LMFDB - Embedded newform 983.6.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,6,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	983.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:	$157.657294876$
Analytic rank:	$0$
Dimension:	$218$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-9.61332 q^{2} +27.9669 q^{3} +60.4159 q^{4} -41.3834 q^{5} -268.854 q^{6} +221.300 q^{7} -273.171 q^{8} +539.145 q^{9} +397.832 q^{10} +72.0069 q^{11} +1689.64 q^{12} +378.554 q^{13} -2127.43 q^{14} -1157.36 q^{15} +692.774 q^{16} +447.425 q^{17} -5182.98 q^{18} -2941.48 q^{19} -2500.22 q^{20} +6189.06 q^{21} -692.226 q^{22} -3381.87 q^{23} -7639.74 q^{24} -1412.41 q^{25} -3639.16 q^{26} +8282.26 q^{27} +13370.0 q^{28} -1168.22 q^{29} +11126.1 q^{30} +6533.14 q^{31} +2081.63 q^{32} +2013.81 q^{33} -4301.24 q^{34} -9158.14 q^{35} +32573.0 q^{36} +5918.56 q^{37} +28277.4 q^{38} +10587.0 q^{39} +11304.8 q^{40} -6233.63 q^{41} -59497.4 q^{42} +8857.78 q^{43} +4350.36 q^{44} -22311.7 q^{45} +32511.0 q^{46} -3800.48 q^{47} +19374.7 q^{48} +32166.6 q^{49} +13578.0 q^{50} +12513.1 q^{51} +22870.7 q^{52} +15138.0 q^{53} -79620.0 q^{54} -2979.89 q^{55} -60452.7 q^{56} -82264.1 q^{57} +11230.5 q^{58} -11335.5 q^{59} -69923.3 q^{60} +41481.0 q^{61} -62805.2 q^{62} +119313. q^{63} -42180.1 q^{64} -15665.9 q^{65} -19359.4 q^{66} +38017.7 q^{67} +27031.6 q^{68} -94580.3 q^{69} +88040.2 q^{70} -2192.43 q^{71} -147279. q^{72} -30480.5 q^{73} -56897.0 q^{74} -39500.7 q^{75} -177712. q^{76} +15935.1 q^{77} -101776. q^{78} +41047.7 q^{79} -28669.4 q^{80} +100616. q^{81} +59925.9 q^{82} +111799. q^{83} +373918. q^{84} -18516.0 q^{85} -85152.6 q^{86} -32671.5 q^{87} -19670.2 q^{88} +29925.8 q^{89} +214489. q^{90} +83773.9 q^{91} -204319. q^{92} +182711. q^{93} +36535.2 q^{94} +121729. q^{95} +58216.5 q^{96} +117393. q^{97} -309228. q^{98} +38822.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16}+ \cdots + 627643 q^{99}+O(q^{100}) $ 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * 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 $

$2$	−9.61332	−1.69941	−0.849705	−	0.527258i	$-0.823220\pi$
$2$	−9.61332	−1.69941	−0.849705	+	0.527258i	$0.823220\pi$
$3$	27.9669	1.79408	0.897038	−	0.441954i	$-0.145715\pi$
$3$	27.9669	1.79408	0.897038	+	0.441954i	$0.145715\pi$
$4$	60.4159	1.88800
$5$	−41.3834	−0.740289	−0.370145	−	0.928974i	$-0.620692\pi$
$5$	−41.3834	−0.740289	−0.370145	+	0.928974i	$0.620692\pi$
$6$	−268.854	−3.04887
$7$	221.300	1.70701	0.853505	−	0.521085i	$-0.174473\pi$
$7$	221.300	1.70701	0.853505	+	0.521085i	$0.174473\pi$
$8$	−273.171	−1.50907
$9$	539.145	2.21871
$10$	397.832	1.25806
$11$	72.0069	0.179429	0.0897145	−	0.995968i	$-0.471405\pi$
$11$	72.0069	0.179429	0.0897145	+	0.995968i	$0.471405\pi$
$12$	1689.64	3.38721
$13$	378.554	0.621254	0.310627	−	0.950532i	$-0.399461\pi$
$13$	378.554	0.621254	0.310627	+	0.950532i	$0.399461\pi$
$14$	−2127.43	−2.90091
$15$	−1157.36	−1.32813
$16$	692.774	0.676537
$17$	447.425	0.375490	0.187745	−	0.982218i	$-0.439882\pi$
$17$	447.425	0.375490	0.187745	+	0.982218i	$0.439882\pi$
$18$	−5182.98	−3.77049
$19$	−2941.48	−1.86931	−0.934657	−	0.355550i	$-0.884293\pi$
$19$	−2941.48	−1.86931	−0.934657	+	0.355550i	$0.884293\pi$
$20$	−2500.22	−1.39766
$21$	6189.06	3.06250
$22$	−692.226	−0.304924
$23$	−3381.87	−1.33302	−0.666511	−	0.745495i	$-0.732213\pi$
$23$	−3381.87	−1.33302	−0.666511	+	0.745495i	$0.732213\pi$
$24$	−7639.74	−2.70739
$25$	−1412.41	−0.451972
$26$	−3639.16	−1.05577
$27$	8282.26	2.18645
$28$	13370.0	3.22283
$29$	−1168.22	−0.257947	−0.128973	−	0.991648i	$-0.541168\pi$
$29$	−1168.22	−0.257947	−0.128973	+	0.991648i	$0.541168\pi$
$30$	11126.1	2.25705
$31$	6533.14	1.22101	0.610503	−	0.792014i	$-0.290967\pi$
$31$	6533.14	1.22101	0.610503	+	0.792014i	$0.290967\pi$
$32$	2081.63	0.359358
$33$	2013.81	0.321909
$34$	−4301.24	−0.638112
$35$	−9158.14	−1.26368
$36$	32573.0	4.18891
$37$	5918.56	0.710741	0.355371	−	0.934725i	$-0.384355\pi$
$37$	5918.56	0.710741	0.355371	+	0.934725i	$0.384355\pi$
$38$	28277.4	3.17673
$39$	10587.0	1.11458
$40$	11304.8	1.11715
$41$	−6233.63	−0.579137	−0.289569	−	0.957157i	$-0.593512\pi$
$41$	−6233.63	−0.579137	−0.289569	+	0.957157i	$0.593512\pi$
$42$	−59497.4	−5.20445
$43$	8857.78	0.730556	0.365278	−	0.930898i	$-0.380974\pi$
$43$	8857.78	0.730556	0.365278	+	0.930898i	$0.380974\pi$
$44$	4350.36	0.338761
$45$	−22311.7	−1.64248
$46$	32511.0	2.26535
$47$	−3800.48	−0.250954	−0.125477	−	0.992097i	$-0.540046\pi$
$47$	−3800.48	−0.250954	−0.125477	+	0.992097i	$0.540046\pi$
$48$	19374.7	1.21376
$49$	32166.6	1.91388
$50$	13578.0	0.768085
$51$	12513.1	0.673657
$52$	22870.7	1.17293
$53$	15138.0	0.740248	0.370124	−	0.928982i	$-0.379315\pi$
$53$	15138.0	0.740248	0.370124	+	0.928982i	$0.379315\pi$
$54$	−79620.0	−3.71568
$55$	−2979.89	−0.132829
$56$	−60452.7	−2.57600
$57$	−82264.1	−3.35369
$58$	11230.5	0.438358
$59$	−11335.5	−0.423948	−0.211974	−	0.977275i	$-0.567989\pi$
$59$	−11335.5	−0.423948	−0.211974	+	0.977275i	$0.567989\pi$
$60$	−69923.3	−2.50752
$61$	41481.0	1.42733	0.713665	−	0.700488i	$-0.247034\pi$
$61$	41481.0	1.42733	0.713665	+	0.700488i	$0.247034\pi$
$62$	−62805.2	−2.07499
$63$	119313.	3.78735
$64$	−42180.1	−1.28723
$65$	−15665.9	−0.459908
$66$	−19359.4	−0.547056
$67$	38017.7	1.03466	0.517332	−	0.855785i	$-0.326925\pi$
$67$	38017.7	1.03466	0.517332	+	0.855785i	$0.326925\pi$
$68$	27031.6	0.708924
$69$	−94580.3	−2.39154
$70$	88040.2	2.14751
$71$	−2192.43	−0.0516154	−0.0258077	−	0.999667i	$-0.508216\pi$
$71$	−2192.43	−0.0516154	−0.0258077	+	0.999667i	$0.508216\pi$
$72$	−147279.	−3.34819
$73$	−30480.5	−0.669446	−0.334723	−	0.942317i	$-0.608643\pi$
$73$	−30480.5	−0.669446	−0.334723	+	0.942317i	$0.608643\pi$
$74$	−56897.0	−1.20784
$75$	−39500.7	−0.810871
$76$	−177712.	−3.52926
$77$	15935.1	0.306287
$78$	−101776.	−1.89412
$79$	41047.7	0.739982	0.369991	−	0.929035i	$-0.379361\pi$
$79$	41047.7	0.739982	0.369991	+	0.929035i	$0.379361\pi$
$80$	−28669.4	−0.500833
$81$	100616.	1.70395
$82$	59925.9	0.984192
$83$	111799.	1.78132	0.890662	−	0.454667i	$-0.150242\pi$
$83$	111799.	1.78132	0.890662	+	0.454667i	$0.150242\pi$
$84$	373918.	5.78200
$85$	−18516.0	−0.277971
$86$	−85152.6	−1.24151
$87$	−32671.5	−0.462776
$88$	−19670.2	−0.270771
$89$	29925.8	0.400471	0.200236	−	0.979748i	$-0.435829\pi$
$89$	29925.8	0.400471	0.200236	+	0.979748i	$0.435829\pi$
$90$	214489.	2.79126
$91$	83773.9	1.06049
$92$	−204319.	−2.51674
$93$	182711.	2.19058
$94$	36535.2	0.426473
$95$	121729.	1.38383
$96$	58216.5	0.644716
$97$	117393.	1.26681	0.633406	−	0.773820i	$-0.281656\pi$
$97$	117393.	1.26681	0.633406	+	0.773820i	$0.281656\pi$
$98$	−309228.	−3.25247
$99$	38822.2	0.398100
$100$	−85332.1	−0.853321
$101$	147248.	1.43630	0.718149	−	0.695889i	$-0.244989\pi$
$101$	147248.	1.43630	0.718149	+	0.695889i	$0.244989\pi$
$102$	−120292.	−1.14482
$103$	−2714.26	−0.0252092	−0.0126046	−	0.999921i	$-0.504012\pi$
$103$	−2714.26	−0.0252092	−0.0126046	+	0.999921i	$0.504012\pi$
$104$	−103410.	−0.937518
$105$	−256125.	−2.26714
$106$	−145526.	−1.25799
$107$	−125721.	−1.06157	−0.530785	−	0.847507i	$-0.678103\pi$
$107$	−125721.	−1.06157	−0.530785	+	0.847507i	$0.678103\pi$
$108$	500380.	4.12801
$109$	81943.3	0.660613	0.330307	−	0.943874i	$-0.392848\pi$
$109$	81943.3	0.660613	0.330307	+	0.943874i	$0.392848\pi$
$110$	28646.7	0.225732
$111$	165523.	1.27512
$112$	153311.	1.15485
$113$	226858.	1.67131	0.835656	−	0.549253i	$-0.185088\pi$
$113$	226858.	1.67131	0.835656	+	0.549253i	$0.185088\pi$
$114$	790831.	5.69930
$115$	139953.	0.986822
$116$	−70579.2	−0.487003
$117$	204096.	1.37838
$118$	108972.	0.720461
$119$	99015.1	0.640965
$120$	316159.	2.00425
$121$	−155866.	−0.967805
$122$	−398770.	−2.42562
$123$	−174335.	−1.03902
$124$	394706.	2.30526
$125$	187774.	1.07488
$126$	−1.14699e6	−6.43626
$127$	60898.0	0.335038	0.167519	−	0.985869i	$-0.446424\pi$
$127$	60898.0	0.335038	0.167519	+	0.985869i	$0.446424\pi$
$128$	338879.	1.82818
$129$	247724.	1.31067
$130$	150601.	0.781573
$131$	−275543.	−1.40285	−0.701425	−	0.712743i	$-0.747453\pi$
$131$	−275543.	−1.40285	−0.701425	+	0.712743i	$0.747453\pi$
$132$	121666.	0.607763
$133$	−650949.	−3.19094
$134$	−365477.	−1.75832
$135$	−342748.	−1.61861
$136$	−122224.	−0.566642
$137$	−56717.5	−0.258176	−0.129088	−	0.991633i	$-0.541205\pi$
$137$	−56717.5	−0.258176	−0.129088	+	0.991633i	$0.541205\pi$
$138$	909231.	4.06421
$139$	134717.	0.591406	0.295703	−	0.955280i	$-0.404446\pi$
$139$	134717.	0.591406	0.295703	+	0.955280i	$0.404446\pi$
$140$	−553298.	−2.38583
$141$	−106287.	−0.450230
$142$	21076.5	0.0877157
$143$	27258.5	0.111471
$144$	373506.	1.50104
$145$	48345.0	0.190955
$146$	293019.	1.13766
$147$	899598.	3.43364
$148$	357575.	1.34188
$149$	173667.	0.640841	0.320421	−	0.947275i	$-0.396176\pi$
$149$	173667.	0.640841	0.320421	+	0.947275i	$0.396176\pi$
$150$	379733.	1.37800
$151$	90375.5	0.322558	0.161279	−	0.986909i	$-0.448438\pi$
$151$	90375.5	0.322558	0.161279	+	0.986909i	$0.448438\pi$
$152$	803529.	2.82093
$153$	241227.	0.833102
$154$	−153189.	−0.520507
$155$	−270364.	−0.903898
$156$	639621.	2.10432
$157$	361356.	1.17000	0.585000	−	0.811033i	$-0.301095\pi$
$157$	361356.	1.17000	0.585000	+	0.811033i	$0.301095\pi$
$158$	−394605.	−1.25753
$159$	423361.	1.32806
$160$	−86144.8	−0.266029
$161$	−748407.	−2.27548
$162$	−967258.	−2.89571
$163$	−507005.	−1.49466	−0.747331	−	0.664452i	$-0.768665\pi$
$163$	−507005.	−1.49466	−0.747331	+	0.664452i	$0.768665\pi$
$164$	−376611.	−1.09341
$165$	−83338.3	−0.238306
$166$	−1.07476e6	−3.02720
$167$	−584410.	−1.62154	−0.810768	−	0.585368i	$-0.800950\pi$
$167$	−584410.	−1.62154	−0.810768	+	0.585368i	$0.800950\pi$
$168$	−1.69067e6	−4.62154
$169$	−227990.	−0.614043
$170$	178000.	0.472387
$171$	−1.58589e6	−4.14746
$172$	535151.	1.37929
$173$	540584.	1.37324	0.686622	−	0.727015i	$-0.259093\pi$
$173$	540584.	1.37324	0.686622	+	0.727015i	$0.259093\pi$
$174$	314082.	0.786447
$175$	−312566.	−0.771520
$176$	49884.5	0.121390
$177$	−317020.	−0.760594
$178$	−287687.	−0.680565
$179$	−238123.	−0.555481	−0.277741	−	0.960656i	$-0.589586\pi$
$179$	−238123.	−0.555481	−0.277741	+	0.960656i	$0.589586\pi$
$180$	−1.34798e6	−3.10101
$181$	498347.	1.13067	0.565334	−	0.824862i	$-0.308747\pi$
$181$	498347.	1.13067	0.565334	+	0.824862i	$0.308747\pi$
$182$	−805345.	−1.80220
$183$	1.16009e6	2.56074
$184$	923830.	2.01163
$185$	−244930.	−0.526154
$186$	−1.75646e6	−3.72269
$187$	32217.7	0.0673738
$188$	−229609.	−0.473800
$189$	1.83286e6	3.73229
$190$	−1.17022e6	−2.35170
$191$	−632113.	−1.25375	−0.626876	−	0.779119i	$-0.715667\pi$
$191$	−632113.	−1.25375	−0.626876	+	0.779119i	$0.715667\pi$
$192$	−1.17964e6	−2.30940
$193$	194716.	0.376278	0.188139	−	0.982142i	$-0.439754\pi$
$193$	194716.	0.376278	0.188139	+	0.982142i	$0.439754\pi$
$194$	−1.12853e6	−2.15283
$195$	−438125.	−0.825110
$196$	1.94337e6	3.61340
$197$	−271114.	−0.497722	−0.248861	−	0.968539i	$-0.580056\pi$
$197$	−271114.	−0.497722	−0.248861	+	0.968539i	$0.580056\pi$
$198$	−373210.	−0.676535
$199$	459151.	0.821907	0.410953	−	0.911656i	$-0.365196\pi$
$199$	459151.	0.821907	0.410953	+	0.911656i	$0.365196\pi$
$200$	385830.	0.682058
$201$	1.06324e6	1.85626
$202$	−1.41554e6	−2.44086
$203$	−258527.	−0.440318
$204$	755990.	1.27186
$205$	257969.	0.428729
$206$	26093.0	0.0428407
$207$	−1.82332e6	−2.95758
$208$	262252.	0.420302
$209$	−211807.	−0.335409
$210$	2.46221e6	3.85280
$211$	544846.	0.842495	0.421247	−	0.906946i	$-0.361592\pi$
$211$	544846.	0.842495	0.421247	+	0.906946i	$0.361592\pi$
$212$	914573.	1.39759
$213$	−61315.3	−0.0926019
$214$	1.20860e6	1.80404
$215$	−366565.	−0.540823
$216$	−2.26248e6	−3.29951
$217$	1.44578e6	2.08427
$218$	−787747.	−1.12265
$219$	−852445.	−1.20104
$220$	−180033.	−0.250781
$221$	169375.	0.233275
$222$	−1.59123e6	−2.16696
$223$	781305.	1.05210	0.526052	−	0.850453i	$-0.323672\pi$
$223$	781305.	1.05210	0.526052	+	0.850453i	$0.323672\pi$
$224$	460663.	0.613428
$225$	−761495.	−1.00279
$226$	−2.18086e6	−2.84025
$227$	−265970.	−0.342585	−0.171293	−	0.985220i	$-0.554794\pi$
$227$	−265970.	−0.342585	−0.171293	+	0.985220i	$0.554794\pi$
$228$	−4.97006e6	−6.33176
$229$	1.46288e6	1.84341	0.921703	−	0.387897i	$-0.126798\pi$
$229$	1.46288e6	1.84341	0.921703	+	0.387897i	$0.126798\pi$
$230$	−1.34542e6	−1.67702
$231$	445655.	0.549502
$232$	319125.	0.389261
$233$	229997.	0.277544	0.138772	−	0.990324i	$-0.455685\pi$
$233$	229997.	0.277544	0.138772	+	0.990324i	$0.455685\pi$
$234$	−1.96204e6	−2.34244
$235$	157277.	0.185778
$236$	−684847.	−0.800412
$237$	1.14798e6	1.32758
$238$	−951864.	−1.08926
$239$	−700223.	−0.792942	−0.396471	−	0.918047i	$-0.629765\pi$
$239$	−700223.	−0.792942	−0.396471	+	0.918047i	$0.629765\pi$
$240$	−801792.	−0.898532
$241$	1.02043e6	1.13173	0.565864	−	0.824499i	$-0.308543\pi$
$241$	1.02043e6	1.13173	0.565864	+	0.824499i	$0.308543\pi$
$242$	1.49839e6	1.64470
$243$	801338.	0.870562
$244$	2.50611e6	2.69479
$245$	−1.33116e6	−1.41683
$246$	1.67594e6	1.76571
$247$	−1.11351e6	−1.16132
$248$	−1.78467e6	−1.84259
$249$	3.12667e6	3.19583
$250$	−1.80513e6	−1.82666
$251$	−225106.	−0.225529	−0.112765	−	0.993622i	$-0.535971\pi$
$251$	−225106.	−0.225529	−0.112765	+	0.993622i	$0.535971\pi$
$252$	7.20839e6	7.15051
$253$	−243518.	−0.239183
$254$	−585432.	−0.569367
$255$	−517835.	−0.498701
$256$	−1.90799e6	−1.81960
$257$	133185.	0.125783	0.0628916	−	0.998020i	$-0.479968\pi$
$257$	133185.	0.125783	0.0628916	+	0.998020i	$0.479968\pi$
$258$	−2.38145e6	−2.22737
$259$	1.30978e6	1.21324
$260$	−946468.	−0.868305
$261$	−629841.	−0.572308
$262$	2.64888e6	2.38402
$263$	−1.64581e6	−1.46720	−0.733601	−	0.679580i	$-0.762162\pi$
$263$	−1.64581e6	−1.46720	−0.733601	+	0.679580i	$0.762162\pi$
$264$	−550114.	−0.485784
$265$	−626461.	−0.547998
$266$	6.25779e6	5.42271
$267$	836932.	0.718476
$268$	2.29688e6	1.95344
$269$	743690.	0.626630	0.313315	−	0.949649i	$-0.398560\pi$
$269$	743690.	0.626630	0.313315	+	0.949649i	$0.398560\pi$
$270$	3.29495e6	2.75068
$271$	480954.	0.397814	0.198907	−	0.980018i	$-0.436261\pi$
$271$	480954.	0.397814	0.198907	+	0.980018i	$0.436261\pi$
$272$	309965.	0.254033
$273$	2.34289e6	1.90259
$274$	545243.	0.438747
$275$	−101703.	−0.0810968
$276$	−5.71416e6	−4.51523
$277$	−1.69099e6	−1.32416	−0.662081	−	0.749432i	$-0.730327\pi$
$277$	−1.69099e6	−1.32416	−0.662081	+	0.749432i	$0.730327\pi$
$278$	−1.29508e6	−1.00504
$279$	3.52231e6	2.70905
$280$	2.50174e6	1.90699
$281$	2.28935e6	1.72960	0.864800	−	0.502117i	$-0.167445\pi$
$281$	2.28935e6	1.72960	0.864800	+	0.502117i	$0.167445\pi$
$282$	1.02178e6	0.765125
$283$	−36780.8	−0.0272995	−0.0136498	−	0.999907i	$-0.504345\pi$
$283$	−36780.8	−0.0272995	−0.0136498	+	0.999907i	$0.504345\pi$
$284$	−132457.	−0.0974497
$285$	3.40437e6	2.48270
$286$	−262045.	−0.189435
$287$	−1.37950e6	−0.988593
$288$	1.12230e6	0.797310
$289$	−1.21967e6	−0.859007
$290$	−464756.	−0.324512
$291$	3.28311e6	2.27276
$292$	−1.84151e6	−1.26391
$293$	−2.08471e6	−1.41866	−0.709328	−	0.704878i	$-0.751002\pi$
$293$	−2.08471e6	−1.41866	−0.709328	+	0.704878i	$0.751002\pi$
$294$	−8.64813e6	−5.83517
$295$	469104.	0.313844
$296$	−1.61678e6	−1.07256
$297$	596380.	0.392312
$298$	−1.66951e6	−1.08905
$299$	−1.28022e6	−0.828146
$300$	−2.38647e6	−1.53092
$301$	1.96022e6	1.24707
$302$	−868809.	−0.548159
$303$	4.11805e6	2.57683
$304$	−2.03778e6	−1.26466
$305$	−1.71662e6	−1.05664
$306$	−2.31900e6	−1.41578
$307$	−951017.	−0.575894	−0.287947	−	0.957646i	$-0.592973\pi$
$307$	−951017.	−0.575894	−0.287947	+	0.957646i	$0.592973\pi$
$308$	962734.	0.578269
$309$	−75909.3	−0.0452271
$310$	2.59909e6	1.53609
$311$	286310.	0.167856	0.0839278	−	0.996472i	$-0.473254\pi$
$311$	286310.	0.167856	0.0839278	+	0.996472i	$0.473254\pi$
$312$	−2.89206e6	−1.68198
$313$	−1.10994e6	−0.640380	−0.320190	−	0.947353i	$-0.603747\pi$
$313$	−1.10994e6	−0.640380	−0.320190	+	0.947353i	$0.603747\pi$
$314$	−3.47383e6	−1.98831
$315$	−4.93757e6	−2.80374
$316$	2.47993e6	1.39708
$317$	1.44376e6	0.806952	0.403476	−	0.914990i	$-0.367802\pi$
$317$	1.44376e6	0.806952	0.403476	+	0.914990i	$0.367802\pi$
$318$	−4.06991e6	−2.25692
$319$	−84120.0	−0.0462831
$320$	1.74556e6	0.952926
$321$	−3.51602e6	−1.90453
$322$	7.19468e6	3.86698
$323$	−1.31609e6	−0.701909
$324$	6.07884e6	3.21705
$325$	−534674.	−0.280789
$326$	4.87400e6	2.54005
$327$	2.29170e6	1.18519
$328$	1.70285e6	0.873960
$329$	−841045.	−0.428380
$330$	801158.	0.404980
$331$	−3.18244e6	−1.59658	−0.798289	−	0.602274i	$-0.794261\pi$
$331$	−3.18244e6	−1.59658	−0.798289	+	0.602274i	$0.794261\pi$
$332$	6.75444e6	3.36313
$333$	3.19096e6	1.57693
$334$	5.61812e6	2.75566
$335$	−1.57330e6	−0.765951
$336$	4.28762e6	2.07190
$337$	3.15071e6	1.51124	0.755620	−	0.655010i	$-0.227336\pi$
$337$	3.15071e6	1.51124	0.755620	+	0.655010i	$0.227336\pi$
$338$	2.19174e6	1.04351
$339$	6.34450e6	2.99846
$340$	−1.11866e6	−0.524809
$341$	470431.	0.219084
$342$	1.52456e7	7.04824
$343$	3.39907e6	1.56000
$344$	−2.41969e6	−1.10246
$345$	3.91406e6	1.77043
$346$	−5.19680e6	−2.33371
$347$	−3.28842e6	−1.46610	−0.733050	−	0.680175i	$-0.761904\pi$
$347$	−3.28842e6	−1.46610	−0.733050	+	0.680175i	$0.761904\pi$
$348$	−1.97388e6	−0.873720
$349$	−3.03326e6	−1.33305	−0.666524	−	0.745483i	$-0.732219\pi$
$349$	−3.03326e6	−1.33305	−0.666524	+	0.745483i	$0.732219\pi$
$350$	3.00480e6	1.31113
$351$	3.13528e6	1.35834
$352$	149891.	0.0644793
$353$	3.60028e6	1.53780	0.768900	−	0.639369i	$-0.220805\pi$
$353$	3.60028e6	1.53780	0.768900	+	0.639369i	$0.220805\pi$
$354$	3.04761e6	1.29256
$355$	90730.1	0.0382103
$356$	1.80800e6	0.756089
$357$	2.76914e6	1.14994
$358$	2.28916e6	0.943991
$359$	−2.98440e6	−1.22214	−0.611070	−	0.791576i	$-0.709261\pi$
$359$	−2.98440e6	−1.22214	−0.611070	+	0.791576i	$0.709261\pi$
$360$	6.09491e6	2.47863
$361$	6.17622e6	2.49434
$362$	−4.79076e6	−1.92147
$363$	−4.35908e6	−1.73632
$364$	5.06128e6	2.00220
$365$	1.26139e6	0.495583
$366$	−1.11523e7	−4.35174
$367$	−3.22401e6	−1.24948	−0.624742	−	0.780831i	$-0.714796\pi$
$367$	−3.22401e6	−1.24948	−0.624742	+	0.780831i	$0.714796\pi$
$368$	−2.34287e6	−0.901839
$369$	−3.36083e6	−1.28494
$370$	2.35459e6	0.894152
$371$	3.35003e6	1.26361
$372$	1.10387e7	4.13580
$373$	−566079.	−0.210671	−0.105335	−	0.994437i	$-0.533592\pi$
$373$	−566079.	−0.210671	−0.105335	+	0.994437i	$0.533592\pi$
$374$	−309719.	−0.114496
$375$	5.25144e6	1.92841
$376$	1.03818e6	0.378707
$377$	−442235.	−0.160251
$378$	−1.76199e7	−6.34269
$379$	2.06578e6	0.738731	0.369366	−	0.929284i	$-0.379575\pi$
$379$	2.06578e6	0.738731	0.369366	+	0.929284i	$0.379575\pi$
$380$	7.35435e6	2.61267
$381$	1.70313e6	0.601083
$382$	6.07671e6	2.13064
$383$	1.26408e6	0.440330	0.220165	−	0.975463i	$-0.429340\pi$
$383$	1.26408e6	0.440330	0.220165	+	0.975463i	$0.429340\pi$
$384$	9.47738e6	3.27990
$385$	−659450.	−0.226741
$386$	−1.87187e6	−0.639451
$387$	4.77563e6	1.62089
$388$	7.09239e6	2.39174
$389$	3.37044e6	1.12931	0.564655	−	0.825327i	$-0.309009\pi$
$389$	3.37044e6	1.12931	0.564655	+	0.825327i	$0.309009\pi$
$390$	4.21184e6	1.40220
$391$	−1.51314e6	−0.500537
$392$	−8.78699e6	−2.88818
$393$	−7.70608e6	−2.51682
$394$	2.60631e6	0.845834
$395$	−1.69869e6	−0.547801
$396$	2.34548e6	0.751612
$397$	3.62630e6	1.15475	0.577374	−	0.816479i	$-0.304077\pi$
$397$	3.62630e6	1.15475	0.577374	+	0.816479i	$0.304077\pi$
$398$	−4.41396e6	−1.39676
$399$	−1.82050e7	−5.72478
$400$	−978481.	−0.305775
$401$	−3.12403e6	−0.970184	−0.485092	−	0.874463i	$-0.661214\pi$
$401$	−3.12403e6	−0.970184	−0.485092	+	0.874463i	$0.661214\pi$
$402$	−1.02212e7	−3.15456
$403$	2.47315e6	0.758555
$404$	8.89610e6	2.71173
$405$	−4.16385e6	−1.26142
$406$	2.48530e6	0.748281
$407$	426177.	0.127528
$408$	−3.41822e6	−1.01660
$409$	1.08397e6	0.320412	0.160206	−	0.987084i	$-0.448784\pi$
$409$	1.08397e6	0.320412	0.160206	+	0.987084i	$0.448784\pi$
$410$	−2.47994e6	−0.728587
$411$	−1.58621e6	−0.463187
$412$	−163984.	−0.0475948
$413$	−2.50855e6	−0.723682
$414$	1.75282e7	5.02615
$415$	−4.62663e6	−1.31869
$416$	788008.	0.223253
$417$	3.76762e6	1.06103
$418$	2.03617e6	0.569998
$419$	−3.15770e6	−0.878689	−0.439345	−	0.898319i	$-0.644789\pi$
$419$	−3.15770e6	−0.878689	−0.439345	+	0.898319i	$0.644789\pi$
$420$	−1.54740e7	−4.28035
$421$	−4.19127e6	−1.15250	−0.576249	−	0.817274i	$-0.695484\pi$
$421$	−4.19127e6	−1.15250	−0.576249	+	0.817274i	$0.695484\pi$
$422$	−5.23778e6	−1.43175
$423$	−2.04901e6	−0.556792
$424$	−4.13525e6	−1.11709
$425$	−631949.	−0.169711
$426$	589443.	0.157369
$427$	9.17972e6	2.43646
$428$	−7.59555e6	−2.00424
$429$	762335.	0.199987
$430$	3.52391e6	0.919080
$431$	−93524.3	−0.0242511	−0.0121255	−	0.999926i	$-0.503860\pi$
$431$	−93524.3	−0.0242511	−0.0121255	+	0.999926i	$0.503860\pi$
$432$	5.73773e6	1.47921
$433$	−4.47008e6	−1.14576	−0.572882	−	0.819638i	$-0.694175\pi$
$433$	−4.47008e6	−1.14576	−0.572882	+	0.819638i	$0.694175\pi$
$434$	−1.38988e7	−3.54203
$435$	1.35206e6	0.342588
$436$	4.95068e6	1.24724
$437$	9.94772e6	2.49184
$438$	8.19482e6	2.04105
$439$	5.13107e6	1.27071	0.635356	−	0.772220i	$-0.280854\pi$
$439$	5.13107e6	1.27071	0.635356	+	0.772220i	$0.280854\pi$
$440$	814022.	0.200449
$441$	1.73425e7	4.24634
$442$	−1.62825e6	−0.396430
$443$	476162.	0.115278	0.0576388	−	0.998338i	$-0.481643\pi$
$443$	476162.	0.115278	0.0576388	+	0.998338i	$0.481643\pi$
$444$	1.00003e7	2.40743
$445$	−1.23843e6	−0.296465
$446$	−7.51093e6	−1.78796
$447$	4.85691e6	1.14972
$448$	−9.33444e6	−2.19732
$449$	−1.81216e6	−0.424210	−0.212105	−	0.977247i	$-0.568032\pi$
$449$	−1.81216e6	−0.424210	−0.212105	+	0.977247i	$0.568032\pi$
$450$	7.32049e6	1.70416
$451$	−448865.	−0.103914
$452$	1.37058e7	3.15543
$453$	2.52752e6	0.578694
$454$	2.55686e6	0.582193
$455$	−3.46685e6	−0.785067
$456$	2.24722e7	5.06096
$457$	8.38656e6	1.87842	0.939212	−	0.343338i	$-0.111558\pi$
$457$	8.38656e6	1.87842	0.939212	+	0.343338i	$0.111558\pi$
$458$	−1.40632e7	−3.13270
$459$	3.70569e6	0.820990
$460$	8.45542e6	1.86312
$461$	6.04043e6	1.32378	0.661890	−	0.749601i	$-0.269755\pi$
$461$	6.04043e6	1.32378	0.661890	+	0.749601i	$0.269755\pi$
$462$	−4.28423e6	−0.933829
$463$	−6.55857e6	−1.42186	−0.710929	−	0.703264i	$-0.751725\pi$
$463$	−6.55857e6	−1.42186	−0.710929	+	0.703264i	$0.751725\pi$
$464$	−809313.	−0.174511
$465$	−7.56123e6	−1.62166
$466$	−2.21103e6	−0.471661
$467$	−2.24534e6	−0.476419	−0.238210	−	0.971214i	$-0.576560\pi$
$467$	−2.24534e6	−0.476419	−0.238210	+	0.971214i	$0.576560\pi$
$468$	1.23306e7	2.60238
$469$	8.41331e6	1.76618
$470$	−1.51195e6	−0.315714
$471$	1.01060e7	2.09907
$472$	3.09654e6	0.639768
$473$	637821.	0.131083
$474$	−1.10359e7	−2.25611
$475$	4.15458e6	0.844877
$476$	5.98209e6	1.21014
$477$	8.16156e6	1.64239
$478$	6.73147e6	1.34753
$479$	4.21405e6	0.839192	0.419596	−	0.907711i	$-0.362172\pi$
$479$	4.21405e6	0.839192	0.419596	+	0.907711i	$0.362172\pi$
$480$	−2.40920e6	−0.477276
$481$	2.24049e6	0.441551
$482$	−9.80975e6	−1.92327
$483$	−2.09306e7	−4.08238
$484$	−9.41679e6	−1.82721
$485$	−4.85812e6	−0.937807
$486$	−7.70352e6	−1.47944
$487$	5.90930e6	1.12905	0.564525	−	0.825416i	$-0.309059\pi$
$487$	5.90930e6	1.12905	0.564525	+	0.825416i	$0.309059\pi$
$488$	−1.13314e7	−2.15394
$489$	−1.41793e7	−2.68154
$490$	1.27969e7	2.40777
$491$	3.40576e6	0.637544	0.318772	−	0.947831i	$-0.396730\pi$
$491$	3.40576e6	0.637544	0.318772	+	0.947831i	$0.396730\pi$
$492$	−1.05326e7	−1.96166
$493$	−522692.	−0.0968565
$494$	1.07045e7	1.97356
$495$	−1.60660e6	−0.294709
$496$	4.52599e6	0.826056
$497$	−485183.	−0.0881079
$498$	−3.00577e7	−5.43103
$499$	−2.77937e6	−0.499683	−0.249841	−	0.968287i	$-0.580378\pi$
$499$	−2.77937e6	−0.499683	−0.249841	+	0.968287i	$0.580378\pi$
$500$	1.13445e7	2.02937
$501$	−1.63441e7	−2.90916
$502$	2.16402e6	0.383267
$503$	−1.06879e7	−1.88354	−0.941768	−	0.336263i	$-0.890837\pi$
$503$	−1.06879e7	−1.88354	−0.941768	+	0.336263i	$0.890837\pi$
$504$	−3.25928e7	−5.71539
$505$	−6.09361e6	−1.06328
$506$	2.34102e6	0.406470
$507$	−6.37616e6	−1.10164
$508$	3.67921e6	0.632550
$509$	3.22149e6	0.551140	0.275570	−	0.961281i	$-0.411133\pi$
$509$	3.22149e6	0.551140	0.275570	+	0.961281i	$0.411133\pi$
$510$	4.97811e6	0.847499
$511$	−6.74533e6	−1.14275
$512$	7.49797e6	1.26406
$513$	−2.43621e7	−4.08716
$514$	−1.28035e6	−0.213757
$515$	112325.	0.0186621
$516$	1.49665e7	2.47455
$517$	−273661.	−0.0450284
$518$	−1.25913e7	−2.06180
$519$	1.51184e7	2.46370
$520$	4.27947e6	0.694035
$521$	4.89753e6	0.790465	0.395233	−	0.918581i	$-0.370664\pi$
$521$	4.89753e6	0.790465	0.395233	+	0.918581i	$0.370664\pi$
$522$	6.05487e6	0.972587
$523$	22067.8	0.00352780	0.00176390	−	0.999998i	$-0.499439\pi$
$523$	22067.8	0.00352780	0.00176390	+	0.999998i	$0.499439\pi$
$524$	−1.66472e7	−2.64858
$525$	−8.74150e6	−1.38416
$526$	1.58217e7	2.49338
$527$	2.92309e6	0.458476
$528$	1.39511e6	0.217783
$529$	5.00071e6	0.776948
$530$	6.02237e6	0.931274
$531$	−6.11150e6	−0.940615
$532$	−3.93277e7	−6.02448
$533$	−2.35977e6	−0.359792
$534$	−8.04569e6	−1.22099
$535$	5.20277e6	0.785868
$536$	−1.03854e7	−1.56138
$537$	−6.65957e6	−0.996575
$538$	−7.14933e6	−1.06490
$539$	2.31622e6	0.343405
$540$	−2.07075e7	−3.05592
$541$	−4.31826e6	−0.634330	−0.317165	−	0.948370i	$-0.602731\pi$
$541$	−4.31826e6	−0.634330	−0.317165	+	0.948370i	$0.602731\pi$
$542$	−4.62356e6	−0.676050
$543$	1.39372e7	2.02850
$544$	931372.	0.134935
$545$	−3.39110e6	−0.489045
$546$	−2.25230e7	−3.23329
$547$	−8.24088e6	−1.17762	−0.588810	−	0.808272i	$-0.700403\pi$
$547$	−8.24088e6	−1.17762	−0.588810	+	0.808272i	$0.700403\pi$
$548$	−3.42664e6	−0.487435
$549$	2.23643e7	3.16682
$550$	977707.	0.137817
$551$	3.43630e6	0.482184
$552$	2.58366e7	3.60901
$553$	9.08384e6	1.26316
$554$	1.62560e7	2.25030
$555$	−6.84993e6	−0.943960
$556$	8.13906e6	1.11657
$557$	1.33173e6	0.181877	0.0909386	−	0.995856i	$-0.471013\pi$
$557$	1.33173e6	0.181877	0.0909386	+	0.995856i	$0.471013\pi$
$558$	−3.38611e7	−4.60379
$559$	3.35315e6	0.453861
$560$	−6.34452e6	−0.854927
$561$	901029.	0.120874
$562$	−2.20082e7	−2.93930
$563$	6.35229e6	0.844616	0.422308	−	0.906452i	$-0.361220\pi$
$563$	6.35229e6	0.844616	0.422308	+	0.906452i	$0.361220\pi$
$564$	−6.42145e6	−0.850033
$565$	−9.38815e6	−1.23725
$566$	353585.	0.0463931
$567$	2.22664e7	2.90866
$568$	598908.	0.0778913
$569$	−9.57321e6	−1.23959	−0.619794	−	0.784765i	$-0.712784\pi$
$569$	−9.57321e6	−1.23959	−0.619794	+	0.784765i	$0.712784\pi$
$570$	−3.27273e7	−4.21913
$571$	2.81768e6	0.361661	0.180831	−	0.983514i	$-0.442121\pi$
$571$	2.81768e6	0.361661	0.180831	+	0.983514i	$0.442121\pi$
$572$	1.64685e6	0.210457
$573$	−1.76782e7	−2.24933
$574$	1.32616e7	1.68002
$575$	4.77659e6	0.602488
$576$	−2.27412e7	−2.85599
$577$	−8.37249e6	−1.04692	−0.523462	−	0.852049i	$-0.675360\pi$
$577$	−8.37249e6	−1.04692	−0.523462	+	0.852049i	$0.675360\pi$
$578$	1.17251e7	1.45981
$579$	5.44560e6	0.675071
$580$	2.92081e6	0.360523
$581$	2.47411e7	3.04074
$582$	−3.15616e7	−3.86235
$583$	1.09004e6	0.132822
$584$	8.32640e6	1.01024
$585$	−8.44618e6	−1.02040
$586$	2.00410e7	2.41088
$587$	7.10074e6	0.850566	0.425283	−	0.905060i	$-0.360175\pi$
$587$	7.10074e6	0.850566	0.425283	+	0.905060i	$0.360175\pi$
$588$	5.43501e7	6.48271
$589$	−1.92171e7	−2.28244
$590$	−4.50964e6	−0.533350
$591$	−7.58221e6	−0.892950
$592$	4.10022e6	0.480843
$593$	1.29659e7	1.51414	0.757071	−	0.653332i	$-0.226630\pi$
$593$	1.29659e7	1.51414	0.757071	+	0.653332i	$0.226630\pi$
$594$	−5.73319e6	−0.666700
$595$	−4.09759e6	−0.474500
$596$	1.04922e7	1.20991
$597$	1.28410e7	1.47456
$598$	1.23072e7	1.40736
$599$	7.64236e6	0.870283	0.435142	−	0.900362i	$-0.356698\pi$
$599$	7.64236e6	0.870283	0.435142	+	0.900362i	$0.356698\pi$
$600$	1.07905e7	1.22366
$601$	1.35462e7	1.52979	0.764897	−	0.644153i	$-0.222790\pi$
$601$	1.35462e7	1.52979	0.764897	+	0.644153i	$0.222790\pi$
$602$	−1.88443e7	−2.11928
$603$	2.04971e7	2.29561
$604$	5.46012e6	0.608989
$605$	6.45027e6	0.716456
$606$	−3.95882e7	−4.37909
$607$	−1.40459e7	−1.54731	−0.773655	−	0.633607i	$-0.781574\pi$
$607$	−1.40459e7	−1.54731	−0.773655	+	0.633607i	$0.781574\pi$
$608$	−6.12307e6	−0.671754
$609$	−7.23019e6	−0.789963
$610$	1.65025e7	1.79566
$611$	−1.43869e6	−0.155906
$612$	1.45740e7	1.57289
$613$	7.20030e6	0.773926	0.386963	−	0.922095i	$-0.373524\pi$
$613$	7.20030e6	0.773926	0.386963	+	0.922095i	$0.373524\pi$
$614$	9.14244e6	0.978681
$615$	7.21459e6	0.769172
$616$	−4.35302e6	−0.462209
$617$	−3.09437e6	−0.327235	−0.163618	−	0.986524i	$-0.552316\pi$
$617$	−3.09437e6	−0.327235	−0.163618	+	0.986524i	$0.552316\pi$
$618$	729741.	0.0768595
$619$	5.60446e6	0.587905	0.293952	−	0.955820i	$-0.405029\pi$
$619$	5.60446e6	0.587905	0.293952	+	0.955820i	$0.405029\pi$
$620$	−1.63343e7	−1.70656
$621$	−2.80095e7	−2.91459
$622$	−2.75239e6	−0.285255
$623$	6.62258e6	0.683608
$624$	7.33438e6	0.754053
$625$	−3.35694e6	−0.343750
$626$	1.06702e7	1.08827
$627$	−5.92358e6	−0.601749
$628$	2.18316e7	2.20896
$629$	2.64811e6	0.266876
$630$	4.74665e7	4.76470
$631$	−1.04528e7	−1.04511	−0.522554	−	0.852606i	$-0.675021\pi$
$631$	−1.04528e7	−1.04511	−0.522554	+	0.852606i	$0.675021\pi$
$632$	−1.12131e7	−1.11669
$633$	1.52376e7	1.51150
$634$	−1.38794e7	−1.37134
$635$	−2.52017e6	−0.248025
$636$	2.55777e7	2.50738
$637$	1.21768e7	1.18901
$638$	808673.	0.0786541
$639$	−1.18204e6	−0.114519
$640$	−1.40240e7	−1.35338
$641$	8.54011e6	0.820953	0.410477	−	0.911871i	$-0.365362\pi$
$641$	8.54011e6	0.820953	0.410477	+	0.911871i	$0.365362\pi$
$642$	3.38006e7	3.23659
$643$	1.53192e7	1.46120	0.730598	−	0.682808i	$-0.239242\pi$
$643$	1.53192e7	1.46120	0.730598	+	0.682808i	$0.239242\pi$
$644$	−4.52157e7	−4.29610
$645$	−1.02517e7	−0.970277
$646$	1.26520e7	1.19283
$647$	−1.15425e7	−1.08403	−0.542014	−	0.840370i	$-0.682338\pi$
$647$	−1.15425e7	−1.08403	−0.542014	+	0.840370i	$0.682338\pi$
$648$	−2.74855e7	−2.57138
$649$	−816237.	−0.0760685
$650$	5.13999e6	0.477176
$651$	4.04340e7	3.73933
$652$	−3.06312e7	−2.82192
$653$	−1.48966e7	−1.36711	−0.683554	−	0.729900i	$-0.739567\pi$
$653$	−1.48966e7	−1.36711	−0.683554	+	0.729900i	$0.739567\pi$
$654$	−2.20308e7	−2.01412
$655$	1.14029e7	1.03852
$656$	−4.31850e6	−0.391808
$657$	−1.64334e7	−1.48530
$658$	8.08523e6	0.727994
$659$	1.40051e7	1.25624	0.628119	−	0.778117i	$-0.283825\pi$
$659$	1.40051e7	1.25624	0.628119	+	0.778117i	$0.283825\pi$
$660$	−5.03496e6	−0.449921
$661$	−1.10008e7	−0.979313	−0.489657	−	0.871915i	$-0.662878\pi$
$661$	−1.10008e7	−0.979313	−0.489657	+	0.871915i	$0.662878\pi$
$662$	3.05938e7	2.71324
$663$	4.73688e6	0.418513
$664$	−3.05403e7	−2.68815
$665$	2.69385e7	2.36222
$666$	−3.06758e7	−2.67984
$667$	3.95077e6	0.343849
$668$	−3.53077e7	−3.06146
$669$	2.18506e7	1.88755
$670$	1.51247e7	1.30166
$671$	2.98692e6	0.256104
$672$	1.28833e7	1.10054
$673$	−5.45968e6	−0.464654	−0.232327	−	0.972638i	$-0.574634\pi$
$673$	−5.45968e6	−0.464654	−0.232327	+	0.972638i	$0.574634\pi$
$674$	−3.02888e7	−2.56822
$675$	−1.16980e7	−0.988213
$676$	−1.37742e7	−1.15931
$677$	−7.02343e6	−0.588949	−0.294474	−	0.955659i	$-0.595145\pi$
$677$	−7.02343e6	−0.588949	−0.294474	+	0.955659i	$0.595145\pi$
$678$	−6.09917e7	−5.09561
$679$	2.59790e7	2.16246
$680$	5.05804e6	0.419479
$681$	−7.43835e6	−0.614623
$682$	−4.52241e6	−0.372313
$683$	2.70590e6	0.221952	0.110976	−	0.993823i	$-0.464602\pi$
$683$	2.70590e6	0.221952	0.110976	+	0.993823i	$0.464602\pi$
$684$	−9.58128e7	−7.83039
$685$	2.34716e6	0.191125
$686$	−3.26764e7	−2.65108
$687$	4.09122e7	3.30721
$688$	6.13644e6	0.494248
$689$	5.73053e6	0.459883
$690$	−3.76271e7	−3.00869
$691$	2.07593e7	1.65393	0.826966	−	0.562252i	$-0.190065\pi$
$691$	2.07593e7	1.65393	0.826966	+	0.562252i	$0.190065\pi$
$692$	3.26599e7	2.59268
$693$	8.59134e6	0.679560
$694$	3.16126e7	2.49151
$695$	−5.57506e6	−0.437812
$696$	8.92492e6	0.698363
$697$	−2.78909e6	−0.217460
$698$	2.91597e7	2.26540
$699$	6.43228e6	0.497934
$700$	−1.88840e7	−1.45663
$701$	9.20836e6	0.707762	0.353881	−	0.935290i	$-0.384862\pi$
$701$	9.20836e6	0.707762	0.353881	+	0.935290i	$0.384862\pi$
$702$	−3.01405e7	−2.30838
$703$	−1.74093e7	−1.32860
$704$	−3.03726e6	−0.230967
$705$	4.39854e6	0.333300
$706$	−3.46107e7	−2.61335
$707$	3.25859e7	2.45177
$708$	−1.91530e7	−1.43600
$709$	6.13331e6	0.458226	0.229113	−	0.973400i	$-0.426418\pi$
$709$	6.13331e6	0.458226	0.229113	+	0.973400i	$0.426418\pi$
$710$	−872218.	−0.0649350
$711$	2.21307e7	1.64180
$712$	−8.17488e6	−0.604340
$713$	−2.20942e7	−1.62763
$714$	−2.66207e7	−1.95422
$715$	−1.12805e6	−0.0825208
$716$	−1.43864e7	−1.04875
$717$	−1.95830e7	−1.42260
$718$	2.86900e7	2.07692
$719$	−1.21189e7	−0.874259	−0.437129	−	0.899399i	$-0.644005\pi$
$719$	−1.21189e7	−0.874259	−0.437129	+	0.899399i	$0.644005\pi$
$720$	−1.54570e7	−1.11120
$721$	−600665.	−0.0430323
$722$	−5.93740e7	−4.23890
$723$	2.85383e7	2.03040
$724$	3.01081e7	2.13470
$725$	1.65001e6	0.116585
$726$	4.19053e7	2.95071
$727$	−2.10279e7	−1.47557	−0.737784	−	0.675037i	$-0.764128\pi$
$727$	−2.10279e7	−1.47557	−0.737784	+	0.675037i	$0.764128\pi$
$728$	−2.28846e7	−1.60035
$729$	−2.03890e6	−0.142094
$730$	−1.21261e7	−0.842200
$731$	3.96319e6	0.274317
$732$	7.00880e7	4.83466
$733$	−1.15552e7	−0.794357	−0.397179	−	0.917741i	$-0.630011\pi$
$733$	−1.15552e7	−0.794357	−0.397179	+	0.917741i	$0.630011\pi$
$734$	3.09934e7	2.12339
$735$	−3.72285e7	−2.54189
$736$	−7.03979e6	−0.479033
$737$	2.73754e6	0.185649
$738$	3.23088e7	2.18363
$739$	−1.78123e7	−1.19980	−0.599900	−	0.800075i	$-0.704793\pi$
$739$	−1.78123e7	−1.19980	−0.599900	+	0.800075i	$0.704793\pi$
$740$	−1.47977e7	−0.993378
$741$	−3.11414e7	−2.08349
$742$	−3.22049e7	−2.14739
$743$	−1.66941e7	−1.10941	−0.554704	−	0.832048i	$-0.687169\pi$
$743$	−1.66941e7	−1.10941	−0.554704	+	0.832048i	$0.687169\pi$
$744$	−4.99115e7	−3.30574
$745$	−7.18692e6	−0.474408
$746$	5.44190e6	0.358017
$747$	6.02759e7	3.95223
$748$	1.94646e6	0.127202
$749$	−2.78220e7	−1.81211
$750$	−5.04838e7	−3.27717
$751$	1.51681e7	0.981368	0.490684	−	0.871338i	$-0.336747\pi$
$751$	1.51681e7	0.981368	0.490684	+	0.871338i	$0.336747\pi$
$752$	−2.63287e6	−0.169779
$753$	−6.29551e6	−0.404616
$754$	4.25135e6	0.272332
$755$	−3.74005e6	−0.238787
$756$	1.10734e8	7.04655
$757$	−5.80254e6	−0.368026	−0.184013	−	0.982924i	$-0.558909\pi$
$757$	−5.80254e6	−0.368026	−0.184013	+	0.982924i	$0.558909\pi$
$758$	−1.98590e7	−1.25541
$759$	−6.81044e6	−0.429112
$760$	−3.32528e7	−2.08831
$761$	−1.22810e7	−0.768729	−0.384365	−	0.923181i	$-0.625579\pi$
$761$	−1.22810e7	−0.768729	−0.384365	+	0.923181i	$0.625579\pi$
$762$	−1.63727e7	−1.02149
$763$	1.81340e7	1.12767
$764$	−3.81897e7	−2.36708
$765$	−9.98282e6	−0.616736
$766$	−1.21520e7	−0.748302
$767$	−4.29111e6	−0.263379
$768$	−5.33604e7	−3.26450
$769$	−1.46288e6	−0.0892055	−0.0446027	−	0.999005i	$-0.514202\pi$
$769$	−1.46288e6	−0.0892055	−0.0446027	+	0.999005i	$0.514202\pi$
$770$	6.33950e6	0.385326
$771$	3.72477e6	0.225665
$772$	1.17640e7	0.710412
$773$	5.49947e6	0.331034	0.165517	−	0.986207i	$-0.447071\pi$
$773$	5.49947e6	0.331034	0.165517	+	0.986207i	$0.447071\pi$
$774$	−4.59097e7	−2.75456
$775$	−9.22748e6	−0.551860
$776$	−3.20683e7	−1.91171
$777$	3.66303e7	2.17665
$778$	−3.24012e7	−1.91916
$779$	1.83361e7	1.08259
$780$	−2.64697e7	−1.55780
$781$	−157870.	−0.00926129
$782$	1.45463e7	0.850617
$783$	−9.67551e6	−0.563988
$784$	2.22842e7	1.29481
$785$	−1.49541e7	−0.866139
$786$	7.40810e7	4.27711
$787$	−1.38829e7	−0.798991	−0.399496	−	0.916735i	$-0.630815\pi$
$787$	−1.38829e7	−0.798991	−0.399496	+	0.916735i	$0.630815\pi$
$788$	−1.63796e7	−0.939697
$789$	−4.60281e7	−2.63227
$790$	1.63301e7	0.930938
$791$	5.02036e7	2.85294
$792$	−1.06051e7	−0.600762
$793$	1.57028e7	0.886735
$794$	−3.48608e7	−1.96239
$795$	−1.75201e7	−0.983150
$796$	2.77400e7	1.55176
$797$	1.66216e7	0.926888	0.463444	−	0.886126i	$-0.346613\pi$
$797$	1.66216e7	0.926888	0.463444	+	0.886126i	$0.346613\pi$
$798$	1.75011e8	9.72875
$799$	−1.70043e6	−0.0942306
$800$	−2.94011e6	−0.162420
$801$	1.61344e7	0.888528
$802$	3.00323e7	1.64874
$803$	−2.19481e6	−0.120118
$804$	6.42364e7	3.50462
$805$	3.09717e7	1.68451
$806$	−2.37752e7	−1.28910
$807$	2.07987e7	1.12422
$808$	−4.02238e7	−2.16748
$809$	−2.28866e7	−1.22945	−0.614724	−	0.788742i	$-0.710733\pi$
$809$	−2.28866e7	−1.22945	−0.614724	+	0.788742i	$0.710733\pi$
$810$	4.00285e7	2.14366
$811$	−2.84294e7	−1.51780	−0.758901	−	0.651206i	$-0.774263\pi$
$811$	−2.84294e7	−1.51780	−0.758901	+	0.651206i	$0.774263\pi$
$812$	−1.56192e7	−0.831319
$813$	1.34508e7	0.713708
$814$	−4.09698e6	−0.216722
$815$	2.09816e7	1.10648
$816$	8.66874e6	0.455754
$817$	−2.60550e7	−1.36564
$818$	−1.04206e7	−0.544512
$819$	4.51663e7	2.35291
$820$	1.55854e7	0.809440
$821$	−5.45476e6	−0.282434	−0.141217	−	0.989979i	$-0.545102\pi$
$821$	−5.45476e6	−0.282434	−0.141217	+	0.989979i	$0.545102\pi$
$822$	1.52487e7	0.787144
$823$	−8.37649e6	−0.431084	−0.215542	−	0.976495i	$-0.569152\pi$
$823$	−8.37649e6	−0.431084	−0.215542	+	0.976495i	$0.569152\pi$
$824$	741458.	0.0380424
$825$	−2.84432e6	−0.145494
$826$	2.41155e7	1.22983
$827$	−2.86055e7	−1.45441	−0.727204	−	0.686422i	$-0.759181\pi$
$827$	−2.86055e7	−1.45441	−0.727204	+	0.686422i	$0.759181\pi$
$828$	−1.10158e8	−5.58391
$829$	3.10731e7	1.57036	0.785179	−	0.619269i	$-0.212571\pi$
$829$	3.10731e7	1.57036	0.785179	+	0.619269i	$0.212571\pi$
$830$	4.44773e7	2.24100
$831$	−4.72916e7	−2.37565
$832$	−1.59674e7	−0.799700
$833$	1.43921e7	0.718643
$834$	−3.62193e7	−1.80312
$835$	2.41849e7	1.20041
$836$	−1.27965e7	−0.633252
$837$	5.41092e7	2.66967
$838$	3.03559e7	1.49325
$839$	2.16591e7	1.06227	0.531135	−	0.847287i	$-0.321766\pi$
$839$	2.16591e7	1.06227	0.531135	+	0.847287i	$0.321766\pi$
$840$	6.99659e7	3.42128
$841$	−1.91464e7	−0.933463
$842$	4.02920e7	1.95857
$843$	6.40258e7	3.10303
$844$	3.29173e7	1.59063
$845$	9.43500e6	0.454570
$846$	1.96978e7	0.946219
$847$	−3.44931e7	−1.65205
$848$	1.04872e7	0.500805
$849$	−1.02864e6	−0.0489774
$850$	6.07513e6	0.288408
$851$	−2.00158e7	−0.947434
$852$	−3.70442e6	−0.174832
$853$	1.69604e7	0.798111	0.399055	−	0.916927i	$-0.369338\pi$
$853$	1.69604e7	0.798111	0.399055	+	0.916927i	$0.369338\pi$
$854$	−8.82476e7	−4.14055
$855$	6.56295e7	3.07032
$856$	3.43434e7	1.60198
$857$	−2.00796e7	−0.933908	−0.466954	−	0.884282i	$-0.654649\pi$
$857$	−2.00796e7	−0.933908	−0.466954	+	0.884282i	$0.654649\pi$
$858$	−7.32857e6	−0.339861
$859$	8.66953e6	0.400878	0.200439	−	0.979706i	$-0.435763\pi$
$859$	8.66953e6	0.400878	0.200439	+	0.979706i	$0.435763\pi$
$860$	−2.21464e7	−1.02107
$861$	−3.85803e7	−1.77361
$862$	899079.	0.0412126
$863$	7.31327e6	0.334260	0.167130	−	0.985935i	$-0.446550\pi$
$863$	7.31327e6	0.334260	0.167130	+	0.985935i	$0.446550\pi$
$864$	1.72406e7	0.785719
$865$	−2.23712e7	−1.01660
$866$	4.29723e7	1.94713
$867$	−3.41103e7	−1.54112
$868$	8.73483e7	3.93509
$869$	2.95572e6	0.132774
$870$	−1.29978e7	−0.582198
$871$	1.43918e7	0.642789
$872$	−2.23846e7	−0.996913
$873$	6.32918e7	2.81068
$874$	−9.56306e7	−4.23466
$875$	4.15543e7	1.83483
$876$	−5.15012e7	−2.26755
$877$	9.10111e6	0.399572	0.199786	−	0.979840i	$-0.435975\pi$
$877$	9.10111e6	0.399572	0.199786	+	0.979840i	$0.435975\pi$
$878$	−4.93266e7	−2.15946
$879$	−5.83029e7	−2.54518
$880$	−2.06439e6	−0.0898640
$881$	−1.51265e7	−0.656598	−0.328299	−	0.944574i	$-0.606475\pi$
$881$	−1.51265e7	−0.656598	−0.328299	+	0.944574i	$0.606475\pi$
$882$	−1.66719e8	−7.21627
$883$	−3.50421e7	−1.51248	−0.756238	−	0.654296i	$-0.772965\pi$
$883$	−3.50421e7	−1.51248	−0.756238	+	0.654296i	$0.772965\pi$
$884$	1.02329e7	0.440422
$885$	1.31194e7	0.563060
$886$	−4.57750e6	−0.195904
$887$	1.75635e7	0.749554	0.374777	−	0.927115i	$-0.377719\pi$
$887$	1.75635e7	0.749554	0.374777	+	0.927115i	$0.377719\pi$
$888$	−4.52163e7	−1.92425
$889$	1.34767e7	0.571913
$890$	1.19055e7	0.503815
$891$	7.24508e6	0.305738
$892$	4.72033e7	1.98637
$893$	1.11790e7	0.469111
$894$	−4.66910e7	−1.95384
$895$	9.85437e6	0.411217
$896$	7.49938e7	3.12072
$897$	−3.58038e7	−1.48576
$898$	1.74209e7	0.720907
$899$	−7.63216e6	−0.314955
$900$	−4.60064e7	−1.89327
$901$	6.77311e6	0.277956
$902$	4.31508e6	0.176593
$903$	5.48213e7	2.23733
$904$	−6.19710e7	−2.52213
$905$	−2.06233e7	−0.837021
$906$	−2.42979e7	−0.983439
$907$	464101.	0.0187324	0.00936622	−	0.999956i	$-0.497019\pi$
$907$	464101.	0.0187324	0.00936622	+	0.999956i	$0.497019\pi$
$908$	−1.60688e7	−0.646800
$909$	7.93879e7	3.18672
$910$	3.33280e7	1.33415
$911$	−3.31603e7	−1.32380	−0.661901	−	0.749591i	$-0.730250\pi$
$911$	−3.31603e7	−1.32380	−0.661901	+	0.749591i	$0.730250\pi$
$912$	−5.69904e7	−2.26890
$913$	8.05030e6	0.319621
$914$	−8.06227e7	−3.19221
$915$	−4.80086e7	−1.89569
$916$	8.83814e7	3.48035
$917$	−6.09776e7	−2.39468
$918$	−3.56240e7	−1.39520
$919$	1.03117e7	0.402754	0.201377	−	0.979514i	$-0.435458\pi$
$919$	1.03117e7	0.402754	0.201377	+	0.979514i	$0.435458\pi$
$920$	−3.82313e7	−1.48919
$921$	−2.65970e7	−1.03320
$922$	−5.80686e7	−2.24965
$923$	−829952.	−0.0320663
$924$	2.69247e7	1.03746
$925$	−8.35944e6	−0.321235
$926$	6.30496e7	2.41632
$927$	−1.46338e6	−0.0559317
$928$	−2.43180e6	−0.0926953
$929$	2.64309e7	1.00478	0.502392	−	0.864640i	$-0.332453\pi$
$929$	2.64309e7	1.00478	0.502392	+	0.864640i	$0.332453\pi$
$930$	7.26885e7	2.75587
$931$	−9.46174e7	−3.57764
$932$	1.38955e7	0.524002
$933$	8.00719e6	0.301145
$934$	2.15851e7	0.809632
$935$	−1.33328e6	−0.0498761
$936$	−5.57531e7	−2.08008
$937$	−8.28032e6	−0.308105	−0.154052	−	0.988063i	$-0.549232\pi$
$937$	−8.28032e6	−0.308105	−0.154052	+	0.988063i	$0.549232\pi$
$938$	−8.08799e7	−3.00147
$939$	−3.10415e7	−1.14889
$940$	9.50203e6	0.350749
$941$	7.82029e6	0.287905	0.143952	−	0.989585i	$-0.454019\pi$
$941$	7.82029e6	0.287905	0.143952	+	0.989585i	$0.454019\pi$
$942$	−9.71521e7	−3.56718
$943$	2.10813e7	0.772003
$944$	−7.85297e6	−0.286816
$945$	−7.58501e7	−2.76297
$946$	−6.13158e6	−0.222764
$947$	−3.36374e7	−1.21884	−0.609421	−	0.792847i	$-0.708598\pi$
$947$	−3.36374e7	−1.21884	−0.609421	+	0.792847i	$0.708598\pi$
$948$	6.93560e7	2.50647
$949$	−1.15385e7	−0.415896
$950$	−3.99393e7	−1.43579
$951$	4.03775e7	1.44773
$952$	−2.70481e7	−0.967263
$953$	4.71590e7	1.68203	0.841013	−	0.541015i	$-0.181960\pi$
$953$	4.71590e7	1.68203	0.841013	+	0.541015i	$0.181960\pi$
$954$	−7.84597e7	−2.79110
$955$	2.61590e7	0.928139
$956$	−4.23046e7	−1.49707
$957$	−2.35257e6	−0.0830354
$958$	−4.05110e7	−1.42613
$959$	−1.25516e7	−0.440708
$960$	4.88178e7	1.70962
$961$	1.40528e7	0.490856
$962$	−2.15386e7	−0.750377
$963$	−6.77819e7	−2.35531
$964$	6.16504e7	2.13670
$965$	−8.05802e6	−0.278555
$966$	2.01213e8	6.93765
$967$	2.95205e7	1.01521	0.507607	−	0.861589i	$-0.330530\pi$
$967$	2.95205e7	1.01521	0.507607	+	0.861589i	$0.330530\pi$
$968$	4.25781e7	1.46049
$969$	−3.68070e7	−1.25928
$970$	4.67026e7	1.59372
$971$	4.31812e6	0.146976	0.0734880	−	0.997296i	$-0.476587\pi$
$971$	4.31812e6	0.146976	0.0734880	+	0.997296i	$0.476587\pi$
$972$	4.84136e7	1.64362
$973$	2.98129e7	1.00954
$974$	−5.68079e7	−1.91872
$975$	−1.49532e7	−0.503757
$976$	2.87369e7	0.965641
$977$	−1.50177e7	−0.503347	−0.251673	−	0.967812i	$-0.580981\pi$
$977$	−1.50177e7	−0.503347	−0.251673	+	0.967812i	$0.580981\pi$
$978$	1.36310e8	4.55703
$979$	2.15487e6	0.0718561
$980$	−8.04235e7	−2.67496
$981$	4.41794e7	1.46571
$982$	−3.27407e7	−1.08345
$983$	966289.	0.0318950
$983$	966289.	0.0318950
$984$	4.76234e7	1.56795
$985$	1.12196e7	0.368458
$986$	5.02481e6	0.164599
$987$	−2.35214e7	−0.768546
$988$	−6.72737e7	−2.19257
$989$	−2.99559e7	−0.973847
$990$	1.54447e7	0.500832
$991$	2.78637e7	0.901268	0.450634	−	0.892709i	$-0.351198\pi$
$991$	2.78637e7	0.901268	0.450634	+	0.892709i	$0.351198\pi$
$992$	1.35996e7	0.438779
$993$	−8.90029e7	−2.86438
$994$	4.66422e6	0.149732
$995$	−1.90012e7	−0.608449
$996$	1.88901e8	6.03372
$997$	1.09791e7	0.349808	0.174904	−	0.984586i	$-0.444039\pi$
$997$	1.09791e7	0.349808	0.174904	+	0.984586i	$0.444039\pi$
$998$	2.67189e7	0.849166
$999$	4.90190e7	1.55400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.b.1.20	✓	218

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.b.1.20	✓	218	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-9.61332 q^{2} +27.9669 q^{3} +60.4159 q^{4} -41.3834 q^{5} -268.854 q^{6} +221.300 q^{7} -273.171 q^{8} +539.145 q^{9} +397.832 q^{10} +72.0069 q^{11} +1689.64 q^{12} +378.554 q^{13} -2127.43 q^{14} -1157.36 q^{15} +692.774 q^{16} +447.425 q^{17} -5182.98 q^{18} -2941.48 q^{19} -2500.22 q^{20} +6189.06 q^{21} -692.226 q^{22} -3381.87 q^{23} -7639.74 q^{24} -1412.41 q^{25} -3639.16 q^{26} +8282.26 q^{27} +13370.0 q^{28} -1168.22 q^{29} +11126.1 q^{30} +6533.14 q^{31} +2081.63 q^{32} +2013.81 q^{33} -4301.24 q^{34} -9158.14 q^{35} +32573.0 q^{36} +5918.56 q^{37} +28277.4 q^{38} +10587.0 q^{39} +11304.8 q^{40} -6233.63 q^{41} -59497.4 q^{42} +8857.78 q^{43} +4350.36 q^{44} -22311.7 q^{45} +32511.0 q^{46} -3800.48 q^{47} +19374.7 q^{48} +32166.6 q^{49} +13578.0 q^{50} +12513.1 q^{51} +22870.7 q^{52} +15138.0 q^{53} -79620.0 q^{54} -2979.89 q^{55} -60452.7 q^{56} -82264.1 q^{57} +11230.5 q^{58} -11335.5 q^{59} -69923.3 q^{60} +41481.0 q^{61} -62805.2 q^{62} +119313. q^{63} -42180.1 q^{64} -15665.9 q^{65} -19359.4 q^{66} +38017.7 q^{67} +27031.6 q^{68} -94580.3 q^{69} +88040.2 q^{70} -2192.43 q^{71} -147279. q^{72} -30480.5 q^{73} -56897.0 q^{74} -39500.7 q^{75} -177712. q^{76} +15935.1 q^{77} -101776. q^{78} +41047.7 q^{79} -28669.4 q^{80} +100616. q^{81} +59925.9 q^{82} +111799. q^{83} +373918. q^{84} -18516.0 q^{85} -85152.6 q^{86} -32671.5 q^{87} -19670.2 q^{88} +29925.8 q^{89} +214489. q^{90} +83773.9 q^{91} -204319. q^{92} +182711. q^{93} +36535.2 q^{94} +121729. q^{95} +58216.5 q^{96} +117393. q^{97} -309228. q^{98} +38822.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16}+ \cdots + 627643 q^{99}+O(q^{100}) \) 218 * q + 35 * q^2 + 70 * q^3 + 3685 * q^4 + 253 * q^5 + 529 * q^6 + 1567 * q^7 + 1695 * q^8 + 19812 * q^9 + 2133 * q^10 + 1752 * q^11 + 3512 * q^12 + 5990 * q^13 + 2319 * q^14 + 4639 * q^15 + 66105 * q^16 + 10656 * q^17 + 11911 * q^18 + 11511 * q^19 + 10012 * q^20 + 12225 * q^21 + 19401 * q^22 + 9767 * q^23 + 21725 * q^24 + 185207 * q^25 + 7708 * q^26 + 23764 * q^27 + 77808 * q^28 + 25772 * q^29 + 15736 * q^30 + 35900 * q^31 + 60155 * q^32 + 70026 * q^33 + 17236 * q^34 + 28782 * q^35 + 382874 * q^36 + 126082 * q^37 + 62164 * q^38 + 54264 * q^39 + 102846 * q^40 + 70480 * q^41 + 102244 * q^42 + 137413 * q^43 + 116278 * q^44 + 93481 * q^45 + 126122 * q^46 + 63218 * q^47 + 124701 * q^48 + 732031 * q^49 + 131089 * q^50 + 109902 * q^51 + 229519 * q^52 + 102608 * q^53 + 149130 * q^54 + 167596 * q^55 + 87868 * q^56 + 408318 * q^57 + 304579 * q^58 + 67460 * q^59 + 150523 * q^60 + 195132 * q^61 + 132294 * q^62 + 374425 * q^63 + 1296639 * q^64 + 347092 * q^65 + 147397 * q^66 + 381238 * q^67 + 296321 * q^68 + 139362 * q^69 + 325675 * q^70 + 147818 * q^71 + 646059 * q^72 + 961992 * q^73 + 167410 * q^74 + 167324 * q^75 + 504875 * q^76 + 284328 * q^77 + 284295 * q^78 + 285792 * q^79 + 444932 * q^80 + 1980282 * q^81 + 336676 * q^82 + 276734 * q^83 + 378474 * q^84 + 1021245 * q^85 + 156051 * q^86 + 500457 * q^87 + 1068101 * q^88 + 398983 * q^89 + 463961 * q^90 + 273517 * q^91 + 577884 * q^92 + 967833 * q^93 + 224775 * q^94 + 482817 * q^95 + 780445 * q^96 + 1636277 * q^97 + 495958 * q^98 + 627643 * q^99

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