LMFDB - Embedded newform 1859.4.a.i.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:	$0$
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			1.17
Root			$5.45173$ 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)

$f(q)$	$=$	$q+5.45173 q^{2} +6.71552 q^{3} +21.7213 q^{4} +3.97680 q^{5} +36.6112 q^{6} +10.9778 q^{7} +74.8051 q^{8} +18.0982 q^{9} +O(q^{10})$	\(q+5.45173 q^{2} +6.71552 q^{3} +21.7213 q^{4} +3.97680 q^{5} +36.6112 q^{6} +10.9778 q^{7} +74.8051 q^{8} +18.0982 q^{9} +21.6804 q^{10} -11.0000 q^{11} +145.870 q^{12} +59.8481 q^{14} +26.7063 q^{15} +234.046 q^{16} +133.840 q^{17} +98.6662 q^{18} -49.7682 q^{19} +86.3815 q^{20} +73.7217 q^{21} -59.9690 q^{22} -148.421 q^{23} +502.355 q^{24} -109.185 q^{25} -59.7805 q^{27} +238.453 q^{28} +51.1368 q^{29} +145.595 q^{30} +39.7633 q^{31} +677.516 q^{32} -73.8707 q^{33} +729.662 q^{34} +43.6566 q^{35} +393.116 q^{36} -65.9474 q^{37} -271.322 q^{38} +297.485 q^{40} -169.761 q^{41} +401.911 q^{42} -371.407 q^{43} -238.935 q^{44} +71.9728 q^{45} -809.152 q^{46} +263.114 q^{47} +1571.74 q^{48} -222.488 q^{49} -595.247 q^{50} +898.808 q^{51} +327.504 q^{53} -325.907 q^{54} -43.7448 q^{55} +821.196 q^{56} -334.219 q^{57} +278.784 q^{58} +401.251 q^{59} +580.096 q^{60} -219.064 q^{61} +216.779 q^{62} +198.678 q^{63} +1821.26 q^{64} -402.723 q^{66} -514.978 q^{67} +2907.20 q^{68} -996.725 q^{69} +238.004 q^{70} -86.9248 q^{71} +1353.83 q^{72} -1133.15 q^{73} -359.527 q^{74} -733.234 q^{75} -1081.03 q^{76} -120.756 q^{77} +238.321 q^{79} +930.755 q^{80} -890.107 q^{81} -925.489 q^{82} +474.884 q^{83} +1601.33 q^{84} +532.257 q^{85} -2024.81 q^{86} +343.410 q^{87} -822.856 q^{88} +58.0186 q^{89} +392.376 q^{90} -3223.91 q^{92} +267.031 q^{93} +1434.43 q^{94} -197.918 q^{95} +4549.87 q^{96} +982.259 q^{97} -1212.94 q^{98} -199.080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.45173	1.92748	0.963739	−	0.266848i	$-0.0859822\pi$
$2$	5.45173	1.92748	0.963739	+	0.266848i	$0.0859822\pi$
$3$	6.71552	1.29240	0.646201	−	0.763167i	$-0.276357\pi$
$3$	6.71552	1.29240	0.646201	+	0.763167i	$0.276357\pi$
$4$	21.7213	2.71517
$5$	3.97680	0.355696	0.177848	−	0.984058i	$-0.443086\pi$
$5$	3.97680	0.355696	0.177848	+	0.984058i	$0.443086\pi$
$6$	36.6112	2.49107
$7$	10.9778	0.592746	0.296373	−	0.955072i	$-0.404223\pi$
$7$	10.9778	0.592746	0.296373	+	0.955072i	$0.404223\pi$
$8$	74.8051	3.30595
$9$	18.0982	0.670302
$10$	21.6804	0.685596
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	145.870	3.50909
$13$	0	0
$13$	0	0
$14$	59.8481	1.14251
$15$	26.7063	0.459702
$16$	234.046	3.65697
$17$	133.840	1.90948	0.954738	−	0.297449i	$-0.0961357\pi$
$17$	133.840	1.90948	0.954738	+	0.297449i	$0.0961357\pi$
$18$	98.6662	1.29199
$19$	−49.7682	−0.600926	−0.300463	−	0.953793i	$-0.597141\pi$
$19$	−49.7682	−0.600926	−0.300463	+	0.953793i	$0.597141\pi$
$20$	86.3815	0.965774
$21$	73.7217	0.766066
$22$	−59.9690	−0.581156
$23$	−148.421	−1.34556	−0.672781	−	0.739841i	$-0.734901\pi$
$23$	−148.421	−1.34556	−0.672781	+	0.739841i	$0.734901\pi$
$24$	502.355	4.27261
$25$	−109.185	−0.873480
$26$	0	0
$27$	−59.7805	−0.426102
$28$	238.453	1.60941
$29$	51.1368	0.327443	0.163722	−	0.986507i	$-0.447650\pi$
$29$	51.1368	0.327443	0.163722	+	0.986507i	$0.447650\pi$
$30$	145.595	0.886065
$31$	39.7633	0.230377	0.115189	−	0.993344i	$-0.463253\pi$
$31$	39.7633	0.230377	0.115189	+	0.993344i	$0.463253\pi$
$32$	677.516	3.74278
$33$	−73.8707	−0.389674
$34$	729.662	3.68047
$35$	43.6566	0.210837
$36$	393.116	1.81998
$37$	−65.9474	−0.293018	−0.146509	−	0.989209i	$-0.546804\pi$
$37$	−65.9474	−0.293018	−0.146509	+	0.989209i	$0.546804\pi$
$38$	−271.322	−1.15827
$39$	0	0
$40$	297.485	1.17591
$41$	−169.761	−0.646638	−0.323319	−	0.946290i	$-0.604799\pi$
$41$	−169.761	−0.646638	−0.323319	+	0.946290i	$0.604799\pi$
$42$	401.911	1.47658
$43$	−371.407	−1.31719	−0.658594	−	0.752498i	$-0.728849\pi$
$43$	−371.407	−1.31719	−0.658594	+	0.752498i	$0.728849\pi$
$44$	−238.935	−0.818654
$45$	71.9728	0.238424
$46$	−809.152	−2.59354
$47$	263.114	0.816578	0.408289	−	0.912853i	$-0.366125\pi$
$47$	263.114	0.816578	0.408289	+	0.912853i	$0.366125\pi$
$48$	1571.74	4.72628
$49$	−222.488	−0.648652
$50$	−595.247	−1.68361
$51$	898.808	2.46781
$52$	0	0
$53$	327.504	0.848796	0.424398	−	0.905476i	$-0.360486\pi$
$53$	327.504	0.848796	0.424398	+	0.905476i	$0.360486\pi$
$54$	−325.907	−0.821302
$55$	−43.7448	−0.107246
$56$	821.196	1.95959
$57$	−334.219	−0.776638
$58$	278.784	0.631140
$59$	401.251	0.885398	0.442699	−	0.896670i	$-0.354021\pi$
$59$	401.251	0.885398	0.442699	+	0.896670i	$0.354021\pi$
$60$	580.096	1.24817
$61$	−219.064	−0.459807	−0.229903	−	0.973213i	$-0.573841\pi$
$61$	−219.064	−0.459807	−0.229903	+	0.973213i	$0.573841\pi$
$62$	216.779	0.444047
$63$	198.678	0.397319
$64$	1821.26	3.55716
$65$	0	0
$66$	−402.723	−0.751087
$67$	−514.978	−0.939024	−0.469512	−	0.882926i	$-0.655570\pi$
$67$	−514.978	−0.939024	−0.469512	+	0.882926i	$0.655570\pi$
$68$	2907.20	5.18455
$69$	−996.725	−1.73901
$70$	238.004	0.406384
$71$	−86.9248	−0.145297	−0.0726484	−	0.997358i	$-0.523145\pi$
$71$	−86.9248	−0.145297	−0.0726484	+	0.997358i	$0.523145\pi$
$72$	1353.83	2.21598
$73$	−1133.15	−1.81679	−0.908393	−	0.418118i	$-0.862690\pi$
$73$	−1133.15	−1.81679	−0.908393	+	0.418118i	$0.862690\pi$
$74$	−359.527	−0.564786
$75$	−733.234	−1.12889
$76$	−1081.03	−1.63162
$77$	−120.756	−0.178720
$78$	0	0
$79$	238.321	0.339408	0.169704	−	0.985495i	$-0.445719\pi$
$79$	238.321	0.339408	0.169704	+	0.985495i	$0.445719\pi$
$80$	930.755	1.30077
$81$	−890.107	−1.22100
$82$	−925.489	−1.24638
$83$	474.884	0.628016	0.314008	−	0.949420i	$-0.398328\pi$
$83$	474.884	0.628016	0.314008	+	0.949420i	$0.398328\pi$
$84$	1601.33	2.08000
$85$	532.257	0.679193
$86$	−2024.81	−2.53885
$87$	343.410	0.423188
$88$	−822.856	−0.996781
$89$	58.0186	0.0691006	0.0345503	−	0.999403i	$-0.489000\pi$
$89$	58.0186	0.0691006	0.0345503	+	0.999403i	$0.489000\pi$
$90$	392.376	0.459556
$91$	0	0
$92$	−3223.91	−3.65343
$93$	267.031	0.297740
$94$	1434.43	1.57394
$95$	−197.918	−0.213747
$96$	4549.87	4.83718
$97$	982.259	1.02818	0.514089	−	0.857737i	$-0.328130\pi$
$97$	982.259	1.02818	0.514089	+	0.857737i	$0.328130\pi$
$98$	−1212.94	−1.25026
$99$	−199.080	−0.202104
$100$	−2371.65	−2.37165
$101$	−1476.69	−1.45481	−0.727404	−	0.686209i	$-0.759274\pi$
$101$	−1476.69	−1.45481	−0.727404	+	0.686209i	$0.759274\pi$
$102$	4900.06	4.75665
$103$	564.499	0.540017	0.270009	−	0.962858i	$-0.412973\pi$
$103$	564.499	0.540017	0.270009	+	0.962858i	$0.412973\pi$
$104$	0	0
$105$	293.176	0.272487
$106$	1785.46	1.63603
$107$	2057.44	1.85888	0.929440	−	0.368973i	$-0.120290\pi$
$107$	2057.44	1.85888	0.929440	+	0.368973i	$0.120290\pi$
$108$	−1298.51	−1.15694
$109$	1472.95	1.29434	0.647171	−	0.762345i	$-0.275952\pi$
$109$	1472.95	1.29434	0.647171	+	0.762345i	$0.275952\pi$
$110$	−238.485	−0.206715
$111$	−442.871	−0.378698
$112$	2569.32	2.16766
$113$	1978.47	1.64707	0.823536	−	0.567265i	$-0.191998\pi$
$113$	1978.47	1.64707	0.823536	+	0.567265i	$0.191998\pi$
$114$	−1822.07	−1.49695
$115$	−590.241	−0.478611
$116$	1110.76	0.889064
$117$	0	0
$118$	2187.51	1.70658
$119$	1469.28	1.13183
$120$	1997.76	1.51975
$121$	121.000	0.0909091
$122$	−1194.28	−0.886267
$123$	−1140.03	−0.835716
$124$	863.712	0.625513
$125$	−931.307	−0.666389
$126$	1083.14	0.765824
$127$	−1219.00	−0.851724	−0.425862	−	0.904788i	$-0.640029\pi$
$127$	−1219.00	−0.851724	−0.425862	+	0.904788i	$0.640029\pi$
$128$	4508.91	3.11355
$129$	−2494.19	−1.70234
$130$	0	0
$131$	894.419	0.596532	0.298266	−	0.954483i	$-0.403592\pi$
$131$	894.419	0.596532	0.298266	+	0.954483i	$0.403592\pi$
$132$	−1604.57	−1.05803
$133$	−546.346	−0.356197
$134$	−2807.52	−1.80995
$135$	−237.735	−0.151563
$136$	10011.9	6.31263
$137$	2486.22	1.55046	0.775228	−	0.631681i	$-0.217635\pi$
$137$	2486.22	1.55046	0.775228	+	0.631681i	$0.217635\pi$
$138$	−5433.87	−3.35190
$139$	−3218.28	−1.96382	−0.981909	−	0.189353i	$-0.939361\pi$
$139$	−3218.28	−1.96382	−0.981909	+	0.189353i	$0.939361\pi$
$140$	948.280	0.572459
$141$	1766.95	1.05535
$142$	−473.890	−0.280056
$143$	0	0
$144$	4235.80	2.45128
$145$	203.361	0.116470
$146$	−6177.63	−3.50181
$147$	−1494.12	−0.838319
$148$	−1432.47	−0.795595
$149$	35.8926	0.0197344	0.00986722	−	0.999951i	$-0.496859\pi$
$149$	35.8926	0.0197344	0.00986722	+	0.999951i	$0.496859\pi$
$150$	−3997.39	−2.17591
$151$	−2253.63	−1.21455	−0.607277	−	0.794490i	$-0.707738\pi$
$151$	−2253.63	−1.21455	−0.607277	+	0.794490i	$0.707738\pi$
$152$	−3722.91	−1.98663
$153$	2422.27	1.27993
$154$	−658.329	−0.344478
$155$	158.131	0.0819442
$156$	0	0
$157$	122.106	0.0620709	0.0310355	−	0.999518i	$-0.490120\pi$
$157$	122.106	0.0620709	0.0310355	+	0.999518i	$0.490120\pi$
$158$	1299.26	0.654201
$159$	2199.36	1.09698
$160$	2694.35	1.33129
$161$	−1629.34	−0.797578
$162$	−4852.62	−2.35344
$163$	2989.42	1.43650	0.718250	−	0.695785i	$-0.244943\pi$
$163$	2989.42	1.43650	0.718250	+	0.695785i	$0.244943\pi$
$164$	−3687.43	−1.75573
$165$	−293.769	−0.138605
$166$	2588.94	1.21049
$167$	−4245.43	−1.96719	−0.983597	−	0.180378i	$-0.942268\pi$
$167$	−4245.43	−1.96719	−0.983597	+	0.180378i	$0.942268\pi$
$168$	5514.76	2.53258
$169$	0	0
$170$	2901.72	1.30913
$171$	−900.712	−0.402802
$172$	−8067.47	−3.57639
$173$	2983.52	1.31117	0.655586	−	0.755121i	$-0.272422\pi$
$173$	2983.52	1.31117	0.655586	+	0.755121i	$0.272422\pi$
$174$	1872.18	0.815686
$175$	−1198.61	−0.517752
$176$	−2574.51	−1.10262
$177$	2694.61	1.14429
$178$	316.302	0.133190
$179$	265.175	0.110727	0.0553634	−	0.998466i	$-0.482368\pi$
$179$	265.175	0.110727	0.0553634	+	0.998466i	$0.482368\pi$
$180$	1563.35	0.647360
$181$	−3135.66	−1.28769	−0.643845	−	0.765156i	$-0.722662\pi$
$181$	−3135.66	−1.28769	−0.643845	+	0.765156i	$0.722662\pi$
$182$	0	0
$183$	−1471.12	−0.594255
$184$	−11102.7	−4.44836
$185$	−262.260	−0.104225
$186$	1455.78	0.573887
$187$	−1472.25	−0.575729
$188$	5715.20	2.21715
$189$	−656.259	−0.252570
$190$	−1079.00	−0.411992
$191$	268.014	0.101533	0.0507664	−	0.998711i	$-0.483834\pi$
$191$	268.014	0.101533	0.0507664	+	0.998711i	$0.483834\pi$
$192$	12230.7	4.59727
$193$	2935.01	1.09464	0.547322	−	0.836922i	$-0.315647\pi$
$193$	2935.01	1.09464	0.547322	+	0.836922i	$0.315647\pi$
$194$	5355.01	1.98179
$195$	0	0
$196$	−4832.73	−1.76120
$197$	1842.24	0.666264	0.333132	−	0.942880i	$-0.391895\pi$
$197$	1842.24	0.666264	0.333132	+	0.942880i	$0.391895\pi$
$198$	−1085.33	−0.389550
$199$	−4253.65	−1.51524	−0.757621	−	0.652695i	$-0.773638\pi$
$199$	−4253.65	−1.51524	−0.757621	+	0.652695i	$0.773638\pi$
$200$	−8167.60	−2.88768
$201$	−3458.34	−1.21360
$202$	−8050.49	−2.80411
$203$	561.370	0.194091
$204$	19523.3	6.70052
$205$	−675.104	−0.230006
$206$	3077.50	1.04087
$207$	−2686.15	−0.901934
$208$	0	0
$209$	547.450	0.181186
$210$	1598.32	0.525212
$211$	−828.885	−0.270440	−0.135220	−	0.990816i	$-0.543174\pi$
$211$	−828.885	−0.270440	−0.135220	+	0.990816i	$0.543174\pi$
$212$	7113.83	2.30462
$213$	−583.745	−0.187782
$214$	11216.6	3.58295
$215$	−1477.01	−0.468519
$216$	−4471.88	−1.40867
$217$	436.514	0.136555
$218$	8030.14	2.49482
$219$	−7609.69	−2.34802
$220$	−950.196	−0.291192
$221$	0	0
$222$	−2414.41	−0.729931
$223$	−976.298	−0.293174	−0.146587	−	0.989198i	$-0.546829\pi$
$223$	−976.298	−0.293174	−0.146587	+	0.989198i	$0.546829\pi$
$224$	7437.64	2.21852
$225$	−1976.05	−0.585496
$226$	10786.1	3.17469
$227$	−1692.91	−0.494987	−0.247494	−	0.968890i	$-0.579607\pi$
$227$	−1692.91	−0.494987	−0.247494	+	0.968890i	$0.579607\pi$
$228$	−7259.68	−2.10870
$229$	2909.02	0.839448	0.419724	−	0.907652i	$-0.362127\pi$
$229$	2909.02	0.839448	0.419724	+	0.907652i	$0.362127\pi$
$230$	−3217.84	−0.922512
$231$	−810.939	−0.230978
$232$	3825.29	1.08251
$233$	1181.61	0.332230	0.166115	−	0.986106i	$-0.446878\pi$
$233$	1181.61	0.332230	0.166115	+	0.986106i	$0.446878\pi$
$234$	0	0
$235$	1046.35	0.290454
$236$	8715.72	2.40400
$237$	1600.45	0.438651
$238$	8010.10	2.18159
$239$	−119.971	−0.0324698	−0.0162349	−	0.999868i	$-0.505168\pi$
$239$	−119.971	−0.0324698	−0.0162349	+	0.999868i	$0.505168\pi$
$240$	6250.50	1.68112
$241$	−960.003	−0.256594	−0.128297	−	0.991736i	$-0.540951\pi$
$241$	−960.003	−0.256594	−0.128297	+	0.991736i	$0.540951\pi$
$242$	659.659	0.175225
$243$	−4363.45	−1.15192
$244$	−4758.36	−1.24845
$245$	−884.789	−0.230723
$246$	−6215.14	−1.61082
$247$	0	0
$248$	2974.49	0.761615
$249$	3189.09	0.811649
$250$	−5077.23	−1.28445
$251$	−475.485	−0.119571	−0.0597856	−	0.998211i	$-0.519042\pi$
$251$	−475.485	−0.119571	−0.0597856	+	0.998211i	$0.519042\pi$
$252$	4315.56	1.07879
$253$	1632.63	0.405703
$254$	−6645.67	−1.64168
$255$	3574.38	0.877790
$256$	10011.2	2.44415
$257$	−4114.46	−0.998649	−0.499324	−	0.866415i	$-0.666418\pi$
$257$	−4114.46	−0.998649	−0.499324	+	0.866415i	$0.666418\pi$
$258$	−13597.7	−3.28122
$259$	−723.958	−0.173686
$260$	0	0
$261$	925.481	0.219486
$262$	4876.13	1.14980
$263$	−1223.11	−0.286770	−0.143385	−	0.989667i	$-0.545799\pi$
$263$	−1223.11	−0.286770	−0.143385	+	0.989667i	$0.545799\pi$
$264$	−5525.90	−1.28824
$265$	1302.42	0.301913
$266$	−2978.53	−0.686561
$267$	389.625	0.0893058
$268$	−11186.0	−2.54961
$269$	−5286.07	−1.19813	−0.599066	−	0.800700i	$-0.704461\pi$
$269$	−5286.07	−1.19813	−0.599066	+	0.800700i	$0.704461\pi$
$270$	−1296.07	−0.292134
$271$	6953.59	1.55867	0.779336	−	0.626606i	$-0.215556\pi$
$271$	6953.59	1.55867	0.779336	+	0.626606i	$0.215556\pi$
$272$	31324.9	6.98290
$273$	0	0
$274$	13554.2	2.98847
$275$	1201.04	0.263364
$276$	−21650.2	−4.72170
$277$	−7562.82	−1.64045	−0.820227	−	0.572038i	$-0.806153\pi$
$277$	−7562.82	−1.64045	−0.820227	+	0.572038i	$0.806153\pi$
$278$	−17545.2	−3.78522
$279$	719.642	0.154422
$280$	3265.73	0.697018
$281$	2993.52	0.635510	0.317755	−	0.948173i	$-0.397071\pi$
$281$	2993.52	0.635510	0.317755	+	0.948173i	$0.397071\pi$
$282$	9632.93	2.03416
$283$	−2732.56	−0.573970	−0.286985	−	0.957935i	$-0.592653\pi$
$283$	−2732.56	−0.573970	−0.286985	+	0.957935i	$0.592653\pi$
$284$	−1888.12	−0.394505
$285$	−1329.12	−0.276247
$286$	0	0
$287$	−1863.60	−0.383292
$288$	12261.8	2.50879
$289$	13000.3	2.64610
$290$	1108.67	0.224494
$291$	6596.38	1.32882
$292$	−24613.6	−4.93288
$293$	5089.01	1.01469	0.507343	−	0.861744i	$-0.330628\pi$
$293$	5089.01	1.01469	0.507343	+	0.861744i	$0.330628\pi$
$294$	−8145.53	−1.61584
$295$	1595.70	0.314932
$296$	−4933.20	−0.968704
$297$	657.585	0.128475
$298$	195.676	0.0380377
$299$	0	0
$300$	−15926.8	−3.06512
$301$	−4077.24	−0.780759
$302$	−12286.2	−2.34103
$303$	−9916.70	−1.88020
$304$	−11648.0	−2.19757
$305$	−871.172	−0.163551
$306$	13205.5	2.46703
$307$	−5566.20	−1.03479	−0.517394	−	0.855747i	$-0.673098\pi$
$307$	−5566.20	−1.03479	−0.517394	+	0.855747i	$0.673098\pi$
$308$	−2622.98	−0.485254
$309$	3790.90	0.697919
$310$	862.085	0.157946
$311$	4144.22	0.755618	0.377809	−	0.925884i	$-0.376678\pi$
$311$	4144.22	0.755618	0.377809	+	0.925884i	$0.376678\pi$
$312$	0	0
$313$	3522.79	0.636165	0.318082	−	0.948063i	$-0.396961\pi$
$313$	3522.79	0.636165	0.318082	+	0.948063i	$0.396961\pi$
$314$	665.690	0.119640
$315$	790.104	0.141325
$316$	5176.66	0.921550
$317$	192.587	0.0341222	0.0170611	−	0.999854i	$-0.494569\pi$
$317$	192.587	0.0341222	0.0170611	+	0.999854i	$0.494569\pi$
$318$	11990.3	2.11441
$319$	−562.504	−0.0987279
$320$	7242.80	1.26527
$321$	13816.8	2.40242
$322$	−8882.72	−1.53731
$323$	−6660.99	−1.14745
$324$	−19334.3	−3.31521
$325$	0	0
$326$	16297.5	2.76882
$327$	9891.64	1.67281
$328$	−12699.0	−2.13775
$329$	2888.42	0.484024
$330$	−1601.55	−0.267159
$331$	5223.85	0.867459	0.433729	−	0.901043i	$-0.357197\pi$
$331$	5223.85	0.867459	0.433729	+	0.901043i	$0.357197\pi$
$332$	10315.1	1.70517
$333$	−1193.53	−0.196411
$334$	−23145.0	−3.79172
$335$	−2047.97	−0.334007
$336$	17254.3	2.80148
$337$	−6220.97	−1.00557	−0.502786	−	0.864411i	$-0.667692\pi$
$337$	−6220.97	−1.00557	−0.502786	+	0.864411i	$0.667692\pi$
$338$	0	0
$339$	13286.5	2.12868
$340$	11561.3	1.84412
$341$	−437.396	−0.0694613
$342$	−4910.44	−0.776392
$343$	−6207.82	−0.977232
$344$	−27783.2	−4.35456
$345$	−3963.77	−0.618558
$346$	16265.3	2.52725
$347$	4475.35	0.692361	0.346180	−	0.938168i	$-0.387478\pi$
$347$	4475.35	0.692361	0.346180	+	0.938168i	$0.387478\pi$
$348$	7459.32	1.14903
$349$	8466.92	1.29864	0.649318	−	0.760517i	$-0.275054\pi$
$349$	8466.92	1.29864	0.649318	+	0.760517i	$0.275054\pi$
$350$	−6534.52	−0.997956
$351$	0	0
$352$	−7452.67	−1.12849
$353$	7895.97	1.19054	0.595269	−	0.803527i	$-0.297046\pi$
$353$	7895.97	1.19054	0.595269	+	0.803527i	$0.297046\pi$
$354$	14690.3	2.20559
$355$	−345.682	−0.0516815
$356$	1260.24	0.187620
$357$	9866.95	1.46279
$358$	1445.66	0.213423
$359$	30.3787	0.00446609	0.00223305	−	0.999998i	$-0.499289\pi$
$359$	30.3787	0.00446609	0.00223305	+	0.999998i	$0.499289\pi$
$360$	5383.93	0.788216
$361$	−4382.13	−0.638888
$362$	−17094.8	−2.48199
$363$	812.577	0.117491
$364$	0	0
$365$	−4506.32	−0.646223
$366$	−8020.17	−1.14541
$367$	−3892.34	−0.553619	−0.276810	−	0.960925i	$-0.589277\pi$
$367$	−3892.34	−0.553619	−0.276810	+	0.960925i	$0.589277\pi$
$368$	−34737.4	−4.92069
$369$	−3072.36	−0.433443
$370$	−1429.77	−0.200892
$371$	3595.28	0.503120
$372$	5800.27	0.808414
$373$	−6398.65	−0.888229	−0.444114	−	0.895970i	$-0.646482\pi$
$373$	−6398.65	−0.888229	−0.444114	+	0.895970i	$0.646482\pi$
$374$	−8026.28	−1.10970
$375$	−6254.21	−0.861243
$376$	19682.3	2.69957
$377$	0	0
$378$	−3577.75	−0.486824
$379$	−9010.19	−1.22117	−0.610583	−	0.791952i	$-0.709065\pi$
$379$	−9010.19	−1.22117	−0.610583	+	0.791952i	$0.709065\pi$
$380$	−4299.05	−0.580359
$381$	−8186.23	−1.10077
$382$	1461.14	0.195702
$383$	6320.28	0.843215	0.421607	−	0.906778i	$-0.361466\pi$
$383$	6320.28	0.843215	0.421607	+	0.906778i	$0.361466\pi$
$384$	30279.6	4.02396
$385$	−480.222	−0.0635699
$386$	16000.9	2.10990
$387$	−6721.79	−0.882914
$388$	21336.0	2.79168
$389$	−11800.0	−1.53800	−0.769002	−	0.639247i	$-0.779246\pi$
$389$	−11800.0	−1.53800	−0.769002	+	0.639247i	$0.779246\pi$
$390$	0	0
$391$	−19864.8	−2.56932
$392$	−16643.2	−2.14441
$393$	6006.48	0.770959
$394$	10043.4	1.28421
$395$	947.756	0.120726
$396$	−4324.28	−0.548746
$397$	7152.42	0.904205	0.452103	−	0.891966i	$-0.350674\pi$
$397$	7152.42	0.904205	0.452103	+	0.891966i	$0.350674\pi$
$398$	−23189.7	−2.92059
$399$	−3668.99	−0.460349
$400$	−25554.3	−3.19429
$401$	−1711.25	−0.213106	−0.106553	−	0.994307i	$-0.533981\pi$
$401$	−1711.25	−0.213106	−0.106553	+	0.994307i	$0.533981\pi$
$402$	−18854.0	−2.33918
$403$	0	0
$404$	−32075.6	−3.95005
$405$	−3539.78	−0.434304
$406$	3060.44	0.374106
$407$	725.421	0.0883484
$408$	67235.4	8.15845
$409$	−3685.90	−0.445614	−0.222807	−	0.974863i	$-0.571522\pi$
$409$	−3685.90	−0.445614	−0.222807	+	0.974863i	$0.571522\pi$
$410$	−3680.49	−0.443332
$411$	16696.3	2.00381
$412$	12261.7	1.46624
$413$	4404.86	0.524816
$414$	−14644.2	−1.73846
$415$	1888.52	0.223383
$416$	0	0
$417$	−21612.4	−2.53804
$418$	2984.55	0.349232
$419$	753.382	0.0878403	0.0439202	−	0.999035i	$-0.486015\pi$
$419$	753.382	0.0878403	0.0439202	+	0.999035i	$0.486015\pi$
$420$	6368.19	0.739847
$421$	−4362.81	−0.505060	−0.252530	−	0.967589i	$-0.581263\pi$
$421$	−4362.81	−0.505060	−0.252530	+	0.967589i	$0.581263\pi$
$422$	−4518.86	−0.521267
$423$	4761.89	0.547354
$424$	24499.0	2.80607
$425$	−14613.4	−1.66789
$426$	−3182.42	−0.361945
$427$	−2404.84	−0.272549
$428$	44690.4	5.04717
$429$	0	0
$430$	−8052.28	−0.903059
$431$	1597.38	0.178522	0.0892610	−	0.996008i	$-0.471549\pi$
$431$	1597.38	0.178522	0.0892610	+	0.996008i	$0.471549\pi$
$432$	−13991.4	−1.55824
$433$	1145.60	0.127145	0.0635726	−	0.997977i	$-0.479751\pi$
$433$	1145.60	0.127145	0.0635726	+	0.997977i	$0.479751\pi$
$434$	2379.75	0.263207
$435$	1365.67	0.150526
$436$	31994.5	3.51436
$437$	7386.65	0.808584
$438$	−41486.0	−4.52575
$439$	9769.65	1.06214	0.531071	−	0.847328i	$-0.321790\pi$
$439$	9769.65	1.06214	0.531071	+	0.847328i	$0.321790\pi$
$440$	−3272.33	−0.354551
$441$	−4026.61	−0.434793
$442$	0	0
$443$	−3877.61	−0.415871	−0.207935	−	0.978143i	$-0.566674\pi$
$443$	−3877.61	−0.415871	−0.207935	+	0.978143i	$0.566674\pi$
$444$	−9619.75	−1.02823
$445$	230.728	0.0245788
$446$	−5322.51	−0.565086
$447$	241.037	0.0255048
$448$	19993.5	2.10849
$449$	6379.86	0.670566	0.335283	−	0.942118i	$-0.391168\pi$
$449$	6379.86	0.670566	0.335283	+	0.942118i	$0.391168\pi$
$450$	−10772.9	−1.12853
$451$	1867.37	0.194969
$452$	42975.1	4.47208
$453$	−15134.3	−1.56969
$454$	−9229.27	−0.954077
$455$	0	0
$456$	−25001.3	−2.56753
$457$	707.199	0.0723881	0.0361941	−	0.999345i	$-0.488477\pi$
$457$	707.199	0.0723881	0.0361941	+	0.999345i	$0.488477\pi$
$458$	15859.2	1.61802
$459$	−8001.05	−0.813632
$460$	−12820.8	−1.29951
$461$	15942.8	1.61069	0.805345	−	0.592806i	$-0.201980\pi$
$461$	15942.8	1.61069	0.805345	+	0.592806i	$0.201980\pi$
$462$	−4421.02	−0.445204
$463$	12297.2	1.23434	0.617171	−	0.786829i	$-0.288279\pi$
$463$	12297.2	1.23434	0.617171	+	0.786829i	$0.288279\pi$
$464$	11968.4	1.19745
$465$	1061.93	0.105905
$466$	6441.80	0.640366
$467$	−2715.95	−0.269120	−0.134560	−	0.990905i	$-0.542962\pi$
$467$	−2715.95	−0.269120	−0.134560	+	0.990905i	$0.542962\pi$
$468$	0	0
$469$	−5653.34	−0.556603
$470$	5704.44	0.559843
$471$	820.006	0.0802206
$472$	30015.6	2.92708
$473$	4085.48	0.397147
$474$	8725.22	0.845491
$475$	5433.94	0.524897
$476$	31914.7	3.07312
$477$	5927.22	0.568949
$478$	−654.050	−0.0625848
$479$	3917.41	0.373677	0.186838	−	0.982391i	$-0.440176\pi$
$479$	3917.41	0.373677	0.186838	+	0.982391i	$0.440176\pi$
$480$	18093.9	1.72056
$481$	0	0
$482$	−5233.68	−0.494580
$483$	−10941.9	−1.03079
$484$	2628.28	0.246834
$485$	3906.25	0.365719
$486$	−23788.4	−2.22029
$487$	−2659.99	−0.247506	−0.123753	−	0.992313i	$-0.539493\pi$
$487$	−2659.99	−0.247506	−0.123753	+	0.992313i	$0.539493\pi$
$488$	−16387.1	−1.52010
$489$	20075.5	1.85654
$490$	−4823.63	−0.444713
$491$	16396.5	1.50706	0.753529	−	0.657414i	$-0.228350\pi$
$491$	16396.5	1.50706	0.753529	+	0.657414i	$0.228350\pi$
$492$	−24763.0	−2.26911
$493$	6844.17	0.625245
$494$	0	0
$495$	−791.700	−0.0718874
$496$	9306.44	0.842483
$497$	−954.244	−0.0861241
$498$	17386.1	1.56444
$499$	−12282.4	−1.10187	−0.550937	−	0.834547i	$-0.685730\pi$
$499$	−12282.4	−1.10187	−0.550937	+	0.834547i	$0.685730\pi$
$500$	−20229.2	−1.80936
$501$	−28510.3	−2.54241
$502$	−2592.22	−0.230471
$503$	−3320.74	−0.294362	−0.147181	−	0.989110i	$-0.547020\pi$
$503$	−3320.74	−0.294362	−0.147181	+	0.989110i	$0.547020\pi$
$504$	14862.1	1.31352
$505$	−5872.48	−0.517469
$506$	8900.67	0.781982
$507$	0	0
$508$	−26478.4	−2.31257
$509$	−6220.84	−0.541717	−0.270859	−	0.962619i	$-0.587308\pi$
$509$	−6220.84	−0.541717	−0.270859	+	0.962619i	$0.587308\pi$
$510$	19486.5	1.69192
$511$	−12439.5	−1.07689
$512$	18507.3	1.59749
$513$	2975.16	0.256056
$514$	−22430.9	−1.92487
$515$	2244.90	0.192082
$516$	−54177.2	−4.62213
$517$	−2894.26	−0.246208
$518$	−3946.82	−0.334775
$519$	20035.9	1.69456
$520$	0	0
$521$	761.877	0.0640661	0.0320330	−	0.999487i	$-0.489802\pi$
$521$	761.877	0.0640661	0.0320330	+	0.999487i	$0.489802\pi$
$522$	5045.47	0.423054
$523$	−6377.85	−0.533239	−0.266619	−	0.963802i	$-0.585907\pi$
$523$	−6377.85	−0.533239	−0.266619	+	0.963802i	$0.585907\pi$
$524$	19428.0	1.61969
$525$	−8049.31	−0.669144
$526$	−6668.09	−0.552742
$527$	5321.93	0.439900
$528$	−17289.2	−1.42503
$529$	9861.84	0.810540
$530$	7100.44	0.581931
$531$	7261.91	0.593484
$532$	−11867.4	−0.967134
$533$	0	0
$534$	2124.13	0.172135
$535$	8182.03	0.661196
$536$	−38523.0	−3.10436
$537$	1780.79	0.143104
$538$	−28818.2	−2.30937
$539$	2447.36	0.195576
$540$	−5163.93	−0.411518
$541$	15251.3	1.21202	0.606010	−	0.795457i	$-0.292769\pi$
$541$	15251.3	1.21202	0.606010	+	0.795457i	$0.292769\pi$
$542$	37909.1	3.00431
$543$	−21057.6	−1.66421
$544$	90679.1	7.14675
$545$	5857.64	0.460392
$546$	0	0
$547$	16194.0	1.26583	0.632913	−	0.774223i	$-0.281859\pi$
$547$	16194.0	1.26583	0.632913	+	0.774223i	$0.281859\pi$
$548$	54004.2	4.20975
$549$	−3964.65	−0.308209
$550$	6547.72	0.507629
$551$	−2544.98	−0.196769
$552$	−74560.1	−5.74907
$553$	2616.25	0.201183
$554$	−41230.4	−3.16194
$555$	−1761.21	−0.134701
$556$	−69905.3	−5.33210
$557$	−17280.9	−1.31457	−0.657286	−	0.753641i	$-0.728296\pi$
$557$	−17280.9	−1.31457	−0.657286	+	0.753641i	$0.728296\pi$
$558$	3923.29	0.297645
$559$	0	0
$560$	10217.7	0.771026
$561$	−9886.89	−0.744073
$562$	16319.9	1.22493
$563$	5535.16	0.414350	0.207175	−	0.978304i	$-0.433573\pi$
$563$	5535.16	0.414350	0.207175	+	0.978304i	$0.433573\pi$
$564$	38380.5	2.86545
$565$	7867.99	0.585856
$566$	−14897.2	−1.10631
$567$	−9771.43	−0.723742
$568$	−6502.41	−0.480344
$569$	6461.74	0.476081	0.238041	−	0.971255i	$-0.423495\pi$
$569$	6461.74	0.476081	0.238041	+	0.971255i	$0.423495\pi$
$570$	−7246.01	−0.532460
$571$	−13333.7	−0.977230	−0.488615	−	0.872499i	$-0.662498\pi$
$571$	−13333.7	−0.977230	−0.488615	+	0.872499i	$0.662498\pi$
$572$	0	0
$573$	1799.85	0.131221
$574$	−10159.9	−0.738787
$575$	16205.4	1.17532
$576$	32961.5	2.38437
$577$	−1984.83	−0.143205	−0.0716027	−	0.997433i	$-0.522811\pi$
$577$	−1984.83	−0.143205	−0.0716027	+	0.997433i	$0.522811\pi$
$578$	70874.0	5.10029
$579$	19710.1	1.41472
$580$	4417.27	0.316236
$581$	5213.19	0.372254
$582$	35961.7	2.56127
$583$	−3602.55	−0.255922
$584$	−84765.5	−6.00620
$585$	0	0
$586$	27743.9	1.95579
$587$	−14393.8	−1.01209	−0.506044	−	0.862508i	$-0.668893\pi$
$587$	−14393.8	−1.01209	−0.506044	+	0.862508i	$0.668893\pi$
$588$	−32454.3	−2.27618
$589$	−1978.94	−0.138440
$590$	8699.30	0.607025
$591$	12371.6	0.861080
$592$	−15434.7	−1.07156
$593$	20117.9	1.39316	0.696579	−	0.717480i	$-0.254704\pi$
$593$	20117.9	1.39316	0.696579	+	0.717480i	$0.254704\pi$
$594$	3584.98	0.247632
$595$	5843.02	0.402589
$596$	779.635	0.0535824
$597$	−28565.4	−1.95830
$598$	0	0
$599$	16711.0	1.13989	0.569944	−	0.821684i	$-0.306965\pi$
$599$	16711.0	1.13989	0.569944	+	0.821684i	$0.306965\pi$
$600$	−54849.6	−3.73204
$601$	2686.78	0.182356	0.0911780	−	0.995835i	$-0.470937\pi$
$601$	2686.78	0.182356	0.0911780	+	0.995835i	$0.470937\pi$
$602$	−22228.0	−1.50489
$603$	−9320.16	−0.629430
$604$	−48951.9	−3.29772
$605$	481.193	0.0323360
$606$	−54063.2	−3.62404
$607$	494.542	0.0330690	0.0165345	−	0.999863i	$-0.494737\pi$
$607$	494.542	0.0330690	0.0165345	+	0.999863i	$0.494737\pi$
$608$	−33718.7	−2.24914
$609$	3769.89	0.250843
$610$	−4749.39	−0.315242
$611$	0	0
$612$	52614.9	3.47521
$613$	−6650.73	−0.438206	−0.219103	−	0.975702i	$-0.570313\pi$
$613$	−6650.73	−0.438206	−0.219103	+	0.975702i	$0.570313\pi$
$614$	−30345.4	−1.99453
$615$	−4533.67	−0.297261
$616$	−9033.16	−0.590838
$617$	−2846.14	−0.185707	−0.0928537	−	0.995680i	$-0.529599\pi$
$617$	−2846.14	−0.185707	−0.0928537	+	0.995680i	$0.529599\pi$
$618$	20667.0	1.34522
$619$	22897.7	1.48681	0.743407	−	0.668839i	$-0.233209\pi$
$619$	22897.7	1.48681	0.743407	+	0.668839i	$0.233209\pi$
$620$	3434.81	0.222492
$621$	8872.69	0.573347
$622$	22593.2	1.45644
$623$	636.917	0.0409592
$624$	0	0
$625$	9944.51	0.636449
$626$	19205.3	1.22619
$627$	3676.41	0.234165
$628$	2652.31	0.168533
$629$	−8826.43	−0.559512
$630$	4307.43	0.272400
$631$	−4443.90	−0.280363	−0.140181	−	0.990126i	$-0.544769\pi$
$631$	−4443.90	−0.280363	−0.140181	+	0.990126i	$0.544769\pi$
$632$	17827.6	1.12207
$633$	−5566.39	−0.349517
$634$	1049.93	0.0657699
$635$	−4847.73	−0.302955
$636$	47773.1	2.97850
$637$	0	0
$638$	−3066.62	−0.190296
$639$	−1573.18	−0.0973927
$640$	17931.0	1.10748
$641$	−19359.1	−1.19288	−0.596441	−	0.802657i	$-0.703419\pi$
$641$	−19359.1	−1.19288	−0.596441	+	0.802657i	$0.703419\pi$
$642$	75325.3	4.63061
$643$	−6340.25	−0.388857	−0.194429	−	0.980917i	$-0.562285\pi$
$643$	−6340.25	−0.388857	−0.194429	+	0.980917i	$0.562285\pi$
$644$	−35391.5	−2.16556
$645$	−9918.91	−0.605514
$646$	−36313.9	−2.21169
$647$	−6219.86	−0.377941	−0.188971	−	0.981983i	$-0.560515\pi$
$647$	−6219.86	−0.377941	−0.188971	+	0.981983i	$0.560515\pi$
$648$	−66584.5	−4.03655
$649$	−4413.76	−0.266958
$650$	0	0
$651$	2931.41	0.176484
$652$	64934.3	3.90034
$653$	6310.07	0.378150	0.189075	−	0.981963i	$-0.439451\pi$
$653$	6310.07	0.378150	0.189075	+	0.981963i	$0.439451\pi$
$654$	53926.6	3.22430
$655$	3556.93	0.212184
$656$	−39731.8	−2.36474
$657$	−20507.9	−1.21779
$658$	15746.9	0.932945
$659$	511.092	0.0302114	0.0151057	−	0.999886i	$-0.495192\pi$
$659$	511.092	0.0302114	0.0151057	+	0.999886i	$0.495192\pi$
$660$	−6381.06	−0.376337
$661$	−11679.7	−0.687275	−0.343638	−	0.939102i	$-0.611659\pi$
$661$	−11679.7	−0.687275	−0.343638	+	0.939102i	$0.611659\pi$
$662$	28479.0	1.67201
$663$	0	0
$664$	35523.8	2.07619
$665$	−2172.71	−0.126698
$666$	−6506.78	−0.378578
$667$	−7589.78	−0.440596
$668$	−92216.5	−5.34126
$669$	−6556.35	−0.378898
$670$	−11165.0	−0.643791
$671$	2409.70	0.138637
$672$	49947.6	2.86722
$673$	−2525.96	−0.144678	−0.0723392	−	0.997380i	$-0.523046\pi$
$673$	−2525.96	−0.144678	−0.0723392	+	0.997380i	$0.523046\pi$
$674$	−33915.1	−1.93822
$675$	6527.13	0.372192
$676$	0	0
$677$	−2626.19	−0.149088	−0.0745442	−	0.997218i	$-0.523750\pi$
$677$	−2626.19	−0.149088	−0.0745442	+	0.997218i	$0.523750\pi$
$678$	72434.2	4.10298
$679$	10783.1	0.609449
$680$	39815.5	2.24538
$681$	−11368.7	−0.639723
$682$	−2384.56	−0.133885
$683$	−25494.3	−1.42828	−0.714138	−	0.700005i	$-0.753181\pi$
$683$	−25494.3	−1.42828	−0.714138	+	0.700005i	$0.753181\pi$
$684$	−19564.7	−1.09368
$685$	9887.22	0.551491
$686$	−33843.3	−1.88359
$687$	19535.6	1.08490
$688$	−86926.5	−4.81692
$689$	0	0
$690$	−21609.4	−1.19226
$691$	27615.7	1.52033	0.760166	−	0.649729i	$-0.225117\pi$
$691$	27615.7	1.52033	0.760166	+	0.649729i	$0.225117\pi$
$692$	64806.1	3.56005
$693$	−2185.46	−0.119796
$694$	24398.4	1.33451
$695$	−12798.4	−0.698522
$696$	25688.8	1.39904
$697$	−22720.9	−1.23474
$698$	46159.4	2.50309
$699$	7935.10	0.429375
$700$	−26035.5	−1.40578
$701$	−27810.2	−1.49840	−0.749200	−	0.662344i	$-0.769562\pi$
$701$	−27810.2	−1.49840	−0.749200	+	0.662344i	$0.769562\pi$
$702$	0	0
$703$	3282.08	0.176082
$704$	−20033.9	−1.07252
$705$	7026.80	0.375383
$706$	43046.7	2.29473
$707$	−16210.8	−0.862333
$708$	58530.6	3.10694
$709$	12843.6	0.680328	0.340164	−	0.940366i	$-0.389517\pi$
$709$	12843.6	0.680328	0.340164	+	0.940366i	$0.389517\pi$
$710$	−1884.57	−0.0996148
$711$	4313.17	0.227506
$712$	4340.08	0.228443
$713$	−5901.71	−0.309987
$714$	53791.9	2.81948
$715$	0	0
$716$	5759.96	0.300642
$717$	−805.668	−0.0419640
$718$	165.616	0.00860829
$719$	2499.33	0.129638	0.0648188	−	0.997897i	$-0.479353\pi$
$719$	2499.33	0.129638	0.0648188	+	0.997897i	$0.479353\pi$
$720$	16844.9	0.871909
$721$	6196.97	0.320093
$722$	−23890.2	−1.23144
$723$	−6446.92	−0.331623
$724$	−68110.8	−3.49630
$725$	−5583.37	−0.286015
$726$	4429.95	0.226461
$727$	−26977.9	−1.37628	−0.688139	−	0.725578i	$-0.741572\pi$
$727$	−26977.9	−1.37628	−0.688139	+	0.725578i	$0.741572\pi$
$728$	0	0
$729$	−5269.96	−0.267742
$730$	−24567.2	−1.24558
$731$	−49709.4	−2.51514
$732$	−31954.8	−1.61350
$733$	12358.5	0.622744	0.311372	−	0.950288i	$-0.399211\pi$
$733$	12358.5	0.622744	0.311372	+	0.950288i	$0.399211\pi$
$734$	−21220.0	−1.06709
$735$	−5941.81	−0.298186
$736$	−100558.	−5.03615
$737$	5664.76	0.283126
$738$	−16749.6	−0.835451
$739$	9173.93	0.456656	0.228328	−	0.973584i	$-0.426674\pi$
$739$	9173.93	0.456656	0.228328	+	0.973584i	$0.426674\pi$
$740$	−5696.63	−0.282990
$741$	0	0
$742$	19600.5	0.969753
$743$	33911.3	1.67441	0.837204	−	0.546890i	$-0.184189\pi$
$743$	33911.3	1.67441	0.837204	+	0.546890i	$0.184189\pi$
$744$	19975.3	0.984313
$745$	142.738	0.00701946
$746$	−34883.7	−1.71204
$747$	8594.53	0.420961
$748$	−31979.2	−1.56320
$749$	22586.2	1.10184
$750$	−34096.2	−1.66003
$751$	32020.7	1.55586	0.777932	−	0.628349i	$-0.216269\pi$
$751$	32020.7	1.55586	0.777932	+	0.628349i	$0.216269\pi$
$752$	61580.9	2.98620
$753$	−3193.13	−0.154534
$754$	0	0
$755$	−8962.23	−0.432012
$756$	−14254.8	−0.685771
$757$	30968.5	1.48688	0.743440	−	0.668803i	$-0.233193\pi$
$757$	30968.5	1.48688	0.743440	+	0.668803i	$0.233193\pi$
$758$	−49121.1	−2.35377
$759$	10964.0	0.524331
$760$	−14805.3	−0.706636
$761$	−31926.2	−1.52079	−0.760397	−	0.649458i	$-0.774996\pi$
$761$	−31926.2	−1.52079	−0.760397	+	0.649458i	$0.774996\pi$
$762$	−44629.1	−2.12171
$763$	16169.8	0.767217
$764$	5821.62	0.275679
$765$	9632.87	0.455264
$766$	34456.5	1.62528
$767$	0	0
$768$	67230.6	3.15882
$769$	7542.47	0.353691	0.176846	−	0.984239i	$-0.443411\pi$
$769$	7542.47	0.353691	0.176846	+	0.984239i	$0.443411\pi$
$770$	−2618.04	−0.122529
$771$	−27630.7	−1.29066
$772$	63752.3	2.97214
$773$	4347.18	0.202273	0.101137	−	0.994873i	$-0.467752\pi$
$773$	4347.18	0.202273	0.101137	+	0.994873i	$0.467752\pi$
$774$	−36645.4	−1.70180
$775$	−4341.55	−0.201230
$776$	73478.0	3.39911
$777$	−4861.75	−0.224472
$778$	−64330.4	−2.96447
$779$	8448.68	0.388582
$780$	0	0
$781$	956.172	0.0438086
$782$	−108297.	−4.95231
$783$	−3056.98	−0.139524
$784$	−52072.4	−2.37210
$785$	485.592	0.0220784
$786$	32745.7	1.48601
$787$	27404.1	1.24123	0.620617	−	0.784114i	$-0.286882\pi$
$787$	27404.1	1.24123	0.620617	+	0.784114i	$0.286882\pi$
$788$	40015.9	1.80902
$789$	−8213.84	−0.370622
$790$	5166.91	0.232697
$791$	21719.3	0.976295
$792$	−14892.2	−0.668144
$793$	0	0
$794$	38993.0	1.74284
$795$	8746.42	0.390193
$796$	−92395.0	−4.11414
$797$	9043.77	0.401941	0.200970	−	0.979597i	$-0.435590\pi$
$797$	9043.77	0.401941	0.200970	+	0.979597i	$0.435590\pi$
$798$	−20002.4	−0.887313
$799$	35215.4	1.55924
$800$	−73974.6	−3.26925
$801$	1050.03	0.0463183
$802$	−9329.26	−0.410757
$803$	12464.7	0.547781
$804$	−75119.9	−3.29512
$805$	−6479.56	−0.283695
$806$	0	0
$807$	−35498.7	−1.54847
$808$	−110464.	−4.80952
$809$	−12351.2	−0.536768	−0.268384	−	0.963312i	$-0.586490\pi$
$809$	−12351.2	−0.536768	−0.268384	+	0.963312i	$0.586490\pi$
$810$	−19297.9	−0.837110
$811$	1246.81	0.0539844	0.0269922	−	0.999636i	$-0.491407\pi$
$811$	1246.81	0.0539844	0.0269922	+	0.999636i	$0.491407\pi$
$812$	12193.7	0.526989
$813$	46696.9	2.01443
$814$	3954.80	0.170290
$815$	11888.3	0.510957
$816$	210363.	9.02471
$817$	18484.3	0.791533
$818$	−20094.5	−0.858910
$819$	0	0
$820$	−14664.2	−0.624506
$821$	10073.3	0.428212	0.214106	−	0.976810i	$-0.431316\pi$
$821$	10073.3	0.428212	0.214106	+	0.976810i	$0.431316\pi$
$822$	91023.6	3.86230
$823$	−2495.03	−0.105676	−0.0528379	−	0.998603i	$-0.516827\pi$
$823$	−2495.03	−0.105676	−0.0528379	+	0.998603i	$0.516827\pi$
$824$	42227.4	1.78527
$825$	8065.57	0.340372
$826$	24014.1	1.01157
$827$	−36297.3	−1.52621	−0.763107	−	0.646272i	$-0.776327\pi$
$827$	−36297.3	−1.52621	−0.763107	+	0.646272i	$0.776327\pi$
$828$	−58346.8	−2.44890
$829$	−36624.7	−1.53441	−0.767207	−	0.641400i	$-0.778354\pi$
$829$	−36624.7	−1.53441	−0.767207	+	0.641400i	$0.778354\pi$
$830$	10295.7	0.430565
$831$	−50788.2	−2.12013
$832$	0	0
$833$	−29777.8	−1.23858
$834$	−117825.	−4.89202
$835$	−16883.2	−0.699723
$836$	11891.3	0.491951
$837$	−2377.07	−0.0981642
$838$	4107.23	0.169310
$839$	−31890.7	−1.31226	−0.656132	−	0.754647i	$-0.727808\pi$
$839$	−31890.7	−1.31226	−0.656132	+	0.754647i	$0.727808\pi$
$840$	21931.1	0.900827
$841$	−21774.0	−0.892781
$842$	−23784.9	−0.973492
$843$	20103.0	0.821335
$844$	−18004.5	−0.734290
$845$	0	0
$846$	25960.5	1.05501
$847$	1328.32	0.0538860
$848$	76651.1	3.10402
$849$	−18350.5	−0.741800
$850$	−79668.2	−3.21482
$851$	9787.99	0.394275
$852$	−12679.7	−0.509859
$853$	31015.9	1.24497	0.622487	−	0.782630i	$-0.286122\pi$
$853$	31015.9	1.24497	0.622487	+	0.782630i	$0.286122\pi$
$854$	−13110.5	−0.525332
$855$	−3581.95	−0.143275
$856$	153907.	6.14536
$857$	25713.0	1.02490	0.512449	−	0.858718i	$-0.328738\pi$
$857$	25713.0	1.02490	0.512449	+	0.858718i	$0.328738\pi$
$858$	0	0
$859$	−14363.6	−0.570522	−0.285261	−	0.958450i	$-0.592080\pi$
$859$	−14363.6	−0.570522	−0.285261	+	0.958450i	$0.592080\pi$
$860$	−32082.7	−1.27211
$861$	−12515.0	−0.495368
$862$	8708.47	0.344097
$863$	17576.4	0.693290	0.346645	−	0.937996i	$-0.387321\pi$
$863$	17576.4	0.693290	0.346645	+	0.937996i	$0.387321\pi$
$864$	−40502.2	−1.59481
$865$	11864.9	0.466378
$866$	6245.49	0.245070
$867$	87303.6	3.41982
$868$	9481.67	0.370770
$869$	−2621.53	−0.102335
$870$	7445.27	0.290136
$871$	0	0
$872$	110184.	4.27903
$873$	17777.1	0.689190
$874$	40270.0	1.55853
$875$	−10223.7	−0.395000
$876$	−165293.	−6.37526
$877$	2445.45	0.0941583	0.0470792	−	0.998891i	$-0.485009\pi$
$877$	2445.45	0.0941583	0.0470792	+	0.998891i	$0.485009\pi$
$878$	53261.5	2.04725
$879$	34175.3	1.31138
$880$	−10238.3	−0.392197
$881$	−22281.6	−0.852084	−0.426042	−	0.904703i	$-0.640092\pi$
$881$	−22281.6	−0.852084	−0.426042	+	0.904703i	$0.640092\pi$
$882$	−21952.0	−0.838053
$883$	17954.7	0.684286	0.342143	−	0.939648i	$-0.388847\pi$
$883$	17954.7	0.684286	0.342143	+	0.939648i	$0.388847\pi$
$884$	0	0
$885$	10715.9	0.407019
$886$	−21139.7	−0.801582
$887$	−9547.43	−0.361411	−0.180705	−	0.983537i	$-0.557838\pi$
$887$	−9547.43	−0.361411	−0.180705	+	0.983537i	$0.557838\pi$
$888$	−33129.0	−1.25195
$889$	−13382.0	−0.504856
$890$	1257.87	0.0473751
$891$	9791.18	0.368145
$892$	−21206.5	−0.796017
$893$	−13094.7	−0.490703
$894$	1314.07	0.0491600
$895$	1054.55	0.0393851
$896$	49498.0	1.84555
$897$	0	0
$898$	34781.2	1.29250
$899$	2033.36	0.0754355
$900$	−42922.4	−1.58972
$901$	43833.3	1.62075
$902$	10180.4	0.375798
$903$	−27380.8	−1.00905
$904$	148000.	5.44513
$905$	−12469.9	−0.458026
$906$	−82508.0	−3.02555
$907$	29766.0	1.08971	0.544853	−	0.838531i	$-0.316585\pi$
$907$	29766.0	1.08971	0.544853	+	0.838531i	$0.316585\pi$
$908$	−36772.2	−1.34397
$909$	−26725.3	−0.975161
$910$	0	0
$911$	−41115.3	−1.49529	−0.747646	−	0.664098i	$-0.768816\pi$
$911$	−41115.3	−1.49529	−0.747646	+	0.664098i	$0.768816\pi$
$912$	−78222.7	−2.84014
$913$	−5223.73	−0.189354
$914$	3855.46	0.139526
$915$	−5850.37	−0.211374
$916$	63187.9	2.27924
$917$	9818.77	0.353592
$918$	−43619.5	−1.56826
$919$	34.4854	0.00123783	0.000618916	−	1.00000i	$-0.499803\pi$
$919$	34.4854	0.00123783	0.000618916		1.00000i	$0.499803\pi$
$920$	−44153.0	−1.58226
$921$	−37379.9	−1.33736
$922$	86915.6	3.10457
$923$	0	0
$924$	−17614.7	−0.627143
$925$	7200.47	0.255946
$926$	67041.1	2.37916
$927$	10216.4	0.361975
$928$	34646.0	1.22555
$929$	−27214.9	−0.961134	−0.480567	−	0.876958i	$-0.659569\pi$
$929$	−27214.9	−0.961134	−0.480567	+	0.876958i	$0.659569\pi$
$930$	5789.34	0.204129
$931$	11072.8	0.389792
$932$	25666.1	0.902061
$933$	27830.6	0.976561
$934$	−14806.6	−0.518723
$935$	−5854.83	−0.204784
$936$	0	0
$937$	36687.9	1.27913	0.639563	−	0.768739i	$-0.279116\pi$
$937$	36687.9	1.27913	0.639563	+	0.768739i	$0.279116\pi$
$938$	−30820.5	−1.07284
$939$	23657.3	0.822181
$940$	22728.2	0.788630
$941$	49944.2	1.73022	0.865109	−	0.501584i	$-0.167249\pi$
$941$	49944.2	1.73022	0.865109	+	0.501584i	$0.167249\pi$
$942$	4470.45	0.154623
$943$	25196.1	0.870092
$944$	93911.4	3.23788
$945$	−2609.81	−0.0898383
$946$	22272.9	0.765492
$947$	25008.9	0.858163	0.429081	−	0.903266i	$-0.358837\pi$
$947$	25008.9	0.858163	0.429081	+	0.903266i	$0.358837\pi$
$948$	34763.9	1.19101
$949$	0	0
$950$	29624.4	1.01173
$951$	1293.32	0.0440996
$952$	109909.	3.74179
$953$	−25385.1	−0.862858	−0.431429	−	0.902147i	$-0.641990\pi$
$953$	−25385.1	−0.862858	−0.431429	+	0.902147i	$0.641990\pi$
$954$	32313.6	1.09664
$955$	1065.84	0.0361148
$956$	−2605.93	−0.0881610
$957$	−3777.51	−0.127596
$958$	21356.7	0.720254
$959$	27293.3	0.919027
$960$	48639.1	1.63523
$961$	−28209.9	−0.946926
$962$	0	0
$963$	37235.9	1.24601
$964$	−20852.6	−0.696697
$965$	11671.9	0.389360
$966$	−59652.1	−1.98683
$967$	−6995.49	−0.232637	−0.116318	−	0.993212i	$-0.537109\pi$
$967$	−6995.49	−0.232637	−0.116318	+	0.993212i	$0.537109\pi$
$968$	9051.41	0.300541
$969$	−44732.0	−1.48297
$970$	21295.8	0.704915
$971$	−33645.6	−1.11198	−0.555992	−	0.831187i	$-0.687662\pi$
$971$	−33645.6	−1.11198	−0.555992	+	0.831187i	$0.687662\pi$
$972$	−94780.1	−3.12765
$973$	−35329.7	−1.16405
$974$	−14501.5	−0.477063
$975$	0	0
$976$	−51271.0	−1.68150
$977$	40662.4	1.33153	0.665766	−	0.746161i	$-0.268105\pi$
$977$	40662.4	1.33153	0.665766	+	0.746161i	$0.268105\pi$
$978$	109446.	3.57843
$979$	−638.204	−0.0208346
$980$	−19218.8	−0.626451
$981$	26657.7	0.867601
$982$	89389.5	2.90482
$983$	25908.2	0.840635	0.420317	−	0.907377i	$-0.361919\pi$
$983$	25908.2	0.840635	0.420317	+	0.907377i	$0.361919\pi$
$984$	−85280.1	−2.76283
$985$	7326.21	0.236987
$986$	37312.6	1.20515
$987$	19397.2	0.625553
$988$	0	0
$989$	55124.7	1.77236
$990$	−4316.14	−0.138561
$991$	−28450.1	−0.911954	−0.455977	−	0.889991i	$-0.650710\pi$
$991$	−28450.1	−0.911954	−0.455977	+	0.889991i	$0.650710\pi$
$992$	26940.2	0.862251
$993$	35080.9	1.12111
$994$	−5202.28	−0.166002
$995$	−16915.9	−0.538965
$996$	69271.4	2.20376
$997$	−29757.2	−0.945255	−0.472628	−	0.881262i	$-0.656694\pi$
$997$	−29757.2	−0.945255	−0.472628	+	0.881262i	$0.656694\pi$
$998$	−66960.2	−2.12384
$999$	3942.37	0.124856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.i.1.17		17
13.3	even	3		143.4.e.a.100.1	✓	34
13.9	even	3		143.4.e.a.133.1	yes	34
13.12	even	2		1859.4.a.f.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.1	✓	34	13.3	even	3
143.4.e.a.133.1	yes	34	13.9	even	3
1859.4.a.f.1.1		17	13.12	even	2
1859.4.a.i.1.17		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)

\(f(q)\)	\(=\)	\(q+5.45173 q^{2} +6.71552 q^{3} +21.7213 q^{4} +3.97680 q^{5} +36.6112 q^{6} +10.9778 q^{7} +74.8051 q^{8} +18.0982 q^{9} +O(q^{10})\)	\(q+5.45173 q^{2} +6.71552 q^{3} +21.7213 q^{4} +3.97680 q^{5} +36.6112 q^{6} +10.9778 q^{7} +74.8051 q^{8} +18.0982 q^{9} +21.6804 q^{10} -11.0000 q^{11} +145.870 q^{12} +59.8481 q^{14} +26.7063 q^{15} +234.046 q^{16} +133.840 q^{17} +98.6662 q^{18} -49.7682 q^{19} +86.3815 q^{20} +73.7217 q^{21} -59.9690 q^{22} -148.421 q^{23} +502.355 q^{24} -109.185 q^{25} -59.7805 q^{27} +238.453 q^{28} +51.1368 q^{29} +145.595 q^{30} +39.7633 q^{31} +677.516 q^{32} -73.8707 q^{33} +729.662 q^{34} +43.6566 q^{35} +393.116 q^{36} -65.9474 q^{37} -271.322 q^{38} +297.485 q^{40} -169.761 q^{41} +401.911 q^{42} -371.407 q^{43} -238.935 q^{44} +71.9728 q^{45} -809.152 q^{46} +263.114 q^{47} +1571.74 q^{48} -222.488 q^{49} -595.247 q^{50} +898.808 q^{51} +327.504 q^{53} -325.907 q^{54} -43.7448 q^{55} +821.196 q^{56} -334.219 q^{57} +278.784 q^{58} +401.251 q^{59} +580.096 q^{60} -219.064 q^{61} +216.779 q^{62} +198.678 q^{63} +1821.26 q^{64} -402.723 q^{66} -514.978 q^{67} +2907.20 q^{68} -996.725 q^{69} +238.004 q^{70} -86.9248 q^{71} +1353.83 q^{72} -1133.15 q^{73} -359.527 q^{74} -733.234 q^{75} -1081.03 q^{76} -120.756 q^{77} +238.321 q^{79} +930.755 q^{80} -890.107 q^{81} -925.489 q^{82} +474.884 q^{83} +1601.33 q^{84} +532.257 q^{85} -2024.81 q^{86} +343.410 q^{87} -822.856 q^{88} +58.0186 q^{89} +392.376 q^{90} -3223.91 q^{92} +267.031 q^{93} +1434.43 q^{94} -197.918 q^{95} +4549.87 q^{96} +982.259 q^{97} -1212.94 q^{98} -199.080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more