LMFDB - Embedded newform 1859.4.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.13075 q^{2} +4.07791 q^{3} +18.3246 q^{4} +9.39838 q^{5} -20.9227 q^{6} +18.3779 q^{7} -52.9729 q^{8} -10.3707 q^{9} +O(q^{10})$	\(q-5.13075 q^{2} +4.07791 q^{3} +18.3246 q^{4} +9.39838 q^{5} -20.9227 q^{6} +18.3779 q^{7} -52.9729 q^{8} -10.3707 q^{9} -48.2207 q^{10} -11.0000 q^{11} +74.7260 q^{12} -94.2924 q^{14} +38.3257 q^{15} +125.194 q^{16} -89.6643 q^{17} +53.2093 q^{18} -27.3088 q^{19} +172.221 q^{20} +74.9434 q^{21} +56.4383 q^{22} -16.8091 q^{23} -216.019 q^{24} -36.6705 q^{25} -152.394 q^{27} +336.768 q^{28} +92.4784 q^{29} -196.640 q^{30} -156.111 q^{31} -218.556 q^{32} -44.8570 q^{33} +460.045 q^{34} +172.722 q^{35} -190.038 q^{36} +302.667 q^{37} +140.115 q^{38} -497.860 q^{40} +402.842 q^{41} -384.516 q^{42} -4.90422 q^{43} -201.571 q^{44} -97.4674 q^{45} +86.2433 q^{46} +23.9853 q^{47} +510.530 q^{48} -5.25283 q^{49} +188.147 q^{50} -365.643 q^{51} +455.801 q^{53} +781.896 q^{54} -103.382 q^{55} -973.531 q^{56} -111.363 q^{57} -474.484 q^{58} +656.781 q^{59} +702.303 q^{60} -785.025 q^{61} +800.968 q^{62} -190.591 q^{63} +119.805 q^{64} +230.150 q^{66} +238.815 q^{67} -1643.06 q^{68} -68.5460 q^{69} -886.195 q^{70} -102.212 q^{71} +549.364 q^{72} -709.562 q^{73} -1552.91 q^{74} -149.539 q^{75} -500.424 q^{76} -202.157 q^{77} -629.514 q^{79} +1176.62 q^{80} -341.442 q^{81} -2066.88 q^{82} -1063.98 q^{83} +1373.31 q^{84} -842.698 q^{85} +25.1623 q^{86} +377.118 q^{87} +582.702 q^{88} +918.445 q^{89} +500.081 q^{90} -308.020 q^{92} -636.607 q^{93} -123.063 q^{94} -256.659 q^{95} -891.253 q^{96} -865.441 q^{97} +26.9510 q^{98} +114.077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.13075	−1.81399	−0.906997	−	0.421137i	$-0.861631\pi$
$2$	−5.13075	−1.81399	−0.906997	+	0.421137i	$0.861631\pi$
$3$	4.07791	0.784794	0.392397	−	0.919796i	$-0.371646\pi$
$3$	4.07791	0.784794	0.392397	+	0.919796i	$0.371646\pi$
$4$	18.3246	2.29057
$5$	9.39838	0.840616	0.420308	−	0.907381i	$-0.361922\pi$
$5$	9.39838	0.840616	0.420308	+	0.907381i	$0.361922\pi$
$6$	−20.9227	−1.42361
$7$	18.3779	0.992313	0.496157	−	0.868233i	$-0.334744\pi$
$7$	18.3779	0.992313	0.496157	+	0.868233i	$0.334744\pi$
$8$	−52.9729	−2.34110
$9$	−10.3707	−0.384099
$10$	−48.2207	−1.52487
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	74.7260	1.79763
$13$	0	0
$13$	0	0
$14$	−94.2924	−1.80005
$15$	38.3257	0.659711
$16$	125.194	1.95616
$17$	−89.6643	−1.27922	−0.639611	−	0.768699i	$-0.720905\pi$
$17$	−89.6643	−1.27922	−0.639611	+	0.768699i	$0.720905\pi$
$18$	53.2093	0.696752
$19$	−27.3088	−0.329741	−0.164871	−	0.986315i	$-0.552721\pi$
$19$	−27.3088	−0.329741	−0.164871	+	0.986315i	$0.552721\pi$
$20$	172.221	1.92549
$21$	74.9434	0.778761
$22$	56.4383	0.546940
$23$	−16.8091	−0.152389	−0.0761944	−	0.997093i	$-0.524277\pi$
$23$	−16.8091	−0.152389	−0.0761944	+	0.997093i	$0.524277\pi$
$24$	−216.019	−1.83728
$25$	−36.6705	−0.293364
$26$	0	0
$27$	−152.394	−1.08623
$28$	336.768	2.27297
$29$	92.4784	0.592166	0.296083	−	0.955162i	$-0.404320\pi$
$29$	92.4784	0.592166	0.296083	+	0.955162i	$0.404320\pi$
$30$	−196.640	−1.19671
$31$	−156.111	−0.904465	−0.452232	−	0.891900i	$-0.649372\pi$
$31$	−156.111	−0.904465	−0.452232	+	0.891900i	$0.649372\pi$
$32$	−218.556	−1.20736
$33$	−44.8570	−0.236624
$34$	460.045	2.32050
$35$	172.722	0.834155
$36$	−190.038	−0.879806
$37$	302.667	1.34482	0.672409	−	0.740180i	$-0.265260\pi$
$37$	302.667	1.34482	0.672409	+	0.740180i	$0.265260\pi$
$38$	140.115	0.598148
$39$	0	0
$40$	−497.860	−1.96796
$41$	402.842	1.53447	0.767236	−	0.641365i	$-0.221632\pi$
$41$	402.842	1.53447	0.767236	+	0.641365i	$0.221632\pi$
$42$	−384.516	−1.41267
$43$	−4.90422	−0.0173927	−0.00869636	−	0.999962i	$-0.502768\pi$
$43$	−4.90422	−0.0173927	−0.00869636	+	0.999962i	$0.502768\pi$
$44$	−201.571	−0.690634
$45$	−97.4674	−0.322879
$46$	86.2433	0.276432
$47$	23.9853	0.0744386	0.0372193	−	0.999307i	$-0.488150\pi$
$47$	23.9853	0.0744386	0.0372193	+	0.999307i	$0.488150\pi$
$48$	510.530	1.53518
$49$	−5.25283	−0.0153144
$50$	188.147	0.532161
$51$	−365.643	−1.00393
$52$	0	0
$53$	455.801	1.18130	0.590652	−	0.806927i	$-0.298871\pi$
$53$	455.801	1.18130	0.590652	+	0.806927i	$0.298871\pi$
$54$	781.896	1.97042
$55$	−103.382	−0.253455
$56$	−973.531	−2.32310
$57$	−111.363	−0.258779
$58$	−474.484	−1.07419
$59$	656.781	1.44925	0.724623	−	0.689145i	$-0.242014\pi$
$59$	656.781	1.44925	0.724623	+	0.689145i	$0.242014\pi$
$60$	702.303	1.51112
$61$	−785.025	−1.64774	−0.823870	−	0.566778i	$-0.808190\pi$
$61$	−785.025	−1.64774	−0.823870	+	0.566778i	$0.808190\pi$
$62$	800.968	1.64069
$63$	−190.591	−0.381146
$64$	119.805	0.233994
$65$	0	0
$66$	230.150	0.429235
$67$	238.815	0.435460	0.217730	−	0.976009i	$-0.430135\pi$
$67$	238.815	0.435460	0.217730	+	0.976009i	$0.430135\pi$
$68$	−1643.06	−2.93015
$69$	−68.5460	−0.119594
$70$	−886.195	−1.51315
$71$	−102.212	−0.170851	−0.0854253	−	0.996345i	$-0.527225\pi$
$71$	−102.212	−0.170851	−0.0854253	+	0.996345i	$0.527225\pi$
$72$	549.364	0.899211
$73$	−709.562	−1.13764	−0.568822	−	0.822461i	$-0.692601\pi$
$73$	−709.562	−1.13764	−0.568822	+	0.822461i	$0.692601\pi$
$74$	−1552.91	−2.43949
$75$	−149.539	−0.230231
$76$	−500.424	−0.755296
$77$	−202.157	−0.299194
$78$	0	0
$79$	−629.514	−0.896530	−0.448265	−	0.893901i	$-0.647958\pi$
$79$	−629.514	−0.896530	−0.448265	+	0.893901i	$0.647958\pi$
$80$	1176.62	1.64438
$81$	−341.442	−0.468370
$82$	−2066.88	−2.78352
$83$	−1063.98	−1.40707	−0.703534	−	0.710662i	$-0.748396\pi$
$83$	−1063.98	−1.40707	−0.703534	+	0.710662i	$0.748396\pi$
$84$	1373.31	1.78381
$85$	−842.698	−1.07533
$86$	25.1623	0.0315503
$87$	377.118	0.464728
$88$	582.702	0.705867
$89$	918.445	1.09388	0.546938	−	0.837173i	$-0.315793\pi$
$89$	918.445	1.09388	0.546938	+	0.837173i	$0.315793\pi$
$90$	500.081	0.585701
$91$	0	0
$92$	−308.020	−0.349058
$93$	−636.607	−0.709818
$94$	−123.063	−0.135031
$95$	−256.659	−0.277186
$96$	−891.253	−0.947532
$97$	−865.441	−0.905899	−0.452950	−	0.891536i	$-0.649628\pi$
$97$	−865.441	−0.905899	−0.452950	+	0.891536i	$0.649628\pi$
$98$	26.9510	0.0277802
$99$	114.077	0.115810
$100$	−671.973	−0.671973
$101$	−479.105	−0.472007	−0.236003	−	0.971752i	$-0.575838\pi$
$101$	−479.105	−0.472007	−0.236003	+	0.971752i	$0.575838\pi$
$102$	1876.02	1.82112
$103$	1773.33	1.69643	0.848213	−	0.529655i	$-0.177679\pi$
$103$	1773.33	1.69643	0.848213	+	0.529655i	$0.177679\pi$
$104$	0	0
$105$	704.346	0.654640
$106$	−2338.60	−2.14288
$107$	−1231.11	−1.11230	−0.556149	−	0.831083i	$-0.687722\pi$
$107$	−1231.11	−1.11230	−0.556149	+	0.831083i	$0.687722\pi$
$108$	−2792.56	−2.48810
$109$	−1934.75	−1.70014	−0.850072	−	0.526667i	$-0.823442\pi$
$109$	−1934.75	−1.70014	−0.850072	+	0.526667i	$0.823442\pi$
$110$	530.428	0.459767
$111$	1234.25	1.05540
$112$	2300.80	1.94112
$113$	−1163.42	−0.968542	−0.484271	−	0.874918i	$-0.660915\pi$
$113$	−1163.42	−0.968542	−0.484271	+	0.874918i	$0.660915\pi$
$114$	571.376	0.469423
$115$	−157.978	−0.128100
$116$	1694.63	1.35640
$117$	0	0
$118$	−3369.78	−2.62893
$119$	−1647.84	−1.26939
$120$	−2030.23	−1.54445
$121$	121.000	0.0909091
$122$	4027.77	2.98899
$123$	1642.75	1.20424
$124$	−2860.68	−2.07174
$125$	−1519.44	−1.08722
$126$	977.875	0.691397
$127$	−1507.35	−1.05319	−0.526596	−	0.850116i	$-0.676532\pi$
$127$	−1507.35	−1.05319	−0.526596	+	0.850116i	$0.676532\pi$
$128$	1133.76	0.782901
$129$	−19.9990	−0.0136497
$130$	0	0
$131$	2453.41	1.63630	0.818149	−	0.575006i	$-0.195000\pi$
$131$	2453.41	1.63630	0.818149	+	0.575006i	$0.195000\pi$
$132$	−821.986	−0.542006
$133$	−501.879	−0.327206
$134$	−1225.30	−0.789922
$135$	−1432.26	−0.913104
$136$	4749.78	2.99478
$137$	−866.740	−0.540516	−0.270258	−	0.962788i	$-0.587109\pi$
$137$	−866.740	−0.540516	−0.270258	+	0.962788i	$0.587109\pi$
$138$	351.692	0.216942
$139$	−1826.06	−1.11428	−0.557138	−	0.830420i	$-0.688101\pi$
$139$	−1826.06	−1.11428	−0.557138	+	0.830420i	$0.688101\pi$
$140$	3165.07	1.91069
$141$	97.8099	0.0584190
$142$	524.427	0.309922
$143$	0	0
$144$	−1298.35	−0.751357
$145$	869.147	0.497784
$146$	3640.59	2.06368
$147$	−21.4206	−0.0120186
$148$	5546.26	3.08040
$149$	−2471.76	−1.35902	−0.679511	−	0.733665i	$-0.737808\pi$
$149$	−2471.76	−1.35902	−0.679511	+	0.733665i	$0.737808\pi$
$150$	767.248	0.417637
$151$	1119.18	0.603164	0.301582	−	0.953440i	$-0.402485\pi$
$151$	1119.18	0.603164	0.301582	+	0.953440i	$0.402485\pi$
$152$	1446.63	0.771955
$153$	929.877	0.491347
$154$	1037.22	0.542736
$155$	−1467.19	−0.760308
$156$	0	0
$157$	−3030.57	−1.54055	−0.770273	−	0.637714i	$-0.779880\pi$
$157$	−3030.57	−1.54055	−0.770273	+	0.637714i	$0.779880\pi$
$158$	3229.88	1.62630
$159$	1858.72	0.927080
$160$	−2054.07	−1.01493
$161$	−308.916	−0.151217
$162$	1751.85	0.849620
$163$	−2204.42	−1.05929	−0.529643	−	0.848221i	$-0.677674\pi$
$163$	−2204.42	−1.05929	−0.529643	+	0.848221i	$0.677674\pi$
$164$	7381.91	3.51482
$165$	−421.583	−0.198910
$166$	5459.00	2.55241
$167$	2250.60	1.04286	0.521428	−	0.853295i	$-0.325400\pi$
$167$	2250.60	1.04286	0.521428	+	0.853295i	$0.325400\pi$
$168$	−3969.97	−1.82315
$169$	0	0
$170$	4323.67	1.95065
$171$	283.211	0.126653
$172$	−89.8679	−0.0398393
$173$	−1850.89	−0.813416	−0.406708	−	0.913558i	$-0.633323\pi$
$173$	−1850.89	−0.813416	−0.406708	+	0.913558i	$0.633323\pi$
$174$	−1934.90	−0.843014
$175$	−673.927	−0.291109
$176$	−1377.14	−0.589804
$177$	2678.29	1.13736
$178$	−4712.31	−1.98429
$179$	2375.32	0.991844	0.495922	−	0.868367i	$-0.334830\pi$
$179$	2375.32	0.991844	0.495922	+	0.868367i	$0.334830\pi$
$180$	−1786.05	−0.739580
$181$	2992.20	1.22878	0.614388	−	0.789004i	$-0.289403\pi$
$181$	2992.20	1.22878	0.614388	+	0.789004i	$0.289403\pi$
$182$	0	0
$183$	−3201.26	−1.29314
$184$	890.428	0.356757
$185$	2844.58	1.13048
$186$	3266.27	1.28761
$187$	986.307	0.385700
$188$	439.521	0.170507
$189$	−2800.68	−1.07788
$190$	1316.85	0.502813
$191$	−1389.31	−0.526318	−0.263159	−	0.964752i	$-0.584764\pi$
$191$	−1389.31	−0.526318	−0.263159	+	0.964752i	$0.584764\pi$
$192$	488.553	0.183637
$193$	−2962.15	−1.10477	−0.552383	−	0.833590i	$-0.686281\pi$
$193$	−2962.15	−1.10477	−0.552383	+	0.833590i	$0.686281\pi$
$194$	4440.36	1.64330
$195$	0	0
$196$	−96.2561	−0.0350787
$197$	−804.082	−0.290805	−0.145402	−	0.989373i	$-0.546448\pi$
$197$	−804.082	−0.290805	−0.145402	+	0.989373i	$0.546448\pi$
$198$	−585.302	−0.210079
$199$	1206.40	0.429745	0.214872	−	0.976642i	$-0.431066\pi$
$199$	1206.40	0.429745	0.214872	+	0.976642i	$0.431066\pi$
$200$	1942.55	0.686794
$201$	973.864	0.341747
$202$	2458.17	0.856218
$203$	1699.56	0.587614
$204$	−6700.25	−2.29957
$205$	3786.06	1.28990
$206$	−9098.54	−3.07731
$207$	174.322	0.0585323
$208$	0	0
$209$	300.397	0.0994207
$210$	−3613.82	−1.18751
$211$	−3467.77	−1.13143	−0.565714	−	0.824601i	$-0.691400\pi$
$211$	−3467.77	−1.13143	−0.565714	+	0.824601i	$0.691400\pi$
$212$	8352.37	2.70586
$213$	−416.813	−0.134082
$214$	6316.52	2.01770
$215$	−46.0917	−0.0146206
$216$	8072.77	2.54297
$217$	−2869.00	−0.897512
$218$	9926.73	3.08405
$219$	−2893.53	−0.892816
$220$	−1894.44	−0.580558
$221$	0	0
$222$	−6332.63	−1.91450
$223$	2455.81	0.737459	0.368729	−	0.929537i	$-0.379793\pi$
$223$	2455.81	0.737459	0.368729	+	0.929537i	$0.379793\pi$
$224$	−4016.61	−1.19808
$225$	380.298	0.112681
$226$	5969.21	1.75693
$227$	−2104.45	−0.615320	−0.307660	−	0.951496i	$-0.599546\pi$
$227$	−2104.45	−0.615320	−0.307660	+	0.951496i	$0.599546\pi$
$228$	−2040.68	−0.592752
$229$	1093.57	0.315569	0.157785	−	0.987474i	$-0.449565\pi$
$229$	1093.57	0.315569	0.157785	+	0.987474i	$0.449565\pi$
$230$	810.547	0.232373
$231$	−824.377	−0.234805
$232$	−4898.85	−1.38632
$233$	3127.45	0.879338	0.439669	−	0.898160i	$-0.355096\pi$
$233$	3127.45	0.879338	0.439669	+	0.898160i	$0.355096\pi$
$234$	0	0
$235$	225.423	0.0625743
$236$	12035.2	3.31961
$237$	−2567.10	−0.703591
$238$	8454.66	2.30266
$239$	−4769.79	−1.29093	−0.645464	−	0.763790i	$-0.723336\pi$
$239$	−4769.79	−1.29093	−0.645464	+	0.763790i	$0.723336\pi$
$240$	4798.15	1.29050
$241$	1616.68	0.432115	0.216057	−	0.976381i	$-0.430680\pi$
$241$	1616.68	0.432115	0.216057	+	0.976381i	$0.430680\pi$
$242$	−620.821	−0.164909
$243$	2722.27	0.718658
$244$	−14385.3	−3.77427
$245$	−49.3681	−0.0128735
$246$	−8428.55	−2.18449
$247$	0	0
$248$	8269.67	2.11744
$249$	−4338.80	−1.10426
$250$	7795.87	1.97222
$251$	−3004.02	−0.755427	−0.377713	−	0.925923i	$-0.623290\pi$
$251$	−3004.02	−0.755427	−0.377713	+	0.925923i	$0.623290\pi$
$252$	−3492.50	−0.873044
$253$	184.900	0.0459469
$254$	7733.81	1.91048
$255$	−3436.45	−0.843916
$256$	−6775.49	−1.65417
$257$	−282.776	−0.0686345	−0.0343172	−	0.999411i	$-0.510926\pi$
$257$	−282.776	−0.0686345	−0.0343172	+	0.999411i	$0.510926\pi$
$258$	102.610	0.0247605
$259$	5562.39	1.33448
$260$	0	0
$261$	−959.062	−0.227450
$262$	−12587.8	−2.96824
$263$	−1341.46	−0.314517	−0.157259	−	0.987557i	$-0.550266\pi$
$263$	−1341.46	−0.314517	−0.157259	+	0.987557i	$0.550266\pi$
$264$	2376.21	0.553960
$265$	4283.79	0.993023
$266$	2575.02	0.593550
$267$	3745.34	0.858468
$268$	4376.18	0.997454
$269$	4453.03	1.00932	0.504658	−	0.863319i	$-0.331619\pi$
$269$	4453.03	1.00932	0.504658	+	0.863319i	$0.331619\pi$
$270$	7348.55	1.65637
$271$	−3895.33	−0.873154	−0.436577	−	0.899667i	$-0.643809\pi$
$271$	−3895.33	−0.873154	−0.436577	+	0.899667i	$0.643809\pi$
$272$	−11225.4	−2.50236
$273$	0	0
$274$	4447.03	0.980492
$275$	403.376	0.0884527
$276$	−1256.08	−0.273938
$277$	7275.16	1.57806	0.789029	−	0.614357i	$-0.210584\pi$
$277$	7275.16	1.57806	0.789029	+	0.614357i	$0.210584\pi$
$278$	9369.06	2.02129
$279$	1618.98	0.347404
$280$	−9149.61	−1.95284
$281$	−8933.32	−1.89650	−0.948251	−	0.317522i	$-0.897149\pi$
$281$	−8933.32	−1.89650	−0.948251	+	0.317522i	$0.897149\pi$
$282$	−501.838	−0.105972
$283$	−6654.45	−1.39776	−0.698880	−	0.715239i	$-0.746318\pi$
$283$	−6654.45	−1.39776	−0.698880	+	0.715239i	$0.746318\pi$
$284$	−1873.00	−0.391346
$285$	−1046.63	−0.217534
$286$	0	0
$287$	7403.39	1.52268
$288$	2266.57	0.463747
$289$	3126.68	0.636409
$290$	−4459.37	−0.902978
$291$	−3529.19	−0.710944
$292$	−13002.4	−2.60586
$293$	3824.59	0.762576	0.381288	−	0.924456i	$-0.375481\pi$
$293$	3824.59	0.762576	0.381288	+	0.924456i	$0.375481\pi$
$294$	109.904	0.0218017
$295$	6172.67	1.21826
$296$	−16033.2	−3.14834
$297$	1676.34	0.327511
$298$	12682.0	2.46526
$299$	0	0
$300$	−2740.24	−0.527360
$301$	−90.1293	−0.0172590
$302$	−5742.25	−1.09414
$303$	−1953.75	−0.370428
$304$	−3418.91	−0.645026
$305$	−7377.96	−1.38512
$306$	−4770.97	−0.891301
$307$	5387.31	1.00153	0.500766	−	0.865583i	$-0.333052\pi$
$307$	5387.31	1.00153	0.500766	+	0.865583i	$0.333052\pi$
$308$	−3704.44	−0.685326
$309$	7231.50	1.33134
$310$	7527.80	1.37919
$311$	−5694.63	−1.03830	−0.519152	−	0.854682i	$-0.673752\pi$
$311$	−5694.63	−1.03830	−0.519152	+	0.854682i	$0.673752\pi$
$312$	0	0
$313$	1436.72	0.259451	0.129725	−	0.991550i	$-0.458590\pi$
$313$	1436.72	0.259451	0.129725	+	0.991550i	$0.458590\pi$
$314$	15549.1	2.79454
$315$	−1791.25	−0.320398
$316$	−11535.6	−2.05357
$317$	2222.45	0.393771	0.196886	−	0.980426i	$-0.436917\pi$
$317$	2222.45	0.393771	0.196886	+	0.980426i	$0.436917\pi$
$318$	−9536.60	−1.68172
$319$	−1017.26	−0.178545
$320$	1125.97	0.196699
$321$	−5020.35	−0.872924
$322$	1584.97	0.274307
$323$	2448.63	0.421812
$324$	−6256.78	−1.07284
$325$	0	0
$326$	11310.3	1.92154
$327$	−7889.74	−1.33426
$328$	−21339.7	−3.59234
$329$	440.799	0.0738664
$330$	2163.04	0.360822
$331$	−10932.7	−1.81546	−0.907729	−	0.419556i	$-0.862186\pi$
$331$	−10932.7	−1.81546	−0.907729	+	0.419556i	$0.862186\pi$
$332$	−19496.9	−3.22299
$333$	−3138.86	−0.516542
$334$	−11547.3	−1.89173
$335$	2244.47	0.366055
$336$	9382.47	1.52338
$337$	−9161.53	−1.48089	−0.740446	−	0.672116i	$-0.765385\pi$
$337$	−9161.53	−1.48089	−0.740446	+	0.672116i	$0.765385\pi$
$338$	0	0
$339$	−4744.32	−0.760106
$340$	−15442.1	−2.46313
$341$	1717.22	0.272706
$342$	−1453.08	−0.229748
$343$	−6400.16	−1.00751
$344$	259.791	0.0407180
$345$	−644.221	−0.100532
$346$	9496.48	1.47553
$347$	−9525.27	−1.47361	−0.736806	−	0.676104i	$-0.763667\pi$
$347$	−9525.27	−1.47361	−0.736806	+	0.676104i	$0.763667\pi$
$348$	6910.54	1.06449
$349$	8396.00	1.28776	0.643879	−	0.765127i	$-0.277324\pi$
$349$	8396.00	1.28776	0.643879	+	0.765127i	$0.277324\pi$
$350$	3457.75	0.528071
$351$	0	0
$352$	2404.12	0.364034
$353$	791.832	0.119391	0.0596954	−	0.998217i	$-0.480987\pi$
$353$	791.832	0.119391	0.0596954	+	0.998217i	$0.480987\pi$
$354$	−13741.6	−2.06316
$355$	−960.631	−0.143620
$356$	16830.1	2.50561
$357$	−6719.74	−0.996209
$358$	−12187.2	−1.79920
$359$	−1515.94	−0.222864	−0.111432	−	0.993772i	$-0.535544\pi$
$359$	−1515.94	−0.222864	−0.111432	+	0.993772i	$0.535544\pi$
$360$	5163.13	0.755892
$361$	−6113.23	−0.891271
$362$	−15352.2	−2.22899
$363$	493.427	0.0713449
$364$	0	0
$365$	−6668.73	−0.956322
$366$	16424.9	2.34574
$367$	−960.497	−0.136615	−0.0683073	−	0.997664i	$-0.521760\pi$
$367$	−960.497	−0.136615	−0.0683073	+	0.997664i	$0.521760\pi$
$368$	−2104.40	−0.298096
$369$	−4177.74	−0.589388
$370$	−14594.8	−2.05068
$371$	8376.67	1.17222
$372$	−11665.6	−1.62589
$373$	12095.9	1.67910	0.839549	−	0.543284i	$-0.182819\pi$
$373$	12095.9	1.67910	0.839549	+	0.543284i	$0.182819\pi$
$374$	−5060.49	−0.699657
$375$	−6196.14	−0.853246
$376$	−1270.57	−0.174268
$377$	0	0
$378$	14369.6	1.95527
$379$	−6922.78	−0.938257	−0.469128	−	0.883130i	$-0.655432\pi$
$379$	−6922.78	−0.938257	−0.469128	+	0.883130i	$0.655432\pi$
$380$	−4703.17	−0.634914
$381$	−6146.82	−0.826538
$382$	7128.19	0.954738
$383$	−7774.62	−1.03724	−0.518622	−	0.855004i	$-0.673555\pi$
$383$	−7774.62	−1.03724	−0.518622	+	0.855004i	$0.673555\pi$
$384$	4623.38	0.614416
$385$	−1899.95	−0.251507
$386$	15198.0	2.00404
$387$	50.8600	0.00668052
$388$	−15858.9	−2.07503
$389$	−9328.52	−1.21587	−0.607937	−	0.793985i	$-0.708003\pi$
$389$	−9328.52	−1.21587	−0.607937	+	0.793985i	$0.708003\pi$
$390$	0	0
$391$	1507.18	0.194939
$392$	278.258	0.0358524
$393$	10004.8	1.28416
$394$	4125.55	0.527518
$395$	−5916.41	−0.753638
$396$	2090.42	0.265272
$397$	12361.6	1.56275	0.781376	−	0.624061i	$-0.214518\pi$
$397$	12361.6	1.56275	0.781376	+	0.624061i	$0.214518\pi$
$398$	−6189.72	−0.779555
$399$	−2046.62	−0.256790
$400$	−4590.94	−0.573867
$401$	−2287.69	−0.284892	−0.142446	−	0.989803i	$-0.545497\pi$
$401$	−2287.69	−0.284892	−0.142446	+	0.989803i	$0.545497\pi$
$402$	−4996.65	−0.619926
$403$	0	0
$404$	−8779.40	−1.08117
$405$	−3209.00	−0.393719
$406$	−8720.01	−1.06593
$407$	−3329.34	−0.405478
$408$	19369.2	2.35029
$409$	−4687.13	−0.566660	−0.283330	−	0.959023i	$-0.591439\pi$
$409$	−4687.13	−0.566660	−0.283330	+	0.959023i	$0.591439\pi$
$410$	−19425.3	−2.33987
$411$	−3534.49	−0.424193
$412$	32495.6	3.88579
$413$	12070.2	1.43811
$414$	−894.400	−0.106177
$415$	−9999.65	−1.18280
$416$	0	0
$417$	−7446.50	−0.874477
$418$	−1541.26	−0.180348
$419$	6310.83	0.735809	0.367905	−	0.929864i	$-0.380075\pi$
$419$	6310.83	0.735809	0.367905	+	0.929864i	$0.380075\pi$
$420$	12906.9	1.49950
$421$	−10266.6	−1.18851	−0.594257	−	0.804275i	$-0.702554\pi$
$421$	−10266.6	−1.18851	−0.594257	+	0.804275i	$0.702554\pi$
$422$	17792.3	2.05241
$423$	−248.743	−0.0285918
$424$	−24145.1	−2.76554
$425$	3288.04	0.375278
$426$	2138.56	0.243225
$427$	−14427.1	−1.63507
$428$	−22559.6	−2.54780
$429$	0	0
$430$	236.485	0.0265217
$431$	14881.6	1.66316	0.831582	−	0.555402i	$-0.187436\pi$
$431$	14881.6	1.66316	0.831582	+	0.555402i	$0.187436\pi$
$432$	−19078.9	−2.12484
$433$	−12541.9	−1.39197	−0.695987	−	0.718055i	$-0.745033\pi$
$433$	−12541.9	−1.39197	−0.695987	+	0.718055i	$0.745033\pi$
$434$	14720.1	1.62808
$435$	3544.30	0.390658
$436$	−35453.6	−3.89431
$437$	459.037	0.0502488
$438$	14846.0	1.61956
$439$	724.138	0.0787271	0.0393636	−	0.999225i	$-0.487467\pi$
$439$	724.138	0.0787271	0.0393636	+	0.999225i	$0.487467\pi$
$440$	5476.46	0.593363
$441$	54.4753	0.00588223
$442$	0	0
$443$	−17971.1	−1.92739	−0.963694	−	0.267010i	$-0.913964\pi$
$443$	−17971.1	−1.92739	−0.963694	+	0.267010i	$0.913964\pi$
$444$	22617.1	2.41748
$445$	8631.89	0.919530
$446$	−12600.2	−1.33775
$447$	−10079.6	−1.06655
$448$	2201.76	0.232195
$449$	12094.6	1.27122	0.635610	−	0.772010i	$-0.280749\pi$
$449$	12094.6	1.27122	0.635610	+	0.772010i	$0.280749\pi$
$450$	−1951.21	−0.204402
$451$	−4431.26	−0.462661
$452$	−21319.2	−2.21852
$453$	4563.93	0.473360
$454$	10797.4	1.11619
$455$	0	0
$456$	5899.22	0.605826
$457$	−1308.30	−0.133916	−0.0669582	−	0.997756i	$-0.521329\pi$
$457$	−1308.30	−0.133916	−0.0669582	+	0.997756i	$0.521329\pi$
$458$	−5610.85	−0.572441
$459$	13664.3	1.38953
$460$	−2894.89	−0.293424
$461$	6587.38	0.665520	0.332760	−	0.943012i	$-0.392020\pi$
$461$	6587.38	0.665520	0.332760	+	0.943012i	$0.392020\pi$
$462$	4229.67	0.425936
$463$	−3192.65	−0.320464	−0.160232	−	0.987079i	$-0.551224\pi$
$463$	−3192.65	−0.320464	−0.160232	+	0.987079i	$0.551224\pi$
$464$	11577.8	1.15837
$465$	−5983.07	−0.596685
$466$	−16046.1	−1.59511
$467$	−7298.06	−0.723156	−0.361578	−	0.932342i	$-0.617762\pi$
$467$	−7298.06	−0.723156	−0.361578	+	0.932342i	$0.617762\pi$
$468$	0	0
$469$	4388.91	0.432113
$470$	−1156.59	−0.113509
$471$	−12358.4	−1.20901
$472$	−34791.6	−3.39282
$473$	53.9464	0.00524410
$474$	13171.2	1.27631
$475$	1001.43	0.0967342
$476$	−30196.0	−2.90763
$477$	−4726.96	−0.453737
$478$	24472.6	2.34174
$479$	10439.3	0.995793	0.497896	−	0.867237i	$-0.334106\pi$
$479$	10439.3	0.995793	0.497896	+	0.867237i	$0.334106\pi$
$480$	−8376.33	−0.796511
$481$	0	0
$482$	−8294.79	−0.783853
$483$	−1259.73	−0.118674
$484$	2217.28	0.208234
$485$	−8133.74	−0.761514
$486$	−13967.3	−1.30364
$487$	4881.93	0.454253	0.227126	−	0.973865i	$-0.427067\pi$
$487$	4881.93	0.454253	0.227126	+	0.973865i	$0.427067\pi$
$488$	41585.1	3.85752
$489$	−8989.43	−0.831321
$490$	253.295	0.0233525
$491$	1466.35	0.134777	0.0673884	−	0.997727i	$-0.478533\pi$
$491$	1466.35	0.134777	0.0673884	+	0.997727i	$0.478533\pi$
$492$	30102.8	2.75841
$493$	−8292.01	−0.757512
$494$	0	0
$495$	1072.14	0.0973518
$496$	−19544.2	−1.76928
$497$	−1878.45	−0.169537
$498$	22261.3	2.00312
$499$	5005.78	0.449078	0.224539	−	0.974465i	$-0.427912\pi$
$499$	5005.78	0.449078	0.224539	+	0.974465i	$0.427912\pi$
$500$	−27843.1	−2.49037
$501$	9177.75	0.818427
$502$	15412.9	1.37034
$503$	−7613.76	−0.674912	−0.337456	−	0.941341i	$-0.609566\pi$
$503$	−7613.76	−0.674912	−0.337456	+	0.941341i	$0.609566\pi$
$504$	10096.2	0.892299
$505$	−4502.81	−0.396777
$506$	−948.677	−0.0833475
$507$	0	0
$508$	−27621.5	−2.41241
$509$	17379.1	1.51339	0.756693	−	0.653771i	$-0.226814\pi$
$509$	17379.1	1.51339	0.756693	+	0.653771i	$0.226814\pi$
$510$	17631.6	1.53086
$511$	−13040.3	−1.12890
$512$	25693.2	2.21776
$513$	4161.71	0.358175
$514$	1450.85	0.124503
$515$	16666.5	1.42604
$516$	−366.473	−0.0312656
$517$	−263.838	−0.0224441
$518$	−28539.2	−2.42074
$519$	−7547.78	−0.638364
$520$	0	0
$521$	23476.7	1.97415	0.987074	−	0.160264i	$-0.0512345\pi$
$521$	23476.7	1.97415	0.987074	+	0.160264i	$0.0512345\pi$
$522$	4920.71	0.412593
$523$	12889.7	1.07768	0.538839	−	0.842409i	$-0.318863\pi$
$523$	12889.7	1.07768	0.538839	+	0.842409i	$0.318863\pi$
$524$	44957.7	3.74807
$525$	−2748.21	−0.228461
$526$	6882.70	0.570532
$527$	13997.6	1.15701
$528$	−5615.83	−0.462874
$529$	−11884.5	−0.976778
$530$	−21979.1	−1.80134
$531$	−6811.25	−0.556654
$532$	−9196.74	−0.749491
$533$	0	0
$534$	−19216.4	−1.55726
$535$	−11570.4	−0.935015
$536$	−12650.7	−1.01945
$537$	9686.36	0.778393
$538$	−22847.4	−1.83089
$539$	57.7812	0.00461746
$540$	−26245.5	−2.09153
$541$	20986.2	1.66777	0.833887	−	0.551935i	$-0.186111\pi$
$541$	20986.2	1.66777	0.833887	+	0.551935i	$0.186111\pi$
$542$	19986.0	1.58390
$543$	12201.9	0.964335
$544$	19596.7	1.54449
$545$	−18183.5	−1.42917
$546$	0	0
$547$	−8259.72	−0.645631	−0.322815	−	0.946462i	$-0.604629\pi$
$547$	−8259.72	−0.645631	−0.322815	+	0.946462i	$0.604629\pi$
$548$	−15882.7	−1.23809
$549$	8141.23	0.632895
$550$	−2069.62	−0.160453
$551$	−2525.48	−0.195261
$552$	3631.08	0.279980
$553$	−11569.1	−0.889639
$554$	−37327.0	−2.86259
$555$	11599.9	0.887190
$556$	−33461.8	−2.55233
$557$	−2356.83	−0.179285	−0.0896427	−	0.995974i	$-0.528573\pi$
$557$	−2356.83	−0.179285	−0.0896427	+	0.995974i	$0.528573\pi$
$558$	−8306.56	−0.630188
$559$	0	0
$560$	21623.8	1.63174
$561$	4022.07	0.302695
$562$	45834.6	3.44024
$563$	20563.8	1.53936	0.769680	−	0.638429i	$-0.220416\pi$
$563$	20563.8	1.53936	0.769680	+	0.638429i	$0.220416\pi$
$564$	1792.33	0.133813
$565$	−10934.2	−0.814172
$566$	34142.3	2.53553
$567$	−6274.98	−0.464770
$568$	5414.50	0.399977
$569$	−11186.9	−0.824218	−0.412109	−	0.911135i	$-0.635208\pi$
$569$	−11186.9	−0.824218	−0.412109	+	0.911135i	$0.635208\pi$
$570$	5370.00	0.394605
$571$	−21115.9	−1.54759	−0.773793	−	0.633439i	$-0.781643\pi$
$571$	−21115.9	−1.54759	−0.773793	+	0.633439i	$0.781643\pi$
$572$	0	0
$573$	−5665.47	−0.413051
$574$	−37984.9	−2.76213
$575$	616.399	0.0447054
$576$	−1242.45	−0.0898766
$577$	20388.8	1.47105	0.735527	−	0.677495i	$-0.236935\pi$
$577$	20388.8	1.47105	0.735527	+	0.677495i	$0.236935\pi$
$578$	−16042.2	−1.15444
$579$	−12079.4	−0.867014
$580$	15926.8	1.14021
$581$	−19553.7	−1.39625
$582$	18107.4	1.28965
$583$	−5013.81	−0.356176
$584$	37587.6	2.66333
$585$	0	0
$586$	−19623.0	−1.38331
$587$	548.846	0.0385917	0.0192958	−	0.999814i	$-0.493858\pi$
$587$	548.846	0.0385917	0.0192958	+	0.999814i	$0.493858\pi$
$588$	−392.523	−0.0275296
$589$	4263.22	0.298239
$590$	−31670.4	−2.20992
$591$	−3278.97	−0.228222
$592$	37892.2	2.63067
$593$	−4283.88	−0.296658	−0.148329	−	0.988938i	$-0.547389\pi$
$593$	−4283.88	−0.296658	−0.148329	+	0.988938i	$0.547389\pi$
$594$	−8600.86	−0.594104
$595$	−15487.0	−1.06707
$596$	−45294.0	−3.11294
$597$	4919.58	0.337261
$598$	0	0
$599$	−13440.4	−0.916797	−0.458399	−	0.888747i	$-0.651577\pi$
$599$	−13440.4	−0.916797	−0.458399	+	0.888747i	$0.651577\pi$
$600$	7921.53	0.538992
$601$	−7020.47	−0.476491	−0.238246	−	0.971205i	$-0.576572\pi$
$601$	−7020.47	−0.476491	−0.238246	+	0.971205i	$0.576572\pi$
$602$	462.431	0.0313078
$603$	−2476.66	−0.167260
$604$	20508.6	1.38159
$605$	1137.20	0.0764197
$606$	10024.2	0.671954
$607$	−19321.1	−1.29196	−0.645981	−	0.763353i	$-0.723552\pi$
$607$	−19321.1	−1.29196	−0.645981	+	0.763353i	$0.723552\pi$
$608$	5968.52	0.398118
$609$	6930.65	0.461156
$610$	37854.5	2.51260
$611$	0	0
$612$	17039.6	1.12547
$613$	1990.10	0.131125	0.0655623	−	0.997848i	$-0.479116\pi$
$613$	1990.10	0.131125	0.0655623	+	0.997848i	$0.479116\pi$
$614$	−27640.9	−1.81677
$615$	15439.2	1.01231
$616$	10708.8	0.700441
$617$	−13050.7	−0.851544	−0.425772	−	0.904831i	$-0.639997\pi$
$617$	−13050.7	−0.851544	−0.425772	+	0.904831i	$0.639997\pi$
$618$	−37103.0	−2.41505
$619$	−640.963	−0.0416195	−0.0208098	−	0.999783i	$-0.506624\pi$
$619$	−640.963	−0.0416195	−0.0208098	+	0.999783i	$0.506624\pi$
$620$	−26885.7	−1.74154
$621$	2561.61	0.165530
$622$	29217.7	1.88348
$623$	16879.1	1.08547
$624$	0	0
$625$	−9696.45	−0.620573
$626$	−7371.44	−0.470642
$627$	1224.99	0.0780247
$628$	−55534.0	−3.52874
$629$	−27138.5	−1.72032
$630$	9190.43	0.581199
$631$	18944.7	1.19521	0.597603	−	0.801792i	$-0.296120\pi$
$631$	18944.7	1.19521	0.597603	+	0.801792i	$0.296120\pi$
$632$	33347.2	2.09886
$633$	−14141.3	−0.887938
$634$	−11402.9	−0.714299
$635$	−14166.6	−0.885330
$636$	34060.2	2.12355
$637$	0	0
$638$	5219.32	0.323879
$639$	1060.01	0.0656234
$640$	10655.5	0.658120
$641$	3768.67	0.232221	0.116111	−	0.993236i	$-0.462957\pi$
$641$	3768.67	0.232221	0.116111	+	0.993236i	$0.462957\pi$
$642$	25758.2	1.58348
$643$	−17077.4	−1.04738	−0.523691	−	0.851908i	$-0.675445\pi$
$643$	−17077.4	−1.04738	−0.523691	+	0.851908i	$0.675445\pi$
$644$	−5660.76	−0.346375
$645$	−187.958	−0.0114742
$646$	−12563.3	−0.765164
$647$	5715.66	0.347304	0.173652	−	0.984807i	$-0.444443\pi$
$647$	5715.66	0.347304	0.173652	+	0.984807i	$0.444443\pi$
$648$	18087.2	1.09650
$649$	−7224.59	−0.436964
$650$	0	0
$651$	−11699.5	−0.704362
$652$	−40395.1	−2.42637
$653$	9966.45	0.597270	0.298635	−	0.954367i	$-0.403469\pi$
$653$	9966.45	0.597270	0.298635	+	0.954367i	$0.403469\pi$
$654$	40480.3	2.42034
$655$	23058.0	1.37550
$656$	50433.4	3.00167
$657$	7358.63	0.436967
$658$	−2261.63	−0.133993
$659$	5184.68	0.306474	0.153237	−	0.988189i	$-0.451030\pi$
$659$	5184.68	0.306474	0.153237	+	0.988189i	$0.451030\pi$
$660$	−7725.34	−0.455619
$661$	−22634.1	−1.33187	−0.665933	−	0.746012i	$-0.731966\pi$
$661$	−22634.1	−1.33187	−0.665933	+	0.746012i	$0.731966\pi$
$662$	56093.1	3.29323
$663$	0	0
$664$	56362.0	3.29408
$665$	−4716.85	−0.275055
$666$	16104.7	0.937005
$667$	−1554.48	−0.0902394
$668$	41241.4	2.38874
$669$	10014.6	0.578753
$670$	−11515.8	−0.664022
$671$	8635.28	0.496812
$672$	−16379.3	−0.940249
$673$	20185.0	1.15613	0.578065	−	0.815991i	$-0.303808\pi$
$673$	20185.0	1.15613	0.578065	+	0.815991i	$0.303808\pi$
$674$	47005.5	2.68633
$675$	5588.38	0.318662
$676$	0	0
$677$	10484.9	0.595223	0.297612	−	0.954687i	$-0.403810\pi$
$677$	10484.9	0.595223	0.297612	+	0.954687i	$0.403810\pi$
$678$	24341.9	1.37883
$679$	−15905.0	−0.898936
$680$	44640.2	2.51746
$681$	−8581.77	−0.482899
$682$	−8810.64	−0.494688
$683$	−467.874	−0.0262119	−0.0131059	−	0.999914i	$-0.504172\pi$
$683$	−467.874	−0.0262119	−0.0131059	+	0.999914i	$0.504172\pi$
$684$	5189.72	0.290108
$685$	−8145.95	−0.454366
$686$	32837.6	1.82762
$687$	4459.49	0.247657
$688$	−613.980	−0.0340229
$689$	0	0
$690$	3305.34	0.182365
$691$	6296.45	0.346640	0.173320	−	0.984866i	$-0.444551\pi$
$691$	6296.45	0.346640	0.173320	+	0.984866i	$0.444551\pi$
$692$	−33916.9	−1.86319
$693$	2096.50	0.114920
$694$	48871.8	2.67312
$695$	−17162.0	−0.936678
$696$	−19977.1	−1.08797
$697$	−36120.5	−1.96293
$698$	−43077.8	−2.33599
$699$	12753.4	0.690099
$700$	−12349.4	−0.666808
$701$	25632.4	1.38106	0.690529	−	0.723304i	$-0.257378\pi$
$701$	25632.4	1.38106	0.690529	+	0.723304i	$0.257378\pi$
$702$	0	0
$703$	−8265.50	−0.443441
$704$	−1317.85	−0.0705517
$705$	919.254	0.0491079
$706$	−4062.69	−0.216574
$707$	−8804.94	−0.468379
$708$	49078.6	2.60521
$709$	12359.7	0.654693	0.327347	−	0.944904i	$-0.393846\pi$
$709$	12359.7	0.654693	0.327347	+	0.944904i	$0.393846\pi$
$710$	4928.76	0.260525
$711$	6528.48	0.344356
$712$	−48652.7	−2.56087
$713$	2624.09	0.137830
$714$	34477.3	1.80712
$715$	0	0
$716$	43526.9	2.27189
$717$	−19450.8	−1.01311
$718$	7777.90	0.404274
$719$	13729.6	0.712139	0.356069	−	0.934459i	$-0.384117\pi$
$719$	13729.6	0.712139	0.356069	+	0.934459i	$0.384117\pi$
$720$	−12202.3	−0.631603
$721$	32590.2	1.68339
$722$	31365.4	1.61676
$723$	6592.68	0.339121
$724$	54830.8	2.81460
$725$	−3391.23	−0.173720
$726$	−2531.65	−0.129419
$727$	−255.862	−0.0130528	−0.00652640	−	0.999979i	$-0.502077\pi$
$727$	−255.862	−0.0130528	−0.00652640	+	0.999979i	$0.502077\pi$
$728$	0	0
$729$	20320.1	1.03237
$730$	34215.6	1.73476
$731$	439.733	0.0222491
$732$	−58661.8	−2.96203
$733$	−8488.40	−0.427730	−0.213865	−	0.976863i	$-0.568605\pi$
$733$	−8488.40	−0.427730	−0.213865	+	0.976863i	$0.568605\pi$
$734$	4928.07	0.247818
$735$	−201.319	−0.0101031
$736$	3673.74	0.183989
$737$	−2626.96	−0.131296
$738$	21434.9	1.06915
$739$	4216.58	0.209891	0.104945	−	0.994478i	$-0.466533\pi$
$739$	4216.58	0.209891	0.104945	+	0.994478i	$0.466533\pi$
$740$	52125.8	2.58944
$741$	0	0
$742$	−42978.6	−2.12641
$743$	22669.5	1.11933	0.559665	−	0.828719i	$-0.310930\pi$
$743$	22669.5	1.11933	0.559665	+	0.828719i	$0.310930\pi$
$744$	33723.0	1.66175
$745$	−23230.5	−1.14242
$746$	−62061.2	−3.04587
$747$	11034.1	0.540453
$748$	18073.7	0.883475
$749$	−22625.2	−1.10375
$750$	31790.8	1.54778
$751$	−1183.94	−0.0575268	−0.0287634	−	0.999586i	$-0.509157\pi$
$751$	−1183.94	−0.0575268	−0.0287634	+	0.999586i	$0.509157\pi$
$752$	3002.82	0.145614
$753$	−12250.1	−0.592854
$754$	0	0
$755$	10518.5	0.507030
$756$	−51321.4	−2.46897
$757$	28374.1	1.36232	0.681159	−	0.732136i	$-0.261476\pi$
$757$	28374.1	1.36232	0.681159	+	0.732136i	$0.261476\pi$
$758$	35519.1	1.70199
$759$	754.006	0.0360589
$760$	13596.0	0.648918
$761$	−26337.5	−1.25458	−0.627290	−	0.778786i	$-0.715836\pi$
$761$	−26337.5	−1.25458	−0.627290	+	0.778786i	$0.715836\pi$
$762$	31537.8	1.49934
$763$	−35556.7	−1.68708
$764$	−25458.5	−1.20557
$765$	8739.34	0.413035
$766$	39889.6	1.88155
$767$	0	0
$768$	−27629.8	−1.29818
$769$	1342.27	0.0629434	0.0314717	−	0.999505i	$-0.489981\pi$
$769$	1342.27	0.0629434	0.0314717	+	0.999505i	$0.489981\pi$
$770$	9748.15	0.456232
$771$	−1153.13	−0.0538639
$772$	−54280.1	−2.53055
$773$	9693.60	0.451041	0.225520	−	0.974238i	$-0.427592\pi$
$773$	9693.60	0.451041	0.225520	+	0.974238i	$0.427592\pi$
$774$	−260.950	−0.0121184
$775$	5724.68	0.265338
$776$	45845.0	2.12080
$777$	22682.9	1.04729
$778$	47862.3	2.20559
$779$	−11001.1	−0.505978
$780$	0	0
$781$	1124.34	0.0515134
$782$	−7732.94	−0.353618
$783$	−14093.2	−0.643229
$784$	−657.624	−0.0299574
$785$	−28482.4	−1.29501
$786$	−51332.0	−2.32945
$787$	11997.5	0.543412	0.271706	−	0.962380i	$-0.412412\pi$
$787$	11997.5	0.543412	0.271706	+	0.962380i	$0.412412\pi$
$788$	−14734.5	−0.666109
$789$	−5470.36	−0.246831
$790$	30355.6	1.36709
$791$	−21381.2	−0.961097
$792$	−6043.01	−0.271122
$793$	0	0
$794$	−63424.4	−2.83482
$795$	17468.9	0.779318
$796$	22106.7	0.984363
$797$	928.665	0.0412735	0.0206368	−	0.999787i	$-0.493431\pi$
$797$	928.665	0.0412735	0.0206368	+	0.999787i	$0.493431\pi$
$798$	10500.7	0.465815
$799$	−2150.62	−0.0952235
$800$	8014.58	0.354198
$801$	−9524.88	−0.420156
$802$	11737.6	0.516792
$803$	7805.19	0.343013
$804$	17845.7	0.782796
$805$	−2903.31	−0.127116
$806$	0	0
$807$	18159.1	0.792105
$808$	25379.6	1.10501
$809$	16901.3	0.734507	0.367254	−	0.930121i	$-0.380298\pi$
$809$	16901.3	0.734507	0.367254	+	0.930121i	$0.380298\pi$
$810$	16464.6	0.714204
$811$	25345.2	1.09740	0.548700	−	0.836019i	$-0.315123\pi$
$811$	25345.2	1.09740	0.548700	+	0.836019i	$0.315123\pi$
$812$	31143.7	1.34597
$813$	−15884.8	−0.685246
$814$	17082.0	0.735534
$815$	−20718.0	−0.890453
$816$	−45776.3	−1.96384
$817$	133.929	0.00573509
$818$	24048.5	1.02792
$819$	0	0
$820$	69378.0	2.95462
$821$	−31816.1	−1.35249	−0.676243	−	0.736679i	$-0.736393\pi$
$821$	−31816.1	−1.35249	−0.676243	+	0.736679i	$0.736393\pi$
$822$	18134.6	0.769484
$823$	40293.4	1.70661	0.853304	−	0.521413i	$-0.174595\pi$
$823$	40293.4	1.70661	0.853304	+	0.521413i	$0.174595\pi$
$824$	−93938.7	−3.97149
$825$	1644.93	0.0694171
$826$	−61929.4	−2.60872
$827$	16568.5	0.696666	0.348333	−	0.937371i	$-0.386748\pi$
$827$	16568.5	0.696666	0.348333	+	0.937371i	$0.386748\pi$
$828$	3194.37	0.134073
$829$	−10358.4	−0.433972	−0.216986	−	0.976175i	$-0.569623\pi$
$829$	−10358.4	−0.433972	−0.216986	+	0.976175i	$0.569623\pi$
$830$	51305.7	2.14560
$831$	29667.4	1.23845
$832$	0	0
$833$	470.991	0.0195905
$834$	38206.2	1.58630
$835$	21152.0	0.876641
$836$	5504.66	0.227730
$837$	23790.4	0.982458
$838$	−32379.3	−1.33475
$839$	35867.6	1.47591	0.737955	−	0.674850i	$-0.235792\pi$
$839$	35867.6	1.47591	0.737955	+	0.674850i	$0.235792\pi$
$840$	−37311.3	−1.53257
$841$	−15836.7	−0.649340
$842$	52675.5	2.15596
$843$	−36429.2	−1.48836
$844$	−63545.6	−2.59162
$845$	0	0
$846$	1276.24	0.0518653
$847$	2223.73	0.0902103
$848$	57063.6	2.31082
$849$	−27136.2	−1.09695
$850$	−16870.1	−0.680752
$851$	−5087.57	−0.204935
$852$	−7637.93	−0.307126
$853$	33105.2	1.32884	0.664420	−	0.747359i	$-0.268679\pi$
$853$	33105.2	1.32884	0.664420	+	0.747359i	$0.268679\pi$
$854$	74021.9	2.96602
$855$	2661.72	0.106467
$856$	65215.5	2.60399
$857$	−34332.7	−1.36848	−0.684238	−	0.729259i	$-0.739865\pi$
$857$	−34332.7	−1.36848	−0.684238	+	0.729259i	$0.739865\pi$
$858$	0	0
$859$	−39395.0	−1.56477	−0.782387	−	0.622793i	$-0.785998\pi$
$859$	−39395.0	−1.56477	−0.782387	+	0.622793i	$0.785998\pi$
$860$	−844.612	−0.0334896
$861$	30190.3	1.19499
$862$	−76354.0	−3.01697
$863$	−36038.7	−1.42152	−0.710760	−	0.703435i	$-0.751649\pi$
$863$	−36038.7	−1.42152	−0.710760	+	0.703435i	$0.751649\pi$
$864$	33306.7	1.31148
$865$	−17395.4	−0.683770
$866$	64349.3	2.52503
$867$	12750.3	0.499450
$868$	−52573.2	−2.05582
$869$	6924.66	0.270314
$870$	−18184.9	−0.708651
$871$	0	0
$872$	102490.	3.98020
$873$	8975.20	0.347955
$874$	−2355.21	−0.0911511
$875$	−27924.1	−1.07887
$876$	−53022.8	−2.04506
$877$	14746.6	0.567797	0.283899	−	0.958854i	$-0.408372\pi$
$877$	14746.6	0.567797	0.283899	+	0.958854i	$0.408372\pi$
$878$	−3715.37	−0.142811
$879$	15596.3	0.598465
$880$	−12942.8	−0.495799
$881$	−42327.7	−1.61868	−0.809340	−	0.587340i	$-0.800175\pi$
$881$	−42327.7	−1.61868	−0.809340	+	0.587340i	$0.800175\pi$
$882$	−279.499	−0.0106703
$883$	−17309.6	−0.659697	−0.329849	−	0.944034i	$-0.606998\pi$
$883$	−17309.6	−0.659697	−0.329849	+	0.944034i	$0.606998\pi$
$884$	0	0
$885$	25171.6	0.956083
$886$	92205.2	3.49627
$887$	−22014.9	−0.833358	−0.416679	−	0.909054i	$-0.636806\pi$
$887$	−22014.9	−0.833358	−0.416679	+	0.909054i	$0.636806\pi$
$888$	−65381.9	−2.47080
$889$	−27701.8	−1.04510
$890$	−44288.1	−1.66802
$891$	3755.86	0.141219
$892$	45001.7	1.68920
$893$	−655.011	−0.0245455
$894$	51715.9	1.93472
$895$	22324.2	0.833760
$896$	20836.2	0.776883
$897$	0	0
$898$	−62054.2	−2.30599
$899$	−14436.9	−0.535593
$900$	6968.80	0.258104
$901$	−40869.1	−1.51115
$902$	22735.7	0.839263
$903$	−367.539	−0.0135448
$904$	61629.7	2.26745
$905$	28121.8	1.03293
$906$	−23416.4	−0.858672
$907$	15198.7	0.556411	0.278206	−	0.960522i	$-0.410260\pi$
$907$	15198.7	0.556411	0.278206	+	0.960522i	$0.410260\pi$
$908$	−38563.3	−1.40944
$909$	4968.63	0.181297
$910$	0	0
$911$	3419.47	0.124360	0.0621801	−	0.998065i	$-0.480195\pi$
$911$	3419.47	0.124360	0.0621801	+	0.998065i	$0.480195\pi$
$912$	−13942.0	−0.506212
$913$	11703.7	0.424247
$914$	6712.58	0.242924
$915$	−30086.7	−1.08703
$916$	20039.3	0.722835
$917$	45088.5	1.62372
$918$	−70108.1	−2.52060
$919$	−11210.7	−0.402400	−0.201200	−	0.979550i	$-0.564484\pi$
$919$	−11210.7	−0.402400	−0.201200	+	0.979550i	$0.564484\pi$
$920$	8368.57	0.299895
$921$	21969.0	0.785996
$922$	−33798.2	−1.20725
$923$	0	0
$924$	−15106.4	−0.537839
$925$	−11099.0	−0.394521
$926$	16380.7	0.581320
$927$	−18390.7	−0.651595
$928$	−20211.7	−0.714960
$929$	21836.7	0.771192	0.385596	−	0.922668i	$-0.373996\pi$
$929$	21836.7	0.771192	0.385596	+	0.922668i	$0.373996\pi$
$930$	30697.7	1.08238
$931$	143.449	0.00504978
$932$	57309.2	2.01419
$933$	−23222.2	−0.814855
$934$	37444.5	1.31180
$935$	9269.68	0.324226
$936$	0	0
$937$	2274.53	0.0793017	0.0396509	−	0.999214i	$-0.487375\pi$
$937$	2274.53	0.0793017	0.0396509	+	0.999214i	$0.487375\pi$
$938$	−22518.4	−0.783851
$939$	5858.80	0.203615
$940$	4130.78	0.143331
$941$	50432.4	1.74713	0.873564	−	0.486709i	$-0.161803\pi$
$941$	50432.4	1.74713	0.873564	+	0.486709i	$0.161803\pi$
$942$	63407.8	2.19314
$943$	−6771.41	−0.233836
$944$	82225.1	2.83496
$945$	−26321.9	−0.906086
$946$	−276.786	−0.00951277
$947$	55095.6	1.89057	0.945283	−	0.326251i	$-0.105785\pi$
$947$	55095.6	1.89057	0.945283	+	0.326251i	$0.105785\pi$
$948$	−47041.1	−1.61163
$949$	0	0
$950$	−5138.09	−0.175475
$951$	9062.97	0.309029
$952$	87291.0	2.97176
$953$	8958.40	0.304503	0.152251	−	0.988342i	$-0.451348\pi$
$953$	8958.40	0.304503	0.152251	+	0.988342i	$0.451348\pi$
$954$	24252.8	0.823076
$955$	−13057.2	−0.442432
$956$	−87404.5	−2.95697
$957$	−4148.30	−0.140121
$958$	−53561.5	−1.80636
$959$	−15928.9	−0.536361
$960$	4591.60	0.154368
$961$	−5420.29	−0.181944
$962$	0	0
$963$	12767.4	0.427232
$964$	29625.0	0.989791
$965$	−27839.4	−0.928685
$966$	6463.37	0.215275
$967$	8945.60	0.297488	0.148744	−	0.988876i	$-0.452477\pi$
$967$	8945.60	0.297488	0.148744	+	0.988876i	$0.452477\pi$
$968$	−6409.73	−0.212827
$969$	9985.28	0.331035
$970$	41732.2	1.38138
$971$	41990.4	1.38778	0.693891	−	0.720080i	$-0.255895\pi$
$971$	41990.4	1.38778	0.693891	+	0.720080i	$0.255895\pi$
$972$	49884.6	1.64614
$973$	−33559.1	−1.10571
$974$	−25047.9	−0.824012
$975$	0	0
$976$	−98280.5	−3.22324
$977$	53089.9	1.73848	0.869241	−	0.494388i	$-0.164608\pi$
$977$	53089.9	1.73848	0.869241	+	0.494388i	$0.164608\pi$
$978$	46122.5	1.50801
$979$	−10102.9	−0.329816
$980$	−904.651	−0.0294878
$981$	20064.7	0.653023
$982$	−7523.47	−0.244484
$983$	17570.8	0.570114	0.285057	−	0.958511i	$-0.407987\pi$
$983$	17570.8	0.570114	0.285057	+	0.958511i	$0.407987\pi$
$984$	−87021.4	−2.81925
$985$	−7557.07	−0.244455
$986$	42544.2	1.37412
$987$	1797.54	0.0579699
$988$	0	0
$989$	82.4356	0.00265045
$990$	−5500.89	−0.176596
$991$	−18584.1	−0.595705	−0.297852	−	0.954612i	$-0.596270\pi$
$991$	−18584.1	−0.595705	−0.297852	+	0.954612i	$0.596270\pi$
$992$	34119.1	1.09202
$993$	−44582.6	−1.42476
$994$	9637.86	0.307540
$995$	11338.2	0.361251
$996$	−79506.8	−2.52939
$997$	3343.63	0.106212	0.0531062	−	0.998589i	$-0.483088\pi$
$997$	3343.63	0.106212	0.0531062	+	0.998589i	$0.483088\pi$
$998$	−25683.4	−0.814624
$999$	−46124.8	−1.46078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.2	yes	39
13.12	even	2		1859.4.a.n.1.38	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.38	✓	39	13.12	even	2
1859.4.a.o.1.2	yes	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-5.13075 q^{2} +4.07791 q^{3} +18.3246 q^{4} +9.39838 q^{5} -20.9227 q^{6} +18.3779 q^{7} -52.9729 q^{8} -10.3707 q^{9} +O(q^{10})\)	\(q-5.13075 q^{2} +4.07791 q^{3} +18.3246 q^{4} +9.39838 q^{5} -20.9227 q^{6} +18.3779 q^{7} -52.9729 q^{8} -10.3707 q^{9} -48.2207 q^{10} -11.0000 q^{11} +74.7260 q^{12} -94.2924 q^{14} +38.3257 q^{15} +125.194 q^{16} -89.6643 q^{17} +53.2093 q^{18} -27.3088 q^{19} +172.221 q^{20} +74.9434 q^{21} +56.4383 q^{22} -16.8091 q^{23} -216.019 q^{24} -36.6705 q^{25} -152.394 q^{27} +336.768 q^{28} +92.4784 q^{29} -196.640 q^{30} -156.111 q^{31} -218.556 q^{32} -44.8570 q^{33} +460.045 q^{34} +172.722 q^{35} -190.038 q^{36} +302.667 q^{37} +140.115 q^{38} -497.860 q^{40} +402.842 q^{41} -384.516 q^{42} -4.90422 q^{43} -201.571 q^{44} -97.4674 q^{45} +86.2433 q^{46} +23.9853 q^{47} +510.530 q^{48} -5.25283 q^{49} +188.147 q^{50} -365.643 q^{51} +455.801 q^{53} +781.896 q^{54} -103.382 q^{55} -973.531 q^{56} -111.363 q^{57} -474.484 q^{58} +656.781 q^{59} +702.303 q^{60} -785.025 q^{61} +800.968 q^{62} -190.591 q^{63} +119.805 q^{64} +230.150 q^{66} +238.815 q^{67} -1643.06 q^{68} -68.5460 q^{69} -886.195 q^{70} -102.212 q^{71} +549.364 q^{72} -709.562 q^{73} -1552.91 q^{74} -149.539 q^{75} -500.424 q^{76} -202.157 q^{77} -629.514 q^{79} +1176.62 q^{80} -341.442 q^{81} -2066.88 q^{82} -1063.98 q^{83} +1373.31 q^{84} -842.698 q^{85} +25.1623 q^{86} +377.118 q^{87} +582.702 q^{88} +918.445 q^{89} +500.081 q^{90} -308.020 q^{92} -636.607 q^{93} -123.063 q^{94} -256.659 q^{95} -891.253 q^{96} -865.441 q^{97} +26.9510 q^{98} +114.077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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