LMFDB - Embedded newform 1870.4.a.j.1.5

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,-1] 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:	$1$
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} - x^{9} - 168 x^{8} + 138 x^{7} + 9025 x^{6} - 8357 x^{5} - 177203 x^{4} + 269951 x^{3} + \cdots + 1239820 $ x^10 - x^9 - 168x^8 + 138x^7 + 9025x^6 - 8357x^5 - 177203x^4 + 269951x^3 + 1064495x^2 - 2545931x + 1239820
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			1.5
Root			$1.93833$ 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)

$f(q)$	$=$	\(q-2.00000 q^{2} -1.93833 q^{3} +4.00000 q^{4} -5.00000 q^{5} +3.87666 q^{6} +17.2000 q^{7} -8.00000 q^{8} -23.2429 q^{9} +10.0000 q^{10} -11.0000 q^{11} -7.75332 q^{12} -14.1499 q^{13} -34.4001 q^{14} +9.69165 q^{15} +16.0000 q^{16} +17.0000 q^{17} +46.4858 q^{18} -21.4463 q^{19} -20.0000 q^{20} -33.3394 q^{21} +22.0000 q^{22} -33.4585 q^{23} +15.5066 q^{24} +25.0000 q^{25} +28.2997 q^{26} +97.3872 q^{27} +68.8002 q^{28} +267.732 q^{29} -19.3833 q^{30} +146.383 q^{31} -32.0000 q^{32} +21.3216 q^{33} -34.0000 q^{34} -86.0002 q^{35} -92.9715 q^{36} -342.017 q^{37} +42.8926 q^{38} +27.4271 q^{39} +40.0000 q^{40} -151.800 q^{41} +66.6787 q^{42} +113.445 q^{43} -44.0000 q^{44} +116.214 q^{45} +66.9171 q^{46} +377.453 q^{47} -31.0133 q^{48} -47.1584 q^{49} -50.0000 q^{50} -32.9516 q^{51} -56.5995 q^{52} -242.222 q^{53} -194.774 q^{54} +55.0000 q^{55} -137.600 q^{56} +41.5700 q^{57} -535.464 q^{58} -23.3335 q^{59} +38.7666 q^{60} +481.320 q^{61} -292.765 q^{62} -399.779 q^{63} +64.0000 q^{64} +70.7493 q^{65} -42.6432 q^{66} -384.271 q^{67} +68.0000 q^{68} +64.8537 q^{69} +172.000 q^{70} -778.875 q^{71} +185.943 q^{72} +500.356 q^{73} +684.034 q^{74} -48.4582 q^{75} -85.7853 q^{76} -189.200 q^{77} -54.8542 q^{78} -1025.48 q^{79} -80.0000 q^{80} +438.789 q^{81} +303.600 q^{82} +823.835 q^{83} -133.357 q^{84} -85.0000 q^{85} -226.891 q^{86} -518.953 q^{87} +88.0000 q^{88} +1194.43 q^{89} -232.429 q^{90} -243.378 q^{91} -133.834 q^{92} -283.738 q^{93} -754.906 q^{94} +107.232 q^{95} +62.0265 q^{96} +308.808 q^{97} +94.3169 q^{98} +255.672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 20 q^{2} - q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 4 q^{7} - 80 q^{8} + 67 q^{9} + 100 q^{10} - 110 q^{11} - 4 q^{12} - 7 q^{13} - 8 q^{14} + 5 q^{15} + 160 q^{16} + 170 q^{17} - 134 q^{18} + 11 q^{19}+ \cdots - 737 q^{99}+O(q^{100}) $ 10 * q - 20 * q^2 - q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 4 * q^7 - 80 * q^8 + 67 * q^9 + 100 * q^10 - 110 * q^11 - 4 * q^12 - 7 * q^13 - 8 * q^14 + 5 * q^15 + 160 * q^16 + 170 * q^17 - 134 * q^18 + 11 * q^19 - 200 * q^20 - 162 * q^21 + 220 * q^22 - 124 * q^23 + 8 * q^24 + 250 * q^25 + 14 * q^26 - 37 * q^27 + 16 * q^28 + 91 * q^29 - 10 * q^30 + 29 * q^31 - 320 * q^32 + 11 * q^33 - 340 * q^34 - 20 * q^35 + 268 * q^36 + 468 * q^37 - 22 * q^38 + 161 * q^39 + 400 * q^40 - 698 * q^41 + 324 * q^42 + 726 * q^43 - 440 * q^44 - 335 * q^45 + 248 * q^46 - 181 * q^47 - 16 * q^48 + 638 * q^49 - 500 * q^50 - 17 * q^51 - 28 * q^52 - 335 * q^53 + 74 * q^54 + 550 * q^55 - 32 * q^56 + 11 * q^57 - 182 * q^58 + 649 * q^59 + 20 * q^60 + 13 * q^61 - 58 * q^62 - 460 * q^63 + 640 * q^64 + 35 * q^65 - 22 * q^66 + 1384 * q^67 + 680 * q^68 + 1304 * q^69 + 40 * q^70 - 1655 * q^71 - 536 * q^72 - 1185 * q^73 - 936 * q^74 - 25 * q^75 + 44 * q^76 - 44 * q^77 - 322 * q^78 + 364 * q^79 - 800 * q^80 + 462 * q^81 + 1396 * q^82 - 120 * q^83 - 648 * q^84 - 850 * q^85 - 1452 * q^86 + 3429 * q^87 + 880 * q^88 - 651 * q^89 + 670 * q^90 - 42 * q^91 - 496 * q^92 - 355 * q^93 + 362 * q^94 - 55 * q^95 + 32 * q^96 + 73 * q^97 - 1276 * q^98 - 737 * 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
$3$	−1.93833	−0.373032	−0.186516	−	0.982452i	$-0.559720\pi$
$3$	−1.93833	−0.373032	−0.186516	+	0.982452i	$0.559720\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	3.87666	0.263773
$7$	17.2000	0.928715	0.464358	−	0.885648i	$-0.346285\pi$
$7$	17.2000	0.928715	0.464358	+	0.885648i	$0.346285\pi$
$8$	−8.00000	−0.353553
$9$	−23.2429	−0.860847
$10$	10.0000	0.316228
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−7.75332	−0.186516
$13$	−14.1499	−0.301882	−0.150941	−	0.988543i	$-0.548230\pi$
$13$	−14.1499	−0.301882	−0.150941	+	0.988543i	$0.548230\pi$
$14$	−34.4001	−0.656701
$15$	9.69165	0.166825
$16$	16.0000	0.250000
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	46.4858	0.608711
$19$	−21.4463	−0.258954	−0.129477	−	0.991582i	$-0.541330\pi$
$19$	−21.4463	−0.258954	−0.129477	+	0.991582i	$0.541330\pi$
$20$	−20.0000	−0.223607
$21$	−33.3394	−0.346440
$22$	22.0000	0.213201
$23$	−33.4585	−0.303330	−0.151665	−	0.988432i	$-0.548463\pi$
$23$	−33.4585	−0.303330	−0.151665	+	0.988432i	$0.548463\pi$
$24$	15.5066	0.131887
$25$	25.0000	0.200000
$26$	28.2997	0.213463
$27$	97.3872	0.694155
$28$	68.8002	0.464358
$29$	267.732	1.71437	0.857183	−	0.515012i	$-0.172212\pi$
$29$	267.732	1.71437	0.857183	+	0.515012i	$0.172212\pi$
$30$	−19.3833	−0.117963
$31$	146.383	0.848100	0.424050	−	0.905639i	$-0.360608\pi$
$31$	146.383	0.848100	0.424050	+	0.905639i	$0.360608\pi$
$32$	−32.0000	−0.176777
$33$	21.3216	0.112473
$34$	−34.0000	−0.171499
$35$	−86.0002	−0.415334
$36$	−92.9715	−0.430424
$37$	−342.017	−1.51966	−0.759828	−	0.650124i	$-0.774717\pi$
$37$	−342.017	−1.51966	−0.759828	+	0.650124i	$0.774717\pi$
$38$	42.8926	0.183108
$39$	27.4271	0.112612
$40$	40.0000	0.158114
$41$	−151.800	−0.578223	−0.289112	−	0.957295i	$-0.593360\pi$
$41$	−151.800	−0.578223	−0.289112	+	0.957295i	$0.593360\pi$
$42$	66.6787	0.244970
$43$	113.445	0.402332	0.201166	−	0.979557i	$-0.435527\pi$
$43$	113.445	0.402332	0.201166	+	0.979557i	$0.435527\pi$
$44$	−44.0000	−0.150756
$45$	116.214	0.384983
$46$	66.9171	0.214487
$47$	377.453	1.17143	0.585714	−	0.810518i	$-0.300814\pi$
$47$	377.453	1.17143	0.585714	+	0.810518i	$0.300814\pi$
$48$	−31.0133	−0.0932579
$49$	−47.1584	−0.137488
$50$	−50.0000	−0.141421
$51$	−32.9516	−0.0904735
$52$	−56.5995	−0.150941
$53$	−242.222	−0.627770	−0.313885	−	0.949461i	$-0.601631\pi$
$53$	−242.222	−0.627770	−0.313885	+	0.949461i	$0.601631\pi$
$54$	−194.774	−0.490842
$55$	55.0000	0.134840
$56$	−137.600	−0.328350
$57$	41.5700	0.0965980
$58$	−535.464	−1.21224
$59$	−23.3335	−0.0514874	−0.0257437	−	0.999669i	$-0.508195\pi$
$59$	−23.3335	−0.0514874	−0.0257437	+	0.999669i	$0.508195\pi$
$60$	38.7666	0.0834124
$61$	481.320	1.01027	0.505137	−	0.863039i	$-0.331442\pi$
$61$	481.320	1.01027	0.505137	+	0.863039i	$0.331442\pi$
$62$	−292.765	−0.599697
$63$	−399.779	−0.799482
$64$	64.0000	0.125000
$65$	70.7493	0.135006
$66$	−42.6432	−0.0795306
$67$	−384.271	−0.700689	−0.350345	−	0.936621i	$-0.613935\pi$
$67$	−384.271	−0.700689	−0.350345	+	0.936621i	$0.613935\pi$
$68$	68.0000	0.121268
$69$	64.8537	0.113152
$70$	172.000	0.293686
$71$	−778.875	−1.30191	−0.650954	−	0.759118i	$-0.725631\pi$
$71$	−778.875	−1.30191	−0.650954	+	0.759118i	$0.725631\pi$
$72$	185.943	0.304356
$73$	500.356	0.802223	0.401111	−	0.916029i	$-0.368624\pi$
$73$	500.356	0.802223	0.401111	+	0.916029i	$0.368624\pi$
$74$	684.034	1.07456
$75$	−48.4582	−0.0746063
$76$	−85.7853	−0.129477
$77$	−189.200	−0.280018
$78$	−54.8542	−0.0796284
$79$	−1025.48	−1.46044	−0.730222	−	0.683210i	$-0.760583\pi$
$79$	−1025.48	−1.46044	−0.730222	+	0.683210i	$0.760583\pi$
$80$	−80.0000	−0.111803
$81$	438.789	0.601906
$82$	303.600	0.408866
$83$	823.835	1.08949	0.544745	−	0.838602i	$-0.316627\pi$
$83$	823.835	1.08949	0.544745	+	0.838602i	$0.316627\pi$
$84$	−133.357	−0.173220
$85$	−85.0000	−0.108465
$86$	−226.891	−0.284491
$87$	−518.953	−0.639513
$88$	88.0000	0.106600
$89$	1194.43	1.42258	0.711289	−	0.702899i	$-0.248112\pi$
$89$	1194.43	1.42258	0.711289	+	0.702899i	$0.248112\pi$
$90$	−232.429	−0.272224
$91$	−243.378	−0.280362
$92$	−133.834	−0.151665
$93$	−283.738	−0.316368
$94$	−754.906	−0.828325
$95$	107.232	0.115808
$96$	62.0265	0.0659433
$97$	308.808	0.323244	0.161622	−	0.986853i	$-0.448327\pi$
$97$	308.808	0.323244	0.161622	+	0.986853i	$0.448327\pi$
$98$	94.3169	0.0972188
$99$	255.672	0.259555
$100$	100.000	0.100000
$101$	−183.403	−0.180686	−0.0903428	−	0.995911i	$-0.528796\pi$
$101$	−183.403	−0.180686	−0.0903428	+	0.995911i	$0.528796\pi$
$102$	65.9032	0.0639744
$103$	127.151	0.121636	0.0608181	−	0.998149i	$-0.480629\pi$
$103$	127.151	0.121636	0.0608181	+	0.998149i	$0.480629\pi$
$104$	113.199	0.106731
$105$	166.697	0.154933
$106$	484.445	0.443900
$107$	−1379.15	−1.24605	−0.623025	−	0.782202i	$-0.714096\pi$
$107$	−1379.15	−1.24605	−0.623025	+	0.782202i	$0.714096\pi$
$108$	389.549	0.347077
$109$	1922.70	1.68955	0.844777	−	0.535118i	$-0.179733\pi$
$109$	1922.70	1.68955	0.844777	+	0.535118i	$0.179733\pi$
$110$	−110.000	−0.0953463
$111$	662.942	0.566880
$112$	275.201	0.232179
$113$	−742.009	−0.617719	−0.308860	−	0.951108i	$-0.599947\pi$
$113$	−742.009	−0.617719	−0.308860	+	0.951108i	$0.599947\pi$
$114$	−83.1401	−0.0683051
$115$	167.293	0.135653
$116$	1070.93	0.857183
$117$	328.884	0.259874
$118$	46.6669	0.0364071
$119$	292.401	0.225247
$120$	−77.5332	−0.0589815
$121$	121.000	0.0909091
$122$	−962.641	−0.714372
$123$	294.238	0.215696
$124$	585.530	0.424050
$125$	−125.000	−0.0894427
$126$	799.557	0.565319
$127$	2150.41	1.50250	0.751251	−	0.660016i	$-0.229451\pi$
$127$	2150.41	1.50250	0.751251	+	0.660016i	$0.229451\pi$
$128$	−128.000	−0.0883883
$129$	−219.895	−0.150082
$130$	−141.499	−0.0954635
$131$	−2827.49	−1.88580	−0.942898	−	0.333081i	$-0.891912\pi$
$131$	−2827.49	−1.88580	−0.942898	+	0.333081i	$0.891912\pi$
$132$	85.2865	0.0562366
$133$	−368.878	−0.240494
$134$	768.542	0.495462
$135$	−486.936	−0.310436
$136$	−136.000	−0.0857493
$137$	−2897.09	−1.80668	−0.903340	−	0.428925i	$-0.858892\pi$
$137$	−2897.09	−1.80668	−0.903340	+	0.428925i	$0.858892\pi$
$138$	−129.707	−0.0800103
$139$	2409.78	1.47047	0.735235	−	0.677812i	$-0.237072\pi$
$139$	2409.78	1.47047	0.735235	+	0.677812i	$0.237072\pi$
$140$	−344.001	−0.207667
$141$	−731.628	−0.436980
$142$	1557.75	0.920587
$143$	155.649	0.0910209
$144$	−371.886	−0.215212
$145$	−1338.66	−0.766688
$146$	−1000.71	−0.567257
$147$	91.4086	0.0512874
$148$	−1368.07	−0.759828
$149$	750.050	0.412393	0.206196	−	0.978511i	$-0.433891\pi$
$149$	750.050	0.412393	0.206196	+	0.978511i	$0.433891\pi$
$150$	96.9165	0.0527546
$151$	−1453.49	−0.783331	−0.391665	−	0.920108i	$-0.628101\pi$
$151$	−1453.49	−0.783331	−0.391665	+	0.920108i	$0.628101\pi$
$152$	171.571	0.0915540
$153$	−395.129	−0.208786
$154$	378.401	0.198003
$155$	−731.913	−0.379282
$156$	109.708	0.0563058
$157$	−1137.83	−0.578398	−0.289199	−	0.957269i	$-0.593389\pi$
$157$	−1137.83	−0.578398	−0.289199	+	0.957269i	$0.593389\pi$
$158$	2050.95	1.03269
$159$	469.507	0.234178
$160$	160.000	0.0790569
$161$	−575.488	−0.281707
$162$	−877.578	−0.425612
$163$	1761.13	0.846273	0.423136	−	0.906066i	$-0.360929\pi$
$163$	1761.13	0.846273	0.423136	+	0.906066i	$0.360929\pi$
$164$	−607.199	−0.289112
$165$	−106.608	−0.0502996
$166$	−1647.67	−0.770385
$167$	3538.49	1.63962	0.819810	−	0.572635i	$-0.194079\pi$
$167$	3538.49	1.63962	0.819810	+	0.572635i	$0.194079\pi$
$168$	266.715	0.122485
$169$	−1996.78	−0.908867
$170$	170.000	0.0766965
$171$	498.474	0.222920
$172$	453.782	0.201166
$173$	1238.72	0.544384	0.272192	−	0.962243i	$-0.412251\pi$
$173$	1238.72	0.544384	0.272192	+	0.962243i	$0.412251\pi$
$174$	1037.91	0.452204
$175$	430.001	0.185743
$176$	−176.000	−0.0753778
$177$	45.2279	0.0192064
$178$	−2388.86	−1.00591
$179$	−923.716	−0.385708	−0.192854	−	0.981227i	$-0.561774\pi$
$179$	−923.716	−0.385708	−0.192854	+	0.981227i	$0.561774\pi$
$180$	464.858	0.192491
$181$	3000.36	1.23213	0.616064	−	0.787696i	$-0.288726\pi$
$181$	3000.36	1.23213	0.616064	+	0.787696i	$0.288726\pi$
$182$	486.757	0.198246
$183$	−932.957	−0.376864
$184$	267.668	0.107243
$185$	1710.09	0.679611
$186$	567.475	0.223706
$187$	−187.000	−0.0731272
$188$	1509.81	0.585714
$189$	1675.06	0.644672
$190$	−214.463	−0.0818884
$191$	−1967.61	−0.745400	−0.372700	−	0.927952i	$-0.621568\pi$
$191$	−1967.61	−0.745400	−0.372700	+	0.927952i	$0.621568\pi$
$192$	−124.053	−0.0466290
$193$	691.407	0.257868	0.128934	−	0.991653i	$-0.458844\pi$
$193$	691.407	0.257868	0.128934	+	0.991653i	$0.458844\pi$
$194$	−617.616	−0.228568
$195$	−137.135	−0.0503614
$196$	−188.634	−0.0687441
$197$	−3528.00	−1.27594	−0.637969	−	0.770062i	$-0.720225\pi$
$197$	−3528.00	−1.27594	−0.637969	+	0.770062i	$0.720225\pi$
$198$	−511.343	−0.183533
$199$	1658.43	0.590769	0.295385	−	0.955378i	$-0.404552\pi$
$199$	1658.43	0.590769	0.295385	+	0.955378i	$0.404552\pi$
$200$	−200.000	−0.0707107
$201$	744.844	0.261379
$202$	366.805	0.127764
$203$	4605.01	1.59216
$204$	−131.806	−0.0452367
$205$	758.999	0.258589
$206$	−254.301	−0.0860098
$207$	777.673	0.261121
$208$	−226.398	−0.0754705
$209$	235.910	0.0780775
$210$	−333.394	−0.109554
$211$	−1990.55	−0.649455	−0.324727	−	0.945808i	$-0.605273\pi$
$211$	−1990.55	−0.649455	−0.324727	+	0.945808i	$0.605273\pi$
$212$	−968.889	−0.313885
$213$	1509.72	0.485653
$214$	2758.30	0.881090
$215$	−567.227	−0.179928
$216$	−779.098	−0.245421
$217$	2517.79	0.787643
$218$	−3845.40	−1.19470
$219$	−969.855	−0.299255
$220$	220.000	0.0674200
$221$	−240.548	−0.0732172
$222$	−1325.88	−0.400844
$223$	−5310.11	−1.59458	−0.797290	−	0.603596i	$-0.793734\pi$
$223$	−5310.11	−1.59458	−0.797290	+	0.603596i	$0.793734\pi$
$224$	−550.401	−0.164175
$225$	−581.072	−0.172169
$226$	1484.02	0.436794
$227$	−4714.26	−1.37840	−0.689200	−	0.724572i	$-0.742038\pi$
$227$	−4714.26	−1.37840	−0.689200	+	0.724572i	$0.742038\pi$
$228$	166.280	0.0482990
$229$	−5578.13	−1.60967	−0.804833	−	0.593502i	$-0.797745\pi$
$229$	−5578.13	−1.60967	−0.804833	+	0.593502i	$0.797745\pi$
$230$	−334.585	−0.0959213
$231$	366.733	0.104456
$232$	−2141.86	−0.606120
$233$	1105.86	0.310934	0.155467	−	0.987841i	$-0.450312\pi$
$233$	1105.86	0.310934	0.155467	+	0.987841i	$0.450312\pi$
$234$	−657.767	−0.183759
$235$	−1887.26	−0.523879
$236$	−93.3339	−0.0257437
$237$	1987.71	0.544792
$238$	−584.802	−0.159273
$239$	−4901.87	−1.32668	−0.663339	−	0.748319i	$-0.730861\pi$
$239$	−4901.87	−1.32668	−0.663339	+	0.748319i	$0.730861\pi$
$240$	155.066	0.0417062
$241$	37.0033	0.00989042	0.00494521	−	0.999988i	$-0.498426\pi$
$241$	37.0033	0.00989042	0.00494521	+	0.999988i	$0.498426\pi$
$242$	−242.000	−0.0642824
$243$	−3479.97	−0.918685
$244$	1925.28	0.505137
$245$	235.792	0.0614866
$246$	−588.476	−0.152520
$247$	303.463	0.0781735
$248$	−1171.06	−0.299848
$249$	−1596.86	−0.406414
$250$	250.000	0.0632456
$251$	−716.985	−0.180302	−0.0901508	−	0.995928i	$-0.528735\pi$
$251$	−716.985	−0.180302	−0.0901508	+	0.995928i	$0.528735\pi$
$252$	−1599.11	−0.399741
$253$	368.044	0.0914574
$254$	−4300.81	−1.06243
$255$	164.758	0.0404610
$256$	256.000	0.0625000
$257$	−2888.35	−0.701051	−0.350526	−	0.936553i	$-0.613997\pi$
$257$	−2888.35	−0.701051	−0.350526	+	0.936553i	$0.613997\pi$
$258$	439.789	0.106124
$259$	−5882.71	−1.41133
$260$	282.997	0.0675029
$261$	−6222.87	−1.47581
$262$	5654.99	1.33346
$263$	−6294.73	−1.47585	−0.737927	−	0.674880i	$-0.764195\pi$
$263$	−6294.73	−1.47585	−0.737927	+	0.674880i	$0.764195\pi$
$264$	−170.573	−0.0397653
$265$	1211.11	0.280747
$266$	737.755	0.170055
$267$	−2315.20	−0.530667
$268$	−1537.08	−0.350345
$269$	−6537.25	−1.48172	−0.740861	−	0.671659i	$-0.765582\pi$
$269$	−6537.25	−1.48172	−0.740861	+	0.671659i	$0.765582\pi$
$270$	973.872	0.219511
$271$	−941.790	−0.211106	−0.105553	−	0.994414i	$-0.533661\pi$
$271$	−941.790	−0.211106	−0.105553	+	0.994414i	$0.533661\pi$
$272$	272.000	0.0606339
$273$	471.747	0.104584
$274$	5794.18	1.27752
$275$	−275.000	−0.0603023
$276$	259.415	0.0565758
$277$	5247.18	1.13817	0.569084	−	0.822279i	$-0.307298\pi$
$277$	5247.18	1.13817	0.569084	+	0.822279i	$0.307298\pi$
$278$	−4819.57	−1.03978
$279$	−3402.35	−0.730084
$280$	688.002	0.146843
$281$	−4416.07	−0.937511	−0.468756	−	0.883328i	$-0.655298\pi$
$281$	−4416.07	−0.937511	−0.468756	+	0.883328i	$0.655298\pi$
$282$	1463.26	0.308991
$283$	4800.21	1.00828	0.504140	−	0.863622i	$-0.331810\pi$
$283$	4800.21	1.00828	0.504140	+	0.863622i	$0.331810\pi$
$284$	−3115.50	−0.650954
$285$	−207.850	−0.0431999
$286$	−311.297	−0.0643615
$287$	−2610.96	−0.537005
$288$	743.772	0.152178
$289$	289.000	0.0588235
$290$	2677.32	0.542130
$291$	−598.571	−0.120580
$292$	2001.43	0.401111
$293$	6536.88	1.30337	0.651687	−	0.758488i	$-0.274062\pi$
$293$	6536.88	1.30337	0.651687	+	0.758488i	$0.274062\pi$
$294$	−182.817	−0.0362657
$295$	116.667	0.0230259
$296$	2736.14	0.537279
$297$	−1071.26	−0.209296
$298$	−1500.10	−0.291606
$299$	473.434	0.0915699
$300$	−193.833	−0.0373032
$301$	1951.27	0.373652
$302$	2906.97	0.553899
$303$	355.495	0.0674014
$304$	−343.141	−0.0647385
$305$	−2406.60	−0.451809
$306$	790.258	0.147634
$307$	8499.94	1.58019	0.790093	−	0.612987i	$-0.210032\pi$
$307$	8499.94	1.58019	0.790093	+	0.612987i	$0.210032\pi$
$308$	−756.802	−0.140009
$309$	−246.460	−0.0453742
$310$	1463.83	0.268193
$311$	−8746.25	−1.59471	−0.797354	−	0.603512i	$-0.793768\pi$
$311$	−8746.25	−1.59471	−0.797354	+	0.603512i	$0.793768\pi$
$312$	−219.417	−0.0398142
$313$	6578.30	1.18795	0.593974	−	0.804484i	$-0.297558\pi$
$313$	6578.30	1.18795	0.593974	+	0.804484i	$0.297558\pi$
$314$	2275.65	0.408989
$315$	1998.89	0.357539
$316$	−4101.90	−0.730222
$317$	−3487.51	−0.617911	−0.308956	−	0.951076i	$-0.599979\pi$
$317$	−3487.51	−0.617911	−0.308956	+	0.951076i	$0.599979\pi$
$318$	−939.013	−0.165589
$319$	−2945.05	−0.516901
$320$	−320.000	−0.0559017
$321$	2673.24	0.464816
$322$	1150.98	0.199197
$323$	−364.587	−0.0628055
$324$	1755.16	0.300953
$325$	−353.747	−0.0603764
$326$	−3522.26	−0.598405
$327$	−3726.83	−0.630257
$328$	1214.40	0.204433
$329$	6492.20	1.08792
$330$	213.216	0.0355672
$331$	−8887.34	−1.47581	−0.737904	−	0.674906i	$-0.764184\pi$
$331$	−8887.34	−1.47581	−0.737904	+	0.674906i	$0.764184\pi$
$332$	3295.34	0.544745
$333$	7949.46	1.30819
$334$	−7076.98	−1.15939
$335$	1921.35	0.313358
$336$	−533.430	−0.0866100
$337$	5037.96	0.814347	0.407174	−	0.913351i	$-0.366514\pi$
$337$	5037.96	0.814347	0.407174	+	0.913351i	$0.366514\pi$
$338$	3993.56	0.642666
$339$	1438.26	0.230429
$340$	−340.000	−0.0542326
$341$	−1610.21	−0.255712
$342$	−996.948	−0.157628
$343$	−6710.74	−1.05640
$344$	−907.563	−0.142246
$345$	−324.268	−0.0506030
$346$	−2477.45	−0.384938
$347$	−1594.63	−0.246698	−0.123349	−	0.992363i	$-0.539363\pi$
$347$	−1594.63	−0.246698	−0.123349	+	0.992363i	$0.539363\pi$
$348$	−2075.81	−0.319756
$349$	3930.62	0.602869	0.301435	−	0.953487i	$-0.402535\pi$
$349$	3930.62	0.602869	0.301435	+	0.953487i	$0.402535\pi$
$350$	−860.002	−0.131340
$351$	−1378.02	−0.209553
$352$	352.000	0.0533002
$353$	−6124.92	−0.923503	−0.461752	−	0.887009i	$-0.652779\pi$
$353$	−6124.92	−0.923503	−0.461752	+	0.887009i	$0.652779\pi$
$354$	−90.4559	−0.0135810
$355$	3894.37	0.582231
$356$	4777.73	0.711289
$357$	−566.769	−0.0840241
$358$	1847.43	0.272737
$359$	−7462.03	−1.09702	−0.548511	−	0.836143i	$-0.684805\pi$
$359$	−7462.03	−1.09702	−0.548511	+	0.836143i	$0.684805\pi$
$360$	−929.715	−0.136112
$361$	−6399.06	−0.932943
$362$	−6000.73	−0.871246
$363$	−234.538	−0.0339120
$364$	−973.513	−0.140181
$365$	−2501.78	−0.358765
$366$	1865.91	0.266483
$367$	7346.41	1.04490	0.522451	−	0.852669i	$-0.325018\pi$
$367$	7346.41	1.04490	0.522451	+	0.852669i	$0.325018\pi$
$368$	−535.337	−0.0758325
$369$	3528.27	0.497762
$370$	−3420.17	−0.480557
$371$	−4166.23	−0.583019
$372$	−1134.95	−0.158184
$373$	−6714.17	−0.932028	−0.466014	−	0.884777i	$-0.654310\pi$
$373$	−6714.17	−0.932028	−0.466014	+	0.884777i	$0.654310\pi$
$374$	374.000	0.0517088
$375$	242.291	0.0333650
$376$	−3019.62	−0.414163
$377$	−3788.38	−0.517536
$378$	−3350.13	−0.455852
$379$	−10142.2	−1.37459	−0.687297	−	0.726376i	$-0.741203\pi$
$379$	−10142.2	−1.37459	−0.687297	+	0.726376i	$0.741203\pi$
$380$	428.926	0.0579038
$381$	−4168.20	−0.560481
$382$	3935.22	0.527077
$383$	−1260.63	−0.168186	−0.0840928	−	0.996458i	$-0.526799\pi$
$383$	−1260.63	−0.168186	−0.0840928	+	0.996458i	$0.526799\pi$
$384$	248.106	0.0329716
$385$	946.002	0.125228
$386$	−1382.81	−0.182340
$387$	−2636.80	−0.346346
$388$	1235.23	0.161622
$389$	−12006.7	−1.56494	−0.782472	−	0.622686i	$-0.786041\pi$
$389$	−12006.7	−1.56494	−0.782472	+	0.622686i	$0.786041\pi$
$390$	274.271	0.0356109
$391$	−568.795	−0.0735683
$392$	377.268	0.0486094
$393$	5480.61	0.703462
$394$	7056.00	0.902224
$395$	5127.38	0.653130
$396$	1022.69	0.129778
$397$	−11455.5	−1.44820	−0.724100	−	0.689695i	$-0.757745\pi$
$397$	−11455.5	−1.44820	−0.724100	+	0.689695i	$0.757745\pi$
$398$	−3316.86	−0.417737
$399$	715.006	0.0897120
$400$	400.000	0.0500000
$401$	11625.3	1.44773	0.723867	−	0.689940i	$-0.242363\pi$
$401$	11625.3	1.44773	0.723867	+	0.689940i	$0.242363\pi$
$402$	−1489.69	−0.184823
$403$	−2071.29	−0.256026
$404$	−733.610	−0.0903428
$405$	−2193.95	−0.269180
$406$	−9210.01	−1.12583
$407$	3762.19	0.458193
$408$	263.613	0.0319872
$409$	3760.81	0.454670	0.227335	−	0.973817i	$-0.426999\pi$
$409$	3760.81	0.454670	0.227335	+	0.973817i	$0.426999\pi$
$410$	−1518.00	−0.182850
$411$	5615.52	0.673949
$412$	508.603	0.0608181
$413$	−401.337	−0.0478172
$414$	−1555.35	−0.184640
$415$	−4119.17	−0.487234
$416$	452.796	0.0533657
$417$	−4670.96	−0.548532
$418$	−471.819	−0.0552091
$419$	2038.74	0.237707	0.118853	−	0.992912i	$-0.462078\pi$
$419$	2038.74	0.237707	0.118853	+	0.992912i	$0.462078\pi$
$420$	666.787	0.0774664
$421$	−4758.71	−0.550892	−0.275446	−	0.961317i	$-0.588825\pi$
$421$	−4758.71	−0.550892	−0.275446	+	0.961317i	$0.588825\pi$
$422$	3981.10	0.459234
$423$	−8773.09	−1.00842
$424$	1937.78	0.221950
$425$	425.000	0.0485071
$426$	−3019.43	−0.343408
$427$	8278.73	0.938257
$428$	−5516.59	−0.623025
$429$	−301.698	−0.0339537
$430$	1134.45	0.127228
$431$	−4304.63	−0.481083	−0.240541	−	0.970639i	$-0.577325\pi$
$431$	−4304.63	−0.481083	−0.240541	+	0.970639i	$0.577325\pi$
$432$	1558.20	0.173539
$433$	−4243.91	−0.471015	−0.235507	−	0.971873i	$-0.575675\pi$
$433$	−4243.91	−0.471015	−0.235507	+	0.971873i	$0.575675\pi$
$434$	−5035.57	−0.556948
$435$	2594.77	0.285999
$436$	7690.81	0.844777
$437$	717.563	0.0785484
$438$	1939.71	0.211605
$439$	−12393.5	−1.34740	−0.673701	−	0.739004i	$-0.735296\pi$
$439$	−12393.5	−1.34740	−0.673701	+	0.739004i	$0.735296\pi$
$440$	−440.000	−0.0476731
$441$	1096.10	0.118356
$442$	481.095	0.0517723
$443$	1307.45	0.140223	0.0701116	−	0.997539i	$-0.477664\pi$
$443$	1307.45	0.140223	0.0701116	+	0.997539i	$0.477664\pi$
$444$	2651.77	0.283440
$445$	−5972.16	−0.636196
$446$	10620.2	1.12754
$447$	−1453.84	−0.153836
$448$	1100.80	0.116089
$449$	3970.17	0.417292	0.208646	−	0.977991i	$-0.433094\pi$
$449$	3970.17	0.417292	0.208646	+	0.977991i	$0.433094\pi$
$450$	1162.14	0.121742
$451$	1669.80	0.174341
$452$	−2968.03	−0.308860
$453$	2817.33	0.292207
$454$	9428.53	0.974675
$455$	1216.89	0.125382
$456$	−332.560	−0.0341525
$457$	−17959.7	−1.83833	−0.919167	−	0.393868i	$-0.871137\pi$
$457$	−17959.7	−1.83833	−0.919167	+	0.393868i	$0.871137\pi$
$458$	11156.3	1.13821
$459$	1655.58	0.168357
$460$	669.171	0.0678266
$461$	−3663.49	−0.370121	−0.185060	−	0.982727i	$-0.559248\pi$
$461$	−3663.49	−0.370121	−0.185060	+	0.982727i	$0.559248\pi$
$462$	−733.466	−0.0738613
$463$	7795.16	0.782445	0.391222	−	0.920296i	$-0.372052\pi$
$463$	7795.16	0.782445	0.391222	+	0.920296i	$0.372052\pi$
$464$	4283.72	0.428592
$465$	1418.69	0.141484
$466$	−2211.73	−0.219863
$467$	−13473.9	−1.33512	−0.667558	−	0.744558i	$-0.732660\pi$
$467$	−13473.9	−1.33512	−0.667558	+	0.744558i	$0.732660\pi$
$468$	1315.53	0.129937
$469$	−6609.48	−0.650741
$470$	3774.53	0.370438
$471$	2205.48	0.215761
$472$	186.668	0.0182036
$473$	−1247.90	−0.121308
$474$	−3975.42	−0.385226
$475$	−536.158	−0.0517908
$476$	1169.60	0.112623
$477$	5629.94	0.540414
$478$	9803.75	0.938103
$479$	−5189.88	−0.495056	−0.247528	−	0.968881i	$-0.579618\pi$
$479$	−5189.88	−0.495056	−0.247528	+	0.968881i	$0.579618\pi$
$480$	−310.133	−0.0294907
$481$	4839.50	0.458757
$482$	−74.0066	−0.00699359
$483$	1115.49	0.105086
$484$	484.000	0.0454545
$485$	−1544.04	−0.144559
$486$	6959.95	0.649608
$487$	8633.90	0.803366	0.401683	−	0.915779i	$-0.368425\pi$
$487$	8633.90	0.803366	0.401683	+	0.915779i	$0.368425\pi$
$488$	−3850.56	−0.357186
$489$	−3413.65	−0.315686
$490$	−471.584	−0.0434776
$491$	1163.26	0.106919	0.0534595	−	0.998570i	$-0.482975\pi$
$491$	1163.26	0.106919	0.0534595	+	0.998570i	$0.482975\pi$
$492$	1176.95	0.107848
$493$	4551.45	0.415795
$494$	−606.925	−0.0552770
$495$	−1278.36	−0.116077
$496$	2342.12	0.212025
$497$	−13396.7	−1.20910
$498$	3193.73	0.287378
$499$	−11567.7	−1.03776	−0.518880	−	0.854847i	$-0.673651\pi$
$499$	−11567.7	−1.03776	−0.518880	+	0.854847i	$0.673651\pi$
$500$	−500.000	−0.0447214
$501$	−6858.76	−0.611630
$502$	1433.97	0.127493
$503$	−15945.8	−1.41349	−0.706745	−	0.707468i	$-0.749837\pi$
$503$	−15945.8	−1.41349	−0.706745	+	0.707468i	$0.749837\pi$
$504$	3198.23	0.282660
$505$	917.013	0.0808050
$506$	−736.088	−0.0646702
$507$	3870.42	0.339036
$508$	8601.63	0.751251
$509$	−11873.2	−1.03393	−0.516965	−	0.856006i	$-0.672938\pi$
$509$	−11873.2	−1.03393	−0.516965	+	0.856006i	$0.672938\pi$
$510$	−329.516	−0.0286102
$511$	8606.15	0.745037
$512$	−512.000	−0.0441942
$513$	−2088.60	−0.179754
$514$	5776.70	0.495718
$515$	−635.753	−0.0543974
$516$	−879.578	−0.0750412
$517$	−4151.98	−0.353199
$518$	11765.4	0.997959
$519$	−2401.06	−0.203073
$520$	−565.995	−0.0477317
$521$	−21901.1	−1.84166	−0.920832	−	0.389960i	$-0.872489\pi$
$521$	−21901.1	−1.84166	−0.920832	+	0.389960i	$0.872489\pi$
$522$	12445.7	1.04355
$523$	21487.0	1.79648	0.898241	−	0.439504i	$-0.144846\pi$
$523$	21487.0	1.79648	0.898241	+	0.439504i	$0.144846\pi$
$524$	−11310.0	−0.942898
$525$	−833.484	−0.0692880
$526$	12589.5	1.04359
$527$	2488.50	0.205694
$528$	341.146	0.0281183
$529$	−11047.5	−0.907991
$530$	−2422.22	−0.198518
$531$	542.337	0.0443228
$532$	−1475.51	−0.120247
$533$	2147.95	0.174555
$534$	4630.40	0.375238
$535$	6895.74	0.557250
$536$	3074.17	0.247731
$537$	1790.47	0.143881
$538$	13074.5	1.04773
$539$	518.743	0.0414542
$540$	−1947.74	−0.155218
$541$	13344.1	1.06046	0.530229	−	0.847854i	$-0.322106\pi$
$541$	13344.1	1.06046	0.530229	+	0.847854i	$0.322106\pi$
$542$	1883.58	0.149274
$543$	−5815.69	−0.459623
$544$	−544.000	−0.0428746
$545$	−9613.51	−0.755592
$546$	−943.495	−0.0739521
$547$	−15760.7	−1.23195	−0.615977	−	0.787764i	$-0.711239\pi$
$547$	−15760.7	−1.23195	−0.615977	+	0.787764i	$0.711239\pi$
$548$	−11588.4	−0.903340
$549$	−11187.3	−0.869692
$550$	550.000	0.0426401
$551$	−5741.87	−0.443942
$552$	−518.829	−0.0400051
$553$	−17638.2	−1.35634
$554$	−10494.4	−0.804807
$555$	−3314.71	−0.253516
$556$	9639.14	0.735235
$557$	13535.3	1.02964	0.514819	−	0.857299i	$-0.327859\pi$
$557$	13535.3	1.02964	0.514819	+	0.857299i	$0.327859\pi$
$558$	6804.71	0.516248
$559$	−1605.24	−0.121457
$560$	−1376.00	−0.103834
$561$	362.468	0.0272788
$562$	8832.14	0.662921
$563$	13494.6	1.01017	0.505087	−	0.863069i	$-0.331461\pi$
$563$	13494.6	1.01017	0.505087	+	0.863069i	$0.331461\pi$
$564$	−2926.51	−0.218490
$565$	3710.04	0.276253
$566$	−9600.43	−0.712961
$567$	7547.19	0.558999
$568$	6231.00	0.460294
$569$	−23878.1	−1.75926	−0.879632	−	0.475655i	$-0.842211\pi$
$569$	−23878.1	−1.75926	−0.879632	+	0.475655i	$0.842211\pi$
$570$	415.700	0.0305470
$571$	−9088.62	−0.666107	−0.333053	−	0.942908i	$-0.608079\pi$
$571$	−9088.62	−0.666107	−0.333053	+	0.942908i	$0.608079\pi$
$572$	622.594	0.0455104
$573$	3813.88	0.278058
$574$	5221.93	0.379720
$575$	−836.463	−0.0606660
$576$	−1487.54	−0.107606
$577$	20131.4	1.45248	0.726240	−	0.687441i	$-0.241266\pi$
$577$	20131.4	1.45248	0.726240	+	0.687441i	$0.241266\pi$
$578$	−578.000	−0.0415945
$579$	−1340.17	−0.0961930
$580$	−5354.64	−0.383344
$581$	14170.0	1.01183
$582$	1197.14	0.0852632
$583$	2664.45	0.189280
$584$	−4002.85	−0.283629
$585$	−1644.42	−0.116219
$586$	−13073.8	−0.921624
$587$	16357.3	1.15015	0.575073	−	0.818102i	$-0.304974\pi$
$587$	16357.3	1.15015	0.575073	+	0.818102i	$0.304974\pi$
$588$	365.634	0.0256437
$589$	−3139.37	−0.219619
$590$	−233.335	−0.0162818
$591$	6838.43	0.475965
$592$	−5472.27	−0.379914
$593$	15948.1	1.10440	0.552202	−	0.833711i	$-0.313788\pi$
$593$	15948.1	1.10440	0.552202	+	0.833711i	$0.313788\pi$
$594$	2142.52	0.147994
$595$	−1462.00	−0.100733
$596$	3000.20	0.206196
$597$	−3214.59	−0.220376
$598$	−946.868	−0.0647497
$599$	14557.2	0.992971	0.496486	−	0.868045i	$-0.334624\pi$
$599$	14557.2	0.992971	0.496486	+	0.868045i	$0.334624\pi$
$600$	387.666	0.0263773
$601$	4953.99	0.336235	0.168118	−	0.985767i	$-0.446231\pi$
$601$	4953.99	0.336235	0.168118	+	0.985767i	$0.446231\pi$
$602$	−3902.53	−0.264212
$603$	8931.56	0.603186
$604$	−5813.94	−0.391665
$605$	−605.000	−0.0406558
$606$	−710.989	−0.0476600
$607$	−27024.2	−1.80705	−0.903524	−	0.428537i	$-0.859029\pi$
$607$	−27024.2	−1.80705	−0.903524	+	0.428537i	$0.859029\pi$
$608$	686.282	0.0457770
$609$	−8926.02	−0.593925
$610$	4813.20	0.319477
$611$	−5340.91	−0.353633
$612$	−1580.52	−0.104393
$613$	25098.6	1.65371	0.826855	−	0.562415i	$-0.190128\pi$
$613$	25098.6	1.65371	0.826855	+	0.562415i	$0.190128\pi$
$614$	−16999.9	−1.11736
$615$	−1471.19	−0.0964620
$616$	1513.60	0.0990014
$617$	−6876.47	−0.448681	−0.224341	−	0.974511i	$-0.572023\pi$
$617$	−6876.47	−0.448681	−0.224341	+	0.974511i	$0.572023\pi$
$618$	492.920	0.0320844
$619$	−5145.30	−0.334099	−0.167049	−	0.985949i	$-0.553424\pi$
$619$	−5145.30	−0.334099	−0.167049	+	0.985949i	$0.553424\pi$
$620$	−2927.65	−0.189641
$621$	−3258.43	−0.210558
$622$	17492.5	1.12763
$623$	20544.3	1.32117
$624$	438.834	0.0281529
$625$	625.000	0.0400000
$626$	−13156.6	−0.840006
$627$	−457.270	−0.0291254
$628$	−4551.31	−0.289199
$629$	−5814.29	−0.368571
$630$	−3997.79	−0.252818
$631$	−26571.9	−1.67640	−0.838202	−	0.545359i	$-0.816393\pi$
$631$	−26571.9	−1.67640	−0.838202	+	0.545359i	$0.816393\pi$
$632$	8203.80	0.516345
$633$	3858.34	0.242267
$634$	6975.01	0.436929
$635$	−10752.0	−0.671939
$636$	1878.03	0.117089
$637$	667.286	0.0415052
$638$	5890.11	0.365504
$639$	18103.3	1.12074
$640$	640.000	0.0395285
$641$	−7086.94	−0.436689	−0.218344	−	0.975872i	$-0.570066\pi$
$641$	−7086.94	−0.436689	−0.218344	+	0.975872i	$0.570066\pi$
$642$	−5346.49	−0.328674
$643$	−22685.5	−1.39134	−0.695668	−	0.718363i	$-0.744892\pi$
$643$	−22685.5	−1.39134	−0.695668	+	0.718363i	$0.744892\pi$
$644$	−2301.95	−0.140854
$645$	1099.47	0.0671189
$646$	729.175	0.0444102
$647$	−822.476	−0.0499766	−0.0249883	−	0.999688i	$-0.507955\pi$
$647$	−822.476	−0.0499766	−0.0249883	+	0.999688i	$0.507955\pi$
$648$	−3510.31	−0.212806
$649$	256.668	0.0155240
$650$	707.493	0.0426926
$651$	−4880.30	−0.293816
$652$	7044.52	0.423136
$653$	13293.5	0.796652	0.398326	−	0.917244i	$-0.369591\pi$
$653$	13293.5	0.796652	0.398326	+	0.917244i	$0.369591\pi$
$654$	7453.66	0.445659
$655$	14137.5	0.843354
$656$	−2428.80	−0.144556
$657$	−11629.7	−0.690591
$658$	−12984.4	−0.769278
$659$	12917.6	0.763576	0.381788	−	0.924250i	$-0.375308\pi$
$659$	12917.6	0.763576	0.381788	+	0.924250i	$0.375308\pi$
$660$	−426.432	−0.0251498
$661$	9389.06	0.552484	0.276242	−	0.961088i	$-0.410911\pi$
$661$	9389.06	0.552484	0.276242	+	0.961088i	$0.410911\pi$
$662$	17774.7	1.04355
$663$	466.261	0.0273123
$664$	−6590.68	−0.385193
$665$	1844.39	0.107552
$666$	−15898.9	−0.925031
$667$	−8957.93	−0.520019
$668$	14154.0	0.819810
$669$	10292.7	0.594829
$670$	−3842.71	−0.221577
$671$	−5294.52	−0.304609
$672$	1066.86	0.0612425
$673$	19822.9	1.13539	0.567695	−	0.823239i	$-0.307835\pi$
$673$	19822.9	1.13539	0.567695	+	0.823239i	$0.307835\pi$
$674$	−10075.9	−0.575830
$675$	2434.68	0.138831
$676$	−7987.13	−0.454434
$677$	−17815.7	−1.01140	−0.505698	−	0.862711i	$-0.668765\pi$
$677$	−17815.7	−1.01140	−0.505698	+	0.862711i	$0.668765\pi$
$678$	−2876.51	−0.162938
$679$	5311.51	0.300202
$680$	680.000	0.0383482
$681$	9137.79	0.514187
$682$	3220.42	0.180815
$683$	18866.4	1.05696	0.528479	−	0.848946i	$-0.322763\pi$
$683$	18866.4	1.05696	0.528479	+	0.848946i	$0.322763\pi$
$684$	1993.90	0.111460
$685$	14485.5	0.807972
$686$	13421.5	0.746989
$687$	10812.3	0.600456
$688$	1815.13	0.100583
$689$	3427.41	0.189512
$690$	648.537	0.0357817
$691$	12346.7	0.679724	0.339862	−	0.940475i	$-0.389620\pi$
$691$	12346.7	0.679724	0.339862	+	0.940475i	$0.389620\pi$
$692$	4954.90	0.272192
$693$	4397.56	0.241053
$694$	3189.26	0.174442
$695$	−12048.9	−0.657614
$696$	4151.63	0.226102
$697$	−2580.60	−0.140240
$698$	−7861.24	−0.426293
$699$	−2143.53	−0.115988
$700$	1720.00	0.0928715
$701$	−26388.1	−1.42178	−0.710888	−	0.703306i	$-0.751707\pi$
$701$	−26388.1	−1.42178	−0.710888	+	0.703306i	$0.751707\pi$
$702$	2756.03	0.148176
$703$	7335.01	0.393521
$704$	−704.000	−0.0376889
$705$	3658.14	0.195423
$706$	12249.8	0.653015
$707$	−3154.53	−0.167805
$708$	180.912	0.00960322
$709$	4461.01	0.236300	0.118150	−	0.992996i	$-0.462304\pi$
$709$	4461.01	0.236300	0.118150	+	0.992996i	$0.462304\pi$
$710$	−7788.75	−0.411699
$711$	23835.0	1.25722
$712$	−9555.45	−0.502957
$713$	−4897.75	−0.257254
$714$	1133.54	0.0594140
$715$	−778.243	−0.0407058
$716$	−3694.86	−0.192854
$717$	9501.45	0.494893
$718$	14924.1	0.775712
$719$	25040.0	1.29879	0.649397	−	0.760449i	$-0.275021\pi$
$719$	25040.0	1.29879	0.649397	+	0.760449i	$0.275021\pi$
$720$	1859.43	0.0962457
$721$	2187.00	0.112965
$722$	12798.1	0.659690
$723$	−71.7246	−0.00368944
$724$	12001.5	0.616064
$725$	6693.31	0.342873
$726$	469.076	0.0239794
$727$	712.986	0.0363730	0.0181865	−	0.999835i	$-0.494211\pi$
$727$	712.986	0.0363730	0.0181865	+	0.999835i	$0.494211\pi$
$728$	1947.03	0.0991231
$729$	−5101.97	−0.259207
$730$	5003.56	0.253685
$731$	1928.57	0.0975798
$732$	−3731.83	−0.188432
$733$	−12406.1	−0.625143	−0.312572	−	0.949894i	$-0.601190\pi$
$733$	−12406.1	−0.625143	−0.312572	+	0.949894i	$0.601190\pi$
$734$	−14692.8	−0.738858
$735$	−457.043	−0.0229364
$736$	1070.67	0.0536217
$737$	4226.98	0.211266
$738$	−7056.53	−0.351971
$739$	−23880.9	−1.18873	−0.594366	−	0.804195i	$-0.702597\pi$
$739$	−23880.9	−1.18873	−0.594366	+	0.804195i	$0.702597\pi$
$740$	6840.34	0.339805
$741$	−588.210	−0.0291612
$742$	8332.47	0.412257
$743$	2448.14	0.120880	0.0604399	−	0.998172i	$-0.480750\pi$
$743$	2448.14	0.120880	0.0604399	+	0.998172i	$0.480750\pi$
$744$	2269.90	0.111853
$745$	−3750.25	−0.184428
$746$	13428.3	0.659043
$747$	−19148.3	−0.937884
$748$	−748.000	−0.0365636
$749$	−23721.4	−1.15722
$750$	−484.582	−0.0235926
$751$	12768.7	0.620422	0.310211	−	0.950668i	$-0.399600\pi$
$751$	12768.7	0.620422	0.310211	+	0.950668i	$0.399600\pi$
$752$	6039.24	0.292857
$753$	1389.75	0.0672582
$754$	7576.75	0.365954
$755$	7267.43	0.350316
$756$	6700.26	0.322336
$757$	−7317.50	−0.351333	−0.175666	−	0.984450i	$-0.556208\pi$
$757$	−7317.50	−0.351333	−0.175666	+	0.984450i	$0.556208\pi$
$758$	20284.5	0.971985
$759$	−713.390	−0.0341165
$760$	−857.853	−0.0409442
$761$	−5263.65	−0.250732	−0.125366	−	0.992111i	$-0.540011\pi$
$761$	−5263.65	−0.250732	−0.125366	+	0.992111i	$0.540011\pi$
$762$	8336.40	0.396320
$763$	33070.6	1.56912
$764$	−7870.44	−0.372700
$765$	1975.64	0.0933720
$766$	2521.26	0.118925
$767$	330.165	0.0155431
$768$	−496.212	−0.0233145
$769$	20533.2	0.962867	0.481433	−	0.876483i	$-0.340116\pi$
$769$	20533.2	0.962867	0.481433	+	0.876483i	$0.340116\pi$
$770$	−1892.00	−0.0885495
$771$	5598.57	0.261514
$772$	2765.63	0.128934
$773$	−20834.2	−0.969410	−0.484705	−	0.874678i	$-0.661073\pi$
$773$	−20834.2	−0.969410	−0.484705	+	0.874678i	$0.661073\pi$
$774$	5273.60	0.244904
$775$	3659.56	0.169620
$776$	−2470.46	−0.114284
$777$	11402.6	0.526470
$778$	24013.4	1.10658
$779$	3255.55	0.149733
$780$	−548.542	−0.0251807
$781$	8567.62	0.392540
$782$	1137.59	0.0520206
$783$	26073.7	1.19004
$784$	−754.535	−0.0343720
$785$	5689.14	0.258668
$786$	−10961.2	−0.497422
$787$	1345.92	0.0609619	0.0304809	−	0.999535i	$-0.490296\pi$
$787$	1345.92	0.0609619	0.0304809	+	0.999535i	$0.490296\pi$
$788$	−14112.0	−0.637969
$789$	12201.3	0.550540
$790$	−10254.8	−0.461833
$791$	−12762.6	−0.573685
$792$	−2045.37	−0.0917666
$793$	−6810.62	−0.304984
$794$	22911.0	1.02403
$795$	−2347.53	−0.104728
$796$	6633.72	0.295385
$797$	32198.3	1.43102	0.715511	−	0.698602i	$-0.246194\pi$
$797$	32198.3	1.43102	0.715511	+	0.698602i	$0.246194\pi$
$798$	−1430.01	−0.0634360
$799$	6416.70	0.284113
$800$	−800.000	−0.0353553
$801$	−27762.0	−1.22462
$802$	−23250.6	−1.02370
$803$	−5503.92	−0.241879
$804$	2979.37	0.130690
$805$	2877.44	0.125983
$806$	4142.59	0.181038
$807$	12671.3	0.552729
$808$	1467.22	0.0638820
$809$	23943.4	1.04055	0.520274	−	0.853999i	$-0.325830\pi$
$809$	23943.4	1.04055	0.520274	+	0.853999i	$0.325830\pi$
$810$	4387.89	0.190339
$811$	22846.8	0.989223	0.494611	−	0.869114i	$-0.335310\pi$
$811$	22846.8	0.989223	0.494611	+	0.869114i	$0.335310\pi$
$812$	18420.0	0.796079
$813$	1825.50	0.0787491
$814$	−7524.38	−0.323992
$815$	−8805.65	−0.378465
$816$	−527.226	−0.0226184
$817$	−2432.99	−0.104185
$818$	−7521.61	−0.321500
$819$	5656.81	0.241349
$820$	3036.00	0.129295
$821$	−12883.5	−0.547669	−0.273834	−	0.961777i	$-0.588292\pi$
$821$	−12883.5	−0.547669	−0.273834	+	0.961777i	$0.588292\pi$
$822$	−11231.0	−0.476554
$823$	33725.6	1.42844	0.714218	−	0.699924i	$-0.246783\pi$
$823$	33725.6	1.42844	0.714218	+	0.699924i	$0.246783\pi$
$824$	−1017.21	−0.0430049
$825$	533.041	0.0224947
$826$	802.673	0.0338118
$827$	31258.0	1.31432	0.657162	−	0.753750i	$-0.271757\pi$
$827$	31258.0	1.31432	0.657162	+	0.753750i	$0.271757\pi$
$828$	3110.69	0.130560
$829$	−14741.9	−0.617621	−0.308811	−	0.951124i	$-0.599931\pi$
$829$	−14741.9	−0.617621	−0.308811	+	0.951124i	$0.599931\pi$
$830$	8238.35	0.344527
$831$	−10170.8	−0.424573
$832$	−905.591	−0.0377353
$833$	−801.693	−0.0333458
$834$	9341.91	0.387870
$835$	−17692.5	−0.733260
$836$	943.638	0.0390388
$837$	14255.8	0.588712
$838$	−4077.49	−0.168084
$839$	17338.9	0.713476	0.356738	−	0.934204i	$-0.383889\pi$
$839$	17338.9	0.713476	0.356738	+	0.934204i	$0.383889\pi$
$840$	−1333.57	−0.0547770
$841$	47291.6	1.93905
$842$	9517.42	0.389539
$843$	8559.80	0.349721
$844$	−7962.19	−0.324727
$845$	9983.91	0.406458
$846$	17546.2	0.713062
$847$	2081.21	0.0844287
$848$	−3875.56	−0.156942
$849$	−9304.39	−0.376120
$850$	−850.000	−0.0342997
$851$	11443.4	0.460957
$852$	6038.86	0.242826
$853$	−493.320	−0.0198018	−0.00990091	−	0.999951i	$-0.503152\pi$
$853$	−493.320	−0.0198018	−0.00990091	+	0.999951i	$0.503152\pi$
$854$	−16557.5	−0.663448
$855$	−2492.37	−0.0996927
$856$	11033.2	0.440545
$857$	−15486.1	−0.617266	−0.308633	−	0.951181i	$-0.599871\pi$
$857$	−15486.1	−0.617266	−0.308633	+	0.951181i	$0.599871\pi$
$858$	603.396	0.0240089
$859$	25326.4	1.00597	0.502983	−	0.864296i	$-0.332236\pi$
$859$	25326.4	1.00597	0.502983	+	0.864296i	$0.332236\pi$
$860$	−2268.91	−0.0899641
$861$	5060.91	0.200320
$862$	8609.26	0.340177
$863$	43889.7	1.73120	0.865599	−	0.500738i	$-0.166938\pi$
$863$	43889.7	1.73120	0.865599	+	0.500738i	$0.166938\pi$
$864$	−3116.39	−0.122710
$865$	−6193.62	−0.243456
$866$	8487.82	0.333058
$867$	−560.177	−0.0219430
$868$	10071.1	0.393821
$869$	11280.2	0.440340
$870$	−5189.53	−0.202232
$871$	5437.38	0.211525
$872$	−15381.6	−0.597348
$873$	−7177.58	−0.278264
$874$	−1435.13	−0.0555421
$875$	−2150.01	−0.0830668
$876$	−3879.42	−0.149627
$877$	13941.5	0.536796	0.268398	−	0.963308i	$-0.413506\pi$
$877$	13941.5	0.536796	0.268398	+	0.963308i	$0.413506\pi$
$878$	24787.0	0.952757
$879$	−12670.6	−0.486199
$880$	880.000	0.0337100
$881$	16445.5	0.628904	0.314452	−	0.949273i	$-0.398179\pi$
$881$	16445.5	0.628904	0.314452	+	0.949273i	$0.398179\pi$
$882$	−2192.20	−0.0836906
$883$	4162.10	0.158625	0.0793125	−	0.996850i	$-0.474728\pi$
$883$	4162.10	0.158625	0.0793125	+	0.996850i	$0.474728\pi$
$884$	−962.191	−0.0366086
$885$	−226.140	−0.00858938
$886$	−2614.90	−0.0991528
$887$	−20012.8	−0.757569	−0.378784	−	0.925485i	$-0.623658\pi$
$887$	−20012.8	−0.757569	−0.378784	+	0.925485i	$0.623658\pi$
$888$	−5303.53	−0.200422
$889$	36987.1	1.39540
$890$	11944.3	0.449859
$891$	−4826.68	−0.181481
$892$	−21240.4	−0.797290
$893$	−8094.97	−0.303346
$894$	2907.69	0.108778
$895$	4618.58	0.172494
$896$	−2201.61	−0.0820876
$897$	−917.671	−0.0341585
$898$	−7940.35	−0.295070
$899$	39191.3	1.45395
$900$	−2324.29	−0.0860847
$901$	−4117.78	−0.152257
$902$	−3339.60	−0.123278
$903$	−3782.20	−0.139384
$904$	5936.07	0.218397
$905$	−15001.8	−0.551025
$906$	−5634.67	−0.206622
$907$	31455.2	1.15155	0.575773	−	0.817610i	$-0.304701\pi$
$907$	31455.2	1.15155	0.575773	+	0.817610i	$0.304701\pi$
$908$	−18857.1	−0.689200
$909$	4262.80	0.155543
$910$	−2433.78	−0.0886584
$911$	33962.2	1.23515	0.617574	−	0.786513i	$-0.288116\pi$
$911$	33962.2	1.23515	0.617574	+	0.786513i	$0.288116\pi$
$912$	665.120	0.0241495
$913$	−9062.18	−0.328493
$914$	35919.4	1.29990
$915$	4664.79	0.168539
$916$	−22312.5	−0.804833
$917$	−48633.0	−1.75137
$918$	−3311.17	−0.119047
$919$	−42646.1	−1.53076	−0.765379	−	0.643580i	$-0.777448\pi$
$919$	−42646.1	−1.53076	−0.765379	+	0.643580i	$0.777448\pi$
$920$	−1338.34	−0.0479607
$921$	−16475.7	−0.589459
$922$	7326.98	0.261715
$923$	11021.0	0.393022
$924$	1466.93	0.0522278
$925$	−8550.43	−0.303931
$926$	−15590.3	−0.553272
$927$	−2955.35	−0.104710
$928$	−8567.43	−0.303060
$929$	−34681.3	−1.22482	−0.612410	−	0.790541i	$-0.709800\pi$
$929$	−34681.3	−1.22482	−0.612410	+	0.790541i	$0.709800\pi$
$930$	−2837.38	−0.100044
$931$	1011.37	0.0356031
$932$	4423.45	0.155467
$933$	16953.1	0.594877
$934$	26947.9	0.944070
$935$	935.000	0.0327035
$936$	−2631.07	−0.0918795
$937$	6210.98	0.216546	0.108273	−	0.994121i	$-0.465468\pi$
$937$	6210.98	0.216546	0.108273	+	0.994121i	$0.465468\pi$
$938$	13219.0	0.460143
$939$	−12750.9	−0.443142
$940$	−7549.06	−0.261939
$941$	−45461.7	−1.57493	−0.787466	−	0.616358i	$-0.788607\pi$
$941$	−45461.7	−1.57493	−0.787466	+	0.616358i	$0.788607\pi$
$942$	−4410.97	−0.152566
$943$	5079.00	0.175392
$944$	−373.336	−0.0128719
$945$	−8375.32	−0.288306
$946$	2495.80	0.0857774
$947$	−2420.59	−0.0830609	−0.0415305	−	0.999137i	$-0.513223\pi$
$947$	−2420.59	−0.0830609	−0.0415305	+	0.999137i	$0.513223\pi$
$948$	7950.84	0.272396
$949$	−7079.97	−0.242177
$950$	1072.32	0.0366216
$951$	6759.93	0.230500
$952$	−2339.21	−0.0796367
$953$	32037.3	1.08897	0.544486	−	0.838770i	$-0.316725\pi$
$953$	32037.3	1.08897	0.544486	+	0.838770i	$0.316725\pi$
$954$	−11259.9	−0.382130
$955$	9838.06	0.333353
$956$	−19607.5	−0.663339
$957$	5708.49	0.192820
$958$	10379.8	0.350057
$959$	−49830.1	−1.67789
$960$	620.265	0.0208531
$961$	−8363.14	−0.280727
$962$	−9678.99	−0.324390
$963$	32055.4	1.07266
$964$	148.013	0.00494521
$965$	−3457.03	−0.115322
$966$	−2230.97	−0.0743068
$967$	−15002.6	−0.498917	−0.249458	−	0.968386i	$-0.580253\pi$
$967$	−15002.6	−0.498917	−0.249458	+	0.968386i	$0.580253\pi$
$968$	−968.000	−0.0321412
$969$	706.690	0.0234284
$970$	3088.08	0.102219
$971$	59163.1	1.95534	0.977670	−	0.210146i	$-0.0673940\pi$
$971$	59163.1	1.95534	0.977670	+	0.210146i	$0.0673940\pi$
$972$	−13919.9	−0.459342
$973$	41448.4	1.36565
$974$	−17267.8	−0.568066
$975$	685.677	0.0225223
$976$	7701.12	0.252569
$977$	−51854.7	−1.69803	−0.849017	−	0.528366i	$-0.822805\pi$
$977$	−51854.7	−1.69803	−0.849017	+	0.528366i	$0.822805\pi$
$978$	6827.30	0.223224
$979$	−13138.7	−0.428924
$980$	943.169	0.0307433
$981$	−44689.1	−1.45445
$982$	−2326.52	−0.0756032
$983$	−19402.6	−0.629548	−0.314774	−	0.949167i	$-0.601929\pi$
$983$	−19402.6	−0.629548	−0.314774	+	0.949167i	$0.601929\pi$
$984$	−2353.90	−0.0762599
$985$	17640.0	0.570617
$986$	−9102.90	−0.294011
$987$	−12584.0	−0.405830
$988$	1213.85	0.0390868
$989$	−3795.72	−0.122039
$990$	2556.72	0.0820786
$991$	30543.5	0.979059	0.489530	−	0.871987i	$-0.337168\pi$
$991$	30543.5	0.979059	0.489530	+	0.871987i	$0.337168\pi$
$992$	−4684.24	−0.149924
$993$	17226.6	0.550523
$994$	26793.4	0.854963
$995$	−8292.16	−0.264200
$996$	−6387.45	−0.203207
$997$	−34937.2	−1.10980	−0.554900	−	0.831917i	$-0.687244\pi$
$997$	−34937.2	−1.10980	−0.554900	+	0.831917i	$0.687244\pi$
$998$	23135.4	0.733807
$999$	−33308.1	−1.05488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.4.a.j.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.4.a.j.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -1.93833 q^{3} +4.00000 q^{4} -5.00000 q^{5} +3.87666 q^{6} +17.2000 q^{7} -8.00000 q^{8} -23.2429 q^{9} +10.0000 q^{10} -11.0000 q^{11} -7.75332 q^{12} -14.1499 q^{13} -34.4001 q^{14} +9.69165 q^{15} +16.0000 q^{16} +17.0000 q^{17} +46.4858 q^{18} -21.4463 q^{19} -20.0000 q^{20} -33.3394 q^{21} +22.0000 q^{22} -33.4585 q^{23} +15.5066 q^{24} +25.0000 q^{25} +28.2997 q^{26} +97.3872 q^{27} +68.8002 q^{28} +267.732 q^{29} -19.3833 q^{30} +146.383 q^{31} -32.0000 q^{32} +21.3216 q^{33} -34.0000 q^{34} -86.0002 q^{35} -92.9715 q^{36} -342.017 q^{37} +42.8926 q^{38} +27.4271 q^{39} +40.0000 q^{40} -151.800 q^{41} +66.6787 q^{42} +113.445 q^{43} -44.0000 q^{44} +116.214 q^{45} +66.9171 q^{46} +377.453 q^{47} -31.0133 q^{48} -47.1584 q^{49} -50.0000 q^{50} -32.9516 q^{51} -56.5995 q^{52} -242.222 q^{53} -194.774 q^{54} +55.0000 q^{55} -137.600 q^{56} +41.5700 q^{57} -535.464 q^{58} -23.3335 q^{59} +38.7666 q^{60} +481.320 q^{61} -292.765 q^{62} -399.779 q^{63} +64.0000 q^{64} +70.7493 q^{65} -42.6432 q^{66} -384.271 q^{67} +68.0000 q^{68} +64.8537 q^{69} +172.000 q^{70} -778.875 q^{71} +185.943 q^{72} +500.356 q^{73} +684.034 q^{74} -48.4582 q^{75} -85.7853 q^{76} -189.200 q^{77} -54.8542 q^{78} -1025.48 q^{79} -80.0000 q^{80} +438.789 q^{81} +303.600 q^{82} +823.835 q^{83} -133.357 q^{84} -85.0000 q^{85} -226.891 q^{86} -518.953 q^{87} +88.0000 q^{88} +1194.43 q^{89} -232.429 q^{90} -243.378 q^{91} -133.834 q^{92} -283.738 q^{93} -754.906 q^{94} +107.232 q^{95} +62.0265 q^{96} +308.808 q^{97} +94.3169 q^{98} +255.672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 20 q^{2} - q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 4 q^{7} - 80 q^{8} + 67 q^{9} + 100 q^{10} - 110 q^{11} - 4 q^{12} - 7 q^{13} - 8 q^{14} + 5 q^{15} + 160 q^{16} + 170 q^{17} - 134 q^{18} + 11 q^{19}+ \cdots - 737 q^{99}+O(q^{100}) \) 10 * q - 20 * q^2 - q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 4 * q^7 - 80 * q^8 + 67 * q^9 + 100 * q^10 - 110 * q^11 - 4 * q^12 - 7 * q^13 - 8 * q^14 + 5 * q^15 + 160 * q^16 + 170 * q^17 - 134 * q^18 + 11 * q^19 - 200 * q^20 - 162 * q^21 + 220 * q^22 - 124 * q^23 + 8 * q^24 + 250 * q^25 + 14 * q^26 - 37 * q^27 + 16 * q^28 + 91 * q^29 - 10 * q^30 + 29 * q^31 - 320 * q^32 + 11 * q^33 - 340 * q^34 - 20 * q^35 + 268 * q^36 + 468 * q^37 - 22 * q^38 + 161 * q^39 + 400 * q^40 - 698 * q^41 + 324 * q^42 + 726 * q^43 - 440 * q^44 - 335 * q^45 + 248 * q^46 - 181 * q^47 - 16 * q^48 + 638 * q^49 - 500 * q^50 - 17 * q^51 - 28 * q^52 - 335 * q^53 + 74 * q^54 + 550 * q^55 - 32 * q^56 + 11 * q^57 - 182 * q^58 + 649 * q^59 + 20 * q^60 + 13 * q^61 - 58 * q^62 - 460 * q^63 + 640 * q^64 + 35 * q^65 - 22 * q^66 + 1384 * q^67 + 680 * q^68 + 1304 * q^69 + 40 * q^70 - 1655 * q^71 - 536 * q^72 - 1185 * q^73 - 936 * q^74 - 25 * q^75 + 44 * q^76 - 44 * q^77 - 322 * q^78 + 364 * q^79 - 800 * q^80 + 462 * q^81 + 1396 * q^82 - 120 * q^83 - 648 * q^84 - 850 * q^85 - 1452 * q^86 + 3429 * q^87 + 880 * q^88 - 651 * q^89 + 670 * q^90 - 42 * q^91 - 496 * q^92 - 355 * q^93 + 362 * q^94 - 55 * q^95 + 32 * q^96 + 73 * q^97 - 1276 * q^98 - 737 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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