LMFDB - Embedded newform 1859.4.a.f.1.8

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			1.8
Root			$1.75097$ 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)

$f(q)$	$=$	$q-1.75097 q^{2} +3.47555 q^{3} -4.93410 q^{4} +8.23074 q^{5} -6.08559 q^{6} +17.9650 q^{7} +22.6472 q^{8} -14.9205 q^{9} +O(q^{10})$	\(q-1.75097 q^{2} +3.47555 q^{3} -4.93410 q^{4} +8.23074 q^{5} -6.08559 q^{6} +17.9650 q^{7} +22.6472 q^{8} -14.9205 q^{9} -14.4118 q^{10} +11.0000 q^{11} -17.1487 q^{12} -31.4562 q^{14} +28.6064 q^{15} -0.181784 q^{16} +28.0472 q^{17} +26.1254 q^{18} +44.4394 q^{19} -40.6113 q^{20} +62.4384 q^{21} -19.2607 q^{22} -192.682 q^{23} +78.7116 q^{24} -57.2549 q^{25} -145.697 q^{27} -88.6414 q^{28} -49.2942 q^{29} -50.0889 q^{30} +118.496 q^{31} -180.860 q^{32} +38.2311 q^{33} -49.1098 q^{34} +147.866 q^{35} +73.6194 q^{36} -57.8650 q^{37} -77.8120 q^{38} +186.404 q^{40} -496.817 q^{41} -109.328 q^{42} -226.059 q^{43} -54.2751 q^{44} -122.807 q^{45} +337.380 q^{46} +67.8838 q^{47} -0.631798 q^{48} -20.2574 q^{49} +100.252 q^{50} +97.4796 q^{51} +428.853 q^{53} +255.111 q^{54} +90.5382 q^{55} +406.858 q^{56} +154.451 q^{57} +86.3126 q^{58} +792.083 q^{59} -141.147 q^{60} -691.816 q^{61} -207.483 q^{62} -268.048 q^{63} +318.134 q^{64} -66.9415 q^{66} -700.044 q^{67} -138.388 q^{68} -669.675 q^{69} -258.908 q^{70} -318.160 q^{71} -337.909 q^{72} +189.776 q^{73} +101.320 q^{74} -198.992 q^{75} -219.268 q^{76} +197.615 q^{77} -894.471 q^{79} -1.49621 q^{80} -103.524 q^{81} +869.912 q^{82} -328.861 q^{83} -308.078 q^{84} +230.850 q^{85} +395.823 q^{86} -171.324 q^{87} +249.120 q^{88} -615.226 q^{89} +215.031 q^{90} +950.711 q^{92} +411.838 q^{93} -118.862 q^{94} +365.769 q^{95} -628.587 q^{96} -752.293 q^{97} +35.4701 q^{98} -164.126 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.75097	−0.619061	−0.309531	−	0.950889i	$-0.600172\pi$
$2$	−1.75097	−0.619061	−0.309531	+	0.950889i	$0.600172\pi$
$3$	3.47555	0.668871	0.334435	−	0.942419i	$-0.391454\pi$
$3$	3.47555	0.668871	0.334435	+	0.942419i	$0.391454\pi$
$4$	−4.93410	−0.616763
$5$	8.23074	0.736180	0.368090	−	0.929790i	$-0.380012\pi$
$5$	8.23074	0.736180	0.368090	+	0.929790i	$0.380012\pi$
$6$	−6.08559	−0.414072
$7$	17.9650	0.970021	0.485010	−	0.874508i	$-0.338816\pi$
$7$	17.9650	0.970021	0.485010	+	0.874508i	$0.338816\pi$
$8$	22.6472	1.00088
$9$	−14.9205	−0.552612
$10$	−14.4118	−0.455741
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−17.1487	−0.412535
$13$	0	0
$13$	0	0
$14$	−31.4562	−0.600502
$15$	28.6064	0.492409
$16$	−0.181784	−0.00284037
$17$	28.0472	0.400144	0.200072	−	0.979781i	$-0.435882\pi$
$17$	28.0472	0.400144	0.200072	+	0.979781i	$0.435882\pi$
$18$	26.1254	0.342101
$19$	44.4394	0.536584	0.268292	−	0.963338i	$-0.413541\pi$
$19$	44.4394	0.536584	0.268292	+	0.963338i	$0.413541\pi$
$20$	−40.6113	−0.454049
$21$	62.4384	0.648818
$22$	−19.2607	−0.186654
$23$	−192.682	−1.74682	−0.873410	−	0.486985i	$-0.838097\pi$
$23$	−192.682	−1.74682	−0.873410	+	0.486985i	$0.838097\pi$
$24$	78.7116	0.669456
$25$	−57.2549	−0.458039
$26$	0	0
$27$	−145.697	−1.03850
$28$	−88.6414	−0.598273
$29$	−49.2942	−0.315645	−0.157822	−	0.987468i	$-0.550447\pi$
$29$	−49.2942	−0.315645	−0.157822	+	0.987468i	$0.550447\pi$
$30$	−50.0889	−0.304832
$31$	118.496	0.686531	0.343266	−	0.939238i	$-0.388467\pi$
$31$	118.496	0.686531	0.343266	+	0.939238i	$0.388467\pi$
$32$	−180.860	−0.999117
$33$	38.2311	0.201672
$34$	−49.1098	−0.247714
$35$	147.866	0.714110
$36$	73.6194	0.340831
$37$	−57.8650	−0.257107	−0.128553	−	0.991703i	$-0.541033\pi$
$37$	−57.8650	−0.257107	−0.128553	+	0.991703i	$0.541033\pi$
$38$	−77.8120	−0.332178
$39$	0	0
$40$	186.404	0.736825
$41$	−496.817	−1.89243	−0.946217	−	0.323532i	$-0.895130\pi$
$41$	−496.817	−1.89243	−0.946217	+	0.323532i	$0.895130\pi$
$42$	−109.328	−0.401658
$43$	−226.059	−0.801714	−0.400857	−	0.916141i	$-0.631288\pi$
$43$	−226.059	−0.801714	−0.400857	+	0.916141i	$0.631288\pi$
$44$	−54.2751	−0.185961
$45$	−122.807	−0.406822
$46$	337.380	1.08139
$47$	67.8838	0.210678	0.105339	−	0.994436i	$-0.466407\pi$
$47$	67.8838	0.210678	0.105339	+	0.994436i	$0.466407\pi$
$48$	−0.631798	−0.00189984
$49$	−20.2574	−0.0590595
$50$	100.252	0.283554
$51$	97.4796	0.267645
$52$	0	0
$53$	428.853	1.11146	0.555731	−	0.831362i	$-0.312439\pi$
$53$	428.853	1.11146	0.555731	+	0.831362i	$0.312439\pi$
$54$	255.111	0.642893
$55$	90.5382	0.221967
$56$	406.858	0.970870
$57$	154.451	0.358905
$58$	86.3126	0.195403
$59$	792.083	1.74780	0.873902	−	0.486103i	$-0.161582\pi$
$59$	792.083	1.74780	0.873902	+	0.486103i	$0.161582\pi$
$60$	−141.147	−0.303700
$61$	−691.816	−1.45210	−0.726049	−	0.687643i	$-0.758646\pi$
$61$	−691.816	−1.45210	−0.726049	+	0.687643i	$0.758646\pi$
$62$	−207.483	−0.425005
$63$	−268.048	−0.536045
$64$	318.134	0.621355
$65$	0	0
$66$	−66.9415	−0.124847
$67$	−700.044	−1.27648	−0.638239	−	0.769838i	$-0.720337\pi$
$67$	−700.044	−1.27648	−0.638239	+	0.769838i	$0.720337\pi$
$68$	−138.388	−0.246794
$69$	−669.675	−1.16840
$70$	−258.908	−0.442078
$71$	−318.160	−0.531812	−0.265906	−	0.963999i	$-0.585671\pi$
$71$	−318.160	−0.531812	−0.265906	+	0.963999i	$0.585671\pi$
$72$	−337.909	−0.553096
$73$	189.776	0.304269	0.152134	−	0.988360i	$-0.451385\pi$
$73$	189.776	0.304269	0.152134	+	0.988360i	$0.451385\pi$
$74$	101.320	0.159165
$75$	−198.992	−0.306369
$76$	−219.268	−0.330945
$77$	197.615	0.292472
$78$	0	0
$79$	−894.471	−1.27387	−0.636936	−	0.770917i	$-0.719798\pi$
$79$	−894.471	−1.27387	−0.636936	+	0.770917i	$0.719798\pi$
$80$	−1.49621	−0.00209102
$81$	−103.524	−0.142008
$82$	869.912	1.17153
$83$	−328.861	−0.434906	−0.217453	−	0.976071i	$-0.569775\pi$
$83$	−328.861	−0.434906	−0.217453	+	0.976071i	$0.569775\pi$
$84$	−308.078	−0.400167
$85$	230.850	0.294578
$86$	395.823	0.496310
$87$	−171.324	−0.211125
$88$	249.120	0.301775
$89$	−615.226	−0.732739	−0.366370	−	0.930469i	$-0.619399\pi$
$89$	−615.226	−0.732739	−0.366370	+	0.930469i	$0.619399\pi$
$90$	215.031	0.251848
$91$	0	0
$92$	950.711	1.07737
$93$	411.838	0.459201
$94$	−118.862	−0.130423
$95$	365.769	0.395022
$96$	−628.587	−0.668280
$97$	−752.293	−0.787461	−0.393731	−	0.919226i	$-0.628816\pi$
$97$	−752.293	−0.787461	−0.393731	+	0.919226i	$0.628816\pi$
$98$	35.4701	0.0365615
$99$	−164.126	−0.166619
$100$	282.501	0.282501
$101$	1857.94	1.83042	0.915209	−	0.402979i	$-0.132025\pi$
$101$	1857.94	1.83042	0.915209	+	0.402979i	$0.132025\pi$
$102$	−170.684	−0.165688
$103$	770.052	0.736655	0.368328	−	0.929696i	$-0.379930\pi$
$103$	770.052	0.736655	0.368328	+	0.929696i	$0.379930\pi$
$104$	0	0
$105$	513.915	0.477647
$106$	−750.908	−0.688063
$107$	−775.772	−0.700903	−0.350452	−	0.936581i	$-0.613972\pi$
$107$	−775.772	−0.700903	−0.350452	+	0.936581i	$0.613972\pi$
$108$	718.884	0.640506
$109$	−556.340	−0.488878	−0.244439	−	0.969665i	$-0.578604\pi$
$109$	−556.340	−0.488878	−0.244439	+	0.969665i	$0.578604\pi$
$110$	−158.530	−0.137411
$111$	−201.113	−0.171971
$112$	−3.26575	−0.00275522
$113$	1453.73	1.21023	0.605114	−	0.796139i	$-0.293128\pi$
$113$	1453.73	1.21023	0.605114	+	0.796139i	$0.293128\pi$
$114$	−270.440	−0.222184
$115$	−1585.91	−1.28597
$116$	243.223	0.194678
$117$	0	0
$118$	−1386.91	−1.08200
$119$	503.869	0.388148
$120$	647.855	0.492840
$121$	121.000	0.0909091
$122$	1211.35	0.898938
$123$	−1726.71	−1.26579
$124$	−584.671	−0.423427
$125$	−1500.09	−1.07338
$126$	469.344	0.331845
$127$	737.987	0.515636	0.257818	−	0.966194i	$-0.416997\pi$
$127$	737.987	0.515636	0.257818	+	0.966194i	$0.416997\pi$
$128$	889.833	0.614460
$129$	−785.680	−0.536243
$130$	0	0
$131$	−1770.20	−1.18064	−0.590318	−	0.807171i	$-0.700998\pi$
$131$	−1770.20	−1.18064	−0.590318	+	0.807171i	$0.700998\pi$
$132$	−188.636	−0.124384
$133$	798.355	0.520497
$134$	1225.76	0.790218
$135$	−1199.19	−0.764520
$136$	635.192	0.400495
$137$	−169.035	−0.105413	−0.0527066	−	0.998610i	$-0.516785\pi$
$137$	−169.035	−0.105413	−0.0527066	+	0.998610i	$0.516785\pi$
$138$	1172.58	0.723309
$139$	42.3421	0.0258375	0.0129187	−	0.999917i	$-0.495888\pi$
$139$	42.3421	0.0258375	0.0129187	+	0.999917i	$0.495888\pi$
$140$	−729.584	−0.440437
$141$	235.934	0.140916
$142$	557.089	0.329224
$143$	0	0
$144$	2.71231	0.00156962
$145$	−405.728	−0.232371
$146$	−332.293	−0.188361
$147$	−70.4057	−0.0395032
$148$	285.512	0.158574
$149$	−1461.52	−0.803571	−0.401786	−	0.915734i	$-0.631610\pi$
$149$	−1461.52	−0.803571	−0.401786	+	0.915734i	$0.631610\pi$
$150$	348.430	0.189661
$151$	3250.95	1.75205	0.876023	−	0.482270i	$-0.160188\pi$
$151$	3250.95	1.75205	0.876023	+	0.482270i	$0.160188\pi$
$152$	1006.43	0.537053
$153$	−418.479	−0.221125
$154$	−346.019	−0.181058
$155$	975.308	0.505411
$156$	0	0
$157$	3244.13	1.64911	0.824553	−	0.565785i	$-0.191427\pi$
$157$	3244.13	1.64911	0.824553	+	0.565785i	$0.191427\pi$
$158$	1566.19	0.788605
$159$	1490.50	0.743424
$160$	−1488.61	−0.735530
$161$	−3461.53	−1.69445
$162$	181.267	0.0879114
$163$	2350.78	1.12962	0.564808	−	0.825223i	$-0.308950\pi$
$163$	2350.78	1.12962	0.564808	+	0.825223i	$0.308950\pi$
$164$	2451.35	1.16718
$165$	314.670	0.148467
$166$	575.827	0.269234
$167$	−1155.86	−0.535586	−0.267793	−	0.963477i	$-0.586294\pi$
$167$	−1155.86	−0.535586	−0.267793	+	0.963477i	$0.586294\pi$
$168$	1414.06	0.649386
$169$	0	0
$170$	−404.211	−0.182362
$171$	−663.059	−0.296523
$172$	1115.40	0.494467
$173$	−2196.70	−0.965388	−0.482694	−	0.875789i	$-0.660342\pi$
$173$	−2196.70	−0.965388	−0.482694	+	0.875789i	$0.660342\pi$
$174$	299.984	0.130700
$175$	−1028.59	−0.444307
$176$	−1.99962	−0.000856403 0
$177$	2752.93	1.16905
$178$	1077.24	0.453611
$179$	−2579.32	−1.07702	−0.538512	−	0.842618i	$-0.681013\pi$
$179$	−2579.32	−1.07702	−0.538512	+	0.842618i	$0.681013\pi$
$180$	605.943	0.250913
$181$	3829.30	1.57254	0.786269	−	0.617885i	$-0.212010\pi$
$181$	3829.30	1.57254	0.786269	+	0.617885i	$0.212010\pi$
$182$	0	0
$183$	−2404.44	−0.971266
$184$	−4363.70	−1.74835
$185$	−476.272	−0.189277
$186$	−721.117	−0.284273
$187$	308.519	0.120648
$188$	−334.946	−0.129938
$189$	−2617.45	−1.00736
$190$	−640.450	−0.244543
$191$	−925.668	−0.350675	−0.175338	−	0.984508i	$-0.556102\pi$
$191$	−925.668	−0.350675	−0.175338	+	0.984508i	$0.556102\pi$
$192$	1105.69	0.415606
$193$	−852.061	−0.317786	−0.158893	−	0.987296i	$-0.550792\pi$
$193$	−852.061	−0.317786	−0.158893	+	0.987296i	$0.550792\pi$
$194$	1317.24	0.487487
$195$	0	0
$196$	99.9522	0.0364257
$197$	431.118	0.155918	0.0779592	−	0.996957i	$-0.475160\pi$
$197$	431.118	0.155918	0.0779592	+	0.996957i	$0.475160\pi$
$198$	287.379	0.103147
$199$	−5127.28	−1.82645	−0.913224	−	0.407457i	$-0.866416\pi$
$199$	−5127.28	−1.82645	−0.913224	+	0.407457i	$0.866416\pi$
$200$	−1296.66	−0.458440
$201$	−2433.04	−0.853799
$202$	−3253.20	−1.13314
$203$	−885.571	−0.306182
$204$	−480.975	−0.165073
$205$	−4089.18	−1.39317
$206$	−1348.34	−0.456035
$207$	2874.91	0.965315
$208$	0	0
$209$	488.833	0.161786
$210$	−899.849	−0.295693
$211$	−2047.44	−0.668016	−0.334008	−	0.942570i	$-0.608401\pi$
$211$	−2047.44	−0.668016	−0.334008	+	0.942570i	$0.608401\pi$
$212$	−2116.00	−0.685508
$213$	−1105.78	−0.355713
$214$	1358.35	0.433902
$215$	−1860.63	−0.590206
$216$	−3299.63	−1.03941
$217$	2128.78	0.665950
$218$	974.134	0.302645
$219$	659.578	0.203517
$220$	−446.725	−0.136901
$221$	0	0
$222$	352.143	0.106461
$223$	−2849.80	−0.855769	−0.427885	−	0.903833i	$-0.640741\pi$
$223$	−2849.80	−0.855769	−0.427885	+	0.903833i	$0.640741\pi$
$224$	−3249.15	−0.969165
$225$	854.273	0.253118
$226$	−2545.44	−0.749205
$227$	−2022.66	−0.591404	−0.295702	−	0.955280i	$-0.595554\pi$
$227$	−2022.66	−0.591404	−0.295702	+	0.955280i	$0.595554\pi$
$228$	−762.079	−0.221359
$229$	−1365.28	−0.393975	−0.196988	−	0.980406i	$-0.563116\pi$
$229$	−1365.28	−0.393975	−0.196988	+	0.980406i	$0.563116\pi$
$230$	2776.89	0.796097
$231$	686.823	0.195626
$232$	−1116.38	−0.315921
$233$	−3021.58	−0.849571	−0.424785	−	0.905294i	$-0.639650\pi$
$233$	−3021.58	−0.849571	−0.424785	+	0.905294i	$0.639650\pi$
$234$	0	0
$235$	558.734	0.155097
$236$	−3908.22	−1.07798
$237$	−3108.78	−0.852056
$238$	−882.260	−0.240288
$239$	6559.77	1.77538	0.887691	−	0.460439i	$-0.152308\pi$
$239$	6559.77	1.77538	0.887691	+	0.460439i	$0.152308\pi$
$240$	−5.20017	−0.00139862
$241$	2861.89	0.764941	0.382470	−	0.923968i	$-0.375073\pi$
$241$	2861.89	0.764941	0.382470	+	0.923968i	$0.375073\pi$
$242$	−211.867	−0.0562783
$243$	3574.02	0.943512
$244$	3413.49	0.895601
$245$	−166.734	−0.0434784
$246$	3023.43	0.783604
$247$	0	0
$248$	2683.60	0.687132
$249$	−1142.98	−0.290896
$250$	2626.62	0.664488
$251$	−5029.67	−1.26482	−0.632411	−	0.774633i	$-0.717935\pi$
$251$	−5029.67	−1.26482	−0.632411	+	0.774633i	$0.717935\pi$
$252$	1322.58	0.330613
$253$	−2119.50	−0.526686
$254$	−1292.19	−0.319210
$255$	802.330	0.197035
$256$	−4103.14	−1.00174
$257$	−3947.81	−0.958201	−0.479100	−	0.877760i	$-0.659037\pi$
$257$	−3947.81	−0.958201	−0.479100	+	0.877760i	$0.659037\pi$
$258$	1375.70	0.331967
$259$	−1039.55	−0.249399
$260$	0	0
$261$	735.495	0.174429
$262$	3099.57	0.730886
$263$	16.4413	0.00385480	0.00192740	−	0.999998i	$-0.499386\pi$
$263$	16.4413	0.00385480	0.00192740	+	0.999998i	$0.499386\pi$
$264$	865.828	0.201849
$265$	3529.78	0.818236
$266$	−1397.90	−0.322220
$267$	−2138.25	−0.490108
$268$	3454.09	0.787285
$269$	2473.90	0.560730	0.280365	−	0.959894i	$-0.409545\pi$
$269$	2473.90	0.560730	0.280365	+	0.959894i	$0.409545\pi$
$270$	2099.75	0.473285
$271$	316.738	0.0709981	0.0354990	−	0.999370i	$-0.488698\pi$
$271$	316.738	0.0709981	0.0354990	+	0.999370i	$0.488698\pi$
$272$	−5.09852	−0.00113656
$273$	0	0
$274$	295.975	0.0652572
$275$	−629.803	−0.138104
$276$	3304.25	0.720624
$277$	−6929.35	−1.50305	−0.751524	−	0.659706i	$-0.770681\pi$
$277$	−6929.35	−1.50305	−0.751524	+	0.659706i	$0.770681\pi$
$278$	−74.1398	−0.0159950
$279$	−1768.02	−0.379386
$280$	3348.75	0.714735
$281$	−7453.75	−1.58240	−0.791198	−	0.611560i	$-0.790542\pi$
$281$	−7453.75	−1.58240	−0.791198	+	0.611560i	$0.790542\pi$
$282$	−413.113	−0.0872358
$283$	3543.82	0.744376	0.372188	−	0.928157i	$-0.378608\pi$
$283$	3543.82	0.744376	0.372188	+	0.928157i	$0.378608\pi$
$284$	1569.84	0.328002
$285$	1271.25	0.264219
$286$	0	0
$287$	−8925.34	−1.83570
$288$	2698.52	0.552124
$289$	−4126.35	−0.839885
$290$	710.417	0.143852
$291$	−2614.63	−0.526710
$292$	−936.376	−0.187662
$293$	−2181.32	−0.434929	−0.217464	−	0.976068i	$-0.569779\pi$
$293$	−2181.32	−0.434929	−0.217464	+	0.976068i	$0.569779\pi$
$294$	123.278	0.0244549
$295$	6519.43	1.28670
$296$	−1310.48	−0.257332
$297$	−1602.67	−0.313118
$298$	2559.07	0.497460
$299$	0	0
$300$	981.849	0.188957
$301$	−4061.16	−0.777679
$302$	−5692.32	−1.08462
$303$	6457.38	1.22431
$304$	−8.07834	−0.00152409
$305$	−5694.16	−1.06901
$306$	732.745	0.136890
$307$	6755.87	1.25595	0.627977	−	0.778232i	$-0.283883\pi$
$307$	6755.87	1.25595	0.627977	+	0.778232i	$0.283883\pi$
$308$	−975.055	−0.180386
$309$	2676.36	0.492727
$310$	−1707.74	−0.312880
$311$	410.371	0.0748231	0.0374116	−	0.999300i	$-0.488089\pi$
$311$	410.371	0.0748231	0.0374116	+	0.999300i	$0.488089\pi$
$312$	0	0
$313$	−5628.26	−1.01638	−0.508192	−	0.861244i	$-0.669686\pi$
$313$	−5628.26	−1.01638	−0.508192	+	0.861244i	$0.669686\pi$
$314$	−5680.37	−1.02090
$315$	−2206.23	−0.394626
$316$	4413.42	0.785677
$317$	5955.90	1.05526	0.527629	−	0.849475i	$-0.323081\pi$
$317$	5955.90	1.05526	0.527629	+	0.849475i	$0.323081\pi$
$318$	−2609.82	−0.460225
$319$	−542.236	−0.0951704
$320$	2618.48	0.457429
$321$	−2696.24	−0.468814
$322$	6061.04	1.04897
$323$	1246.40	0.214711
$324$	510.796	0.0875850
$325$	0	0
$326$	−4116.15	−0.699301
$327$	−1933.59	−0.326996
$328$	−11251.5	−1.89409
$329$	1219.53	0.204362
$330$	−550.978	−0.0919102
$331$	4163.82	0.691433	0.345716	−	0.938339i	$-0.387636\pi$
$331$	4163.82	0.691433	0.345716	+	0.938339i	$0.387636\pi$
$332$	1622.64	0.268234
$333$	863.377	0.142080
$334$	2023.87	0.331560
$335$	−5761.89	−0.939718
$336$	−11.3503	−0.00184288
$337$	6456.50	1.04364	0.521822	−	0.853054i	$-0.325252\pi$
$337$	6456.50	1.04364	0.521822	+	0.853054i	$0.325252\pi$
$338$	0	0
$339$	5052.53	0.809486
$340$	−1139.04	−0.181685
$341$	1303.45	0.206997
$342$	1161.00	0.183566
$343$	−6525.93	−1.02731
$344$	−5119.61	−0.802416
$345$	−5511.92	−0.860151
$346$	3846.36	0.597634
$347$	7348.41	1.13684	0.568420	−	0.822739i	$-0.307555\pi$
$347$	7348.41	1.13684	0.568420	+	0.822739i	$0.307555\pi$
$348$	845.333	0.130214
$349$	3819.09	0.585764	0.292882	−	0.956149i	$-0.405386\pi$
$349$	3819.09	0.585764	0.292882	+	0.956149i	$0.405386\pi$
$350$	1801.02	0.275053
$351$	0	0
$352$	−1989.45	−0.301245
$353$	6037.09	0.910260	0.455130	−	0.890425i	$-0.349593\pi$
$353$	6037.09	0.910260	0.455130	+	0.890425i	$0.349593\pi$
$354$	−4820.29	−0.723716
$355$	−2618.69	−0.391510
$356$	3035.59	0.451926
$357$	1751.23	0.259621
$358$	4516.31	0.666744
$359$	−12145.0	−1.78549	−0.892744	−	0.450564i	$-0.851223\pi$
$359$	−12145.0	−1.78549	−0.892744	+	0.450564i	$0.851223\pi$
$360$	−2781.24	−0.407178
$361$	−4884.14	−0.712078
$362$	−6704.98	−0.973497
$363$	420.542	0.0608064
$364$	0	0
$365$	1562.00	0.223997
$366$	4210.11	0.601273
$367$	−5960.56	−0.847789	−0.423895	−	0.905712i	$-0.639337\pi$
$367$	−5960.56	−0.847789	−0.423895	+	0.905712i	$0.639337\pi$
$368$	35.0263	0.00496161
$369$	7412.78	1.04578
$370$	833.939	0.117174
$371$	7704.35	1.07814
$372$	−2032.05	−0.283218
$373$	−3243.42	−0.450236	−0.225118	−	0.974332i	$-0.572277\pi$
$373$	−3243.42	−0.450236	−0.225118	+	0.974332i	$0.572277\pi$
$374$	−540.208	−0.0746885
$375$	−5213.65	−0.717952
$376$	1537.38	0.210862
$377$	0	0
$378$	4583.08	0.623620
$379$	−7601.00	−1.03018	−0.515089	−	0.857137i	$-0.672241\pi$
$379$	−7601.00	−1.03018	−0.515089	+	0.857137i	$0.672241\pi$
$380$	−1804.74	−0.243635
$381$	2564.91	0.344894
$382$	1620.82	0.217090
$383$	1689.30	0.225377	0.112688	−	0.993630i	$-0.464054\pi$
$383$	1689.30	0.225377	0.112688	+	0.993630i	$0.464054\pi$
$384$	3092.66	0.410994
$385$	1626.52	0.215312
$386$	1491.93	0.196729
$387$	3372.92	0.443037
$388$	3711.89	0.485677
$389$	6795.58	0.885732	0.442866	−	0.896588i	$-0.353962\pi$
$389$	6795.58	0.885732	0.442866	+	0.896588i	$0.353962\pi$
$390$	0	0
$391$	−5404.18	−0.698980
$392$	−458.774	−0.0591112
$393$	−6152.44	−0.789693
$394$	−754.875	−0.0965230
$395$	−7362.16	−0.937799
$396$	809.814	0.102764
$397$	−13637.4	−1.72403	−0.862015	−	0.506882i	$-0.830798\pi$
$397$	−13637.4	−1.72403	−0.862015	+	0.506882i	$0.830798\pi$
$398$	8977.71	1.13068
$399$	2774.72	0.348145
$400$	10.4080	0.00130100
$401$	−6609.91	−0.823150	−0.411575	−	0.911376i	$-0.635021\pi$
$401$	−6609.91	−0.823150	−0.411575	+	0.911376i	$0.635021\pi$
$402$	4260.18	0.528554
$403$	0	0
$404$	−9167.28	−1.12893
$405$	−852.076	−0.104543
$406$	1550.61	0.189545
$407$	−636.515	−0.0775206
$408$	2207.64	0.267879
$409$	5984.49	0.723506	0.361753	−	0.932274i	$-0.382178\pi$
$409$	5984.49	0.723506	0.361753	+	0.932274i	$0.382178\pi$
$410$	7160.02	0.862459
$411$	−587.489	−0.0705078
$412$	−3799.52	−0.454342
$413$	14229.8	1.69541
$414$	−5033.88	−0.597589
$415$	−2706.77	−0.320169
$416$	0	0
$417$	147.162	0.0172819
$418$	−855.932	−0.100155
$419$	1525.91	0.177913	0.0889563	−	0.996036i	$-0.471647\pi$
$419$	1525.91	0.177913	0.0889563	+	0.996036i	$0.471647\pi$
$420$	−2535.71	−0.294595
$421$	−13572.9	−1.57126	−0.785631	−	0.618696i	$-0.787661\pi$
$421$	−13572.9	−1.57126	−0.785631	+	0.618696i	$0.787661\pi$
$422$	3585.00	0.413543
$423$	−1012.86	−0.116423
$424$	9712.32	1.11243
$425$	−1605.84	−0.183282
$426$	1936.19	0.220208
$427$	−12428.5	−1.40857
$428$	3827.74	0.432291
$429$	0	0
$430$	3257.91	0.365373
$431$	−7686.82	−0.859074	−0.429537	−	0.903049i	$-0.641323\pi$
$431$	−7686.82	−0.859074	−0.429537	+	0.903049i	$0.641323\pi$
$432$	26.4853	0.00294971
$433$	−5873.05	−0.651827	−0.325913	−	0.945400i	$-0.605672\pi$
$433$	−5873.05	−0.651827	−0.325913	+	0.945400i	$0.605672\pi$
$434$	−3727.43	−0.412264
$435$	−1410.13	−0.155426
$436$	2745.04	0.301522
$437$	−8562.64	−0.937315
$438$	−1154.90	−0.125989
$439$	−7804.57	−0.848500	−0.424250	−	0.905545i	$-0.639462\pi$
$439$	−7804.57	−0.848500	−0.424250	+	0.905545i	$0.639462\pi$
$440$	2050.44	0.222161
$441$	302.251	0.0326370
$442$	0	0
$443$	−870.362	−0.0933458	−0.0466729	−	0.998910i	$-0.514862\pi$
$443$	−870.362	−0.0933458	−0.0466729	+	0.998910i	$0.514862\pi$
$444$	992.313	0.106065
$445$	−5063.76	−0.539428
$446$	4989.91	0.529774
$447$	−5079.58	−0.537485
$448$	5715.29	0.602728
$449$	2769.96	0.291142	0.145571	−	0.989348i	$-0.453498\pi$
$449$	2769.96	0.291142	0.145571	+	0.989348i	$0.453498\pi$
$450$	−1495.81	−0.156695
$451$	−5464.99	−0.570590
$452$	−7172.87	−0.746424
$453$	11298.9	1.17189
$454$	3541.62	0.366115
$455$	0	0
$456$	3497.90	0.359219
$457$	1389.23	0.142200	0.0710998	−	0.997469i	$-0.477349\pi$
$457$	1389.23	0.142200	0.0710998	+	0.997469i	$0.477349\pi$
$458$	2390.57	0.243895
$459$	−4086.40	−0.415548
$460$	7825.06	0.793142
$461$	15251.6	1.54086	0.770429	−	0.637526i	$-0.220042\pi$
$461$	15251.6	1.54086	0.770429	+	0.637526i	$0.220042\pi$
$462$	−1202.61	−0.121105
$463$	−11372.5	−1.14152	−0.570760	−	0.821117i	$-0.693351\pi$
$463$	−11372.5	−1.14152	−0.570760	+	0.821117i	$0.693351\pi$
$464$	8.96087	0.000896547 0
$465$	3389.74	0.338054
$466$	5290.69	0.525937
$467$	−16855.6	−1.67020	−0.835101	−	0.550097i	$-0.814591\pi$
$467$	−16855.6	−1.67020	−0.835101	+	0.550097i	$0.814591\pi$
$468$	0	0
$469$	−12576.3	−1.23821
$470$	−978.326	−0.0960145
$471$	11275.1	1.10304
$472$	17938.5	1.74933
$473$	−2486.65	−0.241726
$474$	5443.39	0.527475
$475$	−2544.37	−0.245776
$476$	−2486.14	−0.239395
$477$	−6398.71	−0.614207
$478$	−11486.0	−1.09907
$479$	13948.4	1.33052	0.665260	−	0.746612i	$-0.268321\pi$
$479$	13948.4	1.33052	0.665260	+	0.746612i	$0.268321\pi$
$480$	−5173.74	−0.491974
$481$	0	0
$482$	−5011.09	−0.473545
$483$	−12030.7	−1.13337
$484$	−597.027	−0.0560694
$485$	−6191.93	−0.579713
$486$	−6258.00	−0.584092
$487$	−17469.8	−1.62553	−0.812763	−	0.582594i	$-0.802038\pi$
$487$	−17469.8	−1.62553	−0.812763	+	0.582594i	$0.802038\pi$
$488$	−15667.7	−1.45337
$489$	8170.26	0.755566
$490$	291.945	0.0269158
$491$	−9166.12	−0.842487	−0.421244	−	0.906948i	$-0.638406\pi$
$491$	−9166.12	−0.842487	−0.421244	+	0.906948i	$0.638406\pi$
$492$	8519.79	0.780695
$493$	−1382.56	−0.126303
$494$	0	0
$495$	−1350.88	−0.122661
$496$	−21.5406	−0.00195000
$497$	−5715.76	−0.515869
$498$	2001.32	0.180083
$499$	10268.0	0.921157	0.460578	−	0.887619i	$-0.347642\pi$
$499$	10268.0	0.921157	0.460578	+	0.887619i	$0.347642\pi$
$500$	7401.62	0.662021
$501$	−4017.24	−0.358237
$502$	8806.81	0.783002
$503$	−4911.90	−0.435409	−0.217705	−	0.976015i	$-0.569857\pi$
$503$	−4911.90	−0.435409	−0.217705	+	0.976015i	$0.569857\pi$
$504$	−6070.54	−0.536515
$505$	15292.3	1.34752
$506$	3711.18	0.326051
$507$	0	0
$508$	−3641.30	−0.318025
$509$	−8141.39	−0.708960	−0.354480	−	0.935064i	$-0.615342\pi$
$509$	−8141.39	−0.708960	−0.354480	+	0.935064i	$0.615342\pi$
$510$	−1404.86	−0.121977
$511$	3409.34	0.295147
$512$	65.8124	0.00568071
$513$	−6474.68	−0.557240
$514$	6912.50	0.593185
$515$	6338.10	0.542311
$516$	3876.63	0.330735
$517$	746.721	0.0635218
$518$	1820.22	0.154393
$519$	−7634.75	−0.645719
$520$	0	0
$521$	2822.17	0.237315	0.118658	−	0.992935i	$-0.462141\pi$
$521$	2822.17	0.237315	0.118658	+	0.992935i	$0.462141\pi$
$522$	−1287.83	−0.107982
$523$	3939.18	0.329347	0.164673	−	0.986348i	$-0.447343\pi$
$523$	3939.18	0.329347	0.164673	+	0.986348i	$0.447343\pi$
$524$	8734.37	0.728173
$525$	−3574.90	−0.297184
$526$	−28.7882	−0.00238636
$527$	3323.48	0.274712
$528$	−6.94978	−0.000572823 0
$529$	24959.2	2.05138
$530$	−6180.53	−0.506538
$531$	−11818.3	−0.965857
$532$	−3939.17	−0.321023
$533$	0	0
$534$	3744.01	0.303407
$535$	−6385.18	−0.515991
$536$	−15854.1	−1.27760
$537$	−8964.55	−0.720389
$538$	−4331.72	−0.347126
$539$	−222.832	−0.0178071
$540$	5916.95	0.471528
$541$	−8326.91	−0.661741	−0.330870	−	0.943676i	$-0.607342\pi$
$541$	−8326.91	−0.661741	−0.330870	+	0.943676i	$0.607342\pi$
$542$	−554.599	−0.0439522
$543$	13308.9	1.05182
$544$	−5072.61	−0.399791
$545$	−4579.09	−0.359902
$546$	0	0
$547$	7772.51	0.607547	0.303774	−	0.952744i	$-0.401753\pi$
$547$	7772.51	0.607547	0.303774	+	0.952744i	$0.401753\pi$
$548$	834.035	0.0650150
$549$	10322.3	0.802447
$550$	1102.77	0.0854948
$551$	−2190.60	−0.169370
$552$	−15166.3	−1.16942
$553$	−16069.2	−1.23568
$554$	12133.1	0.930479
$555$	−1655.31	−0.126602
$556$	−208.920	−0.0159356
$557$	−7765.12	−0.590698	−0.295349	−	0.955389i	$-0.595436\pi$
$557$	−7765.12	−0.590698	−0.295349	+	0.955389i	$0.595436\pi$
$558$	3095.75	0.234863
$559$	0	0
$560$	−26.8795	−0.00202834
$561$	1072.28	0.0806979
$562$	13051.3	0.979601
$563$	2911.64	0.217959	0.108980	−	0.994044i	$-0.465242\pi$
$563$	2911.64	0.217959	0.108980	+	0.994044i	$0.465242\pi$
$564$	−1164.12	−0.0869120
$565$	11965.3	0.890945
$566$	−6205.13	−0.460814
$567$	−1859.80	−0.137750
$568$	−7205.45	−0.532278
$569$	5241.56	0.386182	0.193091	−	0.981181i	$-0.438149\pi$
$569$	5241.56	0.386182	0.193091	+	0.981181i	$0.438149\pi$
$570$	−2225.92	−0.163568
$571$	−10710.3	−0.784959	−0.392479	−	0.919761i	$-0.628383\pi$
$571$	−10710.3	−0.784959	−0.392479	+	0.919761i	$0.628383\pi$
$572$	0	0
$573$	−3217.21	−0.234557
$574$	15628.0	1.13641
$575$	11032.0	0.800112
$576$	−4746.73	−0.343368
$577$	−4891.38	−0.352913	−0.176456	−	0.984308i	$-0.556463\pi$
$577$	−4891.38	−0.352913	−0.176456	+	0.984308i	$0.556463\pi$
$578$	7225.12	0.519940
$579$	−2961.38	−0.212558
$580$	2001.90	0.143318
$581$	−5908.01	−0.421868
$582$	4578.14	0.326066
$583$	4717.38	0.335118
$584$	4297.91	0.304535
$585$	0	0
$586$	3819.43	0.269248
$587$	−5477.65	−0.385156	−0.192578	−	0.981282i	$-0.561685\pi$
$587$	−5477.65	−0.385156	−0.192578	+	0.981282i	$0.561685\pi$
$588$	347.389	0.0243641
$589$	5265.88	0.368381
$590$	−11415.3	−0.796545
$591$	1498.37	0.104289
$592$	10.5189	0.000730278 0
$593$	−4552.12	−0.315233	−0.157617	−	0.987500i	$-0.550381\pi$
$593$	−4552.12	−0.315233	−0.157617	+	0.987500i	$0.550381\pi$
$594$	2806.22	0.193840
$595$	4147.22	0.285747
$596$	7211.27	0.495613
$597$	−17820.1	−1.22166
$598$	0	0
$599$	−14947.9	−1.01962	−0.509810	−	0.860287i	$-0.670284\pi$
$599$	−14947.9	−1.01962	−0.509810	+	0.860287i	$0.670284\pi$
$600$	−4506.62	−0.306637
$601$	22193.9	1.50634	0.753168	−	0.657828i	$-0.228524\pi$
$601$	22193.9	1.50634	0.753168	+	0.657828i	$0.228524\pi$
$602$	7110.97	0.481431
$603$	10445.0	0.705397
$604$	−16040.5	−1.08060
$605$	995.920	0.0669255
$606$	−11306.7	−0.757925
$607$	115.689	0.00773584	0.00386792	−	0.999993i	$-0.498769\pi$
$607$	115.689	0.00773584	0.00386792	+	0.999993i	$0.498769\pi$
$608$	−8037.28	−0.536110
$609$	−3077.85	−0.204796
$610$	9970.31	0.661780
$611$	0	0
$612$	2064.82	0.136381
$613$	14061.7	0.926501	0.463251	−	0.886227i	$-0.346683\pi$
$613$	14061.7	0.926501	0.463251	+	0.886227i	$0.346683\pi$
$614$	−11829.3	−0.777512
$615$	−14212.1	−0.931852
$616$	4475.44	0.292728
$617$	2419.49	0.157868	0.0789342	−	0.996880i	$-0.474848\pi$
$617$	2419.49	0.157868	0.0789342	+	0.996880i	$0.474848\pi$
$618$	−4686.22	−0.305028
$619$	−14866.5	−0.965321	−0.482661	−	0.875808i	$-0.660329\pi$
$619$	−14866.5	−0.965321	−0.482661	+	0.875808i	$0.660329\pi$
$620$	−4812.27	−0.311719
$621$	28073.1	1.81407
$622$	−718.547	−0.0463201
$623$	−11052.6	−0.710772
$624$	0	0
$625$	−5190.02	−0.332161
$626$	9854.91	0.629204
$627$	1698.97	0.108214
$628$	−16006.9	−1.01711
$629$	−1622.95	−0.102880
$630$	3863.05	0.244298
$631$	7536.71	0.475486	0.237743	−	0.971328i	$-0.423592\pi$
$631$	7536.71	0.475486	0.237743	+	0.971328i	$0.423592\pi$
$632$	−20257.3	−1.27499
$633$	−7115.98	−0.446816
$634$	−10428.6	−0.653269
$635$	6074.18	0.379601
$636$	−7354.28	−0.458516
$637$	0	0
$638$	949.438	0.0589163
$639$	4747.12	0.293886
$640$	7323.99	0.452353
$641$	9462.80	0.583086	0.291543	−	0.956558i	$-0.405831\pi$
$641$	9462.80	0.583086	0.291543	+	0.956558i	$0.405831\pi$
$642$	4721.03	0.290224
$643$	−7925.52	−0.486084	−0.243042	−	0.970016i	$-0.578145\pi$
$643$	−7925.52	−0.486084	−0.243042	+	0.970016i	$0.578145\pi$
$644$	17079.6	1.04508
$645$	−6466.73	−0.394771
$646$	−2182.41	−0.132919
$647$	−8700.37	−0.528666	−0.264333	−	0.964431i	$-0.585152\pi$
$647$	−8700.37	−0.528666	−0.264333	+	0.964431i	$0.585152\pi$
$648$	−2344.52	−0.142132
$649$	8712.91	0.526983
$650$	0	0
$651$	7398.69	0.445434
$652$	−11599.0	−0.696705
$653$	28984.3	1.73698	0.868488	−	0.495711i	$-0.165092\pi$
$653$	28984.3	1.73698	0.868488	+	0.495711i	$0.165092\pi$
$654$	3385.66	0.202431
$655$	−14570.1	−0.869161
$656$	90.3132	0.00537521
$657$	−2831.56	−0.168143
$658$	−2135.37	−0.126513
$659$	6634.82	0.392194	0.196097	−	0.980584i	$-0.437173\pi$
$659$	6634.82	0.392194	0.196097	+	0.980584i	$0.437173\pi$
$660$	−1552.62	−0.0915689
$661$	27522.1	1.61949	0.809747	−	0.586779i	$-0.199604\pi$
$661$	27522.1	1.61949	0.809747	+	0.586779i	$0.199604\pi$
$662$	−7290.73	−0.428039
$663$	0	0
$664$	−7447.80	−0.435287
$665$	6571.05	0.383180
$666$	−1511.75	−0.0879565
$667$	9498.07	0.551375
$668$	5703.11	0.330329
$669$	−9904.62	−0.572399
$670$	10088.9	0.581743
$671$	−7609.98	−0.437824
$672$	−11292.6	−0.648246
$673$	812.561	0.0465408	0.0232704	−	0.999729i	$-0.492592\pi$
$673$	812.561	0.0465408	0.0232704	+	0.999729i	$0.492592\pi$
$674$	−11305.1	−0.646080
$675$	8341.86	0.475672
$676$	0	0
$677$	19939.3	1.13195	0.565974	−	0.824423i	$-0.308500\pi$
$677$	19939.3	1.13195	0.565974	+	0.824423i	$0.308500\pi$
$678$	−8846.82	−0.501121
$679$	−13515.0	−0.763854
$680$	5228.10	0.294836
$681$	−7029.87	−0.395573
$682$	−2282.31	−0.128144
$683$	6448.71	0.361278	0.180639	−	0.983549i	$-0.442183\pi$
$683$	6448.71	0.361278	0.180639	+	0.983549i	$0.442183\pi$
$684$	3271.60	0.182884
$685$	−1391.28	−0.0776031
$686$	11426.7	0.635968
$687$	−4745.11	−0.263518
$688$	41.0938	0.00227716
$689$	0	0
$690$	9651.21	0.532486
$691$	32088.0	1.76655	0.883275	−	0.468855i	$-0.155333\pi$
$691$	32088.0	1.76655	0.883275	+	0.468855i	$0.155333\pi$
$692$	10838.7	0.595415
$693$	−2948.53	−0.161624
$694$	−12866.8	−0.703773
$695$	348.507	0.0190210
$696$	−3880.02	−0.211310
$697$	−13934.3	−0.757247
$698$	−6687.12	−0.362624
$699$	−10501.6	−0.568253
$700$	5075.15	0.274032
$701$	29075.6	1.56658	0.783288	−	0.621659i	$-0.213541\pi$
$701$	29075.6	1.56658	0.783288	+	0.621659i	$0.213541\pi$
$702$	0	0
$703$	−2571.49	−0.137959
$704$	3499.47	0.187346
$705$	1941.91	0.103740
$706$	−10570.8	−0.563507
$707$	33378.0	1.77554
$708$	−13583.2	−0.721029
$709$	26303.6	1.39331	0.696653	−	0.717409i	$-0.254672\pi$
$709$	26303.6	1.39331	0.696653	+	0.717409i	$0.254672\pi$
$710$	4585.26	0.242368
$711$	13346.0	0.703957
$712$	−13933.2	−0.733381
$713$	−22832.0	−1.19925
$714$	−3066.34	−0.160721
$715$	0	0
$716$	12726.6	0.664268
$717$	22798.8	1.18750
$718$	21265.6	1.10533
$719$	22921.8	1.18893	0.594465	−	0.804122i	$-0.297364\pi$
$719$	22921.8	1.18893	0.594465	+	0.804122i	$0.297364\pi$
$720$	22.3243	0.00115552
$721$	13834.0	0.714571
$722$	8551.99	0.440820
$723$	9946.66	0.511646
$724$	−18894.1	−0.969883
$725$	2822.33	0.144578
$726$	−736.356	−0.0376429
$727$	35361.6	1.80397	0.901987	−	0.431762i	$-0.142108\pi$
$727$	35361.6	1.80397	0.901987	+	0.431762i	$0.142108\pi$
$728$	0	0
$729$	15216.8	0.773095
$730$	−2735.02	−0.138668
$731$	−6340.33	−0.320801
$732$	11863.8	0.599041
$733$	22245.1	1.12093	0.560465	−	0.828178i	$-0.310623\pi$
$733$	22245.1	1.12093	0.560465	+	0.828178i	$0.310623\pi$
$734$	10436.8	0.524834
$735$	−579.491	−0.0290814
$736$	34848.3	1.74528
$737$	−7700.49	−0.384873
$738$	−12979.5	−0.647403
$739$	−17241.2	−0.858223	−0.429112	−	0.903251i	$-0.641173\pi$
$739$	−17241.2	−0.858223	−0.429112	+	0.903251i	$0.641173\pi$
$740$	2349.98	0.116739
$741$	0	0
$742$	−13490.1	−0.667435
$743$	−22058.3	−1.08915	−0.544577	−	0.838711i	$-0.683310\pi$
$743$	−22058.3	−1.08915	−0.544577	+	0.838711i	$0.683310\pi$
$744$	9327.00	0.459603
$745$	−12029.4	−0.591573
$746$	5679.13	0.278724
$747$	4906.79	0.240335
$748$	−1522.27	−0.0744112
$749$	−13936.8	−0.679891
$750$	9128.95	0.444456
$751$	−14937.4	−0.725797	−0.362898	−	0.931829i	$-0.618213\pi$
$751$	−14937.4	−0.725797	−0.362898	+	0.931829i	$0.618213\pi$
$752$	−12.3402	−0.000598403 0
$753$	−17480.9	−0.846002
$754$	0	0
$755$	26757.8	1.28982
$756$	12914.8	0.621304
$757$	−15681.3	−0.752901	−0.376450	−	0.926437i	$-0.622855\pi$
$757$	−15681.3	−0.752901	−0.376450	+	0.926437i	$0.622855\pi$
$758$	13309.1	0.637743
$759$	−7366.43	−0.352285
$760$	8283.65	0.395368
$761$	−918.028	−0.0437299	−0.0218650	−	0.999761i	$-0.506960\pi$
$761$	−918.028	−0.0437299	−0.0218650	+	0.999761i	$0.506960\pi$
$762$	−4491.09	−0.213510
$763$	−9994.66	−0.474222
$764$	4567.34	0.216284
$765$	−3444.40	−0.162787
$766$	−2957.92	−0.139522
$767$	0	0
$768$	−14260.7	−0.670037
$769$	18397.3	0.862710	0.431355	−	0.902182i	$-0.358036\pi$
$769$	18397.3	0.862710	0.431355	+	0.902182i	$0.358036\pi$
$770$	−2847.99	−0.133292
$771$	−13720.8	−0.640912
$772$	4204.16	0.195999
$773$	34448.9	1.60290	0.801450	−	0.598062i	$-0.204062\pi$
$773$	34448.9	1.60290	0.801450	+	0.598062i	$0.204062\pi$
$774$	−5905.88	−0.274267
$775$	−6784.46	−0.314458
$776$	−17037.3	−0.788151
$777$	−3613.00	−0.166816
$778$	−11898.9	−0.548322
$779$	−22078.2	−1.01545
$780$	0	0
$781$	−3499.76	−0.160347
$782$	9462.56	0.432712
$783$	7182.01	0.327796
$784$	3.68246	0.000167751 0
$785$	26701.6	1.21404
$786$	10772.7	0.488868
$787$	−24528.8	−1.11100	−0.555500	−	0.831516i	$-0.687473\pi$
$787$	−24528.8	−1.11100	−0.555500	+	0.831516i	$0.687473\pi$
$788$	−2127.18	−0.0961647
$789$	57.1425	0.00257836
$790$	12890.9	0.580555
$791$	26116.4	1.17395
$792$	−3716.99	−0.166765
$793$	0	0
$794$	23878.6	1.06728
$795$	12267.9	0.547294
$796$	25298.5	1.12649
$797$	5627.86	0.250124	0.125062	−	0.992149i	$-0.460087\pi$
$797$	5627.86	0.250124	0.125062	+	0.992149i	$0.460087\pi$
$798$	−4858.46	−0.215523
$799$	1903.95	0.0843016
$800$	10355.1	0.457635
$801$	9179.49	0.404921
$802$	11573.8	0.509580
$803$	2087.54	0.0917406
$804$	12004.9	0.526591
$805$	−28491.0	−1.24742
$806$	0	0
$807$	8598.17	0.375056
$808$	42077.3	1.83202
$809$	−2007.99	−0.0872646	−0.0436323	−	0.999048i	$-0.513893\pi$
$809$	−2007.99	−0.0872646	−0.0436323	+	0.999048i	$0.513893\pi$
$810$	1491.96	0.0647186
$811$	−16522.7	−0.715399	−0.357700	−	0.933837i	$-0.616439\pi$
$811$	−16522.7	−0.715399	−0.357700	+	0.933837i	$0.616439\pi$
$812$	4369.50	0.188842
$813$	1100.84	0.0474885
$814$	1114.52	0.0479900
$815$	19348.7	0.831600
$816$	−17.7202	−0.000760209 0
$817$	−10045.9	−0.430186
$818$	−10478.7	−0.447895
$819$	0	0
$820$	20176.4	0.859257
$821$	8895.62	0.378148	0.189074	−	0.981963i	$-0.439451\pi$
$821$	8895.62	0.378148	0.189074	+	0.981963i	$0.439451\pi$
$822$	1028.68	0.0436486
$823$	−2764.09	−0.117072	−0.0585358	−	0.998285i	$-0.518643\pi$
$823$	−2764.09	−0.117072	−0.0585358	+	0.998285i	$0.518643\pi$
$824$	17439.6	0.737300
$825$	−2188.92	−0.0923736
$826$	−24915.9	−1.04956
$827$	−11377.4	−0.478392	−0.239196	−	0.970971i	$-0.576884\pi$
$827$	−11377.4	−0.478392	−0.239196	+	0.970971i	$0.576884\pi$
$828$	−14185.1	−0.595370
$829$	10061.9	0.421548	0.210774	−	0.977535i	$-0.432402\pi$
$829$	10061.9	0.421548	0.210774	+	0.977535i	$0.432402\pi$
$830$	4739.48	0.198205
$831$	−24083.3	−1.00534
$832$	0	0
$833$	−568.164	−0.0236323
$834$	−257.677	−0.0106986
$835$	−9513.55	−0.394288
$836$	−2411.95	−0.0997836
$837$	−17264.5	−0.712960
$838$	−2671.82	−0.110139
$839$	5570.43	0.229216	0.114608	−	0.993411i	$-0.463439\pi$
$839$	5570.43	0.229216	0.114608	+	0.993411i	$0.463439\pi$
$840$	11638.7	0.478065
$841$	−21959.1	−0.900368
$842$	23765.7	0.972707
$843$	−25905.9	−1.05842
$844$	10102.3	0.412008
$845$	0	0
$846$	1773.49	0.0720731
$847$	2173.77	0.0881837
$848$	−77.9584	−0.00315696
$849$	12316.7	0.497891
$850$	2811.78	0.113463
$851$	11149.5	0.449120
$852$	5456.05	0.219391
$853$	15495.5	0.621986	0.310993	−	0.950412i	$-0.399338\pi$
$853$	15495.5	0.621986	0.310993	+	0.950412i	$0.399338\pi$
$854$	21761.9	0.871989
$855$	−5457.47	−0.218294
$856$	−17569.1	−0.701517
$857$	−13089.1	−0.521722	−0.260861	−	0.965376i	$-0.584006\pi$
$857$	−13089.1	−0.521722	−0.260861	+	0.965376i	$0.584006\pi$
$858$	0	0
$859$	4556.12	0.180969	0.0904847	−	0.995898i	$-0.471158\pi$
$859$	4556.12	0.180969	0.0904847	+	0.995898i	$0.471158\pi$
$860$	9180.56	0.364017
$861$	−31020.5	−1.22785
$862$	13459.4	0.531820
$863$	31051.4	1.22480	0.612399	−	0.790549i	$-0.290205\pi$
$863$	31051.4	1.22480	0.612399	+	0.790549i	$0.290205\pi$
$864$	26350.7	1.03758
$865$	−18080.5	−0.710699
$866$	10283.5	0.403521
$867$	−14341.4	−0.561774
$868$	−10503.6	−0.410733
$869$	−9839.19	−0.384087
$870$	2469.09	0.0962184
$871$	0	0
$872$	−12599.6	−0.489306
$873$	11224.6	0.435161
$874$	14992.9	0.580256
$875$	−26949.2	−1.04120
$876$	−3254.42	−0.125521
$877$	−10491.7	−0.403967	−0.201983	−	0.979389i	$-0.564739\pi$
$877$	−10491.7	−0.403967	−0.201983	+	0.979389i	$0.564739\pi$
$878$	13665.6	0.525274
$879$	−7581.30	−0.290911
$880$	−16.4584	−0.000630467 0
$881$	21000.7	0.803102	0.401551	−	0.915837i	$-0.368471\pi$
$881$	21000.7	0.803102	0.401551	+	0.915837i	$0.368471\pi$
$882$	−529.233	−0.0202043
$883$	−15914.6	−0.606535	−0.303267	−	0.952906i	$-0.598078\pi$
$883$	−15914.6	−0.606535	−0.303267	+	0.952906i	$0.598078\pi$
$884$	0	0
$885$	22658.6	0.860634
$886$	1523.98	0.0577867
$887$	16627.4	0.629416	0.314708	−	0.949188i	$-0.398093\pi$
$887$	16627.4	0.629416	0.314708	+	0.949188i	$0.398093\pi$
$888$	−4554.65	−0.172122
$889$	13258.0	0.500177
$890$	8866.50	0.333939
$891$	−1138.76	−0.0428169
$892$	14061.2	0.527807
$893$	3016.71	0.113046
$894$	8894.19	0.332736
$895$	−21229.7	−0.792883
$896$	15985.9	0.596039
$897$	0	0
$898$	−4850.12	−0.180235
$899$	−5841.15	−0.216700
$900$	−4215.07	−0.156114
$901$	12028.1	0.444745
$902$	9569.03	0.353231
$903$	−14114.8	−0.520167
$904$	32923.0	1.21129
$905$	31517.9	1.15767
$906$	−19784.0	−0.725473
$907$	5646.27	0.206705	0.103352	−	0.994645i	$-0.467043\pi$
$907$	5646.27	0.206705	0.103352	+	0.994645i	$0.467043\pi$
$908$	9980.02	0.364756
$909$	−27721.5	−1.01151
$910$	0	0
$911$	41537.1	1.51063	0.755316	−	0.655361i	$-0.227483\pi$
$911$	41537.1	1.51063	0.755316	+	0.655361i	$0.227483\pi$
$912$	−28.0767	−0.00101942
$913$	−3617.48	−0.131129
$914$	−2432.49	−0.0880303
$915$	−19790.4	−0.715027
$916$	6736.44	0.242989
$917$	−31801.8	−1.14524
$918$	7155.16	0.257250
$919$	48137.8	1.72788	0.863939	−	0.503596i	$-0.167990\pi$
$919$	48137.8	1.72788	0.863939	+	0.503596i	$0.167990\pi$
$920$	−35916.5	−1.28710
$921$	23480.4	0.840070
$922$	−26705.0	−0.953886
$923$	0	0
$924$	−3388.86	−0.120655
$925$	3313.05	0.117765
$926$	19912.9	0.706671
$927$	−11489.6	−0.407085
$928$	8915.32	0.315366
$929$	−36873.3	−1.30223	−0.651116	−	0.758979i	$-0.725699\pi$
$929$	−36873.3	−1.30223	−0.651116	+	0.758979i	$0.725699\pi$
$930$	−5935.33	−0.209276
$931$	−900.226	−0.0316904
$932$	14908.8	0.523984
$933$	1426.27	0.0500470
$934$	29513.7	1.03396
$935$	2539.34	0.0888187
$936$	0	0
$937$	−56583.7	−1.97280	−0.986398	−	0.164373i	$-0.947440\pi$
$937$	−56583.7	−1.97280	−0.986398	+	0.164373i	$0.947440\pi$
$938$	22020.8	0.766528
$939$	−19561.3	−0.679829
$940$	−2756.85	−0.0956581
$941$	33822.6	1.17172	0.585859	−	0.810413i	$-0.300757\pi$
$941$	33822.6	1.17172	0.585859	+	0.810413i	$0.300757\pi$
$942$	−19742.4	−0.682848
$943$	95727.5	3.30574
$944$	−143.988	−0.00496440
$945$	−21543.6	−0.741601
$946$	4354.05	0.149643
$947$	20833.2	0.714878	0.357439	−	0.933937i	$-0.383650\pi$
$947$	20833.2	0.714878	0.357439	+	0.933937i	$0.383650\pi$
$948$	15339.1	0.525516
$949$	0	0
$950$	4455.11	0.152151
$951$	20700.0	0.705831
$952$	11411.2	0.388488
$953$	−49746.2	−1.69091	−0.845455	−	0.534047i	$-0.820670\pi$
$953$	−49746.2	−1.69091	−0.845455	+	0.534047i	$0.820670\pi$
$954$	11203.9	0.380232
$955$	−7618.94	−0.258160
$956$	−32366.6	−1.09499
$957$	−1884.57	−0.0636567
$958$	−24423.2	−0.823673
$959$	−3036.71	−0.102253
$960$	9100.66	0.305961
$961$	−15749.7	−0.528675
$962$	0	0
$963$	11574.9	0.387328
$964$	−14120.9	−0.471787
$965$	−7013.09	−0.233948
$966$	21065.5	0.701625
$967$	−46886.0	−1.55921	−0.779604	−	0.626273i	$-0.784579\pi$
$967$	−46886.0	−1.55921	−0.779604	+	0.626273i	$0.784579\pi$
$968$	2740.31	0.0909887
$969$	4331.93	0.143614
$970$	10841.9	0.358878
$971$	43814.9	1.44808	0.724041	−	0.689757i	$-0.242283\pi$
$971$	43814.9	1.44808	0.724041	+	0.689757i	$0.242283\pi$
$972$	−17634.6	−0.581923
$973$	760.678	0.0250629
$974$	30589.1	1.00630
$975$	0	0
$976$	125.761	0.00412449
$977$	−25750.9	−0.843238	−0.421619	−	0.906773i	$-0.638538\pi$
$977$	−25750.9	−0.843238	−0.421619	+	0.906773i	$0.638538\pi$
$978$	−14305.9	−0.467742
$979$	−6767.48	−0.220929
$980$	822.681	0.0268159
$981$	8300.88	0.270160
$982$	16049.6	0.521551
$983$	−95.1851	−0.00308844	−0.00154422	−	0.999999i	$-0.500492\pi$
$983$	−95.1851	−0.00308844	−0.00154422	+	0.999999i	$0.500492\pi$
$984$	−39105.3	−1.26690
$985$	3548.42	0.114784
$986$	2420.83	0.0781895
$987$	4238.56	0.136692
$988$	0	0
$989$	43557.4	1.40045
$990$	2365.35	0.0759350
$991$	35568.1	1.14012	0.570059	−	0.821603i	$-0.306920\pi$
$991$	35568.1	1.14012	0.570059	+	0.821603i	$0.306920\pi$
$992$	−21431.1	−0.685925
$993$	14471.6	0.462479
$994$	10008.1	0.319355
$995$	−42201.3	−1.34460
$996$	5639.56	0.179414
$997$	−50924.0	−1.61763	−0.808816	−	0.588062i	$-0.799891\pi$
$997$	−50924.0	−1.61763	−0.808816	+	0.588062i	$0.799891\pi$
$998$	−17978.9	−0.570253
$999$	8430.76	0.267005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.f.1.8		17
13.4	even	6		143.4.e.a.133.8	yes	34
13.10	even	6		143.4.e.a.100.8	✓	34
13.12	even	2		1859.4.a.i.1.10		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.8	✓	34	13.10	even	6
143.4.e.a.133.8	yes	34	13.4	even	6
1859.4.a.f.1.8		17	1.1	even	1	trivial
1859.4.a.i.1.10		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)

\(f(q)\)	\(=\)	\(q-1.75097 q^{2} +3.47555 q^{3} -4.93410 q^{4} +8.23074 q^{5} -6.08559 q^{6} +17.9650 q^{7} +22.6472 q^{8} -14.9205 q^{9} +O(q^{10})\)	\(q-1.75097 q^{2} +3.47555 q^{3} -4.93410 q^{4} +8.23074 q^{5} -6.08559 q^{6} +17.9650 q^{7} +22.6472 q^{8} -14.9205 q^{9} -14.4118 q^{10} +11.0000 q^{11} -17.1487 q^{12} -31.4562 q^{14} +28.6064 q^{15} -0.181784 q^{16} +28.0472 q^{17} +26.1254 q^{18} +44.4394 q^{19} -40.6113 q^{20} +62.4384 q^{21} -19.2607 q^{22} -192.682 q^{23} +78.7116 q^{24} -57.2549 q^{25} -145.697 q^{27} -88.6414 q^{28} -49.2942 q^{29} -50.0889 q^{30} +118.496 q^{31} -180.860 q^{32} +38.2311 q^{33} -49.1098 q^{34} +147.866 q^{35} +73.6194 q^{36} -57.8650 q^{37} -77.8120 q^{38} +186.404 q^{40} -496.817 q^{41} -109.328 q^{42} -226.059 q^{43} -54.2751 q^{44} -122.807 q^{45} +337.380 q^{46} +67.8838 q^{47} -0.631798 q^{48} -20.2574 q^{49} +100.252 q^{50} +97.4796 q^{51} +428.853 q^{53} +255.111 q^{54} +90.5382 q^{55} +406.858 q^{56} +154.451 q^{57} +86.3126 q^{58} +792.083 q^{59} -141.147 q^{60} -691.816 q^{61} -207.483 q^{62} -268.048 q^{63} +318.134 q^{64} -66.9415 q^{66} -700.044 q^{67} -138.388 q^{68} -669.675 q^{69} -258.908 q^{70} -318.160 q^{71} -337.909 q^{72} +189.776 q^{73} +101.320 q^{74} -198.992 q^{75} -219.268 q^{76} +197.615 q^{77} -894.471 q^{79} -1.49621 q^{80} -103.524 q^{81} +869.912 q^{82} -328.861 q^{83} -308.078 q^{84} +230.850 q^{85} +395.823 q^{86} -171.324 q^{87} +249.120 q^{88} -615.226 q^{89} +215.031 q^{90} +950.711 q^{92} +411.838 q^{93} -118.862 q^{94} +365.769 q^{95} -628.587 q^{96} -752.293 q^{97} +35.4701 q^{98} -164.126 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) \) 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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