LMFDB - Embedded newform 1859.4.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 59x^{7} - 12x^{6} + 1144x^{5} + 345x^{4} - 7888x^{3} - 2245x^{2} + 9710x - 2988 $ x^9 - 59x^7 - 12x^6 + 1144x^5 + 345x^4 - 7888x^3 - 2245x^2 + 9710*x - 2988
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			1.6
Root			$-1.62159$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.62159 q^{2} -2.83913 q^{3} -5.37046 q^{4} +8.40999 q^{5} -4.60389 q^{6} +9.04976 q^{7} -21.6813 q^{8} -18.9393 q^{9} +O(q^{10})$	\(q+1.62159 q^{2} -2.83913 q^{3} -5.37046 q^{4} +8.40999 q^{5} -4.60389 q^{6} +9.04976 q^{7} -21.6813 q^{8} -18.9393 q^{9} +13.6375 q^{10} +11.0000 q^{11} +15.2474 q^{12} +14.6750 q^{14} -23.8771 q^{15} +7.80556 q^{16} +121.995 q^{17} -30.7117 q^{18} -74.4993 q^{19} -45.1655 q^{20} -25.6935 q^{21} +17.8374 q^{22} -159.587 q^{23} +61.5562 q^{24} -54.2720 q^{25} +130.428 q^{27} -48.6014 q^{28} +268.866 q^{29} -38.7187 q^{30} -166.890 q^{31} +186.108 q^{32} -31.2304 q^{33} +197.825 q^{34} +76.1084 q^{35} +101.713 q^{36} -30.7828 q^{37} -120.807 q^{38} -182.340 q^{40} +171.426 q^{41} -41.6641 q^{42} +285.411 q^{43} -59.0751 q^{44} -159.280 q^{45} -258.783 q^{46} +67.0946 q^{47} -22.1610 q^{48} -261.102 q^{49} -88.0067 q^{50} -346.360 q^{51} -422.643 q^{53} +211.500 q^{54} +92.5099 q^{55} -196.211 q^{56} +211.513 q^{57} +435.989 q^{58} -427.541 q^{59} +128.231 q^{60} +128.991 q^{61} -270.626 q^{62} -171.396 q^{63} +239.346 q^{64} -50.6428 q^{66} +622.950 q^{67} -655.170 q^{68} +453.087 q^{69} +123.416 q^{70} +1140.26 q^{71} +410.630 q^{72} -839.061 q^{73} -49.9169 q^{74} +154.085 q^{75} +400.095 q^{76} +99.5474 q^{77} +650.986 q^{79} +65.6447 q^{80} +141.060 q^{81} +277.981 q^{82} -891.619 q^{83} +137.986 q^{84} +1025.98 q^{85} +462.818 q^{86} -763.346 q^{87} -238.495 q^{88} -730.428 q^{89} -258.286 q^{90} +857.053 q^{92} +473.823 q^{93} +108.800 q^{94} -626.538 q^{95} -528.385 q^{96} -1177.21 q^{97} -423.399 q^{98} -208.333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 8 q^{3} + 46 q^{4} - 30 q^{5} - 34 q^{6} - 25 q^{7} - 36 q^{8} + 91 q^{9}+O(q^{10}) $ 9 * q + 8 * q^3 + 46 * q^4 - 30 * q^5 - 34 * q^6 - 25 * q^7 - 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} - 30 q^{5} - 34 q^{6} - 25 q^{7} - 36 q^{8} + 91 q^{9} - 22 q^{10} + 99 q^{11} + 181 q^{12} - 351 q^{15} + 130 q^{16} + 53 q^{17} - 33 q^{18} - 69 q^{19} - 282 q^{20} - 463 q^{21} + 216 q^{23} + 121 q^{24} + 617 q^{25} + 275 q^{27} - 279 q^{28} - 91 q^{29} + 29 q^{30} - 636 q^{31} - 663 q^{32} + 88 q^{33} - 423 q^{34} - 358 q^{35} - 252 q^{36} - 967 q^{37} - 101 q^{38} + 652 q^{40} + 226 q^{41} - 1186 q^{42} + 42 q^{43} + 506 q^{44} - 5 q^{45} + 1127 q^{46} + 269 q^{47} - 1820 q^{48} + 228 q^{49} + 1374 q^{50} - 589 q^{51} + 1227 q^{53} + 2438 q^{54} - 330 q^{55} - 659 q^{56} + 71 q^{57} - 471 q^{58} + 613 q^{59} + 859 q^{60} + 427 q^{61} - 1714 q^{62} - 305 q^{63} - 1194 q^{64} - 374 q^{66} + 271 q^{67} - 2835 q^{68} - 846 q^{69} + 102 q^{70} - 2279 q^{71} + 2400 q^{72} - 3602 q^{73} - 4955 q^{74} - 883 q^{75} - 1126 q^{76} - 275 q^{77} - 1182 q^{79} + 2360 q^{80} + 2697 q^{81} + 1007 q^{82} + 1877 q^{83} - 1618 q^{84} + 441 q^{85} - 830 q^{86} + 1942 q^{87} - 396 q^{88} - 1258 q^{89} - 5669 q^{90} + 1046 q^{92} - 1556 q^{93} + 1439 q^{94} + 2032 q^{95} + 3417 q^{96} - 4002 q^{97} + 1855 q^{98} + 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 - 30 * q^5 - 34 * q^6 - 25 * q^7 - 36 * q^8 + 91 * q^9 - 22 * q^10 + 99 * q^11 + 181 * q^12 - 351 * q^15 + 130 * q^16 + 53 * q^17 - 33 * q^18 - 69 * q^19 - 282 * q^20 - 463 * q^21 + 216 * q^23 + 121 * q^24 + 617 * q^25 + 275 * q^27 - 279 * q^28 - 91 * q^29 + 29 * q^30 - 636 * q^31 - 663 * q^32 + 88 * q^33 - 423 * q^34 - 358 * q^35 - 252 * q^36 - 967 * q^37 - 101 * q^38 + 652 * q^40 + 226 * q^41 - 1186 * q^42 + 42 * q^43 + 506 * q^44 - 5 * q^45 + 1127 * q^46 + 269 * q^47 - 1820 * q^48 + 228 * q^49 + 1374 * q^50 - 589 * q^51 + 1227 * q^53 + 2438 * q^54 - 330 * q^55 - 659 * q^56 + 71 * q^57 - 471 * q^58 + 613 * q^59 + 859 * q^60 + 427 * q^61 - 1714 * q^62 - 305 * q^63 - 1194 * q^64 - 374 * q^66 + 271 * q^67 - 2835 * q^68 - 846 * q^69 + 102 * q^70 - 2279 * q^71 + 2400 * q^72 - 3602 * q^73 - 4955 * q^74 - 883 * q^75 - 1126 * q^76 - 275 * q^77 - 1182 * q^79 + 2360 * q^80 + 2697 * q^81 + 1007 * q^82 + 1877 * q^83 - 1618 * q^84 + 441 * q^85 - 830 * q^86 + 1942 * q^87 - 396 * q^88 - 1258 * q^89 - 5669 * q^90 + 1046 * q^92 - 1556 * q^93 + 1439 * q^94 + 2032 * q^95 + 3417 * q^96 - 4002 * q^97 + 1855 * q^98 + 1001 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.62159	0.573317	0.286658	−	0.958033i	$-0.407456\pi$
$2$	1.62159	0.573317	0.286658	+	0.958033i	$0.407456\pi$
$3$	−2.83913	−0.546391	−0.273196	−	0.961959i	$-0.588081\pi$
$3$	−2.83913	−0.546391	−0.273196	+	0.961959i	$0.588081\pi$
$4$	−5.37046	−0.671308
$5$	8.40999	0.752213	0.376106	−	0.926577i	$-0.377263\pi$
$5$	8.40999	0.752213	0.376106	+	0.926577i	$0.377263\pi$
$6$	−4.60389	−0.313255
$7$	9.04976	0.488641	0.244321	−	0.969695i	$-0.421435\pi$
$7$	9.04976	0.488641	0.244321	+	0.969695i	$0.421435\pi$
$8$	−21.6813	−0.958189
$9$	−18.9393	−0.701457
$10$	13.6375	0.431256
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	15.2474	0.366797
$13$	0	0
$13$	0	0
$14$	14.6750	0.280146
$15$	−23.8771	−0.411002
$16$	7.80556	0.121962
$17$	121.995	1.74048	0.870240	−	0.492628i	$-0.163964\pi$
$17$	121.995	1.74048	0.870240	+	0.492628i	$0.163964\pi$
$18$	−30.7117	−0.402157
$19$	−74.4993	−0.899542	−0.449771	−	0.893144i	$-0.648494\pi$
$19$	−74.4993	−0.899542	−0.449771	+	0.893144i	$0.648494\pi$
$20$	−45.1655	−0.504966
$21$	−25.6935	−0.266989
$22$	17.8374	0.172862
$23$	−159.587	−1.44679	−0.723393	−	0.690436i	$-0.757419\pi$
$23$	−159.587	−1.44679	−0.723393	+	0.690436i	$0.757419\pi$
$24$	61.5562	0.523546
$25$	−54.2720	−0.434176
$26$	0	0
$27$	130.428	0.929661
$28$	−48.6014	−0.328029
$29$	268.866	1.72163	0.860813	−	0.508921i	$-0.169956\pi$
$29$	268.866	1.72163	0.860813	+	0.508921i	$0.169956\pi$
$30$	−38.7187	−0.235635
$31$	−166.890	−0.966914	−0.483457	−	0.875368i	$-0.660619\pi$
$31$	−166.890	−0.966914	−0.483457	+	0.875368i	$0.660619\pi$
$32$	186.108	1.02811
$33$	−31.2304	−0.164743
$34$	197.825	0.997846
$35$	76.1084	0.367562
$36$	101.713	0.470893
$37$	−30.7828	−0.136775	−0.0683873	−	0.997659i	$-0.521785\pi$
$37$	−30.7828	−0.136775	−0.0683873	+	0.997659i	$0.521785\pi$
$38$	−120.807	−0.515723
$39$	0	0
$40$	−182.340	−0.720762
$41$	171.426	0.652980	0.326490	−	0.945201i	$-0.394134\pi$
$41$	171.426	0.652980	0.326490	+	0.945201i	$0.394134\pi$
$42$	−41.6641	−0.153069
$43$	285.411	1.01220	0.506102	−	0.862473i	$-0.331086\pi$
$43$	285.411	1.01220	0.506102	+	0.862473i	$0.331086\pi$
$44$	−59.0751	−0.202407
$45$	−159.280	−0.527645
$46$	−258.783	−0.829467
$47$	67.0946	0.208229	0.104114	−	0.994565i	$-0.466799\pi$
$47$	67.0946	0.208229	0.104114	+	0.994565i	$0.466799\pi$
$48$	−22.1610	−0.0666389
$49$	−261.102	−0.761230
$50$	−88.0067	−0.248921
$51$	−346.360	−0.950983
$52$	0	0
$53$	−422.643	−1.09537	−0.547684	−	0.836685i	$-0.684490\pi$
$53$	−422.643	−1.09537	−0.547684	+	0.836685i	$0.684490\pi$
$54$	211.500	0.532990
$55$	92.5099	0.226801
$56$	−196.211	−0.468211
$57$	211.513	0.491502
$58$	435.989	0.987037
$59$	−427.541	−0.943408	−0.471704	−	0.881757i	$-0.656361\pi$
$59$	−427.541	−0.943408	−0.471704	+	0.881757i	$0.656361\pi$
$60$	128.231	0.275909
$61$	128.991	0.270747	0.135373	−	0.990795i	$-0.456777\pi$
$61$	128.991	0.270747	0.135373	+	0.990795i	$0.456777\pi$
$62$	−270.626	−0.554348
$63$	−171.396	−0.342761
$64$	239.346	0.467472
$65$	0	0
$66$	−50.6428	−0.0944500
$67$	622.950	1.13590	0.567951	−	0.823062i	$-0.307736\pi$
$67$	622.950	1.13590	0.567951	+	0.823062i	$0.307736\pi$
$68$	−655.170	−1.16840
$69$	453.087	0.790511
$70$	123.416	0.210730
$71$	1140.26	1.90597	0.952986	−	0.303013i	$-0.0979926\pi$
$71$	1140.26	1.90597	0.952986	+	0.303013i	$0.0979926\pi$
$72$	410.630	0.672128
$73$	−839.061	−1.34527	−0.672635	−	0.739975i	$-0.734838\pi$
$73$	−839.061	−1.34527	−0.672635	+	0.739975i	$0.734838\pi$
$74$	−49.9169	−0.0784151
$75$	154.085	0.237230
$76$	400.095	0.603870
$77$	99.5474	0.147331
$78$	0	0
$79$	650.986	0.927110	0.463555	−	0.886068i	$-0.346574\pi$
$79$	650.986	0.927110	0.463555	+	0.886068i	$0.346574\pi$
$80$	65.6447	0.0917412
$81$	141.060	0.193499
$82$	277.981	0.374365
$83$	−891.619	−1.17913	−0.589566	−	0.807720i	$-0.700701\pi$
$83$	−891.619	−1.17913	−0.589566	+	0.807720i	$0.700701\pi$
$84$	137.986	0.179232
$85$	1025.98	1.30921
$86$	462.818	0.580314
$87$	−763.346	−0.940681
$88$	−238.495	−0.288905
$89$	−730.428	−0.869946	−0.434973	−	0.900443i	$-0.643242\pi$
$89$	−730.428	−0.869946	−0.434973	+	0.900443i	$0.643242\pi$
$90$	−258.286	−0.302508
$91$	0	0
$92$	857.053	0.971239
$93$	473.823	0.528313
$94$	108.800	0.119381
$95$	−626.538	−0.676647
$96$	−528.385	−0.561751
$97$	−1177.21	−1.23224	−0.616119	−	0.787653i	$-0.711296\pi$
$97$	−1177.21	−1.23224	−0.616119	+	0.787653i	$0.711296\pi$
$98$	−423.399	−0.436426
$99$	−208.333	−0.211497
$100$	291.466	0.291466
$101$	−1179.99	−1.16250	−0.581252	−	0.813724i	$-0.697437\pi$
$101$	−1179.99	−1.16250	−0.581252	+	0.813724i	$0.697437\pi$
$102$	−561.652	−0.545214
$103$	1545.82	1.47878	0.739389	−	0.673278i	$-0.235114\pi$
$103$	1545.82	1.47878	0.739389	+	0.673278i	$0.235114\pi$
$104$	0	0
$105$	−216.082	−0.200833
$106$	−685.351	−0.627993
$107$	−1381.48	−1.24816	−0.624080	−	0.781360i	$-0.714526\pi$
$107$	−1381.48	−1.24816	−0.624080	+	0.781360i	$0.714526\pi$
$108$	−700.458	−0.624088
$109$	−1537.26	−1.35085	−0.675427	−	0.737426i	$-0.736041\pi$
$109$	−1537.26	−1.35085	−0.675427	+	0.737426i	$0.736041\pi$
$110$	150.013	0.130029
$111$	87.3963	0.0747324
$112$	70.6384	0.0595956
$113$	2274.72	1.89369	0.946847	−	0.321684i	$-0.104249\pi$
$113$	2274.72	1.89369	0.946847	+	0.321684i	$0.104249\pi$
$114$	342.987	0.281786
$115$	−1342.12	−1.08829
$116$	−1443.93	−1.15574
$117$	0	0
$118$	−693.294	−0.540872
$119$	1104.03	0.850470
$120$	517.687	0.393818
$121$	121.000	0.0909091
$122$	209.169	0.155224
$123$	−486.700	−0.356783
$124$	896.277	0.649097
$125$	−1507.68	−1.07881
$126$	−277.934	−0.196510
$127$	1456.61	1.01774	0.508870	−	0.860843i	$-0.330063\pi$
$127$	1456.61	1.01774	0.508870	+	0.860843i	$0.330063\pi$
$128$	−1100.75	−0.760102
$129$	−810.320	−0.553059
$130$	0	0
$131$	−2459.68	−1.64048	−0.820242	−	0.572017i	$-0.806161\pi$
$131$	−2459.68	−1.64048	−0.820242	+	0.572017i	$0.806161\pi$
$132$	167.722	0.110593
$133$	−674.200	−0.439553
$134$	1010.17	0.651232
$135$	1096.90	0.699303
$136$	−2645.02	−1.66771
$137$	−2879.54	−1.79573	−0.897867	−	0.440266i	$-0.854884\pi$
$137$	−2879.54	−1.79573	−0.897867	+	0.440266i	$0.854884\pi$
$138$	734.719	0.453213
$139$	−383.930	−0.234277	−0.117139	−	0.993116i	$-0.537372\pi$
$139$	−383.930	−0.234277	−0.117139	+	0.993116i	$0.537372\pi$
$140$	−408.737	−0.246747
$141$	−190.490	−0.113774
$142$	1849.03	1.09273
$143$	0	0
$144$	−147.832	−0.0855510
$145$	2261.16	1.29503
$146$	−1360.61	−0.771266
$147$	741.302	0.415929
$148$	165.318	0.0918178
$149$	242.150	0.133139	0.0665694	−	0.997782i	$-0.478795\pi$
$149$	242.150	0.133139	0.0665694	+	0.997782i	$0.478795\pi$
$150$	249.863	0.136008
$151$	−2316.14	−1.24824	−0.624121	−	0.781328i	$-0.714543\pi$
$151$	−2316.14	−1.24824	−0.624121	+	0.781328i	$0.714543\pi$
$152$	1615.24	0.861931
$153$	−2310.51	−1.22087
$154$	161.425	0.0844673
$155$	−1403.54	−0.727325
$156$	0	0
$157$	1439.81	0.731908	0.365954	−	0.930633i	$-0.380743\pi$
$157$	1439.81	0.731908	0.365954	+	0.930633i	$0.380743\pi$
$158$	1055.63	0.531528
$159$	1199.94	0.598499
$160$	1565.17	0.773359
$161$	−1444.22	−0.706959
$162$	228.741	0.110936
$163$	990.309	0.475871	0.237936	−	0.971281i	$-0.423529\pi$
$163$	990.309	0.475871	0.237936	+	0.971281i	$0.423529\pi$
$164$	−920.635	−0.438351
$165$	−262.648	−0.123922
$166$	−1445.84	−0.676016
$167$	2388.61	1.10680	0.553402	−	0.832915i	$-0.313329\pi$
$167$	2388.61	1.10680	0.553402	+	0.832915i	$0.313329\pi$
$168$	557.069	0.255826
$169$	0	0
$170$	1663.71	0.750593
$171$	1410.97	0.630990
$172$	−1532.79	−0.679501
$173$	−191.001	−0.0839397	−0.0419698	−	0.999119i	$-0.513363\pi$
$173$	−191.001	−0.0839397	−0.0419698	+	0.999119i	$0.513363\pi$
$174$	−1237.83	−0.539308
$175$	−491.149	−0.212156
$176$	85.8611	0.0367729
$177$	1213.84	0.515470
$178$	−1184.45	−0.498755
$179$	−715.726	−0.298860	−0.149430	−	0.988772i	$-0.547744\pi$
$179$	−715.726	−0.298860	−0.149430	+	0.988772i	$0.547744\pi$
$180$	855.405	0.354212
$181$	−2199.99	−0.903447	−0.451724	−	0.892158i	$-0.649191\pi$
$181$	−2199.99	−0.903447	−0.451724	+	0.892158i	$0.649191\pi$
$182$	0	0
$183$	−366.221	−0.147934
$184$	3460.05	1.38629
$185$	−258.883	−0.102884
$186$	768.344	0.302891
$187$	1341.95	0.524774
$188$	−360.329	−0.139786
$189$	1180.34	0.454270
$190$	−1015.98	−0.387933
$191$	−2439.02	−0.923987	−0.461994	−	0.886883i	$-0.652866\pi$
$191$	−2439.02	−0.923987	−0.461994	+	0.886883i	$0.652866\pi$
$192$	−679.534	−0.255423
$193$	−4809.19	−1.79364	−0.896821	−	0.442394i	$-0.854129\pi$
$193$	−4809.19	−1.79364	−0.896821	+	0.442394i	$0.854129\pi$
$194$	−1908.94	−0.706463
$195$	0	0
$196$	1402.24	0.511020
$197$	405.408	0.146620	0.0733099	−	0.997309i	$-0.476644\pi$
$197$	405.408	0.146620	0.0733099	+	0.997309i	$0.476644\pi$
$198$	−337.829	−0.121255
$199$	−1957.65	−0.697356	−0.348678	−	0.937243i	$-0.613369\pi$
$199$	−1957.65	−0.697356	−0.348678	+	0.937243i	$0.613369\pi$
$200$	1176.69	0.416023
$201$	−1768.64	−0.620646
$202$	−1913.45	−0.666483
$203$	2433.17	0.841257
$204$	1860.11	0.638402
$205$	1441.69	0.491180
$206$	2506.68	0.847809
$207$	3022.46	1.01486
$208$	0	0
$209$	−819.492	−0.271222
$210$	−350.395	−0.115141
$211$	−1100.93	−0.359200	−0.179600	−	0.983740i	$-0.557480\pi$
$211$	−1100.93	−0.359200	−0.179600	+	0.983740i	$0.557480\pi$
$212$	2269.79	0.735329
$213$	−3237.35	−1.04141
$214$	−2240.19	−0.715591
$215$	2400.31	0.761393
$216$	−2827.85	−0.890791
$217$	−1510.31	−0.472474
$218$	−2492.80	−0.774468
$219$	2382.20	0.735043
$220$	−496.821	−0.152253
$221$	0	0
$222$	141.721	0.0428453
$223$	−1200.77	−0.360580	−0.180290	−	0.983614i	$-0.557704\pi$
$223$	−1200.77	−0.360580	−0.180290	+	0.983614i	$0.557704\pi$
$224$	1684.23	0.502378
$225$	1027.88	0.304556
$226$	3688.65	1.08569
$227$	−3382.58	−0.989030	−0.494515	−	0.869169i	$-0.664654\pi$
$227$	−3382.58	−0.989030	−0.494515	+	0.869169i	$0.664654\pi$
$228$	−1135.92	−0.329949
$229$	−1606.50	−0.463584	−0.231792	−	0.972765i	$-0.574459\pi$
$229$	−1606.50	−0.463584	−0.231792	+	0.972765i	$0.574459\pi$
$230$	−2176.36	−0.623936
$231$	−282.628	−0.0805002
$232$	−5829.37	−1.64964
$233$	−5429.41	−1.52658	−0.763288	−	0.646058i	$-0.776416\pi$
$233$	−5429.41	−1.52658	−0.763288	+	0.646058i	$0.776416\pi$
$234$	0	0
$235$	564.265	0.156632
$236$	2296.09	0.633317
$237$	−1848.24	−0.506564
$238$	1790.27	0.487589
$239$	2800.44	0.757930	0.378965	−	0.925411i	$-0.376280\pi$
$239$	2800.44	0.757930	0.378965	+	0.925411i	$0.376280\pi$
$240$	−186.374	−0.0501266
$241$	−1561.49	−0.417364	−0.208682	−	0.977984i	$-0.566917\pi$
$241$	−1561.49	−0.417364	−0.208682	+	0.977984i	$0.566917\pi$
$242$	196.212	0.0521197
$243$	−3922.04	−1.03539
$244$	−692.739	−0.181754
$245$	−2195.86	−0.572607
$246$	−789.225	−0.204550
$247$	0	0
$248$	3618.40	0.926486
$249$	2531.42	0.644267
$250$	−2444.83	−0.618497
$251$	3010.04	0.756940	0.378470	−	0.925613i	$-0.376450\pi$
$251$	3010.04	0.756940	0.378470	+	0.925613i	$0.376450\pi$
$252$	920.478	0.230098
$253$	−1755.45	−0.436223
$254$	2362.01	0.583487
$255$	−2912.89	−0.715341
$256$	−3699.72	−0.903251
$257$	−3094.77	−0.751152	−0.375576	−	0.926792i	$-0.622555\pi$
$257$	−3094.77	−0.751152	−0.375576	+	0.926792i	$0.622555\pi$
$258$	−1314.00	−0.317078
$259$	−278.577	−0.0668336
$260$	0	0
$261$	−5092.14	−1.20765
$262$	−3988.58	−0.940517
$263$	−4746.23	−1.11279	−0.556397	−	0.830917i	$-0.687817\pi$
$263$	−4746.23	−1.11279	−0.556397	+	0.830917i	$0.687817\pi$
$264$	677.118	0.157855
$265$	−3554.42	−0.823949
$266$	−1093.27	−0.252003
$267$	2073.78	0.475331
$268$	−3345.53	−0.762540
$269$	4326.50	0.980637	0.490318	−	0.871543i	$-0.336880\pi$
$269$	4326.50	0.980637	0.490318	+	0.871543i	$0.336880\pi$
$270$	1778.71	0.400922
$271$	−998.230	−0.223757	−0.111878	−	0.993722i	$-0.535687\pi$
$271$	−998.230	−0.223757	−0.111878	+	0.993722i	$0.535687\pi$
$272$	952.240	0.212272
$273$	0	0
$274$	−4669.42	−1.02953
$275$	−596.992	−0.130909
$276$	−2433.29	−0.530676
$277$	4716.29	1.02301	0.511506	−	0.859280i	$-0.329088\pi$
$277$	4716.29	1.02301	0.511506	+	0.859280i	$0.329088\pi$
$278$	−622.575	−0.134315
$279$	3160.79	0.678248
$280$	−1650.13	−0.352194
$281$	−4370.32	−0.927800	−0.463900	−	0.885888i	$-0.653550\pi$
$281$	−4370.32	−0.927800	−0.463900	+	0.885888i	$0.653550\pi$
$282$	−308.896	−0.0652287
$283$	−3403.83	−0.714972	−0.357486	−	0.933919i	$-0.616366\pi$
$283$	−3403.83	−0.714972	−0.357486	+	0.933919i	$0.616366\pi$
$284$	−6123.73	−1.27949
$285$	1778.82	0.369714
$286$	0	0
$287$	1551.36	0.319073
$288$	−3524.76	−0.721176
$289$	9969.80	2.02927
$290$	3666.66	0.742462
$291$	3342.24	0.673284
$292$	4506.15	0.903090
$293$	−6760.39	−1.34794	−0.673969	−	0.738759i	$-0.735412\pi$
$293$	−6760.39	−1.34794	−0.673969	+	0.738759i	$0.735412\pi$
$294$	1202.08	0.238459
$295$	−3595.62	−0.709644
$296$	667.412	0.131056
$297$	1434.71	0.280303
$298$	392.666	0.0763307
$299$	0	0
$300$	−827.510	−0.159254
$301$	2582.90	0.494605
$302$	−3755.81	−0.715638
$303$	3350.13	0.635182
$304$	−581.508	−0.109710
$305$	1084.81	0.203659
$306$	−3746.68	−0.699946
$307$	−5570.35	−1.03556	−0.517780	−	0.855514i	$-0.673241\pi$
$307$	−5570.35	−1.03556	−0.517780	+	0.855514i	$0.673241\pi$
$308$	−534.615	−0.0989043
$309$	−4388.79	−0.807991
$310$	−2275.97	−0.416988
$311$	−105.135	−0.0191693	−0.00958463	−	0.999954i	$-0.503051\pi$
$311$	−105.135	−0.0191693	−0.00958463	+	0.999954i	$0.503051\pi$
$312$	0	0
$313$	−8956.96	−1.61750	−0.808750	−	0.588153i	$-0.799855\pi$
$313$	−8956.96	−1.61750	−0.808750	+	0.588153i	$0.799855\pi$
$314$	2334.78	0.419615
$315$	−1441.44	−0.257829
$316$	−3496.10	−0.622376
$317$	−2755.29	−0.488177	−0.244089	−	0.969753i	$-0.578489\pi$
$317$	−2755.29	−0.488177	−0.244089	+	0.969753i	$0.578489\pi$
$318$	1945.80	0.343130
$319$	2957.53	0.519090
$320$	2012.90	0.351638
$321$	3922.22	0.681984
$322$	−2341.92	−0.405312
$323$	−9088.54	−1.56563
$324$	−757.560	−0.129897
$325$	0	0
$326$	1605.87	0.272825
$327$	4364.49	0.738095
$328$	−3716.74	−0.625679
$329$	607.190	0.101749
$330$	−425.906	−0.0710465
$331$	10291.9	1.70904	0.854522	−	0.519415i	$-0.173850\pi$
$331$	10291.9	1.70904	0.854522	+	0.519415i	$0.173850\pi$
$332$	4788.41	0.791560
$333$	583.005	0.0959414
$334$	3873.33	0.634549
$335$	5239.00	0.854440
$336$	−200.552	−0.0325625
$337$	5903.00	0.954175	0.477088	−	0.878856i	$-0.341692\pi$
$337$	5903.00	0.954175	0.477088	+	0.878856i	$0.341692\pi$
$338$	0	0
$339$	−6458.22	−1.03470
$340$	−5509.98	−0.878883
$341$	−1835.79	−0.291536
$342$	2288.00	0.361757
$343$	−5466.98	−0.860609
$344$	−6188.10	−0.969883
$345$	3810.46	0.594632
$346$	−309.725	−0.0481240
$347$	4826.82	0.746735	0.373368	−	0.927683i	$-0.378203\pi$
$347$	4826.82	0.746735	0.373368	+	0.927683i	$0.378203\pi$
$348$	4099.52	0.631486
$349$	1693.32	0.259717	0.129859	−	0.991533i	$-0.458548\pi$
$349$	1693.32	0.259717	0.129859	+	0.991533i	$0.458548\pi$
$350$	−796.439	−0.121633
$351$	0	0
$352$	2047.19	0.309987
$353$	−3036.87	−0.457893	−0.228946	−	0.973439i	$-0.573528\pi$
$353$	−3036.87	−0.457893	−0.228946	+	0.973439i	$0.573528\pi$
$354$	1968.35	0.295528
$355$	9589.59	1.43370
$356$	3922.74	0.584002
$357$	−3134.48	−0.464689
$358$	−1160.61	−0.171341
$359$	−10171.1	−1.49529	−0.747643	−	0.664101i	$-0.768815\pi$
$359$	−10171.1	−1.49529	−0.747643	+	0.664101i	$0.768815\pi$
$360$	3453.40	0.505583
$361$	−1308.86	−0.190824
$362$	−3567.47	−0.517962
$363$	−343.535	−0.0496719
$364$	0	0
$365$	−7056.50	−1.01193
$366$	−593.859	−0.0848129
$367$	−2642.07	−0.375790	−0.187895	−	0.982189i	$-0.560167\pi$
$367$	−2642.07	−0.375790	−0.187895	+	0.982189i	$0.560167\pi$
$368$	−1245.66	−0.176453
$369$	−3246.69	−0.458038
$370$	−419.801	−0.0589849
$371$	−3824.82	−0.535242
$372$	−2544.65	−0.354661
$373$	3015.94	0.418658	0.209329	−	0.977845i	$-0.432872\pi$
$373$	3015.94	0.418658	0.209329	+	0.977845i	$0.432872\pi$
$374$	2176.08	0.300862
$375$	4280.49	0.589450
$376$	−1454.70	−0.199523
$377$	0	0
$378$	1914.02	0.260441
$379$	3559.16	0.482379	0.241190	−	0.970478i	$-0.422462\pi$
$379$	3559.16	0.482379	0.241190	+	0.970478i	$0.422462\pi$
$380$	3364.80	0.454238
$381$	−4135.50	−0.556084
$382$	−3955.09	−0.529738
$383$	1979.76	0.264127	0.132064	−	0.991241i	$-0.457840\pi$
$383$	1979.76	0.264127	0.132064	+	0.991241i	$0.457840\pi$
$384$	3125.16	0.415313
$385$	837.193	0.110824
$386$	−7798.51	−1.02833
$387$	−5405.50	−0.710018
$388$	6322.14	0.827211
$389$	−6847.24	−0.892465	−0.446232	−	0.894917i	$-0.647235\pi$
$389$	−6847.24	−0.892465	−0.446232	+	0.894917i	$0.647235\pi$
$390$	0	0
$391$	−19468.8	−2.51810
$392$	5661.04	0.729402
$393$	6983.36	0.896346
$394$	657.403	0.0840596
$395$	5474.79	0.697384
$396$	1118.84	0.141980
$397$	2400.01	0.303408	0.151704	−	0.988426i	$-0.451524\pi$
$397$	2400.01	0.303408	0.151704	+	0.988426i	$0.451524\pi$
$398$	−3174.49	−0.399806
$399$	1914.14	0.240168
$400$	−423.623	−0.0529529
$401$	−12086.7	−1.50518	−0.752592	−	0.658487i	$-0.771197\pi$
$401$	−12086.7	−1.50518	−0.752592	+	0.658487i	$0.771197\pi$
$402$	−2867.99	−0.355827
$403$	0	0
$404$	6337.06	0.780398
$405$	1186.32	0.145552
$406$	3945.60	0.482307
$407$	−338.610	−0.0412391
$408$	7509.55	0.911221
$409$	−6627.32	−0.801222	−0.400611	−	0.916248i	$-0.631202\pi$
$409$	−6627.32	−0.801222	−0.400611	+	0.916248i	$0.631202\pi$
$410$	2337.82	0.281602
$411$	8175.39	0.981173
$412$	−8301.77	−0.992715
$413$	−3869.14	−0.460988
$414$	4901.18	0.581835
$415$	−7498.51	−0.886958
$416$	0	0
$417$	1090.03	0.128007
$418$	−1328.88	−0.155496
$419$	1404.54	0.163762	0.0818810	−	0.996642i	$-0.473907\pi$
$419$	1404.54	0.163762	0.0818810	+	0.996642i	$0.473907\pi$
$420$	1160.46	0.134820
$421$	7150.76	0.827807	0.413904	−	0.910321i	$-0.364165\pi$
$421$	7150.76	0.827807	0.413904	+	0.910321i	$0.364165\pi$
$422$	−1785.26	−0.205936
$423$	−1270.73	−0.146063
$424$	9163.47	1.04957
$425$	−6620.92	−0.755675
$426$	−5249.64	−0.597056
$427$	1167.33	0.132298
$428$	7419.21	0.837900
$429$	0	0
$430$	3892.30	0.436519
$431$	2311.73	0.258357	0.129179	−	0.991621i	$-0.458766\pi$
$431$	2311.73	0.258357	0.129179	+	0.991621i	$0.458766\pi$
$432$	1018.06	0.113383
$433$	3002.50	0.333236	0.166618	−	0.986022i	$-0.446715\pi$
$433$	3002.50	0.333236	0.166618	+	0.986022i	$0.446715\pi$
$434$	−2449.10	−0.270877
$435$	−6419.73	−0.707592
$436$	8255.82	0.906839
$437$	11889.1	1.30145
$438$	3862.95	0.421413
$439$	324.153	0.0352414	0.0176207	−	0.999845i	$-0.494391\pi$
$439$	324.153	0.0352414	0.0176207	+	0.999845i	$0.494391\pi$
$440$	−2005.74	−0.217318
$441$	4945.10	0.533970
$442$	0	0
$443$	−3685.38	−0.395254	−0.197627	−	0.980277i	$-0.563324\pi$
$443$	−3685.38	−0.395254	−0.197627	+	0.980277i	$0.563324\pi$
$444$	−469.359	−0.0501684
$445$	−6142.89	−0.654385
$446$	−1947.15	−0.206727
$447$	−687.495	−0.0727458
$448$	2166.02	0.228426
$449$	4059.06	0.426635	0.213317	−	0.976983i	$-0.431573\pi$
$449$	4059.06	0.426635	0.213317	+	0.976983i	$0.431573\pi$
$450$	1666.79	0.174607
$451$	1885.68	0.196881
$452$	−12216.3	−1.27125
$453$	6575.81	0.682028
$454$	−5485.14	−0.567028
$455$	0	0
$456$	−4585.89	−0.470952
$457$	2299.36	0.235360	0.117680	−	0.993052i	$-0.462454\pi$
$457$	2299.36	0.235360	0.117680	+	0.993052i	$0.462454\pi$
$458$	−2605.08	−0.265781
$459$	15911.6	1.61806
$460$	7207.81	0.730578
$461$	13576.3	1.37161	0.685805	−	0.727785i	$-0.259450\pi$
$461$	13576.3	1.37161	0.685805	+	0.727785i	$0.259450\pi$
$462$	−458.305	−0.0461522
$463$	−9773.50	−0.981021	−0.490511	−	0.871435i	$-0.663190\pi$
$463$	−9773.50	−0.981021	−0.490511	+	0.871435i	$0.663190\pi$
$464$	2098.65	0.209973
$465$	3984.85	0.397404
$466$	−8804.24	−0.875212
$467$	11504.2	1.13994	0.569969	−	0.821666i	$-0.306955\pi$
$467$	11504.2	1.13994	0.569969	+	0.821666i	$0.306955\pi$
$468$	0	0
$469$	5637.54	0.555048
$470$	915.004	0.0897999
$471$	−4087.82	−0.399908
$472$	9269.66	0.903963
$473$	3139.52	0.305191
$474$	−2997.07	−0.290422
$475$	4043.23	0.390560
$476$	−5929.13	−0.570927
$477$	8004.58	0.768353
$478$	4541.15	0.434534
$479$	3823.46	0.364714	0.182357	−	0.983232i	$-0.441627\pi$
$479$	3823.46	0.364714	0.182357	+	0.983232i	$0.441627\pi$
$480$	−4443.72	−0.422556
$481$	0	0
$482$	−2532.09	−0.239282
$483$	4100.33	0.386276
$484$	−649.826	−0.0610280
$485$	−9900.29	−0.926905
$486$	−6359.92	−0.593605
$487$	−6491.32	−0.604003	−0.302002	−	0.953307i	$-0.597655\pi$
$487$	−6491.32	−0.604003	−0.302002	+	0.953307i	$0.597655\pi$
$488$	−2796.69	−0.259427
$489$	−2811.62	−0.260012
$490$	−3560.78	−0.328285
$491$	−9666.20	−0.888451	−0.444226	−	0.895915i	$-0.646521\pi$
$491$	−9666.20	−0.888451	−0.444226	+	0.895915i	$0.646521\pi$
$492$	2613.80	0.239511
$493$	32800.3	2.99646
$494$	0	0
$495$	−1752.08	−0.159091
$496$	−1302.67	−0.117927
$497$	10319.1	0.931337
$498$	4104.92	0.369369
$499$	9725.54	0.872495	0.436247	−	0.899827i	$-0.356307\pi$
$499$	9725.54	0.872495	0.436247	+	0.899827i	$0.356307\pi$
$500$	8096.92	0.724210
$501$	−6781.58	−0.604747
$502$	4881.04	0.433967
$503$	20469.2	1.81446	0.907232	−	0.420630i	$-0.138191\pi$
$503$	20469.2	1.81446	0.907232	+	0.420630i	$0.138191\pi$
$504$	3716.10	0.328429
$505$	−9923.67	−0.874450
$506$	−2846.61	−0.250094
$507$	0	0
$508$	−7822.65	−0.683217
$509$	2284.29	0.198918	0.0994589	−	0.995042i	$-0.468289\pi$
$509$	2284.29	0.198918	0.0994589	+	0.995042i	$0.468289\pi$
$510$	−4723.49	−0.410117
$511$	−7593.30	−0.657354
$512$	2806.56	0.242253
$513$	−9716.77	−0.836269
$514$	−5018.43	−0.430648
$515$	13000.3	1.11236
$516$	4351.79	0.371273
$517$	738.041	0.0627833
$518$	−451.736	−0.0383169
$519$	542.278	0.0458639
$520$	0	0
$521$	17638.0	1.48318	0.741589	−	0.670855i	$-0.234073\pi$
$521$	17638.0	1.48318	0.741589	+	0.670855i	$0.234073\pi$
$522$	−8257.34	−0.692364
$523$	12465.8	1.04224	0.521119	−	0.853484i	$-0.325515\pi$
$523$	12465.8	1.04224	0.521119	+	0.853484i	$0.325515\pi$
$524$	13209.6	1.10127
$525$	1394.44	0.115920
$526$	−7696.41	−0.637984
$527$	−20359.8	−1.68289
$528$	−243.771	−0.0200924
$529$	13300.9	1.09319
$530$	−5763.80	−0.472384
$531$	8097.34	0.661760
$532$	3620.77	0.295076
$533$	0	0
$534$	3362.81	0.272515
$535$	−11618.3	−0.938882
$536$	−13506.4	−1.08841
$537$	2032.04	0.163294
$538$	7015.79	0.562216
$539$	−2872.12	−0.229519
$540$	−5890.84	−0.469447
$541$	7286.90	0.579091	0.289545	−	0.957164i	$-0.406496\pi$
$541$	7286.90	0.579091	0.289545	+	0.957164i	$0.406496\pi$
$542$	−1618.71	−0.128284
$543$	6246.06	0.493636
$544$	22704.3	1.78941
$545$	−12928.4	−1.01613
$546$	0	0
$547$	10442.6	0.816261	0.408130	−	0.912924i	$-0.366181\pi$
$547$	10442.6	0.816261	0.408130	+	0.912924i	$0.366181\pi$
$548$	15464.5	1.20549
$549$	−2443.00	−0.189917
$550$	−968.074	−0.0750524
$551$	−20030.3	−1.54868
$552$	−9823.53	−0.757459
$553$	5891.27	0.453024
$554$	7647.86	0.586510
$555$	735.002	0.0562146
$556$	2061.88	0.157272
$557$	−5859.40	−0.445728	−0.222864	−	0.974850i	$-0.571541\pi$
$557$	−5859.40	−0.445728	−0.222864	+	0.974850i	$0.571541\pi$
$558$	5125.48	0.388851
$559$	0	0
$560$	594.069	0.0448285
$561$	−3809.96	−0.286732
$562$	−7086.85	−0.531923
$563$	−12954.0	−0.969710	−0.484855	−	0.874595i	$-0.661128\pi$
$563$	−12954.0	−0.969710	−0.484855	+	0.874595i	$0.661128\pi$
$564$	1023.02	0.0763776
$565$	19130.4	1.42446
$566$	−5519.61	−0.409905
$567$	1276.56	0.0945513
$568$	−24722.4	−1.82628
$569$	24532.4	1.80747	0.903737	−	0.428088i	$-0.140813\pi$
$569$	24532.4	1.80747	0.903737	+	0.428088i	$0.140813\pi$
$570$	2884.51	0.211963
$571$	−10872.4	−0.796844	−0.398422	−	0.917202i	$-0.630442\pi$
$571$	−10872.4	−0.796844	−0.398422	+	0.917202i	$0.630442\pi$
$572$	0	0
$573$	6924.71	0.504858
$574$	2515.66	0.182930
$575$	8661.08	0.628160
$576$	−4533.05	−0.327911
$577$	−3961.28	−0.285807	−0.142903	−	0.989737i	$-0.545644\pi$
$577$	−3961.28	−0.285807	−0.142903	+	0.989737i	$0.545644\pi$
$578$	16166.9	1.16341
$579$	13653.9	0.980030
$580$	−12143.5	−0.869363
$581$	−8068.94	−0.576172
$582$	5419.73	0.386005
$583$	−4649.07	−0.330266
$584$	18192.0	1.28902
$585$	0	0
$586$	−10962.5	−0.772796
$587$	10500.4	0.738327	0.369163	−	0.929364i	$-0.379644\pi$
$587$	10500.4	0.738327	0.369163	+	0.929364i	$0.379644\pi$
$588$	−3981.14	−0.279216
$589$	12433.2	0.869780
$590$	−5830.60	−0.406851
$591$	−1151.01	−0.0801117
$592$	−240.277	−0.0166813
$593$	8167.26	0.565580	0.282790	−	0.959182i	$-0.408740\pi$
$593$	8167.26	0.565580	0.282790	+	0.959182i	$0.408740\pi$
$594$	2326.50	0.160703
$595$	9284.85	0.639734
$596$	−1300.46	−0.0893771
$597$	5558.01	0.381029
$598$	0	0
$599$	−5240.52	−0.357466	−0.178733	−	0.983898i	$-0.557200\pi$
$599$	−5240.52	−0.357466	−0.178733	+	0.983898i	$0.557200\pi$
$600$	−3340.78	−0.227311
$601$	14867.4	1.00907	0.504537	−	0.863390i	$-0.331663\pi$
$601$	14867.4	1.00907	0.504537	+	0.863390i	$0.331663\pi$
$602$	4188.40	0.283565
$603$	−11798.3	−0.796786
$604$	12438.7	0.837954
$605$	1017.61	0.0683830
$606$	5432.52	0.364160
$607$	−5770.68	−0.385873	−0.192936	−	0.981211i	$-0.561801\pi$
$607$	−5770.68	−0.385873	−0.192936	+	0.981211i	$0.561801\pi$
$608$	−13864.9	−0.924830
$609$	−6908.09	−0.459655
$610$	1759.11	0.116761
$611$	0	0
$612$	12408.5	0.819580
$613$	−379.495	−0.0250043	−0.0125022	−	0.999922i	$-0.503980\pi$
$613$	−379.495	−0.0250043	−0.0125022	+	0.999922i	$0.503980\pi$
$614$	−9032.80	−0.593704
$615$	−4093.14	−0.268376
$616$	−2158.32	−0.141171
$617$	−28149.7	−1.83673	−0.918367	−	0.395730i	$-0.870492\pi$
$617$	−28149.7	−1.83673	−0.918367	+	0.395730i	$0.870492\pi$
$618$	−7116.79	−0.463235
$619$	17100.1	1.11036	0.555179	−	0.831731i	$-0.312650\pi$
$619$	17100.1	1.11036	0.555179	+	0.831731i	$0.312650\pi$
$620$	7537.68	0.488259
$621$	−20814.5	−1.34502
$622$	−170.485	−0.0109901
$623$	−6610.20	−0.425091
$624$	0	0
$625$	−5895.54	−0.377315
$626$	−14524.5	−0.927340
$627$	2326.64	0.148193
$628$	−7732.46	−0.491335
$629$	−3755.35	−0.238053
$630$	−2337.42	−0.147818
$631$	24567.7	1.54996	0.774980	−	0.631986i	$-0.217760\pi$
$631$	24567.7	1.54996	0.774980	+	0.631986i	$0.217760\pi$
$632$	−14114.3	−0.888346
$633$	3125.69	0.196264
$634$	−4467.93	−0.279880
$635$	12250.1	0.765557
$636$	−6444.23	−0.401777
$637$	0	0
$638$	4795.88	0.297603
$639$	−21595.8	−1.33696
$640$	−9257.26	−0.571758
$641$	−19740.8	−1.21641	−0.608203	−	0.793782i	$-0.708109\pi$
$641$	−19740.8	−1.21641	−0.608203	+	0.793782i	$0.708109\pi$
$642$	6360.21	0.390993
$643$	−8787.40	−0.538944	−0.269472	−	0.963008i	$-0.586849\pi$
$643$	−8787.40	−0.538944	−0.269472	+	0.963008i	$0.586849\pi$
$644$	7756.13	0.474587
$645$	−6814.78	−0.416018
$646$	−14737.8	−0.897605
$647$	12069.0	0.733358	0.366679	−	0.930348i	$-0.380495\pi$
$647$	12069.0	0.733358	0.366679	+	0.930348i	$0.380495\pi$
$648$	−3058.38	−0.185408
$649$	−4702.95	−0.284448
$650$	0	0
$651$	4287.98	0.258156
$652$	−5318.42	−0.319456
$653$	−4127.91	−0.247377	−0.123689	−	0.992321i	$-0.539472\pi$
$653$	−4127.91	−0.247377	−0.123689	+	0.992321i	$0.539472\pi$
$654$	7077.40	0.423162
$655$	−20685.9	−1.23399
$656$	1338.07	0.0796387
$657$	15891.3	0.943649
$658$	984.610	0.0583345
$659$	−866.676	−0.0512305	−0.0256152	−	0.999672i	$-0.508154\pi$
$659$	−866.676	−0.0512305	−0.0256152	+	0.999672i	$0.508154\pi$
$660$	1410.54	0.0831897
$661$	−11325.8	−0.666449	−0.333225	−	0.942847i	$-0.608137\pi$
$661$	−11325.8	−0.666449	−0.333225	+	0.942847i	$0.608137\pi$
$662$	16689.2	0.979824
$663$	0	0
$664$	19331.5	1.12983
$665$	−5670.02	−0.330638
$666$	945.393	0.0550048
$667$	−42907.4	−2.49083
$668$	−12827.9	−0.743006
$669$	3409.14	0.197018
$670$	8495.49	0.489865
$671$	1418.90	0.0816332
$672$	−4781.76	−0.274495
$673$	−2971.35	−0.170189	−0.0850945	−	0.996373i	$-0.527119\pi$
$673$	−2971.35	−0.170189	−0.0850945	+	0.996373i	$0.527119\pi$
$674$	9572.22	0.547045
$675$	−7078.58	−0.403637
$676$	0	0
$677$	13089.6	0.743096	0.371548	−	0.928414i	$-0.378827\pi$
$677$	13089.6	0.743096	0.371548	+	0.928414i	$0.378827\pi$
$678$	−10472.6	−0.593210
$679$	−10653.4	−0.602122
$680$	−22244.6	−1.25447
$681$	9603.59	0.540397
$682$	−2976.89	−0.167142
$683$	552.603	0.0309587	0.0154793	−	0.999880i	$-0.495073\pi$
$683$	552.603	0.0309587	0.0154793	+	0.999880i	$0.495073\pi$
$684$	−7577.54	−0.423588
$685$	−24216.9	−1.35077
$686$	−8865.17	−0.493402
$687$	4561.08	0.253298
$688$	2227.79	0.123450
$689$	0	0
$690$	6178.98	0.340913
$691$	18218.4	1.00298	0.501491	−	0.865163i	$-0.332785\pi$
$691$	18218.4	1.00298	0.501491	+	0.865163i	$0.332785\pi$
$692$	1025.77	0.0563493
$693$	−1885.36	−0.103346
$694$	7827.10	0.428116
$695$	−3228.85	−0.176226
$696$	16550.4	0.901350
$697$	20913.1	1.13650
$698$	2745.86	0.148900
$699$	15414.8	0.834107
$700$	2637.70	0.142422
$701$	6395.52	0.344587	0.172293	−	0.985046i	$-0.444882\pi$
$701$	6395.52	0.344587	0.172293	+	0.985046i	$0.444882\pi$
$702$	0	0
$703$	2293.29	0.123034
$704$	2632.80	0.140948
$705$	−1602.02	−0.0855825
$706$	−4924.54	−0.262518
$707$	−10678.6	−0.568047
$708$	−6518.91	−0.346039
$709$	−23276.9	−1.23298	−0.616488	−	0.787364i	$-0.711445\pi$
$709$	−23276.9	−1.23298	−0.616488	+	0.787364i	$0.711445\pi$
$710$	15550.3	0.821963
$711$	−12329.2	−0.650327
$712$	15836.7	0.833573
$713$	26633.4	1.39892
$714$	−5082.82	−0.266414
$715$	0	0
$716$	3843.78	0.200627
$717$	−7950.81	−0.414126
$718$	−16493.2	−0.857273
$719$	−22544.4	−1.16935	−0.584676	−	0.811267i	$-0.698778\pi$
$719$	−22544.4	−1.16935	−0.584676	+	0.811267i	$0.698778\pi$
$720$	−1243.27	−0.0643525
$721$	13989.3	0.722592
$722$	−2122.43	−0.109403
$723$	4433.28	0.228044
$724$	11815.0	0.606491
$725$	−14591.9	−0.747489
$726$	−557.071	−0.0284777
$727$	−32297.1	−1.64764	−0.823820	−	0.566851i	$-0.808161\pi$
$727$	−32297.1	−1.64764	−0.823820	+	0.566851i	$0.808161\pi$
$728$	0	0
$729$	7326.55	0.372227
$730$	−11442.7	−0.580156
$731$	34818.8	1.76172
$732$	1966.78	0.0993090
$733$	34885.9	1.75790	0.878951	−	0.476913i	$-0.158244\pi$
$733$	34885.9	1.75790	0.878951	+	0.476913i	$0.158244\pi$
$734$	−4284.34	−0.215447
$735$	6234.35	0.312867
$736$	−29700.3	−1.48746
$737$	6852.45	0.342487
$738$	−5264.78	−0.262601
$739$	19302.6	0.960837	0.480418	−	0.877039i	$-0.340485\pi$
$739$	19302.6	0.960837	0.480418	+	0.877039i	$0.340485\pi$
$740$	1390.32	0.0690665
$741$	0	0
$742$	−6202.27	−0.306863
$743$	−5088.50	−0.251250	−0.125625	−	0.992078i	$-0.540094\pi$
$743$	−5088.50	−0.251250	−0.125625	+	0.992078i	$0.540094\pi$
$744$	−10273.1	−0.506224
$745$	2036.48	0.100149
$746$	4890.60	0.240024
$747$	16886.7	0.827110
$748$	−7206.87	−0.352285
$749$	−12502.1	−0.609902
$750$	6941.18	0.337941
$751$	33349.9	1.62045	0.810224	−	0.586120i	$-0.199345\pi$
$751$	33349.9	1.62045	0.810224	+	0.586120i	$0.199345\pi$
$752$	523.711	0.0253960
$753$	−8545.90	−0.413585
$754$	0	0
$755$	−19478.7	−0.938943
$756$	−6338.97	−0.304955
$757$	22322.6	1.07177	0.535885	−	0.844291i	$-0.319978\pi$
$757$	22322.6	1.07177	0.535885	+	0.844291i	$0.319978\pi$
$758$	5771.48	0.276556
$759$	4983.96	0.238348
$760$	13584.2	0.648356
$761$	1730.41	0.0824277	0.0412138	−	0.999150i	$-0.486878\pi$
$761$	1730.41	0.0824277	0.0412138	+	0.999150i	$0.486878\pi$
$762$	−6706.06	−0.318812
$763$	−13911.9	−0.660083
$764$	13098.7	0.620280
$765$	−19431.3	−0.918355
$766$	3210.34	0.151429
$767$	0	0
$768$	10504.0	0.493528
$769$	6648.69	0.311779	0.155889	−	0.987775i	$-0.450176\pi$
$769$	6648.69	0.311779	0.155889	+	0.987775i	$0.450176\pi$
$770$	1357.58	0.0635373
$771$	8786.44	0.410423
$772$	25827.6	1.20409
$773$	11634.8	0.541366	0.270683	−	0.962669i	$-0.412751\pi$
$773$	11634.8	0.541366	0.270683	+	0.962669i	$0.412751\pi$
$774$	−8765.47	−0.407065
$775$	9057.46	0.419811
$776$	25523.4	1.18072
$777$	790.916	0.0365173
$778$	−11103.4	−0.511665
$779$	−12771.1	−0.587383
$780$	0	0
$781$	12542.9	0.574672
$782$	−31570.3	−1.44367
$783$	35067.6	1.60053
$784$	−2038.05	−0.0928410
$785$	12108.8	0.550550
$786$	11324.1	0.513890
$787$	−18991.8	−0.860210	−0.430105	−	0.902779i	$-0.641523\pi$
$787$	−18991.8	−0.860210	−0.430105	+	0.902779i	$0.641523\pi$
$788$	−2177.23	−0.0984270
$789$	13475.2	0.608021
$790$	8877.84	0.399822
$791$	20585.6	0.925337
$792$	4516.93	0.202654
$793$	0	0
$794$	3891.82	0.173949
$795$	10091.5	0.450198
$796$	10513.5	0.468141
$797$	−33330.3	−1.48133	−0.740665	−	0.671875i	$-0.765489\pi$
$797$	−33330.3	−1.48133	−0.740665	+	0.671875i	$0.765489\pi$
$798$	3103.95	0.137692
$799$	8185.21	0.362418
$800$	−10100.5	−0.446382
$801$	13833.8	0.610230
$802$	−19599.5	−0.862947
$803$	−9229.67	−0.405614
$804$	9498.39	0.416645
$805$	−12145.9	−0.531784
$806$	0	0
$807$	−12283.5	−0.535811
$808$	25583.7	1.11390
$809$	3933.25	0.170934	0.0854671	−	0.996341i	$-0.472762\pi$
$809$	3933.25	0.170934	0.0854671	+	0.996341i	$0.472762\pi$
$810$	1923.71	0.0834474
$811$	−43834.0	−1.89793	−0.948965	−	0.315383i	$-0.897867\pi$
$811$	−43834.0	−1.89793	−0.948965	+	0.315383i	$0.897867\pi$
$812$	−13067.3	−0.564742
$813$	2834.10	0.122259
$814$	−549.086	−0.0236431
$815$	8328.49	0.357956
$816$	−2703.53	−0.115984
$817$	−21262.9	−0.910521
$818$	−10746.8	−0.459354
$819$	0	0
$820$	−7742.53	−0.329733
$821$	3483.16	0.148067	0.0740335	−	0.997256i	$-0.476413\pi$
$821$	3483.16	0.148067	0.0740335	+	0.997256i	$0.476413\pi$
$822$	13257.1	0.562523
$823$	3375.08	0.142950	0.0714751	−	0.997442i	$-0.477229\pi$
$823$	3375.08	0.142950	0.0714751	+	0.997442i	$0.477229\pi$
$824$	−33515.5	−1.41695
$825$	1694.94	0.0715275
$826$	−6274.14	−0.264292
$827$	−27025.0	−1.13634	−0.568169	−	0.822912i	$-0.692348\pi$
$827$	−27025.0	−1.13634	−0.568169	+	0.822912i	$0.692348\pi$
$828$	−16232.0	−0.681282
$829$	14939.7	0.625909	0.312954	−	0.949768i	$-0.398681\pi$
$829$	14939.7	0.625909	0.312954	+	0.949768i	$0.398681\pi$
$830$	−12159.5	−0.508508
$831$	−13390.2	−0.558965
$832$	0	0
$833$	−31853.1	−1.32491
$834$	1767.57	0.0733886
$835$	20088.2	0.832551
$836$	4401.05	0.182074
$837$	−21767.1	−0.898902
$838$	2277.58	0.0938876
$839$	−8176.20	−0.336441	−0.168220	−	0.985749i	$-0.553802\pi$
$839$	−8176.20	−0.336441	−0.168220	+	0.985749i	$0.553802\pi$
$840$	4684.94	0.192436
$841$	47899.9	1.96400
$842$	11595.6	0.474596
$843$	12407.9	0.506941
$844$	5912.51	0.241134
$845$	0	0
$846$	−2060.59	−0.0837407
$847$	1095.02	0.0444219
$848$	−3298.96	−0.133593
$849$	9663.93	0.390654
$850$	−10736.4	−0.433241
$851$	4912.52	0.197883
$852$	17386.1	0.699104
$853$	−1432.28	−0.0574918	−0.0287459	−	0.999587i	$-0.509151\pi$
$853$	−1432.28	−0.0574918	−0.0287459	+	0.999587i	$0.509151\pi$
$854$	1892.93	0.0758487
$855$	11866.2	0.474639
$856$	29952.4	1.19597
$857$	−14564.2	−0.580519	−0.290259	−	0.956948i	$-0.593742\pi$
$857$	−14564.2	−0.580519	−0.290259	+	0.956948i	$0.593742\pi$
$858$	0	0
$859$	43414.4	1.72442	0.862212	−	0.506547i	$-0.169078\pi$
$859$	43414.4	1.72442	0.862212	+	0.506547i	$0.169078\pi$
$860$	−12890.8	−0.511129
$861$	−4404.52	−0.174339
$862$	3748.66	0.148121
$863$	29369.8	1.15847	0.579235	−	0.815161i	$-0.303351\pi$
$863$	29369.8	1.15847	0.579235	+	0.815161i	$0.303351\pi$
$864$	24273.7	0.955795
$865$	−1606.32	−0.0631405
$866$	4868.82	0.191050
$867$	−28305.6	−1.10877
$868$	8111.09	0.317175
$869$	7160.85	0.279534
$870$	−10410.1	−0.405674
$871$	0	0
$872$	33329.9	1.29437
$873$	22295.5	0.864362
$874$	19279.1	0.746141
$875$	−13644.1	−0.527149
$876$	−12793.5	−0.493440
$877$	9946.88	0.382990	0.191495	−	0.981494i	$-0.438666\pi$
$877$	9946.88	0.382990	0.191495	+	0.981494i	$0.438666\pi$
$878$	525.642	0.0202045
$879$	19193.6	0.736501
$880$	722.091	0.0276610
$881$	−30801.3	−1.17789	−0.588945	−	0.808173i	$-0.700457\pi$
$881$	−30801.3	−1.17789	−0.588945	+	0.808173i	$0.700457\pi$
$882$	8018.89	0.306134
$883$	6918.20	0.263665	0.131832	−	0.991272i	$-0.457914\pi$
$883$	6918.20	0.263665	0.131832	+	0.991272i	$0.457914\pi$
$884$	0	0
$885$	10208.4	0.387743
$886$	−5976.16	−0.226606
$887$	−9122.53	−0.345327	−0.172663	−	0.984981i	$-0.555237\pi$
$887$	−9122.53	−0.345327	−0.172663	+	0.984981i	$0.555237\pi$
$888$	−1894.87	−0.0716077
$889$	13181.9	0.497309
$890$	−9961.23	−0.375170
$891$	1551.66	0.0583420
$892$	6448.68	0.242060
$893$	−4998.50	−0.187311
$894$	−1114.83	−0.0417064
$895$	−6019.25	−0.224806
$896$	−9961.48	−0.371417
$897$	0	0
$898$	6582.12	0.244597
$899$	−44871.0	−1.66466
$900$	−5520.17	−0.204451
$901$	−51560.4	−1.90646
$902$	3057.79	0.112875
$903$	−7333.20	−0.270248
$904$	−49318.9	−1.81452
$905$	−18501.9	−0.679584
$906$	10663.2	0.391018
$907$	30087.8	1.10149	0.550744	−	0.834674i	$-0.314344\pi$
$907$	30087.8	1.10149	0.550744	+	0.834674i	$0.314344\pi$
$908$	18166.0	0.663944
$909$	22348.1	0.815446
$910$	0	0
$911$	25698.4	0.934607	0.467304	−	0.884097i	$-0.345225\pi$
$911$	25698.4	0.934607	0.467304	+	0.884097i	$0.345225\pi$
$912$	1650.98	0.0599445
$913$	−9807.81	−0.355522
$914$	3728.61	0.134936
$915$	−3079.92	−0.111278
$916$	8627.67	0.311208
$917$	−22259.5	−0.801608
$918$	25801.9	0.927659
$919$	−32000.4	−1.14864	−0.574318	−	0.818632i	$-0.694733\pi$
$919$	−32000.4	−1.14864	−0.574318	+	0.818632i	$0.694733\pi$
$920$	29099.0	1.04279
$921$	15815.0	0.565821
$922$	22015.2	0.786367
$923$	0	0
$924$	1517.84	0.0540404
$925$	1670.64	0.0593842
$926$	−15848.6	−0.562436
$927$	−29276.8	−1.03730
$928$	50038.1	1.77002
$929$	−40327.1	−1.42421	−0.712105	−	0.702073i	$-0.752258\pi$
$929$	−40327.1	−1.42421	−0.712105	+	0.702073i	$0.752258\pi$
$930$	6461.77	0.227838
$931$	19451.9	0.684758
$932$	29158.4	1.02480
$933$	298.491	0.0104739
$934$	18655.1	0.653546
$935$	11285.8	0.394742
$936$	0	0
$937$	−6019.50	−0.209870	−0.104935	−	0.994479i	$-0.533464\pi$
$937$	−6019.50	−0.209870	−0.104935	+	0.994479i	$0.533464\pi$
$938$	9141.76	0.318219
$939$	25430.0	0.883787
$940$	−3030.36	−0.105148
$941$	26288.5	0.910713	0.455357	−	0.890309i	$-0.349512\pi$
$941$	26288.5	0.910713	0.455357	+	0.890309i	$0.349512\pi$
$942$	−6628.74	−0.229274
$943$	−27357.2	−0.944723
$944$	−3337.20	−0.115060
$945$	9926.65	0.341708
$946$	5091.00	0.174971
$947$	−3907.29	−0.134076	−0.0670380	−	0.997750i	$-0.521355\pi$
$947$	−3907.29	−0.134076	−0.0670380	+	0.997750i	$0.521355\pi$
$948$	9925.88	0.340061
$949$	0	0
$950$	6556.43	0.223915
$951$	7822.62	0.266736
$952$	−23936.8	−0.814911
$953$	15742.9	0.535114	0.267557	−	0.963542i	$-0.413784\pi$
$953$	15742.9	0.535114	0.267557	+	0.963542i	$0.413784\pi$
$954$	12980.1	0.440510
$955$	−20512.2	−0.695035
$956$	−15039.6	−0.508804
$957$	−8396.80	−0.283626
$958$	6200.06	0.209097
$959$	−26059.1	−0.877470
$960$	−5714.87	−0.192132
$961$	−1938.71	−0.0650772
$962$	0	0
$963$	26164.4	0.875531
$964$	8385.94	0.280179
$965$	−40445.2	−1.34920
$966$	6649.03	0.221459
$967$	−31581.4	−1.05025	−0.525124	−	0.851026i	$-0.675981\pi$
$967$	−31581.4	−1.05025	−0.525124	+	0.851026i	$0.675981\pi$
$968$	−2623.44	−0.0871081
$969$	25803.6	0.855449
$970$	−16054.2	−0.531410
$971$	−6835.67	−0.225919	−0.112959	−	0.993600i	$-0.536033\pi$
$971$	−6835.67	−0.225919	−0.112959	+	0.993600i	$0.536033\pi$
$972$	21063.2	0.695063
$973$	−3474.48	−0.114477
$974$	−10526.2	−0.346285
$975$	0	0
$976$	1006.84	0.0330208
$977$	4896.64	0.160345	0.0801726	−	0.996781i	$-0.474453\pi$
$977$	4896.64	0.160345	0.0801726	+	0.996781i	$0.474453\pi$
$978$	−4559.28	−0.149069
$979$	−8034.71	−0.262299
$980$	11792.8	0.384395
$981$	29114.8	0.947566
$982$	−15674.6	−0.509364
$983$	−15812.1	−0.513049	−0.256524	−	0.966538i	$-0.582577\pi$
$983$	−15812.1	−0.513049	−0.256524	+	0.966538i	$0.582577\pi$
$984$	10552.3	0.341865
$985$	3409.48	0.110289
$986$	53188.5	1.71792
$987$	−1723.89	−0.0555948
$988$	0	0
$989$	−45547.8	−1.46444
$990$	−2841.14	−0.0912095
$991$	58171.1	1.86465	0.932323	−	0.361626i	$-0.117778\pi$
$991$	58171.1	1.86465	0.932323	+	0.361626i	$0.117778\pi$
$992$	−31059.6	−0.994096
$993$	−29220.0	−0.933806
$994$	16733.3	0.533951
$995$	−16463.8	−0.524560
$996$	−13594.9	−0.432501
$997$	−20051.7	−0.636953	−0.318477	−	0.947931i	$-0.603171\pi$
$997$	−20051.7	−0.636953	−0.318477	+	0.947931i	$0.603171\pi$
$998$	15770.8	0.500216
$999$	−4014.93	−0.127154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.d.1.6		9
13.12	even	2		143.4.a.c.1.4	✓	9
39.38	odd	2		1287.4.a.k.1.6		9
52.51	odd	2		2288.4.a.r.1.7		9
143.142	odd	2		1573.4.a.e.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.c.1.4	✓	9	13.12	even	2
1287.4.a.k.1.6		9	39.38	odd	2
1573.4.a.e.1.6		9	143.142	odd	2
1859.4.a.d.1.6		9	1.1	even	1	trivial
2288.4.a.r.1.7		9	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)

\(f(q)\)	\(=\)	\(q+1.62159 q^{2} -2.83913 q^{3} -5.37046 q^{4} +8.40999 q^{5} -4.60389 q^{6} +9.04976 q^{7} -21.6813 q^{8} -18.9393 q^{9} +O(q^{10})\)	\(q+1.62159 q^{2} -2.83913 q^{3} -5.37046 q^{4} +8.40999 q^{5} -4.60389 q^{6} +9.04976 q^{7} -21.6813 q^{8} -18.9393 q^{9} +13.6375 q^{10} +11.0000 q^{11} +15.2474 q^{12} +14.6750 q^{14} -23.8771 q^{15} +7.80556 q^{16} +121.995 q^{17} -30.7117 q^{18} -74.4993 q^{19} -45.1655 q^{20} -25.6935 q^{21} +17.8374 q^{22} -159.587 q^{23} +61.5562 q^{24} -54.2720 q^{25} +130.428 q^{27} -48.6014 q^{28} +268.866 q^{29} -38.7187 q^{30} -166.890 q^{31} +186.108 q^{32} -31.2304 q^{33} +197.825 q^{34} +76.1084 q^{35} +101.713 q^{36} -30.7828 q^{37} -120.807 q^{38} -182.340 q^{40} +171.426 q^{41} -41.6641 q^{42} +285.411 q^{43} -59.0751 q^{44} -159.280 q^{45} -258.783 q^{46} +67.0946 q^{47} -22.1610 q^{48} -261.102 q^{49} -88.0067 q^{50} -346.360 q^{51} -422.643 q^{53} +211.500 q^{54} +92.5099 q^{55} -196.211 q^{56} +211.513 q^{57} +435.989 q^{58} -427.541 q^{59} +128.231 q^{60} +128.991 q^{61} -270.626 q^{62} -171.396 q^{63} +239.346 q^{64} -50.6428 q^{66} +622.950 q^{67} -655.170 q^{68} +453.087 q^{69} +123.416 q^{70} +1140.26 q^{71} +410.630 q^{72} -839.061 q^{73} -49.9169 q^{74} +154.085 q^{75} +400.095 q^{76} +99.5474 q^{77} +650.986 q^{79} +65.6447 q^{80} +141.060 q^{81} +277.981 q^{82} -891.619 q^{83} +137.986 q^{84} +1025.98 q^{85} +462.818 q^{86} -763.346 q^{87} -238.495 q^{88} -730.428 q^{89} -258.286 q^{90} +857.053 q^{92} +473.823 q^{93} +108.800 q^{94} -626.538 q^{95} -528.385 q^{96} -1177.21 q^{97} -423.399 q^{98} -208.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{3} + 46 q^{4} - 30 q^{5} - 34 q^{6} - 25 q^{7} - 36 q^{8} + 91 q^{9}+O(q^{10}) \) 9 * q + 8 * q^3 + 46 * q^4 - 30 * q^5 - 34 * q^6 - 25 * q^7 - 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} - 30 q^{5} - 34 q^{6} - 25 q^{7} - 36 q^{8} + 91 q^{9} - 22 q^{10} + 99 q^{11} + 181 q^{12} - 351 q^{15} + 130 q^{16} + 53 q^{17} - 33 q^{18} - 69 q^{19} - 282 q^{20} - 463 q^{21} + 216 q^{23} + 121 q^{24} + 617 q^{25} + 275 q^{27} - 279 q^{28} - 91 q^{29} + 29 q^{30} - 636 q^{31} - 663 q^{32} + 88 q^{33} - 423 q^{34} - 358 q^{35} - 252 q^{36} - 967 q^{37} - 101 q^{38} + 652 q^{40} + 226 q^{41} - 1186 q^{42} + 42 q^{43} + 506 q^{44} - 5 q^{45} + 1127 q^{46} + 269 q^{47} - 1820 q^{48} + 228 q^{49} + 1374 q^{50} - 589 q^{51} + 1227 q^{53} + 2438 q^{54} - 330 q^{55} - 659 q^{56} + 71 q^{57} - 471 q^{58} + 613 q^{59} + 859 q^{60} + 427 q^{61} - 1714 q^{62} - 305 q^{63} - 1194 q^{64} - 374 q^{66} + 271 q^{67} - 2835 q^{68} - 846 q^{69} + 102 q^{70} - 2279 q^{71} + 2400 q^{72} - 3602 q^{73} - 4955 q^{74} - 883 q^{75} - 1126 q^{76} - 275 q^{77} - 1182 q^{79} + 2360 q^{80} + 2697 q^{81} + 1007 q^{82} + 1877 q^{83} - 1618 q^{84} + 441 q^{85} - 830 q^{86} + 1942 q^{87} - 396 q^{88} - 1258 q^{89} - 5669 q^{90} + 1046 q^{92} - 1556 q^{93} + 1439 q^{94} + 2032 q^{95} + 3417 q^{96} - 4002 q^{97} + 1855 q^{98} + 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 - 30 * q^5 - 34 * q^6 - 25 * q^7 - 36 * q^8 + 91 * q^9 - 22 * q^10 + 99 * q^11 + 181 * q^12 - 351 * q^15 + 130 * q^16 + 53 * q^17 - 33 * q^18 - 69 * q^19 - 282 * q^20 - 463 * q^21 + 216 * q^23 + 121 * q^24 + 617 * q^25 + 275 * q^27 - 279 * q^28 - 91 * q^29 + 29 * q^30 - 636 * q^31 - 663 * q^32 + 88 * q^33 - 423 * q^34 - 358 * q^35 - 252 * q^36 - 967 * q^37 - 101 * q^38 + 652 * q^40 + 226 * q^41 - 1186 * q^42 + 42 * q^43 + 506 * q^44 - 5 * q^45 + 1127 * q^46 + 269 * q^47 - 1820 * q^48 + 228 * q^49 + 1374 * q^50 - 589 * q^51 + 1227 * q^53 + 2438 * q^54 - 330 * q^55 - 659 * q^56 + 71 * q^57 - 471 * q^58 + 613 * q^59 + 859 * q^60 + 427 * q^61 - 1714 * q^62 - 305 * q^63 - 1194 * q^64 - 374 * q^66 + 271 * q^67 - 2835 * q^68 - 846 * q^69 + 102 * q^70 - 2279 * q^71 + 2400 * q^72 - 3602 * q^73 - 4955 * q^74 - 883 * q^75 - 1126 * q^76 - 275 * q^77 - 1182 * q^79 + 2360 * q^80 + 2697 * q^81 + 1007 * q^82 + 1877 * q^83 - 1618 * q^84 + 441 * q^85 - 830 * q^86 + 1942 * q^87 - 396 * q^88 - 1258 * q^89 - 5669 * q^90 + 1046 * q^92 - 1556 * q^93 + 1439 * q^94 + 2032 * q^95 + 3417 * q^96 - 4002 * q^97 + 1855 * q^98 + 1001 * q^99

Introduction

L-functions

Modular forms

Varieties

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