LMFDB - Embedded newform 1859.4.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$17$
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			1.3
Root			$4.70666$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.70666 q^{2} -10.1964 q^{3} +14.1527 q^{4} -19.7628 q^{5} +47.9909 q^{6} +2.86520 q^{7} -28.9586 q^{8} +76.9660 q^{9} +O(q^{10})$	\(q-4.70666 q^{2} -10.1964 q^{3} +14.1527 q^{4} -19.7628 q^{5} +47.9909 q^{6} +2.86520 q^{7} -28.9586 q^{8} +76.9660 q^{9} +93.0167 q^{10} +11.0000 q^{11} -144.306 q^{12} -13.4855 q^{14} +201.508 q^{15} +23.0771 q^{16} +67.5383 q^{17} -362.253 q^{18} -35.1515 q^{19} -279.696 q^{20} -29.2146 q^{21} -51.7733 q^{22} +93.4585 q^{23} +295.273 q^{24} +265.567 q^{25} -509.471 q^{27} +40.5502 q^{28} -90.3480 q^{29} -948.433 q^{30} -107.147 q^{31} +123.053 q^{32} -112.160 q^{33} -317.880 q^{34} -56.6242 q^{35} +1089.28 q^{36} -144.510 q^{37} +165.447 q^{38} +572.303 q^{40} -110.300 q^{41} +137.503 q^{42} -24.7106 q^{43} +155.680 q^{44} -1521.06 q^{45} -439.878 q^{46} -184.521 q^{47} -235.303 q^{48} -334.791 q^{49} -1249.93 q^{50} -688.645 q^{51} +363.939 q^{53} +2397.91 q^{54} -217.390 q^{55} -82.9722 q^{56} +358.418 q^{57} +425.238 q^{58} +40.9743 q^{59} +2851.89 q^{60} -314.620 q^{61} +504.303 q^{62} +220.523 q^{63} -763.786 q^{64} +527.900 q^{66} -114.194 q^{67} +955.848 q^{68} -952.938 q^{69} +266.511 q^{70} +233.672 q^{71} -2228.83 q^{72} +19.7048 q^{73} +680.160 q^{74} -2707.82 q^{75} -497.489 q^{76} +31.5172 q^{77} +43.9487 q^{79} -456.067 q^{80} +3116.68 q^{81} +519.145 q^{82} +1290.67 q^{83} -413.465 q^{84} -1334.74 q^{85} +116.305 q^{86} +921.222 q^{87} -318.545 q^{88} -1261.46 q^{89} +7159.12 q^{90} +1322.69 q^{92} +1092.51 q^{93} +868.478 q^{94} +694.692 q^{95} -1254.69 q^{96} +288.983 q^{97} +1575.75 q^{98} +846.626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.70666	−1.66406	−0.832029	−	0.554733i	$-0.812820\pi$
$2$	−4.70666	−1.66406	−0.832029	+	0.554733i	$0.812820\pi$
$3$	−10.1964	−1.96229	−0.981146	−	0.193267i	$-0.938092\pi$
$3$	−10.1964	−1.96229	−0.981146	+	0.193267i	$0.938092\pi$
$4$	14.1527	1.76909
$5$	−19.7628	−1.76764	−0.883818	−	0.467831i	$-0.845035\pi$
$5$	−19.7628	−1.76764	−0.883818	+	0.467831i	$0.845035\pi$
$6$	47.9909	3.26537
$7$	2.86520	0.154706	0.0773530	−	0.997004i	$-0.475353\pi$
$7$	2.86520	0.154706	0.0773530	+	0.997004i	$0.475353\pi$
$8$	−28.9586	−1.27980
$9$	76.9660	2.85059
$10$	93.0167	2.94145
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−144.306	−3.47146
$13$	0	0
$13$	0	0
$14$	−13.4855	−0.257440
$15$	201.508	3.46862
$16$	23.0771	0.360580
$17$	67.5383	0.963555	0.481777	−	0.876294i	$-0.339991\pi$
$17$	67.5383	0.963555	0.481777	+	0.876294i	$0.339991\pi$
$18$	−362.253	−4.74355
$19$	−35.1515	−0.424438	−0.212219	−	0.977222i	$-0.568069\pi$
$19$	−35.1515	−0.424438	−0.212219	+	0.977222i	$0.568069\pi$
$20$	−279.696	−3.12710
$21$	−29.2146	−0.303578
$22$	−51.7733	−0.501732
$23$	93.4585	0.847280	0.423640	−	0.905831i	$-0.360752\pi$
$23$	93.4585	0.847280	0.423640	+	0.905831i	$0.360752\pi$
$24$	295.273	2.51135
$25$	265.567	2.12454
$26$	0	0
$27$	−509.471	−3.63140
$28$	40.5502	0.273688
$29$	−90.3480	−0.578524	−0.289262	−	0.957250i	$-0.593410\pi$
$29$	−90.3480	−0.578524	−0.289262	+	0.957250i	$0.593410\pi$
$30$	−948.433	−5.77198
$31$	−107.147	−0.620777	−0.310389	−	0.950610i	$-0.600459\pi$
$31$	−107.147	−0.620777	−0.310389	+	0.950610i	$0.600459\pi$
$32$	123.053	0.679778
$33$	−112.160	−0.591653
$34$	−317.880	−1.60341
$35$	−56.6242	−0.273464
$36$	1089.28	5.04294
$37$	−144.510	−0.642089	−0.321044	−	0.947064i	$-0.604034\pi$
$37$	−144.510	−0.642089	−0.321044	+	0.947064i	$0.604034\pi$
$38$	165.447	0.706289
$39$	0	0
$40$	572.303	2.26223
$41$	−110.300	−0.420146	−0.210073	−	0.977686i	$-0.567370\pi$
$41$	−110.300	−0.420146	−0.210073	+	0.977686i	$0.567370\pi$
$42$	137.503	0.505172
$43$	−24.7106	−0.0876358	−0.0438179	−	0.999040i	$-0.513952\pi$
$43$	−24.7106	−0.0876358	−0.0438179	+	0.999040i	$0.513952\pi$
$44$	155.680	0.533400
$45$	−1521.06	−5.03881
$46$	−439.878	−1.40992
$47$	−184.521	−0.572662	−0.286331	−	0.958131i	$-0.592436\pi$
$47$	−184.521	−0.572662	−0.286331	+	0.958131i	$0.592436\pi$
$48$	−235.303	−0.707563
$49$	−334.791	−0.976066
$50$	−1249.93	−3.53535
$51$	−688.645	−1.89078
$52$	0	0
$53$	363.939	0.943224	0.471612	−	0.881806i	$-0.343672\pi$
$53$	363.939	0.943224	0.471612	+	0.881806i	$0.343672\pi$
$54$	2397.91	6.04286
$55$	−217.390	−0.532962
$56$	−82.9722	−0.197993
$57$	358.418	0.832871
$58$	425.238	0.962697
$59$	40.9743	0.0904137	0.0452068	−	0.998978i	$-0.485605\pi$
$59$	40.9743	0.0904137	0.0452068	+	0.998978i	$0.485605\pi$
$60$	2851.89	6.13628
$61$	−314.620	−0.660376	−0.330188	−	0.943915i	$-0.607112\pi$
$61$	−314.620	−0.660376	−0.330188	+	0.943915i	$0.607112\pi$
$62$	504.303	1.03301
$63$	220.523	0.441004
$64$	−763.786	−1.49177
$65$	0	0
$66$	527.900	0.984545
$67$	−114.194	−0.208225	−0.104112	−	0.994566i	$-0.533200\pi$
$67$	−114.194	−0.208225	−0.104112	+	0.994566i	$0.533200\pi$
$68$	955.848	1.70461
$69$	−952.938	−1.66261
$70$	266.511	0.455059
$71$	233.672	0.390589	0.195294	−	0.980745i	$-0.437434\pi$
$71$	233.672	0.390589	0.195294	+	0.980745i	$0.437434\pi$
$72$	−2228.83	−3.64820
$73$	19.7048	0.0315927	0.0157964	−	0.999875i	$-0.494972\pi$
$73$	19.7048	0.0315927	0.0157964	+	0.999875i	$0.494972\pi$
$74$	680.160	1.06847
$75$	−2707.82	−4.16896
$76$	−497.489	−0.750867
$77$	31.5172	0.0466456
$78$	0	0
$79$	43.9487	0.0625900	0.0312950	−	0.999510i	$-0.490037\pi$
$79$	43.9487	0.0625900	0.0312950	+	0.999510i	$0.490037\pi$
$80$	−456.067	−0.637374
$81$	3116.68	4.27528
$82$	519.145	0.699147
$83$	1290.67	1.70686	0.853432	−	0.521204i	$-0.174517\pi$
$83$	1290.67	1.70686	0.853432	+	0.521204i	$0.174517\pi$
$84$	−413.465	−0.537056
$85$	−1334.74	−1.70321
$86$	116.305	0.145831
$87$	921.222	1.13523
$88$	−318.545	−0.385875
$89$	−1261.46	−1.50241	−0.751205	−	0.660069i	$-0.770527\pi$
$89$	−1261.46	−1.50241	−0.751205	+	0.660069i	$0.770527\pi$
$90$	7159.12	8.38486
$91$	0	0
$92$	1322.69	1.49891
$93$	1092.51	1.21815
$94$	868.478	0.952943
$95$	694.692	0.750251
$96$	−1254.69	−1.33392
$97$	288.983	0.302492	0.151246	−	0.988496i	$-0.451671\pi$
$97$	288.983	0.302492	0.151246	+	0.988496i	$0.451671\pi$
$98$	1575.75	1.62423
$99$	846.626	0.859486
$100$	3758.49	3.75849
$101$	1212.37	1.19441	0.597205	−	0.802089i	$-0.296278\pi$
$101$	1212.37	1.19441	0.597205	+	0.802089i	$0.296278\pi$
$102$	3241.22	3.14636
$103$	−1054.79	−1.00905	−0.504523	−	0.863398i	$-0.668332\pi$
$103$	−1054.79	−1.00905	−0.504523	+	0.863398i	$0.668332\pi$
$104$	0	0
$105$	577.361	0.536616
$106$	−1712.94	−1.56958
$107$	230.225	0.208007	0.104003	−	0.994577i	$-0.466835\pi$
$107$	230.225	0.208007	0.104003	+	0.994577i	$0.466835\pi$
$108$	−7210.39	−6.42426
$109$	−2005.09	−1.76195	−0.880974	−	0.473165i	$-0.843112\pi$
$109$	−2005.09	−1.76195	−0.880974	+	0.473165i	$0.843112\pi$
$110$	1023.18	0.886880
$111$	1473.48	1.25997
$112$	66.1204	0.0557839
$113$	−174.104	−0.144941	−0.0724706	−	0.997371i	$-0.523088\pi$
$113$	−174.104	−0.144941	−0.0724706	+	0.997371i	$0.523088\pi$
$114$	−1686.95	−1.38594
$115$	−1847.00	−1.49768
$116$	−1278.67	−1.02346
$117$	0	0
$118$	−192.852	−0.150453
$119$	193.510	0.149068
$120$	−5835.41	−4.43915
$121$	121.000	0.0909091
$122$	1480.81	1.09890
$123$	1124.66	0.824449
$124$	−1516.41	−1.09821
$125$	−2777.99	−1.98777
$126$	−1037.93	−0.733855
$127$	1848.92	1.29185	0.645925	−	0.763401i	$-0.276472\pi$
$127$	1848.92	1.29185	0.645925	+	0.763401i	$0.276472\pi$
$128$	2610.46	1.80261
$129$	251.959	0.171967
$130$	0	0
$131$	−241.276	−0.160919	−0.0804595	−	0.996758i	$-0.525639\pi$
$131$	−241.276	−0.160919	−0.0804595	+	0.996758i	$0.525639\pi$
$132$	−1587.37	−1.04669
$133$	−100.716	−0.0656631
$134$	537.475	0.346498
$135$	10068.6	6.41899
$136$	−1955.82	−1.23316
$137$	2547.29	1.58854	0.794269	−	0.607567i	$-0.207854\pi$
$137$	2547.29	1.58854	0.794269	+	0.607567i	$0.207854\pi$
$138$	4485.16	2.76668
$139$	1256.69	0.766840	0.383420	−	0.923574i	$-0.374746\pi$
$139$	1256.69	0.766840	0.383420	+	0.923574i	$0.374746\pi$
$140$	−801.385	−0.483781
$141$	1881.44	1.12373
$142$	−1099.82	−0.649962
$143$	0	0
$144$	1776.15	1.02787
$145$	1785.53	1.02262
$146$	−92.7437	−0.0525721
$147$	3413.65	1.91533
$148$	−2045.20	−1.13591
$149$	−1198.49	−0.658952	−0.329476	−	0.944164i	$-0.606872\pi$
$149$	−1198.49	−0.658952	−0.329476	+	0.944164i	$0.606872\pi$
$150$	12744.8	6.93739
$151$	−1618.04	−0.872012	−0.436006	−	0.899944i	$-0.643607\pi$
$151$	−1618.04	−0.872012	−0.436006	+	0.899944i	$0.643607\pi$
$152$	1017.94	0.543197
$153$	5198.15	2.74670
$154$	−148.341	−0.0776210
$155$	2117.51	1.09731
$156$	0	0
$157$	3691.07	1.87630	0.938150	−	0.346229i	$-0.112538\pi$
$157$	3691.07	1.87630	0.938150	+	0.346229i	$0.112538\pi$
$158$	−206.852	−0.104153
$159$	−3710.86	−1.85088
$160$	−2431.87	−1.20160
$161$	267.777	0.131079
$162$	−14669.2	−7.11431
$163$	−1338.94	−0.643396	−0.321698	−	0.946842i	$-0.604254\pi$
$163$	−1338.94	−0.643396	−0.321698	+	0.946842i	$0.604254\pi$
$164$	−1561.04	−0.743274
$165$	2216.59	1.04583
$166$	−6074.77	−2.84032
$167$	−2401.79	−1.11291	−0.556454	−	0.830878i	$-0.687839\pi$
$167$	−2401.79	−1.11291	−0.556454	+	0.830878i	$0.687839\pi$
$168$	846.015	0.388521
$169$	0	0
$170$	6282.19	2.83425
$171$	−2705.47	−1.20990
$172$	−349.722	−0.155035
$173$	−1496.69	−0.657752	−0.328876	−	0.944373i	$-0.606670\pi$
$173$	−1496.69	−0.657752	−0.328876	+	0.944373i	$0.606670\pi$
$174$	−4335.88	−1.88909
$175$	760.901	0.328678
$176$	253.848	0.108719
$177$	−417.790	−0.177418
$178$	5937.27	2.50009
$179$	1155.01	0.482287	0.241143	−	0.970489i	$-0.422478\pi$
$179$	1155.01	0.482287	0.241143	+	0.970489i	$0.422478\pi$
$180$	−21527.1	−8.91408
$181$	−308.002	−0.126484	−0.0632420	−	0.997998i	$-0.520144\pi$
$181$	−308.002	−0.126484	−0.0632420	+	0.997998i	$0.520144\pi$
$182$	0	0
$183$	3207.98	1.29585
$184$	−2706.43	−1.08435
$185$	2855.92	1.13498
$186$	−5142.06	−2.02707
$187$	742.921	0.290523
$188$	−2611.47	−1.01309
$189$	−1459.74	−0.561800
$190$	−3269.68	−1.24846
$191$	2323.00	0.880033	0.440017	−	0.897990i	$-0.354973\pi$
$191$	2323.00	0.880033	0.440017	+	0.897990i	$0.354973\pi$
$192$	7787.84	2.92729
$193$	2502.04	0.933166	0.466583	−	0.884477i	$-0.345485\pi$
$193$	2502.04	0.933166	0.466583	+	0.884477i	$0.345485\pi$
$194$	−1360.14	−0.503364
$195$	0	0
$196$	−4738.19	−1.72674
$197$	−3926.60	−1.42009	−0.710046	−	0.704155i	$-0.751326\pi$
$197$	−3926.60	−1.42009	−0.710046	+	0.704155i	$0.751326\pi$
$198$	−3984.78	−1.43023
$199$	−8.82572	−0.00314391	−0.00157196	−	0.999999i	$-0.500500\pi$
$199$	−8.82572	−0.00314391	−0.00157196	+	0.999999i	$0.500500\pi$
$200$	−7690.46	−2.71899
$201$	1164.37	0.408598
$202$	−5706.22	−1.98757
$203$	−258.865	−0.0895012
$204$	−9746.18	−3.34495
$205$	2179.83	0.742665
$206$	4964.55	1.67911
$207$	7193.12	2.41525
$208$	0	0
$209$	−386.667	−0.127973
$210$	−2717.45	−0.892960
$211$	−589.607	−0.192371	−0.0961853	−	0.995363i	$-0.530664\pi$
$211$	−589.607	−0.192371	−0.0961853	+	0.995363i	$0.530664\pi$
$212$	5150.71	1.66864
$213$	−2382.61	−0.766449
$214$	−1083.59	−0.346135
$215$	488.351	0.154908
$216$	14753.6	4.64748
$217$	−306.996	−0.0960380
$218$	9437.26	2.93198
$219$	−200.917	−0.0619941
$220$	−3076.66	−0.942856
$221$	0	0
$222$	−6935.16	−2.09665
$223$	4485.45	1.34694	0.673471	−	0.739213i	$-0.264802\pi$
$223$	4485.45	1.34694	0.673471	+	0.739213i	$0.264802\pi$
$224$	352.571	0.105166
$225$	20439.6	6.05618
$226$	819.451	0.241191
$227$	−2320.44	−0.678471	−0.339235	−	0.940702i	$-0.610168\pi$
$227$	−2320.44	−0.678471	−0.339235	+	0.940702i	$0.610168\pi$
$228$	5072.58	1.47342
$229$	−2065.95	−0.596165	−0.298083	−	0.954540i	$-0.596347\pi$
$229$	−2065.95	−0.596165	−0.298083	+	0.954540i	$0.596347\pi$
$230$	8693.20	2.49223
$231$	−321.361	−0.0915323
$232$	2616.36	0.740397
$233$	4326.13	1.21637	0.608186	−	0.793795i	$-0.291898\pi$
$233$	4326.13	1.21637	0.608186	+	0.793795i	$0.291898\pi$
$234$	0	0
$235$	3646.64	1.01226
$236$	579.897	0.159950
$237$	−448.117	−0.122820
$238$	−910.788	−0.248057
$239$	5781.53	1.56475	0.782377	−	0.622806i	$-0.214007\pi$
$239$	5781.53	1.56475	0.782377	+	0.622806i	$0.214007\pi$
$240$	4650.23	1.25071
$241$	−4037.02	−1.07903	−0.539517	−	0.841975i	$-0.681393\pi$
$241$	−4037.02	−1.07903	−0.539517	+	0.841975i	$0.681393\pi$
$242$	−569.506	−0.151278
$243$	−18023.1	−4.75795
$244$	−4452.72	−1.16826
$245$	6616.39	1.72533
$246$	−5293.40	−1.37193
$247$	0	0
$248$	3102.82	0.794473
$249$	−13160.2	−3.34937
$250$	13075.1	3.30776
$251$	1295.40	0.325756	0.162878	−	0.986646i	$-0.447922\pi$
$251$	1295.40	0.325756	0.162878	+	0.986646i	$0.447922\pi$
$252$	3120.99	0.780173
$253$	1028.04	0.255465
$254$	−8702.23	−2.14971
$255$	13609.5	3.34220
$256$	−6176.27	−1.50788
$257$	5672.76	1.37688	0.688438	−	0.725295i	$-0.258297\pi$
$257$	5672.76	1.37688	0.688438	+	0.725295i	$0.258297\pi$
$258$	−1185.89	−0.286163
$259$	−414.049	−0.0993350
$260$	0	0
$261$	−6953.72	−1.64914
$262$	1135.61	0.267778
$263$	−7405.78	−1.73635	−0.868175	−	0.496258i	$-0.834707\pi$
$263$	−7405.78	−1.73635	−0.868175	+	0.496258i	$0.834707\pi$
$264$	3248.00	0.757200
$265$	−7192.44	−1.66728
$266$	474.037	0.109267
$267$	12862.3	2.94817
$268$	−1616.16	−0.368368
$269$	1308.86	0.296665	0.148332	−	0.988938i	$-0.452609\pi$
$269$	1308.86	0.296665	0.148332	+	0.988938i	$0.452609\pi$
$270$	−47389.4	−10.6816
$271$	3250.88	0.728696	0.364348	−	0.931263i	$-0.381292\pi$
$271$	3250.88	0.728696	0.364348	+	0.931263i	$0.381292\pi$
$272$	1558.59	0.347438
$273$	0	0
$274$	−11989.2	−2.64342
$275$	2921.24	0.640572
$276$	−13486.6	−2.94130
$277$	−3895.24	−0.844917	−0.422459	−	0.906382i	$-0.638833\pi$
$277$	−3895.24	−0.844917	−0.422459	+	0.906382i	$0.638833\pi$
$278$	−5914.80	−1.27607
$279$	−8246.64	−1.76958
$280$	1639.76	0.349980
$281$	5784.91	1.22811	0.614055	−	0.789263i	$-0.289537\pi$
$281$	5784.91	1.22811	0.614055	+	0.789263i	$0.289537\pi$
$282$	−8855.32	−1.86995
$283$	4490.29	0.943181	0.471590	−	0.881818i	$-0.343680\pi$
$283$	4490.29	0.943181	0.471590	+	0.881818i	$0.343680\pi$
$284$	3307.09	0.690985
$285$	−7083.33	−1.47221
$286$	0	0
$287$	−316.031	−0.0649991
$288$	9470.89	1.93777
$289$	−351.584	−0.0715619
$290$	−8403.87	−1.70170
$291$	−2946.57	−0.593578
$292$	278.875	0.0558902
$293$	−3315.66	−0.661102	−0.330551	−	0.943788i	$-0.607235\pi$
$293$	−3315.66	−0.661102	−0.330551	+	0.943788i	$0.607235\pi$
$294$	−16066.9	−3.18721
$295$	−809.766	−0.159818
$296$	4184.81	0.821747
$297$	−5604.19	−1.09491
$298$	5640.88	1.09653
$299$	0	0
$300$	−38322.9	−7.37525
$301$	−70.8008	−0.0135578
$302$	7615.55	1.45108
$303$	−12361.8	−2.34378
$304$	−811.196	−0.153044
$305$	6217.76	1.16730
$306$	−24465.9	−4.57067
$307$	−9432.75	−1.75360	−0.876800	−	0.480855i	$-0.840326\pi$
$307$	−9432.75	−1.75360	−0.876800	+	0.480855i	$0.840326\pi$
$308$	446.052	0.0825201
$309$	10755.1	1.98004
$310$	−9966.42	−1.82598
$311$	−5599.68	−1.02099	−0.510496	−	0.859880i	$-0.670538\pi$
$311$	−5599.68	−1.02099	−0.510496	+	0.859880i	$0.670538\pi$
$312$	0	0
$313$	−5001.74	−0.903242	−0.451621	−	0.892210i	$-0.649154\pi$
$313$	−5001.74	−0.903242	−0.451621	+	0.892210i	$0.649154\pi$
$314$	−17372.6	−3.12227
$315$	−4358.14	−0.779534
$316$	621.992	0.110727
$317$	587.460	0.104085	0.0520427	−	0.998645i	$-0.483427\pi$
$317$	587.460	0.104085	0.0520427	+	0.998645i	$0.483427\pi$
$318$	17465.8	3.07997
$319$	−993.828	−0.174432
$320$	15094.5	2.63690
$321$	−2347.46	−0.408170
$322$	−1260.34	−0.218124
$323$	−2374.07	−0.408969
$324$	44109.4	7.56334
$325$	0	0
$326$	6301.93	1.07065
$327$	20444.6	3.45746
$328$	3194.14	0.537704
$329$	−528.688	−0.0885943
$330$	−10432.8	−1.74032
$331$	−5226.90	−0.867965	−0.433982	−	0.900921i	$-0.642892\pi$
$331$	−5226.90	−0.867965	−0.433982	+	0.900921i	$0.642892\pi$
$332$	18266.5	3.01959
$333$	−11122.3	−1.83033
$334$	11304.4	1.85194
$335$	2256.80	0.368066
$336$	−674.188	−0.109464
$337$	−6220.94	−1.00557	−0.502784	−	0.864412i	$-0.667691\pi$
$337$	−6220.94	−1.00557	−0.502784	+	0.864412i	$0.667691\pi$
$338$	0	0
$339$	1775.23	0.284417
$340$	−18890.2	−3.01313
$341$	−1178.61	−0.187171
$342$	12733.8	2.01334
$343$	−1942.00	−0.305709
$344$	715.587	0.112157
$345$	18832.7	2.93889
$346$	7044.41	1.09454
$347$	11961.2	1.85046	0.925232	−	0.379401i	$-0.123870\pi$
$347$	11961.2	1.85046	0.925232	+	0.379401i	$0.123870\pi$
$348$	13037.8	2.00833
$349$	−7.69569	−0.00118035	−0.000590173	−	1.00000i	$-0.500188\pi$
$349$	−7.69569	−0.00118035	−0.000590173		1.00000i	$0.500188\pi$
$350$	−3581.31	−0.546940
$351$	0	0
$352$	1353.58	0.204961
$353$	5516.77	0.831807	0.415904	−	0.909409i	$-0.363465\pi$
$353$	5516.77	0.831807	0.415904	+	0.909409i	$0.363465\pi$
$354$	1966.40	0.295234
$355$	−4618.01	−0.690418
$356$	−17853.0	−2.65789
$357$	−1973.10	−0.292514
$358$	−5436.23	−0.802553
$359$	3640.71	0.535235	0.267618	−	0.963525i	$-0.413764\pi$
$359$	3640.71	0.535235	0.267618	+	0.963525i	$0.413764\pi$
$360$	44047.8	6.44868
$361$	−5623.37	−0.819853
$362$	1449.66	0.210477
$363$	−1233.76	−0.178390
$364$	0	0
$365$	−389.421	−0.0558444
$366$	−15098.9	−2.15637
$367$	−554.623	−0.0788858	−0.0394429	−	0.999222i	$-0.512558\pi$
$367$	−554.623	−0.0788858	−0.0394429	+	0.999222i	$0.512558\pi$
$368$	2156.75	0.305512
$369$	−8489.35	−1.19766
$370$	−13441.8	−1.88867
$371$	1042.76	0.145922
$372$	15461.9	2.15501
$373$	−7558.30	−1.04921	−0.524603	−	0.851347i	$-0.675786\pi$
$373$	−7558.30	−1.04921	−0.524603	+	0.851347i	$0.675786\pi$
$374$	−3496.68	−0.483446
$375$	28325.4	3.90058
$376$	5343.47	0.732895
$377$	0	0
$378$	6870.48	0.934867
$379$	8651.52	1.17256	0.586278	−	0.810110i	$-0.300593\pi$
$379$	8651.52	1.17256	0.586278	+	0.810110i	$0.300593\pi$
$380$	9831.76	1.32726
$381$	−18852.2	−2.53499
$382$	−10933.6	−1.46443
$383$	11750.4	1.56768	0.783838	−	0.620965i	$-0.213259\pi$
$383$	11750.4	1.56768	0.783838	+	0.620965i	$0.213259\pi$
$384$	−26617.2	−3.53725
$385$	−622.866	−0.0824525
$386$	−11776.3	−1.55284
$387$	−1901.88	−0.249814
$388$	4089.88	0.535135
$389$	−3652.39	−0.476050	−0.238025	−	0.971259i	$-0.576500\pi$
$389$	−3652.39	−0.476050	−0.238025	+	0.971259i	$0.576500\pi$
$390$	0	0
$391$	6312.03	0.816401
$392$	9695.08	1.24917
$393$	2460.14	0.315770
$394$	18481.2	2.36312
$395$	−868.547	−0.110636
$396$	11982.0	1.52050
$397$	−2898.26	−0.366396	−0.183198	−	0.983076i	$-0.558645\pi$
$397$	−2898.26	−0.366396	−0.183198	+	0.983076i	$0.558645\pi$
$398$	41.5397	0.00523165
$399$	1026.94	0.128850
$400$	6128.52	0.766064
$401$	9925.56	1.23606	0.618029	−	0.786156i	$-0.287932\pi$
$401$	9925.56	1.23606	0.618029	+	0.786156i	$0.287932\pi$
$402$	−5480.29	−0.679931
$403$	0	0
$404$	17158.3	2.11301
$405$	−61594.2	−7.55713
$406$	1218.39	0.148935
$407$	−1589.61	−0.193597
$408$	19942.2	2.41982
$409$	1950.43	0.235800	0.117900	−	0.993025i	$-0.462384\pi$
$409$	1950.43	0.235800	0.117900	+	0.993025i	$0.462384\pi$
$410$	−10259.7	−1.23584
$411$	−25973.1	−3.11717
$412$	−14928.2	−1.78509
$413$	117.400	0.0139875
$414$	−33855.6	−4.01911
$415$	−25507.3	−3.01711
$416$	0	0
$417$	−12813.6	−1.50476
$418$	1819.91	0.212954
$419$	−7457.05	−0.869453	−0.434726	−	0.900563i	$-0.643155\pi$
$419$	−7457.05	−0.869453	−0.434726	+	0.900563i	$0.643155\pi$
$420$	8171.21	0.949320
$421$	5766.40	0.667547	0.333773	−	0.942653i	$-0.391678\pi$
$421$	5766.40	0.667547	0.333773	+	0.942653i	$0.391678\pi$
$422$	2775.08	0.320116
$423$	−14201.8	−1.63243
$424$	−10539.2	−1.20714
$425$	17935.9	2.04711
$426$	11214.1	1.27541
$427$	−901.447	−0.102164
$428$	3258.30	0.367981
$429$	0	0
$430$	−2298.50	−0.257776
$431$	−8580.65	−0.958969	−0.479484	−	0.877550i	$-0.659176\pi$
$431$	−8580.65	−0.958969	−0.479484	+	0.877550i	$0.659176\pi$
$432$	−11757.1	−1.30941
$433$	14707.1	1.63229	0.816143	−	0.577850i	$-0.196108\pi$
$433$	14707.1	1.63229	0.816143	+	0.577850i	$0.196108\pi$
$434$	1444.93	0.159813
$435$	−18205.9	−2.00668
$436$	−28377.3	−3.11704
$437$	−3285.21	−0.359618
$438$	945.649	0.103162
$439$	9486.30	1.03134	0.515668	−	0.856789i	$-0.327544\pi$
$439$	9486.30	1.03134	0.515668	+	0.856789i	$0.327544\pi$
$440$	6295.33	0.682087
$441$	−25767.5	−2.78237
$442$	0	0
$443$	−96.4462	−0.0103438	−0.00517189	−	0.999987i	$-0.501646\pi$
$443$	−96.4462	−0.0103438	−0.00517189	+	0.999987i	$0.501646\pi$
$444$	20853.7	2.22899
$445$	24929.9	2.65571
$446$	−21111.5	−2.24139
$447$	12220.2	1.29306
$448$	−2188.40	−0.230786
$449$	3949.73	0.415143	0.207572	−	0.978220i	$-0.433444\pi$
$449$	3949.73	0.415143	0.207572	+	0.978220i	$0.433444\pi$
$450$	−96202.4	−10.0778
$451$	−1213.30	−0.126679
$452$	−2464.05	−0.256414
$453$	16498.1	1.71114
$454$	10921.5	1.12901
$455$	0	0
$456$	−10379.3	−1.06591
$457$	4521.79	0.462845	0.231423	−	0.972853i	$-0.425662\pi$
$457$	4521.79	0.462845	0.231423	+	0.972853i	$0.425662\pi$
$458$	9723.73	0.992053
$459$	−34408.8	−3.49905
$460$	−26140.0	−2.64953
$461$	−17562.8	−1.77436	−0.887181	−	0.461422i	$-0.847339\pi$
$461$	−17562.8	−1.77436	−0.887181	+	0.461422i	$0.847339\pi$
$462$	1512.54	0.152315
$463$	1201.33	0.120584	0.0602921	−	0.998181i	$-0.480797\pi$
$463$	1201.33	0.120584	0.0602921	+	0.998181i	$0.480797\pi$
$464$	−2084.97	−0.208604
$465$	−21590.9	−2.15324
$466$	−20361.7	−2.02411
$467$	−6638.04	−0.657755	−0.328878	−	0.944373i	$-0.606670\pi$
$467$	−6638.04	−0.657755	−0.328878	+	0.944373i	$0.606670\pi$
$468$	0	0
$469$	−327.189	−0.0322136
$470$	−17163.5	−1.68446
$471$	−37635.5	−3.68185
$472$	−1186.56	−0.115712
$473$	−271.817	−0.0264232
$474$	2109.14	0.204379
$475$	−9335.09	−0.901733
$476$	2738.69	0.263714
$477$	28010.9	2.68874
$478$	−27211.7	−2.60384
$479$	5219.56	0.497887	0.248943	−	0.968518i	$-0.419917\pi$
$479$	5219.56	0.497887	0.248943	+	0.968518i	$0.419917\pi$
$480$	24796.2	2.35789
$481$	0	0
$482$	19000.9	1.79557
$483$	−2730.35	−0.257216
$484$	1712.48	0.160826
$485$	−5711.10	−0.534696
$486$	84828.6	7.91749
$487$	10924.4	1.01649	0.508246	−	0.861212i	$-0.330294\pi$
$487$	10924.4	1.01649	0.508246	+	0.861212i	$0.330294\pi$
$488$	9110.96	0.845151
$489$	13652.3	1.26253
$490$	−31141.1	−2.87105
$491$	−15834.1	−1.45536	−0.727682	−	0.685915i	$-0.759402\pi$
$491$	−15834.1	−1.45536	−0.727682	+	0.685915i	$0.759402\pi$
$492$	15917.0	1.45852
$493$	−6101.95	−0.557440
$494$	0	0
$495$	−16731.7	−1.51926
$496$	−2472.63	−0.223840
$497$	669.517	0.0604264
$498$	61940.6	5.57354
$499$	15354.2	1.37745	0.688725	−	0.725023i	$-0.258171\pi$
$499$	15354.2	1.37745	0.688725	+	0.725023i	$0.258171\pi$
$500$	−39316.1	−3.51653
$501$	24489.5	2.18385
$502$	−6097.00	−0.542077
$503$	−19012.6	−1.68535	−0.842676	−	0.538422i	$-0.819021\pi$
$503$	−19012.6	−1.68535	−0.842676	+	0.538422i	$0.819021\pi$
$504$	−6386.03	−0.564398
$505$	−23959.8	−2.11128
$506$	−4838.66	−0.425108
$507$	0	0
$508$	26167.2	2.28539
$509$	−9433.61	−0.821488	−0.410744	−	0.911751i	$-0.634731\pi$
$509$	−9433.61	−0.821488	−0.410744	+	0.911751i	$0.634731\pi$
$510$	−64055.5	−5.56162
$511$	56.4580	0.00488758
$512$	8185.96	0.706585
$513$	17908.7	1.54130
$514$	−26699.8	−2.29120
$515$	20845.6	1.78363
$516$	3565.90	0.304224
$517$	−2029.73	−0.172664
$518$	1948.79	0.165299
$519$	15260.8	1.29070
$520$	0	0
$521$	11008.8	0.925731	0.462866	−	0.886428i	$-0.346821\pi$
$521$	11008.8	0.925731	0.462866	+	0.886428i	$0.346821\pi$
$522$	32728.8	2.74426
$523$	−18119.0	−1.51489	−0.757446	−	0.652898i	$-0.773553\pi$
$523$	−18119.0	−1.51489	−0.757446	+	0.652898i	$0.773553\pi$
$524$	−3414.71	−0.284680
$525$	−7758.43	−0.644963
$526$	34856.5	2.88939
$527$	−7236.49	−0.598153
$528$	−2588.33	−0.213338
$529$	−3432.51	−0.282116
$530$	33852.4	2.77444
$531$	3153.63	0.257732
$532$	−1425.40	−0.116164
$533$	0	0
$534$	−60538.6	−4.90592
$535$	−4549.88	−0.367680
$536$	3306.92	0.266487
$537$	−11776.9	−0.946388
$538$	−6160.38	−0.493667
$539$	−3682.70	−0.294295
$540$	142497.	11.3558
$541$	13578.0	1.07905	0.539523	−	0.841971i	$-0.318605\pi$
$541$	13578.0	1.07905	0.539523	+	0.841971i	$0.318605\pi$
$542$	−15300.8	−1.21259
$543$	3140.50	0.248199
$544$	8310.78	0.655004
$545$	39626.0	3.11448
$546$	0	0
$547$	23289.2	1.82043	0.910213	−	0.414141i	$-0.135918\pi$
$547$	23289.2	1.82043	0.910213	+	0.414141i	$0.135918\pi$
$548$	36051.0	2.81026
$549$	−24215.0	−1.88246
$550$	−13749.3	−1.06595
$551$	3175.87	0.245548
$552$	27595.8	2.12782
$553$	125.922	0.00968305
$554$	18333.6	1.40599
$555$	−29120.0	−2.22716
$556$	17785.5	1.35661
$557$	23696.1	1.80258	0.901290	−	0.433217i	$-0.142622\pi$
$557$	23696.1	1.80258	0.901290	+	0.433217i	$0.142622\pi$
$558$	38814.2	2.94469
$559$	0	0
$560$	−1306.72	−0.0986055
$561$	−7575.10	−0.570091
$562$	−27227.6	−2.04365
$563$	17928.8	1.34211	0.671054	−	0.741408i	$-0.265842\pi$
$563$	17928.8	1.34211	0.671054	+	0.741408i	$0.265842\pi$
$564$	26627.5	1.98798
$565$	3440.78	0.256203
$566$	−21134.3	−1.56951
$567$	8929.89	0.661411
$568$	−6766.83	−0.499877
$569$	15375.9	1.13285	0.566426	−	0.824113i	$-0.308326\pi$
$569$	15375.9	1.13285	0.566426	+	0.824113i	$0.308326\pi$
$570$	33338.9	2.44985
$571$	1063.08	0.0779131	0.0389565	−	0.999241i	$-0.487597\pi$
$571$	1063.08	0.0779131	0.0389565	+	0.999241i	$0.487597\pi$
$572$	0	0
$573$	−23686.2	−1.72688
$574$	1487.45	0.108162
$575$	24819.5	1.80008
$576$	−58785.5	−4.25242
$577$	1269.80	0.0916162	0.0458081	−	0.998950i	$-0.485414\pi$
$577$	1269.80	0.0916162	0.0458081	+	0.998950i	$0.485414\pi$
$578$	1654.79	0.119083
$579$	−25511.8	−1.83114
$580$	25270.0	1.80910
$581$	3698.03	0.264062
$582$	13868.5	0.987748
$583$	4003.33	0.284393
$584$	−570.623	−0.0404324
$585$	0	0
$586$	15605.7	1.10011
$587$	−3193.97	−0.224582	−0.112291	−	0.993675i	$-0.535819\pi$
$587$	−3193.97	−0.224582	−0.112291	+	0.993675i	$0.535819\pi$
$588$	48312.3	3.38838
$589$	3766.37	0.263481
$590$	3811.30	0.265947
$591$	40037.0	2.78664
$592$	−3334.87	−0.231524
$593$	4830.45	0.334507	0.167253	−	0.985914i	$-0.446510\pi$
$593$	4830.45	0.334507	0.167253	+	0.985914i	$0.446510\pi$
$594$	26377.0	1.82199
$595$	−3824.30	−0.263497
$596$	−16961.8	−1.16574
$597$	89.9903	0.00616928
$598$	0	0
$599$	−24512.2	−1.67203	−0.836013	−	0.548710i	$-0.815119\pi$
$599$	−24512.2	−1.67203	−0.836013	+	0.548710i	$0.815119\pi$
$600$	78414.8	5.33545
$601$	5161.63	0.350328	0.175164	−	0.984539i	$-0.443954\pi$
$601$	5161.63	0.350328	0.175164	+	0.984539i	$0.443954\pi$
$602$	333.236	0.0225609
$603$	−8789.08	−0.593564
$604$	−22899.6	−1.54266
$605$	−2391.29	−0.160694
$606$	58182.7	3.90019
$607$	6528.16	0.436523	0.218262	−	0.975890i	$-0.429961\pi$
$607$	6528.16	0.436523	0.218262	+	0.975890i	$0.429961\pi$
$608$	−4325.50	−0.288524
$609$	2639.48	0.175627
$610$	−29264.9	−1.94246
$611$	0	0
$612$	73567.8	4.85915
$613$	19291.2	1.27107	0.635535	−	0.772072i	$-0.280780\pi$
$613$	19291.2	1.27107	0.635535	+	0.772072i	$0.280780\pi$
$614$	44396.8	2.91809
$615$	−22226.4	−1.45733
$616$	−912.694	−0.0596972
$617$	−1335.28	−0.0871251	−0.0435625	−	0.999051i	$-0.513871\pi$
$617$	−1335.28	−0.0871251	−0.0435625	+	0.999051i	$0.513871\pi$
$618$	−50620.4	−3.29491
$619$	13175.8	0.855539	0.427769	−	0.903888i	$-0.359300\pi$
$619$	13175.8	0.855539	0.427769	+	0.903888i	$0.359300\pi$
$620$	29968.5	1.94123
$621$	−47614.4	−3.07681
$622$	26355.8	1.69899
$623$	−3614.33	−0.232432
$624$	0	0
$625$	21704.9	1.38912
$626$	23541.5	1.50305
$627$	3942.60	0.251120
$628$	52238.5	3.31934
$629$	−9759.95	−0.618688
$630$	20512.3	1.29719
$631$	11481.2	0.724342	0.362171	−	0.932112i	$-0.382036\pi$
$631$	11481.2	0.724342	0.362171	+	0.932112i	$0.382036\pi$
$632$	−1272.69	−0.0801029
$633$	6011.85	0.377488
$634$	−2764.98	−0.173204
$635$	−36539.7	−2.28352
$636$	−52518.6	−3.27437
$637$	0	0
$638$	4677.61	0.290264
$639$	17984.8	1.11341
$640$	−51589.9	−3.18636
$641$	19361.5	1.19303	0.596516	−	0.802601i	$-0.296551\pi$
$641$	19361.5	1.19303	0.596516	+	0.802601i	$0.296551\pi$
$642$	11048.7	0.679218
$643$	11053.7	0.677942	0.338971	−	0.940797i	$-0.389921\pi$
$643$	11053.7	0.677942	0.338971	+	0.940797i	$0.389921\pi$
$644$	3789.76	0.231891
$645$	−4979.40	−0.303975
$646$	11174.0	0.680548
$647$	24637.4	1.49706	0.748528	−	0.663103i	$-0.230761\pi$
$647$	24637.4	1.49706	0.748528	+	0.663103i	$0.230761\pi$
$648$	−90254.8	−5.47152
$649$	450.718	0.0272607
$650$	0	0
$651$	3130.24	0.188455
$652$	−18949.6	−1.13822
$653$	24753.1	1.48341	0.741704	−	0.670728i	$-0.234018\pi$
$653$	24753.1	1.48341	0.741704	+	0.670728i	$0.234018\pi$
$654$	−96225.8	−5.75341
$655$	4768.28	0.284446
$656$	−2545.41	−0.151496
$657$	1516.60	0.0900579
$658$	2488.36	0.147426
$659$	23784.0	1.40591	0.702955	−	0.711234i	$-0.251863\pi$
$659$	23784.0	1.40591	0.702955	+	0.711234i	$0.251863\pi$
$660$	31370.8	1.85016
$661$	1415.63	0.0833007	0.0416503	−	0.999132i	$-0.486738\pi$
$661$	1415.63	0.0833007	0.0416503	+	0.999132i	$0.486738\pi$
$662$	24601.3	1.44434
$663$	0	0
$664$	−37376.1	−2.18445
$665$	1990.43	0.116068
$666$	52349.1	3.04578
$667$	−8443.79	−0.490172
$668$	−33991.7	−1.96883
$669$	−45735.4	−2.64310
$670$	−10622.0	−0.612482
$671$	−3460.82	−0.199111
$672$	−3594.94	−0.206366
$673$	−12872.4	−0.737285	−0.368643	−	0.929571i	$-0.620177\pi$
$673$	−12872.4	−0.737285	−0.368643	+	0.929571i	$0.620177\pi$
$674$	29279.9	1.67332
$675$	−135299.	−7.71504
$676$	0	0
$677$	−21840.6	−1.23988	−0.619942	−	0.784648i	$-0.712844\pi$
$677$	−21840.6	−1.23988	−0.619942	+	0.784648i	$0.712844\pi$
$678$	−8355.43	−0.473286
$679$	827.992	0.0467974
$680$	38652.3	2.17978
$681$	23660.0	1.33136
$682$	5547.33	0.311464
$683$	15237.1	0.853633	0.426817	−	0.904338i	$-0.359635\pi$
$683$	15237.1	0.853633	0.426817	+	0.904338i	$0.359635\pi$
$684$	−38289.7	−2.14041
$685$	−50341.5	−2.80796
$686$	9140.36	0.508718
$687$	21065.2	1.16985
$688$	−570.250	−0.0315997
$689$	0	0
$690$	−88639.1	−4.89048
$691$	13244.9	0.729173	0.364586	−	0.931170i	$-0.381210\pi$
$691$	13244.9	0.729173	0.364586	+	0.931170i	$0.381210\pi$
$692$	−21182.2	−1.16362
$693$	2425.75	0.132968
$694$	−56297.4	−3.07928
$695$	−24835.6	−1.35549
$696$	−26677.3	−1.45288
$697$	−7449.47	−0.404834
$698$	36.2210	0.00196416
$699$	−44110.9	−2.38688
$700$	10768.8	0.581460
$701$	10042.0	0.541057	0.270528	−	0.962712i	$-0.412802\pi$
$701$	10042.0	0.541057	0.270528	+	0.962712i	$0.412802\pi$
$702$	0	0
$703$	5079.75	0.272527
$704$	−8401.64	−0.449785
$705$	−37182.5	−1.98635
$706$	−25965.6	−1.38418
$707$	3473.68	0.184782
$708$	−5912.85	−0.313868
$709$	29782.9	1.57760	0.788802	−	0.614647i	$-0.210702\pi$
$709$	29782.9	1.57760	0.788802	+	0.614647i	$0.210702\pi$
$710$	21735.4	1.14890
$711$	3382.55	0.178419
$712$	36530.1	1.92279
$713$	−10013.8	−0.525972
$714$	9286.73	0.486761
$715$	0	0
$716$	16346.5	0.853207
$717$	−58950.6	−3.07050
$718$	−17135.6	−0.890662
$719$	9331.48	0.484013	0.242007	−	0.970275i	$-0.422194\pi$
$719$	9331.48	0.484013	0.242007	+	0.970275i	$0.422194\pi$
$720$	−35101.7	−1.81689
$721$	−3022.19	−0.156106
$722$	26467.3	1.36428
$723$	41162.9	2.11738
$724$	−4359.06	−0.223761
$725$	−23993.4	−1.22910
$726$	5806.90	0.296852
$727$	−8084.13	−0.412412	−0.206206	−	0.978509i	$-0.566112\pi$
$727$	−8084.13	−0.412412	−0.206206	+	0.978509i	$0.566112\pi$
$728$	0	0
$729$	99619.6	5.06120
$730$	1832.87	0.0929283
$731$	−1668.91	−0.0844419
$732$	45401.5	2.29247
$733$	11147.8	0.561739	0.280869	−	0.959746i	$-0.409377\pi$
$733$	11147.8	0.561739	0.280869	+	0.959746i	$0.409377\pi$
$734$	2610.43	0.131271
$735$	−67463.2	−3.38560
$736$	11500.3	0.575963
$737$	−1256.14	−0.0627822
$738$	39956.5	1.99298
$739$	−16487.3	−0.820699	−0.410349	−	0.911928i	$-0.634593\pi$
$739$	−16487.3	−0.820699	−0.410349	+	0.911928i	$0.634593\pi$
$740$	40418.9	2.00788
$741$	0	0
$742$	−4907.90	−0.242823
$743$	23090.0	1.14009	0.570047	−	0.821612i	$-0.306925\pi$
$743$	23090.0	1.14009	0.570047	+	0.821612i	$0.306925\pi$
$744$	−31637.5	−1.55899
$745$	23685.4	1.16479
$746$	35574.4	1.74594
$747$	99337.9	4.86557
$748$	10514.3	0.513960
$749$	659.640	0.0321799
$750$	−133318.	−6.49079
$751$	18025.1	0.875824	0.437912	−	0.899018i	$-0.355718\pi$
$751$	18025.1	0.875824	0.437912	+	0.899018i	$0.355718\pi$
$752$	−4258.21	−0.206490
$753$	−13208.4	−0.639229
$754$	0	0
$755$	31976.9	1.54140
$756$	−20659.2	−0.993872
$757$	−21654.0	−1.03967	−0.519834	−	0.854267i	$-0.674006\pi$
$757$	−21654.0	−1.03967	−0.519834	+	0.854267i	$0.674006\pi$
$758$	−40719.8	−1.95120
$759$	−10482.3	−0.501296
$760$	−20117.3	−0.960174
$761$	24032.6	1.14478	0.572392	−	0.819980i	$-0.306016\pi$
$761$	24032.6	1.14478	0.572392	+	0.819980i	$0.306016\pi$
$762$	88731.2	4.21836
$763$	−5744.96	−0.272584
$764$	32876.7	1.55685
$765$	−102730.	−4.85517
$766$	−55305.4	−2.60870
$767$	0	0
$768$	62975.6	2.95890
$769$	−20761.9	−0.973595	−0.486798	−	0.873515i	$-0.661835\pi$
$769$	−20761.9	−0.973595	−0.486798	+	0.873515i	$0.661835\pi$
$770$	2931.62	0.137206
$771$	−57841.6	−2.70183
$772$	35410.7	1.65085
$773$	3609.21	0.167936	0.0839678	−	0.996468i	$-0.473241\pi$
$773$	3609.21	0.167936	0.0839678	+	0.996468i	$0.473241\pi$
$774$	8951.50	0.415704
$775$	−28454.6	−1.31886
$776$	−8368.55	−0.387131
$777$	4221.80	0.194924
$778$	17190.6	0.792174
$779$	3877.22	0.178326
$780$	0	0
$781$	2570.39	0.117767
$782$	−29708.6	−1.35854
$783$	46029.7	2.10085
$784$	−7726.00	−0.351950
$785$	−72945.7	−3.31661
$786$	−11579.1	−0.525460
$787$	4567.45	0.206877	0.103438	−	0.994636i	$-0.467016\pi$
$787$	4567.45	0.206877	0.103438	+	0.994636i	$0.467016\pi$
$788$	−55571.9	−2.51227
$789$	75512.1	3.40723
$790$	4087.96	0.184105
$791$	−498.843	−0.0224233
$792$	−24517.1	−1.09997
$793$	0	0
$794$	13641.1	0.609704
$795$	73336.8	3.27168
$796$	−124.908	−0.00556185
$797$	−990.678	−0.0440296	−0.0220148	−	0.999758i	$-0.507008\pi$
$797$	−990.678	−0.0440296	−0.0220148	+	0.999758i	$0.507008\pi$
$798$	−4833.45	−0.214414
$799$	−12462.2	−0.551792
$800$	32678.8	1.44421
$801$	−97089.4	−4.28275
$802$	−46716.3	−2.05687
$803$	216.752	0.00952556
$804$	16478.9	0.722845
$805$	−5292.01	−0.231701
$806$	0	0
$807$	−13345.6	−0.582142
$808$	−35108.6	−1.52861
$809$	−19783.8	−0.859778	−0.429889	−	0.902882i	$-0.641447\pi$
$809$	−19783.8	−0.859778	−0.429889	+	0.902882i	$0.641447\pi$
$810$	289903.	12.5755
$811$	−31391.3	−1.35918	−0.679591	−	0.733592i	$-0.737843\pi$
$811$	−31391.3	−1.35918	−0.679591	+	0.733592i	$0.737843\pi$
$812$	−3663.63	−0.158335
$813$	−33147.1	−1.42992
$814$	7481.76	0.322156
$815$	26461.1	1.13729
$816$	−15891.9	−0.681776
$817$	868.617	0.0371959
$818$	−9180.00	−0.392385
$819$	0	0
$820$	30850.5	1.31384
$821$	−18777.1	−0.798202	−0.399101	−	0.916907i	$-0.630678\pi$
$821$	−18777.1	−0.798202	−0.399101	+	0.916907i	$0.630678\pi$
$822$	122247.	5.18716
$823$	19309.9	0.817860	0.408930	−	0.912566i	$-0.365902\pi$
$823$	19309.9	0.817860	0.408930	+	0.912566i	$0.365902\pi$
$824$	30545.4	1.29138
$825$	−29786.0	−1.25699
$826$	−552.560	−0.0232761
$827$	−33363.2	−1.40284	−0.701422	−	0.712746i	$-0.747451\pi$
$827$	−33363.2	−1.40284	−0.701422	+	0.712746i	$0.747451\pi$
$828$	101802.	4.27279
$829$	−16798.3	−0.703776	−0.351888	−	0.936042i	$-0.614460\pi$
$829$	−16798.3	−0.703776	−0.351888	+	0.936042i	$0.614460\pi$
$830$	120054.	5.02065
$831$	39717.3	1.65797
$832$	0	0
$833$	−22611.2	−0.940493
$834$	60309.5	2.50401
$835$	47465.9	1.96722
$836$	−5472.38	−0.226395
$837$	54588.1	2.25429
$838$	35097.8	1.44682
$839$	33348.2	1.37224	0.686119	−	0.727489i	$-0.259313\pi$
$839$	33348.2	1.37224	0.686119	+	0.727489i	$0.259313\pi$
$840$	−16719.6	−0.686763
$841$	−16226.2	−0.665310
$842$	−27140.5	−1.11084
$843$	−58985.1	−2.40991
$844$	−8344.52	−0.340320
$845$	0	0
$846$	66843.2	2.71645
$847$	346.689	0.0140642
$848$	8398.65	0.340107
$849$	−45784.7	−1.85080
$850$	−84418.4	−3.40650
$851$	−13505.7	−0.544029
$852$	−33720.3	−1.35591
$853$	−14722.9	−0.590974	−0.295487	−	0.955347i	$-0.595482\pi$
$853$	−14722.9	−0.590974	−0.295487	+	0.955347i	$0.595482\pi$
$854$	4242.81	0.170007
$855$	53467.6	2.13866
$856$	−6667.01	−0.266207
$857$	−27939.9	−1.11366	−0.556830	−	0.830626i	$-0.687983\pi$
$857$	−27939.9	−1.11366	−0.556830	+	0.830626i	$0.687983\pi$
$858$	0	0
$859$	−9953.60	−0.395358	−0.197679	−	0.980267i	$-0.563340\pi$
$859$	−9953.60	−0.395358	−0.197679	+	0.980267i	$0.563340\pi$
$860$	6911.48	0.274046
$861$	3222.37	0.127547
$862$	40386.3	1.59578
$863$	−5818.73	−0.229515	−0.114758	−	0.993394i	$-0.536609\pi$
$863$	−5818.73	−0.229515	−0.114758	+	0.993394i	$0.536609\pi$
$864$	−62692.0	−2.46855
$865$	29578.7	1.16267
$866$	−69221.5	−2.71622
$867$	3584.88	0.140425
$868$	−4344.82	−0.169899
$869$	483.435	0.0188716
$870$	85689.0	3.33923
$871$	0	0
$872$	58064.5	2.25495
$873$	22241.8	0.862282
$874$	15462.4	0.598425
$875$	−7959.49	−0.307520
$876$	−2843.52	−0.109673
$877$	−11332.9	−0.436356	−0.218178	−	0.975909i	$-0.570011\pi$
$877$	−11332.9	−0.436356	−0.218178	+	0.975909i	$0.570011\pi$
$878$	−44648.8	−1.71620
$879$	33807.7	1.29728
$880$	−5016.74	−0.192175
$881$	−37635.0	−1.43922	−0.719612	−	0.694377i	$-0.755680\pi$
$881$	−37635.0	−1.43922	−0.719612	+	0.694377i	$0.755680\pi$
$882$	121279.	4.63001
$883$	−27631.7	−1.05309	−0.526547	−	0.850146i	$-0.676513\pi$
$883$	−27631.7	−1.05309	−0.526547	+	0.850146i	$0.676513\pi$
$884$	0	0
$885$	8256.68	0.313610
$886$	453.940	0.0172126
$887$	14257.2	0.539696	0.269848	−	0.962903i	$-0.413026\pi$
$887$	14257.2	0.539696	0.269848	+	0.962903i	$0.413026\pi$
$888$	−42669.9	−1.61251
$889$	5297.51	0.199857
$890$	−117337.	−4.41926
$891$	34283.5	1.28904
$892$	63481.2	2.38286
$893$	6486.19	0.243060
$894$	−57516.5	−2.15172
$895$	−22826.1	−0.852507
$896$	7479.48	0.278875
$897$	0	0
$898$	−18590.1	−0.690822
$899$	9680.48	0.359135
$900$	289276.	10.7139
$901$	24579.8	0.908848
$902$	5710.60	0.210801
$903$	721.911	0.0266043
$904$	5041.83	0.185496
$905$	6086.97	0.223578
$906$	−77651.0	−2.84744
$907$	−36469.9	−1.33513	−0.667566	−	0.744551i	$-0.732664\pi$
$907$	−36469.9	−1.33513	−0.667566	+	0.744551i	$0.732664\pi$
$908$	−32840.4	−1.20027
$909$	93311.3	3.40477
$910$	0	0
$911$	−39720.8	−1.44457	−0.722287	−	0.691593i	$-0.756909\pi$
$911$	−39720.8	−1.44457	−0.722287	+	0.691593i	$0.756909\pi$
$912$	8271.25	0.300316
$913$	14197.4	0.514639
$914$	−21282.5	−0.770201
$915$	−63398.6	−2.29059
$916$	−29238.8	−1.05467
$917$	−691.303	−0.0248951
$918$	161951.	5.82263
$919$	21066.5	0.756168	0.378084	−	0.925771i	$-0.376583\pi$
$919$	21066.5	0.756168	0.378084	+	0.925771i	$0.376583\pi$
$920$	53486.6	1.91674
$921$	96179.8	3.44108
$922$	82662.1	2.95264
$923$	0	0
$924$	−4548.12	−0.161929
$925$	−38377.0	−1.36414
$926$	−5654.25	−0.200659
$927$	−81183.1	−2.87638
$928$	−11117.6	−0.393268
$929$	−25107.2	−0.886697	−0.443349	−	0.896349i	$-0.646210\pi$
$929$	−25107.2	−0.886697	−0.443349	+	0.896349i	$0.646210\pi$
$930$	101621.	3.58311
$931$	11768.4	0.414279
$932$	61226.4	2.15187
$933$	57096.4	2.00349
$934$	31243.0	1.09454
$935$	−14682.2	−0.513538
$936$	0	0
$937$	−35776.6	−1.24736	−0.623678	−	0.781682i	$-0.714362\pi$
$937$	−35776.6	−1.24736	−0.623678	+	0.781682i	$0.714362\pi$
$938$	1539.97	0.0536053
$939$	50999.6	1.77243
$940$	51609.8	1.79077
$941$	−7239.26	−0.250790	−0.125395	−	0.992107i	$-0.540020\pi$
$941$	−7239.26	−0.250790	−0.125395	+	0.992107i	$0.540020\pi$
$942$	177138.	6.12681
$943$	−10308.5	−0.355981
$944$	945.569	0.0326013
$945$	28848.4	0.993057
$946$	1279.35	0.0439697
$947$	9989.93	0.342797	0.171399	−	0.985202i	$-0.445171\pi$
$947$	9989.93	0.342797	0.171399	+	0.985202i	$0.445171\pi$
$948$	−6342.06	−0.217279
$949$	0	0
$950$	43937.1	1.50054
$951$	−5989.96	−0.204246
$952$	−5603.80	−0.190777
$953$	−39737.6	−1.35071	−0.675354	−	0.737493i	$-0.736009\pi$
$953$	−39737.6	−1.35071	−0.675354	+	0.737493i	$0.736009\pi$
$954$	−131838.	−4.47422
$955$	−45908.9	−1.55558
$956$	81824.2	2.76818
$957$	10133.4	0.342286
$958$	−24566.7	−0.828512
$959$	7298.48	0.245756
$960$	−153909.	−5.17438
$961$	−18310.6	−0.614636
$962$	0	0
$963$	17719.5	0.592942
$964$	−57134.7	−1.90890
$965$	−49447.3	−1.64950
$966$	12850.9	0.428022
$967$	49755.7	1.65464	0.827319	−	0.561732i	$-0.189865\pi$
$967$	49755.7	1.65464	0.827319	+	0.561732i	$0.189865\pi$
$968$	−3504.00	−0.116346
$969$	24206.9	0.802517
$970$	26880.2	0.889765
$971$	17825.9	0.589146	0.294573	−	0.955629i	$-0.404823\pi$
$971$	17825.9	0.589146	0.294573	+	0.955629i	$0.404823\pi$
$972$	−255075.	−8.41722
$973$	3600.65	0.118635
$974$	−51417.5	−1.69150
$975$	0	0
$976$	−7260.51	−0.238118
$977$	−19439.5	−0.636566	−0.318283	−	0.947996i	$-0.603106\pi$
$977$	−19439.5	−0.636566	−0.318283	+	0.947996i	$0.603106\pi$
$978$	−64256.8	−2.10092
$979$	−13876.1	−0.452993
$980$	93639.7	3.05226
$981$	−154323.	−5.02259
$982$	74525.8	2.42181
$983$	−42851.2	−1.39038	−0.695189	−	0.718827i	$-0.744680\pi$
$983$	−42851.2	−1.39038	−0.695189	+	0.718827i	$0.744680\pi$
$984$	−32568.6	−1.05513
$985$	77600.4	2.51021
$986$	28719.8	0.927612
$987$	5390.70	0.173848
$988$	0	0
$989$	−2309.42	−0.0742521
$990$	78750.3	2.52813
$991$	50849.4	1.62995	0.814977	−	0.579493i	$-0.196750\pi$
$991$	50849.4	1.62995	0.814977	+	0.579493i	$0.196750\pi$
$992$	−13184.7	−0.421991
$993$	53295.4	1.70320
$994$	−3151.19	−0.100553
$995$	174.421	0.00555729
$996$	−186252.	−5.92532
$997$	−33749.7	−1.07208	−0.536040	−	0.844193i	$-0.680080\pi$
$997$	−33749.7	−1.07208	−0.536040	+	0.844193i	$0.680080\pi$
$998$	−72267.0	−2.29216
$999$	73623.7	2.33168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.f.1.3		17
13.4	even	6		143.4.e.a.133.3	yes	34
13.10	even	6		143.4.e.a.100.3	✓	34
13.12	even	2		1859.4.a.i.1.15		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.3	✓	34	13.10	even	6
143.4.e.a.133.3	yes	34	13.4	even	6
1859.4.a.f.1.3		17	1.1	even	1	trivial
1859.4.a.i.1.15		17	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.70666 q^{2} -10.1964 q^{3} +14.1527 q^{4} -19.7628 q^{5} +47.9909 q^{6} +2.86520 q^{7} -28.9586 q^{8} +76.9660 q^{9} +O(q^{10})\)	\(q-4.70666 q^{2} -10.1964 q^{3} +14.1527 q^{4} -19.7628 q^{5} +47.9909 q^{6} +2.86520 q^{7} -28.9586 q^{8} +76.9660 q^{9} +93.0167 q^{10} +11.0000 q^{11} -144.306 q^{12} -13.4855 q^{14} +201.508 q^{15} +23.0771 q^{16} +67.5383 q^{17} -362.253 q^{18} -35.1515 q^{19} -279.696 q^{20} -29.2146 q^{21} -51.7733 q^{22} +93.4585 q^{23} +295.273 q^{24} +265.567 q^{25} -509.471 q^{27} +40.5502 q^{28} -90.3480 q^{29} -948.433 q^{30} -107.147 q^{31} +123.053 q^{32} -112.160 q^{33} -317.880 q^{34} -56.6242 q^{35} +1089.28 q^{36} -144.510 q^{37} +165.447 q^{38} +572.303 q^{40} -110.300 q^{41} +137.503 q^{42} -24.7106 q^{43} +155.680 q^{44} -1521.06 q^{45} -439.878 q^{46} -184.521 q^{47} -235.303 q^{48} -334.791 q^{49} -1249.93 q^{50} -688.645 q^{51} +363.939 q^{53} +2397.91 q^{54} -217.390 q^{55} -82.9722 q^{56} +358.418 q^{57} +425.238 q^{58} +40.9743 q^{59} +2851.89 q^{60} -314.620 q^{61} +504.303 q^{62} +220.523 q^{63} -763.786 q^{64} +527.900 q^{66} -114.194 q^{67} +955.848 q^{68} -952.938 q^{69} +266.511 q^{70} +233.672 q^{71} -2228.83 q^{72} +19.7048 q^{73} +680.160 q^{74} -2707.82 q^{75} -497.489 q^{76} +31.5172 q^{77} +43.9487 q^{79} -456.067 q^{80} +3116.68 q^{81} +519.145 q^{82} +1290.67 q^{83} -413.465 q^{84} -1334.74 q^{85} +116.305 q^{86} +921.222 q^{87} -318.545 q^{88} -1261.46 q^{89} +7159.12 q^{90} +1322.69 q^{92} +1092.51 q^{93} +868.478 q^{94} +694.692 q^{95} -1254.69 q^{96} +288.983 q^{97} +1575.75 q^{98} +846.626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) \) 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

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Database

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