LMFDB - Embedded newform 935.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(1,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.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:	$7.46601258899$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 21 x^{9} + 20 x^{8} + 161 x^{7} - 148 x^{6} - 536 x^{5} + 481 x^{4} + 689 x^{3} + \cdots + 61 $ x^11 - x^10 - 21x^9 + 20x^8 + 161x^7 - 148x^6 - 536x^5 + 481x^4 + 689x^3 - 587x^2 - 156*x + 61
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.23394$ of defining polynomial
Character	$\chi$	$=$	935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.23394 q^{2} +1.33781 q^{3} -0.477390 q^{4} +1.00000 q^{5} -1.65077 q^{6} -2.41473 q^{7} +3.05695 q^{8} -1.21027 q^{9} +O(q^{10})$	\(q-1.23394 q^{2} +1.33781 q^{3} -0.477390 q^{4} +1.00000 q^{5} -1.65077 q^{6} -2.41473 q^{7} +3.05695 q^{8} -1.21027 q^{9} -1.23394 q^{10} -1.00000 q^{11} -0.638655 q^{12} +5.99070 q^{13} +2.97963 q^{14} +1.33781 q^{15} -2.81732 q^{16} -1.00000 q^{17} +1.49340 q^{18} -3.44044 q^{19} -0.477390 q^{20} -3.23044 q^{21} +1.23394 q^{22} +8.43743 q^{23} +4.08961 q^{24} +1.00000 q^{25} -7.39218 q^{26} -5.63253 q^{27} +1.15277 q^{28} +3.64537 q^{29} -1.65077 q^{30} +8.98705 q^{31} -2.63750 q^{32} -1.33781 q^{33} +1.23394 q^{34} -2.41473 q^{35} +0.577772 q^{36} +4.91313 q^{37} +4.24530 q^{38} +8.01441 q^{39} +3.05695 q^{40} +11.0117 q^{41} +3.98618 q^{42} -8.45703 q^{43} +0.477390 q^{44} -1.21027 q^{45} -10.4113 q^{46} +4.79052 q^{47} -3.76903 q^{48} -1.16908 q^{49} -1.23394 q^{50} -1.33781 q^{51} -2.85990 q^{52} +1.90119 q^{53} +6.95021 q^{54} -1.00000 q^{55} -7.38172 q^{56} -4.60264 q^{57} -4.49817 q^{58} -6.48062 q^{59} -0.638655 q^{60} +1.96375 q^{61} -11.0895 q^{62} +2.92248 q^{63} +8.88916 q^{64} +5.99070 q^{65} +1.65077 q^{66} +9.36951 q^{67} +0.477390 q^{68} +11.2877 q^{69} +2.97963 q^{70} +4.63594 q^{71} -3.69974 q^{72} -6.01487 q^{73} -6.06251 q^{74} +1.33781 q^{75} +1.64243 q^{76} +2.41473 q^{77} -9.88931 q^{78} +9.30990 q^{79} -2.81732 q^{80} -3.90442 q^{81} -13.5878 q^{82} -6.34804 q^{83} +1.54218 q^{84} -1.00000 q^{85} +10.4355 q^{86} +4.87680 q^{87} -3.05695 q^{88} +2.98945 q^{89} +1.49340 q^{90} -14.4659 q^{91} -4.02794 q^{92} +12.0229 q^{93} -5.91122 q^{94} -3.44044 q^{95} -3.52847 q^{96} +14.4946 q^{97} +1.44257 q^{98} +1.21027 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - q^{2} + 5 q^{3} + 21 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} + 26 q^{9}+O(q^{10}) $ 11 * q - q^2 + 5 * q^3 + 21 * q^4 + 11 * q^5 + q^6 - 2 * q^7 + 26 * q^9	\( 11 q - q^{2} + 5 q^{3} + 21 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} + 26 q^{9} - q^{10} - 11 q^{11} + 8 q^{12} + 13 q^{13} + 5 q^{15} + 29 q^{16} - 11 q^{17} + 3 q^{18} + 4 q^{19} + 21 q^{20} + 34 q^{21} + q^{22} - 7 q^{23} - 29 q^{24} + 11 q^{25} + 4 q^{26} + 14 q^{27} + 8 q^{28} + 9 q^{29} + q^{30} + 20 q^{31} - 26 q^{32} - 5 q^{33} + q^{34} - 2 q^{35} + 62 q^{36} - q^{37} - 6 q^{39} - 9 q^{41} - 74 q^{42} + 5 q^{43} - 21 q^{44} + 26 q^{45} - 10 q^{46} + 24 q^{48} + 43 q^{49} - q^{50} - 5 q^{51} + 18 q^{52} + 14 q^{53} - 9 q^{54} - 11 q^{55} - 6 q^{56} - 32 q^{57} - 10 q^{58} + 13 q^{59} + 8 q^{60} + 11 q^{61} - 26 q^{62} - 40 q^{63} + 24 q^{64} + 13 q^{65} - q^{66} + 26 q^{67} - 21 q^{68} + 56 q^{69} - 8 q^{71} - 26 q^{72} + 42 q^{73} + 16 q^{74} + 5 q^{75} - 70 q^{76} + 2 q^{77} - 56 q^{78} - 27 q^{79} + 29 q^{80} + 71 q^{81} + 57 q^{82} - 41 q^{83} + 76 q^{84} - 11 q^{85} + 47 q^{86} + 26 q^{87} + 37 q^{89} + 3 q^{90} + 30 q^{91} - 47 q^{92} - 8 q^{93} + 94 q^{94} + 4 q^{95} - 154 q^{96} + 29 q^{97} - 69 q^{98} - 26 q^{99}+O(q^{100}) \) 11 * q - q^2 + 5 * q^3 + 21 * q^4 + 11 * q^5 + q^6 - 2 * q^7 + 26 * q^9 - q^10 - 11 * q^11 + 8 * q^12 + 13 * q^13 + 5 * q^15 + 29 * q^16 - 11 * q^17 + 3 * q^18 + 4 * q^19 + 21 * q^20 + 34 * q^21 + q^22 - 7 * q^23 - 29 * q^24 + 11 * q^25 + 4 * q^26 + 14 * q^27 + 8 * q^28 + 9 * q^29 + q^30 + 20 * q^31 - 26 * q^32 - 5 * q^33 + q^34 - 2 * q^35 + 62 * q^36 - q^37 - 6 * q^39 - 9 * q^41 - 74 * q^42 + 5 * q^43 - 21 * q^44 + 26 * q^45 - 10 * q^46 + 24 * q^48 + 43 * q^49 - q^50 - 5 * q^51 + 18 * q^52 + 14 * q^53 - 9 * q^54 - 11 * q^55 - 6 * q^56 - 32 * q^57 - 10 * q^58 + 13 * q^59 + 8 * q^60 + 11 * q^61 - 26 * q^62 - 40 * q^63 + 24 * q^64 + 13 * q^65 - q^66 + 26 * q^67 - 21 * q^68 + 56 * q^69 - 8 * q^71 - 26 * q^72 + 42 * q^73 + 16 * q^74 + 5 * q^75 - 70 * q^76 + 2 * q^77 - 56 * q^78 - 27 * q^79 + 29 * q^80 + 71 * q^81 + 57 * q^82 - 41 * q^83 + 76 * q^84 - 11 * q^85 + 47 * q^86 + 26 * q^87 + 37 * q^89 + 3 * q^90 + 30 * q^91 - 47 * q^92 - 8 * q^93 + 94 * q^94 + 4 * q^95 - 154 * q^96 + 29 * q^97 - 69 * q^98 - 26 * 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 $

$2$	−1.23394	−0.872528	−0.436264	−	0.899819i	$-0.643699\pi$
$2$	−1.23394	−0.872528	−0.436264	+	0.899819i	$0.643699\pi$
$3$	1.33781	0.772383	0.386192	−	0.922419i	$-0.373790\pi$
$3$	1.33781	0.772383	0.386192	+	0.922419i	$0.373790\pi$
$4$	−0.477390	−0.238695
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.65077	−0.673926
$7$	−2.41473	−0.912682	−0.456341	−	0.889805i	$-0.650840\pi$
$7$	−2.41473	−0.912682	−0.456341	+	0.889805i	$0.650840\pi$
$8$	3.05695	1.08080
$9$	−1.21027	−0.403424
$10$	−1.23394	−0.390206
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.638655	−0.184364
$13$	5.99070	1.66152	0.830761	−	0.556629i	$-0.187905\pi$
$13$	5.99070	1.66152	0.830761	+	0.556629i	$0.187905\pi$
$14$	2.97963	0.796341
$15$	1.33781	0.345420
$16$	−2.81732	−0.704330
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.49340	0.351999
$19$	−3.44044	−0.789291	−0.394645	−	0.918834i	$-0.629133\pi$
$19$	−3.44044	−0.789291	−0.394645	+	0.918834i	$0.629133\pi$
$20$	−0.477390	−0.106748
$21$	−3.23044	−0.704940
$22$	1.23394	0.263077
$23$	8.43743	1.75933	0.879663	−	0.475597i	$-0.157768\pi$
$23$	8.43743	1.75933	0.879663	+	0.475597i	$0.157768\pi$
$24$	4.08961	0.834789
$25$	1.00000	0.200000
$26$	−7.39218	−1.44972
$27$	−5.63253	−1.08398
$28$	1.15277	0.217853
$29$	3.64537	0.676928	0.338464	−	0.940979i	$-0.390093\pi$
$29$	3.64537	0.676928	0.338464	+	0.940979i	$0.390093\pi$
$30$	−1.65077	−0.301389
$31$	8.98705	1.61412	0.807061	−	0.590468i	$-0.201057\pi$
$31$	8.98705	1.61412	0.807061	+	0.590468i	$0.201057\pi$
$32$	−2.63750	−0.466248
$33$	−1.33781	−0.232882
$34$	1.23394	0.211619
$35$	−2.41473	−0.408164
$36$	0.577772	0.0962953
$37$	4.91313	0.807713	0.403856	−	0.914822i	$-0.367670\pi$
$37$	4.91313	0.807713	0.403856	+	0.914822i	$0.367670\pi$
$38$	4.24530	0.688678
$39$	8.01441	1.28333
$40$	3.05695	0.483347
$41$	11.0117	1.71974	0.859868	−	0.510517i	$-0.170546\pi$
$41$	11.0117	1.71974	0.859868	+	0.510517i	$0.170546\pi$
$42$	3.98618	0.615080
$43$	−8.45703	−1.28969	−0.644843	−	0.764315i	$-0.723077\pi$
$43$	−8.45703	−1.28969	−0.644843	+	0.764315i	$0.723077\pi$
$44$	0.477390	0.0719692
$45$	−1.21027	−0.180417
$46$	−10.4113	−1.53506
$47$	4.79052	0.698769	0.349385	−	0.936979i	$-0.386391\pi$
$47$	4.79052	0.698769	0.349385	+	0.936979i	$0.386391\pi$
$48$	−3.76903	−0.544013
$49$	−1.16908	−0.167011
$50$	−1.23394	−0.174506
$51$	−1.33781	−0.187330
$52$	−2.85990	−0.396597
$53$	1.90119	0.261148	0.130574	−	0.991439i	$-0.458318\pi$
$53$	1.90119	0.261148	0.130574	+	0.991439i	$0.458318\pi$
$54$	6.95021	0.945804
$55$	−1.00000	−0.134840
$56$	−7.38172	−0.986423
$57$	−4.60264	−0.609635
$58$	−4.49817	−0.590638
$59$	−6.48062	−0.843705	−0.421853	−	0.906664i	$-0.638620\pi$
$59$	−6.48062	−0.843705	−0.421853	+	0.906664i	$0.638620\pi$
$60$	−0.638655	−0.0824501
$61$	1.96375	0.251432	0.125716	−	0.992066i	$-0.459877\pi$
$61$	1.96375	0.251432	0.125716	+	0.992066i	$0.459877\pi$
$62$	−11.0895	−1.40837
$63$	2.92248	0.368198
$64$	8.88916	1.11114
$65$	5.99070	0.743055
$66$	1.65077	0.203196
$67$	9.36951	1.14467	0.572334	−	0.820021i	$-0.306038\pi$
$67$	9.36951	1.14467	0.572334	+	0.820021i	$0.306038\pi$
$68$	0.477390	0.0578920
$69$	11.2877	1.35887
$70$	2.97963	0.356134
$71$	4.63594	0.550185	0.275092	−	0.961418i	$-0.411292\pi$
$71$	4.63594	0.550185	0.275092	+	0.961418i	$0.411292\pi$
$72$	−3.69974	−0.436019
$73$	−6.01487	−0.703987	−0.351994	−	0.936002i	$-0.614496\pi$
$73$	−6.01487	−0.703987	−0.351994	+	0.936002i	$0.614496\pi$
$74$	−6.06251	−0.704752
$75$	1.33781	0.154477
$76$	1.64243	0.188400
$77$	2.41473	0.275184
$78$	−9.88931	−1.11974
$79$	9.30990	1.04745	0.523723	−	0.851889i	$-0.324543\pi$
$79$	9.30990	1.04745	0.523723	+	0.851889i	$0.324543\pi$
$80$	−2.81732	−0.314986
$81$	−3.90442	−0.433825
$82$	−13.5878	−1.50052
$83$	−6.34804	−0.696788	−0.348394	−	0.937348i	$-0.613273\pi$
$83$	−6.34804	−0.696788	−0.348394	+	0.937348i	$0.613273\pi$
$84$	1.54218	0.168266
$85$	−1.00000	−0.108465
$86$	10.4355	1.12529
$87$	4.87680	0.522848
$88$	−3.05695	−0.325872
$89$	2.98945	0.316881	0.158441	−	0.987368i	$-0.449353\pi$
$89$	2.98945	0.316881	0.158441	+	0.987368i	$0.449353\pi$
$90$	1.49340	0.157419
$91$	−14.4659	−1.51644
$92$	−4.02794	−0.419942
$93$	12.0229	1.24672
$94$	−5.91122	−0.609696
$95$	−3.44044	−0.352982
$96$	−3.52847	−0.360122
$97$	14.4946	1.47171	0.735854	−	0.677140i	$-0.236781\pi$
$97$	14.4946	1.47171	0.735854	+	0.677140i	$0.236781\pi$
$98$	1.44257	0.145722
$99$	1.21027	0.121637
$100$	−0.477390	−0.0477390
$101$	10.3233	1.02721	0.513605	−	0.858027i	$-0.328310\pi$
$101$	10.3233	1.02721	0.513605	+	0.858027i	$0.328310\pi$
$102$	1.65077	0.163451
$103$	3.70840	0.365400	0.182700	−	0.983169i	$-0.441516\pi$
$103$	3.70840	0.365400	0.182700	+	0.983169i	$0.441516\pi$
$104$	18.3133	1.79577
$105$	−3.23044	−0.315259
$106$	−2.34595	−0.227859
$107$	−20.2079	−1.95358	−0.976788	−	0.214209i	$-0.931283\pi$
$107$	−20.2079	−1.95358	−0.976788	+	0.214209i	$0.931283\pi$
$108$	2.68891	0.258741
$109$	6.50276	0.622852	0.311426	−	0.950270i	$-0.399193\pi$
$109$	6.50276	0.622852	0.311426	+	0.950270i	$0.399193\pi$
$110$	1.23394	0.117652
$111$	6.57281	0.623864
$112$	6.80307	0.642829
$113$	−2.73362	−0.257157	−0.128579	−	0.991699i	$-0.541041\pi$
$113$	−2.73362	−0.257157	−0.128579	+	0.991699i	$0.541041\pi$
$114$	5.67939	0.531924
$115$	8.43743	0.786795
$116$	−1.74026	−0.161579
$117$	−7.25038	−0.670298
$118$	7.99671	0.736156
$119$	2.41473	0.221358
$120$	4.08961	0.373329
$121$	1.00000	0.0909091
$122$	−2.42315	−0.219381
$123$	14.7315	1.32829
$124$	−4.29033	−0.385283
$125$	1.00000	0.0894427
$126$	−3.60617	−0.321263
$127$	3.02996	0.268866	0.134433	−	0.990923i	$-0.457079\pi$
$127$	3.02996	0.268866	0.134433	+	0.990923i	$0.457079\pi$
$128$	−5.69370	−0.503256
$129$	−11.3139	−0.996131
$130$	−7.39218	−0.648337
$131$	−4.39116	−0.383658	−0.191829	−	0.981428i	$-0.561442\pi$
$131$	−4.39116	−0.383658	−0.191829	+	0.981428i	$0.561442\pi$
$132$	0.638655	0.0555878
$133$	8.30773	0.720372
$134$	−11.5614	−0.998755
$135$	−5.63253	−0.484771
$136$	−3.05695	−0.262132
$137$	19.9818	1.70716	0.853580	−	0.520961i	$-0.174426\pi$
$137$	19.9818	1.70716	0.853580	+	0.520961i	$0.174426\pi$
$138$	−13.9283	−1.18566
$139$	17.9238	1.52028	0.760139	−	0.649761i	$-0.225131\pi$
$139$	17.9238	1.52028	0.760139	+	0.649761i	$0.225131\pi$
$140$	1.15277	0.0974266
$141$	6.40879	0.539718
$142$	−5.72048	−0.480052
$143$	−5.99070	−0.500968
$144$	3.40972	0.284144
$145$	3.64537	0.302731
$146$	7.42199	0.614248
$147$	−1.56400	−0.128997
$148$	−2.34548	−0.192797
$149$	−20.5661	−1.68484	−0.842422	−	0.538819i	$-0.818871\pi$
$149$	−20.5661	−1.68484	−0.842422	+	0.538819i	$0.818871\pi$
$150$	−1.65077	−0.134785
$151$	−13.3256	−1.08442	−0.542210	−	0.840243i	$-0.682412\pi$
$151$	−13.3256	−1.08442	−0.542210	+	0.840243i	$0.682412\pi$
$152$	−10.5173	−0.853062
$153$	1.21027	0.0978447
$154$	−2.97963	−0.240106
$155$	8.98705	0.721858
$156$	−3.82600	−0.306325
$157$	−3.51594	−0.280603	−0.140301	−	0.990109i	$-0.544807\pi$
$157$	−3.51594	−0.280603	−0.140301	+	0.990109i	$0.544807\pi$
$158$	−11.4879	−0.913925
$159$	2.54342	0.201707
$160$	−2.63750	−0.208513
$161$	−20.3741	−1.60571
$162$	4.81783	0.378524
$163$	−16.0177	−1.25460	−0.627301	−	0.778777i	$-0.715840\pi$
$163$	−16.0177	−1.25460	−0.627301	+	0.778777i	$0.715840\pi$
$164$	−5.25686	−0.410492
$165$	−1.33781	−0.104148
$166$	7.83310	0.607967
$167$	2.84725	0.220327	0.110163	−	0.993913i	$-0.464863\pi$
$167$	2.84725	0.220327	0.110163	+	0.993913i	$0.464863\pi$
$168$	−9.87531	−0.761897
$169$	22.8885	1.76066
$170$	1.23394	0.0946390
$171$	4.16387	0.318419
$172$	4.03730	0.307841
$173$	−19.0302	−1.44684	−0.723418	−	0.690410i	$-0.757430\pi$
$173$	−19.0302	−1.44684	−0.723418	+	0.690410i	$0.757430\pi$
$174$	−6.01768	−0.456199
$175$	−2.41473	−0.182536
$176$	2.81732	0.212363
$177$	−8.66982	−0.651664
$178$	−3.68881	−0.276488
$179$	1.32898	0.0993324	0.0496662	−	0.998766i	$-0.484184\pi$
$179$	1.32898	0.0993324	0.0496662	+	0.998766i	$0.484184\pi$
$180$	0.577772	0.0430645
$181$	15.4937	1.15164	0.575820	−	0.817577i	$-0.304683\pi$
$181$	15.4937	1.15164	0.575820	+	0.817577i	$0.304683\pi$
$182$	17.8501	1.32314
$183$	2.62711	0.194202
$184$	25.7928	1.90147
$185$	4.91313	0.361220
$186$	−14.8356	−1.08780
$187$	1.00000	0.0731272
$188$	−2.28695	−0.166793
$189$	13.6010	0.989330
$190$	4.24530	0.307986
$191$	−15.7278	−1.13803	−0.569013	−	0.822329i	$-0.692674\pi$
$191$	−15.7278	−1.13803	−0.569013	+	0.822329i	$0.692674\pi$
$192$	11.8920	0.858230
$193$	7.31329	0.526422	0.263211	−	0.964738i	$-0.415218\pi$
$193$	7.31329	0.526422	0.263211	+	0.964738i	$0.415218\pi$
$194$	−17.8855	−1.28411
$195$	8.01441	0.573924
$196$	0.558106	0.0398647
$197$	−21.0661	−1.50090	−0.750449	−	0.660929i	$-0.770162\pi$
$197$	−21.0661	−1.50090	−0.750449	+	0.660929i	$0.770162\pi$
$198$	−1.49340	−0.106132
$199$	2.78470	0.197402	0.0987011	−	0.995117i	$-0.468531\pi$
$199$	2.78470	0.197402	0.0987011	+	0.995117i	$0.468531\pi$
$200$	3.05695	0.216159
$201$	12.5346	0.884122
$202$	−12.7384	−0.896270
$203$	−8.80258	−0.617820
$204$	0.638655	0.0447148
$205$	11.0117	0.769089
$206$	−4.57595	−0.318821
$207$	−10.2116	−0.709754
$208$	−16.8777	−1.17026
$209$	3.44044	0.237980
$210$	3.98618	0.275072
$211$	18.5625	1.27790	0.638949	−	0.769249i	$-0.279369\pi$
$211$	18.5625	1.27790	0.638949	+	0.769249i	$0.279369\pi$
$212$	−0.907608	−0.0623348
$213$	6.20199	0.424954
$214$	24.9354	1.70455
$215$	−8.45703	−0.576765
$216$	−17.2184	−1.17156
$217$	−21.7013	−1.47318
$218$	−8.02403	−0.543456
$219$	−8.04673	−0.543748
$220$	0.477390	0.0321856
$221$	−5.99070	−0.402978
$222$	−8.11046	−0.544339
$223$	−17.1138	−1.14603	−0.573013	−	0.819546i	$-0.694226\pi$
$223$	−17.1138	−1.14603	−0.573013	+	0.819546i	$0.694226\pi$
$224$	6.36885	0.425537
$225$	−1.21027	−0.0806848
$226$	3.37312	0.224377
$227$	−29.8924	−1.98403	−0.992013	−	0.126136i	$-0.959742\pi$
$227$	−29.8924	−1.98403	−0.992013	+	0.126136i	$0.959742\pi$
$228$	2.19725	0.145517
$229$	−2.00284	−0.132351	−0.0661757	−	0.997808i	$-0.521080\pi$
$229$	−2.00284	−0.132351	−0.0661757	+	0.997808i	$0.521080\pi$
$230$	−10.4113	−0.686500
$231$	3.23044	0.212548
$232$	11.1437	0.731621
$233$	−12.0095	−0.786767	−0.393383	−	0.919375i	$-0.628695\pi$
$233$	−12.0095	−0.786767	−0.393383	+	0.919375i	$0.628695\pi$
$234$	8.94654	0.584854
$235$	4.79052	0.312499
$236$	3.09378	0.201388
$237$	12.4548	0.809029
$238$	−2.97963	−0.193141
$239$	1.75736	0.113674	0.0568370	−	0.998383i	$-0.481898\pi$
$239$	1.75736	0.113674	0.0568370	+	0.998383i	$0.481898\pi$
$240$	−3.76903	−0.243290
$241$	−18.9940	−1.22351	−0.611754	−	0.791048i	$-0.709536\pi$
$241$	−18.9940	−1.22351	−0.611754	+	0.791048i	$0.709536\pi$
$242$	−1.23394	−0.0793207
$243$	11.6742	0.748902
$244$	−0.937472	−0.0600155
$245$	−1.16908	−0.0746897
$246$	−18.1778	−1.15897
$247$	−20.6106	−1.31142
$248$	27.4730	1.74454
$249$	−8.49245	−0.538187
$250$	−1.23394	−0.0780413
$251$	−1.48343	−0.0936334	−0.0468167	−	0.998903i	$-0.514908\pi$
$251$	−1.48343	−0.0936334	−0.0468167	+	0.998903i	$0.514908\pi$
$252$	−1.39516	−0.0878870
$253$	−8.43743	−0.530457
$254$	−3.73880	−0.234593
$255$	−1.33781	−0.0837767
$256$	−10.7526	−0.672039
$257$	2.58897	0.161496	0.0807478	−	0.996735i	$-0.474269\pi$
$257$	2.58897	0.161496	0.0807478	+	0.996735i	$0.474269\pi$
$258$	13.9607	0.869153
$259$	−11.8639	−0.737185
$260$	−2.85990	−0.177364
$261$	−4.41189	−0.273089
$262$	5.41844	0.334752
$263$	3.93842	0.242853	0.121427	−	0.992600i	$-0.461253\pi$
$263$	3.93842	0.242853	0.121427	+	0.992600i	$0.461253\pi$
$264$	−4.08961	−0.251698
$265$	1.90119	0.116789
$266$	−10.2512	−0.628544
$267$	3.99931	0.244754
$268$	−4.47291	−0.273226
$269$	−13.6803	−0.834102	−0.417051	−	0.908883i	$-0.636936\pi$
$269$	−13.6803	−0.834102	−0.417051	+	0.908883i	$0.636936\pi$
$270$	6.95021	0.422976
$271$	−4.76224	−0.289285	−0.144643	−	0.989484i	$-0.546203\pi$
$271$	−4.76224	−0.289285	−0.144643	+	0.989484i	$0.546203\pi$
$272$	2.81732	0.170825
$273$	−19.3526	−1.17127
$274$	−24.6564	−1.48955
$275$	−1.00000	−0.0603023
$276$	−5.38861	−0.324356
$277$	−11.6893	−0.702344	−0.351172	−	0.936311i	$-0.614217\pi$
$277$	−11.6893	−0.702344	−0.351172	+	0.936311i	$0.614217\pi$
$278$	−22.1169	−1.32648
$279$	−10.8768	−0.651176
$280$	−7.38172	−0.441142
$281$	−9.05001	−0.539878	−0.269939	−	0.962877i	$-0.587004\pi$
$281$	−9.05001	−0.539878	−0.269939	+	0.962877i	$0.587004\pi$
$282$	−7.90807	−0.470919
$283$	−25.9889	−1.54488	−0.772441	−	0.635087i	$-0.780964\pi$
$283$	−25.9889	−1.54488	−0.772441	+	0.635087i	$0.780964\pi$
$284$	−2.21315	−0.131326
$285$	−4.60264	−0.272637
$286$	7.39218	0.437109
$287$	−26.5902	−1.56957
$288$	3.19209	0.188096
$289$	1.00000	0.0588235
$290$	−4.49817	−0.264142
$291$	19.3910	1.13672
$292$	2.87144	0.168038
$293$	−12.6078	−0.736556	−0.368278	−	0.929716i	$-0.620053\pi$
$293$	−12.6078	−0.736556	−0.368278	+	0.929716i	$0.620053\pi$
$294$	1.92989	0.112553
$295$	−6.48062	−0.377316
$296$	15.0192	0.872973
$297$	5.63253	0.326833
$298$	25.3774	1.47007
$299$	50.5462	2.92316
$300$	−0.638655	−0.0368728
$301$	20.4215	1.17707
$302$	16.4430	0.946187
$303$	13.8106	0.793400
$304$	9.69281	0.555921
$305$	1.96375	0.112444
$306$	−1.49340	−0.0853722
$307$	6.74829	0.385145	0.192573	−	0.981283i	$-0.438317\pi$
$307$	6.74829	0.385145	0.192573	+	0.981283i	$0.438317\pi$
$308$	−1.15277	−0.0656850
$309$	4.96112	0.282229
$310$	−11.0895	−0.629841
$311$	5.47406	0.310406	0.155203	−	0.987883i	$-0.450397\pi$
$311$	5.47406	0.310406	0.155203	+	0.987883i	$0.450397\pi$
$312$	24.4997	1.38702
$313$	−2.34332	−0.132452	−0.0662262	−	0.997805i	$-0.521096\pi$
$313$	−2.34332	−0.132452	−0.0662262	+	0.997805i	$0.521096\pi$
$314$	4.33847	0.244834
$315$	2.92248	0.164663
$316$	−4.44445	−0.250020
$317$	−4.16233	−0.233780	−0.116890	−	0.993145i	$-0.537292\pi$
$317$	−4.16233	−0.233780	−0.116890	+	0.993145i	$0.537292\pi$
$318$	−3.13843	−0.175995
$319$	−3.64537	−0.204101
$320$	8.88916	0.496919
$321$	−27.0343	−1.50891
$322$	25.1405	1.40102
$323$	3.44044	0.191431
$324$	1.86393	0.103552
$325$	5.99070	0.332305
$326$	19.7649	1.09468
$327$	8.69945	0.481080
$328$	33.6622	1.85868
$329$	−11.5678	−0.637754
$330$	1.65077	0.0908722
$331$	14.2161	0.781389	0.390695	−	0.920520i	$-0.372235\pi$
$331$	14.2161	0.781389	0.390695	+	0.920520i	$0.372235\pi$
$332$	3.03049	0.166320
$333$	−5.94622	−0.325851
$334$	−3.51334	−0.192241
$335$	9.36951	0.511911
$336$	9.10119	0.496511
$337$	14.2128	0.774221	0.387110	−	0.922033i	$-0.373473\pi$
$337$	14.2128	0.774221	0.387110	+	0.922033i	$0.373473\pi$
$338$	−28.2431	−1.53622
$339$	−3.65705	−0.198624
$340$	0.477390	0.0258901
$341$	−8.98705	−0.486676
$342$	−5.13797	−0.277829
$343$	19.7261	1.06511
$344$	−25.8527	−1.39389
$345$	11.2877	0.607707
$346$	23.4821	1.26241
$347$	1.24538	0.0668553	0.0334277	−	0.999441i	$-0.489358\pi$
$347$	1.24538	0.0668553	0.0334277	+	0.999441i	$0.489358\pi$
$348$	−2.32813	−0.124801
$349$	17.4562	0.934411	0.467205	−	0.884149i	$-0.345261\pi$
$349$	17.4562	0.934411	0.467205	+	0.884149i	$0.345261\pi$
$350$	2.97963	0.159268
$351$	−33.7428	−1.80106
$352$	2.63750	0.140579
$353$	−27.7611	−1.47757	−0.738787	−	0.673939i	$-0.764601\pi$
$353$	−27.7611	−1.47757	−0.738787	+	0.673939i	$0.764601\pi$
$354$	10.6980	0.568595
$355$	4.63594	0.246050
$356$	−1.42713	−0.0756380
$357$	3.23044	0.170973
$358$	−1.63988	−0.0866703
$359$	9.11940	0.481303	0.240652	−	0.970612i	$-0.422639\pi$
$359$	9.11940	0.481303	0.240652	+	0.970612i	$0.422639\pi$
$360$	−3.69974	−0.194994
$361$	−7.16339	−0.377020
$362$	−19.1183	−1.00484
$363$	1.33781	0.0702167
$364$	6.90589	0.361967
$365$	−6.01487	−0.314833
$366$	−3.24170	−0.169447
$367$	9.59212	0.500704	0.250352	−	0.968155i	$-0.419454\pi$
$367$	9.59212	0.500704	0.250352	+	0.968155i	$0.419454\pi$
$368$	−23.7709	−1.23915
$369$	−13.3271	−0.693783
$370$	−6.06251	−0.315175
$371$	−4.59086	−0.238345
$372$	−5.73963	−0.297586
$373$	18.4660	0.956134	0.478067	−	0.878323i	$-0.341338\pi$
$373$	18.4660	0.956134	0.478067	+	0.878323i	$0.341338\pi$
$374$	−1.23394	−0.0638056
$375$	1.33781	0.0690841
$376$	14.6444	0.755227
$377$	21.8383	1.12473
$378$	−16.7829	−0.863219
$379$	−17.2393	−0.885525	−0.442762	−	0.896639i	$-0.646002\pi$
$379$	−17.2393	−0.885525	−0.442762	+	0.896639i	$0.646002\pi$
$380$	1.64243	0.0842549
$381$	4.05351	0.207668
$382$	19.4072	0.992959
$383$	−3.53718	−0.180742	−0.0903708	−	0.995908i	$-0.528805\pi$
$383$	−3.53718	−0.180742	−0.0903708	+	0.995908i	$0.528805\pi$
$384$	−7.61707	−0.388707
$385$	2.41473	0.123066
$386$	−9.02417	−0.459318
$387$	10.2353	0.520290
$388$	−6.91960	−0.351289
$389$	14.6780	0.744202	0.372101	−	0.928192i	$-0.378637\pi$
$389$	14.6780	0.744202	0.372101	+	0.928192i	$0.378637\pi$
$390$	−9.88931	−0.500764
$391$	−8.43743	−0.426699
$392$	−3.57382	−0.180505
$393$	−5.87453	−0.296331
$394$	25.9943	1.30957
$395$	9.30990	0.468432
$396$	−0.577772	−0.0290341
$397$	22.1812	1.11324	0.556621	−	0.830767i	$-0.312098\pi$
$397$	22.1812	1.11324	0.556621	+	0.830767i	$0.312098\pi$
$398$	−3.43616	−0.172239
$399$	11.1141	0.556403
$400$	−2.81732	−0.140866
$401$	−15.9486	−0.796436	−0.398218	−	0.917291i	$-0.630371\pi$
$401$	−15.9486	−0.796436	−0.398218	+	0.917291i	$0.630371\pi$
$402$	−15.4670	−0.771421
$403$	53.8388	2.68190
$404$	−4.92826	−0.245190
$405$	−3.90442	−0.194012
$406$	10.8619	0.539065
$407$	−4.91313	−0.243535
$408$	−4.08961	−0.202466
$409$	6.30144	0.311586	0.155793	−	0.987790i	$-0.450207\pi$
$409$	6.30144	0.311586	0.155793	+	0.987790i	$0.450207\pi$
$410$	−13.5878	−0.671052
$411$	26.7318	1.31858
$412$	−1.77035	−0.0872190
$413$	15.6490	0.770035
$414$	12.6005	0.619281
$415$	−6.34804	−0.311613
$416$	−15.8005	−0.774682
$417$	23.9786	1.17424
$418$	−4.24530	−0.207644
$419$	5.74293	0.280561	0.140280	−	0.990112i	$-0.455200\pi$
$419$	5.74293	0.280561	0.140280	+	0.990112i	$0.455200\pi$
$420$	1.54218	0.0752507
$421$	35.3133	1.72106	0.860532	−	0.509397i	$-0.170132\pi$
$421$	35.3133	1.72106	0.860532	+	0.509397i	$0.170132\pi$
$422$	−22.9051	−1.11500
$423$	−5.79783	−0.281900
$424$	5.81184	0.282248
$425$	−1.00000	−0.0485071
$426$	−7.65289	−0.370784
$427$	−4.74192	−0.229477
$428$	9.64707	0.466309
$429$	−8.01441	−0.386939
$430$	10.4355	0.503243
$431$	23.1663	1.11588	0.557940	−	0.829881i	$-0.311592\pi$
$431$	23.1663	1.11588	0.557940	+	0.829881i	$0.311592\pi$
$432$	15.8686	0.763480
$433$	12.8510	0.617581	0.308790	−	0.951130i	$-0.400076\pi$
$433$	12.8510	0.617581	0.308790	+	0.951130i	$0.400076\pi$
$434$	26.7781	1.28539
$435$	4.87680	0.233825
$436$	−3.10435	−0.148672
$437$	−29.0285	−1.38862
$438$	9.92919	0.474435
$439$	−25.3359	−1.20922	−0.604609	−	0.796522i	$-0.706671\pi$
$439$	−25.3359	−1.20922	−0.604609	+	0.796522i	$0.706671\pi$
$440$	−3.05695	−0.145734
$441$	1.41490	0.0673763
$442$	7.39218	0.351610
$443$	−31.3720	−1.49053	−0.745264	−	0.666770i	$-0.767677\pi$
$443$	−31.3720	−1.49053	−0.745264	+	0.666770i	$0.767677\pi$
$444$	−3.13779	−0.148913
$445$	2.98945	0.141714
$446$	21.1175	0.999940
$447$	−27.5135	−1.30134
$448$	−21.4649	−1.01412
$449$	−3.26014	−0.153855	−0.0769277	−	0.997037i	$-0.524511\pi$
$449$	−3.26014	−0.153855	−0.0769277	+	0.997037i	$0.524511\pi$
$450$	1.49340	0.0703998
$451$	−11.0117	−0.518520
$452$	1.30500	0.0613821
$453$	−17.8271	−0.837588
$454$	36.8854	1.73112
$455$	−14.4659	−0.678174
$456$	−14.0701	−0.658891
$457$	26.9473	1.26054	0.630271	−	0.776375i	$-0.282944\pi$
$457$	26.9473	1.26054	0.630271	+	0.776375i	$0.282944\pi$
$458$	2.47139	0.115480
$459$	5.63253	0.262904
$460$	−4.02794	−0.187804
$461$	32.8151	1.52835	0.764175	−	0.645009i	$-0.223147\pi$
$461$	32.8151	1.52835	0.764175	+	0.645009i	$0.223147\pi$
$462$	−3.98618	−0.185454
$463$	−22.2453	−1.03383	−0.516913	−	0.856038i	$-0.672919\pi$
$463$	−22.2453	−1.03383	−0.516913	+	0.856038i	$0.672919\pi$
$464$	−10.2702	−0.476780
$465$	12.0229	0.557551
$466$	14.8190	0.686476
$467$	40.0742	1.85441	0.927207	−	0.374548i	$-0.122202\pi$
$467$	40.0742	1.85441	0.927207	+	0.374548i	$0.122202\pi$
$468$	3.46126	0.159997
$469$	−22.6248	−1.04472
$470$	−5.91122	−0.272664
$471$	−4.70366	−0.216733
$472$	−19.8110	−0.911873
$473$	8.45703	0.388855
$474$	−15.3685	−0.705901
$475$	−3.44044	−0.157858
$476$	−1.15277	−0.0528370
$477$	−2.30096	−0.105354
$478$	−2.16848	−0.0991837
$479$	−14.2030	−0.648950	−0.324475	−	0.945894i	$-0.605188\pi$
$479$	−14.2030	−0.648950	−0.324475	+	0.945894i	$0.605188\pi$
$480$	−3.52847	−0.161052
$481$	29.4331	1.34203
$482$	23.4374	1.06755
$483$	−27.2566	−1.24022
$484$	−0.477390	−0.0216995
$485$	14.4946	0.658168
$486$	−14.4053	−0.653438
$487$	7.58673	0.343787	0.171894	−	0.985115i	$-0.445011\pi$
$487$	7.58673	0.343787	0.171894	+	0.985115i	$0.445011\pi$
$488$	6.00308	0.271747
$489$	−21.4286	−0.969034
$490$	1.44257	0.0651688
$491$	21.4850	0.969605	0.484803	−	0.874624i	$-0.338891\pi$
$491$	21.4850	0.969605	0.484803	+	0.874624i	$0.338891\pi$
$492$	−7.03267	−0.317057
$493$	−3.64537	−0.164179
$494$	25.4323	1.14425
$495$	1.21027	0.0543977
$496$	−25.3194	−1.13687
$497$	−11.1945	−0.502144
$498$	10.4792	0.469583
$499$	−30.7518	−1.37664	−0.688321	−	0.725406i	$-0.741652\pi$
$499$	−30.7518	−1.37664	−0.688321	+	0.725406i	$0.741652\pi$
$500$	−0.477390	−0.0213495
$501$	3.80907	0.170177
$502$	1.83047	0.0816978
$503$	25.1135	1.11976	0.559879	−	0.828575i	$-0.310848\pi$
$503$	25.1135	1.11976	0.559879	+	0.828575i	$0.310848\pi$
$504$	8.93388	0.397947
$505$	10.3233	0.459383
$506$	10.4113	0.462838
$507$	30.6205	1.35990
$508$	−1.44647	−0.0641769
$509$	−6.84134	−0.303237	−0.151619	−	0.988439i	$-0.548449\pi$
$509$	−6.84134	−0.303237	−0.151619	+	0.988439i	$0.548449\pi$
$510$	1.65077	0.0730975
$511$	14.5243	0.642516
$512$	24.6555	1.08963
$513$	19.3784	0.855576
$514$	−3.19464	−0.140909
$515$	3.70840	0.163412
$516$	5.40113	0.237771
$517$	−4.79052	−0.210687
$518$	14.6393	0.643215
$519$	−25.4587	−1.11751
$520$	18.3133	0.803091
$521$	−34.5798	−1.51497	−0.757485	−	0.652852i	$-0.773572\pi$
$521$	−34.5798	−1.51497	−0.757485	+	0.652852i	$0.773572\pi$
$522$	5.44401	0.238278
$523$	−4.62535	−0.202253	−0.101126	−	0.994874i	$-0.532245\pi$
$523$	−4.62535	−0.202253	−0.101126	+	0.994874i	$0.532245\pi$
$524$	2.09630	0.0915771
$525$	−3.23044	−0.140988
$526$	−4.85977	−0.211896
$527$	−8.98705	−0.391482
$528$	3.76903	0.164026
$529$	48.1903	2.09523
$530$	−2.34595	−0.101902
$531$	7.84332	0.340371
$532$	−3.96602	−0.171949
$533$	65.9677	2.85738
$534$	−4.93491	−0.213555
$535$	−20.2079	−0.873666
$536$	28.6421	1.23715
$537$	1.77792	0.0767227
$538$	16.8807	0.727777
$539$	1.16908	0.0503558
$540$	2.68891	0.115712
$541$	33.1907	1.42698	0.713491	−	0.700665i	$-0.247113\pi$
$541$	33.1907	1.42698	0.713491	+	0.700665i	$0.247113\pi$
$542$	5.87632	0.252409
$543$	20.7276	0.889507
$544$	2.63750	0.113082
$545$	6.50276	0.278548
$546$	23.8800	1.02197
$547$	40.9416	1.75054	0.875268	−	0.483638i	$-0.160685\pi$
$547$	40.9416	1.75054	0.875268	+	0.483638i	$0.160685\pi$
$548$	−9.53911	−0.407490
$549$	−2.37667	−0.101434
$550$	1.23394	0.0526154
$551$	−12.5417	−0.534293
$552$	34.5058	1.46867
$553$	−22.4809	−0.955985
$554$	14.4240	0.612815
$555$	6.57281	0.279000
$556$	−8.55664	−0.362882
$557$	−3.99055	−0.169085	−0.0845426	−	0.996420i	$-0.526943\pi$
$557$	−3.99055	−0.169085	−0.0845426	+	0.996420i	$0.526943\pi$
$558$	13.4213	0.568169
$559$	−50.6636	−2.14284
$560$	6.80307	0.287482
$561$	1.33781	0.0564823
$562$	11.1672	0.471059
$563$	35.5510	1.49829	0.749147	−	0.662404i	$-0.230464\pi$
$563$	35.5510	1.49829	0.749147	+	0.662404i	$0.230464\pi$
$564$	−3.05949	−0.128828
$565$	−2.73362	−0.115004
$566$	32.0688	1.34795
$567$	9.42813	0.395944
$568$	14.1718	0.594638
$569$	32.8016	1.37511	0.687557	−	0.726131i	$-0.258683\pi$
$569$	32.8016	1.37511	0.687557	+	0.726131i	$0.258683\pi$
$570$	5.67939	0.237883
$571$	−21.0268	−0.879946	−0.439973	−	0.898011i	$-0.645012\pi$
$571$	−21.0268	−0.879946	−0.439973	+	0.898011i	$0.645012\pi$
$572$	2.85990	0.119578
$573$	−21.0408	−0.878992
$574$	32.8108	1.36950
$575$	8.43743	0.351865
$576$	−10.7583	−0.448262
$577$	−8.25080	−0.343485	−0.171743	−	0.985142i	$-0.554940\pi$
$577$	−8.25080	−0.343485	−0.171743	+	0.985142i	$0.554940\pi$
$578$	−1.23394	−0.0513252
$579$	9.78378	0.406600
$580$	−1.74026	−0.0722604
$581$	15.3288	0.635946
$582$	−23.9274	−0.991823
$583$	−1.90119	−0.0787392
$584$	−18.3872	−0.760866
$585$	−7.25038	−0.299766
$586$	15.5573	0.642666
$587$	−25.2181	−1.04086	−0.520430	−	0.853904i	$-0.674228\pi$
$587$	−25.2181	−1.04086	−0.520430	+	0.853904i	$0.674228\pi$
$588$	0.746638	0.0307908
$589$	−30.9194	−1.27401
$590$	7.99671	0.329219
$591$	−28.1824	−1.15927
$592$	−13.8418	−0.568896
$593$	15.4984	0.636443	0.318222	−	0.948016i	$-0.396914\pi$
$593$	15.4984	0.636443	0.318222	+	0.948016i	$0.396914\pi$
$594$	−6.95021	−0.285171
$595$	2.41473	0.0989943
$596$	9.81806	0.402163
$597$	3.72539	0.152470
$598$	−62.3710	−2.55054
$599$	−24.2055	−0.989010	−0.494505	−	0.869175i	$-0.664651\pi$
$599$	−24.2055	−0.989010	−0.494505	+	0.869175i	$0.664651\pi$
$600$	4.08961	0.166958
$601$	−0.482194	−0.0196691	−0.00983455	−	0.999952i	$-0.503130\pi$
$601$	−0.482194	−0.0196691	−0.00983455	+	0.999952i	$0.503130\pi$
$602$	−25.1989	−1.02703
$603$	−11.3397	−0.461787
$604$	6.36150	0.258846
$605$	1.00000	0.0406558
$606$	−17.0415	−0.692264
$607$	−32.3043	−1.31119	−0.655595	−	0.755113i	$-0.727582\pi$
$607$	−32.3043	−1.31119	−0.655595	+	0.755113i	$0.727582\pi$
$608$	9.07415	0.368006
$609$	−11.7762	−0.477194
$610$	−2.42315	−0.0981104
$611$	28.6986	1.16102
$612$	−0.577772	−0.0233550
$613$	−34.1168	−1.37796	−0.688981	−	0.724779i	$-0.741942\pi$
$613$	−34.1168	−1.37796	−0.688981	+	0.724779i	$0.741942\pi$
$614$	−8.32699	−0.336050
$615$	14.7315	0.594031
$616$	7.38172	0.297418
$617$	−2.61004	−0.105076	−0.0525381	−	0.998619i	$-0.516731\pi$
$617$	−2.61004	−0.105076	−0.0525381	+	0.998619i	$0.516731\pi$
$618$	−6.12173	−0.246252
$619$	−5.23893	−0.210570	−0.105285	−	0.994442i	$-0.533576\pi$
$619$	−5.23893	−0.210570	−0.105285	+	0.994442i	$0.533576\pi$
$620$	−4.29033	−0.172304
$621$	−47.5241	−1.90708
$622$	−6.75467	−0.270838
$623$	−7.21872	−0.289212
$624$	−22.5791	−0.903889
$625$	1.00000	0.0400000
$626$	2.89152	0.115568
$627$	4.60264	0.183812
$628$	1.67848	0.0669785
$629$	−4.91313	−0.195899
$630$	−3.60617	−0.143673
$631$	−34.7132	−1.38191	−0.690956	−	0.722897i	$-0.742810\pi$
$631$	−34.7132	−1.38191	−0.690956	+	0.722897i	$0.742810\pi$
$632$	28.4599	1.13207
$633$	24.8331	0.987027
$634$	5.13607	0.203979
$635$	3.02996	0.120240
$636$	−1.21420	−0.0481463
$637$	−7.00360	−0.277493
$638$	4.49817	0.178084
$639$	−5.61075	−0.221958
$640$	−5.69370	−0.225063
$641$	−7.06650	−0.279110	−0.139555	−	0.990214i	$-0.544567\pi$
$641$	−7.06650	−0.279110	−0.139555	+	0.990214i	$0.544567\pi$
$642$	33.3588	1.31657
$643$	8.15696	0.321679	0.160839	−	0.986981i	$-0.448580\pi$
$643$	8.15696	0.321679	0.160839	+	0.986981i	$0.448580\pi$
$644$	9.72640	0.383274
$645$	−11.3139	−0.445484
$646$	−4.24530	−0.167029
$647$	22.2146	0.873348	0.436674	−	0.899620i	$-0.356156\pi$
$647$	22.2146	0.873348	0.436674	+	0.899620i	$0.356156\pi$
$648$	−11.9356	−0.468876
$649$	6.48062	0.254387
$650$	−7.39218	−0.289945
$651$	−29.0322	−1.13786
$652$	7.64668	0.299467
$653$	−33.6327	−1.31615	−0.658074	−	0.752953i	$-0.728629\pi$
$653$	−33.6327	−1.31615	−0.658074	+	0.752953i	$0.728629\pi$
$654$	−10.7346	−0.419756
$655$	−4.39116	−0.171577
$656$	−31.0234	−1.21126
$657$	7.27963	0.284005
$658$	14.2740	0.556458
$659$	−30.8042	−1.19996	−0.599980	−	0.800015i	$-0.704825\pi$
$659$	−30.8042	−1.19996	−0.599980	+	0.800015i	$0.704825\pi$
$660$	0.638655	0.0248596
$661$	−19.3485	−0.752568	−0.376284	−	0.926504i	$-0.622798\pi$
$661$	−19.3485	−0.752568	−0.376284	+	0.926504i	$0.622798\pi$
$662$	−17.5419	−0.681784
$663$	−8.01441	−0.311254
$664$	−19.4057	−0.753085
$665$	8.30773	0.322160
$666$	7.33728	0.284314
$667$	30.7575	1.19094
$668$	−1.35925	−0.0525909
$669$	−22.8950	−0.885172
$670$	−11.5614	−0.446657
$671$	−1.96375	−0.0758096
$672$	8.52029	0.328677
$673$	−2.82236	−0.108794	−0.0543969	−	0.998519i	$-0.517324\pi$
$673$	−2.82236	−0.108794	−0.0543969	+	0.998519i	$0.517324\pi$
$674$	−17.5378	−0.675529
$675$	−5.63253	−0.216796
$676$	−10.9268	−0.420260
$677$	−27.3518	−1.05122	−0.525608	−	0.850727i	$-0.676162\pi$
$677$	−27.3518	−1.05122	−0.525608	+	0.850727i	$0.676162\pi$
$678$	4.51259	0.173305
$679$	−35.0007	−1.34320
$680$	−3.05695	−0.117229
$681$	−39.9902	−1.53243
$682$	11.0895	0.424639
$683$	38.5727	1.47594	0.737972	−	0.674831i	$-0.235784\pi$
$683$	38.5727	1.47594	0.737972	+	0.674831i	$0.235784\pi$
$684$	−1.98779	−0.0760049
$685$	19.9818	0.763465
$686$	−24.3409	−0.929339
$687$	−2.67942	−0.102226
$688$	23.8262	0.908364
$689$	11.3895	0.433904
$690$	−13.9283	−0.530241
$691$	−32.1876	−1.22448	−0.612238	−	0.790674i	$-0.709730\pi$
$691$	−32.1876	−1.22448	−0.612238	+	0.790674i	$0.709730\pi$
$692$	9.08480	0.345352
$693$	−2.92248	−0.111016
$694$	−1.53672	−0.0583331
$695$	17.9238	0.679889
$696$	14.9081	0.565092
$697$	−11.0117	−0.417097
$698$	−21.5400	−0.815299
$699$	−16.0664	−0.607685
$700$	1.15277	0.0435705
$701$	20.7377	0.783253	0.391626	−	0.920124i	$-0.371913\pi$
$701$	20.7377	0.783253	0.391626	+	0.920124i	$0.371913\pi$
$702$	41.6367	1.57147
$703$	−16.9033	−0.637520
$704$	−8.88916	−0.335023
$705$	6.40879	0.241369
$706$	34.2556	1.28923
$707$	−24.9281	−0.937517
$708$	4.13888	0.155549
$709$	41.4231	1.55568	0.777839	−	0.628463i	$-0.216316\pi$
$709$	41.4231	1.55568	0.777839	+	0.628463i	$0.216316\pi$
$710$	−5.72048	−0.214686
$711$	−11.2675	−0.422565
$712$	9.13862	0.342484
$713$	75.8277	2.83977
$714$	−3.98618	−0.149179
$715$	−5.99070	−0.224040
$716$	−0.634440	−0.0237101
$717$	2.35100	0.0877999
$718$	−11.2528	−0.419951
$719$	−6.12396	−0.228385	−0.114193	−	0.993459i	$-0.536428\pi$
$719$	−6.12396	−0.228385	−0.114193	+	0.993459i	$0.536428\pi$
$720$	3.40972	0.127073
$721$	−8.95479	−0.333494
$722$	8.83919	0.328961
$723$	−25.4103	−0.945018
$724$	−7.39654	−0.274890
$725$	3.64537	0.135386
$726$	−1.65077	−0.0612660
$727$	−17.9206	−0.664637	−0.332319	−	0.943167i	$-0.607831\pi$
$727$	−17.9206	−0.664637	−0.332319	+	0.943167i	$0.607831\pi$
$728$	−44.2217	−1.63896
$729$	27.3311	1.01226
$730$	7.42199	0.274700
$731$	8.45703	0.312795
$732$	−1.25416	−0.0463550
$733$	−41.4764	−1.53197	−0.765983	−	0.642861i	$-0.777747\pi$
$733$	−41.4764	−1.53197	−0.765983	+	0.642861i	$0.777747\pi$
$734$	−11.8361	−0.436879
$735$	−1.56400	−0.0576891
$736$	−22.2537	−0.820283
$737$	−9.36951	−0.345130
$738$	16.4449	0.605345
$739$	0.839066	0.0308656	0.0154328	−	0.999881i	$-0.495087\pi$
$739$	0.839066	0.0308656	0.0154328	+	0.999881i	$0.495087\pi$
$740$	−2.34548	−0.0862214
$741$	−27.5731	−1.01292
$742$	5.66485	0.207963
$743$	−38.2537	−1.40339	−0.701696	−	0.712477i	$-0.747573\pi$
$743$	−38.2537	−1.40339	−0.701696	+	0.712477i	$0.747573\pi$
$744$	36.7536	1.34745
$745$	−20.5661	−0.753485
$746$	−22.7860	−0.834253
$747$	7.68285	0.281101
$748$	−0.477390	−0.0174551
$749$	48.7967	1.78299
$750$	−1.65077	−0.0602778
$751$	21.0649	0.768668	0.384334	−	0.923194i	$-0.374431\pi$
$751$	21.0649	0.768668	0.384334	+	0.923194i	$0.374431\pi$
$752$	−13.4964	−0.492164
$753$	−1.98455	−0.0723209
$754$	−26.9472	−0.981359
$755$	−13.3256	−0.484968
$756$	−6.49300	−0.236148
$757$	40.9997	1.49016	0.745080	−	0.666975i	$-0.232411\pi$
$757$	40.9997	1.49016	0.745080	+	0.666975i	$0.232411\pi$
$758$	21.2723	0.772645
$759$	−11.2877	−0.409716
$760$	−10.5173	−0.381501
$761$	0.300937	0.0109090	0.00545448	−	0.999985i	$-0.498264\pi$
$761$	0.300937	0.0109090	0.00545448	+	0.999985i	$0.498264\pi$
$762$	−5.00179	−0.181196
$763$	−15.7024	−0.568466
$764$	7.50830	0.271641
$765$	1.21027	0.0437575
$766$	4.36468	0.157702
$767$	−38.8235	−1.40184
$768$	−14.3849	−0.519072
$769$	−9.51413	−0.343088	−0.171544	−	0.985176i	$-0.554876\pi$
$769$	−9.51413	−0.343088	−0.171544	+	0.985176i	$0.554876\pi$
$770$	−2.97963	−0.107379
$771$	3.46354	0.124737
$772$	−3.49129	−0.125654
$773$	−16.5434	−0.595025	−0.297513	−	0.954718i	$-0.596157\pi$
$773$	−16.5434	−0.595025	−0.297513	+	0.954718i	$0.596157\pi$
$774$	−12.6298	−0.453968
$775$	8.98705	0.322825
$776$	44.3094	1.59062
$777$	−15.8716	−0.569389
$778$	−18.1117	−0.649337
$779$	−37.8850	−1.35737
$780$	−3.82600	−0.136993
$781$	−4.63594	−0.165887
$782$	10.4113	0.372307
$783$	−20.5327	−0.733777
$784$	3.29367	0.117631
$785$	−3.51594	−0.125489
$786$	7.24882	0.258557
$787$	−20.7956	−0.741284	−0.370642	−	0.928776i	$-0.620862\pi$
$787$	−20.7956	−0.741284	−0.370642	+	0.928776i	$0.620862\pi$
$788$	10.0567	0.358256
$789$	5.26884	0.187576
$790$	−11.4879	−0.408720
$791$	6.60095	0.234703
$792$	3.69974	0.131465
$793$	11.7642	0.417760
$794$	−27.3703	−0.971335
$795$	2.54342	0.0902059
$796$	−1.32939	−0.0471189
$797$	−14.2666	−0.505350	−0.252675	−	0.967551i	$-0.581310\pi$
$797$	−14.2666	−0.505350	−0.252675	+	0.967551i	$0.581310\pi$
$798$	−13.7142	−0.485477
$799$	−4.79052	−0.169476
$800$	−2.63750	−0.0932497
$801$	−3.61805	−0.127838
$802$	19.6796	0.694912
$803$	6.01487	0.212260
$804$	−5.98389	−0.211035
$805$	−20.3741	−0.718093
$806$	−66.4339	−2.34003
$807$	−18.3016	−0.644246
$808$	31.5580	1.11021
$809$	−7.23800	−0.254475	−0.127237	−	0.991872i	$-0.540611\pi$
$809$	−7.23800	−0.254475	−0.127237	+	0.991872i	$0.540611\pi$
$810$	4.81783	0.169281
$811$	−5.36765	−0.188484	−0.0942418	−	0.995549i	$-0.530043\pi$
$811$	−5.36765	−0.188484	−0.0942418	+	0.995549i	$0.530043\pi$
$812$	4.20226	0.147470
$813$	−6.37095	−0.223439
$814$	6.06251	0.212491
$815$	−16.0177	−0.561075
$816$	3.76903	0.131942
$817$	29.0959	1.01794
$818$	−7.77560	−0.271867
$819$	17.5077	0.611769
$820$	−5.25686	−0.183578
$821$	48.7059	1.69985	0.849924	−	0.526905i	$-0.176648\pi$
$821$	48.7059	1.69985	0.849924	+	0.526905i	$0.176648\pi$
$822$	−32.9855	−1.15050
$823$	42.8022	1.49199	0.745996	−	0.665950i	$-0.231974\pi$
$823$	42.8022	1.49199	0.745996	+	0.665950i	$0.231974\pi$
$824$	11.3364	0.394922
$825$	−1.33781	−0.0465765
$826$	−19.3099	−0.671877
$827$	−37.5847	−1.30695	−0.653474	−	0.756949i	$-0.726689\pi$
$827$	−37.5847	−1.30695	−0.653474	+	0.756949i	$0.726689\pi$
$828$	4.87491	0.169415
$829$	43.2360	1.50165	0.750823	−	0.660503i	$-0.229657\pi$
$829$	43.2360	1.50165	0.750823	+	0.660503i	$0.229657\pi$
$830$	7.83310	0.271891
$831$	−15.6381	−0.542479
$832$	53.2523	1.84619
$833$	1.16908	0.0405062
$834$	−29.5882	−1.02455
$835$	2.84725	0.0985331
$836$	−1.64243	−0.0568046
$837$	−50.6199	−1.74968
$838$	−7.08644	−0.244797
$839$	53.1197	1.83389	0.916947	−	0.399009i	$-0.130646\pi$
$839$	53.1197	1.83389	0.916947	+	0.399009i	$0.130646\pi$
$840$	−9.87531	−0.340731
$841$	−15.7113	−0.541769
$842$	−43.5745	−1.50168
$843$	−12.1072	−0.416993
$844$	−8.86157	−0.305028
$845$	22.8885	0.787390
$846$	7.15418	0.245966
$847$	−2.41473	−0.0829711
$848$	−5.35626	−0.183935
$849$	−34.7682	−1.19324
$850$	1.23394	0.0423238
$851$	41.4542	1.42103
$852$	−2.96077	−0.101434
$853$	42.1260	1.44237	0.721183	−	0.692745i	$-0.243599\pi$
$853$	42.1260	1.44237	0.721183	+	0.692745i	$0.243599\pi$
$854$	5.85125	0.200226
$855$	4.16387	0.142401
$856$	−61.7747	−2.11142
$857$	37.9248	1.29549	0.647744	−	0.761858i	$-0.275713\pi$
$857$	37.9248	1.29549	0.647744	+	0.761858i	$0.275713\pi$
$858$	9.88931	0.337615
$859$	−51.3968	−1.75364	−0.876819	−	0.480821i	$-0.840339\pi$
$859$	−51.3968	−1.75364	−0.876819	+	0.480821i	$0.840339\pi$
$860$	4.03730	0.137671
$861$	−35.5726	−1.21231
$862$	−28.5858	−0.973636
$863$	51.0886	1.73908	0.869538	−	0.493866i	$-0.164417\pi$
$863$	51.0886	1.73908	0.869538	+	0.493866i	$0.164417\pi$
$864$	14.8558	0.505405
$865$	−19.0302	−0.647045
$866$	−15.8574	−0.538856
$867$	1.33781	0.0454343
$868$	10.3600	0.351641
$869$	−9.30990	−0.315817
$870$	−6.01768	−0.204019
$871$	56.1300	1.90189
$872$	19.8786	0.673176
$873$	−17.5425	−0.593723
$874$	35.8194	1.21161
$875$	−2.41473	−0.0816328
$876$	3.84143	0.129790
$877$	16.9154	0.571194	0.285597	−	0.958350i	$-0.407808\pi$
$877$	16.9154	0.571194	0.285597	+	0.958350i	$0.407808\pi$
$878$	31.2630	1.05508
$879$	−16.8668	−0.568904
$880$	2.81732	0.0949718
$881$	25.2394	0.850337	0.425168	−	0.905114i	$-0.360215\pi$
$881$	25.2394	0.850337	0.425168	+	0.905114i	$0.360215\pi$
$882$	−1.74591	−0.0587877
$883$	14.9184	0.502043	0.251022	−	0.967981i	$-0.419233\pi$
$883$	14.9184	0.502043	0.251022	+	0.967981i	$0.419233\pi$
$884$	2.85990	0.0961889
$885$	−8.66982	−0.291433
$886$	38.7112	1.30053
$887$	−40.9742	−1.37578	−0.687890	−	0.725815i	$-0.741463\pi$
$887$	−40.9742	−1.37578	−0.687890	+	0.725815i	$0.741463\pi$
$888$	20.0928	0.674270
$889$	−7.31655	−0.245389
$890$	−3.68881	−0.123649
$891$	3.90442	0.130803
$892$	8.16997	0.273551
$893$	−16.4815	−0.551532
$894$	33.9501	1.13546
$895$	1.32898	0.0444228
$896$	13.7487	0.459313
$897$	67.6210	2.25780
$898$	4.02282	0.134243
$899$	32.7611	1.09264
$900$	0.577772	0.0192591
$901$	−1.90119	−0.0633378
$902$	13.5878	0.452423
$903$	27.3200	0.909151
$904$	−8.35654	−0.277934
$905$	15.4937	0.515029
$906$	21.9975	0.730819
$907$	−55.7531	−1.85125	−0.925626	−	0.378438i	$-0.876461\pi$
$907$	−55.7531	−1.85125	−0.925626	+	0.378438i	$0.876461\pi$
$908$	14.2703	0.473577
$909$	−12.4940	−0.414401
$910$	17.8501	0.591725
$911$	25.8245	0.855603	0.427802	−	0.903873i	$-0.359288\pi$
$911$	25.8245	0.855603	0.427802	+	0.903873i	$0.359288\pi$
$912$	12.9671	0.429384
$913$	6.34804	0.210089
$914$	−33.2514	−1.09986
$915$	2.62711	0.0868497
$916$	0.956136	0.0315916
$917$	10.6035	0.350158
$918$	−6.95021	−0.229391
$919$	7.98018	0.263242	0.131621	−	0.991300i	$-0.457982\pi$
$919$	7.98018	0.263242	0.131621	+	0.991300i	$0.457982\pi$
$920$	25.7928	0.850364
$921$	9.02791	0.297480
$922$	−40.4918	−1.33353
$923$	27.7725	0.914145
$924$	−1.54218	−0.0507340
$925$	4.91313	0.161543
$926$	27.4494	0.902043
$927$	−4.48817	−0.147411
$928$	−9.61466	−0.315617
$929$	−7.44605	−0.244297	−0.122148	−	0.992512i	$-0.538978\pi$
$929$	−7.44605	−0.244297	−0.122148	+	0.992512i	$0.538978\pi$
$930$	−14.8356	−0.486479
$931$	4.02214	0.131820
$932$	5.73320	0.187797
$933$	7.32324	0.239752
$934$	−49.4492	−1.61803
$935$	1.00000	0.0327035
$936$	−22.1641	−0.724456
$937$	4.35263	0.142194	0.0710971	−	0.997469i	$-0.477350\pi$
$937$	4.35263	0.142194	0.0710971	+	0.997469i	$0.477350\pi$
$938$	27.9177	0.911546
$939$	−3.13491	−0.102304
$940$	−2.28695	−0.0745919
$941$	−46.4557	−1.51441	−0.757206	−	0.653177i	$-0.773436\pi$
$941$	−46.4557	−1.51441	−0.757206	+	0.653177i	$0.773436\pi$
$942$	5.80403	0.189106
$943$	92.9103	3.02558
$944$	18.2580	0.594247
$945$	13.6010	0.442442
$946$	−10.4355	−0.339287
$947$	−48.9668	−1.59121	−0.795604	−	0.605817i	$-0.792846\pi$
$947$	−48.9668	−1.59121	−0.795604	+	0.605817i	$0.792846\pi$
$948$	−5.94582	−0.193111
$949$	−36.0333	−1.16969
$950$	4.24530	0.137736
$951$	−5.56840	−0.180568
$952$	7.38172	0.239243
$953$	−2.48728	−0.0805709	−0.0402854	−	0.999188i	$-0.512827\pi$
$953$	−2.48728	−0.0805709	−0.0402854	+	0.999188i	$0.512827\pi$
$954$	2.83924	0.0919239
$955$	−15.7278	−0.508940
$956$	−0.838944	−0.0271334
$957$	−4.87680	−0.157645
$958$	17.5256	0.566227
$959$	−48.2507	−1.55810
$960$	11.8920	0.383812
$961$	49.7671	1.60539
$962$	−36.3187	−1.17096
$963$	24.4571	0.788119
$964$	9.06752	0.292045
$965$	7.31329	0.235423
$966$	33.6331	1.08213
$967$	32.7700	1.05381	0.526906	−	0.849923i	$-0.323352\pi$
$967$	32.7700	1.05381	0.526906	+	0.849923i	$0.323352\pi$
$968$	3.05695	0.0982542
$969$	4.60264	0.147858
$970$	−17.8855	−0.574270
$971$	−8.27116	−0.265434	−0.132717	−	0.991154i	$-0.542370\pi$
$971$	−8.27116	−0.265434	−0.132717	+	0.991154i	$0.542370\pi$
$972$	−5.57316	−0.178759
$973$	−43.2811	−1.38753
$974$	−9.36158	−0.299964
$975$	8.01441	0.256666
$976$	−5.53250	−0.177091
$977$	−29.2283	−0.935097	−0.467548	−	0.883967i	$-0.654863\pi$
$977$	−29.2283	−0.935097	−0.467548	+	0.883967i	$0.654863\pi$
$978$	26.4416	0.845509
$979$	−2.98945	−0.0955433
$980$	0.558106	0.0178280
$981$	−7.87012	−0.251273
$982$	−26.5112	−0.846008
$983$	−9.09841	−0.290194	−0.145097	−	0.989417i	$-0.546349\pi$
$983$	−9.09841	−0.290194	−0.145097	+	0.989417i	$0.546349\pi$
$984$	45.0335	1.43562
$985$	−21.0661	−0.671222
$986$	4.49817	0.143251
$987$	−15.4755	−0.492591
$988$	9.83931	0.313030
$989$	−71.3556	−2.26898
$990$	−1.49340	−0.0474635
$991$	−32.1602	−1.02160	−0.510801	−	0.859699i	$-0.670651\pi$
$991$	−32.1602	−1.02160	−0.510801	+	0.859699i	$0.670651\pi$
$992$	−23.7033	−0.752582
$993$	19.0184	0.603532
$994$	13.8134	0.438135
$995$	2.78470	0.0882809
$996$	4.05421	0.128463
$997$	−61.8701	−1.95945	−0.979724	−	0.200354i	$-0.935791\pi$
$997$	−61.8701	−1.95945	−0.979724	+	0.200354i	$0.935791\pi$
$998$	37.9460	1.20116
$999$	−27.6733	−0.875546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.a.j.1.5	✓	11
3.2	odd	2		8415.2.a.by.1.7		11
5.4	even	2		4675.2.a.bl.1.7		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.a.j.1.5	✓	11	1.1	even	1	trivial
4675.2.a.bl.1.7		11	5.4	even	2
8415.2.a.by.1.7		11	3.2	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:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.23394 q^{2} +1.33781 q^{3} -0.477390 q^{4} +1.00000 q^{5} -1.65077 q^{6} -2.41473 q^{7} +3.05695 q^{8} -1.21027 q^{9} +O(q^{10})\)	\(q-1.23394 q^{2} +1.33781 q^{3} -0.477390 q^{4} +1.00000 q^{5} -1.65077 q^{6} -2.41473 q^{7} +3.05695 q^{8} -1.21027 q^{9} -1.23394 q^{10} -1.00000 q^{11} -0.638655 q^{12} +5.99070 q^{13} +2.97963 q^{14} +1.33781 q^{15} -2.81732 q^{16} -1.00000 q^{17} +1.49340 q^{18} -3.44044 q^{19} -0.477390 q^{20} -3.23044 q^{21} +1.23394 q^{22} +8.43743 q^{23} +4.08961 q^{24} +1.00000 q^{25} -7.39218 q^{26} -5.63253 q^{27} +1.15277 q^{28} +3.64537 q^{29} -1.65077 q^{30} +8.98705 q^{31} -2.63750 q^{32} -1.33781 q^{33} +1.23394 q^{34} -2.41473 q^{35} +0.577772 q^{36} +4.91313 q^{37} +4.24530 q^{38} +8.01441 q^{39} +3.05695 q^{40} +11.0117 q^{41} +3.98618 q^{42} -8.45703 q^{43} +0.477390 q^{44} -1.21027 q^{45} -10.4113 q^{46} +4.79052 q^{47} -3.76903 q^{48} -1.16908 q^{49} -1.23394 q^{50} -1.33781 q^{51} -2.85990 q^{52} +1.90119 q^{53} +6.95021 q^{54} -1.00000 q^{55} -7.38172 q^{56} -4.60264 q^{57} -4.49817 q^{58} -6.48062 q^{59} -0.638655 q^{60} +1.96375 q^{61} -11.0895 q^{62} +2.92248 q^{63} +8.88916 q^{64} +5.99070 q^{65} +1.65077 q^{66} +9.36951 q^{67} +0.477390 q^{68} +11.2877 q^{69} +2.97963 q^{70} +4.63594 q^{71} -3.69974 q^{72} -6.01487 q^{73} -6.06251 q^{74} +1.33781 q^{75} +1.64243 q^{76} +2.41473 q^{77} -9.88931 q^{78} +9.30990 q^{79} -2.81732 q^{80} -3.90442 q^{81} -13.5878 q^{82} -6.34804 q^{83} +1.54218 q^{84} -1.00000 q^{85} +10.4355 q^{86} +4.87680 q^{87} -3.05695 q^{88} +2.98945 q^{89} +1.49340 q^{90} -14.4659 q^{91} -4.02794 q^{92} +12.0229 q^{93} -5.91122 q^{94} -3.44044 q^{95} -3.52847 q^{96} +14.4946 q^{97} +1.44257 q^{98} +1.21027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - q^{2} + 5 q^{3} + 21 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} + 26 q^{9}+O(q^{10}) \) 11 * q - q^2 + 5 * q^3 + 21 * q^4 + 11 * q^5 + q^6 - 2 * q^7 + 26 * q^9	\( 11 q - q^{2} + 5 q^{3} + 21 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} + 26 q^{9} - q^{10} - 11 q^{11} + 8 q^{12} + 13 q^{13} + 5 q^{15} + 29 q^{16} - 11 q^{17} + 3 q^{18} + 4 q^{19} + 21 q^{20} + 34 q^{21} + q^{22} - 7 q^{23} - 29 q^{24} + 11 q^{25} + 4 q^{26} + 14 q^{27} + 8 q^{28} + 9 q^{29} + q^{30} + 20 q^{31} - 26 q^{32} - 5 q^{33} + q^{34} - 2 q^{35} + 62 q^{36} - q^{37} - 6 q^{39} - 9 q^{41} - 74 q^{42} + 5 q^{43} - 21 q^{44} + 26 q^{45} - 10 q^{46} + 24 q^{48} + 43 q^{49} - q^{50} - 5 q^{51} + 18 q^{52} + 14 q^{53} - 9 q^{54} - 11 q^{55} - 6 q^{56} - 32 q^{57} - 10 q^{58} + 13 q^{59} + 8 q^{60} + 11 q^{61} - 26 q^{62} - 40 q^{63} + 24 q^{64} + 13 q^{65} - q^{66} + 26 q^{67} - 21 q^{68} + 56 q^{69} - 8 q^{71} - 26 q^{72} + 42 q^{73} + 16 q^{74} + 5 q^{75} - 70 q^{76} + 2 q^{77} - 56 q^{78} - 27 q^{79} + 29 q^{80} + 71 q^{81} + 57 q^{82} - 41 q^{83} + 76 q^{84} - 11 q^{85} + 47 q^{86} + 26 q^{87} + 37 q^{89} + 3 q^{90} + 30 q^{91} - 47 q^{92} - 8 q^{93} + 94 q^{94} + 4 q^{95} - 154 q^{96} + 29 q^{97} - 69 q^{98} - 26 q^{99}+O(q^{100}) \) 11 * q - q^2 + 5 * q^3 + 21 * q^4 + 11 * q^5 + q^6 - 2 * q^7 + 26 * q^9 - q^10 - 11 * q^11 + 8 * q^12 + 13 * q^13 + 5 * q^15 + 29 * q^16 - 11 * q^17 + 3 * q^18 + 4 * q^19 + 21 * q^20 + 34 * q^21 + q^22 - 7 * q^23 - 29 * q^24 + 11 * q^25 + 4 * q^26 + 14 * q^27 + 8 * q^28 + 9 * q^29 + q^30 + 20 * q^31 - 26 * q^32 - 5 * q^33 + q^34 - 2 * q^35 + 62 * q^36 - q^37 - 6 * q^39 - 9 * q^41 - 74 * q^42 + 5 * q^43 - 21 * q^44 + 26 * q^45 - 10 * q^46 + 24 * q^48 + 43 * q^49 - q^50 - 5 * q^51 + 18 * q^52 + 14 * q^53 - 9 * q^54 - 11 * q^55 - 6 * q^56 - 32 * q^57 - 10 * q^58 + 13 * q^59 + 8 * q^60 + 11 * q^61 - 26 * q^62 - 40 * q^63 + 24 * q^64 + 13 * q^65 - q^66 + 26 * q^67 - 21 * q^68 + 56 * q^69 - 8 * q^71 - 26 * q^72 + 42 * q^73 + 16 * q^74 + 5 * q^75 - 70 * q^76 + 2 * q^77 - 56 * q^78 - 27 * q^79 + 29 * q^80 + 71 * q^81 + 57 * q^82 - 41 * q^83 + 76 * q^84 - 11 * q^85 + 47 * q^86 + 26 * q^87 + 37 * q^89 + 3 * q^90 + 30 * q^91 - 47 * q^92 - 8 * q^93 + 94 * q^94 + 4 * q^95 - 154 * q^96 + 29 * q^97 - 69 * q^98 - 26 * q^99

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