LMFDB - Embedded newform 6042.2.a.z.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
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} - 4x^{8} - 11x^{7} + 51x^{6} + 25x^{5} - 180x^{4} + 29x^{3} + 119x^{2} - 8x - 14 $ x^9 - 4x^8 - 11x^7 + 51x^6 + 25x^5 - 180x^4 + 29x^3 + 119x^2 - 8x - 14
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.362196$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.82978 q^{5} +1.00000 q^{6} -0.790105 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.82978 q^{5} +1.00000 q^{6} -0.790105 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.82978 q^{10} +0.446910 q^{11} -1.00000 q^{12} +0.193805 q^{13} +0.790105 q^{14} -3.82978 q^{15} +1.00000 q^{16} -4.41306 q^{17} -1.00000 q^{18} -1.00000 q^{19} +3.82978 q^{20} +0.790105 q^{21} -0.446910 q^{22} +4.46341 q^{23} +1.00000 q^{24} +9.66725 q^{25} -0.193805 q^{26} -1.00000 q^{27} -0.790105 q^{28} -3.07194 q^{29} +3.82978 q^{30} +2.03661 q^{31} -1.00000 q^{32} -0.446910 q^{33} +4.41306 q^{34} -3.02593 q^{35} +1.00000 q^{36} -6.71886 q^{37} +1.00000 q^{38} -0.193805 q^{39} -3.82978 q^{40} -0.0299034 q^{41} -0.790105 q^{42} +0.658880 q^{43} +0.446910 q^{44} +3.82978 q^{45} -4.46341 q^{46} +6.54823 q^{47} -1.00000 q^{48} -6.37573 q^{49} -9.66725 q^{50} +4.41306 q^{51} +0.193805 q^{52} +1.00000 q^{53} +1.00000 q^{54} +1.71157 q^{55} +0.790105 q^{56} +1.00000 q^{57} +3.07194 q^{58} -4.62022 q^{59} -3.82978 q^{60} +8.27631 q^{61} -2.03661 q^{62} -0.790105 q^{63} +1.00000 q^{64} +0.742230 q^{65} +0.446910 q^{66} +5.32352 q^{67} -4.41306 q^{68} -4.46341 q^{69} +3.02593 q^{70} +6.92682 q^{71} -1.00000 q^{72} +8.46217 q^{73} +6.71886 q^{74} -9.66725 q^{75} -1.00000 q^{76} -0.353105 q^{77} +0.193805 q^{78} +11.7730 q^{79} +3.82978 q^{80} +1.00000 q^{81} +0.0299034 q^{82} +10.0300 q^{83} +0.790105 q^{84} -16.9011 q^{85} -0.658880 q^{86} +3.07194 q^{87} -0.446910 q^{88} -14.3347 q^{89} -3.82978 q^{90} -0.153126 q^{91} +4.46341 q^{92} -2.03661 q^{93} -6.54823 q^{94} -3.82978 q^{95} +1.00000 q^{96} +13.3255 q^{97} +6.37573 q^{98} +0.446910 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9} + q^{10} + 12 q^{11} - 9 q^{12} - q^{13} - 4 q^{14} + q^{15} + 9 q^{16} + 12 q^{17} - 9 q^{18} - 9 q^{19} - q^{20} - 4 q^{21} - 12 q^{22} + 11 q^{23} + 9 q^{24} + 10 q^{25} + q^{26} - 9 q^{27} + 4 q^{28} + 7 q^{29} - q^{30} - 12 q^{31} - 9 q^{32} - 12 q^{33} - 12 q^{34} + 15 q^{35} + 9 q^{36} - 9 q^{37} + 9 q^{38} + q^{39} + q^{40} - 4 q^{41} + 4 q^{42} + 23 q^{43} + 12 q^{44} - q^{45} - 11 q^{46} + 35 q^{47} - 9 q^{48} + 3 q^{49} - 10 q^{50} - 12 q^{51} - q^{52} + 9 q^{53} + 9 q^{54} + 3 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} + 14 q^{59} + q^{60} + 14 q^{61} + 12 q^{62} + 4 q^{63} + 9 q^{64} + 13 q^{65} + 12 q^{66} - 10 q^{67} + 12 q^{68} - 11 q^{69} - 15 q^{70} + 4 q^{71} - 9 q^{72} - 5 q^{73} + 9 q^{74} - 10 q^{75} - 9 q^{76} + 17 q^{77} - q^{78} - 14 q^{79} - q^{80} + 9 q^{81} + 4 q^{82} + 37 q^{83} - 4 q^{84} - 31 q^{85} - 23 q^{86} - 7 q^{87} - 12 q^{88} - 20 q^{89} + q^{90} - 12 q^{91} + 11 q^{92} + 12 q^{93} - 35 q^{94} + q^{95} + 9 q^{96} - 2 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9 + q^10 + 12 * q^11 - 9 * q^12 - q^13 - 4 * q^14 + q^15 + 9 * q^16 + 12 * q^17 - 9 * q^18 - 9 * q^19 - q^20 - 4 * q^21 - 12 * q^22 + 11 * q^23 + 9 * q^24 + 10 * q^25 + q^26 - 9 * q^27 + 4 * q^28 + 7 * q^29 - q^30 - 12 * q^31 - 9 * q^32 - 12 * q^33 - 12 * q^34 + 15 * q^35 + 9 * q^36 - 9 * q^37 + 9 * q^38 + q^39 + q^40 - 4 * q^41 + 4 * q^42 + 23 * q^43 + 12 * q^44 - q^45 - 11 * q^46 + 35 * q^47 - 9 * q^48 + 3 * q^49 - 10 * q^50 - 12 * q^51 - q^52 + 9 * q^53 + 9 * q^54 + 3 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 + 14 * q^59 + q^60 + 14 * q^61 + 12 * q^62 + 4 * q^63 + 9 * q^64 + 13 * q^65 + 12 * q^66 - 10 * q^67 + 12 * q^68 - 11 * q^69 - 15 * q^70 + 4 * q^71 - 9 * q^72 - 5 * q^73 + 9 * q^74 - 10 * q^75 - 9 * q^76 + 17 * q^77 - q^78 - 14 * q^79 - q^80 + 9 * q^81 + 4 * q^82 + 37 * q^83 - 4 * q^84 - 31 * q^85 - 23 * q^86 - 7 * q^87 - 12 * q^88 - 20 * q^89 + q^90 - 12 * q^91 + 11 * q^92 + 12 * q^93 - 35 * q^94 + q^95 + 9 * q^96 - 2 * q^97 - 3 * q^98 + 12 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.82978	1.71273	0.856366	−	0.516370i	$-0.172717\pi$
$5$	3.82978	1.71273	0.856366	+	0.516370i	$0.172717\pi$
$6$	1.00000	0.408248
$7$	−0.790105	−0.298632	−0.149316	−	0.988790i	$-0.547707\pi$
$7$	−0.790105	−0.298632	−0.149316	+	0.988790i	$0.547707\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.82978	−1.21108
$11$	0.446910	0.134748	0.0673741	−	0.997728i	$-0.478538\pi$
$11$	0.446910	0.134748	0.0673741	+	0.997728i	$0.478538\pi$
$12$	−1.00000	−0.288675
$13$	0.193805	0.0537517	0.0268759	−	0.999639i	$-0.491444\pi$
$13$	0.193805	0.0537517	0.0268759	+	0.999639i	$0.491444\pi$
$14$	0.790105	0.211164
$15$	−3.82978	−0.988846
$16$	1.00000	0.250000
$17$	−4.41306	−1.07032	−0.535162	−	0.844749i	$-0.679750\pi$
$17$	−4.41306	−1.07032	−0.535162	+	0.844749i	$0.679750\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.82978	0.856366
$21$	0.790105	0.172415
$22$	−0.446910	−0.0952814
$23$	4.46341	0.930685	0.465343	−	0.885131i	$-0.345931\pi$
$23$	4.46341	0.930685	0.465343	+	0.885131i	$0.345931\pi$
$24$	1.00000	0.204124
$25$	9.66725	1.93345
$26$	−0.193805	−0.0380082
$27$	−1.00000	−0.192450
$28$	−0.790105	−0.149316
$29$	−3.07194	−0.570446	−0.285223	−	0.958461i	$-0.592068\pi$
$29$	−3.07194	−0.570446	−0.285223	+	0.958461i	$0.592068\pi$
$30$	3.82978	0.699220
$31$	2.03661	0.365786	0.182893	−	0.983133i	$-0.441454\pi$
$31$	2.03661	0.365786	0.182893	+	0.983133i	$0.441454\pi$
$32$	−1.00000	−0.176777
$33$	−0.446910	−0.0777970
$34$	4.41306	0.756834
$35$	−3.02593	−0.511476
$36$	1.00000	0.166667
$37$	−6.71886	−1.10457	−0.552287	−	0.833654i	$-0.686245\pi$
$37$	−6.71886	−1.10457	−0.552287	+	0.833654i	$0.686245\pi$
$38$	1.00000	0.162221
$39$	−0.193805	−0.0310336
$40$	−3.82978	−0.605542
$41$	−0.0299034	−0.00467013	−0.00233507	−	0.999997i	$-0.500743\pi$
$41$	−0.0299034	−0.00467013	−0.00233507	+	0.999997i	$0.500743\pi$
$42$	−0.790105	−0.121916
$43$	0.658880	0.100478	0.0502392	−	0.998737i	$-0.484002\pi$
$43$	0.658880	0.100478	0.0502392	+	0.998737i	$0.484002\pi$
$44$	0.446910	0.0673741
$45$	3.82978	0.570911
$46$	−4.46341	−0.658094
$47$	6.54823	0.955158	0.477579	−	0.878589i	$-0.341515\pi$
$47$	6.54823	0.955158	0.477579	+	0.878589i	$0.341515\pi$
$48$	−1.00000	−0.144338
$49$	−6.37573	−0.910819
$50$	−9.66725	−1.36716
$51$	4.41306	0.617952
$52$	0.193805	0.0268759
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	1.71157	0.230788
$56$	0.790105	0.105582
$57$	1.00000	0.132453
$58$	3.07194	0.403366
$59$	−4.62022	−0.601501	−0.300751	−	0.953703i	$-0.597237\pi$
$59$	−4.62022	−0.601501	−0.300751	+	0.953703i	$0.597237\pi$
$60$	−3.82978	−0.494423
$61$	8.27631	1.05967	0.529837	−	0.848100i	$-0.322253\pi$
$61$	8.27631	1.05967	0.529837	+	0.848100i	$0.322253\pi$
$62$	−2.03661	−0.258650
$63$	−0.790105	−0.0995439
$64$	1.00000	0.125000
$65$	0.742230	0.0920623
$66$	0.446910	0.0550108
$67$	5.32352	0.650372	0.325186	−	0.945650i	$-0.394573\pi$
$67$	5.32352	0.650372	0.325186	+	0.945650i	$0.394573\pi$
$68$	−4.41306	−0.535162
$69$	−4.46341	−0.537331
$70$	3.02593	0.361668
$71$	6.92682	0.822062	0.411031	−	0.911621i	$-0.365169\pi$
$71$	6.92682	0.822062	0.411031	+	0.911621i	$0.365169\pi$
$72$	−1.00000	−0.117851
$73$	8.46217	0.990423	0.495211	−	0.868773i	$-0.335091\pi$
$73$	8.46217	0.990423	0.495211	+	0.868773i	$0.335091\pi$
$74$	6.71886	0.781052
$75$	−9.66725	−1.11628
$76$	−1.00000	−0.114708
$77$	−0.353105	−0.0402401
$78$	0.193805	0.0219441
$79$	11.7730	1.32456	0.662280	−	0.749256i	$-0.269589\pi$
$79$	11.7730	1.32456	0.662280	+	0.749256i	$0.269589\pi$
$80$	3.82978	0.428183
$81$	1.00000	0.111111
$82$	0.0299034	0.00330228
$83$	10.0300	1.10094	0.550468	−	0.834856i	$-0.314449\pi$
$83$	10.0300	1.10094	0.550468	+	0.834856i	$0.314449\pi$
$84$	0.790105	0.0862075
$85$	−16.9011	−1.83318
$86$	−0.658880	−0.0710489
$87$	3.07194	0.329347
$88$	−0.446910	−0.0476407
$89$	−14.3347	−1.51947	−0.759737	−	0.650231i	$-0.774672\pi$
$89$	−14.3347	−1.51947	−0.759737	+	0.650231i	$0.774672\pi$
$90$	−3.82978	−0.403695
$91$	−0.153126	−0.0160520
$92$	4.46341	0.465343
$93$	−2.03661	−0.211187
$94$	−6.54823	−0.675398
$95$	−3.82978	−0.392928
$96$	1.00000	0.102062
$97$	13.3255	1.35300	0.676502	−	0.736441i	$-0.263495\pi$
$97$	13.3255	1.35300	0.676502	+	0.736441i	$0.263495\pi$
$98$	6.37573	0.644046
$99$	0.446910	0.0449161
$100$	9.66725	0.966725
$101$	5.76906	0.574043	0.287021	−	0.957924i	$-0.407335\pi$
$101$	5.76906	0.574043	0.287021	+	0.957924i	$0.407335\pi$
$102$	−4.41306	−0.436958
$103$	−4.31765	−0.425431	−0.212715	−	0.977114i	$-0.568231\pi$
$103$	−4.31765	−0.425431	−0.212715	+	0.977114i	$0.568231\pi$
$104$	−0.193805	−0.0190041
$105$	3.02593	0.295301
$106$	−1.00000	−0.0971286
$107$	14.0342	1.35674	0.678368	−	0.734722i	$-0.262688\pi$
$107$	14.0342	1.35674	0.678368	+	0.734722i	$0.262688\pi$
$108$	−1.00000	−0.0962250
$109$	11.7618	1.12658	0.563289	−	0.826260i	$-0.309536\pi$
$109$	11.7618	1.12658	0.563289	+	0.826260i	$0.309536\pi$
$110$	−1.71157	−0.163192
$111$	6.71886	0.637726
$112$	−0.790105	−0.0746579
$113$	−5.70150	−0.536352	−0.268176	−	0.963370i	$-0.586421\pi$
$113$	−5.70150	−0.536352	−0.268176	+	0.963370i	$0.586421\pi$
$114$	−1.00000	−0.0936586
$115$	17.0939	1.59401
$116$	−3.07194	−0.285223
$117$	0.193805	0.0179172
$118$	4.62022	0.425325
$119$	3.48678	0.319633
$120$	3.82978	0.349610
$121$	−10.8003	−0.981843
$122$	−8.27631	−0.749302
$123$	0.0299034	0.00269630
$124$	2.03661	0.182893
$125$	17.8746	1.59875
$126$	0.790105	0.0703881
$127$	1.60126	0.142089	0.0710444	−	0.997473i	$-0.477367\pi$
$127$	1.60126	0.142089	0.0710444	+	0.997473i	$0.477367\pi$
$128$	−1.00000	−0.0883883
$129$	−0.658880	−0.0580112
$130$	−0.742230	−0.0650979
$131$	12.8066	1.11892	0.559459	−	0.828858i	$-0.311009\pi$
$131$	12.8066	1.11892	0.559459	+	0.828858i	$0.311009\pi$
$132$	−0.446910	−0.0388985
$133$	0.790105	0.0685108
$134$	−5.32352	−0.459883
$135$	−3.82978	−0.329615
$136$	4.41306	0.378417
$137$	6.61702	0.565330	0.282665	−	0.959219i	$-0.408782\pi$
$137$	6.61702	0.565330	0.282665	+	0.959219i	$0.408782\pi$
$138$	4.46341	0.379951
$139$	0.642811	0.0545225	0.0272613	−	0.999628i	$-0.491321\pi$
$139$	0.642811	0.0545225	0.0272613	+	0.999628i	$0.491321\pi$
$140$	−3.02593	−0.255738
$141$	−6.54823	−0.551460
$142$	−6.92682	−0.581286
$143$	0.0866131	0.00724295
$144$	1.00000	0.0833333
$145$	−11.7649	−0.977020
$146$	−8.46217	−0.700335
$147$	6.37573	0.525862
$148$	−6.71886	−0.552287
$149$	0.421009	0.0344904	0.0172452	−	0.999851i	$-0.494510\pi$
$149$	0.421009	0.0344904	0.0172452	+	0.999851i	$0.494510\pi$
$150$	9.66725	0.789328
$151$	13.0626	1.06302	0.531511	−	0.847052i	$-0.321625\pi$
$151$	13.0626	1.06302	0.531511	+	0.847052i	$0.321625\pi$
$152$	1.00000	0.0811107
$153$	−4.41306	−0.356775
$154$	0.353105	0.0284540
$155$	7.79978	0.626493
$156$	−0.193805	−0.0155168
$157$	14.4289	1.15155	0.575775	−	0.817608i	$-0.304700\pi$
$157$	14.4289	1.15155	0.575775	+	0.817608i	$0.304700\pi$
$158$	−11.7730	−0.936606
$159$	−1.00000	−0.0793052
$160$	−3.82978	−0.302771
$161$	−3.52656	−0.277932
$162$	−1.00000	−0.0785674
$163$	18.1071	1.41825	0.709127	−	0.705081i	$-0.249089\pi$
$163$	18.1071	1.41825	0.709127	+	0.705081i	$0.249089\pi$
$164$	−0.0299034	−0.00233507
$165$	−1.71157	−0.133245
$166$	−10.0300	−0.778479
$167$	21.5543	1.66792	0.833960	−	0.551825i	$-0.186068\pi$
$167$	21.5543	1.66792	0.833960	+	0.551825i	$0.186068\pi$
$168$	−0.790105	−0.0609579
$169$	−12.9624	−0.997111
$170$	16.9011	1.29625
$171$	−1.00000	−0.0764719
$172$	0.658880	0.0502392
$173$	−1.64948	−0.125408	−0.0627039	−	0.998032i	$-0.519972\pi$
$173$	−1.64948	−0.125408	−0.0627039	+	0.998032i	$0.519972\pi$
$174$	−3.07194	−0.232883
$175$	−7.63814	−0.577389
$176$	0.446910	0.0336871
$177$	4.62022	0.347277
$178$	14.3347	1.07443
$179$	−24.5074	−1.83177	−0.915885	−	0.401440i	$-0.868510\pi$
$179$	−24.5074	−1.83177	−0.915885	+	0.401440i	$0.868510\pi$
$180$	3.82978	0.285455
$181$	−8.78529	−0.653006	−0.326503	−	0.945196i	$-0.605870\pi$
$181$	−8.78529	−0.653006	−0.326503	+	0.945196i	$0.605870\pi$
$182$	0.153126	0.0113505
$183$	−8.27631	−0.611803
$184$	−4.46341	−0.329047
$185$	−25.7318	−1.89184
$186$	2.03661	0.149332
$187$	−1.97224	−0.144224
$188$	6.54823	0.477579
$189$	0.790105	0.0574717
$190$	3.82978	0.277842
$191$	−7.06173	−0.510969	−0.255485	−	0.966813i	$-0.582235\pi$
$191$	−7.06173	−0.510969	−0.255485	+	0.966813i	$0.582235\pi$
$192$	−1.00000	−0.0721688
$193$	8.35398	0.601333	0.300666	−	0.953729i	$-0.402791\pi$
$193$	8.35398	0.601333	0.300666	+	0.953729i	$0.402791\pi$
$194$	−13.3255	−0.956718
$195$	−0.742230	−0.0531522
$196$	−6.37573	−0.455410
$197$	10.5400	0.750942	0.375471	−	0.926834i	$-0.377481\pi$
$197$	10.5400	0.750942	0.375471	+	0.926834i	$0.377481\pi$
$198$	−0.446910	−0.0317605
$199$	−14.2303	−1.00876	−0.504381	−	0.863481i	$-0.668279\pi$
$199$	−14.2303	−1.00876	−0.504381	+	0.863481i	$0.668279\pi$
$200$	−9.66725	−0.683578
$201$	−5.32352	−0.375492
$202$	−5.76906	−0.405910
$203$	2.42716	0.170353
$204$	4.41306	0.308976
$205$	−0.114524	−0.00799868
$206$	4.31765	0.300825
$207$	4.46341	0.310228
$208$	0.193805	0.0134379
$209$	−0.446910	−0.0309134
$210$	−3.02593	−0.208809
$211$	−22.3210	−1.53664	−0.768319	−	0.640067i	$-0.778907\pi$
$211$	−22.3210	−1.53664	−0.768319	+	0.640067i	$0.778907\pi$
$212$	1.00000	0.0686803
$213$	−6.92682	−0.474618
$214$	−14.0342	−0.959357
$215$	2.52337	0.172092
$216$	1.00000	0.0680414
$217$	−1.60914	−0.109235
$218$	−11.7618	−0.796612
$219$	−8.46217	−0.571821
$220$	1.71157	0.115394
$221$	−0.855272	−0.0575318
$222$	−6.71886	−0.450941
$223$	−12.9146	−0.864828	−0.432414	−	0.901675i	$-0.642338\pi$
$223$	−12.9146	−0.864828	−0.432414	+	0.901675i	$0.642338\pi$
$224$	0.790105	0.0527911
$225$	9.66725	0.644483
$226$	5.70150	0.379258
$227$	−7.82435	−0.519320	−0.259660	−	0.965700i	$-0.583611\pi$
$227$	−7.82435	−0.519320	−0.259660	+	0.965700i	$0.583611\pi$
$228$	1.00000	0.0662266
$229$	−9.42402	−0.622757	−0.311378	−	0.950286i	$-0.600791\pi$
$229$	−9.42402	−0.622757	−0.311378	+	0.950286i	$0.600791\pi$
$230$	−17.0939	−1.12714
$231$	0.353105	0.0232326
$232$	3.07194	0.201683
$233$	−1.78897	−0.117199	−0.0585996	−	0.998282i	$-0.518664\pi$
$233$	−1.78897	−0.117199	−0.0585996	+	0.998282i	$0.518664\pi$
$234$	−0.193805	−0.0126694
$235$	25.0783	1.63593
$236$	−4.62022	−0.300751
$237$	−11.7730	−0.764736
$238$	−3.48678	−0.226015
$239$	16.7328	1.08236	0.541178	−	0.840908i	$-0.317979\pi$
$239$	16.7328	1.08236	0.541178	+	0.840908i	$0.317979\pi$
$240$	−3.82978	−0.247212
$241$	−10.9047	−0.702434	−0.351217	−	0.936294i	$-0.614232\pi$
$241$	−10.9047	−0.702434	−0.351217	+	0.936294i	$0.614232\pi$
$242$	10.8003	0.694268
$243$	−1.00000	−0.0641500
$244$	8.27631	0.529837
$245$	−24.4177	−1.55999
$246$	−0.0299034	−0.00190657
$247$	−0.193805	−0.0123315
$248$	−2.03661	−0.129325
$249$	−10.0300	−0.635626
$250$	−17.8746	−1.13049
$251$	28.9380	1.82655	0.913277	−	0.407340i	$-0.133543\pi$
$251$	28.9380	1.82655	0.913277	+	0.407340i	$0.133543\pi$
$252$	−0.790105	−0.0497719
$253$	1.99474	0.125408
$254$	−1.60126	−0.100472
$255$	16.9011	1.05839
$256$	1.00000	0.0625000
$257$	−2.68567	−0.167528	−0.0837639	−	0.996486i	$-0.526694\pi$
$257$	−2.68567	−0.167528	−0.0837639	+	0.996486i	$0.526694\pi$
$258$	0.658880	0.0410201
$259$	5.30861	0.329861
$260$	0.742230	0.0460311
$261$	−3.07194	−0.190149
$262$	−12.8066	−0.791195
$263$	4.59887	0.283579	0.141789	−	0.989897i	$-0.454714\pi$
$263$	4.59887	0.283579	0.141789	+	0.989897i	$0.454714\pi$
$264$	0.446910	0.0275054
$265$	3.82978	0.235262
$266$	−0.790105	−0.0484444
$267$	14.3347	0.877268
$268$	5.32352	0.325186
$269$	−10.6225	−0.647668	−0.323834	−	0.946114i	$-0.604972\pi$
$269$	−10.6225	−0.647668	−0.323834	+	0.946114i	$0.604972\pi$
$270$	3.82978	0.233073
$271$	−2.73151	−0.165927	−0.0829637	−	0.996553i	$-0.526439\pi$
$271$	−2.73151	−0.165927	−0.0829637	+	0.996553i	$0.526439\pi$
$272$	−4.41306	−0.267581
$273$	0.153126	0.00926761
$274$	−6.61702	−0.399749
$275$	4.32039	0.260529
$276$	−4.46341	−0.268666
$277$	13.3642	0.802980	0.401490	−	0.915864i	$-0.368493\pi$
$277$	13.3642	0.802980	0.401490	+	0.915864i	$0.368493\pi$
$278$	−0.642811	−0.0385532
$279$	2.03661	0.121929
$280$	3.02593	0.180834
$281$	3.02842	0.180660	0.0903302	−	0.995912i	$-0.471208\pi$
$281$	3.02842	0.180660	0.0903302	+	0.995912i	$0.471208\pi$
$282$	6.54823	0.389941
$283$	−17.0084	−1.01104	−0.505521	−	0.862814i	$-0.668700\pi$
$283$	−17.0084	−1.01104	−0.505521	+	0.862814i	$0.668700\pi$
$284$	6.92682	0.411031
$285$	3.82978	0.226857
$286$	−0.0866131	−0.00512154
$287$	0.0236268	0.00139465
$288$	−1.00000	−0.0589256
$289$	2.47512	0.145595
$290$	11.7649	0.690858
$291$	−13.3255	−0.781157
$292$	8.46217	0.495211
$293$	−1.69944	−0.0992826	−0.0496413	−	0.998767i	$-0.515808\pi$
$293$	−1.69944	−0.0992826	−0.0496413	+	0.998767i	$0.515808\pi$
$294$	−6.37573	−0.371840
$295$	−17.6944	−1.03021
$296$	6.71886	0.390526
$297$	−0.446910	−0.0259323
$298$	−0.421009	−0.0243884
$299$	0.865029	0.0500259
$300$	−9.66725	−0.558139
$301$	−0.520585	−0.0300060
$302$	−13.0626	−0.751670
$303$	−5.76906	−0.331424
$304$	−1.00000	−0.0573539
$305$	31.6965	1.81494
$306$	4.41306	0.252278
$307$	10.9862	0.627016	0.313508	−	0.949585i	$-0.398496\pi$
$307$	10.9862	0.627016	0.313508	+	0.949585i	$0.398496\pi$
$308$	−0.353105	−0.0201200
$309$	4.31765	0.245622
$310$	−7.79978	−0.442998
$311$	12.7816	0.724779	0.362389	−	0.932027i	$-0.381961\pi$
$311$	12.7816	0.724779	0.362389	+	0.932027i	$0.381961\pi$
$312$	0.193805	0.0109720
$313$	−9.87055	−0.557916	−0.278958	−	0.960303i	$-0.589989\pi$
$313$	−9.87055	−0.557916	−0.278958	+	0.960303i	$0.589989\pi$
$314$	−14.4289	−0.814269
$315$	−3.02593	−0.170492
$316$	11.7730	0.662280
$317$	6.53804	0.367213	0.183607	−	0.983000i	$-0.441223\pi$
$317$	6.53804	0.367213	0.183607	+	0.983000i	$0.441223\pi$
$318$	1.00000	0.0560772
$319$	−1.37288	−0.0768666
$320$	3.82978	0.214091
$321$	−14.0342	−0.783312
$322$	3.52656	0.196528
$323$	4.41306	0.245549
$324$	1.00000	0.0555556
$325$	1.87356	0.103926
$326$	−18.1071	−1.00286
$327$	−11.7618	−0.650431
$328$	0.0299034	0.00165114
$329$	−5.17379	−0.285240
$330$	1.71157	0.0942187
$331$	−1.85852	−0.102154	−0.0510768	−	0.998695i	$-0.516265\pi$
$331$	−1.85852	−0.102154	−0.0510768	+	0.998695i	$0.516265\pi$
$332$	10.0300	0.550468
$333$	−6.71886	−0.368192
$334$	−21.5543	−1.17940
$335$	20.3880	1.11391
$336$	0.790105	0.0431038
$337$	−5.34743	−0.291293	−0.145647	−	0.989337i	$-0.546526\pi$
$337$	−5.34743	−0.291293	−0.145647	+	0.989337i	$0.546526\pi$
$338$	12.9624	0.705064
$339$	5.70150	0.309663
$340$	−16.9011	−0.916590
$341$	0.910181	0.0492891
$342$	1.00000	0.0540738
$343$	10.5682	0.570631
$344$	−0.658880	−0.0355245
$345$	−17.0939	−0.920304
$346$	1.64948	0.0886767
$347$	23.5161	1.26241	0.631205	−	0.775616i	$-0.282560\pi$
$347$	23.5161	1.26241	0.631205	+	0.775616i	$0.282560\pi$
$348$	3.07194	0.164673
$349$	−18.1502	−0.971556	−0.485778	−	0.874082i	$-0.661464\pi$
$349$	−18.1502	−0.971556	−0.485778	+	0.874082i	$0.661464\pi$
$350$	7.63814	0.408276
$351$	−0.193805	−0.0103445
$352$	−0.446910	−0.0238204
$353$	−9.08780	−0.483695	−0.241847	−	0.970314i	$-0.577753\pi$
$353$	−9.08780	−0.483695	−0.241847	+	0.970314i	$0.577753\pi$
$354$	−4.62022	−0.245562
$355$	26.5282	1.40797
$356$	−14.3347	−0.759737
$357$	−3.48678	−0.184540
$358$	24.5074	1.29526
$359$	12.8542	0.678421	0.339210	−	0.940711i	$-0.389840\pi$
$359$	12.8542	0.678421	0.339210	+	0.940711i	$0.389840\pi$
$360$	−3.82978	−0.201847
$361$	1.00000	0.0526316
$362$	8.78529	0.461745
$363$	10.8003	0.566867
$364$	−0.153126	−0.00802598
$365$	32.4083	1.69633
$366$	8.27631	0.432610
$367$	2.90067	0.151414	0.0757068	−	0.997130i	$-0.475879\pi$
$367$	2.90067	0.151414	0.0757068	+	0.997130i	$0.475879\pi$
$368$	4.46341	0.232671
$369$	−0.0299034	−0.00155671
$370$	25.7318	1.33773
$371$	−0.790105	−0.0410202
$372$	−2.03661	−0.105593
$373$	−21.8174	−1.12966	−0.564832	−	0.825206i	$-0.691059\pi$
$373$	−21.8174	−1.12966	−0.564832	+	0.825206i	$0.691059\pi$
$374$	1.97224	0.101982
$375$	−17.8746	−0.923038
$376$	−6.54823	−0.337699
$377$	−0.595357	−0.0306624
$378$	−0.790105	−0.0406386
$379$	−21.1583	−1.08683	−0.543415	−	0.839464i	$-0.682869\pi$
$379$	−21.1583	−1.08683	−0.543415	+	0.839464i	$0.682869\pi$
$380$	−3.82978	−0.196464
$381$	−1.60126	−0.0820350
$382$	7.06173	0.361310
$383$	8.88087	0.453791	0.226896	−	0.973919i	$-0.427142\pi$
$383$	8.88087	0.453791	0.226896	+	0.973919i	$0.427142\pi$
$384$	1.00000	0.0510310
$385$	−1.35232	−0.0689205
$386$	−8.35398	−0.425206
$387$	0.658880	0.0334928
$388$	13.3255	0.676502
$389$	25.4647	1.29111	0.645556	−	0.763713i	$-0.276626\pi$
$389$	25.4647	1.29111	0.645556	+	0.763713i	$0.276626\pi$
$390$	0.742230	0.0375843
$391$	−19.6973	−0.996135
$392$	6.37573	0.322023
$393$	−12.8066	−0.646008
$394$	−10.5400	−0.530996
$395$	45.0879	2.26862
$396$	0.446910	0.0224580
$397$	−0.921126	−0.0462300	−0.0231150	−	0.999733i	$-0.507358\pi$
$397$	−0.921126	−0.0462300	−0.0231150	+	0.999733i	$0.507358\pi$
$398$	14.2303	0.713302
$399$	−0.790105	−0.0395547
$400$	9.66725	0.483362
$401$	26.0639	1.30157	0.650785	−	0.759262i	$-0.274440\pi$
$401$	26.0639	1.30157	0.650785	+	0.759262i	$0.274440\pi$
$402$	5.32352	0.265513
$403$	0.394705	0.0196616
$404$	5.76906	0.287021
$405$	3.82978	0.190304
$406$	−2.42716	−0.120458
$407$	−3.00272	−0.148840
$408$	−4.41306	−0.218479
$409$	26.3759	1.30420	0.652102	−	0.758131i	$-0.273887\pi$
$409$	26.3759	1.30420	0.652102	+	0.758131i	$0.273887\pi$
$410$	0.114524	0.00565592
$411$	−6.61702	−0.326393
$412$	−4.31765	−0.212715
$413$	3.65046	0.179627
$414$	−4.46341	−0.219365
$415$	38.4127	1.88561
$416$	−0.193805	−0.00950205
$417$	−0.642811	−0.0314786
$418$	0.446910	0.0218591
$419$	15.8308	0.773383	0.386692	−	0.922209i	$-0.373618\pi$
$419$	15.8308	0.773383	0.386692	+	0.922209i	$0.373618\pi$
$420$	3.02593	0.147650
$421$	18.9690	0.924490	0.462245	−	0.886752i	$-0.347044\pi$
$421$	18.9690	0.924490	0.462245	+	0.886752i	$0.347044\pi$
$422$	22.3210	1.08657
$423$	6.54823	0.318386
$424$	−1.00000	−0.0485643
$425$	−42.6622	−2.06942
$426$	6.92682	0.335605
$427$	−6.53915	−0.316452
$428$	14.0342	0.678368
$429$	−0.0866131	−0.00418172
$430$	−2.52337	−0.121688
$431$	15.9307	0.767357	0.383678	−	0.923467i	$-0.374657\pi$
$431$	15.9307	0.767357	0.383678	+	0.923467i	$0.374657\pi$
$432$	−1.00000	−0.0481125
$433$	−15.6597	−0.752555	−0.376277	−	0.926507i	$-0.622796\pi$
$433$	−15.6597	−0.752555	−0.376277	+	0.926507i	$0.622796\pi$
$434$	1.60914	0.0772410
$435$	11.7649	0.564083
$436$	11.7618	0.563289
$437$	−4.46341	−0.213514
$438$	8.46217	0.404338
$439$	−16.6208	−0.793268	−0.396634	−	0.917977i	$-0.629822\pi$
$439$	−16.6208	−0.793268	−0.396634	+	0.917977i	$0.629822\pi$
$440$	−1.71157	−0.0815958
$441$	−6.37573	−0.303606
$442$	0.855272	0.0406811
$443$	−12.9754	−0.616481	−0.308240	−	0.951308i	$-0.599740\pi$
$443$	−12.9754	−0.616481	−0.308240	+	0.951308i	$0.599740\pi$
$444$	6.71886	0.318863
$445$	−54.8987	−2.60245
$446$	12.9146	0.611526
$447$	−0.421009	−0.0199131
$448$	−0.790105	−0.0373289
$449$	−1.70560	−0.0804921	−0.0402460	−	0.999190i	$-0.512814\pi$
$449$	−1.70560	−0.0804921	−0.0402460	+	0.999190i	$0.512814\pi$
$450$	−9.66725	−0.455718
$451$	−0.0133641	−0.000629292 0
$452$	−5.70150	−0.268176
$453$	−13.0626	−0.613736
$454$	7.82435	0.367215
$455$	−0.586439	−0.0274927
$456$	−1.00000	−0.0468293
$457$	−15.7323	−0.735928	−0.367964	−	0.929840i	$-0.619945\pi$
$457$	−15.7323	−0.735928	−0.367964	+	0.929840i	$0.619945\pi$
$458$	9.42402	0.440355
$459$	4.41306	0.205984
$460$	17.0939	0.797007
$461$	30.5681	1.42370	0.711850	−	0.702331i	$-0.247857\pi$
$461$	30.5681	1.42370	0.711850	+	0.702331i	$0.247857\pi$
$462$	−0.353105	−0.0164280
$463$	−4.71049	−0.218915	−0.109457	−	0.993991i	$-0.534911\pi$
$463$	−4.71049	−0.218915	−0.109457	+	0.993991i	$0.534911\pi$
$464$	−3.07194	−0.142611
$465$	−7.79978	−0.361706
$466$	1.78897	0.0828723
$467$	35.6878	1.65143	0.825716	−	0.564086i	$-0.190771\pi$
$467$	35.6878	1.65143	0.825716	+	0.564086i	$0.190771\pi$
$468$	0.193805	0.00895862
$469$	−4.20614	−0.194222
$470$	−25.0783	−1.15678
$471$	−14.4289	−0.664848
$472$	4.62022	0.212663
$473$	0.294460	0.0135393
$474$	11.7730	0.540750
$475$	−9.66725	−0.443564
$476$	3.48678	0.159816
$477$	1.00000	0.0457869
$478$	−16.7328	−0.765341
$479$	26.4955	1.21061	0.605306	−	0.795993i	$-0.293051\pi$
$479$	26.4955	1.21061	0.605306	+	0.795993i	$0.293051\pi$
$480$	3.82978	0.174805
$481$	−1.30215	−0.0593728
$482$	10.9047	0.496696
$483$	3.52656	0.160464
$484$	−10.8003	−0.490921
$485$	51.0339	2.31733
$486$	1.00000	0.0453609
$487$	−6.22402	−0.282037	−0.141019	−	0.990007i	$-0.545038\pi$
$487$	−6.22402	−0.282037	−0.141019	+	0.990007i	$0.545038\pi$
$488$	−8.27631	−0.374651
$489$	−18.1071	−0.818830
$490$	24.4177	1.10308
$491$	−3.70736	−0.167311	−0.0836555	−	0.996495i	$-0.526660\pi$
$491$	−3.70736	−0.167311	−0.0836555	+	0.996495i	$0.526660\pi$
$492$	0.0299034	0.00134815
$493$	13.5567	0.610562
$494$	0.193805	0.00871968
$495$	1.71157	0.0769292
$496$	2.03661	0.0914465
$497$	−5.47291	−0.245494
$498$	10.0300	0.449455
$499$	−26.8514	−1.20203	−0.601016	−	0.799237i	$-0.705237\pi$
$499$	−26.8514	−1.20203	−0.601016	+	0.799237i	$0.705237\pi$
$500$	17.8746	0.799374
$501$	−21.5543	−0.962974
$502$	−28.9380	−1.29157
$503$	−14.8535	−0.662287	−0.331143	−	0.943580i	$-0.607434\pi$
$503$	−14.8535	−0.662287	−0.331143	+	0.943580i	$0.607434\pi$
$504$	0.790105	0.0351941
$505$	22.0943	0.983182
$506$	−1.99474	−0.0886770
$507$	12.9624	0.575682
$508$	1.60126	0.0710444
$509$	16.0631	0.711984	0.355992	−	0.934489i	$-0.384143\pi$
$509$	16.0631	0.711984	0.355992	+	0.934489i	$0.384143\pi$
$510$	−16.9011	−0.748392
$511$	−6.68601	−0.295771
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	2.68567	0.118460
$515$	−16.5357	−0.728648
$516$	−0.658880	−0.0290056
$517$	2.92647	0.128706
$518$	−5.30861	−0.233247
$519$	1.64948	0.0724043
$520$	−0.742230	−0.0325489
$521$	−38.4530	−1.68466	−0.842328	−	0.538966i	$-0.818815\pi$
$521$	−38.4530	−1.68466	−0.842328	+	0.538966i	$0.818815\pi$
$522$	3.07194	0.134455
$523$	4.20178	0.183731	0.0918656	−	0.995771i	$-0.470717\pi$
$523$	4.20178	0.183731	0.0918656	+	0.995771i	$0.470717\pi$
$524$	12.8066	0.559459
$525$	7.63814	0.333356
$526$	−4.59887	−0.200520
$527$	−8.98769	−0.391510
$528$	−0.446910	−0.0194492
$529$	−3.07798	−0.133825
$530$	−3.82978	−0.166355
$531$	−4.62022	−0.200500
$532$	0.790105	0.0342554
$533$	−0.00579542	−0.000251028 0
$534$	−14.3347	−0.620322
$535$	53.7479	2.32372
$536$	−5.32352	−0.229941
$537$	24.5074	1.05757
$538$	10.6225	0.457970
$539$	−2.84938	−0.122731
$540$	−3.82978	−0.164808
$541$	−42.0824	−1.80926	−0.904631	−	0.426196i	$-0.859853\pi$
$541$	−42.0824	−1.80926	−0.904631	+	0.426196i	$0.859853\pi$
$542$	2.73151	0.117328
$543$	8.78529	0.377013
$544$	4.41306	0.189209
$545$	45.0453	1.92953
$546$	−0.153126	−0.00655319
$547$	7.95114	0.339966	0.169983	−	0.985447i	$-0.445629\pi$
$547$	7.95114	0.339966	0.169983	+	0.985447i	$0.445629\pi$
$548$	6.61702	0.282665
$549$	8.27631	0.353224
$550$	−4.32039	−0.184222
$551$	3.07194	0.130869
$552$	4.46341	0.189975
$553$	−9.30187	−0.395556
$554$	−13.3642	−0.567792
$555$	25.7318	1.09225
$556$	0.642811	0.0272613
$557$	9.35756	0.396493	0.198246	−	0.980152i	$-0.436475\pi$
$557$	9.35756	0.396493	0.198246	+	0.980152i	$0.436475\pi$
$558$	−2.03661	−0.0862166
$559$	0.127694	0.00540088
$560$	−3.02593	−0.127869
$561$	1.97224	0.0832680
$562$	−3.02842	−0.127746
$563$	20.1890	0.850864	0.425432	−	0.904990i	$-0.360122\pi$
$563$	20.1890	0.850864	0.425432	+	0.904990i	$0.360122\pi$
$564$	−6.54823	−0.275730
$565$	−21.8355	−0.918628
$566$	17.0084	0.714915
$567$	−0.790105	−0.0331813
$568$	−6.92682	−0.290643
$569$	5.00784	0.209939	0.104970	−	0.994475i	$-0.466525\pi$
$569$	5.00784	0.209939	0.104970	+	0.994475i	$0.466525\pi$
$570$	−3.82978	−0.160412
$571$	−9.85105	−0.412254	−0.206127	−	0.978525i	$-0.566086\pi$
$571$	−9.85105	−0.412254	−0.206127	+	0.978525i	$0.566086\pi$
$572$	0.0866131	0.00362148
$573$	7.06173	0.295008
$574$	−0.0236268	−0.000986166 0
$575$	43.1489	1.79943
$576$	1.00000	0.0416667
$577$	45.6607	1.90088	0.950439	−	0.310911i	$-0.100634\pi$
$577$	45.6607	1.90088	0.950439	+	0.310911i	$0.100634\pi$
$578$	−2.47512	−0.102952
$579$	−8.35398	−0.347179
$580$	−11.7649	−0.488510
$581$	−7.92475	−0.328774
$582$	13.3255	0.552361
$583$	0.446910	0.0185091
$584$	−8.46217	−0.350167
$585$	0.742230	0.0306874
$586$	1.69944	0.0702034
$587$	−30.1982	−1.24641	−0.623207	−	0.782057i	$-0.714171\pi$
$587$	−30.1982	−1.24641	−0.623207	+	0.782057i	$0.714171\pi$
$588$	6.37573	0.262931
$589$	−2.03661	−0.0839171
$590$	17.6944	0.728468
$591$	−10.5400	−0.433556
$592$	−6.71886	−0.276144
$593$	13.9809	0.574128	0.287064	−	0.957911i	$-0.407321\pi$
$593$	13.9809	0.574128	0.287064	+	0.957911i	$0.407321\pi$
$594$	0.446910	0.0183369
$595$	13.3536	0.547445
$596$	0.421009	0.0172452
$597$	14.2303	0.582409
$598$	−0.865029	−0.0353737
$599$	−31.0504	−1.26868	−0.634342	−	0.773053i	$-0.718729\pi$
$599$	−31.0504	−1.26868	−0.634342	+	0.773053i	$0.718729\pi$
$600$	9.66725	0.394664
$601$	36.1523	1.47468	0.737342	−	0.675519i	$-0.236080\pi$
$601$	36.1523	1.47468	0.737342	+	0.675519i	$0.236080\pi$
$602$	0.520585	0.0212174
$603$	5.32352	0.216791
$604$	13.0626	0.531511
$605$	−41.3627	−1.68163
$606$	5.76906	0.234352
$607$	12.7071	0.515763	0.257882	−	0.966176i	$-0.416976\pi$
$607$	12.7071	0.515763	0.257882	+	0.966176i	$0.416976\pi$
$608$	1.00000	0.0405554
$609$	−2.42716	−0.0983534
$610$	−31.6965	−1.28335
$611$	1.26908	0.0513414
$612$	−4.41306	−0.178387
$613$	−10.8643	−0.438803	−0.219402	−	0.975635i	$-0.570411\pi$
$613$	−10.8643	−0.438803	−0.219402	+	0.975635i	$0.570411\pi$
$614$	−10.9862	−0.443368
$615$	0.114524	0.00461804
$616$	0.353105	0.0142270
$617$	−32.6827	−1.31576	−0.657878	−	0.753125i	$-0.728546\pi$
$617$	−32.6827	−1.31576	−0.657878	+	0.753125i	$0.728546\pi$
$618$	−4.31765	−0.173681
$619$	8.72781	0.350800	0.175400	−	0.984497i	$-0.443878\pi$
$619$	8.72781	0.350800	0.175400	+	0.984497i	$0.443878\pi$
$620$	7.79978	0.313247
$621$	−4.46341	−0.179110
$622$	−12.7816	−0.512496
$623$	11.3259	0.453763
$624$	−0.193805	−0.00775839
$625$	20.1195	0.804778
$626$	9.87055	0.394506
$627$	0.446910	0.0178478
$628$	14.4289	0.575775
$629$	29.6508	1.18225
$630$	3.02593	0.120556
$631$	27.2592	1.08517	0.542586	−	0.840000i	$-0.317445\pi$
$631$	27.2592	1.08517	0.542586	+	0.840000i	$0.317445\pi$
$632$	−11.7730	−0.468303
$633$	22.3210	0.887179
$634$	−6.53804	−0.259659
$635$	6.13248	0.243360
$636$	−1.00000	−0.0396526
$637$	−1.23565	−0.0489581
$638$	1.37288	0.0543529
$639$	6.92682	0.274021
$640$	−3.82978	−0.151386
$641$	−13.8963	−0.548870	−0.274435	−	0.961606i	$-0.588491\pi$
$641$	−13.8963	−0.548870	−0.274435	+	0.961606i	$0.588491\pi$
$642$	14.0342	0.553885
$643$	3.63156	0.143215	0.0716073	−	0.997433i	$-0.477187\pi$
$643$	3.63156	0.143215	0.0716073	+	0.997433i	$0.477187\pi$
$644$	−3.52656	−0.138966
$645$	−2.52337	−0.0993576
$646$	−4.41306	−0.173630
$647$	39.8219	1.56556	0.782780	−	0.622299i	$-0.213801\pi$
$647$	39.8219	1.56556	0.782780	+	0.622299i	$0.213801\pi$
$648$	−1.00000	−0.0392837
$649$	−2.06482	−0.0810512
$650$	−1.87356	−0.0734870
$651$	1.60914	0.0630670
$652$	18.1071	0.709127
$653$	−3.81742	−0.149387	−0.0746937	−	0.997207i	$-0.523798\pi$
$653$	−3.81742	−0.149387	−0.0746937	+	0.997207i	$0.523798\pi$
$654$	11.7618	0.459924
$655$	49.0465	1.91641
$656$	−0.0299034	−0.00116753
$657$	8.46217	0.330141
$658$	5.17379	0.201695
$659$	29.3038	1.14151	0.570757	−	0.821119i	$-0.306650\pi$
$659$	29.3038	1.14151	0.570757	+	0.821119i	$0.306650\pi$
$660$	−1.71157	−0.0666227
$661$	−2.97186	−0.115592	−0.0577959	−	0.998328i	$-0.518407\pi$
$661$	−2.97186	−0.115592	−0.0577959	+	0.998328i	$0.518407\pi$
$662$	1.85852	0.0722334
$663$	0.855272	0.0332160
$664$	−10.0300	−0.389240
$665$	3.02593	0.117341
$666$	6.71886	0.260351
$667$	−13.7113	−0.530905
$668$	21.5543	0.833960
$669$	12.9146	0.499309
$670$	−20.3880	−0.787655
$671$	3.69876	0.142789
$672$	−0.790105	−0.0304790
$673$	25.1267	0.968564	0.484282	−	0.874912i	$-0.339081\pi$
$673$	25.1267	0.968564	0.484282	+	0.874912i	$0.339081\pi$
$674$	5.34743	0.205975
$675$	−9.66725	−0.372093
$676$	−12.9624	−0.498555
$677$	−11.5563	−0.444143	−0.222072	−	0.975030i	$-0.571282\pi$
$677$	−11.5563	−0.444143	−0.222072	+	0.975030i	$0.571282\pi$
$678$	−5.70150	−0.218965
$679$	−10.5286	−0.404050
$680$	16.9011	0.648127
$681$	7.82435	0.299830
$682$	−0.910181	−0.0348526
$683$	−48.6571	−1.86181	−0.930907	−	0.365258i	$-0.880981\pi$
$683$	−48.6571	−1.86181	−0.930907	+	0.365258i	$0.880981\pi$
$684$	−1.00000	−0.0382360
$685$	25.3418	0.968259
$686$	−10.5682	−0.403497
$687$	9.42402	0.359549
$688$	0.658880	0.0251196
$689$	0.193805	0.00738337
$690$	17.0939	0.650753
$691$	−10.2327	−0.389272	−0.194636	−	0.980876i	$-0.562353\pi$
$691$	−10.2327	−0.389272	−0.194636	+	0.980876i	$0.562353\pi$
$692$	−1.64948	−0.0627039
$693$	−0.353105	−0.0134134
$694$	−23.5161	−0.892659
$695$	2.46183	0.0933824
$696$	−3.07194	−0.116442
$697$	0.131966	0.00499856
$698$	18.1502	0.686994
$699$	1.78897	0.0676650
$700$	−7.63814	−0.288695
$701$	21.7552	0.821681	0.410841	−	0.911707i	$-0.365235\pi$
$701$	21.7552	0.821681	0.410841	+	0.911707i	$0.365235\pi$
$702$	0.193805	0.00731468
$703$	6.71886	0.253407
$704$	0.446910	0.0168435
$705$	−25.0783	−0.944504
$706$	9.08780	0.342024
$707$	−4.55816	−0.171427
$708$	4.62022	0.173638
$709$	−3.93319	−0.147714	−0.0738571	−	0.997269i	$-0.523531\pi$
$709$	−3.93319	−0.147714	−0.0738571	+	0.997269i	$0.523531\pi$
$710$	−26.5282	−0.995586
$711$	11.7730	0.441520
$712$	14.3347	0.537215
$713$	9.09023	0.340432
$714$	3.48678	0.130490
$715$	0.331710	0.0124052
$716$	−24.5074	−0.915885
$717$	−16.7328	−0.624898
$718$	−12.8542	−0.479716
$719$	25.9932	0.969382	0.484691	−	0.874685i	$-0.338932\pi$
$719$	25.9932	0.969382	0.484691	+	0.874685i	$0.338932\pi$
$720$	3.82978	0.142728
$721$	3.41140	0.127047
$722$	−1.00000	−0.0372161
$723$	10.9047	0.405550
$724$	−8.78529	−0.326503
$725$	−29.6972	−1.10293
$726$	−10.8003	−0.400836
$727$	14.5643	0.540159	0.270079	−	0.962838i	$-0.412950\pi$
$727$	14.5643	0.540159	0.270079	+	0.962838i	$0.412950\pi$
$728$	0.153126	0.00567523
$729$	1.00000	0.0370370
$730$	−32.4083	−1.19949
$731$	−2.90768	−0.107544
$732$	−8.27631	−0.305901
$733$	−27.1835	−1.00405	−0.502023	−	0.864854i	$-0.667411\pi$
$733$	−27.1835	−1.00405	−0.502023	+	0.864854i	$0.667411\pi$
$734$	−2.90067	−0.107066
$735$	24.4177	0.900660
$736$	−4.46341	−0.164523
$737$	2.37913	0.0876365
$738$	0.0299034	0.00110076
$739$	3.08182	0.113367	0.0566833	−	0.998392i	$-0.481947\pi$
$739$	3.08182	0.113367	0.0566833	+	0.998392i	$0.481947\pi$
$740$	−25.7318	−0.945920
$741$	0.193805	0.00711959
$742$	0.790105	0.0290057
$743$	40.4728	1.48480	0.742401	−	0.669956i	$-0.233687\pi$
$743$	40.4728	1.48480	0.742401	+	0.669956i	$0.233687\pi$
$744$	2.03661	0.0746658
$745$	1.61238	0.0590729
$746$	21.8174	0.798793
$747$	10.0300	0.366979
$748$	−1.97224	−0.0721122
$749$	−11.0885	−0.405164
$750$	17.8746	0.652686
$751$	19.7039	0.719006	0.359503	−	0.933144i	$-0.382946\pi$
$751$	19.7039	0.719006	0.359503	+	0.933144i	$0.382946\pi$
$752$	6.54823	0.238789
$753$	−28.9380	−1.05456
$754$	0.595357	0.0216816
$755$	50.0270	1.82067
$756$	0.790105	0.0287358
$757$	7.27408	0.264381	0.132190	−	0.991224i	$-0.457799\pi$
$757$	7.27408	0.264381	0.132190	+	0.991224i	$0.457799\pi$
$758$	21.1583	0.768504
$759$	−1.99474	−0.0724045
$760$	3.82978	0.138921
$761$	−16.4669	−0.596924	−0.298462	−	0.954421i	$-0.596474\pi$
$761$	−16.4669	−0.596924	−0.298462	+	0.954421i	$0.596474\pi$
$762$	1.60126	0.0580075
$763$	−9.29308	−0.336432
$764$	−7.06173	−0.255485
$765$	−16.9011	−0.611060
$766$	−8.88087	−0.320879
$767$	−0.895419	−0.0323317
$768$	−1.00000	−0.0360844
$769$	29.1904	1.05263	0.526316	−	0.850289i	$-0.323573\pi$
$769$	29.1904	1.05263	0.526316	+	0.850289i	$0.323573\pi$
$770$	1.35232	0.0487341
$771$	2.68567	0.0967222
$772$	8.35398	0.300666
$773$	37.0093	1.33113	0.665566	−	0.746339i	$-0.268190\pi$
$773$	37.0093	1.33113	0.665566	+	0.746339i	$0.268190\pi$
$774$	−0.658880	−0.0236830
$775$	19.6884	0.707229
$776$	−13.3255	−0.478359
$777$	−5.30861	−0.190445
$778$	−25.4647	−0.912954
$779$	0.0299034	0.00107140
$780$	−0.742230	−0.0265761
$781$	3.09566	0.110771
$782$	19.6973	0.704374
$783$	3.07194	0.109782
$784$	−6.37573	−0.227705
$785$	55.2595	1.97230
$786$	12.8066	0.456796
$787$	14.3131	0.510205	0.255103	−	0.966914i	$-0.417891\pi$
$787$	14.3131	0.510205	0.255103	+	0.966914i	$0.417891\pi$
$788$	10.5400	0.375471
$789$	−4.59887	−0.163724
$790$	−45.0879	−1.60415
$791$	4.50479	0.160172
$792$	−0.446910	−0.0158802
$793$	1.60399	0.0569593
$794$	0.921126	0.0326895
$795$	−3.82978	−0.135828
$796$	−14.2303	−0.504381
$797$	40.3661	1.42984	0.714921	−	0.699205i	$-0.246463\pi$
$797$	40.3661	1.42984	0.714921	+	0.699205i	$0.246463\pi$
$798$	0.790105	0.0279694
$799$	−28.8978	−1.02233
$800$	−9.66725	−0.341789
$801$	−14.3347	−0.506491
$802$	−26.0639	−0.920349
$803$	3.78183	0.133458
$804$	−5.32352	−0.187746
$805$	−13.5060	−0.476023
$806$	−0.394705	−0.0139029
$807$	10.6225	0.373931
$808$	−5.76906	−0.202955
$809$	3.57253	0.125603	0.0628017	−	0.998026i	$-0.479996\pi$
$809$	3.57253	0.125603	0.0628017	+	0.998026i	$0.479996\pi$
$810$	−3.82978	−0.134565
$811$	−48.6333	−1.70775	−0.853874	−	0.520480i	$-0.825753\pi$
$811$	−48.6333	−1.70775	−0.853874	+	0.520480i	$0.825753\pi$
$812$	2.42716	0.0851765
$813$	2.73151	0.0957983
$814$	3.00272	0.105245
$815$	69.3461	2.42909
$816$	4.41306	0.154488
$817$	−0.658880	−0.0230513
$818$	−26.3759	−0.922212
$819$	−0.153126	−0.00535065
$820$	−0.114524	−0.00399934
$821$	21.1794	0.739167	0.369583	−	0.929198i	$-0.379500\pi$
$821$	21.1794	0.739167	0.369583	+	0.929198i	$0.379500\pi$
$822$	6.61702	0.230795
$823$	48.0999	1.67666	0.838328	−	0.545166i	$-0.183533\pi$
$823$	48.0999	1.67666	0.838328	+	0.545166i	$0.183533\pi$
$824$	4.31765	0.150412
$825$	−4.32039	−0.150417
$826$	−3.65046	−0.127016
$827$	39.7274	1.38146	0.690729	−	0.723113i	$-0.257290\pi$
$827$	39.7274	1.38146	0.690729	+	0.723113i	$0.257290\pi$
$828$	4.46341	0.155114
$829$	−29.2919	−1.01735	−0.508675	−	0.860959i	$-0.669864\pi$
$829$	−29.2919	−1.01735	−0.508675	+	0.860959i	$0.669864\pi$
$830$	−38.4127	−1.33333
$831$	−13.3642	−0.463600
$832$	0.193805	0.00671897
$833$	28.1365	0.974872
$834$	0.642811	0.0222587
$835$	82.5482	2.85670
$836$	−0.446910	−0.0154567
$837$	−2.03661	−0.0703956
$838$	−15.8308	−0.546865
$839$	−10.4066	−0.359277	−0.179639	−	0.983733i	$-0.557493\pi$
$839$	−10.4066	−0.359277	−0.179639	+	0.983733i	$0.557493\pi$
$840$	−3.02593	−0.104405
$841$	−19.5632	−0.674592
$842$	−18.9690	−0.653713
$843$	−3.02842	−0.104304
$844$	−22.3210	−0.768319
$845$	−49.6433	−1.70778
$846$	−6.54823	−0.225133
$847$	8.53335	0.293209
$848$	1.00000	0.0343401
$849$	17.0084	0.583726
$850$	42.6622	1.46330
$851$	−29.9890	−1.02801
$852$	−6.92682	−0.237309
$853$	48.3345	1.65494	0.827470	−	0.561510i	$-0.189779\pi$
$853$	48.3345	1.65494	0.827470	+	0.561510i	$0.189779\pi$
$854$	6.53915	0.223765
$855$	−3.82978	−0.130976
$856$	−14.0342	−0.479679
$857$	47.7651	1.63162	0.815812	−	0.578318i	$-0.196291\pi$
$857$	47.7651	1.63162	0.815812	+	0.578318i	$0.196291\pi$
$858$	0.0866131	0.00295692
$859$	−15.5166	−0.529420	−0.264710	−	0.964328i	$-0.585276\pi$
$859$	−15.5166	−0.529420	−0.264710	+	0.964328i	$0.585276\pi$
$860$	2.52337	0.0860462
$861$	−0.0236268	−0.000805201 0
$862$	−15.9307	−0.542603
$863$	−4.16698	−0.141846	−0.0709229	−	0.997482i	$-0.522594\pi$
$863$	−4.16698	−0.141846	−0.0709229	+	0.997482i	$0.522594\pi$
$864$	1.00000	0.0340207
$865$	−6.31716	−0.214790
$866$	15.6597	0.532137
$867$	−2.47512	−0.0840596
$868$	−1.60914	−0.0546176
$869$	5.26145	0.178482
$870$	−11.7649	−0.398867
$871$	1.03172	0.0349586
$872$	−11.7618	−0.398306
$873$	13.3255	0.451001
$874$	4.46341	0.150977
$875$	−14.1228	−0.477437
$876$	−8.46217	−0.285910
$877$	−13.5310	−0.456911	−0.228455	−	0.973554i	$-0.573367\pi$
$877$	−13.5310	−0.456911	−0.228455	+	0.973554i	$0.573367\pi$
$878$	16.6208	0.560925
$879$	1.69944	0.0573208
$880$	1.71157	0.0576969
$881$	−13.4714	−0.453862	−0.226931	−	0.973911i	$-0.572869\pi$
$881$	−13.4714	−0.453862	−0.226931	+	0.973911i	$0.572869\pi$
$882$	6.37573	0.214682
$883$	−20.1862	−0.679321	−0.339661	−	0.940548i	$-0.610312\pi$
$883$	−20.1862	−0.679321	−0.339661	+	0.940548i	$0.610312\pi$
$884$	−0.855272	−0.0287659
$885$	17.6944	0.594792
$886$	12.9754	0.435918
$887$	−31.2512	−1.04931	−0.524657	−	0.851314i	$-0.675806\pi$
$887$	−31.2512	−1.04931	−0.524657	+	0.851314i	$0.675806\pi$
$888$	−6.71886	−0.225470
$889$	−1.26516	−0.0424322
$890$	54.8987	1.84021
$891$	0.446910	0.0149720
$892$	−12.9146	−0.432414
$893$	−6.54823	−0.219128
$894$	0.421009	0.0140807
$895$	−93.8582	−3.13733
$896$	0.790105	0.0263956
$897$	−0.865029	−0.0288825
$898$	1.70560	0.0569165
$899$	−6.25635	−0.208661
$900$	9.66725	0.322242
$901$	−4.41306	−0.147020
$902$	0.0133641	0.000444977 0
$903$	0.520585	0.0173240
$904$	5.70150	0.189629
$905$	−33.6458	−1.11842
$906$	13.0626	0.433977
$907$	−20.5963	−0.683887	−0.341944	−	0.939720i	$-0.611085\pi$
$907$	−20.5963	−0.683887	−0.341944	+	0.939720i	$0.611085\pi$
$908$	−7.82435	−0.259660
$909$	5.76906	0.191348
$910$	0.586439	0.0194403
$911$	8.68508	0.287750	0.143875	−	0.989596i	$-0.454044\pi$
$911$	8.68508	0.287750	0.143875	+	0.989596i	$0.454044\pi$
$912$	1.00000	0.0331133
$913$	4.48250	0.148349
$914$	15.7323	0.520379
$915$	−31.6965	−1.04785
$916$	−9.42402	−0.311378
$917$	−10.1186	−0.334144
$918$	−4.41306	−0.145653
$919$	−23.4638	−0.774000	−0.387000	−	0.922080i	$-0.626489\pi$
$919$	−23.4638	−0.774000	−0.387000	+	0.922080i	$0.626489\pi$
$920$	−17.0939	−0.563569
$921$	−10.9862	−0.362008
$922$	−30.5681	−1.00671
$923$	1.34245	0.0441873
$924$	0.353105	0.0116163
$925$	−64.9529	−2.13564
$926$	4.71049	0.154796
$927$	−4.31765	−0.141810
$928$	3.07194	0.100841
$929$	−50.8711	−1.66903	−0.834513	−	0.550988i	$-0.814251\pi$
$929$	−50.8711	−1.66903	−0.834513	+	0.550988i	$0.814251\pi$
$930$	7.79978	0.255765
$931$	6.37573	0.208956
$932$	−1.78897	−0.0585996
$933$	−12.7816	−0.418451
$934$	−35.6878	−1.16774
$935$	−7.55325	−0.247018
$936$	−0.193805	−0.00633470
$937$	7.18033	0.234571	0.117286	−	0.993098i	$-0.462581\pi$
$937$	7.18033	0.234571	0.117286	+	0.993098i	$0.462581\pi$
$938$	4.20614	0.137335
$939$	9.87055	0.322113
$940$	25.0783	0.817964
$941$	−55.7667	−1.81794	−0.908972	−	0.416858i	$-0.863131\pi$
$941$	−55.7667	−1.81794	−0.908972	+	0.416858i	$0.863131\pi$
$942$	14.4289	0.470119
$943$	−0.133471	−0.00434642
$944$	−4.62022	−0.150375
$945$	3.02593	0.0984336
$946$	−0.294460	−0.00957372
$947$	−52.8254	−1.71660	−0.858298	−	0.513151i	$-0.828478\pi$
$947$	−52.8254	−1.71660	−0.858298	+	0.513151i	$0.828478\pi$
$948$	−11.7730	−0.382368
$949$	1.64001	0.0532369
$950$	9.66725	0.313647
$951$	−6.53804	−0.212011
$952$	−3.48678	−0.113007
$953$	−24.3972	−0.790302	−0.395151	−	0.918616i	$-0.629308\pi$
$953$	−24.3972	−0.790302	−0.395151	+	0.918616i	$0.629308\pi$
$954$	−1.00000	−0.0323762
$955$	−27.0449	−0.875153
$956$	16.7328	0.541178
$957$	1.37288	0.0443789
$958$	−26.4955	−0.856031
$959$	−5.22814	−0.168825
$960$	−3.82978	−0.123606
$961$	−26.8522	−0.866201
$962$	1.30215	0.0419829
$963$	14.0342	0.452245
$964$	−10.9047	−0.351217
$965$	31.9939	1.02992
$966$	−3.52656	−0.113465
$967$	−18.3483	−0.590042	−0.295021	−	0.955491i	$-0.595327\pi$
$967$	−18.3483	−0.590042	−0.295021	+	0.955491i	$0.595327\pi$
$968$	10.8003	0.347134
$969$	−4.41306	−0.141768
$970$	−51.0339	−1.63860
$971$	34.7578	1.11543	0.557716	−	0.830032i	$-0.311678\pi$
$971$	34.7578	1.11543	0.557716	+	0.830032i	$0.311678\pi$
$972$	−1.00000	−0.0320750
$973$	−0.507888	−0.0162821
$974$	6.22402	0.199430
$975$	−1.87356	−0.0600019
$976$	8.27631	0.264918
$977$	56.8459	1.81866	0.909331	−	0.416074i	$-0.136594\pi$
$977$	56.8459	1.81866	0.909331	+	0.416074i	$0.136594\pi$
$978$	18.1071	0.579000
$979$	−6.40631	−0.204746
$980$	−24.4177	−0.779994
$981$	11.7618	0.375526
$982$	3.70736	0.118307
$983$	−21.4247	−0.683342	−0.341671	−	0.939820i	$-0.610993\pi$
$983$	−21.4247	−0.683342	−0.341671	+	0.939820i	$0.610993\pi$
$984$	−0.0299034	−0.000953287 0
$985$	40.3658	1.28616
$986$	−13.5567	−0.431733
$987$	5.17379	0.164684
$988$	−0.193805	−0.00616575
$989$	2.94085	0.0935137
$990$	−1.71157	−0.0543972
$991$	−32.3546	−1.02778	−0.513889	−	0.857857i	$-0.671796\pi$
$991$	−32.3546	−1.02778	−0.513889	+	0.857857i	$0.671796\pi$
$992$	−2.03661	−0.0646625
$993$	1.85852	0.0589784
$994$	5.47291	0.173590
$995$	−54.4991	−1.72774
$996$	−10.0300	−0.317813
$997$	−41.5468	−1.31580	−0.657900	−	0.753105i	$-0.728555\pi$
$997$	−41.5468	−1.31580	−0.657900	+	0.753105i	$0.728555\pi$
$998$	26.8514	0.849965
$999$	6.71886	0.212575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.z.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.z.1.9	✓	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.82978 q^{5} +1.00000 q^{6} -0.790105 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.82978 q^{5} +1.00000 q^{6} -0.790105 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.82978 q^{10} +0.446910 q^{11} -1.00000 q^{12} +0.193805 q^{13} +0.790105 q^{14} -3.82978 q^{15} +1.00000 q^{16} -4.41306 q^{17} -1.00000 q^{18} -1.00000 q^{19} +3.82978 q^{20} +0.790105 q^{21} -0.446910 q^{22} +4.46341 q^{23} +1.00000 q^{24} +9.66725 q^{25} -0.193805 q^{26} -1.00000 q^{27} -0.790105 q^{28} -3.07194 q^{29} +3.82978 q^{30} +2.03661 q^{31} -1.00000 q^{32} -0.446910 q^{33} +4.41306 q^{34} -3.02593 q^{35} +1.00000 q^{36} -6.71886 q^{37} +1.00000 q^{38} -0.193805 q^{39} -3.82978 q^{40} -0.0299034 q^{41} -0.790105 q^{42} +0.658880 q^{43} +0.446910 q^{44} +3.82978 q^{45} -4.46341 q^{46} +6.54823 q^{47} -1.00000 q^{48} -6.37573 q^{49} -9.66725 q^{50} +4.41306 q^{51} +0.193805 q^{52} +1.00000 q^{53} +1.00000 q^{54} +1.71157 q^{55} +0.790105 q^{56} +1.00000 q^{57} +3.07194 q^{58} -4.62022 q^{59} -3.82978 q^{60} +8.27631 q^{61} -2.03661 q^{62} -0.790105 q^{63} +1.00000 q^{64} +0.742230 q^{65} +0.446910 q^{66} +5.32352 q^{67} -4.41306 q^{68} -4.46341 q^{69} +3.02593 q^{70} +6.92682 q^{71} -1.00000 q^{72} +8.46217 q^{73} +6.71886 q^{74} -9.66725 q^{75} -1.00000 q^{76} -0.353105 q^{77} +0.193805 q^{78} +11.7730 q^{79} +3.82978 q^{80} +1.00000 q^{81} +0.0299034 q^{82} +10.0300 q^{83} +0.790105 q^{84} -16.9011 q^{85} -0.658880 q^{86} +3.07194 q^{87} -0.446910 q^{88} -14.3347 q^{89} -3.82978 q^{90} -0.153126 q^{91} +4.46341 q^{92} -2.03661 q^{93} -6.54823 q^{94} -3.82978 q^{95} +1.00000 q^{96} +13.3255 q^{97} +6.37573 q^{98} +0.446910 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9} + q^{10} + 12 q^{11} - 9 q^{12} - q^{13} - 4 q^{14} + q^{15} + 9 q^{16} + 12 q^{17} - 9 q^{18} - 9 q^{19} - q^{20} - 4 q^{21} - 12 q^{22} + 11 q^{23} + 9 q^{24} + 10 q^{25} + q^{26} - 9 q^{27} + 4 q^{28} + 7 q^{29} - q^{30} - 12 q^{31} - 9 q^{32} - 12 q^{33} - 12 q^{34} + 15 q^{35} + 9 q^{36} - 9 q^{37} + 9 q^{38} + q^{39} + q^{40} - 4 q^{41} + 4 q^{42} + 23 q^{43} + 12 q^{44} - q^{45} - 11 q^{46} + 35 q^{47} - 9 q^{48} + 3 q^{49} - 10 q^{50} - 12 q^{51} - q^{52} + 9 q^{53} + 9 q^{54} + 3 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} + 14 q^{59} + q^{60} + 14 q^{61} + 12 q^{62} + 4 q^{63} + 9 q^{64} + 13 q^{65} + 12 q^{66} - 10 q^{67} + 12 q^{68} - 11 q^{69} - 15 q^{70} + 4 q^{71} - 9 q^{72} - 5 q^{73} + 9 q^{74} - 10 q^{75} - 9 q^{76} + 17 q^{77} - q^{78} - 14 q^{79} - q^{80} + 9 q^{81} + 4 q^{82} + 37 q^{83} - 4 q^{84} - 31 q^{85} - 23 q^{86} - 7 q^{87} - 12 q^{88} - 20 q^{89} + q^{90} - 12 q^{91} + 11 q^{92} + 12 q^{93} - 35 q^{94} + q^{95} + 9 q^{96} - 2 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9 + q^10 + 12 * q^11 - 9 * q^12 - q^13 - 4 * q^14 + q^15 + 9 * q^16 + 12 * q^17 - 9 * q^18 - 9 * q^19 - q^20 - 4 * q^21 - 12 * q^22 + 11 * q^23 + 9 * q^24 + 10 * q^25 + q^26 - 9 * q^27 + 4 * q^28 + 7 * q^29 - q^30 - 12 * q^31 - 9 * q^32 - 12 * q^33 - 12 * q^34 + 15 * q^35 + 9 * q^36 - 9 * q^37 + 9 * q^38 + q^39 + q^40 - 4 * q^41 + 4 * q^42 + 23 * q^43 + 12 * q^44 - q^45 - 11 * q^46 + 35 * q^47 - 9 * q^48 + 3 * q^49 - 10 * q^50 - 12 * q^51 - q^52 + 9 * q^53 + 9 * q^54 + 3 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 + 14 * q^59 + q^60 + 14 * q^61 + 12 * q^62 + 4 * q^63 + 9 * q^64 + 13 * q^65 + 12 * q^66 - 10 * q^67 + 12 * q^68 - 11 * q^69 - 15 * q^70 + 4 * q^71 - 9 * q^72 - 5 * q^73 + 9 * q^74 - 10 * q^75 - 9 * q^76 + 17 * q^77 - q^78 - 14 * q^79 - q^80 + 9 * q^81 + 4 * q^82 + 37 * q^83 - 4 * q^84 - 31 * q^85 - 23 * q^86 - 7 * q^87 - 12 * q^88 - 20 * q^89 + q^90 - 12 * q^91 + 11 * q^92 + 12 * q^93 - 35 * q^94 + q^95 + 9 * q^96 - 2 * q^97 - 3 * q^98 + 12 * q^99

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