LMFDB - Embedded newform 1859.4.a.q.1.11

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:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-3.69645 q^{2} +1.78714 q^{3} +5.66374 q^{4} +8.08739 q^{5} -6.60608 q^{6} +3.93004 q^{7} +8.63587 q^{8} -23.8061 q^{9} +O(q^{10})$	\(q-3.69645 q^{2} +1.78714 q^{3} +5.66374 q^{4} +8.08739 q^{5} -6.60608 q^{6} +3.93004 q^{7} +8.63587 q^{8} -23.8061 q^{9} -29.8946 q^{10} +11.0000 q^{11} +10.1219 q^{12} -14.5272 q^{14} +14.4533 q^{15} -77.2320 q^{16} +91.3760 q^{17} +87.9981 q^{18} +133.273 q^{19} +45.8049 q^{20} +7.02353 q^{21} -40.6609 q^{22} +102.296 q^{23} +15.4335 q^{24} -59.5941 q^{25} -90.7977 q^{27} +22.2587 q^{28} +242.556 q^{29} -53.4259 q^{30} -168.362 q^{31} +216.397 q^{32} +19.6586 q^{33} -337.767 q^{34} +31.7838 q^{35} -134.832 q^{36} -80.8938 q^{37} -492.638 q^{38} +69.8416 q^{40} -466.724 q^{41} -25.9621 q^{42} +272.122 q^{43} +62.3011 q^{44} -192.529 q^{45} -378.133 q^{46} +161.979 q^{47} -138.024 q^{48} -327.555 q^{49} +220.287 q^{50} +163.302 q^{51} +542.455 q^{53} +335.629 q^{54} +88.9613 q^{55} +33.9393 q^{56} +238.178 q^{57} -896.597 q^{58} -133.553 q^{59} +81.8598 q^{60} +797.554 q^{61} +622.341 q^{62} -93.5590 q^{63} -182.045 q^{64} -72.6668 q^{66} -41.0714 q^{67} +517.530 q^{68} +182.818 q^{69} -117.487 q^{70} +1011.56 q^{71} -205.587 q^{72} -360.066 q^{73} +299.020 q^{74} -106.503 q^{75} +754.826 q^{76} +43.2304 q^{77} -916.538 q^{79} -624.605 q^{80} +480.497 q^{81} +1725.22 q^{82} +1439.65 q^{83} +39.7795 q^{84} +738.993 q^{85} -1005.88 q^{86} +433.482 q^{87} +94.9946 q^{88} -1317.83 q^{89} +711.675 q^{90} +579.380 q^{92} -300.886 q^{93} -598.747 q^{94} +1077.83 q^{95} +386.732 q^{96} -1063.97 q^{97} +1210.79 q^{98} -261.867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * 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 $

$2$	−3.69645	−1.30689	−0.653446	−	0.756973i	$-0.726677\pi$
$2$	−3.69645	−1.30689	−0.653446	+	0.756973i	$0.726677\pi$
$3$	1.78714	0.343935	0.171968	−	0.985103i	$-0.444988\pi$
$3$	1.78714	0.343935	0.171968	+	0.985103i	$0.444988\pi$
$4$	5.66374	0.707967
$5$	8.08739	0.723358	0.361679	−	0.932303i	$-0.382204\pi$
$5$	8.08739	0.723358	0.361679	+	0.932303i	$0.382204\pi$
$6$	−6.60608	−0.449487
$7$	3.93004	0.212202	0.106101	−	0.994355i	$-0.466163\pi$
$7$	3.93004	0.212202	0.106101	+	0.994355i	$0.466163\pi$
$8$	8.63587	0.381655
$9$	−23.8061	−0.881708
$10$	−29.8946	−0.945351
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	10.1219	0.243495
$13$	0	0
$13$	0	0
$14$	−14.5272	−0.277325
$15$	14.4533	0.248789
$16$	−77.2320	−1.20675
$17$	91.3760	1.30364	0.651822	−	0.758372i	$-0.274005\pi$
$17$	91.3760	1.30364	0.651822	+	0.758372i	$0.274005\pi$
$18$	87.9981	1.15230
$19$	133.273	1.60921	0.804606	−	0.593810i	$-0.202377\pi$
$19$	133.273	1.60921	0.804606	+	0.593810i	$0.202377\pi$
$20$	45.8049	0.512114
$21$	7.02353	0.0729838
$22$	−40.6609	−0.394043
$23$	102.296	0.927402	0.463701	−	0.885992i	$-0.346521\pi$
$23$	102.296	0.927402	0.463701	+	0.885992i	$0.346521\pi$
$24$	15.4335	0.131265
$25$	−59.5941	−0.476753
$26$	0	0
$27$	−90.7977	−0.647186
$28$	22.2587	0.150232
$29$	242.556	1.55316	0.776579	−	0.630020i	$-0.216953\pi$
$29$	242.556	1.55316	0.776579	+	0.630020i	$0.216953\pi$
$30$	−53.4259	−0.325140
$31$	−168.362	−0.975441	−0.487721	−	0.873000i	$-0.662172\pi$
$31$	−168.362	−0.975441	−0.487721	+	0.873000i	$0.662172\pi$
$32$	216.397	1.19544
$33$	19.6586	0.103700
$34$	−337.767	−1.70372
$35$	31.7838	0.153498
$36$	−134.832	−0.624221
$37$	−80.8938	−0.359428	−0.179714	−	0.983719i	$-0.557517\pi$
$37$	−80.8938	−0.359428	−0.179714	+	0.983719i	$0.557517\pi$
$38$	−492.638	−2.10307
$39$	0	0
$40$	69.8416	0.276073
$41$	−466.724	−1.77781	−0.888904	−	0.458094i	$-0.848532\pi$
$41$	−466.724	−1.77781	−0.888904	+	0.458094i	$0.848532\pi$
$42$	−25.9621	−0.0953820
$43$	272.122	0.965074	0.482537	−	0.875876i	$-0.339715\pi$
$43$	272.122	0.965074	0.482537	+	0.875876i	$0.339715\pi$
$44$	62.3011	0.213460
$45$	−192.529	−0.637791
$46$	−378.133	−1.21202
$47$	161.979	0.502704	0.251352	−	0.967896i	$-0.419125\pi$
$47$	161.979	0.502704	0.251352	+	0.967896i	$0.419125\pi$
$48$	−138.024	−0.415044
$49$	−327.555	−0.954970
$50$	220.287	0.623065
$51$	163.302	0.448369
$52$	0	0
$53$	542.455	1.40589	0.702943	−	0.711246i	$-0.251869\pi$
$53$	542.455	1.40589	0.702943	+	0.711246i	$0.251869\pi$
$54$	335.629	0.845803
$55$	88.9613	0.218101
$56$	33.9393	0.0809880
$57$	238.178	0.553465
$58$	−896.597	−2.02981
$59$	−133.553	−0.294697	−0.147348	−	0.989085i	$-0.547074\pi$
$59$	−133.553	−0.294697	−0.147348	+	0.989085i	$0.547074\pi$
$60$	81.8598	0.176134
$61$	797.554	1.67404	0.837019	−	0.547174i	$-0.184296\pi$
$61$	797.554	1.67404	0.837019	+	0.547174i	$0.184296\pi$
$62$	622.341	1.27480
$63$	−93.5590	−0.187100
$64$	−182.045	−0.355557
$65$	0	0
$66$	−72.6668	−0.135525
$67$	−41.0714	−0.0748905	−0.0374453	−	0.999299i	$-0.511922\pi$
$67$	−41.0714	−0.0748905	−0.0374453	+	0.999299i	$0.511922\pi$
$68$	517.530	0.922937
$69$	182.818	0.318967
$70$	−117.487	−0.200606
$71$	1011.56	1.69085	0.845424	−	0.534096i	$-0.179348\pi$
$71$	1011.56	1.69085	0.845424	+	0.534096i	$0.179348\pi$
$72$	−205.587	−0.336509
$73$	−360.066	−0.577296	−0.288648	−	0.957435i	$-0.593206\pi$
$73$	−360.066	−0.577296	−0.288648	+	0.957435i	$0.593206\pi$
$74$	299.020	0.469734
$75$	−106.503	−0.163972
$76$	754.826	1.13927
$77$	43.2304	0.0639814
$78$	0	0
$79$	−916.538	−1.30530	−0.652649	−	0.757660i	$-0.726342\pi$
$79$	−916.538	−1.30530	−0.652649	+	0.757660i	$0.726342\pi$
$80$	−624.605	−0.872912
$81$	480.497	0.659118
$82$	1725.22	2.32340
$83$	1439.65	1.90388	0.951940	−	0.306284i	$-0.0990859\pi$
$83$	1439.65	1.90388	0.951940	+	0.306284i	$0.0990859\pi$
$84$	39.7795	0.0516702
$85$	738.993	0.943001
$86$	−1005.88	−1.26125
$87$	433.482	0.534186
$88$	94.9946	0.115073
$89$	−1317.83	−1.56955	−0.784775	−	0.619780i	$-0.787222\pi$
$89$	−1317.83	−1.56955	−0.784775	+	0.619780i	$0.787222\pi$
$90$	711.675	0.833524
$91$	0	0
$92$	579.380	0.656571
$93$	−300.886	−0.335489
$94$	−598.747	−0.656980
$95$	1077.83	1.16404
$96$	386.732	0.411153
$97$	−1063.97	−1.11371	−0.556856	−	0.830609i	$-0.687992\pi$
$97$	−1063.97	−1.11371	−0.556856	+	0.830609i	$0.687992\pi$
$98$	1210.79	1.24804
$99$	−261.867	−0.265845
$100$	−337.526	−0.337526
$101$	−1347.65	−1.32769	−0.663843	−	0.747872i	$-0.731076\pi$
$101$	−1347.65	−1.32769	−0.663843	+	0.747872i	$0.731076\pi$
$102$	−603.637	−0.585970
$103$	−878.304	−0.840212	−0.420106	−	0.907475i	$-0.638007\pi$
$103$	−878.304	−0.840212	−0.420106	+	0.907475i	$0.638007\pi$
$104$	0	0
$105$	56.8021	0.0527935
$106$	−2005.16	−1.83734
$107$	172.025	0.155423	0.0777116	−	0.996976i	$-0.475239\pi$
$107$	172.025	0.155423	0.0777116	+	0.996976i	$0.475239\pi$
$108$	−514.255	−0.458187
$109$	1137.49	0.999554	0.499777	−	0.866154i	$-0.333415\pi$
$109$	1137.49	0.999554	0.499777	+	0.866154i	$0.333415\pi$
$110$	−328.841	−0.285034
$111$	−144.569	−0.123620
$112$	−303.525	−0.256075
$113$	1991.83	1.65819	0.829097	−	0.559105i	$-0.188855\pi$
$113$	1991.83	1.65819	0.829097	+	0.559105i	$0.188855\pi$
$114$	−880.414	−0.723319
$115$	827.310	0.670844
$116$	1373.78	1.09958
$117$	0	0
$118$	493.672	0.385137
$119$	359.111	0.276636
$120$	124.817	0.0949514
$121$	121.000	0.0909091
$122$	−2948.12	−2.18779
$123$	−834.102	−0.611451
$124$	−953.557	−0.690581
$125$	−1492.88	−1.06822
$126$	345.836	0.244520
$127$	681.565	0.476213	0.238107	−	0.971239i	$-0.423473\pi$
$127$	681.565	0.476213	0.238107	+	0.971239i	$0.423473\pi$
$128$	−1058.26	−0.730762
$129$	486.320	0.331923
$130$	0	0
$131$	2225.67	1.48441	0.742205	−	0.670173i	$-0.233780\pi$
$131$	2225.67	1.48441	0.742205	+	0.670173i	$0.233780\pi$
$132$	111.341	0.0734165
$133$	523.770	0.341478
$134$	151.818	0.0978738
$135$	−734.317	−0.468147
$136$	789.111	0.497542
$137$	566.142	0.353057	0.176528	−	0.984296i	$-0.443513\pi$
$137$	566.142	0.353057	0.176528	+	0.984296i	$0.443513\pi$
$138$	−675.777	−0.416855
$139$	−1333.75	−0.813863	−0.406931	−	0.913459i	$-0.633401\pi$
$139$	−1333.75	−0.813863	−0.406931	+	0.913459i	$0.633401\pi$
$140$	180.015	0.108672
$141$	289.479	0.172898
$142$	−3739.18	−2.20976
$143$	0	0
$144$	1838.59	1.06400
$145$	1961.65	1.12349
$146$	1330.97	0.754463
$147$	−585.387	−0.328448
$148$	−458.161	−0.254464
$149$	−2274.29	−1.25045	−0.625226	−	0.780444i	$-0.714993\pi$
$149$	−2274.29	−1.25045	−0.625226	+	0.780444i	$0.714993\pi$
$150$	393.683	0.214294
$151$	−1547.28	−0.833878	−0.416939	−	0.908934i	$-0.636897\pi$
$151$	−1547.28	−0.833878	−0.416939	+	0.908934i	$0.636897\pi$
$152$	1150.93	0.614164
$153$	−2175.31	−1.14943
$154$	−159.799	−0.0836167
$155$	−1361.61	−0.705593
$156$	0	0
$157$	−191.231	−0.0972093	−0.0486047	−	0.998818i	$-0.515477\pi$
$157$	−191.231	−0.0972093	−0.0486047	+	0.998818i	$0.515477\pi$
$158$	3387.94	1.70588
$159$	969.444	0.483534
$160$	1750.09	0.864729
$161$	402.029	0.196797
$162$	−1776.13	−0.861396
$163$	−849.338	−0.408131	−0.204065	−	0.978957i	$-0.565415\pi$
$163$	−849.338	−0.408131	−0.204065	+	0.978957i	$0.565415\pi$
$164$	−2643.41	−1.25863
$165$	158.986	0.0750126
$166$	−5321.59	−2.48817
$167$	−84.3101	−0.0390665	−0.0195333	−	0.999809i	$-0.506218\pi$
$167$	−84.3101	−0.0390665	−0.0195333	+	0.999809i	$0.506218\pi$
$168$	60.6543	0.0278547
$169$	0	0
$170$	−2731.65	−1.23240
$171$	−3172.72	−1.41886
$172$	1541.23	0.683241
$173$	−127.660	−0.0561029	−0.0280514	−	0.999606i	$-0.508930\pi$
$173$	−127.660	−0.0561029	−0.0280514	+	0.999606i	$0.508930\pi$
$174$	−1602.34	−0.698123
$175$	−234.207	−0.101168
$176$	−849.552	−0.363849
$177$	−238.678	−0.101357
$178$	4871.30	2.05123
$179$	−48.1158	−0.0200913	−0.0100457	−	0.999950i	$-0.503198\pi$
$179$	−48.1158	−0.0200913	−0.0100457	+	0.999950i	$0.503198\pi$
$180$	−1090.44	−0.451535
$181$	−780.026	−0.320325	−0.160163	−	0.987091i	$-0.551202\pi$
$181$	−780.026	−0.320325	−0.160163	+	0.987091i	$0.551202\pi$
$182$	0	0
$183$	1425.34	0.575761
$184$	883.418	0.353948
$185$	−654.219	−0.259996
$186$	1112.21	0.438448
$187$	1005.14	0.393063
$188$	917.407	0.355898
$189$	−356.839	−0.137334
$190$	−3984.16	−1.52127
$191$	551.713	0.209008	0.104504	−	0.994524i	$-0.466674\pi$
$191$	551.713	0.209008	0.104504	+	0.994524i	$0.466674\pi$
$192$	−325.341	−0.122289
$193$	4071.21	1.51840	0.759201	−	0.650856i	$-0.225590\pi$
$193$	4071.21	1.51840	0.759201	+	0.650856i	$0.225590\pi$
$194$	3932.92	1.45550
$195$	0	0
$196$	−1855.18	−0.676088
$197$	−2918.86	−1.05563	−0.527817	−	0.849358i	$-0.676989\pi$
$197$	−2918.86	−1.05563	−0.527817	+	0.849358i	$0.676989\pi$
$198$	967.980	0.347431
$199$	−1713.15	−0.610261	−0.305131	−	0.952310i	$-0.598700\pi$
$199$	−1713.15	−0.610261	−0.305131	+	0.952310i	$0.598700\pi$
$200$	−514.647	−0.181955
$201$	−73.4003	−0.0257575
$202$	4981.52	1.73514
$203$	953.255	0.329583
$204$	924.899	0.317431
$205$	−3774.58	−1.28599
$206$	3246.61	1.09807
$207$	−2435.28	−0.817699
$208$	0	0
$209$	1466.01	0.485195
$210$	−209.966	−0.0689954
$211$	−1246.06	−0.406552	−0.203276	−	0.979121i	$-0.565159\pi$
$211$	−1246.06	−0.406552	−0.203276	+	0.979121i	$0.565159\pi$
$212$	3072.33	0.995322
$213$	1807.80	0.581542
$214$	−635.881	−0.203121
$215$	2200.76	0.698094
$216$	−784.117	−0.247002
$217$	−661.668	−0.206991
$218$	−4204.66	−1.30631
$219$	−643.489	−0.198552
$220$	503.854	0.154408
$221$	0	0
$222$	534.390	0.161558
$223$	5148.09	1.54593	0.772963	−	0.634451i	$-0.218774\pi$
$223$	5148.09	1.54593	0.772963	+	0.634451i	$0.218774\pi$
$224$	850.449	0.253674
$225$	1418.71	0.420357
$226$	−7362.71	−2.16708
$227$	3585.49	1.04836	0.524179	−	0.851608i	$-0.324372\pi$
$227$	3585.49	1.04836	0.524179	+	0.851608i	$0.324372\pi$
$228$	1348.98	0.391835
$229$	−2964.18	−0.855363	−0.427682	−	0.903929i	$-0.640670\pi$
$229$	−2964.18	−0.855363	−0.427682	+	0.903929i	$0.640670\pi$
$230$	−3058.11	−0.876721
$231$	77.2589	0.0220055
$232$	2094.68	0.592770
$233$	4612.26	1.29682	0.648411	−	0.761291i	$-0.275434\pi$
$233$	4612.26	1.29682	0.648411	+	0.761291i	$0.275434\pi$
$234$	0	0
$235$	1309.99	0.363635
$236$	−756.409	−0.208636
$237$	−1637.98	−0.448938
$238$	−1327.44	−0.361533
$239$	−1232.20	−0.333491	−0.166746	−	0.986000i	$-0.553326\pi$
$239$	−1232.20	−0.333491	−0.166746	+	0.986000i	$0.553326\pi$
$240$	−1116.26	−0.300225
$241$	2241.15	0.599025	0.299513	−	0.954092i	$-0.403176\pi$
$241$	2241.15	0.599025	0.299513	+	0.954092i	$0.403176\pi$
$242$	−447.270	−0.118808
$243$	3310.25	0.873880
$244$	4517.14	1.18516
$245$	−2649.06	−0.690786
$246$	3083.22	0.799101
$247$	0	0
$248$	−1453.95	−0.372282
$249$	2572.86	0.654812
$250$	5518.37	1.39605
$251$	−208.397	−0.0524061	−0.0262030	−	0.999657i	$-0.508342\pi$
$251$	−208.397	−0.0524061	−0.0262030	+	0.999657i	$0.508342\pi$
$252$	−529.894	−0.132461
$253$	1125.26	0.279622
$254$	−2519.37	−0.622359
$255$	1320.69	0.324332
$256$	5368.15	1.31058
$257$	2255.31	0.547403	0.273702	−	0.961815i	$-0.411752\pi$
$257$	2255.31	0.547403	0.273702	+	0.961815i	$0.411752\pi$
$258$	−1797.66	−0.433788
$259$	−317.916	−0.0762715
$260$	0	0
$261$	−5774.32	−1.36943
$262$	−8227.08	−1.93996
$263$	4262.91	0.999477	0.499739	−	0.866176i	$-0.333429\pi$
$263$	4262.91	0.999477	0.499739	+	0.866176i	$0.333429\pi$
$264$	169.769	0.0395778
$265$	4387.05	1.01696
$266$	−1936.09	−0.446275
$267$	−2355.15	−0.539824
$268$	−232.617	−0.0530201
$269$	7082.90	1.60540	0.802699	−	0.596384i	$-0.203397\pi$
$269$	7082.90	1.60540	0.802699	+	0.596384i	$0.203397\pi$
$270$	2714.36	0.611818
$271$	66.0511	0.0148056	0.00740280	−	0.999973i	$-0.497644\pi$
$271$	66.0511	0.0148056	0.00740280	+	0.999973i	$0.497644\pi$
$272$	−7057.15	−1.57317
$273$	0	0
$274$	−2092.71	−0.461407
$275$	−655.535	−0.143746
$276$	1035.43	0.225818
$277$	−3143.52	−0.681861	−0.340931	−	0.940088i	$-0.610742\pi$
$277$	−3143.52	−0.681861	−0.340931	+	0.940088i	$0.610742\pi$
$278$	4930.13	1.06363
$279$	4008.04	0.860055
$280$	274.480	0.0585834
$281$	−8204.64	−1.74181	−0.870904	−	0.491454i	$-0.836466\pi$
$281$	−8204.64	−1.74181	−0.870904	+	0.491454i	$0.836466\pi$
$282$	−1070.05	−0.225959
$283$	539.452	0.113311	0.0566557	−	0.998394i	$-0.481956\pi$
$283$	539.452	0.113311	0.0566557	+	0.998394i	$0.481956\pi$
$284$	5729.22	1.19707
$285$	1926.24	0.400353
$286$	0	0
$287$	−1834.24	−0.377255
$288$	−5151.58	−1.05403
$289$	3436.58	0.699486
$290$	−7251.13	−1.46828
$291$	−1901.47	−0.383045
$292$	−2039.32	−0.408707
$293$	−5913.10	−1.17900	−0.589500	−	0.807769i	$-0.700675\pi$
$293$	−5913.10	−1.17900	−0.589500	+	0.807769i	$0.700675\pi$
$294$	2163.85	0.429246
$295$	−1080.10	−0.213171
$296$	−698.588	−0.137178
$297$	−998.775	−0.195134
$298$	8406.81	1.63421
$299$	0	0
$300$	−603.206	−0.116087
$301$	1069.45	0.204791
$302$	5719.43	1.08979
$303$	−2408.44	−0.456638
$304$	−10293.0	−1.94192
$305$	6450.13	1.21093
$306$	8040.92	1.50219
$307$	868.481	0.161455	0.0807277	−	0.996736i	$-0.474276\pi$
$307$	868.481	0.161455	0.0807277	+	0.996736i	$0.474276\pi$
$308$	244.846	0.0452967
$309$	−1569.65	−0.288979
$310$	5033.11	0.922134
$311$	3977.40	0.725201	0.362601	−	0.931945i	$-0.381889\pi$
$311$	3977.40	0.725201	0.362601	+	0.931945i	$0.381889\pi$
$312$	0	0
$313$	1614.34	0.291527	0.145763	−	0.989319i	$-0.453436\pi$
$313$	1614.34	0.291527	0.145763	+	0.989319i	$0.453436\pi$
$314$	706.874	0.127042
$315$	−756.648	−0.135341
$316$	−5191.03	−0.924109
$317$	−3030.42	−0.536925	−0.268462	−	0.963290i	$-0.586516\pi$
$317$	−3030.42	−0.536925	−0.268462	+	0.963290i	$0.586516\pi$
$318$	−3583.50	−0.631927
$319$	2668.12	0.468295
$320$	−1472.27	−0.257195
$321$	307.433	0.0534555
$322$	−1486.08	−0.257192
$323$	12178.0	2.09784
$324$	2721.41	0.466634
$325$	0	0
$326$	3139.53	0.533383
$327$	2032.85	0.343782
$328$	−4030.57	−0.678509
$329$	636.584	0.106675
$330$	−587.685	−0.0980333
$331$	−1187.19	−0.197142	−0.0985709	−	0.995130i	$-0.531427\pi$
$331$	−1187.19	−0.197142	−0.0985709	+	0.995130i	$0.531427\pi$
$332$	8153.80	1.34789
$333$	1925.77	0.316911
$334$	311.648	0.0510557
$335$	−332.160	−0.0541727
$336$	−542.441	−0.0880732
$337$	4277.59	0.691439	0.345720	−	0.938338i	$-0.387635\pi$
$337$	4277.59	0.691439	0.345720	+	0.938338i	$0.387635\pi$
$338$	0	0
$339$	3559.69	0.570312
$340$	4185.47	0.667614
$341$	−1851.98	−0.294107
$342$	11727.8	1.85429
$343$	−2635.31	−0.414849
$344$	2350.01	0.368326
$345$	1478.52	0.230727
$346$	471.888	0.0733204
$347$	−6577.97	−1.01765	−0.508824	−	0.860871i	$-0.669920\pi$
$347$	−6577.97	−1.01765	−0.508824	+	0.860871i	$0.669920\pi$
$348$	2455.13	0.378186
$349$	4377.20	0.671365	0.335682	−	0.941975i	$-0.391033\pi$
$349$	4377.20	0.671365	0.335682	+	0.941975i	$0.391033\pi$
$350$	865.735	0.132216
$351$	0	0
$352$	2380.37	0.360438
$353$	−4699.39	−0.708565	−0.354282	−	0.935138i	$-0.615275\pi$
$353$	−4699.39	−0.708565	−0.354282	+	0.935138i	$0.615275\pi$
$354$	882.261	0.132462
$355$	8180.89	1.22309
$356$	−7463.86	−1.11119
$357$	641.782	0.0951449
$358$	177.858	0.0262572
$359$	7883.06	1.15892	0.579459	−	0.815001i	$-0.303264\pi$
$359$	7883.06	1.15892	0.579459	+	0.815001i	$0.303264\pi$
$360$	−1662.66	−0.243416
$361$	10902.8	1.58956
$362$	2883.33	0.418631
$363$	216.244	0.0312669
$364$	0	0
$365$	−2912.00	−0.417592
$366$	−5268.70	−0.752458
$367$	6974.17	0.991958	0.495979	−	0.868334i	$-0.334809\pi$
$367$	6974.17	0.991958	0.495979	+	0.868334i	$0.334809\pi$
$368$	−7900.55	−1.11914
$369$	11110.9	1.56751
$370$	2418.29	0.339786
$371$	2131.87	0.298332
$372$	−1704.14	−0.237515
$373$	8432.72	1.17059	0.585294	−	0.810821i	$-0.300979\pi$
$373$	8432.72	1.17059	0.585294	+	0.810821i	$0.300979\pi$
$374$	−3715.44	−0.513691
$375$	−2668.00	−0.367399
$376$	1398.83	0.191859
$377$	0	0
$378$	1319.04	0.179481
$379$	7675.14	1.04023	0.520113	−	0.854097i	$-0.325890\pi$
$379$	7675.14	1.04023	0.520113	+	0.854097i	$0.325890\pi$
$380$	6104.57	0.824100
$381$	1218.05	0.163787
$382$	−2039.38	−0.273151
$383$	11494.6	1.53354	0.766769	−	0.641924i	$-0.221863\pi$
$383$	11494.6	1.53354	0.766769	+	0.641924i	$0.221863\pi$
$384$	−1891.25	−0.251335
$385$	349.621	0.0462814
$386$	−15049.0	−1.98439
$387$	−6478.17	−0.850914
$388$	−6026.06	−0.788472
$389$	−2911.60	−0.379496	−0.189748	−	0.981833i	$-0.560767\pi$
$389$	−2911.60	−0.379496	−0.189748	+	0.981833i	$0.560767\pi$
$390$	0	0
$391$	9347.43	1.20900
$392$	−2828.72	−0.364469
$393$	3977.59	0.510541
$394$	10789.4	1.37960
$395$	−7412.40	−0.944198
$396$	−1483.15	−0.188210
$397$	5375.40	0.679555	0.339778	−	0.940506i	$-0.389648\pi$
$397$	5375.40	0.679555	0.339778	+	0.940506i	$0.389648\pi$
$398$	6332.57	0.797546
$399$	936.050	0.117446
$400$	4602.57	0.575321
$401$	10359.5	1.29009	0.645046	−	0.764144i	$-0.276838\pi$
$401$	10359.5	1.29009	0.645046	+	0.764144i	$0.276838\pi$
$402$	271.321	0.0336623
$403$	0	0
$404$	−7632.74	−0.939958
$405$	3885.97	0.476778
$406$	−3523.66	−0.430730
$407$	−889.831	−0.108372
$408$	1410.25	0.171122
$409$	6971.07	0.842781	0.421391	−	0.906879i	$-0.361542\pi$
$409$	6971.07	0.842781	0.421391	+	0.906879i	$0.361542\pi$
$410$	13952.6	1.68065
$411$	1011.78	0.121429
$412$	−4974.49	−0.594843
$413$	−524.868	−0.0625353
$414$	9001.89	1.06864
$415$	11643.0	1.37719
$416$	0	0
$417$	−2383.59	−0.279916
$418$	−5419.02	−0.634098
$419$	7077.26	0.825171	0.412585	−	0.910919i	$-0.364626\pi$
$419$	7077.26	0.825171	0.412585	+	0.910919i	$0.364626\pi$
$420$	321.712	0.0373760
$421$	−6505.96	−0.753162	−0.376581	−	0.926384i	$-0.622900\pi$
$421$	−6505.96	−0.753162	−0.376581	+	0.926384i	$0.622900\pi$
$422$	4606.00	0.531319
$423$	−3856.09	−0.443238
$424$	4684.57	0.536564
$425$	−5445.47	−0.621516
$426$	−6682.45	−0.760013
$427$	3134.42	0.355235
$428$	974.304	0.110035
$429$	0	0
$430$	−8134.98	−0.912334
$431$	−13358.6	−1.49295	−0.746476	−	0.665412i	$-0.768256\pi$
$431$	−13358.6	−1.49295	−0.746476	+	0.665412i	$0.768256\pi$
$432$	7012.49	0.780992
$433$	16278.9	1.80673	0.903364	−	0.428874i	$-0.141090\pi$
$433$	16278.9	1.80673	0.903364	+	0.428874i	$0.141090\pi$
$434$	2445.82	0.270515
$435$	3505.74	0.386408
$436$	6442.42	0.707652
$437$	13633.4	1.49239
$438$	2378.63	0.259487
$439$	−13910.3	−1.51231	−0.756154	−	0.654393i	$-0.772924\pi$
$439$	−13910.3	−1.51231	−0.756154	+	0.654393i	$0.772924\pi$
$440$	768.258	0.0832392
$441$	7797.81	0.842005
$442$	0	0
$443$	−5092.06	−0.546119	−0.273060	−	0.961997i	$-0.588036\pi$
$443$	−5092.06	−0.546119	−0.273060	+	0.961997i	$0.588036\pi$
$444$	−818.799	−0.0875191
$445$	−10657.8	−1.13535
$446$	−19029.6	−2.02036
$447$	−4064.48	−0.430075
$448$	−715.445	−0.0754500
$449$	−17384.3	−1.82721	−0.913604	−	0.406606i	$-0.866712\pi$
$449$	−17384.3	−1.82721	−0.913604	+	0.406606i	$0.866712\pi$
$450$	−5244.17	−0.549361
$451$	−5133.97	−0.536029
$452$	11281.2	1.17395
$453$	−2765.20	−0.286800
$454$	−13253.6	−1.37009
$455$	0	0
$456$	2056.88	0.211233
$457$	11894.4	1.21750	0.608749	−	0.793363i	$-0.291671\pi$
$457$	11894.4	1.21750	0.608749	+	0.793363i	$0.291671\pi$
$458$	10956.9	1.11787
$459$	−8296.73	−0.843700
$460$	4685.67	0.474936
$461$	4566.95	0.461397	0.230699	−	0.973025i	$-0.425899\pi$
$461$	4566.95	0.461397	0.230699	+	0.973025i	$0.425899\pi$
$462$	−285.584	−0.0287588
$463$	−1613.59	−0.161965	−0.0809824	−	0.996716i	$-0.525806\pi$
$463$	−1613.59	−0.161965	−0.0809824	+	0.996716i	$0.525806\pi$
$464$	−18733.1	−1.87427
$465$	−2433.38	−0.242679
$466$	−17049.0	−1.69481
$467$	14921.8	1.47858	0.739290	−	0.673387i	$-0.235161\pi$
$467$	14921.8	1.47858	0.739290	+	0.673387i	$0.235161\pi$
$468$	0	0
$469$	−161.412	−0.0158919
$470$	−4842.30	−0.475232
$471$	−341.756	−0.0334337
$472$	−1153.35	−0.112473
$473$	2993.34	0.290981
$474$	6054.72	0.586714
$475$	−7942.31	−0.767196
$476$	2033.91	0.195849
$477$	−12913.8	−1.23958
$478$	4554.77	0.435837
$479$	11969.3	1.14173	0.570867	−	0.821043i	$-0.306607\pi$
$479$	11969.3	1.14173	0.570867	+	0.821043i	$0.306607\pi$
$480$	3127.65	0.297411
$481$	0	0
$482$	−8284.29	−0.782861
$483$	718.482	0.0676854
$484$	685.312	0.0643607
$485$	−8604.76	−0.805612
$486$	−12236.2	−1.14207
$487$	8999.25	0.837361	0.418681	−	0.908134i	$-0.362493\pi$
$487$	8999.25	0.837361	0.418681	+	0.908134i	$0.362493\pi$
$488$	6887.57	0.638905
$489$	−1517.89	−0.140371
$490$	9792.13	0.902782
$491$	21069.6	1.93657	0.968285	−	0.249849i	$-0.0803810\pi$
$491$	21069.6	1.93657	0.968285	+	0.249849i	$0.0803810\pi$
$492$	−4724.14	−0.432887
$493$	22163.8	2.02476
$494$	0	0
$495$	−2117.82	−0.192301
$496$	13002.9	1.17711
$497$	3975.47	0.358802
$498$	−9510.43	−0.855769
$499$	1663.20	0.149208	0.0746042	−	0.997213i	$-0.476231\pi$
$499$	1663.20	0.149208	0.0746042	+	0.997213i	$0.476231\pi$
$500$	−8455.31	−0.756266
$501$	−150.674	−0.0134364
$502$	770.331	0.0684891
$503$	22319.4	1.97847	0.989237	−	0.146322i	$-0.0467437\pi$
$503$	22319.4	1.97847	0.989237	+	0.146322i	$0.0467437\pi$
$504$	−807.963	−0.0714078
$505$	−10899.0	−0.960392
$506$	−4159.47	−0.365436
$507$	0	0
$508$	3860.20	0.337143
$509$	774.081	0.0674078	0.0337039	−	0.999432i	$-0.489270\pi$
$509$	774.081	0.0674078	0.0337039	+	0.999432i	$0.489270\pi$
$510$	−4881.85	−0.423866
$511$	−1415.07	−0.122503
$512$	−11377.1	−0.982030
$513$	−12100.9	−1.04146
$514$	−8336.65	−0.715397
$515$	−7103.19	−0.607775
$516$	2754.39	0.234991
$517$	1781.77	0.151571
$518$	1175.16	0.0996786
$519$	−228.146	−0.0192958
$520$	0	0
$521$	10497.7	0.882746	0.441373	−	0.897324i	$-0.354492\pi$
$521$	10497.7	0.882746	0.441373	+	0.897324i	$0.354492\pi$
$522$	21344.5	1.78970
$523$	−384.791	−0.0321716	−0.0160858	−	0.999871i	$-0.505120\pi$
$523$	−384.791	−0.0321716	−0.0160858	+	0.999871i	$0.505120\pi$
$524$	12605.6	1.05091
$525$	−418.561	−0.0347953
$526$	−15757.6	−1.30621
$527$	−15384.2	−1.27163
$528$	−1518.27	−0.125140
$529$	−1702.46	−0.139925
$530$	−16216.5	−1.32906
$531$	3179.38	0.259837
$532$	2966.49	0.241755
$533$	0	0
$534$	8705.71	0.705492
$535$	1391.23	0.112427
$536$	−354.687	−0.0285824
$537$	−85.9898	−0.00691012
$538$	−26181.6	−2.09808
$539$	−3603.10	−0.287934
$540$	−4158.98	−0.331433
$541$	20219.9	1.60688	0.803438	−	0.595389i	$-0.203002\pi$
$541$	20219.9	1.60688	0.803438	+	0.595389i	$0.203002\pi$
$542$	−244.155	−0.0193493
$543$	−1394.02	−0.110171
$544$	19773.5	1.55842
$545$	9199.29	0.723035
$546$	0	0
$547$	12116.4	0.947095	0.473547	−	0.880768i	$-0.342973\pi$
$547$	12116.4	0.947095	0.473547	+	0.880768i	$0.342973\pi$
$548$	3206.48	0.249953
$549$	−18986.7	−1.47601
$550$	2423.15	0.187861
$551$	32326.3	2.49936
$552$	1578.79	0.121735
$553$	−3602.03	−0.276987
$554$	11619.9	0.891119
$555$	−1169.18	−0.0894217
$556$	−7553.99	−0.576188
$557$	−1640.42	−0.124788	−0.0623940	−	0.998052i	$-0.519874\pi$
$557$	−1640.42	−0.124788	−0.0623940	+	0.998052i	$0.519874\pi$
$558$	−14815.5	−1.12400
$559$	0	0
$560$	−2454.72	−0.185234
$561$	1796.32	0.135188
$562$	30328.0	2.27635
$563$	4503.47	0.337120	0.168560	−	0.985691i	$-0.446088\pi$
$563$	4503.47	0.337120	0.168560	+	0.985691i	$0.446088\pi$
$564$	1639.54	0.122406
$565$	16108.7	1.19947
$566$	−1994.06	−0.148086
$567$	1888.37	0.139866
$568$	8735.71	0.645321
$569$	−6117.64	−0.450729	−0.225365	−	0.974274i	$-0.572357\pi$
$569$	−6117.64	−0.450729	−0.225365	+	0.974274i	$0.572357\pi$
$570$	−7120.25	−0.523219
$571$	−12352.9	−0.905350	−0.452675	−	0.891676i	$-0.649530\pi$
$571$	−12352.9	−0.905350	−0.452675	+	0.891676i	$0.649530\pi$
$572$	0	0
$573$	985.988	0.0718853
$574$	6780.19	0.493031
$575$	−6096.26	−0.442142
$576$	4333.79	0.313498
$577$	5007.93	0.361322	0.180661	−	0.983545i	$-0.442176\pi$
$577$	5007.93	0.361322	0.180661	+	0.983545i	$0.442176\pi$
$578$	−12703.1	−0.914153
$579$	7275.82	0.522233
$580$	11110.3	0.795394
$581$	5657.88	0.404007
$582$	7028.68	0.500598
$583$	5967.01	0.423891
$584$	−3109.49	−0.220328
$585$	0	0
$586$	21857.5	1.54083
$587$	9935.11	0.698579	0.349290	−	0.937015i	$-0.386423\pi$
$587$	9935.11	0.698579	0.349290	+	0.937015i	$0.386423\pi$
$588$	−3315.48	−0.232531
$589$	−22438.2	−1.56969
$590$	3992.52	0.278592
$591$	−5216.41	−0.363070
$592$	6247.59	0.433740
$593$	7730.60	0.535342	0.267671	−	0.963510i	$-0.413746\pi$
$593$	7730.60	0.535342	0.267671	+	0.963510i	$0.413746\pi$
$594$	3691.92	0.255019
$595$	2904.27	0.200107
$596$	−12881.0	−0.885279
$597$	−3061.64	−0.209891
$598$	0	0
$599$	−1516.15	−0.103419	−0.0517096	−	0.998662i	$-0.516467\pi$
$599$	−1516.15	−0.103419	−0.0517096	+	0.998662i	$0.516467\pi$
$600$	−919.747	−0.0625808
$601$	−19345.2	−1.31299	−0.656495	−	0.754331i	$-0.727962\pi$
$601$	−19345.2	−1.31299	−0.656495	+	0.754331i	$0.727962\pi$
$602$	−3953.17	−0.267640
$603$	977.750	0.0660316
$604$	−8763.37	−0.590359
$605$	978.574	0.0657598
$606$	8902.68	0.596777
$607$	15626.1	1.04488	0.522441	−	0.852675i	$-0.325021\pi$
$607$	15626.1	1.04488	0.522441	+	0.852675i	$0.325021\pi$
$608$	28840.0	1.92371
$609$	1703.60	0.113355
$610$	−23842.6	−1.58255
$611$	0	0
$612$	−12320.4	−0.813761
$613$	−22895.5	−1.50855	−0.754273	−	0.656561i	$-0.772011\pi$
$613$	−22895.5	−1.50855	−0.754273	+	0.656561i	$0.772011\pi$
$614$	−3210.29	−0.211005
$615$	−6745.71	−0.442298
$616$	373.332	0.0244188
$617$	−10412.4	−0.679394	−0.339697	−	0.940535i	$-0.610324\pi$
$617$	−10412.4	−0.679394	−0.339697	+	0.940535i	$0.610324\pi$
$618$	5802.14	0.377664
$619$	−18692.4	−1.21375	−0.606874	−	0.794798i	$-0.707577\pi$
$619$	−18692.4	−1.21375	−0.606874	+	0.794798i	$0.707577\pi$
$620$	−7711.79	−0.499537
$621$	−9288.27	−0.600202
$622$	−14702.3	−0.947760
$623$	−5179.13	−0.333062
$624$	0	0
$625$	−4624.28	−0.295954
$626$	−5967.32	−0.380994
$627$	2619.96	0.166876
$628$	−1083.08	−0.0688211
$629$	−7391.75	−0.468567
$630$	2796.91	0.176876
$631$	−6880.36	−0.434077	−0.217039	−	0.976163i	$-0.569640\pi$
$631$	−6880.36	−0.434077	−0.217039	+	0.976163i	$0.569640\pi$
$632$	−7915.10	−0.498174
$633$	−2226.89	−0.139828
$634$	11201.8	0.701703
$635$	5512.08	0.344473
$636$	5490.68	0.342326
$637$	0	0
$638$	−9862.56	−0.612010
$639$	−24081.3	−1.49083
$640$	−8558.53	−0.528602
$641$	−2315.64	−0.142687	−0.0713436	−	0.997452i	$-0.522729\pi$
$641$	−2315.64	−0.142687	−0.0713436	+	0.997452i	$0.522729\pi$
$642$	−1136.41	−0.0698606
$643$	−21914.4	−1.34404	−0.672022	−	0.740531i	$-0.734574\pi$
$643$	−21914.4	−1.34404	−0.672022	+	0.740531i	$0.734574\pi$
$644$	2276.98	0.139326
$645$	3933.06	0.240099
$646$	−45015.3	−2.74165
$647$	−3809.57	−0.231483	−0.115741	−	0.993279i	$-0.536924\pi$
$647$	−3809.57	−0.231483	−0.115741	+	0.993279i	$0.536924\pi$
$648$	4149.51	0.251556
$649$	−1469.08	−0.0888545
$650$	0	0
$651$	−1182.49	−0.0711914
$652$	−4810.43	−0.288943
$653$	−12573.4	−0.753501	−0.376750	−	0.926315i	$-0.622959\pi$
$653$	−12573.4	−0.753501	−0.376750	+	0.926315i	$0.622959\pi$
$654$	−7514.32	−0.449286
$655$	17999.9	1.07376
$656$	36046.0	2.14537
$657$	8571.79	0.509006
$658$	−2353.10	−0.139412
$659$	19038.5	1.12540	0.562698	−	0.826663i	$-0.309763\pi$
$659$	19038.5	1.12540	0.562698	+	0.826663i	$0.309763\pi$
$660$	900.457	0.0531064
$661$	484.052	0.0284833	0.0142416	−	0.999899i	$-0.495467\pi$
$661$	484.052	0.0284833	0.0142416	+	0.999899i	$0.495467\pi$
$662$	4388.39	0.257643
$663$	0	0
$664$	12432.6	0.726626
$665$	4235.93	0.247011
$666$	−7118.50	−0.414169
$667$	24812.6	1.44040
$668$	−477.510	−0.0276578
$669$	9200.36	0.531699
$670$	1227.81	0.0707978
$671$	8773.10	0.504742
$672$	1519.87	0.0872475
$673$	8800.42	0.504059	0.252029	−	0.967720i	$-0.418902\pi$
$673$	8800.42	0.504059	0.252029	+	0.967720i	$0.418902\pi$
$674$	−15811.9	−0.903636
$675$	5411.01	0.308548
$676$	0	0
$677$	8824.31	0.500954	0.250477	−	0.968123i	$-0.419413\pi$
$677$	8824.31	0.500954	0.250477	+	0.968123i	$0.419413\pi$
$678$	−13158.2	−0.745336
$679$	−4181.45	−0.236332
$680$	6381.85	0.359901
$681$	6407.78	0.360568
$682$	6845.75	0.384366
$683$	−25946.8	−1.45362	−0.726812	−	0.686837i	$-0.758999\pi$
$683$	−25946.8	−1.45362	−0.726812	+	0.686837i	$0.758999\pi$
$684$	−17969.5	−1.00450
$685$	4578.61	0.255386
$686$	9741.28	0.542163
$687$	−5297.40	−0.294190
$688$	−21016.5	−1.16460
$689$	0	0
$690$	−5465.27	−0.301535
$691$	7520.52	0.414029	0.207015	−	0.978338i	$-0.433625\pi$
$691$	7520.52	0.414029	0.207015	+	0.978338i	$0.433625\pi$
$692$	−723.032	−0.0397190
$693$	−1029.15	−0.0564129
$694$	24315.1	1.32996
$695$	−10786.5	−0.588714
$696$	3743.50	0.203875
$697$	−42647.4	−2.31763
$698$	−16180.1	−0.877402
$699$	8242.77	0.446023
$700$	−1326.49	−0.0716237
$701$	−15949.9	−0.859372	−0.429686	−	0.902978i	$-0.641376\pi$
$701$	−15949.9	−0.859372	−0.429686	+	0.902978i	$0.641376\pi$
$702$	0	0
$703$	−10781.0	−0.578396
$704$	−2002.50	−0.107205
$705$	2341.13	0.125067
$706$	17371.1	0.926018
$707$	−5296.32	−0.281738
$708$	−1351.81	−0.0717573
$709$	31560.8	1.67178	0.835889	−	0.548898i	$-0.184953\pi$
$709$	31560.8	1.67178	0.835889	+	0.548898i	$0.184953\pi$
$710$	−30240.2	−1.59844
$711$	21819.2	1.15089
$712$	−11380.6	−0.599027
$713$	−17222.8	−0.904627
$714$	−2372.32	−0.124344
$715$	0	0
$716$	−272.516	−0.0142240
$717$	−2202.12	−0.114699
$718$	−29139.3	−1.51458
$719$	−32385.1	−1.67978	−0.839890	−	0.542757i	$-0.817380\pi$
$719$	−32385.1	−1.67978	−0.839890	+	0.542757i	$0.817380\pi$
$720$	14869.4	0.769654
$721$	−3451.77	−0.178295
$722$	−40301.6	−2.07739
$723$	4005.25	0.206026
$724$	−4417.86	−0.226780
$725$	−14454.9	−0.740472
$726$	−799.335	−0.0408624
$727$	1589.27	0.0810769	0.0405385	−	0.999178i	$-0.487093\pi$
$727$	1589.27	0.0810769	0.0405385	+	0.999178i	$0.487093\pi$
$728$	0	0
$729$	−7057.53	−0.358560
$730$	10764.1	0.545747
$731$	24865.4	1.25811
$732$	8072.76	0.407620
$733$	4096.04	0.206399	0.103200	−	0.994661i	$-0.467092\pi$
$733$	4096.04	0.206399	0.103200	+	0.994661i	$0.467092\pi$
$734$	−25779.7	−1.29638
$735$	−4734.25	−0.237586
$736$	22136.6	1.10865
$737$	−451.785	−0.0225803
$738$	−41070.9	−2.04856
$739$	−10127.9	−0.504144	−0.252072	−	0.967708i	$-0.581112\pi$
$739$	−10127.9	−0.504144	−0.252072	+	0.967708i	$0.581112\pi$
$740$	−3705.33	−0.184068
$741$	0	0
$742$	−7880.35	−0.389888
$743$	33858.2	1.67179	0.835894	−	0.548892i	$-0.184950\pi$
$743$	33858.2	1.67179	0.835894	+	0.548892i	$0.184950\pi$
$744$	−2598.41	−0.128041
$745$	−18393.1	−0.904525
$746$	−31171.1	−1.52983
$747$	−34272.5	−1.67867
$748$	5692.83	0.278276
$749$	676.065	0.0329811
$750$	9862.11	0.480151
$751$	6390.64	0.310516	0.155258	−	0.987874i	$-0.450379\pi$
$751$	6390.64	0.310516	0.155258	+	0.987874i	$0.450379\pi$
$752$	−12510.0	−0.606637
$753$	−372.436	−0.0180243
$754$	0	0
$755$	−12513.4	−0.603193
$756$	−2021.04	−0.0972282
$757$	−33254.3	−1.59663	−0.798313	−	0.602242i	$-0.794274\pi$
$757$	−33254.3	−1.59663	−0.798313	+	0.602242i	$0.794274\pi$
$758$	−28370.8	−1.35946
$759$	2011.00	0.0961720
$760$	9308.03	0.444260
$761$	−30798.9	−1.46709	−0.733546	−	0.679639i	$-0.762136\pi$
$761$	−30798.9	−1.46709	−0.733546	+	0.679639i	$0.762136\pi$
$762$	−4502.47	−0.214051
$763$	4470.36	0.212107
$764$	3124.76	0.147971
$765$	−17592.6	−0.831452
$766$	−42489.1	−2.00417
$767$	0	0
$768$	9593.64	0.450756
$769$	9196.97	0.431276	0.215638	−	0.976473i	$-0.430817\pi$
$769$	9196.97	0.431276	0.215638	+	0.976473i	$0.430817\pi$
$770$	−1292.36	−0.0604848
$771$	4030.56	0.188271
$772$	23058.2	1.07498
$773$	13133.4	0.611095	0.305547	−	0.952177i	$-0.401161\pi$
$773$	13133.4	0.611095	0.305547	+	0.952177i	$0.401161\pi$
$774$	23946.2	1.11205
$775$	10033.4	0.465044
$776$	−9188.33	−0.425054
$777$	−568.160	−0.0262325
$778$	10762.6	0.495960
$779$	−62201.9	−2.86087
$780$	0	0
$781$	11127.2	0.509810
$782$	−34552.3	−1.58004
$783$	−22023.5	−1.00518
$784$	25297.7	1.15241
$785$	−1546.56	−0.0703172
$786$	−14702.9	−0.667222
$787$	−17072.5	−0.773277	−0.386638	−	0.922231i	$-0.626364\pi$
$787$	−17072.5	−0.773277	−0.386638	+	0.922231i	$0.626364\pi$
$788$	−16531.6	−0.747355
$789$	7618.43	0.343756
$790$	27399.6	1.23397
$791$	7827.98	0.351872
$792$	−2261.45	−0.101461
$793$	0	0
$794$	−19869.9	−0.888106
$795$	7840.28	0.349768
$796$	−9702.84	−0.432045
$797$	15885.1	0.705998	0.352999	−	0.935624i	$-0.385162\pi$
$797$	15885.1	0.705998	0.352999	+	0.935624i	$0.385162\pi$
$798$	−3460.06	−0.153490
$799$	14801.0	0.655346
$800$	−12896.0	−0.569928
$801$	31372.5	1.38389
$802$	−38293.2	−1.68601
$803$	−3960.73	−0.174061
$804$	−415.720	−0.0182355
$805$	3251.36	0.142355
$806$	0	0
$807$	12658.1	0.552153
$808$	−11638.1	−0.506718
$809$	10911.8	0.474213	0.237107	−	0.971484i	$-0.423801\pi$
$809$	10911.8	0.474213	0.237107	+	0.971484i	$0.423801\pi$
$810$	−14364.3	−0.623098
$811$	25455.7	1.10218	0.551091	−	0.834445i	$-0.314212\pi$
$811$	25455.7	1.10218	0.551091	+	0.834445i	$0.314212\pi$
$812$	5398.99	0.233334
$813$	118.043	0.00509217
$814$	3289.22	0.141630
$815$	−6868.93	−0.295225
$816$	−12612.1	−0.541069
$817$	36266.6	1.55301
$818$	−25768.2	−1.10142
$819$	0	0
$820$	−21378.2	−0.910440
$821$	−7236.14	−0.307604	−0.153802	−	0.988102i	$-0.549152\pi$
$821$	−7236.14	−0.307604	−0.153802	+	0.988102i	$0.549152\pi$
$822$	−3739.98	−0.158694
$823$	30247.8	1.28113	0.640567	−	0.767903i	$-0.278700\pi$
$823$	30247.8	1.28113	0.640567	+	0.767903i	$0.278700\pi$
$824$	−7584.92	−0.320671
$825$	−1171.53	−0.0494395
$826$	1940.15	0.0817269
$827$	14690.6	0.617703	0.308852	−	0.951110i	$-0.400055\pi$
$827$	14690.6	0.617703	0.308852	+	0.951110i	$0.400055\pi$
$828$	−13792.8	−0.578904
$829$	24759.3	1.03730	0.518652	−	0.854986i	$-0.326434\pi$
$829$	24759.3	1.03730	0.518652	+	0.854986i	$0.326434\pi$
$830$	−43037.8	−1.79984
$831$	−5617.91	−0.234516
$832$	0	0
$833$	−29930.7	−1.24494
$834$	8810.83	0.365820
$835$	−681.849	−0.0282591
$836$	8303.08	0.343503
$837$	15286.9	0.631292
$838$	−26160.7	−1.07841
$839$	−33729.8	−1.38794	−0.693970	−	0.720004i	$-0.744140\pi$
$839$	−33729.8	−1.38794	−0.693970	+	0.720004i	$0.744140\pi$
$840$	490.535	0.0201489
$841$	34444.5	1.41230
$842$	24049.0	0.984301
$843$	−14662.8	−0.599069
$844$	−7057.37	−0.287825
$845$	0	0
$846$	14253.9	0.579264
$847$	475.535	0.0192911
$848$	−41894.9	−1.69655
$849$	964.078	0.0389718
$850$	20128.9	0.812254
$851$	−8275.14	−0.333335
$852$	10238.9	0.411713
$853$	113.552	0.00455795	0.00227897	−	0.999997i	$-0.499275\pi$
$853$	113.552	0.00455795	0.00227897	+	0.999997i	$0.499275\pi$
$854$	−11586.2	−0.464253
$855$	−25659.1	−1.02634
$856$	1485.58	0.0593180
$857$	14128.0	0.563130	0.281565	−	0.959542i	$-0.409147\pi$
$857$	14128.0	0.563130	0.281565	+	0.959542i	$0.409147\pi$
$858$	0	0
$859$	6930.78	0.275291	0.137646	−	0.990482i	$-0.456047\pi$
$859$	6930.78	0.275291	0.137646	+	0.990482i	$0.456047\pi$
$860$	12464.5	0.494228
$861$	−3278.05	−0.129751
$862$	49379.5	1.95113
$863$	33107.8	1.30591	0.652957	−	0.757395i	$-0.273528\pi$
$863$	33107.8	1.30591	0.652957	+	0.757395i	$0.273528\pi$
$864$	−19648.4	−0.773670
$865$	−1032.43	−0.0405825
$866$	−60174.1	−2.36120
$867$	6141.65	0.240578
$868$	−3747.52	−0.146543
$869$	−10081.9	−0.393562
$870$	−12958.8	−0.504993
$871$	0	0
$872$	9823.18	0.381485
$873$	25329.1	0.981969
$874$	−50395.1	−1.95039
$875$	−5867.09	−0.226679
$876$	−3644.56	−0.140569
$877$	−25735.6	−0.990913	−0.495457	−	0.868633i	$-0.664999\pi$
$877$	−25735.6	−0.990913	−0.495457	+	0.868633i	$0.664999\pi$
$878$	51418.8	1.97642
$879$	−10567.5	−0.405500
$880$	−6870.66	−0.263193
$881$	−30493.4	−1.16612	−0.583058	−	0.812430i	$-0.698144\pi$
$881$	−30493.4	−1.16612	−0.583058	+	0.812430i	$0.698144\pi$
$882$	−28824.2	−1.10041
$883$	46096.1	1.75680	0.878401	−	0.477923i	$-0.158610\pi$
$883$	46096.1	1.75680	0.878401	+	0.477923i	$0.158610\pi$
$884$	0	0
$885$	−1930.28	−0.0733172
$886$	18822.5	0.713719
$887$	−34959.2	−1.32335	−0.661676	−	0.749790i	$-0.730155\pi$
$887$	−34959.2	−1.32335	−0.661676	+	0.749790i	$0.730155\pi$
$888$	−1248.48	−0.0471803
$889$	2678.58	0.101053
$890$	39396.1	1.48378
$891$	5285.47	0.198732
$892$	29157.4	1.09447
$893$	21587.5	0.808957
$894$	15024.2	0.562061
$895$	−389.132	−0.0145332
$896$	−4158.99	−0.155069
$897$	0	0
$898$	64260.2	2.38796
$899$	−40837.2	−1.51501
$900$	8035.18	0.297599
$901$	49567.4	1.83277
$902$	18977.5	0.700532
$903$	1911.26	0.0704348
$904$	17201.2	0.632858
$905$	−6308.37	−0.231710
$906$	10221.4	0.374817
$907$	7318.40	0.267920	0.133960	−	0.990987i	$-0.457231\pi$
$907$	7318.40	0.267920	0.133960	+	0.990987i	$0.457231\pi$
$908$	20307.3	0.742203
$909$	32082.3	1.17063
$910$	0	0
$911$	−46091.3	−1.67626	−0.838131	−	0.545469i	$-0.816351\pi$
$911$	−46091.3	−1.67626	−0.838131	+	0.545469i	$0.816351\pi$
$912$	−18395.0	−0.667893
$913$	15836.1	0.574041
$914$	−43967.1	−1.59114
$915$	11527.3	0.416482
$916$	−16788.3	−0.605569
$917$	8746.97	0.314995
$918$	30668.5	1.10263
$919$	15316.8	0.549789	0.274894	−	0.961474i	$-0.411357\pi$
$919$	15316.8	0.549789	0.274894	+	0.961474i	$0.411357\pi$
$920$	7144.54	0.256031
$921$	1552.10	0.0555302
$922$	−16881.5	−0.602996
$923$	0	0
$924$	437.574	0.0155791
$925$	4820.79	0.171359
$926$	5964.54	0.211670
$927$	20909.0	0.740822
$928$	52488.5	1.85670
$929$	4995.25	0.176414	0.0882071	−	0.996102i	$-0.471886\pi$
$929$	4995.25	0.176414	0.0882071	+	0.996102i	$0.471886\pi$
$930$	8994.88	0.317155
$931$	−43654.3	−1.53675
$932$	26122.7	0.918108
$933$	7108.17	0.249422
$934$	−55157.6	−1.93234
$935$	8128.93	0.284326
$936$	0	0
$937$	−36672.8	−1.27860	−0.639300	−	0.768957i	$-0.720776\pi$
$937$	−36672.8	−1.27860	−0.639300	+	0.768957i	$0.720776\pi$
$938$	596.651	0.0207690
$939$	2885.05	0.100266
$940$	7419.43	0.257442
$941$	11312.9	0.391914	0.195957	−	0.980613i	$-0.437219\pi$
$941$	11312.9	0.391914	0.195957	+	0.980613i	$0.437219\pi$
$942$	1263.28	0.0436943
$943$	−47744.2	−1.64874
$944$	10314.6	0.355625
$945$	−2885.89	−0.0993419
$946$	−11064.7	−0.380281
$947$	−27693.3	−0.950276	−0.475138	−	0.879911i	$-0.657602\pi$
$947$	−27693.3	−0.950276	−0.475138	+	0.879911i	$0.657602\pi$
$948$	−9277.11	−0.317834
$949$	0	0
$950$	29358.4	1.00264
$951$	−5415.78	−0.184668
$952$	3101.24	0.105580
$953$	44807.5	1.52304	0.761520	−	0.648141i	$-0.224453\pi$
$953$	44807.5	1.52304	0.761520	+	0.648141i	$0.224453\pi$
$954$	47735.1	1.62000
$955$	4461.92	0.151188
$956$	−6978.86	−0.236101
$957$	4768.30	0.161063
$958$	−44243.8	−1.49212
$959$	2224.96	0.0749194
$960$	−2631.16	−0.0884586
$961$	−1445.30	−0.0485146
$962$	0	0
$963$	−4095.25	−0.137038
$964$	12693.3	0.424090
$965$	32925.4	1.09835
$966$	−2655.83	−0.0884575
$967$	9264.68	0.308099	0.154050	−	0.988063i	$-0.450768\pi$
$967$	9264.68	0.308099	0.154050	+	0.988063i	$0.450768\pi$
$968$	1044.94	0.0346959
$969$	21763.8	0.721521
$970$	31807.1	1.05285
$971$	−19565.5	−0.646640	−0.323320	−	0.946290i	$-0.604799\pi$
$971$	−19565.5	−0.646640	−0.323320	+	0.946290i	$0.604799\pi$
$972$	18748.4	0.618679
$973$	−5241.68	−0.172703
$974$	−33265.3	−1.09434
$975$	0	0
$976$	−61596.7	−2.02015
$977$	11474.5	0.375745	0.187873	−	0.982193i	$-0.439841\pi$
$977$	11474.5	0.375745	0.187873	+	0.982193i	$0.439841\pi$
$978$	5610.79	0.183449
$979$	−14496.2	−0.473237
$980$	−15003.6	−0.489054
$981$	−27079.1	−0.881315
$982$	−77882.5	−2.53089
$983$	−55973.1	−1.81614	−0.908070	−	0.418819i	$-0.862444\pi$
$983$	−55973.1	−1.81614	−0.908070	+	0.418819i	$0.862444\pi$
$984$	−7203.20	−0.233363
$985$	−23605.9	−0.763601
$986$	−81927.4	−2.64615
$987$	1137.67	0.0366892
$988$	0	0
$989$	27837.1	0.895012
$990$	7828.43	0.251317
$991$	49461.2	1.58546	0.792729	−	0.609575i	$-0.208660\pi$
$991$	49461.2	1.58546	0.792729	+	0.609575i	$0.208660\pi$
$992$	−36433.0	−1.16608
$993$	−2121.68	−0.0678040
$994$	−14695.1	−0.468915
$995$	−13854.9	−0.441438
$996$	14572.0	0.463585
$997$	−16174.9	−0.513807	−0.256903	−	0.966437i	$-0.582702\pi$
$997$	−16174.9	−0.513807	−0.256903	+	0.966437i	$0.582702\pi$
$998$	−6147.93	−0.194999
$999$	7344.97	0.232617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.11	yes	51
13.12	even	2		1859.4.a.p.1.41	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.41	✓	51	13.12	even	2
1859.4.a.q.1.11	yes	51	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)

\(f(q)\)	\(=\)	\(q-3.69645 q^{2} +1.78714 q^{3} +5.66374 q^{4} +8.08739 q^{5} -6.60608 q^{6} +3.93004 q^{7} +8.63587 q^{8} -23.8061 q^{9} +O(q^{10})\)	\(q-3.69645 q^{2} +1.78714 q^{3} +5.66374 q^{4} +8.08739 q^{5} -6.60608 q^{6} +3.93004 q^{7} +8.63587 q^{8} -23.8061 q^{9} -29.8946 q^{10} +11.0000 q^{11} +10.1219 q^{12} -14.5272 q^{14} +14.4533 q^{15} -77.2320 q^{16} +91.3760 q^{17} +87.9981 q^{18} +133.273 q^{19} +45.8049 q^{20} +7.02353 q^{21} -40.6609 q^{22} +102.296 q^{23} +15.4335 q^{24} -59.5941 q^{25} -90.7977 q^{27} +22.2587 q^{28} +242.556 q^{29} -53.4259 q^{30} -168.362 q^{31} +216.397 q^{32} +19.6586 q^{33} -337.767 q^{34} +31.7838 q^{35} -134.832 q^{36} -80.8938 q^{37} -492.638 q^{38} +69.8416 q^{40} -466.724 q^{41} -25.9621 q^{42} +272.122 q^{43} +62.3011 q^{44} -192.529 q^{45} -378.133 q^{46} +161.979 q^{47} -138.024 q^{48} -327.555 q^{49} +220.287 q^{50} +163.302 q^{51} +542.455 q^{53} +335.629 q^{54} +88.9613 q^{55} +33.9393 q^{56} +238.178 q^{57} -896.597 q^{58} -133.553 q^{59} +81.8598 q^{60} +797.554 q^{61} +622.341 q^{62} -93.5590 q^{63} -182.045 q^{64} -72.6668 q^{66} -41.0714 q^{67} +517.530 q^{68} +182.818 q^{69} -117.487 q^{70} +1011.56 q^{71} -205.587 q^{72} -360.066 q^{73} +299.020 q^{74} -106.503 q^{75} +754.826 q^{76} +43.2304 q^{77} -916.538 q^{79} -624.605 q^{80} +480.497 q^{81} +1725.22 q^{82} +1439.65 q^{83} +39.7795 q^{84} +738.993 q^{85} -1005.88 q^{86} +433.482 q^{87} +94.9946 q^{88} -1317.83 q^{89} +711.675 q^{90} +579.380 q^{92} -300.886 q^{93} -598.747 q^{94} +1077.83 q^{95} +386.732 q^{96} -1063.97 q^{97} +1210.79 q^{98} -261.867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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