LMFDB - Embedded newform 301.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [301,2,Mod(1,301)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(301, 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("301.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 301 = 7 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	301.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:	$2.40349710084$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.81509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 5x^{3} + 3x^{2} + 5x - 2 $ x^5 - x^4 - 5x^3 + 3x^2 + 5*x - 2
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			1.2
Root			$1.21568$ of defining polynomial
Character	$\chi$	$=$	301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.09263 q^{2} +2.42092 q^{3} -0.806154 q^{4} -3.85042 q^{5} -2.64518 q^{6} -1.00000 q^{7} +3.06610 q^{8} +2.86085 q^{9} +O(q^{10})$	\(q-1.09263 q^{2} +2.42092 q^{3} -0.806154 q^{4} -3.85042 q^{5} -2.64518 q^{6} -1.00000 q^{7} +3.06610 q^{8} +2.86085 q^{9} +4.20709 q^{10} -5.95348 q^{11} -1.95163 q^{12} +1.59479 q^{13} +1.09263 q^{14} -9.32156 q^{15} -1.73781 q^{16} -5.09448 q^{17} -3.12586 q^{18} -4.59233 q^{19} +3.10403 q^{20} -2.42092 q^{21} +6.50497 q^{22} -1.92122 q^{23} +7.42277 q^{24} +9.82573 q^{25} -1.74252 q^{26} -0.336868 q^{27} +0.806154 q^{28} +7.91837 q^{29} +10.1850 q^{30} +4.05321 q^{31} -4.23340 q^{32} -14.4129 q^{33} +5.56640 q^{34} +3.85042 q^{35} -2.30629 q^{36} -7.46889 q^{37} +5.01773 q^{38} +3.86085 q^{39} -11.8058 q^{40} -1.41722 q^{41} +2.64518 q^{42} -1.00000 q^{43} +4.79942 q^{44} -11.0155 q^{45} +2.09919 q^{46} +6.31948 q^{47} -4.20709 q^{48} +1.00000 q^{49} -10.7359 q^{50} -12.3333 q^{51} -1.28564 q^{52} -1.23340 q^{53} +0.368073 q^{54} +22.9234 q^{55} -3.06610 q^{56} -11.1177 q^{57} -8.65187 q^{58} -6.76822 q^{59} +7.51461 q^{60} +6.01958 q^{61} -4.42867 q^{62} -2.86085 q^{63} +8.10117 q^{64} -6.14060 q^{65} +15.7480 q^{66} +10.5197 q^{67} +4.10694 q^{68} -4.65113 q^{69} -4.20709 q^{70} -13.5331 q^{71} +8.77164 q^{72} -2.80712 q^{73} +8.16075 q^{74} +23.7873 q^{75} +3.70212 q^{76} +5.95348 q^{77} -4.21849 q^{78} +14.9658 q^{79} +6.69129 q^{80} -9.39808 q^{81} +1.54850 q^{82} +2.18241 q^{83} +1.95163 q^{84} +19.6159 q^{85} +1.09263 q^{86} +19.1697 q^{87} -18.2540 q^{88} +4.09791 q^{89} +12.0359 q^{90} -1.59479 q^{91} +1.54880 q^{92} +9.81248 q^{93} -6.90487 q^{94} +17.6824 q^{95} -10.2487 q^{96} -14.2330 q^{97} -1.09263 q^{98} -17.0320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{3} + 2 q^{4} - 6 q^{5} - 10 q^{6} - 5 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 5 * q - 3 * q^3 + 2 * q^4 - 6 * q^5 - 10 * q^6 - 5 * q^7 - 3 * q^8 + 6 * q^9	\( 5 q - 3 q^{3} + 2 q^{4} - 6 q^{5} - 10 q^{6} - 5 q^{7} - 3 q^{8} + 6 q^{9} - q^{10} - 16 q^{11} - 8 q^{12} - 2 q^{13} - 8 q^{15} - 8 q^{17} + 17 q^{18} - 10 q^{19} - 6 q^{20} + 3 q^{21} - 5 q^{22} - 2 q^{23} + 10 q^{24} + 11 q^{25} - 24 q^{26} - 9 q^{27} - 2 q^{28} - 4 q^{29} + 24 q^{30} - 6 q^{31} + 4 q^{32} + 14 q^{33} + 17 q^{34} + 6 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + 11 q^{39} - 20 q^{40} - 16 q^{41} + 10 q^{42} - 5 q^{43} - 11 q^{44} - 14 q^{45} + 17 q^{46} - 11 q^{47} + q^{48} + 5 q^{49} + 12 q^{50} - 6 q^{51} + 24 q^{52} + 19 q^{53} - 23 q^{54} + 25 q^{55} + 3 q^{56} - 5 q^{57} - 31 q^{59} + 43 q^{60} - 2 q^{61} + 7 q^{62} - 6 q^{63} - 17 q^{64} + 6 q^{65} + 59 q^{66} + 11 q^{67} + 13 q^{68} - 17 q^{69} + q^{70} - 15 q^{71} + 23 q^{72} + 13 q^{73} + 22 q^{74} + 4 q^{75} + 34 q^{76} + 16 q^{77} + 17 q^{78} + 24 q^{79} + 11 q^{80} + 5 q^{81} - 36 q^{83} + 8 q^{84} - 19 q^{85} + 23 q^{87} - 13 q^{88} - 15 q^{89} - 17 q^{90} + 2 q^{91} - 35 q^{92} + 39 q^{93} + 32 q^{94} - 14 q^{95} - 2 q^{96} - 13 q^{97} - 63 q^{99}+O(q^{100}) \) 5 * q - 3 * q^3 + 2 * q^4 - 6 * q^5 - 10 * q^6 - 5 * q^7 - 3 * q^8 + 6 * q^9 - q^10 - 16 * q^11 - 8 * q^12 - 2 * q^13 - 8 * q^15 - 8 * q^17 + 17 * q^18 - 10 * q^19 - 6 * q^20 + 3 * q^21 - 5 * q^22 - 2 * q^23 + 10 * q^24 + 11 * q^25 - 24 * q^26 - 9 * q^27 - 2 * q^28 - 4 * q^29 + 24 * q^30 - 6 * q^31 + 4 * q^32 + 14 * q^33 + 17 * q^34 + 6 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + 11 * q^39 - 20 * q^40 - 16 * q^41 + 10 * q^42 - 5 * q^43 - 11 * q^44 - 14 * q^45 + 17 * q^46 - 11 * q^47 + q^48 + 5 * q^49 + 12 * q^50 - 6 * q^51 + 24 * q^52 + 19 * q^53 - 23 * q^54 + 25 * q^55 + 3 * q^56 - 5 * q^57 - 31 * q^59 + 43 * q^60 - 2 * q^61 + 7 * q^62 - 6 * q^63 - 17 * q^64 + 6 * q^65 + 59 * q^66 + 11 * q^67 + 13 * q^68 - 17 * q^69 + q^70 - 15 * q^71 + 23 * q^72 + 13 * q^73 + 22 * q^74 + 4 * q^75 + 34 * q^76 + 16 * q^77 + 17 * q^78 + 24 * q^79 + 11 * q^80 + 5 * q^81 - 36 * q^83 + 8 * q^84 - 19 * q^85 + 23 * q^87 - 13 * q^88 - 15 * q^89 - 17 * q^90 + 2 * q^91 - 35 * q^92 + 39 * q^93 + 32 * q^94 - 14 * q^95 - 2 * q^96 - 13 * q^97 - 63 * 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 $

$2$	−1.09263	−0.772608	−0.386304	−	0.922372i	$-0.626248\pi$
$2$	−1.09263	−0.772608	−0.386304	+	0.922372i	$0.626248\pi$
$3$	2.42092	1.39772	0.698859	−	0.715259i	$-0.253691\pi$
$3$	2.42092	1.39772	0.698859	+	0.715259i	$0.253691\pi$
$4$	−0.806154	−0.403077
$5$	−3.85042	−1.72196	−0.860980	−	0.508639i	$-0.830149\pi$
$5$	−3.85042	−1.72196	−0.860980	+	0.508639i	$0.830149\pi$
$6$	−2.64518	−1.07989
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.06610	1.08403
$9$	2.86085	0.953617
$10$	4.20709	1.33040
$11$	−5.95348	−1.79504	−0.897521	−	0.440971i	$-0.854634\pi$
$11$	−5.95348	−1.79504	−0.897521	+	0.440971i	$0.854634\pi$
$12$	−1.95163	−0.563388
$13$	1.59479	0.442314	0.221157	−	0.975238i	$-0.429017\pi$
$13$	1.59479	0.442314	0.221157	+	0.975238i	$0.429017\pi$
$14$	1.09263	0.292018
$15$	−9.32156	−2.40682
$16$	−1.73781	−0.434452
$17$	−5.09448	−1.23559	−0.617797	−	0.786338i	$-0.711975\pi$
$17$	−5.09448	−1.23559	−0.617797	+	0.786338i	$0.711975\pi$
$18$	−3.12586	−0.736772
$19$	−4.59233	−1.05355	−0.526776	−	0.850004i	$-0.676599\pi$
$19$	−4.59233	−1.05355	−0.526776	+	0.850004i	$0.676599\pi$
$20$	3.10403	0.694082
$21$	−2.42092	−0.528288
$22$	6.50497	1.38686
$23$	−1.92122	−0.400603	−0.200301	−	0.979734i	$-0.564192\pi$
$23$	−1.92122	−0.400603	−0.200301	+	0.979734i	$0.564192\pi$
$24$	7.42277	1.51517
$25$	9.82573	1.96515
$26$	−1.74252	−0.341736
$27$	−0.336868	−0.0648302
$28$	0.806154	0.152349
$29$	7.91837	1.47040	0.735202	−	0.677848i	$-0.237087\pi$
$29$	7.91837	1.47040	0.735202	+	0.677848i	$0.237087\pi$
$30$	10.1850	1.85952
$31$	4.05321	0.727977	0.363989	−	0.931403i	$-0.381415\pi$
$31$	4.05321	0.727977	0.363989	+	0.931403i	$0.381415\pi$
$32$	−4.23340	−0.748367
$33$	−14.4129	−2.50896
$34$	5.56640	0.954630
$35$	3.85042	0.650840
$36$	−2.30629	−0.384381
$37$	−7.46889	−1.22788	−0.613939	−	0.789354i	$-0.710416\pi$
$37$	−7.46889	−1.22788	−0.613939	+	0.789354i	$0.710416\pi$
$38$	5.01773	0.813983
$39$	3.86085	0.618231
$40$	−11.8058	−1.86665
$41$	−1.41722	−0.221332	−0.110666	−	0.993858i	$-0.535298\pi$
$41$	−1.41722	−0.221332	−0.110666	+	0.993858i	$0.535298\pi$
$42$	2.64518	0.408159
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	4.79942	0.723540
$45$	−11.0155	−1.64209
$46$	2.09919	0.309509
$47$	6.31948	0.921791	0.460895	−	0.887455i	$-0.347528\pi$
$47$	6.31948	0.921791	0.460895	+	0.887455i	$0.347528\pi$
$48$	−4.20709	−0.607242
$49$	1.00000	0.142857
$50$	−10.7359	−1.51829
$51$	−12.3333	−1.72701
$52$	−1.28564	−0.178287
$53$	−1.23340	−0.169421	−0.0847106	−	0.996406i	$-0.526997\pi$
$53$	−1.23340	−0.169421	−0.0847106	+	0.996406i	$0.526997\pi$
$54$	0.368073	0.0500883
$55$	22.9234	3.09099
$56$	−3.06610	−0.409724
$57$	−11.1177	−1.47257
$58$	−8.65187	−1.13605
$59$	−6.76822	−0.881147	−0.440574	−	0.897717i	$-0.645225\pi$
$59$	−6.76822	−0.881147	−0.440574	+	0.897717i	$0.645225\pi$
$60$	7.51461	0.970132
$61$	6.01958	0.770728	0.385364	−	0.922765i	$-0.374076\pi$
$61$	6.01958	0.770728	0.385364	+	0.922765i	$0.374076\pi$
$62$	−4.42867	−0.562441
$63$	−2.86085	−0.360433
$64$	8.10117	1.01265
$65$	−6.14060	−0.761648
$66$	15.7480	1.93845
$67$	10.5197	1.28519	0.642594	−	0.766207i	$-0.277858\pi$
$67$	10.5197	1.28519	0.642594	+	0.766207i	$0.277858\pi$
$68$	4.10694	0.498039
$69$	−4.65113	−0.559930
$70$	−4.20709	−0.502844
$71$	−13.5331	−1.60609	−0.803044	−	0.595920i	$-0.796787\pi$
$71$	−13.5331	−1.60609	−0.803044	+	0.595920i	$0.796787\pi$
$72$	8.77164	1.03375
$73$	−2.80712	−0.328549	−0.164274	−	0.986415i	$-0.552528\pi$
$73$	−2.80712	−0.328549	−0.164274	+	0.986415i	$0.552528\pi$
$74$	8.16075	0.948668
$75$	23.7873	2.74672
$76$	3.70212	0.424663
$77$	5.95348	0.678462
$78$	−4.21849	−0.477650
$79$	14.9658	1.68379	0.841895	−	0.539642i	$-0.181440\pi$
$79$	14.9658	1.68379	0.841895	+	0.539642i	$0.181440\pi$
$80$	6.69129	0.748109
$81$	−9.39808	−1.04423
$82$	1.54850	0.171003
$83$	2.18241	0.239550	0.119775	−	0.992801i	$-0.461783\pi$
$83$	2.18241	0.239550	0.119775	+	0.992801i	$0.461783\pi$
$84$	1.95163	0.212941
$85$	19.6159	2.12764
$86$	1.09263	0.117822
$87$	19.1697	2.05521
$88$	−18.2540	−1.94588
$89$	4.09791	0.434377	0.217189	−	0.976130i	$-0.430311\pi$
$89$	4.09791	0.434377	0.217189	+	0.976130i	$0.430311\pi$
$90$	12.0359	1.26869
$91$	−1.59479	−0.167179
$92$	1.54880	0.161474
$93$	9.81248	1.01751
$94$	−6.90487	−0.712183
$95$	17.6824	1.81418
$96$	−10.2487	−1.04601
$97$	−14.2330	−1.44514	−0.722571	−	0.691296i	$-0.757040\pi$
$97$	−14.2330	−1.44514	−0.722571	+	0.691296i	$0.757040\pi$
$98$	−1.09263	−0.110373
$99$	−17.0320	−1.71178
$100$	−7.92105	−0.792105
$101$	−2.63884	−0.262575	−0.131287	−	0.991344i	$-0.541911\pi$
$101$	−2.63884	−0.262575	−0.131287	+	0.991344i	$0.541911\pi$
$102$	13.4758	1.33430
$103$	−3.32173	−0.327300	−0.163650	−	0.986518i	$-0.552327\pi$
$103$	−3.32173	−0.327300	−0.163650	+	0.986518i	$0.552327\pi$
$104$	4.88977	0.479481
$105$	9.32156	0.909691
$106$	1.34766	0.130896
$107$	−12.9763	−1.25446	−0.627232	−	0.778832i	$-0.715812\pi$
$107$	−12.9763	−1.25446	−0.627232	+	0.778832i	$0.715812\pi$
$108$	0.271567	0.0261316
$109$	−9.36731	−0.897226	−0.448613	−	0.893726i	$-0.648082\pi$
$109$	−9.36731	−0.897226	−0.448613	+	0.893726i	$0.648082\pi$
$110$	−25.0469	−2.38813
$111$	−18.0816	−1.71623
$112$	1.73781	0.164207
$113$	0.515443	0.0484888	0.0242444	−	0.999706i	$-0.492282\pi$
$113$	0.515443	0.0484888	0.0242444	+	0.999706i	$0.492282\pi$
$114$	12.1475	1.13772
$115$	7.39752	0.689822
$116$	−6.38342	−0.592686
$117$	4.56245	0.421799
$118$	7.39518	0.680781
$119$	5.09448	0.467011
$120$	−28.5808	−2.60906
$121$	24.4440	2.22218
$122$	−6.57719	−0.595471
$123$	−3.43097	−0.309360
$124$	−3.26751	−0.293431
$125$	−18.5811	−1.66194
$126$	3.12586	0.278474
$127$	−4.66410	−0.413872	−0.206936	−	0.978354i	$-0.566349\pi$
$127$	−4.66410	−0.413872	−0.206936	+	0.978354i	$0.566349\pi$
$128$	−0.384798	−0.0340117
$129$	−2.42092	−0.213150
$130$	6.70942	0.588455
$131$	−8.45173	−0.738431	−0.369215	−	0.929344i	$-0.620374\pi$
$131$	−8.45173	−0.738431	−0.369215	+	0.929344i	$0.620374\pi$
$132$	11.6190	1.01131
$133$	4.59233	0.398205
$134$	−11.4942	−0.992946
$135$	1.29708	0.111635
$136$	−15.6202	−1.33942
$137$	15.4319	1.31844	0.659219	−	0.751951i	$-0.270887\pi$
$137$	15.4319	1.31844	0.659219	+	0.751951i	$0.270887\pi$
$138$	5.08197	0.432606
$139$	−19.0572	−1.61641	−0.808205	−	0.588901i	$-0.799561\pi$
$139$	−19.0572	−1.61641	−0.808205	+	0.588901i	$0.799561\pi$
$140$	−3.10403	−0.262338
$141$	15.2989	1.28840
$142$	14.7867	1.24088
$143$	−9.49454	−0.793973
$144$	−4.97161	−0.414301
$145$	−30.4890	−2.53198
$146$	3.06715	0.253839
$147$	2.42092	0.199674
$148$	6.02107	0.494929
$149$	0.323656	0.0265149	0.0132575	−	0.999912i	$-0.495780\pi$
$149$	0.323656	0.0265149	0.0132575	+	0.999912i	$0.495780\pi$
$150$	−25.9908	−2.12214
$151$	6.44574	0.524547	0.262273	−	0.964994i	$-0.415528\pi$
$151$	6.44574	0.524547	0.262273	+	0.964994i	$0.415528\pi$
$152$	−14.0805	−1.14208
$153$	−14.5746	−1.17828
$154$	−6.50497	−0.524186
$155$	−15.6065	−1.25355
$156$	−3.11244	−0.249195
$157$	2.21137	0.176486	0.0882431	−	0.996099i	$-0.471875\pi$
$157$	2.21137	0.176486	0.0882431	+	0.996099i	$0.471875\pi$
$158$	−16.3522	−1.30091
$159$	−2.98597	−0.236803
$160$	16.3004	1.28866
$161$	1.92122	0.151414
$162$	10.2687	0.806782
$163$	8.74957	0.685319	0.342659	−	0.939460i	$-0.388672\pi$
$163$	8.74957	0.685319	0.342659	+	0.939460i	$0.388672\pi$
$164$	1.14250	0.0892139
$165$	55.4957	4.32034
$166$	−2.38457	−0.185079
$167$	−6.81368	−0.527258	−0.263629	−	0.964624i	$-0.584920\pi$
$167$	−6.81368	−0.527258	−0.263629	+	0.964624i	$0.584920\pi$
$168$	−7.42277	−0.572679
$169$	−10.4567	−0.804358
$170$	−21.4330	−1.64383
$171$	−13.1380	−1.00469
$172$	0.806154	0.0614686
$173$	−18.6576	−1.41851	−0.709255	−	0.704952i	$-0.750969\pi$
$173$	−18.6576	−1.41851	−0.709255	+	0.704952i	$0.750969\pi$
$174$	−20.9455	−1.58787
$175$	−9.82573	−0.742756
$176$	10.3460	0.779860
$177$	−16.3853	−1.23160
$178$	−4.47751	−0.335603
$179$	−12.8771	−0.962479	−0.481239	−	0.876589i	$-0.659813\pi$
$179$	−12.8771	−0.962479	−0.481239	+	0.876589i	$0.659813\pi$
$180$	8.88017	0.661889
$181$	−17.3630	−1.29058	−0.645290	−	0.763938i	$-0.723263\pi$
$181$	−17.3630	−1.29058	−0.645290	+	0.763938i	$0.723263\pi$
$182$	1.74252	0.129164
$183$	14.5729	1.07726
$184$	−5.89065	−0.434265
$185$	28.7584	2.11436
$186$	−10.7214	−0.786134
$187$	30.3299	2.21794
$188$	−5.09447	−0.371553
$189$	0.336868	0.0245035
$190$	−19.3204	−1.40165
$191$	16.9725	1.22809	0.614045	−	0.789271i	$-0.289541\pi$
$191$	16.9725	1.22809	0.614045	+	0.789271i	$0.289541\pi$
$192$	19.6123	1.41539
$193$	−2.04204	−0.146989	−0.0734945	−	0.997296i	$-0.523415\pi$
$193$	−2.04204	−0.146989	−0.0734945	+	0.997296i	$0.523415\pi$
$194$	15.5514	1.11653
$195$	−14.8659	−1.06457
$196$	−0.806154	−0.0575824
$197$	23.4284	1.66921	0.834603	−	0.550852i	$-0.185697\pi$
$197$	23.4284	1.66921	0.834603	+	0.550852i	$0.185697\pi$
$198$	18.6098	1.32254
$199$	−2.33014	−0.165179	−0.0825895	−	0.996584i	$-0.526319\pi$
$199$	−2.33014	−0.165179	−0.0825895	+	0.996584i	$0.526319\pi$
$200$	30.1266	2.13027
$201$	25.4674	1.79633
$202$	2.88329	0.202867
$203$	−7.91837	−0.555760
$204$	9.94256	0.696119
$205$	5.45689	0.381125
$206$	3.62943	0.252874
$207$	−5.49633	−0.382022
$208$	−2.77143	−0.192164
$209$	27.3404	1.89117
$210$	−10.1850	−0.702834
$211$	−5.01816	−0.345465	−0.172732	−	0.984969i	$-0.555260\pi$
$211$	−5.01816	−0.345465	−0.172732	+	0.984969i	$0.555260\pi$
$212$	0.994314	0.0682897
$213$	−32.7626	−2.24486
$214$	14.1783	0.969209
$215$	3.85042	0.262596
$216$	−1.03287	−0.0702778
$217$	−4.05321	−0.275150
$218$	10.2350	0.693204
$219$	−6.79581	−0.459218
$220$	−18.4798	−1.24591
$221$	−8.12462	−0.546521
$222$	19.7565	1.32597
$223$	−16.6042	−1.11190	−0.555948	−	0.831217i	$-0.687645\pi$
$223$	−16.6042	−1.11190	−0.555948	+	0.831217i	$0.687645\pi$
$224$	4.23340	0.282856
$225$	28.1100	1.87400
$226$	−0.563190	−0.0374629
$227$	−27.0896	−1.79800	−0.898999	−	0.437950i	$-0.855705\pi$
$227$	−27.0896	−1.79800	−0.898999	+	0.437950i	$0.855705\pi$
$228$	8.96254	0.593559
$229$	−7.08405	−0.468127	−0.234064	−	0.972221i	$-0.575202\pi$
$229$	−7.08405	−0.468127	−0.234064	+	0.972221i	$0.575202\pi$
$230$	−8.08277	−0.532962
$231$	14.4129	0.948300
$232$	24.2785	1.59396
$233$	−1.52120	−0.0996574	−0.0498287	−	0.998758i	$-0.515868\pi$
$233$	−1.52120	−0.0996574	−0.0498287	+	0.998758i	$0.515868\pi$
$234$	−4.98508	−0.325885
$235$	−24.3326	−1.58729
$236$	5.45622	0.355170
$237$	36.2311	2.35346
$238$	−5.56640	−0.360816
$239$	−22.7727	−1.47304	−0.736520	−	0.676415i	$-0.763532\pi$
$239$	−22.7727	−1.47304	−0.736520	+	0.676415i	$0.763532\pi$
$240$	16.1991	1.04565
$241$	7.45556	0.480255	0.240127	−	0.970741i	$-0.422811\pi$
$241$	7.45556	0.480255	0.240127	+	0.970741i	$0.422811\pi$
$242$	−26.7083	−1.71687
$243$	−21.7414	−1.39471
$244$	−4.85271	−0.310663
$245$	−3.85042	−0.245994
$246$	3.74879	0.239014
$247$	−7.32379	−0.466001
$248$	12.4275	0.789148
$249$	5.28343	0.334824
$250$	20.3023	1.28403
$251$	−11.0868	−0.699792	−0.349896	−	0.936789i	$-0.613783\pi$
$251$	−11.0868	−0.699792	−0.349896	+	0.936789i	$0.613783\pi$
$252$	2.30629	0.145282
$253$	11.4380	0.719099
$254$	5.09615	0.319761
$255$	47.4885	2.97385
$256$	−15.7819	−0.986369
$257$	−6.33515	−0.395176	−0.197588	−	0.980285i	$-0.563311\pi$
$257$	−6.33515	−0.395176	−0.197588	+	0.980285i	$0.563311\pi$
$258$	2.64518	0.164681
$259$	7.46889	0.464094
$260$	4.95027	0.307003
$261$	22.6533	1.40220
$262$	9.23464	0.570518
$263$	23.1950	1.43027	0.715134	−	0.698987i	$-0.246366\pi$
$263$	23.1950	1.43027	0.715134	+	0.698987i	$0.246366\pi$
$264$	−44.1913	−2.71979
$265$	4.74912	0.291736
$266$	−5.01773	−0.307657
$267$	9.92071	0.607137
$268$	−8.48051	−0.518029
$269$	17.8316	1.08721	0.543605	−	0.839341i	$-0.317059\pi$
$269$	17.8316	1.08721	0.543605	+	0.839341i	$0.317059\pi$
$270$	−1.41723	−0.0862501
$271$	−18.0899	−1.09888	−0.549442	−	0.835532i	$-0.685160\pi$
$271$	−18.0899	−1.09888	−0.549442	+	0.835532i	$0.685160\pi$
$272$	8.85324	0.536806
$273$	−3.86085	−0.233669
$274$	−16.8614	−1.01864
$275$	−58.4973	−3.52752
$276$	3.74952	0.225695
$277$	−11.0720	−0.665251	−0.332626	−	0.943059i	$-0.607935\pi$
$277$	−11.0720	−0.665251	−0.332626	+	0.943059i	$0.607935\pi$
$278$	20.8225	1.24885
$279$	11.5956	0.694212
$280$	11.8058	0.705529
$281$	11.7863	0.703109	0.351555	−	0.936167i	$-0.385653\pi$
$281$	11.7863	0.703109	0.351555	+	0.936167i	$0.385653\pi$
$282$	−16.7161	−0.995431
$283$	−11.9325	−0.709313	−0.354656	−	0.934997i	$-0.615402\pi$
$283$	−11.9325	−0.709313	−0.354656	+	0.934997i	$0.615402\pi$
$284$	10.9098	0.647377
$285$	42.8077	2.53571
$286$	10.3740	0.613430
$287$	1.41722	0.0836557
$288$	−12.1111	−0.713656
$289$	8.95376	0.526692
$290$	33.3133	1.95623
$291$	−34.4570	−2.01990
$292$	2.26297	0.132430
$293$	−2.20089	−0.128577	−0.0642887	−	0.997931i	$-0.520478\pi$
$293$	−2.20089	−0.128577	−0.0642887	+	0.997931i	$0.520478\pi$
$294$	−2.64518	−0.154270
$295$	26.0605	1.51730
$296$	−22.9003	−1.33105
$297$	2.00554	0.116373
$298$	−0.353637	−0.0204857
$299$	−3.06394	−0.177192
$300$	−19.1762	−1.10714
$301$	1.00000	0.0576390
$302$	−7.04282	−0.405269
$303$	−6.38843	−0.367006
$304$	7.98059	0.457718
$305$	−23.1779	−1.32716
$306$	15.9246	0.910351
$307$	9.12748	0.520933	0.260466	−	0.965483i	$-0.416124\pi$
$307$	9.12748	0.520933	0.260466	+	0.965483i	$0.416124\pi$
$308$	−4.79942	−0.273473
$309$	−8.04164	−0.457473
$310$	17.0522	0.968501
$311$	9.16544	0.519724	0.259862	−	0.965646i	$-0.416323\pi$
$311$	9.16544	0.519724	0.259862	+	0.965646i	$0.416323\pi$
$312$	11.8377	0.670180
$313$	16.6069	0.938680	0.469340	−	0.883018i	$-0.344492\pi$
$313$	16.6069	0.938680	0.469340	+	0.883018i	$0.344492\pi$
$314$	−2.41621	−0.136355
$315$	11.0155	0.620652
$316$	−12.0648	−0.678697
$317$	25.2309	1.41711	0.708554	−	0.705657i	$-0.249348\pi$
$317$	25.2309	1.41711	0.708554	+	0.705657i	$0.249348\pi$
$318$	3.26257	0.182956
$319$	−47.1419	−2.63944
$320$	−31.1929	−1.74374
$321$	−31.4145	−1.75339
$322$	−2.09919	−0.116983
$323$	23.3955	1.30176
$324$	7.57630	0.420906
$325$	15.6700	0.869213
$326$	−9.56006	−0.529483
$327$	−22.6775	−1.25407
$328$	−4.34533	−0.239930
$329$	−6.31948	−0.348404
$330$	−60.6365	−3.33793
$331$	−18.3516	−1.00870	−0.504349	−	0.863500i	$-0.668267\pi$
$331$	−18.3516	−1.00870	−0.504349	+	0.863500i	$0.668267\pi$
$332$	−1.75936	−0.0965572
$333$	−21.3674	−1.17092
$334$	7.44485	0.407364
$335$	−40.5053	−2.21304
$336$	4.20709	0.229516
$337$	11.9227	0.649472	0.324736	−	0.945805i	$-0.394725\pi$
$337$	11.9227	0.649472	0.324736	+	0.945805i	$0.394725\pi$
$338$	11.4253	0.621453
$339$	1.24785	0.0677737
$340$	−15.8134	−0.857604
$341$	−24.1307	−1.30675
$342$	14.3550	0.776228
$343$	−1.00000	−0.0539949
$344$	−3.06610	−0.165313
$345$	17.9088	0.964177
$346$	20.3859	1.09595
$347$	33.5972	1.80359	0.901796	−	0.432162i	$-0.142249\pi$
$347$	33.5972	1.80359	0.901796	+	0.432162i	$0.142249\pi$
$348$	−15.4537	−0.828408
$349$	3.37739	0.180788	0.0903938	−	0.995906i	$-0.471187\pi$
$349$	3.37739	0.180788	0.0903938	+	0.995906i	$0.471187\pi$
$350$	10.7359	0.573859
$351$	−0.537232	−0.0286753
$352$	25.2035	1.34335
$353$	4.51114	0.240104	0.120052	−	0.992768i	$-0.461694\pi$
$353$	4.51114	0.240104	0.120052	+	0.992768i	$0.461694\pi$
$354$	17.9031	0.951541
$355$	52.1082	2.76562
$356$	−3.30354	−0.175087
$357$	12.3333	0.652749
$358$	14.0699	0.743619
$359$	14.8084	0.781556	0.390778	−	0.920485i	$-0.372206\pi$
$359$	14.8084	0.781556	0.390778	+	0.920485i	$0.372206\pi$
$360$	−33.7745	−1.78007
$361$	2.08949	0.109973
$362$	18.9713	0.997112
$363$	59.1769	3.10598
$364$	1.28564	0.0673860
$365$	10.8086	0.565748
$366$	−15.9228	−0.832301
$367$	1.56099	0.0814832	0.0407416	−	0.999170i	$-0.487028\pi$
$367$	1.56099	0.0814832	0.0407416	+	0.999170i	$0.487028\pi$
$368$	3.33872	0.174043
$369$	−4.05445	−0.211066
$370$	−31.4223	−1.63357
$371$	1.23340	0.0640352
$372$	−7.91037	−0.410134
$373$	12.2655	0.635083	0.317541	−	0.948244i	$-0.397143\pi$
$373$	12.2655	0.635083	0.317541	+	0.948244i	$0.397143\pi$
$374$	−33.1395	−1.71360
$375$	−44.9833	−2.32293
$376$	19.3761	0.999247
$377$	12.6281	0.650381
$378$	−0.368073	−0.0189316
$379$	4.76826	0.244929	0.122464	−	0.992473i	$-0.460920\pi$
$379$	4.76826	0.244929	0.122464	+	0.992473i	$0.460920\pi$
$380$	−14.2547	−0.731252
$381$	−11.2914	−0.578476
$382$	−18.5447	−0.948832
$383$	31.8891	1.62945	0.814727	−	0.579844i	$-0.196887\pi$
$383$	31.8891	1.62945	0.814727	+	0.579844i	$0.196887\pi$
$384$	−0.931565	−0.0475387
$385$	−22.9234	−1.16829
$386$	2.23119	0.113565
$387$	−2.86085	−0.145425
$388$	11.4740	0.582504
$389$	28.5879	1.44947	0.724733	−	0.689030i	$-0.241963\pi$
$389$	28.5879	1.44947	0.724733	+	0.689030i	$0.241963\pi$
$390$	16.2430	0.822495
$391$	9.78764	0.494982
$392$	3.06610	0.154861
$393$	−20.4610	−1.03212
$394$	−25.5987	−1.28964
$395$	−57.6248	−2.89942
$396$	13.7304	0.689980
$397$	11.7849	0.591465	0.295732	−	0.955271i	$-0.404436\pi$
$397$	11.7849	0.591465	0.295732	+	0.955271i	$0.404436\pi$
$398$	2.54598	0.127619
$399$	11.1177	0.556579
$400$	−17.0752	−0.853762
$401$	−31.5575	−1.57591	−0.787953	−	0.615735i	$-0.788859\pi$
$401$	−31.5575	−1.57591	−0.787953	+	0.615735i	$0.788859\pi$
$402$	−27.8265	−1.38786
$403$	6.46400	0.321995
$404$	2.12731	0.105838
$405$	36.1866	1.79813
$406$	8.65187	0.429385
$407$	44.4659	2.20409
$408$	−37.8152	−1.87213
$409$	−15.8722	−0.784830	−0.392415	−	0.919788i	$-0.628360\pi$
$409$	−15.8722	−0.784830	−0.392415	+	0.919788i	$0.628360\pi$
$410$	−5.96237	−0.294461
$411$	37.3594	1.84280
$412$	2.67782	0.131927
$413$	6.76822	0.333042
$414$	6.00547	0.295153
$415$	−8.40319	−0.412496
$416$	−6.75138	−0.331014
$417$	−46.1359	−2.25929
$418$	−29.8730	−1.46113
$419$	17.5249	0.856149	0.428074	−	0.903743i	$-0.359192\pi$
$419$	17.5249	0.856149	0.428074	+	0.903743i	$0.359192\pi$
$420$	−7.51461	−0.366675
$421$	13.2659	0.646542	0.323271	−	0.946306i	$-0.395217\pi$
$421$	13.2659	0.646542	0.323271	+	0.946306i	$0.395217\pi$
$422$	5.48301	0.266909
$423$	18.0791	0.879035
$424$	−3.78174	−0.183657
$425$	−50.0570	−2.42812
$426$	35.7975	1.73440
$427$	−6.01958	−0.291308
$428$	10.4609	0.505646
$429$	−22.9855	−1.10975
$430$	−4.20709	−0.202884
$431$	12.9595	0.624235	0.312118	−	0.950043i	$-0.398962\pi$
$431$	12.9595	0.624235	0.312118	+	0.950043i	$0.398962\pi$
$432$	0.585411	0.0281656
$433$	24.6907	1.18656	0.593280	−	0.804996i	$-0.297833\pi$
$433$	24.6907	1.18656	0.593280	+	0.804996i	$0.297833\pi$
$434$	4.42867	0.212583
$435$	−73.8115	−3.53899
$436$	7.55150	0.361651
$437$	8.82289	0.422056
$438$	7.42533	0.354796
$439$	8.97964	0.428575	0.214287	−	0.976771i	$-0.431257\pi$
$439$	8.97964	0.428575	0.214287	+	0.976771i	$0.431257\pi$
$440$	70.2854	3.35072
$441$	2.86085	0.136231
$442$	8.87722	0.422246
$443$	21.9781	1.04421	0.522106	−	0.852881i	$-0.325147\pi$
$443$	21.9781	1.04421	0.522106	+	0.852881i	$0.325147\pi$
$444$	14.5765	0.691771
$445$	−15.7787	−0.747981
$446$	18.1423	0.859061
$447$	0.783546	0.0370604
$448$	−8.10117	−0.382744
$449$	20.5006	0.967482	0.483741	−	0.875211i	$-0.339278\pi$
$449$	20.5006	0.967482	0.483741	+	0.875211i	$0.339278\pi$
$450$	−30.7139	−1.44787
$451$	8.43739	0.397301
$452$	−0.415527	−0.0195447
$453$	15.6046	0.733169
$454$	29.5990	1.38915
$455$	6.14060	0.287876
$456$	−34.0878	−1.59631
$457$	−22.8403	−1.06843	−0.534213	−	0.845350i	$-0.679392\pi$
$457$	−22.8403	−1.06843	−0.534213	+	0.845350i	$0.679392\pi$
$458$	7.74027	0.361679
$459$	1.71617	0.0801038
$460$	−5.96354	−0.278051
$461$	−28.0662	−1.30717	−0.653586	−	0.756852i	$-0.726736\pi$
$461$	−28.0662	−1.30717	−0.653586	+	0.756852i	$0.726736\pi$
$462$	−15.7480	−0.732664
$463$	24.4586	1.13669	0.568344	−	0.822791i	$-0.307584\pi$
$463$	24.4586	1.13669	0.568344	+	0.822791i	$0.307584\pi$
$464$	−13.7606	−0.638820
$465$	−37.7822	−1.75211
$466$	1.66212	0.0769961
$467$	−10.9762	−0.507916	−0.253958	−	0.967215i	$-0.581733\pi$
$467$	−10.9762	−0.507916	−0.253958	+	0.967215i	$0.581733\pi$
$468$	−3.67804	−0.170017
$469$	−10.5197	−0.485755
$470$	26.5866	1.22635
$471$	5.35354	0.246678
$472$	−20.7520	−0.955188
$473$	5.95348	0.273741
$474$	−39.5873	−1.81830
$475$	−45.1230	−2.07039
$476$	−4.10694	−0.188241
$477$	−3.52859	−0.161563
$478$	24.8822	1.13808
$479$	−28.0996	−1.28390	−0.641952	−	0.766745i	$-0.721875\pi$
$479$	−28.0996	−1.28390	−0.641952	+	0.766745i	$0.721875\pi$
$480$	39.4619	1.80118
$481$	−11.9113	−0.543108
$482$	−8.14619	−0.371049
$483$	4.65113	0.211634
$484$	−19.7056	−0.895709
$485$	54.8030	2.48848
$486$	23.7554	1.07757
$487$	−30.1220	−1.36496	−0.682478	−	0.730906i	$-0.739098\pi$
$487$	−30.1220	−1.36496	−0.682478	+	0.730906i	$0.739098\pi$
$488$	18.4566	0.835491
$489$	21.1820	0.957883
$490$	4.20709	0.190057
$491$	0.591620	0.0266994	0.0133497	−	0.999911i	$-0.495751\pi$
$491$	0.591620	0.0266994	0.0133497	+	0.999911i	$0.495751\pi$
$492$	2.76589	0.124696
$493$	−40.3400	−1.81682
$494$	8.00221	0.360036
$495$	65.5805	2.94762
$496$	−7.04370	−0.316271
$497$	13.5331	0.607044
$498$	−5.77285	−0.258688
$499$	−19.6906	−0.881472	−0.440736	−	0.897637i	$-0.645283\pi$
$499$	−19.6906	−0.881472	−0.440736	+	0.897637i	$0.645283\pi$
$500$	14.9792	0.669891
$501$	−16.4954	−0.736959
$502$	12.1138	0.540665
$503$	−7.96818	−0.355283	−0.177642	−	0.984095i	$-0.556847\pi$
$503$	−7.96818	−0.355283	−0.177642	+	0.984095i	$0.556847\pi$
$504$	−8.77164	−0.390720
$505$	10.1607	0.452143
$506$	−12.4975	−0.555582
$507$	−25.3147	−1.12427
$508$	3.75998	0.166822
$509$	−7.89790	−0.350068	−0.175034	−	0.984562i	$-0.556004\pi$
$509$	−7.89790	−0.350068	−0.175034	+	0.984562i	$0.556004\pi$
$510$	−51.8875	−2.29762
$511$	2.80712	0.124180
$512$	18.0134	0.796088
$513$	1.54701	0.0683020
$514$	6.92199	0.305316
$515$	12.7900	0.563597
$516$	1.95163	0.0859159
$517$	−37.6229	−1.65465
$518$	−8.16075	−0.358563
$519$	−45.1685	−1.98268
$520$	−18.8277	−0.825648
$521$	25.2812	1.10759	0.553796	−	0.832653i	$-0.313179\pi$
$521$	25.2812	1.10759	0.553796	+	0.832653i	$0.313179\pi$
$522$	−24.7517	−1.08335
$523$	−40.2551	−1.76023	−0.880117	−	0.474757i	$-0.842536\pi$
$523$	−40.2551	−1.76023	−0.880117	+	0.474757i	$0.842536\pi$
$524$	6.81339	0.297644
$525$	−23.7873	−1.03816
$526$	−25.3437	−1.10504
$527$	−20.6490	−0.899484
$528$	25.0469	1.09003
$529$	−19.3089	−0.839517
$530$	−5.18905	−0.225398
$531$	−19.3629	−0.840277
$532$	−3.70212	−0.160507
$533$	−2.26016	−0.0978985
$534$	−10.8397	−0.469079
$535$	49.9641	2.16014
$536$	32.2544	1.39318
$537$	−31.1744	−1.34527
$538$	−19.4834	−0.839987
$539$	−5.95348	−0.256435
$540$	−1.04565	−0.0449975
$541$	−9.13566	−0.392773	−0.196386	−	0.980527i	$-0.562921\pi$
$541$	−9.13566	−0.392773	−0.196386	+	0.980527i	$0.562921\pi$
$542$	19.7656	0.849006
$543$	−42.0343	−1.80387
$544$	21.5670	0.924678
$545$	36.0681	1.54499
$546$	4.21849	0.180535
$547$	15.5362	0.664280	0.332140	−	0.943230i	$-0.392229\pi$
$547$	15.5362	0.664280	0.332140	+	0.943230i	$0.392229\pi$
$548$	−12.4405	−0.531432
$549$	17.2211	0.734980
$550$	63.9161	2.72539
$551$	−36.3637	−1.54915
$552$	−14.2608	−0.606980
$553$	−14.9658	−0.636413
$554$	12.0976	0.513978
$555$	69.6217	2.95527
$556$	15.3630	0.651538
$557$	18.8594	0.799100	0.399550	−	0.916711i	$-0.369166\pi$
$557$	18.8594	0.799100	0.399550	+	0.916711i	$0.369166\pi$
$558$	−12.6698	−0.536353
$559$	−1.59479	−0.0674523
$560$	−6.69129	−0.282759
$561$	73.4263	3.10006
$562$	−12.8780	−0.543228
$563$	−40.0127	−1.68634	−0.843168	−	0.537651i	$-0.819312\pi$
$563$	−40.0127	−1.68634	−0.843168	+	0.537651i	$0.819312\pi$
$564$	−12.3333	−0.519326
$565$	−1.98467	−0.0834958
$566$	13.0378	0.548021
$567$	9.39808	0.394682
$568$	−41.4939	−1.74104
$569$	−20.1928	−0.846527	−0.423264	−	0.906007i	$-0.639116\pi$
$569$	−20.1928	−0.846527	−0.423264	+	0.906007i	$0.639116\pi$
$570$	−46.7730	−1.95911
$571$	−18.9978	−0.795033	−0.397516	−	0.917595i	$-0.630128\pi$
$571$	−18.9978	−0.795033	−0.397516	+	0.917595i	$0.630128\pi$
$572$	7.65406	0.320032
$573$	41.0891	1.71652
$574$	−1.54850	−0.0646331
$575$	−18.8774	−0.787243
$576$	23.1763	0.965677
$577$	24.8388	1.03405	0.517026	−	0.855970i	$-0.327039\pi$
$577$	24.8388	1.03405	0.517026	+	0.855970i	$0.327039\pi$
$578$	−9.78317	−0.406926
$579$	−4.94360	−0.205449
$580$	24.5788	1.02058
$581$	−2.18241	−0.0905415
$582$	37.6488	1.56059
$583$	7.34305	0.304118
$584$	−8.60690	−0.356156
$585$	−17.5673	−0.726320
$586$	2.40476	0.0993399
$587$	28.5915	1.18010	0.590048	−	0.807368i	$-0.299109\pi$
$587$	28.5915	1.18010	0.590048	+	0.807368i	$0.299109\pi$
$588$	−1.95163	−0.0804840
$589$	−18.6137	−0.766962
$590$	−28.4745	−1.17228
$591$	56.7183	2.33308
$592$	12.9795	0.533454
$593$	14.5533	0.597634	0.298817	−	0.954310i	$-0.403408\pi$
$593$	14.5533	0.597634	0.298817	+	0.954310i	$0.403408\pi$
$594$	−2.19131	−0.0899107
$595$	−19.6159	−0.804173
$596$	−0.260917	−0.0106876
$597$	−5.64108	−0.230874
$598$	3.34776	0.136900
$599$	18.2078	0.743950	0.371975	−	0.928243i	$-0.378681\pi$
$599$	18.2078	0.743950	0.371975	+	0.928243i	$0.378681\pi$
$600$	72.9342	2.97752
$601$	−25.2134	−1.02848	−0.514238	−	0.857648i	$-0.671925\pi$
$601$	−25.2134	−1.02848	−0.514238	+	0.857648i	$0.671925\pi$
$602$	−1.09263	−0.0445324
$603$	30.0953	1.22558
$604$	−5.19626	−0.211433
$605$	−94.1196	−3.82650
$606$	6.98021	0.283552
$607$	−15.4229	−0.625997	−0.312998	−	0.949754i	$-0.601333\pi$
$607$	−15.4229	−0.625997	−0.312998	+	0.949754i	$0.601333\pi$
$608$	19.4412	0.788444
$609$	−19.1697	−0.776797
$610$	25.3249	1.02538
$611$	10.0782	0.407721
$612$	11.7493	0.474939
$613$	−2.71686	−0.109733	−0.0548665	−	0.998494i	$-0.517473\pi$
$613$	−2.71686	−0.109733	−0.0548665	+	0.998494i	$0.517473\pi$
$614$	−9.97299	−0.402477
$615$	13.2107	0.532706
$616$	18.2540	0.735473
$617$	2.81241	0.113224	0.0566118	−	0.998396i	$-0.481970\pi$
$617$	2.81241	0.113224	0.0566118	+	0.998396i	$0.481970\pi$
$618$	8.78656	0.353447
$619$	33.8153	1.35915	0.679576	−	0.733605i	$-0.262164\pi$
$619$	33.8153	1.35915	0.679576	+	0.733605i	$0.262164\pi$
$620$	12.5813	0.505276
$621$	0.647198	0.0259712
$622$	−10.0145	−0.401543
$623$	−4.09791	−0.164179
$624$	−6.70942	−0.268592
$625$	22.4164	0.896655
$626$	−18.1453	−0.725232
$627$	66.1888	2.64333
$628$	−1.78270	−0.0711375
$629$	38.0501	1.51716
$630$	−12.0359	−0.479521
$631$	−39.0876	−1.55605	−0.778027	−	0.628231i	$-0.783779\pi$
$631$	−39.0876	−1.55605	−0.778027	+	0.628231i	$0.783779\pi$
$632$	45.8867	1.82528
$633$	−12.1486	−0.482862
$634$	−27.5681	−1.09487
$635$	17.9587	0.712671
$636$	2.40715	0.0954498
$637$	1.59479	0.0631878
$638$	51.5087	2.03925
$639$	−38.7163	−1.53159
$640$	1.48163	0.0585667
$641$	30.0577	1.18721	0.593604	−	0.804757i	$-0.297704\pi$
$641$	30.0577	1.18721	0.593604	+	0.804757i	$0.297704\pi$
$642$	34.3245	1.35468
$643$	−4.31741	−0.170262	−0.0851310	−	0.996370i	$-0.527131\pi$
$643$	−4.31741	−0.170262	−0.0851310	+	0.996370i	$0.527131\pi$
$644$	−1.54880	−0.0610313
$645$	9.32156	0.367036
$646$	−25.5627	−1.00575
$647$	−7.24150	−0.284693	−0.142346	−	0.989817i	$-0.545465\pi$
$647$	−7.24150	−0.284693	−0.142346	+	0.989817i	$0.545465\pi$
$648$	−28.8154	−1.13198
$649$	40.2945	1.58170
$650$	−17.1215	−0.671561
$651$	−9.81248	−0.384582
$652$	−7.05349	−0.276236
$653$	35.0049	1.36985	0.684924	−	0.728614i	$-0.259835\pi$
$653$	35.0049	1.36985	0.684924	+	0.728614i	$0.259835\pi$
$654$	24.7782	0.968904
$655$	32.5427	1.27155
$656$	2.46285	0.0961583
$657$	−8.03075	−0.313310
$658$	6.90487	0.269180
$659$	−33.6189	−1.30961	−0.654804	−	0.755799i	$-0.727249\pi$
$659$	−33.6189	−1.30961	−0.654804	+	0.755799i	$0.727249\pi$
$660$	−44.7381	−1.74143
$661$	−27.3726	−1.06467	−0.532334	−	0.846534i	$-0.678685\pi$
$661$	−27.3726	−1.06467	−0.532334	+	0.846534i	$0.678685\pi$
$662$	20.0516	0.779328
$663$	−19.6690	−0.763882
$664$	6.69147	0.259679
$665$	−17.6824	−0.685694
$666$	23.3467	0.904666
$667$	−15.2129	−0.589048
$668$	5.49287	0.212526
$669$	−40.1973	−1.55412
$670$	44.2574	1.70981
$671$	−35.8375	−1.38349
$672$	10.2487	0.395353
$673$	33.4546	1.28958	0.644791	−	0.764359i	$-0.276944\pi$
$673$	33.4546	1.28958	0.644791	+	0.764359i	$0.276944\pi$
$674$	−13.0272	−0.501787
$675$	−3.30997	−0.127401
$676$	8.42967	0.324218
$677$	−41.5865	−1.59830	−0.799149	−	0.601132i	$-0.794716\pi$
$677$	−41.5865	−1.59830	−0.799149	+	0.601132i	$0.794716\pi$
$678$	−1.36344	−0.0523625
$679$	14.2330	0.546213
$680$	60.1442	2.30643
$681$	−65.5817	−2.51310
$682$	26.3660	1.00961
$683$	−11.5517	−0.442014	−0.221007	−	0.975272i	$-0.570934\pi$
$683$	−11.5517	−0.442014	−0.221007	+	0.975272i	$0.570934\pi$
$684$	10.5912	0.404966
$685$	−59.4194	−2.27030
$686$	1.09263	0.0417169
$687$	−17.1499	−0.654310
$688$	1.73781	0.0662533
$689$	−1.96702	−0.0749374
$690$	−19.5677	−0.744931
$691$	45.7535	1.74054	0.870272	−	0.492571i	$-0.163943\pi$
$691$	45.7535	1.74054	0.870272	+	0.492571i	$0.163943\pi$
$692$	15.0409	0.571769
$693$	17.0320	0.646993
$694$	−36.7094	−1.39347
$695$	73.3782	2.78339
$696$	58.7762	2.22791
$697$	7.21999	0.273477
$698$	−3.69025	−0.139678
$699$	−3.68271	−0.139293
$700$	7.92105	0.299388
$701$	−13.9065	−0.525240	−0.262620	−	0.964899i	$-0.584587\pi$
$701$	−13.9065	−0.525240	−0.262620	+	0.964899i	$0.584587\pi$
$702$	0.586997	0.0221548
$703$	34.2996	1.29363
$704$	−48.2302	−1.81774
$705$	−58.9074	−2.21858
$706$	−4.92902	−0.185506
$707$	2.63884	0.0992440
$708$	13.2091	0.496428
$709$	−5.31400	−0.199572	−0.0997858	−	0.995009i	$-0.531816\pi$
$709$	−5.31400	−0.199572	−0.0997858	+	0.995009i	$0.531816\pi$
$710$	−56.9352	−2.13674
$711$	42.8151	1.60569
$712$	12.5646	0.470877
$713$	−7.78711	−0.291630
$714$	−13.4758	−0.504319
$715$	36.5580	1.36719
$716$	10.3809	0.387953
$717$	−55.1308	−2.05890
$718$	−16.1801	−0.603837
$719$	2.98056	0.111156	0.0555780	−	0.998454i	$-0.482300\pi$
$719$	2.98056	0.111156	0.0555780	+	0.998454i	$0.482300\pi$
$720$	19.1428	0.713410
$721$	3.32173	0.123708
$722$	−2.28304	−0.0849659
$723$	18.0493	0.671261
$724$	13.9972	0.520203
$725$	77.8038	2.88956
$726$	−64.6586	−2.39971
$727$	−4.52994	−0.168006	−0.0840032	−	0.996465i	$-0.526771\pi$
$727$	−4.52994	−0.168006	−0.0840032	+	0.996465i	$0.526771\pi$
$728$	−4.88977	−0.181227
$729$	−24.4399	−0.905183
$730$	−11.8098	−0.437101
$731$	5.09448	0.188426
$732$	−11.7480	−0.434219
$733$	−1.65527	−0.0611387	−0.0305694	−	0.999533i	$-0.509732\pi$
$733$	−1.65527	−0.0611387	−0.0305694	+	0.999533i	$0.509732\pi$
$734$	−1.70559	−0.0629545
$735$	−9.32156	−0.343831
$736$	8.13331	0.299798
$737$	−62.6289	−2.30697
$738$	4.43003	0.163071
$739$	−5.41342	−0.199136	−0.0995679	−	0.995031i	$-0.531746\pi$
$739$	−5.41342	−0.199136	−0.0995679	+	0.995031i	$0.531746\pi$
$740$	−23.1837	−0.852248
$741$	−17.7303	−0.651339
$742$	−1.34766	−0.0494741
$743$	−35.3874	−1.29824	−0.649120	−	0.760686i	$-0.724863\pi$
$743$	−35.3874	−1.29824	−0.649120	+	0.760686i	$0.724863\pi$
$744$	30.0860	1.10301
$745$	−1.24621	−0.0456577
$746$	−13.4017	−0.490670
$747$	6.24355	0.228439
$748$	−24.4506	−0.894002
$749$	12.9763	0.474143
$750$	49.1503	1.79471
$751$	21.3373	0.778609	0.389305	−	0.921109i	$-0.372715\pi$
$751$	21.3373	0.778609	0.389305	+	0.921109i	$0.372715\pi$
$752$	−10.9820	−0.400474
$753$	−26.8402	−0.978112
$754$	−13.7979	−0.502489
$755$	−24.8188	−0.903248
$756$	−0.271567	−0.00987680
$757$	−12.5426	−0.455868	−0.227934	−	0.973677i	$-0.573197\pi$
$757$	−12.5426	−0.455868	−0.227934	+	0.973677i	$0.573197\pi$
$758$	−5.20995	−0.189234
$759$	27.6904	1.00510
$760$	54.2159	1.96662
$761$	46.9566	1.70218	0.851089	−	0.525022i	$-0.175943\pi$
$761$	46.9566	1.70218	0.851089	+	0.525022i	$0.175943\pi$
$762$	12.3374	0.446935
$763$	9.36731	0.339120
$764$	−13.6825	−0.495014
$765$	56.1182	2.02896
$766$	−34.8430	−1.25893
$767$	−10.7939	−0.389744
$768$	−38.2067	−1.37867
$769$	28.8811	1.04148	0.520739	−	0.853716i	$-0.325656\pi$
$769$	28.8811	1.04148	0.520739	+	0.853716i	$0.325656\pi$
$770$	25.0469	0.902627
$771$	−15.3369	−0.552344
$772$	1.64619	0.0592478
$773$	47.4997	1.70845	0.854223	−	0.519908i	$-0.174034\pi$
$773$	47.4997	1.70845	0.854223	+	0.519908i	$0.174034\pi$
$774$	3.12586	0.112357
$775$	39.8257	1.43058
$776$	−43.6398	−1.56658
$777$	18.0816	0.648673
$778$	−31.2361	−1.11987
$779$	6.50833	0.233185
$780$	11.9842	0.429103
$781$	80.5693	2.88300
$782$	−10.6943	−0.382427
$783$	−2.66744	−0.0953266
$784$	−1.73781	−0.0620646
$785$	−8.51469	−0.303902
$786$	22.3563	0.797423
$787$	−54.5836	−1.94570	−0.972848	−	0.231447i	$-0.925654\pi$
$787$	−54.5836	−1.94570	−0.972848	+	0.231447i	$0.925654\pi$
$788$	−18.8869	−0.672818
$789$	56.1533	1.99911
$790$	62.9627	2.24011
$791$	−0.515443	−0.0183271
$792$	−52.2218	−1.85562
$793$	9.59995	0.340904
$794$	−12.8765	−0.456970
$795$	11.4972	0.407765
$796$	1.87845	0.0665799
$797$	8.63417	0.305838	0.152919	−	0.988239i	$-0.451133\pi$
$797$	8.63417	0.305838	0.152919	+	0.988239i	$0.451133\pi$
$798$	−12.1475	−0.430017
$799$	−32.1945	−1.13896
$800$	−41.5963	−1.47065
$801$	11.7235	0.414230
$802$	34.4808	1.21756
$803$	16.7121	0.589759
$804$	−20.5306	−0.724059
$805$	−7.39752	−0.260728
$806$	−7.06278	−0.248776
$807$	43.1688	1.51961
$808$	−8.09095	−0.284639
$809$	−41.7646	−1.46837	−0.734183	−	0.678952i	$-0.762434\pi$
$809$	−41.7646	−1.46837	−0.734183	+	0.678952i	$0.762434\pi$
$810$	−39.5386	−1.38925
$811$	12.2988	0.431868	0.215934	−	0.976408i	$-0.430720\pi$
$811$	12.2988	0.431868	0.215934	+	0.976408i	$0.430720\pi$
$812$	6.38342	0.224014
$813$	−43.7942	−1.53593
$814$	−48.5849	−1.70290
$815$	−33.6895	−1.18009
$816$	21.4330	0.750304
$817$	4.59233	0.160665
$818$	17.3425	0.606366
$819$	−4.56245	−0.159425
$820$	−4.39909	−0.153623
$821$	−31.3138	−1.09286	−0.546430	−	0.837505i	$-0.684014\pi$
$821$	−31.3138	−1.09286	−0.546430	+	0.837505i	$0.684014\pi$
$822$	−40.8201	−1.42377
$823$	−9.67687	−0.337315	−0.168657	−	0.985675i	$-0.553943\pi$
$823$	−9.67687	−0.337315	−0.168657	+	0.985675i	$0.553943\pi$
$824$	−10.1847	−0.354802
$825$	−141.617	−4.93048
$826$	−7.39518	−0.257311
$827$	−11.1983	−0.389403	−0.194702	−	0.980863i	$-0.562374\pi$
$827$	−11.1983	−0.389403	−0.194702	+	0.980863i	$0.562374\pi$
$828$	4.43089	0.153984
$829$	38.3359	1.33146	0.665730	−	0.746192i	$-0.268120\pi$
$829$	38.3359	1.33146	0.665730	+	0.746192i	$0.268120\pi$
$830$	9.18160	0.318698
$831$	−26.8044	−0.929834
$832$	12.9196	0.447908
$833$	−5.09448	−0.176513
$834$	50.4096	1.74554
$835$	26.2355	0.907918
$836$	−22.0405	−0.762288
$837$	−1.36539	−0.0471949
$838$	−19.1483	−0.661467
$839$	−20.6731	−0.713714	−0.356857	−	0.934159i	$-0.616152\pi$
$839$	−20.6731	−0.713714	−0.356857	+	0.934159i	$0.616152\pi$
$840$	28.5808	0.986131
$841$	33.7005	1.16209
$842$	−14.4948	−0.499523
$843$	28.5336	0.982749
$844$	4.04541	0.139249
$845$	40.2625	1.38507
$846$	−19.7538	−0.679150
$847$	−24.4440	−0.839905
$848$	2.14342	0.0736054
$849$	−28.8876	−0.991420
$850$	54.6940	1.87599
$851$	14.3494	0.491891
$852$	26.4117	0.904850
$853$	15.8745	0.543532	0.271766	−	0.962363i	$-0.412392\pi$
$853$	15.8745	0.543532	0.271766	+	0.962363i	$0.412392\pi$
$854$	6.57719	0.225067
$855$	50.5867	1.73003
$856$	−39.7865	−1.35987
$857$	−8.81251	−0.301030	−0.150515	−	0.988608i	$-0.548093\pi$
$857$	−8.81251	−0.301030	−0.150515	+	0.988608i	$0.548093\pi$
$858$	25.1147	0.857403
$859$	8.06809	0.275280	0.137640	−	0.990482i	$-0.456048\pi$
$859$	8.06809	0.275280	0.137640	+	0.990482i	$0.456048\pi$
$860$	−3.10403	−0.105847
$861$	3.43097	0.116927
$862$	−14.1599	−0.482289
$863$	12.1082	0.412169	0.206084	−	0.978534i	$-0.433928\pi$
$863$	12.1082	0.412169	0.206084	+	0.978534i	$0.433928\pi$
$864$	1.42610	0.0485168
$865$	71.8396	2.44262
$866$	−26.9779	−0.916746
$867$	21.6763	0.736167
$868$	3.26751	0.110906
$869$	−89.0989	−3.02247
$870$	80.6489	2.73425
$871$	16.7767	0.568457
$872$	−28.7211	−0.972619
$873$	−40.7185	−1.37811
$874$	−9.64018	−0.326084
$875$	18.5811	0.628156
$876$	5.47847	0.185100
$877$	−36.4929	−1.23228	−0.616138	−	0.787638i	$-0.711304\pi$
$877$	−36.4929	−1.23228	−0.616138	+	0.787638i	$0.711304\pi$
$878$	−9.81145	−0.331120
$879$	−5.32818	−0.179715
$880$	−39.8365	−1.34289
$881$	16.2090	0.546095	0.273047	−	0.962001i	$-0.411968\pi$
$881$	16.2090	0.546095	0.273047	+	0.962001i	$0.411968\pi$
$882$	−3.12586	−0.105253
$883$	12.0114	0.404215	0.202107	−	0.979363i	$-0.435221\pi$
$883$	12.0114	0.404215	0.202107	+	0.979363i	$0.435221\pi$
$884$	6.54969	0.220290
$885$	63.0903	2.12076
$886$	−24.0140	−0.806766
$887$	−36.9421	−1.24040	−0.620198	−	0.784446i	$-0.712948\pi$
$887$	−36.9421	−1.24040	−0.620198	+	0.784446i	$0.712948\pi$
$888$	−55.4398	−1.86044
$889$	4.66410	0.156429
$890$	17.2403	0.577896
$891$	55.9513	1.87444
$892$	13.3855	0.448180
$893$	−29.0211	−0.971155
$894$	−0.856127	−0.0286332
$895$	49.5822	1.65735
$896$	0.384798	0.0128552
$897$	−7.41756	−0.247665
$898$	−22.3996	−0.747484
$899$	32.0948	1.07042
$900$	−22.6610	−0.755365
$901$	6.28356	0.209336
$902$	−9.21896	−0.306958
$903$	2.42092	0.0805632
$904$	1.58040	0.0525633
$905$	66.8547	2.22233
$906$	−17.0501	−0.566452
$907$	−13.8924	−0.461290	−0.230645	−	0.973038i	$-0.574084\pi$
$907$	−13.8924	−0.461290	−0.230645	+	0.973038i	$0.574084\pi$
$908$	21.8384	0.724732
$909$	−7.54934	−0.250396
$910$	−6.70942	−0.222415
$911$	−34.7150	−1.15016	−0.575080	−	0.818097i	$-0.695029\pi$
$911$	−34.7150	−1.15016	−0.575080	+	0.818097i	$0.695029\pi$
$912$	19.3204	0.639761
$913$	−12.9929	−0.430003
$914$	24.9561	0.825474
$915$	−56.1119	−1.85500
$916$	5.71084	0.188691
$917$	8.45173	0.279101
$918$	−1.87514	−0.0618888
$919$	−29.6657	−0.978583	−0.489291	−	0.872120i	$-0.662745\pi$
$919$	−29.6657	−0.978583	−0.489291	+	0.872120i	$0.662745\pi$
$920$	22.6815	0.747787
$921$	22.0969	0.728118
$922$	30.6660	1.00993
$923$	−21.5825	−0.710395
$924$	−11.6190	−0.382238
$925$	−73.3873	−2.41296
$926$	−26.7243	−0.878214
$927$	−9.50297	−0.312118
$928$	−33.5216	−1.10040
$929$	24.1242	0.791490	0.395745	−	0.918360i	$-0.370486\pi$
$929$	24.1242	0.791490	0.395745	+	0.918360i	$0.370486\pi$
$930$	41.2821	1.35369
$931$	−4.59233	−0.150508
$932$	1.22632	0.0401696
$933$	22.1888	0.726428
$934$	11.9929	0.392420
$935$	−116.783	−3.81921
$936$	13.9889	0.457242
$937$	−17.1631	−0.560695	−0.280348	−	0.959899i	$-0.590450\pi$
$937$	−17.1631	−0.560695	−0.280348	+	0.959899i	$0.590450\pi$
$938$	11.4942	0.375298
$939$	40.2041	1.31201
$940$	19.6159	0.639799
$941$	−18.4514	−0.601498	−0.300749	−	0.953703i	$-0.597237\pi$
$941$	−18.4514	−0.601498	−0.300749	+	0.953703i	$0.597237\pi$
$942$	−5.84945	−0.190585
$943$	2.72279	0.0886663
$944$	11.7619	0.382816
$945$	−1.29708	−0.0421941
$946$	−6.50497	−0.211495
$947$	−38.1114	−1.23845	−0.619227	−	0.785212i	$-0.712554\pi$
$947$	−38.1114	−1.23845	−0.619227	+	0.785212i	$0.712554\pi$
$948$	−29.2078	−0.948627
$949$	−4.47676	−0.145322
$950$	49.3029	1.59960
$951$	61.0819	1.98072
$952$	15.6202	0.506253
$953$	29.2642	0.947960	0.473980	−	0.880536i	$-0.342817\pi$
$953$	29.2642	0.947960	0.473980	+	0.880536i	$0.342817\pi$
$954$	3.85545	0.124825
$955$	−65.3514	−2.11472
$956$	18.3583	0.593749
$957$	−114.127	−3.68919
$958$	30.7025	0.991954
$959$	−15.4319	−0.498323
$960$	−75.5155	−2.43725
$961$	−14.5715	−0.470049
$962$	13.0147	0.419609
$963$	−37.1232	−1.19628
$964$	−6.01033	−0.193580
$965$	7.86269	0.253109
$966$	−5.08197	−0.163510
$967$	−43.9933	−1.41473	−0.707364	−	0.706850i	$-0.750116\pi$
$967$	−43.9933	−1.41473	−0.707364	+	0.706850i	$0.750116\pi$
$968$	74.9476	2.40891
$969$	56.6387	1.81950
$970$	−59.8796	−1.92262
$971$	−5.60326	−0.179817	−0.0899087	−	0.995950i	$-0.528658\pi$
$971$	−5.60326	−0.179817	−0.0899087	+	0.995950i	$0.528658\pi$
$972$	17.5269	0.562176
$973$	19.0572	0.610946
$974$	32.9123	1.05458
$975$	37.9357	1.21491
$976$	−10.4609	−0.334845
$977$	39.5893	1.26657	0.633287	−	0.773917i	$-0.281705\pi$
$977$	39.5893	1.26657	0.633287	+	0.773917i	$0.281705\pi$
$978$	−23.1441	−0.740068
$979$	−24.3968	−0.779726
$980$	3.10403	0.0991546
$981$	−26.7985	−0.855610
$982$	−0.646424	−0.0206282
$983$	−17.7419	−0.565877	−0.282939	−	0.959138i	$-0.591309\pi$
$983$	−17.7419	−0.565877	−0.282939	+	0.959138i	$0.591309\pi$
$984$	−10.5197	−0.335355
$985$	−90.2093	−2.87431
$986$	44.0768	1.40369
$987$	−15.2989	−0.486971
$988$	5.90410	0.187834
$989$	1.92122	0.0610913
$990$	−71.6554	−2.27736
$991$	−39.4489	−1.25314	−0.626568	−	0.779367i	$-0.715541\pi$
$991$	−39.4489	−1.25314	−0.626568	+	0.779367i	$0.715541\pi$
$992$	−17.1589	−0.544794
$993$	−44.4279	−1.40988
$994$	−14.7867	−0.469007
$995$	8.97201	0.284432
$996$	−4.25926	−0.134960
$997$	−15.4833	−0.490362	−0.245181	−	0.969477i	$-0.578847\pi$
$997$	−15.4833	−0.490362	−0.245181	+	0.969477i	$0.578847\pi$
$998$	21.5146	0.681032
$999$	2.51603	0.0796036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	301.2.a.b.1.2	✓	5
3.2	odd	2		2709.2.a.k.1.4		5
4.3	odd	2		4816.2.a.s.1.1		5
5.4	even	2		7525.2.a.g.1.4		5
7.6	odd	2		2107.2.a.f.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
301.2.a.b.1.2	✓	5	1.1	even	1	trivial
2107.2.a.f.1.2		5	7.6	odd	2
2709.2.a.k.1.4		5	3.2	odd	2
4816.2.a.s.1.1		5	4.3	odd	2
7525.2.a.g.1.4		5	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:	\( N \)	\(=\)	\( 301 = 7 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	301.a (trivial)

\(f(q)\)	\(=\)	\(q-1.09263 q^{2} +2.42092 q^{3} -0.806154 q^{4} -3.85042 q^{5} -2.64518 q^{6} -1.00000 q^{7} +3.06610 q^{8} +2.86085 q^{9} +O(q^{10})\)	\(q-1.09263 q^{2} +2.42092 q^{3} -0.806154 q^{4} -3.85042 q^{5} -2.64518 q^{6} -1.00000 q^{7} +3.06610 q^{8} +2.86085 q^{9} +4.20709 q^{10} -5.95348 q^{11} -1.95163 q^{12} +1.59479 q^{13} +1.09263 q^{14} -9.32156 q^{15} -1.73781 q^{16} -5.09448 q^{17} -3.12586 q^{18} -4.59233 q^{19} +3.10403 q^{20} -2.42092 q^{21} +6.50497 q^{22} -1.92122 q^{23} +7.42277 q^{24} +9.82573 q^{25} -1.74252 q^{26} -0.336868 q^{27} +0.806154 q^{28} +7.91837 q^{29} +10.1850 q^{30} +4.05321 q^{31} -4.23340 q^{32} -14.4129 q^{33} +5.56640 q^{34} +3.85042 q^{35} -2.30629 q^{36} -7.46889 q^{37} +5.01773 q^{38} +3.86085 q^{39} -11.8058 q^{40} -1.41722 q^{41} +2.64518 q^{42} -1.00000 q^{43} +4.79942 q^{44} -11.0155 q^{45} +2.09919 q^{46} +6.31948 q^{47} -4.20709 q^{48} +1.00000 q^{49} -10.7359 q^{50} -12.3333 q^{51} -1.28564 q^{52} -1.23340 q^{53} +0.368073 q^{54} +22.9234 q^{55} -3.06610 q^{56} -11.1177 q^{57} -8.65187 q^{58} -6.76822 q^{59} +7.51461 q^{60} +6.01958 q^{61} -4.42867 q^{62} -2.86085 q^{63} +8.10117 q^{64} -6.14060 q^{65} +15.7480 q^{66} +10.5197 q^{67} +4.10694 q^{68} -4.65113 q^{69} -4.20709 q^{70} -13.5331 q^{71} +8.77164 q^{72} -2.80712 q^{73} +8.16075 q^{74} +23.7873 q^{75} +3.70212 q^{76} +5.95348 q^{77} -4.21849 q^{78} +14.9658 q^{79} +6.69129 q^{80} -9.39808 q^{81} +1.54850 q^{82} +2.18241 q^{83} +1.95163 q^{84} +19.6159 q^{85} +1.09263 q^{86} +19.1697 q^{87} -18.2540 q^{88} +4.09791 q^{89} +12.0359 q^{90} -1.59479 q^{91} +1.54880 q^{92} +9.81248 q^{93} -6.90487 q^{94} +17.6824 q^{95} -10.2487 q^{96} -14.2330 q^{97} -1.09263 q^{98} -17.0320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{3} + 2 q^{4} - 6 q^{5} - 10 q^{6} - 5 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 5 * q - 3 * q^3 + 2 * q^4 - 6 * q^5 - 10 * q^6 - 5 * q^7 - 3 * q^8 + 6 * q^9	\( 5 q - 3 q^{3} + 2 q^{4} - 6 q^{5} - 10 q^{6} - 5 q^{7} - 3 q^{8} + 6 q^{9} - q^{10} - 16 q^{11} - 8 q^{12} - 2 q^{13} - 8 q^{15} - 8 q^{17} + 17 q^{18} - 10 q^{19} - 6 q^{20} + 3 q^{21} - 5 q^{22} - 2 q^{23} + 10 q^{24} + 11 q^{25} - 24 q^{26} - 9 q^{27} - 2 q^{28} - 4 q^{29} + 24 q^{30} - 6 q^{31} + 4 q^{32} + 14 q^{33} + 17 q^{34} + 6 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + 11 q^{39} - 20 q^{40} - 16 q^{41} + 10 q^{42} - 5 q^{43} - 11 q^{44} - 14 q^{45} + 17 q^{46} - 11 q^{47} + q^{48} + 5 q^{49} + 12 q^{50} - 6 q^{51} + 24 q^{52} + 19 q^{53} - 23 q^{54} + 25 q^{55} + 3 q^{56} - 5 q^{57} - 31 q^{59} + 43 q^{60} - 2 q^{61} + 7 q^{62} - 6 q^{63} - 17 q^{64} + 6 q^{65} + 59 q^{66} + 11 q^{67} + 13 q^{68} - 17 q^{69} + q^{70} - 15 q^{71} + 23 q^{72} + 13 q^{73} + 22 q^{74} + 4 q^{75} + 34 q^{76} + 16 q^{77} + 17 q^{78} + 24 q^{79} + 11 q^{80} + 5 q^{81} - 36 q^{83} + 8 q^{84} - 19 q^{85} + 23 q^{87} - 13 q^{88} - 15 q^{89} - 17 q^{90} + 2 q^{91} - 35 q^{92} + 39 q^{93} + 32 q^{94} - 14 q^{95} - 2 q^{96} - 13 q^{97} - 63 q^{99}+O(q^{100}) \) 5 * q - 3 * q^3 + 2 * q^4 - 6 * q^5 - 10 * q^6 - 5 * q^7 - 3 * q^8 + 6 * q^9 - q^10 - 16 * q^11 - 8 * q^12 - 2 * q^13 - 8 * q^15 - 8 * q^17 + 17 * q^18 - 10 * q^19 - 6 * q^20 + 3 * q^21 - 5 * q^22 - 2 * q^23 + 10 * q^24 + 11 * q^25 - 24 * q^26 - 9 * q^27 - 2 * q^28 - 4 * q^29 + 24 * q^30 - 6 * q^31 + 4 * q^32 + 14 * q^33 + 17 * q^34 + 6 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + 11 * q^39 - 20 * q^40 - 16 * q^41 + 10 * q^42 - 5 * q^43 - 11 * q^44 - 14 * q^45 + 17 * q^46 - 11 * q^47 + q^48 + 5 * q^49 + 12 * q^50 - 6 * q^51 + 24 * q^52 + 19 * q^53 - 23 * q^54 + 25 * q^55 + 3 * q^56 - 5 * q^57 - 31 * q^59 + 43 * q^60 - 2 * q^61 + 7 * q^62 - 6 * q^63 - 17 * q^64 + 6 * q^65 + 59 * q^66 + 11 * q^67 + 13 * q^68 - 17 * q^69 + q^70 - 15 * q^71 + 23 * q^72 + 13 * q^73 + 22 * q^74 + 4 * q^75 + 34 * q^76 + 16 * q^77 + 17 * q^78 + 24 * q^79 + 11 * q^80 + 5 * q^81 - 36 * q^83 + 8 * q^84 - 19 * q^85 + 23 * q^87 - 13 * q^88 - 15 * q^89 - 17 * q^90 + 2 * q^91 - 35 * q^92 + 39 * q^93 + 32 * q^94 - 14 * q^95 - 2 * q^96 - 13 * q^97 - 63 * q^99

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