LMFDB - Embedded newform 1617.4.a.bd.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.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:	$95.4060884793$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 92 x^{14} + 346 x^{13} + 3385 x^{12} - 11756 x^{11} - 63875 x^{10} + 199466 x^{9} + \cdots - 738304 $ x^16 - 4x^15 - 92x^14 + 346x^13 + 3385x^12 - 11756x^11 - 63875x^10 + 199466x^9 + 657606x^8 - 1772388x^7 - 3590705x^6 + 7831536x^5 + 8898560x^4 - 14389664x^3 - 4854640x^2 + 6896896*x - 738304
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-3.48862$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.48862 q^{2} +3.00000 q^{3} +4.17050 q^{4} -0.768490 q^{5} +10.4659 q^{6} -13.3597 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+3.48862 q^{2} +3.00000 q^{3} +4.17050 q^{4} -0.768490 q^{5} +10.4659 q^{6} -13.3597 q^{8} +9.00000 q^{9} -2.68097 q^{10} -11.0000 q^{11} +12.5115 q^{12} -37.4965 q^{13} -2.30547 q^{15} -79.9709 q^{16} +22.4707 q^{17} +31.3976 q^{18} +74.1954 q^{19} -3.20499 q^{20} -38.3749 q^{22} +195.196 q^{23} -40.0791 q^{24} -124.409 q^{25} -130.811 q^{26} +27.0000 q^{27} +48.3627 q^{29} -8.04292 q^{30} -287.913 q^{31} -172.111 q^{32} -33.0000 q^{33} +78.3919 q^{34} +37.5345 q^{36} -251.325 q^{37} +258.840 q^{38} -112.490 q^{39} +10.2668 q^{40} +223.117 q^{41} -472.383 q^{43} -45.8755 q^{44} -6.91641 q^{45} +680.967 q^{46} -329.863 q^{47} -239.913 q^{48} -434.018 q^{50} +67.4121 q^{51} -156.379 q^{52} +569.160 q^{53} +94.1929 q^{54} +8.45339 q^{55} +222.586 q^{57} +168.719 q^{58} -869.686 q^{59} -9.61496 q^{60} -768.920 q^{61} -1004.42 q^{62} +39.3368 q^{64} +28.8157 q^{65} -115.125 q^{66} -942.990 q^{67} +93.7141 q^{68} +585.589 q^{69} -320.206 q^{71} -120.237 q^{72} -963.122 q^{73} -876.779 q^{74} -373.228 q^{75} +309.432 q^{76} -392.434 q^{78} +620.919 q^{79} +61.4569 q^{80} +81.0000 q^{81} +778.371 q^{82} -594.378 q^{83} -17.2685 q^{85} -1647.97 q^{86} +145.088 q^{87} +146.957 q^{88} +53.7887 q^{89} -24.1288 q^{90} +814.066 q^{92} -863.739 q^{93} -1150.77 q^{94} -57.0185 q^{95} -516.333 q^{96} -1477.54 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9} - 178 q^{10} - 176 q^{11} + 216 q^{12} - 104 q^{13} + 220 q^{16} - 220 q^{17} - 36 q^{18} - 152 q^{19} - 182 q^{20} + 44 q^{22} - 180 q^{23} - 198 q^{24} + 284 q^{25} - 10 q^{26} + 432 q^{27} - 604 q^{29} - 534 q^{30} - 380 q^{31} - 592 q^{32} - 528 q^{33} - 632 q^{34} + 648 q^{36} + 148 q^{37} - 266 q^{38} - 312 q^{39} - 1792 q^{40} - 60 q^{41} + 252 q^{43} - 792 q^{44} - 116 q^{46} - 1468 q^{47} + 660 q^{48} - 850 q^{50} - 660 q^{51} - 310 q^{52} - 1456 q^{53} - 108 q^{54} - 456 q^{57} - 1350 q^{58} - 1312 q^{59} - 546 q^{60} - 2880 q^{61} - 708 q^{62} + 630 q^{64} - 4064 q^{65} + 132 q^{66} + 1220 q^{67} - 4956 q^{68} - 540 q^{69} - 2040 q^{71} - 594 q^{72} - 1628 q^{73} - 3126 q^{74} + 852 q^{75} - 6286 q^{76} - 30 q^{78} - 416 q^{79} + 874 q^{80} + 1296 q^{81} - 3040 q^{82} - 3724 q^{83} + 628 q^{85} - 1608 q^{86} - 1812 q^{87} + 726 q^{88} - 752 q^{89} - 1602 q^{90} - 32 q^{92} - 1140 q^{93} - 610 q^{94} - 912 q^{95} - 1776 q^{96} - 1088 q^{97} - 1584 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9 - 178 * q^10 - 176 * q^11 + 216 * q^12 - 104 * q^13 + 220 * q^16 - 220 * q^17 - 36 * q^18 - 152 * q^19 - 182 * q^20 + 44 * q^22 - 180 * q^23 - 198 * q^24 + 284 * q^25 - 10 * q^26 + 432 * q^27 - 604 * q^29 - 534 * q^30 - 380 * q^31 - 592 * q^32 - 528 * q^33 - 632 * q^34 + 648 * q^36 + 148 * q^37 - 266 * q^38 - 312 * q^39 - 1792 * q^40 - 60 * q^41 + 252 * q^43 - 792 * q^44 - 116 * q^46 - 1468 * q^47 + 660 * q^48 - 850 * q^50 - 660 * q^51 - 310 * q^52 - 1456 * q^53 - 108 * q^54 - 456 * q^57 - 1350 * q^58 - 1312 * q^59 - 546 * q^60 - 2880 * q^61 - 708 * q^62 + 630 * q^64 - 4064 * q^65 + 132 * q^66 + 1220 * q^67 - 4956 * q^68 - 540 * q^69 - 2040 * q^71 - 594 * q^72 - 1628 * q^73 - 3126 * q^74 + 852 * q^75 - 6286 * q^76 - 30 * q^78 - 416 * q^79 + 874 * q^80 + 1296 * q^81 - 3040 * q^82 - 3724 * q^83 + 628 * q^85 - 1608 * q^86 - 1812 * q^87 + 726 * q^88 - 752 * q^89 - 1602 * q^90 - 32 * q^92 - 1140 * q^93 - 610 * q^94 - 912 * q^95 - 1776 * q^96 - 1088 * q^97 - 1584 * 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 $

$2$	3.48862	1.23341	0.616707	−	0.787192i	$-0.288466\pi$
$2$	3.48862	1.23341	0.616707	+	0.787192i	$0.288466\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.17050	0.521312
$5$	−0.768490	−0.0687359	−0.0343679	−	0.999409i	$-0.510942\pi$
$5$	−0.768490	−0.0687359	−0.0343679	+	0.999409i	$0.510942\pi$
$6$	10.4659	0.712112
$7$	0	0
$7$	0	0
$8$	−13.3597	−0.590420
$9$	9.00000	0.333333
$10$	−2.68097	−0.0847798
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	12.5115	0.300980
$13$	−37.4965	−0.799975	−0.399987	−	0.916521i	$-0.630985\pi$
$13$	−37.4965	−0.799975	−0.399987	+	0.916521i	$0.630985\pi$
$14$	0	0
$15$	−2.30547	−0.0396847
$16$	−79.9709	−1.24955
$17$	22.4707	0.320585	0.160293	−	0.987070i	$-0.448756\pi$
$17$	22.4707	0.320585	0.160293	+	0.987070i	$0.448756\pi$
$18$	31.3976	0.411138
$19$	74.1954	0.895874	0.447937	−	0.894065i	$-0.352159\pi$
$19$	74.1954	0.895874	0.447937	+	0.894065i	$0.352159\pi$
$20$	−3.20499	−0.0358329
$21$	0	0
$22$	−38.3749	−0.371889
$23$	195.196	1.76962	0.884810	−	0.465952i	$-0.154288\pi$
$23$	195.196	1.76962	0.884810	+	0.465952i	$0.154288\pi$
$24$	−40.0791	−0.340879
$25$	−124.409	−0.995275
$26$	−130.811	−0.986701
$27$	27.0000	0.192450
$28$	0	0
$29$	48.3627	0.309680	0.154840	−	0.987940i	$-0.450514\pi$
$29$	48.3627	0.309680	0.154840	+	0.987940i	$0.450514\pi$
$30$	−8.04292	−0.0489477
$31$	−287.913	−1.66809	−0.834044	−	0.551699i	$-0.813980\pi$
$31$	−287.913	−1.66809	−0.834044	+	0.551699i	$0.813980\pi$
$32$	−172.111	−0.950788
$33$	−33.0000	−0.174078
$34$	78.3919	0.395415
$35$	0	0
$36$	37.5345	0.173771
$37$	−251.325	−1.11669	−0.558346	−	0.829608i	$-0.688564\pi$
$37$	−251.325	−1.11669	−0.558346	+	0.829608i	$0.688564\pi$
$38$	258.840	1.10498
$39$	−112.490	−0.461866
$40$	10.2668	0.0405831
$41$	223.117	0.849878	0.424939	−	0.905222i	$-0.360296\pi$
$41$	223.117	0.849878	0.424939	+	0.905222i	$0.360296\pi$
$42$	0	0
$43$	−472.383	−1.67530	−0.837649	−	0.546209i	$-0.816070\pi$
$43$	−472.383	−1.67530	−0.837649	+	0.546209i	$0.816070\pi$
$44$	−45.8755	−0.157182
$45$	−6.91641	−0.0229120
$46$	680.967	2.18268
$47$	−329.863	−1.02373	−0.511866	−	0.859065i	$-0.671046\pi$
$47$	−329.863	−1.02373	−0.511866	+	0.859065i	$0.671046\pi$
$48$	−239.913	−0.721426
$49$	0	0
$50$	−434.018	−1.22759
$51$	67.4121	0.185090
$52$	−156.379	−0.417037
$53$	569.160	1.47510	0.737548	−	0.675294i	$-0.235983\pi$
$53$	569.160	1.47510	0.737548	+	0.675294i	$0.235983\pi$
$54$	94.1929	0.237371
$55$	8.45339	0.0207246
$56$	0	0
$57$	222.586	0.517233
$58$	168.719	0.381964
$59$	−869.686	−1.91904	−0.959521	−	0.281638i	$-0.909122\pi$
$59$	−869.686	−1.91904	−0.959521	+	0.281638i	$0.909122\pi$
$60$	−9.61496	−0.0206881
$61$	−768.920	−1.61394	−0.806968	−	0.590595i	$-0.798893\pi$
$61$	−768.920	−1.61394	−0.806968	+	0.590595i	$0.798893\pi$
$62$	−1004.42	−2.05744
$63$	0	0
$64$	39.3368	0.0768298
$65$	28.8157	0.0549870
$66$	−115.125	−0.214710
$67$	−942.990	−1.71947	−0.859735	−	0.510740i	$-0.829371\pi$
$67$	−942.990	−1.71947	−0.859735	+	0.510740i	$0.829371\pi$
$68$	93.7141	0.167125
$69$	585.589	1.02169
$70$	0	0
$71$	−320.206	−0.535231	−0.267616	−	0.963526i	$-0.586236\pi$
$71$	−320.206	−0.535231	−0.267616	+	0.963526i	$0.586236\pi$
$72$	−120.237	−0.196807
$73$	−963.122	−1.54418	−0.772088	−	0.635515i	$-0.780788\pi$
$73$	−963.122	−1.54418	−0.772088	+	0.635515i	$0.780788\pi$
$74$	−876.779	−1.37735
$75$	−373.228	−0.574623
$76$	309.432	0.467030
$77$	0	0
$78$	−392.434	−0.569672
$79$	620.919	0.884289	0.442144	−	0.896944i	$-0.354218\pi$
$79$	620.919	0.884289	0.442144	+	0.896944i	$0.354218\pi$
$80$	61.4569	0.0858886
$81$	81.0000	0.111111
$82$	778.371	1.04825
$83$	−594.378	−0.786041	−0.393021	−	0.919530i	$-0.628570\pi$
$83$	−594.378	−0.786041	−0.393021	+	0.919530i	$0.628570\pi$
$84$	0	0
$85$	−17.2685	−0.0220357
$86$	−1647.97	−2.06634
$87$	145.088	0.178794
$88$	146.957	0.178018
$89$	53.7887	0.0640628	0.0320314	−	0.999487i	$-0.489802\pi$
$89$	53.7887	0.0640628	0.0320314	+	0.999487i	$0.489802\pi$
$90$	−24.1288	−0.0282599
$91$	0	0
$92$	814.066	0.922525
$93$	−863.739	−0.963071
$94$	−1150.77	−1.26269
$95$	−57.0185	−0.0615787
$96$	−516.333	−0.548938
$97$	−1477.54	−1.54661	−0.773306	−	0.634033i	$-0.781398\pi$
$97$	−1477.54	−1.54661	−0.773306	+	0.634033i	$0.781398\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	−518.849	−0.518849
$101$	940.073	0.926147	0.463073	−	0.886320i	$-0.346747\pi$
$101$	940.073	0.926147	0.463073	+	0.886320i	$0.346747\pi$
$102$	235.176	0.228293
$103$	838.640	0.802268	0.401134	−	0.916019i	$-0.368616\pi$
$103$	838.640	0.802268	0.401134	+	0.916019i	$0.368616\pi$
$104$	500.942	0.472321
$105$	0	0
$106$	1985.59	1.81941
$107$	148.716	0.134364	0.0671821	−	0.997741i	$-0.478599\pi$
$107$	148.716	0.134364	0.0671821	+	0.997741i	$0.478599\pi$
$108$	112.603	0.100327
$109$	2196.36	1.93002	0.965012	−	0.262205i	$-0.0844495\pi$
$109$	2196.36	1.93002	0.965012	+	0.262205i	$0.0844495\pi$
$110$	29.4907	0.0255621
$111$	−753.976	−0.644723
$112$	0	0
$113$	−521.485	−0.434135	−0.217067	−	0.976157i	$-0.569649\pi$
$113$	−521.485	−0.434135	−0.217067	+	0.976157i	$0.569649\pi$
$114$	776.520	0.637963
$115$	−150.007	−0.121636
$116$	201.696	0.161440
$117$	−337.469	−0.266658
$118$	−3034.01	−2.36697
$119$	0	0
$120$	30.8004	0.0234306
$121$	121.000	0.0909091
$122$	−2682.47	−1.99065
$123$	669.350	0.490677
$124$	−1200.74	−0.869594
$125$	191.669	0.137147
$126$	0	0
$127$	−331.554	−0.231659	−0.115830	−	0.993269i	$-0.536953\pi$
$127$	−331.554	−0.231659	−0.115830	+	0.993269i	$0.536953\pi$
$128$	1514.12	1.04555
$129$	−1417.15	−0.967234
$130$	100.527	0.0678217
$131$	−494.168	−0.329585	−0.164793	−	0.986328i	$-0.552696\pi$
$131$	−494.168	−0.329585	−0.164793	+	0.986328i	$0.552696\pi$
$132$	−137.626	−0.0907488
$133$	0	0
$134$	−3289.74	−2.12082
$135$	−20.7492	−0.0132282
$136$	−300.202	−0.189280
$137$	2464.59	1.53696	0.768482	−	0.639872i	$-0.221013\pi$
$137$	2464.59	1.53696	0.768482	+	0.639872i	$0.221013\pi$
$138$	2042.90	1.26017
$139$	2180.64	1.33064	0.665322	−	0.746557i	$-0.268294\pi$
$139$	2180.64	1.33064	0.665322	+	0.746557i	$0.268294\pi$
$140$	0	0
$141$	−989.588	−0.591052
$142$	−1117.08	−0.660162
$143$	412.462	0.241201
$144$	−719.738	−0.416515
$145$	−37.1662	−0.0212861
$146$	−3359.97	−1.90461
$147$	0	0
$148$	−1048.15	−0.582146
$149$	−500.000	−0.274910	−0.137455	−	0.990508i	$-0.543892\pi$
$149$	−500.000	−0.274910	−0.137455	+	0.990508i	$0.543892\pi$
$150$	−1302.05	−0.708748
$151$	2114.76	1.13971	0.569856	−	0.821745i	$-0.306999\pi$
$151$	2114.76	1.13971	0.569856	+	0.821745i	$0.306999\pi$
$152$	−991.228	−0.528942
$153$	202.236	0.106862
$154$	0	0
$155$	221.258	0.114657
$156$	−469.138	−0.240776
$157$	−2311.39	−1.17496	−0.587480	−	0.809238i	$-0.699880\pi$
$157$	−2311.39	−1.17496	−0.587480	+	0.809238i	$0.699880\pi$
$158$	2166.15	1.09069
$159$	1707.48	0.851648
$160$	132.266	0.0653532
$161$	0	0
$162$	282.579	0.137046
$163$	528.928	0.254165	0.127082	−	0.991892i	$-0.459439\pi$
$163$	528.928	0.254165	0.127082	+	0.991892i	$0.459439\pi$
$164$	930.508	0.443052
$165$	25.3602	0.0119654
$166$	−2073.56	−0.969515
$167$	−3873.09	−1.79466	−0.897332	−	0.441356i	$-0.854498\pi$
$167$	−3873.09	−1.79466	−0.897332	+	0.441356i	$0.854498\pi$
$168$	0	0
$169$	−791.009	−0.360040
$170$	−60.2434	−0.0271792
$171$	667.759	0.298625
$172$	−1970.07	−0.873353
$173$	206.597	0.0907935	0.0453968	−	0.998969i	$-0.485545\pi$
$173$	206.597	0.0907935	0.0453968	+	0.998969i	$0.485545\pi$
$174$	506.157	0.220527
$175$	0	0
$176$	879.680	0.376752
$177$	−2609.06	−1.10796
$178$	187.648	0.0790160
$179$	−257.868	−0.107676	−0.0538379	−	0.998550i	$-0.517145\pi$
$179$	−257.868	−0.107676	−0.0538379	+	0.998550i	$0.517145\pi$
$180$	−28.8449	−0.0119443
$181$	−2006.48	−0.823981	−0.411990	−	0.911188i	$-0.635166\pi$
$181$	−2006.48	−0.823981	−0.411990	+	0.911188i	$0.635166\pi$
$182$	0	0
$183$	−2306.76	−0.931806
$184$	−2607.76	−1.04482
$185$	193.141	0.0767568
$186$	−3013.26	−1.18787
$187$	−247.178	−0.0966601
$188$	−1375.69	−0.533684
$189$	0	0
$190$	−198.916	−0.0759520
$191$	1529.00	0.579239	0.289620	−	0.957142i	$-0.406471\pi$
$191$	1529.00	0.579239	0.289620	+	0.957142i	$0.406471\pi$
$192$	118.011	0.0443577
$193$	2045.71	0.762969	0.381485	−	0.924375i	$-0.375413\pi$
$193$	2045.71	0.762969	0.381485	+	0.924375i	$0.375413\pi$
$194$	−5154.58	−1.90761
$195$	86.4472	0.0317467
$196$	0	0
$197$	−8.68219	−0.00314000	−0.00157000	−	0.999999i	$-0.500500\pi$
$197$	−8.68219	−0.00314000	−0.00157000	+	0.999999i	$0.500500\pi$
$198$	−345.374	−0.123963
$199$	3331.52	1.18676	0.593380	−	0.804922i	$-0.297793\pi$
$199$	3331.52	1.18676	0.593380	+	0.804922i	$0.297793\pi$
$200$	1662.07	0.587631
$201$	−2828.97	−0.992737
$202$	3279.56	1.14232
$203$	0	0
$204$	281.142	0.0964897
$205$	−171.463	−0.0584171
$206$	2925.70	0.989530
$207$	1756.77	0.589873
$208$	2998.63	0.999605
$209$	−816.150	−0.270116
$210$	0	0
$211$	4511.71	1.47203	0.736016	−	0.676964i	$-0.236705\pi$
$211$	4511.71	1.47203	0.736016	+	0.676964i	$0.236705\pi$
$212$	2373.68	0.768986
$213$	−960.617	−0.309016
$214$	518.816	0.165727
$215$	363.022	0.115153
$216$	−360.712	−0.113626
$217$	0	0
$218$	7662.26	2.38052
$219$	−2889.37	−0.891531
$220$	35.2549	0.0108040
$221$	−842.574	−0.256460
$222$	−2630.34	−0.795211
$223$	−330.609	−0.0992790	−0.0496395	−	0.998767i	$-0.515807\pi$
$223$	−330.609	−0.0992790	−0.0496395	+	0.998767i	$0.515807\pi$
$224$	0	0
$225$	−1119.68	−0.331758
$226$	−1819.27	−0.535468
$227$	1895.47	0.554216	0.277108	−	0.960839i	$-0.410624\pi$
$227$	1895.47	0.554216	0.277108	+	0.960839i	$0.410624\pi$
$228$	928.296	0.269640
$229$	2177.25	0.628283	0.314141	−	0.949376i	$-0.398283\pi$
$229$	2177.25	0.628283	0.314141	+	0.949376i	$0.398283\pi$
$230$	−523.317	−0.150028
$231$	0	0
$232$	−646.110	−0.182841
$233$	−3701.95	−1.04087	−0.520436	−	0.853901i	$-0.674230\pi$
$233$	−3701.95	−1.04087	−0.520436	+	0.853901i	$0.674230\pi$
$234$	−1177.30	−0.328900
$235$	253.496	0.0703671
$236$	−3627.02	−1.00042
$237$	1862.76	0.510544
$238$	0	0
$239$	−2004.49	−0.542509	−0.271255	−	0.962508i	$-0.587439\pi$
$239$	−2004.49	−0.542509	−0.271255	+	0.962508i	$0.587439\pi$
$240$	184.371	0.0495878
$241$	−5059.31	−1.35228	−0.676138	−	0.736775i	$-0.736348\pi$
$241$	−5059.31	−1.35228	−0.676138	+	0.736775i	$0.736348\pi$
$242$	422.124	0.112129
$243$	243.000	0.0641500
$244$	−3206.78	−0.841365
$245$	0	0
$246$	2335.11	0.605209
$247$	−2782.07	−0.716676
$248$	3846.43	0.984873
$249$	−1783.13	−0.453821
$250$	668.660	0.169159
$251$	3282.62	0.825486	0.412743	−	0.910847i	$-0.364571\pi$
$251$	3282.62	0.825486	0.412743	+	0.910847i	$0.364571\pi$
$252$	0	0
$253$	−2147.16	−0.533561
$254$	−1156.67	−0.285732
$255$	−51.8056	−0.0127223
$256$	4967.50	1.21277
$257$	−6037.12	−1.46531	−0.732656	−	0.680599i	$-0.761720\pi$
$257$	−6037.12	−1.46531	−0.732656	+	0.680599i	$0.761720\pi$
$258$	−4943.90	−1.19300
$259$	0	0
$260$	120.176	0.0286654
$261$	435.264	0.103227
$262$	−1723.97	−0.406516
$263$	8135.21	1.90737	0.953686	−	0.300805i	$-0.0972555\pi$
$263$	8135.21	1.90737	0.953686	+	0.300805i	$0.0972555\pi$
$264$	440.870	0.102779
$265$	−437.394	−0.101392
$266$	0	0
$267$	161.366	0.0369867
$268$	−3932.74	−0.896381
$269$	6484.92	1.46986	0.734931	−	0.678142i	$-0.237215\pi$
$269$	6484.92	1.46986	0.734931	+	0.678142i	$0.237215\pi$
$270$	−72.3863	−0.0163159
$271$	−814.547	−0.182584	−0.0912919	−	0.995824i	$-0.529100\pi$
$271$	−814.547	−0.182584	−0.0912919	+	0.995824i	$0.529100\pi$
$272$	−1797.00	−0.400586
$273$	0	0
$274$	8598.02	1.89571
$275$	1368.50	0.300087
$276$	2442.20	0.532620
$277$	−2776.73	−0.602303	−0.301151	−	0.953576i	$-0.597371\pi$
$277$	−2776.73	−0.602303	−0.301151	+	0.953576i	$0.597371\pi$
$278$	7607.43	1.64124
$279$	−2591.22	−0.556029
$280$	0	0
$281$	−4486.86	−0.952541	−0.476270	−	0.879299i	$-0.658012\pi$
$281$	−4486.86	−0.952541	−0.476270	+	0.879299i	$0.658012\pi$
$282$	−3452.30	−0.729012
$283$	−2968.58	−0.623548	−0.311774	−	0.950156i	$-0.600923\pi$
$283$	−2968.58	−0.623548	−0.311774	+	0.950156i	$0.600923\pi$
$284$	−1335.42	−0.279023
$285$	−171.055	−0.0355525
$286$	1438.93	0.297501
$287$	0	0
$288$	−1549.00	−0.316929
$289$	−4408.07	−0.897225
$290$	−129.659	−0.0262546
$291$	−4432.62	−0.892937
$292$	−4016.70	−0.804998
$293$	−3548.40	−0.707508	−0.353754	−	0.935339i	$-0.615095\pi$
$293$	−3548.40	−0.707508	−0.353754	+	0.935339i	$0.615095\pi$
$294$	0	0
$295$	668.345	0.131907
$296$	3357.63	0.659318
$297$	−297.000	−0.0580259
$298$	−1744.31	−0.339078
$299$	−7319.19	−1.41565
$300$	−1556.55	−0.299558
$301$	0	0
$302$	7377.59	1.40574
$303$	2820.22	0.534711
$304$	−5933.48	−1.11944
$305$	590.907	0.110935
$306$	705.527	0.131805
$307$	−310.414	−0.0577077	−0.0288538	−	0.999584i	$-0.509186\pi$
$307$	−310.414	−0.0577077	−0.0288538	+	0.999584i	$0.509186\pi$
$308$	0	0
$309$	2515.92	0.463190
$310$	771.887	0.141420
$311$	4116.51	0.750565	0.375282	−	0.926910i	$-0.377546\pi$
$311$	4116.51	0.750565	0.375282	+	0.926910i	$0.377546\pi$
$312$	1502.83	0.272695
$313$	74.1250	0.0133859	0.00669296	−	0.999978i	$-0.497870\pi$
$313$	74.1250	0.0133859	0.00669296	+	0.999978i	$0.497870\pi$
$314$	−8063.57	−1.44921
$315$	0	0
$316$	2589.54	0.460991
$317$	−370.888	−0.0657134	−0.0328567	−	0.999460i	$-0.510460\pi$
$317$	−370.888	−0.0657134	−0.0328567	+	0.999460i	$0.510460\pi$
$318$	5956.76	1.05043
$319$	−531.989	−0.0933720
$320$	−30.2300	−0.00528096
$321$	446.149	0.0775752
$322$	0	0
$323$	1667.22	0.287204
$324$	337.810	0.0579236
$325$	4664.92	0.796195
$326$	1845.23	0.313491
$327$	6589.07	1.11430
$328$	−2980.77	−0.501785
$329$	0	0
$330$	88.4721	0.0147583
$331$	−147.078	−0.0244234	−0.0122117	−	0.999925i	$-0.503887\pi$
$331$	−147.078	−0.0244234	−0.0122117	+	0.999925i	$0.503887\pi$
$332$	−2478.85	−0.409773
$333$	−2261.93	−0.372231
$334$	−13511.8	−2.21357
$335$	724.678	0.118189
$336$	0	0
$337$	6464.63	1.04496	0.522479	−	0.852652i	$-0.325007\pi$
$337$	6464.63	1.04496	0.522479	+	0.852652i	$0.325007\pi$
$338$	−2759.53	−0.444079
$339$	−1564.46	−0.250648
$340$	−72.0184	−0.0114875
$341$	3167.04	0.502947
$342$	2329.56	0.368328
$343$	0	0
$344$	6310.90	0.989130
$345$	−450.020	−0.0702268
$346$	720.739	0.111986
$347$	2803.08	0.433653	0.216826	−	0.976210i	$-0.430429\pi$
$347$	2803.08	0.433653	0.216826	+	0.976210i	$0.430429\pi$
$348$	605.089	0.0932074
$349$	8850.57	1.35748	0.678739	−	0.734379i	$-0.262527\pi$
$349$	8850.57	1.35748	0.678739	+	0.734379i	$0.262527\pi$
$350$	0	0
$351$	−1012.41	−0.153955
$352$	1893.22	0.286673
$353$	11853.2	1.78720	0.893600	−	0.448863i	$-0.148171\pi$
$353$	11853.2	1.78720	0.893600	+	0.448863i	$0.148171\pi$
$354$	−9102.02	−1.36657
$355$	246.075	0.0367896
$356$	224.326	0.0333967
$357$	0	0
$358$	−899.606	−0.132809
$359$	−12245.7	−1.80028	−0.900142	−	0.435596i	$-0.856538\pi$
$359$	−12245.7	−1.80028	−0.900142	+	0.435596i	$0.856538\pi$
$360$	92.4011	0.0135277
$361$	−1354.04	−0.197410
$362$	−6999.86	−1.01631
$363$	363.000	0.0524864
$364$	0	0
$365$	740.150	0.106140
$366$	−8047.42	−1.14930
$367$	2253.02	0.320454	0.160227	−	0.987080i	$-0.448777\pi$
$367$	2253.02	0.320454	0.160227	+	0.987080i	$0.448777\pi$
$368$	−15610.0	−2.21122
$369$	2008.05	0.283293
$370$	673.797	0.0946730
$371$	0	0
$372$	−3602.22	−0.502061
$373$	−9980.79	−1.38548	−0.692742	−	0.721185i	$-0.743598\pi$
$373$	−9980.79	−1.38548	−0.692742	+	0.721185i	$0.743598\pi$
$374$	−862.310	−0.119222
$375$	575.006	0.0791818
$376$	4406.86	0.604432
$377$	−1813.43	−0.247736
$378$	0	0
$379$	10487.7	1.42141	0.710705	−	0.703490i	$-0.248376\pi$
$379$	10487.7	1.42141	0.710705	+	0.703490i	$0.248376\pi$
$380$	−237.795	−0.0321017
$381$	−994.663	−0.133748
$382$	5334.11	0.714442
$383$	−2564.53	−0.342145	−0.171073	−	0.985258i	$-0.554723\pi$
$383$	−2564.53	−0.342145	−0.171073	+	0.985258i	$0.554723\pi$
$384$	4542.36	0.603649
$385$	0	0
$386$	7136.70	0.941058
$387$	−4251.45	−0.558433
$388$	−6162.07	−0.806268
$389$	−7953.52	−1.03666	−0.518328	−	0.855182i	$-0.673445\pi$
$389$	−7953.52	−1.03666	−0.518328	+	0.855182i	$0.673445\pi$
$390$	301.582	0.0391569
$391$	4386.20	0.567314
$392$	0	0
$393$	−1482.51	−0.190286
$394$	−30.2889	−0.00387293
$395$	−477.170	−0.0607823
$396$	−412.879	−0.0523939
$397$	13872.0	1.75369	0.876843	−	0.480776i	$-0.159645\pi$
$397$	13872.0	1.75369	0.876843	+	0.480776i	$0.159645\pi$
$398$	11622.4	1.46377
$399$	0	0
$400$	9949.14	1.24364
$401$	11144.2	1.38781	0.693906	−	0.720066i	$-0.255888\pi$
$401$	11144.2	1.38781	0.693906	+	0.720066i	$0.255888\pi$
$402$	−9869.21	−1.22446
$403$	10795.7	1.33443
$404$	3920.58	0.482812
$405$	−62.2477	−0.00763732
$406$	0	0
$407$	2764.58	0.336695
$408$	−900.605	−0.109281
$409$	−8948.96	−1.08190	−0.540951	−	0.841054i	$-0.681935\pi$
$409$	−8948.96	−1.08190	−0.540951	+	0.841054i	$0.681935\pi$
$410$	−598.170	−0.0720525
$411$	7393.76	0.887366
$412$	3497.55	0.418232
$413$	0	0
$414$	6128.70	0.727559
$415$	456.774	0.0540292
$416$	6453.57	0.760606
$417$	6541.92	0.768247
$418$	−2847.24	−0.333165
$419$	−14331.8	−1.67101	−0.835506	−	0.549482i	$-0.814825\pi$
$419$	−14331.8	−1.67101	−0.835506	+	0.549482i	$0.814825\pi$
$420$	0	0
$421$	−5712.73	−0.661334	−0.330667	−	0.943748i	$-0.607274\pi$
$421$	−5712.73	−0.661334	−0.330667	+	0.943748i	$0.607274\pi$
$422$	15739.7	1.81563
$423$	−2968.76	−0.341244
$424$	−7603.80	−0.870927
$425$	−2795.57	−0.319071
$426$	−3351.23	−0.381145
$427$	0	0
$428$	620.222	0.0700457
$429$	1237.39	0.139258
$430$	1266.45	0.142031
$431$	16106.5	1.80006	0.900028	−	0.435833i	$-0.143546\pi$
$431$	16106.5	1.80006	0.900028	+	0.435833i	$0.143546\pi$
$432$	−2159.22	−0.240475
$433$	10329.9	1.14648	0.573238	−	0.819389i	$-0.305687\pi$
$433$	10329.9	1.14648	0.573238	+	0.819389i	$0.305687\pi$
$434$	0	0
$435$	−111.499	−0.0122896
$436$	9159.90	1.00615
$437$	14482.7	1.58536
$438$	−10079.9	−1.09963
$439$	−17183.9	−1.86821	−0.934105	−	0.356998i	$-0.883800\pi$
$439$	−17183.9	−1.86821	−0.934105	+	0.356998i	$0.883800\pi$
$440$	−112.935	−0.0122363
$441$	0	0
$442$	−2939.42	−0.316322
$443$	3732.13	0.400268	0.200134	−	0.979769i	$-0.435862\pi$
$443$	3732.13	0.400268	0.200134	+	0.979769i	$0.435862\pi$
$444$	−3144.46	−0.336102
$445$	−41.3361	−0.00440341
$446$	−1153.37	−0.122452
$447$	−1500.00	−0.158719
$448$	0	0
$449$	822.408	0.0864406	0.0432203	−	0.999066i	$-0.486238\pi$
$449$	822.408	0.0864406	0.0432203	+	0.999066i	$0.486238\pi$
$450$	−3906.16	−0.409196
$451$	−2454.28	−0.256248
$452$	−2174.85	−0.226320
$453$	6344.27	0.658013
$454$	6612.59	0.683578
$455$	0	0
$456$	−2973.68	−0.305385
$457$	−3510.61	−0.359343	−0.179671	−	0.983727i	$-0.557503\pi$
$457$	−3510.61	−0.359343	−0.179671	+	0.983727i	$0.557503\pi$
$458$	7595.61	0.774933
$459$	606.709	0.0616966
$460$	−625.602	−0.0634106
$461$	−241.013	−0.0243494	−0.0121747	−	0.999926i	$-0.503875\pi$
$461$	−241.013	−0.0243494	−0.0121747	+	0.999926i	$0.503875\pi$
$462$	0	0
$463$	−17334.2	−1.73993	−0.869967	−	0.493111i	$-0.835860\pi$
$463$	−17334.2	−1.73993	−0.869967	+	0.493111i	$0.835860\pi$
$464$	−3867.61	−0.386959
$465$	663.775	0.0661975
$466$	−12914.7	−1.28383
$467$	3664.67	0.363128	0.181564	−	0.983379i	$-0.441884\pi$
$467$	3664.67	0.363128	0.181564	+	0.983379i	$0.441884\pi$
$468$	−1407.41	−0.139012
$469$	0	0
$470$	884.353	0.0867918
$471$	−6934.17	−0.678364
$472$	11618.7	1.13304
$473$	5196.22	0.505121
$474$	6498.46	0.629713
$475$	−9230.61	−0.891641
$476$	0	0
$477$	5122.44	0.491699
$478$	−6992.92	−0.669139
$479$	−11966.7	−1.14149	−0.570745	−	0.821128i	$-0.693345\pi$
$479$	−11966.7	−1.14149	−0.570745	+	0.821128i	$0.693345\pi$
$480$	396.797	0.0377317
$481$	9423.83	0.893326
$482$	−17650.0	−1.66792
$483$	0	0
$484$	504.630	0.0473920
$485$	1135.47	0.106308
$486$	847.736	0.0791236
$487$	−9427.54	−0.877213	−0.438606	−	0.898679i	$-0.644528\pi$
$487$	−9427.54	−0.877213	−0.438606	+	0.898679i	$0.644528\pi$
$488$	10272.5	0.952901
$489$	1586.79	0.146742
$490$	0	0
$491$	−9725.76	−0.893925	−0.446963	−	0.894553i	$-0.647494\pi$
$491$	−9725.76	−0.893925	−0.446963	+	0.894553i	$0.647494\pi$
$492$	2791.52	0.255796
$493$	1086.74	0.0992788
$494$	−9705.61	−0.883959
$495$	76.0805	0.00690821
$496$	23024.7	2.08435
$497$	0	0
$498$	−6220.68	−0.559750
$499$	9374.00	0.840958	0.420479	−	0.907302i	$-0.361862\pi$
$499$	9374.00	0.840958	0.420479	+	0.907302i	$0.361862\pi$
$500$	799.354	0.0714964
$501$	−11619.3	−1.03615
$502$	11451.8	1.01817
$503$	860.872	0.0763109	0.0381554	−	0.999272i	$-0.487852\pi$
$503$	860.872	0.0763109	0.0381554	+	0.999272i	$0.487852\pi$
$504$	0	0
$505$	−722.437	−0.0636595
$506$	−7490.64	−0.658102
$507$	−2373.03	−0.207869
$508$	−1382.75	−0.120767
$509$	6158.61	0.536298	0.268149	−	0.963377i	$-0.413588\pi$
$509$	6158.61	0.536298	0.268149	+	0.963377i	$0.413588\pi$
$510$	−180.730	−0.0156919
$511$	0	0
$512$	5216.78	0.450296
$513$	2003.28	0.172411
$514$	−21061.3	−1.80734
$515$	−644.486	−0.0551446
$516$	−5910.22	−0.504231
$517$	3628.49	0.308667
$518$	0	0
$519$	619.791	0.0524197
$520$	−384.969	−0.0324654
$521$	1636.83	0.137641	0.0688204	−	0.997629i	$-0.478076\pi$
$521$	1636.83	0.137641	0.0688204	+	0.997629i	$0.478076\pi$
$522$	1518.47	0.127321
$523$	−8891.04	−0.743361	−0.371681	−	0.928361i	$-0.621218\pi$
$523$	−8891.04	−0.743361	−0.371681	+	0.928361i	$0.621218\pi$
$524$	−2060.93	−0.171817
$525$	0	0
$526$	28380.7	2.35258
$527$	−6469.61	−0.534764
$528$	2639.04	0.217518
$529$	25934.6	2.13156
$530$	−1525.90	−0.125058
$531$	−7827.17	−0.639680
$532$	0	0
$533$	−8366.11	−0.679881
$534$	562.945	0.0456199
$535$	−114.287	−0.00923564
$536$	12598.0	1.01521
$537$	−773.605	−0.0621667
$538$	22623.5	1.81295
$539$	0	0
$540$	−86.5347	−0.00689604
$541$	−16379.4	−1.30167	−0.650837	−	0.759217i	$-0.725582\pi$
$541$	−16379.4	−1.30167	−0.650837	+	0.759217i	$0.725582\pi$
$542$	−2841.65	−0.225202
$543$	−6019.44	−0.475725
$544$	−3867.46	−0.304808
$545$	−1687.88	−0.132662
$546$	0	0
$547$	3765.27	0.294317	0.147159	−	0.989113i	$-0.452987\pi$
$547$	3765.27	0.294317	0.147159	+	0.989113i	$0.452987\pi$
$548$	10278.6	0.801238
$549$	−6920.28	−0.537979
$550$	4774.19	0.370132
$551$	3588.29	0.277434
$552$	−7823.29	−0.603227
$553$	0	0
$554$	−9686.98	−0.742889
$555$	579.423	0.0443156
$556$	9094.35	0.693681
$557$	−22661.3	−1.72386	−0.861929	−	0.507029i	$-0.830744\pi$
$557$	−22661.3	−1.72386	−0.861929	+	0.507029i	$0.830744\pi$
$558$	−9039.78	−0.685814
$559$	17712.7	1.34020
$560$	0	0
$561$	−741.533	−0.0558067
$562$	−15653.0	−1.17488
$563$	18708.3	1.40046	0.700231	−	0.713916i	$-0.253080\pi$
$563$	18708.3	1.40046	0.700231	+	0.713916i	$0.253080\pi$
$564$	−4127.07	−0.308123
$565$	400.756	0.0298406
$566$	−10356.3	−0.769093
$567$	0	0
$568$	4277.85	0.316012
$569$	9400.73	0.692617	0.346308	−	0.938121i	$-0.387435\pi$
$569$	9400.73	0.692617	0.346308	+	0.938121i	$0.387435\pi$
$570$	−596.748	−0.0438509
$571$	4176.00	0.306060	0.153030	−	0.988222i	$-0.451097\pi$
$571$	4176.00	0.306060	0.153030	+	0.988222i	$0.451097\pi$
$572$	1720.17	0.125741
$573$	4587.01	0.334424
$574$	0	0
$575$	−24284.3	−1.76126
$576$	354.032	0.0256099
$577$	1535.32	0.110773	0.0553866	−	0.998465i	$-0.482361\pi$
$577$	1535.32	0.110773	0.0553866	+	0.998465i	$0.482361\pi$
$578$	−15378.1	−1.10665
$579$	6137.12	0.440501
$580$	−155.002	−0.0110967
$581$	0	0
$582$	−15463.7	−1.10136
$583$	−6260.76	−0.444758
$584$	12867.0	0.911714
$585$	259.342	0.0183290
$586$	−12379.0	−0.872651
$587$	24464.0	1.72017	0.860083	−	0.510154i	$-0.170412\pi$
$587$	24464.0	1.72017	0.860083	+	0.510154i	$0.170412\pi$
$588$	0	0
$589$	−21361.8	−1.49440
$590$	2331.61	0.162696
$591$	−26.0466	−0.00181288
$592$	20098.7	1.39536
$593$	8416.48	0.582839	0.291419	−	0.956595i	$-0.405873\pi$
$593$	8416.48	0.582839	0.291419	+	0.956595i	$0.405873\pi$
$594$	−1036.12	−0.0715700
$595$	0	0
$596$	−2085.25	−0.143314
$597$	9994.56	0.685176
$598$	−25533.9	−1.74609
$599$	3986.79	0.271946	0.135973	−	0.990713i	$-0.456584\pi$
$599$	3986.79	0.271946	0.135973	+	0.990713i	$0.456584\pi$
$600$	4986.21	0.339269
$601$	−8565.32	−0.581342	−0.290671	−	0.956823i	$-0.593879\pi$
$601$	−8565.32	−0.581342	−0.290671	+	0.956823i	$0.593879\pi$
$602$	0	0
$603$	−8486.91	−0.573157
$604$	8819.59	0.594146
$605$	−92.9873	−0.00624872
$606$	9838.69	0.659520
$607$	1024.58	0.0685117	0.0342558	−	0.999413i	$-0.489094\pi$
$607$	1024.58	0.0685117	0.0342558	+	0.999413i	$0.489094\pi$
$608$	−12769.8	−0.851786
$609$	0	0
$610$	2061.45	0.136829
$611$	12368.7	0.818960
$612$	843.427	0.0557083
$613$	20537.5	1.35318	0.676592	−	0.736358i	$-0.263456\pi$
$613$	20537.5	1.35318	0.676592	+	0.736358i	$0.263456\pi$
$614$	−1082.92	−0.0711775
$615$	−514.389	−0.0337271
$616$	0	0
$617$	−27993.5	−1.82654	−0.913270	−	0.407354i	$-0.866451\pi$
$617$	−27993.5	−1.82654	−0.913270	+	0.407354i	$0.866451\pi$
$618$	8777.10	0.571305
$619$	420.662	0.0273147	0.0136574	−	0.999907i	$-0.495653\pi$
$619$	420.662	0.0273147	0.0136574	+	0.999907i	$0.495653\pi$
$620$	922.758	0.0597723
$621$	5270.30	0.340564
$622$	14360.9	0.925758
$623$	0	0
$624$	8995.90	0.577122
$625$	15403.9	0.985848
$626$	258.594	0.0165104
$627$	−2448.45	−0.155952
$628$	−9639.64	−0.612522
$629$	−5647.46	−0.357995
$630$	0	0
$631$	−24749.2	−1.56141	−0.780704	−	0.624900i	$-0.785140\pi$
$631$	−24749.2	−1.56141	−0.780704	+	0.624900i	$0.785140\pi$
$632$	−8295.28	−0.522102
$633$	13535.1	0.849878
$634$	−1293.89	−0.0810519
$635$	254.796	0.0159233
$636$	7121.04	0.443974
$637$	0	0
$638$	−1855.91	−0.115166
$639$	−2881.85	−0.178410
$640$	−1163.59	−0.0718669
$641$	15192.3	0.936129	0.468065	−	0.883694i	$-0.344951\pi$
$641$	15192.3	0.936129	0.468065	+	0.883694i	$0.344951\pi$
$642$	1556.45	0.0956824
$643$	−11698.5	−0.717488	−0.358744	−	0.933436i	$-0.616795\pi$
$643$	−11698.5	−0.717488	−0.358744	+	0.933436i	$0.616795\pi$
$644$	0	0
$645$	1089.07	0.0664836
$646$	5816.32	0.354241
$647$	−14679.8	−0.891995	−0.445997	−	0.895034i	$-0.647151\pi$
$647$	−14679.8	−0.891995	−0.445997	+	0.895034i	$0.647151\pi$
$648$	−1082.13	−0.0656023
$649$	9566.54	0.578613
$650$	16274.2	0.982039
$651$	0	0
$652$	2205.90	0.132499
$653$	−2715.52	−0.162736	−0.0813679	−	0.996684i	$-0.525929\pi$
$653$	−2715.52	−0.162736	−0.0813679	+	0.996684i	$0.525929\pi$
$654$	22986.8	1.37439
$655$	379.764	0.0226543
$656$	−17842.9	−1.06196
$657$	−8668.10	−0.514726
$658$	0	0
$659$	19444.7	1.14940	0.574701	−	0.818363i	$-0.305118\pi$
$659$	19444.7	1.14940	0.574701	+	0.818363i	$0.305118\pi$
$660$	105.765	0.00623770
$661$	−8824.48	−0.519262	−0.259631	−	0.965708i	$-0.583601\pi$
$661$	−8824.48	−0.519262	−0.259631	+	0.965708i	$0.583601\pi$
$662$	−513.099	−0.0301241
$663$	−2527.72	−0.148067
$664$	7940.70	0.464095
$665$	0	0
$666$	−7891.01	−0.459115
$667$	9440.22	0.548016
$668$	−16152.7	−0.935581
$669$	−991.828	−0.0573188
$670$	2528.13	0.145776
$671$	8458.12	0.486620
$672$	0	0
$673$	−572.852	−0.0328110	−0.0164055	−	0.999865i	$-0.505222\pi$
$673$	−572.852	−0.0328110	−0.0164055	+	0.999865i	$0.505222\pi$
$674$	22552.7	1.28887
$675$	−3359.05	−0.191541
$676$	−3298.90	−0.187694
$677$	9148.28	0.519346	0.259673	−	0.965697i	$-0.416385\pi$
$677$	9148.28	0.519346	0.259673	+	0.965697i	$0.416385\pi$
$678$	−5457.80	−0.309153
$679$	0	0
$680$	230.702	0.0130103
$681$	5686.42	0.319977
$682$	11048.6	0.620343
$683$	−3299.50	−0.184849	−0.0924244	−	0.995720i	$-0.529462\pi$
$683$	−3299.50	−0.184849	−0.0924244	+	0.995720i	$0.529462\pi$
$684$	2784.89	0.155677
$685$	−1894.01	−0.105645
$686$	0	0
$687$	6531.75	0.362739
$688$	37776.9	2.09336
$689$	−21341.5	−1.18004
$690$	−1569.95	−0.0866188
$691$	1222.95	0.0673273	0.0336636	−	0.999433i	$-0.489283\pi$
$691$	1222.95	0.0673273	0.0336636	+	0.999433i	$0.489283\pi$
$692$	861.612	0.0473318
$693$	0	0
$694$	9778.91	0.534873
$695$	−1675.80	−0.0914629
$696$	−1938.33	−0.105564
$697$	5013.59	0.272458
$698$	30876.3	1.67433
$699$	−11105.9	−0.600947
$700$	0	0
$701$	−18067.6	−0.973474	−0.486737	−	0.873548i	$-0.661813\pi$
$701$	−18067.6	−0.973474	−0.486737	+	0.873548i	$0.661813\pi$
$702$	−3531.91	−0.189891
$703$	−18647.2	−1.00042
$704$	−432.705	−0.0231651
$705$	760.489	0.0406265
$706$	41351.3	2.20436
$707$	0	0
$708$	−10881.1	−0.577593
$709$	8771.36	0.464619	0.232310	−	0.972642i	$-0.425372\pi$
$709$	8771.36	0.464619	0.232310	+	0.972642i	$0.425372\pi$
$710$	858.463	0.0453768
$711$	5588.27	0.294763
$712$	−718.600	−0.0378240
$713$	−56199.6	−2.95188
$714$	0	0
$715$	−316.973	−0.0165792
$716$	−1075.44	−0.0561328
$717$	−6013.47	−0.313218
$718$	−42720.6	−2.22050
$719$	−19097.4	−0.990559	−0.495279	−	0.868734i	$-0.664934\pi$
$719$	−19097.4	−0.990559	−0.495279	+	0.868734i	$0.664934\pi$
$720$	553.112	0.0286295
$721$	0	0
$722$	−4723.73	−0.243489
$723$	−15177.9	−0.780737
$724$	−8368.02	−0.429551
$725$	−6016.77	−0.308217
$726$	1266.37	0.0647375
$727$	10949.6	0.558593	0.279296	−	0.960205i	$-0.409899\pi$
$727$	10949.6	0.558593	0.279296	+	0.960205i	$0.409899\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	2582.11	0.130915
$731$	−10614.8	−0.537076
$732$	−9620.34	−0.485762
$733$	−30245.4	−1.52406	−0.762031	−	0.647540i	$-0.775798\pi$
$733$	−30245.4	−1.52406	−0.762031	+	0.647540i	$0.775798\pi$
$734$	7859.93	0.395252
$735$	0	0
$736$	−33595.5	−1.68253
$737$	10372.9	0.518440
$738$	7005.34	0.349417
$739$	37646.1	1.87393	0.936966	−	0.349422i	$-0.113622\pi$
$739$	37646.1	1.87393	0.936966	+	0.349422i	$0.113622\pi$
$740$	805.495	0.0400143
$741$	−8346.22	−0.413773
$742$	0	0
$743$	−1445.38	−0.0713670	−0.0356835	−	0.999363i	$-0.511361\pi$
$743$	−1445.38	−0.0713670	−0.0356835	+	0.999363i	$0.511361\pi$
$744$	11539.3	0.568617
$745$	384.245	0.0188962
$746$	−34819.2	−1.70888
$747$	−5349.40	−0.262014
$748$	−1030.85	−0.0503901
$749$	0	0
$750$	2005.98	0.0976641
$751$	20129.8	0.978090	0.489045	−	0.872259i	$-0.337345\pi$
$751$	20129.8	0.978090	0.489045	+	0.872259i	$0.337345\pi$
$752$	26379.4	1.27920
$753$	9847.86	0.476595
$754$	−6326.39	−0.305562
$755$	−1625.17	−0.0783391
$756$	0	0
$757$	−3160.13	−0.151726	−0.0758632	−	0.997118i	$-0.524171\pi$
$757$	−3160.13	−0.151726	−0.0758632	+	0.997118i	$0.524171\pi$
$758$	36587.5	1.75319
$759$	−6441.48	−0.308051
$760$	761.749	0.0363573
$761$	23052.0	1.09807	0.549037	−	0.835798i	$-0.314995\pi$
$761$	23052.0	1.09807	0.549037	+	0.835798i	$0.314995\pi$
$762$	−3470.01	−0.164967
$763$	0	0
$764$	6376.70	0.301965
$765$	−155.417	−0.00734523
$766$	−8946.70	−0.422007
$767$	32610.2	1.53518
$768$	14902.5	0.700192
$769$	−883.438	−0.0414273	−0.0207136	−	0.999785i	$-0.506594\pi$
$769$	−883.438	−0.0414273	−0.0207136	+	0.999785i	$0.506594\pi$
$770$	0	0
$771$	−18111.4	−0.845999
$772$	8531.61	0.397745
$773$	−20547.3	−0.956059	−0.478029	−	0.878344i	$-0.658649\pi$
$773$	−20547.3	−0.956059	−0.478029	+	0.878344i	$0.658649\pi$
$774$	−14831.7	−0.688779
$775$	35819.1	1.66021
$776$	19739.5	0.913151
$777$	0	0
$778$	−27746.8	−1.27863
$779$	16554.2	0.761383
$780$	360.528	0.0165500
$781$	3522.26	0.161378
$782$	15301.8	0.699734
$783$	1305.79	0.0595980
$784$	0	0
$785$	1776.28	0.0807620
$786$	−5171.90	−0.234702
$787$	−22179.7	−1.00460	−0.502299	−	0.864694i	$-0.667512\pi$
$787$	−22179.7	−1.00460	−0.502299	+	0.864694i	$0.667512\pi$
$788$	−36.2091	−0.00163692
$789$	24405.6	1.10122
$790$	−1664.67	−0.0749699
$791$	0	0
$792$	1322.61	0.0593395
$793$	28831.8	1.29111
$794$	48394.0	2.16302
$795$	−1312.18	−0.0585387
$796$	13894.1	0.618673
$797$	26409.4	1.17374	0.586869	−	0.809682i	$-0.300360\pi$
$797$	26409.4	1.17374	0.586869	+	0.809682i	$0.300360\pi$
$798$	0	0
$799$	−7412.25	−0.328193
$800$	21412.2	0.946296
$801$	484.098	0.0213543
$802$	38877.8	1.71175
$803$	10594.3	0.465587
$804$	−11798.2	−0.517526
$805$	0	0
$806$	37662.3	1.64590
$807$	19454.8	0.848625
$808$	−12559.1	−0.546816
$809$	22702.8	0.986637	0.493319	−	0.869849i	$-0.335784\pi$
$809$	22702.8	0.986637	0.493319	+	0.869849i	$0.335784\pi$
$810$	−217.159	−0.00941998
$811$	2393.33	0.103626	0.0518132	−	0.998657i	$-0.483500\pi$
$811$	2393.33	0.103626	0.0518132	+	0.998657i	$0.483500\pi$
$812$	0	0
$813$	−2443.64	−0.105415
$814$	9644.57	0.415285
$815$	−406.476	−0.0174702
$816$	−5391.01	−0.231278
$817$	−35048.7	−1.50085
$818$	−31219.6	−1.33443
$819$	0	0
$820$	−715.087	−0.0304535
$821$	5386.96	0.228996	0.114498	−	0.993423i	$-0.463474\pi$
$821$	5386.96	0.228996	0.114498	+	0.993423i	$0.463474\pi$
$822$	25794.1	1.09449
$823$	−16151.7	−0.684097	−0.342048	−	0.939682i	$-0.611121\pi$
$823$	−16151.7	−0.684097	−0.342048	+	0.939682i	$0.611121\pi$
$824$	−11204.0	−0.473676
$825$	4105.51	0.173255
$826$	0	0
$827$	−31420.7	−1.32117	−0.660584	−	0.750752i	$-0.729691\pi$
$827$	−31420.7	−1.32117	−0.660584	+	0.750752i	$0.729691\pi$
$828$	7326.60	0.307508
$829$	4715.64	0.197564	0.0987822	−	0.995109i	$-0.468505\pi$
$829$	4715.64	0.197564	0.0987822	+	0.995109i	$0.468505\pi$
$830$	1593.51	0.0666405
$831$	−8330.20	−0.347740
$832$	−1475.00	−0.0614619
$833$	0	0
$834$	22822.3	0.947568
$835$	2976.43	0.123358
$836$	−3403.75	−0.140815
$837$	−7773.65	−0.321024
$838$	−49998.2	−2.06105
$839$	−20163.8	−0.829717	−0.414859	−	0.909886i	$-0.636169\pi$
$839$	−20163.8	−0.829717	−0.414859	+	0.909886i	$0.636169\pi$
$840$	0	0
$841$	−22050.1	−0.904098
$842$	−19929.6	−0.815699
$843$	−13460.6	−0.549950
$844$	18816.1	0.767389
$845$	607.883	0.0247477
$846$	−10356.9	−0.420895
$847$	0	0
$848$	−45516.3	−1.84320
$849$	−8905.75	−0.360006
$850$	−9752.69	−0.393546
$851$	−49057.8	−1.97612
$852$	−4006.25	−0.161094
$853$	−14994.7	−0.601886	−0.300943	−	0.953642i	$-0.597301\pi$
$853$	−14994.7	−0.601886	−0.300943	+	0.953642i	$0.597301\pi$
$854$	0	0
$855$	−513.166	−0.0205262
$856$	−1986.81	−0.0793314
$857$	1662.28	0.0662571	0.0331285	−	0.999451i	$-0.489453\pi$
$857$	1662.28	0.0662571	0.0331285	+	0.999451i	$0.489453\pi$
$858$	4316.78	0.171763
$859$	26977.9	1.07156	0.535781	−	0.844357i	$-0.320017\pi$
$859$	26977.9	1.07156	0.535781	+	0.844357i	$0.320017\pi$
$860$	1513.98	0.0600307
$861$	0	0
$862$	56189.6	2.22022
$863$	−5933.48	−0.234042	−0.117021	−	0.993129i	$-0.537334\pi$
$863$	−5933.48	−0.234042	−0.117021	+	0.993129i	$0.537334\pi$
$864$	−4647.00	−0.182979
$865$	−158.768	−0.00624077
$866$	36037.2	1.41408
$867$	−13224.2	−0.518013
$868$	0	0
$869$	−6830.10	−0.266623
$870$	−388.977	−0.0151581
$871$	35358.9	1.37553
$872$	−29342.6	−1.13953
$873$	−13297.9	−0.515537
$874$	50524.6	1.95540
$875$	0	0
$876$	−12050.1	−0.464766
$877$	−6675.62	−0.257035	−0.128517	−	0.991707i	$-0.541022\pi$
$877$	−6675.62	−0.257035	−0.128517	+	0.991707i	$0.541022\pi$
$878$	−59948.3	−2.30428
$879$	−10645.2	−0.408480
$880$	−676.026	−0.0258964
$881$	30685.9	1.17348	0.586738	−	0.809777i	$-0.300412\pi$
$881$	30685.9	1.17348	0.586738	+	0.809777i	$0.300412\pi$
$882$	0	0
$883$	45293.0	1.72620	0.863098	−	0.505036i	$-0.168521\pi$
$883$	45293.0	1.72620	0.863098	+	0.505036i	$0.168521\pi$
$884$	−3513.95	−0.133696
$885$	2005.04	0.0761565
$886$	13020.0	0.493697
$887$	−18151.7	−0.687121	−0.343560	−	0.939131i	$-0.611633\pi$
$887$	−18151.7	−0.687121	−0.343560	+	0.939131i	$0.611633\pi$
$888$	10072.9	0.380657
$889$	0	0
$890$	−144.206	−0.00543123
$891$	−891.000	−0.0335013
$892$	−1378.81	−0.0517554
$893$	−24474.3	−0.917134
$894$	−5232.93	−0.195767
$895$	198.169	0.00740119
$896$	0	0
$897$	−21957.6	−0.817327
$898$	2869.07	0.106617
$899$	−13924.2	−0.516573
$900$	−4669.64	−0.172950
$901$	12789.4	0.472894
$902$	−8562.08	−0.316060
$903$	0	0
$904$	6966.88	0.256322
$905$	1541.96	0.0566370
$906$	22132.8	0.811603
$907$	−22537.9	−0.825092	−0.412546	−	0.910937i	$-0.635360\pi$
$907$	−22537.9	−0.825092	−0.412546	+	0.910937i	$0.635360\pi$
$908$	7905.07	0.288919
$909$	8460.66	0.308716
$910$	0	0
$911$	12495.9	0.454454	0.227227	−	0.973842i	$-0.427034\pi$
$911$	12495.9	0.454454	0.227227	+	0.973842i	$0.427034\pi$
$912$	−17800.4	−0.646306
$913$	6538.16	0.237000
$914$	−12247.2	−0.443218
$915$	1772.72	0.0640485
$916$	9080.22	0.327532
$917$	0	0
$918$	2116.58	0.0760976
$919$	53913.2	1.93518	0.967592	−	0.252519i	$-0.0812591\pi$
$919$	53913.2	1.93518	0.967592	+	0.252519i	$0.0812591\pi$
$920$	2004.04	0.0718166
$921$	−931.241	−0.0333175
$922$	−840.804	−0.0300330
$923$	12006.6	0.428172
$924$	0	0
$925$	31267.2	1.11142
$926$	−60472.5	−2.14606
$927$	7547.76	0.267423
$928$	−8323.75	−0.294440
$929$	−45018.7	−1.58990	−0.794950	−	0.606676i	$-0.792503\pi$
$929$	−45018.7	−1.58990	−0.794950	+	0.606676i	$0.792503\pi$
$930$	2315.66	0.0816490
$931$	0	0
$932$	−15439.0	−0.542619
$933$	12349.5	0.433339
$934$	12784.7	0.447887
$935$	189.954	0.00664401
$936$	4508.48	0.157440
$937$	11293.3	0.393742	0.196871	−	0.980429i	$-0.436922\pi$
$937$	11293.3	0.393742	0.196871	+	0.980429i	$0.436922\pi$
$938$	0	0
$939$	222.375	0.00772836
$940$	1057.21	0.0366832
$941$	17140.9	0.593811	0.296906	−	0.954907i	$-0.404045\pi$
$941$	17140.9	0.593811	0.296906	+	0.954907i	$0.404045\pi$
$942$	−24190.7	−0.836704
$943$	43551.6	1.50396
$944$	69549.6	2.39793
$945$	0	0
$946$	18127.7	0.623024
$947$	−8991.92	−0.308551	−0.154276	−	0.988028i	$-0.549304\pi$
$947$	−8991.92	−0.308551	−0.154276	+	0.988028i	$0.549304\pi$
$948$	7768.62	0.266153
$949$	36113.8	1.23530
$950$	−32202.1	−1.09976
$951$	−1112.66	−0.0379397
$952$	0	0
$953$	−8554.35	−0.290769	−0.145384	−	0.989375i	$-0.546442\pi$
$953$	−8554.35	−0.290769	−0.145384	+	0.989375i	$0.546442\pi$
$954$	17870.3	0.606469
$955$	−1175.02	−0.0398145
$956$	−8359.73	−0.282817
$957$	−1595.97	−0.0539084
$958$	−41747.4	−1.40793
$959$	0	0
$960$	−90.6900	−0.00304896
$961$	53102.9	1.78251
$962$	32876.2	1.10184
$963$	1338.45	0.0447881
$964$	−21099.8	−0.704958
$965$	−1572.10	−0.0524434
$966$	0	0
$967$	5074.71	0.168761	0.0843804	−	0.996434i	$-0.473109\pi$
$967$	5074.71	0.168761	0.0843804	+	0.996434i	$0.473109\pi$
$968$	−1616.52	−0.0536746
$969$	5001.67	0.165817
$970$	3961.24	0.131122
$971$	−9033.56	−0.298559	−0.149279	−	0.988795i	$-0.547695\pi$
$971$	−9033.56	−0.298559	−0.149279	+	0.988795i	$0.547695\pi$
$972$	1013.43	0.0334422
$973$	0	0
$974$	−32889.1	−1.08197
$975$	13994.8	0.459683
$976$	61491.2	2.01669
$977$	26813.5	0.878033	0.439017	−	0.898479i	$-0.355327\pi$
$977$	26813.5	0.878033	0.439017	+	0.898479i	$0.355327\pi$
$978$	5535.70	0.180994
$979$	−591.675	−0.0193157
$980$	0	0
$981$	19767.2	0.643342
$982$	−33929.5	−1.10258
$983$	−59245.3	−1.92231	−0.961155	−	0.276010i	$-0.910988\pi$
$983$	−59245.3	−1.92231	−0.961155	+	0.276010i	$0.910988\pi$
$984$	−8942.31	−0.289706
$985$	6.67218	0.000215831 0
$986$	3791.24	0.122452
$987$	0	0
$988$	−11602.6	−0.373612
$989$	−92207.6	−2.96464
$990$	265.416	0.00852070
$991$	56437.5	1.80908	0.904540	−	0.426390i	$-0.140215\pi$
$991$	56437.5	1.80908	0.904540	+	0.426390i	$0.140215\pi$
$992$	49553.0	1.58600
$993$	−441.234	−0.0141008
$994$	0	0
$995$	−2560.24	−0.0815730
$996$	−7436.56	−0.236583
$997$	−19313.3	−0.613500	−0.306750	−	0.951790i	$-0.599242\pi$
$997$	−19313.3	−0.613500	−0.306750	+	0.951790i	$0.599242\pi$
$998$	32702.4	1.03725
$999$	−6785.78	−0.214908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.bd.1.13	yes	16
7.6	odd	2		1617.4.a.bc.1.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.bc.1.13	✓	16	7.6	odd	2
1617.4.a.bd.1.13	yes	16	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+3.48862 q^{2} +3.00000 q^{3} +4.17050 q^{4} -0.768490 q^{5} +10.4659 q^{6} -13.3597 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+3.48862 q^{2} +3.00000 q^{3} +4.17050 q^{4} -0.768490 q^{5} +10.4659 q^{6} -13.3597 q^{8} +9.00000 q^{9} -2.68097 q^{10} -11.0000 q^{11} +12.5115 q^{12} -37.4965 q^{13} -2.30547 q^{15} -79.9709 q^{16} +22.4707 q^{17} +31.3976 q^{18} +74.1954 q^{19} -3.20499 q^{20} -38.3749 q^{22} +195.196 q^{23} -40.0791 q^{24} -124.409 q^{25} -130.811 q^{26} +27.0000 q^{27} +48.3627 q^{29} -8.04292 q^{30} -287.913 q^{31} -172.111 q^{32} -33.0000 q^{33} +78.3919 q^{34} +37.5345 q^{36} -251.325 q^{37} +258.840 q^{38} -112.490 q^{39} +10.2668 q^{40} +223.117 q^{41} -472.383 q^{43} -45.8755 q^{44} -6.91641 q^{45} +680.967 q^{46} -329.863 q^{47} -239.913 q^{48} -434.018 q^{50} +67.4121 q^{51} -156.379 q^{52} +569.160 q^{53} +94.1929 q^{54} +8.45339 q^{55} +222.586 q^{57} +168.719 q^{58} -869.686 q^{59} -9.61496 q^{60} -768.920 q^{61} -1004.42 q^{62} +39.3368 q^{64} +28.8157 q^{65} -115.125 q^{66} -942.990 q^{67} +93.7141 q^{68} +585.589 q^{69} -320.206 q^{71} -120.237 q^{72} -963.122 q^{73} -876.779 q^{74} -373.228 q^{75} +309.432 q^{76} -392.434 q^{78} +620.919 q^{79} +61.4569 q^{80} +81.0000 q^{81} +778.371 q^{82} -594.378 q^{83} -17.2685 q^{85} -1647.97 q^{86} +145.088 q^{87} +146.957 q^{88} +53.7887 q^{89} -24.1288 q^{90} +814.066 q^{92} -863.739 q^{93} -1150.77 q^{94} -57.0185 q^{95} -516.333 q^{96} -1477.54 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9	\( 16 q - 4 q^{2} + 48 q^{3} + 72 q^{4} - 12 q^{6} - 66 q^{8} + 144 q^{9} - 178 q^{10} - 176 q^{11} + 216 q^{12} - 104 q^{13} + 220 q^{16} - 220 q^{17} - 36 q^{18} - 152 q^{19} - 182 q^{20} + 44 q^{22} - 180 q^{23} - 198 q^{24} + 284 q^{25} - 10 q^{26} + 432 q^{27} - 604 q^{29} - 534 q^{30} - 380 q^{31} - 592 q^{32} - 528 q^{33} - 632 q^{34} + 648 q^{36} + 148 q^{37} - 266 q^{38} - 312 q^{39} - 1792 q^{40} - 60 q^{41} + 252 q^{43} - 792 q^{44} - 116 q^{46} - 1468 q^{47} + 660 q^{48} - 850 q^{50} - 660 q^{51} - 310 q^{52} - 1456 q^{53} - 108 q^{54} - 456 q^{57} - 1350 q^{58} - 1312 q^{59} - 546 q^{60} - 2880 q^{61} - 708 q^{62} + 630 q^{64} - 4064 q^{65} + 132 q^{66} + 1220 q^{67} - 4956 q^{68} - 540 q^{69} - 2040 q^{71} - 594 q^{72} - 1628 q^{73} - 3126 q^{74} + 852 q^{75} - 6286 q^{76} - 30 q^{78} - 416 q^{79} + 874 q^{80} + 1296 q^{81} - 3040 q^{82} - 3724 q^{83} + 628 q^{85} - 1608 q^{86} - 1812 q^{87} + 726 q^{88} - 752 q^{89} - 1602 q^{90} - 32 q^{92} - 1140 q^{93} - 610 q^{94} - 912 q^{95} - 1776 q^{96} - 1088 q^{97} - 1584 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 48 * q^3 + 72 * q^4 - 12 * q^6 - 66 * q^8 + 144 * q^9 - 178 * q^10 - 176 * q^11 + 216 * q^12 - 104 * q^13 + 220 * q^16 - 220 * q^17 - 36 * q^18 - 152 * q^19 - 182 * q^20 + 44 * q^22 - 180 * q^23 - 198 * q^24 + 284 * q^25 - 10 * q^26 + 432 * q^27 - 604 * q^29 - 534 * q^30 - 380 * q^31 - 592 * q^32 - 528 * q^33 - 632 * q^34 + 648 * q^36 + 148 * q^37 - 266 * q^38 - 312 * q^39 - 1792 * q^40 - 60 * q^41 + 252 * q^43 - 792 * q^44 - 116 * q^46 - 1468 * q^47 + 660 * q^48 - 850 * q^50 - 660 * q^51 - 310 * q^52 - 1456 * q^53 - 108 * q^54 - 456 * q^57 - 1350 * q^58 - 1312 * q^59 - 546 * q^60 - 2880 * q^61 - 708 * q^62 + 630 * q^64 - 4064 * q^65 + 132 * q^66 + 1220 * q^67 - 4956 * q^68 - 540 * q^69 - 2040 * q^71 - 594 * q^72 - 1628 * q^73 - 3126 * q^74 + 852 * q^75 - 6286 * q^76 - 30 * q^78 - 416 * q^79 + 874 * q^80 + 1296 * q^81 - 3040 * q^82 - 3724 * q^83 + 628 * q^85 - 1608 * q^86 - 1812 * q^87 + 726 * q^88 - 752 * q^89 - 1602 * q^90 - 32 * q^92 - 1140 * q^93 - 610 * q^94 - 912 * q^95 - 1776 * q^96 - 1088 * q^97 - 1584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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