LMFDB - Embedded newform 1931.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1931,2,Mod(1,1931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1931, 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("1931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1931 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1931.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:	$15.4191126303$
Analytic rank:	$0$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	1931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80220 q^{2} +3.00833 q^{3} +5.85234 q^{4} +3.47491 q^{5} -8.42994 q^{6} +3.27757 q^{7} -10.7951 q^{8} +6.05002 q^{9} +O(q^{10})$	\(q-2.80220 q^{2} +3.00833 q^{3} +5.85234 q^{4} +3.47491 q^{5} -8.42994 q^{6} +3.27757 q^{7} -10.7951 q^{8} +6.05002 q^{9} -9.73740 q^{10} +3.94598 q^{11} +17.6058 q^{12} -3.16567 q^{13} -9.18441 q^{14} +10.4537 q^{15} +18.5452 q^{16} +3.48588 q^{17} -16.9534 q^{18} -2.55373 q^{19} +20.3364 q^{20} +9.85999 q^{21} -11.0574 q^{22} -7.75246 q^{23} -32.4750 q^{24} +7.07498 q^{25} +8.87086 q^{26} +9.17546 q^{27} +19.1814 q^{28} -10.1472 q^{29} -29.2933 q^{30} +1.25295 q^{31} -30.3774 q^{32} +11.8708 q^{33} -9.76816 q^{34} +11.3892 q^{35} +35.4068 q^{36} -3.31060 q^{37} +7.15608 q^{38} -9.52338 q^{39} -37.5118 q^{40} -5.30193 q^{41} -27.6297 q^{42} +2.48485 q^{43} +23.0932 q^{44} +21.0233 q^{45} +21.7240 q^{46} +2.97505 q^{47} +55.7901 q^{48} +3.74244 q^{49} -19.8255 q^{50} +10.4867 q^{51} -18.5266 q^{52} -2.16818 q^{53} -25.7115 q^{54} +13.7119 q^{55} -35.3815 q^{56} -7.68246 q^{57} +28.4346 q^{58} -9.52858 q^{59} +61.1784 q^{60} +11.6925 q^{61} -3.51102 q^{62} +19.8294 q^{63} +48.0333 q^{64} -11.0004 q^{65} -33.2644 q^{66} +0.689655 q^{67} +20.4006 q^{68} -23.3219 q^{69} -31.9150 q^{70} +15.3566 q^{71} -65.3103 q^{72} -6.96810 q^{73} +9.27697 q^{74} +21.2839 q^{75} -14.9453 q^{76} +12.9332 q^{77} +26.6864 q^{78} -3.55863 q^{79} +64.4430 q^{80} +9.45270 q^{81} +14.8571 q^{82} -12.6714 q^{83} +57.7040 q^{84} +12.1131 q^{85} -6.96305 q^{86} -30.5262 q^{87} -42.5971 q^{88} +2.67831 q^{89} -58.9115 q^{90} -10.3757 q^{91} -45.3701 q^{92} +3.76928 q^{93} -8.33669 q^{94} -8.87399 q^{95} -91.3852 q^{96} -3.10303 q^{97} -10.4871 q^{98} +23.8733 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9}+O(q^{10}) $ 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9} + 14 q^{10} + 29 q^{11} + 15 q^{12} + 41 q^{13} + 4 q^{14} + 22 q^{15} + 187 q^{16} + 9 q^{17} + 11 q^{18} + 34 q^{19} + 42 q^{20} + 72 q^{21} + 17 q^{22} + 19 q^{23} + 33 q^{24} + 172 q^{25} + 28 q^{26} + 36 q^{27} + 47 q^{28} + 68 q^{29} + q^{30} + 76 q^{31} + 9 q^{32} + 8 q^{33} + 50 q^{34} + 7 q^{35} + 198 q^{36} + 141 q^{37} - 13 q^{38} + 42 q^{39} + 32 q^{40} + 35 q^{41} - 46 q^{42} + 45 q^{43} + 67 q^{44} + 106 q^{45} + 86 q^{46} - 5 q^{47} + 7 q^{48} + 203 q^{49} + 4 q^{50} + 5 q^{51} + 30 q^{52} + 47 q^{53} + 20 q^{54} + 11 q^{55} - 4 q^{56} + 19 q^{57} + 92 q^{58} + 30 q^{59} + 35 q^{60} + 153 q^{61} - 20 q^{62} + 19 q^{63} + 276 q^{64} - 7 q^{65} - 18 q^{66} + 39 q^{67} - 7 q^{68} + 55 q^{69} - 8 q^{70} + 47 q^{71} - 4 q^{72} + 86 q^{73} + 9 q^{74} + 11 q^{75} + 50 q^{76} + 15 q^{77} - 15 q^{78} + 89 q^{79} + 26 q^{80} + 201 q^{81} - 9 q^{82} - 15 q^{83} + 60 q^{84} + 239 q^{85} + 13 q^{86} - 22 q^{87} + 5 q^{88} + 14 q^{89} - 85 q^{90} + 58 q^{91} - 4 q^{92} + 86 q^{93} + 21 q^{94} - 10 q^{95} + 6 q^{96} + 46 q^{97} - 68 q^{98} + 100 q^{99}+O(q^{100}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9 + 14 * q^10 + 29 * q^11 + 15 * q^12 + 41 * q^13 + 4 * q^14 + 22 * q^15 + 187 * q^16 + 9 * q^17 + 11 * q^18 + 34 * q^19 + 42 * q^20 + 72 * q^21 + 17 * q^22 + 19 * q^23 + 33 * q^24 + 172 * q^25 + 28 * q^26 + 36 * q^27 + 47 * q^28 + 68 * q^29 + q^30 + 76 * q^31 + 9 * q^32 + 8 * q^33 + 50 * q^34 + 7 * q^35 + 198 * q^36 + 141 * q^37 - 13 * q^38 + 42 * q^39 + 32 * q^40 + 35 * q^41 - 46 * q^42 + 45 * q^43 + 67 * q^44 + 106 * q^45 + 86 * q^46 - 5 * q^47 + 7 * q^48 + 203 * q^49 + 4 * q^50 + 5 * q^51 + 30 * q^52 + 47 * q^53 + 20 * q^54 + 11 * q^55 - 4 * q^56 + 19 * q^57 + 92 * q^58 + 30 * q^59 + 35 * q^60 + 153 * q^61 - 20 * q^62 + 19 * q^63 + 276 * q^64 - 7 * q^65 - 18 * q^66 + 39 * q^67 - 7 * q^68 + 55 * q^69 - 8 * q^70 + 47 * q^71 - 4 * q^72 + 86 * q^73 + 9 * q^74 + 11 * q^75 + 50 * q^76 + 15 * q^77 - 15 * q^78 + 89 * q^79 + 26 * q^80 + 201 * q^81 - 9 * q^82 - 15 * q^83 + 60 * q^84 + 239 * q^85 + 13 * q^86 - 22 * q^87 + 5 * q^88 + 14 * q^89 - 85 * q^90 + 58 * q^91 - 4 * q^92 + 86 * q^93 + 21 * q^94 - 10 * q^95 + 6 * q^96 + 46 * q^97 - 68 * q^98 + 100 * 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 $

$2$	−2.80220	−1.98146	−0.990729	−	0.135857i	$-0.956621\pi$
$2$	−2.80220	−1.98146	−0.990729	+	0.135857i	$0.956621\pi$
$3$	3.00833	1.73686	0.868429	−	0.495814i	$-0.165130\pi$
$3$	3.00833	1.73686	0.868429	+	0.495814i	$0.165130\pi$
$4$	5.85234	2.92617
$5$	3.47491	1.55403	0.777013	−	0.629485i	$-0.216734\pi$
$5$	3.47491	1.55403	0.777013	+	0.629485i	$0.216734\pi$
$6$	−8.42994	−3.44151
$7$	3.27757	1.23880	0.619402	−	0.785074i	$-0.287375\pi$
$7$	3.27757	1.23880	0.619402	+	0.785074i	$0.287375\pi$
$8$	−10.7951	−3.81663
$9$	6.05002	2.01667
$10$	−9.73740	−3.07924
$11$	3.94598	1.18976	0.594879	−	0.803815i	$-0.297200\pi$
$11$	3.94598	1.18976	0.594879	+	0.803815i	$0.297200\pi$
$12$	17.6058	5.08234
$13$	−3.16567	−0.878000	−0.439000	−	0.898487i	$-0.644667\pi$
$13$	−3.16567	−0.878000	−0.439000	+	0.898487i	$0.644667\pi$
$14$	−9.18441	−2.45464
$15$	10.4537	2.69912
$16$	18.5452	4.63631
$17$	3.48588	0.845451	0.422726	−	0.906258i	$-0.361073\pi$
$17$	3.48588	0.845451	0.422726	+	0.906258i	$0.361073\pi$
$18$	−16.9534	−3.99595
$19$	−2.55373	−0.585867	−0.292933	−	0.956133i	$-0.594631\pi$
$19$	−2.55373	−0.585867	−0.292933	+	0.956133i	$0.594631\pi$
$20$	20.3364	4.54735
$21$	9.85999	2.15163
$22$	−11.0574	−2.35746
$23$	−7.75246	−1.61650	−0.808250	−	0.588839i	$-0.799585\pi$
$23$	−7.75246	−1.61650	−0.808250	+	0.588839i	$0.799585\pi$
$24$	−32.4750	−6.62894
$25$	7.07498	1.41500
$26$	8.87086	1.73972
$27$	9.17546	1.76582
$28$	19.1814	3.62495
$29$	−10.1472	−1.88430	−0.942148	−	0.335199i	$-0.891197\pi$
$29$	−10.1472	−1.88430	−0.942148	+	0.335199i	$0.891197\pi$
$30$	−29.2933	−5.34819
$31$	1.25295	0.225036	0.112518	−	0.993650i	$-0.464108\pi$
$31$	1.25295	0.225036	0.112518	+	0.993650i	$0.464108\pi$
$32$	−30.3774	−5.37002
$33$	11.8708	2.06644
$34$	−9.76816	−1.67522
$35$	11.3892	1.92513
$36$	35.4068	5.90114
$37$	−3.31060	−0.544259	−0.272129	−	0.962261i	$-0.587728\pi$
$37$	−3.31060	−0.544259	−0.272129	+	0.962261i	$0.587728\pi$
$38$	7.15608	1.16087
$39$	−9.52338	−1.52496
$40$	−37.5118	−5.93114
$41$	−5.30193	−0.828023	−0.414011	−	0.910272i	$-0.635873\pi$
$41$	−5.30193	−0.828023	−0.414011	+	0.910272i	$0.635873\pi$
$42$	−27.6297	−4.26335
$43$	2.48485	0.378936	0.189468	−	0.981887i	$-0.439324\pi$
$43$	2.48485	0.378936	0.189468	+	0.981887i	$0.439324\pi$
$44$	23.0932	3.48144
$45$	21.0233	3.13396
$46$	21.7240	3.20303
$47$	2.97505	0.433955	0.216978	−	0.976177i	$-0.430380\pi$
$47$	2.97505	0.433955	0.216978	+	0.976177i	$0.430380\pi$
$48$	55.7901	8.05261
$49$	3.74244	0.534635
$50$	−19.8255	−2.80375
$51$	10.4867	1.46843
$52$	−18.5266	−2.56918
$53$	−2.16818	−0.297822	−0.148911	−	0.988851i	$-0.547577\pi$
$53$	−2.16818	−0.297822	−0.148911	+	0.988851i	$0.547577\pi$
$54$	−25.7115	−3.49889
$55$	13.7119	1.84892
$56$	−35.3815	−4.72805
$57$	−7.68246	−1.01757
$58$	28.4346	3.73365
$59$	−9.52858	−1.24052	−0.620258	−	0.784398i	$-0.712972\pi$
$59$	−9.52858	−1.24052	−0.620258	+	0.784398i	$0.712972\pi$
$60$	61.1784	7.89809
$61$	11.6925	1.49708	0.748539	−	0.663091i	$-0.230756\pi$
$61$	11.6925	1.49708	0.748539	+	0.663091i	$0.230756\pi$
$62$	−3.51102	−0.445900
$63$	19.8294	2.49826
$64$	48.0333	6.00416
$65$	−11.0004	−1.36443
$66$	−33.2644	−4.09456
$67$	0.689655	0.0842547	0.0421274	−	0.999112i	$-0.486586\pi$
$67$	0.689655	0.0842547	0.0421274	+	0.999112i	$0.486586\pi$
$68$	20.4006	2.47394
$69$	−23.3219	−2.80763
$70$	−31.9150	−3.81457
$71$	15.3566	1.82249	0.911245	−	0.411866i	$-0.135123\pi$
$71$	15.3566	1.82249	0.911245	+	0.411866i	$0.135123\pi$
$72$	−65.3103	−7.69689
$73$	−6.96810	−0.815555	−0.407777	−	0.913081i	$-0.633696\pi$
$73$	−6.96810	−0.815555	−0.407777	+	0.913081i	$0.633696\pi$
$74$	9.27697	1.07843
$75$	21.2839	2.45765
$76$	−14.9453	−1.71435
$77$	12.9332	1.47388
$78$	26.6864	3.02164
$79$	−3.55863	−0.400378	−0.200189	−	0.979757i	$-0.564156\pi$
$79$	−3.55863	−0.400378	−0.200189	+	0.979757i	$0.564156\pi$
$80$	64.4430	7.20495
$81$	9.45270	1.05030
$82$	14.8571	1.64069
$83$	−12.6714	−1.39087	−0.695435	−	0.718589i	$-0.744788\pi$
$83$	−12.6714	−1.39087	−0.695435	+	0.718589i	$0.744788\pi$
$84$	57.7040	6.29603
$85$	12.1131	1.31385
$86$	−6.96305	−0.750845
$87$	−30.5262	−3.27275
$88$	−42.5971	−4.54086
$89$	2.67831	0.283901	0.141950	−	0.989874i	$-0.454663\pi$
$89$	2.67831	0.283901	0.141950	+	0.989874i	$0.454663\pi$
$90$	−58.9115	−6.20981
$91$	−10.3757	−1.08767
$92$	−45.3701	−4.73016
$93$	3.76928	0.390856
$94$	−8.33669	−0.859863
$95$	−8.87399	−0.910452
$96$	−91.3852	−9.32697
$97$	−3.10303	−0.315065	−0.157532	−	0.987514i	$-0.550354\pi$
$97$	−3.10303	−0.315065	−0.157532	+	0.987514i	$0.550354\pi$
$98$	−10.4871	−1.05936
$99$	23.8733	2.39936
$100$	41.4052	4.14052
$101$	−2.04236	−0.203222	−0.101611	−	0.994824i	$-0.532400\pi$
$101$	−2.04236	−0.203222	−0.101611	+	0.994824i	$0.532400\pi$
$102$	−29.3858	−2.90963
$103$	−5.29484	−0.521716	−0.260858	−	0.965377i	$-0.584005\pi$
$103$	−5.29484	−0.521716	−0.260858	+	0.965377i	$0.584005\pi$
$104$	34.1736	3.35100
$105$	34.2625	3.34368
$106$	6.07567	0.590121
$107$	−3.52187	−0.340472	−0.170236	−	0.985403i	$-0.554453\pi$
$107$	−3.52187	−0.340472	−0.170236	+	0.985403i	$0.554453\pi$
$108$	53.6980	5.16709
$109$	9.61036	0.920505	0.460253	−	0.887788i	$-0.347759\pi$
$109$	9.61036	0.920505	0.460253	+	0.887788i	$0.347759\pi$
$110$	−38.4236	−3.66355
$111$	−9.95935	−0.945300
$112$	60.7833	5.74348
$113$	−2.12087	−0.199515	−0.0997574	−	0.995012i	$-0.531807\pi$
$113$	−2.12087	−0.199515	−0.0997574	+	0.995012i	$0.531807\pi$
$114$	21.5278	2.01626
$115$	−26.9391	−2.51208
$116$	−59.3851	−5.51377
$117$	−19.1524	−1.77064
$118$	26.7010	2.45803
$119$	11.4252	1.04735
$120$	−112.848	−10.3015
$121$	4.57078	0.415525
$122$	−32.7649	−2.96639
$123$	−15.9499	−1.43816
$124$	7.33269	0.658495
$125$	7.21037	0.644915
$126$	−55.5659	−4.95020
$127$	11.1710	0.991266	0.495633	−	0.868532i	$-0.334936\pi$
$127$	11.1710	0.991266	0.495633	+	0.868532i	$0.334936\pi$
$128$	−73.8441	−6.52696
$129$	7.47523	0.658158
$130$	30.8254	2.70357
$131$	−14.5132	−1.26802	−0.634011	−	0.773324i	$-0.718593\pi$
$131$	−14.5132	−1.26802	−0.634011	+	0.773324i	$0.718593\pi$
$132$	69.4720	6.04676
$133$	−8.37003	−0.725774
$134$	−1.93255	−0.166947
$135$	31.8839	2.74413
$136$	−37.6303	−3.22677
$137$	−13.5947	−1.16147	−0.580737	−	0.814092i	$-0.697235\pi$
$137$	−13.5947	−1.16147	−0.580737	+	0.814092i	$0.697235\pi$
$138$	65.3528	5.56320
$139$	−5.20401	−0.441398	−0.220699	−	0.975342i	$-0.570834\pi$
$139$	−5.20401	−0.441398	−0.220699	+	0.975342i	$0.570834\pi$
$140$	66.6538	5.63327
$141$	8.94991	0.753718
$142$	−43.0322	−3.61118
$143$	−12.4917	−1.04461
$144$	112.199	9.34993
$145$	−35.2607	−2.92824
$146$	19.5260	1.61599
$147$	11.2585	0.928584
$148$	−19.3748	−1.59259
$149$	−9.66787	−0.792023	−0.396011	−	0.918246i	$-0.629606\pi$
$149$	−9.66787	−0.792023	−0.396011	+	0.918246i	$0.629606\pi$
$150$	−59.6417	−4.86972
$151$	16.6236	1.35281	0.676406	−	0.736529i	$-0.263537\pi$
$151$	16.6236	1.35281	0.676406	+	0.736529i	$0.263537\pi$
$152$	27.5677	2.23603
$153$	21.0897	1.70500
$154$	−36.2415	−2.92042
$155$	4.35388	0.349712
$156$	−55.7341	−4.46230
$157$	−2.38601	−0.190425	−0.0952123	−	0.995457i	$-0.530353\pi$
$157$	−2.38601	−0.190425	−0.0952123	+	0.995457i	$0.530353\pi$
$158$	9.97202	0.793331
$159$	−6.52258	−0.517274
$160$	−105.559	−8.34516
$161$	−25.4092	−2.00253
$162$	−26.4884	−2.08113
$163$	−6.99963	−0.548253	−0.274127	−	0.961694i	$-0.588389\pi$
$163$	−6.99963	−0.548253	−0.274127	+	0.961694i	$0.588389\pi$
$164$	−31.0287	−2.42294
$165$	41.2499	3.21130
$166$	35.5079	2.75595
$167$	−10.9266	−0.845526	−0.422763	−	0.906240i	$-0.638940\pi$
$167$	−10.9266	−0.845526	−0.422763	+	0.906240i	$0.638940\pi$
$168$	−106.439	−8.21195
$169$	−2.97851	−0.229116
$170$	−33.9434	−2.60334
$171$	−15.4501	−1.18150
$172$	14.5422	1.10883
$173$	−15.3322	−1.16568	−0.582842	−	0.812586i	$-0.698059\pi$
$173$	−15.3322	−1.16568	−0.582842	+	0.812586i	$0.698059\pi$
$174$	85.5406	6.48482
$175$	23.1887	1.75290
$176$	73.1792	5.51609
$177$	−28.6651	−2.15460
$178$	−7.50518	−0.562537
$179$	0.319940	0.0239134	0.0119567	−	0.999929i	$-0.496194\pi$
$179$	0.319940	0.0239134	0.0119567	+	0.999929i	$0.496194\pi$
$180$	123.035	9.17052
$181$	17.8746	1.32861	0.664305	−	0.747462i	$-0.268728\pi$
$181$	17.8746	1.32861	0.664305	+	0.747462i	$0.268728\pi$
$182$	29.0748	2.15517
$183$	35.1750	2.60021
$184$	83.6882	6.16958
$185$	−11.5040	−0.845792
$186$	−10.5623	−0.774464
$187$	13.7552	1.00588
$188$	17.4110	1.26983
$189$	30.0732	2.18750
$190$	24.8667	1.80402
$191$	10.9771	0.794273	0.397137	−	0.917759i	$-0.370004\pi$
$191$	10.9771	0.794273	0.397137	+	0.917759i	$0.370004\pi$
$192$	144.500	10.4284
$193$	9.59116	0.690387	0.345193	−	0.938532i	$-0.387813\pi$
$193$	9.59116	0.690387	0.345193	+	0.938532i	$0.387813\pi$
$194$	8.69531	0.624287
$195$	−33.0929	−2.36983
$196$	21.9021	1.56443
$197$	15.5341	1.10676	0.553379	−	0.832930i	$-0.313338\pi$
$197$	15.5341	1.10676	0.553379	+	0.832930i	$0.313338\pi$
$198$	−66.8978	−4.75422
$199$	−10.1524	−0.719682	−0.359841	−	0.933014i	$-0.617169\pi$
$199$	−10.1524	−0.719682	−0.359841	+	0.933014i	$0.617169\pi$
$200$	−76.3748	−5.40051
$201$	2.07471	0.146338
$202$	5.72311	0.402677
$203$	−33.2583	−2.33427
$204$	61.3716	4.29687
$205$	−18.4237	−1.28677
$206$	14.8372	1.03376
$207$	−46.9026	−3.25995
$208$	−58.7082	−4.07068
$209$	−10.0770	−0.697040
$210$	−96.0106	−6.62536
$211$	11.5077	0.792222	0.396111	−	0.918203i	$-0.370360\pi$
$211$	11.5077	0.792222	0.396111	+	0.918203i	$0.370360\pi$
$212$	−12.6889	−0.871478
$213$	46.1975	3.16540
$214$	9.86901	0.674632
$215$	8.63462	0.588876
$216$	−99.0496	−6.73947
$217$	4.10662	0.278776
$218$	−26.9302	−1.82394
$219$	−20.9623	−1.41650
$220$	80.2469	5.41025
$221$	−11.0352	−0.742306
$222$	27.9081	1.87307
$223$	19.3861	1.29819	0.649096	−	0.760707i	$-0.275147\pi$
$223$	19.3861	1.29819	0.649096	+	0.760707i	$0.275147\pi$
$224$	−99.5641	−6.65240
$225$	42.8038	2.85359
$226$	5.94311	0.395330
$227$	23.2215	1.54127	0.770634	−	0.637279i	$-0.219940\pi$
$227$	23.2215	1.54127	0.770634	+	0.637279i	$0.219940\pi$
$228$	−44.9604	−2.97758
$229$	3.73572	0.246863	0.123432	−	0.992353i	$-0.460610\pi$
$229$	3.73572	0.246863	0.123432	+	0.992353i	$0.460610\pi$
$230$	75.4888	4.97758
$231$	38.9073	2.55991
$232$	109.540	7.19165
$233$	−16.2430	−1.06411	−0.532056	−	0.846709i	$-0.678580\pi$
$233$	−16.2430	−1.06411	−0.532056	+	0.846709i	$0.678580\pi$
$234$	53.6689	3.50845
$235$	10.3380	0.674378
$236$	−55.7645	−3.62996
$237$	−10.7055	−0.695399
$238$	−32.0158	−2.07528
$239$	0.872851	0.0564600	0.0282300	−	0.999601i	$-0.491013\pi$
$239$	0.872851	0.0564600	0.0282300	+	0.999601i	$0.491013\pi$
$240$	193.866	12.5140
$241$	15.3923	0.991507	0.495754	−	0.868463i	$-0.334892\pi$
$241$	15.3923	0.991507	0.495754	+	0.868463i	$0.334892\pi$
$242$	−12.8083	−0.823346
$243$	0.910431	0.0584042
$244$	68.4288	4.38071
$245$	13.0046	0.830836
$246$	44.6950	2.84965
$247$	8.08428	0.514391
$248$	−13.5256	−0.858880
$249$	−38.1198	−2.41574
$250$	−20.2049	−1.27787
$251$	7.47837	0.472031	0.236015	−	0.971749i	$-0.424158\pi$
$251$	7.47837	0.472031	0.236015	+	0.971749i	$0.424158\pi$
$252$	116.048	7.31035
$253$	−30.5911	−1.92324
$254$	−31.3034	−1.96415
$255$	36.4402	2.28198
$256$	110.860	6.92873
$257$	5.14870	0.321167	0.160584	−	0.987022i	$-0.448662\pi$
$257$	5.14870	0.321167	0.160584	+	0.987022i	$0.448662\pi$
$258$	−20.9471	−1.30411
$259$	−10.8507	−0.674230
$260$	−64.3783	−3.99257
$261$	−61.3910	−3.80001
$262$	40.6689	2.51253
$263$	28.3820	1.75011	0.875055	−	0.484023i	$-0.160825\pi$
$263$	28.3820	1.75011	0.875055	+	0.484023i	$0.160825\pi$
$264$	−128.146	−7.88684
$265$	−7.53421	−0.462823
$266$	23.4545	1.43809
$267$	8.05724	0.493095
$268$	4.03610	0.246544
$269$	−3.43072	−0.209175	−0.104587	−	0.994516i	$-0.533352\pi$
$269$	−3.43072	−0.209175	−0.104587	+	0.994516i	$0.533352\pi$
$270$	−89.3451	−5.43737
$271$	−10.4566	−0.635194	−0.317597	−	0.948226i	$-0.602876\pi$
$271$	−10.4566	−0.635194	−0.317597	+	0.948226i	$0.602876\pi$
$272$	64.6466	3.91977
$273$	−31.2135	−1.88913
$274$	38.0951	2.30141
$275$	27.9178	1.68350
$276$	−136.488	−8.21561
$277$	13.4247	0.806613	0.403307	−	0.915065i	$-0.367861\pi$
$277$	13.4247	0.806613	0.403307	+	0.915065i	$0.367861\pi$
$278$	14.5827	0.874611
$279$	7.58037	0.453825
$280$	−122.947	−7.34752
$281$	−4.08604	−0.243753	−0.121876	−	0.992545i	$-0.538891\pi$
$281$	−4.08604	−0.243753	−0.121876	+	0.992545i	$0.538891\pi$
$282$	−25.0795	−1.49346
$283$	−9.03943	−0.537338	−0.268669	−	0.963233i	$-0.586584\pi$
$283$	−9.03943	−0.537338	−0.268669	+	0.963233i	$0.586584\pi$
$284$	89.8719	5.33292
$285$	−26.6958	−1.58132
$286$	35.0043	2.06985
$287$	−17.3774	−1.02576
$288$	−183.784	−10.8296
$289$	−4.84861	−0.285212
$290$	98.8077	5.80219
$291$	−9.33491	−0.547222
$292$	−40.7797	−2.38645
$293$	22.2818	1.30172	0.650858	−	0.759199i	$-0.274409\pi$
$293$	22.2818	1.30172	0.650858	+	0.759199i	$0.274409\pi$
$294$	−31.5486	−1.83995
$295$	−33.1109	−1.92779
$296$	35.7381	2.07723
$297$	36.2062	2.10090
$298$	27.0913	1.56936
$299$	24.5418	1.41929
$300$	124.560	7.19150
$301$	8.14426	0.469427
$302$	−46.5828	−2.68054
$303$	−6.14408	−0.352968
$304$	−47.3596	−2.71626
$305$	40.6305	2.32650
$306$	−59.0976	−3.37838
$307$	−3.11506	−0.177786	−0.0888929	−	0.996041i	$-0.528333\pi$
$307$	−3.11506	−0.177786	−0.0888929	+	0.996041i	$0.528333\pi$
$308$	75.6897	4.31282
$309$	−15.9286	−0.906147
$310$	−12.2005	−0.692940
$311$	−11.7983	−0.669019	−0.334510	−	0.942392i	$-0.608571\pi$
$311$	−11.7983	−0.669019	−0.334510	+	0.942392i	$0.608571\pi$
$312$	102.805	5.82021
$313$	−19.9090	−1.12532	−0.562661	−	0.826688i	$-0.690222\pi$
$313$	−19.9090	−1.12532	−0.562661	+	0.826688i	$0.690222\pi$
$314$	6.68609	0.377318
$315$	68.9052	3.88237
$316$	−20.8264	−1.17157
$317$	−0.451454	−0.0253562	−0.0126781	−	0.999920i	$-0.504036\pi$
$317$	−0.451454	−0.0253562	−0.0126781	+	0.999920i	$0.504036\pi$
$318$	18.2776	1.02496
$319$	−40.0408	−2.24186
$320$	166.911	9.33062
$321$	−10.5949	−0.591352
$322$	71.2018	3.96792
$323$	−8.90202	−0.495321
$324$	55.3205	3.07336
$325$	−22.3971	−1.24237
$326$	19.6144	1.08634
$327$	28.9111	1.59879
$328$	57.2346	3.16025
$329$	9.75091	0.537585
$330$	−115.591	−6.36306
$331$	−12.2653	−0.674163	−0.337081	−	0.941476i	$-0.609440\pi$
$331$	−12.2653	−0.674163	−0.337081	+	0.941476i	$0.609440\pi$
$332$	−74.1575	−4.06992
$333$	−20.0292	−1.09759
$334$	30.6186	1.67537
$335$	2.39649	0.130934
$336$	182.856	9.97560
$337$	−15.0703	−0.820932	−0.410466	−	0.911876i	$-0.634634\pi$
$337$	−15.0703	−0.820932	−0.410466	+	0.911876i	$0.634634\pi$
$338$	8.34639	0.453984
$339$	−6.38027	−0.346529
$340$	70.8902	3.84456
$341$	4.94411	0.267739
$342$	43.2944	2.34110
$343$	−10.6769	−0.576496
$344$	−26.8241	−1.44626
$345$	−81.0416	−4.36313
$346$	42.9639	2.30975
$347$	16.9293	0.908811	0.454406	−	0.890795i	$-0.349852\pi$
$347$	16.9293	0.908811	0.454406	+	0.890795i	$0.349852\pi$
$348$	−178.650	−9.57664
$349$	22.5275	1.20587	0.602936	−	0.797790i	$-0.293997\pi$
$349$	22.5275	1.20587	0.602936	+	0.797790i	$0.293997\pi$
$350$	−64.9795	−3.47330
$351$	−29.0465	−1.55039
$352$	−119.869	−6.38903
$353$	7.40332	0.394039	0.197019	−	0.980400i	$-0.436874\pi$
$353$	7.40332	0.394039	0.197019	+	0.980400i	$0.436874\pi$
$354$	80.3254	4.26925
$355$	53.3626	2.83220
$356$	15.6744	0.830742
$357$	34.3708	1.81909
$358$	−0.896536	−0.0473834
$359$	16.6334	0.877875	0.438938	−	0.898518i	$-0.355355\pi$
$359$	16.6334	0.877875	0.438938	+	0.898518i	$0.355355\pi$
$360$	−226.947	−11.9612
$361$	−12.4784	−0.656760
$362$	−50.0883	−2.63258
$363$	13.7504	0.721708
$364$	−60.7222	−3.18271
$365$	−24.2135	−1.26739
$366$	−98.5675	−5.15220
$367$	−21.3146	−1.11261	−0.556306	−	0.830978i	$-0.687782\pi$
$367$	−21.3146	−1.11261	−0.556306	+	0.830978i	$0.687782\pi$
$368$	−143.771	−7.49460
$369$	−32.0768	−1.66985
$370$	32.2366	1.67590
$371$	−7.10634	−0.368943
$372$	22.0591	1.14371
$373$	13.7501	0.711951	0.355976	−	0.934495i	$-0.384149\pi$
$373$	13.7501	0.711951	0.355976	+	0.934495i	$0.384149\pi$
$374$	−38.5450	−1.99311
$375$	21.6912	1.12013
$376$	−32.1158	−1.65624
$377$	32.1228	1.65441
$378$	−84.2712	−4.33444
$379$	29.2279	1.50134	0.750669	−	0.660679i	$-0.229731\pi$
$379$	29.2279	1.50134	0.750669	+	0.660679i	$0.229731\pi$
$380$	−51.9336	−2.66414
$381$	33.6060	1.72169
$382$	−30.7600	−1.57382
$383$	14.0727	0.719083	0.359541	−	0.933129i	$-0.382933\pi$
$383$	14.0727	0.719083	0.359541	+	0.933129i	$0.382933\pi$
$384$	−222.147	−11.3364
$385$	44.9417	2.29044
$386$	−26.8764	−1.36797
$387$	15.0334	0.764190
$388$	−18.1600	−0.921933
$389$	14.9485	0.757921	0.378960	−	0.925413i	$-0.376282\pi$
$389$	14.9485	0.757921	0.378960	+	0.925413i	$0.376282\pi$
$390$	92.7329	4.69571
$391$	−27.0242	−1.36667
$392$	−40.3999	−2.04050
$393$	−43.6604	−2.20238
$394$	−43.5297	−2.19299
$395$	−12.3659	−0.622197
$396$	139.715	7.02093
$397$	6.45424	0.323929	0.161964	−	0.986797i	$-0.448217\pi$
$397$	6.45424	0.323929	0.161964	+	0.986797i	$0.448217\pi$
$398$	28.4490	1.42602
$399$	−25.1798	−1.26057
$400$	131.207	6.56036
$401$	−4.96728	−0.248054	−0.124027	−	0.992279i	$-0.539581\pi$
$401$	−4.96728	−0.248054	−0.124027	+	0.992279i	$0.539581\pi$
$402$	−5.81375	−0.289963
$403$	−3.96643	−0.197582
$404$	−11.9526	−0.594664
$405$	32.8473	1.63219
$406$	93.1964	4.62526
$407$	−13.0636	−0.647537
$408$	−113.204	−5.60444
$409$	11.7635	0.581667	0.290834	−	0.956774i	$-0.406067\pi$
$409$	11.7635	0.581667	0.290834	+	0.956774i	$0.406067\pi$
$410$	51.6270	2.54968
$411$	−40.8973	−2.01731
$412$	−30.9872	−1.52663
$413$	−31.2306	−1.53676
$414$	131.431	6.45946
$415$	−44.0320	−2.16145
$416$	96.1651	4.71488
$417$	−15.6553	−0.766645
$418$	28.2378	1.38115
$419$	24.8034	1.21173	0.605864	−	0.795569i	$-0.292828\pi$
$419$	24.8034	1.21173	0.605864	+	0.795569i	$0.292828\pi$
$420$	200.516	9.78419
$421$	13.3850	0.652346	0.326173	−	0.945310i	$-0.394241\pi$
$421$	13.3850	0.652346	0.326173	+	0.945310i	$0.394241\pi$
$422$	−32.2469	−1.56975
$423$	17.9991	0.875146
$424$	23.4056	1.13667
$425$	24.6626	1.19631
$426$	−129.455	−6.27211
$427$	38.3231	1.85458
$428$	−20.6112	−0.996281
$429$	−37.5791	−1.81434
$430$	−24.1960	−1.16683
$431$	8.53060	0.410905	0.205452	−	0.978667i	$-0.434133\pi$
$431$	8.53060	0.410905	0.205452	+	0.978667i	$0.434133\pi$
$432$	170.161	8.18688
$433$	20.7368	0.996548	0.498274	−	0.867020i	$-0.333967\pi$
$433$	20.7368	0.996548	0.498274	+	0.867020i	$0.333967\pi$
$434$	−11.5076	−0.552382
$435$	−106.076	−5.08594
$436$	56.2431	2.69356
$437$	19.7977	0.947053
$438$	58.7407	2.80674
$439$	−31.7694	−1.51627	−0.758136	−	0.652096i	$-0.773890\pi$
$439$	−31.7694	−1.51627	−0.758136	+	0.652096i	$0.773890\pi$
$440$	−148.021	−7.05662
$441$	22.6419	1.07818
$442$	30.9228	1.47085
$443$	0.683737	0.0324853	0.0162427	−	0.999868i	$-0.494830\pi$
$443$	0.683737	0.0324853	0.0162427	+	0.999868i	$0.494830\pi$
$444$	−58.2856	−2.76611
$445$	9.30689	0.441189
$446$	−54.3239	−2.57231
$447$	−29.0841	−1.37563
$448$	157.432	7.43798
$449$	23.1891	1.09436	0.547180	−	0.837015i	$-0.315701\pi$
$449$	23.1891	1.09436	0.547180	+	0.837015i	$0.315701\pi$
$450$	−119.945	−5.65426
$451$	−20.9213	−0.985147
$452$	−12.4121	−0.583814
$453$	50.0093	2.34964
$454$	−65.0715	−3.05395
$455$	−36.0546	−1.69027
$456$	82.9325	3.88367
$457$	3.29091	0.153942	0.0769711	−	0.997033i	$-0.475475\pi$
$457$	3.29091	0.153942	0.0769711	+	0.997033i	$0.475475\pi$
$458$	−10.4682	−0.489149
$459$	31.9846	1.49291
$460$	−157.657	−7.35079
$461$	40.0943	1.86738	0.933689	−	0.358086i	$-0.116571\pi$
$461$	40.0943	1.86738	0.933689	+	0.358086i	$0.116571\pi$
$462$	−109.026	−5.07236
$463$	−12.1401	−0.564200	−0.282100	−	0.959385i	$-0.591031\pi$
$463$	−12.1401	−0.564200	−0.282100	+	0.959385i	$0.591031\pi$
$464$	−188.183	−8.73618
$465$	13.0979	0.607400
$466$	45.5161	2.10849
$467$	−25.5876	−1.18405	−0.592026	−	0.805919i	$-0.701672\pi$
$467$	−25.5876	−1.18405	−0.592026	+	0.805919i	$0.701672\pi$
$468$	−112.086	−5.18120
$469$	2.26039	0.104375
$470$	−28.9692	−1.33625
$471$	−7.17790	−0.330740
$472$	102.862	4.73459
$473$	9.80517	0.450842
$474$	29.9991	1.37790
$475$	−18.0676	−0.828999
$476$	66.8643	3.06472
$477$	−13.1175	−0.600610
$478$	−2.44590	−0.111873
$479$	30.2186	1.38072	0.690361	−	0.723465i	$-0.257452\pi$
$479$	30.2186	1.38072	0.690361	+	0.723465i	$0.257452\pi$
$480$	−317.555	−14.4943
$481$	10.4803	0.477859
$482$	−43.1324	−1.96463
$483$	−76.4392	−3.47810
$484$	26.7498	1.21590
$485$	−10.7827	−0.489619
$486$	−2.55121	−0.115725
$487$	7.57067	0.343060	0.171530	−	0.985179i	$-0.445129\pi$
$487$	7.57067	0.343060	0.171530	+	0.985179i	$0.445129\pi$
$488$	−126.222	−5.71379
$489$	−21.0572	−0.952237
$490$	−36.4417	−1.64627
$491$	−30.3763	−1.37086	−0.685432	−	0.728137i	$-0.740387\pi$
$491$	−30.3763	−1.37086	−0.685432	+	0.728137i	$0.740387\pi$
$492$	−93.3445	−4.20830
$493$	−35.3721	−1.59308
$494$	−22.6538	−1.01924
$495$	82.9575	3.72866
$496$	23.2362	1.04334
$497$	50.3322	2.25771
$498$	106.819	4.78669
$499$	39.4823	1.76747	0.883735	−	0.467988i	$-0.155021\pi$
$499$	39.4823	1.76747	0.883735	+	0.467988i	$0.155021\pi$
$500$	42.1976	1.88713
$501$	−32.8708	−1.46856
$502$	−20.9559	−0.935308
$503$	21.3163	0.950448	0.475224	−	0.879865i	$-0.342367\pi$
$503$	21.3163	0.950448	0.475224	+	0.879865i	$0.342367\pi$
$504$	−214.059	−9.53494
$505$	−7.09701	−0.315813
$506$	85.7224	3.81083
$507$	−8.96033	−0.397942
$508$	65.3765	2.90061
$509$	−26.7125	−1.18401	−0.592005	−	0.805934i	$-0.701664\pi$
$509$	−26.7125	−1.18401	−0.592005	+	0.805934i	$0.701664\pi$
$510$	−102.113	−4.52164
$511$	−22.8384	−1.01031
$512$	−162.963	−7.20203
$513$	−23.4317	−1.03453
$514$	−14.4277	−0.636379
$515$	−18.3991	−0.810760
$516$	43.7476	1.92588
$517$	11.7395	0.516302
$518$	30.4059	1.33596
$519$	−46.1242	−2.02463
$520$	118.750	5.20754
$521$	7.12440	0.312126	0.156063	−	0.987747i	$-0.450120\pi$
$521$	7.12440	0.312126	0.156063	+	0.987747i	$0.450120\pi$
$522$	172.030	7.52955
$523$	12.1175	0.529863	0.264931	−	0.964267i	$-0.414651\pi$
$523$	12.1175	0.529863	0.264931	+	0.964267i	$0.414651\pi$
$524$	−84.9362	−3.71045
$525$	69.7592	3.04454
$526$	−79.5322	−3.46777
$527$	4.36763	0.190257
$528$	220.147	9.58066
$529$	37.1007	1.61307
$530$	21.1124	0.917063
$531$	−57.6481	−2.50172
$532$	−48.9843	−2.12374
$533$	16.7842	0.727004
$534$	−22.5780	−0.977047
$535$	−12.2382	−0.529103
$536$	−7.44486	−0.321569
$537$	0.962483	0.0415342
$538$	9.61357	0.414470
$539$	14.7676	0.636086
$540$	186.595	8.02979
$541$	38.7365	1.66541	0.832705	−	0.553716i	$-0.186791\pi$
$541$	38.7365	1.66541	0.832705	+	0.553716i	$0.186791\pi$
$542$	29.3015	1.25861
$543$	53.7727	2.30761
$544$	−105.892	−4.54009
$545$	33.3951	1.43049
$546$	87.4666	3.74322
$547$	34.3473	1.46858	0.734292	−	0.678834i	$-0.237514\pi$
$547$	34.3473	1.46858	0.734292	+	0.678834i	$0.237514\pi$
$548$	−79.5608	−3.39867
$549$	70.7402	3.01912
$550$	−78.2312	−3.33579
$551$	25.9133	1.10395
$552$	251.761	10.7157
$553$	−11.6637	−0.495989
$554$	−37.6188	−1.59827
$555$	−34.6078	−1.46902
$556$	−30.4556	−1.29161
$557$	−13.4145	−0.568390	−0.284195	−	0.958767i	$-0.591726\pi$
$557$	−13.4145	−0.568390	−0.284195	+	0.958767i	$0.591726\pi$
$558$	−21.2417	−0.899234
$559$	−7.86622	−0.332706
$560$	211.216	8.92552
$561$	41.3802	1.74707
$562$	11.4499	0.482986
$563$	−13.1113	−0.552574	−0.276287	−	0.961075i	$-0.589104\pi$
$563$	−13.1113	−0.552574	−0.276287	+	0.961075i	$0.589104\pi$
$564$	52.3779	2.20551
$565$	−7.36983	−0.310051
$566$	25.3303	1.06471
$567$	30.9819	1.30112
$568$	−165.775	−6.95576
$569$	−42.5621	−1.78430	−0.892149	−	0.451742i	$-0.850803\pi$
$569$	−42.5621	−1.78430	−0.892149	+	0.451742i	$0.850803\pi$
$570$	74.8072	3.13333
$571$	−3.10954	−0.130130	−0.0650652	−	0.997881i	$-0.520726\pi$
$571$	−3.10954	−0.130130	−0.0650652	+	0.997881i	$0.520726\pi$
$572$	−73.1057	−3.05670
$573$	33.0226	1.37954
$574$	48.6951	2.03250
$575$	−54.8485	−2.28734
$576$	290.602	12.1084
$577$	−14.4810	−0.602854	−0.301427	−	0.953489i	$-0.597463\pi$
$577$	−14.4810	−0.602854	−0.301427	+	0.953489i	$0.597463\pi$
$578$	13.5868	0.565136
$579$	28.8533	1.19910
$580$	−206.358	−8.56854
$581$	−41.5314	−1.72301
$582$	26.1583	1.08430
$583$	−8.55558	−0.354336
$584$	75.2210	3.11267
$585$	−66.5528	−2.75162
$586$	−62.4381	−2.57929
$587$	41.5195	1.71369	0.856847	−	0.515571i	$-0.172420\pi$
$587$	41.5195	1.71369	0.856847	+	0.515571i	$0.172420\pi$
$588$	65.8885	2.71720
$589$	−3.19970	−0.131841
$590$	92.7836	3.81984
$591$	46.7316	1.92228
$592$	−61.3958	−2.52335
$593$	27.2253	1.11801	0.559005	−	0.829164i	$-0.311183\pi$
$593$	27.2253	1.11801	0.559005	+	0.829164i	$0.311183\pi$
$594$	−101.457	−4.16284
$595$	39.7016	1.62761
$596$	−56.5797	−2.31759
$597$	−30.5416	−1.24998
$598$	−68.7710	−2.81226
$599$	17.3478	0.708812	0.354406	−	0.935092i	$-0.384683\pi$
$599$	17.3478	0.708812	0.354406	+	0.935092i	$0.384683\pi$
$600$	−229.760	−9.37992
$601$	−45.0476	−1.83753	−0.918765	−	0.394804i	$-0.870812\pi$
$601$	−45.0476	−1.83753	−0.918765	+	0.394804i	$0.870812\pi$
$602$	−22.8219	−0.930150
$603$	4.17243	0.169914
$604$	97.2872	3.95856
$605$	15.8830	0.645737
$606$	17.2170	0.699392
$607$	2.95614	0.119986	0.0599929	−	0.998199i	$-0.480892\pi$
$607$	2.95614	0.119986	0.0599929	+	0.998199i	$0.480892\pi$
$608$	77.5759	3.14612
$609$	−100.052	−4.05430
$610$	−113.855	−4.60985
$611$	−9.41803	−0.381013
$612$	123.424	4.98912
$613$	−21.1374	−0.853732	−0.426866	−	0.904315i	$-0.640382\pi$
$613$	−21.1374	−0.853732	−0.426866	+	0.904315i	$0.640382\pi$
$614$	8.72903	0.352275
$615$	−55.4246	−2.23493
$616$	−139.615	−5.62524
$617$	−32.2072	−1.29661	−0.648306	−	0.761380i	$-0.724522\pi$
$617$	−32.2072	−1.29661	−0.648306	+	0.761380i	$0.724522\pi$
$618$	44.6352	1.79549
$619$	−37.5281	−1.50838	−0.754192	−	0.656654i	$-0.771971\pi$
$619$	−37.5281	−1.50838	−0.754192	+	0.656654i	$0.771971\pi$
$620$	25.4804	1.02332
$621$	−71.1324	−2.85445
$622$	33.0612	1.32563
$623$	8.77835	0.351697
$624$	−176.613	−7.07019
$625$	−10.3195	−0.412781
$626$	55.7890	2.22978
$627$	−30.3149	−1.21066
$628$	−13.9638	−0.557215
$629$	−11.5404	−0.460144
$630$	−193.086	−7.69274
$631$	41.5482	1.65401	0.827004	−	0.562197i	$-0.190044\pi$
$631$	41.5482	1.65401	0.827004	+	0.562197i	$0.190044\pi$
$632$	38.4156	1.52809
$633$	34.6189	1.37598
$634$	1.26507	0.0502422
$635$	38.8182	1.54045
$636$	−38.1724	−1.51363
$637$	−11.8474	−0.469409
$638$	112.203	4.44214
$639$	92.9076	3.67537
$640$	−256.602	−10.1431
$641$	14.8761	0.587570	0.293785	−	0.955872i	$-0.405085\pi$
$641$	14.8761	0.587570	0.293785	+	0.955872i	$0.405085\pi$
$642$	29.6892	1.17174
$643$	−34.8774	−1.37543	−0.687715	−	0.725981i	$-0.741386\pi$
$643$	−34.8774	−1.37543	−0.687715	+	0.725981i	$0.741386\pi$
$644$	−148.703	−5.85974
$645$	25.9757	1.02279
$646$	24.9453	0.981458
$647$	4.30487	0.169242	0.0846210	−	0.996413i	$-0.473032\pi$
$647$	4.30487	0.169242	0.0846210	+	0.996413i	$0.473032\pi$
$648$	−102.042	−4.00861
$649$	−37.5996	−1.47591
$650$	62.7612	2.46170
$651$	12.3541	0.484194
$652$	−40.9642	−1.60428
$653$	15.3579	0.601001	0.300501	−	0.953782i	$-0.402846\pi$
$653$	15.3579	0.601001	0.300501	+	0.953782i	$0.402846\pi$
$654$	−81.0147	−3.16793
$655$	−50.4320	−1.97054
$656$	−98.3256	−3.83897
$657$	−42.1572	−1.64471
$658$	−27.3240	−1.06520
$659$	8.11817	0.316239	0.158120	−	0.987420i	$-0.449457\pi$
$659$	8.11817	0.316239	0.158120	+	0.987420i	$0.449457\pi$
$660$	241.409	9.39683
$661$	9.00197	0.350136	0.175068	−	0.984556i	$-0.443985\pi$
$661$	9.00197	0.350136	0.175068	+	0.984556i	$0.443985\pi$
$662$	34.3699	1.33582
$663$	−33.1974	−1.28928
$664$	136.789	5.30843
$665$	−29.0851	−1.12787
$666$	56.1259	2.17483
$667$	78.6661	3.04596
$668$	−63.9462	−2.47415
$669$	58.3198	2.25477
$670$	−6.71544	−0.259440
$671$	46.1386	1.78116
$672$	−299.521	−11.5543
$673$	−2.15883	−0.0832169	−0.0416084	−	0.999134i	$-0.513248\pi$
$673$	−2.15883	−0.0832169	−0.0416084	+	0.999134i	$0.513248\pi$
$674$	42.2301	1.62664
$675$	64.9162	2.49863
$676$	−17.4313	−0.670433
$677$	−3.74781	−0.144040	−0.0720201	−	0.997403i	$-0.522945\pi$
$677$	−3.74781	−0.144040	−0.0720201	+	0.997403i	$0.522945\pi$
$678$	17.8788	0.686632
$679$	−10.1704	−0.390303
$680$	−130.762	−5.01449
$681$	69.8579	2.67696
$682$	−13.8544	−0.530513
$683$	−35.3611	−1.35306	−0.676528	−	0.736417i	$-0.736516\pi$
$683$	−35.3611	−1.35306	−0.676528	+	0.736417i	$0.736516\pi$
$684$	−90.4195	−3.45728
$685$	−47.2403	−1.80496
$686$	29.9187	1.14230
$687$	11.2383	0.428766
$688$	46.0821	1.75686
$689$	6.86374	0.261488
$690$	227.095	8.64536
$691$	28.9290	1.10051	0.550255	−	0.834997i	$-0.314531\pi$
$691$	28.9290	1.10051	0.550255	+	0.834997i	$0.314531\pi$
$692$	−89.7291	−3.41099
$693$	78.2463	2.97233
$694$	−47.4393	−1.80077
$695$	−18.0834	−0.685944
$696$	329.532	12.4909
$697$	−18.4819	−0.700053
$698$	−63.1268	−2.38938
$699$	−48.8641	−1.84821
$700$	135.708	5.12930
$701$	50.1604	1.89453	0.947267	−	0.320446i	$-0.103833\pi$
$701$	50.1604	1.89453	0.947267	+	0.320446i	$0.103833\pi$
$702$	81.3942	3.07203
$703$	8.45438	0.318863
$704$	189.538	7.14350
$705$	31.1001	1.17130
$706$	−20.7456	−0.780771
$707$	−6.69397	−0.251753
$708$	−167.758	−6.30473
$709$	13.6065	0.511003	0.255502	−	0.966809i	$-0.417759\pi$
$709$	13.6065	0.511003	0.255502	+	0.966809i	$0.417759\pi$
$710$	−149.533	−5.61187
$711$	−21.5298	−0.807431
$712$	−28.9125	−1.08354
$713$	−9.71344	−0.363771
$714$	−96.3139	−3.60446
$715$	−43.4075	−1.62335
$716$	1.87240	0.0699748
$717$	2.62582	0.0980630
$718$	−46.6101	−1.73947
$719$	−38.2527	−1.42658	−0.713292	−	0.700867i	$-0.752797\pi$
$719$	−38.2527	−1.42658	−0.713292	+	0.700867i	$0.752797\pi$
$720$	389.882	14.5300
$721$	−17.3542	−0.646304
$722$	34.9672	1.30134
$723$	46.3051	1.72211
$724$	104.608	3.88774
$725$	−71.7915	−2.66627
$726$	−38.5314	−1.43003
$727$	−0.911151	−0.0337927	−0.0168964	−	0.999857i	$-0.505379\pi$
$727$	−0.911151	−0.0337927	−0.0168964	+	0.999857i	$0.505379\pi$
$728$	112.006	4.15123
$729$	−25.6192	−0.948861
$730$	67.8512	2.51129
$731$	8.66190	0.320372
$732$	205.856	7.60866
$733$	−16.3933	−0.605499	−0.302749	−	0.953070i	$-0.597904\pi$
$733$	−16.3933	−0.605499	−0.302749	+	0.953070i	$0.597904\pi$
$734$	59.7278	2.20459
$735$	39.1222	1.44304
$736$	235.500	8.68064
$737$	2.72137	0.100243
$738$	89.8858	3.30874
$739$	48.9314	1.79997	0.899985	−	0.435921i	$-0.143577\pi$
$739$	48.9314	1.79997	0.899985	+	0.435921i	$0.143577\pi$
$740$	−67.3255	−2.47493
$741$	24.3202	0.893423
$742$	19.9134	0.731044
$743$	−0.149508	−0.00548490	−0.00274245	−	0.999996i	$-0.500873\pi$
$743$	−0.149508	−0.00548490	−0.00274245	+	0.999996i	$0.500873\pi$
$744$	−40.6896	−1.49175
$745$	−33.5950	−1.23082
$746$	−38.5305	−1.41070
$747$	−76.6624	−2.80493
$748$	80.5004	2.94339
$749$	−11.5432	−0.421779
$750$	−60.7830	−2.21948
$751$	−13.8104	−0.503948	−0.251974	−	0.967734i	$-0.581080\pi$
$751$	−13.8104	−0.503948	−0.251974	+	0.967734i	$0.581080\pi$
$752$	55.1730	2.01195
$753$	22.4974	0.819850
$754$	−90.0148	−3.27814
$755$	57.7656	2.10230
$756$	175.999	6.40101
$757$	27.0371	0.982679	0.491340	−	0.870968i	$-0.336507\pi$
$757$	27.0371	0.982679	0.491340	+	0.870968i	$0.336507\pi$
$758$	−81.9026	−2.97484
$759$	−92.0279	−3.34040
$760$	95.7951	3.47485
$761$	−33.4645	−1.21309	−0.606544	−	0.795050i	$-0.707444\pi$
$761$	−33.4645	−1.21309	−0.606544	+	0.795050i	$0.707444\pi$
$762$	−94.1709	−3.41145
$763$	31.4986	1.14033
$764$	64.2416	2.32418
$765$	73.2847	2.64961
$766$	−39.4346	−1.42483
$767$	30.1644	1.08917
$768$	333.502	12.0342
$769$	43.9202	1.58380	0.791902	−	0.610649i	$-0.209091\pi$
$769$	43.9202	1.58380	0.791902	+	0.610649i	$0.209091\pi$
$770$	−125.936	−4.53842
$771$	15.4890	0.557822
$772$	56.1308	2.02019
$773$	20.1646	0.725270	0.362635	−	0.931931i	$-0.381877\pi$
$773$	20.1646	0.725270	0.362635	+	0.931931i	$0.381877\pi$
$774$	−42.1266	−1.51421
$775$	8.86459	0.318426
$776$	33.4973	1.20248
$777$	−32.6424	−1.17104
$778$	−41.8888	−1.50179
$779$	13.5397	0.485111
$780$	−193.671	−6.93453
$781$	60.5967	2.16832
$782$	75.7273	2.70800
$783$	−93.1056	−3.32732
$784$	69.4045	2.47873
$785$	−8.29117	−0.295925
$786$	122.345	4.36391
$787$	6.52808	0.232701	0.116351	−	0.993208i	$-0.462880\pi$
$787$	6.52808	0.232701	0.116351	+	0.993208i	$0.462880\pi$
$788$	90.9108	3.23856
$789$	85.3824	3.03969
$790$	34.6518	1.23286
$791$	−6.95129	−0.247160
$792$	−257.713	−9.15744
$793$	−37.0148	−1.31443
$794$	−18.0861	−0.641851
$795$	−22.6654	−0.803857
$796$	−59.4151	−2.10591
$797$	37.0374	1.31193	0.655965	−	0.754791i	$-0.272262\pi$
$797$	37.0374	1.31193	0.655965	+	0.754791i	$0.272262\pi$
$798$	70.5588	2.49776
$799$	10.3707	0.366888
$800$	−214.920	−7.59856
$801$	16.2039	0.572535
$802$	13.9193	0.491509
$803$	−27.4960	−0.970313
$804$	12.1419	0.428211
$805$	−88.2947	−3.11198
$806$	11.1147	0.391500
$807$	−10.3207	−0.363306
$808$	22.0474	0.775624
$809$	53.5025	1.88105	0.940523	−	0.339730i	$-0.110336\pi$
$809$	53.5025	1.88105	0.940523	+	0.339730i	$0.110336\pi$
$810$	−92.0447	−3.23412
$811$	−4.46138	−0.156660	−0.0783301	−	0.996927i	$-0.524959\pi$
$811$	−4.46138	−0.156660	−0.0783301	+	0.996927i	$0.524959\pi$
$812$	−194.639	−6.83048
$813$	−31.4569	−1.10324
$814$	36.6067	1.28307
$815$	−24.3231	−0.851999
$816$	194.478	6.80809
$817$	−6.34564	−0.222006
$818$	−32.9637	−1.15255
$819$	−62.7733	−2.19348
$820$	−107.822	−3.76531
$821$	18.0992	0.631668	0.315834	−	0.948814i	$-0.397716\pi$
$821$	18.0992	0.631668	0.315834	+	0.948814i	$0.397716\pi$
$822$	114.602	3.99722
$823$	9.22157	0.321444	0.160722	−	0.987000i	$-0.448618\pi$
$823$	9.22157	0.321444	0.160722	+	0.987000i	$0.448618\pi$
$824$	57.1581	1.99120
$825$	83.9857	2.92401
$826$	87.5144	3.04501
$827$	20.0188	0.696120	0.348060	−	0.937472i	$-0.386840\pi$
$827$	20.0188	0.696120	0.348060	+	0.937472i	$0.386840\pi$
$828$	−274.490	−9.53919
$829$	−40.2588	−1.39824	−0.699122	−	0.715002i	$-0.746426\pi$
$829$	−40.2588	−1.39824	−0.699122	+	0.715002i	$0.746426\pi$
$830$	123.387	4.28281
$831$	40.3859	1.40097
$832$	−152.058	−5.27165
$833$	13.0457	0.452008
$834$	43.8695	1.51907
$835$	−37.9689	−1.31397
$836$	−58.9740	−2.03966
$837$	11.4964	0.397373
$838$	−69.5043	−2.40099
$839$	−24.0466	−0.830180	−0.415090	−	0.909780i	$-0.636250\pi$
$839$	−24.0466	−0.830180	−0.415090	+	0.909780i	$0.636250\pi$
$840$	−369.866	−12.7616
$841$	73.9665	2.55057
$842$	−37.5076	−1.29260
$843$	−12.2921	−0.423364
$844$	67.3470	2.31818
$845$	−10.3500	−0.356052
$846$	−50.4371	−1.73406
$847$	14.9810	0.514754
$848$	−40.2093	−1.38079
$849$	−27.1935	−0.933280
$850$	−69.1095	−2.37044
$851$	25.6653	0.879794
$852$	270.364	9.26252
$853$	−15.6826	−0.536961	−0.268481	−	0.963285i	$-0.586522\pi$
$853$	−15.6826	−0.536961	−0.268481	+	0.963285i	$0.586522\pi$
$854$	−107.389	−3.67478
$855$	−53.6878	−1.83608
$856$	38.0188	1.29946
$857$	−54.0058	−1.84480	−0.922401	−	0.386234i	$-0.873776\pi$
$857$	−54.0058	−1.84480	−0.922401	+	0.386234i	$0.873776\pi$
$858$	105.304	3.59503
$859$	44.1969	1.50798	0.753989	−	0.656887i	$-0.228127\pi$
$859$	44.1969	1.50798	0.753989	+	0.656887i	$0.228127\pi$
$860$	50.5328	1.72315
$861$	−52.2770	−1.78160
$862$	−23.9045	−0.814190
$863$	53.4624	1.81988	0.909940	−	0.414739i	$-0.136127\pi$
$863$	53.4624	1.81988	0.909940	+	0.414739i	$0.136127\pi$
$864$	−278.727	−9.48248
$865$	−53.2779	−1.81150
$866$	−58.1088	−1.97462
$867$	−14.5862	−0.495373
$868$	24.0334	0.815746
$869$	−14.0423	−0.476353
$870$	297.246	10.0776
$871$	−2.18322	−0.0739756
$872$	−103.744	−3.51323
$873$	−18.7734	−0.635383
$874$	−55.4772	−1.87655
$875$	23.6325	0.798924
$876$	−122.679	−4.14493
$877$	−42.3687	−1.43069	−0.715344	−	0.698772i	$-0.753730\pi$
$877$	−42.3687	−1.43069	−0.715344	+	0.698772i	$0.753730\pi$
$878$	89.0244	3.00443
$879$	67.0309	2.26090
$880$	254.291	8.57215
$881$	−14.5249	−0.489356	−0.244678	−	0.969604i	$-0.578682\pi$
$881$	−14.5249	−0.489356	−0.244678	+	0.969604i	$0.578682\pi$
$882$	−63.4471	−2.13638
$883$	−32.0676	−1.07916	−0.539580	−	0.841934i	$-0.681417\pi$
$883$	−32.0676	−1.07916	−0.539580	+	0.841934i	$0.681417\pi$
$884$	−64.5816	−2.17211
$885$	−99.6085	−3.34830
$886$	−1.91597	−0.0643683
$887$	−41.7644	−1.40231	−0.701155	−	0.713008i	$-0.747332\pi$
$887$	−41.7644	−1.40231	−0.701155	+	0.713008i	$0.747332\pi$
$888$	107.512	3.60786
$889$	36.6137	1.22798
$890$	−26.0798	−0.874197
$891$	37.3002	1.24960
$892$	113.454	3.79873
$893$	−7.59747	−0.254240
$894$	81.4996	2.72575
$895$	1.11176	0.0371621
$896$	−242.029	−8.08562
$897$	73.8296	2.46510
$898$	−64.9805	−2.16843
$899$	−12.7140	−0.424035
$900$	250.503	8.35009
$901$	−7.55801	−0.251794
$902$	58.6258	1.95203
$903$	24.5006	0.815328
$904$	22.8949	0.761473
$905$	62.1126	2.06469
$906$	−140.136	−4.65571
$907$	−43.7098	−1.45136	−0.725681	−	0.688032i	$-0.758475\pi$
$907$	−43.7098	−1.45136	−0.725681	+	0.688032i	$0.758475\pi$
$908$	135.900	4.51001
$909$	−12.3563	−0.409833
$910$	101.032	3.34919
$911$	−10.1703	−0.336958	−0.168479	−	0.985705i	$-0.553885\pi$
$911$	−10.1703	−0.336958	−0.168479	+	0.985705i	$0.553885\pi$
$912$	−142.473	−4.71776
$913$	−50.0012	−1.65480
$914$	−9.22179	−0.305030
$915$	122.230	4.04079
$916$	21.8627	0.722364
$917$	−47.5679	−1.57083
$918$	−89.6273	−2.95814
$919$	−23.9666	−0.790584	−0.395292	−	0.918556i	$-0.629357\pi$
$919$	−23.9666	−0.790584	−0.395292	+	0.918556i	$0.629357\pi$
$920$	290.809	9.58768
$921$	−9.37111	−0.308789
$922$	−112.352	−3.70013
$923$	−48.6139	−1.60015
$924$	227.699	7.49075
$925$	−23.4224	−0.770124
$926$	34.0191	1.11794
$927$	−32.0339	−1.05213
$928$	308.247	10.1187
$929$	36.5020	1.19759	0.598796	−	0.800902i	$-0.295646\pi$
$929$	36.5020	1.19759	0.598796	+	0.800902i	$0.295646\pi$
$930$	−36.7030	−1.20354
$931$	−9.55720	−0.313225
$932$	−95.0594	−3.11378
$933$	−35.4931	−1.16199
$934$	71.7016	2.34615
$935$	47.7982	1.56317
$936$	206.751	6.75787
$937$	−33.9283	−1.10839	−0.554194	−	0.832387i	$-0.686973\pi$
$937$	−33.9283	−1.10839	−0.554194	+	0.832387i	$0.686973\pi$
$938$	−6.33407	−0.206815
$939$	−59.8927	−1.95452
$940$	60.5016	1.97334
$941$	−29.5654	−0.963805	−0.481902	−	0.876225i	$-0.660054\pi$
$941$	−29.5654	−0.963805	−0.481902	+	0.876225i	$0.660054\pi$
$942$	20.1139	0.655348
$943$	41.1030	1.33850
$944$	−176.710	−5.75142
$945$	104.502	3.39944
$946$	−27.4761	−0.893324
$947$	−49.0058	−1.59248	−0.796238	−	0.604984i	$-0.793180\pi$
$947$	−49.0058	−1.59248	−0.796238	+	0.604984i	$0.793180\pi$
$948$	−62.6524	−2.03486
$949$	22.0587	0.716057
$950$	50.6291	1.64263
$951$	−1.35812	−0.0440401
$952$	−123.336	−3.99734
$953$	10.8532	0.351571	0.175785	−	0.984428i	$-0.443753\pi$
$953$	10.8532	0.351571	0.175785	+	0.984428i	$0.443753\pi$
$954$	36.7579	1.19008
$955$	38.1443	1.23432
$956$	5.10822	0.165212
$957$	−120.456	−3.89378
$958$	−84.6786	−2.73584
$959$	−44.5575	−1.43884
$960$	502.123	16.2060
$961$	−29.4301	−0.949359
$962$	−29.3678	−0.946857
$963$	−21.3074	−0.686622
$964$	90.0812	2.90132
$965$	33.3284	1.07288
$966$	214.198	6.89171
$967$	−52.5240	−1.68906	−0.844529	−	0.535509i	$-0.820120\pi$
$967$	−52.5240	−1.68906	−0.844529	+	0.535509i	$0.820120\pi$
$968$	−49.3418	−1.58591
$969$	−26.7802	−0.860303
$970$	30.2154	0.970158
$971$	10.5463	0.338446	0.169223	−	0.985578i	$-0.445874\pi$
$971$	10.5463	0.338446	0.169223	+	0.985578i	$0.445874\pi$
$972$	5.32815	0.170901
$973$	−17.0565	−0.546805
$974$	−21.2146	−0.679758
$975$	−67.3777	−2.15781
$976$	216.841	6.94091
$977$	−4.02429	−0.128749	−0.0643743	−	0.997926i	$-0.520505\pi$
$977$	−4.02429	−0.128749	−0.0643743	+	0.997926i	$0.520505\pi$
$978$	59.0064	1.88682
$979$	10.5686	0.337773
$980$	76.1076	2.43117
$981$	58.1429	1.85636
$982$	85.1206	2.71631
$983$	−50.4805	−1.61008	−0.805039	−	0.593222i	$-0.797856\pi$
$983$	−50.4805	−1.61008	−0.805039	+	0.593222i	$0.797856\pi$
$984$	172.180	5.48891
$985$	53.9795	1.71993
$986$	99.1198	3.15662
$987$	29.3339	0.933709
$988$	47.3120	1.50520
$989$	−19.2637	−0.612550
$990$	−232.464	−7.38818
$991$	−25.9026	−0.822823	−0.411411	−	0.911450i	$-0.634964\pi$
$991$	−25.9026	−0.822823	−0.411411	+	0.911450i	$0.634964\pi$
$992$	−38.0614	−1.20845
$993$	−36.8981	−1.17092
$994$	−141.041	−4.47355
$995$	−35.2785	−1.11840
$996$	−223.090	−7.06888
$997$	−52.4834	−1.66217	−0.831083	−	0.556149i	$-0.812279\pi$
$997$	−52.4834	−1.66217	−0.831083	+	0.556149i	$0.812279\pi$
$998$	−110.637	−3.50216
$999$	−30.3763	−0.961062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1931.2.a.b.1.2	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1931.2.a.b.1.2	✓	101	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:	\( N \)	\(=\)	\( 1931 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1931.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80220 q^{2} +3.00833 q^{3} +5.85234 q^{4} +3.47491 q^{5} -8.42994 q^{6} +3.27757 q^{7} -10.7951 q^{8} +6.05002 q^{9} +O(q^{10})\)	\(q-2.80220 q^{2} +3.00833 q^{3} +5.85234 q^{4} +3.47491 q^{5} -8.42994 q^{6} +3.27757 q^{7} -10.7951 q^{8} +6.05002 q^{9} -9.73740 q^{10} +3.94598 q^{11} +17.6058 q^{12} -3.16567 q^{13} -9.18441 q^{14} +10.4537 q^{15} +18.5452 q^{16} +3.48588 q^{17} -16.9534 q^{18} -2.55373 q^{19} +20.3364 q^{20} +9.85999 q^{21} -11.0574 q^{22} -7.75246 q^{23} -32.4750 q^{24} +7.07498 q^{25} +8.87086 q^{26} +9.17546 q^{27} +19.1814 q^{28} -10.1472 q^{29} -29.2933 q^{30} +1.25295 q^{31} -30.3774 q^{32} +11.8708 q^{33} -9.76816 q^{34} +11.3892 q^{35} +35.4068 q^{36} -3.31060 q^{37} +7.15608 q^{38} -9.52338 q^{39} -37.5118 q^{40} -5.30193 q^{41} -27.6297 q^{42} +2.48485 q^{43} +23.0932 q^{44} +21.0233 q^{45} +21.7240 q^{46} +2.97505 q^{47} +55.7901 q^{48} +3.74244 q^{49} -19.8255 q^{50} +10.4867 q^{51} -18.5266 q^{52} -2.16818 q^{53} -25.7115 q^{54} +13.7119 q^{55} -35.3815 q^{56} -7.68246 q^{57} +28.4346 q^{58} -9.52858 q^{59} +61.1784 q^{60} +11.6925 q^{61} -3.51102 q^{62} +19.8294 q^{63} +48.0333 q^{64} -11.0004 q^{65} -33.2644 q^{66} +0.689655 q^{67} +20.4006 q^{68} -23.3219 q^{69} -31.9150 q^{70} +15.3566 q^{71} -65.3103 q^{72} -6.96810 q^{73} +9.27697 q^{74} +21.2839 q^{75} -14.9453 q^{76} +12.9332 q^{77} +26.6864 q^{78} -3.55863 q^{79} +64.4430 q^{80} +9.45270 q^{81} +14.8571 q^{82} -12.6714 q^{83} +57.7040 q^{84} +12.1131 q^{85} -6.96305 q^{86} -30.5262 q^{87} -42.5971 q^{88} +2.67831 q^{89} -58.9115 q^{90} -10.3757 q^{91} -45.3701 q^{92} +3.76928 q^{93} -8.33669 q^{94} -8.87399 q^{95} -91.3852 q^{96} -3.10303 q^{97} -10.4871 q^{98} +23.8733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9}+O(q^{10}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9} + 14 q^{10} + 29 q^{11} + 15 q^{12} + 41 q^{13} + 4 q^{14} + 22 q^{15} + 187 q^{16} + 9 q^{17} + 11 q^{18} + 34 q^{19} + 42 q^{20} + 72 q^{21} + 17 q^{22} + 19 q^{23} + 33 q^{24} + 172 q^{25} + 28 q^{26} + 36 q^{27} + 47 q^{28} + 68 q^{29} + q^{30} + 76 q^{31} + 9 q^{32} + 8 q^{33} + 50 q^{34} + 7 q^{35} + 198 q^{36} + 141 q^{37} - 13 q^{38} + 42 q^{39} + 32 q^{40} + 35 q^{41} - 46 q^{42} + 45 q^{43} + 67 q^{44} + 106 q^{45} + 86 q^{46} - 5 q^{47} + 7 q^{48} + 203 q^{49} + 4 q^{50} + 5 q^{51} + 30 q^{52} + 47 q^{53} + 20 q^{54} + 11 q^{55} - 4 q^{56} + 19 q^{57} + 92 q^{58} + 30 q^{59} + 35 q^{60} + 153 q^{61} - 20 q^{62} + 19 q^{63} + 276 q^{64} - 7 q^{65} - 18 q^{66} + 39 q^{67} - 7 q^{68} + 55 q^{69} - 8 q^{70} + 47 q^{71} - 4 q^{72} + 86 q^{73} + 9 q^{74} + 11 q^{75} + 50 q^{76} + 15 q^{77} - 15 q^{78} + 89 q^{79} + 26 q^{80} + 201 q^{81} - 9 q^{82} - 15 q^{83} + 60 q^{84} + 239 q^{85} + 13 q^{86} - 22 q^{87} + 5 q^{88} + 14 q^{89} - 85 q^{90} + 58 q^{91} - 4 q^{92} + 86 q^{93} + 21 q^{94} - 10 q^{95} + 6 q^{96} + 46 q^{97} - 68 q^{98} + 100 q^{99}+O(q^{100}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9 + 14 * q^10 + 29 * q^11 + 15 * q^12 + 41 * q^13 + 4 * q^14 + 22 * q^15 + 187 * q^16 + 9 * q^17 + 11 * q^18 + 34 * q^19 + 42 * q^20 + 72 * q^21 + 17 * q^22 + 19 * q^23 + 33 * q^24 + 172 * q^25 + 28 * q^26 + 36 * q^27 + 47 * q^28 + 68 * q^29 + q^30 + 76 * q^31 + 9 * q^32 + 8 * q^33 + 50 * q^34 + 7 * q^35 + 198 * q^36 + 141 * q^37 - 13 * q^38 + 42 * q^39 + 32 * q^40 + 35 * q^41 - 46 * q^42 + 45 * q^43 + 67 * q^44 + 106 * q^45 + 86 * q^46 - 5 * q^47 + 7 * q^48 + 203 * q^49 + 4 * q^50 + 5 * q^51 + 30 * q^52 + 47 * q^53 + 20 * q^54 + 11 * q^55 - 4 * q^56 + 19 * q^57 + 92 * q^58 + 30 * q^59 + 35 * q^60 + 153 * q^61 - 20 * q^62 + 19 * q^63 + 276 * q^64 - 7 * q^65 - 18 * q^66 + 39 * q^67 - 7 * q^68 + 55 * q^69 - 8 * q^70 + 47 * q^71 - 4 * q^72 + 86 * q^73 + 9 * q^74 + 11 * q^75 + 50 * q^76 + 15 * q^77 - 15 * q^78 + 89 * q^79 + 26 * q^80 + 201 * q^81 - 9 * q^82 - 15 * q^83 + 60 * q^84 + 239 * q^85 + 13 * q^86 - 22 * q^87 + 5 * q^88 + 14 * q^89 - 85 * q^90 + 58 * q^91 - 4 * q^92 + 86 * q^93 + 21 * q^94 - 10 * q^95 + 6 * q^96 + 46 * q^97 - 68 * q^98 + 100 * q^99

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