LMFDB - Embedded newform 1859.4.a.f.1.17

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			1.17
Root			$-5.36576$ 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)

$f(q)$	$=$	$q+5.36576 q^{2} -0.836231 q^{3} +20.7914 q^{4} -1.92861 q^{5} -4.48702 q^{6} -17.6723 q^{7} +68.6355 q^{8} -26.3007 q^{9} +O(q^{10})$	\(q+5.36576 q^{2} -0.836231 q^{3} +20.7914 q^{4} -1.92861 q^{5} -4.48702 q^{6} -17.6723 q^{7} +68.6355 q^{8} -26.3007 q^{9} -10.3485 q^{10} +11.0000 q^{11} -17.3864 q^{12} -94.8252 q^{14} +1.61276 q^{15} +201.951 q^{16} -29.3238 q^{17} -141.123 q^{18} +78.8200 q^{19} -40.0985 q^{20} +14.7781 q^{21} +59.0234 q^{22} -167.985 q^{23} -57.3952 q^{24} -121.280 q^{25} +44.5717 q^{27} -367.431 q^{28} -191.141 q^{29} +8.65370 q^{30} -47.7682 q^{31} +534.535 q^{32} -9.19854 q^{33} -157.345 q^{34} +34.0829 q^{35} -546.828 q^{36} +27.3197 q^{37} +422.929 q^{38} -132.371 q^{40} +297.685 q^{41} +79.2958 q^{42} -522.466 q^{43} +228.705 q^{44} +50.7238 q^{45} -901.369 q^{46} +27.8453 q^{47} -168.878 q^{48} -30.6909 q^{49} -650.762 q^{50} +24.5215 q^{51} -179.517 q^{53} +239.161 q^{54} -21.2147 q^{55} -1212.95 q^{56} -65.9118 q^{57} -1025.62 q^{58} -92.1021 q^{59} +33.5316 q^{60} +824.335 q^{61} -256.313 q^{62} +464.793 q^{63} +1252.58 q^{64} -49.3572 q^{66} -224.066 q^{67} -609.683 q^{68} +140.475 q^{69} +182.881 q^{70} +461.784 q^{71} -1805.16 q^{72} -883.333 q^{73} +146.591 q^{74} +101.419 q^{75} +1638.78 q^{76} -194.395 q^{77} -150.626 q^{79} -389.484 q^{80} +672.847 q^{81} +1597.31 q^{82} -1136.83 q^{83} +307.257 q^{84} +56.5542 q^{85} -2803.43 q^{86} +159.838 q^{87} +754.991 q^{88} -1356.14 q^{89} +272.172 q^{90} -3492.65 q^{92} +39.9453 q^{93} +149.411 q^{94} -152.013 q^{95} -446.995 q^{96} +328.044 q^{97} -164.680 q^{98} -289.308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.36576	1.89708	0.948541	−	0.316653i	$-0.102559\pi$
$2$	5.36576	1.89708	0.948541	+	0.316653i	$0.102559\pi$
$3$	−0.836231	−0.160933	−0.0804664	−	0.996757i	$-0.525641\pi$
$3$	−0.836231	−0.160933	−0.0804664	+	0.996757i	$0.525641\pi$
$4$	20.7914	2.59892
$5$	−1.92861	−0.172500	−0.0862501	−	0.996274i	$-0.527488\pi$
$5$	−1.92861	−0.172500	−0.0862501	+	0.996274i	$0.527488\pi$
$6$	−4.48702	−0.305303
$7$	−17.6723	−0.954213	−0.477106	−	0.878846i	$-0.658314\pi$
$7$	−17.6723	−0.954213	−0.477106	+	0.878846i	$0.658314\pi$
$8$	68.6355	3.03329
$9$	−26.3007	−0.974101
$10$	−10.3485	−0.327247
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−17.3864	−0.418252
$13$	0	0
$13$	0	0
$14$	−94.8252	−1.81022
$15$	1.61276	0.0277609
$16$	201.951	3.15548
$17$	−29.3238	−0.418357	−0.209178	−	0.977877i	$-0.567079\pi$
$17$	−29.3238	−0.418357	−0.209178	+	0.977877i	$0.567079\pi$
$18$	−141.123	−1.84795
$19$	78.8200	0.951713	0.475857	−	0.879523i	$-0.342138\pi$
$19$	78.8200	0.951713	0.475857	+	0.879523i	$0.342138\pi$
$20$	−40.0985	−0.448315
$21$	14.7781	0.153564
$22$	59.0234	0.571992
$23$	−167.985	−1.52293	−0.761464	−	0.648207i	$-0.775519\pi$
$23$	−167.985	−1.52293	−0.761464	+	0.648207i	$0.775519\pi$
$24$	−57.3952	−0.488156
$25$	−121.280	−0.970244
$26$	0	0
$27$	44.5717	0.317697
$28$	−367.431	−2.47993
$29$	−191.141	−1.22393	−0.611964	−	0.790885i	$-0.709620\pi$
$29$	−191.141	−1.22393	−0.611964	+	0.790885i	$0.709620\pi$
$30$	8.65370	0.0526648
$31$	−47.7682	−0.276756	−0.138378	−	0.990380i	$-0.544189\pi$
$31$	−47.7682	−0.276756	−0.138378	+	0.990380i	$0.544189\pi$
$32$	534.535	2.95292
$33$	−9.19854	−0.0485231
$34$	−157.345	−0.793658
$35$	34.0829	0.164602
$36$	−546.828	−2.53161
$37$	27.3197	0.121387	0.0606937	−	0.998156i	$-0.480669\pi$
$37$	27.3197	0.121387	0.0606937	+	0.998156i	$0.480669\pi$
$38$	422.929	1.80548
$39$	0	0
$40$	−132.371	−0.523243
$41$	297.685	1.13392	0.566959	−	0.823746i	$-0.308120\pi$
$41$	297.685	1.13392	0.566959	+	0.823746i	$0.308120\pi$
$42$	79.2958	0.291324
$43$	−522.466	−1.85292	−0.926458	−	0.376399i	$-0.877162\pi$
$43$	−522.466	−1.85292	−0.926458	+	0.376399i	$0.877162\pi$
$44$	228.705	0.783605
$45$	50.7238	0.168032
$46$	−901.369	−2.88912
$47$	27.8453	0.0864183	0.0432091	−	0.999066i	$-0.486242\pi$
$47$	27.8453	0.0864183	0.0432091	+	0.999066i	$0.486242\pi$
$48$	−168.878	−0.507820
$49$	−30.6909	−0.0894779
$50$	−650.762	−1.84063
$51$	24.5215	0.0673273
$52$	0	0
$53$	−179.517	−0.465257	−0.232628	−	0.972566i	$-0.574733\pi$
$53$	−179.517	−0.465257	−0.232628	+	0.972566i	$0.574733\pi$
$54$	239.161	0.602698
$55$	−21.2147	−0.0520107
$56$	−1212.95	−2.89440
$57$	−65.9118	−0.153162
$58$	−1025.62	−2.32189
$59$	−92.1021	−0.203232	−0.101616	−	0.994824i	$-0.532401\pi$
$59$	−92.1021	−0.203232	−0.101616	+	0.994824i	$0.532401\pi$
$60$	33.5316	0.0721485
$61$	824.335	1.73025	0.865126	−	0.501555i	$-0.167239\pi$
$61$	824.335	1.73025	0.865126	+	0.501555i	$0.167239\pi$
$62$	−256.313	−0.525028
$63$	464.793	0.929499
$64$	1252.58	2.44645
$65$	0	0
$66$	−49.3572	−0.0920523
$67$	−224.066	−0.408568	−0.204284	−	0.978912i	$-0.565487\pi$
$67$	−224.066	−0.408568	−0.204284	+	0.978912i	$0.565487\pi$
$68$	−609.683	−1.08728
$69$	140.475	0.245089
$70$	182.881	0.312263
$71$	461.784	0.771882	0.385941	−	0.922523i	$-0.373877\pi$
$71$	461.784	0.771882	0.385941	+	0.922523i	$0.373877\pi$
$72$	−1805.16	−2.95473
$73$	−883.333	−1.41625	−0.708125	−	0.706087i	$-0.750459\pi$
$73$	−883.333	−1.41625	−0.708125	+	0.706087i	$0.750459\pi$
$74$	146.591	0.230282
$75$	101.419	0.156144
$76$	1638.78	2.47343
$77$	−194.395	−0.287706
$78$	0	0
$79$	−150.626	−0.214516	−0.107258	−	0.994231i	$-0.534207\pi$
$79$	−150.626	−0.214516	−0.107258	+	0.994231i	$0.534207\pi$
$80$	−389.484	−0.544321
$81$	672.847	0.922973
$82$	1597.31	2.15114
$83$	−1136.83	−1.50342	−0.751709	−	0.659495i	$-0.770770\pi$
$83$	−1136.83	−1.50342	−0.751709	+	0.659495i	$0.770770\pi$
$84$	307.257	0.399101
$85$	56.5542	0.0721666
$86$	−2803.43	−3.51513
$87$	159.838	0.196970
$88$	754.991	0.914572
$89$	−1356.14	−1.61517	−0.807586	−	0.589750i	$-0.799226\pi$
$89$	−1356.14	−1.61517	−0.807586	+	0.589750i	$0.799226\pi$
$90$	272.172	0.318772
$91$	0	0
$92$	−3492.65	−3.95797
$93$	39.9453	0.0445390
$94$	149.411	0.163943
$95$	−152.013	−0.164171
$96$	−446.995	−0.475221
$97$	328.044	0.343380	0.171690	−	0.985151i	$-0.445077\pi$
$97$	328.044	0.343380	0.171690	+	0.985151i	$0.445077\pi$
$98$	−164.680	−0.169747
$99$	−289.308	−0.293702
$100$	−2521.59	−2.52159
$101$	9.15157	0.00901600	0.00450800	−	0.999990i	$-0.498565\pi$
$101$	9.15157	0.00901600	0.00450800	+	0.999990i	$0.498565\pi$
$102$	131.576	0.127726
$103$	433.807	0.414993	0.207496	−	0.978236i	$-0.433469\pi$
$103$	433.807	0.414993	0.207496	+	0.978236i	$0.433469\pi$
$104$	0	0
$105$	−28.5012	−0.0264898
$106$	−963.247	−0.882631
$107$	1121.57	1.01333	0.506666	−	0.862142i	$-0.330878\pi$
$107$	1121.57	1.01333	0.506666	+	0.862142i	$0.330878\pi$
$108$	926.708	0.825672
$109$	−1530.67	−1.34506	−0.672530	−	0.740070i	$-0.734792\pi$
$109$	−1530.67	−1.34506	−0.672530	+	0.740070i	$0.734792\pi$
$110$	−113.833	−0.0986687
$111$	−22.8456	−0.0195352
$112$	−3568.93	−3.01100
$113$	−1551.47	−1.29159	−0.645795	−	0.763511i	$-0.723474\pi$
$113$	−1551.47	−1.29159	−0.645795	+	0.763511i	$0.723474\pi$
$114$	−353.667	−0.290561
$115$	323.978	0.262705
$116$	−3974.08	−3.18090
$117$	0	0
$118$	−494.198	−0.385547
$119$	518.218	0.399202
$120$	110.693	0.0842069
$121$	121.000	0.0909091
$122$	4423.19	3.28243
$123$	−248.934	−0.182485
$124$	−993.167	−0.719267
$125$	474.979	0.339867
$126$	2493.97	1.76334
$127$	2007.37	1.40256	0.701281	−	0.712885i	$-0.252612\pi$
$127$	2007.37	1.40256	0.701281	+	0.712885i	$0.252612\pi$
$128$	2444.77	1.68820
$129$	436.903	0.298195
$130$	0	0
$131$	−1738.38	−1.15941	−0.579705	−	0.814826i	$-0.696832\pi$
$131$	−1738.38	−1.15941	−0.579705	+	0.814826i	$0.696832\pi$
$132$	−191.250	−0.126108
$133$	−1392.93	−0.908137
$134$	−1202.29	−0.775087
$135$	−85.9615	−0.0548029
$136$	−2012.66	−1.26900
$137$	483.868	0.301749	0.150875	−	0.988553i	$-0.451791\pi$
$137$	483.868	0.301749	0.150875	+	0.988553i	$0.451791\pi$
$138$	753.753	0.464954
$139$	−897.744	−0.547810	−0.273905	−	0.961757i	$-0.588315\pi$
$139$	−897.744	−0.547810	−0.273905	+	0.961757i	$0.588315\pi$
$140$	708.631	0.427788
$141$	−23.2851	−0.0139075
$142$	2477.82	1.46433
$143$	0	0
$144$	−5311.45	−3.07376
$145$	368.636	0.211128
$146$	−4739.75	−2.68675
$147$	25.6647	0.0143999
$148$	568.015	0.315476
$149$	1550.19	0.852327	0.426163	−	0.904646i	$-0.359865\pi$
$149$	1550.19	0.852327	0.426163	+	0.904646i	$0.359865\pi$
$150$	544.187	0.296218
$151$	−634.843	−0.342138	−0.171069	−	0.985259i	$-0.554722\pi$
$151$	−634.843	−0.342138	−0.171069	+	0.985259i	$0.554722\pi$
$152$	5409.85	2.88682
$153$	771.237	0.407522
$154$	−1043.08	−0.545802
$155$	92.1262	0.0477404
$156$	0	0
$157$	3199.63	1.62649	0.813244	−	0.581923i	$-0.197699\pi$
$157$	3199.63	1.62649	0.813244	+	0.581923i	$0.197699\pi$
$158$	−808.224	−0.406955
$159$	150.118	0.0748751
$160$	−1030.91	−0.509379
$161$	2968.68	1.45320
$162$	3610.34	1.75096
$163$	−870.348	−0.418226	−0.209113	−	0.977891i	$-0.567058\pi$
$163$	−870.348	−0.418226	−0.209113	+	0.977891i	$0.567058\pi$
$164$	6189.29	2.94697
$165$	17.7404	0.00837023
$166$	−6099.97	−2.85211
$167$	113.049	0.0523833	0.0261917	−	0.999657i	$-0.491662\pi$
$167$	113.049	0.0523833	0.0261917	+	0.999657i	$0.491662\pi$
$168$	1014.30	0.465805
$169$	0	0
$170$	303.456	0.136906
$171$	−2073.02	−0.927065
$172$	−10862.8	−4.81558
$173$	116.385	0.0511478	0.0255739	−	0.999673i	$-0.491859\pi$
$173$	116.385	0.0511478	0.0255739	+	0.999673i	$0.491859\pi$
$174$	857.651	0.373669
$175$	2143.30	0.925819
$176$	2221.46	0.951413
$177$	77.0186	0.0327066
$178$	−7276.71	−3.06411
$179$	1937.25	0.808921	0.404461	−	0.914555i	$-0.367459\pi$
$179$	1937.25	0.808921	0.404461	+	0.914555i	$0.367459\pi$
$180$	1054.62	0.436704
$181$	−4239.34	−1.74093	−0.870463	−	0.492233i	$-0.836181\pi$
$181$	−4239.34	−1.74093	−0.870463	+	0.492233i	$0.836181\pi$
$182$	0	0
$183$	−689.335	−0.278454
$184$	−11529.8	−4.61948
$185$	−52.6891	−0.0209393
$186$	214.337	0.0844942
$187$	−322.562	−0.126139
$188$	578.943	0.224594
$189$	−787.683	−0.303151
$190$	−815.666	−0.311445
$191$	2247.01	0.851245	0.425622	−	0.904901i	$-0.360055\pi$
$191$	2247.01	0.851245	0.425622	+	0.904901i	$0.360055\pi$
$192$	−1047.45	−0.393714
$193$	4205.94	1.56866	0.784328	−	0.620347i	$-0.213008\pi$
$193$	4205.94	1.56866	0.784328	+	0.620347i	$0.213008\pi$
$194$	1760.21	0.651420
$195$	0	0
$196$	−638.107	−0.232546
$197$	1423.27	0.514739	0.257370	−	0.966313i	$-0.417144\pi$
$197$	1423.27	0.514739	0.257370	+	0.966313i	$0.417144\pi$
$198$	−1552.36	−0.557178
$199$	3048.14	1.08581	0.542906	−	0.839793i	$-0.317324\pi$
$199$	3048.14	1.08581	0.542906	+	0.839793i	$0.317324\pi$
$200$	−8324.15	−2.94303
$201$	187.371	0.0657520
$202$	49.1052	0.0171041
$203$	3377.89	1.16789
$204$	509.836	0.174979
$205$	−574.119	−0.195601
$206$	2327.70	0.787275
$207$	4418.13	1.48349
$208$	0	0
$209$	867.020	0.286952
$210$	−152.931	−0.0502534
$211$	−3354.62	−1.09451	−0.547255	−	0.836966i	$-0.684327\pi$
$211$	−3354.62	−1.09451	−0.547255	+	0.836966i	$0.684327\pi$
$212$	−3732.42	−1.20917
$213$	−386.158	−0.124221
$214$	6018.09	1.92238
$215$	1007.63	0.319628
$216$	3059.20	0.963669
$217$	844.172	0.264084
$218$	−8213.21	−2.55169
$219$	738.671	0.227921
$220$	−441.083	−0.135172
$221$	0	0
$222$	−122.584	−0.0370599
$223$	−1756.04	−0.527324	−0.263662	−	0.964615i	$-0.584930\pi$
$223$	−1756.04	−0.527324	−0.263662	+	0.964615i	$0.584930\pi$
$224$	−9446.45	−2.81771
$225$	3189.76	0.945115
$226$	−8324.79	−2.45025
$227$	2374.03	0.694142	0.347071	−	0.937839i	$-0.387176\pi$
$227$	2374.03	0.694142	0.347071	+	0.937839i	$0.387176\pi$
$228$	−1370.40	−0.398056
$229$	5172.77	1.49269	0.746346	−	0.665558i	$-0.231806\pi$
$229$	5172.77	1.49269	0.746346	+	0.665558i	$0.231806\pi$
$230$	1738.39	0.498374
$231$	162.559	0.0463013
$232$	−13119.0	−3.71253
$233$	1059.46	0.297887	0.148944	−	0.988846i	$-0.452413\pi$
$233$	1059.46	0.297887	0.148944	+	0.988846i	$0.452413\pi$
$234$	0	0
$235$	−53.7028	−0.0149072
$236$	−1914.93	−0.528184
$237$	125.958	0.0345227
$238$	2780.64	0.757318
$239$	−4494.00	−1.21629	−0.608144	−	0.793827i	$-0.708086\pi$
$239$	−4494.00	−1.21629	−0.608144	+	0.793827i	$0.708086\pi$
$240$	325.699	0.0875990
$241$	−5088.34	−1.36004	−0.680018	−	0.733195i	$-0.738028\pi$
$241$	−5088.34	−1.36004	−0.680018	+	0.733195i	$0.738028\pi$
$242$	649.257	0.172462
$243$	−1766.09	−0.466234
$244$	17139.1	4.49679
$245$	59.1908	0.0154349
$246$	−1335.72	−0.346188
$247$	0	0
$248$	−3278.60	−0.839480
$249$	950.655	0.241949
$250$	2548.62	0.644756
$251$	1008.84	0.253695	0.126848	−	0.991922i	$-0.459514\pi$
$251$	1008.84	0.253695	0.126848	+	0.991922i	$0.459514\pi$
$252$	9663.70	2.41570
$253$	−1847.84	−0.459180
$254$	10771.1	2.66078
$255$	−47.2924	−0.0116140
$256$	3097.41	0.756203
$257$	−4054.04	−0.983984	−0.491992	−	0.870600i	$-0.663731\pi$
$257$	−4054.04	−0.983984	−0.491992	+	0.870600i	$0.663731\pi$
$258$	2344.31	0.565700
$259$	−482.801	−0.115829
$260$	0	0
$261$	5027.14	1.19223
$262$	−9327.72	−2.19950
$263$	3027.58	0.709841	0.354921	−	0.934896i	$-0.384508\pi$
$263$	3027.58	0.709841	0.354921	+	0.934896i	$0.384508\pi$
$264$	−631.347	−0.147185
$265$	346.219	0.0802568
$266$	−7474.12	−1.72281
$267$	1134.04	0.259934
$268$	−4658.65	−1.06184
$269$	7492.67	1.69827	0.849137	−	0.528172i	$-0.177122\pi$
$269$	7492.67	1.69827	0.849137	+	0.528172i	$0.177122\pi$
$270$	−461.249	−0.103966
$271$	−6105.30	−1.36853	−0.684263	−	0.729235i	$-0.739876\pi$
$271$	−6105.30	−1.36853	−0.684263	+	0.729235i	$0.739876\pi$
$272$	−5921.96	−1.32012
$273$	0	0
$274$	2596.32	0.572444
$275$	−1334.09	−0.292539
$276$	2920.66	0.636968
$277$	7649.53	1.65926	0.829631	−	0.558311i	$-0.188551\pi$
$277$	7649.53	1.65926	0.829631	+	0.558311i	$0.188551\pi$
$278$	−4817.08	−1.03924
$279$	1256.34	0.269588
$280$	2339.30	0.499285
$281$	3781.25	0.802743	0.401371	−	0.915915i	$-0.368534\pi$
$281$	3781.25	0.802743	0.401371	+	0.915915i	$0.368534\pi$
$282$	−124.942	−0.0263837
$283$	−2397.31	−0.503552	−0.251776	−	0.967785i	$-0.581015\pi$
$283$	−2397.31	−0.503552	−0.251776	+	0.967785i	$0.581015\pi$
$284$	9601.13	2.00606
$285$	127.118	0.0264204
$286$	0	0
$287$	−5260.78	−1.08200
$288$	−14058.7	−2.87644
$289$	−4053.11	−0.824977
$290$	1978.01	0.400527
$291$	−274.321	−0.0552610
$292$	−18365.7	−3.68073
$293$	4962.87	0.989535	0.494768	−	0.869025i	$-0.335253\pi$
$293$	4962.87	0.989535	0.494768	+	0.869025i	$0.335253\pi$
$294$	137.711	0.0273178
$295$	177.629	0.0350575
$296$	1875.10	0.368203
$297$	490.289	0.0957894
$298$	8317.96	1.61693
$299$	0	0
$300$	2108.63	0.405806
$301$	9233.16	1.76808
$302$	−3406.41	−0.649063
$303$	−7.65283	−0.00145097
$304$	15917.8	3.00311
$305$	−1589.82	−0.298469
$306$	4138.27	0.773103
$307$	−4710.51	−0.875711	−0.437856	−	0.899045i	$-0.644262\pi$
$307$	−4710.51	−0.875711	−0.437856	+	0.899045i	$0.644262\pi$
$308$	−4041.74	−0.747726
$309$	−362.763	−0.0667859
$310$	494.327	0.0905674
$311$	−5374.03	−0.979849	−0.489925	−	0.871765i	$-0.662976\pi$
$311$	−5374.03	−0.979849	−0.489925	+	0.871765i	$0.662976\pi$
$312$	0	0
$313$	−2109.35	−0.380918	−0.190459	−	0.981695i	$-0.560998\pi$
$313$	−2109.35	−0.380918	−0.190459	+	0.981695i	$0.560998\pi$
$314$	17168.5	3.08558
$315$	−896.405	−0.160339
$316$	−3131.73	−0.557511
$317$	5723.36	1.01406	0.507028	−	0.861929i	$-0.330744\pi$
$317$	5723.36	1.01406	0.507028	+	0.861929i	$0.330744\pi$
$318$	805.497	0.142044
$319$	−2102.55	−0.369028
$320$	−2415.74	−0.422013
$321$	−937.895	−0.163078
$322$	15929.2	2.75684
$323$	−2311.30	−0.398156
$324$	13989.4	2.39874
$325$	0	0
$326$	−4670.08	−0.793410
$327$	1279.99	0.216464
$328$	20431.8	3.43950
$329$	−492.090	−0.0824614
$330$	95.1908	0.0158790
$331$	9545.23	1.58506	0.792528	−	0.609836i	$-0.208765\pi$
$331$	9545.23	1.58506	0.792528	+	0.609836i	$0.208765\pi$
$332$	−23636.3	−3.90727
$333$	−718.528	−0.118244
$334$	606.595	0.0993755
$335$	432.136	0.0704780
$336$	2984.45	0.484569
$337$	9912.83	1.60233	0.801167	−	0.598441i	$-0.204213\pi$
$337$	9912.83	1.60233	0.801167	+	0.598441i	$0.204213\pi$
$338$	0	0
$339$	1297.38	0.207859
$340$	1175.84	0.187556
$341$	−525.450	−0.0834449
$342$	−11123.3	−1.75872
$343$	6603.97	1.03959
$344$	−35859.7	−5.62043
$345$	−270.921	−0.0422779
$346$	624.493	0.0970316
$347$	−570.072	−0.0881933	−0.0440966	−	0.999027i	$-0.514041\pi$
$347$	−570.072	−0.0881933	−0.0440966	+	0.999027i	$0.514041\pi$
$348$	3323.25	0.511911
$349$	−9184.71	−1.40873	−0.704365	−	0.709838i	$-0.748768\pi$
$349$	−9184.71	−1.40873	−0.704365	+	0.709838i	$0.748768\pi$
$350$	11500.4	1.75636
$351$	0	0
$352$	5879.89	0.890338
$353$	8144.04	1.22794	0.613971	−	0.789329i	$-0.289571\pi$
$353$	8144.04	1.22794	0.613971	+	0.789329i	$0.289571\pi$
$354$	413.264	0.0620472
$355$	−890.601	−0.133150
$356$	−28196.0	−4.19771
$357$	−433.350	−0.0642446
$358$	10394.8	1.53459
$359$	−6407.26	−0.941956	−0.470978	−	0.882145i	$-0.656099\pi$
$359$	−6407.26	−0.941956	−0.470978	+	0.882145i	$0.656099\pi$
$360$	3481.46	0.509691
$361$	−646.403	−0.0942416
$362$	−22747.3	−3.30268
$363$	−101.184	−0.0146303
$364$	0	0
$365$	1703.60	0.244303
$366$	−3698.81	−0.528251
$367$	5232.25	0.744200	0.372100	−	0.928193i	$-0.378638\pi$
$367$	5232.25	0.744200	0.372100	+	0.928193i	$0.378638\pi$
$368$	−33924.7	−4.80557
$369$	−7829.34	−1.10455
$370$	−282.717	−0.0397236
$371$	3172.48	0.443954
$372$	830.517	0.115754
$373$	−1045.59	−0.145144	−0.0725720	−	0.997363i	$-0.523121\pi$
$373$	−1045.59	−0.145144	−0.0725720	+	0.997363i	$0.523121\pi$
$374$	−1730.79	−0.239297
$375$	−397.192	−0.0546958
$376$	1911.18	0.262132
$377$	0	0
$378$	−4226.52	−0.575103
$379$	3110.36	0.421553	0.210776	−	0.977534i	$-0.432401\pi$
$379$	3110.36	0.421553	0.210776	+	0.977534i	$0.432401\pi$
$380$	−3160.56	−0.426667
$381$	−1678.63	−0.225718
$382$	12056.9	1.61488
$383$	3301.27	0.440437	0.220218	−	0.975451i	$-0.429323\pi$
$383$	3301.27	0.440437	0.220218	+	0.975451i	$0.429323\pi$
$384$	−2044.39	−0.271686
$385$	374.912	0.0496293
$386$	22568.1	2.97587
$387$	13741.2	1.80493
$388$	6820.49	0.892417
$389$	−5485.87	−0.715024	−0.357512	−	0.933908i	$-0.616375\pi$
$389$	−5485.87	−0.715024	−0.357512	+	0.933908i	$0.616375\pi$
$390$	0	0
$391$	4925.97	0.637128
$392$	−2106.49	−0.271412
$393$	1453.69	0.186587
$394$	7636.92	0.976503
$395$	290.499	0.0370041
$396$	−6015.11	−0.763310
$397$	4213.85	0.532712	0.266356	−	0.963875i	$-0.414180\pi$
$397$	4213.85	0.532712	0.266356	+	0.963875i	$0.414180\pi$
$398$	16355.6	2.05988
$399$	1164.81	0.146149
$400$	−24492.7	−3.06158
$401$	−12222.4	−1.52208	−0.761042	−	0.648703i	$-0.775312\pi$
$401$	−12222.4	−1.52208	−0.761042	+	0.648703i	$0.775312\pi$
$402$	1005.39	0.124737
$403$	0	0
$404$	190.274	0.0234319
$405$	−1297.66	−0.159213
$406$	18124.9	2.21558
$407$	300.517	0.0365997
$408$	1683.05	0.204223
$409$	−10069.0	−1.21731	−0.608653	−	0.793436i	$-0.708290\pi$
$409$	−10069.0	−1.21731	−0.608653	+	0.793436i	$0.708290\pi$
$410$	−3080.58	−0.371071
$411$	−404.626	−0.0485614
$412$	9019.44	1.07853
$413$	1627.65	0.193926
$414$	23706.6	2.81429
$415$	2192.51	0.259340
$416$	0	0
$417$	750.721	0.0881606
$418$	4652.22	0.544372
$419$	4128.87	0.481404	0.240702	−	0.970599i	$-0.422622\pi$
$419$	4128.87	0.481404	0.240702	+	0.970599i	$0.422622\pi$
$420$	−592.579	−0.0688450
$421$	−15503.2	−1.79472	−0.897361	−	0.441297i	$-0.854518\pi$
$421$	−15503.2	−1.79472	−0.897361	+	0.441297i	$0.854518\pi$
$422$	−18000.1	−2.07637
$423$	−732.352	−0.0841801
$424$	−12321.3	−1.41126
$425$	3556.41	0.405908
$426$	−2072.03	−0.235658
$427$	−14567.9	−1.65103
$428$	23319.1	2.63357
$429$	0	0
$430$	5406.72	0.606361
$431$	−8425.34	−0.941611	−0.470805	−	0.882237i	$-0.656037\pi$
$431$	−8425.34	−0.941611	−0.470805	+	0.882237i	$0.656037\pi$
$432$	9001.29	1.00249
$433$	−839.007	−0.0931180	−0.0465590	−	0.998916i	$-0.514826\pi$
$433$	−839.007	−0.0931180	−0.0465590	+	0.998916i	$0.514826\pi$
$434$	4529.63	0.500989
$435$	−308.265	−0.0339774
$436$	−31824.7	−3.49571
$437$	−13240.6	−1.44939
$438$	3963.53	0.432385
$439$	−16884.5	−1.83565	−0.917826	−	0.396982i	$-0.870058\pi$
$439$	−16884.5	−1.83565	−0.917826	+	0.396982i	$0.870058\pi$
$440$	−1456.08	−0.157764
$441$	807.193	0.0871605
$442$	0	0
$443$	6295.93	0.675234	0.337617	−	0.941284i	$-0.390379\pi$
$443$	6295.93	0.675234	0.337617	+	0.941284i	$0.390379\pi$
$444$	−474.992	−0.0507705
$445$	2615.46	0.278617
$446$	−9422.50	−1.00038
$447$	−1296.32	−0.137167
$448$	−22136.0	−2.33443
$449$	−5091.46	−0.535147	−0.267574	−	0.963537i	$-0.586222\pi$
$449$	−5091.46	−0.535147	−0.267574	+	0.963537i	$0.586222\pi$
$450$	17115.5	1.79296
$451$	3274.54	0.341889
$452$	−32257.1	−3.35674
$453$	530.875	0.0550611
$454$	12738.5	1.31684
$455$	0	0
$456$	−4523.89	−0.464584
$457$	−7677.35	−0.785845	−0.392923	−	0.919572i	$-0.628536\pi$
$457$	−7677.35	−0.785845	−0.392923	+	0.919572i	$0.628536\pi$
$458$	27755.9	2.83176
$459$	−1307.01	−0.132911
$460$	6735.95	0.682751
$461$	9600.97	0.969982	0.484991	−	0.874519i	$-0.338823\pi$
$461$	9600.97	0.969982	0.484991	+	0.874519i	$0.338823\pi$
$462$	872.253	0.0878375
$463$	12832.1	1.28803	0.644014	−	0.765014i	$-0.277268\pi$
$463$	12832.1	1.28803	0.644014	+	0.765014i	$0.277268\pi$
$464$	−38601.0	−3.86208
$465$	−77.0388	−0.00768299
$466$	5684.83	0.565117
$467$	−5051.74	−0.500571	−0.250286	−	0.968172i	$-0.580525\pi$
$467$	−5051.74	−0.500571	−0.250286	+	0.968172i	$0.580525\pi$
$468$	0	0
$469$	3959.76	0.389861
$470$	−288.156	−0.0282801
$471$	−2675.63	−0.261755
$472$	−6321.48	−0.616461
$473$	−5747.13	−0.558675
$474$	675.862	0.0654924
$475$	−9559.33	−0.923394
$476$	10774.5	1.03749
$477$	4721.44	0.453207
$478$	−24113.7	−2.30740
$479$	−20709.5	−1.97545	−0.987726	−	0.156198i	$-0.950076\pi$
$479$	−20709.5	−1.97545	−0.987726	+	0.156198i	$0.950076\pi$
$480$	862.079	0.0819757
$481$	0	0
$482$	−27302.8	−2.58010
$483$	−2482.50	−0.233867
$484$	2515.76	0.236266
$485$	−632.669	−0.0592330
$486$	−9476.43	−0.884485
$487$	16823.1	1.56536	0.782679	−	0.622426i	$-0.213853\pi$
$487$	16823.1	1.56536	0.782679	+	0.622426i	$0.213853\pi$
$488$	56578.7	5.24835
$489$	727.812	0.0673063
$490$	317.604	0.0292814
$491$	20006.3	1.83885	0.919423	−	0.393271i	$-0.128657\pi$
$491$	20006.3	1.83885	0.919423	+	0.393271i	$0.128657\pi$
$492$	−5175.68	−0.474263
$493$	5604.97	0.512039
$494$	0	0
$495$	557.962	0.0506637
$496$	−9646.82	−0.873297
$497$	−8160.77	−0.736540
$498$	5100.99	0.458997
$499$	−6663.08	−0.597757	−0.298878	−	0.954291i	$-0.596612\pi$
$499$	−6663.08	−0.597757	−0.298878	+	0.954291i	$0.596612\pi$
$500$	9875.47	0.883289
$501$	−94.5353	−0.00843019
$502$	5413.20	0.481281
$503$	−21648.6	−1.91902	−0.959508	−	0.281681i	$-0.909108\pi$
$503$	−21648.6	−1.91902	−0.959508	+	0.281681i	$0.909108\pi$
$504$	31901.3	2.81944
$505$	−17.6498	−0.00155526
$506$	−9915.06	−0.871103
$507$	0	0
$508$	41736.0	3.64515
$509$	6607.17	0.575359	0.287679	−	0.957727i	$-0.407116\pi$
$509$	6607.17	0.575359	0.287679	+	0.957727i	$0.407116\pi$
$510$	−253.760	−0.0220327
$511$	15610.5	1.35140
$512$	−2938.22	−0.253617
$513$	3513.14	0.302357
$514$	−21753.0	−1.86670
$515$	−836.644	−0.0715863
$516$	9083.81	0.774985
$517$	306.299	0.0260561
$518$	−2590.60	−0.219738
$519$	−97.3245	−0.00823136
$520$	0	0
$521$	−6677.59	−0.561517	−0.280759	−	0.959778i	$-0.590586\pi$
$521$	−6677.59	−0.561517	−0.280759	+	0.959778i	$0.590586\pi$
$522$	26974.4	2.26176
$523$	−21813.2	−1.82376	−0.911879	−	0.410460i	$-0.865368\pi$
$523$	−21813.2	−1.82376	−0.911879	+	0.410460i	$0.865368\pi$
$524$	−36143.3	−3.01322
$525$	−1792.30	−0.148995
$526$	16245.2	1.34663
$527$	1400.75	0.115783
$528$	−1857.65	−0.153114
$529$	16052.1	1.31931
$530$	1857.73	0.152254
$531$	2422.35	0.197968
$532$	−28960.9	−2.36018
$533$	0	0
$534$	6085.01	0.493116
$535$	−2163.08	−0.174800
$536$	−15378.9	−1.23931
$537$	−1619.99	−0.130182
$538$	40203.9	3.22177
$539$	−337.600	−0.0269786
$540$	−1787.26	−0.142428
$541$	−10655.7	−0.846807	−0.423403	−	0.905941i	$-0.639165\pi$
$541$	−10655.7	−0.846807	−0.423403	+	0.905941i	$0.639165\pi$
$542$	−32759.6	−2.59621
$543$	3545.07	0.280172
$544$	−15674.6	−1.23537
$545$	2952.06	0.232023
$546$	0	0
$547$	15842.0	1.23831	0.619155	−	0.785269i	$-0.287475\pi$
$547$	15842.0	1.23831	0.619155	+	0.785269i	$0.287475\pi$
$548$	10060.3	0.784224
$549$	−21680.6	−1.68544
$550$	−7158.38	−0.554972
$551$	−15065.7	−1.16483
$552$	9641.54	0.743426
$553$	2661.91	0.204694
$554$	41045.6	3.14776
$555$	44.0602	0.00336982
$556$	−18665.3	−1.42372
$557$	−1236.65	−0.0940730	−0.0470365	−	0.998893i	$-0.514978\pi$
$557$	−1236.65	−0.0940730	−0.0470365	+	0.998893i	$0.514978\pi$
$558$	6741.21	0.511430
$559$	0	0
$560$	6883.07	0.519398
$561$	269.736	0.0203000
$562$	20289.3	1.52287
$563$	10958.9	0.820357	0.410178	−	0.912005i	$-0.365466\pi$
$563$	10958.9	0.820357	0.410178	+	0.912005i	$0.365466\pi$
$564$	−484.130	−0.0361446
$565$	2992.17	0.222799
$566$	−12863.4	−0.955281
$567$	−11890.7	−0.880712
$568$	31694.8	2.34134
$569$	15552.0	1.14582	0.572911	−	0.819617i	$-0.305814\pi$
$569$	15552.0	1.14582	0.572911	+	0.819617i	$0.305814\pi$
$570$	682.085	0.0501218
$571$	19712.6	1.44474	0.722372	−	0.691505i	$-0.243052\pi$
$571$	19712.6	1.44474	0.722372	+	0.691505i	$0.243052\pi$
$572$	0	0
$573$	−1879.02	−0.136993
$574$	−28228.1	−2.05264
$575$	20373.3	1.47761
$576$	−32943.8	−2.38309
$577$	19914.2	1.43681	0.718405	−	0.695625i	$-0.244872\pi$
$577$	19914.2	1.43681	0.718405	+	0.695625i	$0.244872\pi$
$578$	−21748.0	−1.56505
$579$	−3517.14	−0.252448
$580$	7664.45	0.548705
$581$	20090.4	1.43458
$582$	−1471.94	−0.104835
$583$	−1974.69	−0.140280
$584$	−60628.0	−4.29590
$585$	0	0
$586$	26629.6	1.87723
$587$	25477.6	1.79144	0.895720	−	0.444619i	$-0.146661\pi$
$587$	25477.6	1.79144	0.895720	+	0.444619i	$0.146661\pi$
$588$	533.605	0.0374243
$589$	−3765.09	−0.263392
$590$	953.115	0.0665070
$591$	−1190.18	−0.0828384
$592$	5517.24	0.383035
$593$	6770.95	0.468887	0.234443	−	0.972130i	$-0.424673\pi$
$593$	6770.95	0.468887	0.234443	+	0.972130i	$0.424673\pi$
$594$	2630.77	0.181720
$595$	−999.441	−0.0688623
$596$	32230.7	2.21513
$597$	−2548.95	−0.174743
$598$	0	0
$599$	−12620.3	−0.860853	−0.430427	−	0.902626i	$-0.641637\pi$
$599$	−12620.3	−0.860853	−0.430427	+	0.902626i	$0.641637\pi$
$600$	6960.91	0.473630
$601$	−1900.70	−0.129004	−0.0645018	−	0.997918i	$-0.520546\pi$
$601$	−1900.70	−0.129004	−0.0645018	+	0.997918i	$0.520546\pi$
$602$	49542.9	3.35419
$603$	5893.10	0.397986
$604$	−13199.3	−0.889189
$605$	−233.362	−0.0156818
$606$	−41.0633	−0.00275261
$607$	456.457	0.0305223	0.0152611	−	0.999884i	$-0.495142\pi$
$607$	456.457	0.0305223	0.0152611	+	0.999884i	$0.495142\pi$
$608$	42132.1	2.81033
$609$	−2824.70	−0.187952
$610$	−8530.60	−0.566219
$611$	0	0
$612$	16035.1	1.05912
$613$	18634.5	1.22780	0.613900	−	0.789384i	$-0.289600\pi$
$613$	18634.5	1.22780	0.613900	+	0.789384i	$0.289600\pi$
$614$	−25275.5	−1.66130
$615$	480.096	0.0314786
$616$	−13342.4	−0.872696
$617$	5740.18	0.374540	0.187270	−	0.982309i	$-0.440036\pi$
$617$	5740.18	0.374540	0.187270	+	0.982309i	$0.440036\pi$
$618$	−1946.50	−0.126698
$619$	8498.19	0.551811	0.275906	−	0.961185i	$-0.411022\pi$
$619$	8498.19	0.551811	0.275906	+	0.961185i	$0.411022\pi$
$620$	1915.43	0.124074
$621$	−7487.39	−0.483830
$622$	−28835.7	−1.85885
$623$	23966.0	1.54122
$624$	0	0
$625$	14244.0	0.911617
$626$	−11318.3	−0.722634
$627$	−725.029	−0.0461800
$628$	66524.8	4.22712
$629$	−801.118	−0.0507832
$630$	−4809.89	−0.304176
$631$	17384.3	1.09677	0.548383	−	0.836227i	$-0.315244\pi$
$631$	17384.3	1.09677	0.548383	+	0.836227i	$0.315244\pi$
$632$	−10338.3	−0.650690
$633$	2805.24	0.176142
$634$	30710.2	1.92375
$635$	−3871.43	−0.241942
$636$	3121.16	0.194595
$637$	0	0
$638$	−11281.8	−0.700077
$639$	−12145.2	−0.751891
$640$	−4715.01	−0.291214
$641$	−2936.80	−0.180962	−0.0904811	−	0.995898i	$-0.528840\pi$
$641$	−2936.80	−0.180962	−0.0904811	+	0.995898i	$0.528840\pi$
$642$	−5032.52	−0.309373
$643$	−14265.8	−0.874943	−0.437471	−	0.899232i	$-0.644126\pi$
$643$	−14265.8	−0.874943	−0.437471	+	0.899232i	$0.644126\pi$
$644$	61723.0	3.77675
$645$	−842.615	−0.0514386
$646$	−12401.9	−0.755335
$647$	8247.81	0.501167	0.250583	−	0.968095i	$-0.419378\pi$
$647$	8247.81	0.501167	0.250583	+	0.968095i	$0.419378\pi$
$648$	46181.2	2.79964
$649$	−1013.12	−0.0612767
$650$	0	0
$651$	−705.923	−0.0424997
$652$	−18095.7	−1.08694
$653$	−27149.0	−1.62699	−0.813493	−	0.581575i	$-0.802437\pi$
$653$	−27149.0	−1.62699	−0.813493	+	0.581575i	$0.802437\pi$
$654$	6868.14	0.410651
$655$	3352.65	0.199998
$656$	60117.8	3.57806
$657$	23232.3	1.37957
$658$	−2640.44	−0.156436
$659$	11338.9	0.670259	0.335129	−	0.942172i	$-0.391220\pi$
$659$	11338.9	0.670259	0.335129	+	0.942172i	$0.391220\pi$
$660$	368.848	0.0217536
$661$	−14772.8	−0.869281	−0.434641	−	0.900604i	$-0.643125\pi$
$661$	−14772.8	−0.869281	−0.434641	+	0.900604i	$0.643125\pi$
$662$	51217.4	3.00698
$663$	0	0
$664$	−78027.1	−4.56030
$665$	2686.42	0.156654
$666$	−3855.45	−0.224318
$667$	32108.8	1.86396
$668$	2350.45	0.136140
$669$	1468.46	0.0848637
$670$	2318.74	0.133703
$671$	9067.69	0.521690
$672$	7899.41	0.453462
$673$	18985.2	1.08741	0.543705	−	0.839276i	$-0.317021\pi$
$673$	18985.2	1.08741	0.543705	+	0.839276i	$0.317021\pi$
$674$	53189.9	3.03976
$675$	−5405.68	−0.308244
$676$	0	0
$677$	−25767.5	−1.46281	−0.731407	−	0.681941i	$-0.761136\pi$
$677$	−25767.5	−1.46281	−0.731407	+	0.681941i	$0.761136\pi$
$678$	6961.45	0.394326
$679$	−5797.28	−0.327657
$680$	3881.63	0.218902
$681$	−1985.24	−0.111710
$682$	−2819.44	−0.158302
$683$	−14934.3	−0.836668	−0.418334	−	0.908293i	$-0.637386\pi$
$683$	−14934.3	−0.836668	−0.418334	+	0.908293i	$0.637386\pi$
$684$	−43101.0	−2.40937
$685$	−933.193	−0.0520518
$686$	35435.3	1.97220
$687$	−4325.64	−0.240223
$688$	−105512.	−5.84684
$689$	0	0
$690$	−1453.69	−0.0802047
$691$	−6757.88	−0.372043	−0.186022	−	0.982546i	$-0.559559\pi$
$691$	−6757.88	−0.372043	−0.186022	+	0.982546i	$0.559559\pi$
$692$	2419.80	0.132929
$693$	5112.73	0.280255
$694$	−3058.87	−0.167310
$695$	1731.40	0.0944973
$696$	10970.6	0.597468
$697$	−8729.27	−0.474383
$698$	−49283.0	−2.67248
$699$	−885.957	−0.0479399
$700$	44562.2	2.40613
$701$	−5330.17	−0.287186	−0.143593	−	0.989637i	$-0.545866\pi$
$701$	−5330.17	−0.287186	−0.143593	+	0.989637i	$0.545866\pi$
$702$	0	0
$703$	2153.34	0.115526
$704$	13778.4	0.737632
$705$	44.9079	0.00239905
$706$	43698.9	2.32951
$707$	−161.729	−0.00860318
$708$	1601.32	0.0850021
$709$	−1554.08	−0.0823199	−0.0411599	−	0.999153i	$-0.513105\pi$
$709$	−1554.08	−0.0823199	−0.0411599	+	0.999153i	$0.513105\pi$
$710$	−4778.75	−0.252596
$711$	3961.58	0.208960
$712$	−93079.2	−4.89928
$713$	8024.35	0.421479
$714$	−2325.25	−0.121877
$715$	0	0
$716$	40278.1	2.10232
$717$	3758.03	0.195741
$718$	−34379.8	−1.78697
$719$	9131.70	0.473651	0.236825	−	0.971552i	$-0.423893\pi$
$719$	9131.70	0.473651	0.236825	+	0.971552i	$0.423893\pi$
$720$	10243.7	0.530223
$721$	−7666.35	−0.395991
$722$	−3468.44	−0.178784
$723$	4255.03	0.218874
$724$	−88141.8	−4.52454
$725$	23181.6	1.18751
$726$	−542.929	−0.0277548
$727$	−15859.2	−0.809056	−0.404528	−	0.914526i	$-0.632564\pi$
$727$	−15859.2	−0.809056	−0.404528	+	0.914526i	$0.632564\pi$
$728$	0	0
$729$	−16690.0	−0.847940
$730$	9141.14	0.463464
$731$	15320.7	0.775180
$732$	−14332.2	−0.723681
$733$	−20446.2	−1.03028	−0.515142	−	0.857105i	$-0.672261\pi$
$733$	−20446.2	−1.03028	−0.515142	+	0.857105i	$0.672261\pi$
$734$	28075.0	1.41181
$735$	−49.4972	−0.00248399
$736$	−89794.0	−4.49708
$737$	−2464.73	−0.123188
$738$	−42010.4	−2.09542
$739$	−320.521	−0.0159547	−0.00797737	−	0.999968i	$-0.502539\pi$
$739$	−320.521	−0.0159547	−0.00797737	+	0.999968i	$0.502539\pi$
$740$	−1095.48	−0.0544197
$741$	0	0
$742$	17022.8	0.842217
$743$	−7905.15	−0.390326	−0.195163	−	0.980771i	$-0.562524\pi$
$743$	−7905.15	−0.390326	−0.195163	+	0.980771i	$0.562524\pi$
$744$	2741.66	0.135100
$745$	−2989.72	−0.147026
$746$	−5610.40	−0.275350
$747$	29899.5	1.46448
$748$	−6706.51	−0.327827
$749$	−19820.7	−0.966935
$750$	−2131.24	−0.103762
$751$	−12503.1	−0.607516	−0.303758	−	0.952749i	$-0.598241\pi$
$751$	−12503.1	−0.607516	−0.303758	+	0.952749i	$0.598241\pi$
$752$	5623.39	0.272691
$753$	−843.625	−0.0408279
$754$	0	0
$755$	1224.36	0.0590188
$756$	−16377.0	−0.787866
$757$	−3371.62	−0.161881	−0.0809404	−	0.996719i	$-0.525792\pi$
$757$	−3371.62	−0.161881	−0.0809404	+	0.996719i	$0.525792\pi$
$758$	16689.5	0.799721
$759$	1545.22	0.0738971
$760$	−10433.5	−0.497977
$761$	−33063.5	−1.57497	−0.787485	−	0.616334i	$-0.788617\pi$
$761$	−33063.5	−1.57497	−0.787485	+	0.616334i	$0.788617\pi$
$762$	−9007.10	−0.428206
$763$	27050.4	1.28347
$764$	46718.4	2.21232
$765$	−1487.42	−0.0702976
$766$	17713.9	0.835545
$767$	0	0
$768$	−2590.15	−0.121698
$769$	−10817.8	−0.507281	−0.253640	−	0.967299i	$-0.581628\pi$
$769$	−10817.8	−0.507281	−0.253640	+	0.967299i	$0.581628\pi$
$770$	2011.69	0.0941509
$771$	3390.11	0.158355
$772$	87447.4	4.07682
$773$	33763.5	1.57101	0.785504	−	0.618856i	$-0.212404\pi$
$773$	33763.5	1.57101	0.785504	+	0.618856i	$0.212404\pi$
$774$	73732.2	3.42409
$775$	5793.35	0.268520
$776$	22515.5	1.04157
$777$	403.733	0.0186407
$778$	−29435.8	−1.35646
$779$	23463.6	1.07917
$780$	0	0
$781$	5079.62	0.232731
$782$	26431.6	1.20868
$783$	−8519.47	−0.388839
$784$	−6198.05	−0.282346
$785$	−6170.85	−0.280569
$786$	7800.13	0.353971
$787$	26156.8	1.18474	0.592369	−	0.805667i	$-0.298193\pi$
$787$	26156.8	1.18474	0.592369	+	0.805667i	$0.298193\pi$
$788$	29591.7	1.33777
$789$	−2531.75	−0.114237
$790$	1558.75	0.0701998
$791$	27417.9	1.23245
$792$	−19856.8	−0.890885
$793$	0	0
$794$	22610.5	1.01060
$795$	−289.519	−0.0129160
$796$	63375.0	2.82194
$797$	−16665.6	−0.740687	−0.370343	−	0.928895i	$-0.620760\pi$
$797$	−16665.6	−0.740687	−0.370343	+	0.928895i	$0.620760\pi$
$798$	6250.09	0.277257
$799$	−816.531	−0.0361537
$800$	−64828.7	−2.86505
$801$	35667.4	1.57334
$802$	−65582.2	−2.88752
$803$	−9716.66	−0.427016
$804$	3895.71	0.170884
$805$	−5725.43	−0.250677
$806$	0	0
$807$	−6265.60	−0.273308
$808$	628.123	0.0273481
$809$	9167.23	0.398396	0.199198	−	0.979959i	$-0.436166\pi$
$809$	9167.23	0.398396	0.199198	+	0.979959i	$0.436166\pi$
$810$	−6962.93	−0.302040
$811$	−10969.3	−0.474949	−0.237474	−	0.971394i	$-0.576320\pi$
$811$	−10969.3	−0.474949	−0.237474	+	0.971394i	$0.576320\pi$
$812$	70231.0	3.03525
$813$	5105.44	0.220241
$814$	1612.50	0.0694326
$815$	1678.56	0.0721441
$816$	4952.13	0.212450
$817$	−41180.8	−1.76344
$818$	−54027.7	−2.30933
$819$	0	0
$820$	−11936.7	−0.508352
$821$	7469.59	0.317528	0.158764	−	0.987317i	$-0.449249\pi$
$821$	7469.59	0.317528	0.158764	+	0.987317i	$0.449249\pi$
$822$	−2171.13	−0.0921250
$823$	−19559.3	−0.828425	−0.414213	−	0.910180i	$-0.635943\pi$
$823$	−19559.3	−0.828425	−0.414213	+	0.910180i	$0.635943\pi$
$824$	29774.5	1.25879
$825$	1115.60	0.0470792
$826$	8733.60	0.367894
$827$	−585.253	−0.0246085	−0.0123043	−	0.999924i	$-0.503917\pi$
$827$	−585.253	−0.0246085	−0.0123043	+	0.999924i	$0.503917\pi$
$828$	91859.1	3.85547
$829$	−21296.7	−0.892238	−0.446119	−	0.894974i	$-0.647194\pi$
$829$	−21296.7	−0.892238	−0.446119	+	0.894974i	$0.647194\pi$
$830$	11764.5	0.491989
$831$	−6396.78	−0.267030
$832$	0	0
$833$	899.974	0.0374337
$834$	4028.19	0.167248
$835$	−218.028	−0.00903613
$836$	18026.6	0.745767
$837$	−2129.11	−0.0879245
$838$	22154.5	0.913263
$839$	−41750.4	−1.71798	−0.858989	−	0.511994i	$-0.828907\pi$
$839$	−41750.4	−1.71798	−0.858989	+	0.511994i	$0.828907\pi$
$840$	−1956.19	−0.0803513
$841$	12145.8	0.498001
$842$	−83186.3	−3.40474
$843$	−3162.00	−0.129188
$844$	−69747.2	−2.84455
$845$	0	0
$846$	−3929.63	−0.159697
$847$	−2138.34	−0.0867466
$848$	−36253.7	−1.46811
$849$	2004.71	0.0810381
$850$	19082.8	0.770042
$851$	−4589.31	−0.184864
$852$	−8028.76	−0.322841
$853$	18390.2	0.738181	0.369091	−	0.929393i	$-0.379669\pi$
$853$	18390.2	0.738181	0.369091	+	0.929393i	$0.379669\pi$
$854$	−78167.7	−3.13214
$855$	3998.05	0.159919
$856$	76979.8	3.07373
$857$	−11567.3	−0.461063	−0.230532	−	0.973065i	$-0.574047\pi$
$857$	−11567.3	−0.461063	−0.230532	+	0.973065i	$0.574047\pi$
$858$	0	0
$859$	27503.1	1.09243	0.546213	−	0.837646i	$-0.316069\pi$
$859$	27503.1	1.09243	0.546213	+	0.837646i	$0.316069\pi$
$860$	20950.1	0.830689
$861$	4399.22	0.174129
$862$	−45208.3	−1.78631
$863$	−18424.0	−0.726719	−0.363360	−	0.931649i	$-0.618370\pi$
$863$	−18424.0	−0.726719	−0.363360	+	0.931649i	$0.618370\pi$
$864$	23825.1	0.938134
$865$	−224.461	−0.00882300
$866$	−4501.91	−0.176653
$867$	3389.34	0.132766
$868$	17551.5	0.686333
$869$	−1656.89	−0.0646791
$870$	−1654.07	−0.0644579
$871$	0	0
$872$	−105058.	−4.07996
$873$	−8627.79	−0.334486
$874$	−71045.9	−2.74962
$875$	−8393.96	−0.324306
$876$	15358.0	0.592350
$877$	−10714.4	−0.412543	−0.206271	−	0.978495i	$-0.566133\pi$
$877$	−10714.4	−0.412543	−0.206271	+	0.978495i	$0.566133\pi$
$878$	−90598.0	−3.48239
$879$	−4150.10	−0.159249
$880$	−4284.33	−0.164119
$881$	12186.1	0.466016	0.233008	−	0.972475i	$-0.425143\pi$
$881$	12186.1	0.466016	0.233008	+	0.972475i	$0.425143\pi$
$882$	4331.20	0.165351
$883$	4835.55	0.184291	0.0921457	−	0.995746i	$-0.470627\pi$
$883$	4835.55	0.184291	0.0921457	+	0.995746i	$0.470627\pi$
$884$	0	0
$885$	−148.539	−0.00564190
$886$	33782.4	1.28097
$887$	−10765.8	−0.407533	−0.203766	−	0.979020i	$-0.565318\pi$
$887$	−10765.8	−0.407533	−0.203766	+	0.979020i	$0.565318\pi$
$888$	−1568.02	−0.0592560
$889$	−35474.8	−1.33834
$890$	14033.9	0.528560
$891$	7401.32	0.278287
$892$	−36510.5	−1.37047
$893$	2194.77	0.0822454
$894$	−6955.74	−0.260218
$895$	−3736.20	−0.139539
$896$	−43204.7	−1.61090
$897$	0	0
$898$	−27319.6	−1.01522
$899$	9130.45	0.338729
$900$	66319.6	2.45628
$901$	5264.13	0.194643
$902$	17570.4	0.648592
$903$	−7721.06	−0.284541
$904$	−106486.	−3.91777
$905$	8176.04	0.300310
$906$	2848.55	0.104456
$907$	12515.9	0.458195	0.229098	−	0.973403i	$-0.426423\pi$
$907$	12515.9	0.458195	0.229098	+	0.973403i	$0.426423\pi$
$908$	49359.5	1.80402
$909$	−240.693	−0.00878249
$910$	0	0
$911$	−39336.8	−1.43061	−0.715305	−	0.698812i	$-0.753712\pi$
$911$	−39336.8	−1.43061	−0.715305	+	0.698812i	$0.753712\pi$
$912$	−13310.9	−0.483299
$913$	−12505.2	−0.453297
$914$	−41194.8	−1.49081
$915$	1329.46	0.0480334
$916$	107549.	3.87939
$917$	30721.1	1.10632
$918$	−7013.12	−0.252143
$919$	18801.4	0.674867	0.337433	−	0.941349i	$-0.390441\pi$
$919$	18801.4	0.674867	0.337433	+	0.941349i	$0.390441\pi$
$920$	22236.4	0.796861
$921$	3939.08	0.140931
$922$	51516.5	1.84014
$923$	0	0
$924$	3379.83	0.120334
$925$	−3313.35	−0.117775
$926$	68853.8	2.44350
$927$	−11409.4	−0.404245
$928$	−102171.	−3.61416
$929$	−5332.10	−0.188311	−0.0941554	−	0.995558i	$-0.530015\pi$
$929$	−5332.10	−0.188311	−0.0941554	+	0.995558i	$0.530015\pi$
$930$	−413.372	−0.0145753
$931$	−2419.06	−0.0851573
$932$	22027.7	0.774187
$933$	4493.93	0.157690
$934$	−27106.5	−0.949626
$935$	622.096	0.0217591
$936$	0	0
$937$	−39200.1	−1.36671	−0.683357	−	0.730085i	$-0.739481\pi$
$937$	−39200.1	−1.36671	−0.683357	+	0.730085i	$0.739481\pi$
$938$	21247.1	0.739598
$939$	1763.90	0.0613022
$940$	−1116.56	−0.0387426
$941$	−13215.6	−0.457828	−0.228914	−	0.973447i	$-0.573517\pi$
$941$	−13215.6	−0.457828	−0.228914	+	0.973447i	$0.573517\pi$
$942$	−14356.8	−0.496571
$943$	−50006.8	−1.72688
$944$	−18600.1	−0.641294
$945$	1519.13	0.0522936
$946$	−30837.7	−1.05985
$947$	−56828.4	−1.95003	−0.975014	−	0.222144i	$-0.928694\pi$
$947$	−56828.4	−1.95003	−0.975014	+	0.222144i	$0.928694\pi$
$948$	2618.85	0.0897218
$949$	0	0
$950$	−51293.1	−1.75175
$951$	−4786.05	−0.163195
$952$	35568.2	1.21089
$953$	8193.30	0.278496	0.139248	−	0.990258i	$-0.455531\pi$
$953$	8193.30	0.278496	0.139248	+	0.990258i	$0.455531\pi$
$954$	25334.1	0.859771
$955$	−4333.60	−0.146840
$956$	−93436.6	−3.16104
$957$	1758.22	0.0593888
$958$	−111122.	−3.74760
$959$	−8551.05	−0.287933
$960$	2020.12	0.0679157
$961$	−27509.2	−0.923406
$962$	0	0
$963$	−29498.2	−0.987088
$964$	−105794.	−3.53463
$965$	−8111.62	−0.270593
$966$	−13320.5	−0.443665
$967$	−17140.7	−0.570018	−0.285009	−	0.958525i	$-0.591997\pi$
$967$	−17140.7	−0.570018	−0.285009	+	0.958525i	$0.591997\pi$
$968$	8304.90	0.275754
$969$	1932.78	0.0640763
$970$	−3394.75	−0.112370
$971$	3941.82	0.130277	0.0651386	−	0.997876i	$-0.479251\pi$
$971$	3941.82	0.130277	0.0651386	+	0.997876i	$0.479251\pi$
$972$	−36719.5	−1.21171
$973$	15865.2	0.522728
$974$	90268.9	2.96961
$975$	0	0
$976$	166475.	5.45977
$977$	−38582.1	−1.26341	−0.631705	−	0.775209i	$-0.717645\pi$
$977$	−38582.1	−1.26341	−0.631705	+	0.775209i	$0.717645\pi$
$978$	3905.26	0.127686
$979$	−14917.5	−0.486992
$980$	1230.66	0.0401142
$981$	40257.7	1.31022
$982$	107349.	3.48844
$983$	−54684.3	−1.77432	−0.887161	−	0.461460i	$-0.847326\pi$
$983$	−54684.3	−1.77432	−0.887161	+	0.461460i	$0.847326\pi$
$984$	−17085.7	−0.553529
$985$	−2744.93	−0.0887926
$986$	30074.9	0.971381
$987$	411.501	0.0132707
$988$	0	0
$989$	87766.6	2.82186
$990$	2993.89	0.0961132
$991$	−17001.3	−0.544969	−0.272485	−	0.962160i	$-0.587845\pi$
$991$	−17001.3	−0.544969	−0.272485	+	0.962160i	$0.587845\pi$
$992$	−25533.8	−0.817236
$993$	−7982.02	−0.255087
$994$	−43788.7	−1.39728
$995$	−5878.67	−0.187303
$996$	19765.4	0.628807
$997$	10524.5	0.334316	0.167158	−	0.985930i	$-0.446541\pi$
$997$	10524.5	0.334316	0.167158	+	0.985930i	$0.446541\pi$
$998$	−35752.5	−1.13399
$999$	1217.69	0.0385645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.f.1.17		17
13.4	even	6		143.4.e.a.133.17	yes	34
13.10	even	6		143.4.e.a.100.17	✓	34
13.12	even	2		1859.4.a.i.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.17	✓	34	13.10	even	6
143.4.e.a.133.17	yes	34	13.4	even	6
1859.4.a.f.1.17		17	1.1	even	1	trivial
1859.4.a.i.1.1		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)

\(f(q)\)	\(=\)	\(q+5.36576 q^{2} -0.836231 q^{3} +20.7914 q^{4} -1.92861 q^{5} -4.48702 q^{6} -17.6723 q^{7} +68.6355 q^{8} -26.3007 q^{9} +O(q^{10})\)	\(q+5.36576 q^{2} -0.836231 q^{3} +20.7914 q^{4} -1.92861 q^{5} -4.48702 q^{6} -17.6723 q^{7} +68.6355 q^{8} -26.3007 q^{9} -10.3485 q^{10} +11.0000 q^{11} -17.3864 q^{12} -94.8252 q^{14} +1.61276 q^{15} +201.951 q^{16} -29.3238 q^{17} -141.123 q^{18} +78.8200 q^{19} -40.0985 q^{20} +14.7781 q^{21} +59.0234 q^{22} -167.985 q^{23} -57.3952 q^{24} -121.280 q^{25} +44.5717 q^{27} -367.431 q^{28} -191.141 q^{29} +8.65370 q^{30} -47.7682 q^{31} +534.535 q^{32} -9.19854 q^{33} -157.345 q^{34} +34.0829 q^{35} -546.828 q^{36} +27.3197 q^{37} +422.929 q^{38} -132.371 q^{40} +297.685 q^{41} +79.2958 q^{42} -522.466 q^{43} +228.705 q^{44} +50.7238 q^{45} -901.369 q^{46} +27.8453 q^{47} -168.878 q^{48} -30.6909 q^{49} -650.762 q^{50} +24.5215 q^{51} -179.517 q^{53} +239.161 q^{54} -21.2147 q^{55} -1212.95 q^{56} -65.9118 q^{57} -1025.62 q^{58} -92.1021 q^{59} +33.5316 q^{60} +824.335 q^{61} -256.313 q^{62} +464.793 q^{63} +1252.58 q^{64} -49.3572 q^{66} -224.066 q^{67} -609.683 q^{68} +140.475 q^{69} +182.881 q^{70} +461.784 q^{71} -1805.16 q^{72} -883.333 q^{73} +146.591 q^{74} +101.419 q^{75} +1638.78 q^{76} -194.395 q^{77} -150.626 q^{79} -389.484 q^{80} +672.847 q^{81} +1597.31 q^{82} -1136.83 q^{83} +307.257 q^{84} +56.5542 q^{85} -2803.43 q^{86} +159.838 q^{87} +754.991 q^{88} -1356.14 q^{89} +272.172 q^{90} -3492.65 q^{92} +39.9453 q^{93} +149.411 q^{94} -152.013 q^{95} -446.995 q^{96} +328.044 q^{97} -164.680 q^{98} -289.308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) \) 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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