LMFDB - Embedded newform 119.4.a.e.1.6

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			1.6
Root			$0.923542$ 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)

$f(q)$	$=$	$q+0.923542 q^{2} +8.63083 q^{3} -7.14707 q^{4} +12.8089 q^{5} +7.97094 q^{6} +7.00000 q^{7} -13.9890 q^{8} +47.4913 q^{9} +O(q^{10})$	\(q+0.923542 q^{2} +8.63083 q^{3} -7.14707 q^{4} +12.8089 q^{5} +7.97094 q^{6} +7.00000 q^{7} -13.9890 q^{8} +47.4913 q^{9} +11.8296 q^{10} -25.1461 q^{11} -61.6852 q^{12} +44.3092 q^{13} +6.46480 q^{14} +110.551 q^{15} +44.2572 q^{16} +17.0000 q^{17} +43.8602 q^{18} -128.215 q^{19} -91.5461 q^{20} +60.4158 q^{21} -23.2235 q^{22} -34.3519 q^{23} -120.736 q^{24} +39.0678 q^{25} +40.9214 q^{26} +176.857 q^{27} -50.0295 q^{28} +217.720 q^{29} +102.099 q^{30} -168.787 q^{31} +152.785 q^{32} -217.032 q^{33} +15.7002 q^{34} +89.6623 q^{35} -339.424 q^{36} +110.738 q^{37} -118.412 q^{38} +382.426 q^{39} -179.183 q^{40} -139.358 q^{41} +55.7966 q^{42} -505.289 q^{43} +179.721 q^{44} +608.311 q^{45} -31.7254 q^{46} +49.3243 q^{47} +381.976 q^{48} +49.0000 q^{49} +36.0808 q^{50} +146.724 q^{51} -316.681 q^{52} -451.668 q^{53} +163.335 q^{54} -322.094 q^{55} -97.9227 q^{56} -1106.61 q^{57} +201.074 q^{58} -534.869 q^{59} -790.119 q^{60} -499.909 q^{61} -155.882 q^{62} +332.439 q^{63} -212.954 q^{64} +567.552 q^{65} -200.438 q^{66} -35.9387 q^{67} -121.500 q^{68} -296.485 q^{69} +82.8069 q^{70} +46.6169 q^{71} -664.354 q^{72} +1014.63 q^{73} +102.271 q^{74} +337.188 q^{75} +916.364 q^{76} -176.023 q^{77} +353.186 q^{78} +322.720 q^{79} +566.885 q^{80} +244.159 q^{81} -128.703 q^{82} +215.368 q^{83} -431.796 q^{84} +217.751 q^{85} -466.656 q^{86} +1879.10 q^{87} +351.768 q^{88} +243.588 q^{89} +561.801 q^{90} +310.165 q^{91} +245.515 q^{92} -1456.77 q^{93} +45.5531 q^{94} -1642.30 q^{95} +1318.66 q^{96} +1061.03 q^{97} +45.2536 q^{98} -1194.22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.923542	0.326522	0.163261	−	0.986583i	$-0.447799\pi$
$2$	0.923542	0.326522	0.163261	+	0.986583i	$0.447799\pi$
$3$	8.63083	1.66100	0.830502	−	0.557015i	$-0.188053\pi$
$3$	8.63083	1.66100	0.830502	+	0.557015i	$0.188053\pi$
$4$	−7.14707	−0.893384
$5$	12.8089	1.14566	0.572831	−	0.819673i	$-0.305845\pi$
$5$	12.8089	1.14566	0.572831	+	0.819673i	$0.305845\pi$
$6$	7.97094	0.542354
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−13.9890	−0.618231
$9$	47.4913	1.75894
$10$	11.8296	0.374083
$11$	−25.1461	−0.689259	−0.344629	−	0.938739i	$-0.611995\pi$
$11$	−25.1461	−0.689259	−0.344629	+	0.938739i	$0.611995\pi$
$12$	−61.6852	−1.48391
$13$	44.3092	0.945321	0.472660	−	0.881245i	$-0.343294\pi$
$13$	44.3092	0.945321	0.472660	+	0.881245i	$0.343294\pi$
$14$	6.46480	0.123414
$15$	110.551	1.90295
$16$	44.2572	0.691518
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	43.8602	0.574331
$19$	−128.215	−1.54814	−0.774069	−	0.633102i	$-0.781782\pi$
$19$	−128.215	−1.54814	−0.774069	+	0.633102i	$0.781782\pi$
$20$	−91.5461	−1.02352
$21$	60.4158	0.627801
$22$	−23.2235	−0.225058
$23$	−34.3519	−0.311429	−0.155714	−	0.987802i	$-0.549768\pi$
$23$	−34.3519	−0.311429	−0.155714	+	0.987802i	$0.549768\pi$
$24$	−120.736	−1.02688
$25$	39.0678	0.312542
$26$	40.9214	0.308668
$27$	176.857	1.26060
$28$	−50.0295	−0.337667
$29$	217.720	1.39412	0.697062	−	0.717011i	$-0.254490\pi$
$29$	217.720	1.39412	0.697062	+	0.717011i	$0.254490\pi$
$30$	102.099	0.621354
$31$	−168.787	−0.977903	−0.488952	−	0.872311i	$-0.662621\pi$
$31$	−168.787	−0.977903	−0.488952	+	0.872311i	$0.662621\pi$
$32$	152.785	0.844026
$33$	−217.032	−1.14486
$34$	15.7002	0.0791931
$35$	89.6623	0.433020
$36$	−339.424	−1.57141
$37$	110.738	0.492031	0.246015	−	0.969266i	$-0.420879\pi$
$37$	110.738	0.492031	0.246015	+	0.969266i	$0.420879\pi$
$38$	−118.412	−0.505500
$39$	382.426	1.57018
$40$	−179.183	−0.708284
$41$	−139.358	−0.530829	−0.265414	−	0.964134i	$-0.585509\pi$
$41$	−139.358	−0.530829	−0.265414	+	0.964134i	$0.585509\pi$
$42$	55.7966	0.204990
$43$	−505.289	−1.79200	−0.895999	−	0.444056i	$-0.853539\pi$
$43$	−505.289	−1.79200	−0.895999	+	0.444056i	$0.853539\pi$
$44$	179.721	0.615773
$45$	608.311	2.01515
$46$	−31.7254	−0.101688
$47$	49.3243	0.153078	0.0765392	−	0.997067i	$-0.475613\pi$
$47$	49.3243	0.153078	0.0765392	+	0.997067i	$0.475613\pi$
$48$	381.976	1.14861
$49$	49.0000	0.142857
$50$	36.0808	0.102052
$51$	146.724	0.402853
$52$	−316.681	−0.844534
$53$	−451.668	−1.17059	−0.585296	−	0.810820i	$-0.699022\pi$
$53$	−451.668	−1.17059	−0.585296	+	0.810820i	$0.699022\pi$
$54$	163.335	0.411612
$55$	−322.094	−0.789658
$56$	−97.9227	−0.233669
$57$	−1106.61	−2.57146
$58$	201.074	0.455211
$59$	−534.869	−1.18024	−0.590119	−	0.807316i	$-0.700919\pi$
$59$	−534.869	−1.18024	−0.590119	+	0.807316i	$0.700919\pi$
$60$	−790.119	−1.70007
$61$	−499.909	−1.04929	−0.524646	−	0.851320i	$-0.675802\pi$
$61$	−499.909	−1.04929	−0.524646	+	0.851320i	$0.675802\pi$
$62$	−155.882	−0.319306
$63$	332.439	0.664816
$64$	−212.954	−0.415925
$65$	567.552	1.08302
$66$	−200.438	−0.373822
$67$	−35.9387	−0.0655315	−0.0327657	−	0.999463i	$-0.510432\pi$
$67$	−35.9387	−0.0655315	−0.0327657	+	0.999463i	$0.510432\pi$
$68$	−121.500	−0.216677
$69$	−296.485	−0.517284
$70$	82.8069	0.141390
$71$	46.6169	0.0779212	0.0389606	−	0.999241i	$-0.487595\pi$
$71$	46.6169	0.0779212	0.0389606	+	0.999241i	$0.487595\pi$
$72$	−664.354	−1.08743
$73$	1014.63	1.62676	0.813382	−	0.581730i	$-0.197624\pi$
$73$	1014.63	1.62676	0.813382	+	0.581730i	$0.197624\pi$
$74$	102.271	0.160659
$75$	337.188	0.519135
$76$	916.364	1.38308
$77$	−176.023	−0.260515
$78$	353.186	0.512698
$79$	322.720	0.459606	0.229803	−	0.973237i	$-0.426192\pi$
$79$	322.720	0.459606	0.229803	+	0.973237i	$0.426192\pi$
$80$	566.885	0.792246
$81$	244.159	0.334923
$82$	−128.703	−0.173327
$83$	215.368	0.284816	0.142408	−	0.989808i	$-0.454516\pi$
$83$	215.368	0.284816	0.142408	+	0.989808i	$0.454516\pi$
$84$	−431.796	−0.560867
$85$	217.751	0.277864
$86$	−466.656	−0.585126
$87$	1879.10	2.31565
$88$	351.768	0.426121
$89$	243.588	0.290115	0.145058	−	0.989423i	$-0.453663\pi$
$89$	243.588	0.290115	0.145058	+	0.989423i	$0.453663\pi$
$90$	561.801	0.657989
$91$	310.165	0.357298
$92$	245.515	0.278225
$93$	−1456.77	−1.62430
$94$	45.5531	0.0499834
$95$	−1642.30	−1.77364
$96$	1318.66	1.40193
$97$	1061.03	1.11064	0.555318	−	0.831638i	$-0.312597\pi$
$97$	1061.03	1.11064	0.555318	+	0.831638i	$0.312597\pi$
$98$	45.2536	0.0466459
$99$	−1194.22	−1.21236
$100$	−279.220	−0.279220
$101$	−1439.52	−1.41820	−0.709099	−	0.705109i	$-0.750898\pi$
$101$	−1439.52	−1.41820	−0.709099	+	0.705109i	$0.750898\pi$
$102$	135.506	0.131540
$103$	1809.72	1.73124	0.865618	−	0.500705i	$-0.166926\pi$
$103$	1809.72	1.73124	0.865618	+	0.500705i	$0.166926\pi$
$104$	−619.840	−0.584426
$105$	773.860	0.719248
$106$	−417.135	−0.382223
$107$	2090.20	1.88848	0.944242	−	0.329253i	$-0.106797\pi$
$107$	2090.20	1.88848	0.944242	+	0.329253i	$0.106797\pi$
$108$	−1264.01	−1.12620
$109$	910.372	0.799980	0.399990	−	0.916520i	$-0.369014\pi$
$109$	910.372	0.799980	0.399990	+	0.916520i	$0.369014\pi$
$110$	−297.468	−0.257840
$111$	955.757	0.817265
$112$	309.800	0.261369
$113$	−446.879	−0.372025	−0.186012	−	0.982547i	$-0.559556\pi$
$113$	−446.879	−0.372025	−0.186012	+	0.982547i	$0.559556\pi$
$114$	−1022.00	−0.839638
$115$	−440.009	−0.356792
$116$	−1556.06	−1.24549
$117$	2104.30	1.66276
$118$	−493.974	−0.385373
$119$	119.000	0.0916698
$120$	−1546.50	−1.17646
$121$	−698.671	−0.524922
$122$	−461.687	−0.342617
$123$	−1202.77	−0.881709
$124$	1206.33	0.873643
$125$	−1100.70	−0.787594
$126$	307.022	0.217077
$127$	2404.28	1.67988	0.839941	−	0.542678i	$-0.182590\pi$
$127$	2404.28	1.67988	0.839941	+	0.542678i	$0.182590\pi$
$128$	−1418.95	−0.979835
$129$	−4361.07	−2.97652
$130$	524.159	0.353629
$131$	2536.27	1.69156	0.845781	−	0.533531i	$-0.179135\pi$
$131$	2536.27	1.69156	0.845781	+	0.533531i	$0.179135\pi$
$132$	1551.14	1.02280
$133$	−897.507	−0.585141
$134$	−33.1909	−0.0213974
$135$	2265.34	1.44422
$136$	−237.812	−0.149943
$137$	1563.86	0.975254	0.487627	−	0.873052i	$-0.337863\pi$
$137$	1563.86	0.975254	0.487627	+	0.873052i	$0.337863\pi$
$138$	−273.817	−0.168904
$139$	−1258.88	−0.768178	−0.384089	−	0.923296i	$-0.625484\pi$
$139$	−1258.88	−0.768178	−0.384089	+	0.923296i	$0.625484\pi$
$140$	−640.822	−0.386853
$141$	425.710	0.254264
$142$	43.0527	0.0254430
$143$	−1114.21	−0.651571
$144$	2101.83	1.21634
$145$	2788.75	1.59719
$146$	937.057	0.531174
$147$	422.911	0.237286
$148$	−791.449	−0.439572
$149$	2787.63	1.53269	0.766347	−	0.642426i	$-0.222072\pi$
$149$	2787.63	1.53269	0.766347	+	0.642426i	$0.222072\pi$
$150$	311.407	0.169509
$151$	−2669.54	−1.43870	−0.719351	−	0.694646i	$-0.755561\pi$
$151$	−2669.54	−1.43870	−0.719351	+	0.694646i	$0.755561\pi$
$152$	1793.60	0.957106
$153$	807.352	0.426605
$154$	−162.565	−0.0850639
$155$	−2161.97	−1.12035
$156$	−2733.22	−1.40278
$157$	2376.31	1.20796	0.603980	−	0.796999i	$-0.293581\pi$
$157$	2376.31	1.20796	0.603980	+	0.796999i	$0.293581\pi$
$158$	298.046	0.150071
$159$	−3898.27	−1.94436
$160$	1957.01	0.966969
$161$	−240.463	−0.117709
$162$	225.491	0.109359
$163$	3728.18	1.79149	0.895747	−	0.444565i	$-0.146642\pi$
$163$	3728.18	1.79149	0.895747	+	0.444565i	$0.146642\pi$
$164$	995.998	0.474234
$165$	−2779.94	−1.31163
$166$	198.901	0.0929985
$167$	−1447.60	−0.670773	−0.335386	−	0.942081i	$-0.608867\pi$
$167$	−1447.60	−0.670773	−0.335386	+	0.942081i	$0.608867\pi$
$168$	−845.155	−0.388126
$169$	−233.693	−0.106369
$170$	201.102	0.0907286
$171$	−6089.11	−2.72308
$172$	3611.34	1.60094
$173$	−2075.47	−0.912111	−0.456055	−	0.889951i	$-0.650738\pi$
$173$	−2075.47	−0.912111	−0.456055	+	0.889951i	$0.650738\pi$
$174$	1735.43	0.756108
$175$	273.475	0.118130
$176$	−1112.90	−0.476635
$177$	−4616.37	−1.96038
$178$	224.964	0.0947289
$179$	−4088.16	−1.70706	−0.853530	−	0.521044i	$-0.825543\pi$
$179$	−4088.16	−1.70706	−0.853530	+	0.521044i	$0.825543\pi$
$180$	−4347.64	−1.80030
$181$	−1719.45	−0.706107	−0.353054	−	0.935603i	$-0.614857\pi$
$181$	−1719.45	−0.706107	−0.353054	+	0.935603i	$0.614857\pi$
$182$	286.450	0.116665
$183$	−4314.63	−1.74288
$184$	480.547	0.192535
$185$	1418.43	0.563701
$186$	−1345.39	−0.530370
$187$	−427.484	−0.167170
$188$	−352.524	−0.136758
$189$	1238.00	0.476461
$190$	−1516.73	−0.579133
$191$	515.598	0.195326	0.0976632	−	0.995220i	$-0.468863\pi$
$191$	515.598	0.195326	0.0976632	+	0.995220i	$0.468863\pi$
$192$	−1837.97	−0.690854
$193$	1426.60	0.532065	0.266033	−	0.963964i	$-0.414287\pi$
$193$	1426.60	0.532065	0.266033	+	0.963964i	$0.414287\pi$
$194$	979.909	0.362646
$195$	4898.45	1.79890
$196$	−350.206	−0.127626
$197$	4024.33	1.45544	0.727720	−	0.685875i	$-0.240580\pi$
$197$	4024.33	1.45544	0.727720	+	0.685875i	$0.240580\pi$
$198$	−1102.92	−0.395863
$199$	−2624.70	−0.934976	−0.467488	−	0.883999i	$-0.654841\pi$
$199$	−2624.70	−0.934976	−0.467488	+	0.883999i	$0.654841\pi$
$200$	−546.518	−0.193223
$201$	−310.181	−0.108848
$202$	−1329.46	−0.463072
$203$	1524.04	0.526929
$204$	−1048.65	−0.359902
$205$	−1785.02	−0.608151
$206$	1671.36	0.565286
$207$	−1631.41	−0.547783
$208$	1961.00	0.653706
$209$	3224.12	1.06707
$210$	714.693	0.234850
$211$	1140.64	0.372157	0.186079	−	0.982535i	$-0.440422\pi$
$211$	1140.64	0.372157	0.186079	+	0.982535i	$0.440422\pi$
$212$	3228.10	1.04579
$213$	402.343	0.129427
$214$	1930.39	0.616630
$215$	−6472.20	−2.05302
$216$	−2474.05	−0.779340
$217$	−1181.51	−0.369613
$218$	840.767	0.261211
$219$	8757.13	2.70206
$220$	2302.03	0.705468
$221$	753.257	0.229274
$222$	882.682	0.266855
$223$	−2272.97	−0.682554	−0.341277	−	0.939963i	$-0.610859\pi$
$223$	−2272.97	−0.682554	−0.341277	+	0.939963i	$0.610859\pi$
$224$	1069.50	0.319012
$225$	1855.38	0.549743
$226$	−412.711	−0.121474
$227$	2837.33	0.829604	0.414802	−	0.909912i	$-0.363851\pi$
$227$	2837.33	0.829604	0.414802	+	0.909912i	$0.363851\pi$
$228$	7908.98	2.29730
$229$	153.243	0.0442210	0.0221105	−	0.999756i	$-0.492961\pi$
$229$	153.243	0.0442210	0.0221105	+	0.999756i	$0.492961\pi$
$230$	−406.367	−0.116500
$231$	−1519.23	−0.432717
$232$	−3045.67	−0.861889
$233$	−4108.46	−1.15517	−0.577585	−	0.816331i	$-0.696005\pi$
$233$	−4108.46	−1.15517	−0.577585	+	0.816331i	$0.696005\pi$
$234$	1943.41	0.542927
$235$	631.790	0.175376
$236$	3822.75	1.05441
$237$	2785.35	0.763408
$238$	109.902	0.0299322
$239$	−3041.48	−0.823168	−0.411584	−	0.911372i	$-0.635024\pi$
$239$	−3041.48	−0.823168	−0.411584	+	0.911372i	$0.635024\pi$
$240$	4892.69	1.31593
$241$	4011.67	1.07226	0.536129	−	0.844136i	$-0.319886\pi$
$241$	4011.67	1.07226	0.536129	+	0.844136i	$0.319886\pi$
$242$	−645.253	−0.171398
$243$	−2667.85	−0.704290
$244$	3572.89	0.937421
$245$	627.636	0.163666
$246$	−1110.81	−0.287897
$247$	−5681.12	−1.46349
$248$	2361.15	0.604570
$249$	1858.81	0.473080
$250$	−1016.54	−0.257166
$251$	−6694.08	−1.68337	−0.841687	−	0.539966i	$-0.818437\pi$
$251$	−6694.08	−1.68337	−0.841687	+	0.539966i	$0.818437\pi$
$252$	−2375.97	−0.593936
$253$	863.817	0.214655
$254$	2220.45	0.548517
$255$	1879.37	0.461533
$256$	393.168	0.0959883
$257$	1001.05	0.242973	0.121487	−	0.992593i	$-0.461234\pi$
$257$	1001.05	0.242973	0.121487	+	0.992593i	$0.461234\pi$
$258$	−4027.63	−0.971897
$259$	775.163	0.185970
$260$	−4056.34	−0.967551
$261$	10339.8	2.45217
$262$	2342.35	0.552331
$263$	−2228.69	−0.522537	−0.261268	−	0.965266i	$-0.584141\pi$
$263$	−2228.69	−0.522537	−0.261268	+	0.965266i	$0.584141\pi$
$264$	3036.06	0.707789
$265$	−5785.37	−1.34110
$266$	−828.886	−0.191061
$267$	2102.37	0.481883
$268$	256.856	0.0585448
$269$	−2222.34	−0.503711	−0.251855	−	0.967765i	$-0.581041\pi$
$269$	−2222.34	−0.503711	−0.251855	+	0.967765i	$0.581041\pi$
$270$	2092.14	0.471569
$271$	5388.84	1.20793	0.603965	−	0.797011i	$-0.293587\pi$
$271$	5388.84	1.20793	0.603965	+	0.797011i	$0.293587\pi$
$272$	752.372	0.167718
$273$	2676.98	0.593473
$274$	1444.29	0.318441
$275$	−982.405	−0.215423
$276$	2119.00	0.462133
$277$	2231.61	0.484059	0.242029	−	0.970269i	$-0.422187\pi$
$277$	2231.61	0.484059	0.242029	+	0.970269i	$0.422187\pi$
$278$	−1162.63	−0.250827
$279$	−8015.90	−1.72007
$280$	−1254.28	−0.267706
$281$	−68.6799	−0.0145804	−0.00729022	−	0.999973i	$-0.502321\pi$
$281$	−68.6799	−0.0145804	−0.00729022	+	0.999973i	$0.502321\pi$
$282$	393.161	0.0830227
$283$	7248.99	1.52264	0.761321	−	0.648375i	$-0.224551\pi$
$283$	7248.99	1.52264	0.761321	+	0.648375i	$0.224551\pi$
$284$	−333.174	−0.0696135
$285$	−14174.4	−2.94603
$286$	−1029.02	−0.212752
$287$	−975.503	−0.200634
$288$	7255.96	1.48459
$289$	289.000	0.0588235
$290$	2575.53	0.521518
$291$	9157.60	1.84477
$292$	−7251.65	−1.45332
$293$	−5623.57	−1.12127	−0.560635	−	0.828063i	$-0.689443\pi$
$293$	−5623.57	−1.12127	−0.560635	+	0.828063i	$0.689443\pi$
$294$	390.576	0.0774791
$295$	−6851.08	−1.35215
$296$	−1549.10	−0.304188
$297$	−4447.27	−0.868879
$298$	2574.49	0.500458
$299$	−1522.10	−0.294400
$300$	−2409.90	−0.463786
$301$	−3537.03	−0.677312
$302$	−2465.43	−0.469767
$303$	−12424.3	−2.35563
$304$	−5674.45	−1.07057
$305$	−6403.29	−1.20213
$306$	745.624	0.139296
$307$	2371.03	0.440787	0.220394	−	0.975411i	$-0.429266\pi$
$307$	2371.03	0.440787	0.220394	+	0.975411i	$0.429266\pi$
$308$	1258.05	0.232740
$309$	15619.4	2.87559
$310$	−1996.67	−0.365817
$311$	218.383	0.0398179	0.0199090	−	0.999802i	$-0.493662\pi$
$311$	218.383	0.0398179	0.0199090	+	0.999802i	$0.493662\pi$
$312$	−5349.74	−0.970735
$313$	8268.53	1.49318	0.746589	−	0.665285i	$-0.231690\pi$
$313$	8268.53	1.49318	0.746589	+	0.665285i	$0.231690\pi$
$314$	2194.62	0.394425
$315$	4258.18	0.761654
$316$	−2306.50	−0.410604
$317$	−892.805	−0.158186	−0.0790930	−	0.996867i	$-0.525202\pi$
$317$	−892.805	−0.158186	−0.0790930	+	0.996867i	$0.525202\pi$
$318$	−3600.22	−0.634875
$319$	−5474.82	−0.960912
$320$	−2727.70	−0.476510
$321$	18040.2	3.13678
$322$	−222.078	−0.0384345
$323$	−2179.66	−0.375478
$324$	−1745.02	−0.299214
$325$	1731.06	0.295453
$326$	3443.13	0.584961
$327$	7857.27	1.32877
$328$	1949.47	0.328175
$329$	345.270	0.0578582
$330$	−2567.40	−0.428274
$331$	−4580.22	−0.760578	−0.380289	−	0.924868i	$-0.624176\pi$
$331$	−4580.22	−0.760578	−0.380289	+	0.924868i	$0.624176\pi$
$332$	−1539.25	−0.254450
$333$	5259.07	0.865451
$334$	−1336.92	−0.219022
$335$	−460.335	−0.0750770
$336$	2673.83	0.434136
$337$	1126.30	0.182057	0.0910286	−	0.995848i	$-0.470985\pi$
$337$	1126.30	0.182057	0.0910286	+	0.995848i	$0.470985\pi$
$338$	−215.825	−0.0347318
$339$	−3856.94	−0.617935
$340$	−1556.28	−0.248239
$341$	4244.34	0.674029
$342$	−5623.55	−0.889143
$343$	343.000	0.0539949
$344$	7068.47	1.10787
$345$	−3797.65	−0.592633
$346$	−1916.79	−0.297824
$347$	−10261.9	−1.58758	−0.793789	−	0.608193i	$-0.791895\pi$
$347$	−10261.9	−1.58758	−0.793789	+	0.608193i	$0.791895\pi$
$348$	−13430.1	−2.06876
$349$	7233.38	1.10944	0.554719	−	0.832037i	$-0.312826\pi$
$349$	7233.38	1.10944	0.554719	+	0.832037i	$0.312826\pi$
$350$	252.565	0.0385720
$351$	7836.40	1.19167
$352$	−3841.96	−0.581753
$353$	−6562.11	−0.989422	−0.494711	−	0.869058i	$-0.664726\pi$
$353$	−6562.11	−0.989422	−0.494711	+	0.869058i	$0.664726\pi$
$354$	−4263.41	−0.640107
$355$	597.111	0.0892714
$356$	−1740.94	−0.259184
$357$	1027.07	0.152264
$358$	−3775.59	−0.557392
$359$	−6102.05	−0.897086	−0.448543	−	0.893761i	$-0.648057\pi$
$359$	−6102.05	−0.897086	−0.448543	+	0.893761i	$0.648057\pi$
$360$	−8509.64	−1.24583
$361$	9580.17	1.39673
$362$	−1587.98	−0.230559
$363$	−6030.12	−0.871898
$364$	−2216.77	−0.319204
$365$	12996.3	1.86372
$366$	−3984.75	−0.569088
$367$	11539.8	1.64135	0.820674	−	0.571397i	$-0.193598\pi$
$367$	11539.8	1.64135	0.820674	+	0.571397i	$0.193598\pi$
$368$	−1520.32	−0.215358
$369$	−6618.27	−0.933695
$370$	1309.98	0.184061
$371$	−3161.68	−0.442442
$372$	10411.6	1.45112
$373$	3649.00	0.506536	0.253268	−	0.967396i	$-0.418495\pi$
$373$	3649.00	0.506536	0.253268	+	0.967396i	$0.418495\pi$
$374$	−394.800	−0.0545846
$375$	−9499.93	−1.30820
$376$	−689.996	−0.0946378
$377$	9647.00	1.31789
$378$	1143.34	0.155575
$379$	−4826.70	−0.654171	−0.327085	−	0.944995i	$-0.606066\pi$
$379$	−4826.70	−0.654171	−0.327085	+	0.944995i	$0.606066\pi$
$380$	11737.6	1.58454
$381$	20750.9	2.79029
$382$	476.176	0.0637783
$383$	366.260	0.0488642	0.0244321	−	0.999701i	$-0.492222\pi$
$383$	366.260	0.0488642	0.0244321	+	0.999701i	$0.492222\pi$
$384$	−12246.7	−1.62751
$385$	−2254.66	−0.298463
$386$	1317.52	0.173731
$387$	−23996.9	−3.15201
$388$	−7583.28	−0.992224
$389$	−1607.00	−0.209455	−0.104727	−	0.994501i	$-0.533397\pi$
$389$	−1607.00	−0.209455	−0.104727	+	0.994501i	$0.533397\pi$
$390$	4523.93	0.587379
$391$	−583.981	−0.0755325
$392$	−685.459	−0.0883186
$393$	21890.1	2.80969
$394$	3716.64	0.475232
$395$	4133.69	0.526553
$396$	8535.20	1.08311
$397$	−8375.29	−1.05880	−0.529400	−	0.848372i	$-0.677583\pi$
$397$	−8375.29	−1.05880	−0.529400	+	0.848372i	$0.677583\pi$
$398$	−2424.02	−0.305290
$399$	−7746.24	−0.971922
$400$	1729.03	0.216129
$401$	278.263	0.0346528	0.0173264	−	0.999850i	$-0.494485\pi$
$401$	278.263	0.0346528	0.0173264	+	0.999850i	$0.494485\pi$
$402$	−286.465	−0.0355413
$403$	−7478.81	−0.924432
$404$	10288.4	1.26699
$405$	3127.40	0.383708
$406$	1407.51	0.172054
$407$	−2784.62	−0.339137
$408$	−2052.52	−0.249056
$409$	−4596.08	−0.555652	−0.277826	−	0.960631i	$-0.589614\pi$
$409$	−4596.08	−0.555652	−0.277826	+	0.960631i	$0.589614\pi$
$410$	−1648.54	−0.198574
$411$	13497.4	1.61990
$412$	−12934.2	−1.54666
$413$	−3744.09	−0.446088
$414$	−1506.68	−0.178863
$415$	2758.63	0.326303
$416$	6769.79	0.797875
$417$	−10865.2	−1.27595
$418$	2977.61	0.348421
$419$	1770.51	0.206432	0.103216	−	0.994659i	$-0.467087\pi$
$419$	1770.51	0.206432	0.103216	+	0.994659i	$0.467087\pi$
$420$	−5530.83	−0.642564
$421$	−1457.08	−0.168678	−0.0843392	−	0.996437i	$-0.526878\pi$
$421$	−1457.08	−0.168678	−0.0843392	+	0.996437i	$0.526878\pi$
$422$	1053.43	0.121517
$423$	2342.48	0.269255
$424$	6318.37	0.723696
$425$	664.153	0.0758027
$426$	371.580	0.0422609
$427$	−3499.37	−0.396595
$428$	−14938.8	−1.68714
$429$	−9616.53	−1.08226
$430$	−5977.35	−0.670357
$431$	−13452.5	−1.50344	−0.751722	−	0.659480i	$-0.770777\pi$
$431$	−13452.5	−1.50344	−0.751722	+	0.659480i	$0.770777\pi$
$432$	7827.19	0.871727
$433$	−14767.8	−1.63902	−0.819512	−	0.573063i	$-0.805755\pi$
$433$	−14767.8	−1.63902	−0.819512	+	0.573063i	$0.805755\pi$
$434$	−1091.17	−0.120686
$435$	24069.3	2.65295
$436$	−6506.49	−0.714689
$437$	4404.43	0.482134
$438$	8087.58	0.882282
$439$	−4574.75	−0.497360	−0.248680	−	0.968586i	$-0.579997\pi$
$439$	−4574.75	−0.497360	−0.248680	+	0.968586i	$0.579997\pi$
$440$	4505.77	0.488191
$441$	2327.07	0.251277
$442$	695.665	0.0748629
$443$	6288.13	0.674397	0.337199	−	0.941433i	$-0.390521\pi$
$443$	6288.13	0.674397	0.337199	+	0.941433i	$0.390521\pi$
$444$	−6830.86	−0.730132
$445$	3120.09	0.332374
$446$	−2099.19	−0.222869
$447$	24059.6	2.54581
$448$	−1490.68	−0.157205
$449$	−399.444	−0.0419842	−0.0209921	−	0.999780i	$-0.506682\pi$
$449$	−399.444	−0.0419842	−0.0209921	+	0.999780i	$0.506682\pi$
$450$	1713.52	0.179503
$451$	3504.30	0.365879
$452$	3193.87	0.332361
$453$	−23040.4	−2.38969
$454$	2620.39	0.270884
$455$	3972.87	0.409342
$456$	15480.3	1.58976
$457$	10220.8	1.04619	0.523097	−	0.852273i	$-0.324776\pi$
$457$	10220.8	1.04619	0.523097	+	0.852273i	$0.324776\pi$
$458$	141.527	0.0144391
$459$	3006.57	0.305740
$460$	3144.78	0.318752
$461$	6880.74	0.695159	0.347579	−	0.937651i	$-0.387004\pi$
$461$	6880.74	0.695159	0.347579	+	0.937651i	$0.387004\pi$
$462$	−1403.07	−0.141292
$463$	−7460.45	−0.748847	−0.374424	−	0.927258i	$-0.622159\pi$
$463$	−7460.45	−0.748847	−0.374424	+	0.927258i	$0.622159\pi$
$464$	9635.66	0.964061
$465$	−18659.6	−1.86090
$466$	−3794.34	−0.377188
$467$	1948.09	0.193034	0.0965169	−	0.995331i	$-0.469230\pi$
$467$	1948.09	0.193034	0.0965169	+	0.995331i	$0.469230\pi$
$468$	−15039.6	−1.48548
$469$	−251.571	−0.0247686
$470$	583.485	0.0572641
$471$	20509.5	2.00643
$472$	7482.27	0.729659
$473$	12706.1	1.23515
$474$	2572.38	0.249269
$475$	−5009.09	−0.483859
$476$	−850.501	−0.0818963
$477$	−21450.3	−2.05900
$478$	−2808.94	−0.268782
$479$	9843.24	0.938933	0.469467	−	0.882950i	$-0.344446\pi$
$479$	9843.24	0.938933	0.469467	+	0.882950i	$0.344446\pi$
$480$	16890.6	1.60614
$481$	4906.69	0.465127
$482$	3704.94	0.350115
$483$	−2075.40	−0.195515
$484$	4993.45	0.468957
$485$	13590.7	1.27241
$486$	−2463.87	−0.229966
$487$	1874.30	0.174400	0.0871998	−	0.996191i	$-0.472208\pi$
$487$	1874.30	0.174400	0.0871998	+	0.996191i	$0.472208\pi$
$488$	6993.21	0.648705
$489$	32177.3	2.97568
$490$	579.648	0.0534405
$491$	5815.57	0.534527	0.267264	−	0.963623i	$-0.413881\pi$
$491$	5815.57	0.534527	0.267264	+	0.963623i	$0.413881\pi$
$492$	8596.29	0.787705
$493$	3701.24	0.338124
$494$	−5246.76	−0.477860
$495$	−15296.7	−1.38896
$496$	−7470.02	−0.676238
$497$	326.318	0.0294514
$498$	1716.69	0.154471
$499$	7739.44	0.694318	0.347159	−	0.937806i	$-0.387146\pi$
$499$	7739.44	0.694318	0.347159	+	0.937806i	$0.387146\pi$
$500$	7866.75	0.703624
$501$	−12494.0	−1.11416
$502$	−6182.27	−0.549658
$503$	−4060.20	−0.359911	−0.179956	−	0.983675i	$-0.557595\pi$
$503$	−4060.20	−0.359911	−0.179956	+	0.983675i	$0.557595\pi$
$504$	−4650.48	−0.411009
$505$	−18438.7	−1.62478
$506$	797.771	0.0700894
$507$	−2016.96	−0.176679
$508$	−17183.5	−1.50078
$509$	4530.63	0.394532	0.197266	−	0.980350i	$-0.436794\pi$
$509$	4530.63	0.394532	0.197266	+	0.980350i	$0.436794\pi$
$510$	1735.68	0.150701
$511$	7102.43	0.614859
$512$	11714.7	1.01118
$513$	−22675.8	−1.95158
$514$	924.516	0.0793359
$515$	23180.6	1.98341
$516$	31168.9	2.65917
$517$	−1240.32	−0.105511
$518$	715.895	0.0607232
$519$	−17913.0	−1.51502
$520$	−7939.47	−0.669555
$521$	−1524.81	−0.128221	−0.0641105	−	0.997943i	$-0.520421\pi$
$521$	−1524.81	−0.128221	−0.0641105	+	0.997943i	$0.520421\pi$
$522$	9549.24	0.800688
$523$	16602.5	1.38810	0.694051	−	0.719926i	$-0.255824\pi$
$523$	16602.5	1.38810	0.694051	+	0.719926i	$0.255824\pi$
$524$	−18126.9	−1.51121
$525$	2360.31	0.196214
$526$	−2058.29	−0.170620
$527$	−2869.38	−0.237176
$528$	−9605.23	−0.791693
$529$	−10987.0	−0.903012
$530$	−5343.03	−0.437899
$531$	−25401.6	−2.07596
$532$	6414.55	0.522755
$533$	−6174.82	−0.501803
$534$	1941.63	0.157345
$535$	26773.2	2.16356
$536$	502.745	0.0405136
$537$	−35284.3	−2.83543
$538$	−2052.42	−0.164472
$539$	−1232.16	−0.0984656
$540$	−16190.6	−1.29024
$541$	−13862.2	−1.10163	−0.550815	−	0.834627i	$-0.685683\pi$
$541$	−13862.2	−1.10163	−0.550815	+	0.834627i	$0.685683\pi$
$542$	4976.82	0.394415
$543$	−14840.3	−1.17285
$544$	2597.35	0.204706
$545$	11660.9	0.916507
$546$	2472.30	0.193782
$547$	11227.8	0.877631	0.438816	−	0.898577i	$-0.355398\pi$
$547$	11227.8	0.877631	0.438816	+	0.898577i	$0.355398\pi$
$548$	−11177.0	−0.871276
$549$	−23741.3	−1.84564
$550$	−907.292	−0.0703401
$551$	−27915.0	−2.15829
$552$	4147.52	0.319801
$553$	2259.04	0.173715
$554$	2060.98	0.158056
$555$	12242.2	0.936310
$556$	8997.29	0.686277
$557$	6981.57	0.531093	0.265546	−	0.964098i	$-0.414448\pi$
$557$	6981.57	0.531093	0.265546	+	0.964098i	$0.414448\pi$
$558$	−7403.03	−0.561640
$559$	−22389.0	−1.69401
$560$	3968.20	0.299441
$561$	−3689.55	−0.277670
$562$	−63.4288	−0.00476083
$563$	12172.4	0.911199	0.455599	−	0.890185i	$-0.349425\pi$
$563$	12172.4	0.911199	0.455599	+	0.890185i	$0.349425\pi$
$564$	−3042.58	−0.227155
$565$	−5724.02	−0.426215
$566$	6694.75	0.497176
$567$	1709.11	0.126589
$568$	−652.122	−0.0481733
$569$	15981.0	1.17743	0.588715	−	0.808341i	$-0.299634\pi$
$569$	15981.0	1.17743	0.588715	+	0.808341i	$0.299634\pi$
$570$	−13090.6	−0.961942
$571$	−4249.75	−0.311465	−0.155732	−	0.987799i	$-0.549774\pi$
$571$	−4249.75	−0.311465	−0.155732	+	0.987799i	$0.549774\pi$
$572$	7963.31	0.582103
$573$	4450.04	0.324438
$574$	−900.918	−0.0655115
$575$	−1342.05	−0.0973346
$576$	−10113.5	−0.731587
$577$	−5624.58	−0.405814	−0.202907	−	0.979198i	$-0.565039\pi$
$577$	−5624.58	−0.405814	−0.202907	+	0.979198i	$0.565039\pi$
$578$	266.904	0.0192071
$579$	12312.7	0.883763
$580$	−19931.4	−1.42691
$581$	1507.58	0.107650
$582$	8457.44	0.602357
$583$	11357.7	0.806841
$584$	−14193.7	−1.00572
$585$	26953.8	1.90496
$586$	−5193.60	−0.366119
$587$	19602.6	1.37834	0.689169	−	0.724601i	$-0.257976\pi$
$587$	19602.6	1.37834	0.689169	+	0.724601i	$0.257976\pi$
$588$	−3022.57	−0.211988
$589$	21641.0	1.51393
$590$	−6327.27	−0.441508
$591$	34733.3	2.41749
$592$	4900.93	0.340248
$593$	−11403.4	−0.789679	−0.394840	−	0.918750i	$-0.629200\pi$
$593$	−11403.4	−0.789679	−0.394840	+	0.918750i	$0.629200\pi$
$594$	−4107.24	−0.283708
$595$	1524.26	0.105023
$596$	−19923.4	−1.36928
$597$	−22653.4	−1.55300
$598$	−1405.73	−0.0961279
$599$	−19347.4	−1.31972	−0.659861	−	0.751388i	$-0.729385\pi$
$599$	−19347.4	−1.31972	−0.659861	+	0.751388i	$0.729385\pi$
$600$	−4716.91	−0.320945
$601$	−8504.09	−0.577187	−0.288593	−	0.957452i	$-0.593188\pi$
$601$	−8504.09	−0.577187	−0.288593	+	0.957452i	$0.593188\pi$
$602$	−3266.59	−0.221157
$603$	−1706.78	−0.115266
$604$	19079.4	1.28531
$605$	−8949.21	−0.601384
$606$	−11474.4	−0.769165
$607$	−15367.3	−1.02758	−0.513788	−	0.857917i	$-0.671758\pi$
$607$	−15367.3	−1.02758	−0.513788	+	0.857917i	$0.671758\pi$
$608$	−19589.4	−1.30667
$609$	13153.7	0.875232
$610$	−5913.71	−0.392523
$611$	2185.52	0.144708
$612$	−5770.20	−0.381122
$613$	−7823.33	−0.515467	−0.257734	−	0.966216i	$-0.582976\pi$
$613$	−7823.33	−0.515467	−0.257734	+	0.966216i	$0.582976\pi$
$614$	2189.74	0.143927
$615$	−15406.2	−1.01014
$616$	2462.38	0.161059
$617$	−23795.3	−1.55261	−0.776307	−	0.630356i	$-0.782909\pi$
$617$	−23795.3	−1.55261	−0.776307	+	0.630356i	$0.782909\pi$
$618$	14425.2	0.938942
$619$	4405.91	0.286088	0.143044	−	0.989716i	$-0.454311\pi$
$619$	4405.91	0.286088	0.143044	+	0.989716i	$0.454311\pi$
$620$	15451.8	1.00090
$621$	−6075.37	−0.392586
$622$	201.686	0.0130014
$623$	1705.12	0.109653
$624$	16925.1	1.08581
$625$	−18982.2	−1.21486
$626$	7636.34	0.487555
$627$	27826.9	1.77240
$628$	−16983.6	−1.07917
$629$	1882.54	0.119335
$630$	3932.61	0.248697
$631$	16515.1	1.04193	0.520963	−	0.853579i	$-0.325573\pi$
$631$	16515.1	1.04193	0.520963	+	0.853579i	$0.325573\pi$
$632$	−4514.52	−0.284142
$633$	9844.70	0.618155
$634$	−824.543	−0.0516511
$635$	30796.1	1.92458
$636$	27861.2	1.73706
$637$	2171.15	0.135046
$638$	−5056.22	−0.313758
$639$	2213.90	0.137058
$640$	−18175.2	−1.12256
$641$	25434.3	1.56723	0.783614	−	0.621248i	$-0.213374\pi$
$641$	25434.3	1.56723	0.783614	+	0.621248i	$0.213374\pi$
$642$	16660.9	1.02423
$643$	5355.13	0.328438	0.164219	−	0.986424i	$-0.447490\pi$
$643$	5355.13	0.328438	0.164219	+	0.986424i	$0.447490\pi$
$644$	1718.61	0.105159
$645$	−55860.5	−3.41008
$646$	−2013.01	−0.122602
$647$	−28127.0	−1.70910	−0.854548	−	0.519373i	$-0.826166\pi$
$647$	−28127.0	−1.70910	−0.854548	+	0.519373i	$0.826166\pi$
$648$	−3415.53	−0.207059
$649$	13449.9	0.813490
$650$	1598.71	0.0964717
$651$	−10197.4	−0.613928
$652$	−26645.5	−1.60049
$653$	−2.94464	−0.000176467 0	−8.82333e−5	−	1.00000i	$-0.500028\pi$
$653$	−2.94464	−0.000176467 0	−8.82333e−5		1.00000i	$0.500028\pi$
$654$	7256.52	0.433872
$655$	32486.8	1.93796
$656$	−6167.57	−0.367078
$657$	48186.2	2.86138
$658$	318.872	0.0188920
$659$	−20993.5	−1.24096	−0.620480	−	0.784222i	$-0.713062\pi$
$659$	−20993.5	−1.24096	−0.620480	+	0.784222i	$0.713062\pi$
$660$	19868.4	1.17179
$661$	−13976.2	−0.822408	−0.411204	−	0.911543i	$-0.634892\pi$
$661$	−13976.2	−0.822408	−0.411204	+	0.911543i	$0.634892\pi$
$662$	−4230.02	−0.248345
$663$	6501.23	0.380825
$664$	−3012.77	−0.176082
$665$	−11496.1	−0.670374
$666$	4856.97	0.282588
$667$	−7479.08	−0.434170
$668$	10346.1	0.599257
$669$	−19617.7	−1.13373
$670$	−425.139	−0.0245142
$671$	12570.8	0.723234
$672$	9230.64	0.529880
$673$	32423.6	1.85712	0.928559	−	0.371186i	$-0.121049\pi$
$673$	32423.6	1.85712	0.928559	+	0.371186i	$0.121049\pi$
$674$	1040.18	0.0594456
$675$	6909.42	0.393990
$676$	1670.22	0.0950283
$677$	−24903.8	−1.41378	−0.706892	−	0.707322i	$-0.749903\pi$
$677$	−24903.8	−1.41378	−0.706892	+	0.707322i	$0.749903\pi$
$678$	−3562.04	−0.201769
$679$	7427.23	0.419781
$680$	−3046.11	−0.171784
$681$	24488.5	1.37798
$682$	3919.82	0.220085
$683$	−9688.33	−0.542773	−0.271386	−	0.962470i	$-0.587482\pi$
$683$	−9688.33	−0.542773	−0.271386	+	0.962470i	$0.587482\pi$
$684$	43519.3	2.43275
$685$	20031.3	1.11731
$686$	316.775	0.0176305
$687$	1322.62	0.0734513
$688$	−22362.7	−1.23920
$689$	−20013.1	−1.10658
$690$	−3507.29	−0.193507
$691$	−10264.5	−0.565096	−0.282548	−	0.959253i	$-0.591180\pi$
$691$	−10264.5	−0.565096	−0.282548	+	0.959253i	$0.591180\pi$
$692$	14833.5	0.814865
$693$	−8359.56	−0.458230
$694$	−9477.33	−0.518378
$695$	−16124.8	−0.880072
$696$	−26286.7	−1.43160
$697$	−2369.08	−0.128745
$698$	6680.34	0.362256
$699$	−35459.5	−1.91874
$700$	−1954.54	−0.105535
$701$	−16145.8	−0.869928	−0.434964	−	0.900448i	$-0.643239\pi$
$701$	−16145.8	−0.869928	−0.434964	+	0.900448i	$0.643239\pi$
$702$	7237.25	0.389106
$703$	−14198.2	−0.761731
$704$	5354.97	0.286680
$705$	5452.87	0.291301
$706$	−6060.39	−0.323067
$707$	−10076.7	−0.536028
$708$	32993.5	1.75137
$709$	−33674.4	−1.78373	−0.891867	−	0.452297i	$-0.850605\pi$
$709$	−33674.4	−1.78373	−0.891867	+	0.452297i	$0.850605\pi$
$710$	551.457	0.0291490
$711$	15326.4	0.808418
$712$	−3407.54	−0.179358
$713$	5798.14	0.304547
$714$	948.542	0.0497175
$715$	−14271.8	−0.746480
$716$	29218.4	1.52506
$717$	−26250.5	−1.36729
$718$	−5635.50	−0.292918
$719$	25786.1	1.33750	0.668748	−	0.743489i	$-0.266831\pi$
$719$	25786.1	1.33750	0.668748	+	0.743489i	$0.266831\pi$
$720$	26922.1	1.39351
$721$	12668.1	0.654346
$722$	8847.69	0.456062
$723$	34624.0	1.78103
$724$	12289.0	0.630825
$725$	8505.84	0.435723
$726$	−5569.07	−0.284694
$727$	16593.5	0.846518	0.423259	−	0.906009i	$-0.360886\pi$
$727$	16593.5	0.846518	0.423259	+	0.906009i	$0.360886\pi$
$728$	−4338.88	−0.220892
$729$	−29618.0	−1.50475
$730$	12002.7	0.608546
$731$	−8589.92	−0.434623
$732$	30837.0	1.55706
$733$	35099.4	1.76866	0.884329	−	0.466864i	$-0.154616\pi$
$733$	35099.4	1.76866	0.884329	+	0.466864i	$0.154616\pi$
$734$	10657.5	0.535935
$735$	5417.02	0.271850
$736$	−5248.45	−0.262854
$737$	903.720	0.0451682
$738$	−6112.25	−0.304871
$739$	−2378.49	−0.118395	−0.0591977	−	0.998246i	$-0.518854\pi$
$739$	−2378.49	−0.118395	−0.0591977	+	0.998246i	$0.518854\pi$
$740$	−10137.6	−0.503601
$741$	−49032.8	−2.43086
$742$	−2919.94	−0.144467
$743$	3700.16	0.182700	0.0913498	−	0.995819i	$-0.470882\pi$
$743$	3700.16	0.182700	0.0913498	+	0.995819i	$0.470882\pi$
$744$	20378.7	1.00419
$745$	35706.5	1.75595
$746$	3370.00	0.165395
$747$	10228.1	0.500973
$748$	3055.26	0.149347
$749$	14631.4	0.713780
$750$	−8773.59	−0.427155
$751$	−20632.4	−1.00251	−0.501256	−	0.865299i	$-0.667128\pi$
$751$	−20632.4	−1.00251	−0.501256	+	0.865299i	$0.667128\pi$
$752$	2182.95	0.105857
$753$	−57775.5	−2.79609
$754$	8909.41	0.430320
$755$	−34193.9	−1.64827
$756$	−8848.07	−0.425663
$757$	−673.353	−0.0323295	−0.0161648	−	0.999869i	$-0.505146\pi$
$757$	−673.353	−0.0323295	−0.0161648	+	0.999869i	$0.505146\pi$
$758$	−4457.66	−0.213601
$759$	7455.46	0.356543
$760$	22974.0	1.09652
$761$	23822.4	1.13477	0.567386	−	0.823452i	$-0.307955\pi$
$761$	23822.4	1.13477	0.567386	+	0.823452i	$0.307955\pi$
$762$	19164.3	0.911090
$763$	6372.60	0.302364
$764$	−3685.01	−0.174501
$765$	10341.3	0.488745
$766$	338.256	0.0159552
$767$	−23699.6	−1.11570
$768$	3393.37	0.159437
$769$	9036.48	0.423750	0.211875	−	0.977297i	$-0.432043\pi$
$769$	9036.48	0.423750	0.211875	+	0.977297i	$0.432043\pi$
$770$	−2082.27	−0.0974545
$771$	8639.94	0.403579
$772$	−10196.0	−0.475338
$773$	−19411.9	−0.903231	−0.451616	−	0.892213i	$-0.649152\pi$
$773$	−19411.9	−0.903231	−0.451616	+	0.892213i	$0.649152\pi$
$774$	−22162.1	−1.02920
$775$	−6594.13	−0.305636
$776$	−14842.8	−0.686629
$777$	6690.30	0.308897
$778$	−1484.13	−0.0683915
$779$	17867.8	0.821796
$780$	−35009.6	−1.60711
$781$	−1172.23	−0.0537079
$782$	−539.332	−0.0246630
$783$	38505.3	1.75743
$784$	2168.60	0.0987883
$785$	30437.8	1.38391
$786$	20216.4	0.917425
$787$	12672.0	0.573961	0.286981	−	0.957936i	$-0.407348\pi$
$787$	12672.0	0.573961	0.286981	+	0.957936i	$0.407348\pi$
$788$	−28762.2	−1.30027
$789$	−19235.5	−0.867936
$790$	3817.64	0.171931
$791$	−3128.15	−0.140612
$792$	16705.9	0.749520
$793$	−22150.6	−0.991918
$794$	−7734.94	−0.345721
$795$	−49932.6	−2.22758
$796$	18758.9	0.835292
$797$	24632.8	1.09478	0.547389	−	0.836878i	$-0.315622\pi$
$797$	24632.8	1.09478	0.547389	+	0.836878i	$0.315622\pi$
$798$	−7153.98	−0.317353
$799$	838.513	0.0371270
$800$	5968.98	0.263794
$801$	11568.3	0.510295
$802$	256.987	0.0113149
$803$	−25514.1	−1.12126
$804$	2216.88	0.0972431
$805$	−3080.06	−0.134855
$806$	−6907.00	−0.301847
$807$	−19180.6	−0.836666
$808$	20137.4	0.876773
$809$	−3588.52	−0.155952	−0.0779762	−	0.996955i	$-0.524846\pi$
$809$	−3588.52	−0.155952	−0.0779762	+	0.996955i	$0.524846\pi$
$810$	2888.29	0.125289
$811$	5225.50	0.226254	0.113127	−	0.993581i	$-0.463913\pi$
$811$	5225.50	0.226254	0.113127	+	0.993581i	$0.463913\pi$
$812$	−10892.4	−0.470750
$813$	46510.2	2.00638
$814$	−2571.72	−0.110735
$815$	47753.8	2.05245
$816$	6493.60	0.278580
$817$	64785.8	2.77426
$818$	−4244.68	−0.181432
$819$	14730.1	0.628464
$820$	12757.6	0.543312
$821$	−28768.6	−1.22294	−0.611469	−	0.791268i	$-0.709421\pi$
$821$	−28768.6	−1.22294	−0.611469	+	0.791268i	$0.709421\pi$
$822$	12465.5	0.528933
$823$	−38037.5	−1.61106	−0.805530	−	0.592555i	$-0.798119\pi$
$823$	−38037.5	−1.61106	−0.805530	+	0.592555i	$0.798119\pi$
$824$	−25316.1	−1.07030
$825$	−8478.97	−0.357818
$826$	−3457.82	−0.145657
$827$	−16986.2	−0.714228	−0.357114	−	0.934061i	$-0.616239\pi$
$827$	−16986.2	−0.714228	−0.357114	+	0.934061i	$0.616239\pi$
$828$	11659.8	0.489381
$829$	10407.1	0.436009	0.218005	−	0.975948i	$-0.430045\pi$
$829$	10407.1	0.436009	0.218005	+	0.975948i	$0.430045\pi$
$830$	2547.71	0.106545
$831$	19260.6	0.804024
$832$	−9435.82	−0.393183
$833$	833.000	0.0346479
$834$	−10034.4	−0.416624
$835$	−18542.2	−0.768479
$836$	−23043.0	−0.953301
$837$	−29851.1	−1.23274
$838$	1635.14	0.0674046
$839$	38356.6	1.57833	0.789164	−	0.614182i	$-0.210514\pi$
$839$	38356.6	1.57833	0.789164	+	0.614182i	$0.210514\pi$
$840$	−10825.5	−0.444661
$841$	23012.9	0.943579
$842$	−1345.67	−0.0550772
$843$	−592.765	−0.0242182
$844$	−8152.26	−0.332479
$845$	−2993.34	−0.121863
$846$	2163.37	0.0879177
$847$	−4890.70	−0.198402
$848$	−19989.5	−0.809486
$849$	62564.8	2.52912
$850$	613.373	0.0247512
$851$	−3804.04	−0.153232
$852$	−2875.57	−0.115628
$853$	25006.9	1.00378	0.501888	−	0.864933i	$-0.332639\pi$
$853$	25006.9	1.00378	0.501888	+	0.864933i	$0.332639\pi$
$854$	−3231.81	−0.129497
$855$	−77994.8	−3.11973
$856$	−29239.8	−1.16752
$857$	−37731.5	−1.50395	−0.751974	−	0.659193i	$-0.770898\pi$
$857$	−37731.5	−1.50395	−0.751974	+	0.659193i	$0.770898\pi$
$858$	−8881.27	−0.353382
$859$	10015.4	0.397815	0.198907	−	0.980018i	$-0.436261\pi$
$859$	10015.4	0.397815	0.198907	+	0.980018i	$0.436261\pi$
$860$	46257.3	1.83414
$861$	−8419.40	−0.333255
$862$	−12424.0	−0.490907
$863$	24605.4	0.970541	0.485270	−	0.874364i	$-0.338721\pi$
$863$	24605.4	0.970541	0.485270	+	0.874364i	$0.338721\pi$
$864$	27021.1	1.06398
$865$	−26584.5	−1.04497
$866$	−13638.7	−0.535176
$867$	2494.31	0.0977062
$868$	8444.32	0.330206
$869$	−8115.17	−0.316788
$870$	22229.0	0.866245
$871$	−1592.42	−0.0619483
$872$	−12735.2	−0.494572
$873$	50389.9	1.95354
$874$	4067.68	0.157427
$875$	−7704.88	−0.297683
$876$	−62587.8	−2.41398
$877$	6130.71	0.236054	0.118027	−	0.993010i	$-0.462343\pi$
$877$	6130.71	0.236054	0.118027	+	0.993010i	$0.462343\pi$
$878$	−4224.98	−0.162399
$879$	−48536.1	−1.86244
$880$	−14255.0	−0.546063
$881$	−25445.9	−0.973093	−0.486547	−	0.873655i	$-0.661744\pi$
$881$	−25445.9	−0.973093	−0.486547	+	0.873655i	$0.661744\pi$
$882$	2149.15	0.0820473
$883$	−39741.9	−1.51463	−0.757317	−	0.653047i	$-0.773490\pi$
$883$	−39741.9	−1.51463	−0.757317	+	0.653047i	$0.773490\pi$
$884$	−5383.58	−0.204830
$885$	−59130.6	−2.24594
$886$	5807.35	0.220205
$887$	7874.04	0.298066	0.149033	−	0.988832i	$-0.452384\pi$
$887$	7874.04	0.298066	0.149033	+	0.988832i	$0.452384\pi$
$888$	−13370.0	−0.505258
$889$	16829.9	0.634936
$890$	2881.54	0.108527
$891$	−6139.65	−0.230848
$892$	16245.1	0.609783
$893$	−6324.13	−0.236987
$894$	22220.0	0.831263
$895$	−52364.8	−1.95571
$896$	−9932.67	−0.370343
$897$	−13137.0	−0.488999
$898$	−368.903	−0.0137088
$899$	−36748.2	−1.36332
$900$	−13260.5	−0.491131
$901$	−7678.36	−0.283910
$902$	3236.37	0.119467
$903$	−30527.5	−1.12502
$904$	6251.37	0.229997
$905$	−22024.2	−0.808961
$906$	−21278.7	−0.780286
$907$	23000.7	0.842036	0.421018	−	0.907052i	$-0.361673\pi$
$907$	23000.7	0.842036	0.421018	+	0.907052i	$0.361673\pi$
$908$	−20278.6	−0.741155
$909$	−68364.9	−2.49452
$910$	3669.11	0.133659
$911$	41283.3	1.50140	0.750701	−	0.660642i	$-0.229716\pi$
$911$	41283.3	1.50140	0.750701	+	0.660642i	$0.229716\pi$
$912$	−48975.2	−1.77821
$913$	−5415.67	−0.196312
$914$	9439.38	0.341605
$915$	−55265.7	−1.99675
$916$	−1095.24	−0.0395063
$917$	17753.9	0.639350
$918$	2776.69	0.0998307
$919$	−5372.29	−0.192835	−0.0964176	−	0.995341i	$-0.530738\pi$
$919$	−5372.29	−0.192835	−0.0964176	+	0.995341i	$0.530738\pi$
$920$	6155.27	0.220580
$921$	20463.9	0.732150
$922$	6354.66	0.226984
$923$	2065.56	0.0736605
$924$	10858.0	0.386583
$925$	4326.27	0.153780
$926$	−6890.04	−0.244515
$927$	85946.1	3.04513
$928$	33264.3	1.17668
$929$	42029.5	1.48433	0.742165	−	0.670217i	$-0.233799\pi$
$929$	42029.5	1.48433	0.742165	+	0.670217i	$0.233799\pi$
$930$	−17233.0	−0.607624
$931$	−6282.55	−0.221162
$932$	29363.5	1.03201
$933$	1884.83	0.0661377
$934$	1799.14	0.0630297
$935$	−5475.60	−0.191520
$936$	−29437.0	−1.02797
$937$	30940.8	1.07875	0.539376	−	0.842065i	$-0.318660\pi$
$937$	30940.8	1.07875	0.539376	+	0.842065i	$0.318660\pi$
$938$	−232.336	−0.00808747
$939$	71364.3	2.48018
$940$	−4515.45	−0.156678
$941$	−14300.7	−0.495419	−0.247710	−	0.968834i	$-0.579678\pi$
$941$	−14300.7	−0.495419	−0.247710	+	0.968834i	$0.579678\pi$
$942$	18941.4	0.655142
$943$	4787.19	0.165315
$944$	−23671.8	−0.816156
$945$	15857.4	0.545864
$946$	11734.6	0.403303
$947$	16921.0	0.580632	0.290316	−	0.956931i	$-0.406240\pi$
$947$	16921.0	0.580632	0.290316	+	0.956931i	$0.406240\pi$
$948$	−19907.1	−0.682016
$949$	44957.6	1.53781
$950$	−4626.11	−0.157990
$951$	−7705.65	−0.262748
$952$	−1664.69	−0.0566731
$953$	46473.9	1.57968	0.789841	−	0.613311i	$-0.210163\pi$
$953$	46473.9	1.57968	0.789841	+	0.613311i	$0.210163\pi$
$954$	−19810.3	−0.672307
$955$	6604.24	0.223778
$956$	21737.7	0.735405
$957$	−47252.2	−1.59608
$958$	9090.65	0.306582
$959$	10947.0	0.368611
$960$	−23542.4	−0.791486
$961$	−1302.03	−0.0437053
$962$	4531.54	0.151874
$963$	99266.5	3.32172
$964$	−28671.7	−0.957938
$965$	18273.1	0.609567
$966$	−1916.72	−0.0638399
$967$	25406.9	0.844912	0.422456	−	0.906383i	$-0.361168\pi$
$967$	25406.9	0.844912	0.422456	+	0.906383i	$0.361168\pi$
$968$	9773.68	0.324523
$969$	−18812.3	−0.623672
$970$	12551.6	0.415470
$971$	−33318.0	−1.10116	−0.550580	−	0.834783i	$-0.685593\pi$
$971$	−33318.0	−1.10116	−0.550580	+	0.834783i	$0.685593\pi$
$972$	19067.3	0.629201
$973$	−8812.15	−0.290344
$974$	1731.00	0.0569452
$975$	14940.5	0.490749
$976$	−22124.6	−0.725605
$977$	32933.1	1.07843	0.539213	−	0.842169i	$-0.318722\pi$
$977$	32933.1	1.07843	0.539213	+	0.842169i	$0.318722\pi$
$978$	29717.1	0.971623
$979$	−6125.30	−0.199965
$980$	−4485.76	−0.146217
$981$	43234.8	1.40711
$982$	5370.92	0.174535
$983$	−52466.3	−1.70235	−0.851177	−	0.524879i	$-0.824111\pi$
$983$	−52466.3	−1.70235	−0.851177	+	0.524879i	$0.824111\pi$
$984$	16825.5	0.545100
$985$	51547.2	1.66744
$986$	3418.25	0.110405
$987$	2979.97	0.0961028
$988$	40603.4	1.30745
$989$	17357.6	0.558079
$990$	−14127.1	−0.453525
$991$	−16779.9	−0.537872	−0.268936	−	0.963158i	$-0.586672\pi$
$991$	−16779.9	−0.537872	−0.268936	+	0.963158i	$0.586672\pi$
$992$	−25788.1	−0.825376
$993$	−39531.1	−1.26332
$994$	301.369	0.00961653
$995$	−33619.5	−1.07117
$996$	−13285.0	−0.422642
$997$	18850.4	0.598794	0.299397	−	0.954129i	$-0.403215\pi$
$997$	18850.4	0.598794	0.299397	+	0.954129i	$0.403215\pi$
$998$	7147.70	0.226710
$999$	19584.7	0.620253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.4.a.e.1.6	✓	9
3.2	odd	2		1071.4.a.r.1.4		9
4.3	odd	2		1904.4.a.s.1.2		9
7.6	odd	2		833.4.a.g.1.6		9
17.16	even	2		2023.4.a.h.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.e.1.6	✓	9	1.1	even	1	trivial
833.4.a.g.1.6		9	7.6	odd	2
1071.4.a.r.1.4		9	3.2	odd	2
1904.4.a.s.1.2		9	4.3	odd	2
2023.4.a.h.1.6		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)

\(f(q)\)	\(=\)	\(q+0.923542 q^{2} +8.63083 q^{3} -7.14707 q^{4} +12.8089 q^{5} +7.97094 q^{6} +7.00000 q^{7} -13.9890 q^{8} +47.4913 q^{9} +O(q^{10})\)	\(q+0.923542 q^{2} +8.63083 q^{3} -7.14707 q^{4} +12.8089 q^{5} +7.97094 q^{6} +7.00000 q^{7} -13.9890 q^{8} +47.4913 q^{9} +11.8296 q^{10} -25.1461 q^{11} -61.6852 q^{12} +44.3092 q^{13} +6.46480 q^{14} +110.551 q^{15} +44.2572 q^{16} +17.0000 q^{17} +43.8602 q^{18} -128.215 q^{19} -91.5461 q^{20} +60.4158 q^{21} -23.2235 q^{22} -34.3519 q^{23} -120.736 q^{24} +39.0678 q^{25} +40.9214 q^{26} +176.857 q^{27} -50.0295 q^{28} +217.720 q^{29} +102.099 q^{30} -168.787 q^{31} +152.785 q^{32} -217.032 q^{33} +15.7002 q^{34} +89.6623 q^{35} -339.424 q^{36} +110.738 q^{37} -118.412 q^{38} +382.426 q^{39} -179.183 q^{40} -139.358 q^{41} +55.7966 q^{42} -505.289 q^{43} +179.721 q^{44} +608.311 q^{45} -31.7254 q^{46} +49.3243 q^{47} +381.976 q^{48} +49.0000 q^{49} +36.0808 q^{50} +146.724 q^{51} -316.681 q^{52} -451.668 q^{53} +163.335 q^{54} -322.094 q^{55} -97.9227 q^{56} -1106.61 q^{57} +201.074 q^{58} -534.869 q^{59} -790.119 q^{60} -499.909 q^{61} -155.882 q^{62} +332.439 q^{63} -212.954 q^{64} +567.552 q^{65} -200.438 q^{66} -35.9387 q^{67} -121.500 q^{68} -296.485 q^{69} +82.8069 q^{70} +46.6169 q^{71} -664.354 q^{72} +1014.63 q^{73} +102.271 q^{74} +337.188 q^{75} +916.364 q^{76} -176.023 q^{77} +353.186 q^{78} +322.720 q^{79} +566.885 q^{80} +244.159 q^{81} -128.703 q^{82} +215.368 q^{83} -431.796 q^{84} +217.751 q^{85} -466.656 q^{86} +1879.10 q^{87} +351.768 q^{88} +243.588 q^{89} +561.801 q^{90} +310.165 q^{91} +245.515 q^{92} -1456.77 q^{93} +45.5531 q^{94} -1642.30 q^{95} +1318.66 q^{96} +1061.03 q^{97} +45.2536 q^{98} -1194.22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 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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