LMFDB - Embedded newform 1859.4.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 64 x^{9} + 268 x^{8} + 1564 x^{7} - 4963 x^{6} - 16942 x^{5} + 37082 x^{4} + \cdots + 16256 $ x^11 - 5x^10 - 64x^9 + 268x^8 + 1564x^7 - 4963x^6 - 16942x^5 + 37082x^4 + 68209x^3 - 90926x^2 - 1672x + 16256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$5.65354$ 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)

$f(q)$	$=$	$q+4.65354 q^{2} +8.62383 q^{3} +13.6554 q^{4} +21.5680 q^{5} +40.1313 q^{6} -9.18213 q^{7} +26.3178 q^{8} +47.3704 q^{9} +O(q^{10})$	\(q+4.65354 q^{2} +8.62383 q^{3} +13.6554 q^{4} +21.5680 q^{5} +40.1313 q^{6} -9.18213 q^{7} +26.3178 q^{8} +47.3704 q^{9} +100.367 q^{10} -11.0000 q^{11} +117.762 q^{12} -42.7294 q^{14} +185.999 q^{15} +13.2273 q^{16} +83.6163 q^{17} +220.440 q^{18} -78.8085 q^{19} +294.520 q^{20} -79.1851 q^{21} -51.1889 q^{22} -77.8165 q^{23} +226.960 q^{24} +340.178 q^{25} +175.671 q^{27} -125.386 q^{28} +47.4099 q^{29} +865.552 q^{30} -233.815 q^{31} -148.988 q^{32} -94.8621 q^{33} +389.112 q^{34} -198.040 q^{35} +646.863 q^{36} +102.147 q^{37} -366.738 q^{38} +567.621 q^{40} -15.0495 q^{41} -368.491 q^{42} +451.167 q^{43} -150.210 q^{44} +1021.68 q^{45} -362.122 q^{46} -450.232 q^{47} +114.070 q^{48} -258.688 q^{49} +1583.03 q^{50} +721.092 q^{51} -480.812 q^{53} +817.490 q^{54} -237.248 q^{55} -241.653 q^{56} -679.631 q^{57} +220.624 q^{58} -291.810 q^{59} +2539.89 q^{60} +649.237 q^{61} -1088.07 q^{62} -434.961 q^{63} -799.141 q^{64} -441.444 q^{66} +580.541 q^{67} +1141.82 q^{68} -671.076 q^{69} -921.587 q^{70} +11.1556 q^{71} +1246.68 q^{72} +268.170 q^{73} +475.346 q^{74} +2933.64 q^{75} -1076.16 q^{76} +101.003 q^{77} -964.479 q^{79} +285.287 q^{80} +235.952 q^{81} -70.0334 q^{82} -158.499 q^{83} -1081.31 q^{84} +1803.43 q^{85} +2099.52 q^{86} +408.854 q^{87} -289.495 q^{88} -671.305 q^{89} +4754.44 q^{90} -1062.62 q^{92} -2016.38 q^{93} -2095.17 q^{94} -1699.74 q^{95} -1284.85 q^{96} +1296.73 q^{97} -1203.82 q^{98} -521.074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) $ 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9 + 48 * q^10 - 121 * q^11 + 105 * q^12 - 48 * q^14 + 125 * q^15 + 394 * q^16 + 265 * q^17 - 405 * q^18 - 127 * q^19 + 46 * q^20 + 287 * q^21 + 66 * q^22 + 42 * q^23 + 83 * q^24 + 737 * q^25 + 69 * q^27 - 675 * q^28 + 435 * q^29 + 785 * q^30 + 174 * q^31 - 315 * q^32 - 66 * q^33 - 497 * q^34 + 844 * q^35 + 1572 * q^36 - 187 * q^37 - 1813 * q^38 - 1470 * q^40 - 128 * q^41 - 2630 * q^42 + 696 * q^43 - 726 * q^44 + 1537 * q^45 - 785 * q^46 + 355 * q^47 - 516 * q^48 + 1758 * q^49 + 3414 * q^50 - 25 * q^51 - 693 * q^53 + 4150 * q^54 - 44 * q^55 - 3123 * q^56 - 99 * q^57 + 287 * q^58 + 609 * q^59 + 5013 * q^60 + 1625 * q^61 - 882 * q^62 - 1365 * q^63 - 914 * q^64 - 154 * q^66 - 633 * q^67 + 2873 * q^68 - 2192 * q^69 + 2054 * q^70 + 1937 * q^71 - 3242 * q^72 - 404 * q^73 - 447 * q^74 + 1781 * q^75 + 1814 * q^76 + 495 * q^77 + 1670 * q^79 + 1568 * q^80 + 2619 * q^81 + 1283 * q^82 - 785 * q^83 + 11750 * q^84 - 3189 * q^85 + 5950 * q^86 + 46 * q^87 + 858 * q^88 - 1464 * q^89 + 401 * q^90 - 3786 * q^92 - 1826 * q^93 - 2597 * q^94 - 2356 * q^95 - 4513 * q^96 - 1184 * q^97 - 2823 * q^98 - 1485 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.65354	1.64527	0.822637	−	0.568566i	$-0.192502\pi$
$2$	4.65354	1.64527	0.822637	+	0.568566i	$0.192502\pi$
$3$	8.62383	1.65966	0.829828	−	0.558019i	$-0.188438\pi$
$3$	8.62383	1.65966	0.829828	+	0.558019i	$0.188438\pi$
$4$	13.6554	1.70693
$5$	21.5680	1.92910	0.964550	−	0.263902i	$-0.0850094\pi$
$5$	21.5680	1.92910	0.964550	+	0.263902i	$0.0850094\pi$
$6$	40.1313	2.73059
$7$	−9.18213	−0.495788	−0.247894	−	0.968787i	$-0.579739\pi$
$7$	−9.18213	−0.495788	−0.247894	+	0.968787i	$0.579739\pi$
$8$	26.3178	1.16309
$9$	47.3704	1.75446
$10$	100.367	3.17390
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	117.762	2.83291
$13$	0	0
$13$	0	0
$14$	−42.7294	−0.815708
$15$	185.999	3.20164
$16$	13.2273	0.206677
$17$	83.6163	1.19294	0.596468	−	0.802637i	$-0.296570\pi$
$17$	83.6163	1.19294	0.596468	+	0.802637i	$0.296570\pi$
$18$	220.440	2.88657
$19$	−78.8085	−0.951574	−0.475787	−	0.879561i	$-0.657837\pi$
$19$	−78.8085	−0.951574	−0.475787	+	0.879561i	$0.657837\pi$
$20$	294.520	3.29283
$21$	−79.1851	−0.822838
$22$	−51.1889	−0.496069
$23$	−77.8165	−0.705472	−0.352736	−	0.935723i	$-0.614749\pi$
$23$	−77.8165	−0.705472	−0.352736	+	0.935723i	$0.614749\pi$
$24$	226.960	1.93033
$25$	340.178	2.72142
$26$	0	0
$27$	175.671	1.25214
$28$	−125.386	−0.846276
$29$	47.4099	0.303579	0.151790	−	0.988413i	$-0.451496\pi$
$29$	47.4099	0.303579	0.151790	+	0.988413i	$0.451496\pi$
$30$	865.552	5.26758
$31$	−233.815	−1.35466	−0.677331	−	0.735679i	$-0.736863\pi$
$31$	−233.815	−1.35466	−0.677331	+	0.735679i	$0.736863\pi$
$32$	−148.988	−0.823051
$33$	−94.8621	−0.500405
$34$	389.112	1.96271
$35$	−198.040	−0.956425
$36$	646.863	2.99474
$37$	102.147	0.453862	0.226931	−	0.973911i	$-0.427131\pi$
$37$	102.147	0.453862	0.226931	+	0.973911i	$0.427131\pi$
$38$	−366.738	−1.56560
$39$	0	0
$40$	567.621	2.24372
$41$	−15.0495	−0.0573252	−0.0286626	−	0.999589i	$-0.509125\pi$
$41$	−15.0495	−0.0573252	−0.0286626	+	0.999589i	$0.509125\pi$
$42$	−368.491	−1.35379
$43$	451.167	1.60005	0.800026	−	0.599965i	$-0.204819\pi$
$43$	451.167	1.60005	0.800026	+	0.599965i	$0.204819\pi$
$44$	−150.210	−0.514658
$45$	1021.68	3.38452
$46$	−362.122	−1.16069
$47$	−450.232	−1.39730	−0.698650	−	0.715464i	$-0.746215\pi$
$47$	−450.232	−1.39730	−0.698650	+	0.715464i	$0.746215\pi$
$48$	114.070	0.343013
$49$	−258.688	−0.754194
$50$	1583.03	4.47749
$51$	721.092	1.97986
$52$	0	0
$53$	−480.812	−1.24613	−0.623063	−	0.782172i	$-0.714112\pi$
$53$	−480.812	−1.24613	−0.623063	+	0.782172i	$0.714112\pi$
$54$	817.490	2.06012
$55$	−237.248	−0.581645
$56$	−241.653	−0.576648
$57$	−679.631	−1.57929
$58$	220.624	0.499471
$59$	−291.810	−0.643905	−0.321952	−	0.946756i	$-0.604339\pi$
$59$	−291.810	−0.643905	−0.321952	+	0.946756i	$0.604339\pi$
$60$	2539.89	5.46497
$61$	649.237	1.36273	0.681363	−	0.731945i	$-0.261387\pi$
$61$	649.237	1.36273	0.681363	+	0.731945i	$0.261387\pi$
$62$	−1088.07	−2.22879
$63$	−434.961	−0.869840
$64$	−799.141	−1.56082
$65$	0	0
$66$	−441.444	−0.823304
$67$	580.541	1.05857	0.529286	−	0.848443i	$-0.322460\pi$
$67$	580.541	1.05857	0.529286	+	0.848443i	$0.322460\pi$
$68$	1141.82	2.03626
$69$	−671.076	−1.17084
$70$	−921.587	−1.57358
$71$	11.1556	0.0186469	0.00932346	−	0.999957i	$-0.497032\pi$
$71$	11.1556	0.0186469	0.00932346	+	0.999957i	$0.497032\pi$
$72$	1246.68	2.04060
$73$	268.170	0.429957	0.214979	−	0.976619i	$-0.431032\pi$
$73$	268.170	0.429957	0.214979	+	0.976619i	$0.431032\pi$
$74$	475.346	0.746728
$75$	2933.64	4.51663
$76$	−1076.16	−1.62427
$77$	101.003	0.149486
$78$	0	0
$79$	−964.479	−1.37357	−0.686787	−	0.726859i	$-0.740979\pi$
$79$	−964.479	−1.37357	−0.686787	+	0.726859i	$0.740979\pi$
$80$	285.287	0.398701
$81$	235.952	0.323665
$82$	−70.0334	−0.0943158
$83$	−158.499	−0.209609	−0.104804	−	0.994493i	$-0.533422\pi$
$83$	−158.499	−0.209609	−0.104804	+	0.994493i	$0.533422\pi$
$84$	−1081.31	−1.40453
$85$	1803.43	2.30129
$86$	2099.52	2.63253
$87$	408.854	0.503837
$88$	−289.495	−0.350685
$89$	−671.305	−0.799530	−0.399765	−	0.916618i	$-0.630908\pi$
$89$	−671.305	−0.799530	−0.399765	+	0.916618i	$0.630908\pi$
$90$	4754.44	5.56847
$91$	0	0
$92$	−1062.62	−1.20419
$93$	−2016.38	−2.24827
$94$	−2095.17	−2.29894
$95$	−1699.74	−1.83568
$96$	−1284.85	−1.36598
$97$	1296.73	1.35735	0.678673	−	0.734441i	$-0.262555\pi$
$97$	1296.73	1.35735	0.678673	+	0.734441i	$0.262555\pi$
$98$	−1203.82	−1.24086
$99$	−521.074	−0.528989
$100$	4645.28	4.64528
$101$	−947.341	−0.933306	−0.466653	−	0.884440i	$-0.654540\pi$
$101$	−947.341	−0.933306	−0.466653	+	0.884440i	$0.654540\pi$
$102$	3355.63	3.25742
$103$	989.251	0.946348	0.473174	−	0.880969i	$-0.343108\pi$
$103$	989.251	0.946348	0.473174	+	0.880969i	$0.343108\pi$
$104$	0	0
$105$	−1707.86	−1.58734
$106$	−2237.48	−2.05022
$107$	228.059	0.206049	0.103025	−	0.994679i	$-0.467148\pi$
$107$	228.059	0.206049	0.103025	+	0.994679i	$0.467148\pi$
$108$	2398.86	2.13732
$109$	1603.85	1.40937	0.704686	−	0.709520i	$-0.251088\pi$
$109$	1603.85	1.40937	0.704686	+	0.709520i	$0.251088\pi$
$110$	−1104.04	−0.956966
$111$	880.900	0.753255
$112$	−121.455	−0.102468
$113$	−1014.62	−0.844665	−0.422332	−	0.906441i	$-0.638788\pi$
$113$	−1014.62	−0.844665	−0.422332	+	0.906441i	$0.638788\pi$
$114$	−3162.69	−2.59836
$115$	−1678.34	−1.36093
$116$	647.402	0.518188
$117$	0	0
$118$	−1357.95	−1.05940
$119$	−767.776	−0.591444
$120$	4895.07	3.72380
$121$	121.000	0.0909091
$122$	3021.25	2.24206
$123$	−129.784	−0.0951402
$124$	−3192.85	−2.31231
$125$	4640.95	3.32080
$126$	−2024.11	−1.43113
$127$	−289.637	−0.202371	−0.101186	−	0.994868i	$-0.532264\pi$
$127$	−289.637	−0.202371	−0.101186	+	0.994868i	$0.532264\pi$
$128$	−2526.93	−1.74493
$129$	3890.78	2.65554
$130$	0	0
$131$	488.349	0.325704	0.162852	−	0.986650i	$-0.447931\pi$
$131$	488.349	0.325704	0.162852	+	0.986650i	$0.447931\pi$
$132$	−1295.38	−0.854156
$133$	723.630	0.471779
$134$	2701.57	1.74164
$135$	3788.86	2.41550
$136$	2200.59	1.38750
$137$	−2365.73	−1.47531	−0.737657	−	0.675176i	$-0.764068\pi$
$137$	−2365.73	−1.47531	−0.737657	+	0.675176i	$0.764068\pi$
$138$	−3122.88	−1.92635
$139$	745.228	0.454744	0.227372	−	0.973808i	$-0.426987\pi$
$139$	745.228	0.454744	0.227372	+	0.973808i	$0.426987\pi$
$140$	−2704.32	−1.63255
$141$	−3882.72	−2.31904
$142$	51.9132	0.0306793
$143$	0	0
$144$	626.584	0.362606
$145$	1022.54	0.585634
$146$	1247.94	0.707398
$147$	−2230.88	−1.25170
$148$	1394.86	0.774711
$149$	3097.89	1.70328	0.851641	−	0.524126i	$-0.175608\pi$
$149$	3097.89	1.70328	0.851641	+	0.524126i	$0.175608\pi$
$150$	13651.8	7.43109
$151$	1373.15	0.740035	0.370017	−	0.929025i	$-0.379352\pi$
$151$	1373.15	0.740035	0.370017	+	0.929025i	$0.379352\pi$
$152$	−2074.06	−1.10677
$153$	3960.93	2.09296
$154$	470.023	0.245945
$155$	−5042.93	−2.61328
$156$	0	0
$157$	−716.774	−0.364361	−0.182181	−	0.983265i	$-0.558316\pi$
$157$	−716.774	−0.364361	−0.182181	+	0.983265i	$0.558316\pi$
$158$	−4488.24	−2.25991
$159$	−4146.44	−2.06814
$160$	−3213.38	−1.58775
$161$	714.521	0.349765
$162$	1098.01	0.532518
$163$	−2280.28	−1.09574	−0.547869	−	0.836564i	$-0.684561\pi$
$163$	−2280.28	−1.09574	−0.547869	+	0.836564i	$0.684561\pi$
$164$	−205.507	−0.0978501
$165$	−2045.98	−0.965331
$166$	−737.582	−0.344864
$167$	−2583.60	−1.19716	−0.598579	−	0.801064i	$-0.704268\pi$
$167$	−2583.60	−1.19716	−0.598579	+	0.801064i	$0.704268\pi$
$168$	−2083.97	−0.957037
$169$	0	0
$170$	8392.35	3.78626
$171$	−3733.19	−1.66950
$172$	6160.87	2.73118
$173$	1267.36	0.556970	0.278485	−	0.960441i	$-0.410168\pi$
$173$	1267.36	0.556970	0.278485	+	0.960441i	$0.410168\pi$
$174$	1902.62	0.828950
$175$	−3123.56	−1.34925
$176$	−145.501	−0.0623155
$177$	−2516.51	−1.06866
$178$	−3123.94	−1.31545
$179$	−1763.41	−0.736332	−0.368166	−	0.929760i	$-0.620014\pi$
$179$	−1763.41	−0.736332	−0.368166	+	0.929760i	$0.620014\pi$
$180$	13951.5	5.77714
$181$	357.138	0.146662	0.0733312	−	0.997308i	$-0.476637\pi$
$181$	357.138	0.146662	0.0733312	+	0.997308i	$0.476637\pi$
$182$	0	0
$183$	5598.91	2.26166
$184$	−2047.96	−0.820529
$185$	2203.11	0.875545
$186$	−9383.32	−3.69902
$187$	−919.779	−0.359684
$188$	−6148.11	−2.38509
$189$	−1613.03	−0.620797
$190$	−7909.81	−3.02020
$191$	2834.52	1.07381	0.536907	−	0.843641i	$-0.319593\pi$
$191$	2834.52	1.07381	0.536907	+	0.843641i	$0.319593\pi$
$192$	−6891.66	−2.59043
$193$	−2318.42	−0.864680	−0.432340	−	0.901711i	$-0.642312\pi$
$193$	−2318.42	−0.864680	−0.432340	+	0.901711i	$0.642312\pi$
$194$	6034.36	2.23321
$195$	0	0
$196$	−3532.50	−1.28736
$197$	−1111.83	−0.402103	−0.201051	−	0.979581i	$-0.564436\pi$
$197$	−1111.83	−0.402103	−0.201051	+	0.979581i	$0.564436\pi$
$198$	−2424.84	−0.870332
$199$	3773.16	1.34408	0.672041	−	0.740514i	$-0.265418\pi$
$199$	3773.16	1.34408	0.672041	+	0.740514i	$0.265418\pi$
$200$	8952.72	3.16527
$201$	5006.48	1.75687
$202$	−4408.49	−1.53555
$203$	−435.324	−0.150511
$204$	9846.82	3.37949
$205$	−324.587	−0.110586
$206$	4603.52	1.55700
$207$	−3686.19	−1.23772
$208$	0	0
$209$	866.893	0.286910
$210$	−7947.61	−2.61160
$211$	−4332.85	−1.41368	−0.706838	−	0.707376i	$-0.749879\pi$
$211$	−4332.85	−1.41368	−0.706838	+	0.707376i	$0.749879\pi$
$212$	−6565.70	−2.12705
$213$	96.2043	0.0309475
$214$	1061.28	0.339008
$215$	9730.75	3.08666
$216$	4623.26	1.45636
$217$	2146.92	0.671625
$218$	7463.60	2.31880
$219$	2312.65	0.713581
$220$	−3239.72	−0.992827
$221$	0	0
$222$	4099.30	1.23931
$223$	2243.94	0.673835	0.336918	−	0.941534i	$-0.390616\pi$
$223$	2243.94	0.673835	0.336918	+	0.941534i	$0.390616\pi$
$224$	1368.03	0.408059
$225$	16114.4	4.77462
$226$	−4721.56	−1.38971
$227$	−1953.68	−0.571235	−0.285618	−	0.958344i	$-0.592199\pi$
$227$	−1953.68	−0.571235	−0.285618	+	0.958344i	$0.592199\pi$
$228$	−9280.65	−2.69573
$229$	2252.20	0.649912	0.324956	−	0.945729i	$-0.394651\pi$
$229$	2252.20	0.649912	0.324956	+	0.945729i	$0.394651\pi$
$230$	−7810.24	−2.23910
$231$	871.036	0.248095
$232$	1247.72	0.353090
$233$	−1491.02	−0.419226	−0.209613	−	0.977784i	$-0.567220\pi$
$233$	−1491.02	−0.419226	−0.209613	+	0.977784i	$0.567220\pi$
$234$	0	0
$235$	−9710.59	−2.69553
$236$	−3984.79	−1.09910
$237$	−8317.49	−2.27966
$238$	−3572.87	−0.973088
$239$	−3771.04	−1.02062	−0.510311	−	0.859990i	$-0.670470\pi$
$239$	−3771.04	−1.02062	−0.510311	+	0.859990i	$0.670470\pi$
$240$	2460.27	0.661706
$241$	4068.97	1.08758	0.543788	−	0.839223i	$-0.316990\pi$
$241$	4068.97	1.08758	0.543788	+	0.839223i	$0.316990\pi$
$242$	563.078	0.149570
$243$	−2708.30	−0.714968
$244$	8865.61	2.32608
$245$	−5579.39	−1.45491
$246$	−603.956	−0.156532
$247$	0	0
$248$	−6153.50	−1.57560
$249$	−1366.87	−0.347879
$250$	21596.9	5.46362
$251$	−6162.31	−1.54965	−0.774824	−	0.632178i	$-0.782161\pi$
$251$	−6162.31	−1.54965	−0.774824	+	0.632178i	$0.782161\pi$
$252$	−5939.58	−1.48476
$253$	855.981	0.212708
$254$	−1347.84	−0.332956
$255$	15552.5	3.81936
$256$	−5366.04	−1.31007
$257$	−5209.34	−1.26440	−0.632198	−	0.774807i	$-0.717847\pi$
$257$	−5209.34	−1.26440	−0.632198	+	0.774807i	$0.717847\pi$
$258$	18105.9	4.36909
$259$	−937.929	−0.225020
$260$	0	0
$261$	2245.82	0.532617
$262$	2272.55	0.535873
$263$	3342.54	0.783688	0.391844	−	0.920032i	$-0.371837\pi$
$263$	3342.54	0.783688	0.391844	+	0.920032i	$0.371837\pi$
$264$	−2496.56	−0.582017
$265$	−10370.2	−2.40390
$266$	3367.44	0.776207
$267$	−5789.21	−1.32694
$268$	7927.54	1.80691
$269$	−3946.10	−0.894416	−0.447208	−	0.894430i	$-0.647582\pi$
$269$	−3946.10	−0.894416	−0.447208	+	0.894430i	$0.647582\pi$
$270$	17631.6	3.97417
$271$	−20.7302	−0.00464675	−0.00232337	−	0.999997i	$-0.500740\pi$
$271$	−20.7302	−0.00464675	−0.00232337	+	0.999997i	$0.500740\pi$
$272$	1106.02	0.246553
$273$	0	0
$274$	−11009.0	−2.42730
$275$	−3741.96	−0.820540
$276$	−9163.83	−1.99854
$277$	3912.84	0.848737	0.424368	−	0.905490i	$-0.360496\pi$
$277$	3912.84	0.848737	0.424368	+	0.905490i	$0.360496\pi$
$278$	3467.95	0.748179
$279$	−11075.9	−2.37670
$280$	−5211.97	−1.11241
$281$	−2337.97	−0.496341	−0.248170	−	0.968716i	$-0.579829\pi$
$281$	−2337.97	−0.496341	−0.248170	+	0.968716i	$0.579829\pi$
$282$	−18068.4	−3.81545
$283$	2915.26	0.612348	0.306174	−	0.951976i	$-0.400951\pi$
$283$	2915.26	0.612348	0.306174	+	0.951976i	$0.400951\pi$
$284$	152.335	0.0318290
$285$	−14658.3	−3.04660
$286$	0	0
$287$	138.186	0.0284212
$288$	−7057.63	−1.44401
$289$	2078.68	0.423098
$290$	4758.41	0.963529
$291$	11182.7	2.25273
$292$	3661.97	0.733906
$293$	−63.0586	−0.0125731	−0.00628656	−	0.999980i	$-0.502001\pi$
$293$	−63.0586	−0.0125731	−0.00628656	+	0.999980i	$0.502001\pi$
$294$	−10381.5	−2.05939
$295$	−6293.74	−1.24216
$296$	2688.29	0.527884
$297$	−1932.38	−0.377535
$298$	14416.2	2.80237
$299$	0	0
$300$	40060.1	7.70956
$301$	−4142.67	−0.793288
$302$	6390.00	1.21756
$303$	−8169.70	−1.54897
$304$	−1042.43	−0.196669
$305$	14002.7	2.62883
$306$	18432.4	3.44349
$307$	1055.65	0.196250	0.0981252	−	0.995174i	$-0.468715\pi$
$307$	1055.65	0.196250	0.0981252	+	0.995174i	$0.468715\pi$
$308$	1379.25	0.255162
$309$	8531.13	1.57061
$310$	−23467.5	−4.29956
$311$	6329.09	1.15399	0.576993	−	0.816749i	$-0.304226\pi$
$311$	6329.09	1.15399	0.576993	+	0.816749i	$0.304226\pi$
$312$	0	0
$313$	3904.10	0.705025	0.352513	−	0.935807i	$-0.385327\pi$
$313$	3904.10	0.705025	0.352513	+	0.935807i	$0.385327\pi$
$314$	−3335.53	−0.599475
$315$	−9381.23	−1.67801
$316$	−13170.4	−2.34459
$317$	−2672.48	−0.473506	−0.236753	−	0.971570i	$-0.576083\pi$
$317$	−2672.48	−0.473506	−0.236753	+	0.971570i	$0.576083\pi$
$318$	−19295.6	−3.40266
$319$	−521.509	−0.0915325
$320$	−17235.9	−3.01098
$321$	1966.74	0.341971
$322$	3325.05	0.575459
$323$	−6589.67	−1.13517
$324$	3222.03	0.552474
$325$	0	0
$326$	−10611.4	−1.80279
$327$	13831.4	2.33907
$328$	−396.069	−0.0666745
$329$	4134.09	0.692765
$330$	−9521.07	−1.58823
$331$	616.645	0.102398	0.0511992	−	0.998688i	$-0.483696\pi$
$331$	616.645	0.102398	0.0511992	+	0.998688i	$0.483696\pi$
$332$	−2164.37	−0.357787
$333$	4838.75	0.796282
$334$	−12022.9	−1.96965
$335$	12521.1	2.04209
$336$	−1047.41	−0.170062
$337$	1753.55	0.283447	0.141724	−	0.989906i	$-0.454736\pi$
$337$	1753.55	0.283447	0.141724	+	0.989906i	$0.454736\pi$
$338$	0	0
$339$	−8749.88	−1.40185
$340$	24626.7	3.92814
$341$	2571.97	0.408446
$342$	−17372.5	−2.74678
$343$	5524.78	0.869709
$344$	11873.7	1.86101
$345$	−14473.7	−2.25867
$346$	5897.73	0.916369
$347$	10322.8	1.59699	0.798497	−	0.601999i	$-0.205629\pi$
$347$	10322.8	1.59699	0.798497	+	0.601999i	$0.205629\pi$
$348$	5583.08	0.860013
$349$	9590.66	1.47099	0.735496	−	0.677529i	$-0.236949\pi$
$349$	9590.66	1.47099	0.735496	+	0.677529i	$0.236949\pi$
$350$	−14535.6	−2.21989
$351$	0	0
$352$	1638.87	0.248159
$353$	−5401.46	−0.814421	−0.407211	−	0.913334i	$-0.633499\pi$
$353$	−5401.46	−0.814421	−0.407211	+	0.913334i	$0.633499\pi$
$354$	−11710.7	−1.75824
$355$	240.605	0.0359718
$356$	−9166.95	−1.36474
$357$	−6621.16	−0.981594
$358$	−8206.10	−1.21147
$359$	829.295	0.121918	0.0609589	−	0.998140i	$-0.480584\pi$
$359$	829.295	0.121918	0.0609589	+	0.998140i	$0.480584\pi$
$360$	26888.4	3.93651
$361$	−648.223	−0.0945069
$362$	1661.96	0.241300
$363$	1043.48	0.150878
$364$	0	0
$365$	5783.88	0.829430
$366$	26054.7	3.72105
$367$	7651.69	1.08832	0.544162	−	0.838980i	$-0.316848\pi$
$367$	7651.69	1.08832	0.544162	+	0.838980i	$0.316848\pi$
$368$	−1029.30	−0.145805
$369$	−712.900	−0.100575
$370$	10252.3	1.44051
$371$	4414.88	0.617815
$372$	−27534.6	−3.83764
$373$	11101.4	1.54104	0.770520	−	0.637416i	$-0.219996\pi$
$373$	11101.4	1.54104	0.770520	+	0.637416i	$0.219996\pi$
$374$	−4280.23	−0.591779
$375$	40022.8	5.51138
$376$	−11849.1	−1.62519
$377$	0	0
$378$	−7506.30	−1.02138
$379$	7282.78	0.987048	0.493524	−	0.869732i	$-0.335708\pi$
$379$	7282.78	0.987048	0.493524	+	0.869732i	$0.335708\pi$
$380$	−23210.7	−3.13338
$381$	−2497.78	−0.335867
$382$	13190.5	1.76672
$383$	4341.21	0.579179	0.289589	−	0.957151i	$-0.406481\pi$
$383$	4341.21	0.579179	0.289589	+	0.957151i	$0.406481\pi$
$384$	−21791.8	−2.89598
$385$	2178.44	0.288373
$386$	−10788.8	−1.42264
$387$	21371.9	2.80723
$388$	17707.3	2.31689
$389$	−6304.38	−0.821709	−0.410854	−	0.911701i	$-0.634770\pi$
$389$	−6304.38	−0.821709	−0.410854	+	0.911701i	$0.634770\pi$
$390$	0	0
$391$	−6506.72	−0.841583
$392$	−6808.10	−0.877197
$393$	4211.44	0.540557
$394$	−5173.92	−0.661570
$395$	−20801.9	−2.64976
$396$	−7115.49	−0.902947
$397$	4817.17	0.608984	0.304492	−	0.952515i	$-0.401513\pi$
$397$	4817.17	0.608984	0.304492	+	0.952515i	$0.401513\pi$
$398$	17558.6	2.21138
$399$	6240.46	0.782991
$400$	4499.65	0.562456
$401$	2065.79	0.257259	0.128629	−	0.991693i	$-0.458942\pi$
$401$	2065.79	0.257259	0.128629	+	0.991693i	$0.458942\pi$
$402$	23297.9	2.89053
$403$	0	0
$404$	−12936.3	−1.59309
$405$	5089.01	0.624383
$406$	−2025.80	−0.247632
$407$	−1123.62	−0.136845
$408$	18977.5	2.30277
$409$	5428.26	0.656260	0.328130	−	0.944633i	$-0.393582\pi$
$409$	5428.26	0.656260	0.328130	+	0.944633i	$0.393582\pi$
$410$	−1510.48	−0.181944
$411$	−20401.6	−2.44851
$412$	13508.7	1.61535
$413$	2679.43	0.319240
$414$	−17153.9	−2.03639
$415$	−3418.51	−0.404356
$416$	0	0
$417$	6426.72	0.754719
$418$	4034.12	0.472046
$419$	−7647.83	−0.891697	−0.445849	−	0.895108i	$-0.647098\pi$
$419$	−7647.83	−0.891697	−0.445849	+	0.895108i	$0.647098\pi$
$420$	−23321.6	−2.70947
$421$	11817.4	1.36804	0.684020	−	0.729463i	$-0.260230\pi$
$421$	11817.4	1.36804	0.684020	+	0.729463i	$0.260230\pi$
$422$	−20163.1	−2.32588
$423$	−21327.6	−2.45150
$424$	−12653.9	−1.44936
$425$	28444.4	3.24649
$426$	447.691	0.0509171
$427$	−5961.38	−0.675624
$428$	3114.24	0.351711
$429$	0	0
$430$	45282.4	5.07840
$431$	−11660.9	−1.30321	−0.651605	−	0.758558i	$-0.725904\pi$
$431$	−11660.9	−1.30321	−0.651605	+	0.758558i	$0.725904\pi$
$432$	2323.65	0.258789
$433$	3.98657	0.000442454 0	0.000221227	−	1.00000i	$-0.499930\pi$
$433$	3.98657	0.000442454 0	0.000221227		1.00000i	$0.499930\pi$
$434$	9990.80	1.10501
$435$	8818.17	0.971951
$436$	21901.3	2.40570
$437$	6132.60	0.671309
$438$	10762.0	1.17404
$439$	−16432.2	−1.78649	−0.893243	−	0.449574i	$-0.851576\pi$
$439$	−16432.2	−1.78649	−0.893243	+	0.449574i	$0.851576\pi$
$440$	−6243.83	−0.676507
$441$	−12254.2	−1.32320
$442$	0	0
$443$	3538.09	0.379458	0.189729	−	0.981836i	$-0.439239\pi$
$443$	3538.09	0.379458	0.189729	+	0.981836i	$0.439239\pi$
$444$	12029.1	1.28575
$445$	−14478.7	−1.54237
$446$	10442.3	1.10864
$447$	26715.7	2.82686
$448$	7337.82	0.773838
$449$	8875.96	0.932923	0.466462	−	0.884541i	$-0.345529\pi$
$449$	8875.96	0.932923	0.466462	+	0.884541i	$0.345529\pi$
$450$	74988.8	7.85557
$451$	165.544	0.0172842
$452$	−13855.0	−1.44178
$453$	11841.8	1.22820
$454$	−9091.53	−0.939839
$455$	0	0
$456$	−17886.4	−1.83685
$457$	9376.91	0.959811	0.479905	−	0.877320i	$-0.340671\pi$
$457$	9376.91	0.959811	0.479905	+	0.877320i	$0.340671\pi$
$458$	10480.7	1.06928
$459$	14688.9	1.49373
$460$	−22918.5	−2.32300
$461$	2985.81	0.301655	0.150828	−	0.988560i	$-0.451806\pi$
$461$	2985.81	0.301655	0.150828	+	0.988560i	$0.451806\pi$
$462$	4053.40	0.408185
$463$	6928.66	0.695469	0.347735	−	0.937593i	$-0.386951\pi$
$463$	6928.66	0.695469	0.347735	+	0.937593i	$0.386951\pi$
$464$	627.106	0.0627428
$465$	−43489.3	−4.33714
$466$	−6938.50	−0.689742
$467$	−11130.9	−1.10295	−0.551474	−	0.834192i	$-0.685935\pi$
$467$	−11130.9	−1.10295	−0.551474	+	0.834192i	$0.685935\pi$
$468$	0	0
$469$	−5330.60	−0.524828
$470$	−45188.6	−4.43488
$471$	−6181.33	−0.604715
$472$	−7679.78	−0.748920
$473$	−4962.83	−0.482434
$474$	−38705.8	−3.75067
$475$	−26808.9	−2.58964
$476$	−10484.3	−1.00955
$477$	−22776.3	−2.18627
$478$	−17548.7	−1.67920
$479$	5172.28	0.493377	0.246689	−	0.969095i	$-0.420658\pi$
$479$	5172.28	0.493377	0.246689	+	0.969095i	$0.420658\pi$
$480$	−27711.6	−2.63512
$481$	0	0
$482$	18935.1	1.78936
$483$	6161.90	0.580489
$484$	1652.31	0.155175
$485$	27967.8	2.61845
$486$	−12603.2	−1.17632
$487$	−942.628	−0.0877095	−0.0438548	−	0.999038i	$-0.513964\pi$
$487$	−942.628	−0.0877095	−0.0438548	+	0.999038i	$0.513964\pi$
$488$	17086.5	1.58498
$489$	−19664.8	−1.81855
$490$	−25963.9	−2.39373
$491$	9205.28	0.846087	0.423043	−	0.906109i	$-0.360962\pi$
$491$	9205.28	0.846087	0.423043	+	0.906109i	$0.360962\pi$
$492$	−1772.26	−0.162398
$493$	3964.24	0.362151
$494$	0	0
$495$	−11238.5	−1.02047
$496$	−3092.76	−0.279978
$497$	−102.433	−0.00924493
$498$	−6360.78	−0.572356
$499$	2256.27	0.202413	0.101207	−	0.994865i	$-0.467730\pi$
$499$	2256.27	0.202413	0.101207	+	0.994865i	$0.467730\pi$
$500$	63374.2	5.66836
$501$	−22280.6	−1.98687
$502$	−28676.5	−2.54960
$503$	−16858.5	−1.49440	−0.747202	−	0.664597i	$-0.768603\pi$
$503$	−16858.5	−1.49440	−0.747202	+	0.664597i	$0.768603\pi$
$504$	−11447.2	−1.01170
$505$	−20432.2	−1.80044
$506$	3983.34	0.349963
$507$	0	0
$508$	−3955.12	−0.345433
$509$	9608.77	0.836741	0.418370	−	0.908276i	$-0.362601\pi$
$509$	9608.77	0.836741	0.418370	+	0.908276i	$0.362601\pi$
$510$	72374.2	6.28389
$511$	−2462.37	−0.213168
$512$	−4755.63	−0.410490
$513$	−13844.3	−1.19150
$514$	−24241.9	−2.08028
$515$	21336.2	1.82560
$516$	53130.3	4.53281
$517$	4952.55	0.421302
$518$	−4364.69	−0.370219
$519$	10929.5	0.924379
$520$	0	0
$521$	−8639.31	−0.726478	−0.363239	−	0.931696i	$-0.618329\pi$
$521$	−8639.31	−0.726478	−0.363239	+	0.931696i	$0.618329\pi$
$522$	10451.0	0.876301
$523$	1413.67	0.118194	0.0590971	−	0.998252i	$-0.481178\pi$
$523$	1413.67	0.118194	0.0590971	+	0.998252i	$0.481178\pi$
$524$	6668.61	0.555954
$525$	−26937.0	−2.23929
$526$	15554.6	1.28938
$527$	−19550.8	−1.61603
$528$	−1254.77	−0.103422
$529$	−6111.60	−0.502309
$530$	−48257.9	−3.95508
$531$	−13823.1	−1.12970
$532$	9881.48	0.805294
$533$	0	0
$534$	−26940.3	−2.18319
$535$	4918.77	0.397490
$536$	15278.5	1.23122
$537$	−15207.3	−1.22206
$538$	−18363.3	−1.47156
$539$	2845.57	0.227398
$540$	51738.5	4.12309
$541$	−19863.9	−1.57859	−0.789294	−	0.614015i	$-0.789553\pi$
$541$	−19863.9	−1.57859	−0.789294	+	0.614015i	$0.789553\pi$
$542$	−96.4687	−0.00764518
$543$	3079.90	0.243409
$544$	−12457.8	−0.981848
$545$	34591.9	2.71882
$546$	0	0
$547$	−2752.50	−0.215153	−0.107576	−	0.994197i	$-0.534309\pi$
$547$	−2752.50	−0.215153	−0.107576	+	0.994197i	$0.534309\pi$
$548$	−32305.1	−2.51826
$549$	30754.6	2.39085
$550$	−17413.3	−1.35001
$551$	−3736.30	−0.288878
$552$	−17661.2	−1.36180
$553$	8855.97	0.681002
$554$	18208.6	1.39640
$555$	18999.2	1.45310
$556$	10176.4	0.776216
$557$	9630.30	0.732583	0.366292	−	0.930500i	$-0.380627\pi$
$557$	9630.30	0.732583	0.366292	+	0.930500i	$0.380627\pi$
$558$	−51542.3	−3.91032
$559$	0	0
$560$	−2619.54	−0.197671
$561$	−7932.01	−0.596952
$562$	−10879.9	−0.816617
$563$	6622.36	0.495736	0.247868	−	0.968794i	$-0.420270\pi$
$563$	6622.36	0.495736	0.247868	+	0.968794i	$0.420270\pi$
$564$	−53020.2	−3.95843
$565$	−21883.2	−1.62944
$566$	13566.3	1.00748
$567$	−2166.54	−0.160470
$568$	293.592	0.0216881
$569$	−16480.9	−1.21426	−0.607130	−	0.794603i	$-0.707679\pi$
$569$	−16480.9	−1.21426	−0.607130	+	0.794603i	$0.707679\pi$
$570$	−68212.8	−5.01249
$571$	−24409.5	−1.78898	−0.894489	−	0.447089i	$-0.852461\pi$
$571$	−24409.5	−1.78898	−0.894489	+	0.447089i	$0.852461\pi$
$572$	0	0
$573$	24444.4	1.78216
$574$	643.056	0.0467607
$575$	−26471.4	−1.91989
$576$	−37855.6	−2.73840
$577$	7347.12	0.530095	0.265047	−	0.964235i	$-0.414612\pi$
$577$	7347.12	0.530095	0.265047	+	0.964235i	$0.414612\pi$
$578$	9673.23	0.696113
$579$	−19993.6	−1.43507
$580$	13963.2	0.999636
$581$	1455.36	0.103922
$582$	52039.3	3.70635
$583$	5288.94	0.375721
$584$	7057.62	0.500080
$585$	0	0
$586$	−293.446	−0.0206862
$587$	11215.6	0.788616	0.394308	−	0.918978i	$-0.370984\pi$
$587$	11215.6	0.788616	0.394308	+	0.918978i	$0.370984\pi$
$588$	−30463.7	−2.13657
$589$	18426.6	1.28906
$590$	−29288.2	−2.04369
$591$	−9588.19	−0.667353
$592$	1351.14	0.0938030
$593$	−988.627	−0.0684621	−0.0342311	−	0.999414i	$-0.510898\pi$
$593$	−988.627	−0.0684621	−0.0342311	+	0.999414i	$0.510898\pi$
$594$	−8992.39	−0.621148
$595$	−16559.4	−1.14095
$596$	42303.0	2.90738
$597$	32539.1	2.23071
$598$	0	0
$599$	2001.97	0.136558	0.0682790	−	0.997666i	$-0.478249\pi$
$599$	2001.97	0.136558	0.0682790	+	0.997666i	$0.478249\pi$
$600$	77206.7	5.25325
$601$	18163.2	1.23276	0.616382	−	0.787447i	$-0.288598\pi$
$601$	18163.2	1.23276	0.616382	+	0.787447i	$0.288598\pi$
$602$	−19278.1	−1.30518
$603$	27500.4	1.85722
$604$	18750.9	1.26319
$605$	2609.73	0.175373
$606$	−38018.0	−2.54848
$607$	−20894.0	−1.39714	−0.698569	−	0.715542i	$-0.746180\pi$
$607$	−20894.0	−1.39714	−0.698569	+	0.715542i	$0.746180\pi$
$608$	11741.5	0.783194
$609$	−3754.15	−0.249796
$610$	65162.3	4.32516
$611$	0	0
$612$	54088.3	3.57253
$613$	3160.11	0.208215	0.104107	−	0.994566i	$-0.466801\pi$
$613$	3160.11	0.208215	0.104107	+	0.994566i	$0.466801\pi$
$614$	4912.49	0.322886
$615$	−2799.18	−0.183535
$616$	2658.18	0.173866
$617$	13285.8	0.866883	0.433442	−	0.901182i	$-0.357299\pi$
$617$	13285.8	0.866883	0.433442	+	0.901182i	$0.357299\pi$
$618$	39700.0	2.58409
$619$	−3336.82	−0.216669	−0.108335	−	0.994114i	$-0.534552\pi$
$619$	−3336.82	−0.216669	−0.108335	+	0.994114i	$0.534552\pi$
$620$	−68863.4	−4.46068
$621$	−13670.1	−0.883350
$622$	29452.7	1.89862
$623$	6164.01	0.396398
$624$	0	0
$625$	57573.8	3.68472
$626$	18167.9	1.15996
$627$	7475.94	0.476173
$628$	−9787.85	−0.621939
$629$	8541.17	0.541429
$630$	−43655.9	−2.76078
$631$	−8844.83	−0.558014	−0.279007	−	0.960289i	$-0.590005\pi$
$631$	−8844.83	−0.558014	−0.279007	+	0.960289i	$0.590005\pi$
$632$	−25382.9	−1.59759
$633$	−37365.7	−2.34622
$634$	−12436.5	−0.779048
$635$	−6246.89	−0.390394
$636$	−56621.4	−3.53017
$637$	0	0
$638$	−2426.86	−0.150596
$639$	528.447	0.0327152
$640$	−54500.8	−3.36614
$641$	25390.4	1.56453	0.782263	−	0.622948i	$-0.214065\pi$
$641$	25390.4	1.56453	0.782263	+	0.622948i	$0.214065\pi$
$642$	9152.30	0.562636
$643$	12101.7	0.742214	0.371107	−	0.928590i	$-0.378978\pi$
$643$	12101.7	0.742214	0.371107	+	0.928590i	$0.378978\pi$
$644$	9757.09	0.597024
$645$	83916.3	5.12279
$646$	−30665.3	−1.86766
$647$	4291.21	0.260750	0.130375	−	0.991465i	$-0.458382\pi$
$647$	4291.21	0.260750	0.130375	+	0.991465i	$0.458382\pi$
$648$	6209.73	0.376453
$649$	3209.91	0.194145
$650$	0	0
$651$	18514.7	1.11467
$652$	−31138.2	−1.87035
$653$	−27279.0	−1.63478	−0.817389	−	0.576086i	$-0.804579\pi$
$653$	−27279.0	−1.63478	−0.817389	+	0.576086i	$0.804579\pi$
$654$	64364.8	3.84841
$655$	10532.7	0.628316
$656$	−199.065	−0.0118478
$657$	12703.3	0.754342
$658$	19238.1	1.13979
$659$	20168.4	1.19219	0.596093	−	0.802916i	$-0.296719\pi$
$659$	20168.4	1.19219	0.596093	+	0.802916i	$0.296719\pi$
$660$	−27938.8	−1.64775
$661$	−27107.4	−1.59509	−0.797546	−	0.603258i	$-0.793869\pi$
$661$	−27107.4	−1.59509	−0.797546	+	0.603258i	$0.793869\pi$
$662$	2869.58	0.168474
$663$	0	0
$664$	−4171.34	−0.243794
$665$	15607.2	0.910109
$666$	22517.3	1.31010
$667$	−3689.27	−0.214166
$668$	−35280.2	−2.04346
$669$	19351.3	1.11833
$670$	58267.4	3.35980
$671$	−7141.61	−0.410878
$672$	11797.6	0.677238
$673$	28937.5	1.65744	0.828722	−	0.559661i	$-0.189068\pi$
$673$	28937.5	1.65744	0.828722	+	0.559661i	$0.189068\pi$
$674$	8160.19	0.466349
$675$	59759.2	3.40761
$676$	0	0
$677$	−7639.16	−0.433673	−0.216837	−	0.976208i	$-0.569574\pi$
$677$	−7639.16	−0.433673	−0.216837	+	0.976208i	$0.569574\pi$
$678$	−40717.9	−2.30643
$679$	−11906.7	−0.672956
$680$	47462.4	2.67662
$681$	−16848.2	−0.948054
$682$	11968.8	0.672005
$683$	−14233.4	−0.797403	−0.398701	−	0.917081i	$-0.630539\pi$
$683$	−14233.4	−0.797403	−0.398701	+	0.917081i	$0.630539\pi$
$684$	−50978.3	−2.84971
$685$	−51024.0	−2.84603
$686$	25709.8	1.43091
$687$	19422.6	1.07863
$688$	5967.73	0.330694
$689$	0	0
$690$	−67354.2	−3.71613
$691$	−36008.9	−1.98241	−0.991203	−	0.132348i	$-0.957748\pi$
$691$	−36008.9	−1.98241	−0.991203	+	0.132348i	$0.957748\pi$
$692$	17306.4	0.950709
$693$	4784.57	0.262267
$694$	48037.6	2.62749
$695$	16073.1	0.877247
$696$	10760.1	0.586009
$697$	−1258.38	−0.0683854
$698$	44630.5	2.42019
$699$	−12858.3	−0.695771
$700$	−42653.5	−2.30307
$701$	−5499.81	−0.296327	−0.148163	−	0.988963i	$-0.547336\pi$
$701$	−5499.81	−0.296327	−0.148163	+	0.988963i	$0.547336\pi$
$702$	0	0
$703$	−8050.07	−0.431884
$704$	8790.55	0.470606
$705$	−83742.5	−4.47365
$706$	−25135.9	−1.33995
$707$	8698.61	0.462723
$708$	−34364.1	−1.82413
$709$	17007.8	0.900903	0.450452	−	0.892801i	$-0.351263\pi$
$709$	17007.8	0.900903	0.450452	+	0.892801i	$0.351263\pi$
$710$	1119.66	0.0591834
$711$	−45687.7	−2.40988
$712$	−17667.2	−0.929927
$713$	18194.7	0.955675
$714$	−30811.8	−1.61499
$715$	0	0
$716$	−24080.1	−1.25687
$717$	−32520.8	−1.69388
$718$	3859.16	0.200588
$719$	−12235.4	−0.634638	−0.317319	−	0.948319i	$-0.602783\pi$
$719$	−12235.4	−0.634638	−0.317319	+	0.948319i	$0.602783\pi$
$720$	13514.2	0.699504
$721$	−9083.43	−0.469188
$722$	−3016.53	−0.155490
$723$	35090.1	1.80500
$724$	4876.88	0.250342
$725$	16127.8	0.826167
$726$	4855.89	0.248235
$727$	12760.0	0.650953	0.325477	−	0.945550i	$-0.394475\pi$
$727$	12760.0	0.650953	0.325477	+	0.945550i	$0.394475\pi$
$728$	0	0
$729$	−29726.6	−1.51027
$730$	26915.5	1.36464
$731$	37724.9	1.90876
$732$	76455.5	3.86049
$733$	−9307.43	−0.469001	−0.234500	−	0.972116i	$-0.575345\pi$
$733$	−9307.43	−0.469001	−0.234500	+	0.972116i	$0.575345\pi$
$734$	35607.4	1.79059
$735$	−48115.7	−2.41466
$736$	11593.7	0.580640
$737$	−6385.95	−0.319172
$738$	−3317.51	−0.165473
$739$	−23212.7	−1.15547	−0.577735	−	0.816224i	$-0.696063\pi$
$739$	−23212.7	−1.15547	−0.577735	+	0.816224i	$0.696063\pi$
$740$	30084.4	1.49449
$741$	0	0
$742$	20544.8	1.01647
$743$	−27858.0	−1.37552	−0.687760	−	0.725938i	$-0.741406\pi$
$743$	−27858.0	−1.37552	−0.687760	+	0.725938i	$0.741406\pi$
$744$	−53066.7	−2.61495
$745$	66815.2	3.28580
$746$	51660.8	2.53543
$747$	−7508.16	−0.367750
$748$	−12560.0	−0.613955
$749$	−2094.07	−0.102157
$750$	186248.	9.06774
$751$	15823.4	0.768847	0.384423	−	0.923157i	$-0.374400\pi$
$751$	15823.4	0.768847	0.384423	+	0.923157i	$0.374400\pi$
$752$	−5955.37	−0.288790
$753$	−53142.7	−2.57188
$754$	0	0
$755$	29616.0	1.42760
$756$	−22026.6	−1.05966
$757$	15406.6	0.739713	0.369856	−	0.929089i	$-0.379407\pi$
$757$	15406.6	0.739713	0.369856	+	0.929089i	$0.379407\pi$
$758$	33890.7	1.62397
$759$	7381.83	0.353022
$760$	−44733.4	−2.13507
$761$	10695.3	0.509466	0.254733	−	0.967011i	$-0.418012\pi$
$761$	10695.3	0.509466	0.254733	+	0.967011i	$0.418012\pi$
$762$	−11623.5	−0.552593
$763$	−14726.8	−0.698750
$764$	38706.6	1.83292
$765$	85429.4	4.03752
$766$	20202.0	0.952908
$767$	0	0
$768$	−46275.8	−2.17426
$769$	26544.4	1.24475	0.622377	−	0.782717i	$-0.286167\pi$
$769$	26544.4	1.24475	0.622377	+	0.782717i	$0.286167\pi$
$770$	10137.5	0.474453
$771$	−44924.4	−2.09846
$772$	−31659.0	−1.47595
$773$	34406.2	1.60091	0.800456	−	0.599391i	$-0.204591\pi$
$773$	34406.2	1.60091	0.800456	+	0.599391i	$0.204591\pi$
$774$	99455.1	4.61866
$775$	−79538.9	−3.68661
$776$	34126.9	1.57872
$777$	−8088.54	−0.373455
$778$	−29337.7	−1.35194
$779$	1186.03	0.0545492
$780$	0	0
$781$	−122.712	−0.00562226
$782$	−30279.3	−1.38464
$783$	8328.52	0.380124
$784$	−3421.76	−0.155875
$785$	−15459.4	−0.702889
$786$	19598.1	0.889365
$787$	36787.1	1.66623	0.833113	−	0.553103i	$-0.186556\pi$
$787$	36787.1	1.66623	0.833113	+	0.553103i	$0.186556\pi$
$788$	−15182.5	−0.686361
$789$	28825.5	1.30065
$790$	−96802.3	−4.35958
$791$	9316.34	0.418775
$792$	−13713.5	−0.615263
$793$	0	0
$794$	22416.9	1.00195
$795$	−89430.4	−3.98965
$796$	51524.1	2.29425
$797$	−33504.4	−1.48907	−0.744534	−	0.667584i	$-0.767328\pi$
$797$	−33504.4	−1.48907	−0.744534	+	0.667584i	$0.767328\pi$
$798$	29040.2	1.28824
$799$	−37646.7	−1.66689
$800$	−50682.5	−2.23987
$801$	−31800.0	−1.40274
$802$	9613.24	0.423261
$803$	−2949.87	−0.129637
$804$	68365.7	2.99885
$805$	15410.8	0.674731
$806$	0	0
$807$	−34030.5	−1.48442
$808$	−24931.9	−1.08552
$809$	1167.95	0.0507576	0.0253788	−	0.999678i	$-0.491921\pi$
$809$	1167.95	0.0507576	0.0253788	+	0.999678i	$0.491921\pi$
$810$	23681.9	1.02728
$811$	5911.53	0.255958	0.127979	−	0.991777i	$-0.459151\pi$
$811$	5911.53	0.255958	0.127979	+	0.991777i	$0.459151\pi$
$812$	−5944.53	−0.256911
$813$	−178.774	−0.00771201
$814$	−5228.81	−0.225147
$815$	−49181.1	−2.11379
$816$	9538.13	0.409193
$817$	−35555.8	−1.52257
$818$	25260.6	1.07973
$819$	0	0
$820$	−4432.38	−0.188763
$821$	15733.5	0.668824	0.334412	−	0.942427i	$-0.391462\pi$
$821$	15733.5	0.668824	0.334412	+	0.942427i	$0.391462\pi$
$822$	−94939.9	−4.02848
$823$	9931.39	0.420640	0.210320	−	0.977633i	$-0.432549\pi$
$823$	9931.39	0.420640	0.210320	+	0.977633i	$0.432549\pi$
$824$	26034.9	1.10069
$825$	−32270.0	−1.36181
$826$	12468.8	0.525238
$827$	15309.4	0.643726	0.321863	−	0.946786i	$-0.395691\pi$
$827$	15309.4	0.643726	0.321863	+	0.946786i	$0.395691\pi$
$828$	−50336.6	−2.11270
$829$	179.433	0.00751745	0.00375873	−	0.999993i	$-0.498804\pi$
$829$	179.433	0.00751745	0.00375873	+	0.999993i	$0.498804\pi$
$830$	−15908.2	−0.665277
$831$	33743.7	1.40861
$832$	0	0
$833$	−21630.6	−0.899706
$834$	29907.0	1.24172
$835$	−55723.1	−2.30944
$836$	11837.8	0.489736
$837$	−41074.5	−1.69623
$838$	−35589.5	−1.46709
$839$	−1665.25	−0.0685230	−0.0342615	−	0.999413i	$-0.510908\pi$
$839$	−1665.25	−0.0685230	−0.0342615	+	0.999413i	$0.510908\pi$
$840$	−44947.1	−1.84622
$841$	−22141.3	−0.907840
$842$	54992.8	2.25080
$843$	−20162.3	−0.823755
$844$	−59166.9	−2.41304
$845$	0	0
$846$	−99249.0	−4.03340
$847$	−1111.04	−0.0450717
$848$	−6359.87	−0.257546
$849$	25140.7	1.01629
$850$	132367.	5.34136
$851$	−7948.74	−0.320187
$852$	1313.71	0.0528251
$853$	16304.7	0.654469	0.327235	−	0.944943i	$-0.393883\pi$
$853$	16304.7	0.654469	0.327235	+	0.944943i	$0.393883\pi$
$854$	−27741.5	−1.11159
$855$	−80517.3	−3.22062
$856$	6002.00	0.239654
$857$	32473.8	1.29438	0.647190	−	0.762329i	$-0.275944\pi$
$857$	32473.8	1.29438	0.647190	+	0.762329i	$0.275944\pi$
$858$	0	0
$859$	−2564.74	−0.101872	−0.0509358	−	0.998702i	$-0.516220\pi$
$859$	−2564.74	−0.101872	−0.0509358	+	0.998702i	$0.516220\pi$
$860$	132878.	5.26871
$861$	1191.69	0.0471694
$862$	−54264.3	−2.14414
$863$	32017.8	1.26292	0.631460	−	0.775409i	$-0.282456\pi$
$863$	32017.8	1.26292	0.631460	+	0.775409i	$0.282456\pi$
$864$	−26172.8	−1.03058
$865$	27334.5	1.07445
$866$	18.5517	0.000727958 0
$867$	17926.2	0.702198
$868$	29317.2	1.14642
$869$	10609.3	0.414148
$870$	41035.7	1.59913
$871$	0	0
$872$	42209.9	1.63923
$873$	61426.4	2.38141
$874$	28538.3	1.10449
$875$	−42613.8	−1.64641
$876$	31580.2	1.21803
$877$	−47065.4	−1.81218	−0.906092	−	0.423080i	$-0.860949\pi$
$877$	−47065.4	−1.81218	−0.906092	+	0.423080i	$0.860949\pi$
$878$	−76468.0	−2.93926
$879$	−543.806	−0.0208670
$880$	−3138.16	−0.120213
$881$	−16125.2	−0.616653	−0.308327	−	0.951281i	$-0.599769\pi$
$881$	−16125.2	−0.616653	−0.308327	+	0.951281i	$0.599769\pi$
$882$	−57025.3	−2.17703
$883$	−47457.6	−1.80869	−0.904345	−	0.426801i	$-0.859640\pi$
$883$	−47457.6	−1.80869	−0.904345	+	0.426801i	$0.859640\pi$
$884$	0	0
$885$	−54276.2	−2.06155
$886$	16464.7	0.624313
$887$	32926.0	1.24639	0.623195	−	0.782067i	$-0.285834\pi$
$887$	32926.0	1.24639	0.623195	+	0.782067i	$0.285834\pi$
$888$	23183.3	0.876105
$889$	2659.49	0.100333
$890$	−67377.1	−2.53763
$891$	−2595.47	−0.0975888
$892$	30641.9	1.15019
$893$	35482.1	1.32963
$894$	124322.	4.65096
$895$	−38033.2	−1.42046
$896$	23202.6	0.865116
$897$	0	0
$898$	41304.6	1.53492
$899$	−11085.2	−0.411247
$900$	220048.	8.14994
$901$	−40203.7	−1.48655
$902$	770.367	0.0284373
$903$	−35725.7	−1.31658
$904$	−26702.4	−0.982423
$905$	7702.76	0.282926
$906$	55106.3	2.02073
$907$	−5630.61	−0.206132	−0.103066	−	0.994675i	$-0.532865\pi$
$907$	−5630.61	−0.206132	−0.103066	+	0.994675i	$0.532865\pi$
$908$	−26678.4	−0.975058
$909$	−44875.9	−1.63745
$910$	0	0
$911$	−2360.04	−0.0858306	−0.0429153	−	0.999079i	$-0.513665\pi$
$911$	−2360.04	−0.0858306	−0.0429153	+	0.999079i	$0.513665\pi$
$912$	−8989.70	−0.326402
$913$	1743.49	0.0631995
$914$	43635.8	1.57915
$915$	120757.	4.36296
$916$	30754.8	1.10935
$917$	−4484.08	−0.161480
$918$	68355.5	2.45759
$919$	2167.72	0.0778092	0.0389046	−	0.999243i	$-0.487613\pi$
$919$	2167.72	0.0778092	0.0389046	+	0.999243i	$0.487613\pi$
$920$	−44170.3	−1.58288
$921$	9103.70	0.325708
$922$	13894.6	0.496306
$923$	0	0
$924$	11894.4	0.423481
$925$	34748.2	1.23515
$926$	32242.8	1.14424
$927$	46861.2	1.66033
$928$	−7063.51	−0.249861
$929$	−37059.5	−1.30881	−0.654405	−	0.756145i	$-0.727081\pi$
$929$	−37059.5	−1.30881	−0.654405	+	0.756145i	$0.727081\pi$
$930$	−202379.	−7.13579
$931$	20386.8	0.717671
$932$	−20360.5	−0.715589
$933$	54581.0	1.91522
$934$	−51798.1	−1.81465
$935$	−19837.8	−0.693866
$936$	0	0
$937$	−20903.4	−0.728800	−0.364400	−	0.931243i	$-0.618726\pi$
$937$	−20903.4	−0.728800	−0.364400	+	0.931243i	$0.618726\pi$
$938$	−24806.2	−0.863486
$939$	33668.3	1.17010
$940$	−132602.	−4.60108
$941$	−45.5123	−0.00157668	−0.000788342	−	1.00000i	$-0.500251\pi$
$941$	−45.5123	−0.00157668	−0.000788342		1.00000i	$0.500251\pi$
$942$	−28765.1	−0.994922
$943$	1171.10	0.0404413
$944$	−3859.86	−0.133080
$945$	−34789.8	−1.19758
$946$	−23094.7	−0.793736
$947$	20301.1	0.696618	0.348309	−	0.937380i	$-0.386756\pi$
$947$	20301.1	0.696618	0.348309	+	0.937380i	$0.386756\pi$
$948$	−113579.	−3.89122
$949$	0	0
$950$	−124756.	−4.26066
$951$	−23047.0	−0.785858
$952$	−20206.1	−0.687904
$953$	24503.7	0.832899	0.416449	−	0.909159i	$-0.363274\pi$
$953$	24503.7	0.832899	0.416449	+	0.909159i	$0.363274\pi$
$954$	−105990.	−3.59702
$955$	61134.8	2.07149
$956$	−51495.2	−1.74213
$957$	−4497.40	−0.151912
$958$	24069.4	0.811741
$959$	21722.4	0.731444
$960$	−148639.	−4.99719
$961$	24878.7	0.835107
$962$	0	0
$963$	10803.2	0.361505
$964$	55563.6	1.85641
$965$	−50003.5	−1.66805
$966$	28674.7	0.955064
$967$	18164.6	0.604070	0.302035	−	0.953297i	$-0.402334\pi$
$967$	18164.6	0.604070	0.302035	+	0.953297i	$0.402334\pi$
$968$	3184.45	0.105736
$969$	−56828.2	−1.88399
$970$	130149.	4.30808
$971$	4866.82	0.160848	0.0804242	−	0.996761i	$-0.474373\pi$
$971$	4866.82	0.160848	0.0804242	+	0.996761i	$0.474373\pi$
$972$	−36982.9	−1.22040
$973$	−6842.78	−0.225457
$974$	−4386.55	−0.144306
$975$	0	0
$976$	8587.68	0.281644
$977$	10257.3	0.335885	0.167942	−	0.985797i	$-0.446288\pi$
$977$	10257.3	0.335885	0.167942	+	0.985797i	$0.446288\pi$
$978$	−91510.7	−2.99201
$979$	7384.35	0.241067
$980$	−76189.0	−2.48344
$981$	75975.2	2.47268
$982$	42837.1	1.39205
$983$	−51703.2	−1.67760	−0.838798	−	0.544442i	$-0.816741\pi$
$983$	−51703.2	−1.67760	−0.838798	+	0.544442i	$0.816741\pi$
$984$	−3415.63	−0.110657
$985$	−23979.8	−0.775696
$986$	18447.7	0.595837
$987$	35651.6	1.14975
$988$	0	0
$989$	−35108.2	−1.12879
$990$	−52298.9	−1.67896
$991$	335.759	0.0107626	0.00538129	−	0.999986i	$-0.498287\pi$
$991$	335.759	0.0107626	0.00538129	+	0.999986i	$0.498287\pi$
$992$	34835.7	1.11496
$993$	5317.84	0.169946
$994$	−476.674	−0.0152104
$995$	81379.5	2.59287
$996$	−18665.2	−0.593804
$997$	30041.2	0.954276	0.477138	−	0.878828i	$-0.341674\pi$
$997$	30041.2	0.954276	0.477138	+	0.878828i	$0.341674\pi$
$998$	10499.6	0.333026
$999$	17944.3	0.568300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.e.1.10		11
13.12	even	2		143.4.a.d.1.2	✓	11
39.38	odd	2		1287.4.a.m.1.10		11
52.51	odd	2		2288.4.a.u.1.2		11
143.142	odd	2		1573.4.a.f.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.d.1.2	✓	11	13.12	even	2
1287.4.a.m.1.10		11	39.38	odd	2
1573.4.a.f.1.10		11	143.142	odd	2
1859.4.a.e.1.10		11	1.1	even	1	trivial
2288.4.a.u.1.2		11	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+4.65354 q^{2} +8.62383 q^{3} +13.6554 q^{4} +21.5680 q^{5} +40.1313 q^{6} -9.18213 q^{7} +26.3178 q^{8} +47.3704 q^{9} +O(q^{10})\)	\(q+4.65354 q^{2} +8.62383 q^{3} +13.6554 q^{4} +21.5680 q^{5} +40.1313 q^{6} -9.18213 q^{7} +26.3178 q^{8} +47.3704 q^{9} +100.367 q^{10} -11.0000 q^{11} +117.762 q^{12} -42.7294 q^{14} +185.999 q^{15} +13.2273 q^{16} +83.6163 q^{17} +220.440 q^{18} -78.8085 q^{19} +294.520 q^{20} -79.1851 q^{21} -51.1889 q^{22} -77.8165 q^{23} +226.960 q^{24} +340.178 q^{25} +175.671 q^{27} -125.386 q^{28} +47.4099 q^{29} +865.552 q^{30} -233.815 q^{31} -148.988 q^{32} -94.8621 q^{33} +389.112 q^{34} -198.040 q^{35} +646.863 q^{36} +102.147 q^{37} -366.738 q^{38} +567.621 q^{40} -15.0495 q^{41} -368.491 q^{42} +451.167 q^{43} -150.210 q^{44} +1021.68 q^{45} -362.122 q^{46} -450.232 q^{47} +114.070 q^{48} -258.688 q^{49} +1583.03 q^{50} +721.092 q^{51} -480.812 q^{53} +817.490 q^{54} -237.248 q^{55} -241.653 q^{56} -679.631 q^{57} +220.624 q^{58} -291.810 q^{59} +2539.89 q^{60} +649.237 q^{61} -1088.07 q^{62} -434.961 q^{63} -799.141 q^{64} -441.444 q^{66} +580.541 q^{67} +1141.82 q^{68} -671.076 q^{69} -921.587 q^{70} +11.1556 q^{71} +1246.68 q^{72} +268.170 q^{73} +475.346 q^{74} +2933.64 q^{75} -1076.16 q^{76} +101.003 q^{77} -964.479 q^{79} +285.287 q^{80} +235.952 q^{81} -70.0334 q^{82} -158.499 q^{83} -1081.31 q^{84} +1803.43 q^{85} +2099.52 q^{86} +408.854 q^{87} -289.495 q^{88} -671.305 q^{89} +4754.44 q^{90} -1062.62 q^{92} -2016.38 q^{93} -2095.17 q^{94} -1699.74 q^{95} -1284.85 q^{96} +1296.73 q^{97} -1203.82 q^{98} -521.074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9 + 48 * q^10 - 121 * q^11 + 105 * q^12 - 48 * q^14 + 125 * q^15 + 394 * q^16 + 265 * q^17 - 405 * q^18 - 127 * q^19 + 46 * q^20 + 287 * q^21 + 66 * q^22 + 42 * q^23 + 83 * q^24 + 737 * q^25 + 69 * q^27 - 675 * q^28 + 435 * q^29 + 785 * q^30 + 174 * q^31 - 315 * q^32 - 66 * q^33 - 497 * q^34 + 844 * q^35 + 1572 * q^36 - 187 * q^37 - 1813 * q^38 - 1470 * q^40 - 128 * q^41 - 2630 * q^42 + 696 * q^43 - 726 * q^44 + 1537 * q^45 - 785 * q^46 + 355 * q^47 - 516 * q^48 + 1758 * q^49 + 3414 * q^50 - 25 * q^51 - 693 * q^53 + 4150 * q^54 - 44 * q^55 - 3123 * q^56 - 99 * q^57 + 287 * q^58 + 609 * q^59 + 5013 * q^60 + 1625 * q^61 - 882 * q^62 - 1365 * q^63 - 914 * q^64 - 154 * q^66 - 633 * q^67 + 2873 * q^68 - 2192 * q^69 + 2054 * q^70 + 1937 * q^71 - 3242 * q^72 - 404 * q^73 - 447 * q^74 + 1781 * q^75 + 1814 * q^76 + 495 * q^77 + 1670 * q^79 + 1568 * q^80 + 2619 * q^81 + 1283 * q^82 - 785 * q^83 + 11750 * q^84 - 3189 * q^85 + 5950 * q^86 + 46 * q^87 + 858 * q^88 - 1464 * q^89 + 401 * q^90 - 3786 * q^92 - 1826 * q^93 - 2597 * q^94 - 2356 * q^95 - 4513 * q^96 - 1184 * q^97 - 2823 * q^98 - 1485 * q^99

Introduction

L-functions

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Database

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