LMFDB - Embedded newform 119.4.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [119,4,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, 4, names="a")

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

chi := DirichletCharacter("119.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
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:	$7.02122729068$
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} - 2x^{8} - 53x^{7} + 90x^{6} + 880x^{5} - 1087x^{4} - 4674x^{3} + 2515x^{2} + 1814x + 36 $ x^9 - 2x^8 - 53x^7 + 90x^6 + 880x^5 - 1087x^4 - 4674x^3 + 2515x^2 + 1814x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$4.42628$ 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)

$f(q)$	$=$	$q+4.42628 q^{2} -5.22352 q^{3} +11.5919 q^{4} +16.9037 q^{5} -23.1207 q^{6} +7.00000 q^{7} +15.8988 q^{8} +0.285172 q^{9} +O(q^{10})$	\(q+4.42628 q^{2} -5.22352 q^{3} +11.5919 q^{4} +16.9037 q^{5} -23.1207 q^{6} +7.00000 q^{7} +15.8988 q^{8} +0.285172 q^{9} +74.8205 q^{10} +22.2449 q^{11} -60.5506 q^{12} +69.0502 q^{13} +30.9839 q^{14} -88.2969 q^{15} -22.3627 q^{16} +17.0000 q^{17} +1.26225 q^{18} +6.54805 q^{19} +195.946 q^{20} -36.5646 q^{21} +98.4621 q^{22} -202.353 q^{23} -83.0479 q^{24} +160.735 q^{25} +305.635 q^{26} +139.545 q^{27} +81.1434 q^{28} -8.82223 q^{29} -390.826 q^{30} -297.162 q^{31} -226.174 q^{32} -116.197 q^{33} +75.2467 q^{34} +118.326 q^{35} +3.30569 q^{36} -343.891 q^{37} +28.9835 q^{38} -360.685 q^{39} +268.749 q^{40} -151.543 q^{41} -161.845 q^{42} +150.940 q^{43} +257.861 q^{44} +4.82046 q^{45} -895.670 q^{46} -308.563 q^{47} +116.812 q^{48} +49.0000 q^{49} +711.459 q^{50} -88.7999 q^{51} +800.424 q^{52} +570.022 q^{53} +617.667 q^{54} +376.021 q^{55} +111.292 q^{56} -34.2039 q^{57} -39.0496 q^{58} +539.811 q^{59} -1023.53 q^{60} +27.4019 q^{61} -1315.32 q^{62} +1.99620 q^{63} -822.208 q^{64} +1167.20 q^{65} -514.319 q^{66} +19.7566 q^{67} +197.063 q^{68} +1057.00 q^{69} +523.743 q^{70} -69.4533 q^{71} +4.53390 q^{72} +320.158 q^{73} -1522.16 q^{74} -839.605 q^{75} +75.9044 q^{76} +155.714 q^{77} -1596.49 q^{78} -372.464 q^{79} -378.013 q^{80} -736.618 q^{81} -670.772 q^{82} +312.615 q^{83} -423.854 q^{84} +287.363 q^{85} +668.101 q^{86} +46.0831 q^{87} +353.668 q^{88} -443.861 q^{89} +21.3367 q^{90} +483.351 q^{91} -2345.66 q^{92} +1552.23 q^{93} -1365.79 q^{94} +110.686 q^{95} +1181.43 q^{96} +1415.74 q^{97} +216.888 q^{98} +6.34361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9	\( 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9} + 134 q^{10} - 8 q^{11} + 56 q^{12} + 164 q^{13} + 14 q^{14} + 34 q^{15} + 178 q^{16} + 153 q^{17} + 98 q^{18} + 244 q^{19} - 41 q^{20} + 77 q^{21} - 80 q^{22} - 14 q^{23} + 298 q^{24} + 684 q^{25} + 326 q^{26} + 218 q^{27} + 266 q^{28} - 234 q^{29} - 335 q^{30} + 555 q^{31} - 181 q^{32} + 458 q^{33} + 34 q^{34} - 21 q^{35} - 1221 q^{36} - 364 q^{37} - 714 q^{38} - 52 q^{39} + 123 q^{40} - 45 q^{41} + 63 q^{42} - 135 q^{43} - 748 q^{44} - 844 q^{45} - 1576 q^{46} - 172 q^{47} - 949 q^{48} + 441 q^{49} - 2901 q^{50} + 187 q^{51} - 1596 q^{52} + 101 q^{53} - 1163 q^{54} + 1260 q^{55} + 168 q^{56} - 602 q^{57} + 1062 q^{58} + 280 q^{59} - 1727 q^{60} + 639 q^{61} - 1708 q^{62} + 518 q^{63} - 2390 q^{64} + 638 q^{65} - 2476 q^{66} + 35 q^{67} + 646 q^{68} + 1288 q^{69} + 938 q^{70} - 1616 q^{71} + 1335 q^{72} + 1049 q^{73} - 370 q^{74} + 1260 q^{75} + 4964 q^{76} - 56 q^{77} - 4714 q^{78} + 2304 q^{79} - 3996 q^{80} - 791 q^{81} - 215 q^{82} + 2508 q^{83} + 392 q^{84} - 51 q^{85} + 623 q^{86} + 166 q^{87} - 416 q^{88} + 2762 q^{89} + 2935 q^{90} + 1148 q^{91} - 2392 q^{92} + 2784 q^{93} - 862 q^{94} - 3462 q^{95} + 2928 q^{96} + 3107 q^{97} + 98 q^{98} - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9 + 134 * q^10 - 8 * q^11 + 56 * q^12 + 164 * q^13 + 14 * q^14 + 34 * q^15 + 178 * q^16 + 153 * q^17 + 98 * q^18 + 244 * q^19 - 41 * q^20 + 77 * q^21 - 80 * q^22 - 14 * q^23 + 298 * q^24 + 684 * q^25 + 326 * q^26 + 218 * q^27 + 266 * q^28 - 234 * q^29 - 335 * q^30 + 555 * q^31 - 181 * q^32 + 458 * q^33 + 34 * q^34 - 21 * q^35 - 1221 * q^36 - 364 * q^37 - 714 * q^38 - 52 * q^39 + 123 * q^40 - 45 * q^41 + 63 * q^42 - 135 * q^43 - 748 * q^44 - 844 * q^45 - 1576 * q^46 - 172 * q^47 - 949 * q^48 + 441 * q^49 - 2901 * q^50 + 187 * q^51 - 1596 * q^52 + 101 * q^53 - 1163 * q^54 + 1260 * q^55 + 168 * q^56 - 602 * q^57 + 1062 * q^58 + 280 * q^59 - 1727 * q^60 + 639 * q^61 - 1708 * q^62 + 518 * q^63 - 2390 * q^64 + 638 * q^65 - 2476 * q^66 + 35 * q^67 + 646 * q^68 + 1288 * q^69 + 938 * q^70 - 1616 * q^71 + 1335 * q^72 + 1049 * q^73 - 370 * q^74 + 1260 * q^75 + 4964 * q^76 - 56 * q^77 - 4714 * q^78 + 2304 * q^79 - 3996 * q^80 - 791 * q^81 - 215 * q^82 + 2508 * q^83 + 392 * q^84 - 51 * q^85 + 623 * q^86 + 166 * q^87 - 416 * q^88 + 2762 * q^89 + 2935 * q^90 + 1148 * q^91 - 2392 * q^92 + 2784 * q^93 - 862 * q^94 - 3462 * q^95 + 2928 * q^96 + 3107 * q^97 + 98 * q^98 - 2396 * 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 $

$2$	4.42628	1.56492	0.782462	−	0.622698i	$-0.213963\pi$
$2$	4.42628	1.56492	0.782462	+	0.622698i	$0.213963\pi$
$3$	−5.22352	−1.00527	−0.502634	−	0.864500i	$-0.667635\pi$
$3$	−5.22352	−1.00527	−0.502634	+	0.864500i	$0.667635\pi$
$4$	11.5919	1.44899
$5$	16.9037	1.51191	0.755957	−	0.654621i	$-0.227172\pi$
$5$	16.9037	1.51191	0.755957	+	0.654621i	$0.227172\pi$
$6$	−23.1207	−1.57317
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	15.8988	0.702636
$9$	0.285172	0.0105619
$10$	74.8205	2.36603
$11$	22.2449	0.609735	0.304868	−	0.952395i	$-0.401388\pi$
$11$	22.2449	0.609735	0.304868	+	0.952395i	$0.401388\pi$
$12$	−60.5506	−1.45662
$13$	69.0502	1.47316	0.736580	−	0.676350i	$-0.236439\pi$
$13$	69.0502	1.47316	0.736580	+	0.676350i	$0.236439\pi$
$14$	30.9839	0.591486
$15$	−88.2969	−1.51988
$16$	−22.3627	−0.349418
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	1.26225	0.0165286
$19$	6.54805	0.0790645	0.0395322	−	0.999218i	$-0.487413\pi$
$19$	6.54805	0.0790645	0.0395322	+	0.999218i	$0.487413\pi$
$20$	195.946	2.19075
$21$	−36.5646	−0.379955
$22$	98.4621	0.954190
$23$	−202.353	−1.83450	−0.917251	−	0.398311i	$-0.869597\pi$
$23$	−202.353	−1.83450	−0.917251	+	0.398311i	$0.869597\pi$
$24$	−83.0479	−0.706337
$25$	160.735	1.28588
$26$	305.635	2.30538
$27$	139.545	0.994650
$28$	81.1434	0.547667
$29$	−8.82223	−0.0564913	−0.0282456	−	0.999601i	$-0.508992\pi$
$29$	−8.82223	−0.0564913	−0.0282456	+	0.999601i	$0.508992\pi$
$30$	−390.826	−2.37849
$31$	−297.162	−1.72168	−0.860838	−	0.508879i	$-0.830060\pi$
$31$	−297.162	−1.72168	−0.860838	+	0.508879i	$0.830060\pi$
$32$	−226.174	−1.24945
$33$	−116.197	−0.612947
$34$	75.2467	0.379550
$35$	118.326	0.571450
$36$	3.30569	0.0153041
$37$	−343.891	−1.52798	−0.763992	−	0.645226i	$-0.776763\pi$
$37$	−343.891	−1.52798	−0.763992	+	0.645226i	$0.776763\pi$
$38$	28.9835	0.123730
$39$	−360.685	−1.48092
$40$	268.749	1.06232
$41$	−151.543	−0.577245	−0.288623	−	0.957443i	$-0.593197\pi$
$41$	−151.543	−0.577245	−0.288623	+	0.957443i	$0.593197\pi$
$42$	−161.845	−0.594601
$43$	150.940	0.535305	0.267652	−	0.963516i	$-0.413752\pi$
$43$	150.940	0.535305	0.267652	+	0.963516i	$0.413752\pi$
$44$	257.861	0.883500
$45$	4.82046	0.0159687
$46$	−895.670	−2.87086
$47$	−308.563	−0.957629	−0.478815	−	0.877916i	$-0.658933\pi$
$47$	−308.563	−0.957629	−0.478815	+	0.877916i	$0.658933\pi$
$48$	116.812	0.351258
$49$	49.0000	0.142857
$50$	711.459	2.01231
$51$	−88.7999	−0.243813
$52$	800.424	2.13459
$53$	570.022	1.47733	0.738665	−	0.674073i	$-0.235457\pi$
$53$	570.022	1.47733	0.738665	+	0.674073i	$0.235457\pi$
$54$	617.667	1.55655
$55$	376.021	0.921867
$56$	111.292	0.265571
$57$	−34.2039	−0.0794809
$58$	−39.0496	−0.0884046
$59$	539.811	1.19114	0.595571	−	0.803302i	$-0.296926\pi$
$59$	539.811	1.19114	0.595571	+	0.803302i	$0.296926\pi$
$60$	−1023.53	−2.20229
$61$	27.4019	0.0575157	0.0287579	−	0.999586i	$-0.490845\pi$
$61$	27.4019	0.0575157	0.0287579	+	0.999586i	$0.490845\pi$
$62$	−1315.32	−2.69429
$63$	1.99620	0.00399203
$64$	−822.208	−1.60588
$65$	1167.20	2.22729
$66$	−514.319	−0.959216
$67$	19.7566	0.0360246	0.0180123	−	0.999838i	$-0.494266\pi$
$67$	19.7566	0.0360246	0.0180123	+	0.999838i	$0.494266\pi$
$68$	197.063	0.351432
$69$	1057.00	1.84416
$70$	523.743	0.894276
$71$	−69.4533	−0.116093	−0.0580464	−	0.998314i	$-0.518487\pi$
$71$	−69.4533	−0.116093	−0.0580464	+	0.998314i	$0.518487\pi$
$72$	4.53390	0.00742118
$73$	320.158	0.513310	0.256655	−	0.966503i	$-0.417380\pi$
$73$	320.158	0.513310	0.256655	+	0.966503i	$0.417380\pi$
$74$	−1522.16	−2.39118
$75$	−839.605	−1.29266
$76$	75.9044	0.114564
$77$	155.714	0.230458
$78$	−1596.49	−2.31753
$79$	−372.464	−0.530449	−0.265225	−	0.964187i	$-0.585446\pi$
$79$	−372.464	−0.530449	−0.265225	+	0.964187i	$0.585446\pi$
$80$	−378.013	−0.528290
$81$	−736.618	−1.01045
$82$	−670.772	−0.903346
$83$	312.615	0.413421	0.206711	−	0.978402i	$-0.433724\pi$
$83$	312.615	0.413421	0.206711	+	0.978402i	$0.433724\pi$
$84$	−423.854	−0.550551
$85$	287.363	0.366693
$86$	668.101	0.837712
$87$	46.0831	0.0567888
$88$	353.668	0.428422
$89$	−443.861	−0.528642	−0.264321	−	0.964435i	$-0.585148\pi$
$89$	−443.861	−0.528642	−0.264321	+	0.964435i	$0.585148\pi$
$90$	21.3367	0.0249898
$91$	483.351	0.556802
$92$	−2345.66	−2.65817
$93$	1552.23	1.73074
$94$	−1365.79	−1.49862
$95$	110.686	0.119539
$96$	1181.43	1.25603
$97$	1415.74	1.48193	0.740964	−	0.671545i	$-0.234369\pi$
$97$	1415.74	1.48193	0.740964	+	0.671545i	$0.234369\pi$
$98$	216.888	0.223561
$99$	6.34361	0.00643997
$100$	1863.23	1.86323
$101$	1119.77	1.10318	0.551592	−	0.834114i	$-0.314020\pi$
$101$	1119.77	1.10318	0.551592	+	0.834114i	$0.314020\pi$
$102$	−393.053	−0.381549
$103$	−930.310	−0.889963	−0.444981	−	0.895540i	$-0.646790\pi$
$103$	−930.310	−0.889963	−0.444981	+	0.895540i	$0.646790\pi$
$104$	1097.82	1.03510
$105$	−618.078	−0.574460
$106$	2523.07	2.31191
$107$	−939.841	−0.849139	−0.424569	−	0.905395i	$-0.639574\pi$
$107$	−939.841	−0.849139	−0.424569	+	0.905395i	$0.639574\pi$
$108$	1617.60	1.44124
$109$	250.597	0.220210	0.110105	−	0.993920i	$-0.464881\pi$
$109$	250.597	0.220210	0.110105	+	0.993920i	$0.464881\pi$
$110$	1664.37	1.44265
$111$	1796.32	1.53603
$112$	−156.539	−0.132068
$113$	758.427	0.631387	0.315694	−	0.948861i	$-0.397763\pi$
$113$	758.427	0.631387	0.315694	+	0.948861i	$0.397763\pi$
$114$	−151.396	−0.124382
$115$	−3420.52	−2.77361
$116$	−102.267	−0.0818553
$117$	19.6912	0.0155594
$118$	2389.35	1.86405
$119$	119.000	0.0916698
$120$	−1403.82	−1.06792
$121$	−836.165	−0.628223
$122$	121.289	0.0900078
$123$	791.589	0.580286
$124$	−3444.68	−2.49469
$125$	604.060	0.432230
$126$	8.83574	0.00624722
$127$	−794.380	−0.555038	−0.277519	−	0.960720i	$-0.589512\pi$
$127$	−794.380	−0.555038	−0.277519	+	0.960720i	$0.589512\pi$
$128$	−1829.93	−1.26363
$129$	−788.437	−0.538124
$130$	5166.37	3.48554
$131$	1633.80	1.08966	0.544831	−	0.838546i	$-0.316594\pi$
$131$	1633.80	1.08966	0.544831	+	0.838546i	$0.316594\pi$
$132$	−1346.94	−0.888154
$133$	45.8363	0.0298836
$134$	87.4480	0.0563758
$135$	2358.84	1.50382
$136$	270.280	0.170414
$137$	−810.805	−0.505633	−0.252817	−	0.967514i	$-0.581357\pi$
$137$	−810.805	−0.505633	−0.252817	+	0.967514i	$0.581357\pi$
$138$	4678.55	2.88598
$139$	−3035.90	−1.85253	−0.926266	−	0.376870i	$-0.877000\pi$
$139$	−3035.90	−1.85253	−0.926266	+	0.376870i	$0.877000\pi$
$140$	1371.63	0.828025
$141$	1611.79	0.962673
$142$	−307.419	−0.181676
$143$	1536.01	0.898238
$144$	−6.37722	−0.00369052
$145$	−149.128	−0.0854099
$146$	1417.11	0.803291
$147$	−255.953	−0.143610
$148$	−3986.36	−2.21403
$149$	2210.48	1.21537	0.607684	−	0.794179i	$-0.292099\pi$
$149$	2210.48	1.21537	0.607684	+	0.794179i	$0.292099\pi$
$150$	−3716.32	−2.02291
$151$	13.3482	0.00719378	0.00359689	−	0.999994i	$-0.498855\pi$
$151$	13.3482	0.00719378	0.00359689	+	0.999994i	$0.498855\pi$
$152$	104.106	0.0555535
$153$	4.84792	0.00256164
$154$	689.234	0.360650
$155$	−5023.15	−2.60303
$156$	−4181.03	−2.14584
$157$	1189.54	0.604684	0.302342	−	0.953200i	$-0.402232\pi$
$157$	1189.54	0.604684	0.302342	+	0.953200i	$0.402232\pi$
$158$	−1648.63	−0.830113
$159$	−2977.52	−1.48511
$160$	−3823.18	−1.88906
$161$	−1416.47	−0.693376
$162$	−3260.48	−1.58128
$163$	3487.28	1.67574	0.837868	−	0.545873i	$-0.183802\pi$
$163$	3487.28	1.67574	0.837868	+	0.545873i	$0.183802\pi$
$164$	−1756.68	−0.836423
$165$	−1964.15	−0.926723
$166$	1383.72	0.646973
$167$	−3091.88	−1.43268	−0.716338	−	0.697754i	$-0.754183\pi$
$167$	−3091.88	−1.43268	−0.716338	+	0.697754i	$0.754183\pi$
$168$	−581.335	−0.266970
$169$	2570.93	1.17020
$170$	1271.95	0.573847
$171$	1.86732	0.000835072 0
$172$	1749.68	0.775651
$173$	−3139.53	−1.37973	−0.689867	−	0.723936i	$-0.742331\pi$
$173$	−3139.53	−1.37973	−0.689867	+	0.723936i	$0.742331\pi$
$174$	203.977	0.0888702
$175$	1125.15	0.486018
$176$	−497.457	−0.213052
$177$	−2819.71	−1.19742
$178$	−1964.65	−0.827285
$179$	3822.18	1.59600	0.797998	−	0.602660i	$-0.205893\pi$
$179$	3822.18	1.59600	0.797998	+	0.602660i	$0.205893\pi$
$180$	55.8784	0.0231385
$181$	2158.69	0.886487	0.443244	−	0.896401i	$-0.353828\pi$
$181$	2158.69	0.886487	0.443244	+	0.896401i	$0.353828\pi$
$182$	2139.45	0.871354
$183$	−143.135	−0.0578187
$184$	−3217.18	−1.28899
$185$	−5813.04	−2.31018
$186$	6870.62	2.70848
$187$	378.163	0.147883
$188$	−3576.84	−1.38760
$189$	976.818	0.375942
$190$	489.928	0.187069
$191$	−1055.33	−0.399797	−0.199899	−	0.979817i	$-0.564061\pi$
$191$	−1055.33	−0.399797	−0.199899	+	0.979817i	$0.564061\pi$
$192$	4294.82	1.61433
$193$	102.145	0.0380960	0.0190480	−	0.999819i	$-0.493936\pi$
$193$	102.145	0.0380960	0.0190480	+	0.999819i	$0.493936\pi$
$194$	6266.47	2.31911
$195$	−6096.92	−2.23902
$196$	568.004	0.206999
$197$	−4360.12	−1.57688	−0.788440	−	0.615111i	$-0.789111\pi$
$197$	−4360.12	−1.57688	−0.788440	+	0.615111i	$0.789111\pi$
$198$	28.0786	0.0100781
$199$	3775.79	1.34502	0.672510	−	0.740088i	$-0.265216\pi$
$199$	3775.79	1.34502	0.672510	+	0.740088i	$0.265216\pi$
$200$	2555.50	0.903507
$201$	−103.199	−0.0362144
$202$	4956.43	1.72640
$203$	−61.7556	−0.0213517
$204$	−1029.36	−0.353283
$205$	−2561.64	−0.872745
$206$	−4117.81	−1.39272
$207$	−57.7053	−0.0193758
$208$	−1544.15	−0.514748
$209$	145.661	0.0482084
$210$	−2735.78	−0.898986
$211$	5842.83	1.90634	0.953168	−	0.302443i	$-0.0978021\pi$
$211$	5842.83	1.90634	0.953168	+	0.302443i	$0.0978021\pi$
$212$	6607.65	2.14064
$213$	362.791	0.116704
$214$	−4159.99	−1.32884
$215$	2551.44	0.809334
$216$	2218.61	0.698876
$217$	−2080.14	−0.650732
$218$	1109.21	0.344612
$219$	−1672.35	−0.516013
$220$	4358.81	1.33578
$221$	1173.85	0.357294
$222$	7951.03	2.40377
$223$	6090.44	1.82891	0.914454	−	0.404691i	$-0.132621\pi$
$223$	6090.44	1.82891	0.914454	+	0.404691i	$0.132621\pi$
$224$	−1583.22	−0.472247
$225$	45.8372	0.0135814
$226$	3357.01	0.988074
$227$	−5109.99	−1.49410	−0.747052	−	0.664765i	$-0.768532\pi$
$227$	−5109.99	−1.49410	−0.747052	+	0.664765i	$0.768532\pi$
$228$	−396.488	−0.115167
$229$	2493.77	0.719619	0.359809	−	0.933026i	$-0.382842\pi$
$229$	2493.77	0.719619	0.359809	+	0.933026i	$0.382842\pi$
$230$	−15140.2	−4.34049
$231$	−813.377	−0.231672
$232$	−140.263	−0.0396928
$233$	2113.26	0.594182	0.297091	−	0.954849i	$-0.403983\pi$
$233$	2113.26	0.594182	0.297091	+	0.954849i	$0.403983\pi$
$234$	87.1585	0.0243493
$235$	−5215.86	−1.44785
$236$	6257.45	1.72595
$237$	1945.57	0.533243
$238$	526.727	0.143456
$239$	−4230.50	−1.14497	−0.572486	−	0.819915i	$-0.694021\pi$
$239$	−4230.50	−1.14497	−0.572486	+	0.819915i	$0.694021\pi$
$240$	1974.56	0.531072
$241$	3922.05	1.04830	0.524152	−	0.851625i	$-0.324382\pi$
$241$	3922.05	1.04830	0.524152	+	0.851625i	$0.324382\pi$
$242$	−3701.10	−0.983122
$243$	80.0136	0.0211229
$244$	317.641	0.0833397
$245$	828.282	0.215988
$246$	3503.79	0.908104
$247$	452.144	0.116475
$248$	−4724.54	−1.20971
$249$	−1632.95	−0.415599
$250$	2673.74	0.676408
$251$	0.674614	0.000169646 0	8.48232e−5	−	1.00000i	$-0.499973\pi$
$251$	0.674614	0.000169646 0	8.48232e−5		1.00000i	$0.499973\pi$
$252$	23.1398	0.00578441
$253$	−4501.32	−1.11856
$254$	−3516.15	−0.868593
$255$	−1501.05	−0.368624
$256$	−1522.09	−0.371604
$257$	5160.55	1.25255	0.626277	−	0.779601i	$-0.284578\pi$
$257$	5160.55	1.25255	0.626277	+	0.779601i	$0.284578\pi$
$258$	−3489.84	−0.842124
$259$	−2407.24	−0.577524
$260$	13530.1	3.22732
$261$	−2.51585	−0.000596656 0
$262$	7231.64	1.70524
$263$	−3100.41	−0.726918	−0.363459	−	0.931610i	$-0.618404\pi$
$263$	−3100.41	−0.726918	−0.363459	+	0.931610i	$0.618404\pi$
$264$	−1847.39	−0.430678
$265$	9635.48	2.23360
$266$	202.884	0.0467655
$267$	2318.52	0.531427
$268$	229.017	0.0521993
$269$	−2982.89	−0.676097	−0.338048	−	0.941129i	$-0.609767\pi$
$269$	−2982.89	−0.676097	−0.338048	+	0.941129i	$0.609767\pi$
$270$	10440.9	2.35337
$271$	−630.039	−0.141226	−0.0706128	−	0.997504i	$-0.522495\pi$
$271$	−630.039	−0.141226	−0.0706128	+	0.997504i	$0.522495\pi$
$272$	−380.167	−0.0847463
$273$	−2524.80	−0.559735
$274$	−3588.85	−0.791278
$275$	3575.54	0.784048
$276$	12252.6	2.67217
$277$	−6451.11	−1.39931	−0.699656	−	0.714480i	$-0.746664\pi$
$277$	−6451.11	−1.39931	−0.699656	+	0.714480i	$0.746664\pi$
$278$	−13437.7	−2.89907
$279$	−84.7423	−0.0181842
$280$	1881.24	0.401521
$281$	−6936.02	−1.47248	−0.736242	−	0.676718i	$-0.763402\pi$
$281$	−6936.02	−1.47248	−0.736242	+	0.676718i	$0.763402\pi$
$282$	7134.21	1.50651
$283$	−3194.87	−0.671078	−0.335539	−	0.942026i	$-0.608918\pi$
$283$	−3194.87	−0.671078	−0.335539	+	0.942026i	$0.608918\pi$
$284$	−805.097	−0.168217
$285$	−578.172	−0.120168
$286$	6798.83	1.40567
$287$	−1060.80	−0.218178
$288$	−64.4985	−0.0131966
$289$	289.000	0.0588235
$290$	−660.083	−0.133660
$291$	−7395.17	−1.48973
$292$	3711.24	0.743781
$293$	9221.06	1.83857	0.919283	−	0.393597i	$-0.128770\pi$
$293$	9221.06	1.83857	0.919283	+	0.393597i	$0.128770\pi$
$294$	−1132.92	−0.224738
$295$	9124.81	1.80090
$296$	−5467.47	−1.07362
$297$	3104.17	0.606473
$298$	9784.21	1.90196
$299$	−13972.5	−2.70251
$300$	−9732.63	−1.87305
$301$	1056.58	0.202326
$302$	59.0828	0.0112577
$303$	−5849.16	−1.10899
$304$	−146.432	−0.0276265
$305$	463.195	0.0869588
$306$	21.4582	0.00400877
$307$	166.875	0.0310230	0.0155115	−	0.999880i	$-0.495062\pi$
$307$	166.875	0.0310230	0.0155115	+	0.999880i	$0.495062\pi$
$308$	1805.03	0.333932
$309$	4859.49	0.894650
$310$	−22233.8	−4.07354
$311$	−604.942	−0.110299	−0.0551497	−	0.998478i	$-0.517564\pi$
$311$	−604.942	−0.110299	−0.0551497	+	0.998478i	$0.517564\pi$
$312$	−5734.47	−1.04055
$313$	−6192.74	−1.11832	−0.559160	−	0.829060i	$-0.688876\pi$
$313$	−6192.74	−1.11832	−0.559160	+	0.829060i	$0.688876\pi$
$314$	5265.22	0.946285
$315$	33.7432	0.00603560
$316$	−4317.58	−0.768616
$317$	1803.66	0.319571	0.159785	−	0.987152i	$-0.448920\pi$
$317$	1803.66	0.319571	0.159785	+	0.987152i	$0.448920\pi$
$318$	−13179.3	−2.32409
$319$	−196.250	−0.0344447
$320$	−13898.4	−2.42794
$321$	4909.28	0.853611
$322$	−6269.69	−1.08508
$323$	111.317	0.0191760
$324$	−8538.82	−1.46413
$325$	11098.8	1.89431
$326$	15435.7	2.62240
$327$	−1309.00	−0.221370
$328$	−2409.36	−0.405593
$329$	−2159.94	−0.361950
$330$	−8693.89	−1.45025
$331$	5111.31	0.848771	0.424385	−	0.905482i	$-0.360490\pi$
$331$	5111.31	0.848771	0.424385	+	0.905482i	$0.360490\pi$
$332$	3623.81	0.599043
$333$	−98.0681	−0.0161384
$334$	−13685.5	−2.24203
$335$	333.959	0.0544661
$336$	817.686	0.132763
$337$	3865.00	0.624748	0.312374	−	0.949959i	$-0.398876\pi$
$337$	3865.00	0.624748	0.312374	+	0.949959i	$0.398876\pi$
$338$	11379.6	1.83128
$339$	−3961.66	−0.634713
$340$	3331.09	0.531334
$341$	−6610.35	−1.04977
$342$	8.26526	0.00130683
$343$	343.000	0.0539949
$344$	2399.77	0.376124
$345$	17867.1	2.78822
$346$	−13896.4	−2.15918
$347$	27.8871	0.00431428	0.00215714	−	0.999998i	$-0.499313\pi$
$347$	27.8871	0.00431428	0.00215714	+	0.999998i	$0.499313\pi$
$348$	534.192	0.0822864
$349$	4895.68	0.750888	0.375444	−	0.926845i	$-0.377490\pi$
$349$	4895.68	0.750888	0.375444	+	0.926845i	$0.377490\pi$
$350$	4980.21	0.760582
$351$	9635.64	1.46528
$352$	−5031.22	−0.761833
$353$	3996.67	0.602609	0.301305	−	0.953528i	$-0.402578\pi$
$353$	3996.67	0.602609	0.301305	+	0.953528i	$0.402578\pi$
$354$	−12480.8	−1.87387
$355$	−1174.02	−0.175522
$356$	−5145.20	−0.765997
$357$	−621.599	−0.0921527
$358$	16918.0	2.49761
$359$	482.472	0.0709300	0.0354650	−	0.999371i	$-0.488709\pi$
$359$	482.472	0.0709300	0.0354650	+	0.999371i	$0.488709\pi$
$360$	76.6397	0.0112202
$361$	−6816.12	−0.993749
$362$	9554.96	1.38729
$363$	4367.72	0.631532
$364$	5602.97	0.806801
$365$	5411.85	0.776080
$366$	−633.553	−0.0904819
$367$	5495.14	0.781592	0.390796	−	0.920477i	$-0.372200\pi$
$367$	5495.14	0.781592	0.390796	+	0.920477i	$0.372200\pi$
$368$	4525.17	0.641007
$369$	−43.2158	−0.00609681
$370$	−25730.1	−3.61526
$371$	3990.15	0.558378
$372$	17993.4	2.50783
$373$	−3038.90	−0.421845	−0.210922	−	0.977503i	$-0.567647\pi$
$373$	−3038.90	−0.421845	−0.210922	+	0.977503i	$0.567647\pi$
$374$	1673.85	0.231425
$375$	−3155.32	−0.434507
$376$	−4905.80	−0.672865
$377$	−609.177	−0.0832207
$378$	4323.67	0.588321
$379$	13910.5	1.88531	0.942654	−	0.333770i	$-0.108321\pi$
$379$	13910.5	1.88531	0.942654	+	0.333770i	$0.108321\pi$
$380$	1283.07	0.173210
$381$	4149.46	0.557962
$382$	−4671.20	−0.625653
$383$	4187.26	0.558640	0.279320	−	0.960198i	$-0.409891\pi$
$383$	4187.26	0.558640	0.279320	+	0.960198i	$0.409891\pi$
$384$	9558.65	1.27028
$385$	2632.15	0.348433
$386$	452.120	0.0596174
$387$	43.0437	0.00565384
$388$	16411.2	2.14730
$389$	−7416.22	−0.966626	−0.483313	−	0.875448i	$-0.660567\pi$
$389$	−7416.22	−0.966626	−0.483313	+	0.875448i	$0.660567\pi$
$390$	−26986.6	−3.50390
$391$	−3440.00	−0.444932
$392$	779.043	0.100377
$393$	−8534.18	−1.09540
$394$	−19299.1	−2.46770
$395$	−6296.03	−0.801993
$396$	73.5347	0.00933145
$397$	11937.9	1.50918	0.754590	−	0.656197i	$-0.227836\pi$
$397$	11937.9	1.50918	0.754590	+	0.656197i	$0.227836\pi$
$398$	16712.7	2.10485
$399$	−239.427	−0.0300410
$400$	−3594.48	−0.449310
$401$	−15219.6	−1.89533	−0.947667	−	0.319260i	$-0.896566\pi$
$401$	−15219.6	−1.89533	−0.947667	+	0.319260i	$0.896566\pi$
$402$	−456.787	−0.0566728
$403$	−20519.1	−2.53630
$404$	12980.3	1.59850
$405$	−12451.6	−1.52771
$406$	−273.347	−0.0334138
$407$	−7649.83	−0.931666
$408$	−1411.81	−0.171312
$409$	7534.85	0.910940	0.455470	−	0.890251i	$-0.349471\pi$
$409$	7534.85	0.910940	0.455470	+	0.890251i	$0.349471\pi$
$410$	−11338.5	−1.36578
$411$	4235.26	0.508296
$412$	−10784.1	−1.28955
$413$	3778.68	0.450210
$414$	−255.420	−0.0303217
$415$	5284.35	0.625057
$416$	−15617.4	−1.84064
$417$	15858.1	1.86229
$418$	644.734	0.0754425
$419$	3895.36	0.454179	0.227089	−	0.973874i	$-0.427079\pi$
$419$	3895.36	0.454179	0.227089	+	0.973874i	$0.427079\pi$
$420$	−7164.71	−0.832386
$421$	−8636.29	−0.999779	−0.499889	−	0.866089i	$-0.666626\pi$
$421$	−8636.29	−0.999779	−0.499889	+	0.866089i	$0.666626\pi$
$422$	25862.0	2.98327
$423$	−87.9935	−0.0101144
$424$	9062.68	1.03803
$425$	2732.50	0.311872
$426$	1605.81	0.182633
$427$	191.814	0.0217389
$428$	−10894.6	−1.23039
$429$	−8023.40	−0.902969
$430$	11293.4	1.26655
$431$	9927.45	1.10949	0.554743	−	0.832022i	$-0.312817\pi$
$431$	9927.45	1.10949	0.554743	+	0.832022i	$0.312817\pi$
$432$	−3120.62	−0.347548
$433$	−6576.00	−0.729844	−0.364922	−	0.931038i	$-0.618904\pi$
$433$	−6576.00	−0.729844	−0.364922	+	0.931038i	$0.618904\pi$
$434$	−9207.26	−1.01835
$435$	778.975	0.0858598
$436$	2904.90	0.319082
$437$	−1325.02	−0.145044
$438$	−7402.28	−0.807522
$439$	9719.62	1.05670	0.528351	−	0.849026i	$-0.322811\pi$
$439$	9719.62	1.05670	0.528351	+	0.849026i	$0.322811\pi$
$440$	5978.30	0.647737
$441$	13.9734	0.00150884
$442$	5195.80	0.559138
$443$	−11347.5	−1.21702	−0.608508	−	0.793548i	$-0.708232\pi$
$443$	−11347.5	−1.21702	−0.608508	+	0.793548i	$0.708232\pi$
$444$	20822.8	2.22570
$445$	−7502.90	−0.799261
$446$	26958.0	2.86210
$447$	−11546.5	−1.22177
$448$	−5755.46	−0.606964
$449$	16453.2	1.72934	0.864672	−	0.502338i	$-0.167527\pi$
$449$	16453.2	1.72934	0.864672	+	0.502338i	$0.167527\pi$
$450$	202.888	0.0212538
$451$	−3371.06	−0.351967
$452$	8791.62	0.914874
$453$	−69.7246	−0.00723167
$454$	−22618.2	−2.33816
$455$	8170.43	0.841837
$456$	−543.802	−0.0558461
$457$	−2402.41	−0.245908	−0.122954	−	0.992412i	$-0.539237\pi$
$457$	−2402.41	−0.245908	−0.122954	+	0.992412i	$0.539237\pi$
$458$	11038.1	1.12615
$459$	2372.27	0.241238
$460$	−39650.4	−4.01893
$461$	12582.2	1.27117	0.635586	−	0.772030i	$-0.280759\pi$
$461$	12582.2	1.27117	0.635586	+	0.772030i	$0.280759\pi$
$462$	−3600.23	−0.362550
$463$	−4320.33	−0.433656	−0.216828	−	0.976210i	$-0.569571\pi$
$463$	−4320.33	−0.433656	−0.216828	+	0.976210i	$0.569571\pi$
$464$	197.289	0.0197391
$465$	26238.5	2.61674
$466$	9353.88	0.929851
$467$	−453.197	−0.0449068	−0.0224534	−	0.999748i	$-0.507148\pi$
$467$	−453.197	−0.0449068	−0.0224534	+	0.999748i	$0.507148\pi$
$468$	228.258	0.0225454
$469$	138.296	0.0136160
$470$	−23086.9	−2.26578
$471$	−6213.57	−0.607869
$472$	8582.37	0.836939
$473$	3357.64	0.326394
$474$	8611.65	0.834486
$475$	1052.50	0.101668
$476$	1379.44	0.132829
$477$	162.554	0.0156034
$478$	−18725.4	−1.79180
$479$	−7262.14	−0.692726	−0.346363	−	0.938101i	$-0.612583\pi$
$479$	−7262.14	−0.692726	−0.346363	+	0.938101i	$0.612583\pi$
$480$	19970.5	1.89901
$481$	−23745.8	−2.25096
$482$	17360.1	1.64052
$483$	7398.97	0.697028
$484$	−9692.75	−0.910289
$485$	23931.3	2.24055
$486$	354.162	0.0330558
$487$	−10655.0	−0.991425	−0.495712	−	0.868487i	$-0.665093\pi$
$487$	−10655.0	−0.991425	−0.495712	+	0.868487i	$0.665093\pi$
$488$	435.659	0.0404126
$489$	−18215.9	−1.68456
$490$	3666.20	0.338004
$491$	21324.2	1.95998	0.979990	−	0.199048i	$-0.0637851\pi$
$491$	21324.2	1.95998	0.979990	+	0.199048i	$0.0637851\pi$
$492$	9176.03	0.840828
$493$	−149.978	−0.0137011
$494$	2001.31	0.182274
$495$	107.231	0.00973668
$496$	6645.37	0.601584
$497$	−486.173	−0.0438789
$498$	−7227.89	−0.650381
$499$	−6043.52	−0.542175	−0.271087	−	0.962555i	$-0.587383\pi$
$499$	−6043.52	−0.542175	−0.271087	+	0.962555i	$0.587383\pi$
$500$	7002.22	0.626297
$501$	16150.5	1.44022
$502$	2.98603	0.000265484 0
$503$	−1741.30	−0.154355	−0.0771775	−	0.997017i	$-0.524591\pi$
$503$	−1741.30	−0.154355	−0.0771775	+	0.997017i	$0.524591\pi$
$504$	31.7373	0.00280494
$505$	18928.3	1.66792
$506$	−19924.1	−1.75046
$507$	−13429.3	−1.17636
$508$	−9208.39	−0.804245
$509$	−7405.78	−0.644902	−0.322451	−	0.946586i	$-0.604507\pi$
$509$	−7405.78	−0.644902	−0.322451	+	0.946586i	$0.604507\pi$
$510$	−6644.05	−0.576869
$511$	2241.10	0.194013
$512$	7902.21	0.682093
$513$	913.750	0.0786414
$514$	22842.0	1.96015
$515$	−15725.7	−1.34555
$516$	−9139.50	−0.779737
$517$	−6863.96	−0.583900
$518$	−10655.1	−0.903781
$519$	16399.4	1.38700
$520$	18557.2	1.56497
$521$	−19487.0	−1.63866	−0.819331	−	0.573321i	$-0.805655\pi$
$521$	−19487.0	−1.63866	−0.819331	+	0.573321i	$0.805655\pi$
$522$	−11.1358	−0.000933722 0
$523$	4971.34	0.415643	0.207822	−	0.978167i	$-0.433363\pi$
$523$	4971.34	0.415643	0.207822	+	0.978167i	$0.433363\pi$
$524$	18938.9	1.57891
$525$	−5877.23	−0.488578
$526$	−13723.3	−1.13757
$527$	−5051.76	−0.417568
$528$	2598.48	0.214175
$529$	28779.8	2.36539
$530$	42649.3	3.49541
$531$	153.939	0.0125807
$532$	531.331	0.0433010
$533$	−10464.1	−0.850375
$534$	10262.4	0.831643
$535$	−15886.8	−1.28382
$536$	314.106	0.0253122
$537$	−19965.2	−1.60440
$538$	−13203.1	−1.05804
$539$	1090.00	0.0871050
$540$	27343.4	2.17903
$541$	−3403.45	−0.270472	−0.135236	−	0.990813i	$-0.543179\pi$
$541$	−3403.45	−0.270472	−0.135236	+	0.990813i	$0.543179\pi$
$542$	−2788.73	−0.221008
$543$	−11276.0	−0.891157
$544$	−3844.96	−0.303036
$545$	4236.02	0.332938
$546$	−11175.4	−0.875943
$547$	−9897.33	−0.773637	−0.386818	−	0.922156i	$-0.626426\pi$
$547$	−9897.33	−0.773637	−0.386818	+	0.922156i	$0.626426\pi$
$548$	−9398.79	−0.732658
$549$	7.81426	0.000607476 0
$550$	15826.3	1.22698
$551$	−57.7684	−0.00446645
$552$	16805.0	1.29578
$553$	−2607.25	−0.200491
$554$	−28554.4	−2.18982
$555$	30364.5	2.32235
$556$	−35192.0	−2.68430
$557$	−13722.2	−1.04386	−0.521930	−	0.852988i	$-0.674788\pi$
$557$	−13722.2	−1.04386	−0.521930	+	0.852988i	$0.674788\pi$
$558$	−375.093	−0.0284569
$559$	10422.4	0.788589
$560$	−2646.09	−0.199675
$561$	−1975.34	−0.148661
$562$	−30700.7	−2.30433
$563$	−6833.01	−0.511504	−0.255752	−	0.966742i	$-0.582323\pi$
$563$	−6833.01	−0.511504	−0.255752	+	0.966742i	$0.582323\pi$
$564$	18683.7	1.39490
$565$	12820.2	0.954603
$566$	−14141.4	−1.05019
$567$	−5156.33	−0.381914
$568$	−1104.23	−0.0815709
$569$	8285.15	0.610425	0.305212	−	0.952284i	$-0.401273\pi$
$569$	8285.15	0.610425	0.305212	+	0.952284i	$0.401273\pi$
$570$	−2559.15	−0.188054
$571$	12246.2	0.897526	0.448763	−	0.893651i	$-0.351865\pi$
$571$	12246.2	0.897526	0.448763	+	0.893651i	$0.351865\pi$
$572$	17805.4	1.30154
$573$	5512.56	0.401903
$574$	−4695.40	−0.341433
$575$	−32525.3	−2.35895
$576$	−234.470	−0.0169611
$577$	552.177	0.0398396	0.0199198	−	0.999802i	$-0.493659\pi$
$577$	552.177	0.0398396	0.0199198	+	0.999802i	$0.493659\pi$
$578$	1279.19	0.0920544
$579$	−533.554	−0.0382966
$580$	−1728.68	−0.123758
$581$	2188.30	0.156258
$582$	−32733.1	−2.33132
$583$	12680.1	0.900780
$584$	5090.13	0.360670
$585$	332.854	0.0235244
$586$	40814.9	2.87722
$587$	−16616.0	−1.16834	−0.584170	−	0.811631i	$-0.698580\pi$
$587$	−16616.0	−1.16834	−0.584170	+	0.811631i	$0.698580\pi$
$588$	−2966.98	−0.208089
$589$	−1945.83	−0.136123
$590$	40388.9	2.81828
$591$	22775.2	1.58519
$592$	7690.35	0.533905
$593$	8807.53	0.609919	0.304959	−	0.952365i	$-0.401357\pi$
$593$	8807.53	0.609919	0.304959	+	0.952365i	$0.401357\pi$
$594$	13739.9	0.949085
$595$	2011.54	0.138597
$596$	25623.7	1.76106
$597$	−19722.9	−1.35210
$598$	−61846.2	−4.22923
$599$	1706.32	0.116391	0.0581957	−	0.998305i	$-0.481465\pi$
$599$	1706.32	0.116391	0.0581957	+	0.998305i	$0.481465\pi$
$600$	−13348.7	−0.908266
$601$	7869.44	0.534111	0.267056	−	0.963681i	$-0.413949\pi$
$601$	7869.44	0.534111	0.267056	+	0.963681i	$0.413949\pi$
$602$	4676.71	0.316625
$603$	5.63401	0.000380489 0
$604$	154.731	0.0104237
$605$	−14134.3	−0.949819
$606$	−25890.0	−1.73549
$607$	9589.90	0.641256	0.320628	−	0.947205i	$-0.396106\pi$
$607$	9589.90	0.641256	0.320628	+	0.947205i	$0.396106\pi$
$608$	−1481.00	−0.0987870
$609$	322.582	0.0214642
$610$	2050.23	0.136084
$611$	−21306.4	−1.41074
$612$	56.1967	0.00371179
$613$	−19106.4	−1.25889	−0.629446	−	0.777045i	$-0.716718\pi$
$613$	−19106.4	−1.25889	−0.629446	+	0.777045i	$0.716718\pi$
$614$	738.636	0.0485487
$615$	13380.8	0.877342
$616$	2475.68	0.161928
$617$	−20503.2	−1.33781	−0.668905	−	0.743348i	$-0.733237\pi$
$617$	−20503.2	−1.33781	−0.668905	+	0.743348i	$0.733237\pi$
$618$	21509.5	1.40006
$619$	2652.77	0.172252	0.0861258	−	0.996284i	$-0.472551\pi$
$619$	2652.77	0.172252	0.0861258	+	0.996284i	$0.472551\pi$
$620$	−58227.9	−3.77176
$621$	−28237.4	−1.82469
$622$	−2677.64	−0.172610
$623$	−3107.03	−0.199808
$624$	8065.91	0.517460
$625$	−9881.06	−0.632388
$626$	−27410.8	−1.75009
$627$	−760.861	−0.0484623
$628$	13789.0	0.876181
$629$	−5846.15	−0.370591
$630$	149.357	0.00944526
$631$	15223.5	0.960440	0.480220	−	0.877148i	$-0.340557\pi$
$631$	15223.5	0.960440	0.480220	+	0.877148i	$0.340557\pi$
$632$	−5921.75	−0.372713
$633$	−30520.1	−1.91638
$634$	7983.51	0.500104
$635$	−13428.0	−0.839170
$636$	−34515.2	−2.15191
$637$	3383.46	0.210451
$638$	−868.655	−0.0539034
$639$	−19.8061	−0.00122616
$640$	−30932.5	−1.91049
$641$	8978.54	0.553247	0.276623	−	0.960978i	$-0.410785\pi$
$641$	8978.54	0.553247	0.276623	+	0.960978i	$0.410785\pi$
$642$	21729.8	1.33584
$643$	−13807.1	−0.846810	−0.423405	−	0.905940i	$-0.639165\pi$
$643$	−13807.1	−0.846810	−0.423405	+	0.905940i	$0.639165\pi$
$644$	−16419.6	−1.00470
$645$	−13327.5	−0.813597
$646$	492.719	0.0300089
$647$	5033.05	0.305826	0.152913	−	0.988240i	$-0.451135\pi$
$647$	5033.05	0.305826	0.152913	+	0.988240i	$0.451135\pi$
$648$	−11711.4	−0.709979
$649$	12008.0	0.726282
$650$	49126.4	2.96446
$651$	10865.6	0.654160
$652$	40424.3	2.42812
$653$	10208.1	0.611754	0.305877	−	0.952071i	$-0.401050\pi$
$653$	10208.1	0.611754	0.305877	+	0.952071i	$0.401050\pi$
$654$	−5794.00	−0.346427
$655$	27617.2	1.64747
$656$	3388.92	0.201700
$657$	91.2999	0.00542153
$658$	−9560.50	−0.566424
$659$	15428.3	0.911990	0.455995	−	0.889982i	$-0.349284\pi$
$659$	15428.3	0.911990	0.455995	+	0.889982i	$0.349284\pi$
$660$	−22768.3	−1.34281
$661$	22651.9	1.33291	0.666457	−	0.745544i	$-0.267810\pi$
$661$	22651.9	1.33291	0.666457	+	0.745544i	$0.267810\pi$
$662$	22624.1	1.32826
$663$	−6131.65	−0.359176
$664$	4970.21	0.290484
$665$	774.804	0.0451814
$666$	−434.076	−0.0252554
$667$	1785.20	0.103633
$668$	−35840.8	−2.07593
$669$	−31813.6	−1.83854
$670$	1478.20	0.0852354
$671$	609.553	0.0350694
$672$	8269.98	0.474734
$673$	−17291.4	−0.990393	−0.495196	−	0.868781i	$-0.664904\pi$
$673$	−17291.4	−0.990393	−0.495196	+	0.868781i	$0.664904\pi$
$674$	17107.6	0.977684
$675$	22429.9	1.27900
$676$	29802.0	1.69561
$677$	−8539.36	−0.484777	−0.242389	−	0.970179i	$-0.577931\pi$
$677$	−8539.36	−0.484777	−0.242389	+	0.970179i	$0.577931\pi$
$678$	−17535.4	−0.993278
$679$	9910.21	0.560116
$680$	4568.74	0.257652
$681$	26692.1	1.50197
$682$	−29259.2	−1.64281
$683$	1930.75	0.108167	0.0540835	−	0.998536i	$-0.482776\pi$
$683$	1930.75	0.108167	0.0540835	+	0.998536i	$0.482776\pi$
$684$	21.6458	0.00121001
$685$	−13705.6	−0.764474
$686$	1518.21	0.0844980
$687$	−13026.2	−0.723409
$688$	−3375.43	−0.187045
$689$	39360.1	2.17634
$690$	79084.9	4.36335
$691$	32951.2	1.81407	0.907036	−	0.421054i	$-0.138340\pi$
$691$	32951.2	1.81407	0.907036	+	0.421054i	$0.138340\pi$
$692$	−36393.2	−1.99922
$693$	44.4053	0.00243408
$694$	123.436	0.00675153
$695$	−51318.0	−2.80087
$696$	732.668	0.0399019
$697$	−2576.23	−0.140003
$698$	21669.6	1.17508
$699$	−11038.7	−0.597312
$700$	13042.6	0.704235
$701$	−21147.5	−1.13941	−0.569707	−	0.821848i	$-0.692943\pi$
$701$	−21147.5	−1.13941	−0.569707	+	0.821848i	$0.692943\pi$
$702$	42650.0	2.29305
$703$	−2251.82	−0.120809
$704$	−18289.9	−0.979159
$705$	27245.2	1.45548
$706$	17690.3	0.943038
$707$	7838.41	0.416965
$708$	−32685.9	−1.73504
$709$	−14069.8	−0.745279	−0.372639	−	0.927976i	$-0.621547\pi$
$709$	−14069.8	−0.745279	−0.372639	+	0.927976i	$0.621547\pi$
$710$	−5196.53	−0.274679
$711$	−106.216	−0.00560256
$712$	−7056.87	−0.371443
$713$	60131.7	3.15842
$714$	−2751.37	−0.144212
$715$	25964.3	1.35806
$716$	44306.4	2.31258
$717$	22098.1	1.15100
$718$	2135.55	0.111000
$719$	−10892.1	−0.564959	−0.282479	−	0.959273i	$-0.591157\pi$
$719$	−10892.1	−0.564959	−0.282479	+	0.959273i	$0.591157\pi$
$720$	−107.799	−0.00557975
$721$	−6512.17	−0.336374
$722$	−30170.0	−1.55514
$723$	−20486.9	−1.05383
$724$	25023.4	1.28451
$725$	−1418.04	−0.0726412
$726$	19332.7	0.988300
$727$	−4947.43	−0.252394	−0.126197	−	0.992005i	$-0.540277\pi$
$727$	−4947.43	−0.252394	−0.126197	+	0.992005i	$0.540277\pi$
$728$	7684.72	0.391229
$729$	19470.7	0.989216
$730$	23954.3	1.21451
$731$	2565.98	0.129830
$732$	−1659.21	−0.0837787
$733$	−3023.86	−0.152372	−0.0761861	−	0.997094i	$-0.524274\pi$
$733$	−3023.86	−0.152372	−0.0761861	+	0.997094i	$0.524274\pi$
$734$	24323.0	1.22313
$735$	−4326.55	−0.217125
$736$	45767.1	2.29211
$737$	439.483	0.0219655
$738$	−191.285	−0.00954106
$739$	22602.2	1.12508	0.562541	−	0.826769i	$-0.309824\pi$
$739$	22602.2	1.12508	0.562541	+	0.826769i	$0.309824\pi$
$740$	−67384.3	−3.34743
$741$	−2361.78	−0.117088
$742$	17661.5	0.873820
$743$	−4371.41	−0.215843	−0.107922	−	0.994159i	$-0.534420\pi$
$743$	−4371.41	−0.215843	−0.107922	+	0.994159i	$0.534420\pi$
$744$	24678.7	1.21608
$745$	37365.4	1.83753
$746$	−13451.0	−0.660155
$747$	89.1489	0.00436652
$748$	4383.64	0.214280
$749$	−6578.88	−0.320944
$750$	−13966.3	−0.679971
$751$	−9415.34	−0.457484	−0.228742	−	0.973487i	$-0.573461\pi$
$751$	−9415.34	−0.457484	−0.228742	+	0.973487i	$0.573461\pi$
$752$	6900.32	0.334613
$753$	−3.52386	−0.000170540 0
$754$	−2696.38	−0.130234
$755$	225.634	0.0108764
$756$	11323.2	0.544737
$757$	−20071.8	−0.963704	−0.481852	−	0.876253i	$-0.660036\pi$
$757$	−20071.8	−0.963704	−0.481852	+	0.876253i	$0.660036\pi$
$758$	61571.5	2.95037
$759$	23512.8	1.12445
$760$	1759.78	0.0839921
$761$	420.505	0.0200306	0.0100153	−	0.999950i	$-0.496812\pi$
$761$	420.505	0.0200306	0.0100153	+	0.999950i	$0.496812\pi$
$762$	18366.7	0.873168
$763$	1754.18	0.0832315
$764$	−12233.4	−0.579303
$765$	81.9478	0.00387298
$766$	18534.0	0.874229
$767$	37274.1	1.75474
$768$	7950.68	0.373562
$769$	−21370.8	−1.00215	−0.501074	−	0.865405i	$-0.667061\pi$
$769$	−21370.8	−1.00215	−0.501074	+	0.865405i	$0.667061\pi$
$770$	11650.6	0.545272
$771$	−26956.2	−1.25915
$772$	1184.05	0.0552007
$773$	−34813.4	−1.61986	−0.809929	−	0.586527i	$-0.800495\pi$
$773$	−34813.4	−1.61986	−0.809929	+	0.586527i	$0.800495\pi$
$774$	190.523	0.00884784
$775$	−47764.5	−2.21387
$776$	22508.7	1.04126
$777$	12574.3	0.580566
$778$	−32826.3	−1.51270
$779$	−992.312	−0.0456396
$780$	−70675.0	−3.24432
$781$	−1544.98	−0.0707859
$782$	−15226.4	−0.696285
$783$	−1231.10	−0.0561890
$784$	−1095.77	−0.0499168
$785$	20107.6	0.914230
$786$	−37774.6	−1.71422
$787$	−23937.8	−1.08423	−0.542115	−	0.840304i	$-0.682376\pi$
$787$	−23937.8	−1.08423	−0.542115	+	0.840304i	$0.682376\pi$
$788$	−50542.1	−2.28488
$789$	16195.1	0.730747
$790$	−27867.9	−1.25506
$791$	5308.99	0.238642
$792$	100.856	0.00452495
$793$	1892.11	0.0847299
$794$	52840.3	2.36175
$795$	−50331.1	−2.24536
$796$	43768.7	1.94892
$797$	−14091.2	−0.626267	−0.313134	−	0.949709i	$-0.601379\pi$
$797$	−14091.2	−0.626267	−0.313134	+	0.949709i	$0.601379\pi$
$798$	−1059.77	−0.0470119
$799$	−5245.58	−0.232259
$800$	−36354.2	−1.60664
$801$	−126.577	−0.00558347
$802$	−67366.0	−2.96606
$803$	7121.87	0.312983
$804$	−1196.27	−0.0524743
$805$	−23943.6	−1.04832
$806$	−90823.3	−3.96913
$807$	15581.2	0.679658
$808$	17803.1	0.775137
$809$	−35107.7	−1.52574	−0.762868	−	0.646554i	$-0.776210\pi$
$809$	−35107.7	−1.52574	−0.762868	+	0.646554i	$0.776210\pi$
$810$	−55114.1	−2.39076
$811$	−7397.43	−0.320295	−0.160147	−	0.987093i	$-0.551197\pi$
$811$	−7397.43	−0.320295	−0.160147	+	0.987093i	$0.551197\pi$
$812$	−715.866	−0.0309384
$813$	3291.02	0.141969
$814$	−33860.3	−1.45799
$815$	58948.0	2.53357
$816$	1985.81	0.0851926
$817$	988.361	0.0423236
$818$	33351.3	1.42555
$819$	137.838	0.00588090
$820$	−29694.3	−1.26460
$821$	−19148.5	−0.813993	−0.406997	−	0.913430i	$-0.633424\pi$
$821$	−19148.5	−0.813993	−0.406997	+	0.913430i	$0.633424\pi$
$822$	18746.4	0.795446
$823$	6580.95	0.278733	0.139367	−	0.990241i	$-0.455493\pi$
$823$	6580.95	0.278733	0.139367	+	0.990241i	$0.455493\pi$
$824$	−14790.8	−0.625320
$825$	−18676.9	−0.788178
$826$	16725.5	0.704544
$827$	−5487.32	−0.230729	−0.115364	−	0.993323i	$-0.536804\pi$
$827$	−5487.32	−0.230729	−0.115364	+	0.993323i	$0.536804\pi$
$828$	−668.916	−0.0280754
$829$	−21781.2	−0.912537	−0.456269	−	0.889842i	$-0.650814\pi$
$829$	−21781.2	−0.912537	−0.456269	+	0.889842i	$0.650814\pi$
$830$	23390.0	0.978167
$831$	33697.5	1.40668
$832$	−56773.6	−2.36571
$833$	833.000	0.0346479
$834$	70192.4	2.91434
$835$	−52264.2	−2.16608
$836$	1688.49	0.0698535
$837$	−41467.7	−1.71246
$838$	17242.0	0.710756
$839$	9781.70	0.402505	0.201252	−	0.979539i	$-0.435499\pi$
$839$	9781.70	0.402505	0.201252	+	0.979539i	$0.435499\pi$
$840$	−9826.72	−0.403636
$841$	−24311.2	−0.996809
$842$	−38226.6	−1.56458
$843$	36230.4	1.48024
$844$	67729.6	2.76226
$845$	43458.3	1.76924
$846$	−389.484	−0.0158283
$847$	−5853.15	−0.237446
$848$	−12747.2	−0.516205
$849$	16688.5	0.674613
$850$	12094.8	0.488057
$851$	69587.5	2.80309
$852$	4205.44	0.169103
$853$	42400.6	1.70196	0.850978	−	0.525202i	$-0.176010\pi$
$853$	42400.6	1.70196	0.850978	+	0.525202i	$0.176010\pi$
$854$	849.020	0.0340198
$855$	31.5646	0.00126256
$856$	−14942.4	−0.596635
$857$	33492.7	1.33499	0.667497	−	0.744612i	$-0.267366\pi$
$857$	33492.7	1.33499	0.667497	+	0.744612i	$0.267366\pi$
$858$	−35513.8	−1.41308
$859$	17039.5	0.676810	0.338405	−	0.941001i	$-0.390113\pi$
$859$	17039.5	0.676810	0.338405	+	0.941001i	$0.390113\pi$
$860$	29576.1	1.17272
$861$	5541.12	0.219327
$862$	43941.7	1.73626
$863$	13005.4	0.512988	0.256494	−	0.966546i	$-0.417433\pi$
$863$	13005.4	0.512988	0.256494	+	0.966546i	$0.417433\pi$
$864$	−31561.6	−1.24276
$865$	−53069.7	−2.08604
$866$	−29107.2	−1.14215
$867$	−1509.60	−0.0591334
$868$	−24112.8	−0.942905
$869$	−8285.43	−0.323434
$870$	3447.96	0.134364
$871$	1364.20	0.0530700
$872$	3984.21	0.154727
$873$	403.730	0.0156520
$874$	−5864.89	−0.226983
$875$	4228.42	0.163368
$876$	−19385.8	−0.747698
$877$	−24871.7	−0.957647	−0.478824	−	0.877911i	$-0.658937\pi$
$877$	−24871.7	−0.957647	−0.478824	+	0.877911i	$0.658937\pi$
$878$	43021.7	1.65366
$879$	−48166.4	−1.84825
$880$	−8408.86	−0.322117
$881$	−5392.80	−0.206229	−0.103115	−	0.994669i	$-0.532881\pi$
$881$	−5392.80	−0.206229	−0.103115	+	0.994669i	$0.532881\pi$
$882$	61.8502	0.00236123
$883$	−24850.0	−0.947077	−0.473539	−	0.880773i	$-0.657024\pi$
$883$	−24850.0	−0.947077	−0.473539	+	0.880773i	$0.657024\pi$
$884$	13607.2	0.517715
$885$	−47663.6	−1.81039
$886$	−50227.4	−1.90454
$887$	−23725.5	−0.898111	−0.449056	−	0.893504i	$-0.648239\pi$
$887$	−23725.5	−0.898111	−0.449056	+	0.893504i	$0.648239\pi$
$888$	28559.5	1.07927
$889$	−5560.66	−0.209785
$890$	−33209.9	−1.25078
$891$	−16386.0	−0.616107
$892$	70599.9	2.65007
$893$	−2020.49	−0.0757145
$894$	−51108.0	−1.91198
$895$	64609.0	2.41301
$896$	−12809.5	−0.477606
$897$	72985.7	2.71675
$898$	72826.5	2.70629
$899$	2621.64	0.0972597
$900$	531.341	0.0196793
$901$	9690.37	0.358305
$902$	−14921.2	−0.550802
$903$	−5519.06	−0.203392
$904$	12058.1	0.443635
$905$	36489.9	1.34029
$906$	−308.620	−0.0113170
$907$	47638.2	1.74399	0.871996	−	0.489513i	$-0.162825\pi$
$907$	47638.2	1.74399	0.871996	+	0.489513i	$0.162825\pi$
$908$	−59234.6	−2.16494
$909$	319.328	0.0116517
$910$	36164.6	1.31741
$911$	−20622.7	−0.750013	−0.375007	−	0.927022i	$-0.622360\pi$
$911$	−20622.7	−0.750013	−0.375007	+	0.927022i	$0.622360\pi$
$912$	764.892	0.0277720
$913$	6954.09	0.252077
$914$	−10633.7	−0.384827
$915$	−2419.51	−0.0874168
$916$	28907.5	1.04272
$917$	11436.6	0.411853
$918$	10500.3	0.377519
$919$	−4491.12	−0.161206	−0.0806030	−	0.996746i	$-0.525685\pi$
$919$	−4491.12	−0.161206	−0.0806030	+	0.996746i	$0.525685\pi$
$920$	−54382.2	−1.94884
$921$	−871.676	−0.0311864
$922$	55692.1	1.98929
$923$	−4795.76	−0.171023
$924$	−9428.60	−0.335691
$925$	−55275.5	−1.96481
$926$	−19123.0	−0.678639
$927$	−265.298	−0.00939971
$928$	1995.36	0.0705829
$929$	−19354.9	−0.683544	−0.341772	−	0.939783i	$-0.611027\pi$
$929$	−19354.9	−0.683544	−0.341772	+	0.939783i	$0.611027\pi$
$930$	116139.	4.09500
$931$	320.854	0.0112949
$932$	24496.8	0.860964
$933$	3159.93	0.110880
$934$	−2005.98	−0.0702757
$935$	6392.36	0.223586
$936$	313.066	0.0109326
$937$	−18723.3	−0.652788	−0.326394	−	0.945234i	$-0.605834\pi$
$937$	−18723.3	−0.652788	−0.326394	+	0.945234i	$0.605834\pi$
$938$	612.136	0.0213081
$939$	32347.9	1.12421
$940$	−60461.9	−2.09792
$941$	−28104.8	−0.973634	−0.486817	−	0.873504i	$-0.661842\pi$
$941$	−28104.8	−0.973634	−0.486817	+	0.873504i	$0.661842\pi$
$942$	−27503.0	−0.951269
$943$	30665.2	1.05896
$944$	−12071.7	−0.416206
$945$	16511.9	0.568392
$946$	14861.8	0.510782
$947$	−47298.0	−1.62300	−0.811498	−	0.584355i	$-0.801348\pi$
$947$	−47298.0	−1.62300	−0.811498	+	0.584355i	$0.801348\pi$
$948$	22552.9	0.772664
$949$	22107.0	0.756188
$950$	4658.67	0.159102
$951$	−9421.48	−0.321254
$952$	1891.96	0.0644105
$953$	−31810.9	−1.08128	−0.540639	−	0.841255i	$-0.681817\pi$
$953$	−31810.9	−1.08128	−0.540639	+	0.841255i	$0.681817\pi$
$954$	719.509	0.0244182
$955$	−17839.1	−0.604459
$956$	−49039.6	−1.65905
$957$	1025.11	0.0346261
$958$	−32144.2	−1.08406
$959$	−5675.64	−0.191111
$960$	72598.4	2.44073
$961$	58514.5	1.96417
$962$	−105105.	−3.52259
$963$	−268.016	−0.00896853
$964$	45464.1	1.51898
$965$	1726.62	0.0575978
$966$	32749.9	1.09080
$967$	5938.61	0.197490	0.0987450	−	0.995113i	$-0.468517\pi$
$967$	5938.61	0.197490	0.0987450	+	0.995113i	$0.468517\pi$
$968$	−13294.0	−0.441412
$969$	−581.466	−0.0192770
$970$	105927.	3.50629
$971$	16153.1	0.533860	0.266930	−	0.963716i	$-0.413991\pi$
$971$	16153.1	0.533860	0.266930	+	0.963716i	$0.413991\pi$
$972$	927.511	0.0306069
$973$	−21251.3	−0.700191
$974$	−47161.9	−1.55151
$975$	−57974.9	−1.90429
$976$	−612.783	−0.0200970
$977$	−49414.9	−1.61814	−0.809070	−	0.587713i	$-0.800029\pi$
$977$	−49414.9	−1.61814	−0.809070	+	0.587713i	$0.800029\pi$
$978$	−80628.5	−2.63621
$979$	−9873.64	−0.322332
$980$	9601.38	0.312964
$981$	71.4632	0.00232584
$982$	94387.0	3.06722
$983$	−43923.2	−1.42516	−0.712581	−	0.701590i	$-0.752474\pi$
$983$	−43923.2	−1.42516	−0.712581	+	0.701590i	$0.752474\pi$
$984$	12585.3	0.407730
$985$	−73702.1	−2.38411
$986$	−663.844	−0.0214413
$987$	11282.5	0.363856
$988$	5241.22	0.168771
$989$	−30543.1	−0.982017
$990$	474.632	0.0152372
$991$	24956.2	0.799961	0.399980	−	0.916524i	$-0.369017\pi$
$991$	24956.2	0.799961	0.399980	+	0.916524i	$0.369017\pi$
$992$	67210.5	2.15115
$993$	−26699.0	−0.853241
$994$	−2151.94	−0.0686672
$995$	63824.9	2.03355
$996$	−18929.0	−0.602198
$997$	51762.8	1.64428	0.822138	−	0.569288i	$-0.192781\pi$
$997$	51762.8	1.64428	0.822138	+	0.569288i	$0.192781\pi$
$998$	−26750.3	−0.848463
$999$	−47988.5	−1.51981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.4.a.e.1.8	✓	9
3.2	odd	2		1071.4.a.r.1.2		9
4.3	odd	2		1904.4.a.s.1.8		9
7.6	odd	2		833.4.a.g.1.8		9
17.16	even	2		2023.4.a.h.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.e.1.8	✓	9	1.1	even	1	trivial
833.4.a.g.1.8		9	7.6	odd	2
1071.4.a.r.1.2		9	3.2	odd	2
1904.4.a.s.1.8		9	4.3	odd	2
2023.4.a.h.1.8		9	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)

\(f(q)\)	\(=\)	\(q+4.42628 q^{2} -5.22352 q^{3} +11.5919 q^{4} +16.9037 q^{5} -23.1207 q^{6} +7.00000 q^{7} +15.8988 q^{8} +0.285172 q^{9} +O(q^{10})\)	\(q+4.42628 q^{2} -5.22352 q^{3} +11.5919 q^{4} +16.9037 q^{5} -23.1207 q^{6} +7.00000 q^{7} +15.8988 q^{8} +0.285172 q^{9} +74.8205 q^{10} +22.2449 q^{11} -60.5506 q^{12} +69.0502 q^{13} +30.9839 q^{14} -88.2969 q^{15} -22.3627 q^{16} +17.0000 q^{17} +1.26225 q^{18} +6.54805 q^{19} +195.946 q^{20} -36.5646 q^{21} +98.4621 q^{22} -202.353 q^{23} -83.0479 q^{24} +160.735 q^{25} +305.635 q^{26} +139.545 q^{27} +81.1434 q^{28} -8.82223 q^{29} -390.826 q^{30} -297.162 q^{31} -226.174 q^{32} -116.197 q^{33} +75.2467 q^{34} +118.326 q^{35} +3.30569 q^{36} -343.891 q^{37} +28.9835 q^{38} -360.685 q^{39} +268.749 q^{40} -151.543 q^{41} -161.845 q^{42} +150.940 q^{43} +257.861 q^{44} +4.82046 q^{45} -895.670 q^{46} -308.563 q^{47} +116.812 q^{48} +49.0000 q^{49} +711.459 q^{50} -88.7999 q^{51} +800.424 q^{52} +570.022 q^{53} +617.667 q^{54} +376.021 q^{55} +111.292 q^{56} -34.2039 q^{57} -39.0496 q^{58} +539.811 q^{59} -1023.53 q^{60} +27.4019 q^{61} -1315.32 q^{62} +1.99620 q^{63} -822.208 q^{64} +1167.20 q^{65} -514.319 q^{66} +19.7566 q^{67} +197.063 q^{68} +1057.00 q^{69} +523.743 q^{70} -69.4533 q^{71} +4.53390 q^{72} +320.158 q^{73} -1522.16 q^{74} -839.605 q^{75} +75.9044 q^{76} +155.714 q^{77} -1596.49 q^{78} -372.464 q^{79} -378.013 q^{80} -736.618 q^{81} -670.772 q^{82} +312.615 q^{83} -423.854 q^{84} +287.363 q^{85} +668.101 q^{86} +46.0831 q^{87} +353.668 q^{88} -443.861 q^{89} +21.3367 q^{90} +483.351 q^{91} -2345.66 q^{92} +1552.23 q^{93} -1365.79 q^{94} +110.686 q^{95} +1181.43 q^{96} +1415.74 q^{97} +216.888 q^{98} +6.34361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9	\( 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9} + 134 q^{10} - 8 q^{11} + 56 q^{12} + 164 q^{13} + 14 q^{14} + 34 q^{15} + 178 q^{16} + 153 q^{17} + 98 q^{18} + 244 q^{19} - 41 q^{20} + 77 q^{21} - 80 q^{22} - 14 q^{23} + 298 q^{24} + 684 q^{25} + 326 q^{26} + 218 q^{27} + 266 q^{28} - 234 q^{29} - 335 q^{30} + 555 q^{31} - 181 q^{32} + 458 q^{33} + 34 q^{34} - 21 q^{35} - 1221 q^{36} - 364 q^{37} - 714 q^{38} - 52 q^{39} + 123 q^{40} - 45 q^{41} + 63 q^{42} - 135 q^{43} - 748 q^{44} - 844 q^{45} - 1576 q^{46} - 172 q^{47} - 949 q^{48} + 441 q^{49} - 2901 q^{50} + 187 q^{51} - 1596 q^{52} + 101 q^{53} - 1163 q^{54} + 1260 q^{55} + 168 q^{56} - 602 q^{57} + 1062 q^{58} + 280 q^{59} - 1727 q^{60} + 639 q^{61} - 1708 q^{62} + 518 q^{63} - 2390 q^{64} + 638 q^{65} - 2476 q^{66} + 35 q^{67} + 646 q^{68} + 1288 q^{69} + 938 q^{70} - 1616 q^{71} + 1335 q^{72} + 1049 q^{73} - 370 q^{74} + 1260 q^{75} + 4964 q^{76} - 56 q^{77} - 4714 q^{78} + 2304 q^{79} - 3996 q^{80} - 791 q^{81} - 215 q^{82} + 2508 q^{83} + 392 q^{84} - 51 q^{85} + 623 q^{86} + 166 q^{87} - 416 q^{88} + 2762 q^{89} + 2935 q^{90} + 1148 q^{91} - 2392 q^{92} + 2784 q^{93} - 862 q^{94} - 3462 q^{95} + 2928 q^{96} + 3107 q^{97} + 98 q^{98} - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9 + 134 * q^10 - 8 * q^11 + 56 * q^12 + 164 * q^13 + 14 * q^14 + 34 * q^15 + 178 * q^16 + 153 * q^17 + 98 * q^18 + 244 * q^19 - 41 * q^20 + 77 * q^21 - 80 * q^22 - 14 * q^23 + 298 * q^24 + 684 * q^25 + 326 * q^26 + 218 * q^27 + 266 * q^28 - 234 * q^29 - 335 * q^30 + 555 * q^31 - 181 * q^32 + 458 * q^33 + 34 * q^34 - 21 * q^35 - 1221 * q^36 - 364 * q^37 - 714 * q^38 - 52 * q^39 + 123 * q^40 - 45 * q^41 + 63 * q^42 - 135 * q^43 - 748 * q^44 - 844 * q^45 - 1576 * q^46 - 172 * q^47 - 949 * q^48 + 441 * q^49 - 2901 * q^50 + 187 * q^51 - 1596 * q^52 + 101 * q^53 - 1163 * q^54 + 1260 * q^55 + 168 * q^56 - 602 * q^57 + 1062 * q^58 + 280 * q^59 - 1727 * q^60 + 639 * q^61 - 1708 * q^62 + 518 * q^63 - 2390 * q^64 + 638 * q^65 - 2476 * q^66 + 35 * q^67 + 646 * q^68 + 1288 * q^69 + 938 * q^70 - 1616 * q^71 + 1335 * q^72 + 1049 * q^73 - 370 * q^74 + 1260 * q^75 + 4964 * q^76 - 56 * q^77 - 4714 * q^78 + 2304 * q^79 - 3996 * q^80 - 791 * q^81 - 215 * q^82 + 2508 * q^83 + 392 * q^84 - 51 * q^85 + 623 * q^86 + 166 * q^87 - 416 * q^88 + 2762 * q^89 + 2935 * q^90 + 1148 * q^91 - 2392 * q^92 + 2784 * q^93 - 862 * q^94 - 3462 * q^95 + 2928 * q^96 + 3107 * q^97 + 98 * q^98 - 2396 * q^99

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