LMFDB - Embedded newform 26.6.a.c.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,6,Mod(1,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	26.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$4.16997931514$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{849}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 212 $ x^2 - x - 212
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-14.0688$ of defining polynomial
Character	$\chi$	$=$	26.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} +19.0688 q^{3} +16.0000 q^{4} -7.20641 q^{5} +76.2752 q^{6} -53.6192 q^{7} +64.0000 q^{8} +120.619 q^{9} -28.8256 q^{10} +239.651 q^{11} +305.101 q^{12} -169.000 q^{13} -214.477 q^{14} -137.418 q^{15} +256.000 q^{16} -1973.88 q^{17} +482.477 q^{18} -373.872 q^{19} -115.303 q^{20} -1022.45 q^{21} +958.605 q^{22} +51.4306 q^{23} +1220.40 q^{24} -3073.07 q^{25} -676.000 q^{26} -2333.65 q^{27} -857.908 q^{28} +4796.16 q^{29} -549.670 q^{30} +6906.01 q^{31} +1024.00 q^{32} +4569.86 q^{33} -7895.50 q^{34} +386.402 q^{35} +1929.91 q^{36} +11481.2 q^{37} -1495.49 q^{38} -3222.63 q^{39} -461.210 q^{40} +12547.8 q^{41} -4089.82 q^{42} +1156.07 q^{43} +3834.42 q^{44} -869.231 q^{45} +205.723 q^{46} -18644.9 q^{47} +4881.61 q^{48} -13932.0 q^{49} -12292.3 q^{50} -37639.4 q^{51} -2704.00 q^{52} +9318.90 q^{53} -9334.62 q^{54} -1727.02 q^{55} -3431.63 q^{56} -7129.29 q^{57} +19184.7 q^{58} -5066.63 q^{59} -2198.68 q^{60} +54271.7 q^{61} +27624.0 q^{62} -6467.51 q^{63} +4096.00 q^{64} +1217.88 q^{65} +18279.4 q^{66} +40241.0 q^{67} -31582.0 q^{68} +980.721 q^{69} +1545.61 q^{70} -65236.5 q^{71} +7719.63 q^{72} +68506.2 q^{73} +45924.7 q^{74} -58599.7 q^{75} -5981.95 q^{76} -12849.9 q^{77} -12890.5 q^{78} +10627.3 q^{79} -1844.84 q^{80} -73810.5 q^{81} +50191.1 q^{82} -2357.98 q^{83} -16359.3 q^{84} +14224.5 q^{85} +4624.27 q^{86} +91457.1 q^{87} +15337.7 q^{88} -93620.0 q^{89} -3476.92 q^{90} +9061.65 q^{91} +822.890 q^{92} +131689. q^{93} -74579.5 q^{94} +2694.27 q^{95} +19526.5 q^{96} -31195.8 q^{97} -55727.9 q^{98} +28906.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 9 q^{3} + 32 q^{4} + 73 q^{5} + 36 q^{6} + 155 q^{7} + 128 q^{8} - 21 q^{9} + 292 q^{10} - 220 q^{11} + 144 q^{12} - 338 q^{13} + 620 q^{14} - 945 q^{15} + 512 q^{16} - 189 q^{17} - 84 q^{18}+ \cdots + 94002 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 + 9 * q^3 + 32 * q^4 + 73 * q^5 + 36 * q^6 + 155 * q^7 + 128 * q^8 - 21 * q^9 + 292 * q^10 - 220 * q^11 + 144 * q^12 - 338 * q^13 + 620 * q^14 - 945 * q^15 + 512 * q^16 - 189 * q^17 - 84 * q^18 - 2496 * q^19 + 1168 * q^20 - 3123 * q^21 - 880 * q^22 - 3044 * q^23 + 576 * q^24 + 235 * q^25 - 1352 * q^26 + 1539 * q^27 + 2480 * q^28 + 1900 * q^29 - 3780 * q^30 + 2798 * q^31 + 2048 * q^32 + 9198 * q^33 - 756 * q^34 + 17119 * q^35 - 336 * q^36 + 17805 * q^37 - 9984 * q^38 - 1521 * q^39 + 4672 * q^40 + 11634 * q^41 - 12492 * q^42 - 4069 * q^43 - 3520 * q^44 - 12228 * q^45 - 12176 * q^46 - 25489 * q^47 + 2304 * q^48 + 12783 * q^49 + 940 * q^50 - 55611 * q^51 - 5408 * q^52 - 4614 * q^53 + 6156 * q^54 - 38594 * q^55 + 9920 * q^56 + 14238 * q^57 + 7600 * q^58 - 23420 * q^59 - 15120 * q^60 + 96830 * q^61 + 11192 * q^62 - 36012 * q^63 + 8192 * q^64 - 12337 * q^65 + 36792 * q^66 + 72440 * q^67 - 3024 * q^68 + 32148 * q^69 + 68476 * q^70 - 36679 * q^71 - 1344 * q^72 + 47152 * q^73 + 71220 * q^74 - 91908 * q^75 - 39936 * q^76 - 108742 * q^77 - 6084 * q^78 + 52024 * q^79 + 18688 * q^80 - 78390 * q^81 + 46536 * q^82 - 37758 * q^83 - 49968 * q^84 + 157383 * q^85 - 16276 * q^86 + 120618 * q^87 - 14080 * q^88 - 105072 * q^89 - 48912 * q^90 - 26195 * q^91 - 48704 * q^92 + 173052 * q^93 - 101956 * q^94 - 167514 * q^95 + 9216 * q^96 + 104392 * q^97 + 51132 * q^98 + 94002 * 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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	19.0688	1.22326	0.611632	−	0.791142i	$-0.290513\pi$
$3$	19.0688	1.22326	0.611632	+	0.791142i	$0.290513\pi$
$4$	16.0000	0.500000
$5$	−7.20641	−0.128912	−0.0644561	−	0.997921i	$-0.520531\pi$
$5$	−7.20641	−0.128912	−0.0644561	+	0.997921i	$0.520531\pi$
$6$	76.2752	0.864978
$7$	−53.6192	−0.413595	−0.206798	−	0.978384i	$-0.566304\pi$
$7$	−53.6192	−0.413595	−0.206798	+	0.978384i	$0.566304\pi$
$8$	64.0000	0.353553
$9$	120.619	0.496375
$10$	−28.8256	−0.0911546
$11$	239.651	0.597170	0.298585	−	0.954383i	$-0.403485\pi$
$11$	239.651	0.597170	0.298585	+	0.954383i	$0.403485\pi$
$12$	305.101	0.611632
$13$	−169.000	−0.277350
$13$	−169.000	−0.277350
$14$	−214.477	−0.292456
$15$	−137.418	−0.157694
$16$	256.000	0.250000
$17$	−1973.88	−1.65652	−0.828261	−	0.560342i	$-0.810670\pi$
$17$	−1973.88	−1.65652	−0.828261	+	0.560342i	$0.810670\pi$
$18$	482.477	0.350990
$19$	−373.872	−0.237596	−0.118798	−	0.992918i	$-0.537904\pi$
$19$	−373.872	−0.237596	−0.118798	+	0.992918i	$0.537904\pi$
$20$	−115.303	−0.0644561
$21$	−1022.45	−0.505936
$22$	958.605	0.422263
$23$	51.4306	0.0202723	0.0101361	−	0.999949i	$-0.496774\pi$
$23$	51.4306	0.0202723	0.0101361	+	0.999949i	$0.496774\pi$
$24$	1220.40	0.432489
$25$	−3073.07	−0.983382
$26$	−676.000	−0.196116
$27$	−2333.65	−0.616066
$28$	−857.908	−0.206798
$29$	4796.16	1.05901	0.529504	−	0.848308i	$-0.322378\pi$
$29$	4796.16	1.05901	0.529504	+	0.848308i	$0.322378\pi$
$30$	−549.670	−0.111506
$31$	6906.01	1.29069	0.645346	−	0.763890i	$-0.276713\pi$
$31$	6906.01	1.29069	0.645346	+	0.763890i	$0.276713\pi$
$32$	1024.00	0.176777
$33$	4569.86	0.730497
$34$	−7895.50	−1.17134
$35$	386.402	0.0533174
$36$	1929.91	0.248188
$37$	11481.2	1.37874	0.689370	−	0.724410i	$-0.257888\pi$
$37$	11481.2	1.37874	0.689370	+	0.724410i	$0.257888\pi$
$38$	−1495.49	−0.168006
$39$	−3222.63	−0.339272
$40$	−461.210	−0.0455773
$41$	12547.8	1.16576	0.582878	−	0.812560i	$-0.301927\pi$
$41$	12547.8	1.16576	0.582878	+	0.812560i	$0.301927\pi$
$42$	−4089.82	−0.357751
$43$	1156.07	0.0953481	0.0476741	−	0.998863i	$-0.484819\pi$
$43$	1156.07	0.0953481	0.0476741	+	0.998863i	$0.484819\pi$
$44$	3834.42	0.298585
$45$	−869.231	−0.0639888
$46$	205.723	0.0143347
$47$	−18644.9	−1.23116	−0.615580	−	0.788074i	$-0.711078\pi$
$47$	−18644.9	−1.23116	−0.615580	+	0.788074i	$0.711078\pi$
$48$	4881.61	0.305816
$49$	−13932.0	−0.828939
$50$	−12292.3	−0.695356
$51$	−37639.4	−2.02637
$52$	−2704.00	−0.138675
$53$	9318.90	0.455696	0.227848	−	0.973697i	$-0.426831\pi$
$53$	9318.90	0.455696	0.227848	+	0.973697i	$0.426831\pi$
$54$	−9334.62	−0.435624
$55$	−1727.02	−0.0769825
$56$	−3431.63	−0.146228
$57$	−7129.29	−0.290642
$58$	19184.7	0.748831
$59$	−5066.63	−0.189491	−0.0947456	−	0.995502i	$-0.530204\pi$
$59$	−5066.63	−0.189491	−0.0947456	+	0.995502i	$0.530204\pi$
$60$	−2198.68	−0.0788468
$61$	54271.7	1.86745	0.933724	−	0.357994i	$-0.116539\pi$
$61$	54271.7	1.86745	0.933724	+	0.357994i	$0.116539\pi$
$62$	27624.0	0.912657
$63$	−6467.51	−0.205298
$64$	4096.00	0.125000
$65$	1217.88	0.0357538
$66$	18279.4	0.516539
$67$	40241.0	1.09517	0.547585	−	0.836750i	$-0.315547\pi$
$67$	40241.0	1.09517	0.547585	+	0.836750i	$0.315547\pi$
$68$	−31582.0	−0.828261
$69$	980.721	0.0247983
$70$	1545.61	0.0377011
$71$	−65236.5	−1.53584	−0.767918	−	0.640549i	$-0.778707\pi$
$71$	−65236.5	−1.53584	−0.767918	+	0.640549i	$0.778707\pi$
$72$	7719.63	0.175495
$73$	68506.2	1.50461	0.752303	−	0.658818i	$-0.228943\pi$
$73$	68506.2	1.50461	0.752303	+	0.658818i	$0.228943\pi$
$74$	45924.7	0.974916
$75$	−58599.7	−1.20294
$76$	−5981.95	−0.118798
$77$	−12849.9	−0.246987
$78$	−12890.5	−0.239902
$79$	10627.3	0.191583	0.0957915	−	0.995401i	$-0.469462\pi$
$79$	10627.3	0.191583	0.0957915	+	0.995401i	$0.469462\pi$
$80$	−1844.84	−0.0322280
$81$	−73810.5	−1.24999
$82$	50191.1	0.824314
$83$	−2357.98	−0.0375703	−0.0187851	−	0.999824i	$-0.505980\pi$
$83$	−2357.98	−0.0375703	−0.0187851	+	0.999824i	$0.505980\pi$
$84$	−16359.3	−0.252968
$85$	14224.5	0.213546
$86$	4624.27	0.0674213
$87$	91457.1	1.29545
$88$	15337.7	0.211131
$89$	−93620.0	−1.25283	−0.626417	−	0.779488i	$-0.715479\pi$
$89$	−93620.0	−1.25283	−0.626417	+	0.779488i	$0.715479\pi$
$90$	−3476.92	−0.0452469
$91$	9061.65	0.114711
$92$	822.890	0.0101361
$93$	131689.	1.57886
$94$	−74579.5	−0.870562
$95$	2694.27	0.0306290
$96$	19526.5	0.216245
$97$	−31195.8	−0.336641	−0.168321	−	0.985732i	$-0.553834\pi$
$97$	−31195.8	−0.336641	−0.168321	+	0.985732i	$0.553834\pi$
$98$	−55727.9	−0.586148
$99$	28906.5	0.296421
$100$	−49169.1	−0.491691
$101$	−86948.6	−0.848124	−0.424062	−	0.905633i	$-0.639396\pi$
$101$	−86948.6	−0.848124	−0.424062	+	0.905633i	$0.639396\pi$
$102$	−150558.	−1.43286
$103$	−43111.1	−0.400402	−0.200201	−	0.979755i	$-0.564159\pi$
$103$	−43111.1	−0.400402	−0.200201	+	0.979755i	$0.564159\pi$
$104$	−10816.0	−0.0980581
$105$	7368.22	0.0652213
$106$	37275.6	0.322226
$107$	−175966.	−1.48583	−0.742913	−	0.669388i	$-0.766557\pi$
$107$	−175966.	−1.48583	−0.742913	+	0.669388i	$0.766557\pi$
$108$	−37338.5	−0.308033
$109$	119578.	0.964020	0.482010	−	0.876166i	$-0.339907\pi$
$109$	119578.	0.964020	0.482010	+	0.876166i	$0.339907\pi$
$110$	−6908.10	−0.0544348
$111$	218932.	1.68656
$112$	−13726.5	−0.103399
$113$	47558.0	0.350370	0.175185	−	0.984536i	$-0.443948\pi$
$113$	47558.0	0.350370	0.175185	+	0.984536i	$0.443948\pi$
$114$	−28517.2	−0.205515
$115$	−370.630	−0.00261334
$116$	76738.6	0.529504
$117$	−20384.6	−0.137670
$118$	−20266.5	−0.133990
$119$	105838.	0.685130
$120$	−8794.72	−0.0557531
$121$	−103618.	−0.643388
$122$	217087.	1.32049
$123$	239271.	1.42603
$124$	110496.	0.645346
$125$	44665.8	0.255682
$126$	−25870.0	−0.145168
$127$	−108774.	−0.598433	−0.299217	−	0.954185i	$-0.596725\pi$
$127$	−108774.	−0.598433	−0.299217	+	0.954185i	$0.596725\pi$
$128$	16384.0	0.0883883
$129$	22044.8	0.116636
$130$	4871.53	0.0252817
$131$	−340486.	−1.73349	−0.866744	−	0.498753i	$-0.833791\pi$
$131$	−340486.	−1.73349	−0.866744	+	0.498753i	$0.833791\pi$
$132$	73117.8	0.365248
$133$	20046.7	0.0982685
$134$	160964.	0.774402
$135$	16817.3	0.0794184
$136$	−126328.	−0.585669
$137$	48143.4	0.219147	0.109574	−	0.993979i	$-0.465051\pi$
$137$	48143.4	0.219147	0.109574	+	0.993979i	$0.465051\pi$
$138$	3922.88	0.0175351
$139$	323803.	1.42149	0.710745	−	0.703450i	$-0.248358\pi$
$139$	323803.	1.42149	0.710745	+	0.703450i	$0.248358\pi$
$140$	6182.43	0.0266587
$141$	−355535.	−1.50603
$142$	−260946.	−1.08600
$143$	−40501.1	−0.165625
$144$	30878.5	0.124094
$145$	−34563.1	−0.136519
$146$	274025.	1.06392
$147$	−265666.	−1.01401
$148$	183699.	0.689370
$149$	372945.	1.37619	0.688096	−	0.725620i	$-0.258447\pi$
$149$	372945.	1.37619	0.688096	+	0.725620i	$0.258447\pi$
$150$	−234399.	−0.850604
$151$	−159735.	−0.570110	−0.285055	−	0.958511i	$-0.592012\pi$
$151$	−159735.	−0.570110	−0.285055	+	0.958511i	$0.592012\pi$
$152$	−23927.8	−0.0840028
$153$	−238087.	−0.822257
$154$	−51399.7	−0.174646
$155$	−49767.5	−0.166386
$156$	−51562.0	−0.169636
$157$	−484134.	−1.56753	−0.783765	−	0.621057i	$-0.786704\pi$
$157$	−484134.	−1.56753	−0.783765	+	0.621057i	$0.786704\pi$
$158$	42509.4	0.135470
$159$	177700.	0.557437
$160$	−7379.36	−0.0227887
$161$	−2757.67	−0.00838451
$162$	−295242.	−0.883874
$163$	−140172.	−0.413232	−0.206616	−	0.978422i	$-0.566245\pi$
$163$	−140172.	−0.413232	−0.206616	+	0.978422i	$0.566245\pi$
$164$	200765.	0.582878
$165$	−32932.3	−0.0941699
$166$	−9431.91	−0.0265662
$167$	218046.	0.605002	0.302501	−	0.953149i	$-0.402178\pi$
$167$	218046.	0.605002	0.302501	+	0.953149i	$0.402178\pi$
$168$	−65437.1	−0.178875
$169$	28561.0	0.0769231
$170$	56898.2	0.151000
$171$	−45096.1	−0.117937
$172$	18497.1	0.0476741
$173$	−384852.	−0.977638	−0.488819	−	0.872385i	$-0.662572\pi$
$173$	−384852.	−0.977638	−0.488819	+	0.872385i	$0.662572\pi$
$174$	365828.	0.916019
$175$	164775.	0.406722
$176$	61350.7	0.149293
$177$	−96614.5	−0.231798
$178$	−374480.	−0.885888
$179$	498273.	1.16234	0.581172	−	0.813781i	$-0.302595\pi$
$179$	498273.	1.16234	0.581172	+	0.813781i	$0.302595\pi$
$180$	−13907.7	−0.0319944
$181$	152201.	0.345320	0.172660	−	0.984981i	$-0.444764\pi$
$181$	152201.	0.345320	0.172660	+	0.984981i	$0.444764\pi$
$182$	36246.6	0.0811127
$183$	1.03490e6	2.28438
$184$	3291.56	0.00716733
$185$	−82738.0	−0.177736
$186$	526757.	1.11642
$187$	−473042.	−0.989226
$188$	−298318.	−0.615580
$189$	125129.	0.254802
$190$	10777.1	0.0216580
$191$	600284.	1.19062	0.595310	−	0.803496i	$-0.297029\pi$
$191$	600284.	1.19062	0.595310	+	0.803496i	$0.297029\pi$
$192$	78105.8	0.152908
$193$	350804.	0.677909	0.338955	−	0.940803i	$-0.389927\pi$
$193$	350804.	0.677909	0.338955	+	0.940803i	$0.389927\pi$
$194$	−124783.	−0.238041
$195$	23223.6	0.0437363
$196$	−222912.	−0.414470
$197$	−321145.	−0.589571	−0.294785	−	0.955563i	$-0.595248\pi$
$197$	−321145.	−0.589571	−0.294785	+	0.955563i	$0.595248\pi$
$198$	115626.	0.209601
$199$	561416.	1.00497	0.502484	−	0.864586i	$-0.332420\pi$
$199$	561416.	1.00497	0.502484	+	0.864586i	$0.332420\pi$
$200$	−196676.	−0.347678
$201$	767347.	1.33968
$202$	−347794.	−0.599714
$203$	−257167.	−0.438000
$204$	−602231.	−1.01318
$205$	−90424.5	−0.150280
$206$	−172444.	−0.283127
$207$	6203.52	0.0100627
$208$	−43264.0	−0.0693375
$209$	−89598.9	−0.141885
$210$	29472.9	0.0461184
$211$	−751002.	−1.16127	−0.580637	−	0.814162i	$-0.697196\pi$
$211$	−751002.	−1.16127	−0.580637	+	0.814162i	$0.697196\pi$
$212$	149102.	0.227848
$213$	−1.24398e6	−1.87873
$214$	−703862.	−1.05064
$215$	−8331.09	−0.0122915
$216$	−149354.	−0.217812
$217$	−370295.	−0.533824
$218$	478313.	0.681665
$219$	1.30633e6	1.84053
$220$	−27632.4	−0.0384912
$221$	333585.	0.459437
$222$	875729.	1.19258
$223$	−598906.	−0.806485	−0.403243	−	0.915093i	$-0.632117\pi$
$223$	−598906.	−0.806485	−0.403243	+	0.915093i	$0.632117\pi$
$224$	−54906.1	−0.0731140
$225$	−370671.	−0.488126
$226$	190232.	0.247749
$227$	−1.32303e6	−1.70414	−0.852071	−	0.523426i	$-0.824654\pi$
$227$	−1.32303e6	−1.70414	−0.852071	+	0.523426i	$0.824654\pi$
$228$	−114069.	−0.145321
$229$	115752.	0.145861	0.0729307	−	0.997337i	$-0.476765\pi$
$229$	115752.	0.145861	0.0729307	+	0.997337i	$0.476765\pi$
$230$	−1482.52	−0.00184791
$231$	−245032.	−0.302130
$232$	306954.	0.374416
$233$	1.21925e6	1.47131	0.735655	−	0.677357i	$-0.236875\pi$
$233$	1.21925e6	1.47131	0.735655	+	0.677357i	$0.236875\pi$
$234$	−81538.6	−0.0973472
$235$	134362.	0.158711
$236$	−81066.0	−0.0947456
$237$	202651.	0.234357
$238$	423351.	0.484460
$239$	−1.66823e6	−1.88913	−0.944565	−	0.328323i	$-0.893516\pi$
$239$	−1.66823e6	−1.88913	−0.944565	+	0.328323i	$0.893516\pi$
$240$	−35178.9	−0.0394234
$241$	847710.	0.940167	0.470083	−	0.882622i	$-0.344224\pi$
$241$	847710.	0.940167	0.470083	+	0.882622i	$0.344224\pi$
$242$	−414473.	−0.454944
$243$	−840399.	−0.912998
$244$	868347.	0.933724
$245$	100400.	0.106860
$246$	957085.	1.00835
$247$	63184.3	0.0658972
$248$	441984.	0.456329
$249$	−44963.8	−0.0459584
$250$	178663.	0.180794
$251$	−1.09148e6	−1.09353	−0.546765	−	0.837286i	$-0.684141\pi$
$251$	−1.09148e6	−1.09353	−0.546765	+	0.837286i	$0.684141\pi$
$252$	−103480.	−0.102649
$253$	12325.4	0.0121060
$254$	−435096.	−0.423156
$255$	271245.	0.261223
$256$	65536.0	0.0625000
$257$	−10510.6	−0.00992644	−0.00496322	−	0.999988i	$-0.501580\pi$
$257$	−10510.6	−0.00992644	−0.00496322	+	0.999988i	$0.501580\pi$
$258$	88179.3	0.0824741
$259$	−615612.	−0.570240
$260$	19486.1	0.0178769
$261$	578510.	0.525665
$262$	−1.36194e6	−1.22576
$263$	1.66350e6	1.48297	0.741487	−	0.670967i	$-0.234121\pi$
$263$	1.66350e6	1.48297	0.741487	+	0.670967i	$0.234121\pi$
$264$	292471.	0.258270
$265$	−67155.8	−0.0587447
$266$	80186.9	0.0694863
$267$	−1.78522e6	−1.53255
$268$	643856.	0.547585
$269$	−123097.	−0.103721	−0.0518606	−	0.998654i	$-0.516515\pi$
$269$	−123097.	−0.103721	−0.0518606	+	0.998654i	$0.516515\pi$
$270$	67269.1	0.0561573
$271$	2.14956e6	1.77798	0.888991	−	0.457925i	$-0.151407\pi$
$271$	2.14956e6	1.77798	0.888991	+	0.457925i	$0.151407\pi$
$272$	−505312.	−0.414131
$273$	172795.	0.140321
$274$	192574.	0.154960
$275$	−736465.	−0.587246
$276$	15691.5	0.0123992
$277$	818582.	0.641007	0.320503	−	0.947247i	$-0.396148\pi$
$277$	818582.	0.641007	0.320503	+	0.947247i	$0.396148\pi$
$278$	1.29521e6	1.00514
$279$	832997.	0.640668
$280$	24729.7	0.0188506
$281$	1.38003e6	1.04261	0.521305	−	0.853370i	$-0.325445\pi$
$281$	1.38003e6	1.04261	0.521305	+	0.853370i	$0.325445\pi$
$282$	−1.42214e6	−1.06493
$283$	395823.	0.293788	0.146894	−	0.989152i	$-0.453072\pi$
$283$	395823.	0.293788	0.146894	+	0.989152i	$0.453072\pi$
$284$	−1.04378e6	−0.767918
$285$	51376.6	0.0374673
$286$	−162004.	−0.117115
$287$	−672803.	−0.482151
$288$	123514.	0.0877476
$289$	2.47633e6	1.74407
$290$	−138252.	−0.0965334
$291$	−594867.	−0.411801
$292$	1.09610e6	0.752303
$293$	382789.	0.260490	0.130245	−	0.991482i	$-0.458424\pi$
$293$	382789.	0.260490	0.130245	+	0.991482i	$0.458424\pi$
$294$	−1.06266e6	−0.717014
$295$	36512.2	0.0244277
$296$	734795.	0.487458
$297$	−559263.	−0.367896
$298$	1.49178e6	0.973115
$299$	−8691.78	−0.00562252
$300$	−937596.	−0.601468
$301$	−61987.4	−0.0394355
$302$	−638941.	−0.403129
$303$	−1.65801e6	−1.03748
$304$	−95711.2	−0.0593990
$305$	−391104.	−0.240737
$306$	−952349.	−0.581424
$307$	−2.95976e6	−1.79230	−0.896150	−	0.443751i	$-0.853648\pi$
$307$	−2.95976e6	−1.79230	−0.896150	+	0.443751i	$0.853648\pi$
$308$	−205599.	−0.123493
$309$	−822077.	−0.489797
$310$	−199070.	−0.117653
$311$	−536900.	−0.314770	−0.157385	−	0.987537i	$-0.550306\pi$
$311$	−536900.	−0.314770	−0.157385	+	0.987537i	$0.550306\pi$
$312$	−206248.	−0.119951
$313$	−3.33301e6	−1.92299	−0.961493	−	0.274829i	$-0.911379\pi$
$313$	−3.33301e6	−1.92299	−0.961493	+	0.274829i	$0.911379\pi$
$314$	−1.93653e6	−1.10841
$315$	46607.5	0.0264655
$316$	170038.	0.0957915
$317$	1.50100e6	0.838943	0.419472	−	0.907768i	$-0.362215\pi$
$317$	1.50100e6	0.838943	0.419472	+	0.907768i	$0.362215\pi$
$318$	710801.	0.394167
$319$	1.14941e6	0.632407
$320$	−29517.4	−0.0161140
$321$	−3.35545e6	−1.81756
$322$	−11030.7	−0.00592875
$323$	737977.	0.393583
$324$	−1.18097e6	−0.624993
$325$	519348.	0.272741
$326$	−560690.	−0.292199
$327$	2.28022e6	1.17925
$328$	803058.	0.412157
$329$	999723.	0.509202
$330$	−131729.	−0.0665882
$331$	2.17404e6	1.09068	0.545341	−	0.838214i	$-0.316400\pi$
$331$	2.17404e6	1.09068	0.545341	+	0.838214i	$0.316400\pi$
$332$	−37727.7	−0.0187851
$333$	1.38485e6	0.684372
$334$	872184.	0.427801
$335$	−289993.	−0.141181
$336$	−261748.	−0.126484
$337$	821494.	0.394030	0.197015	−	0.980400i	$-0.436875\pi$
$337$	821494.	0.394030	0.197015	+	0.980400i	$0.436875\pi$
$338$	114244.	0.0543928
$339$	906874.	0.428595
$340$	227593.	0.106773
$341$	1.65503e6	0.770763
$342$	−180385.	−0.0833939
$343$	1.64820e6	0.756440
$344$	73988.3	0.0337107
$345$	−7067.47	−0.00319681
$346$	−1.53941e6	−0.691295
$347$	1.75897e6	0.784216	0.392108	−	0.919919i	$-0.371746\pi$
$347$	1.75897e6	0.784216	0.392108	+	0.919919i	$0.371746\pi$
$348$	1.46331e6	0.647723
$349$	−3.15359e6	−1.38593	−0.692965	−	0.720971i	$-0.743696\pi$
$349$	−3.15359e6	−1.38593	−0.692965	+	0.720971i	$0.743696\pi$
$350$	659102.	0.287596
$351$	394388.	0.170866
$352$	245403.	0.105566
$353$	−1.51456e6	−0.646918	−0.323459	−	0.946242i	$-0.604846\pi$
$353$	−1.51456e6	−0.646918	−0.323459	+	0.946242i	$0.604846\pi$
$354$	−386458.	−0.163906
$355$	470121.	0.197988
$356$	−1.49792e6	−0.626417
$357$	2.01820e6	0.838095
$358$	1.99309e6	0.821901
$359$	1.68935e6	0.691803	0.345902	−	0.938271i	$-0.387573\pi$
$359$	1.68935e6	0.691803	0.345902	+	0.938271i	$0.387573\pi$
$360$	−55630.8	−0.0226235
$361$	−2.33632e6	−0.943548
$362$	608805.	0.244178
$363$	−1.97588e6	−0.787033
$364$	144986.	0.0573553
$365$	−493683.	−0.193962
$366$	4.13958e6	1.61530
$367$	−1.87184e6	−0.725443	−0.362722	−	0.931898i	$-0.618152\pi$
$367$	−1.87184e6	−0.725443	−0.362722	+	0.931898i	$0.618152\pi$
$368$	13166.2	0.00506807
$369$	1.51350e6	0.578652
$370$	−330952.	−0.125678
$371$	−499672.	−0.188474
$372$	2.10703e6	0.789429
$373$	628003.	0.233717	0.116858	−	0.993149i	$-0.462718\pi$
$373$	628003.	0.233717	0.116858	+	0.993149i	$0.462718\pi$
$374$	−1.89217e6	−0.699488
$375$	851723.	0.312767
$376$	−1.19327e6	−0.435281
$377$	−810552.	−0.293716
$378$	500515.	0.180172
$379$	478225.	0.171015	0.0855076	−	0.996338i	$-0.472749\pi$
$379$	478225.	0.171015	0.0855076	+	0.996338i	$0.472749\pi$
$380$	43108.4	0.0153145
$381$	−2.07419e6	−0.732042
$382$	2.40114e6	0.841895
$383$	−4.58548e6	−1.59731	−0.798653	−	0.601791i	$-0.794454\pi$
$383$	−4.58548e6	−1.59731	−0.798653	+	0.601791i	$0.794454\pi$
$384$	312423.	0.108122
$385$	92601.7	0.0318396
$386$	1.40322e6	0.479354
$387$	139444.	0.0473285
$388$	−499133.	−0.168321
$389$	2.62136e6	0.878318	0.439159	−	0.898409i	$-0.355276\pi$
$389$	2.62136e6	0.878318	0.439159	+	0.898409i	$0.355276\pi$
$390$	92894.3	0.0309263
$391$	−101518.	−0.0335815
$392$	−891647.	−0.293074
$393$	−6.49266e6	−2.12051
$394$	−1.28458e6	−0.416890
$395$	−76585.0	−0.0246974
$396$	462505.	0.148210
$397$	961154.	0.306067	0.153034	−	0.988221i	$-0.451096\pi$
$397$	961154.	0.306067	0.153034	+	0.988221i	$0.451096\pi$
$398$	2.24567e6	0.710620
$399$	382267.	0.120208
$400$	−786705.	−0.245845
$401$	−4.00559e6	−1.24396	−0.621978	−	0.783034i	$-0.713671\pi$
$401$	−4.00559e6	−1.24396	−0.621978	+	0.783034i	$0.713671\pi$
$402$	3.06939e6	0.947299
$403$	−1.16712e6	−0.357974
$404$	−1.39118e6	−0.424062
$405$	531908.	0.161138
$406$	−1.02867e6	−0.309713
$407$	2.75148e6	0.823342
$408$	−2.40892e6	−0.716428
$409$	−3.12530e6	−0.923813	−0.461906	−	0.886929i	$-0.652834\pi$
$409$	−3.12530e6	−0.923813	−0.461906	+	0.886929i	$0.652834\pi$
$410$	−361698.	−0.106264
$411$	918038.	0.268075
$412$	−689777.	−0.200201
$413$	271669.	0.0783726
$414$	24814.1	0.00711537
$415$	16992.6	0.00484327
$416$	−173056.	−0.0490290
$417$	6.17453e6	1.73886
$418$	−358395.	−0.100328
$419$	−3.34877e6	−0.931859	−0.465929	−	0.884822i	$-0.654280\pi$
$419$	−3.34877e6	−0.931859	−0.465929	+	0.884822i	$0.654280\pi$
$420$	117892.	0.0326106
$421$	−3.01332e6	−0.828591	−0.414295	−	0.910143i	$-0.635972\pi$
$421$	−3.01332e6	−0.828591	−0.414295	+	0.910143i	$0.635972\pi$
$422$	−3.00401e6	−0.821145
$423$	−2.24893e6	−0.611118
$424$	596410.	0.161113
$425$	6.06585e6	1.62899
$426$	−4.97593e6	−1.32846
$427$	−2.91000e6	−0.772367
$428$	−2.81545e6	−0.742913
$429$	−772307.	−0.202603
$430$	−33324.4	−0.00869142
$431$	3.35224e6	0.869245	0.434623	−	0.900613i	$-0.356882\pi$
$431$	3.35224e6	0.869245	0.434623	+	0.900613i	$0.356882\pi$
$432$	−597416.	−0.154016
$433$	1.62188e6	0.415719	0.207859	−	0.978159i	$-0.433350\pi$
$433$	1.62188e6	0.415719	0.207859	+	0.978159i	$0.433350\pi$
$434$	−1.48118e6	−0.377471
$435$	−659077.	−0.166999
$436$	1.91325e6	0.482010
$437$	−19228.5	−0.00481661
$438$	5.22532e6	1.30145
$439$	7.48948e6	1.85477	0.927386	−	0.374106i	$-0.122050\pi$
$439$	7.48948e6	1.85477	0.927386	+	0.374106i	$0.122050\pi$
$440$	−110530.	−0.0272174
$441$	−1.68046e6	−0.411465
$442$	1.33434e6	0.324871
$443$	1.90156e6	0.460364	0.230182	−	0.973148i	$-0.426068\pi$
$443$	1.90156e6	0.460364	0.230182	+	0.973148i	$0.426068\pi$
$444$	3.50292e6	0.843281
$445$	674664.	0.161506
$446$	−2.39562e6	−0.570271
$447$	7.11161e6	1.68345
$448$	−219624.	−0.0516994
$449$	1.62580e6	0.380585	0.190293	−	0.981727i	$-0.439056\pi$
$449$	1.62580e6	0.380585	0.190293	+	0.981727i	$0.439056\pi$
$450$	−1.48268e6	−0.345158
$451$	3.00709e6	0.696154
$452$	760928.	0.175185
$453$	−3.04596e6	−0.697395
$454$	−5.29213e6	−1.20501
$455$	−65301.9	−0.0147876
$456$	−456274.	−0.102758
$457$	1.50323e6	0.336694	0.168347	−	0.985728i	$-0.446157\pi$
$457$	1.50323e6	0.336694	0.168347	+	0.985728i	$0.446157\pi$
$458$	463009.	0.103140
$459$	4.60634e6	1.02053
$460$	−5930.08	−0.00130667
$461$	549546.	0.120435	0.0602173	−	0.998185i	$-0.480821\pi$
$461$	549546.	0.120435	0.0602173	+	0.998185i	$0.480821\pi$
$462$	−980130.	−0.213638
$463$	−3.34547e6	−0.725279	−0.362640	−	0.931929i	$-0.618124\pi$
$463$	−3.34547e6	−0.725279	−0.362640	+	0.931929i	$0.618124\pi$
$464$	1.22782e6	0.264752
$465$	−949007.	−0.203534
$466$	4.87701e6	1.04037
$467$	2.20487e6	0.467833	0.233916	−	0.972257i	$-0.424846\pi$
$467$	2.20487e6	0.467833	0.233916	+	0.972257i	$0.424846\pi$
$468$	−326154.	−0.0688349
$469$	−2.15769e6	−0.452957
$470$	537450.	0.112226
$471$	−9.23185e6	−1.91750
$472$	−324264.	−0.0669952
$473$	277053.	0.0569390
$474$	810603.	0.165715
$475$	1.14893e6	0.233647
$476$	1.69340e6	0.342565
$477$	1.12404e6	0.226196
$478$	−6.67293e6	−1.33582
$479$	−655516.	−0.130540	−0.0652702	−	0.997868i	$-0.520791\pi$
$479$	−655516.	−0.130540	−0.0652702	+	0.997868i	$0.520791\pi$
$480$	−140716.	−0.0278766
$481$	−1.94032e6	−0.382393
$482$	3.39084e6	0.664798
$483$	−52585.5	−0.0102565
$484$	−1.65789e6	−0.321694
$485$	224810.	0.0433971
$486$	−3.36160e6	−0.645587
$487$	1.70140e6	0.325076	0.162538	−	0.986702i	$-0.448032\pi$
$487$	1.70140e6	0.325076	0.162538	+	0.986702i	$0.448032\pi$
$488$	3.47339e6	0.660243
$489$	−2.67292e6	−0.505491
$490$	401598.	0.0755616
$491$	1.54564e6	0.289338	0.144669	−	0.989480i	$-0.453788\pi$
$491$	1.54564e6	0.289338	0.144669	+	0.989480i	$0.453788\pi$
$492$	3.82834e6	0.713014
$493$	−9.46703e6	−1.75427
$494$	252737.	0.0465964
$495$	−208312.	−0.0382122
$496$	1.76794e6	0.322673
$497$	3.49793e6	0.635214
$498$	−179855.	−0.0324975
$499$	5.57437e6	1.00218	0.501089	−	0.865396i	$-0.332933\pi$
$499$	5.57437e6	1.00218	0.501089	+	0.865396i	$0.332933\pi$
$500$	714653.	0.127841
$501$	4.15788e6	0.740078
$502$	−4.36591e6	−0.773243
$503$	318350.	0.0561028	0.0280514	−	0.999606i	$-0.491070\pi$
$503$	318350.	0.0561028	0.0280514	+	0.999606i	$0.491070\pi$
$504$	−413921.	−0.0725840
$505$	626587.	0.109333
$506$	49301.7	0.00856023
$507$	544624.	0.0940972
$508$	−1.74038e6	−0.299217
$509$	265194.	0.0453701	0.0226851	−	0.999743i	$-0.492779\pi$
$509$	265194.	0.0453701	0.0226851	+	0.999743i	$0.492779\pi$
$510$	1.08498e6	0.184713
$511$	−3.67325e6	−0.622297
$512$	262144.	0.0441942
$513$	872488.	0.146375
$514$	−42042.3	−0.00701906
$515$	310676.	0.0516166
$516$	352717.	0.0583180
$517$	−4.46827e6	−0.735212
$518$	−2.46245e6	−0.403220
$519$	−7.33866e6	−1.19591
$520$	77944.5	0.0126409
$521$	1.91132e6	0.308489	0.154245	−	0.988033i	$-0.450706\pi$
$521$	1.91132e6	0.308489	0.154245	+	0.988033i	$0.450706\pi$
$522$	2.31404e6	0.371701
$523$	4.75910e6	0.760801	0.380400	−	0.924822i	$-0.375786\pi$
$523$	4.75910e6	0.760801	0.380400	+	0.924822i	$0.375786\pi$
$524$	−5.44777e6	−0.866744
$525$	3.14207e6	0.497528
$526$	6.65400e6	1.04862
$527$	−1.36316e7	−2.13806
$528$	1.16988e6	0.182624
$529$	−6.43370e6	−0.999589
$530$	−268623.	−0.0415388
$531$	−611132.	−0.0940587
$532$	320747.	0.0491342
$533$	−2.12058e6	−0.323322
$534$	−7.14089e6	−1.08367
$535$	1.26808e6	0.191541
$536$	2.57542e6	0.387201
$537$	9.50146e6	1.42185
$538$	−492389.	−0.0733420
$539$	−3.33882e6	−0.495018
$540$	269076.	0.0397092
$541$	−1.03919e7	−1.52652	−0.763261	−	0.646090i	$-0.776403\pi$
$541$	−1.03919e7	−1.52652	−0.763261	+	0.646090i	$0.776403\pi$
$542$	8.59826e6	1.25722
$543$	2.90230e6	0.422418
$544$	−2.02125e6	−0.292835
$545$	−861730.	−0.124274
$546$	691179.	0.0992222
$547$	−9.00790e6	−1.28723	−0.643614	−	0.765350i	$-0.722566\pi$
$547$	−9.00790e6	−1.28723	−0.643614	+	0.765350i	$0.722566\pi$
$548$	770295.	0.109574
$549$	6.54621e6	0.926955
$550$	−2.94586e6	−0.415246
$551$	−1.79315e6	−0.251616
$552$	62766.1	0.00876754
$553$	−569830.	−0.0792378
$554$	3.27433e6	0.453260
$555$	−1.57772e6	−0.217418
$556$	5.18084e6	0.710745
$557$	1.61153e6	0.220090	0.110045	−	0.993927i	$-0.464901\pi$
$557$	1.61153e6	0.220090	0.110045	+	0.993927i	$0.464901\pi$
$558$	3.33199e6	0.453021
$559$	−195375.	−0.0264448
$560$	98918.9	0.0133294
$561$	−9.02034e6	−1.21008
$562$	5.52011e6	0.737237
$563$	−5.73380e6	−0.762380	−0.381190	−	0.924497i	$-0.624486\pi$
$563$	−5.73380e6	−0.762380	−0.381190	+	0.924497i	$0.624486\pi$
$564$	−5.68856e6	−0.753017
$565$	−342722.	−0.0451670
$566$	1.58329e6	0.207740
$567$	3.95766e6	0.516988
$568$	−4.17513e6	−0.543000
$569$	4.81958e6	0.624063	0.312032	−	0.950072i	$-0.398991\pi$
$569$	4.81958e6	0.624063	0.312032	+	0.950072i	$0.398991\pi$
$570$	205506.	0.0264934
$571$	7.86132e6	1.00903	0.504517	−	0.863402i	$-0.331671\pi$
$571$	7.86132e6	1.00903	0.504517	+	0.863402i	$0.331671\pi$
$572$	−648017.	−0.0828126
$573$	1.14467e7	1.45644
$574$	−2.69121e6	−0.340932
$575$	−158050.	−0.0199354
$576$	494056.	0.0620469
$577$	1.55342e7	1.94244	0.971221	−	0.238179i	$-0.0765504\pi$
$577$	1.55342e7	1.94244	0.971221	+	0.238179i	$0.0765504\pi$
$578$	9.90531e6	1.23324
$579$	6.68942e6	0.829262
$580$	−553010.	−0.0682594
$581$	126433.	0.0155389
$582$	−2.37947e6	−0.291187
$583$	2.23329e6	0.272128
$584$	4.38440e6	0.531958
$585$	146900.	0.0177473
$586$	1.53116e6	0.184194
$587$	−1.84016e6	−0.220425	−0.110212	−	0.993908i	$-0.535153\pi$
$587$	−1.84016e6	−0.220425	−0.110212	+	0.993908i	$0.535153\pi$
$588$	−4.25066e6	−0.507006
$589$	−2.58196e6	−0.306663
$590$	146049.	0.0172730
$591$	−6.12386e6	−0.721201
$592$	2.93918e6	0.344685
$593$	1.11019e7	1.29646	0.648230	−	0.761445i	$-0.275510\pi$
$593$	1.11019e7	1.29646	0.648230	+	0.761445i	$0.275510\pi$
$594$	−2.23705e6	−0.260142
$595$	−762709.	−0.0883215
$596$	5.96712e6	0.688096
$597$	1.07055e7	1.22934
$598$	−34767.1	−0.00397572
$599$	−1.34553e7	−1.53224	−0.766122	−	0.642696i	$-0.777816\pi$
$599$	−1.34553e7	−1.53224	−0.766122	+	0.642696i	$0.777816\pi$
$600$	−3.75038e6	−0.425302
$601$	1.49829e7	1.69204	0.846020	−	0.533151i	$-0.178992\pi$
$601$	1.49829e7	1.69204	0.846020	+	0.533151i	$0.178992\pi$
$602$	−247950.	−0.0278851
$603$	4.85384e6	0.543616
$604$	−2.55577e6	−0.285055
$605$	746715.	0.0829405
$606$	−6.63202e6	−0.733609
$607$	−1.18436e7	−1.30471	−0.652353	−	0.757915i	$-0.726218\pi$
$607$	−1.18436e7	−1.30471	−0.652353	+	0.757915i	$0.726218\pi$
$608$	−382845.	−0.0420014
$609$	−4.90386e6	−0.535790
$610$	−1.56441e6	−0.170227
$611$	3.15098e6	0.341462
$612$	−3.80940e6	−0.411129
$613$	6.44924e6	0.693198	0.346599	−	0.938013i	$-0.387336\pi$
$613$	6.44924e6	0.693198	0.346599	+	0.938013i	$0.387336\pi$
$614$	−1.18390e7	−1.26735
$615$	−1.72429e6	−0.183832
$616$	−822394.	−0.0873229
$617$	−1.10487e7	−1.16842	−0.584210	−	0.811602i	$-0.698596\pi$
$617$	−1.10487e7	−1.16842	−0.584210	+	0.811602i	$0.698596\pi$
$618$	−3.28831e6	−0.346339
$619$	7.71392e6	0.809186	0.404593	−	0.914497i	$-0.367413\pi$
$619$	7.71392e6	0.809186	0.404593	+	0.914497i	$0.367413\pi$
$620$	−796280.	−0.0831930
$621$	−120021.	−0.0124891
$622$	−2.14760e6	−0.222576
$623$	5.01983e6	0.518166
$624$	−824993.	−0.0848181
$625$	9.28146e6	0.950421
$626$	−1.33321e7	−1.35976
$627$	−1.70854e6	−0.173563
$628$	−7.74614e6	−0.783765
$629$	−2.26624e7	−2.28391
$630$	186430.	0.0187139
$631$	−9.79932e6	−0.979767	−0.489883	−	0.871788i	$-0.662961\pi$
$631$	−9.79932e6	−0.979767	−0.489883	+	0.871788i	$0.662961\pi$
$632$	680150.	0.0677348
$633$	−1.43207e7	−1.42055
$634$	6.00400e6	0.593222
$635$	783870.	0.0771453
$636$	2.84321e6	0.278718
$637$	2.35450e6	0.229906
$638$	4.59763e6	0.447180
$639$	−7.86877e6	−0.762351
$640$	−118070.	−0.0113943
$641$	1.53393e7	1.47455	0.737275	−	0.675593i	$-0.236112\pi$
$641$	1.53393e7	1.47455	0.737275	+	0.675593i	$0.236112\pi$
$642$	−1.34218e7	−1.28521
$643$	1.45341e7	1.38631	0.693155	−	0.720789i	$-0.256220\pi$
$643$	1.45341e7	1.38631	0.693155	+	0.720789i	$0.256220\pi$
$644$	−44122.7	−0.00419226
$645$	−158864.	−0.0150358
$646$	2.95191e6	0.278305
$647$	−1.26902e7	−1.19181	−0.595904	−	0.803055i	$-0.703206\pi$
$647$	−1.26902e7	−1.19181	−0.595904	+	0.803055i	$0.703206\pi$
$648$	−4.72387e6	−0.441937
$649$	−1.21422e6	−0.113158
$650$	2.07739e6	0.192857
$651$	−7.06108e6	−0.653008
$652$	−2.24276e6	−0.206616
$653$	−4.48209e6	−0.411337	−0.205669	−	0.978622i	$-0.565937\pi$
$653$	−4.48209e6	−0.411337	−0.205669	+	0.978622i	$0.565937\pi$
$654$	9.12086e6	0.833857
$655$	2.45368e6	0.223468
$656$	3.21223e6	0.291439
$657$	8.26316e6	0.746849
$658$	3.99889e6	0.360060
$659$	−1.76267e7	−1.58109	−0.790545	−	0.612403i	$-0.790203\pi$
$659$	−1.76267e7	−1.58109	−0.790545	+	0.612403i	$0.790203\pi$
$660$	−526917.	−0.0470849
$661$	1.03733e7	0.923447	0.461724	−	0.887024i	$-0.347231\pi$
$661$	1.03733e7	0.923447	0.461724	+	0.887024i	$0.347231\pi$
$662$	8.69617e6	0.771229
$663$	6.36107e6	0.562013
$664$	−150911.	−0.0132831
$665$	−144465.	−0.0126680
$666$	5.53940e6	0.483924
$667$	246670.	0.0214685
$668$	3.48874e6	0.302501
$669$	−1.14204e7	−0.986545
$670$	−1.15997e6	−0.0998298
$671$	1.30063e7	1.11518
$672$	−1.04699e6	−0.0894377
$673$	4.76273e6	0.405339	0.202669	−	0.979247i	$-0.435038\pi$
$673$	4.76273e6	0.405339	0.202669	+	0.979247i	$0.435038\pi$
$674$	3.28598e6	0.278622
$675$	7.17148e6	0.605828
$676$	456976.	0.0384615
$677$	1.68783e7	1.41533	0.707665	−	0.706548i	$-0.249749\pi$
$677$	1.68783e7	1.41533	0.707665	+	0.706548i	$0.249749\pi$
$678$	3.62750e6	0.303063
$679$	1.67270e6	0.139233
$680$	910371.	0.0754999
$681$	−2.52286e7	−2.08462
$682$	6.62013e6	0.545012
$683$	−1.87331e7	−1.53659	−0.768294	−	0.640097i	$-0.778894\pi$
$683$	−1.87331e7	−1.53659	−0.768294	+	0.640097i	$0.778894\pi$
$684$	−721538.	−0.0589684
$685$	−346941.	−0.0282507
$686$	6.59280e6	0.534884
$687$	2.20726e6	0.178427
$688$	295953.	0.0238370
$689$	−1.57489e6	−0.126387
$690$	−28269.9	−0.00226048
$691$	2.12121e7	1.69000	0.845002	−	0.534763i	$-0.179599\pi$
$691$	2.12121e7	1.69000	0.845002	+	0.534763i	$0.179599\pi$
$692$	−6.15763e6	−0.488819
$693$	−1.54995e6	−0.122598
$694$	7.03590e6	0.554525
$695$	−2.33345e6	−0.183247
$696$	5.85325e6	0.458009
$697$	−2.47678e7	−1.93110
$698$	−1.26143e7	−0.980000
$699$	2.32497e7	1.79980
$700$	2.63641e6	0.203361
$701$	2.61831e6	0.201246	0.100623	−	0.994925i	$-0.467916\pi$
$701$	2.61831e6	0.201246	0.100623	+	0.994925i	$0.467916\pi$
$702$	1.57755e6	0.120820
$703$	−4.29249e6	−0.327583
$704$	981612.	0.0746463
$705$	2.56213e6	0.194146
$706$	−6.05824e6	−0.457440
$707$	4.66212e6	0.350780
$708$	−1.54583e6	−0.115899
$709$	1.41825e7	1.05959	0.529794	−	0.848127i	$-0.322269\pi$
$709$	1.41825e7	1.05959	0.529794	+	0.848127i	$0.322269\pi$
$710$	1.88048e6	0.139998
$711$	1.28186e6	0.0950971
$712$	−5.99168e6	−0.442944
$713$	355180.	0.0261653
$714$	8.07279e6	0.592622
$715$	291867.	0.0213511
$716$	7.97236e6	0.581172
$717$	−3.18112e7	−2.31091
$718$	6.75739e6	0.489179
$719$	1.39362e6	0.100536	0.0502681	−	0.998736i	$-0.483992\pi$
$719$	1.39362e6	0.100536	0.0502681	+	0.998736i	$0.483992\pi$
$720$	−222523.	−0.0159972
$721$	2.31158e6	0.165604
$722$	−9.34528e6	−0.667189
$723$	1.61648e7	1.15007
$724$	2.43522e6	0.172660
$725$	−1.47389e7	−1.04141
$726$	−7.90351e6	−0.556517
$727$	5.67972e6	0.398557	0.199279	−	0.979943i	$-0.436140\pi$
$727$	5.67972e6	0.398557	0.199279	+	0.979943i	$0.436140\pi$
$728$	579945.	0.0405563
$729$	1.91054e6	0.133149
$730$	−1.97473e6	−0.137152
$731$	−2.28193e6	−0.157946
$732$	1.65583e7	1.14219
$733$	−1.55611e7	−1.06974	−0.534872	−	0.844933i	$-0.679640\pi$
$733$	−1.55611e7	−1.06974	−0.534872	+	0.844933i	$0.679640\pi$
$734$	−7.48736e6	−0.512966
$735$	1.91450e6	0.130718
$736$	52665.0	0.00358367
$737$	9.64380e6	0.654003
$738$	6.05402e6	0.409169
$739$	1.54351e7	1.03968	0.519839	−	0.854264i	$-0.325992\pi$
$739$	1.54351e7	1.03968	0.519839	+	0.854264i	$0.325992\pi$
$740$	−1.32381e6	−0.0888681
$741$	1.20485e6	0.0806097
$742$	−1.99869e6	−0.133271
$743$	−8.72110e6	−0.579561	−0.289781	−	0.957093i	$-0.593582\pi$
$743$	−8.72110e6	−0.579561	−0.289781	+	0.957093i	$0.593582\pi$
$744$	8.42811e6	0.558211
$745$	−2.68759e6	−0.177408
$746$	2.51201e6	0.165263
$747$	−284417.	−0.0186490
$748$	−7.56867e6	−0.494613
$749$	9.43514e6	0.614531
$750$	3.40689e6	0.221159
$751$	1.07940e7	0.698365	0.349183	−	0.937055i	$-0.386459\pi$
$751$	1.07940e7	0.698365	0.349183	+	0.937055i	$0.386459\pi$
$752$	−4.77309e6	−0.307790
$753$	−2.08132e7	−1.33768
$754$	−3.24221e6	−0.207688
$755$	1.15112e6	0.0734941
$756$	2.00206e6	0.127401
$757$	1.87309e7	1.18801	0.594005	−	0.804462i	$-0.297546\pi$
$757$	1.87309e7	1.18801	0.594005	+	0.804462i	$0.297546\pi$
$758$	1.91290e6	0.120926
$759$	235031.	0.0148088
$760$	172433.	0.0108290
$761$	−1.41785e7	−0.887498	−0.443749	−	0.896151i	$-0.646352\pi$
$761$	−1.41785e7	−0.887498	−0.443749	+	0.896151i	$0.646352\pi$
$762$	−8.29676e6	−0.517632
$763$	−6.41170e6	−0.398714
$764$	9.60454e6	0.595310
$765$	1.71575e6	0.105999
$766$	−1.83419e7	−1.12947
$767$	856260.	0.0525554
$768$	1.24969e6	0.0764540
$769$	−1.90780e7	−1.16337	−0.581683	−	0.813416i	$-0.697605\pi$
$769$	−1.90780e7	−1.16337	−0.581683	+	0.813416i	$0.697605\pi$
$770$	370407.	0.0225140
$771$	−200424.	−0.0121427
$772$	5.61287e6	0.338955
$773$	1.31787e7	0.793276	0.396638	−	0.917975i	$-0.370177\pi$
$773$	1.31787e7	0.793276	0.396638	+	0.917975i	$0.370177\pi$
$774$	557776.	0.0334663
$775$	−2.12226e7	−1.26924
$776$	−1.99653e6	−0.119021
$777$	−1.17390e7	−0.697554
$778$	1.04854e7	0.621065
$779$	−4.69126e6	−0.276979
$780$	371577.	0.0218682
$781$	−1.56340e7	−0.917155
$782$	−406071.	−0.0237457
$783$	−1.11926e7	−0.652418
$784$	−3.56659e6	−0.207235
$785$	3.48886e6	0.202074
$786$	−2.59706e7	−1.49943
$787$	−2.47284e7	−1.42318	−0.711589	−	0.702596i	$-0.752024\pi$
$787$	−2.47284e7	−1.42318	−0.711589	+	0.702596i	$0.752024\pi$
$788$	−5.13832e6	−0.294785
$789$	3.17210e7	1.81407
$790$	−306340.	−0.0174637
$791$	−2.55002e6	−0.144911
$792$	1.85002e6	0.104800
$793$	−9.17191e6	−0.517937
$794$	3.84461e6	0.216422
$795$	−1.28058e6	−0.0718603
$796$	8.98266e6	0.502484
$797$	−2.11191e7	−1.17769	−0.588843	−	0.808248i	$-0.700416\pi$
$797$	−2.11191e7	−1.17769	−0.588843	+	0.808248i	$0.700416\pi$
$798$	1.52907e6	0.0850001
$799$	3.68026e7	2.03945
$800$	−3.14682e6	−0.173839
$801$	−1.12924e7	−0.621876
$802$	−1.60223e7	−0.879610
$803$	1.64176e7	0.898505
$804$	1.22776e7	0.669841
$805$	19872.9	0.00108087
$806$	−4.66846e6	−0.253126
$807$	−2.34732e6	−0.126878
$808$	−5.56471e6	−0.299857
$809$	1.62945e7	0.875326	0.437663	−	0.899139i	$-0.355806\pi$
$809$	1.62945e7	0.875326	0.437663	+	0.899139i	$0.355806\pi$
$810$	2.12763e6	0.113942
$811$	2.00401e7	1.06991	0.534954	−	0.844881i	$-0.320329\pi$
$811$	2.00401e7	1.06991	0.534954	+	0.844881i	$0.320329\pi$
$812$	−4.11467e6	−0.219000
$813$	4.09896e7	2.17494
$814$	1.10059e7	0.582191
$815$	1.01014e6	0.0532706
$816$	−9.63570e6	−0.506591
$817$	−432221.	−0.0226543
$818$	−1.25012e7	−0.653234
$819$	1.09301e6	0.0569395
$820$	−1.44679e6	−0.0751400
$821$	3.51296e7	1.81893	0.909463	−	0.415784i	$-0.136493\pi$
$821$	3.51296e7	1.81893	0.909463	+	0.415784i	$0.136493\pi$
$822$	3.67215e6	0.189558
$823$	−2.51324e7	−1.29341	−0.646703	−	0.762742i	$-0.723853\pi$
$823$	−2.51324e7	−1.29341	−0.646703	+	0.762742i	$0.723853\pi$
$824$	−2.75911e6	−0.141563
$825$	−1.40435e7	−0.718357
$826$	1.08667e6	0.0554178
$827$	−1.66576e7	−0.846934	−0.423467	−	0.905911i	$-0.639187\pi$
$827$	−1.66576e7	−0.846934	−0.423467	+	0.905911i	$0.639187\pi$
$828$	99256.4	0.00503133
$829$	−1.46404e7	−0.739887	−0.369944	−	0.929054i	$-0.620623\pi$
$829$	−1.46404e7	−0.739887	−0.369944	+	0.929054i	$0.620623\pi$
$830$	67970.2	0.00342471
$831$	1.56094e7	0.784121
$832$	−692224.	−0.0346688
$833$	2.75000e7	1.37316
$834$	2.46981e7	1.22956
$835$	−1.57133e6	−0.0779921
$836$	−1.43358e6	−0.0709425
$837$	−1.61162e7	−0.795152
$838$	−1.33951e7	−0.658924
$839$	2.79895e7	1.37275	0.686374	−	0.727249i	$-0.259201\pi$
$839$	2.79895e7	1.37275	0.686374	+	0.727249i	$0.259201\pi$
$840$	471566.	0.0230592
$841$	2.49204e6	0.121497
$842$	−1.20533e7	−0.585902
$843$	2.63155e7	1.27539
$844$	−1.20160e7	−0.580637
$845$	−205822.	−0.00991632
$846$	−8.99572e6	−0.432125
$847$	5.55593e6	0.266102
$848$	2.38564e6	0.113924
$849$	7.54787e6	0.359381
$850$	2.42634e7	1.15187
$851$	590484.	0.0279502
$852$	−1.99037e7	−0.939366
$853$	−2.22248e7	−1.04584	−0.522919	−	0.852382i	$-0.675157\pi$
$853$	−2.22248e7	−1.04584	−0.522919	+	0.852382i	$0.675157\pi$
$854$	−1.16400e7	−0.546146
$855$	324981.	0.0152035
$856$	−1.12618e7	−0.525319
$857$	7.83995e6	0.364637	0.182319	−	0.983239i	$-0.441640\pi$
$857$	7.83995e6	0.364637	0.182319	+	0.983239i	$0.441640\pi$
$858$	−3.08923e6	−0.143262
$859$	−3.08215e7	−1.42518	−0.712592	−	0.701579i	$-0.752479\pi$
$859$	−3.08215e7	−1.42518	−0.712592	+	0.701579i	$0.752479\pi$
$860$	−133298.	−0.00614576
$861$	−1.28295e7	−0.589798
$862$	1.34090e7	0.614649
$863$	−4.53439e6	−0.207249	−0.103624	−	0.994617i	$-0.533044\pi$
$863$	−4.53439e6	−0.207249	−0.103624	+	0.994617i	$0.533044\pi$
$864$	−2.38966e6	−0.108906
$865$	2.77340e6	0.126029
$866$	6.48753e6	0.293957
$867$	4.72206e7	2.13346
$868$	−5.92472e6	−0.266912
$869$	2.54686e6	0.114408
$870$	−2.63631e6	−0.118086
$871$	−6.80073e6	−0.303746
$872$	7.65301e6	0.340833
$873$	−3.76282e6	−0.167100
$874$	−76913.9	−0.00340586
$875$	−2.39495e6	−0.105749
$876$	2.09013e7	0.920265
$877$	3.31312e7	1.45458	0.727292	−	0.686328i	$-0.240779\pi$
$877$	3.31312e7	1.45458	0.727292	+	0.686328i	$0.240779\pi$
$878$	2.99579e7	1.31152
$879$	7.29933e6	0.318648
$880$	−442118.	−0.0192456
$881$	6.36611e6	0.276334	0.138167	−	0.990409i	$-0.455879\pi$
$881$	6.36611e6	0.276334	0.138167	+	0.990409i	$0.455879\pi$
$882$	−6.72186e6	−0.290950
$883$	−3.09630e7	−1.33641	−0.668207	−	0.743975i	$-0.732938\pi$
$883$	−3.09630e7	−1.33641	−0.668207	+	0.743975i	$0.732938\pi$
$884$	5.33736e6	0.229718
$885$	696243.	0.0298815
$886$	7.60626e6	0.325527
$887$	−4.17692e7	−1.78257	−0.891287	−	0.453440i	$-0.850197\pi$
$887$	−4.17692e7	−1.78257	−0.891287	+	0.453440i	$0.850197\pi$
$888$	1.40117e7	0.596290
$889$	5.83238e6	0.247509
$890$	2.69866e6	0.114202
$891$	−1.76888e7	−0.746455
$892$	−9.58250e6	−0.403243
$893$	6.97079e6	0.292519
$894$	2.84465e7	1.19038
$895$	−3.59075e6	−0.149840
$896$	−878497.	−0.0365570
$897$	−165742.	−0.00687782
$898$	6.50321e6	0.269114
$899$	3.31223e7	1.36685
$900$	−5.93074e6	−0.244063
$901$	−1.83944e7	−0.754871
$902$	1.20284e7	0.492255
$903$	−1.18203e6	−0.0482401
$904$	3.04371e6	0.123875
$905$	−1.09682e6	−0.0445159
$906$	−1.21838e7	−0.493133
$907$	−4.51182e7	−1.82110	−0.910550	−	0.413399i	$-0.864342\pi$
$907$	−4.51182e7	−1.82110	−0.910550	+	0.413399i	$0.864342\pi$
$908$	−2.11685e7	−0.852071
$909$	−1.04877e7	−0.420988
$910$	−261208.	−0.0104564
$911$	2.93224e6	0.117059	0.0585293	−	0.998286i	$-0.481359\pi$
$911$	2.93224e6	0.117059	0.0585293	+	0.998286i	$0.481359\pi$
$912$	−1.82510e6	−0.0726606
$913$	−565092.	−0.0224359
$914$	6.01293e6	0.238079
$915$	−7.45788e6	−0.294485
$916$	1.85203e6	0.0729307
$917$	1.82566e7	0.716962
$918$	1.84254e7	0.721622
$919$	1.06534e7	0.416101	0.208051	−	0.978118i	$-0.433288\pi$
$919$	1.06534e7	0.416101	0.208051	+	0.978118i	$0.433288\pi$
$920$	−23720.3	−0.000923956 0
$921$	−5.64391e7	−2.19246
$922$	2.19818e6	0.0851602
$923$	1.10250e7	0.425964
$924$	−3.92052e6	−0.151065
$925$	−3.52824e7	−1.35583
$926$	−1.33819e7	−0.512850
$927$	−5.20003e6	−0.198750
$928$	4.91127e6	0.187208
$929$	−1.93436e7	−0.735355	−0.367677	−	0.929953i	$-0.619847\pi$
$929$	−1.93436e7	−0.735355	−0.367677	+	0.929953i	$0.619847\pi$
$930$	−3.79603e6	−0.143920
$931$	5.20878e6	0.196952
$932$	1.95081e7	0.735655
$933$	−1.02380e7	−0.385046
$934$	8.81947e6	0.330808
$935$	3.40893e6	0.127523
$936$	−1.30462e6	−0.0486736
$937$	−5.62445e6	−0.209282	−0.104641	−	0.994510i	$-0.533369\pi$
$937$	−5.62445e6	−0.209282	−0.104641	+	0.994510i	$0.533369\pi$
$938$	−8.63076e6	−0.320289
$939$	−6.35566e7	−2.35232
$940$	2.14980e6	0.0793557
$941$	−2.18961e7	−0.806106	−0.403053	−	0.915177i	$-0.632051\pi$
$941$	−2.18961e7	−0.806106	−0.403053	+	0.915177i	$0.632051\pi$
$942$	−3.69274e7	−1.35588
$943$	645341.	0.0236325
$944$	−1.29706e6	−0.0473728
$945$	−901729.	−0.0328471
$946$	1.10821e6	0.0402620
$947$	931486.	0.0337522	0.0168761	−	0.999858i	$-0.494628\pi$
$947$	931486.	0.0337522	0.0168761	+	0.999858i	$0.494628\pi$
$948$	3.24241e6	0.117178
$949$	−1.15775e7	−0.417302
$950$	4.59573e6	0.165214
$951$	2.86223e7	1.02625
$952$	6.77361e6	0.242230
$953$	4.06914e7	1.45135	0.725673	−	0.688040i	$-0.241529\pi$
$953$	4.06914e7	1.45135	0.725673	+	0.688040i	$0.241529\pi$
$954$	4.49616e6	0.159945
$955$	−4.32589e6	−0.153485
$956$	−2.66917e7	−0.944565
$957$	2.19178e7	0.773601
$958$	−2.62206e6	−0.0923059
$959$	−2.58141e6	−0.0906382
$960$	−562862.	−0.0197117
$961$	1.90638e7	0.665887
$962$	−7.76128e6	−0.270393
$963$	−2.12248e7	−0.737528
$964$	1.35634e7	0.470083
$965$	−2.52804e6	−0.0873907
$966$	−210342.	−0.00725242
$967$	1.43608e7	0.493869	0.246934	−	0.969032i	$-0.420577\pi$
$967$	1.43608e7	0.493869	0.246934	+	0.969032i	$0.420577\pi$
$968$	−6.63157e6	−0.227472
$969$	1.40723e7	0.481456
$970$	899239.	0.0306864
$971$	4.38037e6	0.149095	0.0745475	−	0.997217i	$-0.476249\pi$
$971$	4.38037e6	0.149095	0.0745475	+	0.997217i	$0.476249\pi$
$972$	−1.34464e7	−0.456499
$973$	−1.73621e7	−0.587921
$974$	6.80562e6	0.229864
$975$	9.90335e6	0.333634
$976$	1.38935e7	0.466862
$977$	2.87093e7	0.962247	0.481123	−	0.876653i	$-0.340229\pi$
$977$	2.87093e7	0.962247	0.481123	+	0.876653i	$0.340229\pi$
$978$	−1.06917e7	−0.357436
$979$	−2.24362e7	−0.748155
$980$	1.60639e6	0.0534301
$981$	1.44234e7	0.478516
$982$	6.18257e6	0.204593
$983$	5.36798e7	1.77185	0.885925	−	0.463829i	$-0.153525\pi$
$983$	5.36798e7	1.77185	0.885925	+	0.463829i	$0.153525\pi$
$984$	1.53134e7	0.504177
$985$	2.31430e6	0.0760028
$986$	−3.78681e7	−1.24046
$987$	1.90635e7	0.622888
$988$	1.01095e6	0.0329486
$989$	59457.3	0.00193292
$990$	−833249.	−0.0270201
$991$	2.18434e7	0.706539	0.353269	−	0.935522i	$-0.385070\pi$
$991$	2.18434e7	0.706539	0.353269	+	0.935522i	$0.385070\pi$
$992$	7.07175e6	0.228164
$993$	4.14564e7	1.33419
$994$	1.39917e7	0.449164
$995$	−4.04579e6	−0.129553
$996$	−719421.	−0.0229792
$997$	4.14924e7	1.32200	0.660999	−	0.750387i	$-0.270133\pi$
$997$	4.14924e7	1.32200	0.660999	+	0.750387i	$0.270133\pi$
$998$	2.22975e7	0.708646
$999$	−2.67931e7	−0.849394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.6.a.c.1.2	✓	2
3.2	odd	2		234.6.a.h.1.2		2
4.3	odd	2		208.6.a.g.1.1		2
5.2	odd	4		650.6.b.h.599.3		4
5.3	odd	4		650.6.b.h.599.2		4
5.4	even	2		650.6.a.b.1.1		2
8.3	odd	2		832.6.a.m.1.2		2
8.5	even	2		832.6.a.k.1.1		2
13.5	odd	4		338.6.b.b.337.2		4
13.8	odd	4		338.6.b.b.337.4		4
13.12	even	2		338.6.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.a.c.1.2	✓	2	1.1	even	1	trivial
208.6.a.g.1.1		2	4.3	odd	2
234.6.a.h.1.2		2	3.2	odd	2
338.6.a.f.1.2		2	13.12	even	2
338.6.b.b.337.2		4	13.5	odd	4
338.6.b.b.337.4		4	13.8	odd	4
650.6.a.b.1.1		2	5.4	even	2
650.6.b.h.599.2		4	5.3	odd	4
650.6.b.h.599.3		4	5.2	odd	4
832.6.a.k.1.1		2	8.5	even	2
832.6.a.m.1.2		2	8.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	26.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +19.0688 q^{3} +16.0000 q^{4} -7.20641 q^{5} +76.2752 q^{6} -53.6192 q^{7} +64.0000 q^{8} +120.619 q^{9} -28.8256 q^{10} +239.651 q^{11} +305.101 q^{12} -169.000 q^{13} -214.477 q^{14} -137.418 q^{15} +256.000 q^{16} -1973.88 q^{17} +482.477 q^{18} -373.872 q^{19} -115.303 q^{20} -1022.45 q^{21} +958.605 q^{22} +51.4306 q^{23} +1220.40 q^{24} -3073.07 q^{25} -676.000 q^{26} -2333.65 q^{27} -857.908 q^{28} +4796.16 q^{29} -549.670 q^{30} +6906.01 q^{31} +1024.00 q^{32} +4569.86 q^{33} -7895.50 q^{34} +386.402 q^{35} +1929.91 q^{36} +11481.2 q^{37} -1495.49 q^{38} -3222.63 q^{39} -461.210 q^{40} +12547.8 q^{41} -4089.82 q^{42} +1156.07 q^{43} +3834.42 q^{44} -869.231 q^{45} +205.723 q^{46} -18644.9 q^{47} +4881.61 q^{48} -13932.0 q^{49} -12292.3 q^{50} -37639.4 q^{51} -2704.00 q^{52} +9318.90 q^{53} -9334.62 q^{54} -1727.02 q^{55} -3431.63 q^{56} -7129.29 q^{57} +19184.7 q^{58} -5066.63 q^{59} -2198.68 q^{60} +54271.7 q^{61} +27624.0 q^{62} -6467.51 q^{63} +4096.00 q^{64} +1217.88 q^{65} +18279.4 q^{66} +40241.0 q^{67} -31582.0 q^{68} +980.721 q^{69} +1545.61 q^{70} -65236.5 q^{71} +7719.63 q^{72} +68506.2 q^{73} +45924.7 q^{74} -58599.7 q^{75} -5981.95 q^{76} -12849.9 q^{77} -12890.5 q^{78} +10627.3 q^{79} -1844.84 q^{80} -73810.5 q^{81} +50191.1 q^{82} -2357.98 q^{83} -16359.3 q^{84} +14224.5 q^{85} +4624.27 q^{86} +91457.1 q^{87} +15337.7 q^{88} -93620.0 q^{89} -3476.92 q^{90} +9061.65 q^{91} +822.890 q^{92} +131689. q^{93} -74579.5 q^{94} +2694.27 q^{95} +19526.5 q^{96} -31195.8 q^{97} -55727.9 q^{98} +28906.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 9 q^{3} + 32 q^{4} + 73 q^{5} + 36 q^{6} + 155 q^{7} + 128 q^{8} - 21 q^{9} + 292 q^{10} - 220 q^{11} + 144 q^{12} - 338 q^{13} + 620 q^{14} - 945 q^{15} + 512 q^{16} - 189 q^{17} - 84 q^{18}+ \cdots + 94002 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 9 * q^3 + 32 * q^4 + 73 * q^5 + 36 * q^6 + 155 * q^7 + 128 * q^8 - 21 * q^9 + 292 * q^10 - 220 * q^11 + 144 * q^12 - 338 * q^13 + 620 * q^14 - 945 * q^15 + 512 * q^16 - 189 * q^17 - 84 * q^18 - 2496 * q^19 + 1168 * q^20 - 3123 * q^21 - 880 * q^22 - 3044 * q^23 + 576 * q^24 + 235 * q^25 - 1352 * q^26 + 1539 * q^27 + 2480 * q^28 + 1900 * q^29 - 3780 * q^30 + 2798 * q^31 + 2048 * q^32 + 9198 * q^33 - 756 * q^34 + 17119 * q^35 - 336 * q^36 + 17805 * q^37 - 9984 * q^38 - 1521 * q^39 + 4672 * q^40 + 11634 * q^41 - 12492 * q^42 - 4069 * q^43 - 3520 * q^44 - 12228 * q^45 - 12176 * q^46 - 25489 * q^47 + 2304 * q^48 + 12783 * q^49 + 940 * q^50 - 55611 * q^51 - 5408 * q^52 - 4614 * q^53 + 6156 * q^54 - 38594 * q^55 + 9920 * q^56 + 14238 * q^57 + 7600 * q^58 - 23420 * q^59 - 15120 * q^60 + 96830 * q^61 + 11192 * q^62 - 36012 * q^63 + 8192 * q^64 - 12337 * q^65 + 36792 * q^66 + 72440 * q^67 - 3024 * q^68 + 32148 * q^69 + 68476 * q^70 - 36679 * q^71 - 1344 * q^72 + 47152 * q^73 + 71220 * q^74 - 91908 * q^75 - 39936 * q^76 - 108742 * q^77 - 6084 * q^78 + 52024 * q^79 + 18688 * q^80 - 78390 * q^81 + 46536 * q^82 - 37758 * q^83 - 49968 * q^84 + 157383 * q^85 - 16276 * q^86 + 120618 * q^87 - 14080 * q^88 - 105072 * q^89 - 48912 * q^90 - 26195 * q^91 - 48704 * q^92 + 173052 * q^93 - 101956 * q^94 - 167514 * q^95 + 9216 * q^96 + 104392 * q^97 + 51132 * q^98 + 94002 * q^99

Introduction

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