LMFDB - Embedded newform 1997.4.a.a.1.19

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			1.19
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)

$f(q)$	$=$	$q-4.85005 q^{2} -9.72090 q^{3} +15.5230 q^{4} -21.5228 q^{5} +47.1469 q^{6} -0.473007 q^{7} -36.4868 q^{8} +67.4960 q^{9} +O(q^{10})$	\(q-4.85005 q^{2} -9.72090 q^{3} +15.5230 q^{4} -21.5228 q^{5} +47.1469 q^{6} -0.473007 q^{7} -36.4868 q^{8} +67.4960 q^{9} +104.387 q^{10} +26.4818 q^{11} -150.897 q^{12} -60.6157 q^{13} +2.29411 q^{14} +209.222 q^{15} +52.7790 q^{16} +72.2326 q^{17} -327.359 q^{18} -31.2577 q^{19} -334.099 q^{20} +4.59806 q^{21} -128.438 q^{22} +17.8922 q^{23} +354.685 q^{24} +338.233 q^{25} +293.989 q^{26} -393.658 q^{27} -7.34248 q^{28} -180.215 q^{29} -1014.73 q^{30} -17.7085 q^{31} +35.9137 q^{32} -257.427 q^{33} -350.332 q^{34} +10.1805 q^{35} +1047.74 q^{36} +183.854 q^{37} +151.601 q^{38} +589.240 q^{39} +785.300 q^{40} -60.2701 q^{41} -22.3008 q^{42} -559.218 q^{43} +411.076 q^{44} -1452.71 q^{45} -86.7781 q^{46} -394.736 q^{47} -513.060 q^{48} -342.776 q^{49} -1640.45 q^{50} -702.167 q^{51} -940.937 q^{52} -431.679 q^{53} +1909.26 q^{54} -569.963 q^{55} +17.2585 q^{56} +303.853 q^{57} +874.053 q^{58} +327.739 q^{59} +3247.74 q^{60} -494.324 q^{61} +85.8873 q^{62} -31.9261 q^{63} -596.415 q^{64} +1304.62 q^{65} +1248.53 q^{66} +641.404 q^{67} +1121.27 q^{68} -173.928 q^{69} -49.3758 q^{70} +939.893 q^{71} -2462.71 q^{72} +200.181 q^{73} -891.702 q^{74} -3287.93 q^{75} -485.212 q^{76} -12.5261 q^{77} -2857.84 q^{78} +444.061 q^{79} -1135.95 q^{80} +2004.32 q^{81} +292.313 q^{82} -881.886 q^{83} +71.3756 q^{84} -1554.65 q^{85} +2712.24 q^{86} +1751.85 q^{87} -966.235 q^{88} +1261.87 q^{89} +7045.69 q^{90} +28.6717 q^{91} +277.740 q^{92} +172.143 q^{93} +1914.49 q^{94} +672.754 q^{95} -349.114 q^{96} -1176.54 q^{97} +1662.48 q^{98} +1787.41 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.85005	−1.71475	−0.857376	−	0.514691i	$-0.827907\pi$
$2$	−4.85005	−1.71475	−0.857376	+	0.514691i	$0.827907\pi$
$3$	−9.72090	−1.87079	−0.935394	−	0.353606i	$-0.884955\pi$
$3$	−9.72090	−1.87079	−0.935394	+	0.353606i	$0.884955\pi$
$4$	15.5230	1.94037
$5$	−21.5228	−1.92506	−0.962531	−	0.271172i	$-0.912589\pi$
$5$	−21.5228	−1.92506	−0.962531	+	0.271172i	$0.912589\pi$
$6$	47.1469	3.20794
$7$	−0.473007	−0.0255400	−0.0127700	−	0.999918i	$-0.504065\pi$
$7$	−0.473007	−0.0255400	−0.0127700	+	0.999918i	$0.504065\pi$
$8$	−36.4868	−1.61250
$9$	67.4960	2.49985
$10$	104.387	3.30100
$11$	26.4818	0.725868	0.362934	−	0.931815i	$-0.381775\pi$
$11$	26.4818	0.725868	0.362934	+	0.931815i	$0.381775\pi$
$12$	−150.897	−3.63003
$13$	−60.6157	−1.29321	−0.646607	−	0.762823i	$-0.723813\pi$
$13$	−60.6157	−1.29321	−0.646607	+	0.762823i	$0.723813\pi$
$14$	2.29411	0.0437947
$15$	209.222	3.60138
$16$	52.7790	0.824672
$17$	72.2326	1.03053	0.515264	−	0.857031i	$-0.327694\pi$
$17$	72.2326	1.03053	0.515264	+	0.857031i	$0.327694\pi$
$18$	−327.359	−4.28662
$19$	−31.2577	−0.377421	−0.188711	−	0.982033i	$-0.560431\pi$
$19$	−31.2577	−0.377421	−0.188711	+	0.982033i	$0.560431\pi$
$20$	−334.099	−3.73534
$21$	4.59806	0.0477799
$22$	−128.438	−1.24468
$23$	17.8922	0.162208	0.0811040	−	0.996706i	$-0.474155\pi$
$23$	17.8922	0.162208	0.0811040	+	0.996706i	$0.474155\pi$
$24$	354.685	3.01666
$25$	338.233	2.70586
$26$	293.989	2.21754
$27$	−393.658	−2.80591
$28$	−7.34248	−0.0495571
$29$	−180.215	−1.15397	−0.576985	−	0.816755i	$-0.695771\pi$
$29$	−180.215	−1.15397	−0.576985	+	0.816755i	$0.695771\pi$
$30$	−1014.73	−6.17548
$31$	−17.7085	−0.102598	−0.0512991	−	0.998683i	$-0.516336\pi$
$31$	−17.7085	−0.102598	−0.0512991	+	0.998683i	$0.516336\pi$
$32$	35.9137	0.198397
$33$	−257.427	−1.35795
$34$	−350.332	−1.76710
$35$	10.1805	0.0491661
$36$	1047.74	4.85064
$37$	183.854	0.816904	0.408452	−	0.912780i	$-0.366069\pi$
$37$	183.854	0.816904	0.408452	+	0.912780i	$0.366069\pi$
$38$	151.601	0.647183
$39$	589.240	2.41933
$40$	785.300	3.10417
$41$	−60.2701	−0.229576	−0.114788	−	0.993390i	$-0.536619\pi$
$41$	−60.2701	−0.229576	−0.114788	+	0.993390i	$0.536619\pi$
$42$	−22.3008	−0.0819307
$43$	−559.218	−1.98326	−0.991628	−	0.129128i	$-0.958782\pi$
$43$	−559.218	−1.98326	−0.991628	+	0.129128i	$0.958782\pi$
$44$	411.076	1.40845
$45$	−1452.71	−4.81237
$46$	−86.7781	−0.278146
$47$	−394.736	−1.22507	−0.612533	−	0.790445i	$-0.709849\pi$
$47$	−394.736	−1.22507	−0.612533	+	0.790445i	$0.709849\pi$
$48$	−513.060	−1.54279
$49$	−342.776	−0.999348
$50$	−1640.45	−4.63988
$51$	−702.167	−1.92790
$52$	−940.937	−2.50932
$53$	−431.679	−1.11879	−0.559393	−	0.828903i	$-0.688966\pi$
$53$	−431.679	−1.11879	−0.559393	+	0.828903i	$0.688966\pi$
$54$	1909.26	4.81143
$55$	−569.963	−1.39734
$56$	17.2585	0.0411834
$57$	303.853	0.706075
$58$	874.053	1.97877
$59$	327.739	0.723186	0.361593	−	0.932336i	$-0.382233\pi$
$59$	327.739	0.723186	0.361593	+	0.932336i	$0.382233\pi$
$60$	3247.74	6.98803
$61$	−494.324	−1.03757	−0.518784	−	0.854905i	$-0.673615\pi$
$61$	−494.324	−1.03757	−0.518784	+	0.854905i	$0.673615\pi$
$62$	85.8873	0.175931
$63$	−31.9261	−0.0638462
$64$	−596.415	−1.16487
$65$	1304.62	2.48952
$66$	1248.53	2.32854
$67$	641.404	1.16955	0.584776	−	0.811195i	$-0.301182\pi$
$67$	641.404	1.16955	0.584776	+	0.811195i	$0.301182\pi$
$68$	1121.27	1.99961
$69$	−173.928	−0.303457
$70$	−49.3758	−0.0843076
$71$	939.893	1.57105	0.785527	−	0.618827i	$-0.212392\pi$
$71$	939.893	1.57105	0.785527	+	0.618827i	$0.212392\pi$
$72$	−2462.71	−4.03102
$73$	200.181	0.320950	0.160475	−	0.987040i	$-0.448697\pi$
$73$	200.181	0.320950	0.160475	+	0.987040i	$0.448697\pi$
$74$	−891.702	−1.40079
$75$	−3287.93	−5.06210
$76$	−485.212	−0.732337
$77$	−12.5261	−0.0185387
$78$	−2857.84	−4.14855
$79$	444.061	0.632415	0.316207	−	0.948690i	$-0.397590\pi$
$79$	444.061	0.632415	0.316207	+	0.948690i	$0.397590\pi$
$80$	−1135.95	−1.58754
$81$	2004.32	2.74941
$82$	292.313	0.393665
$83$	−881.886	−1.16626	−0.583130	−	0.812379i	$-0.698172\pi$
$83$	−881.886	−1.16626	−0.583130	+	0.812379i	$0.698172\pi$
$84$	71.3756	0.0927109
$85$	−1554.65	−1.98383
$86$	2712.24	3.40079
$87$	1751.85	2.15883
$88$	−966.235	−1.17047
$89$	1261.87	1.50290	0.751448	−	0.659793i	$-0.229356\pi$
$89$	1261.87	1.50290	0.751448	+	0.659793i	$0.229356\pi$
$90$	7045.69	8.25202
$91$	28.6717	0.0330287
$92$	277.740	0.314744
$93$	172.143	0.191940
$94$	1914.49	2.10068
$95$	672.754	0.726559
$96$	−349.114	−0.371159
$97$	−1176.54	−1.23154	−0.615772	−	0.787924i	$-0.711156\pi$
$97$	−1176.54	−1.23154	−0.615772	+	0.787924i	$0.711156\pi$
$98$	1662.48	1.71363
$99$	1787.41	1.81456
$100$	5250.38	5.25038
$101$	782.077	0.770491	0.385245	−	0.922814i	$-0.374117\pi$
$101$	782.077	0.770491	0.385245	+	0.922814i	$0.374117\pi$
$102$	3405.54	3.30587
$103$	−706.354	−0.675720	−0.337860	−	0.941196i	$-0.609703\pi$
$103$	−706.354	−0.675720	−0.337860	+	0.941196i	$0.609703\pi$
$104$	2211.67	2.08531
$105$	−98.9633	−0.0919793
$106$	2093.66	1.91844
$107$	−1136.39	−1.02672	−0.513360	−	0.858173i	$-0.671600\pi$
$107$	−1136.39	−1.02672	−0.513360	+	0.858173i	$0.671600\pi$
$108$	−6110.74	−5.44450
$109$	−235.684	−0.207105	−0.103552	−	0.994624i	$-0.533021\pi$
$109$	−235.684	−0.207105	−0.103552	+	0.994624i	$0.533021\pi$
$110$	2764.35	2.39609
$111$	−1787.23	−1.52825
$112$	−24.9649	−0.0210621
$113$	−386.695	−0.321922	−0.160961	−	0.986961i	$-0.551459\pi$
$113$	−386.695	−0.321922	−0.160961	+	0.986961i	$0.551459\pi$
$114$	−1473.70	−1.21074
$115$	−385.091	−0.312260
$116$	−2797.48	−2.23913
$117$	−4091.32	−3.23284
$118$	−1589.55	−1.24008
$119$	−34.1666	−0.0263197
$120$	−7633.83	−5.80725
$121$	−629.716	−0.473115
$122$	2397.49	1.77917
$123$	585.880	0.429488
$124$	−274.889	−0.199079
$125$	−4589.38	−3.28389
$126$	154.843	0.109480
$127$	783.324	0.547313	0.273657	−	0.961827i	$-0.411767\pi$
$127$	783.324	0.547313	0.273657	+	0.961827i	$0.411767\pi$
$128$	2605.33	1.79907
$129$	5436.11	3.71025
$130$	−6327.49	−4.26890
$131$	1707.32	1.13870	0.569348	−	0.822096i	$-0.307196\pi$
$131$	1707.32	1.13870	0.569348	+	0.822096i	$0.307196\pi$
$132$	−3996.03	−2.63492
$133$	14.7851	0.00963933
$134$	−3110.84	−2.00549
$135$	8472.63	5.40154
$136$	−2635.54	−1.66173
$137$	3038.97	1.89516	0.947578	−	0.319524i	$-0.103523\pi$
$137$	3038.97	1.89516	0.947578	+	0.319524i	$0.103523\pi$
$138$	843.562	0.520353
$139$	−2548.68	−1.55522	−0.777612	−	0.628745i	$-0.783569\pi$
$139$	−2548.68	−1.55522	−0.777612	+	0.628745i	$0.783569\pi$
$140$	158.031	0.0954005
$141$	3837.19	2.29184
$142$	−4558.53	−2.69397
$143$	−1605.21	−0.938703
$144$	3562.37	2.06156
$145$	3878.74	2.22146
$146$	−970.886	−0.550350
$147$	3332.10	1.86957
$148$	2853.96	1.58510
$149$	1563.26	0.859511	0.429756	−	0.902945i	$-0.358600\pi$
$149$	1563.26	0.859511	0.429756	+	0.902945i	$0.358600\pi$
$150$	15946.6	8.68024
$151$	2011.62	1.08413	0.542063	−	0.840338i	$-0.317643\pi$
$151$	2011.62	1.08413	0.542063	+	0.840338i	$0.317643\pi$
$152$	1140.49	0.608593
$153$	4875.41	2.57617
$154$	60.7520	0.0317892
$155$	381.138	0.197508
$156$	9146.76	4.69440
$157$	73.5848	0.0374058	0.0187029	−	0.999825i	$-0.494046\pi$
$157$	73.5848	0.0374058	0.0187029	+	0.999825i	$0.494046\pi$
$158$	−2153.72	−1.08443
$159$	4196.31	2.09301
$160$	−772.965	−0.381927
$161$	−8.46315	−0.00414279
$162$	−9721.04	−4.71455
$163$	466.706	0.224265	0.112133	−	0.993693i	$-0.464232\pi$
$163$	466.706	0.224265	0.112133	+	0.993693i	$0.464232\pi$
$164$	−935.571	−0.445462
$165$	5540.55	2.61413
$166$	4277.19	1.99985
$167$	−655.134	−0.303567	−0.151784	−	0.988414i	$-0.548502\pi$
$167$	−655.134	−0.303567	−0.151784	+	0.988414i	$0.548502\pi$
$168$	−167.769	−0.0770454
$169$	1477.27	0.672402
$170$	7540.14	3.40178
$171$	−2109.77	−0.943497
$172$	−8680.73	−3.84825
$173$	−267.876	−0.117724	−0.0588619	−	0.998266i	$-0.518747\pi$
$173$	−267.876	−0.117724	−0.0588619	+	0.998266i	$0.518747\pi$
$174$	−8496.58	−3.70186
$175$	−159.987	−0.0691077
$176$	1397.68	0.598603
$177$	−3185.92	−1.35293
$178$	−6120.12	−2.57709
$179$	2156.84	0.900614	0.450307	−	0.892874i	$-0.351315\pi$
$179$	2156.84	0.900614	0.450307	+	0.892874i	$0.351315\pi$
$180$	−22550.3	−9.33779
$181$	3081.07	1.26527	0.632637	−	0.774449i	$-0.281973\pi$
$181$	3081.07	1.26527	0.632637	+	0.774449i	$0.281973\pi$
$182$	−139.059	−0.0566360
$183$	4805.27	1.94107
$184$	−652.830	−0.261561
$185$	−3957.07	−1.57259
$186$	−834.902	−0.329129
$187$	1912.85	0.748028
$188$	−6127.47	−2.37708
$189$	186.203	0.0716628
$190$	−3262.89	−1.24587
$191$	2405.23	0.911185	0.455593	−	0.890188i	$-0.349427\pi$
$191$	2405.23	0.911185	0.455593	+	0.890188i	$0.349427\pi$
$192$	5797.70	2.17923
$193$	−2852.66	−1.06393	−0.531966	−	0.846766i	$-0.678547\pi$
$193$	−2852.66	−1.06393	−0.531966	+	0.846766i	$0.678547\pi$
$194$	5706.29	2.11179
$195$	−12682.1	−4.65736
$196$	−5320.91	−1.93911
$197$	4047.80	1.46393	0.731963	−	0.681344i	$-0.238604\pi$
$197$	4047.80	1.46393	0.731963	+	0.681344i	$0.238604\pi$
$198$	−8669.04	−3.11152
$199$	5229.24	1.86277	0.931384	−	0.364038i	$-0.118602\pi$
$199$	5229.24	1.86277	0.931384	+	0.364038i	$0.118602\pi$
$200$	−12341.0	−4.36322
$201$	−6235.03	−2.18798
$202$	−3793.11	−1.32120
$203$	85.2431	0.0294724
$204$	−10899.7	−3.74085
$205$	1297.18	0.441947
$206$	3425.85	1.15869
$207$	1207.65	0.405496
$208$	−3199.24	−1.06648
$209$	−827.758	−0.273958
$210$	479.977	0.157722
$211$	−2321.97	−0.757587	−0.378793	−	0.925481i	$-0.623661\pi$
$211$	−2321.97	−0.757587	−0.378793	+	0.925481i	$0.623661\pi$
$212$	−6700.94	−2.17086
$213$	−9136.61	−2.93911
$214$	5511.56	1.76057
$215$	12036.0	3.81789
$216$	14363.3	4.52454
$217$	8.37627	0.00262036
$218$	1143.08	0.355133
$219$	−1945.94	−0.600430
$220$	−8847.52	−2.71136
$221$	−4378.43	−1.33269
$222$	8668.15	2.62058
$223$	221.841	0.0666168	0.0333084	−	0.999445i	$-0.489396\pi$
$223$	221.841	0.0666168	0.0333084	+	0.999445i	$0.489396\pi$
$224$	−16.9875	−0.00506706
$225$	22829.4	6.76426
$226$	1875.49	0.552016
$227$	−1333.79	−0.389985	−0.194993	−	0.980805i	$-0.562468\pi$
$227$	−1333.79	−0.389985	−0.194993	+	0.980805i	$0.562468\pi$
$228$	4716.70	1.37005
$229$	−1545.81	−0.446071	−0.223035	−	0.974810i	$-0.571597\pi$
$229$	−1545.81	−0.446071	−0.223035	+	0.974810i	$0.571597\pi$
$230$	1867.71	0.535449
$231$	121.765	0.0346819
$232$	6575.48	1.86078
$233$	−1141.00	−0.320812	−0.160406	−	0.987051i	$-0.551280\pi$
$233$	−1141.00	−0.320812	−0.160406	+	0.987051i	$0.551280\pi$
$234$	19843.1	5.54352
$235$	8495.84	2.35833
$236$	5087.49	1.40325
$237$	−4316.67	−1.18311
$238$	165.710	0.0451317
$239$	1819.02	0.492313	0.246157	−	0.969230i	$-0.420832\pi$
$239$	1819.02	0.492313	0.246157	+	0.969230i	$0.420832\pi$
$240$	11042.5	2.96996
$241$	−3998.99	−1.06887	−0.534435	−	0.845210i	$-0.679475\pi$
$241$	−3998.99	−1.06887	−0.534435	+	0.845210i	$0.679475\pi$
$242$	3054.15	0.811275
$243$	−8855.02	−2.33765
$244$	−7673.38	−2.01327
$245$	7377.52	1.92381
$246$	−2841.55	−0.736465
$247$	1894.71	0.488086
$248$	646.128	0.165440
$249$	8572.73	2.18183
$250$	22258.7	5.63106
$251$	−4066.81	−1.02269	−0.511344	−	0.859376i	$-0.670852\pi$
$251$	−4066.81	−1.02269	−0.511344	+	0.859376i	$0.670852\pi$
$252$	−495.588	−0.123885
$253$	473.817	0.117742
$254$	−3799.16	−0.938506
$255$	15112.6	3.71133
$256$	−7864.67	−1.92009
$257$	−2998.69	−0.727832	−0.363916	−	0.931432i	$-0.618561\pi$
$257$	−2998.69	−0.727832	−0.363916	+	0.931432i	$0.618561\pi$
$258$	−26365.4	−6.36216
$259$	−86.9644	−0.0208637
$260$	20251.6	4.83059
$261$	−12163.8	−2.88475
$262$	−8280.59	−1.95258
$263$	−5126.15	−1.20187	−0.600935	−	0.799298i	$-0.705205\pi$
$263$	−5126.15	−1.20187	−0.600935	+	0.799298i	$0.705205\pi$
$264$	9392.68	2.18969
$265$	9290.95	2.15373
$266$	−71.7085	−0.0165291
$267$	−12266.5	−2.81160
$268$	9956.50	2.26937
$269$	4205.41	0.953190	0.476595	−	0.879123i	$-0.341871\pi$
$269$	4205.41	0.953190	0.476595	+	0.879123i	$0.341871\pi$
$270$	−41092.7	−9.26230
$271$	−4447.95	−0.997024	−0.498512	−	0.866883i	$-0.666120\pi$
$271$	−4447.95	−0.997024	−0.498512	+	0.866883i	$0.666120\pi$
$272$	3812.37	0.849848
$273$	−278.715	−0.0617897
$274$	−14739.1	−3.24972
$275$	8957.00	1.96410
$276$	−2699.89	−0.588819
$277$	3207.03	0.695638	0.347819	−	0.937562i	$-0.386922\pi$
$277$	3207.03	0.695638	0.347819	+	0.937562i	$0.386922\pi$
$278$	12361.2	2.66682
$279$	−1195.26	−0.256480
$280$	−371.453	−0.0792805
$281$	3914.09	0.830943	0.415471	−	0.909606i	$-0.363617\pi$
$281$	3914.09	0.830943	0.415471	+	0.909606i	$0.363617\pi$
$282$	−18610.6	−3.92994
$283$	2543.50	0.534258	0.267129	−	0.963661i	$-0.413925\pi$
$283$	2543.50	0.534258	0.267129	+	0.963661i	$0.413925\pi$
$284$	14589.9	3.04843
$285$	−6539.78	−1.35924
$286$	7785.35	1.60964
$287$	28.5082	0.00586336
$288$	2424.03	0.495963
$289$	304.555	0.0619896
$290$	−18812.1	−3.80926
$291$	11437.1	2.30396
$292$	3107.40	0.622763
$293$	4979.65	0.992881	0.496441	−	0.868071i	$-0.334640\pi$
$293$	4979.65	0.992881	0.496441	+	0.868071i	$0.334640\pi$
$294$	−16160.8	−3.20585
$295$	−7053.88	−1.39218
$296$	−6708.25	−1.31726
$297$	−10424.7	−2.03672
$298$	−7581.89	−1.47385
$299$	−1084.55	−0.209770
$300$	−51038.5	−9.82236
$301$	264.514	0.0506523
$302$	−9756.45	−1.85901
$303$	−7602.50	−1.44143
$304$	−1649.75	−0.311249
$305$	10639.3	1.99738
$306$	−23646.0	−4.41749
$307$	3657.49	0.679948	0.339974	−	0.940435i	$-0.389582\pi$
$307$	3657.49	0.679948	0.339974	+	0.940435i	$0.389582\pi$
$308$	−194.442	−0.0359719
$309$	6866.40	1.26413
$310$	−1848.54	−0.338677
$311$	10882.0	1.98411	0.992057	−	0.125787i	$-0.0401455\pi$
$311$	10882.0	1.98411	0.992057	+	0.125787i	$0.0401455\pi$
$312$	−21499.5	−3.90118
$313$	−9682.33	−1.74849	−0.874245	−	0.485485i	$-0.838643\pi$
$313$	−9682.33	−1.74849	−0.874245	+	0.485485i	$0.838643\pi$
$314$	−356.890	−0.0641416
$315$	687.141	0.122908
$316$	6893.15	1.22712
$317$	−9074.06	−1.60773	−0.803864	−	0.594813i	$-0.797226\pi$
$317$	−9074.06	−1.60773	−0.803864	+	0.594813i	$0.797226\pi$
$318$	−20352.3	−3.58899
$319$	−4772.42	−0.837630
$320$	12836.6	2.24245
$321$	11046.8	1.92078
$322$	41.0467	0.00710386
$323$	−2257.82	−0.388943
$324$	31113.0	5.33487
$325$	−20502.2	−3.49926
$326$	−2263.55	−0.384559
$327$	2291.06	0.387450
$328$	2199.06	0.370192
$329$	186.713	0.0312882
$330$	−26872.0	−4.48258
$331$	−6245.90	−1.03718	−0.518589	−	0.855024i	$-0.673542\pi$
$331$	−6245.90	−1.03718	−0.518589	+	0.855024i	$0.673542\pi$
$332$	−13689.5	−2.26298
$333$	12409.4	2.04214
$334$	3177.43	0.520543
$335$	−13804.8	−2.25146
$336$	242.681	0.0394028
$337$	8708.85	1.40772	0.703860	−	0.710339i	$-0.251458\pi$
$337$	8708.85	1.40772	0.703860	+	0.710339i	$0.251458\pi$
$338$	−7164.82	−1.15300
$339$	3759.02	0.602248
$340$	−24132.8	−3.84937
$341$	−468.953	−0.0744728
$342$	10232.5	1.61786
$343$	324.377	0.0510633
$344$	20404.1	3.19801
$345$	3743.44	0.584173
$346$	1299.21	0.201867
$347$	6430.05	0.994763	0.497382	−	0.867532i	$-0.334295\pi$
$347$	6430.05	0.994763	0.497382	+	0.867532i	$0.334295\pi$
$348$	27194.0	4.18894
$349$	−4524.16	−0.693905	−0.346953	−	0.937883i	$-0.612784\pi$
$349$	−4524.16	−0.693905	−0.346953	+	0.937883i	$0.612784\pi$
$350$	775.943	0.118503
$351$	23861.8	3.62864
$352$	951.059	0.144010
$353$	−10017.2	−1.51038	−0.755189	−	0.655507i	$-0.772455\pi$
$353$	−10017.2	−1.51038	−0.755189	+	0.655507i	$0.772455\pi$
$354$	15451.9	2.31994
$355$	−20229.2	−3.02438
$356$	19587.9	2.91618
$357$	332.130	0.0492386
$358$	−10460.8	−1.54433
$359$	−2113.15	−0.310662	−0.155331	−	0.987862i	$-0.549644\pi$
$359$	−2113.15	−0.310662	−0.155331	+	0.987862i	$0.549644\pi$
$360$	53004.6	7.75997
$361$	−5881.96	−0.857553
$362$	−14943.4	−2.16963
$363$	6121.41	0.885099
$364$	445.070	0.0640879
$365$	−4308.46	−0.617849
$366$	−23305.8	−3.32845
$367$	−9760.52	−1.38827	−0.694135	−	0.719845i	$-0.744213\pi$
$367$	−9760.52	−1.38827	−0.694135	+	0.719845i	$0.744213\pi$
$368$	944.333	0.133768
$369$	−4067.99	−0.573905
$370$	19192.0	2.69660
$371$	204.187	0.0285738
$372$	2672.17	0.372435
$373$	3602.99	0.500150	0.250075	−	0.968227i	$-0.419545\pi$
$373$	3602.99	0.500150	0.250075	+	0.968227i	$0.419545\pi$
$374$	−9277.41	−1.28268
$375$	44612.9	6.14347
$376$	14402.6	1.97542
$377$	10923.9	1.49233
$378$	−903.094	−0.122884
$379$	−12148.7	−1.64653	−0.823267	−	0.567655i	$-0.807851\pi$
$379$	−12148.7	−1.64653	−0.823267	+	0.567655i	$0.807851\pi$
$380$	10443.1	1.40979
$381$	−7614.62	−1.02391
$382$	−11665.5	−1.56246
$383$	6659.36	0.888452	0.444226	−	0.895915i	$-0.353479\pi$
$383$	6659.36	0.888452	0.444226	+	0.895915i	$0.353479\pi$
$384$	−25326.2	−3.36568
$385$	269.597	0.0356881
$386$	13835.5	1.82438
$387$	−37745.0	−4.95785
$388$	−18263.4	−2.38965
$389$	8826.53	1.15044	0.575222	−	0.817997i	$-0.304916\pi$
$389$	8826.53	1.15044	0.575222	+	0.817997i	$0.304916\pi$
$390$	61508.9	7.98621
$391$	1292.40	0.167160
$392$	12506.8	1.61145
$393$	−16596.7	−2.13026
$394$	−19632.0	−2.51027
$395$	−9557.46	−1.21744
$396$	27746.0	3.52093
$397$	12081.3	1.52731	0.763655	−	0.645624i	$-0.223403\pi$
$397$	12081.3	1.52731	0.763655	+	0.645624i	$0.223403\pi$
$398$	−25362.1	−3.19418
$399$	−143.725	−0.0180332
$400$	17851.6	2.23145
$401$	3356.58	0.418004	0.209002	−	0.977915i	$-0.432979\pi$
$401$	3356.58	0.418004	0.209002	+	0.977915i	$0.432979\pi$
$402$	30240.2	3.75185
$403$	1073.42	0.132682
$404$	12140.2	1.49504
$405$	−43138.6	−5.29278
$406$	−413.433	−0.0505378
$407$	4868.78	0.592965
$408$	25619.8	3.10875
$409$	4961.22	0.599796	0.299898	−	0.953971i	$-0.403047\pi$
$409$	4961.22	0.599796	0.299898	+	0.953971i	$0.403047\pi$
$410$	−6291.40	−0.757830
$411$	−29541.5	−3.54544
$412$	−10964.7	−1.31115
$413$	−155.023	−0.0184702
$414$	−5857.17	−0.695325
$415$	18980.7	2.24512
$416$	−2176.94	−0.256570
$417$	24775.5	2.90950
$418$	4014.67	0.469770
$419$	8634.66	1.00676	0.503378	−	0.864066i	$-0.332090\pi$
$419$	8634.66	1.00676	0.503378	+	0.864066i	$0.332090\pi$
$420$	−1536.21	−0.178474
$421$	15330.9	1.77478	0.887389	−	0.461022i	$-0.152517\pi$
$421$	15330.9	1.77478	0.887389	+	0.461022i	$0.152517\pi$
$422$	11261.7	1.29907
$423$	−26643.1	−3.06248
$424$	15750.6	1.80405
$425$	24431.5	2.78847
$426$	44313.0	5.03984
$427$	233.819	0.0264995
$428$	−17640.2	−1.99222
$429$	15604.1	1.75612
$430$	−58375.0	−6.54673
$431$	2015.50	0.225251	0.112626	−	0.993637i	$-0.464074\pi$
$431$	2015.50	0.225251	0.112626	+	0.993637i	$0.464074\pi$
$432$	−20776.9	−2.31395
$433$	−11396.9	−1.26490	−0.632451	−	0.774601i	$-0.717951\pi$
$433$	−11396.9	−1.26490	−0.632451	+	0.774601i	$0.717951\pi$
$434$	−40.6253	−0.00449327
$435$	−37704.9	−4.15589
$436$	−3658.52	−0.401861
$437$	−559.269	−0.0612207
$438$	9437.89	1.02959
$439$	5042.59	0.548222	0.274111	−	0.961698i	$-0.411616\pi$
$439$	5042.59	0.548222	0.274111	+	0.961698i	$0.411616\pi$
$440$	20796.1	2.25322
$441$	−23136.0	−2.49822
$442$	21235.6	2.28524
$443$	7672.28	0.822847	0.411423	−	0.911444i	$-0.365032\pi$
$443$	7672.28	0.822847	0.411423	+	0.911444i	$0.365032\pi$
$444$	−27743.1	−2.96538
$445$	−27159.0	−2.89317
$446$	−1075.94	−0.114231
$447$	−15196.3	−1.60796
$448$	282.109	0.0297509
$449$	3867.38	0.406488	0.203244	−	0.979128i	$-0.434852\pi$
$449$	3867.38	0.406488	0.203244	+	0.979128i	$0.434852\pi$
$450$	−110724.	−11.5990
$451$	−1596.06	−0.166642
$452$	−6002.65	−0.624648
$453$	−19554.7	−2.02817
$454$	6468.94	0.668728
$455$	−617.096	−0.0635822
$456$	−11086.6	−1.13855
$457$	9956.94	1.01918	0.509591	−	0.860417i	$-0.329797\pi$
$457$	9956.94	1.01918	0.509591	+	0.860417i	$0.329797\pi$
$458$	7497.27	0.764901
$459$	−28434.9	−2.89157
$460$	−5977.76	−0.605901
$461$	6196.82	0.626062	0.313031	−	0.949743i	$-0.398656\pi$
$461$	6196.82	0.626062	0.313031	+	0.949743i	$0.398656\pi$
$462$	−590.565	−0.0594709
$463$	−11626.0	−1.16696	−0.583482	−	0.812126i	$-0.698310\pi$
$463$	−11626.0	−1.16696	−0.583482	+	0.812126i	$0.698310\pi$
$464$	−9511.58	−0.951646
$465$	−3705.01	−0.369496
$466$	5533.89	0.550113
$467$	5488.67	0.543865	0.271933	−	0.962316i	$-0.412337\pi$
$467$	5488.67	0.543865	0.271933	+	0.962316i	$0.412337\pi$
$468$	−63509.4	−6.27292
$469$	−303.389	−0.0298704
$470$	−41205.2	−4.04395
$471$	−715.311	−0.0699783
$472$	−11958.2	−1.16614
$473$	−14809.1	−1.43958
$474$	20936.1	2.02875
$475$	−10572.4	−1.02125
$476$	−530.367	−0.0510700
$477$	−29136.6	−2.79680
$478$	−8822.36	−0.844195
$479$	3230.81	0.308183	0.154092	−	0.988057i	$-0.450755\pi$
$479$	3230.81	0.308183	0.154092	+	0.988057i	$0.450755\pi$
$480$	7513.92	0.714504
$481$	−11144.5	−1.05643
$482$	19395.3	1.83285
$483$	82.2694	0.00775029
$484$	−9775.07	−0.918019
$485$	25322.5	2.37080
$486$	42947.3	4.00849
$487$	3108.47	0.289236	0.144618	−	0.989488i	$-0.453805\pi$
$487$	3108.47	0.289236	0.144618	+	0.989488i	$0.453805\pi$
$488$	18036.3	1.67308
$489$	−4536.81	−0.419553
$490$	−35781.3	−3.29885
$491$	−436.429	−0.0401136	−0.0200568	−	0.999799i	$-0.506385\pi$
$491$	−436.429	−0.0401136	−0.0200568	+	0.999799i	$0.506385\pi$
$492$	9094.60	0.833366
$493$	−13017.4	−1.18920
$494$	−9189.42	−0.836946
$495$	−38470.2	−3.49315
$496$	−934.639	−0.0846099
$497$	−444.577	−0.0401247
$498$	−41578.2	−3.74129
$499$	19520.5	1.75122	0.875610	−	0.483018i	$-0.160459\pi$
$499$	19520.5	1.75122	0.875610	+	0.483018i	$0.160459\pi$
$500$	−71240.8	−6.37197
$501$	6368.49	0.567911
$502$	19724.2	1.75365
$503$	−5698.28	−0.505117	−0.252559	−	0.967582i	$-0.581272\pi$
$503$	−5698.28	−0.505117	−0.252559	+	0.967582i	$0.581272\pi$
$504$	1164.88	0.102952
$505$	−16832.5	−1.48324
$506$	−2298.04	−0.201898
$507$	−14360.4	−1.25792
$508$	12159.5	1.06199
$509$	1540.91	0.134184	0.0670918	−	0.997747i	$-0.478628\pi$
$509$	1540.91	0.134184	0.0670918	+	0.997747i	$0.478628\pi$
$510$	−73297.0	−6.36401
$511$	−94.6869	−0.00819707
$512$	17301.4	1.49340
$513$	12304.8	1.05901
$514$	14543.8	1.24805
$515$	15202.8	1.30080
$516$	84384.6	7.19927
$517$	−10453.3	−0.889237
$518$	421.782	0.0357761
$519$	2604.00	0.220237
$520$	−47601.5	−4.01436
$521$	−6396.69	−0.537897	−0.268948	−	0.963155i	$-0.586676\pi$
$521$	−6396.69	−0.537897	−0.268948	+	0.963155i	$0.586676\pi$
$522$	58995.0	4.94663
$523$	8119.63	0.678866	0.339433	−	0.940630i	$-0.389765\pi$
$523$	8119.63	0.678866	0.339433	+	0.940630i	$0.389765\pi$
$524$	26502.7	2.20950
$525$	1555.21	0.129286
$526$	24862.1	2.06091
$527$	−1279.13	−0.105730
$528$	−13586.7	−1.11986
$529$	−11846.9	−0.973689
$530$	−45061.6	−3.69311
$531$	22121.1	1.80786
$532$	229.509	0.0187039
$533$	3653.32	0.296891
$534$	59493.1	4.82120
$535$	24458.4	1.97650
$536$	−23402.8	−1.88591
$537$	−20966.5	−1.68486
$538$	−20396.4	−1.63448
$539$	−9077.32	−0.725395
$540$	131520.	10.4810
$541$	2101.94	0.167042	0.0835209	−	0.996506i	$-0.473383\pi$
$541$	2101.94	0.167042	0.0835209	+	0.996506i	$0.473383\pi$
$542$	21572.8	1.70965
$543$	−29950.8	−2.36706
$544$	2594.14	0.204454
$545$	5072.59	0.398690
$546$	1351.78	0.105954
$547$	−2738.27	−0.214040	−0.107020	−	0.994257i	$-0.534131\pi$
$547$	−2738.27	−0.214040	−0.107020	+	0.994257i	$0.534131\pi$
$548$	47173.8	3.67731
$549$	−33364.9	−2.59377
$550$	−43441.9	−3.36794
$551$	5633.11	0.435533
$552$	6346.10	0.489326
$553$	−210.044	−0.0161519
$554$	−15554.3	−1.19285
$555$	38466.3	2.94199
$556$	−39563.1	−3.01771
$557$	−17062.4	−1.29794	−0.648972	−	0.760812i	$-0.724801\pi$
$557$	−17062.4	−1.29794	−0.648972	+	0.760812i	$0.724801\pi$
$558$	5797.05	0.439800
$559$	33897.4	2.56477
$560$	537.315	0.0405459
$561$	−18594.6	−1.39940
$562$	−18983.5	−1.42486
$563$	8917.52	0.667546	0.333773	−	0.942653i	$-0.391678\pi$
$563$	8917.52	0.667546	0.333773	+	0.942653i	$0.391678\pi$
$564$	59564.6	4.44702
$565$	8322.77	0.619720
$566$	−12336.1	−0.916120
$567$	−948.057	−0.0702198
$568$	−34293.7	−2.53333
$569$	−26614.7	−1.96089	−0.980446	−	0.196788i	$-0.936949\pi$
$569$	−26614.7	−1.96089	−0.980446	+	0.196788i	$0.936949\pi$
$570$	31718.2	2.33076
$571$	17130.2	1.25548	0.627739	−	0.778424i	$-0.283981\pi$
$571$	17130.2	1.25548	0.627739	+	0.778424i	$0.283981\pi$
$572$	−24917.7	−1.82143
$573$	−23381.0	−1.70464
$574$	−138.266	−0.0100542
$575$	6051.73	0.438913
$576$	−40255.6	−2.91201
$577$	−5903.10	−0.425908	−0.212954	−	0.977062i	$-0.568309\pi$
$577$	−5903.10	−0.425908	−0.212954	+	0.977062i	$0.568309\pi$
$578$	−1477.11	−0.106297
$579$	27730.4	1.99039
$580$	60209.7	4.31047
$581$	417.139	0.0297863
$582$	−55470.3	−3.95072
$583$	−11431.6	−0.812091
$584$	−7303.95	−0.517534
$585$	88056.8	6.22342
$586$	−24151.5	−1.70254
$587$	20907.7	1.47010	0.735052	−	0.678010i	$-0.237158\pi$
$587$	20907.7	1.47010	0.735052	+	0.678010i	$0.237158\pi$
$588$	51724.0	3.62766
$589$	553.527	0.0387228
$590$	34211.6	2.38724
$591$	−39348.3	−2.73870
$592$	9703.64	0.673678
$593$	67.1816	0.00465230	0.00232615	−	0.999997i	$-0.499260\pi$
$593$	67.1816	0.00465230	0.00232615	+	0.999997i	$0.499260\pi$
$594$	50560.5	3.49246
$595$	735.362	0.0506671
$596$	24266.4	1.66777
$597$	−50832.9	−3.48485
$598$	5260.12	0.359703
$599$	12224.4	0.833850	0.416925	−	0.908941i	$-0.363108\pi$
$599$	12224.4	0.833850	0.416925	+	0.908941i	$0.363108\pi$
$600$	119966.	8.16266
$601$	24713.0	1.67731	0.838655	−	0.544663i	$-0.183343\pi$
$601$	24713.0	1.67731	0.838655	+	0.544663i	$0.183343\pi$
$602$	−1282.91	−0.0868562
$603$	43292.2	2.92371
$604$	31226.3	2.10361
$605$	13553.3	0.910776
$606$	36872.5	2.47169
$607$	15321.1	1.02449	0.512246	−	0.858839i	$-0.328814\pi$
$607$	15321.1	1.02449	0.512246	+	0.858839i	$0.328814\pi$
$608$	−1122.58	−0.0748793
$609$	−828.640	−0.0551366
$610$	−51600.9	−3.42502
$611$	23927.2	1.58427
$612$	75680.9	4.99873
$613$	20916.5	1.37816	0.689079	−	0.724687i	$-0.258015\pi$
$613$	20916.5	1.37816	0.689079	+	0.724687i	$0.258015\pi$
$614$	−17739.0	−1.16594
$615$	−12609.8	−0.826791
$616$	457.036	0.0298937
$617$	−8178.88	−0.533662	−0.266831	−	0.963743i	$-0.585977\pi$
$617$	−8178.88	−0.533662	−0.266831	+	0.963743i	$0.585977\pi$
$618$	−33302.4	−2.16767
$619$	−17695.1	−1.14899	−0.574495	−	0.818508i	$-0.694801\pi$
$619$	−17695.1	−1.14899	−0.574495	+	0.818508i	$0.694801\pi$
$620$	5916.40	0.383239
$621$	−7043.41	−0.455140
$622$	−52778.1	−3.40226
$623$	−596.873	−0.0383839
$624$	31099.5	1.99515
$625$	56497.4	3.61583
$626$	46959.8	2.99823
$627$	8046.56	0.512518
$628$	1142.26	0.0725811
$629$	13280.3	0.841843
$630$	−3332.67	−0.210756
$631$	20980.0	1.32361	0.661807	−	0.749674i	$-0.269790\pi$
$631$	20980.0	1.32361	0.661807	+	0.749674i	$0.269790\pi$
$632$	−16202.4	−1.01977
$633$	22571.6	1.41728
$634$	44009.6	2.75685
$635$	−16859.4	−1.05361
$636$	65139.2	4.06122
$637$	20777.6	1.29237
$638$	23146.5	1.43633
$639$	63439.0	3.92740
$640$	−56074.2	−3.46332
$641$	9847.00	0.606760	0.303380	−	0.952870i	$-0.401885\pi$
$641$	9847.00	0.606760	0.303380	+	0.952870i	$0.401885\pi$
$642$	−53577.3	−3.29366
$643$	−1787.27	−0.109616	−0.0548081	−	0.998497i	$-0.517455\pi$
$643$	−1787.27	−0.109616	−0.0548081	+	0.998497i	$0.517455\pi$
$644$	−131.373	−0.00803856
$645$	−117001.	−7.14247
$646$	10950.6	0.666941
$647$	1101.29	0.0669181	0.0334590	−	0.999440i	$-0.489348\pi$
$647$	1101.29	0.0669181	0.0334590	+	0.999440i	$0.489348\pi$
$648$	−73131.1	−4.43343
$649$	8679.11	0.524938
$650$	99436.8	6.00036
$651$	−81.4249	−0.00490214
$652$	7244.67	0.435158
$653$	2594.37	0.155476	0.0777379	−	0.996974i	$-0.475230\pi$
$653$	2594.37	0.155476	0.0777379	+	0.996974i	$0.475230\pi$
$654$	−11111.8	−0.664380
$655$	−36746.4	−2.19206
$656$	−3180.99	−0.189325
$657$	13511.4	0.802328
$658$	−905.567	−0.0536515
$659$	−3915.77	−0.231467	−0.115733	−	0.993280i	$-0.536922\pi$
$659$	−3915.77	−0.231467	−0.115733	+	0.993280i	$0.536922\pi$
$660$	86005.9	5.07239
$661$	−10254.5	−0.603410	−0.301705	−	0.953401i	$-0.597556\pi$
$661$	−10254.5	−0.603410	−0.301705	+	0.953401i	$0.597556\pi$
$662$	30292.9	1.77850
$663$	42562.3	2.49319
$664$	32177.2	1.88060
$665$	−318.218	−0.0185563
$666$	−60186.3	−3.50176
$667$	−3224.45	−0.187183
$668$	−10169.6	−0.589034
$669$	−2156.49	−0.124626
$670$	66954.2	3.86069
$671$	−13090.6	−0.753138
$672$	165.133	0.00947940
$673$	−22918.5	−1.31269	−0.656346	−	0.754460i	$-0.727899\pi$
$673$	−22918.5	−1.31269	−0.656346	+	0.754460i	$0.727899\pi$
$674$	−42238.4	−2.41389
$675$	−133148.	−7.59240
$676$	22931.6	1.30471
$677$	22232.9	1.26215	0.631077	−	0.775720i	$-0.282613\pi$
$677$	22232.9	1.26215	0.631077	+	0.775720i	$0.282613\pi$
$678$	−18231.4	−1.03271
$679$	556.513	0.0314536
$680$	56724.3	3.19894
$681$	12965.6	0.729581
$682$	2274.45	0.127702
$683$	15483.9	0.867461	0.433730	−	0.901043i	$-0.357197\pi$
$683$	15483.9	0.867461	0.433730	+	0.901043i	$0.357197\pi$
$684$	−32749.9	−1.83073
$685$	−65407.2	−3.64829
$686$	−1573.25	−0.0875609
$687$	15026.7	0.834504
$688$	−29515.0	−1.63554
$689$	26166.5	1.44683
$690$	−18155.8	−1.00171
$691$	−17461.8	−0.961330	−0.480665	−	0.876904i	$-0.659605\pi$
$691$	−17461.8	−0.961330	−0.480665	+	0.876904i	$0.659605\pi$
$692$	−4158.23	−0.228428
$693$	−845.459	−0.0463439
$694$	−31186.0	−1.70577
$695$	54854.8	2.99390
$696$	−63919.6	−3.48113
$697$	−4353.47	−0.236584
$698$	21942.4	1.18988
$699$	11091.5	0.600171
$700$	−2483.47	−0.134095
$701$	12095.4	0.651692	0.325846	−	0.945423i	$-0.394351\pi$
$701$	12095.4	0.651692	0.325846	+	0.945423i	$0.394351\pi$
$702$	−115731.	−6.22221
$703$	−5746.85	−0.308317
$704$	−15794.1	−0.845545
$705$	−82587.2	−4.41194
$706$	48584.0	2.58992
$707$	−369.928	−0.0196783
$708$	−49455.0	−2.62519
$709$	−22787.9	−1.20708	−0.603538	−	0.797334i	$-0.706243\pi$
$709$	−22787.9	−1.20708	−0.603538	+	0.797334i	$0.706243\pi$
$710$	98112.5	5.18605
$711$	29972.3	1.58094
$712$	−46041.5	−2.42343
$713$	−316.845	−0.0166423
$714$	−1610.85	−0.0844320
$715$	34548.7	1.80706
$716$	33480.6	1.74753
$717$	−17682.6	−0.921015
$718$	10248.9	0.532708
$719$	−18981.7	−0.984559	−0.492279	−	0.870437i	$-0.663836\pi$
$719$	−18981.7	−0.984559	−0.492279	+	0.870437i	$0.663836\pi$
$720$	−76672.4	−3.96863
$721$	334.111	0.0172579
$722$	28527.8	1.47049
$723$	38873.8	1.99963
$724$	47827.4	2.45510
$725$	−60954.7	−3.12248
$726$	−29689.1	−1.51772
$727$	3922.17	0.200090	0.100045	−	0.994983i	$-0.468101\pi$
$727$	3922.17	0.200090	0.100045	+	0.994983i	$0.468101\pi$
$728$	−1046.14	−0.0532589
$729$	31962.2	1.62385
$730$	20896.2	1.05946
$731$	−40393.8	−2.04380
$732$	74592.2	3.76640
$733$	31569.6	1.59079	0.795395	−	0.606092i	$-0.207264\pi$
$733$	31569.6	1.59079	0.795395	+	0.606092i	$0.207264\pi$
$734$	47339.0	2.38054
$735$	−71716.2	−3.59904
$736$	642.576	0.0321816
$737$	16985.5	0.848941
$738$	19729.9	0.984105
$739$	−18098.8	−0.900911	−0.450456	−	0.892799i	$-0.648738\pi$
$739$	−18098.8	−0.900911	−0.450456	+	0.892799i	$0.648738\pi$
$740$	−61425.4	−3.05141
$741$	−18418.3	−0.913106
$742$	−990.318	−0.0489969
$743$	−8069.09	−0.398420	−0.199210	−	0.979957i	$-0.563838\pi$
$743$	−8069.09	−0.398420	−0.199210	+	0.979957i	$0.563838\pi$
$744$	−6280.95	−0.309504
$745$	−33645.8	−1.65461
$746$	−17474.7	−0.857632
$747$	−59523.8	−2.91548
$748$	29693.1	1.45145
$749$	537.522	0.0262224
$750$	−216375.	−10.5345
$751$	−25727.5	−1.25008	−0.625039	−	0.780594i	$-0.714917\pi$
$751$	−25727.5	−1.25008	−0.625039	+	0.780594i	$0.714917\pi$
$752$	−20833.8	−1.01028
$753$	39533.0	1.91323
$754$	−52981.3	−2.55897
$755$	−43295.7	−2.08701
$756$	2890.42	0.139053
$757$	20550.7	0.986693	0.493347	−	0.869833i	$-0.335773\pi$
$757$	20550.7	0.986693	0.493347	+	0.869833i	$0.335773\pi$
$758$	58921.7	2.82340
$759$	−4605.93	−0.220270
$760$	−24546.6	−1.17158
$761$	8327.73	0.396689	0.198344	−	0.980132i	$-0.436444\pi$
$761$	8327.73	0.396689	0.198344	+	0.980132i	$0.436444\pi$
$762$	36931.3	1.75575
$763$	111.480	0.00528946
$764$	37336.3	1.76804
$765$	−104933.	−4.95928
$766$	−32298.2	−1.52347
$767$	−19866.1	−0.935234
$768$	76451.8	3.59208
$769$	−4652.06	−0.218150	−0.109075	−	0.994034i	$-0.534789\pi$
$769$	−4652.06	−0.218150	−0.109075	+	0.994034i	$0.534789\pi$
$770$	−1307.56	−0.0611962
$771$	29149.9	1.36162
$772$	−44281.8	−2.06442
$773$	22213.5	1.03359	0.516795	−	0.856109i	$-0.327125\pi$
$773$	22213.5	1.03359	0.516795	+	0.856109i	$0.327125\pi$
$774$	183065.	8.50147
$775$	−5989.61	−0.277617
$776$	42928.3	1.98587
$777$	845.373	0.0390316
$778$	−42809.1	−1.97273
$779$	1883.90	0.0866467
$780$	−196864.	−9.03701
$781$	24890.0	1.14038
$782$	−6268.21	−0.286638
$783$	70943.1	3.23793
$784$	−18091.4	−0.824134
$785$	−1583.75	−0.0720084
$786$	80494.8	3.65287
$787$	39687.6	1.79760	0.898799	−	0.438360i	$-0.144441\pi$
$787$	39687.6	1.79760	0.898799	+	0.438360i	$0.144441\pi$
$788$	62833.9	2.84056
$789$	49830.8	2.24845
$790$	46354.1	2.08760
$791$	182.909	0.00822188
$792$	−65217.0	−2.92599
$793$	29963.8	1.34180
$794$	−58594.8	−2.61896
$795$	−90316.5	−4.02918
$796$	81173.3	3.61446
$797$	9111.53	0.404952	0.202476	−	0.979287i	$-0.435101\pi$
$797$	9111.53	0.404952	0.202476	+	0.979287i	$0.435101\pi$
$798$	697.071	0.0309224
$799$	−28512.8	−1.26247
$800$	12147.2	0.536836
$801$	85171.0	3.75702
$802$	−16279.6	−0.716772
$803$	5301.14	0.232968
$804$	−96786.2	−4.24550
$805$	182.151	0.00797513
$806$	−5206.12	−0.227516
$807$	−40880.3	−1.78322
$808$	−28535.5	−1.24242
$809$	−13942.7	−0.605931	−0.302965	−	0.953002i	$-0.597977\pi$
$809$	−13942.7	−0.605931	−0.302965	+	0.953002i	$0.597977\pi$
$810$	209224.	9.07580
$811$	−5530.55	−0.239462	−0.119731	−	0.992806i	$-0.538203\pi$
$811$	−5530.55	−0.239462	−0.119731	+	0.992806i	$0.538203\pi$
$812$	1323.23	0.0571874
$813$	43238.1	1.86522
$814$	−23613.8	−1.01679
$815$	−10044.8	−0.431725
$816$	−37059.7	−1.58989
$817$	17479.9	0.748523
$818$	−24062.2	−1.02850
$819$	1935.22	0.0825668
$820$	20136.2	0.857543
$821$	3789.13	0.161074	0.0805369	−	0.996752i	$-0.474337\pi$
$821$	3789.13	0.161074	0.0805369	+	0.996752i	$0.474337\pi$
$822$	143278.	6.07954
$823$	18978.0	0.803804	0.401902	−	0.915683i	$-0.368349\pi$
$823$	18978.0	0.803804	0.401902	+	0.915683i	$0.368349\pi$
$824$	25772.6	1.08960
$825$	−87070.2	−3.67442
$826$	751.869	0.0316718
$827$	−6372.10	−0.267932	−0.133966	−	0.990986i	$-0.542771\pi$
$827$	−6372.10	−0.267932	−0.133966	+	0.990986i	$0.542771\pi$
$828$	18746.4	0.786813
$829$	38906.7	1.63002	0.815010	−	0.579447i	$-0.196731\pi$
$829$	38906.7	1.63002	0.815010	+	0.579447i	$0.196731\pi$
$830$	−92057.3	−3.84983
$831$	−31175.2	−1.30139
$832$	36152.2	1.50643
$833$	−24759.6	−1.02986
$834$	−120162.	−4.98906
$835$	14100.3	0.584386
$836$	−12849.3	−0.531580
$837$	6971.10	0.287881
$838$	−41878.5	−1.72634
$839$	17156.2	0.705955	0.352978	−	0.935632i	$-0.385169\pi$
$839$	17156.2	0.705955	0.352978	+	0.935632i	$0.385169\pi$
$840$	3610.86	0.148317
$841$	8088.52	0.331646
$842$	−74355.5	−3.04330
$843$	−38048.5	−1.55452
$844$	−36043.8	−1.47000
$845$	−31795.0	−1.29442
$846$	129220.	5.25140
$847$	297.860	0.0120834
$848$	−22783.6	−0.922631
$849$	−24725.1	−0.999485
$850$	−118494.	−4.78153
$851$	3289.56	0.132508
$852$	−141827.	−5.70297
$853$	18068.5	0.725268	0.362634	−	0.931932i	$-0.381878\pi$
$853$	18068.5	0.725268	0.362634	+	0.931932i	$0.381878\pi$
$854$	−1134.03	−0.0454400
$855$	45408.2	1.81629
$856$	41463.3	1.65559
$857$	45313.3	1.80615	0.903077	−	0.429478i	$-0.141302\pi$
$857$	45313.3	1.80615	0.903077	+	0.429478i	$0.141302\pi$
$858$	−75680.7	−3.01130
$859$	−6723.86	−0.267072	−0.133536	−	0.991044i	$-0.542633\pi$
$859$	−6723.86	−0.267072	−0.133536	+	0.991044i	$0.542633\pi$
$860$	186834.	7.40813
$861$	−277.125	−0.0109691
$862$	−9775.29	−0.386250
$863$	−30514.0	−1.20360	−0.601802	−	0.798646i	$-0.705550\pi$
$863$	−30514.0	−1.20360	−0.601802	+	0.798646i	$0.705550\pi$
$864$	−14137.7	−0.556684
$865$	5765.45	0.226626
$866$	55275.8	2.16899
$867$	−2960.55	−0.115969
$868$	130.025	0.00508447
$869$	11759.5	0.459050
$870$	182871.	7.12632
$871$	−38879.2	−1.51248
$872$	8599.36	0.333958
$873$	−79411.9	−3.07868
$874$	2712.48	0.104978
$875$	2170.81	0.0838706
$876$	−30206.7	−1.16506
$877$	39522.0	1.52174	0.760868	−	0.648906i	$-0.224773\pi$
$877$	39522.0	1.52174	0.760868	+	0.648906i	$0.224773\pi$
$878$	−24456.8	−0.940065
$879$	−48406.7	−1.85747
$880$	−30082.1	−1.15235
$881$	−21185.1	−0.810153	−0.405076	−	0.914283i	$-0.632755\pi$
$881$	−21185.1	−0.810153	−0.405076	+	0.914283i	$0.632755\pi$
$882$	112211.	4.28383
$883$	−33290.5	−1.26876	−0.634380	−	0.773021i	$-0.718745\pi$
$883$	−33290.5	−1.26876	−0.634380	+	0.773021i	$0.718745\pi$
$884$	−67966.3	−2.58592
$885$	68570.1	2.60447
$886$	−37210.9	−1.41098
$887$	15782.5	0.597433	0.298716	−	0.954342i	$-0.403442\pi$
$887$	15782.5	0.597433	0.298716	+	0.954342i	$0.403442\pi$
$888$	65210.3	2.46432
$889$	−370.518	−0.0139784
$890$	131722.	4.96106
$891$	53077.8	1.99571
$892$	3443.63	0.129261
$893$	12338.5	0.462366
$894$	73702.8	2.75726
$895$	−46421.4	−1.73374
$896$	−1232.34	−0.0459483
$897$	10542.8	0.392435
$898$	−18757.0	−0.697026
$899$	3191.35	0.118395
$900$	354380.	13.1252
$901$	−31181.3	−1.15294
$902$	7740.96	0.285749
$903$	−2571.32	−0.0947599
$904$	14109.3	0.519100
$905$	−66313.5	−2.43573
$906$	94841.5	3.47781
$907$	31722.4	1.16133	0.580664	−	0.814143i	$-0.302793\pi$
$907$	31722.4	1.16133	0.580664	+	0.814143i	$0.302793\pi$
$908$	−20704.4	−0.756717
$909$	52787.1	1.92611
$910$	2992.95	0.109028
$911$	−22227.3	−0.808368	−0.404184	−	0.914678i	$-0.632444\pi$
$911$	−22227.3	−0.808368	−0.404184	+	0.914678i	$0.632444\pi$
$912$	16037.0	0.582280
$913$	−23353.9	−0.846551
$914$	−48291.7	−1.74764
$915$	−103423.	−3.73668
$916$	−23995.6	−0.865543
$917$	−807.575	−0.0290823
$918$	137911.	4.95832
$919$	7769.51	0.278882	0.139441	−	0.990230i	$-0.455469\pi$
$919$	7769.51	0.278882	0.139441	+	0.990230i	$0.455469\pi$
$920$	14050.8	0.503521
$921$	−35554.1	−1.27204
$922$	−30054.9	−1.07354
$923$	−56972.3	−2.03171
$924$	1890.15	0.0672959
$925$	62185.5	2.21043
$926$	56386.5	2.00105
$927$	−47676.1	−1.68920
$928$	−6472.20	−0.228944
$929$	−51128.3	−1.80567	−0.902834	−	0.429990i	$-0.858517\pi$
$929$	−51128.3	−1.80567	−0.902834	+	0.429990i	$0.858517\pi$
$930$	17969.5	0.633594
$931$	10714.4	0.377175
$932$	−17711.7	−0.622494
$933$	−105783.	−3.71186
$934$	−26620.3	−0.932594
$935$	−41169.9	−1.44000
$936$	149279.	5.21297
$937$	21841.6	0.761510	0.380755	−	0.924676i	$-0.375664\pi$
$937$	21841.6	0.761510	0.380755	+	0.924676i	$0.375664\pi$
$938$	1471.45	0.0512202
$939$	94121.0	3.27106
$940$	131881.	4.57604
$941$	−12080.5	−0.418505	−0.209252	−	0.977862i	$-0.567103\pi$
$941$	−12080.5	−0.418505	−0.209252	+	0.977862i	$0.567103\pi$
$942$	3469.29	0.119995
$943$	−1078.37	−0.0372390
$944$	17297.7	0.596391
$945$	−4007.62	−0.137955
$946$	71824.8	2.46853
$947$	−48324.6	−1.65822	−0.829112	−	0.559083i	$-0.811153\pi$
$947$	−48324.6	−1.65822	−0.829112	+	0.559083i	$0.811153\pi$
$948$	−67007.6	−2.29568
$949$	−12134.1	−0.415057
$950$	51276.5	1.75119
$951$	88208.1	3.00772
$952$	1246.63	0.0424406
$953$	46034.2	1.56474	0.782368	−	0.622816i	$-0.214011\pi$
$953$	46034.2	1.56474	0.782368	+	0.622816i	$0.214011\pi$
$954$	141314.	4.79581
$955$	−51767.4	−1.75409
$956$	28236.7	0.955271
$957$	46392.2	1.56703
$958$	−15669.6	−0.528457
$959$	−1437.45	−0.0484023
$960$	−124783.	−4.19516
$961$	−29477.4	−0.989474
$962$	54051.2	1.81152
$963$	−76701.9	−2.56665
$964$	−62076.2	−2.07400
$965$	61397.4	2.04814
$966$	−399.011	−0.0132898
$967$	−464.873	−0.0154595	−0.00772973	−	0.999970i	$-0.502460\pi$
$967$	−464.873	−0.0154595	−0.00772973	+	0.999970i	$0.502460\pi$
$968$	22976.3	0.762900
$969$	21948.1	0.727631
$970$	−122816.	−4.06533
$971$	−12806.6	−0.423259	−0.211629	−	0.977350i	$-0.567877\pi$
$971$	−12806.6	−0.423259	−0.211629	+	0.977350i	$0.567877\pi$
$972$	−137456.	−4.53592
$973$	1205.54	0.0397204
$974$	−15076.2	−0.495968
$975$	199300.	6.54638
$976$	−26089.9	−0.855653
$977$	−1781.23	−0.0583280	−0.0291640	−	0.999575i	$-0.509285\pi$
$977$	−1781.23	−0.0583280	−0.0291640	+	0.999575i	$0.509285\pi$
$978$	22003.7	0.719430
$979$	33416.5	1.09090
$980$	114521.	3.73290
$981$	−15907.7	−0.517732
$982$	2116.70	0.0687848
$983$	2344.42	0.0760685	0.0380343	−	0.999276i	$-0.487890\pi$
$983$	2344.42	0.0760685	0.0380343	+	0.999276i	$0.487890\pi$
$984$	−21376.9	−0.692551
$985$	−87120.1	−2.81815
$986$	63135.1	2.03918
$987$	−1815.02	−0.0585336
$988$	29411.5	0.947069
$989$	−10005.7	−0.321700
$990$	186582.	5.98988
$991$	−8598.10	−0.275608	−0.137804	−	0.990460i	$-0.544004\pi$
$991$	−8598.10	−0.275608	−0.137804	+	0.990460i	$0.544004\pi$
$992$	−635.979	−0.0203552
$993$	60715.8	1.94034
$994$	2156.22	0.0688039
$995$	−112548.	−3.58594
$996$	133074.	4.23356
$997$	46226.2	1.46840	0.734202	−	0.678931i	$-0.237556\pi$
$997$	46226.2	1.46840	0.734202	+	0.678931i	$0.237556\pi$
$998$	−94675.6	−3.00291
$999$	−72375.6	−2.29216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1997.4.a.a.1.19	✓	239

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1997.4.a.a.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-4.85005 q^{2} -9.72090 q^{3} +15.5230 q^{4} -21.5228 q^{5} +47.1469 q^{6} -0.473007 q^{7} -36.4868 q^{8} +67.4960 q^{9} +O(q^{10})\)	\(q-4.85005 q^{2} -9.72090 q^{3} +15.5230 q^{4} -21.5228 q^{5} +47.1469 q^{6} -0.473007 q^{7} -36.4868 q^{8} +67.4960 q^{9} +104.387 q^{10} +26.4818 q^{11} -150.897 q^{12} -60.6157 q^{13} +2.29411 q^{14} +209.222 q^{15} +52.7790 q^{16} +72.2326 q^{17} -327.359 q^{18} -31.2577 q^{19} -334.099 q^{20} +4.59806 q^{21} -128.438 q^{22} +17.8922 q^{23} +354.685 q^{24} +338.233 q^{25} +293.989 q^{26} -393.658 q^{27} -7.34248 q^{28} -180.215 q^{29} -1014.73 q^{30} -17.7085 q^{31} +35.9137 q^{32} -257.427 q^{33} -350.332 q^{34} +10.1805 q^{35} +1047.74 q^{36} +183.854 q^{37} +151.601 q^{38} +589.240 q^{39} +785.300 q^{40} -60.2701 q^{41} -22.3008 q^{42} -559.218 q^{43} +411.076 q^{44} -1452.71 q^{45} -86.7781 q^{46} -394.736 q^{47} -513.060 q^{48} -342.776 q^{49} -1640.45 q^{50} -702.167 q^{51} -940.937 q^{52} -431.679 q^{53} +1909.26 q^{54} -569.963 q^{55} +17.2585 q^{56} +303.853 q^{57} +874.053 q^{58} +327.739 q^{59} +3247.74 q^{60} -494.324 q^{61} +85.8873 q^{62} -31.9261 q^{63} -596.415 q^{64} +1304.62 q^{65} +1248.53 q^{66} +641.404 q^{67} +1121.27 q^{68} -173.928 q^{69} -49.3758 q^{70} +939.893 q^{71} -2462.71 q^{72} +200.181 q^{73} -891.702 q^{74} -3287.93 q^{75} -485.212 q^{76} -12.5261 q^{77} -2857.84 q^{78} +444.061 q^{79} -1135.95 q^{80} +2004.32 q^{81} +292.313 q^{82} -881.886 q^{83} +71.3756 q^{84} -1554.65 q^{85} +2712.24 q^{86} +1751.85 q^{87} -966.235 q^{88} +1261.87 q^{89} +7045.69 q^{90} +28.6717 q^{91} +277.740 q^{92} +172.143 q^{93} +1914.49 q^{94} +672.754 q^{95} -349.114 q^{96} -1176.54 q^{97} +1662.48 q^{98} +1787.41 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) \) 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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