LMFDB - Embedded newform 1859.4.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + \cdots + 2596992 $ x^17 - 4x^16 - 99x^15 + 375x^14 + 3949x^13 - 13998x^12 - 81750x^11 + 267574x^10 + 941923x^9 - 2799440x^8 - 6021311x^7 + 15765187x^6 + 20197463x^5 - 42560950x^4 - 32766128x^3 + 37775816x^2 + 27375104x + 2596992
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.74484$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74484 q^{2} -4.19208 q^{3} -0.465832 q^{4} -5.57379 q^{5} +11.5066 q^{6} +6.88148 q^{7} +23.2374 q^{8} -9.42645 q^{9} +O(q^{10})$	\(q-2.74484 q^{2} -4.19208 q^{3} -0.465832 q^{4} -5.57379 q^{5} +11.5066 q^{6} +6.88148 q^{7} +23.2374 q^{8} -9.42645 q^{9} +15.2992 q^{10} +11.0000 q^{11} +1.95281 q^{12} -18.8886 q^{14} +23.3658 q^{15} -60.0563 q^{16} -96.9572 q^{17} +25.8741 q^{18} +91.3208 q^{19} +2.59645 q^{20} -28.8477 q^{21} -30.1933 q^{22} +4.92652 q^{23} -97.4130 q^{24} -93.9329 q^{25} +152.703 q^{27} -3.20562 q^{28} +120.698 q^{29} -64.1354 q^{30} -62.6271 q^{31} -21.0538 q^{32} -46.1129 q^{33} +266.132 q^{34} -38.3559 q^{35} +4.39115 q^{36} -59.9413 q^{37} -250.661 q^{38} -129.520 q^{40} +54.8955 q^{41} +79.1826 q^{42} -418.966 q^{43} -5.12415 q^{44} +52.5411 q^{45} -13.5225 q^{46} +158.651 q^{47} +251.761 q^{48} -295.645 q^{49} +257.831 q^{50} +406.453 q^{51} +89.8532 q^{53} -419.145 q^{54} -61.3117 q^{55} +159.908 q^{56} -382.824 q^{57} -331.298 q^{58} -658.045 q^{59} -10.8845 q^{60} +439.684 q^{61} +171.901 q^{62} -64.8680 q^{63} +538.240 q^{64} +126.573 q^{66} +1051.80 q^{67} +45.1658 q^{68} -20.6524 q^{69} +105.281 q^{70} -1077.54 q^{71} -219.046 q^{72} +338.912 q^{73} +164.530 q^{74} +393.774 q^{75} -42.5402 q^{76} +75.6963 q^{77} +664.285 q^{79} +334.741 q^{80} -385.628 q^{81} -150.680 q^{82} +1011.19 q^{83} +13.4382 q^{84} +540.419 q^{85} +1150.00 q^{86} -505.977 q^{87} +255.611 q^{88} +237.802 q^{89} -144.217 q^{90} -2.29493 q^{92} +262.538 q^{93} -435.472 q^{94} -509.003 q^{95} +88.2593 q^{96} +150.055 q^{97} +811.500 q^{98} -103.691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 95 q^{12} - 60 q^{14} + 28 q^{15} + 350 q^{16} + 118 q^{17} - 478 q^{18} - 403 q^{19} - 98 q^{20} - 220 q^{21} - 44 q^{22} - 215 q^{23} - 26 q^{24} + 319 q^{25} - 384 q^{27} + 396 q^{28} - 7 q^{29} - 1269 q^{30} - 682 q^{31} - 813 q^{32} - 66 q^{33} - 738 q^{34} + 10 q^{35} + 560 q^{36} - 1084 q^{37} + 410 q^{38} + 95 q^{40} - 240 q^{41} + 393 q^{42} - 435 q^{43} + 858 q^{44} - 1242 q^{45} - 1671 q^{46} - 549 q^{47} + 894 q^{48} + 403 q^{49} + 651 q^{50} + 1552 q^{51} - 566 q^{53} - 311 q^{54} - 176 q^{55} - 1925 q^{56} + 534 q^{57} - 618 q^{58} - 2010 q^{59} + 411 q^{60} + 460 q^{61} - 823 q^{62} - 820 q^{63} + 3171 q^{64} - 154 q^{66} + 232 q^{67} + 1795 q^{68} - 1608 q^{69} - 207 q^{70} - 489 q^{71} - 2556 q^{72} - 290 q^{73} + 2653 q^{74} - 2852 q^{75} - 2421 q^{76} + 66 q^{77} - 732 q^{79} - 4915 q^{80} + 2393 q^{81} - 1772 q^{82} + 117 q^{83} - 4161 q^{84} - 4858 q^{85} - 1034 q^{86} + 3032 q^{87} - 693 q^{88} - 4113 q^{89} + 15145 q^{90} - 3554 q^{92} - 802 q^{93} + 2325 q^{94} - 3924 q^{95} - 2601 q^{96} - 2793 q^{97} - 533 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 95 * q^12 - 60 * q^14 + 28 * q^15 + 350 * q^16 + 118 * q^17 - 478 * q^18 - 403 * q^19 - 98 * q^20 - 220 * q^21 - 44 * q^22 - 215 * q^23 - 26 * q^24 + 319 * q^25 - 384 * q^27 + 396 * q^28 - 7 * q^29 - 1269 * q^30 - 682 * q^31 - 813 * q^32 - 66 * q^33 - 738 * q^34 + 10 * q^35 + 560 * q^36 - 1084 * q^37 + 410 * q^38 + 95 * q^40 - 240 * q^41 + 393 * q^42 - 435 * q^43 + 858 * q^44 - 1242 * q^45 - 1671 * q^46 - 549 * q^47 + 894 * q^48 + 403 * q^49 + 651 * q^50 + 1552 * q^51 - 566 * q^53 - 311 * q^54 - 176 * q^55 - 1925 * q^56 + 534 * q^57 - 618 * q^58 - 2010 * q^59 + 411 * q^60 + 460 * q^61 - 823 * q^62 - 820 * q^63 + 3171 * q^64 - 154 * q^66 + 232 * q^67 + 1795 * q^68 - 1608 * q^69 - 207 * q^70 - 489 * q^71 - 2556 * q^72 - 290 * q^73 + 2653 * q^74 - 2852 * q^75 - 2421 * q^76 + 66 * q^77 - 732 * q^79 - 4915 * q^80 + 2393 * q^81 - 1772 * q^82 + 117 * q^83 - 4161 * q^84 - 4858 * q^85 - 1034 * q^86 + 3032 * q^87 - 693 * q^88 - 4113 * q^89 + 15145 * q^90 - 3554 * q^92 - 802 * q^93 + 2325 * q^94 - 3924 * q^95 - 2601 * q^96 - 2793 * q^97 - 533 * q^98 + 1485 * 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 $

$2$	−2.74484	−0.970449	−0.485224	−	0.874390i	$-0.661262\pi$
$2$	−2.74484	−0.970449	−0.485224	+	0.874390i	$0.661262\pi$
$3$	−4.19208	−0.806766	−0.403383	−	0.915031i	$-0.632166\pi$
$3$	−4.19208	−0.806766	−0.403383	+	0.915031i	$0.632166\pi$
$4$	−0.465832	−0.0582290
$5$	−5.57379	−0.498535	−0.249267	−	0.968435i	$-0.580190\pi$
$5$	−5.57379	−0.498535	−0.249267	+	0.968435i	$0.580190\pi$
$6$	11.5066	0.782926
$7$	6.88148	0.371565	0.185783	−	0.982591i	$-0.440518\pi$
$7$	6.88148	0.371565	0.185783	+	0.982591i	$0.440518\pi$
$8$	23.2374	1.02696
$9$	−9.42645	−0.349128
$10$	15.2992	0.483803
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	1.95281	0.0469772
$13$	0	0
$13$	0	0
$14$	−18.8886	−0.360585
$15$	23.3658	0.402201
$16$	−60.0563	−0.938380
$17$	−96.9572	−1.38327	−0.691635	−	0.722247i	$-0.743109\pi$
$17$	−96.9572	−1.38327	−0.691635	+	0.722247i	$0.743109\pi$
$18$	25.8741	0.338811
$19$	91.3208	1.10265	0.551327	−	0.834289i	$-0.314122\pi$
$19$	91.3208	1.10265	0.551327	+	0.834289i	$0.314122\pi$
$20$	2.59645	0.0290292
$21$	−28.8477	−0.299766
$22$	−30.1933	−0.292601
$23$	4.92652	0.0446630	0.0223315	−	0.999751i	$-0.492891\pi$
$23$	4.92652	0.0446630	0.0223315	+	0.999751i	$0.492891\pi$
$24$	−97.4130	−0.828515
$25$	−93.9329	−0.751463
$26$	0	0
$27$	152.703	1.08843
$28$	−3.20562	−0.0216359
$29$	120.698	0.772865	0.386433	−	0.922318i	$-0.373707\pi$
$29$	120.698	0.772865	0.386433	+	0.922318i	$0.373707\pi$
$30$	−64.1354	−0.390316
$31$	−62.6271	−0.362844	−0.181422	−	0.983405i	$-0.558070\pi$
$31$	−62.6271	−0.362844	−0.181422	+	0.983405i	$0.558070\pi$
$32$	−21.0538	−0.116307
$33$	−46.1129	−0.243249
$34$	266.132	1.34239
$35$	−38.3559	−0.185238
$36$	4.39115	0.0203294
$37$	−59.9413	−0.266332	−0.133166	−	0.991094i	$-0.542514\pi$
$37$	−59.9413	−0.266332	−0.133166	+	0.991094i	$0.542514\pi$
$38$	−250.661	−1.07007
$39$	0	0
$40$	−129.520	−0.511974
$41$	54.8955	0.209103	0.104552	−	0.994519i	$-0.466659\pi$
$41$	54.8955	0.209103	0.104552	+	0.994519i	$0.466659\pi$
$42$	79.1826	0.290908
$43$	−418.966	−1.48585	−0.742927	−	0.669373i	$-0.766563\pi$
$43$	−418.966	−1.48585	−0.742927	+	0.669373i	$0.766563\pi$
$44$	−5.12415	−0.0175567
$45$	52.5411	0.174052
$46$	−13.5225	−0.0433432
$47$	158.651	0.492375	0.246187	−	0.969222i	$-0.420822\pi$
$47$	158.651	0.492375	0.246187	+	0.969222i	$0.420822\pi$
$48$	251.761	0.757054
$49$	−295.645	−0.861939
$50$	257.831	0.729256
$51$	406.453	1.11598
$52$	0	0
$53$	89.8532	0.232873	0.116437	−	0.993198i	$-0.462853\pi$
$53$	89.8532	0.232873	0.116437	+	0.993198i	$0.462853\pi$
$54$	−419.145	−1.05627
$55$	−61.3117	−0.150314
$56$	159.908	0.381582
$57$	−382.824	−0.889584
$58$	−331.298	−0.750026
$59$	−658.045	−1.45204	−0.726018	−	0.687676i	$-0.758631\pi$
$59$	−658.045	−1.45204	−0.726018	+	0.687676i	$0.758631\pi$
$60$	−10.8845	−0.0234198
$61$	439.684	0.922881	0.461441	−	0.887171i	$-0.347333\pi$
$61$	439.684	0.922881	0.461441	+	0.887171i	$0.347333\pi$
$62$	171.901	0.352121
$63$	−64.8680	−0.129724
$64$	538.240	1.05125
$65$	0	0
$66$	126.573	0.236061
$67$	1051.80	1.91788	0.958941	−	0.283605i	$-0.0915304\pi$
$67$	1051.80	1.91788	0.958941	+	0.283605i	$0.0915304\pi$
$68$	45.1658	0.0805464
$69$	−20.6524	−0.0360326
$70$	105.281	0.179764
$71$	−1077.54	−1.80114	−0.900570	−	0.434710i	$-0.856851\pi$
$71$	−1077.54	−1.80114	−0.900570	+	0.434710i	$0.856851\pi$
$72$	−219.046	−0.358539
$73$	338.912	0.543379	0.271689	−	0.962385i	$-0.412418\pi$
$73$	338.912	0.543379	0.271689	+	0.962385i	$0.412418\pi$
$74$	164.530	0.258462
$75$	393.774	0.606255
$76$	−42.5402	−0.0642065
$77$	75.6963	0.112031
$78$	0	0
$79$	664.285	0.946049	0.473024	−	0.881049i	$-0.343162\pi$
$79$	664.285	0.946049	0.473024	+	0.881049i	$0.343162\pi$
$80$	334.741	0.467815
$81$	−385.628	−0.528982
$82$	−150.680	−0.202924
$83$	1011.19	1.33726	0.668628	−	0.743597i	$-0.266882\pi$
$83$	1011.19	1.33726	0.668628	+	0.743597i	$0.266882\pi$
$84$	13.4382	0.0174551
$85$	540.419	0.689608
$86$	1150.00	1.44194
$87$	−505.977	−0.623522
$88$	255.611	0.309639
$89$	237.802	0.283224	0.141612	−	0.989922i	$-0.454771\pi$
$89$	237.802	0.283224	0.141612	+	0.989922i	$0.454771\pi$
$90$	−144.217	−0.168909
$91$	0	0
$92$	−2.29493	−0.00260068
$93$	262.538	0.292730
$94$	−435.472	−0.477824
$95$	−509.003	−0.549711
$96$	88.2593	0.0938326
$97$	150.055	0.157069	0.0785347	−	0.996911i	$-0.474976\pi$
$97$	150.055	0.157069	0.0785347	+	0.996911i	$0.474976\pi$
$98$	811.500	0.836468
$99$	−103.691	−0.105266
$100$	43.7570	0.0437570
$101$	1632.70	1.60851	0.804254	−	0.594286i	$-0.202565\pi$
$101$	1632.70	1.60851	0.804254	+	0.594286i	$0.202565\pi$
$102$	−1115.65	−1.08300
$103$	−38.9576	−0.0372681	−0.0186340	−	0.999826i	$-0.505932\pi$
$103$	−38.9576	−0.0372681	−0.0186340	+	0.999826i	$0.505932\pi$
$104$	0	0
$105$	160.791	0.149444
$106$	−246.633	−0.225992
$107$	296.619	0.267993	0.133996	−	0.990982i	$-0.457219\pi$
$107$	296.619	0.267993	0.133996	+	0.990982i	$0.457219\pi$
$108$	−71.1338	−0.0633783
$109$	1405.78	1.23532	0.617658	−	0.786447i	$-0.288082\pi$
$109$	1405.78	1.23532	0.617658	+	0.786447i	$0.288082\pi$
$110$	168.291	0.145872
$111$	251.279	0.214868
$112$	−413.277	−0.348670
$113$	1459.72	1.21521	0.607607	−	0.794238i	$-0.292130\pi$
$113$	1459.72	1.21521	0.607607	+	0.794238i	$0.292130\pi$
$114$	1050.79	0.863296
$115$	−27.4594	−0.0222661
$116$	−56.2251	−0.0450032
$117$	0	0
$118$	1806.23	1.40913
$119$	−667.210	−0.513975
$120$	542.960	0.413043
$121$	121.000	0.0909091
$122$	−1206.86	−0.895609
$123$	−230.127	−0.168698
$124$	29.1737	0.0211280
$125$	1220.29	0.873165
$126$	178.053	0.125890
$127$	−2229.27	−1.55760	−0.778801	−	0.627272i	$-0.784172\pi$
$127$	−2229.27	−1.55760	−0.778801	+	0.627272i	$0.784172\pi$
$128$	−1308.95	−0.903878
$129$	1756.34	1.19874
$130$	0	0
$131$	804.754	0.536730	0.268365	−	0.963317i	$-0.413517\pi$
$131$	804.754	0.536730	0.268365	+	0.963317i	$0.413517\pi$
$132$	21.4809	0.0141642
$133$	628.423	0.409708
$134$	−2887.03	−1.86121
$135$	−851.132	−0.542621
$136$	−2253.03	−1.42056
$137$	2048.95	1.27776	0.638881	−	0.769306i	$-0.279398\pi$
$137$	2048.95	1.27776	0.638881	+	0.769306i	$0.279398\pi$
$138$	56.6875	0.0349678
$139$	843.182	0.514516	0.257258	−	0.966343i	$-0.417181\pi$
$139$	843.182	0.514516	0.257258	+	0.966343i	$0.417181\pi$
$140$	17.8674	0.0107862
$141$	−665.077	−0.397231
$142$	2957.69	1.74791
$143$	0	0
$144$	566.118	0.327615
$145$	−672.746	−0.385300
$146$	−930.261	−0.527321
$147$	1239.37	0.695384
$148$	27.9226	0.0155083
$149$	−3159.85	−1.73735	−0.868674	−	0.495385i	$-0.835027\pi$
$149$	−3159.85	−1.73735	−0.868674	+	0.495385i	$0.835027\pi$
$150$	−1080.85	−0.588340
$151$	−2493.03	−1.34357	−0.671787	−	0.740745i	$-0.734473\pi$
$151$	−2493.03	−1.34357	−0.671787	+	0.740745i	$0.734473\pi$
$152$	2122.06	1.13238
$153$	913.963	0.482938
$154$	−207.775	−0.108720
$155$	349.070	0.180890
$156$	0	0
$157$	176.934	0.0899421	0.0449710	−	0.998988i	$-0.485680\pi$
$157$	176.934	0.0899421	0.0449710	+	0.998988i	$0.485680\pi$
$158$	−1823.36	−0.918092
$159$	−376.672	−0.187874
$160$	117.350	0.0579831
$161$	33.9017	0.0165952
$162$	1058.49	0.513350
$163$	1020.11	0.490193	0.245097	−	0.969499i	$-0.421180\pi$
$163$	1020.11	0.490193	0.245097	+	0.969499i	$0.421180\pi$
$164$	−25.5721	−0.0121759
$165$	257.024	0.121268
$166$	−2775.55	−1.29774
$167$	245.512	0.113762	0.0568812	−	0.998381i	$-0.481884\pi$
$167$	245.512	0.113762	0.0568812	+	0.998381i	$0.481884\pi$
$168$	−670.346	−0.307847
$169$	0	0
$170$	−1483.37	−0.669229
$171$	−860.831	−0.384967
$172$	195.168	0.0865198
$173$	−1090.74	−0.479350	−0.239675	−	0.970853i	$-0.577041\pi$
$173$	−1090.74	−0.479350	−0.239675	+	0.970853i	$0.577041\pi$
$174$	1388.83	0.605096
$175$	−646.398	−0.279218
$176$	−660.620	−0.282932
$177$	2758.58	1.17145
$178$	−652.729	−0.274855
$179$	3377.85	1.41046	0.705229	−	0.708979i	$-0.250844\pi$
$179$	3377.85	1.41046	0.705229	+	0.708979i	$0.250844\pi$
$180$	−24.4753	−0.0101349
$181$	3464.79	1.42285	0.711424	−	0.702763i	$-0.248051\pi$
$181$	3464.79	1.42285	0.711424	+	0.702763i	$0.248051\pi$
$182$	0	0
$183$	−1843.19	−0.744550
$184$	114.479	0.0458670
$185$	334.100	0.132776
$186$	−720.625	−0.284079
$187$	−1066.53	−0.417072
$188$	−73.9047	−0.0286705
$189$	1050.82	0.404423
$190$	1397.13	0.533467
$191$	2903.39	1.09991	0.549953	−	0.835196i	$-0.314646\pi$
$191$	2903.39	1.09991	0.549953	+	0.835196i	$0.314646\pi$
$192$	−2256.35	−0.848113
$193$	−4605.72	−1.71776	−0.858878	−	0.512180i	$-0.828838\pi$
$193$	−4605.72	−1.71776	−0.858878	+	0.512180i	$0.828838\pi$
$194$	−411.877	−0.152428
$195$	0	0
$196$	137.721	0.0501899
$197$	−25.4797	−0.00921500	−0.00460750	−	0.999989i	$-0.501467\pi$
$197$	−25.4797	−0.00921500	−0.00460750	+	0.999989i	$0.501467\pi$
$198$	284.616	0.102155
$199$	−2697.05	−0.960748	−0.480374	−	0.877064i	$-0.659499\pi$
$199$	−2697.05	−0.960748	−0.480374	+	0.877064i	$0.659499\pi$
$200$	−2182.75	−0.771720
$201$	−4409.24	−1.54728
$202$	−4481.49	−1.56097
$203$	830.583	0.287170
$204$	−189.339	−0.0649822
$205$	−305.976	−0.104245
$206$	106.933	0.0361667
$207$	−46.4396	−0.0155931
$208$	0	0
$209$	1004.53	0.332463
$210$	−441.347	−0.145028
$211$	−3381.79	−1.10337	−0.551687	−	0.834051i	$-0.686016\pi$
$211$	−3381.79	−1.10337	−0.551687	+	0.834051i	$0.686016\pi$
$212$	−41.8565	−0.0135600
$213$	4517.15	1.45310
$214$	−814.173	−0.260073
$215$	2335.23	0.740750
$216$	3548.41	1.11777
$217$	−430.967	−0.134820
$218$	−3858.65	−1.19881
$219$	−1420.75	−0.438380
$220$	28.5610	0.00875263
$221$	0	0
$222$	−689.722	−0.208518
$223$	−3980.55	−1.19533	−0.597663	−	0.801747i	$-0.703904\pi$
$223$	−3980.55	−1.19533	−0.597663	+	0.801747i	$0.703904\pi$
$224$	−144.882	−0.0432156
$225$	885.454	0.262357
$226$	−4006.71	−1.17930
$227$	−1307.72	−0.382363	−0.191181	−	0.981555i	$-0.561232\pi$
$227$	−1307.72	−0.382363	−0.191181	+	0.981555i	$0.561232\pi$
$228$	178.332	0.0517996
$229$	3204.14	0.924611	0.462305	−	0.886721i	$-0.347022\pi$
$229$	3204.14	0.924611	0.462305	+	0.886721i	$0.347022\pi$
$230$	75.3717	0.0216081
$231$	−317.325	−0.0903830
$232$	2804.71	0.793699
$233$	308.568	0.0867596	0.0433798	−	0.999059i	$-0.486187\pi$
$233$	308.568	0.0867596	0.0433798	+	0.999059i	$0.486187\pi$
$234$	0	0
$235$	−884.286	−0.245466
$236$	306.538	0.0845506
$237$	−2784.74	−0.763241
$238$	1831.39	0.498786
$239$	−3295.42	−0.891895	−0.445948	−	0.895059i	$-0.647133\pi$
$239$	−3295.42	−0.891895	−0.445948	+	0.895059i	$0.647133\pi$
$240$	−1403.26	−0.377418
$241$	−5144.69	−1.37510	−0.687549	−	0.726138i	$-0.741313\pi$
$241$	−5144.69	−1.37510	−0.687549	+	0.726138i	$0.741313\pi$
$242$	−332.126	−0.0882226
$243$	−2506.39	−0.661666
$244$	−204.819	−0.0537385
$245$	1647.86	0.429707
$246$	631.661	0.163712
$247$	0	0
$248$	−1455.29	−0.372625
$249$	−4238.98	−1.07885
$250$	−3349.49	−0.847362
$251$	−678.142	−0.170534	−0.0852668	−	0.996358i	$-0.527174\pi$
$251$	−678.142	−0.170534	−0.0852668	+	0.996358i	$0.527174\pi$
$252$	30.2176	0.00755369
$253$	54.1917	0.0134664
$254$	6118.99	1.51157
$255$	−2265.48	−0.556353
$256$	−713.045	−0.174083
$257$	927.443	0.225106	0.112553	−	0.993646i	$-0.464097\pi$
$257$	927.443	0.225106	0.112553	+	0.993646i	$0.464097\pi$
$258$	−4820.88	−1.16331
$259$	−412.485	−0.0989599
$260$	0	0
$261$	−1137.76	−0.269829
$262$	−2208.92	−0.520869
$263$	−2468.42	−0.578742	−0.289371	−	0.957217i	$-0.593446\pi$
$263$	−2468.42	−0.578742	−0.289371	+	0.957217i	$0.593446\pi$
$264$	−1071.54	−0.249807
$265$	−500.823	−0.116096
$266$	−1724.92	−0.397601
$267$	−996.885	−0.228496
$268$	−489.963	−0.111676
$269$	−1161.84	−0.263340	−0.131670	−	0.991294i	$-0.542034\pi$
$269$	−1161.84	−0.263340	−0.131670	+	0.991294i	$0.542034\pi$
$270$	2336.23	0.526586
$271$	4535.04	1.01655	0.508273	−	0.861196i	$-0.330284\pi$
$271$	4535.04	1.01655	0.508273	+	0.861196i	$0.330284\pi$
$272$	5822.90	1.29803
$273$	0	0
$274$	−5624.04	−1.24000
$275$	−1033.26	−0.226575
$276$	9.62053	0.00209815
$277$	2214.86	0.480426	0.240213	−	0.970720i	$-0.422783\pi$
$277$	2214.86	0.480426	0.240213	+	0.970720i	$0.422783\pi$
$278$	−2314.40	−0.499311
$279$	590.351	0.126679
$280$	−891.292	−0.190232
$281$	1806.53	0.383518	0.191759	−	0.981442i	$-0.438581\pi$
$281$	1806.53	0.383518	0.191759	+	0.981442i	$0.438581\pi$
$282$	1825.53	0.385493
$283$	6881.60	1.44547	0.722736	−	0.691125i	$-0.242884\pi$
$283$	6881.60	1.44547	0.722736	+	0.691125i	$0.242884\pi$
$284$	501.955	0.104879
$285$	2133.78	0.443489
$286$	0	0
$287$	377.763	0.0776956
$288$	198.463	0.0406060
$289$	4487.71	0.913435
$290$	1846.58	0.373914
$291$	−629.041	−0.126718
$292$	−157.876	−0.0316404
$293$	−845.454	−0.168573	−0.0842866	−	0.996442i	$-0.526861\pi$
$293$	−845.454	−0.168573	−0.0842866	+	0.996442i	$0.526861\pi$
$294$	−3401.87	−0.674834
$295$	3667.80	0.723890
$296$	−1392.88	−0.273512
$297$	1679.73	0.328174
$298$	8673.29	1.68601
$299$	0	0
$300$	−183.433	−0.0353016
$301$	−2883.11	−0.552092
$302$	6842.97	1.30387
$303$	−6844.39	−1.29769
$304$	−5484.39	−1.03471
$305$	−2450.71	−0.460088
$306$	−2508.69	−0.468667
$307$	−3457.05	−0.642685	−0.321342	−	0.946963i	$-0.604134\pi$
$307$	−3457.05	−0.642685	−0.321342	+	0.946963i	$0.604134\pi$
$308$	−35.2618	−0.00652346
$309$	163.314	0.0300666
$310$	−958.143	−0.175545
$311$	−1756.56	−0.320275	−0.160137	−	0.987095i	$-0.551194\pi$
$311$	−1756.56	−0.320275	−0.160137	+	0.987095i	$0.551194\pi$
$312$	0	0
$313$	−4815.76	−0.869659	−0.434829	−	0.900513i	$-0.643191\pi$
$313$	−4815.76	−0.869659	−0.434829	+	0.900513i	$0.643191\pi$
$314$	−485.657	−0.0872842
$315$	361.561	0.0646718
$316$	−309.445	−0.0550875
$317$	1278.25	0.226479	0.113239	−	0.993568i	$-0.463877\pi$
$317$	1278.25	0.226479	0.113239	+	0.993568i	$0.463877\pi$
$318$	1033.91	0.182323
$319$	1327.68	0.233028
$320$	−3000.04	−0.524085
$321$	−1243.45	−0.216208
$322$	−93.0550	−0.0161048
$323$	−8854.21	−1.52527
$324$	179.638	0.0308021
$325$	0	0
$326$	−2800.05	−0.475707
$327$	−5893.15	−0.996611
$328$	1275.63	0.214740
$329$	1091.75	0.182949
$330$	−705.489	−0.117685
$331$	5940.96	0.986539	0.493270	−	0.869876i	$-0.335802\pi$
$331$	5940.96	0.986539	0.493270	+	0.869876i	$0.335802\pi$
$332$	−471.043	−0.0778671
$333$	565.034	0.0929841
$334$	−673.893	−0.110401
$335$	−5862.53	−0.956131
$336$	1732.49	0.281295
$337$	−4606.79	−0.744652	−0.372326	−	0.928102i	$-0.621440\pi$
$337$	−4606.79	−0.744652	−0.372326	+	0.928102i	$0.621440\pi$
$338$	0	0
$339$	−6119.28	−0.980394
$340$	−251.745	−0.0401552
$341$	−688.898	−0.109401
$342$	2362.85	0.373591
$343$	−4394.83	−0.691832
$344$	−9735.67	−1.52591
$345$	115.112	0.0179635
$346$	2993.91	0.465184
$347$	−10457.6	−1.61786	−0.808928	−	0.587908i	$-0.799952\pi$
$347$	−10457.6	−1.61786	−0.808928	+	0.587908i	$0.799952\pi$
$348$	235.700	0.0363071
$349$	5867.84	0.899996	0.449998	−	0.893030i	$-0.351425\pi$
$349$	5867.84	0.899996	0.449998	+	0.893030i	$0.351425\pi$
$350$	1774.26	0.270966
$351$	0	0
$352$	−231.592	−0.0350679
$353$	−4876.00	−0.735194	−0.367597	−	0.929985i	$-0.619819\pi$
$353$	−4876.00	−0.735194	−0.367597	+	0.929985i	$0.619819\pi$
$354$	−7571.86	−1.13684
$355$	6006.00	0.897931
$356$	−110.776	−0.0164919
$357$	2797.00	0.414658
$358$	−9271.66	−1.36878
$359$	−5199.25	−0.764362	−0.382181	−	0.924087i	$-0.624827\pi$
$359$	−5199.25	−0.764362	−0.382181	+	0.924087i	$0.624827\pi$
$360$	1220.92	0.178744
$361$	1480.49	0.215846
$362$	−9510.29	−1.38080
$363$	−507.242	−0.0733424
$364$	0	0
$365$	−1889.02	−0.270893
$366$	5059.27	0.722547
$367$	−6154.64	−0.875394	−0.437697	−	0.899122i	$-0.644206\pi$
$367$	−6154.64	−0.875394	−0.437697	+	0.899122i	$0.644206\pi$
$368$	−295.869	−0.0419109
$369$	−517.470	−0.0730039
$370$	−917.053	−0.128852
$371$	618.324	0.0865277
$372$	−122.299	−0.0170454
$373$	10952.0	1.52030	0.760151	−	0.649747i	$-0.225125\pi$
$373$	10952.0	1.52030	0.760151	+	0.649747i	$0.225125\pi$
$374$	2927.46	0.404747
$375$	−5115.54	−0.704440
$376$	3686.63	0.505648
$377$	0	0
$378$	−2884.34	−0.392472
$379$	−2139.45	−0.289963	−0.144982	−	0.989434i	$-0.546312\pi$
$379$	−2139.45	−0.289963	−0.144982	+	0.989434i	$0.546312\pi$
$380$	237.110	0.0320092
$381$	9345.26	1.25662
$382$	−7969.36	−1.06740
$383$	2695.52	0.359620	0.179810	−	0.983701i	$-0.442452\pi$
$383$	2695.52	0.359620	0.179810	+	0.983701i	$0.442452\pi$
$384$	5487.24	0.729218
$385$	−421.915	−0.0558514
$386$	12642.0	1.66699
$387$	3949.36	0.518753
$388$	−69.9003	−0.00914600
$389$	−9522.84	−1.24120	−0.620600	−	0.784127i	$-0.713111\pi$
$389$	−9522.84	−1.24120	−0.620600	+	0.784127i	$0.713111\pi$
$390$	0	0
$391$	−477.661	−0.0617810
$392$	−6870.02	−0.885175
$393$	−3373.59	−0.433016
$394$	69.9378	0.00894268
$395$	−3702.58	−0.471638
$396$	48.3026	0.00612954
$397$	4313.11	0.545261	0.272630	−	0.962119i	$-0.412106\pi$
$397$	4313.11	0.545261	0.272630	+	0.962119i	$0.412106\pi$
$398$	7402.98	0.932357
$399$	−2634.40	−0.330539
$400$	5641.27	0.705158
$401$	14532.0	1.80971	0.904853	−	0.425725i	$-0.139981\pi$
$401$	14532.0	1.80971	0.904853	+	0.425725i	$0.139981\pi$
$402$	12102.7	1.50156
$403$	0	0
$404$	−760.562	−0.0936618
$405$	2149.41	0.263716
$406$	−2279.82	−0.278684
$407$	−659.355	−0.0803022
$408$	9444.90	1.14606
$409$	−10546.2	−1.27501	−0.637504	−	0.770447i	$-0.720033\pi$
$409$	−10546.2	−1.27501	−0.637504	+	0.770447i	$0.720033\pi$
$410$	839.857	0.101165
$411$	−8589.35	−1.03085
$412$	18.1477	0.00217008
$413$	−4528.32	−0.539526
$414$	127.469	0.0151323
$415$	−5636.14	−0.666668
$416$	0	0
$417$	−3534.69	−0.415094
$418$	−2757.27	−0.322638
$419$	−12463.7	−1.45320	−0.726602	−	0.687058i	$-0.758902\pi$
$419$	−12463.7	−1.45320	−0.726602	+	0.687058i	$0.758902\pi$
$420$	−74.9017	−0.00870198
$421$	5963.21	0.690330	0.345165	−	0.938542i	$-0.387823\pi$
$421$	5963.21	0.690330	0.345165	+	0.938542i	$0.387823\pi$
$422$	9282.48	1.07077
$423$	−1495.52	−0.171902
$424$	2087.95	0.239151
$425$	9107.47	1.03948
$426$	−12398.9	−1.41016
$427$	3025.68	0.342911
$428$	−138.175	−0.0156050
$429$	0	0
$430$	−6409.83	−0.718860
$431$	129.688	0.0144939	0.00724694	−	0.999974i	$-0.497693\pi$
$431$	129.688	0.0144939	0.00724694	+	0.999974i	$0.497693\pi$
$432$	−9170.76	−1.02136
$433$	−6991.05	−0.775908	−0.387954	−	0.921679i	$-0.626818\pi$
$433$	−6991.05	−0.775908	−0.387954	+	0.921679i	$0.626818\pi$
$434$	1182.94	0.130836
$435$	2820.21	0.310847
$436$	−654.858	−0.0719312
$437$	449.893	0.0492479
$438$	3899.73	0.425425
$439$	−4073.08	−0.442819	−0.221410	−	0.975181i	$-0.571066\pi$
$439$	−4073.08	−0.442819	−0.221410	+	0.975181i	$0.571066\pi$
$440$	−1424.72	−0.154366
$441$	2786.89	0.300927
$442$	0	0
$443$	9000.98	0.965348	0.482674	−	0.875800i	$-0.339666\pi$
$443$	9000.98	0.965348	0.482674	+	0.875800i	$0.339666\pi$
$444$	−117.054	−0.0125116
$445$	−1325.46	−0.141197
$446$	10926.0	1.16000
$447$	13246.3	1.40163
$448$	3703.89	0.390608
$449$	−14909.6	−1.56710	−0.783551	−	0.621328i	$-0.786593\pi$
$449$	−14909.6	−1.56710	−0.783551	+	0.621328i	$0.786593\pi$
$450$	−2430.43	−0.254604
$451$	603.851	0.0630471
$452$	−679.986	−0.0707607
$453$	10451.0	1.08395
$454$	3589.48	0.371063
$455$	0	0
$456$	−8895.83	−0.913565
$457$	−12358.5	−1.26500	−0.632502	−	0.774559i	$-0.717972\pi$
$457$	−12358.5	−1.26500	−0.632502	+	0.774559i	$0.717972\pi$
$458$	−8794.88	−0.897287
$459$	−14805.6	−1.50559
$460$	12.7915	0.00129653
$461$	767.522	0.0775424	0.0387712	−	0.999248i	$-0.487656\pi$
$461$	767.522	0.0775424	0.0387712	+	0.999248i	$0.487656\pi$
$462$	871.008	0.0877120
$463$	2323.66	0.233239	0.116620	−	0.993177i	$-0.462794\pi$
$463$	2323.66	0.233239	0.116620	+	0.993177i	$0.462794\pi$
$464$	−7248.69	−0.725241
$465$	−1463.33	−0.145936
$466$	−846.972	−0.0841958
$467$	5615.29	0.556413	0.278206	−	0.960521i	$-0.410260\pi$
$467$	5615.29	0.556413	0.278206	+	0.960521i	$0.410260\pi$
$468$	0	0
$469$	7237.96	0.712619
$470$	2427.23	0.238212
$471$	−741.723	−0.0725622
$472$	−15291.2	−1.49118
$473$	−4608.62	−0.448002
$474$	7643.66	0.740686
$475$	−8578.03	−0.828604
$476$	310.808	0.0299283
$477$	−846.997	−0.0813026
$478$	9045.41	0.865539
$479$	11072.0	1.05614	0.528070	−	0.849201i	$-0.322916\pi$
$479$	11072.0	1.05614	0.528070	+	0.849201i	$0.322916\pi$
$480$	−491.939	−0.0467788
$481$	0	0
$482$	14121.4	1.33446
$483$	−142.119	−0.0133885
$484$	−56.3657	−0.00529355
$485$	−836.373	−0.0783046
$486$	6879.65	0.642113
$487$	8597.17	0.799949	0.399974	−	0.916526i	$-0.369019\pi$
$487$	8597.17	0.799949	0.399974	+	0.916526i	$0.369019\pi$
$488$	10217.1	0.947759
$489$	−4276.40	−0.395471
$490$	−4523.13	−0.417008
$491$	−8208.03	−0.754426	−0.377213	−	0.926126i	$-0.623118\pi$
$491$	−8208.03	−0.754426	−0.377213	+	0.926126i	$0.623118\pi$
$492$	107.200	0.00982310
$493$	−11702.6	−1.06908
$494$	0	0
$495$	577.952	0.0524788
$496$	3761.15	0.340485
$497$	−7415.10	−0.669241
$498$	11635.3	1.04697
$499$	−9787.67	−0.878069	−0.439034	−	0.898470i	$-0.644679\pi$
$499$	−9787.67	−0.878069	−0.439034	+	0.898470i	$0.644679\pi$
$500$	−568.448	−0.0508436
$501$	−1029.21	−0.0917797
$502$	1861.39	0.165494
$503$	17677.7	1.56702	0.783508	−	0.621382i	$-0.213428\pi$
$503$	17677.7	1.56702	0.783508	+	0.621382i	$0.213428\pi$
$504$	−1507.36	−0.133221
$505$	−9100.30	−0.801897
$506$	−148.748	−0.0130685
$507$	0	0
$508$	1038.46	0.0906976
$509$	−9611.63	−0.836990	−0.418495	−	0.908219i	$-0.637442\pi$
$509$	−9611.63	−0.836990	−0.418495	+	0.908219i	$0.637442\pi$
$510$	6218.39	0.539912
$511$	2332.22	0.201901
$512$	12428.8	1.07282
$513$	13944.9	1.20016
$514$	−2545.69	−0.218454
$515$	217.142	0.0185794
$516$	−818.159	−0.0698013
$517$	1745.16	0.148457
$518$	1132.21	0.0960355
$519$	4572.48	0.386723
$520$	0	0
$521$	3095.56	0.260305	0.130152	−	0.991494i	$-0.458453\pi$
$521$	3095.56	0.260305	0.130152	+	0.991494i	$0.458453\pi$
$522$	3122.96	0.261855
$523$	9957.66	0.832539	0.416270	−	0.909241i	$-0.363337\pi$
$523$	9957.66	0.832539	0.416270	+	0.909241i	$0.363337\pi$
$524$	−374.880	−0.0312533
$525$	2709.75	0.225263
$526$	6775.42	0.561640
$527$	6072.15	0.501911
$528$	2769.37	0.228260
$529$	−12142.7	−0.998005
$530$	1374.68	0.112665
$531$	6203.03	0.506946
$532$	−292.740	−0.0238569
$533$	0	0
$534$	2736.29	0.221743
$535$	−1653.29	−0.133604
$536$	24441.1	1.96958
$537$	−14160.2	−1.13791
$538$	3189.07	0.255558
$539$	−3252.10	−0.259884
$540$	396.485	0.0315963
$541$	−2425.98	−0.192793	−0.0963965	−	0.995343i	$-0.530732\pi$
$541$	−2425.98	−0.192793	−0.0963965	+	0.995343i	$0.530732\pi$
$542$	−12448.0	−0.986506
$543$	−14524.7	−1.14791
$544$	2041.32	0.160884
$545$	−7835.53	−0.615848
$546$	0	0
$547$	−20777.9	−1.62413	−0.812064	−	0.583568i	$-0.801656\pi$
$547$	−20777.9	−1.62413	−0.812064	+	0.583568i	$0.801656\pi$
$548$	−954.465	−0.0744028
$549$	−4144.66	−0.322204
$550$	2836.14	0.219879
$551$	11022.3	0.852203
$552$	−479.907	−0.0370040
$553$	4571.27	0.351519
$554$	−6079.44	−0.466229
$555$	−1400.58	−0.107119
$556$	−392.781	−0.0299598
$557$	−19780.4	−1.50470	−0.752352	−	0.658761i	$-0.771081\pi$
$557$	−19780.4	−1.50470	−0.752352	+	0.658761i	$0.771081\pi$
$558$	−1620.42	−0.122935
$559$	0	0
$560$	2303.52	0.173824
$561$	4470.98	0.336479
$562$	−4958.65	−0.372185
$563$	−8441.16	−0.631887	−0.315943	−	0.948778i	$-0.602321\pi$
$563$	−8441.16	−0.631887	−0.315943	+	0.948778i	$0.602321\pi$
$564$	309.814	0.0231304
$565$	−8136.19	−0.605826
$566$	−18888.9	−1.40276
$567$	−2653.69	−0.196551
$568$	−25039.3	−1.84969
$569$	23677.8	1.74451	0.872254	−	0.489053i	$-0.162658\pi$
$569$	23677.8	1.74451	0.872254	+	0.489053i	$0.162658\pi$
$570$	−5856.90	−0.430383
$571$	−22123.9	−1.62147	−0.810734	−	0.585415i	$-0.800932\pi$
$571$	−22123.9	−1.62147	−0.810734	+	0.585415i	$0.800932\pi$
$572$	0	0
$573$	−12171.3	−0.887367
$574$	−1036.90	−0.0753996
$575$	−462.762	−0.0335626
$576$	−5073.70	−0.367021
$577$	−3030.42	−0.218645	−0.109323	−	0.994006i	$-0.534868\pi$
$577$	−3030.42	−0.218645	−0.109323	+	0.994006i	$0.534868\pi$
$578$	−12318.1	−0.886442
$579$	19307.6	1.38583
$580$	313.387	0.0224357
$581$	6958.47	0.496878
$582$	1726.62	0.122974
$583$	988.386	0.0702140
$584$	7875.43	0.558027
$585$	0	0
$586$	2320.64	0.163592
$587$	13752.7	0.967006	0.483503	−	0.875343i	$-0.339364\pi$
$587$	13752.7	0.967006	0.483503	+	0.875343i	$0.339364\pi$
$588$	−577.338	−0.0404915
$589$	−5719.15	−0.400091
$590$	−10067.5	−0.702498
$591$	106.813	0.00743435
$592$	3599.86	0.249921
$593$	−25257.1	−1.74905	−0.874524	−	0.484983i	$-0.838826\pi$
$593$	−25257.1	−1.74905	−0.874524	+	0.484983i	$0.838826\pi$
$594$	−4610.59	−0.318476
$595$	3718.89	0.256234
$596$	1471.96	0.101164
$597$	11306.3	0.775099
$598$	0	0
$599$	13380.9	0.912735	0.456367	−	0.889791i	$-0.349150\pi$
$599$	13380.9	0.912735	0.456367	+	0.889791i	$0.349150\pi$
$600$	9150.29	0.622598
$601$	−13498.9	−0.916195	−0.458098	−	0.888902i	$-0.651469\pi$
$601$	−13498.9	−0.916195	−0.458098	+	0.888902i	$0.651469\pi$
$602$	7913.68	0.535777
$603$	−9914.77	−0.669586
$604$	1161.33	0.0782350
$605$	−674.428	−0.0453213
$606$	18786.8	1.25934
$607$	−26685.0	−1.78436	−0.892182	−	0.451676i	$-0.850826\pi$
$607$	−26685.0	−1.78436	−0.892182	+	0.451676i	$0.850826\pi$
$608$	−1922.65	−0.128246
$609$	−3481.87	−0.231679
$610$	6726.80	0.446492
$611$	0	0
$612$	−425.753	−0.0281210
$613$	11935.7	0.786425	0.393212	−	0.919448i	$-0.371364\pi$
$613$	11935.7	0.786425	0.393212	+	0.919448i	$0.371364\pi$
$614$	9489.06	0.623693
$615$	1282.68	0.0841016
$616$	1758.99	0.115051
$617$	−11001.0	−0.717801	−0.358900	−	0.933376i	$-0.616848\pi$
$617$	−11001.0	−0.717801	−0.358900	+	0.933376i	$0.616848\pi$
$618$	−448.270	−0.0291781
$619$	16473.1	1.06964	0.534821	−	0.844965i	$-0.320379\pi$
$619$	16473.1	1.06964	0.534821	+	0.844965i	$0.320379\pi$
$620$	−162.608	−0.0105331
$621$	752.292	0.0486126
$622$	4821.49	0.310810
$623$	1636.43	0.105236
$624$	0	0
$625$	4940.00	0.316160
$626$	13218.5	0.843959
$627$	−4211.07	−0.268220
$628$	−82.4217	−0.00523724
$629$	5811.75	0.368409
$630$	−992.427	−0.0627607
$631$	−18621.0	−1.17479	−0.587394	−	0.809301i	$-0.699846\pi$
$631$	−18621.0	−1.17479	−0.587394	+	0.809301i	$0.699846\pi$
$632$	15436.2	0.971552
$633$	14176.7	0.890165
$634$	−3508.60	−0.219786
$635$	12425.5	0.776518
$636$	175.466	0.0109397
$637$	0	0
$638$	−3644.27	−0.226141
$639$	10157.4	0.628829
$640$	7295.84	0.450615
$641$	−17638.9	−1.08688	−0.543442	−	0.839447i	$-0.682879\pi$
$641$	−17638.9	−1.08688	−0.543442	+	0.839447i	$0.682879\pi$
$642$	3413.08	0.209819
$643$	3116.85	0.191161	0.0955805	−	0.995422i	$-0.469529\pi$
$643$	3116.85	0.191161	0.0955805	+	0.995422i	$0.469529\pi$
$644$	−15.7925	−0.000966324 0
$645$	−9789.46	−0.597612
$646$	24303.4	1.48019
$647$	−4611.77	−0.280228	−0.140114	−	0.990135i	$-0.544747\pi$
$647$	−4611.77	−0.280228	−0.140114	+	0.990135i	$0.544747\pi$
$648$	−8960.98	−0.543242
$649$	−7238.49	−0.437805
$650$	0	0
$651$	1806.65	0.108768
$652$	−475.202	−0.0285435
$653$	−23189.2	−1.38968	−0.694841	−	0.719164i	$-0.744525\pi$
$653$	−23189.2	−1.38968	−0.694841	+	0.719164i	$0.744525\pi$
$654$	16175.8	0.967160
$655$	−4485.53	−0.267579
$656$	−3296.82	−0.196219
$657$	−3194.74	−0.189709
$658$	−2996.69	−0.177543
$659$	20632.6	1.21962	0.609812	−	0.792546i	$-0.291245\pi$
$659$	20632.6	1.21962	0.609812	+	0.792546i	$0.291245\pi$
$660$	−119.730	−0.00706133
$661$	15114.0	0.889359	0.444679	−	0.895690i	$-0.353318\pi$
$661$	15114.0	0.889359	0.444679	+	0.895690i	$0.353318\pi$
$662$	−16307.0	−0.957386
$663$	0	0
$664$	23497.3	1.37330
$665$	−3502.70	−0.204254
$666$	−1550.93	−0.0902363
$667$	594.622	0.0345185
$668$	−114.368	−0.00662427
$669$	16686.8	0.964349
$670$	16091.7	0.927876
$671$	4836.52	0.278259
$672$	607.355	0.0348649
$673$	17153.6	0.982499	0.491249	−	0.871019i	$-0.336540\pi$
$673$	17153.6	0.982499	0.491249	+	0.871019i	$0.336540\pi$
$674$	12644.9	0.722647
$675$	−14343.8	−0.817916
$676$	0	0
$677$	9987.36	0.566980	0.283490	−	0.958975i	$-0.408508\pi$
$677$	9987.36	0.566980	0.283490	+	0.958975i	$0.408508\pi$
$678$	16796.5	0.951422
$679$	1032.60	0.0583616
$680$	12557.9	0.708198
$681$	5482.06	0.308477
$682$	1890.92	0.106169
$683$	15590.0	0.873405	0.436702	−	0.899606i	$-0.356146\pi$
$683$	15590.0	0.873405	0.436702	+	0.899606i	$0.356146\pi$
$684$	401.003	0.0224163
$685$	−11420.4	−0.637008
$686$	12063.1	0.671388
$687$	−13432.0	−0.745945
$688$	25161.6	1.39430
$689$	0	0
$690$	−315.964	−0.0174327
$691$	14518.7	0.799304	0.399652	−	0.916667i	$-0.369131\pi$
$691$	14518.7	0.799304	0.399652	+	0.916667i	$0.369131\pi$
$692$	508.102	0.0279121
$693$	−713.548	−0.0391132
$694$	28704.6	1.57005
$695$	−4699.72	−0.256504
$696$	−11757.6	−0.640330
$697$	−5322.52	−0.289246
$698$	−16106.3	−0.873400
$699$	−1293.54	−0.0699947
$700$	301.113	0.0162586
$701$	−17959.6	−0.967650	−0.483825	−	0.875165i	$-0.660753\pi$
$701$	−17959.6	−0.967650	−0.483825	+	0.875165i	$0.660753\pi$
$702$	0	0
$703$	−5473.89	−0.293672
$704$	5920.64	0.316964
$705$	3707.00	0.198034
$706$	13383.9	0.713468
$707$	11235.4	0.597666
$708$	−1285.03	−0.0682126
$709$	−67.5784	−0.00357963	−0.00178982	−	0.999998i	$-0.500570\pi$
$709$	−67.5784	−0.00357963	−0.00178982	+	0.999998i	$0.500570\pi$
$710$	−16485.5	−0.871396
$711$	−6261.85	−0.330292
$712$	5525.89	0.290859
$713$	−308.533	−0.0162057
$714$	−7677.32	−0.402404
$715$	0	0
$716$	−1573.51	−0.0821296
$717$	13814.7	0.719551
$718$	14271.1	0.741775
$719$	6924.60	0.359171	0.179586	−	0.983742i	$-0.442524\pi$
$719$	6924.60	0.359171	0.179586	+	0.983742i	$0.442524\pi$
$720$	−3155.42	−0.163327
$721$	−268.086	−0.0138475
$722$	−4063.71	−0.209468
$723$	21567.0	1.10938
$724$	−1614.01	−0.0828510
$725$	−11337.5	−0.580780
$726$	1392.30	0.0711750
$727$	−31335.3	−1.59857	−0.799287	−	0.600950i	$-0.794789\pi$
$727$	−31335.3	−1.59857	−0.799287	+	0.600950i	$0.794789\pi$
$728$	0	0
$729$	20918.9	1.06279
$730$	5185.08	0.262888
$731$	40621.8	2.05534
$732$	858.618	0.0433544
$733$	−165.612	−0.00834517	−0.00417258	−	0.999991i	$-0.501328\pi$
$733$	−165.612	−0.00834517	−0.00417258	+	0.999991i	$0.501328\pi$
$734$	16893.5	0.849525
$735$	−6907.98	−0.346673
$736$	−103.722	−0.00519462
$737$	11569.8	0.578263
$738$	1420.37	0.0708465
$739$	−21103.6	−1.05048	−0.525242	−	0.850953i	$-0.676025\pi$
$739$	−21103.6	−1.05048	−0.525242	+	0.850953i	$0.676025\pi$
$740$	−155.635	−0.00773141
$741$	0	0
$742$	−1697.20	−0.0839707
$743$	19069.7	0.941589	0.470795	−	0.882243i	$-0.343967\pi$
$743$	19069.7	0.941589	0.470795	+	0.882243i	$0.343967\pi$
$744$	6100.69	0.300621
$745$	17612.3	0.866128
$746$	−30061.5	−1.47537
$747$	−9531.91	−0.466873
$748$	496.824	0.0242857
$749$	2041.18	0.0995769
$750$	14041.3	0.683623
$751$	8966.42	0.435672	0.217836	−	0.975985i	$-0.430100\pi$
$751$	8966.42	0.435672	0.217836	+	0.975985i	$0.430100\pi$
$752$	−9527.99	−0.462035
$753$	2842.83	0.137581
$754$	0	0
$755$	13895.6	0.669818
$756$	−489.506	−0.0235492
$757$	38368.4	1.84217	0.921085	−	0.389362i	$-0.127304\pi$
$757$	38368.4	1.84217	0.921085	+	0.389362i	$0.127304\pi$
$758$	5872.45	0.281394
$759$	−227.176	−0.0108642
$760$	−11827.9	−0.564530
$761$	20959.7	0.998406	0.499203	−	0.866485i	$-0.333626\pi$
$761$	20959.7	0.998406	0.499203	+	0.866485i	$0.333626\pi$
$762$	−25651.3	−1.21949
$763$	9673.86	0.459000
$764$	−1352.49	−0.0640465
$765$	−5094.24	−0.240761
$766$	−7398.78	−0.348993
$767$	0	0
$768$	2989.14	0.140445
$769$	−24396.7	−1.14404	−0.572021	−	0.820239i	$-0.693840\pi$
$769$	−24396.7	−1.14404	−0.572021	+	0.820239i	$0.693840\pi$
$770$	1158.09	0.0542010
$771$	−3887.92	−0.181608
$772$	2145.49	0.100023
$773$	11301.5	0.525855	0.262927	−	0.964816i	$-0.415312\pi$
$773$	11301.5	0.525855	0.262927	+	0.964816i	$0.415312\pi$
$774$	−10840.4	−0.503423
$775$	5882.74	0.272664
$776$	3486.88	0.161304
$777$	1729.17	0.0798375
$778$	26138.7	1.20452
$779$	5013.10	0.230569
$780$	0	0
$781$	−11853.0	−0.543064
$782$	1311.11	0.0599553
$783$	18430.9	0.841210
$784$	17755.4	0.808827
$785$	−986.195	−0.0448392
$786$	9259.99	0.420220
$787$	20542.2	0.930431	0.465215	−	0.885198i	$-0.345977\pi$
$787$	20542.2	0.930431	0.465215	+	0.885198i	$0.345977\pi$
$788$	11.8693	0.000536580 0
$789$	10347.8	0.466910
$790$	10163.0	0.457701
$791$	10045.1	0.451531
$792$	−2409.51	−0.108104
$793$	0	0
$794$	−11838.8	−0.529148
$795$	2099.49	0.0936620
$796$	1256.37	0.0559434
$797$	−24044.4	−1.06863	−0.534313	−	0.845287i	$-0.679430\pi$
$797$	−24044.4	−1.06863	−0.534313	+	0.845287i	$0.679430\pi$
$798$	7231.01	0.320771
$799$	−15382.4	−0.681087
$800$	1977.65	0.0874004
$801$	−2241.63	−0.0988815
$802$	−39888.0	−1.75623
$803$	3728.03	0.163835
$804$	2053.97	0.0900968
$805$	−188.961	−0.00827330
$806$	0	0
$807$	4870.52	0.212454
$808$	37939.6	1.65187
$809$	20153.3	0.875839	0.437919	−	0.899014i	$-0.355716\pi$
$809$	20153.3	0.875839	0.437919	+	0.899014i	$0.355716\pi$
$810$	−5899.79	−0.255923
$811$	−22525.4	−0.975305	−0.487653	−	0.873038i	$-0.662147\pi$
$811$	−22525.4	−0.975305	−0.487653	+	0.873038i	$0.662147\pi$
$812$	−386.912	−0.0167216
$813$	−19011.2	−0.820115
$814$	1809.83	0.0779292
$815$	−5685.90	−0.244378
$816$	−24410.1	−1.04721
$817$	−38260.3	−1.63838
$818$	28947.8	1.23733
$819$	0	0
$820$	142.533	0.00607010
$821$	−24043.1	−1.02206	−0.511029	−	0.859564i	$-0.670735\pi$
$821$	−24043.1	−1.02206	−0.511029	+	0.859564i	$0.670735\pi$
$822$	23576.4	1.00039
$823$	21709.9	0.919515	0.459758	−	0.888044i	$-0.347936\pi$
$823$	21709.9	0.919515	0.459758	+	0.888044i	$0.347936\pi$
$824$	−905.274	−0.0382727
$825$	4331.52	0.182793
$826$	12429.5	0.523582
$827$	4842.01	0.203595	0.101797	−	0.994805i	$-0.467541\pi$
$827$	4842.01	0.203595	0.101797	+	0.994805i	$0.467541\pi$
$828$	21.6331	0.000907972 0
$829$	−36772.6	−1.54061	−0.770304	−	0.637677i	$-0.779895\pi$
$829$	−36772.6	−1.54061	−0.770304	+	0.637677i	$0.779895\pi$
$830$	15470.3	0.646967
$831$	−9284.86	−0.387591
$832$	0	0
$833$	28664.9	1.19229
$834$	9702.16	0.402828
$835$	−1368.43	−0.0567145
$836$	−467.942	−0.0193590
$837$	−9563.32	−0.394930
$838$	34211.0	1.41026
$839$	3261.95	0.134225	0.0671126	−	0.997745i	$-0.478621\pi$
$839$	3261.95	0.134225	0.0671126	+	0.997745i	$0.478621\pi$
$840$	3736.37	0.153473
$841$	−9820.95	−0.402680
$842$	−16368.1	−0.669930
$843$	−7573.13	−0.309410
$844$	1575.35	0.0642484
$845$	0	0
$846$	4104.96	0.166822
$847$	832.660	0.0337787
$848$	−5396.26	−0.218524
$849$	−28848.2	−1.16616
$850$	−24998.6	−1.00876
$851$	−295.302	−0.0118952
$852$	−2104.24	−0.0846126
$853$	−7398.89	−0.296991	−0.148495	−	0.988913i	$-0.547443\pi$
$853$	−7398.89	−0.296991	−0.148495	+	0.988913i	$0.547443\pi$
$854$	−8305.01	−0.332777
$855$	4798.09	0.191920
$856$	6892.65	0.275217
$857$	21584.3	0.860332	0.430166	−	0.902750i	$-0.358455\pi$
$857$	21584.3	0.860332	0.430166	+	0.902750i	$0.358455\pi$
$858$	0	0
$859$	−11879.3	−0.471848	−0.235924	−	0.971771i	$-0.575812\pi$
$859$	−11879.3	−0.471848	−0.235924	+	0.971771i	$0.575812\pi$
$860$	−1087.82	−0.0431331
$861$	−1583.61	−0.0626822
$862$	−355.974	−0.0140656
$863$	−6366.72	−0.251131	−0.125565	−	0.992085i	$-0.540074\pi$
$863$	−6366.72	−0.251131	−0.125565	+	0.992085i	$0.540074\pi$
$864$	−3214.97	−0.126592
$865$	6079.56	0.238973
$866$	19189.3	0.752979
$867$	−18812.8	−0.736929
$868$	200.758	0.00785044
$869$	7307.13	0.285245
$870$	−7741.03	−0.301661
$871$	0	0
$872$	32666.7	1.26862
$873$	−1414.48	−0.0548373
$874$	−1234.89	−0.0477925
$875$	8397.38	0.324438
$876$	661.830	0.0255264
$877$	−17337.2	−0.667542	−0.333771	−	0.942654i	$-0.608321\pi$
$877$	−17337.2	−0.667542	−0.333771	+	0.942654i	$0.608321\pi$
$878$	11180.0	0.429733
$879$	3544.21	0.135999
$880$	3682.16	0.141052
$881$	37166.4	1.42130	0.710651	−	0.703545i	$-0.248400\pi$
$881$	37166.4	1.42130	0.710651	+	0.703545i	$0.248400\pi$
$882$	−7649.57	−0.292034
$883$	−30523.4	−1.16330	−0.581651	−	0.813438i	$-0.697593\pi$
$883$	−30523.4	−1.16330	−0.581651	+	0.813438i	$0.697593\pi$
$884$	0	0
$885$	−15375.7	−0.584010
$886$	−24706.3	−0.936821
$887$	41231.1	1.56077	0.780386	−	0.625299i	$-0.215023\pi$
$887$	41231.1	1.56077	0.780386	+	0.625299i	$0.215023\pi$
$888$	5839.07	0.220660
$889$	−15340.7	−0.578751
$890$	3638.17	0.137025
$891$	−4241.90	−0.159494
$892$	1854.27	0.0696027
$893$	14488.1	0.542919
$894$	−36359.1	−1.36021
$895$	−18827.4	−0.703163
$896$	−9007.55	−0.335850
$897$	0	0
$898$	40924.6	1.52079
$899$	−7558.97	−0.280429
$900$	−412.473	−0.0152768
$901$	−8711.92	−0.322127
$902$	−1657.48	−0.0611839
$903$	12086.2	0.445409
$904$	33920.1	1.24797
$905$	−19312.0	−0.709339
$906$	−28686.3	−1.05192
$907$	−16628.8	−0.608766	−0.304383	−	0.952550i	$-0.598450\pi$
$907$	−16628.8	−0.608766	−0.304383	+	0.952550i	$0.598450\pi$
$908$	609.177	0.0222646
$909$	−15390.5	−0.561575
$910$	0	0
$911$	46330.1	1.68495	0.842473	−	0.538739i	$-0.181099\pi$
$911$	46330.1	1.68495	0.842473	+	0.538739i	$0.181099\pi$
$912$	22991.0	0.834768
$913$	11123.1	0.403198
$914$	33922.2	1.22762
$915$	10273.6	0.371184
$916$	−1492.59	−0.0538392
$917$	5537.90	0.199430
$918$	40639.1	1.46110
$919$	−18488.1	−0.663618	−0.331809	−	0.943347i	$-0.607659\pi$
$919$	−18488.1	−0.663618	−0.331809	+	0.943347i	$0.607659\pi$
$920$	−638.084	−0.0228663
$921$	14492.2	0.518496
$922$	−2106.73	−0.0752509
$923$	0	0
$924$	147.820	0.00526291
$925$	5630.46	0.200139
$926$	−6378.09	−0.226347
$927$	367.232	0.0130113
$928$	−2541.16	−0.0898896
$929$	17200.9	0.607474	0.303737	−	0.952756i	$-0.401766\pi$
$929$	17200.9	0.607474	0.303737	+	0.952756i	$0.401766\pi$
$930$	4016.61	0.141624
$931$	−26998.6	−0.950421
$932$	−143.741	−0.00505193
$933$	7363.65	0.258387
$934$	−15413.1	−0.539970
$935$	5944.61	0.207925
$936$	0	0
$937$	−34989.5	−1.21991	−0.609955	−	0.792436i	$-0.708813\pi$
$937$	−34989.5	−1.21991	−0.609955	+	0.792436i	$0.708813\pi$
$938$	−19867.1	−0.691560
$939$	20188.1	0.701611
$940$	411.929	0.0142932
$941$	31179.6	1.08015	0.540077	−	0.841616i	$-0.318395\pi$
$941$	31179.6	1.08015	0.540077	+	0.841616i	$0.318395\pi$
$942$	2035.91	0.0704179
$943$	270.444	0.00933919
$944$	39519.7	1.36256
$945$	−5857.05	−0.201619
$946$	12650.0	0.434763
$947$	33273.5	1.14176	0.570879	−	0.821034i	$-0.306603\pi$
$947$	33273.5	1.14176	0.570879	+	0.821034i	$0.306603\pi$
$948$	1297.22	0.0444428
$949$	0	0
$950$	23545.3	0.804118
$951$	−5358.54	−0.182716
$952$	−15504.2	−0.527830
$953$	16842.6	0.572491	0.286246	−	0.958156i	$-0.407593\pi$
$953$	16842.6	0.572491	0.286246	+	0.958156i	$0.407593\pi$
$954$	2324.88	0.0789000
$955$	−16182.9	−0.548342
$956$	1535.11	0.0519342
$957$	−5565.74	−0.187999
$958$	−30390.8	−1.02493
$959$	14099.8	0.474772
$960$	12576.4	0.422814
$961$	−25868.9	−0.868345
$962$	0	0
$963$	−2796.07	−0.0935638
$964$	2396.56	0.0800706
$965$	25671.3	0.856361
$966$	390.094	0.0129928
$967$	44144.9	1.46805	0.734025	−	0.679122i	$-0.237639\pi$
$967$	44144.9	1.46805	0.734025	+	0.679122i	$0.237639\pi$
$968$	2811.72	0.0933597
$969$	37117.6	1.23054
$970$	2295.71	0.0759906
$971$	18193.8	0.601304	0.300652	−	0.953734i	$-0.402796\pi$
$971$	18193.8	0.601304	0.300652	+	0.953734i	$0.402796\pi$
$972$	1167.56	0.0385282
$973$	5802.34	0.191176
$974$	−23597.9	−0.776309
$975$	0	0
$976$	−26405.8	−0.866014
$977$	−17584.9	−0.575833	−0.287917	−	0.957655i	$-0.592963\pi$
$977$	−17584.9	−0.575833	−0.287917	+	0.957655i	$0.592963\pi$
$978$	11738.1	0.383785
$979$	2615.82	0.0853953
$980$	−767.628	−0.0250214
$981$	−13251.5	−0.431283
$982$	22529.8	0.732132
$983$	−16945.0	−0.549808	−0.274904	−	0.961472i	$-0.588646\pi$
$983$	−16945.0	−0.549808	−0.274904	+	0.961472i	$0.588646\pi$
$984$	−5347.54	−0.173245
$985$	142.019	0.00459400
$986$	32121.7	1.03749
$987$	−4576.72	−0.147597
$988$	0	0
$989$	−2064.04	−0.0663627
$990$	−1586.39	−0.0509280
$991$	109.868	0.00352176	0.00176088	−	0.999998i	$-0.499439\pi$
$991$	109.868	0.00352176	0.00176088	+	0.999998i	$0.499439\pi$
$992$	1318.54	0.0422012
$993$	−24905.0	−0.795907
$994$	20353.3	0.649464
$995$	15032.8	0.478966
$996$	1974.65	0.0628205
$997$	48317.7	1.53484	0.767421	−	0.641143i	$-0.221540\pi$
$997$	48317.7	1.53484	0.767421	+	0.641143i	$0.221540\pi$
$998$	26865.6	0.852121
$999$	−9153.20	−0.289884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.f.1.6		17
13.4	even	6		143.4.e.a.133.6	yes	34
13.10	even	6		143.4.e.a.100.6	✓	34
13.12	even	2		1859.4.a.i.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.6	✓	34	13.10	even	6
143.4.e.a.133.6	yes	34	13.4	even	6
1859.4.a.f.1.6		17	1.1	even	1	trivial
1859.4.a.i.1.12		17	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74484 q^{2} -4.19208 q^{3} -0.465832 q^{4} -5.57379 q^{5} +11.5066 q^{6} +6.88148 q^{7} +23.2374 q^{8} -9.42645 q^{9} +O(q^{10})\)	\(q-2.74484 q^{2} -4.19208 q^{3} -0.465832 q^{4} -5.57379 q^{5} +11.5066 q^{6} +6.88148 q^{7} +23.2374 q^{8} -9.42645 q^{9} +15.2992 q^{10} +11.0000 q^{11} +1.95281 q^{12} -18.8886 q^{14} +23.3658 q^{15} -60.0563 q^{16} -96.9572 q^{17} +25.8741 q^{18} +91.3208 q^{19} +2.59645 q^{20} -28.8477 q^{21} -30.1933 q^{22} +4.92652 q^{23} -97.4130 q^{24} -93.9329 q^{25} +152.703 q^{27} -3.20562 q^{28} +120.698 q^{29} -64.1354 q^{30} -62.6271 q^{31} -21.0538 q^{32} -46.1129 q^{33} +266.132 q^{34} -38.3559 q^{35} +4.39115 q^{36} -59.9413 q^{37} -250.661 q^{38} -129.520 q^{40} +54.8955 q^{41} +79.1826 q^{42} -418.966 q^{43} -5.12415 q^{44} +52.5411 q^{45} -13.5225 q^{46} +158.651 q^{47} +251.761 q^{48} -295.645 q^{49} +257.831 q^{50} +406.453 q^{51} +89.8532 q^{53} -419.145 q^{54} -61.3117 q^{55} +159.908 q^{56} -382.824 q^{57} -331.298 q^{58} -658.045 q^{59} -10.8845 q^{60} +439.684 q^{61} +171.901 q^{62} -64.8680 q^{63} +538.240 q^{64} +126.573 q^{66} +1051.80 q^{67} +45.1658 q^{68} -20.6524 q^{69} +105.281 q^{70} -1077.54 q^{71} -219.046 q^{72} +338.912 q^{73} +164.530 q^{74} +393.774 q^{75} -42.5402 q^{76} +75.6963 q^{77} +664.285 q^{79} +334.741 q^{80} -385.628 q^{81} -150.680 q^{82} +1011.19 q^{83} +13.4382 q^{84} +540.419 q^{85} +1150.00 q^{86} -505.977 q^{87} +255.611 q^{88} +237.802 q^{89} -144.217 q^{90} -2.29493 q^{92} +262.538 q^{93} -435.472 q^{94} -509.003 q^{95} +88.2593 q^{96} +150.055 q^{97} +811.500 q^{98} -103.691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 95 q^{12} - 60 q^{14} + 28 q^{15} + 350 q^{16} + 118 q^{17} - 478 q^{18} - 403 q^{19} - 98 q^{20} - 220 q^{21} - 44 q^{22} - 215 q^{23} - 26 q^{24} + 319 q^{25} - 384 q^{27} + 396 q^{28} - 7 q^{29} - 1269 q^{30} - 682 q^{31} - 813 q^{32} - 66 q^{33} - 738 q^{34} + 10 q^{35} + 560 q^{36} - 1084 q^{37} + 410 q^{38} + 95 q^{40} - 240 q^{41} + 393 q^{42} - 435 q^{43} + 858 q^{44} - 1242 q^{45} - 1671 q^{46} - 549 q^{47} + 894 q^{48} + 403 q^{49} + 651 q^{50} + 1552 q^{51} - 566 q^{53} - 311 q^{54} - 176 q^{55} - 1925 q^{56} + 534 q^{57} - 618 q^{58} - 2010 q^{59} + 411 q^{60} + 460 q^{61} - 823 q^{62} - 820 q^{63} + 3171 q^{64} - 154 q^{66} + 232 q^{67} + 1795 q^{68} - 1608 q^{69} - 207 q^{70} - 489 q^{71} - 2556 q^{72} - 290 q^{73} + 2653 q^{74} - 2852 q^{75} - 2421 q^{76} + 66 q^{77} - 732 q^{79} - 4915 q^{80} + 2393 q^{81} - 1772 q^{82} + 117 q^{83} - 4161 q^{84} - 4858 q^{85} - 1034 q^{86} + 3032 q^{87} - 693 q^{88} - 4113 q^{89} + 15145 q^{90} - 3554 q^{92} - 802 q^{93} + 2325 q^{94} - 3924 q^{95} - 2601 q^{96} - 2793 q^{97} - 533 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - 6 * q^3 + 78 * q^4 - 16 * q^5 - 14 * q^6 + 6 * q^7 - 63 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 95 * q^12 - 60 * q^14 + 28 * q^15 + 350 * q^16 + 118 * q^17 - 478 * q^18 - 403 * q^19 - 98 * q^20 - 220 * q^21 - 44 * q^22 - 215 * q^23 - 26 * q^24 + 319 * q^25 - 384 * q^27 + 396 * q^28 - 7 * q^29 - 1269 * q^30 - 682 * q^31 - 813 * q^32 - 66 * q^33 - 738 * q^34 + 10 * q^35 + 560 * q^36 - 1084 * q^37 + 410 * q^38 + 95 * q^40 - 240 * q^41 + 393 * q^42 - 435 * q^43 + 858 * q^44 - 1242 * q^45 - 1671 * q^46 - 549 * q^47 + 894 * q^48 + 403 * q^49 + 651 * q^50 + 1552 * q^51 - 566 * q^53 - 311 * q^54 - 176 * q^55 - 1925 * q^56 + 534 * q^57 - 618 * q^58 - 2010 * q^59 + 411 * q^60 + 460 * q^61 - 823 * q^62 - 820 * q^63 + 3171 * q^64 - 154 * q^66 + 232 * q^67 + 1795 * q^68 - 1608 * q^69 - 207 * q^70 - 489 * q^71 - 2556 * q^72 - 290 * q^73 + 2653 * q^74 - 2852 * q^75 - 2421 * q^76 + 66 * q^77 - 732 * q^79 - 4915 * q^80 + 2393 * q^81 - 1772 * q^82 + 117 * q^83 - 4161 * q^84 - 4858 * q^85 - 1034 * q^86 + 3032 * q^87 - 693 * q^88 - 4113 * q^89 + 15145 * q^90 - 3554 * q^92 - 802 * q^93 + 2325 * q^94 - 3924 * q^95 - 2601 * q^96 - 2793 * q^97 - 533 * q^98 + 1485 * q^99

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