LMFDB - Embedded newform 1859.4.a.e.1.11

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 64 x^{9} + 268 x^{8} + 1564 x^{7} - 4963 x^{6} - 16942 x^{5} + 37082 x^{4} + \cdots + 16256 $ x^11 - 5x^10 - 64x^9 + 268x^8 + 1564x^7 - 4963x^6 - 16942x^5 + 37082x^4 + 68209x^3 - 90926x^2 - 1672x + 16256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$6.09923$ 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)

$f(q)$	$=$	$q+5.09923 q^{2} -3.26338 q^{3} +18.0021 q^{4} -18.2348 q^{5} -16.6407 q^{6} -29.9777 q^{7} +51.0031 q^{8} -16.3503 q^{9} +O(q^{10})$	\(q+5.09923 q^{2} -3.26338 q^{3} +18.0021 q^{4} -18.2348 q^{5} -16.6407 q^{6} -29.9777 q^{7} +51.0031 q^{8} -16.3503 q^{9} -92.9834 q^{10} -11.0000 q^{11} -58.7479 q^{12} -152.863 q^{14} +59.5072 q^{15} +116.060 q^{16} +19.4381 q^{17} -83.3740 q^{18} -94.9053 q^{19} -328.265 q^{20} +97.8288 q^{21} -56.0915 q^{22} -179.289 q^{23} -166.443 q^{24} +207.508 q^{25} +141.469 q^{27} -539.662 q^{28} +90.3548 q^{29} +303.441 q^{30} +259.905 q^{31} +183.789 q^{32} +35.8972 q^{33} +99.1191 q^{34} +546.637 q^{35} -294.340 q^{36} -212.422 q^{37} -483.944 q^{38} -930.032 q^{40} +234.195 q^{41} +498.851 q^{42} +305.510 q^{43} -198.023 q^{44} +298.145 q^{45} -914.237 q^{46} -222.720 q^{47} -378.747 q^{48} +555.663 q^{49} +1058.13 q^{50} -63.4339 q^{51} -36.5237 q^{53} +721.382 q^{54} +200.583 q^{55} -1528.96 q^{56} +309.713 q^{57} +460.740 q^{58} +175.175 q^{59} +1071.26 q^{60} +173.729 q^{61} +1325.32 q^{62} +490.145 q^{63} +8.70598 q^{64} +183.048 q^{66} -773.117 q^{67} +349.927 q^{68} +585.090 q^{69} +2787.43 q^{70} +1121.34 q^{71} -833.917 q^{72} -816.392 q^{73} -1083.19 q^{74} -677.178 q^{75} -1708.50 q^{76} +329.755 q^{77} -88.8016 q^{79} -2116.32 q^{80} -20.2085 q^{81} +1194.21 q^{82} -276.084 q^{83} +1761.13 q^{84} -354.449 q^{85} +1557.86 q^{86} -294.862 q^{87} -561.034 q^{88} -376.590 q^{89} +1520.31 q^{90} -3227.59 q^{92} -848.171 q^{93} -1135.70 q^{94} +1730.58 q^{95} -599.774 q^{96} -793.710 q^{97} +2833.45 q^{98} +179.854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) $ 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9 + 48 * q^10 - 121 * q^11 + 105 * q^12 - 48 * q^14 + 125 * q^15 + 394 * q^16 + 265 * q^17 - 405 * q^18 - 127 * q^19 + 46 * q^20 + 287 * q^21 + 66 * q^22 + 42 * q^23 + 83 * q^24 + 737 * q^25 + 69 * q^27 - 675 * q^28 + 435 * q^29 + 785 * q^30 + 174 * q^31 - 315 * q^32 - 66 * q^33 - 497 * q^34 + 844 * q^35 + 1572 * q^36 - 187 * q^37 - 1813 * q^38 - 1470 * q^40 - 128 * q^41 - 2630 * q^42 + 696 * q^43 - 726 * q^44 + 1537 * q^45 - 785 * q^46 + 355 * q^47 - 516 * q^48 + 1758 * q^49 + 3414 * q^50 - 25 * q^51 - 693 * q^53 + 4150 * q^54 - 44 * q^55 - 3123 * q^56 - 99 * q^57 + 287 * q^58 + 609 * q^59 + 5013 * q^60 + 1625 * q^61 - 882 * q^62 - 1365 * q^63 - 914 * q^64 - 154 * q^66 - 633 * q^67 + 2873 * q^68 - 2192 * q^69 + 2054 * q^70 + 1937 * q^71 - 3242 * q^72 - 404 * q^73 - 447 * q^74 + 1781 * q^75 + 1814 * q^76 + 495 * q^77 + 1670 * q^79 + 1568 * q^80 + 2619 * q^81 + 1283 * q^82 - 785 * q^83 + 11750 * q^84 - 3189 * q^85 + 5950 * q^86 + 46 * q^87 + 858 * q^88 - 1464 * q^89 + 401 * q^90 - 3786 * q^92 - 1826 * q^93 - 2597 * q^94 - 2356 * q^95 - 4513 * q^96 - 1184 * q^97 - 2823 * 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 $

$2$	5.09923	1.80285	0.901425	−	0.432936i	$-0.142522\pi$
$2$	5.09923	1.80285	0.901425	+	0.432936i	$0.142522\pi$
$3$	−3.26338	−0.628039	−0.314019	−	0.949417i	$-0.601676\pi$
$3$	−3.26338	−0.628039	−0.314019	+	0.949417i	$0.601676\pi$
$4$	18.0021	2.25027
$5$	−18.2348	−1.63097	−0.815485	−	0.578778i	$-0.803530\pi$
$5$	−18.2348	−1.63097	−0.815485	+	0.578778i	$0.803530\pi$
$6$	−16.6407	−1.13226
$7$	−29.9777	−1.61864	−0.809322	−	0.587365i	$-0.800165\pi$
$7$	−29.9777	−1.61864	−0.809322	+	0.587365i	$0.800165\pi$
$8$	51.0031	2.25404
$9$	−16.3503	−0.605567
$10$	−92.9834	−2.94039
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−58.7479	−1.41325
$13$	0	0
$13$	0	0
$14$	−152.863	−2.91817
$15$	59.5072	1.02431
$16$	116.060	1.81343
$17$	19.4381	0.277319	0.138660	−	0.990340i	$-0.455721\pi$
$17$	19.4381	0.277319	0.138660	+	0.990340i	$0.455721\pi$
$18$	−83.3740	−1.09175
$19$	−94.9053	−1.14594	−0.572968	−	0.819578i	$-0.694208\pi$
$19$	−94.9053	−1.14594	−0.572968	+	0.819578i	$0.694208\pi$
$20$	−328.265	−3.67012
$21$	97.8288	1.01657
$22$	−56.0915	−0.543580
$23$	−179.289	−1.62541	−0.812704	−	0.582677i	$-0.802005\pi$
$23$	−179.289	−1.62541	−0.812704	+	0.582677i	$0.802005\pi$
$24$	−166.443	−1.41562
$25$	207.508	1.66006
$26$	0	0
$27$	141.469	1.00836
$28$	−539.662	−3.64238
$29$	90.3548	0.578568	0.289284	−	0.957243i	$-0.406583\pi$
$29$	90.3548	0.578568	0.289284	+	0.957243i	$0.406583\pi$
$30$	303.441	1.84668
$31$	259.905	1.50582	0.752909	−	0.658124i	$-0.228650\pi$
$31$	259.905	1.50582	0.752909	+	0.658124i	$0.228650\pi$
$32$	183.789	1.01530
$33$	35.8972	0.189361
$34$	99.1191	0.499964
$35$	546.637	2.63996
$36$	−294.340	−1.36269
$37$	−212.422	−0.943838	−0.471919	−	0.881642i	$-0.656438\pi$
$37$	−212.422	−0.943838	−0.471919	+	0.881642i	$0.656438\pi$
$38$	−483.944	−2.06595
$39$	0	0
$40$	−930.032	−3.67627
$41$	234.195	0.892075	0.446037	−	0.895014i	$-0.352835\pi$
$41$	234.195	0.892075	0.446037	+	0.895014i	$0.352835\pi$
$42$	498.851	1.83272
$43$	305.510	1.08348	0.541742	−	0.840545i	$-0.317765\pi$
$43$	305.510	1.08348	0.541742	+	0.840545i	$0.317765\pi$
$44$	−198.023	−0.678481
$45$	298.145	0.987662
$46$	−914.237	−2.93037
$47$	−222.720	−0.691213	−0.345607	−	0.938380i	$-0.612327\pi$
$47$	−222.720	−0.691213	−0.345607	+	0.938380i	$0.612327\pi$
$48$	−378.747	−1.13890
$49$	555.663	1.62001
$50$	1058.13	2.99285
$51$	−63.4339	−0.174167
$52$	0	0
$53$	−36.5237	−0.0946589	−0.0473294	−	0.998879i	$-0.515071\pi$
$53$	−36.5237	−0.0946589	−0.0473294	+	0.998879i	$0.515071\pi$
$54$	721.382	1.81792
$55$	200.583	0.491756
$56$	−1528.96	−3.64849
$57$	309.713	0.719692
$58$	460.740	1.04307
$59$	175.175	0.386540	0.193270	−	0.981146i	$-0.438091\pi$
$59$	175.175	0.386540	0.193270	+	0.981146i	$0.438091\pi$
$60$	1071.26	2.30498
$61$	173.729	0.364652	0.182326	−	0.983238i	$-0.441637\pi$
$61$	173.729	0.364652	0.182326	+	0.983238i	$0.441637\pi$
$62$	1325.32	2.71476
$63$	490.145	0.980198
$64$	8.70598	0.0170039
$65$	0	0
$66$	183.048	0.341389
$67$	−773.117	−1.40972	−0.704860	−	0.709346i	$-0.748990\pi$
$67$	−773.117	−1.40972	−0.704860	+	0.709346i	$0.748990\pi$
$68$	349.927	0.624041
$69$	585.090	1.02082
$70$	2787.43	4.75945
$71$	1121.34	1.87435	0.937173	−	0.348866i	$-0.113433\pi$
$71$	1121.34	1.87435	0.937173	+	0.348866i	$0.113433\pi$
$72$	−833.917	−1.36497
$73$	−816.392	−1.30892	−0.654462	−	0.756095i	$-0.727105\pi$
$73$	−816.392	−1.30892	−0.654462	+	0.756095i	$0.727105\pi$
$74$	−1083.19	−1.70160
$75$	−677.178	−1.04258
$76$	−1708.50	−2.57866
$77$	329.755	0.488039
$78$	0	0
$79$	−88.8016	−0.126468	−0.0632339	−	0.997999i	$-0.520141\pi$
$79$	−88.8016	−0.126468	−0.0632339	+	0.997999i	$0.520141\pi$
$80$	−2116.32	−2.95765
$81$	−20.2085	−0.0277208
$82$	1194.21	1.60828
$83$	−276.084	−0.365110	−0.182555	−	0.983196i	$-0.558437\pi$
$83$	−276.084	−0.365110	−0.182555	+	0.983196i	$0.558437\pi$
$84$	1761.13	2.28755
$85$	−354.449	−0.452299
$86$	1557.86	1.95336
$87$	−294.862	−0.363363
$88$	−561.034	−0.679619
$89$	−376.590	−0.448522	−0.224261	−	0.974529i	$-0.571997\pi$
$89$	−376.590	−0.448522	−0.224261	+	0.974529i	$0.571997\pi$
$90$	1520.31	1.78061
$91$	0	0
$92$	−3227.59	−3.65760
$93$	−848.171	−0.945712
$94$	−1135.70	−1.24615
$95$	1730.58	1.86899
$96$	−599.774	−0.637648
$97$	−793.710	−0.830815	−0.415407	−	0.909635i	$-0.636361\pi$
$97$	−793.710	−0.830815	−0.415407	+	0.909635i	$0.636361\pi$
$98$	2833.45	2.92063
$99$	179.854	0.182585
$100$	3735.59	3.73559
$101$	917.556	0.903963	0.451981	−	0.892027i	$-0.350717\pi$
$101$	917.556	0.903963	0.451981	+	0.892027i	$0.350717\pi$
$102$	−323.464	−0.313997
$103$	−109.316	−0.104575	−0.0522874	−	0.998632i	$-0.516651\pi$
$103$	−109.316	−0.104575	−0.0522874	+	0.998632i	$0.516651\pi$
$104$	0	0
$105$	−1783.89	−1.65800
$106$	−186.243	−0.170656
$107$	−1470.21	−1.32832	−0.664160	−	0.747590i	$-0.731211\pi$
$107$	−1470.21	−1.32832	−0.664160	+	0.747590i	$0.731211\pi$
$108$	2546.74	2.26907
$109$	1321.91	1.16162	0.580808	−	0.814041i	$-0.302737\pi$
$109$	1321.91	1.16162	0.580808	+	0.814041i	$0.302737\pi$
$110$	1022.82	0.886562
$111$	693.215	0.592767
$112$	−3479.20	−2.93530
$113$	1430.99	1.19129	0.595646	−	0.803247i	$-0.296896\pi$
$113$	1430.99	1.19129	0.595646	+	0.803247i	$0.296896\pi$
$114$	1579.29	1.29750
$115$	3269.30	2.65099
$116$	1626.58	1.30193
$117$	0	0
$118$	893.259	0.696874
$119$	−582.709	−0.448881
$120$	3035.05	2.30884
$121$	121.000	0.0909091
$122$	885.885	0.657412
$123$	−764.267	−0.560257
$124$	4678.85	3.38849
$125$	−1504.52	−1.07654
$126$	2499.36	1.76715
$127$	−1812.55	−1.26644	−0.633218	−	0.773974i	$-0.718266\pi$
$127$	−1812.55	−1.26644	−0.633218	+	0.773974i	$0.718266\pi$
$128$	−1425.92	−0.984645
$129$	−996.996	−0.680470
$130$	0	0
$131$	1586.78	1.05831	0.529153	−	0.848527i	$-0.322510\pi$
$131$	1586.78	1.05831	0.529153	+	0.848527i	$0.322510\pi$
$132$	646.227	0.426112
$133$	2845.04	1.85486
$134$	−3942.30	−2.54151
$135$	−2579.66	−1.64460
$136$	991.402	0.625088
$137$	468.055	0.291888	0.145944	−	0.989293i	$-0.453378\pi$
$137$	468.055	0.291888	0.145944	+	0.989293i	$0.453378\pi$
$138$	2983.51	1.84038
$139$	−1195.19	−0.729313	−0.364657	−	0.931142i	$-0.618814\pi$
$139$	−1195.19	−0.729313	−0.364657	+	0.931142i	$0.618814\pi$
$140$	9840.64	5.94061
$141$	726.820	0.434109
$142$	5717.97	3.37916
$143$	0	0
$144$	−1897.61	−1.09815
$145$	−1647.60	−0.943627
$146$	−4162.97	−2.35979
$147$	−1813.34	−1.01743
$148$	−3824.05	−2.12389
$149$	−399.410	−0.219604	−0.109802	−	0.993954i	$-0.535022\pi$
$149$	−399.410	−0.219604	−0.109802	+	0.993954i	$0.535022\pi$
$150$	−3453.09	−1.87962
$151$	1486.27	0.801001	0.400501	−	0.916297i	$-0.368836\pi$
$151$	1486.27	0.801001	0.400501	+	0.916297i	$0.368836\pi$
$152$	−4840.47	−2.58298
$153$	−317.819	−0.167935
$154$	1681.49	0.879862
$155$	−4739.32	−2.45594
$156$	0	0
$157$	−520.075	−0.264373	−0.132186	−	0.991225i	$-0.542200\pi$
$157$	−520.075	−0.264373	−0.132186	+	0.991225i	$0.542200\pi$
$158$	−452.819	−0.228002
$159$	119.191	0.0594494
$160$	−3351.36	−1.65593
$161$	5374.68	2.63096
$162$	−103.048	−0.0499765
$163$	2773.77	1.33287	0.666436	−	0.745562i	$-0.267819\pi$
$163$	2773.77	1.33287	0.666436	+	0.745562i	$0.267819\pi$
$164$	4216.00	2.00741
$165$	−654.579	−0.308842
$166$	−1407.82	−0.658239
$167$	560.240	0.259597	0.129798	−	0.991540i	$-0.458567\pi$
$167$	560.240	0.259597	0.129798	+	0.991540i	$0.458567\pi$
$168$	4989.57	2.29139
$169$	0	0
$170$	−1807.42	−0.815427
$171$	1551.73	0.693941
$172$	5499.83	2.43813
$173$	2310.65	1.01547	0.507733	−	0.861514i	$-0.330484\pi$
$173$	2310.65	1.01547	0.507733	+	0.861514i	$0.330484\pi$
$174$	−1503.57	−0.655089
$175$	−6220.61	−2.68705
$176$	−1276.65	−0.546770
$177$	−571.664	−0.242762
$178$	−1920.32	−0.808617
$179$	−4688.97	−1.95794	−0.978968	−	0.204016i	$-0.934601\pi$
$179$	−4688.97	−1.95794	−0.978968	+	0.204016i	$0.934601\pi$
$180$	5367.24	2.22250
$181$	1023.21	0.420191	0.210096	−	0.977681i	$-0.432622\pi$
$181$	1023.21	0.420191	0.210096	+	0.977681i	$0.432622\pi$
$182$	0	0
$183$	−566.946	−0.229015
$184$	−9144.31	−3.66374
$185$	3873.48	1.53937
$186$	−4325.02	−1.70498
$187$	−213.819	−0.0836148
$188$	−4009.43	−1.55541
$189$	−4240.91	−1.63217
$190$	8824.62	3.36950
$191$	−4083.15	−1.54684	−0.773420	−	0.633894i	$-0.781456\pi$
$191$	−4083.15	−1.54684	−0.773420	+	0.633894i	$0.781456\pi$
$192$	−28.4110	−0.0106791
$193$	2470.14	0.921266	0.460633	−	0.887591i	$-0.347622\pi$
$193$	2470.14	0.921266	0.460633	+	0.887591i	$0.347622\pi$
$194$	−4047.31	−1.49783
$195$	0	0
$196$	10003.1	3.64545
$197$	−2272.98	−0.822048	−0.411024	−	0.911625i	$-0.634829\pi$
$197$	−2272.98	−0.822048	−0.411024	+	0.911625i	$0.634829\pi$
$198$	917.114	0.329174
$199$	3285.32	1.17030	0.585150	−	0.810925i	$-0.301035\pi$
$199$	3285.32	1.17030	0.585150	+	0.810925i	$0.301035\pi$
$200$	10583.6	3.74185
$201$	2522.98	0.885359
$202$	4678.83	1.62971
$203$	−2708.63	−0.936495
$204$	−1141.94	−0.391922
$205$	−4270.49	−1.45495
$206$	−557.426	−0.188533
$207$	2931.44	0.984294
$208$	0	0
$209$	1043.96	0.345513
$210$	−9096.45	−2.98912
$211$	2369.93	0.773236	0.386618	−	0.922240i	$-0.373643\pi$
$211$	2369.93	0.773236	0.386618	+	0.922240i	$0.373643\pi$
$212$	−657.505	−0.213008
$213$	−3659.36	−1.17716
$214$	−7496.92	−2.39476
$215$	−5570.91	−1.76713
$216$	7215.35	2.27288
$217$	−7791.36	−2.43738
$218$	6740.72	2.09422
$219$	2664.20	0.822055
$220$	3610.92	1.10658
$221$	0	0
$222$	3534.86	1.06867
$223$	790.841	0.237483	0.118741	−	0.992925i	$-0.462114\pi$
$223$	790.841	0.237483	0.118741	+	0.992925i	$0.462114\pi$
$224$	−5509.57	−1.64341
$225$	−3392.82	−1.00528
$226$	7296.93	2.14772
$227$	1016.15	0.297111	0.148555	−	0.988904i	$-0.452538\pi$
$227$	1016.15	0.297111	0.148555	+	0.988904i	$0.452538\pi$
$228$	5575.48	1.61950
$229$	4103.08	1.18401	0.592007	−	0.805933i	$-0.298336\pi$
$229$	4103.08	1.18401	0.592007	+	0.805933i	$0.298336\pi$
$230$	16670.9	4.77934
$231$	−1076.12	−0.306508
$232$	4608.38	1.30412
$233$	3355.91	0.943574	0.471787	−	0.881713i	$-0.343609\pi$
$233$	3355.91	0.943574	0.471787	+	0.881713i	$0.343609\pi$
$234$	0	0
$235$	4061.25	1.12735
$236$	3153.53	0.869818
$237$	289.794	0.0794267
$238$	−2971.36	−0.809264
$239$	−5909.10	−1.59928	−0.799640	−	0.600479i	$-0.794976\pi$
$239$	−5909.10	−1.59928	−0.799640	+	0.600479i	$0.794976\pi$
$240$	6906.38	1.85752
$241$	1778.48	0.475361	0.237680	−	0.971343i	$-0.423613\pi$
$241$	1778.48	0.475361	0.237680	+	0.971343i	$0.423613\pi$
$242$	617.007	0.163895
$243$	−3753.71	−0.990949
$244$	3127.50	0.820563
$245$	−10132.4	−2.64218
$246$	−3897.17	−1.01006
$247$	0	0
$248$	13256.0	3.39418
$249$	900.969	0.229304
$250$	−7671.87	−1.94085
$251$	6866.72	1.72679	0.863393	−	0.504532i	$-0.168335\pi$
$251$	6866.72	1.72679	0.863393	+	0.504532i	$0.168335\pi$
$252$	8823.65	2.20571
$253$	1972.18	0.490079
$254$	−9242.58	−2.28319
$255$	1156.70	0.284061
$256$	−7340.73	−1.79217
$257$	−3516.47	−0.853506	−0.426753	−	0.904368i	$-0.640343\pi$
$257$	−3516.47	−0.853506	−0.426753	+	0.904368i	$0.640343\pi$
$258$	−5083.91	−1.22679
$259$	6367.93	1.52774
$260$	0	0
$261$	−1477.33	−0.350362
$262$	8091.37	1.90796
$263$	−5940.77	−1.39287	−0.696433	−	0.717622i	$-0.745231\pi$
$263$	−5940.77	−1.39287	−0.696433	+	0.717622i	$0.745231\pi$
$264$	1830.87	0.426827
$265$	666.003	0.154386
$266$	14507.5	3.34404
$267$	1228.96	0.281689
$268$	−13917.8	−3.17225
$269$	2777.92	0.629638	0.314819	−	0.949152i	$-0.398056\pi$
$269$	2777.92	0.629638	0.314819	+	0.949152i	$0.398056\pi$
$270$	−13154.2	−2.96497
$271$	615.293	0.137920	0.0689601	−	0.997619i	$-0.478032\pi$
$271$	615.293	0.137920	0.0689601	+	0.997619i	$0.478032\pi$
$272$	2255.97	0.502899
$273$	0	0
$274$	2386.72	0.526229
$275$	−2282.59	−0.500528
$276$	10532.9	2.29711
$277$	−4917.70	−1.06670	−0.533350	−	0.845895i	$-0.679067\pi$
$277$	−4917.70	−1.06670	−0.533350	+	0.845895i	$0.679067\pi$
$278$	−6094.54	−1.31484
$279$	−4249.53	−0.911874
$280$	27880.2	5.95058
$281$	−2167.87	−0.460228	−0.230114	−	0.973164i	$-0.573910\pi$
$281$	−2167.87	−0.460228	−0.230114	+	0.973164i	$0.573910\pi$
$282$	3706.22	0.782632
$283$	−635.027	−0.133387	−0.0666933	−	0.997774i	$-0.521245\pi$
$283$	−635.027	−0.133387	−0.0666933	+	0.997774i	$0.521245\pi$
$284$	20186.5	4.21777
$285$	−5647.55	−1.17380
$286$	0	0
$287$	−7020.62	−1.44395
$288$	−3005.01	−0.614833
$289$	−4535.16	−0.923094
$290$	−8401.50	−1.70122
$291$	2590.18	0.521784
$292$	−14696.8	−2.94543
$293$	−5394.05	−1.07551	−0.537754	−	0.843102i	$-0.680727\pi$
$293$	−5394.05	−1.07551	−0.537754	+	0.843102i	$0.680727\pi$
$294$	−9246.64	−1.83427
$295$	−3194.29	−0.630436
$296$	−10834.2	−2.12745
$297$	−1556.16	−0.304032
$298$	−2036.68	−0.395912
$299$	0	0
$300$	−12190.7	−2.34609
$301$	−9158.49	−1.75378
$302$	7578.84	1.44408
$303$	−2994.34	−0.567724
$304$	−11014.7	−2.07807
$305$	−3167.92	−0.594736
$306$	−1620.63	−0.302762
$307$	−538.274	−0.100068	−0.0500341	−	0.998748i	$-0.515933\pi$
$307$	−538.274	−0.100068	−0.0500341	+	0.998748i	$0.515933\pi$
$308$	5936.29	1.09822
$309$	356.739	0.0656770
$310$	−24166.9	−4.42770
$311$	−997.613	−0.181895	−0.0909477	−	0.995856i	$-0.528990\pi$
$311$	−997.613	−0.181895	−0.0909477	+	0.995856i	$0.528990\pi$
$312$	0	0
$313$	−1524.60	−0.275322	−0.137661	−	0.990479i	$-0.543958\pi$
$313$	−1524.60	−0.275322	−0.137661	+	0.990479i	$0.543958\pi$
$314$	−2651.98	−0.476624
$315$	−8937.70	−1.59867
$316$	−1598.62	−0.284586
$317$	4457.20	0.789721	0.394860	−	0.918741i	$-0.370793\pi$
$317$	4457.20	0.789721	0.394860	+	0.918741i	$0.370793\pi$
$318$	607.782	0.107178
$319$	−993.903	−0.174445
$320$	−158.752	−0.0277328
$321$	4797.85	0.834237
$322$	27406.7	4.74322
$323$	−1844.78	−0.317790
$324$	−363.796	−0.0623793
$325$	0	0
$326$	14144.1	2.40297
$327$	−4313.90	−0.729539
$328$	11944.7	2.01077
$329$	6676.63	1.11883
$330$	−3337.85	−0.556795
$331$	−308.201	−0.0511791	−0.0255895	−	0.999673i	$-0.508146\pi$
$331$	−308.201	−0.0511791	−0.0255895	+	0.999673i	$0.508146\pi$
$332$	−4970.10	−0.821596
$333$	3473.17	0.571557
$334$	2856.79	0.468014
$335$	14097.6	2.29921
$336$	11354.0	1.84348
$337$	3278.03	0.529868	0.264934	−	0.964267i	$-0.414650\pi$
$337$	3278.03	0.529868	0.264934	+	0.964267i	$0.414650\pi$
$338$	0	0
$339$	−4669.86	−0.748177
$340$	−6380.84	−1.01779
$341$	−2858.96	−0.454021
$342$	7912.64	1.25107
$343$	−6375.14	−1.00357
$344$	15582.0	2.44222
$345$	−10669.0	−1.66493
$346$	11782.5	1.83073
$347$	−7069.22	−1.09365	−0.546824	−	0.837248i	$-0.684163\pi$
$347$	−7069.22	−1.09365	−0.546824	+	0.837248i	$0.684163\pi$
$348$	−5308.15	−0.817663
$349$	5822.01	0.892965	0.446483	−	0.894792i	$-0.352676\pi$
$349$	5822.01	0.892965	0.446483	+	0.894792i	$0.352676\pi$
$350$	−31720.3	−4.84435
$351$	0	0
$352$	−2021.68	−0.306125
$353$	7098.02	1.07022	0.535112	−	0.844781i	$-0.320269\pi$
$353$	7098.02	1.07022	0.535112	+	0.844781i	$0.320269\pi$
$354$	−2915.05	−0.437664
$355$	−20447.4	−3.05700
$356$	−6779.41	−1.00929
$357$	1901.60	0.281914
$358$	−23910.1	−3.52986
$359$	11618.5	1.70808	0.854040	−	0.520207i	$-0.174145\pi$
$359$	11618.5	1.70808	0.854040	+	0.520207i	$0.174145\pi$
$360$	15206.3	2.22623
$361$	2148.02	0.313168
$362$	5217.58	0.757541
$363$	−394.870	−0.0570944
$364$	0	0
$365$	14886.8	2.13482
$366$	−2890.98	−0.412880
$367$	−6680.49	−0.950188	−0.475094	−	0.879935i	$-0.657586\pi$
$367$	−6680.49	−0.950188	−0.475094	+	0.879935i	$0.657586\pi$
$368$	−20808.2	−2.94756
$369$	−3829.16	−0.540211
$370$	19751.7	2.77525
$371$	1094.90	0.153219
$372$	−15268.9	−2.12810
$373$	−9090.83	−1.26195	−0.630973	−	0.775805i	$-0.717344\pi$
$373$	−9090.83	−1.26195	−0.630973	+	0.775805i	$0.717344\pi$
$374$	−1090.31	−0.150745
$375$	4909.82	0.676112
$376$	−11359.4	−1.55802
$377$	0	0
$378$	−21625.4	−2.94256
$379$	3418.99	0.463381	0.231691	−	0.972790i	$-0.425574\pi$
$379$	3418.99	0.463381	0.231691	+	0.972790i	$0.425574\pi$
$380$	31154.1	4.20572
$381$	5915.03	0.795371
$382$	−20820.9	−2.78872
$383$	−485.274	−0.0647424	−0.0323712	−	0.999476i	$-0.510306\pi$
$383$	−485.274	−0.0647424	−0.0323712	+	0.999476i	$0.510306\pi$
$384$	4653.32	0.618395
$385$	−6013.01	−0.795978
$386$	12595.8	1.66090
$387$	−4995.18	−0.656123
$388$	−14288.5	−1.86955
$389$	7132.62	0.929661	0.464831	−	0.885400i	$-0.346115\pi$
$389$	7132.62	0.929661	0.464831	+	0.885400i	$0.346115\pi$
$390$	0	0
$391$	−3485.04	−0.450757
$392$	28340.5	3.65156
$393$	−5178.29	−0.664657
$394$	−11590.5	−1.48203
$395$	1619.28	0.206265
$396$	3237.75	0.410866
$397$	12204.4	1.54287	0.771434	−	0.636309i	$-0.219540\pi$
$397$	12204.4	1.54287	0.771434	+	0.636309i	$0.219540\pi$
$398$	16752.6	2.10988
$399$	−9284.47	−1.16492
$400$	24083.3	3.01041
$401$	−2610.95	−0.325149	−0.162575	−	0.986696i	$-0.551980\pi$
$401$	−2610.95	−0.325149	−0.162575	+	0.986696i	$0.551980\pi$
$402$	12865.2	1.59617
$403$	0	0
$404$	16518.0	2.03416
$405$	368.498	0.0452119
$406$	−13811.9	−1.68836
$407$	2336.64	0.284578
$408$	−3235.33	−0.392580
$409$	−3783.03	−0.457356	−0.228678	−	0.973502i	$-0.573440\pi$
$409$	−3783.03	−0.457356	−0.228678	+	0.973502i	$0.573440\pi$
$410$	−21776.2	−2.62305
$411$	−1527.44	−0.183317
$412$	−1967.92	−0.235321
$413$	−5251.35	−0.625671
$414$	14948.1	1.77453
$415$	5034.34	0.595484
$416$	0	0
$417$	3900.36	0.458037
$418$	5323.38	0.622907
$419$	492.553	0.0574291	0.0287145	−	0.999588i	$-0.490859\pi$
$419$	492.553	0.0574291	0.0287145	+	0.999588i	$0.490859\pi$
$420$	−32113.8	−3.73093
$421$	3255.75	0.376901	0.188451	−	0.982083i	$-0.439653\pi$
$421$	3255.75	0.376901	0.188451	+	0.982083i	$0.439653\pi$
$422$	12084.8	1.39403
$423$	3641.54	0.418576
$424$	−1862.82	−0.213365
$425$	4033.55	0.460367
$426$	−18659.9	−2.12224
$427$	−5208.01	−0.590241
$428$	−26466.9	−2.98907
$429$	0	0
$430$	−28407.4	−3.18587
$431$	17457.0	1.95098	0.975492	−	0.220033i	$-0.0706165\pi$
$431$	17457.0	1.95098	0.975492	+	0.220033i	$0.0706165\pi$
$432$	16418.8	1.82859
$433$	181.735	0.0201701	0.0100850	−	0.999949i	$-0.496790\pi$
$433$	181.735	0.0201701	0.0100850	+	0.999949i	$0.496790\pi$
$434$	−39729.9	−4.39424
$435$	5376.76	0.592634
$436$	23797.2	2.61394
$437$	17015.5	1.86261
$438$	13585.4	1.48204
$439$	7494.12	0.814749	0.407374	−	0.913261i	$-0.366444\pi$
$439$	7494.12	0.814749	0.407374	+	0.913261i	$0.366444\pi$
$440$	10230.3	1.10844
$441$	−9085.26	−0.981024
$442$	0	0
$443$	−2677.27	−0.287135	−0.143568	−	0.989640i	$-0.545857\pi$
$443$	−2677.27	−0.287135	−0.143568	+	0.989640i	$0.545857\pi$
$444$	12479.4	1.33388
$445$	6867.04	0.731525
$446$	4032.68	0.428145
$447$	1303.43	0.137920
$448$	−260.985	−0.0275232
$449$	−8738.34	−0.918458	−0.459229	−	0.888318i	$-0.651874\pi$
$449$	−8738.34	−0.918458	−0.459229	+	0.888318i	$0.651874\pi$
$450$	−17300.8	−1.81237
$451$	−2576.14	−0.268971
$452$	25760.8	2.68072
$453$	−4850.28	−0.503060
$454$	5181.58	0.535646
$455$	0	0
$456$	15796.3	1.62221
$457$	5170.94	0.529292	0.264646	−	0.964346i	$-0.414745\pi$
$457$	5170.94	0.529292	0.264646	+	0.964346i	$0.414745\pi$
$458$	20922.5	2.13460
$459$	2749.88	0.279637
$460$	58854.4	5.96544
$461$	11583.5	1.17027	0.585137	−	0.810935i	$-0.301041\pi$
$461$	11583.5	1.17027	0.585137	+	0.810935i	$0.301041\pi$
$462$	−5487.36	−0.552587
$463$	−11419.2	−1.14621	−0.573106	−	0.819481i	$-0.694262\pi$
$463$	−11419.2	−1.14621	−0.573106	+	0.819481i	$0.694262\pi$
$464$	10486.5	1.04919
$465$	15466.2	1.54243
$466$	17112.5	1.70112
$467$	7698.58	0.762844	0.381422	−	0.924401i	$-0.375435\pi$
$467$	7698.58	0.762844	0.381422	+	0.924401i	$0.375435\pi$
$468$	0	0
$469$	23176.3	2.28184
$470$	20709.2	2.03244
$471$	1697.21	0.166036
$472$	8934.49	0.871278
$473$	−3360.61	−0.326683
$474$	1477.72	0.143194
$475$	−19693.6	−1.90233
$476$	−10490.0	−1.01010
$477$	597.175	0.0573223
$478$	−30131.9	−2.88326
$479$	12684.3	1.20994	0.604971	−	0.796248i	$-0.293185\pi$
$479$	12684.3	1.20994	0.604971	+	0.796248i	$0.293185\pi$
$480$	10936.8	1.03999
$481$	0	0
$482$	9068.87	0.857004
$483$	−17539.6	−1.65234
$484$	2178.26	0.204570
$485$	14473.1	1.35503
$486$	−19141.0	−1.78653
$487$	8331.58	0.775236	0.387618	−	0.921820i	$-0.373298\pi$
$487$	8331.58	0.775236	0.387618	+	0.921820i	$0.373298\pi$
$488$	8860.74	0.821940
$489$	−9051.87	−0.837096
$490$	−51667.4	−4.76346
$491$	−4003.46	−0.367970	−0.183985	−	0.982929i	$-0.558900\pi$
$491$	−4003.46	−0.367970	−0.183985	+	0.982929i	$0.558900\pi$
$492$	−13758.4	−1.26073
$493$	1756.32	0.160448
$494$	0	0
$495$	−3279.59	−0.297791
$496$	30164.5	2.73070
$497$	−33615.2	−3.03390
$498$	4594.24	0.413400
$499$	8016.96	0.719215	0.359607	−	0.933104i	$-0.382911\pi$
$499$	8016.96	0.719215	0.359607	+	0.933104i	$0.382911\pi$
$500$	−27084.5	−2.42251
$501$	−1828.28	−0.163037
$502$	35014.9	3.11313
$503$	6609.88	0.585925	0.292962	−	0.956124i	$-0.405359\pi$
$503$	6609.88	0.585925	0.292962	+	0.956124i	$0.405359\pi$
$504$	24998.9	2.20941
$505$	−16731.5	−1.47434
$506$	10056.6	0.883539
$507$	0	0
$508$	−32629.7	−2.84982
$509$	−14143.9	−1.23166	−0.615831	−	0.787878i	$-0.711180\pi$
$509$	−14143.9	−1.23166	−0.615831	+	0.787878i	$0.711180\pi$
$510$	5898.30	0.512120
$511$	24473.6	2.11868
$512$	−26024.7	−2.24637
$513$	−13426.1	−1.15551
$514$	−17931.3	−1.53874
$515$	1993.35	0.170558
$516$	−17948.1	−1.53124
$517$	2449.92	0.208409
$518$	32471.5	2.75428
$519$	−7540.55	−0.637752
$520$	0	0
$521$	1511.29	0.127084	0.0635421	−	0.997979i	$-0.479760\pi$
$521$	1511.29	0.127084	0.0635421	+	0.997979i	$0.479760\pi$
$522$	−7533.24	−0.631649
$523$	−9516.70	−0.795671	−0.397836	−	0.917457i	$-0.630239\pi$
$523$	−9516.70	−0.795671	−0.397836	+	0.917457i	$0.630239\pi$
$524$	28565.5	2.38147
$525$	20300.3	1.68757
$526$	−30293.4	−2.51113
$527$	5052.06	0.417592
$528$	4166.22	0.343393
$529$	19977.6	1.64195
$530$	3396.10	0.278334
$531$	−2864.17	−0.234076
$532$	51216.8	4.17393
$533$	0	0
$534$	6266.73	0.507843
$535$	26808.9	2.16645
$536$	−39431.4	−3.17757
$537$	15301.9	1.22966
$538$	14165.2	1.13514
$539$	−6112.29	−0.488451
$540$	−46439.3	−3.70079
$541$	−3720.66	−0.295681	−0.147841	−	0.989011i	$-0.547232\pi$
$541$	−3720.66	−0.295681	−0.147841	+	0.989011i	$0.547232\pi$
$542$	3137.52	0.248649
$543$	−3339.13	−0.263896
$544$	3572.50	0.281562
$545$	−24104.8	−1.89456
$546$	0	0
$547$	20271.6	1.58456	0.792278	−	0.610160i	$-0.208895\pi$
$547$	20271.6	1.58456	0.792278	+	0.610160i	$0.208895\pi$
$548$	8425.98	0.656825
$549$	−2840.53	−0.220821
$550$	−11639.4	−0.902377
$551$	−8575.15	−0.663001
$552$	29841.4	2.30097
$553$	2662.07	0.204706
$554$	−25076.5	−1.92310
$555$	−12640.6	−0.966785
$556$	−21515.9	−1.64115
$557$	−7595.31	−0.577780	−0.288890	−	0.957362i	$-0.593286\pi$
$557$	−7595.31	−0.577780	−0.288890	+	0.957362i	$0.593286\pi$
$558$	−21669.3	−1.64397
$559$	0	0
$560$	63442.5	4.78738
$561$	697.773	0.0525134
$562$	−11054.5	−0.829722
$563$	22521.5	1.68591	0.842957	−	0.537981i	$-0.180813\pi$
$563$	22521.5	1.68591	0.842957	+	0.537981i	$0.180813\pi$
$564$	13084.3	0.976860
$565$	−26093.8	−1.94296
$566$	−3238.15	−0.240476
$567$	605.804	0.0448702
$568$	57191.8	4.22485
$569$	482.001	0.0355123	0.0177562	−	0.999842i	$-0.494348\pi$
$569$	482.001	0.0355123	0.0177562	+	0.999842i	$0.494348\pi$
$570$	−28798.1	−2.11618
$571$	−9489.01	−0.695451	−0.347726	−	0.937596i	$-0.613046\pi$
$571$	−9489.01	−0.695451	−0.347726	+	0.937596i	$0.613046\pi$
$572$	0	0
$573$	13324.9	0.971476
$574$	−35799.7	−2.60323
$575$	−37203.9	−2.69828
$576$	−142.346	−0.0102970
$577$	18661.7	1.34644	0.673220	−	0.739442i	$-0.264911\pi$
$577$	18661.7	1.34644	0.673220	+	0.739442i	$0.264911\pi$
$578$	−23125.8	−1.66420
$579$	−8061.00	−0.578591
$580$	−29660.3	−2.12341
$581$	8276.37	0.590984
$582$	13207.9	0.940698
$583$	401.761	0.0285407
$584$	−41638.6	−2.95037
$585$	0	0
$586$	−27505.5	−1.93898
$587$	2243.14	0.157724	0.0788621	−	0.996886i	$-0.474871\pi$
$587$	2243.14	0.157724	0.0788621	+	0.996886i	$0.474871\pi$
$588$	−32644.0	−2.28948
$589$	−24666.4	−1.72557
$590$	−16288.4	−1.13658
$591$	7417.62	0.516278
$592$	−24653.6	−1.71158
$593$	12377.0	0.857103	0.428552	−	0.903517i	$-0.359024\pi$
$593$	12377.0	0.857103	0.428552	+	0.903517i	$0.359024\pi$
$594$	−7935.20	−0.548123
$595$	10625.6	0.732111
$596$	−7190.23	−0.494167
$597$	−10721.3	−0.734994
$598$	0	0
$599$	−9628.45	−0.656774	−0.328387	−	0.944543i	$-0.606505\pi$
$599$	−9628.45	−0.656774	−0.328387	+	0.944543i	$0.606505\pi$
$600$	−34538.2	−2.35003
$601$	7371.09	0.500288	0.250144	−	0.968209i	$-0.419522\pi$
$601$	7371.09	0.500288	0.250144	+	0.968209i	$0.419522\pi$
$602$	−46701.2	−3.16179
$603$	12640.7	0.853681
$604$	26756.1	1.80247
$605$	−2206.41	−0.148270
$606$	−15268.8	−1.02352
$607$	−3850.12	−0.257449	−0.128724	−	0.991680i	$-0.541088\pi$
$607$	−3850.12	−0.257449	−0.128724	+	0.991680i	$0.541088\pi$
$608$	−17442.6	−1.16347
$609$	8839.30	0.588155
$610$	−16153.9	−1.07222
$611$	0	0
$612$	−5721.41	−0.377899
$613$	−17029.7	−1.12206	−0.561032	−	0.827794i	$-0.689595\pi$
$613$	−17029.7	−1.12206	−0.561032	+	0.827794i	$0.689595\pi$
$614$	−2744.78	−0.180408
$615$	13936.3	0.913763
$616$	16818.5	1.10006
$617$	−23834.5	−1.55517	−0.777587	−	0.628776i	$-0.783556\pi$
$617$	−23834.5	−1.55517	−0.777587	+	0.628776i	$0.783556\pi$
$618$	1819.10	0.118406
$619$	287.420	0.0186630	0.00933148	−	0.999956i	$-0.497030\pi$
$619$	287.420	0.0186630	0.00933148	+	0.999956i	$0.497030\pi$
$620$	−85317.9	−5.52653
$621$	−25363.8	−1.63899
$622$	−5087.06	−0.327930
$623$	11289.3	0.725997
$624$	0	0
$625$	1496.07	0.0957484
$626$	−7774.30	−0.496363
$627$	−3406.84	−0.216995
$628$	−9362.46	−0.594909
$629$	−4129.08	−0.261744
$630$	−45575.4	−2.88217
$631$	4776.42	0.301341	0.150671	−	0.988584i	$-0.451857\pi$
$631$	4776.42	0.301341	0.150671	+	0.988584i	$0.451857\pi$
$632$	−4529.16	−0.285064
$633$	−7734.00	−0.485622
$634$	22728.3	1.42375
$635$	33051.4	2.06552
$636$	2145.69	0.133777
$637$	0	0
$638$	−5068.14	−0.314498
$639$	−18334.3	−1.13504
$640$	26001.3	1.60593
$641$	−14591.9	−0.899136	−0.449568	−	0.893246i	$-0.648422\pi$
$641$	−14591.9	−0.899136	−0.449568	+	0.893246i	$0.648422\pi$
$642$	24465.3	1.50400
$643$	−24853.3	−1.52429	−0.762146	−	0.647405i	$-0.775854\pi$
$643$	−24853.3	−1.52429	−0.762146	+	0.647405i	$0.775854\pi$
$644$	96755.7	5.92035
$645$	18180.0	1.10983
$646$	−9406.93	−0.572927
$647$	3573.79	0.217156	0.108578	−	0.994088i	$-0.465370\pi$
$647$	3573.79	0.217156	0.108578	+	0.994088i	$0.465370\pi$
$648$	−1030.70	−0.0624839
$649$	−1926.93	−0.116546
$650$	0	0
$651$	25426.2	1.53077
$652$	49933.7	2.99932
$653$	14004.8	0.839278	0.419639	−	0.907691i	$-0.362157\pi$
$653$	14004.8	0.839278	0.419639	+	0.907691i	$0.362157\pi$
$654$	−21997.6	−1.31525
$655$	−28934.7	−1.72606
$656$	27180.5	1.61772
$657$	13348.3	0.792642
$658$	34045.6	2.01708
$659$	7498.88	0.443270	0.221635	−	0.975130i	$-0.428861\pi$
$659$	7498.88	0.443270	0.221635	+	0.975130i	$0.428861\pi$
$660$	−11783.8	−0.694976
$661$	22575.5	1.32842	0.664211	−	0.747545i	$-0.268768\pi$
$661$	22575.5	1.32842	0.664211	+	0.747545i	$0.268768\pi$
$662$	−1571.59	−0.0922682
$663$	0	0
$664$	−14081.2	−0.822974
$665$	−51878.8	−3.02522
$666$	17710.5	1.03043
$667$	−16199.6	−0.940409
$668$	10085.5	0.584161
$669$	−2580.82	−0.149148
$670$	71887.1	4.14513
$671$	−1911.02	−0.109947
$672$	17979.9	1.03213
$673$	19283.0	1.10446	0.552231	−	0.833691i	$-0.313777\pi$
$673$	19283.0	1.10446	0.552231	+	0.833691i	$0.313777\pi$
$674$	16715.4	0.955272
$675$	29355.9	1.67394
$676$	0	0
$677$	−24238.0	−1.37598	−0.687991	−	0.725719i	$-0.741507\pi$
$677$	−24238.0	−1.37598	−0.687991	+	0.725719i	$0.741507\pi$
$678$	−23812.7	−1.34885
$679$	23793.6	1.34479
$680$	−18078.0	−1.01950
$681$	−3316.09	−0.186597
$682$	−14578.5	−0.818532
$683$	32117.5	1.79933	0.899666	−	0.436580i	$-0.143810\pi$
$683$	32117.5	1.79933	0.899666	+	0.436580i	$0.143810\pi$
$684$	27934.5	1.56155
$685$	−8534.88	−0.476060
$686$	−32508.3	−1.80929
$687$	−13389.9	−0.743606
$688$	35457.3	1.96482
$689$	0	0
$690$	−54403.6	−3.00161
$691$	−29415.4	−1.61941	−0.809707	−	0.586835i	$-0.800374\pi$
$691$	−29415.4	−1.61941	−0.809707	+	0.586835i	$0.800374\pi$
$692$	41596.7	2.28507
$693$	−5391.59	−0.295541
$694$	−36047.6	−1.97168
$695$	21794.0	1.18949
$696$	−15038.9	−0.819035
$697$	4552.29	0.247389
$698$	29687.7	1.60988
$699$	−10951.6	−0.592601
$700$	−111984.	−6.04658
$701$	−8891.19	−0.479052	−0.239526	−	0.970890i	$-0.576992\pi$
$701$	−8891.19	−0.479052	−0.239526	+	0.970890i	$0.576992\pi$
$702$	0	0
$703$	20160.0	1.08158
$704$	−95.7658	−0.00512686
$705$	−13253.4	−0.708018
$706$	36194.4	1.92945
$707$	−27506.2	−1.46319
$708$	−10291.2	−0.546280
$709$	−1699.71	−0.0900338	−0.0450169	−	0.998986i	$-0.514334\pi$
$709$	−1699.71	−0.0900338	−0.0450169	+	0.998986i	$0.514334\pi$
$710$	−104266.	−5.51131
$711$	1451.93	0.0765848
$712$	−19207.2	−1.01099
$713$	−46598.2	−2.44757
$714$	9696.70	0.508249
$715$	0	0
$716$	−84411.5	−4.40587
$717$	19283.7	1.00441
$718$	59245.4	3.07941
$719$	26223.5	1.36018	0.680091	−	0.733127i	$-0.261940\pi$
$719$	26223.5	1.36018	0.680091	+	0.733127i	$0.261940\pi$
$720$	34602.5	1.79106
$721$	3277.03	0.169269
$722$	10953.2	0.564594
$723$	−5803.86	−0.298545
$724$	18420.0	0.945542
$725$	18749.3	0.960459
$726$	−2013.53	−0.102933
$727$	29843.4	1.52246	0.761232	−	0.648479i	$-0.224595\pi$
$727$	29843.4	1.52246	0.761232	+	0.648479i	$0.224595\pi$
$728$	0	0
$729$	12795.4	0.650075
$730$	75910.9	3.84875
$731$	5938.52	0.300471
$732$	−10206.2	−0.515346
$733$	34648.9	1.74596	0.872978	−	0.487760i	$-0.162186\pi$
$733$	34648.9	1.74596	0.872978	+	0.487760i	$0.162186\pi$
$734$	−34065.4	−1.71305
$735$	33065.9	1.65939
$736$	−32951.4	−1.65028
$737$	8504.29	0.425047
$738$	−19525.7	−0.973920
$739$	−7820.04	−0.389262	−0.194631	−	0.980876i	$-0.562351\pi$
$739$	−7820.04	−0.389262	−0.194631	+	0.980876i	$0.562351\pi$
$740$	69730.8	3.46399
$741$	0	0
$742$	5583.13	0.276231
$743$	4314.73	0.213045	0.106522	−	0.994310i	$-0.466028\pi$
$743$	4314.73	0.213045	0.106522	+	0.994310i	$0.466028\pi$
$744$	−43259.4	−2.13167
$745$	7283.16	0.358167
$746$	−46356.2	−2.27510
$747$	4514.06	0.221099
$748$	−3849.19	−0.188156
$749$	44073.4	2.15008
$750$	25036.3	1.21893
$751$	−18032.8	−0.876199	−0.438099	−	0.898927i	$-0.644348\pi$
$751$	−18032.8	−0.876199	−0.438099	+	0.898927i	$0.644348\pi$
$752$	−25848.7	−1.25347
$753$	−22408.7	−1.08449
$754$	0	0
$755$	−27101.9	−1.30641
$756$	−76345.4	−3.67282
$757$	−35332.2	−1.69640	−0.848198	−	0.529680i	$-0.822312\pi$
$757$	−35332.2	−1.69640	−0.848198	+	0.529680i	$0.822312\pi$
$758$	17434.2	0.835407
$759$	−6435.99	−0.307789
$760$	88265.0	4.21277
$761$	−25658.7	−1.22225	−0.611123	−	0.791536i	$-0.709282\pi$
$761$	−25658.7	−1.22225	−0.611123	+	0.791536i	$0.709282\pi$
$762$	30162.1	1.43393
$763$	−39627.8	−1.88024
$764$	−73505.4	−3.48080
$765$	5795.36	0.273898
$766$	−2474.52	−0.116721
$767$	0	0
$768$	23955.6	1.12555
$769$	6212.48	0.291324	0.145662	−	0.989334i	$-0.453469\pi$
$769$	6212.48	0.291324	0.145662	+	0.989334i	$0.453469\pi$
$770$	−30661.7	−1.43503
$771$	11475.6	0.536035
$772$	44467.7	2.07309
$773$	1918.95	0.0892881	0.0446440	−	0.999003i	$-0.485785\pi$
$773$	1918.95	0.0892881	0.0446440	+	0.999003i	$0.485785\pi$
$774$	−25471.6	−1.18289
$775$	53932.4	2.49975
$776$	−40481.7	−1.87269
$777$	−20781.0	−0.959478
$778$	36370.9	1.67604
$779$	−22226.3	−1.02226
$780$	0	0
$781$	−12334.7	−0.565136
$782$	−17771.0	−0.812646
$783$	12782.4	0.583404
$784$	64489.9	2.93777
$785$	9483.47	0.431184
$786$	−26405.3	−1.19828
$787$	−9987.67	−0.452379	−0.226189	−	0.974083i	$-0.572627\pi$
$787$	−9987.67	−0.452379	−0.226189	+	0.974083i	$0.572627\pi$
$788$	−40918.5	−1.84983
$789$	19387.0	0.874774
$790$	8257.07	0.371865
$791$	−42897.7	−1.92828
$792$	9173.09	0.411555
$793$	0	0
$794$	62232.8	2.78156
$795$	−2173.42	−0.0969602
$796$	59142.7	2.63349
$797$	−31816.1	−1.41403	−0.707016	−	0.707198i	$-0.749959\pi$
$797$	−31816.1	−1.41403	−0.707016	+	0.707198i	$0.749959\pi$
$798$	−47343.6	−2.10018
$799$	−4329.24	−0.191687
$800$	38137.7	1.68546
$801$	6157.36	0.271610
$802$	−13313.8	−0.586195
$803$	8980.32	0.394656
$804$	45419.0	1.99229
$805$	−98006.2	−4.29101
$806$	0	0
$807$	−9065.42	−0.395437
$808$	46798.2	2.03757
$809$	−23062.0	−1.00225	−0.501123	−	0.865376i	$-0.667080\pi$
$809$	−23062.0	−1.00225	−0.501123	+	0.865376i	$0.667080\pi$
$810$	1879.05	0.0815102
$811$	8164.70	0.353516	0.176758	−	0.984254i	$-0.443439\pi$
$811$	8164.70	0.353516	0.176758	+	0.984254i	$0.443439\pi$
$812$	−48761.1	−2.10736
$813$	−2007.94	−0.0866192
$814$	11915.1	0.513051
$815$	−50579.1	−2.17388
$816$	−7362.11	−0.315840
$817$	−28994.5	−1.24160
$818$	−19290.5	−0.824544
$819$	0	0
$820$	−76878.0	−3.27402
$821$	495.439	0.0210608	0.0105304	−	0.999945i	$-0.496648\pi$
$821$	495.439	0.0210608	0.0105304	+	0.999945i	$0.496648\pi$
$822$	−7788.78	−0.330492
$823$	29869.4	1.26510	0.632552	−	0.774518i	$-0.282007\pi$
$823$	29869.4	1.26510	0.632552	+	0.774518i	$0.282007\pi$
$824$	−5575.44	−0.235716
$825$	7448.96	0.314351
$826$	−26777.8	−1.12799
$827$	−17107.6	−0.719335	−0.359668	−	0.933081i	$-0.617110\pi$
$827$	−17107.6	−0.719335	−0.359668	+	0.933081i	$0.617110\pi$
$828$	52772.1	2.21492
$829$	42894.3	1.79708	0.898542	−	0.438888i	$-0.144628\pi$
$829$	42894.3	1.79708	0.898542	+	0.438888i	$0.144628\pi$
$830$	25671.2	1.07357
$831$	16048.3	0.669929
$832$	0	0
$833$	10801.0	0.449259
$834$	19888.8	0.825772
$835$	−10215.9	−0.423394
$836$	18793.5	0.777495
$837$	36768.5	1.51840
$838$	2511.64	0.103536
$839$	39564.5	1.62803	0.814015	−	0.580844i	$-0.197277\pi$
$839$	39564.5	1.62803	0.814015	+	0.580844i	$0.197277\pi$
$840$	−90983.9	−3.73719
$841$	−16225.0	−0.665259
$842$	16601.8	0.679496
$843$	7074.59	0.289041
$844$	42663.8	1.73999
$845$	0	0
$846$	18569.0	0.754630
$847$	−3627.30	−0.147149
$848$	−4238.93	−0.171657
$849$	2072.34	0.0837720
$850$	20568.0	0.829973
$851$	38085.0	1.53412
$852$	−65876.3	−2.64893
$853$	4021.91	0.161439	0.0807195	−	0.996737i	$-0.474278\pi$
$853$	4021.91	0.161439	0.0807195	+	0.996737i	$0.474278\pi$
$854$	−26556.8	−1.06412
$855$	−28295.5	−1.13180
$856$	−74985.2	−2.99409
$857$	42082.3	1.67737	0.838684	−	0.544618i	$-0.183325\pi$
$857$	42082.3	1.67737	0.838684	+	0.544618i	$0.183325\pi$
$858$	0	0
$859$	−27251.7	−1.08244	−0.541219	−	0.840881i	$-0.682037\pi$
$859$	−27251.7	−1.08244	−0.541219	+	0.840881i	$0.682037\pi$
$860$	−100288.	−3.97651
$861$	22911.0	0.906857
$862$	89017.3	3.51733
$863$	13531.3	0.533732	0.266866	−	0.963734i	$-0.414012\pi$
$863$	13531.3	0.533732	0.266866	+	0.963734i	$0.414012\pi$
$864$	26000.4	1.02379
$865$	−42134.3	−1.65620
$866$	926.709	0.0363636
$867$	14800.0	0.579739
$868$	−140261.	−5.48476
$869$	976.817	0.0381315
$870$	27417.3	1.06843
$871$	0	0
$872$	67421.6	2.61833
$873$	12977.4	0.503114
$874$	86765.9	3.35801
$875$	45102.0	1.74254
$876$	47961.3	1.84984
$877$	1171.03	0.0450888	0.0225444	−	0.999746i	$-0.492823\pi$
$877$	1171.03	0.0450888	0.0225444	+	0.999746i	$0.492823\pi$
$878$	38214.2	1.46887
$879$	17602.9	0.675460
$880$	23279.5	0.891765
$881$	−37175.4	−1.42165	−0.710824	−	0.703370i	$-0.751678\pi$
$881$	−37175.4	−1.42165	−0.710824	+	0.703370i	$0.751678\pi$
$882$	−46327.8	−1.76864
$883$	−26849.7	−1.02329	−0.511645	−	0.859197i	$-0.670964\pi$
$883$	−26849.7	−1.02329	−0.511645	+	0.859197i	$0.670964\pi$
$884$	0	0
$885$	10424.2	0.395938
$886$	−13652.0	−0.517662
$887$	34365.3	1.30087	0.650437	−	0.759560i	$-0.274586\pi$
$887$	34365.3	1.30087	0.650437	+	0.759560i	$0.274586\pi$
$888$	35356.1	1.33612
$889$	54335.9	2.04991
$890$	35016.6	1.31883
$891$	222.293	0.00835815
$892$	14236.8	0.534399
$893$	21137.3	0.792085
$894$	6646.48	0.248648
$895$	85502.5	3.19333
$896$	42745.8	1.59379
$897$	0	0
$898$	−44558.8	−1.65584
$899$	23483.7	0.871218
$900$	−61078.0	−2.26215
$901$	−709.951	−0.0262507
$902$	−13136.3	−0.484914
$903$	29887.7	1.10144
$904$	72984.8	2.68522
$905$	−18658.0	−0.685319
$906$	−24732.7	−0.906941
$907$	19967.3	0.730983	0.365492	−	0.930815i	$-0.380901\pi$
$907$	19967.3	0.730983	0.365492	+	0.930815i	$0.380901\pi$
$908$	18292.8	0.668579
$909$	−15002.3	−0.547410
$910$	0	0
$911$	−32045.9	−1.16545	−0.582726	−	0.812669i	$-0.698014\pi$
$911$	−32045.9	−1.16545	−0.582726	+	0.812669i	$0.698014\pi$
$912$	35945.1	1.30511
$913$	3036.93	0.110085
$914$	26367.8	0.954234
$915$	10338.1	0.373517
$916$	73864.1	2.66434
$917$	−47568.1	−1.71302
$918$	14022.3	0.504143
$919$	6857.41	0.246143	0.123071	−	0.992398i	$-0.460726\pi$
$919$	6857.41	0.246143	0.123071	+	0.992398i	$0.460726\pi$
$920$	166745.	5.97544
$921$	1756.60	0.0628467
$922$	59066.8	2.10983
$923$	0	0
$924$	−19372.4	−0.689724
$925$	−44079.3	−1.56683
$926$	−58229.2	−2.06645
$927$	1787.35	0.0633271
$928$	16606.2	0.587420
$929$	6240.76	0.220401	0.110201	−	0.993909i	$-0.464851\pi$
$929$	6240.76	0.220401	0.110201	+	0.993909i	$0.464851\pi$
$930$	78865.8	2.78077
$931$	−52735.3	−1.85642
$932$	60413.4	2.12329
$933$	3255.60	0.114237
$934$	39256.8	1.37529
$935$	3898.94	0.136373
$936$	0	0
$937$	41474.3	1.44601	0.723003	−	0.690845i	$-0.242761\pi$
$937$	41474.3	1.44601	0.723003	+	0.690845i	$0.242761\pi$
$938$	118181.	4.11381
$939$	4975.37	0.172913
$940$	73111.1	2.53683
$941$	23022.8	0.797578	0.398789	−	0.917043i	$-0.369431\pi$
$941$	23022.8	0.797578	0.398789	+	0.917043i	$0.369431\pi$
$942$	8654.44	0.299339
$943$	−41988.6	−1.44999
$944$	20330.8	0.700964
$945$	77332.1	2.66203
$946$	−17136.5	−0.588960
$947$	16856.3	0.578411	0.289205	−	0.957267i	$-0.406609\pi$
$947$	16856.3	0.578411	0.289205	+	0.957267i	$0.406609\pi$
$948$	5216.90	0.178731
$949$	0	0
$950$	−100422.	−3.42961
$951$	−14545.6	−0.495975
$952$	−29720.0	−1.01180
$953$	38211.6	1.29884	0.649421	−	0.760429i	$-0.275011\pi$
$953$	38211.6	1.29884	0.649421	+	0.760429i	$0.275011\pi$
$954$	3045.13	0.103343
$955$	74455.5	2.52285
$956$	−106376.	−3.59881
$957$	3243.49	0.109558
$958$	64680.3	2.18134
$959$	−14031.2	−0.472462
$960$	518.068	0.0174173
$961$	37759.8	1.26749
$962$	0	0
$963$	24038.4	0.804388
$964$	32016.4	1.06969
$965$	−45042.4	−1.50256
$966$	−89438.7	−2.97893
$967$	−52395.7	−1.74243	−0.871217	−	0.490899i	$-0.836668\pi$
$967$	−52395.7	−1.74243	−0.871217	+	0.490899i	$0.836668\pi$
$968$	6171.38	0.204913
$969$	6020.21	0.199584
$970$	73801.9	2.44292
$971$	−9570.84	−0.316316	−0.158158	−	0.987414i	$-0.550556\pi$
$971$	−9570.84	−0.316316	−0.158158	+	0.987414i	$0.550556\pi$
$972$	−67574.7	−2.22990
$973$	35829.0	1.18050
$974$	42484.6	1.39763
$975$	0	0
$976$	20162.9	0.661271
$977$	28678.1	0.939093	0.469547	−	0.882908i	$-0.344417\pi$
$977$	28678.1	0.939093	0.469547	+	0.882908i	$0.344417\pi$
$978$	−46157.6	−1.50916
$979$	4142.49	0.135234
$980$	−182405.	−5.94562
$981$	−21613.7	−0.703436
$982$	−20414.5	−0.663395
$983$	−38437.3	−1.24716	−0.623581	−	0.781758i	$-0.714323\pi$
$983$	−38437.3	−1.24716	−0.623581	+	0.781758i	$0.714323\pi$
$984$	−38980.0	−1.26284
$985$	41447.4	1.34074
$986$	8955.89	0.289263
$987$	−21788.4	−0.702667
$988$	0	0
$989$	−54774.6	−1.76110
$990$	−16723.4	−0.536873
$991$	−5046.00	−0.161747	−0.0808736	−	0.996724i	$-0.525771\pi$
$991$	−5046.00	−0.161747	−0.0808736	+	0.996724i	$0.525771\pi$
$992$	47767.7	1.52886
$993$	1005.78	0.0321424
$994$	−171411.	−5.46966
$995$	−59907.1	−1.90873
$996$	16219.4	0.515994
$997$	−33004.8	−1.04842	−0.524209	−	0.851590i	$-0.675639\pi$
$997$	−33004.8	−1.04842	−0.524209	+	0.851590i	$0.675639\pi$
$998$	40880.3	1.29664
$999$	−30051.1	−0.951727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.e.1.11		11
13.12	even	2		143.4.a.d.1.1	✓	11
39.38	odd	2		1287.4.a.m.1.11		11
52.51	odd	2		2288.4.a.u.1.8		11
143.142	odd	2		1573.4.a.f.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.d.1.1	✓	11	13.12	even	2
1287.4.a.m.1.11		11	39.38	odd	2
1573.4.a.f.1.11		11	143.142	odd	2
1859.4.a.e.1.11		11	1.1	even	1	trivial
2288.4.a.u.1.8		11	52.51	odd	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)

\(f(q)\)	\(=\)	\(q+5.09923 q^{2} -3.26338 q^{3} +18.0021 q^{4} -18.2348 q^{5} -16.6407 q^{6} -29.9777 q^{7} +51.0031 q^{8} -16.3503 q^{9} +O(q^{10})\)	\(q+5.09923 q^{2} -3.26338 q^{3} +18.0021 q^{4} -18.2348 q^{5} -16.6407 q^{6} -29.9777 q^{7} +51.0031 q^{8} -16.3503 q^{9} -92.9834 q^{10} -11.0000 q^{11} -58.7479 q^{12} -152.863 q^{14} +59.5072 q^{15} +116.060 q^{16} +19.4381 q^{17} -83.3740 q^{18} -94.9053 q^{19} -328.265 q^{20} +97.8288 q^{21} -56.0915 q^{22} -179.289 q^{23} -166.443 q^{24} +207.508 q^{25} +141.469 q^{27} -539.662 q^{28} +90.3548 q^{29} +303.441 q^{30} +259.905 q^{31} +183.789 q^{32} +35.8972 q^{33} +99.1191 q^{34} +546.637 q^{35} -294.340 q^{36} -212.422 q^{37} -483.944 q^{38} -930.032 q^{40} +234.195 q^{41} +498.851 q^{42} +305.510 q^{43} -198.023 q^{44} +298.145 q^{45} -914.237 q^{46} -222.720 q^{47} -378.747 q^{48} +555.663 q^{49} +1058.13 q^{50} -63.4339 q^{51} -36.5237 q^{53} +721.382 q^{54} +200.583 q^{55} -1528.96 q^{56} +309.713 q^{57} +460.740 q^{58} +175.175 q^{59} +1071.26 q^{60} +173.729 q^{61} +1325.32 q^{62} +490.145 q^{63} +8.70598 q^{64} +183.048 q^{66} -773.117 q^{67} +349.927 q^{68} +585.090 q^{69} +2787.43 q^{70} +1121.34 q^{71} -833.917 q^{72} -816.392 q^{73} -1083.19 q^{74} -677.178 q^{75} -1708.50 q^{76} +329.755 q^{77} -88.8016 q^{79} -2116.32 q^{80} -20.2085 q^{81} +1194.21 q^{82} -276.084 q^{83} +1761.13 q^{84} -354.449 q^{85} +1557.86 q^{86} -294.862 q^{87} -561.034 q^{88} -376.590 q^{89} +1520.31 q^{90} -3227.59 q^{92} -848.171 q^{93} -1135.70 q^{94} +1730.58 q^{95} -599.774 q^{96} -793.710 q^{97} +2833.45 q^{98} +179.854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9 + 48 * q^10 - 121 * q^11 + 105 * q^12 - 48 * q^14 + 125 * q^15 + 394 * q^16 + 265 * q^17 - 405 * q^18 - 127 * q^19 + 46 * q^20 + 287 * q^21 + 66 * q^22 + 42 * q^23 + 83 * q^24 + 737 * q^25 + 69 * q^27 - 675 * q^28 + 435 * q^29 + 785 * q^30 + 174 * q^31 - 315 * q^32 - 66 * q^33 - 497 * q^34 + 844 * q^35 + 1572 * q^36 - 187 * q^37 - 1813 * q^38 - 1470 * q^40 - 128 * q^41 - 2630 * q^42 + 696 * q^43 - 726 * q^44 + 1537 * q^45 - 785 * q^46 + 355 * q^47 - 516 * q^48 + 1758 * q^49 + 3414 * q^50 - 25 * q^51 - 693 * q^53 + 4150 * q^54 - 44 * q^55 - 3123 * q^56 - 99 * q^57 + 287 * q^58 + 609 * q^59 + 5013 * q^60 + 1625 * q^61 - 882 * q^62 - 1365 * q^63 - 914 * q^64 - 154 * q^66 - 633 * q^67 + 2873 * q^68 - 2192 * q^69 + 2054 * q^70 + 1937 * q^71 - 3242 * q^72 - 404 * q^73 - 447 * q^74 + 1781 * q^75 + 1814 * q^76 + 495 * q^77 + 1670 * q^79 + 1568 * q^80 + 2619 * q^81 + 1283 * q^82 - 785 * q^83 + 11750 * q^84 - 3189 * q^85 + 5950 * q^86 + 46 * q^87 + 858 * q^88 - 1464 * q^89 + 401 * q^90 - 3786 * q^92 - 1826 * q^93 - 2597 * q^94 - 2356 * q^95 - 4513 * q^96 - 1184 * q^97 - 2823 * q^98 - 1485 * q^99

Introduction

L-functions

Modular forms

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Database

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