LMFDB - Embedded newform 1441.4.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.96967 q^{2} +4.89807 q^{3} +16.6976 q^{4} +5.95481 q^{5} -24.3418 q^{6} +15.7482 q^{7} -43.2240 q^{8} -3.00887 q^{9} +O(q^{10})$	\(q-4.96967 q^{2} +4.89807 q^{3} +16.6976 q^{4} +5.95481 q^{5} -24.3418 q^{6} +15.7482 q^{7} -43.2240 q^{8} -3.00887 q^{9} -29.5934 q^{10} -11.0000 q^{11} +81.7859 q^{12} +24.5395 q^{13} -78.2632 q^{14} +29.1671 q^{15} +81.2283 q^{16} -28.1591 q^{17} +14.9531 q^{18} -71.2174 q^{19} +99.4308 q^{20} +77.1357 q^{21} +54.6663 q^{22} +28.7688 q^{23} -211.714 q^{24} -89.5403 q^{25} -121.953 q^{26} -146.986 q^{27} +262.956 q^{28} -83.5623 q^{29} -144.951 q^{30} +184.473 q^{31} -57.8854 q^{32} -53.8788 q^{33} +139.942 q^{34} +93.7774 q^{35} -50.2408 q^{36} -131.535 q^{37} +353.926 q^{38} +120.196 q^{39} -257.391 q^{40} +244.871 q^{41} -383.339 q^{42} +312.208 q^{43} -183.673 q^{44} -17.9172 q^{45} -142.971 q^{46} -128.399 q^{47} +397.862 q^{48} -94.9950 q^{49} +444.985 q^{50} -137.926 q^{51} +409.750 q^{52} -637.831 q^{53} +730.470 q^{54} -65.5029 q^{55} -680.699 q^{56} -348.828 q^{57} +415.277 q^{58} -466.571 q^{59} +487.020 q^{60} -759.706 q^{61} -916.768 q^{62} -47.3842 q^{63} -362.155 q^{64} +146.128 q^{65} +267.760 q^{66} +590.720 q^{67} -470.189 q^{68} +140.912 q^{69} -466.042 q^{70} -135.791 q^{71} +130.055 q^{72} -1083.68 q^{73} +653.687 q^{74} -438.575 q^{75} -1189.16 q^{76} -173.230 q^{77} -597.335 q^{78} +833.437 q^{79} +483.699 q^{80} -638.707 q^{81} -1216.93 q^{82} -454.743 q^{83} +1287.98 q^{84} -167.682 q^{85} -1551.57 q^{86} -409.295 q^{87} +475.464 q^{88} +21.0437 q^{89} +89.0427 q^{90} +386.452 q^{91} +480.370 q^{92} +903.561 q^{93} +638.102 q^{94} -424.086 q^{95} -283.527 q^{96} +291.774 q^{97} +472.093 q^{98} +33.0976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) $ 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.96967	−1.75704	−0.878521	−	0.477704i	$-0.841469\pi$
$2$	−4.96967	−1.75704	−0.878521	+	0.477704i	$0.841469\pi$
$3$	4.89807	0.942635	0.471317	−	0.881964i	$-0.343779\pi$
$3$	4.89807	0.942635	0.471317	+	0.881964i	$0.343779\pi$
$4$	16.6976	2.08720
$5$	5.95481	0.532614	0.266307	−	0.963888i	$-0.414196\pi$
$5$	5.95481	0.532614	0.266307	+	0.963888i	$0.414196\pi$
$6$	−24.3418	−1.65625
$7$	15.7482	0.850322	0.425161	−	0.905118i	$-0.360218\pi$
$7$	15.7482	0.850322	0.425161	+	0.905118i	$0.360218\pi$
$8$	−43.2240	−1.91025
$9$	−3.00887	−0.111440
$10$	−29.5934	−0.935826
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	81.7859	1.96746
$13$	24.5395	0.523541	0.261770	−	0.965130i	$-0.415694\pi$
$13$	24.5395	0.523541	0.261770	+	0.965130i	$0.415694\pi$
$14$	−78.2632	−1.49405
$15$	29.1671	0.502061
$16$	81.2283	1.26919
$17$	−28.1591	−0.401741	−0.200870	−	0.979618i	$-0.564377\pi$
$17$	−28.1591	−0.401741	−0.200870	+	0.979618i	$0.564377\pi$
$18$	14.9531	0.195804
$19$	−71.2174	−0.859915	−0.429957	−	0.902849i	$-0.641471\pi$
$19$	−71.2174	−0.859915	−0.429957	+	0.902849i	$0.641471\pi$
$20$	99.4308	1.11167
$21$	77.1357	0.801543
$22$	54.6663	0.529768
$23$	28.7688	0.260814	0.130407	−	0.991461i	$-0.458372\pi$
$23$	28.7688	0.260814	0.130407	+	0.991461i	$0.458372\pi$
$24$	−211.714	−1.80067
$25$	−89.5403	−0.716322
$26$	−121.953	−0.919883
$27$	−146.986	−1.04768
$28$	262.956	1.77479
$29$	−83.5623	−0.535074	−0.267537	−	0.963548i	$-0.586210\pi$
$29$	−83.5623	−0.535074	−0.267537	+	0.963548i	$0.586210\pi$
$30$	−144.951	−0.882142
$31$	184.473	1.06878	0.534392	−	0.845237i	$-0.320541\pi$
$31$	184.473	1.06878	0.534392	+	0.845237i	$0.320541\pi$
$32$	−57.8854	−0.319775
$33$	−53.8788	−0.284215
$34$	139.942	0.705876
$35$	93.7774	0.452893
$36$	−50.2408	−0.232596
$37$	−131.535	−0.584440	−0.292220	−	0.956351i	$-0.594394\pi$
$37$	−131.535	−0.584440	−0.292220	+	0.956351i	$0.594394\pi$
$38$	353.926	1.51091
$39$	120.196	0.493508
$40$	−257.391	−1.01743
$41$	244.871	0.932743	0.466372	−	0.884589i	$-0.345561\pi$
$41$	244.871	0.932743	0.466372	+	0.884589i	$0.345561\pi$
$42$	−383.339	−1.40834
$43$	312.208	1.10724	0.553619	−	0.832770i	$-0.313246\pi$
$43$	312.208	1.10724	0.553619	+	0.832770i	$0.313246\pi$
$44$	−183.673	−0.629313
$45$	−17.9172	−0.0593543
$46$	−142.971	−0.458261
$47$	−128.399	−0.398489	−0.199245	−	0.979950i	$-0.563849\pi$
$47$	−128.399	−0.398489	−0.199245	+	0.979950i	$0.563849\pi$
$48$	397.862	1.19639
$49$	−94.9950	−0.276953
$50$	444.985	1.25861
$51$	−137.926	−0.378695
$52$	409.750	1.09273
$53$	−637.831	−1.65307	−0.826536	−	0.562884i	$-0.809692\pi$
$53$	−637.831	−1.65307	−0.826536	+	0.562884i	$0.809692\pi$
$54$	730.470	1.84082
$55$	−65.5029	−0.160589
$56$	−680.699	−1.62433
$57$	−348.828	−0.810586
$58$	415.277	0.940147
$59$	−466.571	−1.02953	−0.514766	−	0.857331i	$-0.672121\pi$
$59$	−466.571	−1.02953	−0.514766	+	0.857331i	$0.672121\pi$
$60$	487.020	1.04790
$61$	−759.706	−1.59460	−0.797299	−	0.603585i	$-0.793738\pi$
$61$	−759.706	−1.59460	−0.797299	+	0.603585i	$0.793738\pi$
$62$	−916.768	−1.87790
$63$	−47.3842	−0.0947595
$64$	−362.155	−0.707335
$65$	146.128	0.278845
$66$	267.760	0.499378
$67$	590.720	1.07713	0.538567	−	0.842583i	$-0.318966\pi$
$67$	590.720	1.07713	0.538567	+	0.842583i	$0.318966\pi$
$68$	−470.189	−0.838512
$69$	140.912	0.245852
$70$	−466.042	−0.795753
$71$	−135.791	−0.226978	−0.113489	−	0.993539i	$-0.536203\pi$
$71$	−135.791	−0.226978	−0.113489	+	0.993539i	$0.536203\pi$
$72$	130.055	0.212877
$73$	−1083.68	−1.73747	−0.868737	−	0.495273i	$-0.835068\pi$
$73$	−1083.68	−1.73747	−0.868737	+	0.495273i	$0.835068\pi$
$74$	653.687	1.02689
$75$	−438.575	−0.675230
$76$	−1189.16	−1.79481
$77$	−173.230	−0.256382
$78$	−597.335	−0.867114
$79$	833.437	1.18695	0.593475	−	0.804852i	$-0.297756\pi$
$79$	833.437	1.18695	0.593475	+	0.804852i	$0.297756\pi$
$80$	483.699	0.675990
$81$	−638.707	−0.876142
$82$	−1216.93	−1.63887
$83$	−454.743	−0.601379	−0.300690	−	0.953722i	$-0.597217\pi$
$83$	−454.743	−0.601379	−0.300690	+	0.953722i	$0.597217\pi$
$84$	1287.98	1.67298
$85$	−167.682	−0.213973
$86$	−1551.57	−1.94546
$87$	−409.295	−0.504379
$88$	475.464	0.575962
$89$	21.0437	0.0250632	0.0125316	−	0.999921i	$-0.496011\pi$
$89$	21.0437	0.0250632	0.0125316	+	0.999921i	$0.496011\pi$
$90$	89.0427	0.104288
$91$	386.452	0.445178
$92$	480.370	0.544370
$93$	903.561	1.00747
$94$	638.102	0.700162
$95$	−424.086	−0.458003
$96$	−283.527	−0.301431
$97$	291.774	0.305414	0.152707	−	0.988272i	$-0.451201\pi$
$97$	291.774	0.305414	0.152707	+	0.988272i	$0.451201\pi$
$98$	472.093	0.486619
$99$	33.0976	0.0336003
$100$	−1495.10	−1.49510
$101$	−1674.07	−1.64926	−0.824632	−	0.565669i	$-0.808618\pi$
$101$	−1674.07	−1.64926	−0.824632	+	0.565669i	$0.808618\pi$
$102$	685.444	0.665383
$103$	−597.991	−0.572056	−0.286028	−	0.958221i	$-0.592335\pi$
$103$	−597.991	−0.572056	−0.286028	+	0.958221i	$0.592335\pi$
$104$	−1060.69	−1.00009
$105$	459.329	0.426913
$106$	3169.81	2.90452
$107$	−2034.83	−1.83845	−0.919225	−	0.393732i	$-0.871184\pi$
$107$	−2034.83	−1.83845	−0.919225	+	0.393732i	$0.871184\pi$
$108$	−2454.30	−2.18672
$109$	1700.49	1.49429	0.747145	−	0.664661i	$-0.231424\pi$
$109$	1700.49	1.49429	0.747145	+	0.664661i	$0.231424\pi$
$110$	325.527	0.282162
$111$	−644.270	−0.550914
$112$	1279.20	1.07922
$113$	177.853	0.148062	0.0740309	−	0.997256i	$-0.476414\pi$
$113$	177.853	0.148062	0.0740309	+	0.997256i	$0.476414\pi$
$114$	1733.56	1.42423
$115$	171.313	0.138913
$116$	−1395.29	−1.11680
$117$	−73.8361	−0.0583431
$118$	2318.70	1.80893
$119$	−443.455	−0.341609
$120$	−1260.72	−0.959061
$121$	121.000	0.0909091
$122$	3775.49	2.80177
$123$	1199.40	0.879236
$124$	3080.25	2.23076
$125$	−1277.55	−0.914138
$126$	235.484	0.166496
$127$	782.468	0.546715	0.273357	−	0.961913i	$-0.411866\pi$
$127$	782.468	0.546715	0.273357	+	0.961913i	$0.411866\pi$
$128$	2262.87	1.56259
$129$	1529.22	1.04372
$130$	−726.207	−0.489943
$131$	131.000	0.0873704
$131$	131.000	0.0873704
$132$	−899.645	−0.593213
$133$	−1121.54	−0.731204
$134$	−2935.68	−1.89257
$135$	−875.272	−0.558010
$136$	1217.15	0.767426
$137$	−2424.19	−1.51177	−0.755887	−	0.654702i	$-0.772794\pi$
$137$	−2424.19	−1.51177	−0.755887	+	0.654702i	$0.772794\pi$
$138$	−700.285	−0.431973
$139$	2683.42	1.63744	0.818722	−	0.574190i	$-0.194683\pi$
$139$	2683.42	1.63744	0.818722	+	0.574190i	$0.194683\pi$
$140$	1565.85	0.945277
$141$	−628.910	−0.375630
$142$	674.836	0.398810
$143$	−269.934	−0.157853
$144$	−244.405	−0.141438
$145$	−497.598	−0.284988
$146$	5385.55	3.05282
$147$	−465.292	−0.261066
$148$	−2196.32	−1.21984
$149$	−1149.28	−0.631900	−0.315950	−	0.948776i	$-0.602323\pi$
$149$	−1149.28	−0.631900	−0.315950	+	0.948776i	$0.602323\pi$
$150$	2179.57	1.18641
$151$	1615.46	0.870622	0.435311	−	0.900280i	$-0.356638\pi$
$151$	1615.46	0.870622	0.435311	+	0.900280i	$0.356638\pi$
$152$	3078.30	1.64265
$153$	84.7272	0.0447698
$154$	860.895	0.450473
$155$	1098.50	0.569249
$156$	2006.98	1.03005
$157$	−2139.43	−1.08755	−0.543774	−	0.839232i	$-0.683005\pi$
$157$	−2139.43	−1.08755	−0.543774	+	0.839232i	$0.683005\pi$
$158$	−4141.91	−2.08552
$159$	−3124.14	−1.55824
$160$	−344.697	−0.170317
$161$	453.057	0.221776
$162$	3174.16	1.53942
$163$	−2627.86	−1.26276	−0.631379	−	0.775474i	$-0.717511\pi$
$163$	−2627.86	−1.26276	−0.631379	+	0.775474i	$0.717511\pi$
$164$	4088.76	1.94682
$165$	−320.838	−0.151377
$166$	2259.92	1.05665
$167$	2629.35	1.21835	0.609177	−	0.793034i	$-0.291500\pi$
$167$	2629.35	1.21835	0.609177	+	0.793034i	$0.291500\pi$
$168$	−3334.12	−1.53115
$169$	−1594.81	−0.725905
$170$	833.325	0.375959
$171$	214.284	0.0958286
$172$	5213.11	2.31102
$173$	3649.05	1.60365	0.801827	−	0.597556i	$-0.203862\pi$
$173$	3649.05	1.60365	0.801827	+	0.597556i	$0.203862\pi$
$174$	2034.06	0.886215
$175$	−1410.10	−0.609104
$176$	−893.512	−0.382676
$177$	−2285.30	−0.970472
$178$	−104.580	−0.0440371
$179$	−304.529	−0.127160	−0.0635798	−	0.997977i	$-0.520252\pi$
$179$	−304.529	−0.127160	−0.0635798	+	0.997977i	$0.520252\pi$
$180$	−299.174	−0.123884
$181$	4251.89	1.74608	0.873040	−	0.487649i	$-0.162145\pi$
$181$	4251.89	1.74608	0.873040	+	0.487649i	$0.162145\pi$
$182$	−1920.54	−0.782196
$183$	−3721.10	−1.50312
$184$	−1243.50	−0.498219
$185$	−783.268	−0.311281
$186$	−4490.40	−1.77017
$187$	309.751	0.121129
$188$	−2143.96	−0.831725
$189$	−2314.76	−0.890866
$190$	2107.56	0.804730
$191$	1222.77	0.463227	0.231614	−	0.972808i	$-0.425599\pi$
$191$	1222.77	0.463227	0.231614	+	0.972808i	$0.425599\pi$
$192$	−1773.86	−0.666759
$193$	2688.90	1.00285	0.501427	−	0.865200i	$-0.332808\pi$
$193$	2688.90	1.00285	0.501427	+	0.865200i	$0.332808\pi$
$194$	−1450.02	−0.536625
$195$	715.745	0.262849
$196$	−1586.19	−0.578056
$197$	4616.84	1.66973	0.834864	−	0.550457i	$-0.185546\pi$
$197$	4616.84	1.66973	0.834864	+	0.550457i	$0.185546\pi$
$198$	−164.484	−0.0590371
$199$	−1050.36	−0.374160	−0.187080	−	0.982345i	$-0.559902\pi$
$199$	−1050.36	−0.374160	−0.187080	+	0.982345i	$0.559902\pi$
$200$	3870.29	1.36835
$201$	2893.39	1.01534
$202$	8319.54	2.89783
$203$	−1315.95	−0.454985
$204$	−2303.02	−0.790411
$205$	1458.16	0.496792
$206$	2971.81	1.00513
$207$	−86.5616	−0.0290650
$208$	1993.30	0.664474
$209$	783.391	0.259274
$210$	−2282.71	−0.750104
$211$	429.966	0.140285	0.0701423	−	0.997537i	$-0.477655\pi$
$211$	429.966	0.140285	0.0701423	+	0.997537i	$0.477655\pi$
$212$	−10650.2	−3.45029
$213$	−665.115	−0.213957
$214$	10112.4	3.23024
$215$	1859.14	0.589731
$216$	6353.31	2.00133
$217$	2905.11	0.908809
$218$	−8450.87	−2.62553
$219$	−5307.97	−1.63780
$220$	−1093.74	−0.335181
$221$	−691.011	−0.210328
$222$	3201.81	0.967978
$223$	−3038.92	−0.912562	−0.456281	−	0.889836i	$-0.650819\pi$
$223$	−3038.92	−0.912562	−0.456281	+	0.889836i	$0.650819\pi$
$224$	−911.589	−0.271911
$225$	269.415	0.0798266
$226$	−883.869	−0.260151
$227$	5782.14	1.69064	0.845318	−	0.534264i	$-0.179411\pi$
$227$	5782.14	1.69064	0.845318	+	0.534264i	$0.179411\pi$
$228$	−5824.58	−1.69185
$229$	2800.82	0.808225	0.404112	−	0.914709i	$-0.367580\pi$
$229$	2800.82	0.808225	0.404112	+	0.914709i	$0.367580\pi$
$230$	−851.368	−0.244076
$231$	−848.493	−0.241674
$232$	3611.90	1.02212
$233$	−1601.02	−0.450156	−0.225078	−	0.974341i	$-0.572264\pi$
$233$	−1601.02	−0.450156	−0.225078	+	0.974341i	$0.572264\pi$
$234$	366.941	0.102511
$235$	−764.594	−0.212241
$236$	−7790.60	−2.14883
$237$	4082.24	1.11886
$238$	2203.82	0.600221
$239$	−2358.37	−0.638286	−0.319143	−	0.947707i	$-0.603395\pi$
$239$	−2358.37	−0.638286	−0.319143	+	0.947707i	$0.603395\pi$
$240$	2369.19	0.637212
$241$	−2759.49	−0.737571	−0.368785	−	0.929515i	$-0.620226\pi$
$241$	−2759.49	−0.737571	−0.368785	+	0.929515i	$0.620226\pi$
$242$	−601.329	−0.159731
$243$	840.177	0.221800
$244$	−12685.3	−3.32824
$245$	−565.677	−0.147509
$246$	−5960.61	−1.54486
$247$	−1747.64	−0.450200
$248$	−7973.65	−2.04164
$249$	−2227.36	−0.566881
$250$	6348.98	1.60618
$251$	−7217.11	−1.81490	−0.907450	−	0.420161i	$-0.861974\pi$
$251$	−7217.11	−1.81490	−0.907450	+	0.420161i	$0.861974\pi$
$252$	−791.201	−0.197782
$253$	−316.457	−0.0786383
$254$	−3888.60	−0.960601
$255$	−821.320	−0.201698
$256$	−8348.49	−2.03820
$257$	−7567.32	−1.83672	−0.918358	−	0.395750i	$-0.870485\pi$
$257$	−7567.32	−1.83672	−0.918358	+	0.395750i	$0.870485\pi$
$258$	−7599.69	−1.83386
$259$	−2071.44	−0.496962
$260$	2439.98	0.582005
$261$	251.428	0.0596284
$262$	−651.026	−0.153513
$263$	−2444.32	−0.573091	−0.286546	−	0.958067i	$-0.592507\pi$
$263$	−2444.32	−0.573091	−0.286546	+	0.958067i	$0.592507\pi$
$264$	2328.86	0.542922
$265$	−3798.16	−0.880450
$266$	5573.70	1.28476
$267$	103.073	0.0236254
$268$	9863.60	2.24819
$269$	−2570.24	−0.582567	−0.291283	−	0.956637i	$-0.594082\pi$
$269$	−2570.24	−0.582567	−0.291283	+	0.956637i	$0.594082\pi$
$270$	4349.81	0.980447
$271$	−1013.38	−0.227154	−0.113577	−	0.993529i	$-0.536231\pi$
$271$	−1013.38	−0.227154	−0.113577	+	0.993529i	$0.536231\pi$
$272$	−2287.32	−0.509887
$273$	1892.87	0.419640
$274$	12047.4	2.65625
$275$	984.943	0.215979
$276$	2352.89	0.513142
$277$	−3798.96	−0.824034	−0.412017	−	0.911176i	$-0.635176\pi$
$277$	−3798.96	−0.824034	−0.412017	+	0.911176i	$0.635176\pi$
$278$	−13335.7	−2.87706
$279$	−555.054	−0.119105
$280$	−4053.43	−0.865139
$281$	−4068.46	−0.863715	−0.431858	−	0.901942i	$-0.642142\pi$
$281$	−4068.46	−0.863715	−0.431858	+	0.901942i	$0.642142\pi$
$282$	3125.47	0.659997
$283$	−3942.82	−0.828185	−0.414092	−	0.910235i	$-0.635901\pi$
$283$	−3942.82	−0.828185	−0.414092	+	0.910235i	$0.635901\pi$
$284$	−2267.38	−0.473748
$285$	−2077.20	−0.431730
$286$	1341.48	0.277355
$287$	3856.28	0.793132
$288$	174.170	0.0356356
$289$	−4120.06	−0.838604
$290$	2472.89	0.500736
$291$	1429.13	0.287894
$292$	−18094.9	−3.62645
$293$	−5420.26	−1.08073	−0.540367	−	0.841430i	$-0.681714\pi$
$293$	−5420.26	−1.08073	−0.540367	+	0.841430i	$0.681714\pi$
$294$	2312.35	0.458704
$295$	−2778.34	−0.548343
$296$	5685.49	1.11643
$297$	1616.84	0.315888
$298$	5711.56	1.11027
$299$	705.972	0.136547
$300$	−7323.13	−1.40934
$301$	4916.70	0.941508
$302$	−8028.27	−1.52972
$303$	−8199.70	−1.55465
$304$	−5784.87	−1.09140
$305$	−4523.91	−0.849305
$306$	−421.066	−0.0786625
$307$	−5822.32	−1.08240	−0.541201	−	0.840893i	$-0.682030\pi$
$307$	−5822.32	−1.08240	−0.541201	+	0.840893i	$0.682030\pi$
$308$	−2892.52	−0.535119
$309$	−2929.00	−0.539240
$310$	−5459.18	−1.00019
$311$	−627.433	−0.114400	−0.0572001	−	0.998363i	$-0.518217\pi$
$311$	−627.433	−0.114400	−0.0572001	+	0.998363i	$0.518217\pi$
$312$	−5195.36	−0.942723
$313$	5968.89	1.07790	0.538949	−	0.842339i	$-0.318822\pi$
$313$	5968.89	1.07790	0.538949	+	0.842339i	$0.318822\pi$
$314$	10632.2	1.91087
$315$	−282.164	−0.0504703
$316$	13916.4	2.47740
$317$	897.492	0.159016	0.0795081	−	0.996834i	$-0.474665\pi$
$317$	897.492	0.159016	0.0795081	+	0.996834i	$0.474665\pi$
$318$	15525.9	2.73790
$319$	919.186	0.161331
$320$	−2156.57	−0.376737
$321$	−9966.74	−1.73299
$322$	−2251.54	−0.389669
$323$	2005.42	0.345463
$324$	−10664.9	−1.82868
$325$	−2197.27	−0.375024
$326$	13059.6	2.21872
$327$	8329.13	1.40857
$328$	−10584.3	−1.78177
$329$	−2022.06	−0.338844
$330$	1594.46	0.265976
$331$	7762.35	1.28899	0.644497	−	0.764607i	$-0.277067\pi$
$331$	7762.35	1.28899	0.644497	+	0.764607i	$0.277067\pi$
$332$	−7593.10	−1.25520
$333$	395.773	0.0651298
$334$	−13067.0	−2.14070
$335$	3517.63	0.573697
$336$	6265.61	1.01731
$337$	−4813.21	−0.778019	−0.389009	−	0.921234i	$-0.627183\pi$
$337$	−4813.21	−0.778019	−0.389009	+	0.921234i	$0.627183\pi$
$338$	7925.69	1.27545
$339$	871.136	0.139568
$340$	−2799.89	−0.446604
$341$	−2029.20	−0.322250
$342$	−1064.92	−0.168375
$343$	−6897.62	−1.08582
$344$	−13494.9	−2.11510
$345$	839.103	0.130944
$346$	−18134.6	−2.81769
$347$	−4232.90	−0.654853	−0.327427	−	0.944877i	$-0.606181\pi$
$347$	−4232.90	−0.654853	−0.327427	+	0.944877i	$0.606181\pi$
$348$	−6834.22	−1.05274
$349$	2199.50	0.337354	0.168677	−	0.985671i	$-0.446050\pi$
$349$	2199.50	0.337354	0.168677	+	0.985671i	$0.446050\pi$
$350$	7007.70	1.07022
$351$	−3606.95	−0.548504
$352$	636.739	0.0964157
$353$	−9002.97	−1.35745	−0.678725	−	0.734393i	$-0.737467\pi$
$353$	−9002.97	−1.35745	−0.678725	+	0.734393i	$0.737467\pi$
$354$	11357.2	1.70516
$355$	−808.610	−0.120892
$356$	351.378	0.0523118
$357$	−2172.08	−0.322013
$358$	1513.41	0.223425
$359$	9564.65	1.40614	0.703068	−	0.711122i	$-0.251813\pi$
$359$	9564.65	1.40614	0.703068	+	0.711122i	$0.251813\pi$
$360$	774.455	0.113382
$361$	−1787.09	−0.260546
$362$	−21130.5	−3.06794
$363$	592.667	0.0856941
$364$	6452.81	0.929174
$365$	−6453.13	−0.925404
$366$	18492.6	2.64105
$367$	10495.2	1.49277	0.746384	−	0.665515i	$-0.231788\pi$
$367$	10495.2	1.49277	0.746384	+	0.665515i	$0.231788\pi$
$368$	2336.84	0.331023
$369$	−736.786	−0.103945
$370$	3892.58	0.546934
$371$	−10044.7	−1.40564
$372$	15087.3	2.10279
$373$	980.652	0.136129	0.0680647	−	0.997681i	$-0.478318\pi$
$373$	980.652	0.136129	0.0680647	+	0.997681i	$0.478318\pi$
$374$	−1539.36	−0.212830
$375$	−6257.52	−0.861698
$376$	5549.94	0.761214
$377$	−2050.58	−0.280133
$378$	11503.6	1.56529
$379$	−2679.52	−0.363160	−0.181580	−	0.983376i	$-0.558121\pi$
$379$	−2679.52	−0.363160	−0.181580	+	0.983376i	$0.558121\pi$
$380$	−7081.20	−0.955942
$381$	3832.58	0.515352
$382$	−6076.75	−0.813910
$383$	13688.6	1.82625	0.913127	−	0.407676i	$-0.133661\pi$
$383$	13688.6	1.82625	0.913127	+	0.407676i	$0.133661\pi$
$384$	11083.7	1.47295
$385$	−1031.55	−0.136552
$386$	−13362.9	−1.76206
$387$	−939.392	−0.123390
$388$	4871.91	0.637459
$389$	−7268.32	−0.947348	−0.473674	−	0.880700i	$-0.657073\pi$
$389$	−7268.32	−0.947348	−0.473674	+	0.880700i	$0.657073\pi$
$390$	−3557.01	−0.461837
$391$	−810.106	−0.104780
$392$	4106.06	0.529050
$393$	641.648	0.0823584
$394$	−22944.2	−2.93378
$395$	4962.96	0.632186
$396$	552.649	0.0701304
$397$	1388.41	0.175522	0.0877612	−	0.996142i	$-0.472029\pi$
$397$	1388.41	0.175522	0.0877612	+	0.996142i	$0.472029\pi$
$398$	5219.92	0.657415
$399$	−5493.40	−0.689259
$400$	−7273.20	−0.909151
$401$	5724.66	0.712907	0.356454	−	0.934313i	$-0.383986\pi$
$401$	5724.66	0.712907	0.356454	+	0.934313i	$0.383986\pi$
$402$	−14379.2	−1.78400
$403$	4526.86	0.559551
$404$	−27952.8	−3.44234
$405$	−3803.38	−0.466646
$406$	6539.85	0.799427
$407$	1446.89	0.176215
$408$	5961.70	0.723402
$409$	15275.0	1.84670	0.923348	−	0.383964i	$-0.125441\pi$
$409$	15275.0	1.84670	0.923348	+	0.383964i	$0.125441\pi$
$410$	−7246.58	−0.872885
$411$	−11873.9	−1.42505
$412$	−9984.99	−1.19399
$413$	−7347.64	−0.875433
$414$	430.182	0.0510684
$415$	−2707.91	−0.320303
$416$	−1420.48	−0.167415
$417$	13143.6	1.54351
$418$	−3893.19	−0.455555
$419$	102.720	0.0119767	0.00598833	−	0.999982i	$-0.498094\pi$
$419$	102.720	0.0119767	0.00598833	+	0.999982i	$0.498094\pi$
$420$	7669.67	0.891051
$421$	15654.2	1.81221	0.906104	−	0.423056i	$-0.139043\pi$
$421$	15654.2	1.81221	0.906104	+	0.423056i	$0.139043\pi$
$422$	−2136.79	−0.246486
$423$	386.337	0.0444075
$424$	27569.6	3.15778
$425$	2521.38	0.287776
$426$	3305.40	0.375932
$427$	−11964.0	−1.35592
$428$	−33976.7	−3.83721
$429$	−1322.16	−0.148798
$430$	−9239.29	−1.03618
$431$	−13858.0	−1.54876	−0.774380	−	0.632721i	$-0.781938\pi$
$431$	−13858.0	−1.54876	−0.774380	+	0.632721i	$0.781938\pi$
$432$	−11939.4	−1.32971
$433$	−13936.7	−1.54678	−0.773389	−	0.633932i	$-0.781440\pi$
$433$	−13936.7	−1.54678	−0.773389	+	0.633932i	$0.781440\pi$
$434$	−14437.4	−1.59682
$435$	−2437.27	−0.268640
$436$	28394.1	3.11888
$437$	−2048.84	−0.224278
$438$	26378.8	2.87769
$439$	13447.3	1.46197	0.730987	−	0.682391i	$-0.239060\pi$
$439$	13447.3	1.46197	0.730987	+	0.682391i	$0.239060\pi$
$440$	2831.30	0.306766
$441$	285.827	0.0308636
$442$	3434.09	0.369555
$443$	13161.5	1.41156	0.705780	−	0.708431i	$-0.250597\pi$
$443$	13161.5	1.41156	0.705780	+	0.708431i	$0.250597\pi$
$444$	−10757.7	−1.14986
$445$	125.311	0.0133490
$446$	15102.4	1.60341
$447$	−5629.28	−0.595651
$448$	−5703.29	−0.601462
$449$	−10375.7	−1.09055	−0.545277	−	0.838256i	$-0.683575\pi$
$449$	−10375.7	−1.09055	−0.545277	+	0.838256i	$0.683575\pi$
$450$	−1338.90	−0.140259
$451$	−2693.58	−0.281233
$452$	2969.71	0.309034
$453$	7912.62	0.820678
$454$	−28735.3	−2.97052
$455$	2301.25	0.237108
$456$	15077.7	1.54842
$457$	−5565.22	−0.569649	−0.284825	−	0.958580i	$-0.591935\pi$
$457$	−5565.22	−0.569649	−0.284825	+	0.958580i	$0.591935\pi$
$458$	−13919.1	−1.42008
$459$	4138.99	0.420897
$460$	2860.51	0.289939
$461$	3392.13	0.342706	0.171353	−	0.985210i	$-0.445186\pi$
$461$	3392.13	0.342706	0.171353	+	0.985210i	$0.445186\pi$
$462$	4216.73	0.424632
$463$	1278.31	0.128311	0.0641556	−	0.997940i	$-0.479565\pi$
$463$	1278.31	0.128311	0.0641556	+	0.997940i	$0.479565\pi$
$464$	−6787.63	−0.679111
$465$	5380.53	0.536594
$466$	7956.54	0.790944
$467$	−11506.5	−1.14017	−0.570085	−	0.821586i	$-0.693090\pi$
$467$	−11506.5	−1.14017	−0.570085	+	0.821586i	$0.693090\pi$
$468$	−1232.88	−0.121774
$469$	9302.77	0.915910
$470$	3799.78	0.372916
$471$	−10479.1	−1.02516
$472$	20167.1	1.96666
$473$	−3434.28	−0.333845
$474$	−20287.4	−1.96588
$475$	6376.82	0.615976
$476$	−7404.62	−0.713005
$477$	1919.15	0.184218
$478$	11720.3	1.12149
$479$	−2883.32	−0.275036	−0.137518	−	0.990499i	$-0.543913\pi$
$479$	−2883.32	−0.275036	−0.137518	+	0.990499i	$0.543913\pi$
$480$	−1688.35	−0.160546
$481$	−3227.81	−0.305978
$482$	13713.8	1.29594
$483$	2219.11	0.209053
$484$	2020.41	0.189745
$485$	1737.46	0.162668
$486$	−4175.40	−0.389712
$487$	−15494.1	−1.44169	−0.720847	−	0.693094i	$-0.756247\pi$
$487$	−15494.1	−1.44169	−0.720847	+	0.693094i	$0.756247\pi$
$488$	32837.6	3.04608
$489$	−12871.4	−1.19032
$490$	2811.22	0.259180
$491$	−5016.85	−0.461114	−0.230557	−	0.973059i	$-0.574055\pi$
$491$	−5016.85	−0.461114	−0.230557	+	0.973059i	$0.574055\pi$
$492$	20027.0	1.83514
$493$	2353.04	0.214961
$494$	8685.17	0.791021
$495$	197.090	0.0178960
$496$	14984.4	1.35649
$497$	−2138.46	−0.193004
$498$	11069.3	0.996034
$499$	6348.36	0.569523	0.284761	−	0.958598i	$-0.408086\pi$
$499$	6348.36	0.569523	0.284761	+	0.958598i	$0.408086\pi$
$500$	−21331.9	−1.90798
$501$	12878.7	1.14846
$502$	35866.6	3.18885
$503$	2703.69	0.239665	0.119833	−	0.992794i	$-0.461764\pi$
$503$	2703.69	0.239665	0.119833	+	0.992794i	$0.461764\pi$
$504$	2048.14	0.181014
$505$	−9968.74	−0.878422
$506$	1572.69	0.138171
$507$	−7811.52	−0.684264
$508$	13065.3	1.14110
$509$	−10143.9	−0.883338	−0.441669	−	0.897178i	$-0.645613\pi$
$509$	−10143.9	−0.883338	−0.441669	+	0.897178i	$0.645613\pi$
$510$	4081.69	0.354393
$511$	−17066.0	−1.47741
$512$	23386.2	2.01862
$513$	10467.9	0.900917
$514$	37607.0	3.22719
$515$	−3560.92	−0.304685
$516$	25534.2	2.17845
$517$	1412.39	0.120149
$518$	10294.4	0.873183
$519$	17873.3	1.51166
$520$	−6316.24	−0.532664
$521$	−4740.76	−0.398649	−0.199325	−	0.979934i	$-0.563875\pi$
$521$	−4740.76	−0.398649	−0.199325	+	0.979934i	$0.563875\pi$
$522$	−1249.51	−0.104770
$523$	10820.2	0.904657	0.452329	−	0.891851i	$-0.350593\pi$
$523$	10820.2	0.904657	0.452329	+	0.891851i	$0.350593\pi$
$524$	2187.38	0.182359
$525$	−6906.75	−0.574163
$526$	12147.4	1.00695
$527$	−5194.59	−0.429374
$528$	−4376.49	−0.360724
$529$	−11339.4	−0.931976
$530$	18875.6	1.54699
$531$	1403.85	0.114731
$532$	−18727.1	−1.52617
$533$	6009.02	0.488329
$534$	−512.241	−0.0415109
$535$	−12117.0	−0.979185
$536$	−25533.3	−2.05760
$537$	−1491.61	−0.119865
$538$	12773.2	1.02359
$539$	1044.94	0.0835046
$540$	−14614.9	−1.16468
$541$	16350.3	1.29936	0.649682	−	0.760206i	$-0.274902\pi$
$541$	16350.3	1.29936	0.649682	+	0.760206i	$0.274902\pi$
$542$	5036.18	0.399119
$543$	20826.1	1.64592
$544$	1630.00	0.128467
$545$	10126.1	0.795880
$546$	−9406.93	−0.737325
$547$	−20509.1	−1.60312	−0.801558	−	0.597917i	$-0.795995\pi$
$547$	−20509.1	−1.60312	−0.801558	+	0.597917i	$0.795995\pi$
$548$	−40478.2	−3.15537
$549$	2285.86	0.177701
$550$	−4894.84	−0.379485
$551$	5951.09	0.460118
$552$	−6090.78	−0.469639
$553$	13125.1	1.00929
$554$	18879.6	1.44786
$555$	−3836.50	−0.293424
$556$	44806.6	3.41767
$557$	−21578.5	−1.64149	−0.820747	−	0.571292i	$-0.806442\pi$
$557$	−21578.5	−1.64149	−0.820747	+	0.571292i	$0.806442\pi$
$558$	2758.43	0.209272
$559$	7661.41	0.579684
$560$	7617.38	0.574809
$561$	1517.18	0.114181
$562$	20218.9	1.51758
$563$	21049.8	1.57574	0.787872	−	0.615838i	$-0.211183\pi$
$563$	21049.8	1.57574	0.787872	+	0.615838i	$0.211183\pi$
$564$	−10501.3	−0.784013
$565$	1059.08	0.0788598
$566$	19594.5	1.45516
$567$	−10058.5	−0.745002
$568$	5869.44	0.433585
$569$	−16084.6	−1.18507	−0.592534	−	0.805546i	$-0.701872\pi$
$569$	−16084.6	−1.18507	−0.592534	+	0.805546i	$0.701872\pi$
$570$	10323.0	0.758567
$571$	1145.41	0.0839471	0.0419735	−	0.999119i	$-0.486635\pi$
$571$	1145.41	0.0839471	0.0419735	+	0.999119i	$0.486635\pi$
$572$	−4507.25	−0.329471
$573$	5989.21	0.436654
$574$	−19164.4	−1.39357
$575$	−2575.97	−0.186827
$576$	1089.68	0.0788251
$577$	−24700.4	−1.78214	−0.891068	−	0.453871i	$-0.850043\pi$
$577$	−24700.4	−1.78214	−0.891068	+	0.453871i	$0.850043\pi$
$578$	20475.3	1.47346
$579$	13170.4	0.945326
$580$	−8308.67	−0.594826
$581$	−7161.37	−0.511366
$582$	−7102.30	−0.505841
$583$	7016.14	0.498420
$584$	46841.2	3.31901
$585$	−439.680	−0.0310744
$586$	26936.9	1.89889
$587$	22388.1	1.57420	0.787100	−	0.616826i	$-0.211582\pi$
$587$	22388.1	1.57420	0.787100	+	0.616826i	$0.211582\pi$
$588$	−7769.25	−0.544896
$589$	−13137.7	−0.919063
$590$	13807.4	0.963462
$591$	22613.6	1.57394
$592$	−10684.4	−0.741767
$593$	−2699.17	−0.186917	−0.0934583	−	0.995623i	$-0.529792\pi$
$593$	−2699.17	−0.186917	−0.0934583	+	0.995623i	$0.529792\pi$
$594$	−8035.16	−0.555028
$595$	−2640.69	−0.181946
$596$	−19190.3	−1.31890
$597$	−5144.73	−0.352696
$598$	−3508.45	−0.239918
$599$	−8019.16	−0.547001	−0.273501	−	0.961872i	$-0.588182\pi$
$599$	−8019.16	−0.547001	−0.273501	+	0.961872i	$0.588182\pi$
$600$	18957.0	1.28986
$601$	−18975.7	−1.28791	−0.643955	−	0.765063i	$-0.722708\pi$
$601$	−18975.7	−1.28791	−0.643955	+	0.765063i	$0.722708\pi$
$602$	−24434.4	−1.65427
$603$	−1777.40	−0.120035
$604$	26974.2	1.81716
$605$	720.532	0.0484195
$606$	40749.7	2.73159
$607$	2129.41	0.142389	0.0711943	−	0.997462i	$-0.477319\pi$
$607$	2129.41	0.142389	0.0711943	+	0.997462i	$0.477319\pi$
$608$	4122.45	0.274979
$609$	−6445.64	−0.428884
$610$	22482.3	1.49227
$611$	−3150.86	−0.208625
$612$	1414.74	0.0934435
$613$	−12459.1	−0.820908	−0.410454	−	0.911881i	$-0.634630\pi$
$613$	−12459.1	−0.820908	−0.410454	+	0.911881i	$0.634630\pi$
$614$	28935.0	1.90183
$615$	7142.19	0.468294
$616$	7487.69	0.489753
$617$	23406.3	1.52723	0.763616	−	0.645671i	$-0.223422\pi$
$617$	23406.3	1.52723	0.763616	+	0.645671i	$0.223422\pi$
$618$	14556.2	0.947467
$619$	5340.79	0.346793	0.173396	−	0.984852i	$-0.444526\pi$
$619$	5340.79	0.346793	0.173396	+	0.984852i	$0.444526\pi$
$620$	18342.3	1.18813
$621$	−4228.61	−0.273250
$622$	3118.13	0.201006
$623$	331.399	0.0213118
$624$	9763.34	0.626356
$625$	3584.99	0.229439
$626$	−29663.4	−1.89391
$627$	3837.11	0.244401
$628$	−35723.3	−2.26993
$629$	3703.92	0.234794
$630$	1402.26	0.0886784
$631$	17846.7	1.12593	0.562967	−	0.826479i	$-0.309660\pi$
$631$	17846.7	1.12593	0.562967	+	0.826479i	$0.309660\pi$
$632$	−36024.5	−2.26737
$633$	2106.00	0.132237
$634$	−4460.23	−0.279398
$635$	4659.44	0.291188
$636$	−52165.6	−3.25236
$637$	−2331.13	−0.144996
$638$	−4568.05	−0.283465
$639$	408.578	0.0252943
$640$	13475.0	0.832259
$641$	−26064.0	−1.60603	−0.803015	−	0.595959i	$-0.796772\pi$
$641$	−26064.0	−1.60603	−0.803015	+	0.595959i	$0.796772\pi$
$642$	49531.4	3.04493
$643$	−1346.04	−0.0825544	−0.0412772	−	0.999148i	$-0.513143\pi$
$643$	−1346.04	−0.0825544	−0.0412772	+	0.999148i	$0.513143\pi$
$644$	7564.95	0.462889
$645$	9106.19	0.555901
$646$	−9966.27	−0.606993
$647$	2464.52	0.149753	0.0748766	−	0.997193i	$-0.476144\pi$
$647$	2464.52	0.149753	0.0748766	+	0.997193i	$0.476144\pi$
$648$	27607.5	1.67365
$649$	5132.28	0.310415
$650$	10919.7	0.658932
$651$	14229.4	0.856675
$652$	−43878.8	−2.63563
$653$	28941.5	1.73441	0.867205	−	0.497952i	$-0.165914\pi$
$653$	28941.5	1.73441	0.867205	+	0.497952i	$0.165914\pi$
$654$	−41393.0	−2.47492
$655$	780.080	0.0465347
$656$	19890.5	1.18383
$657$	3260.66	0.193623
$658$	10048.9	0.595363
$659$	6971.46	0.412094	0.206047	−	0.978542i	$-0.433940\pi$
$659$	6971.46	0.412094	0.206047	+	0.978542i	$0.433940\pi$
$660$	−5357.22	−0.315954
$661$	12602.3	0.741560	0.370780	−	0.928721i	$-0.379090\pi$
$661$	12602.3	0.741560	0.370780	+	0.928721i	$0.379090\pi$
$662$	−38576.3	−2.26482
$663$	−3384.62	−0.198262
$664$	19655.8	1.14878
$665$	−6678.58	−0.389450
$666$	−1966.86	−0.114436
$667$	−2403.99	−0.139555
$668$	43903.7	2.54294
$669$	−14884.9	−0.860212
$670$	−17481.4	−1.00801
$671$	8356.77	0.480789
$672$	−4465.03	−0.256313
$673$	17488.8	1.00170	0.500851	−	0.865534i	$-0.333021\pi$
$673$	17488.8	1.00170	0.500851	+	0.865534i	$0.333021\pi$
$674$	23920.1	1.36701
$675$	13161.1	0.750477
$676$	−26629.5	−1.51511
$677$	7113.51	0.403832	0.201916	−	0.979403i	$-0.435283\pi$
$677$	7113.51	0.403832	0.201916	+	0.979403i	$0.435283\pi$
$678$	−4329.25	−0.245227
$679$	4594.91	0.259700
$680$	7247.90	0.408742
$681$	28321.4	1.59365
$682$	10084.4	0.566207
$683$	−5278.77	−0.295734	−0.147867	−	0.989007i	$-0.547241\pi$
$683$	−5278.77	−0.295734	−0.147867	+	0.989007i	$0.547241\pi$
$684$	3578.02	0.200013
$685$	−14435.6	−0.805192
$686$	34278.9	1.90783
$687$	13718.6	0.761861
$688$	25360.1	1.40530
$689$	−15652.0	−0.865450
$690$	−4170.06	−0.230075
$691$	−26571.7	−1.46286	−0.731429	−	0.681918i	$-0.761146\pi$
$691$	−26571.7	−1.46286	−0.731429	+	0.681918i	$0.761146\pi$
$692$	60930.3	3.34714
$693$	521.226	0.0285711
$694$	21036.1	1.15060
$695$	15979.3	0.872126
$696$	17691.4	0.963490
$697$	−6895.37	−0.374721
$698$	−10930.8	−0.592745
$699$	−7841.93	−0.424333
$700$	−23545.2	−1.27132
$701$	−17047.9	−0.918533	−0.459266	−	0.888299i	$-0.651888\pi$
$701$	−17047.9	−0.918533	−0.459266	+	0.888299i	$0.651888\pi$
$702$	17925.3	0.963744
$703$	9367.60	0.502569
$704$	3983.71	0.213269
$705$	−3745.04	−0.200066
$706$	44741.7	2.38510
$707$	−26363.5	−1.40241
$708$	−38158.9	−2.02557
$709$	−6326.22	−0.335100	−0.167550	−	0.985864i	$-0.553586\pi$
$709$	−6326.22	−0.335100	−0.167550	+	0.985864i	$0.553586\pi$
$710$	4018.52	0.212412
$711$	−2507.70	−0.132273
$712$	−909.592	−0.0478770
$713$	5307.06	0.278753
$714$	10794.5	0.565790
$715$	−1607.41	−0.0840750
$716$	−5084.90	−0.265407
$717$	−11551.5	−0.601670
$718$	−47533.1	−2.47064
$719$	−15860.4	−0.822662	−0.411331	−	0.911486i	$-0.634936\pi$
$719$	−15860.4	−0.822662	−0.411331	+	0.911486i	$0.634936\pi$
$720$	−1455.39	−0.0753320
$721$	−9417.26	−0.486432
$722$	8881.23	0.457791
$723$	−13516.2	−0.695260
$724$	70996.2	3.64441
$725$	7482.19	0.383285
$726$	−2945.36	−0.150568
$727$	−688.809	−0.0351396	−0.0175698	−	0.999846i	$-0.505593\pi$
$727$	−688.809	−0.0351396	−0.0175698	+	0.999846i	$0.505593\pi$
$728$	−16704.0	−0.850401
$729$	21360.3	1.08522
$730$	32069.9	1.62597
$731$	−8791.50	−0.444823
$732$	−62133.3	−3.13731
$733$	28259.6	1.42400	0.712001	−	0.702178i	$-0.247789\pi$
$733$	28259.6	1.42400	0.712001	+	0.702178i	$0.247789\pi$
$734$	−52157.7	−2.62286
$735$	−2770.73	−0.139047
$736$	−1665.30	−0.0834016
$737$	−6497.92	−0.324768
$738$	3661.58	0.182635
$739$	−12980.5	−0.646137	−0.323069	−	0.946376i	$-0.604714\pi$
$739$	−12980.5	−0.646137	−0.323069	+	0.946376i	$0.604714\pi$
$740$	−13078.7	−0.649705
$741$	−8560.06	−0.424375
$742$	49918.7	2.46977
$743$	15009.7	0.741121	0.370560	−	0.928808i	$-0.379166\pi$
$743$	15009.7	0.741121	0.370560	+	0.928808i	$0.379166\pi$
$744$	−39055.5	−1.92452
$745$	−6843.77	−0.336559
$746$	−4873.51	−0.239185
$747$	1368.26	0.0670175
$748$	5172.08	0.252821
$749$	−32044.8	−1.56327
$750$	31097.8	1.51404
$751$	−5063.61	−0.246037	−0.123019	−	0.992404i	$-0.539257\pi$
$751$	−5063.61	−0.246037	−0.123019	+	0.992404i	$0.539257\pi$
$752$	−10429.7	−0.505759
$753$	−35349.9	−1.71079
$754$	10190.7	0.492205
$755$	9619.73	0.463706
$756$	−38650.8	−1.85941
$757$	−1681.62	−0.0807392	−0.0403696	−	0.999185i	$-0.512854\pi$
$757$	−1681.62	−0.0807392	−0.0403696	+	0.999185i	$0.512854\pi$
$758$	13316.3	0.638088
$759$	−1550.03	−0.0741272
$760$	18330.7	0.874900
$761$	−29935.8	−1.42598	−0.712991	−	0.701173i	$-0.752660\pi$
$761$	−29935.8	−1.42598	−0.712991	+	0.701173i	$0.752660\pi$
$762$	−19046.7	−0.905496
$763$	26779.6	1.27063
$764$	20417.3	0.966846
$765$	504.534	0.0238451
$766$	−68027.8	−3.20880
$767$	−11449.4	−0.539002
$768$	−40891.5	−1.92128
$769$	−1726.90	−0.0809802	−0.0404901	−	0.999180i	$-0.512892\pi$
$769$	−1726.90	−0.0809802	−0.0404901	+	0.999180i	$0.512892\pi$
$770$	5126.46	0.239928
$771$	−37065.3	−1.73135
$772$	44898.0	2.09315
$773$	−10131.7	−0.471427	−0.235714	−	0.971823i	$-0.575743\pi$
$773$	−10131.7	−0.471427	−0.235714	+	0.971823i	$0.575743\pi$
$774$	4668.46	0.216802
$775$	−16517.7	−0.765593
$776$	−12611.6	−0.583417
$777$	−10146.1	−0.468454
$778$	36121.1	1.66453
$779$	−17439.1	−0.802080
$780$	11951.2	0.548618
$781$	1493.70	0.0684365
$782$	4025.95	0.184102
$783$	12282.5	0.560587
$784$	−7716.28	−0.351507
$785$	−12739.9	−0.579243
$786$	−3188.77	−0.144707
$787$	−15988.3	−0.724171	−0.362086	−	0.932145i	$-0.617935\pi$
$787$	−15988.3	−0.724171	−0.362086	+	0.932145i	$0.617935\pi$
$788$	77090.0	3.48505
$789$	−11972.4	−0.540216
$790$	−24664.3	−1.11078
$791$	2800.86	0.125900
$792$	−1430.61	−0.0641850
$793$	−18642.8	−0.834836
$794$	−6899.94	−0.308400
$795$	−18603.7	−0.829943
$796$	−17538.4	−0.780945
$797$	21332.7	0.948111	0.474055	−	0.880495i	$-0.342790\pi$
$797$	21332.7	0.948111	0.474055	+	0.880495i	$0.342790\pi$
$798$	27300.4	1.21106
$799$	3615.62	0.160089
$800$	5183.07	0.229062
$801$	−63.3177	−0.00279303
$802$	−28449.6	−1.25261
$803$	11920.5	0.523868
$804$	48312.6	2.11922
$805$	2697.87	0.118121
$806$	−22497.0	−0.983155
$807$	−12589.2	−0.549148
$808$	72359.8	3.15051
$809$	−2687.86	−0.116811	−0.0584056	−	0.998293i	$-0.518602\pi$
$809$	−2687.86	−0.116811	−0.0584056	+	0.998293i	$0.518602\pi$
$810$	18901.5	0.819916
$811$	−43323.4	−1.87582	−0.937909	−	0.346881i	$-0.887241\pi$
$811$	−43323.4	−1.87582	−0.937909	+	0.346881i	$0.887241\pi$
$812$	−21973.2	−0.949642
$813$	−4963.63	−0.214123
$814$	−7190.55	−0.309618
$815$	−15648.4	−0.672563
$816$	−11203.5	−0.480637
$817$	−22234.6	−0.952130
$818$	−75911.5	−3.24472
$819$	−1162.78	−0.0496104
$820$	24347.8	1.03690
$821$	−5215.04	−0.221688	−0.110844	−	0.993838i	$-0.535355\pi$
$821$	−5215.04	−0.221688	−0.110844	+	0.993838i	$0.535355\pi$
$822$	59009.2	2.50387
$823$	−5333.50	−0.225898	−0.112949	−	0.993601i	$-0.536030\pi$
$823$	−5333.50	−0.225898	−0.112949	+	0.993601i	$0.536030\pi$
$824$	25847.6	1.09277
$825$	4824.32	0.203590
$826$	36515.3	1.53817
$827$	−19700.1	−0.828343	−0.414171	−	0.910199i	$-0.635929\pi$
$827$	−19700.1	−0.828343	−0.414171	+	0.910199i	$0.635929\pi$
$828$	−1445.37	−0.0606643
$829$	31461.0	1.31807	0.659037	−	0.752110i	$-0.270964\pi$
$829$	31461.0	1.31807	0.659037	+	0.752110i	$0.270964\pi$
$830$	13457.4	0.562786
$831$	−18607.6	−0.776763
$832$	−8887.11	−0.370319
$833$	2674.98	0.111263
$834$	−65319.3	−2.71202
$835$	15657.3	0.648913
$836$	13080.7	0.541156
$837$	−27114.8	−1.11974
$838$	−510.486	−0.0210435
$839$	−8007.99	−0.329519	−0.164760	−	0.986334i	$-0.552685\pi$
$839$	−8007.99	−0.329519	−0.164760	+	0.986334i	$0.552685\pi$
$840$	−19854.0	−0.815511
$841$	−17406.3	−0.713696
$842$	−77796.2	−3.18412
$843$	−19927.6	−0.814168
$844$	7179.38	0.292802
$845$	−9496.81	−0.386628
$846$	−1919.97	−0.0780258
$847$	1905.53	0.0773020
$848$	−51809.9	−2.09807
$849$	−19312.2	−0.780676
$850$	−12530.4	−0.505634
$851$	−3784.12	−0.152430
$852$	−11105.8	−0.446571
$853$	33502.2	1.34478	0.672388	−	0.740199i	$-0.265269\pi$
$853$	33502.2	1.34478	0.672388	+	0.740199i	$0.265269\pi$
$854$	59457.0	2.38241
$855$	1276.02	0.0510397
$856$	87953.4	3.51190
$857$	7065.70	0.281633	0.140817	−	0.990036i	$-0.455027\pi$
$857$	7065.70	0.281633	0.140817	+	0.990036i	$0.455027\pi$
$858$	6570.68	0.261445
$859$	−1301.13	−0.0516808	−0.0258404	−	0.999666i	$-0.508226\pi$
$859$	−1301.13	−0.0516808	−0.0258404	+	0.999666i	$0.508226\pi$
$860$	31043.1	1.23088
$861$	18888.3	0.747634
$862$	68869.6	2.72124
$863$	5240.51	0.206708	0.103354	−	0.994645i	$-0.467043\pi$
$863$	5240.51	0.206708	0.103354	+	0.994645i	$0.467043\pi$
$864$	8508.32	0.335022
$865$	21729.4	0.854129
$866$	69260.7	2.71775
$867$	−20180.4	−0.790498
$868$	48508.3	1.89686
$869$	−9167.81	−0.357879
$870$	12112.4	0.472011
$871$	14496.0	0.563923
$872$	−73502.1	−2.85447
$873$	−877.909	−0.0340352
$874$	10182.1	0.394065
$875$	−20119.0	−0.777311
$876$	−88630.1	−3.41842
$877$	47646.4	1.83456	0.917278	−	0.398248i	$-0.130382\pi$
$877$	47646.4	1.83456	0.917278	+	0.398248i	$0.130382\pi$
$878$	−66828.8	−2.56875
$879$	−26548.8	−1.01874
$880$	−5320.69	−0.203819
$881$	−20851.5	−0.797395	−0.398698	−	0.917082i	$-0.630538\pi$
$881$	−20851.5	−0.797395	−0.398698	+	0.917082i	$0.630538\pi$
$882$	−1420.47	−0.0542286
$883$	34694.6	1.32227	0.661135	−	0.750267i	$-0.270075\pi$
$883$	34694.6	1.32227	0.661135	+	0.750267i	$0.270075\pi$
$884$	−11538.2	−0.438995
$885$	−13608.5	−0.516887
$886$	−65408.1	−2.48017
$887$	−37066.0	−1.40311	−0.701554	−	0.712617i	$-0.747510\pi$
$887$	−37066.0	−1.40311	−0.701554	+	0.712617i	$0.747510\pi$
$888$	27847.9	1.05238
$889$	12322.4	0.464883
$890$	−622.754	−0.0234548
$891$	7025.78	0.264167
$892$	−50742.6	−1.90470
$893$	9144.27	0.342667
$894$	27975.6	1.04658
$895$	−1813.41	−0.0677270
$896$	35636.1	1.32871
$897$	3457.90	0.128714
$898$	51563.6	1.91615
$899$	−15415.0	−0.571878
$900$	4498.57	0.166614
$901$	17960.8	0.664107
$902$	13386.2	0.494138
$903$	24082.4	0.887498
$904$	−7687.51	−0.282835
$905$	25319.2	0.929987
$906$	−39323.1	−1.44197
$907$	5981.51	0.218978	0.109489	−	0.993988i	$-0.465079\pi$
$907$	5981.51	0.218978	0.109489	+	0.993988i	$0.465079\pi$
$908$	96547.7	3.52869
$909$	5037.04	0.183793
$910$	−11436.4	−0.416609
$911$	39447.0	1.43462	0.717308	−	0.696756i	$-0.245374\pi$
$911$	39447.0	1.43462	0.717308	+	0.696756i	$0.245374\pi$
$912$	−28334.7	−1.02879
$913$	5002.17	0.181323
$914$	27657.3	1.00090
$915$	−22158.4	−0.800585
$916$	46766.9	1.68692
$917$	2063.01	0.0742929
$918$	−20569.4	−0.739533
$919$	30242.5	1.08553	0.542767	−	0.839883i	$-0.317377\pi$
$919$	30242.5	1.08553	0.542767	+	0.839883i	$0.317377\pi$
$920$	−7404.83	−0.265359
$921$	−28518.2	−1.02031
$922$	−16857.8	−0.602148
$923$	−3332.24	−0.118832
$924$	−14167.8	−0.504422
$925$	11777.7	0.418647
$926$	−6352.77	−0.225448
$927$	1799.28	0.0637497
$928$	4837.04	0.171103
$929$	52251.4	1.84533	0.922666	−	0.385601i	$-0.126006\pi$
$929$	52251.4	1.84533	0.922666	+	0.385601i	$0.126006\pi$
$930$	−26739.4	−0.942818
$931$	6765.29	0.238156
$932$	−26733.2	−0.939565
$933$	−3073.21	−0.107838
$934$	57183.7	2.00333
$935$	1844.51	0.0645153
$936$	3191.49	0.111450
$937$	25875.9	0.902165	0.451083	−	0.892482i	$-0.351038\pi$
$937$	25875.9	0.902165	0.451083	+	0.892482i	$0.351038\pi$
$938$	−46231.6	−1.60929
$939$	29236.1	1.01606
$940$	−12766.9	−0.442989
$941$	−8943.37	−0.309825	−0.154913	−	0.987928i	$-0.549510\pi$
$941$	−8943.37	−0.309825	−0.154913	+	0.987928i	$0.549510\pi$
$942$	52077.5	1.80125
$943$	7044.66	0.243272
$944$	−37898.8	−1.30667
$945$	−13783.9	−0.474488
$946$	17067.2	0.586579
$947$	15070.9	0.517147	0.258574	−	0.965992i	$-0.416748\pi$
$947$	15070.9	0.517147	0.258574	+	0.965992i	$0.416748\pi$
$948$	68163.5	2.33528
$949$	−26593.0	−0.909638
$950$	−31690.7	−1.08230
$951$	4395.98	0.149894
$952$	19167.9	0.652558
$953$	−19645.7	−0.667773	−0.333887	−	0.942613i	$-0.608360\pi$
$953$	−19645.7	−0.667773	−0.333887	+	0.942613i	$0.608360\pi$
$954$	−9537.53	−0.323678
$955$	7281.35	0.246721
$956$	−39379.0	−1.33223
$957$	4502.24	0.152076
$958$	14329.2	0.483251
$959$	−38176.6	−1.28549
$960$	−10563.0	−0.355125
$961$	4239.18	0.142297
$962$	16041.1	0.537616
$963$	6122.53	0.204876
$964$	−46076.8	−1.53945
$965$	16011.9	0.534135
$966$	−11028.2	−0.367316
$967$	46135.9	1.53426	0.767131	−	0.641491i	$-0.221684\pi$
$967$	46135.9	1.53426	0.767131	+	0.641491i	$0.221684\pi$
$968$	−5230.11	−0.173659
$969$	9822.70	0.325645
$970$	−8634.58	−0.285814
$971$	−4246.06	−0.140332	−0.0701661	−	0.997535i	$-0.522353\pi$
$971$	−4246.06	−0.140332	−0.0701661	+	0.997535i	$0.522353\pi$
$972$	14028.9	0.462940
$973$	42259.0	1.39235
$974$	77000.5	2.53312
$975$	−10762.4	−0.353510
$976$	−61709.7	−2.02385
$977$	−38163.5	−1.24970	−0.624850	−	0.780745i	$-0.714840\pi$
$977$	−38163.5	−1.24970	−0.624850	+	0.780745i	$0.714840\pi$
$978$	63966.7	2.09144
$979$	−231.480	−0.00755684
$980$	−9445.43	−0.307881
$981$	−5116.56	−0.166523
$982$	24932.1	0.810197
$983$	9609.22	0.311787	0.155894	−	0.987774i	$-0.450174\pi$
$983$	9609.22	0.311787	0.155894	+	0.987774i	$0.450174\pi$
$984$	−51842.8	−1.67956
$985$	27492.4	0.889321
$986$	−11693.8	−0.377696
$987$	−9904.19	−0.319406
$988$	−29181.3	−0.939657
$989$	8981.85	0.288783
$990$	−979.469	−0.0314440
$991$	3957.81	0.126866	0.0634329	−	0.997986i	$-0.479795\pi$
$991$	3957.81	0.126866	0.0634329	+	0.997986i	$0.479795\pi$
$992$	−10678.3	−0.341770
$993$	38020.6	1.21505
$994$	10627.4	0.339117
$995$	−6254.68	−0.199283
$996$	−37191.6	−1.18319
$997$	−20172.6	−0.640796	−0.320398	−	0.947283i	$-0.603817\pi$
$997$	−20172.6	−0.640796	−0.320398	+	0.947283i	$0.603817\pi$
$998$	−31549.2	−1.00068
$999$	19333.8	0.612307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.a.1.7	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.a.1.7	✓	77	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-4.96967 q^{2} +4.89807 q^{3} +16.6976 q^{4} +5.95481 q^{5} -24.3418 q^{6} +15.7482 q^{7} -43.2240 q^{8} -3.00887 q^{9} +O(q^{10})\)	\(q-4.96967 q^{2} +4.89807 q^{3} +16.6976 q^{4} +5.95481 q^{5} -24.3418 q^{6} +15.7482 q^{7} -43.2240 q^{8} -3.00887 q^{9} -29.5934 q^{10} -11.0000 q^{11} +81.7859 q^{12} +24.5395 q^{13} -78.2632 q^{14} +29.1671 q^{15} +81.2283 q^{16} -28.1591 q^{17} +14.9531 q^{18} -71.2174 q^{19} +99.4308 q^{20} +77.1357 q^{21} +54.6663 q^{22} +28.7688 q^{23} -211.714 q^{24} -89.5403 q^{25} -121.953 q^{26} -146.986 q^{27} +262.956 q^{28} -83.5623 q^{29} -144.951 q^{30} +184.473 q^{31} -57.8854 q^{32} -53.8788 q^{33} +139.942 q^{34} +93.7774 q^{35} -50.2408 q^{36} -131.535 q^{37} +353.926 q^{38} +120.196 q^{39} -257.391 q^{40} +244.871 q^{41} -383.339 q^{42} +312.208 q^{43} -183.673 q^{44} -17.9172 q^{45} -142.971 q^{46} -128.399 q^{47} +397.862 q^{48} -94.9950 q^{49} +444.985 q^{50} -137.926 q^{51} +409.750 q^{52} -637.831 q^{53} +730.470 q^{54} -65.5029 q^{55} -680.699 q^{56} -348.828 q^{57} +415.277 q^{58} -466.571 q^{59} +487.020 q^{60} -759.706 q^{61} -916.768 q^{62} -47.3842 q^{63} -362.155 q^{64} +146.128 q^{65} +267.760 q^{66} +590.720 q^{67} -470.189 q^{68} +140.912 q^{69} -466.042 q^{70} -135.791 q^{71} +130.055 q^{72} -1083.68 q^{73} +653.687 q^{74} -438.575 q^{75} -1189.16 q^{76} -173.230 q^{77} -597.335 q^{78} +833.437 q^{79} +483.699 q^{80} -638.707 q^{81} -1216.93 q^{82} -454.743 q^{83} +1287.98 q^{84} -167.682 q^{85} -1551.57 q^{86} -409.295 q^{87} +475.464 q^{88} +21.0437 q^{89} +89.0427 q^{90} +386.452 q^{91} +480.370 q^{92} +903.561 q^{93} +638.102 q^{94} -424.086 q^{95} -283.527 q^{96} +291.774 q^{97} +472.093 q^{98} +33.0976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9}+O(q^{10}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9	\( 77 q - 14 q^{2} - 10 q^{3} + 296 q^{4} - 42 q^{5} - 13 q^{6} - 59 q^{7} - 150 q^{8} + 541 q^{9} + 2 q^{10} - 847 q^{11} - 88 q^{12} - 20 q^{13} - 282 q^{14} - 330 q^{15} + 936 q^{16} - 56 q^{17} - 343 q^{18} - 157 q^{19} - 450 q^{20} - 122 q^{21} + 154 q^{22} - 764 q^{23} - 346 q^{24} + 1413 q^{25} - 408 q^{26} - 358 q^{27} - 228 q^{28} - 557 q^{29} - 267 q^{30} - 780 q^{31} - 1739 q^{32} + 110 q^{33} - 1104 q^{34} - 1254 q^{35} + 375 q^{36} - 541 q^{37} - 2133 q^{38} - 1458 q^{39} - 554 q^{40} - 1723 q^{41} - 5 q^{42} - 688 q^{43} - 3256 q^{44} - 1588 q^{45} + 276 q^{46} - 3086 q^{47} - 4280 q^{48} + 2452 q^{49} - 2234 q^{50} - 1570 q^{51} - 715 q^{52} - 1230 q^{53} - 5166 q^{54} + 462 q^{55} - 3203 q^{56} + 1024 q^{57} - 3016 q^{58} - 5408 q^{59} - 8221 q^{60} + 566 q^{61} - 3642 q^{62} - 3035 q^{63} + 1084 q^{64} - 1794 q^{65} + 143 q^{66} - 1925 q^{67} - 1105 q^{68} - 3710 q^{69} - 5875 q^{70} - 9614 q^{71} - 2198 q^{72} - 384 q^{73} - 2378 q^{74} - 3888 q^{75} - 2809 q^{76} + 649 q^{77} - 1731 q^{78} - 1086 q^{79} - 4357 q^{80} + 2329 q^{81} - 3167 q^{82} - 3045 q^{83} - 5359 q^{84} + 2582 q^{85} - 6468 q^{86} - 4432 q^{87} + 1650 q^{88} - 2831 q^{89} + 512 q^{90} - 6002 q^{91} - 7134 q^{92} - 4428 q^{93} + 1697 q^{94} - 10434 q^{95} + 195 q^{96} - 2506 q^{97} - 3435 q^{98} - 5951 q^{99}+O(q^{100}) \) 77 * q - 14 * q^2 - 10 * q^3 + 296 * q^4 - 42 * q^5 - 13 * q^6 - 59 * q^7 - 150 * q^8 + 541 * q^9 + 2 * q^10 - 847 * q^11 - 88 * q^12 - 20 * q^13 - 282 * q^14 - 330 * q^15 + 936 * q^16 - 56 * q^17 - 343 * q^18 - 157 * q^19 - 450 * q^20 - 122 * q^21 + 154 * q^22 - 764 * q^23 - 346 * q^24 + 1413 * q^25 - 408 * q^26 - 358 * q^27 - 228 * q^28 - 557 * q^29 - 267 * q^30 - 780 * q^31 - 1739 * q^32 + 110 * q^33 - 1104 * q^34 - 1254 * q^35 + 375 * q^36 - 541 * q^37 - 2133 * q^38 - 1458 * q^39 - 554 * q^40 - 1723 * q^41 - 5 * q^42 - 688 * q^43 - 3256 * q^44 - 1588 * q^45 + 276 * q^46 - 3086 * q^47 - 4280 * q^48 + 2452 * q^49 - 2234 * q^50 - 1570 * q^51 - 715 * q^52 - 1230 * q^53 - 5166 * q^54 + 462 * q^55 - 3203 * q^56 + 1024 * q^57 - 3016 * q^58 - 5408 * q^59 - 8221 * q^60 + 566 * q^61 - 3642 * q^62 - 3035 * q^63 + 1084 * q^64 - 1794 * q^65 + 143 * q^66 - 1925 * q^67 - 1105 * q^68 - 3710 * q^69 - 5875 * q^70 - 9614 * q^71 - 2198 * q^72 - 384 * q^73 - 2378 * q^74 - 3888 * q^75 - 2809 * q^76 + 649 * q^77 - 1731 * q^78 - 1086 * q^79 - 4357 * q^80 + 2329 * q^81 - 3167 * q^82 - 3045 * q^83 - 5359 * q^84 + 2582 * q^85 - 6468 * q^86 - 4432 * q^87 + 1650 * q^88 - 2831 * q^89 + 512 * q^90 - 6002 * q^91 - 7134 * q^92 - 4428 * q^93 + 1697 * q^94 - 10434 * q^95 + 195 * q^96 - 2506 * q^97 - 3435 * q^98 - 5951 * q^99

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