LMFDB - Embedded newform 197.6.a.b.1.15

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			1.15
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)

$f(q)$	$=$	\(q-5.19771 q^{2} +3.76016 q^{3} -4.98380 q^{4} +5.57792 q^{5} -19.5442 q^{6} +75.5206 q^{7} +192.231 q^{8} -228.861 q^{9} -28.9924 q^{10} +535.511 q^{11} -18.7399 q^{12} -703.883 q^{13} -392.534 q^{14} +20.9739 q^{15} -839.680 q^{16} +1823.54 q^{17} +1189.55 q^{18} -2264.64 q^{19} -27.7992 q^{20} +283.970 q^{21} -2783.43 q^{22} -711.106 q^{23} +722.820 q^{24} -3093.89 q^{25} +3658.58 q^{26} -1774.28 q^{27} -376.379 q^{28} +4657.25 q^{29} -109.016 q^{30} +8116.66 q^{31} -1786.98 q^{32} +2013.61 q^{33} -9478.21 q^{34} +421.248 q^{35} +1140.60 q^{36} -66.5124 q^{37} +11770.9 q^{38} -2646.72 q^{39} +1072.25 q^{40} -10115.6 q^{41} -1475.99 q^{42} -9329.01 q^{43} -2668.88 q^{44} -1276.57 q^{45} +3696.12 q^{46} +22696.0 q^{47} -3157.34 q^{48} -11103.6 q^{49} +16081.1 q^{50} +6856.79 q^{51} +3508.01 q^{52} +34630.8 q^{53} +9222.17 q^{54} +2987.04 q^{55} +14517.4 q^{56} -8515.42 q^{57} -24207.1 q^{58} -7445.49 q^{59} -104.530 q^{60} +48629.2 q^{61} -42188.0 q^{62} -17283.7 q^{63} +36158.0 q^{64} -3926.20 q^{65} -10466.2 q^{66} +49198.6 q^{67} -9088.14 q^{68} -2673.88 q^{69} -2189.52 q^{70} +60666.4 q^{71} -43994.2 q^{72} +69639.7 q^{73} +345.712 q^{74} -11633.5 q^{75} +11286.5 q^{76} +40442.1 q^{77} +13756.9 q^{78} +36459.9 q^{79} -4683.67 q^{80} +48941.7 q^{81} +52578.2 q^{82} -33146.0 q^{83} -1415.25 q^{84} +10171.5 q^{85} +48489.5 q^{86} +17512.0 q^{87} +102942. q^{88} +52330.9 q^{89} +6635.24 q^{90} -53157.7 q^{91} +3544.01 q^{92} +30520.0 q^{93} -117967. q^{94} -12632.0 q^{95} -6719.34 q^{96} -69399.8 q^{97} +57713.5 q^{98} -122558. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.19771	−0.918834	−0.459417	−	0.888221i	$-0.651942\pi$
$2$	−5.19771	−0.918834	−0.459417	+	0.888221i	$0.651942\pi$
$3$	3.76016	0.241215	0.120607	−	0.992700i	$-0.461516\pi$
$3$	3.76016	0.241215	0.120607	+	0.992700i	$0.461516\pi$
$4$	−4.98380	−0.155744
$5$	5.57792	0.0997809	0.0498904	−	0.998755i	$-0.484113\pi$
$5$	5.57792	0.0997809	0.0498904	+	0.998755i	$0.484113\pi$
$6$	−19.5442	−0.221636
$7$	75.5206	0.582532	0.291266	−	0.956642i	$-0.405923\pi$
$7$	75.5206	0.582532	0.291266	+	0.956642i	$0.405923\pi$
$8$	192.231	1.06194
$9$	−228.861	−0.941816
$10$	−28.9924	−0.0916821
$11$	535.511	1.33440	0.667201	−	0.744878i	$-0.267492\pi$
$11$	535.511	1.33440	0.667201	+	0.744878i	$0.267492\pi$
$12$	−18.7399	−0.0375677
$13$	−703.883	−1.15516	−0.577580	−	0.816334i	$-0.696003\pi$
$13$	−703.883	−1.15516	−0.577580	+	0.816334i	$0.696003\pi$
$14$	−392.534	−0.535251
$15$	20.9739	0.0240686
$16$	−839.680	−0.820000
$17$	1823.54	1.53035	0.765177	−	0.643820i	$-0.222651\pi$
$17$	1823.54	1.53035	0.765177	+	0.643820i	$0.222651\pi$
$18$	1189.55	0.865372
$19$	−2264.64	−1.43918	−0.719590	−	0.694399i	$-0.755670\pi$
$19$	−2264.64	−1.43918	−0.719590	+	0.694399i	$0.755670\pi$
$20$	−27.7992	−0.0155402
$21$	283.970	0.140515
$22$	−2783.43	−1.22609
$23$	−711.106	−0.280295	−0.140147	−	0.990131i	$-0.544758\pi$
$23$	−711.106	−0.280295	−0.140147	+	0.990131i	$0.544758\pi$
$24$	722.820	0.256155
$25$	−3093.89	−0.990044
$26$	3658.58	1.06140
$27$	−1774.28	−0.468394
$28$	−376.379	−0.0907258
$29$	4657.25	1.02834	0.514168	−	0.857690i	$-0.328101\pi$
$29$	4657.25	1.02834	0.514168	+	0.857690i	$0.328101\pi$
$30$	−109.016	−0.0221151
$31$	8116.66	1.51696	0.758478	−	0.651699i	$-0.225943\pi$
$31$	8116.66	1.51696	0.758478	+	0.651699i	$0.225943\pi$
$32$	−1786.98	−0.308493
$33$	2013.61	0.321877
$34$	−9478.21	−1.40614
$35$	421.248	0.0581256
$36$	1140.60	0.146682
$37$	−66.5124	−0.00798727	−0.00399363	−	0.999992i	$-0.501271\pi$
$37$	−66.5124	−0.00798727	−0.00399363	+	0.999992i	$0.501271\pi$
$38$	11770.9	1.32237
$39$	−2646.72	−0.278642
$40$	1072.25	0.105961
$41$	−10115.6	−0.939796	−0.469898	−	0.882721i	$-0.655709\pi$
$41$	−10115.6	−0.939796	−0.469898	+	0.882721i	$0.655709\pi$
$42$	−1475.99	−0.129110
$43$	−9329.01	−0.769422	−0.384711	−	0.923037i	$-0.625699\pi$
$43$	−9329.01	−0.769422	−0.384711	+	0.923037i	$0.625699\pi$
$44$	−2668.88	−0.207825
$45$	−1276.57	−0.0939752
$46$	3696.12	0.257544
$47$	22696.0	1.49866	0.749332	−	0.662194i	$-0.230375\pi$
$47$	22696.0	1.49866	0.749332	+	0.662194i	$0.230375\pi$
$48$	−3157.34	−0.197796
$49$	−11103.6	−0.660656
$50$	16081.1	0.909686
$51$	6856.79	0.369144
$52$	3508.01	0.179909
$53$	34630.8	1.69345	0.846725	−	0.532031i	$-0.178571\pi$
$53$	34630.8	1.69345	0.846725	+	0.532031i	$0.178571\pi$
$54$	9222.17	0.430377
$55$	2987.04	0.133148
$56$	14517.4	0.618613
$57$	−8515.42	−0.347151
$58$	−24207.1	−0.944870
$59$	−7445.49	−0.278460	−0.139230	−	0.990260i	$-0.544463\pi$
$59$	−7445.49	−0.278460	−0.139230	+	0.990260i	$0.544463\pi$
$60$	−104.530	−0.00374853
$61$	48629.2	1.67330	0.836648	−	0.547741i	$-0.184512\pi$
$61$	48629.2	1.67330	0.836648	+	0.547741i	$0.184512\pi$
$62$	−42188.0	−1.39383
$63$	−17283.7	−0.548638
$64$	36158.0	1.10345
$65$	−3926.20	−0.115263
$66$	−10466.2	−0.295752
$67$	49198.6	1.33896	0.669478	−	0.742832i	$-0.266518\pi$
$67$	49198.6	1.33896	0.669478	+	0.742832i	$0.266518\pi$
$68$	−9088.14	−0.238343
$69$	−2673.88	−0.0676112
$70$	−2189.52	−0.0534078
$71$	60666.4	1.42824	0.714122	−	0.700021i	$-0.246826\pi$
$71$	60666.4	1.42824	0.714122	+	0.700021i	$0.246826\pi$
$72$	−43994.2	−1.00015
$73$	69639.7	1.52950	0.764750	−	0.644327i	$-0.222862\pi$
$73$	69639.7	1.52950	0.764750	+	0.644327i	$0.222862\pi$
$74$	345.712	0.00733897
$75$	−11633.5	−0.238813
$76$	11286.5	0.224143
$77$	40442.1	0.777332
$78$	13756.9	0.256025
$79$	36459.9	0.657276	0.328638	−	0.944456i	$-0.393410\pi$
$79$	36459.9	0.657276	0.328638	+	0.944456i	$0.393410\pi$
$80$	−4683.67	−0.0818203
$81$	48941.7	0.828832
$82$	52578.2	0.863517
$83$	−33146.0	−0.528123	−0.264062	−	0.964506i	$-0.585062\pi$
$83$	−33146.0	−0.528123	−0.264062	+	0.964506i	$0.585062\pi$
$84$	−1415.25	−0.0218844
$85$	10171.5	0.152700
$86$	48489.5	0.706971
$87$	17512.0	0.248050
$88$	102942.	1.41705
$89$	52330.9	0.700299	0.350149	−	0.936694i	$-0.386131\pi$
$89$	52330.9	0.700299	0.350149	+	0.936694i	$0.386131\pi$
$90$	6635.24	0.0863476
$91$	−53157.7	−0.672919
$92$	3544.01	0.0436541
$93$	30520.0	0.365912
$94$	−117967.	−1.37702
$95$	−12632.0	−0.143603
$96$	−6719.34	−0.0744129
$97$	−69399.8	−0.748909	−0.374454	−	0.927245i	$-0.622170\pi$
$97$	−69399.8	−0.748909	−0.374454	+	0.927245i	$0.622170\pi$
$98$	57713.5	0.607033
$99$	−122558.	−1.25676
$100$	15419.3	0.154193
$101$	25233.5	0.246135	0.123068	−	0.992398i	$-0.460727\pi$
$101$	25233.5	0.246135	0.123068	+	0.992398i	$0.460727\pi$
$102$	−35639.6	−0.339182
$103$	−75257.5	−0.698968	−0.349484	−	0.936942i	$-0.613643\pi$
$103$	−75257.5	−0.698968	−0.349484	+	0.936942i	$0.613643\pi$
$104$	−135308.	−1.22671
$105$	1583.96	0.0140207
$106$	−180001.	−1.55600
$107$	−157044.	−1.32606	−0.663028	−	0.748594i	$-0.730729\pi$
$107$	−157044.	−1.32606	−0.663028	+	0.748594i	$0.730729\pi$
$108$	8842.63	0.0729495
$109$	208857.	1.68377	0.841885	−	0.539656i	$-0.181446\pi$
$109$	208857.	1.68377	0.841885	+	0.539656i	$0.181446\pi$
$110$	−15525.8	−0.122341
$111$	−250.097	−0.00192665
$112$	−63413.1	−0.477677
$113$	45591.5	0.335883	0.167942	−	0.985797i	$-0.446288\pi$
$113$	45591.5	0.335883	0.167942	+	0.985797i	$0.446288\pi$
$114$	44260.7	0.318975
$115$	−3966.49	−0.0279680
$116$	−23210.8	−0.160157
$117$	161092.	1.08795
$118$	38699.5	0.255859
$119$	137714.	0.891481
$120$	4031.83	0.0255593
$121$	125721.	0.780628
$122$	−252761.	−1.53748
$123$	−38036.5	−0.226693
$124$	−40451.8	−0.236256
$125$	−34688.4	−0.198568
$126$	89835.8	0.504107
$127$	−194477.	−1.06994	−0.534969	−	0.844872i	$-0.679677\pi$
$127$	−194477.	−1.06994	−0.534969	+	0.844872i	$0.679677\pi$
$128$	−130755.	−0.705398
$129$	−35078.6	−0.185596
$130$	20407.3	0.105908
$131$	20848.1	0.106142	0.0530711	−	0.998591i	$-0.483099\pi$
$131$	20848.1	0.106142	0.0530711	+	0.998591i	$0.483099\pi$
$132$	−10035.4	−0.0501303
$133$	−171027.	−0.838369
$134$	−255720.	−1.23028
$135$	−9896.76	−0.0467368
$136$	350540.	1.62514
$137$	8886.47	0.0404509	0.0202254	−	0.999795i	$-0.493562\pi$
$137$	8886.47	0.0404509	0.0202254	+	0.999795i	$0.493562\pi$
$138$	13898.0	0.0621234
$139$	−55059.5	−0.241710	−0.120855	−	0.992670i	$-0.538564\pi$
$139$	−55059.5	−0.241710	−0.120855	+	0.992670i	$0.538564\pi$
$140$	−2099.41	−0.00905269
$141$	85340.6	0.361500
$142$	−315327.	−1.31232
$143$	−376937.	−1.54145
$144$	192170.	0.772289
$145$	25977.8	0.102608
$146$	−361967.	−1.40536
$147$	−41751.5	−0.159360
$148$	331.484	0.00124397
$149$	275661.	1.01721	0.508604	−	0.861000i	$-0.330162\pi$
$149$	275661.	1.01721	0.508604	+	0.861000i	$0.330162\pi$
$150$	60467.7	0.219430
$151$	−187066.	−0.667657	−0.333828	−	0.942634i	$-0.608341\pi$
$151$	−187066.	−0.667657	−0.333828	+	0.942634i	$0.608341\pi$
$152$	−435334.	−1.52832
$153$	−417337.	−1.44131
$154$	−210206.	−0.714240
$155$	45274.0	0.151363
$156$	13190.7	0.0433967
$157$	−431171.	−1.39605	−0.698023	−	0.716075i	$-0.745937\pi$
$157$	−431171.	−1.39605	−0.698023	+	0.716075i	$0.745937\pi$
$158$	−189508.	−0.603927
$159$	130217.	0.408485
$160$	−9967.63	−0.0307817
$161$	−53703.1	−0.163281
$162$	−254385.	−0.761559
$163$	266240.	0.784882	0.392441	−	0.919777i	$-0.371631\pi$
$163$	266240.	0.784882	0.392441	+	0.919777i	$0.371631\pi$
$164$	50414.3	0.146367
$165$	11231.7	0.0321172
$166$	172283.	0.485258
$167$	212836.	0.590546	0.295273	−	0.955413i	$-0.404589\pi$
$167$	212836.	0.590546	0.295273	+	0.955413i	$0.404589\pi$
$168$	54587.8	0.149218
$169$	124159.	0.334396
$170$	−52868.7	−0.140306
$171$	518288.	1.35544
$172$	46493.9	0.119833
$173$	696415.	1.76910	0.884551	−	0.466443i	$-0.154465\pi$
$173$	696415.	1.76910	0.884551	+	0.466443i	$0.154465\pi$
$174$	−91022.5	−0.227916
$175$	−233652.	−0.576733
$176$	−449658.	−1.09421
$177$	−27996.2	−0.0671687
$178$	−272001.	−0.643459
$179$	−451438.	−1.05309	−0.526545	−	0.850148i	$-0.676513\pi$
$179$	−451438.	−1.05309	−0.526545	+	0.850148i	$0.676513\pi$
$180$	6362.16	0.0146360
$181$	717221.	1.62726	0.813629	−	0.581385i	$-0.197489\pi$
$181$	717221.	1.62726	0.813629	+	0.581385i	$0.197489\pi$
$182$	276298.	0.618301
$183$	182854.	0.403623
$184$	−136697.	−0.297655
$185$	−371.001	−0.000796976 0
$186$	−158634.	−0.336212
$187$	976523.	2.04211
$188$	−113112.	−0.233408
$189$	−133994.	−0.272855
$190$	65657.4	0.131947
$191$	588227.	1.16671	0.583354	−	0.812218i	$-0.301740\pi$
$191$	588227.	1.16671	0.583354	+	0.812218i	$0.301740\pi$
$192$	135960.	0.266169
$193$	−224178.	−0.433211	−0.216606	−	0.976259i	$-0.569499\pi$
$193$	−224178.	−0.433211	−0.216606	+	0.976259i	$0.569499\pi$
$194$	360720.	0.688123
$195$	−14763.2	−0.0278031
$196$	55338.3	0.102893
$197$	38809.0	0.0712470
$197$	38809.0	0.0712470
$198$	637019.	1.15475
$199$	324.370	0.000580642 0	0.000290321	−	1.00000i	$-0.499908\pi$
$199$	324.370	0.000580642 0	0.000290321		1.00000i	$0.499908\pi$
$200$	−594741.	−1.05136
$201$	184995.	0.322976
$202$	−131156.	−0.226157
$203$	351718.	0.599039
$204$	−34172.9	−0.0574918
$205$	−56424.2	−0.0937737
$206$	391167.	0.642235
$207$	162745.	0.263986
$208$	591037.	0.947232
$209$	−1.21274e6	−1.92044
$210$	−8232.97	−0.0128827
$211$	−185429.	−0.286729	−0.143364	−	0.989670i	$-0.545792\pi$
$211$	−185429.	−0.286729	−0.143364	+	0.989670i	$0.545792\pi$
$212$	−172593.	−0.263744
$213$	228116.	0.344513
$214$	816269.	1.21843
$215$	−52036.5	−0.0767735
$216$	−341071.	−0.497405
$217$	612974.	0.883676
$218$	−1.08558e6	−1.54711
$219$	261857.	0.368938
$220$	−14886.8	−0.0207369
$221$	−1.28356e6	−1.76781
$222$	1299.93	0.00177027
$223$	−975718.	−1.31390	−0.656950	−	0.753935i	$-0.728154\pi$
$223$	−975718.	−1.31390	−0.656950	+	0.753935i	$0.728154\pi$
$224$	−134954.	−0.179707
$225$	708071.	0.932439
$226$	−236972.	−0.308621
$227$	1.43184e6	1.84429	0.922143	−	0.386848i	$-0.126436\pi$
$227$	1.43184e6	1.84429	0.922143	+	0.386848i	$0.126436\pi$
$228$	42439.1	0.0540666
$229$	−1.36811e6	−1.72398	−0.861992	−	0.506922i	$-0.830783\pi$
$229$	−1.36811e6	−1.72398	−0.861992	+	0.506922i	$0.830783\pi$
$230$	20616.7	0.0256980
$231$	152069.	0.187504
$232$	895269.	1.09203
$233$	341372.	0.411944	0.205972	−	0.978558i	$-0.433964\pi$
$233$	341372.	0.411944	0.205972	+	0.978558i	$0.433964\pi$
$234$	−837308.	−0.999644
$235$	126596.	0.149538
$236$	37106.8	0.0433684
$237$	137095.	0.158545
$238$	−715800.	−0.819123
$239$	258337.	0.292544	0.146272	−	0.989244i	$-0.453272\pi$
$239$	258337.	0.292544	0.146272	+	0.989244i	$0.453272\pi$
$240$	−17611.4	−0.0197363
$241$	742372.	0.823340	0.411670	−	0.911333i	$-0.364946\pi$
$241$	742372.	0.823340	0.411670	+	0.911333i	$0.364946\pi$
$242$	−653461.	−0.717267
$243$	615178.	0.668321
$244$	−242358.	−0.260605
$245$	−61935.2	−0.0659208
$246$	197703.	0.208293
$247$	1.59404e6	1.66248
$248$	1.56027e6	1.61091
$249$	−124634.	−0.127391
$250$	180301.	0.182451
$251$	1.76033e6	1.76364	0.881821	−	0.471583i	$-0.156317\pi$
$251$	1.76033e6	1.76364	0.881821	+	0.471583i	$0.156317\pi$
$252$	86138.6	0.0854469
$253$	−380805.	−0.374026
$254$	1.01083e6	0.983096
$255$	38246.6	0.0368335
$256$	−477427.	−0.455310
$257$	−769457.	−0.726694	−0.363347	−	0.931654i	$-0.618366\pi$
$257$	−769457.	−0.726694	−0.363347	+	0.931654i	$0.618366\pi$
$258$	182328.	0.170532
$259$	−5023.05	−0.00465284
$260$	19567.4	0.0179515
$261$	−1.06586e6	−0.968502
$262$	−108362.	−0.0975271
$263$	−874387.	−0.779497	−0.389748	−	0.920921i	$-0.627438\pi$
$263$	−874387.	−0.779497	−0.389748	+	0.920921i	$0.627438\pi$
$264$	387078.	0.341813
$265$	193168.	0.168974
$266$	888949.	0.770322
$267$	196773.	0.168922
$268$	−245196.	−0.208534
$269$	−26277.9	−0.0221417	−0.0110708	−	0.999939i	$-0.503524\pi$
$269$	−26277.9	−0.0221417	−0.0110708	+	0.999939i	$0.503524\pi$
$270$	51440.5	0.0429434
$271$	395415.	0.327062	0.163531	−	0.986538i	$-0.447712\pi$
$271$	395415.	0.327062	0.163531	+	0.986538i	$0.447712\pi$
$272$	−1.53119e6	−1.25489
$273$	−199882.	−0.162318
$274$	−46189.3	−0.0371676
$275$	−1.65681e6	−1.32112
$276$	13326.1	0.0105300
$277$	1.49333e6	1.16938	0.584690	−	0.811257i	$-0.301216\pi$
$277$	1.49333e6	1.16938	0.584690	+	0.811257i	$0.301216\pi$
$278$	286183.	0.222092
$279$	−1.85759e6	−1.42869
$280$	80976.9	0.0617257
$281$	−1.44166e6	−1.08918	−0.544588	−	0.838704i	$-0.683314\pi$
$281$	−1.44166e6	−1.08918	−0.544588	+	0.838704i	$0.683314\pi$
$282$	−443576.	−0.332158
$283$	963140.	0.714864	0.357432	−	0.933939i	$-0.383652\pi$
$283$	963140.	0.714864	0.357432	+	0.933939i	$0.383652\pi$
$284$	−302349.	−0.222440
$285$	−47498.3	−0.0346391
$286$	1.95921e6	1.41634
$287$	−763939.	−0.547462
$288$	408970.	0.290543
$289$	1.90543e6	1.34198
$290$	−135025.	−0.0942799
$291$	−260955.	−0.180648
$292$	−347070.	−0.238210
$293$	−1.90757e6	−1.29811	−0.649055	−	0.760742i	$-0.724835\pi$
$293$	−1.90757e6	−1.29811	−0.649055	+	0.760742i	$0.724835\pi$
$294$	217012.	0.146425
$295$	−41530.3	−0.0277850
$296$	−12785.7	−0.00848197
$297$	−950144.	−0.625026
$298$	−1.43281e6	−0.934646
$299$	500536.	0.323785
$300$	57979.1	0.0371936
$301$	−704532.	−0.448213
$302$	972317.	0.613466
$303$	94882.0	0.0593714
$304$	1.90157e6	1.18013
$305$	271250.	0.166963
$306$	2.16920e6	1.32433
$307$	1.16830e6	0.707472	0.353736	−	0.935345i	$-0.384911\pi$
$307$	1.16830e6	0.707472	0.353736	+	0.935345i	$0.384911\pi$
$308$	−201555.	−0.121065
$309$	−282981.	−0.168601
$310$	−235321.	−0.139078
$311$	380703.	0.223195	0.111598	−	0.993753i	$-0.464403\pi$
$311$	380703.	0.223195	0.111598	+	0.993753i	$0.464403\pi$
$312$	−508781.	−0.295900
$313$	1.50517e6	0.868411	0.434205	−	0.900814i	$-0.357029\pi$
$313$	1.50517e6	0.868411	0.434205	+	0.900814i	$0.357029\pi$
$314$	2.24110e6	1.28274
$315$	−96407.2	−0.0547436
$316$	−181709.	−0.102367
$317$	−138597.	−0.0774653	−0.0387326	−	0.999250i	$-0.512332\pi$
$317$	−138597.	−0.0774653	−0.0387326	+	0.999250i	$0.512332\pi$
$318$	−676832.	−0.375330
$319$	2.49401e6	1.37221
$320$	201686.	0.110104
$321$	−590511.	−0.319864
$322$	279133.	0.150028
$323$	−4.12965e6	−2.20246
$324$	−243916.	−0.129085
$325$	2.17774e6	1.14366
$326$	−1.38384e6	−0.721177
$327$	785337.	0.406150
$328$	−1.94454e6	−0.998004
$329$	1.71401e6	0.873021
$330$	−58379.4	−0.0295104
$331$	−3.93334e6	−1.97330	−0.986648	−	0.162870i	$-0.947925\pi$
$331$	−3.93334e6	−1.97330	−0.986648	+	0.162870i	$0.947925\pi$
$332$	165193.	0.0822519
$333$	15222.1	0.00752253
$334$	−1.10626e6	−0.542614
$335$	274426.	0.133602
$336$	−238444.	−0.115223
$337$	3.45853e6	1.65889	0.829444	−	0.558590i	$-0.188658\pi$
$337$	3.45853e6	1.65889	0.829444	+	0.558590i	$0.188658\pi$
$338$	−645342.	−0.307254
$339$	171432.	0.0810199
$340$	−50692.9	−0.0237821
$341$	4.34656e6	2.02423
$342$	−2.69391e6	−1.24543
$343$	−2.10783e6	−0.967386
$344$	−1.79333e6	−0.817077
$345$	−14914.7	−0.00674630
$346$	−3.61977e6	−1.62551
$347$	−1.65303e6	−0.736981	−0.368490	−	0.929632i	$-0.620125\pi$
$347$	−1.65303e6	−0.736981	−0.368490	+	0.929632i	$0.620125\pi$
$348$	−87276.4	−0.0386322
$349$	751225.	0.330146	0.165073	−	0.986281i	$-0.447214\pi$
$349$	751225.	0.330146	0.165073	+	0.986281i	$0.447214\pi$
$350$	1.21446e6	0.529922
$351$	1.24888e6	0.541071
$352$	−956947.	−0.411653
$353$	−722241.	−0.308493	−0.154246	−	0.988032i	$-0.549295\pi$
$353$	−722241.	−0.308493	−0.154246	+	0.988032i	$0.549295\pi$
$354$	145516.	0.0617169
$355$	338392.	0.142511
$356$	−260807.	−0.109067
$357$	517829.	0.215038
$358$	2.34644e6	0.967614
$359$	−335743.	−0.137490	−0.0687449	−	0.997634i	$-0.521899\pi$
$359$	−335743.	−0.137490	−0.0687449	+	0.997634i	$0.521899\pi$
$360$	−245396.	−0.0997957
$361$	2.65250e6	1.07124
$362$	−3.72791e6	−1.49518
$363$	472731.	0.188299
$364$	264927.	0.104803
$365$	388444.	0.152615
$366$	−950422.	−0.370863
$367$	2.22140e6	0.860918	0.430459	−	0.902610i	$-0.358352\pi$
$367$	2.22140e6	0.860918	0.430459	+	0.902610i	$0.358352\pi$
$368$	597102.	0.229842
$369$	2.31508e6	0.885115
$370$	1928.35	0.000732289 0
$371$	2.61533e6	0.986490
$372$	−152105.	−0.0569885
$373$	−864573.	−0.321758	−0.160879	−	0.986974i	$-0.551433\pi$
$373$	−864573.	−0.321758	−0.160879	+	0.986974i	$0.551433\pi$
$374$	−5.07569e6	−1.87636
$375$	−130434.	−0.0478976
$376$	4.36287e6	1.59149
$377$	−3.27816e6	−1.18789
$378$	696464.	0.250708
$379$	4.99610e6	1.78662	0.893311	−	0.449439i	$-0.148376\pi$
$379$	4.99610e6	1.78662	0.893311	+	0.449439i	$0.148376\pi$
$380$	62955.2	0.0223652
$381$	−731265.	−0.258085
$382$	−3.05744e6	−1.07201
$383$	−4.18551e6	−1.45798	−0.728990	−	0.684524i	$-0.760010\pi$
$383$	−4.18551e6	−1.45798	−0.728990	+	0.684524i	$0.760010\pi$
$384$	−491662.	−0.170152
$385$	225583.	0.0775629
$386$	1.16521e6	0.398049
$387$	2.13505e6	0.724653
$388$	345875.	0.116638
$389$	−3.48494e6	−1.16767	−0.583836	−	0.811872i	$-0.698449\pi$
$389$	−3.48494e6	−1.16767	−0.583836	+	0.811872i	$0.698449\pi$
$390$	76734.7	0.0255464
$391$	−1.29673e6	−0.428950
$392$	−2.13447e6	−0.701575
$393$	78392.3	0.0256031
$394$	−201718.	−0.0654642
$395$	203370.	0.0655835
$396$	610803.	0.195732
$397$	899629.	0.286475	0.143238	−	0.989688i	$-0.454249\pi$
$397$	899629.	0.286475	0.143238	+	0.989688i	$0.454249\pi$
$398$	−1685.98	−0.000533513 0
$399$	−643089.	−0.202227
$400$	2.59788e6	0.811836
$401$	−4.00012e6	−1.24226	−0.621129	−	0.783709i	$-0.713326\pi$
$401$	−4.00012e6	−1.24226	−0.621129	+	0.783709i	$0.713326\pi$
$402$	−961550.	−0.296761
$403$	−5.71318e6	−1.75233
$404$	−125759.	−0.0383340
$405$	272993.	0.0827016
$406$	−1.82813e6	−0.550417
$407$	−35618.1	−0.0106582
$408$	1.31809e6	0.392007
$409$	−3.35798e6	−0.992590	−0.496295	−	0.868154i	$-0.665306\pi$
$409$	−3.35798e6	−0.992590	−0.496295	+	0.868154i	$0.665306\pi$
$410$	293277.	0.0861625
$411$	33414.6	0.00975734
$412$	375068.	0.108860
$413$	−562287.	−0.162212
$414$	−845899.	−0.242559
$415$	−184885.	−0.0526966
$416$	1.25783e6	0.356358
$417$	−207033.	−0.0583040
$418$	6.30347e6	1.76457
$419$	727261.	0.202374	0.101187	−	0.994867i	$-0.467736\pi$
$419$	727261.	0.202374	0.101187	+	0.994867i	$0.467736\pi$
$420$	−7894.14	−0.00218364
$421$	−5.18504e6	−1.42576	−0.712881	−	0.701285i	$-0.752610\pi$
$421$	−5.18504e6	−1.42576	−0.712881	+	0.701285i	$0.752610\pi$
$422$	963806.	0.263456
$423$	−5.19423e6	−1.41147
$424$	6.65711e6	1.79834
$425$	−5.64181e6	−1.51512
$426$	−1.18568e6	−0.316551
$427$	3.67251e6	0.974749
$428$	782676.	0.206525
$429$	−1.41735e6	−0.371820
$430$	270470.	0.0705422
$431$	−13997.1	−0.00362947	−0.00181474	−	0.999998i	$-0.500578\pi$
$431$	−13997.1	−0.00362947	−0.00181474	+	0.999998i	$0.500578\pi$
$432$	1.48982e6	0.384083
$433$	4.94322e6	1.26704	0.633519	−	0.773727i	$-0.281610\pi$
$433$	4.94322e6	1.26704	0.633519	+	0.773727i	$0.281610\pi$
$434$	−3.18606e6	−0.811952
$435$	97680.7	0.0247506
$436$	−1.04090e6	−0.262237
$437$	1.61040e6	0.403394
$438$	−1.36105e6	−0.338993
$439$	−3.75112e6	−0.928965	−0.464482	−	0.885582i	$-0.653760\pi$
$439$	−3.75112e6	−0.928965	−0.464482	+	0.885582i	$0.653760\pi$
$440$	574201.	0.141394
$441$	2.54119e6	0.622216
$442$	6.67156e6	1.62432
$443$	−1.46686e6	−0.355123	−0.177561	−	0.984110i	$-0.556821\pi$
$443$	−1.46686e6	−0.355123	−0.177561	+	0.984110i	$0.556821\pi$
$444$	1246.44	0.000300063 0
$445$	291898.	0.0698764
$446$	5.07150e6	1.20726
$447$	1.03653e6	0.245366
$448$	2.73067e6	0.642798
$449$	7.39536e6	1.73119	0.865593	−	0.500748i	$-0.166942\pi$
$449$	7.39536e6	1.73119	0.865593	+	0.500748i	$0.166942\pi$
$450$	−3.68035e6	−0.856756
$451$	−5.41703e6	−1.25407
$452$	−227219.	−0.0523117
$453$	−703400.	−0.161049
$454$	−7.44227e6	−1.69459
$455$	−296509.	−0.0671444
$456$	−1.63693e6	−0.368653
$457$	−4.56751e6	−1.02303	−0.511516	−	0.859274i	$-0.670916\pi$
$457$	−4.56751e6	−1.02303	−0.511516	+	0.859274i	$0.670916\pi$
$458$	7.11105e6	1.58406
$459$	−3.23545e6	−0.716809
$460$	19768.2	0.00435585
$461$	−7.21344e6	−1.58085	−0.790424	−	0.612560i	$-0.790140\pi$
$461$	−7.21344e6	−1.58085	−0.790424	+	0.612560i	$0.790140\pi$
$462$	−790410.	−0.172285
$463$	−3.18009e6	−0.689424	−0.344712	−	0.938708i	$-0.612023\pi$
$463$	−3.18009e6	−0.689424	−0.344712	+	0.938708i	$0.612023\pi$
$464$	−3.91060e6	−0.843235
$465$	170238.	0.0365110
$466$	−1.77435e6	−0.378508
$467$	−337722.	−0.0716584	−0.0358292	−	0.999358i	$-0.511407\pi$
$467$	−337722.	−0.0716584	−0.0358292	+	0.999358i	$0.511407\pi$
$468$	−802848.	−0.169441
$469$	3.71551e6	0.779985
$470$	−658012.	−0.137401
$471$	−1.62127e6	−0.336747
$472$	−1.43125e6	−0.295707
$473$	−4.99579e6	−1.02672
$474$	−712581.	−0.145676
$475$	7.00654e6	1.42485
$476$	−686341.	−0.138843
$477$	−7.92564e6	−1.59492
$478$	−1.34276e6	−0.268800
$479$	5.47597e6	1.09049	0.545246	−	0.838276i	$-0.316436\pi$
$479$	5.47597e6	1.09049	0.545246	+	0.838276i	$0.316436\pi$
$480$	−37479.9	−0.00742499
$481$	46817.0	0.00922657
$482$	−3.85864e6	−0.756513
$483$	−201933.	−0.0393857
$484$	−626567.	−0.121578
$485$	−387106.	−0.0747267
$486$	−3.19752e6	−0.614076
$487$	2.13877e6	0.408640	0.204320	−	0.978904i	$-0.434502\pi$
$487$	2.13877e6	0.408640	0.204320	+	0.978904i	$0.434502\pi$
$488$	9.34805e6	1.77693
$489$	1.00111e6	0.189325
$490$	321921.	0.0605703
$491$	7.48997e6	1.40209	0.701046	−	0.713116i	$-0.252717\pi$
$491$	7.48997e6	1.40209	0.701046	+	0.713116i	$0.252717\pi$
$492$	189566.	0.0353059
$493$	8.49267e6	1.57372
$494$	−8.28537e6	−1.52755
$495$	−683617.	−0.125401
$496$	−6.81540e6	−1.24390
$497$	4.58156e6	0.831999
$498$	647813.	0.117051
$499$	2.96062e6	0.532268	0.266134	−	0.963936i	$-0.414254\pi$
$499$	2.96062e6	0.532268	0.266134	+	0.963936i	$0.414254\pi$
$500$	172880.	0.0309258
$501$	800298.	0.142448
$502$	−9.14971e6	−1.62050
$503$	9.55380e6	1.68367	0.841833	−	0.539738i	$-0.181477\pi$
$503$	9.55380e6	1.68367	0.841833	+	0.539738i	$0.181477\pi$
$504$	−3.32247e6	−0.582619
$505$	140750.	0.0245596
$506$	1.97931e6	0.343668
$507$	466858.	0.0806612
$508$	969233.	0.166636
$509$	−8.17902e6	−1.39929	−0.699643	−	0.714492i	$-0.746658\pi$
$509$	−8.17902e6	−1.39929	−0.699643	+	0.714492i	$0.746658\pi$
$510$	−198795.	−0.0338439
$511$	5.25923e6	0.890983
$512$	6.66570e6	1.12375
$513$	4.01810e6	0.674104
$514$	3.99942e6	0.667712
$515$	−419781.	−0.0697436
$516$	174825.	0.0289054
$517$	1.21539e7	1.99982
$518$	26108.4	0.00427519
$519$	2.61864e6	0.426733
$520$	−754739.	−0.122402
$521$	−9.47540e6	−1.52934	−0.764669	−	0.644424i	$-0.777097\pi$
$521$	−9.47540e6	−1.52934	−0.764669	+	0.644424i	$0.777097\pi$
$522$	5.54006e6	0.889893
$523$	−1.07462e7	−1.71791	−0.858953	−	0.512055i	$-0.828884\pi$
$523$	−1.07462e7	−1.71791	−0.858953	+	0.512055i	$0.828884\pi$
$524$	−103903.	−0.0165310
$525$	−878570.	−0.139116
$526$	4.54481e6	0.716228
$527$	1.48010e7	2.32148
$528$	−1.69079e6	−0.263939
$529$	−5.93067e6	−0.921435
$530$	−1.00403e6	−0.155259
$531$	1.70398e6	0.262258
$532$	852364.	0.130571
$533$	7.12023e6	1.08562
$534$	−1.02277e6	−0.155212
$535$	−875979.	−0.132315
$536$	9.45751e6	1.42189
$537$	−1.69748e6	−0.254021
$538$	136585.	0.0203445
$539$	−5.94612e6	−0.881580
$540$	49323.5	0.00727896
$541$	−6.91734e6	−1.01612	−0.508061	−	0.861321i	$-0.669638\pi$
$541$	−6.91734e6	−1.01612	−0.508061	+	0.861321i	$0.669638\pi$
$542$	−2.05525e6	−0.300516
$543$	2.69687e6	0.392518
$544$	−3.25862e6	−0.472103
$545$	1.16499e6	0.168008
$546$	1.03893e6	0.149143
$547$	6.66329e6	0.952183	0.476091	−	0.879396i	$-0.342053\pi$
$547$	6.66329e6	0.952183	0.476091	+	0.879396i	$0.342053\pi$
$548$	−44288.4	−0.00629997
$549$	−1.11293e7	−1.57594
$550$	8.61162e6	1.21389
$551$	−1.05470e7	−1.47996
$552$	−514002.	−0.0717988
$553$	2.75347e6	0.382884
$554$	−7.76189e6	−1.07447
$555$	−1395.02	−0.000192242 0
$556$	274405.	0.0376448
$557$	684613.	0.0934991	0.0467495	−	0.998907i	$-0.485114\pi$
$557$	684613.	0.0934991	0.0467495	+	0.998907i	$0.485114\pi$
$558$	9.65520e6	1.31273
$559$	6.56653e6	0.888805
$560$	−353713.	−0.0476630
$561$	3.67189e6	0.492586
$562$	7.49335e6	1.00077
$563$	480541.	0.0638939	0.0319470	−	0.999490i	$-0.489829\pi$
$563$	480541.	0.0638939	0.0319470	+	0.999490i	$0.489829\pi$
$564$	−425321.	−0.0563013
$565$	254306.	0.0335147
$566$	−5.00613e6	−0.656842
$567$	3.69610e6	0.482822
$568$	1.16620e7	1.51671
$569$	6.88712e6	0.891779	0.445889	−	0.895088i	$-0.352887\pi$
$569$	6.88712e6	0.891779	0.445889	+	0.895088i	$0.352887\pi$
$570$	246883.	0.0318276
$571$	613961.	0.0788044	0.0394022	−	0.999223i	$-0.487455\pi$
$571$	613961.	0.0788044	0.0394022	+	0.999223i	$0.487455\pi$
$572$	1.87858e6	0.240071
$573$	2.21183e6	0.281427
$574$	3.97073e6	0.503027
$575$	2.20008e6	0.277504
$576$	−8.27516e6	−1.03925
$577$	−2.21463e6	−0.276925	−0.138462	−	0.990368i	$-0.544216\pi$
$577$	−2.21463e6	−0.276925	−0.138462	+	0.990368i	$0.544216\pi$
$578$	−9.90386e6	−1.23306
$579$	−842946.	−0.104497
$580$	−129468.	−0.0159806
$581$	−2.50320e6	−0.307649
$582$	1.35637e6	0.165985
$583$	1.85451e7	2.25974
$584$	1.33869e7	1.62423
$585$	898556.	0.108556
$586$	9.91499e6	1.19275
$587$	1.10037e7	1.31809	0.659044	−	0.752105i	$-0.270961\pi$
$587$	1.10037e7	1.31809	0.659044	+	0.752105i	$0.270961\pi$
$588$	208081.	0.0248193
$589$	−1.83813e7	−2.18317
$590$	215863.	0.0255298
$591$	145928.	0.0171858
$592$	55849.1	0.00654956
$593$	−6.21747e6	−0.726067	−0.363034	−	0.931776i	$-0.618259\pi$
$593$	−6.21747e6	−0.726067	−0.363034	+	0.931776i	$0.618259\pi$
$594$	4.93857e6	0.574295
$595$	768160.	0.0889528
$596$	−1.37384e6	−0.158424
$597$	1219.68	0.000140059 0
$598$	−2.60164e6	−0.297505
$599$	−6.94013e6	−0.790315	−0.395158	−	0.918613i	$-0.629310\pi$
$599$	−6.94013e6	−0.790315	−0.395158	+	0.918613i	$0.629310\pi$
$600$	−2.23632e6	−0.253604
$601$	−6.03770e6	−0.681845	−0.340922	−	0.940091i	$-0.610739\pi$
$601$	−6.03770e6	−0.681845	−0.340922	+	0.940091i	$0.610739\pi$
$602$	3.66195e6	0.411834
$603$	−1.12597e7	−1.26105
$604$	932301.	0.103983
$605$	701261.	0.0778917
$606$	−493169.	−0.0545525
$607$	9.86943e6	1.08723	0.543613	−	0.839336i	$-0.317056\pi$
$607$	9.86943e6	1.08723	0.543613	+	0.839336i	$0.317056\pi$
$608$	4.04687e6	0.443976
$609$	1.32252e6	0.144497
$610$	−1.40988e6	−0.153411
$611$	−1.59753e7	−1.73120
$612$	2.07992e6	0.224475
$613$	1.25306e6	0.134685	0.0673426	−	0.997730i	$-0.478548\pi$
$613$	1.25306e6	0.134685	0.0673426	+	0.997730i	$0.478548\pi$
$614$	−6.07250e6	−0.650049
$615$	−212164.	−0.0226196
$616$	7.77423e6	0.825478
$617$	3.05448e6	0.323016	0.161508	−	0.986871i	$-0.448364\pi$
$617$	3.05448e6	0.323016	0.161508	+	0.986871i	$0.448364\pi$
$618$	1.47085e6	0.154917
$619$	−1.75579e7	−1.84181	−0.920905	−	0.389787i	$-0.872549\pi$
$619$	−1.75579e7	−1.84181	−0.920905	+	0.389787i	$0.872549\pi$
$620$	−225637.	−0.0235739
$621$	1.26170e6	0.131288
$622$	−1.97878e6	−0.205079
$623$	3.95206e6	0.407947
$624$	2.22240e6	0.228486
$625$	9.47491e6	0.970230
$626$	−7.82345e6	−0.797926
$627$	−4.56010e6	−0.463239
$628$	2.14887e6	0.217425
$629$	−121288.	−0.0122233
$630$	501097.	0.0503003
$631$	1.13580e7	1.13561	0.567806	−	0.823163i	$-0.307793\pi$
$631$	1.13580e7	1.13561	0.567806	+	0.823163i	$0.307793\pi$
$632$	7.00872e6	0.697985
$633$	−697243.	−0.0691632
$634$	720390.	0.0711778
$635$	−1.08478e6	−0.106759
$636$	−648977.	−0.0636189
$637$	7.81567e6	0.763164
$638$	−1.29631e7	−1.26084
$639$	−1.38842e7	−1.34514
$640$	−729343.	−0.0703853
$641$	1.83468e7	1.76366	0.881829	−	0.471569i	$-0.156312\pi$
$641$	1.83468e7	1.76366	0.881829	+	0.471569i	$0.156312\pi$
$642$	3.06931e6	0.293902
$643$	−8.68139e6	−0.828060	−0.414030	−	0.910263i	$-0.635879\pi$
$643$	−8.68139e6	−0.828060	−0.414030	+	0.910263i	$0.635879\pi$
$644$	267646.	0.0254299
$645$	−195666.	−0.0185189
$646$	2.14647e7	2.02369
$647$	4.39313e6	0.412584	0.206292	−	0.978490i	$-0.433860\pi$
$647$	4.39313e6	0.412584	0.206292	+	0.978490i	$0.433860\pi$
$648$	9.40812e6	0.880167
$649$	−3.98714e6	−0.371578
$650$	−1.13192e7	−1.05083
$651$	2.30488e6	0.213156
$652$	−1.32689e6	−0.122240
$653$	2.86980e6	0.263372	0.131686	−	0.991291i	$-0.457961\pi$
$653$	2.86980e6	0.263372	0.131686	+	0.991291i	$0.457961\pi$
$654$	−4.08195e6	−0.373185
$655$	116289.	0.0105910
$656$	8.49390e6	0.770633
$657$	−1.59378e7	−1.44051
$658$	−8.90895e6	−0.802161
$659$	−1.18400e7	−1.06203	−0.531017	−	0.847361i	$-0.678190\pi$
$659$	−1.18400e7	−1.06203	−0.531017	+	0.847361i	$0.678190\pi$
$660$	−55976.8	−0.00500205
$661$	1.07309e7	0.955281	0.477641	−	0.878555i	$-0.341492\pi$
$661$	1.07309e7	0.955281	0.477641	+	0.878555i	$0.341492\pi$
$662$	2.04444e7	1.81313
$663$	−4.82638e6	−0.426420
$664$	−6.37168e6	−0.560834
$665$	−953974.	−0.0836532
$666$	−79120.1	−0.00691196
$667$	−3.31180e6	−0.288237
$668$	−1.06073e6	−0.0919739
$669$	−3.66886e6	−0.316932
$670$	−1.42639e6	−0.122758
$671$	2.60415e7	2.23285
$672$	−507448.	−0.0433479
$673$	−2.07757e7	−1.76814	−0.884071	−	0.467353i	$-0.845208\pi$
$673$	−2.07757e7	−1.76814	−0.884071	+	0.467353i	$0.845208\pi$
$674$	−1.79764e7	−1.52424
$675$	5.48941e6	0.463731
$676$	−618783.	−0.0520800
$677$	1.84359e7	1.54594	0.772969	−	0.634444i	$-0.218771\pi$
$677$	1.84359e7	1.54594	0.772969	+	0.634444i	$0.218771\pi$
$678$	−891052.	−0.0744439
$679$	−5.24111e6	−0.436264
$680$	1.95529e6	0.162158
$681$	5.38394e6	0.444869
$682$	−2.25921e7	−1.85993
$683$	−1.10599e7	−0.907191	−0.453596	−	0.891208i	$-0.649859\pi$
$683$	−1.10599e7	−0.907191	−0.453596	+	0.891208i	$0.649859\pi$
$684$	−2.58304e6	−0.211102
$685$	49568.0	0.00403622
$686$	1.09559e7	0.888867
$687$	−5.14433e6	−0.415850
$688$	7.83338e6	0.630926
$689$	−2.43760e7	−1.95621
$690$	77522.1	0.00619873
$691$	−7.08758e6	−0.564680	−0.282340	−	0.959314i	$-0.591111\pi$
$691$	−7.08758e6	−0.564680	−0.282340	+	0.959314i	$0.591111\pi$
$692$	−3.47079e6	−0.275527
$693$	−9.25562e6	−0.732104
$694$	8.59196e6	0.677163
$695$	−307117.	−0.0241181
$696$	3.36636e6	0.263413
$697$	−1.84462e7	−1.43822
$698$	−3.90465e6	−0.303350
$699$	1.28362e6	0.0993669
$700$	1.16447e6	0.0898225
$701$	7.26755e6	0.558590	0.279295	−	0.960205i	$-0.409899\pi$
$701$	7.26755e6	0.558590	0.279295	+	0.960205i	$0.409899\pi$
$702$	−6.49133e6	−0.497154
$703$	150627.	0.0114951
$704$	1.93630e7	1.47245
$705$	476023.	0.0360708
$706$	3.75400e6	0.283454
$707$	1.90565e6	0.143382
$708$	139528.	0.0104611
$709$	−1.53263e7	−1.14504	−0.572520	−	0.819891i	$-0.694034\pi$
$709$	−1.53263e7	−1.14504	−0.572520	+	0.819891i	$0.694034\pi$
$710$	−1.75887e6	−0.130944
$711$	−8.34425e6	−0.619032
$712$	1.00596e7	0.743673
$713$	−5.77180e6	−0.425194
$714$	−2.69153e6	−0.197585
$715$	−2.10253e6	−0.153807
$716$	2.24987e6	0.164012
$717$	971389.	0.0705660
$718$	1.74509e6	0.126330
$719$	9.07927e6	0.654981	0.327490	−	0.944855i	$-0.393797\pi$
$719$	9.07927e6	0.654981	0.327490	+	0.944855i	$0.393797\pi$
$720$	1.07191e6	0.0770596
$721$	−5.68349e6	−0.407171
$722$	−1.37869e7	−0.984292
$723$	2.79144e6	0.198602
$724$	−3.57448e6	−0.253435
$725$	−1.44090e7	−1.01810
$726$	−2.45712e6	−0.173015
$727$	−2.08130e7	−1.46049	−0.730245	−	0.683185i	$-0.760594\pi$
$727$	−2.08130e7	−1.46049	−0.730245	+	0.683185i	$0.760594\pi$
$728$	−1.02186e7	−0.714597
$729$	−9.57966e6	−0.667623
$730$	−2.01902e6	−0.140228
$731$	−1.70118e7	−1.17749
$732$	−911307.	−0.0628618
$733$	−1.84241e7	−1.26656	−0.633282	−	0.773921i	$-0.718293\pi$
$733$	−1.84241e7	−1.26656	−0.633282	+	0.773921i	$0.718293\pi$
$734$	−1.15462e7	−0.791041
$735$	−232887.	−0.0159011
$736$	1.27073e6	0.0864688
$737$	2.63464e7	1.78670
$738$	−1.20331e7	−0.813274
$739$	1.18203e7	0.796189	0.398095	−	0.917344i	$-0.369672\pi$
$739$	1.18203e7	0.796189	0.398095	+	0.917344i	$0.369672\pi$
$740$	1848.99	0.000124124 0
$741$	5.99386e6	0.401016
$742$	−1.35938e7	−0.906420
$743$	−7.93755e6	−0.527490	−0.263745	−	0.964592i	$-0.584958\pi$
$743$	−7.93755e6	−0.527490	−0.263745	+	0.964592i	$0.584958\pi$
$744$	5.86688e6	0.388575
$745$	1.53762e6	0.101498
$746$	4.49380e6	0.295642
$747$	7.58582e6	0.497395
$748$	−4.86680e6	−0.318045
$749$	−1.18601e7	−0.772471
$750$	677960.	0.0440099
$751$	3.47806e6	0.225029	0.112514	−	0.993650i	$-0.464110\pi$
$751$	3.47806e6	0.225029	0.112514	+	0.993650i	$0.464110\pi$
$752$	−1.90574e7	−1.22891
$753$	6.61914e6	0.425416
$754$	1.70389e7	1.09148
$755$	−1.04344e6	−0.0666194
$756$	667800.	0.0424954
$757$	−1.81981e7	−1.15421	−0.577106	−	0.816669i	$-0.695818\pi$
$757$	−1.81981e7	−1.15421	−0.577106	+	0.816669i	$0.695818\pi$
$758$	−2.59683e7	−1.64161
$759$	−1.43189e6	−0.0902204
$760$	−2.42826e6	−0.152497
$761$	−1.88105e7	−1.17744	−0.588720	−	0.808337i	$-0.700368\pi$
$761$	−1.88105e7	−1.17744	−0.588720	+	0.808337i	$0.700368\pi$
$762$	3.80090e6	0.237137
$763$	1.57730e7	0.980851
$764$	−2.93161e6	−0.181707
$765$	−2.32787e6	−0.143815
$766$	2.17551e7	1.33964
$767$	5.24075e6	0.321666
$768$	−1.79520e6	−0.109827
$769$	−7.31422e6	−0.446018	−0.223009	−	0.974816i	$-0.571588\pi$
$769$	−7.31422e6	−0.446018	−0.223009	+	0.974816i	$0.571588\pi$
$770$	−1.17251e6	−0.0712674
$771$	−2.89329e6	−0.175289
$772$	1.11726e6	0.0674699
$773$	2.74174e7	1.65036	0.825179	−	0.564872i	$-0.191074\pi$
$773$	2.74174e7	1.65036	0.825179	+	0.564872i	$0.191074\pi$
$774$	−1.10974e7	−0.665836
$775$	−2.51120e7	−1.50185
$776$	−1.33408e7	−0.795294
$777$	−18887.5	−0.00112233
$778$	1.81137e7	1.07290
$779$	2.29083e7	1.35254
$780$	73576.7	0.00433016
$781$	3.24875e7	1.90585
$782$	6.74001e6	0.394134
$783$	−8.26325e6	−0.481666
$784$	9.32351e6	0.541738
$785$	−2.40503e6	−0.139299
$786$	−407460.	−0.0235250
$787$	2.87493e7	1.65459	0.827294	−	0.561769i	$-0.189879\pi$
$787$	2.87493e7	1.65459	0.827294	+	0.561769i	$0.189879\pi$
$788$	−193416.	−0.0110963
$789$	−3.28784e6	−0.188026
$790$	−1.05706e6	−0.0602604
$791$	3.44310e6	0.195663
$792$	−2.35594e7	−1.33460
$793$	−3.42293e7	−1.93293
$794$	−4.67601e6	−0.263223
$795$	726342.	0.0407590
$796$	−1616.59	−9.04313e−5 0
$797$	5.42597e6	0.302574	0.151287	−	0.988490i	$-0.451658\pi$
$797$	5.42597e6	0.302574	0.151287	+	0.988490i	$0.451658\pi$
$798$	3.34259e6	0.185813
$799$	4.13870e7	2.29349
$800$	5.52871e6	0.305421
$801$	−1.19765e7	−0.659552
$802$	2.07914e7	1.14143
$803$	3.72928e7	2.04097
$804$	−921977.	−0.0503014
$805$	−299552.	−0.0162923
$806$	2.96955e7	1.61010
$807$	−98809.2	−0.00534089
$808$	4.85066e6	0.261380
$809$	−2.21881e7	−1.19193	−0.595963	−	0.803012i	$-0.703230\pi$
$809$	−2.21881e7	−1.19193	−0.595963	+	0.803012i	$0.703230\pi$
$810$	−1.41894e6	−0.0759890
$811$	−3.34953e7	−1.78826	−0.894131	−	0.447805i	$-0.852206\pi$
$811$	−3.34953e7	−1.78826	−0.894131	+	0.447805i	$0.852206\pi$
$812$	−1.75289e6	−0.0932965
$813$	1.48683e6	0.0788921
$814$	185133.	0.00979314
$815$	1.48507e6	0.0783162
$816$	−5.75751e6	−0.302698
$817$	2.11268e7	1.10734
$818$	1.74538e7	0.912025
$819$	1.21657e7	0.633765
$820$	281207.	0.0146047
$821$	−1.24443e7	−0.644338	−0.322169	−	0.946682i	$-0.604412\pi$
$821$	−1.24443e7	−0.644338	−0.322169	+	0.946682i	$0.604412\pi$
$822$	−173679.	−0.00896538
$823$	6.78002e6	0.348925	0.174462	−	0.984664i	$-0.444181\pi$
$823$	6.78002e6	0.348925	0.174462	+	0.984664i	$0.444181\pi$
$824$	−1.44668e7	−0.742259
$825$	−6.22988e6	−0.318673
$826$	2.92261e6	0.149046
$827$	−3.17778e7	−1.61570	−0.807849	−	0.589390i	$-0.799368\pi$
$827$	−3.17778e7	−1.61570	−0.807849	+	0.589390i	$0.799368\pi$
$828$	−811086.	−0.0411141
$829$	−2.96573e7	−1.49881	−0.749403	−	0.662114i	$-0.769660\pi$
$829$	−2.96573e7	−1.49881	−0.749403	+	0.662114i	$0.769660\pi$
$830$	960981.	0.0484194
$831$	5.61516e6	0.282072
$832$	−2.54510e7	−1.27467
$833$	−2.02479e7	−1.01104
$834$	1.07610e6	0.0535718
$835$	1.18718e6	0.0589252
$836$	6.04405e6	0.299097
$837$	−1.44012e7	−0.710533
$838$	−3.78009e6	−0.185948
$839$	3.06249e7	1.50200	0.751000	−	0.660303i	$-0.229572\pi$
$839$	3.06249e7	1.50200	0.751000	+	0.660303i	$0.229572\pi$
$840$	304486.	0.0148891
$841$	1.17886e6	0.0574739
$842$	2.69504e7	1.31004
$843$	−5.42089e6	−0.262725
$844$	924140.	0.0446562
$845$	692548.	0.0333663
$846$	2.69981e7	1.29690
$847$	9.49451e6	0.454741
$848$	−2.90788e7	−1.38863
$849$	3.62157e6	0.172436
$850$	2.93245e7	1.39214
$851$	47297.3	0.00223879
$852$	−1.13688e6	−0.0536558
$853$	4.13271e7	1.94474	0.972371	−	0.233442i	$-0.0749988\pi$
$853$	4.13271e7	1.94474	0.972371	+	0.233442i	$0.0749988\pi$
$854$	−1.90886e7	−0.895633
$855$	2.89097e6	0.135247
$856$	−3.01887e7	−1.40819
$857$	−1.33030e6	−0.0618724	−0.0309362	−	0.999521i	$-0.509849\pi$
$857$	−1.33030e6	−0.0618724	−0.0309362	+	0.999521i	$0.509849\pi$
$858$	7.36695e6	0.341641
$859$	9.95944e6	0.460524	0.230262	−	0.973129i	$-0.426042\pi$
$859$	9.95944e6	0.460524	0.230262	+	0.973129i	$0.426042\pi$
$860$	259339.	0.0119570
$861$	−2.87254e6	−0.132056
$862$	72752.6	0.00333488
$863$	7.55868e6	0.345477	0.172738	−	0.984968i	$-0.444738\pi$
$863$	7.55868e6	0.345477	0.172738	+	0.984968i	$0.444738\pi$
$864$	3.17059e6	0.144496
$865$	3.88455e6	0.176523
$866$	−2.56934e7	−1.16420
$867$	7.16472e6	0.323706
$868$	−3.05494e6	−0.137627
$869$	1.95247e7	0.877070
$870$	−507716.	−0.0227417
$871$	−3.46301e7	−1.54671
$872$	4.01488e7	1.78806
$873$	1.58829e7	0.705334
$874$	−8.37039e6	−0.370653
$875$	−2.61969e6	−0.115672
$876$	−1.30504e6	−0.0574597
$877$	−1.14551e7	−0.502922	−0.251461	−	0.967867i	$-0.580911\pi$
$877$	−1.14551e7	−0.502922	−0.251461	+	0.967867i	$0.580911\pi$
$878$	1.94972e7	0.853565
$879$	−7.17277e6	−0.313123
$880$	−2.50816e6	−0.109181
$881$	−1.45015e7	−0.629466	−0.314733	−	0.949180i	$-0.601915\pi$
$881$	−1.45015e7	−0.629466	−0.314733	+	0.949180i	$0.601915\pi$
$882$	−1.32084e7	−0.571713
$883$	3.57921e7	1.54485	0.772424	−	0.635107i	$-0.219044\pi$
$883$	3.57921e7	1.54485	0.772424	+	0.635107i	$0.219044\pi$
$884$	6.39699e6	0.275324
$885$	−156161.	−0.00670215
$886$	7.62430e6	0.326299
$887$	4.62246e6	0.197271	0.0986356	−	0.995124i	$-0.468552\pi$
$887$	4.62246e6	0.197271	0.0986356	+	0.995124i	$0.468552\pi$
$888$	−48076.5	−0.00204598
$889$	−1.46870e7	−0.623274
$890$	−1.51720e6	−0.0642048
$891$	2.62088e7	1.10599
$892$	4.86278e6	0.204632
$893$	−5.13982e7	−2.15685
$894$	−5.38759e6	−0.225450
$895$	−2.51808e6	−0.105078
$896$	−9.87472e6	−0.410918
$897$	1.88210e6	0.0781017
$898$	−3.84390e7	−1.59067
$899$	3.78013e7	1.55994
$900$	−3.52888e6	−0.145221
$901$	6.31504e7	2.59158
$902$	2.81562e7	1.15228
$903$	−2.64916e6	−0.108116
$904$	8.76411e6	0.356687
$905$	4.00060e6	0.162369
$906$	3.65607e6	0.147977
$907$	3.19267e7	1.28865	0.644325	−	0.764752i	$-0.277138\pi$
$907$	3.19267e7	1.28865	0.644325	+	0.764752i	$0.277138\pi$
$908$	−7.13598e6	−0.287236
$909$	−5.77496e6	−0.231814
$910$	1.54117e6	0.0616946
$911$	−1.68727e7	−0.673581	−0.336790	−	0.941580i	$-0.609341\pi$
$911$	−1.68727e7	−0.673581	−0.336790	+	0.941580i	$0.609341\pi$
$912$	7.15023e6	0.284664
$913$	−1.77500e7	−0.704729
$914$	2.37406e7	0.939997
$915$	1.01994e6	0.0402739
$916$	6.81840e6	0.268500
$917$	1.57446e6	0.0618313
$918$	1.68170e7	0.658629
$919$	−7.70898e6	−0.301098	−0.150549	−	0.988603i	$-0.548104\pi$
$919$	−7.70898e6	−0.301098	−0.150549	+	0.988603i	$0.548104\pi$
$920$	−762483.	−0.0297003
$921$	4.39301e6	0.170653
$922$	3.74934e7	1.45254
$923$	−4.27021e7	−1.64985
$924$	−757881.	−0.0292026
$925$	205782.	0.00790774
$926$	1.65292e7	0.633467
$927$	1.72235e7	0.658298
$928$	−8.32242e6	−0.317234
$929$	1.49959e7	0.570076	0.285038	−	0.958516i	$-0.407994\pi$
$929$	1.49959e7	0.570076	0.285038	+	0.958516i	$0.407994\pi$
$930$	−884847.	−0.0335476
$931$	2.51458e7	0.950803
$932$	−1.70133e6	−0.0641577
$933$	1.43150e6	0.0538380
$934$	1.75538e6	0.0658422
$935$	5.44697e6	0.203763
$936$	3.09668e7	1.15533
$937$	−3.09311e7	−1.15092	−0.575462	−	0.817829i	$-0.695178\pi$
$937$	−3.09311e7	−1.15092	−0.575462	+	0.817829i	$0.695178\pi$
$938$	−1.93121e7	−0.716677
$939$	5.65969e6	0.209473
$940$	−630931.	−0.0232896
$941$	−1.45145e7	−0.534352	−0.267176	−	0.963648i	$-0.586091\pi$
$941$	−1.45145e7	−0.534352	−0.267176	+	0.963648i	$0.586091\pi$
$942$	8.42690e6	0.309415
$943$	7.19329e6	0.263420
$944$	6.25183e6	0.228337
$945$	−747409.	−0.0272257
$946$	2.59666e7	0.943383
$947$	−1.70022e7	−0.616070	−0.308035	−	0.951375i	$-0.599671\pi$
$947$	−1.70022e7	−0.616070	−0.308035	+	0.951375i	$0.599671\pi$
$948$	−683255.	−0.0246923
$949$	−4.90182e7	−1.76682
$950$	−3.64180e7	−1.30920
$951$	−521149.	−0.0186858
$952$	2.64730e7	0.946697
$953$	4.26676e7	1.52183	0.760914	−	0.648853i	$-0.224751\pi$
$953$	4.26676e7	1.52183	0.760914	+	0.648853i	$0.224751\pi$
$954$	4.11952e7	1.46546
$955$	3.28109e6	0.116415
$956$	−1.28750e6	−0.0455619
$957$	9.37788e6	0.330998
$958$	−2.84625e7	−1.00198
$959$	671111.	0.0235639
$960$	758373.	0.0265586
$961$	3.72509e7	1.30115
$962$	−243341.	−0.00847769
$963$	3.59413e7	1.24890
$964$	−3.69983e6	−0.128230
$965$	−1.25045e6	−0.0432262
$966$	1.04959e6	0.0361889
$967$	2.51343e7	0.864371	0.432185	−	0.901785i	$-0.357743\pi$
$967$	2.51343e7	0.864371	0.432185	+	0.901785i	$0.357743\pi$
$968$	2.41675e7	0.828977
$969$	−1.55282e7	−0.531265
$970$	2.01207e6	0.0686615
$971$	2.42214e7	0.824425	0.412213	−	0.911088i	$-0.364756\pi$
$971$	2.42214e7	0.824425	0.412213	+	0.911088i	$0.364756\pi$
$972$	−3.06592e6	−0.104087
$973$	−4.15812e6	−0.140804
$974$	−1.11167e7	−0.375473
$975$	8.18864e6	0.275867
$976$	−4.08330e7	−1.37210
$977$	4.57307e7	1.53275	0.766376	−	0.642393i	$-0.222058\pi$
$977$	4.57307e7	1.53275	0.766376	+	0.642393i	$0.222058\pi$
$978$	−5.20346e6	−0.173958
$979$	2.80238e7	0.934480
$980$	308673.	0.0102668
$981$	−4.77993e7	−1.58580
$982$	−3.89307e7	−1.28829
$983$	142068.	0.00468936	0.00234468	−	0.999997i	$-0.499254\pi$
$983$	142068.	0.00468936	0.00234468	+	0.999997i	$0.499254\pi$
$984$	−7.31179e6	−0.240733
$985$	216473.	0.00710909
$986$	−4.41424e7	−1.44599
$987$	6.44497e6	0.210585
$988$	−7.94439e6	−0.258921
$989$	6.63391e6	0.215665
$990$	3.55324e6	0.115222
$991$	−3.50168e7	−1.13264	−0.566321	−	0.824185i	$-0.691634\pi$
$991$	−3.50168e7	−1.13264	−0.566321	+	0.824185i	$0.691634\pi$
$992$	−1.45043e7	−0.467970
$993$	−1.47900e7	−0.475988
$994$	−2.38136e7	−0.764469
$995$	1809.31	5.79369e−5 0
$996$	621152.	0.0198404
$997$	1.06621e7	0.339707	0.169854	−	0.985469i	$-0.445670\pi$
$997$	1.06621e7	0.339707	0.169854	+	0.985469i	$0.445670\pi$
$998$	−1.53884e7	−0.489066
$999$	118011.	0.00374119

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.6.a.b.1.15	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.6.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-5.19771 q^{2} +3.76016 q^{3} -4.98380 q^{4} +5.57792 q^{5} -19.5442 q^{6} +75.5206 q^{7} +192.231 q^{8} -228.861 q^{9} -28.9924 q^{10} +535.511 q^{11} -18.7399 q^{12} -703.883 q^{13} -392.534 q^{14} +20.9739 q^{15} -839.680 q^{16} +1823.54 q^{17} +1189.55 q^{18} -2264.64 q^{19} -27.7992 q^{20} +283.970 q^{21} -2783.43 q^{22} -711.106 q^{23} +722.820 q^{24} -3093.89 q^{25} +3658.58 q^{26} -1774.28 q^{27} -376.379 q^{28} +4657.25 q^{29} -109.016 q^{30} +8116.66 q^{31} -1786.98 q^{32} +2013.61 q^{33} -9478.21 q^{34} +421.248 q^{35} +1140.60 q^{36} -66.5124 q^{37} +11770.9 q^{38} -2646.72 q^{39} +1072.25 q^{40} -10115.6 q^{41} -1475.99 q^{42} -9329.01 q^{43} -2668.88 q^{44} -1276.57 q^{45} +3696.12 q^{46} +22696.0 q^{47} -3157.34 q^{48} -11103.6 q^{49} +16081.1 q^{50} +6856.79 q^{51} +3508.01 q^{52} +34630.8 q^{53} +9222.17 q^{54} +2987.04 q^{55} +14517.4 q^{56} -8515.42 q^{57} -24207.1 q^{58} -7445.49 q^{59} -104.530 q^{60} +48629.2 q^{61} -42188.0 q^{62} -17283.7 q^{63} +36158.0 q^{64} -3926.20 q^{65} -10466.2 q^{66} +49198.6 q^{67} -9088.14 q^{68} -2673.88 q^{69} -2189.52 q^{70} +60666.4 q^{71} -43994.2 q^{72} +69639.7 q^{73} +345.712 q^{74} -11633.5 q^{75} +11286.5 q^{76} +40442.1 q^{77} +13756.9 q^{78} +36459.9 q^{79} -4683.67 q^{80} +48941.7 q^{81} +52578.2 q^{82} -33146.0 q^{83} -1415.25 q^{84} +10171.5 q^{85} +48489.5 q^{86} +17512.0 q^{87} +102942. q^{88} +52330.9 q^{89} +6635.24 q^{90} -53157.7 q^{91} +3544.01 q^{92} +30520.0 q^{93} -117967. q^{94} -12632.0 q^{95} -6719.34 q^{96} -69399.8 q^{97} +57713.5 q^{98} -122558. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 12 q^{2} + 98 q^{3} + 752 q^{4} + 146 q^{5} + 144 q^{6} + 831 q^{7} + 699 q^{8} + 3725 q^{9} + 1033 q^{10} + 1370 q^{11} + 3136 q^{12} + 2948 q^{13} + 929 q^{14} + 1859 q^{15} + 14080 q^{16} + 1545 q^{17}+ \cdots + 119867 q^{99}+O(q^{100}) \) 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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