LMFDB - Embedded newform 4022.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.43557 q^{3} +1.00000 q^{4} +0.846052 q^{5} -2.43557 q^{6} +3.32195 q^{7} +1.00000 q^{8} +2.93199 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.43557 q^{3} +1.00000 q^{4} +0.846052 q^{5} -2.43557 q^{6} +3.32195 q^{7} +1.00000 q^{8} +2.93199 q^{9} +0.846052 q^{10} -5.24665 q^{11} -2.43557 q^{12} -0.00893602 q^{13} +3.32195 q^{14} -2.06062 q^{15} +1.00000 q^{16} +5.00903 q^{17} +2.93199 q^{18} -1.94555 q^{19} +0.846052 q^{20} -8.09084 q^{21} -5.24665 q^{22} -8.50701 q^{23} -2.43557 q^{24} -4.28420 q^{25} -0.00893602 q^{26} +0.165651 q^{27} +3.32195 q^{28} +6.22917 q^{29} -2.06062 q^{30} -9.47858 q^{31} +1.00000 q^{32} +12.7786 q^{33} +5.00903 q^{34} +2.81054 q^{35} +2.93199 q^{36} -10.2865 q^{37} -1.94555 q^{38} +0.0217643 q^{39} +0.846052 q^{40} -0.134813 q^{41} -8.09084 q^{42} +9.26520 q^{43} -5.24665 q^{44} +2.48061 q^{45} -8.50701 q^{46} -7.87366 q^{47} -2.43557 q^{48} +4.03536 q^{49} -4.28420 q^{50} -12.1998 q^{51} -0.00893602 q^{52} +6.77672 q^{53} +0.165651 q^{54} -4.43894 q^{55} +3.32195 q^{56} +4.73852 q^{57} +6.22917 q^{58} -8.05274 q^{59} -2.06062 q^{60} -3.55046 q^{61} -9.47858 q^{62} +9.73992 q^{63} +1.00000 q^{64} -0.00756033 q^{65} +12.7786 q^{66} +0.680426 q^{67} +5.00903 q^{68} +20.7194 q^{69} +2.81054 q^{70} -8.60377 q^{71} +2.93199 q^{72} +0.767273 q^{73} -10.2865 q^{74} +10.4344 q^{75} -1.94555 q^{76} -17.4291 q^{77} +0.0217643 q^{78} -5.46148 q^{79} +0.846052 q^{80} -9.19941 q^{81} -0.134813 q^{82} +6.43940 q^{83} -8.09084 q^{84} +4.23790 q^{85} +9.26520 q^{86} -15.1716 q^{87} -5.24665 q^{88} +4.46154 q^{89} +2.48061 q^{90} -0.0296850 q^{91} -8.50701 q^{92} +23.0857 q^{93} -7.87366 q^{94} -1.64604 q^{95} -2.43557 q^{96} +3.36313 q^{97} +4.03536 q^{98} -15.3831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.43557	−1.40618	−0.703088	−	0.711103i	$-0.748196\pi$
$3$	−2.43557	−1.40618	−0.703088	+	0.711103i	$0.748196\pi$
$4$	1.00000	0.500000
$5$	0.846052	0.378366	0.189183	−	0.981942i	$-0.439416\pi$
$5$	0.846052	0.378366	0.189183	+	0.981942i	$0.439416\pi$
$6$	−2.43557	−0.994316
$7$	3.32195	1.25558	0.627790	−	0.778383i	$-0.283960\pi$
$7$	3.32195	1.25558	0.627790	+	0.778383i	$0.283960\pi$
$8$	1.00000	0.353553
$9$	2.93199	0.977329
$10$	0.846052	0.267545
$11$	−5.24665	−1.58192	−0.790962	−	0.611866i	$-0.790419\pi$
$11$	−5.24665	−1.58192	−0.790962	+	0.611866i	$0.790419\pi$
$12$	−2.43557	−0.703088
$13$	−0.00893602	−0.00247840	−0.00123920	−	0.999999i	$-0.500394\pi$
$13$	−0.00893602	−0.00247840	−0.00123920	+	0.999999i	$0.500394\pi$
$14$	3.32195	0.887829
$15$	−2.06062	−0.532049
$16$	1.00000	0.250000
$17$	5.00903	1.21487	0.607434	−	0.794370i	$-0.292199\pi$
$17$	5.00903	1.21487	0.607434	+	0.794370i	$0.292199\pi$
$18$	2.93199	0.691076
$19$	−1.94555	−0.446340	−0.223170	−	0.974780i	$-0.571641\pi$
$19$	−1.94555	−0.446340	−0.223170	+	0.974780i	$0.571641\pi$
$20$	0.846052	0.189183
$21$	−8.09084	−1.76557
$22$	−5.24665	−1.11859
$23$	−8.50701	−1.77383	−0.886917	−	0.461928i	$-0.847158\pi$
$23$	−8.50701	−1.77383	−0.886917	+	0.461928i	$0.847158\pi$
$24$	−2.43557	−0.497158
$25$	−4.28420	−0.856839
$26$	−0.00893602	−0.00175250
$27$	0.165651	0.0318795
$28$	3.32195	0.627790
$29$	6.22917	1.15673	0.578364	−	0.815779i	$-0.303691\pi$
$29$	6.22917	1.15673	0.578364	+	0.815779i	$0.303691\pi$
$30$	−2.06062	−0.376215
$31$	−9.47858	−1.70240	−0.851202	−	0.524838i	$-0.824126\pi$
$31$	−9.47858	−1.70240	−0.851202	+	0.524838i	$0.824126\pi$
$32$	1.00000	0.176777
$33$	12.7786	2.22446
$34$	5.00903	0.859042
$35$	2.81054	0.475069
$36$	2.93199	0.488664
$37$	−10.2865	−1.69109	−0.845543	−	0.533907i	$-0.820723\pi$
$37$	−10.2865	−1.69109	−0.845543	+	0.533907i	$0.820723\pi$
$38$	−1.94555	−0.315610
$39$	0.0217643	0.00348507
$40$	0.846052	0.133773
$41$	−0.134813	−0.0210542	−0.0105271	−	0.999945i	$-0.503351\pi$
$41$	−0.134813	−0.0210542	−0.0105271	+	0.999945i	$0.503351\pi$
$42$	−8.09084	−1.24844
$43$	9.26520	1.41293	0.706465	−	0.707748i	$-0.250289\pi$
$43$	9.26520	1.41293	0.706465	+	0.707748i	$0.250289\pi$
$44$	−5.24665	−0.790962
$45$	2.48061	0.369788
$46$	−8.50701	−1.25429
$47$	−7.87366	−1.14849	−0.574246	−	0.818683i	$-0.694705\pi$
$47$	−7.87366	−1.14849	−0.574246	+	0.818683i	$0.694705\pi$
$48$	−2.43557	−0.351544
$49$	4.03536	0.576481
$50$	−4.28420	−0.605877
$51$	−12.1998	−1.70832
$52$	−0.00893602	−0.00123920
$53$	6.77672	0.930853	0.465427	−	0.885086i	$-0.345901\pi$
$53$	6.77672	0.930853	0.465427	+	0.885086i	$0.345901\pi$
$54$	0.165651	0.0225422
$55$	−4.43894	−0.598546
$56$	3.32195	0.443914
$57$	4.73852	0.627632
$58$	6.22917	0.817930
$59$	−8.05274	−1.04838	−0.524189	−	0.851602i	$-0.675631\pi$
$59$	−8.05274	−1.04838	−0.524189	+	0.851602i	$0.675631\pi$
$60$	−2.06062	−0.266024
$61$	−3.55046	−0.454590	−0.227295	−	0.973826i	$-0.572988\pi$
$61$	−3.55046	−0.454590	−0.227295	+	0.973826i	$0.572988\pi$
$62$	−9.47858	−1.20378
$63$	9.73992	1.22711
$64$	1.00000	0.125000
$65$	−0.00756033	−0.000937744 0
$66$	12.7786	1.57293
$67$	0.680426	0.0831273	0.0415637	−	0.999136i	$-0.486766\pi$
$67$	0.680426	0.0831273	0.0415637	+	0.999136i	$0.486766\pi$
$68$	5.00903	0.607434
$69$	20.7194	2.49432
$70$	2.81054	0.335924
$71$	−8.60377	−1.02108	−0.510540	−	0.859854i	$-0.670554\pi$
$71$	−8.60377	−1.02108	−0.510540	+	0.859854i	$0.670554\pi$
$72$	2.93199	0.345538
$73$	0.767273	0.0898025	0.0449012	−	0.998991i	$-0.485703\pi$
$73$	0.767273	0.0898025	0.0449012	+	0.998991i	$0.485703\pi$
$74$	−10.2865	−1.19578
$75$	10.4344	1.20487
$76$	−1.94555	−0.223170
$77$	−17.4291	−1.98623
$78$	0.0217643	0.00246432
$79$	−5.46148	−0.614465	−0.307232	−	0.951634i	$-0.599403\pi$
$79$	−5.46148	−0.614465	−0.307232	+	0.951634i	$0.599403\pi$
$80$	0.846052	0.0945915
$81$	−9.19941	−1.02216
$82$	−0.134813	−0.0148876
$83$	6.43940	0.706816	0.353408	−	0.935469i	$-0.385023\pi$
$83$	6.43940	0.706816	0.353408	+	0.935469i	$0.385023\pi$
$84$	−8.09084	−0.882783
$85$	4.23790	0.459665
$86$	9.26520	0.999092
$87$	−15.1716	−1.62656
$88$	−5.24665	−0.559294
$89$	4.46154	0.472922	0.236461	−	0.971641i	$-0.424012\pi$
$89$	4.46154	0.472922	0.236461	+	0.971641i	$0.424012\pi$
$90$	2.48061	0.261480
$91$	−0.0296850	−0.00311184
$92$	−8.50701	−0.886917
$93$	23.0857	2.39388
$94$	−7.87366	−0.812106
$95$	−1.64604	−0.168880
$96$	−2.43557	−0.248579
$97$	3.36313	0.341474	0.170737	−	0.985317i	$-0.445385\pi$
$97$	3.36313	0.341474	0.170737	+	0.985317i	$0.445385\pi$
$98$	4.03536	0.407633
$99$	−15.3831	−1.54606
$100$	−4.28420	−0.428420
$101$	18.9163	1.88224	0.941121	−	0.338069i	$-0.109774\pi$
$101$	18.9163	1.88224	0.941121	+	0.338069i	$0.109774\pi$
$102$	−12.1998	−1.20796
$103$	5.21269	0.513622	0.256811	−	0.966462i	$-0.417328\pi$
$103$	5.21269	0.513622	0.256811	+	0.966462i	$0.417328\pi$
$104$	−0.00893602	−0.000876248 0
$105$	−6.84527	−0.668030
$106$	6.77672	0.658213
$107$	1.11897	0.108175	0.0540873	−	0.998536i	$-0.482775\pi$
$107$	1.11897	0.108175	0.0540873	+	0.998536i	$0.482775\pi$
$108$	0.165651	0.0159398
$109$	−3.86262	−0.369971	−0.184986	−	0.982741i	$-0.559224\pi$
$109$	−3.86262	−0.369971	−0.184986	+	0.982741i	$0.559224\pi$
$110$	−4.43894	−0.423236
$111$	25.0534	2.37796
$112$	3.32195	0.313895
$113$	−14.8774	−1.39955	−0.699774	−	0.714364i	$-0.746716\pi$
$113$	−14.8774	−1.39955	−0.699774	+	0.714364i	$0.746716\pi$
$114$	4.73852	0.443803
$115$	−7.19737	−0.671159
$116$	6.22917	0.578364
$117$	−0.0262003	−0.00242222
$118$	−8.05274	−0.741315
$119$	16.6398	1.52536
$120$	−2.06062	−0.188108
$121$	16.5273	1.50248
$122$	−3.55046	−0.321444
$123$	0.328346	0.0296059
$124$	−9.47858	−0.851202
$125$	−7.85491	−0.702565
$126$	9.73992	0.867701
$127$	21.3026	1.89030	0.945149	−	0.326640i	$-0.105916\pi$
$127$	21.3026	1.89030	0.945149	+	0.326640i	$0.105916\pi$
$128$	1.00000	0.0883883
$129$	−22.5660	−1.98683
$130$	−0.00756033	−0.000663085 0
$131$	9.92475	0.867130	0.433565	−	0.901122i	$-0.357256\pi$
$131$	9.92475	0.867130	0.433565	+	0.901122i	$0.357256\pi$
$132$	12.7786	1.11223
$133$	−6.46303	−0.560416
$134$	0.680426	0.0587799
$135$	0.140149	0.0120621
$136$	5.00903	0.429521
$137$	−23.0430	−1.96870	−0.984349	−	0.176233i	$-0.943609\pi$
$137$	−23.0430	−1.96870	−0.984349	+	0.176233i	$0.943609\pi$
$138$	20.7194	1.76375
$139$	−20.7623	−1.76103	−0.880517	−	0.474015i	$-0.842804\pi$
$139$	−20.7623	−1.76103	−0.880517	+	0.474015i	$0.842804\pi$
$140$	2.81054	0.237534
$141$	19.1768	1.61498
$142$	−8.60377	−0.722013
$143$	0.0468841	0.00392065
$144$	2.93199	0.244332
$145$	5.27020	0.437667
$146$	0.767273	0.0634999
$147$	−9.82840	−0.810633
$148$	−10.2865	−0.845543
$149$	−7.09545	−0.581282	−0.290641	−	0.956832i	$-0.593868\pi$
$149$	−7.09545	−0.581282	−0.290641	+	0.956832i	$0.593868\pi$
$150$	10.4344	0.851969
$151$	−6.72230	−0.547053	−0.273526	−	0.961865i	$-0.588190\pi$
$151$	−6.72230	−0.547053	−0.273526	+	0.961865i	$0.588190\pi$
$152$	−1.94555	−0.157805
$153$	14.6864	1.18733
$154$	−17.4291	−1.40448
$155$	−8.01938	−0.644132
$156$	0.0217643	0.00174254
$157$	11.1012	0.885969	0.442984	−	0.896529i	$-0.353920\pi$
$157$	11.1012	0.885969	0.442984	+	0.896529i	$0.353920\pi$
$158$	−5.46148	−0.434492
$159$	−16.5051	−1.30894
$160$	0.846052	0.0668863
$161$	−28.2599	−2.22719
$162$	−9.19941	−0.722774
$163$	−5.37013	−0.420621	−0.210311	−	0.977635i	$-0.567448\pi$
$163$	−5.37013	−0.420621	−0.210311	+	0.977635i	$0.567448\pi$
$164$	−0.134813	−0.0105271
$165$	10.8113	0.841661
$166$	6.43940	0.499795
$167$	−13.5523	−1.04871	−0.524354	−	0.851500i	$-0.675693\pi$
$167$	−13.5523	−1.04871	−0.524354	+	0.851500i	$0.675693\pi$
$168$	−8.09084	−0.624222
$169$	−12.9999	−0.999994
$170$	4.23790	0.325032
$171$	−5.70433	−0.436221
$172$	9.26520	0.706465
$173$	−1.74260	−0.132487	−0.0662435	−	0.997803i	$-0.521101\pi$
$173$	−1.74260	−0.132487	−0.0662435	+	0.997803i	$0.521101\pi$
$174$	−15.1716	−1.15015
$175$	−14.2319	−1.07583
$176$	−5.24665	−0.395481
$177$	19.6130	1.47420
$178$	4.46154	0.334407
$179$	−19.9857	−1.49380	−0.746902	−	0.664934i	$-0.768460\pi$
$179$	−19.9857	−1.49380	−0.746902	+	0.664934i	$0.768460\pi$
$180$	2.48061	0.184894
$181$	−16.5282	−1.22853	−0.614264	−	0.789100i	$-0.710547\pi$
$181$	−16.5282	−1.22853	−0.614264	+	0.789100i	$0.710547\pi$
$182$	−0.0296850	−0.00220040
$183$	8.64739	0.639233
$184$	−8.50701	−0.627145
$185$	−8.70289	−0.639849
$186$	23.0857	1.69273
$187$	−26.2806	−1.92183
$188$	−7.87366	−0.574246
$189$	0.550284	0.0400273
$190$	−1.64604	−0.119416
$191$	2.82072	0.204100	0.102050	−	0.994779i	$-0.467460\pi$
$191$	2.82072	0.204100	0.102050	+	0.994779i	$0.467460\pi$
$192$	−2.43557	−0.175772
$193$	−7.99480	−0.575478	−0.287739	−	0.957709i	$-0.592904\pi$
$193$	−7.99480	−0.575478	−0.287739	+	0.957709i	$0.592904\pi$
$194$	3.36313	0.241459
$195$	0.0184137	0.00131863
$196$	4.03536	0.288240
$197$	2.79123	0.198867	0.0994335	−	0.995044i	$-0.468297\pi$
$197$	2.79123	0.198867	0.0994335	+	0.995044i	$0.468297\pi$
$198$	−15.3831	−1.09323
$199$	−17.4753	−1.23879	−0.619395	−	0.785079i	$-0.712622\pi$
$199$	−17.4753	−1.23879	−0.619395	+	0.785079i	$0.712622\pi$
$200$	−4.28420	−0.302938
$201$	−1.65722	−0.116892
$202$	18.9163	1.33095
$203$	20.6930	1.45236
$204$	−12.1998	−0.854159
$205$	−0.114059	−0.00796620
$206$	5.21269	0.363185
$207$	−24.9424	−1.73362
$208$	−0.00893602	−0.000619601 0
$209$	10.2076	0.706076
$210$	−6.84527	−0.472368
$211$	−13.7405	−0.945938	−0.472969	−	0.881079i	$-0.656818\pi$
$211$	−13.7405	−0.945938	−0.472969	+	0.881079i	$0.656818\pi$
$212$	6.77672	0.465427
$213$	20.9551	1.43582
$214$	1.11897	0.0764911
$215$	7.83884	0.534605
$216$	0.165651	0.0112711
$217$	−31.4874	−2.13750
$218$	−3.86262	−0.261609
$219$	−1.86874	−0.126278
$220$	−4.43894	−0.299273
$221$	−0.0447608	−0.00301094
$222$	25.0534	1.68147
$223$	20.8205	1.39425	0.697123	−	0.716952i	$-0.254463\pi$
$223$	20.8205	1.39425	0.697123	+	0.716952i	$0.254463\pi$
$224$	3.32195	0.221957
$225$	−12.5612	−0.837414
$226$	−14.8774	−0.989630
$227$	−0.476877	−0.0316515	−0.0158257	−	0.999875i	$-0.505038\pi$
$227$	−0.476877	−0.0316515	−0.0158257	+	0.999875i	$0.505038\pi$
$228$	4.73852	0.313816
$229$	−23.3736	−1.54457	−0.772285	−	0.635276i	$-0.780886\pi$
$229$	−23.3736	−1.54457	−0.772285	+	0.635276i	$0.780886\pi$
$230$	−7.19737	−0.474581
$231$	42.4498	2.79299
$232$	6.22917	0.408965
$233$	−13.0917	−0.857664	−0.428832	−	0.903384i	$-0.641075\pi$
$233$	−13.0917	−0.857664	−0.428832	+	0.903384i	$0.641075\pi$
$234$	−0.0262003	−0.00171277
$235$	−6.66153	−0.434550
$236$	−8.05274	−0.524189
$237$	13.3018	0.864045
$238$	16.6398	1.07860
$239$	28.5946	1.84963	0.924815	−	0.380417i	$-0.124220\pi$
$239$	28.5946	1.84963	0.924815	+	0.380417i	$0.124220\pi$
$240$	−2.06062	−0.133012
$241$	12.2783	0.790917	0.395459	−	0.918484i	$-0.370586\pi$
$241$	12.2783	0.790917	0.395459	+	0.918484i	$0.370586\pi$
$242$	16.5273	1.06241
$243$	21.9088	1.40545
$244$	−3.55046	−0.227295
$245$	3.41413	0.218121
$246$	0.328346	0.0209346
$247$	0.0173855	0.00110621
$248$	−9.47858	−0.601891
$249$	−15.6836	−0.993908
$250$	−7.85491	−0.496788
$251$	−14.1522	−0.893279	−0.446639	−	0.894714i	$-0.647379\pi$
$251$	−14.1522	−0.893279	−0.446639	+	0.894714i	$0.647379\pi$
$252$	9.73992	0.613557
$253$	44.6333	2.80607
$254$	21.3026	1.33664
$255$	−10.3217	−0.646369
$256$	1.00000	0.0625000
$257$	−6.01526	−0.375222	−0.187611	−	0.982243i	$-0.560074\pi$
$257$	−6.01526	−0.375222	−0.187611	+	0.982243i	$0.560074\pi$
$258$	−22.5660	−1.40490
$259$	−34.1712	−2.12329
$260$	−0.00756033	−0.000468872 0
$261$	18.2639	1.13050
$262$	9.92475	0.613153
$263$	2.30132	0.141906	0.0709529	−	0.997480i	$-0.477396\pi$
$263$	2.30132	0.141906	0.0709529	+	0.997480i	$0.477396\pi$
$264$	12.7786	0.786466
$265$	5.73345	0.352203
$266$	−6.46303	−0.396274
$267$	−10.8664	−0.665012
$268$	0.680426	0.0415637
$269$	9.96215	0.607403	0.303701	−	0.952767i	$-0.401777\pi$
$269$	9.96215	0.607403	0.303701	+	0.952767i	$0.401777\pi$
$270$	0.140149	0.00852921
$271$	−26.8977	−1.63392	−0.816958	−	0.576697i	$-0.804341\pi$
$271$	−26.8977	−1.63392	−0.816958	+	0.576697i	$0.804341\pi$
$272$	5.00903	0.303717
$273$	0.0722998	0.00437579
$274$	−23.0430	−1.39208
$275$	22.4777	1.35545
$276$	20.7194	1.24716
$277$	1.84141	0.110640	0.0553198	−	0.998469i	$-0.482382\pi$
$277$	1.84141	0.110640	0.0553198	+	0.998469i	$0.482382\pi$
$278$	−20.7623	−1.24524
$279$	−27.7911	−1.66381
$280$	2.81054	0.167962
$281$	12.4916	0.745187	0.372594	−	0.927995i	$-0.378469\pi$
$281$	12.4916	0.745187	0.372594	+	0.927995i	$0.378469\pi$
$282$	19.1768	1.14196
$283$	23.9588	1.42420	0.712101	−	0.702077i	$-0.247744\pi$
$283$	23.9588	1.42420	0.712101	+	0.702077i	$0.247744\pi$
$284$	−8.60377	−0.510540
$285$	4.00904	0.237475
$286$	0.0468841	0.00277232
$287$	−0.447842	−0.0264353
$288$	2.93199	0.172769
$289$	8.09039	0.475905
$290$	5.27020	0.309477
$291$	−8.19113	−0.480173
$292$	0.767273	0.0449012
$293$	−2.01164	−0.117521	−0.0587606	−	0.998272i	$-0.518715\pi$
$293$	−2.01164	−0.117521	−0.0587606	+	0.998272i	$0.518715\pi$
$294$	−9.82840	−0.573204
$295$	−6.81304	−0.396670
$296$	−10.2865	−0.597889
$297$	−0.869112	−0.0504310
$298$	−7.09545	−0.411028
$299$	0.0760188	0.00439628
$300$	10.4344	0.602433
$301$	30.7786	1.77405
$302$	−6.72230	−0.386825
$303$	−46.0719	−2.64676
$304$	−1.94555	−0.111585
$305$	−3.00388	−0.172001
$306$	14.6864	0.839566
$307$	−18.9572	−1.08195	−0.540973	−	0.841040i	$-0.681944\pi$
$307$	−18.9572	−1.08195	−0.540973	+	0.841040i	$0.681944\pi$
$308$	−17.4291	−0.993116
$309$	−12.6959	−0.722242
$310$	−8.01938	−0.455470
$311$	−20.6180	−1.16914	−0.584568	−	0.811344i	$-0.698736\pi$
$311$	−20.6180	−1.16914	−0.584568	+	0.811344i	$0.698736\pi$
$312$	0.0217643	0.00123216
$313$	−25.1376	−1.42086	−0.710431	−	0.703767i	$-0.751500\pi$
$313$	−25.1376	−1.42086	−0.710431	+	0.703767i	$0.751500\pi$
$314$	11.1012	0.626475
$315$	8.24048	0.464298
$316$	−5.46148	−0.307232
$317$	13.6355	0.765849	0.382924	−	0.923780i	$-0.374917\pi$
$317$	13.6355	0.765849	0.382924	+	0.923780i	$0.374917\pi$
$318$	−16.5051	−0.925563
$319$	−32.6823	−1.82986
$320$	0.846052	0.0472957
$321$	−2.72532	−0.152113
$322$	−28.2599	−1.57486
$323$	−9.74533	−0.542245
$324$	−9.19941	−0.511079
$325$	0.0382836	0.00212359
$326$	−5.37013	−0.297424
$327$	9.40766	0.520245
$328$	−0.134813	−0.00744379
$329$	−26.1559	−1.44202
$330$	10.8113	0.595144
$331$	−6.13266	−0.337082	−0.168541	−	0.985695i	$-0.553905\pi$
$331$	−6.13266	−0.337082	−0.168541	+	0.985695i	$0.553905\pi$
$332$	6.43940	0.353408
$333$	−30.1598	−1.65275
$334$	−13.5523	−0.741549
$335$	0.575676	0.0314526
$336$	−8.09084	−0.441391
$337$	31.2562	1.70263	0.851317	−	0.524651i	$-0.175804\pi$
$337$	31.2562	1.70263	0.851317	+	0.524651i	$0.175804\pi$
$338$	−12.9999	−0.707102
$339$	36.2349	1.96801
$340$	4.23790	0.229832
$341$	49.7308	2.69307
$342$	−5.70433	−0.308455
$343$	−9.84838	−0.531762
$344$	9.26520	0.499546
$345$	17.5297	0.943767
$346$	−1.74260	−0.0936825
$347$	29.1026	1.56231	0.781154	−	0.624339i	$-0.214631\pi$
$347$	29.1026	1.56231	0.781154	+	0.624339i	$0.214631\pi$
$348$	−15.1716	−0.813281
$349$	−23.6692	−1.26698	−0.633491	−	0.773750i	$-0.718379\pi$
$349$	−23.6692	−1.26698	−0.633491	+	0.773750i	$0.718379\pi$
$350$	−14.2319	−0.760727
$351$	−0.00148026	−7.90104e−5 0
$352$	−5.24665	−0.279647
$353$	31.5820	1.68094	0.840471	−	0.541856i	$-0.182278\pi$
$353$	31.5820	1.68094	0.840471	+	0.541856i	$0.182278\pi$
$354$	19.6130	1.04242
$355$	−7.27924	−0.386342
$356$	4.46154	0.236461
$357$	−40.5272	−2.14493
$358$	−19.9857	−1.05628
$359$	−1.44604	−0.0763192	−0.0381596	−	0.999272i	$-0.512150\pi$
$359$	−1.44604	−0.0763192	−0.0381596	+	0.999272i	$0.512150\pi$
$360$	2.48061	0.130740
$361$	−15.2148	−0.800780
$362$	−16.5282	−0.868701
$363$	−40.2533	−2.11275
$364$	−0.0296850	−0.00155592
$365$	0.649152	0.0339782
$366$	8.64739	0.452006
$367$	−16.4485	−0.858607	−0.429303	−	0.903160i	$-0.641241\pi$
$367$	−16.4485	−0.858607	−0.429303	+	0.903160i	$0.641241\pi$
$368$	−8.50701	−0.443459
$369$	−0.395269	−0.0205769
$370$	−8.70289	−0.452442
$371$	22.5119	1.16876
$372$	23.0857	1.19694
$373$	11.3899	0.589748	0.294874	−	0.955536i	$-0.404722\pi$
$373$	11.3899	0.589748	0.294874	+	0.955536i	$0.404722\pi$
$374$	−26.2806	−1.35894
$375$	19.1312	0.987929
$376$	−7.87366	−0.406053
$377$	−0.0556640	−0.00286684
$378$	0.550284	0.0283036
$379$	1.55238	0.0797403	0.0398702	−	0.999205i	$-0.487306\pi$
$379$	1.55238	0.0797403	0.0398702	+	0.999205i	$0.487306\pi$
$380$	−1.64604	−0.0844400
$381$	−51.8838	−2.65809
$382$	2.82072	0.144321
$383$	27.0832	1.38389	0.691945	−	0.721951i	$-0.256754\pi$
$383$	27.0832	1.38389	0.691945	+	0.721951i	$0.256754\pi$
$384$	−2.43557	−0.124290
$385$	−14.7459	−0.751522
$386$	−7.99480	−0.406925
$387$	27.1654	1.38090
$388$	3.36313	0.170737
$389$	4.24993	0.215480	0.107740	−	0.994179i	$-0.465639\pi$
$389$	4.24993	0.215480	0.107740	+	0.994179i	$0.465639\pi$
$390$	0.0184137	0.000932414 0
$391$	−42.6119	−2.15498
$392$	4.03536	0.203817
$393$	−24.1724	−1.21934
$394$	2.79123	0.140620
$395$	−4.62070	−0.232493
$396$	−15.3831	−0.773030
$397$	−29.5029	−1.48071	−0.740354	−	0.672218i	$-0.765342\pi$
$397$	−29.5029	−1.48071	−0.740354	+	0.672218i	$0.765342\pi$
$398$	−17.4753	−0.875957
$399$	15.7411	0.788043
$400$	−4.28420	−0.214210
$401$	2.65450	0.132559	0.0662796	−	0.997801i	$-0.478887\pi$
$401$	2.65450	0.132559	0.0662796	+	0.997801i	$0.478887\pi$
$402$	−1.65722	−0.0826548
$403$	0.0847008	0.00421925
$404$	18.9163	0.941121
$405$	−7.78318	−0.386749
$406$	20.6930	1.02698
$407$	53.9695	2.67517
$408$	−12.1998	−0.603982
$409$	20.0265	0.990248	0.495124	−	0.868822i	$-0.335123\pi$
$409$	20.0265	0.990248	0.495124	+	0.868822i	$0.335123\pi$
$410$	−0.114059	−0.00563296
$411$	56.1228	2.76833
$412$	5.21269	0.256811
$413$	−26.7508	−1.31632
$414$	−24.9424	−1.22585
$415$	5.44807	0.267435
$416$	−0.00893602	−0.000438124 0
$417$	50.5679	2.47632
$418$	10.2076	0.499271
$419$	17.5586	0.857794	0.428897	−	0.903353i	$-0.358902\pi$
$419$	17.5586	0.857794	0.428897	+	0.903353i	$0.358902\pi$
$420$	−6.84527	−0.334015
$421$	29.8894	1.45672	0.728360	−	0.685195i	$-0.240283\pi$
$421$	29.8894	1.45672	0.728360	+	0.685195i	$0.240283\pi$
$422$	−13.7405	−0.668879
$423$	−23.0855	−1.12245
$424$	6.77672	0.329106
$425$	−21.4597	−1.04095
$426$	20.9551	1.01528
$427$	−11.7945	−0.570774
$428$	1.11897	0.0540873
$429$	−0.114189	−0.00551312
$430$	7.83884	0.378023
$431$	−27.4073	−1.32016	−0.660081	−	0.751194i	$-0.729478\pi$
$431$	−27.4073	−1.32016	−0.660081	+	0.751194i	$0.729478\pi$
$432$	0.165651	0.00796988
$433$	−32.7173	−1.57229	−0.786146	−	0.618041i	$-0.787927\pi$
$433$	−32.7173	−1.57229	−0.786146	+	0.618041i	$0.787927\pi$
$434$	−31.4874	−1.51144
$435$	−12.8359	−0.615436
$436$	−3.86262	−0.184986
$437$	16.5508	0.791733
$438$	−1.86874	−0.0892920
$439$	0.0754612	0.00360157	0.00180078	−	0.999998i	$-0.499427\pi$
$439$	0.0754612	0.00360157	0.00180078	+	0.999998i	$0.499427\pi$
$440$	−4.43894	−0.211618
$441$	11.8316	0.563411
$442$	−0.0447608	−0.00212905
$443$	25.9651	1.23364	0.616821	−	0.787104i	$-0.288420\pi$
$443$	25.9651	1.23364	0.616821	+	0.787104i	$0.288420\pi$
$444$	25.0534	1.18898
$445$	3.77470	0.178938
$446$	20.8205	0.985881
$447$	17.2814	0.817384
$448$	3.32195	0.156947
$449$	−23.9242	−1.12905	−0.564526	−	0.825415i	$-0.690941\pi$
$449$	−23.9242	−1.12905	−0.564526	+	0.825415i	$0.690941\pi$
$450$	−12.5612	−0.592141
$451$	0.707315	0.0333062
$452$	−14.8774	−0.699774
$453$	16.3726	0.769252
$454$	−0.476877	−0.0223810
$455$	−0.0251151	−0.00117741
$456$	4.73852	0.221902
$457$	17.5263	0.819847	0.409923	−	0.912120i	$-0.365555\pi$
$457$	17.5263	0.819847	0.409923	+	0.912120i	$0.365555\pi$
$458$	−23.3736	−1.09218
$459$	0.829751	0.0387294
$460$	−7.19737	−0.335579
$461$	18.9214	0.881256	0.440628	−	0.897690i	$-0.354756\pi$
$461$	18.9214	0.881256	0.440628	+	0.897690i	$0.354756\pi$
$462$	42.4498	1.97494
$463$	−42.1825	−1.96039	−0.980194	−	0.198039i	$-0.936543\pi$
$463$	−42.1825	−1.96039	−0.980194	+	0.198039i	$0.936543\pi$
$464$	6.22917	0.289182
$465$	19.5317	0.905762
$466$	−13.0917	−0.606460
$467$	−9.65035	−0.446565	−0.223282	−	0.974754i	$-0.571677\pi$
$467$	−9.65035	−0.446565	−0.223282	+	0.974754i	$0.571677\pi$
$468$	−0.0262003	−0.00121111
$469$	2.26034	0.104373
$470$	−6.66153	−0.307273
$471$	−27.0376	−1.24583
$472$	−8.05274	−0.370657
$473$	−48.6112	−2.23515
$474$	13.3018	0.610972
$475$	8.33512	0.382442
$476$	16.6398	0.762682
$477$	19.8692	0.909750
$478$	28.5946	1.30789
$479$	28.1811	1.28763	0.643814	−	0.765182i	$-0.277351\pi$
$479$	28.1811	1.28763	0.643814	+	0.765182i	$0.277351\pi$
$480$	−2.06062	−0.0940538
$481$	0.0919201	0.00419120
$482$	12.2783	0.559263
$483$	68.8288	3.13182
$484$	16.5273	0.751241
$485$	2.84538	0.129202
$486$	21.9088	0.993805
$487$	31.7225	1.43748	0.718741	−	0.695277i	$-0.244719\pi$
$487$	31.7225	1.43748	0.718741	+	0.695277i	$0.244719\pi$
$488$	−3.55046	−0.160722
$489$	13.0793	0.591467
$490$	3.41413	0.154235
$491$	−3.10373	−0.140069	−0.0700347	−	0.997545i	$-0.522311\pi$
$491$	−3.10373	−0.140069	−0.0700347	+	0.997545i	$0.522311\pi$
$492$	0.328346	0.0148030
$493$	31.2021	1.40527
$494$	0.0173855	0.000782210 0
$495$	−13.0149	−0.584976
$496$	−9.47858	−0.425601
$497$	−28.5813	−1.28205
$498$	−15.6836	−0.702799
$499$	27.5361	1.23269	0.616343	−	0.787478i	$-0.288614\pi$
$499$	27.5361	1.23269	0.616343	+	0.787478i	$0.288614\pi$
$500$	−7.85491	−0.351282
$501$	33.0075	1.47467
$502$	−14.1522	−0.631643
$503$	−7.00674	−0.312415	−0.156207	−	0.987724i	$-0.549927\pi$
$503$	−7.00674	−0.312415	−0.156207	+	0.987724i	$0.549927\pi$
$504$	9.73992	0.433850
$505$	16.0042	0.712177
$506$	44.6333	1.98419
$507$	31.6622	1.40617
$508$	21.3026	0.945149
$509$	26.5854	1.17838	0.589189	−	0.807995i	$-0.299447\pi$
$509$	26.5854	1.17838	0.589189	+	0.807995i	$0.299447\pi$
$510$	−10.3217	−0.457052
$511$	2.54884	0.112754
$512$	1.00000	0.0441942
$513$	−0.322282	−0.0142291
$514$	−6.01526	−0.265322
$515$	4.41021	0.194337
$516$	−22.5660	−0.993414
$517$	41.3103	1.81683
$518$	−34.1712	−1.50140
$519$	4.24421	0.186300
$520$	−0.00756033	−0.000331543 0
$521$	18.3885	0.805614	0.402807	−	0.915285i	$-0.368035\pi$
$521$	18.3885	0.805614	0.402807	+	0.915285i	$0.368035\pi$
$522$	18.2639	0.799387
$523$	−4.21858	−0.184466	−0.0922328	−	0.995737i	$-0.529400\pi$
$523$	−4.21858	−0.184466	−0.0922328	+	0.995737i	$0.529400\pi$
$524$	9.92475	0.433565
$525$	34.6627	1.51281
$526$	2.30132	0.100343
$527$	−47.4785	−2.06820
$528$	12.7786	0.556115
$529$	49.3692	2.14649
$530$	5.73345	0.249045
$531$	−23.6105	−1.02461
$532$	−6.46303	−0.280208
$533$	0.00120469	5.21809e−5 0
$534$	−10.8664	−0.470234
$535$	0.946705	0.0409296
$536$	0.680426	0.0293899
$537$	48.6766	2.10055
$538$	9.96215	0.429499
$539$	−21.1721	−0.911948
$540$	0.140149	0.00603107
$541$	37.2515	1.60157	0.800783	−	0.598955i	$-0.204417\pi$
$541$	37.2515	1.60157	0.800783	+	0.598955i	$0.204417\pi$
$542$	−26.8977	−1.15535
$543$	40.2554	1.72753
$544$	5.00903	0.214760
$545$	−3.26797	−0.139985
$546$	0.0722998	0.00309415
$547$	−22.2912	−0.953105	−0.476552	−	0.879146i	$-0.658114\pi$
$547$	−22.2912	−0.953105	−0.476552	+	0.879146i	$0.658114\pi$
$548$	−23.0430	−0.984349
$549$	−10.4099	−0.444284
$550$	22.4777	0.958451
$551$	−12.1192	−0.516294
$552$	20.7194	0.881876
$553$	−18.1428	−0.771510
$554$	1.84141	0.0782340
$555$	21.1965	0.899740
$556$	−20.7623	−0.880517
$557$	21.5856	0.914613	0.457307	−	0.889309i	$-0.348814\pi$
$557$	21.5856	0.914613	0.457307	+	0.889309i	$0.348814\pi$
$558$	−27.7911	−1.17649
$559$	−0.0827940	−0.00350181
$560$	2.81054	0.118767
$561$	64.0082	2.70243
$562$	12.4916	0.526927
$563$	20.9162	0.881512	0.440756	−	0.897627i	$-0.354710\pi$
$563$	20.9162	0.881512	0.440756	+	0.897627i	$0.354710\pi$
$564$	19.1768	0.807490
$565$	−12.5871	−0.529541
$566$	23.9588	1.00706
$567$	−30.5600	−1.28340
$568$	−8.60377	−0.361006
$569$	4.95334	0.207655	0.103827	−	0.994595i	$-0.466891\pi$
$569$	4.95334	0.207655	0.103827	+	0.994595i	$0.466891\pi$
$570$	4.00904	0.167920
$571$	11.8625	0.496430	0.248215	−	0.968705i	$-0.420156\pi$
$571$	11.8625	0.496430	0.248215	+	0.968705i	$0.420156\pi$
$572$	0.0468841	0.00196032
$573$	−6.87006	−0.287001
$574$	−0.447842	−0.0186926
$575$	36.4457	1.51989
$576$	2.93199	0.122166
$577$	−25.5318	−1.06290	−0.531451	−	0.847089i	$-0.678353\pi$
$577$	−25.5318	−1.06290	−0.531451	+	0.847089i	$0.678353\pi$
$578$	8.09039	0.336516
$579$	19.4719	0.809223
$580$	5.27020	0.218833
$581$	21.3914	0.887464
$582$	−8.19113	−0.339533
$583$	−35.5550	−1.47254
$584$	0.767273	0.0317500
$585$	−0.0221668	−0.000916484 0
$586$	−2.01164	−0.0831001
$587$	13.8808	0.572923	0.286461	−	0.958092i	$-0.407521\pi$
$587$	13.8808	0.572923	0.286461	+	0.958092i	$0.407521\pi$
$588$	−9.82840	−0.405316
$589$	18.4411	0.759851
$590$	−6.81304	−0.280488
$591$	−6.79823	−0.279642
$592$	−10.2865	−0.422771
$593$	−10.6237	−0.436262	−0.218131	−	0.975920i	$-0.569996\pi$
$593$	−10.6237	−0.436262	−0.218131	+	0.975920i	$0.569996\pi$
$594$	−0.869112	−0.0356601
$595$	14.0781	0.577146
$596$	−7.09545	−0.290641
$597$	42.5622	1.74196
$598$	0.0760188	0.00310864
$599$	−37.4412	−1.52981	−0.764904	−	0.644145i	$-0.777214\pi$
$599$	−37.4412	−1.52981	−0.764904	+	0.644145i	$0.777214\pi$
$600$	10.4344	0.425984
$601$	4.97617	0.202982	0.101491	−	0.994836i	$-0.467639\pi$
$601$	4.97617	0.202982	0.101491	+	0.994836i	$0.467639\pi$
$602$	30.7786	1.25444
$603$	1.99500	0.0812427
$604$	−6.72230	−0.273526
$605$	13.9830	0.568488
$606$	−46.0719	−1.87154
$607$	−24.4535	−0.992538	−0.496269	−	0.868169i	$-0.665297\pi$
$607$	−24.4535	−0.992538	−0.496269	+	0.868169i	$0.665297\pi$
$608$	−1.94555	−0.0789025
$609$	−50.3992	−2.04228
$610$	−3.00388	−0.121623
$611$	0.0703592	0.00284643
$612$	14.6864	0.593663
$613$	30.4328	1.22917	0.614584	−	0.788852i	$-0.289324\pi$
$613$	30.4328	1.22917	0.614584	+	0.788852i	$0.289324\pi$
$614$	−18.9572	−0.765052
$615$	0.277798	0.0112019
$616$	−17.4291	−0.702239
$617$	−4.81293	−0.193761	−0.0968806	−	0.995296i	$-0.530886\pi$
$617$	−4.81293	−0.193761	−0.0968806	+	0.995296i	$0.530886\pi$
$618$	−12.6959	−0.510702
$619$	8.04690	0.323432	0.161716	−	0.986837i	$-0.448297\pi$
$619$	8.04690	0.323432	0.161716	+	0.986837i	$0.448297\pi$
$620$	−8.01938	−0.322066
$621$	−1.40919	−0.0565490
$622$	−20.6180	−0.826705
$623$	14.8210	0.593792
$624$	0.0217643	0.000871268 0
$625$	14.7753	0.591013
$626$	−25.1376	−1.00470
$627$	−24.8613	−0.992866
$628$	11.1012	0.442984
$629$	−51.5253	−2.05445
$630$	8.24048	0.328309
$631$	3.69386	0.147050	0.0735252	−	0.997293i	$-0.476575\pi$
$631$	3.69386	0.147050	0.0735252	+	0.997293i	$0.476575\pi$
$632$	−5.46148	−0.217246
$633$	33.4660	1.33015
$634$	13.6355	0.541537
$635$	18.0231	0.715224
$636$	−16.5051	−0.654472
$637$	−0.0360601	−0.00142875
$638$	−32.6823	−1.29390
$639$	−25.2261	−0.997931
$640$	0.846052	0.0334431
$641$	−10.6350	−0.420058	−0.210029	−	0.977695i	$-0.567356\pi$
$641$	−10.6350	−0.420058	−0.210029	+	0.977695i	$0.567356\pi$
$642$	−2.72532	−0.107560
$643$	−12.9684	−0.511422	−0.255711	−	0.966753i	$-0.582310\pi$
$643$	−12.9684	−0.511422	−0.255711	+	0.966753i	$0.582310\pi$
$644$	−28.2599	−1.11360
$645$	−19.0920	−0.751748
$646$	−9.74533	−0.383425
$647$	−8.78565	−0.345400	−0.172700	−	0.984974i	$-0.555249\pi$
$647$	−8.78565	−0.345400	−0.172700	+	0.984974i	$0.555249\pi$
$648$	−9.19941	−0.361387
$649$	42.2499	1.65845
$650$	0.0382836	0.00150161
$651$	76.6897	3.00571
$652$	−5.37013	−0.210311
$653$	36.1556	1.41488	0.707439	−	0.706774i	$-0.249850\pi$
$653$	36.1556	1.41488	0.707439	+	0.706774i	$0.249850\pi$
$654$	9.40766	0.367869
$655$	8.39686	0.328092
$656$	−0.134813	−0.00526356
$657$	2.24963	0.0877665
$658$	−26.1559	−1.01966
$659$	5.30490	0.206649	0.103325	−	0.994648i	$-0.467052\pi$
$659$	5.30490	0.206649	0.103325	+	0.994648i	$0.467052\pi$
$660$	10.8113	0.420830
$661$	−15.8066	−0.614807	−0.307403	−	0.951579i	$-0.599460\pi$
$661$	−15.8066	−0.614807	−0.307403	+	0.951579i	$0.599460\pi$
$662$	−6.13266	−0.238353
$663$	0.109018	0.00423390
$664$	6.43940	0.249897
$665$	−5.46806	−0.212042
$666$	−30.1598	−1.16867
$667$	−52.9916	−2.05184
$668$	−13.5523	−0.524354
$669$	−50.7098	−1.96055
$670$	0.575676	0.0222403
$671$	18.6280	0.719127
$672$	−8.09084	−0.312111
$673$	4.78927	0.184613	0.0923064	−	0.995731i	$-0.470576\pi$
$673$	4.78927	0.184613	0.0923064	+	0.995731i	$0.470576\pi$
$674$	31.2562	1.20394
$675$	−0.709681	−0.0273156
$676$	−12.9999	−0.499997
$677$	−25.6518	−0.985880	−0.492940	−	0.870063i	$-0.664078\pi$
$677$	−25.6518	−0.985880	−0.492940	+	0.870063i	$0.664078\pi$
$678$	36.2349	1.39159
$679$	11.1722	0.428748
$680$	4.23790	0.162516
$681$	1.16147	0.0445075
$682$	49.7308	1.90429
$683$	13.8348	0.529376	0.264688	−	0.964334i	$-0.414731\pi$
$683$	13.8348	0.529376	0.264688	+	0.964334i	$0.414731\pi$
$684$	−5.70433	−0.218111
$685$	−19.4956	−0.744888
$686$	−9.84838	−0.376013
$687$	56.9279	2.17194
$688$	9.26520	0.353233
$689$	−0.0605568	−0.00230703
$690$	17.5297	0.667344
$691$	−37.7011	−1.43422	−0.717108	−	0.696962i	$-0.754535\pi$
$691$	−37.7011	−1.43422	−0.717108	+	0.696962i	$0.754535\pi$
$692$	−1.74260	−0.0662435
$693$	−51.1019	−1.94120
$694$	29.1026	1.10472
$695$	−17.5660	−0.666315
$696$	−15.1716	−0.575077
$697$	−0.675282	−0.0255781
$698$	−23.6692	−0.895892
$699$	31.8856	1.20603
$700$	−14.2319	−0.537915
$701$	33.8385	1.27806	0.639031	−	0.769181i	$-0.279336\pi$
$701$	33.8385	1.27806	0.639031	+	0.769181i	$0.279336\pi$
$702$	−0.00148026	−5.58688e−5 0
$703$	20.0129	0.754799
$704$	−5.24665	−0.197740
$705$	16.2246	0.611054
$706$	31.5820	1.18861
$707$	62.8391	2.36331
$708$	19.6130	0.737101
$709$	−32.2493	−1.21115	−0.605575	−	0.795789i	$-0.707057\pi$
$709$	−32.2493	−1.21115	−0.605575	+	0.795789i	$0.707057\pi$
$710$	−7.27924	−0.273185
$711$	−16.0130	−0.600534
$712$	4.46154	0.167203
$713$	80.6344	3.01978
$714$	−40.5272	−1.51669
$715$	0.0396664	0.00148344
$716$	−19.9857	−0.746902
$717$	−69.6440	−2.60090
$718$	−1.44604	−0.0539658
$719$	−26.5729	−0.991001	−0.495500	−	0.868608i	$-0.665015\pi$
$719$	−26.5729	−0.991001	−0.495500	+	0.868608i	$0.665015\pi$
$720$	2.48061	0.0924470
$721$	17.3163	0.644893
$722$	−15.2148	−0.566237
$723$	−29.9047	−1.11217
$724$	−16.5282	−0.614264
$725$	−26.6870	−0.991130
$726$	−40.2533	−1.49394
$727$	1.98984	0.0737991	0.0368996	−	0.999319i	$-0.488252\pi$
$727$	1.98984	0.0737991	0.0368996	+	0.999319i	$0.488252\pi$
$728$	−0.0296850	−0.00110020
$729$	−25.7622	−0.954155
$730$	0.649152	0.0240262
$731$	46.4097	1.71652
$732$	8.64739	0.319617
$733$	−18.3398	−0.677397	−0.338698	−	0.940895i	$-0.609987\pi$
$733$	−18.3398	−0.677397	−0.338698	+	0.940895i	$0.609987\pi$
$734$	−16.4485	−0.607127
$735$	−8.31534	−0.306716
$736$	−8.50701	−0.313573
$737$	−3.56996	−0.131501
$738$	−0.395269	−0.0145501
$739$	8.22811	0.302676	0.151338	−	0.988482i	$-0.451642\pi$
$739$	8.22811	0.302676	0.151338	+	0.988482i	$0.451642\pi$
$740$	−8.70289	−0.319925
$741$	−0.0423435	−0.00155553
$742$	22.5119	0.826439
$743$	46.0433	1.68917	0.844583	−	0.535425i	$-0.179849\pi$
$743$	46.0433	1.68917	0.844583	+	0.535425i	$0.179849\pi$
$744$	23.0857	0.846364
$745$	−6.00312	−0.219937
$746$	11.3899	0.417015
$747$	18.8802	0.690792
$748$	−26.2806	−0.960914
$749$	3.71716	0.135822
$750$	19.1312	0.698571
$751$	14.8785	0.542923	0.271461	−	0.962449i	$-0.412493\pi$
$751$	14.8785	0.542923	0.271461	+	0.962449i	$0.412493\pi$
$752$	−7.87366	−0.287123
$753$	34.4686	1.25611
$754$	−0.0556640	−0.00202716
$755$	−5.68741	−0.206986
$756$	0.550284	0.0200136
$757$	−14.1605	−0.514672	−0.257336	−	0.966322i	$-0.582845\pi$
$757$	−14.1605	−0.514672	−0.257336	+	0.966322i	$0.582845\pi$
$758$	1.55238	0.0563849
$759$	−108.707	−3.94583
$760$	−1.64604	−0.0597081
$761$	−11.8936	−0.431143	−0.215572	−	0.976488i	$-0.569161\pi$
$761$	−11.8936	−0.431143	−0.215572	+	0.976488i	$0.569161\pi$
$762$	−51.8838	−1.87955
$763$	−12.8314	−0.464529
$764$	2.82072	0.102050
$765$	12.4255	0.449244
$766$	27.0832	0.978557
$767$	0.0719594	0.00259830
$768$	−2.43557	−0.0878860
$769$	15.7711	0.568719	0.284360	−	0.958718i	$-0.408219\pi$
$769$	15.7711	0.568719	0.284360	+	0.958718i	$0.408219\pi$
$770$	−14.7459	−0.531406
$771$	14.6506	0.527628
$772$	−7.99480	−0.287739
$773$	−50.9860	−1.83384	−0.916919	−	0.399073i	$-0.869332\pi$
$773$	−50.9860	−1.83384	−0.916919	+	0.399073i	$0.869332\pi$
$774$	27.1654	0.976442
$775$	40.6081	1.45869
$776$	3.36313	0.120729
$777$	83.2262	2.98572
$778$	4.24993	0.152367
$779$	0.262285	0.00939735
$780$	0.0184137	0.000659316 0
$781$	45.1410	1.61527
$782$	−42.6119	−1.52380
$783$	1.03187	0.0368760
$784$	4.03536	0.144120
$785$	9.39216	0.335220
$786$	−24.1724	−0.862201
$787$	−3.60205	−0.128399	−0.0641996	−	0.997937i	$-0.520449\pi$
$787$	−3.60205	−0.128399	−0.0641996	+	0.997937i	$0.520449\pi$
$788$	2.79123	0.0994335
$789$	−5.60503	−0.199544
$790$	−4.62070	−0.164397
$791$	−49.4220	−1.75724
$792$	−15.3831	−0.546615
$793$	0.0317270	0.00112666
$794$	−29.5029	−1.04702
$795$	−13.9642	−0.495260
$796$	−17.4753	−0.619395
$797$	−0.323025	−0.0114421	−0.00572106	−	0.999984i	$-0.501821\pi$
$797$	−0.323025	−0.0114421	−0.00572106	+	0.999984i	$0.501821\pi$
$798$	15.7411	0.557230
$799$	−39.4394	−1.39527
$800$	−4.28420	−0.151469
$801$	13.0812	0.462201
$802$	2.65450	0.0937335
$803$	−4.02561	−0.142061
$804$	−1.65722	−0.0584458
$805$	−23.9093	−0.842693
$806$	0.0847008	0.00298346
$807$	−24.2635	−0.854115
$808$	18.9163	0.665473
$809$	−3.79637	−0.133473	−0.0667366	−	0.997771i	$-0.521259\pi$
$809$	−3.79637	−0.133473	−0.0667366	+	0.997771i	$0.521259\pi$
$810$	−7.78318	−0.273473
$811$	46.3459	1.62743	0.813713	−	0.581267i	$-0.197443\pi$
$811$	46.3459	1.62743	0.813713	+	0.581267i	$0.197443\pi$
$812$	20.6930	0.726182
$813$	65.5110	2.29757
$814$	53.9695	1.89163
$815$	−4.54341	−0.159149
$816$	−12.1998	−0.427079
$817$	−18.0259	−0.630647
$818$	20.0265	0.700211
$819$	−0.0870361	−0.00304129
$820$	−0.114059	−0.00398310
$821$	22.1236	0.772118	0.386059	−	0.922474i	$-0.373836\pi$
$821$	22.1236	0.772118	0.386059	+	0.922474i	$0.373836\pi$
$822$	56.1228	1.95751
$823$	−23.8011	−0.829653	−0.414826	−	0.909901i	$-0.636158\pi$
$823$	−23.8011	−0.829653	−0.414826	+	0.909901i	$0.636158\pi$
$824$	5.21269	0.181593
$825$	−54.7459	−1.90601
$826$	−26.7508	−0.930780
$827$	−5.95868	−0.207204	−0.103602	−	0.994619i	$-0.533037\pi$
$827$	−5.95868	−0.207204	−0.103602	+	0.994619i	$0.533037\pi$
$828$	−24.9424	−0.866810
$829$	−29.8920	−1.03819	−0.519096	−	0.854716i	$-0.673731\pi$
$829$	−29.8920	−1.03819	−0.519096	+	0.854716i	$0.673731\pi$
$830$	5.44807	0.189105
$831$	−4.48488	−0.155579
$832$	−0.00893602	−0.000309801 0
$833$	20.2133	0.700348
$834$	50.5679	1.75102
$835$	−11.4659	−0.396796
$836$	10.2076	0.353038
$837$	−1.57014	−0.0542718
$838$	17.5586	0.606552
$839$	19.6832	0.679540	0.339770	−	0.940509i	$-0.389651\pi$
$839$	19.6832	0.679540	0.339770	+	0.940509i	$0.389651\pi$
$840$	−6.84527	−0.236184
$841$	9.80259	0.338020
$842$	29.8894	1.03006
$843$	−30.4242	−1.04786
$844$	−13.7405	−0.472969
$845$	−10.9986	−0.378364
$846$	−23.0855	−0.793695
$847$	54.9029	1.88649
$848$	6.77672	0.232713
$849$	−58.3532	−2.00268
$850$	−21.4597	−0.736061
$851$	87.5071	2.99971
$852$	20.9551	0.717909
$853$	18.3748	0.629141	0.314571	−	0.949234i	$-0.398139\pi$
$853$	18.3748	0.629141	0.314571	+	0.949234i	$0.398139\pi$
$854$	−11.7945	−0.403598
$855$	−4.82616	−0.165051
$856$	1.11897	0.0382455
$857$	−14.6281	−0.499686	−0.249843	−	0.968286i	$-0.580379\pi$
$857$	−14.6281	−0.499686	−0.249843	+	0.968286i	$0.580379\pi$
$858$	−0.114189	−0.00389836
$859$	49.3388	1.68342	0.841708	−	0.539932i	$-0.181550\pi$
$859$	49.3388	1.68342	0.841708	+	0.539932i	$0.181550\pi$
$860$	7.83884	0.267302
$861$	1.09075	0.0371726
$862$	−27.4073	−0.933496
$863$	23.1921	0.789467	0.394733	−	0.918796i	$-0.370837\pi$
$863$	23.1921	0.789467	0.394733	+	0.918796i	$0.370837\pi$
$864$	0.165651	0.00563556
$865$	−1.47433	−0.0501286
$866$	−32.7173	−1.11178
$867$	−19.7047	−0.669206
$868$	−31.4874	−1.06875
$869$	28.6545	0.972037
$870$	−12.8359	−0.435179
$871$	−0.00608030	−0.000206023 0
$872$	−3.86262	−0.130805
$873$	9.86066	0.333733
$874$	16.5508	0.559840
$875$	−26.0936	−0.882126
$876$	−1.86874	−0.0631390
$877$	43.9083	1.48268	0.741339	−	0.671131i	$-0.234191\pi$
$877$	43.9083	1.48268	0.741339	+	0.671131i	$0.234191\pi$
$878$	0.0754612	0.00254669
$879$	4.89948	0.165256
$880$	−4.43894	−0.149637
$881$	26.8120	0.903318	0.451659	−	0.892191i	$-0.350832\pi$
$881$	26.8120	0.903318	0.451659	+	0.892191i	$0.350832\pi$
$882$	11.8316	0.398392
$883$	17.5404	0.590282	0.295141	−	0.955454i	$-0.404633\pi$
$883$	17.5404	0.590282	0.295141	+	0.955454i	$0.404633\pi$
$884$	−0.0447608	−0.00150547
$885$	16.5936	0.557788
$886$	25.9651	0.872316
$887$	−1.30906	−0.0439538	−0.0219769	−	0.999758i	$-0.506996\pi$
$887$	−1.30906	−0.0439538	−0.0219769	+	0.999758i	$0.506996\pi$
$888$	25.0534	0.840737
$889$	70.7661	2.37342
$890$	3.77470	0.126528
$891$	48.2661	1.61697
$892$	20.8205	0.697123
$893$	15.3186	0.512618
$894$	17.2814	0.577978
$895$	−16.9090	−0.565205
$896$	3.32195	0.110979
$897$	−0.185149	−0.00618194
$898$	−23.9242	−0.798361
$899$	−59.0437	−1.96922
$900$	−12.5612	−0.418707
$901$	33.9448	1.13086
$902$	0.707315	0.0235510
$903$	−74.9632	−2.49462
$904$	−14.8774	−0.494815
$905$	−13.9837	−0.464833
$906$	16.3726	0.543943
$907$	2.11662	0.0702813	0.0351406	−	0.999382i	$-0.488812\pi$
$907$	2.11662	0.0702813	0.0351406	+	0.999382i	$0.488812\pi$
$908$	−0.476877	−0.0158257
$909$	55.4624	1.83957
$910$	−0.0251151	−0.000832556 0
$911$	23.0778	0.764600	0.382300	−	0.924038i	$-0.375132\pi$
$911$	23.0778	0.764600	0.382300	+	0.924038i	$0.375132\pi$
$912$	4.73852	0.156908
$913$	−33.7853	−1.11813
$914$	17.5263	0.579719
$915$	7.31614	0.241864
$916$	−23.3736	−0.772285
$917$	32.9696	1.08875
$918$	0.829751	0.0273858
$919$	−45.7099	−1.50783	−0.753915	−	0.656972i	$-0.771837\pi$
$919$	−45.7099	−1.50783	−0.753915	+	0.656972i	$0.771837\pi$
$920$	−7.19737	−0.237290
$921$	46.1716	1.52141
$922$	18.9214	0.623142
$923$	0.0768834	0.00253065
$924$	42.4498	1.39649
$925$	44.0693	1.44899
$926$	−42.1825	−1.38620
$927$	15.2835	0.501977
$928$	6.22917	0.204483
$929$	25.8251	0.847294	0.423647	−	0.905827i	$-0.360750\pi$
$929$	25.8251	0.847294	0.423647	+	0.905827i	$0.360750\pi$
$930$	19.5317	0.640471
$931$	−7.85101	−0.257306
$932$	−13.0917	−0.428832
$933$	50.2164	1.64401
$934$	−9.65035	−0.315769
$935$	−22.2348	−0.727155
$936$	−0.0262003	−0.000856383 0
$937$	−19.9827	−0.652806	−0.326403	−	0.945231i	$-0.605837\pi$
$937$	−19.9827	−0.652806	−0.326403	+	0.945231i	$0.605837\pi$
$938$	2.26034	0.0738028
$939$	61.2244	1.99798
$940$	−6.66153	−0.217275
$941$	−5.34909	−0.174375	−0.0871876	−	0.996192i	$-0.527788\pi$
$941$	−5.34909	−0.174375	−0.0871876	+	0.996192i	$0.527788\pi$
$942$	−27.0376	−0.880933
$943$	1.14685	0.0373467
$944$	−8.05274	−0.262094
$945$	0.465569	0.0151450
$946$	−48.6112	−1.58049
$947$	−18.4021	−0.597988	−0.298994	−	0.954255i	$-0.596651\pi$
$947$	−18.4021	−0.597988	−0.298994	+	0.954255i	$0.596651\pi$
$948$	13.3018	0.432023
$949$	−0.00685636	−0.000222567 0
$950$	8.33512	0.270427
$951$	−33.2103	−1.07692
$952$	16.6398	0.539298
$953$	23.6906	0.767413	0.383706	−	0.923455i	$-0.374647\pi$
$953$	23.6906	0.767413	0.383706	+	0.923455i	$0.374647\pi$
$954$	19.8692	0.643290
$955$	2.38648	0.0772246
$956$	28.5946	0.924815
$957$	79.5998	2.57310
$958$	28.1811	0.910491
$959$	−76.5478	−2.47186
$960$	−2.06062	−0.0665061
$961$	58.8436	1.89818
$962$	0.0919201	0.00296362
$963$	3.28080	0.105722
$964$	12.2783	0.395459
$965$	−6.76402	−0.217741
$966$	68.8288	2.21453
$967$	43.5328	1.39992	0.699961	−	0.714181i	$-0.253201\pi$
$967$	43.5328	1.39992	0.699961	+	0.714181i	$0.253201\pi$
$968$	16.5273	0.531207
$969$	23.7354	0.762491
$970$	2.84538	0.0913598
$971$	12.8499	0.412374	0.206187	−	0.978513i	$-0.433894\pi$
$971$	12.8499	0.412374	0.206187	+	0.978513i	$0.433894\pi$
$972$	21.9088	0.702726
$973$	−68.9713	−2.21112
$974$	31.7225	1.01645
$975$	−0.0932424	−0.00298615
$976$	−3.55046	−0.113648
$977$	−55.5594	−1.77750	−0.888751	−	0.458389i	$-0.848427\pi$
$977$	−55.5594	−1.77750	−0.888751	+	0.458389i	$0.848427\pi$
$978$	13.0793	0.418230
$979$	−23.4081	−0.748127
$980$	3.41413	0.109060
$981$	−11.3251	−0.361584
$982$	−3.10373	−0.0990440
$983$	19.7049	0.628490	0.314245	−	0.949342i	$-0.398249\pi$
$983$	19.7049	0.628490	0.314245	+	0.949342i	$0.398249\pi$
$984$	0.328346	0.0104673
$985$	2.36153	0.0752445
$986$	31.2021	0.993678
$987$	63.7045	2.02774
$988$	0.0173855	0.000553106 0
$989$	−78.8192	−2.50630
$990$	−13.0149	−0.413641
$991$	−41.5203	−1.31894	−0.659469	−	0.751732i	$-0.729219\pi$
$991$	−41.5203	−1.31894	−0.659469	+	0.751732i	$0.729219\pi$
$992$	−9.47858	−0.300945
$993$	14.9365	0.473996
$994$	−28.5813	−0.906544
$995$	−14.7850	−0.468716
$996$	−15.6836	−0.496954
$997$	−38.9357	−1.23311	−0.616554	−	0.787313i	$-0.711472\pi$
$997$	−38.9357	−1.23311	−0.616554	+	0.787313i	$0.711472\pi$
$998$	27.5361	0.871641
$999$	−1.70396	−0.0539110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.c.1.8	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.c.1.8	✓	31	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.43557 q^{3} +1.00000 q^{4} +0.846052 q^{5} -2.43557 q^{6} +3.32195 q^{7} +1.00000 q^{8} +2.93199 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.43557 q^{3} +1.00000 q^{4} +0.846052 q^{5} -2.43557 q^{6} +3.32195 q^{7} +1.00000 q^{8} +2.93199 q^{9} +0.846052 q^{10} -5.24665 q^{11} -2.43557 q^{12} -0.00893602 q^{13} +3.32195 q^{14} -2.06062 q^{15} +1.00000 q^{16} +5.00903 q^{17} +2.93199 q^{18} -1.94555 q^{19} +0.846052 q^{20} -8.09084 q^{21} -5.24665 q^{22} -8.50701 q^{23} -2.43557 q^{24} -4.28420 q^{25} -0.00893602 q^{26} +0.165651 q^{27} +3.32195 q^{28} +6.22917 q^{29} -2.06062 q^{30} -9.47858 q^{31} +1.00000 q^{32} +12.7786 q^{33} +5.00903 q^{34} +2.81054 q^{35} +2.93199 q^{36} -10.2865 q^{37} -1.94555 q^{38} +0.0217643 q^{39} +0.846052 q^{40} -0.134813 q^{41} -8.09084 q^{42} +9.26520 q^{43} -5.24665 q^{44} +2.48061 q^{45} -8.50701 q^{46} -7.87366 q^{47} -2.43557 q^{48} +4.03536 q^{49} -4.28420 q^{50} -12.1998 q^{51} -0.00893602 q^{52} +6.77672 q^{53} +0.165651 q^{54} -4.43894 q^{55} +3.32195 q^{56} +4.73852 q^{57} +6.22917 q^{58} -8.05274 q^{59} -2.06062 q^{60} -3.55046 q^{61} -9.47858 q^{62} +9.73992 q^{63} +1.00000 q^{64} -0.00756033 q^{65} +12.7786 q^{66} +0.680426 q^{67} +5.00903 q^{68} +20.7194 q^{69} +2.81054 q^{70} -8.60377 q^{71} +2.93199 q^{72} +0.767273 q^{73} -10.2865 q^{74} +10.4344 q^{75} -1.94555 q^{76} -17.4291 q^{77} +0.0217643 q^{78} -5.46148 q^{79} +0.846052 q^{80} -9.19941 q^{81} -0.134813 q^{82} +6.43940 q^{83} -8.09084 q^{84} +4.23790 q^{85} +9.26520 q^{86} -15.1716 q^{87} -5.24665 q^{88} +4.46154 q^{89} +2.48061 q^{90} -0.0296850 q^{91} -8.50701 q^{92} +23.0857 q^{93} -7.87366 q^{94} -1.64604 q^{95} -2.43557 q^{96} +3.36313 q^{97} +4.03536 q^{98} -15.3831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - q^99

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