LMFDB - Embedded newform 4021.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, 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("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55186 q^{2} -0.0699266 q^{3} +4.51199 q^{4} -3.83680 q^{5} +0.178443 q^{6} +5.05477 q^{7} -6.41025 q^{8} -2.99511 q^{9} +O(q^{10})$	\(q-2.55186 q^{2} -0.0699266 q^{3} +4.51199 q^{4} -3.83680 q^{5} +0.178443 q^{6} +5.05477 q^{7} -6.41025 q^{8} -2.99511 q^{9} +9.79098 q^{10} -3.29610 q^{11} -0.315508 q^{12} +0.104999 q^{13} -12.8991 q^{14} +0.268294 q^{15} +7.33408 q^{16} -4.20070 q^{17} +7.64310 q^{18} -6.70384 q^{19} -17.3116 q^{20} -0.353463 q^{21} +8.41119 q^{22} +6.20974 q^{23} +0.448247 q^{24} +9.72105 q^{25} -0.267943 q^{26} +0.419217 q^{27} +22.8071 q^{28} +7.54890 q^{29} -0.684650 q^{30} +7.66074 q^{31} -5.89504 q^{32} +0.230485 q^{33} +10.7196 q^{34} -19.3942 q^{35} -13.5139 q^{36} -0.991053 q^{37} +17.1073 q^{38} -0.00734224 q^{39} +24.5949 q^{40} +11.1283 q^{41} +0.901988 q^{42} -5.32191 q^{43} -14.8720 q^{44} +11.4916 q^{45} -15.8464 q^{46} -7.10812 q^{47} -0.512847 q^{48} +18.5507 q^{49} -24.8068 q^{50} +0.293740 q^{51} +0.473756 q^{52} -0.425922 q^{53} -1.06978 q^{54} +12.6465 q^{55} -32.4024 q^{56} +0.468776 q^{57} -19.2637 q^{58} -4.35401 q^{59} +1.21054 q^{60} -1.28873 q^{61} -19.5491 q^{62} -15.1396 q^{63} +0.375164 q^{64} -0.402861 q^{65} -0.588166 q^{66} -14.6493 q^{67} -18.9535 q^{68} -0.434226 q^{69} +49.4912 q^{70} +2.79688 q^{71} +19.1994 q^{72} -0.264229 q^{73} +2.52903 q^{74} -0.679760 q^{75} -30.2476 q^{76} -16.6610 q^{77} +0.0187364 q^{78} -1.50862 q^{79} -28.1394 q^{80} +8.95602 q^{81} -28.3978 q^{82} +12.8104 q^{83} -1.59482 q^{84} +16.1173 q^{85} +13.5808 q^{86} -0.527869 q^{87} +21.1288 q^{88} +3.43528 q^{89} -29.3251 q^{90} +0.530747 q^{91} +28.0183 q^{92} -0.535689 q^{93} +18.1389 q^{94} +25.7213 q^{95} +0.412220 q^{96} +6.27274 q^{97} -47.3389 q^{98} +9.87219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.55186	−1.80444	−0.902219	−	0.431279i	$-0.858063\pi$
$2$	−2.55186	−1.80444	−0.902219	+	0.431279i	$0.858063\pi$
$3$	−0.0699266	−0.0403721	−0.0201861	−	0.999796i	$-0.506426\pi$
$3$	−0.0699266	−0.0403721	−0.0201861	+	0.999796i	$0.506426\pi$
$4$	4.51199	2.25600
$5$	−3.83680	−1.71587	−0.857935	−	0.513758i	$-0.828253\pi$
$5$	−3.83680	−1.71587	−0.857935	+	0.513758i	$0.828253\pi$
$6$	0.178443	0.0728490
$7$	5.05477	1.91052	0.955262	−	0.295759i	$-0.0955726\pi$
$7$	5.05477	1.91052	0.955262	+	0.295759i	$0.0955726\pi$
$8$	−6.41025	−2.26636
$9$	−2.99511	−0.998370
$10$	9.79098	3.09618
$11$	−3.29610	−0.993812	−0.496906	−	0.867804i	$-0.665531\pi$
$11$	−3.29610	−0.993812	−0.496906	+	0.867804i	$0.665531\pi$
$12$	−0.315508	−0.0910793
$13$	0.104999	0.0291216	0.0145608	−	0.999894i	$-0.495365\pi$
$13$	0.104999	0.0291216	0.0145608	+	0.999894i	$0.495365\pi$
$14$	−12.8991	−3.44742
$15$	0.268294	0.0692733
$16$	7.33408	1.83352
$17$	−4.20070	−1.01882	−0.509410	−	0.860524i	$-0.670136\pi$
$17$	−4.20070	−1.01882	−0.509410	+	0.860524i	$0.670136\pi$
$18$	7.64310	1.80150
$19$	−6.70384	−1.53797	−0.768983	−	0.639270i	$-0.779237\pi$
$19$	−6.70384	−1.53797	−0.768983	+	0.639270i	$0.779237\pi$
$20$	−17.3116	−3.87099
$21$	−0.353463	−0.0771319
$22$	8.41119	1.79327
$23$	6.20974	1.29482	0.647410	−	0.762142i	$-0.275852\pi$
$23$	6.20974	1.29482	0.647410	+	0.762142i	$0.275852\pi$
$24$	0.448247	0.0914980
$25$	9.72105	1.94421
$26$	−0.267943	−0.0525480
$27$	0.419217	0.0806784
$28$	22.8071	4.31013
$29$	7.54890	1.40180	0.700898	−	0.713262i	$-0.252783\pi$
$29$	7.54890	1.40180	0.700898	+	0.713262i	$0.252783\pi$
$30$	−0.684650	−0.124999
$31$	7.66074	1.37591	0.687955	−	0.725753i	$-0.258509\pi$
$31$	7.66074	1.37591	0.687955	+	0.725753i	$0.258509\pi$
$32$	−5.89504	−1.04211
$33$	0.230485	0.0401223
$34$	10.7196	1.83840
$35$	−19.3942	−3.27821
$36$	−13.5139	−2.25232
$37$	−0.991053	−0.162928	−0.0814641	−	0.996676i	$-0.525960\pi$
$37$	−0.991053	−0.162928	−0.0814641	+	0.996676i	$0.525960\pi$
$38$	17.1073	2.77516
$39$	−0.00734224	−0.00117570
$40$	24.5949	3.88879
$41$	11.1283	1.73794	0.868972	−	0.494861i	$-0.164781\pi$
$41$	11.1283	1.73794	0.868972	+	0.494861i	$0.164781\pi$
$42$	0.901988	0.139180
$43$	−5.32191	−0.811584	−0.405792	−	0.913965i	$-0.633004\pi$
$43$	−5.32191	−0.811584	−0.405792	+	0.913965i	$0.633004\pi$
$44$	−14.8720	−2.24203
$45$	11.4916	1.71307
$46$	−15.8464	−2.33642
$47$	−7.10812	−1.03683	−0.518413	−	0.855130i	$-0.673477\pi$
$47$	−7.10812	−1.03683	−0.518413	+	0.855130i	$0.673477\pi$
$48$	−0.512847	−0.0740230
$49$	18.5507	2.65011
$50$	−24.8068	−3.50821
$51$	0.293740	0.0411319
$52$	0.473756	0.0656981
$53$	−0.425922	−0.0585049	−0.0292524	−	0.999572i	$-0.509313\pi$
$53$	−0.425922	−0.0585049	−0.0292524	+	0.999572i	$0.509313\pi$
$54$	−1.06978	−0.145579
$55$	12.6465	1.70525
$56$	−32.4024	−4.32995
$57$	0.468776	0.0620909
$58$	−19.2637	−2.52945
$59$	−4.35401	−0.566844	−0.283422	−	0.958995i	$-0.591470\pi$
$59$	−4.35401	−0.566844	−0.283422	+	0.958995i	$0.591470\pi$
$60$	1.21054	0.156280
$61$	−1.28873	−0.165005	−0.0825023	−	0.996591i	$-0.526291\pi$
$61$	−1.28873	−0.165005	−0.0825023	+	0.996591i	$0.526291\pi$
$62$	−19.5491	−2.48274
$63$	−15.1396	−1.90741
$64$	0.375164	0.0468956
$65$	−0.402861	−0.0499688
$66$	−0.588166	−0.0723982
$67$	−14.6493	−1.78970	−0.894849	−	0.446368i	$-0.852717\pi$
$67$	−14.6493	−1.78970	−0.894849	+	0.446368i	$0.852717\pi$
$68$	−18.9535	−2.29845
$69$	−0.434226	−0.0522746
$70$	49.4912	5.91533
$71$	2.79688	0.331929	0.165964	−	0.986132i	$-0.446926\pi$
$71$	2.79688	0.331929	0.165964	+	0.986132i	$0.446926\pi$
$72$	19.1994	2.26267
$73$	−0.264229	−0.0309257	−0.0154628	−	0.999880i	$-0.504922\pi$
$73$	−0.264229	−0.0309257	−0.0154628	+	0.999880i	$0.504922\pi$
$74$	2.52903	0.293994
$75$	−0.679760	−0.0784919
$76$	−30.2476	−3.46964
$77$	−16.6610	−1.89870
$78$	0.0187364	0.00212148
$79$	−1.50862	−0.169733	−0.0848663	−	0.996392i	$-0.527046\pi$
$79$	−1.50862	−0.169733	−0.0848663	+	0.996392i	$0.527046\pi$
$80$	−28.1394	−3.14608
$81$	8.95602	0.995113
$82$	−28.3978	−3.13601
$83$	12.8104	1.40612	0.703060	−	0.711131i	$-0.251817\pi$
$83$	12.8104	1.40612	0.703060	+	0.711131i	$0.251817\pi$
$84$	−1.59482	−0.174009
$85$	16.1173	1.74816
$86$	13.5808	1.46445
$87$	−0.527869	−0.0565935
$88$	21.1288	2.25234
$89$	3.43528	0.364139	0.182070	−	0.983286i	$-0.441720\pi$
$89$	3.43528	0.364139	0.182070	+	0.983286i	$0.441720\pi$
$90$	−29.3251	−3.09113
$91$	0.530747	0.0556375
$92$	28.0183	2.92111
$93$	−0.535689	−0.0555484
$94$	18.1389	1.87089
$95$	25.7213	2.63895
$96$	0.412220	0.0420720
$97$	6.27274	0.636900	0.318450	−	0.947940i	$-0.396838\pi$
$97$	6.27274	0.636900	0.318450	+	0.947940i	$0.396838\pi$
$98$	−47.3389	−4.78195
$99$	9.87219	0.992192
$100$	43.8613	4.38613
$101$	−18.4475	−1.83559	−0.917797	−	0.397050i	$-0.870034\pi$
$101$	−18.4475	−1.83559	−0.917797	+	0.397050i	$0.870034\pi$
$102$	−0.749585	−0.0742199
$103$	2.40901	0.237367	0.118684	−	0.992932i	$-0.462133\pi$
$103$	2.40901	0.237367	0.118684	+	0.992932i	$0.462133\pi$
$104$	−0.673071	−0.0660001
$105$	1.35617	0.132348
$106$	1.08689	0.105568
$107$	−3.76410	−0.363889	−0.181945	−	0.983309i	$-0.558239\pi$
$107$	−3.76410	−0.363889	−0.181945	+	0.983309i	$0.558239\pi$
$108$	1.89151	0.182010
$109$	10.0952	0.966950	0.483475	−	0.875358i	$-0.339374\pi$
$109$	10.0952	0.966950	0.483475	+	0.875358i	$0.339374\pi$
$110$	−32.2721	−3.07702
$111$	0.0693009	0.00657775
$112$	37.0721	3.50298
$113$	1.67540	0.157608	0.0788041	−	0.996890i	$-0.474890\pi$
$113$	1.67540	0.157608	0.0788041	+	0.996890i	$0.474890\pi$
$114$	−1.19625	−0.112039
$115$	−23.8255	−2.22174
$116$	34.0606	3.16244
$117$	−0.314484	−0.0290741
$118$	11.1108	1.02283
$119$	−21.2336	−1.94648
$120$	−1.71983	−0.156999
$121$	−0.135718	−0.0123380
$122$	3.28865	0.297740
$123$	−0.778162	−0.0701645
$124$	34.5652	3.10405
$125$	−18.1138	−1.62014
$126$	38.6342	3.44180
$127$	3.73200	0.331162	0.165581	−	0.986196i	$-0.447050\pi$
$127$	3.73200	0.331162	0.165581	+	0.986196i	$0.447050\pi$
$128$	10.8327	0.957485
$129$	0.372143	0.0327654
$130$	1.02805	0.0901656
$131$	−10.0037	−0.874031	−0.437015	−	0.899454i	$-0.643964\pi$
$131$	−10.0037	−0.874031	−0.437015	+	0.899454i	$0.643964\pi$
$132$	1.03995	0.0905157
$133$	−33.8864	−2.93832
$134$	37.3830	3.22940
$135$	−1.60845	−0.138434
$136$	26.9275	2.30902
$137$	1.93052	0.164936	0.0824679	−	0.996594i	$-0.473720\pi$
$137$	1.93052	0.164936	0.0824679	+	0.996594i	$0.473720\pi$
$138$	1.10808	0.0943263
$139$	18.1287	1.53766	0.768830	−	0.639454i	$-0.220839\pi$
$139$	18.1287	1.53766	0.768830	+	0.639454i	$0.220839\pi$
$140$	−87.5063	−7.39563
$141$	0.497047	0.0418589
$142$	−7.13725	−0.598945
$143$	−0.346088	−0.0289413
$144$	−21.9664	−1.83053
$145$	−28.9636	−2.40530
$146$	0.674276	0.0558034
$147$	−1.29719	−0.106990
$148$	−4.47162	−0.367565
$149$	21.8520	1.79019	0.895094	−	0.445878i	$-0.147108\pi$
$149$	21.8520	1.79019	0.895094	+	0.445878i	$0.147108\pi$
$150$	1.73465	0.141634
$151$	−17.3909	−1.41525	−0.707626	−	0.706587i	$-0.750234\pi$
$151$	−17.3909	−1.41525	−0.707626	+	0.706587i	$0.750234\pi$
$152$	42.9732	3.48559
$153$	12.5816	1.01716
$154$	42.5167	3.42609
$155$	−29.3928	−2.36088
$156$	−0.0331281	−0.00265237
$157$	−3.40046	−0.271386	−0.135693	−	0.990751i	$-0.543326\pi$
$157$	−3.40046	−0.271386	−0.135693	+	0.990751i	$0.543326\pi$
$158$	3.84978	0.306272
$159$	0.0297833	0.00236197
$160$	22.6181	1.78812
$161$	31.3888	2.47379
$162$	−22.8545	−1.79562
$163$	14.6356	1.14635	0.573173	−	0.819434i	$-0.305712\pi$
$163$	14.6356	1.14635	0.573173	+	0.819434i	$0.305712\pi$
$164$	50.2107	3.92079
$165$	−0.884325	−0.0688446
$166$	−32.6902	−2.53726
$167$	13.4307	1.03930	0.519651	−	0.854379i	$-0.326062\pi$
$167$	13.4307	1.03930	0.519651	+	0.854379i	$0.326062\pi$
$168$	2.26579	0.174809
$169$	−12.9890	−0.999152
$170$	−41.1290	−3.15445
$171$	20.0787	1.53546
$172$	−24.0124	−1.83093
$173$	−13.4586	−1.02324	−0.511621	−	0.859211i	$-0.670955\pi$
$173$	−13.4586	−1.02324	−0.511621	+	0.859211i	$0.670955\pi$
$174$	1.34705	0.102119
$175$	49.1377	3.71446
$176$	−24.1739	−1.82217
$177$	0.304461	0.0228847
$178$	−8.76636	−0.657066
$179$	−21.4162	−1.60072	−0.800362	−	0.599517i	$-0.795359\pi$
$179$	−21.4162	−1.60072	−0.800362	+	0.599517i	$0.795359\pi$
$180$	51.8502	3.86469
$181$	−17.0020	−1.26375	−0.631874	−	0.775071i	$-0.717714\pi$
$181$	−17.0020	−1.26375	−0.631874	+	0.775071i	$0.717714\pi$
$182$	−1.35439	−0.100394
$183$	0.0901162	0.00666158
$184$	−39.8060	−2.93453
$185$	3.80247	0.279563
$186$	1.36700	0.100234
$187$	13.8459	1.01251
$188$	−32.0718	−2.33908
$189$	2.11905	0.154138
$190$	−65.6371	−4.76182
$191$	−16.9262	−1.22474	−0.612369	−	0.790572i	$-0.709783\pi$
$191$	−16.9262	−1.22474	−0.612369	+	0.790572i	$0.709783\pi$
$192$	−0.0262340	−0.00189327
$193$	4.25800	0.306498	0.153249	−	0.988188i	$-0.451026\pi$
$193$	4.25800	0.306498	0.153249	+	0.988188i	$0.451026\pi$
$194$	−16.0071	−1.14925
$195$	0.0281707	0.00201735
$196$	83.7008	5.97863
$197$	2.42449	0.172737	0.0863687	−	0.996263i	$-0.472474\pi$
$197$	2.42449	0.172737	0.0863687	+	0.996263i	$0.472474\pi$
$198$	−25.1924	−1.79035
$199$	13.6794	0.969704	0.484852	−	0.874596i	$-0.338873\pi$
$199$	13.6794	0.969704	0.484852	+	0.874596i	$0.338873\pi$
$200$	−62.3144	−4.40629
$201$	1.02438	0.0722539
$202$	47.0754	3.31221
$203$	38.1580	2.67817
$204$	1.32535	0.0927933
$205$	−42.6970	−2.98209
$206$	−6.14747	−0.428314
$207$	−18.5988	−1.29271
$208$	0.770072	0.0533949
$209$	22.0965	1.52845
$210$	−3.46075	−0.238814
$211$	−11.5803	−0.797218	−0.398609	−	0.917121i	$-0.630507\pi$
$211$	−11.5803	−0.797218	−0.398609	+	0.917121i	$0.630507\pi$
$212$	−1.92176	−0.131987
$213$	−0.195576	−0.0134007
$214$	9.60545	0.656615
$215$	20.4191	1.39257
$216$	−2.68729	−0.182847
$217$	38.7233	2.62871
$218$	−25.7617	−1.74480
$219$	0.0184766	0.00124853
$220$	57.0608	3.84704
$221$	−0.441070	−0.0296696
$222$	−0.176846	−0.0118691
$223$	−23.5577	−1.57754	−0.788771	−	0.614687i	$-0.789282\pi$
$223$	−23.5577	−1.57754	−0.788771	+	0.614687i	$0.789282\pi$
$224$	−29.7981	−1.99097
$225$	−29.1156	−1.94104
$226$	−4.27538	−0.284394
$227$	−10.0661	−0.668112	−0.334056	−	0.942553i	$-0.608418\pi$
$227$	−10.0661	−0.668112	−0.334056	+	0.942553i	$0.608418\pi$
$228$	2.11511	0.140077
$229$	24.9055	1.64580	0.822902	−	0.568183i	$-0.192353\pi$
$229$	24.9055	1.64580	0.822902	+	0.568183i	$0.192353\pi$
$230$	60.7994	4.00900
$231$	1.16505	0.0766546
$232$	−48.3903	−3.17698
$233$	−23.8065	−1.55961	−0.779806	−	0.626021i	$-0.784682\pi$
$233$	−23.8065	−1.55961	−0.779806	+	0.626021i	$0.784682\pi$
$234$	0.802520	0.0524624
$235$	27.2725	1.77906
$236$	−19.6453	−1.27880
$237$	0.105492	0.00685247
$238$	54.1851	3.51230
$239$	−20.6144	−1.33343	−0.666716	−	0.745311i	$-0.732301\pi$
$239$	−20.6144	−1.33343	−0.666716	+	0.745311i	$0.732301\pi$
$240$	1.96769	0.127014
$241$	10.5754	0.681219	0.340609	−	0.940205i	$-0.389367\pi$
$241$	10.5754	0.681219	0.340609	+	0.940205i	$0.389367\pi$
$242$	0.346334	0.0222632
$243$	−1.88392	−0.120853
$244$	−5.81472	−0.372249
$245$	−71.1755	−4.54724
$246$	1.98576	0.126607
$247$	−0.703898	−0.0447879
$248$	−49.1073	−3.11831
$249$	−0.895784	−0.0567680
$250$	46.2238	2.92345
$251$	−0.00619179	−0.000390822 0	−0.000195411	−	1.00000i	$-0.500062\pi$
$251$	−0.00619179	−0.000390822 0	−0.000195411		1.00000i	$0.500062\pi$
$252$	−68.3098	−4.30311
$253$	−20.4679	−1.28681
$254$	−9.52355	−0.597560
$255$	−1.12702	−0.0705770
$256$	−28.3939	−1.77462
$257$	−0.677985	−0.0422916	−0.0211458	−	0.999776i	$-0.506731\pi$
$257$	−0.677985	−0.0422916	−0.0211458	+	0.999776i	$0.506731\pi$
$258$	−0.949657	−0.0591231
$259$	−5.00955	−0.311278
$260$	−1.81771	−0.112729
$261$	−22.6098	−1.39951
$262$	25.5281	1.57713
$263$	18.7153	1.15404	0.577018	−	0.816731i	$-0.304216\pi$
$263$	18.7153	1.15404	0.577018	+	0.816731i	$0.304216\pi$
$264$	−1.47747	−0.0909317
$265$	1.63418	0.100387
$266$	86.4733	5.30202
$267$	−0.240217	−0.0147011
$268$	−66.0976	−4.03755
$269$	−18.6097	−1.13465	−0.567326	−	0.823493i	$-0.692022\pi$
$269$	−18.6097	−1.13465	−0.567326	+	0.823493i	$0.692022\pi$
$270$	4.10455	0.249795
$271$	−23.8451	−1.44848	−0.724242	−	0.689546i	$-0.757810\pi$
$271$	−23.8451	−1.44848	−0.724242	+	0.689546i	$0.757810\pi$
$272$	−30.8082	−1.86802
$273$	−0.0371133	−0.00224620
$274$	−4.92643	−0.297616
$275$	−32.0416	−1.93218
$276$	−1.95922	−0.117931
$277$	2.36408	0.142044	0.0710220	−	0.997475i	$-0.477374\pi$
$277$	2.36408	0.142044	0.0710220	+	0.997475i	$0.477374\pi$
$278$	−46.2620	−2.77461
$279$	−22.9448	−1.37367
$280$	124.321	7.42963
$281$	1.94304	0.115912	0.0579561	−	0.998319i	$-0.481542\pi$
$281$	1.94304	0.115912	0.0579561	+	0.998319i	$0.481542\pi$
$282$	−1.26839	−0.0755317
$283$	25.8890	1.53894	0.769469	−	0.638684i	$-0.220521\pi$
$283$	25.8890	1.53894	0.769469	+	0.638684i	$0.220521\pi$
$284$	12.6195	0.748830
$285$	−1.79860	−0.106540
$286$	0.883168	0.0522228
$287$	56.2509	3.32039
$288$	17.6563	1.04041
$289$	0.645874	0.0379926
$290$	73.9112	4.34021
$291$	−0.438631	−0.0257130
$292$	−1.19220	−0.0697682
$293$	−20.0867	−1.17348	−0.586738	−	0.809777i	$-0.699588\pi$
$293$	−20.0867	−1.17348	−0.586738	+	0.809777i	$0.699588\pi$
$294$	3.31025	0.193057
$295$	16.7055	0.972631
$296$	6.35290	0.369255
$297$	−1.38178	−0.0801792
$298$	−55.7633	−3.23028
$299$	0.652018	0.0377072
$300$	−3.06707	−0.177077
$301$	−26.9011	−1.55055
$302$	44.3792	2.55373
$303$	1.28997	0.0741068
$304$	−49.1664	−2.81989
$305$	4.94459	0.283126
$306$	−32.1064	−1.83540
$307$	−0.0372543	−0.00212621	−0.00106311	−	0.999999i	$-0.500338\pi$
$307$	−0.0372543	−0.00212621	−0.00106311	+	0.999999i	$0.500338\pi$
$308$	−75.1745	−4.28346
$309$	−0.168454	−0.00958302
$310$	75.0062	4.26007
$311$	5.31652	0.301472	0.150736	−	0.988574i	$-0.451836\pi$
$311$	5.31652	0.301472	0.150736	+	0.988574i	$0.451836\pi$
$312$	0.0470656	0.00266456
$313$	0.881024	0.0497984	0.0248992	−	0.999690i	$-0.492074\pi$
$313$	0.881024	0.0497984	0.0248992	+	0.999690i	$0.492074\pi$
$314$	8.67750	0.489700
$315$	58.0877	3.27287
$316$	−6.80687	−0.382916
$317$	16.7395	0.940187	0.470093	−	0.882617i	$-0.344220\pi$
$317$	16.7395	0.940187	0.470093	+	0.882617i	$0.344220\pi$
$318$	−0.0760027	−0.00426202
$319$	−24.8819	−1.39312
$320$	−1.43943	−0.0804667
$321$	0.263211	0.0146910
$322$	−80.0999	−4.46379
$323$	28.1608	1.56691
$324$	40.4095	2.24497
$325$	1.02070	0.0566184
$326$	−37.3479	−2.06851
$327$	−0.705926	−0.0390378
$328$	−71.3350	−3.93882
$329$	−35.9300	−1.98088
$330$	2.25667	0.124226
$331$	3.54997	0.195124	0.0975620	−	0.995229i	$-0.468896\pi$
$331$	3.54997	0.195124	0.0975620	+	0.995229i	$0.468896\pi$
$332$	57.8002	3.17220
$333$	2.96831	0.162663
$334$	−34.2734	−1.87535
$335$	56.2065	3.07089
$336$	−2.59232	−0.141423
$337$	−27.5821	−1.50249	−0.751247	−	0.660021i	$-0.770547\pi$
$337$	−27.5821	−1.50249	−0.751247	+	0.660021i	$0.770547\pi$
$338$	33.1460	1.80291
$339$	−0.117155	−0.00636298
$340$	72.7209	3.94384
$341$	−25.2506	−1.36740
$342$	−51.2381	−2.77064
$343$	58.3864	3.15257
$344$	34.1148	1.83935
$345$	1.66604	0.0896965
$346$	34.3446	1.84638
$347$	−4.44577	−0.238662	−0.119331	−	0.992855i	$-0.538075\pi$
$347$	−4.44577	−0.238662	−0.119331	+	0.992855i	$0.538075\pi$
$348$	−2.38174	−0.127675
$349$	16.7492	0.896565	0.448283	−	0.893892i	$-0.352036\pi$
$349$	16.7492	0.896565	0.448283	+	0.893892i	$0.352036\pi$
$350$	−125.393	−6.70252
$351$	0.0440175	0.00234948
$352$	19.4306	1.03566
$353$	10.5532	0.561688	0.280844	−	0.959753i	$-0.409386\pi$
$353$	10.5532	0.561688	0.280844	+	0.959753i	$0.409386\pi$
$354$	−0.776942	−0.0412940
$355$	−10.7311	−0.569547
$356$	15.5000	0.821496
$357$	1.48479	0.0785835
$358$	54.6512	2.88841
$359$	−8.14562	−0.429909	−0.214955	−	0.976624i	$-0.568960\pi$
$359$	−8.14562	−0.429909	−0.214955	+	0.976624i	$0.568960\pi$
$360$	−73.6643	−3.88245
$361$	25.9414	1.36534
$362$	43.3867	2.28036
$363$	0.00949031	0.000498112 0
$364$	2.39473	0.125518
$365$	1.01379	0.0530644
$366$	−0.229964	−0.0120204
$367$	3.56361	0.186019	0.0930096	−	0.995665i	$-0.470351\pi$
$367$	3.56361	0.186019	0.0930096	+	0.995665i	$0.470351\pi$
$368$	45.5427	2.37408
$369$	−33.3304	−1.73511
$370$	−9.70338	−0.504455
$371$	−2.15294	−0.111775
$372$	−2.41703	−0.125317
$373$	−28.8752	−1.49510	−0.747551	−	0.664205i	$-0.768770\pi$
$373$	−28.8752	−1.49510	−0.747551	+	0.664205i	$0.768770\pi$
$374$	−35.3329	−1.82702
$375$	1.26663	0.0654086
$376$	45.5648	2.34983
$377$	0.792629	0.0408225
$378$	−5.40752	−0.278133
$379$	−19.0986	−0.981027	−0.490513	−	0.871434i	$-0.663191\pi$
$379$	−19.0986	−0.981027	−0.490513	+	0.871434i	$0.663191\pi$
$380$	116.054	5.95346
$381$	−0.260966	−0.0133697
$382$	43.1933	2.20996
$383$	−10.1817	−0.520258	−0.260129	−	0.965574i	$-0.583765\pi$
$383$	−10.1817	−0.520258	−0.260129	+	0.965574i	$0.583765\pi$
$384$	−0.757494	−0.0386557
$385$	63.9251	3.25793
$386$	−10.8658	−0.553056
$387$	15.9397	0.810261
$388$	28.3025	1.43684
$389$	20.1542	1.02186	0.510928	−	0.859623i	$-0.329302\pi$
$389$	20.1542	1.02186	0.510928	+	0.859623i	$0.329302\pi$
$390$	−0.0718877	−0.00364018
$391$	−26.0852	−1.31919
$392$	−118.915	−6.00611
$393$	0.699527	0.0352865
$394$	−6.18695	−0.311694
$395$	5.78827	0.291239
$396$	44.5432	2.23838
$397$	−16.7873	−0.842530	−0.421265	−	0.906938i	$-0.638414\pi$
$397$	−16.7873	−0.842530	−0.421265	+	0.906938i	$0.638414\pi$
$398$	−34.9078	−1.74977
$399$	2.36956	0.118626
$400$	71.2949	3.56475
$401$	9.31170	0.465004	0.232502	−	0.972596i	$-0.425309\pi$
$401$	9.31170	0.465004	0.232502	+	0.972596i	$0.425309\pi$
$402$	−2.61406	−0.130378
$403$	0.804372	0.0400686
$404$	−83.2349	−4.14109
$405$	−34.3625	−1.70748
$406$	−97.3738	−4.83258
$407$	3.26661	0.161920
$408$	−1.88295	−0.0932199
$409$	−1.45538	−0.0719637	−0.0359819	−	0.999352i	$-0.511456\pi$
$409$	−1.45538	−0.0719637	−0.0359819	+	0.999352i	$0.511456\pi$
$410$	108.957	5.38099
$411$	−0.134995	−0.00665881
$412$	10.8694	0.535499
$413$	−22.0085	−1.08297
$414$	47.4617	2.33261
$415$	−49.1508	−2.41272
$416$	−0.618975	−0.0303477
$417$	−1.26768	−0.0620786
$418$	−56.3872	−2.75799
$419$	36.0159	1.75949	0.879747	−	0.475442i	$-0.157712\pi$
$419$	36.0159	1.75949	0.879747	+	0.475442i	$0.157712\pi$
$420$	6.11901	0.298577
$421$	−17.1091	−0.833847	−0.416924	−	0.908942i	$-0.636892\pi$
$421$	−17.1091	−0.833847	−0.416924	+	0.908942i	$0.636892\pi$
$422$	29.5512	1.43853
$423$	21.2896	1.03514
$424$	2.73027	0.132593
$425$	−40.8352	−1.98080
$426$	0.499084	0.0241807
$427$	−6.51422	−0.315245
$428$	−16.9836	−0.820932
$429$	0.0242008	0.00116842
$430$	−52.1068	−2.51281
$431$	−12.0575	−0.580788	−0.290394	−	0.956907i	$-0.593786\pi$
$431$	−12.0575	−0.580788	−0.290394	+	0.956907i	$0.593786\pi$
$432$	3.07457	0.147925
$433$	−6.12824	−0.294505	−0.147252	−	0.989099i	$-0.547043\pi$
$433$	−6.12824	−0.294505	−0.147252	+	0.989099i	$0.547043\pi$
$434$	−98.8165	−4.74334
$435$	2.02533	0.0971070
$436$	45.5497	2.18143
$437$	−41.6291	−1.99139
$438$	−0.0471498	−0.00225290
$439$	−17.8873	−0.853715	−0.426857	−	0.904319i	$-0.640379\pi$
$439$	−17.8873	−0.853715	−0.426857	+	0.904319i	$0.640379\pi$
$440$	−81.0671	−3.86472
$441$	−55.5615	−2.64579
$442$	1.12555	0.0535369
$443$	−37.3692	−1.77546	−0.887732	−	0.460360i	$-0.847720\pi$
$443$	−37.3692	−1.77546	−0.887732	+	0.460360i	$0.847720\pi$
$444$	0.312685	0.0148394
$445$	−13.1805	−0.624815
$446$	60.1160	2.84658
$447$	−1.52804	−0.0722737
$448$	1.89637	0.0895951
$449$	−29.0342	−1.37021	−0.685104	−	0.728445i	$-0.740243\pi$
$449$	−29.0342	−1.37021	−0.685104	+	0.728445i	$0.740243\pi$
$450$	74.2990	3.50249
$451$	−36.6799	−1.72719
$452$	7.55938	0.355564
$453$	1.21609	0.0571367
$454$	25.6874	1.20557
$455$	−2.03637	−0.0954666
$456$	−3.00497	−0.140721
$457$	−32.1162	−1.50233	−0.751167	−	0.660112i	$-0.770509\pi$
$457$	−32.1162	−1.50233	−0.751167	+	0.660112i	$0.770509\pi$
$458$	−63.5555	−2.96975
$459$	−1.76101	−0.0821967
$460$	−107.501	−5.01224
$461$	−2.08862	−0.0972768	−0.0486384	−	0.998816i	$-0.515488\pi$
$461$	−2.08862	−0.0972768	−0.0486384	+	0.998816i	$0.515488\pi$
$462$	−2.97304	−0.138319
$463$	−26.4301	−1.22831	−0.614156	−	0.789184i	$-0.710504\pi$
$463$	−26.4301	−1.22831	−0.614156	+	0.789184i	$0.710504\pi$
$464$	55.3642	2.57022
$465$	2.05533	0.0953139
$466$	60.7507	2.81422
$467$	6.63443	0.307005	0.153503	−	0.988148i	$-0.450945\pi$
$467$	6.63443	0.307005	0.153503	+	0.988148i	$0.450945\pi$
$468$	−1.41895	−0.0655910
$469$	−74.0490	−3.41926
$470$	−69.5955	−3.21020
$471$	0.237783	0.0109564
$472$	27.9103	1.28468
$473$	17.5416	0.806562
$474$	−0.269202	−0.0123649
$475$	−65.1683	−2.99013
$476$	−95.8057	−4.39125
$477$	1.27568	0.0584095
$478$	52.6050	2.40610
$479$	−32.7173	−1.49489	−0.747446	−	0.664323i	$-0.768720\pi$
$479$	−32.7173	−1.49489	−0.747446	+	0.664323i	$0.768720\pi$
$480$	−1.58161	−0.0721901
$481$	−0.104060	−0.00474472
$482$	−26.9868	−1.22922
$483$	−2.19491	−0.0998720
$484$	−0.612359	−0.0278345
$485$	−24.0672	−1.09284
$486$	4.80749	0.218072
$487$	41.7607	1.89236	0.946179	−	0.323644i	$-0.104908\pi$
$487$	41.7607	1.89236	0.946179	+	0.323644i	$0.104908\pi$
$488$	8.26106	0.373961
$489$	−1.02342	−0.0462804
$490$	181.630	8.20521
$491$	34.9468	1.57713	0.788564	−	0.614953i	$-0.210825\pi$
$491$	34.9468	1.57713	0.788564	+	0.614953i	$0.210825\pi$
$492$	−3.51106	−0.158291
$493$	−31.7107	−1.42818
$494$	1.79625	0.0808170
$495$	−37.8776	−1.70247
$496$	56.1845	2.52276
$497$	14.1376	0.634158
$498$	2.28592	0.102434
$499$	−7.81803	−0.349983	−0.174991	−	0.984570i	$-0.555990\pi$
$499$	−7.81803	−0.349983	−0.174991	+	0.984570i	$0.555990\pi$
$500$	−81.7291	−3.65504
$501$	−0.939165	−0.0419588
$502$	0.0158006	0.000705214 0
$503$	14.0350	0.625792	0.312896	−	0.949787i	$-0.398701\pi$
$503$	14.0350	0.625792	0.312896	+	0.949787i	$0.398701\pi$
$504$	97.0486	4.32289
$505$	70.7794	3.14964
$506$	52.2313	2.32196
$507$	0.908274	0.0403379
$508$	16.8388	0.747099
$509$	−20.2314	−0.896742	−0.448371	−	0.893848i	$-0.647996\pi$
$509$	−20.2314	−0.896742	−0.448371	+	0.893848i	$0.647996\pi$
$510$	2.87601	0.127352
$511$	−1.33562	−0.0590843
$512$	50.7918	2.24470
$513$	−2.81036	−0.124081
$514$	1.73012	0.0763125
$515$	−9.24291	−0.407291
$516$	1.67911	0.0739185
$517$	23.4291	1.03041
$518$	12.7837	0.561682
$519$	0.941116	0.0413104
$520$	2.58244	0.113248
$521$	−15.0517	−0.659425	−0.329712	−	0.944081i	$-0.606952\pi$
$521$	−15.0517	−0.659425	−0.329712	+	0.944081i	$0.606952\pi$
$522$	57.6970	2.52533
$523$	15.1074	0.660602	0.330301	−	0.943876i	$-0.392850\pi$
$523$	15.1074	0.660602	0.330301	+	0.943876i	$0.392850\pi$
$524$	−45.1368	−1.97181
$525$	−3.43603	−0.149961
$526$	−47.7589	−2.08239
$527$	−32.1805	−1.40180
$528$	1.69039	0.0735650
$529$	15.5608	0.676558
$530$	−4.17020	−0.181142
$531$	13.0407	0.565920
$532$	−152.895	−6.62884
$533$	1.16846	0.0506116
$534$	0.613001	0.0265272
$535$	14.4421	0.624387
$536$	93.9057	4.05611
$537$	1.49756	0.0646246
$538$	47.4893	2.04741
$539$	−61.1451	−2.63371
$540$	−7.25733	−0.312306
$541$	−27.2509	−1.17161	−0.585804	−	0.810453i	$-0.699221\pi$
$541$	−27.2509	−1.17161	−0.585804	+	0.810453i	$0.699221\pi$
$542$	60.8493	2.61370
$543$	1.18889	0.0510202
$544$	24.7633	1.06172
$545$	−38.7335	−1.65916
$546$	0.0947081	0.00405313
$547$	−42.0407	−1.79753	−0.898766	−	0.438428i	$-0.855535\pi$
$547$	−42.0407	−1.79753	−0.898766	+	0.438428i	$0.855535\pi$
$548$	8.71051	0.372094
$549$	3.85988	0.164736
$550$	81.7656	3.48650
$551$	−50.6066	−2.15591
$552$	2.78349	0.118473
$553$	−7.62572	−0.324279
$554$	−6.03281	−0.256310
$555$	−0.265894	−0.0112866
$556$	81.7967	3.46895
$557$	11.0497	0.468190	0.234095	−	0.972214i	$-0.424787\pi$
$557$	11.0497	0.468190	0.234095	+	0.972214i	$0.424787\pi$
$558$	58.5519	2.47870
$559$	−0.558797	−0.0236346
$560$	−142.238	−6.01067
$561$	−0.968198	−0.0408774
$562$	−4.95837	−0.209156
$563$	15.2149	0.641231	0.320615	−	0.947209i	$-0.396110\pi$
$563$	15.2149	0.641231	0.320615	+	0.947209i	$0.396110\pi$
$564$	2.24267	0.0944334
$565$	−6.42818	−0.270435
$566$	−66.0650	−2.77692
$567$	45.2706	1.90119
$568$	−17.9287	−0.752272
$569$	−2.11369	−0.0886106	−0.0443053	−	0.999018i	$-0.514107\pi$
$569$	−2.11369	−0.0886106	−0.0443053	+	0.999018i	$0.514107\pi$
$570$	4.58978	0.192245
$571$	−22.6474	−0.947763	−0.473881	−	0.880589i	$-0.657147\pi$
$571$	−22.6474	−0.947763	−0.473881	+	0.880589i	$0.657147\pi$
$572$	−1.56155	−0.0652915
$573$	1.18359	0.0494453
$574$	−143.544	−5.99143
$575$	60.3652	2.51740
$576$	−1.12366	−0.0468191
$577$	2.27368	0.0946547	0.0473274	−	0.998879i	$-0.484930\pi$
$577$	2.27368	0.0946547	0.0473274	+	0.998879i	$0.484930\pi$
$578$	−1.64818	−0.0685552
$579$	−0.297747	−0.0123740
$580$	−130.684	−5.42634
$581$	64.7535	2.68643
$582$	1.11932	0.0463975
$583$	1.40388	0.0581429
$584$	1.69377	0.0700888
$585$	1.20661	0.0498874
$586$	51.2584	2.11746
$587$	35.7563	1.47582	0.737910	−	0.674900i	$-0.235813\pi$
$587$	35.7563	1.47582	0.737910	+	0.674900i	$0.235813\pi$
$588$	−5.85291	−0.241370
$589$	−51.3564	−2.11610
$590$	−42.6301	−1.75505
$591$	−0.169536	−0.00697378
$592$	−7.26846	−0.298732
$593$	16.7074	0.686091	0.343046	−	0.939319i	$-0.388541\pi$
$593$	16.7074	0.686091	0.343046	+	0.939319i	$0.388541\pi$
$594$	3.52612	0.144678
$595$	81.4691	3.33991
$596$	98.5961	4.03865
$597$	−0.956551	−0.0391490
$598$	−1.66386	−0.0680402
$599$	−3.80565	−0.155495	−0.0777474	−	0.996973i	$-0.524773\pi$
$599$	−3.80565	−0.155495	−0.0777474	+	0.996973i	$0.524773\pi$
$600$	4.35743	0.177891
$601$	−42.5924	−1.73738	−0.868690	−	0.495357i	$-0.835037\pi$
$601$	−42.5924	−1.73738	−0.868690	+	0.495357i	$0.835037\pi$
$602$	68.6478	2.79787
$603$	43.8763	1.78678
$604$	−78.4676	−3.19280
$605$	0.520724	0.0211704
$606$	−3.29182	−0.133721
$607$	−10.1298	−0.411154	−0.205577	−	0.978641i	$-0.565907\pi$
$607$	−10.1298	−0.411154	−0.205577	+	0.978641i	$0.565907\pi$
$608$	39.5194	1.60272
$609$	−2.66826	−0.108123
$610$	−12.6179	−0.510884
$611$	−0.746348	−0.0301940
$612$	56.7679	2.29470
$613$	−34.7742	−1.40452	−0.702258	−	0.711923i	$-0.747825\pi$
$613$	−34.7742	−1.40452	−0.702258	+	0.711923i	$0.747825\pi$
$614$	0.0950677	0.00383662
$615$	2.98565	0.120393
$616$	106.801	4.30315
$617$	26.7131	1.07543	0.537714	−	0.843127i	$-0.319288\pi$
$617$	26.7131	1.07543	0.537714	+	0.843127i	$0.319288\pi$
$618$	0.429871	0.0172920
$619$	−17.9579	−0.721790	−0.360895	−	0.932606i	$-0.617529\pi$
$619$	−17.9579	−0.721790	−0.360895	+	0.932606i	$0.617529\pi$
$620$	−132.620	−5.32614
$621$	2.60323	0.104464
$622$	−13.5670	−0.543988
$623$	17.3646	0.695697
$624$	−0.0538485	−0.00215567
$625$	20.8936	0.835745
$626$	−2.24825	−0.0898581
$627$	−1.54513	−0.0617067
$628$	−15.3428	−0.612246
$629$	4.16312	0.165994
$630$	−148.232	−5.90569
$631$	15.2920	0.608765	0.304382	−	0.952550i	$-0.401550\pi$
$631$	15.2920	0.608765	0.304382	+	0.952550i	$0.401550\pi$
$632$	9.67061	0.384676
$633$	0.809768	0.0321854
$634$	−42.7170	−1.69651
$635$	−14.3190	−0.568230
$636$	0.134382	0.00532858
$637$	1.94781	0.0771752
$638$	63.4952	2.51380
$639$	−8.37697	−0.331388
$640$	−41.5630	−1.64292
$641$	11.8646	0.468623	0.234311	−	0.972162i	$-0.424716\pi$
$641$	11.8646	0.468623	0.234311	+	0.972162i	$0.424716\pi$
$642$	−0.671676	−0.0265090
$643$	−13.8624	−0.546678	−0.273339	−	0.961918i	$-0.588128\pi$
$643$	−13.8624	−0.546678	−0.273339	+	0.961918i	$0.588128\pi$
$644$	141.626	5.58085
$645$	−1.42784	−0.0562211
$646$	−71.8624	−2.82739
$647$	9.82362	0.386206	0.193103	−	0.981178i	$-0.438145\pi$
$647$	9.82362	0.386206	0.193103	+	0.981178i	$0.438145\pi$
$648$	−57.4103	−2.25529
$649$	14.3513	0.563336
$650$	−2.60469	−0.102164
$651$	−2.70779	−0.106127
$652$	66.0356	2.58615
$653$	−13.0019	−0.508805	−0.254402	−	0.967098i	$-0.581879\pi$
$653$	−13.0019	−0.508805	−0.254402	+	0.967098i	$0.581879\pi$
$654$	1.80142	0.0704413
$655$	38.3824	1.49972
$656$	81.6156	3.18655
$657$	0.791395	0.0308753
$658$	91.6882	3.57438
$659$	18.9191	0.736984	0.368492	−	0.929631i	$-0.379874\pi$
$659$	18.9191	0.736984	0.368492	+	0.929631i	$0.379874\pi$
$660$	−3.99007	−0.155313
$661$	28.0454	1.09084	0.545420	−	0.838163i	$-0.316370\pi$
$661$	28.0454	1.09084	0.545420	+	0.838163i	$0.316370\pi$
$662$	−9.05902	−0.352089
$663$	0.0308425	0.00119782
$664$	−82.1176	−3.18678
$665$	130.015	5.04178
$666$	−7.57472	−0.293514
$667$	46.8767	1.81507
$668$	60.5993	2.34466
$669$	1.64731	0.0636887
$670$	−143.431	−5.54123
$671$	4.24777	0.163983
$672$	2.08368	0.0803796
$673$	2.82026	0.108713	0.0543564	−	0.998522i	$-0.482689\pi$
$673$	2.82026	0.108713	0.0543564	+	0.998522i	$0.482689\pi$
$674$	70.3857	2.71116
$675$	4.07524	0.156856
$676$	−58.6061	−2.25408
$677$	−4.28988	−0.164874	−0.0824368	−	0.996596i	$-0.526270\pi$
$677$	−4.28988	−0.164874	−0.0824368	+	0.996596i	$0.526270\pi$
$678$	0.298963	0.0114816
$679$	31.7073	1.21681
$680$	−103.316	−3.96197
$681$	0.703890	0.0269731
$682$	64.4360	2.46738
$683$	−30.0178	−1.14860	−0.574299	−	0.818646i	$-0.694725\pi$
$683$	−30.0178	−1.14860	−0.574299	+	0.818646i	$0.694725\pi$
$684$	90.5950	3.46399
$685$	−7.40704	−0.283009
$686$	−148.994	−5.68861
$687$	−1.74156	−0.0664446
$688$	−39.0313	−1.48805
$689$	−0.0447215	−0.00170375
$690$	−4.25150	−0.161852
$691$	−35.6264	−1.35529	−0.677645	−	0.735389i	$-0.736999\pi$
$691$	−35.6264	−1.35529	−0.677645	+	0.735389i	$0.736999\pi$
$692$	−60.7252	−2.30843
$693$	49.9017	1.89561
$694$	11.3450	0.430650
$695$	−69.5564	−2.63842
$696$	3.38377	0.128261
$697$	−46.7465	−1.77065
$698$	−42.7417	−1.61780
$699$	1.66470	0.0629649
$700$	221.709	8.37981
$701$	16.0352	0.605641	0.302821	−	0.953048i	$-0.402072\pi$
$701$	16.0352	0.605641	0.302821	+	0.953048i	$0.402072\pi$
$702$	−0.112327	−0.00423949
$703$	6.64386	0.250578
$704$	−1.23658	−0.0466054
$705$	−1.90707	−0.0718244
$706$	−26.9302	−1.01353
$707$	−93.2479	−3.50695
$708$	1.37373	0.0516278
$709$	47.2994	1.77637	0.888183	−	0.459489i	$-0.151967\pi$
$709$	47.2994	1.77637	0.888183	+	0.459489i	$0.151967\pi$
$710$	27.3842	1.02771
$711$	4.51847	0.169456
$712$	−22.0210	−0.825272
$713$	47.5712	1.78156
$714$	−3.78898	−0.141799
$715$	1.32787	0.0496596
$716$	−96.6298	−3.61122
$717$	1.44149	0.0538335
$718$	20.7865	0.775744
$719$	−37.6295	−1.40334	−0.701671	−	0.712501i	$-0.747563\pi$
$719$	−37.6295	−1.40334	−0.701671	+	0.712501i	$0.747563\pi$
$720$	84.2806	3.14095
$721$	12.1770	0.453496
$722$	−66.1989	−2.46367
$723$	−0.739499	−0.0275023
$724$	−76.7128	−2.85101
$725$	73.3833	2.72539
$726$	−0.0242179	−0.000898812 0
$727$	−37.7959	−1.40177	−0.700886	−	0.713273i	$-0.747212\pi$
$727$	−37.7959	−1.40177	−0.700886	+	0.713273i	$0.747212\pi$
$728$	−3.40222	−0.126095
$729$	−26.7363	−0.990234
$730$	−2.58706	−0.0957515
$731$	22.3558	0.826858
$732$	0.406604	0.0150285
$733$	−2.92343	−0.107979	−0.0539897	−	0.998541i	$-0.517194\pi$
$733$	−2.92343	−0.107979	−0.0539897	+	0.998541i	$0.517194\pi$
$734$	−9.09385	−0.335660
$735$	4.97706	0.183582
$736$	−36.6066	−1.34934
$737$	48.2856	1.77862
$738$	85.0545	3.13090
$739$	−20.0479	−0.737472	−0.368736	−	0.929534i	$-0.620209\pi$
$739$	−20.0479	−0.737472	−0.368736	+	0.929534i	$0.620209\pi$
$740$	17.1567	0.630694
$741$	0.0492211	0.00180818
$742$	5.49400	0.201691
$743$	−38.8844	−1.42653	−0.713266	−	0.700894i	$-0.752785\pi$
$743$	−38.8844	−1.42653	−0.713266	+	0.700894i	$0.752785\pi$
$744$	3.43390	0.125893
$745$	−83.8419	−3.07173
$746$	73.6855	2.69782
$747$	−38.3684	−1.40383
$748$	62.4727	2.28423
$749$	−19.0267	−0.695219
$750$	−3.23227	−0.118026
$751$	−25.8045	−0.941620	−0.470810	−	0.882235i	$-0.656038\pi$
$751$	−25.8045	−0.941620	−0.470810	+	0.882235i	$0.656038\pi$
$752$	−52.1315	−1.90104
$753$	0.000432970 0	1.57783e−5 0
$754$	−2.02268	−0.0736616
$755$	66.7255	2.42839
$756$	9.56113	0.347735
$757$	−35.2349	−1.28063	−0.640316	−	0.768111i	$-0.721197\pi$
$757$	−35.2349	−1.28063	−0.640316	+	0.768111i	$0.721197\pi$
$758$	48.7368	1.77020
$759$	1.43125	0.0519511
$760$	−164.880	−5.98082
$761$	18.9475	0.686846	0.343423	−	0.939181i	$-0.388414\pi$
$761$	18.9475	0.686846	0.343423	+	0.939181i	$0.388414\pi$
$762$	0.665949	0.0241248
$763$	51.0292	1.84738
$764$	−76.3709	−2.76300
$765$	−48.2730	−1.74531
$766$	25.9822	0.938773
$767$	−0.457168	−0.0165074
$768$	1.98549	0.0716451
$769$	42.6208	1.53694	0.768472	−	0.639884i	$-0.221017\pi$
$769$	42.6208	1.53694	0.768472	+	0.639884i	$0.221017\pi$
$770$	−163.128	−5.87873
$771$	0.0474092	0.00170740
$772$	19.2121	0.691457
$773$	32.3988	1.16530	0.582652	−	0.812722i	$-0.302015\pi$
$773$	32.3988	1.16530	0.582652	+	0.812722i	$0.302015\pi$
$774$	−40.6759	−1.46207
$775$	74.4705	2.67506
$776$	−40.2098	−1.44345
$777$	0.350301	0.0125670
$778$	−51.4306	−1.84388
$779$	−74.6021	−2.67290
$780$	0.127106	0.00455112
$781$	−9.21881	−0.329875
$782$	66.5659	2.38039
$783$	3.16463	0.113095
$784$	136.053	4.85902
$785$	13.0469	0.465664
$786$	−1.78510	−0.0636722
$787$	10.9329	0.389716	0.194858	−	0.980831i	$-0.437575\pi$
$787$	10.9329	0.389716	0.194858	+	0.980831i	$0.437575\pi$
$788$	10.9393	0.389695
$789$	−1.30870	−0.0465909
$790$	−14.7708	−0.525523
$791$	8.46876	0.301115
$792$	−63.2832	−2.24867
$793$	−0.135315	−0.00480519
$794$	42.8388	1.52029
$795$	−0.114273	−0.00405283
$796$	61.7212	2.18765
$797$	10.1461	0.359395	0.179697	−	0.983722i	$-0.442488\pi$
$797$	10.1461	0.359395	0.179697	+	0.983722i	$0.442488\pi$
$798$	−6.04678	−0.214054
$799$	29.8591	1.05634
$800$	−57.3060	−2.02607
$801$	−10.2890	−0.363546
$802$	−23.7622	−0.839071
$803$	0.870926	0.0307343
$804$	4.62198	0.163004
$805$	−120.433	−4.24470
$806$	−2.05265	−0.0723014
$807$	1.30131	0.0458083
$808$	118.253	4.16013
$809$	−42.8627	−1.50697	−0.753487	−	0.657463i	$-0.771629\pi$
$809$	−42.8627	−1.50697	−0.753487	+	0.657463i	$0.771629\pi$
$810$	87.6882	3.08105
$811$	15.8601	0.556925	0.278462	−	0.960447i	$-0.410175\pi$
$811$	15.8601	0.556925	0.278462	+	0.960447i	$0.410175\pi$
$812$	172.168	6.04193
$813$	1.66740	0.0584784
$814$	−8.33593	−0.292174
$815$	−56.1538	−1.96698
$816$	2.15431	0.0754161
$817$	35.6772	1.24819
$818$	3.71392	0.129854
$819$	−1.58965	−0.0555468
$820$	−192.648	−6.72757
$821$	−34.4485	−1.20226	−0.601130	−	0.799151i	$-0.705283\pi$
$821$	−34.4485	−1.20226	−0.601130	+	0.799151i	$0.705283\pi$
$822$	0.344488	0.0120154
$823$	−23.8436	−0.831137	−0.415569	−	0.909562i	$-0.636417\pi$
$823$	−23.8436	−0.831137	−0.415569	+	0.909562i	$0.636417\pi$
$824$	−15.4424	−0.537961
$825$	2.24056	0.0780062
$826$	56.1627	1.95415
$827$	7.18826	0.249960	0.124980	−	0.992159i	$-0.460113\pi$
$827$	7.18826	0.249960	0.124980	+	0.992159i	$0.460113\pi$
$828$	−83.9178	−2.91635
$829$	−16.8362	−0.584744	−0.292372	−	0.956305i	$-0.594445\pi$
$829$	−16.8362	−0.584744	−0.292372	+	0.956305i	$0.594445\pi$
$830$	125.426	4.35360
$831$	−0.165312	−0.00573462
$832$	0.0393920	0.00136567
$833$	−77.9261	−2.69998
$834$	3.23494	0.112017
$835$	−51.5311	−1.78331
$836$	99.6993	3.44817
$837$	3.21152	0.111006
$838$	−91.9077	−3.17490
$839$	11.0407	0.381169	0.190584	−	0.981671i	$-0.438962\pi$
$839$	11.0407	0.381169	0.190584	+	0.981671i	$0.438962\pi$
$840$	−8.69337	−0.299950
$841$	27.9859	0.965031
$842$	43.6601	1.50463
$843$	−0.135870	−0.00467962
$844$	−52.2500	−1.79852
$845$	49.8361	1.71442
$846$	−54.3281	−1.86784
$847$	−0.686025	−0.0235721
$848$	−3.12374	−0.107270
$849$	−1.81033	−0.0621302
$850$	104.206	3.57423
$851$	−6.15418	−0.210963
$852$	−0.882439	−0.0302318
$853$	11.5489	0.395427	0.197713	−	0.980260i	$-0.436648\pi$
$853$	11.5489	0.395427	0.197713	+	0.980260i	$0.436648\pi$
$854$	16.6234	0.568841
$855$	−77.0381	−2.63465
$856$	24.1288	0.824706
$857$	37.0391	1.26523	0.632615	−	0.774466i	$-0.281981\pi$
$857$	37.0391	1.26523	0.632615	+	0.774466i	$0.281981\pi$
$858$	−0.0617569	−0.00210835
$859$	31.4361	1.07259	0.536293	−	0.844032i	$-0.319824\pi$
$859$	31.4361	1.07259	0.536293	+	0.844032i	$0.319824\pi$
$860$	92.1309	3.14164
$861$	−3.93343	−0.134051
$862$	30.7690	1.04800
$863$	24.2719	0.826225	0.413112	−	0.910680i	$-0.364442\pi$
$863$	24.2719	0.826225	0.413112	+	0.910680i	$0.364442\pi$
$864$	−2.47130	−0.0840754
$865$	51.6381	1.75575
$866$	15.6384	0.531415
$867$	−0.0451637	−0.00153384
$868$	174.719	5.93036
$869$	4.97255	0.168682
$870$	−5.16835	−0.175224
$871$	−1.53817	−0.0521188
$872$	−64.7131	−2.19146
$873$	−18.7875	−0.635862
$874$	106.232	3.59334
$875$	−91.5609	−3.09532
$876$	0.0833664	0.00281669
$877$	28.6360	0.966969	0.483485	−	0.875353i	$-0.339371\pi$
$877$	28.6360	0.966969	0.483485	+	0.875353i	$0.339371\pi$
$878$	45.6459	1.54047
$879$	1.40459	0.0473757
$880$	92.7503	3.12661
$881$	−40.3805	−1.36045	−0.680227	−	0.733001i	$-0.738119\pi$
$881$	−40.3805	−1.36045	−0.680227	+	0.733001i	$0.738119\pi$
$882$	141.785	4.77416
$883$	58.8707	1.98116	0.990578	−	0.136949i	$-0.0437296\pi$
$883$	58.8707	1.98116	0.990578	+	0.136949i	$0.0437296\pi$
$884$	−1.99010	−0.0669345
$885$	−1.16816	−0.0392672
$886$	95.3610	3.20371
$887$	12.2882	0.412598	0.206299	−	0.978489i	$-0.433858\pi$
$887$	12.2882	0.412598	0.206299	+	0.978489i	$0.433858\pi$
$888$	−0.444236	−0.0149076
$889$	18.8644	0.632693
$890$	33.6348	1.12744
$891$	−29.5199	−0.988955
$892$	−106.292	−3.55893
$893$	47.6517	1.59460
$894$	3.89934	0.130413
$895$	82.1698	2.74663
$896$	54.7569	1.82930
$897$	−0.0455934	−0.00152232
$898$	74.0912	2.47246
$899$	57.8302	1.92874
$900$	−131.369	−4.37898
$901$	1.78917	0.0596059
$902$	93.6020	3.11661
$903$	1.88110	0.0625991
$904$	−10.7397	−0.357198
$905$	65.2333	2.16843
$906$	−3.10328	−0.103100
$907$	−46.6836	−1.55010	−0.775052	−	0.631897i	$-0.782277\pi$
$907$	−46.6836	−1.55010	−0.775052	+	0.631897i	$0.782277\pi$
$908$	−45.4183	−1.50726
$909$	55.2523	1.83260
$910$	5.19654	0.172264
$911$	0.0924527	0.00306310	0.00153155	−	0.999999i	$-0.499512\pi$
$911$	0.0924527	0.00306310	0.00153155	+	0.999999i	$0.499512\pi$
$912$	3.43804	0.113845
$913$	−42.2242	−1.39742
$914$	81.9562	2.71087
$915$	−0.345758	−0.0114304
$916$	112.374	3.71293
$917$	−50.5666	−1.66986
$918$	4.49384	0.148319
$919$	−29.4693	−0.972103	−0.486051	−	0.873930i	$-0.661563\pi$
$919$	−29.4693	−0.972103	−0.486051	+	0.873930i	$0.661563\pi$
$920$	152.728	5.03528
$921$	0.00260506	8.58398e−5 0
$922$	5.32987	0.175530
$923$	0.293671	0.00966628
$924$	5.25669	0.172932
$925$	−9.63408	−0.316767
$926$	67.4460	2.21641
$927$	−7.21526	−0.236980
$928$	−44.5011	−1.46082
$929$	17.2398	0.565618	0.282809	−	0.959176i	$-0.408734\pi$
$929$	17.2398	0.565618	0.282809	+	0.959176i	$0.408734\pi$
$930$	−5.24493	−0.171988
$931$	−124.361	−4.07577
$932$	−107.414	−3.51848
$933$	−0.371766	−0.0121711
$934$	−16.9301	−0.553971
$935$	−53.1241	−1.73734
$936$	2.01592	0.0658925
$937$	24.6238	0.804424	0.402212	−	0.915547i	$-0.368241\pi$
$937$	24.6238	0.804424	0.402212	+	0.915547i	$0.368241\pi$
$938$	188.963	6.16985
$939$	−0.0616070	−0.00201047
$940$	123.053	4.01355
$941$	−31.6013	−1.03017	−0.515087	−	0.857138i	$-0.672240\pi$
$941$	−31.6013	−1.03017	−0.515087	+	0.857138i	$0.672240\pi$
$942$	−0.606788	−0.0197702
$943$	69.1037	2.25032
$944$	−31.9326	−1.03932
$945$	−8.13037	−0.264481
$946$	−44.7636	−1.45539
$947$	12.9131	0.419620	0.209810	−	0.977742i	$-0.432715\pi$
$947$	12.9131	0.419620	0.209810	+	0.977742i	$0.432715\pi$
$948$	0.475981	0.0154591
$949$	−0.0277438	−0.000900603 0
$950$	166.301	5.39550
$951$	−1.17054	−0.0379573
$952$	136.113	4.41143
$953$	50.0525	1.62136	0.810679	−	0.585491i	$-0.199098\pi$
$953$	50.0525	1.62136	0.810679	+	0.585491i	$0.199098\pi$
$954$	−3.25537	−0.105396
$955$	64.9426	2.10149
$956$	−93.0118	−3.00822
$957$	1.73991	0.0562433
$958$	83.4900	2.69744
$959$	9.75837	0.315114
$960$	0.100655	0.00324861
$961$	27.6870	0.893129
$962$	0.265546	0.00856155
$963$	11.2739	0.363296
$964$	47.7159	1.53683
$965$	−16.3371	−0.525910
$966$	5.60111	0.180213
$967$	−18.9828	−0.610445	−0.305222	−	0.952281i	$-0.598731\pi$
$967$	−18.9828	−0.610445	−0.305222	+	0.952281i	$0.598731\pi$
$968$	0.869987	0.0279625
$969$	−1.96919	−0.0632594
$970$	61.4163	1.97196
$971$	−18.8688	−0.605529	−0.302765	−	0.953065i	$-0.597910\pi$
$971$	−18.8688	−0.605529	−0.302765	+	0.953065i	$0.597910\pi$
$972$	−8.50021	−0.272644
$973$	91.6367	2.93774
$974$	−106.567	−3.41464
$975$	−0.0713743	−0.00228581
$976$	−9.45162	−0.302539
$977$	24.2194	0.774847	0.387423	−	0.921902i	$-0.373365\pi$
$977$	24.2194	0.774847	0.387423	+	0.921902i	$0.373365\pi$
$978$	2.61161	0.0835102
$979$	−11.3230	−0.361886
$980$	−321.143	−10.2585
$981$	−30.2364	−0.965373
$982$	−89.1794	−2.84583
$983$	3.58745	0.114422	0.0572109	−	0.998362i	$-0.481779\pi$
$983$	3.58745	0.114422	0.0572109	+	0.998362i	$0.481779\pi$
$984$	4.98821	0.159018
$985$	−9.30227	−0.296395
$986$	80.9212	2.57706
$987$	2.51246	0.0799724
$988$	−3.17598	−0.101041
$989$	−33.0477	−1.05086
$990$	96.6584	3.07201
$991$	−34.6510	−1.10073	−0.550363	−	0.834926i	$-0.685511\pi$
$991$	−34.6510	−1.10073	−0.550363	+	0.834926i	$0.685511\pi$
$992$	−45.1604	−1.43384
$993$	−0.248237	−0.00787757
$994$	−36.0772	−1.14430
$995$	−52.4850	−1.66389
$996$	−4.04177	−0.128068
$997$	3.35063	0.106116	0.0530578	−	0.998591i	$-0.483103\pi$
$997$	3.35063	0.106116	0.0530578	+	0.998591i	$0.483103\pi$
$998$	19.9505	0.631522
$999$	−0.415467	−0.0131448

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.9	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.9	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55186 q^{2} -0.0699266 q^{3} +4.51199 q^{4} -3.83680 q^{5} +0.178443 q^{6} +5.05477 q^{7} -6.41025 q^{8} -2.99511 q^{9} +O(q^{10})\)	\(q-2.55186 q^{2} -0.0699266 q^{3} +4.51199 q^{4} -3.83680 q^{5} +0.178443 q^{6} +5.05477 q^{7} -6.41025 q^{8} -2.99511 q^{9} +9.79098 q^{10} -3.29610 q^{11} -0.315508 q^{12} +0.104999 q^{13} -12.8991 q^{14} +0.268294 q^{15} +7.33408 q^{16} -4.20070 q^{17} +7.64310 q^{18} -6.70384 q^{19} -17.3116 q^{20} -0.353463 q^{21} +8.41119 q^{22} +6.20974 q^{23} +0.448247 q^{24} +9.72105 q^{25} -0.267943 q^{26} +0.419217 q^{27} +22.8071 q^{28} +7.54890 q^{29} -0.684650 q^{30} +7.66074 q^{31} -5.89504 q^{32} +0.230485 q^{33} +10.7196 q^{34} -19.3942 q^{35} -13.5139 q^{36} -0.991053 q^{37} +17.1073 q^{38} -0.00734224 q^{39} +24.5949 q^{40} +11.1283 q^{41} +0.901988 q^{42} -5.32191 q^{43} -14.8720 q^{44} +11.4916 q^{45} -15.8464 q^{46} -7.10812 q^{47} -0.512847 q^{48} +18.5507 q^{49} -24.8068 q^{50} +0.293740 q^{51} +0.473756 q^{52} -0.425922 q^{53} -1.06978 q^{54} +12.6465 q^{55} -32.4024 q^{56} +0.468776 q^{57} -19.2637 q^{58} -4.35401 q^{59} +1.21054 q^{60} -1.28873 q^{61} -19.5491 q^{62} -15.1396 q^{63} +0.375164 q^{64} -0.402861 q^{65} -0.588166 q^{66} -14.6493 q^{67} -18.9535 q^{68} -0.434226 q^{69} +49.4912 q^{70} +2.79688 q^{71} +19.1994 q^{72} -0.264229 q^{73} +2.52903 q^{74} -0.679760 q^{75} -30.2476 q^{76} -16.6610 q^{77} +0.0187364 q^{78} -1.50862 q^{79} -28.1394 q^{80} +8.95602 q^{81} -28.3978 q^{82} +12.8104 q^{83} -1.59482 q^{84} +16.1173 q^{85} +13.5808 q^{86} -0.527869 q^{87} +21.1288 q^{88} +3.43528 q^{89} -29.3251 q^{90} +0.530747 q^{91} +28.0183 q^{92} -0.535689 q^{93} +18.1389 q^{94} +25.7213 q^{95} +0.412220 q^{96} +6.27274 q^{97} -47.3389 q^{98} +9.87219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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