LMFDB - Embedded newform 1334.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 44x^{6} + 87x^{5} - 209x^{4} - 160x^{3} + 348x^{2} + 12x - 100 $ x^9 - 3x^8 - 16x^7 + 44x^6 + 87x^5 - 209x^4 - 160x^3 + 348x^2 + 12x - 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.11529$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.11529 q^{3} +1.00000 q^{4} +2.08342 q^{5} +3.11529 q^{6} -4.29295 q^{7} -1.00000 q^{8} +6.70504 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.11529 q^{3} +1.00000 q^{4} +2.08342 q^{5} +3.11529 q^{6} -4.29295 q^{7} -1.00000 q^{8} +6.70504 q^{9} -2.08342 q^{10} -5.59308 q^{11} -3.11529 q^{12} -2.42515 q^{13} +4.29295 q^{14} -6.49047 q^{15} +1.00000 q^{16} -1.01224 q^{17} -6.70504 q^{18} +5.83724 q^{19} +2.08342 q^{20} +13.3738 q^{21} +5.59308 q^{22} -1.00000 q^{23} +3.11529 q^{24} -0.659343 q^{25} +2.42515 q^{26} -11.5423 q^{27} -4.29295 q^{28} +1.00000 q^{29} +6.49047 q^{30} -3.59308 q^{31} -1.00000 q^{32} +17.4241 q^{33} +1.01224 q^{34} -8.94403 q^{35} +6.70504 q^{36} -7.58614 q^{37} -5.83724 q^{38} +7.55505 q^{39} -2.08342 q^{40} -9.58614 q^{41} -13.3738 q^{42} -0.637507 q^{43} -5.59308 q^{44} +13.9694 q^{45} +1.00000 q^{46} -2.11142 q^{47} -3.11529 q^{48} +11.4294 q^{49} +0.659343 q^{50} +3.15343 q^{51} -2.42515 q^{52} +9.32666 q^{53} +11.5423 q^{54} -11.6528 q^{55} +4.29295 q^{56} -18.1847 q^{57} -1.00000 q^{58} +3.63843 q^{59} -6.49047 q^{60} -11.4413 q^{61} +3.59308 q^{62} -28.7844 q^{63} +1.00000 q^{64} -5.05262 q^{65} -17.4241 q^{66} -5.74676 q^{67} -1.01224 q^{68} +3.11529 q^{69} +8.94403 q^{70} +9.47177 q^{71} -6.70504 q^{72} +16.0728 q^{73} +7.58614 q^{74} +2.05405 q^{75} +5.83724 q^{76} +24.0108 q^{77} -7.55505 q^{78} +16.5811 q^{79} +2.08342 q^{80} +15.8425 q^{81} +9.58614 q^{82} +11.0368 q^{83} +13.3738 q^{84} -2.10893 q^{85} +0.637507 q^{86} -3.11529 q^{87} +5.59308 q^{88} +5.85083 q^{89} -13.9694 q^{90} +10.4110 q^{91} -1.00000 q^{92} +11.1935 q^{93} +2.11142 q^{94} +12.1615 q^{95} +3.11529 q^{96} +5.12271 q^{97} -11.4294 q^{98} -37.5018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.11529	−1.79861	−0.899307	−	0.437317i	$-0.855929\pi$
$3$	−3.11529	−1.79861	−0.899307	+	0.437317i	$0.855929\pi$
$4$	1.00000	0.500000
$5$	2.08342	0.931736	0.465868	−	0.884854i	$-0.345742\pi$
$5$	2.08342	0.931736	0.465868	+	0.884854i	$0.345742\pi$
$6$	3.11529	1.27181
$7$	−4.29295	−1.62258	−0.811291	−	0.584643i	$-0.801235\pi$
$7$	−4.29295	−1.62258	−0.811291	+	0.584643i	$0.801235\pi$
$8$	−1.00000	−0.353553
$9$	6.70504	2.23501
$10$	−2.08342	−0.658837
$11$	−5.59308	−1.68638	−0.843188	−	0.537619i	$-0.819324\pi$
$11$	−5.59308	−1.68638	−0.843188	+	0.537619i	$0.819324\pi$
$12$	−3.11529	−0.899307
$13$	−2.42515	−0.672615	−0.336308	−	0.941752i	$-0.609178\pi$
$13$	−2.42515	−0.672615	−0.336308	+	0.941752i	$0.609178\pi$
$14$	4.29295	1.14734
$15$	−6.49047	−1.67583
$16$	1.00000	0.250000
$17$	−1.01224	−0.245505	−0.122752	−	0.992437i	$-0.539172\pi$
$17$	−1.01224	−0.245505	−0.122752	+	0.992437i	$0.539172\pi$
$18$	−6.70504	−1.58039
$19$	5.83724	1.33916	0.669578	−	0.742742i	$-0.266475\pi$
$19$	5.83724	1.33916	0.669578	+	0.742742i	$0.266475\pi$
$20$	2.08342	0.465868
$21$	13.3738	2.91840
$22$	5.59308	1.19245
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.11529	0.635906
$25$	−0.659343	−0.131869
$26$	2.42515	0.475611
$27$	−11.5423	−2.22131
$28$	−4.29295	−0.811291
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	6.49047	1.18499
$31$	−3.59308	−0.645336	−0.322668	−	0.946512i	$-0.604580\pi$
$31$	−3.59308	−0.645336	−0.322668	+	0.946512i	$0.604580\pi$
$32$	−1.00000	−0.176777
$33$	17.4241	3.03314
$34$	1.01224	0.173598
$35$	−8.94403	−1.51182
$36$	6.70504	1.11751
$37$	−7.58614	−1.24715	−0.623577	−	0.781762i	$-0.714321\pi$
$37$	−7.58614	−1.24715	−0.623577	+	0.781762i	$0.714321\pi$
$38$	−5.83724	−0.946926
$39$	7.55505	1.20978
$40$	−2.08342	−0.329418
$41$	−9.58614	−1.49710	−0.748552	−	0.663076i	$-0.769250\pi$
$41$	−9.58614	−1.49710	−0.748552	+	0.663076i	$0.769250\pi$
$42$	−13.3738	−2.06362
$43$	−0.637507	−0.0972189	−0.0486095	−	0.998818i	$-0.515479\pi$
$43$	−0.637507	−0.0972189	−0.0486095	+	0.998818i	$0.515479\pi$
$44$	−5.59308	−0.843188
$45$	13.9694	2.08244
$46$	1.00000	0.147442
$47$	−2.11142	−0.307982	−0.153991	−	0.988072i	$-0.549213\pi$
$47$	−2.11142	−0.307982	−0.153991	+	0.988072i	$0.549213\pi$
$48$	−3.11529	−0.449654
$49$	11.4294	1.63277
$50$	0.659343	0.0932452
$51$	3.15343	0.441568
$52$	−2.42515	−0.336308
$53$	9.32666	1.28112	0.640558	−	0.767910i	$-0.278703\pi$
$53$	9.32666	1.28112	0.640558	+	0.767910i	$0.278703\pi$
$54$	11.5423	1.57071
$55$	−11.6528	−1.57126
$56$	4.29295	0.573669
$57$	−18.1847	−2.40862
$58$	−1.00000	−0.131306
$59$	3.63843	0.473683	0.236842	−	0.971548i	$-0.423888\pi$
$59$	3.63843	0.473683	0.236842	+	0.971548i	$0.423888\pi$
$60$	−6.49047	−0.837917
$61$	−11.4413	−1.46491	−0.732457	−	0.680813i	$-0.761627\pi$
$61$	−11.4413	−1.46491	−0.732457	+	0.680813i	$0.761627\pi$
$62$	3.59308	0.456321
$63$	−28.7844	−3.62649
$64$	1.00000	0.125000
$65$	−5.05262	−0.626700
$66$	−17.4241	−2.14475
$67$	−5.74676	−0.702078	−0.351039	−	0.936361i	$-0.614172\pi$
$67$	−5.74676	−0.702078	−0.351039	+	0.936361i	$0.614172\pi$
$68$	−1.01224	−0.122752
$69$	3.11529	0.375037
$70$	8.94403	1.06902
$71$	9.47177	1.12409	0.562046	−	0.827106i	$-0.310014\pi$
$71$	9.47177	1.12409	0.562046	+	0.827106i	$0.310014\pi$
$72$	−6.70504	−0.790197
$73$	16.0728	1.88117	0.940587	−	0.339554i	$-0.110276\pi$
$73$	16.0728	1.88117	0.940587	+	0.339554i	$0.110276\pi$
$74$	7.58614	0.881871
$75$	2.05405	0.237181
$76$	5.83724	0.669578
$77$	24.0108	2.73628
$78$	−7.55505	−0.855441
$79$	16.5811	1.86552	0.932760	−	0.360499i	$-0.117394\pi$
$79$	16.5811	1.86552	0.932760	+	0.360499i	$0.117394\pi$
$80$	2.08342	0.232934
$81$	15.8425	1.76027
$82$	9.58614	1.05861
$83$	11.0368	1.21145	0.605726	−	0.795674i	$-0.292883\pi$
$83$	11.0368	1.21145	0.605726	+	0.795674i	$0.292883\pi$
$84$	13.3738	1.45920
$85$	−2.10893	−0.228745
$86$	0.637507	0.0687442
$87$	−3.11529	−0.333994
$88$	5.59308	0.596224
$89$	5.85083	0.620187	0.310093	−	0.950706i	$-0.399640\pi$
$89$	5.85083	0.620187	0.310093	+	0.950706i	$0.399640\pi$
$90$	−13.9694	−1.47251
$91$	10.4110	1.09137
$92$	−1.00000	−0.104257
$93$	11.1935	1.16071
$94$	2.11142	0.217776
$95$	12.1615	1.24774
$96$	3.11529	0.317953
$97$	5.12271	0.520132	0.260066	−	0.965591i	$-0.416256\pi$
$97$	5.12271	0.520132	0.260066	+	0.965591i	$0.416256\pi$
$98$	−11.4294	−1.15454
$99$	−37.5018	−3.76907
$100$	−0.659343	−0.0659343
$101$	0.124875	0.0124255	0.00621275	−	0.999981i	$-0.498022\pi$
$101$	0.124875	0.0124255	0.00621275	+	0.999981i	$0.498022\pi$
$102$	−3.15343	−0.312236
$103$	−9.83539	−0.969109	−0.484555	−	0.874761i	$-0.661018\pi$
$103$	−9.83539	−0.969109	−0.484555	+	0.874761i	$0.661018\pi$
$104$	2.42515	0.237805
$105$	27.8633	2.71918
$106$	−9.32666	−0.905885
$107$	2.73816	0.264708	0.132354	−	0.991203i	$-0.457747\pi$
$107$	2.73816	0.264708	0.132354	+	0.991203i	$0.457747\pi$
$108$	−11.5423	−1.11066
$109$	13.2033	1.26465	0.632323	−	0.774705i	$-0.282101\pi$
$109$	13.2033	1.26465	0.632323	+	0.774705i	$0.282101\pi$
$110$	11.6528	1.11105
$111$	23.6330	2.24315
$112$	−4.29295	−0.405645
$113$	−17.7235	−1.66729	−0.833644	−	0.552301i	$-0.813750\pi$
$113$	−17.7235	−1.66729	−0.833644	+	0.552301i	$0.813750\pi$
$114$	18.1847	1.70315
$115$	−2.08342	−0.194280
$116$	1.00000	0.0928477
$117$	−16.2607	−1.50331
$118$	−3.63843	−0.334945
$119$	4.34550	0.398351
$120$	6.49047	0.592497
$121$	20.2825	1.84386
$122$	11.4413	1.03585
$123$	29.8636	2.69271
$124$	−3.59308	−0.322668
$125$	−11.7908	−1.05460
$126$	28.7844	2.56432
$127$	6.99266	0.620499	0.310249	−	0.950655i	$-0.399587\pi$
$127$	6.99266	0.620499	0.310249	+	0.950655i	$0.399587\pi$
$128$	−1.00000	−0.0883883
$129$	1.98602	0.174859
$130$	5.05262	0.443144
$131$	−0.00748124	−0.000653639 0	−0.000326819	−	1.00000i	$-0.500104\pi$
$131$	−0.00748124	−0.000653639 0	−0.000326819		1.00000i	$0.500104\pi$
$132$	17.4241	1.51657
$133$	−25.0590	−2.17289
$134$	5.74676	0.496444
$135$	−24.0475	−2.06968
$136$	1.01224	0.0867990
$137$	−1.90791	−0.163004	−0.0815020	−	0.996673i	$-0.525972\pi$
$137$	−1.90791	−0.163004	−0.0815020	+	0.996673i	$0.525972\pi$
$138$	−3.11529	−0.265191
$139$	0.487667	0.0413634	0.0206817	−	0.999786i	$-0.493416\pi$
$139$	0.487667	0.0413634	0.0206817	+	0.999786i	$0.493416\pi$
$140$	−8.94403	−0.755909
$141$	6.57769	0.553941
$142$	−9.47177	−0.794854
$143$	13.5640	1.13428
$144$	6.70504	0.558754
$145$	2.08342	0.173019
$146$	−16.0728	−1.33019
$147$	−35.6059	−2.93673
$148$	−7.58614	−0.623577
$149$	7.24420	0.593468	0.296734	−	0.954960i	$-0.404103\pi$
$149$	7.24420	0.593468	0.296734	+	0.954960i	$0.404103\pi$
$150$	−2.05405	−0.167712
$151$	7.27734	0.592222	0.296111	−	0.955154i	$-0.404310\pi$
$151$	7.27734	0.592222	0.296111	+	0.955154i	$0.404310\pi$
$152$	−5.83724	−0.473463
$153$	−6.78712	−0.548706
$154$	−24.0108	−1.93484
$155$	−7.48590	−0.601282
$156$	7.55505	0.604888
$157$	20.8674	1.66540	0.832701	−	0.553723i	$-0.186793\pi$
$157$	20.8674	1.66540	0.832701	+	0.553723i	$0.186793\pi$
$158$	−16.5811	−1.31912
$159$	−29.0553	−2.30423
$160$	−2.08342	−0.164709
$161$	4.29295	0.338332
$162$	−15.8425	−1.24470
$163$	8.61816	0.675027	0.337513	−	0.941321i	$-0.390414\pi$
$163$	8.61816	0.675027	0.337513	+	0.941321i	$0.390414\pi$
$164$	−9.58614	−0.748552
$165$	36.3017	2.82608
$166$	−11.0368	−0.856625
$167$	−24.9412	−1.93001	−0.965003	−	0.262240i	$-0.915539\pi$
$167$	−24.9412	−1.93001	−0.965003	+	0.262240i	$0.915539\pi$
$168$	−13.3738	−1.03181
$169$	−7.11865	−0.547588
$170$	2.10893	0.161747
$171$	39.1390	2.99303
$172$	−0.637507	−0.0486095
$173$	11.0613	0.840976	0.420488	−	0.907298i	$-0.361859\pi$
$173$	11.0613	0.840976	0.420488	+	0.907298i	$0.361859\pi$
$174$	3.11529	0.236170
$175$	2.83052	0.213968
$176$	−5.59308	−0.421594
$177$	−11.3348	−0.851974
$178$	−5.85083	−0.438538
$179$	6.49238	0.485264	0.242632	−	0.970118i	$-0.421989\pi$
$179$	6.49238	0.485264	0.242632	+	0.970118i	$0.421989\pi$
$180$	13.9694	1.04122
$181$	25.1472	1.86918	0.934589	−	0.355731i	$-0.115768\pi$
$181$	25.1472	1.86918	0.934589	+	0.355731i	$0.115768\pi$
$182$	−10.4110	−0.771718
$183$	35.6431	2.63482
$184$	1.00000	0.0737210
$185$	−15.8051	−1.16202
$186$	−11.1935	−0.820746
$187$	5.66154	0.414013
$188$	−2.11142	−0.153991
$189$	49.5504	3.60426
$190$	−12.1615	−0.882285
$191$	−25.2961	−1.83036	−0.915181	−	0.403042i	$-0.867953\pi$
$191$	−25.2961	−1.83036	−0.915181	+	0.403042i	$0.867953\pi$
$192$	−3.11529	−0.224827
$193$	10.2906	0.740735	0.370367	−	0.928885i	$-0.379232\pi$
$193$	10.2906	0.740735	0.370367	+	0.928885i	$0.379232\pi$
$194$	−5.12271	−0.367789
$195$	15.7404	1.12719
$196$	11.4294	0.816385
$197$	4.22908	0.301310	0.150655	−	0.988586i	$-0.451862\pi$
$197$	4.22908	0.301310	0.150655	+	0.988586i	$0.451862\pi$
$198$	37.5018	2.66514
$199$	4.85379	0.344076	0.172038	−	0.985090i	$-0.444965\pi$
$199$	4.85379	0.344076	0.172038	+	0.985090i	$0.444965\pi$
$200$	0.659343	0.0466226
$201$	17.9028	1.26277
$202$	−0.124875	−0.00878615
$203$	−4.29295	−0.301306
$204$	3.15343	0.220784
$205$	−19.9720	−1.39490
$206$	9.83539	0.685264
$207$	−6.70504	−0.466033
$208$	−2.42515	−0.168154
$209$	−32.6482	−2.25832
$210$	−27.8633	−1.92275
$211$	−5.09858	−0.351001	−0.175500	−	0.984479i	$-0.556154\pi$
$211$	−5.09858	−0.351001	−0.175500	+	0.984479i	$0.556154\pi$
$212$	9.32666	0.640558
$213$	−29.5073	−2.02181
$214$	−2.73816	−0.187176
$215$	−1.32820	−0.0905824
$216$	11.5423	0.785353
$217$	15.4249	1.04711
$218$	−13.2033	−0.894240
$219$	−50.0713	−3.38351
$220$	−11.6528	−0.785628
$221$	2.45484	0.165130
$222$	−23.6330	−1.58615
$223$	12.0707	0.808317	0.404158	−	0.914689i	$-0.367564\pi$
$223$	12.0707	0.808317	0.404158	+	0.914689i	$0.367564\pi$
$224$	4.29295	0.286835
$225$	−4.42092	−0.294728
$226$	17.7235	1.17895
$227$	23.5612	1.56381	0.781905	−	0.623397i	$-0.214248\pi$
$227$	23.5612	1.56381	0.781905	+	0.623397i	$0.214248\pi$
$228$	−18.1847	−1.20431
$229$	21.2241	1.40253	0.701263	−	0.712902i	$-0.252620\pi$
$229$	21.2241	1.40253	0.701263	+	0.712902i	$0.252620\pi$
$230$	2.08342	0.137377
$231$	−74.8006	−4.92152
$232$	−1.00000	−0.0656532
$233$	−10.4877	−0.687074	−0.343537	−	0.939139i	$-0.611625\pi$
$233$	−10.4877	−0.687074	−0.343537	+	0.939139i	$0.611625\pi$
$234$	16.2607	1.06300
$235$	−4.39898	−0.286958
$236$	3.63843	0.236842
$237$	−51.6549	−3.35535
$238$	−4.34550	−0.281677
$239$	26.7499	1.73031	0.865153	−	0.501508i	$-0.167221\pi$
$239$	26.7499	1.73031	0.865153	+	0.501508i	$0.167221\pi$
$240$	−6.49047	−0.418958
$241$	−9.75386	−0.628301	−0.314151	−	0.949373i	$-0.601720\pi$
$241$	−9.75386	−0.628301	−0.314151	+	0.949373i	$0.601720\pi$
$242$	−20.2825	−1.30381
$243$	−14.7270	−0.944740
$244$	−11.4413	−0.732457
$245$	23.8123	1.52131
$246$	−29.8636	−1.90404
$247$	−14.1562	−0.900737
$248$	3.59308	0.228161
$249$	−34.3830	−2.17893
$250$	11.7908	0.745716
$251$	−14.7728	−0.932454	−0.466227	−	0.884665i	$-0.654387\pi$
$251$	−14.7728	−0.932454	−0.466227	+	0.884665i	$0.654387\pi$
$252$	−28.7844	−1.81325
$253$	5.59308	0.351634
$254$	−6.99266	−0.438759
$255$	6.56993	0.411425
$256$	1.00000	0.0625000
$257$	−21.7809	−1.35866	−0.679328	−	0.733835i	$-0.737728\pi$
$257$	−21.7809	−1.35866	−0.679328	+	0.733835i	$0.737728\pi$
$258$	−1.98602	−0.123644
$259$	32.5669	2.02361
$260$	−5.05262	−0.313350
$261$	6.70504	0.415032
$262$	0.00748124	0.000462192 0
$263$	20.5775	1.26887	0.634433	−	0.772978i	$-0.281234\pi$
$263$	20.5775	1.26887	0.634433	+	0.772978i	$0.281234\pi$
$264$	−17.4241	−1.07238
$265$	19.4314	1.19366
$266$	25.0590	1.53646
$267$	−18.2270	−1.11548
$268$	−5.74676	−0.351039
$269$	−6.42493	−0.391735	−0.195867	−	0.980630i	$-0.562752\pi$
$269$	−6.42493	−0.391735	−0.195867	+	0.980630i	$0.562752\pi$
$270$	24.0475	1.46348
$271$	1.35972	0.0825971	0.0412986	−	0.999147i	$-0.486851\pi$
$271$	1.35972	0.0825971	0.0412986	+	0.999147i	$0.486851\pi$
$272$	−1.01224	−0.0613762
$273$	−32.4334	−1.96296
$274$	1.90791	0.115261
$275$	3.68776	0.222380
$276$	3.11529	0.187519
$277$	−21.2687	−1.27792	−0.638958	−	0.769242i	$-0.720634\pi$
$277$	−21.2687	−1.27792	−0.638958	+	0.769242i	$0.720634\pi$
$278$	−0.487667	−0.0292483
$279$	−24.0917	−1.44233
$280$	8.94403	0.534508
$281$	−22.6386	−1.35051	−0.675253	−	0.737586i	$-0.735966\pi$
$281$	−22.6386	−1.35051	−0.675253	+	0.737586i	$0.735966\pi$
$282$	−6.57769	−0.391696
$283$	7.06466	0.419950	0.209975	−	0.977707i	$-0.432662\pi$
$283$	7.06466	0.419950	0.209975	+	0.977707i	$0.432662\pi$
$284$	9.47177	0.562046
$285$	−37.8865	−2.24420
$286$	−13.5640	−0.802059
$287$	41.1528	2.42917
$288$	−6.70504	−0.395098
$289$	−15.9754	−0.939727
$290$	−2.08342	−0.122343
$291$	−15.9587	−0.935517
$292$	16.0728	0.940587
$293$	−16.7387	−0.977887	−0.488944	−	0.872315i	$-0.662618\pi$
$293$	−16.7387	−0.977887	−0.488944	+	0.872315i	$0.662618\pi$
$294$	35.6059	2.07658
$295$	7.58040	0.441348
$296$	7.58614	0.440935
$297$	64.5569	3.74597
$298$	−7.24420	−0.419645
$299$	2.42515	0.140250
$300$	2.05405	0.118590
$301$	2.73678	0.157746
$302$	−7.27734	−0.418764
$303$	−0.389021	−0.0223487
$304$	5.83724	0.334789
$305$	−23.8372	−1.36491
$306$	6.78712	0.387994
$307$	−4.64415	−0.265056	−0.132528	−	0.991179i	$-0.542309\pi$
$307$	−4.64415	−0.265056	−0.132528	+	0.991179i	$0.542309\pi$
$308$	24.0108	1.36814
$309$	30.6401	1.74305
$310$	7.48590	0.425171
$311$	−12.7133	−0.720908	−0.360454	−	0.932777i	$-0.617378\pi$
$311$	−12.7133	−0.720908	−0.360454	+	0.932777i	$0.617378\pi$
$312$	−7.55505	−0.427720
$313$	5.72039	0.323335	0.161668	−	0.986845i	$-0.448313\pi$
$313$	5.72039	0.323335	0.161668	+	0.986845i	$0.448313\pi$
$314$	−20.8674	−1.17762
$315$	−59.9701	−3.37893
$316$	16.5811	0.932760
$317$	−13.8371	−0.777169	−0.388584	−	0.921413i	$-0.627036\pi$
$317$	−13.8371	−0.777169	−0.388584	+	0.921413i	$0.627036\pi$
$318$	29.0553	1.62934
$319$	−5.59308	−0.313152
$320$	2.08342	0.116467
$321$	−8.53015	−0.476107
$322$	−4.29295	−0.239237
$323$	−5.90870	−0.328769
$324$	15.8425	0.880137
$325$	1.59901	0.0886969
$326$	−8.61816	−0.477316
$327$	−41.1321	−2.27461
$328$	9.58614	0.529306
$329$	9.06422	0.499726
$330$	−36.3017	−1.99834
$331$	18.2367	1.00238	0.501190	−	0.865337i	$-0.332896\pi$
$331$	18.2367	1.00238	0.501190	+	0.865337i	$0.332896\pi$
$332$	11.0368	0.605726
$333$	−50.8654	−2.78741
$334$	24.9412	1.36472
$335$	−11.9729	−0.654151
$336$	13.3738	0.729600
$337$	13.1078	0.714026	0.357013	−	0.934099i	$-0.383795\pi$
$337$	13.1078	0.714026	0.357013	+	0.934099i	$0.383795\pi$
$338$	7.11865	0.387203
$339$	55.2139	2.99881
$340$	−2.10893	−0.114373
$341$	20.0963	1.08828
$342$	−39.1390	−2.11639
$343$	−19.0152	−1.02672
$344$	0.637507	0.0343721
$345$	6.49047	0.349435
$346$	−11.0613	−0.594660
$347$	0.180848	0.00970844	0.00485422	−	0.999988i	$-0.498455\pi$
$347$	0.180848	0.00970844	0.00485422	+	0.999988i	$0.498455\pi$
$348$	−3.11529	−0.166997
$349$	−18.8127	−1.00702	−0.503511	−	0.863989i	$-0.667959\pi$
$349$	−18.8127	−1.00702	−0.503511	+	0.863989i	$0.667959\pi$
$350$	−2.83052	−0.151298
$351$	27.9918	1.49409
$352$	5.59308	0.298112
$353$	−6.96488	−0.370703	−0.185352	−	0.982672i	$-0.559342\pi$
$353$	−6.96488	−0.370703	−0.185352	+	0.982672i	$0.559342\pi$
$354$	11.3348	0.602436
$355$	19.7337	1.04736
$356$	5.85083	0.310093
$357$	−13.5375	−0.716480
$358$	−6.49238	−0.343133
$359$	−22.3497	−1.17957	−0.589785	−	0.807560i	$-0.700787\pi$
$359$	−22.3497	−1.17957	−0.589785	+	0.807560i	$0.700787\pi$
$360$	−13.9694	−0.736255
$361$	15.0734	0.793338
$362$	−25.1472	−1.32171
$363$	−63.1859	−3.31640
$364$	10.4110	0.545687
$365$	33.4864	1.75276
$366$	−35.6431	−1.86310
$367$	−1.79712	−0.0938091	−0.0469046	−	0.998899i	$-0.514936\pi$
$367$	−1.79712	−0.0938091	−0.0469046	+	0.998899i	$0.514936\pi$
$368$	−1.00000	−0.0521286
$369$	−64.2755	−3.34605
$370$	15.8051	0.821671
$371$	−40.0389	−2.07871
$372$	11.1935	0.580355
$373$	15.1627	0.785093	0.392547	−	0.919732i	$-0.371594\pi$
$373$	15.1627	0.785093	0.392547	+	0.919732i	$0.371594\pi$
$374$	−5.66154	−0.292751
$375$	36.7318	1.89682
$376$	2.11142	0.108888
$377$	−2.42515	−0.124902
$378$	−49.5504	−2.54860
$379$	−5.84836	−0.300410	−0.150205	−	0.988655i	$-0.547993\pi$
$379$	−5.84836	−0.300410	−0.150205	+	0.988655i	$0.547993\pi$
$380$	12.1615	0.623870
$381$	−21.7842	−1.11604
$382$	25.2961	1.29426
$383$	36.0050	1.83977	0.919884	−	0.392190i	$-0.128282\pi$
$383$	36.0050	1.83977	0.919884	+	0.392190i	$0.128282\pi$
$384$	3.11529	0.158977
$385$	50.0246	2.54949
$386$	−10.2906	−0.523778
$387$	−4.27451	−0.217286
$388$	5.12271	0.260066
$389$	−16.8129	−0.852446	−0.426223	−	0.904618i	$-0.640156\pi$
$389$	−16.8129	−0.852446	−0.426223	+	0.904618i	$0.640156\pi$
$390$	−15.7404	−0.797045
$391$	1.01224	0.0511913
$392$	−11.4294	−0.577272
$393$	0.0233062	0.00117564
$394$	−4.22908	−0.213058
$395$	34.5455	1.73817
$396$	−37.5018	−1.88454
$397$	10.3689	0.520401	0.260201	−	0.965555i	$-0.416211\pi$
$397$	10.3689	0.520401	0.260201	+	0.965555i	$0.416211\pi$
$398$	−4.85379	−0.243298
$399$	78.0660	3.90819
$400$	−0.659343	−0.0329672
$401$	5.20531	0.259941	0.129970	−	0.991518i	$-0.458512\pi$
$401$	5.20531	0.259941	0.129970	+	0.991518i	$0.458512\pi$
$402$	−17.9028	−0.892912
$403$	8.71375	0.434063
$404$	0.124875	0.00621275
$405$	33.0066	1.64011
$406$	4.29295	0.213055
$407$	42.4299	2.10317
$408$	−3.15343	−0.156118
$409$	14.8300	0.733297	0.366648	−	0.930360i	$-0.380505\pi$
$409$	14.8300	0.733297	0.366648	+	0.930360i	$0.380505\pi$
$410$	19.9720	0.986347
$411$	5.94371	0.293181
$412$	−9.83539	−0.484555
$413$	−15.6196	−0.768590
$414$	6.70504	0.329535
$415$	22.9944	1.12875
$416$	2.42515	0.118903
$417$	−1.51923	−0.0743968
$418$	32.6482	1.59687
$419$	−5.31761	−0.259782	−0.129891	−	0.991528i	$-0.541463\pi$
$419$	−5.31761	−0.259782	−0.129891	+	0.991528i	$0.541463\pi$
$420$	27.8633	1.35959
$421$	−9.33097	−0.454764	−0.227382	−	0.973806i	$-0.573017\pi$
$421$	−9.33097	−0.454764	−0.227382	+	0.973806i	$0.573017\pi$
$422$	5.09858	0.248195
$423$	−14.1572	−0.688345
$424$	−9.32666	−0.452943
$425$	0.667414	0.0323744
$426$	29.5073	1.42964
$427$	49.1171	2.37694
$428$	2.73816	0.132354
$429$	−42.2560	−2.04014
$430$	1.32820	0.0640514
$431$	−22.5088	−1.08421	−0.542105	−	0.840311i	$-0.682373\pi$
$431$	−22.5088	−1.08421	−0.542105	+	0.840311i	$0.682373\pi$
$432$	−11.5423	−0.555329
$433$	−17.6029	−0.845943	−0.422971	−	0.906143i	$-0.639013\pi$
$433$	−17.6029	−0.845943	−0.422971	+	0.906143i	$0.639013\pi$
$434$	−15.4249	−0.740418
$435$	−6.49047	−0.311194
$436$	13.2033	0.632323
$437$	−5.83724	−0.279233
$438$	50.0713	2.39250
$439$	24.3103	1.16027	0.580134	−	0.814521i	$-0.303000\pi$
$439$	24.3103	1.16027	0.580134	+	0.814521i	$0.303000\pi$
$440$	11.6528	0.555523
$441$	76.6346	3.64927
$442$	−2.45484	−0.116765
$443$	−16.1133	−0.765567	−0.382783	−	0.923838i	$-0.625034\pi$
$443$	−16.1133	−0.765567	−0.382783	+	0.923838i	$0.625034\pi$
$444$	23.6330	1.12157
$445$	12.1898	0.577850
$446$	−12.0707	−0.571566
$447$	−22.5678	−1.06742
$448$	−4.29295	−0.202823
$449$	−9.72200	−0.458810	−0.229405	−	0.973331i	$-0.573678\pi$
$449$	−9.72200	−0.458810	−0.229405	+	0.973331i	$0.573678\pi$
$450$	4.42092	0.208404
$451$	53.6160	2.52468
$452$	−17.7235	−0.833644
$453$	−22.6711	−1.06518
$454$	−23.5612	−1.10578
$455$	21.6906	1.01687
$456$	18.1847	0.851577
$457$	−28.1428	−1.31647	−0.658233	−	0.752814i	$-0.728696\pi$
$457$	−28.1428	−1.31647	−0.658233	+	0.752814i	$0.728696\pi$
$458$	−21.2241	−0.991736
$459$	11.6836	0.545343
$460$	−2.08342	−0.0971402
$461$	−0.187607	−0.00873772	−0.00436886	−	0.999990i	$-0.501391\pi$
$461$	−0.187607	−0.00873772	−0.00436886	+	0.999990i	$0.501391\pi$
$462$	74.8006	3.48004
$463$	10.1401	0.471252	0.235626	−	0.971844i	$-0.424286\pi$
$463$	10.1401	0.471252	0.235626	+	0.971844i	$0.424286\pi$
$464$	1.00000	0.0464238
$465$	23.3208	1.08147
$466$	10.4877	0.485835
$467$	15.8714	0.734441	0.367220	−	0.930134i	$-0.380310\pi$
$467$	15.8714	0.734441	0.367220	+	0.930134i	$0.380310\pi$
$468$	−16.2607	−0.751653
$469$	24.6705	1.13918
$470$	4.39898	0.202910
$471$	−65.0081	−2.99542
$472$	−3.63843	−0.167472
$473$	3.56563	0.163948
$474$	51.6549	2.37259
$475$	−3.84875	−0.176593
$476$	4.34550	0.199176
$477$	62.5356	2.86331
$478$	−26.7499	−1.22351
$479$	−7.31386	−0.334179	−0.167089	−	0.985942i	$-0.553437\pi$
$479$	−7.31386	−0.334179	−0.167089	+	0.985942i	$0.553437\pi$
$480$	6.49047	0.296248
$481$	18.3975	0.838855
$482$	9.75386	0.444276
$483$	−13.3738	−0.608528
$484$	20.2825	0.921932
$485$	10.6728	0.484626
$486$	14.7270	0.668032
$487$	21.9044	0.992583	0.496291	−	0.868156i	$-0.334695\pi$
$487$	21.9044	0.992583	0.496291	+	0.868156i	$0.334695\pi$
$488$	11.4413	0.517926
$489$	−26.8481	−1.21411
$490$	−23.8123	−1.07573
$491$	−35.0527	−1.58190	−0.790952	−	0.611878i	$-0.790414\pi$
$491$	−35.0527	−1.58190	−0.790952	+	0.611878i	$0.790414\pi$
$492$	29.8636	1.34636
$493$	−1.01224	−0.0455891
$494$	14.1562	0.636917
$495$	−78.1322	−3.51178
$496$	−3.59308	−0.161334
$497$	−40.6618	−1.82393
$498$	34.3830	1.54074
$499$	−32.3564	−1.44847	−0.724236	−	0.689552i	$-0.757807\pi$
$499$	−32.3564	−1.44847	−0.724236	+	0.689552i	$0.757807\pi$
$500$	−11.7908	−0.527301
$501$	77.6990	3.47134
$502$	14.7728	0.659344
$503$	−11.5726	−0.515997	−0.257999	−	0.966145i	$-0.583063\pi$
$503$	−11.5726	−0.515997	−0.257999	+	0.966145i	$0.583063\pi$
$504$	28.7844	1.28216
$505$	0.260167	0.0115773
$506$	−5.59308	−0.248643
$507$	22.1767	0.984900
$508$	6.99266	0.310249
$509$	17.7938	0.788695	0.394348	−	0.918961i	$-0.370971\pi$
$509$	17.7938	0.788695	0.394348	+	0.918961i	$0.370971\pi$
$510$	−6.56993	−0.290921
$511$	−68.9995	−3.05236
$512$	−1.00000	−0.0441942
$513$	−67.3751	−2.97469
$514$	21.7809	0.960714
$515$	−20.4913	−0.902954
$516$	1.98602	0.0874297
$517$	11.8093	0.519374
$518$	−32.5669	−1.43091
$519$	−34.4592	−1.51259
$520$	5.05262	0.221572
$521$	−19.3505	−0.847762	−0.423881	−	0.905718i	$-0.639332\pi$
$521$	−19.3505	−0.847762	−0.423881	+	0.905718i	$0.639332\pi$
$522$	−6.70504	−0.293472
$523$	31.6001	1.38178	0.690888	−	0.722962i	$-0.257220\pi$
$523$	31.6001	1.38178	0.690888	+	0.722962i	$0.257220\pi$
$524$	−0.00748124	−0.000326819 0
$525$	−8.81791	−0.384845
$526$	−20.5775	−0.897223
$527$	3.63706	0.158433
$528$	17.4241	0.758285
$529$	1.00000	0.0434783
$530$	−19.4314	−0.844046
$531$	24.3958	1.05869
$532$	−25.0590	−1.08644
$533$	23.2478	1.00698
$534$	18.2270	0.788761
$535$	5.70474	0.246637
$536$	5.74676	0.248222
$537$	−20.2257	−0.872802
$538$	6.42493	0.276998
$539$	−63.9255	−2.75347
$540$	−24.0475	−1.03484
$541$	20.2787	0.871851	0.435926	−	0.899983i	$-0.356421\pi$
$541$	20.2787	0.871851	0.435926	+	0.899983i	$0.356421\pi$
$542$	−1.35972	−0.0584050
$543$	−78.3409	−3.36193
$544$	1.01224	0.0433995
$545$	27.5081	1.17832
$546$	32.4334	1.38802
$547$	−3.92415	−0.167785	−0.0838923	−	0.996475i	$-0.526735\pi$
$547$	−3.92415	−0.167785	−0.0838923	+	0.996475i	$0.526735\pi$
$548$	−1.90791	−0.0815020
$549$	−76.7147	−3.27410
$550$	−3.68776	−0.157246
$551$	5.83724	0.248675
$552$	−3.11529	−0.132596
$553$	−71.1818	−3.02696
$554$	21.2687	0.903623
$555$	49.2376	2.09002
$556$	0.487667	0.0206817
$557$	25.2858	1.07139	0.535696	−	0.844411i	$-0.320049\pi$
$557$	25.2858	1.07139	0.535696	+	0.844411i	$0.320049\pi$
$558$	24.0917	1.01988
$559$	1.54605	0.0653910
$560$	−8.94403	−0.377954
$561$	−17.6374	−0.744650
$562$	22.6386	0.954952
$563$	36.5269	1.53943	0.769713	−	0.638390i	$-0.220399\pi$
$563$	36.5269	1.53943	0.769713	+	0.638390i	$0.220399\pi$
$564$	6.57769	0.276971
$565$	−36.9256	−1.55347
$566$	−7.06466	−0.296950
$567$	−68.0109	−2.85619
$568$	−9.47177	−0.397427
$569$	32.4133	1.35884	0.679418	−	0.733751i	$-0.262232\pi$
$569$	32.4133	1.35884	0.679418	+	0.733751i	$0.262232\pi$
$570$	37.8865	1.58689
$571$	−16.6621	−0.697288	−0.348644	−	0.937255i	$-0.613358\pi$
$571$	−16.6621	−0.697288	−0.348644	+	0.937255i	$0.613358\pi$
$572$	13.5640	0.567141
$573$	78.8048	3.29212
$574$	−41.1528	−1.71768
$575$	0.659343	0.0274965
$576$	6.70504	0.279377
$577$	35.3544	1.47182	0.735912	−	0.677077i	$-0.236754\pi$
$577$	35.3544	1.47182	0.735912	+	0.677077i	$0.236754\pi$
$578$	15.9754	0.664488
$579$	−32.0583	−1.33230
$580$	2.08342	0.0865095
$581$	−47.3806	−1.96568
$582$	15.9587	0.661510
$583$	−52.1647	−2.16044
$584$	−16.0728	−0.665095
$585$	−33.8780	−1.40068
$586$	16.7387	0.691471
$587$	12.7410	0.525879	0.262939	−	0.964812i	$-0.415308\pi$
$587$	12.7410	0.525879	0.262939	+	0.964812i	$0.415308\pi$
$588$	−35.6059	−1.46836
$589$	−20.9737	−0.864205
$590$	−7.58040	−0.312080
$591$	−13.1748	−0.541940
$592$	−7.58614	−0.311788
$593$	−37.9961	−1.56031	−0.780156	−	0.625585i	$-0.784860\pi$
$593$	−37.9961	−1.56031	−0.780156	+	0.625585i	$0.784860\pi$
$594$	−64.5569	−2.64880
$595$	9.05352	0.371158
$596$	7.24420	0.296734
$597$	−15.1210	−0.618860
$598$	−2.42515	−0.0991717
$599$	−35.2369	−1.43974	−0.719870	−	0.694108i	$-0.755799\pi$
$599$	−35.2369	−1.43974	−0.719870	+	0.694108i	$0.755799\pi$
$600$	−2.05405	−0.0838561
$601$	12.4868	0.509347	0.254673	−	0.967027i	$-0.418032\pi$
$601$	12.4868	0.509347	0.254673	+	0.967027i	$0.418032\pi$
$602$	−2.73678	−0.111543
$603$	−38.5323	−1.56915
$604$	7.27734	0.296111
$605$	42.2571	1.71799
$606$	0.389021	0.0158029
$607$	−18.9793	−0.770346	−0.385173	−	0.922844i	$-0.625858\pi$
$607$	−18.9793	−0.770346	−0.385173	+	0.922844i	$0.625858\pi$
$608$	−5.83724	−0.236732
$609$	13.3738	0.541933
$610$	23.8372	0.965139
$611$	5.12051	0.207154
$612$	−6.78712	−0.274353
$613$	−22.2325	−0.897961	−0.448981	−	0.893541i	$-0.648213\pi$
$613$	−22.2325	−0.897961	−0.448981	+	0.893541i	$0.648213\pi$
$614$	4.64415	0.187423
$615$	62.2186	2.50890
$616$	−24.0108	−0.967422
$617$	48.0344	1.93379	0.966897	−	0.255167i	$-0.0821305\pi$
$617$	48.0344	1.93379	0.966897	+	0.255167i	$0.0821305\pi$
$618$	−30.6401	−1.23253
$619$	−32.1051	−1.29041	−0.645207	−	0.764007i	$-0.723229\pi$
$619$	−32.1051	−1.29041	−0.645207	+	0.764007i	$0.723229\pi$
$620$	−7.48590	−0.300641
$621$	11.5423	0.463176
$622$	12.7133	0.509759
$623$	−25.1173	−1.00630
$624$	7.55505	0.302444
$625$	−21.2686	−0.850742
$626$	−5.72039	−0.228633
$627$	101.709	4.06185
$628$	20.8674	0.832701
$629$	7.67901	0.306182
$630$	59.9701	2.38927
$631$	9.67378	0.385107	0.192554	−	0.981286i	$-0.438323\pi$
$631$	9.67378	0.385107	0.192554	+	0.981286i	$0.438323\pi$
$632$	−16.5811	−0.659561
$633$	15.8836	0.631315
$634$	13.8371	0.549541
$635$	14.5687	0.578141
$636$	−29.0553	−1.15212
$637$	−27.7180	−1.09823
$638$	5.59308	0.221432
$639$	63.5086	2.51236
$640$	−2.08342	−0.0823546
$641$	11.2143	0.442939	0.221469	−	0.975167i	$-0.428915\pi$
$641$	11.2143	0.442939	0.221469	+	0.975167i	$0.428915\pi$
$642$	8.53015	0.336658
$643$	10.9416	0.431494	0.215747	−	0.976449i	$-0.430781\pi$
$643$	10.9416	0.431494	0.215747	+	0.976449i	$0.430781\pi$
$644$	4.29295	0.169166
$645$	4.13772	0.162923
$646$	5.90870	0.232475
$647$	−25.1019	−0.986857	−0.493428	−	0.869786i	$-0.664256\pi$
$647$	−25.1019	−0.986857	−0.493428	+	0.869786i	$0.664256\pi$
$648$	−15.8425	−0.622351
$649$	−20.3500	−0.798808
$650$	−1.59901	−0.0627182
$651$	−48.0530	−1.88335
$652$	8.61816	0.337513
$653$	14.2104	0.556096	0.278048	−	0.960567i	$-0.410313\pi$
$653$	14.2104	0.556096	0.278048	+	0.960567i	$0.410313\pi$
$654$	41.1321	1.60839
$655$	−0.0155866	−0.000609019 0
$656$	−9.58614	−0.374276
$657$	107.768	4.20445
$658$	−9.06422	−0.353360
$659$	28.4749	1.10922	0.554612	−	0.832109i	$-0.312867\pi$
$659$	28.4749	1.10922	0.554612	+	0.832109i	$0.312867\pi$
$660$	36.3017	1.41304
$661$	−8.27948	−0.322035	−0.161017	−	0.986952i	$-0.551477\pi$
$661$	−8.27948	−0.322035	−0.161017	+	0.986952i	$0.551477\pi$
$662$	−18.2367	−0.708790
$663$	−7.64753	−0.297006
$664$	−11.0368	−0.428313
$665$	−52.2085	−2.02456
$666$	50.8654	1.97099
$667$	−1.00000	−0.0387202
$668$	−24.9412	−0.965003
$669$	−37.6039	−1.45385
$670$	11.9729	0.462555
$671$	63.9923	2.47040
$672$	−13.3738	−0.515905
$673$	0.0933122	0.00359692	0.00179846	−	0.999998i	$-0.499428\pi$
$673$	0.0933122	0.00359692	0.00179846	+	0.999998i	$0.499428\pi$
$674$	−13.1078	−0.504893
$675$	7.61033	0.292922
$676$	−7.11865	−0.273794
$677$	6.44257	0.247608	0.123804	−	0.992307i	$-0.460491\pi$
$677$	6.44257	0.247608	0.123804	+	0.992307i	$0.460491\pi$
$678$	−55.2139	−2.12048
$679$	−21.9915	−0.843957
$680$	2.10893	0.0808737
$681$	−73.4000	−2.81269
$682$	−20.0963	−0.769529
$683$	−24.9257	−0.953757	−0.476878	−	0.878969i	$-0.658232\pi$
$683$	−24.9257	−0.953757	−0.476878	+	0.878969i	$0.658232\pi$
$684$	39.1390	1.49652
$685$	−3.97499	−0.151877
$686$	19.0152	0.726002
$687$	−66.1192	−2.52260
$688$	−0.637507	−0.0243047
$689$	−22.6185	−0.861698
$690$	−6.49047	−0.247088
$691$	40.4202	1.53766	0.768829	−	0.639454i	$-0.220840\pi$
$691$	40.4202	1.53766	0.768829	+	0.639454i	$0.220840\pi$
$692$	11.0613	0.420488
$693$	160.993	6.11563
$694$	−0.180848	−0.00686491
$695$	1.01602	0.0385397
$696$	3.11529	0.118085
$697$	9.70349	0.367546
$698$	18.8127	0.712072
$699$	32.6723	1.23578
$700$	2.83052	0.106984
$701$	39.4576	1.49029	0.745146	−	0.666902i	$-0.232380\pi$
$701$	39.4576	1.49029	0.745146	+	0.666902i	$0.232380\pi$
$702$	−27.9918	−1.05648
$703$	−44.2822	−1.67013
$704$	−5.59308	−0.210797
$705$	13.7041	0.516127
$706$	6.96488	0.262127
$707$	−0.536080	−0.0201614
$708$	−11.3348	−0.425987
$709$	−21.4733	−0.806445	−0.403223	−	0.915102i	$-0.632110\pi$
$709$	−21.4733	−0.806445	−0.403223	+	0.915102i	$0.632110\pi$
$710$	−19.7337	−0.740593
$711$	111.177	4.16946
$712$	−5.85083	−0.219269
$713$	3.59308	0.134562
$714$	13.5375	0.506628
$715$	28.2597	1.05685
$716$	6.49238	0.242632
$717$	−83.3337	−3.11215
$718$	22.3497	0.834082
$719$	5.71462	0.213120	0.106560	−	0.994306i	$-0.466016\pi$
$719$	5.71462	0.213120	0.106560	+	0.994306i	$0.466016\pi$
$720$	13.9694	0.520611
$721$	42.2228	1.57246
$722$	−15.0734	−0.560975
$723$	30.3861	1.13007
$724$	25.1472	0.934589
$725$	−0.659343	−0.0244874
$726$	63.1859	2.34505
$727$	−46.2708	−1.71609	−0.858044	−	0.513576i	$-0.828320\pi$
$727$	−46.2708	−1.71609	−0.858044	+	0.513576i	$0.828320\pi$
$728$	−10.4110	−0.385859
$729$	−1.64839	−0.0610515
$730$	−33.4864	−1.23939
$731$	0.645311	0.0238677
$732$	35.6431	1.31741
$733$	36.4508	1.34634	0.673171	−	0.739487i	$-0.264932\pi$
$733$	36.4508	1.34634	0.673171	+	0.739487i	$0.264932\pi$
$734$	1.79712	0.0663331
$735$	−74.1822	−2.73625
$736$	1.00000	0.0368605
$737$	32.1421	1.18397
$738$	64.2755	2.36601
$739$	49.2655	1.81226	0.906130	−	0.422998i	$-0.139022\pi$
$739$	49.2655	1.81226	0.906130	+	0.422998i	$0.139022\pi$
$740$	−15.8051	−0.581009
$741$	44.1007	1.62008
$742$	40.0389	1.46987
$743$	−32.7759	−1.20243	−0.601215	−	0.799087i	$-0.705316\pi$
$743$	−32.7759	−1.20243	−0.601215	+	0.799087i	$0.705316\pi$
$744$	−11.1935	−0.410373
$745$	15.0927	0.552955
$746$	−15.1627	−0.555145
$747$	74.0025	2.70761
$748$	5.66154	0.207007
$749$	−11.7548	−0.429510
$750$	−36.7318	−1.34126
$751$	−22.8885	−0.835214	−0.417607	−	0.908628i	$-0.637131\pi$
$751$	−22.8885	−0.835214	−0.417607	+	0.908628i	$0.637131\pi$
$752$	−2.11142	−0.0769956
$753$	46.0217	1.67712
$754$	2.42515	0.0883187
$755$	15.1618	0.551794
$756$	49.5504	1.80213
$757$	21.5955	0.784903	0.392452	−	0.919773i	$-0.371627\pi$
$757$	21.5955	0.784903	0.392452	+	0.919773i	$0.371627\pi$
$758$	5.84836	0.212422
$759$	−17.4241	−0.632453
$760$	−12.1615	−0.441142
$761$	34.3524	1.24527	0.622637	−	0.782511i	$-0.286061\pi$
$761$	34.3524	1.24527	0.622637	+	0.782511i	$0.286061\pi$
$762$	21.7842	0.789158
$763$	−56.6811	−2.05199
$764$	−25.2961	−0.915181
$765$	−14.1405	−0.511249
$766$	−36.0050	−1.30091
$767$	−8.82374	−0.318607
$768$	−3.11529	−0.112413
$769$	35.6652	1.28612	0.643060	−	0.765816i	$-0.277664\pi$
$769$	35.6652	1.28612	0.643060	+	0.765816i	$0.277664\pi$
$770$	−50.0246	−1.80276
$771$	67.8538	2.44370
$772$	10.2906	0.370367
$773$	15.7186	0.565357	0.282679	−	0.959215i	$-0.408777\pi$
$773$	15.7186	0.565357	0.282679	+	0.959215i	$0.408777\pi$
$774$	4.27451	0.153644
$775$	2.36907	0.0850995
$776$	−5.12271	−0.183894
$777$	−101.455	−3.63969
$778$	16.8129	0.602771
$779$	−55.9566	−2.00485
$780$	15.7404	0.563596
$781$	−52.9763	−1.89564
$782$	−1.01224	−0.0361977
$783$	−11.5423	−0.412488
$784$	11.4294	0.408193
$785$	43.4757	1.55171
$786$	−0.0233062	−0.000831306 0
$787$	46.4087	1.65429	0.827145	−	0.561988i	$-0.189963\pi$
$787$	46.4087	1.65429	0.827145	+	0.561988i	$0.189963\pi$
$788$	4.22908	0.150655
$789$	−64.1050	−2.28220
$790$	−34.5455	−1.22907
$791$	76.0862	2.70531
$792$	37.5018	1.33257
$793$	27.7470	0.985324
$794$	−10.3689	−0.367979
$795$	−60.5344	−2.14694
$796$	4.85379	0.172038
$797$	−1.91781	−0.0679322	−0.0339661	−	0.999423i	$-0.510814\pi$
$797$	−1.91781	−0.0679322	−0.0339661	+	0.999423i	$0.510814\pi$
$798$	−78.0660	−2.76351
$799$	2.13727	0.0756111
$800$	0.659343	0.0233113
$801$	39.2301	1.38613
$802$	−5.20531	−0.183806
$803$	−89.8961	−3.17237
$804$	17.9028	0.631384
$805$	8.94403	0.315236
$806$	−8.71375	−0.306929
$807$	20.0155	0.704580
$808$	−0.124875	−0.00439308
$809$	−17.7557	−0.624256	−0.312128	−	0.950040i	$-0.601042\pi$
$809$	−17.7557	−0.624256	−0.312128	+	0.950040i	$0.601042\pi$
$810$	−33.0066	−1.15973
$811$	38.2928	1.34464	0.672322	−	0.740259i	$-0.265297\pi$
$811$	38.2928	1.34464	0.672322	+	0.740259i	$0.265297\pi$
$812$	−4.29295	−0.150653
$813$	−4.23593	−0.148560
$814$	−42.4299	−1.48717
$815$	17.9553	0.628946
$816$	3.15343	0.110392
$817$	−3.72129	−0.130191
$818$	−14.8300	−0.518519
$819$	69.8065	2.43924
$820$	−19.9720	−0.697452
$821$	30.6039	1.06808	0.534041	−	0.845459i	$-0.320673\pi$
$821$	30.6039	1.06808	0.534041	+	0.845459i	$0.320673\pi$
$822$	−5.94371	−0.207311
$823$	0.219791	0.00766144	0.00383072	−	0.999993i	$-0.498781\pi$
$823$	0.219791	0.00766144	0.00383072	+	0.999993i	$0.498781\pi$
$824$	9.83539	0.342632
$825$	−11.4884	−0.399976
$826$	15.6196	0.543475
$827$	22.8810	0.795650	0.397825	−	0.917461i	$-0.369765\pi$
$827$	22.8810	0.795650	0.397825	+	0.917461i	$0.369765\pi$
$828$	−6.70504	−0.233016
$829$	39.7419	1.38029	0.690147	−	0.723670i	$-0.257546\pi$
$829$	39.7419	1.38029	0.690147	+	0.723670i	$0.257546\pi$
$830$	−22.9944	−0.798148
$831$	66.2584	2.29848
$832$	−2.42515	−0.0840769
$833$	−11.5693	−0.400853
$834$	1.51923	0.0526065
$835$	−51.9630	−1.79825
$836$	−32.6482	−1.12916
$837$	41.4723	1.43349
$838$	5.31761	0.183694
$839$	−13.2386	−0.457048	−0.228524	−	0.973538i	$-0.573390\pi$
$839$	−13.2386	−0.457048	−0.228524	+	0.973538i	$0.573390\pi$
$840$	−27.8633	−0.961374
$841$	1.00000	0.0344828
$842$	9.33097	0.321567
$843$	70.5259	2.42904
$844$	−5.09858	−0.175500
$845$	−14.8312	−0.510208
$846$	14.1572	0.486733
$847$	−87.0717	−2.99182
$848$	9.32666	0.320279
$849$	−22.0085	−0.755329
$850$	−0.667414	−0.0228921
$851$	7.58614	0.260050
$852$	−29.5073	−1.01090
$853$	17.7775	0.608689	0.304345	−	0.952562i	$-0.401563\pi$
$853$	17.7775	0.608689	0.304345	+	0.952562i	$0.401563\pi$
$854$	−49.1171	−1.68075
$855$	81.5431	2.78871
$856$	−2.73816	−0.0935882
$857$	−12.7178	−0.434431	−0.217216	−	0.976124i	$-0.569697\pi$
$857$	−12.7178	−0.434431	−0.217216	+	0.976124i	$0.569697\pi$
$858$	42.2560	1.44259
$859$	17.6699	0.602891	0.301445	−	0.953483i	$-0.402531\pi$
$859$	17.6699	0.602891	0.301445	+	0.953483i	$0.402531\pi$
$860$	−1.32820	−0.0452912
$861$	−128.203	−4.36915
$862$	22.5088	0.766653
$863$	−45.7945	−1.55886	−0.779431	−	0.626488i	$-0.784492\pi$
$863$	−45.7945	−1.55886	−0.779431	+	0.626488i	$0.784492\pi$
$864$	11.5423	0.392677
$865$	23.0454	0.783567
$866$	17.6029	0.598172
$867$	49.7679	1.69021
$868$	15.4249	0.523555
$869$	−92.7393	−3.14597
$870$	6.49047	0.220048
$871$	13.9368	0.472229
$872$	−13.2033	−0.447120
$873$	34.3480	1.16250
$874$	5.83724	0.197448
$875$	50.6173	1.71118
$876$	−50.0713	−1.69175
$877$	−31.0576	−1.04874	−0.524371	−	0.851490i	$-0.675699\pi$
$877$	−31.0576	−1.04874	−0.524371	+	0.851490i	$0.675699\pi$
$878$	−24.3103	−0.820434
$879$	52.1460	1.75884
$880$	−11.6528	−0.392814
$881$	−16.8923	−0.569116	−0.284558	−	0.958659i	$-0.591847\pi$
$881$	−16.8923	−0.569116	−0.284558	+	0.958659i	$0.591847\pi$
$882$	−76.6346	−2.58042
$883$	−27.9962	−0.942147	−0.471074	−	0.882094i	$-0.656133\pi$
$883$	−27.9962	−0.942147	−0.471074	+	0.882094i	$0.656133\pi$
$884$	2.45484	0.0825651
$885$	−23.6151	−0.793814
$886$	16.1133	0.541338
$887$	34.1078	1.14523	0.572613	−	0.819826i	$-0.305930\pi$
$887$	34.1078	1.14523	0.572613	+	0.819826i	$0.305930\pi$
$888$	−23.6330	−0.793073
$889$	−30.0191	−1.00681
$890$	−12.1898	−0.408602
$891$	−88.6081	−2.96848
$892$	12.0707	0.404158
$893$	−12.3249	−0.412436
$894$	22.5678	0.754780
$895$	13.5264	0.452137
$896$	4.29295	0.143417
$897$	−7.55505	−0.252256
$898$	9.72200	0.324427
$899$	−3.59308	−0.119836
$900$	−4.42092	−0.147364
$901$	−9.44083	−0.314520
$902$	−53.6160	−1.78522
$903$	−8.52588	−0.283724
$904$	17.7235	0.589476
$905$	52.3923	1.74158
$906$	22.6711	0.753195
$907$	−2.60686	−0.0865595	−0.0432797	−	0.999063i	$-0.513781\pi$
$907$	−2.60686	−0.0865595	−0.0432797	+	0.999063i	$0.513781\pi$
$908$	23.5612	0.781905
$909$	0.837290	0.0277712
$910$	−21.6906	−0.719037
$911$	−12.7211	−0.421468	−0.210734	−	0.977543i	$-0.567585\pi$
$911$	−12.7211	−0.421468	−0.210734	+	0.977543i	$0.567585\pi$
$912$	−18.1847	−0.602156
$913$	−61.7299	−2.04296
$914$	28.1428	0.930882
$915$	74.2598	2.45495
$916$	21.2241	0.701263
$917$	0.0321166	0.00106058
$918$	−11.6836	−0.385616
$919$	14.6136	0.482058	0.241029	−	0.970518i	$-0.422515\pi$
$919$	14.6136	0.482058	0.241029	+	0.970518i	$0.422515\pi$
$920$	2.08342	0.0686885
$921$	14.4679	0.476733
$922$	0.187607	0.00617850
$923$	−22.9705	−0.756082
$924$	−74.8006	−2.46076
$925$	5.00187	0.164460
$926$	−10.1401	−0.333226
$927$	−65.9467	−2.16597
$928$	−1.00000	−0.0328266
$929$	2.79813	0.0918038	0.0459019	−	0.998946i	$-0.485384\pi$
$929$	2.79813	0.0918038	0.0459019	+	0.998946i	$0.485384\pi$
$930$	−23.3208	−0.764718
$931$	66.7162	2.18653
$932$	−10.4877	−0.343537
$933$	39.6058	1.29663
$934$	−15.8714	−0.519328
$935$	11.7954	0.385751
$936$	16.2607	0.531499
$937$	−59.1555	−1.93252	−0.966262	−	0.257560i	$-0.917082\pi$
$937$	−59.1555	−1.93252	−0.966262	+	0.257560i	$0.917082\pi$
$938$	−24.6705	−0.805521
$939$	−17.8207	−0.581556
$940$	−4.39898	−0.143479
$941$	57.3169	1.86848	0.934238	−	0.356650i	$-0.116081\pi$
$941$	57.3169	1.86848	0.934238	+	0.356650i	$0.116081\pi$
$942$	65.0081	2.11808
$943$	9.58614	0.312168
$944$	3.63843	0.118421
$945$	103.235	3.35822
$946$	−3.56563	−0.115929
$947$	7.98072	0.259338	0.129669	−	0.991557i	$-0.458608\pi$
$947$	7.98072	0.259338	0.129669	+	0.991557i	$0.458608\pi$
$948$	−51.6549	−1.67767
$949$	−38.9788	−1.26531
$950$	3.84875	0.124870
$951$	43.1066	1.39783
$952$	−4.34550	−0.140838
$953$	−14.1361	−0.457912	−0.228956	−	0.973437i	$-0.573531\pi$
$953$	−14.1361	−0.457912	−0.228956	+	0.973437i	$0.573531\pi$
$954$	−62.5356	−2.02467
$955$	−52.7025	−1.70541
$956$	26.7499	0.865153
$957$	17.4241	0.563240
$958$	7.31386	0.236300
$959$	8.19057	0.264487
$960$	−6.49047	−0.209479
$961$	−18.0898	−0.583542
$962$	−18.3975	−0.593160
$963$	18.3595	0.591625
$964$	−9.75386	−0.314151
$965$	21.4397	0.690169
$966$	13.3738	0.430294
$967$	34.9899	1.12520	0.562600	−	0.826729i	$-0.309801\pi$
$967$	34.9899	1.12520	0.562600	+	0.826729i	$0.309801\pi$
$968$	−20.2825	−0.651904
$969$	18.4073	0.591329
$970$	−10.6728	−0.342682
$971$	12.6871	0.407147	0.203573	−	0.979060i	$-0.434744\pi$
$971$	12.6871	0.407147	0.203573	+	0.979060i	$0.434744\pi$
$972$	−14.7270	−0.472370
$973$	−2.09353	−0.0671155
$974$	−21.9044	−0.701862
$975$	−4.98137	−0.159531
$976$	−11.4413	−0.366229
$977$	55.3887	1.77204	0.886021	−	0.463645i	$-0.153459\pi$
$977$	55.3887	1.77204	0.886021	+	0.463645i	$0.153459\pi$
$978$	26.8481	0.858507
$979$	−32.7241	−1.04587
$980$	23.8123	0.760655
$981$	88.5287	2.82650
$982$	35.0527	1.11858
$983$	4.72570	0.150727	0.0753633	−	0.997156i	$-0.475988\pi$
$983$	4.72570	0.150727	0.0753633	+	0.997156i	$0.475988\pi$
$984$	−29.8636	−0.952018
$985$	8.81097	0.280741
$986$	1.01224	0.0322363
$987$	−28.2377	−0.898815
$988$	−14.1562	−0.450368
$989$	0.637507	0.0202715
$990$	78.1322	2.48320
$991$	−50.6191	−1.60797	−0.803984	−	0.594650i	$-0.797291\pi$
$991$	−50.6191	−1.60797	−0.803984	+	0.594650i	$0.797291\pi$
$992$	3.59308	0.114080
$993$	−56.8127	−1.80290
$994$	40.6618	1.28971
$995$	10.1125	0.320588
$996$	−34.3830	−1.08947
$997$	−3.69046	−0.116878	−0.0584390	−	0.998291i	$-0.518612\pi$
$997$	−3.69046	−0.116878	−0.0584390	+	0.998291i	$0.518612\pi$
$998$	32.3564	1.02422
$999$	87.5614	2.77032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.j.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.j.1.2	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.11529 q^{3} +1.00000 q^{4} +2.08342 q^{5} +3.11529 q^{6} -4.29295 q^{7} -1.00000 q^{8} +6.70504 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.11529 q^{3} +1.00000 q^{4} +2.08342 q^{5} +3.11529 q^{6} -4.29295 q^{7} -1.00000 q^{8} +6.70504 q^{9} -2.08342 q^{10} -5.59308 q^{11} -3.11529 q^{12} -2.42515 q^{13} +4.29295 q^{14} -6.49047 q^{15} +1.00000 q^{16} -1.01224 q^{17} -6.70504 q^{18} +5.83724 q^{19} +2.08342 q^{20} +13.3738 q^{21} +5.59308 q^{22} -1.00000 q^{23} +3.11529 q^{24} -0.659343 q^{25} +2.42515 q^{26} -11.5423 q^{27} -4.29295 q^{28} +1.00000 q^{29} +6.49047 q^{30} -3.59308 q^{31} -1.00000 q^{32} +17.4241 q^{33} +1.01224 q^{34} -8.94403 q^{35} +6.70504 q^{36} -7.58614 q^{37} -5.83724 q^{38} +7.55505 q^{39} -2.08342 q^{40} -9.58614 q^{41} -13.3738 q^{42} -0.637507 q^{43} -5.59308 q^{44} +13.9694 q^{45} +1.00000 q^{46} -2.11142 q^{47} -3.11529 q^{48} +11.4294 q^{49} +0.659343 q^{50} +3.15343 q^{51} -2.42515 q^{52} +9.32666 q^{53} +11.5423 q^{54} -11.6528 q^{55} +4.29295 q^{56} -18.1847 q^{57} -1.00000 q^{58} +3.63843 q^{59} -6.49047 q^{60} -11.4413 q^{61} +3.59308 q^{62} -28.7844 q^{63} +1.00000 q^{64} -5.05262 q^{65} -17.4241 q^{66} -5.74676 q^{67} -1.01224 q^{68} +3.11529 q^{69} +8.94403 q^{70} +9.47177 q^{71} -6.70504 q^{72} +16.0728 q^{73} +7.58614 q^{74} +2.05405 q^{75} +5.83724 q^{76} +24.0108 q^{77} -7.55505 q^{78} +16.5811 q^{79} +2.08342 q^{80} +15.8425 q^{81} +9.58614 q^{82} +11.0368 q^{83} +13.3738 q^{84} -2.10893 q^{85} +0.637507 q^{86} -3.11529 q^{87} +5.59308 q^{88} +5.85083 q^{89} -13.9694 q^{90} +10.4110 q^{91} -1.00000 q^{92} +11.1935 q^{93} +2.11142 q^{94} +12.1615 q^{95} +3.11529 q^{96} +5.12271 q^{97} -11.4294 q^{98} -37.5018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * q^99

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