391641	−	0.920118i	$-0.628093\pi$
$839$	−22.6882	−0.783283	−0.391641	+	0.920118i	$0.628093\pi$
$840$	−31.7516	−1.09553
$841$	1.00000	0.0344828
$842$	28.3340	0.976455
$843$	17.1577	0.590944
$844$	8.08766	0.278389
$845$	−13.5713	−0.466866
$846$	9.82147	0.337669
$847$	−6.60875	−0.227079
$848$	−3.19348	−0.109664
$849$	−42.7506	−1.46720
$850$	53.8540	1.84718
$851$	0.533936	0.0183031
$852$	6.79276	0.232716
$853$	−10.1981	−0.349175	−0.174587	−	0.984642i	$-0.555859\pi$
$853$	−10.1981	−0.349175	−0.174587	+	0.984642i	$0.555859\pi$
$854$	49.4395	1.69178
$855$	15.3612	0.525342
$856$	17.7205	0.605675
$857$	−52.7786	−1.80288	−0.901441	−	0.432901i	$-0.857490\pi$
$857$	−52.7786	−1.80288	−0.901441	+	0.432901i	$0.857490\pi$
$858$	19.2647	0.657686
$859$	−47.9536	−1.63616	−0.818078	−	0.575107i	$-0.804961\pi$
$859$	−47.9536	−1.63616	−0.818078	+	0.575107i	$0.804961\pi$
$860$	26.3128	0.897259
$861$	−21.9740	−0.748872
$862$	5.50963	0.187659
$863$	−34.7156	−1.18173	−0.590867	−	0.806769i	$-0.701214\pi$
$863$	−34.7156	−1.18173	−0.590867	+	0.806769i	$0.701214\pi$
$864$	3.63387	0.123627
$865$	75.8361	2.57850
$866$	−28.7766	−0.977869
$867$	49.4731	1.68019
$868$	−4.51423	−0.153223
$869$	27.9778	0.949083
$870$	−7.53401	−0.255427
$871$	−16.0898	−0.545182
$872$	13.0276	0.441170
$873$	22.2331	0.752478
$874$	3.39989	0.115003
$875$	52.5597	1.77684
$876$	−12.6725	−0.428164
$877$	10.2973	0.347715	0.173858	−	0.984771i	$-0.444377\pi$
$877$	10.2973	0.347715	0.173858	+	0.984771i	$0.444377\pi$
$878$	32.4587	1.09543
$879$	4.09240	0.138033
$880$	−11.2448	−0.379061
$881$	16.1496	0.544092	0.272046	−	0.962284i	$-0.412300\pi$
$881$	16.1496	0.544092	0.272046	+	0.962284i	$0.412300\pi$
$882$	−13.2794	−0.447140
$883$	−33.8012	−1.13750	−0.568750	−	0.822510i	$-0.692573\pi$
$883$	−33.8012	−1.13750	−0.568750	+	0.822510i	$0.692573\pi$
$884$	−19.5303	−0.656877
$885$	−63.8648	−2.14679
$886$	34.2159	1.14951
$887$	−22.3873	−0.751693	−0.375846	−	0.926682i	$-0.622648\pi$
$887$	−22.3873	−0.751693	−0.375846	+	0.926682i	$0.622648\pi$
$888$	1.09866	0.0368686
$889$	−48.8333	−1.63782
$890$	−13.9000	−0.465928
$891$	34.3329	1.15020
$892$	−25.1121	−0.840815
$893$	−27.0604	−0.905541
$894$	34.3037	1.14729
$895$	81.0315	2.70859
$896$	−4.21443	−0.140794
$897$	−6.27282	−0.209443
$898$	3.41946	0.114109
$899$	−1.07114	−0.0357244
$900$	10.3730	0.345767
$901$	20.4590	0.681589
$902$	−7.78206	−0.259114
$903$	62.3202	2.07389
$904$	−8.97667	−0.298560
$905$	22.1940	0.737753
$906$	−42.3312	−1.40636
$907$	−11.7379	−0.389749	−0.194875	−	0.980828i	$-0.562430\pi$
$907$	−11.7379	−0.389749	−0.194875	+	0.980828i	$0.562430\pi$
$908$	−2.67321	−0.0887135
$909$	14.2059	0.471179
$910$	−47.0413	−1.55940
$911$	20.2791	0.671878	0.335939	−	0.941884i	$-0.390946\pi$
$911$	20.2791	0.671878	0.335939	+	0.941884i	$0.390946\pi$
$912$	6.99584	0.231655
$913$	−41.8795	−1.38601
$914$	−28.3384	−0.937352
$915$	−88.3815	−2.92180
$916$	−17.8685	−0.590393
$917$	17.9498	0.592756
$918$	−23.2804	−0.768369
$919$	−0.399258	−0.0131703	−0.00658516	−	0.999978i	$-0.502096\pi$
$919$	−0.399258	−0.0131703	−0.00658516	+	0.999978i	$0.502096\pi$
$920$	3.66144	0.120714
$921$	32.4157	1.06813
$922$	2.30643	0.0759582
$923$	10.0638	0.331253
$924$	−26.6325	−0.876146
$925$	−4.48834	−0.147576
$926$	30.1156	0.989659
$927$	3.07679	0.101055
$928$	−1.00000	−0.0328266
$929$	14.2250	0.466706	0.233353	−	0.972392i	$-0.425030\pi$
$929$	14.2250	0.466706	0.233353	+	0.972392i	$0.425030\pi$
$930$	8.06995	0.264624
$931$	36.5877	1.19911
$932$	22.0601	0.722603
$933$	−51.8166	−1.69640
$934$	23.5775	0.771479
$935$	72.0398	2.35595
$936$	−3.76181	−0.122959
$937$	−18.2098	−0.594887	−0.297444	−	0.954739i	$-0.596134\pi$
$937$	−18.2098	−0.594887	−0.297444	+	0.954739i	$0.596134\pi$
$938$	22.2434	0.726272
$939$	40.4640	1.32049
$940$	−29.1421	−0.950509
$941$	6.07886	0.198165	0.0990827	−	0.995079i	$-0.468409\pi$
$941$	6.07886	0.198165	0.0990827	+	0.995079i	$0.468409\pi$
$942$	−23.4411	−0.763752
$943$	2.53394	0.0825163
$944$	−8.47686	−0.275898
$945$	−56.0739	−1.82408
$946$	22.0706	0.717577
$947$	50.8776	1.65330	0.826650	−	0.562716i	$-0.190244\pi$
$947$	50.8776	1.65330	0.826650	+	0.562716i	$0.190244\pi$
$948$	−18.7452	−0.608815
$949$	−18.7749	−0.609458
$950$	−28.5800	−0.927257
$951$	−55.0626	−1.78553
$952$	26.9998	0.875068
$953$	22.8374	0.739775	0.369887	−	0.929077i	$-0.379396\pi$
$953$	22.8374	0.739775	0.369887	+	0.929077i	$0.379396\pi$
$954$	3.94069	0.127585
$955$	−43.0258	−1.39228
$956$	−1.49350	−0.0483031
$957$	−6.31937	−0.204276
$958$	−37.9145	−1.22496
$959$	38.7764	1.25216
$960$	7.53401	0.243159
$961$	−29.8527	−0.962989
$962$	1.62771	0.0524795
$963$	−21.8668	−0.704647
$964$	−18.1496	−0.584559
$965$	82.0150	2.64015
$966$	8.67188	0.279013
$967$	−8.44594	−0.271603	−0.135802	−	0.990736i	$-0.543361\pi$
$967$	−8.44594	−0.271603	−0.135802	+	0.990736i	$0.543361\pi$
$968$	1.56812	0.0504014
$969$	−44.8189	−1.43979
$970$	−65.9697	−2.11816
$971$	−56.6974	−1.81951	−0.909753	−	0.415150i	$-0.863729\pi$
$971$	−56.6974	−1.81951	−0.909753	+	0.415150i	$0.863729\pi$
$972$	−12.1015	−0.388155
$973$	3.95968	0.126941
$974$	8.85727	0.283805
$975$	52.7302	1.68872
$976$	−11.7310	−0.375500
$977$	−31.1904	−0.997869	−0.498934	−	0.866640i	$-0.666275\pi$
$977$	−31.1904	−0.997869	−0.498934	+	0.866640i	$0.666275\pi$
$978$	24.9360	0.797366
$979$	−11.6590	−0.372623
$980$	39.4023	1.25866
$981$	−16.0758	−0.513260
$982$	5.17434	0.165120
$983$	−5.77328	−0.184139	−0.0920696	−	0.995753i	$-0.529348\pi$
$983$	−5.77328	−0.184139	−0.0920696	+	0.995753i	$0.529348\pi$
$984$	5.21399	0.166216
$985$	15.8640	0.505470
$986$	6.40651	0.204025
$987$	−69.0211	−2.19697
$988$	10.3646	0.329743
$989$	−7.18646	−0.228516
$990$	13.8758	0.441003
$991$	−51.4911	−1.63567	−0.817835	−	0.575453i	$-0.804826\pi$
$991$	−51.4911	−1.63567	−0.817835	+	0.575453i	$0.804826\pi$
$992$	1.07114	0.0340086
$993$	−59.9007	−1.90089
$994$	−13.9127	−0.441284
$995$	43.8741	1.39090
$996$	28.0593	0.889093
$997$	−48.6789	−1.54168	−0.770838	−	0.637031i	$-0.780162\pi$
$997$	−48.6789	−1.54168	−0.770838	+	0.637031i	$0.780162\pi$
$998$	−29.1059	−0.921332
$999$	1.94026	0.0613870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.j.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.j.1.7	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.05766 q^{3} +1.00000 q^{4} +3.66144 q^{5} -2.05766 q^{6} +4.21443 q^{7} -1.00000 q^{8} +1.23398 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.05766 q^{3} +1.00000 q^{4} +3.66144 q^{5} -2.05766 q^{6} +4.21443 q^{7} -1.00000 q^{8} +1.23398 q^{9} -3.66144 q^{10} -3.07114 q^{11} +2.05766 q^{12} +3.04852 q^{13} -4.21443 q^{14} +7.53401 q^{15} +1.00000 q^{16} -6.40651 q^{17} -1.23398 q^{18} +3.39989 q^{19} +3.66144 q^{20} +8.67188 q^{21} +3.07114 q^{22} -1.00000 q^{23} -2.05766 q^{24} +8.40614 q^{25} -3.04852 q^{26} -3.63387 q^{27} +4.21443 q^{28} +1.00000 q^{29} -7.53401 q^{30} -1.07114 q^{31} -1.00000 q^{32} -6.31937 q^{33} +6.40651 q^{34} +15.4309 q^{35} +1.23398 q^{36} -0.533936 q^{37} -3.39989 q^{38} +6.27282 q^{39} -3.66144 q^{40} -2.53394 q^{41} -8.67188 q^{42} +7.18646 q^{43} -3.07114 q^{44} +4.51814 q^{45} +1.00000 q^{46} -7.95918 q^{47} +2.05766 q^{48} +10.7614 q^{49} -8.40614 q^{50} -13.1824 q^{51} +3.04852 q^{52} -3.19348 q^{53} +3.63387 q^{54} -11.2448 q^{55} -4.21443 q^{56} +6.99584 q^{57} -1.00000 q^{58} -8.47686 q^{59} +7.53401 q^{60} -11.7310 q^{61} +1.07114 q^{62} +5.20053 q^{63} +1.00000 q^{64} +11.1620 q^{65} +6.31937 q^{66} -5.27790 q^{67} -6.40651 q^{68} -2.05766 q^{69} -15.4309 q^{70} +3.30120 q^{71} -1.23398 q^{72} -6.15868 q^{73} +0.533936 q^{74} +17.2970 q^{75} +3.39989 q^{76} -12.9431 q^{77} -6.27282 q^{78} -9.10993 q^{79} +3.66144 q^{80} -11.1792 q^{81} +2.53394 q^{82} +13.6365 q^{83} +8.67188 q^{84} -23.4570 q^{85} -7.18646 q^{86} +2.05766 q^{87} +3.07114 q^{88} +3.79632 q^{89} -4.51814 q^{90} +12.8478 q^{91} -1.00000 q^{92} -2.20404 q^{93} +7.95918 q^{94} +12.4485 q^{95} -2.05766 q^{96} +18.0174 q^{97} -10.7614 q^{98} -3.78972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * q^99

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