LMFDB - Embedded newform 1997.4.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q-5.59440 q^{2} -8.36152 q^{3} +23.2974 q^{4} -4.51522 q^{5} +46.7777 q^{6} -9.81959 q^{7} -85.5797 q^{8} +42.9151 q^{9} +O(q^{10})$	\(q-5.59440 q^{2} -8.36152 q^{3} +23.2974 q^{4} -4.51522 q^{5} +46.7777 q^{6} -9.81959 q^{7} -85.5797 q^{8} +42.9151 q^{9} +25.2599 q^{10} +22.4851 q^{11} -194.801 q^{12} -38.3746 q^{13} +54.9348 q^{14} +37.7541 q^{15} +292.388 q^{16} -104.691 q^{17} -240.084 q^{18} +62.9168 q^{19} -105.193 q^{20} +82.1068 q^{21} -125.791 q^{22} +60.7523 q^{23} +715.576 q^{24} -104.613 q^{25} +214.683 q^{26} -133.074 q^{27} -228.771 q^{28} +191.820 q^{29} -211.212 q^{30} -279.869 q^{31} -951.102 q^{32} -188.010 q^{33} +585.683 q^{34} +44.3376 q^{35} +999.808 q^{36} +199.967 q^{37} -351.982 q^{38} +320.870 q^{39} +386.411 q^{40} -4.98648 q^{41} -459.338 q^{42} +69.3206 q^{43} +523.845 q^{44} -193.771 q^{45} -339.873 q^{46} +342.363 q^{47} -2444.81 q^{48} -246.576 q^{49} +585.247 q^{50} +875.375 q^{51} -894.027 q^{52} -307.469 q^{53} +744.470 q^{54} -101.525 q^{55} +840.358 q^{56} -526.080 q^{57} -1073.12 q^{58} +761.526 q^{59} +879.571 q^{60} -725.327 q^{61} +1565.70 q^{62} -421.408 q^{63} +2981.74 q^{64} +173.270 q^{65} +1051.80 q^{66} +8.42525 q^{67} -2439.02 q^{68} -507.982 q^{69} -248.042 q^{70} -670.699 q^{71} -3672.66 q^{72} -881.638 q^{73} -1118.70 q^{74} +874.722 q^{75} +1465.79 q^{76} -220.795 q^{77} -1795.08 q^{78} -1135.31 q^{79} -1320.20 q^{80} -46.0047 q^{81} +27.8964 q^{82} -201.036 q^{83} +1912.87 q^{84} +472.702 q^{85} -387.807 q^{86} -1603.90 q^{87} -1924.27 q^{88} -180.375 q^{89} +1084.03 q^{90} +376.823 q^{91} +1415.37 q^{92} +2340.13 q^{93} -1915.31 q^{94} -284.083 q^{95} +7952.66 q^{96} +628.015 q^{97} +1379.44 q^{98} +964.951 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.59440	−1.97792	−0.988960	−	0.148180i	$-0.952659\pi$
$2$	−5.59440	−1.97792	−0.988960	+	0.148180i	$0.952659\pi$
$3$	−8.36152	−1.60918	−0.804588	−	0.593834i	$-0.797614\pi$
$3$	−8.36152	−1.60918	−0.804588	+	0.593834i	$0.797614\pi$
$4$	23.2974	2.91217
$5$	−4.51522	−0.403853	−0.201927	−	0.979401i	$-0.564720\pi$
$5$	−4.51522	−0.403853	−0.201927	+	0.979401i	$0.564720\pi$
$6$	46.7777	3.18282
$7$	−9.81959	−0.530208	−0.265104	−	0.964220i	$-0.585406\pi$
$7$	−9.81959	−0.530208	−0.265104	+	0.964220i	$0.585406\pi$
$8$	−85.5797	−3.78212
$9$	42.9151	1.58945
$10$	25.2599	0.798790
$11$	22.4851	0.616320	0.308160	−	0.951334i	$-0.400287\pi$
$11$	22.4851	0.616320	0.308160	+	0.951334i	$0.400287\pi$
$12$	−194.801	−4.68619
$13$	−38.3746	−0.818708	−0.409354	−	0.912376i	$-0.634246\pi$
$13$	−38.3746	−0.818708	−0.409354	+	0.912376i	$0.634246\pi$
$14$	54.9348	1.04871
$15$	37.7541	0.649871
$16$	292.388	4.56857
$17$	−104.691	−1.49360	−0.746802	−	0.665046i	$-0.768412\pi$
$17$	−104.691	−1.49360	−0.746802	+	0.665046i	$0.768412\pi$
$18$	−240.084	−3.14380
$19$	62.9168	0.759689	0.379845	−	0.925050i	$-0.375977\pi$
$19$	62.9168	0.759689	0.379845	+	0.925050i	$0.375977\pi$
$20$	−105.193	−1.17609
$21$	82.1068	0.853198
$22$	−125.791	−1.21903
$23$	60.7523	0.550771	0.275385	−	0.961334i	$-0.411195\pi$
$23$	60.7523	0.550771	0.275385	+	0.961334i	$0.411195\pi$
$24$	715.576	6.08610
$25$	−104.613	−0.836903
$26$	214.683	1.61934
$27$	−133.074	−0.948523
$28$	−228.771	−1.54406
$29$	191.820	1.22828	0.614138	−	0.789198i	$-0.289504\pi$
$29$	191.820	1.22828	0.614138	+	0.789198i	$0.289504\pi$
$30$	−211.212	−1.28539
$31$	−279.869	−1.62148	−0.810740	−	0.585406i	$-0.800935\pi$
$31$	−279.869	−1.62148	−0.810740	+	0.585406i	$0.800935\pi$
$32$	−951.102	−5.25414
$33$	−188.010	−0.991768
$34$	585.683	2.95423
$35$	44.3376	0.214126
$36$	999.808	4.62874
$37$	199.967	0.888496	0.444248	−	0.895904i	$-0.353471\pi$
$37$	199.967	0.888496	0.444248	+	0.895904i	$0.353471\pi$
$38$	−351.982	−1.50261
$39$	320.870	1.31744
$40$	386.411	1.52742
$41$	−4.98648	−0.0189941	−0.00949704	−	0.999955i	$-0.503023\pi$
$41$	−4.98648	−0.0189941	−0.00949704	+	0.999955i	$0.503023\pi$
$42$	−459.338	−1.68756
$43$	69.3206	0.245844	0.122922	−	0.992416i	$-0.460774\pi$
$43$	69.3206	0.245844	0.122922	+	0.992416i	$0.460774\pi$
$44$	523.845	1.79483
$45$	−193.771	−0.641903
$46$	−339.873	−1.08938
$47$	342.363	1.06253	0.531263	−	0.847207i	$-0.321718\pi$
$47$	342.363	1.06253	0.531263	+	0.847207i	$0.321718\pi$
$48$	−2444.81	−7.35163
$49$	−246.576	−0.718879
$50$	585.247	1.65533
$51$	875.375	2.40347
$52$	−894.027	−2.38422
$53$	−307.469	−0.796869	−0.398434	−	0.917197i	$-0.630446\pi$
$53$	−307.469	−0.796869	−0.398434	+	0.917197i	$0.630446\pi$
$54$	744.470	1.87610
$55$	−101.525	−0.248903
$56$	840.358	2.00531
$57$	−526.080	−1.22247
$58$	−1073.12	−2.42943
$59$	761.526	1.68038	0.840188	−	0.542295i	$-0.182444\pi$
$59$	761.526	1.68038	0.840188	+	0.542295i	$0.182444\pi$
$60$	879.571	1.89253
$61$	−725.327	−1.52244	−0.761219	−	0.648495i	$-0.775399\pi$
$61$	−725.327	−1.52244	−0.761219	+	0.648495i	$0.775399\pi$
$62$	1565.70	3.20716
$63$	−421.408	−0.842738
$64$	2981.74	5.82371
$65$	173.270	0.330638
$66$	1051.80	1.96164
$67$	8.42525	0.0153628	0.00768141	−	0.999970i	$-0.497555\pi$
$67$	8.42525	0.0153628	0.00768141	+	0.999970i	$0.497555\pi$
$68$	−2439.02	−4.34963
$69$	−507.982	−0.886287
$70$	−248.042	−0.423525
$71$	−670.699	−1.12109	−0.560544	−	0.828125i	$-0.689408\pi$
$71$	−670.699	−1.12109	−0.560544	+	0.828125i	$0.689408\pi$
$72$	−3672.66	−6.01148
$73$	−881.638	−1.41353	−0.706767	−	0.707447i	$-0.749847\pi$
$73$	−881.638	−1.41353	−0.706767	+	0.707447i	$0.749847\pi$
$74$	−1118.70	−1.75737
$75$	874.722	1.34672
$76$	1465.79	2.21234
$77$	−220.795	−0.326778
$78$	−1795.08	−2.60580
$79$	−1135.31	−1.61687	−0.808434	−	0.588587i	$-0.799684\pi$
$79$	−1135.31	−1.61687	−0.808434	+	0.588587i	$0.799684\pi$
$80$	−1320.20	−1.84503
$81$	−46.0047	−0.0631065
$82$	27.8964	0.0375688
$83$	−201.036	−0.265862	−0.132931	−	0.991125i	$-0.542439\pi$
$83$	−201.036	−0.265862	−0.132931	+	0.991125i	$0.542439\pi$
$84$	1912.87	2.48466
$85$	472.702	0.603197
$86$	−387.807	−0.486260
$87$	−1603.90	−1.97651
$88$	−1924.27	−2.33100
$89$	−180.375	−0.214828	−0.107414	−	0.994214i	$-0.534257\pi$
$89$	−180.375	−0.214828	−0.107414	+	0.994214i	$0.534257\pi$
$90$	1084.03	1.26963
$91$	376.823	0.434086
$92$	1415.37	1.60394
$93$	2340.13	2.60925
$94$	−1915.31	−2.10159
$95$	−284.083	−0.306803
$96$	7952.66	8.45484
$97$	628.015	0.657374	0.328687	−	0.944439i	$-0.393394\pi$
$97$	628.015	0.657374	0.328687	+	0.944439i	$0.393394\pi$
$98$	1379.44	1.42189
$99$	964.951	0.979608
$100$	−2437.20	−2.43720
$101$	957.067	0.942888	0.471444	−	0.881896i	$-0.343733\pi$
$101$	957.067	0.942888	0.471444	+	0.881896i	$0.343733\pi$
$102$	−4897.20	−4.75388
$103$	−1225.41	−1.17226	−0.586131	−	0.810216i	$-0.699350\pi$
$103$	−1225.41	−1.17226	−0.586131	+	0.810216i	$0.699350\pi$
$104$	3284.09	3.09645
$105$	−370.730	−0.344567
$106$	1720.10	1.57614
$107$	740.535	0.669067	0.334534	−	0.942384i	$-0.391421\pi$
$107$	740.535	0.669067	0.334534	+	0.942384i	$0.391421\pi$
$108$	−3100.28	−2.76226
$109$	2171.98	1.90860	0.954301	−	0.298846i	$-0.0966015\pi$
$109$	2171.98	1.90860	0.954301	+	0.298846i	$0.0966015\pi$
$110$	567.973	0.492310
$111$	−1672.03	−1.42975
$112$	−2871.13	−2.42229
$113$	103.817	0.0864276	0.0432138	−	0.999066i	$-0.486240\pi$
$113$	103.817	0.0864276	0.0432138	+	0.999066i	$0.486240\pi$
$114$	2943.10	2.41796
$115$	−274.310	−0.222430
$116$	4468.89	3.57695
$117$	−1646.85	−1.30129
$118$	−4260.28	−3.32365
$119$	1028.02	0.791921
$120$	−3230.98	−2.45789
$121$	−825.418	−0.620149
$122$	4057.78	3.01126
$123$	41.6945	0.0305648
$124$	−6520.20	−4.72203
$125$	1036.75	0.741839
$126$	2357.53	1.66687
$127$	1694.66	1.18407	0.592033	−	0.805914i	$-0.298325\pi$
$127$	1694.66	1.18407	0.592033	+	0.805914i	$0.298325\pi$
$128$	−9072.25	−6.26470
$129$	−579.626	−0.395606
$130$	−969.340	−0.653975
$131$	2547.01	1.69872	0.849362	−	0.527810i	$-0.176987\pi$
$131$	2547.01	1.69872	0.849362	+	0.527810i	$0.176987\pi$
$132$	−4380.14	−2.88820
$133$	−617.817	−0.402794
$134$	−47.1343	−0.0303864
$135$	600.858	0.383064
$136$	8959.41	5.64899
$137$	1446.01	0.901757	0.450879	−	0.892585i	$-0.351111\pi$
$137$	1446.01	0.901757	0.450879	+	0.892585i	$0.351111\pi$
$138$	2841.85	1.75301
$139$	1440.60	0.879063	0.439531	−	0.898227i	$-0.355145\pi$
$139$	1440.60	0.879063	0.439531	+	0.898227i	$0.355145\pi$
$140$	1032.95	0.623572
$141$	−2862.67	−1.70979
$142$	3752.16	2.21742
$143$	−862.859	−0.504586
$144$	12547.9	7.26149
$145$	−866.107	−0.496043
$146$	4932.24	2.79586
$147$	2061.75	1.15680
$148$	4658.70	2.58745
$149$	−1803.97	−0.991859	−0.495930	−	0.868363i	$-0.665173\pi$
$149$	−1803.97	−0.991859	−0.495930	+	0.868363i	$0.665173\pi$
$150$	−4893.55	−2.66371
$151$	1394.55	0.751570	0.375785	−	0.926707i	$-0.377373\pi$
$151$	1394.55	0.751570	0.375785	+	0.926707i	$0.377373\pi$
$152$	−5384.40	−2.87324
$153$	−4492.82	−2.37400
$154$	1235.22	0.646341
$155$	1263.67	0.654840
$156$	7475.43	3.83662
$157$	1661.94	0.844824	0.422412	−	0.906404i	$-0.361184\pi$
$157$	1661.94	0.844824	0.422412	+	0.906404i	$0.361184\pi$
$158$	6351.39	3.19804
$159$	2570.91	1.28230
$160$	4294.43	2.12190
$161$	−596.563	−0.292023
$162$	257.369	0.124820
$163$	−791.981	−0.380569	−0.190285	−	0.981729i	$-0.560941\pi$
$163$	−791.981	−0.380569	−0.190285	+	0.981729i	$0.560941\pi$
$164$	−116.172	−0.0553140
$165$	848.906	0.400529
$166$	1124.68	0.525854
$167$	3375.24	1.56398	0.781989	−	0.623292i	$-0.214205\pi$
$167$	3375.24	1.56398	0.781989	+	0.623292i	$0.214205\pi$
$168$	−7026.67	−3.22690
$169$	−724.389	−0.329717
$170$	−2644.49	−1.19308
$171$	2700.08	1.20749
$172$	1614.99	0.715940
$173$	−149.473	−0.0656890	−0.0328445	−	0.999460i	$-0.510457\pi$
$173$	−149.473	−0.0656890	−0.0328445	+	0.999460i	$0.510457\pi$
$174$	8972.89	3.90939
$175$	1027.26	0.443733
$176$	6574.39	2.81570
$177$	−6367.51	−2.70402
$178$	1009.09	0.424913
$179$	−826.193	−0.344986	−0.172493	−	0.985011i	$-0.555182\pi$
$179$	−826.193	−0.344986	−0.172493	+	0.985011i	$0.555182\pi$
$180$	−4514.35	−1.86933
$181$	2588.26	1.06290	0.531448	−	0.847091i	$-0.321648\pi$
$181$	2588.26	1.06290	0.531448	+	0.847091i	$0.321648\pi$
$182$	−2108.10	−0.858587
$183$	6064.84	2.44987
$184$	−5199.16	−2.08308
$185$	−902.893	−0.358822
$186$	−13091.6	−5.16088
$187$	−2353.99	−0.920539
$188$	7976.15	3.09426
$189$	1306.73	0.502915
$190$	1589.27	0.606832
$191$	−660.056	−0.250052	−0.125026	−	0.992153i	$-0.539901\pi$
$191$	−660.056	−0.250052	−0.125026	+	0.992153i	$0.539901\pi$
$192$	−24931.9	−9.37137
$193$	3503.42	1.30664	0.653321	−	0.757081i	$-0.273375\pi$
$193$	3503.42	1.30664	0.653321	+	0.757081i	$0.273375\pi$
$194$	−3513.37	−1.30023
$195$	−1448.80	−0.532054
$196$	−5744.56	−2.09350
$197$	931.407	0.336853	0.168426	−	0.985714i	$-0.446131\pi$
$197$	931.407	0.336853	0.168426	+	0.985714i	$0.446131\pi$
$198$	−5398.33	−1.93759
$199$	−3479.66	−1.23953	−0.619764	−	0.784788i	$-0.712772\pi$
$199$	−3479.66	−1.23953	−0.619764	+	0.784788i	$0.712772\pi$
$200$	8952.73	3.16527
$201$	−70.4479	−0.0247215
$202$	−5354.22	−1.86496
$203$	−1883.59	−0.651243
$204$	20393.9	6.99932
$205$	22.5150	0.00767082
$206$	6855.42	2.31864
$207$	2607.19	0.875420
$208$	−11220.3	−3.74032
$209$	1414.69	0.468212
$210$	2074.01	0.681526
$211$	1678.98	0.547800	0.273900	−	0.961758i	$-0.411686\pi$
$211$	1678.98	0.547800	0.273900	+	0.961758i	$0.411686\pi$
$212$	−7163.21	−2.32062
$213$	5608.06	1.80403
$214$	−4142.85	−1.32336
$215$	−312.997	−0.0992848
$216$	11388.4	3.58743
$217$	2748.20	0.859722
$218$	−12150.9	−3.77507
$219$	7371.84	2.27462
$220$	−2365.27	−0.724848
$221$	4017.47	1.22283
$222$	9354.00	2.82792
$223$	−1544.21	−0.463714	−0.231857	−	0.972750i	$-0.574480\pi$
$223$	−1544.21	−0.463714	−0.231857	+	0.972750i	$0.574480\pi$
$224$	9339.43	2.78579
$225$	−4489.47	−1.33021
$226$	−580.797	−0.170947
$227$	−3636.90	−1.06339	−0.531695	−	0.846936i	$-0.678445\pi$
$227$	−3636.90	−1.06339	−0.531695	+	0.846936i	$0.678445\pi$
$228$	−12256.3	−3.56005
$229$	2603.21	0.751201	0.375600	−	0.926782i	$-0.377437\pi$
$229$	2603.21	0.751201	0.375600	+	0.926782i	$0.377437\pi$
$230$	1534.60	0.439950
$231$	1846.18	0.525844
$232$	−16415.9	−4.64549
$233$	−1120.11	−0.314939	−0.157470	−	0.987524i	$-0.550334\pi$
$233$	−1120.11	−0.314939	−0.157470	+	0.987524i	$0.550334\pi$
$234$	9213.14	2.57385
$235$	−1545.84	−0.429104
$236$	17741.5	4.89354
$237$	9492.93	2.60182
$238$	−5751.17	−1.56636
$239$	4287.31	1.16035	0.580174	−	0.814492i	$-0.302984\pi$
$239$	4287.31	1.16035	0.580174	+	0.814492i	$0.302984\pi$
$240$	11038.9	2.96898
$241$	2285.68	0.610927	0.305463	−	0.952204i	$-0.401189\pi$
$241$	2285.68	0.610927	0.305463	+	0.952204i	$0.401189\pi$
$242$	4617.72	1.22661
$243$	3977.67	1.05007
$244$	−16898.2	−4.43360
$245$	1113.34	0.290322
$246$	−233.256	−0.0604548
$247$	−2414.41	−0.621964
$248$	23951.1	6.13264
$249$	1680.96	0.427818
$250$	−5800.01	−1.46730
$251$	6007.68	1.51076	0.755382	−	0.655285i	$-0.227452\pi$
$251$	6007.68	1.51076	0.755382	+	0.655285i	$0.227452\pi$
$252$	−9817.71	−2.45420
$253$	1366.02	0.339451
$254$	−9480.59	−2.34199
$255$	−3952.51	−0.970650
$256$	26899.9	6.56736
$257$	7486.58	1.81712	0.908560	−	0.417755i	$-0.137183\pi$
$257$	7486.58	1.81712	0.908560	+	0.417755i	$0.137183\pi$
$258$	3242.66	0.782477
$259$	−1963.59	−0.471088
$260$	4036.73	0.962874
$261$	8231.95	1.95228
$262$	−14249.0	−3.35994
$263$	3836.94	0.899603	0.449802	−	0.893128i	$-0.351495\pi$
$263$	3836.94	0.899603	0.449802	+	0.893128i	$0.351495\pi$
$264$	16089.8	3.75099
$265$	1388.29	0.321818
$266$	3456.32	0.796694
$267$	1508.21	0.345696
$268$	196.286	0.0447391
$269$	−6154.34	−1.39493	−0.697466	−	0.716618i	$-0.745689\pi$
$269$	−6154.34	−1.39493	−0.697466	+	0.716618i	$0.745689\pi$
$270$	−3361.44	−0.757670
$271$	−3459.88	−0.775546	−0.387773	−	0.921755i	$-0.626756\pi$
$271$	−3459.88	−0.775546	−0.387773	+	0.921755i	$0.626756\pi$
$272$	−30610.4	−6.82363
$273$	−3150.81	−0.698520
$274$	−8089.55	−1.78360
$275$	−2352.23	−0.515800
$276$	−11834.6	−2.58102
$277$	4166.96	0.903857	0.451928	−	0.892054i	$-0.350736\pi$
$277$	4166.96	0.903857	0.451928	+	0.892054i	$0.350736\pi$
$278$	−8059.28	−1.73872
$279$	−12010.6	−2.57726
$280$	−3794.40	−0.809852
$281$	−4177.99	−0.886968	−0.443484	−	0.896282i	$-0.646258\pi$
$281$	−4177.99	−0.886968	−0.443484	+	0.896282i	$0.646258\pi$
$282$	16014.9	3.38183
$283$	−7368.71	−1.54779	−0.773895	−	0.633314i	$-0.781694\pi$
$283$	−7368.71	−1.54779	−0.773895	+	0.633314i	$0.781694\pi$
$284$	−15625.5	−3.26480
$285$	2375.36	0.493700
$286$	4827.18	0.998032
$287$	48.9652	0.0100708
$288$	−40816.6	−8.35118
$289$	6047.19	1.23085
$290$	4845.36	0.981135
$291$	−5251.16	−1.05783
$292$	−20539.8	−4.11645
$293$	4023.52	0.802240	0.401120	−	0.916026i	$-0.368621\pi$
$293$	4023.52	0.802240	0.401120	+	0.916026i	$0.368621\pi$
$294$	−11534.2	−2.28806
$295$	−3438.45	−0.678625
$296$	−17113.1	−3.36040
$297$	−2992.19	−0.584594
$298$	10092.1	1.96182
$299$	−2331.34	−0.450920
$300$	20378.7	3.92189
$301$	−680.700	−0.130348
$302$	−7801.69	−1.48655
$303$	−8002.53	−1.51727
$304$	18396.1	3.47069
$305$	3275.01	0.614841
$306$	25134.6	4.69559
$307$	8772.85	1.63092	0.815461	−	0.578812i	$-0.196483\pi$
$307$	8772.85	1.63092	0.815461	+	0.578812i	$0.196483\pi$
$308$	−5143.94	−0.951634
$309$	10246.3	1.88637
$310$	−7069.47	−1.29522
$311$	−1863.56	−0.339785	−0.169892	−	0.985463i	$-0.554342\pi$
$311$	−1863.56	−0.339785	−0.169892	+	0.985463i	$0.554342\pi$
$312$	−27460.0	−4.98274
$313$	6505.63	1.17482	0.587412	−	0.809288i	$-0.300147\pi$
$313$	6505.63	1.17482	0.587412	+	0.809288i	$0.300147\pi$
$314$	−9297.57	−1.67099
$315$	1902.75	0.340342
$316$	−26449.8	−4.70859
$317$	1304.65	0.231156	0.115578	−	0.993298i	$-0.463128\pi$
$317$	1304.65	0.231156	0.115578	+	0.993298i	$0.463128\pi$
$318$	−14382.7	−2.53629
$319$	4313.09	0.757012
$320$	−13463.2	−2.35192
$321$	−6192.00	−1.07665
$322$	3337.41	0.577599
$323$	−6586.81	−1.13468
$324$	−1071.79	−0.183777
$325$	4014.48	0.685179
$326$	4430.66	0.752736
$327$	−18161.0	−3.07128
$328$	426.741	0.0718379
$329$	−3361.86	−0.563360
$330$	−4749.12	−0.792214
$331$	−2795.96	−0.464289	−0.232144	−	0.972681i	$-0.574574\pi$
$331$	−2795.96	−0.464289	−0.232144	+	0.972681i	$0.574574\pi$
$332$	−4683.60	−0.774235
$333$	8581.59	1.41222
$334$	−18882.5	−3.09342
$335$	−38.0418	−0.00620432
$336$	24007.1	3.89789
$337$	−2681.48	−0.433441	−0.216721	−	0.976234i	$-0.569536\pi$
$337$	−2681.48	−0.433441	−0.216721	+	0.976234i	$0.569536\pi$
$338$	4052.53	0.652155
$339$	−868.072	−0.139077
$340$	11012.7	1.75661
$341$	−6292.89	−0.999351
$342$	−15105.3	−2.38831
$343$	5789.39	0.911364
$344$	−5932.43	−0.929812
$345$	2293.65	0.357930
$346$	836.211	0.129928
$347$	−1466.34	−0.226851	−0.113426	−	0.993546i	$-0.536182\pi$
$347$	−1466.34	−0.226851	−0.113426	+	0.993546i	$0.536182\pi$
$348$	−37366.8	−5.75594
$349$	164.216	0.0251871	0.0125935	−	0.999921i	$-0.495991\pi$
$349$	164.216	0.0251871	0.0125935	+	0.999921i	$0.495991\pi$
$350$	−5746.88	−0.877668
$351$	5106.67	0.776563
$352$	−21385.7	−3.23824
$353$	−4936.25	−0.744278	−0.372139	−	0.928177i	$-0.621376\pi$
$353$	−4936.25	−0.744278	−0.372139	+	0.928177i	$0.621376\pi$
$354$	35622.5	5.34834
$355$	3028.35	0.452755
$356$	−4202.26	−0.625616
$357$	−8595.83	−1.27434
$358$	4622.06	0.682356
$359$	5925.57	0.871141	0.435571	−	0.900155i	$-0.356547\pi$
$359$	5925.57	0.871141	0.435571	+	0.900155i	$0.356547\pi$
$360$	16582.8	2.42776
$361$	−2900.48	−0.422872
$362$	−14479.8	−2.10232
$363$	6901.75	0.997929
$364$	8778.99	1.26413
$365$	3980.79	0.570860
$366$	−33929.2	−4.84565
$367$	−3424.07	−0.487016	−0.243508	−	0.969899i	$-0.578298\pi$
$367$	−3424.07	−0.487016	−0.243508	+	0.969899i	$0.578298\pi$
$368$	17763.3	2.51623
$369$	−213.995	−0.0301901
$370$	5051.15	0.709721
$371$	3019.22	0.422506
$372$	54518.8	7.59857
$373$	−4108.67	−0.570346	−0.285173	−	0.958476i	$-0.592051\pi$
$373$	−4108.67	−0.570346	−0.285173	+	0.958476i	$0.592051\pi$
$374$	13169.2	1.82075
$375$	−8668.82	−1.19375
$376$	−29299.3	−4.01860
$377$	−7361.01	−1.00560
$378$	−7310.40	−0.994725
$379$	−9071.99	−1.22954	−0.614771	−	0.788705i	$-0.710752\pi$
$379$	−9071.99	−1.22954	−0.614771	+	0.788705i	$0.710752\pi$
$380$	−6618.38	−0.893462
$381$	−14169.9	−1.90537
$382$	3692.62	0.494584
$383$	−4006.86	−0.534572	−0.267286	−	0.963617i	$-0.586127\pi$
$383$	−4006.86	−0.534572	−0.267286	+	0.963617i	$0.586127\pi$
$384$	75857.8	10.0810
$385$	996.937	0.131970
$386$	−19599.6	−2.58443
$387$	2974.90	0.390756
$388$	14631.1	1.91439
$389$	8479.13	1.10516	0.552582	−	0.833458i	$-0.313642\pi$
$389$	8479.13	1.10516	0.552582	+	0.833458i	$0.313642\pi$
$390$	8105.16	1.05236
$391$	−6360.21	−0.822634
$392$	21101.9	2.71889
$393$	−21296.8	−2.73355
$394$	−5210.67	−0.666268
$395$	5126.18	0.652977
$396$	22480.8	2.85279
$397$	6373.70	0.805760	0.402880	−	0.915253i	$-0.368009\pi$
$397$	6373.70	0.805760	0.402880	+	0.915253i	$0.368009\pi$
$398$	19466.6	2.45169
$399$	5165.89	0.648166
$400$	−30587.6	−3.82345
$401$	−1067.38	−0.132923	−0.0664617	−	0.997789i	$-0.521171\pi$
$401$	−1067.38	−0.132923	−0.0664617	+	0.997789i	$0.521171\pi$
$402$	394.114	0.0488971
$403$	10739.8	1.32752
$404$	22297.1	2.74585
$405$	207.721	0.0254858
$406$	10537.6	1.28811
$407$	4496.28	0.547598
$408$	−74914.3	−9.09023
$409$	−13584.3	−1.64231	−0.821153	−	0.570709i	$-0.806669\pi$
$409$	−13584.3	−1.64231	−0.821153	+	0.570709i	$0.806669\pi$
$410$	−125.958	−0.0151723
$411$	−12090.8	−1.45109
$412$	−28548.8	−3.41383
$413$	−7477.87	−0.890949
$414$	−14585.7	−1.73151
$415$	907.720	0.107369
$416$	36498.1	4.30161
$417$	−12045.6	−1.41457
$418$	−7914.36	−0.926086
$419$	−2034.43	−0.237204	−0.118602	−	0.992942i	$-0.537841\pi$
$419$	−2034.43	−0.237204	−0.118602	+	0.992942i	$0.537841\pi$
$420$	−8637.03	−1.00344
$421$	15400.8	1.78288	0.891438	−	0.453142i	$-0.149697\pi$
$421$	15400.8	1.78288	0.891438	+	0.453142i	$0.149697\pi$
$422$	−9392.90	−1.08350
$423$	14692.5	1.68883
$424$	26313.1	3.01386
$425$	10952.0	1.25000
$426$	−31373.8	−3.56822
$427$	7122.42	0.807209
$428$	17252.5	1.94844
$429$	7214.81	0.811968
$430$	1751.03	0.196378
$431$	1336.96	0.149418	0.0747088	−	0.997205i	$-0.476197\pi$
$431$	1336.96	0.149418	0.0747088	+	0.997205i	$0.476197\pi$
$432$	−38909.3	−4.33339
$433$	−9690.87	−1.07555	−0.537775	−	0.843088i	$-0.680735\pi$
$433$	−9690.87	−1.07555	−0.537775	+	0.843088i	$0.680735\pi$
$434$	−15374.5	−1.70046
$435$	7241.98	0.798221
$436$	50601.4	5.55818
$437$	3822.34	0.418415
$438$	−41241.0	−4.49903
$439$	−4014.04	−0.436400	−0.218200	−	0.975904i	$-0.570019\pi$
$439$	−4014.04	−0.436400	−0.218200	+	0.975904i	$0.570019\pi$
$440$	8688.50	0.941381
$441$	−10581.8	−1.14262
$442$	−22475.4	−2.41865
$443$	−14188.1	−1.52167	−0.760833	−	0.648948i	$-0.775209\pi$
$443$	−14188.1	−1.52167	−0.760833	+	0.648948i	$0.775209\pi$
$444$	−38953.8	−4.16366
$445$	814.432	0.0867591
$446$	8638.96	0.917190
$447$	15083.9	1.59608
$448$	−29279.5	−3.08778
$449$	11788.0	1.23900	0.619499	−	0.784997i	$-0.287336\pi$
$449$	11788.0	1.23900	0.619499	+	0.784997i	$0.287336\pi$
$450$	25115.9	2.63105
$451$	−112.122	−0.0117064
$452$	2418.67	0.251692
$453$	−11660.6	−1.20941
$454$	20346.3	2.10330
$455$	−1701.44	−0.175307
$456$	45021.7	4.62354
$457$	202.402	0.0207177	0.0103589	−	0.999946i	$-0.496703\pi$
$457$	202.402	0.0207177	0.0103589	+	0.999946i	$0.496703\pi$
$458$	−14563.4	−1.48582
$459$	13931.6	1.41672
$460$	−6390.69	−0.647756
$461$	−9205.38	−0.930016	−0.465008	−	0.885306i	$-0.653949\pi$
$461$	−9205.38	−0.930016	−0.465008	+	0.885306i	$0.653949\pi$
$462$	−10328.3	−1.04008
$463$	1949.71	0.195703	0.0978515	−	0.995201i	$-0.468803\pi$
$463$	1949.71	0.195703	0.0978515	+	0.995201i	$0.468803\pi$
$464$	56085.9	5.61147
$465$	−10566.2	−1.05375
$466$	6266.34	0.622924
$467$	−13273.4	−1.31524	−0.657621	−	0.753349i	$-0.728437\pi$
$467$	−13273.4	−1.31524	−0.657621	+	0.753349i	$0.728437\pi$
$468$	−38367.2	−3.78959
$469$	−82.7326	−0.00814549
$470$	8648.06	0.848734
$471$	−13896.4	−1.35947
$472$	−65171.1	−6.35539
$473$	1558.68	0.151519
$474$	−53107.3	−5.14620
$475$	−6581.90	−0.635786
$476$	23950.2	2.30621
$477$	−13195.0	−1.26658
$478$	−23985.0	−2.29508
$479$	−19264.9	−1.83765	−0.918826	−	0.394663i	$-0.870861\pi$
$479$	−19264.9	−1.83765	−0.918826	+	0.394663i	$0.870861\pi$
$480$	−35908.0	−3.41451
$481$	−7673.65	−0.727418
$482$	−12787.0	−1.20836
$483$	4988.17	0.469917
$484$	−19230.1	−1.80598
$485$	−2835.62	−0.265483
$486$	−22252.7	−2.07696
$487$	11283.7	1.04993	0.524963	−	0.851125i	$-0.324079\pi$
$487$	11283.7	1.04993	0.524963	+	0.851125i	$0.324079\pi$
$488$	62073.3	5.75804
$489$	6622.17	0.612403
$490$	−6228.49	−0.574233
$491$	7562.17	0.695063	0.347531	−	0.937668i	$-0.387020\pi$
$491$	7562.17	0.695063	0.347531	+	0.937668i	$0.387020\pi$
$492$	971.373	0.0890099
$493$	−20081.8	−1.83456
$494$	13507.2	1.23019
$495$	−4356.96	−0.395618
$496$	−81830.3	−7.40784
$497$	6585.99	0.594410
$498$	−9404.00	−0.846191
$499$	14544.6	1.30482	0.652408	−	0.757868i	$-0.273759\pi$
$499$	14544.6	1.30482	0.652408	+	0.757868i	$0.273759\pi$
$500$	24153.6	2.16036
$501$	−28222.2	−2.51672
$502$	−33609.4	−2.98817
$503$	19399.4	1.71963	0.859817	−	0.510602i	$-0.170577\pi$
$503$	19399.4	1.71963	0.859817	+	0.510602i	$0.170577\pi$
$504$	36064.0	3.18734
$505$	−4321.36	−0.380788
$506$	−7642.09	−0.671408
$507$	6057.00	0.530573
$508$	39481.0	3.44820
$509$	−838.617	−0.0730276	−0.0365138	−	0.999333i	$-0.511625\pi$
$509$	−838.617	−0.0730276	−0.0365138	+	0.999333i	$0.511625\pi$
$510$	22111.9	1.91987
$511$	8657.33	0.749467
$512$	−77911.0	−6.72503
$513$	−8372.59	−0.720583
$514$	−41882.9	−3.59412
$515$	5532.98	0.473422
$516$	−13503.7	−1.15207
$517$	7698.07	0.654856
$518$	10985.1	0.931774
$519$	1249.82	0.105705
$520$	−14828.4	−1.25051
$521$	−2470.69	−0.207760	−0.103880	−	0.994590i	$-0.533126\pi$
$521$	−2470.69	−0.207760	−0.103880	+	0.994590i	$0.533126\pi$
$522$	−46052.9	−3.86146
$523$	−21408.5	−1.78992	−0.894959	−	0.446149i	$-0.852795\pi$
$523$	−21408.5	−1.78992	−0.894959	+	0.446149i	$0.852795\pi$
$524$	59338.5	4.94698
$525$	−8589.42	−0.714044
$526$	−21465.4	−1.77934
$527$	29299.7	2.42185
$528$	−54971.9	−4.53096
$529$	−8476.16	−0.696652
$530$	−7766.64	−0.636531
$531$	32680.9	2.67087
$532$	−14393.5	−1.17300
$533$	191.354	0.0155506
$534$	−8437.53	−0.683760
$535$	−3343.67	−0.270205
$536$	−721.030	−0.0581040
$537$	6908.23	0.555144
$538$	34429.9	2.75907
$539$	−5544.29	−0.443060
$540$	13998.4	1.11555
$541$	−17767.8	−1.41201	−0.706006	−	0.708206i	$-0.749505\pi$
$541$	−17767.8	−1.41201	−0.706006	+	0.708206i	$0.749505\pi$
$542$	19356.0	1.53397
$543$	−21641.8	−1.71039
$544$	99571.7	7.84761
$545$	−9806.95	−0.770795
$546$	17626.9	1.38162
$547$	13956.7	1.09094	0.545472	−	0.838129i	$-0.316350\pi$
$547$	13956.7	1.09094	0.545472	+	0.838129i	$0.316350\pi$
$548$	33688.2	2.62607
$549$	−31127.5	−2.41983
$550$	13159.4	1.02021
$551$	12068.7	0.933109
$552$	43472.9	3.35205
$553$	11148.3	0.857276
$554$	−23311.7	−1.78776
$555$	7549.56	0.577407
$556$	33562.1	2.55998
$557$	4295.55	0.326765	0.163383	−	0.986563i	$-0.447760\pi$
$557$	4295.55	0.326765	0.163383	+	0.986563i	$0.447760\pi$
$558$	67192.0	5.09761
$559$	−2660.15	−0.201274
$560$	12963.8	0.978250
$561$	19682.9	1.48131
$562$	23373.4	1.75435
$563$	18448.0	1.38098	0.690488	−	0.723344i	$-0.257396\pi$
$563$	18448.0	1.38098	0.690488	+	0.723344i	$0.257396\pi$
$564$	−66692.7	−4.97920
$565$	−468.758	−0.0349041
$566$	41223.6	3.06141
$567$	451.747	0.0334596
$568$	57398.2	4.24009
$569$	23370.2	1.72184	0.860921	−	0.508738i	$-0.169888\pi$
$569$	23370.2	1.72184	0.860921	+	0.508738i	$0.169888\pi$
$570$	−13288.8	−0.976499
$571$	6006.46	0.440215	0.220107	−	0.975476i	$-0.429359\pi$
$571$	6006.46	0.440215	0.220107	+	0.975476i	$0.429359\pi$
$572$	−20102.3	−1.46944
$573$	5519.07	0.402378
$574$	−273.931	−0.0199193
$575$	−6355.47	−0.460941
$576$	127962.	9.25648
$577$	−6123.37	−0.441801	−0.220900	−	0.975296i	$-0.570900\pi$
$577$	−6123.37	−0.441801	−0.220900	+	0.975296i	$0.570900\pi$
$578$	−33830.4	−2.43453
$579$	−29293.9	−2.10262
$580$	−20178.0	−1.44456
$581$	1974.09	0.140962
$582$	29377.1	2.09230
$583$	−6913.47	−0.491127
$584$	75450.3	5.34616
$585$	7435.88	0.525531
$586$	−22509.2	−1.58677
$587$	−5177.80	−0.364072	−0.182036	−	0.983292i	$-0.558269\pi$
$587$	−5177.80	−0.364072	−0.182036	+	0.983292i	$0.558269\pi$
$588$	48033.3	3.36881
$589$	−17608.4	−1.23182
$590$	19236.1	1.34227
$591$	−7787.98	−0.542056
$592$	58468.0	4.05915
$593$	25022.9	1.73283	0.866413	−	0.499328i	$-0.166420\pi$
$593$	25022.9	1.73283	0.866413	+	0.499328i	$0.166420\pi$
$594$	16739.5	1.15628
$595$	−4641.74	−0.319820
$596$	−42027.8	−2.88846
$597$	29095.2	1.99462
$598$	13042.5	0.891885
$599$	−4159.49	−0.283726	−0.141863	−	0.989886i	$-0.545309\pi$
$599$	−4159.49	−0.283726	−0.141863	+	0.989886i	$0.545309\pi$
$600$	−74858.5	−5.09347
$601$	15468.5	1.04987	0.524936	−	0.851142i	$-0.324089\pi$
$601$	15468.5	1.04987	0.524936	+	0.851142i	$0.324089\pi$
$602$	3808.11	0.257819
$603$	361.570	0.0244184
$604$	32489.4	2.18870
$605$	3726.94	0.250449
$606$	44769.4	3.00104
$607$	3222.10	0.215455	0.107727	−	0.994180i	$-0.465643\pi$
$607$	3222.10	0.215455	0.107727	+	0.994180i	$0.465643\pi$
$608$	−59840.2	−3.99152
$609$	15749.7	1.04796
$610$	−18321.7	−1.21611
$611$	−13138.0	−0.869898
$612$	−104671.	−6.91351
$613$	5840.71	0.384835	0.192418	−	0.981313i	$-0.438367\pi$
$613$	5840.71	0.384835	0.192418	+	0.981313i	$0.438367\pi$
$614$	−49078.9	−3.22584
$615$	−188.260	−0.0123437
$616$	18895.6	1.23592
$617$	61.0466	0.00398321	0.00199161	−	0.999998i	$-0.499366\pi$
$617$	61.0466	0.00398321	0.00199161	+	0.999998i	$0.499366\pi$
$618$	−57321.8	−3.73110
$619$	−24695.2	−1.60353	−0.801763	−	0.597642i	$-0.796105\pi$
$619$	−24695.2	−1.60353	−0.801763	+	0.597642i	$0.796105\pi$
$620$	29440.1	1.90701
$621$	−8084.55	−0.522419
$622$	10425.5	0.672067
$623$	1771.21	0.113904
$624$	93818.7	6.01884
$625$	8395.45	0.537309
$626$	−36395.1	−2.32371
$627$	−11829.0	−0.753435
$628$	38718.9	2.46027
$629$	−20934.7	−1.32706
$630$	−10644.8	−0.673170
$631$	−24193.8	−1.52637	−0.763185	−	0.646180i	$-0.776365\pi$
$631$	−24193.8	−1.52637	−0.763185	+	0.646180i	$0.776365\pi$
$632$	97159.6	6.11519
$633$	−14038.8	−0.881506
$634$	−7298.75	−0.457209
$635$	−7651.74	−0.478189
$636$	59895.3	3.73428
$637$	9462.24	0.588552
$638$	−24129.2	−1.49731
$639$	−28783.1	−1.78191
$640$	40963.2	2.53002
$641$	28605.2	1.76262	0.881310	−	0.472539i	$-0.156662\pi$
$641$	28605.2	1.76262	0.881310	+	0.472539i	$0.156662\pi$
$642$	34640.5	2.12952
$643$	12479.3	0.765377	0.382688	−	0.923877i	$-0.374998\pi$
$643$	12479.3	0.765377	0.382688	+	0.923877i	$0.374998\pi$
$644$	−13898.3	−0.850421
$645$	2617.13	0.159767
$646$	36849.3	2.24430
$647$	−27767.4	−1.68725	−0.843623	−	0.536935i	$-0.819582\pi$
$647$	−27767.4	−1.68725	−0.843623	+	0.536935i	$0.819582\pi$
$648$	3937.06	0.238677
$649$	17123.0	1.03565
$650$	−22458.6	−1.35523
$651$	−22979.1	−1.38344
$652$	−18451.1	−1.10828
$653$	−19256.1	−1.15398	−0.576989	−	0.816752i	$-0.695773\pi$
$653$	−19256.1	−1.15398	−0.576989	+	0.816752i	$0.695773\pi$
$654$	101600.	6.07474
$655$	−11500.3	−0.686035
$656$	−1457.99	−0.0867757
$657$	−37835.5	−2.24674
$658$	18807.6	1.11428
$659$	17328.5	1.02431	0.512157	−	0.858892i	$-0.328846\pi$
$659$	17328.5	1.02431	0.512157	+	0.858892i	$0.328846\pi$
$660$	19777.3	1.16641
$661$	25559.0	1.50398	0.751990	−	0.659174i	$-0.229094\pi$
$661$	25559.0	1.50398	0.751990	+	0.659174i	$0.229094\pi$
$662$	15641.7	0.918327
$663$	−33592.2	−1.96774
$664$	17204.6	1.00552
$665$	2789.58	0.162669
$666$	−48008.9	−2.79325
$667$	11653.5	0.676499
$668$	78634.3	4.55457
$669$	12912.0	0.746197
$670$	212.821	0.0122717
$671$	−16309.1	−0.938309
$672$	−78091.9	−4.48283
$673$	7055.03	0.404088	0.202044	−	0.979376i	$-0.435242\pi$
$673$	7055.03	0.404088	0.202044	+	0.979376i	$0.435242\pi$
$674$	15001.3	0.857313
$675$	13921.3	0.793821
$676$	−16876.4	−0.960194
$677$	−15241.3	−0.865246	−0.432623	−	0.901575i	$-0.642412\pi$
$677$	−15241.3	−0.865246	−0.432623	+	0.901575i	$0.642412\pi$
$678$	4856.34	0.275084
$679$	−6166.85	−0.348545
$680$	−40453.7	−2.28136
$681$	30410.0	1.71118
$682$	35204.9	1.97664
$683$	−10985.3	−0.615435	−0.307717	−	0.951478i	$-0.599565\pi$
$683$	−10985.3	−0.615435	−0.307717	+	0.951478i	$0.599565\pi$
$684$	62904.7	3.51640
$685$	−6529.04	−0.364178
$686$	−32388.2	−1.80261
$687$	−21766.8	−1.20881
$688$	20268.5	1.12315
$689$	11799.0	0.652403
$690$	−12831.6	−0.707957
$691$	−12193.9	−0.671315	−0.335658	−	0.941984i	$-0.608959\pi$
$691$	−12193.9	−0.671315	−0.335658	+	0.941984i	$0.608959\pi$
$692$	−3482.32	−0.191298
$693$	−9475.43	−0.519396
$694$	8203.32	0.448694
$695$	−6504.60	−0.355012
$696$	137262.	7.47542
$697$	522.039	0.0283696
$698$	−918.691	−0.0498180
$699$	9365.82	0.506792
$700$	23932.3	1.29223
$701$	−13204.0	−0.711425	−0.355712	−	0.934595i	$-0.615762\pi$
$701$	−13204.0	−0.711425	−0.355712	+	0.934595i	$0.615762\pi$
$702$	−28568.8	−1.53598
$703$	12581.3	0.674981
$704$	67044.9	3.58927
$705$	12925.6	0.690504
$706$	27615.4	1.47212
$707$	−9398.01	−0.499927
$708$	−148346.	−7.87457
$709$	−24800.5	−1.31368	−0.656841	−	0.754029i	$-0.728108\pi$
$709$	−24800.5	−1.31368	−0.656841	+	0.754029i	$0.728108\pi$
$710$	−16941.8	−0.895514
$711$	−48722.0	−2.56992
$712$	15436.4	0.812507
$713$	−17002.7	−0.893064
$714$	48088.6	2.52054
$715$	3895.99	0.203779
$716$	−19248.1	−1.00466
$717$	−35848.5	−1.86720
$718$	−33150.1	−1.72305
$719$	−8757.26	−0.454229	−0.227115	−	0.973868i	$-0.572929\pi$
$719$	−8757.26	−0.454229	−0.227115	+	0.973868i	$0.572929\pi$
$720$	−56656.3	−2.93258
$721$	12033.0	0.621543
$722$	16226.5	0.836408
$723$	−19111.7	−0.983088
$724$	60299.7	3.09533
$725$	−20066.8	−1.02795
$726$	−38611.2	−1.97382
$727$	−13501.0	−0.688755	−0.344377	−	0.938831i	$-0.611910\pi$
$727$	−13501.0	−0.688755	−0.344377	+	0.938831i	$0.611910\pi$
$728$	−32248.4	−1.64176
$729$	−32017.2	−1.62664
$730$	−22270.1	−1.12912
$731$	−7257.23	−0.367194
$732$	141295.	7.13444
$733$	−10493.8	−0.528782	−0.264391	−	0.964416i	$-0.585171\pi$
$733$	−10493.8	−0.528782	−0.264391	+	0.964416i	$0.585171\pi$
$734$	19155.6	0.963279
$735$	−9309.23	−0.467179
$736$	−57781.6	−2.89383
$737$	189.443	0.00946842
$738$	1197.17	0.0597136
$739$	19203.8	0.955916	0.477958	−	0.878383i	$-0.341377\pi$
$739$	19203.8	0.955916	0.477958	+	0.878383i	$0.341377\pi$
$740$	−21035.0	−1.04495
$741$	20188.1	1.00085
$742$	−16890.7	−0.835684
$743$	10882.1	0.537314	0.268657	−	0.963236i	$-0.413420\pi$
$743$	10882.1	0.537314	0.268657	+	0.963236i	$0.413420\pi$
$744$	−200267.	−9.86849
$745$	8145.32	0.400566
$746$	22985.6	1.12810
$747$	−8627.46	−0.422573
$748$	−54841.8	−2.68077
$749$	−7271.75	−0.354745
$750$	48496.9	2.36114
$751$	3550.93	0.172537	0.0862685	−	0.996272i	$-0.472506\pi$
$751$	3550.93	0.172537	0.0862685	+	0.996272i	$0.472506\pi$
$752$	100103.	4.85422
$753$	−50233.4	−2.43108
$754$	41180.5	1.98900
$755$	−6296.71	−0.303524
$756$	30443.4	1.46457
$757$	29875.7	1.43441	0.717207	−	0.696860i	$-0.245420\pi$
$757$	29875.7	1.43441	0.717207	+	0.696860i	$0.245420\pi$
$758$	50752.4	2.43194
$759$	−11422.0	−0.546237
$760$	24311.7	1.16037
$761$	14484.0	0.689942	0.344971	−	0.938613i	$-0.387889\pi$
$761$	14484.0	0.689942	0.344971	+	0.938613i	$0.387889\pi$
$762$	79272.2	3.76867
$763$	−21327.9	−1.01196
$764$	−15377.6	−0.728195
$765$	20286.0	0.958749
$766$	22416.0	1.05734
$767$	−29223.3	−1.37574
$768$	−224924.	−10.5680
$769$	−36051.8	−1.69059	−0.845293	−	0.534303i	$-0.820574\pi$
$769$	−36051.8	−1.69059	−0.845293	+	0.534303i	$0.820574\pi$
$770$	−5577.27	−0.261027
$771$	−62599.2	−2.92406
$772$	81620.5	3.80516
$773$	−31485.9	−1.46503	−0.732516	−	0.680750i	$-0.761654\pi$
$773$	−31485.9	−1.46503	−0.732516	+	0.680750i	$0.761654\pi$
$774$	−16642.8	−0.772884
$775$	29277.8	1.35702
$776$	−53745.3	−2.48627
$777$	16418.6	0.758063
$778$	−47435.7	−2.18593
$779$	−313.733	−0.0144296
$780$	−33753.2	−1.54943
$781$	−15080.8	−0.690950
$782$	35581.6	1.62710
$783$	−25526.2	−1.16505
$784$	−72095.8	−3.28425
$785$	−7504.02	−0.341185
$786$	119143.	5.40674
$787$	−10899.5	−0.493678	−0.246839	−	0.969057i	$-0.579392\pi$
$787$	−10899.5	−0.493678	−0.246839	+	0.969057i	$0.579392\pi$
$788$	21699.3	0.980973
$789$	−32082.6	−1.44762
$790$	−28677.9	−1.29154
$791$	−1019.44	−0.0458246
$792$	−82580.2	−3.70500
$793$	27834.2	1.24643
$794$	−35657.1	−1.59373
$795$	−11608.2	−0.517862
$796$	−81066.8	−3.60972
$797$	30343.4	1.34858	0.674289	−	0.738468i	$-0.264450\pi$
$797$	30343.4	1.34858	0.674289	+	0.738468i	$0.264450\pi$
$798$	−28900.1	−1.28202
$799$	−35842.2	−1.58699
$800$	99497.4	4.39721
$801$	−7740.80	−0.341458
$802$	5971.34	0.262912
$803$	−19823.8	−0.871190
$804$	−1641.25	−0.0719931
$805$	2693.61	0.117934
$806$	−60083.1	−2.62573
$807$	51459.7	2.24469
$808$	−81905.4	−3.56612
$809$	231.655	0.0100674	0.00503372	−	0.999987i	$-0.498398\pi$
$809$	231.655	0.0100674	0.00503372	+	0.999987i	$0.498398\pi$
$810$	−1162.08	−0.0504089
$811$	3704.65	0.160404	0.0802022	−	0.996779i	$-0.474443\pi$
$811$	3704.65	0.160404	0.0802022	+	0.996779i	$0.474443\pi$
$812$	−43882.7	−1.89653
$813$	28929.9	1.24799
$814$	−25154.0	−1.08311
$815$	3575.97	0.153694
$816$	255950.	10.9804
$817$	4361.43	0.186765
$818$	75996.3	3.24835
$819$	16171.4	0.689956
$820$	524.541	0.0223387
$821$	13510.5	0.574326	0.287163	−	0.957882i	$-0.407288\pi$
$821$	13510.5	0.574326	0.287163	+	0.957882i	$0.407288\pi$
$822$	67641.0	2.87013
$823$	−23575.3	−0.998523	−0.499262	−	0.866451i	$-0.666395\pi$
$823$	−23575.3	−0.998523	−0.499262	+	0.866451i	$0.666395\pi$
$824$	104870.	4.43364
$825$	19668.3	0.830013
$826$	41834.2	1.76223
$827$	−10981.4	−0.461741	−0.230871	−	0.972984i	$-0.574157\pi$
$827$	−10981.4	−0.461741	−0.230871	+	0.972984i	$0.574157\pi$
$828$	60740.6	2.54937
$829$	−15131.0	−0.633923	−0.316962	−	0.948438i	$-0.602663\pi$
$829$	−15131.0	−0.633923	−0.316962	+	0.948438i	$0.602663\pi$
$830$	−5078.15	−0.212368
$831$	−34842.1	−1.45446
$832$	−114423.	−4.76792
$833$	25814.2	1.07372
$834$	67387.8	2.79790
$835$	−15240.0	−0.631617
$836$	32958.6	1.36351
$837$	37243.3	1.53801
$838$	11381.4	0.469171
$839$	2706.81	0.111382	0.0556910	−	0.998448i	$-0.482264\pi$
$839$	2706.81	0.111382	0.0556910	+	0.998448i	$0.482264\pi$
$840$	31726.9	1.30319
$841$	12405.8	0.508664
$842$	−86158.5	−3.52639
$843$	34934.3	1.42729
$844$	39115.8	1.59529
$845$	3270.77	0.133157
$846$	−82195.8	−3.34037
$847$	8105.27	0.328808
$848$	−89900.2	−3.64055
$849$	61613.7	2.49067
$850$	−61270.0	−2.47240
$851$	12148.4	0.489357
$852$	130653.	5.25364
$853$	−9236.12	−0.370737	−0.185368	−	0.982669i	$-0.559348\pi$
$853$	−9236.12	−0.370737	−0.185368	+	0.982669i	$0.559348\pi$
$854$	−39845.7	−1.59659
$855$	−12191.4	−0.487647
$856$	−63374.7	−2.53049
$857$	25834.8	1.02976	0.514878	−	0.857264i	$-0.327837\pi$
$857$	25834.8	1.02976	0.514878	+	0.857264i	$0.327837\pi$
$858$	−40362.6	−1.60601
$859$	18529.0	0.735973	0.367987	−	0.929831i	$-0.380047\pi$
$859$	18529.0	0.735973	0.367987	+	0.929831i	$0.380047\pi$
$860$	−7292.01	−0.289134
$861$	−409.424	−0.0162057
$862$	−7479.48	−0.295536
$863$	−3685.86	−0.145386	−0.0726931	−	0.997354i	$-0.523159\pi$
$863$	−3685.86	−0.145386	−0.0726931	+	0.997354i	$0.523159\pi$
$864$	126567.	4.98367
$865$	674.902	0.0265287
$866$	54214.7	2.12735
$867$	−50563.7	−1.98066
$868$	64025.7	2.50366
$869$	−25527.6	−0.996509
$870$	−40514.5	−1.57882
$871$	−323.316	−0.0125777
$872$	−185877.	−7.21857
$873$	26951.3	1.04486
$874$	−21383.7	−0.827591
$875$	−10180.5	−0.393329
$876$	171744.	6.62409
$877$	−42733.3	−1.64538	−0.822691	−	0.568488i	$-0.807529\pi$
$877$	−42733.3	−1.64538	−0.822691	+	0.568488i	$0.807529\pi$
$878$	22456.2	0.863165
$879$	−33642.7	−1.29095
$880$	−29684.8	−1.13713
$881$	−37775.7	−1.44460	−0.722302	−	0.691578i	$-0.756916\pi$
$881$	−37775.7	−1.44460	−0.722302	+	0.691578i	$0.756916\pi$
$882$	59198.9	2.26001
$883$	−36336.1	−1.38483	−0.692417	−	0.721498i	$-0.743454\pi$
$883$	−36336.1	−1.38483	−0.692417	+	0.721498i	$0.743454\pi$
$884$	93596.5	3.56108
$885$	28750.7	1.09203
$886$	79374.1	3.00973
$887$	22488.6	0.851290	0.425645	−	0.904890i	$-0.360047\pi$
$887$	22488.6	0.851290	0.425645	+	0.904890i	$0.360047\pi$
$888$	143091.	5.40747
$889$	−16640.8	−0.627802
$890$	−4556.26	−0.171603
$891$	−1034.42	−0.0388939
$892$	−35976.1	−1.35041
$893$	21540.3	0.807189
$894$	−84385.7	−3.15691
$895$	3730.44	0.139324
$896$	89085.8	3.32159
$897$	19493.6	0.725610
$898$	−65946.9	−2.45064
$899$	−53684.3	−1.99163
$900$	−104593.	−3.87380
$901$	32189.2	1.19021
$902$	627.254	0.0231544
$903$	5691.69	0.209754
$904$	−8884.66	−0.326880
$905$	−11686.6	−0.429254
$906$	65234.0	2.39211
$907$	−20709.5	−0.758157	−0.379078	−	0.925365i	$-0.623759\pi$
$907$	−20709.5	−0.758157	−0.379078	+	0.925365i	$0.623759\pi$
$908$	−84730.2	−3.09677
$909$	41072.6	1.49867
$910$	9518.53	0.346743
$911$	31685.9	1.15236	0.576180	−	0.817323i	$-0.304543\pi$
$911$	31685.9	1.15236	0.576180	+	0.817323i	$0.304543\pi$
$912$	−153820.	−5.58495
$913$	−4520.32	−0.163856
$914$	−1132.32	−0.0409780
$915$	−27384.1	−0.989387
$916$	60647.9	2.18762
$917$	−25010.6	−0.900678
$918$	−77939.3	−2.80216
$919$	−14632.4	−0.525221	−0.262611	−	0.964902i	$-0.584583\pi$
$919$	−14632.4	−0.525221	−0.262611	+	0.964902i	$0.584583\pi$
$920$	23475.3	0.841259
$921$	−73354.4	−2.62444
$922$	51498.6	1.83950
$923$	25737.8	0.917844
$924$	43011.2	1.53135
$925$	−20919.1	−0.743584
$926$	−10907.4	−0.387085
$927$	−52588.4	−1.86325
$928$	−182440.	−6.45354
$929$	−39546.3	−1.39663	−0.698316	−	0.715789i	$-0.746067\pi$
$929$	−39546.3	−1.39663	−0.698316	+	0.715789i	$0.746067\pi$
$930$	59111.5	2.08424
$931$	−15513.7	−0.546125
$932$	−26095.6	−0.917156
$933$	15582.2	0.546773
$934$	74256.6	2.60145
$935$	10628.8	0.371763
$936$	140937.	4.92165
$937$	37072.2	1.29253	0.646263	−	0.763115i	$-0.276331\pi$
$937$	37072.2	1.29253	0.646263	+	0.763115i	$0.276331\pi$
$938$	462.840	0.0161111
$939$	−54396.9	−1.89050
$940$	−36014.0	−1.24963
$941$	−18007.6	−0.623838	−0.311919	−	0.950109i	$-0.600972\pi$
$941$	−18007.6	−0.623838	−0.311919	+	0.950109i	$0.600972\pi$
$942$	77741.9	2.68892
$943$	−302.940	−0.0104614
$944$	222661.	7.67691
$945$	−5900.18	−0.203104
$946$	−8719.90	−0.299692
$947$	20060.1	0.688347	0.344174	−	0.938906i	$-0.388159\pi$
$947$	20060.1	0.688347	0.344174	+	0.938906i	$0.388159\pi$
$948$	221160.	7.57696
$949$	33832.5	1.15727
$950$	36821.8	1.25753
$951$	−10908.9	−0.371971
$952$	−87977.8	−2.99514
$953$	−13323.5	−0.452877	−0.226439	−	0.974025i	$-0.572708\pi$
$953$	−13323.5	−0.452877	−0.226439	+	0.974025i	$0.572708\pi$
$954$	73818.3	2.50520
$955$	2980.30	0.100984
$956$	99883.1	3.37913
$957$	−36064.0	−1.21817
$958$	107776.	3.63473
$959$	−14199.2	−0.478119
$960$	112573.	3.78466
$961$	48535.4	1.62920
$962$	42929.5	1.43878
$963$	31780.1	1.06345
$964$	53250.2	1.77912
$965$	−15818.7	−0.527691
$966$	−27905.9	−0.929458
$967$	−2988.49	−0.0993829	−0.0496914	−	0.998765i	$-0.515824\pi$
$967$	−2988.49	−0.0993829	−0.0496914	+	0.998765i	$0.515824\pi$
$968$	70639.0	2.34548
$969$	55075.8	1.82589
$970$	15863.6	0.525103
$971$	8786.97	0.290409	0.145205	−	0.989402i	$-0.453616\pi$
$971$	8786.97	0.290409	0.145205	+	0.989402i	$0.453616\pi$
$972$	92669.2	3.05799
$973$	−14146.1	−0.466086
$974$	−63125.7	−2.07667
$975$	−33567.1	−1.10257
$976$	−212077.	−6.95536
$977$	−9941.53	−0.325545	−0.162773	−	0.986664i	$-0.552044\pi$
$977$	−9941.53	−0.325545	−0.162773	+	0.986664i	$0.552044\pi$
$978$	−37047.1	−1.21128
$979$	−4055.76	−0.132403
$980$	25937.9	0.845466
$981$	93210.5	3.03362
$982$	−42305.8	−1.37478
$983$	−13695.1	−0.444359	−0.222180	−	0.975006i	$-0.571317\pi$
$983$	−13695.1	−0.444359	−0.222180	+	0.975006i	$0.571317\pi$
$984$	−3568.21	−0.115600
$985$	−4205.51	−0.136039
$986$	112346.	3.62861
$987$	28110.3	0.906545
$988$	−56249.3	−1.81126
$989$	4211.38	0.135404
$990$	24374.6	0.782501
$991$	−21577.9	−0.691668	−0.345834	−	0.938296i	$-0.612404\pi$
$991$	−21577.9	−0.691668	−0.345834	+	0.938296i	$0.612404\pi$
$992$	266183.	8.51949
$993$	23378.4	0.747122
$994$	−36844.7	−1.17570
$995$	15711.4	0.500588
$996$	39162.0	1.24588
$997$	2206.56	0.0700927	0.0350463	−	0.999386i	$-0.488842\pi$
$997$	2206.56	0.0700927	0.0350463	+	0.999386i	$0.488842\pi$
$998$	−81368.1	−2.58082
$999$	−26610.4	−0.842758

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1997.4.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-5.59440 q^{2} -8.36152 q^{3} +23.2974 q^{4} -4.51522 q^{5} +46.7777 q^{6} -9.81959 q^{7} -85.5797 q^{8} +42.9151 q^{9} +O(q^{10})\)	\(q-5.59440 q^{2} -8.36152 q^{3} +23.2974 q^{4} -4.51522 q^{5} +46.7777 q^{6} -9.81959 q^{7} -85.5797 q^{8} +42.9151 q^{9} +25.2599 q^{10} +22.4851 q^{11} -194.801 q^{12} -38.3746 q^{13} +54.9348 q^{14} +37.7541 q^{15} +292.388 q^{16} -104.691 q^{17} -240.084 q^{18} +62.9168 q^{19} -105.193 q^{20} +82.1068 q^{21} -125.791 q^{22} +60.7523 q^{23} +715.576 q^{24} -104.613 q^{25} +214.683 q^{26} -133.074 q^{27} -228.771 q^{28} +191.820 q^{29} -211.212 q^{30} -279.869 q^{31} -951.102 q^{32} -188.010 q^{33} +585.683 q^{34} +44.3376 q^{35} +999.808 q^{36} +199.967 q^{37} -351.982 q^{38} +320.870 q^{39} +386.411 q^{40} -4.98648 q^{41} -459.338 q^{42} +69.3206 q^{43} +523.845 q^{44} -193.771 q^{45} -339.873 q^{46} +342.363 q^{47} -2444.81 q^{48} -246.576 q^{49} +585.247 q^{50} +875.375 q^{51} -894.027 q^{52} -307.469 q^{53} +744.470 q^{54} -101.525 q^{55} +840.358 q^{56} -526.080 q^{57} -1073.12 q^{58} +761.526 q^{59} +879.571 q^{60} -725.327 q^{61} +1565.70 q^{62} -421.408 q^{63} +2981.74 q^{64} +173.270 q^{65} +1051.80 q^{66} +8.42525 q^{67} -2439.02 q^{68} -507.982 q^{69} -248.042 q^{70} -670.699 q^{71} -3672.66 q^{72} -881.638 q^{73} -1118.70 q^{74} +874.722 q^{75} +1465.79 q^{76} -220.795 q^{77} -1795.08 q^{78} -1135.31 q^{79} -1320.20 q^{80} -46.0047 q^{81} +27.8964 q^{82} -201.036 q^{83} +1912.87 q^{84} +472.702 q^{85} -387.807 q^{86} -1603.90 q^{87} -1924.27 q^{88} -180.375 q^{89} +1084.03 q^{90} +376.823 q^{91} +1415.37 q^{92} +2340.13 q^{93} -1915.31 q^{94} -284.083 q^{95} +7952.66 q^{96} +628.015 q^{97} +1379.44 q^{98} +964.951 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) \) 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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