LMFDB - Embedded newform 1859.4.a.i.1.15

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			1.15
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	$-0.187180\pi$
$2$	4.70666	1.66406	0.832029	+	0.554733i	$0.187180\pi$
$3$	−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	$-0.154965\pi$
$5$	19.7628	1.76764	0.883818	+	0.467831i	$0.154965\pi$
$6$	−47.9909	−3.26537
$7$	−2.86520	−0.154706	−0.0773530	−	0.997004i	$-0.524647\pi$
$7$	−2.86520	−0.154706	−0.0773530	+	0.997004i	$0.524647\pi$
$8$	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	$-0.431931\pi$
$19$	35.1515	0.424438	0.212219	+	0.977222i	$0.431931\pi$
$20$	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	$-0.399541\pi$
$31$	107.147	0.620777	0.310389	+	0.950610i	$0.399541\pi$
$32$	−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	$-0.395966\pi$
$37$	144.510	0.642089	0.321044	+	0.947064i	$0.395966\pi$
$38$	165.447	0.706289
$39$	0	0
$40$	572.303	2.26223
$41$	110.300	0.420146	0.210073	−	0.977686i	$-0.432630\pi$
$41$	110.300	0.420146	0.210073	+	0.977686i	$0.432630\pi$
$42$	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	$-0.407564\pi$
$47$	184.521	0.572662	0.286331	+	0.958131i	$0.407564\pi$
$48$	−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	$-0.514395\pi$
$59$	−40.9743	−0.0904137	−0.0452068	+	0.998978i	$0.514395\pi$
$60$	−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	$-0.466800\pi$
$67$	114.194	0.208225	0.104112	+	0.994566i	$0.466800\pi$
$68$	955.848	1.70461
$69$	−952.938	−1.66261
$70$	−266.511	−0.455059
$71$	−233.672	−0.390589	−0.195294	−	0.980745i	$-0.562566\pi$
$71$	−233.672	−0.390589	−0.195294	+	0.980745i	$0.562566\pi$
$72$	2228.83	3.64820
$73$	−19.7048	−0.0315927	−0.0157964	−	0.999875i	$-0.505028\pi$
$73$	−19.7048	−0.0315927	−0.0157964	+	0.999875i	$0.505028\pi$
$74$	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	$-0.825483\pi$
$83$	−1290.67	−1.70686	−0.853432	+	0.521204i	$0.825483\pi$
$84$	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	$-0.229473\pi$
$89$	1261.46	1.50241	0.751205	+	0.660069i	$0.229473\pi$
$90$	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	$-0.548329\pi$
$97$	−288.983	−0.302492	−0.151246	+	0.988496i	$0.548329\pi$
$98$	−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	$-0.156888\pi$
$109$	2005.09	1.76195	0.880974	+	0.473165i	$0.156888\pi$
$110$	−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	$-0.792146\pi$
$137$	−2547.29	−1.58854	−0.794269	+	0.607567i	$0.792146\pi$
$138$	−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	$-0.393128\pi$
$149$	1198.49	0.658952	0.329476	+	0.944164i	$0.393128\pi$
$150$	−12744.8	−6.93739
$151$	1618.04	0.872012	0.436006	−	0.899944i	$-0.356393\pi$
$151$	1618.04	0.872012	0.436006	+	0.899944i	$0.356393\pi$
$152$	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	$-0.395746\pi$
$163$	1338.94	0.643396	0.321698	+	0.946842i	$0.395746\pi$
$164$	1561.04	0.743274
$165$	2216.59	1.04583
$166$	−6074.77	−2.84032
$167$	2401.79	1.11291	0.556454	−	0.830878i	$-0.312161\pi$
$167$	2401.79	1.11291	0.556454	+	0.830878i	$0.312161\pi$
$168$	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	$-0.654515\pi$
$193$	−2502.04	−0.933166	−0.466583	+	0.884477i	$0.654515\pi$
$194$	−1360.14	−0.503364
$195$	0	0
$196$	−4738.19	−1.72674
$197$	3926.60	1.42009	0.710046	−	0.704155i	$-0.248674\pi$
$197$	3926.60	1.42009	0.710046	+	0.704155i	$0.248674\pi$
$198$	−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	$-0.735198\pi$
$223$	−4485.45	−1.34694	−0.673471	+	0.739213i	$0.735198\pi$
$224$	352.571	0.105166
$225$	20439.6	6.05618
$226$	−819.451	−0.241191
$227$	2320.44	0.678471	0.339235	−	0.940702i	$-0.389832\pi$
$227$	2320.44	0.678471	0.339235	+	0.940702i	$0.389832\pi$
$228$	−5072.58	−1.47342
$229$	2065.95	0.596165	0.298083	−	0.954540i	$-0.403653\pi$
$229$	2065.95	0.596165	0.298083	+	0.954540i	$0.403653\pi$
$230$	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	$-0.785993\pi$
$239$	−5781.53	−1.56475	−0.782377	+	0.622806i	$0.785993\pi$
$240$	−4650.23	−1.25071
$241$	4037.02	1.07903	0.539517	−	0.841975i	$-0.318607\pi$
$241$	4037.02	1.07903	0.539517	+	0.841975i	$0.318607\pi$
$242$	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	$-0.618708\pi$
$271$	−3250.88	−0.728696	−0.364348	+	0.931263i	$0.618708\pi$
$272$	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	$-0.710463\pi$
$281$	−5784.91	−1.22811	−0.614055	+	0.789263i	$0.710463\pi$
$282$	−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	$-0.392765\pi$
$293$	3315.66	0.661102	0.330551	+	0.943788i	$0.392765\pi$
$294$	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	$-0.159674\pi$
$307$	9432.75	1.75360	0.876800	+	0.480855i	$0.159674\pi$
$308$	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	$-0.516573\pi$
$317$	−587.460	−0.104085	−0.0520427	+	0.998645i	$0.516573\pi$
$318$	−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	$-0.357108\pi$
$331$	5226.90	0.867965	0.433982	+	0.900921i	$0.357108\pi$
$332$	−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	$-0.499812\pi$
$349$	7.69569	0.00118035	0.000590173		1.00000i	$0.499812\pi$
$350$	−3581.31	−0.546940
$351$	0	0
$352$	1353.58	0.204961
$353$	−5516.77	−0.831807	−0.415904	−	0.909409i	$-0.636535\pi$
$353$	−5516.77	−0.831807	−0.415904	+	0.909409i	$0.636535\pi$
$354$	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	$-0.586236\pi$
$359$	−3640.71	−0.535235	−0.267618	+	0.963525i	$0.586236\pi$
$360$	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	$-0.699407\pi$
$379$	−8651.52	−1.17256	−0.586278	+	0.810110i	$0.699407\pi$
$380$	9831.76	1.32726
$381$	−18852.2	−2.53499
$382$	10933.6	1.46443
$383$	−11750.4	−1.56768	−0.783838	−	0.620965i	$-0.786741\pi$
$383$	−11750.4	−1.56768	−0.783838	+	0.620965i	$0.786741\pi$
$384$	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	$-0.441355\pi$
$397$	2898.26	0.366396	0.183198	+	0.983076i	$0.441355\pi$
$398$	−41.5397	−0.00523165
$399$	1026.94	0.128850
$400$	6128.52	0.766064
$401$	−9925.56	−1.23606	−0.618029	−	0.786156i	$-0.712068\pi$
$401$	−9925.56	−1.23606	−0.618029	+	0.786156i	$0.712068\pi$
$402$	−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	$-0.537616\pi$
$409$	−1950.43	−0.235800	−0.117900	+	0.993025i	$0.537616\pi$
$410$	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	$-0.608322\pi$
$421$	−5766.40	−0.667547	−0.333773	+	0.942653i	$0.608322\pi$
$422$	−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	$-0.340824\pi$
$431$	8580.65	0.958969	0.479484	+	0.877550i	$0.340824\pi$
$432$	−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	$-0.566556\pi$
$449$	−3949.73	−0.415143	−0.207572	+	0.978220i	$0.566556\pi$
$450$	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	$-0.574338\pi$
$457$	−4521.79	−0.462845	−0.231423	+	0.972853i	$0.574338\pi$
$458$	9723.73	0.992053
$459$	−34408.8	−3.49905
$460$	26140.0	2.64953
$461$	17562.8	1.77436	0.887181	−	0.461422i	$-0.152661\pi$
$461$	17562.8	1.77436	0.887181	+	0.461422i	$0.152661\pi$
$462$	−1512.54	−0.152315
$463$	−1201.33	−0.120584	−0.0602921	−	0.998181i	$-0.519203\pi$
$463$	−1201.33	−0.120584	−0.0602921	+	0.998181i	$0.519203\pi$
$464$	−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	$-0.580083\pi$
$479$	−5219.56	−0.497887	−0.248943	+	0.968518i	$0.580083\pi$
$480$	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	$-0.669706\pi$
$487$	−10924.4	−1.01649	−0.508246	+	0.861212i	$0.669706\pi$
$488$	−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	$-0.741829\pi$
$499$	−15354.2	−1.37745	−0.688725	+	0.725023i	$0.741829\pi$
$500$	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	$-0.365269\pi$
$509$	9433.61	0.821488	0.410744	+	0.911751i	$0.365269\pi$
$510$	−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	$-0.681395\pi$
$541$	−13578.0	−1.07905	−0.539523	+	0.841971i	$0.681395\pi$
$542$	−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	$-0.857378\pi$
$557$	−23696.1	−1.80258	−0.901290	+	0.433217i	$0.857378\pi$
$558$	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	$-0.514586\pi$
$577$	−1269.80	−0.0916162	−0.0458081	+	0.998950i	$0.514586\pi$
$578$	−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	$-0.464181\pi$
$587$	3193.97	0.224582	0.112291	+	0.993675i	$0.464181\pi$
$588$	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	$-0.553490\pi$
$593$	−4830.45	−0.334507	−0.167253	+	0.985914i	$0.553490\pi$
$594$	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	$-0.719220\pi$
$613$	−19291.2	−1.27107	−0.635535	+	0.772072i	$0.719220\pi$
$614$	44396.8	2.91809
$615$	−22226.4	−1.45733
$616$	912.694	0.0596972
$617$	1335.28	0.0871251	0.0435625	−	0.999051i	$-0.486129\pi$
$617$	1335.28	0.0871251	0.0435625	+	0.999051i	$0.486129\pi$
$618$	50620.4	3.29491
$619$	−13175.8	−0.855539	−0.427769	−	0.903888i	$-0.640700\pi$
$619$	−13175.8	−0.855539	−0.427769	+	0.903888i	$0.640700\pi$
$620$	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	$-0.617964\pi$
$631$	−11481.2	−0.724342	−0.362171	+	0.932112i	$0.617964\pi$
$632$	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	$-0.610079\pi$
$643$	−11053.7	−0.677942	−0.338971	+	0.940797i	$0.610079\pi$
$644$	−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	$-0.513262\pi$
$661$	−1415.63	−0.0833007	−0.0416503	+	0.999132i	$0.513262\pi$
$662$	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	$-0.640365\pi$
$683$	−15237.1	−0.853633	−0.426817	+	0.904338i	$0.640365\pi$
$684$	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	$-0.618790\pi$
$691$	−13244.9	−0.729173	−0.364586	+	0.931170i	$0.618790\pi$
$692$	−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	$-0.789298\pi$
$709$	−29782.9	−1.57760	−0.788802	+	0.614647i	$0.789298\pi$
$710$	−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	$-0.590623\pi$
$733$	−11147.8	−0.561739	−0.280869	+	0.959746i	$0.590623\pi$
$734$	−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	$-0.365407\pi$
$739$	16487.3	0.820699	0.410349	+	0.911928i	$0.365407\pi$
$740$	40418.9	2.00788
$741$	0	0
$742$	−4907.90	−0.242823
$743$	−23090.0	−1.14009	−0.570047	−	0.821612i	$-0.693075\pi$
$743$	−23090.0	−1.14009	−0.570047	+	0.821612i	$0.693075\pi$
$744$	−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	$-0.693984\pi$
$761$	−24032.6	−1.14478	−0.572392	+	0.819980i	$0.693984\pi$
$762$	−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	$-0.338165\pi$
$769$	20761.9	0.973595	0.486798	+	0.873515i	$0.338165\pi$
$770$	2931.62	0.137206
$771$	−57841.6	−2.70183
$772$	−35410.7	−1.65085
$773$	−3609.21	−0.167936	−0.0839678	−	0.996468i	$-0.526759\pi$
$773$	−3609.21	−0.167936	−0.0839678	+	0.996468i	$0.526759\pi$
$774$	−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	$-0.532984\pi$
$787$	−4567.45	−0.206877	−0.103438	+	0.994636i	$0.532984\pi$
$788$	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	$-0.262157\pi$
$811$	31391.3	1.35918	0.679591	+	0.733592i	$0.262157\pi$
$812$	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	$-0.369322\pi$
$821$	18777.1	0.798202	0.399101	+	0.916907i	$0.369322\pi$
$822$	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	$-0.252549\pi$
$827$	33363.2	1.40284	0.701422	+	0.712746i	$0.252549\pi$
$828$	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	$-0.740687\pi$
$839$	−33348.2	−1.37224	−0.686119	+	0.727489i	$0.740687\pi$
$840$	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	$-0.404518\pi$
$853$	14722.9	0.590974	0.295487	+	0.955347i	$0.404518\pi$
$854$	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	$-0.463391\pi$
$863$	5818.73	0.229515	0.114758	+	0.993394i	$0.463391\pi$
$864$	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	$-0.429989\pi$
$877$	11332.9	0.436356	0.218178	+	0.975909i	$0.429989\pi$
$878$	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	$-0.353790\pi$
$929$	25107.2	0.886697	0.443349	+	0.896349i	$0.353790\pi$
$930$	−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	$-0.459980\pi$
$941$	7239.26	0.250790	0.125395	+	0.992107i	$0.459980\pi$
$942$	−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	$-0.554829\pi$
$947$	−9989.93	−0.342797	−0.171399	+	0.985202i	$0.554829\pi$
$948$	−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	$-0.810135\pi$
$967$	−49755.7	−1.65464	−0.827319	+	0.561732i	$0.810135\pi$
$968$	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	$-0.396894\pi$
$977$	19439.5	0.636566	0.318283	+	0.947996i	$0.396894\pi$
$978$	−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	$-0.255320\pi$
$983$	42851.2	1.39038	0.695189	+	0.718827i	$0.255320\pi$
$984$	−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.i.1.15		17
13.3	even	3		143.4.e.a.100.3	✓	34
13.9	even	3		143.4.e.a.133.3	yes	34
13.12	even	2		1859.4.a.f.1.3		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.3	✓	34	13.3	even	3
143.4.e.a.133.3	yes	34	13.9	even	3
1859.4.a.f.1.3		17	13.12	even	2
1859.4.a.i.1.15		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)

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

Varieties

Fields

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