LMFDB - Embedded newform 6001.2.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58651 q^{2} -0.844986 q^{3} +4.69006 q^{4} -0.771482 q^{5} +2.18557 q^{6} -2.98561 q^{7} -6.95787 q^{8} -2.28600 q^{9} +O(q^{10})$	\(q-2.58651 q^{2} -0.844986 q^{3} +4.69006 q^{4} -0.771482 q^{5} +2.18557 q^{6} -2.98561 q^{7} -6.95787 q^{8} -2.28600 q^{9} +1.99545 q^{10} +2.21423 q^{11} -3.96303 q^{12} -1.82519 q^{13} +7.72234 q^{14} +0.651891 q^{15} +8.61652 q^{16} -1.00000 q^{17} +5.91277 q^{18} -3.33212 q^{19} -3.61829 q^{20} +2.52280 q^{21} -5.72714 q^{22} +6.31794 q^{23} +5.87930 q^{24} -4.40482 q^{25} +4.72087 q^{26} +4.46659 q^{27} -14.0027 q^{28} +2.28181 q^{29} -1.68613 q^{30} -6.05518 q^{31} -8.37101 q^{32} -1.87099 q^{33} +2.58651 q^{34} +2.30335 q^{35} -10.7215 q^{36} +2.57541 q^{37} +8.61857 q^{38} +1.54226 q^{39} +5.36787 q^{40} -3.79925 q^{41} -6.52526 q^{42} +11.8225 q^{43} +10.3849 q^{44} +1.76361 q^{45} -16.3414 q^{46} -3.12298 q^{47} -7.28083 q^{48} +1.91390 q^{49} +11.3931 q^{50} +0.844986 q^{51} -8.56023 q^{52} -0.00490433 q^{53} -11.5529 q^{54} -1.70824 q^{55} +20.7735 q^{56} +2.81559 q^{57} -5.90194 q^{58} -10.0910 q^{59} +3.05741 q^{60} +2.89373 q^{61} +15.6618 q^{62} +6.82511 q^{63} +4.41869 q^{64} +1.40810 q^{65} +4.83935 q^{66} +5.55525 q^{67} -4.69006 q^{68} -5.33857 q^{69} -5.95764 q^{70} +1.30409 q^{71} +15.9057 q^{72} +10.3119 q^{73} -6.66133 q^{74} +3.72201 q^{75} -15.6278 q^{76} -6.61083 q^{77} -3.98907 q^{78} +7.21369 q^{79} -6.64749 q^{80} +3.08379 q^{81} +9.82682 q^{82} +11.4580 q^{83} +11.8321 q^{84} +0.771482 q^{85} -30.5790 q^{86} -1.92810 q^{87} -15.4063 q^{88} +9.57081 q^{89} -4.56160 q^{90} +5.44930 q^{91} +29.6315 q^{92} +5.11654 q^{93} +8.07764 q^{94} +2.57067 q^{95} +7.07338 q^{96} -3.70810 q^{97} -4.95032 q^{98} -5.06173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.58651	−1.82894	−0.914471	−	0.404652i	$-0.867393\pi$
$2$	−2.58651	−1.82894	−0.914471	+	0.404652i	$0.867393\pi$
$3$	−0.844986	−0.487853	−0.243926	−	0.969794i	$-0.578436\pi$
$3$	−0.844986	−0.487853	−0.243926	+	0.969794i	$0.578436\pi$
$4$	4.69006	2.34503
$5$	−0.771482	−0.345017	−0.172509	−	0.985008i	$-0.555187\pi$
$5$	−0.771482	−0.345017	−0.172509	+	0.985008i	$0.555187\pi$
$6$	2.18557	0.892254
$7$	−2.98561	−1.12846	−0.564228	−	0.825619i	$-0.690826\pi$
$7$	−2.98561	−1.12846	−0.564228	+	0.825619i	$0.690826\pi$
$8$	−6.95787	−2.45998
$9$	−2.28600	−0.762000
$10$	1.99545	0.631017
$11$	2.21423	0.667615	0.333808	−	0.942641i	$-0.391666\pi$
$11$	2.21423	0.667615	0.333808	+	0.942641i	$0.391666\pi$
$12$	−3.96303	−1.14403
$13$	−1.82519	−0.506216	−0.253108	−	0.967438i	$-0.581453\pi$
$13$	−1.82519	−0.506216	−0.253108	+	0.967438i	$0.581453\pi$
$14$	7.72234	2.06388
$15$	0.651891	0.168318
$16$	8.61652	2.15413
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.91277	1.39365
$19$	−3.33212	−0.764440	−0.382220	−	0.924071i	$-0.624840\pi$
$19$	−3.33212	−0.764440	−0.382220	+	0.924071i	$0.624840\pi$
$20$	−3.61829	−0.809075
$21$	2.52280	0.550520
$22$	−5.72714	−1.22103
$23$	6.31794	1.31738	0.658691	−	0.752414i	$-0.271110\pi$
$23$	6.31794	1.31738	0.658691	+	0.752414i	$0.271110\pi$
$24$	5.87930	1.20011
$25$	−4.40482	−0.880963
$26$	4.72087	0.925839
$27$	4.46659	0.859596
$28$	−14.0027	−2.64626
$29$	2.28181	0.423722	0.211861	−	0.977300i	$-0.432048\pi$
$29$	2.28181	0.423722	0.211861	+	0.977300i	$0.432048\pi$
$30$	−1.68613	−0.307843
$31$	−6.05518	−1.08754	−0.543771	−	0.839234i	$-0.683004\pi$
$31$	−6.05518	−1.08754	−0.543771	+	0.839234i	$0.683004\pi$
$32$	−8.37101	−1.47980
$33$	−1.87099	−0.325698
$34$	2.58651	0.443584
$35$	2.30335	0.389337
$36$	−10.7215	−1.78691
$37$	2.57541	0.423394	0.211697	−	0.977335i	$-0.432101\pi$
$37$	2.57541	0.423394	0.211697	+	0.977335i	$0.432101\pi$
$38$	8.61857	1.39812
$39$	1.54226	0.246959
$40$	5.36787	0.848735
$41$	−3.79925	−0.593343	−0.296672	−	0.954980i	$-0.595877\pi$
$41$	−3.79925	−0.593343	−0.296672	+	0.954980i	$0.595877\pi$
$42$	−6.52526	−1.00687
$43$	11.8225	1.80291	0.901455	−	0.432872i	$-0.142500\pi$
$43$	11.8225	1.80291	0.901455	+	0.432872i	$0.142500\pi$
$44$	10.3849	1.56558
$45$	1.76361	0.262903
$46$	−16.3414	−2.40942
$47$	−3.12298	−0.455534	−0.227767	−	0.973716i	$-0.573142\pi$
$47$	−3.12298	−0.455534	−0.227767	+	0.973716i	$0.573142\pi$
$48$	−7.28083	−1.05090
$49$	1.91390	0.273414
$50$	11.3931	1.61123
$51$	0.844986	0.118322
$52$	−8.56023	−1.18709
$53$	−0.00490433	−0.000673661 0	−0.000336831	−	1.00000i	$-0.500107\pi$
$53$	−0.00490433	−0.000673661 0	−0.000336831		1.00000i	$0.500107\pi$
$54$	−11.5529	−1.57215
$55$	−1.70824	−0.230339
$56$	20.7735	2.77598
$57$	2.81559	0.372934
$58$	−5.90194	−0.774963
$59$	−10.0910	−1.31373	−0.656866	−	0.754007i	$-0.728118\pi$
$59$	−10.0910	−1.31373	−0.656866	+	0.754007i	$0.728118\pi$
$60$	3.05741	0.394710
$61$	2.89373	0.370504	0.185252	−	0.982691i	$-0.440690\pi$
$61$	2.89373	0.370504	0.185252	+	0.982691i	$0.440690\pi$
$62$	15.6618	1.98905
$63$	6.82511	0.859884
$64$	4.41869	0.552337
$65$	1.40810	0.174653
$66$	4.83935	0.595682
$67$	5.55525	0.678681	0.339341	−	0.940664i	$-0.389796\pi$
$67$	5.55525	0.678681	0.339341	+	0.940664i	$0.389796\pi$
$68$	−4.69006	−0.568753
$69$	−5.33857	−0.642688
$70$	−5.95764	−0.712075
$71$	1.30409	0.154767	0.0773833	−	0.997001i	$-0.475343\pi$
$71$	1.30409	0.154767	0.0773833	+	0.997001i	$0.475343\pi$
$72$	15.9057	1.87450
$73$	10.3119	1.20692	0.603460	−	0.797393i	$-0.293788\pi$
$73$	10.3119	1.20692	0.603460	+	0.797393i	$0.293788\pi$
$74$	−6.66133	−0.774364
$75$	3.72201	0.429780
$76$	−15.6278	−1.79263
$77$	−6.61083	−0.753375
$78$	−3.98907	−0.451673
$79$	7.21369	0.811604	0.405802	−	0.913961i	$-0.366992\pi$
$79$	7.21369	0.811604	0.405802	+	0.913961i	$0.366992\pi$
$80$	−6.64749	−0.743212
$81$	3.08379	0.342644
$82$	9.82682	1.08519
$83$	11.4580	1.25767	0.628837	−	0.777537i	$-0.283531\pi$
$83$	11.4580	1.25767	0.628837	+	0.777537i	$0.283531\pi$
$84$	11.8321	1.29099
$85$	0.771482	0.0836790
$86$	−30.5790	−3.29742
$87$	−1.92810	−0.206714
$88$	−15.4063	−1.64232
$89$	9.57081	1.01450	0.507252	−	0.861798i	$-0.330661\pi$
$89$	9.57081	1.01450	0.507252	+	0.861798i	$0.330661\pi$
$90$	−4.56160	−0.480835
$91$	5.44930	0.571242
$92$	29.6315	3.08930
$93$	5.11654	0.530560
$94$	8.07764	0.833145
$95$	2.57067	0.263745
$96$	7.07338	0.721924
$97$	−3.70810	−0.376501	−0.188250	−	0.982121i	$-0.560282\pi$
$97$	−3.70810	−0.376501	−0.188250	+	0.982121i	$0.560282\pi$
$98$	−4.95032	−0.500058
$99$	−5.06173	−0.508723
$100$	−20.6588	−2.06588
$101$	−4.85896	−0.483484	−0.241742	−	0.970341i	$-0.577719\pi$
$101$	−4.85896	−0.483484	−0.241742	+	0.970341i	$0.577719\pi$
$102$	−2.18557	−0.216403
$103$	15.7181	1.54875	0.774373	−	0.632729i	$-0.218065\pi$
$103$	15.7181	1.54875	0.774373	+	0.632729i	$0.218065\pi$
$104$	12.6994	1.24528
$105$	−1.94630	−0.189939
$106$	0.0126851	0.00123209
$107$	−17.2504	−1.66766	−0.833830	−	0.552021i	$-0.813857\pi$
$107$	−17.2504	−1.66766	−0.833830	+	0.552021i	$0.813857\pi$
$108$	20.9486	2.01578
$109$	18.8661	1.80704	0.903522	−	0.428542i	$-0.140973\pi$
$109$	18.8661	1.80704	0.903522	+	0.428542i	$0.140973\pi$
$110$	4.41838	0.421276
$111$	−2.17618	−0.206554
$112$	−25.7256	−2.43084
$113$	−12.8216	−1.20615	−0.603077	−	0.797683i	$-0.706059\pi$
$113$	−12.8216	−1.20615	−0.603077	+	0.797683i	$0.706059\pi$
$114$	−7.28257	−0.682075
$115$	−4.87418	−0.454520
$116$	10.7018	0.993640
$117$	4.17237	0.385736
$118$	26.1004	2.40274
$119$	2.98561	0.273691
$120$	−4.53577	−0.414058
$121$	−6.09719	−0.554290
$122$	−7.48467	−0.677630
$123$	3.21031	0.289464
$124$	−28.3991	−2.55032
$125$	7.25565	0.648965
$126$	−17.6533	−1.57268
$127$	13.6770	1.21363	0.606817	−	0.794841i	$-0.292446\pi$
$127$	13.6770	1.21363	0.606817	+	0.794841i	$0.292446\pi$
$128$	5.31300	0.469607
$129$	−9.98982	−0.879555
$130$	−3.64207	−0.319430
$131$	−1.05547	−0.0922172	−0.0461086	−	0.998936i	$-0.514682\pi$
$131$	−1.05547	−0.0922172	−0.0461086	+	0.998936i	$0.514682\pi$
$132$	−8.77506	−0.763771
$133$	9.94842	0.862637
$134$	−14.3687	−1.24127
$135$	−3.44590	−0.296576
$136$	6.95787	0.596632
$137$	−1.74754	−0.149302	−0.0746512	−	0.997210i	$-0.523784\pi$
$137$	−1.74754	−0.149302	−0.0746512	+	0.997210i	$0.523784\pi$
$138$	13.8083	1.17544
$139$	−11.1699	−0.947417	−0.473708	−	0.880682i	$-0.657085\pi$
$139$	−11.1699	−0.947417	−0.473708	+	0.880682i	$0.657085\pi$
$140$	10.8028	0.913006
$141$	2.63888	0.222233
$142$	−3.37304	−0.283059
$143$	−4.04138	−0.337957
$144$	−19.6974	−1.64145
$145$	−1.76038	−0.146191
$146$	−26.6720	−2.20739
$147$	−1.61721	−0.133386
$148$	12.0788	0.992872
$149$	0.226786	0.0185790	0.00928951	−	0.999957i	$-0.497043\pi$
$149$	0.226786	0.0185790	0.00928951	+	0.999957i	$0.497043\pi$
$150$	−9.62702	−0.786043
$151$	−8.70485	−0.708390	−0.354195	−	0.935172i	$-0.615245\pi$
$151$	−8.70485	−0.708390	−0.354195	+	0.935172i	$0.615245\pi$
$152$	23.1844	1.88051
$153$	2.28600	0.184812
$154$	17.0990	1.37788
$155$	4.67146	0.375221
$156$	7.23327	0.579125
$157$	15.7561	1.25747	0.628735	−	0.777619i	$-0.283573\pi$
$157$	15.7561	1.25747	0.628735	+	0.777619i	$0.283573\pi$
$158$	−18.6583	−1.48438
$159$	0.00414409	0.000328647 0
$160$	6.45808	0.510556
$161$	−18.8629	−1.48661
$162$	−7.97627	−0.626675
$163$	2.42899	0.190253	0.0951264	−	0.995465i	$-0.469674\pi$
$163$	2.42899	0.190253	0.0951264	+	0.995465i	$0.469674\pi$
$164$	−17.8187	−1.39141
$165$	1.44344	0.112371
$166$	−29.6362	−2.30021
$167$	−20.2462	−1.56670	−0.783348	−	0.621583i	$-0.786490\pi$
$167$	−20.2462	−1.56670	−0.783348	+	0.621583i	$0.786490\pi$
$168$	−17.5533	−1.35427
$169$	−9.66870	−0.743746
$170$	−1.99545	−0.153044
$171$	7.61722	0.582503
$172$	55.4481	4.22788
$173$	−18.6430	−1.41740	−0.708699	−	0.705511i	$-0.750717\pi$
$173$	−18.6430	−1.41740	−0.708699	+	0.705511i	$0.750717\pi$
$174$	4.98705	0.378068
$175$	13.1511	0.994128
$176$	19.0789	1.43813
$177$	8.52673	0.640908
$178$	−24.7550	−1.85547
$179$	−0.746448	−0.0557921	−0.0278961	−	0.999611i	$-0.508881\pi$
$179$	−0.746448	−0.0557921	−0.0278961	+	0.999611i	$0.508881\pi$
$180$	8.27142	0.616515
$181$	−9.09236	−0.675830	−0.337915	−	0.941177i	$-0.609722\pi$
$181$	−9.09236	−0.675830	−0.337915	+	0.941177i	$0.609722\pi$
$182$	−14.0947	−1.04477
$183$	−2.44516	−0.180751
$184$	−43.9594	−3.24073
$185$	−1.98688	−0.146078
$186$	−13.2340	−0.970364
$187$	−2.21423	−0.161920
$188$	−14.6470	−1.06824
$189$	−13.3355	−0.970017
$190$	−6.64907	−0.482374
$191$	16.5629	1.19845	0.599224	−	0.800581i	$-0.295476\pi$
$191$	16.5629	1.19845	0.599224	+	0.800581i	$0.295476\pi$
$192$	−3.73373	−0.269459
$193$	8.06999	0.580891	0.290445	−	0.956892i	$-0.406197\pi$
$193$	8.06999	0.580891	0.290445	+	0.956892i	$0.406197\pi$
$194$	9.59105	0.688598
$195$	−1.18982	−0.0852050
$196$	8.97628	0.641163
$197$	−19.3870	−1.38126	−0.690632	−	0.723207i	$-0.742667\pi$
$197$	−19.3870	−1.38126	−0.690632	+	0.723207i	$0.742667\pi$
$198$	13.0922	0.930424
$199$	12.1352	0.860239	0.430120	−	0.902772i	$-0.358471\pi$
$199$	12.1352	0.860239	0.430120	+	0.902772i	$0.358471\pi$
$200$	30.6481	2.16715
$201$	−4.69410	−0.331096
$202$	12.5678	0.884265
$203$	−6.81261	−0.478152
$204$	3.96303	0.277468
$205$	2.93105	0.204714
$206$	−40.6550	−2.83257
$207$	−14.4428	−1.00384
$208$	−15.7267	−1.09045
$209$	−7.37807	−0.510352
$210$	5.03412	0.347387
$211$	24.3742	1.67799	0.838994	−	0.544141i	$-0.183144\pi$
$211$	24.3742	1.67799	0.838994	+	0.544141i	$0.183144\pi$
$212$	−0.0230016	−0.00157975
$213$	−1.10193	−0.0755033
$214$	44.6184	3.05005
$215$	−9.12083	−0.622035
$216$	−31.0780	−2.11459
$217$	18.0784	1.22724
$218$	−48.7974	−3.30498
$219$	−8.71343	−0.588799
$220$	−8.01173	−0.540151
$221$	1.82519	0.122775
$222$	5.62873	0.377775
$223$	19.5542	1.30945	0.654724	−	0.755868i	$-0.272785\pi$
$223$	19.5542	1.30945	0.654724	+	0.755868i	$0.272785\pi$
$224$	24.9926	1.66989
$225$	10.0694	0.671294
$226$	33.1632	2.20598
$227$	−22.7228	−1.50816	−0.754082	−	0.656780i	$-0.771918\pi$
$227$	−22.7228	−1.50816	−0.754082	+	0.656780i	$0.771918\pi$
$228$	13.2053	0.874541
$229$	−12.6051	−0.832971	−0.416486	−	0.909142i	$-0.636738\pi$
$229$	−12.6051	−0.832971	−0.416486	+	0.909142i	$0.636738\pi$
$230$	12.6071	0.831290
$231$	5.58606	0.367536
$232$	−15.8766	−1.04235
$233$	6.68294	0.437814	0.218907	−	0.975746i	$-0.429751\pi$
$233$	6.68294	0.437814	0.218907	+	0.975746i	$0.429751\pi$
$234$	−10.7919	−0.705489
$235$	2.40933	0.157167
$236$	−47.3272	−3.08074
$237$	−6.09547	−0.395943
$238$	−7.72234	−0.500565
$239$	14.6789	0.949500	0.474750	−	0.880121i	$-0.342538\pi$
$239$	14.6789	0.949500	0.474750	+	0.880121i	$0.342538\pi$
$240$	5.61703	0.362578
$241$	1.38389	0.0891443	0.0445722	−	0.999006i	$-0.485808\pi$
$241$	1.38389	0.0891443	0.0445722	+	0.999006i	$0.485808\pi$
$242$	15.7705	1.01376
$243$	−16.0055	−1.02676
$244$	13.5718	0.868842
$245$	−1.47654	−0.0943324
$246$	−8.30352	−0.529413
$247$	6.08174	0.386972
$248$	42.1311	2.67533
$249$	−9.68181	−0.613560
$250$	−18.7668	−1.18692
$251$	10.0398	0.633708	0.316854	−	0.948474i	$-0.397374\pi$
$251$	10.0398	0.633708	0.316854	+	0.948474i	$0.397374\pi$
$252$	32.0102	2.01645
$253$	13.9894	0.879504
$254$	−35.3757	−2.21967
$255$	−0.651891	−0.0408230
$256$	−22.5795	−1.41122
$257$	30.7975	1.92110	0.960548	−	0.278115i	$-0.0897096\pi$
$257$	30.7975	1.92110	0.960548	+	0.278115i	$0.0897096\pi$
$258$	25.8388	1.60865
$259$	−7.68917	−0.477782
$260$	6.60406	0.409567
$261$	−5.21622	−0.322876
$262$	2.73000	0.168660
$263$	4.00375	0.246882	0.123441	−	0.992352i	$-0.460607\pi$
$263$	4.00375	0.246882	0.123441	+	0.992352i	$0.460607\pi$
$264$	13.0181	0.801210
$265$	0.00378360	0.000232425 0
$266$	−25.7317	−1.57771
$267$	−8.08720	−0.494928
$268$	26.0544	1.59153
$269$	−4.14118	−0.252492	−0.126246	−	0.991999i	$-0.540293\pi$
$269$	−4.14118	−0.252492	−0.126246	+	0.991999i	$0.540293\pi$
$270$	8.91286	0.542419
$271$	−16.2642	−0.987981	−0.493990	−	0.869467i	$-0.664462\pi$
$271$	−16.2642	−0.987981	−0.493990	+	0.869467i	$0.664462\pi$
$272$	−8.61652	−0.522453
$273$	−4.60458	−0.278682
$274$	4.52004	0.273066
$275$	−9.75327	−0.588144
$276$	−25.0382	−1.50712
$277$	−8.52687	−0.512330	−0.256165	−	0.966633i	$-0.582459\pi$
$277$	−8.52687	−0.512330	−0.256165	+	0.966633i	$0.582459\pi$
$278$	28.8910	1.73277
$279$	13.8421	0.828707
$280$	−16.0264	−0.957761
$281$	−20.5734	−1.22731	−0.613653	−	0.789575i	$-0.710301\pi$
$281$	−20.5734	−1.22731	−0.613653	+	0.789575i	$0.710301\pi$
$282$	−6.82549	−0.406452
$283$	10.5852	0.629223	0.314612	−	0.949221i	$-0.398126\pi$
$283$	10.5852	0.629223	0.314612	+	0.949221i	$0.398126\pi$
$284$	6.11624	0.362932
$285$	−2.17218	−0.128669
$286$	10.4531	0.618104
$287$	11.3431	0.669562
$288$	19.1361	1.12761
$289$	1.00000	0.0588235
$290$	4.55324	0.267376
$291$	3.13329	0.183677
$292$	48.3635	2.83026
$293$	28.0976	1.64148	0.820741	−	0.571301i	$-0.193561\pi$
$293$	28.0976	1.64148	0.820741	+	0.571301i	$0.193561\pi$
$294$	4.18295	0.243954
$295$	7.78501	0.453261
$296$	−17.9193	−1.04154
$297$	9.89006	0.573879
$298$	−0.586585	−0.0339799
$299$	−11.5314	−0.666879
$300$	17.4564	1.00785
$301$	−35.2974	−2.03451
$302$	22.5152	1.29560
$303$	4.10575	0.235869
$304$	−28.7113	−1.64670
$305$	−2.23246	−0.127830
$306$	−5.91277	−0.338011
$307$	−4.58617	−0.261747	−0.130873	−	0.991399i	$-0.541778\pi$
$307$	−4.58617	−0.261747	−0.130873	+	0.991399i	$0.541778\pi$
$308$	−31.0052	−1.76668
$309$	−13.2815	−0.755560
$310$	−12.0828	−0.686257
$311$	7.83970	0.444549	0.222274	−	0.974984i	$-0.428652\pi$
$311$	7.83970	0.444549	0.222274	+	0.974984i	$0.428652\pi$
$312$	−10.7308	−0.607513
$313$	11.2472	0.635731	0.317866	−	0.948136i	$-0.397034\pi$
$313$	11.2472	0.635731	0.317866	+	0.948136i	$0.397034\pi$
$314$	−40.7533	−2.29984
$315$	−5.26545	−0.296675
$316$	33.8326	1.90323
$317$	17.5933	0.988139	0.494070	−	0.869422i	$-0.335509\pi$
$317$	17.5933	0.988139	0.494070	+	0.869422i	$0.335509\pi$
$318$	−0.0107187	−0.000601077 0
$319$	5.05245	0.282883
$320$	−3.40894	−0.190566
$321$	14.5763	0.813572
$322$	48.7893	2.71892
$323$	3.33212	0.185404
$324$	14.4632	0.803509
$325$	8.03961	0.445957
$326$	−6.28261	−0.347961
$327$	−15.9416	−0.881571
$328$	26.4347	1.45961
$329$	9.32402	0.514050
$330$	−3.73347	−0.205521
$331$	−3.68185	−0.202373	−0.101186	−	0.994867i	$-0.532264\pi$
$331$	−3.68185	−0.202373	−0.101186	+	0.994867i	$0.532264\pi$
$332$	53.7385	2.94928
$333$	−5.88738	−0.322626
$334$	52.3670	2.86540
$335$	−4.28577	−0.234157
$336$	21.7378	1.18589
$337$	−1.23726	−0.0673977	−0.0336988	−	0.999432i	$-0.510729\pi$
$337$	−1.23726	−0.0673977	−0.0336988	+	0.999432i	$0.510729\pi$
$338$	25.0082	1.36027
$339$	10.8341	0.588425
$340$	3.61829	0.196230
$341$	−13.4075	−0.726059
$342$	−19.7020	−1.06536
$343$	15.1851	0.819921
$344$	−82.2593	−4.43512
$345$	4.11861	0.221739
$346$	48.2203	2.59234
$347$	−4.57641	−0.245675	−0.122837	−	0.992427i	$-0.539199\pi$
$347$	−4.57641	−0.245675	−0.122837	+	0.992427i	$0.539199\pi$
$348$	−9.04289	−0.484750
$349$	−1.08278	−0.0579601	−0.0289800	−	0.999580i	$-0.509226\pi$
$349$	−1.08278	−0.0579601	−0.0289800	+	0.999580i	$0.509226\pi$
$350$	−34.0155	−1.81820
$351$	−8.15236	−0.435141
$352$	−18.5353	−0.987936
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−22.0545	−1.17218
$355$	−1.00608	−0.0533972
$356$	44.8877	2.37904
$357$	−2.52280	−0.133521
$358$	1.93070	0.102041
$359$	28.2867	1.49291	0.746457	−	0.665433i	$-0.231753\pi$
$359$	28.2867	1.49291	0.746457	+	0.665433i	$0.231753\pi$
$360$	−12.2710	−0.646736
$361$	−7.89699	−0.415631
$362$	23.5175	1.23605
$363$	5.15204	0.270412
$364$	25.5575	1.33958
$365$	−7.95547	−0.416408
$366$	6.32444	0.330584
$367$	33.3486	1.74078	0.870391	−	0.492362i	$-0.163866\pi$
$367$	33.3486	1.74078	0.870391	+	0.492362i	$0.163866\pi$
$368$	54.4387	2.83781
$369$	8.68508	0.452127
$370$	5.13910	0.267169
$371$	0.0146424	0.000760197 0
$372$	23.9968	1.24418
$373$	27.9646	1.44795	0.723976	−	0.689825i	$-0.242313\pi$
$373$	27.9646	1.44795	0.723976	+	0.689825i	$0.242313\pi$
$374$	5.72714	0.296143
$375$	−6.13092	−0.316599
$376$	21.7293	1.12060
$377$	−4.16473	−0.214495
$378$	34.4925	1.77410
$379$	−19.9130	−1.02286	−0.511431	−	0.859324i	$-0.670884\pi$
$379$	−19.9130	−1.02286	−0.511431	+	0.859324i	$0.670884\pi$
$380$	12.0566	0.618490
$381$	−11.5568	−0.592075
$382$	−42.8402	−2.19189
$383$	−34.1606	−1.74552	−0.872762	−	0.488145i	$-0.837674\pi$
$383$	−34.1606	−1.74552	−0.872762	+	0.488145i	$0.837674\pi$
$384$	−4.48941	−0.229099
$385$	5.10014	0.259927
$386$	−20.8731	−1.06242
$387$	−27.0262	−1.37382
$388$	−17.3912	−0.882904
$389$	−18.9749	−0.962064	−0.481032	−	0.876703i	$-0.659738\pi$
$389$	−18.9749	−0.962064	−0.481032	+	0.876703i	$0.659738\pi$
$390$	3.07749	0.155835
$391$	−6.31794	−0.319512
$392$	−13.3166	−0.672592
$393$	0.891860	0.0449884
$394$	50.1446	2.52625
$395$	−5.56524	−0.280017
$396$	−23.7398	−1.19297
$397$	2.90166	0.145630	0.0728150	−	0.997345i	$-0.476802\pi$
$397$	2.90166	0.145630	0.0728150	+	0.997345i	$0.476802\pi$
$398$	−31.3878	−1.57333
$399$	−8.40627	−0.420840
$400$	−37.9542	−1.89771
$401$	27.6538	1.38097	0.690483	−	0.723349i	$-0.257398\pi$
$401$	27.6538	1.38097	0.690483	+	0.723349i	$0.257398\pi$
$402$	12.1414	0.605556
$403$	11.0518	0.550531
$404$	−22.7888	−1.13378
$405$	−2.37909	−0.118218
$406$	17.6209	0.874511
$407$	5.70254	0.282664
$408$	−5.87930	−0.291069
$409$	−5.16074	−0.255182	−0.127591	−	0.991827i	$-0.540724\pi$
$409$	−5.16074	−0.255182	−0.127591	+	0.991827i	$0.540724\pi$
$410$	−7.58121	−0.374409
$411$	1.47665	0.0728376
$412$	73.7186	3.63185
$413$	30.1278	1.48249
$414$	37.3565	1.83597
$415$	−8.83961	−0.433919
$416$	15.2786	0.749097
$417$	9.43838	0.462200
$418$	19.0835	0.933404
$419$	−26.5363	−1.29638	−0.648191	−	0.761478i	$-0.724474\pi$
$419$	−26.5363	−1.29638	−0.648191	+	0.761478i	$0.724474\pi$
$420$	−9.12824	−0.445412
$421$	−33.6934	−1.64212	−0.821058	−	0.570845i	$-0.806616\pi$
$421$	−33.6934	−1.64212	−0.821058	+	0.570845i	$0.806616\pi$
$422$	−63.0442	−3.06894
$423$	7.13914	0.347117
$424$	0.0341237	0.00165719
$425$	4.40482	0.213665
$426$	2.85017	0.138091
$427$	−8.63956	−0.418098
$428$	−80.9054	−3.91071
$429$	3.41491	0.164873
$430$	23.5912	1.13767
$431$	−22.6221	−1.08967	−0.544834	−	0.838544i	$-0.683407\pi$
$431$	−22.6221	−1.08967	−0.544834	+	0.838544i	$0.683407\pi$
$432$	38.4865	1.85168
$433$	−25.8518	−1.24236	−0.621179	−	0.783669i	$-0.713346\pi$
$433$	−25.8518	−1.24236	−0.621179	+	0.783669i	$0.713346\pi$
$434$	−46.7601	−2.24456
$435$	1.48749	0.0713198
$436$	88.4830	4.23757
$437$	−21.0521	−1.00706
$438$	22.5374	1.07688
$439$	−19.6428	−0.937498	−0.468749	−	0.883331i	$-0.655295\pi$
$439$	−19.6428	−0.937498	−0.468749	+	0.883331i	$0.655295\pi$
$440$	11.8857	0.566628
$441$	−4.37516	−0.208341
$442$	−4.72087	−0.224549
$443$	24.8429	1.18032	0.590162	−	0.807285i	$-0.299064\pi$
$443$	24.8429	1.18032	0.590162	+	0.807285i	$0.299064\pi$
$444$	−10.2064	−0.484375
$445$	−7.38371	−0.350021
$446$	−50.5773	−2.39490
$447$	−0.191631	−0.00906382
$448$	−13.1925	−0.623288
$449$	−25.1327	−1.18609	−0.593043	−	0.805171i	$-0.702074\pi$
$449$	−25.1327	−1.18609	−0.593043	+	0.805171i	$0.702074\pi$
$450$	−26.0447	−1.22776
$451$	−8.41241	−0.396125
$452$	−60.1340	−2.82846
$453$	7.35547	0.345590
$454$	58.7728	2.75835
$455$	−4.20404	−0.197088
$456$	−19.5905	−0.917410
$457$	30.6610	1.43426	0.717131	−	0.696938i	$-0.245455\pi$
$457$	30.6610	1.43426	0.717131	+	0.696938i	$0.245455\pi$
$458$	32.6034	1.52346
$459$	−4.46659	−0.208483
$460$	−22.8602	−1.06586
$461$	−26.6752	−1.24239	−0.621194	−	0.783657i	$-0.713352\pi$
$461$	−26.6752	−1.24239	−0.621194	+	0.783657i	$0.713352\pi$
$462$	−14.4484	−0.672202
$463$	−31.7189	−1.47410	−0.737052	−	0.675836i	$-0.763783\pi$
$463$	−31.7189	−1.47410	−0.737052	+	0.675836i	$0.763783\pi$
$464$	19.6613	0.912752
$465$	−3.94732	−0.183052
$466$	−17.2855	−0.800736
$467$	−7.61091	−0.352191	−0.176095	−	0.984373i	$-0.556347\pi$
$467$	−7.61091	−0.352191	−0.176095	+	0.984373i	$0.556347\pi$
$468$	19.5687	0.904562
$469$	−16.5858	−0.765862
$470$	−6.23176	−0.287449
$471$	−13.3136	−0.613460
$472$	70.2117	3.23175
$473$	26.1777	1.20365
$474$	15.7660	0.724157
$475$	14.6774	0.673444
$476$	14.0027	0.641813
$477$	0.0112113	0.000513330 0
$478$	−37.9672	−1.73658
$479$	−15.7148	−0.718029	−0.359015	−	0.933332i	$-0.616887\pi$
$479$	−15.7148	−0.718029	−0.359015	+	0.933332i	$0.616887\pi$
$480$	−5.45699	−0.249076
$481$	−4.70060	−0.214329
$482$	−3.57946	−0.163040
$483$	15.9389	0.725246
$484$	−28.5962	−1.29983
$485$	2.86073	0.129899
$486$	41.3986	1.87788
$487$	−8.10133	−0.367106	−0.183553	−	0.983010i	$-0.558760\pi$
$487$	−8.10133	−0.367106	−0.183553	+	0.983010i	$0.558760\pi$
$488$	−20.1342	−0.911432
$489$	−2.05246	−0.0928154
$490$	3.81908	0.172529
$491$	−6.81158	−0.307402	−0.153701	−	0.988117i	$-0.549119\pi$
$491$	−6.81158	−0.307402	−0.153701	+	0.988117i	$0.549119\pi$
$492$	15.0565	0.678801
$493$	−2.28181	−0.102768
$494$	−15.7305	−0.707748
$495$	3.90503	0.175518
$496$	−52.1745	−2.34271
$497$	−3.89350	−0.174647
$498$	25.0421	1.12216
$499$	−24.9162	−1.11540	−0.557700	−	0.830042i	$-0.688316\pi$
$499$	−24.9162	−1.11540	−0.557700	+	0.830042i	$0.688316\pi$
$500$	34.0294	1.52184
$501$	17.1077	0.764317
$502$	−25.9681	−1.15901
$503$	−18.1273	−0.808254	−0.404127	−	0.914703i	$-0.632425\pi$
$503$	−18.1273	−0.808254	−0.404127	+	0.914703i	$0.632425\pi$
$504$	−47.4883	−2.11529
$505$	3.74860	0.166810
$506$	−36.1837	−1.60856
$507$	8.16991	0.362838
$508$	64.1458	2.84601
$509$	−2.53522	−0.112372	−0.0561859	−	0.998420i	$-0.517894\pi$
$509$	−2.53522	−0.112372	−0.0561859	+	0.998420i	$0.517894\pi$
$510$	1.68613	0.0746629
$511$	−30.7875	−1.36196
$512$	47.7763	2.11143
$513$	−14.8832	−0.657110
$514$	−79.6582	−3.51357
$515$	−12.1262	−0.534344
$516$	−46.8528	−2.06258
$517$	−6.91500	−0.304121
$518$	19.8882	0.873836
$519$	15.7530	0.691481
$520$	−9.79737	−0.429643
$521$	−26.8443	−1.17607	−0.588035	−	0.808836i	$-0.700098\pi$
$521$	−26.8443	−1.17607	−0.588035	+	0.808836i	$0.700098\pi$
$522$	13.4918	0.590521
$523$	−24.6668	−1.07860	−0.539302	−	0.842112i	$-0.681312\pi$
$523$	−24.6668	−1.07860	−0.539302	+	0.842112i	$0.681312\pi$
$524$	−4.95023	−0.216252
$525$	−11.1125	−0.484988
$526$	−10.3558	−0.451533
$527$	6.05518	0.263768
$528$	−16.1214	−0.701595
$529$	16.9164	0.735496
$530$	−0.00978634	−0.000425091 0
$531$	23.0680	1.00106
$532$	46.6587	2.02291
$533$	6.93434	0.300360
$534$	20.9177	0.905195
$535$	13.3084	0.575372
$536$	−38.6527	−1.66954
$537$	0.630738	0.0272183
$538$	10.7112	0.461793
$539$	4.23780	0.182535
$540$	−16.1615	−0.695478
$541$	−4.35811	−0.187370	−0.0936848	−	0.995602i	$-0.529865\pi$
$541$	−4.35811	−0.187370	−0.0936848	+	0.995602i	$0.529865\pi$
$542$	42.0676	1.80696
$543$	7.68292	0.329705
$544$	8.37101	0.358904
$545$	−14.5549	−0.623461
$546$	11.9098	0.509693
$547$	20.3148	0.868599	0.434299	−	0.900769i	$-0.356996\pi$
$547$	20.3148	0.868599	0.434299	+	0.900769i	$0.356996\pi$
$548$	−8.19606	−0.350119
$549$	−6.61506	−0.282324
$550$	25.2270	1.07568
$551$	−7.60327	−0.323910
$552$	37.1451	1.58100
$553$	−21.5373	−0.915860
$554$	22.0549	0.937022
$555$	1.67889	0.0712647
$556$	−52.3874	−2.22172
$557$	−25.4640	−1.07894	−0.539471	−	0.842004i	$-0.681376\pi$
$557$	−25.4640	−1.07894	−0.539471	+	0.842004i	$0.681376\pi$
$558$	−35.8029	−1.51566
$559$	−21.5782	−0.912662
$560$	19.8468	0.838682
$561$	1.87099	0.0789933
$562$	53.2134	2.24467
$563$	11.9697	0.504463	0.252231	−	0.967667i	$-0.418836\pi$
$563$	11.9697	0.504463	0.252231	+	0.967667i	$0.418836\pi$
$564$	12.3765	0.521144
$565$	9.89163	0.416144
$566$	−27.3787	−1.15081
$567$	−9.20701	−0.386658
$568$	−9.07367	−0.380723
$569$	22.3301	0.936128	0.468064	−	0.883694i	$-0.344952\pi$
$569$	22.3301	0.936128	0.468064	+	0.883694i	$0.344952\pi$
$570$	5.61837	0.235328
$571$	30.8423	1.29071	0.645356	−	0.763882i	$-0.276709\pi$
$571$	30.8423	1.29071	0.645356	+	0.763882i	$0.276709\pi$
$572$	−18.9543	−0.792519
$573$	−13.9954	−0.584666
$574$	−29.3391	−1.22459
$575$	−27.8294	−1.16056
$576$	−10.1011	−0.420881
$577$	27.7342	1.15459	0.577294	−	0.816536i	$-0.304108\pi$
$577$	27.7342	1.15459	0.577294	+	0.816536i	$0.304108\pi$
$578$	−2.58651	−0.107585
$579$	−6.81902	−0.283389
$580$	−8.25627	−0.342823
$581$	−34.2090	−1.41923
$582$	−8.10430	−0.335934
$583$	−0.0108593	−0.000449746 0
$584$	−71.7491	−2.96900
$585$	−3.21891	−0.133086
$586$	−72.6749	−3.00217
$587$	−0.914088	−0.0377285	−0.0188642	−	0.999822i	$-0.506005\pi$
$587$	−0.914088	−0.0377285	−0.0188642	+	0.999822i	$0.506005\pi$
$588$	−7.58483	−0.312793
$589$	20.1766	0.831361
$590$	−20.1360	−0.828987
$591$	16.3817	0.673853
$592$	22.1910	0.912046
$593$	−39.6376	−1.62772	−0.813861	−	0.581060i	$-0.802638\pi$
$593$	−39.6376	−1.62772	−0.813861	+	0.581060i	$0.802638\pi$
$594$	−25.5808	−1.04959
$595$	−2.30335	−0.0944281
$596$	1.06364	0.0435683
$597$	−10.2540	−0.419670
$598$	29.8262	1.21968
$599$	28.3739	1.15933	0.579664	−	0.814856i	$-0.303184\pi$
$599$	28.3739	1.15933	0.579664	+	0.814856i	$0.303184\pi$
$600$	−25.8972	−1.05725
$601$	−9.12725	−0.372308	−0.186154	−	0.982521i	$-0.559602\pi$
$601$	−9.12725	−0.372308	−0.186154	+	0.982521i	$0.559602\pi$
$602$	91.2971	3.72099
$603$	−12.6993	−0.517155
$604$	−40.8262	−1.66120
$605$	4.70387	0.191240
$606$	−10.6196	−0.431391
$607$	−10.8362	−0.439827	−0.219913	−	0.975519i	$-0.570577\pi$
$607$	−10.8362	−0.439827	−0.219913	+	0.975519i	$0.570577\pi$
$608$	27.8932	1.13122
$609$	5.75656	0.233268
$610$	5.77429	0.233794
$611$	5.70003	0.230598
$612$	10.7215	0.433390
$613$	−1.01669	−0.0410637	−0.0205318	−	0.999789i	$-0.506536\pi$
$613$	−1.01669	−0.0410637	−0.0205318	+	0.999789i	$0.506536\pi$
$614$	11.8622	0.478720
$615$	−2.47670	−0.0998701
$616$	45.9973	1.85329
$617$	39.1146	1.57470	0.787348	−	0.616509i	$-0.211454\pi$
$617$	39.1146	1.57470	0.787348	+	0.616509i	$0.211454\pi$
$618$	34.3529	1.38187
$619$	18.5676	0.746297	0.373148	−	0.927772i	$-0.378278\pi$
$619$	18.5676	0.746297	0.373148	+	0.927772i	$0.378278\pi$
$620$	21.9094	0.879903
$621$	28.2197	1.13242
$622$	−20.2775	−0.813054
$623$	−28.5748	−1.14482
$624$	13.2889	0.531981
$625$	16.4265	0.657059
$626$	−29.0911	−1.16272
$627$	6.23436	0.248977
$628$	73.8968	2.94880
$629$	−2.57541	−0.102688
$630$	13.6192	0.542601
$631$	−18.3123	−0.729002	−0.364501	−	0.931203i	$-0.618760\pi$
$631$	−18.3123	−0.729002	−0.364501	+	0.931203i	$0.618760\pi$
$632$	−50.1919	−1.99653
$633$	−20.5958	−0.818611
$634$	−45.5054	−1.80725
$635$	−10.5515	−0.418725
$636$	0.0194360	0.000770687 0
$637$	−3.49322	−0.138406
$638$	−13.0682	−0.517377
$639$	−2.98114	−0.117932
$640$	−4.09888	−0.162023
$641$	27.7836	1.09739	0.548694	−	0.836024i	$-0.315125\pi$
$641$	27.7836	1.09739	0.548694	+	0.836024i	$0.315125\pi$
$642$	−37.7019	−1.48798
$643$	−6.78349	−0.267515	−0.133757	−	0.991014i	$-0.542704\pi$
$643$	−6.78349	−0.267515	−0.133757	+	0.991014i	$0.542704\pi$
$644$	−88.4683	−3.48614
$645$	7.70697	0.303462
$646$	−8.61857	−0.339093
$647$	−44.7803	−1.76049	−0.880247	−	0.474516i	$-0.842623\pi$
$647$	−44.7803	−1.76049	−0.880247	+	0.474516i	$0.842623\pi$
$648$	−21.4566	−0.842896
$649$	−22.3437	−0.877068
$650$	−20.7946	−0.815630
$651$	−15.2760	−0.598714
$652$	11.3921	0.446148
$653$	−31.4289	−1.22991	−0.614954	−	0.788563i	$-0.710826\pi$
$653$	−31.4289	−1.22991	−0.614954	+	0.788563i	$0.710826\pi$
$654$	41.2331	1.61234
$655$	0.814279	0.0318165
$656$	−32.7363	−1.27814
$657$	−23.5731	−0.919673
$658$	−24.1167	−0.940168
$659$	−40.1638	−1.56456	−0.782280	−	0.622927i	$-0.785944\pi$
$659$	−40.1638	−1.56456	−0.782280	+	0.622927i	$0.785944\pi$
$660$	6.76980	0.263514
$661$	−17.9348	−0.697582	−0.348791	−	0.937201i	$-0.613408\pi$
$661$	−17.9348	−0.697582	−0.348791	+	0.937201i	$0.613408\pi$
$662$	9.52316	0.370128
$663$	−1.54226	−0.0598963
$664$	−79.7230	−3.09385
$665$	−7.67503	−0.297625
$666$	15.2278	0.590065
$667$	14.4164	0.558204
$668$	−94.9558	−3.67395
$669$	−16.5230	−0.638817
$670$	11.0852	0.428259
$671$	6.40738	0.247354
$672$	−21.1184	−0.814659
$673$	−24.7247	−0.953066	−0.476533	−	0.879157i	$-0.658107\pi$
$673$	−24.7247	−0.953066	−0.476533	+	0.879157i	$0.658107\pi$
$674$	3.20018	0.123266
$675$	−19.6745	−0.757273
$676$	−45.3467	−1.74410
$677$	45.4076	1.74515	0.872577	−	0.488476i	$-0.162447\pi$
$677$	45.4076	1.74515	0.872577	+	0.488476i	$0.162447\pi$
$678$	−28.0224	−1.07620
$679$	11.0710	0.424864
$680$	−5.36787	−0.205849
$681$	19.2004	0.735762
$682$	34.6788	1.32792
$683$	−14.9076	−0.570423	−0.285211	−	0.958465i	$-0.592064\pi$
$683$	−14.9076	−0.570423	−0.285211	+	0.958465i	$0.592064\pi$
$684$	35.7252	1.36599
$685$	1.34820	0.0515119
$686$	−39.2766	−1.49959
$687$	10.6512	0.406367
$688$	101.869	3.88370
$689$	0.00895131	0.000341018 0
$690$	−10.6528	−0.405547
$691$	−43.0597	−1.63807	−0.819034	−	0.573744i	$-0.805490\pi$
$691$	−43.0597	−1.63807	−0.819034	+	0.573744i	$0.805490\pi$
$692$	−87.4365	−3.32384
$693$	15.1124	0.574071
$694$	11.8370	0.449325
$695$	8.61736	0.326875
$696$	13.4155	0.508512
$697$	3.79925	0.143907
$698$	2.80064	0.106006
$699$	−5.64699	−0.213589
$700$	61.6793	2.33126
$701$	24.8187	0.937389	0.468694	−	0.883360i	$-0.344725\pi$
$701$	24.8187	0.937389	0.468694	+	0.883360i	$0.344725\pi$
$702$	21.0862	0.795848
$703$	−8.58156	−0.323660
$704$	9.78400	0.368748
$705$	−2.03585	−0.0766744
$706$	2.58651	0.0973448
$707$	14.5070	0.545591
$708$	39.9908	1.50295
$709$	25.8753	0.971767	0.485884	−	0.874024i	$-0.338498\pi$
$709$	25.8753	0.971767	0.485884	+	0.874024i	$0.338498\pi$
$710$	2.60224	0.0976603
$711$	−16.4905	−0.618442
$712$	−66.5925	−2.49566
$713$	−38.2563	−1.43271
$714$	6.52526	0.244202
$715$	3.11785	0.116601
$716$	−3.50088	−0.130834
$717$	−12.4035	−0.463216
$718$	−73.1640	−2.73045
$719$	13.7866	0.514154	0.257077	−	0.966391i	$-0.417241\pi$
$719$	13.7866	0.514154	0.257077	+	0.966391i	$0.417241\pi$
$720$	15.1962	0.566327
$721$	−46.9281	−1.74769
$722$	20.4257	0.760165
$723$	−1.16937	−0.0434893
$724$	−42.6437	−1.58484
$725$	−10.0510	−0.373283
$726$	−13.3258	−0.494568
$727$	−42.1429	−1.56299	−0.781497	−	0.623908i	$-0.785544\pi$
$727$	−42.1429	−1.56299	−0.781497	+	0.623908i	$0.785544\pi$
$728$	−37.9155	−1.40524
$729$	4.27307	0.158262
$730$	20.5769	0.761587
$731$	−11.8225	−0.437270
$732$	−11.4679	−0.423867
$733$	−19.0239	−0.702664	−0.351332	−	0.936251i	$-0.614271\pi$
$733$	−19.0239	−0.702664	−0.351332	+	0.936251i	$0.614271\pi$
$734$	−86.2566	−3.18379
$735$	1.24765	0.0460203
$736$	−52.8875	−1.94946
$737$	12.3006	0.453098
$738$	−22.4641	−0.826915
$739$	−6.73954	−0.247918	−0.123959	−	0.992287i	$-0.539559\pi$
$739$	−6.73954	−0.247918	−0.123959	+	0.992287i	$0.539559\pi$
$740$	−9.31858	−0.342558
$741$	−5.13898	−0.188785
$742$	−0.0378729	−0.00139036
$743$	−18.8982	−0.693308	−0.346654	−	0.937993i	$-0.612682\pi$
$743$	−18.8982	−0.693308	−0.346654	+	0.937993i	$0.612682\pi$
$744$	−35.6002	−1.30517
$745$	−0.174961	−0.00641008
$746$	−72.3309	−2.64822
$747$	−26.1929	−0.958347
$748$	−10.3849	−0.379708
$749$	51.5031	1.88188
$750$	15.8577	0.579042
$751$	−11.5625	−0.421923	−0.210961	−	0.977494i	$-0.567659\pi$
$751$	−11.5625	−0.421923	−0.210961	+	0.977494i	$0.567659\pi$
$752$	−26.9092	−0.981279
$753$	−8.48350	−0.309156
$754$	10.7721	0.392298
$755$	6.71563	0.244407
$756$	−62.5444	−2.27472
$757$	−47.1196	−1.71259	−0.856295	−	0.516488i	$-0.827239\pi$
$757$	−47.1196	−1.71259	−0.856295	+	0.516488i	$0.827239\pi$
$758$	51.5053	1.87076
$759$	−11.8208	−0.429068
$760$	−17.8864	−0.648807
$761$	34.0772	1.23530	0.617650	−	0.786453i	$-0.288085\pi$
$761$	34.0772	1.23530	0.617650	+	0.786453i	$0.288085\pi$
$762$	29.8919	1.08287
$763$	−56.3269	−2.03917
$764$	77.6809	2.81040
$765$	−1.76361	−0.0637634
$766$	88.3569	3.19246
$767$	18.4179	0.665032
$768$	19.0794	0.688468
$769$	−19.9855	−0.720694	−0.360347	−	0.932818i	$-0.617342\pi$
$769$	−19.9855	−0.720694	−0.360347	+	0.932818i	$0.617342\pi$
$770$	−13.1916	−0.475392
$771$	−26.0234	−0.937212
$772$	37.8487	1.36220
$773$	−16.0292	−0.576531	−0.288265	−	0.957551i	$-0.593079\pi$
$773$	−16.0292	−0.576531	−0.288265	+	0.957551i	$0.593079\pi$
$774$	69.9036	2.51263
$775$	26.6719	0.958084
$776$	25.8005	0.926183
$777$	6.49724	0.233087
$778$	49.0788	1.75956
$779$	12.6595	0.453575
$780$	−5.58034	−0.199808
$781$	2.88755	0.103325
$782$	16.3414	0.584369
$783$	10.1919	0.364230
$784$	16.4911	0.588968
$785$	−12.1555	−0.433849
$786$	−2.30681	−0.0822812
$787$	−44.2097	−1.57591	−0.787953	−	0.615736i	$-0.788859\pi$
$787$	−44.2097	−1.57591	−0.787953	+	0.615736i	$0.788859\pi$
$788$	−90.9259	−3.23910
$789$	−3.38311	−0.120442
$790$	14.3946	0.512136
$791$	38.2803	1.36109
$792$	35.2188	1.25145
$793$	−5.28159	−0.187555
$794$	−7.50518	−0.266349
$795$	−0.00319709	−0.000113389 0
$796$	56.9146	2.01729
$797$	−41.1652	−1.45815	−0.729073	−	0.684436i	$-0.760049\pi$
$797$	−41.1652	−1.45815	−0.729073	+	0.684436i	$0.760049\pi$
$798$	21.7429	0.769692
$799$	3.12298	0.110483
$800$	36.8727	1.30365
$801$	−21.8789	−0.773052
$802$	−71.5270	−2.52571
$803$	22.8330	0.805758
$804$	−22.0156	−0.776431
$805$	14.5524	0.512906
$806$	−28.5857	−1.00689
$807$	3.49924	0.123179
$808$	33.8080	1.18936
$809$	10.2843	0.361578	0.180789	−	0.983522i	$-0.442135\pi$
$809$	10.2843	0.361578	0.180789	+	0.983522i	$0.442135\pi$
$810$	6.15355	0.216214
$811$	41.8235	1.46862	0.734311	−	0.678813i	$-0.237505\pi$
$811$	41.8235	1.46862	0.734311	+	0.678813i	$0.237505\pi$
$812$	−31.9515	−1.12128
$813$	13.7430	0.481989
$814$	−14.7497	−0.516977
$815$	−1.87392	−0.0656405
$816$	7.28083	0.254880
$817$	−39.3939	−1.37822
$818$	13.3483	0.466713
$819$	−12.4571	−0.435286
$820$	13.7468	0.480059
$821$	18.7619	0.654794	0.327397	−	0.944887i	$-0.393828\pi$
$821$	18.7619	0.654794	0.327397	+	0.944887i	$0.393828\pi$
$822$	−3.81937	−0.133216
$823$	−26.5919	−0.926934	−0.463467	−	0.886114i	$-0.653395\pi$
$823$	−26.5919	−0.926934	−0.463467	+	0.886114i	$0.653395\pi$
$824$	−109.364	−3.80988
$825$	8.24137	0.286928
$826$	−77.9259	−2.71139
$827$	−21.3871	−0.743702	−0.371851	−	0.928292i	$-0.621277\pi$
$827$	−21.3871	−0.743702	−0.371851	+	0.928292i	$0.621277\pi$
$828$	−67.7376	−2.35404
$829$	−34.0459	−1.18246	−0.591231	−	0.806502i	$-0.701358\pi$
$829$	−34.0459	−1.18246	−0.591231	+	0.806502i	$0.701358\pi$
$830$	22.8638	0.793613
$831$	7.20508	0.249942
$832$	−8.06494	−0.279601
$833$	−1.91390	−0.0663126
$834$	−24.4125	−0.845336
$835$	15.6196	0.540538
$836$	−34.6036	−1.19679
$837$	−27.0460	−0.934847
$838$	68.6365	2.37101
$839$	10.1363	0.349943	0.174972	−	0.984573i	$-0.444017\pi$
$839$	10.1363	0.349943	0.174972	+	0.984573i	$0.444017\pi$
$840$	13.5421	0.467246
$841$	−23.7933	−0.820460
$842$	87.1484	3.00333
$843$	17.3842	0.598745
$844$	114.316	3.93493
$845$	7.45923	0.256605
$846$	−18.4655	−0.634856
$847$	18.2039	0.625492
$848$	−0.0422582	−0.00145115
$849$	−8.94432	−0.306968
$850$	−11.3931	−0.390781
$851$	16.2713	0.557772
$852$	−5.16814	−0.177057
$853$	−32.2154	−1.10303	−0.551517	−	0.834164i	$-0.685951\pi$
$853$	−32.2154	−1.10303	−0.551517	+	0.834164i	$0.685951\pi$
$854$	22.3463	0.764676
$855$	−5.87655	−0.200974
$856$	120.026	4.10241
$857$	37.0020	1.26396	0.631982	−	0.774983i	$-0.282242\pi$
$857$	37.0020	1.26396	0.631982	+	0.774983i	$0.282242\pi$
$858$	−8.83271	−0.301544
$859$	17.9749	0.613295	0.306647	−	0.951823i	$-0.400793\pi$
$859$	17.9749	0.613295	0.306647	+	0.951823i	$0.400793\pi$
$860$	−42.7772	−1.45869
$861$	−9.58475	−0.326648
$862$	58.5124	1.99294
$863$	−12.0972	−0.411795	−0.205897	−	0.978574i	$-0.566011\pi$
$863$	−12.0972	−0.411795	−0.205897	+	0.978574i	$0.566011\pi$
$864$	−37.3899	−1.27203
$865$	14.3827	0.489027
$866$	66.8660	2.27220
$867$	−0.844986	−0.0286972
$868$	84.7888	2.87792
$869$	15.9728	0.541839
$870$	−3.84742	−0.130440
$871$	−10.1394	−0.343559
$872$	−131.268	−4.44529
$873$	8.47672	0.286893
$874$	54.4516	1.84185
$875$	−21.6626	−0.732328
$876$	−40.8665	−1.38075
$877$	9.60482	0.324332	0.162166	−	0.986764i	$-0.448152\pi$
$877$	9.60482	0.324332	0.162166	+	0.986764i	$0.448152\pi$
$878$	50.8063	1.71463
$879$	−23.7421	−0.800801
$880$	−14.7191	−0.496180
$881$	−3.58217	−0.120686	−0.0603432	−	0.998178i	$-0.519220\pi$
$881$	−3.58217	−0.120686	−0.0603432	+	0.998178i	$0.519220\pi$
$882$	11.3164	0.381044
$883$	46.5400	1.56619	0.783097	−	0.621899i	$-0.213639\pi$
$883$	46.5400	1.56619	0.783097	+	0.621899i	$0.213639\pi$
$884$	8.56023	0.287912
$885$	−6.57822	−0.221124
$886$	−64.2566	−2.15874
$887$	−19.4337	−0.652519	−0.326260	−	0.945280i	$-0.605788\pi$
$887$	−19.4337	−0.652519	−0.326260	+	0.945280i	$0.605788\pi$
$888$	15.1416	0.508119
$889$	−40.8342	−1.36953
$890$	19.0981	0.640169
$891$	6.82822	0.228754
$892$	91.7104	3.07069
$893$	10.4061	0.348228
$894$	0.495656	0.0165772
$895$	0.575871	0.0192493
$896$	−15.8626	−0.529931
$897$	9.74388	0.325339
$898$	65.0061	2.16928
$899$	−13.8168	−0.460815
$900$	47.2261	1.57420
$901$	0.00490433	0.000163387 0
$902$	21.7588	0.724489
$903$	29.8258	0.992539
$904$	89.2109	2.96711
$905$	7.01460	0.233173
$906$	−19.0250	−0.632064
$907$	−18.9805	−0.630238	−0.315119	−	0.949052i	$-0.602044\pi$
$907$	−18.9805	−0.630238	−0.315119	+	0.949052i	$0.602044\pi$
$908$	−106.571	−3.53669
$909$	11.1076	0.368415
$910$	10.8738	0.360463
$911$	−5.34493	−0.177086	−0.0885428	−	0.996072i	$-0.528221\pi$
$911$	−5.34493	−0.177086	−0.0885428	+	0.996072i	$0.528221\pi$
$912$	24.2606	0.803348
$913$	25.3705	0.839642
$914$	−79.3052	−2.62318
$915$	1.88640	0.0623623
$916$	−59.1188	−1.95334
$917$	3.15124	0.104063
$918$	11.5529	0.381303
$919$	−27.2717	−0.899609	−0.449804	−	0.893127i	$-0.648506\pi$
$919$	−27.2717	−0.899609	−0.449804	+	0.893127i	$0.648506\pi$
$920$	33.9139	1.11811
$921$	3.87525	0.127694
$922$	68.9958	2.27226
$923$	−2.38020	−0.0783453
$924$	26.1989	0.861882
$925$	−11.3442	−0.372995
$926$	82.0415	2.69605
$927$	−35.9315	−1.18014
$928$	−19.1011	−0.627023
$929$	46.6417	1.53027	0.765133	−	0.643873i	$-0.222673\pi$
$929$	46.6417	1.53027	0.765133	+	0.643873i	$0.222673\pi$
$930$	10.2098	0.334792
$931$	−6.37733	−0.209008
$932$	31.3434	1.02669
$933$	−6.62444	−0.216874
$934$	19.6857	0.644137
$935$	1.70824	0.0558654
$936$	−29.0308	−0.948903
$937$	24.1531	0.789046	0.394523	−	0.918886i	$-0.370910\pi$
$937$	24.1531	0.789046	0.394523	+	0.918886i	$0.370910\pi$
$938$	42.8995	1.40072
$939$	−9.50375	−0.310143
$940$	11.2999	0.368561
$941$	36.2870	1.18292	0.591462	−	0.806333i	$-0.298551\pi$
$941$	36.2870	1.18292	0.591462	+	0.806333i	$0.298551\pi$
$942$	34.4359	1.12198
$943$	−24.0034	−0.781660
$944$	−86.9491	−2.82995
$945$	10.2881	0.334673
$946$	−67.7089	−2.20141
$947$	−35.2300	−1.14482	−0.572411	−	0.819967i	$-0.693992\pi$
$947$	−35.2300	−1.14482	−0.572411	+	0.819967i	$0.693992\pi$
$948$	−28.5881	−0.928498
$949$	−18.8212	−0.610962
$950$	−37.9632	−1.23169
$951$	−14.8661	−0.482066
$952$	−20.7735	−0.673274
$953$	−39.0403	−1.26464	−0.632320	−	0.774708i	$-0.717897\pi$
$953$	−39.0403	−1.26464	−0.632320	+	0.774708i	$0.717897\pi$
$954$	−0.0289982	−0.000938850 0
$955$	−12.7780	−0.413486
$956$	68.8450	2.22661
$957$	−4.26925	−0.138005
$958$	40.6467	1.31323
$959$	5.21748	0.168481
$960$	2.88051	0.0929680
$961$	5.66517	0.182748
$962$	12.1582	0.391995
$963$	39.4344	1.27076
$964$	6.49053	0.209046
$965$	−6.22585	−0.200417
$966$	−41.2262	−1.32643
$967$	−7.88199	−0.253468	−0.126734	−	0.991937i	$-0.540449\pi$
$967$	−7.88199	−0.253468	−0.126734	+	0.991937i	$0.540449\pi$
$968$	42.4235	1.36354
$969$	−2.81559	−0.0904498
$970$	−7.39933	−0.237578
$971$	57.1328	1.83348	0.916739	−	0.399487i	$-0.130812\pi$
$971$	57.1328	1.83348	0.916739	+	0.399487i	$0.130812\pi$
$972$	−75.0669	−2.40777
$973$	33.3490	1.06912
$974$	20.9542	0.671416
$975$	−6.79335	−0.217561
$976$	24.9339	0.798114
$977$	−39.2339	−1.25520	−0.627602	−	0.778534i	$-0.715963\pi$
$977$	−39.2339	−1.25520	−0.627602	+	0.778534i	$0.715963\pi$
$978$	5.30871	0.169754
$979$	21.1920	0.677298
$980$	−6.92504	−0.221212
$981$	−43.1279	−1.37697
$982$	17.6182	0.562221
$983$	−22.8104	−0.727538	−0.363769	−	0.931489i	$-0.618510\pi$
$983$	−22.8104	−0.727538	−0.363769	+	0.931489i	$0.618510\pi$
$984$	−22.3369	−0.712075
$985$	14.9567	0.476560
$986$	5.90194	0.187956
$987$	−7.87867	−0.250781
$988$	28.5237	0.907459
$989$	74.6937	2.37512
$990$	−10.1004	−0.321012
$991$	−37.4088	−1.18833	−0.594165	−	0.804343i	$-0.702518\pi$
$991$	−37.4088	−1.18833	−0.594165	+	0.804343i	$0.702518\pi$
$992$	50.6879	1.60934
$993$	3.11111	0.0987281
$994$	10.0706	0.319420
$995$	−9.36207	−0.296797
$996$	−45.4082	−1.43881
$997$	−9.61246	−0.304430	−0.152215	−	0.988347i	$-0.548641\pi$
$997$	−9.61246	−0.304430	−0.152215	+	0.988347i	$0.548641\pi$
$998$	64.4460	2.04000
$999$	11.5033	0.363948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.8	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.8	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58651 q^{2} -0.844986 q^{3} +4.69006 q^{4} -0.771482 q^{5} +2.18557 q^{6} -2.98561 q^{7} -6.95787 q^{8} -2.28600 q^{9} +O(q^{10})\)	\(q-2.58651 q^{2} -0.844986 q^{3} +4.69006 q^{4} -0.771482 q^{5} +2.18557 q^{6} -2.98561 q^{7} -6.95787 q^{8} -2.28600 q^{9} +1.99545 q^{10} +2.21423 q^{11} -3.96303 q^{12} -1.82519 q^{13} +7.72234 q^{14} +0.651891 q^{15} +8.61652 q^{16} -1.00000 q^{17} +5.91277 q^{18} -3.33212 q^{19} -3.61829 q^{20} +2.52280 q^{21} -5.72714 q^{22} +6.31794 q^{23} +5.87930 q^{24} -4.40482 q^{25} +4.72087 q^{26} +4.46659 q^{27} -14.0027 q^{28} +2.28181 q^{29} -1.68613 q^{30} -6.05518 q^{31} -8.37101 q^{32} -1.87099 q^{33} +2.58651 q^{34} +2.30335 q^{35} -10.7215 q^{36} +2.57541 q^{37} +8.61857 q^{38} +1.54226 q^{39} +5.36787 q^{40} -3.79925 q^{41} -6.52526 q^{42} +11.8225 q^{43} +10.3849 q^{44} +1.76361 q^{45} -16.3414 q^{46} -3.12298 q^{47} -7.28083 q^{48} +1.91390 q^{49} +11.3931 q^{50} +0.844986 q^{51} -8.56023 q^{52} -0.00490433 q^{53} -11.5529 q^{54} -1.70824 q^{55} +20.7735 q^{56} +2.81559 q^{57} -5.90194 q^{58} -10.0910 q^{59} +3.05741 q^{60} +2.89373 q^{61} +15.6618 q^{62} +6.82511 q^{63} +4.41869 q^{64} +1.40810 q^{65} +4.83935 q^{66} +5.55525 q^{67} -4.69006 q^{68} -5.33857 q^{69} -5.95764 q^{70} +1.30409 q^{71} +15.9057 q^{72} +10.3119 q^{73} -6.66133 q^{74} +3.72201 q^{75} -15.6278 q^{76} -6.61083 q^{77} -3.98907 q^{78} +7.21369 q^{79} -6.64749 q^{80} +3.08379 q^{81} +9.82682 q^{82} +11.4580 q^{83} +11.8321 q^{84} +0.771482 q^{85} -30.5790 q^{86} -1.92810 q^{87} -15.4063 q^{88} +9.57081 q^{89} -4.56160 q^{90} +5.44930 q^{91} +29.6315 q^{92} +5.11654 q^{93} +8.07764 q^{94} +2.57067 q^{95} +7.07338 q^{96} -3.70810 q^{97} -4.95032 q^{98} -5.06173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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