LMFDB - Embedded newform 1859.4.a.c.1.2

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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 34x^{4} - 26x^{3} + 249x^{2} + 274x - 200 $ x^6 - 34x^4 - 26x^3 + 249x^2 + 274x - 200
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.2
Root			$3.11199$ 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)

$f(q)$	$=$	$q-2.11199 q^{2} +4.05013 q^{3} -3.53950 q^{4} +16.1679 q^{5} -8.55384 q^{6} +9.75779 q^{7} +24.3713 q^{8} -10.5964 q^{9} +O(q^{10})$	\(q-2.11199 q^{2} +4.05013 q^{3} -3.53950 q^{4} +16.1679 q^{5} -8.55384 q^{6} +9.75779 q^{7} +24.3713 q^{8} -10.5964 q^{9} -34.1465 q^{10} -11.0000 q^{11} -14.3354 q^{12} -20.6084 q^{14} +65.4822 q^{15} -23.1560 q^{16} +0.385518 q^{17} +22.3796 q^{18} -37.1986 q^{19} -57.2263 q^{20} +39.5203 q^{21} +23.2319 q^{22} -15.2996 q^{23} +98.7070 q^{24} +136.402 q^{25} -152.271 q^{27} -34.5377 q^{28} +123.881 q^{29} -138.298 q^{30} -85.7031 q^{31} -146.065 q^{32} -44.5514 q^{33} -0.814209 q^{34} +157.763 q^{35} +37.5060 q^{36} +294.472 q^{37} +78.5631 q^{38} +394.034 q^{40} +231.369 q^{41} -83.4666 q^{42} -481.201 q^{43} +38.9345 q^{44} -171.322 q^{45} +32.3126 q^{46} +292.929 q^{47} -93.7848 q^{48} -247.785 q^{49} -288.080 q^{50} +1.56140 q^{51} +504.448 q^{53} +321.594 q^{54} -177.847 q^{55} +237.810 q^{56} -150.659 q^{57} -261.636 q^{58} +274.649 q^{59} -231.774 q^{60} +783.829 q^{61} +181.004 q^{62} -103.398 q^{63} +493.736 q^{64} +94.0922 q^{66} +774.702 q^{67} -1.36454 q^{68} -61.9654 q^{69} -333.195 q^{70} -477.187 q^{71} -258.249 q^{72} -0.557393 q^{73} -621.922 q^{74} +552.446 q^{75} +131.664 q^{76} -107.336 q^{77} +1065.02 q^{79} -374.384 q^{80} -330.612 q^{81} -488.649 q^{82} +402.398 q^{83} -139.882 q^{84} +6.23302 q^{85} +1016.29 q^{86} +501.735 q^{87} -268.084 q^{88} +829.936 q^{89} +361.831 q^{90} +54.1529 q^{92} -347.109 q^{93} -618.664 q^{94} -601.424 q^{95} -591.583 q^{96} +185.252 q^{97} +523.320 q^{98} +116.561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} + 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 + 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} + 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8} - 52 q^{10} - 66 q^{11} - 19 q^{12} - 120 q^{14} + 23 q^{15} + 26 q^{16} - 117 q^{17} + 27 q^{18} + 67 q^{19} - 10 q^{20} - 19 q^{21} - 66 q^{22} - 158 q^{23} + 609 q^{24} - 234 q^{25} - 531 q^{27} + 670 q^{28} - 145 q^{29} - 211 q^{30} + 58 q^{31} + 364 q^{32} + 66 q^{33} - 43 q^{34} - 210 q^{35} + 383 q^{36} + 753 q^{37} + 738 q^{38} + 4 q^{40} + 232 q^{41} + 1593 q^{42} - 390 q^{43} - 286 q^{44} + 107 q^{45} - 5 q^{46} + 205 q^{47} + 1625 q^{48} + 491 q^{49} - 938 q^{50} + 363 q^{51} - 65 q^{53} - 1917 q^{54} - 88 q^{55} + 1816 q^{56} + 1657 q^{57} + 1685 q^{58} - 1735 q^{59} - 871 q^{60} + 421 q^{61} + 3394 q^{62} + 125 q^{63} + 570 q^{64} - 165 q^{66} + 703 q^{67} + 209 q^{68} - 272 q^{69} - 1968 q^{70} - 445 q^{71} - 1035 q^{72} + 2340 q^{73} + 1135 q^{74} + 1941 q^{75} + 1208 q^{76} - 583 q^{77} - 1234 q^{79} - 2766 q^{80} + 606 q^{81} - 897 q^{82} + 1601 q^{83} + 7 q^{84} + 2245 q^{85} + 1146 q^{86} + 2462 q^{87} - 396 q^{88} + 442 q^{89} + 113 q^{90} + 2737 q^{92} + 982 q^{93} + 2733 q^{94} - 504 q^{95} + 1153 q^{96} + 2682 q^{97} - 2036 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 + 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8 - 52 * q^10 - 66 * q^11 - 19 * q^12 - 120 * q^14 + 23 * q^15 + 26 * q^16 - 117 * q^17 + 27 * q^18 + 67 * q^19 - 10 * q^20 - 19 * q^21 - 66 * q^22 - 158 * q^23 + 609 * q^24 - 234 * q^25 - 531 * q^27 + 670 * q^28 - 145 * q^29 - 211 * q^30 + 58 * q^31 + 364 * q^32 + 66 * q^33 - 43 * q^34 - 210 * q^35 + 383 * q^36 + 753 * q^37 + 738 * q^38 + 4 * q^40 + 232 * q^41 + 1593 * q^42 - 390 * q^43 - 286 * q^44 + 107 * q^45 - 5 * q^46 + 205 * q^47 + 1625 * q^48 + 491 * q^49 - 938 * q^50 + 363 * q^51 - 65 * q^53 - 1917 * q^54 - 88 * q^55 + 1816 * q^56 + 1657 * q^57 + 1685 * q^58 - 1735 * q^59 - 871 * q^60 + 421 * q^61 + 3394 * q^62 + 125 * q^63 + 570 * q^64 - 165 * q^66 + 703 * q^67 + 209 * q^68 - 272 * q^69 - 1968 * q^70 - 445 * q^71 - 1035 * q^72 + 2340 * q^73 + 1135 * q^74 + 1941 * q^75 + 1208 * q^76 - 583 * q^77 - 1234 * q^79 - 2766 * q^80 + 606 * q^81 - 897 * q^82 + 1601 * q^83 + 7 * q^84 + 2245 * q^85 + 1146 * q^86 + 2462 * q^87 - 396 * q^88 + 442 * q^89 + 113 * q^90 + 2737 * q^92 + 982 * q^93 + 2733 * q^94 - 504 * q^95 + 1153 * q^96 + 2682 * q^97 - 2036 * q^98

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 $

$2$	−2.11199	−0.746701	−0.373351	−	0.927690i	$-0.621791\pi$
$2$	−2.11199	−0.746701	−0.373351	+	0.927690i	$0.621791\pi$
$3$	4.05013	0.779448	0.389724	−	0.920932i	$-0.372570\pi$
$3$	4.05013	0.779448	0.389724	+	0.920932i	$0.372570\pi$
$4$	−3.53950	−0.442437
$5$	16.1679	1.44610	0.723052	−	0.690794i	$-0.242739\pi$
$5$	16.1679	1.44610	0.723052	+	0.690794i	$0.242739\pi$
$6$	−8.55384	−0.582015
$7$	9.75779	0.526871	0.263436	−	0.964677i	$-0.415144\pi$
$7$	9.75779	0.526871	0.263436	+	0.964677i	$0.415144\pi$
$8$	24.3713	1.07707
$9$	−10.5964	−0.392460
$10$	−34.1465	−1.07981
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−14.3354	−0.344857
$13$	0	0
$13$	0	0
$14$	−20.6084	−0.393415
$15$	65.4822	1.12716
$16$	−23.1560	−0.361812
$17$	0.385518	0.00550010	0.00275005	−	0.999996i	$-0.499125\pi$
$17$	0.385518	0.00550010	0.00275005	+	0.999996i	$0.499125\pi$
$18$	22.3796	0.293051
$19$	−37.1986	−0.449155	−0.224577	−	0.974456i	$-0.572100\pi$
$19$	−37.1986	−0.449155	−0.224577	+	0.974456i	$0.572100\pi$
$20$	−57.2263	−0.639810
$21$	39.5203	0.410669
$22$	23.2319	0.225139
$23$	−15.2996	−0.138704	−0.0693519	−	0.997592i	$-0.522093\pi$
$23$	−15.2996	−0.138704	−0.0693519	+	0.997592i	$0.522093\pi$
$24$	98.7070	0.839520
$25$	136.402	1.09122
$26$	0	0
$27$	−152.271	−1.08535
$28$	−34.5377	−0.233107
$29$	123.881	0.793246	0.396623	−	0.917982i	$-0.370182\pi$
$29$	123.881	0.793246	0.396623	+	0.917982i	$0.370182\pi$
$30$	−138.298	−0.841654
$31$	−85.7031	−0.496540	−0.248270	−	0.968691i	$-0.579862\pi$
$31$	−85.7031	−0.496540	−0.248270	+	0.968691i	$0.579862\pi$
$32$	−146.065	−0.806904
$33$	−44.5514	−0.235012
$34$	−0.814209	−0.00410693
$35$	157.763	0.761911
$36$	37.5060	0.173639
$37$	294.472	1.30840	0.654201	−	0.756321i	$-0.273005\pi$
$37$	294.472	1.30840	0.654201	+	0.756321i	$0.273005\pi$
$38$	78.5631	0.335385
$39$	0	0
$40$	394.034	1.55755
$41$	231.369	0.881312	0.440656	−	0.897676i	$-0.354746\pi$
$41$	231.369	0.881312	0.440656	+	0.897676i	$0.354746\pi$
$42$	−83.4666	−0.306647
$43$	−481.201	−1.70657	−0.853285	−	0.521445i	$-0.825393\pi$
$43$	−481.201	−1.70657	−0.853285	+	0.521445i	$0.825393\pi$
$44$	38.9345	0.133400
$45$	−171.322	−0.567539
$46$	32.3126	0.103570
$47$	292.929	0.909109	0.454555	−	0.890719i	$-0.349798\pi$
$47$	292.929	0.909109	0.454555	+	0.890719i	$0.349798\pi$
$48$	−93.7848	−0.282014
$49$	−247.785	−0.722407
$50$	−288.080	−0.814812
$51$	1.56140	0.00428704
$52$	0	0
$53$	504.448	1.30738	0.653691	−	0.756762i	$-0.273220\pi$
$53$	504.448	1.30738	0.653691	+	0.756762i	$0.273220\pi$
$54$	321.594	0.810433
$55$	−177.847	−0.436017
$56$	237.810	0.567477
$57$	−150.659	−0.350093
$58$	−261.636	−0.592318
$59$	274.649	0.606037	0.303019	−	0.952985i	$-0.402006\pi$
$59$	274.649	0.606037	0.303019	+	0.952985i	$0.402006\pi$
$60$	−231.774	−0.498699
$61$	783.829	1.64523	0.822615	−	0.568599i	$-0.192514\pi$
$61$	783.829	1.64523	0.822615	+	0.568599i	$0.192514\pi$
$62$	181.004	0.370767
$63$	−103.398	−0.206776
$64$	493.736	0.964329
$65$	0	0
$66$	94.0922	0.175484
$67$	774.702	1.41261	0.706305	−	0.707908i	$-0.250361\pi$
$67$	774.702	1.41261	0.706305	+	0.707908i	$0.250361\pi$
$68$	−1.36454	−0.00243345
$69$	−61.9654	−0.108112
$70$	−333.195	−0.568920
$71$	−477.187	−0.797629	−0.398814	−	0.917032i	$-0.630578\pi$
$71$	−477.187	−0.797629	−0.398814	+	0.917032i	$0.630578\pi$
$72$	−258.249	−0.422707
$73$	−0.557393	−0.000893670 0	−0.000446835	−	1.00000i	$-0.500142\pi$
$73$	−0.557393	−0.000893670 0	−0.000446835		1.00000i	$0.500142\pi$
$74$	−621.922	−0.976985
$75$	552.446	0.850546
$76$	131.664	0.198723
$77$	−107.336	−0.158858
$78$	0	0
$79$	1065.02	1.51676	0.758380	−	0.651812i	$-0.225991\pi$
$79$	1065.02	1.51676	0.758380	+	0.651812i	$0.225991\pi$
$80$	−374.384	−0.523218
$81$	−330.612	−0.453514
$82$	−488.649	−0.658077
$83$	402.398	0.532155	0.266078	−	0.963952i	$-0.414272\pi$
$83$	402.398	0.532155	0.266078	+	0.963952i	$0.414272\pi$
$84$	−139.882	−0.181695
$85$	6.23302	0.00795372
$86$	1016.29	1.27430
$87$	501.735	0.618294
$88$	−268.084	−0.324749
$89$	829.936	0.988461	0.494231	−	0.869331i	$-0.335450\pi$
$89$	829.936	0.988461	0.494231	+	0.869331i	$0.335450\pi$
$90$	361.831	0.423782
$91$	0	0
$92$	54.1529	0.0613677
$93$	−347.109	−0.387027
$94$	−618.664	−0.678833
$95$	−601.424	−0.649524
$96$	−591.583	−0.628940
$97$	185.252	0.193912	0.0969562	−	0.995289i	$-0.469089\pi$
$97$	185.252	0.193912	0.0969562	+	0.995289i	$0.469089\pi$
$98$	523.320	0.539422
$99$	116.561	0.118331
$100$	−482.794	−0.482794
$101$	869.730	0.856846	0.428423	−	0.903578i	$-0.359069\pi$
$101$	869.730	0.856846	0.428423	+	0.903578i	$0.359069\pi$
$102$	−3.29765	−0.00320114
$103$	−190.031	−0.181789	−0.0908946	−	0.995861i	$-0.528973\pi$
$103$	−190.031	−0.181789	−0.0908946	+	0.995861i	$0.528973\pi$
$104$	0	0
$105$	638.962	0.593870
$106$	−1065.39	−0.976223
$107$	−1184.51	−1.07020	−0.535100	−	0.844789i	$-0.679726\pi$
$107$	−1184.51	−1.07020	−0.535100	+	0.844789i	$0.679726\pi$
$108$	538.961	0.480200
$109$	715.090	0.628378	0.314189	−	0.949360i	$-0.398267\pi$
$109$	715.090	0.628378	0.314189	+	0.949360i	$0.398267\pi$
$110$	375.612	0.325574
$111$	1192.65	1.01983
$112$	−225.951	−0.190628
$113$	624.662	0.520029	0.260014	−	0.965605i	$-0.416273\pi$
$113$	624.662	0.520029	0.260014	+	0.965605i	$0.416273\pi$
$114$	318.191	0.261415
$115$	−247.363	−0.200580
$116$	−438.477	−0.350962
$117$	0	0
$118$	−580.055	−0.452529
$119$	3.76180	0.00289785
$120$	1595.89	1.21403
$121$	121.000	0.0909091
$122$	−1655.44	−1.22849
$123$	937.076	0.686937
$124$	303.346	0.219688
$125$	184.346	0.131907
$126$	218.375	0.154400
$127$	−1759.85	−1.22962	−0.614809	−	0.788676i	$-0.710767\pi$
$127$	−1759.85	−1.22962	−0.614809	+	0.788676i	$0.710767\pi$
$128$	125.756	0.0868387
$129$	−1948.93	−1.33018
$130$	0	0
$131$	−295.876	−0.197334	−0.0986671	−	0.995120i	$-0.531458\pi$
$131$	−295.876	−0.197334	−0.0986671	+	0.995120i	$0.531458\pi$
$132$	157.690	0.103978
$133$	−362.976	−0.236647
$134$	−1636.16	−1.05480
$135$	−2461.90	−1.56953
$136$	9.39556	0.00592399
$137$	−182.011	−0.113506	−0.0567528	−	0.998388i	$-0.518075\pi$
$137$	−182.011	−0.113506	−0.0567528	+	0.998388i	$0.518075\pi$
$138$	130.870	0.0807276
$139$	−2069.27	−1.26268	−0.631342	−	0.775504i	$-0.717496\pi$
$139$	−2069.27	−1.26268	−0.631342	+	0.775504i	$0.717496\pi$
$140$	−558.403	−0.337098
$141$	1186.40	0.708604
$142$	1007.81	0.595590
$143$	0	0
$144$	245.371	0.141997
$145$	2002.90	1.14712
$146$	1.17721	0.000667305 0
$147$	−1003.56	−0.563079
$148$	−1042.28	−0.578886
$149$	2281.69	1.25452	0.627259	−	0.778811i	$-0.284177\pi$
$149$	2281.69	1.25452	0.627259	+	0.778811i	$0.284177\pi$
$150$	−1166.76	−0.635104
$151$	923.083	0.497479	0.248740	−	0.968570i	$-0.419984\pi$
$151$	923.083	0.497479	0.248740	+	0.968570i	$0.419984\pi$
$152$	−906.578	−0.483771
$153$	−4.08511	−0.00215857
$154$	226.692	0.118619
$155$	−1385.64	−0.718048
$156$	0	0
$157$	1757.14	0.893215	0.446608	−	0.894730i	$-0.352632\pi$
$157$	1757.14	0.893215	0.446608	+	0.894730i	$0.352632\pi$
$158$	−2249.31	−1.13257
$159$	2043.08	1.01904
$160$	−2361.57	−1.16687
$161$	−149.290	−0.0730790
$162$	698.249	0.338640
$163$	−1504.48	−0.722947	−0.361473	−	0.932382i	$-0.617726\pi$
$163$	−1504.48	−0.722947	−0.361473	+	0.932382i	$0.617726\pi$
$164$	−818.931	−0.389925
$165$	−720.305	−0.339852
$166$	−849.860	−0.397361
$167$	−1848.36	−0.856468	−0.428234	−	0.903668i	$-0.640864\pi$
$167$	−1848.36	−0.856468	−0.428234	+	0.903668i	$0.640864\pi$
$168$	963.162	0.442319
$169$	0	0
$170$	−13.1641	−0.00593905
$171$	394.172	0.176276
$172$	1703.21	0.755050
$173$	211.565	0.0929769	0.0464884	−	0.998919i	$-0.485197\pi$
$173$	211.565	0.0929769	0.0464884	+	0.998919i	$0.485197\pi$
$174$	−1059.66	−0.461681
$175$	1330.98	0.574930
$176$	254.716	0.109090
$177$	1112.36	0.472375
$178$	−1752.82	−0.738085
$179$	2565.47	1.07124	0.535620	−	0.844459i	$-0.320078\pi$
$179$	2565.47	1.07124	0.535620	+	0.844459i	$0.320078\pi$
$180$	606.395	0.251100
$181$	−4546.30	−1.86698	−0.933490	−	0.358603i	$-0.883253\pi$
$181$	−4546.30	−1.86698	−0.933490	+	0.358603i	$0.883253\pi$
$182$	0	0
$183$	3174.61	1.28237
$184$	−372.871	−0.149394
$185$	4761.00	1.89208
$186$	733.090	0.288994
$187$	−4.24069	−0.00165834
$188$	−1036.82	−0.402224
$189$	−1485.82	−0.571840
$190$	1270.20	0.485001
$191$	5249.68	1.98876	0.994381	−	0.105865i	$-0.0337610\pi$
$191$	5249.68	1.98876	0.994381	+	0.105865i	$0.0337610\pi$
$192$	1999.70	0.751644
$193$	4527.59	1.68862	0.844308	−	0.535858i	$-0.180012\pi$
$193$	4527.59	1.68862	0.844308	+	0.535858i	$0.180012\pi$
$194$	−391.251	−0.144795
$195$	0	0
$196$	877.036	0.319620
$197$	−125.108	−0.0452468	−0.0226234	−	0.999744i	$-0.507202\pi$
$197$	−125.108	−0.0452468	−0.0226234	+	0.999744i	$0.507202\pi$
$198$	−246.175	−0.0883581
$199$	−4233.12	−1.50793	−0.753964	−	0.656916i	$-0.771861\pi$
$199$	−4233.12	−1.50793	−0.753964	+	0.656916i	$0.771861\pi$
$200$	3324.29	1.17532
$201$	3137.64	1.10106
$202$	−1836.86	−0.639808
$203$	1208.81	0.417939
$204$	−5.52656	−0.00189675
$205$	3740.76	1.27447
$206$	401.343	0.135742
$207$	162.121	0.0544357
$208$	0	0
$209$	409.185	0.135425
$210$	−1349.48	−0.443443
$211$	810.272	0.264367	0.132184	−	0.991225i	$-0.457801\pi$
$211$	810.272	0.264367	0.132184	+	0.991225i	$0.457801\pi$
$212$	−1785.49	−0.578434
$213$	−1932.67	−0.621710
$214$	2501.68	0.799119
$215$	−7780.03	−2.46788
$216$	−3711.03	−1.16900
$217$	−836.273	−0.261613
$218$	−1510.26	−0.469211
$219$	−2.25751	−0.000696569 0
$220$	629.490	0.192910
$221$	0	0
$222$	−2518.86	−0.761509
$223$	−4033.32	−1.21117	−0.605585	−	0.795781i	$-0.707061\pi$
$223$	−4033.32	−1.21117	−0.605585	+	0.795781i	$0.707061\pi$
$224$	−1425.27	−0.425135
$225$	−1445.37	−0.428259
$226$	−1319.28	−0.388306
$227$	−2825.13	−0.826038	−0.413019	−	0.910722i	$-0.635526\pi$
$227$	−2825.13	−0.826038	−0.413019	+	0.910722i	$0.635526\pi$
$228$	533.258	0.154894
$229$	−1040.51	−0.300258	−0.150129	−	0.988666i	$-0.547969\pi$
$229$	−1040.51	−0.300258	−0.150129	+	0.988666i	$0.547969\pi$
$230$	522.428	0.149773
$231$	−434.724	−0.123821
$232$	3019.14	0.854381
$233$	5030.10	1.41430	0.707152	−	0.707061i	$-0.249979\pi$
$233$	5030.10	1.41430	0.707152	+	0.707061i	$0.249979\pi$
$234$	0	0
$235$	4736.06	1.31467
$236$	−972.118	−0.268133
$237$	4313.47	1.18224
$238$	−7.94488	−0.00216383
$239$	4121.29	1.11541	0.557707	−	0.830038i	$-0.311681\pi$
$239$	4121.29	1.11541	0.557707	+	0.830038i	$0.311681\pi$
$240$	−1516.31	−0.407821
$241$	−28.1710	−0.00752968	−0.00376484	−	0.999993i	$-0.501198\pi$
$241$	−28.1710	−0.00752968	−0.00376484	+	0.999993i	$0.501198\pi$
$242$	−255.551	−0.0678819
$243$	2772.28	0.731860
$244$	−2774.36	−0.727911
$245$	−4006.18	−1.04467
$246$	−1979.09	−0.512937
$247$	0	0
$248$	−2088.70	−0.534808
$249$	1629.76	0.414787
$250$	−389.337	−0.0984954
$251$	1740.83	0.437771	0.218885	−	0.975751i	$-0.429758\pi$
$251$	1740.83	0.437771	0.218885	+	0.975751i	$0.429758\pi$
$252$	365.976	0.0914855
$253$	168.295	0.0418207
$254$	3716.79	0.918157
$255$	25.2446	0.00619951
$256$	−4215.48	−1.02917
$257$	4642.14	1.12673	0.563364	−	0.826209i	$-0.309507\pi$
$257$	4642.14	1.12673	0.563364	+	0.826209i	$0.309507\pi$
$258$	4116.12	0.993249
$259$	2873.39	0.689359
$260$	0	0
$261$	−1312.70	−0.311318
$262$	624.887	0.147350
$263$	−2764.53	−0.648168	−0.324084	−	0.946028i	$-0.605056\pi$
$263$	−2764.53	−0.648168	−0.324084	+	0.946028i	$0.605056\pi$
$264$	−1085.78	−0.253125
$265$	8155.87	1.89061
$266$	766.602	0.176704
$267$	3361.35	0.770454
$268$	−2742.05	−0.624991
$269$	2741.76	0.621443	0.310721	−	0.950501i	$-0.399429\pi$
$269$	2741.76	0.621443	0.310721	+	0.950501i	$0.399429\pi$
$270$	5199.51	1.17197
$271$	3520.26	0.789079	0.394539	−	0.918879i	$-0.370904\pi$
$271$	3520.26	0.789079	0.394539	+	0.918879i	$0.370904\pi$
$272$	−8.92704	−0.00199000
$273$	0	0
$274$	384.406	0.0847548
$275$	−1500.42	−0.329014
$276$	219.326	0.0478329
$277$	−6856.52	−1.48725	−0.743625	−	0.668596i	$-0.766895\pi$
$277$	−6856.52	−1.48725	−0.743625	+	0.668596i	$0.766895\pi$
$278$	4370.28	0.942848
$279$	908.147	0.194872
$280$	3844.90	0.820631
$281$	5295.02	1.12411	0.562054	−	0.827100i	$-0.310011\pi$
$281$	5295.02	1.12411	0.562054	+	0.827100i	$0.310011\pi$
$282$	−2505.67	−0.529115
$283$	5945.57	1.24886	0.624431	−	0.781080i	$-0.285331\pi$
$283$	5945.57	1.24886	0.624431	+	0.781080i	$0.285331\pi$
$284$	1689.00	0.352901
$285$	−2435.85	−0.506271
$286$	0	0
$287$	2257.65	0.464338
$288$	1547.77	0.316678
$289$	−4912.85	−0.999970
$290$	−4230.11	−0.856553
$291$	750.295	0.151145
$292$	1.97289	0.000395393 0
$293$	20.2960	0.00404678	0.00202339	−	0.999998i	$-0.499356\pi$
$293$	20.2960	0.00404678	0.00202339	+	0.999998i	$0.499356\pi$
$294$	2119.52	0.420451
$295$	4440.50	0.876393
$296$	7176.66	1.40924
$297$	1674.98	0.327246
$298$	−4818.90	−0.936750
$299$	0	0
$300$	−1955.38	−0.376313
$301$	−4695.46	−0.899143
$302$	−1949.54	−0.371469
$303$	3522.52	0.667867
$304$	861.370	0.162510
$305$	12672.9	2.37917
$306$	8.62771	0.00161181
$307$	4100.52	0.762310	0.381155	−	0.924511i	$-0.375526\pi$
$307$	4100.52	0.762310	0.381155	+	0.924511i	$0.375526\pi$
$308$	379.915	0.0702845
$309$	−769.650	−0.141695
$310$	2926.46	0.536167
$311$	5848.10	1.06629	0.533144	−	0.846025i	$-0.321010\pi$
$311$	5848.10	1.06629	0.533144	+	0.846025i	$0.321010\pi$
$312$	0	0
$313$	−7841.90	−1.41614	−0.708068	−	0.706144i	$-0.750433\pi$
$313$	−7841.90	−1.41614	−0.708068	+	0.706144i	$0.750433\pi$
$314$	−3711.06	−0.666965
$315$	−1671.73	−0.299020
$316$	−3769.63	−0.671071
$317$	2587.83	0.458509	0.229254	−	0.973367i	$-0.426371\pi$
$317$	2587.83	0.458509	0.229254	+	0.973367i	$0.426371\pi$
$318$	−4314.96	−0.760916
$319$	−1362.69	−0.239173
$320$	7982.69	1.39452
$321$	−4797.44	−0.834165
$322$	315.300	0.0545682
$323$	−14.3407	−0.00247040
$324$	1170.20	0.200652
$325$	0	0
$326$	3177.46	0.539825
$327$	2896.21	0.489788
$328$	5638.77	0.949235
$329$	2858.34	0.478984
$330$	1521.28	0.253768
$331$	−11760.1	−1.95284	−0.976421	−	0.215873i	$-0.930740\pi$
$331$	−11760.1	−1.95284	−0.976421	+	0.215873i	$0.930740\pi$
$332$	−1424.29	−0.235445
$333$	−3120.35	−0.513496
$334$	3903.71	0.639526
$335$	12525.3	2.04278
$336$	−915.132	−0.148585
$337$	−457.887	−0.0740139	−0.0370069	−	0.999315i	$-0.511782\pi$
$337$	−457.887	−0.0740139	−0.0370069	+	0.999315i	$0.511782\pi$
$338$	0	0
$339$	2529.96	0.405336
$340$	−22.0618	−0.00351902
$341$	942.734	0.149712
$342$	−832.488	−0.131625
$343$	−5764.76	−0.907487
$344$	−11727.5	−1.83809
$345$	−1001.85	−0.156342
$346$	−446.823	−0.0694260
$347$	4490.86	0.694760	0.347380	−	0.937724i	$-0.387071\pi$
$347$	4490.86	0.694760	0.347380	+	0.937724i	$0.387071\pi$
$348$	−1775.89	−0.273556
$349$	3847.92	0.590185	0.295093	−	0.955469i	$-0.404650\pi$
$349$	3847.92	0.590185	0.295093	+	0.955469i	$0.404650\pi$
$350$	−2811.02	−0.429301
$351$	0	0
$352$	1606.72	0.243291
$353$	−7540.48	−1.13694	−0.568469	−	0.822704i	$-0.692464\pi$
$353$	−7540.48	−1.13694	−0.568469	+	0.822704i	$0.692464\pi$
$354$	−2349.30	−0.352723
$355$	−7715.12	−1.15345
$356$	−2937.56	−0.437332
$357$	15.2358	0.00225872
$358$	−5418.24	−0.799896
$359$	2079.90	0.305775	0.152887	−	0.988244i	$-0.451143\pi$
$359$	2079.90	0.305775	0.152887	+	0.988244i	$0.451143\pi$
$360$	−4175.35	−0.611279
$361$	−5475.26	−0.798260
$362$	9601.73	1.39408
$363$	490.066	0.0708589
$364$	0	0
$365$	−9.01189	−0.00129234
$366$	−6704.74	−0.957548
$367$	−5578.62	−0.793465	−0.396732	−	0.917934i	$-0.629856\pi$
$367$	−5578.62	−0.793465	−0.396732	+	0.917934i	$0.629856\pi$
$368$	354.277	0.0501847
$369$	−2451.69	−0.345880
$370$	−10055.2	−1.41282
$371$	4922.30	0.688822
$372$	1228.59	0.171235
$373$	1565.52	0.217319	0.108659	−	0.994079i	$-0.465344\pi$
$373$	1565.52	0.217319	0.108659	+	0.994079i	$0.465344\pi$
$374$	8.95630	0.00123829
$375$	746.626	0.102815
$376$	7139.07	0.979174
$377$	0	0
$378$	3138.05	0.426994
$379$	916.224	0.124177	0.0620887	−	0.998071i	$-0.480224\pi$
$379$	916.224	0.124177	0.0620887	+	0.998071i	$0.480224\pi$
$380$	2128.74	0.287374
$381$	−7127.63	−0.958424
$382$	−11087.3	−1.48501
$383$	9216.29	1.22958	0.614792	−	0.788690i	$-0.289240\pi$
$383$	9216.29	1.22958	0.614792	+	0.788690i	$0.289240\pi$
$384$	509.328	0.0676863
$385$	−1735.40	−0.229725
$386$	−9562.23	−1.26089
$387$	5099.02	0.669761
$388$	−655.699	−0.0857940
$389$	7812.32	1.01825	0.509127	−	0.860692i	$-0.329969\pi$
$389$	7812.32	1.01825	0.509127	+	0.860692i	$0.329969\pi$
$390$	0	0
$391$	−5.89826	−0.000762884 0
$392$	−6038.86	−0.778082
$393$	−1198.34	−0.153812
$394$	264.228	0.0337858
$395$	17219.2	2.19339
$396$	−412.567	−0.0523542
$397$	12153.6	1.53646	0.768228	−	0.640176i	$-0.221139\pi$
$397$	12153.6	1.53646	0.768228	+	0.640176i	$0.221139\pi$
$398$	8940.30	1.12597
$399$	−1470.10	−0.184454
$400$	−3158.52	−0.394815
$401$	−8043.11	−1.00163	−0.500815	−	0.865554i	$-0.666966\pi$
$401$	−8043.11	−1.00163	−0.500815	+	0.865554i	$0.666966\pi$
$402$	−6626.67	−0.822160
$403$	0	0
$404$	−3078.41	−0.379100
$405$	−5345.31	−0.655829
$406$	−2552.99	−0.312075
$407$	−3239.19	−0.394498
$408$	38.0533	0.00461745
$409$	1940.80	0.234637	0.117318	−	0.993094i	$-0.462570\pi$
$409$	1940.80	0.234637	0.117318	+	0.993094i	$0.462570\pi$
$410$	−7900.45	−0.951647
$411$	−737.169	−0.0884717
$412$	672.614	0.0804303
$413$	2679.96	0.319304
$414$	−342.398	−0.0406472
$415$	6505.94	0.769552
$416$	0	0
$417$	−8380.81	−0.984197
$418$	−864.194	−0.101122
$419$	12059.1	1.40602	0.703012	−	0.711178i	$-0.251838\pi$
$419$	12059.1	1.40602	0.703012	+	0.711178i	$0.251838\pi$
$420$	−2261.61	−0.262750
$421$	−14054.0	−1.62696	−0.813482	−	0.581591i	$-0.802431\pi$
$421$	−14054.0	−1.62696	−0.813482	+	0.581591i	$0.802431\pi$
$422$	−1711.29	−0.197403
$423$	−3104.01	−0.356789
$424$	12294.0	1.40814
$425$	52.5853	0.00600180
$426$	4081.78	0.464232
$427$	7648.44	0.866824
$428$	4192.58	0.473496
$429$	0	0
$430$	16431.3	1.84277
$431$	−3528.78	−0.394374	−0.197187	−	0.980366i	$-0.563181\pi$
$431$	−3528.78	−0.394374	−0.197187	+	0.980366i	$0.563181\pi$
$432$	3525.97	0.392693
$433$	13470.5	1.49504	0.747521	−	0.664238i	$-0.231244\pi$
$433$	13470.5	1.49504	0.747521	+	0.664238i	$0.231244\pi$
$434$	1766.20	0.195346
$435$	8112.01	0.894118
$436$	−2531.06	−0.278018
$437$	569.123	0.0622994
$438$	4.76785	0.000520129 0
$439$	10320.9	1.12208	0.561038	−	0.827790i	$-0.310402\pi$
$439$	10320.9	1.12208	0.561038	+	0.827790i	$0.310402\pi$
$440$	−4334.37	−0.469620
$441$	2625.64	0.283516
$442$	0	0
$443$	−6631.41	−0.711214	−0.355607	−	0.934635i	$-0.615726\pi$
$443$	−6631.41	−0.711214	−0.355607	+	0.934635i	$0.615726\pi$
$444$	−4221.38	−0.451211
$445$	13418.3	1.42942
$446$	8518.32	0.904382
$447$	9241.14	0.977832
$448$	4817.78	0.508077
$449$	11689.9	1.22868	0.614341	−	0.789041i	$-0.289422\pi$
$449$	11689.9	1.22868	0.614341	+	0.789041i	$0.289422\pi$
$450$	3052.62	0.319782
$451$	−2545.06	−0.265726
$452$	−2210.99	−0.230080
$453$	3738.61	0.387759
$454$	5966.65	0.616804
$455$	0	0
$456$	−3671.76	−0.377075
$457$	18611.4	1.90504	0.952522	−	0.304469i	$-0.0984791\pi$
$457$	18611.4	1.90504	0.952522	+	0.304469i	$0.0984791\pi$
$458$	2197.55	0.224203
$459$	−58.7029	−0.00596954
$460$	875.540	0.0887440
$461$	10451.6	1.05592	0.527960	−	0.849269i	$-0.322957\pi$
$461$	10451.6	1.05592	0.527960	+	0.849269i	$0.322957\pi$
$462$	918.132	0.0924575
$463$	−4486.92	−0.450378	−0.225189	−	0.974315i	$-0.572300\pi$
$463$	−4486.92	−0.450378	−0.225189	+	0.974315i	$0.572300\pi$
$464$	−2868.59	−0.287006
$465$	−5612.03	−0.559681
$466$	−10623.5	−1.05606
$467$	756.360	0.0749468	0.0374734	−	0.999298i	$-0.488069\pi$
$467$	756.360	0.0749468	0.0374734	+	0.999298i	$0.488069\pi$
$468$	0	0
$469$	7559.38	0.744264
$470$	−10002.5	−0.981663
$471$	7116.64	0.696215
$472$	6693.55	0.652744
$473$	5293.21	0.514550
$474$	−9110.01	−0.882777
$475$	−5073.96	−0.490125
$476$	−13.3149	−0.00128211
$477$	−5345.35	−0.513096
$478$	−8704.13	−0.832882
$479$	333.637	0.0318252	0.0159126	−	0.999873i	$-0.494935\pi$
$479$	333.637	0.0318252	0.0159126	+	0.999873i	$0.494935\pi$
$480$	−9564.68	−0.909512
$481$	0	0
$482$	59.4968	0.00562242
$483$	−604.645	−0.0569613
$484$	−428.279	−0.0402216
$485$	2995.14	0.280417
$486$	−5855.03	−0.546481
$487$	15192.9	1.41367	0.706834	−	0.707379i	$-0.250123\pi$
$487$	15192.9	1.41367	0.706834	+	0.707379i	$0.250123\pi$
$488$	19102.9	1.77203
$489$	−6093.36	−0.563499
$490$	8461.01	0.780060
$491$	−16039.9	−1.47428	−0.737139	−	0.675741i	$-0.763824\pi$
$491$	−16039.9	−1.47428	−0.737139	+	0.675741i	$0.763824\pi$
$492$	−3316.78	−0.303927
$493$	47.7583	0.00436293
$494$	0	0
$495$	1884.55	0.171119
$496$	1984.54	0.179654
$497$	−4656.29	−0.420248
$498$	−3442.04	−0.309722
$499$	6334.59	0.568287	0.284144	−	0.958782i	$-0.408291\pi$
$499$	6334.59	0.568287	0.284144	+	0.958782i	$0.408291\pi$
$500$	−652.493	−0.0583607
$501$	−7486.09	−0.667572
$502$	−3676.62	−0.326884
$503$	6691.01	0.593116	0.296558	−	0.955015i	$-0.404161\pi$
$503$	6691.01	0.593116	0.296558	+	0.955015i	$0.404161\pi$
$504$	−2519.94	−0.222712
$505$	14061.7	1.23909
$506$	−355.438	−0.0312276
$507$	0	0
$508$	6228.99	0.544029
$509$	−15333.3	−1.33524	−0.667618	−	0.744504i	$-0.732686\pi$
$509$	−15333.3	−1.33524	−0.667618	+	0.744504i	$0.732686\pi$
$510$	−53.3162	−0.00462918
$511$	−5.43892	−0.000470849 0
$512$	7897.02	0.681645
$513$	5664.25	0.487491
$514$	−9804.16	−0.841329
$515$	−3072.41	−0.262886
$516$	6898.23	0.588522
$517$	−3222.22	−0.274107
$518$	−6068.58	−0.514746
$519$	856.867	0.0724707
$520$	0	0
$521$	1223.34	0.102871	0.0514354	−	0.998676i	$-0.483620\pi$
$521$	1223.34	0.102871	0.0514354	+	0.998676i	$0.483620\pi$
$522$	2772.40	0.232461
$523$	2578.82	0.215610	0.107805	−	0.994172i	$-0.465618\pi$
$523$	2578.82	0.215610	0.107805	+	0.994172i	$0.465618\pi$
$524$	1047.25	0.0873080
$525$	5390.65	0.448128
$526$	5838.66	0.483988
$527$	−33.0400	−0.00273102
$528$	1031.63	0.0850304
$529$	−11932.9	−0.980761
$530$	−17225.1	−1.41172
$531$	−2910.30	−0.237846
$532$	1284.75	0.104701
$533$	0	0
$534$	−7099.14	−0.575299
$535$	−19151.1	−1.54762
$536$	18880.5	1.52148
$537$	10390.5	0.834976
$538$	−5790.57	−0.464032
$539$	2725.64	0.217814
$540$	8713.88	0.694418
$541$	707.235	0.0562041	0.0281020	−	0.999605i	$-0.491054\pi$
$541$	707.235	0.0562041	0.0281020	+	0.999605i	$0.491054\pi$
$542$	−7434.75	−0.589206
$543$	−18413.1	−1.45521
$544$	−56.3107	−0.00443805
$545$	11561.5	0.908699
$546$	0	0
$547$	376.197	0.0294059	0.0147029	−	0.999892i	$-0.495320\pi$
$547$	376.197	0.0294059	0.0147029	+	0.999892i	$0.495320\pi$
$548$	644.228	0.0502191
$549$	−8305.79	−0.645687
$550$	3168.88	0.245675
$551$	−4608.20	−0.356290
$552$	−1510.18	−0.116445
$553$	10392.2	0.799137
$554$	14480.9	1.11053
$555$	19282.7	1.47478
$556$	7324.17	0.558658
$557$	14363.8	1.09267	0.546333	−	0.837568i	$-0.316023\pi$
$557$	14363.8	1.09267	0.546333	+	0.837568i	$0.316023\pi$
$558$	−1918.00	−0.145511
$559$	0	0
$560$	−3653.16	−0.275669
$561$	−17.1754	−0.00129259
$562$	−11183.0	−0.839374
$563$	−14272.3	−1.06839	−0.534196	−	0.845360i	$-0.679386\pi$
$563$	−14272.3	−1.06839	−0.534196	+	0.845360i	$0.679386\pi$
$564$	−4199.27	−0.313513
$565$	10099.5	0.752016
$566$	−12557.0	−0.932526
$567$	−3226.04	−0.238944
$568$	−11629.7	−0.859102
$569$	−15602.5	−1.14955	−0.574773	−	0.818313i	$-0.694910\pi$
$569$	−15602.5	−1.14955	−0.574773	+	0.818313i	$0.694910\pi$
$570$	5144.49	0.378033
$571$	9814.46	0.719304	0.359652	−	0.933087i	$-0.382895\pi$
$571$	9814.46	0.719304	0.359652	+	0.933087i	$0.382895\pi$
$572$	0	0
$573$	21261.9	1.55014
$574$	−4768.14	−0.346722
$575$	−2086.89	−0.151356
$576$	−5231.84	−0.378461
$577$	−233.820	−0.0168701	−0.00843506	−	0.999964i	$-0.502685\pi$
$577$	−233.820	−0.0168701	−0.00843506	+	0.999964i	$0.502685\pi$
$578$	10375.9	0.746679
$579$	18337.3	1.31619
$580$	−7089.26	−0.507527
$581$	3926.51	0.280377
$582$	−1584.62	−0.112860
$583$	−5548.92	−0.394190
$584$	−13.5844	−0.000962545 0
$585$	0	0
$586$	−42.8651	−0.00302174
$587$	20376.0	1.43272	0.716360	−	0.697730i	$-0.245807\pi$
$587$	20376.0	1.43272	0.716360	+	0.697730i	$0.245807\pi$
$588$	3552.11	0.249127
$589$	3188.03	0.223023
$590$	−9378.29	−0.654404
$591$	−506.706	−0.0352675
$592$	−6818.78	−0.473396
$593$	−17139.6	−1.18691	−0.593456	−	0.804867i	$-0.702237\pi$
$593$	−17139.6	−1.18691	−0.593456	+	0.804867i	$0.702237\pi$
$594$	−3537.53	−0.244355
$595$	60.8205	0.00419059
$596$	−8076.03	−0.555045
$597$	−17144.7	−1.17535
$598$	0	0
$599$	−24002.2	−1.63724	−0.818619	−	0.574338i	$-0.805260\pi$
$599$	−24002.2	−1.63724	−0.818619	+	0.574338i	$0.805260\pi$
$600$	13463.8	0.916097
$601$	−10807.8	−0.733546	−0.366773	−	0.930311i	$-0.619537\pi$
$601$	−10807.8	−0.733546	−0.366773	+	0.930311i	$0.619537\pi$
$602$	9916.77	0.671391
$603$	−8209.08	−0.554394
$604$	−3267.25	−0.220103
$605$	1956.32	0.131464
$606$	−7439.53	−0.498697
$607$	19058.8	1.27442	0.637211	−	0.770689i	$-0.280088\pi$
$607$	19058.8	1.27442	0.637211	+	0.770689i	$0.280088\pi$
$608$	5433.42	0.362425
$609$	4895.82	0.325762
$610$	−26765.0	−1.77653
$611$	0	0
$612$	14.4592	0.000955033 0
$613$	27904.3	1.83857	0.919285	−	0.393592i	$-0.128768\pi$
$613$	27904.3	1.83857	0.919285	+	0.393592i	$0.128768\pi$
$614$	−8660.26	−0.569218
$615$	15150.6	0.993382
$616$	−2615.91	−0.171101
$617$	−17966.5	−1.17229	−0.586147	−	0.810205i	$-0.699356\pi$
$617$	−17966.5	−1.17229	−0.586147	+	0.810205i	$0.699356\pi$
$618$	1625.49	0.105804
$619$	8345.06	0.541868	0.270934	−	0.962598i	$-0.412667\pi$
$619$	8345.06	0.541868	0.270934	+	0.962598i	$0.412667\pi$
$620$	4904.47	0.317691
$621$	2329.68	0.150542
$622$	−12351.1	−0.796198
$623$	8098.34	0.520792
$624$	0	0
$625$	−14069.7	−0.900464
$626$	16562.0	1.05743
$627$	1657.25	0.105557
$628$	−6219.38	−0.395192
$629$	113.524	0.00719634
$630$	3530.67	0.223278
$631$	−4863.53	−0.306837	−0.153418	−	0.988161i	$-0.549028\pi$
$631$	−4863.53	−0.306837	−0.153418	+	0.988161i	$0.549028\pi$
$632$	25955.9	1.63366
$633$	3281.71	0.206060
$634$	−5465.48	−0.342369
$635$	−28453.1	−1.77816
$636$	−7231.47	−0.450859
$637$	0	0
$638$	2877.99	0.178591
$639$	5056.48	0.313038
$640$	2033.21	0.125578
$641$	351.160	0.0216380	0.0108190	−	0.999941i	$-0.496556\pi$
$641$	351.160	0.0216380	0.0108190	+	0.999941i	$0.496556\pi$
$642$	10132.1	0.622872
$643$	3694.84	0.226610	0.113305	−	0.993560i	$-0.463856\pi$
$643$	3694.84	0.226610	0.113305	+	0.993560i	$0.463856\pi$
$644$	528.412	0.0323329
$645$	−31510.1	−1.92358
$646$	30.2874	0.00184465
$647$	−21804.1	−1.32489	−0.662447	−	0.749109i	$-0.730482\pi$
$647$	−21804.1	−1.32489	−0.662447	+	0.749109i	$0.730482\pi$
$648$	−8057.44	−0.488467
$649$	−3021.13	−0.182727
$650$	0	0
$651$	−3387.02	−0.203913
$652$	5325.12	0.319858
$653$	−22622.6	−1.35573	−0.677865	−	0.735186i	$-0.737095\pi$
$653$	−22622.6	−1.35573	−0.677865	+	0.735186i	$0.737095\pi$
$654$	−6116.76	−0.365725
$655$	−4783.70	−0.285366
$656$	−5357.58	−0.318869
$657$	5.90638	0.000350730 0
$658$	−6036.79	−0.357658
$659$	16699.5	0.987134	0.493567	−	0.869708i	$-0.335693\pi$
$659$	16699.5	0.987134	0.493567	+	0.869708i	$0.335693\pi$
$660$	2549.52	0.150363
$661$	−6257.30	−0.368201	−0.184101	−	0.982907i	$-0.558937\pi$
$661$	−6257.30	−0.368201	−0.184101	+	0.982907i	$0.558937\pi$
$662$	24837.1	1.45819
$663$	0	0
$664$	9806.96	0.573168
$665$	−5868.57	−0.342216
$666$	6590.15	0.383428
$667$	−1895.33	−0.110026
$668$	6542.25	0.378933
$669$	−16335.5	−0.944044
$670$	−26453.4	−1.52535
$671$	−8622.12	−0.496055
$672$	−5772.55	−0.331370
$673$	14100.0	0.807600	0.403800	−	0.914847i	$-0.367689\pi$
$673$	14100.0	0.807600	0.403800	+	0.914847i	$0.367689\pi$
$674$	967.052	0.0552663
$675$	−20770.0	−1.18435
$676$	0	0
$677$	−26784.2	−1.52053	−0.760267	−	0.649611i	$-0.774932\pi$
$677$	−26784.2	−1.52053	−0.760267	+	0.649611i	$0.774932\pi$
$678$	−5343.26	−0.302665
$679$	1807.65	0.102167
$680$	151.907	0.00856671
$681$	−11442.2	−0.643854
$682$	−1991.04	−0.111790
$683$	28421.6	1.59227	0.796136	−	0.605118i	$-0.206874\pi$
$683$	28421.6	1.59227	0.796136	+	0.605118i	$0.206874\pi$
$684$	−1395.17	−0.0779909
$685$	−2942.74	−0.164141
$686$	12175.1	0.677621
$687$	−4214.22	−0.234036
$688$	11142.7	0.617458
$689$	0	0
$690$	2115.90	0.116741
$691$	−32230.8	−1.77441	−0.887206	−	0.461374i	$-0.847357\pi$
$691$	−32230.8	−1.77441	−0.887206	+	0.461374i	$0.847357\pi$
$692$	−748.834	−0.0411364
$693$	1137.38	0.0623454
$694$	−9484.65	−0.518778
$695$	−33455.8	−1.82597
$696$	12227.9	0.665946
$697$	89.1969	0.00484731
$698$	−8126.78	−0.440692
$699$	20372.6	1.10238
$700$	−4711.01	−0.254371
$701$	3549.25	0.191231	0.0956157	−	0.995418i	$-0.469518\pi$
$701$	3549.25	0.191231	0.0956157	+	0.995418i	$0.469518\pi$
$702$	0	0
$703$	−10953.9	−0.587675
$704$	−5431.10	−0.290756
$705$	19181.7	1.02471
$706$	15925.4	0.848954
$707$	8486.65	0.451447
$708$	−3937.21	−0.208996
$709$	−21974.7	−1.16400	−0.582002	−	0.813188i	$-0.697730\pi$
$709$	−21974.7	−1.16400	−0.582002	+	0.813188i	$0.697730\pi$
$710$	16294.3	0.861285
$711$	−11285.4	−0.595268
$712$	20226.6	1.06464
$713$	1311.22	0.0688719
$714$	−32.1778	−0.00168659
$715$	0	0
$716$	−9080.46	−0.473956
$717$	16691.8	0.869408
$718$	−4392.74	−0.228322
$719$	−28642.7	−1.48567	−0.742833	−	0.669477i	$-0.766518\pi$
$719$	−28642.7	−1.48567	−0.742833	+	0.669477i	$0.766518\pi$
$720$	3967.14	0.205342
$721$	−1854.28	−0.0957795
$722$	11563.7	0.596062
$723$	−114.096	−0.00586900
$724$	16091.6	0.826022
$725$	16897.6	0.865603
$726$	−1035.01	−0.0529105
$727$	23124.1	1.17968	0.589838	−	0.807522i	$-0.299192\pi$
$727$	23124.1	1.17968	0.589838	+	0.807522i	$0.299192\pi$
$728$	0	0
$729$	20154.6	1.02396
$730$	19.0330	0.000964992 0
$731$	−185.511	−0.00938631
$732$	−11236.5	−0.567369
$733$	−34977.5	−1.76252	−0.881258	−	0.472636i	$-0.843302\pi$
$733$	−34977.5	−1.76252	−0.881258	+	0.472636i	$0.843302\pi$
$734$	11782.0	0.592481
$735$	−16225.5	−0.814270
$736$	2234.74	0.111921
$737$	−8521.72	−0.425918
$738$	5177.94	0.258269
$739$	−4724.81	−0.235189	−0.117595	−	0.993062i	$-0.537518\pi$
$739$	−4724.81	−0.235189	−0.117595	+	0.993062i	$0.537518\pi$
$740$	−16851.5	−0.837129
$741$	0	0
$742$	−10395.8	−0.514344
$743$	17773.4	0.877579	0.438789	−	0.898590i	$-0.355407\pi$
$743$	17773.4	0.877579	0.438789	+	0.898590i	$0.355407\pi$
$744$	−8459.49	−0.416855
$745$	36890.2	1.81416
$746$	−3306.37	−0.162272
$747$	−4263.98	−0.208850
$748$	15.0099	0.000733713 0
$749$	−11558.2	−0.563857
$750$	−1576.87	−0.0767721
$751$	−32065.3	−1.55803	−0.779013	−	0.627007i	$-0.784280\pi$
$751$	−32065.3	−1.55803	−0.779013	+	0.627007i	$0.784280\pi$
$752$	−6783.07	−0.328927
$753$	7050.61	0.341220
$754$	0	0
$755$	14924.3	0.719407
$756$	5259.07	0.253003
$757$	−29867.9	−1.43404	−0.717018	−	0.697054i	$-0.754494\pi$
$757$	−29867.9	−1.43404	−0.717018	+	0.697054i	$0.754494\pi$
$758$	−1935.06	−0.0927235
$759$	681.619	0.0325971
$760$	−14657.5	−0.699583
$761$	−15515.7	−0.739087	−0.369544	−	0.929213i	$-0.620486\pi$
$761$	−15515.7	−0.739087	−0.369544	+	0.929213i	$0.620486\pi$
$762$	15053.5	0.715656
$763$	6977.70	0.331074
$764$	−18581.2	−0.879902
$765$	−66.0478	−0.00312152
$766$	−19464.7	−0.918132
$767$	0	0
$768$	−17073.3	−0.802186
$769$	34784.7	1.63117	0.815584	−	0.578639i	$-0.196416\pi$
$769$	34784.7	1.63117	0.815584	+	0.578639i	$0.196416\pi$
$770$	3665.14	0.171536
$771$	18801.3	0.878226
$772$	−16025.4	−0.747107
$773$	−17790.3	−0.827780	−0.413890	−	0.910327i	$-0.635830\pi$
$773$	−17790.3	−0.827780	−0.413890	+	0.910327i	$0.635830\pi$
$774$	−10769.1	−0.500111
$775$	−11690.1	−0.541832
$776$	4514.83	0.208857
$777$	11637.6	0.537320
$778$	−16499.5	−0.760331
$779$	−8606.61	−0.395846
$780$	0	0
$781$	5249.05	0.240494
$782$	12.4571	0.000569647 0
$783$	−18863.4	−0.860950
$784$	5737.72	0.261376
$785$	28409.3	1.29168
$786$	2530.87	0.114852
$787$	8427.80	0.381726	0.190863	−	0.981617i	$-0.438871\pi$
$787$	8427.80	0.381726	0.190863	+	0.981617i	$0.438871\pi$
$788$	442.821	0.0200188
$789$	−11196.7	−0.505213
$790$	−36366.7	−1.63781
$791$	6095.32	0.273988
$792$	2840.74	0.127451
$793$	0	0
$794$	−25668.4	−1.14727
$795$	33032.4	1.47363
$796$	14983.1	0.667163
$797$	31835.9	1.41491	0.707457	−	0.706757i	$-0.249842\pi$
$797$	31835.9	1.41491	0.707457	+	0.706757i	$0.249842\pi$
$798$	3104.84	0.137732
$799$	112.929	0.00500019
$800$	−19923.6	−0.880506
$801$	−8794.36	−0.387932
$802$	16987.0	0.747918
$803$	6.13132	0.000269452 0
$804$	−11105.7	−0.487148
$805$	−2413.71	−0.105680
$806$	0	0
$807$	11104.5	0.484383
$808$	21196.5	0.922882
$809$	−44601.6	−1.93833	−0.969165	−	0.246411i	$-0.920749\pi$
$809$	−44601.6	−1.93833	−0.969165	+	0.246411i	$0.920749\pi$
$810$	11289.2	0.489708
$811$	−6856.78	−0.296885	−0.148443	−	0.988921i	$-0.547426\pi$
$811$	−6856.78	−0.296885	−0.148443	+	0.988921i	$0.547426\pi$
$812$	−4278.57	−0.184912
$813$	14257.5	0.615046
$814$	6841.14	0.294572
$815$	−24324.4	−1.04546
$816$	−36.1557	−0.00155110
$817$	17900.0	0.766514
$818$	−4098.95	−0.175204
$819$	0	0
$820$	−13240.4	−0.563872
$821$	2359.70	0.100309	0.0501547	−	0.998741i	$-0.484029\pi$
$821$	2359.70	0.100309	0.0501547	+	0.998741i	$0.484029\pi$
$822$	1556.89	0.0660620
$823$	−25686.3	−1.08793	−0.543967	−	0.839107i	$-0.683078\pi$
$823$	−25686.3	−1.08793	−0.543967	+	0.839107i	$0.683078\pi$
$824$	−4631.30	−0.195800
$825$	−6076.91	−0.256449
$826$	−5660.06	−0.238424
$827$	−36731.5	−1.54448	−0.772238	−	0.635334i	$-0.780863\pi$
$827$	−36731.5	−1.54448	−0.772238	+	0.635334i	$0.780863\pi$
$828$	−573.827	−0.0240844
$829$	−1822.39	−0.0763500	−0.0381750	−	0.999271i	$-0.512154\pi$
$829$	−1822.39	−0.0763500	−0.0381750	+	0.999271i	$0.512154\pi$
$830$	−13740.5	−0.574625
$831$	−27769.8	−1.15924
$832$	0	0
$833$	−95.5256	−0.00397331
$834$	17700.2	0.734901
$835$	−29884.1	−1.23854
$836$	−1448.31	−0.0599172
$837$	13050.1	0.538920
$838$	−25468.7	−1.04988
$839$	−30967.0	−1.27426	−0.637128	−	0.770758i	$-0.719878\pi$
$839$	−30967.0	−1.27426	−0.637128	+	0.770758i	$0.719878\pi$
$840$	15572.3	0.639639
$841$	−9042.48	−0.370761
$842$	29682.0	1.21486
$843$	21445.5	0.876185
$844$	−2867.96	−0.116966
$845$	0	0
$846$	6555.63	0.266415
$847$	1180.69	0.0478974
$848$	−11681.0	−0.473026
$849$	24080.4	0.973423
$850$	−111.060	−0.00448155
$851$	−4505.30	−0.181480
$852$	6840.68	0.275068
$853$	2050.88	0.0823220	0.0411610	−	0.999153i	$-0.486894\pi$
$853$	2050.88	0.0823220	0.0411610	+	0.999153i	$0.486894\pi$
$854$	−16153.4	−0.647259
$855$	6372.95	0.254913
$856$	−28868.2	−1.15268
$857$	23377.3	0.931800	0.465900	−	0.884837i	$-0.345731\pi$
$857$	23377.3	0.931800	0.465900	+	0.884837i	$0.345731\pi$
$858$	0	0
$859$	29591.1	1.17536	0.587681	−	0.809093i	$-0.300041\pi$
$859$	29591.1	1.17536	0.587681	+	0.809093i	$0.300041\pi$
$860$	27537.4	1.09188
$861$	9143.79	0.361928
$862$	7452.74	0.294480
$863$	26229.6	1.03461	0.517304	−	0.855802i	$-0.326936\pi$
$863$	26229.6	1.03461	0.517304	+	0.855802i	$0.326936\pi$
$864$	22241.4	0.875774
$865$	3420.57	0.134454
$866$	−28449.7	−1.11635
$867$	−19897.7	−0.779425
$868$	2959.99	0.115747
$869$	−11715.2	−0.457320
$870$	−17132.5	−0.667639
$871$	0	0
$872$	17427.7	0.676807
$873$	−1963.01	−0.0761029
$874$	−1201.98	−0.0465191
$875$	1798.81	0.0694982
$876$	7.99047	0.000308188 0
$877$	23916.9	0.920887	0.460444	−	0.887689i	$-0.347690\pi$
$877$	23916.9	0.920887	0.460444	+	0.887689i	$0.347690\pi$
$878$	−21797.7	−0.837855
$879$	82.2017	0.00315426
$880$	4118.23	0.157756
$881$	−4711.76	−0.180185	−0.0900927	−	0.995933i	$-0.528716\pi$
$881$	−4711.76	−0.180185	−0.0900927	+	0.995933i	$0.528716\pi$
$882$	−5545.33	−0.211702
$883$	3184.99	0.121386	0.0606928	−	0.998156i	$-0.480669\pi$
$883$	3184.99	0.121386	0.0606928	+	0.998156i	$0.480669\pi$
$884$	0	0
$885$	17984.6	0.683103
$886$	14005.5	0.531065
$887$	−27813.9	−1.05287	−0.526436	−	0.850214i	$-0.676472\pi$
$887$	−27813.9	−1.05287	−0.526436	+	0.850214i	$0.676472\pi$
$888$	29066.4	1.09843
$889$	−17172.3	−0.647851
$890$	−28339.4	−1.06735
$891$	3636.73	0.136740
$892$	14275.9	0.535866
$893$	−10896.6	−0.408331
$894$	−19517.2	−0.730148
$895$	41478.3	1.54912
$896$	1227.10	0.0457528
$897$	0	0
$898$	−24688.9	−0.917458
$899$	−10617.0	−0.393878
$900$	5115.90	0.189478
$901$	194.473	0.00719073
$902$	5375.14	0.198418
$903$	−19017.2	−0.700835
$904$	15223.8	0.560107
$905$	−73504.2	−2.69985
$906$	−7895.90	−0.289540
$907$	−14183.8	−0.519255	−0.259628	−	0.965709i	$-0.583600\pi$
$907$	−14183.8	−0.519255	−0.259628	+	0.965709i	$0.583600\pi$
$908$	9999.55	0.365470
$909$	−9216.04	−0.336278
$910$	0	0
$911$	−16285.7	−0.592284	−0.296142	−	0.955144i	$-0.595700\pi$
$911$	−16285.7	−0.592284	−0.296142	+	0.955144i	$0.595700\pi$
$912$	3488.66	0.126668
$913$	−4426.37	−0.160451
$914$	−39307.1	−1.42250
$915$	51326.9	1.85444
$916$	3682.90	0.132845
$917$	−2887.10	−0.103970
$918$	123.980	0.00445746
$919$	26604.5	0.954954	0.477477	−	0.878644i	$-0.341551\pi$
$919$	26604.5	0.954954	0.477477	+	0.878644i	$0.341551\pi$
$920$	−6028.55	−0.216039
$921$	16607.6	0.594181
$922$	−22073.7	−0.788457
$923$	0	0
$924$	1538.70	0.0547832
$925$	40166.5	1.42775
$926$	9476.33	0.336298
$927$	2013.65	0.0713451
$928$	−18094.7	−0.640074
$929$	−1552.21	−0.0548183	−0.0274092	−	0.999624i	$-0.508726\pi$
$929$	−1552.21	−0.0548183	−0.0274092	+	0.999624i	$0.508726\pi$
$930$	11852.6	0.417915
$931$	9217.27	0.324472
$932$	−17804.0	−0.625741
$933$	23685.6	0.831116
$934$	−1597.42	−0.0559629
$935$	−68.5632	−0.00239814
$936$	0	0
$937$	14903.1	0.519599	0.259800	−	0.965663i	$-0.416343\pi$
$937$	14903.1	0.519599	0.259800	+	0.965663i	$0.416343\pi$
$938$	−15965.3	−0.555743
$939$	−31760.7	−1.10380
$940$	−16763.3	−0.581657
$941$	−49348.2	−1.70957	−0.854785	−	0.518982i	$-0.826311\pi$
$941$	−49348.2	−1.70957	−0.854785	+	0.518982i	$0.826311\pi$
$942$	−15030.3	−0.519865
$943$	−3539.85	−0.122241
$944$	−6359.76	−0.219272
$945$	−24022.7	−0.826940
$946$	−11179.2	−0.384215
$947$	−42644.2	−1.46331	−0.731653	−	0.681678i	$-0.761251\pi$
$947$	−42644.2	−1.46331	−0.731653	+	0.681678i	$0.761251\pi$
$948$	−15267.5	−0.523065
$949$	0	0
$950$	10716.2	0.365977
$951$	10481.1	0.357384
$952$	91.6800	0.00312118
$953$	−21045.0	−0.715336	−0.357668	−	0.933849i	$-0.616428\pi$
$953$	−21045.0	−0.715336	−0.357668	+	0.933849i	$0.616428\pi$
$954$	11289.3	0.383129
$955$	84876.4	2.87595
$956$	−14587.3	−0.493501
$957$	−5519.08	−0.186423
$958$	−704.638	−0.0237639
$959$	−1776.03	−0.0598029
$960$	32331.0	1.08696
$961$	−22446.0	−0.753448
$962$	0	0
$963$	12551.6	0.420011
$964$	99.7111	0.00333141
$965$	73201.8	2.44191
$966$	1277.00	0.0425331
$967$	21384.7	0.711152	0.355576	−	0.934647i	$-0.384285\pi$
$967$	21384.7	0.711152	0.355576	+	0.934647i	$0.384285\pi$
$968$	2948.93	0.0979154
$969$	−58.0818	−0.00192555
$970$	−6325.71	−0.209388
$971$	19482.8	0.643906	0.321953	−	0.946756i	$-0.395661\pi$
$971$	19482.8	0.643906	0.321953	+	0.946756i	$0.395661\pi$
$972$	−9812.48	−0.323802
$973$	−20191.5	−0.665272
$974$	−32087.3	−1.05559
$975$	0	0
$976$	−18150.3	−0.595264
$977$	−13909.6	−0.455484	−0.227742	−	0.973722i	$-0.573134\pi$
$977$	−13909.6	−0.455484	−0.227742	+	0.973722i	$0.573134\pi$
$978$	12869.1	0.420766
$979$	−9129.30	−0.298032
$980$	14179.9	0.462203
$981$	−7577.40	−0.246613
$982$	33876.1	1.10084
$983$	−42850.3	−1.39035	−0.695174	−	0.718842i	$-0.744673\pi$
$983$	−42850.3	−1.39035	−0.695174	+	0.718842i	$0.744673\pi$
$984$	22837.8	0.739879
$985$	−2022.75	−0.0654315
$986$	−100.865	−0.00325781
$987$	11576.7	0.373343
$988$	0	0
$989$	7362.18	0.236708
$990$	−3980.14	−0.127775
$991$	−9059.31	−0.290392	−0.145196	−	0.989403i	$-0.546381\pi$
$991$	−9059.31	−0.290392	−0.145196	+	0.989403i	$0.546381\pi$
$992$	12518.2	0.400660
$993$	−47629.8	−1.52214
$994$	9834.03	0.313799
$995$	−68440.7	−2.18062
$996$	−5768.54	−0.183517
$997$	14894.6	0.473135	0.236568	−	0.971615i	$-0.423978\pi$
$997$	14894.6	0.473135	0.236568	+	0.971615i	$0.423978\pi$
$998$	−13378.6	−0.424341
$999$	−44839.4	−1.42007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.c.1.2		6
13.12	even	2		143.4.a.b.1.5	✓	6
39.38	odd	2		1287.4.a.f.1.2		6
52.51	odd	2		2288.4.a.m.1.2		6
143.142	odd	2		1573.4.a.d.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.b.1.5	✓	6	13.12	even	2
1287.4.a.f.1.2		6	39.38	odd	2
1573.4.a.d.1.2		6	143.142	odd	2
1859.4.a.c.1.2		6	1.1	even	1	trivial
2288.4.a.m.1.2		6	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)

\(f(q)\)	\(=\)	\(q-2.11199 q^{2} +4.05013 q^{3} -3.53950 q^{4} +16.1679 q^{5} -8.55384 q^{6} +9.75779 q^{7} +24.3713 q^{8} -10.5964 q^{9} +O(q^{10})\)	\(q-2.11199 q^{2} +4.05013 q^{3} -3.53950 q^{4} +16.1679 q^{5} -8.55384 q^{6} +9.75779 q^{7} +24.3713 q^{8} -10.5964 q^{9} -34.1465 q^{10} -11.0000 q^{11} -14.3354 q^{12} -20.6084 q^{14} +65.4822 q^{15} -23.1560 q^{16} +0.385518 q^{17} +22.3796 q^{18} -37.1986 q^{19} -57.2263 q^{20} +39.5203 q^{21} +23.2319 q^{22} -15.2996 q^{23} +98.7070 q^{24} +136.402 q^{25} -152.271 q^{27} -34.5377 q^{28} +123.881 q^{29} -138.298 q^{30} -85.7031 q^{31} -146.065 q^{32} -44.5514 q^{33} -0.814209 q^{34} +157.763 q^{35} +37.5060 q^{36} +294.472 q^{37} +78.5631 q^{38} +394.034 q^{40} +231.369 q^{41} -83.4666 q^{42} -481.201 q^{43} +38.9345 q^{44} -171.322 q^{45} +32.3126 q^{46} +292.929 q^{47} -93.7848 q^{48} -247.785 q^{49} -288.080 q^{50} +1.56140 q^{51} +504.448 q^{53} +321.594 q^{54} -177.847 q^{55} +237.810 q^{56} -150.659 q^{57} -261.636 q^{58} +274.649 q^{59} -231.774 q^{60} +783.829 q^{61} +181.004 q^{62} -103.398 q^{63} +493.736 q^{64} +94.0922 q^{66} +774.702 q^{67} -1.36454 q^{68} -61.9654 q^{69} -333.195 q^{70} -477.187 q^{71} -258.249 q^{72} -0.557393 q^{73} -621.922 q^{74} +552.446 q^{75} +131.664 q^{76} -107.336 q^{77} +1065.02 q^{79} -374.384 q^{80} -330.612 q^{81} -488.649 q^{82} +402.398 q^{83} -139.882 q^{84} +6.23302 q^{85} +1016.29 q^{86} +501.735 q^{87} -268.084 q^{88} +829.936 q^{89} +361.831 q^{90} +54.1529 q^{92} -347.109 q^{93} -618.664 q^{94} -601.424 q^{95} -591.583 q^{96} +185.252 q^{97} +523.320 q^{98} +116.561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} + 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 + 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8	\( 6 q + 6 q^{2} - 6 q^{3} + 26 q^{4} + 8 q^{5} + 15 q^{6} + 53 q^{7} + 36 q^{8} - 52 q^{10} - 66 q^{11} - 19 q^{12} - 120 q^{14} + 23 q^{15} + 26 q^{16} - 117 q^{17} + 27 q^{18} + 67 q^{19} - 10 q^{20} - 19 q^{21} - 66 q^{22} - 158 q^{23} + 609 q^{24} - 234 q^{25} - 531 q^{27} + 670 q^{28} - 145 q^{29} - 211 q^{30} + 58 q^{31} + 364 q^{32} + 66 q^{33} - 43 q^{34} - 210 q^{35} + 383 q^{36} + 753 q^{37} + 738 q^{38} + 4 q^{40} + 232 q^{41} + 1593 q^{42} - 390 q^{43} - 286 q^{44} + 107 q^{45} - 5 q^{46} + 205 q^{47} + 1625 q^{48} + 491 q^{49} - 938 q^{50} + 363 q^{51} - 65 q^{53} - 1917 q^{54} - 88 q^{55} + 1816 q^{56} + 1657 q^{57} + 1685 q^{58} - 1735 q^{59} - 871 q^{60} + 421 q^{61} + 3394 q^{62} + 125 q^{63} + 570 q^{64} - 165 q^{66} + 703 q^{67} + 209 q^{68} - 272 q^{69} - 1968 q^{70} - 445 q^{71} - 1035 q^{72} + 2340 q^{73} + 1135 q^{74} + 1941 q^{75} + 1208 q^{76} - 583 q^{77} - 1234 q^{79} - 2766 q^{80} + 606 q^{81} - 897 q^{82} + 1601 q^{83} + 7 q^{84} + 2245 q^{85} + 1146 q^{86} + 2462 q^{87} - 396 q^{88} + 442 q^{89} + 113 q^{90} + 2737 q^{92} + 982 q^{93} + 2733 q^{94} - 504 q^{95} + 1153 q^{96} + 2682 q^{97} - 2036 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 26 * q^4 + 8 * q^5 + 15 * q^6 + 53 * q^7 + 36 * q^8 - 52 * q^10 - 66 * q^11 - 19 * q^12 - 120 * q^14 + 23 * q^15 + 26 * q^16 - 117 * q^17 + 27 * q^18 + 67 * q^19 - 10 * q^20 - 19 * q^21 - 66 * q^22 - 158 * q^23 + 609 * q^24 - 234 * q^25 - 531 * q^27 + 670 * q^28 - 145 * q^29 - 211 * q^30 + 58 * q^31 + 364 * q^32 + 66 * q^33 - 43 * q^34 - 210 * q^35 + 383 * q^36 + 753 * q^37 + 738 * q^38 + 4 * q^40 + 232 * q^41 + 1593 * q^42 - 390 * q^43 - 286 * q^44 + 107 * q^45 - 5 * q^46 + 205 * q^47 + 1625 * q^48 + 491 * q^49 - 938 * q^50 + 363 * q^51 - 65 * q^53 - 1917 * q^54 - 88 * q^55 + 1816 * q^56 + 1657 * q^57 + 1685 * q^58 - 1735 * q^59 - 871 * q^60 + 421 * q^61 + 3394 * q^62 + 125 * q^63 + 570 * q^64 - 165 * q^66 + 703 * q^67 + 209 * q^68 - 272 * q^69 - 1968 * q^70 - 445 * q^71 - 1035 * q^72 + 2340 * q^73 + 1135 * q^74 + 1941 * q^75 + 1208 * q^76 - 583 * q^77 - 1234 * q^79 - 2766 * q^80 + 606 * q^81 - 897 * q^82 + 1601 * q^83 + 7 * q^84 + 2245 * q^85 + 1146 * q^86 + 2462 * q^87 - 396 * q^88 + 442 * q^89 + 113 * q^90 + 2737 * q^92 + 982 * q^93 + 2733 * q^94 - 504 * q^95 + 1153 * q^96 + 2682 * q^97 - 2036 * q^98

Introduction

L-functions

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