LMFDB - Embedded newform 119.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [119,2,Mod(1,119)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(119, 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("119.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	119.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:	$0.950219784053$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.453749.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 10x^{2} + x - 3 $ x^5 - 2x^4 - 5x^3 + 10*x^2 + x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.544198$ of defining polynomial
Character	$\chi$	$=$	119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.40868 q^{2} +2.55982 q^{3} -0.0156267 q^{4} +1.76660 q^{5} -3.60597 q^{6} -1.00000 q^{7} +2.83937 q^{8} +3.55270 q^{9} -2.48857 q^{10} -5.40770 q^{11} -0.0400016 q^{12} +5.90575 q^{13} +1.40868 q^{14} +4.52218 q^{15} -3.96850 q^{16} +1.00000 q^{17} -5.00461 q^{18} +3.08840 q^{19} -0.0276061 q^{20} -2.55982 q^{21} +7.61770 q^{22} -6.03125 q^{23} +7.26829 q^{24} -1.87913 q^{25} -8.31930 q^{26} +1.41482 q^{27} +0.0156267 q^{28} -8.99415 q^{29} -6.37030 q^{30} -2.26465 q^{31} -0.0883958 q^{32} -13.8428 q^{33} -1.40868 q^{34} -1.76660 q^{35} -0.0555169 q^{36} -1.67874 q^{37} -4.35055 q^{38} +15.1177 q^{39} +5.01603 q^{40} +4.25753 q^{41} +3.60597 q^{42} +4.06177 q^{43} +0.0845043 q^{44} +6.27620 q^{45} +8.49609 q^{46} -4.30229 q^{47} -10.1587 q^{48} +1.00000 q^{49} +2.64708 q^{50} +2.55982 q^{51} -0.0922873 q^{52} -0.552702 q^{53} -1.99303 q^{54} -9.55324 q^{55} -2.83937 q^{56} +7.90575 q^{57} +12.6699 q^{58} -2.17679 q^{59} -0.0706667 q^{60} +3.74247 q^{61} +3.19017 q^{62} -3.55270 q^{63} +8.06153 q^{64} +10.4331 q^{65} +19.5000 q^{66} +8.58396 q^{67} -0.0156267 q^{68} -15.4390 q^{69} +2.48857 q^{70} +5.26519 q^{71} +10.0874 q^{72} -1.43821 q^{73} +2.36480 q^{74} -4.81023 q^{75} -0.0482614 q^{76} +5.40770 q^{77} -21.2960 q^{78} -5.93700 q^{79} -7.01075 q^{80} -7.03641 q^{81} -5.99749 q^{82} +9.02540 q^{83} +0.0400016 q^{84} +1.76660 q^{85} -5.72173 q^{86} -23.0234 q^{87} -15.3544 q^{88} +14.0996 q^{89} -8.84115 q^{90} -5.90575 q^{91} +0.0942485 q^{92} -5.79712 q^{93} +6.06055 q^{94} +5.45596 q^{95} -0.226278 q^{96} -0.119116 q^{97} -1.40868 q^{98} -19.2119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - q^{6} - 5 q^{7} + 6 q^{8} + 11 q^{9} + 4 q^{10} - 2 q^{11} - 22 q^{12} + 2 q^{13} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 5 q^{17} - 18 q^{18} + 6 q^{19} - 19 q^{20} + 2 q^{21}+ \cdots - 62 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - q^6 - 5 * q^7 + 6 * q^8 + 11 * q^9 + 4 * q^10 - 2 * q^11 - 22 * q^12 + 2 * q^13 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 5 * q^17 - 18 * q^18 + 6 * q^19 - 19 * q^20 + 2 * q^21 + 6 * q^22 - 10 * q^23 + 2 * q^24 + 21 * q^25 - 26 * q^26 - 26 * q^27 - 10 * q^28 - 8 * q^29 - 51 * q^30 + 9 * q^32 + 6 * q^33 + 2 * q^34 + 39 * q^36 + 8 * q^37 + 14 * q^38 + 14 * q^39 + 5 * q^40 + 18 * q^41 + q^42 + 8 * q^43 - 14 * q^44 + 8 * q^46 - 10 * q^47 - 27 * q^48 + 5 * q^49 + 27 * q^50 - 2 * q^51 + 4 * q^52 + 4 * q^53 + 5 * q^54 - 24 * q^55 - 6 * q^56 + 12 * q^57 + 12 * q^58 + 8 * q^59 - 7 * q^60 + 22 * q^61 + 16 * q^62 - 11 * q^63 - 16 * q^64 - 30 * q^65 + 68 * q^66 + 16 * q^67 + 10 * q^68 - 32 * q^69 - 4 * q^70 - 2 * q^71 + 9 * q^72 + 10 * q^73 - 40 * q^74 - 14 * q^75 + 24 * q^76 + 2 * q^77 + 30 * q^78 + 18 * q^79 - 4 * q^80 + 25 * q^81 - 31 * q^82 - 12 * q^83 + 22 * q^84 + 23 * q^86 - 26 * q^87 - 46 * q^88 + 20 * q^89 + 97 * q^90 - 2 * q^91 + 28 * q^92 - 28 * q^93 - 42 * q^94 - 22 * q^95 - 18 * q^96 + 12 * q^97 + 2 * q^98 - 62 * q^99

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 $

$2$	−1.40868	−0.996086	−0.498043	−	0.867152i	$-0.665948\pi$
$2$	−1.40868	−0.996086	−0.498043	+	0.867152i	$0.665948\pi$
$3$	2.55982	1.47792	0.738958	−	0.673752i	$-0.235318\pi$
$3$	2.55982	1.47792	0.738958	+	0.673752i	$0.235318\pi$
$4$	−0.0156267	−0.00781334
$5$	1.76660	0.790047	0.395024	−	0.918671i	$-0.370736\pi$
$5$	1.76660	0.790047	0.395024	+	0.918671i	$0.370736\pi$
$6$	−3.60597	−1.47213
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.83937	1.00387
$9$	3.55270	1.18423
$10$	−2.48857	−0.786955
$11$	−5.40770	−1.63048	−0.815241	−	0.579122i	$-0.803396\pi$
$11$	−5.40770	−1.63048	−0.815241	+	0.579122i	$0.803396\pi$
$12$	−0.0400016	−0.0115475
$13$	5.90575	1.63796	0.818980	−	0.573822i	$-0.194540\pi$
$13$	5.90575	1.63796	0.818980	+	0.573822i	$0.194540\pi$
$14$	1.40868	0.376485
$15$	4.52218	1.16762
$16$	−3.96850	−0.992126
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−5.00461	−1.17960
$19$	3.08840	0.708527	0.354263	−	0.935146i	$-0.384732\pi$
$19$	3.08840	0.708527	0.354263	+	0.935146i	$0.384732\pi$
$20$	−0.0276061	−0.00617291
$21$	−2.55982	−0.558600
$22$	7.61770	1.62410
$23$	−6.03125	−1.25760	−0.628802	−	0.777566i	$-0.716454\pi$
$23$	−6.03125	−1.25760	−0.628802	+	0.777566i	$0.716454\pi$
$24$	7.26829	1.48363
$25$	−1.87913	−0.375825
$26$	−8.31930	−1.63155
$27$	1.41482	0.272282
$28$	0.0156267	0.00295316
$29$	−8.99415	−1.67017	−0.835086	−	0.550120i	$-0.814582\pi$
$29$	−8.99415	−1.67017	−0.835086	+	0.550120i	$0.814582\pi$
$30$	−6.37030	−1.16305
$31$	−2.26465	−0.406744	−0.203372	−	0.979102i	$-0.565190\pi$
$31$	−2.26465	−0.406744	−0.203372	+	0.979102i	$0.565190\pi$
$32$	−0.0883958	−0.0156263
$33$	−13.8428	−2.40971
$34$	−1.40868	−0.241586
$35$	−1.76660	−0.298610
$36$	−0.0555169	−0.00925282
$37$	−1.67874	−0.275983	−0.137991	−	0.990433i	$-0.544065\pi$
$37$	−1.67874	−0.275983	−0.137991	+	0.990433i	$0.544065\pi$
$38$	−4.35055	−0.705753
$39$	15.1177	2.42077
$40$	5.01603	0.793104
$41$	4.25753	0.664915	0.332457	−	0.943118i	$-0.392122\pi$
$41$	4.25753	0.664915	0.332457	+	0.943118i	$0.392122\pi$
$42$	3.60597	0.556413
$43$	4.06177	0.619414	0.309707	−	0.950832i	$-0.399769\pi$
$43$	4.06177	0.619414	0.309707	+	0.950832i	$0.399769\pi$
$44$	0.0845043	0.0127395
$45$	6.27620	0.935601
$46$	8.49609	1.25268
$47$	−4.30229	−0.627554	−0.313777	−	0.949497i	$-0.601594\pi$
$47$	−4.30229	−0.627554	−0.313777	+	0.949497i	$0.601594\pi$
$48$	−10.1587	−1.46628
$49$	1.00000	0.142857
$50$	2.64708	0.374354
$51$	2.55982	0.358447
$52$	−0.0922873	−0.0127979
$53$	−0.552702	−0.0759194	−0.0379597	−	0.999279i	$-0.512086\pi$
$53$	−0.552702	−0.0759194	−0.0379597	+	0.999279i	$0.512086\pi$
$54$	−1.99303	−0.271216
$55$	−9.55324	−1.28816
$56$	−2.83937	−0.379427
$57$	7.90575	1.04714
$58$	12.6699	1.66363
$59$	−2.17679	−0.283394	−0.141697	−	0.989910i	$-0.545256\pi$
$59$	−2.17679	−0.283394	−0.141697	+	0.989910i	$0.545256\pi$
$60$	−0.0706667	−0.00912304
$61$	3.74247	0.479174	0.239587	−	0.970875i	$-0.422988\pi$
$61$	3.74247	0.479174	0.239587	+	0.970875i	$0.422988\pi$
$62$	3.19017	0.405152
$63$	−3.55270	−0.447598
$64$	8.06153	1.00769
$65$	10.4331	1.29407
$66$	19.5000	2.40028
$67$	8.58396	1.04870	0.524349	−	0.851504i	$-0.324309\pi$
$67$	8.58396	1.04870	0.524349	+	0.851504i	$0.324309\pi$
$68$	−0.0156267	−0.00189501
$69$	−15.4390	−1.85863
$70$	2.48857	0.297441
$71$	5.26519	0.624863	0.312431	−	0.949940i	$-0.398857\pi$
$71$	5.26519	0.624863	0.312431	+	0.949940i	$0.398857\pi$
$72$	10.0874	1.18882
$73$	−1.43821	−0.168330	−0.0841651	−	0.996452i	$-0.526822\pi$
$73$	−1.43821	−0.168330	−0.0841651	+	0.996452i	$0.526822\pi$
$74$	2.36480	0.274902
$75$	−4.81023	−0.555438
$76$	−0.0482614	−0.00553596
$77$	5.40770	0.616264
$78$	−21.2960	−2.41129
$79$	−5.93700	−0.667965	−0.333983	−	0.942579i	$-0.608393\pi$
$79$	−5.93700	−0.667965	−0.333983	+	0.942579i	$0.608393\pi$
$80$	−7.01075	−0.783826
$81$	−7.03641	−0.781824
$82$	−5.99749	−0.662312
$83$	9.02540	0.990666	0.495333	−	0.868703i	$-0.335046\pi$
$83$	9.02540	0.990666	0.495333	+	0.868703i	$0.335046\pi$
$84$	0.0400016	0.00436453
$85$	1.76660	0.191615
$86$	−5.72173	−0.616990
$87$	−23.0234	−2.46837
$88$	−15.3544	−1.63679
$89$	14.0996	1.49455	0.747275	−	0.664515i	$-0.231362\pi$
$89$	14.0996	1.49455	0.747275	+	0.664515i	$0.231362\pi$
$90$	−8.84115	−0.931939
$91$	−5.90575	−0.619091
$92$	0.0942485	0.00982608
$93$	−5.79712	−0.601133
$94$	6.06055	0.625098
$95$	5.45596	0.559770
$96$	−0.226278	−0.0230944
$97$	−0.119116	−0.0120944	−0.00604718	−	0.999982i	$-0.501925\pi$
$97$	−0.119116	−0.0120944	−0.00604718	+	0.999982i	$0.501925\pi$
$98$	−1.40868	−0.142298
$99$	−19.2119	−1.93087
$100$	0.0293645	0.00293645
$101$	9.74124	0.969290	0.484645	−	0.874711i	$-0.338949\pi$
$101$	9.74124	0.969290	0.484645	+	0.874711i	$0.338949\pi$
$102$	−3.60597	−0.357044
$103$	−14.8486	−1.46308	−0.731538	−	0.681800i	$-0.761197\pi$
$103$	−14.8486	−1.46308	−0.731538	+	0.681800i	$0.761197\pi$
$104$	16.7686	1.64430
$105$	−4.52218	−0.441320
$106$	0.778579	0.0756223
$107$	−2.86138	−0.276620	−0.138310	−	0.990389i	$-0.544167\pi$
$107$	−2.86138	−0.276620	−0.138310	+	0.990389i	$0.544167\pi$
$108$	−0.0221089	−0.00212743
$109$	16.8154	1.61062	0.805311	−	0.592852i	$-0.201998\pi$
$109$	16.8154	1.61062	0.805311	+	0.592852i	$0.201998\pi$
$110$	13.4574	1.28312
$111$	−4.29727	−0.407879
$112$	3.96850	0.374988
$113$	−12.5273	−1.17847	−0.589237	−	0.807960i	$-0.700571\pi$
$113$	−12.5273	−1.17847	−0.589237	+	0.807960i	$0.700571\pi$
$114$	−11.1367	−1.04304
$115$	−10.6548	−0.993566
$116$	0.140549	0.0130496
$117$	20.9814	1.93973
$118$	3.06640	0.282285
$119$	−1.00000	−0.0916698
$120$	12.8402	1.17214
$121$	18.2432	1.65847
$122$	−5.27193	−0.477298
$123$	10.8985	0.982688
$124$	0.0353890	0.00317803
$125$	−12.1527	−1.08697
$126$	5.00461	0.445846
$127$	0.0546476	0.00484919	0.00242460	−	0.999997i	$-0.499228\pi$
$127$	0.0546476	0.00484919	0.00242460	+	0.999997i	$0.499228\pi$
$128$	−11.1793	−0.988120
$129$	10.3974	0.915442
$130$	−14.6969	−1.28900
$131$	5.63471	0.492307	0.246154	−	0.969231i	$-0.420833\pi$
$131$	5.63471	0.492307	0.246154	+	0.969231i	$0.420833\pi$
$132$	0.216316	0.0188279
$133$	−3.08840	−0.267798
$134$	−12.0920	−1.04459
$135$	2.49942	0.215116
$136$	2.83937	0.243474
$137$	19.1717	1.63795	0.818973	−	0.573832i	$-0.194544\pi$
$137$	19.1717	1.63795	0.818973	+	0.573832i	$0.194544\pi$
$138$	21.7485	1.85136
$139$	21.6094	1.83288	0.916441	−	0.400170i	$-0.131049\pi$
$139$	21.6094	1.83288	0.916441	+	0.400170i	$0.131049\pi$
$140$	0.0276061	0.00233314
$141$	−11.0131	−0.927472
$142$	−7.41695	−0.622417
$143$	−31.9365	−2.67067
$144$	−14.0989	−1.17491
$145$	−15.8891	−1.31951
$146$	2.02598	0.167671
$147$	2.55982	0.211131
$148$	0.0262331	0.00215635
$149$	−4.41731	−0.361881	−0.180940	−	0.983494i	$-0.557914\pi$
$149$	−4.41731	−0.361881	−0.180940	+	0.983494i	$0.557914\pi$
$150$	6.77607	0.553264
$151$	−12.9929	−1.05735	−0.528675	−	0.848825i	$-0.677311\pi$
$151$	−12.9929	−1.05735	−0.528675	+	0.848825i	$0.677311\pi$
$152$	8.76909	0.711267
$153$	3.55270	0.287219
$154$	−7.61770	−0.613852
$155$	−4.00074	−0.321347
$156$	−0.236239	−0.0189143
$157$	−13.8355	−1.10419	−0.552096	−	0.833780i	$-0.686172\pi$
$157$	−13.8355	−1.10419	−0.552096	+	0.833780i	$0.686172\pi$
$158$	8.36333	0.665351
$159$	−1.41482	−0.112203
$160$	−0.156160	−0.0123455
$161$	6.03125	0.475329
$162$	9.91204	0.778764
$163$	16.5444	1.29585	0.647927	−	0.761703i	$-0.275636\pi$
$163$	16.5444	1.29585	0.647927	+	0.761703i	$0.275636\pi$
$164$	−0.0665311	−0.00519520
$165$	−24.4546	−1.90379
$166$	−12.7139	−0.986789
$167$	−6.68337	−0.517174	−0.258587	−	0.965988i	$-0.583257\pi$
$167$	−6.68337	−0.517174	−0.258587	+	0.965988i	$0.583257\pi$
$168$	−7.26829	−0.560760
$169$	21.8779	1.68292
$170$	−2.48857	−0.190865
$171$	10.9721	0.839061
$172$	−0.0634720	−0.00483969
$173$	18.6204	1.41568	0.707840	−	0.706373i	$-0.249670\pi$
$173$	18.6204	1.41568	0.707840	+	0.706373i	$0.249670\pi$
$174$	32.4326	2.45871
$175$	1.87913	0.142049
$176$	21.4605	1.61764
$177$	−5.57220	−0.418833
$178$	−19.8617	−1.48870
$179$	−8.70037	−0.650296	−0.325148	−	0.945663i	$-0.605414\pi$
$179$	−8.70037	−0.650296	−0.325148	+	0.945663i	$0.605414\pi$
$180$	−0.0980762	−0.00731017
$181$	2.99611	0.222699	0.111349	−	0.993781i	$-0.464483\pi$
$181$	2.99611	0.222699	0.111349	+	0.993781i	$0.464483\pi$
$182$	8.31930	0.616668
$183$	9.58006	0.708179
$184$	−17.1250	−1.26247
$185$	−2.96566	−0.218039
$186$	8.16627	0.598780
$187$	−5.40770	−0.395450
$188$	0.0672306	0.00490329
$189$	−1.41482	−0.102913
$190$	−7.68569	−0.557578
$191$	1.76856	0.127969	0.0639843	−	0.997951i	$-0.479619\pi$
$191$	1.76856	0.127969	0.0639843	+	0.997951i	$0.479619\pi$
$192$	20.6361	1.48928
$193$	−7.54046	−0.542774	−0.271387	−	0.962470i	$-0.587482\pi$
$193$	−7.54046	−0.542774	−0.271387	+	0.962470i	$0.587482\pi$
$194$	0.167795	0.0120470
$195$	26.7069	1.91252
$196$	−0.0156267	−0.00111619
$197$	−26.0165	−1.85360	−0.926800	−	0.375555i	$-0.877452\pi$
$197$	−26.0165	−1.85360	−0.926800	+	0.375555i	$0.877452\pi$
$198$	27.0634	1.92331
$199$	−8.50657	−0.603015	−0.301508	−	0.953464i	$-0.597490\pi$
$199$	−8.50657	−0.603015	−0.301508	+	0.953464i	$0.597490\pi$
$200$	−5.33553	−0.377279
$201$	21.9734	1.54989
$202$	−13.7223	−0.965496
$203$	8.99415	0.631265
$204$	−0.0400016	−0.00280067
$205$	7.52135	0.525314
$206$	20.9169	1.45735
$207$	−21.4272	−1.48930
$208$	−23.4370	−1.62506
$209$	−16.7011	−1.15524
$210$	6.37030	0.439593
$211$	−14.9389	−1.02844	−0.514219	−	0.857659i	$-0.671918\pi$
$211$	−14.9389	−1.02844	−0.514219	+	0.857659i	$0.671918\pi$
$212$	0.00863690	0.000593184 0
$213$	13.4780	0.923494
$214$	4.03076	0.275537
$215$	7.17552	0.489367
$216$	4.01720	0.273336
$217$	2.26465	0.153735
$218$	−23.6875	−1.60432
$219$	−3.68158	−0.248778
$220$	0.149285	0.0100648
$221$	5.90575	0.397264
$222$	6.05347	0.406283
$223$	−1.84521	−0.123564	−0.0617821	−	0.998090i	$-0.519678\pi$
$223$	−1.84521	−0.123564	−0.0617821	+	0.998090i	$0.519678\pi$
$224$	0.0883958	0.00590619
$225$	−6.67597	−0.445065
$226$	17.6470	1.17386
$227$	4.55074	0.302043	0.151022	−	0.988530i	$-0.451744\pi$
$227$	4.55074	0.302043	0.151022	+	0.988530i	$0.451744\pi$
$228$	−0.123541	−0.00818168
$229$	11.1709	0.738196	0.369098	−	0.929390i	$-0.379667\pi$
$229$	11.1709	0.738196	0.369098	+	0.929390i	$0.379667\pi$
$230$	15.0092	0.989677
$231$	13.8428	0.910787
$232$	−25.5377	−1.67663
$233$	6.33159	0.414796	0.207398	−	0.978257i	$-0.433500\pi$
$233$	6.33159	0.414796	0.207398	+	0.978257i	$0.433500\pi$
$234$	−29.5560	−1.93214
$235$	−7.60043	−0.495797
$236$	0.0340160	0.00221425
$237$	−15.1977	−0.987196
$238$	1.40868	0.0913110
$239$	4.12428	0.266777	0.133389	−	0.991064i	$-0.457414\pi$
$239$	4.12428	0.266777	0.133389	+	0.991064i	$0.457414\pi$
$240$	−17.9463	−1.15843
$241$	27.0098	1.73985	0.869927	−	0.493181i	$-0.164166\pi$
$241$	27.0098	1.73985	0.869927	+	0.493181i	$0.164166\pi$
$242$	−25.6988	−1.65198
$243$	−22.2564	−1.42775
$244$	−0.0584824	−0.00374395
$245$	1.76660	0.112864
$246$	−15.3525	−0.978841
$247$	18.2393	1.16054
$248$	−6.43019	−0.408317
$249$	23.1034	1.46412
$250$	17.1192	1.08271
$251$	−16.1431	−1.01894	−0.509471	−	0.860488i	$-0.670159\pi$
$251$	−16.1431	−1.01894	−0.509471	+	0.860488i	$0.670159\pi$
$252$	0.0555169	0.00349724
$253$	32.6152	2.05050
$254$	−0.0769809	−0.00483021
$255$	4.52218	0.283190
$256$	−0.375017	−0.0234386
$257$	−8.38484	−0.523032	−0.261516	−	0.965199i	$-0.584222\pi$
$257$	−8.38484	−0.523032	−0.261516	+	0.965199i	$0.584222\pi$
$258$	−14.6466	−0.911858
$259$	1.67874	0.104312
$260$	−0.163035	−0.0101110
$261$	−31.9535	−1.97787
$262$	−7.93749	−0.490380
$263$	23.8115	1.46828	0.734140	−	0.678998i	$-0.237586\pi$
$263$	23.8115	1.46828	0.734140	+	0.678998i	$0.237586\pi$
$264$	−39.3047	−2.41904
$265$	−0.976403	−0.0599800
$266$	4.35055	0.266750
$267$	36.0924	2.20882
$268$	−0.134139	−0.00819383
$269$	−1.11039	−0.0677019	−0.0338509	−	0.999427i	$-0.510777\pi$
$269$	−1.11039	−0.0677019	−0.0338509	+	0.999427i	$0.510777\pi$
$270$	−3.52088	−0.214274
$271$	−8.45905	−0.513851	−0.256925	−	0.966431i	$-0.582709\pi$
$271$	−8.45905	−0.513851	−0.256925	+	0.966431i	$0.582709\pi$
$272$	−3.96850	−0.240626
$273$	−15.1177	−0.914964
$274$	−27.0067	−1.63154
$275$	10.1617	0.612776
$276$	0.241260	0.0145221
$277$	−23.4030	−1.40615	−0.703074	−	0.711116i	$-0.748190\pi$
$277$	−23.4030	−1.40615	−0.703074	+	0.711116i	$0.748190\pi$
$278$	−30.4406	−1.82571
$279$	−8.04564	−0.481680
$280$	−5.01603	−0.299765
$281$	−17.1406	−1.02252	−0.511261	−	0.859425i	$-0.670821\pi$
$281$	−17.1406	−1.02252	−0.511261	+	0.859425i	$0.670821\pi$
$282$	15.5139	0.923841
$283$	6.54967	0.389338	0.194669	−	0.980869i	$-0.437637\pi$
$283$	6.54967	0.389338	0.194669	+	0.980869i	$0.437637\pi$
$284$	−0.0822774	−0.00488227
$285$	13.9663	0.827292
$286$	44.9883	2.66021
$287$	−4.25753	−0.251314
$288$	−0.314044	−0.0185052
$289$	1.00000	0.0588235
$290$	22.3826	1.31435
$291$	−0.304915	−0.0178744
$292$	0.0224745	0.00131522
$293$	−1.27837	−0.0746829	−0.0373415	−	0.999303i	$-0.511889\pi$
$293$	−1.27837	−0.0746829	−0.0373415	+	0.999303i	$0.511889\pi$
$294$	−3.60597	−0.210304
$295$	−3.84552	−0.223895
$296$	−4.76655	−0.277050
$297$	−7.65092	−0.443951
$298$	6.22257	0.360464
$299$	−35.6191	−2.05990
$300$	0.0751680	0.00433982
$301$	−4.06177	−0.234117
$302$	18.3028	1.05321
$303$	24.9359	1.43253
$304$	−12.2563	−0.702947
$305$	6.61144	0.378570
$306$	−5.00461	−0.286095
$307$	−17.0396	−0.972504	−0.486252	−	0.873819i	$-0.661636\pi$
$307$	−17.0396	−0.972504	−0.486252	+	0.873819i	$0.661636\pi$
$308$	−0.0845043	−0.00481508
$309$	−38.0098	−2.16230
$310$	5.63575	0.320089
$311$	21.4961	1.21893	0.609467	−	0.792811i	$-0.291383\pi$
$311$	21.4961	1.21893	0.609467	+	0.792811i	$0.291383\pi$
$312$	42.9247	2.43013
$313$	−15.6171	−0.882731	−0.441366	−	0.897327i	$-0.645506\pi$
$313$	−15.6171	−0.882731	−0.441366	+	0.897327i	$0.645506\pi$
$314$	19.4898	1.09987
$315$	−6.27620	−0.353624
$316$	0.0927757	0.00521904
$317$	1.63195	0.0916594	0.0458297	−	0.998949i	$-0.485407\pi$
$317$	1.63195	0.0916594	0.0458297	+	0.998949i	$0.485407\pi$
$318$	1.99303	0.111763
$319$	48.6376	2.72318
$320$	14.2415	0.796123
$321$	−7.32464	−0.408821
$322$	−8.49609	−0.473469
$323$	3.08840	0.171843
$324$	0.109956	0.00610866
$325$	−11.0977	−0.615587
$326$	−23.3057	−1.29078
$327$	43.0445	2.38036
$328$	12.0887	0.667487
$329$	4.30229	0.237193
$330$	34.4487	1.89634
$331$	−28.8456	−1.58550	−0.792748	−	0.609550i	$-0.791350\pi$
$331$	−28.8456	−1.58550	−0.792748	+	0.609550i	$0.791350\pi$
$332$	−0.141037	−0.00774041
$333$	−5.96405	−0.326828
$334$	9.41471	0.515150
$335$	15.1644	0.828520
$336$	10.1587	0.554201
$337$	3.80896	0.207487	0.103744	−	0.994604i	$-0.466918\pi$
$337$	3.80896	0.207487	0.103744	+	0.994604i	$0.466918\pi$
$338$	−30.8189	−1.67633
$339$	−32.0678	−1.74168
$340$	−0.0276061	−0.00149715
$341$	12.2466	0.663189
$342$	−15.4562	−0.835777
$343$	−1.00000	−0.0539949
$344$	11.5329	0.621810
$345$	−27.2744	−1.46841
$346$	−26.2301	−1.41014
$347$	5.04437	0.270796	0.135398	−	0.990791i	$-0.456769\pi$
$347$	5.04437	0.270796	0.135398	+	0.990791i	$0.456769\pi$
$348$	0.359780	0.0192862
$349$	−24.7187	−1.32316	−0.661581	−	0.749874i	$-0.730114\pi$
$349$	−24.7187	−1.32316	−0.661581	+	0.749874i	$0.730114\pi$
$350$	−2.64708	−0.141493
$351$	8.35558	0.445988
$352$	0.478018	0.0254784
$353$	24.8057	1.32027	0.660136	−	0.751146i	$-0.270499\pi$
$353$	24.8057	1.32027	0.660136	+	0.751146i	$0.270499\pi$
$354$	7.84944	0.417193
$355$	9.30148	0.493671
$356$	−0.220329	−0.0116774
$357$	−2.55982	−0.135480
$358$	12.2560	0.647751
$359$	3.95420	0.208695	0.104347	−	0.994541i	$-0.466725\pi$
$359$	3.95420	0.208695	0.104347	+	0.994541i	$0.466725\pi$
$360$	17.8205	0.939220
$361$	−9.46181	−0.497990
$362$	−4.22055	−0.221827
$363$	46.6994	2.45108
$364$	0.0922873	0.00483717
$365$	−2.54075	−0.132989
$366$	−13.4952	−0.705407
$367$	14.1828	0.740338	0.370169	−	0.928964i	$-0.379300\pi$
$367$	14.1828	0.740338	0.370169	+	0.928964i	$0.379300\pi$
$368$	23.9350	1.24770
$369$	15.1257	0.787415
$370$	4.17765	0.217186
$371$	0.552702	0.0286949
$372$	0.0905897	0.00469686
$373$	−6.55256	−0.339279	−0.169639	−	0.985506i	$-0.554260\pi$
$373$	−6.55256	−0.339279	−0.169639	+	0.985506i	$0.554260\pi$
$374$	7.61770	0.393902
$375$	−31.1087	−1.60645
$376$	−12.2158	−0.629982
$377$	−53.1172	−2.73567
$378$	1.99303	0.102510
$379$	29.6732	1.52421	0.762106	−	0.647453i	$-0.224166\pi$
$379$	29.6732	1.52421	0.762106	+	0.647453i	$0.224166\pi$
$380$	−0.0852585	−0.00437367
$381$	0.139888	0.00716670
$382$	−2.49133	−0.127468
$383$	35.1010	1.79358	0.896788	−	0.442460i	$-0.145894\pi$
$383$	35.1010	1.79358	0.896788	+	0.442460i	$0.145894\pi$
$384$	−28.6171	−1.46036
$385$	9.55324	0.486878
$386$	10.6221	0.540650
$387$	14.4303	0.733531
$388$	0.00186138	9.44973e−5 0
$389$	−21.6738	−1.09891	−0.549453	−	0.835524i	$-0.685164\pi$
$389$	−21.6738	−1.09891	−0.549453	+	0.835524i	$0.685164\pi$
$390$	−37.6214	−1.90503
$391$	−6.03125	−0.305014
$392$	2.83937	0.143410
$393$	14.4239	0.727588
$394$	36.6489	1.84634
$395$	−10.4883	−0.527724
$396$	0.300219	0.0150866
$397$	−5.05272	−0.253589	−0.126794	−	0.991929i	$-0.540469\pi$
$397$	−5.05272	−0.253589	−0.126794	+	0.991929i	$0.540469\pi$
$398$	11.9830	0.600655
$399$	−7.90575	−0.395783
$400$	7.45732	0.372866
$401$	12.5084	0.624639	0.312319	−	0.949977i	$-0.398894\pi$
$401$	12.5084	0.624639	0.312319	+	0.949977i	$0.398894\pi$
$402$	−30.9535	−1.54382
$403$	−13.3745	−0.666230
$404$	−0.152223	−0.00757339
$405$	−12.4305	−0.617678
$406$	−12.6699	−0.628794
$407$	9.07810	0.449985
$408$	7.26829	0.359834
$409$	35.1679	1.73894	0.869471	−	0.493985i	$-0.164460\pi$
$409$	35.1679	1.73894	0.869471	+	0.493985i	$0.164460\pi$
$410$	−10.5952	−0.523258
$411$	49.0761	2.42075
$412$	0.232034	0.0114315
$413$	2.17679	0.107113
$414$	30.1841	1.48347
$415$	15.9443	0.782673
$416$	−0.522044	−0.0255953
$417$	55.3162	2.70884
$418$	23.5265	1.15072
$419$	−7.43256	−0.363105	−0.181552	−	0.983381i	$-0.558112\pi$
$419$	−7.43256	−0.363105	−0.181552	+	0.983381i	$0.558112\pi$
$420$	0.0706667	0.00344818
$421$	17.3069	0.843488	0.421744	−	0.906715i	$-0.361418\pi$
$421$	17.3069	0.843488	0.421744	+	0.906715i	$0.361418\pi$
$422$	21.0441	1.02441
$423$	−15.2848	−0.743171
$424$	−1.56932	−0.0762131
$425$	−1.87913	−0.0911510
$426$	−18.9861	−0.919879
$427$	−3.74247	−0.181111
$428$	0.0447139	0.00216133
$429$	−81.7519	−3.94702
$430$	−10.1080	−0.487451
$431$	3.64198	0.175428	0.0877139	−	0.996146i	$-0.472044\pi$
$431$	3.64198	0.175428	0.0877139	+	0.996146i	$0.472044\pi$
$432$	−5.61472	−0.270138
$433$	−7.23197	−0.347546	−0.173773	−	0.984786i	$-0.555596\pi$
$433$	−7.23197	−0.347546	−0.173773	+	0.984786i	$0.555596\pi$
$434$	−3.19017	−0.153133
$435$	−40.6732	−1.95013
$436$	−0.262769	−0.0125843
$437$	−18.6269	−0.891045
$438$	5.18615	0.247804
$439$	−33.7913	−1.61277	−0.806386	−	0.591390i	$-0.798579\pi$
$439$	−33.7913	−1.61277	−0.806386	+	0.591390i	$0.798579\pi$
$440$	−27.1252	−1.29314
$441$	3.55270	0.169176
$442$	−8.31930	−0.395709
$443$	−12.2276	−0.580950	−0.290475	−	0.956883i	$-0.593813\pi$
$443$	−12.2276	−0.580950	−0.290475	+	0.956883i	$0.593813\pi$
$444$	0.0671521	0.00318690
$445$	24.9083	1.18076
$446$	2.59930	0.123080
$447$	−11.3076	−0.534829
$448$	−8.06153	−0.380871
$449$	−31.8397	−1.50261	−0.751305	−	0.659955i	$-0.770575\pi$
$449$	−31.8397	−1.50261	−0.751305	+	0.659955i	$0.770575\pi$
$450$	9.40430	0.443323
$451$	−23.0234	−1.08413
$452$	0.195761	0.00920781
$453$	−33.2596	−1.56267
$454$	−6.41053	−0.300861
$455$	−10.4331	−0.489111
$456$	22.4473	1.05119
$457$	−4.37698	−0.204746	−0.102373	−	0.994746i	$-0.532644\pi$
$457$	−4.37698	−0.204746	−0.102373	+	0.994746i	$0.532644\pi$
$458$	−15.7363	−0.735307
$459$	1.41482	0.0660381
$460$	0.166499	0.00776307
$461$	14.1763	0.660256	0.330128	−	0.943936i	$-0.392908\pi$
$461$	14.1763	0.660256	0.330128	+	0.943936i	$0.392908\pi$
$462$	−19.5000	−0.907221
$463$	0.854854	0.0397284	0.0198642	−	0.999803i	$-0.493677\pi$
$463$	0.854854	0.0397284	0.0198642	+	0.999803i	$0.493677\pi$
$464$	35.6933	1.65702
$465$	−10.2412	−0.474924
$466$	−8.91916	−0.413172
$467$	17.4052	0.805419	0.402709	−	0.915328i	$-0.368069\pi$
$467$	17.4052	0.805419	0.402709	+	0.915328i	$0.368069\pi$
$468$	−0.327869	−0.0151558
$469$	−8.58396	−0.396370
$470$	10.7066	0.493857
$471$	−35.4164	−1.63190
$472$	−6.18071	−0.284490
$473$	−21.9648	−1.00994
$474$	21.4087	0.983332
$475$	−5.80349	−0.266282
$476$	0.0156267	0.000716248 0
$477$	−1.96359	−0.0899064
$478$	−5.80978	−0.265733
$479$	7.22937	0.330318	0.165159	−	0.986267i	$-0.447186\pi$
$479$	7.22937	0.330318	0.165159	+	0.986267i	$0.447186\pi$
$480$	−0.399742	−0.0182457
$481$	−9.91421	−0.452049
$482$	−38.0481	−1.73304
$483$	15.4390	0.702497
$484$	−0.285080	−0.0129582
$485$	−0.210429	−0.00955511
$486$	31.3522	1.42216
$487$	−8.08148	−0.366207	−0.183103	−	0.983094i	$-0.558614\pi$
$487$	−8.08148	−0.366207	−0.183103	+	0.983094i	$0.558614\pi$
$488$	10.6262	0.481028
$489$	42.3506	1.91516
$490$	−2.48857	−0.112422
$491$	−20.5372	−0.926829	−0.463415	−	0.886142i	$-0.653376\pi$
$491$	−20.5372	−0.926829	−0.463415	+	0.886142i	$0.653376\pi$
$492$	−0.170308	−0.00767807
$493$	−8.99415	−0.405076
$494$	−25.6933	−1.15600
$495$	−33.9398	−1.52548
$496$	8.98728	0.403541
$497$	−5.26519	−0.236176
$498$	−32.5453	−1.45839
$499$	25.9293	1.16075	0.580376	−	0.814348i	$-0.302905\pi$
$499$	25.9293	1.16075	0.580376	+	0.814348i	$0.302905\pi$
$500$	0.189906	0.00849284
$501$	−17.1082	−0.764340
$502$	22.7404	1.01495
$503$	29.5089	1.31574	0.657869	−	0.753133i	$-0.271458\pi$
$503$	29.5089	1.31574	0.657869	+	0.753133i	$0.271458\pi$
$504$	−10.0874	−0.449330
$505$	17.2089	0.765785
$506$	−45.9443	−2.04247
$507$	56.0036	2.48721
$508$	−0.000853961 0	−3.78884e−5 0
$509$	−10.5926	−0.469509	−0.234755	−	0.972055i	$-0.575429\pi$
$509$	−10.5926	−0.469509	−0.234755	+	0.972055i	$0.575429\pi$
$510$	−6.37030	−0.282082
$511$	1.43821	0.0636229
$512$	22.8869	1.01147
$513$	4.36952	0.192919
$514$	11.8115	0.520984
$515$	−26.2315	−1.15590
$516$	−0.162477	−0.00715266
$517$	23.2655	1.02322
$518$	−2.36480	−0.103903
$519$	47.6649	2.09226
$520$	29.6234	1.29907
$521$	7.62040	0.333856	0.166928	−	0.985969i	$-0.446615\pi$
$521$	7.62040	0.333856	0.166928	+	0.985969i	$0.446615\pi$
$522$	45.0122	1.97013
$523$	−16.0195	−0.700486	−0.350243	−	0.936659i	$-0.613901\pi$
$523$	−16.0195	−0.700486	−0.350243	+	0.936659i	$0.613901\pi$
$524$	−0.0880518	−0.00384656
$525$	4.81023	0.209936
$526$	−33.5427	−1.46253
$527$	−2.26465	−0.0986499
$528$	54.9350	2.39074
$529$	13.3760	0.581566
$530$	1.37544	0.0597452
$531$	−7.73349	−0.335605
$532$	0.0482614	0.00209240
$533$	25.1439	1.08910
$534$	−50.8425	−2.20017
$535$	−5.05492	−0.218543
$536$	24.3730	1.05275
$537$	−22.2714	−0.961083
$538$	1.56419	0.0674369
$539$	−5.40770	−0.232926
$540$	−0.0390576	−0.00168077
$541$	−13.5513	−0.582615	−0.291307	−	0.956630i	$-0.594090\pi$
$541$	−13.5513	−0.582615	−0.291307	+	0.956630i	$0.594090\pi$
$542$	11.9161	0.511839
$543$	7.66951	0.329130
$544$	−0.0883958	−0.00378994
$545$	29.7061	1.27247
$546$	21.2960	0.911383
$547$	−10.6651	−0.456008	−0.228004	−	0.973660i	$-0.573220\pi$
$547$	−10.6651	−0.456008	−0.228004	+	0.973660i	$0.573220\pi$
$548$	−0.299590	−0.0127978
$549$	13.2959	0.567454
$550$	−14.3146	−0.610378
$551$	−27.7775	−1.18336
$552$	−43.8369	−1.86582
$553$	5.93700	0.252467
$554$	32.9673	1.40064
$555$	−7.59156	−0.322244
$556$	−0.337682	−0.0143209
$557$	14.0285	0.594406	0.297203	−	0.954814i	$-0.403946\pi$
$557$	14.0285	0.594406	0.297203	+	0.954814i	$0.403946\pi$
$558$	11.3337	0.479794
$559$	23.9878	1.01458
$560$	7.01075	0.296258
$561$	−13.8428	−0.584442
$562$	24.1456	1.01852
$563$	−15.5220	−0.654174	−0.327087	−	0.944994i	$-0.606067\pi$
$563$	−15.5220	−0.654174	−0.327087	+	0.944994i	$0.606067\pi$
$564$	0.172098	0.00724665
$565$	−22.1308	−0.931050
$566$	−9.22638	−0.387814
$567$	7.03641	0.295502
$568$	14.9498	0.627280
$569$	31.4968	1.32041	0.660207	−	0.751084i	$-0.270469\pi$
$569$	31.4968	1.32041	0.660207	+	0.751084i	$0.270469\pi$
$570$	−19.6740	−0.824054
$571$	−23.3199	−0.975908	−0.487954	−	0.872869i	$-0.662257\pi$
$571$	−23.3199	−0.975908	−0.487954	+	0.872869i	$0.662257\pi$
$572$	0.499062	0.0208668
$573$	4.52721	0.189127
$574$	5.99749	0.250330
$575$	11.3335	0.472639
$576$	28.6402	1.19334
$577$	28.7655	1.19752	0.598761	−	0.800927i	$-0.295660\pi$
$577$	28.7655	1.19752	0.598761	+	0.800927i	$0.295660\pi$
$578$	−1.40868	−0.0585933
$579$	−19.3023	−0.802175
$580$	0.248293	0.0103098
$581$	−9.02540	−0.374437
$582$	0.429527	0.0178045
$583$	2.98884	0.123785
$584$	−4.08362	−0.168981
$585$	37.0657	1.53248
$586$	1.80081	0.0743906
$587$	−6.73037	−0.277792	−0.138896	−	0.990307i	$-0.544355\pi$
$587$	−6.73037	−0.277792	−0.138896	+	0.990307i	$0.544355\pi$
$588$	−0.0400016	−0.00164964
$589$	−6.99415	−0.288189
$590$	5.41710	0.223018
$591$	−66.5977	−2.73946
$592$	6.66207	0.273810
$593$	−18.4424	−0.757337	−0.378668	−	0.925532i	$-0.623618\pi$
$593$	−18.4424	−0.757337	−0.378668	+	0.925532i	$0.623618\pi$
$594$	10.7777	0.442214
$595$	−1.76660	−0.0724235
$596$	0.0690280	0.00282750
$597$	−21.7753	−0.891205
$598$	50.1758	2.05184
$599$	31.5457	1.28892	0.644462	−	0.764636i	$-0.277081\pi$
$599$	31.5457	1.28892	0.644462	+	0.764636i	$0.277081\pi$
$600$	−13.6580	−0.557587
$601$	42.7597	1.74420	0.872102	−	0.489324i	$-0.162756\pi$
$601$	42.7597	1.74420	0.872102	+	0.489324i	$0.162756\pi$
$602$	5.72173	0.233200
$603$	30.4962	1.24190
$604$	0.203036	0.00826143
$605$	32.2284	1.31027
$606$	−35.1266	−1.42692
$607$	−8.13465	−0.330175	−0.165088	−	0.986279i	$-0.552791\pi$
$607$	−8.13465	−0.330175	−0.165088	+	0.986279i	$0.552791\pi$
$608$	−0.273001	−0.0110717
$609$	23.0234	0.932957
$610$	−9.31339	−0.377088
$611$	−25.4083	−1.02791
$612$	−0.0555169	−0.00224414
$613$	−36.1718	−1.46096	−0.730482	−	0.682932i	$-0.760705\pi$
$613$	−36.1718	−1.46096	−0.730482	+	0.682932i	$0.760705\pi$
$614$	24.0034	0.968697
$615$	19.2533	0.776370
$616$	15.3544	0.618648
$617$	−38.7539	−1.56017	−0.780086	−	0.625672i	$-0.784825\pi$
$617$	−38.7539	−1.56017	−0.780086	+	0.625672i	$0.784825\pi$
$618$	53.5436	2.15384
$619$	25.7713	1.03584	0.517918	−	0.855430i	$-0.326707\pi$
$619$	25.7713	1.03584	0.517918	+	0.855430i	$0.326707\pi$
$620$	0.0625182	0.00251079
$621$	−8.53314	−0.342423
$622$	−30.2811	−1.21416
$623$	−14.0996	−0.564887
$624$	−59.9946	−2.40171
$625$	−12.0733	−0.482930
$626$	21.9995	0.879276
$627$	−42.7519	−1.70735
$628$	0.216203	0.00862743
$629$	−1.67874	−0.0669356
$630$	8.84115	0.352240
$631$	−34.2365	−1.36293	−0.681467	−	0.731849i	$-0.738658\pi$
$631$	−34.2365	−1.36293	−0.681467	+	0.731849i	$0.738658\pi$
$632$	−16.8573	−0.670549
$633$	−38.2411	−1.51995
$634$	−2.29889	−0.0913006
$635$	0.0965405	0.00383109
$636$	0.0221089	0.000876676 0
$637$	5.90575	0.233994
$638$	−68.5147	−2.71252
$639$	18.7056	0.739984
$640$	−19.7493	−0.780662
$641$	−11.8185	−0.466802	−0.233401	−	0.972381i	$-0.574985\pi$
$641$	−11.8185	−0.466802	−0.233401	+	0.972381i	$0.574985\pi$
$642$	10.3181	0.407221
$643$	−35.9141	−1.41631	−0.708156	−	0.706056i	$-0.750473\pi$
$643$	−35.9141	−1.41631	−0.708156	+	0.706056i	$0.750473\pi$
$644$	−0.0942485	−0.00371391
$645$	18.3681	0.723242
$646$	−4.35055	−0.171170
$647$	−0.160585	−0.00631325	−0.00315663	−	0.999995i	$-0.501005\pi$
$647$	−0.160585	−0.00631325	−0.00315663	+	0.999995i	$0.501005\pi$
$648$	−19.9790	−0.784848
$649$	11.7714	0.462069
$650$	15.6330	0.613177
$651$	5.79712	0.227207
$652$	−0.258533	−0.0101249
$653$	−22.6671	−0.887032	−0.443516	−	0.896266i	$-0.646269\pi$
$653$	−22.6671	−0.887032	−0.443516	+	0.896266i	$0.646269\pi$
$654$	−60.6358	−2.37105
$655$	9.95428	0.388946
$656$	−16.8960	−0.659679
$657$	−5.10955	−0.199342
$658$	−6.06055	−0.236265
$659$	11.8789	0.462737	0.231369	−	0.972866i	$-0.425680\pi$
$659$	11.8789	0.462737	0.231369	+	0.972866i	$0.425680\pi$
$660$	0.382144	0.0148749
$661$	27.1431	1.05574	0.527872	−	0.849324i	$-0.322990\pi$
$661$	27.1431	1.05574	0.527872	+	0.849324i	$0.322990\pi$
$662$	40.6341	1.57929
$663$	15.1177	0.587122
$664$	25.6264	0.994499
$665$	−5.45596	−0.211573
$666$	8.40143	0.325549
$667$	54.2460	2.10041
$668$	0.104439	0.00404086
$669$	−4.72340	−0.182617
$670$	−21.3618	−0.825277
$671$	−20.2381	−0.781285
$672$	0.226278	0.00872885
$673$	20.7262	0.798935	0.399468	−	0.916747i	$-0.369195\pi$
$673$	20.7262	0.798935	0.399468	+	0.916747i	$0.369195\pi$
$674$	−5.36560	−0.206675
$675$	−2.65863	−0.102331
$676$	−0.341879	−0.0131492
$677$	−13.4864	−0.518325	−0.259162	−	0.965834i	$-0.583446\pi$
$677$	−13.4864	−0.518325	−0.259162	+	0.965834i	$0.583446\pi$
$678$	45.1732	1.73487
$679$	0.119116	0.00457123
$680$	5.01603	0.192356
$681$	11.6491	0.446394
$682$	−17.2515	−0.660593
$683$	21.3520	0.817010	0.408505	−	0.912756i	$-0.366050\pi$
$683$	21.3520	0.817010	0.408505	+	0.912756i	$0.366050\pi$
$684$	−0.171458	−0.00655587
$685$	33.8687	1.29406
$686$	1.40868	0.0537836
$687$	28.5956	1.09099
$688$	−16.1191	−0.614537
$689$	−3.26412	−0.124353
$690$	38.4209	1.46266
$691$	8.67019	0.329829	0.164915	−	0.986308i	$-0.447265\pi$
$691$	8.67019	0.329829	0.164915	+	0.986308i	$0.447265\pi$
$692$	−0.290975	−0.0110612
$693$	19.2119	0.729801
$694$	−7.10589	−0.269736
$695$	38.1751	1.44806
$696$	−65.3720	−2.47792
$697$	4.25753	0.161265
$698$	34.8207	1.31798
$699$	16.2077	0.613033
$700$	−0.0293645	−0.00110987
$701$	48.2784	1.82345	0.911725	−	0.410801i	$-0.134751\pi$
$701$	48.2784	1.82345	0.911725	+	0.410801i	$0.134751\pi$
$702$	−11.7703	−0.444242
$703$	−5.18461	−0.195541
$704$	−43.5943	−1.64302
$705$	−19.4558	−0.732747
$706$	−34.9432	−1.31510
$707$	−9.74124	−0.366357
$708$	0.0870751	0.00327248
$709$	20.1791	0.757841	0.378920	−	0.925429i	$-0.376295\pi$
$709$	20.1791	0.757841	0.378920	+	0.925429i	$0.376295\pi$
$710$	−13.1028	−0.491739
$711$	−21.0924	−0.791027
$712$	40.0338	1.50033
$713$	13.6587	0.511522
$714$	3.60597	0.134950
$715$	−56.4190	−2.10995
$716$	0.135958	0.00508099
$717$	10.5574	0.394274
$718$	−5.57020	−0.207878
$719$	−19.4245	−0.724413	−0.362207	−	0.932098i	$-0.617977\pi$
$719$	−19.4245	−0.724413	−0.362207	+	0.932098i	$0.617977\pi$
$720$	−24.9071	−0.928234
$721$	14.8486	0.552991
$722$	13.3286	0.496041
$723$	69.1403	2.57136
$724$	−0.0468192	−0.00174002
$725$	16.9011	0.627692
$726$	−65.7844	−2.44149
$727$	−5.10313	−0.189265	−0.0946323	−	0.995512i	$-0.530168\pi$
$727$	−5.10313	−0.189265	−0.0946323	+	0.995512i	$0.530168\pi$
$728$	−16.7686	−0.621486
$729$	−35.8634	−1.32827
$730$	3.57910	0.132468
$731$	4.06177	0.150230
$732$	−0.149705	−0.00553324
$733$	50.6264	1.86993	0.934965	−	0.354741i	$-0.115431\pi$
$733$	50.6264	1.86993	0.934965	+	0.354741i	$0.115431\pi$
$734$	−19.9790	−0.737440
$735$	4.52218	0.166803
$736$	0.533138	0.0196517
$737$	−46.4194	−1.70988
$738$	−21.3073	−0.784332
$739$	−41.2855	−1.51871	−0.759355	−	0.650676i	$-0.774486\pi$
$739$	−41.2855	−1.51871	−0.759355	+	0.650676i	$0.774486\pi$
$740$	0.0463434	0.00170362
$741$	46.6894	1.71518
$742$	−0.778579	−0.0285825
$743$	−0.115352	−0.00423186	−0.00211593	−	0.999998i	$-0.500674\pi$
$743$	−0.115352	−0.00423186	−0.00211593	+	0.999998i	$0.500674\pi$
$744$	−16.4602	−0.603458
$745$	−7.80363	−0.285903
$746$	9.23045	0.337951
$747$	32.0646	1.17318
$748$	0.0845043	0.00308978
$749$	2.86138	0.104553
$750$	43.8221	1.60016
$751$	−52.3422	−1.90999	−0.954997	−	0.296616i	$-0.904142\pi$
$751$	−52.3422	−1.90999	−0.954997	+	0.296616i	$0.904142\pi$
$752$	17.0737	0.622612
$753$	−41.3235	−1.50591
$754$	74.8250	2.72497
$755$	−22.9533	−0.835356
$756$	0.0221089	0.000804094 0
$757$	−19.1277	−0.695207	−0.347604	−	0.937642i	$-0.613005\pi$
$757$	−19.1277	−0.695207	−0.347604	+	0.937642i	$0.613005\pi$
$758$	−41.8000	−1.51825
$759$	83.4892	3.03046
$760$	15.4915	0.561935
$761$	2.04547	0.0741482	0.0370741	−	0.999313i	$-0.488196\pi$
$761$	2.04547	0.0741482	0.0370741	+	0.999313i	$0.488196\pi$
$762$	−0.197058	−0.00713865
$763$	−16.8154	−0.608758
$764$	−0.0276367	−0.000999862 0
$765$	6.27620	0.226917
$766$	−49.4460	−1.78656
$767$	−12.8556	−0.464188
$768$	−0.959979	−0.0346402
$769$	−45.2661	−1.63234	−0.816168	−	0.577814i	$-0.803906\pi$
$769$	−45.2661	−1.63234	−0.816168	+	0.577814i	$0.803906\pi$
$770$	−13.4574	−0.484972
$771$	−21.4637	−0.772997
$772$	0.117832	0.00424088
$773$	−2.73655	−0.0984269	−0.0492135	−	0.998788i	$-0.515671\pi$
$773$	−2.73655	−0.0984269	−0.0492135	+	0.998788i	$0.515671\pi$
$774$	−20.3276	−0.730660
$775$	4.25557	0.152865
$776$	−0.338213	−0.0121411
$777$	4.29727	0.154164
$778$	30.5314	1.09461
$779$	13.1489	0.471110
$780$	−0.417340	−0.0149432
$781$	−28.4725	−1.01883
$782$	8.49609	0.303820
$783$	−12.7251	−0.454758
$784$	−3.96850	−0.141732
$785$	−24.4418	−0.872364
$786$	−20.3186	−0.724740
$787$	−22.9559	−0.818290	−0.409145	−	0.912469i	$-0.634173\pi$
$787$	−22.9559	−0.818290	−0.409145	+	0.912469i	$0.634173\pi$
$788$	0.406552	0.0144828
$789$	60.9533	2.16999
$790$	14.7747	0.525658
$791$	12.5273	0.445421
$792$	−54.5498	−1.93834
$793$	22.1021	0.784868
$794$	7.11765	0.252596
$795$	−2.49942	−0.0886453
$796$	0.132929	0.00471156
$797$	−23.9778	−0.849337	−0.424669	−	0.905349i	$-0.639609\pi$
$797$	−23.9778	−0.849337	−0.424669	+	0.905349i	$0.639609\pi$
$798$	11.1367	0.394233
$799$	−4.30229	−0.152204
$800$	0.166107	0.00587277
$801$	50.0915	1.76990
$802$	−17.6203	−0.622194
$803$	7.77743	0.274459
$804$	−0.343372	−0.0121098
$805$	10.6548	0.375533
$806$	18.8403	0.663623
$807$	−2.84241	−0.100058
$808$	27.6590	0.973040
$809$	0.547871	0.0192621	0.00963106	−	0.999954i	$-0.496934\pi$
$809$	0.547871	0.0192621	0.00963106	+	0.999954i	$0.496934\pi$
$810$	17.5106	0.615260
$811$	37.1882	1.30585	0.652927	−	0.757421i	$-0.273541\pi$
$811$	37.1882	1.30585	0.652927	+	0.757421i	$0.273541\pi$
$812$	−0.140549	−0.00493229
$813$	−21.6537	−0.759428
$814$	−12.7881	−0.448223
$815$	29.2272	1.02379
$816$	−10.1587	−0.355625
$817$	12.5444	0.438871
$818$	−49.5403	−1.73213
$819$	−20.9814	−0.733149
$820$	−0.117534	−0.00410446
$821$	−7.27943	−0.254054	−0.127027	−	0.991899i	$-0.540543\pi$
$821$	−7.27943	−0.254054	−0.127027	+	0.991899i	$0.540543\pi$
$822$	−69.1325	−2.41127
$823$	14.6436	0.510444	0.255222	−	0.966883i	$-0.417852\pi$
$823$	14.6436	0.510444	0.255222	+	0.966883i	$0.417852\pi$
$824$	−42.1607	−1.46874
$825$	26.0123	0.905631
$826$	−3.06640	−0.106694
$827$	−12.0435	−0.418795	−0.209397	−	0.977831i	$-0.567150\pi$
$827$	−12.0435	−0.418795	−0.209397	+	0.977831i	$0.567150\pi$
$828$	0.334837	0.0116364
$829$	−26.2739	−0.912529	−0.456264	−	0.889844i	$-0.650813\pi$
$829$	−26.2739	−0.912529	−0.456264	+	0.889844i	$0.650813\pi$
$830$	−22.4603	−0.779610
$831$	−59.9075	−2.07817
$832$	47.6094	1.65056
$833$	1.00000	0.0346479
$834$	−77.9227	−2.69824
$835$	−11.8068	−0.408592
$836$	0.260983	0.00902628
$837$	−3.20408	−0.110749
$838$	10.4701	0.361683
$839$	45.9248	1.58550	0.792750	−	0.609547i	$-0.208648\pi$
$839$	45.9248	1.58550	0.792750	+	0.609547i	$0.208648\pi$
$840$	−12.8402	−0.443027
$841$	51.8947	1.78947
$842$	−24.3799	−0.840186
$843$	−43.8769	−1.51120
$844$	0.233446	0.00803554
$845$	38.6495	1.32958
$846$	21.5313	0.740262
$847$	−18.2432	−0.626843
$848$	2.19340	0.0753216
$849$	16.7660	0.575408
$850$	2.64708	0.0907942
$851$	10.1249	0.347077
$852$	−0.210616	−0.00721557
$853$	−10.4825	−0.358915	−0.179457	−	0.983766i	$-0.557434\pi$
$853$	−10.4825	−0.358915	−0.179457	+	0.983766i	$0.557434\pi$
$854$	5.27193	0.180402
$855$	19.3834	0.662898
$856$	−8.12452	−0.277690
$857$	−41.9217	−1.43202	−0.716009	−	0.698091i	$-0.754033\pi$
$857$	−41.9217	−1.43202	−0.716009	+	0.698091i	$0.754033\pi$
$858$	115.162	3.93157
$859$	10.5131	0.358702	0.179351	−	0.983785i	$-0.442600\pi$
$859$	10.5131	0.358702	0.179351	+	0.983785i	$0.442600\pi$
$860$	−0.112130	−0.00382359
$861$	−10.8985	−0.371421
$862$	−5.13037	−0.174741
$863$	−18.8193	−0.640617	−0.320309	−	0.947313i	$-0.603787\pi$
$863$	−18.8193	−0.640617	−0.320309	+	0.947313i	$0.603787\pi$
$864$	−0.125064	−0.00425477
$865$	32.8947	1.11845
$866$	10.1875	0.346186
$867$	2.55982	0.0869362
$868$	−0.0353890	−0.00120118
$869$	32.1055	1.08911
$870$	57.2954	1.94250
$871$	50.6947	1.71772
$872$	47.7451	1.61685
$873$	−0.423182	−0.0143225
$874$	26.2393	0.887558
$875$	12.1527	0.410835
$876$	0.0575308	0.00194379
$877$	−52.4834	−1.77224	−0.886119	−	0.463457i	$-0.846609\pi$
$877$	−52.4834	−1.77224	−0.886119	+	0.463457i	$0.846609\pi$
$878$	47.6011	1.60646
$879$	−3.27239	−0.110375
$880$	37.9120	1.27801
$881$	−1.43758	−0.0484335	−0.0242167	−	0.999707i	$-0.507709\pi$
$881$	−1.43758	−0.0484335	−0.0242167	+	0.999707i	$0.507709\pi$
$882$	−5.00461	−0.168514
$883$	−3.17781	−0.106942	−0.0534710	−	0.998569i	$-0.517028\pi$
$883$	−3.17781	−0.106942	−0.0534710	+	0.998569i	$0.517028\pi$
$884$	−0.0922873	−0.00310396
$885$	−9.84385	−0.330898
$886$	17.2247	0.578676
$887$	−3.77435	−0.126730	−0.0633652	−	0.997990i	$-0.520183\pi$
$887$	−3.77435	−0.126730	−0.0633652	+	0.997990i	$0.520183\pi$
$888$	−12.2015	−0.409457
$889$	−0.0546476	−0.00183282
$890$	−35.0877	−1.17614
$891$	38.0508	1.27475
$892$	0.0288344	0.000965449 0
$893$	−13.2872	−0.444639
$894$	15.9287	0.532735
$895$	−15.3701	−0.513765
$896$	11.1793	0.373474
$897$	−91.1786	−3.04437
$898$	44.8519	1.49673
$899$	20.3686	0.679332
$900$	0.104323	0.00347744
$901$	−0.552702	−0.0184132
$902$	32.4326	1.07989
$903$	−10.3974	−0.346004
$904$	−35.5698	−1.18303
$905$	5.29292	0.175943
$906$	46.8521	1.55656
$907$	−48.6919	−1.61679	−0.808395	−	0.588641i	$-0.799663\pi$
$907$	−48.6919	−1.61679	−0.808395	+	0.588641i	$0.799663\pi$
$908$	−0.0711130	−0.00235997
$909$	34.6077	1.14787
$910$	14.6969	0.487197
$911$	52.2254	1.73030	0.865152	−	0.501510i	$-0.167222\pi$
$911$	52.2254	1.73030	0.865152	+	0.501510i	$0.167222\pi$
$912$	−31.3740	−1.03890
$913$	−48.8066	−1.61526
$914$	6.16575	0.203945
$915$	16.9241	0.559495
$916$	−0.174565	−0.00576778
$917$	−5.63471	−0.186075
$918$	−1.99303	−0.0657796
$919$	56.9695	1.87925	0.939625	−	0.342205i	$-0.111174\pi$
$919$	56.9695	1.87925	0.939625	+	0.342205i	$0.111174\pi$
$920$	−30.2529	−0.997410
$921$	−43.6185	−1.43728
$922$	−19.9698	−0.657672
$923$	31.0949	1.02350
$924$	−0.216316	−0.00711628
$925$	3.15456	0.103721
$926$	−1.20421	−0.0395729
$927$	−52.7527	−1.73263
$928$	0.795045	0.0260986
$929$	−11.1387	−0.365450	−0.182725	−	0.983164i	$-0.558492\pi$
$929$	−11.1387	−0.365450	−0.182725	+	0.983164i	$0.558492\pi$
$930$	14.4265	0.473064
$931$	3.08840	0.101218
$932$	−0.0989417	−0.00324094
$933$	55.0263	1.80148
$934$	−24.5184	−0.802266
$935$	−9.55324	−0.312424
$936$	59.5739	1.94723
$937$	18.6644	0.609740	0.304870	−	0.952394i	$-0.401387\pi$
$937$	18.6644	0.609740	0.304870	+	0.952394i	$0.401387\pi$
$938$	12.0920	0.394819
$939$	−39.9771	−1.30460
$940$	0.118769	0.00387383
$941$	−43.2984	−1.41149	−0.705743	−	0.708467i	$-0.749387\pi$
$941$	−43.2984	−1.41149	−0.705743	+	0.708467i	$0.749387\pi$
$942$	49.8903	1.62552
$943$	−25.6782	−0.836199
$944$	8.63860	0.281163
$945$	−2.49942	−0.0813061
$946$	30.9414	1.00599
$947$	18.7279	0.608576	0.304288	−	0.952580i	$-0.401582\pi$
$947$	18.7279	0.608576	0.304288	+	0.952580i	$0.401582\pi$
$948$	0.237489	0.00771330
$949$	−8.49374	−0.275718
$950$	8.17524	0.265240
$951$	4.17750	0.135465
$952$	−2.83937	−0.0920245
$953$	−22.3380	−0.723598	−0.361799	−	0.932256i	$-0.617837\pi$
$953$	−22.3380	−0.723598	−0.361799	+	0.932256i	$0.617837\pi$
$954$	2.76606	0.0895545
$955$	3.12434	0.101101
$956$	−0.0644488	−0.00208442
$957$	124.504	4.02464
$958$	−10.1839	−0.329025
$959$	−19.1717	−0.619086
$960$	36.4557	1.17660
$961$	−25.8713	−0.834559
$962$	13.9659	0.450279
$963$	−10.1656	−0.327583
$964$	−0.422073	−0.0135941
$965$	−13.3210	−0.428817
$966$	−21.7485	−0.699747
$967$	−40.0648	−1.28840	−0.644199	−	0.764858i	$-0.722809\pi$
$967$	−40.0648	−1.28840	−0.644199	+	0.764858i	$0.722809\pi$
$968$	51.7991	1.66489
$969$	7.90575	0.253969
$970$	0.296427	0.00951771
$971$	−7.71048	−0.247441	−0.123721	−	0.992317i	$-0.539483\pi$
$971$	−7.71048	−0.247441	−0.123721	+	0.992317i	$0.539483\pi$
$972$	0.347794	0.0111555
$973$	−21.6094	−0.692764
$974$	11.3842	0.364773
$975$	−28.4080	−0.909785
$976$	−14.8520	−0.475401
$977$	14.3134	0.457926	0.228963	−	0.973435i	$-0.426466\pi$
$977$	14.3134	0.457926	0.228963	+	0.973435i	$0.426466\pi$
$978$	−59.6584	−1.90767
$979$	−76.2461	−2.43684
$980$	−0.0276061	−0.000881844 0
$981$	59.7401	1.90735
$982$	28.9303	0.923201
$983$	−20.5625	−0.655843	−0.327922	−	0.944705i	$-0.606348\pi$
$983$	−20.5625	−0.655843	−0.327922	+	0.944705i	$0.606348\pi$
$984$	30.9450	0.986489
$985$	−45.9608	−1.46443
$986$	12.6699	0.403490
$987$	11.0131	0.350551
$988$	−0.285020	−0.00906768
$989$	−24.4976	−0.778977
$990$	47.8102	1.51951
$991$	17.4906	0.555606	0.277803	−	0.960638i	$-0.410394\pi$
$991$	17.4906	0.555606	0.277803	+	0.960638i	$0.410394\pi$
$992$	0.200186	0.00635591
$993$	−73.8396	−2.34323
$994$	7.41695	0.235251
$995$	−15.0277	−0.476410
$996$	−0.361030	−0.0114397
$997$	−51.7506	−1.63896	−0.819479	−	0.573109i	$-0.805737\pi$
$997$	−51.7506	−1.63896	−0.819479	+	0.573109i	$0.805737\pi$
$998$	−36.5260	−1.15621
$999$	−2.37511	−0.0751452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.2.a.b.1.2	✓	5
3.2	odd	2		1071.2.a.m.1.4		5
4.3	odd	2		1904.2.a.t.1.1		5
5.4	even	2		2975.2.a.m.1.4		5
7.2	even	3		833.2.e.i.18.4		10
7.3	odd	6		833.2.e.h.324.4		10
7.4	even	3		833.2.e.i.324.4		10
7.5	odd	6		833.2.e.h.18.4		10
7.6	odd	2		833.2.a.g.1.2		5
8.3	odd	2		7616.2.a.bq.1.5		5
8.5	even	2		7616.2.a.bt.1.1		5
17.16	even	2		2023.2.a.j.1.2		5
21.20	even	2		7497.2.a.br.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.a.b.1.2	✓	5	1.1	even	1	trivial
833.2.a.g.1.2		5	7.6	odd	2
833.2.e.h.18.4		10	7.5	odd	6
833.2.e.h.324.4		10	7.3	odd	6
833.2.e.i.18.4		10	7.2	even	3
833.2.e.i.324.4		10	7.4	even	3
1071.2.a.m.1.4		5	3.2	odd	2
1904.2.a.t.1.1		5	4.3	odd	2
2023.2.a.j.1.2		5	17.16	even	2
2975.2.a.m.1.4		5	5.4	even	2
7497.2.a.br.1.4		5	21.20	even	2
7616.2.a.bq.1.5		5	8.3	odd	2
7616.2.a.bt.1.1		5	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)

\(f(q)\)	\(=\)	\(q-1.40868 q^{2} +2.55982 q^{3} -0.0156267 q^{4} +1.76660 q^{5} -3.60597 q^{6} -1.00000 q^{7} +2.83937 q^{8} +3.55270 q^{9} -2.48857 q^{10} -5.40770 q^{11} -0.0400016 q^{12} +5.90575 q^{13} +1.40868 q^{14} +4.52218 q^{15} -3.96850 q^{16} +1.00000 q^{17} -5.00461 q^{18} +3.08840 q^{19} -0.0276061 q^{20} -2.55982 q^{21} +7.61770 q^{22} -6.03125 q^{23} +7.26829 q^{24} -1.87913 q^{25} -8.31930 q^{26} +1.41482 q^{27} +0.0156267 q^{28} -8.99415 q^{29} -6.37030 q^{30} -2.26465 q^{31} -0.0883958 q^{32} -13.8428 q^{33} -1.40868 q^{34} -1.76660 q^{35} -0.0555169 q^{36} -1.67874 q^{37} -4.35055 q^{38} +15.1177 q^{39} +5.01603 q^{40} +4.25753 q^{41} +3.60597 q^{42} +4.06177 q^{43} +0.0845043 q^{44} +6.27620 q^{45} +8.49609 q^{46} -4.30229 q^{47} -10.1587 q^{48} +1.00000 q^{49} +2.64708 q^{50} +2.55982 q^{51} -0.0922873 q^{52} -0.552702 q^{53} -1.99303 q^{54} -9.55324 q^{55} -2.83937 q^{56} +7.90575 q^{57} +12.6699 q^{58} -2.17679 q^{59} -0.0706667 q^{60} +3.74247 q^{61} +3.19017 q^{62} -3.55270 q^{63} +8.06153 q^{64} +10.4331 q^{65} +19.5000 q^{66} +8.58396 q^{67} -0.0156267 q^{68} -15.4390 q^{69} +2.48857 q^{70} +5.26519 q^{71} +10.0874 q^{72} -1.43821 q^{73} +2.36480 q^{74} -4.81023 q^{75} -0.0482614 q^{76} +5.40770 q^{77} -21.2960 q^{78} -5.93700 q^{79} -7.01075 q^{80} -7.03641 q^{81} -5.99749 q^{82} +9.02540 q^{83} +0.0400016 q^{84} +1.76660 q^{85} -5.72173 q^{86} -23.0234 q^{87} -15.3544 q^{88} +14.0996 q^{89} -8.84115 q^{90} -5.90575 q^{91} +0.0942485 q^{92} -5.79712 q^{93} +6.06055 q^{94} +5.45596 q^{95} -0.226278 q^{96} -0.119116 q^{97} -1.40868 q^{98} -19.2119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - q^{6} - 5 q^{7} + 6 q^{8} + 11 q^{9} + 4 q^{10} - 2 q^{11} - 22 q^{12} + 2 q^{13} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 5 q^{17} - 18 q^{18} + 6 q^{19} - 19 q^{20} + 2 q^{21}+ \cdots - 62 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - q^6 - 5 * q^7 + 6 * q^8 + 11 * q^9 + 4 * q^10 - 2 * q^11 - 22 * q^12 + 2 * q^13 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 5 * q^17 - 18 * q^18 + 6 * q^19 - 19 * q^20 + 2 * q^21 + 6 * q^22 - 10 * q^23 + 2 * q^24 + 21 * q^25 - 26 * q^26 - 26 * q^27 - 10 * q^28 - 8 * q^29 - 51 * q^30 + 9 * q^32 + 6 * q^33 + 2 * q^34 + 39 * q^36 + 8 * q^37 + 14 * q^38 + 14 * q^39 + 5 * q^40 + 18 * q^41 + q^42 + 8 * q^43 - 14 * q^44 + 8 * q^46 - 10 * q^47 - 27 * q^48 + 5 * q^49 + 27 * q^50 - 2 * q^51 + 4 * q^52 + 4 * q^53 + 5 * q^54 - 24 * q^55 - 6 * q^56 + 12 * q^57 + 12 * q^58 + 8 * q^59 - 7 * q^60 + 22 * q^61 + 16 * q^62 - 11 * q^63 - 16 * q^64 - 30 * q^65 + 68 * q^66 + 16 * q^67 + 10 * q^68 - 32 * q^69 - 4 * q^70 - 2 * q^71 + 9 * q^72 + 10 * q^73 - 40 * q^74 - 14 * q^75 + 24 * q^76 + 2 * q^77 + 30 * q^78 + 18 * q^79 - 4 * q^80 + 25 * q^81 - 31 * q^82 - 12 * q^83 + 22 * q^84 + 23 * q^86 - 26 * q^87 - 46 * q^88 + 20 * q^89 + 97 * q^90 - 2 * q^91 + 28 * q^92 - 28 * q^93 - 42 * q^94 - 22 * q^95 - 18 * q^96 + 12 * q^97 + 2 * q^98 - 62 * q^99

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