LMFDB - Embedded newform 1997.4.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1997,4,Mod(1,1997)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1997, 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("1997.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1997 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1997.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:	$117.826814281$
Analytic rank:	$1$
Dimension:	$239$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1997.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.27417 q^{2} -3.32423 q^{3} +19.8169 q^{4} -16.6866 q^{5} +17.5325 q^{6} -23.2918 q^{7} -62.3242 q^{8} -15.9495 q^{9} +O(q^{10})$	\(q-5.27417 q^{2} -3.32423 q^{3} +19.8169 q^{4} -16.6866 q^{5} +17.5325 q^{6} -23.2918 q^{7} -62.3242 q^{8} -15.9495 q^{9} +88.0082 q^{10} -15.8034 q^{11} -65.8758 q^{12} -79.0896 q^{13} +122.845 q^{14} +55.4702 q^{15} +170.173 q^{16} -86.2172 q^{17} +84.1205 q^{18} -87.9498 q^{19} -330.677 q^{20} +77.4272 q^{21} +83.3497 q^{22} -28.2883 q^{23} +207.180 q^{24} +153.444 q^{25} +417.132 q^{26} +142.774 q^{27} -461.571 q^{28} -197.636 q^{29} -292.559 q^{30} -7.78381 q^{31} -398.930 q^{32} +52.5340 q^{33} +454.724 q^{34} +388.662 q^{35} -316.070 q^{36} -377.592 q^{37} +463.862 q^{38} +262.912 q^{39} +1039.98 q^{40} +370.825 q^{41} -408.364 q^{42} -133.233 q^{43} -313.173 q^{44} +266.144 q^{45} +149.197 q^{46} -326.071 q^{47} -565.695 q^{48} +199.508 q^{49} -809.290 q^{50} +286.605 q^{51} -1567.31 q^{52} +747.834 q^{53} -753.014 q^{54} +263.705 q^{55} +1451.64 q^{56} +292.365 q^{57} +1042.36 q^{58} +322.501 q^{59} +1099.25 q^{60} +830.937 q^{61} +41.0531 q^{62} +371.493 q^{63} +742.637 q^{64} +1319.74 q^{65} -277.073 q^{66} -573.161 q^{67} -1708.55 q^{68} +94.0366 q^{69} -2049.87 q^{70} -699.511 q^{71} +994.041 q^{72} -1058.29 q^{73} +1991.49 q^{74} -510.083 q^{75} -1742.89 q^{76} +368.089 q^{77} -1386.64 q^{78} -299.686 q^{79} -2839.62 q^{80} -43.9757 q^{81} -1955.80 q^{82} +384.319 q^{83} +1534.36 q^{84} +1438.68 q^{85} +702.691 q^{86} +656.985 q^{87} +984.932 q^{88} -1252.22 q^{89} -1403.69 q^{90} +1842.14 q^{91} -560.585 q^{92} +25.8751 q^{93} +1719.75 q^{94} +1467.59 q^{95} +1326.13 q^{96} -1528.35 q^{97} -1052.24 q^{98} +252.056 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) $ 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9} - 273 q^{10} - 294 q^{11} - 864 q^{12} - 797 q^{13} - 220 q^{14} - 580 q^{15} + 2816 q^{16} - 439 q^{17} - 536 q^{18} - 1704 q^{19} - 933 q^{20} - 596 q^{21} - 1046 q^{22} - 829 q^{23} - 1237 q^{24} + 4364 q^{25} - 818 q^{26} - 3670 q^{27} - 3690 q^{28} - 316 q^{29} - 888 q^{30} - 2595 q^{31} - 1881 q^{32} - 2066 q^{33} - 2605 q^{34} - 2450 q^{35} + 5863 q^{36} - 1912 q^{37} - 1709 q^{38} - 914 q^{39} - 3582 q^{40} - 1064 q^{41} - 3228 q^{42} - 5184 q^{43} - 2656 q^{44} - 3967 q^{45} - 2521 q^{46} - 4909 q^{47} - 7461 q^{48} + 7193 q^{49} - 1906 q^{50} - 3240 q^{51} - 9614 q^{52} - 2722 q^{53} - 3754 q^{54} - 6018 q^{55} - 2347 q^{56} - 2032 q^{57} - 6709 q^{58} - 6318 q^{59} - 5821 q^{60} - 2990 q^{61} - 2117 q^{62} - 8738 q^{63} + 6866 q^{64} - 1738 q^{65} - 3080 q^{66} - 14729 q^{67} - 3897 q^{68} - 2080 q^{69} - 7445 q^{70} - 3240 q^{71} - 8263 q^{72} - 8828 q^{73} - 3103 q^{74} - 12716 q^{75} - 14843 q^{76} - 3818 q^{77} - 8029 q^{78} - 4794 q^{79} - 10336 q^{80} + 11899 q^{81} - 13447 q^{82} - 11434 q^{83} - 7957 q^{84} - 8188 q^{85} - 5196 q^{86} - 11266 q^{87} - 11861 q^{88} - 4845 q^{89} - 7759 q^{90} - 12734 q^{91} - 8644 q^{92} - 10130 q^{93} - 6909 q^{94} - 3686 q^{95} - 11958 q^{96} - 16108 q^{97} - 6845 q^{98} - 12372 q^{99}+O(q^{100}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9 - 273 * q^10 - 294 * q^11 - 864 * q^12 - 797 * q^13 - 220 * q^14 - 580 * q^15 + 2816 * q^16 - 439 * q^17 - 536 * q^18 - 1704 * q^19 - 933 * q^20 - 596 * q^21 - 1046 * q^22 - 829 * q^23 - 1237 * q^24 + 4364 * q^25 - 818 * q^26 - 3670 * q^27 - 3690 * q^28 - 316 * q^29 - 888 * q^30 - 2595 * q^31 - 1881 * q^32 - 2066 * q^33 - 2605 * q^34 - 2450 * q^35 + 5863 * q^36 - 1912 * q^37 - 1709 * q^38 - 914 * q^39 - 3582 * q^40 - 1064 * q^41 - 3228 * q^42 - 5184 * q^43 - 2656 * q^44 - 3967 * q^45 - 2521 * q^46 - 4909 * q^47 - 7461 * q^48 + 7193 * q^49 - 1906 * q^50 - 3240 * q^51 - 9614 * q^52 - 2722 * q^53 - 3754 * q^54 - 6018 * q^55 - 2347 * q^56 - 2032 * q^57 - 6709 * q^58 - 6318 * q^59 - 5821 * q^60 - 2990 * q^61 - 2117 * q^62 - 8738 * q^63 + 6866 * q^64 - 1738 * q^65 - 3080 * q^66 - 14729 * q^67 - 3897 * q^68 - 2080 * q^69 - 7445 * q^70 - 3240 * q^71 - 8263 * q^72 - 8828 * q^73 - 3103 * q^74 - 12716 * q^75 - 14843 * q^76 - 3818 * q^77 - 8029 * q^78 - 4794 * q^79 - 10336 * q^80 + 11899 * q^81 - 13447 * q^82 - 11434 * q^83 - 7957 * q^84 - 8188 * q^85 - 5196 * q^86 - 11266 * q^87 - 11861 * q^88 - 4845 * q^89 - 7759 * q^90 - 12734 * q^91 - 8644 * q^92 - 10130 * q^93 - 6909 * q^94 - 3686 * q^95 - 11958 * q^96 - 16108 * q^97 - 6845 * q^98 - 12372 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.27417	−1.86470	−0.932350	−	0.361556i	$-0.882246\pi$
$2$	−5.27417	−1.86470	−0.932350	+	0.361556i	$0.882246\pi$
$3$	−3.32423	−0.639748	−0.319874	−	0.947460i	$-0.603641\pi$
$3$	−3.32423	−0.639748	−0.319874	+	0.947460i	$0.603641\pi$
$4$	19.8169	2.47711
$5$	−16.6866	−1.49250	−0.746249	−	0.665666i	$-0.768147\pi$
$5$	−16.6866	−1.49250	−0.746249	+	0.665666i	$0.768147\pi$
$6$	17.5325	1.19294
$7$	−23.2918	−1.25764	−0.628819	−	0.777551i	$-0.716462\pi$
$7$	−23.2918	−1.25764	−0.628819	+	0.777551i	$0.716462\pi$
$8$	−62.3242	−2.75437
$9$	−15.9495	−0.590723
$10$	88.0082	2.78306
$11$	−15.8034	−0.433172	−0.216586	−	0.976264i	$-0.569492\pi$
$11$	−15.8034	−0.433172	−0.216586	+	0.976264i	$0.569492\pi$
$12$	−65.8758	−1.58472
$13$	−79.0896	−1.68735	−0.843673	−	0.536857i	$-0.819611\pi$
$13$	−79.0896	−1.68735	−0.843673	+	0.536857i	$0.819611\pi$
$14$	122.845	2.34512
$15$	55.4702	0.954823
$16$	170.173	2.65896
$17$	−86.2172	−1.23004	−0.615022	−	0.788510i	$-0.710853\pi$
$17$	−86.2172	−1.23004	−0.615022	+	0.788510i	$0.710853\pi$
$18$	84.1205	1.10152
$19$	−87.9498	−1.06195	−0.530976	−	0.847387i	$-0.678174\pi$
$19$	−87.9498	−1.06195	−0.530976	+	0.847387i	$0.678174\pi$
$20$	−330.677	−3.69708
$21$	77.4272	0.804571
$22$	83.3497	0.807737
$23$	−28.2883	−0.256457	−0.128228	−	0.991745i	$-0.540929\pi$
$23$	−28.2883	−0.256457	−0.128228	+	0.991745i	$0.540929\pi$
$24$	207.180	1.76210
$25$	153.444	1.22755
$26$	417.132	3.14640
$27$	142.774	1.01766
$28$	−461.571	−3.11531
$29$	−197.636	−1.26552	−0.632759	−	0.774349i	$-0.718077\pi$
$29$	−197.636	−1.26552	−0.632759	+	0.774349i	$0.718077\pi$
$30$	−292.559	−1.78046
$31$	−7.78381	−0.0450972	−0.0225486	−	0.999746i	$-0.507178\pi$
$31$	−7.78381	−0.0450972	−0.0225486	+	0.999746i	$0.507178\pi$
$32$	−398.930	−2.20380
$33$	52.5340	0.277121
$34$	454.724	2.29366
$35$	388.662	1.87702
$36$	−316.070	−1.46329
$37$	−377.592	−1.67772	−0.838862	−	0.544344i	$-0.816779\pi$
$37$	−377.592	−1.67772	−0.838862	+	0.544344i	$0.816779\pi$
$38$	463.862	1.98022
$39$	262.912	1.07948
$40$	1039.98	4.11089
$41$	370.825	1.41252	0.706258	−	0.707954i	$-0.250382\pi$
$41$	370.825	1.41252	0.706258	+	0.707954i	$0.250382\pi$
$42$	−408.364	−1.50028
$43$	−133.233	−0.472507	−0.236253	−	0.971692i	$-0.575920\pi$
$43$	−133.233	−0.472507	−0.236253	+	0.971692i	$0.575920\pi$
$44$	−313.173	−1.07302
$45$	266.144	0.881653
$46$	149.197	0.478215
$47$	−326.071	−1.01196	−0.505982	−	0.862544i	$-0.668870\pi$
$47$	−326.071	−1.01196	−0.505982	+	0.862544i	$0.668870\pi$
$48$	−565.695	−1.70106
$49$	199.508	0.581656
$50$	−809.290	−2.28902
$51$	286.605	0.786917
$52$	−1567.31	−4.17974
$53$	747.834	1.93817	0.969084	−	0.246731i	$-0.0793563\pi$
$53$	747.834	1.93817	0.969084	+	0.246731i	$0.0793563\pi$
$54$	−753.014	−1.89763
$55$	263.705	0.646509
$56$	1451.64	3.46400
$57$	292.365	0.679381
$58$	1042.36	2.35981
$59$	322.501	0.711629	0.355814	−	0.934557i	$-0.384204\pi$
$59$	322.501	0.711629	0.355814	+	0.934557i	$0.384204\pi$
$60$	1099.25	2.36520
$61$	830.937	1.74411	0.872054	−	0.489410i	$-0.162788\pi$
$61$	830.937	1.74411	0.872054	+	0.489410i	$0.162788\pi$
$62$	41.0531	0.0840928
$63$	371.493	0.742916
$64$	742.637	1.45046
$65$	1319.74	2.51836
$66$	−277.073	−0.516748
$67$	−573.161	−1.04512	−0.522558	−	0.852604i	$-0.675022\pi$
$67$	−573.161	−1.04512	−0.522558	+	0.852604i	$0.675022\pi$
$68$	−1708.55	−3.04695
$69$	94.0366	0.164068
$70$	−2049.87	−3.50009
$71$	−699.511	−1.16925	−0.584625	−	0.811304i	$-0.698758\pi$
$71$	−699.511	−1.16925	−0.584625	+	0.811304i	$0.698758\pi$
$72$	994.041	1.62707
$73$	−1058.29	−1.69676	−0.848381	−	0.529386i	$-0.822423\pi$
$73$	−1058.29	−1.69676	−0.848381	+	0.529386i	$0.822423\pi$
$74$	1991.49	3.12845
$75$	−510.083	−0.785324
$76$	−1742.89	−2.63057
$77$	368.089	0.544774
$78$	−1386.64	−2.01290
$79$	−299.686	−0.426802	−0.213401	−	0.976965i	$-0.568454\pi$
$79$	−299.686	−0.426802	−0.213401	+	0.976965i	$0.568454\pi$
$80$	−2839.62	−3.96849
$81$	−43.9757	−0.0603234
$82$	−1955.80	−2.63392
$83$	384.319	0.508247	0.254123	−	0.967172i	$-0.418213\pi$
$83$	384.319	0.508247	0.254123	+	0.967172i	$0.418213\pi$
$84$	1534.36	1.99301
$85$	1438.68	1.83584
$86$	702.691	0.881083
$87$	656.985	0.809612
$88$	984.932	1.19312
$89$	−1252.22	−1.49141	−0.745703	−	0.666279i	$-0.767886\pi$
$89$	−1252.22	−1.49141	−0.745703	+	0.666279i	$0.767886\pi$
$90$	−1403.69	−1.64402
$91$	1842.14	2.12207
$92$	−560.585	−0.635272
$93$	25.8751	0.0288508
$94$	1719.75	1.88701
$95$	1467.59	1.58496
$96$	1326.13	1.40987
$97$	−1528.35	−1.59980	−0.799899	−	0.600135i	$-0.795113\pi$
$97$	−1528.35	−1.59980	−0.799899	+	0.600135i	$0.795113\pi$
$98$	−1052.24	−1.08461
$99$	252.056	0.255885
$100$	3040.78	3.04078
$101$	1715.88	1.69046	0.845229	−	0.534404i	$-0.179464\pi$
$101$	1715.88	1.69046	0.845229	+	0.534404i	$0.179464\pi$
$102$	−1511.61	−1.46737
$103$	1280.14	1.22462	0.612312	−	0.790616i	$-0.290240\pi$
$103$	1280.14	1.22462	0.612312	+	0.790616i	$0.290240\pi$
$104$	4929.19	4.64757
$105$	−1292.00	−1.20082
$106$	−3944.20	−3.61410
$107$	−428.744	−0.387367	−0.193684	−	0.981064i	$-0.562044\pi$
$107$	−428.744	−0.387367	−0.193684	+	0.981064i	$0.562044\pi$
$108$	2829.33	2.52086
$109$	−702.333	−0.617168	−0.308584	−	0.951197i	$-0.599855\pi$
$109$	−702.333	−0.617168	−0.308584	+	0.951197i	$0.599855\pi$
$110$	−1390.83	−1.20555
$111$	1255.20	1.07332
$112$	−3963.64	−3.34401
$113$	975.285	0.811921	0.405961	−	0.913891i	$-0.366937\pi$
$113$	975.285	0.811921	0.405961	+	0.913891i	$0.366937\pi$
$114$	−1541.98	−1.26684
$115$	472.036	0.382762
$116$	−3916.52	−3.13482
$117$	1261.44	0.996754
$118$	−1700.93	−1.32697
$119$	2008.15	1.54695
$120$	−3457.13	−2.62993
$121$	−1081.25	−0.812362
$122$	−4382.50	−3.25224
$123$	−1232.71	−0.903654
$124$	−154.251	−0.111711
$125$	−474.637	−0.339622
$126$	−1959.32	−1.38532
$127$	−784.872	−0.548395	−0.274198	−	0.961673i	$-0.588412\pi$
$127$	−784.872	−0.548395	−0.274198	+	0.961673i	$0.588412\pi$
$128$	−725.355	−0.500882
$129$	442.895	0.302285
$130$	−6960.53	−4.69599
$131$	−1321.12	−0.881123	−0.440562	−	0.897722i	$-0.645221\pi$
$131$	−1321.12	−0.881123	−0.440562	+	0.897722i	$0.645221\pi$
$132$	1041.06	0.686459
$133$	2048.51	1.33555
$134$	3022.95	1.94883
$135$	−2382.42	−1.51886
$136$	5373.42	3.38799
$137$	−890.215	−0.555155	−0.277577	−	0.960703i	$-0.589532\pi$
$137$	−890.215	−0.555155	−0.277577	+	0.960703i	$0.589532\pi$
$138$	−495.965	−0.305937
$139$	−872.061	−0.532138	−0.266069	−	0.963954i	$-0.585725\pi$
$139$	−872.061	−0.532138	−0.266069	+	0.963954i	$0.585725\pi$
$140$	7702.06	4.64959
$141$	1083.93	0.647402
$142$	3689.34	2.18030
$143$	1249.88	0.730912
$144$	−2714.18	−1.57071
$145$	3297.87	1.88878
$146$	5581.61	3.16395
$147$	−663.209	−0.372113
$148$	−7482.70	−4.15591
$149$	−1074.73	−0.590909	−0.295455	−	0.955357i	$-0.595471\pi$
$149$	−1074.73	−0.590909	−0.295455	+	0.955357i	$0.595471\pi$
$150$	2690.26	1.46439
$151$	350.091	0.188676	0.0943378	−	0.995540i	$-0.469927\pi$
$151$	350.091	0.188676	0.0943378	+	0.995540i	$0.469927\pi$
$152$	5481.40	2.92500
$153$	1375.12	0.726615
$154$	−1941.36	−1.01584
$155$	129.886	0.0673075
$156$	5210.09	2.67398
$157$	−2998.00	−1.52399	−0.761995	−	0.647582i	$-0.775780\pi$
$157$	−2998.00	−1.52399	−0.761995	+	0.647582i	$0.775780\pi$
$158$	1580.60	0.795857
$159$	−2485.97	−1.23994
$160$	6656.80	3.28916
$161$	658.884	0.322530
$162$	231.936	0.112485
$163$	3740.56	1.79744	0.898722	−	0.438519i	$-0.144497\pi$
$163$	3740.56	1.79744	0.898722	+	0.438519i	$0.144497\pi$
$164$	7348.60	3.49896
$165$	−876.616	−0.413603
$166$	−2026.96	−0.947728
$167$	2101.64	0.973830	0.486915	−	0.873449i	$-0.338122\pi$
$167$	2101.64	0.973830	0.486915	+	0.873449i	$0.338122\pi$
$168$	−4825.59	−2.21608
$169$	4058.16	1.84714
$170$	−7587.82	−3.42329
$171$	1402.76	0.627319
$172$	−2640.25	−1.17045
$173$	−1408.53	−0.619008	−0.309504	−	0.950898i	$-0.600163\pi$
$173$	−1408.53	−0.619008	−0.309504	+	0.950898i	$0.600163\pi$
$174$	−3465.05	−1.50968
$175$	−3573.99	−1.54382
$176$	−2689.31	−1.15179
$177$	−1072.07	−0.455263
$178$	6604.42	2.78103
$179$	3922.35	1.63782	0.818911	−	0.573921i	$-0.194578\pi$
$179$	3922.35	1.63782	0.818911	+	0.573921i	$0.194578\pi$
$180$	5274.14	2.18395
$181$	−1120.42	−0.460110	−0.230055	−	0.973178i	$-0.573891\pi$
$181$	−1120.42	−0.460110	−0.230055	+	0.973178i	$0.573891\pi$
$182$	−9715.75	−3.95703
$183$	−2762.22	−1.11579
$184$	1763.04	0.706376
$185$	6300.75	2.50400
$186$	−136.470	−0.0537982
$187$	1362.52	0.532821
$188$	−6461.70	−2.50675
$189$	−3325.46	−1.27985
$190$	−7740.31	−2.95548
$191$	4648.68	1.76108	0.880541	−	0.473971i	$-0.157180\pi$
$191$	4648.68	1.76108	0.880541	+	0.473971i	$0.157180\pi$
$192$	−2468.69	−0.927930
$193$	2492.75	0.929699	0.464850	−	0.885390i	$-0.346108\pi$
$193$	2492.75	0.929699	0.464850	+	0.885390i	$0.346108\pi$
$194$	8060.77	2.98314
$195$	−4387.11	−1.61112
$196$	3953.62	1.44082
$197$	−791.813	−0.286367	−0.143184	−	0.989696i	$-0.545734\pi$
$197$	−791.813	−0.286367	−0.143184	+	0.989696i	$0.545734\pi$
$198$	−1329.39	−0.477149
$199$	2520.01	0.897684	0.448842	−	0.893611i	$-0.351837\pi$
$199$	2520.01	0.897684	0.448842	+	0.893611i	$0.351837\pi$
$200$	−9563.28	−3.38113
$201$	1905.32	0.668611
$202$	−9049.83	−3.15220
$203$	4603.29	1.59156
$204$	5679.62	1.94928
$205$	−6187.83	−2.10818
$206$	−6751.70	−2.28356
$207$	451.184	0.151495
$208$	−13458.9	−4.48658
$209$	1389.90	0.460008
$210$	6814.23	2.23917
$211$	2397.00	0.782069	0.391034	−	0.920376i	$-0.372117\pi$
$211$	2397.00	0.782069	0.391034	+	0.920376i	$0.372117\pi$
$212$	14819.7	4.80105
$213$	2325.33	0.748024
$214$	2261.27	0.722324
$215$	2223.21	0.705215
$216$	−8898.27	−2.80301
$217$	181.299	0.0567160
$218$	3704.22	1.15083
$219$	3518.00	1.08550
$220$	5225.81	1.60147
$221$	6818.88	2.07551
$222$	−6620.15	−2.00142
$223$	−1559.07	−0.468176	−0.234088	−	0.972215i	$-0.575210\pi$
$223$	−1559.07	−0.468176	−0.234088	+	0.972215i	$0.575210\pi$
$224$	9291.79	2.77158
$225$	−2447.36	−0.725144
$226$	−5143.82	−1.51399
$227$	6083.35	1.77871	0.889353	−	0.457221i	$-0.151155\pi$
$227$	6083.35	1.77871	0.889353	+	0.457221i	$0.151155\pi$
$228$	5793.76	1.68290
$229$	−2211.36	−0.638125	−0.319063	−	0.947734i	$-0.603368\pi$
$229$	−2211.36	−0.638125	−0.319063	+	0.947734i	$0.603368\pi$
$230$	−2489.60	−0.713736
$231$	−1223.61	−0.348518
$232$	12317.5	3.48570
$233$	−3288.85	−0.924721	−0.462360	−	0.886692i	$-0.652997\pi$
$233$	−3288.85	−0.924721	−0.462360	+	0.886692i	$0.652997\pi$
$234$	−6653.05	−1.85865
$235$	5441.03	1.51036
$236$	6390.97	1.76278
$237$	996.225	0.273045
$238$	−10591.3	−2.88460
$239$	−126.525	−0.0342436	−0.0171218	−	0.999853i	$-0.505450\pi$
$239$	−126.525	−0.0342436	−0.0171218	+	0.999853i	$0.505450\pi$
$240$	9439.55	2.53883
$241$	7043.64	1.88266	0.941330	−	0.337489i	$-0.109577\pi$
$241$	7043.64	1.88266	0.941330	+	0.337489i	$0.109577\pi$
$242$	5702.71	1.51481
$243$	−3708.71	−0.979070
$244$	16466.6	4.32034
$245$	−3329.12	−0.868120
$246$	6501.51	1.68504
$247$	6955.92	1.79188
$248$	485.120	0.124214
$249$	−1277.56	−0.325150
$250$	2503.31	0.633294
$251$	−6610.02	−1.66223	−0.831117	−	0.556097i	$-0.812298\pi$
$251$	−6610.02	−1.66223	−0.831117	+	0.556097i	$0.812298\pi$
$252$	7361.83	1.84028
$253$	447.050	0.111090
$254$	4139.55	1.02259
$255$	−4782.48	−1.17447
$256$	−2115.45	−0.516468
$257$	−2632.04	−0.638842	−0.319421	−	0.947613i	$-0.603488\pi$
$257$	−2632.04	−0.638842	−0.319421	+	0.947613i	$0.603488\pi$
$258$	−2335.91	−0.563671
$259$	8794.81	2.10997
$260$	26153.1	6.23826
$261$	3152.19	0.747570
$262$	6967.83	1.64303
$263$	1252.72	0.293710	0.146855	−	0.989158i	$-0.453085\pi$
$263$	1252.72	0.293710	0.146855	+	0.989158i	$0.453085\pi$
$264$	−3274.14	−0.763293
$265$	−12478.8	−2.89271
$266$	−10804.2	−2.49040
$267$	4162.66	0.954123
$268$	−11358.3	−2.58887
$269$	−4485.80	−1.01674	−0.508372	−	0.861137i	$-0.669753\pi$
$269$	−4485.80	−1.01674	−0.508372	+	0.861137i	$0.669753\pi$
$270$	12565.3	2.83222
$271$	6752.59	1.51362	0.756810	−	0.653635i	$-0.226757\pi$
$271$	6752.59	1.51362	0.756810	+	0.653635i	$0.226757\pi$
$272$	−14671.9	−3.27063
$273$	−6123.68	−1.35759
$274$	4695.15	1.03520
$275$	−2424.93	−0.531742
$276$	1863.51	0.406414
$277$	−5084.54	−1.10289	−0.551445	−	0.834211i	$-0.685923\pi$
$277$	−5084.54	−1.10289	−0.551445	+	0.834211i	$0.685923\pi$
$278$	4599.40	0.992279
$279$	124.148	0.0266400
$280$	−24223.0	−5.17001
$281$	−5292.43	−1.12356	−0.561779	−	0.827287i	$-0.689883\pi$
$281$	−5292.43	−1.12356	−0.561779	+	0.827287i	$0.689883\pi$
$282$	−5716.85	−1.20721
$283$	−2624.36	−0.551244	−0.275622	−	0.961266i	$-0.588884\pi$
$283$	−2624.36	−0.551244	−0.275622	+	0.961266i	$0.588884\pi$
$284$	−13862.1	−2.89636
$285$	−4878.59	−1.01398
$286$	−6592.09	−1.36293
$287$	−8637.19	−1.77644
$288$	6362.74	1.30183
$289$	2520.40	0.513007
$290$	−17393.5	−3.52201
$291$	5080.58	1.02347
$292$	−20972.0	−4.20307
$293$	2747.87	0.547892	0.273946	−	0.961745i	$-0.411671\pi$
$293$	2747.87	0.547892	0.273946	+	0.961745i	$0.411671\pi$
$294$	3497.88	0.693879
$295$	−5381.46	−1.06210
$296$	23533.1	4.62107
$297$	−2256.31	−0.440823
$298$	5668.32	1.10187
$299$	2237.31	0.432732
$300$	−10108.2	−1.94533
$301$	3103.23	0.594243
$302$	−1846.44	−0.351823
$303$	−5703.97	−1.08147
$304$	−14966.7	−2.82369
$305$	−13865.5	−2.60308
$306$	−7252.63	−1.35492
$307$	−2685.46	−0.499243	−0.249621	−	0.968344i	$-0.580306\pi$
$307$	−2685.46	−0.499243	−0.249621	+	0.968344i	$0.580306\pi$
$308$	7294.37	1.34947
$309$	−4255.49	−0.783451
$310$	−685.039	−0.125508
$311$	−6412.85	−1.16926	−0.584629	−	0.811301i	$-0.698760\pi$
$311$	−6412.85	−1.16926	−0.584629	+	0.811301i	$0.698760\pi$
$312$	−16385.8	−2.97327
$313$	−4056.59	−0.732563	−0.366281	−	0.930504i	$-0.619369\pi$
$313$	−4056.59	−0.732563	−0.366281	+	0.930504i	$0.619369\pi$
$314$	15812.0	2.84179
$315$	−6198.97	−1.10880
$316$	−5938.84	−1.05723
$317$	−1879.78	−0.333056	−0.166528	−	0.986037i	$-0.553256\pi$
$317$	−1879.78	−0.333056	−0.166528	+	0.986037i	$0.553256\pi$
$318$	13111.4	2.31211
$319$	3123.31	0.548187
$320$	−12392.1	−2.16481
$321$	1425.24	0.247817
$322$	−3475.07	−0.601422
$323$	7582.79	1.30625
$324$	−871.462	−0.149428
$325$	−12135.8	−2.07131
$326$	−19728.3	−3.35169
$327$	2334.71	0.394831
$328$	−23111.4	−3.89059
$329$	7594.78	1.27269
$330$	4623.42	0.771245
$331$	1293.34	0.214769	0.107385	−	0.994218i	$-0.465752\pi$
$331$	1293.34	0.214769	0.107385	+	0.994218i	$0.465752\pi$
$332$	7616.00	1.25898
$333$	6022.42	0.991070
$334$	−11084.4	−1.81590
$335$	9564.14	1.55983
$336$	13176.0	2.13932
$337$	5066.45	0.818953	0.409476	−	0.912321i	$-0.365711\pi$
$337$	5066.45	0.818953	0.409476	+	0.912321i	$0.365711\pi$
$338$	−21403.4	−3.44436
$339$	−3242.07	−0.519425
$340$	28510.0	4.54757
$341$	123.010	0.0195349
$342$	−7398.38	−1.16976
$343$	3342.19	0.526126
$344$	8303.61	1.30146
$345$	−1569.15	−0.244871
$346$	7428.81	1.15426
$347$	8263.36	1.27839	0.639194	−	0.769046i	$-0.279268\pi$
$347$	8263.36	1.27839	0.639194	+	0.769046i	$0.279268\pi$
$348$	13019.4	2.00550
$349$	−4383.15	−0.672276	−0.336138	−	0.941813i	$-0.609121\pi$
$349$	−4383.15	−0.672276	−0.336138	+	0.941813i	$0.609121\pi$
$350$	18849.8	2.87876
$351$	−11291.9	−1.71715
$352$	6304.44	0.954624
$353$	−7227.74	−1.08978	−0.544892	−	0.838506i	$-0.683429\pi$
$353$	−7227.74	−1.08978	−0.544892	+	0.838506i	$0.683429\pi$
$354$	5654.26	0.848929
$355$	11672.5	1.74510
$356$	−24815.1	−3.69437
$357$	−6675.56	−0.989658
$358$	−20687.1	−3.05405
$359$	708.174	0.104111	0.0520557	−	0.998644i	$-0.483423\pi$
$359$	708.174	0.104111	0.0520557	+	0.998644i	$0.483423\pi$
$360$	−16587.2	−2.42840
$361$	876.175	0.127741
$362$	5909.27	0.857967
$363$	3594.33	0.519706
$364$	36505.4	5.25660
$365$	17659.3	2.53242
$366$	14568.4	2.08061
$367$	−11184.8	−1.59085	−0.795425	−	0.606052i	$-0.792752\pi$
$367$	−11184.8	−1.59085	−0.795425	+	0.606052i	$0.792752\pi$
$368$	−4813.91	−0.681908
$369$	−5914.49	−0.834406
$370$	−33231.2	−4.66921
$371$	−17418.4	−2.43752
$372$	512.764	0.0714666
$373$	3929.25	0.545440	0.272720	−	0.962093i	$-0.412077\pi$
$373$	3929.25	0.545440	0.272720	+	0.962093i	$0.412077\pi$
$374$	−7186.17	−0.993551
$375$	1577.80	0.217273
$376$	20322.1	2.78732
$377$	15630.9	2.13537
$378$	17539.0	2.38654
$379$	−13167.4	−1.78461	−0.892303	−	0.451438i	$-0.850911\pi$
$379$	−13167.4	−1.78461	−0.892303	+	0.451438i	$0.850911\pi$
$380$	29083.0	3.92612
$381$	2609.09	0.350834
$382$	−24517.9	−3.28389
$383$	−6762.21	−0.902175	−0.451087	−	0.892480i	$-0.648964\pi$
$383$	−6762.21	−0.902175	−0.451087	+	0.892480i	$0.648964\pi$
$384$	2411.24	0.320438
$385$	−6142.17	−0.813075
$386$	−13147.2	−1.73361
$387$	2125.00	0.279120
$388$	−30287.1	−3.96287
$389$	1123.08	0.146381	0.0731905	−	0.997318i	$-0.476682\pi$
$389$	1123.08	0.146381	0.0731905	+	0.997318i	$0.476682\pi$
$390$	23138.4	3.00425
$391$	2438.93	0.315453
$392$	−12434.2	−1.60209
$393$	4391.71	0.563696
$394$	4176.16	0.533989
$395$	5000.76	0.637001
$396$	4994.97	0.633855
$397$	−7002.64	−0.885271	−0.442635	−	0.896702i	$-0.645956\pi$
$397$	−7002.64	−0.885271	−0.442635	+	0.896702i	$0.645956\pi$
$398$	−13291.0	−1.67391
$399$	−6809.71	−0.854416
$400$	26112.1	3.26401
$401$	−3571.09	−0.444718	−0.222359	−	0.974965i	$-0.571376\pi$
$401$	−3571.09	−0.444718	−0.222359	+	0.974965i	$0.571376\pi$
$402$	−10049.0	−1.24676
$403$	615.618	0.0760946
$404$	34003.3	4.18745
$405$	733.808	0.0900326
$406$	−24278.5	−2.96779
$407$	5967.23	0.726744
$408$	−17862.4	−2.16746
$409$	−10372.1	−1.25395	−0.626976	−	0.779038i	$-0.715708\pi$
$409$	−10372.1	−1.25395	−0.626976	+	0.779038i	$0.715708\pi$
$410$	32635.7	3.93112
$411$	2959.28	0.355159
$412$	25368.4	3.03353
$413$	−7511.63	−0.894972
$414$	−2379.62	−0.282493
$415$	−6412.99	−0.758558
$416$	31551.2	3.71857
$417$	2898.93	0.340434
$418$	−7330.59	−0.857777
$419$	6652.23	0.775616	0.387808	−	0.921740i	$-0.373232\pi$
$419$	6652.23	0.775616	0.387808	+	0.921740i	$0.373232\pi$
$420$	−25603.4	−2.97457
$421$	−1516.08	−0.175509	−0.0877543	−	0.996142i	$-0.527969\pi$
$421$	−1516.08	−0.175509	−0.0877543	+	0.996142i	$0.527969\pi$
$422$	−12642.2	−1.45832
$423$	5200.67	0.597791
$424$	−46608.1	−5.33842
$425$	−13229.5	−1.50994
$426$	−12264.2	−1.39484
$427$	−19354.0	−2.19346
$428$	−8496.37	−0.959551
$429$	−4154.89	−0.467599
$430$	−11725.6	−1.31502
$431$	−5519.81	−0.616891	−0.308445	−	0.951242i	$-0.599809\pi$
$431$	−5519.81	−0.616891	−0.308445	+	0.951242i	$0.599809\pi$
$432$	24296.3	2.70592
$433$	14945.9	1.65878	0.829391	−	0.558668i	$-0.188687\pi$
$433$	14945.9	1.65878	0.829391	+	0.558668i	$0.188687\pi$
$434$	−956.201	−0.105758
$435$	−10962.9	−1.20834
$436$	−13918.0	−1.52879
$437$	2487.95	0.272345
$438$	−18554.5	−2.02413
$439$	1538.57	0.167271	0.0836354	−	0.996496i	$-0.473347\pi$
$439$	1538.57	0.167271	0.0836354	+	0.996496i	$0.473347\pi$
$440$	−16435.2	−1.78072
$441$	−3182.05	−0.343597
$442$	−35963.9	−3.87020
$443$	−246.695	−0.0264579	−0.0132290	−	0.999912i	$-0.504211\pi$
$443$	−246.695	−0.0264579	−0.0132290	+	0.999912i	$0.504211\pi$
$444$	24874.2	2.65873
$445$	20895.4	2.22592
$446$	8222.81	0.873008
$447$	3572.65	0.378033
$448$	−17297.3	−1.82416
$449$	−80.8889	−0.00850197	−0.00425099	−	0.999991i	$-0.501353\pi$
$449$	−80.8889	−0.00850197	−0.00425099	+	0.999991i	$0.501353\pi$
$450$	12907.8	1.35218
$451$	−5860.29	−0.611863
$452$	19327.1	2.01122
$453$	−1163.78	−0.120705
$454$	−32084.6	−3.31676
$455$	−30739.1	−3.16719
$456$	−18221.4	−1.87126
$457$	−7311.33	−0.748380	−0.374190	−	0.927352i	$-0.622079\pi$
$457$	−7311.33	−0.748380	−0.374190	+	0.927352i	$0.622079\pi$
$458$	11663.1	1.18991
$459$	−12309.6	−1.25177
$460$	9354.28	0.948142
$461$	3427.72	0.346301	0.173150	−	0.984895i	$-0.444605\pi$
$461$	3427.72	0.346301	0.173150	+	0.984895i	$0.444605\pi$
$462$	6453.53	0.649882
$463$	−5714.43	−0.573590	−0.286795	−	0.957992i	$-0.592590\pi$
$463$	−5714.43	−0.573590	−0.286795	+	0.957992i	$0.592590\pi$
$464$	−33632.3	−3.36496
$465$	−431.769	−0.0430598
$466$	17346.0	1.72433
$467$	−1068.49	−0.105875	−0.0529377	−	0.998598i	$-0.516858\pi$
$467$	−1068.49	−0.105875	−0.0529377	+	0.998598i	$0.516858\pi$
$468$	24997.8	2.46907
$469$	13350.0	1.31438
$470$	−28696.9	−2.81636
$471$	9966.04	0.974970
$472$	−20099.6	−1.96009
$473$	2105.52	0.204677
$474$	−5254.26	−0.509148
$475$	−13495.4	−1.30360
$476$	39795.3	3.83196
$477$	−11927.6	−1.14492
$478$	667.314	0.0638540
$479$	13115.6	1.25108	0.625541	−	0.780191i	$-0.284878\pi$
$479$	13115.6	1.25108	0.625541	+	0.780191i	$0.284878\pi$
$480$	−22128.7	−2.10424
$481$	29863.6	2.83090
$482$	−37149.4	−3.51060
$483$	−2190.28	−0.206338
$484$	−21427.1	−2.01231
$485$	25503.0	2.38770
$486$	19560.4	1.82567
$487$	−12244.6	−1.13934	−0.569669	−	0.821874i	$-0.692929\pi$
$487$	−12244.6	−1.13934	−0.569669	+	0.821874i	$0.692929\pi$
$488$	−51787.5	−4.80391
$489$	−12434.5	−1.14991
$490$	17558.3	1.61878
$491$	4223.43	0.388189	0.194095	−	0.980983i	$-0.437823\pi$
$491$	4223.43	0.388189	0.194095	+	0.980983i	$0.437823\pi$
$492$	−24428.4	−2.23845
$493$	17039.6	1.55664
$494$	−36686.7	−3.34132
$495$	−4205.97	−0.381908
$496$	−1324.60	−0.119912
$497$	16292.9	1.47049
$498$	6738.08	0.606307
$499$	7982.87	0.716157	0.358078	−	0.933692i	$-0.383432\pi$
$499$	7982.87	0.716157	0.358078	+	0.933692i	$0.383432\pi$
$500$	−9405.81	−0.841281
$501$	−6986.32	−0.623006
$502$	34862.4	3.09957
$503$	2025.12	0.179514	0.0897571	−	0.995964i	$-0.471391\pi$
$503$	2025.12	0.179514	0.0897571	+	0.995964i	$0.471391\pi$
$504$	−23153.0	−2.04626
$505$	−28632.2	−2.52301
$506$	−2357.82	−0.207150
$507$	−13490.2	−1.18170
$508$	−15553.7	−1.35843
$509$	−18714.8	−1.62970	−0.814850	−	0.579671i	$-0.803181\pi$
$509$	−18714.8	−1.62970	−0.814850	+	0.579671i	$0.803181\pi$
$510$	25223.6	2.19004
$511$	24649.5	2.13391
$512$	16960.1	1.46394
$513$	−12556.9	−1.08071
$514$	13881.8	1.19125
$515$	−21361.3	−1.82775
$516$	8776.80	0.748793
$517$	5153.02	0.438355
$518$	−46385.3	−3.93447
$519$	4682.26	0.396009
$520$	−82251.7	−6.93649
$521$	13165.4	1.10708	0.553539	−	0.832824i	$-0.313277\pi$
$521$	13165.4	1.10708	0.553539	+	0.832824i	$0.313277\pi$
$522$	−16625.2	−1.39399
$523$	−17080.9	−1.42810	−0.714048	−	0.700097i	$-0.753140\pi$
$523$	−17080.9	−1.42810	−0.714048	+	0.700097i	$0.753140\pi$
$524$	−26180.5	−2.18264
$525$	11880.7	0.987654
$526$	−6607.04	−0.547681
$527$	671.098	0.0554715
$528$	8939.89	0.736853
$529$	−11366.8	−0.934230
$530$	65815.5	5.39405
$531$	−5143.74	−0.420375
$532$	40595.1	3.30831
$533$	−29328.4	−2.38341
$534$	−21954.6	−1.77915
$535$	7154.31	0.578145
$536$	35721.8	2.87863
$537$	−13038.8	−1.04779
$538$	23658.9	1.89592
$539$	−3152.90	−0.251957
$540$	−47212.1	−3.76238
$541$	10755.5	0.854741	0.427370	−	0.904077i	$-0.359440\pi$
$541$	10755.5	0.854741	0.427370	+	0.904077i	$0.359440\pi$
$542$	−35614.3	−2.82245
$543$	3724.52	0.294354
$544$	34394.6	2.71077
$545$	11719.6	0.921122
$546$	32297.4	2.53150
$547$	−19048.0	−1.48891	−0.744453	−	0.667675i	$-0.767290\pi$
$547$	−19048.0	−1.48891	−0.744453	+	0.667675i	$0.767290\pi$
$548$	−17641.3	−1.37518
$549$	−13253.0	−1.03028
$550$	12789.5	0.991540
$551$	17382.0	1.34392
$552$	−5860.75	−0.451902
$553$	6980.23	0.536762
$554$	26816.8	2.05656
$555$	−20945.1	−1.60193
$556$	−17281.5	−1.31816
$557$	20378.7	1.55022	0.775110	−	0.631826i	$-0.217694\pi$
$557$	20378.7	1.55022	0.775110	+	0.631826i	$0.217694\pi$
$558$	−654.778	−0.0496755
$559$	10537.3	0.797282
$560$	66139.9	4.99093
$561$	−4529.33	−0.340871
$562$	27913.2	2.09510
$563$	−6339.79	−0.474583	−0.237292	−	0.971438i	$-0.576260\pi$
$563$	−6339.79	−0.474583	−0.237292	+	0.971438i	$0.576260\pi$
$564$	21480.2	1.60368
$565$	−16274.2	−1.21179
$566$	13841.3	1.02790
$567$	1024.27	0.0758650
$568$	43596.5	3.22054
$569$	8215.19	0.605270	0.302635	−	0.953107i	$-0.402134\pi$
$569$	8215.19	0.605270	0.302635	+	0.953107i	$0.402134\pi$
$570$	25730.5	1.89076
$571$	−3096.95	−0.226976	−0.113488	−	0.993539i	$-0.536202\pi$
$571$	−3096.95	−0.226976	−0.113488	+	0.993539i	$0.536202\pi$
$572$	24768.7	1.81055
$573$	−15453.3	−1.12665
$574$	45554.0	3.31252
$575$	−4340.67	−0.314814
$576$	−11844.7	−0.856822
$577$	13344.0	0.962769	0.481385	−	0.876509i	$-0.340134\pi$
$577$	13344.0	0.962769	0.481385	+	0.876509i	$0.340134\pi$
$578$	−13293.0	−0.956604
$579$	−8286.46	−0.594773
$580$	65353.5	4.67872
$581$	−8951.48	−0.639191
$582$	−26795.8	−1.90846
$583$	−11818.3	−0.839561
$584$	65957.2	4.67351
$585$	−21049.2	−1.48765
$586$	−14492.7	−1.02165
$587$	−17696.9	−1.24435	−0.622173	−	0.782880i	$-0.713750\pi$
$587$	−17696.9	−1.24435	−0.622173	+	0.782880i	$0.713750\pi$
$588$	−13142.7	−0.921764
$589$	684.585	0.0478910
$590$	28382.8	1.98051
$591$	2632.17	0.183203
$592$	−64256.2	−4.46100
$593$	22344.3	1.54734	0.773669	−	0.633590i	$-0.218419\pi$
$593$	22344.3	1.54734	0.773669	+	0.633590i	$0.218419\pi$
$594$	11900.2	0.822002
$595$	−33509.3	−2.30882
$596$	−21297.8	−1.46375
$597$	−8377.10	−0.574291
$598$	−11799.9	−0.806915
$599$	13410.6	0.914762	0.457381	−	0.889271i	$-0.348788\pi$
$599$	13410.6	0.914762	0.457381	+	0.889271i	$0.348788\pi$
$600$	31790.5	2.16307
$601$	−5207.19	−0.353420	−0.176710	−	0.984263i	$-0.556546\pi$
$601$	−5207.19	−0.353420	−0.176710	+	0.984263i	$0.556546\pi$
$602$	−16366.9	−1.10808
$603$	9141.65	0.617374
$604$	6937.71	0.467370
$605$	18042.5	1.21245
$606$	30083.7	2.01661
$607$	21840.6	1.46043	0.730217	−	0.683215i	$-0.239419\pi$
$607$	21840.6	1.46043	0.730217	+	0.683215i	$0.239419\pi$
$608$	35085.8	2.34033
$609$	−15302.4	−1.01820
$610$	73129.2	4.85396
$611$	25788.8	1.70753
$612$	27250.6	1.79990
$613$	6796.50	0.447811	0.223905	−	0.974611i	$-0.428119\pi$
$613$	6796.50	0.447811	0.223905	+	0.974611i	$0.428119\pi$
$614$	14163.6	0.930938
$615$	20569.8	1.34870
$616$	−22940.8	−1.50051
$617$	−18237.7	−1.18999	−0.594994	−	0.803730i	$-0.702846\pi$
$617$	−18237.7	−1.18999	−0.594994	+	0.803730i	$0.702846\pi$
$618$	22444.2	1.46090
$619$	305.296	0.0198237	0.00991185	−	0.999951i	$-0.496845\pi$
$619$	305.296	0.0198237	0.00991185	+	0.999951i	$0.496845\pi$
$620$	2573.93	0.166728
$621$	−4038.82	−0.260986
$622$	33822.5	2.18032
$623$	29166.5	1.87565
$624$	44740.6	2.87028
$625$	−11260.4	−0.720667
$626$	21395.2	1.36601
$627$	−4620.36	−0.294289
$628$	−59411.0	−3.77509
$629$	32555.0	2.06367
$630$	32694.4	2.06758
$631$	−20214.5	−1.27532	−0.637659	−	0.770319i	$-0.720097\pi$
$631$	−20214.5	−1.27532	−0.637659	+	0.770319i	$0.720097\pi$
$632$	18677.7	1.17557
$633$	−7968.18	−0.500327
$634$	9914.27	0.621050
$635$	13096.9	0.818479
$636$	−49264.1	−3.07146
$637$	−15779.0	−0.981454
$638$	−16472.9	−1.02220
$639$	11156.9	0.690702
$640$	12103.7	0.747566
$641$	28377.2	1.74857	0.874284	−	0.485415i	$-0.161331\pi$
$641$	28377.2	1.74857	0.874284	+	0.485415i	$0.161331\pi$
$642$	−7516.98	−0.462105
$643$	−1205.94	−0.0739622	−0.0369811	−	0.999316i	$-0.511774\pi$
$643$	−1205.94	−0.0739622	−0.0369811	+	0.999316i	$0.511774\pi$
$644$	13057.0	0.798942
$645$	−7390.44	−0.451160
$646$	−39992.9	−2.43576
$647$	14431.9	0.876936	0.438468	−	0.898747i	$-0.355521\pi$
$647$	14431.9	0.876936	0.438468	+	0.898747i	$0.355521\pi$
$648$	2740.75	0.166153
$649$	−5096.61	−0.308258
$650$	64006.4	3.86237
$651$	−602.679	−0.0362839
$652$	74126.2	4.45246
$653$	−12600.8	−0.755144	−0.377572	−	0.925980i	$-0.623241\pi$
$653$	−12600.8	−0.755144	−0.377572	+	0.925980i	$0.623241\pi$
$654$	−12313.7	−0.736243
$655$	22045.1	1.31508
$656$	63104.6	3.75582
$657$	16879.2	1.00232
$658$	−40056.1	−2.37318
$659$	−20687.5	−1.22287	−0.611433	−	0.791296i	$-0.709407\pi$
$659$	−20687.5	−1.22287	−0.611433	+	0.791296i	$0.709407\pi$
$660$	−17371.8	−1.02454
$661$	983.370	0.0578649	0.0289324	−	0.999581i	$-0.490789\pi$
$661$	983.370	0.0578649	0.0289324	+	0.999581i	$0.490789\pi$
$662$	−6821.32	−0.400480
$663$	−22667.5	−1.32780
$664$	−23952.4	−1.39990
$665$	−34182.8	−1.99331
$666$	−31763.3	−1.84805
$667$	5590.76	0.324551
$668$	41647.9	2.41228
$669$	5182.71	0.299514
$670$	−50442.9	−2.90863
$671$	−13131.6	−0.755499
$672$	−30888.0	−1.77311
$673$	−19296.9	−1.10526	−0.552632	−	0.833425i	$-0.686376\pi$
$673$	−19296.9	−1.10526	−0.552632	+	0.833425i	$0.686376\pi$
$674$	−26721.3	−1.52710
$675$	21907.8	1.24923
$676$	80420.0	4.57556
$677$	6799.96	0.386032	0.193016	−	0.981196i	$-0.438173\pi$
$677$	6799.96	0.386032	0.193016	+	0.981196i	$0.438173\pi$
$678$	17099.2	0.968571
$679$	35598.0	2.01197
$680$	−89664.3	−5.05657
$681$	−20222.4	−1.13792
$682$	−648.778	−0.0364267
$683$	−22932.8	−1.28477	−0.642387	−	0.766380i	$-0.722056\pi$
$683$	−22932.8	−1.28477	−0.642387	+	0.766380i	$0.722056\pi$
$684$	27798.3	1.55394
$685$	14854.7	0.828568
$686$	−17627.3	−0.981068
$687$	7351.05	0.408239
$688$	−22672.6	−1.25638
$689$	−59145.9	−3.27036
$690$	8275.99	0.456611
$691$	−31721.8	−1.74639	−0.873194	−	0.487373i	$-0.837955\pi$
$691$	−31721.8	−1.74639	−0.873194	+	0.487373i	$0.837955\pi$
$692$	−27912.6	−1.53335
$693$	−5870.84	−0.321811
$694$	−43582.4	−2.38381
$695$	14551.8	0.794216
$696$	−40946.1	−2.22997
$697$	−31971.5	−1.73746
$698$	23117.5	1.25359
$699$	10932.9	0.591588
$700$	−70825.3	−3.82421
$701$	−18667.0	−1.00577	−0.502883	−	0.864354i	$-0.667727\pi$
$701$	−18667.0	−1.00577	−0.502883	+	0.864354i	$0.667727\pi$
$702$	59555.6	3.20197
$703$	33209.2	1.78166
$704$	−11736.2	−0.628300
$705$	−18087.2	−0.966246
$706$	38120.3	2.03212
$707$	−39965.9	−2.12599
$708$	−21245.0	−1.12774
$709$	10799.5	0.572048	0.286024	−	0.958222i	$-0.407666\pi$
$709$	10799.5	0.572048	0.286024	+	0.958222i	$0.407666\pi$
$710$	−61562.7	−3.25410
$711$	4779.85	0.252122
$712$	78043.6	4.10788
$713$	220.190	0.0115655
$714$	35208.0	1.84542
$715$	−20856.3	−1.09088
$716$	77728.7	4.05706
$717$	420.597	0.0219073
$718$	−3735.03	−0.194136
$719$	29576.4	1.53409	0.767047	−	0.641591i	$-0.221726\pi$
$719$	29576.4	1.53409	0.767047	+	0.641591i	$0.221726\pi$
$720$	45290.6	2.34428
$721$	−29816.9	−1.54014
$722$	−4621.10	−0.238199
$723$	−23414.7	−1.20443
$724$	−22203.1	−1.13974
$725$	−30326.0	−1.55349
$726$	−18957.1	−0.969097
$727$	8787.47	0.448293	0.224147	−	0.974555i	$-0.428041\pi$
$727$	8787.47	0.448293	0.224147	+	0.974555i	$0.428041\pi$
$728$	−114810.	−5.84496
$729$	13515.9	0.686681
$730$	−93138.4	−4.72220
$731$	11486.9	0.581204
$732$	−54738.6	−2.76393
$733$	−6885.93	−0.346982	−0.173491	−	0.984835i	$-0.555505\pi$
$733$	−6885.93	−0.346982	−0.173491	+	0.984835i	$0.555505\pi$
$734$	58990.6	2.96646
$735$	11066.7	0.555378
$736$	11285.0	0.565179
$737$	9057.88	0.452716
$738$	31194.0	1.55592
$739$	37600.1	1.87164	0.935821	−	0.352475i	$-0.114660\pi$
$739$	37600.1	1.87164	0.935821	+	0.352475i	$0.114660\pi$
$740$	124861.	6.20268
$741$	−23123.0	−1.14635
$742$	91867.6	4.54524
$743$	12251.9	0.604950	0.302475	−	0.953157i	$-0.402187\pi$
$743$	12251.9	0.604950	0.302475	+	0.953157i	$0.402187\pi$
$744$	−1612.65	−0.0794657
$745$	17933.7	0.881931
$746$	−20723.5	−1.01708
$747$	−6129.70	−0.300233
$748$	27000.9	1.31986
$749$	9986.23	0.487168
$750$	−8321.58	−0.405148
$751$	−2206.91	−0.107232	−0.0536161	−	0.998562i	$-0.517075\pi$
$751$	−2206.91	−0.107232	−0.0536161	+	0.998562i	$0.517075\pi$
$752$	−55488.6	−2.69077
$753$	21973.2	1.06341
$754$	−82440.1	−3.98182
$755$	−5841.84	−0.281598
$756$	−65900.2	−3.17033
$757$	−6601.17	−0.316940	−0.158470	−	0.987364i	$-0.550656\pi$
$757$	−6601.17	−0.316940	−0.158470	+	0.987364i	$0.550656\pi$
$758$	69447.3	3.32776
$759$	−1486.09	−0.0710696
$760$	−91466.2	−4.36556
$761$	10382.6	0.494573	0.247286	−	0.968942i	$-0.420461\pi$
$761$	10382.6	0.494573	0.247286	+	0.968942i	$0.420461\pi$
$762$	−13760.8	−0.654201
$763$	16358.6	0.776174
$764$	92122.2	4.36239
$765$	−22946.2	−1.08447
$766$	35665.1	1.68229
$767$	−25506.5	−1.20076
$768$	7032.24	0.330409
$769$	−17970.0	−0.842671	−0.421336	−	0.906905i	$-0.638439\pi$
$769$	−17970.0	−0.842671	−0.421336	+	0.906905i	$0.638439\pi$
$770$	32394.8	1.51614
$771$	8749.51	0.408697
$772$	49398.5	2.30297
$773$	−16580.4	−0.771484	−0.385742	−	0.922607i	$-0.626055\pi$
$773$	−16580.4	−0.771484	−0.385742	+	0.922607i	$0.626055\pi$
$774$	−11207.6	−0.520476
$775$	−1194.38	−0.0553592
$776$	95253.1	4.40643
$777$	−29235.9	−1.34985
$778$	−5923.29	−0.272957
$779$	−32614.0	−1.50002
$780$	−86938.8	−3.99091
$781$	11054.6	0.506486
$782$	−12863.4	−0.588226
$783$	−28217.2	−1.28787
$784$	33950.9	1.54660
$785$	50026.6	2.27455
$786$	−23162.6	−1.05113
$787$	13507.6	0.611811	0.305906	−	0.952062i	$-0.401041\pi$
$787$	13507.6	0.611811	0.305906	+	0.952062i	$0.401041\pi$
$788$	−15691.3	−0.709363
$789$	−4164.31	−0.187900
$790$	−26374.8	−1.18782
$791$	−22716.1	−1.02110
$792$	−15709.2	−0.704801
$793$	−65718.4	−2.94291
$794$	36933.1	1.65077
$795$	41482.5	1.85061
$796$	49938.8	2.22366
$797$	3108.80	0.138167	0.0690837	−	0.997611i	$-0.477992\pi$
$797$	3108.80	0.138167	0.0690837	+	0.997611i	$0.477992\pi$
$798$	35915.6	1.59323
$799$	28112.9	1.24476
$800$	−61213.4	−2.70528
$801$	19972.3	0.881008
$802$	18834.6	0.829266
$803$	16724.6	0.734991
$804$	37757.4	1.65622
$805$	−10994.6	−0.481376
$806$	−3246.88	−0.141894
$807$	14911.8	0.650460
$808$	−106941.	−4.65614
$809$	−1379.34	−0.0599442	−0.0299721	−	0.999551i	$-0.509542\pi$
$809$	−1379.34	−0.0599442	−0.0299721	+	0.999551i	$0.509542\pi$
$810$	−3870.23	−0.167884
$811$	−32664.4	−1.41431	−0.707153	−	0.707061i	$-0.750021\pi$
$811$	−32664.4	−1.41431	−0.707153	+	0.707061i	$0.750021\pi$
$812$	91222.7	3.94248
$813$	−22447.1	−0.968334
$814$	−31472.2	−1.35516
$815$	−62417.4	−2.68268
$816$	48772.6	2.09238
$817$	11717.8	0.501779
$818$	54704.1	2.33825
$819$	−29381.2	−1.25356
$820$	−122623.	−5.22219
$821$	33669.8	1.43128	0.715642	−	0.698467i	$-0.246134\pi$
$821$	33669.8	1.43128	0.715642	+	0.698467i	$0.246134\pi$
$822$	−15607.7	−0.662265
$823$	−4803.76	−0.203461	−0.101730	−	0.994812i	$-0.532438\pi$
$823$	−4803.76	−0.203461	−0.101730	+	0.994812i	$0.532438\pi$
$824$	−79783.9	−3.37306
$825$	8061.03	0.340181
$826$	39617.6	1.66885
$827$	−38285.9	−1.60983	−0.804917	−	0.593388i	$-0.797790\pi$
$827$	−38285.9	−1.60983	−0.804917	+	0.593388i	$0.797790\pi$
$828$	8941.06	0.375270
$829$	−9248.63	−0.387477	−0.193738	−	0.981053i	$-0.562061\pi$
$829$	−9248.63	−0.387477	−0.193738	+	0.981053i	$0.562061\pi$
$830$	33823.2	1.41448
$831$	16902.2	0.705572
$832$	−58734.8	−2.44743
$833$	−17201.0	−0.715462
$834$	−15289.4	−0.634808
$835$	−35069.3	−1.45344
$836$	27543.5	1.13949
$837$	−1111.33	−0.0458937
$838$	−35085.0	−1.44629
$839$	−23533.9	−0.968393	−0.484197	−	0.874959i	$-0.660888\pi$
$839$	−23533.9	−0.968393	−0.484197	+	0.874959i	$0.660888\pi$
$840$	80522.9	3.30750
$841$	14670.8	0.601534
$842$	7996.05	0.327271
$843$	17593.2	0.718794
$844$	47501.1	1.93727
$845$	−67717.1	−2.75685
$846$	−27429.2	−1.11470
$847$	25184.3	1.02166
$848$	127261.	5.15351
$849$	8723.97	0.352657
$850$	69774.7	2.81559
$851$	10681.4	0.430264
$852$	46080.8	1.85294
$853$	22568.1	0.905883	0.452941	−	0.891540i	$-0.350375\pi$
$853$	22568.1	0.905883	0.452941	+	0.891540i	$0.350375\pi$
$854$	102076.	4.09014
$855$	−23407.3	−0.936273
$856$	26721.1	1.06695
$857$	12832.3	0.511485	0.255742	−	0.966745i	$-0.417680\pi$
$857$	12832.3	0.511485	0.255742	+	0.966745i	$0.417680\pi$
$858$	21913.6	0.871932
$859$	−10188.8	−0.404702	−0.202351	−	0.979313i	$-0.564858\pi$
$859$	−10188.8	−0.404702	−0.202351	+	0.979313i	$0.564858\pi$
$860$	44057.0	1.74690
$861$	28712.0	1.13647
$862$	29112.4	1.15032
$863$	48640.6	1.91859	0.959296	−	0.282403i	$-0.0911316\pi$
$863$	48640.6	1.91859	0.959296	+	0.282403i	$0.0911316\pi$
$864$	−56956.8	−2.24272
$865$	23503.6	0.923868
$866$	−78827.1	−3.09313
$867$	−8378.39	−0.328195
$868$	3592.78	0.140492
$869$	4736.05	0.184879
$870$	57820.1	2.25320
$871$	45331.1	1.76347
$872$	43772.3	1.69991
$873$	24376.4	0.945037
$874$	−13121.9	−0.507842
$875$	11055.1	0.427122
$876$	69715.8	2.68890
$877$	−21565.8	−0.830359	−0.415179	−	0.909740i	$-0.636281\pi$
$877$	−21565.8	−0.830359	−0.415179	+	0.909740i	$0.636281\pi$
$878$	−8114.67	−0.311910
$879$	−9134.54	−0.350512
$880$	44875.6	1.71904
$881$	22657.2	0.866448	0.433224	−	0.901286i	$-0.357376\pi$
$881$	22657.2	0.866448	0.433224	+	0.901286i	$0.357376\pi$
$882$	16782.7	0.640706
$883$	−49052.5	−1.86948	−0.934738	−	0.355338i	$-0.884366\pi$
$883$	−49052.5	−1.86948	−0.934738	+	0.355338i	$0.884366\pi$
$884$	135129.	5.14126
$885$	17889.2	0.679479
$886$	1301.11	0.0493361
$887$	3816.26	0.144462	0.0722308	−	0.997388i	$-0.476988\pi$
$887$	3816.26	0.144462	0.0722308	+	0.997388i	$0.476988\pi$
$888$	−78229.5	−2.95632
$889$	18281.1	0.689683
$890$	−110206.	−4.15068
$891$	694.965	0.0261304
$892$	−30895.9	−1.15972
$893$	28677.9	1.07466
$894$	−18842.8	−0.704918
$895$	−65450.8	−2.44445
$896$	16894.8	0.629929
$897$	−7437.31	−0.276839
$898$	426.622	0.0158536
$899$	1538.36	0.0570713
$900$	−48499.0	−1.79626
$901$	−64476.1	−2.38403
$902$	30908.2	1.14094
$903$	−10315.8	−0.380165
$904$	−60783.8	−2.23633
$905$	18696.0	0.686714
$906$	6137.98	0.225078
$907$	28312.4	1.03649	0.518246	−	0.855232i	$-0.326585\pi$
$907$	28312.4	1.03649	0.518246	+	0.855232i	$0.326585\pi$
$908$	120553.	4.40605
$909$	−27367.4	−0.998592
$910$	162123.	5.90586
$911$	−7979.74	−0.290209	−0.145105	−	0.989416i	$-0.546352\pi$
$911$	−7979.74	−0.290209	−0.145105	+	0.989416i	$0.546352\pi$
$912$	49752.8	1.80645
$913$	−6073.53	−0.220158
$914$	38561.2	1.39550
$915$	46092.2	1.66531
$916$	−43822.2	−1.58071
$917$	30771.3	1.10813
$918$	64922.7	2.33417
$919$	43894.5	1.57557	0.787784	−	0.615951i	$-0.211228\pi$
$919$	43894.5	1.57557	0.787784	+	0.615951i	$0.211228\pi$
$920$	−29419.3	−1.05427
$921$	8927.09	0.319389
$922$	−18078.4	−0.645747
$923$	55324.0	1.97293
$924$	−24248.1	−0.863317
$925$	−57939.3	−2.05950
$926$	30138.9	1.06957
$927$	−20417.7	−0.723414
$928$	78842.7	2.78894
$929$	4919.11	0.173725	0.0868626	−	0.996220i	$-0.472316\pi$
$929$	4919.11	0.173725	0.0868626	+	0.996220i	$0.472316\pi$
$930$	2277.22	0.0802937
$931$	−17546.7	−0.617690
$932$	−65174.8	−2.29063
$933$	21317.8	0.748030
$934$	5635.40	0.197426
$935$	−22735.9	−0.795234
$936$	−78618.3	−2.74543
$937$	8208.62	0.286194	0.143097	−	0.989709i	$-0.454294\pi$
$937$	8208.62	0.286194	0.143097	+	0.989709i	$0.454294\pi$
$938$	−70409.9	−2.45092
$939$	13485.0	0.468655
$940$	107824.	3.74131
$941$	12853.2	0.445275	0.222637	−	0.974901i	$-0.428533\pi$
$941$	12853.2	0.445275	0.222637	+	0.974901i	$0.428533\pi$
$942$	−52562.6	−1.81803
$943$	−10490.0	−0.362250
$944$	54881.1	1.89219
$945$	55490.8	1.91018
$946$	−11104.9	−0.381661
$947$	10919.6	0.374699	0.187349	−	0.982293i	$-0.440010\pi$
$947$	10919.6	0.374699	0.187349	+	0.982293i	$0.440010\pi$
$948$	19742.1	0.676363
$949$	83699.8	2.86303
$950$	71177.0	2.43083
$951$	6248.81	0.213072
$952$	−125157.	−4.26087
$953$	−12381.7	−0.420863	−0.210432	−	0.977609i	$-0.567487\pi$
$953$	−12381.7	−0.420863	−0.210432	+	0.977609i	$0.567487\pi$
$954$	62908.2	2.13493
$955$	−77570.8	−2.62841
$956$	−2507.33	−0.0848251
$957$	−10382.6	−0.350701
$958$	−69174.0	−2.33289
$959$	20734.7	0.698184
$960$	41194.2	1.38493
$961$	−29730.4	−0.997966
$962$	−157506.	−5.27879
$963$	6838.27	0.228827
$964$	139583.	4.66355
$965$	−41595.6	−1.38758
$966$	11551.9	0.384758
$967$	−3601.12	−0.119756	−0.0598781	−	0.998206i	$-0.519071\pi$
$967$	−3601.12	−0.119756	−0.0598781	+	0.998206i	$0.519071\pi$
$968$	67388.2	2.23754
$969$	−25206.9	−0.835668
$970$	−134507.	−4.45234
$971$	−36151.8	−1.19482	−0.597408	−	0.801937i	$-0.703803\pi$
$971$	−36151.8	−1.19482	−0.597408	+	0.801937i	$0.703803\pi$
$972$	−73495.0	−2.42526
$973$	20311.9	0.669238
$974$	64580.3	2.12453
$975$	40342.2	1.32511
$976$	141403.	4.63751
$977$	15862.8	0.519443	0.259722	−	0.965684i	$-0.416369\pi$
$977$	15862.8	0.519443	0.259722	+	0.965684i	$0.416369\pi$
$978$	65581.5	2.14424
$979$	19789.3	0.646036
$980$	−65972.7	−2.15043
$981$	11201.9	0.364575
$982$	−22275.1	−0.723857
$983$	−6176.81	−0.200417	−0.100208	−	0.994966i	$-0.531951\pi$
$983$	−6176.81	−0.200417	−0.100208	+	0.994966i	$0.531951\pi$
$984$	76827.5	2.48899
$985$	13212.7	0.427403
$986$	−89869.6	−2.90267
$987$	−25246.8	−0.814198
$988$	137844.	4.43868
$989$	3768.92	0.121178
$990$	22183.0	0.712144
$991$	19965.1	0.639971	0.319986	−	0.947422i	$-0.396322\pi$
$991$	19965.1	0.639971	0.319986	+	0.947422i	$0.396322\pi$
$992$	3105.19	0.0993851
$993$	−4299.37	−0.137398
$994$	−85931.4	−2.74203
$995$	−42050.6	−1.33979
$996$	−25317.3	−0.805431
$997$	−20869.5	−0.662934	−0.331467	−	0.943467i	$-0.607543\pi$
$997$	−20869.5	−0.662934	−0.331467	+	0.943467i	$0.607543\pi$
$998$	−42103.0	−1.33542
$999$	−53910.3	−1.70736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1997.4.a.a.1.10	✓	239

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1997.4.a.a.1.10	✓	239	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:	\( N \)	\(=\)	\( 1997 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1997.a (trivial)

\(f(q)\)	\(=\)	\(q-5.27417 q^{2} -3.32423 q^{3} +19.8169 q^{4} -16.6866 q^{5} +17.5325 q^{6} -23.2918 q^{7} -62.3242 q^{8} -15.9495 q^{9} +O(q^{10})\)	\(q-5.27417 q^{2} -3.32423 q^{3} +19.8169 q^{4} -16.6866 q^{5} +17.5325 q^{6} -23.2918 q^{7} -62.3242 q^{8} -15.9495 q^{9} +88.0082 q^{10} -15.8034 q^{11} -65.8758 q^{12} -79.0896 q^{13} +122.845 q^{14} +55.4702 q^{15} +170.173 q^{16} -86.2172 q^{17} +84.1205 q^{18} -87.9498 q^{19} -330.677 q^{20} +77.4272 q^{21} +83.3497 q^{22} -28.2883 q^{23} +207.180 q^{24} +153.444 q^{25} +417.132 q^{26} +142.774 q^{27} -461.571 q^{28} -197.636 q^{29} -292.559 q^{30} -7.78381 q^{31} -398.930 q^{32} +52.5340 q^{33} +454.724 q^{34} +388.662 q^{35} -316.070 q^{36} -377.592 q^{37} +463.862 q^{38} +262.912 q^{39} +1039.98 q^{40} +370.825 q^{41} -408.364 q^{42} -133.233 q^{43} -313.173 q^{44} +266.144 q^{45} +149.197 q^{46} -326.071 q^{47} -565.695 q^{48} +199.508 q^{49} -809.290 q^{50} +286.605 q^{51} -1567.31 q^{52} +747.834 q^{53} -753.014 q^{54} +263.705 q^{55} +1451.64 q^{56} +292.365 q^{57} +1042.36 q^{58} +322.501 q^{59} +1099.25 q^{60} +830.937 q^{61} +41.0531 q^{62} +371.493 q^{63} +742.637 q^{64} +1319.74 q^{65} -277.073 q^{66} -573.161 q^{67} -1708.55 q^{68} +94.0366 q^{69} -2049.87 q^{70} -699.511 q^{71} +994.041 q^{72} -1058.29 q^{73} +1991.49 q^{74} -510.083 q^{75} -1742.89 q^{76} +368.089 q^{77} -1386.64 q^{78} -299.686 q^{79} -2839.62 q^{80} -43.9757 q^{81} -1955.80 q^{82} +384.319 q^{83} +1534.36 q^{84} +1438.68 q^{85} +702.691 q^{86} +656.985 q^{87} +984.932 q^{88} -1252.22 q^{89} -1403.69 q^{90} +1842.14 q^{91} -560.585 q^{92} +25.8751 q^{93} +1719.75 q^{94} +1467.59 q^{95} +1326.13 q^{96} -1528.35 q^{97} -1052.24 q^{98} +252.056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9} - 273 q^{10} - 294 q^{11} - 864 q^{12} - 797 q^{13} - 220 q^{14} - 580 q^{15} + 2816 q^{16} - 439 q^{17} - 536 q^{18} - 1704 q^{19} - 933 q^{20} - 596 q^{21} - 1046 q^{22} - 829 q^{23} - 1237 q^{24} + 4364 q^{25} - 818 q^{26} - 3670 q^{27} - 3690 q^{28} - 316 q^{29} - 888 q^{30} - 2595 q^{31} - 1881 q^{32} - 2066 q^{33} - 2605 q^{34} - 2450 q^{35} + 5863 q^{36} - 1912 q^{37} - 1709 q^{38} - 914 q^{39} - 3582 q^{40} - 1064 q^{41} - 3228 q^{42} - 5184 q^{43} - 2656 q^{44} - 3967 q^{45} - 2521 q^{46} - 4909 q^{47} - 7461 q^{48} + 7193 q^{49} - 1906 q^{50} - 3240 q^{51} - 9614 q^{52} - 2722 q^{53} - 3754 q^{54} - 6018 q^{55} - 2347 q^{56} - 2032 q^{57} - 6709 q^{58} - 6318 q^{59} - 5821 q^{60} - 2990 q^{61} - 2117 q^{62} - 8738 q^{63} + 6866 q^{64} - 1738 q^{65} - 3080 q^{66} - 14729 q^{67} - 3897 q^{68} - 2080 q^{69} - 7445 q^{70} - 3240 q^{71} - 8263 q^{72} - 8828 q^{73} - 3103 q^{74} - 12716 q^{75} - 14843 q^{76} - 3818 q^{77} - 8029 q^{78} - 4794 q^{79} - 10336 q^{80} + 11899 q^{81} - 13447 q^{82} - 11434 q^{83} - 7957 q^{84} - 8188 q^{85} - 5196 q^{86} - 11266 q^{87} - 11861 q^{88} - 4845 q^{89} - 7759 q^{90} - 12734 q^{91} - 8644 q^{92} - 10130 q^{93} - 6909 q^{94} - 3686 q^{95} - 11958 q^{96} - 16108 q^{97} - 6845 q^{98} - 12372 q^{99}+O(q^{100}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9 - 273 * q^10 - 294 * q^11 - 864 * q^12 - 797 * q^13 - 220 * q^14 - 580 * q^15 + 2816 * q^16 - 439 * q^17 - 536 * q^18 - 1704 * q^19 - 933 * q^20 - 596 * q^21 - 1046 * q^22 - 829 * q^23 - 1237 * q^24 + 4364 * q^25 - 818 * q^26 - 3670 * q^27 - 3690 * q^28 - 316 * q^29 - 888 * q^30 - 2595 * q^31 - 1881 * q^32 - 2066 * q^33 - 2605 * q^34 - 2450 * q^35 + 5863 * q^36 - 1912 * q^37 - 1709 * q^38 - 914 * q^39 - 3582 * q^40 - 1064 * q^41 - 3228 * q^42 - 5184 * q^43 - 2656 * q^44 - 3967 * q^45 - 2521 * q^46 - 4909 * q^47 - 7461 * q^48 + 7193 * q^49 - 1906 * q^50 - 3240 * q^51 - 9614 * q^52 - 2722 * q^53 - 3754 * q^54 - 6018 * q^55 - 2347 * q^56 - 2032 * q^57 - 6709 * q^58 - 6318 * q^59 - 5821 * q^60 - 2990 * q^61 - 2117 * q^62 - 8738 * q^63 + 6866 * q^64 - 1738 * q^65 - 3080 * q^66 - 14729 * q^67 - 3897 * q^68 - 2080 * q^69 - 7445 * q^70 - 3240 * q^71 - 8263 * q^72 - 8828 * q^73 - 3103 * q^74 - 12716 * q^75 - 14843 * q^76 - 3818 * q^77 - 8029 * q^78 - 4794 * q^79 - 10336 * q^80 + 11899 * q^81 - 13447 * q^82 - 11434 * q^83 - 7957 * q^84 - 8188 * q^85 - 5196 * q^86 - 11266 * q^87 - 11861 * q^88 - 4845 * q^89 - 7759 * q^90 - 12734 * q^91 - 8644 * q^92 - 10130 * q^93 - 6909 * q^94 - 3686 * q^95 - 11958 * q^96 - 16108 * q^97 - 6845 * q^98 - 12372 * q^99

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