LMFDB - Embedded newform 667.4.a.a.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,4,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.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:	$39.3542739738$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.60367 q^{2} +1.17941 q^{3} +4.98643 q^{4} -5.88126 q^{5} +4.25019 q^{6} +15.2314 q^{7} -10.8599 q^{8} -25.6090 q^{9} +O(q^{10})$	\(q+3.60367 q^{2} +1.17941 q^{3} +4.98643 q^{4} -5.88126 q^{5} +4.25019 q^{6} +15.2314 q^{7} -10.8599 q^{8} -25.6090 q^{9} -21.1941 q^{10} +45.5935 q^{11} +5.88104 q^{12} -26.6791 q^{13} +54.8890 q^{14} -6.93640 q^{15} -79.0269 q^{16} -95.3500 q^{17} -92.2864 q^{18} -111.188 q^{19} -29.3265 q^{20} +17.9640 q^{21} +164.304 q^{22} +23.0000 q^{23} -12.8082 q^{24} -90.4108 q^{25} -96.1428 q^{26} -62.0474 q^{27} +75.9504 q^{28} -29.0000 q^{29} -24.9965 q^{30} +252.794 q^{31} -197.908 q^{32} +53.7734 q^{33} -343.610 q^{34} -89.5798 q^{35} -127.698 q^{36} +306.197 q^{37} -400.686 q^{38} -31.4656 q^{39} +63.8698 q^{40} +163.768 q^{41} +64.7365 q^{42} -391.207 q^{43} +227.349 q^{44} +150.613 q^{45} +82.8844 q^{46} -304.869 q^{47} -93.2050 q^{48} -111.004 q^{49} -325.811 q^{50} -112.457 q^{51} -133.034 q^{52} -636.234 q^{53} -223.598 q^{54} -268.147 q^{55} -165.411 q^{56} -131.136 q^{57} -104.506 q^{58} +213.668 q^{59} -34.5879 q^{60} -713.978 q^{61} +910.985 q^{62} -390.061 q^{63} -80.9789 q^{64} +156.907 q^{65} +193.781 q^{66} -782.849 q^{67} -475.457 q^{68} +27.1264 q^{69} -322.816 q^{70} +988.013 q^{71} +278.111 q^{72} -438.171 q^{73} +1103.43 q^{74} -106.631 q^{75} -554.434 q^{76} +694.454 q^{77} -113.392 q^{78} +278.665 q^{79} +464.778 q^{80} +618.264 q^{81} +590.167 q^{82} -726.517 q^{83} +89.5765 q^{84} +560.778 q^{85} -1409.78 q^{86} -34.2028 q^{87} -495.141 q^{88} -469.945 q^{89} +542.760 q^{90} -406.361 q^{91} +114.688 q^{92} +298.147 q^{93} -1098.65 q^{94} +653.928 q^{95} -233.414 q^{96} +9.51710 q^{97} -400.022 q^{98} -1167.60 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) $ 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9 - 52 * q^10 - 126 * q^11 - 173 * q^12 - 252 * q^13 + 112 * q^14 - 32 * q^15 + 312 * q^16 - 332 * q^17 - 225 * q^18 - 2 * q^19 - 747 * q^20 - 202 * q^21 - 127 * q^22 + 805 * q^23 - 494 * q^24 + 315 * q^25 - 677 * q^26 - 694 * q^27 - 529 * q^28 - 1015 * q^29 + 389 * q^30 - 652 * q^31 + 320 * q^32 - 290 * q^33 - 455 * q^34 - 940 * q^35 + 34 * q^36 - 528 * q^37 - 1218 * q^38 - 268 * q^39 - 806 * q^40 - 68 * q^41 - 1484 * q^42 - 162 * q^43 - 1817 * q^44 - 356 * q^45 - 138 * q^46 - 1200 * q^47 - 2153 * q^48 + 93 * q^49 - 1369 * q^50 - 270 * q^51 - 3134 * q^52 - 1892 * q^53 - 1221 * q^54 - 794 * q^55 + 191 * q^56 - 1764 * q^57 + 174 * q^58 - 1354 * q^59 + 159 * q^60 - 1274 * q^61 - 5413 * q^62 - 2904 * q^63 - 926 * q^64 - 548 * q^65 - 2477 * q^66 - 3212 * q^67 - 3901 * q^68 - 506 * q^69 - 2768 * q^70 - 2342 * q^71 - 2381 * q^72 + 916 * q^73 + 661 * q^74 - 4708 * q^75 - 2810 * q^76 - 5536 * q^77 - 2434 * q^78 + 2622 * q^79 - 5444 * q^80 + 607 * q^81 - 3687 * q^82 - 2702 * q^83 + 346 * q^84 - 3304 * q^85 - 5789 * q^86 + 638 * q^87 - 2252 * q^88 - 1620 * q^89 - 3933 * q^90 - 4016 * q^91 + 2668 * q^92 - 4942 * q^93 - 1413 * q^94 - 4528 * q^95 - 7920 * q^96 + 682 * q^97 + 152 * q^98 - 582 * 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 $

$2$	3.60367	1.27409	0.637045	−	0.770827i	$-0.280157\pi$
$2$	3.60367	1.27409	0.637045	+	0.770827i	$0.280157\pi$
$3$	1.17941	0.226977	0.113489	−	0.993539i	$-0.463797\pi$
$3$	1.17941	0.226977	0.113489	+	0.993539i	$0.463797\pi$
$4$	4.98643	0.623304
$5$	−5.88126	−0.526036	−0.263018	−	0.964791i	$-0.584718\pi$
$5$	−5.88126	−0.526036	−0.263018	+	0.964791i	$0.584718\pi$
$6$	4.25019	0.289189
$7$	15.2314	0.822419	0.411209	−	0.911541i	$-0.365107\pi$
$7$	15.2314	0.822419	0.411209	+	0.911541i	$0.365107\pi$
$8$	−10.8599	−0.479944
$9$	−25.6090	−0.948481
$10$	−21.1941	−0.670217
$11$	45.5935	1.24972	0.624862	−	0.780735i	$-0.285155\pi$
$11$	45.5935	1.24972	0.624862	+	0.780735i	$0.285155\pi$
$12$	5.88104	0.141476
$13$	−26.6791	−0.569190	−0.284595	−	0.958648i	$-0.591859\pi$
$13$	−26.6791	−0.569190	−0.284595	+	0.958648i	$0.591859\pi$
$14$	54.8890	1.04784
$15$	−6.93640	−0.119398
$16$	−79.0269	−1.23480
$17$	−95.3500	−1.36034	−0.680170	−	0.733054i	$-0.738094\pi$
$17$	−95.3500	−1.36034	−0.680170	+	0.733054i	$0.738094\pi$
$18$	−92.2864	−1.20845
$19$	−111.188	−1.34255	−0.671273	−	0.741210i	$-0.734252\pi$
$19$	−111.188	−1.34255	−0.671273	+	0.741210i	$0.734252\pi$
$20$	−29.3265	−0.327880
$21$	17.9640	0.186670
$22$	164.304	1.59226
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−12.8082	−0.108936
$25$	−90.4108	−0.723287
$26$	−96.1428	−0.725198
$27$	−62.0474	−0.442261
$28$	75.9504	0.512617
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−24.9965	−0.152124
$31$	252.794	1.46462	0.732308	−	0.680974i	$-0.238443\pi$
$31$	252.794	1.46462	0.732308	+	0.680974i	$0.238443\pi$
$32$	−197.908	−1.09330
$33$	53.7734	0.283659
$34$	−343.610	−1.73320
$35$	−89.5798	−0.432622
$36$	−127.698	−0.591193
$37$	306.197	1.36050	0.680249	−	0.732981i	$-0.261872\pi$
$37$	306.197	1.36050	0.680249	+	0.732981i	$0.261872\pi$
$38$	−400.686	−1.71052
$39$	−31.4656	−0.129193
$40$	63.8698	0.252468
$41$	163.768	0.623813	0.311906	−	0.950113i	$-0.399032\pi$
$41$	163.768	0.623813	0.311906	+	0.950113i	$0.399032\pi$
$42$	64.7365	0.237835
$43$	−391.207	−1.38741	−0.693704	−	0.720260i	$-0.744023\pi$
$43$	−391.207	−1.38741	−0.693704	+	0.720260i	$0.744023\pi$
$44$	227.349	0.778959
$45$	150.613	0.498935
$46$	82.8844	0.265666
$47$	−304.869	−0.946165	−0.473083	−	0.881018i	$-0.656859\pi$
$47$	−304.869	−0.946165	−0.473083	+	0.881018i	$0.656859\pi$
$48$	−93.2050	−0.280270
$49$	−111.004	−0.323627
$50$	−325.811	−0.921532
$51$	−112.457	−0.308766
$52$	−133.034	−0.354778
$53$	−636.234	−1.64893	−0.824466	−	0.565911i	$-0.808524\pi$
$53$	−636.234	−1.64893	−0.824466	+	0.565911i	$0.808524\pi$
$54$	−223.598	−0.563480
$55$	−268.147	−0.657400
$56$	−165.411	−0.394715
$57$	−131.136	−0.304727
$58$	−104.506	−0.236593
$59$	213.668	0.471479	0.235739	−	0.971816i	$-0.424249\pi$
$59$	213.668	0.471479	0.235739	+	0.971816i	$0.424249\pi$
$60$	−34.5879	−0.0744213
$61$	−713.978	−1.49861	−0.749307	−	0.662223i	$-0.769613\pi$
$61$	−713.978	−1.49861	−0.749307	+	0.662223i	$0.769613\pi$
$62$	910.985	1.86605
$63$	−390.061	−0.780049
$64$	−80.9789	−0.158162
$65$	156.907	0.299414
$66$	193.781	0.361407
$67$	−782.849	−1.42747	−0.713733	−	0.700418i	$-0.752997\pi$
$67$	−782.849	−1.42747	−0.713733	+	0.700418i	$0.752997\pi$
$68$	−475.457	−0.847906
$69$	27.1264	0.0473280
$70$	−322.816	−0.551199
$71$	988.013	1.65149	0.825744	−	0.564046i	$-0.190756\pi$
$71$	988.013	1.65149	0.825744	+	0.564046i	$0.190756\pi$
$72$	278.111	0.455218
$73$	−438.171	−0.702522	−0.351261	−	0.936278i	$-0.614247\pi$
$73$	−438.171	−0.702522	−0.351261	+	0.936278i	$0.614247\pi$
$74$	1103.43	1.73340
$75$	−106.631	−0.164169
$76$	−554.434	−0.836815
$77$	694.454	1.02780
$78$	−113.392	−0.164603
$79$	278.665	0.396864	0.198432	−	0.980115i	$-0.436415\pi$
$79$	278.665	0.396864	0.198432	+	0.980115i	$0.436415\pi$
$80$	464.778	0.649547
$81$	618.264	0.848098
$82$	590.167	0.794793
$83$	−726.517	−0.960791	−0.480396	−	0.877052i	$-0.659507\pi$
$83$	−726.517	−0.960791	−0.480396	+	0.877052i	$0.659507\pi$
$84$	89.5765	0.116352
$85$	560.778	0.715587
$86$	−1409.78	−1.76768
$87$	−34.2028	−0.0421486
$88$	−495.141	−0.599798
$89$	−469.945	−0.559708	−0.279854	−	0.960043i	$-0.590286\pi$
$89$	−469.945	−0.559708	−0.279854	+	0.960043i	$0.590286\pi$
$90$	542.760	0.635688
$91$	−406.361	−0.468112
$92$	114.688	0.129968
$93$	298.147	0.332434
$94$	−1098.65	−1.20550
$95$	653.928	0.706227
$96$	−233.414	−0.248153
$97$	9.51710	0.00996201	0.00498100	−	0.999988i	$-0.498414\pi$
$97$	9.51710	0.00996201	0.00498100	+	0.999988i	$0.498414\pi$
$98$	−400.022	−0.412330
$99$	−1167.60	−1.18534
$100$	−450.828	−0.450828
$101$	195.597	0.192699	0.0963496	−	0.995348i	$-0.469283\pi$
$101$	195.597	0.192699	0.0963496	+	0.995348i	$0.469283\pi$
$102$	−405.256	−0.393396
$103$	782.715	0.748769	0.374384	−	0.927274i	$-0.377854\pi$
$103$	782.715	0.748769	0.374384	+	0.927274i	$0.377854\pi$
$104$	289.733	0.273179
$105$	−105.651	−0.0981952
$106$	−2292.78	−2.10089
$107$	−1536.59	−1.38830	−0.694148	−	0.719832i	$-0.744219\pi$
$107$	−1536.59	−1.38830	−0.694148	+	0.719832i	$0.744219\pi$
$108$	−309.396	−0.275663
$109$	1197.24	1.05206	0.526031	−	0.850465i	$-0.323680\pi$
$109$	1197.24	1.05206	0.526031	+	0.850465i	$0.323680\pi$
$110$	−966.314	−0.837586
$111$	361.131	0.308802
$112$	−1203.69	−1.01552
$113$	2327.38	1.93753	0.968767	−	0.247972i	$-0.0797642\pi$
$113$	2327.38	1.93753	0.968767	+	0.247972i	$0.0797642\pi$
$114$	−472.573	−0.388250
$115$	−135.269	−0.109686
$116$	−144.607	−0.115745
$117$	683.226	0.539866
$118$	769.990	0.600706
$119$	−1452.32	−1.11877
$120$	75.3286	0.0573044
$121$	747.771	0.561812
$122$	−2572.94	−1.90937
$123$	193.150	0.141591
$124$	1260.54	0.912901
$125$	1266.89	0.906510
$126$	−1405.65	−0.993852
$127$	−271.370	−0.189608	−0.0948039	−	0.995496i	$-0.530222\pi$
$127$	−271.370	−0.189608	−0.0948039	+	0.995496i	$0.530222\pi$
$128$	1291.44	0.891784
$129$	−461.393	−0.314910
$130$	565.441	0.381480
$131$	−474.530	−0.316488	−0.158244	−	0.987400i	$-0.550583\pi$
$131$	−474.530	−0.316488	−0.158244	+	0.987400i	$0.550583\pi$
$132$	268.137	0.176806
$133$	−1693.56	−1.10414
$134$	−2821.13	−1.81872
$135$	364.917	0.232645
$136$	1035.49	0.652887
$137$	1450.70	0.904681	0.452341	−	0.891845i	$-0.350589\pi$
$137$	1450.70	0.904681	0.452341	+	0.891845i	$0.350589\pi$
$138$	97.7545	0.0603001
$139$	907.082	0.553509	0.276754	−	0.960941i	$-0.410741\pi$
$139$	907.082	0.553509	0.276754	+	0.960941i	$0.410741\pi$
$140$	−446.684	−0.269655
$141$	−359.565	−0.214758
$142$	3560.47	2.10414
$143$	−1216.40	−0.711330
$144$	2023.80	1.17118
$145$	170.556	0.0976824
$146$	−1579.02	−0.895075
$147$	−130.919	−0.0734560
$148$	1526.83	0.848005
$149$	3005.85	1.65268	0.826338	−	0.563174i	$-0.190420\pi$
$149$	3005.85	1.65268	0.826338	+	0.563174i	$0.190420\pi$
$150$	−384.264	−0.209167
$151$	1332.28	0.718009	0.359005	−	0.933336i	$-0.383116\pi$
$151$	1332.28	0.718009	0.359005	+	0.933336i	$0.383116\pi$
$152$	1207.49	0.644347
$153$	2441.82	1.29026
$154$	2502.58	1.30951
$155$	−1486.74	−0.770440
$156$	−156.901	−0.0805265
$157$	2685.70	1.36524	0.682619	−	0.730774i	$-0.260841\pi$
$157$	2685.70	1.36524	0.682619	+	0.730774i	$0.260841\pi$
$158$	1004.22	0.505641
$159$	−750.379	−0.374270
$160$	1163.95	0.575113
$161$	350.322	0.171486
$162$	2228.02	1.08055
$163$	−928.667	−0.446251	−0.223125	−	0.974790i	$-0.571626\pi$
$163$	−928.667	−0.446251	−0.223125	+	0.974790i	$0.571626\pi$
$164$	816.620	0.388825
$165$	−316.255	−0.149215
$166$	−2618.13	−1.22413
$167$	−690.167	−0.319801	−0.159900	−	0.987133i	$-0.551117\pi$
$167$	−690.167	−0.319801	−0.159900	+	0.987133i	$0.551117\pi$
$168$	−195.088	−0.0895912
$169$	−1485.22	−0.676023
$170$	2020.86	0.911722
$171$	2847.42	1.27338
$172$	−1950.73	−0.864778
$173$	−3064.08	−1.34657	−0.673287	−	0.739381i	$-0.735118\pi$
$173$	−3064.08	−1.34657	−0.673287	+	0.739381i	$0.735118\pi$
$174$	−123.256	−0.0537011
$175$	−1377.08	−0.594844
$176$	−3603.12	−1.54315
$177$	252.002	0.107015
$178$	−1693.53	−0.713119
$179$	−1066.54	−0.445344	−0.222672	−	0.974893i	$-0.571478\pi$
$179$	−1066.54	−0.445344	−0.222672	+	0.974893i	$0.571478\pi$
$180$	751.022	0.310988
$181$	3824.80	1.57069	0.785345	−	0.619058i	$-0.212486\pi$
$181$	3824.80	1.57069	0.785345	+	0.619058i	$0.212486\pi$
$182$	−1464.39	−0.596417
$183$	−842.071	−0.340151
$184$	−249.778	−0.100075
$185$	−1800.82	−0.715671
$186$	1074.42	0.423551
$187$	−4347.35	−1.70005
$188$	−1520.21	−0.589749
$189$	−945.070	−0.363723
$190$	2356.54	0.899797
$191$	−1482.44	−0.561601	−0.280801	−	0.959766i	$-0.590600\pi$
$191$	−1482.44	−0.561601	−0.280801	+	0.959766i	$0.590600\pi$
$192$	−95.5072	−0.0358991
$193$	275.906	0.102902	0.0514512	−	0.998676i	$-0.483615\pi$
$193$	275.906	0.102902	0.0514512	+	0.998676i	$0.483615\pi$
$194$	34.2965	0.0126925
$195$	185.057	0.0679601
$196$	−553.515	−0.201718
$197$	225.115	0.0814151	0.0407076	−	0.999171i	$-0.487039\pi$
$197$	225.115	0.0814151	0.0407076	+	0.999171i	$0.487039\pi$
$198$	−4207.66	−1.51023
$199$	2194.35	0.781674	0.390837	−	0.920460i	$-0.372186\pi$
$199$	2194.35	0.781674	0.390837	+	0.920460i	$0.372186\pi$
$200$	981.852	0.347137
$201$	−923.298	−0.324002
$202$	704.867	0.245516
$203$	−441.711	−0.152719
$204$	−560.757	−0.192455
$205$	−963.164	−0.328148
$206$	2820.64	0.953998
$207$	−589.007	−0.197772
$208$	2108.37	0.702833
$209$	−5069.48	−1.67781
$210$	−380.732	−0.125109
$211$	1953.16	0.637256	0.318628	−	0.947880i	$-0.396778\pi$
$211$	1953.16	0.637256	0.318628	+	0.947880i	$0.396778\pi$
$212$	−3172.54	−1.02779
$213$	1165.27	0.374850
$214$	−5537.36	−1.76881
$215$	2300.79	0.729826
$216$	673.829	0.212260
$217$	3850.40	1.20453
$218$	4314.46	1.34042
$219$	−516.783	−0.159456
$220$	−1337.10	−0.409760
$221$	2543.86	0.774291
$222$	1301.40	0.393441
$223$	−4152.44	−1.24694	−0.623471	−	0.781847i	$-0.714278\pi$
$223$	−4152.44	−1.24694	−0.623471	+	0.781847i	$0.714278\pi$
$224$	−3014.42	−0.899148
$225$	2315.33	0.686024
$226$	8387.10	2.46859
$227$	2687.45	0.785782	0.392891	−	0.919585i	$-0.371475\pi$
$227$	2687.45	0.785782	0.392891	+	0.919585i	$0.371475\pi$
$228$	−653.904	−0.189938
$229$	1141.90	0.329513	0.164757	−	0.986334i	$-0.447316\pi$
$229$	1141.90	0.329513	0.164757	+	0.986334i	$0.447316\pi$
$230$	−487.464	−0.139750
$231$	819.044	0.233286
$232$	314.937	0.0891234
$233$	−3046.03	−0.856447	−0.428223	−	0.903673i	$-0.640860\pi$
$233$	−3046.03	−0.856447	−0.428223	+	0.903673i	$0.640860\pi$
$234$	2462.12	0.687837
$235$	1793.02	0.497717
$236$	1065.44	0.293875
$237$	328.660	0.0900791
$238$	−5233.66	−1.42541
$239$	4598.96	1.24469	0.622347	−	0.782741i	$-0.286179\pi$
$239$	4598.96	1.24469	0.622347	+	0.782741i	$0.286179\pi$
$240$	548.162	0.147432
$241$	−1883.74	−0.503495	−0.251748	−	0.967793i	$-0.581005\pi$
$241$	−1883.74	−0.503495	−0.251748	+	0.967793i	$0.581005\pi$
$242$	2694.72	0.715798
$243$	2404.47	0.634759
$244$	−3560.20	−0.934093
$245$	652.844	0.170240
$246$	696.047	0.180400
$247$	2966.41	0.764163
$248$	−2745.31	−0.702933
$249$	−856.860	−0.218078
$250$	4565.44	1.15498
$251$	−3608.53	−0.907445	−0.453722	−	0.891143i	$-0.649904\pi$
$251$	−3608.53	−0.907445	−0.453722	+	0.891143i	$0.649904\pi$
$252$	−1945.01	−0.486208
$253$	1048.65	0.260586
$254$	−977.927	−0.241577
$255$	661.386	0.162422
$256$	5301.76	1.29437
$257$	−3802.69	−0.922978	−0.461489	−	0.887146i	$-0.652685\pi$
$257$	−3802.69	−0.922978	−0.461489	+	0.887146i	$0.652685\pi$
$258$	−1662.71	−0.401224
$259$	4663.81	1.11890
$260$	782.406	0.186626
$261$	742.661	0.176129
$262$	−1710.05	−0.403234
$263$	−8180.58	−1.91801	−0.959005	−	0.283390i	$-0.908541\pi$
$263$	−8180.58	−1.91801	−0.959005	+	0.283390i	$0.908541\pi$
$264$	−583.973	−0.136140
$265$	3741.85	0.867397
$266$	−6103.02	−1.40677
$267$	−554.256	−0.127041
$268$	−3903.62	−0.889745
$269$	−6538.87	−1.48209	−0.741044	−	0.671456i	$-0.765669\pi$
$269$	−6538.87	−1.48209	−0.741044	+	0.671456i	$0.765669\pi$
$270$	1315.04	0.296410
$271$	3560.65	0.798132	0.399066	−	0.916922i	$-0.369334\pi$
$271$	3560.65	0.798132	0.399066	+	0.916922i	$0.369334\pi$
$272$	7535.22	1.67974
$273$	−479.265	−0.106251
$274$	5227.83	1.15264
$275$	−4122.15	−0.903909
$276$	135.264	0.0294997
$277$	98.4069	0.0213455	0.0106727	−	0.999943i	$-0.496603\pi$
$277$	98.4069	0.0213455	0.0106727	+	0.999943i	$0.496603\pi$
$278$	3268.83	0.705220
$279$	−6473.79	−1.38916
$280$	972.827	0.207634
$281$	1532.10	0.325258	0.162629	−	0.986687i	$-0.448003\pi$
$281$	1532.10	0.325258	0.162629	+	0.986687i	$0.448003\pi$
$282$	−1295.75	−0.273621
$283$	−7358.81	−1.54571	−0.772855	−	0.634582i	$-0.781172\pi$
$283$	−7358.81	−1.54571	−0.772855	+	0.634582i	$0.781172\pi$
$284$	4926.66	1.02938
$285$	771.247	0.160297
$286$	−4383.49	−0.906298
$287$	2494.42	0.513035
$288$	5068.22	1.03697
$289$	4178.63	0.850525
$290$	614.629	0.124456
$291$	11.2245	0.00226115
$292$	−2184.91	−0.437885
$293$	5398.98	1.07649	0.538245	−	0.842788i	$-0.319087\pi$
$293$	5398.98	1.07649	0.538245	+	0.842788i	$0.319087\pi$
$294$	−471.789	−0.0935895
$295$	−1256.64	−0.248015
$296$	−3325.27	−0.652963
$297$	−2828.96	−0.552704
$298$	10832.1	2.10566
$299$	−613.620	−0.118684
$300$	−531.709	−0.102328
$301$	−5958.64	−1.14103
$302$	4801.10	0.914808
$303$	230.688	0.0437383
$304$	8786.88	1.65777
$305$	4199.09	0.788325
$306$	8799.51	1.64390
$307$	−7562.01	−1.40582	−0.702910	−	0.711279i	$-0.748116\pi$
$307$	−7562.01	−1.40582	−0.702910	+	0.711279i	$0.748116\pi$
$308$	3462.85	0.640630
$309$	923.139	0.169953
$310$	−5357.74	−0.981609
$311$	4278.38	0.780080	0.390040	−	0.920798i	$-0.372461\pi$
$311$	4278.38	0.780080	0.390040	+	0.920798i	$0.372461\pi$
$312$	341.713	0.0620054
$313$	−1843.51	−0.332912	−0.166456	−	0.986049i	$-0.553232\pi$
$313$	−1843.51	−0.332912	−0.166456	+	0.986049i	$0.553232\pi$
$314$	9678.38	1.73944
$315$	2294.05	0.410334
$316$	1389.55	0.247367
$317$	1207.87	0.214008	0.107004	−	0.994259i	$-0.465874\pi$
$317$	1207.87	0.214008	0.107004	+	0.994259i	$0.465874\pi$
$318$	−2704.12	−0.476853
$319$	−1322.21	−0.232068
$320$	476.258	0.0831989
$321$	−1812.27	−0.315111
$322$	1262.45	0.218489
$323$	10601.8	1.82632
$324$	3082.93	0.528623
$325$	2412.08	0.411687
$326$	−3346.61	−0.568563
$327$	1412.03	0.238794
$328$	−1778.51	−0.299395
$329$	−4643.59	−0.778144
$330$	−1139.68	−0.190113
$331$	−7135.54	−1.18491	−0.592455	−	0.805604i	$-0.701841\pi$
$331$	−7135.54	−1.18491	−0.592455	+	0.805604i	$0.701841\pi$
$332$	−3622.73	−0.598865
$333$	−7841.39	−1.29041
$334$	−2487.13	−0.407455
$335$	4604.13	0.750898
$336$	−1419.64	−0.230500
$337$	−3882.34	−0.627550	−0.313775	−	0.949497i	$-0.601594\pi$
$337$	−3882.34	−0.627550	−0.313775	+	0.949497i	$0.601594\pi$
$338$	−5352.25	−0.861314
$339$	2744.93	0.439776
$340$	2796.28	0.446029
$341$	11525.8	1.83037
$342$	10261.2	1.62240
$343$	−6915.12	−1.08858
$344$	4248.47	0.665879
$345$	−159.537	−0.0248962
$346$	−11041.9	−1.71566
$347$	−8207.02	−1.26967	−0.634836	−	0.772647i	$-0.718932\pi$
$347$	−8207.02	−1.26967	−0.634836	+	0.772647i	$0.718932\pi$
$348$	−170.550	−0.0262714
$349$	1646.41	0.252523	0.126262	−	0.991997i	$-0.459702\pi$
$349$	1646.41	0.252523	0.126262	+	0.991997i	$0.459702\pi$
$350$	−4962.56	−0.757885
$351$	1655.37	0.251730
$352$	−9023.32	−1.36632
$353$	−4193.33	−0.632262	−0.316131	−	0.948716i	$-0.602384\pi$
$353$	−4193.33	−0.632262	−0.316131	+	0.948716i	$0.602384\pi$
$354$	908.132	0.136347
$355$	−5810.76	−0.868741
$356$	−2343.35	−0.348869
$357$	−1712.87	−0.253935
$358$	−3843.44	−0.567409
$359$	4463.75	0.656234	0.328117	−	0.944637i	$-0.393586\pi$
$359$	4463.75	0.656234	0.328117	+	0.944637i	$0.393586\pi$
$360$	−1635.64	−0.239461
$361$	5503.87	0.802431
$362$	13783.3	2.00120
$363$	881.927	0.127518
$364$	−2026.29	−0.291776
$365$	2577.00	0.369551
$366$	−3034.54	−0.433383
$367$	−7448.13	−1.05937	−0.529685	−	0.848194i	$-0.677690\pi$
$367$	−7448.13	−1.05937	−0.529685	+	0.848194i	$0.677690\pi$
$368$	−1817.62	−0.257473
$369$	−4193.94	−0.591675
$370$	−6489.57	−0.911829
$371$	−9690.73	−1.35611
$372$	1486.69	0.207208
$373$	7925.57	1.10019	0.550095	−	0.835102i	$-0.314592\pi$
$373$	7925.57	1.10019	0.550095	+	0.835102i	$0.314592\pi$
$374$	−15666.4	−2.16602
$375$	1494.18	0.205757
$376$	3310.85	0.454106
$377$	773.695	0.105696
$378$	−3405.72	−0.463416
$379$	3711.89	0.503079	0.251540	−	0.967847i	$-0.419063\pi$
$379$	3711.89	0.503079	0.251540	+	0.967847i	$0.419063\pi$
$380$	3260.77	0.440194
$381$	−320.056	−0.0430366
$382$	−5342.23	−0.715530
$383$	−1958.83	−0.261336	−0.130668	−	0.991426i	$-0.541712\pi$
$383$	−1958.83	−0.261336	−0.130668	+	0.991426i	$0.541712\pi$
$384$	1523.14	0.202415
$385$	−4084.26	−0.540658
$386$	994.275	0.131107
$387$	10018.4	1.31593
$388$	47.4564	0.00620936
$389$	−12461.2	−1.62419	−0.812093	−	0.583527i	$-0.801672\pi$
$389$	−12461.2	−1.62419	−0.812093	+	0.583527i	$0.801672\pi$
$390$	666.885	0.0865873
$391$	−2193.05	−0.283650
$392$	1205.49	0.155323
$393$	−559.665	−0.0718355
$394$	811.240	0.103730
$395$	−1638.90	−0.208765
$396$	−5822.19	−0.738828
$397$	12920.6	1.63342	0.816708	−	0.577052i	$-0.195797\pi$
$397$	12920.6	1.63342	0.816708	+	0.577052i	$0.195797\pi$
$398$	7907.70	0.995923
$399$	−1997.39	−0.250613
$400$	7144.89	0.893111
$401$	2635.72	0.328233	0.164117	−	0.986441i	$-0.447523\pi$
$401$	2635.72	0.328233	0.164117	+	0.986441i	$0.447523\pi$
$402$	−3327.26	−0.412807
$403$	−6744.32	−0.833644
$404$	975.331	0.120110
$405$	−3636.17	−0.446130
$406$	−1591.78	−0.194578
$407$	13960.6	1.70025
$408$	1221.27	0.148190
$409$	−4987.34	−0.602954	−0.301477	−	0.953474i	$-0.597480\pi$
$409$	−4987.34	−0.602954	−0.301477	+	0.953474i	$0.597480\pi$
$410$	−3470.92	−0.418090
$411$	1710.96	0.205342
$412$	3902.95	0.466711
$413$	3254.47	0.387753
$414$	−2122.59	−0.251979
$415$	4272.84	0.505410
$416$	5280.01	0.622293
$417$	1069.82	0.125634
$418$	−18268.7	−2.13768
$419$	2740.64	0.319544	0.159772	−	0.987154i	$-0.448924\pi$
$419$	2740.64	0.319544	0.159772	+	0.987154i	$0.448924\pi$
$420$	−526.822	−0.0612055
$421$	9735.47	1.12703	0.563513	−	0.826107i	$-0.309449\pi$
$421$	9735.47	1.12703	0.563513	+	0.826107i	$0.309449\pi$
$422$	7038.54	0.811921
$423$	7807.40	0.897420
$424$	6909.43	0.791395
$425$	8620.67	0.983916
$426$	4199.25	0.477592
$427$	−10874.9	−1.23249
$428$	−7662.10	−0.865331
$429$	−1434.63	−0.161456
$430$	8291.29	0.929864
$431$	−2437.05	−0.272364	−0.136182	−	0.990684i	$-0.543483\pi$
$431$	−2437.05	−0.272364	−0.136182	+	0.990684i	$0.543483\pi$
$432$	4903.42	0.546102
$433$	−14252.5	−1.58183	−0.790916	−	0.611925i	$-0.790395\pi$
$433$	−14252.5	−1.58183	−0.790916	+	0.611925i	$0.790395\pi$
$434$	13875.6	1.53468
$435$	201.156	0.0221717
$436$	5969.96	0.655755
$437$	−2557.33	−0.279940
$438$	−1862.31	−0.203162
$439$	−2710.69	−0.294702	−0.147351	−	0.989084i	$-0.547075\pi$
$439$	−2710.69	−0.294702	−0.147351	+	0.989084i	$0.547075\pi$
$440$	2912.05	0.315515
$441$	2842.71	0.306955
$442$	9167.22	0.986517
$443$	−1492.51	−0.160071	−0.0800354	−	0.996792i	$-0.525503\pi$
$443$	−1492.51	−0.160071	−0.0800354	+	0.996792i	$0.525503\pi$
$444$	1800.76	0.192478
$445$	2763.87	0.294427
$446$	−14964.0	−1.58871
$447$	3545.12	0.375120
$448$	−1233.42	−0.130075
$449$	−14608.0	−1.53540	−0.767700	−	0.640810i	$-0.778599\pi$
$449$	−14608.0	−1.53540	−0.767700	+	0.640810i	$0.778599\pi$
$450$	8343.69	0.874056
$451$	7466.78	0.779594
$452$	11605.3	1.20767
$453$	1571.30	0.162972
$454$	9684.69	1.00116
$455$	2389.91	0.246244
$456$	1424.13	0.146252
$457$	3150.49	0.322481	0.161240	−	0.986915i	$-0.448451\pi$
$457$	3150.49	0.322481	0.161240	+	0.986915i	$0.448451\pi$
$458$	4115.01	0.419830
$459$	5916.23	0.601625
$460$	−674.510	−0.0683678
$461$	−3784.61	−0.382358	−0.191179	−	0.981555i	$-0.561231\pi$
$461$	−3784.61	−0.382358	−0.191179	+	0.981555i	$0.561231\pi$
$462$	2951.56	0.297228
$463$	−2613.70	−0.262352	−0.131176	−	0.991359i	$-0.541875\pi$
$463$	−2613.70	−0.262352	−0.131176	+	0.991359i	$0.541875\pi$
$464$	2291.78	0.229296
$465$	−1753.48	−0.174872
$466$	−10976.9	−1.09119
$467$	−10275.9	−1.01823	−0.509114	−	0.860699i	$-0.670027\pi$
$467$	−10275.9	−1.01823	−0.509114	+	0.860699i	$0.670027\pi$
$468$	3406.86	0.336501
$469$	−11923.9	−1.17397
$470$	6461.44	0.634136
$471$	3167.54	0.309878
$472$	−2320.42	−0.226284
$473$	−17836.5	−1.73388
$474$	1184.38	0.114769
$475$	10052.6	0.971046
$476$	−7241.88	−0.697334
$477$	16293.3	1.56398
$478$	16573.1	1.58585
$479$	5916.07	0.564326	0.282163	−	0.959366i	$-0.408948\pi$
$479$	5916.07	0.564326	0.282163	+	0.959366i	$0.408948\pi$
$480$	1372.77	0.130537
$481$	−8169.07	−0.774382
$482$	−6788.38	−0.641498
$483$	413.173	0.0389234
$484$	3728.71	0.350180
$485$	−55.9725	−0.00524037
$486$	8664.90	0.808740
$487$	446.065	0.0415054	0.0207527	−	0.999785i	$-0.493394\pi$
$487$	446.065	0.0415054	0.0207527	+	0.999785i	$0.493394\pi$
$488$	7753.72	0.719251
$489$	−1095.28	−0.101289
$490$	2352.63	0.216900
$491$	17723.9	1.62906	0.814532	−	0.580119i	$-0.196994\pi$
$491$	17723.9	1.62906	0.814532	+	0.580119i	$0.196994\pi$
$492$	963.128	0.0882544
$493$	2765.15	0.252609
$494$	10690.0	0.973613
$495$	6866.99	0.623531
$496$	−19977.5	−1.80850
$497$	15048.8	1.35821
$498$	−3087.84	−0.277850
$499$	−3277.90	−0.294066	−0.147033	−	0.989132i	$-0.546972\pi$
$499$	−3277.90	−0.294066	−0.147033	+	0.989132i	$0.546972\pi$
$500$	6317.25	0.565032
$501$	−813.988	−0.0725874
$502$	−13004.0	−1.15617
$503$	9072.87	0.804253	0.402127	−	0.915584i	$-0.368271\pi$
$503$	9072.87	0.804253	0.402127	+	0.915584i	$0.368271\pi$
$504$	4236.02	0.374380
$505$	−1150.36	−0.101367
$506$	3778.99	0.332009
$507$	−1751.68	−0.153442
$508$	−1353.17	−0.118183
$509$	−17060.3	−1.48563	−0.742814	−	0.669498i	$-0.766509\pi$
$509$	−17060.3	−1.48563	−0.742814	+	0.669498i	$0.766509\pi$
$510$	2383.42	0.206940
$511$	−6673.97	−0.577767
$512$	8774.26	0.757366
$513$	6898.96	0.593755
$514$	−13703.6	−1.17596
$515$	−4603.35	−0.393879
$516$	−2300.71	−0.196285
$517$	−13900.1	−1.18245
$518$	16806.8	1.42558
$519$	−3613.79	−0.305641
$520$	−1703.99	−0.143702
$521$	−8029.68	−0.675215	−0.337607	−	0.941287i	$-0.609618\pi$
$521$	−8029.68	−0.675215	−0.337607	+	0.941287i	$0.609618\pi$
$522$	2676.30	0.224404
$523$	12402.7	1.03697	0.518483	−	0.855088i	$-0.326497\pi$
$523$	12402.7	1.03697	0.518483	+	0.855088i	$0.326497\pi$
$524$	−2366.22	−0.197268
$525$	−1624.14	−0.135016
$526$	−29480.1	−2.44372
$527$	−24103.9	−1.99237
$528$	−4249.54	−0.350261
$529$	529.000	0.0434783
$530$	13484.4	1.10514
$531$	−5471.83	−0.447189
$532$	−8444.81	−0.688212
$533$	−4369.20	−0.355068
$534$	−1997.36	−0.161862
$535$	9037.08	0.730293
$536$	8501.65	0.685104
$537$	−1257.88	−0.101083
$538$	−23563.9	−1.88831
$539$	−5061.07	−0.404445
$540$	1819.63	0.145009
$541$	−1887.67	−0.150013	−0.0750067	−	0.997183i	$-0.523898\pi$
$541$	−1887.67	−0.150013	−0.0750067	+	0.997183i	$0.523898\pi$
$542$	12831.4	1.01689
$543$	4510.99	0.356511
$544$	18870.5	1.48726
$545$	−7041.27	−0.553422
$546$	−1727.11	−0.135373
$547$	10299.1	0.805045	0.402522	−	0.915410i	$-0.368134\pi$
$547$	10299.1	0.805045	0.402522	+	0.915410i	$0.368134\pi$
$548$	7233.80	0.563892
$549$	18284.3	1.42141
$550$	−14854.9	−1.15166
$551$	3224.47	0.249305
$552$	−294.590	−0.0227148
$553$	4244.46	0.326389
$554$	354.626	0.0271961
$555$	−2123.90	−0.162441
$556$	4523.11	0.345004
$557$	−15294.1	−1.16343	−0.581717	−	0.813391i	$-0.697619\pi$
$557$	−15294.1	−1.16343	−0.581717	+	0.813391i	$0.697619\pi$
$558$	−23329.4	−1.76991
$559$	10437.1	0.789699
$560$	7079.22	0.534199
$561$	−5127.29	−0.385872
$562$	5521.18	0.414408
$563$	20741.5	1.55266	0.776331	−	0.630326i	$-0.217079\pi$
$563$	20741.5	1.55266	0.776331	+	0.630326i	$0.217079\pi$
$564$	−1792.95	−0.133860
$565$	−13687.9	−1.01921
$566$	−26518.7	−1.96937
$567$	9417.03	0.697492
$568$	−10729.7	−0.792621
$569$	−23205.9	−1.70974	−0.854869	−	0.518844i	$-0.826363\pi$
$569$	−23205.9	−1.70974	−0.854869	+	0.518844i	$0.826363\pi$
$570$	2779.32	0.204233
$571$	−1420.92	−0.104139	−0.0520696	−	0.998643i	$-0.516582\pi$
$571$	−1420.92	−0.104139	−0.0520696	+	0.998643i	$0.516582\pi$
$572$	−6065.48	−0.443375
$573$	−1748.40	−0.127471
$574$	8989.08	0.653653
$575$	−2079.45	−0.150816
$576$	2073.79	0.150014
$577$	−17885.0	−1.29040	−0.645202	−	0.764012i	$-0.723227\pi$
$577$	−17885.0	−1.29040	−0.645202	+	0.764012i	$0.723227\pi$
$578$	15058.4	1.08364
$579$	325.406	0.0233565
$580$	850.469	0.0608858
$581$	−11065.9	−0.790173
$582$	40.4495	0.00288090
$583$	−29008.1	−2.06071
$584$	4758.49	0.337171
$585$	−4018.23	−0.283989
$586$	19456.1	1.37155
$587$	−11295.8	−0.794252	−0.397126	−	0.917764i	$-0.629992\pi$
$587$	−11295.8	−0.794252	−0.397126	+	0.917764i	$0.629992\pi$
$588$	−652.820	−0.0457854
$589$	−28107.7	−1.96631
$590$	−4528.51	−0.315993
$591$	265.502	0.0184794
$592$	−24197.8	−1.67994
$593$	−4848.96	−0.335789	−0.167895	−	0.985805i	$-0.553697\pi$
$593$	−4848.96	−0.335789	−0.167895	+	0.985805i	$0.553697\pi$
$594$	−10194.6	−0.704194
$595$	8541.44	0.588512
$596$	14988.5	1.03012
$597$	2588.03	0.177422
$598$	−2211.29	−0.151214
$599$	−9697.34	−0.661473	−0.330737	−	0.943723i	$-0.607297\pi$
$599$	−9697.34	−0.661473	−0.330737	+	0.943723i	$0.607297\pi$
$600$	1158.00	0.0787921
$601$	13419.7	0.910820	0.455410	−	0.890282i	$-0.349493\pi$
$601$	13419.7	0.910820	0.455410	+	0.890282i	$0.349493\pi$
$602$	−21473.0	−1.45378
$603$	20048.0	1.35392
$604$	6643.33	0.447538
$605$	−4397.83	−0.295533
$606$	831.325	0.0557265
$607$	11849.2	0.792330	0.396165	−	0.918179i	$-0.370341\pi$
$607$	11849.2	0.792330	0.396165	+	0.918179i	$0.370341\pi$
$608$	22005.1	1.46780
$609$	−520.957	−0.0346638
$610$	15132.1	1.00440
$611$	8133.66	0.538548
$612$	12176.0	0.804223
$613$	−17736.1	−1.16861	−0.584303	−	0.811535i	$-0.698632\pi$
$613$	−17736.1	−1.16861	−0.584303	+	0.811535i	$0.698632\pi$
$614$	−27251.0	−1.79114
$615$	−1135.96	−0.0744820
$616$	−7541.70	−0.493285
$617$	4606.21	0.300550	0.150275	−	0.988644i	$-0.451984\pi$
$617$	4606.21	0.300550	0.150275	+	0.988644i	$0.451984\pi$
$618$	3326.69	0.216536
$619$	5774.82	0.374975	0.187488	−	0.982267i	$-0.439966\pi$
$619$	5774.82	0.374975	0.187488	+	0.982267i	$0.439966\pi$
$620$	−7413.55	−0.480218
$621$	−1427.09	−0.0922177
$622$	15417.9	0.993892
$623$	−7157.92	−0.460315
$624$	2486.63	0.159527
$625$	3850.47	0.246430
$626$	−6643.42	−0.424160
$627$	−5978.98	−0.380825
$628$	13392.1	0.850959
$629$	−29195.9	−1.85074
$630$	8267.00	0.522802
$631$	−12860.9	−0.811385	−0.405693	−	0.914010i	$-0.632970\pi$
$631$	−12860.9	−0.811385	−0.405693	+	0.914010i	$0.632970\pi$
$632$	−3026.28	−0.190473
$633$	2303.57	0.144642
$634$	4352.75	0.272665
$635$	1596.00	0.0997404
$636$	−3741.71	−0.233284
$637$	2961.50	0.184205
$638$	−4764.82	−0.295675
$639$	−25302.0	−1.56641
$640$	−7595.30	−0.469110
$641$	−14446.6	−0.890181	−0.445090	−	0.895486i	$-0.646828\pi$
$641$	−14446.6	−0.890181	−0.445090	+	0.895486i	$0.646828\pi$
$642$	−6530.80	−0.401480
$643$	−2159.72	−0.132459	−0.0662294	−	0.997804i	$-0.521097\pi$
$643$	−2159.72	−0.132459	−0.0662294	+	0.997804i	$0.521097\pi$
$644$	1746.86	0.106888
$645$	2713.57	0.165654
$646$	38205.5	2.32689
$647$	4489.22	0.272781	0.136391	−	0.990655i	$-0.456450\pi$
$647$	4489.22	0.272781	0.136391	+	0.990655i	$0.456450\pi$
$648$	−6714.28	−0.407040
$649$	9741.90	0.589219
$650$	8692.35	0.524526
$651$	4541.19	0.273400
$652$	−4630.74	−0.278150
$653$	19734.4	1.18265	0.591323	−	0.806435i	$-0.298606\pi$
$653$	19734.4	1.18265	0.591323	+	0.806435i	$0.298606\pi$
$654$	5088.50	0.304245
$655$	2790.84	0.166484
$656$	−12942.1	−0.770282
$657$	11221.1	0.666329
$658$	−16734.0	−0.991425
$659$	−28489.8	−1.68407	−0.842037	−	0.539420i	$-0.818644\pi$
$659$	−28489.8	−1.68407	−0.842037	+	0.539420i	$0.818644\pi$
$660$	−1576.98	−0.0930061
$661$	−26358.2	−1.55101	−0.775503	−	0.631344i	$-0.782504\pi$
$661$	−26358.2	−1.55101	−0.775503	+	0.631344i	$0.782504\pi$
$662$	−25714.1	−1.50968
$663$	3000.24	0.175746
$664$	7889.90	0.461126
$665$	9960.24	0.580815
$666$	−28257.8	−1.64409
$667$	−667.000	−0.0387202
$668$	−3441.47	−0.199333
$669$	−4897.42	−0.283027
$670$	16591.8	0.956711
$671$	−32552.8	−1.87286
$672$	−3555.22	−0.204086
$673$	22062.9	1.26369	0.631844	−	0.775096i	$-0.282298\pi$
$673$	22062.9	1.26369	0.631844	+	0.775096i	$0.282298\pi$
$674$	−13990.7	−0.799555
$675$	5609.76	0.319881
$676$	−7405.97	−0.421368
$677$	31824.2	1.80665	0.903325	−	0.428957i	$-0.141119\pi$
$677$	31824.2	1.80665	0.903325	+	0.428957i	$0.141119\pi$
$678$	9891.81	0.560314
$679$	144.959	0.00819294
$680$	−6089.99	−0.343442
$681$	3169.60	0.178354
$682$	41535.0	2.33205
$683$	−8038.76	−0.450358	−0.225179	−	0.974317i	$-0.572297\pi$
$683$	−8038.76	−0.450358	−0.225179	+	0.974317i	$0.572297\pi$
$684$	14198.5	0.793703
$685$	−8531.92	−0.475895
$686$	−24919.8	−1.38694
$687$	1346.76	0.0747920
$688$	30915.9	1.71317
$689$	16974.2	0.938555
$690$	−574.919	−0.0317200
$691$	10220.9	0.562696	0.281348	−	0.959606i	$-0.409218\pi$
$691$	10220.9	0.562696	0.281348	+	0.959606i	$0.409218\pi$
$692$	−15278.8	−0.839326
$693$	−17784.3	−0.974846
$694$	−29575.4	−1.61768
$695$	−5334.79	−0.291165
$696$	371.439	0.0202290
$697$	−15615.3	−0.848597
$698$	5933.13	0.321737
$699$	−3592.51	−0.194394
$700$	−6866.74	−0.370769
$701$	32741.0	1.76406	0.882032	−	0.471189i	$-0.156175\pi$
$701$	32741.0	1.76406	0.882032	+	0.471189i	$0.156175\pi$
$702$	5965.42	0.320727
$703$	−34045.6	−1.82653
$704$	−3692.12	−0.197659
$705$	2114.70	0.112970
$706$	−15111.4	−0.805559
$707$	2979.22	0.158479
$708$	1256.59	0.0667029
$709$	−5246.50	−0.277907	−0.138954	−	0.990299i	$-0.544374\pi$
$709$	−5246.50	−0.277907	−0.138954	+	0.990299i	$0.544374\pi$
$710$	−20940.1	−1.10685
$711$	−7136.34	−0.376419
$712$	5103.55	0.268629
$713$	5814.25	0.305393
$714$	−6172.62	−0.323536
$715$	7153.94	0.374185
$716$	−5318.21	−0.277585
$717$	5424.05	0.282517
$718$	16085.9	0.836100
$719$	−30675.9	−1.59112	−0.795562	−	0.605873i	$-0.792824\pi$
$719$	−30675.9	−1.59112	−0.795562	+	0.605873i	$0.792824\pi$
$720$	−11902.5	−0.616083
$721$	11921.8	0.615801
$722$	19834.1	1.02237
$723$	−2221.70	−0.114282
$724$	19072.1	0.979018
$725$	2621.91	0.134311
$726$	3178.17	0.162470
$727$	−5657.91	−0.288639	−0.144319	−	0.989531i	$-0.546099\pi$
$727$	−5657.91	−0.288639	−0.144319	+	0.989531i	$0.546099\pi$
$728$	4413.04	0.224668
$729$	−13857.3	−0.704023
$730$	9286.65	0.470842
$731$	37301.6	1.88735
$732$	−4198.93	−0.212018
$733$	−33290.6	−1.67751	−0.838757	−	0.544506i	$-0.816717\pi$
$733$	−33290.6	−1.67751	−0.838757	+	0.544506i	$0.816717\pi$
$734$	−26840.6	−1.34973
$735$	769.969	0.0386405
$736$	−4551.88	−0.227968
$737$	−35692.8	−1.78394
$738$	−15113.6	−0.753847
$739$	−23382.6	−1.16393	−0.581963	−	0.813215i	$-0.697715\pi$
$739$	−23382.6	−1.16393	−0.581963	+	0.813215i	$0.697715\pi$
$740$	−8979.68	−0.446081
$741$	3498.61	0.173448
$742$	−34922.2	−1.72781
$743$	−23083.9	−1.13979	−0.569896	−	0.821717i	$-0.693017\pi$
$743$	−23083.9	−1.13979	−0.569896	+	0.821717i	$0.693017\pi$
$744$	−3237.84	−0.159550
$745$	−17678.2	−0.869367
$746$	28561.2	1.40174
$747$	18605.4	0.911292
$748$	−21677.8	−1.05965
$749$	−23404.4	−1.14176
$750$	5384.51	0.262153
$751$	17996.5	0.874436	0.437218	−	0.899356i	$-0.355964\pi$
$751$	17996.5	0.874436	0.437218	+	0.899356i	$0.355964\pi$
$752$	24092.9	1.16832
$753$	−4255.93	−0.205969
$754$	2788.14	0.134666
$755$	−7835.48	−0.377698
$756$	−4712.53	−0.226710
$757$	31212.2	1.49858	0.749291	−	0.662241i	$-0.230394\pi$
$757$	31212.2	1.49858	0.749291	+	0.662241i	$0.230394\pi$
$758$	13376.4	0.640968
$759$	1236.79	0.0591470
$760$	−7101.59	−0.338950
$761$	13653.7	0.650389	0.325194	−	0.945647i	$-0.394570\pi$
$761$	13653.7	0.650389	0.325194	+	0.945647i	$0.394570\pi$
$762$	−1153.37	−0.0548325
$763$	18235.6	0.865235
$764$	−7392.10	−0.350048
$765$	−14361.0	−0.678721
$766$	−7058.98	−0.332965
$767$	−5700.49	−0.268361
$768$	6252.93	0.293793
$769$	14672.3	0.688032	0.344016	−	0.938964i	$-0.388213\pi$
$769$	14672.3	0.688032	0.344016	+	0.938964i	$0.388213\pi$
$770$	−14718.3	−0.688847
$771$	−4484.92	−0.209495
$772$	1375.79	0.0641395
$773$	3926.31	0.182690	0.0913450	−	0.995819i	$-0.470883\pi$
$773$	3926.31	0.182690	0.0913450	+	0.995819i	$0.470883\pi$
$774$	36103.1	1.67661
$775$	−22855.3	−1.05934
$776$	−103.355	−0.00478121
$777$	5500.53	0.253965
$778$	−44906.1	−2.06936
$779$	−18209.2	−0.837498
$780$	922.776	0.0423598
$781$	45047.0	2.06390
$782$	−7903.03	−0.361396
$783$	1799.38	0.0821257
$784$	8772.32	0.399614
$785$	−15795.3	−0.718164
$786$	−2016.85	−0.0915249
$787$	15384.9	0.696837	0.348419	−	0.937339i	$-0.386719\pi$
$787$	15384.9	0.696837	0.348419	+	0.937339i	$0.386719\pi$
$788$	1122.52	0.0507464
$789$	−9648.24	−0.435344
$790$	−5906.06	−0.265985
$791$	35449.3	1.59346
$792$	12680.1	0.568897
$793$	19048.3	0.852996
$794$	46561.5	2.08112
$795$	4413.17	0.196879
$796$	10942.0	0.487221
$797$	−30345.3	−1.34867	−0.674333	−	0.738427i	$-0.735569\pi$
$797$	−30345.3	−1.34867	−0.674333	+	0.738427i	$0.735569\pi$
$798$	−7197.95	−0.319304
$799$	29069.3	1.28711
$800$	17893.0	0.790767
$801$	12034.8	0.530873
$802$	9498.27	0.418199
$803$	−19977.8	−0.877958
$804$	−4603.96	−0.201952
$805$	−2060.34	−0.0902078
$806$	−24304.3	−1.06214
$807$	−7711.99	−0.336400
$808$	−2124.16	−0.0924848
$809$	18784.5	0.816350	0.408175	−	0.912904i	$-0.366165\pi$
$809$	18784.5	0.816350	0.408175	+	0.912904i	$0.366165\pi$
$810$	−13103.5	−0.568410
$811$	6745.25	0.292056	0.146028	−	0.989280i	$-0.453351\pi$
$811$	6745.25	0.292056	0.146028	+	0.989280i	$0.453351\pi$
$812$	−2202.56	−0.0951906
$813$	4199.45	0.181158
$814$	50309.4	2.16627
$815$	5461.73	0.234744
$816$	8887.10	0.381263
$817$	43497.8	1.86266
$818$	−17972.7	−0.768217
$819$	10406.5	0.443996
$820$	−4802.75	−0.204536
$821$	28192.8	1.19846	0.599230	−	0.800577i	$-0.295474\pi$
$821$	28192.8	1.19846	0.599230	+	0.800577i	$0.295474\pi$
$822$	6165.74	0.261624
$823$	−13574.7	−0.574951	−0.287475	−	0.957788i	$-0.592816\pi$
$823$	−13574.7	−0.574951	−0.287475	+	0.957788i	$0.592816\pi$
$824$	−8500.20	−0.359367
$825$	−4861.69	−0.205167
$826$	11728.0	0.494032
$827$	−17679.6	−0.743384	−0.371692	−	0.928356i	$-0.621222\pi$
$827$	−17679.6	−0.743384	−0.371692	+	0.928356i	$0.621222\pi$
$828$	−2937.04	−0.123272
$829$	−37818.7	−1.58444	−0.792219	−	0.610237i	$-0.791074\pi$
$829$	−37818.7	−1.58444	−0.792219	+	0.610237i	$0.791074\pi$
$830$	15397.9	0.643938
$831$	116.062	0.00484493
$832$	2160.45	0.0900242
$833$	10584.3	0.440243
$834$	3855.28	0.160069
$835$	4059.05	0.168226
$836$	−25278.6	−1.04579
$837$	−15685.2	−0.647742
$838$	9876.35	0.407128
$839$	6360.48	0.261726	0.130863	−	0.991400i	$-0.458225\pi$
$839$	6360.48	0.261726	0.130863	+	0.991400i	$0.458225\pi$
$840$	1147.36	0.0471282
$841$	841.000	0.0344828
$842$	35083.4	1.43593
$843$	1806.97	0.0738260
$844$	9739.30	0.397204
$845$	8734.98	0.355612
$846$	28135.3	1.14339
$847$	11389.6	0.462044
$848$	50279.6	2.03609
$849$	−8679.04	−0.350841
$850$	31066.1	1.25360
$851$	7042.53	0.283684
$852$	5810.54	0.233645
$853$	−3652.06	−0.146593	−0.0732966	−	0.997310i	$-0.523352\pi$
$853$	−3652.06	−0.146593	−0.0732966	+	0.997310i	$0.523352\pi$
$854$	−39189.5	−1.57030
$855$	−16746.4	−0.669843
$856$	16687.2	0.666305
$857$	−17631.9	−0.702793	−0.351397	−	0.936227i	$-0.614293\pi$
$857$	−17631.9	−0.702793	−0.351397	+	0.936227i	$0.614293\pi$
$858$	−5169.92	−0.205709
$859$	11840.8	0.470317	0.235159	−	0.971957i	$-0.424439\pi$
$859$	11840.8	0.470317	0.235159	+	0.971957i	$0.424439\pi$
$860$	11472.7	0.454904
$861$	2941.94	0.116447
$862$	−8782.33	−0.347016
$863$	41010.6	1.61763	0.808815	−	0.588063i	$-0.200109\pi$
$863$	41010.6	1.61763	0.808815	+	0.588063i	$0.200109\pi$
$864$	12279.7	0.483522
$865$	18020.6	0.708346
$866$	−51361.4	−2.01539
$867$	4928.31	0.193050
$868$	19199.8	0.750787
$869$	12705.3	0.495971
$870$	724.898	0.0282487
$871$	20885.7	0.812498
$872$	−13001.9	−0.504931
$873$	−243.723	−0.00944878
$874$	−9215.79	−0.356669
$875$	19296.5	0.745531
$876$	−2576.90	−0.0993898
$877$	−42880.6	−1.65105	−0.825527	−	0.564363i	$-0.809122\pi$
$877$	−42880.6	−1.65105	−0.825527	+	0.564363i	$0.809122\pi$
$878$	−9768.45	−0.375477
$879$	6367.59	0.244339
$880$	21190.9	0.811755
$881$	−36645.3	−1.40138	−0.700688	−	0.713468i	$-0.747123\pi$
$881$	−36645.3	−1.40138	−0.700688	+	0.713468i	$0.747123\pi$
$882$	10244.2	0.391088
$883$	−26863.8	−1.02383	−0.511914	−	0.859037i	$-0.671063\pi$
$883$	−26863.8	−1.02383	−0.511914	+	0.859037i	$0.671063\pi$
$884$	12684.8	0.482619
$885$	−1482.09	−0.0562937
$886$	−5378.52	−0.203945
$887$	−9899.40	−0.374734	−0.187367	−	0.982290i	$-0.559995\pi$
$887$	−9899.40	−0.374734	−0.187367	+	0.982290i	$0.559995\pi$
$888$	−3921.84	−0.148208
$889$	−4133.35	−0.155937
$890$	9960.06	0.375126
$891$	28188.8	1.05989
$892$	−20705.9	−0.777224
$893$	33898.0	1.27027
$894$	12775.4	0.477936
$895$	6272.57	0.234267
$896$	19670.5	0.733420
$897$	−723.708	−0.0269386
$898$	−52642.4	−1.95624
$899$	−7331.01	−0.271972
$900$	11545.2	0.427602
$901$	60664.9	2.24311
$902$	26907.8	0.993273
$903$	−7027.66	−0.258988
$904$	−25275.1	−0.929908
$905$	−22494.6	−0.826239
$906$	5662.45	0.207640
$907$	−3680.50	−0.134740	−0.0673699	−	0.997728i	$-0.521461\pi$
$907$	−3680.50	−0.134740	−0.0673699	+	0.997728i	$0.521461\pi$
$908$	13400.8	0.489781
$909$	−5009.04	−0.182772
$910$	8612.46	0.313737
$911$	−3424.94	−0.124559	−0.0622795	−	0.998059i	$-0.519837\pi$
$911$	−3424.94	−0.124559	−0.0622795	+	0.998059i	$0.519837\pi$
$912$	10363.3	0.376276
$913$	−33124.5	−1.20072
$914$	11353.3	0.410869
$915$	4952.43	0.178932
$916$	5693.99	0.205387
$917$	−7227.77	−0.260286
$918$	21320.1	0.766524
$919$	1193.22	0.0428299	0.0214149	−	0.999771i	$-0.493183\pi$
$919$	1193.22	0.0428299	0.0214149	+	0.999771i	$0.493183\pi$
$920$	1469.01	0.0526431
$921$	−8918.70	−0.319089
$922$	−13638.5	−0.487158
$923$	−26359.4	−0.940009
$924$	4084.11	0.145408
$925$	−27683.5	−0.984030
$926$	−9418.90	−0.334260
$927$	−20044.5	−0.710193
$928$	5739.33	0.203020
$929$	−20010.0	−0.706680	−0.353340	−	0.935495i	$-0.614954\pi$
$929$	−20010.0	−0.706680	−0.353340	+	0.935495i	$0.614954\pi$
$930$	−6318.95	−0.222803
$931$	12342.4	0.434485
$932$	−15188.8	−0.533827
$933$	5045.96	0.177060
$934$	−37031.0	−1.29731
$935$	25567.9	0.894287
$936$	−7419.76	−0.259105
$937$	28273.2	0.985748	0.492874	−	0.870101i	$-0.335946\pi$
$937$	28273.2	0.985748	0.492874	+	0.870101i	$0.335946\pi$
$938$	−42969.8	−1.49575
$939$	−2174.25	−0.0755635
$940$	8940.75	0.310229
$941$	−31630.5	−1.09578	−0.547888	−	0.836552i	$-0.684568\pi$
$941$	−31630.5	−1.09578	−0.547888	+	0.836552i	$0.684568\pi$
$942$	11414.8	0.394812
$943$	3766.67	0.130074
$944$	−16885.6	−0.582180
$945$	5558.20	0.191331
$946$	−64277.0	−2.20912
$947$	−19159.1	−0.657430	−0.328715	−	0.944429i	$-0.606616\pi$
$947$	−19159.1	−0.657430	−0.328715	+	0.944429i	$0.606616\pi$
$948$	1638.84	0.0561467
$949$	11690.0	0.399868
$950$	36226.4	1.23720
$951$	1424.57	0.0485749
$952$	15772.0	0.536947
$953$	28653.5	0.973953	0.486977	−	0.873415i	$-0.338100\pi$
$953$	28653.5	0.973953	0.486977	+	0.873415i	$0.338100\pi$
$954$	58715.7	1.99265
$955$	8718.63	0.295422
$956$	22932.4	0.775823
$957$	−1559.43	−0.0526741
$958$	21319.6	0.719002
$959$	22096.1	0.744027
$960$	561.702	0.0188842
$961$	34113.6	1.14510
$962$	−29438.6	−0.986632
$963$	39350.5	1.31677
$964$	−9393.15	−0.313831
$965$	−1622.68	−0.0541303
$966$	1488.94	0.0495919
$967$	29602.1	0.984427	0.492213	−	0.870475i	$-0.336188\pi$
$967$	29602.1	0.984427	0.492213	+	0.870475i	$0.336188\pi$
$968$	−8120.72	−0.269638
$969$	12503.9	0.414533
$970$	−201.706	−0.00667670
$971$	8493.50	0.280710	0.140355	−	0.990101i	$-0.455176\pi$
$971$	8493.50	0.280710	0.140355	+	0.990101i	$0.455176\pi$
$972$	11989.7	0.395648
$973$	13816.1	0.455216
$974$	1607.47	0.0528816
$975$	2844.83	0.0934435
$976$	56423.5	1.85048
$977$	5132.14	0.168057	0.0840285	−	0.996463i	$-0.473221\pi$
$977$	5132.14	0.168057	0.0840285	+	0.996463i	$0.473221\pi$
$978$	−3947.02	−0.129051
$979$	−21426.5	−0.699481
$980$	3255.37	0.106111
$981$	−30660.1	−0.997861
$982$	63871.2	2.07557
$983$	−3034.98	−0.0984750	−0.0492375	−	0.998787i	$-0.515679\pi$
$983$	−3034.98	−0.0984750	−0.0492375	+	0.998787i	$0.515679\pi$
$984$	−2097.58	−0.0679558
$985$	−1323.96	−0.0428273
$986$	9964.69	0.321846
$987$	−5476.69	−0.176621
$988$	14791.8	0.476306
$989$	−8997.77	−0.289295
$990$	24746.3	0.794435
$991$	−42982.6	−1.37779	−0.688894	−	0.724862i	$-0.741904\pi$
$991$	−42982.6	−1.37779	−0.688894	+	0.724862i	$0.741904\pi$
$992$	−50029.8	−1.60126
$993$	−8415.71	−0.268947
$994$	54231.0	1.73049
$995$	−12905.5	−0.411188
$996$	−4272.68	−0.135929
$997$	31531.3	1.00161	0.500805	−	0.865560i	$-0.333037\pi$
$997$	31531.3	1.00161	0.500805	+	0.865560i	$0.333037\pi$
$998$	−11812.5	−0.374667
$999$	−18998.7	−0.601695

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.a.1.28	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.a.1.28	✓	35	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+3.60367 q^{2} +1.17941 q^{3} +4.98643 q^{4} -5.88126 q^{5} +4.25019 q^{6} +15.2314 q^{7} -10.8599 q^{8} -25.6090 q^{9} +O(q^{10})\)	\(q+3.60367 q^{2} +1.17941 q^{3} +4.98643 q^{4} -5.88126 q^{5} +4.25019 q^{6} +15.2314 q^{7} -10.8599 q^{8} -25.6090 q^{9} -21.1941 q^{10} +45.5935 q^{11} +5.88104 q^{12} -26.6791 q^{13} +54.8890 q^{14} -6.93640 q^{15} -79.0269 q^{16} -95.3500 q^{17} -92.2864 q^{18} -111.188 q^{19} -29.3265 q^{20} +17.9640 q^{21} +164.304 q^{22} +23.0000 q^{23} -12.8082 q^{24} -90.4108 q^{25} -96.1428 q^{26} -62.0474 q^{27} +75.9504 q^{28} -29.0000 q^{29} -24.9965 q^{30} +252.794 q^{31} -197.908 q^{32} +53.7734 q^{33} -343.610 q^{34} -89.5798 q^{35} -127.698 q^{36} +306.197 q^{37} -400.686 q^{38} -31.4656 q^{39} +63.8698 q^{40} +163.768 q^{41} +64.7365 q^{42} -391.207 q^{43} +227.349 q^{44} +150.613 q^{45} +82.8844 q^{46} -304.869 q^{47} -93.2050 q^{48} -111.004 q^{49} -325.811 q^{50} -112.457 q^{51} -133.034 q^{52} -636.234 q^{53} -223.598 q^{54} -268.147 q^{55} -165.411 q^{56} -131.136 q^{57} -104.506 q^{58} +213.668 q^{59} -34.5879 q^{60} -713.978 q^{61} +910.985 q^{62} -390.061 q^{63} -80.9789 q^{64} +156.907 q^{65} +193.781 q^{66} -782.849 q^{67} -475.457 q^{68} +27.1264 q^{69} -322.816 q^{70} +988.013 q^{71} +278.111 q^{72} -438.171 q^{73} +1103.43 q^{74} -106.631 q^{75} -554.434 q^{76} +694.454 q^{77} -113.392 q^{78} +278.665 q^{79} +464.778 q^{80} +618.264 q^{81} +590.167 q^{82} -726.517 q^{83} +89.5765 q^{84} +560.778 q^{85} -1409.78 q^{86} -34.2028 q^{87} -495.141 q^{88} -469.945 q^{89} +542.760 q^{90} -406.361 q^{91} +114.688 q^{92} +298.147 q^{93} -1098.65 q^{94} +653.928 q^{95} -233.414 q^{96} +9.51710 q^{97} -400.022 q^{98} -1167.60 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9 - 52 * q^10 - 126 * q^11 - 173 * q^12 - 252 * q^13 + 112 * q^14 - 32 * q^15 + 312 * q^16 - 332 * q^17 - 225 * q^18 - 2 * q^19 - 747 * q^20 - 202 * q^21 - 127 * q^22 + 805 * q^23 - 494 * q^24 + 315 * q^25 - 677 * q^26 - 694 * q^27 - 529 * q^28 - 1015 * q^29 + 389 * q^30 - 652 * q^31 + 320 * q^32 - 290 * q^33 - 455 * q^34 - 940 * q^35 + 34 * q^36 - 528 * q^37 - 1218 * q^38 - 268 * q^39 - 806 * q^40 - 68 * q^41 - 1484 * q^42 - 162 * q^43 - 1817 * q^44 - 356 * q^45 - 138 * q^46 - 1200 * q^47 - 2153 * q^48 + 93 * q^49 - 1369 * q^50 - 270 * q^51 - 3134 * q^52 - 1892 * q^53 - 1221 * q^54 - 794 * q^55 + 191 * q^56 - 1764 * q^57 + 174 * q^58 - 1354 * q^59 + 159 * q^60 - 1274 * q^61 - 5413 * q^62 - 2904 * q^63 - 926 * q^64 - 548 * q^65 - 2477 * q^66 - 3212 * q^67 - 3901 * q^68 - 506 * q^69 - 2768 * q^70 - 2342 * q^71 - 2381 * q^72 + 916 * q^73 + 661 * q^74 - 4708 * q^75 - 2810 * q^76 - 5536 * q^77 - 2434 * q^78 + 2622 * q^79 - 5444 * q^80 + 607 * q^81 - 3687 * q^82 - 2702 * q^83 + 346 * q^84 - 3304 * q^85 - 5789 * q^86 + 638 * q^87 - 2252 * q^88 - 1620 * q^89 - 3933 * q^90 - 4016 * q^91 + 2668 * q^92 - 4942 * q^93 - 1413 * q^94 - 4528 * q^95 - 7920 * q^96 + 682 * q^97 + 152 * q^98 - 582 * q^99

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