LMFDB - Embedded newform 1859.4.a.i.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + \cdots + 2596992 $ x^17 - 4x^16 - 99x^15 + 375x^14 + 3949x^13 - 13998x^12 - 81750x^11 + 267574x^10 + 941923x^9 - 2799440x^8 - 6021311x^7 + 15765187x^6 + 20197463x^5 - 42560950x^4 - 32766128x^3 + 37775816x^2 + 27375104x + 2596992
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.02345$ 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)

$f(q)$	$=$	$q+2.02345 q^{2} -7.47211 q^{3} -3.90564 q^{4} -6.22433 q^{5} -15.1195 q^{6} +28.5679 q^{7} -24.0905 q^{8} +28.8324 q^{9} +O(q^{10})$	\(q+2.02345 q^{2} -7.47211 q^{3} -3.90564 q^{4} -6.22433 q^{5} -15.1195 q^{6} +28.5679 q^{7} -24.0905 q^{8} +28.8324 q^{9} -12.5946 q^{10} -11.0000 q^{11} +29.1833 q^{12} +57.8058 q^{14} +46.5089 q^{15} -17.5009 q^{16} -6.87065 q^{17} +58.3411 q^{18} +74.9116 q^{19} +24.3100 q^{20} -213.462 q^{21} -22.2580 q^{22} +35.5439 q^{23} +180.007 q^{24} -86.2577 q^{25} -13.6922 q^{27} -111.576 q^{28} -238.076 q^{29} +94.1085 q^{30} +67.6726 q^{31} +157.312 q^{32} +82.1932 q^{33} -13.9024 q^{34} -177.816 q^{35} -112.609 q^{36} +163.331 q^{37} +151.580 q^{38} +149.947 q^{40} -499.460 q^{41} -431.931 q^{42} +72.9317 q^{43} +42.9620 q^{44} -179.463 q^{45} +71.9214 q^{46} -167.830 q^{47} +130.769 q^{48} +473.123 q^{49} -174.539 q^{50} +51.3382 q^{51} -25.3435 q^{53} -27.7054 q^{54} +68.4676 q^{55} -688.214 q^{56} -559.748 q^{57} -481.737 q^{58} -84.2856 q^{59} -181.647 q^{60} -699.623 q^{61} +136.932 q^{62} +823.681 q^{63} +458.320 q^{64} +166.314 q^{66} -24.3552 q^{67} +26.8343 q^{68} -265.588 q^{69} -359.802 q^{70} -917.389 q^{71} -694.588 q^{72} -651.592 q^{73} +330.492 q^{74} +644.527 q^{75} -292.577 q^{76} -314.247 q^{77} +709.665 q^{79} +108.931 q^{80} -676.166 q^{81} -1010.63 q^{82} +412.149 q^{83} +833.706 q^{84} +42.7652 q^{85} +147.574 q^{86} +1778.93 q^{87} +264.995 q^{88} -454.838 q^{89} -363.134 q^{90} -138.821 q^{92} -505.657 q^{93} -339.595 q^{94} -466.274 q^{95} -1175.45 q^{96} +1389.40 q^{97} +957.343 q^{98} -317.157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19} + 98 q^{20} + 220 q^{21} - 44 q^{22} - 215 q^{23} + 26 q^{24} + 319 q^{25} - 384 q^{27} - 396 q^{28} - 7 q^{29} - 1269 q^{30} + 682 q^{31} + 813 q^{32} + 66 q^{33} + 738 q^{34} + 10 q^{35} + 560 q^{36} + 1084 q^{37} + 410 q^{38} + 95 q^{40} + 240 q^{41} + 393 q^{42} - 435 q^{43} - 858 q^{44} + 1242 q^{45} + 1671 q^{46} + 549 q^{47} + 894 q^{48} + 403 q^{49} - 651 q^{50} + 1552 q^{51} - 566 q^{53} + 311 q^{54} - 176 q^{55} - 1925 q^{56} - 534 q^{57} + 618 q^{58} + 2010 q^{59} - 411 q^{60} + 460 q^{61} - 823 q^{62} + 820 q^{63} + 3171 q^{64} - 154 q^{66} - 232 q^{67} + 1795 q^{68} - 1608 q^{69} + 207 q^{70} + 489 q^{71} + 2556 q^{72} + 290 q^{73} + 2653 q^{74} - 2852 q^{75} + 2421 q^{76} + 66 q^{77} - 732 q^{79} + 4915 q^{80} + 2393 q^{81} - 1772 q^{82} - 117 q^{83} + 4161 q^{84} + 4858 q^{85} + 1034 q^{86} + 3032 q^{87} - 693 q^{88} + 4113 q^{89} + 15145 q^{90} - 3554 q^{92} + 802 q^{93} + 2325 q^{94} - 3924 q^{95} + 2601 q^{96} + 2793 q^{97} + 533 q^{98} - 1485 q^{99}+O(q^{100}) \) 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 95 * q^12 - 60 * q^14 - 28 * q^15 + 350 * q^16 + 118 * q^17 + 478 * q^18 + 403 * q^19 + 98 * q^20 + 220 * q^21 - 44 * q^22 - 215 * q^23 + 26 * q^24 + 319 * q^25 - 384 * q^27 - 396 * q^28 - 7 * q^29 - 1269 * q^30 + 682 * q^31 + 813 * q^32 + 66 * q^33 + 738 * q^34 + 10 * q^35 + 560 * q^36 + 1084 * q^37 + 410 * q^38 + 95 * q^40 + 240 * q^41 + 393 * q^42 - 435 * q^43 - 858 * q^44 + 1242 * q^45 + 1671 * q^46 + 549 * q^47 + 894 * q^48 + 403 * q^49 - 651 * q^50 + 1552 * q^51 - 566 * q^53 + 311 * q^54 - 176 * q^55 - 1925 * q^56 - 534 * q^57 + 618 * q^58 + 2010 * q^59 - 411 * q^60 + 460 * q^61 - 823 * q^62 + 820 * q^63 + 3171 * q^64 - 154 * q^66 - 232 * q^67 + 1795 * q^68 - 1608 * q^69 + 207 * q^70 + 489 * q^71 + 2556 * q^72 + 290 * q^73 + 2653 * q^74 - 2852 * q^75 + 2421 * q^76 + 66 * q^77 - 732 * q^79 + 4915 * q^80 + 2393 * q^81 - 1772 * q^82 - 117 * q^83 + 4161 * q^84 + 4858 * q^85 + 1034 * q^86 + 3032 * q^87 - 693 * q^88 + 4113 * q^89 + 15145 * q^90 - 3554 * q^92 + 802 * q^93 + 2325 * q^94 - 3924 * q^95 + 2601 * q^96 + 2793 * q^97 + 533 * 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 $

$2$	2.02345	0.715399	0.357699	−	0.933837i	$-0.383561\pi$
$2$	2.02345	0.715399	0.357699	+	0.933837i	$0.383561\pi$
$3$	−7.47211	−1.43801	−0.719004	−	0.695006i	$-0.755402\pi$
$3$	−7.47211	−1.43801	−0.719004	+	0.695006i	$0.755402\pi$
$4$	−3.90564	−0.488205
$5$	−6.22433	−0.556721	−0.278360	−	0.960477i	$-0.589791\pi$
$5$	−6.22433	−0.556721	−0.278360	+	0.960477i	$0.589791\pi$
$6$	−15.1195	−1.02875
$7$	28.5679	1.54252	0.771260	−	0.636520i	$-0.219627\pi$
$7$	28.5679	1.54252	0.771260	+	0.636520i	$0.219627\pi$
$8$	−24.0905	−1.06466
$9$	28.8324	1.06787
$10$	−12.5946	−0.398277
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	29.1833	0.702042
$13$	0	0
$13$	0	0
$14$	57.8058	1.10352
$15$	46.5089	0.800569
$16$	−17.5009	−0.273452
$17$	−6.87065	−0.0980222	−0.0490111	−	0.998798i	$-0.515607\pi$
$17$	−6.87065	−0.0980222	−0.0490111	+	0.998798i	$0.515607\pi$
$18$	58.3411	0.763951
$19$	74.9116	0.904521	0.452260	−	0.891886i	$-0.350618\pi$
$19$	74.9116	0.904521	0.452260	+	0.891886i	$0.350618\pi$
$20$	24.3100	0.271794
$21$	−213.462	−2.21816
$22$	−22.2580	−0.215701
$23$	35.5439	0.322235	0.161118	−	0.986935i	$-0.448490\pi$
$23$	35.5439	0.322235	0.161118	+	0.986935i	$0.448490\pi$
$24$	180.007	1.53099
$25$	−86.2577	−0.690062
$26$	0	0
$27$	−13.6922	−0.0975947
$28$	−111.576	−0.753065
$29$	−238.076	−1.52447	−0.762236	−	0.647299i	$-0.775898\pi$
$29$	−238.076	−1.52447	−0.762236	+	0.647299i	$0.775898\pi$
$30$	94.1085	0.572726
$31$	67.6726	0.392076	0.196038	−	0.980596i	$-0.437192\pi$
$31$	67.6726	0.392076	0.196038	+	0.980596i	$0.437192\pi$
$32$	157.312	0.869033
$33$	82.1932	0.433576
$34$	−13.9024	−0.0701250
$35$	−177.816	−0.858753
$36$	−112.609	−0.521338
$37$	163.331	0.725713	0.362856	−	0.931845i	$-0.381802\pi$
$37$	163.331	0.725713	0.362856	+	0.931845i	$0.381802\pi$
$38$	151.580	0.647093
$39$	0	0
$40$	149.947	0.592718
$41$	−499.460	−1.90250	−0.951250	−	0.308420i	$-0.900200\pi$
$41$	−499.460	−1.90250	−0.951250	+	0.308420i	$0.900200\pi$
$42$	−431.931	−1.58687
$43$	72.9317	0.258651	0.129325	−	0.991602i	$-0.458719\pi$
$43$	72.9317	0.258651	0.129325	+	0.991602i	$0.458719\pi$
$44$	42.9620	0.147199
$45$	−179.463	−0.594504
$46$	71.9214	0.230527
$47$	−167.830	−0.520861	−0.260430	−	0.965493i	$-0.583864\pi$
$47$	−167.830	−0.520861	−0.260430	+	0.965493i	$0.583864\pi$
$48$	130.769	0.393226
$49$	473.123	1.37937
$50$	−174.539	−0.493669
$51$	51.3382	0.140957
$52$	0	0
$53$	−25.3435	−0.0656829	−0.0328414	−	0.999461i	$-0.510456\pi$
$53$	−25.3435	−0.0656829	−0.0328414	+	0.999461i	$0.510456\pi$
$54$	−27.7054	−0.0698191
$55$	68.4676	0.167858
$56$	−688.214	−1.64226
$57$	−559.748	−1.30071
$58$	−481.737	−1.09061
$59$	−84.2856	−0.185984	−0.0929919	−	0.995667i	$-0.529643\pi$
$59$	−84.2856	−0.185984	−0.0929919	+	0.995667i	$0.529643\pi$
$60$	−181.647	−0.390842
$61$	−699.623	−1.46849	−0.734243	−	0.678887i	$-0.762463\pi$
$61$	−699.623	−1.46849	−0.734243	+	0.678887i	$0.762463\pi$
$62$	136.932	0.280491
$63$	823.681	1.64721
$64$	458.320	0.895157
$65$	0	0
$66$	166.314	0.310180
$67$	−24.3552	−0.0444098	−0.0222049	−	0.999753i	$-0.507069\pi$
$67$	−24.3552	−0.0444098	−0.0222049	+	0.999753i	$0.507069\pi$
$68$	26.8343	0.0478549
$69$	−265.588	−0.463377
$70$	−359.802	−0.614351
$71$	−917.389	−1.53344	−0.766719	−	0.641983i	$-0.778112\pi$
$71$	−917.389	−1.53344	−0.766719	+	0.641983i	$0.778112\pi$
$72$	−694.588	−1.13692
$73$	−651.592	−1.04470	−0.522350	−	0.852731i	$-0.674944\pi$
$73$	−651.592	−1.04470	−0.522350	+	0.852731i	$0.674944\pi$
$74$	330.492	0.519174
$75$	644.527	0.992315
$76$	−292.577	−0.441591
$77$	−314.247	−0.465087
$78$	0	0
$79$	709.665	1.01068	0.505339	−	0.862921i	$-0.331367\pi$
$79$	709.665	1.01068	0.505339	+	0.862921i	$0.331367\pi$
$80$	108.931	0.152236
$81$	−676.166	−0.927526
$82$	−1010.63	−1.36105
$83$	412.149	0.545051	0.272525	−	0.962149i	$-0.412141\pi$
$83$	412.149	0.545051	0.272525	+	0.962149i	$0.412141\pi$
$84$	833.706	1.08291
$85$	42.7652	0.0545710
$86$	147.574	0.185038
$87$	1778.93	2.19220
$88$	264.995	0.321007
$89$	−454.838	−0.541716	−0.270858	−	0.962619i	$-0.587307\pi$
$89$	−454.838	−0.541716	−0.270858	+	0.962619i	$0.587307\pi$
$90$	−363.134	−0.425308
$91$	0	0
$92$	−138.821	−0.157317
$93$	−505.657	−0.563808
$94$	−339.595	−0.372623
$95$	−466.274	−0.503566
$96$	−1175.45	−1.24968
$97$	1389.40	1.45435	0.727174	−	0.686453i	$-0.240833\pi$
$97$	1389.40	1.45435	0.727174	+	0.686453i	$0.240833\pi$
$98$	957.343	0.986798
$99$	−317.157	−0.321974
$100$	336.891	0.336891
$101$	−1182.45	−1.16493	−0.582464	−	0.812856i	$-0.697911\pi$
$101$	−1182.45	−1.16493	−0.582464	+	0.812856i	$0.697911\pi$
$102$	103.881	0.100840
$103$	1476.20	1.41218	0.706088	−	0.708124i	$-0.250458\pi$
$103$	1476.20	1.41218	0.706088	+	0.708124i	$0.250458\pi$
$104$	0	0
$105$	1328.66	1.23489
$106$	−51.2813	−0.0469895
$107$	911.165	0.823230	0.411615	−	0.911358i	$-0.364965\pi$
$107$	911.165	0.823230	0.411615	+	0.911358i	$0.364965\pi$
$108$	53.4766	0.0476462
$109$	−1451.55	−1.27553	−0.637765	−	0.770231i	$-0.720141\pi$
$109$	−1451.55	−1.27553	−0.637765	+	0.770231i	$0.720141\pi$
$110$	138.541	0.120085
$111$	−1220.42	−1.04358
$112$	−499.964	−0.421805
$113$	967.808	0.805697	0.402848	−	0.915267i	$-0.368020\pi$
$113$	967.808	0.805697	0.402848	+	0.915267i	$0.368020\pi$
$114$	−1132.62	−0.930525
$115$	−221.237	−0.179395
$116$	929.840	0.744254
$117$	0	0
$118$	−170.548	−0.133053
$119$	−196.280	−0.151201
$120$	−1120.42	−0.852334
$121$	121.000	0.0909091
$122$	−1415.66	−1.05055
$123$	3732.02	2.73581
$124$	−264.304	−0.191413
$125$	1314.94	0.940893
$126$	1666.68	1.17841
$127$	2752.08	1.92290	0.961449	−	0.274984i	$-0.0886726\pi$
$127$	2752.08	1.92290	0.961449	+	0.274984i	$0.0886726\pi$
$128$	−331.104	−0.228639
$129$	−544.954	−0.371942
$130$	0	0
$131$	1018.24	0.679113	0.339557	−	0.940586i	$-0.389723\pi$
$131$	1018.24	0.679113	0.339557	+	0.940586i	$0.389723\pi$
$132$	−321.017	−0.211674
$133$	2140.06	1.39524
$134$	−49.2816	−0.0317707
$135$	85.2245	0.0543330
$136$	165.517	0.104360
$137$	−1067.78	−0.665891	−0.332945	−	0.942946i	$-0.608042\pi$
$137$	−1067.78	−0.665891	−0.332945	+	0.942946i	$0.608042\pi$
$138$	−537.404	−0.331499
$139$	1830.63	1.11707	0.558534	−	0.829482i	$-0.311364\pi$
$139$	1830.63	1.11707	0.558534	+	0.829482i	$0.311364\pi$
$140$	694.484	0.419247
$141$	1254.04	0.749002
$142$	−1856.29	−1.09702
$143$	0	0
$144$	−504.594	−0.292010
$145$	1481.87	0.848705
$146$	−1318.47	−0.747377
$147$	−3535.23	−1.98354
$148$	−637.910	−0.354296
$149$	3177.27	1.74693	0.873464	−	0.486889i	$-0.161869\pi$
$149$	3177.27	1.74693	0.873464	+	0.486889i	$0.161869\pi$
$150$	1304.17	0.709901
$151$	−2853.15	−1.53766	−0.768829	−	0.639455i	$-0.779160\pi$
$151$	−2853.15	−1.53766	−0.768829	+	0.639455i	$0.779160\pi$
$152$	−1804.66	−0.963007
$153$	−198.098	−0.104675
$154$	−635.863	−0.332723
$155$	−421.216	−0.218277
$156$	0	0
$157$	−874.275	−0.444425	−0.222213	−	0.974998i	$-0.571328\pi$
$157$	−874.275	−0.444425	−0.222213	+	0.974998i	$0.571328\pi$
$158$	1435.97	0.723038
$159$	189.369	0.0944525
$160$	−979.160	−0.483809
$161$	1015.41	0.497054
$162$	−1368.19	−0.663551
$163$	2874.64	1.38135	0.690673	−	0.723167i	$-0.257315\pi$
$163$	2874.64	1.38135	0.690673	+	0.723167i	$0.257315\pi$
$164$	1950.71	0.928810
$165$	−511.597	−0.241381
$166$	833.964	0.389929
$167$	−754.795	−0.349747	−0.174874	−	0.984591i	$-0.555952\pi$
$167$	−754.795	−0.349747	−0.174874	+	0.984591i	$0.555952\pi$
$168$	5142.41	2.36158
$169$	0	0
$170$	86.5333	0.0390400
$171$	2159.88	0.965909
$172$	−284.845	−0.126275
$173$	1462.70	0.642814	0.321407	−	0.946941i	$-0.395844\pi$
$173$	1462.70	0.642814	0.321407	+	0.946941i	$0.395844\pi$
$174$	3599.59	1.56830
$175$	−2464.20	−1.06443
$176$	192.510	0.0824488
$177$	629.791	0.267446
$178$	−920.344	−0.387543
$179$	−2715.48	−1.13388	−0.566940	−	0.823759i	$-0.691873\pi$
$179$	−2715.48	−1.13388	−0.566940	+	0.823759i	$0.691873\pi$
$180$	700.915	0.290240
$181$	−267.773	−0.109964	−0.0549818	−	0.998487i	$-0.517510\pi$
$181$	−267.773	−0.109964	−0.0549818	+	0.998487i	$0.517510\pi$
$182$	0	0
$183$	5227.66	2.11169
$184$	−856.270	−0.343071
$185$	−1016.62	−0.404019
$186$	−1023.17	−0.403348
$187$	75.5771	0.0295548
$188$	655.481	0.254287
$189$	−391.156	−0.150542
$190$	−943.484	−0.360250
$191$	1515.51	0.574127	0.287063	−	0.957912i	$-0.407321\pi$
$191$	1515.51	0.574127	0.287063	+	0.957912i	$0.407321\pi$
$192$	−3424.62	−1.28724
$193$	−2958.19	−1.10329	−0.551645	−	0.834079i	$-0.686000\pi$
$193$	−2958.19	−1.10329	−0.551645	+	0.834079i	$0.686000\pi$
$194$	2811.38	1.04044
$195$	0	0
$196$	−1847.85	−0.673414
$197$	4174.44	1.50973	0.754865	−	0.655880i	$-0.227702\pi$
$197$	4174.44	1.50973	0.754865	+	0.655880i	$0.227702\pi$
$198$	−641.752	−0.230340
$199$	2786.30	0.992540	0.496270	−	0.868168i	$-0.334703\pi$
$199$	2786.30	0.992540	0.496270	+	0.868168i	$0.334703\pi$
$200$	2077.99	0.734681
$201$	181.985	0.0638617
$202$	−2392.62	−0.833388
$203$	−6801.34	−2.35153
$204$	−200.509	−0.0688157
$205$	3108.80	1.05916
$206$	2987.02	1.01027
$207$	1024.82	0.344105
$208$	0	0
$209$	−824.027	−0.272723
$210$	2688.48	0.883442
$211$	2408.66	0.785872	0.392936	−	0.919566i	$-0.371459\pi$
$211$	2408.66	0.785872	0.392936	+	0.919566i	$0.371459\pi$
$212$	98.9824	0.0320667
$213$	6854.83	2.20510
$214$	1843.70	0.588938
$215$	−453.951	−0.143996
$216$	329.851	0.103905
$217$	1933.26	0.604785
$218$	−2937.13	−0.912513
$219$	4868.77	1.50229
$220$	−267.410	−0.0819489
$221$	0	0
$222$	−2469.47	−0.746577
$223$	−729.590	−0.219089	−0.109545	−	0.993982i	$-0.534939\pi$
$223$	−729.590	−0.219089	−0.109545	+	0.993982i	$0.534939\pi$
$224$	4494.06	1.34050
$225$	−2487.02	−0.736895
$226$	1958.31	0.576395
$227$	1485.77	0.434424	0.217212	−	0.976125i	$-0.430304\pi$
$227$	1485.77	0.434424	0.217212	+	0.976125i	$0.430304\pi$
$228$	2186.17	0.635012
$229$	2686.75	0.775309	0.387654	−	0.921805i	$-0.373285\pi$
$229$	2686.75	0.775309	0.387654	+	0.921805i	$0.373285\pi$
$230$	−447.662	−0.128339
$231$	2348.09	0.668799
$232$	5735.38	1.62304
$233$	−857.503	−0.241102	−0.120551	−	0.992707i	$-0.538466\pi$
$233$	−857.503	−0.241102	−0.120551	+	0.992707i	$0.538466\pi$
$234$	0	0
$235$	1044.63	0.289974
$236$	329.189	0.0907982
$237$	−5302.70	−1.45336
$238$	−397.163	−0.108169
$239$	4980.70	1.34801	0.674005	−	0.738727i	$-0.264573\pi$
$239$	4980.70	1.34801	0.674005	+	0.738727i	$0.264573\pi$
$240$	−813.947	−0.218917
$241$	−5477.02	−1.46392	−0.731962	−	0.681345i	$-0.761395\pi$
$241$	−5477.02	−1.46392	−0.731962	+	0.681345i	$0.761395\pi$
$242$	244.838	0.0650363
$243$	5422.08	1.43138
$244$	2732.47	0.716921
$245$	−2944.87	−0.767923
$246$	7551.57	1.95720
$247$	0	0
$248$	−1630.27	−0.417427
$249$	−3079.62	−0.783788
$250$	2660.71	0.673113
$251$	1220.43	0.306903	0.153452	−	0.988156i	$-0.450961\pi$
$251$	1220.43	0.306903	0.153452	+	0.988156i	$0.450961\pi$
$252$	−3217.00	−0.804174
$253$	−390.983	−0.0971576
$254$	5568.71	1.37564
$255$	−319.546	−0.0784735
$256$	−4336.54	−1.05872
$257$	1597.75	0.387802	0.193901	−	0.981021i	$-0.437886\pi$
$257$	1597.75	0.387802	0.193901	+	0.981021i	$0.437886\pi$
$258$	−1102.69	−0.266087
$259$	4666.01	1.11943
$260$	0	0
$261$	−6864.32	−1.62793
$262$	2060.36	0.485837
$263$	−5306.40	−1.24413	−0.622066	−	0.782965i	$-0.713707\pi$
$263$	−5306.40	−1.24413	−0.622066	+	0.782965i	$0.713707\pi$
$264$	−1980.08	−0.461611
$265$	157.746	0.0365670
$266$	4330.32	0.998154
$267$	3398.60	0.778992
$268$	95.1225	0.0216811
$269$	−1870.34	−0.423929	−0.211964	−	0.977277i	$-0.567986\pi$
$269$	−1870.34	−0.423929	−0.211964	+	0.977277i	$0.567986\pi$
$270$	172.448	0.0388698
$271$	6939.99	1.55562	0.777812	−	0.628496i	$-0.216329\pi$
$271$	6939.99	1.55562	0.777812	+	0.628496i	$0.216329\pi$
$272$	120.243	0.0268043
$273$	0	0
$274$	−2160.61	−0.476377
$275$	948.835	0.208062
$276$	1037.29	0.226223
$277$	4458.79	0.967158	0.483579	−	0.875301i	$-0.339337\pi$
$277$	4458.79	0.967158	0.483579	+	0.875301i	$0.339337\pi$
$278$	3704.20	0.799149
$279$	1951.16	0.418685
$280$	4283.67	0.914280
$281$	606.369	0.128729	0.0643646	−	0.997926i	$-0.479498\pi$
$281$	606.369	0.128729	0.0643646	+	0.997926i	$0.479498\pi$
$282$	2537.49	0.535835
$283$	2925.95	0.614593	0.307296	−	0.951614i	$-0.400576\pi$
$283$	2925.95	0.614593	0.307296	+	0.951614i	$0.400576\pi$
$284$	3582.99	0.748631
$285$	3484.05	0.724131
$286$	0	0
$287$	−14268.5	−2.93465
$288$	4535.68	0.928012
$289$	−4865.79	−0.990392
$290$	2998.49	0.607163
$291$	−10381.7	−2.09137
$292$	2544.88	0.510027
$293$	−5376.06	−1.07192	−0.535961	−	0.844243i	$-0.680050\pi$
$293$	−5376.06	−1.07192	−0.535961	+	0.844243i	$0.680050\pi$
$294$	−7153.37	−1.41902
$295$	524.621	0.103541
$296$	−3934.71	−0.772637
$297$	150.614	0.0294259
$298$	6429.06	1.24975
$299$	0	0
$300$	−2517.29	−0.484453
$301$	2083.50	0.398974
$302$	−5773.22	−1.10004
$303$	8835.37	1.67518
$304$	−1311.02	−0.247343
$305$	4354.69	0.817536
$306$	−400.841	−0.0748842
$307$	8365.85	1.55526	0.777629	−	0.628724i	$-0.216422\pi$
$307$	8365.85	1.55526	0.777629	+	0.628724i	$0.216422\pi$
$308$	1227.33	0.227058
$309$	−11030.3	−2.03072
$310$	−852.311	−0.156155
$311$	−6559.08	−1.19592	−0.597960	−	0.801526i	$-0.704022\pi$
$311$	−6559.08	−1.19592	−0.597960	+	0.801526i	$0.704022\pi$
$312$	0	0
$313$	−2492.21	−0.450058	−0.225029	−	0.974352i	$-0.572248\pi$
$313$	−2492.21	−0.450058	−0.225029	+	0.974352i	$0.572248\pi$
$314$	−1769.06	−0.317941
$315$	−5126.86	−0.917035
$316$	−2771.69	−0.493418
$317$	11108.0	1.96809	0.984045	−	0.177919i	$-0.0569364\pi$
$317$	11108.0	1.96809	0.984045	+	0.177919i	$0.0569364\pi$
$318$	383.180	0.0675712
$319$	2618.84	0.459646
$320$	−2852.74	−0.498352
$321$	−6808.32	−1.18381
$322$	2054.64	0.355592
$323$	−514.691	−0.0886631
$324$	2640.86	0.452822
$325$	0	0
$326$	5816.70	0.988213
$327$	10846.1	1.83422
$328$	12032.2	2.02552
$329$	−4794.53	−0.803438
$330$	−1035.19	−0.172683
$331$	4184.82	0.694919	0.347460	−	0.937695i	$-0.387044\pi$
$331$	4184.82	0.694919	0.347460	+	0.937695i	$0.387044\pi$
$332$	−1609.70	−0.266096
$333$	4709.22	0.774966
$334$	−1527.29	−0.250209
$335$	151.595	0.0247239
$336$	3735.78	0.606559
$337$	577.319	0.0933192	0.0466596	−	0.998911i	$-0.485142\pi$
$337$	577.319	0.0933192	0.0466596	+	0.998911i	$0.485142\pi$
$338$	0	0
$339$	−7231.57	−1.15860
$340$	−167.025	−0.0266418
$341$	−744.398	−0.118215
$342$	4370.42	0.691010
$343$	3717.34	0.585183
$344$	−1756.96	−0.275375
$345$	1653.11	0.257972
$346$	2959.70	0.459868
$347$	1640.43	0.253784	0.126892	−	0.991917i	$-0.459500\pi$
$347$	1640.43	0.253784	0.126892	+	0.991917i	$0.459500\pi$
$348$	−6947.87	−1.07024
$349$	422.988	0.0648769	0.0324385	−	0.999474i	$-0.489673\pi$
$349$	422.988	0.0648769	0.0324385	+	0.999474i	$0.489673\pi$
$350$	−4986.19	−0.761495
$351$	0	0
$352$	−1730.43	−0.262023
$353$	6958.28	1.04916	0.524578	−	0.851363i	$-0.324223\pi$
$353$	6958.28	1.04916	0.524578	+	0.851363i	$0.324223\pi$
$354$	1274.35	0.191331
$355$	5710.13	0.853696
$356$	1776.43	0.264468
$357$	1466.62	0.217429
$358$	−5494.65	−0.811177
$359$	−2567.96	−0.377526	−0.188763	−	0.982023i	$-0.560448\pi$
$359$	−2567.96	−0.377526	−0.188763	+	0.982023i	$0.560448\pi$
$360$	4323.34	0.632945
$361$	−1247.25	−0.181842
$362$	−541.826	−0.0786678
$363$	−904.125	−0.130728
$364$	0	0
$365$	4055.72	0.581606
$366$	10577.9	1.51070
$367$	−7566.35	−1.07619	−0.538093	−	0.842885i	$-0.680855\pi$
$367$	−7566.35	−1.07619	−0.538093	+	0.842885i	$0.680855\pi$
$368$	−622.050	−0.0881158
$369$	−14400.6	−2.03162
$370$	−2057.09	−0.289035
$371$	−724.009	−0.101317
$372$	1974.91	0.275254
$373$	11896.4	1.65140	0.825699	−	0.564111i	$-0.190781\pi$
$373$	11896.4	1.65140	0.825699	+	0.564111i	$0.190781\pi$
$374$	152.927	0.0211435
$375$	−9825.36	−1.35301
$376$	4043.10	0.554539
$377$	0	0
$378$	−791.485	−0.107697
$379$	−2575.83	−0.349106	−0.174553	−	0.984648i	$-0.555848\pi$
$379$	−2575.83	−0.349106	−0.174553	+	0.984648i	$0.555848\pi$
$380$	1821.10	0.245843
$381$	−20563.9	−2.76514
$382$	3066.56	0.410730
$383$	−9211.61	−1.22896	−0.614479	−	0.788933i	$-0.710634\pi$
$383$	−9211.61	−1.22896	−0.614479	+	0.788933i	$0.710634\pi$
$384$	2474.05	0.328785
$385$	1955.97	0.258924
$386$	−5985.76	−0.789293
$387$	2102.80	0.276205
$388$	−5426.48	−0.710020
$389$	−13789.8	−1.79736	−0.898679	−	0.438606i	$-0.855472\pi$
$389$	−13789.8	−1.79736	−0.898679	+	0.438606i	$0.855472\pi$
$390$	0	0
$391$	−244.210	−0.0315862
$392$	−11397.8	−1.46856
$393$	−7608.39	−0.976571
$394$	8446.79	1.08006
$395$	−4417.19	−0.562666
$396$	1238.70	0.157189
$397$	−12713.6	−1.60725	−0.803626	−	0.595134i	$-0.797099\pi$
$397$	−12713.6	−1.60725	−0.803626	+	0.595134i	$0.797099\pi$
$398$	5637.94	0.710062
$399$	−15990.8	−2.00637
$400$	1509.59	0.188699
$401$	−10825.0	−1.34807	−0.674034	−	0.738701i	$-0.735440\pi$
$401$	−10825.0	−1.34807	−0.674034	+	0.738701i	$0.735440\pi$
$402$	368.237	0.0456866
$403$	0	0
$404$	4618.21	0.568723
$405$	4208.68	0.516373
$406$	−13762.2	−1.68228
$407$	−1796.64	−0.218811
$408$	−1236.76	−0.150071
$409$	11550.0	1.39636	0.698178	−	0.715924i	$-0.253994\pi$
$409$	11550.0	1.39636	0.698178	+	0.715924i	$0.253994\pi$
$410$	6290.51	0.757723
$411$	7978.61	0.957556
$412$	−5765.49	−0.689431
$413$	−2407.86	−0.286884
$414$	2073.67	0.246172
$415$	−2565.35	−0.303441
$416$	0	0
$417$	−13678.7	−1.60635
$418$	−1667.38	−0.195106
$419$	2943.28	0.343171	0.171586	−	0.985169i	$-0.445111\pi$
$419$	2943.28	0.343171	0.171586	+	0.985169i	$0.445111\pi$
$420$	−5189.26	−0.602881
$421$	13675.1	1.58310	0.791549	−	0.611106i	$-0.209275\pi$
$421$	13675.1	1.58310	0.791549	+	0.611106i	$0.209275\pi$
$422$	4873.81	0.562212
$423$	−4838.93	−0.556210
$424$	610.537	0.0699299
$425$	592.647	0.0676414
$426$	13870.4	1.57752
$427$	−19986.8	−2.26517
$428$	−3558.68	−0.401905
$429$	0	0
$430$	−918.549	−0.103015
$431$	13778.2	1.53984	0.769921	−	0.638139i	$-0.220295\pi$
$431$	13778.2	1.53984	0.769921	+	0.638139i	$0.220295\pi$
$432$	239.625	0.0266874
$433$	4870.36	0.540541	0.270271	−	0.962784i	$-0.412887\pi$
$433$	4870.36	0.540541	0.270271	+	0.962784i	$0.412887\pi$
$434$	3911.86	0.432662
$435$	−11072.7	−1.22045
$436$	5669.21	0.622720
$437$	2662.65	0.291469
$438$	9851.72	1.07473
$439$	13242.5	1.43970	0.719852	−	0.694128i	$-0.244210\pi$
$439$	13242.5	1.43970	0.719852	+	0.694128i	$0.244210\pi$
$440$	−1649.42	−0.178711
$441$	13641.3	1.47298
$442$	0	0
$443$	16788.6	1.80057	0.900285	−	0.435302i	$-0.143358\pi$
$443$	16788.6	1.80057	0.900285	+	0.435302i	$0.143358\pi$
$444$	4766.53	0.509481
$445$	2831.06	0.301585
$446$	−1476.29	−0.156736
$447$	−23740.9	−2.51210
$448$	13093.2	1.38080
$449$	−9873.11	−1.03773	−0.518865	−	0.854856i	$-0.673645\pi$
$449$	−9873.11	−1.03773	−0.518865	+	0.854856i	$0.673645\pi$
$450$	−5032.37	−0.527174
$451$	5494.06	0.573625
$452$	−3779.91	−0.393345
$453$	21319.1	2.21116
$454$	3006.39	0.310786
$455$	0	0
$456$	13484.6	1.38481
$457$	7415.00	0.758992	0.379496	−	0.925193i	$-0.376097\pi$
$457$	7415.00	0.758992	0.379496	+	0.925193i	$0.376097\pi$
$458$	5436.52	0.554655
$459$	94.0740	0.00956644
$460$	864.070	0.0875815
$461$	−16622.4	−1.67935	−0.839675	−	0.543089i	$-0.817255\pi$
$461$	−16622.4	−1.67935	−0.839675	+	0.543089i	$0.817255\pi$
$462$	4751.24	0.478458
$463$	−6476.10	−0.650043	−0.325021	−	0.945707i	$-0.605371\pi$
$463$	−6476.10	−0.650043	−0.325021	+	0.945707i	$0.605371\pi$
$464$	4166.55	0.416869
$465$	3147.37	0.313884
$466$	−1735.12	−0.172484
$467$	2811.15	0.278554	0.139277	−	0.990253i	$-0.455522\pi$
$467$	2811.15	0.278554	0.139277	+	0.990253i	$0.455522\pi$
$468$	0	0
$469$	−695.776	−0.0685031
$470$	2113.75	0.207447
$471$	6532.68	0.639087
$472$	2030.48	0.198010
$473$	−802.249	−0.0779862
$474$	−10729.8	−1.03973
$475$	−6461.70	−0.624175
$476$	766.598	0.0738171
$477$	−730.714	−0.0701407
$478$	10078.2	0.964365
$479$	3252.28	0.310231	0.155116	−	0.987896i	$-0.450425\pi$
$479$	3252.28	0.310231	0.155116	+	0.987896i	$0.450425\pi$
$480$	7316.39	0.695721
$481$	0	0
$482$	−11082.5	−1.04729
$483$	−7587.28	−0.714768
$484$	−472.582	−0.0443822
$485$	−8648.06	−0.809666
$486$	10971.3	1.02401
$487$	9852.25	0.916731	0.458365	−	0.888764i	$-0.348435\pi$
$487$	9852.25	0.916731	0.458365	+	0.888764i	$0.348435\pi$
$488$	16854.3	1.56344
$489$	−21479.6	−1.98639
$490$	−5958.82	−0.549371
$491$	−3244.81	−0.298241	−0.149120	−	0.988819i	$-0.547644\pi$
$491$	−3244.81	−0.298241	−0.149120	+	0.988819i	$0.547644\pi$
$492$	−14575.9	−1.33564
$493$	1635.74	0.149432
$494$	0	0
$495$	1974.09	0.179250
$496$	−1184.33	−0.107214
$497$	−26207.9	−2.36536
$498$	−6231.47	−0.560721
$499$	−3484.45	−0.312596	−0.156298	−	0.987710i	$-0.549956\pi$
$499$	−3484.45	−0.312596	−0.156298	+	0.987710i	$0.549956\pi$
$500$	−5135.67	−0.459348
$501$	5639.91	0.502940
$502$	2469.48	0.219558
$503$	20404.4	1.80872	0.904360	−	0.426771i	$-0.140349\pi$
$503$	20404.4	1.80872	0.904360	+	0.426771i	$0.140349\pi$
$504$	−19842.9	−1.75372
$505$	7359.93	0.648540
$506$	−791.135	−0.0695064
$507$	0	0
$508$	−10748.6	−0.938767
$509$	4551.87	0.396381	0.198191	−	0.980164i	$-0.436494\pi$
$509$	4551.87	0.396381	0.198191	+	0.980164i	$0.436494\pi$
$510$	−646.587	−0.0561399
$511$	−18614.6	−1.61147
$512$	−6125.94	−0.528771
$513$	−1025.70	−0.0882764
$514$	3232.98	0.277433
$515$	−9188.34	−0.786188
$516$	2128.39	0.181584
$517$	1846.12	0.157045
$518$	9441.45	0.800836
$519$	−10929.4	−0.924371
$520$	0	0
$521$	10772.2	0.905834	0.452917	−	0.891553i	$-0.350383\pi$
$521$	10772.2	0.905834	0.452917	+	0.891553i	$0.350383\pi$
$522$	−13889.6	−1.16462
$523$	−12805.4	−1.07063	−0.535316	−	0.844652i	$-0.679808\pi$
$523$	−12805.4	−1.07063	−0.535316	+	0.844652i	$0.679808\pi$
$524$	−3976.87	−0.331546
$525$	18412.8	1.53067
$526$	−10737.3	−0.890051
$527$	−464.954	−0.0384321
$528$	−1438.46	−0.118562
$529$	−10903.6	−0.896164
$530$	319.192	0.0261600
$531$	−2430.16	−0.198606
$532$	−8358.31	−0.681163
$533$	0	0
$534$	6876.91	0.557290
$535$	−5671.39	−0.458309
$536$	586.729	0.0472814
$537$	20290.4	1.63053
$538$	−3784.55	−0.303278
$539$	−5204.36	−0.415895
$540$	−332.856	−0.0265256
$541$	17.6173	0.00140005	0.000700025	−	1.00000i	$-0.499777\pi$
$541$	17.6173	0.00140005	0.000700025		1.00000i	$0.499777\pi$
$542$	14042.7	1.11289
$543$	2000.83	0.158128
$544$	−1080.83	−0.0851845
$545$	9034.90	0.710115
$546$	0	0
$547$	23349.6	1.82515	0.912573	−	0.408914i	$-0.134092\pi$
$547$	23349.6	1.82515	0.912573	+	0.408914i	$0.134092\pi$
$548$	4170.38	0.325091
$549$	−20171.8	−1.56815
$550$	1919.92	0.148847
$551$	−17834.7	−1.37892
$552$	6398.14	0.493339
$553$	20273.6	1.55899
$554$	9022.15	0.691904
$555$	7596.32	0.580983
$556$	−7149.79	−0.545358
$557$	−8339.26	−0.634373	−0.317187	−	0.948363i	$-0.602738\pi$
$557$	−8339.26	−0.634373	−0.317187	+	0.948363i	$0.602738\pi$
$558$	3948.09	0.299527
$559$	0	0
$560$	3111.94	0.234827
$561$	−564.721	−0.0425001
$562$	1226.96	0.0920928
$563$	−5935.50	−0.444319	−0.222159	−	0.975010i	$-0.571311\pi$
$563$	−5935.50	−0.444319	−0.222159	+	0.975010i	$0.571311\pi$
$564$	−4897.83	−0.365666
$565$	−6023.96	−0.448548
$566$	5920.52	0.439679
$567$	−19316.6	−1.43073
$568$	22100.4	1.63259
$569$	−4011.59	−0.295562	−0.147781	−	0.989020i	$-0.547213\pi$
$569$	−4011.59	−0.295562	−0.147781	+	0.989020i	$0.547213\pi$
$570$	7049.82	0.518043
$571$	−16401.5	−1.20207	−0.601034	−	0.799224i	$-0.705244\pi$
$571$	−16401.5	−1.20207	−0.601034	+	0.799224i	$0.705244\pi$
$572$	0	0
$573$	−11324.0	−0.825599
$574$	−28871.7	−2.09944
$575$	−3065.93	−0.222362
$576$	13214.5	0.955909
$577$	−2795.55	−0.201699	−0.100849	−	0.994902i	$-0.532156\pi$
$577$	−2795.55	−0.201699	−0.100849	+	0.994902i	$0.532156\pi$
$578$	−9845.71	−0.708525
$579$	22103.9	1.58654
$580$	−5787.63	−0.414342
$581$	11774.2	0.840752
$582$	−21006.9	−1.49616
$583$	278.778	0.0198041
$584$	15697.2	1.11225
$585$	0	0
$586$	−10878.2	−0.766851
$587$	6231.90	0.438191	0.219096	−	0.975703i	$-0.429689\pi$
$587$	6231.90	0.438191	0.219096	+	0.975703i	$0.429689\pi$
$588$	13807.3	0.968375
$589$	5069.46	0.354641
$590$	1061.55	0.0740732
$591$	−31191.9	−2.17100
$592$	−2858.43	−0.198447
$593$	9911.55	0.686372	0.343186	−	0.939267i	$-0.388494\pi$
$593$	9911.55	0.686372	0.343186	+	0.939267i	$0.388494\pi$
$594$	304.760	0.0210513
$595$	1221.71	0.0841768
$596$	−12409.3	−0.852858
$597$	−20819.5	−1.42728
$598$	0	0
$599$	3960.39	0.270146	0.135073	−	0.990836i	$-0.456873\pi$
$599$	3960.39	0.270146	0.135073	+	0.990836i	$0.456873\pi$
$600$	−15527.0	−1.05648
$601$	9871.10	0.669968	0.334984	−	0.942224i	$-0.391269\pi$
$601$	9871.10	0.669968	0.334984	+	0.942224i	$0.391269\pi$
$602$	4215.87	0.285426
$603$	−702.219	−0.0474238
$604$	11143.4	0.750691
$605$	−753.144	−0.0506110
$606$	17878.0	1.19842
$607$	−21222.1	−1.41908	−0.709539	−	0.704666i	$-0.751097\pi$
$607$	−21222.1	−1.41908	−0.709539	+	0.704666i	$0.751097\pi$
$608$	11784.5	0.786058
$609$	50820.3	3.38152
$610$	8811.50	0.584864
$611$	0	0
$612$	773.697	0.0511027
$613$	−8526.41	−0.561792	−0.280896	−	0.959738i	$-0.590632\pi$
$613$	−8526.41	−0.561792	−0.280896	+	0.959738i	$0.590632\pi$
$614$	16927.9	1.11263
$615$	−23229.3	−1.52308
$616$	7570.36	0.495160
$617$	10705.4	0.698511	0.349256	−	0.937027i	$-0.386434\pi$
$617$	10705.4	0.698511	0.349256	+	0.937027i	$0.386434\pi$
$618$	−22319.3	−1.45277
$619$	16469.2	1.06939	0.534697	−	0.845044i	$-0.320426\pi$
$619$	16469.2	1.06939	0.534697	+	0.845044i	$0.320426\pi$
$620$	1645.12	0.106564
$621$	−486.672	−0.0314484
$622$	−13272.0	−0.855560
$623$	−12993.8	−0.835608
$624$	0	0
$625$	2597.62	0.166247
$626$	−5042.88	−0.321971
$627$	6157.22	0.392178
$628$	3414.60	0.216971
$629$	−1122.19	−0.0711360
$630$	−10374.0	−0.656046
$631$	6369.05	0.401819	0.200910	−	0.979610i	$-0.435610\pi$
$631$	6369.05	0.401819	0.200910	+	0.979610i	$0.435610\pi$
$632$	−17096.2	−1.07603
$633$	−17997.8	−1.13009
$634$	22476.4	1.40797
$635$	−17129.9	−1.07052
$636$	−739.607	−0.0461122
$637$	0	0
$638$	5299.10	0.328830
$639$	−26450.6	−1.63751
$640$	2060.90	0.127288
$641$	7227.54	0.445352	0.222676	−	0.974892i	$-0.428521\pi$
$641$	7227.54	0.445352	0.222676	+	0.974892i	$0.428521\pi$
$642$	−13776.3	−0.846897
$643$	−15746.8	−0.965773	−0.482886	−	0.875683i	$-0.660412\pi$
$643$	−15746.8	−0.965773	−0.482886	+	0.875683i	$0.660412\pi$
$644$	−3965.83	−0.242664
$645$	3391.97	0.207068
$646$	−1041.45	−0.0634295
$647$	21246.4	1.29101	0.645505	−	0.763756i	$-0.276647\pi$
$647$	21246.4	1.29101	0.645505	+	0.763756i	$0.276647\pi$
$648$	16289.2	0.987500
$649$	927.142	0.0560763
$650$	0	0
$651$	−14445.5	−0.869686
$652$	−11227.3	−0.674379
$653$	13567.9	0.813099	0.406550	−	0.913629i	$-0.366732\pi$
$653$	13567.9	0.813099	0.406550	+	0.913629i	$0.366732\pi$
$654$	21946.6	1.31220
$655$	−6337.85	−0.378077
$656$	8741.00	0.520242
$657$	−18787.0	−1.11560
$658$	−9701.51	−0.574779
$659$	−23554.7	−1.39236	−0.696178	−	0.717869i	$-0.745117\pi$
$659$	−23554.7	−1.39236	−0.696178	+	0.717869i	$0.745117\pi$
$660$	1998.11	0.117843
$661$	−4896.06	−0.288101	−0.144050	−	0.989570i	$-0.546013\pi$
$661$	−4896.06	−0.288101	−0.144050	+	0.989570i	$0.546013\pi$
$662$	8467.78	0.497144
$663$	0	0
$664$	−9928.87	−0.580294
$665$	−13320.5	−0.776760
$666$	9528.88	0.554409
$667$	−8462.16	−0.491239
$668$	2947.96	0.170748
$669$	5451.57	0.315052
$670$	306.745	0.0176874
$671$	7695.86	0.442765
$672$	−33580.1	−1.92765
$673$	−4833.14	−0.276826	−0.138413	−	0.990375i	$-0.544200\pi$
$673$	−4833.14	−0.276826	−0.138413	+	0.990375i	$0.544200\pi$
$674$	1168.18	0.0667604
$675$	1181.05	0.0673464
$676$	0	0
$677$	12643.5	0.717769	0.358885	−	0.933382i	$-0.383157\pi$
$677$	12643.5	0.717769	0.358885	+	0.933382i	$0.383157\pi$
$678$	−14632.7	−0.828860
$679$	39692.1	2.24336
$680$	−1030.23	−0.0580995
$681$	−11101.9	−0.624705
$682$	−1506.25	−0.0845711
$683$	−3424.73	−0.191865	−0.0959324	−	0.995388i	$-0.530583\pi$
$683$	−3424.73	−0.191865	−0.0959324	+	0.995388i	$0.530583\pi$
$684$	−8435.72	−0.471561
$685$	6646.24	0.370715
$686$	7521.87	0.418639
$687$	−20075.7	−1.11490
$688$	−1276.37	−0.0707285
$689$	0	0
$690$	3344.98	0.184553
$691$	23910.3	1.31634	0.658171	−	0.752869i	$-0.271330\pi$
$691$	23910.3	1.31634	0.658171	+	0.752869i	$0.271330\pi$
$692$	−5712.76	−0.313825
$693$	−9060.49	−0.496652
$694$	3319.34	0.181557
$695$	−11394.5	−0.621895
$696$	−42855.4	−2.33395
$697$	3431.61	0.186487
$698$	855.897	0.0464129
$699$	6407.36	0.346707
$700$	9624.27	0.519662
$701$	−17651.3	−0.951041	−0.475521	−	0.879705i	$-0.657740\pi$
$701$	−17651.3	−0.951041	−0.475521	+	0.879705i	$0.657740\pi$
$702$	0	0
$703$	12235.4	0.656422
$704$	−5041.52	−0.269900
$705$	−7805.56	−0.416985
$706$	14079.8	0.750564
$707$	−33780.0	−1.79693
$708$	−2459.74	−0.130569
$709$	31971.3	1.69352	0.846762	−	0.531972i	$-0.178549\pi$
$709$	31971.3	1.69352	0.846762	+	0.531972i	$0.178549\pi$
$710$	11554.2	0.610733
$711$	20461.4	1.07927
$712$	10957.3	0.576743
$713$	2405.35	0.126341
$714$	2967.65	0.155548
$715$	0	0
$716$	10605.7	0.553566
$717$	−37216.3	−1.93845
$718$	−5196.15	−0.270082
$719$	−16995.5	−0.881535	−0.440768	−	0.897621i	$-0.645294\pi$
$719$	−16995.5	−0.881535	−0.440768	+	0.897621i	$0.645294\pi$
$720$	3140.76	0.162568
$721$	42171.8	2.17831
$722$	−2523.76	−0.130090
$723$	40924.9	2.10514
$724$	1045.82	0.0536847
$725$	20535.9	1.05198
$726$	−1829.46	−0.0935227
$727$	12210.5	0.622918	0.311459	−	0.950260i	$-0.399182\pi$
$727$	12210.5	0.622918	0.311459	+	0.950260i	$0.399182\pi$
$728$	0	0
$729$	−22257.9	−1.13082
$730$	8206.56	0.416080
$731$	−501.088	−0.0253535
$732$	−20417.4	−1.03094
$733$	19072.5	0.961060	0.480530	−	0.876978i	$-0.340444\pi$
$733$	19072.5	0.961060	0.480530	+	0.876978i	$0.340444\pi$
$734$	−15310.2	−0.769902
$735$	22004.4	1.10428
$736$	5591.47	0.280033
$737$	267.907	0.0133901
$738$	−29139.0	−1.45342
$739$	−16439.4	−0.818314	−0.409157	−	0.912464i	$-0.634177\pi$
$739$	−16439.4	−0.818314	−0.409157	+	0.912464i	$0.634177\pi$
$740$	3970.56	0.197244
$741$	0	0
$742$	−1465.00	−0.0724822
$743$	20182.0	0.996507	0.498254	−	0.867031i	$-0.333975\pi$
$743$	20182.0	0.996507	0.498254	+	0.867031i	$0.333975\pi$
$744$	12181.5	0.600264
$745$	−19776.4	−0.972551
$746$	24071.8	1.18141
$747$	11883.3	0.582042
$748$	−295.177	−0.0144288
$749$	26030.0	1.26985
$750$	−19881.2	−0.967943
$751$	−22540.7	−1.09523	−0.547617	−	0.836729i	$-0.684465\pi$
$751$	−22540.7	−1.09523	−0.547617	+	0.836729i	$0.684465\pi$
$752$	2937.17	0.142430
$753$	−9119.17	−0.441330
$754$	0	0
$755$	17759.0	0.856046
$756$	1527.71	0.0734952
$757$	12276.4	0.589425	0.294712	−	0.955586i	$-0.404776\pi$
$757$	12276.4	0.589425	0.294712	+	0.955586i	$0.404776\pi$
$758$	−5212.07	−0.249750
$759$	2921.47	0.139713
$760$	11232.8	0.536126
$761$	10301.3	0.490700	0.245350	−	0.969435i	$-0.421097\pi$
$761$	10301.3	0.490700	0.245350	+	0.969435i	$0.421097\pi$
$762$	−41610.0	−1.97818
$763$	−41467.6	−1.96753
$764$	−5919.02	−0.280291
$765$	1233.02	0.0582746
$766$	−18639.3	−0.879196
$767$	0	0
$768$	32403.1	1.52245
$769$	−26926.5	−1.26267	−0.631337	−	0.775509i	$-0.717493\pi$
$769$	−26926.5	−1.26267	−0.631337	+	0.775509i	$0.717493\pi$
$770$	3957.82	0.185234
$771$	−11938.6	−0.557662
$772$	11553.6	0.538632
$773$	38711.5	1.80124	0.900619	−	0.434609i	$-0.143113\pi$
$773$	38711.5	1.80124	0.900619	+	0.434609i	$0.143113\pi$
$774$	4254.92	0.197597
$775$	−5837.28	−0.270557
$776$	−33471.3	−1.54839
$777$	−34864.9	−1.60974
$778$	−27903.1	−1.28583
$779$	−37415.3	−1.72085
$780$	0	0
$781$	10091.3	0.462349
$782$	−494.147	−0.0225967
$783$	3259.78	0.148780
$784$	−8280.09	−0.377190
$785$	5441.78	0.247421
$786$	−15395.2	−0.698638
$787$	−13899.6	−0.629564	−0.314782	−	0.949164i	$-0.601931\pi$
$787$	−13899.6	−0.629564	−0.314782	+	0.949164i	$0.601931\pi$
$788$	−16303.9	−0.737057
$789$	39650.0	1.78907
$790$	−8937.98	−0.402530
$791$	27648.2	1.24280
$792$	7640.47	0.342793
$793$	0	0
$794$	−25725.4	−1.14983
$795$	−1178.70	−0.0525837
$796$	−10882.3	−0.484562
$797$	32389.2	1.43950	0.719752	−	0.694231i	$-0.244256\pi$
$797$	32389.2	1.43950	0.719752	+	0.694231i	$0.244256\pi$
$798$	−32356.6	−1.43535
$799$	1153.10	0.0510559
$800$	−13569.4	−0.599686
$801$	−13114.1	−0.578481
$802$	−21903.9	−0.964406
$803$	7167.51	0.314989
$804$	−710.766	−0.0311776
$805$	−6320.26	−0.276720
$806$	0	0
$807$	13975.4	0.609613
$808$	28485.7	1.24025
$809$	−27518.4	−1.19592	−0.597958	−	0.801527i	$-0.704021\pi$
$809$	−27518.4	−1.19592	−0.597958	+	0.801527i	$0.704021\pi$
$810$	8516.07	0.369413
$811$	34869.9	1.50980	0.754901	−	0.655839i	$-0.227685\pi$
$811$	34869.9	1.50980	0.754901	+	0.655839i	$0.227685\pi$
$812$	26563.6	1.14803
$813$	−51856.4	−2.23700
$814$	−3635.41	−0.156537
$815$	−17892.7	−0.769024
$816$	−898.466	−0.0385448
$817$	5463.43	0.233955
$818$	23370.8	0.998951
$819$	0	0
$820$	−12141.9	−0.517088
$821$	43853.7	1.86420	0.932098	−	0.362206i	$-0.117976\pi$
$821$	43853.7	1.86420	0.932098	+	0.362206i	$0.117976\pi$
$822$	16144.3	0.685034
$823$	19592.4	0.829826	0.414913	−	0.909861i	$-0.363812\pi$
$823$	19592.4	0.829826	0.414913	+	0.909861i	$0.363812\pi$
$824$	−35562.3	−1.50349
$825$	−7089.80	−0.299194
$826$	−4872.19	−0.205236
$827$	15922.0	0.669481	0.334741	−	0.942310i	$-0.391351\pi$
$827$	15922.0	0.669481	0.334741	+	0.942310i	$0.391351\pi$
$828$	−4002.56	−0.167994
$829$	−1603.28	−0.0671704	−0.0335852	−	0.999436i	$-0.510693\pi$
$829$	−1603.28	−0.0671704	−0.0335852	+	0.999436i	$0.510693\pi$
$830$	−5190.87	−0.217081
$831$	−33316.6	−1.39078
$832$	0	0
$833$	−3250.66	−0.135209
$834$	−27678.2	−1.14918
$835$	4698.09	0.194712
$836$	3218.35	0.133145
$837$	−926.583	−0.0382645
$838$	5955.59	0.245504
$839$	9245.15	0.380427	0.190213	−	0.981743i	$-0.439082\pi$
$839$	9245.15	0.380427	0.190213	+	0.981743i	$0.439082\pi$
$840$	−32008.1	−1.31474
$841$	32291.4	1.32401
$842$	27670.9	1.13255
$843$	−4530.85	−0.185114
$844$	−9407.35	−0.383666
$845$	0	0
$846$	−9791.36	−0.397912
$847$	3456.71	0.140229
$848$	443.534	0.0179611
$849$	−21863.0	−0.883789
$850$	1199.19	0.0483906
$851$	5805.40	0.233850
$852$	−26772.5	−1.07654
$853$	10500.9	0.421505	0.210752	−	0.977540i	$-0.432409\pi$
$853$	10500.9	0.421505	0.210752	+	0.977540i	$0.432409\pi$
$854$	−40442.3	−1.62050
$855$	−13443.8	−0.537742
$856$	−21950.4	−0.876460
$857$	4493.39	0.179103	0.0895515	−	0.995982i	$-0.471457\pi$
$857$	4493.39	0.179103	0.0895515	+	0.995982i	$0.471457\pi$
$858$	0	0
$859$	−7099.08	−0.281976	−0.140988	−	0.990011i	$-0.545028\pi$
$859$	−7099.08	−0.281976	−0.140988	+	0.990011i	$0.545028\pi$
$860$	1772.97	0.0702997
$861$	106616.	4.22004
$862$	27879.5	1.10160
$863$	4803.24	0.189460	0.0947301	−	0.995503i	$-0.469801\pi$
$863$	4803.24	0.189460	0.0947301	+	0.995503i	$0.469801\pi$
$864$	−2153.94	−0.0848130
$865$	−9104.30	−0.357868
$866$	9854.94	0.386703
$867$	36357.8	1.42419
$868$	−7550.62	−0.295259
$869$	−7806.32	−0.304731
$870$	−22405.0	−0.873105
$871$	0	0
$872$	34968.5	1.35801
$873$	40059.7	1.55305
$874$	5387.74	0.208516
$875$	37565.0	1.45135
$876$	−19015.6	−0.733423
$877$	−35671.6	−1.37348	−0.686742	−	0.726901i	$-0.740960\pi$
$877$	−35671.6	−1.37348	−0.686742	+	0.726901i	$0.740960\pi$
$878$	26795.6	1.02996
$879$	40170.5	1.54143
$880$	−1198.25	−0.0459009
$881$	19997.8	0.764746	0.382373	−	0.924008i	$-0.375107\pi$
$881$	19997.8	0.764746	0.382373	+	0.924008i	$0.375107\pi$
$882$	27602.5	1.05377
$883$	38256.3	1.45802	0.729008	−	0.684505i	$-0.239982\pi$
$883$	38256.3	1.45802	0.729008	+	0.684505i	$0.239982\pi$
$884$	0	0
$885$	−3920.03	−0.148893
$886$	33971.0	1.28812
$887$	−14546.0	−0.550627	−0.275314	−	0.961354i	$-0.588782\pi$
$887$	−14546.0	−0.550627	−0.275314	+	0.961354i	$0.588782\pi$
$888$	29400.6	1.11106
$889$	78621.2	2.96611
$890$	5728.52	0.215753
$891$	7437.83	0.279660
$892$	2849.51	0.106960
$893$	−12572.4	−0.471129
$894$	−48038.6	−1.79715
$895$	16902.0	0.631255
$896$	−9458.95	−0.352680
$897$	0	0
$898$	−19977.8	−0.742391
$899$	−16111.2	−0.597709
$900$	9713.40	0.359756
$901$	174.126	0.00643838
$902$	11117.0	0.410371
$903$	−15568.2	−0.573728
$904$	−23315.0	−0.857793
$905$	1666.71	0.0612190
$906$	43138.1	1.58186
$907$	−1993.62	−0.0729845	−0.0364922	−	0.999334i	$-0.511618\pi$
$907$	−1993.62	−0.0729845	−0.0364922	+	0.999334i	$0.511618\pi$
$908$	−5802.89	−0.212088
$909$	−34092.8	−1.24399
$910$	0	0
$911$	45291.6	1.64718	0.823589	−	0.567188i	$-0.191969\pi$
$911$	45291.6	1.64718	0.823589	+	0.567188i	$0.191969\pi$
$912$	9796.09	0.355681
$913$	−4533.64	−0.164339
$914$	15003.9	0.542982
$915$	−32538.7	−1.17562
$916$	−10493.5	−0.378509
$917$	29088.9	1.04755
$918$	190.354	0.00684382
$919$	2542.94	0.0912775	0.0456387	−	0.998958i	$-0.485468\pi$
$919$	2542.94	0.0912775	0.0456387	+	0.998958i	$0.485468\pi$
$920$	5329.70	0.190995
$921$	−62510.5	−2.23647
$922$	−33634.6	−1.20141
$923$	0	0
$924$	−9170.77	−0.326511
$925$	−14088.5	−0.500787
$926$	−13104.1	−0.465040
$927$	42562.4	1.50802
$928$	−37452.2	−1.32482
$929$	6788.80	0.239756	0.119878	−	0.992789i	$-0.461750\pi$
$929$	6788.80	0.239756	0.119878	+	0.992789i	$0.461750\pi$
$930$	6368.56	0.224552
$931$	35442.4	1.24767
$932$	3349.09	0.117707
$933$	49010.2	1.71974
$934$	5688.23	0.199277
$935$	−470.417	−0.0164538
$936$	0	0
$937$	−1.53958	−5.36775e−5 0	−2.68387e−5	−	1.00000i	$-0.500009\pi$
$937$	−1.53958	−5.36775e−5 0	−2.68387e−5		1.00000i	$0.500009\pi$
$938$	−1407.87	−0.0490070
$939$	18622.1	0.647187
$940$	−4079.93	−0.141567
$941$	23228.0	0.804688	0.402344	−	0.915489i	$-0.368196\pi$
$941$	23228.0	0.804688	0.402344	+	0.915489i	$0.368196\pi$
$942$	13218.6	0.457202
$943$	−17752.7	−0.613053
$944$	1475.07	0.0508576
$945$	2434.68	0.0838097
$946$	−1623.31	−0.0557912
$947$	−19107.8	−0.655670	−0.327835	−	0.944735i	$-0.606319\pi$
$947$	−19107.8	−0.655670	−0.327835	+	0.944735i	$0.606319\pi$
$948$	20710.4	0.709539
$949$	0	0
$950$	−13075.0	−0.446534
$951$	−82999.8	−2.83013
$952$	4728.48	0.160978
$953$	45983.1	1.56300	0.781500	−	0.623905i	$-0.214455\pi$
$953$	45983.1	1.56300	0.781500	+	0.623905i	$0.214455\pi$
$954$	−1478.57	−0.0501785
$955$	−9433.01	−0.319628
$956$	−19452.8	−0.658105
$957$	−19568.3	−0.660974
$958$	6580.85	0.221939
$959$	−30504.3	−1.02715
$960$	21316.0	0.716635
$961$	−25211.4	−0.846277
$962$	0	0
$963$	26271.1	0.879101
$964$	21391.2	0.714695
$965$	18412.7	0.614225
$966$	−15352.5	−0.511344
$967$	21246.7	0.706566	0.353283	−	0.935517i	$-0.385065\pi$
$967$	21246.7	0.706566	0.353283	+	0.935517i	$0.385065\pi$
$968$	−2914.95	−0.0967872
$969$	3845.83	0.127498
$970$	−17498.9	−0.579234
$971$	46394.1	1.53332	0.766661	−	0.642052i	$-0.221917\pi$
$971$	46394.1	1.53332	0.766661	+	0.642052i	$0.221917\pi$
$972$	−21176.7	−0.698809
$973$	52297.3	1.72310
$974$	19935.6	0.655828
$975$	0	0
$976$	12244.0	0.401560
$977$	16959.3	0.555350	0.277675	−	0.960675i	$-0.410436\pi$
$977$	16959.3	0.555350	0.277675	+	0.960675i	$0.410436\pi$
$978$	−43463.0	−1.42106
$979$	5003.22	0.163334
$980$	11501.6	0.374903
$981$	−41851.6	−1.36210
$982$	−6565.72	−0.213361
$983$	48366.5	1.56933	0.784665	−	0.619919i	$-0.212835\pi$
$983$	48366.5	1.56933	0.784665	+	0.619919i	$0.212835\pi$
$984$	−89906.2	−2.91271
$985$	−25983.1	−0.840498
$986$	3309.84	0.106904
$987$	35825.3	1.15535
$988$	0	0
$989$	2592.28	0.0833464
$990$	3994.47	0.128235
$991$	4514.41	0.144707	0.0723537	−	0.997379i	$-0.476949\pi$
$991$	4514.41	0.144707	0.0723537	+	0.997379i	$0.476949\pi$
$992$	10645.7	0.340727
$993$	−31269.4	−0.999300
$994$	−53030.4	−1.69217
$995$	−17342.8	−0.552567
$996$	12027.9	0.382649
$997$	−32603.7	−1.03568	−0.517838	−	0.855478i	$-0.673263\pi$
$997$	−32603.7	−1.03568	−0.517838	+	0.855478i	$0.673263\pi$
$998$	−7050.62	−0.223631
$999$	−2236.35	−0.0708257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.i.1.11		17
13.3	even	3		143.4.e.a.100.7	✓	34
13.9	even	3		143.4.e.a.133.7	yes	34
13.12	even	2		1859.4.a.f.1.7		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.7	✓	34	13.3	even	3
143.4.e.a.133.7	yes	34	13.9	even	3
1859.4.a.f.1.7		17	13.12	even	2
1859.4.a.i.1.11		17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.02345 q^{2} -7.47211 q^{3} -3.90564 q^{4} -6.22433 q^{5} -15.1195 q^{6} +28.5679 q^{7} -24.0905 q^{8} +28.8324 q^{9} +O(q^{10})\)	\(q+2.02345 q^{2} -7.47211 q^{3} -3.90564 q^{4} -6.22433 q^{5} -15.1195 q^{6} +28.5679 q^{7} -24.0905 q^{8} +28.8324 q^{9} -12.5946 q^{10} -11.0000 q^{11} +29.1833 q^{12} +57.8058 q^{14} +46.5089 q^{15} -17.5009 q^{16} -6.87065 q^{17} +58.3411 q^{18} +74.9116 q^{19} +24.3100 q^{20} -213.462 q^{21} -22.2580 q^{22} +35.5439 q^{23} +180.007 q^{24} -86.2577 q^{25} -13.6922 q^{27} -111.576 q^{28} -238.076 q^{29} +94.1085 q^{30} +67.6726 q^{31} +157.312 q^{32} +82.1932 q^{33} -13.9024 q^{34} -177.816 q^{35} -112.609 q^{36} +163.331 q^{37} +151.580 q^{38} +149.947 q^{40} -499.460 q^{41} -431.931 q^{42} +72.9317 q^{43} +42.9620 q^{44} -179.463 q^{45} +71.9214 q^{46} -167.830 q^{47} +130.769 q^{48} +473.123 q^{49} -174.539 q^{50} +51.3382 q^{51} -25.3435 q^{53} -27.7054 q^{54} +68.4676 q^{55} -688.214 q^{56} -559.748 q^{57} -481.737 q^{58} -84.2856 q^{59} -181.647 q^{60} -699.623 q^{61} +136.932 q^{62} +823.681 q^{63} +458.320 q^{64} +166.314 q^{66} -24.3552 q^{67} +26.8343 q^{68} -265.588 q^{69} -359.802 q^{70} -917.389 q^{71} -694.588 q^{72} -651.592 q^{73} +330.492 q^{74} +644.527 q^{75} -292.577 q^{76} -314.247 q^{77} +709.665 q^{79} +108.931 q^{80} -676.166 q^{81} -1010.63 q^{82} +412.149 q^{83} +833.706 q^{84} +42.7652 q^{85} +147.574 q^{86} +1778.93 q^{87} +264.995 q^{88} -454.838 q^{89} -363.134 q^{90} -138.821 q^{92} -505.657 q^{93} -339.595 q^{94} -466.274 q^{95} -1175.45 q^{96} +1389.40 q^{97} +957.343 q^{98} -317.157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19} + 98 q^{20} + 220 q^{21} - 44 q^{22} - 215 q^{23} + 26 q^{24} + 319 q^{25} - 384 q^{27} - 396 q^{28} - 7 q^{29} - 1269 q^{30} + 682 q^{31} + 813 q^{32} + 66 q^{33} + 738 q^{34} + 10 q^{35} + 560 q^{36} + 1084 q^{37} + 410 q^{38} + 95 q^{40} + 240 q^{41} + 393 q^{42} - 435 q^{43} - 858 q^{44} + 1242 q^{45} + 1671 q^{46} + 549 q^{47} + 894 q^{48} + 403 q^{49} - 651 q^{50} + 1552 q^{51} - 566 q^{53} + 311 q^{54} - 176 q^{55} - 1925 q^{56} - 534 q^{57} + 618 q^{58} + 2010 q^{59} - 411 q^{60} + 460 q^{61} - 823 q^{62} + 820 q^{63} + 3171 q^{64} - 154 q^{66} - 232 q^{67} + 1795 q^{68} - 1608 q^{69} + 207 q^{70} + 489 q^{71} + 2556 q^{72} + 290 q^{73} + 2653 q^{74} - 2852 q^{75} + 2421 q^{76} + 66 q^{77} - 732 q^{79} + 4915 q^{80} + 2393 q^{81} - 1772 q^{82} - 117 q^{83} + 4161 q^{84} + 4858 q^{85} + 1034 q^{86} + 3032 q^{87} - 693 q^{88} + 4113 q^{89} + 15145 q^{90} - 3554 q^{92} + 802 q^{93} + 2325 q^{94} - 3924 q^{95} + 2601 q^{96} + 2793 q^{97} + 533 q^{98} - 1485 q^{99}+O(q^{100}) \) 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 95 * q^12 - 60 * q^14 - 28 * q^15 + 350 * q^16 + 118 * q^17 + 478 * q^18 + 403 * q^19 + 98 * q^20 + 220 * q^21 - 44 * q^22 - 215 * q^23 + 26 * q^24 + 319 * q^25 - 384 * q^27 - 396 * q^28 - 7 * q^29 - 1269 * q^30 + 682 * q^31 + 813 * q^32 + 66 * q^33 + 738 * q^34 + 10 * q^35 + 560 * q^36 + 1084 * q^37 + 410 * q^38 + 95 * q^40 + 240 * q^41 + 393 * q^42 - 435 * q^43 - 858 * q^44 + 1242 * q^45 + 1671 * q^46 + 549 * q^47 + 894 * q^48 + 403 * q^49 - 651 * q^50 + 1552 * q^51 - 566 * q^53 + 311 * q^54 - 176 * q^55 - 1925 * q^56 - 534 * q^57 + 618 * q^58 + 2010 * q^59 - 411 * q^60 + 460 * q^61 - 823 * q^62 + 820 * q^63 + 3171 * q^64 - 154 * q^66 - 232 * q^67 + 1795 * q^68 - 1608 * q^69 + 207 * q^70 + 489 * q^71 + 2556 * q^72 + 290 * q^73 + 2653 * q^74 - 2852 * q^75 + 2421 * q^76 + 66 * q^77 - 732 * q^79 + 4915 * q^80 + 2393 * q^81 - 1772 * q^82 - 117 * q^83 + 4161 * q^84 + 4858 * q^85 + 1034 * q^86 + 3032 * q^87 - 693 * q^88 + 4113 * q^89 + 15145 * q^90 - 3554 * q^92 + 802 * q^93 + 2325 * q^94 - 3924 * q^95 + 2601 * q^96 + 2793 * q^97 + 533 * q^98 - 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more