LMFDB - Embedded newform 671.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29453 q^{2} +3.40741 q^{3} -0.324186 q^{4} +2.94198 q^{5} -4.41100 q^{6} -0.962580 q^{7} +3.00873 q^{8} +8.61042 q^{9} +O(q^{10})$	\(q-1.29453 q^{2} +3.40741 q^{3} -0.324186 q^{4} +2.94198 q^{5} -4.41100 q^{6} -0.962580 q^{7} +3.00873 q^{8} +8.61042 q^{9} -3.80849 q^{10} -1.00000 q^{11} -1.10463 q^{12} -1.22524 q^{13} +1.24609 q^{14} +10.0245 q^{15} -3.24653 q^{16} +4.62899 q^{17} -11.1465 q^{18} -5.94052 q^{19} -0.953749 q^{20} -3.27990 q^{21} +1.29453 q^{22} -0.745508 q^{23} +10.2520 q^{24} +3.65525 q^{25} +1.58611 q^{26} +19.1170 q^{27} +0.312055 q^{28} -2.48163 q^{29} -12.9771 q^{30} -7.01525 q^{31} -1.81473 q^{32} -3.40741 q^{33} -5.99237 q^{34} -2.83189 q^{35} -2.79138 q^{36} +8.66581 q^{37} +7.69019 q^{38} -4.17488 q^{39} +8.85164 q^{40} +4.87491 q^{41} +4.24594 q^{42} -7.47335 q^{43} +0.324186 q^{44} +25.3317 q^{45} +0.965085 q^{46} +5.10409 q^{47} -11.0623 q^{48} -6.07344 q^{49} -4.73184 q^{50} +15.7728 q^{51} +0.397205 q^{52} -12.5071 q^{53} -24.7476 q^{54} -2.94198 q^{55} -2.89615 q^{56} -20.2418 q^{57} +3.21254 q^{58} -4.29739 q^{59} -3.24981 q^{60} +1.00000 q^{61} +9.08147 q^{62} -8.28822 q^{63} +8.84229 q^{64} -3.60462 q^{65} +4.41100 q^{66} -6.70005 q^{67} -1.50065 q^{68} -2.54025 q^{69} +3.66597 q^{70} -5.44678 q^{71} +25.9065 q^{72} +13.4494 q^{73} -11.2182 q^{74} +12.4549 q^{75} +1.92583 q^{76} +0.962580 q^{77} +5.40452 q^{78} -3.09980 q^{79} -9.55123 q^{80} +39.3081 q^{81} -6.31073 q^{82} +11.8714 q^{83} +1.06330 q^{84} +13.6184 q^{85} +9.67450 q^{86} -8.45591 q^{87} -3.00873 q^{88} +13.7818 q^{89} -32.7927 q^{90} +1.17939 q^{91} +0.241683 q^{92} -23.9038 q^{93} -6.60741 q^{94} -17.4769 q^{95} -6.18352 q^{96} +16.5554 q^{97} +7.86226 q^{98} -8.61042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.29453	−0.915373	−0.457686	−	0.889114i	$-0.651322\pi$
$2$	−1.29453	−0.915373	−0.457686	+	0.889114i	$0.651322\pi$
$3$	3.40741	1.96727	0.983634	−	0.180179i	$-0.0576679\pi$
$3$	3.40741	1.96727	0.983634	+	0.180179i	$0.0576679\pi$
$4$	−0.324186	−0.162093
$5$	2.94198	1.31569	0.657847	−	0.753152i	$-0.271467\pi$
$5$	2.94198	1.31569	0.657847	+	0.753152i	$0.271467\pi$
$6$	−4.41100	−1.80078
$7$	−0.962580	−0.363821	−0.181911	−	0.983315i	$-0.558228\pi$
$7$	−0.962580	−0.363821	−0.181911	+	0.983315i	$0.558228\pi$
$8$	3.00873	1.06375
$9$	8.61042	2.87014
$10$	−3.80849	−1.20435
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.10463	−0.318880
$13$	−1.22524	−0.339820	−0.169910	−	0.985460i	$-0.554348\pi$
$13$	−1.22524	−0.339820	−0.169910	+	0.985460i	$0.554348\pi$
$14$	1.24609	0.333032
$15$	10.0245	2.58832
$16$	−3.24653	−0.811633
$17$	4.62899	1.12269	0.561347	−	0.827580i	$-0.310283\pi$
$17$	4.62899	1.12269	0.561347	+	0.827580i	$0.310283\pi$
$18$	−11.1465	−2.62725
$19$	−5.94052	−1.36285	−0.681424	−	0.731889i	$-0.738639\pi$
$19$	−5.94052	−1.36285	−0.681424	+	0.731889i	$0.738639\pi$
$20$	−0.953749	−0.213265
$21$	−3.27990	−0.715733
$22$	1.29453	0.275995
$23$	−0.745508	−0.155449	−0.0777246	−	0.996975i	$-0.524765\pi$
$23$	−0.745508	−0.155449	−0.0777246	+	0.996975i	$0.524765\pi$
$24$	10.2520	2.09268
$25$	3.65525	0.731050
$26$	1.58611	0.311062
$27$	19.1170	3.67907
$28$	0.312055	0.0589728
$29$	−2.48163	−0.460826	−0.230413	−	0.973093i	$-0.574008\pi$
$29$	−2.48163	−0.460826	−0.230413	+	0.973093i	$0.574008\pi$
$30$	−12.9771	−2.36928
$31$	−7.01525	−1.25998	−0.629988	−	0.776605i	$-0.716940\pi$
$31$	−7.01525	−1.25998	−0.629988	+	0.776605i	$0.716940\pi$
$32$	−1.81473	−0.320802
$33$	−3.40741	−0.593153
$34$	−5.99237	−1.02768
$35$	−2.83189	−0.478677
$36$	−2.79138	−0.465230
$37$	8.66581	1.42465	0.712325	−	0.701849i	$-0.247642\pi$
$37$	8.66581	1.42465	0.712325	+	0.701849i	$0.247642\pi$
$38$	7.69019	1.24751
$39$	−4.17488	−0.668516
$40$	8.85164	1.39957
$41$	4.87491	0.761333	0.380666	−	0.924712i	$-0.375695\pi$
$41$	4.87491	0.761333	0.380666	+	0.924712i	$0.375695\pi$
$42$	4.24594	0.655163
$43$	−7.47335	−1.13968	−0.569838	−	0.821757i	$-0.692994\pi$
$43$	−7.47335	−1.13968	−0.569838	+	0.821757i	$0.692994\pi$
$44$	0.324186	0.0488729
$45$	25.3317	3.77623
$46$	0.965085	0.142294
$47$	5.10409	0.744508	0.372254	−	0.928131i	$-0.378585\pi$
$47$	5.10409	0.744508	0.372254	+	0.928131i	$0.378585\pi$
$48$	−11.0623	−1.59670
$49$	−6.07344	−0.867634
$50$	−4.73184	−0.669183
$51$	15.7728	2.20864
$52$	0.397205	0.0550824
$53$	−12.5071	−1.71799	−0.858994	−	0.511986i	$-0.828910\pi$
$53$	−12.5071	−1.71799	−0.858994	+	0.511986i	$0.828910\pi$
$54$	−24.7476	−3.36772
$55$	−2.94198	−0.396697
$56$	−2.89615	−0.387014
$57$	−20.2418	−2.68109
$58$	3.21254	0.421828
$59$	−4.29739	−0.559473	−0.279736	−	0.960077i	$-0.590247\pi$
$59$	−4.29739	−0.559473	−0.279736	+	0.960077i	$0.590247\pi$
$60$	−3.24981	−0.419549
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	9.08147	1.15335
$63$	−8.28822	−1.04422
$64$	8.84229	1.10529
$65$	−3.60462	−0.447099
$66$	4.41100	0.542956
$67$	−6.70005	−0.818542	−0.409271	−	0.912413i	$-0.634217\pi$
$67$	−6.70005	−0.818542	−0.409271	+	0.912413i	$0.634217\pi$
$68$	−1.50065	−0.181981
$69$	−2.54025	−0.305810
$70$	3.66597	0.438168
$71$	−5.44678	−0.646414	−0.323207	−	0.946328i	$-0.604761\pi$
$71$	−5.44678	−0.646414	−0.323207	+	0.946328i	$0.604761\pi$
$72$	25.9065	3.05311
$73$	13.4494	1.57413	0.787064	−	0.616872i	$-0.211600\pi$
$73$	13.4494	1.57413	0.787064	+	0.616872i	$0.211600\pi$
$74$	−11.2182	−1.30409
$75$	12.4549	1.43817
$76$	1.92583	0.220908
$77$	0.962580	0.109696
$78$	5.40452	0.611942
$79$	−3.09980	−0.348754	−0.174377	−	0.984679i	$-0.555791\pi$
$79$	−3.09980	−0.348754	−0.174377	+	0.984679i	$0.555791\pi$
$80$	−9.55123	−1.06786
$81$	39.3081	4.36757
$82$	−6.31073	−0.696903
$83$	11.8714	1.30306	0.651528	−	0.758624i	$-0.274128\pi$
$83$	11.8714	1.30306	0.651528	+	0.758624i	$0.274128\pi$
$84$	1.06330	0.116015
$85$	13.6184	1.47712
$86$	9.67450	1.04323
$87$	−8.45591	−0.906569
$88$	−3.00873	−0.320732
$89$	13.7818	1.46087	0.730433	−	0.682984i	$-0.239318\pi$
$89$	13.7818	1.46087	0.730433	+	0.682984i	$0.239318\pi$
$90$	−32.7927	−3.45665
$91$	1.17939	0.123634
$92$	0.241683	0.0251972
$93$	−23.9038	−2.47871
$94$	−6.60741	−0.681503
$95$	−17.4769	−1.79309
$96$	−6.18352	−0.631103
$97$	16.5554	1.68095	0.840475	−	0.541850i	$-0.182276\pi$
$97$	16.5554	1.68095	0.840475	+	0.541850i	$0.182276\pi$
$98$	7.86226	0.794209
$99$	−8.61042	−0.865380
$100$	−1.18498	−0.118498
$101$	0.888072	0.0883665	0.0441832	−	0.999023i	$-0.485931\pi$
$101$	0.888072	0.0883665	0.0441832	+	0.999023i	$0.485931\pi$
$102$	−20.4185	−2.02173
$103$	−2.85528	−0.281339	−0.140670	−	0.990057i	$-0.544926\pi$
$103$	−2.85528	−0.281339	−0.140670	+	0.990057i	$0.544926\pi$
$104$	−3.68641	−0.361483
$105$	−9.64941	−0.941686
$106$	16.1909	1.57260
$107$	−3.10491	−0.300163	−0.150081	−	0.988674i	$-0.547954\pi$
$107$	−3.10491	−0.300163	−0.150081	+	0.988674i	$0.547954\pi$
$108$	−6.19746	−0.596351
$109$	−0.543978	−0.0521037	−0.0260518	−	0.999661i	$-0.508293\pi$
$109$	−0.543978	−0.0521037	−0.0260518	+	0.999661i	$0.508293\pi$
$110$	3.80849	0.363125
$111$	29.5280	2.80267
$112$	3.12505	0.295289
$113$	−8.55519	−0.804804	−0.402402	−	0.915463i	$-0.631825\pi$
$113$	−8.55519	−0.804804	−0.402402	+	0.915463i	$0.631825\pi$
$114$	26.2036	2.45419
$115$	−2.19327	−0.204524
$116$	0.804508	0.0746967
$117$	−10.5498	−0.975331
$118$	5.56311	0.512126
$119$	−4.45577	−0.408460
$120$	30.1611	2.75332
$121$	1.00000	0.0909091
$122$	−1.29453	−0.117201
$123$	16.6108	1.49775
$124$	2.27425	0.204233
$125$	−3.95623	−0.353856
$126$	10.7294	0.955848
$127$	8.12429	0.720914	0.360457	−	0.932776i	$-0.382621\pi$
$127$	8.12429	0.720914	0.360457	+	0.932776i	$0.382621\pi$
$128$	−7.81717	−0.690947
$129$	−25.4648	−2.24205
$130$	4.66630	0.409262
$131$	−20.2316	−1.76765	−0.883823	−	0.467821i	$-0.845039\pi$
$131$	−20.2316	−1.76765	−0.883823	+	0.467821i	$0.845039\pi$
$132$	1.10463	0.0961460
$133$	5.71823	0.495833
$134$	8.67344	0.749271
$135$	56.2418	4.84053
$136$	13.9274	1.19426
$137$	−5.35686	−0.457668	−0.228834	−	0.973465i	$-0.573491\pi$
$137$	−5.35686	−0.457668	−0.228834	+	0.973465i	$0.573491\pi$
$138$	3.28844	0.279930
$139$	−7.84674	−0.665552	−0.332776	−	0.943006i	$-0.607985\pi$
$139$	−7.84674	−0.665552	−0.332776	+	0.943006i	$0.607985\pi$
$140$	0.918060	0.0775902
$141$	17.3917	1.46465
$142$	7.05103	0.591709
$143$	1.22524	0.102460
$144$	−27.9540	−2.32950
$145$	−7.30089	−0.606306
$146$	−17.4106	−1.44091
$147$	−20.6947	−1.70687
$148$	−2.80934	−0.230926
$149$	−21.4540	−1.75758	−0.878792	−	0.477205i	$-0.841650\pi$
$149$	−21.4540	−1.75758	−0.878792	+	0.477205i	$0.841650\pi$
$150$	−16.1233	−1.31646
$151$	1.98491	0.161530	0.0807649	−	0.996733i	$-0.474264\pi$
$151$	1.98491	0.161530	0.0807649	+	0.996733i	$0.474264\pi$
$152$	−17.8734	−1.44973
$153$	39.8575	3.22229
$154$	−1.24609	−0.100413
$155$	−20.6387	−1.65774
$156$	1.35344	0.108362
$157$	−6.43117	−0.513263	−0.256631	−	0.966509i	$-0.582613\pi$
$157$	−6.43117	−0.513263	−0.256631	+	0.966509i	$0.582613\pi$
$158$	4.01279	0.319240
$159$	−42.6169	−3.37974
$160$	−5.33889	−0.422077
$161$	0.717612	0.0565557
$162$	−50.8856	−3.99795
$163$	5.86870	0.459672	0.229836	−	0.973229i	$-0.426181\pi$
$163$	5.86870	0.459672	0.229836	+	0.973229i	$0.426181\pi$
$164$	−1.58038	−0.123407
$165$	−10.0245	−0.780408
$166$	−15.3679	−1.19278
$167$	7.77784	0.601867	0.300934	−	0.953645i	$-0.402702\pi$
$167$	7.77784	0.601867	0.300934	+	0.953645i	$0.402702\pi$
$168$	−9.86835	−0.761360
$169$	−11.4988	−0.884523
$170$	−17.6294	−1.35212
$171$	−51.1504	−3.91157
$172$	2.42276	0.184733
$173$	1.52361	0.115838	0.0579189	−	0.998321i	$-0.481554\pi$
$173$	1.52361	0.115838	0.0579189	+	0.998321i	$0.481554\pi$
$174$	10.9464	0.829848
$175$	−3.51847	−0.265971
$176$	3.24653	0.244717
$177$	−14.6430	−1.10063
$178$	−17.8410	−1.33724
$179$	−14.1271	−1.05591	−0.527953	−	0.849274i	$-0.677040\pi$
$179$	−14.1271	−1.05591	−0.527953	+	0.849274i	$0.677040\pi$
$180$	−8.21218	−0.612100
$181$	−6.80507	−0.505816	−0.252908	−	0.967490i	$-0.581387\pi$
$181$	−6.80507	−0.505816	−0.252908	+	0.967490i	$0.581387\pi$
$182$	−1.52676	−0.113171
$183$	3.40741	0.251883
$184$	−2.24304	−0.165359
$185$	25.4947	1.87440
$186$	30.9443	2.26894
$187$	−4.62899	−0.338505
$188$	−1.65468	−0.120680
$189$	−18.4016	−1.33852
$190$	22.6244	1.64135
$191$	18.7503	1.35673	0.678364	−	0.734726i	$-0.262689\pi$
$191$	18.7503	1.35673	0.678364	+	0.734726i	$0.262689\pi$
$192$	30.1293	2.17439
$193$	15.7510	1.13378	0.566891	−	0.823793i	$-0.308146\pi$
$193$	15.7510	1.13378	0.566891	+	0.823793i	$0.308146\pi$
$194$	−21.4316	−1.53870
$195$	−12.2824	−0.879563
$196$	1.96892	0.140637
$197$	−19.6194	−1.39782	−0.698910	−	0.715209i	$-0.746331\pi$
$197$	−19.6194	−1.39782	−0.698910	+	0.715209i	$0.746331\pi$
$198$	11.1465	0.792145
$199$	3.05553	0.216601	0.108300	−	0.994118i	$-0.465459\pi$
$199$	3.05553	0.216601	0.108300	+	0.994118i	$0.465459\pi$
$200$	10.9977	0.777653
$201$	−22.8298	−1.61029
$202$	−1.14964	−0.0808883
$203$	2.38876	0.167658
$204$	−5.11334	−0.358005
$205$	14.3419	1.00168
$206$	3.69625	0.257530
$207$	−6.41914	−0.446161
$208$	3.97777	0.275809
$209$	5.94052	0.410914
$210$	12.4915	0.861993
$211$	−13.2527	−0.912353	−0.456177	−	0.889889i	$-0.650781\pi$
$211$	−13.2527	−0.912353	−0.456177	+	0.889889i	$0.650781\pi$
$212$	4.05464	0.278474
$213$	−18.5594	−1.27167
$214$	4.01940	0.274761
$215$	−21.9865	−1.49946
$216$	57.5180	3.91360
$217$	6.75274	0.458406
$218$	0.704197	0.0476943
$219$	45.8274	3.09673
$220$	0.953749	0.0643017
$221$	−5.67161	−0.381514
$222$	−38.2249	−2.56549
$223$	−25.8228	−1.72922	−0.864612	−	0.502440i	$-0.832436\pi$
$223$	−25.8228	−1.72922	−0.864612	+	0.502440i	$0.832436\pi$
$224$	1.74682	0.116714
$225$	31.4732	2.09822
$226$	11.0750	0.736696
$227$	20.5042	1.36091	0.680454	−	0.732790i	$-0.261782\pi$
$227$	20.5042	1.36091	0.680454	+	0.732790i	$0.261782\pi$
$228$	6.56210	0.434586
$229$	−14.1285	−0.933639	−0.466819	−	0.884353i	$-0.654600\pi$
$229$	−14.1285	−0.933639	−0.466819	+	0.884353i	$0.654600\pi$
$230$	2.83926	0.187215
$231$	3.27990	0.215802
$232$	−7.46655	−0.490203
$233$	−23.5630	−1.54366	−0.771832	−	0.635826i	$-0.780659\pi$
$233$	−23.5630	−1.54366	−0.771832	+	0.635826i	$0.780659\pi$
$234$	13.6571	0.892791
$235$	15.0161	0.979545
$236$	1.39315	0.0906866
$237$	−10.5623	−0.686093
$238$	5.76814	0.373893
$239$	0.840460	0.0543649	0.0271824	−	0.999630i	$-0.491346\pi$
$239$	0.840460	0.0543649	0.0271824	+	0.999630i	$0.491346\pi$
$240$	−32.5449	−2.10077
$241$	−0.326981	−0.0210627	−0.0105313	−	0.999945i	$-0.503352\pi$
$241$	−0.326981	−0.0210627	−0.0105313	+	0.999945i	$0.503352\pi$
$242$	−1.29453	−0.0832157
$243$	76.5878	4.91311
$244$	−0.324186	−0.0207539
$245$	−17.8679	−1.14154
$246$	−21.5032	−1.37099
$247$	7.27855	0.463123
$248$	−21.1070	−1.34030
$249$	40.4507	2.56346
$250$	5.12147	0.323910
$251$	−6.54627	−0.413197	−0.206598	−	0.978426i	$-0.566239\pi$
$251$	−6.54627	−0.413197	−0.206598	+	0.978426i	$0.566239\pi$
$252$	2.68693	0.169260
$253$	0.745508	0.0468697
$254$	−10.5172	−0.659905
$255$	46.4034	2.90589
$256$	−7.56499	−0.472812
$257$	14.6146	0.911631	0.455816	−	0.890074i	$-0.349348\pi$
$257$	14.6146	0.911631	0.455816	+	0.890074i	$0.349348\pi$
$258$	32.9650	2.05231
$259$	−8.34154	−0.518318
$260$	1.16857	0.0724716
$261$	−21.3678	−1.32264
$262$	26.1905	1.61805
$263$	7.05354	0.434940	0.217470	−	0.976067i	$-0.430220\pi$
$263$	7.05354	0.434940	0.217470	+	0.976067i	$0.430220\pi$
$264$	−10.2520	−0.630966
$265$	−36.7958	−2.26035
$266$	−7.40243	−0.453872
$267$	46.9601	2.87391
$268$	2.17206	0.132680
$269$	−5.31730	−0.324201	−0.162101	−	0.986774i	$-0.551827\pi$
$269$	−5.31730	−0.324201	−0.162101	+	0.986774i	$0.551827\pi$
$270$	−72.8069	−4.43089
$271$	29.6220	1.79941	0.899704	−	0.436501i	$-0.143782\pi$
$271$	29.6220	1.79941	0.899704	+	0.436501i	$0.143782\pi$
$272$	−15.0282	−0.911216
$273$	4.01866	0.243220
$274$	6.93463	0.418937
$275$	−3.65525	−0.220420
$276$	0.823514	0.0495697
$277$	−3.25940	−0.195838	−0.0979192	−	0.995194i	$-0.531219\pi$
$277$	−3.25940	−0.195838	−0.0979192	+	0.995194i	$0.531219\pi$
$278$	10.1579	0.609228
$279$	−60.4043	−3.61631
$280$	−8.52041	−0.509192
$281$	8.69897	0.518937	0.259468	−	0.965752i	$-0.416453\pi$
$281$	8.69897	0.518937	0.259468	+	0.965752i	$0.416453\pi$
$282$	−22.5141	−1.34070
$283$	24.9271	1.48176	0.740881	−	0.671637i	$-0.234408\pi$
$283$	24.9271	1.48176	0.740881	+	0.671637i	$0.234408\pi$
$284$	1.76577	0.104779
$285$	−59.5509	−3.52749
$286$	−1.58611	−0.0937886
$287$	−4.69249	−0.276989
$288$	−15.6256	−0.920746
$289$	4.42753	0.260443
$290$	9.45124	0.554996
$291$	56.4111	3.30688
$292$	−4.36009	−0.255155
$293$	−23.5261	−1.37441	−0.687204	−	0.726464i	$-0.741162\pi$
$293$	−23.5261	−1.37441	−0.687204	+	0.726464i	$0.741162\pi$
$294$	26.7899	1.56242
$295$	−12.6428	−0.736095
$296$	26.0731	1.51547
$297$	−19.1170	−1.10928
$298$	27.7729	1.60884
$299$	0.913425	0.0528247
$300$	−4.03771	−0.233117
$301$	7.19370	0.414638
$302$	−2.56953	−0.147860
$303$	3.02602	0.173841
$304$	19.2861	1.10613
$305$	2.94198	0.168457
$306$	−51.5969	−2.94960
$307$	11.8721	0.677576	0.338788	−	0.940863i	$-0.389983\pi$
$307$	11.8721	0.677576	0.338788	+	0.940863i	$0.389983\pi$
$308$	−0.312055	−0.0177810
$309$	−9.72910	−0.553469
$310$	26.7175	1.51745
$311$	−4.11507	−0.233344	−0.116672	−	0.993170i	$-0.537223\pi$
$311$	−4.11507	−0.233344	−0.116672	+	0.993170i	$0.537223\pi$
$312$	−12.5611	−0.711133
$313$	−6.63578	−0.375077	−0.187538	−	0.982257i	$-0.560051\pi$
$313$	−6.63578	−0.375077	−0.187538	+	0.982257i	$0.560051\pi$
$314$	8.32535	0.469827
$315$	−24.3838	−1.37387
$316$	1.00491	0.0565306
$317$	16.6483	0.935061	0.467530	−	0.883977i	$-0.345144\pi$
$317$	16.6483	0.935061	0.467530	+	0.883977i	$0.345144\pi$
$318$	55.1690	3.09372
$319$	2.48163	0.138944
$320$	26.0138	1.45422
$321$	−10.5797	−0.590500
$322$	−0.928971	−0.0517695
$323$	−27.4986	−1.53006
$324$	−12.7431	−0.707953
$325$	−4.47855	−0.248425
$326$	−7.59722	−0.420771
$327$	−1.85356	−0.102502
$328$	14.6673	0.809866
$329$	−4.91310	−0.270868
$330$	12.9771	0.714364
$331$	−3.64936	−0.200587	−0.100293	−	0.994958i	$-0.531978\pi$
$331$	−3.64936	−0.200587	−0.100293	+	0.994958i	$0.531978\pi$
$332$	−3.84855	−0.211216
$333$	74.6163	4.08895
$334$	−10.0687	−0.550933
$335$	−19.7114	−1.07695
$336$	10.6483	0.580913
$337$	28.4702	1.55087	0.775436	−	0.631427i	$-0.217530\pi$
$337$	28.4702	1.55087	0.775436	+	0.631427i	$0.217530\pi$
$338$	14.8856	0.809668
$339$	−29.1510	−1.58327
$340$	−4.41489	−0.239431
$341$	7.01525	0.379897
$342$	66.2158	3.58054
$343$	12.5842	0.679485
$344$	−22.4853	−1.21233
$345$	−7.47337	−0.402353
$346$	−1.97236	−0.106035
$347$	5.92554	0.318100	0.159050	−	0.987271i	$-0.449157\pi$
$347$	5.92554	0.318100	0.159050	+	0.987271i	$0.449157\pi$
$348$	2.74129	0.146948
$349$	−2.60651	−0.139523	−0.0697616	−	0.997564i	$-0.522224\pi$
$349$	−2.60651	−0.139523	−0.0697616	+	0.997564i	$0.522224\pi$
$350$	4.55477	0.243463
$351$	−23.4229	−1.25022
$352$	1.81473	0.0967253
$353$	9.84606	0.524053	0.262026	−	0.965061i	$-0.415609\pi$
$353$	9.84606	0.524053	0.262026	+	0.965061i	$0.415609\pi$
$354$	18.9558	1.00749
$355$	−16.0243	−0.850482
$356$	−4.46786	−0.236796
$357$	−15.1826	−0.803550
$358$	18.2879	0.966547
$359$	25.4699	1.34425	0.672125	−	0.740438i	$-0.265382\pi$
$359$	25.4699	1.34425	0.672125	+	0.740438i	$0.265382\pi$
$360$	76.2163	4.01695
$361$	16.2898	0.857356
$362$	8.80938	0.463011
$363$	3.40741	0.178842
$364$	−0.382341	−0.0200401
$365$	39.5677	2.07107
$366$	−4.41100	−0.230567
$367$	13.5461	0.707102	0.353551	−	0.935415i	$-0.384974\pi$
$367$	13.5461	0.707102	0.353551	+	0.935415i	$0.384974\pi$
$368$	2.42032	0.126168
$369$	41.9750	2.18513
$370$	−33.0037	−1.71578
$371$	12.0391	0.625040
$372$	7.74928	0.401782
$373$	−37.1332	−1.92269	−0.961343	−	0.275354i	$-0.911205\pi$
$373$	−37.1332	−1.92269	−0.961343	+	0.275354i	$0.911205\pi$
$374$	5.99237	0.309858
$375$	−13.4805	−0.696130
$376$	15.3569	0.791969
$377$	3.04058	0.156598
$378$	23.8215	1.22525
$379$	21.3790	1.09817	0.549083	−	0.835768i	$-0.314977\pi$
$379$	21.3790	1.09817	0.549083	+	0.835768i	$0.314977\pi$
$380$	5.66576	0.290648
$381$	27.6828	1.41823
$382$	−24.2729	−1.24191
$383$	−20.5316	−1.04912	−0.524558	−	0.851375i	$-0.675770\pi$
$383$	−20.5316	−1.04912	−0.524558	+	0.851375i	$0.675770\pi$
$384$	−26.6363	−1.35928
$385$	2.83189	0.144327
$386$	−20.3902	−1.03783
$387$	−64.3487	−3.27103
$388$	−5.36704	−0.272470
$389$	−2.54805	−0.129191	−0.0645957	−	0.997912i	$-0.520576\pi$
$389$	−2.54805	−0.129191	−0.0645957	+	0.997912i	$0.520576\pi$
$390$	15.9000	0.805128
$391$	−3.45095	−0.174522
$392$	−18.2734	−0.922944
$393$	−68.9374	−3.47743
$394$	25.3979	1.27953
$395$	−9.11954	−0.458854
$396$	2.79138	0.140272
$397$	−9.93497	−0.498622	−0.249311	−	0.968424i	$-0.580204\pi$
$397$	−9.93497	−0.498622	−0.249311	+	0.968424i	$0.580204\pi$
$398$	−3.95549	−0.198271
$399$	19.4843	0.975436
$400$	−11.8669	−0.593344
$401$	−10.3974	−0.519223	−0.259612	−	0.965713i	$-0.583595\pi$
$401$	−10.3974	−0.519223	−0.259612	+	0.965713i	$0.583595\pi$
$402$	29.5539	1.47402
$403$	8.59535	0.428165
$404$	−0.287901	−0.0143236
$405$	115.644	5.74638
$406$	−3.09233	−0.153470
$407$	−8.66581	−0.429548
$408$	47.4563	2.34944
$409$	3.14695	0.155607	0.0778033	−	0.996969i	$-0.475209\pi$
$409$	3.14695	0.155607	0.0778033	+	0.996969i	$0.475209\pi$
$410$	−18.5660	−0.916911
$411$	−18.2530	−0.900355
$412$	0.925642	0.0456031
$413$	4.13658	0.203548
$414$	8.30979	0.408404
$415$	34.9255	1.71442
$416$	2.22347	0.109015
$417$	−26.7370	−1.30932
$418$	−7.69019	−0.376140
$419$	31.9845	1.56254	0.781272	−	0.624190i	$-0.214571\pi$
$419$	31.9845	1.56254	0.781272	+	0.624190i	$0.214571\pi$
$420$	3.12820	0.152641
$421$	17.1307	0.834898	0.417449	−	0.908700i	$-0.362924\pi$
$421$	17.1307	0.834898	0.417449	+	0.908700i	$0.362924\pi$
$422$	17.1560	0.835143
$423$	43.9484	2.13684
$424$	−37.6307	−1.82751
$425$	16.9201	0.820745
$426$	24.0257	1.16405
$427$	−0.962580	−0.0465825
$428$	1.00657	0.0486543
$429$	4.17488	0.201565
$430$	28.4622	1.37257
$431$	−34.2444	−1.64949	−0.824747	−	0.565501i	$-0.808683\pi$
$431$	−34.2444	−1.64949	−0.824747	+	0.565501i	$0.808683\pi$
$432$	−62.0639	−2.98605
$433$	−0.831844	−0.0399759	−0.0199879	−	0.999800i	$-0.506363\pi$
$433$	−0.831844	−0.0399759	−0.0199879	+	0.999800i	$0.506363\pi$
$434$	−8.74164	−0.419612
$435$	−24.8771	−1.19277
$436$	0.176350	0.00844564
$437$	4.42871	0.211854
$438$	−59.3251	−2.83466
$439$	23.0292	1.09913	0.549563	−	0.835452i	$-0.314794\pi$
$439$	23.0292	1.09913	0.549563	+	0.835452i	$0.314794\pi$
$440$	−8.85164	−0.421985
$441$	−52.2949	−2.49023
$442$	7.34208	0.349227
$443$	−4.09693	−0.194651	−0.0973255	−	0.995253i	$-0.531029\pi$
$443$	−4.09693	−0.194651	−0.0973255	+	0.995253i	$0.531029\pi$
$444$	−9.57255	−0.454293
$445$	40.5457	1.92205
$446$	33.4285	1.58288
$447$	−73.1027	−3.45764
$448$	−8.51141	−0.402126
$449$	38.8738	1.83457	0.917285	−	0.398231i	$-0.130376\pi$
$449$	38.8738	1.83457	0.917285	+	0.398231i	$0.130376\pi$
$450$	−40.7431	−1.92065
$451$	−4.87491	−0.229550
$452$	2.77347	0.130453
$453$	6.76340	0.317772
$454$	−26.5433	−1.24574
$455$	3.46974	0.162664
$456$	−60.9021	−2.85200
$457$	28.7219	1.34355	0.671777	−	0.740753i	$-0.265531\pi$
$457$	28.7219	1.34355	0.671777	+	0.740753i	$0.265531\pi$
$458$	18.2898	0.854628
$459$	88.4924	4.13047
$460$	0.711028	0.0331518
$461$	36.1721	1.68470	0.842351	−	0.538929i	$-0.181171\pi$
$461$	36.1721	1.68470	0.842351	+	0.538929i	$0.181171\pi$
$462$	−4.24594	−0.197539
$463$	−19.3506	−0.899298	−0.449649	−	0.893205i	$-0.648451\pi$
$463$	−19.3506	−0.899298	−0.449649	+	0.893205i	$0.648451\pi$
$464$	8.05668	0.374022
$465$	−70.3245	−3.26122
$466$	30.5031	1.41303
$467$	28.6014	1.32352	0.661758	−	0.749718i	$-0.269811\pi$
$467$	28.6014	1.32352	0.661758	+	0.749718i	$0.269811\pi$
$468$	3.42010	0.158094
$469$	6.44934	0.297803
$470$	−19.4389	−0.896649
$471$	−21.9136	−1.00973
$472$	−12.9297	−0.595138
$473$	7.47335	0.343625
$474$	13.6732	0.628031
$475$	−21.7141	−0.996310
$476$	1.44450	0.0662085
$477$	−107.692	−4.93087
$478$	−1.08800	−0.0497641
$479$	−5.94666	−0.271710	−0.135855	−	0.990729i	$-0.543378\pi$
$479$	−5.94666	−0.271710	−0.135855	+	0.990729i	$0.543378\pi$
$480$	−18.1918	−0.830338
$481$	−10.6177	−0.484125
$482$	0.423287	0.0192802
$483$	2.44519	0.111260
$484$	−0.324186	−0.0147357
$485$	48.7058	2.21162
$486$	−99.1454	−4.49733
$487$	−15.9869	−0.724436	−0.362218	−	0.932093i	$-0.617980\pi$
$487$	−15.9869	−0.724436	−0.362218	+	0.932093i	$0.617980\pi$
$488$	3.00873	0.136199
$489$	19.9970	0.904297
$490$	23.1306	1.04494
$491$	−14.3736	−0.648671	−0.324335	−	0.945942i	$-0.605141\pi$
$491$	−14.3736	−0.648671	−0.324335	+	0.945942i	$0.605141\pi$
$492$	−5.38499	−0.242774
$493$	−11.4874	−0.517367
$494$	−9.42231	−0.423930
$495$	−25.3317	−1.13858
$496$	22.7752	1.02264
$497$	5.24296	0.235179
$498$	−52.3648	−2.34652
$499$	−27.4728	−1.22985	−0.614925	−	0.788586i	$-0.710814\pi$
$499$	−27.4728	−1.22985	−0.614925	+	0.788586i	$0.710814\pi$
$500$	1.28256	0.0573577
$501$	26.5023	1.18403
$502$	8.47436	0.378229
$503$	12.4426	0.554787	0.277393	−	0.960756i	$-0.410530\pi$
$503$	12.4426	0.554787	0.277393	+	0.960756i	$0.410530\pi$
$504$	−24.9371	−1.11078
$505$	2.61269	0.116263
$506$	−0.965085	−0.0429033
$507$	−39.1811	−1.74009
$508$	−2.63378	−0.116855
$509$	8.43341	0.373804	0.186902	−	0.982379i	$-0.440155\pi$
$509$	8.43341	0.373804	0.186902	+	0.982379i	$0.440155\pi$
$510$	−60.0707	−2.65998
$511$	−12.9461	−0.572701
$512$	25.4275	1.12375
$513$	−113.565	−5.01401
$514$	−18.9190	−0.834482
$515$	−8.40018	−0.370156
$516$	8.25532	0.363420
$517$	−5.10409	−0.224478
$518$	10.7984	0.474454
$519$	5.19156	0.227884
$520$	−10.8454	−0.475600
$521$	32.9612	1.44406	0.722029	−	0.691863i	$-0.243210\pi$
$521$	32.9612	1.44406	0.722029	+	0.691863i	$0.243210\pi$
$522$	27.6614	1.21071
$523$	35.4687	1.55094	0.775469	−	0.631386i	$-0.217514\pi$
$523$	35.4687	1.55094	0.775469	+	0.631386i	$0.217514\pi$
$524$	6.55881	0.286523
$525$	−11.9889	−0.523236
$526$	−9.13104	−0.398132
$527$	−32.4735	−1.41457
$528$	11.0623	0.481423
$529$	−22.4442	−0.975836
$530$	47.6333	2.06906
$531$	−37.0024	−1.60577
$532$	−1.85377	−0.0803711
$533$	−5.97292	−0.258716
$534$	−60.7914	−2.63070
$535$	−9.13457	−0.394922
$536$	−20.1587	−0.870722
$537$	−48.1366	−2.07725
$538$	6.88341	0.296765
$539$	6.07344	0.261602
$540$	−18.2328	−0.784616
$541$	34.5067	1.48356	0.741779	−	0.670645i	$-0.233982\pi$
$541$	34.5067	1.48356	0.741779	+	0.670645i	$0.233982\pi$
$542$	−38.3466	−1.64713
$543$	−23.1876	−0.995076
$544$	−8.40035	−0.360162
$545$	−1.60037	−0.0685525
$546$	−5.20228	−0.222637
$547$	−21.0533	−0.900172	−0.450086	−	0.892985i	$-0.648607\pi$
$547$	−21.0533	−0.900172	−0.450086	+	0.892985i	$0.648607\pi$
$548$	1.73662	0.0741848
$549$	8.61042	0.367484
$550$	4.73184	0.201766
$551$	14.7421	0.628036
$552$	−7.64294	−0.325305
$553$	2.98380	0.126884
$554$	4.21940	0.179265
$555$	86.8707	3.68745
$556$	2.54380	0.107881
$557$	2.07457	0.0879023	0.0439512	−	0.999034i	$-0.486005\pi$
$557$	2.07457	0.0879023	0.0439512	+	0.999034i	$0.486005\pi$
$558$	78.1953	3.31027
$559$	9.15663	0.387284
$560$	9.19382	0.388510
$561$	−15.7728	−0.665930
$562$	−11.2611	−0.475021
$563$	5.85850	0.246906	0.123453	−	0.992350i	$-0.460603\pi$
$563$	5.85850	0.246906	0.123453	+	0.992350i	$0.460603\pi$
$564$	−5.63815	−0.237409
$565$	−25.1692	−1.05888
$566$	−32.2689	−1.35636
$567$	−37.8372	−1.58901
$568$	−16.3879	−0.687621
$569$	−0.644417	−0.0270154	−0.0135077	−	0.999909i	$-0.504300\pi$
$569$	−0.644417	−0.0270154	−0.0135077	+	0.999909i	$0.504300\pi$
$570$	77.0905	3.22897
$571$	−16.3535	−0.684374	−0.342187	−	0.939632i	$-0.611168\pi$
$571$	−16.3535	−0.684374	−0.342187	+	0.939632i	$0.611168\pi$
$572$	−0.397205	−0.0166080
$573$	63.8901	2.66905
$574$	6.07458	0.253548
$575$	−2.72502	−0.113641
$576$	76.1358	3.17233
$577$	−0.157078	−0.00653926	−0.00326963	−	0.999995i	$-0.501041\pi$
$577$	−0.157078	−0.00653926	−0.00326963	+	0.999995i	$0.501041\pi$
$578$	−5.73158	−0.238402
$579$	53.6701	2.23045
$580$	2.36685	0.0982780
$581$	−11.4272	−0.474080
$582$	−73.0260	−3.02703
$583$	12.5071	0.517993
$584$	40.4655	1.67448
$585$	−31.0373	−1.28324
$586$	30.4553	1.25810
$587$	−6.89197	−0.284462	−0.142231	−	0.989833i	$-0.545428\pi$
$587$	−6.89197	−0.284462	−0.142231	+	0.989833i	$0.545428\pi$
$588$	6.70893	0.276671
$589$	41.6742	1.71716
$590$	16.3666	0.673801
$591$	−66.8511	−2.74989
$592$	−28.1338	−1.15629
$593$	−19.9356	−0.818658	−0.409329	−	0.912387i	$-0.634237\pi$
$593$	−19.9356	−0.818658	−0.409329	+	0.912387i	$0.634237\pi$
$594$	24.7476	1.01541
$595$	−13.1088	−0.537408
$596$	6.95510	0.284892
$597$	10.4114	0.426112
$598$	−1.18246	−0.0483543
$599$	34.3967	1.40541	0.702706	−	0.711480i	$-0.251975\pi$
$599$	34.3967	1.40541	0.702706	+	0.711480i	$0.251975\pi$
$600$	37.4735	1.52985
$601$	8.45470	0.344874	0.172437	−	0.985021i	$-0.444836\pi$
$601$	8.45470	0.344874	0.172437	+	0.985021i	$0.444836\pi$
$602$	−9.31248	−0.379548
$603$	−57.6903	−2.34933
$604$	−0.643480	−0.0261828
$605$	2.94198	0.119609
$606$	−3.91729	−0.159129
$607$	−9.29798	−0.377393	−0.188697	−	0.982035i	$-0.560426\pi$
$607$	−9.29798	−0.377393	−0.188697	+	0.982035i	$0.560426\pi$
$608$	10.7804	0.437204
$609$	8.13949	0.329829
$610$	−3.80849	−0.154201
$611$	−6.25373	−0.252999
$612$	−12.9213	−0.522311
$613$	−38.5718	−1.55790	−0.778950	−	0.627086i	$-0.784247\pi$
$613$	−38.5718	−1.55790	−0.778950	+	0.627086i	$0.784247\pi$
$614$	−15.3688	−0.620234
$615$	48.8686	1.97057
$616$	2.89615	0.116689
$617$	−8.66174	−0.348709	−0.174354	−	0.984683i	$-0.555784\pi$
$617$	−8.66174	−0.348709	−0.174354	+	0.984683i	$0.555784\pi$
$618$	12.5946	0.506630
$619$	27.0814	1.08849	0.544247	−	0.838925i	$-0.316815\pi$
$619$	27.0814	1.08849	0.544247	+	0.838925i	$0.316815\pi$
$620$	6.69079	0.268708
$621$	−14.2519	−0.571908
$622$	5.32709	0.213597
$623$	−13.2661	−0.531494
$624$	13.5539	0.542590
$625$	−29.9154	−1.19662
$626$	8.59023	0.343335
$627$	20.2418	0.808378
$628$	2.08489	0.0831963
$629$	40.1139	1.59945
$630$	31.5656	1.25760
$631$	0.783379	0.0311858	0.0155929	−	0.999878i	$-0.495036\pi$
$631$	0.783379	0.0311858	0.0155929	+	0.999878i	$0.495036\pi$
$632$	−9.32646	−0.370987
$633$	−45.1573	−1.79484
$634$	−21.5517	−0.855929
$635$	23.9015	0.948502
$636$	13.8158	0.547832
$637$	7.44141	0.294839
$638$	−3.21254	−0.127186
$639$	−46.8991	−1.85530
$640$	−22.9980	−0.909074
$641$	−5.68122	−0.224395	−0.112197	−	0.993686i	$-0.535789\pi$
$641$	−5.68122	−0.224395	−0.112197	+	0.993686i	$0.535789\pi$
$642$	13.6957	0.540528
$643$	−3.46757	−0.136747	−0.0683737	−	0.997660i	$-0.521781\pi$
$643$	−3.46757	−0.136747	−0.0683737	+	0.997660i	$0.521781\pi$
$644$	−0.232640	−0.00916729
$645$	−74.9168	−2.94985
$646$	35.5978	1.40058
$647$	−27.6703	−1.08783	−0.543916	−	0.839139i	$-0.683059\pi$
$647$	−27.6703	−1.08783	−0.543916	+	0.839139i	$0.683059\pi$
$648$	118.268	4.64599
$649$	4.29739	0.168687
$650$	5.79762	0.227401
$651$	23.0093	0.901807
$652$	−1.90255	−0.0745096
$653$	9.74591	0.381387	0.190693	−	0.981650i	$-0.438926\pi$
$653$	9.74591	0.381387	0.190693	+	0.981650i	$0.438926\pi$
$654$	2.39949	0.0938274
$655$	−59.5211	−2.32568
$656$	−15.8265	−0.617923
$657$	115.805	4.51797
$658$	6.36016	0.247945
$659$	−6.98292	−0.272016	−0.136008	−	0.990708i	$-0.543427\pi$
$659$	−6.98292	−0.272016	−0.136008	+	0.990708i	$0.543427\pi$
$660$	3.24981	0.126499
$661$	16.5002	0.641783	0.320891	−	0.947116i	$-0.396018\pi$
$661$	16.5002	0.641783	0.320891	+	0.947116i	$0.396018\pi$
$662$	4.72421	0.183612
$663$	−19.3255	−0.750540
$664$	35.7179	1.38612
$665$	16.8229	0.652364
$666$	−96.5933	−3.74291
$667$	1.85007	0.0716351
$668$	−2.52147	−0.0975585
$669$	−87.9889	−3.40185
$670$	25.5171	0.985811
$671$	−1.00000	−0.0386046
$672$	5.95213	0.229608
$673$	37.4769	1.44463	0.722314	−	0.691566i	$-0.243079\pi$
$673$	37.4769	1.44463	0.722314	+	0.691566i	$0.243079\pi$
$674$	−36.8556	−1.41963
$675$	69.8774	2.68958
$676$	3.72775	0.143375
$677$	30.4331	1.16964	0.584820	−	0.811163i	$-0.301165\pi$
$677$	30.4331	1.16964	0.584820	+	0.811163i	$0.301165\pi$
$678$	37.7369	1.44928
$679$	−15.9359	−0.611565
$680$	40.9741	1.57129
$681$	69.8660	2.67727
$682$	−9.08147	−0.347747
$683$	36.6336	1.40174	0.700872	−	0.713287i	$-0.252794\pi$
$683$	36.6336	1.40174	0.700872	+	0.713287i	$0.252794\pi$
$684$	16.5822	0.634038
$685$	−15.7598	−0.602151
$686$	−16.2907	−0.621982
$687$	−48.1416	−1.83672
$688$	24.2625	0.924998
$689$	15.3242	0.583806
$690$	9.67452	0.368303
$691$	22.3610	0.850653	0.425327	−	0.905040i	$-0.360159\pi$
$691$	22.3610	0.850653	0.425327	+	0.905040i	$0.360159\pi$
$692$	−0.493933	−0.0187765
$693$	8.28822	0.314844
$694$	−7.67081	−0.291180
$695$	−23.0850	−0.875663
$696$	−25.4416	−0.964361
$697$	22.5659	0.854744
$698$	3.37421	0.127716
$699$	−80.2888	−3.03680
$700$	1.14064	0.0431121
$701$	−7.55175	−0.285226	−0.142613	−	0.989779i	$-0.545550\pi$
$701$	−7.55175	−0.285226	−0.142613	+	0.989779i	$0.545550\pi$
$702$	30.3217	1.14442
$703$	−51.4794	−1.94158
$704$	−8.84229	−0.333256
$705$	51.1661	1.92703
$706$	−12.7460	−0.479704
$707$	−0.854841	−0.0321496
$708$	4.74704	0.178405
$709$	43.6759	1.64028	0.820141	−	0.572161i	$-0.193895\pi$
$709$	43.6759	1.64028	0.820141	+	0.572161i	$0.193895\pi$
$710$	20.7440	0.778508
$711$	−26.6906	−1.00097
$712$	41.4657	1.55399
$713$	5.22993	0.195862
$714$	19.6544	0.735547
$715$	3.60462	0.134805
$716$	4.57979	0.171155
$717$	2.86379	0.106950
$718$	−32.9716	−1.23049
$719$	7.45445	0.278004	0.139002	−	0.990292i	$-0.455611\pi$
$719$	7.45445	0.278004	0.139002	+	0.990292i	$0.455611\pi$
$720$	−82.2402	−3.06491
$721$	2.74843	0.102357
$722$	−21.0876	−0.784800
$723$	−1.11416	−0.0414359
$724$	2.20611	0.0819893
$725$	−9.07096	−0.336887
$726$	−4.41100	−0.163708
$727$	−41.2110	−1.52843	−0.764215	−	0.644961i	$-0.776873\pi$
$727$	−41.2110	−1.52843	−0.764215	+	0.644961i	$0.776873\pi$
$728$	3.54847	0.131515
$729$	143.041	5.29783
$730$	−51.2217	−1.89580
$731$	−34.5941	−1.27951
$732$	−1.10463	−0.0408284
$733$	5.91454	0.218458	0.109229	−	0.994017i	$-0.465162\pi$
$733$	5.91454	0.218458	0.109229	+	0.994017i	$0.465162\pi$
$734$	−17.5359	−0.647262
$735$	−60.8833	−2.24572
$736$	1.35290	0.0498684
$737$	6.70005	0.246800
$738$	−54.3380	−2.00021
$739$	−50.8314	−1.86986	−0.934932	−	0.354826i	$-0.884540\pi$
$739$	−50.8314	−1.86986	−0.934932	+	0.354826i	$0.884540\pi$
$740$	−8.26501	−0.303828
$741$	24.8010	0.911087
$742$	−15.5850	−0.572145
$743$	−1.25274	−0.0459585	−0.0229793	−	0.999736i	$-0.507315\pi$
$743$	−1.25274	−0.0459585	−0.0229793	+	0.999736i	$0.507315\pi$
$744$	−71.9202	−2.63672
$745$	−63.1174	−2.31244
$746$	48.0702	1.75997
$747$	102.218	3.73996
$748$	1.50065	0.0548693
$749$	2.98872	0.109205
$750$	17.4509	0.637219
$751$	47.7300	1.74169	0.870846	−	0.491555i	$-0.163571\pi$
$751$	47.7300	1.74169	0.870846	+	0.491555i	$0.163571\pi$
$752$	−16.5706	−0.604267
$753$	−22.3058	−0.812869
$754$	−3.93613	−0.143345
$755$	5.83957	0.212524
$756$	5.96556	0.216965
$757$	45.7727	1.66364	0.831819	−	0.555047i	$-0.187300\pi$
$757$	45.7727	1.66364	0.831819	+	0.555047i	$0.187300\pi$
$758$	−27.6758	−1.00523
$759$	2.54025	0.0922053
$760$	−52.5833	−1.90740
$761$	19.6606	0.712698	0.356349	−	0.934353i	$-0.384022\pi$
$761$	19.6606	0.712698	0.356349	+	0.934353i	$0.384022\pi$
$762$	−35.8362	−1.29821
$763$	0.523623	0.0189564
$764$	−6.07860	−0.219916
$765$	117.260	4.23955
$766$	26.5788	0.960333
$767$	5.26532	0.190120
$768$	−25.7770	−0.930148
$769$	−5.37674	−0.193890	−0.0969451	−	0.995290i	$-0.530907\pi$
$769$	−5.37674	−0.193890	−0.0969451	+	0.995290i	$0.530907\pi$
$770$	−3.66597	−0.132113
$771$	49.7978	1.79342
$772$	−5.10625	−0.183778
$773$	10.1558	0.365277	0.182639	−	0.983180i	$-0.441536\pi$
$773$	10.1558	0.365277	0.182639	+	0.983180i	$0.441536\pi$
$774$	83.3015	2.99421
$775$	−25.6425	−0.921105
$776$	49.8109	1.78811
$777$	−28.4230	−1.01967
$778$	3.29854	0.118258
$779$	−28.9595	−1.03758
$780$	3.98179	0.142571
$781$	5.44678	0.194901
$782$	4.46737	0.159753
$783$	−47.4412	−1.69541
$784$	19.7176	0.704200
$785$	−18.9204	−0.675297
$786$	89.2417	3.18315
$787$	38.1398	1.35954	0.679768	−	0.733427i	$-0.262081\pi$
$787$	38.1398	1.35954	0.679768	+	0.733427i	$0.262081\pi$
$788$	6.36032	0.226577
$789$	24.0343	0.855644
$790$	11.8055	0.420022
$791$	8.23505	0.292805
$792$	−25.9065	−0.920547
$793$	−1.22524	−0.0435095
$794$	12.8611	0.456425
$795$	−125.378	−4.44670
$796$	−0.990561	−0.0351095
$797$	−38.8028	−1.37446	−0.687232	−	0.726438i	$-0.741174\pi$
$797$	−38.8028	−1.37446	−0.687232	+	0.726438i	$0.741174\pi$
$798$	−25.2231	−0.892888
$799$	23.6268	0.835855
$800$	−6.63328	−0.234522
$801$	118.667	4.19289
$802$	13.4598	0.475283
$803$	−13.4494	−0.474617
$804$	7.40111	0.261017
$805$	2.11120	0.0744100
$806$	−11.1270	−0.391930
$807$	−18.1182	−0.637791
$808$	2.67197	0.0939997
$809$	4.44997	0.156453	0.0782263	−	0.996936i	$-0.475074\pi$
$809$	4.44997	0.156453	0.0782263	+	0.996936i	$0.475074\pi$
$810$	−149.705	−5.26008
$811$	31.9572	1.12217	0.561084	−	0.827759i	$-0.310384\pi$
$811$	31.9572	1.12217	0.561084	+	0.827759i	$0.310384\pi$
$812$	−0.774404	−0.0271762
$813$	100.934	3.53992
$814$	11.2182	0.393197
$815$	17.2656	0.604787
$816$	−51.2070	−1.79260
$817$	44.3956	1.55321
$818$	−4.07383	−0.142438
$819$	10.1550	0.354846
$820$	−4.64944	−0.162365
$821$	14.8173	0.517126	0.258563	−	0.965994i	$-0.416751\pi$
$821$	14.8173	0.517126	0.258563	+	0.965994i	$0.416751\pi$
$822$	23.6291	0.824160
$823$	−7.72139	−0.269151	−0.134575	−	0.990903i	$-0.542967\pi$
$823$	−7.72139	−0.269151	−0.134575	+	0.990903i	$0.542967\pi$
$824$	−8.59078	−0.299274
$825$	−12.4549	−0.433625
$826$	−5.35494	−0.186322
$827$	−27.3551	−0.951230	−0.475615	−	0.879654i	$-0.657774\pi$
$827$	−27.3551	−0.951230	−0.475615	+	0.879654i	$0.657774\pi$
$828$	2.08100	0.0723196
$829$	−27.3766	−0.950829	−0.475415	−	0.879762i	$-0.657702\pi$
$829$	−27.3766	−0.950829	−0.475415	+	0.879762i	$0.657702\pi$
$830$	−45.2121	−1.56934
$831$	−11.1061	−0.385266
$832$	−10.8339	−0.375598
$833$	−28.1139	−0.974088
$834$	34.6120	1.19851
$835$	22.8823	0.791873
$836$	−1.92583	−0.0666063
$837$	−134.111	−4.63554
$838$	−41.4050	−1.43031
$839$	−36.1380	−1.24762	−0.623812	−	0.781575i	$-0.714417\pi$
$839$	−36.1380	−1.24762	−0.623812	+	0.781575i	$0.714417\pi$
$840$	−29.0325	−1.00172
$841$	−22.8415	−0.787639
$842$	−22.1762	−0.764243
$843$	29.6409	1.02089
$844$	4.29634	0.147886
$845$	−33.8292	−1.16376
$846$	−56.8926	−1.95601
$847$	−0.962580	−0.0330746
$848$	40.6048	1.39438
$849$	84.9367	2.91502
$850$	−21.9036	−0.751288
$851$	−6.46044	−0.221461
$852$	6.01670	0.206129
$853$	−13.5704	−0.464642	−0.232321	−	0.972639i	$-0.574632\pi$
$853$	−13.5704	−0.464642	−0.232321	+	0.972639i	$0.574632\pi$
$854$	1.24609	0.0426404
$855$	−150.483	−5.14643
$856$	−9.34184	−0.319297
$857$	6.06053	0.207024	0.103512	−	0.994628i	$-0.466992\pi$
$857$	6.06053	0.207024	0.103512	+	0.994628i	$0.466992\pi$
$858$	−5.40452	−0.184507
$859$	9.74217	0.332399	0.166199	−	0.986092i	$-0.446850\pi$
$859$	9.74217	0.332399	0.166199	+	0.986092i	$0.446850\pi$
$860$	7.12770	0.243053
$861$	−15.9892	−0.544911
$862$	44.3305	1.50990
$863$	18.4875	0.629324	0.314662	−	0.949204i	$-0.398109\pi$
$863$	18.4875	0.629324	0.314662	+	0.949204i	$0.398109\pi$
$864$	−34.6922	−1.18025
$865$	4.48243	0.152407
$866$	1.07685	0.0365928
$867$	15.0864	0.512360
$868$	−2.18914	−0.0743044
$869$	3.09980	0.105153
$870$	32.2042	1.09183
$871$	8.20916	0.278157
$872$	−1.63669	−0.0554252
$873$	142.549	4.82457
$874$	−5.73311	−0.193925
$875$	3.80819	0.128740
$876$	−14.8566	−0.501958
$877$	−19.7849	−0.668087	−0.334044	−	0.942558i	$-0.608413\pi$
$877$	−19.7849	−0.668087	−0.334044	+	0.942558i	$0.608413\pi$
$878$	−29.8121	−1.00611
$879$	−80.1629	−2.70383
$880$	9.55123	0.321972
$881$	−1.52612	−0.0514164	−0.0257082	−	0.999669i	$-0.508184\pi$
$881$	−1.52612	−0.0514164	−0.0257082	+	0.999669i	$0.508184\pi$
$882$	67.6974	2.27949
$883$	−25.3892	−0.854413	−0.427207	−	0.904154i	$-0.640502\pi$
$883$	−25.3892	−0.854413	−0.427207	+	0.904154i	$0.640502\pi$
$884$	1.83866	0.0618407
$885$	−43.0793	−1.44809
$886$	5.30361	0.178178
$887$	36.2066	1.21570	0.607849	−	0.794053i	$-0.292033\pi$
$887$	36.2066	1.21570	0.607849	+	0.794053i	$0.292033\pi$
$888$	88.8418	2.98133
$889$	−7.82028	−0.262284
$890$	−52.4878	−1.75939
$891$	−39.3081	−1.31687
$892$	8.37140	0.280295
$893$	−30.3210	−1.01465
$894$	94.6338	3.16503
$895$	−41.5615	−1.38925
$896$	7.52465	0.251381
$897$	3.11241	0.103920
$898$	−50.3235	−1.67932
$899$	17.4092	0.580630
$900$	−10.2032	−0.340106
$901$	−57.8954	−1.92878
$902$	6.31073	0.210124
$903$	24.5119	0.815704
$904$	−25.7403	−0.856109
$905$	−20.0204	−0.665500
$906$	−8.75544	−0.290880
$907$	−32.1998	−1.06918	−0.534589	−	0.845112i	$-0.679534\pi$
$907$	−32.1998	−1.06918	−0.534589	+	0.845112i	$0.679534\pi$
$908$	−6.64716	−0.220594
$909$	7.64668	0.253624
$910$	−4.49169	−0.148898
$911$	−42.9132	−1.42178	−0.710889	−	0.703305i	$-0.751707\pi$
$911$	−42.9132	−1.42178	−0.710889	+	0.703305i	$0.751707\pi$
$912$	65.7155	2.17606
$913$	−11.8714	−0.392886
$914$	−37.1815	−1.22985
$915$	10.0245	0.331401
$916$	4.58027	0.151336
$917$	19.4746	0.643107
$918$	−114.556	−3.78092
$919$	8.99125	0.296594	0.148297	−	0.988943i	$-0.452621\pi$
$919$	8.99125	0.296594	0.148297	+	0.988943i	$0.452621\pi$
$920$	−6.59897	−0.217562
$921$	40.4530	1.33297
$922$	−46.8259	−1.54213
$923$	6.67360	0.219664
$924$	−1.06330	−0.0349800
$925$	31.6757	1.04149
$926$	25.0500	0.823193
$927$	−24.5852	−0.807483
$928$	4.50348	0.147834
$929$	9.98673	0.327654	0.163827	−	0.986489i	$-0.447616\pi$
$929$	9.98673	0.327654	0.163827	+	0.986489i	$0.447616\pi$
$930$	91.0374	2.98523
$931$	36.0794	1.18245
$932$	7.63880	0.250217
$933$	−14.0217	−0.459050
$934$	−37.0255	−1.21151
$935$	−13.6184	−0.445369
$936$	−31.7416	−1.03751
$937$	−50.8038	−1.65969	−0.829844	−	0.557995i	$-0.811571\pi$
$937$	−50.8038	−1.65969	−0.829844	+	0.557995i	$0.811571\pi$
$938$	−8.34888	−0.272600
$939$	−22.6108	−0.737876
$940$	−4.86802	−0.158777
$941$	45.3227	1.47748	0.738739	−	0.673991i	$-0.235421\pi$
$941$	45.3227	1.47748	0.738739	+	0.673991i	$0.235421\pi$
$942$	28.3679	0.924275
$943$	−3.63429	−0.118349
$944$	13.9516	0.454086
$945$	−54.1373	−1.76109
$946$	−9.67450	−0.314545
$947$	−16.2837	−0.529150	−0.264575	−	0.964365i	$-0.585232\pi$
$947$	−16.2837	−0.529150	−0.264575	+	0.964365i	$0.585232\pi$
$948$	3.42414	0.111211
$949$	−16.4787	−0.534920
$950$	28.1096	0.911995
$951$	56.7275	1.83951
$952$	−13.4062	−0.434498
$953$	−44.2183	−1.43237	−0.716185	−	0.697910i	$-0.754113\pi$
$953$	−44.2183	−1.43237	−0.716185	+	0.697910i	$0.754113\pi$
$954$	139.410	4.51358
$955$	55.1632	1.78504
$956$	−0.272466	−0.00881216
$957$	8.45591	0.273341
$958$	7.69815	0.248716
$959$	5.15641	0.166509
$960$	88.6397	2.86083
$961$	18.2137	0.587540
$962$	13.7449	0.443154
$963$	−26.7346	−0.861509
$964$	0.106003	0.00341411
$965$	46.3391	1.49171
$966$	−3.16538	−0.101845
$967$	−27.9526	−0.898896	−0.449448	−	0.893306i	$-0.648379\pi$
$967$	−27.9526	−0.898896	−0.449448	+	0.893306i	$0.648379\pi$
$968$	3.00873	0.0967044
$969$	−93.6989	−3.01004
$970$	−63.0512	−2.02445
$971$	36.4599	1.17005	0.585027	−	0.811014i	$-0.301084\pi$
$971$	36.4599	1.17005	0.585027	+	0.811014i	$0.301084\pi$
$972$	−24.8287	−0.796381
$973$	7.55312	0.242142
$974$	20.6956	0.663129
$975$	−15.2602	−0.488719
$976$	−3.24653	−0.103919
$977$	46.8173	1.49782	0.748910	−	0.662672i	$-0.230578\pi$
$977$	46.8173	1.49782	0.748910	+	0.662672i	$0.230578\pi$
$978$	−25.8868	−0.827769
$979$	−13.7818	−0.440468
$980$	5.79254	0.185036
$981$	−4.68388	−0.149545
$982$	18.6071	0.593775
$983$	−0.591052	−0.0188516	−0.00942582	−	0.999956i	$-0.503000\pi$
$983$	−0.591052	−0.0188516	−0.00942582	+	0.999956i	$0.503000\pi$
$984$	49.9775	1.59322
$985$	−57.7197	−1.83910
$986$	14.8708	0.473584
$987$	−16.7409	−0.532869
$988$	−2.35960	−0.0750690
$989$	5.57145	0.177162
$990$	32.7927	1.04222
$991$	−12.8064	−0.406809	−0.203405	−	0.979095i	$-0.565201\pi$
$991$	−12.8064	−0.406809	−0.203405	+	0.979095i	$0.565201\pi$
$992$	12.7308	0.404202
$993$	−12.4349	−0.394608
$994$	−6.78718	−0.215276
$995$	8.98932	0.284981
$996$	−13.1136	−0.415519
$997$	59.2470	1.87637	0.938186	−	0.346131i	$-0.112505\pi$
$997$	59.2470	1.87637	0.938186	+	0.346131i	$0.112505\pi$
$998$	35.5644	1.12577
$999$	165.664	5.24139

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.8	✓	21
3.2	odd	2		6039.2.a.l.1.14		21
11.10	odd	2		7381.2.a.j.1.14		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.8	✓	21	1.1	even	1	trivial
6039.2.a.l.1.14		21	3.2	odd	2
7381.2.a.j.1.14		21	11.10	odd	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-1.29453 q^{2} +3.40741 q^{3} -0.324186 q^{4} +2.94198 q^{5} -4.41100 q^{6} -0.962580 q^{7} +3.00873 q^{8} +8.61042 q^{9} +O(q^{10})\)	\(q-1.29453 q^{2} +3.40741 q^{3} -0.324186 q^{4} +2.94198 q^{5} -4.41100 q^{6} -0.962580 q^{7} +3.00873 q^{8} +8.61042 q^{9} -3.80849 q^{10} -1.00000 q^{11} -1.10463 q^{12} -1.22524 q^{13} +1.24609 q^{14} +10.0245 q^{15} -3.24653 q^{16} +4.62899 q^{17} -11.1465 q^{18} -5.94052 q^{19} -0.953749 q^{20} -3.27990 q^{21} +1.29453 q^{22} -0.745508 q^{23} +10.2520 q^{24} +3.65525 q^{25} +1.58611 q^{26} +19.1170 q^{27} +0.312055 q^{28} -2.48163 q^{29} -12.9771 q^{30} -7.01525 q^{31} -1.81473 q^{32} -3.40741 q^{33} -5.99237 q^{34} -2.83189 q^{35} -2.79138 q^{36} +8.66581 q^{37} +7.69019 q^{38} -4.17488 q^{39} +8.85164 q^{40} +4.87491 q^{41} +4.24594 q^{42} -7.47335 q^{43} +0.324186 q^{44} +25.3317 q^{45} +0.965085 q^{46} +5.10409 q^{47} -11.0623 q^{48} -6.07344 q^{49} -4.73184 q^{50} +15.7728 q^{51} +0.397205 q^{52} -12.5071 q^{53} -24.7476 q^{54} -2.94198 q^{55} -2.89615 q^{56} -20.2418 q^{57} +3.21254 q^{58} -4.29739 q^{59} -3.24981 q^{60} +1.00000 q^{61} +9.08147 q^{62} -8.28822 q^{63} +8.84229 q^{64} -3.60462 q^{65} +4.41100 q^{66} -6.70005 q^{67} -1.50065 q^{68} -2.54025 q^{69} +3.66597 q^{70} -5.44678 q^{71} +25.9065 q^{72} +13.4494 q^{73} -11.2182 q^{74} +12.4549 q^{75} +1.92583 q^{76} +0.962580 q^{77} +5.40452 q^{78} -3.09980 q^{79} -9.55123 q^{80} +39.3081 q^{81} -6.31073 q^{82} +11.8714 q^{83} +1.06330 q^{84} +13.6184 q^{85} +9.67450 q^{86} -8.45591 q^{87} -3.00873 q^{88} +13.7818 q^{89} -32.7927 q^{90} +1.17939 q^{91} +0.241683 q^{92} -23.9038 q^{93} -6.60741 q^{94} -17.4769 q^{95} -6.18352 q^{96} +16.5554 q^{97} +7.86226 q^{98} -8.61042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * q^99

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