LMFDB - Embedded newform 1859.4.a.i.1.7

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:	$0$
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			1.7
Root			$-1.07101$ 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)

$f(q)$	$=$	$q-1.07101 q^{2} -5.99193 q^{3} -6.85294 q^{4} +0.973634 q^{5} +6.41740 q^{6} -28.3191 q^{7} +15.9076 q^{8} +8.90321 q^{9} +O(q^{10})$	\(q-1.07101 q^{2} -5.99193 q^{3} -6.85294 q^{4} +0.973634 q^{5} +6.41740 q^{6} -28.3191 q^{7} +15.9076 q^{8} +8.90321 q^{9} -1.04277 q^{10} -11.0000 q^{11} +41.0623 q^{12} +30.3300 q^{14} -5.83395 q^{15} +37.7863 q^{16} +29.1130 q^{17} -9.53541 q^{18} +150.207 q^{19} -6.67226 q^{20} +169.686 q^{21} +11.7811 q^{22} -45.7247 q^{23} -95.3173 q^{24} -124.052 q^{25} +108.435 q^{27} +194.069 q^{28} -148.278 q^{29} +6.24821 q^{30} -142.017 q^{31} -167.730 q^{32} +65.9112 q^{33} -31.1803 q^{34} -27.5725 q^{35} -61.0132 q^{36} -213.748 q^{37} -160.873 q^{38} +15.4882 q^{40} -183.076 q^{41} -181.735 q^{42} -332.638 q^{43} +75.3824 q^{44} +8.66847 q^{45} +48.9716 q^{46} -458.202 q^{47} -226.413 q^{48} +458.974 q^{49} +132.861 q^{50} -174.443 q^{51} +27.0534 q^{53} -116.134 q^{54} -10.7100 q^{55} -450.490 q^{56} -900.031 q^{57} +158.807 q^{58} -608.037 q^{59} +39.9797 q^{60} +612.902 q^{61} +152.102 q^{62} -252.131 q^{63} -122.650 q^{64} -70.5915 q^{66} +180.650 q^{67} -199.510 q^{68} +273.979 q^{69} +29.5304 q^{70} +507.734 q^{71} +141.629 q^{72} -478.584 q^{73} +228.925 q^{74} +743.311 q^{75} -1029.36 q^{76} +311.511 q^{77} -69.9336 q^{79} +36.7901 q^{80} -890.120 q^{81} +196.075 q^{82} -1069.48 q^{83} -1162.85 q^{84} +28.3454 q^{85} +356.258 q^{86} +888.472 q^{87} -174.984 q^{88} +887.954 q^{89} -9.28400 q^{90} +313.349 q^{92} +850.957 q^{93} +490.738 q^{94} +146.247 q^{95} +1005.03 q^{96} -1420.05 q^{97} -491.564 q^{98} -97.9353 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.07101	−0.378659	−0.189329	−	0.981914i	$-0.560631\pi$
$2$	−1.07101	−0.378659	−0.189329	+	0.981914i	$0.560631\pi$
$3$	−5.99193	−1.15315	−0.576574	−	0.817045i	$-0.695611\pi$
$3$	−5.99193	−1.15315	−0.576574	+	0.817045i	$0.695611\pi$
$4$	−6.85294	−0.856618
$5$	0.973634	0.0870845	0.0435423	−	0.999052i	$-0.486136\pi$
$5$	0.973634	0.0870845	0.0435423	+	0.999052i	$0.486136\pi$
$6$	6.41740	0.436649
$7$	−28.3191	−1.52909	−0.764545	−	0.644571i	$-0.777036\pi$
$7$	−28.3191	−1.52909	−0.764545	+	0.644571i	$0.777036\pi$
$8$	15.9076	0.703024
$9$	8.90321	0.329748
$10$	−1.04277	−0.0329753
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	41.0623	0.987806
$13$	0	0
$13$	0	0
$14$	30.3300	0.579003
$15$	−5.83395	−0.100421
$16$	37.7863	0.590412
$17$	29.1130	0.415350	0.207675	−	0.978198i	$-0.433410\pi$
$17$	29.1130	0.415350	0.207675	+	0.978198i	$0.433410\pi$
$18$	−9.53541	−0.124862
$19$	150.207	1.81368	0.906839	−	0.421477i	$-0.138488\pi$
$19$	150.207	1.81368	0.906839	+	0.421477i	$0.138488\pi$
$20$	−6.67226	−0.0745981
$21$	169.686	1.76327
$22$	11.7811	0.114170
$23$	−45.7247	−0.414533	−0.207267	−	0.978284i	$-0.566457\pi$
$23$	−45.7247	−0.414533	−0.207267	+	0.978284i	$0.566457\pi$
$24$	−95.3173	−0.810690
$25$	−124.052	−0.992416
$26$	0	0
$27$	108.435	0.772899
$28$	194.069	1.30985
$29$	−148.278	−0.949468	−0.474734	−	0.880129i	$-0.657456\pi$
$29$	−148.278	−0.949468	−0.474734	+	0.880129i	$0.657456\pi$
$30$	6.24821	0.0380254
$31$	−142.017	−0.822808	−0.411404	−	0.911453i	$-0.634961\pi$
$31$	−142.017	−0.822808	−0.411404	+	0.911453i	$0.634961\pi$
$32$	−167.730	−0.926589
$33$	65.9112	0.347687
$34$	−31.1803	−0.157276
$35$	−27.5725	−0.133160
$36$	−61.0132	−0.282468
$37$	−213.748	−0.949727	−0.474863	−	0.880060i	$-0.657503\pi$
$37$	−213.748	−0.949727	−0.474863	+	0.880060i	$0.657503\pi$
$38$	−160.873	−0.686765
$39$	0	0
$40$	15.4882	0.0612225
$41$	−183.076	−0.697356	−0.348678	−	0.937243i	$-0.613369\pi$
$41$	−183.076	−0.697356	−0.348678	+	0.937243i	$0.613369\pi$
$42$	−181.735	−0.667676
$43$	−332.638	−1.17969	−0.589846	−	0.807516i	$-0.700812\pi$
$43$	−332.638	−1.17969	−0.589846	+	0.807516i	$0.700812\pi$
$44$	75.3824	0.258280
$45$	8.66847	0.0287160
$46$	48.9716	0.156967
$47$	−458.202	−1.42203	−0.711017	−	0.703175i	$-0.751765\pi$
$47$	−458.202	−1.42203	−0.711017	+	0.703175i	$0.751765\pi$
$48$	−226.413	−0.680831
$49$	458.974	1.33812
$50$	132.861	0.375787
$51$	−174.443	−0.478959
$52$	0	0
$53$	27.0534	0.0701146	0.0350573	−	0.999385i	$-0.488839\pi$
$53$	27.0534	0.0701146	0.0350573	+	0.999385i	$0.488839\pi$
$54$	−116.134	−0.292665
$55$	−10.7100	−0.0262570
$56$	−450.490	−1.07499
$57$	−900.031	−2.09144
$58$	158.807	0.359524
$59$	−608.037	−1.34169	−0.670845	−	0.741598i	$-0.734068\pi$
$59$	−608.037	−1.34169	−0.670845	+	0.741598i	$0.734068\pi$
$60$	39.9797	0.0860226
$61$	612.902	1.28646	0.643230	−	0.765673i	$-0.277594\pi$
$61$	612.902	1.28646	0.643230	+	0.765673i	$0.277594\pi$
$62$	152.102	0.311563
$63$	−252.131	−0.504215
$64$	−122.650	−0.239551
$65$	0	0
$66$	−70.5915	−0.131655
$67$	180.650	0.329402	0.164701	−	0.986344i	$-0.447334\pi$
$67$	180.650	0.329402	0.164701	+	0.986344i	$0.447334\pi$
$68$	−199.510	−0.355796
$69$	273.979	0.478018
$70$	29.5304	0.0504222
$71$	507.734	0.848690	0.424345	−	0.905501i	$-0.360504\pi$
$71$	507.734	0.848690	0.424345	+	0.905501i	$0.360504\pi$
$72$	141.629	0.231821
$73$	−478.584	−0.767316	−0.383658	−	0.923475i	$-0.625336\pi$
$73$	−478.584	−0.767316	−0.383658	+	0.923475i	$0.625336\pi$
$74$	228.925	0.359622
$75$	743.311	1.14440
$76$	−1029.36	−1.55363
$77$	311.511	0.461038
$78$	0	0
$79$	−69.9336	−0.0995968	−0.0497984	−	0.998759i	$-0.515858\pi$
$79$	−69.9336	−0.0995968	−0.0497984	+	0.998759i	$0.515858\pi$
$80$	36.7901	0.0514157
$81$	−890.120	−1.22101
$82$	196.075	0.264060
$83$	−1069.48	−1.41434	−0.707171	−	0.707043i	$-0.750029\pi$
$83$	−1069.48	−1.41434	−0.707171	+	0.707043i	$0.750029\pi$
$84$	−1162.85	−1.51044
$85$	28.3454	0.0361705
$86$	356.258	0.446701
$87$	888.472	1.09488
$88$	−174.984	−0.211970
$89$	887.954	1.05756	0.528781	−	0.848759i	$-0.322649\pi$
$89$	887.954	1.05756	0.528781	+	0.848759i	$0.322649\pi$
$90$	−9.28400	−0.0108736
$91$	0	0
$92$	313.349	0.355097
$93$	850.957	0.948819
$94$	490.738	0.538466
$95$	146.247	0.157943
$96$	1005.03	1.06849
$97$	−1420.05	−1.48644	−0.743219	−	0.669048i	$-0.766702\pi$
$97$	−1420.05	−1.48644	−0.743219	+	0.669048i	$0.766702\pi$
$98$	−491.564	−0.506689
$99$	−97.9353	−0.0994229
$100$	850.121	0.850121
$101$	−977.569	−0.963087	−0.481543	−	0.876422i	$-0.659924\pi$
$101$	−977.569	−0.963087	−0.481543	+	0.876422i	$0.659924\pi$
$102$	186.830	0.181362
$103$	358.449	0.342903	0.171452	−	0.985193i	$-0.445154\pi$
$103$	358.449	0.342903	0.171452	+	0.985193i	$0.445154\pi$
$104$	0	0
$105$	165.212	0.153553
$106$	−28.9744	−0.0265495
$107$	−2090.46	−1.88872	−0.944358	−	0.328920i	$-0.893315\pi$
$107$	−2090.46	−1.88872	−0.944358	+	0.328920i	$0.893315\pi$
$108$	−743.097	−0.662079
$109$	880.013	0.773303	0.386651	−	0.922226i	$-0.373632\pi$
$109$	880.013	0.773303	0.386651	+	0.922226i	$0.373632\pi$
$110$	11.4705	0.00994243
$111$	1280.76	1.09517
$112$	−1070.08	−0.902792
$113$	−1954.74	−1.62731	−0.813657	−	0.581345i	$-0.802527\pi$
$113$	−1954.74	−1.62731	−0.813657	+	0.581345i	$0.802527\pi$
$114$	963.940	0.791941
$115$	−44.5192	−0.0360994
$116$	1016.14	0.813331
$117$	0	0
$118$	651.213	0.508042
$119$	−824.456	−0.635107
$120$	−92.8042	−0.0705986
$121$	121.000	0.0909091
$122$	−656.423	−0.487129
$123$	1096.98	0.804154
$124$	973.236	0.704832
$125$	−242.486	−0.173509
$126$	270.035	0.190925
$127$	−1709.15	−1.19419	−0.597095	−	0.802170i	$-0.703679\pi$
$127$	−1709.15	−1.19419	−0.597095	+	0.802170i	$0.703679\pi$
$128$	1473.20	1.01730
$129$	1993.14	1.36036
$130$	0	0
$131$	−829.069	−0.552947	−0.276474	−	0.961022i	$-0.589166\pi$
$131$	−829.069	−0.552947	−0.276474	+	0.961022i	$0.589166\pi$
$132$	−451.686	−0.297835
$133$	−4253.74	−2.77328
$134$	−193.478	−0.124731
$135$	105.576	0.0673075
$136$	463.119	0.292001
$137$	2067.73	1.28947	0.644737	−	0.764404i	$-0.276967\pi$
$137$	2067.73	1.28947	0.644737	+	0.764404i	$0.276967\pi$
$138$	−293.434	−0.181006
$139$	163.946	0.100041	0.0500205	−	0.998748i	$-0.484071\pi$
$139$	163.946	0.100041	0.0500205	+	0.998748i	$0.484071\pi$
$140$	188.953	0.114067
$141$	2745.51	1.63982
$142$	−543.788	−0.321364
$143$	0	0
$144$	336.420	0.194687
$145$	−144.369	−0.0826839
$146$	512.568	0.290551
$147$	−2750.14	−1.54304
$148$	1464.80	0.813553
$149$	−2856.69	−1.57067	−0.785333	−	0.619073i	$-0.787509\pi$
$149$	−2856.69	−1.57067	−0.785333	+	0.619073i	$0.787509\pi$
$150$	−796.092	−0.433338
$151$	−2865.44	−1.54428	−0.772139	−	0.635454i	$-0.780813\pi$
$151$	−2865.44	−1.54428	−0.772139	+	0.635454i	$0.780813\pi$
$152$	2389.44	1.27506
$153$	259.199	0.136961
$154$	−333.630	−0.174576
$155$	−138.273	−0.0716538
$156$	0	0
$157$	−207.978	−0.105723	−0.0528613	−	0.998602i	$-0.516834\pi$
$157$	−207.978	−0.105723	−0.0528613	+	0.998602i	$0.516834\pi$
$158$	74.8995	0.0377132
$159$	−162.102	−0.0808525
$160$	−163.308	−0.0806915
$161$	1294.88	0.633859
$162$	953.325	0.462348
$163$	775.090	0.372452	0.186226	−	0.982507i	$-0.440374\pi$
$163$	775.090	0.372452	0.186226	+	0.982507i	$0.440374\pi$
$164$	1254.61	0.597367
$165$	64.1734	0.0302781
$166$	1145.42	0.535552
$167$	−2587.61	−1.19901	−0.599506	−	0.800370i	$-0.704636\pi$
$167$	−2587.61	−1.19901	−0.599506	+	0.800370i	$0.704636\pi$
$168$	2699.30	1.23962
$169$	0	0
$170$	−30.3582	−0.0136963
$171$	1337.33	0.598058
$172$	2279.55	1.01055
$173$	2454.02	1.07847	0.539237	−	0.842154i	$-0.318713\pi$
$173$	2454.02	1.07847	0.539237	+	0.842154i	$0.318713\pi$
$174$	−951.561	−0.414584
$175$	3513.05	1.51749
$176$	−415.650	−0.178016
$177$	3643.31	1.54717
$178$	−951.006	−0.400455
$179$	1201.60	0.501743	0.250871	−	0.968020i	$-0.419283\pi$
$179$	1201.60	0.501743	0.250871	+	0.968020i	$0.419283\pi$
$180$	−59.4045	−0.0245986
$181$	−2024.53	−0.831393	−0.415697	−	0.909503i	$-0.636462\pi$
$181$	−2024.53	−0.831393	−0.415697	+	0.909503i	$0.636462\pi$
$182$	0	0
$183$	−3672.46	−1.48348
$184$	−727.372	−0.291427
$185$	−208.112	−0.0827065
$186$	−911.382	−0.359278
$187$	−320.243	−0.125233
$188$	3140.03	1.21814
$189$	−3070.78	−1.18183
$190$	−156.632	−0.0598066
$191$	−2123.18	−0.804334	−0.402167	−	0.915566i	$-0.631743\pi$
$191$	−2123.18	−0.804334	−0.402167	+	0.915566i	$0.631743\pi$
$192$	734.910	0.276237
$193$	−473.881	−0.176739	−0.0883696	−	0.996088i	$-0.528166\pi$
$193$	−473.881	−0.176739	−0.0883696	+	0.996088i	$0.528166\pi$
$194$	1520.89	0.562852
$195$	0	0
$196$	−3145.32	−1.14625
$197$	4630.19	1.67456	0.837278	−	0.546778i	$-0.184146\pi$
$197$	4630.19	1.67456	0.837278	+	0.546778i	$0.184146\pi$
$198$	104.890	0.0376473
$199$	346.794	0.123536	0.0617678	−	0.998091i	$-0.480326\pi$
$199$	346.794	0.123536	0.0617678	+	0.998091i	$0.480326\pi$
$200$	−1973.37	−0.697693
$201$	−1082.44	−0.379849
$202$	1046.98	0.364681
$203$	4199.11	1.45182
$204$	1195.45	0.410285
$205$	−178.249	−0.0607289
$206$	−383.902	−0.129843
$207$	−407.097	−0.136692
$208$	0	0
$209$	−1652.28	−0.546845
$210$	−176.944	−0.0581442
$211$	−403.272	−0.131575	−0.0657876	−	0.997834i	$-0.520956\pi$
$211$	−403.272	−0.131575	−0.0657876	+	0.997834i	$0.520956\pi$
$212$	−185.396	−0.0600614
$213$	−3042.31	−0.978665
$214$	2238.90	0.715178
$215$	−323.868	−0.102733
$216$	1724.94	0.543366
$217$	4021.80	1.25815
$218$	−942.501	−0.292818
$219$	2867.64	0.884828
$220$	73.3949	0.0224922
$221$	0	0
$222$	−1371.70	−0.414697
$223$	2901.52	0.871300	0.435650	−	0.900116i	$-0.356518\pi$
$223$	2901.52	0.871300	0.435650	+	0.900116i	$0.356518\pi$
$224$	4749.98	1.41684
$225$	−1104.46	−0.327248
$226$	2093.54	0.616196
$227$	4992.37	1.45972	0.729858	−	0.683599i	$-0.239586\pi$
$227$	4992.37	1.45972	0.729858	+	0.683599i	$0.239586\pi$
$228$	6167.86	1.79156
$229$	−3219.87	−0.929149	−0.464575	−	0.885534i	$-0.653793\pi$
$229$	−3219.87	−0.929149	−0.464575	+	0.885534i	$0.653793\pi$
$230$	47.6804	0.0136694
$231$	−1866.55	−0.531645
$232$	−2358.75	−0.667499
$233$	4783.62	1.34500	0.672501	−	0.740096i	$-0.265220\pi$
$233$	4783.62	1.34500	0.672501	+	0.740096i	$0.265220\pi$
$234$	0	0
$235$	−446.121	−0.123837
$236$	4166.84	1.14932
$237$	419.037	0.114850
$238$	882.999	0.240489
$239$	3591.51	0.972030	0.486015	−	0.873950i	$-0.338450\pi$
$239$	3591.51	0.972030	0.486015	+	0.873950i	$0.338450\pi$
$240$	−220.444	−0.0592899
$241$	874.794	0.233819	0.116910	−	0.993143i	$-0.462701\pi$
$241$	874.794	0.233819	0.116910	+	0.993143i	$0.462701\pi$
$242$	−129.592	−0.0344235
$243$	2405.80	0.635111
$244$	−4200.18	−1.10200
$245$	446.872	0.116529
$246$	−1174.87	−0.304500
$247$	0	0
$248$	−2259.16	−0.578454
$249$	6408.23	1.63094
$250$	259.704	0.0657005
$251$	−5994.46	−1.50744	−0.753719	−	0.657196i	$-0.771742\pi$
$251$	−5994.46	−1.50744	−0.753719	+	0.657196i	$0.771742\pi$
$252$	1727.84	0.431919
$253$	502.972	0.124986
$254$	1830.51	0.452191
$255$	−169.844	−0.0417099
$256$	−596.612	−0.145657
$257$	4874.61	1.18315	0.591576	−	0.806249i	$-0.298506\pi$
$257$	4874.61	1.18315	0.591576	+	0.806249i	$0.298506\pi$
$258$	−2134.67	−0.515112
$259$	6053.15	1.45222
$260$	0	0
$261$	−1320.15	−0.313086
$262$	887.939	0.209378
$263$	−3195.28	−0.749160	−0.374580	−	0.927195i	$-0.622213\pi$
$263$	−3195.28	−0.749160	−0.374580	+	0.927195i	$0.622213\pi$
$264$	1048.49	0.244432
$265$	26.3401	0.00610589
$266$	4555.79	1.05013
$267$	−5320.56	−1.21952
$268$	−1237.99	−0.282172
$269$	−2033.06	−0.460811	−0.230405	−	0.973095i	$-0.574005\pi$
$269$	−2033.06	−0.460811	−0.230405	+	0.973095i	$0.574005\pi$
$270$	−113.072	−0.0254866
$271$	5270.53	1.18141	0.590705	−	0.806888i	$-0.298850\pi$
$271$	5270.53	1.18141	0.590705	+	0.806888i	$0.298850\pi$
$272$	1100.07	0.245227
$273$	0	0
$274$	−2214.55	−0.488271
$275$	1364.57	0.299225
$276$	−1877.56	−0.409479
$277$	−6583.92	−1.42812	−0.714060	−	0.700084i	$-0.753146\pi$
$277$	−6583.92	−1.42812	−0.714060	+	0.700084i	$0.753146\pi$
$278$	−175.587	−0.0378814
$279$	−1264.41	−0.271320
$280$	−438.613	−0.0936147
$281$	−631.673	−0.134101	−0.0670507	−	0.997750i	$-0.521359\pi$
$281$	−631.673	−0.134101	−0.0670507	+	0.997750i	$0.521359\pi$
$282$	−2940.47	−0.620930
$283$	−4624.73	−0.971418	−0.485709	−	0.874120i	$-0.661439\pi$
$283$	−4624.73	−0.971418	−0.485709	+	0.874120i	$0.661439\pi$
$284$	−3479.47	−0.727003
$285$	−876.301	−0.182132
$286$	0	0
$287$	5184.54	1.06632
$288$	−1493.34	−0.305541
$289$	−4065.43	−0.827485
$290$	154.620	0.0313090
$291$	8508.85	1.71408
$292$	3279.71	0.657296
$293$	−6447.68	−1.28559	−0.642795	−	0.766038i	$-0.722225\pi$
$293$	−6447.68	−1.28559	−0.642795	+	0.766038i	$0.722225\pi$
$294$	2945.42	0.584287
$295$	−592.006	−0.116840
$296$	−3400.22	−0.667681
$297$	−1192.78	−0.233038
$298$	3059.54	0.594747
$299$	0	0
$300$	−5093.87	−0.980315
$301$	9420.01	1.80386
$302$	3068.91	0.584754
$303$	5857.52	1.11058
$304$	5675.78	1.07082
$305$	596.742	0.112031
$306$	−277.605	−0.0518614
$307$	−337.550	−0.0627524	−0.0313762	−	0.999508i	$-0.509989\pi$
$307$	−337.550	−0.0627524	−0.0313762	+	0.999508i	$0.509989\pi$
$308$	−2134.76	−0.394933
$309$	−2147.80	−0.395418
$310$	148.091	0.0271323
$311$	1128.06	0.205680	0.102840	−	0.994698i	$-0.467207\pi$
$311$	1128.06	0.205680	0.102840	+	0.994698i	$0.467207\pi$
$312$	0	0
$313$	−6416.52	−1.15873	−0.579366	−	0.815068i	$-0.696700\pi$
$313$	−6416.52	−1.15873	−0.579366	+	0.815068i	$0.696700\pi$
$314$	222.746	0.0400327
$315$	−245.484	−0.0439093
$316$	479.251	0.0853164
$317$	5310.60	0.940925	0.470462	−	0.882420i	$-0.344087\pi$
$317$	5310.60	0.940925	0.470462	+	0.882420i	$0.344087\pi$
$318$	173.613	0.0306155
$319$	1631.06	0.286275
$320$	−119.416	−0.0208612
$321$	12525.9	2.17797
$322$	−1386.83	−0.240016
$323$	4372.98	0.753311
$324$	6099.94	1.04594
$325$	0	0
$326$	−830.128	−0.141032
$327$	−5272.98	−0.891732
$328$	−2912.30	−0.490258
$329$	12975.9	2.17442
$330$	−68.7303	−0.0114651
$331$	82.4419	0.0136901	0.00684504	−	0.999977i	$-0.497821\pi$
$331$	82.4419	0.0136901	0.00684504	+	0.999977i	$0.497821\pi$
$332$	7329.06	1.21155
$333$	−1903.04	−0.313171
$334$	2771.35	0.454016
$335$	175.887	0.0286858
$336$	6411.82	1.04105
$337$	3617.31	0.584710	0.292355	−	0.956310i	$-0.405561\pi$
$337$	3617.31	0.584710	0.292355	+	0.956310i	$0.405561\pi$
$338$	0	0
$339$	11712.7	1.87653
$340$	−194.250	−0.0309843
$341$	1562.19	0.248086
$342$	−1432.29	−0.226460
$343$	−3284.27	−0.517009
$344$	−5291.48	−0.829352
$345$	266.756	0.0416280
$346$	−2628.28	−0.408373
$347$	−1725.03	−0.266871	−0.133436	−	0.991057i	$-0.542601\pi$
$347$	−1725.03	−0.266871	−0.133436	+	0.991057i	$0.542601\pi$
$348$	−6088.65	−0.937890
$349$	1334.04	0.204611	0.102306	−	0.994753i	$-0.467378\pi$
$349$	1334.04	0.204611	0.102306	+	0.994753i	$0.467378\pi$
$350$	−3762.50	−0.574612
$351$	0	0
$352$	1845.03	0.279377
$353$	1084.94	0.163586	0.0817929	−	0.996649i	$-0.473935\pi$
$353$	1084.94	0.163586	0.0817929	+	0.996649i	$0.473935\pi$
$354$	−3902.02	−0.585848
$355$	494.348	0.0739078
$356$	−6085.10	−0.905926
$357$	4940.08	0.732372
$358$	−1286.93	−0.189989
$359$	−2967.16	−0.436214	−0.218107	−	0.975925i	$-0.569988\pi$
$359$	−2967.16	−0.436214	−0.218107	+	0.975925i	$0.569988\pi$
$360$	137.895	0.0201880
$361$	15703.2	2.28943
$362$	2168.29	0.314814
$363$	−725.023	−0.104832
$364$	0	0
$365$	−465.966	−0.0668213
$366$	3933.24	0.561731
$367$	−5908.23	−0.840346	−0.420173	−	0.907444i	$-0.638031\pi$
$367$	−5908.23	−0.840346	−0.420173	+	0.907444i	$0.638031\pi$
$368$	−1727.77	−0.244745
$369$	−1629.96	−0.229952
$370$	222.890	0.0313175
$371$	−766.130	−0.107212
$372$	−5831.56	−0.812775
$373$	−10198.1	−1.41564	−0.707822	−	0.706391i	$-0.750322\pi$
$373$	−10198.1	−1.41564	−0.707822	+	0.706391i	$0.750322\pi$
$374$	342.983	0.0474204
$375$	1452.96	0.200081
$376$	−7288.90	−0.999725
$377$	0	0
$378$	3288.83	0.447511
$379$	5208.16	0.705871	0.352936	−	0.935648i	$-0.385183\pi$
$379$	5208.16	0.705871	0.352936	+	0.935648i	$0.385183\pi$
$380$	−1002.22	−0.135297
$381$	10241.1	1.37708
$382$	2273.94	0.304568
$383$	7477.95	0.997664	0.498832	−	0.866699i	$-0.333762\pi$
$383$	7477.95	0.997664	0.498832	+	0.866699i	$0.333762\pi$
$384$	−8827.33	−1.17309
$385$	303.297	0.0401493
$386$	507.530	0.0669238
$387$	−2961.54	−0.389002
$388$	9731.54	1.27331
$389$	8729.55	1.13780	0.568902	−	0.822405i	$-0.307368\pi$
$389$	8729.55	1.13780	0.568902	+	0.822405i	$0.307368\pi$
$390$	0	0
$391$	−1331.18	−0.172176
$392$	7301.18	0.940727
$393$	4967.72	0.637629
$394$	−4958.97	−0.634085
$395$	−68.0898	−0.00867334
$396$	671.145	0.0851674
$397$	−728.269	−0.0920674	−0.0460337	−	0.998940i	$-0.514658\pi$
$397$	−728.269	−0.0920674	−0.0460337	+	0.998940i	$0.514658\pi$
$398$	−371.420	−0.0467778
$399$	25488.1	3.19800
$400$	−4687.47	−0.585934
$401$	3015.18	0.375488	0.187744	−	0.982218i	$-0.439882\pi$
$401$	3015.18	0.375488	0.187744	+	0.982218i	$0.439882\pi$
$402$	1159.31	0.143833
$403$	0	0
$404$	6699.22	0.824997
$405$	−866.651	−0.106331
$406$	−4497.28	−0.549745
$407$	2351.22	0.286353
$408$	−2774.98	−0.336720
$409$	−10453.7	−1.26382	−0.631909	−	0.775043i	$-0.717728\pi$
$409$	−10453.7	−1.26382	−0.631909	+	0.775043i	$0.717728\pi$
$410$	190.906	0.0229955
$411$	−12389.7	−1.48695
$412$	−2456.43	−0.293737
$413$	17219.1	2.05156
$414$	436.004	0.0517595
$415$	−1041.28	−0.123167
$416$	0	0
$417$	−982.352	−0.115362
$418$	1769.60	0.207067
$419$	−8163.66	−0.951840	−0.475920	−	0.879489i	$-0.657885\pi$
$419$	−8163.66	−0.951840	−0.475920	+	0.879489i	$0.657885\pi$
$420$	−1132.19	−0.131536
$421$	4236.26	0.490410	0.245205	−	0.969471i	$-0.421145\pi$
$421$	4236.26	0.490410	0.245205	+	0.969471i	$0.421145\pi$
$422$	431.908	0.0498221
$423$	−4079.47	−0.468914
$424$	430.356	0.0492923
$425$	−3611.53	−0.412200
$426$	3258.34	0.370580
$427$	−17356.8	−1.96711
$428$	14325.8	1.61791
$429$	0	0
$430$	346.865	0.0389007
$431$	−10416.1	−1.16410	−0.582050	−	0.813153i	$-0.697749\pi$
$431$	−10416.1	−1.16410	−0.582050	+	0.813153i	$0.697749\pi$
$432$	4097.35	0.456328
$433$	−11452.2	−1.27103	−0.635516	−	0.772087i	$-0.719213\pi$
$433$	−11452.2	−1.27103	−0.635516	+	0.772087i	$0.719213\pi$
$434$	−4307.39	−0.476408
$435$	865.047	0.0953467
$436$	−6030.68	−0.662425
$437$	−6868.18	−0.751830
$438$	−3071.27	−0.335048
$439$	−9205.82	−1.00084	−0.500421	−	0.865782i	$-0.666821\pi$
$439$	−9205.82	−1.00084	−0.500421	+	0.865782i	$0.666821\pi$
$440$	−170.370	−0.0184593
$441$	4086.34	0.441242
$442$	0	0
$443$	−6256.61	−0.671016	−0.335508	−	0.942037i	$-0.608908\pi$
$443$	−6256.61	−0.671016	−0.335508	+	0.942037i	$0.608908\pi$
$444$	−8776.97	−0.938146
$445$	864.543	0.0920972
$446$	−3107.55	−0.329925
$447$	17117.1	1.81121
$448$	3473.34	0.366295
$449$	13495.9	1.41851	0.709253	−	0.704954i	$-0.249033\pi$
$449$	13495.9	1.41851	0.709253	+	0.704954i	$0.249033\pi$
$450$	1182.89	0.123915
$451$	2013.83	0.210261
$452$	13395.7	1.39399
$453$	17169.5	1.78078
$454$	−5346.87	−0.552734
$455$	0	0
$456$	−14317.3	−1.47033
$457$	8790.96	0.899833	0.449916	−	0.893071i	$-0.351454\pi$
$457$	8790.96	0.899833	0.449916	+	0.893071i	$0.351454\pi$
$458$	3448.51	0.351830
$459$	3156.86	0.321023
$460$	305.087	0.0309234
$461$	5419.11	0.547491	0.273745	−	0.961802i	$-0.411737\pi$
$461$	5419.11	0.547491	0.273745	+	0.961802i	$0.411737\pi$
$462$	1999.09	0.201312
$463$	−13061.9	−1.31110	−0.655549	−	0.755153i	$-0.727563\pi$
$463$	−13061.9	−1.31110	−0.655549	+	0.755153i	$0.727563\pi$
$464$	−5602.89	−0.560577
$465$	828.521	0.0826274
$466$	−5123.30	−0.509297
$467$	−13749.5	−1.36242	−0.681212	−	0.732086i	$-0.738547\pi$
$467$	−13749.5	−1.36242	−0.681212	+	0.732086i	$0.738547\pi$
$468$	0	0
$469$	−5115.86	−0.503686
$470$	477.799	0.0468920
$471$	1246.19	0.121914
$472$	−9672.42	−0.943240
$473$	3659.02	0.355691
$474$	−448.792	−0.0434889
$475$	−18633.5	−1.79992
$476$	5649.95	0.544044
$477$	240.862	0.0231202
$478$	−3846.53	−0.368068
$479$	2129.65	0.203144	0.101572	−	0.994828i	$-0.467613\pi$
$479$	2129.65	0.203144	0.101572	+	0.994828i	$0.467613\pi$
$480$	978.531	0.0930492
$481$	0	0
$482$	−936.912	−0.0885377
$483$	−7758.86	−0.730932
$484$	−829.206	−0.0778743
$485$	−1382.61	−0.129446
$486$	−2576.63	−0.240490
$487$	−8553.79	−0.795912	−0.397956	−	0.917404i	$-0.630280\pi$
$487$	−8553.79	−0.795912	−0.397956	+	0.917404i	$0.630280\pi$
$488$	9749.81	0.904412
$489$	−4644.29	−0.429493
$490$	−478.604	−0.0441247
$491$	6449.71	0.592813	0.296406	−	0.955062i	$-0.404212\pi$
$491$	6449.71	0.592813	0.296406	+	0.955062i	$0.404212\pi$
$492$	−7517.51	−0.688853
$493$	−4316.82	−0.394361
$494$	0	0
$495$	−95.3532	−0.00865819
$496$	−5366.31	−0.485795
$497$	−14378.6	−1.29772
$498$	−6863.26	−0.617571
$499$	−10425.5	−0.935286	−0.467643	−	0.883917i	$-0.654897\pi$
$499$	−10425.5	−0.935286	−0.467643	+	0.883917i	$0.654897\pi$
$500$	1661.74	0.148631
$501$	15504.8	1.38264
$502$	6420.12	0.570805
$503$	11304.7	1.00209	0.501047	−	0.865420i	$-0.332949\pi$
$503$	11304.7	1.00209	0.501047	+	0.865420i	$0.332949\pi$
$504$	−4010.81	−0.354475
$505$	−951.795	−0.0838699
$506$	−538.687	−0.0473272
$507$	0	0
$508$	11712.7	1.02296
$509$	−8463.59	−0.737018	−0.368509	−	0.929624i	$-0.620132\pi$
$509$	−8463.59	−0.737018	−0.368509	+	0.929624i	$0.620132\pi$
$510$	181.904	0.0157938
$511$	13553.1	1.17329
$512$	−11146.6	−0.962142
$513$	16287.7	1.40179
$514$	−5220.75	−0.448011
$515$	348.999	0.0298616
$516$	−13658.9	−1.16531
$517$	5040.22	0.428760
$518$	−6482.97	−0.549895
$519$	−14704.3	−1.24364
$520$	0	0
$521$	9534.19	0.801728	0.400864	−	0.916137i	$-0.368710\pi$
$521$	9534.19	0.801728	0.400864	+	0.916137i	$0.368710\pi$
$522$	1413.89	0.118553
$523$	−17777.0	−1.48630	−0.743150	−	0.669124i	$-0.766669\pi$
$523$	−17777.0	−1.48630	−0.743150	+	0.669124i	$0.766669\pi$
$524$	5681.56	0.473664
$525$	−21049.9	−1.74989
$526$	3422.17	0.283676
$527$	−4134.55	−0.341753
$528$	2490.54	0.205278
$529$	−10076.2	−0.828162
$530$	−28.2105	−0.00231205
$531$	−5413.48	−0.442420
$532$	29150.6	2.37564
$533$	0	0
$534$	5698.36	0.461783
$535$	−2035.35	−0.164478
$536$	2873.72	0.231578
$537$	−7199.91	−0.578583
$538$	2177.43	0.174490
$539$	−5048.71	−0.403457
$540$	−723.504	−0.0576568
$541$	9780.03	0.777221	0.388610	−	0.921402i	$-0.372955\pi$
$541$	9780.03	0.777221	0.388610	+	0.921402i	$0.372955\pi$
$542$	−5644.78	−0.447351
$543$	12130.8	0.958719
$544$	−4883.14	−0.384858
$545$	856.811	0.0673427
$546$	0	0
$547$	9105.56	0.711747	0.355873	−	0.934534i	$-0.384183\pi$
$547$	9105.56	0.711747	0.355873	+	0.934534i	$0.384183\pi$
$548$	−14170.0	−1.10459
$549$	5456.79	0.424208
$550$	−1461.47	−0.113304
$551$	−22272.4	−1.72203
$552$	4358.36	0.336058
$553$	1980.46	0.152292
$554$	7051.43	0.540770
$555$	1246.99	0.0953727
$556$	−1123.51	−0.0856970
$557$	−7197.53	−0.547521	−0.273760	−	0.961798i	$-0.588268\pi$
$557$	−7197.53	−0.547521	−0.273760	+	0.961798i	$0.588268\pi$
$558$	1354.19	0.102738
$559$	0	0
$560$	−1041.86	−0.0786192
$561$	1918.87	0.144412
$562$	676.527	0.0507786
$563$	−22365.5	−1.67423	−0.837116	−	0.547025i	$-0.815760\pi$
$563$	−22365.5	−1.67423	−0.837116	+	0.547025i	$0.815760\pi$
$564$	−18814.8	−1.40469
$565$	−1903.20	−0.141714
$566$	4953.12	0.367836
$567$	25207.4	1.86704
$568$	8076.85	0.596650
$569$	−3004.48	−0.221361	−0.110680	−	0.993856i	$-0.535303\pi$
$569$	−3004.48	−0.221361	−0.110680	+	0.993856i	$0.535303\pi$
$570$	938.525	0.0689658
$571$	−5523.03	−0.404784	−0.202392	−	0.979305i	$-0.564871\pi$
$571$	−5523.03	−0.404784	−0.202392	+	0.979305i	$0.564871\pi$
$572$	0	0
$573$	12721.9	0.927515
$574$	−5552.69	−0.403771
$575$	5672.25	0.411390
$576$	−1091.98	−0.0789915
$577$	23138.3	1.66943	0.834715	−	0.550682i	$-0.185632\pi$
$577$	23138.3	1.66943	0.834715	+	0.550682i	$0.185632\pi$
$578$	4354.11	0.313334
$579$	2839.46	0.203806
$580$	989.350	0.0708285
$581$	30286.7	2.16265
$582$	−9113.05	−0.649052
$583$	−297.588	−0.0211403
$584$	−7613.14	−0.539442
$585$	0	0
$586$	6905.52	0.486800
$587$	−15775.0	−1.10921	−0.554603	−	0.832115i	$-0.687130\pi$
$587$	−15775.0	−1.10921	−0.554603	+	0.832115i	$0.687130\pi$
$588$	18846.5	1.32180
$589$	−21332.0	−1.49231
$590$	634.043	0.0442426
$591$	−27743.8	−1.93101
$592$	−8076.74	−0.560730
$593$	−8187.00	−0.566947	−0.283474	−	0.958980i	$-0.591487\pi$
$593$	−8187.00	−0.566947	−0.283474	+	0.958980i	$0.591487\pi$
$594$	1277.48	0.0882417
$595$	−802.718	−0.0553080
$596$	19576.7	1.34546
$597$	−2077.97	−0.142455
$598$	0	0
$599$	21609.5	1.47402	0.737012	−	0.675879i	$-0.236236\pi$
$599$	21609.5	1.47402	0.737012	+	0.675879i	$0.236236\pi$
$600$	11824.3	0.804542
$601$	8845.34	0.600348	0.300174	−	0.953885i	$-0.402955\pi$
$601$	8845.34	0.600348	0.300174	+	0.953885i	$0.402955\pi$
$602$	−10088.9	−0.683045
$603$	1608.37	0.108620
$604$	19636.7	1.32286
$605$	117.810	0.00791677
$606$	−6273.46	−0.420531
$607$	1526.91	0.102101	0.0510504	−	0.998696i	$-0.483743\pi$
$607$	1526.91	0.102101	0.0510504	+	0.998696i	$0.483743\pi$
$608$	−25194.3	−1.68053
$609$	−25160.8	−1.67416
$610$	−639.116	−0.0424214
$611$	0	0
$612$	−1776.28	−0.117323
$613$	21782.1	1.43519	0.717595	−	0.696461i	$-0.245243\pi$
$613$	21782.1	1.43519	0.717595	+	0.696461i	$0.245243\pi$
$614$	361.519	0.0237617
$615$	1068.05	0.0700294
$616$	4955.39	0.324121
$617$	4267.88	0.278474	0.139237	−	0.990259i	$-0.455535\pi$
$617$	4267.88	0.278474	0.139237	+	0.990259i	$0.455535\pi$
$618$	2300.31	0.149728
$619$	14846.7	0.964041	0.482020	−	0.876160i	$-0.339903\pi$
$619$	14846.7	0.964041	0.482020	+	0.876160i	$0.339903\pi$
$620$	947.576	0.0613799
$621$	−4958.15	−0.320392
$622$	−1208.16	−0.0778824
$623$	−25146.1	−1.61711
$624$	0	0
$625$	15270.4	0.977306
$626$	6872.14	0.438764
$627$	9900.34	0.630592
$628$	1425.26	0.0905638
$629$	−6222.84	−0.394469
$630$	262.915	0.0166266
$631$	10338.3	0.652235	0.326117	−	0.945329i	$-0.394260\pi$
$631$	10338.3	0.652235	0.326117	+	0.945329i	$0.394260\pi$
$632$	−1112.48	−0.0700190
$633$	2416.38	0.151726
$634$	−5687.70	−0.356289
$635$	−1664.08	−0.103996
$636$	1110.88	0.0692596
$637$	0	0
$638$	−1746.88	−0.108401
$639$	4520.47	0.279854
$640$	1434.36	0.0885908
$641$	−2328.77	−0.143496	−0.0717479	−	0.997423i	$-0.522858\pi$
$641$	−2328.77	−0.143496	−0.0717479	+	0.997423i	$0.522858\pi$
$642$	−13415.3	−0.824706
$643$	−17023.7	−1.04409	−0.522043	−	0.852919i	$-0.674830\pi$
$643$	−17023.7	−1.04409	−0.522043	+	0.852919i	$0.674830\pi$
$644$	−8873.77	−0.542974
$645$	1940.59	0.118466
$646$	−4683.50	−0.285248
$647$	−10199.6	−0.619767	−0.309884	−	0.950775i	$-0.600290\pi$
$647$	−10199.6	−0.619767	−0.309884	+	0.950775i	$0.600290\pi$
$648$	−14159.7	−0.858403
$649$	6688.41	0.404535
$650$	0	0
$651$	−24098.4	−1.45083
$652$	−5311.65	−0.319049
$653$	−17119.3	−1.02593	−0.512963	−	0.858411i	$-0.671452\pi$
$653$	−17119.3	−1.02593	−0.512963	+	0.858411i	$0.671452\pi$
$654$	5647.40	0.337662
$655$	−807.210	−0.0481531
$656$	−6917.75	−0.411727
$657$	−4260.94	−0.253021
$658$	−13897.3	−0.823362
$659$	−18093.9	−1.06956	−0.534780	−	0.844992i	$-0.679605\pi$
$659$	−18093.9	−1.06956	−0.534780	+	0.844992i	$0.679605\pi$
$660$	−439.777	−0.0259368
$661$	26437.4	1.55567	0.777833	−	0.628472i	$-0.216319\pi$
$661$	26437.4	1.55567	0.777833	+	0.628472i	$0.216319\pi$
$662$	−88.2960	−0.00518387
$663$	0	0
$664$	−17012.8	−0.994316
$665$	−4141.59	−0.241509
$666$	2038.17	0.118585
$667$	6779.98	0.393586
$668$	17732.7	1.02710
$669$	−17385.7	−1.00474
$670$	−188.377	−0.0108621
$671$	−6741.92	−0.387882
$672$	−28461.6	−1.63382
$673$	6660.43	0.381487	0.190743	−	0.981640i	$-0.438910\pi$
$673$	6660.43	0.381487	0.190743	+	0.981640i	$0.438910\pi$
$674$	−3874.17	−0.221406
$675$	−13451.5	−0.767037
$676$	0	0
$677$	4950.87	0.281060	0.140530	−	0.990076i	$-0.455119\pi$
$677$	4950.87	0.281060	0.140530	+	0.990076i	$0.455119\pi$
$678$	−12544.4	−0.710565
$679$	40214.7	2.27290
$680$	450.908	0.0254287
$681$	−29913.9	−1.68327
$682$	−1673.12	−0.0939399
$683$	20861.3	1.16872	0.584360	−	0.811495i	$-0.301346\pi$
$683$	20861.3	1.16872	0.584360	+	0.811495i	$0.301346\pi$
$684$	−9164.62	−0.512307
$685$	2013.21	0.112293
$686$	3517.48	0.195770
$687$	19293.3	1.07145
$688$	−12569.2	−0.696504
$689$	0	0
$690$	−285.698	−0.0157628
$691$	−23234.8	−1.27915	−0.639576	−	0.768728i	$-0.720890\pi$
$691$	−23234.8	−1.27915	−0.639576	+	0.768728i	$0.720890\pi$
$692$	−16817.3	−0.923839
$693$	2773.44	0.152027
$694$	1847.52	0.101053
$695$	159.623	0.00871203
$696$	14133.5	0.769724
$697$	−5329.88	−0.289647
$698$	−1428.77	−0.0774779
$699$	−28663.1	−1.55099
$700$	−24074.7	−1.29991
$701$	−12146.3	−0.654437	−0.327219	−	0.944949i	$-0.606111\pi$
$701$	−12146.3	−0.654437	−0.327219	+	0.944949i	$0.606111\pi$
$702$	0	0
$703$	−32106.4	−1.72250
$704$	1349.15	0.0722273
$705$	2673.13	0.142802
$706$	−1161.98	−0.0619432
$707$	27683.9	1.47265
$708$	−24967.4	−1.32533
$709$	14932.8	0.790989	0.395495	−	0.918468i	$-0.370573\pi$
$709$	14932.8	0.790989	0.395495	+	0.918468i	$0.370573\pi$
$710$	−529.450	−0.0279858
$711$	−622.634	−0.0328419
$712$	14125.2	0.743491
$713$	6493.70	0.341081
$714$	−5290.86	−0.277319
$715$	0	0
$716$	−8234.51	−0.429802
$717$	−21520.0	−1.12089
$718$	3177.85	0.165176
$719$	29897.0	1.55073	0.775363	−	0.631516i	$-0.217567\pi$
$719$	29897.0	1.55073	0.775363	+	0.631516i	$0.217567\pi$
$720$	327.550	0.0169542
$721$	−10151.0	−0.524330
$722$	−16818.3	−0.866912
$723$	−5241.71	−0.269628
$724$	13874.0	0.712186
$725$	18394.2	0.942267
$726$	776.506	0.0396954
$727$	333.074	0.0169918	0.00849589	−	0.999964i	$-0.497296\pi$
$727$	333.074	0.0169918	0.00849589	+	0.999964i	$0.497296\pi$
$728$	0	0
$729$	9617.87	0.488638
$730$	499.054	0.0253025
$731$	−9684.09	−0.489985
$732$	25167.2	1.27077
$733$	19412.4	0.978192	0.489096	−	0.872230i	$-0.337327\pi$
$733$	19412.4	0.978192	0.489096	+	0.872230i	$0.337327\pi$
$734$	6327.76	0.318204
$735$	−2677.63	−0.134375
$736$	7669.43	0.384102
$737$	−1987.15	−0.0993185
$738$	1745.70	0.0870733
$739$	12701.9	0.632269	0.316134	−	0.948714i	$-0.397615\pi$
$739$	12701.9	0.632269	0.316134	+	0.948714i	$0.397615\pi$
$740$	1426.18	0.0708478
$741$	0	0
$742$	820.531	0.0405966
$743$	−24418.7	−1.20570	−0.602849	−	0.797855i	$-0.705968\pi$
$743$	−24418.7	−1.20570	−0.602849	+	0.797855i	$0.705968\pi$
$744$	13536.7	0.667042
$745$	−2781.37	−0.136781
$746$	10922.2	0.536046
$747$	−9521.77	−0.466377
$748$	2194.61	0.107276
$749$	59200.1	2.88802
$750$	−1556.13	−0.0757624
$751$	35441.1	1.72205	0.861027	−	0.508559i	$-0.169822\pi$
$751$	35441.1	1.72205	0.861027	+	0.508559i	$0.169822\pi$
$752$	−17313.8	−0.839586
$753$	35918.4	1.73830
$754$	0	0
$755$	−2789.89	−0.134483
$756$	21043.9	1.01238
$757$	24872.8	1.19421	0.597105	−	0.802163i	$-0.296318\pi$
$757$	24872.8	1.19421	0.597105	+	0.802163i	$0.296318\pi$
$758$	−5577.98	−0.267284
$759$	−3013.77	−0.144128
$760$	2326.44	0.111038
$761$	1761.30	0.0838989	0.0419495	−	0.999120i	$-0.486643\pi$
$761$	1761.30	0.0838989	0.0419495	+	0.999120i	$0.486643\pi$
$762$	−10968.3	−0.521442
$763$	−24921.2	−1.18245
$764$	14550.0	0.689006
$765$	252.365	0.0119272
$766$	−8008.95	−0.377774
$767$	0	0
$768$	3574.86	0.167964
$769$	−269.759	−0.0126499	−0.00632495	−	0.999980i	$-0.502013\pi$
$769$	−269.759	−0.0126499	−0.00632495	+	0.999980i	$0.502013\pi$
$770$	−324.834	−0.0152029
$771$	−29208.3	−1.36435
$772$	3247.48	0.151398
$773$	21749.6	1.01200	0.506001	−	0.862533i	$-0.331123\pi$
$773$	21749.6	1.01200	0.506001	+	0.862533i	$0.331123\pi$
$774$	3171.84	0.147299
$775$	17617.5	0.816568
$776$	−22589.7	−1.04500
$777$	−36270.0	−1.67462
$778$	−9349.42	−0.430839
$779$	−27499.3	−1.26478
$780$	0	0
$781$	−5585.08	−0.255890
$782$	1425.71	0.0651960
$783$	−16078.5	−0.733842
$784$	17342.9	0.790039
$785$	−202.494	−0.00920680
$786$	−5320.47	−0.241444
$787$	−15070.5	−0.682597	−0.341299	−	0.939955i	$-0.610867\pi$
$787$	−15070.5	−0.682597	−0.341299	+	0.939955i	$0.610867\pi$
$788$	−31730.4	−1.43445
$789$	19145.9	0.863892
$790$	72.9247	0.00328423
$791$	55356.6	2.48831
$792$	−1557.92	−0.0698967
$793$	0	0
$794$	779.982	0.0348621
$795$	−157.828	−0.00704100
$796$	−2376.56	−0.105823
$797$	26065.4	1.15845	0.579225	−	0.815168i	$-0.303355\pi$
$797$	26065.4	1.15845	0.579225	+	0.815168i	$0.303355\pi$
$798$	−27298.0	−1.21095
$799$	−13339.6	−0.590642
$800$	20807.3	0.919562
$801$	7905.64	0.348729
$802$	−3229.28	−0.142182
$803$	5264.43	0.231354
$804$	7417.93	0.325386
$805$	1260.74	0.0551993
$806$	0	0
$807$	12182.0	0.531383
$808$	−15550.8	−0.677073
$809$	28155.7	1.22361	0.611806	−	0.791008i	$-0.290443\pi$
$809$	28155.7	1.22361	0.611806	+	0.791008i	$0.290443\pi$
$810$	928.190	0.0402633
$811$	17197.4	0.744617	0.372308	−	0.928109i	$-0.378566\pi$
$811$	17197.4	0.744617	0.372308	+	0.928109i	$0.378566\pi$
$812$	−28776.3	−1.24366
$813$	−31580.7	−1.36234
$814$	−2518.18	−0.108430
$815$	754.654	0.0324348
$816$	−6591.57	−0.282783
$817$	−49964.6	−2.13958
$818$	11196.0	0.478555
$819$	0	0
$820$	1221.53	0.0520214
$821$	2536.72	0.107835	0.0539173	−	0.998545i	$-0.482829\pi$
$821$	2536.72	0.107835	0.0539173	+	0.998545i	$0.482829\pi$
$822$	13269.5	0.563048
$823$	37231.5	1.57692	0.788462	−	0.615083i	$-0.210878\pi$
$823$	37231.5	1.57692	0.788462	+	0.615083i	$0.210878\pi$
$824$	5702.08	0.241069
$825$	−8176.42	−0.345050
$826$	−18441.8	−0.776842
$827$	−10645.3	−0.447610	−0.223805	−	0.974634i	$-0.571848\pi$
$827$	−10645.3	−0.447610	−0.223805	+	0.974634i	$0.571848\pi$
$828$	2789.81	0.117093
$829$	27540.8	1.15384	0.576918	−	0.816802i	$-0.304255\pi$
$829$	27540.8	1.15384	0.576918	+	0.816802i	$0.304255\pi$
$830$	1115.22	0.0466383
$831$	39450.4	1.64683
$832$	0	0
$833$	13362.1	0.555786
$834$	1052.11	0.0436829
$835$	−2519.38	−0.104415
$836$	11323.0	0.468437
$837$	−15399.6	−0.635947
$838$	8743.35	0.360422
$839$	−30300.9	−1.24685	−0.623423	−	0.781885i	$-0.714258\pi$
$839$	−30300.9	−1.24685	−0.623423	+	0.781885i	$0.714258\pi$
$840$	2628.14	0.107952
$841$	−2402.58	−0.0985109
$842$	−4537.07	−0.185698
$843$	3784.94	0.154639
$844$	2763.60	0.112710
$845$	0	0
$846$	4369.14	0.177558
$847$	−3426.62	−0.139008
$848$	1022.25	0.0413965
$849$	27711.0	1.12019
$850$	3867.98	0.156083
$851$	9773.55	0.393693
$852$	20848.8	0.838341
$853$	22809.3	0.915563	0.457781	−	0.889065i	$-0.348644\pi$
$853$	22809.3	0.915563	0.457781	+	0.889065i	$0.348644\pi$
$854$	18589.3	0.744864
$855$	1302.07	0.0520816
$856$	−33254.3	−1.32781
$857$	−17283.7	−0.688916	−0.344458	−	0.938802i	$-0.611937\pi$
$857$	−17283.7	−0.688916	−0.344458	+	0.938802i	$0.611937\pi$
$858$	0	0
$859$	9082.83	0.360771	0.180385	−	0.983596i	$-0.442266\pi$
$859$	9082.83	0.360771	0.180385	+	0.983596i	$0.442266\pi$
$860$	2219.45	0.0880029
$861$	−31065.4	−1.22962
$862$	11155.7	0.440796
$863$	43857.4	1.72992	0.864962	−	0.501837i	$-0.167342\pi$
$863$	43857.4	1.72992	0.864962	+	0.501837i	$0.167342\pi$
$864$	−18187.8	−0.716159
$865$	2389.32	0.0939183
$866$	12265.4	0.481287
$867$	24359.8	0.954212
$868$	−27561.2	−1.07775
$869$	769.270	0.0300296
$870$	−926.473	−0.0361039
$871$	0	0
$872$	13998.9	0.543650
$873$	−12643.0	−0.490151
$874$	7355.88	0.284687
$875$	6866.98	0.265310
$876$	−19651.8	−0.757959
$877$	10451.3	0.402411	0.201205	−	0.979549i	$-0.435514\pi$
$877$	10451.3	0.402411	0.201205	+	0.979549i	$0.435514\pi$
$878$	9859.51	0.378978
$879$	38634.1	1.48247
$880$	−404.691	−0.0155024
$881$	−11532.4	−0.441019	−0.220509	−	0.975385i	$-0.570772\pi$
$881$	−11532.4	−0.441019	−0.220509	+	0.975385i	$0.570772\pi$
$882$	−4376.50	−0.167080
$883$	−32728.1	−1.24732	−0.623662	−	0.781694i	$-0.714356\pi$
$883$	−32728.1	−1.24732	−0.623662	+	0.781694i	$0.714356\pi$
$884$	0	0
$885$	3547.26	0.134734
$886$	6700.88	0.254086
$887$	−30741.2	−1.16368	−0.581842	−	0.813302i	$-0.697668\pi$
$887$	−30741.2	−1.16368	−0.581842	+	0.813302i	$0.697668\pi$
$888$	20373.8	0.769934
$889$	48401.6	1.82602
$890$	−925.932	−0.0348734
$891$	9791.31	0.368150
$892$	−19883.9	−0.746371
$893$	−68825.2	−2.57911
$894$	−18332.6	−0.685830
$895$	1169.92	0.0436940
$896$	−41719.8	−1.55554
$897$	0	0
$898$	−14454.2	−0.537129
$899$	21058.1	0.781230
$900$	7568.81	0.280326
$901$	787.607	0.0291221
$902$	−2156.83	−0.0796170
$903$	−56444.1	−2.08011
$904$	−31095.3	−1.14404
$905$	−1971.15	−0.0724015
$906$	−18388.7	−0.674308
$907$	43243.3	1.58310	0.791549	−	0.611105i	$-0.209275\pi$
$907$	43243.3	1.58310	0.791549	+	0.611105i	$0.209275\pi$
$908$	−34212.4	−1.25042
$909$	−8703.50	−0.317576
$910$	0	0
$911$	−29913.5	−1.08790	−0.543950	−	0.839118i	$-0.683072\pi$
$911$	−29913.5	−1.08790	−0.543950	+	0.839118i	$0.683072\pi$
$912$	−34008.9	−1.23481
$913$	11764.2	0.426440
$914$	−9415.19	−0.340729
$915$	−3575.64	−0.129188
$916$	22065.6	0.795926
$917$	23478.5	0.845506
$918$	−3381.02	−0.121558
$919$	−12745.5	−0.457492	−0.228746	−	0.973486i	$-0.573463\pi$
$919$	−12745.5	−0.457492	−0.228746	+	0.973486i	$0.573463\pi$
$920$	−708.194	−0.0253788
$921$	2022.58	0.0723628
$922$	−5803.91	−0.207312
$923$	0	0
$924$	12791.3	0.455416
$925$	26515.8	0.942524
$926$	13989.4	0.496459
$927$	3191.35	0.113072
$928$	24870.8	0.879766
$929$	−31859.8	−1.12517	−0.562587	−	0.826738i	$-0.690194\pi$
$929$	−31859.8	−1.12517	−0.562587	+	0.826738i	$0.690194\pi$
$930$	−887.353	−0.0312876
$931$	68941.1	2.42691
$932$	−32781.9	−1.15215
$933$	−6759.25	−0.237179
$934$	14725.9	0.515894
$935$	−311.800	−0.0109058
$936$	0	0
$937$	−36176.8	−1.26131	−0.630654	−	0.776064i	$-0.717213\pi$
$937$	−36176.8	−1.26131	−0.630654	+	0.776064i	$0.717213\pi$
$938$	5479.13	0.190725
$939$	38447.3	1.33619
$940$	3057.24	0.106081
$941$	−48802.5	−1.69067	−0.845333	−	0.534239i	$-0.820598\pi$
$941$	−48802.5	−1.69067	−0.845333	+	0.534239i	$0.820598\pi$
$942$	−1334.68	−0.0461637
$943$	8371.08	0.289077
$944$	−22975.5	−0.792149
$945$	−2989.81	−0.102919
$946$	−3918.84	−0.134685
$947$	20954.0	0.719021	0.359511	−	0.933141i	$-0.382944\pi$
$947$	20954.0	0.719021	0.359511	+	0.933141i	$0.382944\pi$
$948$	−2871.64	−0.0983824
$949$	0	0
$950$	19956.6	0.681557
$951$	−31820.7	−1.08502
$952$	−13115.1	−0.446495
$953$	−41866.8	−1.42309	−0.711543	−	0.702643i	$-0.752003\pi$
$953$	−41866.8	−1.42309	−0.711543	+	0.702643i	$0.752003\pi$
$954$	−257.965	−0.00875466
$955$	−2067.20	−0.0700450
$956$	−24612.4	−0.832658
$957$	−9773.19	−0.330118
$958$	−2280.87	−0.0769223
$959$	−58556.3	−1.97172
$960$	715.534	0.0240560
$961$	−9622.11	−0.322987
$962$	0	0
$963$	−18611.8	−0.622801
$964$	−5994.92	−0.200294
$965$	−461.386	−0.0153912
$966$	8309.80	0.276774
$967$	−22946.4	−0.763089	−0.381545	−	0.924350i	$-0.624608\pi$
$967$	−22946.4	−0.763089	−0.381545	+	0.924350i	$0.624608\pi$
$968$	1924.82	0.0639113
$969$	−26202.6	−0.868678
$970$	1480.79	0.0490157
$971$	−39666.9	−1.31099	−0.655495	−	0.755199i	$-0.727540\pi$
$971$	−39666.9	−1.31099	−0.655495	+	0.755199i	$0.727540\pi$
$972$	−16486.8	−0.544047
$973$	−4642.81	−0.152972
$974$	9161.18	0.301379
$975$	0	0
$976$	23159.3	0.759540
$977$	16323.7	0.534536	0.267268	−	0.963622i	$-0.413879\pi$
$977$	16323.7	0.534536	0.267268	+	0.963622i	$0.413879\pi$
$978$	4974.07	0.162631
$979$	−9767.49	−0.318867
$980$	−3062.39	−0.0998209
$981$	7834.94	0.254995
$982$	−6907.69	−0.224474
$983$	12666.5	0.410984	0.205492	−	0.978659i	$-0.434120\pi$
$983$	12666.5	0.410984	0.205492	+	0.978659i	$0.434120\pi$
$984$	17450.3	0.565340
$985$	4508.11	0.145828
$986$	4623.35	0.149328
$987$	−77750.6	−2.50742
$988$	0	0
$989$	15209.8	0.489022
$990$	102.124	0.00327850
$991$	−16230.3	−0.520256	−0.260128	−	0.965574i	$-0.583765\pi$
$991$	−16230.3	−0.520256	−0.260128	+	0.965574i	$0.583765\pi$
$992$	23820.6	0.762404
$993$	−493.986	−0.0157867
$994$	15399.6	0.491394
$995$	337.651	0.0107580
$996$	−43915.2	−1.39710
$997$	−10082.5	−0.320278	−0.160139	−	0.987094i	$-0.551194\pi$
$997$	−10082.5	−0.320278	−0.160139	+	0.987094i	$0.551194\pi$
$998$	11165.8	0.354154
$999$	−23177.7	−0.734042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.i.1.7		17
13.3	even	3		143.4.e.a.100.11	✓	34
13.9	even	3		143.4.e.a.133.11	yes	34
13.12	even	2		1859.4.a.f.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.11	✓	34	13.3	even	3
143.4.e.a.133.11	yes	34	13.9	even	3
1859.4.a.f.1.11		17	13.12	even	2
1859.4.a.i.1.7		17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.07101 q^{2} -5.99193 q^{3} -6.85294 q^{4} +0.973634 q^{5} +6.41740 q^{6} -28.3191 q^{7} +15.9076 q^{8} +8.90321 q^{9} +O(q^{10})\)	\(q-1.07101 q^{2} -5.99193 q^{3} -6.85294 q^{4} +0.973634 q^{5} +6.41740 q^{6} -28.3191 q^{7} +15.9076 q^{8} +8.90321 q^{9} -1.04277 q^{10} -11.0000 q^{11} +41.0623 q^{12} +30.3300 q^{14} -5.83395 q^{15} +37.7863 q^{16} +29.1130 q^{17} -9.53541 q^{18} +150.207 q^{19} -6.67226 q^{20} +169.686 q^{21} +11.7811 q^{22} -45.7247 q^{23} -95.3173 q^{24} -124.052 q^{25} +108.435 q^{27} +194.069 q^{28} -148.278 q^{29} +6.24821 q^{30} -142.017 q^{31} -167.730 q^{32} +65.9112 q^{33} -31.1803 q^{34} -27.5725 q^{35} -61.0132 q^{36} -213.748 q^{37} -160.873 q^{38} +15.4882 q^{40} -183.076 q^{41} -181.735 q^{42} -332.638 q^{43} +75.3824 q^{44} +8.66847 q^{45} +48.9716 q^{46} -458.202 q^{47} -226.413 q^{48} +458.974 q^{49} +132.861 q^{50} -174.443 q^{51} +27.0534 q^{53} -116.134 q^{54} -10.7100 q^{55} -450.490 q^{56} -900.031 q^{57} +158.807 q^{58} -608.037 q^{59} +39.9797 q^{60} +612.902 q^{61} +152.102 q^{62} -252.131 q^{63} -122.650 q^{64} -70.5915 q^{66} +180.650 q^{67} -199.510 q^{68} +273.979 q^{69} +29.5304 q^{70} +507.734 q^{71} +141.629 q^{72} -478.584 q^{73} +228.925 q^{74} +743.311 q^{75} -1029.36 q^{76} +311.511 q^{77} -69.9336 q^{79} +36.7901 q^{80} -890.120 q^{81} +196.075 q^{82} -1069.48 q^{83} -1162.85 q^{84} +28.3454 q^{85} +356.258 q^{86} +888.472 q^{87} -174.984 q^{88} +887.954 q^{89} -9.28400 q^{90} +313.349 q^{92} +850.957 q^{93} +490.738 q^{94} +146.247 q^{95} +1005.03 q^{96} -1420.05 q^{97} -491.564 q^{98} -97.9353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9}+O(q^{10}) \) 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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