LMFDB - Embedded newform 1870.4.a.l.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1870,4,Mod(1,1870)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1870, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1870.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 1870 = 2 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1870.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$110.333571711$
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} - 188 x^{8} - 48 x^{7} + 11155 x^{6} + 5616 x^{5} - 235675 x^{4} - 52830 x^{3} + 1553057 x^{2} + \cdots + 133376 $ x^10 - 188x^8 - 48x^7 + 11155x^6 + 5616x^5 - 235675x^4 - 52830x^3 + 1553057x^2 - 900114x + 133376
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.315034$ of defining polynomial
Character	$\chi$	$=$	1870.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} +0.315034 q^{3} +4.00000 q^{4} +5.00000 q^{5} +0.630069 q^{6} -30.9763 q^{7} +8.00000 q^{8} -26.9008 q^{9} +10.0000 q^{10} -11.0000 q^{11} +1.26014 q^{12} -11.6376 q^{13} -61.9526 q^{14} +1.57517 q^{15} +16.0000 q^{16} -17.0000 q^{17} -53.8015 q^{18} -160.502 q^{19} +20.0000 q^{20} -9.75860 q^{21} -22.0000 q^{22} +149.490 q^{23} +2.52028 q^{24} +25.0000 q^{25} -23.2752 q^{26} -16.9806 q^{27} -123.905 q^{28} +183.648 q^{29} +3.15034 q^{30} +56.7691 q^{31} +32.0000 q^{32} -3.46538 q^{33} -34.0000 q^{34} -154.881 q^{35} -107.603 q^{36} -134.463 q^{37} -321.004 q^{38} -3.66625 q^{39} +40.0000 q^{40} +162.505 q^{41} -19.5172 q^{42} +515.901 q^{43} -44.0000 q^{44} -134.504 q^{45} +298.979 q^{46} -12.2499 q^{47} +5.04055 q^{48} +616.531 q^{49} +50.0000 q^{50} -5.35558 q^{51} -46.5505 q^{52} -2.55486 q^{53} -33.9612 q^{54} -55.0000 q^{55} -247.810 q^{56} -50.5637 q^{57} +367.296 q^{58} +52.3867 q^{59} +6.30069 q^{60} -219.657 q^{61} +113.538 q^{62} +833.286 q^{63} +64.0000 q^{64} -58.1881 q^{65} -6.93076 q^{66} +42.0953 q^{67} -68.0000 q^{68} +47.0944 q^{69} -309.763 q^{70} +580.333 q^{71} -215.206 q^{72} +387.175 q^{73} -268.927 q^{74} +7.87586 q^{75} -642.009 q^{76} +340.739 q^{77} -7.33250 q^{78} +667.753 q^{79} +80.0000 q^{80} +720.971 q^{81} +325.011 q^{82} +1065.70 q^{83} -39.0344 q^{84} -85.0000 q^{85} +1031.80 q^{86} +57.8554 q^{87} -88.0000 q^{88} +1134.74 q^{89} -269.008 q^{90} +360.490 q^{91} +597.958 q^{92} +17.8842 q^{93} -24.4998 q^{94} -802.511 q^{95} +10.0811 q^{96} -1294.74 q^{97} +1233.06 q^{98} +295.908 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 20 q^{2} + 40 q^{4} + 50 q^{5} + 17 q^{7} + 80 q^{8} + 106 q^{9} + 100 q^{10} - 110 q^{11} + 118 q^{13} + 34 q^{14} + 160 q^{16} - 170 q^{17} + 212 q^{18} + 146 q^{19} + 200 q^{20} + 136 q^{21} - 220 q^{22}+ \cdots - 1166 q^{99}+O(q^{100}) $ 10 * q + 20 * q^2 + 40 * q^4 + 50 * q^5 + 17 * q^7 + 80 * q^8 + 106 * q^9 + 100 * q^10 - 110 * q^11 + 118 * q^13 + 34 * q^14 + 160 * q^16 - 170 * q^17 + 212 * q^18 + 146 * q^19 + 200 * q^20 + 136 * q^21 - 220 * q^22 + 278 * q^23 + 250 * q^25 + 236 * q^26 + 144 * q^27 + 68 * q^28 + 167 * q^29 + 520 * q^31 + 320 * q^32 - 340 * q^34 + 85 * q^35 + 424 * q^36 + 412 * q^37 + 292 * q^38 + 428 * q^39 + 400 * q^40 + 939 * q^41 + 272 * q^42 + 1398 * q^43 - 440 * q^44 + 530 * q^45 + 556 * q^46 + 569 * q^47 + 467 * q^49 + 500 * q^50 + 472 * q^52 + 1029 * q^53 + 288 * q^54 - 550 * q^55 + 136 * q^56 - 44 * q^57 + 334 * q^58 + 769 * q^59 + 816 * q^61 + 1040 * q^62 + 1427 * q^63 + 640 * q^64 + 590 * q^65 + 173 * q^67 - 680 * q^68 - 994 * q^69 + 170 * q^70 + 1808 * q^71 + 848 * q^72 + 1137 * q^73 + 824 * q^74 + 584 * q^76 - 187 * q^77 + 856 * q^78 - 382 * q^79 + 800 * q^80 + 2902 * q^81 + 1878 * q^82 + 1130 * q^83 + 544 * q^84 - 850 * q^85 + 2796 * q^86 + 2626 * q^87 - 880 * q^88 - 313 * q^89 + 1060 * q^90 + 1418 * q^91 + 1112 * q^92 + 2152 * q^93 + 1138 * q^94 + 730 * q^95 - 58 * q^97 + 934 * q^98 - 1166 * q^99

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	0.315034	0.0606284	0.0303142	−	0.999540i	$-0.490349\pi$
$3$	0.315034	0.0606284	0.0303142	+	0.999540i	$0.490349\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0.630069	0.0428707
$7$	−30.9763	−1.67256	−0.836281	−	0.548301i	$-0.815275\pi$
$7$	−30.9763	−1.67256	−0.836281	+	0.548301i	$0.815275\pi$
$8$	8.00000	0.353553
$9$	−26.9008	−0.996324
$10$	10.0000	0.316228
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	1.26014	0.0303142
$13$	−11.6376	−0.248284	−0.124142	−	0.992264i	$-0.539618\pi$
$13$	−11.6376	−0.248284	−0.124142	+	0.992264i	$0.539618\pi$
$14$	−61.9526	−1.18268
$15$	1.57517	0.0271138
$16$	16.0000	0.250000
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	−53.8015	−0.704508
$19$	−160.502	−1.93799	−0.968993	−	0.247089i	$-0.920526\pi$
$19$	−160.502	−1.93799	−0.968993	+	0.247089i	$0.920526\pi$
$20$	20.0000	0.223607
$21$	−9.75860	−0.101405
$22$	−22.0000	−0.213201
$23$	149.490	1.35525	0.677625	−	0.735408i	$-0.263009\pi$
$23$	149.490	1.35525	0.677625	+	0.735408i	$0.263009\pi$
$24$	2.52028	0.0214354
$25$	25.0000	0.200000
$26$	−23.2752	−0.175564
$27$	−16.9806	−0.121034
$28$	−123.905	−0.836281
$29$	183.648	1.17595	0.587975	−	0.808879i	$-0.299925\pi$
$29$	183.648	1.17595	0.587975	+	0.808879i	$0.299925\pi$
$30$	3.15034	0.0191724
$31$	56.7691	0.328904	0.164452	−	0.986385i	$-0.447414\pi$
$31$	56.7691	0.328904	0.164452	+	0.986385i	$0.447414\pi$
$32$	32.0000	0.176777
$33$	−3.46538	−0.0182801
$34$	−34.0000	−0.171499
$35$	−154.881	−0.747993
$36$	−107.603	−0.498162
$37$	−134.463	−0.597450	−0.298725	−	0.954339i	$-0.596561\pi$
$37$	−134.463	−0.597450	−0.298725	+	0.954339i	$0.596561\pi$
$38$	−321.004	−1.37036
$39$	−3.66625	−0.0150531
$40$	40.0000	0.158114
$41$	162.505	0.619002	0.309501	−	0.950899i	$-0.399838\pi$
$41$	162.505	0.619002	0.309501	+	0.950899i	$0.399838\pi$
$42$	−19.5172	−0.0717040
$43$	515.901	1.82963	0.914816	−	0.403872i	$-0.132336\pi$
$43$	515.901	1.82963	0.914816	+	0.403872i	$0.132336\pi$
$44$	−44.0000	−0.150756
$45$	−134.504	−0.445570
$46$	298.979	0.958306
$47$	−12.2499	−0.0380176	−0.0190088	−	0.999819i	$-0.506051\pi$
$47$	−12.2499	−0.0380176	−0.0190088	+	0.999819i	$0.506051\pi$
$48$	5.04055	0.0151571
$49$	616.531	1.79747
$50$	50.0000	0.141421
$51$	−5.35558	−0.0147045
$52$	−46.5505	−0.124142
$53$	−2.55486	−0.00662144	−0.00331072	−	0.999995i	$-0.501054\pi$
$53$	−2.55486	−0.00662144	−0.00331072	+	0.999995i	$0.501054\pi$
$54$	−33.9612	−0.0855839
$55$	−55.0000	−0.134840
$56$	−247.810	−0.591340
$57$	−50.5637	−0.117497
$58$	367.296	0.831522
$59$	52.3867	0.115596	0.0577980	−	0.998328i	$-0.481592\pi$
$59$	52.3867	0.115596	0.0577980	+	0.998328i	$0.481592\pi$
$60$	6.30069	0.0135569
$61$	−219.657	−0.461052	−0.230526	−	0.973066i	$-0.574045\pi$
$61$	−219.657	−0.461052	−0.230526	+	0.973066i	$0.574045\pi$
$62$	113.538	0.232571
$63$	833.286	1.66641
$64$	64.0000	0.125000
$65$	−58.1881	−0.111036
$66$	−6.93076	−0.0129260
$67$	42.0953	0.0767576	0.0383788	−	0.999263i	$-0.487781\pi$
$67$	42.0953	0.0767576	0.0383788	+	0.999263i	$0.487781\pi$
$68$	−68.0000	−0.121268
$69$	47.0944	0.0821666
$70$	−309.763	−0.528911
$71$	580.333	0.970041	0.485020	−	0.874503i	$-0.338812\pi$
$71$	580.333	0.970041	0.485020	+	0.874503i	$0.338812\pi$
$72$	−215.206	−0.352254
$73$	387.175	0.620759	0.310379	−	0.950613i	$-0.399544\pi$
$73$	387.175	0.620759	0.310379	+	0.950613i	$0.399544\pi$
$74$	−268.927	−0.422461
$75$	7.87586	0.0121257
$76$	−642.009	−0.968993
$77$	340.739	0.504297
$78$	−7.33250	−0.0106441
$79$	667.753	0.950989	0.475494	−	0.879719i	$-0.342269\pi$
$79$	667.753	0.950989	0.475494	+	0.879719i	$0.342269\pi$
$80$	80.0000	0.111803
$81$	720.971	0.988986
$82$	325.011	0.437700
$83$	1065.70	1.40935	0.704673	−	0.709532i	$-0.251094\pi$
$83$	1065.70	1.40935	0.704673	+	0.709532i	$0.251094\pi$
$84$	−39.0344	−0.0507024
$85$	−85.0000	−0.108465
$86$	1031.80	1.29374
$87$	57.8554	0.0712960
$88$	−88.0000	−0.106600
$89$	1134.74	1.35149	0.675744	−	0.737137i	$-0.263823\pi$
$89$	1134.74	1.35149	0.675744	+	0.737137i	$0.263823\pi$
$90$	−269.008	−0.315065
$91$	360.490	0.415271
$92$	597.958	0.677625
$93$	17.8842	0.0199409
$94$	−24.4998	−0.0268825
$95$	−802.511	−0.866694
$96$	10.0811	0.0107177
$97$	−1294.74	−1.35527	−0.677635	−	0.735398i	$-0.736995\pi$
$97$	−1294.74	−1.35527	−0.677635	+	0.735398i	$0.736995\pi$
$98$	1233.06	1.27100
$99$	295.908	0.300403
$100$	100.000	0.100000
$101$	−951.961	−0.937858	−0.468929	−	0.883236i	$-0.655360\pi$
$101$	−951.961	−0.937858	−0.468929	+	0.883236i	$0.655360\pi$
$102$	−10.7112	−0.0103977
$103$	−1026.11	−0.981606	−0.490803	−	0.871270i	$-0.663297\pi$
$103$	−1026.11	−0.981606	−0.490803	+	0.871270i	$0.663297\pi$
$104$	−93.1010	−0.0877818
$105$	−48.7930	−0.0453496
$106$	−5.10971	−0.00468207
$107$	−1632.80	−1.47523	−0.737613	−	0.675224i	$-0.764047\pi$
$107$	−1632.80	−1.47523	−0.737613	+	0.675224i	$0.764047\pi$
$108$	−67.9224	−0.0605170
$109$	724.237	0.636416	0.318208	−	0.948021i	$-0.396919\pi$
$109$	724.237	0.636416	0.318208	+	0.948021i	$0.396919\pi$
$110$	−110.000	−0.0953463
$111$	−42.3606	−0.0362224
$112$	−495.621	−0.418141
$113$	−1315.49	−1.09514	−0.547570	−	0.836760i	$-0.684447\pi$
$113$	−1315.49	−1.09514	−0.547570	+	0.836760i	$0.684447\pi$
$114$	−101.127	−0.0830829
$115$	747.448	0.606086
$116$	734.591	0.587975
$117$	313.061	0.247372
$118$	104.773	0.0817388
$119$	526.597	0.405656
$120$	12.6014	0.00958619
$121$	121.000	0.0909091
$122$	−439.313	−0.326013
$123$	51.1948	0.0375291
$124$	227.077	0.164452
$125$	125.000	0.0894427
$126$	1666.57	1.17833
$127$	411.661	0.287630	0.143815	−	0.989605i	$-0.454063\pi$
$127$	411.661	0.287630	0.143815	+	0.989605i	$0.454063\pi$
$128$	128.000	0.0883883
$129$	162.527	0.110928
$130$	−116.376	−0.0785144
$131$	2584.86	1.72397	0.861984	−	0.506935i	$-0.169222\pi$
$131$	2584.86	1.72397	0.861984	+	0.506935i	$0.169222\pi$
$132$	−13.8615	−0.00914007
$133$	4971.76	3.24140
$134$	84.1906	0.0542758
$135$	−84.9030	−0.0541280
$136$	−136.000	−0.0857493
$137$	−2212.71	−1.37989	−0.689943	−	0.723864i	$-0.742364\pi$
$137$	−2212.71	−1.37989	−0.689943	+	0.723864i	$0.742364\pi$
$138$	94.1887	0.0581006
$139$	2622.24	1.60011	0.800055	−	0.599926i	$-0.204803\pi$
$139$	2622.24	1.60011	0.800055	+	0.599926i	$0.204803\pi$
$140$	−619.526	−0.373996
$141$	−3.85913	−0.00230495
$142$	1160.67	0.685922
$143$	128.014	0.0748605
$144$	−430.412	−0.249081
$145$	918.239	0.525901
$146$	774.350	0.438943
$147$	194.228	0.108977
$148$	−537.854	−0.298725
$149$	−2247.66	−1.23581	−0.617904	−	0.786254i	$-0.712018\pi$
$149$	−2247.66	−1.23581	−0.617904	+	0.786254i	$0.712018\pi$
$150$	15.7517	0.00857415
$151$	1850.83	0.997475	0.498737	−	0.866753i	$-0.333797\pi$
$151$	1850.83	0.997475	0.498737	+	0.866753i	$0.333797\pi$
$152$	−1284.02	−0.685181
$153$	457.313	0.241644
$154$	681.478	0.356592
$155$	283.846	0.147091
$156$	−14.6650	−0.00752654
$157$	1535.65	0.780626	0.390313	−	0.920682i	$-0.372367\pi$
$157$	1535.65	0.780626	0.390313	+	0.920682i	$0.372367\pi$
$158$	1335.51	0.672451
$159$	−0.804867	−0.000401447 0
$160$	160.000	0.0790569
$161$	−4630.63	−2.26674
$162$	1441.94	0.699319
$163$	−19.2882	−0.00926853	−0.00463426	−	0.999989i	$-0.501475\pi$
$163$	−19.2882	−0.00926853	−0.00463426	+	0.999989i	$0.501475\pi$
$164$	650.022	0.309501
$165$	−17.3269	−0.00817513
$166$	2131.40	0.996558
$167$	1389.99	0.644076	0.322038	−	0.946727i	$-0.395632\pi$
$167$	1389.99	0.644076	0.322038	+	0.946727i	$0.395632\pi$
$168$	−78.0688	−0.0358520
$169$	−2061.57	−0.938355
$170$	−170.000	−0.0766965
$171$	4317.63	1.93086
$172$	2063.60	0.914816
$173$	851.871	0.374373	0.187187	−	0.982324i	$-0.440063\pi$
$173$	851.871	0.374373	0.187187	+	0.982324i	$0.440063\pi$
$174$	115.711	0.0504139
$175$	−774.407	−0.334513
$176$	−176.000	−0.0753778
$177$	16.5036	0.00700840
$178$	2269.48	0.955646
$179$	−3819.85	−1.59502	−0.797511	−	0.603305i	$-0.793850\pi$
$179$	−3819.85	−1.59502	−0.797511	+	0.603305i	$0.793850\pi$
$180$	−538.015	−0.222785
$181$	−371.610	−0.152605	−0.0763027	−	0.997085i	$-0.524312\pi$
$181$	−371.610	−0.152605	−0.0763027	+	0.997085i	$0.524312\pi$
$182$	720.981	0.293641
$183$	−69.1994	−0.0279528
$184$	1195.92	0.479153
$185$	−672.317	−0.267188
$186$	35.7685	0.0141004
$187$	187.000	0.0731272
$188$	−48.9995	−0.0190088
$189$	525.996	0.202437
$190$	−1605.02	−0.612845
$191$	−4600.78	−1.74294	−0.871468	−	0.490452i	$-0.836832\pi$
$191$	−4600.78	−1.74294	−0.871468	+	0.490452i	$0.836832\pi$
$192$	20.1622	0.00757855
$193$	462.626	0.172542	0.0862709	−	0.996272i	$-0.472505\pi$
$193$	462.626	0.172542	0.0862709	+	0.996272i	$0.472505\pi$
$194$	−2589.49	−0.958321
$195$	−18.3313	−0.00673194
$196$	2466.12	0.898733
$197$	3863.67	1.39733	0.698667	−	0.715447i	$-0.253777\pi$
$197$	3863.67	1.39733	0.698667	+	0.715447i	$0.253777\pi$
$198$	591.817	0.212417
$199$	−151.938	−0.0541236	−0.0270618	−	0.999634i	$-0.508615\pi$
$199$	−151.938	−0.0541236	−0.0270618	+	0.999634i	$0.508615\pi$
$200$	200.000	0.0707107
$201$	13.2615	0.00465369
$202$	−1903.92	−0.663166
$203$	−5688.73	−1.96685
$204$	−21.4223	−0.00735227
$205$	812.527	0.276826
$206$	−2052.22	−0.694101
$207$	−4021.38	−1.35027
$208$	−186.202	−0.0620711
$209$	1765.52	0.584325
$210$	−97.5860	−0.0320670
$211$	−1971.87	−0.643362	−0.321681	−	0.946848i	$-0.604248\pi$
$211$	−1971.87	−0.643362	−0.321681	+	0.946848i	$0.604248\pi$
$212$	−10.2194	−0.00331072
$213$	182.825	0.0588120
$214$	−3265.61	−1.04314
$215$	2579.50	0.818236
$216$	−135.845	−0.0427920
$217$	−1758.50	−0.550113
$218$	1448.47	0.450014
$219$	121.973	0.0376356
$220$	−220.000	−0.0674200
$221$	197.840	0.0602178
$222$	−84.7212	−0.0256131
$223$	509.282	0.152933	0.0764665	−	0.997072i	$-0.475636\pi$
$223$	509.282	0.152933	0.0764665	+	0.997072i	$0.475636\pi$
$224$	−991.241	−0.295670
$225$	−672.519	−0.199265
$226$	−2630.98	−0.774381
$227$	2247.82	0.657239	0.328619	−	0.944462i	$-0.393417\pi$
$227$	2247.82	0.657239	0.328619	+	0.944462i	$0.393417\pi$
$228$	−202.255	−0.0587485
$229$	−466.583	−0.134640	−0.0673202	−	0.997731i	$-0.521445\pi$
$229$	−466.583	−0.134640	−0.0673202	+	0.997731i	$0.521445\pi$
$230$	1494.90	0.428568
$231$	107.345	0.0305747
$232$	1469.18	0.415761
$233$	3007.52	0.845620	0.422810	−	0.906218i	$-0.361044\pi$
$233$	3007.52	0.845620	0.422810	+	0.906218i	$0.361044\pi$
$234$	626.122	0.174918
$235$	−61.2494	−0.0170020
$236$	209.547	0.0577980
$237$	210.365	0.0576569
$238$	1053.19	0.286842
$239$	−2597.59	−0.703029	−0.351514	−	0.936182i	$-0.614333\pi$
$239$	−2597.59	−0.703029	−0.351514	+	0.936182i	$0.614333\pi$
$240$	25.2028	0.00677846
$241$	−6393.76	−1.70896	−0.854478	−	0.519488i	$-0.826123\pi$
$241$	−6393.76	−1.70896	−0.854478	+	0.519488i	$0.826123\pi$
$242$	242.000	0.0642824
$243$	685.607	0.180995
$244$	−878.627	−0.230526
$245$	3082.65	0.803851
$246$	102.390	0.0265371
$247$	1867.86	0.481171
$248$	454.153	0.116285
$249$	335.732	0.0854464
$250$	250.000	0.0632456
$251$	7265.20	1.82699	0.913497	−	0.406846i	$-0.133371\pi$
$251$	7265.20	1.82699	0.913497	+	0.406846i	$0.133371\pi$
$252$	3333.14	0.833207
$253$	−1644.39	−0.408623
$254$	823.323	0.203385
$255$	−26.7779	−0.00657607
$256$	256.000	0.0625000
$257$	1768.79	0.429316	0.214658	−	0.976689i	$-0.431136\pi$
$257$	1768.79	0.429316	0.214658	+	0.976689i	$0.431136\pi$
$258$	325.053	0.0784377
$259$	4165.18	0.999273
$260$	−232.752	−0.0555181
$261$	−4940.27	−1.17163
$262$	5169.71	1.21903
$263$	−5609.43	−1.31518	−0.657590	−	0.753376i	$-0.728424\pi$
$263$	−5609.43	−1.31518	−0.657590	+	0.753376i	$0.728424\pi$
$264$	−27.7230	−0.00646301
$265$	−12.7743	−0.00296120
$266$	9943.53	2.29202
$267$	357.483	0.0819385
$268$	168.381	0.0383788
$269$	−4947.62	−1.12142	−0.560709	−	0.828013i	$-0.689471\pi$
$269$	−4947.62	−1.12142	−0.560709	+	0.828013i	$0.689471\pi$
$270$	−169.806	−0.0382743
$271$	7160.19	1.60498	0.802492	−	0.596662i	$-0.203507\pi$
$271$	7160.19	1.60498	0.802492	+	0.596662i	$0.203507\pi$
$272$	−272.000	−0.0606339
$273$	113.567	0.0251772
$274$	−4425.41	−0.975726
$275$	−275.000	−0.0603023
$276$	188.377	0.0410833
$277$	−874.235	−0.189631	−0.0948153	−	0.995495i	$-0.530226\pi$
$277$	−874.235	−0.189631	−0.0948153	+	0.995495i	$0.530226\pi$
$278$	5244.48	1.13145
$279$	−1527.13	−0.327695
$280$	−1239.05	−0.264455
$281$	2387.19	0.506790	0.253395	−	0.967363i	$-0.418453\pi$
$281$	2387.19	0.506790	0.253395	+	0.967363i	$0.418453\pi$
$282$	−7.71827	−0.00162984
$283$	1916.75	0.402611	0.201305	−	0.979529i	$-0.435482\pi$
$283$	1916.75	0.402611	0.201305	+	0.979529i	$0.435482\pi$
$284$	2321.33	0.485020
$285$	−252.819	−0.0525462
$286$	256.028	0.0529344
$287$	−5033.81	−1.03532
$288$	−860.824	−0.176127
$289$	289.000	0.0588235
$290$	1836.48	0.371868
$291$	−407.889	−0.0821679
$292$	1548.70	0.310379
$293$	5948.64	1.18609	0.593043	−	0.805171i	$-0.297927\pi$
$293$	5948.64	1.18609	0.593043	+	0.805171i	$0.297927\pi$
$294$	388.457	0.0770587
$295$	261.934	0.0516961
$296$	−1075.71	−0.211231
$297$	186.786	0.0364931
$298$	−4495.32	−0.873848
$299$	−1739.70	−0.336487
$300$	31.5034	0.00606284
$301$	−15980.7	−3.06017
$302$	3701.67	0.705321
$303$	−299.900	−0.0568608
$304$	−2568.04	−0.484496
$305$	−1098.28	−0.206189
$306$	914.626	0.170868
$307$	5335.01	0.991808	0.495904	−	0.868377i	$-0.334837\pi$
$307$	5335.01	0.991808	0.495904	+	0.868377i	$0.334837\pi$
$308$	1362.96	0.252148
$309$	−323.259	−0.0595132
$310$	567.691	0.104009
$311$	144.451	0.0263378	0.0131689	−	0.999913i	$-0.495808\pi$
$311$	144.451	0.0263378	0.0131689	+	0.999913i	$0.495808\pi$
$312$	−29.3300	−0.00532207
$313$	−3950.15	−0.713341	−0.356670	−	0.934230i	$-0.616088\pi$
$313$	−3950.15	−0.713341	−0.356670	+	0.934230i	$0.616088\pi$
$314$	3071.30	0.551986
$315$	4166.43	0.745243
$316$	2671.01	0.475494
$317$	−3622.12	−0.641761	−0.320881	−	0.947120i	$-0.603979\pi$
$317$	−3622.12	−0.641761	−0.320881	+	0.947120i	$0.603979\pi$
$318$	−1.60973	−0.000283866 0
$319$	−2020.13	−0.354562
$320$	320.000	0.0559017
$321$	−514.390	−0.0894406
$322$	−9261.27	−1.60283
$323$	2728.54	0.470031
$324$	2883.88	0.494493
$325$	−290.941	−0.0496569
$326$	−38.5764	−0.00655384
$327$	228.160	0.0385849
$328$	1300.04	0.218850
$329$	379.456	0.0635869
$330$	−34.6538	−0.00578069
$331$	6790.42	1.12760	0.563799	−	0.825912i	$-0.309339\pi$
$331$	6790.42	1.12760	0.563799	+	0.825912i	$0.309339\pi$
$332$	4262.80	0.704673
$333$	3617.17	0.595254
$334$	2779.98	0.455430
$335$	210.476	0.0343270
$336$	−156.138	−0.0253512
$337$	11300.7	1.82668	0.913339	−	0.407201i	$-0.133495\pi$
$337$	11300.7	1.82668	0.913339	+	0.407201i	$0.133495\pi$
$338$	−4123.13	−0.663517
$339$	−414.424	−0.0663966
$340$	−340.000	−0.0542326
$341$	−624.460	−0.0991684
$342$	8635.26	1.36533
$343$	−8472.97	−1.33381
$344$	4127.21	0.646872
$345$	235.472	0.0367460
$346$	1703.74	0.264722
$347$	4692.42	0.725943	0.362972	−	0.931800i	$-0.381762\pi$
$347$	4692.42	0.725943	0.362972	+	0.931800i	$0.381762\pi$
$348$	231.422	0.0356480
$349$	2518.10	0.386221	0.193110	−	0.981177i	$-0.438142\pi$
$349$	2518.10	0.386221	0.193110	+	0.981177i	$0.438142\pi$
$350$	−1548.81	−0.236536
$351$	197.614	0.0300508
$352$	−352.000	−0.0533002
$353$	−2790.36	−0.420725	−0.210362	−	0.977624i	$-0.567464\pi$
$353$	−2790.36	−0.420725	−0.210362	+	0.977624i	$0.567464\pi$
$354$	33.0072	0.00495569
$355$	2901.67	0.433815
$356$	4538.97	0.675744
$357$	165.896	0.0245943
$358$	−7639.69	−1.12785
$359$	4181.16	0.614689	0.307345	−	0.951598i	$-0.400560\pi$
$359$	4181.16	0.614689	0.307345	+	0.951598i	$0.400560\pi$
$360$	−1076.03	−0.157533
$361$	18902.0	2.75579
$362$	−743.221	−0.107908
$363$	38.1192	0.00551167
$364$	1441.96	0.207636
$365$	1935.87	0.277612
$366$	−138.399	−0.0197656
$367$	5305.14	0.754566	0.377283	−	0.926098i	$-0.376858\pi$
$367$	5305.14	0.754566	0.377283	+	0.926098i	$0.376858\pi$
$368$	2391.83	0.338812
$369$	−4371.52	−0.616727
$370$	−1344.63	−0.188930
$371$	79.1399	0.0110748
$372$	71.5369	0.00997047
$373$	8940.59	1.24109	0.620544	−	0.784171i	$-0.286912\pi$
$373$	8940.59	1.24109	0.620544	+	0.784171i	$0.286912\pi$
$374$	374.000	0.0517088
$375$	39.3793	0.00542277
$376$	−97.9990	−0.0134413
$377$	−2137.22	−0.291970
$378$	1051.99	0.143144
$379$	−7970.48	−1.08025	−0.540127	−	0.841584i	$-0.681624\pi$
$379$	−7970.48	−1.08025	−0.540127	+	0.841584i	$0.681624\pi$
$380$	−3210.04	−0.433347
$381$	129.687	0.0174386
$382$	−9201.56	−1.23244
$383$	13425.5	1.79115	0.895577	−	0.444907i	$-0.146763\pi$
$383$	13425.5	1.79115	0.895577	+	0.444907i	$0.146763\pi$
$384$	40.3244	0.00535884
$385$	1703.70	0.225528
$386$	925.253	0.122006
$387$	−13878.1	−1.82291
$388$	−5178.97	−0.677635
$389$	−12675.4	−1.65211	−0.826053	−	0.563593i	$-0.809419\pi$
$389$	−12675.4	−1.65211	−0.826053	+	0.563593i	$0.809419\pi$
$390$	−36.6625	−0.00476020
$391$	−2541.32	−0.328696
$392$	4932.25	0.635500
$393$	814.318	0.104521
$394$	7727.34	0.988065
$395$	3338.77	0.425295
$396$	1183.63	0.150202
$397$	9726.18	1.22958	0.614790	−	0.788691i	$-0.289241\pi$
$397$	9726.18	1.22958	0.614790	+	0.788691i	$0.289241\pi$
$398$	−303.876	−0.0382712
$399$	1566.28	0.196521
$400$	400.000	0.0500000
$401$	73.6351	0.00916998	0.00458499	−	0.999989i	$-0.498541\pi$
$401$	73.6351	0.00916998	0.00458499	+	0.999989i	$0.498541\pi$
$402$	26.5229	0.00329065
$403$	−660.658	−0.0816618
$404$	−3807.84	−0.468929
$405$	3604.85	0.442288
$406$	−11377.5	−1.39077
$407$	1479.10	0.180138
$408$	−42.8447	−0.00519884
$409$	4333.28	0.523880	0.261940	−	0.965084i	$-0.415638\pi$
$409$	4333.28	0.523880	0.261940	+	0.965084i	$0.415638\pi$
$410$	1625.05	0.195746
$411$	−697.079	−0.0836602
$412$	−4104.43	−0.490803
$413$	−1622.75	−0.193342
$414$	−8042.77	−0.954784
$415$	5328.50	0.630279
$416$	−372.404	−0.0438909
$417$	826.095	0.0970121
$418$	3531.05	0.413180
$419$	8948.86	1.04339	0.521695	−	0.853132i	$-0.325300\pi$
$419$	8948.86	1.04339	0.521695	+	0.853132i	$0.325300\pi$
$420$	−195.172	−0.0226748
$421$	−13480.5	−1.56057	−0.780284	−	0.625426i	$-0.784925\pi$
$421$	−13480.5	−1.56057	−0.780284	+	0.625426i	$0.784925\pi$
$422$	−3943.75	−0.454926
$423$	329.531	0.0378779
$424$	−20.4388	−0.00234103
$425$	−425.000	−0.0485071
$426$	365.650	0.0415864
$427$	6804.15	0.771138
$428$	−6531.22	−0.737613
$429$	40.3288	0.00453867
$430$	5159.01	0.578580
$431$	−4480.02	−0.500684	−0.250342	−	0.968157i	$-0.580543\pi$
$431$	−4480.02	−0.500684	−0.250342	+	0.968157i	$0.580543\pi$
$432$	−271.689	−0.0302585
$433$	7930.54	0.880179	0.440090	−	0.897954i	$-0.354947\pi$
$433$	7930.54	0.880179	0.440090	+	0.897954i	$0.354947\pi$
$434$	−3516.99	−0.388989
$435$	289.277	0.0318845
$436$	2896.95	0.318208
$437$	−23993.4	−2.62645
$438$	243.947	0.0266124
$439$	−227.083	−0.0246881	−0.0123441	−	0.999924i	$-0.503929\pi$
$439$	−227.083	−0.0246881	−0.0123441	+	0.999924i	$0.503929\pi$
$440$	−440.000	−0.0476731
$441$	−16585.1	−1.79086
$442$	395.679	0.0425804
$443$	3205.93	0.343834	0.171917	−	0.985111i	$-0.445004\pi$
$443$	3205.93	0.343834	0.171917	+	0.985111i	$0.445004\pi$
$444$	−169.442	−0.0181112
$445$	5673.71	0.604403
$446$	1018.56	0.108140
$447$	−708.090	−0.0749251
$448$	−1982.48	−0.209070
$449$	18856.3	1.98193	0.990963	−	0.134132i	$-0.0428247\pi$
$449$	18856.3	1.98193	0.990963	+	0.134132i	$0.0428247\pi$
$450$	−1345.04	−0.140902
$451$	−1787.56	−0.186636
$452$	−5261.96	−0.547570
$453$	583.076	0.0604753
$454$	4495.65	0.464738
$455$	1802.45	0.185715
$456$	−404.510	−0.0415414
$457$	11466.7	1.17372	0.586858	−	0.809690i	$-0.300365\pi$
$457$	11466.7	1.17372	0.586858	+	0.809690i	$0.300365\pi$
$458$	−933.165	−0.0952052
$459$	288.670	0.0293550
$460$	2989.79	0.303043
$461$	−8207.67	−0.829218	−0.414609	−	0.910000i	$-0.636082\pi$
$461$	−8207.67	−0.829218	−0.414609	+	0.910000i	$0.636082\pi$
$462$	214.689	0.0216196
$463$	7106.53	0.713322	0.356661	−	0.934234i	$-0.383915\pi$
$463$	7106.53	0.713322	0.356661	+	0.934234i	$0.383915\pi$
$464$	2938.37	0.293988
$465$	89.4211	0.00891786
$466$	6015.05	0.597943
$467$	1530.56	0.151661	0.0758307	−	0.997121i	$-0.475839\pi$
$467$	1530.56	0.151661	0.0758307	+	0.997121i	$0.475839\pi$
$468$	1252.24	0.123686
$469$	−1303.96	−0.128382
$470$	−122.499	−0.0120222
$471$	483.783	0.0473281
$472$	419.094	0.0408694
$473$	−5674.91	−0.551655
$474$	420.731	0.0407696
$475$	−4012.55	−0.387597
$476$	2106.39	0.202828
$477$	68.7275	0.00659710
$478$	−5195.17	−0.497116
$479$	7523.95	0.717700	0.358850	−	0.933395i	$-0.383169\pi$
$479$	7523.95	0.717700	0.358850	+	0.933395i	$0.383169\pi$
$480$	50.4055	0.00479310
$481$	1564.83	0.148337
$482$	−12787.5	−1.20841
$483$	−1458.81	−0.137429
$484$	484.000	0.0454545
$485$	−6473.71	−0.606095
$486$	1371.21	0.127982
$487$	−2261.38	−0.210417	−0.105208	−	0.994450i	$-0.533551\pi$
$487$	−2261.38	−0.210417	−0.105208	+	0.994450i	$0.533551\pi$
$488$	−1757.25	−0.163006
$489$	−6.07645	−0.000561936 0
$490$	6165.31	0.568409
$491$	3674.41	0.337727	0.168863	−	0.985639i	$-0.445990\pi$
$491$	3674.41	0.337727	0.168863	+	0.985639i	$0.445990\pi$
$492$	204.779	0.0187645
$493$	−3122.01	−0.285210
$494$	3735.73	0.340240
$495$	1479.54	0.134344
$496$	908.306	0.0822261
$497$	−17976.6	−1.62245
$498$	671.464	0.0604197
$499$	6727.77	0.603560	0.301780	−	0.953378i	$-0.402419\pi$
$499$	6727.77	0.603560	0.301780	+	0.953378i	$0.402419\pi$
$500$	500.000	0.0447214
$501$	437.895	0.0390493
$502$	14530.4	1.29188
$503$	2999.27	0.265867	0.132933	−	0.991125i	$-0.457560\pi$
$503$	2999.27	0.265867	0.132933	+	0.991125i	$0.457560\pi$
$504$	6666.28	0.589167
$505$	−4759.80	−0.419423
$506$	−3288.77	−0.288940
$507$	−649.464	−0.0568910
$508$	1646.65	0.143815
$509$	−2121.92	−0.184779	−0.0923895	−	0.995723i	$-0.529450\pi$
$509$	−2121.92	−0.184779	−0.0923895	+	0.995723i	$0.529450\pi$
$510$	−53.5558	−0.00464999
$511$	−11993.2	−1.03826
$512$	512.000	0.0441942
$513$	2725.42	0.234562
$514$	3537.58	0.303572
$515$	−5130.54	−0.438988
$516$	650.106	0.0554638
$517$	134.749	0.0114627
$518$	8330.36	0.706592
$519$	268.369	0.0226976
$520$	−465.505	−0.0392572
$521$	−20888.5	−1.75651	−0.878256	−	0.478190i	$-0.841293\pi$
$521$	−20888.5	−1.75651	−0.878256	+	0.478190i	$0.841293\pi$
$522$	−9880.53	−0.828466
$523$	9983.79	0.834724	0.417362	−	0.908740i	$-0.362955\pi$
$523$	9983.79	0.834724	0.417362	+	0.908740i	$0.362955\pi$
$524$	10339.4	0.861984
$525$	−243.965	−0.0202810
$526$	−11218.9	−0.929973
$527$	−965.075	−0.0797710
$528$	−55.4461	−0.00457004
$529$	10180.1	0.836701
$530$	−25.5486	−0.00209388
$531$	−1409.24	−0.115171
$532$	19887.1	1.62070
$533$	−1891.18	−0.153688
$534$	714.965	0.0579393
$535$	−8164.02	−0.659741
$536$	336.762	0.0271379
$537$	−1203.38	−0.0967036
$538$	−9895.24	−0.792963
$539$	−6781.84	−0.541956
$540$	−339.612	−0.0270640
$541$	11697.1	0.929569	0.464785	−	0.885424i	$-0.346132\pi$
$541$	11697.1	0.929569	0.464785	+	0.885424i	$0.346132\pi$
$542$	14320.4	1.13490
$543$	−117.070	−0.00925222
$544$	−544.000	−0.0428746
$545$	3621.18	0.284614
$546$	227.134	0.0178030
$547$	−8815.64	−0.689085	−0.344543	−	0.938771i	$-0.611966\pi$
$547$	−8815.64	−0.689085	−0.344543	+	0.938771i	$0.611966\pi$
$548$	−8850.83	−0.689943
$549$	5908.93	0.459357
$550$	−550.000	−0.0426401
$551$	−29475.9	−2.27897
$552$	376.755	0.0290503
$553$	−20684.5	−1.59059
$554$	−1748.47	−0.134089
$555$	−211.803	−0.0161992
$556$	10489.0	0.800055
$557$	6742.24	0.512887	0.256443	−	0.966559i	$-0.417449\pi$
$557$	6742.24	0.512887	0.256443	+	0.966559i	$0.417449\pi$
$558$	−3054.26	−0.231716
$559$	−6003.86	−0.454269
$560$	−2478.10	−0.186998
$561$	58.9114	0.00443359
$562$	4774.39	0.358355
$563$	−7629.93	−0.571160	−0.285580	−	0.958355i	$-0.592186\pi$
$563$	−7629.93	−0.571160	−0.285580	+	0.958355i	$0.592186\pi$
$564$	−15.4365	−0.00115247
$565$	−6577.45	−0.489762
$566$	3833.50	0.284689
$567$	−22333.0	−1.65414
$568$	4642.67	0.342961
$569$	5375.50	0.396050	0.198025	−	0.980197i	$-0.436547\pi$
$569$	5375.50	0.396050	0.198025	+	0.980197i	$0.436547\pi$
$570$	−505.637	−0.0371558
$571$	−9019.06	−0.661009	−0.330504	−	0.943804i	$-0.607219\pi$
$571$	−9019.06	−0.661009	−0.330504	+	0.943804i	$0.607219\pi$
$572$	512.055	0.0374303
$573$	−1449.40	−0.105671
$574$	−10067.6	−0.732081
$575$	3737.24	0.271050
$576$	−1721.65	−0.124541
$577$	−4453.44	−0.321316	−0.160658	−	0.987010i	$-0.551362\pi$
$577$	−4453.44	−0.321316	−0.160658	+	0.987010i	$0.551362\pi$
$578$	578.000	0.0415945
$579$	145.743	0.0104609
$580$	3672.96	0.262950
$581$	−33011.4	−2.35722
$582$	−815.777	−0.0581015
$583$	28.1034	0.00199644
$584$	3097.40	0.219471
$585$	1565.30	0.110628
$586$	11897.3	0.838689
$587$	20944.9	1.47273	0.736363	−	0.676587i	$-0.236542\pi$
$587$	20944.9	1.47273	0.736363	+	0.676587i	$0.236542\pi$
$588$	776.913	0.0544887
$589$	−9111.57	−0.637412
$590$	523.867	0.0365547
$591$	1217.19	0.0847182
$592$	−2151.42	−0.149363
$593$	−4545.66	−0.314786	−0.157393	−	0.987536i	$-0.550309\pi$
$593$	−4545.66	−0.314786	−0.157393	+	0.987536i	$0.550309\pi$
$594$	373.573	0.0258045
$595$	2632.98	0.181415
$596$	−8990.64	−0.617904
$597$	−47.8657	−0.00328143
$598$	−3479.41	−0.237932
$599$	8512.13	0.580628	0.290314	−	0.956931i	$-0.406240\pi$
$599$	8512.13	0.580628	0.290314	+	0.956931i	$0.406240\pi$
$600$	63.0069	0.00428707
$601$	−3664.04	−0.248685	−0.124342	−	0.992239i	$-0.539682\pi$
$601$	−3664.04	−0.248685	−0.124342	+	0.992239i	$0.539682\pi$
$602$	−31961.4	−2.16387
$603$	−1132.39	−0.0764754
$604$	7403.33	0.498737
$605$	605.000	0.0406558
$606$	−599.801	−0.0402067
$607$	−3049.97	−0.203944	−0.101972	−	0.994787i	$-0.532515\pi$
$607$	−3049.97	−0.203944	−0.101972	+	0.994787i	$0.532515\pi$
$608$	−5136.07	−0.342591
$609$	−1792.15	−0.119247
$610$	−2196.57	−0.145797
$611$	142.559	0.00943918
$612$	1829.25	0.120822
$613$	−15534.0	−1.02351	−0.511756	−	0.859131i	$-0.671005\pi$
$613$	−15534.0	−1.02351	−0.511756	+	0.859131i	$0.671005\pi$
$614$	10670.0	0.701314
$615$	255.974	0.0167835
$616$	2725.91	0.178296
$617$	−10255.2	−0.669137	−0.334568	−	0.942371i	$-0.608590\pi$
$617$	−10255.2	−0.669137	−0.334568	+	0.942371i	$0.608590\pi$
$618$	−646.519	−0.0420822
$619$	−1647.51	−0.106978	−0.0534889	−	0.998568i	$-0.517034\pi$
$619$	−1647.51	−0.106978	−0.0534889	+	0.998568i	$0.517034\pi$
$620$	1135.38	0.0735453
$621$	−2538.42	−0.164031
$622$	288.902	0.0186236
$623$	−35150.1	−2.26045
$624$	−58.6600	−0.00376327
$625$	625.000	0.0400000
$626$	−7900.30	−0.504408
$627$	556.201	0.0354267
$628$	6142.60	0.390313
$629$	2285.88	0.144903
$630$	8332.86	0.526967
$631$	17100.9	1.07888	0.539441	−	0.842024i	$-0.318636\pi$
$631$	17100.9	1.07888	0.539441	+	0.842024i	$0.318636\pi$
$632$	5342.03	0.336225
$633$	−621.208	−0.0390060
$634$	−7244.23	−0.453794
$635$	2058.31	0.128632
$636$	−3.21947	−0.000200724 0
$637$	−7174.95	−0.446283
$638$	−4040.25	−0.250713
$639$	−15611.4	−0.966475
$640$	640.000	0.0395285
$641$	−21957.6	−1.35300	−0.676499	−	0.736444i	$-0.736504\pi$
$641$	−21957.6	−1.35300	−0.676499	+	0.736444i	$0.736504\pi$
$642$	−1028.78	−0.0632440
$643$	−47.7394	−0.00292793	−0.00146396	−	0.999999i	$-0.500466\pi$
$643$	−47.7394	−0.00292793	−0.00146396	+	0.999999i	$0.500466\pi$
$644$	−18522.5	−1.13337
$645$	812.633	0.0496083
$646$	5457.07	0.332362
$647$	−11033.9	−0.670460	−0.335230	−	0.942136i	$-0.608814\pi$
$647$	−11033.9	−0.670460	−0.335230	+	0.942136i	$0.608814\pi$
$648$	5767.77	0.349659
$649$	−576.254	−0.0348535
$650$	−581.881	−0.0351127
$651$	−553.987	−0.0333525
$652$	−77.1529	−0.00463426
$653$	−20580.6	−1.23336	−0.616678	−	0.787216i	$-0.711522\pi$
$653$	−20580.6	−1.23336	−0.616678	+	0.787216i	$0.711522\pi$
$654$	456.319	0.0272836
$655$	12924.3	0.770982
$656$	2600.09	0.154750
$657$	−10415.3	−0.618477
$658$	758.912	0.0449627
$659$	−4507.99	−0.266474	−0.133237	−	0.991084i	$-0.542537\pi$
$659$	−4507.99	−0.266474	−0.133237	+	0.991084i	$0.542537\pi$
$660$	−69.3076	−0.00408757
$661$	−26121.5	−1.53708	−0.768538	−	0.639804i	$-0.779016\pi$
$661$	−26121.5	−1.53708	−0.768538	+	0.639804i	$0.779016\pi$
$662$	13580.8	0.797332
$663$	62.3263	0.00365091
$664$	8525.60	0.498279
$665$	24858.8	1.44960
$666$	7234.34	0.420908
$667$	27453.4	1.59371
$668$	5559.96	0.322038
$669$	160.441	0.00927208
$670$	420.953	0.0242729
$671$	2416.22	0.139012
$672$	−312.275	−0.0179260
$673$	14944.9	0.855993	0.427996	−	0.903780i	$-0.359220\pi$
$673$	14944.9	0.855993	0.427996	+	0.903780i	$0.359220\pi$
$674$	22601.5	1.29166
$675$	−424.515	−0.0242068
$676$	−8246.26	−0.469177
$677$	4958.34	0.281484	0.140742	−	0.990046i	$-0.455051\pi$
$677$	4958.34	0.281484	0.140742	+	0.990046i	$0.455051\pi$
$678$	−828.849	−0.0469495
$679$	40106.3	2.26677
$680$	−680.000	−0.0383482
$681$	708.141	0.0398473
$682$	−1248.92	−0.0701227
$683$	−3170.21	−0.177606	−0.0888030	−	0.996049i	$-0.528304\pi$
$683$	−3170.21	−0.177606	−0.0888030	+	0.996049i	$0.528304\pi$
$684$	17270.5	0.965431
$685$	−11063.5	−0.617103
$686$	−16945.9	−0.943147
$687$	−146.990	−0.00816303
$688$	8254.41	0.457408
$689$	29.7324	0.00164400
$690$	470.944	0.0259834
$691$	−15069.1	−0.829605	−0.414803	−	0.909911i	$-0.636149\pi$
$691$	−15069.1	−0.829605	−0.414803	+	0.909911i	$0.636149\pi$
$692$	3407.48	0.187187
$693$	−9166.14	−0.502443
$694$	9384.84	0.513320
$695$	13111.2	0.715591
$696$	462.843	0.0252069
$697$	−2762.59	−0.150130
$698$	5036.21	0.273099
$699$	947.473	0.0512686
$700$	−3097.63	−0.167256
$701$	−2939.80	−0.158395	−0.0791974	−	0.996859i	$-0.525236\pi$
$701$	−2939.80	−0.158395	−0.0791974	+	0.996859i	$0.525236\pi$
$702$	395.227	0.0212491
$703$	21581.7	1.15785
$704$	−704.000	−0.0376889
$705$	−19.2957	−0.00103080
$706$	−5580.72	−0.297497
$707$	29488.2	1.56863
$708$	66.0145	0.00350420
$709$	−11410.9	−0.604437	−0.302219	−	0.953239i	$-0.597727\pi$
$709$	−11410.9	−0.604437	−0.302219	+	0.953239i	$0.597727\pi$
$710$	5803.33	0.306754
$711$	−17963.1	−0.947493
$712$	9077.93	0.477823
$713$	8486.39	0.445747
$714$	331.792	0.0173908
$715$	640.069	0.0334786
$716$	−15279.4	−0.797511
$717$	−818.329	−0.0426235
$718$	8362.33	0.434651
$719$	−9364.00	−0.485700	−0.242850	−	0.970064i	$-0.578082\pi$
$719$	−9364.00	−0.485700	−0.242850	+	0.970064i	$0.578082\pi$
$720$	−2152.06	−0.111392
$721$	31785.0	1.64180
$722$	37803.9	1.94864
$723$	−2014.25	−0.103611
$724$	−1486.44	−0.0763027
$725$	4591.20	0.235190
$726$	76.2383	0.00389734
$727$	1529.82	0.0780436	0.0390218	−	0.999238i	$-0.487576\pi$
$727$	1529.82	0.0780436	0.0390218	+	0.999238i	$0.487576\pi$
$728$	2883.92	0.146820
$729$	−19250.2	−0.978013
$730$	3871.75	0.196301
$731$	−8770.32	−0.443751
$732$	−276.798	−0.0139764
$733$	2866.17	0.144426	0.0722132	−	0.997389i	$-0.476994\pi$
$733$	2866.17	0.144426	0.0722132	+	0.997389i	$0.476994\pi$
$734$	10610.3	0.533559
$735$	971.142	0.0487362
$736$	4783.67	0.239577
$737$	−463.048	−0.0231433
$738$	−8743.03	−0.436092
$739$	29561.9	1.47152	0.735759	−	0.677244i	$-0.236826\pi$
$739$	29561.9	1.47152	0.735759	+	0.677244i	$0.236826\pi$
$740$	−2689.27	−0.133594
$741$	588.441	0.0291727
$742$	158.280	0.00783105
$743$	−17446.3	−0.861431	−0.430715	−	0.902488i	$-0.641739\pi$
$743$	−17446.3	−0.861431	−0.430715	+	0.902488i	$0.641739\pi$
$744$	143.074	0.00705019
$745$	−11238.3	−0.552670
$746$	17881.2	0.877582
$747$	−28668.1	−1.40417
$748$	748.000	0.0365636
$749$	50578.2	2.46741
$750$	78.7586	0.00383448
$751$	−27489.9	−1.33572	−0.667858	−	0.744289i	$-0.732789\pi$
$751$	−27489.9	−1.33572	−0.667858	+	0.744289i	$0.732789\pi$
$752$	−195.998	−0.00950441
$753$	2288.79	0.110768
$754$	−4274.45	−0.206454
$755$	9254.17	0.446084
$756$	2103.98	0.101218
$757$	17803.3	0.854783	0.427392	−	0.904067i	$-0.359433\pi$
$757$	17803.3	0.854783	0.427392	+	0.904067i	$0.359433\pi$
$758$	−15941.0	−0.763855
$759$	−518.038	−0.0247742
$760$	−6420.09	−0.306422
$761$	24234.0	1.15438	0.577190	−	0.816610i	$-0.304149\pi$
$761$	24234.0	1.15438	0.577190	+	0.816610i	$0.304149\pi$
$762$	259.375	0.0123309
$763$	−22434.2	−1.06445
$764$	−18403.1	−0.871468
$765$	2286.56	0.108067
$766$	26851.0	1.26654
$767$	−609.657	−0.0287007
$768$	80.6488	0.00378927
$769$	−18004.2	−0.844277	−0.422139	−	0.906531i	$-0.638720\pi$
$769$	−18004.2	−0.844277	−0.422139	+	0.906531i	$0.638720\pi$
$770$	3407.39	0.159473
$771$	557.230	0.0260287
$772$	1850.51	0.0862709
$773$	37570.2	1.74813	0.874067	−	0.485806i	$-0.161474\pi$
$773$	37570.2	1.74813	0.874067	+	0.485806i	$0.161474\pi$
$774$	−27756.2	−1.28899
$775$	1419.23	0.0657809
$776$	−10357.9	−0.479160
$777$	1312.17	0.0605843
$778$	−25350.8	−1.16822
$779$	−26082.5	−1.19962
$780$	−73.3250	−0.00336597
$781$	−6383.67	−0.292478
$782$	−5082.65	−0.232423
$783$	−3118.45	−0.142330
$784$	9864.49	0.449366
$785$	7678.25	0.349106
$786$	1628.64	0.0739078
$787$	3529.32	0.159856	0.0799281	−	0.996801i	$-0.474531\pi$
$787$	3529.32	0.159856	0.0799281	+	0.996801i	$0.474531\pi$
$788$	15454.7	0.698667
$789$	−1767.16	−0.0797373
$790$	6677.53	0.300729
$791$	40749.0	1.83169
$792$	2367.27	0.106209
$793$	2556.28	0.114472
$794$	19452.4	0.869444
$795$	−4.02434	−0.000179533 0
$796$	−607.752	−0.0270618
$797$	8483.29	0.377031	0.188516	−	0.982070i	$-0.439632\pi$
$797$	8483.29	0.377031	0.188516	+	0.982070i	$0.439632\pi$
$798$	3132.55	0.138961
$799$	208.248	0.00922063
$800$	800.000	0.0353553
$801$	−30525.4	−1.34652
$802$	147.270	0.00648415
$803$	−4258.92	−0.187166
$804$	53.0458	0.00232684
$805$	−23153.2	−1.01372
$806$	−1321.32	−0.0577436
$807$	−1558.67	−0.0679898
$808$	−7615.69	−0.331583
$809$	21406.6	0.930303	0.465152	−	0.885231i	$-0.346000\pi$
$809$	21406.6	0.930303	0.465152	+	0.885231i	$0.346000\pi$
$810$	7209.71	0.312745
$811$	11110.1	0.481044	0.240522	−	0.970644i	$-0.422681\pi$
$811$	11110.1	0.481044	0.240522	+	0.970644i	$0.422681\pi$
$812$	−22754.9	−0.983425
$813$	2255.71	0.0973076
$814$	2958.20	0.127377
$815$	−96.4411	−0.00414501
$816$	−85.6894	−0.00367614
$817$	−82803.2	−3.54580
$818$	8666.56	0.370439
$819$	−9697.46	−0.413745
$820$	3250.11	0.138413
$821$	−28740.5	−1.22174	−0.610871	−	0.791730i	$-0.709181\pi$
$821$	−28740.5	−1.22174	−0.610871	+	0.791730i	$0.709181\pi$
$822$	−1394.16	−0.0591567
$823$	−5059.82	−0.214307	−0.107153	−	0.994243i	$-0.534174\pi$
$823$	−5059.82	−0.214307	−0.107153	+	0.994243i	$0.534174\pi$
$824$	−8208.87	−0.347050
$825$	−86.6345	−0.00365603
$826$	−3245.49	−0.136713
$827$	−39489.4	−1.66044	−0.830219	−	0.557438i	$-0.811784\pi$
$827$	−39489.4	−1.66044	−0.830219	+	0.557438i	$0.811784\pi$
$828$	−16085.5	−0.675134
$829$	−22428.6	−0.939659	−0.469829	−	0.882757i	$-0.655685\pi$
$829$	−22428.6	−0.939659	−0.469829	+	0.882757i	$0.655685\pi$
$830$	10657.0	0.445674
$831$	−275.414	−0.0114970
$832$	−744.808	−0.0310355
$833$	−10481.0	−0.435949
$834$	1652.19	0.0685979
$835$	6949.95	0.288039
$836$	7062.10	0.292162
$837$	−963.973	−0.0398086
$838$	17897.7	0.737788
$839$	−21648.0	−0.890790	−0.445395	−	0.895334i	$-0.646937\pi$
$839$	−21648.0	−0.890790	−0.445395	+	0.895334i	$0.646937\pi$
$840$	−390.344	−0.0160335
$841$	9337.53	0.382858
$842$	−26961.0	−1.10349
$843$	752.048	0.0307259
$844$	−7887.50	−0.321681
$845$	−10307.8	−0.419645
$846$	659.062	0.0267837
$847$	−3748.13	−0.152051
$848$	−40.8777	−0.00165536
$849$	603.842	0.0244096
$850$	−850.000	−0.0342997
$851$	−20100.9	−0.809694
$852$	731.300	0.0294060
$853$	34200.2	1.37279	0.686396	−	0.727228i	$-0.259192\pi$
$853$	34200.2	1.37279	0.686396	+	0.727228i	$0.259192\pi$
$854$	13608.3	0.545277
$855$	21588.1	0.863508
$856$	−13062.4	−0.521571
$857$	−33938.4	−1.35276	−0.676378	−	0.736554i	$-0.736452\pi$
$857$	−33938.4	−1.35276	−0.676378	+	0.736554i	$0.736452\pi$
$858$	80.6575	0.00320933
$859$	17184.0	0.682551	0.341275	−	0.939963i	$-0.389141\pi$
$859$	17184.0	0.682551	0.341275	+	0.939963i	$0.389141\pi$
$860$	10318.0	0.409118
$861$	−1585.82	−0.0627698
$862$	−8960.04	−0.354037
$863$	−13549.8	−0.534461	−0.267230	−	0.963633i	$-0.586108\pi$
$863$	−13549.8	−0.534461	−0.267230	+	0.963633i	$0.586108\pi$
$864$	−543.379	−0.0213960
$865$	4259.35	0.167425
$866$	15861.1	0.622381
$867$	91.0449	0.00356638
$868$	−7033.99	−0.275057
$869$	−7345.29	−0.286734
$870$	578.554	0.0225458
$871$	−489.889	−0.0190577
$872$	5793.90	0.225007
$873$	34829.6	1.35029
$874$	−47986.8	−1.85718
$875$	−3872.04	−0.149599
$876$	487.894	0.0188178
$877$	10086.8	0.388377	0.194189	−	0.980964i	$-0.437793\pi$
$877$	10086.8	0.388377	0.194189	+	0.980964i	$0.437793\pi$
$878$	−454.166	−0.0174571
$879$	1874.02	0.0719105
$880$	−880.000	−0.0337100
$881$	44175.5	1.68934	0.844671	−	0.535286i	$-0.179796\pi$
$881$	44175.5	1.68934	0.844671	+	0.535286i	$0.179796\pi$
$882$	−33170.3	−1.26633
$883$	−8865.89	−0.337894	−0.168947	−	0.985625i	$-0.554037\pi$
$883$	−8865.89	−0.337894	−0.168947	+	0.985625i	$0.554037\pi$
$884$	791.358	0.0301089
$885$	82.5181	0.00313425
$886$	6411.86	0.243127
$887$	−33126.8	−1.25399	−0.626995	−	0.779023i	$-0.715715\pi$
$887$	−33126.8	−1.25399	−0.626995	+	0.779023i	$0.715715\pi$
$888$	−338.885	−0.0128066
$889$	−12751.7	−0.481080
$890$	11347.4	0.427378
$891$	−7930.68	−0.298191
$892$	2037.13	0.0764665
$893$	1966.13	0.0736776
$894$	−1416.18	−0.0529800
$895$	−19099.2	−0.713315
$896$	−3964.97	−0.147835
$897$	−548.067	−0.0204007
$898$	37712.7	1.40143
$899$	10425.5	0.386775
$900$	−2690.08	−0.0996324
$901$	43.4325	0.00160594
$902$	−3575.12	−0.131972
$903$	−5034.47	−0.185533
$904$	−10523.9	−0.387191
$905$	−1858.05	−0.0682472
$906$	1166.15	0.0427625
$907$	45911.1	1.68076	0.840382	−	0.541994i	$-0.182331\pi$
$907$	45911.1	1.68076	0.840382	+	0.541994i	$0.182331\pi$
$908$	8991.29	0.328619
$909$	25608.5	0.934411
$910$	3604.90	0.131320
$911$	33850.9	1.23110	0.615549	−	0.788098i	$-0.288934\pi$
$911$	33850.9	1.23110	0.615549	+	0.788098i	$0.288934\pi$
$912$	−809.019	−0.0293742
$913$	−11722.7	−0.424934
$914$	22933.3	0.829942
$915$	−345.997	−0.0125009
$916$	−1866.33	−0.0673202
$917$	−80069.2	−2.88344
$918$	577.340	0.0207571
$919$	13833.8	0.496556	0.248278	−	0.968689i	$-0.420135\pi$
$919$	13833.8	0.496556	0.248278	+	0.968689i	$0.420135\pi$
$920$	5979.58	0.214284
$921$	1680.71	0.0601318
$922$	−16415.3	−0.586346
$923$	−6753.70	−0.240846
$924$	429.378	0.0152873
$925$	−3361.59	−0.119490
$926$	14213.1	0.504395
$927$	27603.1	0.977998
$928$	5876.73	0.207881
$929$	53615.1	1.89349	0.946747	−	0.321980i	$-0.104348\pi$
$929$	53615.1	1.89349	0.946747	+	0.321980i	$0.104348\pi$
$930$	178.842	0.00630588
$931$	−98954.5	−3.48346
$932$	12030.1	0.422810
$933$	45.5070	0.00159682
$934$	3061.12	0.107241
$935$	935.000	0.0327035
$936$	2504.49	0.0874591
$937$	52673.5	1.83647	0.918233	−	0.396041i	$-0.129616\pi$
$937$	52673.5	1.83647	0.918233	+	0.396041i	$0.129616\pi$
$938$	−2607.91	−0.0907797
$939$	−1244.43	−0.0432487
$940$	−244.998	−0.00850100
$941$	22858.3	0.791880	0.395940	−	0.918276i	$-0.370419\pi$
$941$	22858.3	0.791880	0.395940	+	0.918276i	$0.370419\pi$
$942$	967.565	0.0334660
$943$	24292.9	0.838902
$944$	838.187	0.0288990
$945$	2629.98	0.0905325
$946$	−11349.8	−0.390079
$947$	−17948.2	−0.615880	−0.307940	−	0.951406i	$-0.599640\pi$
$947$	−17948.2	−0.615880	−0.307940	+	0.951406i	$0.599640\pi$
$948$	841.461	0.0288285
$949$	−4505.80	−0.154125
$950$	−8025.11	−0.274073
$951$	−1141.09	−0.0389089
$952$	4212.78	0.143421
$953$	−7633.31	−0.259462	−0.129731	−	0.991549i	$-0.541411\pi$
$953$	−7633.31	−0.259462	−0.129731	+	0.991549i	$0.541411\pi$
$954$	137.455	0.00466486
$955$	−23003.9	−0.779465
$956$	−10390.3	−0.351514
$957$	−636.409	−0.0214965
$958$	15047.9	0.507490
$959$	68541.4	2.30794
$960$	100.811	0.00338923
$961$	−26568.3	−0.891822
$962$	3129.67	0.104890
$963$	43923.7	1.46980
$964$	−25575.0	−0.854478
$965$	2313.13	0.0771631
$966$	−2917.62	−0.0971768
$967$	−12230.0	−0.406712	−0.203356	−	0.979105i	$-0.565185\pi$
$967$	−12230.0	−0.406712	−0.203356	+	0.979105i	$0.565185\pi$
$968$	968.000	0.0321412
$969$	859.583	0.0284972
$970$	−12947.4	−0.428574
$971$	41188.0	1.36126	0.680631	−	0.732626i	$-0.261706\pi$
$971$	41188.0	1.36126	0.680631	+	0.732626i	$0.261706\pi$
$972$	2742.43	0.0904973
$973$	−81227.2	−2.67629
$974$	−4522.77	−0.148787
$975$	−91.6563	−0.00301062
$976$	−3514.51	−0.115263
$977$	−23207.4	−0.759951	−0.379975	−	0.924997i	$-0.624068\pi$
$977$	−23207.4	−0.759951	−0.379975	+	0.924997i	$0.624068\pi$
$978$	−12.1529	−0.000397349 0
$979$	−12482.2	−0.407489
$980$	12330.6	0.401926
$981$	−19482.5	−0.634076
$982$	7348.82	0.238809
$983$	−22302.8	−0.723650	−0.361825	−	0.932246i	$-0.617846\pi$
$983$	−22302.8	−0.723650	−0.361825	+	0.932246i	$0.617846\pi$
$984$	409.558	0.0132685
$985$	19318.3	0.624907
$986$	−6244.03	−0.201674
$987$	119.542	0.00385517
$988$	7471.46	0.240586
$989$	77121.8	2.47961
$990$	2959.08	0.0949958
$991$	46512.6	1.49094	0.745469	−	0.666540i	$-0.232225\pi$
$991$	46512.6	1.49094	0.745469	+	0.666540i	$0.232225\pi$
$992$	1816.61	0.0581426
$993$	2139.21	0.0683645
$994$	−35953.1	−1.14725
$995$	−759.690	−0.0242048
$996$	1342.93	0.0427232
$997$	−42220.8	−1.34117	−0.670585	−	0.741832i	$-0.733957\pi$
$997$	−42220.8	−1.34117	−0.670585	+	0.741832i	$0.733957\pi$
$998$	13455.5	0.426781
$999$	2283.27	0.0723117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.4.a.l.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.4.a.l.1.6	✓	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1870.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +0.315034 q^{3} +4.00000 q^{4} +5.00000 q^{5} +0.630069 q^{6} -30.9763 q^{7} +8.00000 q^{8} -26.9008 q^{9} +10.0000 q^{10} -11.0000 q^{11} +1.26014 q^{12} -11.6376 q^{13} -61.9526 q^{14} +1.57517 q^{15} +16.0000 q^{16} -17.0000 q^{17} -53.8015 q^{18} -160.502 q^{19} +20.0000 q^{20} -9.75860 q^{21} -22.0000 q^{22} +149.490 q^{23} +2.52028 q^{24} +25.0000 q^{25} -23.2752 q^{26} -16.9806 q^{27} -123.905 q^{28} +183.648 q^{29} +3.15034 q^{30} +56.7691 q^{31} +32.0000 q^{32} -3.46538 q^{33} -34.0000 q^{34} -154.881 q^{35} -107.603 q^{36} -134.463 q^{37} -321.004 q^{38} -3.66625 q^{39} +40.0000 q^{40} +162.505 q^{41} -19.5172 q^{42} +515.901 q^{43} -44.0000 q^{44} -134.504 q^{45} +298.979 q^{46} -12.2499 q^{47} +5.04055 q^{48} +616.531 q^{49} +50.0000 q^{50} -5.35558 q^{51} -46.5505 q^{52} -2.55486 q^{53} -33.9612 q^{54} -55.0000 q^{55} -247.810 q^{56} -50.5637 q^{57} +367.296 q^{58} +52.3867 q^{59} +6.30069 q^{60} -219.657 q^{61} +113.538 q^{62} +833.286 q^{63} +64.0000 q^{64} -58.1881 q^{65} -6.93076 q^{66} +42.0953 q^{67} -68.0000 q^{68} +47.0944 q^{69} -309.763 q^{70} +580.333 q^{71} -215.206 q^{72} +387.175 q^{73} -268.927 q^{74} +7.87586 q^{75} -642.009 q^{76} +340.739 q^{77} -7.33250 q^{78} +667.753 q^{79} +80.0000 q^{80} +720.971 q^{81} +325.011 q^{82} +1065.70 q^{83} -39.0344 q^{84} -85.0000 q^{85} +1031.80 q^{86} +57.8554 q^{87} -88.0000 q^{88} +1134.74 q^{89} -269.008 q^{90} +360.490 q^{91} +597.958 q^{92} +17.8842 q^{93} -24.4998 q^{94} -802.511 q^{95} +10.0811 q^{96} -1294.74 q^{97} +1233.06 q^{98} +295.908 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 20 q^{2} + 40 q^{4} + 50 q^{5} + 17 q^{7} + 80 q^{8} + 106 q^{9} + 100 q^{10} - 110 q^{11} + 118 q^{13} + 34 q^{14} + 160 q^{16} - 170 q^{17} + 212 q^{18} + 146 q^{19} + 200 q^{20} + 136 q^{21} - 220 q^{22}+ \cdots - 1166 q^{99}+O(q^{100}) \) 10 * q + 20 * q^2 + 40 * q^4 + 50 * q^5 + 17 * q^7 + 80 * q^8 + 106 * q^9 + 100 * q^10 - 110 * q^11 + 118 * q^13 + 34 * q^14 + 160 * q^16 - 170 * q^17 + 212 * q^18 + 146 * q^19 + 200 * q^20 + 136 * q^21 - 220 * q^22 + 278 * q^23 + 250 * q^25 + 236 * q^26 + 144 * q^27 + 68 * q^28 + 167 * q^29 + 520 * q^31 + 320 * q^32 - 340 * q^34 + 85 * q^35 + 424 * q^36 + 412 * q^37 + 292 * q^38 + 428 * q^39 + 400 * q^40 + 939 * q^41 + 272 * q^42 + 1398 * q^43 - 440 * q^44 + 530 * q^45 + 556 * q^46 + 569 * q^47 + 467 * q^49 + 500 * q^50 + 472 * q^52 + 1029 * q^53 + 288 * q^54 - 550 * q^55 + 136 * q^56 - 44 * q^57 + 334 * q^58 + 769 * q^59 + 816 * q^61 + 1040 * q^62 + 1427 * q^63 + 640 * q^64 + 590 * q^65 + 173 * q^67 - 680 * q^68 - 994 * q^69 + 170 * q^70 + 1808 * q^71 + 848 * q^72 + 1137 * q^73 + 824 * q^74 + 584 * q^76 - 187 * q^77 + 856 * q^78 - 382 * q^79 + 800 * q^80 + 2902 * q^81 + 1878 * q^82 + 1130 * q^83 + 544 * q^84 - 850 * q^85 + 2796 * q^86 + 2626 * q^87 - 880 * q^88 - 313 * q^89 + 1060 * q^90 + 1418 * q^91 + 1112 * q^92 + 2152 * q^93 + 1138 * q^94 + 730 * q^95 - 58 * q^97 + 934 * q^98 - 1166 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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