LMFDB - Embedded newform 4019.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45850 q^{2} -1.74268 q^{3} +4.04423 q^{4} -0.525405 q^{5} +4.28438 q^{6} -0.912805 q^{7} -5.02575 q^{8} +0.0369224 q^{9} +O(q^{10})$	\(q-2.45850 q^{2} -1.74268 q^{3} +4.04423 q^{4} -0.525405 q^{5} +4.28438 q^{6} -0.912805 q^{7} -5.02575 q^{8} +0.0369224 q^{9} +1.29171 q^{10} +2.47795 q^{11} -7.04779 q^{12} +4.18171 q^{13} +2.24413 q^{14} +0.915610 q^{15} +4.26736 q^{16} +1.77201 q^{17} -0.0907739 q^{18} -2.64140 q^{19} -2.12486 q^{20} +1.59072 q^{21} -6.09205 q^{22} -1.38663 q^{23} +8.75826 q^{24} -4.72395 q^{25} -10.2807 q^{26} +5.16369 q^{27} -3.69160 q^{28} -2.97987 q^{29} -2.25103 q^{30} +3.89539 q^{31} -0.439807 q^{32} -4.31827 q^{33} -4.35650 q^{34} +0.479592 q^{35} +0.149323 q^{36} -6.49802 q^{37} +6.49390 q^{38} -7.28736 q^{39} +2.64055 q^{40} -1.29725 q^{41} -3.91080 q^{42} -0.0331256 q^{43} +10.0214 q^{44} -0.0193992 q^{45} +3.40902 q^{46} +3.06608 q^{47} -7.43663 q^{48} -6.16679 q^{49} +11.6138 q^{50} -3.08804 q^{51} +16.9118 q^{52} +8.26111 q^{53} -12.6949 q^{54} -1.30193 q^{55} +4.58753 q^{56} +4.60311 q^{57} +7.32603 q^{58} -11.1754 q^{59} +3.70294 q^{60} +10.0293 q^{61} -9.57681 q^{62} -0.0337030 q^{63} -7.45345 q^{64} -2.19709 q^{65} +10.6165 q^{66} -14.2565 q^{67} +7.16643 q^{68} +2.41644 q^{69} -1.17908 q^{70} +10.8722 q^{71} -0.185563 q^{72} -2.04982 q^{73} +15.9754 q^{74} +8.23232 q^{75} -10.6825 q^{76} -2.26189 q^{77} +17.9160 q^{78} -2.04815 q^{79} -2.24209 q^{80} -9.10940 q^{81} +3.18929 q^{82} +10.9123 q^{83} +6.43326 q^{84} -0.931023 q^{85} +0.0814394 q^{86} +5.19296 q^{87} -12.4536 q^{88} -4.79191 q^{89} +0.0476930 q^{90} -3.81708 q^{91} -5.60784 q^{92} -6.78840 q^{93} -7.53796 q^{94} +1.38781 q^{95} +0.766442 q^{96} +15.6388 q^{97} +15.1611 q^{98} +0.0914921 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * 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 $

$2$	−2.45850	−1.73842	−0.869212	−	0.494440i	$-0.835373\pi$
$2$	−2.45850	−1.73842	−0.869212	+	0.494440i	$0.835373\pi$
$3$	−1.74268	−1.00613	−0.503067	−	0.864247i	$-0.667795\pi$
$3$	−1.74268	−1.00613	−0.503067	+	0.864247i	$0.667795\pi$
$4$	4.04423	2.02212
$5$	−0.525405	−0.234968	−0.117484	−	0.993075i	$-0.537483\pi$
$5$	−0.525405	−0.234968	−0.117484	+	0.993075i	$0.537483\pi$
$6$	4.28438	1.74909
$7$	−0.912805	−0.345008	−0.172504	−	0.985009i	$-0.555186\pi$
$7$	−0.912805	−0.345008	−0.172504	+	0.985009i	$0.555186\pi$
$8$	−5.02575	−1.77687
$9$	0.0369224	0.0123075
$10$	1.29171	0.408474
$11$	2.47795	0.747131	0.373566	−	0.927604i	$-0.378135\pi$
$11$	2.47795	0.747131	0.373566	+	0.927604i	$0.378135\pi$
$12$	−7.04779	−2.03452
$13$	4.18171	1.15980	0.579898	−	0.814689i	$-0.303092\pi$
$13$	4.18171	1.15980	0.579898	+	0.814689i	$0.303092\pi$
$14$	2.24413	0.599770
$15$	0.915610	0.236410
$16$	4.26736	1.06684
$17$	1.77201	0.429776	0.214888	−	0.976639i	$-0.431061\pi$
$17$	1.77201	0.429776	0.214888	+	0.976639i	$0.431061\pi$
$18$	−0.0907739	−0.0213956
$19$	−2.64140	−0.605979	−0.302990	−	0.952994i	$-0.597985\pi$
$19$	−2.64140	−0.605979	−0.302990	+	0.952994i	$0.597985\pi$
$20$	−2.12486	−0.475133
$21$	1.59072	0.347124
$22$	−6.09205	−1.29883
$23$	−1.38663	−0.289132	−0.144566	−	0.989495i	$-0.546179\pi$
$23$	−1.38663	−0.289132	−0.144566	+	0.989495i	$0.546179\pi$
$24$	8.75826	1.78777
$25$	−4.72395	−0.944790
$26$	−10.2807	−2.01622
$27$	5.16369	0.993752
$28$	−3.69160	−0.697646
$29$	−2.97987	−0.553349	−0.276674	−	0.960964i	$-0.589232\pi$
$29$	−2.97987	−0.553349	−0.276674	+	0.960964i	$0.589232\pi$
$30$	−2.25103	−0.410980
$31$	3.89539	0.699632	0.349816	−	0.936818i	$-0.386244\pi$
$31$	3.89539	0.699632	0.349816	+	0.936818i	$0.386244\pi$
$32$	−0.439807	−0.0777477
$33$	−4.31827	−0.751715
$34$	−4.35650	−0.747133
$35$	0.479592	0.0810658
$36$	0.149323	0.0248872
$37$	−6.49802	−1.06827	−0.534134	−	0.845400i	$-0.679362\pi$
$37$	−6.49802	−1.06827	−0.534134	+	0.845400i	$0.679362\pi$
$38$	6.49390	1.05345
$39$	−7.28736	−1.16691
$40$	2.64055	0.417508
$41$	−1.29725	−0.202596	−0.101298	−	0.994856i	$-0.532300\pi$
$41$	−1.29725	−0.202596	−0.101298	+	0.994856i	$0.532300\pi$
$42$	−3.91080	−0.603449
$43$	−0.0331256	−0.00505161	−0.00252580	−	0.999997i	$-0.500804\pi$
$43$	−0.0331256	−0.00505161	−0.00252580	+	0.999997i	$0.500804\pi$
$44$	10.0214	1.51079
$45$	−0.0193992	−0.00289187
$46$	3.40902	0.502633
$47$	3.06608	0.447233	0.223617	−	0.974677i	$-0.428214\pi$
$47$	3.06608	0.447233	0.223617	+	0.974677i	$0.428214\pi$
$48$	−7.43663	−1.07339
$49$	−6.16679	−0.880970
$50$	11.6138	1.64245
$51$	−3.08804	−0.432413
$52$	16.9118	2.34524
$53$	8.26111	1.13475	0.567375	−	0.823459i	$-0.307959\pi$
$53$	8.26111	1.13475	0.567375	+	0.823459i	$0.307959\pi$
$54$	−12.6949	−1.72756
$55$	−1.30193	−0.175552
$56$	4.58753	0.613035
$57$	4.60311	0.609697
$58$	7.32603	0.961954
$59$	−11.1754	−1.45491	−0.727456	−	0.686154i	$-0.759297\pi$
$59$	−11.1754	−1.45491	−0.727456	+	0.686154i	$0.759297\pi$
$60$	3.70294	0.478048
$61$	10.0293	1.28412	0.642061	−	0.766654i	$-0.278080\pi$
$61$	10.0293	1.28412	0.642061	+	0.766654i	$0.278080\pi$
$62$	−9.57681	−1.21626
$63$	−0.0337030	−0.00424618
$64$	−7.45345	−0.931682
$65$	−2.19709	−0.272515
$66$	10.6165	1.30680
$67$	−14.2565	−1.74171	−0.870854	−	0.491541i	$-0.836434\pi$
$67$	−14.2565	−1.74171	−0.870854	+	0.491541i	$0.836434\pi$
$68$	7.16643	0.869058
$69$	2.41644	0.290905
$70$	−1.17908	−0.140927
$71$	10.8722	1.29029	0.645145	−	0.764060i	$-0.276797\pi$
$71$	10.8722	1.29029	0.645145	+	0.764060i	$0.276797\pi$
$72$	−0.185563	−0.0218688
$73$	−2.04982	−0.239913	−0.119957	−	0.992779i	$-0.538276\pi$
$73$	−2.04982	−0.239913	−0.119957	+	0.992779i	$0.538276\pi$
$74$	15.9754	1.85710
$75$	8.23232	0.950586
$76$	−10.6825	−1.22536
$77$	−2.26189	−0.257766
$78$	17.9160	2.02859
$79$	−2.04815	−0.230435	−0.115218	−	0.993340i	$-0.536757\pi$
$79$	−2.04815	−0.230435	−0.115218	+	0.993340i	$0.536757\pi$
$80$	−2.24209	−0.250673
$81$	−9.10940	−1.01216
$82$	3.18929	0.352199
$83$	10.9123	1.19779	0.598893	−	0.800829i	$-0.295608\pi$
$83$	10.9123	1.19779	0.598893	+	0.800829i	$0.295608\pi$
$84$	6.43326	0.701926
$85$	−0.931023	−0.100984
$86$	0.0814394	0.00878184
$87$	5.19296	0.556743
$88$	−12.4536	−1.32756
$89$	−4.79191	−0.507941	−0.253971	−	0.967212i	$-0.581737\pi$
$89$	−4.79191	−0.507941	−0.253971	+	0.967212i	$0.581737\pi$
$90$	0.0476930	0.00502729
$91$	−3.81708	−0.400139
$92$	−5.60784	−0.584658
$93$	−6.78840	−0.703924
$94$	−7.53796	−0.777481
$95$	1.38781	0.142386
$96$	0.766442	0.0782246
$97$	15.6388	1.58788	0.793939	−	0.607997i	$-0.208027\pi$
$97$	15.6388	1.58788	0.793939	+	0.607997i	$0.208027\pi$
$98$	15.1611	1.53150
$99$	0.0914921	0.00919530
$100$	−19.1048	−1.91048
$101$	1.13469	0.112906	0.0564529	−	0.998405i	$-0.482021\pi$
$101$	1.13469	0.112906	0.0564529	+	0.998405i	$0.482021\pi$
$102$	7.59196	0.751717
$103$	−8.16009	−0.804038	−0.402019	−	0.915631i	$-0.631691\pi$
$103$	−8.16009	−0.804038	−0.402019	+	0.915631i	$0.631691\pi$
$104$	−21.0162	−2.06081
$105$	−0.835774	−0.0815631
$106$	−20.3100	−1.97268
$107$	−1.43729	−0.138948	−0.0694742	−	0.997584i	$-0.522132\pi$
$107$	−1.43729	−0.138948	−0.0694742	+	0.997584i	$0.522132\pi$
$108$	20.8832	2.00948
$109$	−5.76637	−0.552318	−0.276159	−	0.961112i	$-0.589062\pi$
$109$	−5.76637	−0.552318	−0.276159	+	0.961112i	$0.589062\pi$
$110$	3.20079	0.305184
$111$	11.3240	1.07482
$112$	−3.89527	−0.368068
$113$	10.9078	1.02612	0.513061	−	0.858352i	$-0.328512\pi$
$113$	10.9078	1.02612	0.513061	+	0.858352i	$0.328512\pi$
$114$	−11.3168	−1.05991
$115$	0.728540	0.0679367
$116$	−12.0513	−1.11894
$117$	0.154399	0.0142742
$118$	27.4747	2.52925
$119$	−1.61750	−0.148276
$120$	−4.60163	−0.420070
$121$	−4.85975	−0.441795
$122$	−24.6571	−2.23235
$123$	2.26069	0.203839
$124$	15.7538	1.41474
$125$	5.10901	0.456964
$126$	0.0828589	0.00738165
$127$	−6.71410	−0.595780	−0.297890	−	0.954600i	$-0.596283\pi$
$127$	−6.71410	−0.595780	−0.297890	+	0.954600i	$0.596283\pi$
$128$	19.2039	1.69741
$129$	0.0577272	0.00508260
$130$	5.40154	0.473747
$131$	3.70898	0.324055	0.162028	−	0.986786i	$-0.448197\pi$
$131$	3.70898	0.324055	0.162028	+	0.986786i	$0.448197\pi$
$132$	−17.4641	−1.52005
$133$	2.41108	0.209068
$134$	35.0496	3.02783
$135$	−2.71302	−0.233500
$136$	−8.90570	−0.763657
$137$	−16.3489	−1.39678	−0.698389	−	0.715719i	$-0.746099\pi$
$137$	−16.3489	−1.39678	−0.698389	+	0.715719i	$0.746099\pi$
$138$	−5.94083	−0.505717
$139$	−0.154772	−0.0131276	−0.00656378	−	0.999978i	$-0.502089\pi$
$139$	−0.154772	−0.0131276	−0.00656378	+	0.999978i	$0.502089\pi$
$140$	1.93958	0.163925
$141$	−5.34318	−0.449977
$142$	−26.7293	−2.24307
$143$	10.3621	0.866520
$144$	0.157561	0.0131301
$145$	1.56564	0.130019
$146$	5.03949	0.417071
$147$	10.7467	0.886374
$148$	−26.2795	−2.16016
$149$	7.55602	0.619013	0.309507	−	0.950897i	$-0.399836\pi$
$149$	7.55602	0.619013	0.309507	+	0.950897i	$0.399836\pi$
$150$	−20.2392	−1.65252
$151$	−5.95974	−0.484997	−0.242498	−	0.970152i	$-0.577967\pi$
$151$	−5.95974	−0.484997	−0.242498	+	0.970152i	$0.577967\pi$
$152$	13.2750	1.07675
$153$	0.0654270	0.00528946
$154$	5.56086	0.448107
$155$	−2.04665	−0.164391
$156$	−29.4718	−2.35963
$157$	10.0576	0.802682	0.401341	−	0.915929i	$-0.368544\pi$
$157$	10.0576	0.802682	0.401341	+	0.915929i	$0.368544\pi$
$158$	5.03539	0.400594
$159$	−14.3964	−1.14171
$160$	0.231077	0.0182682
$161$	1.26572	0.0997526
$162$	22.3955	1.75956
$163$	18.5873	1.45587	0.727934	−	0.685648i	$-0.240481\pi$
$163$	18.5873	1.45587	0.727934	+	0.685648i	$0.240481\pi$
$164$	−5.24638	−0.409674
$165$	2.26884	0.176629
$166$	−26.8280	−2.08226
$167$	21.2599	1.64514	0.822569	−	0.568665i	$-0.192540\pi$
$167$	21.2599	1.64514	0.822569	+	0.568665i	$0.192540\pi$
$168$	−7.99459	−0.616796
$169$	4.48666	0.345127
$170$	2.28892	0.175552
$171$	−0.0975270	−0.00745808
$172$	−0.133968	−0.0102149
$173$	4.23978	0.322345	0.161172	−	0.986926i	$-0.448473\pi$
$173$	4.23978	0.322345	0.161172	+	0.986926i	$0.448473\pi$
$174$	−12.7669	−0.967856
$175$	4.31204	0.325960
$176$	10.5743	0.797069
$177$	19.4751	1.46384
$178$	11.7809	0.883017
$179$	−25.2198	−1.88502	−0.942508	−	0.334183i	$-0.891540\pi$
$179$	−25.2198	−1.88502	−0.942508	+	0.334183i	$0.891540\pi$
$180$	−0.0784550	−0.00584769
$181$	15.1298	1.12459	0.562295	−	0.826937i	$-0.309919\pi$
$181$	15.1298	1.12459	0.562295	+	0.826937i	$0.309919\pi$
$182$	9.38430	0.695611
$183$	−17.4778	−1.29200
$184$	6.96884	0.513750
$185$	3.41409	0.251009
$186$	16.6893	1.22372
$187$	4.39096	0.321099
$188$	12.3999	0.904358
$189$	−4.71344	−0.342852
$190$	−3.41192	−0.247527
$191$	3.88029	0.280768	0.140384	−	0.990097i	$-0.455166\pi$
$191$	3.88029	0.280768	0.140384	+	0.990097i	$0.455166\pi$
$192$	12.9890	0.937397
$193$	−24.1200	−1.73619	−0.868097	−	0.496395i	$-0.834657\pi$
$193$	−24.1200	−1.73619	−0.868097	+	0.496395i	$0.834657\pi$
$194$	−38.4480	−2.76041
$195$	3.82881	0.274187
$196$	−24.9399	−1.78142
$197$	20.3761	1.45174	0.725868	−	0.687834i	$-0.241438\pi$
$197$	20.3761	1.45174	0.725868	+	0.687834i	$0.241438\pi$
$198$	−0.224934	−0.0159853
$199$	10.9665	0.777396	0.388698	−	0.921365i	$-0.372925\pi$
$199$	10.9665	0.777396	0.388698	+	0.921365i	$0.372925\pi$
$200$	23.7414	1.67877
$201$	24.8445	1.75239
$202$	−2.78963	−0.196278
$203$	2.72004	0.190910
$204$	−12.4888	−0.874389
$205$	0.681581	0.0476037
$206$	20.0616	1.39776
$207$	−0.0511976	−0.00355848
$208$	17.8448	1.23732
$209$	−6.54527	−0.452746
$210$	2.05475	0.141791
$211$	16.4860	1.13495	0.567473	−	0.823392i	$-0.307921\pi$
$211$	16.4860	1.13495	0.567473	+	0.823392i	$0.307921\pi$
$212$	33.4099	2.29460
$213$	−18.9467	−1.29821
$214$	3.53359	0.241551
$215$	0.0174043	0.00118697
$216$	−25.9514	−1.76577
$217$	−3.55573	−0.241378
$218$	14.1766	0.960163
$219$	3.57217	0.241385
$220$	−5.26530	−0.354987
$221$	7.41003	0.498453
$222$	−27.8400	−1.86850
$223$	13.2779	0.889157	0.444578	−	0.895740i	$-0.353353\pi$
$223$	13.2779	0.889157	0.444578	+	0.895740i	$0.353353\pi$
$224$	0.401458	0.0268235
$225$	−0.174420	−0.0116280
$226$	−26.8169	−1.78383
$227$	25.0889	1.66521	0.832604	−	0.553869i	$-0.186849\pi$
$227$	25.0889	1.66521	0.832604	+	0.553869i	$0.186849\pi$
$228$	18.6161	1.23288
$229$	−8.48183	−0.560495	−0.280248	−	0.959928i	$-0.590417\pi$
$229$	−8.48183	−0.560495	−0.280248	+	0.959928i	$0.590417\pi$
$230$	−1.79112	−0.118103
$231$	3.94174	0.259347
$232$	14.9761	0.983230
$233$	−15.2219	−0.997218	−0.498609	−	0.866827i	$-0.666156\pi$
$233$	−15.2219	−0.997218	−0.498609	+	0.866827i	$0.666156\pi$
$234$	−0.379590	−0.0248146
$235$	−1.61093	−0.105086
$236$	−45.1959	−2.94200
$237$	3.56927	0.231849
$238$	3.97663	0.257767
$239$	0.247851	0.0160322	0.00801608	−	0.999968i	$-0.497448\pi$
$239$	0.247851	0.0160322	0.00801608	+	0.999968i	$0.497448\pi$
$240$	3.90724	0.252211
$241$	−21.2521	−1.36897	−0.684485	−	0.729027i	$-0.739973\pi$
$241$	−21.2521	−1.36897	−0.684485	+	0.729027i	$0.739973\pi$
$242$	11.9477	0.768027
$243$	0.383688	0.0246136
$244$	40.5609	2.59664
$245$	3.24006	0.207000
$246$	−5.55791	−0.354359
$247$	−11.0456	−0.702813
$248$	−19.5772	−1.24316
$249$	−19.0167	−1.20513
$250$	−12.5605	−0.794396
$251$	−16.2249	−1.02411	−0.512054	−	0.858953i	$-0.671115\pi$
$251$	−16.2249	−1.02411	−0.512054	+	0.858953i	$0.671115\pi$
$252$	−0.136303	−0.00858627
$253$	−3.43600	−0.216019
$254$	16.5066	1.03572
$255$	1.62247	0.101603
$256$	−32.3060	−2.01913
$257$	18.4877	1.15323	0.576615	−	0.817016i	$-0.304373\pi$
$257$	18.4877	1.15323	0.576615	+	0.817016i	$0.304373\pi$
$258$	−0.141923	−0.00883571
$259$	5.93143	0.368561
$260$	−8.88553	−0.551057
$261$	−0.110024	−0.00681033
$262$	−9.11854	−0.563345
$263$	3.02105	0.186286	0.0931430	−	0.995653i	$-0.470309\pi$
$263$	3.02105	0.186286	0.0931430	+	0.995653i	$0.470309\pi$
$264$	21.7026	1.33570
$265$	−4.34042	−0.266630
$266$	−5.92766	−0.363448
$267$	8.35075	0.511058
$268$	−57.6566	−3.52194
$269$	−2.01717	−0.122989	−0.0614945	−	0.998107i	$-0.519587\pi$
$269$	−2.01717	−0.122989	−0.0614945	+	0.998107i	$0.519587\pi$
$270$	6.66998	0.405922
$271$	10.6646	0.647827	0.323914	−	0.946087i	$-0.395001\pi$
$271$	10.6646	0.647827	0.323914	+	0.946087i	$0.395001\pi$
$272$	7.56181	0.458502
$273$	6.65194	0.402594
$274$	40.1937	2.42819
$275$	−11.7057	−0.705882
$276$	9.77266	0.588245
$277$	−24.3257	−1.46159	−0.730795	−	0.682597i	$-0.760851\pi$
$277$	−24.3257	−1.46159	−0.730795	+	0.682597i	$0.760851\pi$
$278$	0.380506	0.0228212
$279$	0.143827	0.00861071
$280$	−2.41031	−0.144044
$281$	−2.40815	−0.143658	−0.0718290	−	0.997417i	$-0.522884\pi$
$281$	−2.40815	−0.143658	−0.0718290	+	0.997417i	$0.522884\pi$
$282$	13.1362	0.782251
$283$	20.0690	1.19298	0.596490	−	0.802620i	$-0.296561\pi$
$283$	20.0690	1.19298	0.596490	+	0.802620i	$0.296561\pi$
$284$	43.9696	2.60912
$285$	−2.41850	−0.143259
$286$	−25.4752	−1.50638
$287$	1.18414	0.0698974
$288$	−0.0162388	−0.000956878 0
$289$	−13.8600	−0.815293
$290$	−3.84913	−0.226029
$291$	−27.2534	−1.59762
$292$	−8.28995	−0.485133
$293$	6.77651	0.395888	0.197944	−	0.980213i	$-0.436574\pi$
$293$	6.77651	0.395888	0.197944	+	0.980213i	$0.436574\pi$
$294$	−26.4208	−1.54089
$295$	5.87160	0.341858
$296$	32.6575	1.89818
$297$	12.7954	0.742463
$298$	−18.5765	−1.07611
$299$	−5.79846	−0.335334
$300$	33.2934	1.92220
$301$	0.0302372	0.00174284
$302$	14.6520	0.843130
$303$	−1.97739	−0.113598
$304$	−11.2718	−0.646483
$305$	−5.26944	−0.301728
$306$	−0.160852	−0.00919532
$307$	−14.9030	−0.850558	−0.425279	−	0.905062i	$-0.639824\pi$
$307$	−14.9030	−0.850558	−0.425279	+	0.905062i	$0.639824\pi$
$308$	−9.14760	−0.521233
$309$	14.2204	0.808970
$310$	5.03170	0.285781
$311$	−23.1148	−1.31072	−0.655360	−	0.755317i	$-0.727483\pi$
$311$	−23.1148	−1.31072	−0.655360	+	0.755317i	$0.727483\pi$
$312$	36.6245	2.07345
$313$	10.0765	0.569557	0.284779	−	0.958593i	$-0.408080\pi$
$313$	10.0765	0.569557	0.284779	+	0.958593i	$0.408080\pi$
$314$	−24.7266	−1.39540
$315$	0.0177077	0.000997716 0
$316$	−8.28321	−0.465967
$317$	−6.91385	−0.388320	−0.194160	−	0.980970i	$-0.562198\pi$
$317$	−6.91385	−0.388320	−0.194160	+	0.980970i	$0.562198\pi$
$318$	35.3937	1.98478
$319$	−7.38399	−0.413424
$320$	3.91608	0.218915
$321$	2.50474	0.139801
$322$	−3.11177	−0.173412
$323$	−4.68060	−0.260435
$324$	−36.8406	−2.04670
$325$	−19.7542	−1.09576
$326$	−45.6968	−2.53091
$327$	10.0489	0.555706
$328$	6.51966	0.359988
$329$	−2.79873	−0.154299
$330$	−5.57795	−0.307056
$331$	−17.0432	−0.936779	−0.468390	−	0.883522i	$-0.655166\pi$
$331$	−17.0432	−0.936779	−0.468390	+	0.883522i	$0.655166\pi$
$332$	44.1321	2.42206
$333$	−0.239923	−0.0131477
$334$	−52.2675	−2.85995
$335$	7.49043	0.409246
$336$	6.78819	0.370326
$337$	13.0268	0.709617	0.354809	−	0.934939i	$-0.384546\pi$
$337$	13.0268	0.709617	0.354809	+	0.934939i	$0.384546\pi$
$338$	−11.0305	−0.599978
$339$	−19.0088	−1.03242
$340$	−3.76528	−0.204201
$341$	9.65258	0.522717
$342$	0.239770	0.0129653
$343$	12.0187	0.648949
$344$	0.166481	0.00897606
$345$	−1.26961	−0.0683535
$346$	−10.4235	−0.560371
$347$	−12.4640	−0.669101	−0.334551	−	0.942378i	$-0.608585\pi$
$347$	−12.4640	−0.669101	−0.334551	+	0.942378i	$0.608585\pi$
$348$	21.0015	1.12580
$349$	−31.9633	−1.71095	−0.855477	−	0.517841i	$-0.826736\pi$
$349$	−31.9633	−1.71095	−0.855477	+	0.517841i	$0.826736\pi$
$350$	−10.6012	−0.566656
$351$	21.5930	1.15255
$352$	−1.08982	−0.0580877
$353$	−35.8982	−1.91067	−0.955334	−	0.295527i	$-0.904505\pi$
$353$	−35.8982	−1.91067	−0.955334	+	0.295527i	$0.904505\pi$
$354$	−47.8796	−2.54477
$355$	−5.71229	−0.303177
$356$	−19.3796	−1.02712
$357$	2.81878	0.149186
$358$	62.0029	3.27696
$359$	30.8028	1.62571	0.812855	−	0.582467i	$-0.197912\pi$
$359$	30.8028	1.62571	0.812855	+	0.582467i	$0.197912\pi$
$360$	0.0974957	0.00513848
$361$	−12.0230	−0.632789
$362$	−37.1967	−1.95501
$363$	8.46897	0.444506
$364$	−15.4372	−0.809127
$365$	1.07698	0.0563719
$366$	42.9693	2.24604
$367$	−17.4872	−0.912824	−0.456412	−	0.889768i	$-0.650866\pi$
$367$	−17.4872	−0.912824	−0.456412	+	0.889768i	$0.650866\pi$
$368$	−5.91723	−0.308457
$369$	−0.0478977	−0.00249345
$370$	−8.39355	−0.436360
$371$	−7.54078	−0.391498
$372$	−27.4539	−1.42342
$373$	−31.8913	−1.65127	−0.825635	−	0.564204i	$-0.809183\pi$
$373$	−31.8913	−1.65127	−0.825635	+	0.564204i	$0.809183\pi$
$374$	−10.7952	−0.558206
$375$	−8.90335	−0.459767
$376$	−15.4094	−0.794677
$377$	−12.4610	−0.641772
$378$	11.5880	0.596022
$379$	−25.9772	−1.33436	−0.667181	−	0.744896i	$-0.732499\pi$
$379$	−25.9772	−1.33436	−0.667181	+	0.744896i	$0.732499\pi$
$380$	5.61261	0.287921
$381$	11.7005	0.599435
$382$	−9.53969	−0.488093
$383$	−25.7404	−1.31527	−0.657635	−	0.753336i	$-0.728443\pi$
$383$	−25.7404	−1.31527	−0.657635	+	0.753336i	$0.728443\pi$
$384$	−33.4663	−1.70782
$385$	1.18841	0.0605668
$386$	59.2990	3.01824
$387$	−0.00122308	−6.21726e−5 0
$388$	63.2469	3.21088
$389$	8.13631	0.412527	0.206264	−	0.978496i	$-0.433870\pi$
$389$	8.13631	0.412527	0.206264	+	0.978496i	$0.433870\pi$
$390$	−9.41315	−0.476653
$391$	−2.45712	−0.124262
$392$	30.9928	1.56537
$393$	−6.46355	−0.326043
$394$	−50.0946	−2.52373
$395$	1.07611	0.0541449
$396$	0.370015	0.0185940
$397$	−6.64857	−0.333682	−0.166841	−	0.985984i	$-0.553357\pi$
$397$	−6.64857	−0.333682	−0.166841	+	0.985984i	$0.553357\pi$
$398$	−26.9612	−1.35144
$399$	−4.20174	−0.210350
$400$	−20.1588	−1.00794
$401$	−26.8284	−1.33975	−0.669874	−	0.742475i	$-0.733652\pi$
$401$	−26.8284	−1.33975	−0.669874	+	0.742475i	$0.733652\pi$
$402$	−61.0802	−3.04640
$403$	16.2894	0.811430
$404$	4.58894	0.228309
$405$	4.78612	0.237824
$406$	−6.68723	−0.331882
$407$	−16.1018	−0.798136
$408$	15.5198	0.768342
$409$	−27.5795	−1.36372	−0.681859	−	0.731484i	$-0.738828\pi$
$409$	−27.5795	−1.36372	−0.681859	+	0.731484i	$0.738828\pi$
$410$	−1.67567	−0.0827554
$411$	28.4908	1.40535
$412$	−33.0013	−1.62586
$413$	10.2009	0.501956
$414$	0.125870	0.00618615
$415$	−5.73340	−0.281441
$416$	−1.83914	−0.0901714
$417$	0.269717	0.0132081
$418$	16.0916	0.787064
$419$	−26.6300	−1.30096	−0.650480	−	0.759524i	$-0.725432\pi$
$419$	−26.6300	−1.30096	−0.650480	+	0.759524i	$0.725432\pi$
$420$	−3.38006	−0.164930
$421$	−29.1166	−1.41906	−0.709528	−	0.704677i	$-0.751092\pi$
$421$	−29.1166	−1.41906	−0.709528	+	0.704677i	$0.751092\pi$
$422$	−40.5310	−1.97302
$423$	0.113207	0.00550432
$424$	−41.5183	−2.01631
$425$	−8.37090	−0.406048
$426$	46.5805	2.25683
$427$	−9.15480	−0.443032
$428$	−5.81275	−0.280970
$429$	−18.0577	−0.871836
$430$	−0.0427886	−0.00206345
$431$	16.6656	0.802756	0.401378	−	0.915913i	$-0.368531\pi$
$431$	16.6656	0.802756	0.401378	+	0.915913i	$0.368531\pi$
$432$	22.0353	1.06017
$433$	8.58445	0.412542	0.206271	−	0.978495i	$-0.433867\pi$
$433$	8.58445	0.412542	0.206271	+	0.978495i	$0.433867\pi$
$434$	8.74176	0.419618
$435$	−2.72840	−0.130817
$436$	−23.3205	−1.11685
$437$	3.66264	0.175208
$438$	−8.78219	−0.419629
$439$	−22.5397	−1.07576	−0.537881	−	0.843021i	$-0.680775\pi$
$439$	−22.5397	−1.07576	−0.537881	+	0.843021i	$0.680775\pi$
$440$	6.54317	0.311933
$441$	−0.227693	−0.0108425
$442$	−18.2176	−0.866522
$443$	−4.76563	−0.226422	−0.113211	−	0.993571i	$-0.536114\pi$
$443$	−4.76563	−0.226422	−0.113211	+	0.993571i	$0.536114\pi$
$444$	45.7967	2.17342
$445$	2.51769	0.119350
$446$	−32.6439	−1.54573
$447$	−13.1677	−0.622811
$448$	6.80355	0.321437
$449$	19.1997	0.906092	0.453046	−	0.891487i	$-0.350337\pi$
$449$	19.1997	0.906092	0.453046	+	0.891487i	$0.350337\pi$
$450$	0.428811	0.0202144
$451$	−3.21453	−0.151366
$452$	44.1138	2.07494
$453$	10.3859	0.487972
$454$	−61.6811	−2.89484
$455$	2.00551	0.0940198
$456$	−23.1341	−1.08335
$457$	−24.9166	−1.16555	−0.582775	−	0.812633i	$-0.698033\pi$
$457$	−24.9166	−1.16555	−0.582775	+	0.812633i	$0.698033\pi$
$458$	20.8526	0.974378
$459$	9.15012	0.427091
$460$	2.94639	0.137376
$461$	−26.4171	−1.23037	−0.615184	−	0.788384i	$-0.710918\pi$
$461$	−26.4171	−1.23037	−0.615184	+	0.788384i	$0.710918\pi$
$462$	−9.69077	−0.450856
$463$	14.4471	0.671413	0.335707	−	0.941967i	$-0.391025\pi$
$463$	14.4471	0.671413	0.335707	+	0.941967i	$0.391025\pi$
$464$	−12.7162	−0.590335
$465$	3.56666	0.165400
$466$	37.4230	1.73359
$467$	−19.7103	−0.912082	−0.456041	−	0.889959i	$-0.650733\pi$
$467$	−19.7103	−0.912082	−0.456041	+	0.889959i	$0.650733\pi$
$468$	0.624425	0.0288640
$469$	13.0134	0.600903
$470$	3.96048	0.182683
$471$	−17.5271	−0.807607
$472$	56.1648	2.58519
$473$	−0.0820837	−0.00377421
$474$	−8.77506	−0.403052
$475$	12.4779	0.572523
$476$	−6.54155	−0.299832
$477$	0.305020	0.0139659
$478$	−0.609343	−0.0278707
$479$	−7.86665	−0.359437	−0.179718	−	0.983718i	$-0.557519\pi$
$479$	−7.86665	−0.359437	−0.179718	+	0.983718i	$0.557519\pi$
$480$	−0.402692	−0.0183803
$481$	−27.1728	−1.23897
$482$	52.2484	2.37985
$483$	−2.20574	−0.100365
$484$	−19.6540	−0.893362
$485$	−8.21669	−0.373101
$486$	−0.943297	−0.0427888
$487$	−14.4532	−0.654937	−0.327468	−	0.944862i	$-0.606195\pi$
$487$	−14.4532	−0.654937	−0.327468	+	0.944862i	$0.606195\pi$
$488$	−50.4048	−2.28172
$489$	−32.3916	−1.46480
$490$	−7.96569	−0.359853
$491$	42.1829	1.90369	0.951843	−	0.306585i	$-0.0991865\pi$
$491$	42.1829	1.90369	0.951843	+	0.306585i	$0.0991865\pi$
$492$	9.14275	0.412187
$493$	−5.28037	−0.237816
$494$	27.1556	1.22179
$495$	−0.0480704	−0.00216060
$496$	16.6230	0.746395
$497$	−9.92418	−0.445160
$498$	46.7526	2.09503
$499$	−7.38143	−0.330438	−0.165219	−	0.986257i	$-0.552833\pi$
$499$	−7.38143	−0.330438	−0.165219	+	0.986257i	$0.552833\pi$
$500$	20.6620	0.924034
$501$	−37.0491	−1.65523
$502$	39.8890	1.78033
$503$	20.9112	0.932385	0.466193	−	0.884683i	$-0.345625\pi$
$503$	20.9112	0.932385	0.466193	+	0.884683i	$0.345625\pi$
$504$	0.169383	0.00754491
$505$	−0.596170	−0.0265292
$506$	8.44740	0.375533
$507$	−7.81879	−0.347245
$508$	−27.1534	−1.20474
$509$	12.0536	0.534264	0.267132	−	0.963660i	$-0.413924\pi$
$509$	12.0536	0.534264	0.267132	+	0.963660i	$0.413924\pi$
$510$	−3.98885	−0.176629
$511$	1.87108	0.0827719
$512$	41.0166	1.81269
$513$	−13.6394	−0.602193
$514$	−45.4520	−2.00480
$515$	4.28735	0.188923
$516$	0.233462	0.0102776
$517$	7.59760	0.334142
$518$	−14.5824	−0.640715
$519$	−7.38857	−0.324322
$520$	11.0420	0.484225
$521$	−31.5002	−1.38005	−0.690023	−	0.723787i	$-0.742400\pi$
$521$	−31.5002	−1.38005	−0.690023	+	0.723787i	$0.742400\pi$
$522$	0.270495	0.0118392
$523$	−27.2082	−1.18973	−0.594866	−	0.803825i	$-0.702795\pi$
$523$	−27.2082	−1.18973	−0.594866	+	0.803825i	$0.702795\pi$
$524$	15.0000	0.655277
$525$	−7.51450	−0.327960
$526$	−7.42726	−0.323844
$527$	6.90267	0.300685
$528$	−18.4276	−0.801959
$529$	−21.0773	−0.916403
$530$	10.6709	0.463516
$531$	−0.412623	−0.0179063
$532$	9.75099	0.422759
$533$	−5.42472	−0.234971
$534$	−20.5303	−0.888435
$535$	0.755160	0.0326484
$536$	71.6497	3.09479
$537$	43.9500	1.89658
$538$	4.95922	0.213807
$539$	−15.2810	−0.658200
$540$	−10.9721	−0.472164
$541$	−19.1427	−0.823008	−0.411504	−	0.911408i	$-0.634996\pi$
$541$	−19.1427	−0.823008	−0.411504	+	0.911408i	$0.634996\pi$
$542$	−26.2189	−1.12620
$543$	−26.3664	−1.13149
$544$	−0.779344	−0.0334141
$545$	3.02968	0.129777
$546$	−16.3538	−0.699878
$547$	35.9278	1.53616	0.768081	−	0.640352i	$-0.221212\pi$
$547$	35.9278	1.53616	0.768081	+	0.640352i	$0.221212\pi$
$548$	−66.1186	−2.82445
$549$	0.370307	0.0158043
$550$	28.7786	1.22712
$551$	7.87105	0.335318
$552$	−12.1444	−0.516902
$553$	1.86956	0.0795020
$554$	59.8048	2.54086
$555$	−5.94966	−0.252549
$556$	−0.625932	−0.0265454
$557$	−7.75918	−0.328767	−0.164383	−	0.986397i	$-0.552563\pi$
$557$	−7.75918	−0.328767	−0.164383	+	0.986397i	$0.552563\pi$
$558$	−0.353599	−0.0149691
$559$	−0.138522	−0.00585884
$560$	2.04659	0.0864843
$561$	−7.65203	−0.323069
$562$	5.92044	0.249739
$563$	13.1787	0.555416	0.277708	−	0.960665i	$-0.410425\pi$
$563$	13.1787	0.555416	0.277708	+	0.960665i	$0.410425\pi$
$564$	−21.6091	−0.909907
$565$	−5.73102	−0.241106
$566$	−49.3398	−2.07391
$567$	8.31511	0.349202
$568$	−54.6409	−2.29268
$569$	−10.1131	−0.423964	−0.211982	−	0.977274i	$-0.567992\pi$
$569$	−10.1131	−0.423964	−0.211982	+	0.977274i	$0.567992\pi$
$570$	5.94588	0.249045
$571$	15.7142	0.657617	0.328808	−	0.944397i	$-0.393353\pi$
$571$	15.7142	0.657617	0.328808	+	0.944397i	$0.393353\pi$
$572$	41.9066	1.75220
$573$	−6.76208	−0.282490
$574$	−2.91120	−0.121511
$575$	6.55035	0.273169
$576$	−0.275200	−0.0114667
$577$	25.0164	1.04145	0.520723	−	0.853726i	$-0.325662\pi$
$577$	25.0164	1.04145	0.520723	+	0.853726i	$0.325662\pi$
$578$	34.0748	1.41732
$579$	42.0333	1.74684
$580$	6.33181	0.262914
$581$	−9.96084	−0.413245
$582$	67.0025	2.77734
$583$	20.4706	0.847807
$584$	10.3019	0.426295
$585$	−0.0811218	−0.00335397
$586$	−16.6601	−0.688221
$587$	−37.1305	−1.53254	−0.766270	−	0.642519i	$-0.777890\pi$
$587$	−37.1305	−1.53254	−0.766270	+	0.642519i	$0.777890\pi$
$588$	43.4622	1.79235
$589$	−10.2893	−0.423962
$590$	−14.4353	−0.594294
$591$	−35.5089	−1.46064
$592$	−27.7294	−1.13967
$593$	14.6884	0.603179	0.301589	−	0.953438i	$-0.402483\pi$
$593$	14.6884	0.603179	0.301589	+	0.953438i	$0.402483\pi$
$594$	−31.4575	−1.29072
$595$	0.849843	0.0348401
$596$	30.5583	1.25172
$597$	−19.1111	−0.782165
$598$	14.2555	0.582952
$599$	34.0343	1.39060	0.695302	−	0.718718i	$-0.255271\pi$
$599$	34.0343	1.39060	0.695302	+	0.718718i	$0.255271\pi$
$600$	−41.3736	−1.68907
$601$	−19.5259	−0.796480	−0.398240	−	0.917281i	$-0.630379\pi$
$601$	−19.5259	−0.796480	−0.398240	+	0.917281i	$0.630379\pi$
$602$	−0.0743383	−0.00302980
$603$	−0.526385	−0.0214360
$604$	−24.1026	−0.980720
$605$	2.55333	0.103808
$606$	4.86143	0.197482
$607$	42.7065	1.73340	0.866702	−	0.498826i	$-0.166235\pi$
$607$	42.7065	1.73340	0.866702	+	0.498826i	$0.166235\pi$
$608$	1.16171	0.0471135
$609$	−4.74016	−0.192081
$610$	12.9549	0.524530
$611$	12.8214	0.518700
$612$	0.264602	0.0106959
$613$	15.7020	0.634199	0.317099	−	0.948392i	$-0.397291\pi$
$613$	15.7020	0.634199	0.317099	+	0.948392i	$0.397291\pi$
$614$	36.6390	1.47863
$615$	−1.18778	−0.0478957
$616$	11.3677	0.458017
$617$	−6.33325	−0.254967	−0.127483	−	0.991841i	$-0.540690\pi$
$617$	−6.33325	−0.254967	−0.127483	+	0.991841i	$0.540690\pi$
$618$	−34.9609	−1.40633
$619$	24.3833	0.980046	0.490023	−	0.871709i	$-0.336988\pi$
$619$	24.3833	0.980046	0.490023	+	0.871709i	$0.336988\pi$
$620$	−8.27714	−0.332418
$621$	−7.16010	−0.287325
$622$	56.8277	2.27858
$623$	4.37408	0.175244
$624$	−31.0978	−1.24491
$625$	20.9355	0.837418
$626$	−24.7731	−0.990132
$627$	11.4063	0.455524
$628$	40.6752	1.62312
$629$	−11.5146	−0.459116
$630$	−0.0435344	−0.00173445
$631$	34.5936	1.37715	0.688575	−	0.725165i	$-0.258237\pi$
$631$	34.5936	1.37715	0.688575	+	0.725165i	$0.258237\pi$
$632$	10.2935	0.409454
$633$	−28.7298	−1.14191
$634$	16.9977	0.675065
$635$	3.52762	0.139989
$636$	−58.2226	−2.30868
$637$	−25.7877	−1.02175
$638$	18.1536	0.718706
$639$	0.401427	0.0158802
$640$	−10.0898	−0.398836
$641$	6.11941	0.241702	0.120851	−	0.992671i	$-0.461438\pi$
$641$	6.11941	0.241702	0.120851	+	0.992671i	$0.461438\pi$
$642$	−6.15790	−0.243033
$643$	9.95211	0.392473	0.196236	−	0.980557i	$-0.437128\pi$
$643$	9.95211	0.392473	0.196236	+	0.980557i	$0.437128\pi$
$644$	5.11886	0.201712
$645$	−0.0303302	−0.00119425
$646$	11.5073	0.452747
$647$	−26.8517	−1.05565	−0.527824	−	0.849354i	$-0.676992\pi$
$647$	−26.8517	−1.05565	−0.527824	+	0.849354i	$0.676992\pi$
$648$	45.7816	1.79847
$649$	−27.6921	−1.08701
$650$	48.5657	1.90490
$651$	6.19648	0.242859
$652$	75.1713	2.94393
$653$	33.5452	1.31273	0.656363	−	0.754445i	$-0.272094\pi$
$653$	33.5452	1.31273	0.656363	+	0.754445i	$0.272094\pi$
$654$	−24.7053	−0.966053
$655$	−1.94872	−0.0761426
$656$	−5.53583	−0.216138
$657$	−0.0756843	−0.00295273
$658$	6.88069	0.268237
$659$	−5.68079	−0.221292	−0.110646	−	0.993860i	$-0.535292\pi$
$659$	−5.68079	−0.221292	−0.110646	+	0.993860i	$0.535292\pi$
$660$	9.17572	0.357164
$661$	34.3752	1.33704	0.668521	−	0.743693i	$-0.266928\pi$
$661$	34.3752	1.33704	0.668521	+	0.743693i	$0.266928\pi$
$662$	41.9008	1.62852
$663$	−12.9133	−0.501511
$664$	−54.8428	−2.12831
$665$	−1.26680	−0.0491242
$666$	0.589851	0.0228563
$667$	4.13197	0.159991
$668$	85.9799	3.32666
$669$	−23.1392	−0.894612
$670$	−18.4152	−0.711443
$671$	24.8522	0.959407
$672$	−0.699612	−0.0269881
$673$	−22.5300	−0.868468	−0.434234	−	0.900800i	$-0.642981\pi$
$673$	−22.5300	−0.868468	−0.434234	+	0.900800i	$0.642981\pi$
$674$	−32.0265	−1.23362
$675$	−24.3930	−0.938887
$676$	18.1451	0.697888
$677$	−28.0581	−1.07836	−0.539180	−	0.842191i	$-0.681266\pi$
$677$	−28.0581	−1.07836	−0.539180	+	0.842191i	$0.681266\pi$
$678$	46.7332	1.79478
$679$	−14.2752	−0.547831
$680$	4.67909	0.179435
$681$	−43.7218	−1.67542
$682$	−23.7309	−0.908703
$683$	−21.7869	−0.833654	−0.416827	−	0.908986i	$-0.636858\pi$
$683$	−21.7869	−0.833654	−0.416827	+	0.908986i	$0.636858\pi$
$684$	−0.394422	−0.0150811
$685$	8.58977	0.328198
$686$	−29.5480	−1.12815
$687$	14.7811	0.563934
$688$	−0.141359	−0.00538926
$689$	34.5455	1.31608
$690$	3.12134	0.118827
$691$	37.1235	1.41225	0.706123	−	0.708089i	$-0.250443\pi$
$691$	37.1235	1.41225	0.706123	+	0.708089i	$0.250443\pi$
$692$	17.1467	0.651818
$693$	−0.0835144	−0.00317245
$694$	30.6427	1.16318
$695$	0.0813177	0.00308456
$696$	−26.0985	−0.989262
$697$	−2.29874	−0.0870711
$698$	78.5817	2.97436
$699$	26.5268	1.00334
$700$	17.4389	0.659129
$701$	−25.1597	−0.950268	−0.475134	−	0.879913i	$-0.657600\pi$
$701$	−25.1597	−0.950268	−0.475134	+	0.879913i	$0.657600\pi$
$702$	−53.0865	−2.00362
$703$	17.1639	0.647349
$704$	−18.4693	−0.696088
$705$	2.80733	0.105730
$706$	88.2558	3.32155
$707$	−1.03575	−0.0389533
$708$	78.7618	2.96005
$709$	−30.4036	−1.14183	−0.570916	−	0.821009i	$-0.693412\pi$
$709$	−30.4036	−1.14183	−0.570916	+	0.821009i	$0.693412\pi$
$710$	14.0437	0.527050
$711$	−0.0756228	−0.00283608
$712$	24.0830	0.902547
$713$	−5.40144	−0.202286
$714$	−6.92998	−0.259348
$715$	−5.44428	−0.203604
$716$	−101.995	−3.81172
$717$	−0.431924	−0.0161305
$718$	−75.7287	−2.82617
$719$	−5.65888	−0.211041	−0.105520	−	0.994417i	$-0.533651\pi$
$719$	−5.65888	−0.211041	−0.105520	+	0.994417i	$0.533651\pi$
$720$	−0.0827835	−0.00308516
$721$	7.44857	0.277399
$722$	29.5586	1.10006
$723$	37.0356	1.37737
$724$	61.1885	2.27405
$725$	14.0768	0.522798
$726$	−20.8210	−0.772739
$727$	−30.5413	−1.13272	−0.566358	−	0.824159i	$-0.691648\pi$
$727$	−30.5413	−1.13272	−0.566358	+	0.824159i	$0.691648\pi$
$728$	19.1837	0.710995
$729$	26.6596	0.987391
$730$	−2.64777	−0.0979983
$731$	−0.0586990	−0.00217106
$732$	−70.6845	−2.61257
$733$	−16.8568	−0.622621	−0.311311	−	0.950308i	$-0.600768\pi$
$733$	−16.8568	−0.622621	−0.311311	+	0.950308i	$0.600768\pi$
$734$	42.9923	1.58688
$735$	−5.64637	−0.208270
$736$	0.609848	0.0224793
$737$	−35.3269	−1.30128
$738$	0.117756	0.00433468
$739$	−46.4463	−1.70855	−0.854277	−	0.519818i	$-0.826000\pi$
$739$	−46.4463	−1.70855	−0.854277	+	0.519818i	$0.826000\pi$
$740$	13.8074	0.507569
$741$	19.2489	0.707124
$742$	18.5390	0.680589
$743$	−45.9238	−1.68478	−0.842391	−	0.538867i	$-0.818853\pi$
$743$	−45.9238	−1.68478	−0.842391	+	0.538867i	$0.818853\pi$
$744$	34.1168	1.25078
$745$	−3.96997	−0.145448
$746$	78.4049	2.87061
$747$	0.402910	0.0147417
$748$	17.7581	0.649300
$749$	1.31197	0.0479383
$750$	21.8889	0.799270
$751$	−35.2859	−1.28760	−0.643800	−	0.765194i	$-0.722643\pi$
$751$	−35.2859	−1.28760	−0.643800	+	0.765194i	$0.722643\pi$
$752$	13.0841	0.477127
$753$	28.2748	1.03039
$754$	30.6353	1.11567
$755$	3.13128	0.113959
$756$	−19.0622	−0.693287
$757$	18.1365	0.659181	0.329590	−	0.944124i	$-0.393089\pi$
$757$	18.1365	0.659181	0.329590	+	0.944124i	$0.393089\pi$
$758$	63.8651	2.31968
$759$	5.98783	0.217344
$760$	−6.97477	−0.253001
$761$	9.26802	0.335965	0.167983	−	0.985790i	$-0.446275\pi$
$761$	9.26802	0.335965	0.167983	+	0.985790i	$0.446275\pi$
$762$	−28.7657	−1.04207
$763$	5.26357	0.190554
$764$	15.6928	0.567745
$765$	−0.0343757	−0.00124285
$766$	63.2827	2.28650
$767$	−46.7322	−1.68740
$768$	56.2990	2.03151
$769$	−52.9619	−1.90985	−0.954927	−	0.296840i	$-0.904067\pi$
$769$	−52.9619	−1.90985	−0.954927	+	0.296840i	$0.904067\pi$
$770$	−2.92170	−0.105291
$771$	−32.2181	−1.16031
$772$	−97.5468	−3.51079
$773$	8.92197	0.320901	0.160451	−	0.987044i	$-0.448705\pi$
$773$	8.92197	0.320901	0.160451	+	0.987044i	$0.448705\pi$
$774$	0.00300694	0.000108082 0
$775$	−18.4016	−0.661005
$776$	−78.5967	−2.82146
$777$	−10.3366	−0.370822
$778$	−20.0031	−0.717147
$779$	3.42656	0.122769
$780$	15.4846	0.554438
$781$	26.9408	0.964016
$782$	6.04083	0.216020
$783$	−15.3871	−0.549891
$784$	−26.3159	−0.939854
$785$	−5.28430	−0.188605
$786$	15.8907	0.566801
$787$	−4.23540	−0.150976	−0.0754879	−	0.997147i	$-0.524051\pi$
$787$	−4.23540	−0.150976	−0.0754879	+	0.997147i	$0.524051\pi$
$788$	82.4056	2.93558
$789$	−5.26471	−0.187429
$790$	−2.64562	−0.0941268
$791$	−9.95671	−0.354020
$792$	−0.459817	−0.0163389
$793$	41.9396	1.48932
$794$	16.3455	0.580081
$795$	7.56396	0.268266
$796$	44.3511	1.57198
$797$	−18.0320	−0.638728	−0.319364	−	0.947632i	$-0.603469\pi$
$797$	−18.0320	−0.638728	−0.319364	+	0.947632i	$0.603469\pi$
$798$	10.3300	0.365678
$799$	5.43313	0.192210
$800$	2.07763	0.0734552
$801$	−0.176929	−0.00625148
$802$	65.9577	2.32905
$803$	−5.07936	−0.179247
$804$	100.477	3.54355
$805$	−0.665015	−0.0234387
$806$	−40.0474	−1.41061
$807$	3.51528	0.123744
$808$	−5.70266	−0.200619
$809$	6.07008	0.213413	0.106706	−	0.994291i	$-0.465970\pi$
$809$	6.07008	0.213413	0.106706	+	0.994291i	$0.465970\pi$
$810$	−11.7667	−0.413439
$811$	−3.74997	−0.131679	−0.0658396	−	0.997830i	$-0.520973\pi$
$811$	−3.74997	−0.131679	−0.0658396	+	0.997830i	$0.520973\pi$
$812$	11.0005	0.386042
$813$	−18.5849	−0.651801
$814$	39.5863	1.38750
$815$	−9.76584	−0.342082
$816$	−13.1778	−0.461315
$817$	0.0874981	0.00306117
$818$	67.8042	2.37072
$819$	−0.140936	−0.00492470
$820$	2.75647	0.0962603
$821$	8.18468	0.285647	0.142824	−	0.989748i	$-0.454382\pi$
$821$	8.18468	0.285647	0.142824	+	0.989748i	$0.454382\pi$
$822$	−70.0447	−2.44309
$823$	−47.5914	−1.65893	−0.829466	−	0.558558i	$-0.811355\pi$
$823$	−47.5914	−1.65893	−0.829466	+	0.558558i	$0.811355\pi$
$824$	41.0106	1.42867
$825$	20.3993	0.710212
$826$	−25.0791	−0.872612
$827$	21.1256	0.734610	0.367305	−	0.930101i	$-0.380281\pi$
$827$	21.1256	0.734610	0.367305	+	0.930101i	$0.380281\pi$
$828$	−0.207055	−0.00719567
$829$	19.0409	0.661316	0.330658	−	0.943751i	$-0.392729\pi$
$829$	19.0409	0.661316	0.330658	+	0.943751i	$0.392729\pi$
$830$	14.0956	0.489264
$831$	42.3919	1.47056
$832$	−31.1681	−1.08056
$833$	−10.9276	−0.378620
$834$	−0.663099	−0.0229613
$835$	−11.1700	−0.386555
$836$	−26.4706	−0.915505
$837$	20.1145	0.695260
$838$	65.4699	2.26162
$839$	12.9587	0.447383	0.223692	−	0.974660i	$-0.428189\pi$
$839$	12.9587	0.447383	0.223692	+	0.974660i	$0.428189\pi$
$840$	4.20039	0.144927
$841$	−20.1204	−0.693805
$842$	71.5833	2.46692
$843$	4.19662	0.144539
$844$	66.6734	2.29499
$845$	−2.35731	−0.0810939
$846$	−0.278320	−0.00956884
$847$	4.43600	0.152423
$848$	35.2531	1.21060
$849$	−34.9739	−1.20030
$850$	20.5799	0.705884
$851$	9.01033	0.308870
$852$	−76.6249	−2.62512
$853$	−31.3891	−1.07474	−0.537372	−	0.843345i	$-0.680583\pi$
$853$	−31.3891	−1.07474	−0.537372	+	0.843345i	$0.680583\pi$
$854$	22.5071	0.770177
$855$	0.0512412	0.00175241
$856$	7.22348	0.246894
$857$	26.1070	0.891797	0.445899	−	0.895083i	$-0.352884\pi$
$857$	26.1070	0.891797	0.445899	+	0.895083i	$0.352884\pi$
$858$	44.3950	1.51562
$859$	10.1402	0.345980	0.172990	−	0.984924i	$-0.444657\pi$
$859$	10.1402	0.345980	0.172990	+	0.984924i	$0.444657\pi$
$860$	0.0703873	0.00240019
$861$	−2.06357	−0.0703262
$862$	−40.9725	−1.39553
$863$	−35.0391	−1.19274	−0.596372	−	0.802708i	$-0.703392\pi$
$863$	−35.0391	−1.19274	−0.596372	+	0.802708i	$0.703392\pi$
$864$	−2.27103	−0.0772619
$865$	−2.22760	−0.0757407
$866$	−21.1049	−0.717173
$867$	24.1535	0.820294
$868$	−14.3802	−0.488095
$869$	−5.07523	−0.172165
$870$	6.70779	0.227415
$871$	−59.6165	−2.02003
$872$	28.9803	0.981398
$873$	0.577423	0.0195428
$874$	−9.00461	−0.304585
$875$	−4.66353	−0.157656
$876$	14.4467	0.488109
$877$	−2.95494	−0.0997813	−0.0498907	−	0.998755i	$-0.515887\pi$
$877$	−2.95494	−0.0997813	−0.0498907	+	0.998755i	$0.515887\pi$
$878$	55.4139	1.87013
$879$	−11.8093	−0.398317
$880$	−5.55580	−0.187286
$881$	19.5634	0.659107	0.329554	−	0.944137i	$-0.393102\pi$
$881$	19.5634	0.659107	0.329554	+	0.944137i	$0.393102\pi$
$882$	0.559783	0.0188489
$883$	−30.1358	−1.01415	−0.507076	−	0.861901i	$-0.669274\pi$
$883$	−30.1358	−1.01415	−0.507076	+	0.861901i	$0.669274\pi$
$884$	29.9679	1.00793
$885$	−10.2323	−0.343955
$886$	11.7163	0.393617
$887$	41.4684	1.39237	0.696187	−	0.717860i	$-0.254878\pi$
$887$	41.4684	1.39237	0.696187	+	0.717860i	$0.254878\pi$
$888$	−56.9114	−1.90982
$889$	6.12866	0.205549
$890$	−6.18975	−0.207481
$891$	−22.5727	−0.756213
$892$	53.6991	1.79798
$893$	−8.09875	−0.271014
$894$	32.3728	1.08271
$895$	13.2506	0.442919
$896$	−17.5295	−0.585618
$897$	10.1048	0.337391
$898$	−47.2026	−1.57517
$899$	−11.6078	−0.387140
$900$	−0.705394	−0.0235131
$901$	14.6388	0.487689
$902$	7.90292	0.263138
$903$	−0.0526937	−0.00175354
$904$	−54.8200	−1.82329
$905$	−7.94927	−0.264243
$906$	−25.5338	−0.848303
$907$	54.0945	1.79618	0.898089	−	0.439813i	$-0.144955\pi$
$907$	54.0945	1.79618	0.898089	+	0.439813i	$0.144955\pi$
$908$	101.465	3.36724
$909$	0.0418955	0.00138958
$910$	−4.93055	−0.163446
$911$	−21.6332	−0.716739	−0.358369	−	0.933580i	$-0.616667\pi$
$911$	−21.6332	−0.716739	−0.358369	+	0.933580i	$0.616667\pi$
$912$	19.6431	0.650449
$913$	27.0403	0.894903
$914$	61.2576	2.02622
$915$	9.18294	0.303579
$916$	−34.3025	−1.13339
$917$	−3.38558	−0.111802
$918$	−22.4956	−0.742465
$919$	47.3259	1.56114	0.780568	−	0.625070i	$-0.214930\pi$
$919$	47.3259	1.56114	0.780568	+	0.625070i	$0.214930\pi$
$920$	−3.66146	−0.120715
$921$	25.9711	0.855777
$922$	64.9465	2.13890
$923$	45.4642	1.49647
$924$	15.9413	0.524431
$925$	30.6963	1.00929
$926$	−35.5182	−1.16720
$927$	−0.301290	−0.00989568
$928$	1.31057	0.0430216
$929$	−22.0567	−0.723656	−0.361828	−	0.932245i	$-0.617847\pi$
$929$	−22.0567	−0.723656	−0.361828	+	0.932245i	$0.617847\pi$
$930$	−8.76863	−0.287535
$931$	16.2890	0.533849
$932$	−61.5608	−2.01649
$933$	40.2816	1.31876
$934$	48.4577	1.58558
$935$	−2.30703	−0.0754480
$936$	−0.775970	−0.0253634
$937$	−12.1536	−0.397042	−0.198521	−	0.980097i	$-0.563614\pi$
$937$	−12.1536	−0.397042	−0.198521	+	0.980097i	$0.563614\pi$
$938$	−31.9935	−1.04462
$939$	−17.5601	−0.573051
$940$	−6.51498	−0.212495
$941$	−9.30261	−0.303256	−0.151628	−	0.988438i	$-0.548452\pi$
$941$	−9.30261	−0.303256	−0.151628	+	0.988438i	$0.548452\pi$
$942$	43.0905	1.40396
$943$	1.79880	0.0585770
$944$	−47.6894	−1.55216
$945$	2.47646	0.0805593
$946$	0.201803	0.00656118
$947$	19.5379	0.634897	0.317449	−	0.948275i	$-0.397174\pi$
$947$	19.5379	0.634897	0.317449	+	0.948275i	$0.397174\pi$
$948$	14.4350	0.468826
$949$	−8.57174	−0.278250
$950$	−30.6768	−0.995288
$951$	12.0486	0.390703
$952$	8.12916	0.263468
$953$	−12.8769	−0.417122	−0.208561	−	0.978009i	$-0.566878\pi$
$953$	−12.8769	−0.417122	−0.208561	+	0.978009i	$0.566878\pi$
$954$	−0.749893	−0.0242787
$955$	−2.03872	−0.0659714
$956$	1.00237	0.0324189
$957$	12.8679	0.415960
$958$	19.3402	0.624853
$959$	14.9233	0.481899
$960$	−6.82446	−0.220258
$961$	−15.8260	−0.510515
$962$	66.8044	2.15386
$963$	−0.0530684	−0.00171010
$964$	−85.9486	−2.76822
$965$	12.6727	0.407950
$966$	5.42282	0.174476
$967$	1.11625	0.0358960	0.0179480	−	0.999839i	$-0.494287\pi$
$967$	1.11625	0.0358960	0.0179480	+	0.999839i	$0.494287\pi$
$968$	24.4239	0.785014
$969$	8.15677	0.262033
$970$	20.2008	0.648607
$971$	−31.0693	−0.997061	−0.498530	−	0.866872i	$-0.666127\pi$
$971$	−31.0693	−0.997061	−0.498530	+	0.866872i	$0.666127\pi$
$972$	1.55172	0.0497715
$973$	0.141276	0.00452911
$974$	35.5332	1.13856
$975$	34.4251	1.10249
$976$	42.7987	1.36995
$977$	5.65932	0.181058	0.0905288	−	0.995894i	$-0.471144\pi$
$977$	5.65932	0.181058	0.0905288	+	0.995894i	$0.471144\pi$
$978$	79.6348	2.54644
$979$	−11.8741	−0.379499
$980$	13.1036	0.418578
$981$	−0.212908	−0.00679764
$982$	−103.707	−3.30941
$983$	−16.5052	−0.526434	−0.263217	−	0.964737i	$-0.584784\pi$
$983$	−16.5052	−0.526434	−0.263217	+	0.964737i	$0.584784\pi$
$984$	−11.3617	−0.362197
$985$	−10.7057	−0.341112
$986$	12.9818	0.413425
$987$	4.87728	0.155246
$988$	−44.6709	−1.42117
$989$	0.0459328	0.00146058
$990$	0.118181	0.00375604
$991$	−17.6147	−0.559550	−0.279775	−	0.960066i	$-0.590260\pi$
$991$	−17.6147	−0.559550	−0.279775	+	0.960066i	$0.590260\pi$
$992$	−1.71322	−0.0543947
$993$	29.7008	0.942526
$994$	24.3986	0.773877
$995$	−5.76186	−0.182663
$996$	−76.9080	−2.43692
$997$	6.70596	0.212380	0.106190	−	0.994346i	$-0.466135\pi$
$997$	6.70596	0.212380	0.106190	+	0.994346i	$0.466135\pi$
$998$	18.1473	0.574442
$999$	−33.5538	−1.06159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.11	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.11	✓	149	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45850 q^{2} -1.74268 q^{3} +4.04423 q^{4} -0.525405 q^{5} +4.28438 q^{6} -0.912805 q^{7} -5.02575 q^{8} +0.0369224 q^{9} +O(q^{10})\)	\(q-2.45850 q^{2} -1.74268 q^{3} +4.04423 q^{4} -0.525405 q^{5} +4.28438 q^{6} -0.912805 q^{7} -5.02575 q^{8} +0.0369224 q^{9} +1.29171 q^{10} +2.47795 q^{11} -7.04779 q^{12} +4.18171 q^{13} +2.24413 q^{14} +0.915610 q^{15} +4.26736 q^{16} +1.77201 q^{17} -0.0907739 q^{18} -2.64140 q^{19} -2.12486 q^{20} +1.59072 q^{21} -6.09205 q^{22} -1.38663 q^{23} +8.75826 q^{24} -4.72395 q^{25} -10.2807 q^{26} +5.16369 q^{27} -3.69160 q^{28} -2.97987 q^{29} -2.25103 q^{30} +3.89539 q^{31} -0.439807 q^{32} -4.31827 q^{33} -4.35650 q^{34} +0.479592 q^{35} +0.149323 q^{36} -6.49802 q^{37} +6.49390 q^{38} -7.28736 q^{39} +2.64055 q^{40} -1.29725 q^{41} -3.91080 q^{42} -0.0331256 q^{43} +10.0214 q^{44} -0.0193992 q^{45} +3.40902 q^{46} +3.06608 q^{47} -7.43663 q^{48} -6.16679 q^{49} +11.6138 q^{50} -3.08804 q^{51} +16.9118 q^{52} +8.26111 q^{53} -12.6949 q^{54} -1.30193 q^{55} +4.58753 q^{56} +4.60311 q^{57} +7.32603 q^{58} -11.1754 q^{59} +3.70294 q^{60} +10.0293 q^{61} -9.57681 q^{62} -0.0337030 q^{63} -7.45345 q^{64} -2.19709 q^{65} +10.6165 q^{66} -14.2565 q^{67} +7.16643 q^{68} +2.41644 q^{69} -1.17908 q^{70} +10.8722 q^{71} -0.185563 q^{72} -2.04982 q^{73} +15.9754 q^{74} +8.23232 q^{75} -10.6825 q^{76} -2.26189 q^{77} +17.9160 q^{78} -2.04815 q^{79} -2.24209 q^{80} -9.10940 q^{81} +3.18929 q^{82} +10.9123 q^{83} +6.43326 q^{84} -0.931023 q^{85} +0.0814394 q^{86} +5.19296 q^{87} -12.4536 q^{88} -4.79191 q^{89} +0.0476930 q^{90} -3.81708 q^{91} -5.60784 q^{92} -6.78840 q^{93} -7.53796 q^{94} +1.38781 q^{95} +0.766442 q^{96} +15.6388 q^{97} +15.1611 q^{98} +0.0914921 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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