LMFDB - Embedded newform 983.4.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,4,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	983.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:	$57.9988775356$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.67338 q^{2} +5.53617 q^{3} +13.8405 q^{4} -1.05395 q^{5} -25.8727 q^{6} +16.9979 q^{7} -27.2950 q^{8} +3.64920 q^{9} +O(q^{10})$	\(q-4.67338 q^{2} +5.53617 q^{3} +13.8405 q^{4} -1.05395 q^{5} -25.8727 q^{6} +16.9979 q^{7} -27.2950 q^{8} +3.64920 q^{9} +4.92552 q^{10} +47.2420 q^{11} +76.6235 q^{12} +60.2959 q^{13} -79.4379 q^{14} -5.83485 q^{15} +16.8358 q^{16} -135.744 q^{17} -17.0541 q^{18} -115.332 q^{19} -14.5872 q^{20} +94.1036 q^{21} -220.780 q^{22} -52.9846 q^{23} -151.110 q^{24} -123.889 q^{25} -281.786 q^{26} -129.274 q^{27} +235.260 q^{28} +293.162 q^{29} +27.2685 q^{30} -128.230 q^{31} +139.680 q^{32} +261.540 q^{33} +634.386 q^{34} -17.9150 q^{35} +50.5068 q^{36} -414.712 q^{37} +538.991 q^{38} +333.809 q^{39} +28.7676 q^{40} -292.462 q^{41} -439.782 q^{42} -226.691 q^{43} +653.854 q^{44} -3.84607 q^{45} +247.617 q^{46} -290.498 q^{47} +93.2058 q^{48} -54.0698 q^{49} +578.982 q^{50} -751.504 q^{51} +834.527 q^{52} -689.987 q^{53} +604.147 q^{54} -49.7907 q^{55} -463.959 q^{56} -638.498 q^{57} -1370.06 q^{58} +354.171 q^{59} -80.7574 q^{60} +69.9644 q^{61} +599.269 q^{62} +62.0289 q^{63} -787.463 q^{64} -63.5489 q^{65} -1222.28 q^{66} +315.999 q^{67} -1878.77 q^{68} -293.332 q^{69} +83.7237 q^{70} +287.499 q^{71} -99.6048 q^{72} +162.156 q^{73} +1938.11 q^{74} -685.872 q^{75} -1596.26 q^{76} +803.017 q^{77} -1560.02 q^{78} -1091.77 q^{79} -17.7441 q^{80} -814.212 q^{81} +1366.79 q^{82} +979.290 q^{83} +1302.44 q^{84} +143.068 q^{85} +1059.42 q^{86} +1623.00 q^{87} -1289.47 q^{88} +1513.79 q^{89} +17.9742 q^{90} +1024.91 q^{91} -733.334 q^{92} -709.905 q^{93} +1357.61 q^{94} +121.554 q^{95} +773.291 q^{96} -1641.07 q^{97} +252.689 q^{98} +172.395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) $ 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9 - 243 * q^10 - 126 * q^11 - 280 * q^12 - 458 * q^13 - 177 * q^14 - 314 * q^15 + 1009 * q^16 - 594 * q^17 - 671 * q^18 - 491 * q^19 - 500 * q^20 - 660 * q^21 - 899 * q^22 - 487 * q^23 - 811 * q^24 + 705 * q^25 - 104 * q^26 - 842 * q^27 - 2648 * q^28 - 820 * q^29 - 728 * q^30 - 965 * q^31 - 1669 * q^32 - 2196 * q^33 - 508 * q^34 - 846 * q^35 + 1358 * q^36 - 3209 * q^37 - 1136 * q^38 - 1326 * q^39 - 3234 * q^40 - 1961 * q^41 - 2240 * q^42 - 2999 * q^43 - 1922 * q^44 - 2234 * q^45 - 2962 * q^46 - 1903 * q^47 - 2787 * q^48 + 1186 * q^49 - 2309 * q^50 - 2436 * q^51 - 4897 * q^52 - 1825 * q^53 - 3306 * q^54 - 2888 * q^55 - 1820 * q^56 - 6684 * q^57 - 4813 * q^58 - 1537 * q^59 - 3869 * q^60 - 2276 * q^61 - 1950 * q^62 - 6491 * q^63 - 89 * q^64 - 5546 * q^65 - 3527 * q^66 - 5005 * q^67 - 4183 * q^68 - 3018 * q^69 - 2993 * q^70 - 2014 * q^71 - 9549 * q^72 - 12904 * q^73 - 2714 * q^74 - 3379 * q^75 - 6293 * q^76 - 3258 * q^77 - 4593 * q^78 - 5005 * q^79 - 3988 * q^80 + 249 * q^81 - 5116 * q^82 - 2854 * q^83 - 4158 * q^84 - 11742 * q^85 - 2709 * q^86 - 2412 * q^87 - 10451 * q^88 - 2519 * q^89 - 8095 * q^90 - 2438 * q^91 - 6660 * q^92 - 10668 * q^93 - 4281 * q^94 - 4482 * q^95 - 6515 * q^96 - 16628 * q^97 - 5708 * q^98 - 6308 * 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 $

$2$	−4.67338	−1.65229	−0.826145	−	0.563457i	$-0.809471\pi$
$2$	−4.67338	−1.65229	−0.826145	+	0.563457i	$0.809471\pi$
$3$	5.53617	1.06544	0.532718	−	0.846293i	$-0.321171\pi$
$3$	5.53617	1.06544	0.532718	+	0.846293i	$0.321171\pi$
$4$	13.8405	1.73006
$5$	−1.05395	−0.0942682	−0.0471341	−	0.998889i	$-0.515009\pi$
$5$	−1.05395	−0.0942682	−0.0471341	+	0.998889i	$0.515009\pi$
$6$	−25.8727	−1.76041
$7$	16.9979	0.917803	0.458901	−	0.888487i	$-0.348243\pi$
$7$	16.9979	0.917803	0.458901	+	0.888487i	$0.348243\pi$
$8$	−27.2950	−1.20628
$9$	3.64920	0.135155
$10$	4.92552	0.155758
$11$	47.2420	1.29491	0.647454	−	0.762104i	$-0.275834\pi$
$11$	47.2420	1.29491	0.647454	+	0.762104i	$0.275834\pi$
$12$	76.6235	1.84327
$13$	60.2959	1.28639	0.643195	−	0.765702i	$-0.277608\pi$
$13$	60.2959	1.28639	0.643195	+	0.765702i	$0.277608\pi$
$14$	−79.4379	−1.51648
$15$	−5.83485	−0.100437
$16$	16.8358	0.263059
$17$	−135.744	−1.93664	−0.968319	−	0.249717i	$-0.919663\pi$
$17$	−135.744	−1.93664	−0.968319	+	0.249717i	$0.919663\pi$
$18$	−17.0541	−0.223316
$19$	−115.332	−1.39258	−0.696289	−	0.717761i	$-0.745167\pi$
$19$	−115.332	−1.39258	−0.696289	+	0.717761i	$0.745167\pi$
$20$	−14.5872	−0.163090
$21$	94.1036	0.977861
$22$	−220.780	−2.13957
$23$	−52.9846	−0.480350	−0.240175	−	0.970730i	$-0.577205\pi$
$23$	−52.9846	−0.480350	−0.240175	+	0.970730i	$0.577205\pi$
$24$	−151.110	−1.28521
$25$	−123.889	−0.991114
$26$	−281.786	−2.12549
$27$	−129.274	−0.921437
$28$	235.260	1.58786
$29$	293.162	1.87720	0.938601	−	0.345004i	$-0.112122\pi$
$29$	293.162	1.87720	0.938601	+	0.345004i	$0.112122\pi$
$30$	27.2685	0.165951
$31$	−128.230	−0.742930	−0.371465	−	0.928447i	$-0.621144\pi$
$31$	−128.230	−0.742930	−0.371465	+	0.928447i	$0.621144\pi$
$32$	139.680	0.771629
$33$	261.540	1.37964
$34$	634.386	3.19989
$35$	−17.9150	−0.0865196
$36$	50.5068	0.233828
$37$	−414.712	−1.84265	−0.921326	−	0.388790i	$-0.872893\pi$
$37$	−414.712	−1.84265	−0.921326	+	0.388790i	$0.872893\pi$
$38$	538.991	2.30095
$39$	333.809	1.37057
$40$	28.7676	0.113714
$41$	−292.462	−1.11402	−0.557010	−	0.830506i	$-0.688052\pi$
$41$	−292.462	−1.11402	−0.557010	+	0.830506i	$0.688052\pi$
$42$	−439.782	−1.61571
$43$	−226.691	−0.803956	−0.401978	−	0.915649i	$-0.631677\pi$
$43$	−226.691	−0.803956	−0.401978	+	0.915649i	$0.631677\pi$
$44$	653.854	2.24028
$45$	−3.84607	−0.0127409
$46$	247.617	0.793678
$47$	−290.498	−0.901564	−0.450782	−	0.892634i	$-0.648855\pi$
$47$	−290.498	−0.901564	−0.450782	+	0.892634i	$0.648855\pi$
$48$	93.2058	0.280273
$49$	−54.0698	−0.157638
$50$	578.982	1.63761
$51$	−751.504	−2.06337
$52$	834.527	2.22554
$53$	−689.987	−1.78825	−0.894123	−	0.447821i	$-0.852200\pi$
$53$	−689.987	−1.78825	−0.894123	+	0.447821i	$0.852200\pi$
$54$	604.147	1.52248
$55$	−49.7907	−0.122069
$56$	−463.959	−1.10713
$57$	−638.498	−1.48370
$58$	−1370.06	−3.10168
$59$	354.171	0.781511	0.390755	−	0.920495i	$-0.372214\pi$
$59$	354.171	0.781511	0.390755	+	0.920495i	$0.372214\pi$
$60$	−80.7574	−0.173762
$61$	69.9644	0.146853	0.0734264	−	0.997301i	$-0.476607\pi$
$61$	69.9644	0.146853	0.0734264	+	0.997301i	$0.476607\pi$
$62$	599.269	1.22754
$63$	62.0289	0.124046
$64$	−787.463	−1.53801
$65$	−63.5489	−0.121266
$66$	−1222.28	−2.27957
$67$	315.999	0.576201	0.288101	−	0.957600i	$-0.406976\pi$
$67$	315.999	0.576201	0.288101	+	0.957600i	$0.406976\pi$
$68$	−1878.77	−3.35051
$69$	−293.332	−0.511783
$70$	83.7237	0.142956
$71$	287.499	0.480561	0.240280	−	0.970704i	$-0.422761\pi$
$71$	287.499	0.480561	0.240280	+	0.970704i	$0.422761\pi$
$72$	−99.6048	−0.163035
$73$	162.156	0.259986	0.129993	−	0.991515i	$-0.458505\pi$
$73$	162.156	0.259986	0.129993	+	0.991515i	$0.458505\pi$
$74$	1938.11	3.04460
$75$	−685.872	−1.05597
$76$	−1596.26	−2.40925
$77$	803.017	1.18847
$78$	−1560.02	−2.26458
$79$	−1091.77	−1.55486	−0.777430	−	0.628969i	$-0.783477\pi$
$79$	−1091.77	−1.55486	−0.777430	+	0.628969i	$0.783477\pi$
$80$	−17.7441	−0.0247981
$81$	−814.212	−1.11689
$82$	1366.79	1.84069
$83$	979.290	1.29507	0.647537	−	0.762034i	$-0.275799\pi$
$83$	979.290	1.29507	0.647537	+	0.762034i	$0.275799\pi$
$84$	1302.44	1.69176
$85$	143.068	0.182563
$86$	1059.42	1.32837
$87$	1623.00	2.00004
$88$	−1289.47	−1.56202
$89$	1513.79	1.80294	0.901469	−	0.432843i	$-0.142489\pi$
$89$	1513.79	1.80294	0.901469	+	0.432843i	$0.142489\pi$
$90$	17.9742	0.0210516
$91$	1024.91	1.18065
$92$	−733.334	−0.831037
$93$	−709.905	−0.791545
$94$	1357.61	1.48965
$95$	121.554	0.131276
$96$	773.291	0.822122
$97$	−1641.07	−1.71779	−0.858895	−	0.512152i	$-0.828848\pi$
$97$	−1641.07	−1.71779	−0.858895	+	0.512152i	$0.828848\pi$
$98$	252.689	0.260464
$99$	172.395	0.175014
$100$	−1714.69	−1.71469
$101$	−1371.06	−1.35075	−0.675373	−	0.737477i	$-0.736017\pi$
$101$	−1371.06	−1.35075	−0.675373	+	0.737477i	$0.736017\pi$
$102$	3512.07	3.40928
$103$	667.937	0.638969	0.319484	−	0.947592i	$-0.396490\pi$
$103$	667.937	0.638969	0.319484	+	0.947592i	$0.396490\pi$
$104$	−1645.78	−1.55175
$105$	−99.1805	−0.0921812
$106$	3224.58	2.95470
$107$	126.317	0.114127	0.0570633	−	0.998371i	$-0.481826\pi$
$107$	126.317	0.114127	0.0570633	+	0.998371i	$0.481826\pi$
$108$	−1789.22	−1.59415
$109$	−103.251	−0.0907309	−0.0453655	−	0.998970i	$-0.514445\pi$
$109$	−103.251	−0.0907309	−0.0453655	+	0.998970i	$0.514445\pi$
$110$	232.691	0.201693
$111$	−2295.91	−1.96323
$112$	286.174	0.241437
$113$	890.253	0.741133	0.370566	−	0.928806i	$-0.379164\pi$
$113$	890.253	0.741133	0.370566	+	0.928806i	$0.379164\pi$
$114$	2983.95	2.45151
$115$	55.8432	0.0452818
$116$	4057.52	3.24768
$117$	220.032	0.173863
$118$	−1655.18	−1.29128
$119$	−2307.38	−1.77745
$120$	159.262	0.121155
$121$	900.805	0.676788
$122$	−326.970	−0.242644
$123$	−1619.12	−1.18692
$124$	−1774.77	−1.28532
$125$	262.317	0.187699
$126$	−289.885	−0.204960
$127$	1612.44	1.12662	0.563312	−	0.826244i	$-0.309527\pi$
$127$	1612.44	1.12662	0.563312	+	0.826244i	$0.309527\pi$
$128$	2562.68	1.76962
$129$	−1255.00	−0.856564
$130$	296.989	0.200366
$131$	345.456	0.230402	0.115201	−	0.993342i	$-0.463249\pi$
$131$	345.456	0.230402	0.115201	+	0.993342i	$0.463249\pi$
$132$	3619.85	2.38687
$133$	−1960.41	−1.27811
$134$	−1476.79	−0.952052
$135$	136.248	0.0868622
$136$	3705.14	2.33613
$137$	1360.64	0.848520	0.424260	−	0.905541i	$-0.360534\pi$
$137$	1360.64	0.848520	0.424260	+	0.905541i	$0.360534\pi$
$138$	1370.85	0.845614
$139$	955.304	0.582934	0.291467	−	0.956581i	$-0.405857\pi$
$139$	955.304	0.582934	0.291467	+	0.956581i	$0.405857\pi$
$140$	−247.953	−0.149685
$141$	−1608.25	−0.960559
$142$	−1343.59	−0.794026
$143$	2848.50	1.66576
$144$	61.4371	0.0355539
$145$	−308.979	−0.176961
$146$	−757.819	−0.429572
$147$	−299.340	−0.167953
$148$	−5739.82	−3.18791
$149$	1454.07	0.799475	0.399737	−	0.916630i	$-0.369101\pi$
$149$	1454.07	0.799475	0.399737	+	0.916630i	$0.369101\pi$
$150$	3205.34	1.74477
$151$	−441.046	−0.237694	−0.118847	−	0.992913i	$-0.537920\pi$
$151$	−441.046	−0.237694	−0.118847	+	0.992913i	$0.537920\pi$
$152$	3147.99	1.67984
$153$	−495.358	−0.261747
$154$	−3752.81	−1.96370
$155$	135.148	0.0700347
$156$	4620.08	2.37117
$157$	446.234	0.226836	0.113418	−	0.993547i	$-0.463820\pi$
$157$	446.234	0.226836	0.113418	+	0.993547i	$0.463820\pi$
$158$	5102.27	2.56908
$159$	−3819.89	−1.90526
$160$	−147.216	−0.0727401
$161$	−900.630	−0.440867
$162$	3805.12	1.84542
$163$	1112.95	0.534802	0.267401	−	0.963585i	$-0.413835\pi$
$163$	1112.95	0.534802	0.267401	+	0.963585i	$0.413835\pi$
$164$	−4047.82	−1.92733
$165$	−275.650	−0.130057
$166$	−4576.60	−2.13984
$167$	302.733	0.140277	0.0701383	−	0.997537i	$-0.477656\pi$
$167$	302.733	0.140277	0.0701383	+	0.997537i	$0.477656\pi$
$168$	−2568.55	−1.17957
$169$	1438.60	0.654801
$170$	−668.611	−0.301648
$171$	−420.870	−0.188215
$172$	−3137.53	−1.39090
$173$	−1088.61	−0.478414	−0.239207	−	0.970969i	$-0.576887\pi$
$173$	−1088.61	−0.478414	−0.239207	+	0.970969i	$0.576887\pi$
$174$	−7584.89	−3.30465
$175$	−2105.86	−0.909647
$176$	795.356	0.340638
$177$	1960.75	0.832650
$178$	−7074.53	−2.97898
$179$	−3444.60	−1.43833	−0.719167	−	0.694837i	$-0.755476\pi$
$179$	−3444.60	−1.43833	−0.719167	+	0.694837i	$0.755476\pi$
$180$	−53.2317	−0.0220425
$181$	−84.7952	−0.0348220	−0.0174110	−	0.999848i	$-0.505542\pi$
$181$	−84.7952	−0.0348220	−0.0174110	+	0.999848i	$0.505542\pi$
$182$	−4789.78	−1.95078
$183$	387.335	0.156462
$184$	1446.21	0.579437
$185$	437.085	0.173704
$186$	3317.66	1.30786
$187$	−6412.83	−2.50777
$188$	−4020.64	−1.55976
$189$	−2197.39	−0.845698
$190$	−568.070	−0.216906
$191$	−3781.75	−1.43266	−0.716329	−	0.697762i	$-0.754179\pi$
$191$	−3781.75	−1.43266	−0.716329	+	0.697762i	$0.754179\pi$
$192$	−4359.53	−1.63866
$193$	−2264.73	−0.844657	−0.422328	−	0.906443i	$-0.638787\pi$
$193$	−2264.73	−0.844657	−0.422328	+	0.906443i	$0.638787\pi$
$194$	7669.36	2.83829
$195$	−351.818	−0.129201
$196$	−748.354	−0.272724
$197$	3812.04	1.37866	0.689331	−	0.724446i	$-0.257905\pi$
$197$	3812.04	1.37866	0.689331	+	0.724446i	$0.257905\pi$
$198$	−805.670	−0.289174
$199$	−3479.95	−1.23964	−0.619818	−	0.784746i	$-0.712793\pi$
$199$	−3479.95	−1.23964	−0.619818	+	0.784746i	$0.712793\pi$
$200$	3381.55	1.19556
$201$	1749.43	0.613906
$202$	6407.48	2.23182
$203$	4983.16	1.72290
$204$	−10401.2	−3.56976
$205$	308.240	0.105017
$206$	−3121.53	−1.05576
$207$	−193.351	−0.0649220
$208$	1015.13	0.338397
$209$	−5448.52	−1.80326
$210$	463.509	0.152310
$211$	4731.67	1.54380	0.771899	−	0.635746i	$-0.219307\pi$
$211$	4731.67	1.54380	0.771899	+	0.635746i	$0.219307\pi$
$212$	−9549.78	−3.09378
$213$	1591.64	0.512007
$214$	−590.329	−0.188570
$215$	238.921	0.0757875
$216$	3528.53	1.11151
$217$	−2179.65	−0.681863
$218$	482.532	0.149914
$219$	897.725	0.276998
$220$	−689.129	−0.211187
$221$	−8184.83	−2.49127
$222$	10729.7	3.24383
$223$	−5547.11	−1.66575	−0.832874	−	0.553462i	$-0.813306\pi$
$223$	−5547.11	−1.66575	−0.832874	+	0.553462i	$0.813306\pi$
$224$	2374.27	0.708203
$225$	−452.096	−0.133954
$226$	−4160.49	−1.22457
$227$	−1277.48	−0.373522	−0.186761	−	0.982405i	$-0.559799\pi$
$227$	−1277.48	−0.373522	−0.186761	+	0.982405i	$0.559799\pi$
$228$	−8837.15	−2.56691
$229$	3127.79	0.902577	0.451288	−	0.892378i	$-0.350965\pi$
$229$	3127.79	0.902577	0.451288	+	0.892378i	$0.350965\pi$
$230$	−260.977	−0.0748186
$231$	4445.64	1.26624
$232$	−8001.86	−2.26443
$233$	2894.98	0.813976	0.406988	−	0.913434i	$-0.366579\pi$
$233$	2894.98	0.813976	0.406988	+	0.913434i	$0.366579\pi$
$234$	−1028.29	−0.287272
$235$	306.171	0.0849888
$236$	4901.91	1.35206
$237$	−6044.24	−1.65661
$238$	10783.3	2.93687
$239$	2651.40	0.717592	0.358796	−	0.933416i	$-0.383187\pi$
$239$	2651.40	0.717592	0.358796	+	0.933416i	$0.383187\pi$
$240$	−98.2344	−0.0264208
$241$	6070.20	1.62247	0.811236	−	0.584719i	$-0.198795\pi$
$241$	6070.20	1.62247	0.811236	+	0.584719i	$0.198795\pi$
$242$	−4209.81	−1.11825
$243$	−1017.22	−0.268537
$244$	968.343	0.254065
$245$	56.9869	0.0148602
$246$	7566.76	1.96113
$247$	−6954.05	−1.79140
$248$	3500.04	0.896181
$249$	5421.52	1.37982
$250$	−1225.91	−0.310133
$251$	−5475.86	−1.37702	−0.688512	−	0.725225i	$-0.741736\pi$
$251$	−5475.86	−1.37702	−0.688512	+	0.725225i	$0.741736\pi$
$252$	858.512	0.214608
$253$	−2503.10	−0.622010
$254$	−7535.57	−1.86151
$255$	792.048	0.194510
$256$	−5676.68	−1.38591
$257$	−1725.31	−0.418762	−0.209381	−	0.977834i	$-0.567145\pi$
$257$	−1725.31	−0.418762	−0.209381	+	0.977834i	$0.567145\pi$
$258$	5865.11	1.41529
$259$	−7049.25	−1.69119
$260$	−879.550	−0.209798
$261$	1069.81	0.253714
$262$	−1614.45	−0.380691
$263$	−5185.16	−1.21571	−0.607853	−	0.794050i	$-0.707969\pi$
$263$	−5185.16	−1.21571	−0.607853	+	0.794050i	$0.707969\pi$
$264$	−7138.72	−1.66424
$265$	727.212	0.168575
$266$	9161.74	2.11181
$267$	8380.61	1.92092
$268$	4373.60	0.996865
$269$	−2406.13	−0.545369	−0.272685	−	0.962103i	$-0.587912\pi$
$269$	−2406.13	−0.545369	−0.272685	+	0.962103i	$0.587912\pi$
$270$	−636.741	−0.143522
$271$	−6776.17	−1.51890	−0.759452	−	0.650563i	$-0.774533\pi$
$271$	−6776.17	−1.51890	−0.759452	+	0.650563i	$0.774533\pi$
$272$	−2285.36	−0.509451
$273$	5674.06	1.25791
$274$	−6358.79	−1.40200
$275$	−5852.77	−1.28340
$276$	−4059.87	−0.885417
$277$	68.3949	0.0148356	0.00741779	−	0.999972i	$-0.497639\pi$
$277$	68.3949	0.0148356	0.00741779	+	0.999972i	$0.497639\pi$
$278$	−4464.50	−0.963176
$279$	−467.938	−0.100411
$280$	488.990	0.104367
$281$	−2360.17	−0.501053	−0.250526	−	0.968110i	$-0.580604\pi$
$281$	−2360.17	−0.501053	−0.250526	+	0.968110i	$0.580604\pi$
$282$	7515.96	1.58712
$283$	2321.34	0.487595	0.243797	−	0.969826i	$-0.421607\pi$
$283$	2321.34	0.487595	0.243797	+	0.969826i	$0.421607\pi$
$284$	3979.13	0.831402
$285$	672.946	0.139866
$286$	−13312.1	−2.75232
$287$	−4971.25	−1.02245
$288$	509.719	0.104290
$289$	13513.5	2.75057
$290$	1443.98	0.292390
$291$	−9085.26	−1.83020
$292$	2244.33	0.449792
$293$	9379.21	1.87010	0.935050	−	0.354515i	$-0.115354\pi$
$293$	9379.21	1.87010	0.935050	+	0.354515i	$0.115354\pi$
$294$	1398.93	0.277508
$295$	−373.279	−0.0736716
$296$	11319.5	2.22275
$297$	−6107.16	−1.19318
$298$	−6795.41	−1.32096
$299$	−3194.76	−0.617918
$300$	−9492.82	−1.82689
$301$	−3853.29	−0.737873
$302$	2061.18	0.392740
$303$	−7590.41	−1.43913
$304$	−1941.71	−0.366331
$305$	−73.7390	−0.0138436
$306$	2315.00	0.432483
$307$	−8350.94	−1.55249	−0.776243	−	0.630434i	$-0.782877\pi$
$307$	−8350.94	−1.55249	−0.776243	+	0.630434i	$0.782877\pi$
$308$	11114.2	2.05613
$309$	3697.81	0.680781
$310$	−631.600	−0.115718
$311$	3770.99	0.687567	0.343783	−	0.939049i	$-0.388291\pi$
$311$	3770.99	0.687567	0.343783	+	0.939049i	$0.388291\pi$
$312$	−9111.30	−1.65329
$313$	1017.49	0.183745	0.0918724	−	0.995771i	$-0.470715\pi$
$313$	1017.49	0.183745	0.0918724	+	0.995771i	$0.470715\pi$
$314$	−2085.42	−0.374800
$315$	−65.3754	−0.0116936
$316$	−15110.7	−2.69001
$317$	−3575.86	−0.633565	−0.316783	−	0.948498i	$-0.602603\pi$
$317$	−3575.86	−0.633565	−0.316783	+	0.948498i	$0.602603\pi$
$318$	17851.8	3.14805
$319$	13849.6	2.43081
$320$	829.948	0.144986
$321$	699.314	0.121595
$322$	4208.99	0.728440
$323$	15655.7	2.69692
$324$	−11269.1	−1.93229
$325$	−7470.01	−1.27496
$326$	−5201.23	−0.883649
$327$	−571.616	−0.0966680
$328$	7982.74	1.34382
$329$	−4937.87	−0.827458
$330$	1288.22	0.214891
$331$	−1189.84	−0.197582	−0.0987912	−	0.995108i	$-0.531498\pi$
$331$	−1189.84	−0.197582	−0.0987912	+	0.995108i	$0.531498\pi$
$332$	13553.9	2.24056
$333$	−1513.36	−0.249045
$334$	−1414.79	−0.231778
$335$	−333.048	−0.0543175
$336$	1584.31	0.257235
$337$	−7759.37	−1.25424	−0.627122	−	0.778921i	$-0.715767\pi$
$337$	−7759.37	−1.25424	−0.627122	+	0.778921i	$0.715767\pi$
$338$	−6723.12	−1.08192
$339$	4928.59	0.789630
$340$	1980.13	0.315846
$341$	−6057.85	−0.962027
$342$	1966.89	0.310985
$343$	−6749.37	−1.06248
$344$	6187.54	0.969795
$345$	309.157	0.0482448
$346$	5087.50	0.790479
$347$	−4574.35	−0.707677	−0.353839	−	0.935306i	$-0.615124\pi$
$347$	−4574.35	−0.707677	−0.353839	+	0.935306i	$0.615124\pi$
$348$	22463.1	3.46020
$349$	2487.87	0.381584	0.190792	−	0.981630i	$-0.438894\pi$
$349$	2487.87	0.381584	0.190792	+	0.981630i	$0.438894\pi$
$350$	9841.50	1.50300
$351$	−7794.70	−1.18533
$352$	6598.75	0.999189
$353$	6993.13	1.05441	0.527205	−	0.849738i	$-0.323240\pi$
$353$	6993.13	1.05441	0.527205	+	0.849738i	$0.323240\pi$
$354$	−9163.34	−1.37578
$355$	−303.010	−0.0453016
$356$	20951.7	3.11920
$357$	−12774.0	−1.89376
$358$	16098.0	2.37655
$359$	−3752.07	−0.551607	−0.275804	−	0.961214i	$-0.588944\pi$
$359$	−3752.07	−0.551607	−0.275804	+	0.961214i	$0.588944\pi$
$360$	104.979	0.0153690
$361$	6442.49	0.939276
$362$	396.280	0.0575360
$363$	4987.01	0.721075
$364$	14185.2	2.04261
$365$	−170.905	−0.0245084
$366$	−1810.16	−0.258521
$367$	−1105.05	−0.157174	−0.0785871	−	0.996907i	$-0.525041\pi$
$367$	−1105.05	−0.157174	−0.0785871	+	0.996907i	$0.525041\pi$
$368$	−892.038	−0.126361
$369$	−1067.25	−0.150566
$370$	−2042.67	−0.287009
$371$	−11728.4	−1.64126
$372$	−9825.45	−1.36942
$373$	−5321.73	−0.738736	−0.369368	−	0.929283i	$-0.620426\pi$
$373$	−5321.73	−0.738736	−0.369368	+	0.929283i	$0.620426\pi$
$374$	29969.6	4.14356
$375$	1452.23	0.199981
$376$	7929.14	1.08754
$377$	17676.5	2.41482
$378$	10269.3	1.39734
$379$	5710.02	0.773889	0.386944	−	0.922103i	$-0.373531\pi$
$379$	5710.02	0.773889	0.386944	+	0.922103i	$0.373531\pi$
$380$	1682.37	0.227116
$381$	8926.77	1.20035
$382$	17673.6	2.36717
$383$	2164.09	0.288721	0.144360	−	0.989525i	$-0.453888\pi$
$383$	2164.09	0.288721	0.144360	+	0.989525i	$0.453888\pi$
$384$	14187.4	1.88542
$385$	−846.340	−0.112035
$386$	10583.9	1.39562
$387$	−827.242	−0.108659
$388$	−22713.3	−2.97189
$389$	−7910.39	−1.03104	−0.515518	−	0.856879i	$-0.672400\pi$
$389$	−7910.39	−1.03104	−0.515518	+	0.856879i	$0.672400\pi$
$390$	1644.18	0.213478
$391$	7192.36	0.930264
$392$	1475.83	0.190155
$393$	1912.51	0.245479
$394$	−17815.1	−2.27795
$395$	1150.67	0.146574
$396$	2386.04	0.302786
$397$	−2555.70	−0.323091	−0.161545	−	0.986865i	$-0.551648\pi$
$397$	−2555.70	−0.323091	−0.161545	+	0.986865i	$0.551648\pi$
$398$	16263.2	2.04824
$399$	−10853.2	−1.36175
$400$	−2085.77	−0.260722
$401$	−4185.98	−0.521291	−0.260645	−	0.965435i	$-0.583935\pi$
$401$	−4185.98	−0.521291	−0.260645	+	0.965435i	$0.583935\pi$
$402$	−8175.75	−1.01435
$403$	−7731.76	−0.955698
$404$	−18976.1	−2.33688
$405$	858.139	0.105287
$406$	−23288.2	−2.84674
$407$	−19591.8	−2.38607
$408$	20512.3	2.48899
$409$	4393.47	0.531156	0.265578	−	0.964089i	$-0.414437\pi$
$409$	4393.47	0.531156	0.265578	+	0.964089i	$0.414437\pi$
$410$	−1440.52	−0.173518
$411$	7532.73	0.904044
$412$	9244.59	1.10546
$413$	6020.18	0.717273
$414$	903.605	0.107270
$415$	−1032.12	−0.122084
$416$	8422.12	0.992616
$417$	5288.73	0.621079
$418$	25463.0	2.97951
$419$	−801.150	−0.0934098	−0.0467049	−	0.998909i	$-0.514872\pi$
$419$	−801.150	−0.0934098	−0.0467049	+	0.998909i	$0.514872\pi$
$420$	−1372.71	−0.159479
$421$	15257.4	1.76627	0.883137	−	0.469116i	$-0.155427\pi$
$421$	15257.4	1.76627	0.883137	+	0.469116i	$0.155427\pi$
$422$	−22112.9	−2.55080
$423$	−1060.08	−0.121851
$424$	18833.2	2.15712
$425$	16817.3	1.91943
$426$	−7438.36	−0.845985
$427$	1189.25	0.134782
$428$	1748.30	0.197446
$429$	15769.8	1.77476
$430$	−1116.57	−0.125223
$431$	9162.44	1.02399	0.511995	−	0.858989i	$-0.328907\pi$
$431$	9162.44	1.02399	0.511995	+	0.858989i	$0.328907\pi$
$432$	−2176.43	−0.242393
$433$	−8883.94	−0.985993	−0.492996	−	0.870031i	$-0.664098\pi$
$433$	−8883.94	−0.985993	−0.492996	+	0.870031i	$0.664098\pi$
$434$	10186.3	1.12664
$435$	−1710.56	−0.188540
$436$	−1429.05	−0.156970
$437$	6110.83	0.668926
$438$	−4195.41	−0.457682
$439$	2084.12	0.226582	0.113291	−	0.993562i	$-0.463861\pi$
$439$	2084.12	0.226582	0.113291	+	0.993562i	$0.463861\pi$
$440$	1359.04	0.147249
$441$	−197.311	−0.0213056
$442$	38250.9	4.11631
$443$	−2203.48	−0.236321	−0.118161	−	0.992994i	$-0.537700\pi$
$443$	−2203.48	−0.236321	−0.118161	+	0.992994i	$0.537700\pi$
$444$	−31776.6	−3.39652
$445$	−1595.46	−0.169960
$446$	25923.8	2.75230
$447$	8049.96	0.851790
$448$	−13385.3	−1.41159
$449$	11349.6	1.19292	0.596458	−	0.802644i	$-0.296574\pi$
$449$	11349.6	1.19292	0.596458	+	0.802644i	$0.296574\pi$
$450$	2112.82	0.221332
$451$	−13816.5	−1.44256
$452$	12321.6	1.28221
$453$	−2441.71	−0.253248
$454$	5970.17	0.617167
$455$	−1080.20	−0.111298
$456$	17427.8	1.78976
$457$	−3022.81	−0.309412	−0.154706	−	0.987961i	$-0.549443\pi$
$457$	−3022.81	−0.309412	−0.154706	+	0.987961i	$0.549443\pi$
$458$	−14617.4	−1.49132
$459$	17548.2	1.78449
$460$	772.898	0.0783404
$461$	−7384.02	−0.746005	−0.373002	−	0.927830i	$-0.621672\pi$
$461$	−7384.02	−0.746005	−0.373002	+	0.927830i	$0.621672\pi$
$462$	−20776.2	−2.09220
$463$	9672.25	0.970859	0.485430	−	0.874276i	$-0.338663\pi$
$463$	9672.25	0.970859	0.485430	+	0.874276i	$0.338663\pi$
$464$	4935.62	0.493816
$465$	748.204	0.0746175
$466$	−13529.3	−1.34492
$467$	15866.6	1.57220	0.786102	−	0.618096i	$-0.212096\pi$
$467$	15866.6	1.57220	0.786102	+	0.618096i	$0.212096\pi$
$468$	3045.35	0.300794
$469$	5371.34	0.528839
$470$	−1430.85	−0.140426
$471$	2470.43	0.241680
$472$	−9667.09	−0.942720
$473$	−10709.3	−1.04105
$474$	28247.0	2.73719
$475$	14288.4	1.38020
$476$	−31935.3	−3.07511
$477$	−2517.90	−0.241691
$478$	−12391.0	−1.18567
$479$	4135.72	0.394501	0.197251	−	0.980353i	$-0.436799\pi$
$479$	4135.72	0.394501	0.197251	+	0.980353i	$0.436799\pi$
$480$	−815.011	−0.0774999
$481$	−25005.4	−2.37037
$482$	−28368.4	−2.68079
$483$	−4986.04	−0.469716
$484$	12467.6	1.17089
$485$	1729.61	0.161933
$486$	4753.84	0.443701
$487$	15611.6	1.45263	0.726315	−	0.687362i	$-0.241231\pi$
$487$	15611.6	1.45263	0.726315	+	0.687362i	$0.241231\pi$
$488$	−1909.68	−0.177145
$489$	6161.47	0.569798
$490$	−266.322	−0.0245534
$491$	6669.21	0.612988	0.306494	−	0.951873i	$-0.400844\pi$
$491$	6669.21	0.612988	0.306494	+	0.951873i	$0.400844\pi$
$492$	−22409.4	−2.05345
$493$	−39795.1	−3.63546
$494$	32499.0	2.95991
$495$	−181.696	−0.0164983
$496$	−2158.86	−0.195435
$497$	4886.89	0.441060
$498$	−25336.8	−2.27986
$499$	−17948.8	−1.61022	−0.805110	−	0.593126i	$-0.797894\pi$
$499$	−17948.8	−1.61022	−0.805110	+	0.593126i	$0.797894\pi$
$500$	3630.60	0.324731
$501$	1675.98	0.149456
$502$	25590.8	2.27525
$503$	533.127	0.0472584	0.0236292	−	0.999721i	$-0.492478\pi$
$503$	533.127	0.0472584	0.0236292	+	0.999721i	$0.492478\pi$
$504$	−1693.08	−0.149634
$505$	1445.03	0.127332
$506$	11697.9	1.02774
$507$	7964.33	0.697649
$508$	22317.1	1.94913
$509$	5873.31	0.511454	0.255727	−	0.966749i	$-0.417685\pi$
$509$	5873.31	0.511454	0.255727	+	0.966749i	$0.417685\pi$
$510$	−3701.55	−0.321387
$511$	2756.32	0.238616
$512$	6027.88	0.520307
$513$	14909.4	1.28317
$514$	8063.04	0.691917
$515$	−703.972	−0.0602344
$516$	−17369.9	−1.48191
$517$	−13723.7	−1.16744
$518$	32943.8	2.79434
$519$	−6026.74	−0.509720
$520$	1734.57	0.146280
$521$	16510.4	1.38835	0.694177	−	0.719804i	$-0.255768\pi$
$521$	16510.4	1.38835	0.694177	+	0.719804i	$0.255768\pi$
$522$	−4999.62	−0.419210
$523$	−14457.1	−1.20873	−0.604364	−	0.796709i	$-0.706573\pi$
$523$	−14457.1	−1.20873	−0.604364	+	0.796709i	$0.706573\pi$
$524$	4781.29	0.398610
$525$	−11658.4	−0.969171
$526$	24232.2	2.00870
$527$	17406.5	1.43879
$528$	4403.23	0.362928
$529$	−9359.63	−0.769264
$530$	−3398.54	−0.278534
$531$	1292.44	0.105625
$532$	−27133.1	−2.21122
$533$	−17634.2	−1.43307
$534$	−39165.8	−3.17391
$535$	−133.132	−0.0107585
$536$	−8625.20	−0.695059
$537$	−19069.9	−1.53245
$538$	11244.8	0.901109
$539$	−2554.36	−0.204127
$540$	1885.75	0.150277
$541$	−18937.1	−1.50493	−0.752466	−	0.658631i	$-0.771136\pi$
$541$	−18937.1	−1.50493	−0.752466	+	0.658631i	$0.771136\pi$
$542$	31667.6	2.50967
$543$	−469.441	−0.0371006
$544$	−18960.7	−1.49437
$545$	108.822	0.00855304
$546$	−26517.1	−2.07844
$547$	−16683.0	−1.30405	−0.652025	−	0.758197i	$-0.726080\pi$
$547$	−16683.0	−1.30405	−0.652025	+	0.758197i	$0.726080\pi$
$548$	18831.9	1.46799
$549$	255.314	0.0198480
$550$	27352.2	2.12055
$551$	−33811.0	−2.61415
$552$	8006.49	0.617353
$553$	−18557.9	−1.42705
$554$	−319.636	−0.0245127
$555$	2419.78	0.185070
$556$	13221.9	1.00851
$557$	−12101.1	−0.920542	−0.460271	−	0.887778i	$-0.652248\pi$
$557$	−12101.1	−0.920542	−0.460271	+	0.887778i	$0.652248\pi$
$558$	2186.85	0.165908
$559$	−13668.6	−1.03420
$560$	−301.613	−0.0227598
$561$	−35502.5	−2.67187
$562$	11030.0	0.827884
$563$	−4938.81	−0.369709	−0.184854	−	0.982766i	$-0.559181\pi$
$563$	−4938.81	−0.369709	−0.184854	+	0.982766i	$0.559181\pi$
$564$	−22259.0	−1.66183
$565$	−938.283	−0.0698652
$566$	−10848.5	−0.805648
$567$	−13839.9	−1.02508
$568$	−7847.27	−0.579691
$569$	21215.5	1.56309	0.781545	−	0.623849i	$-0.214432\pi$
$569$	21215.5	1.56309	0.781545	+	0.623849i	$0.214432\pi$
$570$	−3144.93	−0.231100
$571$	16351.9	1.19843	0.599216	−	0.800587i	$-0.295479\pi$
$571$	16351.9	1.19843	0.599216	+	0.800587i	$0.295479\pi$
$572$	39424.7	2.88187
$573$	−20936.4	−1.52641
$574$	23232.6	1.68939
$575$	6564.22	0.476082
$576$	−2873.61	−0.207871
$577$	11918.7	0.859933	0.429966	−	0.902845i	$-0.358525\pi$
$577$	11918.7	0.859933	0.429966	+	0.902845i	$0.358525\pi$
$578$	−63153.9	−4.54474
$579$	−12537.9	−0.899928
$580$	−4276.42	−0.306153
$581$	16645.9	1.18862
$582$	42458.9	3.02402
$583$	−32596.4	−2.31562
$584$	−4426.05	−0.313615
$585$	−231.903	−0.0163897
$586$	−43832.7	−3.08995
$587$	−4887.62	−0.343669	−0.171835	−	0.985126i	$-0.554969\pi$
$587$	−4887.62	−0.343669	−0.171835	+	0.985126i	$0.554969\pi$
$588$	−4143.02	−0.290570
$589$	14789.1	1.03459
$590$	1744.47	0.121727
$591$	21104.1	1.46888
$592$	−6982.00	−0.484727
$593$	3882.92	0.268891	0.134446	−	0.990921i	$-0.457075\pi$
$593$	3882.92	0.268891	0.134446	+	0.990921i	$0.457075\pi$
$594$	28541.1	1.97148
$595$	2431.86	0.167557
$596$	20125.0	1.38314
$597$	−19265.6	−1.32075
$598$	14930.3	1.02098
$599$	15385.3	1.04946	0.524730	−	0.851269i	$-0.324166\pi$
$599$	15385.3	1.04946	0.524730	+	0.851269i	$0.324166\pi$
$600$	18720.9	1.27379
$601$	−2879.25	−0.195419	−0.0977095	−	0.995215i	$-0.531152\pi$
$601$	−2879.25	−0.195419	−0.0977095	+	0.995215i	$0.531152\pi$
$602$	18007.9	1.21918
$603$	1153.14	0.0778768
$604$	−6104.30	−0.411226
$605$	−949.404	−0.0637996
$606$	35472.9	2.37787
$607$	16409.5	1.09727	0.548634	−	0.836063i	$-0.315148\pi$
$607$	16409.5	1.09727	0.548634	+	0.836063i	$0.315148\pi$
$608$	−16109.6	−1.07455
$609$	27587.6	1.83564
$610$	344.611	0.0228736
$611$	−17515.8	−1.15976
$612$	−6856.01	−0.452840
$613$	−11966.5	−0.788453	−0.394227	−	0.919013i	$-0.628988\pi$
$613$	−11966.5	−0.788453	−0.394227	+	0.919013i	$0.628988\pi$
$614$	39027.1	2.56516
$615$	1706.47	0.111889
$616$	−21918.3	−1.43363
$617$	12697.6	0.828502	0.414251	−	0.910163i	$-0.364044\pi$
$617$	12697.6	0.828502	0.414251	+	0.910163i	$0.364044\pi$
$618$	−17281.3	−1.12485
$619$	−1540.18	−0.100008	−0.0500041	−	0.998749i	$-0.515923\pi$
$619$	−1540.18	−0.100008	−0.0500041	+	0.998749i	$0.515923\pi$
$620$	1870.52	0.121165
$621$	6849.54	0.442613
$622$	−17623.3	−1.13606
$623$	25731.3	1.65474
$624$	5619.93	0.360541
$625$	15209.7	0.973419
$626$	−4755.14	−0.303600
$627$	−30163.9	−1.92126
$628$	6176.10	0.392442
$629$	56294.8	3.56855
$630$	305.524	0.0193212
$631$	20411.1	1.28772	0.643860	−	0.765143i	$-0.277332\pi$
$631$	20411.1	1.28772	0.643860	+	0.765143i	$0.277332\pi$
$632$	29799.9	1.87560
$633$	26195.3	1.64482
$634$	16711.4	1.04683
$635$	−1699.44	−0.106205
$636$	−52869.2	−3.29623
$637$	−3260.19	−0.202784
$638$	−64724.4	−4.01640
$639$	1049.14	0.0649505
$640$	−2700.94	−0.166819
$641$	7319.00	0.450987	0.225494	−	0.974245i	$-0.427600\pi$
$641$	7319.00	0.450987	0.225494	+	0.974245i	$0.427600\pi$
$642$	−3268.16	−0.200910
$643$	17540.0	1.07576	0.537878	−	0.843022i	$-0.319226\pi$
$643$	17540.0	1.07576	0.537878	+	0.843022i	$0.319226\pi$
$644$	−12465.2	−0.762728
$645$	1322.71	0.0807468
$646$	−73165.0	−4.45610
$647$	−4919.79	−0.298944	−0.149472	−	0.988766i	$-0.547757\pi$
$647$	−4919.79	−0.298944	−0.149472	+	0.988766i	$0.547757\pi$
$648$	22223.9	1.34728
$649$	16731.7	1.01198
$650$	34910.2	2.10660
$651$	−12066.9	−0.726482
$652$	15403.8	0.925243
$653$	−19226.3	−1.15220	−0.576098	−	0.817380i	$-0.695425\pi$
$653$	−19226.3	−1.15220	−0.576098	+	0.817380i	$0.695425\pi$
$654$	2671.38	0.159724
$655$	−364.094	−0.0217196
$656$	−4923.82	−0.293053
$657$	591.741	0.0351385
$658$	23076.6	1.36720
$659$	−24915.2	−1.47277	−0.736387	−	0.676561i	$-0.763470\pi$
$659$	−24915.2	−1.47277	−0.736387	+	0.676561i	$0.763470\pi$
$660$	−3815.14	−0.225006
$661$	−17293.1	−1.01758	−0.508791	−	0.860890i	$-0.669907\pi$
$661$	−17293.1	−1.01758	−0.508791	+	0.860890i	$0.669907\pi$
$662$	5560.60	0.326464
$663$	−45312.6	−2.65429
$664$	−26729.7	−1.56222
$665$	2066.17	0.120485
$666$	7072.53	0.411494
$667$	−15533.1	−0.901715
$668$	4189.99	0.242688
$669$	−30709.8	−1.77475
$670$	1556.46	0.0897482
$671$	3305.26	0.190161
$672$	13144.4	0.754546
$673$	−25470.7	−1.45888	−0.729439	−	0.684046i	$-0.760219\pi$
$673$	−25470.7	−1.45888	−0.729439	+	0.684046i	$0.760219\pi$
$674$	36262.5	2.07237
$675$	16015.7	0.913249
$676$	19910.9	1.13285
$677$	11807.8	0.670327	0.335164	−	0.942160i	$-0.391208\pi$
$677$	11807.8	0.670327	0.335164	+	0.942160i	$0.391208\pi$
$678$	−23033.2	−1.30470
$679$	−27894.9	−1.57659
$680$	−3905.03	−0.220222
$681$	−7072.36	−0.397964
$682$	28310.7	1.58955
$683$	−20280.4	−1.13618	−0.568088	−	0.822968i	$-0.692317\pi$
$683$	−20280.4	−1.13618	−0.568088	+	0.822968i	$0.692317\pi$
$684$	−5825.05	−0.325624
$685$	−1434.05	−0.0799884
$686$	31542.4	1.75553
$687$	17316.0	0.961638
$688$	−3816.53	−0.211488
$689$	−41603.4	−2.30038
$690$	−1444.81	−0.0797145
$691$	−16666.5	−0.917542	−0.458771	−	0.888554i	$-0.651710\pi$
$691$	−16666.5	−0.917542	−0.458771	+	0.888554i	$0.651710\pi$
$692$	−15066.9	−0.827687
$693$	2930.37	0.160628
$694$	21377.7	1.16929
$695$	−1006.84	−0.0549521
$696$	−44299.7	−2.41261
$697$	39700.0	2.15745
$698$	−11626.8	−0.630488
$699$	16027.1	0.867240
$700$	−29146.2	−1.57375
$701$	19893.6	1.07185	0.535927	−	0.844264i	$-0.319962\pi$
$701$	19893.6	1.07185	0.535927	+	0.844264i	$0.319962\pi$
$702$	36427.6	1.95851
$703$	47829.6	2.56604
$704$	−37201.3	−1.99159
$705$	1695.01	0.0905502
$706$	−32681.6	−1.74219
$707$	−23305.2	−1.23972
$708$	27137.8	1.44054
$709$	15747.6	0.834154	0.417077	−	0.908871i	$-0.363055\pi$
$709$	15747.6	0.834154	0.417077	+	0.908871i	$0.363055\pi$
$710$	1416.08	0.0748514
$711$	−3984.09	−0.210148
$712$	−41318.9	−2.17485
$713$	6794.23	0.356867
$714$	59697.9	3.12905
$715$	−3002.18	−0.157028
$716$	−47675.1	−2.48841
$717$	14678.6	0.764549
$718$	17534.9	0.911415
$719$	17381.3	0.901546	0.450773	−	0.892639i	$-0.351148\pi$
$719$	17381.3	0.901546	0.450773	+	0.892639i	$0.351148\pi$
$720$	−64.7517	−0.00335160
$721$	11353.6	0.586447
$722$	−30108.2	−1.55196
$723$	33605.6	1.72864
$724$	−1173.61	−0.0602443
$725$	−36319.6	−1.86052
$726$	−23306.2	−1.19143
$727$	7941.49	0.405135	0.202568	−	0.979268i	$-0.435071\pi$
$727$	7941.49	0.405135	0.202568	+	0.979268i	$0.435071\pi$
$728$	−27974.8	−1.42420
$729$	16352.2	0.830779
$730$	798.704	0.0404950
$731$	30772.1	1.55697
$732$	5360.91	0.270690
$733$	591.406	0.0298009	0.0149005	−	0.999889i	$-0.495257\pi$
$733$	591.406	0.0298009	0.0149005	+	0.999889i	$0.495257\pi$
$734$	5164.31	0.259698
$735$	315.489	0.0158326
$736$	−7400.88	−0.370652
$737$	14928.4	0.746128
$738$	4987.67	0.248779
$739$	−18701.5	−0.930913	−0.465457	−	0.885071i	$-0.654110\pi$
$739$	−18701.5	−0.930913	−0.465457	+	0.885071i	$0.654110\pi$
$740$	6049.49	0.300518
$741$	−38498.8	−1.90862
$742$	54811.2	2.71183
$743$	−12540.5	−0.619200	−0.309600	−	0.950867i	$-0.600195\pi$
$743$	−12540.5	−0.619200	−0.309600	+	0.950867i	$0.600195\pi$
$744$	19376.8	0.954824
$745$	−1532.51	−0.0753650
$746$	24870.5	1.22061
$747$	3573.62	0.175036
$748$	−88756.9	−4.33860
$749$	2147.13	0.104746
$750$	−6786.84	−0.330427
$751$	−29384.4	−1.42777	−0.713883	−	0.700265i	$-0.753065\pi$
$751$	−29384.4	−1.42777	−0.713883	+	0.700265i	$0.753065\pi$
$752$	−4890.76	−0.237165
$753$	−30315.3	−1.46713
$754$	−82609.0	−3.98998
$755$	464.841	0.0224070
$756$	−30413.1	−1.46311
$757$	−21447.8	−1.02977	−0.514884	−	0.857260i	$-0.672165\pi$
$757$	−21447.8	−1.02977	−0.514884	+	0.857260i	$0.672165\pi$
$758$	−26685.1	−1.27869
$759$	−13857.6	−0.662712
$760$	−3317.82	−0.158355
$761$	6307.25	0.300444	0.150222	−	0.988652i	$-0.452001\pi$
$761$	6307.25	0.300444	0.150222	+	0.988652i	$0.452001\pi$
$762$	−41718.2	−1.98332
$763$	−1755.06	−0.0832731
$764$	−52341.4	−2.47859
$765$	522.083	0.0246744
$766$	−10113.6	−0.477050
$767$	21355.1	1.00533
$768$	−31427.1	−1.47660
$769$	16223.8	0.760788	0.380394	−	0.924824i	$-0.375788\pi$
$769$	16223.8	0.760788	0.380394	+	0.924824i	$0.375788\pi$
$770$	3955.27	0.185114
$771$	−9551.61	−0.446165
$772$	−31345.0	−1.46131
$773$	−8105.20	−0.377133	−0.188566	−	0.982060i	$-0.560384\pi$
$773$	−8105.20	−0.377133	−0.188566	+	0.982060i	$0.560384\pi$
$774$	3866.02	0.179536
$775$	15886.3	0.736328
$776$	44793.0	2.07213
$777$	−39025.8	−1.80186
$778$	36968.3	1.70357
$779$	33730.2	1.55136
$780$	−4869.34	−0.223526
$781$	13582.0	0.622283
$782$	−33612.7	−1.53707
$783$	−37898.3	−1.72972
$784$	−910.308	−0.0414681
$785$	−470.308	−0.0213835
$786$	−8937.87	−0.405602
$787$	33311.9	1.50882	0.754409	−	0.656405i	$-0.227924\pi$
$787$	33311.9	1.50882	0.754409	+	0.656405i	$0.227924\pi$
$788$	52760.6	2.38517
$789$	−28705.9	−1.29526
$790$	−5377.54	−0.242183
$791$	15132.5	0.680214
$792$	−4705.53	−0.211116
$793$	4218.57	0.188910
$794$	11943.8	0.533840
$795$	4025.97	0.179606
$796$	−48164.4	−2.14465
$797$	1588.26	0.0705886	0.0352943	−	0.999377i	$-0.488763\pi$
$797$	1588.26	0.0705886	0.0352943	+	0.999377i	$0.488763\pi$
$798$	50721.0	2.25000
$799$	39433.5	1.74600
$800$	−17304.8	−0.764772
$801$	5524.13	0.243677
$802$	19562.7	0.861324
$803$	7660.59	0.336658
$804$	24213.0	1.06210
$805$	949.219	0.0415597
$806$	36133.5	1.57909
$807$	−13320.8	−0.581057
$808$	37423.0	1.62938
$809$	35451.3	1.54067	0.770335	−	0.637640i	$-0.220089\pi$
$809$	35451.3	1.54067	0.770335	+	0.637640i	$0.220089\pi$
$810$	−4010.41	−0.173965
$811$	−41495.3	−1.79667	−0.898333	−	0.439314i	$-0.855221\pi$
$811$	−41495.3	−1.79667	−0.898333	+	0.439314i	$0.855221\pi$
$812$	68969.5	2.98073
$813$	−37514.0	−1.61830
$814$	91560.0	3.94248
$815$	−1172.99	−0.0504149
$816$	−12652.2	−0.542787
$817$	26144.8	1.11957
$818$	−20532.4	−0.877625
$819$	3740.09	0.159572
$820$	4266.20	0.181686
$821$	29008.1	1.23312	0.616559	−	0.787308i	$-0.288526\pi$
$821$	29008.1	1.23312	0.616559	+	0.787308i	$0.288526\pi$
$822$	−35203.3	−1.49374
$823$	17260.0	0.731041	0.365520	−	0.930803i	$-0.380891\pi$
$823$	17260.0	0.731041	0.365520	+	0.930803i	$0.380891\pi$
$824$	−18231.3	−0.770775
$825$	−32401.9	−1.36738
$826$	−28134.6	−1.18514
$827$	−34353.2	−1.44447	−0.722236	−	0.691646i	$-0.756886\pi$
$827$	−34353.2	−1.44447	−0.722236	+	0.691646i	$0.756886\pi$
$828$	−2676.08	−0.112319
$829$	−2732.55	−0.114482	−0.0572408	−	0.998360i	$-0.518230\pi$
$829$	−2732.55	−0.114482	−0.0572408	+	0.998360i	$0.518230\pi$
$830$	4823.51	0.201719
$831$	378.646	0.0158064
$832$	−47480.8	−1.97849
$833$	7339.67	0.305288
$834$	−24716.3	−1.02620
$835$	−319.066	−0.0132236
$836$	−75410.3	−3.11976
$837$	16576.8	0.684563
$838$	3744.08	0.154340
$839$	−453.007	−0.0186407	−0.00932033	−	0.999957i	$-0.502967\pi$
$839$	−453.007	−0.0186407	−0.00932033	+	0.999957i	$0.502967\pi$
$840$	2707.13	0.111196
$841$	61555.2	2.52389
$842$	−71303.8	−2.91840
$843$	−13066.3	−0.533840
$844$	65488.7	2.67087
$845$	−1516.21	−0.0617269
$846$	4954.18	0.201334
$847$	15311.8	0.621158
$848$	−11616.5	−0.470415
$849$	12851.3	0.519501
$850$	−78593.5	−3.17145
$851$	21973.3	0.885119
$852$	22029.2	0.885806
$853$	−18164.7	−0.729131	−0.364566	−	0.931178i	$-0.618782\pi$
$853$	−18164.7	−0.729131	−0.364566	+	0.931178i	$0.618782\pi$
$854$	−5557.83	−0.222699
$855$	443.576	0.0177427
$856$	−3447.83	−0.137669
$857$	12879.4	0.513365	0.256682	−	0.966496i	$-0.417371\pi$
$857$	12879.4	0.513365	0.256682	+	0.966496i	$0.417371\pi$
$858$	−73698.2	−2.93242
$859$	−2123.86	−0.0843597	−0.0421799	−	0.999110i	$-0.513430\pi$
$859$	−2123.86	−0.0843597	−0.0421799	+	0.999110i	$0.513430\pi$
$860$	3306.80	0.131117
$861$	−27521.7	−1.08936
$862$	−42819.6	−1.69193
$863$	−12344.0	−0.486902	−0.243451	−	0.969913i	$-0.578279\pi$
$863$	−12344.0	−0.486902	−0.243451	+	0.969913i	$0.578279\pi$
$864$	−18057.0	−0.711007
$865$	1147.34	0.0450992
$866$	41518.1	1.62915
$867$	74813.2	2.93055
$868$	−30167.5	−1.17967
$869$	−51577.5	−2.01340
$870$	7994.10	0.311523
$871$	19053.5	0.741220
$872$	2818.24	0.109447
$873$	−5988.60	−0.232169
$874$	−28558.2	−1.10526
$875$	4458.85	0.172270
$876$	12425.0	0.479225
$877$	1811.73	0.0697582	0.0348791	−	0.999392i	$-0.488895\pi$
$877$	1811.73	0.0697582	0.0348791	+	0.999392i	$0.488895\pi$
$878$	−9739.90	−0.374380
$879$	51924.9	1.99247
$880$	−838.266	−0.0321113
$881$	−7073.83	−0.270515	−0.135257	−	0.990811i	$-0.543186\pi$
$881$	−7073.83	−0.270515	−0.135257	+	0.990811i	$0.543186\pi$
$882$	922.112	0.0352031
$883$	45490.3	1.73372	0.866858	−	0.498554i	$-0.166136\pi$
$883$	45490.3	1.73372	0.866858	+	0.498554i	$0.166136\pi$
$884$	−113282.	−4.31006
$885$	−2066.54	−0.0784924
$886$	10297.7	0.390471
$887$	−30038.8	−1.13710	−0.568548	−	0.822650i	$-0.692494\pi$
$887$	−30038.8	−1.13710	−0.568548	+	0.822650i	$0.692494\pi$
$888$	62666.9	2.36820
$889$	27408.2	1.03402
$890$	7456.20	0.280823
$891$	−38465.0	−1.44627
$892$	−76774.9	−2.88185
$893$	33503.7	1.25550
$894$	−37620.5	−1.40740
$895$	3630.44	0.135589
$896$	43560.3	1.62416
$897$	−17686.7	−0.658353
$898$	−53040.9	−1.97104
$899$	−37592.3	−1.39463
$900$	−6257.25	−0.231750
$901$	93661.9	3.46319
$902$	64569.7	2.38352
$903$	−21332.5	−0.786157
$904$	−24299.4	−0.894013
$905$	89.3699	0.00328260
$906$	11411.0	0.418439
$907$	19222.4	0.703714	0.351857	−	0.936054i	$-0.385550\pi$
$907$	19222.4	0.703714	0.351857	+	0.936054i	$0.385550\pi$
$908$	−17681.0	−0.646217
$909$	−5003.26	−0.182561
$910$	5048.20	0.183897
$911$	−53177.7	−1.93398	−0.966989	−	0.254817i	$-0.917985\pi$
$911$	−53177.7	−1.93398	−0.966989	+	0.254817i	$0.917985\pi$
$912$	−10749.6	−0.390302
$913$	46263.6	1.67700
$914$	14126.8	0.511238
$915$	−408.232	−0.0147494
$916$	43290.2	1.56152
$917$	5872.05	0.211464
$918$	−82009.6	−2.94850
$919$	−20851.1	−0.748439	−0.374219	−	0.927340i	$-0.622089\pi$
$919$	−20851.1	−0.748439	−0.374219	+	0.927340i	$0.622089\pi$
$920$	−1524.24	−0.0546224
$921$	−46232.2	−1.65408
$922$	34508.4	1.23262
$923$	17335.0	0.618189
$924$	61529.9	2.19068
$925$	51378.3	1.82628
$926$	−45202.2	−1.60414
$927$	2437.43	0.0863601
$928$	40948.8	1.44850
$929$	−34927.2	−1.23350	−0.616752	−	0.787157i	$-0.711552\pi$
$929$	−34927.2	−1.23350	−0.616752	+	0.787157i	$0.711552\pi$
$930$	−3496.65	−0.123290
$931$	6235.98	0.219523
$932$	40068.0	1.40823
$933$	20876.9	0.732559
$934$	−74150.8	−2.59774
$935$	6758.81	0.236403
$936$	−6005.76	−0.209727
$937$	−27104.3	−0.944992	−0.472496	−	0.881333i	$-0.656647\pi$
$937$	−27104.3	−0.944992	−0.472496	+	0.881333i	$0.656647\pi$
$938$	−25102.3	−0.873796
$939$	5633.02	0.195768
$940$	4237.56	0.147036
$941$	−35275.1	−1.22204	−0.611018	−	0.791617i	$-0.709240\pi$
$941$	−35275.1	−1.22204	−0.611018	+	0.791617i	$0.709240\pi$
$942$	−11545.2	−0.399325
$943$	15496.0	0.535120
$944$	5962.75	0.205584
$945$	2315.94	0.0797224
$946$	50048.9	1.72012
$947$	−28257.2	−0.969627	−0.484813	−	0.874618i	$-0.661112\pi$
$947$	−28257.2	−0.969627	−0.484813	+	0.874618i	$0.661112\pi$
$948$	−83655.4	−2.86603
$949$	9777.36	0.334443
$950$	−66775.2	−2.28050
$951$	−19796.6	−0.675024
$952$	62979.8	2.14410
$953$	20958.0	0.712379	0.356189	−	0.934414i	$-0.384076\pi$
$953$	20958.0	0.712379	0.356189	+	0.934414i	$0.384076\pi$
$954$	11767.1	0.399344
$955$	3985.78	0.135054
$956$	36696.7	1.24148
$957$	76673.6	2.58987
$958$	−19327.8	−0.651831
$959$	23128.1	0.778774
$960$	4594.73	0.154473
$961$	−13348.0	−0.448055
$962$	116860.	3.91654
$963$	460.957	0.0154248
$964$	84014.7	2.80698
$965$	2386.91	0.0796243
$966$	23301.7	0.776107
$967$	−16980.5	−0.564689	−0.282345	−	0.959313i	$-0.591112\pi$
$967$	−16980.5	−0.564689	−0.282345	+	0.959313i	$0.591112\pi$
$968$	−24587.5	−0.816396
$969$	86672.5	2.87340
$970$	−8083.13	−0.267560
$971$	−44653.2	−1.47579	−0.737893	−	0.674918i	$-0.764179\pi$
$971$	−44653.2	−1.47579	−0.737893	+	0.674918i	$0.764179\pi$
$972$	−14078.8	−0.464586
$973$	16238.2	0.535018
$974$	−72959.2	−2.40017
$975$	−41355.3	−1.35839
$976$	1177.91	0.0386310
$977$	−31095.9	−1.01827	−0.509133	−	0.860688i	$-0.670034\pi$
$977$	−31095.9	−1.01827	−0.509133	+	0.860688i	$0.670034\pi$
$978$	−28794.9	−0.941472
$979$	71514.5	2.33464
$980$	788.728	0.0257092
$981$	−376.784	−0.0122628
$982$	−31167.8	−1.01283
$983$	983.000	0.0318950
$983$	983.000	0.0318950
$984$	44193.8	1.43176
$985$	−4017.70	−0.129964
$986$	185978.	6.00684
$987$	−27336.9	−0.881604
$988$	−96247.7	−3.09924
$989$	12011.2	0.386180
$990$	849.136	0.0272599
$991$	−28088.8	−0.900372	−0.450186	−	0.892935i	$-0.648642\pi$
$991$	−28088.8	−0.900372	−0.450186	+	0.892935i	$0.648642\pi$
$992$	−17911.2	−0.573266
$993$	−6587.19	−0.210512
$994$	−22838.3	−0.728760
$995$	3667.70	0.116858
$996$	75036.6	2.38718
$997$	36961.8	1.17411	0.587057	−	0.809546i	$-0.300287\pi$
$997$	36961.8	1.17411	0.587057	+	0.809546i	$0.300287\pi$
$998$	83881.7	2.66055
$999$	53611.4	1.69789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.a.1.13	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.a.1.13	✓	109	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-4.67338 q^{2} +5.53617 q^{3} +13.8405 q^{4} -1.05395 q^{5} -25.8727 q^{6} +16.9979 q^{7} -27.2950 q^{8} +3.64920 q^{9} +O(q^{10})\)	\(q-4.67338 q^{2} +5.53617 q^{3} +13.8405 q^{4} -1.05395 q^{5} -25.8727 q^{6} +16.9979 q^{7} -27.2950 q^{8} +3.64920 q^{9} +4.92552 q^{10} +47.2420 q^{11} +76.6235 q^{12} +60.2959 q^{13} -79.4379 q^{14} -5.83485 q^{15} +16.8358 q^{16} -135.744 q^{17} -17.0541 q^{18} -115.332 q^{19} -14.5872 q^{20} +94.1036 q^{21} -220.780 q^{22} -52.9846 q^{23} -151.110 q^{24} -123.889 q^{25} -281.786 q^{26} -129.274 q^{27} +235.260 q^{28} +293.162 q^{29} +27.2685 q^{30} -128.230 q^{31} +139.680 q^{32} +261.540 q^{33} +634.386 q^{34} -17.9150 q^{35} +50.5068 q^{36} -414.712 q^{37} +538.991 q^{38} +333.809 q^{39} +28.7676 q^{40} -292.462 q^{41} -439.782 q^{42} -226.691 q^{43} +653.854 q^{44} -3.84607 q^{45} +247.617 q^{46} -290.498 q^{47} +93.2058 q^{48} -54.0698 q^{49} +578.982 q^{50} -751.504 q^{51} +834.527 q^{52} -689.987 q^{53} +604.147 q^{54} -49.7907 q^{55} -463.959 q^{56} -638.498 q^{57} -1370.06 q^{58} +354.171 q^{59} -80.7574 q^{60} +69.9644 q^{61} +599.269 q^{62} +62.0289 q^{63} -787.463 q^{64} -63.5489 q^{65} -1222.28 q^{66} +315.999 q^{67} -1878.77 q^{68} -293.332 q^{69} +83.7237 q^{70} +287.499 q^{71} -99.6048 q^{72} +162.156 q^{73} +1938.11 q^{74} -685.872 q^{75} -1596.26 q^{76} +803.017 q^{77} -1560.02 q^{78} -1091.77 q^{79} -17.7441 q^{80} -814.212 q^{81} +1366.79 q^{82} +979.290 q^{83} +1302.44 q^{84} +143.068 q^{85} +1059.42 q^{86} +1623.00 q^{87} -1289.47 q^{88} +1513.79 q^{89} +17.9742 q^{90} +1024.91 q^{91} -733.334 q^{92} -709.905 q^{93} +1357.61 q^{94} +121.554 q^{95} +773.291 q^{96} -1641.07 q^{97} +252.689 q^{98} +172.395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9 - 243 * q^10 - 126 * q^11 - 280 * q^12 - 458 * q^13 - 177 * q^14 - 314 * q^15 + 1009 * q^16 - 594 * q^17 - 671 * q^18 - 491 * q^19 - 500 * q^20 - 660 * q^21 - 899 * q^22 - 487 * q^23 - 811 * q^24 + 705 * q^25 - 104 * q^26 - 842 * q^27 - 2648 * q^28 - 820 * q^29 - 728 * q^30 - 965 * q^31 - 1669 * q^32 - 2196 * q^33 - 508 * q^34 - 846 * q^35 + 1358 * q^36 - 3209 * q^37 - 1136 * q^38 - 1326 * q^39 - 3234 * q^40 - 1961 * q^41 - 2240 * q^42 - 2999 * q^43 - 1922 * q^44 - 2234 * q^45 - 2962 * q^46 - 1903 * q^47 - 2787 * q^48 + 1186 * q^49 - 2309 * q^50 - 2436 * q^51 - 4897 * q^52 - 1825 * q^53 - 3306 * q^54 - 2888 * q^55 - 1820 * q^56 - 6684 * q^57 - 4813 * q^58 - 1537 * q^59 - 3869 * q^60 - 2276 * q^61 - 1950 * q^62 - 6491 * q^63 - 89 * q^64 - 5546 * q^65 - 3527 * q^66 - 5005 * q^67 - 4183 * q^68 - 3018 * q^69 - 2993 * q^70 - 2014 * q^71 - 9549 * q^72 - 12904 * q^73 - 2714 * q^74 - 3379 * q^75 - 6293 * q^76 - 3258 * q^77 - 4593 * q^78 - 5005 * q^79 - 3988 * q^80 + 249 * q^81 - 5116 * q^82 - 2854 * q^83 - 4158 * q^84 - 11742 * q^85 - 2709 * q^86 - 2412 * q^87 - 10451 * q^88 - 2519 * q^89 - 8095 * q^90 - 2438 * q^91 - 6660 * q^92 - 10668 * q^93 - 4281 * q^94 - 4482 * q^95 - 6515 * q^96 - 16628 * q^97 - 5708 * q^98 - 6308 * q^99

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