LMFDB - Embedded newform 289.4.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.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:	$17.0515519917$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2555057.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 21x^{2} - 4x + 36 $ x^4 - x^3 - 21x^2 - 4x + 36
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			1.4
Root			$5.04171$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.04171 q^{2} +2.60975 q^{3} +17.4188 q^{4} +13.4166 q^{5} +13.1576 q^{6} +22.2015 q^{7} +47.4869 q^{8} -20.1892 q^{9} +O(q^{10})$	\(q+5.04171 q^{2} +2.60975 q^{3} +17.4188 q^{4} +13.4166 q^{5} +13.1576 q^{6} +22.2015 q^{7} +47.4869 q^{8} -20.1892 q^{9} +67.6428 q^{10} -33.6445 q^{11} +45.4588 q^{12} -73.4255 q^{13} +111.933 q^{14} +35.0141 q^{15} +100.065 q^{16} -101.788 q^{18} -42.5131 q^{19} +233.702 q^{20} +57.9404 q^{21} -169.626 q^{22} -59.2553 q^{23} +123.929 q^{24} +55.0063 q^{25} -370.190 q^{26} -123.152 q^{27} +386.724 q^{28} -21.3559 q^{29} +176.531 q^{30} +42.2667 q^{31} +124.601 q^{32} -87.8038 q^{33} +297.869 q^{35} -351.672 q^{36} +265.496 q^{37} -214.339 q^{38} -191.622 q^{39} +637.115 q^{40} +80.0523 q^{41} +292.118 q^{42} +353.946 q^{43} -586.048 q^{44} -270.871 q^{45} -298.748 q^{46} +52.4119 q^{47} +261.144 q^{48} +149.906 q^{49} +277.325 q^{50} -1278.98 q^{52} +551.066 q^{53} -620.897 q^{54} -451.396 q^{55} +1054.28 q^{56} -110.949 q^{57} -107.670 q^{58} +508.032 q^{59} +609.904 q^{60} +671.496 q^{61} +213.096 q^{62} -448.230 q^{63} -172.314 q^{64} -985.123 q^{65} -442.681 q^{66} -859.787 q^{67} -154.642 q^{69} +1501.77 q^{70} +147.724 q^{71} -958.723 q^{72} +522.518 q^{73} +1338.55 q^{74} +143.553 q^{75} -740.528 q^{76} -746.958 q^{77} -966.103 q^{78} -245.472 q^{79} +1342.53 q^{80} +223.712 q^{81} +403.600 q^{82} -293.554 q^{83} +1009.25 q^{84} +1784.49 q^{86} -55.7336 q^{87} -1597.67 q^{88} -72.0418 q^{89} -1365.65 q^{90} -1630.15 q^{91} -1032.16 q^{92} +110.305 q^{93} +264.245 q^{94} -570.383 q^{95} +325.178 q^{96} -1386.68 q^{97} +755.782 q^{98} +679.256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} + 11 q^{4} + 14 q^{5} + 38 q^{6} + 36 q^{7} + 60 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 + 11 * q^4 + 14 * q^5 + 38 * q^6 + 36 * q^7 + 60 * q^8 + 6 * q^9	\( 4 q + q^{2} - 2 q^{3} + 11 q^{4} + 14 q^{5} + 38 q^{6} + 36 q^{7} + 60 q^{8} + 6 q^{9} - 7 q^{10} + 10 q^{11} - 29 q^{12} - 22 q^{13} + 73 q^{14} + 54 q^{15} + 63 q^{16} - 334 q^{18} + 22 q^{19} + 330 q^{20} - 352 q^{21} - 79 q^{22} + 380 q^{23} + 159 q^{24} + 378 q^{25} - 448 q^{26} - 494 q^{27} + 608 q^{28} - 78 q^{29} + 313 q^{30} + 362 q^{31} + 331 q^{32} + 94 q^{33} - 242 q^{35} + 141 q^{36} + 512 q^{37} - 524 q^{38} + 12 q^{39} + 1381 q^{40} + 840 q^{41} + 1455 q^{42} - 114 q^{43} - 1041 q^{44} + 648 q^{45} - 1051 q^{46} + 10 q^{47} + 998 q^{48} + 1006 q^{49} + 805 q^{50} - 1537 q^{52} + 50 q^{53} + 581 q^{54} - 1316 q^{55} + 411 q^{56} + 358 q^{57} - 376 q^{58} + 996 q^{59} - 217 q^{60} + 448 q^{61} - 73 q^{62} + 766 q^{63} - 150 q^{64} - 372 q^{65} - 1090 q^{66} - 868 q^{67} - 1128 q^{69} + 1052 q^{70} + 1116 q^{71} - 39 q^{72} + 540 q^{73} + 1630 q^{74} + 1070 q^{75} - 873 q^{76} - 894 q^{77} - 1245 q^{78} + 940 q^{79} + 307 q^{80} + 1080 q^{81} - 334 q^{82} + 850 q^{83} + 443 q^{84} + 2411 q^{86} - 384 q^{87} - 2252 q^{88} + 784 q^{89} - 2069 q^{90} - 2858 q^{91} - 1566 q^{92} - 1550 q^{93} + 1119 q^{94} + 2494 q^{95} - 2643 q^{96} - 518 q^{97} - 1877 q^{98} - 1406 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 + 11 * q^4 + 14 * q^5 + 38 * q^6 + 36 * q^7 + 60 * q^8 + 6 * q^9 - 7 * q^10 + 10 * q^11 - 29 * q^12 - 22 * q^13 + 73 * q^14 + 54 * q^15 + 63 * q^16 - 334 * q^18 + 22 * q^19 + 330 * q^20 - 352 * q^21 - 79 * q^22 + 380 * q^23 + 159 * q^24 + 378 * q^25 - 448 * q^26 - 494 * q^27 + 608 * q^28 - 78 * q^29 + 313 * q^30 + 362 * q^31 + 331 * q^32 + 94 * q^33 - 242 * q^35 + 141 * q^36 + 512 * q^37 - 524 * q^38 + 12 * q^39 + 1381 * q^40 + 840 * q^41 + 1455 * q^42 - 114 * q^43 - 1041 * q^44 + 648 * q^45 - 1051 * q^46 + 10 * q^47 + 998 * q^48 + 1006 * q^49 + 805 * q^50 - 1537 * q^52 + 50 * q^53 + 581 * q^54 - 1316 * q^55 + 411 * q^56 + 358 * q^57 - 376 * q^58 + 996 * q^59 - 217 * q^60 + 448 * q^61 - 73 * q^62 + 766 * q^63 - 150 * q^64 - 372 * q^65 - 1090 * q^66 - 868 * q^67 - 1128 * q^69 + 1052 * q^70 + 1116 * q^71 - 39 * q^72 + 540 * q^73 + 1630 * q^74 + 1070 * q^75 - 873 * q^76 - 894 * q^77 - 1245 * q^78 + 940 * q^79 + 307 * q^80 + 1080 * q^81 - 334 * q^82 + 850 * q^83 + 443 * q^84 + 2411 * q^86 - 384 * q^87 - 2252 * q^88 + 784 * q^89 - 2069 * q^90 - 2858 * q^91 - 1566 * q^92 - 1550 * q^93 + 1119 * q^94 + 2494 * q^95 - 2643 * q^96 - 518 * q^97 - 1877 * q^98 - 1406 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5.04171	1.78251	0.891256	−	0.453500i	$-0.149825\pi$
$2$	5.04171	1.78251	0.891256	+	0.453500i	$0.149825\pi$
$3$	2.60975	0.502247	0.251123	−	0.967955i	$-0.419200\pi$
$3$	2.60975	0.502247	0.251123	+	0.967955i	$0.419200\pi$
$4$	17.4188	2.17735
$5$	13.4166	1.20002	0.600010	−	0.799992i	$-0.295163\pi$
$5$	13.4166	1.20002	0.600010	+	0.799992i	$0.295163\pi$
$6$	13.1576	0.895262
$7$	22.2015	1.19877	0.599384	−	0.800462i	$-0.295412\pi$
$7$	22.2015	1.19877	0.599384	+	0.800462i	$0.295412\pi$
$8$	47.4869	2.09865
$9$	−20.1892	−0.747748
$10$	67.6428	2.13905
$11$	−33.6445	−0.922200	−0.461100	−	0.887348i	$-0.652545\pi$
$11$	−33.6445	−0.922200	−0.461100	+	0.887348i	$0.652545\pi$
$12$	45.4588	1.09357
$13$	−73.4255	−1.56650	−0.783252	−	0.621704i	$-0.786441\pi$
$13$	−73.4255	−1.56650	−0.783252	+	0.621704i	$0.786441\pi$
$14$	111.933	2.13682
$15$	35.0141	0.602707
$16$	100.065	1.56351
$17$	0	0
$17$	0	0
$18$	−101.788	−1.33287
$19$	−42.5131	−0.513325	−0.256663	−	0.966501i	$-0.582623\pi$
$19$	−42.5131	−0.513325	−0.256663	+	0.966501i	$0.582623\pi$
$20$	233.702	2.61287
$21$	57.9404	0.602077
$22$	−169.626	−1.64383
$23$	−59.2553	−0.537199	−0.268599	−	0.963252i	$-0.586561\pi$
$23$	−59.2553	−0.537199	−0.268599	+	0.963252i	$0.586561\pi$
$24$	123.929	1.05404
$25$	55.0063	0.440050
$26$	−370.190	−2.79231
$27$	−123.152	−0.877801
$28$	386.724	2.61014
$29$	−21.3559	−0.136748	−0.0683740	−	0.997660i	$-0.521781\pi$
$29$	−21.3559	−0.136748	−0.0683740	+	0.997660i	$0.521781\pi$
$30$	176.531	1.07433
$31$	42.2667	0.244881	0.122441	−	0.992476i	$-0.460928\pi$
$31$	42.2667	0.244881	0.122441	+	0.992476i	$0.460928\pi$
$32$	124.601	0.688331
$33$	−87.8038	−0.463172
$34$	0	0
$35$	297.869	1.43855
$36$	−351.672	−1.62811
$37$	265.496	1.17965	0.589827	−	0.807530i	$-0.299196\pi$
$37$	265.496	1.17965	0.589827	+	0.807530i	$0.299196\pi$
$38$	−214.339	−0.915008
$39$	−191.622	−0.786772
$40$	637.115	2.51842
$41$	80.0523	0.304929	0.152464	−	0.988309i	$-0.451279\pi$
$41$	80.0523	0.304929	0.152464	+	0.988309i	$0.451279\pi$
$42$	292.118	1.07321
$43$	353.946	1.25526	0.627632	−	0.778510i	$-0.284024\pi$
$43$	353.946	1.25526	0.627632	+	0.778510i	$0.284024\pi$
$44$	−586.048	−2.00795
$45$	−270.871	−0.897313
$46$	−298.748	−0.957564
$47$	52.4119	0.162661	0.0813304	−	0.996687i	$-0.474083\pi$
$47$	52.4119	0.162661	0.0813304	+	0.996687i	$0.474083\pi$
$48$	261.144	0.785268
$49$	149.906	0.437044
$50$	277.325	0.784395
$51$	0	0
$52$	−1278.98	−3.41083
$53$	551.066	1.42820	0.714101	−	0.700043i	$-0.246836\pi$
$53$	551.066	1.42820	0.714101	+	0.700043i	$0.246836\pi$
$54$	−620.897	−1.56469
$55$	−451.396	−1.10666
$56$	1054.28	2.51579
$57$	−110.949	−0.257816
$58$	−107.670	−0.243755
$59$	508.032	1.12102	0.560510	−	0.828148i	$-0.310605\pi$
$59$	508.032	1.12102	0.560510	+	0.828148i	$0.310605\pi$
$60$	609.904	1.31230
$61$	671.496	1.40945	0.704723	−	0.709482i	$-0.251071\pi$
$61$	671.496	1.40945	0.704723	+	0.709482i	$0.251071\pi$
$62$	213.096	0.436504
$63$	−448.230	−0.896376
$64$	−172.314	−0.336551
$65$	−985.123	−1.87984
$66$	−442.681	−0.825611
$67$	−859.787	−1.56776	−0.783878	−	0.620915i	$-0.786761\pi$
$67$	−859.787	−1.56776	−0.783878	+	0.620915i	$0.786761\pi$
$68$	0	0
$69$	−154.642	−0.269807
$70$	1501.77	2.56423
$71$	147.724	0.246924	0.123462	−	0.992349i	$-0.460600\pi$
$71$	147.724	0.246924	0.123462	+	0.992349i	$0.460600\pi$
$72$	−958.723	−1.56926
$73$	522.518	0.837755	0.418878	−	0.908043i	$-0.362424\pi$
$73$	522.518	0.837755	0.418878	+	0.908043i	$0.362424\pi$
$74$	1338.55	2.10275
$75$	143.553	0.221014
$76$	−740.528	−1.11769
$77$	−746.958	−1.10550
$78$	−966.103	−1.40243
$79$	−245.472	−0.349592	−0.174796	−	0.984605i	$-0.555927\pi$
$79$	−245.472	−0.349592	−0.174796	+	0.984605i	$0.555927\pi$
$80$	1342.53	1.87624
$81$	223.712	0.306875
$82$	403.600	0.543539
$83$	−293.554	−0.388213	−0.194107	−	0.980980i	$-0.562181\pi$
$83$	−293.554	−0.388213	−0.194107	+	0.980980i	$0.562181\pi$
$84$	1009.25	1.31093
$85$	0	0
$86$	1784.49	2.23752
$87$	−55.7336	−0.0686813
$88$	−1597.67	−1.93537
$89$	−72.0418	−0.0858024	−0.0429012	−	0.999079i	$-0.513660\pi$
$89$	−72.0418	−0.0858024	−0.0429012	+	0.999079i	$0.513660\pi$
$90$	−1365.65	−1.59947
$91$	−1630.15	−1.87787
$92$	−1032.16	−1.16967
$93$	110.305	0.122991
$94$	264.245	0.289945
$95$	−570.383	−0.616001
$96$	325.178	0.345712
$97$	−1386.68	−1.45151	−0.725754	−	0.687955i	$-0.758509\pi$
$97$	−1386.68	−1.45151	−0.725754	+	0.687955i	$0.758509\pi$
$98$	755.782	0.779036
$99$	679.256	0.689574
$100$	958.144	0.958144
$101$	−1455.68	−1.43412	−0.717059	−	0.697012i	$-0.754512\pi$
$101$	−1455.68	−1.43412	−0.717059	+	0.697012i	$0.754512\pi$
$102$	0	0
$103$	−349.197	−0.334052	−0.167026	−	0.985952i	$-0.553416\pi$
$103$	−349.197	−0.334052	−0.167026	+	0.985952i	$0.553416\pi$
$104$	−3486.75	−3.28754
$105$	777.365	0.722505
$106$	2778.31	2.54579
$107$	−1213.83	−1.09669	−0.548344	−	0.836253i	$-0.684742\pi$
$107$	−1213.83	−1.09669	−0.548344	+	0.836253i	$0.684742\pi$
$108$	−2145.16	−1.91128
$109$	981.173	0.862196	0.431098	−	0.902305i	$-0.358126\pi$
$109$	981.173	0.862196	0.431098	+	0.902305i	$0.358126\pi$
$110$	−2275.81	−1.97264
$111$	692.877	0.592478
$112$	2221.58	1.87428
$113$	1354.85	1.12791	0.563953	−	0.825807i	$-0.309280\pi$
$113$	1354.85	1.12791	0.563953	+	0.825807i	$0.309280\pi$
$114$	−559.371	−0.459560
$115$	−795.007	−0.644650
$116$	−371.995	−0.297749
$117$	1482.40	1.17135
$118$	2561.35	1.99823
$119$	0	0
$120$	1662.71	1.26487
$121$	−199.046	−0.149546
$122$	3385.48	2.51236
$123$	208.917	0.153149
$124$	736.235	0.533193
$125$	−939.081	−0.671952
$126$	−2259.85	−1.59780
$127$	2377.49	1.66116	0.830582	−	0.556897i	$-0.188008\pi$
$127$	2377.49	1.66116	0.830582	+	0.556897i	$0.188008\pi$
$128$	−1865.57	−1.28824
$129$	923.712	0.630452
$130$	−4966.70	−3.35084
$131$	2397.58	1.59907	0.799533	−	0.600622i	$-0.205080\pi$
$131$	2397.58	1.59907	0.799533	+	0.600622i	$0.205080\pi$
$132$	−1529.44	−1.00849
$133$	−943.854	−0.615357
$134$	−4334.79	−2.79455
$135$	−1652.29	−1.05338
$136$	0	0
$137$	1595.27	0.994838	0.497419	−	0.867510i	$-0.334281\pi$
$137$	1595.27	0.994838	0.497419	+	0.867510i	$0.334281\pi$
$138$	−779.657	−0.480934
$139$	−362.559	−0.221236	−0.110618	−	0.993863i	$-0.535283\pi$
$139$	−362.559	−0.221236	−0.110618	+	0.993863i	$0.535283\pi$
$140$	5188.53	3.13222
$141$	136.782	0.0816959
$142$	744.781	0.440145
$143$	2470.36	1.44463
$144$	−2020.22	−1.16911
$145$	−286.525	−0.164101
$146$	2634.38	1.49331
$147$	391.218	0.219504
$148$	4624.62	2.56852
$149$	−520.649	−0.286263	−0.143132	−	0.989704i	$-0.545717\pi$
$149$	−520.649	−0.286263	−0.143132	+	0.989704i	$0.545717\pi$
$150$	723.751	0.393960
$151$	−1157.02	−0.623555	−0.311778	−	0.950155i	$-0.600924\pi$
$151$	−1157.02	−0.623555	−0.311778	+	0.950155i	$0.600924\pi$
$152$	−2018.82	−1.07729
$153$	0	0
$154$	−3765.95	−1.97058
$155$	567.077	0.293863
$156$	−3337.83	−1.71308
$157$	−2287.62	−1.16288	−0.581440	−	0.813590i	$-0.697510\pi$
$157$	−2287.62	−1.16288	−0.581440	+	0.813590i	$0.697510\pi$
$158$	−1237.60	−0.623152
$159$	1438.14	0.717310
$160$	1671.73	0.826012
$161$	−1315.55	−0.643977
$162$	1127.89	0.547009
$163$	3471.88	1.66834	0.834168	−	0.551510i	$-0.185948\pi$
$163$	3471.88	1.66834	0.834168	+	0.551510i	$0.185948\pi$
$164$	1394.42	0.663937
$165$	−1178.03	−0.555816
$166$	−1480.01	−0.691995
$167$	611.808	0.283492	0.141746	−	0.989903i	$-0.454728\pi$
$167$	611.808	0.283492	0.141746	+	0.989903i	$0.454728\pi$
$168$	2751.41	1.26355
$169$	3194.30	1.45394
$170$	0	0
$171$	858.305	0.383838
$172$	6165.33	2.73315
$173$	−1074.13	−0.472049	−0.236024	−	0.971747i	$-0.575845\pi$
$173$	−1074.13	−0.472049	−0.236024	+	0.971747i	$0.575845\pi$
$174$	−280.993	−0.122425
$175$	1221.22	0.527518
$176$	−3366.63	−1.44187
$177$	1325.84	0.563029
$178$	−363.214	−0.152944
$179$	1326.09	0.553724	0.276862	−	0.960910i	$-0.410706\pi$
$179$	1326.09	0.553724	0.276862	+	0.960910i	$0.410706\pi$
$180$	−4718.26	−1.95377
$181$	−2450.13	−1.00617	−0.503085	−	0.864237i	$-0.667802\pi$
$181$	−2450.13	−1.00617	−0.503085	+	0.864237i	$0.667802\pi$
$182$	−8218.76	−3.34734
$183$	1752.44	0.707890
$184$	−2813.85	−1.12739
$185$	3562.06	1.41561
$186$	556.128	0.219233
$187$	0	0
$188$	912.953	0.354170
$189$	−2734.16	−1.05228
$190$	−2875.70	−1.09803
$191$	−3177.92	−1.20391	−0.601953	−	0.798532i	$-0.705610\pi$
$191$	−3177.92	−1.20391	−0.601953	+	0.798532i	$0.705610\pi$
$192$	−449.697	−0.169032
$193$	504.377	0.188113	0.0940566	−	0.995567i	$-0.470017\pi$
$193$	504.377	0.188113	0.0940566	+	0.995567i	$0.470017\pi$
$194$	−6991.24	−2.58733
$195$	−2570.93	−0.944143
$196$	2611.19	0.951598
$197$	−4707.42	−1.70249	−0.851244	−	0.524770i	$-0.824151\pi$
$197$	−4707.42	−1.70249	−0.851244	+	0.524770i	$0.824151\pi$
$198$	3424.61	1.22917
$199$	3864.28	1.37654	0.688269	−	0.725455i	$-0.258371\pi$
$199$	3864.28	1.37654	0.688269	+	0.725455i	$0.258371\pi$
$200$	2612.08	0.923509
$201$	−2243.83	−0.787401
$202$	−7339.13	−2.55634
$203$	−474.133	−0.163929
$204$	0	0
$205$	1074.03	0.365921
$206$	−1760.55	−0.595452
$207$	1196.32	0.401689
$208$	−7347.29	−2.44924
$209$	1430.33	0.473389
$210$	3919.25	1.28788
$211$	−2431.92	−0.793462	−0.396731	−	0.917935i	$-0.629855\pi$
$211$	−2431.92	−0.793462	−0.396731	+	0.917935i	$0.629855\pi$
$212$	9598.91	3.10970
$213$	385.523	0.124017
$214$	−6119.79	−1.95486
$215$	4748.77	1.50634
$216$	−5848.11	−1.84219
$217$	938.383	0.293556
$218$	4946.79	1.53688
$219$	1363.64	0.420760
$220$	−7862.79	−2.40959
$221$	0	0
$222$	3493.29	1.05610
$223$	584.515	0.175525	0.0877624	−	0.996141i	$-0.472028\pi$
$223$	584.515	0.175525	0.0877624	+	0.996141i	$0.472028\pi$
$224$	2766.33	0.825149
$225$	−1110.53	−0.329047
$226$	6830.75	2.01051
$227$	−3235.58	−0.946048	−0.473024	−	0.881049i	$-0.656838\pi$
$227$	−3235.58	−0.946048	−0.473024	+	0.881049i	$0.656838\pi$
$228$	−1932.59	−0.561356
$229$	−3039.00	−0.876955	−0.438477	−	0.898742i	$-0.644482\pi$
$229$	−3039.00	−0.876955	−0.438477	+	0.898742i	$0.644482\pi$
$230$	−4008.19	−1.14910
$231$	−1949.38	−0.555236
$232$	−1014.13	−0.286986
$233$	5387.38	1.51476	0.757380	−	0.652974i	$-0.226479\pi$
$233$	5387.38	1.51476	0.757380	+	0.652974i	$0.226479\pi$
$234$	7473.83	2.08795
$235$	703.191	0.195196
$236$	8849.32	2.44085
$237$	−640.621	−0.175582
$238$	0	0
$239$	−6534.43	−1.76852	−0.884262	−	0.466991i	$-0.845338\pi$
$239$	−6534.43	−1.76852	−0.884262	+	0.466991i	$0.845338\pi$
$240$	3503.67	0.942338
$241$	−2242.97	−0.599511	−0.299756	−	0.954016i	$-0.596905\pi$
$241$	−2242.97	−0.599511	−0.299756	+	0.954016i	$0.596905\pi$
$242$	−1003.53	−0.266568
$243$	3908.94	1.03193
$244$	11696.7	3.06886
$245$	2011.24	0.524462
$246$	1053.30	0.272991
$247$	3121.54	0.804126
$248$	2007.11	0.513919
$249$	−766.102	−0.194979
$250$	−4734.57	−1.19776
$251$	1846.41	0.464319	0.232160	−	0.972678i	$-0.425421\pi$
$251$	1846.41	0.464319	0.232160	+	0.972678i	$0.425421\pi$
$252$	−7807.64	−1.95173
$253$	1993.61	0.495405
$254$	11986.6	2.96105
$255$	0	0
$256$	−8027.13	−1.95975
$257$	−1556.43	−0.377772	−0.188886	−	0.981999i	$-0.560488\pi$
$257$	−1556.43	−0.377772	−0.188886	+	0.981999i	$0.560488\pi$
$258$	4657.09	1.12379
$259$	5894.40	1.41413
$260$	−17159.7	−4.09307
$261$	431.159	0.102253
$262$	12087.9	2.85036
$263$	−2926.03	−0.686033	−0.343017	−	0.939329i	$-0.611449\pi$
$263$	−2926.03	−0.686033	−0.343017	+	0.939329i	$0.611449\pi$
$264$	−4169.53	−0.972034
$265$	7393.45	1.71387
$266$	−4758.64	−1.09688
$267$	−188.011	−0.0430940
$268$	−14976.5	−3.41356
$269$	6835.44	1.54931	0.774655	−	0.632384i	$-0.217923\pi$
$269$	6835.44	1.54931	0.774655	+	0.632384i	$0.217923\pi$
$270$	−8330.35	−1.87766
$271$	−1404.62	−0.314850	−0.157425	−	0.987531i	$-0.550319\pi$
$271$	−1404.62	−0.314850	−0.157425	+	0.987531i	$0.550319\pi$
$272$	0	0
$273$	−4254.30	−0.943157
$274$	8042.87	1.77331
$275$	−1850.66	−0.405814
$276$	−2693.67	−0.587464
$277$	2147.18	0.465745	0.232872	−	0.972507i	$-0.425188\pi$
$277$	2147.18	0.465745	0.232872	+	0.972507i	$0.425188\pi$
$278$	−1827.92	−0.394357
$279$	−853.330	−0.183109
$280$	14144.9	3.01900
$281$	−437.112	−0.0927968	−0.0463984	−	0.998923i	$-0.514774\pi$
$281$	−437.112	−0.0927968	−0.0463984	+	0.998923i	$0.514774\pi$
$282$	689.615	0.145624
$283$	6747.75	1.41736	0.708678	−	0.705532i	$-0.249292\pi$
$283$	6747.75	1.41736	0.708678	+	0.705532i	$0.249292\pi$
$284$	2573.18	0.537641
$285$	−1488.56	−0.309384
$286$	12454.9	2.57507
$287$	1777.28	0.365539
$288$	−2515.60	−0.514698
$289$	0	0
$290$	−1444.57	−0.292511
$291$	−3618.89	−0.729015
$292$	9101.65	1.82409
$293$	1219.13	0.243081	0.121540	−	0.992586i	$-0.461217\pi$
$293$	1219.13	0.243081	0.121540	+	0.992586i	$0.461217\pi$
$294$	1972.40	0.391269
$295$	6816.09	1.34525
$296$	12607.6	2.47567
$297$	4143.39	0.809509
$298$	−2624.96	−0.510268
$299$	4350.84	0.841524
$300$	2500.52	0.481225
$301$	7858.14	1.50477
$302$	−5833.35	−1.11150
$303$	−3798.97	−0.720282
$304$	−4254.06	−0.802589
$305$	9009.22	1.69136
$306$	0	0
$307$	9237.79	1.71736	0.858679	−	0.512514i	$-0.171286\pi$
$307$	9237.79	1.71736	0.858679	+	0.512514i	$0.171286\pi$
$308$	−13011.1	−2.40707
$309$	−911.316	−0.167777
$310$	2859.03	0.523814
$311$	−741.272	−0.135157	−0.0675783	−	0.997714i	$-0.521527\pi$
$311$	−741.272	−0.135157	−0.0675783	+	0.997714i	$0.521527\pi$
$312$	−9099.55	−1.65116
$313$	−188.399	−0.0340221	−0.0170110	−	0.999855i	$-0.505415\pi$
$313$	−188.399	−0.0340221	−0.0170110	+	0.999855i	$0.505415\pi$
$314$	−11533.5	−2.07285
$315$	−6013.74	−1.07567
$316$	−4275.83	−0.761185
$317$	−6282.92	−1.11320	−0.556599	−	0.830781i	$-0.687894\pi$
$317$	−6282.92	−1.11320	−0.556599	+	0.830781i	$0.687894\pi$
$318$	7250.70	1.27861
$319$	718.510	0.126109
$320$	−2311.87	−0.403868
$321$	−3167.80	−0.550808
$322$	−6632.64	−1.14790
$323$	0	0
$324$	3896.80	0.668175
$325$	−4038.86	−0.689340
$326$	17504.2	2.97383
$327$	2560.62	0.433035
$328$	3801.44	0.639937
$329$	1163.62	0.194993
$330$	−5939.30	−0.990750
$331$	−252.673	−0.0419582	−0.0209791	−	0.999780i	$-0.506678\pi$
$331$	−252.673	−0.0419582	−0.0209791	+	0.999780i	$0.506678\pi$
$332$	−5113.36	−0.845277
$333$	−5360.14	−0.882084
$334$	3084.56	0.505328
$335$	−11535.5	−1.88134
$336$	5797.78	0.941354
$337$	−5809.35	−0.939038	−0.469519	−	0.882922i	$-0.655573\pi$
$337$	−5809.35	−0.939038	−0.469519	+	0.882922i	$0.655573\pi$
$338$	16104.7	2.59166
$339$	3535.82	0.566487
$340$	0	0
$341$	−1422.04	−0.225830
$342$	4327.33	0.684196
$343$	−4286.97	−0.674854
$344$	16807.8	2.63435
$345$	−2074.77	−0.323773
$346$	−5415.44	−0.841433
$347$	−5961.59	−0.922291	−0.461146	−	0.887324i	$-0.652561\pi$
$347$	−5961.59	−0.922291	−0.461146	+	0.887324i	$0.652561\pi$
$348$	−970.814	−0.149543
$349$	−600.801	−0.0921494	−0.0460747	−	0.998938i	$-0.514671\pi$
$349$	−600.801	−0.0921494	−0.0460747	+	0.998938i	$0.514671\pi$
$350$	6157.04	0.940307
$351$	9042.50	1.37508
$352$	−4192.15	−0.634779
$353$	9716.67	1.46506	0.732530	−	0.680735i	$-0.238339\pi$
$353$	9716.67	1.46506	0.732530	+	0.680735i	$0.238339\pi$
$354$	6684.49	1.00361
$355$	1981.96	0.296314
$356$	−1254.88	−0.186822
$357$	0	0
$358$	6685.76	0.987020
$359$	−7176.43	−1.05504	−0.527518	−	0.849544i	$-0.676877\pi$
$359$	−7176.43	−1.05504	−0.527518	+	0.849544i	$0.676877\pi$
$360$	−12862.8	−1.88314
$361$	−5051.64	−0.736497
$362$	−12352.9	−1.79351
$363$	−519.461	−0.0751092
$364$	−28395.4	−4.08879
$365$	7010.44	1.00532
$366$	8835.28	1.26182
$367$	4524.36	0.643513	0.321757	−	0.946822i	$-0.395727\pi$
$367$	4524.36	0.643513	0.321757	+	0.946822i	$0.395727\pi$
$368$	−5929.35	−0.839916
$369$	−1616.19	−0.228010
$370$	17958.9	2.52334
$371$	12234.5	1.71208
$372$	1921.39	0.267794
$373$	−2266.68	−0.314650	−0.157325	−	0.987547i	$-0.550287\pi$
$373$	−2266.68	−0.314650	−0.157325	+	0.987547i	$0.550287\pi$
$374$	0	0
$375$	−2450.77	−0.337486
$376$	2488.88	0.341367
$377$	1568.07	0.214216
$378$	−13784.8	−1.87570
$379$	−5930.46	−0.803765	−0.401883	−	0.915691i	$-0.631644\pi$
$379$	−5930.46	−0.803765	−0.401883	+	0.915691i	$0.631644\pi$
$380$	−9935.40	−1.34125
$381$	6204.65	0.834314
$382$	−16022.1	−2.14598
$383$	11373.3	1.51736	0.758678	−	0.651466i	$-0.225846\pi$
$383$	11373.3	1.51736	0.758678	+	0.651466i	$0.225846\pi$
$384$	−4868.67	−0.647013
$385$	−10021.7	−1.32663
$386$	2542.92	0.335314
$387$	−7145.89	−0.938621
$388$	−24154.4	−3.16044
$389$	−12707.2	−1.65625	−0.828123	−	0.560546i	$-0.810591\pi$
$389$	−12707.2	−1.65625	−0.828123	+	0.560546i	$0.810591\pi$
$390$	−12961.9	−1.68295
$391$	0	0
$392$	7118.58	0.917200
$393$	6257.09	0.803126
$394$	−23733.5	−3.03471
$395$	−3293.41	−0.419518
$396$	11831.8	1.50144
$397$	−12102.6	−1.53000	−0.765002	−	0.644028i	$-0.777262\pi$
$397$	−12102.6	−1.53000	−0.765002	+	0.644028i	$0.777262\pi$
$398$	19482.5	2.45370
$399$	−2463.23	−0.309061
$400$	5504.18	0.688023
$401$	−9678.17	−1.20525	−0.602624	−	0.798025i	$-0.705878\pi$
$401$	−9678.17	−1.20525	−0.602624	+	0.798025i	$0.705878\pi$
$402$	−11312.7	−1.40355
$403$	−3103.45	−0.383607
$404$	−25356.3	−3.12258
$405$	3001.46	0.368257
$406$	−2390.44	−0.292206
$407$	−8932.47	−1.08788
$408$	0	0
$409$	4382.11	0.529784	0.264892	−	0.964278i	$-0.414664\pi$
$409$	4382.11	0.529784	0.264892	+	0.964278i	$0.414664\pi$
$410$	5414.96	0.652258
$411$	4163.25	0.499655
$412$	−6082.59	−0.727349
$413$	11279.1	1.34384
$414$	6031.48	0.716017
$415$	−3938.51	−0.465864
$416$	−9148.90	−1.07827
$417$	−946.189	−0.111115
$418$	7211.32	0.843821
$419$	−2651.71	−0.309176	−0.154588	−	0.987979i	$-0.549405\pi$
$419$	−2651.71	−0.309176	−0.154588	+	0.987979i	$0.549405\pi$
$420$	13540.8	1.57315
$421$	−1133.25	−0.131191	−0.0655954	−	0.997846i	$-0.520895\pi$
$421$	−1133.25	−0.131191	−0.0655954	+	0.997846i	$0.520895\pi$
$422$	−12261.0	−1.41436
$423$	−1058.15	−0.121629
$424$	26168.4	2.99729
$425$	0	0
$426$	1943.69	0.221062
$427$	14908.2	1.68960
$428$	−21143.5	−2.38788
$429$	6447.04	0.725562
$430$	23941.9	2.68507
$431$	16138.0	1.80357	0.901787	−	0.432180i	$-0.142256\pi$
$431$	16138.0	1.80357	0.901787	+	0.432180i	$0.142256\pi$
$432$	−12323.2	−1.37245
$433$	−1273.94	−0.141390	−0.0706950	−	0.997498i	$-0.522522\pi$
$433$	−1273.94	−0.141390	−0.0706950	+	0.997498i	$0.522522\pi$
$434$	4731.05	0.523267
$435$	−747.758	−0.0824190
$436$	17090.9	1.87730
$437$	2519.12	0.275758
$438$	6875.09	0.750010
$439$	−5326.71	−0.579112	−0.289556	−	0.957161i	$-0.593508\pi$
$439$	−5326.71	−0.579112	−0.289556	+	0.957161i	$0.593508\pi$
$440$	−21435.4	−2.32249
$441$	−3026.48	−0.326799
$442$	0	0
$443$	−2382.90	−0.255564	−0.127782	−	0.991802i	$-0.540786\pi$
$443$	−2382.90	−0.255564	−0.127782	+	0.991802i	$0.540786\pi$
$444$	12069.1	1.29003
$445$	−966.559	−0.102965
$446$	2946.96	0.312875
$447$	−1358.76	−0.143775
$448$	−3825.63	−0.403446
$449$	−8253.53	−0.867501	−0.433750	−	0.901033i	$-0.642810\pi$
$449$	−8253.53	−0.867501	−0.433750	+	0.901033i	$0.642810\pi$
$450$	−5598.98	−0.586530
$451$	−2693.32	−0.281205
$452$	23599.9	2.45585
$453$	−3019.53	−0.313179
$454$	−16312.8	−1.68634
$455$	−21871.2	−2.25349
$456$	−5268.61	−0.541064
$457$	−4710.14	−0.482125	−0.241063	−	0.970510i	$-0.577496\pi$
$457$	−4710.14	−0.482125	−0.241063	+	0.970510i	$0.577496\pi$
$458$	−15321.7	−1.56318
$459$	0	0
$460$	−13848.1	−1.40363
$461$	10294.3	1.04003	0.520016	−	0.854157i	$-0.325926\pi$
$461$	10294.3	1.04003	0.520016	+	0.854157i	$0.325926\pi$
$462$	−9828.18	−0.989715
$463$	3454.44	0.346742	0.173371	−	0.984857i	$-0.444534\pi$
$463$	3454.44	0.346742	0.173371	+	0.984857i	$0.444534\pi$
$464$	−2136.97	−0.213807
$465$	1479.93	0.147592
$466$	27161.6	2.70008
$467$	2128.17	0.210878	0.105439	−	0.994426i	$-0.466375\pi$
$467$	2128.17	0.210878	0.105439	+	0.994426i	$0.466375\pi$
$468$	25821.7	2.55044
$469$	−19088.5	−1.87938
$470$	3545.29	0.347940
$471$	−5970.12	−0.584053
$472$	24124.9	2.35262
$473$	−11908.4	−1.15760
$474$	−3229.83	−0.312976
$475$	−2338.49	−0.225889
$476$	0	0
$477$	−11125.6	−1.06793
$478$	−32944.7	−3.15242
$479$	12574.1	1.19942	0.599712	−	0.800216i	$-0.295282\pi$
$479$	12574.1	1.19942	0.599712	+	0.800216i	$0.295282\pi$
$480$	4362.80	0.414862
$481$	−19494.1	−1.84793
$482$	−11308.4	−1.06864
$483$	−3433.27	−0.323435
$484$	−3467.15	−0.325615
$485$	−18604.6	−1.74184
$486$	19707.7	1.83943
$487$	−20485.6	−1.90615	−0.953073	−	0.302740i	$-0.902099\pi$
$487$	−20485.6	−1.90615	−0.953073	+	0.302740i	$0.902099\pi$
$488$	31887.3	2.95793
$489$	9060.75	0.837917
$490$	10140.1	0.934860
$491$	10450.5	0.960539	0.480270	−	0.877121i	$-0.340539\pi$
$491$	10450.5	0.960539	0.480270	+	0.877121i	$0.340539\pi$
$492$	3639.08	0.333460
$493$	0	0
$494$	15737.9	1.43336
$495$	9113.33	0.827503
$496$	4229.40	0.382874
$497$	3279.69	0.296005
$498$	−3862.46	−0.347553
$499$	−6819.20	−0.611762	−0.305881	−	0.952070i	$-0.598951\pi$
$499$	−6819.20	−0.611762	−0.305881	+	0.952070i	$0.598951\pi$
$500$	−16357.7	−1.46308
$501$	1596.67	0.142383
$502$	9309.04	0.827655
$503$	8988.46	0.796771	0.398386	−	0.917218i	$-0.369571\pi$
$503$	8988.46	0.796771	0.398386	+	0.917218i	$0.369571\pi$
$504$	−21285.1	−1.88118
$505$	−19530.4	−1.72097
$506$	10051.2	0.883066
$507$	8336.32	0.730235
$508$	41413.0	3.61694
$509$	4660.74	0.405862	0.202931	−	0.979193i	$-0.434953\pi$
$509$	4660.74	0.405862	0.202931	+	0.979193i	$0.434953\pi$
$510$	0	0
$511$	11600.7	1.00427
$512$	−25545.9	−2.20504
$513$	5235.58	0.450597
$514$	−7847.06	−0.673383
$515$	−4685.05	−0.400869
$516$	16090.0	1.37272
$517$	−1763.37	−0.150006
$518$	29717.8	2.52071
$519$	−2803.21	−0.237085
$520$	−46780.5	−3.94511
$521$	2931.59	0.246517	0.123258	−	0.992375i	$-0.460666\pi$
$521$	2931.59	0.246517	0.123258	+	0.992375i	$0.460666\pi$
$522$	2173.78	0.182267
$523$	−4855.55	−0.405963	−0.202981	−	0.979183i	$-0.565063\pi$
$523$	−4855.55	−0.405963	−0.202981	+	0.979183i	$0.565063\pi$
$524$	41763.0	3.48173
$525$	3187.08	0.264944
$526$	−14752.2	−1.22286
$527$	0	0
$528$	−8786.06	−0.724174
$529$	−8655.81	−0.711417
$530$	37275.6	3.05500
$531$	−10256.8	−0.838240
$532$	−16440.8	−1.33985
$533$	−5877.88	−0.477672
$534$	−947.897	−0.0768156
$535$	−16285.6	−1.31605
$536$	−40828.6	−3.29016
$537$	3460.76	0.278106
$538$	34462.3	2.76167
$539$	−5043.52	−0.403042
$540$	−28780.9	−2.29358
$541$	−14604.2	−1.16060	−0.580300	−	0.814403i	$-0.697065\pi$
$541$	−14604.2	−1.16060	−0.580300	+	0.814403i	$0.697065\pi$
$542$	−7081.67	−0.561225
$543$	−6394.24	−0.505346
$544$	0	0
$545$	13164.0	1.03465
$546$	−21448.9	−1.68119
$547$	10928.1	0.854209	0.427105	−	0.904202i	$-0.359534\pi$
$547$	10928.1	0.854209	0.427105	+	0.904202i	$0.359534\pi$
$548$	27787.7	2.16611
$549$	−13557.0	−1.05391
$550$	−9330.48	−0.723369
$551$	907.906	0.0701962
$552$	−7343.45	−0.566228
$553$	−5449.85	−0.419080
$554$	10825.4	0.830196
$555$	9296.09	0.710985
$556$	−6315.35	−0.481710
$557$	20141.0	1.53214	0.766071	−	0.642756i	$-0.222209\pi$
$557$	20141.0	1.53214	0.766071	+	0.642756i	$0.222209\pi$
$558$	−4302.24	−0.326395
$559$	−25988.7	−1.96638
$560$	29806.2	2.24918
$561$	0	0
$562$	−2203.79	−0.165411
$563$	7089.55	0.530708	0.265354	−	0.964151i	$-0.414511\pi$
$563$	7089.55	0.530708	0.265354	+	0.964151i	$0.414511\pi$
$564$	2382.58	0.177881
$565$	18177.5	1.35351
$566$	34020.2	2.52646
$567$	4966.74	0.367872
$568$	7014.96	0.518206
$569$	22613.5	1.66609	0.833046	−	0.553204i	$-0.186595\pi$
$569$	22613.5	1.66609	0.833046	+	0.553204i	$0.186595\pi$
$570$	−7504.88	−0.551482
$571$	1483.70	0.108741	0.0543705	−	0.998521i	$-0.482685\pi$
$571$	1483.70	0.108741	0.0543705	+	0.998521i	$0.482685\pi$
$572$	43030.8	3.14547
$573$	−8293.57	−0.604658
$574$	8960.53	0.651577
$575$	−3259.41	−0.236394
$576$	3478.88	0.251655
$577$	23288.0	1.68023	0.840115	−	0.542408i	$-0.182487\pi$
$577$	23288.0	1.68023	0.840115	+	0.542408i	$0.182487\pi$
$578$	0	0
$579$	1316.30	0.0944792
$580$	−4990.92	−0.357305
$581$	−6517.33	−0.465378
$582$	−18245.4	−1.29948
$583$	−18540.3	−1.31709
$584$	24812.8	1.75815
$585$	19888.8	1.40565
$586$	6146.52	0.433294
$587$	3330.73	0.234197	0.117099	−	0.993120i	$-0.462641\pi$
$587$	3330.73	0.234197	0.117099	+	0.993120i	$0.462641\pi$
$588$	6814.55	0.477937
$589$	−1796.89	−0.125704
$590$	34364.7	2.39792
$591$	−12285.2	−0.855069
$592$	26566.7	1.84440
$593$	−5795.34	−0.401326	−0.200663	−	0.979660i	$-0.564310\pi$
$593$	−5795.34	−0.401326	−0.200663	+	0.979660i	$0.564310\pi$
$594$	20889.8	1.44296
$595$	0	0
$596$	−9069.08	−0.623295
$597$	10084.8	0.691362
$598$	21935.7	1.50003
$599$	9822.45	0.670007	0.335004	−	0.942217i	$-0.391262\pi$
$599$	9822.45	0.670007	0.335004	+	0.942217i	$0.391262\pi$
$600$	6816.87	0.463830
$601$	−24976.8	−1.69522	−0.847609	−	0.530622i	$-0.821958\pi$
$601$	−24976.8	−1.69522	−0.847609	+	0.530622i	$0.821958\pi$
$602$	39618.4	2.68227
$603$	17358.4	1.17229
$604$	−20153.9	−1.35770
$605$	−2670.53	−0.179459
$606$	−19153.3	−1.28391
$607$	12602.3	0.842689	0.421344	−	0.906901i	$-0.361558\pi$
$607$	12602.3	0.842689	0.421344	+	0.906901i	$0.361558\pi$
$608$	−5297.19	−0.353338
$609$	−1237.37	−0.0823329
$610$	45421.8	3.01488
$611$	−3848.37	−0.254809
$612$	0	0
$613$	−6503.06	−0.428476	−0.214238	−	0.976781i	$-0.568727\pi$
$613$	−6503.06	−0.428476	−0.214238	+	0.976781i	$0.568727\pi$
$614$	46574.3	3.06121
$615$	2802.96	0.183783
$616$	−35470.8	−2.32006
$617$	15511.7	1.01212	0.506061	−	0.862498i	$-0.331101\pi$
$617$	15511.7	1.01212	0.506061	+	0.862498i	$0.331101\pi$
$618$	−4594.59	−0.299064
$619$	−27666.3	−1.79645	−0.898226	−	0.439534i	$-0.855144\pi$
$619$	−27666.3	−1.79645	−0.898226	+	0.439534i	$0.855144\pi$
$620$	9877.80	0.639842
$621$	7297.41	0.471554
$622$	−3737.28	−0.240918
$623$	−1599.43	−0.102857
$624$	−19174.6	−1.23013
$625$	−19475.1	−1.24641
$626$	−949.850	−0.0606448
$627$	3732.81	0.237758
$628$	−39847.7	−2.53200
$629$	0	0
$630$	−30319.5	−1.91740
$631$	5269.63	0.332458	0.166229	−	0.986087i	$-0.446841\pi$
$631$	5269.63	0.332458	0.166229	+	0.986087i	$0.446841\pi$
$632$	−11656.7	−0.733670
$633$	−6346.72	−0.398514
$634$	−31676.6	−1.98429
$635$	31897.9	1.99343
$636$	25050.8	1.56184
$637$	−11006.9	−0.684631
$638$	3622.51	0.224791
$639$	−2982.43	−0.184637
$640$	−25029.6	−1.54591
$641$	−8458.94	−0.521230	−0.260615	−	0.965443i	$-0.583925\pi$
$641$	−8458.94	−0.521230	−0.260615	+	0.965443i	$0.583925\pi$
$642$	−15971.1	−0.981823
$643$	25746.8	1.57909	0.789545	−	0.613693i	$-0.210317\pi$
$643$	25746.8	1.57909	0.789545	+	0.613693i	$0.210317\pi$
$644$	−22915.4	−1.40216
$645$	12393.1	0.756556
$646$	0	0
$647$	−13724.8	−0.833968	−0.416984	−	0.908914i	$-0.636913\pi$
$647$	−13724.8	−0.833968	−0.416984	+	0.908914i	$0.636913\pi$
$648$	10623.4	0.644022
$649$	−17092.5	−1.03380
$650$	−20362.7	−1.22876
$651$	2448.95	0.147437
$652$	60476.1	3.63256
$653$	14415.2	0.863877	0.431939	−	0.901903i	$-0.357830\pi$
$653$	14415.2	0.863877	0.431939	+	0.901903i	$0.357830\pi$
$654$	12909.9	0.771891
$655$	32167.5	1.91891
$656$	8010.41	0.476759
$657$	−10549.2	−0.626430
$658$	5866.64	0.347577
$659$	−7405.85	−0.437771	−0.218885	−	0.975751i	$-0.570242\pi$
$659$	−7405.85	−0.437771	−0.218885	+	0.975751i	$0.570242\pi$
$660$	−20519.9	−1.21021
$661$	−19937.3	−1.17318	−0.586589	−	0.809885i	$-0.699530\pi$
$661$	−19937.3	−1.17318	−0.586589	+	0.809885i	$0.699530\pi$
$662$	−1273.90	−0.0747910
$663$	0	0
$664$	−13940.0	−0.814722
$665$	−12663.4	−0.738442
$666$	−27024.3	−1.57233
$667$	1265.45	0.0734609
$668$	10657.0	0.617262
$669$	1525.44	0.0881568
$670$	−58158.4	−3.35351
$671$	−22592.2	−1.29979
$672$	7219.44	0.414429
$673$	13809.6	0.790965	0.395483	−	0.918473i	$-0.370577\pi$
$673$	13809.6	0.790965	0.395483	+	0.918473i	$0.370577\pi$
$674$	−29289.1	−1.67385
$675$	−6774.14	−0.386276
$676$	55640.9	3.16573
$677$	6869.29	0.389968	0.194984	−	0.980806i	$-0.437535\pi$
$677$	6869.29	0.389968	0.194984	+	0.980806i	$0.437535\pi$
$678$	17826.6	1.00977
$679$	−30786.4	−1.74002
$680$	0	0
$681$	−8444.06	−0.475150
$682$	−7169.52	−0.402544
$683$	−4911.19	−0.275141	−0.137571	−	0.990492i	$-0.543929\pi$
$683$	−4911.19	−0.275141	−0.137571	+	0.990492i	$0.543929\pi$
$684$	14950.7	0.835750
$685$	21403.1	1.19383
$686$	−21613.7	−1.20294
$687$	−7931.03	−0.440448
$688$	35417.5	1.96262
$689$	−40462.2	−2.23728
$690$	−10460.4	−0.577130
$691$	30039.7	1.65378	0.826891	−	0.562363i	$-0.190108\pi$
$691$	30039.7	1.65378	0.826891	+	0.562363i	$0.190108\pi$
$692$	−18710.0	−1.02782
$693$	15080.5	0.826638
$694$	−30056.6	−1.64400
$695$	−4864.33	−0.265488
$696$	−2646.62	−0.144138
$697$	0	0
$698$	−3029.06	−0.164257
$699$	14059.7	0.760784
$700$	21272.2	1.14859
$701$	−4144.68	−0.223313	−0.111657	−	0.993747i	$-0.535616\pi$
$701$	−4144.68	−0.223313	−0.111657	+	0.993747i	$0.535616\pi$
$702$	45589.6	2.45110
$703$	−11287.0	−0.605546
$704$	5797.42	0.310367
$705$	1835.16	0.0980368
$706$	48988.6	2.61149
$707$	−32318.4	−1.71918
$708$	23094.5	1.22591
$709$	−18027.8	−0.954935	−0.477468	−	0.878649i	$-0.658445\pi$
$709$	−18027.8	−0.954935	−0.477468	+	0.878649i	$0.658445\pi$
$710$	9992.46	0.528184
$711$	4955.89	0.261407
$712$	−3421.04	−0.180069
$713$	−2504.52	−0.131550
$714$	0	0
$715$	33144.0	1.73359
$716$	23098.9	1.20565
$717$	−17053.2	−0.888236
$718$	−36181.5	−1.88061
$719$	4482.73	0.232514	0.116257	−	0.993219i	$-0.462910\pi$
$719$	4482.73	0.232514	0.116257	+	0.993219i	$0.462910\pi$
$720$	−27104.6	−1.40296
$721$	−7752.68	−0.400451
$722$	−25468.9	−1.31282
$723$	−5853.59	−0.301103
$724$	−42678.4	−2.19079
$725$	−1174.71	−0.0601760
$726$	−2618.97	−0.133883
$727$	15342.7	0.782709	0.391355	−	0.920240i	$-0.372007\pi$
$727$	15342.7	0.782709	0.391355	+	0.920240i	$0.372007\pi$
$728$	−77411.0	−3.94099
$729$	4161.14	0.211408
$730$	35344.6	1.79200
$731$	0	0
$732$	30525.4	1.54133
$733$	−35022.1	−1.76476	−0.882381	−	0.470536i	$-0.844061\pi$
$733$	−35022.1	−1.76476	−0.882381	+	0.470536i	$0.844061\pi$
$734$	22810.5	1.14707
$735$	5248.83	0.263409
$736$	−7383.28	−0.369771
$737$	28927.1	1.44579
$738$	−8148.37	−0.406430
$739$	−8292.46	−0.412778	−0.206389	−	0.978470i	$-0.566171\pi$
$739$	−8292.46	−0.412778	−0.206389	+	0.978470i	$0.566171\pi$
$740$	62046.8	3.08228
$741$	8146.45	0.403870
$742$	61682.7	3.05181
$743$	29918.5	1.47726	0.738630	−	0.674111i	$-0.235473\pi$
$743$	29918.5	1.47726	0.738630	+	0.674111i	$0.235473\pi$
$744$	5238.07	0.258114
$745$	−6985.36	−0.343522
$746$	−11428.0	−0.560867
$747$	5926.61	0.290286
$748$	0	0
$749$	−26948.9	−1.31467
$750$	−12356.1	−0.601572
$751$	−3090.08	−0.150145	−0.0750723	−	0.997178i	$-0.523919\pi$
$751$	−3090.08	−0.150145	−0.0750723	+	0.997178i	$0.523919\pi$
$752$	5244.58	0.254322
$753$	4818.66	0.233203
$754$	7905.74	0.381844
$755$	−15523.3	−0.748279
$756$	−47625.8	−2.29118
$757$	−8344.86	−0.400659	−0.200330	−	0.979729i	$-0.564201\pi$
$757$	−8344.86	−0.400659	−0.200330	+	0.979729i	$0.564201\pi$
$758$	−29899.6	−1.43272
$759$	5202.84	0.248816
$760$	−27085.7	−1.29277
$761$	−4825.17	−0.229845	−0.114923	−	0.993374i	$-0.536662\pi$
$761$	−4825.17	−0.229845	−0.114923	+	0.993374i	$0.536662\pi$
$762$	31282.0	1.48718
$763$	21783.5	1.03357
$764$	−55355.5	−2.62133
$765$	0	0
$766$	57340.7	2.70471
$767$	−37302.5	−1.75608
$768$	−20948.8	−0.984278
$769$	−14268.8	−0.669110	−0.334555	−	0.942376i	$-0.608586\pi$
$769$	−14268.8	−0.669110	−0.334555	+	0.942376i	$0.608586\pi$
$770$	−50526.3	−2.36473
$771$	−4061.89	−0.189735
$772$	8785.65	0.409588
$773$	4746.48	0.220853	0.110426	−	0.993884i	$-0.464778\pi$
$773$	4746.48	0.220853	0.110426	+	0.993884i	$0.464778\pi$
$774$	−36027.5	−1.67310
$775$	2324.93	0.107760
$776$	−65849.2	−3.04620
$777$	15382.9	0.710243
$778$	−64065.9	−2.95228
$779$	−3403.27	−0.156527
$780$	−44782.5	−2.05573
$781$	−4970.10	−0.227714
$782$	0	0
$783$	2630.03	0.120038
$784$	15000.3	0.683322
$785$	−30692.2	−1.39548
$786$	31546.4	1.43158
$787$	4925.33	0.223086	0.111543	−	0.993760i	$-0.464421\pi$
$787$	4925.33	0.223086	0.111543	+	0.993760i	$0.464421\pi$
$788$	−81997.8	−3.70691
$789$	−7636.21	−0.344558
$790$	−16604.4	−0.747796
$791$	30079.6	1.35210
$792$	32255.8	1.44717
$793$	−49304.9	−2.20790
$794$	−61017.7	−2.72725
$795$	19295.1	0.860787
$796$	67311.1	2.99721
$797$	38377.6	1.70565	0.852826	−	0.522195i	$-0.174887\pi$
$797$	38377.6	1.70565	0.852826	+	0.522195i	$0.174887\pi$
$798$	−12418.9	−0.550906
$799$	0	0
$800$	6853.85	0.302900
$801$	1454.47	0.0641586
$802$	−48794.5	−2.14837
$803$	−17579.9	−0.772578
$804$	−39084.9	−1.71445
$805$	−17650.3	−0.772785
$806$	−15646.7	−0.683785
$807$	17838.8	0.778136
$808$	−69126.0	−3.00971
$809$	9966.44	0.433129	0.216565	−	0.976268i	$-0.430515\pi$
$809$	9966.44	0.433129	0.216565	+	0.976268i	$0.430515\pi$
$810$	15132.5	0.656422
$811$	35469.1	1.53574	0.767871	−	0.640604i	$-0.221316\pi$
$811$	35469.1	1.53574	0.767871	+	0.640604i	$0.221316\pi$
$812$	−8258.84	−0.356931
$813$	−3665.70	−0.158133
$814$	−45034.9	−1.93916
$815$	46581.0	2.00204
$816$	0	0
$817$	−15047.4	−0.644358
$818$	22093.3	0.944346
$819$	32911.5	1.40418
$820$	18708.4	0.796738
$821$	−19408.8	−0.825058	−0.412529	−	0.910944i	$-0.635354\pi$
$821$	−19408.8	−0.825058	−0.412529	+	0.910944i	$0.635354\pi$
$822$	20989.9	0.890641
$823$	19804.6	0.838815	0.419407	−	0.907798i	$-0.362238\pi$
$823$	19804.6	0.838815	0.419407	+	0.907798i	$0.362238\pi$
$824$	−16582.3	−0.701057
$825$	−4829.76	−0.203819
$826$	56865.8	2.39542
$827$	30581.1	1.28586	0.642932	−	0.765923i	$-0.277718\pi$
$827$	30581.1	1.28586	0.642932	+	0.765923i	$0.277718\pi$
$828$	20838.4	0.874619
$829$	15945.5	0.668046	0.334023	−	0.942565i	$-0.391594\pi$
$829$	15945.5	0.668046	0.334023	+	0.942565i	$0.391594\pi$
$830$	−19856.8	−0.830409
$831$	5603.60	0.233919
$832$	12652.2	0.527208
$833$	0	0
$834$	−4770.41	−0.198065
$835$	8208.41	0.340196
$836$	24914.7	1.03073
$837$	−5205.23	−0.214957
$838$	−13369.2	−0.551110
$839$	20434.3	0.840848	0.420424	−	0.907328i	$-0.361881\pi$
$839$	20434.3	0.840848	0.420424	+	0.907328i	$0.361881\pi$
$840$	36914.7	1.51628
$841$	−23932.9	−0.981300
$842$	−5713.53	−0.233849
$843$	−1140.75	−0.0466069
$844$	−42361.2	−1.72765
$845$	42856.7	1.74475
$846$	−5334.90	−0.216806
$847$	−4419.12	−0.179271
$848$	55142.2	2.23301
$849$	17609.9	0.711863
$850$	0	0
$851$	−15732.0	−0.633709
$852$	6715.35	0.270028
$853$	7508.30	0.301382	0.150691	−	0.988581i	$-0.451850\pi$
$853$	7508.30	0.301382	0.150691	+	0.988581i	$0.451850\pi$
$854$	75162.8	3.01173
$855$	11515.6	0.460613
$856$	−57641.2	−2.30156
$857$	4013.00	0.159955	0.0799776	−	0.996797i	$-0.474515\pi$
$857$	4013.00	0.159955	0.0799776	+	0.996797i	$0.474515\pi$
$858$	32504.1	1.29332
$859$	32674.1	1.29782	0.648910	−	0.760865i	$-0.275225\pi$
$859$	32674.1	1.29782	0.648910	+	0.760865i	$0.275225\pi$
$860$	82718.0	3.27984
$861$	4638.26	0.183591
$862$	81363.1	3.21489
$863$	−9829.13	−0.387703	−0.193851	−	0.981031i	$-0.562098\pi$
$863$	−9829.13	−0.387703	−0.193851	+	0.981031i	$0.562098\pi$
$864$	−15344.9	−0.604218
$865$	−14411.2	−0.566469
$866$	−6422.85	−0.252029
$867$	0	0
$868$	16345.5	0.639174
$869$	8258.79	0.322394
$870$	−3769.98	−0.146913
$871$	63130.2	2.45590
$872$	46592.9	1.80944
$873$	27996.0	1.08536
$874$	12700.7	0.491542
$875$	−20849.0	−0.805514
$876$	23753.0	0.916143
$877$	17731.1	0.682711	0.341356	−	0.939934i	$-0.389114\pi$
$877$	17731.1	0.682711	0.341356	+	0.939934i	$0.389114\pi$
$878$	−26855.7	−1.03227
$879$	3181.64	0.122086
$880$	−45168.8	−1.73027
$881$	18721.4	0.715937	0.357969	−	0.933734i	$-0.383470\pi$
$881$	18721.4	0.715937	0.357969	+	0.933734i	$0.383470\pi$
$882$	−15258.6	−0.582523
$883$	−19025.1	−0.725079	−0.362539	−	0.931968i	$-0.618090\pi$
$883$	−19025.1	−0.725079	−0.362539	+	0.931968i	$0.618090\pi$
$884$	0	0
$885$	17788.3	0.675646
$886$	−12013.9	−0.455546
$887$	30933.2	1.17095	0.585476	−	0.810689i	$-0.300907\pi$
$887$	30933.2	1.17095	0.585476	+	0.810689i	$0.300907\pi$
$888$	32902.6	1.24340
$889$	52783.7	1.99135
$890$	−4873.11	−0.183536
$891$	−7526.68	−0.283000
$892$	10181.6	0.382179
$893$	−2228.19	−0.0834979
$894$	−6850.49	−0.256280
$895$	17791.7	0.664480
$896$	−41418.4	−1.54430
$897$	11354.6	0.422653
$898$	−41611.9	−1.54633
$899$	−902.643	−0.0334870
$900$	−19344.2	−0.716450
$901$	0	0
$902$	−13578.9	−0.501252
$903$	20507.8	0.755766
$904$	64337.6	2.36707
$905$	−32872.6	−1.20743
$906$	−15223.6	−0.558245
$907$	−17462.3	−0.639280	−0.319640	−	0.947539i	$-0.603562\pi$
$907$	−17462.3	−0.639280	−0.319640	+	0.947539i	$0.603562\pi$
$908$	−56360.0	−2.05988
$909$	29389.1	1.07236
$910$	−110268.	−4.01687
$911$	50841.6	1.84902	0.924510	−	0.381158i	$-0.124475\pi$
$911$	50841.6	1.84902	0.924510	+	0.381158i	$0.124475\pi$
$912$	−11102.0	−0.403098
$913$	9876.48	0.358011
$914$	−23747.2	−0.859394
$915$	23511.8	0.849483
$916$	−52935.7	−1.90944
$917$	53229.9	1.91691
$918$	0	0
$919$	−2252.46	−0.0808508	−0.0404254	−	0.999183i	$-0.512871\pi$
$919$	−2252.46	−0.0808508	−0.0404254	+	0.999183i	$0.512871\pi$
$920$	−37752.4	−1.35289
$921$	24108.3	0.862538
$922$	51901.0	1.85387
$923$	−10846.7	−0.386808
$924$	−33955.8	−1.20894
$925$	14603.9	0.519107
$926$	17416.3	0.618073
$927$	7050.00	0.249787
$928$	−2660.97	−0.0941279
$929$	15783.0	0.557398	0.278699	−	0.960379i	$-0.410097\pi$
$929$	15783.0	0.557398	0.278699	+	0.960379i	$0.410097\pi$
$930$	7461.37	0.263084
$931$	−6372.97	−0.224346
$932$	93841.8	3.29817
$933$	−1934.54	−0.0678820
$934$	10729.6	0.375892
$935$	0	0
$936$	70394.6	2.45825
$937$	−51506.8	−1.79579	−0.897894	−	0.440211i	$-0.854904\pi$
$937$	−51506.8	−1.79579	−0.897894	+	0.440211i	$0.854904\pi$
$938$	−96238.9	−3.35001
$939$	−491.673	−0.0170875
$940$	12248.8	0.425011
$941$	−7103.99	−0.246104	−0.123052	−	0.992400i	$-0.539268\pi$
$941$	−7103.99	−0.246104	−0.123052	+	0.992400i	$0.539268\pi$
$942$	−30099.6	−1.04108
$943$	−4743.52	−0.163807
$944$	50836.1	1.75273
$945$	−36683.2	−1.26276
$946$	−60038.5	−2.06344
$947$	−24874.2	−0.853542	−0.426771	−	0.904360i	$-0.640349\pi$
$947$	−24874.2	−0.853542	−0.426771	+	0.904360i	$0.640349\pi$
$948$	−11158.9	−0.382303
$949$	−38366.1	−1.31235
$950$	−11790.0	−0.402650
$951$	−16396.9	−0.559101
$952$	0	0
$953$	15169.7	0.515630	0.257815	−	0.966194i	$-0.416997\pi$
$953$	15169.7	0.515630	0.257815	+	0.966194i	$0.416997\pi$
$954$	−56091.9	−1.90361
$955$	−42637.0	−1.44471
$956$	−113822.	−3.85070
$957$	1875.13	0.0633379
$958$	63394.8	2.13799
$959$	35417.3	1.19258
$960$	−6033.42	−0.202841
$961$	−28004.5	−0.940033
$962$	−98283.7	−3.29396
$963$	24506.3	0.820047
$964$	−39069.8	−1.30535
$965$	6767.04	0.225740
$966$	−17309.6	−0.576528
$967$	44604.0	1.48332	0.741659	−	0.670777i	$-0.234039\pi$
$967$	44604.0	1.48332	0.741659	+	0.670777i	$0.234039\pi$
$968$	−9452.09	−0.313845
$969$	0	0
$970$	−93799.0	−3.10485
$971$	−7770.42	−0.256812	−0.128406	−	0.991722i	$-0.540986\pi$
$971$	−7770.42	−0.256812	−0.128406	+	0.991722i	$0.540986\pi$
$972$	68089.1	2.24687
$973$	−8049.35	−0.265211
$974$	−103283.	−3.39773
$975$	−10540.4	−0.346219
$976$	67193.0	2.20368
$977$	−40455.1	−1.32474	−0.662371	−	0.749176i	$-0.730450\pi$
$977$	−40455.1	−1.32474	−0.662371	+	0.749176i	$0.730450\pi$
$978$	45681.7	1.49360
$979$	2423.81	0.0791270
$980$	35033.3	1.14194
$981$	−19809.1	−0.644705
$982$	52688.4	1.71217
$983$	16755.2	0.543649	0.271825	−	0.962347i	$-0.412373\pi$
$983$	16755.2	0.543649	0.271825	+	0.962347i	$0.412373\pi$
$984$	9920.81	0.321406
$985$	−63157.8	−2.04302
$986$	0	0
$987$	3036.76	0.0979344
$988$	54373.6	1.75087
$989$	−20973.2	−0.674326
$990$	45946.8	1.47503
$991$	7953.79	0.254955	0.127478	−	0.991841i	$-0.459312\pi$
$991$	7953.79	0.254955	0.127478	+	0.991841i	$0.459312\pi$
$992$	5266.48	0.168559
$993$	−659.414	−0.0210734
$994$	16535.2	0.527632
$995$	51845.6	1.65188
$996$	−13344.6	−0.424538
$997$	−27528.7	−0.874466	−0.437233	−	0.899348i	$-0.644041\pi$
$997$	−27528.7	−0.874466	−0.437233	+	0.899348i	$0.644041\pi$
$998$	−34380.4	−1.09047
$999$	−32696.3	−1.03550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.a.c.1.4	✓	4
17.4	even	4		289.4.b.d.288.1		8
17.13	even	4		289.4.b.d.288.2		8
17.16	even	2		289.4.a.d.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.4.a.c.1.4	✓	4	1.1	even	1	trivial
289.4.a.d.1.4	yes	4	17.16	even	2
289.4.b.d.288.1		8	17.4	even	4
289.4.b.d.288.2		8	17.13	even	4

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+5.04171 q^{2} +2.60975 q^{3} +17.4188 q^{4} +13.4166 q^{5} +13.1576 q^{6} +22.2015 q^{7} +47.4869 q^{8} -20.1892 q^{9} +O(q^{10})\)	\(q+5.04171 q^{2} +2.60975 q^{3} +17.4188 q^{4} +13.4166 q^{5} +13.1576 q^{6} +22.2015 q^{7} +47.4869 q^{8} -20.1892 q^{9} +67.6428 q^{10} -33.6445 q^{11} +45.4588 q^{12} -73.4255 q^{13} +111.933 q^{14} +35.0141 q^{15} +100.065 q^{16} -101.788 q^{18} -42.5131 q^{19} +233.702 q^{20} +57.9404 q^{21} -169.626 q^{22} -59.2553 q^{23} +123.929 q^{24} +55.0063 q^{25} -370.190 q^{26} -123.152 q^{27} +386.724 q^{28} -21.3559 q^{29} +176.531 q^{30} +42.2667 q^{31} +124.601 q^{32} -87.8038 q^{33} +297.869 q^{35} -351.672 q^{36} +265.496 q^{37} -214.339 q^{38} -191.622 q^{39} +637.115 q^{40} +80.0523 q^{41} +292.118 q^{42} +353.946 q^{43} -586.048 q^{44} -270.871 q^{45} -298.748 q^{46} +52.4119 q^{47} +261.144 q^{48} +149.906 q^{49} +277.325 q^{50} -1278.98 q^{52} +551.066 q^{53} -620.897 q^{54} -451.396 q^{55} +1054.28 q^{56} -110.949 q^{57} -107.670 q^{58} +508.032 q^{59} +609.904 q^{60} +671.496 q^{61} +213.096 q^{62} -448.230 q^{63} -172.314 q^{64} -985.123 q^{65} -442.681 q^{66} -859.787 q^{67} -154.642 q^{69} +1501.77 q^{70} +147.724 q^{71} -958.723 q^{72} +522.518 q^{73} +1338.55 q^{74} +143.553 q^{75} -740.528 q^{76} -746.958 q^{77} -966.103 q^{78} -245.472 q^{79} +1342.53 q^{80} +223.712 q^{81} +403.600 q^{82} -293.554 q^{83} +1009.25 q^{84} +1784.49 q^{86} -55.7336 q^{87} -1597.67 q^{88} -72.0418 q^{89} -1365.65 q^{90} -1630.15 q^{91} -1032.16 q^{92} +110.305 q^{93} +264.245 q^{94} -570.383 q^{95} +325.178 q^{96} -1386.68 q^{97} +755.782 q^{98} +679.256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} + 11 q^{4} + 14 q^{5} + 38 q^{6} + 36 q^{7} + 60 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 + 11 * q^4 + 14 * q^5 + 38 * q^6 + 36 * q^7 + 60 * q^8 + 6 * q^9	\( 4 q + q^{2} - 2 q^{3} + 11 q^{4} + 14 q^{5} + 38 q^{6} + 36 q^{7} + 60 q^{8} + 6 q^{9} - 7 q^{10} + 10 q^{11} - 29 q^{12} - 22 q^{13} + 73 q^{14} + 54 q^{15} + 63 q^{16} - 334 q^{18} + 22 q^{19} + 330 q^{20} - 352 q^{21} - 79 q^{22} + 380 q^{23} + 159 q^{24} + 378 q^{25} - 448 q^{26} - 494 q^{27} + 608 q^{28} - 78 q^{29} + 313 q^{30} + 362 q^{31} + 331 q^{32} + 94 q^{33} - 242 q^{35} + 141 q^{36} + 512 q^{37} - 524 q^{38} + 12 q^{39} + 1381 q^{40} + 840 q^{41} + 1455 q^{42} - 114 q^{43} - 1041 q^{44} + 648 q^{45} - 1051 q^{46} + 10 q^{47} + 998 q^{48} + 1006 q^{49} + 805 q^{50} - 1537 q^{52} + 50 q^{53} + 581 q^{54} - 1316 q^{55} + 411 q^{56} + 358 q^{57} - 376 q^{58} + 996 q^{59} - 217 q^{60} + 448 q^{61} - 73 q^{62} + 766 q^{63} - 150 q^{64} - 372 q^{65} - 1090 q^{66} - 868 q^{67} - 1128 q^{69} + 1052 q^{70} + 1116 q^{71} - 39 q^{72} + 540 q^{73} + 1630 q^{74} + 1070 q^{75} - 873 q^{76} - 894 q^{77} - 1245 q^{78} + 940 q^{79} + 307 q^{80} + 1080 q^{81} - 334 q^{82} + 850 q^{83} + 443 q^{84} + 2411 q^{86} - 384 q^{87} - 2252 q^{88} + 784 q^{89} - 2069 q^{90} - 2858 q^{91} - 1566 q^{92} - 1550 q^{93} + 1119 q^{94} + 2494 q^{95} - 2643 q^{96} - 518 q^{97} - 1877 q^{98} - 1406 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 + 11 * q^4 + 14 * q^5 + 38 * q^6 + 36 * q^7 + 60 * q^8 + 6 * q^9 - 7 * q^10 + 10 * q^11 - 29 * q^12 - 22 * q^13 + 73 * q^14 + 54 * q^15 + 63 * q^16 - 334 * q^18 + 22 * q^19 + 330 * q^20 - 352 * q^21 - 79 * q^22 + 380 * q^23 + 159 * q^24 + 378 * q^25 - 448 * q^26 - 494 * q^27 + 608 * q^28 - 78 * q^29 + 313 * q^30 + 362 * q^31 + 331 * q^32 + 94 * q^33 - 242 * q^35 + 141 * q^36 + 512 * q^37 - 524 * q^38 + 12 * q^39 + 1381 * q^40 + 840 * q^41 + 1455 * q^42 - 114 * q^43 - 1041 * q^44 + 648 * q^45 - 1051 * q^46 + 10 * q^47 + 998 * q^48 + 1006 * q^49 + 805 * q^50 - 1537 * q^52 + 50 * q^53 + 581 * q^54 - 1316 * q^55 + 411 * q^56 + 358 * q^57 - 376 * q^58 + 996 * q^59 - 217 * q^60 + 448 * q^61 - 73 * q^62 + 766 * q^63 - 150 * q^64 - 372 * q^65 - 1090 * q^66 - 868 * q^67 - 1128 * q^69 + 1052 * q^70 + 1116 * q^71 - 39 * q^72 + 540 * q^73 + 1630 * q^74 + 1070 * q^75 - 873 * q^76 - 894 * q^77 - 1245 * q^78 + 940 * q^79 + 307 * q^80 + 1080 * q^81 - 334 * q^82 + 850 * q^83 + 443 * q^84 + 2411 * q^86 - 384 * q^87 - 2252 * q^88 + 784 * q^89 - 2069 * q^90 - 2858 * q^91 - 1566 * q^92 - 1550 * q^93 + 1119 * q^94 + 2494 * q^95 - 2643 * q^96 - 518 * q^97 - 1877 * q^98 - 1406 * q^99

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