LMFDB - Embedded newform 6009.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, 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("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60458 q^{2} +1.00000 q^{3} +4.78383 q^{4} +2.52259 q^{5} -2.60458 q^{6} -2.57820 q^{7} -7.25072 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.60458 q^{2} +1.00000 q^{3} +4.78383 q^{4} +2.52259 q^{5} -2.60458 q^{6} -2.57820 q^{7} -7.25072 q^{8} +1.00000 q^{9} -6.57030 q^{10} +5.19554 q^{11} +4.78383 q^{12} +3.62708 q^{13} +6.71514 q^{14} +2.52259 q^{15} +9.31741 q^{16} -3.49479 q^{17} -2.60458 q^{18} +5.94067 q^{19} +12.0677 q^{20} -2.57820 q^{21} -13.5322 q^{22} -2.02165 q^{23} -7.25072 q^{24} +1.36348 q^{25} -9.44703 q^{26} +1.00000 q^{27} -12.3337 q^{28} +7.65499 q^{29} -6.57030 q^{30} -0.472724 q^{31} -9.76649 q^{32} +5.19554 q^{33} +9.10247 q^{34} -6.50377 q^{35} +4.78383 q^{36} +0.0743106 q^{37} -15.4729 q^{38} +3.62708 q^{39} -18.2906 q^{40} +3.58949 q^{41} +6.71514 q^{42} +6.08419 q^{43} +24.8546 q^{44} +2.52259 q^{45} +5.26556 q^{46} +9.60297 q^{47} +9.31741 q^{48} -0.352861 q^{49} -3.55130 q^{50} -3.49479 q^{51} +17.3514 q^{52} -4.68468 q^{53} -2.60458 q^{54} +13.1062 q^{55} +18.6938 q^{56} +5.94067 q^{57} -19.9380 q^{58} -6.87657 q^{59} +12.0677 q^{60} +9.32916 q^{61} +1.23125 q^{62} -2.57820 q^{63} +6.80278 q^{64} +9.14966 q^{65} -13.5322 q^{66} -4.92583 q^{67} -16.7185 q^{68} -2.02165 q^{69} +16.9396 q^{70} +9.52356 q^{71} -7.25072 q^{72} -8.47128 q^{73} -0.193548 q^{74} +1.36348 q^{75} +28.4192 q^{76} -13.3952 q^{77} -9.44703 q^{78} -8.03670 q^{79} +23.5040 q^{80} +1.00000 q^{81} -9.34911 q^{82} -2.85967 q^{83} -12.3337 q^{84} -8.81595 q^{85} -15.8468 q^{86} +7.65499 q^{87} -37.6714 q^{88} +4.13000 q^{89} -6.57030 q^{90} -9.35136 q^{91} -9.67125 q^{92} -0.472724 q^{93} -25.0117 q^{94} +14.9859 q^{95} -9.76649 q^{96} +4.03928 q^{97} +0.919054 q^{98} +5.19554 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.60458	−1.84172	−0.920858	−	0.389898i	$-0.872510\pi$
$2$	−2.60458	−1.84172	−0.920858	+	0.389898i	$0.872510\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.78383	2.39192
$5$	2.52259	1.12814	0.564069	−	0.825727i	$-0.309235\pi$
$5$	2.52259	1.12814	0.564069	+	0.825727i	$0.309235\pi$
$6$	−2.60458	−1.06332
$7$	−2.57820	−0.974470	−0.487235	−	0.873271i	$-0.661994\pi$
$7$	−2.57820	−0.974470	−0.487235	+	0.873271i	$0.661994\pi$
$8$	−7.25072	−2.56352
$9$	1.00000	0.333333
$10$	−6.57030	−2.07771
$11$	5.19554	1.56651	0.783257	−	0.621698i	$-0.213557\pi$
$11$	5.19554	1.56651	0.783257	+	0.621698i	$0.213557\pi$
$12$	4.78383	1.38097
$13$	3.62708	1.00597	0.502986	−	0.864295i	$-0.332235\pi$
$13$	3.62708	1.00597	0.502986	+	0.864295i	$0.332235\pi$
$14$	6.71514	1.79470
$15$	2.52259	0.651331
$16$	9.31741	2.32935
$17$	−3.49479	−0.847612	−0.423806	−	0.905753i	$-0.639306\pi$
$17$	−3.49479	−0.847612	−0.423806	+	0.905753i	$0.639306\pi$
$18$	−2.60458	−0.613905
$19$	5.94067	1.36288	0.681441	−	0.731873i	$-0.261354\pi$
$19$	5.94067	1.36288	0.681441	+	0.731873i	$0.261354\pi$
$20$	12.0677	2.69841
$21$	−2.57820	−0.562610
$22$	−13.5322	−2.88508
$23$	−2.02165	−0.421544	−0.210772	−	0.977535i	$-0.567598\pi$
$23$	−2.02165	−0.421544	−0.210772	+	0.977535i	$0.567598\pi$
$24$	−7.25072	−1.48005
$25$	1.36348	0.272697
$26$	−9.44703	−1.85271
$27$	1.00000	0.192450
$28$	−12.3337	−2.33085
$29$	7.65499	1.42150	0.710748	−	0.703447i	$-0.248357\pi$
$29$	7.65499	1.42150	0.710748	+	0.703447i	$0.248357\pi$
$30$	−6.57030	−1.19957
$31$	−0.472724	−0.0849038	−0.0424519	−	0.999099i	$-0.513517\pi$
$31$	−0.472724	−0.0849038	−0.0424519	+	0.999099i	$0.513517\pi$
$32$	−9.76649	−1.72649
$33$	5.19554	0.904428
$34$	9.10247	1.56106
$35$	−6.50377	−1.09934
$36$	4.78383	0.797306
$37$	0.0743106	0.0122166	0.00610830	−	0.999981i	$-0.498056\pi$
$37$	0.0743106	0.0122166	0.00610830	+	0.999981i	$0.498056\pi$
$38$	−15.4729	−2.51004
$39$	3.62708	0.580798
$40$	−18.2906	−2.89200
$41$	3.58949	0.560584	0.280292	−	0.959915i	$-0.409569\pi$
$41$	3.58949	0.560584	0.280292	+	0.959915i	$0.409569\pi$
$42$	6.71514	1.03617
$43$	6.08419	0.927830	0.463915	−	0.885880i	$-0.346444\pi$
$43$	6.08419	0.927830	0.463915	+	0.885880i	$0.346444\pi$
$44$	24.8546	3.74697
$45$	2.52259	0.376046
$46$	5.26556	0.776364
$47$	9.60297	1.40074	0.700368	−	0.713781i	$-0.253019\pi$
$47$	9.60297	1.40074	0.700368	+	0.713781i	$0.253019\pi$
$48$	9.31741	1.34485
$49$	−0.352861	−0.0504087
$50$	−3.55130	−0.502230
$51$	−3.49479	−0.489369
$52$	17.3514	2.40620
$53$	−4.68468	−0.643490	−0.321745	−	0.946826i	$-0.604269\pi$
$53$	−4.68468	−0.643490	−0.321745	+	0.946826i	$0.604269\pi$
$54$	−2.60458	−0.354438
$55$	13.1062	1.76725
$56$	18.6938	2.49807
$57$	5.94067	0.786861
$58$	−19.9380	−2.61799
$59$	−6.87657	−0.895253	−0.447626	−	0.894221i	$-0.647731\pi$
$59$	−6.87657	−0.895253	−0.447626	+	0.894221i	$0.647731\pi$
$60$	12.0677	1.55793
$61$	9.32916	1.19448	0.597239	−	0.802064i	$-0.296265\pi$
$61$	9.32916	1.19448	0.597239	+	0.802064i	$0.296265\pi$
$62$	1.23125	0.156369
$63$	−2.57820	−0.324823
$64$	6.80278	0.850347
$65$	9.14966	1.13488
$66$	−13.5322	−1.66570
$67$	−4.92583	−0.601786	−0.300893	−	0.953658i	$-0.597285\pi$
$67$	−4.92583	−0.601786	−0.300893	+	0.953658i	$0.597285\pi$
$68$	−16.7185	−2.02742
$69$	−2.02165	−0.243378
$70$	16.9396	2.02467
$71$	9.52356	1.13024	0.565119	−	0.825009i	$-0.308830\pi$
$71$	9.52356	1.13024	0.565119	+	0.825009i	$0.308830\pi$
$72$	−7.25072	−0.854505
$73$	−8.47128	−0.991488	−0.495744	−	0.868469i	$-0.665105\pi$
$73$	−8.47128	−0.991488	−0.495744	+	0.868469i	$0.665105\pi$
$74$	−0.193548	−0.0224995
$75$	1.36348	0.157442
$76$	28.4192	3.25990
$77$	−13.3952	−1.52652
$78$	−9.44703	−1.06967
$79$	−8.03670	−0.904199	−0.452100	−	0.891967i	$-0.649325\pi$
$79$	−8.03670	−0.904199	−0.452100	+	0.891967i	$0.649325\pi$
$80$	23.5040	2.62783
$81$	1.00000	0.111111
$82$	−9.34911	−1.03244
$83$	−2.85967	−0.313890	−0.156945	−	0.987607i	$-0.550165\pi$
$83$	−2.85967	−0.313890	−0.156945	+	0.987607i	$0.550165\pi$
$84$	−12.3337	−1.34572
$85$	−8.81595	−0.956224
$86$	−15.8468	−1.70880
$87$	7.65499	0.820701
$88$	−37.6714	−4.01579
$89$	4.13000	0.437779	0.218889	−	0.975750i	$-0.429757\pi$
$89$	4.13000	0.437779	0.218889	+	0.975750i	$0.429757\pi$
$90$	−6.57030	−0.692570
$91$	−9.35136	−0.980289
$92$	−9.67125	−1.00830
$93$	−0.472724	−0.0490192
$94$	−25.0117	−2.57976
$95$	14.9859	1.53752
$96$	−9.76649	−0.996788
$97$	4.03928	0.410126	0.205063	−	0.978749i	$-0.434260\pi$
$97$	4.03928	0.410126	0.205063	+	0.978749i	$0.434260\pi$
$98$	0.919054	0.0928385
$99$	5.19554	0.522172
$100$	6.52268	0.652268
$101$	8.75247	0.870903	0.435452	−	0.900212i	$-0.356589\pi$
$101$	8.75247	0.870903	0.435452	+	0.900212i	$0.356589\pi$
$102$	9.10247	0.901279
$103$	−10.2782	−1.01274	−0.506371	−	0.862316i	$-0.669013\pi$
$103$	−10.2782	−1.01274	−0.506371	+	0.862316i	$0.669013\pi$
$104$	−26.2990	−2.57883
$105$	−6.50377	−0.634703
$106$	12.2016	1.18513
$107$	−7.20549	−0.696581	−0.348290	−	0.937387i	$-0.613238\pi$
$107$	−7.20549	−0.696581	−0.348290	+	0.937387i	$0.613238\pi$
$108$	4.78383	0.460325
$109$	−18.0671	−1.73051	−0.865256	−	0.501330i	$-0.832844\pi$
$109$	−18.0671	−1.73051	−0.865256	+	0.501330i	$0.832844\pi$
$110$	−34.1363	−3.25476
$111$	0.0743106	0.00705325
$112$	−24.0222	−2.26988
$113$	16.7097	1.57192	0.785960	−	0.618277i	$-0.212169\pi$
$113$	16.7097	1.57192	0.785960	+	0.618277i	$0.212169\pi$
$114$	−15.4729	−1.44917
$115$	−5.09981	−0.475560
$116$	36.6202	3.40010
$117$	3.62708	0.335324
$118$	17.9106	1.64880
$119$	9.01029	0.825972
$120$	−18.2906	−1.66970
$121$	15.9937	1.45397
$122$	−24.2986	−2.19989
$123$	3.58949	0.323653
$124$	−2.26144	−0.203083
$125$	−9.17346	−0.820499
$126$	6.71514	0.598232
$127$	3.93060	0.348784	0.174392	−	0.984676i	$-0.444204\pi$
$127$	3.93060	0.348784	0.174392	+	0.984676i	$0.444204\pi$
$128$	1.81459	0.160389
$129$	6.08419	0.535683
$130$	−23.8310	−2.09012
$131$	−8.70422	−0.760491	−0.380246	−	0.924886i	$-0.624161\pi$
$131$	−8.70422	−0.760491	−0.380246	+	0.924886i	$0.624161\pi$
$132$	24.8546	2.16332
$133$	−15.3163	−1.32809
$134$	12.8297	1.10832
$135$	2.52259	0.217110
$136$	25.3398	2.17287
$137$	0.0777857	0.00664568	0.00332284	−	0.999994i	$-0.498942\pi$
$137$	0.0777857	0.00664568	0.00332284	+	0.999994i	$0.498942\pi$
$138$	5.26556	0.448234
$139$	−0.0658496	−0.00558529	−0.00279265	−	0.999996i	$-0.500889\pi$
$139$	−0.0658496	−0.00558529	−0.00279265	+	0.999996i	$0.500889\pi$
$140$	−31.1129	−2.62952
$141$	9.60297	0.808716
$142$	−24.8049	−2.08158
$143$	18.8447	1.57587
$144$	9.31741	0.776450
$145$	19.3104	1.60364
$146$	22.0641	1.82604
$147$	−0.352861	−0.0291035
$148$	0.355490	0.0292211
$149$	11.0648	0.906468	0.453234	−	0.891392i	$-0.350270\pi$
$149$	11.0648	0.906468	0.453234	+	0.891392i	$0.350270\pi$
$150$	−3.55130	−0.289963
$151$	19.0366	1.54918	0.774588	−	0.632466i	$-0.217957\pi$
$151$	19.0366	1.54918	0.774588	+	0.632466i	$0.217957\pi$
$152$	−43.0741	−3.49377
$153$	−3.49479	−0.282537
$154$	34.8888	2.81142
$155$	−1.19249	−0.0957833
$156$	17.3514	1.38922
$157$	−19.2897	−1.53948	−0.769742	−	0.638355i	$-0.779615\pi$
$157$	−19.2897	−1.53948	−0.769742	+	0.638355i	$0.779615\pi$
$158$	20.9322	1.66528
$159$	−4.68468	−0.371519
$160$	−24.6369	−1.94772
$161$	5.21224	0.410782
$162$	−2.60458	−0.204635
$163$	−0.439878	−0.0344539	−0.0172270	−	0.999852i	$-0.505484\pi$
$163$	−0.439878	−0.0344539	−0.0172270	+	0.999852i	$0.505484\pi$
$164$	17.1715	1.34087
$165$	13.1062	1.02032
$166$	7.44824	0.578096
$167$	5.23509	0.405103	0.202552	−	0.979272i	$-0.435077\pi$
$167$	5.23509	0.405103	0.202552	+	0.979272i	$0.435077\pi$
$168$	18.6938	1.44226
$169$	0.155730	0.0119792
$170$	22.9618	1.76109
$171$	5.94067	0.454294
$172$	29.1058	2.21929
$173$	−11.3785	−0.865094	−0.432547	−	0.901611i	$-0.642385\pi$
$173$	−11.3785	−0.865094	−0.432547	+	0.901611i	$0.642385\pi$
$174$	−19.9380	−1.51150
$175$	−3.51534	−0.265735
$176$	48.4090	3.64896
$177$	−6.87657	−0.516874
$178$	−10.7569	−0.806264
$179$	22.0903	1.65111	0.825555	−	0.564322i	$-0.190862\pi$
$179$	22.0903	1.65111	0.825555	+	0.564322i	$0.190862\pi$
$180$	12.0677	0.899471
$181$	−8.39410	−0.623929	−0.311964	−	0.950094i	$-0.600987\pi$
$181$	−8.39410	−0.623929	−0.311964	+	0.950094i	$0.600987\pi$
$182$	24.3564	1.80541
$183$	9.32916	0.689632
$184$	14.6584	1.08063
$185$	0.187456	0.0137820
$186$	1.23125	0.0902795
$187$	−18.1573	−1.32780
$188$	45.9390	3.35045
$189$	−2.57820	−0.187537
$190$	−39.0320	−2.83168
$191$	12.6708	0.916827	0.458414	−	0.888739i	$-0.348418\pi$
$191$	12.6708	0.916827	0.458414	+	0.888739i	$0.348418\pi$
$192$	6.80278	0.490948
$193$	16.3035	1.17355	0.586774	−	0.809750i	$-0.300398\pi$
$193$	16.3035	1.17355	0.586774	+	0.809750i	$0.300398\pi$
$194$	−10.5206	−0.755336
$195$	9.14966	0.655221
$196$	−1.68803	−0.120573
$197$	11.3947	0.811838	0.405919	−	0.913909i	$-0.366951\pi$
$197$	11.3947	0.811838	0.405919	+	0.913909i	$0.366951\pi$
$198$	−13.5322	−0.961692
$199$	−20.7278	−1.46936	−0.734678	−	0.678416i	$-0.762667\pi$
$199$	−20.7278	−1.46936	−0.734678	+	0.678416i	$0.762667\pi$
$200$	−9.88624	−0.699063
$201$	−4.92583	−0.347441
$202$	−22.7965	−1.60396
$203$	−19.7361	−1.38521
$204$	−16.7185	−1.17053
$205$	9.05482	0.632416
$206$	26.7704	1.86518
$207$	−2.02165	−0.140515
$208$	33.7950	2.34326
$209$	30.8650	2.13498
$210$	16.9396	1.16894
$211$	−6.53272	−0.449731	−0.224865	−	0.974390i	$-0.572194\pi$
$211$	−6.53272	−0.449731	−0.224865	+	0.974390i	$0.572194\pi$
$212$	−22.4107	−1.53918
$213$	9.52356	0.652544
$214$	18.7673	1.28290
$215$	15.3479	1.04672
$216$	−7.25072	−0.493349
$217$	1.21878	0.0827362
$218$	47.0572	3.18711
$219$	−8.47128	−0.572436
$220$	62.6981	4.22711
$221$	−12.6759	−0.852674
$222$	−0.193548	−0.0129901
$223$	0.536414	0.0359209	0.0179605	−	0.999839i	$-0.494283\pi$
$223$	0.536414	0.0359209	0.0179605	+	0.999839i	$0.494283\pi$
$224$	25.1800	1.68241
$225$	1.36348	0.0908989
$226$	−43.5219	−2.89503
$227$	4.00873	0.266069	0.133034	−	0.991111i	$-0.457528\pi$
$227$	4.00873	0.266069	0.133034	+	0.991111i	$0.457528\pi$
$228$	28.4192	1.88211
$229$	15.9234	1.05225	0.526124	−	0.850408i	$-0.323645\pi$
$229$	15.9234	1.05225	0.526124	+	0.850408i	$0.323645\pi$
$230$	13.2829	0.875846
$231$	−13.3952	−0.881337
$232$	−55.5042	−3.64403
$233$	7.49718	0.491156	0.245578	−	0.969377i	$-0.421022\pi$
$233$	7.49718	0.491156	0.245578	+	0.969377i	$0.421022\pi$
$234$	−9.44703	−0.617571
$235$	24.2244	1.58023
$236$	−32.8964	−2.14137
$237$	−8.03670	−0.522040
$238$	−23.4680	−1.52121
$239$	−14.9906	−0.969661	−0.484830	−	0.874608i	$-0.661119\pi$
$239$	−14.9906	−0.969661	−0.484830	+	0.874608i	$0.661119\pi$
$240$	23.5040	1.51718
$241$	−21.9399	−1.41328	−0.706638	−	0.707575i	$-0.749789\pi$
$241$	−21.9399	−1.41328	−0.706638	+	0.707575i	$0.749789\pi$
$242$	−41.6567	−2.67780
$243$	1.00000	0.0641500
$244$	44.6292	2.85709
$245$	−0.890125	−0.0568680
$246$	−9.34911	−0.596077
$247$	21.5473	1.37102
$248$	3.42759	0.217652
$249$	−2.85967	−0.181224
$250$	23.8930	1.51113
$251$	11.9314	0.753104	0.376552	−	0.926395i	$-0.377110\pi$
$251$	11.9314	0.753104	0.376552	+	0.926395i	$0.377110\pi$
$252$	−12.3337	−0.776950
$253$	−10.5036	−0.660355
$254$	−10.2375	−0.642361
$255$	−8.81595	−0.552076
$256$	−18.3318	−1.14574
$257$	−10.2389	−0.638686	−0.319343	−	0.947639i	$-0.603462\pi$
$257$	−10.2389	−0.638686	−0.319343	+	0.947639i	$0.603462\pi$
$258$	−15.8468	−0.986576
$259$	−0.191588	−0.0119047
$260$	43.7705	2.71453
$261$	7.65499	0.473832
$262$	22.6708	1.40061
$263$	20.0822	1.23832	0.619162	−	0.785263i	$-0.287472\pi$
$263$	20.0822	1.23832	0.619162	+	0.785263i	$0.287472\pi$
$264$	−37.6714	−2.31852
$265$	−11.8176	−0.725946
$266$	39.8924	2.44596
$267$	4.13000	0.252752
$268$	−23.5644	−1.43942
$269$	−8.12042	−0.495111	−0.247555	−	0.968874i	$-0.579627\pi$
$269$	−8.12042	−0.495111	−0.247555	+	0.968874i	$0.579627\pi$
$270$	−6.57030	−0.399856
$271$	−15.3946	−0.935156	−0.467578	−	0.883952i	$-0.654873\pi$
$271$	−15.3946	−0.935156	−0.467578	+	0.883952i	$0.654873\pi$
$272$	−32.5624	−1.97439
$273$	−9.35136	−0.565970
$274$	−0.202599	−0.0122395
$275$	7.08404	0.427184
$276$	−9.67125	−0.582141
$277$	4.76504	0.286303	0.143152	−	0.989701i	$-0.454276\pi$
$277$	4.76504	0.286303	0.143152	+	0.989701i	$0.454276\pi$
$278$	0.171511	0.0102865
$279$	−0.472724	−0.0283013
$280$	47.1570	2.81817
$281$	12.5110	0.746343	0.373171	−	0.927762i	$-0.378270\pi$
$281$	12.5110	0.746343	0.373171	+	0.927762i	$0.378270\pi$
$282$	−25.0117	−1.48942
$283$	4.64864	0.276333	0.138166	−	0.990409i	$-0.455879\pi$
$283$	4.64864	0.276333	0.138166	+	0.990409i	$0.455879\pi$
$284$	45.5591	2.70344
$285$	14.9859	0.887688
$286$	−49.0824	−2.90230
$287$	−9.25444	−0.546272
$288$	−9.76649	−0.575496
$289$	−4.78642	−0.281554
$290$	−50.2956	−2.95346
$291$	4.03928	0.236786
$292$	−40.5252	−2.37156
$293$	8.34247	0.487372	0.243686	−	0.969854i	$-0.421643\pi$
$293$	8.34247	0.487372	0.243686	+	0.969854i	$0.421643\pi$
$294$	0.919054	0.0536003
$295$	−17.3468	−1.00997
$296$	−0.538806	−0.0313174
$297$	5.19554	0.301476
$298$	−28.8193	−1.66946
$299$	−7.33270	−0.424061
$300$	6.52268	0.376587
$301$	−15.6863	−0.904143
$302$	−49.5823	−2.85314
$303$	8.75247	0.502816
$304$	55.3516	3.17463
$305$	23.5337	1.34754
$306$	9.10247	0.520353
$307$	−8.66895	−0.494763	−0.247382	−	0.968918i	$-0.579570\pi$
$307$	−8.66895	−0.494763	−0.247382	+	0.968918i	$0.579570\pi$
$308$	−64.0803	−3.65131
$309$	−10.2782	−0.584707
$310$	3.10594	0.176406
$311$	−14.1689	−0.803447	−0.401723	−	0.915761i	$-0.631589\pi$
$311$	−14.1689	−0.803447	−0.401723	+	0.915761i	$0.631589\pi$
$312$	−26.2990	−1.48889
$313$	−20.0106	−1.13107	−0.565533	−	0.824726i	$-0.691329\pi$
$313$	−20.0106	−1.13107	−0.565533	+	0.824726i	$0.691329\pi$
$314$	50.2415	2.83529
$315$	−6.50377	−0.366446
$316$	−38.4462	−2.16277
$317$	−18.5183	−1.04009	−0.520046	−	0.854138i	$-0.674085\pi$
$317$	−18.5183	−1.04009	−0.520046	+	0.854138i	$0.674085\pi$
$318$	12.2016	0.684233
$319$	39.7718	2.22680
$320$	17.1607	0.959310
$321$	−7.20549	−0.402171
$322$	−13.5757	−0.756543
$323$	−20.7614	−1.15520
$324$	4.78383	0.265769
$325$	4.94547	0.274325
$326$	1.14570	0.0634543
$327$	−18.0671	−0.999112
$328$	−26.0264	−1.43707
$329$	−24.7584	−1.36498
$330$	−34.1363	−1.87914
$331$	9.57680	0.526389	0.263194	−	0.964743i	$-0.415224\pi$
$331$	9.57680	0.526389	0.263194	+	0.964743i	$0.415224\pi$
$332$	−13.6802	−0.750798
$333$	0.0743106	0.00407220
$334$	−13.6352	−0.746085
$335$	−12.4259	−0.678898
$336$	−24.0222	−1.31052
$337$	20.1711	1.09879	0.549395	−	0.835563i	$-0.314858\pi$
$337$	20.1711	1.09879	0.549395	+	0.835563i	$0.314858\pi$
$338$	−0.405611	−0.0220623
$339$	16.7097	0.907549
$340$	−42.1740	−2.28721
$341$	−2.45606	−0.133003
$342$	−15.4729	−0.836681
$343$	18.9572	1.02359
$344$	−44.1148	−2.37851
$345$	−5.09981	−0.274565
$346$	29.6363	1.59326
$347$	−7.52820	−0.404135	−0.202067	−	0.979372i	$-0.564766\pi$
$347$	−7.52820	−0.404135	−0.202067	+	0.979372i	$0.564766\pi$
$348$	36.6202	1.96305
$349$	13.3971	0.717131	0.358565	−	0.933505i	$-0.383266\pi$
$349$	13.3971	0.717131	0.358565	+	0.933505i	$0.383266\pi$
$350$	9.15598	0.489408
$351$	3.62708	0.193599
$352$	−50.7422	−2.70457
$353$	−16.0724	−0.855447	−0.427724	−	0.903910i	$-0.640684\pi$
$353$	−16.0724	−0.855447	−0.427724	+	0.903910i	$0.640684\pi$
$354$	17.9106	0.951936
$355$	24.0241	1.27507
$356$	19.7572	1.04713
$357$	9.01029	0.476875
$358$	−57.5360	−3.04087
$359$	21.9625	1.15913	0.579567	−	0.814924i	$-0.303222\pi$
$359$	21.9625	1.15913	0.579567	+	0.814924i	$0.303222\pi$
$360$	−18.2906	−0.964001
$361$	16.2915	0.857449
$362$	21.8631	1.14910
$363$	15.9937	0.839449
$364$	−44.7354	−2.34477
$365$	−21.3696	−1.11854
$366$	−24.2986	−1.27011
$367$	−12.1577	−0.634626	−0.317313	−	0.948321i	$-0.602781\pi$
$367$	−12.1577	−0.634626	−0.317313	+	0.948321i	$0.602781\pi$
$368$	−18.8366	−0.981924
$369$	3.58949	0.186861
$370$	−0.488243	−0.0253826
$371$	12.0781	0.627062
$372$	−2.26144	−0.117250
$373$	−10.9816	−0.568604	−0.284302	−	0.958735i	$-0.591762\pi$
$373$	−10.9816	−0.568604	−0.284302	+	0.958735i	$0.591762\pi$
$374$	47.2923	2.44542
$375$	−9.17346	−0.473715
$376$	−69.6284	−3.59081
$377$	27.7653	1.42999
$378$	6.71514	0.345389
$379$	−36.0103	−1.84973	−0.924863	−	0.380301i	$-0.875821\pi$
$379$	−36.0103	−1.84973	−0.924863	+	0.380301i	$0.875821\pi$
$380$	71.6900	3.67762
$381$	3.93060	0.201370
$382$	−33.0021	−1.68854
$383$	5.17409	0.264384	0.132192	−	0.991224i	$-0.457798\pi$
$383$	5.17409	0.264384	0.132192	+	0.991224i	$0.457798\pi$
$384$	1.81459	0.0926005
$385$	−33.7906	−1.72213
$386$	−42.4637	−2.16134
$387$	6.08419	0.309277
$388$	19.3232	0.980988
$389$	−21.8758	−1.10915	−0.554574	−	0.832134i	$-0.687119\pi$
$389$	−21.8758	−1.10915	−0.554574	+	0.832134i	$0.687119\pi$
$390$	−23.8310	−1.20673
$391$	7.06526	0.357306
$392$	2.55849	0.129223
$393$	−8.70422	−0.439070
$394$	−29.6784	−1.49518
$395$	−20.2733	−1.02006
$396$	24.8546	1.24899
$397$	−15.8640	−0.796190	−0.398095	−	0.917344i	$-0.630329\pi$
$397$	−15.8640	−0.796190	−0.398095	+	0.917344i	$0.630329\pi$
$398$	53.9872	2.70614
$399$	−15.3163	−0.766772
$400$	12.7041	0.635207
$401$	6.75338	0.337248	0.168624	−	0.985680i	$-0.446068\pi$
$401$	6.75338	0.337248	0.168624	+	0.985680i	$0.446068\pi$
$402$	12.8297	0.639888
$403$	−1.71461	−0.0854108
$404$	41.8704	2.08313
$405$	2.52259	0.125349
$406$	51.4043	2.55115
$407$	0.386084	0.0191375
$408$	25.3398	1.25451
$409$	39.4027	1.94834	0.974168	−	0.225823i	$-0.0725072\pi$
$409$	39.4027	1.94834	0.974168	+	0.225823i	$0.0725072\pi$
$410$	−23.5840	−1.16473
$411$	0.0777857	0.00383689
$412$	−49.1692	−2.42239
$413$	17.7292	0.872397
$414$	5.26556	0.258788
$415$	−7.21379	−0.354111
$416$	−35.4239	−1.73680
$417$	−0.0658496	−0.00322467
$418$	−80.3903	−3.93202
$419$	36.9511	1.80518	0.902589	−	0.430502i	$-0.141664\pi$
$419$	36.9511	1.80518	0.902589	+	0.430502i	$0.141664\pi$
$420$	−31.1129	−1.51816
$421$	8.52040	0.415259	0.207630	−	0.978208i	$-0.433425\pi$
$421$	8.52040	0.415259	0.207630	+	0.978208i	$0.433425\pi$
$422$	17.0150	0.828276
$423$	9.60297	0.466912
$424$	33.9673	1.64960
$425$	−4.76510	−0.231141
$426$	−24.8049	−1.20180
$427$	−24.0525	−1.16398
$428$	−34.4699	−1.66616
$429$	18.8447	0.909829
$430$	−39.9750	−1.92776
$431$	−5.28126	−0.254389	−0.127195	−	0.991878i	$-0.540597\pi$
$431$	−5.28126	−0.254389	−0.127195	+	0.991878i	$0.540597\pi$
$432$	9.31741	0.448284
$433$	10.2846	0.494247	0.247124	−	0.968984i	$-0.420515\pi$
$433$	10.2846	0.494247	0.247124	+	0.968984i	$0.420515\pi$
$434$	−3.17441	−0.152377
$435$	19.3104	0.925865
$436$	−86.4299	−4.13924
$437$	−12.0100	−0.574515
$438$	22.0641	1.05426
$439$	−26.2370	−1.25222	−0.626112	−	0.779733i	$-0.715355\pi$
$439$	−26.2370	−1.25222	−0.626112	+	0.779733i	$0.715355\pi$
$440$	−95.0297	−4.53036
$441$	−0.352861	−0.0168029
$442$	33.0154	1.57038
$443$	−15.3390	−0.728780	−0.364390	−	0.931246i	$-0.618723\pi$
$443$	−15.3390	−0.728780	−0.364390	+	0.931246i	$0.618723\pi$
$444$	0.355490	0.0168708
$445$	10.4183	0.493875
$446$	−1.39713	−0.0661561
$447$	11.0648	0.523349
$448$	−17.5390	−0.828638
$449$	−10.4104	−0.491296	−0.245648	−	0.969359i	$-0.579001\pi$
$449$	−10.4104	−0.491296	−0.245648	+	0.969359i	$0.579001\pi$
$450$	−3.55130	−0.167410
$451$	18.6493	0.878163
$452$	79.9367	3.75990
$453$	19.0366	0.894417
$454$	−10.4411	−0.490023
$455$	−23.5897	−1.10590
$456$	−43.0741	−2.01713
$457$	−5.08934	−0.238069	−0.119035	−	0.992890i	$-0.537980\pi$
$457$	−5.08934	−0.238069	−0.119035	+	0.992890i	$0.537980\pi$
$458$	−41.4738	−1.93794
$459$	−3.49479	−0.163123
$460$	−24.3967	−1.13750
$461$	0.676590	0.0315119	0.0157560	−	0.999876i	$-0.494985\pi$
$461$	0.676590	0.0315119	0.0157560	+	0.999876i	$0.494985\pi$
$462$	34.8888	1.62317
$463$	2.07252	0.0963181	0.0481591	−	0.998840i	$-0.484665\pi$
$463$	2.07252	0.0963181	0.0481591	+	0.998840i	$0.484665\pi$
$464$	71.3247	3.31116
$465$	−1.19249	−0.0553005
$466$	−19.5270	−0.904571
$467$	−20.0140	−0.926138	−0.463069	−	0.886322i	$-0.653252\pi$
$467$	−20.0140	−0.926138	−0.463069	+	0.886322i	$0.653252\pi$
$468$	17.3514	0.802067
$469$	12.6998	0.586422
$470$	−63.0944	−2.91033
$471$	−19.2897	−0.888821
$472$	49.8601	2.29500
$473$	31.6107	1.45346
$474$	20.9322	0.961449
$475$	8.10000	0.371654
$476$	43.1038	1.97566
$477$	−4.68468	−0.214497
$478$	39.0442	1.78584
$479$	−17.3962	−0.794851	−0.397425	−	0.917635i	$-0.630096\pi$
$479$	−17.3962	−0.794851	−0.397425	+	0.917635i	$0.630096\pi$
$480$	−24.6369	−1.12451
$481$	0.269531	0.0122896
$482$	57.1443	2.60285
$483$	5.21224	0.237165
$484$	76.5110	3.47777
$485$	10.1895	0.462679
$486$	−2.60458	−0.118146
$487$	−28.6182	−1.29681	−0.648407	−	0.761294i	$-0.724565\pi$
$487$	−28.6182	−1.29681	−0.648407	+	0.761294i	$0.724565\pi$
$488$	−67.6432	−3.06206
$489$	−0.439878	−0.0198920
$490$	2.31840	0.104735
$491$	27.1236	1.22407	0.612035	−	0.790830i	$-0.290351\pi$
$491$	27.1236	1.22407	0.612035	+	0.790830i	$0.290351\pi$
$492$	17.1715	0.774152
$493$	−26.7526	−1.20488
$494$	−56.1216	−2.52503
$495$	13.1062	0.589082
$496$	−4.40456	−0.197771
$497$	−24.5537	−1.10138
$498$	7.44824	0.333764
$499$	16.7830	0.751309	0.375654	−	0.926760i	$-0.377418\pi$
$499$	16.7830	0.751309	0.375654	+	0.926760i	$0.377418\pi$
$500$	−43.8843	−1.96257
$501$	5.23509	0.233887
$502$	−31.0763	−1.38700
$503$	15.8888	0.708445	0.354222	−	0.935161i	$-0.384746\pi$
$503$	15.8888	0.708445	0.354222	+	0.935161i	$0.384746\pi$
$504$	18.6938	0.832690
$505$	22.0789	0.982499
$506$	27.3574	1.21619
$507$	0.155730	0.00691621
$508$	18.8033	0.834262
$509$	−10.0724	−0.446451	−0.223226	−	0.974767i	$-0.571659\pi$
$509$	−10.0724	−0.446451	−0.223226	+	0.974767i	$0.571659\pi$
$510$	22.9618	1.01677
$511$	21.8407	0.966175
$512$	44.1175	1.94974
$513$	5.94067	0.262287
$514$	26.6681	1.17628
$515$	−25.9277	−1.14251
$516$	29.1058	1.28131
$517$	49.8926	2.19428
$518$	0.499006	0.0219251
$519$	−11.3785	−0.499462
$520$	−66.3416	−2.90927
$521$	−35.4287	−1.55216	−0.776081	−	0.630633i	$-0.782795\pi$
$521$	−35.4287	−1.55216	−0.776081	+	0.630633i	$0.782795\pi$
$522$	−19.9380	−0.872664
$523$	34.5111	1.50906	0.754532	−	0.656264i	$-0.227864\pi$
$523$	34.5111	1.50906	0.754532	+	0.656264i	$0.227864\pi$
$524$	−41.6396	−1.81903
$525$	−3.51534	−0.153422
$526$	−52.3058	−2.28064
$527$	1.65207	0.0719655
$528$	48.4090	2.10673
$529$	−18.9129	−0.822301
$530$	30.7798	1.33699
$531$	−6.87657	−0.298418
$532$	−73.2704	−3.17668
$533$	13.0194	0.563932
$534$	−10.7569	−0.465497
$535$	−18.1765	−0.785840
$536$	35.7158	1.54269
$537$	22.0903	0.953268
$538$	21.1503	0.911854
$539$	−1.83330	−0.0789659
$540$	12.0677	0.519310
$541$	12.2106	0.524974	0.262487	−	0.964935i	$-0.415457\pi$
$541$	12.2106	0.524974	0.262487	+	0.964935i	$0.415457\pi$
$542$	40.0965	1.72229
$543$	−8.39410	−0.360225
$544$	34.1319	1.46339
$545$	−45.5759	−1.95226
$546$	24.3564	1.04236
$547$	−5.48515	−0.234528	−0.117264	−	0.993101i	$-0.537412\pi$
$547$	−5.48515	−0.234528	−0.117264	+	0.993101i	$0.537412\pi$
$548$	0.372114	0.0158959
$549$	9.32916	0.398159
$550$	−18.4509	−0.786751
$551$	45.4758	1.93733
$552$	14.6584	0.623905
$553$	20.7203	0.881115
$554$	−12.4109	−0.527289
$555$	0.187456	0.00795705
$556$	−0.315014	−0.0133596
$557$	−5.56402	−0.235755	−0.117877	−	0.993028i	$-0.537609\pi$
$557$	−5.56402	−0.235755	−0.117877	+	0.993028i	$0.537609\pi$
$558$	1.23125	0.0521229
$559$	22.0679	0.933371
$560$	−60.5982	−2.56074
$561$	−18.1573	−0.766604
$562$	−32.5858	−1.37455
$563$	−24.6724	−1.03982	−0.519908	−	0.854222i	$-0.674034\pi$
$563$	−24.6724	−1.03982	−0.519908	+	0.854222i	$0.674034\pi$
$564$	45.9390	1.93438
$565$	42.1519	1.77334
$566$	−12.1077	−0.508926
$567$	−2.57820	−0.108274
$568$	−69.0527	−2.89739
$569$	13.8894	0.582274	0.291137	−	0.956681i	$-0.405966\pi$
$569$	13.8894	0.582274	0.291137	+	0.956681i	$0.405966\pi$
$570$	−39.0320	−1.63487
$571$	10.8216	0.452870	0.226435	−	0.974026i	$-0.427293\pi$
$571$	10.8216	0.452870	0.226435	+	0.974026i	$0.427293\pi$
$572$	90.1497	3.76935
$573$	12.6708	0.529330
$574$	24.1039	1.00608
$575$	−2.75649	−0.114954
$576$	6.80278	0.283449
$577$	23.0415	0.959232	0.479616	−	0.877478i	$-0.340776\pi$
$577$	23.0415	0.959232	0.479616	+	0.877478i	$0.340776\pi$
$578$	12.4666	0.518543
$579$	16.3035	0.677549
$580$	92.3780	3.83579
$581$	7.37282	0.305876
$582$	−10.5206	−0.436093
$583$	−24.3395	−1.00804
$584$	61.4229	2.54170
$585$	9.14966	0.378292
$586$	−21.7286	−0.897601
$587$	32.6550	1.34782	0.673908	−	0.738815i	$-0.264614\pi$
$587$	32.6550	1.34782	0.673908	+	0.738815i	$0.264614\pi$
$588$	−1.68803	−0.0696131
$589$	−2.80830	−0.115714
$590$	45.1811	1.86008
$591$	11.3947	0.468715
$592$	0.692382	0.0284567
$593$	41.6689	1.71113	0.855567	−	0.517691i	$-0.173208\pi$
$593$	41.6689	1.71113	0.855567	+	0.517691i	$0.173208\pi$
$594$	−13.5322	−0.555233
$595$	22.7293	0.931811
$596$	52.9324	2.16820
$597$	−20.7278	−0.848333
$598$	19.0986	0.781000
$599$	41.6162	1.70039	0.850195	−	0.526468i	$-0.176484\pi$
$599$	41.6162	1.70039	0.850195	+	0.526468i	$0.176484\pi$
$600$	−9.88624	−0.403604
$601$	−6.55341	−0.267319	−0.133660	−	0.991027i	$-0.542673\pi$
$601$	−6.55341	−0.267319	−0.133660	+	0.991027i	$0.542673\pi$
$602$	40.8562	1.66517
$603$	−4.92583	−0.200595
$604$	91.0679	3.70550
$605$	40.3455	1.64028
$606$	−22.7965	−0.926044
$607$	22.6287	0.918471	0.459235	−	0.888315i	$-0.348123\pi$
$607$	22.6287	0.918471	0.459235	+	0.888315i	$0.348123\pi$
$608$	−58.0194	−2.35300
$609$	−19.7361	−0.799749
$610$	−61.2954	−2.48178
$611$	34.8308	1.40910
$612$	−16.7185	−0.675806
$613$	20.1238	0.812793	0.406397	−	0.913697i	$-0.366785\pi$
$613$	20.1238	0.812793	0.406397	+	0.913697i	$0.366785\pi$
$614$	22.5790	0.911213
$615$	9.05482	0.365126
$616$	97.1246	3.91326
$617$	−36.2501	−1.45938	−0.729688	−	0.683781i	$-0.760334\pi$
$617$	−36.2501	−1.45938	−0.729688	+	0.683781i	$0.760334\pi$
$618$	26.7704	1.07686
$619$	26.3090	1.05745	0.528724	−	0.848794i	$-0.322671\pi$
$619$	26.3090	1.05745	0.528724	+	0.848794i	$0.322671\pi$
$620$	−5.70468	−0.229106
$621$	−2.02165	−0.0811261
$622$	36.9041	1.47972
$623$	−10.6480	−0.426602
$624$	33.7950	1.35288
$625$	−29.9583	−1.19833
$626$	52.1192	2.08310
$627$	30.8650	1.23263
$628$	−92.2786	−3.68232
$629$	−0.259700	−0.0103549
$630$	16.9396	0.674889
$631$	19.0142	0.756943	0.378472	−	0.925613i	$-0.376450\pi$
$631$	19.0142	0.756943	0.378472	+	0.925613i	$0.376450\pi$
$632$	58.2719	2.31793
$633$	−6.53272	−0.259652
$634$	48.2325	1.91556
$635$	9.91530	0.393477
$636$	−22.4107	−0.888644
$637$	−1.27986	−0.0507097
$638$	−103.589	−4.10112
$639$	9.52356	0.376746
$640$	4.57748	0.180941
$641$	32.1528	1.26996	0.634979	−	0.772530i	$-0.281009\pi$
$641$	32.1528	1.26996	0.634979	+	0.772530i	$0.281009\pi$
$642$	18.7673	0.740685
$643$	24.3029	0.958415	0.479207	−	0.877702i	$-0.340924\pi$
$643$	24.3029	0.958415	0.479207	+	0.877702i	$0.340924\pi$
$644$	24.9345	0.982556
$645$	15.3479	0.604325
$646$	54.0747	2.12754
$647$	−11.9455	−0.469627	−0.234814	−	0.972040i	$-0.575448\pi$
$647$	−11.9455	−0.469627	−0.234814	+	0.972040i	$0.575448\pi$
$648$	−7.25072	−0.284835
$649$	−35.7275	−1.40243
$650$	−12.8809	−0.505229
$651$	1.21878	0.0477678
$652$	−2.10431	−0.0824109
$653$	5.17466	0.202500	0.101250	−	0.994861i	$-0.467716\pi$
$653$	5.17466	0.202500	0.101250	+	0.994861i	$0.467716\pi$
$654$	47.0572	1.84008
$655$	−21.9572	−0.857940
$656$	33.4447	1.30580
$657$	−8.47128	−0.330496
$658$	64.4853	2.51390
$659$	−0.778075	−0.0303095	−0.0151547	−	0.999885i	$-0.504824\pi$
$659$	−0.778075	−0.0303095	−0.0151547	+	0.999885i	$0.504824\pi$
$660$	62.6981	2.44052
$661$	−33.0093	−1.28391	−0.641957	−	0.766740i	$-0.721877\pi$
$661$	−33.0093	−1.28391	−0.641957	+	0.766740i	$0.721877\pi$
$662$	−24.9435	−0.969458
$663$	−12.6759	−0.492291
$664$	20.7347	0.804662
$665$	−38.6367	−1.49827
$666$	−0.193548	−0.00749983
$667$	−15.4757	−0.599223
$668$	25.0438	0.968974
$669$	0.536414	0.0207389
$670$	32.3642	1.25034
$671$	48.4701	1.87117
$672$	25.1800	0.971340
$673$	−40.9410	−1.57816	−0.789080	−	0.614290i	$-0.789442\pi$
$673$	−40.9410	−1.57816	−0.789080	+	0.614290i	$0.789442\pi$
$674$	−52.5372	−2.02366
$675$	1.36348	0.0524805
$676$	0.744987	0.0286533
$677$	22.1279	0.850444	0.425222	−	0.905089i	$-0.360196\pi$
$677$	22.1279	0.850444	0.425222	+	0.905089i	$0.360196\pi$
$678$	−43.5219	−1.67145
$679$	−10.4141	−0.399656
$680$	63.9220	2.45130
$681$	4.00873	0.153615
$682$	6.39700	0.244954
$683$	−6.00196	−0.229659	−0.114829	−	0.993385i	$-0.536632\pi$
$683$	−6.00196	−0.229659	−0.114829	+	0.993385i	$0.536632\pi$
$684$	28.4192	1.08663
$685$	0.196222	0.00749725
$686$	−49.3755	−1.88516
$687$	15.9234	0.607516
$688$	56.6889	2.16124
$689$	−16.9917	−0.647333
$690$	13.2829	0.505670
$691$	−24.3873	−0.927738	−0.463869	−	0.885904i	$-0.653539\pi$
$691$	−24.3873	−0.927738	−0.463869	+	0.885904i	$0.653539\pi$
$692$	−54.4330	−2.06923
$693$	−13.3952	−0.508840
$694$	19.6078	0.744301
$695$	−0.166112	−0.00630099
$696$	−55.5042	−2.10388
$697$	−12.5445	−0.475158
$698$	−34.8938	−1.32075
$699$	7.49718	0.283569
$700$	−16.8168	−0.635616
$701$	15.2543	0.576147	0.288074	−	0.957608i	$-0.406985\pi$
$701$	15.2543	0.576147	0.288074	+	0.957608i	$0.406985\pi$
$702$	−9.44703	−0.356555
$703$	0.441455	0.0166498
$704$	35.3441	1.33208
$705$	24.2244	0.912344
$706$	41.8618	1.57549
$707$	−22.5657	−0.848669
$708$	−32.8964	−1.23632
$709$	−17.3742	−0.652503	−0.326252	−	0.945283i	$-0.605786\pi$
$709$	−17.3742	−0.652503	−0.326252	+	0.945283i	$0.605786\pi$
$710$	−62.5726	−2.34831
$711$	−8.03670	−0.301400
$712$	−29.9455	−1.12225
$713$	0.955685	0.0357907
$714$	−23.4680	−0.878269
$715$	47.5374	1.77780
$716$	105.677	3.94932
$717$	−14.9906	−0.559834
$718$	−57.2030	−2.13480
$719$	−15.5973	−0.581680	−0.290840	−	0.956772i	$-0.593935\pi$
$719$	−15.5973	−0.581680	−0.290840	+	0.956772i	$0.593935\pi$
$720$	23.5040	0.875944
$721$	26.4993	0.986886
$722$	−42.4326	−1.57918
$723$	−21.9399	−0.815955
$724$	−40.1560	−1.49239
$725$	10.4375	0.387638
$726$	−41.6567	−1.54603
$727$	−9.78659	−0.362965	−0.181482	−	0.983394i	$-0.558090\pi$
$727$	−9.78659	−0.362965	−0.181482	+	0.983394i	$0.558090\pi$
$728$	67.8041	2.51299
$729$	1.00000	0.0370370
$730$	55.6588	2.06003
$731$	−21.2630	−0.786440
$732$	44.6292	1.64954
$733$	37.6641	1.39115	0.695577	−	0.718451i	$-0.255149\pi$
$733$	37.6641	1.39115	0.695577	+	0.718451i	$0.255149\pi$
$734$	31.6657	1.16880
$735$	−0.890125	−0.0328327
$736$	19.7444	0.727790
$737$	−25.5924	−0.942707
$738$	−9.34911	−0.344145
$739$	12.1258	0.446054	0.223027	−	0.974812i	$-0.428406\pi$
$739$	12.1258	0.446054	0.223027	+	0.974812i	$0.428406\pi$
$740$	0.896757	0.0329654
$741$	21.5473	0.791560
$742$	−31.4583	−1.15487
$743$	−21.7285	−0.797142	−0.398571	−	0.917138i	$-0.630494\pi$
$743$	−21.7285	−0.797142	−0.398571	+	0.917138i	$0.630494\pi$
$744$	3.42759	0.125662
$745$	27.9121	1.02262
$746$	28.6024	1.04721
$747$	−2.85967	−0.104630
$748$	−86.8617	−3.17598
$749$	18.5772	0.678797
$750$	23.8930	0.872449
$751$	17.3375	0.632656	0.316328	−	0.948650i	$-0.397550\pi$
$751$	17.3375	0.632656	0.316328	+	0.948650i	$0.397550\pi$
$752$	89.4748	3.26281
$753$	11.9314	0.434805
$754$	−72.3169	−2.63363
$755$	48.0216	1.74769
$756$	−12.3337	−0.448573
$757$	7.56347	0.274899	0.137449	−	0.990509i	$-0.456110\pi$
$757$	7.56347	0.274899	0.137449	+	0.990509i	$0.456110\pi$
$758$	93.7917	3.40667
$759$	−10.5036	−0.381256
$760$	−108.659	−3.94146
$761$	−23.2204	−0.841738	−0.420869	−	0.907121i	$-0.638275\pi$
$761$	−23.2204	−0.841738	−0.420869	+	0.907121i	$0.638275\pi$
$762$	−10.2375	−0.370867
$763$	46.5806	1.68633
$764$	60.6150	2.19297
$765$	−8.81595	−0.318741
$766$	−13.4763	−0.486920
$767$	−24.9419	−0.900599
$768$	−18.3318	−0.661492
$769$	−13.5804	−0.489721	−0.244860	−	0.969558i	$-0.578742\pi$
$769$	−13.5804	−0.489721	−0.244860	+	0.969558i	$0.578742\pi$
$770$	88.0103	3.17167
$771$	−10.2389	−0.368746
$772$	77.9931	2.80703
$773$	17.2134	0.619124	0.309562	−	0.950879i	$-0.399818\pi$
$773$	17.2134	0.619124	0.309562	+	0.950879i	$0.399818\pi$
$774$	−15.8468	−0.569600
$775$	−0.644552	−0.0231530
$776$	−29.2876	−1.05137
$777$	−0.191588	−0.00687318
$778$	56.9773	2.04274
$779$	21.3240	0.764010
$780$	43.7705	1.56723
$781$	49.4801	1.77054
$782$	−18.4020	−0.658055
$783$	7.65499	0.273567
$784$	−3.28775	−0.117420
$785$	−48.6600	−1.73675
$786$	22.6708	0.808642
$787$	36.9254	1.31625	0.658125	−	0.752909i	$-0.271350\pi$
$787$	36.9254	1.31625	0.658125	+	0.752909i	$0.271350\pi$
$788$	54.5103	1.94185
$789$	20.0822	0.714947
$790$	52.8035	1.87866
$791$	−43.0811	−1.53179
$792$	−37.6714	−1.33860
$793$	33.8377	1.20161
$794$	41.3190	1.46636
$795$	−11.8176	−0.419125
$796$	−99.1584	−3.51458
$797$	16.0179	0.567383	0.283692	−	0.958916i	$-0.408441\pi$
$797$	16.0179	0.567383	0.283692	+	0.958916i	$0.408441\pi$
$798$	39.8924	1.41218
$799$	−33.5604	−1.18728
$800$	−13.3164	−0.470808
$801$	4.13000	0.145926
$802$	−17.5897	−0.621115
$803$	−44.0129	−1.55318
$804$	−23.5644	−0.831051
$805$	13.1484	0.463419
$806$	4.46584	0.157302
$807$	−8.12042	−0.285852
$808$	−63.4617	−2.23257
$809$	30.3586	1.06735	0.533676	−	0.845689i	$-0.320810\pi$
$809$	30.3586	1.06735	0.533676	+	0.845689i	$0.320810\pi$
$810$	−6.57030	−0.230857
$811$	−34.0865	−1.19694	−0.598469	−	0.801146i	$-0.704224\pi$
$811$	−34.0865	−1.19694	−0.598469	+	0.801146i	$0.704224\pi$
$812$	−94.4144	−3.31330
$813$	−15.3946	−0.539913
$814$	−1.00559	−0.0352458
$815$	−1.10963	−0.0388688
$816$	−32.5624	−1.13991
$817$	36.1442	1.26452
$818$	−102.627	−3.58828
$819$	−9.35136	−0.326763
$820$	43.3168	1.51269
$821$	4.21241	0.147014	0.0735070	−	0.997295i	$-0.476581\pi$
$821$	4.21241	0.147014	0.0735070	+	0.997295i	$0.476581\pi$
$822$	−0.202599	−0.00706646
$823$	19.9133	0.694136	0.347068	−	0.937840i	$-0.387177\pi$
$823$	19.9133	0.694136	0.347068	+	0.937840i	$0.387177\pi$
$824$	74.5244	2.59618
$825$	7.08404	0.246635
$826$	−46.1771	−1.60671
$827$	−47.9558	−1.66759	−0.833794	−	0.552076i	$-0.813836\pi$
$827$	−47.9558	−1.66759	−0.833794	+	0.552076i	$0.813836\pi$
$828$	−9.67125	−0.336099
$829$	−50.0885	−1.73965	−0.869823	−	0.493364i	$-0.835767\pi$
$829$	−50.0885	−1.73965	−0.869823	+	0.493364i	$0.835767\pi$
$830$	18.7889	0.652172
$831$	4.76504	0.165297
$832$	24.6742	0.855426
$833$	1.23318	0.0427270
$834$	0.171511	0.00593893
$835$	13.2060	0.457013
$836$	147.653	5.10669
$837$	−0.472724	−0.0163397
$838$	−96.2421	−3.32463
$839$	−19.8506	−0.685318	−0.342659	−	0.939460i	$-0.611328\pi$
$839$	−19.8506	−0.685318	−0.342659	+	0.939460i	$0.611328\pi$
$840$	47.1570	1.62707
$841$	29.5989	1.02065
$842$	−22.1921	−0.764789
$843$	12.5110	0.430901
$844$	−31.2514	−1.07572
$845$	0.392844	0.0135142
$846$	−25.0117	−0.859920
$847$	−41.2349	−1.41685
$848$	−43.6491	−1.49892
$849$	4.64864	0.159541
$850$	12.4111	0.425696
$851$	−0.150230	−0.00514983
$852$	45.5591	1.56083
$853$	−49.6045	−1.69842	−0.849212	−	0.528051i	$-0.822923\pi$
$853$	−49.6045	−1.69842	−0.849212	+	0.528051i	$0.822923\pi$
$854$	62.6466	2.14372
$855$	14.9859	0.512507
$856$	52.2450	1.78570
$857$	−14.1401	−0.483017	−0.241509	−	0.970399i	$-0.577642\pi$
$857$	−14.1401	−0.483017	−0.241509	+	0.970399i	$0.577642\pi$
$858$	−49.0824	−1.67565
$859$	53.5982	1.82875	0.914373	−	0.404873i	$-0.132684\pi$
$859$	53.5982	1.82875	0.914373	+	0.404873i	$0.132684\pi$
$860$	73.4220	2.50367
$861$	−9.25444	−0.315390
$862$	13.7555	0.468513
$863$	34.9654	1.19024	0.595119	−	0.803638i	$-0.297105\pi$
$863$	34.9654	1.19024	0.595119	+	0.803638i	$0.297105\pi$
$864$	−9.76649	−0.332263
$865$	−28.7034	−0.975946
$866$	−26.7871	−0.910263
$867$	−4.78642	−0.162555
$868$	5.83044	0.197898
$869$	−41.7550	−1.41644
$870$	−50.2956	−1.70518
$871$	−17.8664	−0.605380
$872$	130.999	4.43620
$873$	4.03928	0.136709
$874$	31.2809	1.05809
$875$	23.6510	0.799551
$876$	−40.5252	−1.36922
$877$	12.3979	0.418647	0.209324	−	0.977846i	$-0.432874\pi$
$877$	12.3979	0.418647	0.209324	+	0.977846i	$0.432874\pi$
$878$	68.3364	2.30624
$879$	8.34247	0.281384
$880$	122.116	4.11654
$881$	−20.6966	−0.697286	−0.348643	−	0.937256i	$-0.613357\pi$
$881$	−20.6966	−0.697286	−0.348643	+	0.937256i	$0.613357\pi$
$882$	0.919054	0.0309462
$883$	54.5891	1.83707	0.918534	−	0.395341i	$-0.129374\pi$
$883$	54.5891	1.83707	0.918534	+	0.395341i	$0.129374\pi$
$884$	−60.6394	−2.03953
$885$	−17.3468	−0.583106
$886$	39.9518	1.34221
$887$	−42.3258	−1.42116	−0.710581	−	0.703616i	$-0.751568\pi$
$887$	−42.3258	−1.42116	−0.710581	+	0.703616i	$0.751568\pi$
$888$	−0.538806	−0.0180811
$889$	−10.1339	−0.339879
$890$	−27.1353	−0.909578
$891$	5.19554	0.174057
$892$	2.56611	0.0859198
$893$	57.0480	1.90904
$894$	−28.8193	−0.963861
$895$	55.7250	1.86268
$896$	−4.67839	−0.156294
$897$	−7.33270	−0.244832
$898$	27.1147	0.904828
$899$	−3.61870	−0.120690
$900$	6.52268	0.217423
$901$	16.3720	0.545430
$902$	−48.5737	−1.61733
$903$	−15.6863	−0.522007
$904$	−121.158	−4.02964
$905$	−21.1749	−0.703878
$906$	−49.5823	−1.64726
$907$	39.5934	1.31468	0.657339	−	0.753595i	$-0.271682\pi$
$907$	39.5934	1.31468	0.657339	+	0.753595i	$0.271682\pi$
$908$	19.1771	0.636414
$909$	8.75247	0.290301
$910$	61.4412	2.03676
$911$	35.4593	1.17482	0.587409	−	0.809290i	$-0.300148\pi$
$911$	35.4593	1.17482	0.587409	+	0.809290i	$0.300148\pi$
$912$	55.3516	1.83287
$913$	−14.8575	−0.491713
$914$	13.2556	0.438456
$915$	23.5337	0.778000
$916$	76.1749	2.51689
$917$	22.4413	0.741076
$918$	9.10247	0.300426
$919$	9.11640	0.300722	0.150361	−	0.988631i	$-0.451956\pi$
$919$	9.11640	0.300722	0.150361	+	0.988631i	$0.451956\pi$
$920$	36.9773	1.21911
$921$	−8.66895	−0.285652
$922$	−1.76223	−0.0580360
$923$	34.5427	1.13699
$924$	−64.0803	−2.10809
$925$	0.101321	0.00333143
$926$	−5.39804	−0.177391
$927$	−10.2782	−0.337581
$928$	−74.7624	−2.45420
$929$	−52.2758	−1.71511	−0.857556	−	0.514390i	$-0.828018\pi$
$929$	−52.2758	−1.71511	−0.857556	+	0.514390i	$0.828018\pi$
$930$	3.10594	0.101848
$931$	−2.09623	−0.0687011
$932$	35.8653	1.17481
$933$	−14.1689	−0.463870
$934$	52.1281	1.70568
$935$	−45.8036	−1.49794
$936$	−26.2990	−0.859608
$937$	−51.8213	−1.69293	−0.846465	−	0.532445i	$-0.821273\pi$
$937$	−51.8213	−1.69293	−0.846465	+	0.532445i	$0.821273\pi$
$938$	−33.0776	−1.08002
$939$	−20.0106	−0.653021
$940$	115.886	3.77977
$941$	28.0363	0.913956	0.456978	−	0.889478i	$-0.348932\pi$
$941$	28.0363	0.913956	0.456978	+	0.889478i	$0.348932\pi$
$942$	50.2415	1.63696
$943$	−7.25670	−0.236311
$944$	−64.0718	−2.08536
$945$	−6.50377	−0.211568
$946$	−82.3325	−2.67686
$947$	7.66933	0.249220	0.124610	−	0.992206i	$-0.460232\pi$
$947$	7.66933	0.249220	0.124610	+	0.992206i	$0.460232\pi$
$948$	−38.4462	−1.24868
$949$	−30.7260	−0.997409
$950$	−21.0971	−0.684481
$951$	−18.5183	−0.600498
$952$	−65.3311	−2.11739
$953$	17.8771	0.579095	0.289547	−	0.957164i	$-0.406495\pi$
$953$	17.8771	0.579095	0.289547	+	0.957164i	$0.406495\pi$
$954$	12.2016	0.395042
$955$	31.9633	1.03431
$956$	−71.7125	−2.31935
$957$	39.7718	1.28564
$958$	45.3097	1.46389
$959$	−0.200548	−0.00647602
$960$	17.1607	0.553858
$961$	−30.7765	−0.992791
$962$	−0.702015	−0.0226339
$963$	−7.20549	−0.232194
$964$	−104.957	−3.38044
$965$	41.1270	1.32393
$966$	−13.5757	−0.436790
$967$	24.9196	0.801360	0.400680	−	0.916218i	$-0.368774\pi$
$967$	24.9196	0.801360	0.400680	+	0.916218i	$0.368774\pi$
$968$	−115.965	−3.72727
$969$	−20.7614	−0.666952
$970$	−26.5392	−0.852124
$971$	49.6346	1.59285	0.796425	−	0.604737i	$-0.206722\pi$
$971$	49.6346	1.59285	0.796425	+	0.604737i	$0.206722\pi$
$972$	4.78383	0.153442
$973$	0.169774	0.00544270
$974$	74.5384	2.38836
$975$	4.94547	0.158382
$976$	86.9236	2.78236
$977$	−39.5306	−1.26470	−0.632348	−	0.774684i	$-0.717909\pi$
$977$	−39.5306	−1.26470	−0.632348	+	0.774684i	$0.717909\pi$
$978$	1.14570	0.0366354
$979$	21.4576	0.685787
$980$	−4.25821	−0.136024
$981$	−18.0671	−0.576838
$982$	−70.6456	−2.25439
$983$	36.5481	1.16570	0.582852	−	0.812579i	$-0.301937\pi$
$983$	36.5481	1.16570	0.582852	+	0.812579i	$0.301937\pi$
$984$	−26.0264	−0.829690
$985$	28.7442	0.915866
$986$	69.6793	2.21904
$987$	−24.7584	−0.788069
$988$	103.079	3.27937
$989$	−12.3001	−0.391121
$990$	−34.1363	−1.08492
$991$	−31.1968	−0.991000	−0.495500	−	0.868608i	$-0.665015\pi$
$991$	−31.1968	−0.991000	−0.495500	+	0.868608i	$0.665015\pi$
$992$	4.61686	0.146585
$993$	9.57680	0.303911
$994$	63.9520	2.02844
$995$	−52.2879	−1.65764
$996$	−13.6802	−0.433474
$997$	−46.3323	−1.46736	−0.733680	−	0.679495i	$-0.762199\pi$
$997$	−46.3323	−1.46736	−0.733680	+	0.679495i	$0.762199\pi$
$998$	−43.7126	−1.38370
$999$	0.0743106	0.00235108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.c.1.4	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.c.1.4	✓	92	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:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60458 q^{2} +1.00000 q^{3} +4.78383 q^{4} +2.52259 q^{5} -2.60458 q^{6} -2.57820 q^{7} -7.25072 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.60458 q^{2} +1.00000 q^{3} +4.78383 q^{4} +2.52259 q^{5} -2.60458 q^{6} -2.57820 q^{7} -7.25072 q^{8} +1.00000 q^{9} -6.57030 q^{10} +5.19554 q^{11} +4.78383 q^{12} +3.62708 q^{13} +6.71514 q^{14} +2.52259 q^{15} +9.31741 q^{16} -3.49479 q^{17} -2.60458 q^{18} +5.94067 q^{19} +12.0677 q^{20} -2.57820 q^{21} -13.5322 q^{22} -2.02165 q^{23} -7.25072 q^{24} +1.36348 q^{25} -9.44703 q^{26} +1.00000 q^{27} -12.3337 q^{28} +7.65499 q^{29} -6.57030 q^{30} -0.472724 q^{31} -9.76649 q^{32} +5.19554 q^{33} +9.10247 q^{34} -6.50377 q^{35} +4.78383 q^{36} +0.0743106 q^{37} -15.4729 q^{38} +3.62708 q^{39} -18.2906 q^{40} +3.58949 q^{41} +6.71514 q^{42} +6.08419 q^{43} +24.8546 q^{44} +2.52259 q^{45} +5.26556 q^{46} +9.60297 q^{47} +9.31741 q^{48} -0.352861 q^{49} -3.55130 q^{50} -3.49479 q^{51} +17.3514 q^{52} -4.68468 q^{53} -2.60458 q^{54} +13.1062 q^{55} +18.6938 q^{56} +5.94067 q^{57} -19.9380 q^{58} -6.87657 q^{59} +12.0677 q^{60} +9.32916 q^{61} +1.23125 q^{62} -2.57820 q^{63} +6.80278 q^{64} +9.14966 q^{65} -13.5322 q^{66} -4.92583 q^{67} -16.7185 q^{68} -2.02165 q^{69} +16.9396 q^{70} +9.52356 q^{71} -7.25072 q^{72} -8.47128 q^{73} -0.193548 q^{74} +1.36348 q^{75} +28.4192 q^{76} -13.3952 q^{77} -9.44703 q^{78} -8.03670 q^{79} +23.5040 q^{80} +1.00000 q^{81} -9.34911 q^{82} -2.85967 q^{83} -12.3337 q^{84} -8.81595 q^{85} -15.8468 q^{86} +7.65499 q^{87} -37.6714 q^{88} +4.13000 q^{89} -6.57030 q^{90} -9.35136 q^{91} -9.67125 q^{92} -0.472724 q^{93} -25.0117 q^{94} +14.9859 q^{95} -9.76649 q^{96} +4.03928 q^{97} +0.919054 q^{98} +5.19554 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * q^99

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