LMFDB - Embedded newform 435.4.a.i.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,4,Mod(1,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("435.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$25.6658308525$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 $ x^7 - 2x^6 - 37x^5 + 55x^4 + 336x^3 - 227x^2 - 824x - 166
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.58378$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.58378 q^{2} -3.00000 q^{3} -1.32408 q^{4} +5.00000 q^{5} -7.75134 q^{6} -26.6398 q^{7} -24.0914 q^{8} +9.00000 q^{9} +12.9189 q^{10} -8.03338 q^{11} +3.97225 q^{12} +49.9367 q^{13} -68.8314 q^{14} -15.0000 q^{15} -51.6541 q^{16} +116.617 q^{17} +23.2540 q^{18} +22.6617 q^{19} -6.62041 q^{20} +79.9195 q^{21} -20.7565 q^{22} +38.2616 q^{23} +72.2741 q^{24} +25.0000 q^{25} +129.025 q^{26} -27.0000 q^{27} +35.2733 q^{28} +29.0000 q^{29} -38.7567 q^{30} -8.82528 q^{31} +59.2681 q^{32} +24.1002 q^{33} +301.312 q^{34} -133.199 q^{35} -11.9167 q^{36} +301.022 q^{37} +58.5529 q^{38} -149.810 q^{39} -120.457 q^{40} +305.401 q^{41} +206.494 q^{42} +275.872 q^{43} +10.6369 q^{44} +45.0000 q^{45} +98.8596 q^{46} -479.282 q^{47} +154.962 q^{48} +366.680 q^{49} +64.5945 q^{50} -349.850 q^{51} -66.1204 q^{52} -496.683 q^{53} -69.7621 q^{54} -40.1669 q^{55} +641.790 q^{56} -67.9852 q^{57} +74.9296 q^{58} -563.505 q^{59} +19.8612 q^{60} +485.346 q^{61} -22.8026 q^{62} -239.758 q^{63} +566.369 q^{64} +249.684 q^{65} +62.2695 q^{66} +217.176 q^{67} -154.410 q^{68} -114.785 q^{69} -344.157 q^{70} +628.023 q^{71} -216.822 q^{72} -682.502 q^{73} +777.773 q^{74} -75.0000 q^{75} -30.0060 q^{76} +214.008 q^{77} -387.076 q^{78} +1159.26 q^{79} -258.271 q^{80} +81.0000 q^{81} +789.089 q^{82} +668.594 q^{83} -105.820 q^{84} +583.084 q^{85} +712.792 q^{86} -87.0000 q^{87} +193.535 q^{88} +798.300 q^{89} +116.270 q^{90} -1330.31 q^{91} -50.6616 q^{92} +26.4758 q^{93} -1238.36 q^{94} +113.309 q^{95} -177.804 q^{96} +867.116 q^{97} +947.421 q^{98} -72.3005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19}+ \cdots + 684 q^{99}+O(q^{100}) $ 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * 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 $

$2$	2.58378	0.913504	0.456752	−	0.889594i	$-0.349013\pi$
$2$	2.58378	0.913504	0.456752	+	0.889594i	$0.349013\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−1.32408	−0.165510
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−7.75134	−0.527412
$7$	−26.6398	−1.43842	−0.719208	−	0.694795i	$-0.755495\pi$
$7$	−26.6398	−1.43842	−0.719208	+	0.694795i	$0.755495\pi$
$8$	−24.0914	−1.06470
$9$	9.00000	0.333333
$10$	12.9189	0.408531
$11$	−8.03338	−0.220196	−0.110098	−	0.993921i	$-0.535116\pi$
$11$	−8.03338	−0.220196	−0.110098	+	0.993921i	$0.535116\pi$
$12$	3.97225	0.0955574
$13$	49.9367	1.06538	0.532691	−	0.846310i	$-0.321181\pi$
$13$	49.9367	1.06538	0.532691	+	0.846310i	$0.321181\pi$
$14$	−68.8314	−1.31400
$15$	−15.0000	−0.258199
$16$	−51.6541	−0.807096
$17$	116.617	1.66375	0.831874	−	0.554964i	$-0.187268\pi$
$17$	116.617	1.66375	0.831874	+	0.554964i	$0.187268\pi$
$18$	23.2540	0.304501
$19$	22.6617	0.273629	0.136815	−	0.990597i	$-0.456314\pi$
$19$	22.6617	0.273629	0.136815	+	0.990597i	$0.456314\pi$
$20$	−6.62041	−0.0740185
$21$	79.9195	0.830470
$22$	−20.7565	−0.201150
$23$	38.2616	0.346874	0.173437	−	0.984845i	$-0.444513\pi$
$23$	38.2616	0.346874	0.173437	+	0.984845i	$0.444513\pi$
$24$	72.2741	0.614704
$25$	25.0000	0.200000
$26$	129.025	0.973230
$27$	−27.0000	−0.192450
$28$	35.2733	0.238073
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−38.7567	−0.235866
$31$	−8.82528	−0.0511312	−0.0255656	−	0.999673i	$-0.508139\pi$
$31$	−8.82528	−0.0511312	−0.0255656	+	0.999673i	$0.508139\pi$
$32$	59.2681	0.327413
$33$	24.1002	0.127130
$34$	301.312	1.51984
$35$	−133.199	−0.643279
$36$	−11.9167	−0.0551701
$37$	301.022	1.33750	0.668752	−	0.743486i	$-0.266829\pi$
$37$	301.022	1.33750	0.668752	+	0.743486i	$0.266829\pi$
$38$	58.5529	0.249962
$39$	−149.810	−0.615098
$40$	−120.457	−0.476148
$41$	305.401	1.16331	0.581654	−	0.813436i	$-0.302406\pi$
$41$	305.401	1.16331	0.581654	+	0.813436i	$0.302406\pi$
$42$	206.494	0.758637
$43$	275.872	0.978374	0.489187	−	0.872179i	$-0.337294\pi$
$43$	275.872	0.978374	0.489187	+	0.872179i	$0.337294\pi$
$44$	10.6369	0.0364447
$45$	45.0000	0.149071
$46$	98.8596	0.316871
$47$	−479.282	−1.48746	−0.743729	−	0.668481i	$-0.766945\pi$
$47$	−479.282	−1.48746	−0.743729	+	0.668481i	$0.766945\pi$
$48$	154.962	0.465977
$49$	366.680	1.06904
$50$	64.5945	0.182701
$51$	−349.850	−0.960566
$52$	−66.1204	−0.176332
$53$	−496.683	−1.28726	−0.643629	−	0.765338i	$-0.722572\pi$
$53$	−496.683	−1.28726	−0.643629	+	0.765338i	$0.722572\pi$
$54$	−69.7621	−0.175804
$55$	−40.1669	−0.0984747
$56$	641.790	1.53148
$57$	−67.9852	−0.157980
$58$	74.9296	0.169633
$59$	−563.505	−1.24342	−0.621712	−	0.783246i	$-0.713563\pi$
$59$	−563.505	−1.24342	−0.621712	+	0.783246i	$0.713563\pi$
$60$	19.8612	0.0427346
$61$	485.346	1.01872	0.509362	−	0.860552i	$-0.329881\pi$
$61$	485.346	1.01872	0.509362	+	0.860552i	$0.329881\pi$
$62$	−22.8026	−0.0467085
$63$	−239.758	−0.479472
$64$	566.369	1.10619
$65$	249.684	0.476453
$66$	62.2695	0.116134
$67$	217.176	0.396004	0.198002	−	0.980202i	$-0.436555\pi$
$67$	217.176	0.396004	0.198002	+	0.980202i	$0.436555\pi$
$68$	−154.410	−0.275368
$69$	−114.785	−0.200268
$70$	−344.157	−0.587638
$71$	628.023	1.04975	0.524877	−	0.851178i	$-0.324111\pi$
$71$	628.023	1.04975	0.524877	+	0.851178i	$0.324111\pi$
$72$	−216.822	−0.354899
$73$	−682.502	−1.09426	−0.547128	−	0.837049i	$-0.684279\pi$
$73$	−682.502	−1.09426	−0.547128	+	0.837049i	$0.684279\pi$
$74$	777.773	1.22182
$75$	−75.0000	−0.115470
$76$	−30.0060	−0.0452885
$77$	214.008	0.316733
$78$	−387.076	−0.561895
$79$	1159.26	1.65097	0.825484	−	0.564425i	$-0.190902\pi$
$79$	1159.26	1.65097	0.825484	+	0.564425i	$0.190902\pi$
$80$	−258.271	−0.360944
$81$	81.0000	0.111111
$82$	789.089	1.06269
$83$	668.594	0.884189	0.442095	−	0.896968i	$-0.354236\pi$
$83$	668.594	0.884189	0.442095	+	0.896968i	$0.354236\pi$
$84$	−105.820	−0.137451
$85$	583.084	0.744051
$86$	712.792	0.893748
$87$	−87.0000	−0.107211
$88$	193.535	0.234442
$89$	798.300	0.950782	0.475391	−	0.879775i	$-0.342307\pi$
$89$	798.300	0.950782	0.475391	+	0.879775i	$0.342307\pi$
$90$	116.270	0.136177
$91$	−1330.31	−1.53246
$92$	−50.6616	−0.0574112
$93$	26.4758	0.0295206
$94$	−1238.36	−1.35880
$95$	113.309	0.122371
$96$	−177.804	−0.189032
$97$	867.116	0.907653	0.453826	−	0.891090i	$-0.350059\pi$
$97$	867.116	0.907653	0.453826	+	0.891090i	$0.350059\pi$
$98$	947.421	0.976571
$99$	−72.3005	−0.0733987
$100$	−33.1021	−0.0331021
$101$	1270.57	1.25174	0.625872	−	0.779926i	$-0.284743\pi$
$101$	1270.57	1.25174	0.625872	+	0.779926i	$0.284743\pi$
$102$	−903.936	−0.877481
$103$	−884.596	−0.846232	−0.423116	−	0.906076i	$-0.639064\pi$
$103$	−884.596	−0.846232	−0.423116	+	0.906076i	$0.639064\pi$
$104$	−1203.04	−1.13431
$105$	399.597	0.371397
$106$	−1283.32	−1.17591
$107$	925.937	0.836577	0.418288	−	0.908314i	$-0.362630\pi$
$107$	925.937	0.836577	0.418288	+	0.908314i	$0.362630\pi$
$108$	35.7502	0.0318525
$109$	73.4989	0.0645864	0.0322932	−	0.999478i	$-0.489719\pi$
$109$	73.4989	0.0645864	0.0322932	+	0.999478i	$0.489719\pi$
$110$	−103.782	−0.0899570
$111$	−903.065	−0.772208
$112$	1376.06	1.16094
$113$	−2068.68	−1.72217	−0.861086	−	0.508459i	$-0.830215\pi$
$113$	−2068.68	−1.72217	−0.861086	+	0.508459i	$0.830215\pi$
$114$	−175.659	−0.144315
$115$	191.308	0.155127
$116$	−38.3984	−0.0307345
$117$	449.431	0.355127
$118$	−1455.97	−1.13587
$119$	−3106.65	−2.39316
$120$	361.371	0.274904
$121$	−1266.46	−0.951514
$122$	1254.03	0.930609
$123$	−916.204	−0.671637
$124$	11.6854	0.00846274
$125$	125.000	0.0894427
$126$	−619.483	−0.437999
$127$	−708.738	−0.495199	−0.247600	−	0.968862i	$-0.579642\pi$
$127$	−708.738	−0.495199	−0.247600	+	0.968862i	$0.579642\pi$
$128$	989.228	0.683095
$129$	−827.616	−0.564864
$130$	645.127	0.435242
$131$	−2033.80	−1.35644	−0.678220	−	0.734859i	$-0.737248\pi$
$131$	−2033.80	−1.35644	−0.678220	+	0.734859i	$0.737248\pi$
$132$	−31.9106	−0.0210414
$133$	−603.705	−0.393593
$134$	561.135	0.361752
$135$	−135.000	−0.0860663
$136$	−2809.46	−1.77139
$137$	2635.96	1.64383	0.821917	−	0.569608i	$-0.192905\pi$
$137$	2635.96	1.64383	0.821917	+	0.569608i	$0.192905\pi$
$138$	−296.579	−0.182945
$139$	−1284.05	−0.783539	−0.391769	−	0.920063i	$-0.628137\pi$
$139$	−1284.05	−0.783539	−0.391769	+	0.920063i	$0.628137\pi$
$140$	176.367	0.106469
$141$	1437.85	0.858784
$142$	1622.67	0.958955
$143$	−401.161	−0.234593
$144$	−464.887	−0.269032
$145$	145.000	0.0830455
$146$	−1763.43	−0.999608
$147$	−1100.04	−0.617210
$148$	−398.578	−0.221371
$149$	261.843	0.143966	0.0719832	−	0.997406i	$-0.477067\pi$
$149$	261.843	0.143966	0.0719832	+	0.997406i	$0.477067\pi$
$150$	−193.783	−0.105482
$151$	2760.20	1.48756	0.743781	−	0.668424i	$-0.233031\pi$
$151$	2760.20	1.48756	0.743781	+	0.668424i	$0.233031\pi$
$152$	−545.952	−0.291333
$153$	1049.55	0.554583
$154$	552.949	0.289337
$155$	−44.1264	−0.0228666
$156$	198.361	0.101805
$157$	1922.00	0.977019	0.488509	−	0.872559i	$-0.337541\pi$
$157$	1922.00	0.977019	0.488509	+	0.872559i	$0.337541\pi$
$158$	2995.26	1.50817
$159$	1490.05	0.743198
$160$	296.340	0.146424
$161$	−1019.28	−0.498949
$162$	209.286	0.101500
$163$	−2784.04	−1.33781	−0.668904	−	0.743349i	$-0.733236\pi$
$163$	−2784.04	−1.33781	−0.668904	+	0.743349i	$0.733236\pi$
$164$	−404.376	−0.192540
$165$	120.501	0.0568544
$166$	1727.50	0.807711
$167$	−1669.58	−0.773627	−0.386814	−	0.922158i	$-0.626424\pi$
$167$	−1669.58	−0.773627	−0.386814	+	0.922158i	$0.626424\pi$
$168$	−1925.37	−0.884200
$169$	296.677	0.135037
$170$	1506.56	0.679694
$171$	203.956	0.0912098
$172$	−365.277	−0.161931
$173$	−3488.62	−1.53315	−0.766574	−	0.642156i	$-0.778040\pi$
$173$	−3488.62	−1.53315	−0.766574	+	0.642156i	$0.778040\pi$
$174$	−224.789	−0.0979379
$175$	−665.996	−0.287683
$176$	414.958	0.177719
$177$	1690.51	0.717892
$178$	2062.63	0.868543
$179$	4016.48	1.67713	0.838564	−	0.544803i	$-0.183396\pi$
$179$	4016.48	1.67713	0.838564	+	0.544803i	$0.183396\pi$
$180$	−59.5837	−0.0246728
$181$	−2275.81	−0.934583	−0.467291	−	0.884103i	$-0.654770\pi$
$181$	−2275.81	−0.934583	−0.467291	+	0.884103i	$0.654770\pi$
$182$	−3437.22	−1.39991
$183$	−1456.04	−0.588161
$184$	−921.775	−0.369316
$185$	1505.11	0.598150
$186$	68.4077	0.0269672
$187$	−936.827	−0.366351
$188$	634.610	0.246190
$189$	719.275	0.276823
$190$	292.765	0.111786
$191$	3204.35	1.21392	0.606961	−	0.794732i	$-0.292389\pi$
$191$	3204.35	1.21392	0.606961	+	0.794732i	$0.292389\pi$
$192$	−1699.11	−0.638659
$193$	−71.0310	−0.0264918	−0.0132459	−	0.999912i	$-0.504216\pi$
$193$	−71.0310	−0.0264918	−0.0132459	+	0.999912i	$0.504216\pi$
$194$	2240.44	0.829144
$195$	−749.051	−0.275080
$196$	−485.515	−0.176937
$197$	1260.52	0.455881	0.227941	−	0.973675i	$-0.426801\pi$
$197$	1260.52	0.455881	0.227941	+	0.973675i	$0.426801\pi$
$198$	−186.808	−0.0670500
$199$	2365.21	0.842539	0.421270	−	0.906935i	$-0.361585\pi$
$199$	2365.21	0.842539	0.421270	+	0.906935i	$0.361585\pi$
$200$	−602.284	−0.212940
$201$	−651.529	−0.228633
$202$	3282.87	1.14347
$203$	−772.555	−0.267107
$204$	463.231	0.158984
$205$	1527.01	0.520247
$206$	−2285.60	−0.773036
$207$	344.355	0.115625
$208$	−2579.44	−0.859865
$209$	−182.050	−0.0602521
$210$	1032.47	0.339273
$211$	−1604.41	−0.523468	−0.261734	−	0.965140i	$-0.584294\pi$
$211$	−1604.41	−0.523468	−0.261734	+	0.965140i	$0.584294\pi$
$212$	657.649	0.213054
$213$	−1884.07	−0.606076
$214$	2392.42	0.764216
$215$	1379.36	0.437542
$216$	650.467	0.204901
$217$	235.104	0.0735479
$218$	189.905	0.0589999
$219$	2047.50	0.631770
$220$	53.1843	0.0162986
$221$	5823.46	1.77253
$222$	−2333.32	−0.705415
$223$	−2789.26	−0.837591	−0.418795	−	0.908081i	$-0.637548\pi$
$223$	−2789.26	−0.837591	−0.418795	+	0.908081i	$0.637548\pi$
$224$	−1578.89	−0.470956
$225$	225.000	0.0666667
$226$	−5345.02	−1.57321
$227$	3091.67	0.903971	0.451985	−	0.892025i	$-0.350716\pi$
$227$	3091.67	0.903971	0.451985	+	0.892025i	$0.350716\pi$
$228$	90.0180	0.0261473
$229$	−6479.99	−1.86991	−0.934955	−	0.354766i	$-0.884561\pi$
$229$	−6479.99	−1.86991	−0.934955	+	0.354766i	$0.884561\pi$
$230$	494.298	0.141709
$231$	−642.024	−0.182866
$232$	−698.650	−0.197710
$233$	−3647.01	−1.02542	−0.512712	−	0.858561i	$-0.671359\pi$
$233$	−3647.01	−1.02542	−0.512712	+	0.858561i	$0.671359\pi$
$234$	1161.23	0.324410
$235$	−2396.41	−0.665211
$236$	746.127	0.205800
$237$	−3477.77	−0.953187
$238$	−8026.90	−2.18616
$239$	3863.00	1.04551	0.522754	−	0.852483i	$-0.324905\pi$
$239$	3863.00	1.04551	0.522754	+	0.852483i	$0.324905\pi$
$240$	774.812	0.208391
$241$	6207.76	1.65924	0.829620	−	0.558329i	$-0.188557\pi$
$241$	6207.76	1.65924	0.829620	+	0.558329i	$0.188557\pi$
$242$	−3272.27	−0.869212
$243$	−243.000	−0.0641500
$244$	−642.638	−0.168609
$245$	1833.40	0.478089
$246$	−2367.27	−0.613543
$247$	1131.65	0.291520
$248$	212.613	0.0544393
$249$	−2005.78	−0.510487
$250$	322.972	0.0817063
$251$	4942.68	1.24294	0.621472	−	0.783436i	$-0.286535\pi$
$251$	4942.68	1.24294	0.621472	+	0.783436i	$0.286535\pi$
$252$	317.460	0.0793575
$253$	−307.370	−0.0763803
$254$	−1831.22	−0.452367
$255$	−1749.25	−0.429578
$256$	−1975.00	−0.482179
$257$	3343.25	0.811465	0.405732	−	0.913992i	$-0.367016\pi$
$257$	3343.25	0.811465	0.405732	+	0.913992i	$0.367016\pi$
$258$	−2138.38	−0.516006
$259$	−8019.16	−1.92389
$260$	−330.602	−0.0788579
$261$	261.000	0.0618984
$262$	−5254.88	−1.23911
$263$	1053.61	0.247027	0.123514	−	0.992343i	$-0.460584\pi$
$263$	1053.61	0.247027	0.123514	+	0.992343i	$0.460584\pi$
$264$	−580.606	−0.135355
$265$	−2483.41	−0.575679
$266$	−1559.84	−0.359549
$267$	−2394.90	−0.548934
$268$	−287.559	−0.0655428
$269$	2348.05	0.532205	0.266103	−	0.963945i	$-0.414264\pi$
$269$	2348.05	0.532205	0.266103	+	0.963945i	$0.414264\pi$
$270$	−348.810	−0.0786219
$271$	4230.65	0.948316	0.474158	−	0.880440i	$-0.342753\pi$
$271$	4230.65	0.948316	0.474158	+	0.880440i	$0.342753\pi$
$272$	−6023.74	−1.34280
$273$	3990.92	0.884767
$274$	6810.74	1.50165
$275$	−200.835	−0.0440392
$276$	151.985	0.0331464
$277$	2146.72	0.465647	0.232823	−	0.972519i	$-0.425204\pi$
$277$	2146.72	0.465647	0.232823	+	0.972519i	$0.425204\pi$
$278$	−3317.71	−0.715766
$279$	−79.4275	−0.0170437
$280$	3208.95	0.684898
$281$	−1445.80	−0.306937	−0.153469	−	0.988154i	$-0.549044\pi$
$281$	−1445.80	−0.306937	−0.153469	+	0.988154i	$0.549044\pi$
$282$	3715.08	0.784503
$283$	3775.85	0.793113	0.396557	−	0.918010i	$-0.370205\pi$
$283$	3775.85	0.793113	0.396557	+	0.918010i	$0.370205\pi$
$284$	−831.554	−0.173745
$285$	−339.926	−0.0706508
$286$	−1036.51	−0.214301
$287$	−8135.83	−1.67332
$288$	533.413	0.109138
$289$	8686.48	1.76806
$290$	374.648	0.0758624
$291$	−2601.35	−0.524033
$292$	903.688	0.181111
$293$	6451.38	1.28633	0.643164	−	0.765729i	$-0.277622\pi$
$293$	6451.38	1.28633	0.643164	+	0.765729i	$0.277622\pi$
$294$	−2842.26	−0.563824
$295$	−2817.52	−0.556076
$296$	−7252.02	−1.42404
$297$	216.901	0.0423767
$298$	676.544	0.131514
$299$	1910.66	0.369553
$300$	99.3062	0.0191115
$301$	−7349.18	−1.40731
$302$	7131.74	1.35889
$303$	−3811.70	−0.722695
$304$	−1170.57	−0.220845
$305$	2426.73	0.455587
$306$	2711.81	0.506614
$307$	4197.07	0.780258	0.390129	−	0.920760i	$-0.372430\pi$
$307$	4197.07	0.780258	0.390129	+	0.920760i	$0.372430\pi$
$308$	−283.364	−0.0524227
$309$	2653.79	0.488572
$310$	−114.013	−0.0208887
$311$	6909.28	1.25977	0.629886	−	0.776687i	$-0.283102\pi$
$311$	6909.28	1.25977	0.629886	+	0.776687i	$0.283102\pi$
$312$	3609.13	0.654894
$313$	835.311	0.150845	0.0754226	−	0.997152i	$-0.475969\pi$
$313$	835.311	0.150845	0.0754226	+	0.997152i	$0.475969\pi$
$314$	4966.01	0.892510
$315$	−1198.79	−0.214426
$316$	−1534.95	−0.273252
$317$	−454.133	−0.0804626	−0.0402313	−	0.999190i	$-0.512809\pi$
$317$	−454.133	−0.0804626	−0.0402313	+	0.999190i	$0.512809\pi$
$318$	3849.96	0.678915
$319$	−232.968	−0.0408894
$320$	2831.84	0.494703
$321$	−2777.81	−0.482998
$322$	−2633.60	−0.455792
$323$	2642.74	0.455250
$324$	−107.251	−0.0183900
$325$	1248.42	0.213076
$326$	−7193.34	−1.22209
$327$	−220.497	−0.0372890
$328$	−7357.53	−1.23857
$329$	12768.0	2.13958
$330$	311.347	0.0519367
$331$	−6368.25	−1.05749	−0.528747	−	0.848779i	$-0.677338\pi$
$331$	−6368.25	−1.05749	−0.528747	+	0.848779i	$0.677338\pi$
$332$	−885.274	−0.146343
$333$	2709.19	0.445835
$334$	−4313.82	−0.706712
$335$	1085.88	0.177099
$336$	−4128.17	−0.670269
$337$	−8096.70	−1.30877	−0.654384	−	0.756162i	$-0.727072\pi$
$337$	−8096.70	−1.30877	−0.654384	+	0.756162i	$0.727072\pi$
$338$	766.547	0.123357
$339$	6206.05	0.994297
$340$	−772.051	−0.123148
$341$	70.8968	0.0112589
$342$	526.976	0.0833205
$343$	−630.841	−0.0993067
$344$	−6646.13	−1.04167
$345$	−573.924	−0.0895625
$346$	−9013.82	−1.40054
$347$	−2438.20	−0.377202	−0.188601	−	0.982054i	$-0.560395\pi$
$347$	−2438.20	−0.377202	−0.188601	+	0.982054i	$0.560395\pi$
$348$	115.195	0.0177446
$349$	−777.284	−0.119218	−0.0596090	−	0.998222i	$-0.518985\pi$
$349$	−777.284	−0.119218	−0.0596090	+	0.998222i	$0.518985\pi$
$350$	−1720.79	−0.262800
$351$	−1348.29	−0.205033
$352$	−476.123	−0.0720950
$353$	−9649.81	−1.45498	−0.727489	−	0.686119i	$-0.759313\pi$
$353$	−9649.81	−1.45498	−0.727489	+	0.686119i	$0.759313\pi$
$354$	4367.92	0.655797
$355$	3140.11	0.469465
$356$	−1057.02	−0.157364
$357$	9319.95	1.38169
$358$	10377.7	1.53206
$359$	9657.56	1.41980	0.709898	−	0.704304i	$-0.248741\pi$
$359$	9657.56	1.41980	0.709898	+	0.704304i	$0.248741\pi$
$360$	−1084.11	−0.158716
$361$	−6345.45	−0.925127
$362$	−5880.19	−0.853745
$363$	3799.39	0.549357
$364$	1761.43	0.253638
$365$	−3412.51	−0.489367
$366$	−3762.08	−0.537287
$367$	−9173.93	−1.30484	−0.652419	−	0.757859i	$-0.726246\pi$
$367$	−9173.93	−1.30484	−0.652419	+	0.757859i	$0.726246\pi$
$368$	−1976.37	−0.279961
$369$	2748.61	0.387770
$370$	3888.87	0.546412
$371$	13231.5	1.85161
$372$	−35.0562	−0.00488597
$373$	2899.69	0.402521	0.201261	−	0.979538i	$-0.435496\pi$
$373$	2899.69	0.402521	0.201261	+	0.979538i	$0.435496\pi$
$374$	−2420.56	−0.334663
$375$	−375.000	−0.0516398
$376$	11546.6	1.58369
$377$	1448.17	0.197836
$378$	1858.45	0.252879
$379$	−5819.59	−0.788739	−0.394370	−	0.918952i	$-0.629037\pi$
$379$	−5819.59	−0.788739	−0.394370	+	0.918952i	$0.629037\pi$
$380$	−150.030	−0.0202536
$381$	2126.21	0.285903
$382$	8279.34	1.10892
$383$	−5805.80	−0.774576	−0.387288	−	0.921959i	$-0.626588\pi$
$383$	−5805.80	−0.774576	−0.387288	+	0.921959i	$0.626588\pi$
$384$	−2967.68	−0.394385
$385$	1070.04	0.141647
$386$	−183.528	−0.0242004
$387$	2482.85	0.326125
$388$	−1148.13	−0.150226
$389$	7690.82	1.00242	0.501208	−	0.865327i	$-0.332889\pi$
$389$	7690.82	1.00242	0.501208	+	0.865327i	$0.332889\pi$
$390$	−1935.38	−0.251287
$391$	4461.95	0.577111
$392$	−8833.83	−1.13820
$393$	6101.39	0.783141
$394$	3256.92	0.416449
$395$	5796.28	0.738336
$396$	95.7318	0.0121482
$397$	−1638.24	−0.207105	−0.103553	−	0.994624i	$-0.533021\pi$
$397$	−1638.24	−0.207105	−0.103553	+	0.994624i	$0.533021\pi$
$398$	6111.18	0.769663
$399$	1811.11	0.227241
$400$	−1291.35	−0.161419
$401$	3780.89	0.470845	0.235422	−	0.971893i	$-0.424353\pi$
$401$	3780.89	0.470845	0.235422	+	0.971893i	$0.424353\pi$
$402$	−1683.41	−0.208857
$403$	−440.705	−0.0544742
$404$	−1682.34	−0.207177
$405$	405.000	0.0496904
$406$	−1996.11	−0.244003
$407$	−2418.22	−0.294513
$408$	8428.38	1.02271
$409$	−330.980	−0.0400145	−0.0200073	−	0.999800i	$-0.506369\pi$
$409$	−330.980	−0.0400145	−0.0200073	+	0.999800i	$0.506369\pi$
$410$	3945.45	0.475248
$411$	−7907.88	−0.949068
$412$	1171.28	0.140060
$413$	15011.7	1.78856
$414$	889.736	0.105624
$415$	3342.97	0.395422
$416$	2959.65	0.348820
$417$	3852.16	0.452376
$418$	−470.378	−0.0550405
$419$	9913.43	1.15585	0.577927	−	0.816089i	$-0.303862\pi$
$419$	9913.43	1.15585	0.577927	+	0.816089i	$0.303862\pi$
$420$	−529.100	−0.0614701
$421$	6286.56	0.727763	0.363881	−	0.931445i	$-0.381451\pi$
$421$	6286.56	0.727763	0.363881	+	0.931445i	$0.381451\pi$
$422$	−4145.43	−0.478190
$423$	−4313.54	−0.495819
$424$	11965.8	1.37054
$425$	2915.42	0.332750
$426$	−4868.02	−0.553653
$427$	−12929.5	−1.46535
$428$	−1226.02	−0.138462
$429$	1203.48	0.135442
$430$	3563.96	0.399696
$431$	5798.56	0.648044	0.324022	−	0.946050i	$-0.394965\pi$
$431$	5798.56	0.648044	0.324022	+	0.946050i	$0.394965\pi$
$432$	1394.66	0.155326
$433$	11476.3	1.27371	0.636856	−	0.770983i	$-0.280235\pi$
$433$	11476.3	1.27371	0.636856	+	0.770983i	$0.280235\pi$
$434$	607.457	0.0671863
$435$	−435.000	−0.0479463
$436$	−97.3186	−0.0106897
$437$	867.075	0.0949149
$438$	5290.30	0.577124
$439$	14429.5	1.56875	0.784377	−	0.620285i	$-0.212983\pi$
$439$	14429.5	1.56875	0.784377	+	0.620285i	$0.212983\pi$
$440$	967.676	0.104846
$441$	3300.12	0.356346
$442$	15046.5	1.61921
$443$	−11892.0	−1.27541	−0.637703	−	0.770283i	$-0.720115\pi$
$443$	−11892.0	−1.27541	−0.637703	+	0.770283i	$0.720115\pi$
$444$	1195.73	0.127808
$445$	3991.50	0.425203
$446$	−7206.84	−0.765143
$447$	−785.528	−0.0831190
$448$	−15088.0	−1.59116
$449$	−9881.53	−1.03862	−0.519308	−	0.854587i	$-0.673810\pi$
$449$	−9881.53	−1.03862	−0.519308	+	0.854587i	$0.673810\pi$
$450$	581.350	0.0609003
$451$	−2453.40	−0.256156
$452$	2739.11	0.285037
$453$	−8280.59	−0.858844
$454$	7988.20	0.825781
$455$	−6651.53	−0.685337
$456$	1637.86	0.168201
$457$	11641.2	1.19158	0.595792	−	0.803139i	$-0.296838\pi$
$457$	11641.2	1.19158	0.595792	+	0.803139i	$0.296838\pi$
$458$	−16742.9	−1.70817
$459$	−3148.65	−0.320189
$460$	−253.308	−0.0256751
$461$	−8045.29	−0.812812	−0.406406	−	0.913693i	$-0.633218\pi$
$461$	−8045.29	−0.812812	−0.406406	+	0.913693i	$0.633218\pi$
$462$	−1658.85	−0.167049
$463$	−4340.54	−0.435684	−0.217842	−	0.975984i	$-0.569902\pi$
$463$	−4340.54	−0.435684	−0.217842	+	0.975984i	$0.569902\pi$
$464$	−1497.97	−0.149874
$465$	132.379	0.0132020
$466$	−9423.08	−0.936729
$467$	−3461.65	−0.343011	−0.171506	−	0.985183i	$-0.554863\pi$
$467$	−3461.65	−0.343011	−0.171506	+	0.985183i	$0.554863\pi$
$468$	−595.083	−0.0587772
$469$	−5785.54	−0.569619
$470$	−6191.80	−0.607673
$471$	−5765.99	−0.564082
$472$	13575.6	1.32387
$473$	−2216.18	−0.215434
$474$	−8985.79	−0.870740
$475$	566.543	0.0547259
$476$	4113.46	0.396093
$477$	−4470.14	−0.429086
$478$	9981.14	0.955076
$479$	6284.62	0.599481	0.299741	−	0.954021i	$-0.403100\pi$
$479$	6284.62	0.599481	0.299741	+	0.954021i	$0.403100\pi$
$480$	−889.021	−0.0845377
$481$	15032.0	1.42495
$482$	16039.5	1.51572
$483$	3057.85	0.288068
$484$	1676.90	0.157485
$485$	4335.58	0.405915
$486$	−627.858	−0.0586013
$487$	−1809.63	−0.168382	−0.0841912	−	0.996450i	$-0.526831\pi$
$487$	−1809.63	−0.168382	−0.0841912	+	0.996450i	$0.526831\pi$
$488$	−11692.7	−1.08463
$489$	8352.12	0.772384
$490$	4737.11	0.436736
$491$	9550.28	0.877796	0.438898	−	0.898537i	$-0.355369\pi$
$491$	9550.28	0.877796	0.438898	+	0.898537i	$0.355369\pi$
$492$	1213.13	0.111163
$493$	3381.89	0.308950
$494$	2923.94	0.266304
$495$	−361.502	−0.0328249
$496$	455.862	0.0412678
$497$	−16730.4	−1.50998
$498$	−5182.50	−0.466332
$499$	−13672.9	−1.22662	−0.613309	−	0.789843i	$-0.710162\pi$
$499$	−13672.9	−1.22662	−0.613309	+	0.789843i	$0.710162\pi$
$500$	−165.510	−0.0148037
$501$	5008.73	0.446654
$502$	12770.8	1.13544
$503$	13406.0	1.18836	0.594181	−	0.804332i	$-0.297476\pi$
$503$	13406.0	1.18836	0.594181	+	0.804332i	$0.297476\pi$
$504$	5776.11	0.510493
$505$	6352.84	0.559797
$506$	−794.177	−0.0697737
$507$	−890.030	−0.0779638
$508$	938.428	0.0819606
$509$	−13537.0	−1.17882	−0.589409	−	0.807835i	$-0.700639\pi$
$509$	−13537.0	−1.17882	−0.589409	+	0.807835i	$0.700639\pi$
$510$	−4519.68	−0.392421
$511$	18181.7	1.57400
$512$	−13016.8	−1.12357
$513$	−611.867	−0.0526600
$514$	8638.23	0.741276
$515$	−4422.98	−0.378446
$516$	1095.83	0.0934909
$517$	3850.26	0.327532
$518$	−20719.8	−1.75748
$519$	10465.9	0.885163
$520$	−6015.22	−0.507279
$521$	−6612.84	−0.556073	−0.278036	−	0.960571i	$-0.589684\pi$
$521$	−6612.84	−0.556073	−0.278036	+	0.960571i	$0.589684\pi$
$522$	674.366	0.0565445
$523$	−11689.8	−0.977363	−0.488682	−	0.872462i	$-0.662522\pi$
$523$	−11689.8	−0.977363	−0.488682	+	0.872462i	$0.662522\pi$
$524$	2692.91	0.224505
$525$	1997.99	0.166094
$526$	2722.29	0.225660
$527$	−1029.18	−0.0850694
$528$	−1244.87	−0.102606
$529$	−10703.0	−0.879678
$530$	−6416.59	−0.525885
$531$	−5071.54	−0.414475
$532$	799.355	0.0651437
$533$	15250.7	1.23937
$534$	−6187.89	−0.501454
$535$	4629.68	0.374128
$536$	−5232.07	−0.421625
$537$	−12049.4	−0.968290
$538$	6066.85	0.486172
$539$	−2945.68	−0.235398
$540$	178.751	0.0142449
$541$	−170.114	−0.0135190	−0.00675951	−	0.999977i	$-0.502152\pi$
$541$	−170.114	−0.0135190	−0.00675951	+	0.999977i	$0.502152\pi$
$542$	10931.1	0.866291
$543$	6827.42	0.539582
$544$	6911.65	0.544733
$545$	367.494	0.0288839
$546$	10311.7	0.808238
$547$	−6453.08	−0.504413	−0.252206	−	0.967673i	$-0.581156\pi$
$547$	−6453.08	−0.504413	−0.252206	+	0.967673i	$0.581156\pi$
$548$	−3490.23	−0.272071
$549$	4368.11	0.339575
$550$	−518.912	−0.0402300
$551$	657.190	0.0508117
$552$	2765.33	0.213225
$553$	−30882.4	−2.37478
$554$	5546.66	0.425370
$555$	−4515.32	−0.345342
$556$	1700.19	0.129684
$557$	−12800.7	−0.973759	−0.486879	−	0.873469i	$-0.661865\pi$
$557$	−12800.7	−0.973759	−0.486879	+	0.873469i	$0.661865\pi$
$558$	−205.223	−0.0155695
$559$	13776.1	1.04234
$560$	6880.29	0.519188
$561$	2810.48	0.211513
$562$	−3735.63	−0.280388
$563$	6454.48	0.483169	0.241584	−	0.970380i	$-0.422333\pi$
$563$	6454.48	0.483169	0.241584	+	0.970380i	$0.422333\pi$
$564$	−1903.83	−0.142138
$565$	−10343.4	−0.770179
$566$	9755.97	0.724512
$567$	−2157.83	−0.159824
$568$	−15129.9	−1.11767
$569$	2900.88	0.213728	0.106864	−	0.994274i	$-0.465919\pi$
$569$	2900.88	0.213728	0.106864	+	0.994274i	$0.465919\pi$
$570$	−878.294	−0.0645398
$571$	−13437.3	−0.984823	−0.492411	−	0.870363i	$-0.663884\pi$
$571$	−13437.3	−0.984823	−0.492411	+	0.870363i	$0.663884\pi$
$572$	531.170	0.0388275
$573$	−9613.06	−0.700858
$574$	−21021.2	−1.52859
$575$	956.541	0.0693748
$576$	5097.32	0.368730
$577$	−5402.33	−0.389778	−0.194889	−	0.980825i	$-0.562435\pi$
$577$	−5402.33	−0.389778	−0.194889	+	0.980825i	$0.562435\pi$
$578$	22443.9	1.61513
$579$	213.093	0.0152951
$580$	−191.992	−0.0137449
$581$	−17811.2	−1.27183
$582$	−6721.31	−0.478707
$583$	3990.04	0.283449
$584$	16442.4	1.16505
$585$	2247.15	0.158818
$586$	16669.0	1.17507
$587$	−17702.2	−1.24471	−0.622357	−	0.782733i	$-0.713825\pi$
$587$	−17702.2	−1.24471	−0.622357	+	0.782733i	$0.713825\pi$
$588$	1456.55	0.102155
$589$	−199.996	−0.0139910
$590$	−7279.86	−0.507978
$591$	−3781.57	−0.263203
$592$	−15549.0	−1.07949
$593$	−13235.5	−0.916558	−0.458279	−	0.888808i	$-0.651534\pi$
$593$	−13235.5	−0.916558	−0.458279	+	0.888808i	$0.651534\pi$
$594$	560.425	0.0387113
$595$	−15533.3	−1.07025
$596$	−346.701	−0.0238279
$597$	−7095.63	−0.486440
$598$	4936.73	0.337588
$599$	−22931.4	−1.56419	−0.782095	−	0.623159i	$-0.785849\pi$
$599$	−22931.4	−1.56419	−0.782095	+	0.623159i	$0.785849\pi$
$600$	1806.85	0.122941
$601$	−11714.0	−0.795051	−0.397525	−	0.917591i	$-0.630131\pi$
$601$	−11714.0	−0.795051	−0.397525	+	0.917591i	$0.630131\pi$
$602$	−18988.7	−1.28558
$603$	1954.59	0.132001
$604$	−3654.73	−0.246207
$605$	−6332.32	−0.425530
$606$	−9848.60	−0.660185
$607$	4567.18	0.305397	0.152699	−	0.988273i	$-0.451204\pi$
$607$	4567.18	0.305397	0.152699	+	0.988273i	$0.451204\pi$
$608$	1343.12	0.0895898
$609$	2317.66	0.154214
$610$	6270.14	0.416181
$611$	−23933.8	−1.58471
$612$	−1389.69	−0.0917892
$613$	−19389.4	−1.27754	−0.638768	−	0.769399i	$-0.720556\pi$
$613$	−19389.4	−1.27754	−0.638768	+	0.769399i	$0.720556\pi$
$614$	10844.3	0.712769
$615$	−4581.02	−0.300365
$616$	−5155.75	−0.337226
$617$	−1918.52	−0.125181	−0.0625905	−	0.998039i	$-0.519936\pi$
$617$	−1918.52	−0.125181	−0.0625905	+	0.998039i	$0.519936\pi$
$618$	6856.81	0.446313
$619$	25281.1	1.64157	0.820785	−	0.571237i	$-0.193536\pi$
$619$	25281.1	1.64157	0.820785	+	0.571237i	$0.193536\pi$
$620$	58.4270	0.00378465
$621$	−1033.06	−0.0667559
$622$	17852.1	1.15081
$623$	−21266.6	−1.36762
$624$	7738.32	0.496443
$625$	625.000	0.0400000
$626$	2158.26	0.137798
$627$	546.151	0.0347866
$628$	−2544.88	−0.161707
$629$	35104.2	2.22527
$630$	−3097.41	−0.195879
$631$	−21718.6	−1.37022	−0.685108	−	0.728442i	$-0.740245\pi$
$631$	−21718.6	−1.37022	−0.685108	+	0.728442i	$0.740245\pi$
$632$	−27928.1	−1.75778
$633$	4813.22	0.302225
$634$	−1173.38	−0.0735029
$635$	−3543.69	−0.221460
$636$	−1972.95	−0.123007
$637$	18310.8	1.13893
$638$	−601.938	−0.0373526
$639$	5652.20	0.349918
$640$	4946.14	0.305489
$641$	9371.00	0.577429	0.288715	−	0.957415i	$-0.406772\pi$
$641$	9371.00	0.577429	0.288715	+	0.957415i	$0.406772\pi$
$642$	−7177.25	−0.441220
$643$	−7538.94	−0.462375	−0.231187	−	0.972909i	$-0.574261\pi$
$643$	−7538.94	−0.462375	−0.231187	+	0.972909i	$0.574261\pi$
$644$	1349.62	0.0825812
$645$	−4138.08	−0.252615
$646$	6828.25	0.415873
$647$	15345.6	0.932455	0.466228	−	0.884665i	$-0.345613\pi$
$647$	15345.6	0.932455	0.466228	+	0.884665i	$0.345613\pi$
$648$	−1951.40	−0.118300
$649$	4526.85	0.273797
$650$	3225.64	0.194646
$651$	−705.312	−0.0424629
$652$	3686.30	0.221421
$653$	−19648.0	−1.17747	−0.588735	−	0.808326i	$-0.700374\pi$
$653$	−19648.0	−1.17747	−0.588735	+	0.808326i	$0.700374\pi$
$654$	−569.715	−0.0340636
$655$	−10169.0	−0.606618
$656$	−15775.2	−0.938902
$657$	−6142.51	−0.364752
$658$	32989.7	1.95452
$659$	−24207.8	−1.43096	−0.715481	−	0.698633i	$-0.753792\pi$
$659$	−24207.8	−1.43096	−0.715481	+	0.698633i	$0.753792\pi$
$660$	−159.553	−0.00940999
$661$	3864.20	0.227383	0.113691	−	0.993516i	$-0.463733\pi$
$661$	3864.20	0.227383	0.113691	+	0.993516i	$0.463733\pi$
$662$	−16454.2	−0.966026
$663$	−17470.4	−1.02337
$664$	−16107.3	−0.941395
$665$	−3018.52	−0.176020
$666$	6999.96	0.407272
$667$	1109.59	0.0644129
$668$	2210.66	0.128043
$669$	8367.78	0.483583
$670$	2805.68	0.161780
$671$	−3898.97	−0.224319
$672$	4736.67	0.271907
$673$	17574.4	1.00660	0.503300	−	0.864112i	$-0.332119\pi$
$673$	17574.4	1.00660	0.503300	+	0.864112i	$0.332119\pi$
$674$	−20920.1	−1.19557
$675$	−675.000	−0.0384900
$676$	−392.825	−0.0223501
$677$	−26672.9	−1.51421	−0.757106	−	0.653292i	$-0.773387\pi$
$677$	−26672.9	−1.51421	−0.757106	+	0.653292i	$0.773387\pi$
$678$	16035.1	0.908294
$679$	−23099.8	−1.30558
$680$	−14047.3	−0.792190
$681$	−9275.01	−0.521908
$682$	183.182	0.0102850
$683$	2985.36	0.167250	0.0836249	−	0.996497i	$-0.473350\pi$
$683$	2985.36	0.167250	0.0836249	+	0.996497i	$0.473350\pi$
$684$	−270.054	−0.0150962
$685$	13179.8	0.735145
$686$	−1629.95	−0.0907171
$687$	19440.0	1.07959
$688$	−14249.9	−0.789642
$689$	−24802.7	−1.37142
$690$	−1482.89	−0.0818157
$691$	15067.6	0.829518	0.414759	−	0.909931i	$-0.363866\pi$
$691$	15067.6	0.829518	0.414759	+	0.909931i	$0.363866\pi$
$692$	4619.22	0.253752
$693$	1926.07	0.105578
$694$	−6299.76	−0.344576
$695$	−6420.26	−0.350409
$696$	2095.95	0.114148
$697$	35614.9	1.93545
$698$	−2008.33	−0.108906
$699$	10941.0	0.592029
$700$	881.833	0.0476145
$701$	32060.7	1.72741	0.863707	−	0.503994i	$-0.168137\pi$
$701$	32060.7	1.72741	0.863707	+	0.503994i	$0.168137\pi$
$702$	−3483.69	−0.187298
$703$	6821.67	0.365980
$704$	−4549.86	−0.243578
$705$	7189.24	0.384060
$706$	−24933.0	−1.32913
$707$	−33847.7	−1.80053
$708$	−2238.38	−0.118818
$709$	−6089.76	−0.322575	−0.161288	−	0.986907i	$-0.551565\pi$
$709$	−6089.76	−0.322575	−0.161288	+	0.986907i	$0.551565\pi$
$710$	8113.36	0.428858
$711$	10433.3	0.550323
$712$	−19232.1	−1.01230
$713$	−337.669	−0.0177361
$714$	24080.7	1.26218
$715$	−2005.80	−0.104913
$716$	−5318.15	−0.277582
$717$	−11589.0	−0.603625
$718$	24953.0	1.29699
$719$	2735.79	0.141902	0.0709511	−	0.997480i	$-0.477397\pi$
$719$	2735.79	0.141902	0.0709511	+	0.997480i	$0.477397\pi$
$720$	−2324.44	−0.120315
$721$	23565.5	1.21723
$722$	−16395.2	−0.845107
$723$	−18623.3	−0.957963
$724$	3013.36	0.154683
$725$	725.000	0.0371391
$726$	9816.80	0.501840
$727$	−23072.1	−1.17702	−0.588511	−	0.808489i	$-0.700286\pi$
$727$	−23072.1	−1.17702	−0.588511	+	0.808489i	$0.700286\pi$
$728$	32048.9	1.63161
$729$	729.000	0.0370370
$730$	−8817.17	−0.447038
$731$	32171.3	1.62777
$732$	1927.92	0.0973467
$733$	2341.92	0.118009	0.0590047	−	0.998258i	$-0.481207\pi$
$733$	2341.92	0.118009	0.0590047	+	0.998258i	$0.481207\pi$
$734$	−23703.4	−1.19197
$735$	−5500.21	−0.276025
$736$	2267.69	0.113571
$737$	−1744.66	−0.0871986
$738$	7101.80	0.354229
$739$	30372.4	1.51186	0.755932	−	0.654651i	$-0.227184\pi$
$739$	30372.4	1.51186	0.755932	+	0.654651i	$0.227184\pi$
$740$	−1992.89	−0.0990000
$741$	−3394.96	−0.168309
$742$	34187.4	1.69145
$743$	16456.7	0.812566	0.406283	−	0.913747i	$-0.366825\pi$
$743$	16456.7	0.812566	0.406283	+	0.913747i	$0.366825\pi$
$744$	−637.839	−0.0314305
$745$	1309.21	0.0643837
$746$	7492.17	0.367705
$747$	6017.35	0.294730
$748$	1240.44	0.0606349
$749$	−24666.8	−1.20334
$750$	−968.917	−0.0471731
$751$	−28265.3	−1.37339	−0.686694	−	0.726947i	$-0.740939\pi$
$751$	−28265.3	−1.37339	−0.686694	+	0.726947i	$0.740939\pi$
$752$	24756.9	1.20052
$753$	−14828.0	−0.717615
$754$	3741.74	0.180724
$755$	13801.0	0.665258
$756$	−952.380	−0.0458171
$757$	30213.7	1.45064	0.725320	−	0.688412i	$-0.241692\pi$
$757$	30213.7	1.45064	0.725320	+	0.688412i	$0.241692\pi$
$758$	−15036.5	−0.720517
$759$	922.111	0.0440982
$760$	−2729.76	−0.130288
$761$	7521.30	0.358274	0.179137	−	0.983824i	$-0.442669\pi$
$761$	7521.30	0.358274	0.179137	+	0.983824i	$0.442669\pi$
$762$	5493.67	0.261174
$763$	−1958.00	−0.0929020
$764$	−4242.83	−0.200916
$765$	5247.76	0.248017
$766$	−15000.9	−0.707578
$767$	−28139.6	−1.32472
$768$	5925.01	0.278386
$769$	−31256.5	−1.46572	−0.732859	−	0.680380i	$-0.761815\pi$
$769$	−31256.5	−1.46572	−0.732859	+	0.680380i	$0.761815\pi$
$770$	2764.75	0.129396
$771$	−10029.8	−0.468499
$772$	94.0510	0.00438467
$773$	6657.91	0.309791	0.154895	−	0.987931i	$-0.450496\pi$
$773$	6657.91	0.309791	0.154895	+	0.987931i	$0.450496\pi$
$774$	6415.13	0.297916
$775$	−220.632	−0.0102262
$776$	−20890.0	−0.966376
$777$	24057.5	1.11076
$778$	19871.4	0.915711
$779$	6920.92	0.318315
$780$	991.805	0.0455286
$781$	−5045.15	−0.231152
$782$	11528.7	0.527193
$783$	−783.000	−0.0357371
$784$	−18940.6	−0.862817
$785$	9609.98	0.436936
$786$	15764.6	0.715402
$787$	18918.1	0.856872	0.428436	−	0.903572i	$-0.359065\pi$
$787$	18918.1	0.856872	0.428436	+	0.903572i	$0.359065\pi$
$788$	−1669.04	−0.0754531
$789$	−3160.82	−0.142621
$790$	14976.3	0.674473
$791$	55109.4	2.47720
$792$	1741.82	0.0781475
$793$	24236.6	1.08533
$794$	−4232.84	−0.189191
$795$	7450.24	0.332368
$796$	−3131.73	−0.139449
$797$	−16329.2	−0.725734	−0.362867	−	0.931841i	$-0.618202\pi$
$797$	−16329.2	−0.725734	−0.362867	+	0.931841i	$0.618202\pi$
$798$	4679.52	0.207585
$799$	−55892.4	−2.47476
$800$	1481.70	0.0654826
$801$	7184.70	0.316927
$802$	9768.99	0.430119
$803$	5482.80	0.240951
$804$	862.678	0.0378412
$805$	−5096.42	−0.223137
$806$	−1138.69	−0.0497624
$807$	−7044.16	−0.307269
$808$	−30609.7	−1.33273
$809$	−2755.55	−0.119753	−0.0598764	−	0.998206i	$-0.519071\pi$
$809$	−2755.55	−0.119753	−0.0598764	+	0.998206i	$0.519071\pi$
$810$	1046.43	0.0453924
$811$	−8552.83	−0.370321	−0.185161	−	0.982708i	$-0.559281\pi$
$811$	−8552.83	−0.370321	−0.185161	+	0.982708i	$0.559281\pi$
$812$	1022.93	0.0442090
$813$	−12692.0	−0.547511
$814$	−6248.15	−0.269039
$815$	−13920.2	−0.598286
$816$	18071.2	0.775269
$817$	6251.73	0.267712
$818$	−855.181	−0.0365534
$819$	−11972.8	−0.510820
$820$	−2021.88	−0.0861063
$821$	20670.4	0.878686	0.439343	−	0.898319i	$-0.355211\pi$
$821$	20670.4	0.878686	0.439343	+	0.898319i	$0.355211\pi$
$822$	−20432.2	−0.866977
$823$	474.045	0.0200780	0.0100390	−	0.999950i	$-0.496804\pi$
$823$	474.045	0.0200780	0.0100390	+	0.999950i	$0.496804\pi$
$824$	21311.1	0.900981
$825$	602.504	0.0254260
$826$	38786.8	1.63386
$827$	25547.5	1.07421	0.537106	−	0.843515i	$-0.319517\pi$
$827$	25547.5	1.07421	0.537106	+	0.843515i	$0.319517\pi$
$828$	−455.954	−0.0191371
$829$	−36219.9	−1.51745	−0.758726	−	0.651410i	$-0.774178\pi$
$829$	−36219.9	−1.51745	−0.758726	+	0.651410i	$0.774178\pi$
$830$	8637.50	0.361219
$831$	−6440.17	−0.268841
$832$	28282.6	1.17851
$833$	42761.1	1.77861
$834$	9953.13	0.413248
$835$	−8347.89	−0.345977
$836$	241.050	0.00997235
$837$	238.283	0.00984020
$838$	25614.1	1.05588
$839$	−17875.0	−0.735535	−0.367767	−	0.929918i	$-0.619878\pi$
$839$	−17875.0	−0.735535	−0.367767	+	0.929918i	$0.619878\pi$
$840$	−9626.85	−0.395426
$841$	841.000	0.0344828
$842$	16243.1	0.664814
$843$	4337.41	0.177210
$844$	2124.37	0.0866394
$845$	1483.38	0.0603905
$846$	−11145.2	−0.452933
$847$	33738.4	1.36867
$848$	25655.7	1.03894
$849$	−11327.6	−0.457904
$850$	7532.80	0.303968
$851$	11517.6	0.463945
$852$	2494.66	0.100312
$853$	−1402.84	−0.0563097	−0.0281549	−	0.999604i	$-0.508963\pi$
$853$	−1402.84	−0.0563097	−0.0281549	+	0.999604i	$0.508963\pi$
$854$	−33407.1	−1.33860
$855$	1019.78	0.0407903
$856$	−22307.1	−0.890702
$857$	32810.4	1.30780	0.653898	−	0.756582i	$-0.273132\pi$
$857$	32810.4	1.30780	0.653898	+	0.756582i	$0.273132\pi$
$858$	3109.53	0.123727
$859$	−19007.6	−0.754982	−0.377491	−	0.926013i	$-0.623213\pi$
$859$	−19007.6	−0.754982	−0.377491	+	0.926013i	$0.623213\pi$
$860$	−1826.39	−0.0724177
$861$	24407.5	0.966092
$862$	14982.2	0.591991
$863$	−6248.92	−0.246484	−0.123242	−	0.992377i	$-0.539329\pi$
$863$	−6248.92	−0.246484	−0.123242	+	0.992377i	$0.539329\pi$
$864$	−1600.24	−0.0630107
$865$	−17443.1	−0.685645
$866$	29652.3	1.16354
$867$	−26059.4	−1.02079
$868$	−311.297	−0.0121729
$869$	−9312.75	−0.363537
$870$	−1123.94	−0.0437992
$871$	10845.1	0.421896
$872$	−1770.69	−0.0687650
$873$	7804.05	0.302551
$874$	2240.33	0.0867051
$875$	−3329.98	−0.128656
$876$	−2711.07	−0.104564
$877$	18018.5	0.693777	0.346888	−	0.937906i	$-0.387238\pi$
$877$	18018.5	0.693777	0.346888	+	0.937906i	$0.387238\pi$
$878$	37282.7	1.43306
$879$	−19354.2	−0.742661
$880$	2074.79	0.0794785
$881$	28136.0	1.07597	0.537983	−	0.842956i	$-0.319186\pi$
$881$	28136.0	1.07597	0.537983	+	0.842956i	$0.319186\pi$
$882$	8526.79	0.325524
$883$	−41964.1	−1.59933	−0.799663	−	0.600450i	$-0.794988\pi$
$883$	−41964.1	−1.59933	−0.799663	+	0.600450i	$0.794988\pi$
$884$	−7710.74	−0.293371
$885$	8452.57	0.321051
$886$	−30726.2	−1.16509
$887$	10526.5	0.398474	0.199237	−	0.979951i	$-0.436154\pi$
$887$	10526.5	0.398474	0.199237	+	0.979951i	$0.436154\pi$
$888$	21756.1	0.822169
$889$	18880.7	0.712302
$890$	10313.2	0.388424
$891$	−650.704	−0.0244662
$892$	3693.21	0.138630
$893$	−10861.4	−0.407012
$894$	−2029.63	−0.0759296
$895$	20082.4	0.750034
$896$	−26352.8	−0.982575
$897$	−5731.98	−0.213362
$898$	−25531.7	−0.948780
$899$	−255.933	−0.00949482
$900$	−297.919	−0.0110340
$901$	−57921.6	−2.14167
$902$	−6339.06	−0.233999
$903$	22047.5	0.812510
$904$	49837.5	1.83359
$905$	−11379.0	−0.417958
$906$	−21395.2	−0.784557
$907$	−41574.7	−1.52201	−0.761006	−	0.648744i	$-0.775294\pi$
$907$	−41574.7	−1.52201	−0.761006	+	0.648744i	$0.775294\pi$
$908$	−4093.63	−0.149617
$909$	11435.1	0.417248
$910$	−17186.1	−0.626058
$911$	−978.851	−0.0355991	−0.0177996	−	0.999842i	$-0.505666\pi$
$911$	−978.851	−0.0355991	−0.0177996	+	0.999842i	$0.505666\pi$
$912$	3511.72	0.127505
$913$	−5371.07	−0.194695
$914$	30078.4	1.08852
$915$	−7280.19	−0.263034
$916$	8580.04	0.309490
$917$	54180.0	1.95112
$918$	−8135.43	−0.292494
$919$	−2296.62	−0.0824358	−0.0412179	−	0.999150i	$-0.513124\pi$
$919$	−2296.62	−0.0824358	−0.0412179	+	0.999150i	$0.513124\pi$
$920$	−4608.88	−0.165163
$921$	−12591.2	−0.450482
$922$	−20787.2	−0.742507
$923$	31361.4	1.11839
$924$	850.093	0.0302662
$925$	7525.54	0.267501
$926$	−11215.0	−0.398000
$927$	−7961.37	−0.282077
$928$	1718.77	0.0607991
$929$	29033.8	1.02537	0.512684	−	0.858578i	$-0.328651\pi$
$929$	29033.8	1.02537	0.512684	+	0.858578i	$0.328651\pi$
$930$	342.039	0.0120601
$931$	8309.61	0.292520
$932$	4828.95	0.169718
$933$	−20727.8	−0.727330
$934$	−8944.15	−0.313342
$935$	−4684.14	−0.163837
$936$	−10827.4	−0.378103
$937$	22945.7	0.800005	0.400002	−	0.916514i	$-0.369009\pi$
$937$	22945.7	0.800005	0.400002	+	0.916514i	$0.369009\pi$
$938$	−14948.5	−0.520349
$939$	−2505.93	−0.0870906
$940$	3173.05	0.110099
$941$	31712.3	1.09861	0.549304	−	0.835622i	$-0.314893\pi$
$941$	31712.3	1.09861	0.549304	+	0.835622i	$0.314893\pi$
$942$	−14898.0	−0.515291
$943$	11685.1	0.403521
$944$	29107.3	1.00356
$945$	3596.38	0.123799
$946$	−5726.13	−0.196800
$947$	−7050.99	−0.241950	−0.120975	−	0.992656i	$-0.538602\pi$
$947$	−7050.99	−0.241950	−0.120975	+	0.992656i	$0.538602\pi$
$948$	4604.85	0.157762
$949$	−34081.9	−1.16580
$950$	1463.82	0.0499923
$951$	1362.40	0.0464551
$952$	74843.5	2.54800
$953$	−12178.0	−0.413938	−0.206969	−	0.978348i	$-0.566360\pi$
$953$	−12178.0	−0.413938	−0.206969	+	0.978348i	$0.566360\pi$
$954$	−11549.9	−0.391972
$955$	16021.8	0.542882
$956$	−5114.93	−0.173043
$957$	698.904	0.0236075
$958$	16238.1	0.547628
$959$	−70221.5	−2.36452
$960$	−8495.53	−0.285617
$961$	−29713.1	−0.997386
$962$	38839.5	1.30170
$963$	8333.43	0.278859
$964$	−8219.58	−0.274621
$965$	−355.155	−0.0118475
$966$	7900.81	0.263151
$967$	−13762.2	−0.457665	−0.228833	−	0.973466i	$-0.573491\pi$
$967$	−13762.2	−0.457665	−0.228833	+	0.973466i	$0.573491\pi$
$968$	30510.9	1.01308
$969$	−7928.22	−0.262839
$970$	11202.2	0.370805
$971$	−33646.0	−1.11200	−0.555999	−	0.831183i	$-0.687664\pi$
$971$	−33646.0	−1.11200	−0.555999	+	0.831183i	$0.687664\pi$
$972$	321.752	0.0106175
$973$	34206.9	1.12705
$974$	−4675.69	−0.153818
$975$	−3745.25	−0.123020
$976$	−25070.1	−0.822208
$977$	−42129.5	−1.37957	−0.689786	−	0.724013i	$-0.742296\pi$
$977$	−42129.5	−1.37957	−0.689786	+	0.724013i	$0.742296\pi$
$978$	21580.0	0.705576
$979$	−6413.05	−0.209358
$980$	−2427.58	−0.0791286
$981$	661.490	0.0215288
$982$	24675.8	0.801870
$983$	−39740.6	−1.28945	−0.644724	−	0.764415i	$-0.723028\pi$
$983$	−39740.6	−1.28945	−0.644724	+	0.764415i	$0.723028\pi$
$984$	22072.6	0.715090
$985$	6302.62	0.203876
$986$	8738.05	0.282227
$987$	−38304.0	−1.23529
$988$	−1498.40	−0.0482495
$989$	10555.3	0.339372
$990$	−934.042	−0.0299857
$991$	34300.8	1.09950	0.549748	−	0.835330i	$-0.314724\pi$
$991$	34300.8	1.09950	0.549748	+	0.835330i	$0.314724\pi$
$992$	−523.057	−0.0167410
$993$	19104.8	0.610545
$994$	−43227.7	−1.37938
$995$	11826.1	0.376795
$996$	2655.82	0.0844909
$997$	−36545.8	−1.16090	−0.580449	−	0.814296i	$-0.697123\pi$
$997$	−36545.8	−1.16090	−0.580449	+	0.814296i	$0.697123\pi$
$998$	−35327.7	−1.12052
$999$	−8127.58	−0.257403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.i.1.6	✓	7
3.2	odd	2		1305.4.a.n.1.2		7
5.4	even	2		2175.4.a.n.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.i.1.6	✓	7	1.1	even	1	trivial
1305.4.a.n.1.2		7	3.2	odd	2
2175.4.a.n.1.2		7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q+2.58378 q^{2} -3.00000 q^{3} -1.32408 q^{4} +5.00000 q^{5} -7.75134 q^{6} -26.6398 q^{7} -24.0914 q^{8} +9.00000 q^{9} +12.9189 q^{10} -8.03338 q^{11} +3.97225 q^{12} +49.9367 q^{13} -68.8314 q^{14} -15.0000 q^{15} -51.6541 q^{16} +116.617 q^{17} +23.2540 q^{18} +22.6617 q^{19} -6.62041 q^{20} +79.9195 q^{21} -20.7565 q^{22} +38.2616 q^{23} +72.2741 q^{24} +25.0000 q^{25} +129.025 q^{26} -27.0000 q^{27} +35.2733 q^{28} +29.0000 q^{29} -38.7567 q^{30} -8.82528 q^{31} +59.2681 q^{32} +24.1002 q^{33} +301.312 q^{34} -133.199 q^{35} -11.9167 q^{36} +301.022 q^{37} +58.5529 q^{38} -149.810 q^{39} -120.457 q^{40} +305.401 q^{41} +206.494 q^{42} +275.872 q^{43} +10.6369 q^{44} +45.0000 q^{45} +98.8596 q^{46} -479.282 q^{47} +154.962 q^{48} +366.680 q^{49} +64.5945 q^{50} -349.850 q^{51} -66.1204 q^{52} -496.683 q^{53} -69.7621 q^{54} -40.1669 q^{55} +641.790 q^{56} -67.9852 q^{57} +74.9296 q^{58} -563.505 q^{59} +19.8612 q^{60} +485.346 q^{61} -22.8026 q^{62} -239.758 q^{63} +566.369 q^{64} +249.684 q^{65} +62.2695 q^{66} +217.176 q^{67} -154.410 q^{68} -114.785 q^{69} -344.157 q^{70} +628.023 q^{71} -216.822 q^{72} -682.502 q^{73} +777.773 q^{74} -75.0000 q^{75} -30.0060 q^{76} +214.008 q^{77} -387.076 q^{78} +1159.26 q^{79} -258.271 q^{80} +81.0000 q^{81} +789.089 q^{82} +668.594 q^{83} -105.820 q^{84} +583.084 q^{85} +712.792 q^{86} -87.0000 q^{87} +193.535 q^{88} +798.300 q^{89} +116.270 q^{90} -1330.31 q^{91} -50.6616 q^{92} +26.4758 q^{93} -1238.36 q^{94} +113.309 q^{95} -177.804 q^{96} +867.116 q^{97} +947.421 q^{98} -72.3005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19}+ \cdots + 684 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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