LMFDB - Embedded newform 723.4.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [723,4,Mod(1,723)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(723, 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("723.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 723 = 3 \cdot 241 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	723.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:	$42.6583809342$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	723.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14536 q^{2} -3.00000 q^{3} -3.39743 q^{4} +15.4086 q^{5} +6.43608 q^{6} -11.8098 q^{7} +24.4516 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.14536 q^{2} -3.00000 q^{3} -3.39743 q^{4} +15.4086 q^{5} +6.43608 q^{6} -11.8098 q^{7} +24.4516 q^{8} +9.00000 q^{9} -33.0569 q^{10} -43.9593 q^{11} +10.1923 q^{12} +41.0277 q^{13} +25.3364 q^{14} -46.2257 q^{15} -25.2780 q^{16} +116.327 q^{17} -19.3082 q^{18} +13.5198 q^{19} -52.3496 q^{20} +35.4295 q^{21} +94.3085 q^{22} -121.889 q^{23} -73.3548 q^{24} +112.424 q^{25} -88.0191 q^{26} -27.0000 q^{27} +40.1232 q^{28} -69.4696 q^{29} +99.1707 q^{30} +109.047 q^{31} -141.382 q^{32} +131.878 q^{33} -249.562 q^{34} -181.973 q^{35} -30.5769 q^{36} +394.488 q^{37} -29.0049 q^{38} -123.083 q^{39} +376.764 q^{40} +85.7192 q^{41} -76.0091 q^{42} -306.810 q^{43} +149.349 q^{44} +138.677 q^{45} +261.496 q^{46} -276.542 q^{47} +75.8339 q^{48} -203.528 q^{49} -241.190 q^{50} -348.980 q^{51} -139.389 q^{52} -588.227 q^{53} +57.9247 q^{54} -677.350 q^{55} -288.769 q^{56} -40.5595 q^{57} +149.037 q^{58} +570.735 q^{59} +157.049 q^{60} +108.993 q^{61} -233.946 q^{62} -106.289 q^{63} +505.540 q^{64} +632.178 q^{65} -282.926 q^{66} -731.737 q^{67} -395.212 q^{68} +365.667 q^{69} +390.397 q^{70} +572.223 q^{71} +220.064 q^{72} -16.9459 q^{73} -846.319 q^{74} -337.272 q^{75} -45.9327 q^{76} +519.153 q^{77} +264.057 q^{78} -162.062 q^{79} -389.497 q^{80} +81.0000 q^{81} -183.899 q^{82} +528.653 q^{83} -120.369 q^{84} +1792.43 q^{85} +658.219 q^{86} +208.409 q^{87} -1074.88 q^{88} +130.255 q^{89} -297.512 q^{90} -484.530 q^{91} +414.110 q^{92} -327.142 q^{93} +593.283 q^{94} +208.321 q^{95} +424.147 q^{96} +1113.98 q^{97} +436.640 q^{98} -395.634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 9 q^{2} - 87 q^{3} + 97 q^{4} + 62 q^{5} - 27 q^{6} - 30 q^{7} + 108 q^{8} + 261 q^{9}+O(q^{10}) $ 29 * q + 9 * q^2 - 87 * q^3 + 97 * q^4 + 62 * q^5 - 27 * q^6 - 30 * q^7 + 108 * q^8 + 261 * q^9	\( 29 q + 9 q^{2} - 87 q^{3} + 97 q^{4} + 62 q^{5} - 27 q^{6} - 30 q^{7} + 108 q^{8} + 261 q^{9} + 51 q^{10} + 46 q^{11} - 291 q^{12} + 250 q^{13} + 84 q^{14} - 186 q^{15} + 333 q^{16} + 128 q^{17} + 81 q^{18} + 58 q^{19} + 405 q^{20} + 90 q^{21} - 48 q^{22} + 232 q^{23} - 324 q^{24} + 707 q^{25} + 238 q^{26} - 783 q^{27} - 89 q^{28} + 590 q^{29} - 153 q^{30} - 468 q^{31} + 1068 q^{32} - 138 q^{33} + 287 q^{34} + 474 q^{35} + 873 q^{36} + 842 q^{37} + 160 q^{38} - 750 q^{39} + 434 q^{40} + 814 q^{41} - 252 q^{42} + 20 q^{43} + 150 q^{44} + 558 q^{45} - 37 q^{46} + 1004 q^{47} - 999 q^{48} + 1239 q^{49} + 839 q^{50} - 384 q^{51} + 1928 q^{52} + 2192 q^{53} - 243 q^{54} + 432 q^{55} + 437 q^{56} - 174 q^{57} - 28 q^{58} + 1288 q^{59} - 1215 q^{60} + 1502 q^{61} + 3059 q^{62} - 270 q^{63} + 3372 q^{64} + 2312 q^{65} + 144 q^{66} + 358 q^{67} + 4990 q^{68} - 696 q^{69} + 5366 q^{70} + 1938 q^{71} + 972 q^{72} + 3266 q^{73} + 2510 q^{74} - 2121 q^{75} + 3591 q^{76} + 5098 q^{77} - 714 q^{78} - 292 q^{79} + 8235 q^{80} + 2349 q^{81} + 4511 q^{82} + 4256 q^{83} + 267 q^{84} + 1998 q^{85} + 6860 q^{86} - 1770 q^{87} + 5935 q^{88} + 6428 q^{89} + 459 q^{90} - 1650 q^{91} + 6823 q^{92} + 1404 q^{93} + 3025 q^{94} + 1802 q^{95} - 3204 q^{96} + 5040 q^{97} + 9410 q^{98} + 414 q^{99}+O(q^{100}) \) 29 * q + 9 * q^2 - 87 * q^3 + 97 * q^4 + 62 * q^5 - 27 * q^6 - 30 * q^7 + 108 * q^8 + 261 * q^9 + 51 * q^10 + 46 * q^11 - 291 * q^12 + 250 * q^13 + 84 * q^14 - 186 * q^15 + 333 * q^16 + 128 * q^17 + 81 * q^18 + 58 * q^19 + 405 * q^20 + 90 * q^21 - 48 * q^22 + 232 * q^23 - 324 * q^24 + 707 * q^25 + 238 * q^26 - 783 * q^27 - 89 * q^28 + 590 * q^29 - 153 * q^30 - 468 * q^31 + 1068 * q^32 - 138 * q^33 + 287 * q^34 + 474 * q^35 + 873 * q^36 + 842 * q^37 + 160 * q^38 - 750 * q^39 + 434 * q^40 + 814 * q^41 - 252 * q^42 + 20 * q^43 + 150 * q^44 + 558 * q^45 - 37 * q^46 + 1004 * q^47 - 999 * q^48 + 1239 * q^49 + 839 * q^50 - 384 * q^51 + 1928 * q^52 + 2192 * q^53 - 243 * q^54 + 432 * q^55 + 437 * q^56 - 174 * q^57 - 28 * q^58 + 1288 * q^59 - 1215 * q^60 + 1502 * q^61 + 3059 * q^62 - 270 * q^63 + 3372 * q^64 + 2312 * q^65 + 144 * q^66 + 358 * q^67 + 4990 * q^68 - 696 * q^69 + 5366 * q^70 + 1938 * q^71 + 972 * q^72 + 3266 * q^73 + 2510 * q^74 - 2121 * q^75 + 3591 * q^76 + 5098 * q^77 - 714 * q^78 - 292 * q^79 + 8235 * q^80 + 2349 * q^81 + 4511 * q^82 + 4256 * q^83 + 267 * q^84 + 1998 * q^85 + 6860 * q^86 - 1770 * q^87 + 5935 * q^88 + 6428 * q^89 + 459 * q^90 - 1650 * q^91 + 6823 * q^92 + 1404 * q^93 + 3025 * q^94 + 1802 * q^95 - 3204 * q^96 + 5040 * q^97 + 9410 * q^98 + 414 * 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 $

$2$	−2.14536	−0.758499	−0.379250	−	0.925294i	$-0.623818\pi$
$2$	−2.14536	−0.758499	−0.379250	+	0.925294i	$0.623818\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−3.39743	−0.424679
$5$	15.4086	1.37818	0.689092	−	0.724674i	$-0.258010\pi$
$5$	15.4086	1.37818	0.689092	+	0.724674i	$0.258010\pi$
$6$	6.43608	0.437920
$7$	−11.8098	−0.637672	−0.318836	−	0.947810i	$-0.603292\pi$
$7$	−11.8098	−0.637672	−0.318836	+	0.947810i	$0.603292\pi$
$8$	24.4516	1.08062
$9$	9.00000	0.333333
$10$	−33.0569	−1.04535
$11$	−43.9593	−1.20493	−0.602465	−	0.798145i	$-0.705815\pi$
$11$	−43.9593	−1.20493	−0.602465	+	0.798145i	$0.705815\pi$
$12$	10.1923	0.245189
$13$	41.0277	0.875310	0.437655	−	0.899143i	$-0.355809\pi$
$13$	41.0277	0.875310	0.437655	+	0.899143i	$0.355809\pi$
$14$	25.3364	0.483673
$15$	−46.2257	−0.795695
$16$	−25.2780	−0.394968
$17$	116.327	1.65961	0.829805	−	0.558054i	$-0.188452\pi$
$17$	116.327	1.65961	0.829805	+	0.558054i	$0.188452\pi$
$18$	−19.3082	−0.252833
$19$	13.5198	0.163245	0.0816227	−	0.996663i	$-0.473990\pi$
$19$	13.5198	0.163245	0.0816227	+	0.996663i	$0.473990\pi$
$20$	−52.3496	−0.585286
$21$	35.4295	0.368160
$22$	94.3085	0.913938
$23$	−121.889	−1.10503	−0.552513	−	0.833504i	$-0.686331\pi$
$23$	−121.889	−1.10503	−0.552513	+	0.833504i	$0.686331\pi$
$24$	−73.3548	−0.623895
$25$	112.424	0.899391
$26$	−88.0191	−0.663922
$27$	−27.0000	−0.192450
$28$	40.1232	0.270806
$29$	−69.4696	−0.444834	−0.222417	−	0.974952i	$-0.571395\pi$
$29$	−69.4696	−0.444834	−0.222417	+	0.974952i	$0.571395\pi$
$30$	99.1707	0.603534
$31$	109.047	0.631790	0.315895	−	0.948794i	$-0.397695\pi$
$31$	109.047	0.631790	0.315895	+	0.948794i	$0.397695\pi$
$32$	−141.382	−0.781035
$33$	131.878	0.695667
$34$	−249.562	−1.25881
$35$	−181.973	−0.878829
$36$	−30.5769	−0.141560
$37$	394.488	1.75280	0.876398	−	0.481588i	$-0.159940\pi$
$37$	394.488	1.75280	0.876398	+	0.481588i	$0.159940\pi$
$38$	−29.0049	−0.123821
$39$	−123.083	−0.505360
$40$	376.764	1.48929
$41$	85.7192	0.326514	0.163257	−	0.986584i	$-0.447800\pi$
$41$	85.7192	0.326514	0.163257	+	0.986584i	$0.447800\pi$
$42$	−76.0091	−0.279249
$43$	−306.810	−1.08810	−0.544048	−	0.839054i	$-0.683109\pi$
$43$	−306.810	−1.08810	−0.544048	+	0.839054i	$0.683109\pi$
$44$	149.349	0.511709
$45$	138.677	0.459395
$46$	261.496	0.838161
$47$	−276.542	−0.858252	−0.429126	−	0.903245i	$-0.641178\pi$
$47$	−276.542	−0.858252	−0.429126	+	0.903245i	$0.641178\pi$
$48$	75.8339	0.228035
$49$	−203.528	−0.593375
$50$	−241.190	−0.682187
$51$	−348.980	−0.958176
$52$	−139.389	−0.371726
$53$	−588.227	−1.52451	−0.762257	−	0.647274i	$-0.775909\pi$
$53$	−588.227	−1.52451	−0.762257	+	0.647274i	$0.775909\pi$
$54$	57.9247	0.145973
$55$	−677.350	−1.66062
$56$	−288.769	−0.689079
$57$	−40.5595	−0.0942498
$58$	149.037	0.337406
$59$	570.735	1.25938	0.629689	−	0.776847i	$-0.283182\pi$
$59$	570.735	1.25938	0.629689	+	0.776847i	$0.283182\pi$
$60$	157.049	0.337915
$61$	108.993	0.228772	0.114386	−	0.993436i	$-0.463510\pi$
$61$	108.993	0.228772	0.114386	+	0.993436i	$0.463510\pi$
$62$	−233.946	−0.479212
$63$	−106.289	−0.212557
$64$	505.540	0.987382
$65$	632.178	1.20634
$66$	−282.926	−0.527663
$67$	−731.737	−1.33427	−0.667133	−	0.744938i	$-0.732479\pi$
$67$	−731.737	−1.33427	−0.667133	+	0.744938i	$0.732479\pi$
$68$	−395.212	−0.704802
$69$	365.667	0.637987
$70$	390.397	0.666591
$71$	572.223	0.956485	0.478242	−	0.878228i	$-0.341274\pi$
$71$	572.223	0.956485	0.478242	+	0.878228i	$0.341274\pi$
$72$	220.064	0.360206
$73$	−16.9459	−0.0271694	−0.0135847	−	0.999908i	$-0.504324\pi$
$73$	−16.9459	−0.0271694	−0.0135847	+	0.999908i	$0.504324\pi$
$74$	−846.319	−1.32949
$75$	−337.272	−0.519263
$76$	−45.9327	−0.0693269
$77$	519.153	0.768350
$78$	264.057	0.383315
$79$	−162.062	−0.230803	−0.115401	−	0.993319i	$-0.536815\pi$
$79$	−162.062	−0.230803	−0.115401	+	0.993319i	$0.536815\pi$
$80$	−389.497	−0.544339
$81$	81.0000	0.111111
$82$	−183.899	−0.247661
$83$	528.653	0.699123	0.349561	−	0.936913i	$-0.386331\pi$
$83$	528.653	0.699123	0.349561	+	0.936913i	$0.386331\pi$
$84$	−120.369	−0.156350
$85$	1792.43	2.28725
$86$	658.219	0.825320
$87$	208.409	0.256825
$88$	−1074.88	−1.30207
$89$	130.255	0.155134	0.0775671	−	0.996987i	$-0.475285\pi$
$89$	130.255	0.155134	0.0775671	+	0.996987i	$0.475285\pi$
$90$	−297.512	−0.348450
$91$	−484.530	−0.558160
$92$	414.110	0.469282
$93$	−327.142	−0.364764
$94$	593.283	0.650983
$95$	208.321	0.224982
$96$	424.147	0.450931
$97$	1113.98	1.16606	0.583028	−	0.812452i	$-0.301868\pi$
$97$	1113.98	1.16606	0.583028	+	0.812452i	$0.301868\pi$
$98$	436.640	0.450074
$99$	−395.634	−0.401643
$100$	−381.953	−0.381953
$101$	627.521	0.618224	0.309112	−	0.951026i	$-0.399968\pi$
$101$	627.521	0.618224	0.309112	+	0.951026i	$0.399968\pi$
$102$	748.687	0.726775
$103$	1487.79	1.42326	0.711631	−	0.702554i	$-0.247957\pi$
$103$	1487.79	1.42326	0.711631	+	0.702554i	$0.247957\pi$
$104$	1003.19	0.945876
$105$	545.918	0.507392
$106$	1261.96	1.15634
$107$	118.196	0.106789	0.0533944	−	0.998574i	$-0.482996\pi$
$107$	118.196	0.106789	0.0533944	+	0.998574i	$0.482996\pi$
$108$	91.7307	0.0817296
$109$	1515.18	1.33145	0.665726	−	0.746196i	$-0.268122\pi$
$109$	1515.18	1.33145	0.665726	+	0.746196i	$0.268122\pi$
$110$	1453.16	1.25958
$111$	−1183.46	−1.01198
$112$	298.529	0.251860
$113$	1274.25	1.06081	0.530405	−	0.847745i	$-0.322040\pi$
$113$	1274.25	1.06081	0.530405	+	0.847745i	$0.322040\pi$
$114$	87.0147	0.0714883
$115$	−1878.13	−1.52293
$116$	236.018	0.188912
$117$	369.249	0.291770
$118$	−1224.43	−0.955237
$119$	−1373.80	−1.05829
$120$	−1130.29	−0.859842
$121$	601.422	0.451857
$122$	−233.828	−0.173523
$123$	−257.158	−0.188513
$124$	−370.481	−0.268308
$125$	−193.780	−0.138658
$126$	228.027	0.161224
$127$	342.312	0.239175	0.119588	−	0.992824i	$-0.461843\pi$
$127$	342.312	0.239175	0.119588	+	0.992824i	$0.461843\pi$
$128$	46.4948	0.0321062
$129$	920.431	0.628213
$130$	−1356.25	−0.915006
$131$	2292.55	1.52902	0.764508	−	0.644614i	$-0.222982\pi$
$131$	2292.55	1.52902	0.764508	+	0.644614i	$0.222982\pi$
$132$	−448.047	−0.295435
$133$	−159.667	−0.104097
$134$	1569.84	1.01204
$135$	−416.031	−0.265232
$136$	2844.37	1.79340
$137$	1225.81	0.764438	0.382219	−	0.924072i	$-0.375160\pi$
$137$	1225.81	0.764438	0.382219	+	0.924072i	$0.375160\pi$
$138$	−784.487	−0.483913
$139$	3046.10	1.85875	0.929376	−	0.369135i	$-0.120346\pi$
$139$	3046.10	1.85875	0.929376	+	0.369135i	$0.120346\pi$
$140$	618.240	0.373220
$141$	829.627	0.495512
$142$	−1227.62	−0.725493
$143$	−1803.55	−1.05469
$144$	−227.502	−0.131656
$145$	−1070.43	−0.613063
$146$	36.3550	0.0206079
$147$	610.583	0.342585
$148$	−1340.25	−0.744376
$149$	2036.65	1.11979	0.559895	−	0.828564i	$-0.310841\pi$
$149$	2036.65	1.11979	0.559895	+	0.828564i	$0.310841\pi$
$150$	723.569	0.393861
$151$	−1950.24	−1.05105	−0.525524	−	0.850779i	$-0.676131\pi$
$151$	−1950.24	−1.05105	−0.525524	+	0.850779i	$0.676131\pi$
$152$	330.581	0.176406
$153$	1046.94	0.553203
$154$	−1113.77	−0.582793
$155$	1680.26	0.870723
$156$	418.166	0.214616
$157$	−3519.52	−1.78910	−0.894548	−	0.446972i	$-0.852502\pi$
$157$	−3519.52	−1.78910	−0.894548	+	0.446972i	$0.852502\pi$
$158$	347.681	0.175064
$159$	1764.68	0.880179
$160$	−2178.50	−1.07641
$161$	1439.49	0.704644
$162$	−173.774	−0.0842777
$163$	1519.91	0.730357	0.365178	−	0.930938i	$-0.381008\pi$
$163$	1519.91	0.730357	0.365178	+	0.930938i	$0.381008\pi$
$164$	−291.225	−0.138664
$165$	2032.05	0.958757
$166$	−1134.15	−0.530284
$167$	1450.87	0.672285	0.336143	−	0.941811i	$-0.390878\pi$
$167$	1450.87	0.672285	0.336143	+	0.941811i	$0.390878\pi$
$168$	866.308	0.397840
$169$	−513.730	−0.233832
$170$	−3845.40	−1.73487
$171$	121.678	0.0544151
$172$	1042.37	0.462092
$173$	−688.008	−0.302360	−0.151180	−	0.988506i	$-0.548307\pi$
$173$	−688.008	−0.302360	−0.151180	+	0.988506i	$0.548307\pi$
$174$	−447.112	−0.194801
$175$	−1327.71	−0.573516
$176$	1111.20	0.475909
$177$	−1712.20	−0.727103
$178$	−279.443	−0.117669
$179$	876.194	0.365865	0.182932	−	0.983126i	$-0.441441\pi$
$179$	876.194	0.365865	0.182932	+	0.983126i	$0.441441\pi$
$180$	−471.146	−0.195095
$181$	1939.88	0.796631	0.398316	−	0.917248i	$-0.369595\pi$
$181$	1939.88	0.796631	0.398316	+	0.917248i	$0.369595\pi$
$182$	1039.49	0.423364
$183$	−326.978	−0.132081
$184$	−2980.38	−1.19411
$185$	6078.50	2.41567
$186$	701.838	0.276673
$187$	−5113.64	−1.99971
$188$	939.534	0.364482
$189$	318.866	0.122720
$190$	−446.924	−0.170649
$191$	1694.89	0.642084	0.321042	−	0.947065i	$-0.395967\pi$
$191$	1694.89	0.642084	0.321042	+	0.947065i	$0.395967\pi$
$192$	−1516.62	−0.570065
$193$	−4150.32	−1.54791	−0.773955	−	0.633241i	$-0.781724\pi$
$193$	−4150.32	−1.54791	−0.773955	+	0.633241i	$0.781724\pi$
$194$	−2389.89	−0.884453
$195$	−1896.53	−0.696480
$196$	691.472	0.251994
$197$	4791.85	1.73302	0.866511	−	0.499158i	$-0.166357\pi$
$197$	4791.85	1.73302	0.866511	+	0.499158i	$0.166357\pi$
$198$	848.777	0.304646
$199$	2052.26	0.731060	0.365530	−	0.930800i	$-0.380888\pi$
$199$	2052.26	0.731060	0.365530	+	0.930800i	$0.380888\pi$
$200$	2748.94	0.971898
$201$	2195.21	0.770339
$202$	−1346.26	−0.468922
$203$	820.425	0.283658
$204$	1185.64	0.406917
$205$	1320.81	0.449997
$206$	−3191.84	−1.07954
$207$	−1097.00	−0.368342
$208$	−1037.10	−0.345720
$209$	−594.323	−0.196699
$210$	−1171.19	−0.384856
$211$	−609.753	−0.198944	−0.0994718	−	0.995040i	$-0.531715\pi$
$211$	−609.753	−0.198944	−0.0994718	+	0.995040i	$0.531715\pi$
$212$	1998.46	0.647430
$213$	−1716.67	−0.552227
$214$	−253.572	−0.0809992
$215$	−4727.51	−1.49960
$216$	−660.193	−0.207965
$217$	−1287.83	−0.402875
$218$	−3250.61	−1.00990
$219$	50.8376	0.0156862
$220$	2301.25	0.705229
$221$	4772.61	1.45267
$222$	2538.96	0.767584
$223$	2883.28	0.865824	0.432912	−	0.901436i	$-0.357486\pi$
$223$	2883.28	0.865824	0.432912	+	0.901436i	$0.357486\pi$
$224$	1669.70	0.498044
$225$	1011.81	0.299797
$226$	−2733.73	−0.804623
$227$	−5431.63	−1.58815	−0.794075	−	0.607820i	$-0.792044\pi$
$227$	−5431.63	−1.58815	−0.794075	+	0.607820i	$0.792044\pi$
$228$	137.798	0.0400259
$229$	−2307.13	−0.665761	−0.332880	−	0.942969i	$-0.608021\pi$
$229$	−2307.13	−0.665761	−0.332880	+	0.942969i	$0.608021\pi$
$230$	4029.27	1.15514
$231$	−1557.46	−0.443607
$232$	−1698.64	−0.480695
$233$	3710.97	1.04341	0.521704	−	0.853127i	$-0.325297\pi$
$233$	3710.97	1.04341	0.521704	+	0.853127i	$0.325297\pi$
$234$	−792.172	−0.221307
$235$	−4261.12	−1.18283
$236$	−1939.03	−0.534832
$237$	486.186	0.133254
$238$	2947.29	0.802709
$239$	−5496.68	−1.48766	−0.743830	−	0.668369i	$-0.766993\pi$
$239$	−5496.68	−1.48766	−0.743830	+	0.668369i	$0.766993\pi$
$240$	1168.49	0.314274
$241$	−241.000	−0.0644157
$241$	−241.000	−0.0644157
$242$	−1290.27	−0.342733
$243$	−243.000	−0.0641500
$244$	−370.295	−0.0971546
$245$	−3136.07	−0.817780
$246$	551.696	0.142987
$247$	554.687	0.142890
$248$	2666.38	0.682724
$249$	−1585.96	−0.403639
$250$	415.729	0.105172
$251$	1003.77	0.252421	0.126211	−	0.992003i	$-0.459719\pi$
$251$	1003.77	0.252421	0.126211	+	0.992003i	$0.459719\pi$
$252$	361.108	0.0902686
$253$	5358.16	1.33148
$254$	−734.382	−0.181414
$255$	−5377.28	−1.32054
$256$	−4144.07	−1.01173
$257$	−124.796	−0.0302901	−0.0151450	−	0.999885i	$-0.504821\pi$
$257$	−124.796	−0.0302901	−0.0151450	+	0.999885i	$0.504821\pi$
$258$	−1974.66	−0.476499
$259$	−4658.84	−1.11771
$260$	−2147.78	−0.512307
$261$	−625.226	−0.148278
$262$	−4918.35	−1.15976
$263$	7085.27	1.66120	0.830601	−	0.556868i	$-0.187997\pi$
$263$	7085.27	1.66120	0.830601	+	0.556868i	$0.187997\pi$
$264$	3224.63	0.751750
$265$	−9063.74	−2.10106
$266$	342.543	0.0789574
$267$	−390.764	−0.0895668
$268$	2486.03	0.566635
$269$	−5749.37	−1.30314	−0.651571	−	0.758588i	$-0.725890\pi$
$269$	−5749.37	−1.30314	−0.651571	+	0.758588i	$0.725890\pi$
$270$	892.536	0.201178
$271$	5398.80	1.21016	0.605081	−	0.796164i	$-0.293141\pi$
$271$	5398.80	1.21016	0.605081	+	0.796164i	$0.293141\pi$
$272$	−2940.50	−0.655493
$273$	1453.59	0.322254
$274$	−2629.80	−0.579825
$275$	−4942.08	−1.08370
$276$	−1242.33	−0.270940
$277$	945.422	0.205072	0.102536	−	0.994729i	$-0.467304\pi$
$277$	945.422	0.205072	0.102536	+	0.994729i	$0.467304\pi$
$278$	−6534.97	−1.40986
$279$	981.427	0.210597
$280$	−4449.52	−0.949678
$281$	−8579.09	−1.82130	−0.910651	−	0.413177i	$-0.864419\pi$
$281$	−8579.09	−1.82130	−0.910651	+	0.413177i	$0.864419\pi$
$282$	−1779.85	−0.375845
$283$	9237.41	1.94031	0.970154	−	0.242491i	$-0.0779644\pi$
$283$	9237.41	1.94031	0.970154	+	0.242491i	$0.0779644\pi$
$284$	−1944.09	−0.406199
$285$	−624.964	−0.129893
$286$	3869.26	0.799979
$287$	−1012.33	−0.208209
$288$	−1272.44	−0.260345
$289$	8618.89	1.75430
$290$	2296.45	0.465007
$291$	−3341.94	−0.673223
$292$	57.5725	0.0115383
$293$	5045.74	1.00606	0.503030	−	0.864269i	$-0.332219\pi$
$293$	5045.74	1.00606	0.503030	+	0.864269i	$0.332219\pi$
$294$	−1309.92	−0.259851
$295$	8794.20	1.73566
$296$	9645.86	1.89410
$297$	1186.90	0.231889
$298$	−4369.34	−0.849360
$299$	−5000.82	−0.967241
$300$	1145.86	0.220520
$301$	3623.38	0.693848
$302$	4183.96	0.797219
$303$	−1882.56	−0.356932
$304$	−341.754	−0.0644767
$305$	1679.42	0.315290
$306$	−2246.06	−0.419604
$307$	−5288.67	−0.983194	−0.491597	−	0.870823i	$-0.663587\pi$
$307$	−5288.67	−0.983194	−0.491597	+	0.870823i	$0.663587\pi$
$308$	−1763.79	−0.326302
$309$	−4463.36	−0.821720
$310$	−3604.77	−0.660442
$311$	2478.17	0.451846	0.225923	−	0.974145i	$-0.427460\pi$
$311$	2478.17	0.451846	0.225923	+	0.974145i	$0.427460\pi$
$312$	−3009.58	−0.546101
$313$	1971.49	0.356023	0.178012	−	0.984028i	$-0.443034\pi$
$313$	1971.49	0.356023	0.178012	+	0.984028i	$0.443034\pi$
$314$	7550.63	1.35703
$315$	−1637.75	−0.292943
$316$	550.595	0.0980171
$317$	10311.4	1.82696	0.913481	−	0.406881i	$-0.133384\pi$
$317$	10311.4	1.82696	0.913481	+	0.406881i	$0.133384\pi$
$318$	−3785.88	−0.667615
$319$	3053.84	0.535994
$320$	7789.64	1.36079
$321$	−354.587	−0.0616546
$322$	−3088.22	−0.534472
$323$	1572.72	0.270924
$324$	−275.192	−0.0471866
$325$	4612.49	0.787246
$326$	−3260.74	−0.553975
$327$	−4545.55	−0.768714
$328$	2095.97	0.352837
$329$	3265.92	0.547283
$330$	−4359.48	−0.727216
$331$	−3653.32	−0.606660	−0.303330	−	0.952886i	$-0.598098\pi$
$331$	−3653.32	−0.606660	−0.303330	+	0.952886i	$0.598098\pi$
$332$	−1796.06	−0.296903
$333$	3550.39	0.584265
$334$	−3112.64	−0.509928
$335$	−11275.0	−1.83886
$336$	−895.586	−0.145411
$337$	−8999.84	−1.45475	−0.727377	−	0.686238i	$-0.759261\pi$
$337$	−8999.84	−1.45475	−0.727377	+	0.686238i	$0.759261\pi$
$338$	1102.14	0.177362
$339$	−3822.75	−0.612459
$340$	−6089.65	−0.971346
$341$	−4793.65	−0.761263
$342$	−261.044	−0.0412738
$343$	6454.41	1.01605
$344$	−7502.00	−1.17582
$345$	5634.40	0.879264
$346$	1476.02	0.229340
$347$	12269.6	1.89818	0.949090	−	0.315004i	$-0.102006\pi$
$347$	12269.6	1.89818	0.949090	+	0.315004i	$0.102006\pi$
$348$	−708.055	−0.109068
$349$	−6332.54	−0.971269	−0.485635	−	0.874162i	$-0.661411\pi$
$349$	−6332.54	−0.971269	−0.485635	+	0.874162i	$0.661411\pi$
$350$	2848.41	0.435011
$351$	−1107.75	−0.168453
$352$	6215.07	0.941093
$353$	4730.35	0.713233	0.356617	−	0.934251i	$-0.383930\pi$
$353$	4730.35	0.713233	0.356617	+	0.934251i	$0.383930\pi$
$354$	3673.29	0.551507
$355$	8817.14	1.31821
$356$	−442.531	−0.0658823
$357$	4121.40	0.611001
$358$	−1879.75	−0.277508
$359$	6355.05	0.934280	0.467140	−	0.884183i	$-0.345284\pi$
$359$	6355.05	0.934280	0.467140	+	0.884183i	$0.345284\pi$
$360$	3390.87	0.496430
$361$	−6676.21	−0.973351
$362$	−4161.74	−0.604244
$363$	−1804.27	−0.260880
$364$	1646.16	0.237039
$365$	−261.111	−0.0374444
$366$	701.485	0.100184
$367$	−6148.41	−0.874508	−0.437254	−	0.899338i	$-0.644049\pi$
$367$	−6148.41	−0.874508	−0.437254	+	0.899338i	$0.644049\pi$
$368$	3081.11	0.436450
$369$	771.473	0.108838
$370$	−13040.6	−1.83229
$371$	6946.87	0.972139
$372$	1111.44	0.154908
$373$	−2357.18	−0.327213	−0.163606	−	0.986526i	$-0.552313\pi$
$373$	−2357.18	−0.327213	−0.163606	+	0.986526i	$0.552313\pi$
$374$	10970.6	1.51678
$375$	581.341	0.0800543
$376$	−6761.90	−0.927442
$377$	−2850.18	−0.389367
$378$	−684.082	−0.0930830
$379$	−855.607	−0.115962	−0.0579810	−	0.998318i	$-0.518466\pi$
$379$	−855.607	−0.115962	−0.0579810	+	0.998318i	$0.518466\pi$
$380$	−707.757	−0.0955452
$381$	−1026.94	−0.138088
$382$	−3636.15	−0.487020
$383$	−2864.58	−0.382175	−0.191087	−	0.981573i	$-0.561201\pi$
$383$	−2864.58	−0.382175	−0.191087	+	0.981573i	$0.561201\pi$
$384$	−139.484	−0.0185366
$385$	7999.40	1.05893
$386$	8903.92	1.17409
$387$	−2761.29	−0.362699
$388$	−3784.67	−0.495200
$389$	323.972	0.0422263	0.0211132	−	0.999777i	$-0.493279\pi$
$389$	323.972	0.0422263	0.0211132	+	0.999777i	$0.493279\pi$
$390$	4068.74	0.528279
$391$	−14178.9	−1.83391
$392$	−4976.57	−0.641212
$393$	−6877.65	−0.882778
$394$	−10280.2	−1.31450
$395$	−2497.14	−0.318088
$396$	1344.14	0.170570
$397$	5077.27	0.641867	0.320933	−	0.947102i	$-0.396003\pi$
$397$	5077.27	0.641867	0.320933	+	0.947102i	$0.396003\pi$
$398$	−4402.84	−0.554508
$399$	479.001	0.0601004
$400$	−2841.85	−0.355231
$401$	−15085.0	−1.87858	−0.939290	−	0.343125i	$-0.888515\pi$
$401$	−15085.0	−1.87858	−0.939290	+	0.343125i	$0.888515\pi$
$402$	−4709.51	−0.584301
$403$	4473.96	0.553012
$404$	−2131.96	−0.262547
$405$	1248.09	0.153132
$406$	−1760.11	−0.215154
$407$	−17341.4	−2.11200
$408$	−8533.11	−1.03542
$409$	9136.86	1.10462	0.552309	−	0.833640i	$-0.313747\pi$
$409$	9136.86	1.10462	0.552309	+	0.833640i	$0.313747\pi$
$410$	−2833.61	−0.341322
$411$	−3677.43	−0.441348
$412$	−5054.66	−0.604430
$413$	−6740.29	−0.803070
$414$	2353.46	0.279387
$415$	8145.78	0.963520
$416$	−5800.59	−0.683648
$417$	−9138.29	−1.07315
$418$	1275.04	0.149196
$419$	813.220	0.0948172	0.0474086	−	0.998876i	$-0.484904\pi$
$419$	813.220	0.0948172	0.0474086	+	0.998876i	$0.484904\pi$
$420$	−1854.72	−0.215479
$421$	−11459.5	−1.32660	−0.663302	−	0.748351i	$-0.730846\pi$
$421$	−11459.5	−1.32660	−0.663302	+	0.748351i	$0.730846\pi$
$422$	1308.14	0.150899
$423$	−2488.88	−0.286084
$424$	−14383.1	−1.64742
$425$	13077.9	1.49264
$426$	3682.87	0.418863
$427$	−1287.19	−0.145881
$428$	−401.562	−0.0453510
$429$	5410.65	0.608924
$430$	10142.2	1.13744
$431$	3799.43	0.424622	0.212311	−	0.977202i	$-0.431901\pi$
$431$	3799.43	0.424622	0.212311	+	0.977202i	$0.431901\pi$
$432$	682.505	0.0760117
$433$	−9828.03	−1.09077	−0.545387	−	0.838185i	$-0.683617\pi$
$433$	−9828.03	−1.09077	−0.545387	+	0.838185i	$0.683617\pi$
$434$	2762.86	0.305580
$435$	3211.28	0.353952
$436$	−5147.74	−0.565440
$437$	−1647.92	−0.180390
$438$	−109.065	−0.0118980
$439$	6386.17	0.694294	0.347147	−	0.937811i	$-0.387150\pi$
$439$	6386.17	0.694294	0.347147	+	0.937811i	$0.387150\pi$
$440$	−16562.3	−1.79449
$441$	−1831.75	−0.197792
$442$	−10239.0	−1.10185
$443$	−2148.02	−0.230374	−0.115187	−	0.993344i	$-0.536747\pi$
$443$	−2148.02	−0.230374	−0.115187	+	0.993344i	$0.536747\pi$
$444$	4020.74	0.429766
$445$	2007.04	0.213804
$446$	−6185.67	−0.656727
$447$	−6109.94	−0.646511
$448$	−5970.34	−0.629626
$449$	4074.71	0.428279	0.214140	−	0.976803i	$-0.431305\pi$
$449$	4074.71	0.428279	0.214140	+	0.976803i	$0.431305\pi$
$450$	−2170.71	−0.227396
$451$	−3768.16	−0.393427
$452$	−4329.18	−0.450504
$453$	5850.72	0.606823
$454$	11652.8	1.20461
$455$	−7465.92	−0.769247
$456$	−991.744	−0.101848
$457$	9286.84	0.950591	0.475296	−	0.879826i	$-0.342341\pi$
$457$	9286.84	0.950591	0.475296	+	0.879826i	$0.342341\pi$
$458$	4949.62	0.504979
$459$	−3140.82	−0.319392
$460$	6380.84	0.646757
$461$	−16325.2	−1.64933	−0.824663	−	0.565624i	$-0.808635\pi$
$461$	−16325.2	−1.64933	−0.824663	+	0.565624i	$0.808635\pi$
$462$	3341.31	0.336475
$463$	10099.6	1.01376	0.506880	−	0.862017i	$-0.330799\pi$
$463$	10099.6	1.01376	0.506880	+	0.862017i	$0.330799\pi$
$464$	1756.05	0.175695
$465$	−5040.79	−0.502712
$466$	−7961.37	−0.791424
$467$	1050.65	0.104107	0.0520537	−	0.998644i	$-0.483423\pi$
$467$	1050.65	0.104107	0.0520537	+	0.998644i	$0.483423\pi$
$468$	−1254.50	−0.123909
$469$	8641.69	0.850824
$470$	9141.63	0.897175
$471$	10558.6	1.03293
$472$	13955.4	1.36091
$473$	13487.2	1.31108
$474$	−1043.04	−0.101073
$475$	1519.95	0.146821
$476$	4667.39	0.449432
$477$	−5294.05	−0.508171
$478$	11792.3	1.12839
$479$	1406.37	0.134152	0.0670760	−	0.997748i	$-0.478633\pi$
$479$	1406.37	0.134152	0.0670760	+	0.997748i	$0.478633\pi$
$480$	6535.50	0.621465
$481$	16184.9	1.53424
$482$	517.032	0.0488592
$483$	−4318.47	−0.406826
$484$	−2043.29	−0.191894
$485$	17164.8	1.60704
$486$	521.322	0.0486577
$487$	13443.6	1.25090	0.625450	−	0.780264i	$-0.284915\pi$
$487$	13443.6	1.25090	0.625450	+	0.780264i	$0.284915\pi$
$488$	2665.04	0.247215
$489$	−4559.72	−0.421672
$490$	6727.99	0.620285
$491$	3422.53	0.314576	0.157288	−	0.987553i	$-0.449725\pi$
$491$	3422.53	0.314576	0.157288	+	0.987553i	$0.449725\pi$
$492$	873.676	0.0800577
$493$	−8081.17	−0.738250
$494$	−1190.00	−0.108382
$495$	−6096.15	−0.553539
$496$	−2756.50	−0.249537
$497$	−6757.87	−0.609923
$498$	3402.45	0.306160
$499$	20828.0	1.86851	0.934257	−	0.356600i	$-0.116064\pi$
$499$	20828.0	1.86851	0.934257	+	0.356600i	$0.116064\pi$
$500$	658.356	0.0588852
$501$	−4352.61	−0.388144
$502$	−2153.46	−0.191461
$503$	−5490.63	−0.486710	−0.243355	−	0.969937i	$-0.578248\pi$
$503$	−5490.63	−0.486710	−0.243355	+	0.969937i	$0.578248\pi$
$504$	−2598.92	−0.229693
$505$	9669.19	0.852026
$506$	−11495.2	−1.00993
$507$	1541.19	0.135003
$508$	−1162.98	−0.101573
$509$	−2519.52	−0.219402	−0.109701	−	0.993965i	$-0.534989\pi$
$509$	−2519.52	−0.219402	−0.109701	+	0.993965i	$0.534989\pi$
$510$	11536.2	1.00163
$511$	200.128	0.0173251
$512$	8518.55	0.735294
$513$	−365.035	−0.0314166
$514$	267.732	0.0229750
$515$	22924.7	1.96152
$516$	−3127.10	−0.266789
$517$	12156.6	1.03413
$518$	9994.89	0.847780
$519$	2064.02	0.174568
$520$	15457.7	1.30359
$521$	−3385.80	−0.284711	−0.142355	−	0.989816i	$-0.545468\pi$
$521$	−3385.80	−0.284711	−0.142355	+	0.989816i	$0.545468\pi$
$522$	1341.34	0.112469
$523$	−2145.79	−0.179405	−0.0897026	−	0.995969i	$-0.528592\pi$
$523$	−2145.79	−0.179405	−0.0897026	+	0.995969i	$0.528592\pi$
$524$	−7788.79	−0.649342
$525$	3983.12	0.331120
$526$	−15200.4	−1.26002
$527$	12685.1	1.04852
$528$	−3333.61	−0.274766
$529$	2689.92	0.221083
$530$	19445.0	1.59365
$531$	5136.61	0.419793
$532$	542.458	0.0442078
$533$	3516.86	0.285801
$534$	838.328	0.0679364
$535$	1821.23	0.147175
$536$	−17892.1	−1.44183
$537$	−2628.58	−0.211232
$538$	12334.5	0.988432
$539$	8946.94	0.714976
$540$	1413.44	0.112638
$541$	6665.33	0.529694	0.264847	−	0.964290i	$-0.414678\pi$
$541$	6665.33	0.529694	0.264847	+	0.964290i	$0.414678\pi$
$542$	−11582.4	−0.917906
$543$	−5819.64	−0.459935
$544$	−16446.5	−1.29621
$545$	23346.8	1.83499
$546$	−3118.47	−0.244429
$547$	5497.88	0.429748	0.214874	−	0.976642i	$-0.431066\pi$
$547$	5497.88	0.429748	0.214874	+	0.976642i	$0.431066\pi$
$548$	−4164.61	−0.324641
$549$	980.934	0.0762573
$550$	10602.5	0.821988
$551$	−939.217	−0.0726171
$552$	8941.14	0.689420
$553$	1913.93	0.147176
$554$	−2028.27	−0.155547
$555$	−18235.5	−1.39469
$556$	−10348.9	−0.789373
$557$	18493.4	1.40680	0.703402	−	0.710792i	$-0.251663\pi$
$557$	18493.4	1.40680	0.703402	+	0.710792i	$0.251663\pi$
$558$	−2105.51	−0.159737
$559$	−12587.7	−0.952422
$560$	4599.90	0.347109
$561$	15340.9	1.15454
$562$	18405.2	1.38146
$563$	3021.55	0.226187	0.113093	−	0.993584i	$-0.463924\pi$
$563$	3021.55	0.226187	0.113093	+	0.993584i	$0.463924\pi$
$564$	−2818.60	−0.210434
$565$	19634.4	1.46199
$566$	−19817.6	−1.47172
$567$	−956.597	−0.0708524
$568$	13991.8	1.03359
$569$	14795.1	1.09006	0.545028	−	0.838418i	$-0.316519\pi$
$569$	14795.1	1.09006	0.545028	+	0.838418i	$0.316519\pi$
$570$	1340.77	0.0985241
$571$	−19086.2	−1.39883	−0.699415	−	0.714716i	$-0.746556\pi$
$571$	−19086.2	−1.39883	−0.699415	+	0.714716i	$0.746556\pi$
$572$	6127.44	0.447904
$573$	−5084.67	−0.370707
$574$	2171.81	0.157926
$575$	−13703.2	−0.993850
$576$	4549.86	0.329127
$577$	−8419.32	−0.607454	−0.303727	−	0.952759i	$-0.598231\pi$
$577$	−8419.32	−0.607454	−0.303727	+	0.952759i	$0.598231\pi$
$578$	−18490.6	−1.33064
$579$	12451.0	0.893686
$580$	3636.70	0.260355
$581$	−6243.31	−0.445811
$582$	7169.66	0.510639
$583$	25858.1	1.83693
$584$	−414.353	−0.0293597
$585$	5689.60	0.402113
$586$	−10824.9	−0.763095
$587$	−4957.54	−0.348585	−0.174292	−	0.984694i	$-0.555764\pi$
$587$	−4957.54	−0.348585	−0.174292	+	0.984694i	$0.555764\pi$
$588$	−2074.42	−0.145489
$589$	1474.30	0.103137
$590$	−18866.7	−1.31649
$591$	−14375.6	−1.00056
$592$	−9971.86	−0.692299
$593$	13939.6	0.965316	0.482658	−	0.875809i	$-0.339672\pi$
$593$	13939.6	0.965316	0.482658	+	0.875809i	$0.339672\pi$
$594$	−2546.33	−0.175888
$595$	−21168.3	−1.45851
$596$	−6919.38	−0.475552
$597$	−6156.78	−0.422078
$598$	10728.6	0.733651
$599$	4282.65	0.292127	0.146064	−	0.989275i	$-0.453340\pi$
$599$	4282.65	0.292127	0.146064	+	0.989275i	$0.453340\pi$
$600$	−8246.83	−0.561125
$601$	27451.2	1.86316	0.931579	−	0.363538i	$-0.118431\pi$
$601$	27451.2	1.86316	0.931579	+	0.363538i	$0.118431\pi$
$602$	−7773.46	−0.526283
$603$	−6585.63	−0.444756
$604$	6625.81	0.446358
$605$	9267.05	0.622742
$606$	4038.77	0.270732
$607$	−4579.55	−0.306224	−0.153112	−	0.988209i	$-0.548930\pi$
$607$	−4579.55	−0.306224	−0.153112	+	0.988209i	$0.548930\pi$
$608$	−1911.47	−0.127500
$609$	−2461.27	−0.163770
$610$	−3602.96	−0.239147
$611$	−11345.9	−0.751237
$612$	−3556.91	−0.234934
$613$	−18881.2	−1.24405	−0.622026	−	0.782997i	$-0.713690\pi$
$613$	−18881.2	−1.24405	−0.622026	+	0.782997i	$0.713690\pi$
$614$	11346.1	0.745751
$615$	−3962.43	−0.259806
$616$	12694.1	0.830292
$617$	−10233.3	−0.667712	−0.333856	−	0.942624i	$-0.608350\pi$
$617$	−10233.3	−0.667712	−0.333856	+	0.942624i	$0.608350\pi$
$618$	9575.51	0.623274
$619$	−23557.7	−1.52967	−0.764833	−	0.644228i	$-0.777179\pi$
$619$	−23557.7	−1.52967	−0.764833	+	0.644228i	$0.777179\pi$
$620$	−5708.59	−0.369778
$621$	3291.00	0.212662
$622$	−5316.56	−0.342724
$623$	−1538.29	−0.0989247
$624$	3111.29	0.199601
$625$	−17038.9	−1.09049
$626$	−4229.56	−0.270043
$627$	1782.97	0.113564
$628$	11957.3	0.759792
$629$	45889.5	2.90896
$630$	3513.57	0.222197
$631$	−15238.8	−0.961403	−0.480701	−	0.876884i	$-0.659618\pi$
$631$	−15238.8	−0.961403	−0.480701	+	0.876884i	$0.659618\pi$
$632$	−3962.67	−0.249409
$633$	1829.26	0.114860
$634$	−22121.7	−1.38575
$635$	5274.53	0.329627
$636$	−5995.39	−0.373794
$637$	−8350.27	−0.519387
$638$	−6551.58	−0.406551
$639$	5150.01	0.318828
$640$	716.418	0.0442483
$641$	27614.5	1.70157	0.850785	−	0.525513i	$-0.176127\pi$
$641$	27614.5	1.70157	0.850785	+	0.525513i	$0.176127\pi$
$642$	760.716	0.0467649
$643$	6901.10	0.423255	0.211627	−	0.977350i	$-0.432124\pi$
$643$	6901.10	0.423255	0.211627	+	0.977350i	$0.432124\pi$
$644$	−4890.57	−0.299248
$645$	14182.5	0.865793
$646$	−3374.04	−0.205495
$647$	892.947	0.0542587	0.0271293	−	0.999632i	$-0.491363\pi$
$647$	892.947	0.0542587	0.0271293	+	0.999632i	$0.491363\pi$
$648$	1980.58	0.120069
$649$	−25089.1	−1.51746
$650$	−9895.45	−0.597125
$651$	3863.50	0.232600
$652$	−5163.78	−0.310167
$653$	−13608.2	−0.815516	−0.407758	−	0.913090i	$-0.633689\pi$
$653$	−13608.2	−0.815516	−0.407758	+	0.913090i	$0.633689\pi$
$654$	9751.84	0.583069
$655$	35324.9	2.10727
$656$	−2166.81	−0.128963
$657$	−152.513	−0.00905645
$658$	−7006.57	−0.415113
$659$	17428.3	1.03021	0.515106	−	0.857127i	$-0.327753\pi$
$659$	17428.3	1.03021	0.515106	+	0.857127i	$0.327753\pi$
$660$	−6903.76	−0.407164
$661$	−7165.65	−0.421651	−0.210826	−	0.977524i	$-0.567615\pi$
$661$	−7165.65	−0.421651	−0.210826	+	0.977524i	$0.567615\pi$
$662$	7837.67	0.460151
$663$	−14317.8	−0.838701
$664$	12926.4	0.755485
$665$	−2460.24	−0.143465
$666$	−7616.87	−0.443165
$667$	8467.58	0.491553
$668$	−4929.23	−0.285506
$669$	−8649.84	−0.499884
$670$	24188.9	1.39478
$671$	−4791.24	−0.275654
$672$	−5009.11	−0.287546
$673$	9013.39	0.516256	0.258128	−	0.966111i	$-0.416894\pi$
$673$	9013.39	0.516256	0.258128	+	0.966111i	$0.416894\pi$
$674$	19307.9	1.10343
$675$	−3035.44	−0.173088
$676$	1745.36	0.0993038
$677$	−10961.0	−0.622255	−0.311128	−	0.950368i	$-0.600707\pi$
$677$	−10961.0	−0.622255	−0.311128	+	0.950368i	$0.600707\pi$
$678$	8201.18	0.464549
$679$	−13155.9	−0.743561
$680$	43827.7	2.47164
$681$	16294.9	0.916919
$682$	10284.1	0.577417
$683$	16736.7	0.937644	0.468822	−	0.883293i	$-0.344679\pi$
$683$	16736.7	0.937644	0.468822	+	0.883293i	$0.344679\pi$
$684$	−413.395	−0.0231090
$685$	18888.0	1.05354
$686$	−13847.0	−0.770673
$687$	6921.38	0.384377
$688$	7755.54	0.429764
$689$	−24133.6	−1.33442
$690$	−12087.8	−0.666921
$691$	−7618.61	−0.419429	−0.209715	−	0.977763i	$-0.567254\pi$
$691$	−7618.61	−0.419429	−0.209715	+	0.977763i	$0.567254\pi$
$692$	2337.46	0.128406
$693$	4672.37	0.256117
$694$	−26322.8	−1.43977
$695$	46936.0	2.56170
$696$	5095.93	0.277530
$697$	9971.43	0.541886
$698$	13585.6	0.736707
$699$	−11132.9	−0.602412
$700$	4510.80	0.243560
$701$	29646.4	1.59733	0.798665	−	0.601776i	$-0.205540\pi$
$701$	29646.4	1.59733	0.798665	+	0.601776i	$0.205540\pi$
$702$	2376.52	0.127772
$703$	5333.41	0.286136
$704$	−22223.2	−1.18973
$705$	12783.4	0.682907
$706$	−10148.3	−0.540987
$707$	−7410.92	−0.394224
$708$	5817.10	0.308785
$709$	−17825.2	−0.944202	−0.472101	−	0.881545i	$-0.656504\pi$
$709$	−17825.2	−0.944202	−0.472101	+	0.881545i	$0.656504\pi$
$710$	−18915.9	−0.999862
$711$	−1458.56	−0.0769342
$712$	3184.93	0.167641
$713$	−13291.7	−0.698145
$714$	−8841.88	−0.463444
$715$	−27790.1	−1.45355
$716$	−2976.81	−0.155375
$717$	16490.0	0.858900
$718$	−13633.9	−0.708651
$719$	−6130.62	−0.317988	−0.158994	−	0.987280i	$-0.550825\pi$
$719$	−6130.62	−0.317988	−0.158994	+	0.987280i	$0.550825\pi$
$720$	−3505.47	−0.181446
$721$	−17570.5	−0.907573
$722$	14322.9	0.738286
$723$	723.000	0.0371904
$724$	−6590.62	−0.338313
$725$	−7810.04	−0.400079
$726$	3870.80	0.197877
$727$	6146.72	0.313575	0.156788	−	0.987632i	$-0.449886\pi$
$727$	6146.72	0.313575	0.156788	+	0.987632i	$0.449886\pi$
$728$	−11847.5	−0.603158
$729$	729.000	0.0370370
$730$	560.178	0.0284015
$731$	−35690.2	−1.80581
$732$	1110.89	0.0560923
$733$	−19579.9	−0.986630	−0.493315	−	0.869851i	$-0.664215\pi$
$733$	−19579.9	−0.986630	−0.493315	+	0.869851i	$0.664215\pi$
$734$	13190.6	0.663314
$735$	9408.21	0.472145
$736$	17233.0	0.863064
$737$	32166.6	1.60770
$738$	−1655.09	−0.0825536
$739$	−13092.6	−0.651718	−0.325859	−	0.945418i	$-0.605653\pi$
$739$	−13092.6	−0.651718	−0.325859	+	0.945418i	$0.605653\pi$
$740$	−20651.3	−1.02589
$741$	−1664.06	−0.0824978
$742$	−14903.5	−0.737367
$743$	1334.40	0.0658876	0.0329438	−	0.999457i	$-0.489512\pi$
$743$	1334.40	0.0658876	0.0329438	+	0.999457i	$0.489512\pi$
$744$	−7999.15	−0.394171
$745$	31381.8	1.54328
$746$	5057.01	0.248190
$747$	4757.88	0.233041
$748$	17373.3	0.849237
$749$	−1395.87	−0.0680962
$750$	−1247.19	−0.0607211
$751$	−6179.38	−0.300251	−0.150126	−	0.988667i	$-0.547968\pi$
$751$	−6179.38	−0.300251	−0.150126	+	0.988667i	$0.547968\pi$
$752$	6990.43	0.338982
$753$	−3011.32	−0.145735
$754$	6114.65	0.295335
$755$	−30050.4	−1.44854
$756$	−1083.33	−0.0521166
$757$	1521.51	0.0730519	0.0365259	−	0.999333i	$-0.488371\pi$
$757$	1521.51	0.0730519	0.0365259	+	0.999333i	$0.488371\pi$
$758$	1835.58	0.0879570
$759$	−16074.5	−0.768730
$760$	5093.78	0.243120
$761$	−32386.3	−1.54271	−0.771355	−	0.636406i	$-0.780420\pi$
$761$	−32386.3	−1.54271	−0.771355	+	0.636406i	$0.780420\pi$
$762$	2203.14	0.104740
$763$	−17894.1	−0.849029
$764$	−5758.28	−0.272680
$765$	16131.8	0.762416
$766$	6145.55	0.289879
$767$	23415.9	1.10235
$768$	12432.2	0.584125
$769$	−6892.50	−0.323212	−0.161606	−	0.986855i	$-0.551667\pi$
$769$	−6892.50	−0.323212	−0.161606	+	0.986855i	$0.551667\pi$
$770$	−17161.6	−0.803195
$771$	374.387	0.0174880
$772$	14100.4	0.657365
$773$	−29678.5	−1.38093	−0.690467	−	0.723364i	$-0.742595\pi$
$773$	−29678.5	−1.38093	−0.690467	+	0.723364i	$0.742595\pi$
$774$	5923.97	0.275107
$775$	12259.5	0.568226
$776$	27238.6	1.26006
$777$	13976.5	0.645309
$778$	−695.037	−0.0320286
$779$	1158.91	0.0533020
$780$	6443.34	0.295780
$781$	−25154.6	−1.15250
$782$	30418.9	1.39102
$783$	1875.68	0.0856083
$784$	5144.76	0.234364
$785$	−54230.7	−2.46570
$786$	14755.0	0.669586
$787$	−26543.4	−1.20225	−0.601124	−	0.799155i	$-0.705280\pi$
$787$	−26543.4	−1.20225	−0.601124	+	0.799155i	$0.705280\pi$
$788$	−16280.0	−0.735979
$789$	−21255.8	−0.959096
$790$	5357.27	0.241270
$791$	−15048.7	−0.676448
$792$	−9673.88	−0.434023
$793$	4471.72	0.200246
$794$	−10892.6	−0.486855
$795$	27191.2	1.21305
$796$	−6972.42	−0.310466
$797$	855.413	0.0380179	0.0190090	−	0.999819i	$-0.493949\pi$
$797$	855.413	0.0380179	0.0190090	+	0.999819i	$0.493949\pi$
$798$	−1027.63	−0.0455861
$799$	−32169.2	−1.42436
$800$	−15894.8	−0.702455
$801$	1172.29	0.0517114
$802$	32362.8	1.42490
$803$	744.929	0.0327372
$804$	−7458.08	−0.327147
$805$	22180.5	0.971129
$806$	−9598.25	−0.419459
$807$	17248.1	0.752369
$808$	15343.9	0.668064
$809$	−1527.02	−0.0663623	−0.0331811	−	0.999449i	$-0.510564\pi$
$809$	−1527.02	−0.0663623	−0.0331811	+	0.999449i	$0.510564\pi$
$810$	−2677.61	−0.116150
$811$	14813.3	0.641386	0.320693	−	0.947183i	$-0.396084\pi$
$811$	14813.3	0.641386	0.320693	+	0.947183i	$0.396084\pi$
$812$	−2787.34	−0.120464
$813$	−16196.4	−0.698687
$814$	37203.6	1.60195
$815$	23419.6	1.00657
$816$	8821.50	0.378449
$817$	−4148.02	−0.177627
$818$	−19601.8	−0.837851
$819$	−4360.77	−0.186053
$820$	−4487.37	−0.191104
$821$	−16452.1	−0.699369	−0.349685	−	0.936867i	$-0.613711\pi$
$821$	−16452.1	−0.699369	−0.349685	+	0.936867i	$0.613711\pi$
$822$	7889.41	0.334762
$823$	−10535.7	−0.446233	−0.223117	−	0.974792i	$-0.571623\pi$
$823$	−10535.7	−0.446233	−0.223117	+	0.974792i	$0.571623\pi$
$824$	36378.7	1.53800
$825$	14826.2	0.625676
$826$	14460.3	0.609128
$827$	25826.6	1.08595	0.542975	−	0.839749i	$-0.317298\pi$
$827$	25826.6	1.08595	0.542975	+	0.839749i	$0.317298\pi$
$828$	3726.99	0.156427
$829$	1824.19	0.0764256	0.0382128	−	0.999270i	$-0.487834\pi$
$829$	1824.19	0.0764256	0.0382128	+	0.999270i	$0.487834\pi$
$830$	−17475.6	−0.730829
$831$	−2836.27	−0.118398
$832$	20741.1	0.864266
$833$	−23675.7	−0.984771
$834$	19604.9	0.813984
$835$	22355.8	0.926533
$836$	2019.17	0.0835341
$837$	−2944.28	−0.121588
$838$	−1744.65	−0.0719187
$839$	6752.41	0.277853	0.138927	−	0.990303i	$-0.455635\pi$
$839$	6752.41	0.277853	0.138927	+	0.990303i	$0.455635\pi$
$840$	13348.6	0.548297
$841$	−19563.0	−0.802123
$842$	24584.7	1.00623
$843$	25737.3	1.05153
$844$	2071.59	0.0844872
$845$	−7915.84	−0.322264
$846$	5339.54	0.216994
$847$	−7102.70	−0.288136
$848$	14869.2	0.602135
$849$	−27712.2	−1.12024
$850$	−28056.8	−1.13216
$851$	−48083.7	−1.93689
$852$	5832.27	0.234519
$853$	−24630.1	−0.988650	−0.494325	−	0.869277i	$-0.664585\pi$
$853$	−24630.1	−0.988650	−0.494325	+	0.869277i	$0.664585\pi$
$854$	2761.48	0.110651
$855$	1874.89	0.0749940
$856$	2890.07	0.115398
$857$	6700.98	0.267096	0.133548	−	0.991042i	$-0.457363\pi$
$857$	6700.98	0.267096	0.133548	+	0.991042i	$0.457363\pi$
$858$	−11607.8	−0.461868
$859$	32774.2	1.30180	0.650898	−	0.759165i	$-0.274393\pi$
$859$	32774.2	1.30180	0.650898	+	0.759165i	$0.274393\pi$
$860$	16061.4	0.636848
$861$	3036.99	0.120210
$862$	−8151.14	−0.322075
$863$	−1551.99	−0.0612170	−0.0306085	−	0.999531i	$-0.509745\pi$
$863$	−1551.99	−0.0612170	−0.0306085	+	0.999531i	$0.509745\pi$
$864$	3817.32	0.150310
$865$	−10601.2	−0.416708
$866$	21084.6	0.827350
$867$	−25856.7	−1.01285
$868$	4375.33	0.171092
$869$	7124.14	0.278101
$870$	−6889.35	−0.268472
$871$	−30021.5	−1.16790
$872$	37048.6	1.43879
$873$	10025.8	0.388686
$874$	3535.38	0.136826
$875$	2288.52	0.0884183
$876$	−172.717	−0.00666162
$877$	18275.2	0.703661	0.351831	−	0.936064i	$-0.385559\pi$
$877$	18275.2	0.703661	0.351831	+	0.936064i	$0.385559\pi$
$878$	−13700.6	−0.526622
$879$	−15137.2	−0.580849
$880$	17122.0	0.655890
$881$	28907.4	1.10547	0.552733	−	0.833358i	$-0.313585\pi$
$881$	28907.4	1.10547	0.552733	+	0.833358i	$0.313585\pi$
$882$	3929.76	0.150025
$883$	−29946.1	−1.14130	−0.570649	−	0.821194i	$-0.693308\pi$
$883$	−29946.1	−1.14130	−0.570649	+	0.821194i	$0.693308\pi$
$884$	−16214.6	−0.616920
$885$	−26382.6	−1.00208
$886$	4608.28	0.174738
$887$	−17164.0	−0.649729	−0.324864	−	0.945761i	$-0.605319\pi$
$887$	−17164.0	−0.649729	−0.324864	+	0.945761i	$0.605319\pi$
$888$	−28937.6	−1.09356
$889$	−4042.65	−0.152515
$890$	−4305.81	−0.162170
$891$	−3560.70	−0.133881
$892$	−9795.76	−0.367697
$893$	−3738.81	−0.140106
$894$	13108.0	0.490378
$895$	13500.9	0.504229
$896$	−549.096	−0.0204732
$897$	15002.5	0.558437
$898$	−8741.72	−0.324850
$899$	−7575.48	−0.281042
$900$	−3437.57	−0.127318
$901$	−68426.5	−2.53010
$902$	8084.05	0.298414
$903$	−10870.1	−0.400593
$904$	31157.5	1.14633
$905$	29890.8	1.09790
$906$	−12551.9	−0.460275
$907$	10389.0	0.380331	0.190165	−	0.981752i	$-0.439098\pi$
$907$	10389.0	0.380331	0.190165	+	0.981752i	$0.439098\pi$
$908$	18453.6	0.674454
$909$	5647.68	0.206075
$910$	16017.1	0.583473
$911$	−47900.9	−1.74207	−0.871035	−	0.491220i	$-0.836551\pi$
$911$	−47900.9	−1.74207	−0.871035	+	0.491220i	$0.836551\pi$
$912$	1025.26	0.0372257
$913$	−23239.2	−0.842394
$914$	−19923.6	−0.721023
$915$	−5038.26	−0.182033
$916$	7838.31	0.282735
$917$	−27074.7	−0.975010
$918$	6738.19	0.242258
$919$	−15975.7	−0.573437	−0.286718	−	0.958015i	$-0.592564\pi$
$919$	−15975.7	−0.573437	−0.286718	+	0.958015i	$0.592564\pi$
$920$	−45923.4	−1.64570
$921$	15866.0	0.567647
$922$	35023.4	1.25101
$923$	23477.0	0.837221
$924$	5291.36	0.188391
$925$	44349.9	1.57645
$926$	−21667.4	−0.768935
$927$	13390.1	0.474421
$928$	9821.78	0.347431
$929$	46881.5	1.65569	0.827844	−	0.560959i	$-0.189567\pi$
$929$	46881.5	1.65569	0.827844	+	0.560959i	$0.189567\pi$
$930$	10814.3	0.381307
$931$	−2751.66	−0.0968657
$932$	−12607.8	−0.443114
$933$	−7434.50	−0.260873
$934$	−2254.02	−0.0789653
$935$	−78793.9	−2.75597
$936$	9028.73	0.315292
$937$	−32509.7	−1.13345	−0.566726	−	0.823906i	$-0.691790\pi$
$937$	−32509.7	−1.13345	−0.566726	+	0.823906i	$0.691790\pi$
$938$	−18539.5	−0.645349
$939$	−5914.47	−0.205550
$940$	14476.9	0.502323
$941$	12955.3	0.448811	0.224406	−	0.974496i	$-0.427956\pi$
$941$	12955.3	0.448811	0.224406	+	0.974496i	$0.427956\pi$
$942$	−22651.9	−0.783480
$943$	−10448.2	−0.360807
$944$	−14427.0	−0.497415
$945$	4913.26	0.169131
$946$	−28934.8	−0.994453
$947$	40884.6	1.40293	0.701464	−	0.712705i	$-0.252530\pi$
$947$	40884.6	1.40293	0.701464	+	0.712705i	$0.252530\pi$
$948$	−1651.79	−0.0565902
$949$	−695.249	−0.0237816
$950$	−3260.84	−0.111364
$951$	−30934.3	−1.05480
$952$	−33591.6	−1.14360
$953$	−38548.1	−1.31028	−0.655139	−	0.755508i	$-0.727390\pi$
$953$	−38548.1	−1.31028	−0.655139	+	0.755508i	$0.727390\pi$
$954$	11357.6	0.385448
$955$	26115.8	0.884910
$956$	18674.6	0.631778
$957$	−9161.51	−0.309456
$958$	−3017.18	−0.101754
$959$	−14476.6	−0.487460
$960$	−23368.9	−0.785655
$961$	−17899.7	−0.600841
$962$	−34722.5	−1.16372
$963$	1063.76	0.0355963
$964$	818.782	0.0273560
$965$	−63950.4	−2.13330
$966$	9264.66	0.308577
$967$	11533.1	0.383535	0.191767	−	0.981440i	$-0.438578\pi$
$967$	11533.1	0.383535	0.191767	+	0.981440i	$0.438578\pi$
$968$	14705.7	0.488285
$969$	−4718.15	−0.156418
$970$	−36824.7	−1.21894
$971$	47910.6	1.58344	0.791722	−	0.610882i	$-0.209185\pi$
$971$	47910.6	1.58344	0.791722	+	0.610882i	$0.209185\pi$
$972$	825.576	0.0272432
$973$	−35973.9	−1.18527
$974$	−28841.4	−0.948806
$975$	−13837.5	−0.454517
$976$	−2755.11	−0.0903576
$977$	14579.8	0.477430	0.238715	−	0.971090i	$-0.423274\pi$
$977$	14579.8	0.477430	0.238715	+	0.971090i	$0.423274\pi$
$978$	9782.23	0.319838
$979$	−5725.90	−0.186926
$980$	10654.6	0.347294
$981$	13636.7	0.443817
$982$	−7342.56	−0.238605
$983$	−48310.4	−1.56751	−0.783754	−	0.621071i	$-0.786698\pi$
$983$	−48310.4	−1.56751	−0.783754	+	0.621071i	$0.786698\pi$
$984$	−6287.91	−0.203711
$985$	73835.6	2.38842
$986$	17337.0	0.559962
$987$	−9797.76	−0.315974
$988$	−1884.51	−0.0606825
$989$	37396.8	1.20238
$990$	13078.4	0.419858
$991$	−747.896	−0.0239735	−0.0119867	−	0.999928i	$-0.503816\pi$
$991$	−747.896	−0.0239735	−0.0119867	+	0.999928i	$0.503816\pi$
$992$	−15417.4	−0.493450
$993$	10959.9	0.350255
$994$	14498.1	0.462626
$995$	31622.4	1.00753
$996$	5388.19	0.171417
$997$	34777.3	1.10472	0.552362	−	0.833604i	$-0.313727\pi$
$997$	34777.3	1.10472	0.552362	+	0.833604i	$0.313727\pi$
$998$	−44683.5	−1.41727
$999$	−10651.2	−0.337326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	723.4.a.b.1.8	✓	29
3.2	odd	2		2169.4.a.c.1.22		29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
723.4.a.b.1.8	✓	29	1.1	even	1	trivial
2169.4.a.c.1.22		29	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 723 = 3 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	723.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14536 q^{2} -3.00000 q^{3} -3.39743 q^{4} +15.4086 q^{5} +6.43608 q^{6} -11.8098 q^{7} +24.4516 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.14536 q^{2} -3.00000 q^{3} -3.39743 q^{4} +15.4086 q^{5} +6.43608 q^{6} -11.8098 q^{7} +24.4516 q^{8} +9.00000 q^{9} -33.0569 q^{10} -43.9593 q^{11} +10.1923 q^{12} +41.0277 q^{13} +25.3364 q^{14} -46.2257 q^{15} -25.2780 q^{16} +116.327 q^{17} -19.3082 q^{18} +13.5198 q^{19} -52.3496 q^{20} +35.4295 q^{21} +94.3085 q^{22} -121.889 q^{23} -73.3548 q^{24} +112.424 q^{25} -88.0191 q^{26} -27.0000 q^{27} +40.1232 q^{28} -69.4696 q^{29} +99.1707 q^{30} +109.047 q^{31} -141.382 q^{32} +131.878 q^{33} -249.562 q^{34} -181.973 q^{35} -30.5769 q^{36} +394.488 q^{37} -29.0049 q^{38} -123.083 q^{39} +376.764 q^{40} +85.7192 q^{41} -76.0091 q^{42} -306.810 q^{43} +149.349 q^{44} +138.677 q^{45} +261.496 q^{46} -276.542 q^{47} +75.8339 q^{48} -203.528 q^{49} -241.190 q^{50} -348.980 q^{51} -139.389 q^{52} -588.227 q^{53} +57.9247 q^{54} -677.350 q^{55} -288.769 q^{56} -40.5595 q^{57} +149.037 q^{58} +570.735 q^{59} +157.049 q^{60} +108.993 q^{61} -233.946 q^{62} -106.289 q^{63} +505.540 q^{64} +632.178 q^{65} -282.926 q^{66} -731.737 q^{67} -395.212 q^{68} +365.667 q^{69} +390.397 q^{70} +572.223 q^{71} +220.064 q^{72} -16.9459 q^{73} -846.319 q^{74} -337.272 q^{75} -45.9327 q^{76} +519.153 q^{77} +264.057 q^{78} -162.062 q^{79} -389.497 q^{80} +81.0000 q^{81} -183.899 q^{82} +528.653 q^{83} -120.369 q^{84} +1792.43 q^{85} +658.219 q^{86} +208.409 q^{87} -1074.88 q^{88} +130.255 q^{89} -297.512 q^{90} -484.530 q^{91} +414.110 q^{92} -327.142 q^{93} +593.283 q^{94} +208.321 q^{95} +424.147 q^{96} +1113.98 q^{97} +436.640 q^{98} -395.634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 9 q^{2} - 87 q^{3} + 97 q^{4} + 62 q^{5} - 27 q^{6} - 30 q^{7} + 108 q^{8} + 261 q^{9}+O(q^{10}) \) 29 * q + 9 * q^2 - 87 * q^3 + 97 * q^4 + 62 * q^5 - 27 * q^6 - 30 * q^7 + 108 * q^8 + 261 * q^9	\( 29 q + 9 q^{2} - 87 q^{3} + 97 q^{4} + 62 q^{5} - 27 q^{6} - 30 q^{7} + 108 q^{8} + 261 q^{9} + 51 q^{10} + 46 q^{11} - 291 q^{12} + 250 q^{13} + 84 q^{14} - 186 q^{15} + 333 q^{16} + 128 q^{17} + 81 q^{18} + 58 q^{19} + 405 q^{20} + 90 q^{21} - 48 q^{22} + 232 q^{23} - 324 q^{24} + 707 q^{25} + 238 q^{26} - 783 q^{27} - 89 q^{28} + 590 q^{29} - 153 q^{30} - 468 q^{31} + 1068 q^{32} - 138 q^{33} + 287 q^{34} + 474 q^{35} + 873 q^{36} + 842 q^{37} + 160 q^{38} - 750 q^{39} + 434 q^{40} + 814 q^{41} - 252 q^{42} + 20 q^{43} + 150 q^{44} + 558 q^{45} - 37 q^{46} + 1004 q^{47} - 999 q^{48} + 1239 q^{49} + 839 q^{50} - 384 q^{51} + 1928 q^{52} + 2192 q^{53} - 243 q^{54} + 432 q^{55} + 437 q^{56} - 174 q^{57} - 28 q^{58} + 1288 q^{59} - 1215 q^{60} + 1502 q^{61} + 3059 q^{62} - 270 q^{63} + 3372 q^{64} + 2312 q^{65} + 144 q^{66} + 358 q^{67} + 4990 q^{68} - 696 q^{69} + 5366 q^{70} + 1938 q^{71} + 972 q^{72} + 3266 q^{73} + 2510 q^{74} - 2121 q^{75} + 3591 q^{76} + 5098 q^{77} - 714 q^{78} - 292 q^{79} + 8235 q^{80} + 2349 q^{81} + 4511 q^{82} + 4256 q^{83} + 267 q^{84} + 1998 q^{85} + 6860 q^{86} - 1770 q^{87} + 5935 q^{88} + 6428 q^{89} + 459 q^{90} - 1650 q^{91} + 6823 q^{92} + 1404 q^{93} + 3025 q^{94} + 1802 q^{95} - 3204 q^{96} + 5040 q^{97} + 9410 q^{98} + 414 q^{99}+O(q^{100}) \) 29 * q + 9 * q^2 - 87 * q^3 + 97 * q^4 + 62 * q^5 - 27 * q^6 - 30 * q^7 + 108 * q^8 + 261 * q^9 + 51 * q^10 + 46 * q^11 - 291 * q^12 + 250 * q^13 + 84 * q^14 - 186 * q^15 + 333 * q^16 + 128 * q^17 + 81 * q^18 + 58 * q^19 + 405 * q^20 + 90 * q^21 - 48 * q^22 + 232 * q^23 - 324 * q^24 + 707 * q^25 + 238 * q^26 - 783 * q^27 - 89 * q^28 + 590 * q^29 - 153 * q^30 - 468 * q^31 + 1068 * q^32 - 138 * q^33 + 287 * q^34 + 474 * q^35 + 873 * q^36 + 842 * q^37 + 160 * q^38 - 750 * q^39 + 434 * q^40 + 814 * q^41 - 252 * q^42 + 20 * q^43 + 150 * q^44 + 558 * q^45 - 37 * q^46 + 1004 * q^47 - 999 * q^48 + 1239 * q^49 + 839 * q^50 - 384 * q^51 + 1928 * q^52 + 2192 * q^53 - 243 * q^54 + 432 * q^55 + 437 * q^56 - 174 * q^57 - 28 * q^58 + 1288 * q^59 - 1215 * q^60 + 1502 * q^61 + 3059 * q^62 - 270 * q^63 + 3372 * q^64 + 2312 * q^65 + 144 * q^66 + 358 * q^67 + 4990 * q^68 - 696 * q^69 + 5366 * q^70 + 1938 * q^71 + 972 * q^72 + 3266 * q^73 + 2510 * q^74 - 2121 * q^75 + 3591 * q^76 + 5098 * q^77 - 714 * q^78 - 292 * q^79 + 8235 * q^80 + 2349 * q^81 + 4511 * q^82 + 4256 * q^83 + 267 * q^84 + 1998 * q^85 + 6860 * q^86 - 1770 * q^87 + 5935 * q^88 + 6428 * q^89 + 459 * q^90 - 1650 * q^91 + 6823 * q^92 + 1404 * q^93 + 3025 * q^94 + 1802 * q^95 - 3204 * q^96 + 5040 * q^97 + 9410 * q^98 + 414 * q^99

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