LMFDB - Embedded newform 2057.4.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2057,4,Mod(1,2057)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2057, 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("2057.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2057 = 11^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2057.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:	$121.366928882$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 55 x^{8} + 72 x^{7} + 1037 x^{6} - 812 x^{5} - 7851 x^{4} + 2526 x^{3} + 20108 x^{2} + \cdots - 5760 $ x^10 - 2x^9 - 55x^8 + 72x^7 + 1037x^6 - 812x^5 - 7851x^4 + 2526x^3 + 20108x^2 + 4072*x - 5760
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.76153$ of defining polynomial
Character	$\chi$	$=$	2057.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.76153 q^{2} -2.80312 q^{3} +14.6722 q^{4} -15.6524 q^{5} +13.3472 q^{6} +31.0159 q^{7} -31.7697 q^{8} -19.1425 q^{9} +O(q^{10})$	\(q-4.76153 q^{2} -2.80312 q^{3} +14.6722 q^{4} -15.6524 q^{5} +13.3472 q^{6} +31.0159 q^{7} -31.7697 q^{8} -19.1425 q^{9} +74.5294 q^{10} -41.1279 q^{12} -22.0201 q^{13} -147.683 q^{14} +43.8757 q^{15} +33.8952 q^{16} +17.0000 q^{17} +91.1476 q^{18} -124.246 q^{19} -229.655 q^{20} -86.9415 q^{21} -171.992 q^{23} +89.0545 q^{24} +119.998 q^{25} +104.850 q^{26} +129.343 q^{27} +455.071 q^{28} -229.202 q^{29} -208.915 q^{30} +12.6553 q^{31} +92.7648 q^{32} -80.9460 q^{34} -485.474 q^{35} -280.862 q^{36} -333.938 q^{37} +591.601 q^{38} +61.7252 q^{39} +497.273 q^{40} +107.501 q^{41} +413.974 q^{42} +432.159 q^{43} +299.626 q^{45} +818.947 q^{46} -515.957 q^{47} -95.0125 q^{48} +618.987 q^{49} -571.375 q^{50} -47.6531 q^{51} -323.083 q^{52} -580.580 q^{53} -615.871 q^{54} -985.368 q^{56} +348.277 q^{57} +1091.35 q^{58} +399.381 q^{59} +643.751 q^{60} -207.426 q^{61} -60.2584 q^{62} -593.722 q^{63} -712.864 q^{64} +344.668 q^{65} +387.291 q^{67} +249.427 q^{68} +482.116 q^{69} +2311.60 q^{70} +252.618 q^{71} +608.152 q^{72} -272.871 q^{73} +1590.05 q^{74} -336.370 q^{75} -1822.96 q^{76} -293.906 q^{78} +730.719 q^{79} -530.542 q^{80} +154.283 q^{81} -511.871 q^{82} -1237.09 q^{83} -1275.62 q^{84} -266.091 q^{85} -2057.74 q^{86} +642.480 q^{87} -1014.85 q^{89} -1426.68 q^{90} -682.975 q^{91} -2523.50 q^{92} -35.4743 q^{93} +2456.74 q^{94} +1944.75 q^{95} -260.031 q^{96} -444.659 q^{97} -2947.33 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{2} - 9 q^{3} + 40 q^{4} - 41 q^{5} - 31 q^{6} + 63 q^{7} + 96 q^{8} + 61 q^{9}+O(q^{10}) $ 10 * q + 8 * q^2 - 9 * q^3 + 40 * q^4 - 41 * q^5 - 31 * q^6 + 63 * q^7 + 96 * q^8 + 61 * q^9	\( 10 q + 8 q^{2} - 9 q^{3} + 40 q^{4} - 41 q^{5} - 31 q^{6} + 63 q^{7} + 96 q^{8} + 61 q^{9} + 47 q^{10} - 171 q^{12} + 99 q^{13} - 95 q^{14} - 150 q^{15} + 180 q^{16} + 170 q^{17} + 207 q^{18} + 73 q^{19} - 343 q^{20} + 152 q^{21} - 58 q^{23} - 157 q^{24} + 529 q^{25} - 285 q^{26} - 246 q^{27} + 1031 q^{28} + 754 q^{29} + 754 q^{30} - 228 q^{31} + 466 q^{32} + 136 q^{34} - 20 q^{35} - 535 q^{36} - 1177 q^{37} - 747 q^{38} + 791 q^{39} - 537 q^{40} + 327 q^{41} - 632 q^{42} + 487 q^{43} - 834 q^{45} + 854 q^{46} - 573 q^{47} - 1857 q^{48} + 2215 q^{49} + 855 q^{50} - 153 q^{51} - 1673 q^{52} - 2022 q^{53} - 3572 q^{54} + 1997 q^{56} + 1310 q^{57} + 4514 q^{58} - 602 q^{59} + 4936 q^{60} + 570 q^{61} - 166 q^{62} + 1903 q^{63} + 968 q^{64} + 2018 q^{65} - 12 q^{67} + 680 q^{68} - 1034 q^{69} + 5460 q^{70} + 636 q^{71} + 2989 q^{72} + 201 q^{73} - 959 q^{74} + 3213 q^{75} - 6999 q^{76} + 3669 q^{78} + 1097 q^{79} - 1409 q^{80} + 3554 q^{81} + 2249 q^{82} + 477 q^{83} - 8476 q^{84} - 697 q^{85} - 1271 q^{86} - 1782 q^{87} - 195 q^{89} - 3292 q^{90} - 1128 q^{91} - 2064 q^{92} - 2632 q^{93} - 465 q^{94} + 1644 q^{95} - 8367 q^{96} - 994 q^{97} - 225 q^{98}+O(q^{100}) \) 10 * q + 8 * q^2 - 9 * q^3 + 40 * q^4 - 41 * q^5 - 31 * q^6 + 63 * q^7 + 96 * q^8 + 61 * q^9 + 47 * q^10 - 171 * q^12 + 99 * q^13 - 95 * q^14 - 150 * q^15 + 180 * q^16 + 170 * q^17 + 207 * q^18 + 73 * q^19 - 343 * q^20 + 152 * q^21 - 58 * q^23 - 157 * q^24 + 529 * q^25 - 285 * q^26 - 246 * q^27 + 1031 * q^28 + 754 * q^29 + 754 * q^30 - 228 * q^31 + 466 * q^32 + 136 * q^34 - 20 * q^35 - 535 * q^36 - 1177 * q^37 - 747 * q^38 + 791 * q^39 - 537 * q^40 + 327 * q^41 - 632 * q^42 + 487 * q^43 - 834 * q^45 + 854 * q^46 - 573 * q^47 - 1857 * q^48 + 2215 * q^49 + 855 * q^50 - 153 * q^51 - 1673 * q^52 - 2022 * q^53 - 3572 * q^54 + 1997 * q^56 + 1310 * q^57 + 4514 * q^58 - 602 * q^59 + 4936 * q^60 + 570 * q^61 - 166 * q^62 + 1903 * q^63 + 968 * q^64 + 2018 * q^65 - 12 * q^67 + 680 * q^68 - 1034 * q^69 + 5460 * q^70 + 636 * q^71 + 2989 * q^72 + 201 * q^73 - 959 * q^74 + 3213 * q^75 - 6999 * q^76 + 3669 * q^78 + 1097 * q^79 - 1409 * q^80 + 3554 * q^81 + 2249 * q^82 + 477 * q^83 - 8476 * q^84 - 697 * q^85 - 1271 * q^86 - 1782 * q^87 - 195 * q^89 - 3292 * q^90 - 1128 * q^91 - 2064 * q^92 - 2632 * q^93 - 465 * q^94 + 1644 * q^95 - 8367 * q^96 - 994 * q^97 - 225 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.76153	−1.68346	−0.841728	−	0.539902i	$-0.818461\pi$
$2$	−4.76153	−1.68346	−0.841728	+	0.539902i	$0.818461\pi$
$3$	−2.80312	−0.539461	−0.269731	−	0.962936i	$-0.586935\pi$
$3$	−2.80312	−0.539461	−0.269731	+	0.962936i	$0.586935\pi$
$4$	14.6722	1.83402
$5$	−15.6524	−1.39999	−0.699997	−	0.714146i	$-0.746815\pi$
$5$	−15.6524	−1.39999	−0.699997	+	0.714146i	$0.746815\pi$
$6$	13.3472	0.908159
$7$	31.0159	1.67470	0.837351	−	0.546665i	$-0.184103\pi$
$7$	31.0159	1.67470	0.837351	+	0.546665i	$0.184103\pi$
$8$	−31.7697	−1.40404
$9$	−19.1425	−0.708981
$10$	74.5294	2.35683
$11$	0	0
$11$	0	0
$12$	−41.1279	−0.989384
$13$	−22.0201	−0.469791	−0.234896	−	0.972021i	$-0.575475\pi$
$13$	−22.0201	−0.469791	−0.234896	+	0.972021i	$0.575475\pi$
$14$	−147.683	−2.81929
$15$	43.8757	0.755243
$16$	33.8952	0.529613
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	91.1476	1.19354
$19$	−124.246	−1.50021	−0.750105	−	0.661319i	$-0.769997\pi$
$19$	−124.246	−1.50021	−0.750105	+	0.661319i	$0.769997\pi$
$20$	−229.655	−2.56762
$21$	−86.9415	−0.903437
$22$	0	0
$23$	−171.992	−1.55926	−0.779628	−	0.626242i	$-0.784592\pi$
$23$	−171.992	−1.55926	−0.779628	+	0.626242i	$0.784592\pi$
$24$	89.0545	0.757424
$25$	119.998	0.959985
$26$	104.850	0.790873
$27$	129.343	0.921930
$28$	455.071	3.07144
$29$	−229.202	−1.46764	−0.733822	−	0.679342i	$-0.762265\pi$
$29$	−229.202	−1.46764	−0.733822	+	0.679342i	$0.762265\pi$
$30$	−208.915	−1.27142
$31$	12.6553	0.0733210	0.0366605	−	0.999328i	$-0.488328\pi$
$31$	12.6553	0.0733210	0.0366605	+	0.999328i	$0.488328\pi$
$32$	92.7648	0.512458
$33$	0	0
$34$	−80.9460	−0.408298
$35$	−485.474	−2.34457
$36$	−280.862	−1.30029
$37$	−333.938	−1.48376	−0.741878	−	0.670535i	$-0.766065\pi$
$37$	−333.938	−1.48376	−0.741878	+	0.670535i	$0.766065\pi$
$38$	591.601	2.52554
$39$	61.7252	0.253434
$40$	497.273	1.96564
$41$	107.501	0.409485	0.204742	−	0.978816i	$-0.434364\pi$
$41$	107.501	0.409485	0.204742	+	0.978816i	$0.434364\pi$
$42$	413.974	1.52090
$43$	432.159	1.53264	0.766321	−	0.642458i	$-0.222085\pi$
$43$	432.159	1.53264	0.766321	+	0.642458i	$0.222085\pi$
$44$	0	0
$45$	299.626	0.992570
$46$	818.947	2.62494
$47$	−515.957	−1.60128	−0.800639	−	0.599147i	$-0.795506\pi$
$47$	−515.957	−1.60128	−0.800639	+	0.599147i	$0.795506\pi$
$48$	−95.0125	−0.285706
$49$	618.987	1.80463
$50$	−571.375	−1.61609
$51$	−47.6531	−0.130839
$52$	−323.083	−0.861607
$53$	−580.580	−1.50469	−0.752347	−	0.658767i	$-0.771078\pi$
$53$	−580.580	−1.50469	−0.752347	+	0.658767i	$0.771078\pi$
$54$	−615.871	−1.55203
$55$	0	0
$56$	−985.368	−2.35134
$57$	348.277	0.809306
$58$	1091.35	2.47071
$59$	399.381	0.881271	0.440636	−	0.897686i	$-0.354753\pi$
$59$	399.381	0.881271	0.440636	+	0.897686i	$0.354753\pi$
$60$	643.751	1.38513
$61$	−207.426	−0.435380	−0.217690	−	0.976018i	$-0.569852\pi$
$61$	−207.426	−0.435380	−0.217690	+	0.976018i	$0.569852\pi$
$62$	−60.2584	−0.123433
$63$	−593.722	−1.18733
$64$	−712.864	−1.39231
$65$	344.668	0.657705
$66$	0	0
$67$	387.291	0.706196	0.353098	−	0.935586i	$-0.385128\pi$
$67$	387.291	0.706196	0.353098	+	0.935586i	$0.385128\pi$
$68$	249.427	0.444815
$69$	482.116	0.841159
$70$	2311.60	3.94699
$71$	252.618	0.422257	0.211129	−	0.977458i	$-0.432286\pi$
$71$	252.618	0.422257	0.211129	+	0.977458i	$0.432286\pi$
$72$	608.152	0.995436
$73$	−272.871	−0.437495	−0.218748	−	0.975781i	$-0.570197\pi$
$73$	−272.871	−0.437495	−0.218748	+	0.975781i	$0.570197\pi$
$74$	1590.05	2.49784
$75$	−336.370	−0.517875
$76$	−1822.96	−2.75142
$77$	0	0
$78$	−293.906	−0.426645
$79$	730.719	1.04066	0.520331	−	0.853964i	$-0.325808\pi$
$79$	730.719	1.04066	0.520331	+	0.853964i	$0.325808\pi$
$80$	−530.542	−0.741455
$81$	154.283	0.211636
$82$	−511.871	−0.689349
$83$	−1237.09	−1.63600	−0.817999	−	0.575220i	$-0.804916\pi$
$83$	−1237.09	−1.63600	−0.817999	+	0.575220i	$0.804916\pi$
$84$	−1275.62	−1.65692
$85$	−266.091	−0.339549
$86$	−2057.74	−2.58013
$87$	642.480	0.791737
$88$	0	0
$89$	−1014.85	−1.20870	−0.604350	−	0.796719i	$-0.706567\pi$
$89$	−1014.85	−1.20870	−0.604350	+	0.796719i	$0.706567\pi$
$90$	−1426.68	−1.67095
$91$	−682.975	−0.786760
$92$	−2523.50	−2.85971
$93$	−35.4743	−0.0395539
$94$	2456.74	2.69568
$95$	1944.75	2.10029
$96$	−260.031	−0.276451
$97$	−444.659	−0.465447	−0.232723	−	0.972543i	$-0.574764\pi$
$97$	−444.659	−0.465447	−0.232723	+	0.972543i	$0.574764\pi$
$98$	−2947.33	−3.03801
$99$	0	0
$100$	1760.63	1.76063
$101$	0.171655	0.000169112 0	8.45561e−5	−	1.00000i	$-0.499973\pi$
$101$	0.171655	0.000169112 0	8.45561e−5		1.00000i	$0.499973\pi$
$102$	226.902	0.220261
$103$	−476.591	−0.455921	−0.227961	−	0.973670i	$-0.573206\pi$
$103$	−476.591	−0.455921	−0.227961	+	0.973670i	$0.573206\pi$
$104$	699.574	0.659604
$105$	1360.84	1.26481
$106$	2764.45	2.53308
$107$	−717.393	−0.648159	−0.324080	−	0.946030i	$-0.605055\pi$
$107$	−717.393	−0.648159	−0.324080	+	0.946030i	$0.605055\pi$
$108$	1897.74	1.69084
$109$	−850.645	−0.747496	−0.373748	−	0.927530i	$-0.621927\pi$
$109$	−850.645	−0.747496	−0.373748	+	0.927530i	$0.621927\pi$
$110$	0	0
$111$	936.068	0.800429
$112$	1051.29	0.886943
$113$	−282.457	−0.235145	−0.117572	−	0.993064i	$-0.537511\pi$
$113$	−282.457	−0.235145	−0.117572	+	0.993064i	$0.537511\pi$
$114$	−1658.33	−1.36243
$115$	2692.10	2.18295
$116$	−3362.88	−2.69169
$117$	421.520	0.333073
$118$	−1901.67	−1.48358
$119$	527.271	0.406175
$120$	−1393.92	−1.06039
$121$	0	0
$122$	987.666	0.732943
$123$	−301.339	−0.220901
$124$	185.680	0.134472
$125$	78.2918	0.0560210
$126$	2827.03	1.99882
$127$	−2029.56	−1.41806	−0.709032	−	0.705177i	$-0.750868\pi$
$127$	−2029.56	−1.41806	−0.709032	+	0.705177i	$0.750868\pi$
$128$	2652.21	1.83144
$129$	−1211.39	−0.826801
$130$	−1641.15	−1.10722
$131$	623.837	0.416068	0.208034	−	0.978122i	$-0.433294\pi$
$131$	623.837	0.416068	0.208034	+	0.978122i	$0.433294\pi$
$132$	0	0
$133$	−3853.60	−2.51241
$134$	−1844.10	−1.18885
$135$	−2024.53	−1.29070
$136$	−540.086	−0.340529
$137$	−2610.47	−1.62794	−0.813969	−	0.580908i	$-0.802698\pi$
$137$	−2610.47	−1.62794	−0.813969	+	0.580908i	$0.802698\pi$
$138$	−2295.61	−1.41605
$139$	263.626	0.160867	0.0804333	−	0.996760i	$-0.474370\pi$
$139$	263.626	0.160867	0.0804333	+	0.996760i	$0.474370\pi$
$140$	−7122.96	−4.30000
$141$	1446.29	0.863828
$142$	−1202.85	−0.710851
$143$	0	0
$144$	−648.839	−0.375485
$145$	3587.56	2.05469
$146$	1299.28	0.736504
$147$	−1735.10	−0.973527
$148$	−4899.59	−2.72124
$149$	222.793	0.122496	0.0612479	−	0.998123i	$-0.480492\pi$
$149$	222.793	0.122496	0.0612479	+	0.998123i	$0.480492\pi$
$150$	1601.63	0.871819
$151$	1212.83	0.653634	0.326817	−	0.945088i	$-0.394024\pi$
$151$	1212.83	0.653634	0.326817	+	0.945088i	$0.394024\pi$
$152$	3947.26	2.10635
$153$	−325.422	−0.171953
$154$	0	0
$155$	−198.085	−0.102649
$156$	905.642	0.464804
$157$	1969.75	1.00130	0.500648	−	0.865651i	$-0.333095\pi$
$157$	1969.75	1.00130	0.500648	+	0.865651i	$0.333095\pi$
$158$	−3479.34	−1.75191
$159$	1627.44	0.811724
$160$	−1451.99	−0.717439
$161$	−5334.50	−2.61129
$162$	−734.621	−0.356280
$163$	−209.486	−0.100664	−0.0503319	−	0.998733i	$-0.516028\pi$
$163$	−209.486	−0.100664	−0.0503319	+	0.998733i	$0.516028\pi$
$164$	1577.28	0.751004
$165$	0	0
$166$	5890.42	2.75413
$167$	138.082	0.0639825	0.0319913	−	0.999488i	$-0.489815\pi$
$167$	138.082	0.0639825	0.0319913	+	0.999488i	$0.489815\pi$
$168$	2762.11	1.26846
$169$	−1712.11	−0.779296
$170$	1267.00	0.571615
$171$	2378.38	1.06362
$172$	6340.71	2.81090
$173$	784.716	0.344861	0.172430	−	0.985022i	$-0.444838\pi$
$173$	784.716	0.344861	0.172430	+	0.985022i	$0.444838\pi$
$174$	−3059.19	−1.33285
$175$	3721.85	1.60769
$176$	0	0
$177$	−1119.51	−0.475412
$178$	4832.26	2.03479
$179$	−3157.39	−1.31841	−0.659203	−	0.751965i	$-0.729106\pi$
$179$	−3157.39	−1.31841	−0.659203	+	0.751965i	$0.729106\pi$
$180$	4396.17	1.82039
$181$	−953.827	−0.391698	−0.195849	−	0.980634i	$-0.562746\pi$
$181$	−953.827	−0.391698	−0.195849	+	0.980634i	$0.562746\pi$
$182$	3252.00	1.32448
$183$	581.441	0.234871
$184$	5464.16	2.18925
$185$	5226.93	2.07725
$186$	168.912	0.0665872
$187$	0	0
$188$	−7570.21	−2.93678
$189$	4011.70	1.54396
$190$	−9259.99	−3.53574
$191$	399.683	0.151414	0.0757068	−	0.997130i	$-0.475879\pi$
$191$	399.683	0.151414	0.0757068	+	0.997130i	$0.475879\pi$
$192$	1998.25	0.751099
$193$	61.1896	0.0228214	0.0114107	−	0.999935i	$-0.496368\pi$
$193$	61.1896	0.0228214	0.0114107	+	0.999935i	$0.496368\pi$
$194$	2117.26	0.783559
$195$	−966.148	−0.354807
$196$	9081.89	3.30973
$197$	−127.209	−0.0460064	−0.0230032	−	0.999735i	$-0.507323\pi$
$197$	−127.209	−0.0460064	−0.0230032	+	0.999735i	$0.507323\pi$
$198$	0	0
$199$	−4613.00	−1.64325	−0.821625	−	0.570029i	$-0.806932\pi$
$199$	−4613.00	−1.64325	−0.821625	+	0.570029i	$0.806932\pi$
$200$	−3812.31	−1.34785
$201$	−1085.63	−0.380966
$202$	−0.817341	−0.000284693 0
$203$	−7108.90	−2.45787
$204$	−699.174	−0.239961
$205$	−1682.65	−0.573277
$206$	2269.30	0.767523
$207$	3292.37	1.10548
$208$	−746.377	−0.248807
$209$	0	0
$210$	−6479.70	−2.12925
$211$	−4880.38	−1.59232	−0.796160	−	0.605086i	$-0.793139\pi$
$211$	−4880.38	−1.59232	−0.796160	+	0.605086i	$0.793139\pi$
$212$	−8518.36	−2.75964
$213$	−708.120	−0.227791
$214$	3415.89	1.09115
$215$	−6764.33	−2.14569
$216$	−4109.20	−1.29442
$217$	392.515	0.122791
$218$	4050.37	1.25838
$219$	764.892	0.236012
$220$	0	0
$221$	−374.342	−0.113941
$222$	−4457.12	−1.34749
$223$	−202.830	−0.0609081	−0.0304540	−	0.999536i	$-0.509695\pi$
$223$	−202.830	−0.0609081	−0.0304540	+	0.999536i	$0.509695\pi$
$224$	2877.19	0.858215
$225$	−2297.06	−0.680611
$226$	1344.93	0.395856
$227$	−4060.39	−1.18721	−0.593606	−	0.804756i	$-0.702296\pi$
$227$	−4060.39	−1.18721	−0.593606	+	0.804756i	$0.702296\pi$
$228$	5109.98	1.48428
$229$	−1827.65	−0.527399	−0.263700	−	0.964605i	$-0.584943\pi$
$229$	−1827.65	−0.527399	−0.263700	+	0.964605i	$0.584943\pi$
$230$	−12818.5	−3.67490
$231$	0	0
$232$	7281.67	2.06063
$233$	669.878	0.188348	0.0941742	−	0.995556i	$-0.469979\pi$
$233$	669.878	0.188348	0.0941742	+	0.995556i	$0.469979\pi$
$234$	−2007.08	−0.560714
$235$	8075.97	2.24178
$236$	5859.79	1.61627
$237$	−2048.30	−0.561397
$238$	−2510.62	−0.683777
$239$	−4835.06	−1.30859	−0.654297	−	0.756238i	$-0.727035\pi$
$239$	−4835.06	−1.30859	−0.654297	+	0.756238i	$0.727035\pi$
$240$	1487.17	0.399986
$241$	1052.95	0.281438	0.140719	−	0.990050i	$-0.455059\pi$
$241$	1052.95	0.281438	0.140719	+	0.990050i	$0.455059\pi$
$242$	0	0
$243$	−3924.74	−1.03610
$244$	−3043.39	−0.798497
$245$	−9688.65	−2.52647
$246$	1434.84	0.371877
$247$	2735.91	0.704786
$248$	−402.054	−0.102945
$249$	3467.70	0.882557
$250$	−372.789	−0.0943089
$251$	1560.98	0.392543	0.196272	−	0.980550i	$-0.437117\pi$
$251$	1560.98	0.392543	0.196272	+	0.980550i	$0.437117\pi$
$252$	−8711.19	−2.17759
$253$	0	0
$254$	9663.80	2.38725
$255$	745.886	0.183173
$256$	−6925.64	−1.69083
$257$	−818.173	−0.198585	−0.0992923	−	0.995058i	$-0.531658\pi$
$257$	−818.173	−0.198585	−0.0992923	+	0.995058i	$0.531658\pi$
$258$	5768.09	1.39188
$259$	−10357.4	−2.48485
$260$	5057.03	1.20625
$261$	4387.49	1.04053
$262$	−2970.42	−0.700432
$263$	3984.23	0.934139	0.467069	−	0.884221i	$-0.345310\pi$
$263$	3984.23	0.934139	0.467069	+	0.884221i	$0.345310\pi$
$264$	0	0
$265$	9087.47	2.10656
$266$	18349.1	4.22952
$267$	2844.76	0.652047
$268$	5682.40	1.29518
$269$	−6572.13	−1.48963	−0.744814	−	0.667273i	$-0.767462\pi$
$269$	−6572.13	−1.48963	−0.744814	+	0.667273i	$0.767462\pi$
$270$	9639.87	2.17283
$271$	−5085.46	−1.13993	−0.569963	−	0.821670i	$-0.693042\pi$
$271$	−5085.46	−1.13993	−0.569963	+	0.821670i	$0.693042\pi$
$272$	576.219	0.128450
$273$	1914.46	0.424427
$274$	12429.8	2.74056
$275$	0	0
$276$	7073.69	1.54270
$277$	12.4725	0.00270542	0.00135271	−	0.999999i	$-0.499569\pi$
$277$	12.4725	0.00270542	0.00135271	+	0.999999i	$0.499569\pi$
$278$	−1255.26	−0.270812
$279$	−242.253	−0.0519832
$280$	15423.4	3.29187
$281$	4741.31	1.00656	0.503279	−	0.864124i	$-0.332127\pi$
$281$	4741.31	1.00656	0.503279	+	0.864124i	$0.332127\pi$
$282$	−6886.56	−1.45422
$283$	−6186.64	−1.29950	−0.649748	−	0.760149i	$-0.725126\pi$
$283$	−6186.64	−1.29950	−0.649748	+	0.760149i	$0.725126\pi$
$284$	3706.46	0.774429
$285$	−5451.38	−1.13302
$286$	0	0
$287$	3334.25	0.685765
$288$	−1775.75	−0.363323
$289$	289.000	0.0588235
$290$	−17082.3	−3.45898
$291$	1246.44	0.251091
$292$	−4003.61	−0.802376
$293$	6913.06	1.37838	0.689190	−	0.724581i	$-0.257967\pi$
$293$	6913.06	1.37838	0.689190	+	0.724581i	$0.257967\pi$
$294$	8261.72	1.63889
$295$	−6251.28	−1.23377
$296$	10609.1	2.08325
$297$	0	0
$298$	−1060.83	−0.206216
$299$	3787.30	0.732525
$300$	−4935.27	−0.949793
$301$	13403.8	2.56672
$302$	−5774.92	−1.10036
$303$	−0.481171	−9.12295e−5 0
$304$	−4211.35	−0.794530
$305$	3246.72	0.609530
$306$	1549.51	0.289476
$307$	61.7594	0.0114814	0.00574070	−	0.999984i	$-0.498173\pi$
$307$	61.7594	0.0114814	0.00574070	+	0.999984i	$0.498173\pi$
$308$	0	0
$309$	1335.94	0.245952
$310$	943.189	0.172805
$311$	3610.52	0.658308	0.329154	−	0.944276i	$-0.393236\pi$
$311$	3610.52	0.658308	0.329154	+	0.944276i	$0.393236\pi$
$312$	−1960.99	−0.355831
$313$	7940.96	1.43402	0.717012	−	0.697061i	$-0.245509\pi$
$313$	7940.96	1.43402	0.717012	+	0.697061i	$0.245509\pi$
$314$	−9379.04	−1.68564
$315$	9293.19	1.66226
$316$	10721.2	1.90860
$317$	−5111.47	−0.905642	−0.452821	−	0.891601i	$-0.649582\pi$
$317$	−5111.47	−0.905642	−0.452821	+	0.891601i	$0.649582\pi$
$318$	−7749.09	−1.36650
$319$	0	0
$320$	11158.0	1.94923
$321$	2010.94	0.349657
$322$	25400.4	4.39599
$323$	−2112.18	−0.363854
$324$	2263.66	0.388145
$325$	−2642.37	−0.450992
$326$	997.472	0.169463
$327$	2384.46	0.403245
$328$	−3415.29	−0.574932
$329$	−16002.9	−2.68166
$330$	0	0
$331$	10925.0	1.81418	0.907091	−	0.420935i	$-0.138298\pi$
$331$	10925.0	1.81418	0.907091	+	0.420935i	$0.138298\pi$
$332$	−18150.7	−3.00045
$333$	6392.40	1.05196
$334$	−657.480	−0.107712
$335$	−6062.04	−0.988671
$336$	−2946.90	−0.478472
$337$	4844.77	0.783120	0.391560	−	0.920152i	$-0.371935\pi$
$337$	4844.77	0.783120	0.391560	+	0.920152i	$0.371935\pi$
$338$	8152.28	1.31191
$339$	791.763	0.126852
$340$	−3904.13	−0.622739
$341$	0	0
$342$	−11324.7	−1.79056
$343$	8560.00	1.34751
$344$	−13729.6	−2.15189
$345$	−7546.28	−1.17762
$346$	−3736.45	−0.580557
$347$	−1631.72	−0.252436	−0.126218	−	0.992003i	$-0.540284\pi$
$347$	−1631.72	−0.252436	−0.126218	+	0.992003i	$0.540284\pi$
$348$	9426.58	1.45206
$349$	4344.57	0.666360	0.333180	−	0.942863i	$-0.391878\pi$
$349$	4344.57	0.666360	0.333180	+	0.942863i	$0.391878\pi$
$350$	−17721.7	−2.70647
$351$	−2848.15	−0.433114
$352$	0	0
$353$	−6826.27	−1.02925	−0.514626	−	0.857415i	$-0.672069\pi$
$353$	−6826.27	−1.02925	−0.514626	+	0.857415i	$0.672069\pi$
$354$	5330.60	0.800335
$355$	−3954.08	−0.591158
$356$	−14890.1	−2.21678
$357$	−1478.00	−0.219116
$358$	15034.0	2.21948
$359$	−10007.4	−1.47123	−0.735614	−	0.677401i	$-0.763106\pi$
$359$	−10007.4	−1.47123	−0.735614	+	0.677401i	$0.763106\pi$
$360$	−9519.05	−1.39361
$361$	8578.08	1.25063
$362$	4541.67	0.659406
$363$	0	0
$364$	−10020.7	−1.44294
$365$	4271.09	0.612491
$366$	−2768.55	−0.395395
$367$	13281.4	1.88906	0.944529	−	0.328429i	$-0.106519\pi$
$367$	13281.4	1.88906	0.944529	+	0.328429i	$0.106519\pi$
$368$	−5829.72	−0.825802
$369$	−2057.84	−0.290317
$370$	−24888.2	−3.49696
$371$	−18007.2	−2.51991
$372$	−520.484	−0.0725426
$373$	4953.44	0.687613	0.343806	−	0.939041i	$-0.388284\pi$
$373$	4953.44	0.687613	0.343806	+	0.939041i	$0.388284\pi$
$374$	0	0
$375$	−219.462	−0.0302212
$376$	16391.8	2.24825
$377$	5047.05	0.689486
$378$	−19101.8	−2.59918
$379$	−6786.85	−0.919834	−0.459917	−	0.887962i	$-0.652121\pi$
$379$	−6786.85	−0.919834	−0.459917	+	0.887962i	$0.652121\pi$
$380$	28533.7	3.85197
$381$	5689.10	0.764990
$382$	−1903.10	−0.254898
$383$	5497.39	0.733429	0.366714	−	0.930334i	$-0.380483\pi$
$383$	5497.39	0.733429	0.366714	+	0.930334i	$0.380483\pi$
$384$	−7434.46	−0.987990
$385$	0	0
$386$	−291.356	−0.0384187
$387$	−8272.60	−1.08661
$388$	−6524.12	−0.853639
$389$	−5139.47	−0.669875	−0.334938	−	0.942240i	$-0.608715\pi$
$389$	−5139.47	−0.669875	−0.334938	+	0.942240i	$0.608715\pi$
$390$	4600.34	0.597301
$391$	−2923.87	−0.378175
$392$	−19665.1	−2.53376
$393$	−1748.69	−0.224453
$394$	605.709	0.0774497
$395$	−11437.5	−1.45692
$396$	0	0
$397$	6764.78	0.855200	0.427600	−	0.903968i	$-0.359359\pi$
$397$	6764.78	0.855200	0.427600	+	0.903968i	$0.359359\pi$
$398$	21964.9	2.76634
$399$	10802.1	1.35535
$400$	4067.36	0.508420
$401$	548.844	0.0683491	0.0341745	−	0.999416i	$-0.489120\pi$
$401$	548.844	0.0683491	0.0341745	+	0.999416i	$0.489120\pi$
$402$	5169.24	0.641339
$403$	−278.671	−0.0344456
$404$	2.51855	0.000310155 0
$405$	−2414.89	−0.296289
$406$	33849.2	4.13771
$407$	0	0
$408$	1513.93	0.183702
$409$	3384.54	0.409180	0.204590	−	0.978848i	$-0.434414\pi$
$409$	3384.54	0.409180	0.204590	+	0.978848i	$0.434414\pi$
$410$	8012.01	0.965086
$411$	7317.47	0.878210
$412$	−6992.62	−0.836169
$413$	12387.2	1.47587
$414$	−15676.7	−1.86103
$415$	19363.4	2.29039
$416$	−2042.69	−0.240748
$417$	−738.976	−0.0867814
$418$	0	0
$419$	−8369.37	−0.975824	−0.487912	−	0.872893i	$-0.662241\pi$
$419$	−8369.37	−0.975824	−0.487912	+	0.872893i	$0.662241\pi$
$420$	19966.5	2.31968
$421$	−397.774	−0.0460483	−0.0230242	−	0.999735i	$-0.507329\pi$
$421$	−397.774	−0.0460483	−0.0230242	+	0.999735i	$0.507329\pi$
$422$	23238.1	2.68060
$423$	9876.70	1.13528
$424$	18444.9	2.11265
$425$	2039.97	0.232831
$426$	3371.73	0.383477
$427$	−6433.51	−0.729132
$428$	−10525.7	−1.18874
$429$	0	0
$430$	32208.6	3.61217
$431$	13682.3	1.52913	0.764563	−	0.644549i	$-0.222955\pi$
$431$	13682.3	1.52913	0.764563	+	0.644549i	$0.222955\pi$
$432$	4384.11	0.488266
$433$	844.229	0.0936976	0.0468488	−	0.998902i	$-0.485082\pi$
$433$	844.229	0.0936976	0.0468488	+	0.998902i	$0.485082\pi$
$434$	−1868.97	−0.206713
$435$	−10056.4	−1.10843
$436$	−12480.8	−1.37092
$437$	21369.4	2.33921
$438$	−3642.05	−0.397315
$439$	10714.4	1.16485	0.582427	−	0.812883i	$-0.302103\pi$
$439$	10714.4	1.16485	0.582427	+	0.812883i	$0.302103\pi$
$440$	0	0
$441$	−11849.0	−1.27945
$442$	1782.44	0.191815
$443$	413.850	0.0443851	0.0221925	−	0.999754i	$-0.492935\pi$
$443$	413.850	0.0443851	0.0221925	+	0.999754i	$0.492935\pi$
$444$	13734.2	1.46800
$445$	15884.9	1.69217
$446$	965.781	0.102536
$447$	−624.515	−0.0660818
$448$	−22110.1	−2.33171
$449$	−506.426	−0.0532287	−0.0266144	−	0.999646i	$-0.508473\pi$
$449$	−506.426	−0.0532287	−0.0266144	+	0.999646i	$0.508473\pi$
$450$	10937.5	1.14578
$451$	0	0
$452$	−4144.26	−0.431260
$453$	−3399.71	−0.352610
$454$	19333.6	1.99862
$455$	10690.2	1.10146
$456$	−11064.7	−1.13630
$457$	−4194.59	−0.429353	−0.214677	−	0.976685i	$-0.568870\pi$
$457$	−4194.59	−0.429353	−0.214677	+	0.976685i	$0.568870\pi$
$458$	8702.41	0.887853
$459$	2198.83	0.223601
$460$	39498.9	4.00358
$461$	5536.37	0.559337	0.279668	−	0.960097i	$-0.409775\pi$
$461$	5536.37	0.559337	0.279668	+	0.960097i	$0.409775\pi$
$462$	0	0
$463$	6354.72	0.637859	0.318930	−	0.947778i	$-0.396677\pi$
$463$	6354.72	0.637859	0.318930	+	0.947778i	$0.396677\pi$
$464$	−7768.83	−0.777282
$465$	555.258	0.0553752
$466$	−3189.64	−0.317076
$467$	−12291.6	−1.21796	−0.608979	−	0.793187i	$-0.708421\pi$
$467$	−12291.6	−1.21796	−0.608979	+	0.793187i	$0.708421\pi$
$468$	6184.62	0.610863
$469$	12012.2	1.18267
$470$	−38454.0	−3.77394
$471$	−5521.46	−0.540161
$472$	−12688.2	−1.23734
$473$	0	0
$474$	9753.03	0.945087
$475$	−14909.3	−1.44018
$476$	7736.20	0.744934
$477$	11113.7	1.06680
$478$	23022.3	2.20296
$479$	9006.05	0.859075	0.429537	−	0.903049i	$-0.358677\pi$
$479$	9006.05	0.859075	0.429537	+	0.903049i	$0.358677\pi$
$480$	4070.12	0.387031
$481$	7353.35	0.697056
$482$	−5013.65	−0.473788
$483$	14953.3	1.40869
$484$	0	0
$485$	6959.99	0.651623
$486$	18687.8	1.74423
$487$	12678.0	1.17966	0.589831	−	0.807527i	$-0.299194\pi$
$487$	12678.0	1.17966	0.589831	+	0.807527i	$0.299194\pi$
$488$	6589.87	0.611290
$489$	587.214	0.0543042
$490$	46132.8	4.25320
$491$	−7761.34	−0.713369	−0.356684	−	0.934225i	$-0.616093\pi$
$491$	−7761.34	−0.713369	−0.356684	+	0.934225i	$0.616093\pi$
$492$	−4421.30	−0.405138
$493$	−3896.43	−0.355956
$494$	−13027.1	−1.18648
$495$	0	0
$496$	428.953	0.0388317
$497$	7835.18	0.707155
$498$	−16511.6	−1.48575
$499$	−19096.3	−1.71316	−0.856581	−	0.516012i	$-0.827416\pi$
$499$	−19096.3	−1.71316	−0.856581	+	0.516012i	$0.827416\pi$
$500$	1148.71	0.102744
$501$	−387.060	−0.0345161
$502$	−7432.67	−0.660829
$503$	7629.52	0.676309	0.338154	−	0.941091i	$-0.390197\pi$
$503$	7629.52	0.676309	0.338154	+	0.941091i	$0.390197\pi$
$504$	18862.4	1.66706
$505$	−2.68682	−0.000236756 0
$506$	0	0
$507$	4799.27	0.420400
$508$	−29778.0	−2.60076
$509$	−13942.3	−1.21411	−0.607054	−	0.794661i	$-0.707649\pi$
$509$	−13942.3	−1.21411	−0.607054	+	0.794661i	$0.707649\pi$
$510$	−3551.56	−0.308364
$511$	−8463.35	−0.732674
$512$	11759.0	1.01500
$513$	−16070.4	−1.38309
$514$	3895.76	0.334308
$515$	7459.79	0.638287
$516$	−17773.8	−1.51637
$517$	0	0
$518$	49317.0	4.18313
$519$	−2199.66	−0.186039
$520$	−10950.0	−0.923443
$521$	6534.64	0.549496	0.274748	−	0.961516i	$-0.411406\pi$
$521$	6534.64	0.549496	0.274748	+	0.961516i	$0.411406\pi$
$522$	−20891.2	−1.75169
$523$	−6138.93	−0.513264	−0.256632	−	0.966509i	$-0.582613\pi$
$523$	−6138.93	−0.513264	−0.256632	+	0.966509i	$0.582613\pi$
$524$	9153.05	0.763078
$525$	−10432.8	−0.867286
$526$	−18971.1	−1.57258
$527$	215.139	0.0177830
$528$	0	0
$529$	17414.4	1.43128
$530$	−43270.3	−3.54630
$531$	−7645.15	−0.624805
$532$	−56540.7	−4.60780
$533$	−2367.19	−0.192372
$534$	−13545.4	−1.09769
$535$	11228.9	0.907420
$536$	−12304.1	−0.991526
$537$	8850.56	0.711229
$538$	31293.4	2.50772
$539$	0	0
$540$	−29704.3	−2.36716
$541$	13473.6	1.07075	0.535375	−	0.844615i	$-0.320170\pi$
$541$	13473.6	1.07075	0.535375	+	0.844615i	$0.320170\pi$
$542$	24214.6	1.91901
$543$	2673.69	0.211306
$544$	1577.00	0.124289
$545$	13314.6	1.04649
$546$	−9115.77	−0.714504
$547$	1192.49	0.0932121	0.0466060	−	0.998913i	$-0.485159\pi$
$547$	1192.49	0.0932121	0.0466060	+	0.998913i	$0.485159\pi$
$548$	−38301.3	−2.98567
$549$	3970.65	0.308676
$550$	0	0
$551$	28477.4	2.20177
$552$	−15316.7	−1.18102
$553$	22663.9	1.74280
$554$	−59.3883	−0.00455446
$555$	−14651.7	−1.12060
$556$	3867.97	0.295033
$557$	19623.6	1.49278	0.746389	−	0.665510i	$-0.231786\pi$
$557$	19623.6	1.49278	0.746389	+	0.665510i	$0.231786\pi$
$558$	1153.50	0.0875114
$559$	−9516.20	−0.720022
$560$	−16455.2	−1.24172
$561$	0	0
$562$	−22575.9	−1.69450
$563$	16856.0	1.26180	0.630902	−	0.775862i	$-0.282685\pi$
$563$	16856.0	1.26180	0.630902	+	0.775862i	$0.282685\pi$
$564$	21220.2	1.58428
$565$	4421.14	0.329201
$566$	29457.9	2.18764
$567$	4785.22	0.354427
$568$	−8025.61	−0.592865
$569$	4743.81	0.349510	0.174755	−	0.984612i	$-0.444087\pi$
$569$	4743.81	0.349510	0.174755	+	0.984612i	$0.444087\pi$
$570$	25956.9	1.90739
$571$	−8010.13	−0.587064	−0.293532	−	0.955949i	$-0.594831\pi$
$571$	−8010.13	−0.587064	−0.293532	+	0.955949i	$0.594831\pi$
$572$	0	0
$573$	−1120.36	−0.0816818
$574$	−15876.1	−1.15446
$575$	−20638.8	−1.49686
$576$	13646.0	0.987124
$577$	8181.80	0.590317	0.295159	−	0.955448i	$-0.404628\pi$
$577$	8181.80	0.590317	0.295159	+	0.955448i	$0.404628\pi$
$578$	−1376.08	−0.0990268
$579$	−171.522	−0.0123112
$580$	52637.3	3.76835
$581$	−38369.3	−2.73981
$582$	−5934.94	−0.422700
$583$	0	0
$584$	8669.05	0.614260
$585$	−6597.81	−0.466301
$586$	−32916.7	−2.32044
$587$	17342.7	1.21944	0.609718	−	0.792618i	$-0.291283\pi$
$587$	17342.7	1.21944	0.609718	+	0.792618i	$0.291283\pi$
$588$	−25457.7	−1.78547
$589$	−1572.37	−0.109997
$590$	29765.7	2.07700
$591$	356.582	0.0248187
$592$	−11318.9	−0.785816
$593$	17046.7	1.18048	0.590240	−	0.807228i	$-0.299033\pi$
$593$	17046.7	1.18048	0.590240	+	0.807228i	$0.299033\pi$
$594$	0	0
$595$	−8253.06	−0.568643
$596$	3268.85	0.224660
$597$	12930.8	0.886470
$598$	−18033.3	−1.23317
$599$	19558.0	1.33408	0.667042	−	0.745020i	$-0.267560\pi$
$599$	19558.0	1.33408	0.667042	+	0.745020i	$0.267560\pi$
$600$	10686.4	0.727116
$601$	−24358.0	−1.65322	−0.826608	−	0.562778i	$-0.809733\pi$
$601$	−24358.0	−1.65322	−0.826608	+	0.562778i	$0.809733\pi$
$602$	−63822.6	−4.32096
$603$	−7413.72	−0.500680
$604$	17794.8	1.19878
$605$	0	0
$606$	2.29111	0.000153581 0
$607$	−10412.5	−0.696261	−0.348131	−	0.937446i	$-0.613183\pi$
$607$	−10412.5	−0.696261	−0.348131	+	0.937446i	$0.613183\pi$
$608$	−11525.7	−0.768795
$609$	19927.1	1.32592
$610$	−15459.4	−1.02612
$611$	11361.4	0.752266
$612$	−4774.65	−0.315366
$613$	−5540.35	−0.365045	−0.182522	−	0.983202i	$-0.558426\pi$
$613$	−5540.35	−0.365045	−0.182522	+	0.983202i	$0.558426\pi$
$614$	−294.069	−0.0193284
$615$	4716.69	0.309261
$616$	0	0
$617$	−519.156	−0.0338743	−0.0169372	−	0.999857i	$-0.505392\pi$
$617$	−519.156	−0.0338743	−0.0169372	+	0.999857i	$0.505392\pi$
$618$	−6361.13	−0.414049
$619$	−20339.0	−1.32067	−0.660335	−	0.750971i	$-0.729586\pi$
$619$	−20339.0	−1.32067	−0.660335	+	0.750971i	$0.729586\pi$
$620$	−2906.34	−0.188261
$621$	−22246.0	−1.43752
$622$	−17191.6	−1.10823
$623$	−31476.6	−2.02421
$624$	2092.19	0.134222
$625$	−16225.2	−1.03841
$626$	−37811.1	−2.41411
$627$	0	0
$628$	28900.6	1.83640
$629$	−5676.94	−0.359864
$630$	−44249.8	−2.79834
$631$	10728.7	0.676865	0.338432	−	0.940991i	$-0.390103\pi$
$631$	10728.7	0.676865	0.338432	+	0.940991i	$0.390103\pi$
$632$	−23214.8	−1.46113
$633$	13680.3	0.858995
$634$	24338.4	1.52461
$635$	31767.5	1.98528
$636$	23878.0	1.48872
$637$	−13630.2	−0.847798
$638$	0	0
$639$	−4835.74	−0.299372
$640$	−41513.4	−2.56400
$641$	−17072.5	−1.05198	−0.525992	−	0.850489i	$-0.676306\pi$
$641$	−17072.5	−1.05198	−0.525992	+	0.850489i	$0.676306\pi$
$642$	−9575.16	−0.588632
$643$	−501.398	−0.0307515	−0.0153758	−	0.999882i	$-0.504894\pi$
$643$	−501.398	−0.0307515	−0.0153758	+	0.999882i	$0.504894\pi$
$644$	−78268.8	−4.78916
$645$	18961.3	1.15752
$646$	10057.2	0.612533
$647$	−21976.0	−1.33534	−0.667671	−	0.744456i	$-0.732709\pi$
$647$	−21976.0	−1.33534	−0.667671	+	0.744456i	$0.732709\pi$
$648$	−4901.52	−0.297145
$649$	0	0
$650$	12581.7	0.759226
$651$	−1100.27	−0.0662409
$652$	−3073.61	−0.184619
$653$	21546.4	1.29124	0.645618	−	0.763661i	$-0.276600\pi$
$653$	21546.4	1.29124	0.645618	+	0.763661i	$0.276600\pi$
$654$	−11353.7	−0.678845
$655$	−9764.56	−0.582493
$656$	3643.78	0.216868
$657$	5223.44	0.310176
$658$	76198.2	4.51446
$659$	−5930.59	−0.350566	−0.175283	−	0.984518i	$-0.556084\pi$
$659$	−5930.59	−0.350566	−0.175283	+	0.984518i	$0.556084\pi$
$660$	0	0
$661$	25181.2	1.48175	0.740874	−	0.671644i	$-0.234412\pi$
$661$	25181.2	1.48175	0.740874	+	0.671644i	$0.234412\pi$
$662$	−52019.9	−3.05409
$663$	1049.33	0.0614668
$664$	39301.9	2.29700
$665$	60318.2	3.51735
$666$	−30437.6	−1.77092
$667$	39420.9	2.28843
$668$	2025.96	0.117345
$669$	568.558	0.0328576
$670$	28864.6	1.66438
$671$	0	0
$672$	−8065.11	−0.462974
$673$	18231.2	1.04422	0.522112	−	0.852877i	$-0.325144\pi$
$673$	18231.2	1.04422	0.522112	+	0.852877i	$0.325144\pi$
$674$	−23068.5	−1.31835
$675$	15520.9	0.885038
$676$	−25120.4	−1.42925
$677$	−16323.2	−0.926662	−0.463331	−	0.886185i	$-0.653346\pi$
$677$	−16323.2	−0.926662	−0.463331	+	0.886185i	$0.653346\pi$
$678$	−3770.00	−0.213549
$679$	−13791.5	−0.779485
$680$	8453.64	0.476739
$681$	11381.8	0.640455
$682$	0	0
$683$	−30438.0	−1.70524	−0.852618	−	0.522534i	$-0.824987\pi$
$683$	−30438.0	−1.70524	−0.852618	+	0.522534i	$0.824987\pi$
$684$	34896.0	1.95070
$685$	40860.2	2.27910
$686$	−40758.7	−2.26848
$687$	5123.13	0.284512
$688$	14648.1	0.811707
$689$	12784.4	0.706892
$690$	35931.9	1.98247
$691$	−7870.58	−0.433301	−0.216650	−	0.976249i	$-0.569513\pi$
$691$	−7870.58	−0.433301	−0.216650	+	0.976249i	$0.569513\pi$
$692$	11513.5	0.632482
$693$	0	0
$694$	7769.47	0.424964
$695$	−4126.38	−0.225212
$696$	−20411.4	−1.11163
$697$	1827.52	0.0993147
$698$	−20686.8	−1.12179
$699$	−1877.75	−0.101607
$700$	54607.6	2.94854
$701$	28057.8	1.51174	0.755870	−	0.654722i	$-0.227214\pi$
$701$	28057.8	1.51174	0.755870	+	0.654722i	$0.227214\pi$
$702$	13561.6	0.729129
$703$	41490.4	2.22595
$704$	0	0
$705$	−22638.0	−1.20935
$706$	32503.5	1.73270
$707$	5.32404	0.000283213 0
$708$	−16425.7	−0.871915
$709$	−34156.2	−1.80926	−0.904628	−	0.426203i	$-0.859851\pi$
$709$	−34156.2	−1.80926	−0.904628	+	0.426203i	$0.859851\pi$
$710$	18827.5	0.995187
$711$	−13987.8	−0.737810
$712$	32241.6	1.69706
$713$	−2176.61	−0.114326
$714$	7037.57	0.368872
$715$	0	0
$716$	−46325.8	−2.41798
$717$	13553.3	0.705936
$718$	47650.6	2.47675
$719$	8494.74	0.440612	0.220306	−	0.975431i	$-0.429294\pi$
$719$	8494.74	0.440612	0.220306	+	0.975431i	$0.429294\pi$
$720$	10155.9	0.525678
$721$	−14781.9	−0.763532
$722$	−40844.8	−2.10538
$723$	−2951.55	−0.151825
$724$	−13994.7	−0.718383
$725$	−27503.7	−1.40892
$726$	0	0
$727$	−25322.6	−1.29183	−0.645916	−	0.763409i	$-0.723524\pi$
$727$	−25322.6	−1.29183	−0.645916	+	0.763409i	$0.723524\pi$
$728$	21697.9	1.10464
$729$	6835.90	0.347300
$730$	−20336.9	−1.03110
$731$	7346.70	0.371720
$732$	8531.00	0.430758
$733$	−21084.6	−1.06245	−0.531225	−	0.847231i	$-0.678268\pi$
$733$	−21084.6	−1.06245	−0.531225	+	0.847231i	$0.678268\pi$
$734$	−63239.8	−3.18014
$735$	27158.5	1.36293
$736$	−15954.9	−0.799054
$737$	0	0
$738$	9798.48	0.488736
$739$	−18988.3	−0.945192	−0.472596	−	0.881279i	$-0.656683\pi$
$739$	−18988.3	−0.945192	−0.472596	+	0.881279i	$0.656683\pi$
$740$	76690.4	3.80972
$741$	−7669.11	−0.380205
$742$	85741.9	4.24216
$743$	−22186.3	−1.09547	−0.547735	−	0.836652i	$-0.684510\pi$
$743$	−22186.3	−1.09547	−0.547735	+	0.836652i	$0.684510\pi$
$744$	1127.01	0.0555351
$745$	−3487.24	−0.171493
$746$	−23586.0	−1.15757
$747$	23680.9	1.15989
$748$	0	0
$749$	−22250.6	−1.08547
$750$	1044.97	0.0508760
$751$	13901.5	0.675464	0.337732	−	0.941242i	$-0.390340\pi$
$751$	13901.5	0.675464	0.337732	+	0.941242i	$0.390340\pi$
$752$	−17488.5	−0.848057
$753$	−4375.63	−0.211762
$754$	−24031.7	−1.16072
$755$	−18983.7	−0.915083
$756$	58860.3	2.83165
$757$	25290.4	1.21426	0.607129	−	0.794603i	$-0.292321\pi$
$757$	25290.4	1.21426	0.607129	+	0.794603i	$0.292321\pi$
$758$	32315.8	1.54850
$759$	0	0
$760$	−61784.2	−2.94888
$761$	10403.7	0.495577	0.247788	−	0.968814i	$-0.420296\pi$
$761$	10403.7	0.495577	0.247788	+	0.968814i	$0.420296\pi$
$762$	−27088.8	−1.28783
$763$	−26383.5	−1.25183
$764$	5864.21	0.277696
$765$	5093.65	0.240734
$766$	−26176.0	−1.23469
$767$	−8794.43	−0.414014
$768$	19413.4	0.912138
$769$	7634.97	0.358029	0.179014	−	0.983846i	$-0.442709\pi$
$769$	7634.97	0.358029	0.179014	+	0.983846i	$0.442709\pi$
$770$	0	0
$771$	2293.44	0.107129
$772$	897.784	0.0418549
$773$	−7342.65	−0.341652	−0.170826	−	0.985301i	$-0.554644\pi$
$773$	−7342.65	−0.341652	−0.170826	+	0.985301i	$0.554644\pi$
$774$	39390.2	1.82927
$775$	1518.61	0.0703871
$776$	14126.7	0.653504
$777$	29033.0	1.34048
$778$	24471.7	1.12770
$779$	−13356.6	−0.614313
$780$	−14175.5	−0.650723
$781$	0	0
$782$	13922.1	0.636641
$783$	−29645.6	−1.35306
$784$	20980.7	0.955754
$785$	−30831.4	−1.40181
$786$	8326.46	0.377856
$787$	−16160.8	−0.731981	−0.365991	−	0.930619i	$-0.619270\pi$
$787$	−16160.8	−0.731981	−0.365991	+	0.930619i	$0.619270\pi$
$788$	−1866.43	−0.0843767
$789$	−11168.3	−0.503932
$790$	54460.1	2.45266
$791$	−8760.67	−0.393797
$792$	0	0
$793$	4567.55	0.204538
$794$	−32210.7	−1.43969
$795$	−25473.3	−1.13641
$796$	−67682.7	−3.01375
$797$	−34853.8	−1.54904	−0.774519	−	0.632551i	$-0.782008\pi$
$797$	−34853.8	−1.54904	−0.774519	+	0.632551i	$0.782008\pi$
$798$	−51434.7	−2.28166
$799$	−8771.27	−0.388367
$800$	11131.6	0.491952
$801$	19426.8	0.856945
$802$	−2613.34	−0.115063
$803$	0	0
$804$	−15928.5	−0.698699
$805$	83497.9	3.65579
$806$	1326.90	0.0579876
$807$	18422.5	0.803596
$808$	−5.45344	−0.000237440 0
$809$	−21825.1	−0.948490	−0.474245	−	0.880393i	$-0.657279\pi$
$809$	−21825.1	−0.948490	−0.474245	+	0.880393i	$0.657279\pi$
$810$	11498.6	0.498789
$811$	−32981.9	−1.42805	−0.714027	−	0.700118i	$-0.753131\pi$
$811$	−32981.9	−1.42805	−0.714027	+	0.700118i	$0.753131\pi$
$812$	−104303.	−4.50778
$813$	14255.2	0.614946
$814$	0	0
$815$	3278.96	0.140929
$816$	−1615.21	−0.0692938
$817$	−53694.0	−2.29929
$818$	−16115.6	−0.688836
$819$	13073.8	0.557799
$820$	−24688.2	−1.05140
$821$	29373.4	1.24865	0.624323	−	0.781166i	$-0.285375\pi$
$821$	29373.4	1.24865	0.624323	+	0.781166i	$0.285375\pi$
$822$	−34842.4	−1.47843
$823$	18054.3	0.764681	0.382341	−	0.924021i	$-0.375118\pi$
$823$	18054.3	0.764681	0.382341	+	0.924021i	$0.375118\pi$
$824$	15141.2	0.640130
$825$	0	0
$826$	−58981.9	−2.48456
$827$	−5138.73	−0.216072	−0.108036	−	0.994147i	$-0.534456\pi$
$827$	−5138.73	−0.216072	−0.108036	+	0.994147i	$0.534456\pi$
$828$	48306.1	2.02748
$829$	25985.7	1.08869	0.544344	−	0.838862i	$-0.316779\pi$
$829$	25985.7	1.08869	0.544344	+	0.838862i	$0.316779\pi$
$830$	−92199.3	−3.85576
$831$	−34.9621	−0.00145947
$832$	15697.4	0.654097
$833$	10522.8	0.437686
$834$	3518.66	0.146093
$835$	−2161.31	−0.0895752
$836$	0	0
$837$	1636.87	0.0675968
$838$	39851.0	1.64276
$839$	−9834.71	−0.404686	−0.202343	−	0.979315i	$-0.564856\pi$
$839$	−9834.71	−0.404686	−0.202343	+	0.979315i	$0.564856\pi$
$840$	−43233.7	−1.77584
$841$	28144.3	1.15398
$842$	1894.01	0.0775202
$843$	−13290.5	−0.542999
$844$	−71605.8	−2.92035
$845$	26798.7	1.09101
$846$	−47028.2	−1.91119
$847$	0	0
$848$	−19678.9	−0.796905
$849$	17341.9	0.701028
$850$	−9713.37	−0.391960
$851$	57434.7	2.31356
$852$	−10389.7	−0.417774
$853$	3826.99	0.153615	0.0768075	−	0.997046i	$-0.475527\pi$
$853$	3826.99	0.153615	0.0768075	+	0.997046i	$0.475527\pi$
$854$	30633.4	1.22746
$855$	−37227.4	−1.48906
$856$	22791.4	0.910040
$857$	978.834	0.0390156	0.0195078	−	0.999810i	$-0.493790\pi$
$857$	978.834	0.0390156	0.0195078	+	0.999810i	$0.493790\pi$
$858$	0	0
$859$	−18936.0	−0.752142	−0.376071	−	0.926591i	$-0.622725\pi$
$859$	−18936.0	−0.752142	−0.376071	+	0.926591i	$0.622725\pi$
$860$	−99247.4	−3.93524
$861$	−9346.32	−0.369944
$862$	−65148.7	−2.57421
$863$	−18757.1	−0.739859	−0.369930	−	0.929060i	$-0.620618\pi$
$863$	−18757.1	−0.739859	−0.369930	+	0.929060i	$0.620618\pi$
$864$	11998.5	0.472450
$865$	−12282.7	−0.482803
$866$	−4019.82	−0.157736
$867$	−810.103	−0.0317330
$868$	5759.04	0.225201
$869$	0	0
$870$	47883.7	1.86599
$871$	−8528.21	−0.331765
$872$	27024.8	1.04951
$873$	8511.89	0.329993
$874$	−101751.	−3.93796
$875$	2428.29	0.0938186
$876$	11222.6	0.432851
$877$	−13776.0	−0.530424	−0.265212	−	0.964190i	$-0.585442\pi$
$877$	−13776.0	−0.530424	−0.265212	+	0.964190i	$0.585442\pi$
$878$	−51017.0	−1.96098
$879$	−19378.2	−0.743583
$880$	0	0
$881$	24259.6	0.927727	0.463863	−	0.885907i	$-0.346463\pi$
$881$	24259.6	0.927727	0.463863	+	0.885907i	$0.346463\pi$
$882$	56419.2	2.15389
$883$	−15361.0	−0.585434	−0.292717	−	0.956199i	$-0.594559\pi$
$883$	−15361.0	−0.585434	−0.292717	+	0.956199i	$0.594559\pi$
$884$	−5492.41	−0.208970
$885$	17523.1	0.665574
$886$	−1970.56	−0.0747203
$887$	23674.9	0.896197	0.448098	−	0.893984i	$-0.352101\pi$
$887$	23674.9	0.896197	0.448098	+	0.893984i	$0.352101\pi$
$888$	−29738.6	−1.12383
$889$	−62948.6	−2.37483
$890$	−75636.5	−2.84870
$891$	0	0
$892$	−2975.96	−0.111707
$893$	64105.6	2.40225
$894$	2973.65	0.111246
$895$	49420.8	1.84576
$896$	82260.6	3.06711
$897$	−10616.3	−0.395169
$898$	2411.36	0.0896082
$899$	−2900.60	−0.107609
$900$	−33702.9	−1.24826
$901$	−9869.85	−0.364942
$902$	0	0
$903$	−37572.5	−1.38465
$904$	8973.60	0.330152
$905$	14929.7	0.548375
$906$	16187.8	0.593603
$907$	−18240.6	−0.667770	−0.333885	−	0.942614i	$-0.608360\pi$
$907$	−18240.6	−0.667770	−0.333885	+	0.942614i	$0.608360\pi$
$908$	−59574.7	−2.17737
$909$	−3.28591	−0.000119897 0
$910$	−50901.7	−1.85426
$911$	9874.55	0.359120	0.179560	−	0.983747i	$-0.442533\pi$
$911$	9874.55	0.359120	0.179560	+	0.983747i	$0.442533\pi$
$912$	11804.9	0.428618
$913$	0	0
$914$	19972.6	0.722797
$915$	−9100.96	−0.328818
$916$	−26815.6	−0.967262
$917$	19348.9	0.696790
$918$	−10469.8	−0.376422
$919$	−13878.0	−0.498143	−0.249072	−	0.968485i	$-0.580125\pi$
$919$	−13878.0	−0.498143	−0.249072	+	0.968485i	$0.580125\pi$
$920$	−85527.2	−3.06494
$921$	−173.119	−0.00619378
$922$	−26361.6	−0.941619
$923$	−5562.68	−0.198373
$924$	0	0
$925$	−40071.9	−1.42438
$926$	−30258.2	−1.07381
$927$	9123.13	0.323239
$928$	−21261.8	−0.752106
$929$	16278.7	0.574905	0.287453	−	0.957795i	$-0.407192\pi$
$929$	16278.7	0.574905	0.287453	+	0.957795i	$0.407192\pi$
$930$	−2643.88	−0.0932217
$931$	−76906.7	−2.70732
$932$	9828.56	0.345435
$933$	−10120.7	−0.355132
$934$	58526.7	2.05038
$935$	0	0
$936$	−13391.6	−0.467647
$937$	−40352.6	−1.40690	−0.703448	−	0.710747i	$-0.748357\pi$
$937$	−40352.6	−1.40690	−0.703448	+	0.710747i	$0.748357\pi$
$938$	−57196.4	−1.99097
$939$	−22259.5	−0.773600
$940$	118492.	4.11147
$941$	−38383.9	−1.32973	−0.664867	−	0.746962i	$-0.731512\pi$
$941$	−38383.9	−1.32973	−0.664867	+	0.746962i	$0.731512\pi$
$942$	26290.6	0.909336
$943$	−18489.4	−0.638492
$944$	13537.1	0.466732
$945$	−62792.7	−2.16153
$946$	0	0
$947$	−11968.7	−0.410697	−0.205349	−	0.978689i	$-0.565833\pi$
$947$	−11968.7	−0.410697	−0.205349	+	0.978689i	$0.565833\pi$
$948$	−30053.0	−1.02961
$949$	6008.66	0.205531
$950$	70991.0	2.42448
$951$	14328.1	0.488559
$952$	−16751.3	−0.570285
$953$	45178.8	1.53566	0.767830	−	0.640654i	$-0.221337\pi$
$953$	45178.8	1.53566	0.767830	+	0.640654i	$0.221337\pi$
$954$	−52918.4	−1.79591
$955$	−6256.00	−0.211978
$956$	−70940.8	−2.39999
$957$	0	0
$958$	−42882.6	−1.44621
$959$	−80966.1	−2.72631
$960$	−31277.4	−1.05153
$961$	−29630.8	−0.994624
$962$	−35013.2	−1.17346
$963$	13732.7	0.459533
$964$	15449.1	0.516163
$965$	−957.765	−0.0319498
$966$	−71200.5	−2.37147
$967$	25079.3	0.834019	0.417010	−	0.908902i	$-0.363078\pi$
$967$	25079.3	0.834019	0.417010	+	0.908902i	$0.363078\pi$
$968$	0	0
$969$	5920.71	0.196285
$970$	−33140.2	−1.09698
$971$	368.571	0.0121813	0.00609063	−	0.999981i	$-0.498061\pi$
$971$	368.571	0.0121813	0.00609063	+	0.999981i	$0.498061\pi$
$972$	−57584.4	−1.90023
$973$	8176.60	0.269404
$974$	−60366.7	−1.98591
$975$	7406.90	0.243293
$976$	−7030.75	−0.230583
$977$	32949.5	1.07896	0.539482	−	0.841997i	$-0.318620\pi$
$977$	32949.5	1.07896	0.539482	+	0.841997i	$0.318620\pi$
$978$	−2796.04	−0.0914187
$979$	0	0
$980$	−142153.	−4.63360
$981$	16283.5	0.529960
$982$	36955.8	1.20092
$983$	46857.1	1.52035	0.760177	−	0.649716i	$-0.225112\pi$
$983$	46857.1	1.52035	0.760177	+	0.649716i	$0.225112\pi$
$984$	9573.48	0.310154
$985$	1991.13	0.0644087
$986$	18552.9	0.599236
$987$	44858.1	1.44665
$988$	40141.8	1.29259
$989$	−74328.1	−2.38978
$990$	0	0
$991$	−32620.8	−1.04565	−0.522823	−	0.852441i	$-0.675121\pi$
$991$	−32620.8	−1.04565	−0.522823	+	0.852441i	$0.675121\pi$
$992$	1173.96	0.0375740
$993$	−30624.2	−0.978681
$994$	−37307.5	−1.19046
$995$	72204.5	2.30054
$996$	50878.7	1.61863
$997$	−44474.9	−1.41277	−0.706385	−	0.707827i	$-0.749675\pi$
$997$	−44474.9	−1.41277	−0.706385	+	0.707827i	$0.749675\pi$
$998$	90927.7	2.88403
$999$	−43192.5	−1.36792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2057.4.a.i.1.1		10
11.10	odd	2		187.4.a.d.1.10	✓	10
33.32	even	2		1683.4.a.m.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.4.a.d.1.10	✓	10	11.10	odd	2
1683.4.a.m.1.1		10	33.32	even	2
2057.4.a.i.1.1		10	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:	\( N \)	\(=\)	\( 2057 = 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2057.a (trivial)

\(f(q)\)	\(=\)	\(q-4.76153 q^{2} -2.80312 q^{3} +14.6722 q^{4} -15.6524 q^{5} +13.3472 q^{6} +31.0159 q^{7} -31.7697 q^{8} -19.1425 q^{9} +O(q^{10})\)	\(q-4.76153 q^{2} -2.80312 q^{3} +14.6722 q^{4} -15.6524 q^{5} +13.3472 q^{6} +31.0159 q^{7} -31.7697 q^{8} -19.1425 q^{9} +74.5294 q^{10} -41.1279 q^{12} -22.0201 q^{13} -147.683 q^{14} +43.8757 q^{15} +33.8952 q^{16} +17.0000 q^{17} +91.1476 q^{18} -124.246 q^{19} -229.655 q^{20} -86.9415 q^{21} -171.992 q^{23} +89.0545 q^{24} +119.998 q^{25} +104.850 q^{26} +129.343 q^{27} +455.071 q^{28} -229.202 q^{29} -208.915 q^{30} +12.6553 q^{31} +92.7648 q^{32} -80.9460 q^{34} -485.474 q^{35} -280.862 q^{36} -333.938 q^{37} +591.601 q^{38} +61.7252 q^{39} +497.273 q^{40} +107.501 q^{41} +413.974 q^{42} +432.159 q^{43} +299.626 q^{45} +818.947 q^{46} -515.957 q^{47} -95.0125 q^{48} +618.987 q^{49} -571.375 q^{50} -47.6531 q^{51} -323.083 q^{52} -580.580 q^{53} -615.871 q^{54} -985.368 q^{56} +348.277 q^{57} +1091.35 q^{58} +399.381 q^{59} +643.751 q^{60} -207.426 q^{61} -60.2584 q^{62} -593.722 q^{63} -712.864 q^{64} +344.668 q^{65} +387.291 q^{67} +249.427 q^{68} +482.116 q^{69} +2311.60 q^{70} +252.618 q^{71} +608.152 q^{72} -272.871 q^{73} +1590.05 q^{74} -336.370 q^{75} -1822.96 q^{76} -293.906 q^{78} +730.719 q^{79} -530.542 q^{80} +154.283 q^{81} -511.871 q^{82} -1237.09 q^{83} -1275.62 q^{84} -266.091 q^{85} -2057.74 q^{86} +642.480 q^{87} -1014.85 q^{89} -1426.68 q^{90} -682.975 q^{91} -2523.50 q^{92} -35.4743 q^{93} +2456.74 q^{94} +1944.75 q^{95} -260.031 q^{96} -444.659 q^{97} -2947.33 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{2} - 9 q^{3} + 40 q^{4} - 41 q^{5} - 31 q^{6} + 63 q^{7} + 96 q^{8} + 61 q^{9}+O(q^{10}) \) 10 * q + 8 * q^2 - 9 * q^3 + 40 * q^4 - 41 * q^5 - 31 * q^6 + 63 * q^7 + 96 * q^8 + 61 * q^9	\( 10 q + 8 q^{2} - 9 q^{3} + 40 q^{4} - 41 q^{5} - 31 q^{6} + 63 q^{7} + 96 q^{8} + 61 q^{9} + 47 q^{10} - 171 q^{12} + 99 q^{13} - 95 q^{14} - 150 q^{15} + 180 q^{16} + 170 q^{17} + 207 q^{18} + 73 q^{19} - 343 q^{20} + 152 q^{21} - 58 q^{23} - 157 q^{24} + 529 q^{25} - 285 q^{26} - 246 q^{27} + 1031 q^{28} + 754 q^{29} + 754 q^{30} - 228 q^{31} + 466 q^{32} + 136 q^{34} - 20 q^{35} - 535 q^{36} - 1177 q^{37} - 747 q^{38} + 791 q^{39} - 537 q^{40} + 327 q^{41} - 632 q^{42} + 487 q^{43} - 834 q^{45} + 854 q^{46} - 573 q^{47} - 1857 q^{48} + 2215 q^{49} + 855 q^{50} - 153 q^{51} - 1673 q^{52} - 2022 q^{53} - 3572 q^{54} + 1997 q^{56} + 1310 q^{57} + 4514 q^{58} - 602 q^{59} + 4936 q^{60} + 570 q^{61} - 166 q^{62} + 1903 q^{63} + 968 q^{64} + 2018 q^{65} - 12 q^{67} + 680 q^{68} - 1034 q^{69} + 5460 q^{70} + 636 q^{71} + 2989 q^{72} + 201 q^{73} - 959 q^{74} + 3213 q^{75} - 6999 q^{76} + 3669 q^{78} + 1097 q^{79} - 1409 q^{80} + 3554 q^{81} + 2249 q^{82} + 477 q^{83} - 8476 q^{84} - 697 q^{85} - 1271 q^{86} - 1782 q^{87} - 195 q^{89} - 3292 q^{90} - 1128 q^{91} - 2064 q^{92} - 2632 q^{93} - 465 q^{94} + 1644 q^{95} - 8367 q^{96} - 994 q^{97} - 225 q^{98}+O(q^{100}) \) 10 * q + 8 * q^2 - 9 * q^3 + 40 * q^4 - 41 * q^5 - 31 * q^6 + 63 * q^7 + 96 * q^8 + 61 * q^9 + 47 * q^10 - 171 * q^12 + 99 * q^13 - 95 * q^14 - 150 * q^15 + 180 * q^16 + 170 * q^17 + 207 * q^18 + 73 * q^19 - 343 * q^20 + 152 * q^21 - 58 * q^23 - 157 * q^24 + 529 * q^25 - 285 * q^26 - 246 * q^27 + 1031 * q^28 + 754 * q^29 + 754 * q^30 - 228 * q^31 + 466 * q^32 + 136 * q^34 - 20 * q^35 - 535 * q^36 - 1177 * q^37 - 747 * q^38 + 791 * q^39 - 537 * q^40 + 327 * q^41 - 632 * q^42 + 487 * q^43 - 834 * q^45 + 854 * q^46 - 573 * q^47 - 1857 * q^48 + 2215 * q^49 + 855 * q^50 - 153 * q^51 - 1673 * q^52 - 2022 * q^53 - 3572 * q^54 + 1997 * q^56 + 1310 * q^57 + 4514 * q^58 - 602 * q^59 + 4936 * q^60 + 570 * q^61 - 166 * q^62 + 1903 * q^63 + 968 * q^64 + 2018 * q^65 - 12 * q^67 + 680 * q^68 - 1034 * q^69 + 5460 * q^70 + 636 * q^71 + 2989 * q^72 + 201 * q^73 - 959 * q^74 + 3213 * q^75 - 6999 * q^76 + 3669 * q^78 + 1097 * q^79 - 1409 * q^80 + 3554 * q^81 + 2249 * q^82 + 477 * q^83 - 8476 * q^84 - 697 * q^85 - 1271 * q^86 - 1782 * q^87 - 195 * q^89 - 3292 * q^90 - 1128 * q^91 - 2064 * q^92 - 2632 * q^93 - 465 * q^94 + 1644 * q^95 - 8367 * q^96 - 994 * q^97 - 225 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more