LMFDB - Embedded newform 197.6.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,6,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	197.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:	$31.5956125032$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.834938 q^{2} +25.3960 q^{3} -31.3029 q^{4} -87.5439 q^{5} -21.2041 q^{6} -171.205 q^{7} +52.8540 q^{8} +401.958 q^{9} +73.0938 q^{10} +131.758 q^{11} -794.969 q^{12} -315.350 q^{13} +142.945 q^{14} -2223.27 q^{15} +957.562 q^{16} +1295.01 q^{17} -335.610 q^{18} +1195.63 q^{19} +2740.38 q^{20} -4347.92 q^{21} -110.010 q^{22} +1036.50 q^{23} +1342.28 q^{24} +4538.94 q^{25} +263.297 q^{26} +4036.91 q^{27} +5359.20 q^{28} +7000.27 q^{29} +1856.29 q^{30} +5369.93 q^{31} -2490.83 q^{32} +3346.13 q^{33} -1081.25 q^{34} +14987.9 q^{35} -12582.4 q^{36} -875.870 q^{37} -998.277 q^{38} -8008.63 q^{39} -4627.04 q^{40} +628.033 q^{41} +3630.24 q^{42} -22948.9 q^{43} -4124.41 q^{44} -35189.0 q^{45} -865.412 q^{46} -8828.97 q^{47} +24318.3 q^{48} +12504.1 q^{49} -3789.73 q^{50} +32888.2 q^{51} +9871.35 q^{52} -7288.61 q^{53} -3370.57 q^{54} -11534.6 q^{55} -9048.85 q^{56} +30364.3 q^{57} -5844.79 q^{58} +40877.9 q^{59} +69594.7 q^{60} -40999.2 q^{61} -4483.56 q^{62} -68817.1 q^{63} -28562.3 q^{64} +27606.9 q^{65} -2793.81 q^{66} +43542.0 q^{67} -40537.6 q^{68} +26323.0 q^{69} -12514.0 q^{70} +27327.1 q^{71} +21245.1 q^{72} +42264.1 q^{73} +731.297 q^{74} +115271. q^{75} -37426.7 q^{76} -22557.6 q^{77} +6686.71 q^{78} +14871.3 q^{79} -83828.8 q^{80} +4845.53 q^{81} -524.368 q^{82} +76584.2 q^{83} +136102. q^{84} -113370. q^{85} +19160.9 q^{86} +177779. q^{87} +6963.93 q^{88} -81131.1 q^{89} +29380.6 q^{90} +53989.3 q^{91} -32445.4 q^{92} +136375. q^{93} +7371.64 q^{94} -104670. q^{95} -63257.2 q^{96} +93274.6 q^{97} -10440.1 q^{98} +52961.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 12 q^{2} + 98 q^{3} + 752 q^{4} + 146 q^{5} + 144 q^{6} + 831 q^{7} + 699 q^{8} + 3725 q^{9} + 1033 q^{10} + 1370 q^{11} + 3136 q^{12} + 2948 q^{13} + 929 q^{14} + 1859 q^{15} + 14080 q^{16} + 1545 q^{17}+ \cdots + 119867 q^{99}+O(q^{100}) $ 43 * q + 12 * q^2 + 98 * q^3 + 752 * q^4 + 146 * q^5 + 144 * q^6 + 831 * q^7 + 699 * q^8 + 3725 * q^9 + 1033 * q^10 + 1370 * q^11 + 3136 * q^12 + 2948 * q^13 + 929 * q^14 + 1859 * q^15 + 14080 * q^16 + 1545 * q^17 + 6757 * q^18 + 12233 * q^19 + 7419 * q^20 + 3674 * q^21 + 10369 * q^22 + 5564 * q^23 + 6813 * q^24 + 35439 * q^25 + 1578 * q^26 + 33755 * q^27 + 38990 * q^28 - 2405 * q^29 + 1483 * q^30 + 31280 * q^31 + 17700 * q^32 + 39326 * q^33 + 9394 * q^34 + 21436 * q^35 + 53290 * q^36 + 35510 * q^37 + 33614 * q^38 + 22963 * q^39 + 50046 * q^40 + 9866 * q^41 + 22195 * q^42 + 51379 * q^43 + 29746 * q^44 + 72219 * q^45 + 35053 * q^46 + 42481 * q^47 + 75938 * q^48 + 175192 * q^49 + 162531 * q^50 + 154051 * q^51 + 210234 * q^52 + 81848 * q^53 + 320743 * q^54 + 105027 * q^55 + 452104 * q^56 + 208589 * q^57 + 159979 * q^58 + 168687 * q^59 + 279933 * q^60 + 148330 * q^61 + 152995 * q^62 + 250849 * q^63 + 540617 * q^64 + 125561 * q^65 + 376032 * q^66 + 395178 * q^67 + 306925 * q^68 + 150249 * q^69 + 271319 * q^70 + 115563 * q^71 + 352975 * q^72 + 247249 * q^73 + 65989 * q^74 + 460002 * q^75 + 440494 * q^76 + 90902 * q^77 + 201225 * q^78 + 222999 * q^79 + 175770 * q^80 + 406335 * q^81 + 172447 * q^82 + 253668 * q^83 - 274214 * q^84 + 114986 * q^85 - 301722 * q^86 + 9553 * q^87 + 79659 * q^88 + 65396 * q^89 - 177829 * q^90 + 360807 * q^91 - 275338 * q^92 - 200055 * q^93 - 249179 * q^94 + 91983 * q^95 - 1089739 * q^96 + 399386 * q^97 - 57978 * q^98 + 119867 * q^99

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 $

$2$	−0.834938	−0.147598	−0.0737988	−	0.997273i	$-0.523512\pi$
$2$	−0.834938	−0.147598	−0.0737988	+	0.997273i	$0.523512\pi$
$3$	25.3960	1.62916	0.814578	−	0.580054i	$-0.196969\pi$
$3$	25.3960	1.62916	0.814578	+	0.580054i	$0.196969\pi$
$4$	−31.3029	−0.978215
$5$	−87.5439	−1.56603	−0.783017	−	0.622001i	$-0.786320\pi$
$5$	−87.5439	−1.56603	−0.783017	+	0.622001i	$0.786320\pi$
$6$	−21.2041	−0.240459
$7$	−171.205	−1.32060	−0.660299	−	0.751003i	$-0.729570\pi$
$7$	−171.205	−1.32060	−0.660299	+	0.751003i	$0.729570\pi$
$8$	52.8540	0.291980
$9$	401.958	1.65415
$10$	73.0938	0.231143
$11$	131.758	0.328319	0.164159	−	0.986434i	$-0.447509\pi$
$11$	131.758	0.328319	0.164159	+	0.986434i	$0.447509\pi$
$12$	−794.969	−1.59366
$13$	−315.350	−0.517528	−0.258764	−	0.965941i	$-0.583315\pi$
$13$	−315.350	−0.517528	−0.258764	+	0.965941i	$0.583315\pi$
$14$	142.945	0.194917
$15$	−2223.27	−2.55131
$16$	957.562	0.935119
$17$	1295.01	1.08680	0.543402	−	0.839472i	$-0.317136\pi$
$17$	1295.01	1.08680	0.543402	+	0.839472i	$0.317136\pi$
$18$	−335.610	−0.244148
$19$	1195.63	0.759824	0.379912	−	0.925023i	$-0.375954\pi$
$19$	1195.63	0.759824	0.379912	+	0.925023i	$0.375954\pi$
$20$	2740.38	1.53192
$21$	−4347.92	−2.15146
$22$	−110.010	−0.0484590
$23$	1036.50	0.408554	0.204277	−	0.978913i	$-0.434516\pi$
$23$	1036.50	0.408554	0.204277	+	0.978913i	$0.434516\pi$
$24$	1342.28	0.475680
$25$	4538.94	1.45246
$26$	263.297	0.0763859
$27$	4036.91	1.06571
$28$	5359.20	1.29183
$29$	7000.27	1.54568	0.772840	−	0.634601i	$-0.218836\pi$
$29$	7000.27	1.54568	0.772840	+	0.634601i	$0.218836\pi$
$30$	1856.29	0.376568
$31$	5369.93	1.00361	0.501805	−	0.864981i	$-0.332670\pi$
$31$	5369.93	1.00361	0.501805	+	0.864981i	$0.332670\pi$
$32$	−2490.83	−0.430001
$33$	3346.13	0.534882
$34$	−1081.25	−0.160410
$35$	14987.9	2.06810
$36$	−12582.4	−1.61811
$37$	−875.870	−0.105181	−0.0525903	−	0.998616i	$-0.516748\pi$
$37$	−875.870	−0.105181	−0.0525903	+	0.998616i	$0.516748\pi$
$38$	−998.277	−0.112148
$39$	−8008.63	−0.843134
$40$	−4627.04	−0.457250
$41$	628.033	0.0583475	0.0291738	−	0.999574i	$-0.490712\pi$
$41$	628.033	0.0583475	0.0291738	+	0.999574i	$0.490712\pi$
$42$	3630.24	0.317550
$43$	−22948.9	−1.89274	−0.946370	−	0.323084i	$-0.895280\pi$
$43$	−22948.9	−1.89274	−0.946370	+	0.323084i	$0.895280\pi$
$44$	−4124.41	−0.321166
$45$	−35189.0	−2.59045
$46$	−865.412	−0.0603015
$47$	−8828.97	−0.582995	−0.291498	−	0.956572i	$-0.594154\pi$
$47$	−8828.97	−0.582995	−0.291498	+	0.956572i	$0.594154\pi$
$48$	24318.3	1.52346
$49$	12504.1	0.743979
$50$	−3789.73	−0.214380
$51$	32888.2	1.77057
$52$	9871.35	0.506254
$53$	−7288.61	−0.356414	−0.178207	−	0.983993i	$-0.557030\pi$
$53$	−7288.61	−0.356414	−0.178207	+	0.983993i	$0.557030\pi$
$54$	−3370.57	−0.157296
$55$	−11534.6	−0.514158
$56$	−9048.85	−0.385588
$57$	30364.3	1.23787
$58$	−5844.79	−0.228139
$59$	40877.9	1.52883	0.764413	−	0.644727i	$-0.223029\pi$
$59$	40877.9	1.52883	0.764413	+	0.644727i	$0.223029\pi$
$60$	69594.7	2.49573
$61$	−40999.2	−1.41075	−0.705376	−	0.708834i	$-0.749222\pi$
$61$	−40999.2	−1.41075	−0.705376	+	0.708834i	$0.749222\pi$
$62$	−4483.56	−0.148130
$63$	−68817.1	−2.18447
$64$	−28562.3	−0.871652
$65$	27606.9	0.810466
$66$	−2793.81	−0.0789473
$67$	43542.0	1.18501	0.592504	−	0.805568i	$-0.298140\pi$
$67$	43542.0	1.18501	0.592504	+	0.805568i	$0.298140\pi$
$68$	−40537.6	−1.06313
$69$	26323.0	0.665598
$70$	−12514.0	−0.305247
$71$	27327.1	0.643351	0.321676	−	0.946850i	$-0.395754\pi$
$71$	27327.1	0.643351	0.321676	+	0.946850i	$0.395754\pi$
$72$	21245.1	0.482978
$73$	42264.1	0.928249	0.464124	−	0.885770i	$-0.346369\pi$
$73$	42264.1	0.928249	0.464124	+	0.885770i	$0.346369\pi$
$74$	731.297	0.0155244
$75$	115271.	2.36629
$76$	−37426.7	−0.743271
$77$	−22557.6	−0.433577
$78$	6686.71	0.124445
$79$	14871.3	0.268090	0.134045	−	0.990975i	$-0.457203\pi$
$79$	14871.3	0.268090	0.134045	+	0.990975i	$0.457203\pi$
$80$	−83828.8	−1.46443
$81$	4845.53	0.0820595
$82$	−524.368	−0.00861196
$83$	76584.2	1.22024	0.610118	−	0.792311i	$-0.291122\pi$
$83$	76584.2	1.22024	0.610118	+	0.792311i	$0.291122\pi$
$84$	136102.	2.10459
$85$	−113370.	−1.70197
$86$	19160.9	0.279364
$87$	177779.	2.51815
$88$	6963.93	0.0958623
$89$	−81131.1	−1.08571	−0.542853	−	0.839828i	$-0.682656\pi$
$89$	−81131.1	−1.08571	−0.542853	+	0.839828i	$0.682656\pi$
$90$	29380.6	0.382344
$91$	53989.3	0.683447
$92$	−32445.4	−0.399653
$93$	136375.	1.63504
$94$	7371.64	0.0860487
$95$	−104670.	−1.18991
$96$	−63257.2	−0.700539
$97$	93274.6	1.00655	0.503274	−	0.864127i	$-0.332129\pi$
$97$	93274.6	1.00655	0.503274	+	0.864127i	$0.332129\pi$
$98$	−10440.1	−0.109809
$99$	52961.2	0.543088
$100$	−142082.	−1.42082
$101$	−70816.1	−0.690762	−0.345381	−	0.938462i	$-0.612250\pi$
$101$	−70816.1	−0.690762	−0.345381	+	0.938462i	$0.612250\pi$
$102$	−27459.6	−0.261332
$103$	32496.5	0.301817	0.150909	−	0.988548i	$-0.451780\pi$
$103$	32496.5	0.301817	0.150909	+	0.988548i	$0.451780\pi$
$104$	−16667.5	−0.151108
$105$	380634.	3.36926
$106$	6085.54	0.0526059
$107$	113929.	0.961998	0.480999	−	0.876721i	$-0.340274\pi$
$107$	113929.	0.961998	0.480999	+	0.876721i	$0.340274\pi$
$108$	−126367.	−1.04249
$109$	138149.	1.11373	0.556866	−	0.830602i	$-0.312004\pi$
$109$	138149.	1.11373	0.556866	+	0.830602i	$0.312004\pi$
$110$	9630.69	0.0758884
$111$	−22243.6	−0.171355
$112$	−163939.	−1.23492
$113$	98757.7	0.727570	0.363785	−	0.931483i	$-0.381484\pi$
$113$	98757.7	0.727570	0.363785	+	0.931483i	$0.381484\pi$
$114$	−25352.3	−0.182707
$115$	−90739.2	−0.639809
$116$	−219128.	−1.51201
$117$	−126757.	−0.856069
$118$	−34130.5	−0.225651
$119$	−221712.	−1.43523
$120$	−117509.	−0.744932
$121$	−143691.	−0.892207
$122$	34231.8	0.208223
$123$	15949.5	0.0950573
$124$	−168094.	−0.981746
$125$	−123782.	−0.708570
$126$	57458.0	0.322422
$127$	155173.	0.853701	0.426851	−	0.904322i	$-0.359623\pi$
$127$	155173.	0.853701	0.426851	+	0.904322i	$0.359623\pi$
$128$	103554.	0.558655
$129$	−582811.	−3.08357
$130$	−23050.1	−0.119623
$131$	70210.6	0.357457	0.178729	−	0.983898i	$-0.442802\pi$
$131$	70210.6	0.357457	0.178729	+	0.983898i	$0.442802\pi$
$132$	−104744.	−0.523230
$133$	−204698.	−1.00342
$134$	−36354.8	−0.174904
$135$	−353407.	−1.66894
$136$	68446.5	0.317325
$137$	402937.	1.83415	0.917076	−	0.398713i	$-0.130543\pi$
$137$	402937.	1.83415	0.917076	+	0.398713i	$0.130543\pi$
$138$	−21978.0	−0.0982406
$139$	−195533.	−0.858388	−0.429194	−	0.903212i	$-0.641202\pi$
$139$	−195533.	−0.858388	−0.429194	+	0.903212i	$0.641202\pi$
$140$	−469166.	−2.02305
$141$	−224221.	−0.949791
$142$	−22816.5	−0.0949571
$143$	−41549.8	−0.169914
$144$	384900.	1.54683
$145$	−612831.	−2.42059
$146$	−35287.9	−0.137007
$147$	317553.	1.21206
$148$	27417.2	0.102889
$149$	302529.	1.11635	0.558176	−	0.829722i	$-0.311501\pi$
$149$	302529.	1.11635	0.558176	+	0.829722i	$0.311501\pi$
$150$	−96244.2	−0.349258
$151$	410360.	1.46461	0.732306	−	0.680975i	$-0.238444\pi$
$151$	410360.	1.46461	0.732306	+	0.680975i	$0.238444\pi$
$152$	63193.8	0.221853
$153$	520541.	1.79774
$154$	18834.2	0.0639949
$155$	−470105.	−1.57169
$156$	250693.	0.824766
$157$	507021.	1.64164	0.820818	−	0.571190i	$-0.193518\pi$
$157$	507021.	1.64164	0.820818	+	0.571190i	$0.193518\pi$
$158$	−12416.6	−0.0395694
$159$	−185102.	−0.580655
$160$	218057.	0.673396
$161$	−177454.	−0.539535
$162$	−4045.72	−0.0121118
$163$	−54010.4	−0.159224	−0.0796119	−	0.996826i	$-0.525368\pi$
$163$	−54010.4	−0.159224	−0.0796119	+	0.996826i	$0.525368\pi$
$164$	−19659.2	−0.0570764
$165$	−292933.	−0.837643
$166$	−63943.0	−0.180104
$167$	−691433.	−1.91849	−0.959244	−	0.282578i	$-0.908810\pi$
$167$	−691433.	−1.91849	−0.959244	+	0.282578i	$0.908810\pi$
$168$	−229805.	−0.628183
$169$	−271848.	−0.732165
$170$	94657.3	0.251207
$171$	480593.	1.25686
$172$	718367.	1.85151
$173$	45452.7	0.115463	0.0577317	−	0.998332i	$-0.481613\pi$
$173$	45452.7	0.115463	0.0577317	+	0.998332i	$0.481613\pi$
$174$	−148434.	−0.371673
$175$	−777088.	−1.91812
$176$	126167.	0.307017
$177$	1.03814e6	2.49070
$178$	67739.4	0.160248
$179$	−268244.	−0.625745	−0.312872	−	0.949795i	$-0.601291\pi$
$179$	−268244.	−0.625745	−0.312872	+	0.949795i	$0.601291\pi$
$180$	1.10152e6	2.53402
$181$	560898.	1.27259	0.636293	−	0.771447i	$-0.280467\pi$
$181$	560898.	1.27259	0.636293	+	0.771447i	$0.280467\pi$
$182$	−45077.7	−0.100875
$183$	−1.04122e6	−2.29833
$184$	54783.1	0.119289
$185$	76677.1	0.164716
$186$	−113865.	−0.241327
$187$	170628.	0.356818
$188$	276372.	0.570295
$189$	−691137.	−1.40737
$190$	87393.1	0.175628
$191$	−613488.	−1.21681	−0.608404	−	0.793627i	$-0.708190\pi$
$191$	−613488.	−1.21681	−0.608404	+	0.793627i	$0.708190\pi$
$192$	−725369.	−1.42006
$193$	605861.	1.17079	0.585396	−	0.810747i	$-0.300939\pi$
$193$	605861.	1.17079	0.585396	+	0.810747i	$0.300939\pi$
$194$	−77878.5	−0.148564
$195$	701107.	1.32038
$196$	−391413.	−0.727771
$197$	38809.0	0.0712470
$197$	38809.0	0.0712470
$198$	−44219.3	−0.0801584
$199$	647497.	1.15906	0.579529	−	0.814952i	$-0.303237\pi$
$199$	647497.	1.15906	0.579529	+	0.814952i	$0.303237\pi$
$200$	239901.	0.424089
$201$	1.10579e6	1.93056
$202$	59127.1	0.101955
$203$	−1.19848e6	−2.04122
$204$	−1.02949e6	−1.73200
$205$	−54980.5	−0.0913742
$206$	−27132.6	−0.0445475
$207$	416629.	0.675809
$208$	−301967.	−0.483951
$209$	157534.	0.249464
$210$	−317806.	−0.497294
$211$	−1.14611e6	−1.77223	−0.886115	−	0.463465i	$-0.846606\pi$
$211$	−1.14611e6	−1.77223	−0.886115	+	0.463465i	$0.846606\pi$
$212$	228155.	0.348650
$213$	694000.	1.04812
$214$	−95123.5	−0.141989
$215$	2.00904e6	2.96410
$216$	213367.	0.311166
$217$	−919358.	−1.32536
$218$	−115346.	−0.164384
$219$	1.07334e6	1.51226
$220$	361067.	0.502957
$221$	−408382.	−0.562452
$222$	18572.0	0.0252916
$223$	−1.00874e6	−1.35836	−0.679181	−	0.733971i	$-0.737665\pi$
$223$	−1.00874e6	−1.35836	−0.679181	+	0.733971i	$0.737665\pi$
$224$	426442.	0.567859
$225$	1.82446e6	2.40259
$226$	−82456.5	−0.107388
$227$	1.12225e6	1.44552	0.722760	−	0.691099i	$-0.242873\pi$
$227$	1.12225e6	1.44552	0.722760	+	0.691099i	$0.242873\pi$
$228$	−950489.	−1.21090
$229$	−1.20306e6	−1.51599	−0.757997	−	0.652257i	$-0.773822\pi$
$229$	−1.20306e6	−1.51599	−0.757997	+	0.652257i	$0.773822\pi$
$230$	75761.6	0.0944343
$231$	−572873.	−0.706364
$232$	369992.	0.451307
$233$	−8724.46	−0.0105281	−0.00526404	−	0.999986i	$-0.501676\pi$
$233$	−8724.46	−0.0105281	−0.00526404	+	0.999986i	$0.501676\pi$
$234$	105835.	0.126354
$235$	772922.	0.912991
$236$	−1.27959e6	−1.49552
$237$	377671.	0.436760
$238$	185116.	0.211837
$239$	−1.12543e6	−1.27445	−0.637227	−	0.770676i	$-0.719919\pi$
$239$	−1.12543e6	−1.27445	−0.637227	+	0.770676i	$0.719919\pi$
$240$	−2.12892e6	−2.38578
$241$	445330.	0.493900	0.246950	−	0.969028i	$-0.420572\pi$
$241$	445330.	0.493900	0.246950	+	0.969028i	$0.420572\pi$
$242$	119973.	0.131688
$243$	−857911.	−0.932023
$244$	1.28339e6	1.38002
$245$	−1.09465e6	−1.16510
$246$	−13316.9	−0.0140302
$247$	−377042.	−0.393230
$248$	283822.	0.293034
$249$	1.94493e6	1.98795
$250$	103350.	0.104583
$251$	1.35982e6	1.36238	0.681188	−	0.732109i	$-0.261464\pi$
$251$	1.35982e6	1.36238	0.681188	+	0.732109i	$0.261464\pi$
$252$	2.15417e6	2.13688
$253$	136567.	0.134136
$254$	−129560.	−0.126004
$255$	−2.87916e6	−2.77278
$256$	827532.	0.789196
$257$	171046.	0.161540	0.0807698	−	0.996733i	$-0.474262\pi$
$257$	171046.	0.161540	0.0807698	+	0.996733i	$0.474262\pi$
$258$	486611.	0.455127
$259$	149953.	0.138901
$260$	−864177.	−0.792810
$261$	2.81381e6	2.55678
$262$	−58621.5	−0.0527598
$263$	−813608.	−0.725314	−0.362657	−	0.931923i	$-0.618130\pi$
$263$	−813608.	−0.725314	−0.362657	+	0.931923i	$0.618130\pi$
$264$	176856.	0.156175
$265$	638074.	0.558157
$266$	170910.	0.148103
$267$	−2.06041e6	−1.76878
$268$	−1.36299e6	−1.15919
$269$	−774708.	−0.652765	−0.326383	−	0.945238i	$-0.605830\pi$
$269$	−774708.	−0.652765	−0.326383	+	0.945238i	$0.605830\pi$
$270$	295073.	0.246331
$271$	506827.	0.419214	0.209607	−	0.977786i	$-0.432781\pi$
$271$	506827.	0.419214	0.209607	+	0.977786i	$0.432781\pi$
$272$	1.24005e6	1.01629
$273$	1.37111e6	1.11344
$274$	−336427.	−0.270716
$275$	598042.	0.476870
$276$	−823984.	−0.651098
$277$	−839340.	−0.657262	−0.328631	−	0.944458i	$-0.606587\pi$
$277$	−839340.	−0.657262	−0.328631	+	0.944458i	$0.606587\pi$
$278$	163258.	0.126696
$279$	2.15849e6	1.66012
$280$	792172.	0.603843
$281$	348090.	0.262982	0.131491	−	0.991317i	$-0.458024\pi$
$281$	348090.	0.262982	0.131491	+	0.991317i	$0.458024\pi$
$282$	187210.	0.140187
$283$	−791577.	−0.587526	−0.293763	−	0.955878i	$-0.594908\pi$
$283$	−791577.	−0.587526	−0.293763	+	0.955878i	$0.594908\pi$
$284$	−855418.	−0.629336
$285$	−2.65821e6	−1.93855
$286$	34691.5	0.0250789
$287$	−107522.	−0.0770537
$288$	−1.00121e6	−0.711286
$289$	257199.	0.181144
$290$	511676.	0.357273
$291$	2.36880e6	1.63982
$292$	−1.32299e6	−0.908027
$293$	−588858.	−0.400720	−0.200360	−	0.979722i	$-0.564211\pi$
$293$	−588858.	−0.400720	−0.200360	+	0.979722i	$0.564211\pi$
$294$	−265137.	−0.178897
$295$	−3.57861e6	−2.39419
$296$	−46293.2	−0.0307106
$297$	531895.	0.349892
$298$	−252593.	−0.164771
$299$	−326860.	−0.211438
$300$	−3.60832e6	−2.31474
$301$	3.92896e6	2.49955
$302$	−342625.	−0.216173
$303$	−1.79845e6	−1.12536
$304$	1.14489e6	0.710526
$305$	3.58923e6	2.20928
$306$	−434619.	−0.265342
$307$	3.16683e6	1.91769	0.958847	−	0.283922i	$-0.0916358\pi$
$307$	3.16683e6	1.91769	0.958847	+	0.283922i	$0.0916358\pi$
$308$	706118.	0.424131
$309$	825282.	0.491707
$310$	392509.	0.231977
$311$	−789002.	−0.462570	−0.231285	−	0.972886i	$-0.574293\pi$
$311$	−789002.	−0.462570	−0.231285	+	0.972886i	$0.574293\pi$
$312$	−423288.	−0.246178
$313$	−22020.8	−0.0127049	−0.00635247	−	0.999980i	$-0.502022\pi$
$313$	−22020.8	−0.0127049	−0.00635247	+	0.999980i	$0.502022\pi$
$314$	−423331.	−0.242301
$315$	6.02452e6	3.42095
$316$	−465514.	−0.262250
$317$	−574777.	−0.321256	−0.160628	−	0.987015i	$-0.551352\pi$
$317$	−574777.	−0.321256	−0.160628	+	0.987015i	$0.551352\pi$
$318$	154549.	0.0857032
$319$	922341.	0.507475
$320$	2.50046e6	1.36504
$321$	2.89334e6	1.56725
$322$	148163.	0.0796341
$323$	1.54836e6	0.825780
$324$	−151679.	−0.0802718
$325$	−1.43135e6	−0.751690
$326$	45095.3	0.0235010
$327$	3.50843e6	1.81444
$328$	33194.0	0.0170363
$329$	1.51156e6	0.769903
$330$	244581.	0.123634
$331$	1.43550e6	0.720168	0.360084	−	0.932920i	$-0.382748\pi$
$331$	1.43550e6	0.720168	0.360084	+	0.932920i	$0.382748\pi$
$332$	−2.39731e6	−1.19365
$333$	−352063.	−0.173984
$334$	577304.	0.283164
$335$	−3.81183e6	−1.85576
$336$	−4.16340e6	−2.01187
$337$	1.57658e6	0.756206	0.378103	−	0.925764i	$-0.376577\pi$
$337$	1.57658e6	0.756206	0.378103	+	0.925764i	$0.376577\pi$
$338$	226976.	0.108066
$339$	2.50805e6	1.18532
$340$	3.54882e6	1.66490
$341$	707532.	0.329504
$342$	−401266.	−0.185510
$343$	736684.	0.338101
$344$	−1.21294e6	−0.552642
$345$	−2.30442e6	−1.04235
$346$	−37950.2	−0.0170421
$347$	−3.50638e6	−1.56327	−0.781637	−	0.623734i	$-0.785615\pi$
$347$	−3.50638e6	−1.56327	−0.781637	+	0.623734i	$0.785615\pi$
$348$	−5.56499e6	−2.46330
$349$	2.21043e6	0.971433	0.485716	−	0.874116i	$-0.338559\pi$
$349$	2.21043e6	0.971433	0.485716	+	0.874116i	$0.338559\pi$
$350$	648820.	0.283109
$351$	−1.27304e6	−0.551535
$352$	−328187.	−0.141177
$353$	2.88495e6	1.23226	0.616130	−	0.787645i	$-0.288700\pi$
$353$	2.88495e6	1.23226	0.616130	+	0.787645i	$0.288700\pi$
$354$	−866779.	−0.367621
$355$	−2.39232e6	−1.00751
$356$	2.53964e6	1.06205
$357$	−5.63061e6	−2.33822
$358$	223967.	0.0923584
$359$	−4.00113e6	−1.63850	−0.819251	−	0.573436i	$-0.805610\pi$
$359$	−4.00113e6	−1.63850	−0.819251	+	0.573436i	$0.805610\pi$
$360$	−1.85988e6	−0.756360
$361$	−1.04657e6	−0.422668
$362$	−468315.	−0.187831
$363$	−3.64918e6	−1.45354
$364$	−1.69002e6	−0.668558
$365$	−3.69996e6	−1.45367
$366$	869351.	0.339228
$367$	−1.46785e6	−0.568873	−0.284436	−	0.958695i	$-0.591806\pi$
$367$	−1.46785e6	−0.568873	−0.284436	+	0.958695i	$0.591806\pi$
$368$	992512.	0.382047
$369$	252443.	0.0965155
$370$	−64020.6	−0.0243117
$371$	1.24785e6	0.470680
$372$	−4.26893e6	−1.59942
$373$	506043.	0.188328	0.0941642	−	0.995557i	$-0.469982\pi$
$373$	506043.	0.188328	0.0941642	+	0.995557i	$0.469982\pi$
$374$	−142464.	−0.0526655
$375$	−3.14357e6	−1.15437
$376$	−466646.	−0.170223
$377$	−2.20753e6	−0.799933
$378$	577057.	0.207725
$379$	3.19756e6	1.14346	0.571730	−	0.820442i	$-0.306273\pi$
$379$	3.19756e6	1.14346	0.571730	+	0.820442i	$0.306273\pi$
$380$	3.27648e6	1.16399
$381$	3.94077e6	1.39081
$382$	512224.	0.179598
$383$	2.88210e6	1.00395	0.501975	−	0.864882i	$-0.332607\pi$
$383$	2.88210e6	1.00395	0.501975	+	0.864882i	$0.332607\pi$
$384$	2.62987e6	0.910136
$385$	1.97478e6	0.678996
$386$	−505857.	−0.172806
$387$	−9.22450e6	−3.13087
$388$	−2.91976e6	−0.984619
$389$	415568.	0.139241	0.0696206	−	0.997574i	$-0.477821\pi$
$389$	415568.	0.139241	0.0696206	+	0.997574i	$0.477821\pi$
$390$	−585381.	−0.194884
$391$	1.34228e6	0.444018
$392$	660889.	0.217227
$393$	1.78307e6	0.582354
$394$	−32403.1	−0.0105159
$395$	−1.30189e6	−0.419838
$396$	−1.65784e6	−0.531256
$397$	2.29734e6	0.731559	0.365780	−	0.930701i	$-0.380802\pi$
$397$	2.29734e6	0.731559	0.365780	+	0.930701i	$0.380802\pi$
$398$	−540620.	−0.171074
$399$	−5.19850e6	−1.63473
$400$	4.34632e6	1.35822
$401$	−1.75497e6	−0.545014	−0.272507	−	0.962154i	$-0.587853\pi$
$401$	−1.75497e6	−0.545014	−0.272507	+	0.962154i	$0.587853\pi$
$402$	−923268.	−0.284946
$403$	−1.69341e6	−0.519396
$404$	2.21675e6	0.675714
$405$	−424197.	−0.128508
$406$	1.00066e6	0.301279
$407$	−115403.	−0.0345327
$408$	1.73827e6	0.516972
$409$	−4.93051e6	−1.45742	−0.728709	−	0.684824i	$-0.759879\pi$
$409$	−4.93051e6	−1.45742	−0.728709	+	0.684824i	$0.759879\pi$
$410$	45905.3	0.0134866
$411$	1.02330e7	2.98812
$412$	−1.01723e6	−0.295242
$413$	−6.99848e6	−2.01897
$414$	−347860.	−0.0997477
$415$	−6.70448e6	−1.91093
$416$	785483.	0.222538
$417$	−4.96577e6	−1.39845
$418$	−131531.	−0.0368203
$419$	−6.23257e6	−1.73433	−0.867165	−	0.498020i	$-0.834061\pi$
$419$	−6.23257e6	−1.73433	−0.867165	+	0.498020i	$0.834061\pi$
$420$	−1.19149e7	−3.29586
$421$	4.10428e6	1.12858	0.564289	−	0.825578i	$-0.309151\pi$
$421$	4.10428e6	1.12858	0.564289	+	0.825578i	$0.309151\pi$
$422$	956930.	0.261577
$423$	−3.54887e6	−0.964361
$424$	−385232.	−0.104066
$425$	5.87798e6	1.57854
$426$	−579447.	−0.154700
$427$	7.01925e6	1.86304
$428$	−3.56630e6	−0.941041
$429$	−1.05520e6	−0.276816
$430$	−1.67742e6	−0.437493
$431$	4.60197e6	1.19330	0.596651	−	0.802501i	$-0.296498\pi$
$431$	4.60197e6	1.19330	0.596651	+	0.802501i	$0.296498\pi$
$432$	3.86559e6	0.996567
$433$	3.61256e6	0.925966	0.462983	−	0.886367i	$-0.346779\pi$
$433$	3.61256e6	0.925966	0.462983	+	0.886367i	$0.346779\pi$
$434$	767607.	0.195621
$435$	−1.55635e7	−3.94351
$436$	−4.32445e6	−1.08947
$437$	1.23927e6	0.310429
$438$	−896172.	−0.223206
$439$	5.20266e6	1.28844	0.644219	−	0.764841i	$-0.277182\pi$
$439$	5.20266e6	1.28844	0.644219	+	0.764841i	$0.277182\pi$
$440$	−609650.	−0.150124
$441$	5.02611e6	1.23065
$442$	340973.	0.0830165
$443$	−3.08808e6	−0.747617	−0.373809	−	0.927506i	$-0.621948\pi$
$443$	−3.08808e6	−0.747617	−0.373809	+	0.927506i	$0.621948\pi$
$444$	696289.	0.167622
$445$	7.10254e6	1.70025
$446$	842233.	0.200491
$447$	7.68303e6	1.81871
$448$	4.89000e6	1.15110
$449$	−4.43448e6	−1.03807	−0.519035	−	0.854753i	$-0.673709\pi$
$449$	−4.43448e6	−1.03807	−0.519035	+	0.854753i	$0.673709\pi$
$450$	−1.52331e6	−0.354616
$451$	82748.3	0.0191566
$452$	−3.09140e6	−0.711720
$453$	1.04215e7	2.38608
$454$	−937007.	−0.213355
$455$	−4.72644e6	−1.07030
$456$	1.60487e6	0.361433
$457$	7.05709e6	1.58065	0.790324	−	0.612689i	$-0.209912\pi$
$457$	7.05709e6	1.58065	0.790324	+	0.612689i	$0.209912\pi$
$458$	1.00448e6	0.223757
$459$	5.22784e6	1.15822
$460$	2.84040e6	0.625871
$461$	1.12098e6	0.245667	0.122834	−	0.992427i	$-0.460802\pi$
$461$	1.12098e6	0.245667	0.122834	+	0.992427i	$0.460802\pi$
$462$	478314.	0.104258
$463$	259268.	0.0562079	0.0281039	−	0.999605i	$-0.491053\pi$
$463$	259268.	0.0562079	0.0281039	+	0.999605i	$0.491053\pi$
$464$	6.70319e6	1.44540
$465$	−1.19388e7	−2.56052
$466$	7284.38	0.00155392
$467$	6.39753e6	1.35744	0.678719	−	0.734398i	$-0.262535\pi$
$467$	6.39753e6	1.35744	0.678719	+	0.734398i	$0.262535\pi$
$468$	3.96787e6	0.837419
$469$	−7.45459e6	−1.56492
$470$	−645342.	−0.134755
$471$	1.28763e7	2.67448
$472$	2.16056e6	0.446386
$473$	−3.02370e6	−0.621422
$474$	−315332.	−0.0644647
$475$	5.42690e6	1.10361
$476$	6.94023e6	1.40397
$477$	−2.92972e6	−0.589562
$478$	939665.	0.188106
$479$	−5.66349e6	−1.12783	−0.563917	−	0.825831i	$-0.690706\pi$
$479$	−5.66349e6	−1.12783	−0.563917	+	0.825831i	$0.690706\pi$
$480$	5.53779e6	1.09707
$481$	276205.	0.0544339
$482$	−371823.	−0.0728985
$483$	−4.50661e6	−0.878987
$484$	4.49794e6	0.872770
$485$	−8.16563e6	−1.57629
$486$	716302.	0.137564
$487$	8.06445e6	1.54082	0.770411	−	0.637548i	$-0.220051\pi$
$487$	8.06445e6	1.54082	0.770411	+	0.637548i	$0.220051\pi$
$488$	−2.16697e6	−0.411911
$489$	−1.37165e6	−0.259400
$490$	913968.	0.171965
$491$	4.65955e6	0.872249	0.436124	−	0.899886i	$-0.356351\pi$
$491$	4.65955e6	0.872249	0.436124	+	0.899886i	$0.356351\pi$
$492$	−499266.	−0.0929864
$493$	9.06543e6	1.67985
$494$	314806.	0.0580398
$495$	−4.63643e6	−0.850494
$496$	5.14205e6	0.938495
$497$	−4.67853e6	−0.849608
$498$	−1.62390e6	−0.293417
$499$	660910.	0.118820	0.0594102	−	0.998234i	$-0.481078\pi$
$499$	660910.	0.118820	0.0594102	+	0.998234i	$0.481078\pi$
$500$	3.87473e6	0.693133
$501$	−1.75597e7	−3.12552
$502$	−1.13536e6	−0.201083
$503$	−6.13270e6	−1.08077	−0.540383	−	0.841419i	$-0.681721\pi$
$503$	−6.13270e6	−1.08077	−0.540383	+	0.841419i	$0.681721\pi$
$504$	−3.63726e6	−0.637820
$505$	6.19952e6	1.08176
$506$	−114025.	−0.0197981
$507$	−6.90385e6	−1.19281
$508$	−4.85735e6	−0.835103
$509$	−9.76923e6	−1.67134	−0.835672	−	0.549229i	$-0.814922\pi$
$509$	−9.76923e6	−1.67134	−0.835672	+	0.549229i	$0.814922\pi$
$510$	2.40392e6	0.409255
$511$	−7.23581e6	−1.22584
$512$	−4.00468e6	−0.675138
$513$	4.82665e6	0.809752
$514$	−142812.	−0.0238429
$515$	−2.84487e6	−0.472656
$516$	1.82437e7	3.01639
$517$	−1.16329e6	−0.191408
$518$	−125201.	−0.0205015
$519$	1.15432e6	0.188108
$520$	1.45914e6	0.236640
$521$	4.02887e6	0.650263	0.325132	−	0.945669i	$-0.394591\pi$
$521$	4.02887e6	0.650263	0.325132	+	0.945669i	$0.394591\pi$
$522$	−2.34936e6	−0.377375
$523$	1.05567e7	1.68761	0.843805	−	0.536649i	$-0.180310\pi$
$523$	1.05567e7	1.68761	0.843805	+	0.536649i	$0.180310\pi$
$524$	−2.19779e6	−0.349670
$525$	−1.97350e7	−3.12491
$526$	679312.	0.107055
$527$	6.95413e6	1.09073
$528$	3.20413e6	0.500179
$529$	−5.36201e6	−0.833084
$530$	−532752.	−0.0823826
$531$	1.64312e7	2.52891
$532$	6.40762e6	0.981562
$533$	−198050.	−0.0301965
$534$	1.72031e6	0.261068
$535$	−9.97378e6	−1.50652
$536$	2.30137e6	0.345998
$537$	−6.81233e6	−1.01944
$538$	646833.	0.0963466
$539$	1.64751e6	0.244262
$540$	1.10626e7	1.63258
$541$	−4.52850e6	−0.665214	−0.332607	−	0.943066i	$-0.607928\pi$
$541$	−4.52850e6	−0.665214	−0.332607	+	0.943066i	$0.607928\pi$
$542$	−423169.	−0.0618750
$543$	1.42446e7	2.07324
$544$	−3.22566e6	−0.467327
$545$	−1.20941e7	−1.74414
$546$	−1.14480e6	−0.164341
$547$	−194902.	−0.0278514	−0.0139257	−	0.999903i	$-0.504433\pi$
$547$	−194902.	−0.0278514	−0.0139257	+	0.999903i	$0.504433\pi$
$548$	−1.26131e7	−1.79419
$549$	−1.64799e7	−2.33359
$550$	−499328.	−0.0703848
$551$	8.36973e6	1.17444
$552$	1.39127e6	0.194341
$553$	−2.54603e6	−0.354039
$554$	700796.	0.0970102
$555$	1.94729e6	0.268348
$556$	6.12075e6	0.839688
$557$	−6.08231e6	−0.830674	−0.415337	−	0.909668i	$-0.636336\pi$
$557$	−6.08231e6	−0.830674	−0.415337	+	0.909668i	$0.636336\pi$
$558$	−1.80220e6	−0.245030
$559$	7.23693e6	0.979546
$560$	1.43519e7	1.93392
$561$	4.33328e6	0.581312
$562$	−290633.	−0.0388155
$563$	−1.16523e7	−1.54932	−0.774661	−	0.632376i	$-0.782080\pi$
$563$	−1.16523e7	−1.54932	−0.774661	+	0.632376i	$0.782080\pi$
$564$	7.01875e6	0.929099
$565$	−8.64564e6	−1.13940
$566$	660918.	0.0867174
$567$	−829578.	−0.108368
$568$	1.44435e6	0.187845
$569$	1.23028e7	1.59303	0.796517	−	0.604616i	$-0.206674\pi$
$569$	1.23028e7	1.59303	0.796517	+	0.604616i	$0.206674\pi$
$570$	2.21944e6	0.286125
$571$	−1.14448e7	−1.46899	−0.734495	−	0.678614i	$-0.762581\pi$
$571$	−1.14448e7	−1.46899	−0.734495	+	0.678614i	$0.762581\pi$
$572$	1.30063e6	0.166212
$573$	−1.55801e7	−1.98237
$574$	89774.3	0.0113729
$575$	4.70461e6	0.593409
$576$	−1.14809e7	−1.44184
$577$	−1.25711e6	−0.157193	−0.0785967	−	0.996906i	$-0.525044\pi$
$577$	−1.25711e6	−0.157193	−0.0785967	+	0.996906i	$0.525044\pi$
$578$	−214745.	−0.0267365
$579$	1.53865e7	1.90740
$580$	1.91834e7	2.36785
$581$	−1.31116e7	−1.61144
$582$	−1.97780e6	−0.242034
$583$	−960333.	−0.117017
$584$	2.23382e6	0.271030
$585$	1.10968e7	1.34063
$586$	491659.	0.0591453
$587$	1.09347e7	1.30982	0.654909	−	0.755708i	$-0.272707\pi$
$587$	1.09347e7	1.30982	0.654909	+	0.755708i	$0.272707\pi$
$588$	−9.94033e6	−1.18565
$589$	6.42046e6	0.762566
$590$	2.98792e6	0.353377
$591$	985594.	0.116073
$592$	−838700.	−0.0983563
$593$	−9.72067e6	−1.13517	−0.567583	−	0.823316i	$-0.692121\pi$
$593$	−9.72067e6	−1.13517	−0.567583	+	0.823316i	$0.692121\pi$
$594$	−444099.	−0.0516433
$595$	1.94096e7	2.24762
$596$	−9.47003e6	−1.09203
$597$	1.64439e7	1.88829
$598$	272907.	0.0312077
$599$	1.28572e7	1.46413	0.732066	−	0.681233i	$-0.238556\pi$
$599$	1.28572e7	1.46413	0.732066	+	0.681233i	$0.238556\pi$
$600$	6.09253e6	0.690907
$601$	−356240.	−0.0402306	−0.0201153	−	0.999798i	$-0.506403\pi$
$601$	−356240.	−0.0402306	−0.0201153	+	0.999798i	$0.506403\pi$
$602$	−3.28044e6	−0.368927
$603$	1.75020e7	1.96018
$604$	−1.28455e7	−1.43271
$605$	1.25793e7	1.39723
$606$	1.50159e6	0.166100
$607$	−5.94207e6	−0.654585	−0.327292	−	0.944923i	$-0.606136\pi$
$607$	−5.94207e6	−0.654585	−0.327292	+	0.944923i	$0.606136\pi$
$608$	−2.97811e6	−0.326725
$609$	−3.04366e7	−3.32547
$610$	−2.99678e6	−0.326085
$611$	2.78421e6	0.301717
$612$	−1.62944e7	−1.75857
$613$	1.62747e7	1.74929	0.874645	−	0.484763i	$-0.161094\pi$
$613$	1.62747e7	1.74929	0.874645	+	0.484763i	$0.161094\pi$
$614$	−2.64411e6	−0.283047
$615$	−1.39629e6	−0.148863
$616$	−1.19226e6	−0.126596
$617$	3.62589e6	0.383444	0.191722	−	0.981449i	$-0.438593\pi$
$617$	3.62589e6	0.383444	0.191722	+	0.981449i	$0.438593\pi$
$618$	−689060.	−0.0725748
$619$	1.85683e7	1.94781	0.973904	−	0.226959i	$-0.0728784\pi$
$619$	1.85683e7	1.94781	0.973904	+	0.226959i	$0.0728784\pi$
$620$	1.47156e7	1.53745
$621$	4.18425e6	0.435400
$622$	658768.	0.0682742
$623$	1.38900e7	1.43378
$624$	−7.66876e6	−0.788431
$625$	−3.34783e6	−0.342817
$626$	18386.0	0.00187522
$627$	4.00074e6	0.406416
$628$	−1.58712e7	−1.60587
$629$	−1.13426e6	−0.114311
$630$	−5.03010e6	−0.504923
$631$	−1.01864e7	−1.01847	−0.509233	−	0.860629i	$-0.670071\pi$
$631$	−1.01864e7	−1.01847	−0.509233	+	0.860629i	$0.670071\pi$
$632$	786006.	0.0782768
$633$	−2.91066e7	−2.88724
$634$	479903.	0.0474166
$635$	−1.35844e7	−1.33692
$636$	5.79422e6	0.568005
$637$	−3.94315e6	−0.385030
$638$	−770098.	−0.0749021
$639$	1.09844e7	1.06420
$640$	−9.06556e6	−0.874872
$641$	−8.63019e6	−0.829613	−0.414806	−	0.909910i	$-0.636151\pi$
$641$	−8.63019e6	−0.829613	−0.414806	+	0.909910i	$0.636151\pi$
$642$	−2.41576e6	−0.231322
$643$	−1.05009e7	−1.00161	−0.500806	−	0.865560i	$-0.666963\pi$
$643$	−1.05009e7	−1.00161	−0.500806	+	0.865560i	$0.666963\pi$
$644$	5.55481e6	0.527782
$645$	5.10216e7	4.82897
$646$	−1.29278e6	−0.121883
$647$	−4.33805e6	−0.407412	−0.203706	−	0.979032i	$-0.565299\pi$
$647$	−4.33805e6	−0.407412	−0.203706	+	0.979032i	$0.565299\pi$
$648$	256106.	0.0239597
$649$	5.38599e6	0.501942
$650$	1.19509e6	0.110948
$651$	−2.33480e7	−2.15923
$652$	1.69068e6	0.155755
$653$	−7.19343e6	−0.660166	−0.330083	−	0.943952i	$-0.607077\pi$
$653$	−7.19343e6	−0.660166	−0.330083	+	0.943952i	$0.607077\pi$
$654$	−2.92932e6	−0.267807
$655$	−6.14651e6	−0.559790
$656$	601380.	0.0545619
$657$	1.69884e7	1.53546
$658$	−1.26206e6	−0.113636
$659$	1.08603e7	0.974160	0.487080	−	0.873357i	$-0.338062\pi$
$659$	1.08603e7	0.974160	0.487080	+	0.873357i	$0.338062\pi$
$660$	9.16966e6	0.819395
$661$	−5.82289e6	−0.518364	−0.259182	−	0.965828i	$-0.583453\pi$
$661$	−5.82289e6	−0.518364	−0.259182	+	0.965828i	$0.583453\pi$
$662$	−1.19856e6	−0.106295
$663$	−1.03713e7	−0.916322
$664$	4.04778e6	0.356284
$665$	1.79200e7	1.57139
$666$	293951.	0.0256796
$667$	7.25577e6	0.631493
$668$	2.16439e7	1.87669
$669$	−2.56179e7	−2.21298
$670$	3.18265e6	0.273906
$671$	−5.40197e6	−0.463176
$672$	1.08299e7	0.925130
$673$	−6.63196e6	−0.564423	−0.282211	−	0.959352i	$-0.591068\pi$
$673$	−6.63196e6	−0.564423	−0.282211	+	0.959352i	$0.591068\pi$
$674$	−1.31634e6	−0.111614
$675$	1.83233e7	1.54790
$676$	8.50961e6	0.716214
$677$	2.41847e6	0.202801	0.101400	−	0.994846i	$-0.467668\pi$
$677$	2.41847e6	0.202801	0.101400	+	0.994846i	$0.467668\pi$
$678$	−2.09407e6	−0.174951
$679$	−1.59691e7	−1.32924
$680$	−5.99208e6	−0.496941
$681$	2.85006e7	2.35498
$682$	−590745.	−0.0486339
$683$	−2.17485e7	−1.78393	−0.891965	−	0.452104i	$-0.850673\pi$
$683$	−2.17485e7	−1.78393	−0.891965	+	0.452104i	$0.850673\pi$
$684$	−1.50440e7	−1.22948
$685$	−3.52747e7	−2.87234
$686$	−615086.	−0.0499028
$687$	−3.05529e7	−2.46979
$688$	−2.19750e7	−1.76994
$689$	2.29846e6	0.184454
$690$	1.92404e6	0.153848
$691$	−2.24676e6	−0.179004	−0.0895018	−	0.995987i	$-0.528527\pi$
$691$	−2.24676e6	−0.179004	−0.0895018	+	0.995987i	$0.528527\pi$
$692$	−1.42280e6	−0.112948
$693$	−9.06721e6	−0.717200
$694$	2.92761e6	0.230735
$695$	1.71177e7	1.34426
$696$	9.39632e6	0.735250
$697$	813310.	0.0634124
$698$	−1.84557e6	−0.143381
$699$	−221567.	−0.0171519
$700$	2.43251e7	1.87633
$701$	1.80035e6	0.138376	0.0691882	−	0.997604i	$-0.477959\pi$
$701$	1.80035e6	0.138376	0.0691882	+	0.997604i	$0.477959\pi$
$702$	1.06291e6	0.0814052
$703$	−1.04722e6	−0.0799187
$704$	−3.76331e6	−0.286180
$705$	1.96292e7	1.48740
$706$	−2.40876e6	−0.181879
$707$	1.21241e7	0.912219
$708$	−3.24966e7	−2.43644
$709$	1.51524e7	1.13205	0.566026	−	0.824388i	$-0.308480\pi$
$709$	1.51524e7	1.13205	0.566026	+	0.824388i	$0.308480\pi$
$710$	1.99744e6	0.148706
$711$	5.97763e6	0.443461
$712$	−4.28810e6	−0.317004
$713$	5.56593e6	0.410028
$714$	4.70121e6	0.345115
$715$	3.63744e6	0.266091
$716$	8.39681e6	0.612113
$717$	−2.85815e7	−2.07628
$718$	3.34070e6	0.241839
$719$	−2.32346e7	−1.67615	−0.838076	−	0.545554i	$-0.816319\pi$
$719$	−2.32346e7	−1.67615	−0.838076	+	0.545554i	$0.816319\pi$
$720$	−3.36957e7	−2.42238
$721$	−5.56356e6	−0.398579
$722$	873818.	0.0623847
$723$	1.13096e7	0.804640
$724$	−1.75577e7	−1.24486
$725$	3.17738e7	2.24504
$726$	3.04684e6	0.214540
$727$	6.19296e6	0.434573	0.217286	−	0.976108i	$-0.430279\pi$
$727$	6.19296e6	0.434573	0.217286	+	0.976108i	$0.430279\pi$
$728$	2.85355e6	0.199553
$729$	−2.29650e7	−1.60047
$730$	3.08924e6	0.214558
$731$	−2.97191e7	−2.05704
$732$	3.25931e7	2.24826
$733$	2.21916e7	1.52556	0.762780	−	0.646659i	$-0.223834\pi$
$733$	2.21916e7	1.52556	0.762780	+	0.646659i	$0.223834\pi$
$734$	1.22556e6	0.0839642
$735$	−2.77999e7	−1.89812
$736$	−2.58174e6	−0.175679
$737$	5.73700e6	0.389060
$738$	−210774.	−0.0142455
$739$	2.35430e7	1.58581	0.792905	−	0.609346i	$-0.208568\pi$
$739$	2.35430e7	1.58581	0.792905	+	0.609346i	$0.208568\pi$
$740$	−2.40021e6	−0.161128
$741$	−9.57536e6	−0.640633
$742$	−1.04187e6	−0.0694712
$743$	−1.70057e7	−1.13012	−0.565058	−	0.825051i	$-0.691146\pi$
$743$	−1.70057e7	−1.13012	−0.565058	+	0.825051i	$0.691146\pi$
$744$	7.20796e6	0.477397
$745$	−2.64846e7	−1.74825
$746$	−422515.	−0.0277968
$747$	3.07836e7	2.01845
$748$	−5.34115e6	−0.349045
$749$	−1.95052e7	−1.27041
$750$	2.62469e6	0.170382
$751$	−2.57097e7	−1.66340	−0.831699	−	0.555226i	$-0.812632\pi$
$751$	−2.57097e7	−1.66340	−0.831699	+	0.555226i	$0.812632\pi$
$752$	−8.45429e6	−0.545170
$753$	3.45340e7	2.21952
$754$	1.84315e6	0.118068
$755$	−3.59245e7	−2.29363
$756$	2.16346e7	1.37672
$757$	8.87571e6	0.562942	0.281471	−	0.959570i	$-0.409178\pi$
$757$	8.87571e6	0.562942	0.281471	+	0.959570i	$0.409178\pi$
$758$	−2.66977e6	−0.168772
$759$	3.46826e6	0.218528
$760$	−5.53224e6	−0.347430
$761$	−4.81848e6	−0.301612	−0.150806	−	0.988563i	$-0.548187\pi$
$761$	−4.81848e6	−0.301612	−0.150806	+	0.988563i	$0.548187\pi$
$762$	−3.29030e6	−0.205280
$763$	−2.36517e7	−1.47079
$764$	1.92039e7	1.19030
$765$	−4.55702e7	−2.81532
$766$	−2.40637e6	−0.148180
$767$	−1.28908e7	−0.791211
$768$	2.10160e7	1.28572
$769$	−8.47775e6	−0.516969	−0.258485	−	0.966015i	$-0.583223\pi$
$769$	−8.47775e6	−0.516969	−0.258485	+	0.966015i	$0.583223\pi$
$770$	−1.64882e6	−0.100218
$771$	4.34388e6	0.263173
$772$	−1.89652e7	−1.14529
$773$	2.81819e6	0.169638	0.0848188	−	0.996396i	$-0.472969\pi$
$773$	2.81819e6	0.169638	0.0848188	+	0.996396i	$0.472969\pi$
$774$	7.70189e6	0.462109
$775$	2.43738e7	1.45770
$776$	4.92993e6	0.293891
$777$	3.80821e6	0.226292
$778$	−346973.	−0.0205517
$779$	750895.	0.0443339
$780$	−2.19467e7	−1.29161
$781$	3.60057e6	0.211224
$782$	−1.12072e6	−0.0655360
$783$	2.82594e7	1.64725
$784$	1.19734e7	0.695709
$785$	−4.43866e7	−2.57086
$786$	−1.48875e6	−0.0859540
$787$	7.39611e6	0.425664	0.212832	−	0.977089i	$-0.431731\pi$
$787$	7.39611e6	0.425664	0.212832	+	0.977089i	$0.431731\pi$
$788$	−1.21483e6	−0.0696949
$789$	−2.06624e7	−1.18165
$790$	1.08700e6	0.0619670
$791$	−1.69078e7	−0.960827
$792$	2.79921e6	0.158571
$793$	1.29291e7	0.730103
$794$	−1.91814e6	−0.107976
$795$	1.62045e7	0.909325
$796$	−2.02685e7	−1.13381
$797$	2.21559e7	1.23550	0.617751	−	0.786374i	$-0.288044\pi$
$797$	2.21559e7	1.23550	0.617751	+	0.786374i	$0.288044\pi$
$798$	4.34043e6	0.241282
$799$	−1.14336e7	−0.633602
$800$	−1.13057e7	−0.624560
$801$	−3.26113e7	−1.79592
$802$	1.46529e6	0.0804428
$803$	5.56863e6	0.304761
$804$	−3.46145e7	−1.88850
$805$	1.55350e7	0.844931
$806$	1.41389e6	0.0766616
$807$	−1.96745e7	−1.06346
$808$	−3.74291e6	−0.201689
$809$	1.35436e7	0.727549	0.363774	−	0.931487i	$-0.381488\pi$
$809$	1.35436e7	0.727549	0.363774	+	0.931487i	$0.381488\pi$
$810$	354178.	0.0189675
$811$	−2.23098e7	−1.19109	−0.595545	−	0.803322i	$-0.703064\pi$
$811$	−2.23098e7	−1.19109	−0.595545	+	0.803322i	$0.703064\pi$
$812$	3.75158e7	1.99675
$813$	1.28714e7	0.682966
$814$	96354.2	0.00509694
$815$	4.72828e6	0.249350
$816$	3.14925e7	1.65570
$817$	−2.74384e7	−1.43815
$818$	4.11667e6	0.215111
$819$	2.17015e7	1.13052
$820$	1.72105e6	0.0893836
$821$	2.15286e7	1.11470	0.557349	−	0.830278i	$-0.311819\pi$
$821$	2.15286e7	1.11470	0.557349	+	0.830278i	$0.311819\pi$
$822$	−8.54391e6	−0.441039
$823$	1.44509e7	0.743698	0.371849	−	0.928293i	$-0.378724\pi$
$823$	1.44509e7	0.743698	0.371849	+	0.928293i	$0.378724\pi$
$824$	1.71757e6	0.0881245
$825$	1.51879e7	0.776895
$826$	5.84330e6	0.297994
$827$	−2.66971e6	−0.135738	−0.0678688	−	0.997694i	$-0.521620\pi$
$827$	−2.66971e6	−0.135738	−0.0678688	+	0.997694i	$0.521620\pi$
$828$	−1.30417e7	−0.661086
$829$	7.23292e6	0.365534	0.182767	−	0.983156i	$-0.441495\pi$
$829$	7.23292e6	0.365534	0.182767	+	0.983156i	$0.441495\pi$
$830$	5.59782e6	0.282049
$831$	−2.13159e7	−1.07078
$832$	9.00711e6	0.451105
$833$	1.61929e7	0.808560
$834$	4.14611e6	0.206407
$835$	6.05308e7	3.00442
$836$	−4.93126e6	−0.244030
$837$	2.16779e7	1.06956
$838$	5.20381e6	0.255983
$839$	−3.28393e7	−1.61060	−0.805302	−	0.592865i	$-0.797997\pi$
$839$	−3.28393e7	−1.61060	−0.805302	+	0.592865i	$0.797997\pi$
$840$	2.01180e7	0.983755
$841$	2.84926e7	1.38913
$842$	−3.42682e6	−0.166575
$843$	8.84010e6	0.428438
$844$	3.58765e7	1.73362
$845$	2.37986e7	1.14659
$846$	2.96309e6	0.142337
$847$	2.46005e7	1.17825
$848$	−6.97930e6	−0.333290
$849$	−2.01029e7	−0.957171
$850$	−4.90775e6	−0.232989
$851$	−907838.	−0.0429719
$852$	−2.17242e7	−1.02529
$853$	−2.86786e7	−1.34954	−0.674769	−	0.738029i	$-0.735757\pi$
$853$	−2.86786e7	−1.34954	−0.674769	+	0.738029i	$0.735757\pi$
$854$	−5.86064e6	−0.274979
$855$	−4.20730e7	−1.96829
$856$	6.02159e6	0.280884
$857$	−2.45015e7	−1.13957	−0.569785	−	0.821794i	$-0.692973\pi$
$857$	−2.45015e7	−1.13957	−0.569785	+	0.821794i	$0.692973\pi$
$858$	881027.	0.0408574
$859$	1.56200e7	0.722266	0.361133	−	0.932514i	$-0.382390\pi$
$859$	1.56200e7	0.722266	0.361133	+	0.932514i	$0.382390\pi$
$860$	−6.28887e7	−2.89952
$861$	−2.73064e6	−0.125532
$862$	−3.84236e6	−0.176128
$863$	8.94840e6	0.408996	0.204498	−	0.978867i	$-0.434444\pi$
$863$	8.94840e6	0.408996	0.204498	+	0.978867i	$0.434444\pi$
$864$	−1.00553e7	−0.458257
$865$	−3.97911e6	−0.180820
$866$	−3.01626e6	−0.136670
$867$	6.53184e6	0.295113
$868$	2.87786e7	1.29649
$869$	1.95941e6	0.0880189
$870$	1.29945e7	0.582053
$871$	−1.37309e7	−0.613275
$872$	7.30171e6	0.325187
$873$	3.74925e7	1.66498
$874$	−1.03471e6	−0.0458186
$875$	2.11921e7	0.935736
$876$	−3.35986e7	−1.47932
$877$	−1.42942e6	−0.0627569	−0.0313785	−	0.999508i	$-0.509990\pi$
$877$	−1.42942e6	−0.0627569	−0.0313785	+	0.999508i	$0.509990\pi$
$878$	−4.34389e6	−0.190170
$879$	−1.49546e7	−0.652836
$880$	−1.10451e7	−0.480799
$881$	8.56181e6	0.371643	0.185821	−	0.982584i	$-0.440505\pi$
$881$	8.56181e6	0.371643	0.185821	+	0.982584i	$0.440505\pi$
$882$	−4.19649e6	−0.181641
$883$	−1.64638e7	−0.710604	−0.355302	−	0.934752i	$-0.615622\pi$
$883$	−1.64638e7	−0.710604	−0.355302	+	0.934752i	$0.615622\pi$
$884$	1.27835e7	0.550199
$885$	−9.08825e7	−3.90051
$886$	2.57836e6	0.110346
$887$	2.46335e7	1.05128	0.525639	−	0.850707i	$-0.323826\pi$
$887$	2.46335e7	1.05128	0.525639	+	0.850707i	$0.323826\pi$
$888$	−1.17566e6	−0.0500323
$889$	−2.65663e7	−1.12740
$890$	−5.93018e6	−0.250953
$891$	638438.	0.0269417
$892$	3.15764e7	1.32877
$893$	−1.05562e7	−0.442974
$894$	−6.41486e6	−0.268437
$895$	2.34831e7	0.979937
$896$	−1.77290e7	−0.737758
$897$	−8.30093e6	−0.344466
$898$	3.70251e6	0.153217
$899$	3.75910e7	1.55126
$900$	−5.71110e7	−2.35025
$901$	−9.43884e6	−0.387353
$902$	−69089.7	−0.00282746
$903$	9.97800e7	4.07216
$904$	5.21974e6	0.212436
$905$	−4.91032e7	−1.99291
$906$	−8.70132e6	−0.352180
$907$	−3.79451e7	−1.53157	−0.765786	−	0.643096i	$-0.777650\pi$
$907$	−3.79451e7	−1.53157	−0.765786	+	0.643096i	$0.777650\pi$
$908$	−3.51296e7	−1.41403
$909$	−2.84651e7	−1.14262
$910$	3.94628e6	0.157974
$911$	4.82815e7	1.92746	0.963729	−	0.266883i	$-0.0859936\pi$
$911$	4.82815e7	1.92746	0.963729	+	0.266883i	$0.0859936\pi$
$912$	2.90757e7	1.15756
$913$	1.00906e7	0.400626
$914$	−5.89223e6	−0.233300
$915$	9.11521e7	3.59927
$916$	3.76592e7	1.48297
$917$	−1.20204e7	−0.472057
$918$	−4.36492e6	−0.170950
$919$	7.56267e6	0.295384	0.147692	−	0.989033i	$-0.452816\pi$
$919$	7.56267e6	0.295384	0.147692	+	0.989033i	$0.452816\pi$
$920$	−4.79593e6	−0.186811
$921$	8.04250e7	3.12422
$922$	−935953.	−0.0362599
$923$	−8.61760e6	−0.332952
$924$	1.79326e7	0.690976
$925$	−3.97552e6	−0.152771
$926$	−216473.	−0.00829614
$927$	1.30622e7	0.499250
$928$	−1.74365e7	−0.664644
$929$	3.76999e7	1.43318	0.716591	−	0.697494i	$-0.245702\pi$
$929$	3.76999e7	1.43318	0.716591	+	0.697494i	$0.245702\pi$
$930$	9.96816e6	0.377927
$931$	1.49502e7	0.565293
$932$	273101.	0.0102987
$933$	−2.00375e7	−0.753598
$934$	−5.34154e6	−0.200355
$935$	−1.49375e7	−0.558789
$936$	−6.69963e6	−0.249955
$937$	1.91262e7	0.711673	0.355836	−	0.934548i	$-0.384196\pi$
$937$	1.91262e7	0.711673	0.355836	+	0.934548i	$0.384196\pi$
$938$	6.22412e6	0.230978
$939$	−559241.	−0.0206983
$940$	−2.41947e7	−0.893101
$941$	−2.42772e7	−0.893769	−0.446885	−	0.894592i	$-0.647467\pi$
$941$	−2.42772e7	−0.893769	−0.446885	+	0.894592i	$0.647467\pi$
$942$	−1.07509e7	−0.394747
$943$	650955.	0.0238381
$944$	3.91431e7	1.42964
$945$	6.05049e7	2.20400
$946$	2.52460e6	0.0917203
$947$	7.17272e6	0.259902	0.129951	−	0.991520i	$-0.458518\pi$
$947$	7.17272e6	0.259902	0.129951	+	0.991520i	$0.458518\pi$
$948$	−1.18222e7	−0.427245
$949$	−1.33280e7	−0.480395
$950$	−4.53112e6	−0.162891
$951$	−1.45971e7	−0.523376
$952$	−1.17184e7	−0.419059
$953$	3.24128e7	1.15607	0.578035	−	0.816012i	$-0.303820\pi$
$953$	3.24128e7	1.15607	0.578035	+	0.816012i	$0.303820\pi$
$954$	2.44613e6	0.0870180
$955$	5.37071e7	1.90556
$956$	3.52292e7	1.24669
$957$	2.34238e7	0.826756
$958$	4.72866e6	0.166466
$959$	−6.89846e7	−2.42218
$960$	6.35017e7	2.22386
$961$	207037.	0.00723169
$962$	−230614.	−0.00803431
$963$	4.57946e7	1.59129
$964$	−1.39401e7	−0.483141
$965$	−5.30395e7	−1.83350
$966$	3.76274e6	0.129736
$967$	−2.09828e6	−0.0721601	−0.0360800	−	0.999349i	$-0.511487\pi$
$967$	−2.09828e6	−0.0721601	−0.0360800	+	0.999349i	$0.511487\pi$
$968$	−7.59463e6	−0.260506
$969$	3.93221e7	1.34532
$970$	6.81779e6	0.232656
$971$	−3.46547e7	−1.17954	−0.589772	−	0.807570i	$-0.700782\pi$
$971$	−3.46547e7	−1.17954	−0.589772	+	0.807570i	$0.700782\pi$
$972$	2.68551e7	0.911719
$973$	3.34762e7	1.13359
$974$	−6.73331e6	−0.227421
$975$	−3.63507e7	−1.22462
$976$	−3.92593e7	−1.31922
$977$	5.84692e6	0.195970	0.0979852	−	0.995188i	$-0.468760\pi$
$977$	5.84692e6	0.195970	0.0979852	+	0.995188i	$0.468760\pi$
$978$	1.14524e6	0.0382869
$979$	−1.06897e7	−0.356457
$980$	3.42658e7	1.13971
$981$	5.55300e7	1.84228
$982$	−3.89044e6	−0.128742
$983$	5.89276e6	0.194507	0.0972535	−	0.995260i	$-0.468994\pi$
$983$	5.89276e6	0.194507	0.0972535	+	0.995260i	$0.468994\pi$
$984$	842996.	0.0277548
$985$	−3.39749e6	−0.111575
$986$	−7.56907e6	−0.247942
$987$	3.83876e7	1.25429
$988$	1.18025e7	0.384664
$989$	−2.37865e7	−0.773286
$990$	3.87113e6	0.125531
$991$	4.69350e7	1.51814	0.759072	−	0.651007i	$-0.225653\pi$
$991$	4.69350e7	1.51814	0.759072	+	0.651007i	$0.225653\pi$
$992$	−1.33756e7	−0.431553
$993$	3.64561e7	1.17327
$994$	3.90628e6	0.125400
$995$	−5.66845e7	−1.81512
$996$	−6.08820e7	−1.94465
$997$	−9.53778e6	−0.303885	−0.151943	−	0.988389i	$-0.548553\pi$
$997$	−9.53778e6	−0.303885	−0.151943	+	0.988389i	$0.548553\pi$
$998$	−551819.	−0.0175376
$999$	−3.53580e6	−0.112092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.6.a.b.1.19	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.6.a.b.1.19	✓	43	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-0.834938 q^{2} +25.3960 q^{3} -31.3029 q^{4} -87.5439 q^{5} -21.2041 q^{6} -171.205 q^{7} +52.8540 q^{8} +401.958 q^{9} +73.0938 q^{10} +131.758 q^{11} -794.969 q^{12} -315.350 q^{13} +142.945 q^{14} -2223.27 q^{15} +957.562 q^{16} +1295.01 q^{17} -335.610 q^{18} +1195.63 q^{19} +2740.38 q^{20} -4347.92 q^{21} -110.010 q^{22} +1036.50 q^{23} +1342.28 q^{24} +4538.94 q^{25} +263.297 q^{26} +4036.91 q^{27} +5359.20 q^{28} +7000.27 q^{29} +1856.29 q^{30} +5369.93 q^{31} -2490.83 q^{32} +3346.13 q^{33} -1081.25 q^{34} +14987.9 q^{35} -12582.4 q^{36} -875.870 q^{37} -998.277 q^{38} -8008.63 q^{39} -4627.04 q^{40} +628.033 q^{41} +3630.24 q^{42} -22948.9 q^{43} -4124.41 q^{44} -35189.0 q^{45} -865.412 q^{46} -8828.97 q^{47} +24318.3 q^{48} +12504.1 q^{49} -3789.73 q^{50} +32888.2 q^{51} +9871.35 q^{52} -7288.61 q^{53} -3370.57 q^{54} -11534.6 q^{55} -9048.85 q^{56} +30364.3 q^{57} -5844.79 q^{58} +40877.9 q^{59} +69594.7 q^{60} -40999.2 q^{61} -4483.56 q^{62} -68817.1 q^{63} -28562.3 q^{64} +27606.9 q^{65} -2793.81 q^{66} +43542.0 q^{67} -40537.6 q^{68} +26323.0 q^{69} -12514.0 q^{70} +27327.1 q^{71} +21245.1 q^{72} +42264.1 q^{73} +731.297 q^{74} +115271. q^{75} -37426.7 q^{76} -22557.6 q^{77} +6686.71 q^{78} +14871.3 q^{79} -83828.8 q^{80} +4845.53 q^{81} -524.368 q^{82} +76584.2 q^{83} +136102. q^{84} -113370. q^{85} +19160.9 q^{86} +177779. q^{87} +6963.93 q^{88} -81131.1 q^{89} +29380.6 q^{90} +53989.3 q^{91} -32445.4 q^{92} +136375. q^{93} +7371.64 q^{94} -104670. q^{95} -63257.2 q^{96} +93274.6 q^{97} -10440.1 q^{98} +52961.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 12 q^{2} + 98 q^{3} + 752 q^{4} + 146 q^{5} + 144 q^{6} + 831 q^{7} + 699 q^{8} + 3725 q^{9} + 1033 q^{10} + 1370 q^{11} + 3136 q^{12} + 2948 q^{13} + 929 q^{14} + 1859 q^{15} + 14080 q^{16} + 1545 q^{17}+ \cdots + 119867 q^{99}+O(q^{100}) \) 43 * q + 12 * q^2 + 98 * q^3 + 752 * q^4 + 146 * q^5 + 144 * q^6 + 831 * q^7 + 699 * q^8 + 3725 * q^9 + 1033 * q^10 + 1370 * q^11 + 3136 * q^12 + 2948 * q^13 + 929 * q^14 + 1859 * q^15 + 14080 * q^16 + 1545 * q^17 + 6757 * q^18 + 12233 * q^19 + 7419 * q^20 + 3674 * q^21 + 10369 * q^22 + 5564 * q^23 + 6813 * q^24 + 35439 * q^25 + 1578 * q^26 + 33755 * q^27 + 38990 * q^28 - 2405 * q^29 + 1483 * q^30 + 31280 * q^31 + 17700 * q^32 + 39326 * q^33 + 9394 * q^34 + 21436 * q^35 + 53290 * q^36 + 35510 * q^37 + 33614 * q^38 + 22963 * q^39 + 50046 * q^40 + 9866 * q^41 + 22195 * q^42 + 51379 * q^43 + 29746 * q^44 + 72219 * q^45 + 35053 * q^46 + 42481 * q^47 + 75938 * q^48 + 175192 * q^49 + 162531 * q^50 + 154051 * q^51 + 210234 * q^52 + 81848 * q^53 + 320743 * q^54 + 105027 * q^55 + 452104 * q^56 + 208589 * q^57 + 159979 * q^58 + 168687 * q^59 + 279933 * q^60 + 148330 * q^61 + 152995 * q^62 + 250849 * q^63 + 540617 * q^64 + 125561 * q^65 + 376032 * q^66 + 395178 * q^67 + 306925 * q^68 + 150249 * q^69 + 271319 * q^70 + 115563 * q^71 + 352975 * q^72 + 247249 * q^73 + 65989 * q^74 + 460002 * q^75 + 440494 * q^76 + 90902 * q^77 + 201225 * q^78 + 222999 * q^79 + 175770 * q^80 + 406335 * q^81 + 172447 * q^82 + 253668 * q^83 - 274214 * q^84 + 114986 * q^85 - 301722 * q^86 + 9553 * q^87 + 79659 * q^88 + 65396 * q^89 - 177829 * q^90 + 360807 * q^91 - 275338 * q^92 - 200055 * q^93 - 249179 * q^94 + 91983 * q^95 - 1089739 * q^96 + 399386 * q^97 - 57978 * q^98 + 119867 * q^99

Introduction

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