LMFDB - Embedded newform 667.4.a.a.1.2

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			1.2
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)

$f(q)$	$=$	$q-5.24031 q^{2} +4.66607 q^{3} +19.4609 q^{4} +9.98386 q^{5} -24.4516 q^{6} -16.6714 q^{7} -60.0584 q^{8} -5.22782 q^{9} +O(q^{10})$	\(q-5.24031 q^{2} +4.66607 q^{3} +19.4609 q^{4} +9.98386 q^{5} -24.4516 q^{6} -16.6714 q^{7} -60.0584 q^{8} -5.22782 q^{9} -52.3185 q^{10} -35.9290 q^{11} +90.8056 q^{12} +36.7562 q^{13} +87.3635 q^{14} +46.5854 q^{15} +159.038 q^{16} +6.49920 q^{17} +27.3954 q^{18} +86.3228 q^{19} +194.294 q^{20} -77.7900 q^{21} +188.279 q^{22} +23.0000 q^{23} -280.237 q^{24} -25.3225 q^{25} -192.614 q^{26} -150.377 q^{27} -324.440 q^{28} -29.0000 q^{29} -244.122 q^{30} +0.154734 q^{31} -352.941 q^{32} -167.647 q^{33} -34.0578 q^{34} -166.445 q^{35} -101.738 q^{36} +114.511 q^{37} -452.358 q^{38} +171.507 q^{39} -599.615 q^{40} -146.654 q^{41} +407.644 q^{42} -39.6845 q^{43} -699.209 q^{44} -52.1938 q^{45} -120.527 q^{46} -11.2626 q^{47} +742.082 q^{48} -65.0634 q^{49} +132.698 q^{50} +30.3257 q^{51} +715.308 q^{52} -285.083 q^{53} +788.023 q^{54} -358.710 q^{55} +1001.26 q^{56} +402.788 q^{57} +151.969 q^{58} -27.7625 q^{59} +906.591 q^{60} -19.3542 q^{61} -0.810855 q^{62} +87.1552 q^{63} +577.216 q^{64} +366.969 q^{65} +878.523 q^{66} -741.100 q^{67} +126.480 q^{68} +107.320 q^{69} +872.225 q^{70} -329.775 q^{71} +313.974 q^{72} -556.329 q^{73} -600.074 q^{74} -118.157 q^{75} +1679.92 q^{76} +598.988 q^{77} -898.750 q^{78} +240.652 q^{79} +1587.81 q^{80} -560.519 q^{81} +768.510 q^{82} +117.558 q^{83} -1513.86 q^{84} +64.8871 q^{85} +207.959 q^{86} -135.316 q^{87} +2157.84 q^{88} -453.690 q^{89} +273.512 q^{90} -612.779 q^{91} +447.600 q^{92} +0.722000 q^{93} +59.0197 q^{94} +861.835 q^{95} -1646.85 q^{96} +427.648 q^{97} +340.952 q^{98} +187.830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.24031	−1.85273	−0.926365	−	0.376628i	$-0.877084\pi$
$2$	−5.24031	−1.85273	−0.926365	+	0.376628i	$0.877084\pi$
$3$	4.66607	0.897985	0.448993	−	0.893536i	$-0.351783\pi$
$3$	4.66607	0.897985	0.448993	+	0.893536i	$0.351783\pi$
$4$	19.4609	2.43261
$5$	9.98386	0.892984	0.446492	−	0.894788i	$-0.352673\pi$
$5$	9.98386	0.892984	0.446492	+	0.894788i	$0.352673\pi$
$6$	−24.4516	−1.66372
$7$	−16.6714	−0.900173	−0.450086	−	0.892985i	$-0.648607\pi$
$7$	−16.6714	−0.900173	−0.450086	+	0.892985i	$0.648607\pi$
$8$	−60.0584	−2.65423
$9$	−5.22782	−0.193623
$10$	−52.3185	−1.65446
$11$	−35.9290	−0.984818	−0.492409	−	0.870364i	$-0.663884\pi$
$11$	−35.9290	−0.984818	−0.492409	+	0.870364i	$0.663884\pi$
$12$	90.8056	2.18444
$13$	36.7562	0.784181	0.392090	−	0.919927i	$-0.371752\pi$
$13$	36.7562	0.784181	0.392090	+	0.919927i	$0.371752\pi$
$14$	87.3635	1.66778
$15$	46.5854	0.801886
$16$	159.038	2.48497
$17$	6.49920	0.0927228	0.0463614	−	0.998925i	$-0.485237\pi$
$17$	6.49920	0.0927228	0.0463614	+	0.998925i	$0.485237\pi$
$18$	27.3954	0.358731
$19$	86.3228	1.04231	0.521153	−	0.853463i	$-0.325502\pi$
$19$	86.3228	1.04231	0.521153	+	0.853463i	$0.325502\pi$
$20$	194.294	2.17228
$21$	−77.7900	−0.808342
$22$	188.279	1.82460
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−280.237	−2.38346
$25$	−25.3225	−0.202580
$26$	−192.614	−1.45287
$27$	−150.377	−1.07186
$28$	−324.440	−2.18977
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−244.122	−1.48568
$31$	0.154734	0.000896486 0	0.000448243	−	1.00000i	$-0.499857\pi$
$31$	0.154734	0.000896486 0	0.000448243		1.00000i	$0.499857\pi$
$32$	−352.941	−1.94974
$33$	−167.647	−0.884352
$34$	−34.0578	−0.171790
$35$	−166.445	−0.803840
$36$	−101.738	−0.471008
$37$	114.511	0.508798	0.254399	−	0.967099i	$-0.418122\pi$
$37$	114.511	0.508798	0.254399	+	0.967099i	$0.418122\pi$
$38$	−452.358	−1.93111
$39$	171.507	0.704182
$40$	−599.615	−2.37019
$41$	−146.654	−0.558621	−0.279310	−	0.960201i	$-0.590106\pi$
$41$	−146.654	−0.558621	−0.279310	+	0.960201i	$0.590106\pi$
$42$	407.644	1.49764
$43$	−39.6845	−0.140740	−0.0703702	−	0.997521i	$-0.522418\pi$
$43$	−39.6845	−0.140740	−0.0703702	+	0.997521i	$0.522418\pi$
$44$	−699.209	−2.39567
$45$	−52.1938	−0.172902
$46$	−120.527	−0.386321
$47$	−11.2626	−0.0349537	−0.0174769	−	0.999847i	$-0.505563\pi$
$47$	−11.2626	−0.0349537	−0.0174769	+	0.999847i	$0.505563\pi$
$48$	742.082	2.23146
$49$	−65.0634	−0.189689
$50$	132.698	0.375326
$51$	30.3257	0.0832637
$52$	715.308	1.90760
$53$	−285.083	−0.738851	−0.369426	−	0.929260i	$-0.620446\pi$
$53$	−285.083	−0.738851	−0.369426	+	0.929260i	$0.620446\pi$
$54$	788.023	1.98586
$55$	−358.710	−0.879426
$56$	1001.26	2.38927
$57$	402.788	0.935975
$58$	151.969	0.344043
$59$	−27.7625	−0.0612605	−0.0306302	−	0.999531i	$-0.509751\pi$
$59$	−27.7625	−0.0612605	−0.0306302	+	0.999531i	$0.509751\pi$
$60$	906.591	1.95067
$61$	−19.3542	−0.0406237	−0.0203119	−	0.999794i	$-0.506466\pi$
$61$	−19.3542	−0.0406237	−0.0203119	+	0.999794i	$0.506466\pi$
$62$	−0.810855	−0.00166095
$63$	87.1552	0.174294
$64$	577.216	1.12737
$65$	366.969	0.700261
$66$	878.523	1.63846
$67$	−741.100	−1.35134	−0.675670	−	0.737204i	$-0.736145\pi$
$67$	−741.100	−1.35134	−0.675670	+	0.737204i	$0.736145\pi$
$68$	126.480	0.225558
$69$	107.320	0.187243
$70$	872.225	1.48930
$71$	−329.775	−0.551227	−0.275614	−	0.961268i	$-0.588881\pi$
$71$	−329.775	−0.551227	−0.275614	+	0.961268i	$0.588881\pi$
$72$	313.974	0.513920
$73$	−556.329	−0.891964	−0.445982	−	0.895042i	$-0.647145\pi$
$73$	−556.329	−0.891964	−0.445982	+	0.895042i	$0.647145\pi$
$74$	−600.074	−0.942665
$75$	−118.157	−0.181914
$76$	1679.92	2.53552
$77$	598.988	0.886506
$78$	−898.750	−1.30466
$79$	240.652	0.342728	0.171364	−	0.985208i	$-0.445183\pi$
$79$	240.652	0.342728	0.171364	+	0.985208i	$0.445183\pi$
$80$	1587.81	2.21904
$81$	−560.519	−0.768887
$82$	768.510	1.03497
$83$	117.558	0.155466	0.0777330	−	0.996974i	$-0.475232\pi$
$83$	117.558	0.155466	0.0777330	+	0.996974i	$0.475232\pi$
$84$	−1513.86	−1.96638
$85$	64.8871	0.0828000
$86$	207.959	0.260754
$87$	−135.316	−0.166752
$88$	2157.84	2.61394
$89$	−453.690	−0.540349	−0.270174	−	0.962811i	$-0.587081\pi$
$89$	−453.690	−0.540349	−0.270174	+	0.962811i	$0.587081\pi$
$90$	273.512	0.320341
$91$	−612.779	−0.705898
$92$	447.600	0.507234
$93$	0.722000	0.000805031 0
$94$	59.0197	0.0647598
$95$	861.835	0.930762
$96$	−1646.85	−1.75084
$97$	427.648	0.447640	0.223820	−	0.974631i	$-0.428147\pi$
$97$	427.648	0.447640	0.223820	+	0.974631i	$0.428147\pi$
$98$	340.952	0.351443
$99$	187.830	0.190683
$100$	−492.798	−0.492798
$101$	453.052	0.446340	0.223170	−	0.974780i	$-0.428359\pi$
$101$	453.052	0.446340	0.223170	+	0.974780i	$0.428359\pi$
$102$	−158.916	−0.154265
$103$	−227.248	−0.217392	−0.108696	−	0.994075i	$-0.534668\pi$
$103$	−227.248	−0.217392	−0.108696	+	0.994075i	$0.534668\pi$
$104$	−2207.52	−2.08140
$105$	−776.645	−0.721836
$106$	1493.92	1.36889
$107$	−1468.19	−1.32650	−0.663249	−	0.748399i	$-0.730823\pi$
$107$	−1468.19	−1.32650	−0.663249	+	0.748399i	$0.730823\pi$
$108$	−2926.47	−2.60740
$109$	−306.687	−0.269498	−0.134749	−	0.990880i	$-0.543023\pi$
$109$	−306.687	−0.269498	−0.134749	+	0.990880i	$0.543023\pi$
$110$	1879.75	1.62934
$111$	534.317	0.456893
$112$	−2651.39	−2.23690
$113$	−1774.53	−1.47729	−0.738647	−	0.674093i	$-0.764535\pi$
$113$	−1774.53	−1.47729	−0.738647	+	0.674093i	$0.764535\pi$
$114$	−2110.73	−1.73411
$115$	229.629	0.186200
$116$	−564.365	−0.451724
$117$	−192.155	−0.151835
$118$	145.484	0.113499
$119$	−108.351	−0.0834666
$120$	−2797.84	−2.12839
$121$	−40.1083	−0.0301339
$122$	101.422	0.0752648
$123$	−684.295	−0.501633
$124$	3.01126	0.00218080
$125$	−1500.80	−1.07388
$126$	−456.720	−0.322920
$127$	1788.87	1.24990	0.624948	−	0.780666i	$-0.285120\pi$
$127$	1788.87	1.24990	0.624948	+	0.780666i	$0.285120\pi$
$128$	−201.263	−0.138979
$129$	−185.171	−0.126383
$130$	−1923.03	−1.29739
$131$	−1724.74	−1.15032	−0.575159	−	0.818042i	$-0.695060\pi$
$131$	−1724.74	−1.15032	−0.575159	+	0.818042i	$0.695060\pi$
$132$	−3262.55	−2.15128
$133$	−1439.12	−0.938255
$134$	3883.59	2.50367
$135$	−1501.34	−0.957150
$136$	−390.332	−0.246108
$137$	−1275.65	−0.795517	−0.397759	−	0.917490i	$-0.630212\pi$
$137$	−1275.65	−0.795517	−0.397759	+	0.917490i	$0.630212\pi$
$138$	−562.388	−0.346910
$139$	2040.37	1.24505	0.622525	−	0.782600i	$-0.286107\pi$
$139$	2040.37	1.24505	0.622525	+	0.782600i	$0.286107\pi$
$140$	−3239.17	−1.95543
$141$	−52.5522	−0.0313879
$142$	1728.13	1.02128
$143$	−1320.61	−0.772275
$144$	−831.421	−0.481147
$145$	−289.532	−0.165823
$146$	2915.34	1.65257
$147$	−303.590	−0.170338
$148$	2228.49	1.23771
$149$	−2561.86	−1.40856	−0.704281	−	0.709921i	$-0.748731\pi$
$149$	−2561.86	−1.40856	−0.704281	+	0.709921i	$0.748731\pi$
$150$	619.177	0.337037
$151$	2368.68	1.27656	0.638278	−	0.769806i	$-0.279647\pi$
$151$	2368.68	1.27656	0.638278	+	0.769806i	$0.279647\pi$
$152$	−5184.41	−2.76652
$153$	−33.9766	−0.0179533
$154$	−3138.88	−1.64246
$155$	1.54484	0.000800547 0
$156$	3337.67	1.71300
$157$	2402.05	1.22105	0.610524	−	0.791998i	$-0.290959\pi$
$157$	2402.05	1.22105	0.610524	+	0.791998i	$0.290959\pi$
$158$	−1261.09	−0.634982
$159$	−1330.22	−0.663478
$160$	−3523.71	−1.74109
$161$	−383.443	−0.187699
$162$	2937.29	1.42454
$163$	−1133.14	−0.544507	−0.272254	−	0.962226i	$-0.587769\pi$
$163$	−1133.14	−0.544507	−0.272254	+	0.962226i	$0.587769\pi$
$164$	−2854.00	−1.35890
$165$	−1673.76	−0.789712
$166$	−616.041	−0.288036
$167$	−160.081	−0.0741764	−0.0370882	−	0.999312i	$-0.511808\pi$
$167$	−160.081	−0.0741764	−0.0370882	+	0.999312i	$0.511808\pi$
$168$	4671.95	2.14553
$169$	−845.978	−0.385061
$170$	−340.029	−0.153406
$171$	−451.280	−0.201814
$172$	−772.295	−0.342366
$173$	−3870.22	−1.70085	−0.850425	−	0.526096i	$-0.823655\pi$
$173$	−3870.22	−1.70085	−0.850425	+	0.526096i	$0.823655\pi$
$174$	709.098	0.308946
$175$	422.162	0.182357
$176$	−5714.07	−2.44724
$177$	−129.542	−0.0550110
$178$	2377.48	1.00112
$179$	862.076	0.359970	0.179985	−	0.983669i	$-0.442395\pi$
$179$	862.076	0.359970	0.179985	+	0.983669i	$0.442395\pi$
$180$	−1015.74	−0.420603
$181$	−1060.45	−0.435486	−0.217743	−	0.976006i	$-0.569869\pi$
$181$	−1060.45	−0.435486	−0.217743	+	0.976006i	$0.569869\pi$
$182$	3211.15	1.30784
$183$	−90.3079	−0.0364795
$184$	−1381.34	−0.553446
$185$	1143.26	0.454348
$186$	−3.78350	−0.00149150
$187$	−233.510	−0.0913151
$188$	−219.181	−0.0850286
$189$	2507.00	0.964855
$190$	−4516.28	−1.72445
$191$	−949.383	−0.359659	−0.179830	−	0.983698i	$-0.557555\pi$
$191$	−949.383	−0.359659	−0.179830	+	0.983698i	$0.557555\pi$
$192$	2693.33	1.01237
$193$	14.6408	0.00546047	0.00273024	−	0.999996i	$-0.499131\pi$
$193$	14.6408	0.00546047	0.00273024	+	0.999996i	$0.499131\pi$
$194$	−2241.01	−0.829355
$195$	1712.30	0.628824
$196$	−1266.19	−0.461439
$197$	2026.85	0.733033	0.366516	−	0.930412i	$-0.380550\pi$
$197$	2026.85	0.733033	0.366516	+	0.930412i	$0.380550\pi$
$198$	−984.288	−0.353284
$199$	−1960.69	−0.698442	−0.349221	−	0.937040i	$-0.613554\pi$
$199$	−1960.69	−0.698442	−0.349221	+	0.937040i	$0.613554\pi$
$200$	1520.83	0.537694
$201$	−3458.02	−1.21348
$202$	−2374.13	−0.826948
$203$	483.472	0.167158
$204$	590.164	0.202548
$205$	−1464.17	−0.498839
$206$	1190.85	0.402769
$207$	−120.240	−0.0403732
$208$	5845.64	1.94866
$209$	−3101.49	−1.02648
$210$	4069.86	1.33737
$211$	4768.46	1.55580	0.777901	−	0.628386i	$-0.216284\pi$
$211$	4768.46	1.55580	0.777901	+	0.628386i	$0.216284\pi$
$212$	−5547.95	−1.79733
$213$	−1538.75	−0.494994
$214$	7693.77	2.45764
$215$	−396.205	−0.125679
$216$	9031.41	2.84495
$217$	−2.57964	−0.000806992 0
$218$	1607.14	0.499307
$219$	−2595.87	−0.800970
$220$	−6980.80	−2.13930
$221$	238.886	0.0727114
$222$	−2799.99	−0.846499
$223$	−3907.55	−1.17340	−0.586702	−	0.809803i	$-0.699574\pi$
$223$	−3907.55	−1.17340	−0.586702	+	0.809803i	$0.699574\pi$
$224$	5884.03	1.75510
$225$	132.381	0.0392241
$226$	9299.11	2.73703
$227$	415.755	0.121562	0.0607811	−	0.998151i	$-0.480641\pi$
$227$	415.755	0.121562	0.0607811	+	0.998151i	$0.480641\pi$
$228$	7838.60	2.27686
$229$	−728.959	−0.210354	−0.105177	−	0.994454i	$-0.533541\pi$
$229$	−728.959	−0.210354	−0.105177	+	0.994454i	$0.533541\pi$
$230$	−1203.33	−0.344978
$231$	2794.92	0.796069
$232$	1741.69	0.492879
$233$	−441.545	−0.124148	−0.0620742	−	0.998072i	$-0.519772\pi$
$233$	−441.545	−0.124148	−0.0620742	+	0.998072i	$0.519772\pi$
$234$	1006.95	0.281310
$235$	−112.445	−0.0312131
$236$	−540.282	−0.149023
$237$	1122.90	0.307764
$238$	567.793	0.154641
$239$	3605.72	0.975877	0.487938	−	0.872878i	$-0.337749\pi$
$239$	3605.72	0.975877	0.487938	+	0.872878i	$0.337749\pi$
$240$	7408.84	1.99266
$241$	5709.71	1.52612	0.763060	−	0.646328i	$-0.223696\pi$
$241$	5709.71	1.52612	0.763060	+	0.646328i	$0.223696\pi$
$242$	210.180	0.0558300
$243$	1444.76	0.381406
$244$	−376.649	−0.0988216
$245$	−649.584	−0.169389
$246$	3585.92	0.929390
$247$	3172.90	0.817356
$248$	−9.29308	−0.00237948
$249$	548.534	0.139606
$250$	7864.65	1.98962
$251$	−3323.40	−0.835742	−0.417871	−	0.908506i	$-0.637224\pi$
$251$	−3323.40	−0.835742	−0.417871	+	0.908506i	$0.637224\pi$
$252$	1696.11	0.423989
$253$	−826.367	−0.205349
$254$	−9374.25	−2.31572
$255$	302.768	0.0743531
$256$	−3563.04	−0.869884
$257$	−4144.88	−1.00603	−0.503017	−	0.864277i	$-0.667777\pi$
$257$	−4144.88	−1.00603	−0.503017	+	0.864277i	$0.667777\pi$
$258$	970.352	0.234153
$259$	−1909.07	−0.458006
$260$	7141.53	1.70346
$261$	151.607	0.0359549
$262$	9038.20	2.13123
$263$	−985.401	−0.231036	−0.115518	−	0.993305i	$-0.536853\pi$
$263$	−985.401	−0.231036	−0.115518	+	0.993305i	$0.536853\pi$
$264$	10068.6	2.34727
$265$	−2846.23	−0.659782
$266$	7541.46	1.73833
$267$	−2116.95	−0.485225
$268$	−14422.4	−3.28728
$269$	−2809.57	−0.636813	−0.318407	−	0.947954i	$-0.603148\pi$
$269$	−2809.57	−0.636813	−0.318407	+	0.947954i	$0.603148\pi$
$270$	7867.51	1.77334
$271$	1762.31	0.395029	0.197515	−	0.980300i	$-0.436713\pi$
$271$	1762.31	0.395029	0.197515	+	0.980300i	$0.436713\pi$
$272$	1033.62	0.230413
$273$	−2859.27	−0.633886
$274$	6684.79	1.47388
$275$	909.812	0.199504
$276$	2088.53	0.455488
$277$	−3248.05	−0.704535	−0.352268	−	0.935899i	$-0.614589\pi$
$277$	−3248.05	−0.704535	−0.352268	+	0.935899i	$0.614589\pi$
$278$	−10692.2	−2.30674
$279$	−0.808921	−0.000173580 0
$280$	9996.44	2.13358
$281$	4346.77	0.922800	0.461400	−	0.887192i	$-0.347347\pi$
$281$	4346.77	0.922800	0.461400	+	0.887192i	$0.347347\pi$
$282$	275.390	0.0581533
$283$	−278.093	−0.0584131	−0.0292066	−	0.999573i	$-0.509298\pi$
$283$	−278.093	−0.0584131	−0.0292066	+	0.999573i	$0.509298\pi$
$284$	−6417.71	−1.34092
$285$	4021.38	0.835811
$286$	6920.43	1.43082
$287$	2444.93	0.502855
$288$	1845.11	0.377514
$289$	−4870.76	−0.991402
$290$	1517.24	0.307225
$291$	1995.43	0.401974
$292$	−10826.6	−2.16980
$293$	−5675.28	−1.13158	−0.565791	−	0.824549i	$-0.691429\pi$
$293$	−5675.28	−1.13158	−0.565791	+	0.824549i	$0.691429\pi$
$294$	1590.91	0.315590
$295$	−277.177	−0.0547046
$296$	−6877.36	−1.35047
$297$	5402.90	1.05558
$298$	13424.9	2.60969
$299$	845.394	0.163513
$300$	−2299.43	−0.442525
$301$	661.598	0.126691
$302$	−12412.6	−2.36511
$303$	2113.97	0.400807
$304$	13728.6	2.59010
$305$	−193.229	−0.0362763
$306$	178.048	0.0332625
$307$	−8181.83	−1.52105	−0.760524	−	0.649309i	$-0.775058\pi$
$307$	−8181.83	−1.52105	−0.760524	+	0.649309i	$0.775058\pi$
$308$	11656.8	2.15652
$309$	−1060.35	−0.195215
$310$	−8.09546	−0.00148320
$311$	4220.43	0.769513	0.384757	−	0.923018i	$-0.374285\pi$
$311$	4220.43	0.769513	0.384757	+	0.923018i	$0.374285\pi$
$312$	−10300.4	−1.86906
$313$	3282.99	0.592861	0.296431	−	0.955054i	$-0.404204\pi$
$313$	3282.99	0.592861	0.296431	+	0.955054i	$0.404204\pi$
$314$	−12587.5	−2.26227
$315$	870.145	0.155642
$316$	4683.30	0.833721
$317$	5179.79	0.917748	0.458874	−	0.888501i	$-0.348253\pi$
$317$	5179.79	0.917748	0.458874	+	0.888501i	$0.348253\pi$
$318$	6970.74	1.22924
$319$	1041.94	0.182876
$320$	5762.84	1.00673
$321$	−6850.67	−1.19118
$322$	2009.36	0.347755
$323$	561.029	0.0966455
$324$	−10908.2	−1.87040
$325$	−930.760	−0.158859
$326$	5938.02	1.00882
$327$	−1431.02	−0.242005
$328$	8807.78	1.48271
$329$	187.764	0.0314644
$330$	8771.05	1.46312
$331$	10506.4	1.74467	0.872333	−	0.488911i	$-0.162606\pi$
$331$	10506.4	1.74467	0.872333	+	0.488911i	$0.162606\pi$
$332$	2287.78	0.378188
$333$	−598.644	−0.0985149
$334$	838.876	0.137429
$335$	−7399.04	−1.20672
$336$	−12371.6	−2.00870
$337$	−7204.80	−1.16460	−0.582300	−	0.812974i	$-0.697847\pi$
$337$	−7204.80	−1.16460	−0.582300	+	0.812974i	$0.697847\pi$
$338$	4433.19	0.713413
$339$	−8280.10	−1.32659
$340$	1262.76	0.201420
$341$	−5.55944	−0.000882875 0
$342$	2364.85	0.373907
$343$	6803.00	1.07093
$344$	2383.39	0.373558
$345$	1071.46	0.167205
$346$	20281.1	3.15121
$347$	−9835.92	−1.52167	−0.760835	−	0.648945i	$-0.775211\pi$
$347$	−9835.92	−1.52167	−0.760835	+	0.648945i	$0.775211\pi$
$348$	−2633.36	−0.405641
$349$	−857.732	−0.131557	−0.0657784	−	0.997834i	$-0.520953\pi$
$349$	−857.732	−0.131557	−0.0657784	+	0.997834i	$0.520953\pi$
$350$	−2212.26	−0.337858
$351$	−5527.30	−0.840528
$352$	12680.8	1.92014
$353$	−12257.7	−1.84820	−0.924098	−	0.382155i	$-0.875182\pi$
$353$	−12257.7	−1.84820	−0.924098	+	0.382155i	$0.875182\pi$
$354$	678.838	0.101920
$355$	−3292.43	−0.492237
$356$	−8829.19	−1.31446
$357$	−505.573	−0.0749517
$358$	−4517.55	−0.666926
$359$	5373.55	0.789987	0.394993	−	0.918684i	$-0.370747\pi$
$359$	5373.55	0.789987	0.394993	+	0.918684i	$0.370747\pi$
$360$	3134.68	0.458922
$361$	592.629	0.0864016
$362$	5557.11	0.806837
$363$	−187.148	−0.0270598
$364$	−11925.2	−1.71717
$365$	−5554.31	−0.796509
$366$	473.241	0.0675867
$367$	10900.8	1.55046	0.775228	−	0.631682i	$-0.217635\pi$
$367$	10900.8	1.55046	0.775228	+	0.631682i	$0.217635\pi$
$368$	3657.87	0.518152
$369$	766.678	0.108162
$370$	−5991.06	−0.841784
$371$	4752.74	0.665094
$372$	14.0507	0.00195832
$373$	1229.70	0.170702	0.0853508	−	0.996351i	$-0.472799\pi$
$373$	1229.70	0.170702	0.0853508	+	0.996351i	$0.472799\pi$
$374$	1223.66	0.169182
$375$	−7002.83	−0.964332
$376$	676.416	0.0927753
$377$	−1065.93	−0.145619
$378$	−13137.5	−1.78762
$379$	−5659.35	−0.767021	−0.383511	−	0.923536i	$-0.625285\pi$
$379$	−5659.35	−0.767021	−0.383511	+	0.923536i	$0.625285\pi$
$380$	16772.0	2.26418
$381$	8347.00	1.12239
$382$	4975.06	0.666351
$383$	−5082.92	−0.678134	−0.339067	−	0.940762i	$-0.610111\pi$
$383$	−5082.92	−0.678134	−0.339067	+	0.940762i	$0.610111\pi$
$384$	−939.106	−0.124801
$385$	5980.21	0.791636
$386$	−76.7226	−0.0101168
$387$	207.464	0.0272506
$388$	8322.39	1.08893
$389$	−5316.07	−0.692893	−0.346446	−	0.938070i	$-0.612612\pi$
$389$	−5316.07	−0.692893	−0.346446	+	0.938070i	$0.612612\pi$
$390$	−8973.00	−1.16504
$391$	149.482	0.0193340
$392$	3907.60	0.503479
$393$	−8047.77	−1.03297
$394$	−10621.3	−1.35811
$395$	2402.64	0.306050
$396$	3655.33	0.463857
$397$	5868.94	0.741949	0.370974	−	0.928643i	$-0.379024\pi$
$397$	5868.94	0.741949	0.370974	+	0.928643i	$0.379024\pi$
$398$	10274.6	1.29402
$399$	−6715.05	−0.842539
$400$	−4027.24	−0.503405
$401$	−5295.98	−0.659523	−0.329761	−	0.944064i	$-0.606968\pi$
$401$	−5295.98	−0.659523	−0.329761	+	0.944064i	$0.606968\pi$
$402$	18121.1	2.24826
$403$	5.68744	0.000703007 0
$404$	8816.78	1.08577
$405$	−5596.14	−0.686604
$406$	−2533.54	−0.309698
$407$	−4114.27	−0.501073
$408$	−1821.31	−0.221001
$409$	−13598.4	−1.64400	−0.822001	−	0.569486i	$-0.807142\pi$
$409$	−13598.4	−1.64400	−0.822001	+	0.569486i	$0.807142\pi$
$410$	7672.70	0.924214
$411$	−5952.25	−0.714363
$412$	−4422.44	−0.528830
$413$	462.840	0.0551450
$414$	630.094	0.0748005
$415$	1173.68	0.138829
$416$	−12972.8	−1.52895
$417$	9520.50	1.11804
$418$	16252.8	1.90179
$419$	4185.21	0.487973	0.243987	−	0.969779i	$-0.421545\pi$
$419$	4185.21	0.487973	0.243987	+	0.969779i	$0.421545\pi$
$420$	−15114.2	−1.75594
$421$	15181.1	1.75744	0.878718	−	0.477341i	$-0.158399\pi$
$421$	15181.1	1.75744	0.878718	+	0.477341i	$0.158399\pi$
$422$	−24988.2	−2.88248
$423$	58.8790	0.00676784
$424$	17121.6	1.96108
$425$	−164.576	−0.0187838
$426$	8063.55	0.917090
$427$	322.662	0.0365684
$428$	−28572.2	−3.22685
$429$	−6162.08	−0.693491
$430$	2076.24	0.232849
$431$	4213.91	0.470944	0.235472	−	0.971881i	$-0.424336\pi$
$431$	4213.91	0.470944	0.235472	+	0.971881i	$0.424336\pi$
$432$	−23915.7	−2.66353
$433$	4617.18	0.512442	0.256221	−	0.966618i	$-0.417523\pi$
$433$	4617.18	0.512442	0.256221	+	0.966618i	$0.417523\pi$
$434$	13.5181	0.00149514
$435$	−1350.98	−0.148907
$436$	−5968.39	−0.655583
$437$	1985.42	0.217336
$438$	13603.2	1.48398
$439$	2984.05	0.324422	0.162211	−	0.986756i	$-0.448138\pi$
$439$	2984.05	0.324422	0.162211	+	0.986756i	$0.448138\pi$
$440$	21543.6	2.33420
$441$	340.139	0.0367281
$442$	−1251.84	−0.134715
$443$	11508.5	1.23428	0.617140	−	0.786853i	$-0.288291\pi$
$443$	11508.5	1.23428	0.617140	+	0.786853i	$0.288291\pi$
$444$	10398.3	1.11144
$445$	−4529.58	−0.482523
$446$	20476.8	2.17400
$447$	−11953.8	−1.26487
$448$	−9623.01	−1.01483
$449$	9865.58	1.03694	0.518469	−	0.855096i	$-0.326502\pi$
$449$	9865.58	1.03694	0.518469	+	0.855096i	$0.326502\pi$
$450$	−693.720	−0.0726717
$451$	5269.11	0.550139
$452$	−34534.0	−3.59367
$453$	11052.4	1.14633
$454$	−2178.69	−0.225222
$455$	−6117.90	−0.630355
$456$	−24190.8	−2.48430
$457$	2180.36	0.223179	0.111590	−	0.993754i	$-0.464406\pi$
$457$	2180.36	0.223179	0.111590	+	0.993754i	$0.464406\pi$
$458$	3819.97	0.389728
$459$	−977.332	−0.0993855
$460$	4468.77	0.452951
$461$	9735.52	0.983576	0.491788	−	0.870715i	$-0.336344\pi$
$461$	9735.52	0.983576	0.491788	+	0.870715i	$0.336344\pi$
$462$	−14646.2	−1.47490
$463$	−10482.2	−1.05216	−0.526079	−	0.850436i	$-0.676338\pi$
$463$	−10482.2	−1.05216	−0.526079	+	0.850436i	$0.676338\pi$
$464$	−4612.10	−0.461447
$465$	7.20834	0.000718879 0
$466$	2313.83	0.230013
$467$	−14354.8	−1.42240	−0.711199	−	0.702991i	$-0.751847\pi$
$467$	−14354.8	−1.42240	−0.711199	+	0.702991i	$0.751847\pi$
$468$	−3739.50	−0.369355
$469$	12355.2	1.21644
$470$	589.245	0.0578294
$471$	11208.1	1.09648
$472$	1667.37	0.162599
$473$	1425.83	0.138604
$474$	−5884.34	−0.570204
$475$	−2185.91	−0.211150
$476$	−2108.60	−0.203041
$477$	1490.36	0.143059
$478$	−18895.1	−1.80804
$479$	18104.7	1.72698	0.863491	−	0.504365i	$-0.168273\pi$
$479$	18104.7	1.72698	0.863491	+	0.504365i	$0.168273\pi$
$480$	−16441.9	−1.56347
$481$	4209.00	0.398989
$482$	−29920.7	−2.82749
$483$	−1789.17	−0.168551
$484$	−780.541	−0.0733040
$485$	4269.58	0.399735
$486$	−7571.01	−0.706642
$487$	−18733.5	−1.74311	−0.871556	−	0.490295i	$-0.836889\pi$
$487$	−18733.5	−1.74311	−0.871556	+	0.490295i	$0.836889\pi$
$488$	1162.38	0.107825
$489$	−5287.32	−0.488959
$490$	3404.02	0.313833
$491$	1852.74	0.170291	0.0851456	−	0.996369i	$-0.472864\pi$
$491$	1852.74	0.170291	0.0851456	+	0.996369i	$0.472864\pi$
$492$	−13317.0	−1.22028
$493$	−188.477	−0.0172182
$494$	−16627.0	−1.51434
$495$	1875.27	0.170277
$496$	24.6086	0.00222774
$497$	5497.83	0.496200
$498$	−2874.49	−0.258652
$499$	8756.55	0.785565	0.392782	−	0.919631i	$-0.371513\pi$
$499$	8756.55	0.785565	0.392782	+	0.919631i	$0.371513\pi$
$500$	−29206.8	−2.61234
$501$	−746.950	−0.0666093
$502$	17415.7	1.54840
$503$	−11005.3	−0.975551	−0.487776	−	0.872969i	$-0.662192\pi$
$503$	−11005.3	−0.975551	−0.487776	+	0.872969i	$0.662192\pi$
$504$	−5234.40	−0.462617
$505$	4523.21	0.398575
$506$	4330.42	0.380456
$507$	−3947.39	−0.345779
$508$	34813.0	3.04050
$509$	5018.41	0.437008	0.218504	−	0.975836i	$-0.429882\pi$
$509$	5018.41	0.437008	0.218504	+	0.975836i	$0.429882\pi$
$510$	−1586.60	−0.137756
$511$	9274.80	0.802922
$512$	20281.6	1.75064
$513$	−12981.0	−1.11720
$514$	21720.5	1.86391
$515$	−2268.81	−0.194128
$516$	−3603.58	−0.307439
$517$	404.655	0.0344230
$518$	10004.1	0.848561
$519$	−18058.7	−1.52734
$520$	−22039.6	−1.85865
$521$	12130.0	1.02001	0.510005	−	0.860171i	$-0.329643\pi$
$521$	12130.0	1.02001	0.510005	+	0.860171i	$0.329643\pi$
$522$	−794.466	−0.0666146
$523$	−133.535	−0.0111646	−0.00558231	−	0.999984i	$-0.501777\pi$
$523$	−133.535	−0.0111646	−0.00558231	+	0.999984i	$0.501777\pi$
$524$	−33565.0	−2.79827
$525$	1969.84	0.163754
$526$	5163.81	0.428047
$527$	1.00565	8.31247e−5 0
$528$	−26662.2	−2.19759
$529$	529.000	0.0434783
$530$	14915.1	1.22240
$531$	145.137	0.0118614
$532$	−28006.6	−2.28241
$533$	−5390.44	−0.438059
$534$	11093.5	0.898991
$535$	−14658.2	−1.18454
$536$	44509.3	3.58677
$537$	4022.50	0.323247
$538$	14723.0	1.17984
$539$	2337.66	0.186809
$540$	−29217.4	−2.32837
$541$	1615.93	0.128418	0.0642091	−	0.997936i	$-0.479548\pi$
$541$	1615.93	0.128418	0.0642091	+	0.997936i	$0.479548\pi$
$542$	−9235.07	−0.731883
$543$	−4948.15	−0.391060
$544$	−2293.83	−0.180785
$545$	−3061.92	−0.240657
$546$	14983.5	1.17442
$547$	2073.16	0.162051	0.0810254	−	0.996712i	$-0.474181\pi$
$547$	2073.16	0.162051	0.0810254	+	0.996712i	$0.474181\pi$
$548$	−24825.2	−1.93518
$549$	101.180	0.00786568
$550$	−4767.70	−0.369628
$551$	−2503.36	−0.193551
$552$	−6445.44	−0.496986
$553$	−4012.02	−0.308514
$554$	17020.8	1.30531
$555$	5334.55	0.407998
$556$	39707.3	3.02872
$557$	20539.1	1.56242	0.781210	−	0.624269i	$-0.214603\pi$
$557$	20539.1	1.56242	0.781210	+	0.624269i	$0.214603\pi$
$558$	4.23900	0.000321597 0
$559$	−1458.65	−0.110366
$560$	−26471.1	−1.99752
$561$	−1089.57	−0.0819996
$562$	−22778.4	−1.70970
$563$	2926.35	0.219060	0.109530	−	0.993983i	$-0.465065\pi$
$563$	2926.35	0.219060	0.109530	+	0.993983i	$0.465065\pi$
$564$	−1022.71	−0.0763544
$565$	−17716.7	−1.31920
$566$	1457.29	0.108224
$567$	9344.65	0.692131
$568$	19805.8	1.46309
$569$	−4757.21	−0.350496	−0.175248	−	0.984524i	$-0.556073\pi$
$569$	−4757.21	−0.350496	−0.175248	+	0.984524i	$0.556073\pi$
$570$	−21073.3	−1.54853
$571$	−14442.5	−1.05849	−0.529247	−	0.848468i	$-0.677526\pi$
$571$	−14442.5	−1.05849	−0.529247	+	0.848468i	$0.677526\pi$
$572$	−25700.3	−1.87864
$573$	−4429.88	−0.322969
$574$	−12812.2	−0.931654
$575$	−582.418	−0.0422409
$576$	−3017.58	−0.218285
$577$	12069.4	0.870806	0.435403	−	0.900236i	$-0.356606\pi$
$577$	12069.4	0.870806	0.435403	+	0.900236i	$0.356606\pi$
$578$	25524.3	1.83680
$579$	68.3152	0.00490342
$580$	−5634.54	−0.403382
$581$	−1959.86	−0.139946
$582$	−10456.7	−0.744749
$583$	10242.7	0.727634
$584$	33412.2	2.36748
$585$	−1918.45	−0.135586
$586$	29740.2	2.09651
$587$	1842.67	0.129566	0.0647829	−	0.997899i	$-0.479364\pi$
$587$	1842.67	0.129566	0.0647829	+	0.997899i	$0.479364\pi$
$588$	−5908.12	−0.414365
$589$	13.3571	0.000934412 0
$590$	1452.49	0.101353
$591$	9457.44	0.658252
$592$	18211.6	1.26435
$593$	22123.8	1.53207	0.766033	−	0.642802i	$-0.222228\pi$
$593$	22123.8	1.53207	0.766033	+	0.642802i	$0.222228\pi$
$594$	−28312.9	−1.95571
$595$	−1081.76	−0.0745343
$596$	−49856.0	−3.42648
$597$	−9148.73	−0.627190
$598$	−4430.12	−0.302945
$599$	−21906.3	−1.49427	−0.747136	−	0.664671i	$-0.768572\pi$
$599$	−21906.3	−1.49427	−0.747136	+	0.664671i	$0.768572\pi$
$600$	7096.29	0.482842
$601$	261.023	0.0177161	0.00885803	−	0.999961i	$-0.497180\pi$
$601$	261.023	0.0177161	0.00885803	+	0.999961i	$0.497180\pi$
$602$	−3466.98	−0.234723
$603$	3874.33	0.261650
$604$	46096.4	3.10536
$605$	−400.435	−0.0269091
$606$	−11077.9	−0.742587
$607$	−4750.72	−0.317670	−0.158835	−	0.987305i	$-0.550774\pi$
$607$	−4750.72	−0.317670	−0.158835	+	0.987305i	$0.550774\pi$
$608$	−30466.8	−2.03223
$609$	2255.91	0.150105
$610$	1012.58	0.0672102
$611$	−413.972	−0.0274100
$612$	−661.214	−0.0436732
$613$	−6986.76	−0.460347	−0.230173	−	0.973150i	$-0.573929\pi$
$613$	−6986.76	−0.460347	−0.230173	+	0.973150i	$0.573929\pi$
$614$	42875.3	2.81809
$615$	−6831.91	−0.447950
$616$	−35974.2	−2.35299
$617$	−1678.76	−0.109537	−0.0547684	−	0.998499i	$-0.517442\pi$
$617$	−1678.76	−0.109537	−0.0547684	+	0.998499i	$0.517442\pi$
$618$	5556.59	0.361681
$619$	11035.1	0.716538	0.358269	−	0.933618i	$-0.383367\pi$
$619$	11035.1	0.716538	0.358269	+	0.933618i	$0.383367\pi$
$620$	30.0640	0.00194742
$621$	−3458.67	−0.223497
$622$	−22116.4	−1.42570
$623$	7563.66	0.486407
$624$	27276.1	1.74987
$625$	−11818.5	−0.756381
$626$	−17203.9	−1.09841
$627$	−14471.8	−0.921765
$628$	46745.9	2.97033
$629$	744.231	0.0471772
$630$	−4559.83	−0.288362
$631$	24684.4	1.55732	0.778662	−	0.627444i	$-0.215899\pi$
$631$	24684.4	1.55732	0.778662	+	0.627444i	$0.215899\pi$
$632$	−14453.2	−0.909679
$633$	22250.0	1.39709
$634$	−27143.7	−1.70034
$635$	17859.9	1.11614
$636$	−25887.1	−1.61398
$637$	−2391.49	−0.148751
$638$	−5460.09	−0.338820
$639$	1724.01	0.106730
$640$	−2009.38	−0.124106
$641$	12656.3	0.779867	0.389933	−	0.920843i	$-0.372498\pi$
$641$	12656.3	0.779867	0.389933	+	0.920843i	$0.372498\pi$
$642$	35899.7	2.20693
$643$	−6059.72	−0.371651	−0.185826	−	0.982583i	$-0.559496\pi$
$643$	−6059.72	−0.371651	−0.185826	+	0.982583i	$0.559496\pi$
$644$	−7462.13	−0.456598
$645$	−1848.72	−0.112858
$646$	−2939.97	−0.179058
$647$	−17520.8	−1.06463	−0.532314	−	0.846547i	$-0.678677\pi$
$647$	−17520.8	−1.06463	−0.532314	+	0.846547i	$0.678677\pi$
$648$	33663.9	2.04081
$649$	997.478	0.0603304
$650$	4877.47	0.294323
$651$	−12.0368	−0.000724667 0
$652$	−22051.9	−1.32457
$653$	−1837.19	−0.110099	−0.0550496	−	0.998484i	$-0.517532\pi$
$653$	−1837.19	−0.110099	−0.0550496	+	0.998484i	$0.517532\pi$
$654$	7499.00	0.448370
$655$	−17219.6	−1.02721
$656$	−23323.5	−1.38815
$657$	2908.39	0.172705
$658$	−983.943	−0.0582950
$659$	−4544.10	−0.268609	−0.134304	−	0.990940i	$-0.542880\pi$
$659$	−4544.10	−0.268609	−0.134304	+	0.990940i	$0.542880\pi$
$660$	−32572.9	−1.92106
$661$	−25659.1	−1.50987	−0.754935	−	0.655799i	$-0.772332\pi$
$661$	−25659.1	−1.50987	−0.754935	+	0.655799i	$0.772332\pi$
$662$	−55056.9	−3.23240
$663$	1114.66	0.0652938
$664$	−7060.35	−0.412643
$665$	−14368.0	−0.837847
$666$	3137.08	0.182521
$667$	−667.000	−0.0387202
$668$	−3115.32	−0.180442
$669$	−18232.9	−1.05370
$670$	38773.3	2.23573
$671$	695.376	0.0400070
$672$	27455.3	1.57606
$673$	−18783.9	−1.07588	−0.537940	−	0.842983i	$-0.680797\pi$
$673$	−18783.9	−1.07588	−0.537940	+	0.842983i	$0.680797\pi$
$674$	37755.4	2.15769
$675$	3807.93	0.217137
$676$	−16463.5	−0.936701
$677$	26086.6	1.48093	0.740465	−	0.672095i	$-0.234605\pi$
$677$	26086.6	1.48093	0.740465	+	0.672095i	$0.234605\pi$
$678$	43390.3	2.45781
$679$	−7129.50	−0.402953
$680$	−3897.02	−0.219770
$681$	1939.94	0.109161
$682$	29.1332	0.00163573
$683$	30777.0	1.72423	0.862115	−	0.506713i	$-0.169140\pi$
$683$	30777.0	1.72423	0.862115	+	0.506713i	$0.169140\pi$
$684$	−8782.29	−0.490935
$685$	−12735.9	−0.710384
$686$	−35649.8	−1.98414
$687$	−3401.37	−0.188894
$688$	−6311.35	−0.349735
$689$	−10478.6	−0.579393
$690$	−5614.80	−0.309785
$691$	15410.4	0.848395	0.424198	−	0.905570i	$-0.360556\pi$
$691$	15410.4	0.848395	0.424198	+	0.905570i	$0.360556\pi$
$692$	−75317.7	−4.13750
$693$	−3131.40	−0.171648
$694$	51543.3	2.81924
$695$	20370.8	1.11181
$696$	8126.86	0.442598
$697$	−953.131	−0.0517969
$698$	4494.78	0.243739
$699$	−2060.28	−0.111483
$700$	8215.64	0.443603
$701$	5557.41	0.299430	0.149715	−	0.988729i	$-0.452164\pi$
$701$	5557.41	0.299430	0.149715	+	0.988729i	$0.452164\pi$
$702$	28964.8	1.55727
$703$	9884.93	0.530323
$704$	−20738.8	−1.11026
$705$	−524.674	−0.0280289
$706$	64234.3	3.42421
$707$	−7553.03	−0.401783
$708$	−2520.99	−0.133820
$709$	15864.2	0.840329	0.420165	−	0.907448i	$-0.361972\pi$
$709$	15864.2	0.840329	0.420165	+	0.907448i	$0.361972\pi$
$710$	17253.4	0.911982
$711$	−1258.09	−0.0663599
$712$	27247.9	1.43421
$713$	3.55888	0.000186930 0
$714$	2649.36	0.138865
$715$	−13184.8	−0.689629
$716$	16776.7	0.875665
$717$	16824.5	0.876323
$718$	−28159.1	−1.46363
$719$	23567.7	1.22243	0.611214	−	0.791466i	$-0.290682\pi$
$719$	23567.7	1.22243	0.611214	+	0.791466i	$0.290682\pi$
$720$	−8300.79	−0.429656
$721$	3788.55	0.195691
$722$	−3105.56	−0.160079
$723$	26641.9	1.37043
$724$	−20637.3	−1.05937
$725$	734.353	0.0376182
$726$	980.713	0.0501345
$727$	34258.7	1.74771	0.873856	−	0.486186i	$-0.161612\pi$
$727$	34258.7	1.74771	0.873856	+	0.486186i	$0.161612\pi$
$728$	36802.6	1.87362
$729$	21875.4	1.11138
$730$	29106.3	1.47572
$731$	−257.918	−0.0130498
$732$	−1757.47	−0.0887403
$733$	27727.4	1.39718	0.698590	−	0.715522i	$-0.253811\pi$
$733$	27727.4	1.39718	0.698590	+	0.715522i	$0.253811\pi$
$734$	−57123.6	−2.87257
$735$	−3031.00	−0.152109
$736$	−8117.64	−0.406549
$737$	26627.0	1.33082
$738$	−4017.63	−0.200394
$739$	33682.5	1.67663	0.838315	−	0.545186i	$-0.183541\pi$
$739$	33682.5	1.67663	0.838315	+	0.545186i	$0.183541\pi$
$740$	22248.9	1.10525
$741$	14805.0	0.733974
$742$	−24905.8	−1.23224
$743$	13459.5	0.664578	0.332289	−	0.943178i	$-0.392179\pi$
$743$	13459.5	0.664578	0.332289	+	0.943178i	$0.392179\pi$
$744$	−43.3622	−0.00213674
$745$	−25577.3	−1.25782
$746$	−6444.03	−0.316264
$747$	−614.572	−0.0301018
$748$	−4544.30	−0.222134
$749$	24476.8	1.19408
$750$	36697.0	1.78665
$751$	−31573.5	−1.53413	−0.767067	−	0.641567i	$-0.778284\pi$
$751$	−31573.5	−1.53413	−0.767067	+	0.641567i	$0.778284\pi$
$752$	−1791.19	−0.0868589
$753$	−15507.2	−0.750484
$754$	5585.81	0.269792
$755$	23648.5	1.13994
$756$	48788.4	2.34711
$757$	6421.33	0.308305	0.154153	−	0.988047i	$-0.450735\pi$
$757$	6421.33	0.308305	0.154153	+	0.988047i	$0.450735\pi$
$758$	29656.7	1.42108
$759$	−3855.88	−0.184400
$760$	−51760.5	−2.47046
$761$	360.810	0.0171870	0.00859352	−	0.999963i	$-0.497265\pi$
$761$	360.810	0.0171870	0.00859352	+	0.999963i	$0.497265\pi$
$762$	−43740.9	−2.07948
$763$	5112.91	0.242595
$764$	−18475.8	−0.874910
$765$	−339.218	−0.0160320
$766$	26636.1	1.25640
$767$	−1020.44	−0.0480393
$768$	−16625.4	−0.781143
$769$	25728.9	1.20651	0.603257	−	0.797547i	$-0.293869\pi$
$769$	25728.9	1.20651	0.603257	+	0.797547i	$0.293869\pi$
$770$	−31338.2	−1.46669
$771$	−19340.3	−0.903403
$772$	284.923	0.0132832
$773$	−1942.26	−0.0903729	−0.0451865	−	0.998979i	$-0.514388\pi$
$773$	−1942.26	−0.0903729	−0.0451865	+	0.998979i	$0.514388\pi$
$774$	−1087.17	−0.0504879
$775$	−3.91825	−0.000181610 0
$776$	−25683.8	−1.18814
$777$	−8907.83	−0.411283
$778$	27857.8	1.28374
$779$	−12659.6	−0.582254
$780$	33322.9	1.52968
$781$	11848.5	0.542859
$782$	−783.330	−0.0358208
$783$	4360.94	0.199039
$784$	−10347.5	−0.471371
$785$	23981.7	1.09038
$786$	42172.8	1.91381
$787$	42081.2	1.90601	0.953006	−	0.302951i	$-0.0979720\pi$
$787$	42081.2	1.90601	0.953006	+	0.302951i	$0.0979720\pi$
$788$	39444.3	1.78318
$789$	−4597.95	−0.207467
$790$	−12590.6	−0.567028
$791$	29584.0	1.32982
$792$	−11280.8	−0.506118
$793$	−711.387	−0.0318563
$794$	−30755.1	−1.37463
$795$	−13280.7	−0.592475
$796$	−38156.8	−1.69903
$797$	7070.55	0.314243	0.157121	−	0.987579i	$-0.449779\pi$
$797$	7070.55	0.314243	0.157121	+	0.987579i	$0.449779\pi$
$798$	35189.0	1.56100
$799$	−73.1982	−0.00324101
$800$	8937.34	0.394979
$801$	2371.81	0.104624
$802$	27752.6	1.22192
$803$	19988.3	0.878422
$804$	−67296.0	−2.95193
$805$	−3828.24	−0.167612
$806$	−29.8040	−0.00130248
$807$	−13109.7	−0.571849
$808$	−27209.6	−1.18469
$809$	−22961.1	−0.997859	−0.498930	−	0.866643i	$-0.666273\pi$
$809$	−22961.1	−0.997859	−0.498930	+	0.866643i	$0.666273\pi$
$810$	29325.5	1.27209
$811$	−35553.4	−1.53939	−0.769697	−	0.638409i	$-0.779593\pi$
$811$	−35553.4	−1.53939	−0.769697	+	0.638409i	$0.779593\pi$
$812$	9408.77	0.406629
$813$	8223.08	0.354730
$814$	21560.1	0.928353
$815$	−11313.1	−0.486236
$816$	4822.94	0.206908
$817$	−3425.68	−0.146695
$818$	71259.7	3.04589
$819$	3203.50	0.136678
$820$	−28494.0	−1.21348
$821$	−12020.6	−0.510987	−0.255494	−	0.966811i	$-0.582238\pi$
$821$	−12020.6	−0.510987	−0.255494	+	0.966811i	$0.582238\pi$
$822$	31191.7	1.32352
$823$	−16574.6	−0.702011	−0.351005	−	0.936373i	$-0.614160\pi$
$823$	−16574.6	−0.702011	−0.351005	+	0.936373i	$0.614160\pi$
$824$	13648.2	0.577010
$825$	4245.24	0.179152
$826$	−2425.43	−0.102169
$827$	−1606.35	−0.0675435	−0.0337717	−	0.999430i	$-0.510752\pi$
$827$	−1606.35	−0.0675435	−0.0337717	+	0.999430i	$0.510752\pi$
$828$	−2339.97	−0.0982120
$829$	−35427.7	−1.48426	−0.742132	−	0.670254i	$-0.766185\pi$
$829$	−35427.7	−1.48426	−0.742132	+	0.670254i	$0.766185\pi$
$830$	−6150.47	−0.257212
$831$	−15155.6	−0.632662
$832$	21216.3	0.884065
$833$	−422.860	−0.0175885
$834$	−49890.4	−2.07142
$835$	−1598.23	−0.0662383
$836$	−60357.7	−2.49703
$837$	−23.2685	−0.000960903 0
$838$	−21931.8	−0.904082
$839$	11048.8	0.454646	0.227323	−	0.973819i	$-0.427003\pi$
$839$	11048.8	0.454646	0.227323	+	0.973819i	$0.427003\pi$
$840$	46644.1	1.91592
$841$	841.000	0.0344828
$842$	−79553.6	−3.25605
$843$	20282.3	0.828660
$844$	92798.3	3.78466
$845$	−8446.13	−0.343853
$846$	−308.544	−0.0125390
$847$	668.662	0.0271257
$848$	−45339.0	−1.83602
$849$	−1297.60	−0.0524541
$850$	862.430	0.0348013
$851$	2633.76	0.106092
$852$	−29945.5	−1.20413
$853$	−17616.2	−0.707112	−0.353556	−	0.935413i	$-0.615028\pi$
$853$	−17616.2	−0.707112	−0.353556	+	0.935413i	$0.615028\pi$
$854$	−1690.85	−0.0677513
$855$	−4505.52	−0.180217
$856$	88177.2	3.52083
$857$	−34949.9	−1.39307	−0.696537	−	0.717521i	$-0.745277\pi$
$857$	−34949.9	−1.39307	−0.696537	+	0.717521i	$0.745277\pi$
$858$	32291.2	1.28485
$859$	20257.4	0.804626	0.402313	−	0.915502i	$-0.368206\pi$
$859$	20257.4	0.804626	0.402313	+	0.915502i	$0.368206\pi$
$860$	−7710.49	−0.305727
$861$	11408.2	0.451556
$862$	−22082.2	−0.872531
$863$	−6884.27	−0.271545	−0.135772	−	0.990740i	$-0.543352\pi$
$863$	−6884.27	−0.271545	−0.135772	+	0.990740i	$0.543352\pi$
$864$	53074.2	2.08984
$865$	−38639.7	−1.51883
$866$	−24195.4	−0.949417
$867$	−22727.3	−0.890265
$868$	−50.2020	−0.00196309
$869$	−8646.39	−0.337524
$870$	7079.53	0.275883
$871$	−27240.0	−1.05969
$872$	18419.1	0.715311
$873$	−2235.66	−0.0866733
$874$	−10404.2	−0.402664
$875$	25020.5	0.966681
$876$	−50517.8	−1.94845
$877$	−3446.74	−0.132712	−0.0663558	−	0.997796i	$-0.521137\pi$
$877$	−3446.74	−0.132712	−0.0663558	+	0.997796i	$0.521137\pi$
$878$	−15637.4	−0.601066
$879$	−26481.2	−1.01614
$880$	−57048.5	−2.18535
$881$	16514.0	0.631520	0.315760	−	0.948839i	$-0.397741\pi$
$881$	16514.0	0.631520	0.315760	+	0.948839i	$0.397741\pi$
$882$	−1782.44	−0.0680473
$883$	−29522.7	−1.12516	−0.562581	−	0.826742i	$-0.690192\pi$
$883$	−29522.7	−1.12516	−0.562581	+	0.826742i	$0.690192\pi$
$884$	4648.93	0.176878
$885$	−1293.33	−0.0491239
$886$	−60308.2	−2.28679
$887$	−10113.3	−0.382830	−0.191415	−	0.981509i	$-0.561308\pi$
$887$	−10113.3	−0.382830	−0.191415	+	0.981509i	$0.561308\pi$
$888$	−32090.2	−1.21270
$889$	−29823.1	−1.12512
$890$	23736.4	0.893984
$891$	20138.9	0.757214
$892$	−76044.3	−2.85443
$893$	−972.223	−0.0364325
$894$	62641.7	2.34346
$895$	8606.85	0.321447
$896$	3355.34	0.125105
$897$	3944.66	0.146832
$898$	−51698.7	−1.92117
$899$	−4.48729	−0.000166473 0
$900$	2576.26	0.0954169
$901$	−1852.81	−0.0685084
$902$	−27611.8	−1.01926
$903$	3087.06	0.113766
$904$	106576.	3.92108
$905$	−10587.4	−0.388882
$906$	−57918.0	−2.12384
$907$	−53029.8	−1.94137	−0.970687	−	0.240345i	$-0.922739\pi$
$907$	−53029.8	−1.94137	−0.970687	+	0.240345i	$0.922739\pi$
$908$	8090.95	0.295713
$909$	−2368.47	−0.0864217
$910$	32059.7	1.16788
$911$	28847.1	1.04912	0.524559	−	0.851374i	$-0.324230\pi$
$911$	28847.1	1.04912	0.524559	+	0.851374i	$0.324230\pi$
$912$	64058.6	2.32587
$913$	−4223.74	−0.153106
$914$	−11425.8	−0.413491
$915$	−901.621	−0.0325756
$916$	−14186.2	−0.511707
$917$	28754.0	1.03548
$918$	5121.52	0.184134
$919$	14361.0	0.515480	0.257740	−	0.966214i	$-0.417022\pi$
$919$	14361.0	0.515480	0.257740	+	0.966214i	$0.417022\pi$
$920$	−13791.1	−0.494218
$921$	−38177.0	−1.36588
$922$	−51017.2	−1.82230
$923$	−12121.3	−0.432262
$924$	54391.4	1.93652
$925$	−2899.71	−0.103072
$926$	54930.0	1.94936
$927$	1188.01	0.0420921
$928$	10235.3	0.362058
$929$	20175.2	0.712514	0.356257	−	0.934388i	$-0.384053\pi$
$929$	20175.2	0.712514	0.356257	+	0.934388i	$0.384053\pi$
$930$	−37.7740	−0.00133189
$931$	−5616.45	−0.197714
$932$	−8592.84	−0.302004
$933$	19692.8	0.691011
$934$	75223.5	2.63532
$935$	−2331.33	−0.0815429
$936$	11540.5	0.403006
$937$	−48414.5	−1.68797	−0.843987	−	0.536364i	$-0.819798\pi$
$937$	−48414.5	−1.68797	−0.843987	+	0.536364i	$0.819798\pi$
$938$	−64745.1	−2.25373
$939$	15318.6	0.532380
$940$	−2188.27	−0.0759292
$941$	40969.1	1.41929	0.709646	−	0.704559i	$-0.248855\pi$
$941$	40969.1	1.41929	0.709646	+	0.704559i	$0.248855\pi$
$942$	−58734.1	−2.03149
$943$	−3373.03	−0.116480
$944$	−4415.29	−0.152230
$945$	25029.6	0.861600
$946$	−7471.77	−0.256795
$947$	−11633.7	−0.399203	−0.199601	−	0.979877i	$-0.563965\pi$
$947$	−11633.7	−0.399203	−0.199601	+	0.979877i	$0.563965\pi$
$948$	21852.6	0.748669
$949$	−20448.6	−0.699461
$950$	11454.8	0.391205
$951$	24169.3	0.824124
$952$	6507.39	0.221540
$953$	−32416.0	−1.10184	−0.550922	−	0.834557i	$-0.685724\pi$
$953$	−32416.0	−1.10184	−0.550922	+	0.834557i	$0.685724\pi$
$954$	−7809.95	−0.265049
$955$	−9478.51	−0.321170
$956$	70170.4	2.37392
$957$	4861.76	0.164220
$958$	−94874.2	−3.19963
$959$	21266.9	0.716103
$960$	26889.8	0.904026
$961$	−29791.0	−0.999999
$962$	−22056.5	−0.739220
$963$	7675.43	0.256840
$964$	111116.	3.71245
$965$	146.172	0.00487611
$966$	9375.81	0.312279
$967$	−2840.17	−0.0944507	−0.0472253	−	0.998884i	$-0.515038\pi$
$967$	−2840.17	−0.0944507	−0.0472253	+	0.998884i	$0.515038\pi$
$968$	2408.84	0.0799825
$969$	2617.80	0.0867863
$970$	−22373.9	−0.740601
$971$	46069.1	1.52258	0.761291	−	0.648411i	$-0.224566\pi$
$971$	46069.1	1.52258	0.761291	+	0.648411i	$0.224566\pi$
$972$	28116.3	0.927811
$973$	−34015.9	−1.12076
$974$	98169.4	3.22952
$975$	−4342.99	−0.142653
$976$	−3078.05	−0.100949
$977$	−38696.5	−1.26716	−0.633578	−	0.773678i	$-0.718415\pi$
$977$	−38696.5	−1.26716	−0.633578	+	0.773678i	$0.718415\pi$
$978$	27707.2	0.905909
$979$	16300.6	0.532145
$980$	−12641.5	−0.412058
$981$	1603.30	0.0521810
$982$	−9708.93	−0.315503
$983$	−23050.5	−0.747911	−0.373956	−	0.927447i	$-0.621999\pi$
$983$	−23050.5	−0.747911	−0.373956	+	0.927447i	$0.621999\pi$
$984$	41097.7	1.33145
$985$	20235.8	0.654586
$986$	987.677	0.0319007
$987$	876.121	0.0282545
$988$	61747.4	1.98831
$989$	−912.744	−0.0293464
$990$	−9827.00	−0.315477
$991$	1533.58	0.0491582	0.0245791	−	0.999698i	$-0.492175\pi$
$991$	1533.58	0.0491582	0.0245791	+	0.999698i	$0.492175\pi$
$992$	−54.6120	−0.00174791
$993$	49023.6	1.56668
$994$	−28810.3	−0.919324
$995$	−19575.3	−0.623697
$996$	10674.9	0.339607
$997$	43303.4	1.37556	0.687779	−	0.725920i	$-0.258586\pi$
$997$	43303.4	1.37556	0.687779	+	0.725920i	$0.258586\pi$
$998$	−45887.0	−1.45544
$999$	−17219.9	−0.545358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.a.1.2	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-5.24031 q^{2} +4.66607 q^{3} +19.4609 q^{4} +9.98386 q^{5} -24.4516 q^{6} -16.6714 q^{7} -60.0584 q^{8} -5.22782 q^{9} +O(q^{10})\)	\(q-5.24031 q^{2} +4.66607 q^{3} +19.4609 q^{4} +9.98386 q^{5} -24.4516 q^{6} -16.6714 q^{7} -60.0584 q^{8} -5.22782 q^{9} -52.3185 q^{10} -35.9290 q^{11} +90.8056 q^{12} +36.7562 q^{13} +87.3635 q^{14} +46.5854 q^{15} +159.038 q^{16} +6.49920 q^{17} +27.3954 q^{18} +86.3228 q^{19} +194.294 q^{20} -77.7900 q^{21} +188.279 q^{22} +23.0000 q^{23} -280.237 q^{24} -25.3225 q^{25} -192.614 q^{26} -150.377 q^{27} -324.440 q^{28} -29.0000 q^{29} -244.122 q^{30} +0.154734 q^{31} -352.941 q^{32} -167.647 q^{33} -34.0578 q^{34} -166.445 q^{35} -101.738 q^{36} +114.511 q^{37} -452.358 q^{38} +171.507 q^{39} -599.615 q^{40} -146.654 q^{41} +407.644 q^{42} -39.6845 q^{43} -699.209 q^{44} -52.1938 q^{45} -120.527 q^{46} -11.2626 q^{47} +742.082 q^{48} -65.0634 q^{49} +132.698 q^{50} +30.3257 q^{51} +715.308 q^{52} -285.083 q^{53} +788.023 q^{54} -358.710 q^{55} +1001.26 q^{56} +402.788 q^{57} +151.969 q^{58} -27.7625 q^{59} +906.591 q^{60} -19.3542 q^{61} -0.810855 q^{62} +87.1552 q^{63} +577.216 q^{64} +366.969 q^{65} +878.523 q^{66} -741.100 q^{67} +126.480 q^{68} +107.320 q^{69} +872.225 q^{70} -329.775 q^{71} +313.974 q^{72} -556.329 q^{73} -600.074 q^{74} -118.157 q^{75} +1679.92 q^{76} +598.988 q^{77} -898.750 q^{78} +240.652 q^{79} +1587.81 q^{80} -560.519 q^{81} +768.510 q^{82} +117.558 q^{83} -1513.86 q^{84} +64.8871 q^{85} +207.959 q^{86} -135.316 q^{87} +2157.84 q^{88} -453.690 q^{89} +273.512 q^{90} -612.779 q^{91} +447.600 q^{92} +0.722000 q^{93} +59.0197 q^{94} +861.835 q^{95} -1646.85 q^{96} +427.648 q^{97} +340.952 q^{98} +187.830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) \) 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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