LMFDB - Embedded newform 211.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,2,Mod(1,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, 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("211.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	211.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:	$1.68484348265$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24698 q^{2} -1.80194 q^{3} +3.04892 q^{4} -1.19806 q^{5} +4.04892 q^{6} +3.93900 q^{7} -2.35690 q^{8} +0.246980 q^{9} +O(q^{10})$	\(q-2.24698 q^{2} -1.80194 q^{3} +3.04892 q^{4} -1.19806 q^{5} +4.04892 q^{6} +3.93900 q^{7} -2.35690 q^{8} +0.246980 q^{9} +2.69202 q^{10} -2.58211 q^{11} -5.49396 q^{12} +0.356896 q^{13} -8.85086 q^{14} +2.15883 q^{15} -0.801938 q^{16} +0.307979 q^{17} -0.554958 q^{18} -6.85086 q^{19} -3.65279 q^{20} -7.09783 q^{21} +5.80194 q^{22} -4.75302 q^{23} +4.24698 q^{24} -3.56465 q^{25} -0.801938 q^{26} +4.96077 q^{27} +12.0097 q^{28} -4.37867 q^{29} -4.85086 q^{30} +3.18598 q^{31} +6.51573 q^{32} +4.65279 q^{33} -0.692021 q^{34} -4.71917 q^{35} +0.753020 q^{36} -8.34481 q^{37} +15.3937 q^{38} -0.643104 q^{39} +2.82371 q^{40} -8.71379 q^{41} +15.9487 q^{42} -1.93900 q^{43} -7.87263 q^{44} -0.295897 q^{45} +10.6799 q^{46} +8.29590 q^{47} +1.44504 q^{48} +8.51573 q^{49} +8.00969 q^{50} -0.554958 q^{51} +1.08815 q^{52} +4.00969 q^{53} -11.1468 q^{54} +3.09352 q^{55} -9.28382 q^{56} +12.3448 q^{57} +9.83877 q^{58} -3.87263 q^{59} +6.58211 q^{60} -1.79225 q^{61} -7.15883 q^{62} +0.972853 q^{63} -13.0368 q^{64} -0.427583 q^{65} -10.4547 q^{66} -2.29590 q^{67} +0.939001 q^{68} +8.56465 q^{69} +10.6039 q^{70} +7.02177 q^{71} -0.582105 q^{72} -15.7995 q^{73} +18.7506 q^{74} +6.42327 q^{75} -20.8877 q^{76} -10.1709 q^{77} +1.44504 q^{78} +4.93362 q^{79} +0.960771 q^{80} -9.67994 q^{81} +19.5797 q^{82} -5.97823 q^{83} -21.6407 q^{84} -0.368977 q^{85} +4.35690 q^{86} +7.89008 q^{87} +6.08575 q^{88} -14.8509 q^{89} +0.664874 q^{90} +1.40581 q^{91} -14.4916 q^{92} -5.74094 q^{93} -18.6407 q^{94} +8.20775 q^{95} -11.7409 q^{96} -6.18060 q^{97} -19.1347 q^{98} -0.637727 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - q^{3} - 8 q^{5} + 3 q^{6} + 2 q^{7} - 3 q^{8} - 4 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - q^3 - 8 * q^5 + 3 * q^6 + 2 * q^7 - 3 * q^8 - 4 * q^9	\( 3 q - 2 q^{2} - q^{3} - 8 q^{5} + 3 q^{6} + 2 q^{7} - 3 q^{8} - 4 q^{9} + 3 q^{10} - 2 q^{11} - 7 q^{12} - 3 q^{13} - 13 q^{14} - 2 q^{15} + 2 q^{16} + 6 q^{17} - 2 q^{18} - 7 q^{19} + 7 q^{20} - 3 q^{21} + 13 q^{22} - 19 q^{23} + 8 q^{24} + 11 q^{25} + 2 q^{26} + 2 q^{27} + 14 q^{28} - 6 q^{29} - q^{30} - 5 q^{31} + 7 q^{32} - 4 q^{33} + 3 q^{34} - 3 q^{35} + 7 q^{36} - 2 q^{37} + 14 q^{38} - 6 q^{39} + q^{40} - 18 q^{41} + 16 q^{42} + 4 q^{43} - 7 q^{44} + 13 q^{45} + 8 q^{46} + 11 q^{47} + 4 q^{48} + 13 q^{49} + 2 q^{50} - 2 q^{51} + 7 q^{52} - 10 q^{53} - 6 q^{54} + 10 q^{55} + 5 q^{56} + 14 q^{57} - 3 q^{58} + 5 q^{59} + 14 q^{60} - 23 q^{61} - 13 q^{62} + 9 q^{63} - 11 q^{64} + 15 q^{65} - 9 q^{66} + 7 q^{67} - 7 q^{68} + 4 q^{69} + 23 q^{70} + 18 q^{71} + 4 q^{72} - 2 q^{73} + 20 q^{74} + 22 q^{75} - 21 q^{76} - 41 q^{77} + 4 q^{78} + 8 q^{79} - 10 q^{80} - 5 q^{81} + 12 q^{82} - 21 q^{83} - 28 q^{84} - 16 q^{85} + 9 q^{86} + 23 q^{87} - 19 q^{88} - 31 q^{89} + 3 q^{90} - 9 q^{91} + 7 q^{92} - 3 q^{93} - 19 q^{94} + 7 q^{95} - 21 q^{96} - 7 q^{97} - 11 q^{98} - 9 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - q^3 - 8 * q^5 + 3 * q^6 + 2 * q^7 - 3 * q^8 - 4 * q^9 + 3 * q^10 - 2 * q^11 - 7 * q^12 - 3 * q^13 - 13 * q^14 - 2 * q^15 + 2 * q^16 + 6 * q^17 - 2 * q^18 - 7 * q^19 + 7 * q^20 - 3 * q^21 + 13 * q^22 - 19 * q^23 + 8 * q^24 + 11 * q^25 + 2 * q^26 + 2 * q^27 + 14 * q^28 - 6 * q^29 - q^30 - 5 * q^31 + 7 * q^32 - 4 * q^33 + 3 * q^34 - 3 * q^35 + 7 * q^36 - 2 * q^37 + 14 * q^38 - 6 * q^39 + q^40 - 18 * q^41 + 16 * q^42 + 4 * q^43 - 7 * q^44 + 13 * q^45 + 8 * q^46 + 11 * q^47 + 4 * q^48 + 13 * q^49 + 2 * q^50 - 2 * q^51 + 7 * q^52 - 10 * q^53 - 6 * q^54 + 10 * q^55 + 5 * q^56 + 14 * q^57 - 3 * q^58 + 5 * q^59 + 14 * q^60 - 23 * q^61 - 13 * q^62 + 9 * q^63 - 11 * q^64 + 15 * q^65 - 9 * q^66 + 7 * q^67 - 7 * q^68 + 4 * q^69 + 23 * q^70 + 18 * q^71 + 4 * q^72 - 2 * q^73 + 20 * q^74 + 22 * q^75 - 21 * q^76 - 41 * q^77 + 4 * q^78 + 8 * q^79 - 10 * q^80 - 5 * q^81 + 12 * q^82 - 21 * q^83 - 28 * q^84 - 16 * q^85 + 9 * q^86 + 23 * q^87 - 19 * q^88 - 31 * q^89 + 3 * q^90 - 9 * q^91 + 7 * q^92 - 3 * q^93 - 19 * q^94 + 7 * q^95 - 21 * q^96 - 7 * q^97 - 11 * q^98 - 9 * 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 $

$2$	−2.24698	−1.58885	−0.794427	−	0.607359i	$-0.792229\pi$
$2$	−2.24698	−1.58885	−0.794427	+	0.607359i	$0.792229\pi$
$3$	−1.80194	−1.04035	−0.520175	−	0.854060i	$-0.674133\pi$
$3$	−1.80194	−1.04035	−0.520175	+	0.854060i	$0.674133\pi$
$4$	3.04892	1.52446
$5$	−1.19806	−0.535790	−0.267895	−	0.963448i	$-0.586328\pi$
$5$	−1.19806	−0.535790	−0.267895	+	0.963448i	$0.586328\pi$
$6$	4.04892	1.65296
$7$	3.93900	1.48880	0.744401	−	0.667733i	$-0.232735\pi$
$7$	3.93900	1.48880	0.744401	+	0.667733i	$0.232735\pi$
$8$	−2.35690	−0.833289
$9$	0.246980	0.0823265
$10$	2.69202	0.851292
$11$	−2.58211	−0.778534	−0.389267	−	0.921125i	$-0.627272\pi$
$11$	−2.58211	−0.778534	−0.389267	+	0.921125i	$0.627272\pi$
$12$	−5.49396	−1.58597
$13$	0.356896	0.0989851	0.0494926	−	0.998774i	$-0.484240\pi$
$13$	0.356896	0.0989851	0.0494926	+	0.998774i	$0.484240\pi$
$14$	−8.85086	−2.36549
$15$	2.15883	0.557408
$16$	−0.801938	−0.200484
$17$	0.307979	0.0746958	0.0373479	−	0.999302i	$-0.488109\pi$
$17$	0.307979	0.0746958	0.0373479	+	0.999302i	$0.488109\pi$
$18$	−0.554958	−0.130805
$19$	−6.85086	−1.57169	−0.785847	−	0.618421i	$-0.787773\pi$
$19$	−6.85086	−1.57169	−0.785847	+	0.618421i	$0.787773\pi$
$20$	−3.65279	−0.816789
$21$	−7.09783	−1.54887
$22$	5.80194	1.23698
$23$	−4.75302	−0.991073	−0.495537	−	0.868587i	$-0.665029\pi$
$23$	−4.75302	−0.991073	−0.495537	+	0.868587i	$0.665029\pi$
$24$	4.24698	0.866911
$25$	−3.56465	−0.712929
$26$	−0.801938	−0.157273
$27$	4.96077	0.954701
$28$	12.0097	2.26962
$29$	−4.37867	−0.813098	−0.406549	−	0.913629i	$-0.633268\pi$
$29$	−4.37867	−0.813098	−0.406549	+	0.913629i	$0.633268\pi$
$30$	−4.85086	−0.885641
$31$	3.18598	0.572219	0.286110	−	0.958197i	$-0.407638\pi$
$31$	3.18598	0.572219	0.286110	+	0.958197i	$0.407638\pi$
$32$	6.51573	1.15183
$33$	4.65279	0.809947
$34$	−0.692021	−0.118681
$35$	−4.71917	−0.797685
$36$	0.753020	0.125503
$37$	−8.34481	−1.37188	−0.685940	−	0.727659i	$-0.740609\pi$
$37$	−8.34481	−1.37188	−0.685940	+	0.727659i	$0.740609\pi$
$38$	15.3937	2.49719
$39$	−0.643104	−0.102979
$40$	2.82371	0.446467
$41$	−8.71379	−1.36087	−0.680433	−	0.732810i	$-0.738208\pi$
$41$	−8.71379	−1.36087	−0.680433	+	0.732810i	$0.738208\pi$
$42$	15.9487	2.46094
$43$	−1.93900	−0.295695	−0.147847	−	0.989010i	$-0.547234\pi$
$43$	−1.93900	−0.295695	−0.147847	+	0.989010i	$0.547234\pi$
$44$	−7.87263	−1.18684
$45$	−0.295897	−0.0441097
$46$	10.6799	1.57467
$47$	8.29590	1.21008	0.605040	−	0.796195i	$-0.293157\pi$
$47$	8.29590	1.21008	0.605040	+	0.796195i	$0.293157\pi$
$48$	1.44504	0.208574
$49$	8.51573	1.21653
$50$	8.00969	1.13274
$51$	−0.554958	−0.0777097
$52$	1.08815	0.150899
$53$	4.00969	0.550773	0.275387	−	0.961334i	$-0.411194\pi$
$53$	4.00969	0.550773	0.275387	+	0.961334i	$0.411194\pi$
$54$	−11.1468	−1.51688
$55$	3.09352	0.417131
$56$	−9.28382	−1.24060
$57$	12.3448	1.63511
$58$	9.83877	1.29189
$59$	−3.87263	−0.504173	−0.252086	−	0.967705i	$-0.581117\pi$
$59$	−3.87263	−0.504173	−0.252086	+	0.967705i	$0.581117\pi$
$60$	6.58211	0.849746
$61$	−1.79225	−0.229474	−0.114737	−	0.993396i	$-0.536603\pi$
$61$	−1.79225	−0.229474	−0.114737	+	0.993396i	$0.536603\pi$
$62$	−7.15883	−0.909173
$63$	0.972853	0.122568
$64$	−13.0368	−1.62960
$65$	−0.427583	−0.0530352
$66$	−10.4547	−1.28689
$67$	−2.29590	−0.280488	−0.140244	−	0.990117i	$-0.544789\pi$
$67$	−2.29590	−0.280488	−0.140244	+	0.990117i	$0.544789\pi$
$68$	0.939001	0.113871
$69$	8.56465	1.03106
$70$	10.6039	1.26741
$71$	7.02177	0.833331	0.416665	−	0.909060i	$-0.363199\pi$
$71$	7.02177	0.833331	0.416665	+	0.909060i	$0.363199\pi$
$72$	−0.582105	−0.0686018
$73$	−15.7995	−1.84920	−0.924598	−	0.380943i	$-0.875599\pi$
$73$	−15.7995	−1.84920	−0.924598	+	0.380943i	$0.875599\pi$
$74$	18.7506	2.17972
$75$	6.42327	0.741696
$76$	−20.8877	−2.39598
$77$	−10.1709	−1.15908
$78$	1.44504	0.163619
$79$	4.93362	0.555076	0.277538	−	0.960715i	$-0.410482\pi$
$79$	4.93362	0.555076	0.277538	+	0.960715i	$0.410482\pi$
$80$	0.960771	0.107418
$81$	−9.67994	−1.07555
$82$	19.5797	2.16222
$83$	−5.97823	−0.656196	−0.328098	−	0.944644i	$-0.606408\pi$
$83$	−5.97823	−0.656196	−0.328098	+	0.944644i	$0.606408\pi$
$84$	−21.6407	−2.36120
$85$	−0.368977	−0.0400212
$86$	4.35690	0.469816
$87$	7.89008	0.845906
$88$	6.08575	0.648743
$89$	−14.8509	−1.57419	−0.787094	−	0.616833i	$-0.788415\pi$
$89$	−14.8509	−1.57419	−0.787094	+	0.616833i	$0.788415\pi$
$90$	0.664874	0.0700839
$91$	1.40581	0.147369
$92$	−14.4916	−1.51085
$93$	−5.74094	−0.595308
$94$	−18.6407	−1.92264
$95$	8.20775	0.842097
$96$	−11.7409	−1.19830
$97$	−6.18060	−0.627545	−0.313773	−	0.949498i	$-0.601593\pi$
$97$	−6.18060	−0.627545	−0.313773	+	0.949498i	$0.601593\pi$
$98$	−19.1347	−1.93289
$99$	−0.637727	−0.0640940
$100$	−10.8683	−1.08683
$101$	−12.4450	−1.23833	−0.619164	−	0.785262i	$-0.712528\pi$
$101$	−12.4450	−1.23833	−0.619164	+	0.785262i	$0.712528\pi$
$102$	1.24698	0.123469
$103$	12.6746	1.24886	0.624431	−	0.781080i	$-0.285331\pi$
$103$	12.6746	1.24886	0.624431	+	0.781080i	$0.285331\pi$
$104$	−0.841166	−0.0824832
$105$	8.50365	0.829871
$106$	−9.00969	−0.875098
$107$	−5.52111	−0.533745	−0.266873	−	0.963732i	$-0.585990\pi$
$107$	−5.52111	−0.533745	−0.266873	+	0.963732i	$0.585990\pi$
$108$	15.1250	1.45540
$109$	19.6896	1.88592	0.942962	−	0.332900i	$-0.108027\pi$
$109$	19.6896	1.88592	0.942962	+	0.332900i	$0.108027\pi$
$110$	−6.95108	−0.662760
$111$	15.0368	1.42723
$112$	−3.15883	−0.298482
$113$	12.0368	1.13233	0.566165	−	0.824292i	$-0.308426\pi$
$113$	12.0368	1.13233	0.566165	+	0.824292i	$0.308426\pi$
$114$	−27.7385	−2.59795
$115$	5.69441	0.531007
$116$	−13.3502	−1.23953
$117$	0.0881460	0.00814910
$118$	8.70171	0.801057
$119$	1.21313	0.111207
$120$	−5.08815	−0.464482
$121$	−4.33273	−0.393885
$122$	4.02715	0.364601
$123$	15.7017	1.41578
$124$	9.71379	0.872324
$125$	10.2610	0.917770
$126$	−2.18598	−0.194743
$127$	6.29590	0.558671	0.279335	−	0.960194i	$-0.409886\pi$
$127$	6.29590	0.558671	0.279335	+	0.960194i	$0.409886\pi$
$128$	16.2620	1.43738
$129$	3.49396	0.307626
$130$	0.960771	0.0842652
$131$	−3.12200	−0.272770	−0.136385	−	0.990656i	$-0.543548\pi$
$131$	−3.12200	−0.272770	−0.136385	+	0.990656i	$0.543548\pi$
$132$	14.1860	1.23473
$133$	−26.9855	−2.33994
$134$	5.15883	0.445655
$135$	−5.94331	−0.511519
$136$	−0.725873	−0.0622431
$137$	19.9812	1.70711	0.853555	−	0.521003i	$-0.174442\pi$
$137$	19.9812	1.70711	0.853555	+	0.521003i	$0.174442\pi$
$138$	−19.2446	−1.63821
$139$	18.0737	1.53299	0.766494	−	0.642251i	$-0.221999\pi$
$139$	18.0737	1.53299	0.766494	+	0.642251i	$0.221999\pi$
$140$	−14.3884	−1.21604
$141$	−14.9487	−1.25891
$142$	−15.7778	−1.32404
$143$	−0.921543	−0.0770633
$144$	−0.198062	−0.0165052
$145$	5.24591	0.435650
$146$	35.5013	2.93810
$147$	−15.3448	−1.26562
$148$	−25.4426	−2.09137
$149$	9.61356	0.787574	0.393787	−	0.919202i	$-0.371165\pi$
$149$	9.61356	0.787574	0.393787	+	0.919202i	$0.371165\pi$
$150$	−14.4330	−1.17845
$151$	8.89008	0.723465	0.361732	−	0.932282i	$-0.382185\pi$
$151$	8.89008	0.723465	0.361732	+	0.932282i	$0.382185\pi$
$152$	16.1468	1.30967
$153$	0.0760644	0.00614944
$154$	22.8538	1.84161
$155$	−3.81700	−0.306589
$156$	−1.96077	−0.156987
$157$	−4.16421	−0.332340	−0.166170	−	0.986097i	$-0.553140\pi$
$157$	−4.16421	−0.332340	−0.166170	+	0.986097i	$0.553140\pi$
$158$	−11.0858	−0.881935
$159$	−7.22521	−0.572996
$160$	−7.80625	−0.617138
$161$	−18.7222	−1.47551
$162$	21.7506	1.70889
$163$	−12.0761	−0.945870	−0.472935	−	0.881097i	$-0.656806\pi$
$163$	−12.0761	−0.945870	−0.472935	+	0.881097i	$0.656806\pi$
$164$	−26.5676	−2.07458
$165$	−5.57434	−0.433961
$166$	13.4330	1.04260
$167$	22.1618	1.71493	0.857466	−	0.514540i	$-0.172037\pi$
$167$	22.1618	1.71493	0.857466	+	0.514540i	$0.172037\pi$
$168$	16.7289	1.29066
$169$	−12.8726	−0.990202
$170$	0.829085	0.0635879
$171$	−1.69202	−0.129392
$172$	−5.91185	−0.450775
$173$	−21.2838	−1.61818	−0.809089	−	0.587686i	$-0.800039\pi$
$173$	−21.2838	−1.61818	−0.809089	+	0.587686i	$0.800039\pi$
$174$	−17.7289	−1.34402
$175$	−14.0411	−1.06141
$176$	2.07069	0.156084
$177$	6.97823	0.524516
$178$	33.3696	2.50115
$179$	16.4993	1.23322	0.616609	−	0.787269i	$-0.288506\pi$
$179$	16.4993	1.23322	0.616609	+	0.787269i	$0.288506\pi$
$180$	−0.902165	−0.0672434
$181$	−15.4644	−1.14946	−0.574731	−	0.818343i	$-0.694893\pi$
$181$	−15.4644	−1.14946	−0.574731	+	0.818343i	$0.694893\pi$
$182$	−3.15883	−0.234148
$183$	3.22952	0.238733
$184$	11.2024	0.825850
$185$	9.99761	0.735039
$186$	12.8998	0.945857
$187$	−0.795233	−0.0581532
$188$	25.2935	1.84472
$189$	19.5405	1.42136
$190$	−18.4426	−1.33797
$191$	10.8605	0.785841	0.392921	−	0.919572i	$-0.371465\pi$
$191$	10.8605	0.785841	0.392921	+	0.919572i	$0.371465\pi$
$192$	23.4916	1.69536
$193$	13.9705	1.00562	0.502808	−	0.864398i	$-0.332300\pi$
$193$	13.9705	1.00562	0.502808	+	0.864398i	$0.332300\pi$
$194$	13.8877	0.997078
$195$	0.770479	0.0551751
$196$	25.9638	1.85455
$197$	12.2838	0.875186	0.437593	−	0.899173i	$-0.355831\pi$
$197$	12.2838	0.875186	0.437593	+	0.899173i	$0.355831\pi$
$198$	1.43296	0.101836
$199$	−21.5066	−1.52456	−0.762282	−	0.647245i	$-0.775921\pi$
$199$	−21.5066	−1.52456	−0.762282	+	0.647245i	$0.775921\pi$
$200$	8.40150	0.594076
$201$	4.13706	0.291806
$202$	27.9638	1.96752
$203$	−17.2476	−1.21054
$204$	−1.69202	−0.118465
$205$	10.4397	0.729138
$206$	−28.4795	−1.98426
$207$	−1.17390	−0.0815916
$208$	−0.286208	−0.0198450
$209$	17.6896	1.22362
$210$	−19.1075	−1.31854
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	12.2252	0.839631
$213$	−12.6528	−0.866955
$214$	12.4058	0.848044
$215$	2.32304	0.158430
$216$	−11.6920	−0.795541
$217$	12.5496	0.851921
$218$	−44.2422	−2.99646
$219$	28.4698	1.92381
$220$	9.43190	0.635898
$221$	0.109916	0.00739377
$222$	−33.7875	−2.26767
$223$	−25.8877	−1.73357	−0.866784	−	0.498684i	$-0.833817\pi$
$223$	−25.8877	−1.73357	−0.866784	+	0.498684i	$0.833817\pi$
$224$	25.6655	1.71485
$225$	−0.880395	−0.0586930
$226$	−27.0465	−1.79911
$227$	0.356896	0.0236880	0.0118440	−	0.999930i	$-0.496230\pi$
$227$	0.356896	0.0236880	0.0118440	+	0.999930i	$0.496230\pi$
$228$	37.6383	2.49266
$229$	11.6189	0.767801	0.383901	−	0.923374i	$-0.374581\pi$
$229$	11.6189	0.767801	0.383901	+	0.923374i	$0.374581\pi$
$230$	−12.7952	−0.843693
$231$	18.3274	1.20585
$232$	10.3201	0.677545
$233$	−25.0291	−1.63971	−0.819854	−	0.572572i	$-0.805946\pi$
$233$	−25.0291	−1.63971	−0.819854	+	0.572572i	$0.805946\pi$
$234$	−0.198062	−0.0129477
$235$	−9.93900	−0.648349
$236$	−11.8073	−0.768591
$237$	−8.89008	−0.577473
$238$	−2.72587	−0.176692
$239$	4.74333	0.306821	0.153410	−	0.988163i	$-0.450974\pi$
$239$	4.74333	0.306821	0.153410	+	0.988163i	$0.450974\pi$
$240$	−1.73125	−0.111752
$241$	−7.48725	−0.482296	−0.241148	−	0.970488i	$-0.577524\pi$
$241$	−7.48725	−0.482296	−0.241148	+	0.970488i	$0.577524\pi$
$242$	9.73556	0.625826
$243$	2.56033	0.164246
$244$	−5.46442	−0.349824
$245$	−10.2024	−0.651806
$246$	−35.2814	−2.24946
$247$	−2.44504	−0.155574
$248$	−7.50902	−0.476824
$249$	10.7724	0.682673
$250$	−23.0562	−1.45820
$251$	−27.4198	−1.73072	−0.865362	−	0.501148i	$-0.832911\pi$
$251$	−27.4198	−1.73072	−0.865362	+	0.501148i	$0.832911\pi$
$252$	2.96615	0.186850
$253$	12.2728	0.771584
$254$	−14.1468	−0.887646
$255$	0.664874	0.0416360
$256$	−10.4668	−0.654176
$257$	12.3623	0.771137	0.385569	−	0.922679i	$-0.374005\pi$
$257$	12.3623	0.771137	0.385569	+	0.922679i	$0.374005\pi$
$258$	−7.85086	−0.488773
$259$	−32.8702	−2.04246
$260$	−1.30367	−0.0808500
$261$	−1.08144	−0.0669395
$262$	7.01507	0.433392
$263$	−2.33273	−0.143842	−0.0719212	−	0.997410i	$-0.522913\pi$
$263$	−2.33273	−0.143842	−0.0719212	+	0.997410i	$0.522913\pi$
$264$	−10.9661	−0.674920
$265$	−4.80386	−0.295099
$266$	60.6359	3.71783
$267$	26.7603	1.63770
$268$	−7.00000	−0.427593
$269$	12.9855	0.791741	0.395871	−	0.918306i	$-0.370443\pi$
$269$	12.9855	0.791741	0.395871	+	0.918306i	$0.370443\pi$
$270$	13.3545	0.812729
$271$	−32.5961	−1.98007	−0.990036	−	0.140813i	$-0.955028\pi$
$271$	−32.5961	−1.98007	−0.990036	+	0.140813i	$0.955028\pi$
$272$	−0.246980	−0.0149753
$273$	−2.53319	−0.153316
$274$	−44.8974	−2.71235
$275$	9.20429	0.555040
$276$	26.1129	1.57181
$277$	−4.07308	−0.244728	−0.122364	−	0.992485i	$-0.539047\pi$
$277$	−4.07308	−0.244728	−0.122364	+	0.992485i	$0.539047\pi$
$278$	−40.6112	−2.43570
$279$	0.786872	0.0471088
$280$	11.1226	0.664702
$281$	17.3110	1.03269	0.516343	−	0.856382i	$-0.327293\pi$
$281$	17.3110	1.03269	0.516343	+	0.856382i	$0.327293\pi$
$282$	33.5894	2.00022
$283$	7.62133	0.453041	0.226521	−	0.974006i	$-0.427265\pi$
$283$	7.62133	0.453041	0.226521	+	0.974006i	$0.427265\pi$
$284$	21.4088	1.27038
$285$	−14.7899	−0.876075
$286$	2.07069	0.122442
$287$	−34.3236	−2.02606
$288$	1.60925	0.0948261
$289$	−16.9051	−0.994421
$290$	−11.7875	−0.692184
$291$	11.1371	0.652866
$292$	−48.1715	−2.81902
$293$	−15.5864	−0.910568	−0.455284	−	0.890346i	$-0.650462\pi$
$293$	−15.5864	−0.910568	−0.455284	+	0.890346i	$0.650462\pi$
$294$	34.4795	2.01088
$295$	4.63965	0.270131
$296$	19.6679	1.14317
$297$	−12.8092	−0.743267
$298$	−21.6015	−1.25134
$299$	−1.69633	−0.0981015
$300$	19.5840	1.13068
$301$	−7.63773	−0.440231
$302$	−19.9758	−1.14948
$303$	22.4252	1.28829
$304$	5.49396	0.315100
$305$	2.14723	0.122950
$306$	−0.170915	−0.00977057
$307$	20.6993	1.18137	0.590686	−	0.806901i	$-0.298857\pi$
$307$	20.6993	1.18137	0.590686	+	0.806901i	$0.298857\pi$
$308$	−31.0103	−1.76697
$309$	−22.8388	−1.29925
$310$	8.57673	0.487125
$311$	−8.67025	−0.491645	−0.245822	−	0.969315i	$-0.579058\pi$
$311$	−8.67025	−0.491645	−0.245822	+	0.969315i	$0.579058\pi$
$312$	1.51573	0.0858113
$313$	33.5308	1.89527	0.947636	−	0.319352i	$-0.103465\pi$
$313$	33.5308	1.89527	0.947636	+	0.319352i	$0.103465\pi$
$314$	9.35690	0.528040
$315$	−1.16554	−0.0656706
$316$	15.0422	0.846191
$317$	20.0707	1.12728	0.563641	−	0.826020i	$-0.309400\pi$
$317$	20.0707	1.12728	0.563641	+	0.826020i	$0.309400\pi$
$318$	16.2349	0.910408
$319$	11.3062	0.633024
$320$	15.6189	0.873125
$321$	9.94869	0.555282
$322$	42.0683	2.34437
$323$	−2.10992	−0.117399
$324$	−29.5133	−1.63963
$325$	−1.27221	−0.0705694
$326$	27.1347	1.50285
$327$	−35.4795	−1.96202
$328$	20.5375	1.13399
$329$	32.6775	1.80157
$330$	12.5254	0.689502
$331$	13.3491	0.733734	0.366867	−	0.930273i	$-0.380430\pi$
$331$	13.3491	0.733734	0.366867	+	0.930273i	$0.380430\pi$
$332$	−18.2271	−1.00034
$333$	−2.06100	−0.112942
$334$	−49.7972	−2.72478
$335$	2.75063	0.150283
$336$	5.69202	0.310525
$337$	−9.72587	−0.529802	−0.264901	−	0.964276i	$-0.585339\pi$
$337$	−9.72587	−0.529802	−0.264901	+	0.964276i	$0.585339\pi$
$338$	28.9245	1.57329
$339$	−21.6896	−1.17802
$340$	−1.12498	−0.0610107
$341$	−8.22654	−0.445492
$342$	3.80194	0.205585
$343$	5.97046	0.322375
$344$	4.57002	0.246399
$345$	−10.2610	−0.552433
$346$	47.8243	2.57105
$347$	−17.3642	−0.932159	−0.466079	−	0.884743i	$-0.654334\pi$
$347$	−17.3642	−0.932159	−0.466079	+	0.884743i	$0.654334\pi$
$348$	24.0562	1.28955
$349$	−6.42327	−0.343830	−0.171915	−	0.985112i	$-0.554995\pi$
$349$	−6.42327	−0.343830	−0.171915	+	0.985112i	$0.554995\pi$
$350$	31.5502	1.68643
$351$	1.77048	0.0945012
$352$	−16.8243	−0.896738
$353$	−4.44073	−0.236356	−0.118178	−	0.992992i	$-0.537705\pi$
$353$	−4.44073	−0.236356	−0.118178	+	0.992992i	$0.537705\pi$
$354$	−15.6799	−0.833379
$355$	−8.41252	−0.446490
$356$	−45.2790	−2.39978
$357$	−2.18598	−0.115694
$358$	−37.0737	−1.95940
$359$	−10.6504	−0.562107	−0.281053	−	0.959692i	$-0.590684\pi$
$359$	−10.6504	−0.562107	−0.281053	+	0.959692i	$0.590684\pi$
$360$	0.697398	0.0367561
$361$	27.9342	1.47022
$362$	34.7482	1.82633
$363$	7.80731	0.409778
$364$	4.28621	0.224658
$365$	18.9288	0.990781
$366$	−7.25667	−0.379312
$367$	−13.3351	−0.696088	−0.348044	−	0.937478i	$-0.613154\pi$
$367$	−13.3351	−0.696088	−0.348044	+	0.937478i	$0.613154\pi$
$368$	3.81163	0.198695
$369$	−2.15213	−0.112035
$370$	−22.4644	−1.16787
$371$	15.7942	0.819992
$372$	−17.5036	−0.907522
$373$	34.2489	1.77334	0.886670	−	0.462402i	$-0.153012\pi$
$373$	34.2489	1.77334	0.886670	+	0.462402i	$0.153012\pi$
$374$	1.78687	0.0923970
$375$	−18.4896	−0.954801
$376$	−19.5526	−1.00835
$377$	−1.56273	−0.0804846
$378$	−43.9071	−2.25834
$379$	−7.85086	−0.403271	−0.201636	−	0.979461i	$-0.564626\pi$
$379$	−7.85086	−0.403271	−0.201636	+	0.979461i	$0.564626\pi$
$380$	25.0248	1.28374
$381$	−11.3448	−0.581212
$382$	−24.4034	−1.24859
$383$	−1.95407	−0.0998481	−0.0499241	−	0.998753i	$-0.515898\pi$
$383$	−1.95407	−0.0998481	−0.0499241	+	0.998753i	$0.515898\pi$
$384$	−29.3032	−1.49537
$385$	12.1854	0.621025
$386$	−31.3913	−1.59778
$387$	−0.478894	−0.0243435
$388$	−18.8442	−0.956667
$389$	−35.5730	−1.80362	−0.901812	−	0.432130i	$-0.857762\pi$
$389$	−35.5730	−1.80362	−0.901812	+	0.432130i	$0.857762\pi$
$390$	−1.73125	−0.0876653
$391$	−1.46383	−0.0740290
$392$	−20.0707	−1.01372
$393$	5.62565	0.283776
$394$	−27.6015	−1.39054
$395$	−5.91079	−0.297404
$396$	−1.94438	−0.0977087
$397$	0.731250	0.0367004	0.0183502	−	0.999832i	$-0.494159\pi$
$397$	0.731250	0.0367004	0.0183502	+	0.999832i	$0.494159\pi$
$398$	48.3250	2.42231
$399$	48.6262	2.43436
$400$	2.85862	0.142931
$401$	−0.862937	−0.0430930	−0.0215465	−	0.999768i	$-0.506859\pi$
$401$	−0.862937	−0.0430930	−0.0215465	+	0.999768i	$0.506859\pi$
$402$	−9.29590	−0.463637
$403$	1.13706	0.0566412
$404$	−37.9439	−1.88778
$405$	11.5972	0.576268
$406$	38.7549	1.92338
$407$	21.5472	1.06805
$408$	1.30798	0.0647546
$409$	17.3913	0.859946	0.429973	−	0.902842i	$-0.358523\pi$
$409$	17.3913	0.859946	0.429973	+	0.902842i	$0.358523\pi$
$410$	−23.4577	−1.15849
$411$	−36.0049	−1.77599
$412$	38.6437	1.90384
$413$	−15.2543	−0.750614
$414$	2.63773	0.129637
$415$	7.16229	0.351583
$416$	2.32544	0.114014
$417$	−32.5676	−1.59484
$418$	−39.7482	−1.94415
$419$	22.5163	1.09999	0.549997	−	0.835167i	$-0.314629\pi$
$419$	22.5163	1.09999	0.549997	+	0.835167i	$0.314629\pi$
$420$	25.9269	1.26510
$421$	−14.1323	−0.688765	−0.344383	−	0.938829i	$-0.611912\pi$
$421$	−14.1323	−0.688765	−0.344383	+	0.938829i	$0.611912\pi$
$422$	2.24698	0.109381
$423$	2.04892	0.0996218
$424$	−9.45042	−0.458953
$425$	−1.09783	−0.0532528
$426$	28.4306	1.37747
$427$	−7.05967	−0.341641
$428$	−16.8334	−0.813673
$429$	1.66056	0.0801727
$430$	−5.21983	−0.251723
$431$	26.7463	1.28832	0.644162	−	0.764889i	$-0.277206\pi$
$431$	26.7463	1.28832	0.644162	+	0.764889i	$0.277206\pi$
$432$	−3.97823	−0.191403
$433$	4.06531	0.195366	0.0976832	−	0.995218i	$-0.468857\pi$
$433$	4.06531	0.195366	0.0976832	+	0.995218i	$0.468857\pi$
$434$	−28.1987	−1.35358
$435$	−9.45281	−0.453228
$436$	60.0320	2.87501
$437$	32.5623	1.55766
$438$	−63.9711	−3.05666
$439$	12.6233	0.602475	0.301237	−	0.953549i	$-0.402600\pi$
$439$	12.6233	0.602475	0.301237	+	0.953549i	$0.402600\pi$
$440$	−7.29111	−0.347590
$441$	2.10321	0.100153
$442$	−0.246980	−0.0117476
$443$	−21.5448	−1.02362	−0.511812	−	0.859097i	$-0.671026\pi$
$443$	−21.5448	−1.02362	−0.511812	+	0.859097i	$0.671026\pi$
$444$	45.8461	2.17576
$445$	17.7922	0.843433
$446$	58.1691	2.75439
$447$	−17.3230	−0.819352
$448$	−51.3521	−2.42616
$449$	−24.7681	−1.16888	−0.584439	−	0.811438i	$-0.698685\pi$
$449$	−24.7681	−1.16888	−0.584439	+	0.811438i	$0.698685\pi$
$450$	1.97823	0.0932546
$451$	22.4999	1.05948
$452$	36.6993	1.72619
$453$	−16.0194	−0.752656
$454$	−0.801938	−0.0376368
$455$	−1.68425	−0.0789589
$456$	−29.0954	−1.36252
$457$	−1.15106	−0.0538445	−0.0269222	−	0.999638i	$-0.508571\pi$
$457$	−1.15106	−0.0538445	−0.0269222	+	0.999638i	$0.508571\pi$
$458$	−26.1075	−1.21992
$459$	1.52781	0.0713121
$460$	17.3618	0.809498
$461$	−21.6286	−1.00735	−0.503673	−	0.863894i	$-0.668018\pi$
$461$	−21.6286	−1.00735	−0.503673	+	0.863894i	$0.668018\pi$
$462$	−41.1812	−1.91592
$463$	28.1196	1.30683	0.653414	−	0.757000i	$-0.273336\pi$
$463$	28.1196	1.30683	0.653414	+	0.757000i	$0.273336\pi$
$464$	3.51142	0.163013
$465$	6.87800	0.318960
$466$	56.2398	2.60526
$467$	−8.71379	−0.403226	−0.201613	−	0.979465i	$-0.564618\pi$
$467$	−8.71379	−0.403226	−0.201613	+	0.979465i	$0.564618\pi$
$468$	0.268750	0.0124230
$469$	−9.04354	−0.417592
$470$	22.3327	1.03013
$471$	7.50365	0.345750
$472$	9.12737	0.420121
$473$	5.00670	0.230209
$474$	19.9758	0.917521
$475$	24.4209	1.12051
$476$	3.69873	0.169531
$477$	0.990311	0.0453432
$478$	−10.6582	−0.487493
$479$	17.0508	0.779073	0.389536	−	0.921011i	$-0.372635\pi$
$479$	17.0508	0.779073	0.389536	+	0.921011i	$0.372635\pi$
$480$	14.0664	0.642039
$481$	−2.97823	−0.135796
$482$	16.8237	0.766299
$483$	33.7362	1.53505
$484$	−13.2101	−0.600461
$485$	7.40475	0.336232
$486$	−5.75302	−0.260962
$487$	−40.0006	−1.81260	−0.906300	−	0.422635i	$-0.861105\pi$
$487$	−40.0006	−1.81260	−0.906300	+	0.422635i	$0.861105\pi$
$488$	4.22414	0.191218
$489$	21.7603	0.984036
$490$	22.9245	1.03562
$491$	31.8799	1.43872	0.719360	−	0.694637i	$-0.244435\pi$
$491$	31.8799	1.43872	0.719360	+	0.694637i	$0.244435\pi$
$492$	47.8732	2.15829
$493$	−1.34854	−0.0607350
$494$	5.49396	0.247185
$495$	0.764037	0.0343409
$496$	−2.55496	−0.114721
$497$	27.6588	1.24066
$498$	−24.2054	−1.08467
$499$	4.35152	0.194801	0.0974004	−	0.995245i	$-0.468947\pi$
$499$	4.35152	0.194801	0.0974004	+	0.995245i	$0.468947\pi$
$500$	31.2849	1.39910
$501$	−39.9342	−1.78413
$502$	61.6118	2.74987
$503$	−15.6625	−0.698356	−0.349178	−	0.937057i	$-0.613539\pi$
$503$	−15.6625	−0.698356	−0.349178	+	0.937057i	$0.613539\pi$
$504$	−2.29291	−0.102134
$505$	14.9099	0.663483
$506$	−27.5767	−1.22594
$507$	23.1957	1.03016
$508$	19.1957	0.851670
$509$	−15.5579	−0.689594	−0.344797	−	0.938677i	$-0.612052\pi$
$509$	−15.5579	−0.689594	−0.344797	+	0.938677i	$0.612052\pi$
$510$	−1.49396	−0.0661536
$511$	−62.2344	−2.75309
$512$	−9.00538	−0.397985
$513$	−33.9855	−1.50050
$514$	−27.7778	−1.22523
$515$	−15.1849	−0.669127
$516$	10.6528	0.468963
$517$	−21.4209	−0.942089
$518$	73.8587	3.24517
$519$	38.3521	1.68347
$520$	1.00777	0.0441936
$521$	−36.5700	−1.60216	−0.801081	−	0.598556i	$-0.795741\pi$
$521$	−36.5700	−1.60216	−0.801081	+	0.598556i	$0.795741\pi$
$522$	2.42998	0.106357
$523$	9.18359	0.401570	0.200785	−	0.979635i	$-0.435651\pi$
$523$	9.18359	0.401570	0.200785	+	0.979635i	$0.435651\pi$
$524$	−9.51871	−0.415827
$525$	25.3013	1.10424
$526$	5.24160	0.228545
$527$	0.981214	0.0427423
$528$	−3.73125	−0.162382
$529$	−0.408797	−0.0177738
$530$	10.7942	0.468869
$531$	−0.956459	−0.0415068
$532$	−82.2766	−3.56714
$533$	−3.10992	−0.134705
$534$	−60.1299	−2.60207
$535$	6.61463	0.285975
$536$	5.41119	0.233728
$537$	−29.7308	−1.28298
$538$	−29.1782	−1.25796
$539$	−21.9885	−0.947112
$540$	−18.1207	−0.779789
$541$	36.7536	1.58016	0.790081	−	0.613003i	$-0.210039\pi$
$541$	36.7536	1.58016	0.790081	+	0.613003i	$0.210039\pi$
$542$	73.2428	3.14605
$543$	27.8659	1.19584
$544$	2.00670	0.0860368
$545$	−23.5894	−1.01046
$546$	5.69202	0.243596
$547$	23.0180	0.984181	0.492090	−	0.870544i	$-0.336233\pi$
$547$	23.0180	0.984181	0.492090	+	0.870544i	$0.336233\pi$
$548$	60.9211	2.60242
$549$	−0.442649	−0.0188918
$550$	−20.6819	−0.881877
$551$	29.9976	1.27794
$552$	−20.1860	−0.859172
$553$	19.4336	0.826399
$554$	9.15213	0.388837
$555$	−18.0151	−0.764697
$556$	55.1051	2.33698
$557$	20.1045	0.851857	0.425928	−	0.904757i	$-0.359948\pi$
$557$	20.1045	0.851857	0.425928	+	0.904757i	$0.359948\pi$
$558$	−1.76809	−0.0748490
$559$	−0.692021	−0.0292694
$560$	3.78448	0.159923
$561$	1.43296	0.0604996
$562$	−38.8974	−1.64079
$563$	−26.3860	−1.11204	−0.556018	−	0.831170i	$-0.687671\pi$
$563$	−26.3860	−1.11204	−0.556018	+	0.831170i	$0.687671\pi$
$564$	−45.5773	−1.91915
$565$	−14.4209	−0.606691
$566$	−17.1250	−0.719817
$567$	−38.1293	−1.60128
$568$	−16.5496	−0.694405
$569$	−34.9202	−1.46393	−0.731966	−	0.681341i	$-0.761397\pi$
$569$	−34.9202	−1.46393	−0.731966	+	0.681341i	$0.761397\pi$
$570$	33.2325	1.39196
$571$	−29.2446	−1.22385	−0.611924	−	0.790917i	$-0.709604\pi$
$571$	−29.2446	−1.22385	−0.611924	+	0.790917i	$0.709604\pi$
$572$	−2.80971	−0.117480
$573$	−19.5700	−0.817549
$574$	77.1245	3.21911
$575$	16.9428	0.706565
$576$	−3.21983	−0.134160
$577$	1.10454	0.0459826	0.0229913	−	0.999736i	$-0.492681\pi$
$577$	1.10454	0.0459826	0.0229913	+	0.999736i	$0.492681\pi$
$578$	37.9855	1.57999
$579$	−25.1739	−1.04619
$580$	15.9944	0.664130
$581$	−23.5483	−0.976946
$582$	−25.0248	−1.03731
$583$	−10.3534	−0.428796
$584$	37.2379	1.54091
$585$	−0.105604	−0.00436620
$586$	35.0224	1.44676
$587$	10.2222	0.421916	0.210958	−	0.977495i	$-0.432342\pi$
$587$	10.2222	0.421916	0.210958	+	0.977495i	$0.432342\pi$
$588$	−46.7851	−1.92938
$589$	−21.8267	−0.899353
$590$	−10.4252	−0.429198
$591$	−22.1347	−0.910499
$592$	6.69202	0.275040
$593$	1.17092	0.0480837	0.0240419	−	0.999711i	$-0.492347\pi$
$593$	1.17092	0.0480837	0.0240419	+	0.999711i	$0.492347\pi$
$594$	28.7821	1.18094
$595$	−1.45340	−0.0595837
$596$	29.3110	1.20062
$597$	38.7536	1.58608
$598$	3.81163	0.155869
$599$	−13.4668	−0.550239	−0.275120	−	0.961410i	$-0.588717\pi$
$599$	−13.4668	−0.550239	−0.275120	+	0.961410i	$0.588717\pi$
$600$	−15.1390	−0.618046
$601$	35.6528	1.45431	0.727154	−	0.686475i	$-0.240843\pi$
$601$	35.6528	1.45431	0.727154	+	0.686475i	$0.240843\pi$
$602$	17.1618	0.699463
$603$	−0.567040	−0.0230916
$604$	27.1051	1.10289
$605$	5.19088	0.211039
$606$	−50.3889	−2.04691
$607$	−1.14185	−0.0463462	−0.0231731	−	0.999731i	$-0.507377\pi$
$607$	−1.14185	−0.0463462	−0.0231731	+	0.999731i	$0.507377\pi$
$608$	−44.6383	−1.81032
$609$	31.0790	1.25939
$610$	−4.82477	−0.195349
$611$	2.96077	0.119780
$612$	0.231914	0.00937457
$613$	−8.68127	−0.350633	−0.175317	−	0.984512i	$-0.556095\pi$
$613$	−8.68127	−0.350633	−0.175317	+	0.984512i	$0.556095\pi$
$614$	−46.5109	−1.87703
$615$	−18.8116	−0.758558
$616$	23.9718	0.965851
$617$	−18.2325	−0.734013	−0.367007	−	0.930218i	$-0.619617\pi$
$617$	−18.2325	−0.734013	−0.367007	+	0.930218i	$0.619617\pi$
$618$	51.3183	2.06432
$619$	2.40150	0.0965245	0.0482622	−	0.998835i	$-0.484632\pi$
$619$	2.40150	0.0965245	0.0482622	+	0.998835i	$0.484632\pi$
$620$	−11.6377	−0.467382
$621$	−23.5786	−0.946179
$622$	19.4819	0.781152
$623$	−58.4975	−2.34365
$624$	0.515729	0.0206457
$625$	5.52994	0.221198
$626$	−75.3430	−3.01131
$627$	−31.8756	−1.27299
$628$	−12.6963	−0.506639
$629$	−2.57002	−0.102474
$630$	2.61894	0.104341
$631$	10.5526	0.420091	0.210045	−	0.977692i	$-0.432639\pi$
$631$	10.5526	0.420091	0.210045	+	0.977692i	$0.432639\pi$
$632$	−11.6280	−0.462539
$633$	1.80194	0.0716206
$634$	−45.0984	−1.79109
$635$	−7.54288	−0.299330
$636$	−22.0291	−0.873509
$637$	3.03923	0.120419
$638$	−25.4047	−1.00578
$639$	1.73423	0.0686052
$640$	−19.4829	−0.770131
$641$	−17.1177	−0.676108	−0.338054	−	0.941127i	$-0.609769\pi$
$641$	−17.1177	−0.676108	−0.338054	+	0.941127i	$0.609769\pi$
$642$	−22.3545	−0.882262
$643$	0.141375	0.00557529	0.00278765	−	0.999996i	$-0.499113\pi$
$643$	0.141375	0.00557529	0.00278765	+	0.999996i	$0.499113\pi$
$644$	−57.0823	−2.24936
$645$	−4.18598	−0.164823
$646$	4.74094	0.186530
$647$	−17.9541	−0.705847	−0.352924	−	0.935652i	$-0.614812\pi$
$647$	−17.9541	−0.705847	−0.352924	+	0.935652i	$0.614812\pi$
$648$	22.8146	0.896243
$649$	9.99953	0.392516
$650$	2.85862	0.112124
$651$	−22.6136	−0.886295
$652$	−36.8189	−1.44194
$653$	7.42626	0.290612	0.145306	−	0.989387i	$-0.453583\pi$
$653$	7.42626	0.290612	0.145306	+	0.989387i	$0.453583\pi$
$654$	79.7217	3.11736
$655$	3.74035	0.146147
$656$	6.98792	0.272832
$657$	−3.90217	−0.152238
$658$	−73.4258	−2.86243
$659$	−21.6920	−0.845001	−0.422501	−	0.906363i	$-0.638848\pi$
$659$	−21.6920	−0.845001	−0.422501	+	0.906363i	$0.638848\pi$
$660$	−16.9957	−0.661556
$661$	4.76941	0.185509	0.0927543	−	0.995689i	$-0.470433\pi$
$661$	4.76941	0.185509	0.0927543	+	0.995689i	$0.470433\pi$
$662$	−29.9952	−1.16580
$663$	−0.198062	−0.00769210
$664$	14.0901	0.546801
$665$	32.3303	1.25372
$666$	4.63102	0.179448
$667$	20.8119	0.805840
$668$	67.5695	2.61434
$669$	46.6480	1.80352
$670$	−6.18060	−0.238778
$671$	4.62778	0.178653
$672$	−46.2476	−1.78404
$673$	5.55389	0.214087	0.107043	−	0.994254i	$-0.465862\pi$
$673$	5.55389	0.214087	0.107043	+	0.994254i	$0.465862\pi$
$674$	21.8538	0.841778
$675$	−17.6834	−0.680634
$676$	−39.2476	−1.50952
$677$	4.45771	0.171324	0.0856619	−	0.996324i	$-0.472699\pi$
$677$	4.45771	0.171324	0.0856619	+	0.996324i	$0.472699\pi$
$678$	48.7362	1.87170
$679$	−24.3454	−0.934291
$680$	0.869641	0.0333492
$681$	−0.643104	−0.0246438
$682$	18.4849	0.707822
$683$	36.8713	1.41084	0.705420	−	0.708789i	$-0.250758\pi$
$683$	36.8713	1.41084	0.705420	+	0.708789i	$0.250758\pi$
$684$	−5.15883	−0.197253
$685$	−23.9387	−0.914652
$686$	−13.4155	−0.512206
$687$	−20.9366	−0.798781
$688$	1.55496	0.0592822
$689$	1.43104	0.0545183
$690$	23.0562	0.877735
$691$	29.1879	1.11036	0.555180	−	0.831730i	$-0.312649\pi$
$691$	29.1879	1.11036	0.555180	+	0.831730i	$0.312649\pi$
$692$	−64.8926	−2.46685
$693$	−2.51201	−0.0954233
$694$	39.0170	1.48106
$695$	−21.6534	−0.821360
$696$	−18.5961	−0.704884
$697$	−2.68366	−0.101651
$698$	14.4330	0.546296
$699$	45.1008	1.70587
$700$	−42.8103	−1.61808
$701$	−44.9952	−1.69945	−0.849723	−	0.527230i	$-0.823231\pi$
$701$	−44.9952	−1.69945	−0.849723	+	0.527230i	$0.823231\pi$
$702$	−3.97823	−0.150149
$703$	57.1691	2.15617
$704$	33.6625	1.26870
$705$	17.9095	0.674509
$706$	9.97823	0.375536
$707$	−49.0210	−1.84363
$708$	21.2760	0.799603
$709$	−20.0586	−0.753317	−0.376658	−	0.926352i	$-0.622927\pi$
$709$	−20.0586	−0.753317	−0.376658	+	0.926352i	$0.622927\pi$
$710$	18.9028	0.709408
$711$	1.21850	0.0456975
$712$	35.0019	1.31175
$713$	−15.1430	−0.567111
$714$	4.91185	0.183822
$715$	1.10407	0.0412897
$716$	50.3051	1.87999
$717$	−8.54719	−0.319201
$718$	23.9312	0.893106
$719$	−14.3461	−0.535021	−0.267510	−	0.963555i	$-0.586201\pi$
$719$	−14.3461	−0.535021	−0.267510	+	0.963555i	$0.586201\pi$
$720$	0.237291	0.00884331
$721$	49.9251	1.85931
$722$	−62.7676	−2.33597
$723$	13.4916	0.501757
$724$	−47.1497	−1.75231
$725$	15.6084	0.579681
$726$	−17.5429	−0.651077
$727$	31.4668	1.16704	0.583520	−	0.812099i	$-0.301675\pi$
$727$	31.4668	1.16704	0.583520	+	0.812099i	$0.301675\pi$
$728$	−3.31336	−0.122801
$729$	24.4263	0.904676
$730$	−42.5327	−1.57421
$731$	−0.597171	−0.0220872
$732$	9.84654	0.363939
$733$	40.2331	1.48604	0.743022	−	0.669267i	$-0.233392\pi$
$733$	40.2331	1.48604	0.743022	+	0.669267i	$0.233392\pi$
$734$	29.9638	1.10598
$735$	18.3840	0.678106
$736$	−30.9694	−1.14155
$737$	5.92825	0.218370
$738$	4.83579	0.178008
$739$	−18.6276	−0.685226	−0.342613	−	0.939477i	$-0.611312\pi$
$739$	−18.6276	−0.685226	−0.342613	+	0.939477i	$0.611312\pi$
$740$	30.4819	1.12054
$741$	4.40581	0.161852
$742$	−35.4892	−1.30285
$743$	6.11098	0.224190	0.112095	−	0.993697i	$-0.464244\pi$
$743$	6.11098	0.224190	0.112095	+	0.993697i	$0.464244\pi$
$744$	13.5308	0.496063
$745$	−11.5176	−0.421974
$746$	−76.9566	−2.81758
$747$	−1.47650	−0.0540223
$748$	−2.42460	−0.0886521
$749$	−21.7476	−0.794642
$750$	41.5459	1.51704
$751$	−42.8558	−1.56383	−0.781914	−	0.623386i	$-0.785757\pi$
$751$	−42.8558	−1.56383	−0.781914	+	0.623386i	$0.785757\pi$
$752$	−6.65279	−0.242602
$753$	49.4088	1.80056
$754$	3.51142	0.127878
$755$	−10.6509	−0.387625
$756$	59.5773	2.16681
$757$	−9.83041	−0.357292	−0.178646	−	0.983913i	$-0.557172\pi$
$757$	−9.83041	−0.357292	−0.178646	+	0.983913i	$0.557172\pi$
$758$	17.6407	0.640739
$759$	−22.1148	−0.802717
$760$	−19.3448	−0.701710
$761$	16.4910	0.597797	0.298899	−	0.954285i	$-0.403381\pi$
$761$	16.4910	0.597797	0.298899	+	0.954285i	$0.403381\pi$
$762$	25.4916	0.923462
$763$	77.5575	2.80777
$764$	33.1129	1.19798
$765$	−0.0911299	−0.00329481
$766$	4.39075	0.158644
$767$	−1.38212	−0.0499056
$768$	18.8605	0.680571
$769$	27.6993	0.998863	0.499431	−	0.866353i	$-0.333542\pi$
$769$	27.6993	0.998863	0.499431	+	0.866353i	$0.333542\pi$
$770$	−27.3803	−0.986718
$771$	−22.2760	−0.802252
$772$	42.5948	1.53302
$773$	9.14808	0.329034	0.164517	−	0.986374i	$-0.447394\pi$
$773$	9.14808	0.329034	0.164517	+	0.986374i	$0.447394\pi$
$774$	1.07606	0.0386783
$775$	−11.3569	−0.407952
$776$	14.5670	0.522926
$777$	59.2301	2.12487
$778$	79.9318	2.86569
$779$	59.6969	2.13886
$780$	2.34913	0.0841122
$781$	−18.1309	−0.648776
$782$	3.28919	0.117621
$783$	−21.7216	−0.776265
$784$	−6.82908	−0.243896
$785$	4.98898	0.178064
$786$	−12.6407	−0.450879
$787$	−30.6708	−1.09330	−0.546649	−	0.837362i	$-0.684097\pi$
$787$	−30.6708	−1.09330	−0.546649	+	0.837362i	$0.684097\pi$
$788$	37.4523	1.33418
$789$	4.20344	0.149646
$790$	13.2814	0.472532
$791$	47.4131	1.68582
$792$	1.50306	0.0534088
$793$	−0.639646	−0.0227145
$794$	−1.64310	−0.0583116
$795$	8.65625	0.307006
$796$	−65.5719	−2.32414
$797$	6.40044	0.226715	0.113358	−	0.993554i	$-0.463839\pi$
$797$	6.40044	0.226715	0.113358	+	0.993554i	$0.463839\pi$
$798$	−109.262	−3.86784
$799$	2.55496	0.0903879
$800$	−23.2263	−0.821173
$801$	−3.66786	−0.129597
$802$	1.93900	0.0684685
$803$	40.7961	1.43966
$804$	12.6136	0.444846
$805$	22.4303	0.790564
$806$	−2.55496	−0.0899946
$807$	−23.3991	−0.823688
$808$	29.3317	1.03188
$809$	−51.9590	−1.82678	−0.913390	−	0.407086i	$-0.866545\pi$
$809$	−51.9590	−1.82678	−0.913390	+	0.407086i	$0.866545\pi$
$810$	−26.0586	−0.915606
$811$	−53.4021	−1.87520	−0.937601	−	0.347714i	$-0.886958\pi$
$811$	−53.4021	−1.87520	−0.937601	+	0.347714i	$0.886958\pi$
$812$	−52.5864	−1.84542
$813$	58.7362	2.05997
$814$	−48.4161	−1.69698
$815$	14.4679	0.506788
$816$	0.445042	0.0155796
$817$	13.2838	0.464742
$818$	−39.0780	−1.36633
$819$	0.347207	0.0121324
$820$	31.8297	1.11154
$821$	22.3556	0.780215	0.390107	−	0.920769i	$-0.372438\pi$
$821$	22.3556	0.780215	0.390107	+	0.920769i	$0.372438\pi$
$822$	80.9023	2.82179
$823$	−30.0834	−1.04864	−0.524320	−	0.851521i	$-0.675680\pi$
$823$	−30.0834	−1.04864	−0.524320	+	0.851521i	$0.675680\pi$
$824$	−29.8726	−1.04066
$825$	−16.5856	−0.577435
$826$	34.2760	1.19262
$827$	28.0670	0.975984	0.487992	−	0.872848i	$-0.337730\pi$
$827$	28.0670	0.975984	0.487992	+	0.872848i	$0.337730\pi$
$828$	−3.57912	−0.124383
$829$	−16.1293	−0.560194	−0.280097	−	0.959972i	$-0.590367\pi$
$829$	−16.1293	−0.560194	−0.280097	+	0.959972i	$0.590367\pi$
$830$	−16.0935	−0.558614
$831$	7.33944	0.254602
$832$	−4.65279	−0.161307
$833$	2.62266	0.0908698
$834$	73.1788	2.53397
$835$	−26.5512	−0.918843
$836$	53.9342	1.86535
$837$	15.8049	0.546298
$838$	−50.5937	−1.74773
$839$	−32.6353	−1.12670	−0.563348	−	0.826219i	$-0.690487\pi$
$839$	−32.6353	−1.12670	−0.563348	+	0.826219i	$0.690487\pi$
$840$	−20.0422	−0.691522
$841$	−9.82728	−0.338872
$842$	31.7549	1.09435
$843$	−31.1933	−1.07435
$844$	−3.04892	−0.104948
$845$	15.4222	0.530540
$846$	−4.60388	−0.158284
$847$	−17.0666	−0.586417
$848$	−3.21552	−0.110421
$849$	−13.7332	−0.471321
$850$	2.46681	0.0846110
$851$	39.6631	1.35963
$852$	−38.5773	−1.32164
$853$	15.1424	0.518467	0.259234	−	0.965815i	$-0.416530\pi$
$853$	15.1424	0.518467	0.259234	+	0.965815i	$0.416530\pi$
$854$	15.8629	0.542819
$855$	2.02715	0.0693270
$856$	13.0127	0.444764
$857$	−21.5351	−0.735625	−0.367813	−	0.929900i	$-0.619893\pi$
$857$	−21.5351	−0.735625	−0.367813	+	0.929900i	$0.619893\pi$
$858$	−3.73125	−0.127383
$859$	7.18406	0.245117	0.122559	−	0.992461i	$-0.460890\pi$
$859$	7.18406	0.245117	0.122559	+	0.992461i	$0.460890\pi$
$860$	7.08277	0.241520
$861$	61.8491	2.10781
$862$	−60.0984	−2.04696
$863$	14.8646	0.505997	0.252998	−	0.967467i	$-0.418583\pi$
$863$	14.8646	0.505997	0.252998	+	0.967467i	$0.418583\pi$
$864$	32.3230	1.09965
$865$	25.4993	0.867003
$866$	−9.13467	−0.310409
$867$	30.4620	1.03454
$868$	38.2626	1.29872
$869$	−12.7391	−0.432146
$870$	21.2403	0.720113
$871$	−0.819396	−0.0277642
$872$	−46.4064	−1.57152
$873$	−1.52648	−0.0516636
$874$	−73.1667	−2.47490
$875$	40.4180	1.36638
$876$	86.8021	2.93277
$877$	7.73556	0.261211	0.130606	−	0.991434i	$-0.458308\pi$
$877$	7.73556	0.261211	0.130606	+	0.991434i	$0.458308\pi$
$878$	−28.3642	−0.957245
$879$	28.0858	0.947309
$880$	−2.48081	−0.0836282
$881$	−11.4149	−0.384578	−0.192289	−	0.981338i	$-0.561591\pi$
$881$	−11.4149	−0.384578	−0.192289	+	0.981338i	$0.561591\pi$
$882$	−4.72587	−0.159128
$883$	−7.99569	−0.269076	−0.134538	−	0.990908i	$-0.542955\pi$
$883$	−7.99569	−0.269076	−0.134538	+	0.990908i	$0.542955\pi$
$884$	0.335126	0.0112715
$885$	−8.36035	−0.281030
$886$	48.4107	1.62639
$887$	35.3779	1.18787	0.593937	−	0.804511i	$-0.297573\pi$
$887$	35.3779	1.18787	0.593937	+	0.804511i	$0.297573\pi$
$888$	−35.4403	−1.18930
$889$	24.7995	0.831750
$890$	−39.9788	−1.34009
$891$	24.9946	0.837351
$892$	−78.9294	−2.64275
$893$	−56.8340	−1.90188
$894$	38.9245	1.30183
$895$	−19.7672	−0.660746
$896$	64.0562	2.13997
$897$	3.05669	0.102060
$898$	55.6534	1.85718
$899$	−13.9503	−0.465270
$900$	−2.68425	−0.0894751
$901$	1.23490	0.0411404
$902$	−50.5569	−1.68336
$903$	13.7627	0.457994
$904$	−28.3696	−0.943558
$905$	18.5273	0.615870
$906$	35.9952	1.19586
$907$	−4.04785	−0.134407	−0.0672034	−	0.997739i	$-0.521408\pi$
$907$	−4.04785	−0.134407	−0.0672034	+	0.997739i	$0.521408\pi$
$908$	1.08815	0.0361114
$909$	−3.07367	−0.101947
$910$	3.78448	0.125454
$911$	−42.8364	−1.41923	−0.709616	−	0.704588i	$-0.751132\pi$
$911$	−42.8364	−1.41923	−0.709616	+	0.704588i	$0.751132\pi$
$912$	−9.89977	−0.327814
$913$	15.4364	0.510871
$914$	2.58642	0.0855511
$915$	−3.86917	−0.127911
$916$	35.4252	1.17048
$917$	−12.2976	−0.406101
$918$	−3.43296	−0.113305
$919$	−28.2234	−0.931004	−0.465502	−	0.885047i	$-0.654126\pi$
$919$	−28.2234	−0.931004	−0.465502	+	0.885047i	$0.654126\pi$
$920$	−13.4211	−0.442482
$921$	−37.2989	−1.22904
$922$	48.5991	1.60053
$923$	2.50604	0.0824873
$924$	55.8786	1.83827
$925$	29.7463	0.978053
$926$	−63.1842	−2.07636
$927$	3.13036	0.102814
$928$	−28.5302	−0.936550
$929$	−15.2034	−0.498809	−0.249404	−	0.968399i	$-0.580235\pi$
$929$	−15.2034	−0.498809	−0.249404	+	0.968399i	$0.580235\pi$
$930$	−15.4547	−0.506781
$931$	−58.3400	−1.91202
$932$	−76.3116	−2.49967
$933$	15.6233	0.511482
$934$	19.5797	0.640668
$935$	0.952739	0.0311579
$936$	−0.207751	−0.00679055
$937$	22.9355	0.749272	0.374636	−	0.927172i	$-0.377768\pi$
$937$	22.9355	0.749272	0.374636	+	0.927172i	$0.377768\pi$
$938$	20.3207	0.663493
$939$	−60.4204	−1.97175
$940$	−30.3032	−0.988381
$941$	−20.6364	−0.672727	−0.336364	−	0.941732i	$-0.609197\pi$
$941$	−20.6364	−0.672727	−0.336364	+	0.941732i	$0.609197\pi$
$942$	−16.8605	−0.549346
$943$	41.4168	1.34872
$944$	3.10560	0.101079
$945$	−23.4107	−0.761551
$946$	−11.2500	−0.365768
$947$	−45.1215	−1.46625	−0.733126	−	0.680093i	$-0.761940\pi$
$947$	−45.1215	−1.46625	−0.733126	+	0.680093i	$0.761940\pi$
$948$	−27.1051	−0.880334
$949$	−5.63879	−0.183043
$950$	−54.8732	−1.78032
$951$	−36.1661	−1.17277
$952$	−2.85922	−0.0926677
$953$	28.8203	0.933579	0.466790	−	0.884368i	$-0.345410\pi$
$953$	28.8203	0.933579	0.466790	+	0.884368i	$0.345410\pi$
$954$	−2.22521	−0.0720438
$955$	−13.0116	−0.421046
$956$	14.4620	0.467735
$957$	−20.3730	−0.658566
$958$	−38.3129	−1.23783
$959$	78.7060	2.54155
$960$	−28.1444	−0.908355
$961$	−20.8495	−0.672565
$962$	6.69202	0.215759
$963$	−1.36360	−0.0439414
$964$	−22.8280	−0.735241
$965$	−16.7375	−0.538799
$966$	−75.8044	−2.43897
$967$	−48.9047	−1.57267	−0.786334	−	0.617801i	$-0.788024\pi$
$967$	−48.9047	−1.57267	−0.786334	+	0.617801i	$0.788024\pi$
$968$	10.2118	0.328220
$969$	3.80194	0.122136
$970$	−16.6383	−0.534224
$971$	17.8461	0.572708	0.286354	−	0.958124i	$-0.407557\pi$
$971$	17.8461	0.572708	0.286354	+	0.958124i	$0.407557\pi$
$972$	7.80625	0.250386
$973$	71.1922	2.28232
$974$	89.8805	2.87996
$975$	2.29244	0.0734168
$976$	1.43727	0.0460060
$977$	28.0670	0.897942	0.448971	−	0.893546i	$-0.351791\pi$
$977$	28.0670	0.897942	0.448971	+	0.893546i	$0.351791\pi$
$978$	−48.8950	−1.56349
$979$	38.3465	1.22556
$980$	−31.1062	−0.993651
$981$	4.86294	0.155262
$982$	−71.6335	−2.28592
$983$	24.6945	0.787633	0.393817	−	0.919189i	$-0.371155\pi$
$983$	24.6945	0.787633	0.393817	+	0.919189i	$0.371155\pi$
$984$	−37.0073	−1.17975
$985$	−14.7168	−0.468915
$986$	3.03013	0.0964990
$987$	−58.8829	−1.87426
$988$	−7.45473	−0.237167
$989$	9.21611	0.293055
$990$	−1.71678	−0.0545627
$991$	52.1094	1.65531	0.827655	−	0.561236i	$-0.189674\pi$
$991$	52.1094	1.65531	0.827655	+	0.561236i	$0.189674\pi$
$992$	20.7590	0.659099
$993$	−24.0543	−0.763340
$994$	−62.1487	−1.97124
$995$	25.7663	0.816846
$996$	32.8442	1.04071
$997$	−51.1008	−1.61838	−0.809190	−	0.587548i	$-0.800093\pi$
$997$	−51.1008	−1.61838	−0.809190	+	0.587548i	$0.800093\pi$
$998$	−9.77777	−0.309510
$999$	−41.3967	−1.30973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.2.a.b.1.1	✓	3
3.2	odd	2		1899.2.a.f.1.3		3
4.3	odd	2		3376.2.a.j.1.3		3
5.4	even	2		5275.2.a.i.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.2.a.b.1.1	✓	3	1.1	even	1	trivial
1899.2.a.f.1.3		3	3.2	odd	2
3376.2.a.j.1.3		3	4.3	odd	2
5275.2.a.i.1.3		3	5.4	even	2

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:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	211.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24698 q^{2} -1.80194 q^{3} +3.04892 q^{4} -1.19806 q^{5} +4.04892 q^{6} +3.93900 q^{7} -2.35690 q^{8} +0.246980 q^{9} +O(q^{10})\)	\(q-2.24698 q^{2} -1.80194 q^{3} +3.04892 q^{4} -1.19806 q^{5} +4.04892 q^{6} +3.93900 q^{7} -2.35690 q^{8} +0.246980 q^{9} +2.69202 q^{10} -2.58211 q^{11} -5.49396 q^{12} +0.356896 q^{13} -8.85086 q^{14} +2.15883 q^{15} -0.801938 q^{16} +0.307979 q^{17} -0.554958 q^{18} -6.85086 q^{19} -3.65279 q^{20} -7.09783 q^{21} +5.80194 q^{22} -4.75302 q^{23} +4.24698 q^{24} -3.56465 q^{25} -0.801938 q^{26} +4.96077 q^{27} +12.0097 q^{28} -4.37867 q^{29} -4.85086 q^{30} +3.18598 q^{31} +6.51573 q^{32} +4.65279 q^{33} -0.692021 q^{34} -4.71917 q^{35} +0.753020 q^{36} -8.34481 q^{37} +15.3937 q^{38} -0.643104 q^{39} +2.82371 q^{40} -8.71379 q^{41} +15.9487 q^{42} -1.93900 q^{43} -7.87263 q^{44} -0.295897 q^{45} +10.6799 q^{46} +8.29590 q^{47} +1.44504 q^{48} +8.51573 q^{49} +8.00969 q^{50} -0.554958 q^{51} +1.08815 q^{52} +4.00969 q^{53} -11.1468 q^{54} +3.09352 q^{55} -9.28382 q^{56} +12.3448 q^{57} +9.83877 q^{58} -3.87263 q^{59} +6.58211 q^{60} -1.79225 q^{61} -7.15883 q^{62} +0.972853 q^{63} -13.0368 q^{64} -0.427583 q^{65} -10.4547 q^{66} -2.29590 q^{67} +0.939001 q^{68} +8.56465 q^{69} +10.6039 q^{70} +7.02177 q^{71} -0.582105 q^{72} -15.7995 q^{73} +18.7506 q^{74} +6.42327 q^{75} -20.8877 q^{76} -10.1709 q^{77} +1.44504 q^{78} +4.93362 q^{79} +0.960771 q^{80} -9.67994 q^{81} +19.5797 q^{82} -5.97823 q^{83} -21.6407 q^{84} -0.368977 q^{85} +4.35690 q^{86} +7.89008 q^{87} +6.08575 q^{88} -14.8509 q^{89} +0.664874 q^{90} +1.40581 q^{91} -14.4916 q^{92} -5.74094 q^{93} -18.6407 q^{94} +8.20775 q^{95} -11.7409 q^{96} -6.18060 q^{97} -19.1347 q^{98} -0.637727 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - q^{3} - 8 q^{5} + 3 q^{6} + 2 q^{7} - 3 q^{8} - 4 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - q^3 - 8 * q^5 + 3 * q^6 + 2 * q^7 - 3 * q^8 - 4 * q^9	\( 3 q - 2 q^{2} - q^{3} - 8 q^{5} + 3 q^{6} + 2 q^{7} - 3 q^{8} - 4 q^{9} + 3 q^{10} - 2 q^{11} - 7 q^{12} - 3 q^{13} - 13 q^{14} - 2 q^{15} + 2 q^{16} + 6 q^{17} - 2 q^{18} - 7 q^{19} + 7 q^{20} - 3 q^{21} + 13 q^{22} - 19 q^{23} + 8 q^{24} + 11 q^{25} + 2 q^{26} + 2 q^{27} + 14 q^{28} - 6 q^{29} - q^{30} - 5 q^{31} + 7 q^{32} - 4 q^{33} + 3 q^{34} - 3 q^{35} + 7 q^{36} - 2 q^{37} + 14 q^{38} - 6 q^{39} + q^{40} - 18 q^{41} + 16 q^{42} + 4 q^{43} - 7 q^{44} + 13 q^{45} + 8 q^{46} + 11 q^{47} + 4 q^{48} + 13 q^{49} + 2 q^{50} - 2 q^{51} + 7 q^{52} - 10 q^{53} - 6 q^{54} + 10 q^{55} + 5 q^{56} + 14 q^{57} - 3 q^{58} + 5 q^{59} + 14 q^{60} - 23 q^{61} - 13 q^{62} + 9 q^{63} - 11 q^{64} + 15 q^{65} - 9 q^{66} + 7 q^{67} - 7 q^{68} + 4 q^{69} + 23 q^{70} + 18 q^{71} + 4 q^{72} - 2 q^{73} + 20 q^{74} + 22 q^{75} - 21 q^{76} - 41 q^{77} + 4 q^{78} + 8 q^{79} - 10 q^{80} - 5 q^{81} + 12 q^{82} - 21 q^{83} - 28 q^{84} - 16 q^{85} + 9 q^{86} + 23 q^{87} - 19 q^{88} - 31 q^{89} + 3 q^{90} - 9 q^{91} + 7 q^{92} - 3 q^{93} - 19 q^{94} + 7 q^{95} - 21 q^{96} - 7 q^{97} - 11 q^{98} - 9 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - q^3 - 8 * q^5 + 3 * q^6 + 2 * q^7 - 3 * q^8 - 4 * q^9 + 3 * q^10 - 2 * q^11 - 7 * q^12 - 3 * q^13 - 13 * q^14 - 2 * q^15 + 2 * q^16 + 6 * q^17 - 2 * q^18 - 7 * q^19 + 7 * q^20 - 3 * q^21 + 13 * q^22 - 19 * q^23 + 8 * q^24 + 11 * q^25 + 2 * q^26 + 2 * q^27 + 14 * q^28 - 6 * q^29 - q^30 - 5 * q^31 + 7 * q^32 - 4 * q^33 + 3 * q^34 - 3 * q^35 + 7 * q^36 - 2 * q^37 + 14 * q^38 - 6 * q^39 + q^40 - 18 * q^41 + 16 * q^42 + 4 * q^43 - 7 * q^44 + 13 * q^45 + 8 * q^46 + 11 * q^47 + 4 * q^48 + 13 * q^49 + 2 * q^50 - 2 * q^51 + 7 * q^52 - 10 * q^53 - 6 * q^54 + 10 * q^55 + 5 * q^56 + 14 * q^57 - 3 * q^58 + 5 * q^59 + 14 * q^60 - 23 * q^61 - 13 * q^62 + 9 * q^63 - 11 * q^64 + 15 * q^65 - 9 * q^66 + 7 * q^67 - 7 * q^68 + 4 * q^69 + 23 * q^70 + 18 * q^71 + 4 * q^72 - 2 * q^73 + 20 * q^74 + 22 * q^75 - 21 * q^76 - 41 * q^77 + 4 * q^78 + 8 * q^79 - 10 * q^80 - 5 * q^81 + 12 * q^82 - 21 * q^83 - 28 * q^84 - 16 * q^85 + 9 * q^86 + 23 * q^87 - 19 * q^88 - 31 * q^89 + 3 * q^90 - 9 * q^91 + 7 * q^92 - 3 * q^93 - 19 * q^94 + 7 * q^95 - 21 * q^96 - 7 * q^97 - 11 * q^98 - 9 * q^99

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