LMFDB - Embedded newform 1617.4.a.z.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.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:	$95.4060884793$
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} - 4 x^{9} - 45 x^{8} + 168 x^{7} + 651 x^{6} - 2176 x^{5} - 3439 x^{4} + 8716 x^{3} + 7840 x^{2} + \cdots - 4032 $ x^10 - 4x^9 - 45x^8 + 168x^7 + 651x^6 - 2176x^5 - 3439x^4 + 8716x^3 + 7840x^2 - 9216*x - 4032
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$4.14909$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.14909 q^{2} +3.00000 q^{3} +9.21491 q^{4} +21.1121 q^{5} +12.4473 q^{6} +5.04076 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.14909 q^{2} +3.00000 q^{3} +9.21491 q^{4} +21.1121 q^{5} +12.4473 q^{6} +5.04076 q^{8} +9.00000 q^{9} +87.5957 q^{10} -11.0000 q^{11} +27.6447 q^{12} +70.8685 q^{13} +63.3362 q^{15} -52.8047 q^{16} -65.4434 q^{17} +37.3418 q^{18} +139.664 q^{19} +194.546 q^{20} -45.6399 q^{22} +16.2797 q^{23} +15.1223 q^{24} +320.719 q^{25} +294.039 q^{26} +27.0000 q^{27} -38.0026 q^{29} +262.787 q^{30} -12.5663 q^{31} -259.417 q^{32} -33.0000 q^{33} -271.530 q^{34} +82.9342 q^{36} -327.482 q^{37} +579.479 q^{38} +212.605 q^{39} +106.421 q^{40} +57.1522 q^{41} -202.383 q^{43} -101.364 q^{44} +190.008 q^{45} +67.5458 q^{46} -226.903 q^{47} -158.414 q^{48} +1330.69 q^{50} -196.330 q^{51} +653.046 q^{52} +503.459 q^{53} +112.025 q^{54} -232.233 q^{55} +418.993 q^{57} -157.676 q^{58} +225.260 q^{59} +583.637 q^{60} -258.774 q^{61} -52.1388 q^{62} -653.907 q^{64} +1496.18 q^{65} -136.920 q^{66} +814.894 q^{67} -603.055 q^{68} +48.8390 q^{69} +1012.06 q^{71} +45.3668 q^{72} +316.707 q^{73} -1358.75 q^{74} +962.156 q^{75} +1286.99 q^{76} +882.118 q^{78} -364.813 q^{79} -1114.82 q^{80} +81.0000 q^{81} +237.129 q^{82} +47.5254 q^{83} -1381.65 q^{85} -839.704 q^{86} -114.008 q^{87} -55.4483 q^{88} -750.827 q^{89} +788.361 q^{90} +150.016 q^{92} -37.6990 q^{93} -941.440 q^{94} +2948.60 q^{95} -778.252 q^{96} -883.329 q^{97} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9} + 44 q^{10} - 110 q^{11} + 78 q^{12} + 82 q^{13} + 60 q^{15} - 10 q^{16} + 164 q^{17} + 36 q^{18} - 76 q^{19} + 356 q^{20} - 44 q^{22} + 140 q^{23} + 108 q^{24} + 472 q^{25} + 360 q^{26} + 270 q^{27} + 40 q^{29} + 132 q^{30} + 24 q^{31} + 112 q^{32} - 330 q^{33} - 262 q^{34} + 234 q^{36} + 412 q^{37} + 16 q^{38} + 246 q^{39} + 828 q^{40} - 228 q^{41} + 530 q^{43} - 286 q^{44} + 180 q^{45} + 1422 q^{46} + 768 q^{47} - 30 q^{48} + 670 q^{50} + 492 q^{51} + 952 q^{52} + 136 q^{53} + 108 q^{54} - 220 q^{55} - 228 q^{57} + 1708 q^{58} + 608 q^{59} + 1068 q^{60} + 1618 q^{61} + 164 q^{62} - 1238 q^{64} + 2764 q^{65} - 132 q^{66} + 1002 q^{67} + 2816 q^{68} + 420 q^{69} + 812 q^{71} + 324 q^{72} + 134 q^{73} + 342 q^{74} + 1416 q^{75} - 450 q^{76} + 1080 q^{78} + 1262 q^{79} - 1316 q^{80} + 810 q^{81} + 982 q^{82} + 1078 q^{83} - 1402 q^{85} + 1692 q^{86} + 120 q^{87} - 396 q^{88} + 2880 q^{89} + 396 q^{90} + 2364 q^{92} + 72 q^{93} - 2362 q^{94} + 2866 q^{95} + 336 q^{96} - 1030 q^{97} - 990 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9 + 44 * q^10 - 110 * q^11 + 78 * q^12 + 82 * q^13 + 60 * q^15 - 10 * q^16 + 164 * q^17 + 36 * q^18 - 76 * q^19 + 356 * q^20 - 44 * q^22 + 140 * q^23 + 108 * q^24 + 472 * q^25 + 360 * q^26 + 270 * q^27 + 40 * q^29 + 132 * q^30 + 24 * q^31 + 112 * q^32 - 330 * q^33 - 262 * q^34 + 234 * q^36 + 412 * q^37 + 16 * q^38 + 246 * q^39 + 828 * q^40 - 228 * q^41 + 530 * q^43 - 286 * q^44 + 180 * q^45 + 1422 * q^46 + 768 * q^47 - 30 * q^48 + 670 * q^50 + 492 * q^51 + 952 * q^52 + 136 * q^53 + 108 * q^54 - 220 * q^55 - 228 * q^57 + 1708 * q^58 + 608 * q^59 + 1068 * q^60 + 1618 * q^61 + 164 * q^62 - 1238 * q^64 + 2764 * q^65 - 132 * q^66 + 1002 * q^67 + 2816 * q^68 + 420 * q^69 + 812 * q^71 + 324 * q^72 + 134 * q^73 + 342 * q^74 + 1416 * q^75 - 450 * q^76 + 1080 * q^78 + 1262 * q^79 - 1316 * q^80 + 810 * q^81 + 982 * q^82 + 1078 * q^83 - 1402 * q^85 + 1692 * q^86 + 120 * q^87 - 396 * q^88 + 2880 * q^89 + 396 * q^90 + 2364 * q^92 + 72 * q^93 - 2362 * q^94 + 2866 * q^95 + 336 * q^96 - 1030 * q^97 - 990 * 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 $

$2$	4.14909	1.46692	0.733462	−	0.679731i	$-0.237903\pi$
$2$	4.14909	1.46692	0.733462	+	0.679731i	$0.237903\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	9.21491	1.15186
$5$	21.1121	1.88832	0.944160	−	0.329488i	$-0.106876\pi$
$5$	21.1121	1.88832	0.944160	+	0.329488i	$0.106876\pi$
$6$	12.4473	0.846928
$7$	0	0
$7$	0	0
$8$	5.04076	0.222772
$9$	9.00000	0.333333
$10$	87.5957	2.77002
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	27.6447	0.665029
$13$	70.8685	1.51195	0.755976	−	0.654599i	$-0.227163\pi$
$13$	70.8685	1.51195	0.755976	+	0.654599i	$0.227163\pi$
$14$	0	0
$15$	63.3362	1.09022
$16$	−52.8047	−0.825074
$17$	−65.4434	−0.933669	−0.466834	−	0.884345i	$-0.654606\pi$
$17$	−65.4434	−0.933669	−0.466834	+	0.884345i	$0.654606\pi$
$18$	37.3418	0.488974
$19$	139.664	1.68638	0.843189	−	0.537617i	$-0.180675\pi$
$19$	139.664	1.68638	0.843189	+	0.537617i	$0.180675\pi$
$20$	194.546	2.17509
$21$	0	0
$22$	−45.6399	−0.442294
$23$	16.2797	0.147589	0.0737945	−	0.997273i	$-0.476489\pi$
$23$	16.2797	0.147589	0.0737945	+	0.997273i	$0.476489\pi$
$24$	15.1223	0.128618
$25$	320.719	2.56575
$26$	294.039	2.21792
$27$	27.0000	0.192450
$28$	0	0
$29$	−38.0026	−0.243341	−0.121671	−	0.992571i	$-0.538825\pi$
$29$	−38.0026	−0.243341	−0.121671	+	0.992571i	$0.538825\pi$
$30$	262.787	1.59927
$31$	−12.5663	−0.0728058	−0.0364029	−	0.999337i	$-0.511590\pi$
$31$	−12.5663	−0.0728058	−0.0364029	+	0.999337i	$0.511590\pi$
$32$	−259.417	−1.43309
$33$	−33.0000	−0.174078
$34$	−271.530	−1.36962
$35$	0	0
$36$	82.9342	0.383954
$37$	−327.482	−1.45507	−0.727537	−	0.686069i	$-0.759335\pi$
$37$	−327.482	−1.45507	−0.727537	+	0.686069i	$0.759335\pi$
$38$	579.479	2.47379
$39$	212.605	0.872926
$40$	106.421	0.420665
$41$	57.1522	0.217699	0.108850	−	0.994058i	$-0.465283\pi$
$41$	57.1522	0.217699	0.108850	+	0.994058i	$0.465283\pi$
$42$	0	0
$43$	−202.383	−0.717746	−0.358873	−	0.933386i	$-0.616839\pi$
$43$	−202.383	−0.717746	−0.358873	+	0.933386i	$0.616839\pi$
$44$	−101.364	−0.347300
$45$	190.008	0.629440
$46$	67.5458	0.216502
$47$	−226.903	−0.704196	−0.352098	−	0.935963i	$-0.614532\pi$
$47$	−226.903	−0.704196	−0.352098	+	0.935963i	$0.614532\pi$
$48$	−158.414	−0.476357
$49$	0	0
$50$	1330.69	3.76376
$51$	−196.330	−0.539054
$52$	653.046	1.74156
$53$	503.459	1.30482	0.652410	−	0.757867i	$-0.273758\pi$
$53$	503.459	1.30482	0.652410	+	0.757867i	$0.273758\pi$
$54$	112.025	0.282309
$55$	−232.233	−0.569350
$56$	0	0
$57$	418.993	0.973631
$58$	−157.676	−0.356963
$59$	225.260	0.497057	0.248528	−	0.968625i	$-0.420053\pi$
$59$	225.260	0.497057	0.248528	+	0.968625i	$0.420053\pi$
$60$	583.637	1.25579
$61$	−258.774	−0.543158	−0.271579	−	0.962416i	$-0.587546\pi$
$61$	−258.774	−0.543158	−0.271579	+	0.962416i	$0.587546\pi$
$62$	−52.1388	−0.106800
$63$	0	0
$64$	−653.907	−1.27716
$65$	1496.18	2.85505
$66$	−136.920	−0.255359
$67$	814.894	1.48590	0.742949	−	0.669348i	$-0.233426\pi$
$67$	814.894	1.48590	0.742949	+	0.669348i	$0.233426\pi$
$68$	−603.055	−1.07546
$69$	48.8390	0.0852106
$70$	0	0
$71$	1012.06	1.69168	0.845842	−	0.533433i	$-0.179098\pi$
$71$	1012.06	1.69168	0.845842	+	0.533433i	$0.179098\pi$
$72$	45.3668	0.0742574
$73$	316.707	0.507778	0.253889	−	0.967233i	$-0.418290\pi$
$73$	316.707	0.507778	0.253889	+	0.967233i	$0.418290\pi$
$74$	−1358.75	−2.13448
$75$	962.156	1.48134
$76$	1286.99	1.94248
$77$	0	0
$78$	882.118	1.28051
$79$	−364.813	−0.519553	−0.259777	−	0.965669i	$-0.583649\pi$
$79$	−364.813	−0.519553	−0.259777	+	0.965669i	$0.583649\pi$
$80$	−1114.82	−1.55800
$81$	81.0000	0.111111
$82$	237.129	0.319348
$83$	47.5254	0.0628504	0.0314252	−	0.999506i	$-0.489995\pi$
$83$	47.5254	0.0628504	0.0314252	+	0.999506i	$0.489995\pi$
$84$	0	0
$85$	−1381.65	−1.76306
$86$	−839.704	−1.05288
$87$	−114.008	−0.140493
$88$	−55.4483	−0.0671683
$89$	−750.827	−0.894242	−0.447121	−	0.894474i	$-0.647551\pi$
$89$	−750.827	−0.894242	−0.447121	+	0.894474i	$0.647551\pi$
$90$	788.361	0.923340
$91$	0	0
$92$	150.016	0.170002
$93$	−37.6990	−0.0420344
$94$	−941.440	−1.03300
$95$	2948.60	3.18442
$96$	−778.252	−0.827396
$97$	−883.329	−0.924624	−0.462312	−	0.886717i	$-0.652980\pi$
$97$	−883.329	−0.924624	−0.462312	+	0.886717i	$0.652980\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	2955.39	2.95539
$101$	273.484	0.269432	0.134716	−	0.990884i	$-0.456988\pi$
$101$	273.484	0.269432	0.134716	+	0.990884i	$0.456988\pi$
$102$	−814.591	−0.790751
$103$	−1598.23	−1.52891	−0.764457	−	0.644675i	$-0.776993\pi$
$103$	−1598.23	−1.52891	−0.764457	+	0.644675i	$0.776993\pi$
$104$	357.231	0.336821
$105$	0	0
$106$	2088.89	1.91407
$107$	−154.045	−0.139178	−0.0695892	−	0.997576i	$-0.522169\pi$
$107$	−154.045	−0.139178	−0.0695892	+	0.997576i	$0.522169\pi$
$108$	248.803	0.221676
$109$	−316.897	−0.278470	−0.139235	−	0.990259i	$-0.544464\pi$
$109$	−316.897	−0.278470	−0.139235	+	0.990259i	$0.544464\pi$
$110$	−963.553	−0.835192
$111$	−982.446	−0.840087
$112$	0	0
$113$	−2185.48	−1.81941	−0.909704	−	0.415258i	$-0.863691\pi$
$113$	−2185.48	−1.81941	−0.909704	+	0.415258i	$0.863691\pi$
$114$	1738.44	1.42824
$115$	343.697	0.278695
$116$	−350.190	−0.280296
$117$	637.816	0.503984
$118$	934.622	0.729144
$119$	0	0
$120$	319.262	0.242871
$121$	121.000	0.0909091
$122$	−1073.68	−0.796771
$123$	171.457	0.125689
$124$	−115.798	−0.0838623
$125$	4132.03	2.95664
$126$	0	0
$127$	−1524.85	−1.06542	−0.532711	−	0.846297i	$-0.678827\pi$
$127$	−1524.85	−1.06542	−0.532711	+	0.846297i	$0.678827\pi$
$128$	−637.777	−0.440406
$129$	−607.149	−0.414391
$130$	6207.77	4.18814
$131$	211.735	0.141217	0.0706084	−	0.997504i	$-0.477506\pi$
$131$	211.735	0.141217	0.0706084	+	0.997504i	$0.477506\pi$
$132$	−304.092	−0.200514
$133$	0	0
$134$	3381.07	2.17970
$135$	570.025	0.363407
$136$	−329.884	−0.207995
$137$	−968.967	−0.604266	−0.302133	−	0.953266i	$-0.597699\pi$
$137$	−968.967	−0.604266	−0.302133	+	0.953266i	$0.597699\pi$
$138$	202.637	0.124997
$139$	−1122.39	−0.684891	−0.342446	−	0.939538i	$-0.611255\pi$
$139$	−1122.39	−0.684891	−0.342446	+	0.939538i	$0.611255\pi$
$140$	0	0
$141$	−680.709	−0.406568
$142$	4199.13	2.48157
$143$	−779.553	−0.455871
$144$	−475.243	−0.275025
$145$	−802.313	−0.459506
$146$	1314.05	0.744871
$147$	0	0
$148$	−3017.72	−1.67605
$149$	−710.182	−0.390472	−0.195236	−	0.980756i	$-0.562547\pi$
$149$	−710.182	−0.390472	−0.195236	+	0.980756i	$0.562547\pi$
$150$	3992.07	2.17301
$151$	3475.23	1.87292	0.936458	−	0.350780i	$-0.114083\pi$
$151$	3475.23	1.87292	0.936458	+	0.350780i	$0.114083\pi$
$152$	704.014	0.375678
$153$	−588.991	−0.311223
$154$	0	0
$155$	−265.301	−0.137481
$156$	1959.14	1.00549
$157$	−484.996	−0.246541	−0.123270	−	0.992373i	$-0.539338\pi$
$157$	−484.996	−0.246541	−0.123270	+	0.992373i	$0.539338\pi$
$158$	−1513.64	−0.762145
$159$	1510.38	0.753338
$160$	−5476.83	−2.70614
$161$	0	0
$162$	336.076	0.162991
$163$	−686.506	−0.329885	−0.164943	−	0.986303i	$-0.552744\pi$
$163$	−686.506	−0.329885	−0.164943	+	0.986303i	$0.552744\pi$
$164$	526.653	0.250760
$165$	−696.698	−0.328714
$166$	197.187	0.0921968
$167$	1474.93	0.683432	0.341716	−	0.939803i	$-0.388992\pi$
$167$	1474.93	0.683432	0.341716	+	0.939803i	$0.388992\pi$
$168$	0	0
$169$	2825.34	1.28600
$170$	−5732.57	−2.58628
$171$	1256.98	0.562126
$172$	−1864.94	−0.826746
$173$	319.384	0.140360	0.0701802	−	0.997534i	$-0.477643\pi$
$173$	319.384	0.140360	0.0701802	+	0.997534i	$0.477643\pi$
$174$	−473.028	−0.206093
$175$	0	0
$176$	580.852	0.248769
$177$	675.780	0.286976
$178$	−3115.25	−1.31178
$179$	−4124.80	−1.72236	−0.861178	−	0.508303i	$-0.830273\pi$
$179$	−4124.80	−1.72236	−0.861178	+	0.508303i	$0.830273\pi$
$180$	1750.91	0.725029
$181$	1019.16	0.418529	0.209265	−	0.977859i	$-0.432893\pi$
$181$	1019.16	0.418529	0.209265	+	0.977859i	$0.432893\pi$
$182$	0	0
$183$	−776.323	−0.313593
$184$	82.0619	0.0328787
$185$	−6913.82	−2.74764
$186$	−156.416	−0.0616613
$187$	719.878	0.281512
$188$	−2090.89	−0.811138
$189$	0	0
$190$	12234.0	4.67130
$191$	−3103.18	−1.17559	−0.587797	−	0.809008i	$-0.700005\pi$
$191$	−3103.18	−1.17559	−0.587797	+	0.809008i	$0.700005\pi$
$192$	−1961.72	−0.737370
$193$	2585.52	0.964301	0.482151	−	0.876088i	$-0.339856\pi$
$193$	2585.52	0.964301	0.482151	+	0.876088i	$0.339856\pi$
$194$	−3665.01	−1.35635
$195$	4488.54	1.64836
$196$	0	0
$197$	4394.32	1.58925	0.794626	−	0.607099i	$-0.207667\pi$
$197$	4394.32	1.58925	0.794626	+	0.607099i	$0.207667\pi$
$198$	−410.759	−0.147431
$199$	−3042.47	−1.08379	−0.541896	−	0.840445i	$-0.682293\pi$
$199$	−3042.47	−1.08379	−0.541896	+	0.840445i	$0.682293\pi$
$200$	1616.67	0.571578
$201$	2444.68	0.857884
$202$	1134.71	0.395236
$203$	0	0
$204$	−1809.17	−0.620916
$205$	1206.60	0.411086
$206$	−6631.18	−2.24280
$207$	146.517	0.0491963
$208$	−3742.19	−1.24747
$209$	−1536.31	−0.508462
$210$	0	0
$211$	−194.479	−0.0634526	−0.0317263	−	0.999497i	$-0.510100\pi$
$211$	−194.479	−0.0634526	−0.0317263	+	0.999497i	$0.510100\pi$
$212$	4639.33	1.50297
$213$	3036.18	0.976695
$214$	−639.145	−0.204164
$215$	−4272.72	−1.35533
$216$	136.100	0.0428725
$217$	0	0
$218$	−1314.83	−0.408494
$219$	950.122	0.293166
$220$	−2140.00	−0.655813
$221$	−4637.88	−1.41166
$222$	−4076.25	−1.23234
$223$	4203.92	1.26240	0.631200	−	0.775620i	$-0.282563\pi$
$223$	4203.92	1.26240	0.631200	+	0.775620i	$0.282563\pi$
$224$	0	0
$225$	2886.47	0.855250
$226$	−9067.76	−2.66893
$227$	1916.90	0.560480	0.280240	−	0.959930i	$-0.409586\pi$
$227$	1916.90	0.560480	0.280240	+	0.959930i	$0.409586\pi$
$228$	3860.98	1.12149
$229$	−5228.83	−1.50887	−0.754434	−	0.656376i	$-0.772089\pi$
$229$	−5228.83	−1.50887	−0.754434	+	0.656376i	$0.772089\pi$
$230$	1426.03	0.408825
$231$	0	0
$232$	−191.562	−0.0542097
$233$	4587.79	1.28994	0.644971	−	0.764207i	$-0.276870\pi$
$233$	4587.79	1.28994	0.644971	+	0.764207i	$0.276870\pi$
$234$	2646.35	0.739306
$235$	−4790.39	−1.32975
$236$	2075.75	0.572541
$237$	−1094.44	−0.299964
$238$	0	0
$239$	2347.65	0.635384	0.317692	−	0.948194i	$-0.397092\pi$
$239$	2347.65	0.635384	0.317692	+	0.948194i	$0.397092\pi$
$240$	−3344.45	−0.899514
$241$	−1567.94	−0.419086	−0.209543	−	0.977799i	$-0.567198\pi$
$241$	−1567.94	−0.419086	−0.209543	+	0.977799i	$0.567198\pi$
$242$	502.039	0.133357
$243$	243.000	0.0641500
$244$	−2384.58	−0.625644
$245$	0	0
$246$	711.388	0.184376
$247$	9897.79	2.54972
$248$	−63.3438	−0.0162191
$249$	142.576	0.0362867
$250$	17144.1	4.33716
$251$	1145.95	0.288173	0.144087	−	0.989565i	$-0.453976\pi$
$251$	1145.95	0.288173	0.144087	+	0.989565i	$0.453976\pi$
$252$	0	0
$253$	−179.076	−0.0444998
$254$	−6326.74	−1.56289
$255$	−4144.94	−1.01791
$256$	2585.07	0.631120
$257$	4867.16	1.18134	0.590671	−	0.806912i	$-0.298863\pi$
$257$	4867.16	1.18134	0.590671	+	0.806912i	$0.298863\pi$
$258$	−2519.11	−0.607880
$259$	0	0
$260$	13787.1	3.28863
$261$	−342.023	−0.0811138
$262$	878.507	0.207154
$263$	−5570.83	−1.30613	−0.653065	−	0.757302i	$-0.726517\pi$
$263$	−5570.83	−1.30613	−0.653065	+	0.757302i	$0.726517\pi$
$264$	−166.345	−0.0387796
$265$	10629.1	2.46392
$266$	0	0
$267$	−2252.48	−0.516291
$268$	7509.17	1.71155
$269$	5613.78	1.27241	0.636205	−	0.771520i	$-0.280503\pi$
$269$	5613.78	1.27241	0.636205	+	0.771520i	$0.280503\pi$
$270$	2365.08	0.533091
$271$	1132.87	0.253937	0.126968	−	0.991907i	$-0.459475\pi$
$271$	1132.87	0.253937	0.126968	+	0.991907i	$0.459475\pi$
$272$	3455.72	0.770346
$273$	0	0
$274$	−4020.33	−0.886412
$275$	−3527.91	−0.773603
$276$	450.047	0.0981509
$277$	−2960.62	−0.642189	−0.321094	−	0.947047i	$-0.604051\pi$
$277$	−2960.62	−0.642189	−0.321094	+	0.947047i	$0.604051\pi$
$278$	−4656.89	−1.00468
$279$	−113.097	−0.0242686
$280$	0	0
$281$	−8768.60	−1.86153	−0.930767	−	0.365614i	$-0.880859\pi$
$281$	−8768.60	−1.86153	−0.930767	+	0.365614i	$0.880859\pi$
$282$	−2824.32	−0.596404
$283$	−5721.53	−1.20180	−0.600901	−	0.799324i	$-0.705191\pi$
$283$	−5721.53	−1.20180	−0.600901	+	0.799324i	$0.705191\pi$
$284$	9326.05	1.94859
$285$	8845.80	1.83853
$286$	−3234.43	−0.668727
$287$	0	0
$288$	−2334.76	−0.477697
$289$	−630.155	−0.128263
$290$	−3328.86	−0.674061
$291$	−2649.99	−0.533832
$292$	2918.43	0.584891
$293$	−2901.41	−0.578505	−0.289253	−	0.957253i	$-0.593407\pi$
$293$	−2901.41	−0.578505	−0.289253	+	0.957253i	$0.593407\pi$
$294$	0	0
$295$	4755.70	0.938602
$296$	−1650.76	−0.324150
$297$	−297.000	−0.0580259
$298$	−2946.60	−0.572793
$299$	1153.72	0.223147
$300$	8866.18	1.70630
$301$	0	0
$302$	14419.0	2.74742
$303$	820.451	0.155557
$304$	−7374.94	−1.39139
$305$	−5463.26	−1.02566
$306$	−2443.77	−0.456540
$307$	−2956.87	−0.549699	−0.274850	−	0.961487i	$-0.588628\pi$
$307$	−2956.87	−0.549699	−0.274850	+	0.961487i	$0.588628\pi$
$308$	0	0
$309$	−4794.68	−0.882719
$310$	−1100.76	−0.201673
$311$	7883.93	1.43748	0.718741	−	0.695278i	$-0.244719\pi$
$311$	7883.93	1.43748	0.718741	+	0.695278i	$0.244719\pi$
$312$	1071.69	0.194463
$313$	−150.281	−0.0271387	−0.0135693	−	0.999908i	$-0.504319\pi$
$313$	−150.281	−0.0271387	−0.0135693	+	0.999908i	$0.504319\pi$
$314$	−2012.29	−0.361657
$315$	0	0
$316$	−3361.72	−0.598454
$317$	−4380.31	−0.776097	−0.388048	−	0.921639i	$-0.626851\pi$
$317$	−4380.31	−0.776097	−0.388048	+	0.921639i	$0.626851\pi$
$318$	6266.68	1.10509
$319$	418.028	0.0733702
$320$	−13805.3	−2.41169
$321$	−462.135	−0.0803546
$322$	0	0
$323$	−9140.11	−1.57452
$324$	746.408	0.127985
$325$	22728.8	3.87929
$326$	−2848.37	−0.483917
$327$	−950.690	−0.160775
$328$	288.090	0.0484974
$329$	0	0
$330$	−2890.66	−0.482199
$331$	−2427.56	−0.403114	−0.201557	−	0.979477i	$-0.564600\pi$
$331$	−2427.56	−0.403114	−0.201557	+	0.979477i	$0.564600\pi$
$332$	437.942	0.0723951
$333$	−2947.34	−0.485024
$334$	6119.59	1.00254
$335$	17204.1	2.80585
$336$	0	0
$337$	5968.91	0.964828	0.482414	−	0.875943i	$-0.339760\pi$
$337$	5968.91	0.964828	0.482414	+	0.875943i	$0.339760\pi$
$338$	11722.6	1.88646
$339$	−6556.45	−1.05044
$340$	−12731.7	−2.03081
$341$	138.230	0.0219518
$342$	5215.31	0.824596
$343$	0	0
$344$	−1020.16	−0.159894
$345$	1031.09	0.160905
$346$	1325.15	0.205898
$347$	9644.76	1.49210	0.746049	−	0.665891i	$-0.231948\pi$
$347$	9644.76	1.49210	0.746049	+	0.665891i	$0.231948\pi$
$348$	−1050.57	−0.161829
$349$	−11134.7	−1.70781	−0.853907	−	0.520425i	$-0.825774\pi$
$349$	−11134.7	−1.70781	−0.853907	+	0.520425i	$0.825774\pi$
$350$	0	0
$351$	1913.45	0.290975
$352$	2853.59	0.432094
$353$	−593.368	−0.0894669	−0.0447334	−	0.998999i	$-0.514244\pi$
$353$	−593.368	−0.0894669	−0.0447334	+	0.998999i	$0.514244\pi$
$354$	2803.87	0.420971
$355$	21366.7	3.19444
$356$	−6918.80	−1.03004
$357$	0	0
$358$	−17114.1	−2.52656
$359$	6131.40	0.901401	0.450700	−	0.892675i	$-0.351174\pi$
$359$	6131.40	0.901401	0.450700	+	0.892675i	$0.351174\pi$
$360$	957.786	0.140222
$361$	12647.1	1.84387
$362$	4228.59	0.613950
$363$	363.000	0.0524864
$364$	0	0
$365$	6686.34	0.958847
$366$	−3221.03	−0.460016
$367$	3995.99	0.568362	0.284181	−	0.958771i	$-0.408278\pi$
$367$	3995.99	0.568362	0.284181	+	0.958771i	$0.408278\pi$
$368$	−859.644	−0.121772
$369$	514.370	0.0725665
$370$	−28686.0	−4.03058
$371$	0	0
$372$	−347.393	−0.0484179
$373$	−9582.86	−1.33025	−0.665123	−	0.746734i	$-0.731621\pi$
$373$	−9582.86	−1.33025	−0.665123	+	0.746734i	$0.731621\pi$
$374$	2986.83	0.412956
$375$	12396.1	1.70702
$376$	−1143.76	−0.156875
$377$	−2693.18	−0.367921
$378$	0	0
$379$	−7515.80	−1.01863	−0.509315	−	0.860580i	$-0.670101\pi$
$379$	−7515.80	−1.01863	−0.509315	+	0.860580i	$0.670101\pi$
$380$	27171.1	3.66802
$381$	−4574.55	−0.615122
$382$	−12875.4	−1.72451
$383$	5778.23	0.770897	0.385449	−	0.922729i	$-0.374047\pi$
$383$	5778.23	0.770897	0.385449	+	0.922729i	$0.374047\pi$
$384$	−1913.33	−0.254269
$385$	0	0
$386$	10727.6	1.41456
$387$	−1821.45	−0.239249
$388$	−8139.80	−1.06504
$389$	−590.988	−0.0770290	−0.0385145	−	0.999258i	$-0.512263\pi$
$389$	−590.988	−0.0770290	−0.0385145	+	0.999258i	$0.512263\pi$
$390$	18623.3	2.41802
$391$	−1065.40	−0.137799
$392$	0	0
$393$	635.206	0.0815315
$394$	18232.4	2.33131
$395$	−7701.96	−0.981082
$396$	−912.276	−0.115767
$397$	−14154.5	−1.78940	−0.894702	−	0.446663i	$-0.852612\pi$
$397$	−14154.5	−1.78940	−0.894702	+	0.446663i	$0.852612\pi$
$398$	−12623.4	−1.58984
$399$	0	0
$400$	−16935.5	−2.11693
$401$	−6493.27	−0.808625	−0.404313	−	0.914621i	$-0.632489\pi$
$401$	−6493.27	−0.808625	−0.404313	+	0.914621i	$0.632489\pi$
$402$	10143.2	1.25845
$403$	−890.556	−0.110079
$404$	2520.13	0.310349
$405$	1710.08	0.209813
$406$	0	0
$407$	3602.30	0.438721
$408$	−989.653	−0.120086
$409$	−12948.9	−1.56548	−0.782742	−	0.622347i	$-0.786179\pi$
$409$	−12948.9	−1.56548	−0.782742	+	0.622347i	$0.786179\pi$
$410$	5006.29	0.603032
$411$	−2906.90	−0.348873
$412$	−14727.5	−1.76110
$413$	0	0
$414$	607.912	0.0721673
$415$	1003.36	0.118682
$416$	−18384.5	−2.16677
$417$	−3367.17	−0.395422
$418$	−6374.27	−0.745875
$419$	−9318.36	−1.08647	−0.543236	−	0.839580i	$-0.682801\pi$
$419$	−9318.36	−1.08647	−0.543236	+	0.839580i	$0.682801\pi$
$420$	0	0
$421$	8939.78	1.03491	0.517457	−	0.855709i	$-0.326879\pi$
$421$	8939.78	1.03491	0.517457	+	0.855709i	$0.326879\pi$
$422$	−806.911	−0.0930801
$423$	−2042.13	−0.234732
$424$	2537.81	0.290677
$425$	−20988.9	−2.39556
$426$	12597.4	1.43274
$427$	0	0
$428$	−1419.51	−0.160314
$429$	−2338.66	−0.263197
$430$	−17727.9	−1.98817
$431$	−2744.83	−0.306761	−0.153380	−	0.988167i	$-0.549016\pi$
$431$	−2744.83	−0.306761	−0.153380	+	0.988167i	$0.549016\pi$
$432$	−1425.73	−0.158786
$433$	−1923.76	−0.213511	−0.106755	−	0.994285i	$-0.534046\pi$
$433$	−1923.76	−0.213511	−0.106755	+	0.994285i	$0.534046\pi$
$434$	0	0
$435$	−2406.94	−0.265296
$436$	−2920.17	−0.320759
$437$	2273.69	0.248891
$438$	3942.14	0.430052
$439$	5973.91	0.649474	0.324737	−	0.945804i	$-0.394724\pi$
$439$	5973.91	0.649474	0.324737	+	0.945804i	$0.394724\pi$
$440$	−1170.63	−0.126835
$441$	0	0
$442$	−19242.9	−2.07080
$443$	−13743.1	−1.47393	−0.736967	−	0.675929i	$-0.763743\pi$
$443$	−13743.1	−1.47393	−0.736967	+	0.675929i	$0.763743\pi$
$444$	−9053.15	−0.967665
$445$	−15851.5	−1.68861
$446$	17442.4	1.85185
$447$	−2130.55	−0.225439
$448$	0	0
$449$	−4050.32	−0.425715	−0.212858	−	0.977083i	$-0.568277\pi$
$449$	−4050.32	−0.425715	−0.212858	+	0.977083i	$0.568277\pi$
$450$	11976.2	1.25459
$451$	−628.675	−0.0656389
$452$	−20139.0	−2.09571
$453$	10425.7	1.08133
$454$	7953.37	0.822181
$455$	0	0
$456$	2112.04	0.216898
$457$	−13436.6	−1.37536	−0.687679	−	0.726015i	$-0.741370\pi$
$457$	−13436.6	−1.37536	−0.687679	+	0.726015i	$0.741370\pi$
$458$	−21694.9	−2.21339
$459$	−1766.97	−0.179685
$460$	3167.14	0.321019
$461$	−5526.31	−0.558321	−0.279160	−	0.960244i	$-0.590056\pi$
$461$	−5526.31	−0.558321	−0.279160	+	0.960244i	$0.590056\pi$
$462$	0	0
$463$	8689.20	0.872185	0.436092	−	0.899902i	$-0.356362\pi$
$463$	8689.20	0.872185	0.436092	+	0.899902i	$0.356362\pi$
$464$	2006.72	0.200775
$465$	−795.903	−0.0793745
$466$	19035.2	1.89225
$467$	1410.42	0.139757	0.0698786	−	0.997556i	$-0.477739\pi$
$467$	1410.42	0.139757	0.0698786	+	0.997556i	$0.477739\pi$
$468$	5877.42	0.580521
$469$	0	0
$470$	−19875.7	−1.95064
$471$	−1454.99	−0.142340
$472$	1135.48	0.110730
$473$	2226.21	0.216409
$474$	−4540.92	−0.440024
$475$	44793.0	4.32683
$476$	0	0
$477$	4531.13	0.434940
$478$	9740.59	0.932059
$479$	−12396.9	−1.18252	−0.591261	−	0.806480i	$-0.701370\pi$
$479$	−12396.9	−1.18252	−0.591261	+	0.806480i	$0.701370\pi$
$480$	−16430.5	−1.56239
$481$	−23208.1	−2.20000
$482$	−6505.51	−0.614768
$483$	0	0
$484$	1115.00	0.104715
$485$	−18648.9	−1.74599
$486$	1008.23	0.0941032
$487$	−15280.4	−1.42181	−0.710904	−	0.703289i	$-0.751714\pi$
$487$	−15280.4	−1.42181	−0.710904	+	0.703289i	$0.751714\pi$
$488$	−1304.42	−0.121000
$489$	−2059.52	−0.190459
$490$	0	0
$491$	16637.4	1.52920	0.764598	−	0.644507i	$-0.222937\pi$
$491$	16637.4	1.52920	0.764598	+	0.644507i	$0.222937\pi$
$492$	1579.96	0.144776
$493$	2487.02	0.227200
$494$	41066.8	3.74025
$495$	−2090.09	−0.189783
$496$	663.562	0.0600702
$497$	0	0
$498$	591.560	0.0532298
$499$	9348.06	0.838630	0.419315	−	0.907841i	$-0.362270\pi$
$499$	9348.06	0.838630	0.419315	+	0.907841i	$0.362270\pi$
$500$	38076.2	3.40564
$501$	4424.78	0.394580
$502$	4754.62	0.422728
$503$	833.934	0.0739230	0.0369615	−	0.999317i	$-0.488232\pi$
$503$	833.934	0.0739230	0.0369615	+	0.999317i	$0.488232\pi$
$504$	0	0
$505$	5773.80	0.508774
$506$	−743.004	−0.0652777
$507$	8476.01	0.742471
$508$	−14051.4	−1.22722
$509$	−5584.02	−0.486262	−0.243131	−	0.969993i	$-0.578174\pi$
$509$	−5584.02	−0.486262	−0.243131	+	0.969993i	$0.578174\pi$
$510$	−17197.7	−1.49319
$511$	0	0
$512$	15827.9	1.36621
$513$	3770.94	0.324544
$514$	20194.2	1.73294
$515$	−33741.9	−2.88708
$516$	−5594.82	−0.477322
$517$	2495.93	0.212323
$518$	0	0
$519$	958.153	0.0810371
$520$	7541.87	0.636025
$521$	−6590.14	−0.554164	−0.277082	−	0.960846i	$-0.589367\pi$
$521$	−6590.14	−0.554164	−0.277082	+	0.960846i	$0.589367\pi$
$522$	−1419.08	−0.118988
$523$	23111.5	1.93231	0.966154	−	0.257967i	$-0.0830526\pi$
$523$	23111.5	1.93231	0.966154	+	0.257967i	$0.0830526\pi$
$524$	1951.12	0.162662
$525$	0	0
$526$	−23113.8	−1.91599
$527$	822.384	0.0679765
$528$	1742.56	0.143627
$529$	−11902.0	−0.978217
$530$	44100.9	3.61437
$531$	2027.34	0.165686
$532$	0	0
$533$	4050.29	0.329151
$534$	−9345.74	−0.757359
$535$	−3252.20	−0.262813
$536$	4107.68	0.331017
$537$	−12374.4	−0.994403
$538$	23292.1	1.86653
$539$	0	0
$540$	5252.73	0.418596
$541$	7263.51	0.577233	0.288616	−	0.957445i	$-0.406805\pi$
$541$	7263.51	0.577233	0.288616	+	0.957445i	$0.406805\pi$
$542$	4700.36	0.372505
$543$	3057.49	0.241638
$544$	16977.2	1.33803
$545$	−6690.34	−0.525840
$546$	0	0
$547$	5332.29	0.416805	0.208402	−	0.978043i	$-0.433174\pi$
$547$	5332.29	0.416805	0.208402	+	0.978043i	$0.433174\pi$
$548$	−8928.94	−0.696032
$549$	−2328.97	−0.181053
$550$	−14637.6	−1.13482
$551$	−5307.60	−0.410366
$552$	246.186	0.0189825
$553$	0	0
$554$	−12283.9	−0.942041
$555$	−20741.5	−1.58635
$556$	−10342.7	−0.788901
$557$	5431.32	0.413164	0.206582	−	0.978429i	$-0.433766\pi$
$557$	5431.32	0.413164	0.206582	+	0.978429i	$0.433766\pi$
$558$	−469.249	−0.0356002
$559$	−14342.6	−1.08520
$560$	0	0
$561$	2159.63	0.162531
$562$	−36381.7	−2.73073
$563$	−898.786	−0.0672812	−0.0336406	−	0.999434i	$-0.510710\pi$
$563$	−898.786	−0.0672812	−0.0336406	+	0.999434i	$0.510710\pi$
$564$	−6272.67	−0.468310
$565$	−46140.1	−3.43562
$566$	−23739.1	−1.76295
$567$	0	0
$568$	5101.56	0.376860
$569$	−10050.3	−0.740474	−0.370237	−	0.928937i	$-0.620724\pi$
$569$	−10050.3	−0.740474	−0.370237	+	0.928937i	$0.620724\pi$
$570$	36702.0	2.69698
$571$	2044.42	0.149836	0.0749178	−	0.997190i	$-0.476131\pi$
$571$	2044.42	0.149836	0.0749178	+	0.997190i	$0.476131\pi$
$572$	−7183.51	−0.525101
$573$	−9309.55	−0.678730
$574$	0	0
$575$	5221.20	0.378677
$576$	−5885.16	−0.425721
$577$	11695.9	0.843860	0.421930	−	0.906629i	$-0.361353\pi$
$577$	11695.9	0.843860	0.421930	+	0.906629i	$0.361353\pi$
$578$	−2614.57	−0.188152
$579$	7756.57	0.556740
$580$	−7393.24	−0.529289
$581$	0	0
$582$	−10995.0	−0.783090
$583$	−5538.05	−0.393418
$584$	1596.44	0.113119
$585$	13465.6	0.951683
$586$	−12038.2	−0.848623
$587$	−14949.2	−1.05114	−0.525569	−	0.850751i	$-0.676148\pi$
$587$	−14949.2	−1.05114	−0.525569	+	0.850751i	$0.676148\pi$
$588$	0	0
$589$	−1755.07	−0.122778
$590$	19731.8	1.37686
$591$	13183.0	0.917555
$592$	17292.6	1.20054
$593$	2181.25	0.151051	0.0755253	−	0.997144i	$-0.475937\pi$
$593$	2181.25	0.151051	0.0755253	+	0.997144i	$0.475937\pi$
$594$	−1232.28	−0.0851195
$595$	0	0
$596$	−6544.26	−0.449771
$597$	−9127.40	−0.625728
$598$	4786.86	0.327340
$599$	14782.1	1.00832	0.504158	−	0.863611i	$-0.331803\pi$
$599$	14782.1	1.00832	0.504158	+	0.863611i	$0.331803\pi$
$600$	4850.00	0.330000
$601$	14164.9	0.961396	0.480698	−	0.876886i	$-0.340383\pi$
$601$	14164.9	0.961396	0.480698	+	0.876886i	$0.340383\pi$
$602$	0	0
$603$	7334.05	0.495299
$604$	32023.9	2.15734
$605$	2554.56	0.171665
$606$	3404.12	0.228190
$607$	−10065.8	−0.673079	−0.336539	−	0.941669i	$-0.609257\pi$
$607$	−10065.8	−0.673079	−0.336539	+	0.941669i	$0.609257\pi$
$608$	−36231.3	−2.41674
$609$	0	0
$610$	−22667.5	−1.50456
$611$	−16080.3	−1.06471
$612$	−5427.50	−0.358486
$613$	22924.4	1.51046	0.755228	−	0.655462i	$-0.227526\pi$
$613$	22924.4	1.51046	0.755228	+	0.655462i	$0.227526\pi$
$614$	−12268.3	−0.806366
$615$	3619.80	0.237341
$616$	0	0
$617$	−6513.86	−0.425021	−0.212511	−	0.977159i	$-0.568164\pi$
$617$	−6513.86	−0.425021	−0.212511	+	0.977159i	$0.568164\pi$
$618$	−19893.6	−1.29488
$619$	−1175.69	−0.0763407	−0.0381703	−	0.999271i	$-0.512153\pi$
$619$	−1175.69	−0.0763407	−0.0381703	+	0.999271i	$0.512153\pi$
$620$	−2444.72	−0.158359
$621$	439.551	0.0284035
$622$	32711.1	2.10868
$623$	0	0
$624$	−11226.6	−0.720228
$625$	47145.7	3.01733
$626$	−623.530	−0.0398104
$627$	−4608.92	−0.293561
$628$	−4469.20	−0.283981
$629$	21431.5	1.35856
$630$	0	0
$631$	−13318.1	−0.840231	−0.420116	−	0.907471i	$-0.638010\pi$
$631$	−13318.1	−0.840231	−0.420116	+	0.907471i	$0.638010\pi$
$632$	−1838.93	−0.115742
$633$	−583.438	−0.0366344
$634$	−18174.3	−1.13847
$635$	−32192.7	−2.01186
$636$	13918.0	0.867742
$637$	0	0
$638$	1734.44	0.107628
$639$	9108.55	0.563895
$640$	−13464.8	−0.831628
$641$	22289.5	1.37345	0.686725	−	0.726918i	$-0.259048\pi$
$641$	22289.5	1.37345	0.686725	+	0.726918i	$0.259048\pi$
$642$	−1917.44	−0.117874
$643$	17465.1	1.07116	0.535580	−	0.844485i	$-0.320093\pi$
$643$	17465.1	1.07116	0.535580	+	0.844485i	$0.320093\pi$
$644$	0	0
$645$	−12818.2	−0.782503
$646$	−37923.1	−2.30970
$647$	7588.03	0.461076	0.230538	−	0.973063i	$-0.425951\pi$
$647$	7588.03	0.461076	0.230538	+	0.973063i	$0.425951\pi$
$648$	408.301	0.0247525
$649$	−2477.86	−0.149868
$650$	94303.9	5.69062
$651$	0	0
$652$	−6326.09	−0.379983
$653$	−465.272	−0.0278829	−0.0139414	−	0.999903i	$-0.504438\pi$
$653$	−465.272	−0.0278829	−0.0139414	+	0.999903i	$0.504438\pi$
$654$	−3944.49	−0.235844
$655$	4470.17	0.266662
$656$	−3017.91	−0.179618
$657$	2850.37	0.169259
$658$	0	0
$659$	2841.34	0.167956	0.0839779	−	0.996468i	$-0.473237\pi$
$659$	2841.34	0.167956	0.0839779	+	0.996468i	$0.473237\pi$
$660$	−6420.01	−0.378634
$661$	−24262.2	−1.42767	−0.713836	−	0.700313i	$-0.753044\pi$
$661$	−24262.2	−1.42767	−0.713836	+	0.700313i	$0.753044\pi$
$662$	−10072.1	−0.591337
$663$	−13913.6	−0.815023
$664$	239.564	0.0140013
$665$	0	0
$666$	−12228.8	−0.711493
$667$	−618.670	−0.0359145
$668$	13591.3	0.787221
$669$	12611.8	0.728848
$670$	71381.2	4.11597
$671$	2846.52	0.163768
$672$	0	0
$673$	3.18434	0.000182388 0	9.11941e−5	−	1.00000i	$-0.499971\pi$
$673$	3.18434	0.000182388 0	9.11941e−5		1.00000i	$0.499971\pi$
$674$	24765.5	1.41533
$675$	8659.41	0.493779
$676$	26035.2	1.48129
$677$	−20650.3	−1.17231	−0.586156	−	0.810198i	$-0.699360\pi$
$677$	−20650.3	−1.17231	−0.586156	+	0.810198i	$0.699360\pi$
$678$	−27203.3	−1.54091
$679$	0	0
$680$	−6964.54	−0.392762
$681$	5750.69	0.323593
$682$	573.526	0.0322016
$683$	−5358.70	−0.300212	−0.150106	−	0.988670i	$-0.547962\pi$
$683$	−5358.70	−0.300212	−0.150106	+	0.988670i	$0.547962\pi$
$684$	11582.9	0.647492
$685$	−20456.9	−1.14105
$686$	0	0
$687$	−15686.5	−0.871145
$688$	10686.8	0.592194
$689$	35679.4	1.97282
$690$	4278.09	0.236035
$691$	14578.8	0.802610	0.401305	−	0.915944i	$-0.368557\pi$
$691$	14578.8	0.802610	0.401305	+	0.915944i	$0.368557\pi$
$692$	2943.10	0.161676
$693$	0	0
$694$	40017.0	2.18879
$695$	−23696.0	−1.29329
$696$	−574.685	−0.0312980
$697$	−3740.24	−0.203259
$698$	−46198.9	−2.50523
$699$	13763.4	0.744748
$700$	0	0
$701$	−20510.3	−1.10509	−0.552543	−	0.833485i	$-0.686342\pi$
$701$	−20510.3	−1.10509	−0.552543	+	0.833485i	$0.686342\pi$
$702$	7939.06	0.426838
$703$	−45737.5	−2.45380
$704$	7192.98	0.385079
$705$	−14371.2	−0.767730
$706$	−2461.94	−0.131241
$707$	0	0
$708$	6227.25	0.330557
$709$	−4726.94	−0.250386	−0.125193	−	0.992132i	$-0.539955\pi$
$709$	−4726.94	−0.250386	−0.125193	+	0.992132i	$0.539955\pi$
$710$	88652.2	4.68600
$711$	−3283.32	−0.173184
$712$	−3784.74	−0.199212
$713$	−204.576	−0.0107453
$714$	0	0
$715$	−16458.0	−0.860829
$716$	−38009.6	−1.98392
$717$	7042.95	0.366839
$718$	25439.7	1.32229
$719$	−1363.54	−0.0707255	−0.0353628	−	0.999375i	$-0.511259\pi$
$719$	−1363.54	−0.0707255	−0.0353628	+	0.999375i	$0.511259\pi$
$720$	−10033.3	−0.519334
$721$	0	0
$722$	52473.9	2.70482
$723$	−4703.82	−0.241960
$724$	9391.49	0.482089
$725$	−12188.1	−0.624354
$726$	1506.12	0.0769935
$727$	−22081.1	−1.12647	−0.563234	−	0.826297i	$-0.690443\pi$
$727$	−22081.1	−1.12647	−0.563234	+	0.826297i	$0.690443\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	27742.2	1.40655
$731$	13244.6	0.670137
$732$	−7153.74	−0.361216
$733$	−17123.6	−0.862857	−0.431428	−	0.902147i	$-0.641990\pi$
$733$	−17123.6	−0.862857	−0.431428	+	0.902147i	$0.641990\pi$
$734$	16579.7	0.833744
$735$	0	0
$736$	−4223.23	−0.211509
$737$	−8963.84	−0.448015
$738$	2134.17	0.106449
$739$	23319.2	1.16077	0.580386	−	0.814342i	$-0.302902\pi$
$739$	23319.2	1.16077	0.580386	+	0.814342i	$0.302902\pi$
$740$	−63710.2	−3.16491
$741$	29693.4	1.47208
$742$	0	0
$743$	−3325.82	−0.164216	−0.0821080	−	0.996623i	$-0.526165\pi$
$743$	−3325.82	−0.164216	−0.0821080	+	0.996623i	$0.526165\pi$
$744$	−190.031	−0.00936410
$745$	−14993.4	−0.737336
$746$	−39760.1	−1.95137
$747$	427.728	0.0209501
$748$	6633.61	0.324263
$749$	0	0
$750$	51432.4	2.50406
$751$	10710.1	0.520396	0.260198	−	0.965555i	$-0.416212\pi$
$751$	10710.1	0.520396	0.260198	+	0.965555i	$0.416212\pi$
$752$	11981.6	0.581014
$753$	3437.84	0.166377
$754$	−11174.3	−0.539711
$755$	73369.3	3.53666
$756$	0	0
$757$	29281.3	1.40588	0.702938	−	0.711251i	$-0.251871\pi$
$757$	29281.3	1.40588	0.702938	+	0.711251i	$0.251871\pi$
$758$	−31183.7	−1.49425
$759$	−537.229	−0.0256920
$760$	14863.2	0.709400
$761$	10791.5	0.514051	0.257025	−	0.966405i	$-0.417258\pi$
$761$	10791.5	0.514051	0.257025	+	0.966405i	$0.417258\pi$
$762$	−18980.2	−0.902337
$763$	0	0
$764$	−28595.6	−1.35412
$765$	−12434.8	−0.587688
$766$	23974.4	1.13085
$767$	15963.8	0.751526
$768$	7755.20	0.364377
$769$	−37681.5	−1.76701	−0.883503	−	0.468425i	$-0.844822\pi$
$769$	−37681.5	−1.76701	−0.883503	+	0.468425i	$0.844822\pi$
$770$	0	0
$771$	14601.5	0.682048
$772$	23825.4	1.11074
$773$	37689.7	1.75369	0.876845	−	0.480772i	$-0.159644\pi$
$773$	37689.7	1.75369	0.876845	+	0.480772i	$0.159644\pi$
$774$	−7557.33	−0.350960
$775$	−4030.26	−0.186801
$776$	−4452.65	−0.205980
$777$	0	0
$778$	−2452.06	−0.112996
$779$	7982.13	0.367124
$780$	41361.4	1.89869
$781$	−11132.7	−0.510062
$782$	−4420.43	−0.202141
$783$	−1026.07	−0.0468311
$784$	0	0
$785$	−10239.3	−0.465548
$786$	2635.52	0.119600
$787$	5798.21	0.262622	0.131311	−	0.991341i	$-0.458081\pi$
$787$	5798.21	0.262622	0.131311	+	0.991341i	$0.458081\pi$
$788$	40493.3	1.83060
$789$	−16712.5	−0.754094
$790$	−31956.1	−1.43917
$791$	0	0
$792$	−499.035	−0.0223894
$793$	−18338.9	−0.821229
$794$	−58728.2	−2.62492
$795$	31887.2	1.42254
$796$	−28036.0	−1.24838
$797$	−27006.7	−1.20028	−0.600142	−	0.799893i	$-0.704889\pi$
$797$	−27006.7	−1.20028	−0.600142	+	0.799893i	$0.704889\pi$
$798$	0	0
$799$	14849.3	0.657486
$800$	−83200.0	−3.67696
$801$	−6757.44	−0.298081
$802$	−26941.1	−1.18619
$803$	−3483.78	−0.153101
$804$	22527.5	0.988165
$805$	0	0
$806$	−3694.99	−0.161477
$807$	16841.4	0.734627
$808$	1378.56	0.0600219
$809$	21675.4	0.941987	0.470994	−	0.882137i	$-0.343895\pi$
$809$	21675.4	0.941987	0.470994	+	0.882137i	$0.343895\pi$
$810$	7095.25	0.307780
$811$	11347.1	0.491307	0.245654	−	0.969358i	$-0.420997\pi$
$811$	11347.1	0.491307	0.245654	+	0.969358i	$0.420997\pi$
$812$	0	0
$813$	3398.60	0.146610
$814$	14946.3	0.643570
$815$	−14493.6	−0.622929
$816$	10367.2	0.444759
$817$	−28265.7	−1.21039
$818$	−53726.2	−2.29644
$819$	0	0
$820$	11118.7	0.473515
$821$	6054.73	0.257383	0.128692	−	0.991685i	$-0.458922\pi$
$821$	6054.73	0.257383	0.128692	+	0.991685i	$0.458922\pi$
$822$	−12061.0	−0.511770
$823$	−353.681	−0.0149800	−0.00748999	−	0.999972i	$-0.502384\pi$
$823$	−353.681	−0.0149800	−0.00748999	+	0.999972i	$0.502384\pi$
$824$	−8056.28	−0.340599
$825$	−10583.7	−0.446640
$826$	0	0
$827$	39897.2	1.67758	0.838792	−	0.544451i	$-0.183262\pi$
$827$	39897.2	1.67758	0.838792	+	0.544451i	$0.183262\pi$
$828$	1350.14	0.0566675
$829$	7626.19	0.319504	0.159752	−	0.987157i	$-0.448931\pi$
$829$	7626.19	0.319504	0.159752	+	0.987157i	$0.448931\pi$
$830$	4163.02	0.174097
$831$	−8881.85	−0.370768
$832$	−46341.4	−1.93101
$833$	0	0
$834$	−13970.7	−0.580054
$835$	31138.7	1.29054
$836$	−14156.9	−0.585679
$837$	−339.291	−0.0140115
$838$	−38662.7	−1.59377
$839$	−19085.5	−0.785345	−0.392672	−	0.919678i	$-0.628449\pi$
$839$	−19085.5	−0.785345	−0.392672	+	0.919678i	$0.628449\pi$
$840$	0	0
$841$	−22944.8	−0.940785
$842$	37091.9	1.51814
$843$	−26305.8	−1.07476
$844$	−1792.11	−0.0730887
$845$	59648.7	2.42838
$846$	−8472.96	−0.344334
$847$	0	0
$848$	−26585.0	−1.07657
$849$	−17164.6	−0.693860
$850$	−87084.9	−3.51410
$851$	−5331.30	−0.214753
$852$	27978.2	1.12502
$853$	−629.361	−0.0252625	−0.0126313	−	0.999920i	$-0.504021\pi$
$853$	−629.361	−0.0252625	−0.0126313	+	0.999920i	$0.504021\pi$
$854$	0	0
$855$	26537.4	1.06147
$856$	−776.503	−0.0310050
$857$	−33261.5	−1.32578	−0.662889	−	0.748718i	$-0.730670\pi$
$857$	−33261.5	−1.32578	−0.662889	+	0.748718i	$0.730670\pi$
$858$	−9703.30	−0.386090
$859$	−4936.04	−0.196060	−0.0980300	−	0.995183i	$-0.531254\pi$
$859$	−4936.04	−0.196060	−0.0980300	+	0.995183i	$0.531254\pi$
$860$	−39372.7	−1.56116
$861$	0	0
$862$	−11388.5	−0.449994
$863$	25546.5	1.00766	0.503832	−	0.863801i	$-0.331923\pi$
$863$	25546.5	1.00766	0.503832	+	0.863801i	$0.331923\pi$
$864$	−7004.27	−0.275799
$865$	6742.86	0.265045
$866$	−7981.85	−0.313204
$867$	−1890.47	−0.0740526
$868$	0	0
$869$	4012.95	0.156651
$870$	−9986.59	−0.389169
$871$	57750.3	2.24661
$872$	−1597.40	−0.0620353
$873$	−7949.97	−0.308208
$874$	9433.73	0.365104
$875$	0	0
$876$	8755.29	0.337687
$877$	−22381.9	−0.861783	−0.430892	−	0.902404i	$-0.641801\pi$
$877$	−22381.9	−0.861783	−0.430892	+	0.902404i	$0.641801\pi$
$878$	24786.3	0.952729
$879$	−8704.22	−0.334000
$880$	12263.0	0.469756
$881$	−22322.3	−0.853642	−0.426821	−	0.904336i	$-0.640366\pi$
$881$	−22322.3	−0.853642	−0.426821	+	0.904336i	$0.640366\pi$
$882$	0	0
$883$	44443.3	1.69381	0.846907	−	0.531741i	$-0.178462\pi$
$883$	44443.3	1.69381	0.846907	+	0.531741i	$0.178462\pi$
$884$	−42737.6	−1.62604
$885$	14267.1	0.541902
$886$	−57021.1	−2.16215
$887$	953.966	0.0361117	0.0180558	−	0.999837i	$-0.494252\pi$
$887$	953.966	0.0361117	0.0180558	+	0.999837i	$0.494252\pi$
$888$	−4952.27	−0.187148
$889$	0	0
$890$	−65769.2	−2.47707
$891$	−891.000	−0.0335013
$892$	38738.8	1.45411
$893$	−31690.2	−1.18754
$894$	−8839.81	−0.330702
$895$	−87082.9	−3.25236
$896$	0	0
$897$	3461.15	0.128834
$898$	−16805.1	−0.624492
$899$	477.553	0.0177167
$900$	26598.6	0.985131
$901$	−32948.1	−1.21827
$902$	−2608.42	−0.0962872
$903$	0	0
$904$	−11016.5	−0.405313
$905$	21516.6	0.790317
$906$	43257.1	1.58623
$907$	−1010.74	−0.0370023	−0.0185011	−	0.999829i	$-0.505889\pi$
$907$	−1010.74	−0.0370023	−0.0185011	+	0.999829i	$0.505889\pi$
$908$	17664.0	0.645596
$909$	2461.35	0.0898107
$910$	0	0
$911$	−24686.9	−0.897819	−0.448909	−	0.893577i	$-0.648187\pi$
$911$	−24686.9	−0.897819	−0.448909	+	0.893577i	$0.648187\pi$
$912$	−22124.8	−0.803318
$913$	−522.779	−0.0189501
$914$	−55749.7	−2.01754
$915$	−16389.8	−0.592163
$916$	−48183.2	−1.73801
$917$	0	0
$918$	−7331.32	−0.263584
$919$	18951.9	0.680267	0.340133	−	0.940377i	$-0.389528\pi$
$919$	18951.9	0.680267	0.340133	+	0.940377i	$0.389528\pi$
$920$	1732.50	0.0620855
$921$	−8870.62	−0.317369
$922$	−22929.1	−0.819014
$923$	71723.2	2.55775
$924$	0	0
$925$	−105030.	−3.73335
$926$	36052.2	1.27943
$927$	−14384.1	−0.509638
$928$	9858.53	0.348731
$929$	1943.51	0.0686377	0.0343189	−	0.999411i	$-0.489074\pi$
$929$	1943.51	0.0686377	0.0343189	+	0.999411i	$0.489074\pi$
$930$	−3302.27	−0.116436
$931$	0	0
$932$	42276.1	1.48584
$933$	23651.8	0.829931
$934$	5851.97	0.205013
$935$	15198.1	0.531584
$936$	3215.08	0.112274
$937$	24789.2	0.864278	0.432139	−	0.901807i	$-0.357759\pi$
$937$	24789.2	0.864278	0.432139	+	0.901807i	$0.357759\pi$
$938$	0	0
$939$	−450.844	−0.0156685
$940$	−44143.0	−1.53169
$941$	16736.7	0.579808	0.289904	−	0.957056i	$-0.406377\pi$
$941$	16736.7	0.579808	0.289904	+	0.957056i	$0.406377\pi$
$942$	−6036.87	−0.208803
$943$	930.420	0.0321301
$944$	−11894.8	−0.410108
$945$	0	0
$946$	9236.74	0.317455
$947$	791.991	0.0271766	0.0135883	−	0.999908i	$-0.495675\pi$
$947$	791.991	0.0271766	0.0135883	+	0.999908i	$0.495675\pi$
$948$	−10085.2	−0.345518
$949$	22444.6	0.767736
$950$	185850.	6.34712
$951$	−13140.9	−0.448080
$952$	0	0
$953$	34651.8	1.17784	0.588921	−	0.808191i	$-0.299553\pi$
$953$	34651.8	1.17784	0.588921	+	0.808191i	$0.299553\pi$
$954$	18800.0	0.638023
$955$	−65514.6	−2.21990
$956$	21633.4	0.731876
$957$	1254.09	0.0423603
$958$	−51435.7	−1.73467
$959$	0	0
$960$	−41416.0	−1.39239
$961$	−29633.1	−0.994699
$962$	−96292.5	−3.22723
$963$	−1386.40	−0.0463928
$964$	−14448.4	−0.482730
$965$	54585.7	1.82091
$966$	0	0
$967$	52591.2	1.74893	0.874467	−	0.485085i	$-0.161211\pi$
$967$	52591.2	1.74893	0.874467	+	0.485085i	$0.161211\pi$
$968$	609.932	0.0202520
$969$	−27420.3	−0.909049
$970$	−77375.9	−2.56123
$971$	37665.3	1.24484	0.622418	−	0.782685i	$-0.286150\pi$
$971$	37665.3	1.24484	0.622418	+	0.782685i	$0.286150\pi$
$972$	2239.22	0.0738921
$973$	0	0
$974$	−63399.6	−2.08568
$975$	68186.5	2.23971
$976$	13664.5	0.448146
$977$	27823.5	0.911107	0.455554	−	0.890208i	$-0.349441\pi$
$977$	27823.5	0.911107	0.455554	+	0.890208i	$0.349441\pi$
$978$	−8545.12	−0.279389
$979$	8259.10	0.269624
$980$	0	0
$981$	−2852.07	−0.0928232
$982$	69030.0	2.24321
$983$	24071.0	0.781025	0.390512	−	0.920598i	$-0.372298\pi$
$983$	24071.0	0.781025	0.390512	+	0.920598i	$0.372298\pi$
$984$	864.271	0.0280000
$985$	92773.2	3.00102
$986$	10318.9	0.333285
$987$	0	0
$988$	91207.2	2.93693
$989$	−3294.73	−0.105932
$990$	−8671.98	−0.278397
$991$	1736.44	0.0556608	0.0278304	−	0.999613i	$-0.491140\pi$
$991$	1736.44	0.0556608	0.0278304	+	0.999613i	$0.491140\pi$
$992$	3259.92	0.104337
$993$	−7282.67	−0.232738
$994$	0	0
$995$	−64232.7	−2.04655
$996$	1313.83	0.0417974
$997$	−1292.79	−0.0410663	−0.0205332	−	0.999789i	$-0.506536\pi$
$997$	−1292.79	−0.0410663	−0.0205332	+	0.999789i	$0.506536\pi$
$998$	38785.9	1.23021
$999$	−8842.01	−0.280029

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.z.1.9		10
7.3	odd	6		231.4.i.b.100.2	yes	20
7.5	odd	6		231.4.i.b.67.2	✓	20
7.6	odd	2		1617.4.a.y.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.i.b.67.2	✓	20	7.5	odd	6
231.4.i.b.100.2	yes	20	7.3	odd	6
1617.4.a.y.1.9		10	7.6	odd	2
1617.4.a.z.1.9		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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+4.14909 q^{2} +3.00000 q^{3} +9.21491 q^{4} +21.1121 q^{5} +12.4473 q^{6} +5.04076 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.14909 q^{2} +3.00000 q^{3} +9.21491 q^{4} +21.1121 q^{5} +12.4473 q^{6} +5.04076 q^{8} +9.00000 q^{9} +87.5957 q^{10} -11.0000 q^{11} +27.6447 q^{12} +70.8685 q^{13} +63.3362 q^{15} -52.8047 q^{16} -65.4434 q^{17} +37.3418 q^{18} +139.664 q^{19} +194.546 q^{20} -45.6399 q^{22} +16.2797 q^{23} +15.1223 q^{24} +320.719 q^{25} +294.039 q^{26} +27.0000 q^{27} -38.0026 q^{29} +262.787 q^{30} -12.5663 q^{31} -259.417 q^{32} -33.0000 q^{33} -271.530 q^{34} +82.9342 q^{36} -327.482 q^{37} +579.479 q^{38} +212.605 q^{39} +106.421 q^{40} +57.1522 q^{41} -202.383 q^{43} -101.364 q^{44} +190.008 q^{45} +67.5458 q^{46} -226.903 q^{47} -158.414 q^{48} +1330.69 q^{50} -196.330 q^{51} +653.046 q^{52} +503.459 q^{53} +112.025 q^{54} -232.233 q^{55} +418.993 q^{57} -157.676 q^{58} +225.260 q^{59} +583.637 q^{60} -258.774 q^{61} -52.1388 q^{62} -653.907 q^{64} +1496.18 q^{65} -136.920 q^{66} +814.894 q^{67} -603.055 q^{68} +48.8390 q^{69} +1012.06 q^{71} +45.3668 q^{72} +316.707 q^{73} -1358.75 q^{74} +962.156 q^{75} +1286.99 q^{76} +882.118 q^{78} -364.813 q^{79} -1114.82 q^{80} +81.0000 q^{81} +237.129 q^{82} +47.5254 q^{83} -1381.65 q^{85} -839.704 q^{86} -114.008 q^{87} -55.4483 q^{88} -750.827 q^{89} +788.361 q^{90} +150.016 q^{92} -37.6990 q^{93} -941.440 q^{94} +2948.60 q^{95} -778.252 q^{96} -883.329 q^{97} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9	\( 10 q + 4 q^{2} + 30 q^{3} + 26 q^{4} + 20 q^{5} + 12 q^{6} + 36 q^{8} + 90 q^{9} + 44 q^{10} - 110 q^{11} + 78 q^{12} + 82 q^{13} + 60 q^{15} - 10 q^{16} + 164 q^{17} + 36 q^{18} - 76 q^{19} + 356 q^{20} - 44 q^{22} + 140 q^{23} + 108 q^{24} + 472 q^{25} + 360 q^{26} + 270 q^{27} + 40 q^{29} + 132 q^{30} + 24 q^{31} + 112 q^{32} - 330 q^{33} - 262 q^{34} + 234 q^{36} + 412 q^{37} + 16 q^{38} + 246 q^{39} + 828 q^{40} - 228 q^{41} + 530 q^{43} - 286 q^{44} + 180 q^{45} + 1422 q^{46} + 768 q^{47} - 30 q^{48} + 670 q^{50} + 492 q^{51} + 952 q^{52} + 136 q^{53} + 108 q^{54} - 220 q^{55} - 228 q^{57} + 1708 q^{58} + 608 q^{59} + 1068 q^{60} + 1618 q^{61} + 164 q^{62} - 1238 q^{64} + 2764 q^{65} - 132 q^{66} + 1002 q^{67} + 2816 q^{68} + 420 q^{69} + 812 q^{71} + 324 q^{72} + 134 q^{73} + 342 q^{74} + 1416 q^{75} - 450 q^{76} + 1080 q^{78} + 1262 q^{79} - 1316 q^{80} + 810 q^{81} + 982 q^{82} + 1078 q^{83} - 1402 q^{85} + 1692 q^{86} + 120 q^{87} - 396 q^{88} + 2880 q^{89} + 396 q^{90} + 2364 q^{92} + 72 q^{93} - 2362 q^{94} + 2866 q^{95} + 336 q^{96} - 1030 q^{97} - 990 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 + 30 * q^3 + 26 * q^4 + 20 * q^5 + 12 * q^6 + 36 * q^8 + 90 * q^9 + 44 * q^10 - 110 * q^11 + 78 * q^12 + 82 * q^13 + 60 * q^15 - 10 * q^16 + 164 * q^17 + 36 * q^18 - 76 * q^19 + 356 * q^20 - 44 * q^22 + 140 * q^23 + 108 * q^24 + 472 * q^25 + 360 * q^26 + 270 * q^27 + 40 * q^29 + 132 * q^30 + 24 * q^31 + 112 * q^32 - 330 * q^33 - 262 * q^34 + 234 * q^36 + 412 * q^37 + 16 * q^38 + 246 * q^39 + 828 * q^40 - 228 * q^41 + 530 * q^43 - 286 * q^44 + 180 * q^45 + 1422 * q^46 + 768 * q^47 - 30 * q^48 + 670 * q^50 + 492 * q^51 + 952 * q^52 + 136 * q^53 + 108 * q^54 - 220 * q^55 - 228 * q^57 + 1708 * q^58 + 608 * q^59 + 1068 * q^60 + 1618 * q^61 + 164 * q^62 - 1238 * q^64 + 2764 * q^65 - 132 * q^66 + 1002 * q^67 + 2816 * q^68 + 420 * q^69 + 812 * q^71 + 324 * q^72 + 134 * q^73 + 342 * q^74 + 1416 * q^75 - 450 * q^76 + 1080 * q^78 + 1262 * q^79 - 1316 * q^80 + 810 * q^81 + 982 * q^82 + 1078 * q^83 - 1402 * q^85 + 1692 * q^86 + 120 * q^87 - 396 * q^88 + 2880 * q^89 + 396 * q^90 + 2364 * q^92 + 72 * q^93 - 2362 * q^94 + 2866 * q^95 + 336 * q^96 - 1030 * q^97 - 990 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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