LMFDB - Embedded newform 1859.4.a.q.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.41499 q^{2} +1.53640 q^{3} -2.16780 q^{4} +15.9482 q^{5} -3.71040 q^{6} -30.4066 q^{7} +24.5552 q^{8} -24.6395 q^{9} +O(q^{10})$	\(q-2.41499 q^{2} +1.53640 q^{3} -2.16780 q^{4} +15.9482 q^{5} -3.71040 q^{6} -30.4066 q^{7} +24.5552 q^{8} -24.6395 q^{9} -38.5149 q^{10} +11.0000 q^{11} -3.33062 q^{12} +73.4317 q^{14} +24.5029 q^{15} -41.9582 q^{16} -90.7790 q^{17} +59.5042 q^{18} +70.9524 q^{19} -34.5726 q^{20} -46.7168 q^{21} -26.5649 q^{22} +209.496 q^{23} +37.7266 q^{24} +129.346 q^{25} -79.3390 q^{27} +65.9154 q^{28} -202.599 q^{29} -59.1744 q^{30} +121.796 q^{31} -95.1126 q^{32} +16.9004 q^{33} +219.231 q^{34} -484.931 q^{35} +53.4135 q^{36} -431.998 q^{37} -171.350 q^{38} +391.612 q^{40} -171.134 q^{41} +112.821 q^{42} -276.890 q^{43} -23.8458 q^{44} -392.956 q^{45} -505.931 q^{46} +353.600 q^{47} -64.4647 q^{48} +581.560 q^{49} -312.370 q^{50} -139.473 q^{51} -348.500 q^{53} +191.603 q^{54} +175.430 q^{55} -746.639 q^{56} +109.011 q^{57} +489.275 q^{58} +702.529 q^{59} -53.1174 q^{60} +810.313 q^{61} -294.138 q^{62} +749.202 q^{63} +565.362 q^{64} -40.8144 q^{66} -735.538 q^{67} +196.791 q^{68} +321.870 q^{69} +1171.11 q^{70} +85.4865 q^{71} -605.027 q^{72} -466.340 q^{73} +1043.27 q^{74} +198.727 q^{75} -153.811 q^{76} -334.472 q^{77} -145.923 q^{79} -669.159 q^{80} +543.369 q^{81} +413.287 q^{82} -321.823 q^{83} +101.273 q^{84} -1447.76 q^{85} +668.687 q^{86} -311.273 q^{87} +270.107 q^{88} -175.825 q^{89} +948.986 q^{90} -454.145 q^{92} +187.128 q^{93} -853.941 q^{94} +1131.56 q^{95} -146.131 q^{96} +62.7289 q^{97} -1404.47 q^{98} -271.034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.41499	−0.853829	−0.426915	−	0.904292i	$-0.640400\pi$
$2$	−2.41499	−0.853829	−0.426915	+	0.904292i	$0.640400\pi$
$3$	1.53640	0.295681	0.147840	−	0.989011i	$-0.452768\pi$
$3$	1.53640	0.295681	0.147840	+	0.989011i	$0.452768\pi$
$4$	−2.16780	−0.270975
$5$	15.9482	1.42645	0.713226	−	0.700934i	$-0.247233\pi$
$5$	15.9482	1.42645	0.713226	+	0.700934i	$0.247233\pi$
$6$	−3.71040	−0.252461
$7$	−30.4066	−1.64180	−0.820901	−	0.571071i	$-0.806528\pi$
$7$	−30.4066	−1.64180	−0.820901	+	0.571071i	$0.806528\pi$
$8$	24.5552	1.08520
$9$	−24.6395	−0.912573
$10$	−38.5149	−1.21795
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−3.33062	−0.0801222
$13$	0	0
$13$	0	0
$14$	73.4317	1.40182
$15$	24.5029	0.421775
$16$	−41.9582	−0.655597
$17$	−90.7790	−1.29513	−0.647563	−	0.762012i	$-0.724212\pi$
$17$	−90.7790	−1.29513	−0.647563	+	0.762012i	$0.724212\pi$
$18$	59.5042	0.779182
$19$	70.9524	0.856715	0.428358	−	0.903609i	$-0.359092\pi$
$19$	70.9524	0.856715	0.428358	+	0.903609i	$0.359092\pi$
$20$	−34.5726	−0.386533
$21$	−46.7168	−0.485449
$22$	−26.5649	−0.257439
$23$	209.496	1.89926	0.949628	−	0.313380i	$-0.101461\pi$
$23$	209.496	1.89926	0.949628	+	0.313380i	$0.101461\pi$
$24$	37.7266	0.320872
$25$	129.346	1.03477
$26$	0	0
$27$	−79.3390	−0.565511
$28$	65.9154	0.444887
$29$	−202.599	−1.29730	−0.648649	−	0.761088i	$-0.724666\pi$
$29$	−202.599	−1.29730	−0.648649	+	0.761088i	$0.724666\pi$
$30$	−59.1744	−0.360124
$31$	121.796	0.705655	0.352827	−	0.935688i	$-0.385220\pi$
$31$	121.796	0.705655	0.352827	+	0.935688i	$0.385220\pi$
$32$	−95.1126	−0.525428
$33$	16.9004	0.0891511
$34$	219.231	1.10582
$35$	−484.931	−2.34195
$36$	53.4135	0.247285
$37$	−431.998	−1.91946	−0.959729	−	0.280926i	$-0.909358\pi$
$37$	−431.998	−1.91946	−0.959729	+	0.280926i	$0.909358\pi$
$38$	−171.350	−0.731489
$39$	0	0
$40$	391.612	1.54798
$41$	−171.134	−0.651869	−0.325934	−	0.945392i	$-0.605679\pi$
$41$	−171.134	−0.651869	−0.325934	+	0.945392i	$0.605679\pi$
$42$	112.821	0.414491
$43$	−276.890	−0.981983	−0.490991	−	0.871164i	$-0.663365\pi$
$43$	−276.890	−0.981983	−0.490991	+	0.871164i	$0.663365\pi$
$44$	−23.8458	−0.0817021
$45$	−392.956	−1.30174
$46$	−505.931	−1.62164
$47$	353.600	1.09740	0.548700	−	0.836019i	$-0.315123\pi$
$47$	353.600	1.09740	0.548700	+	0.836019i	$0.315123\pi$
$48$	−64.4647	−0.193848
$49$	581.560	1.69551
$50$	−312.370	−0.883515
$51$	−139.473	−0.382944
$52$	0	0
$53$	−348.500	−0.903210	−0.451605	−	0.892218i	$-0.649148\pi$
$53$	−348.500	−0.903210	−0.451605	+	0.892218i	$0.649148\pi$
$54$	191.603	0.482850
$55$	175.430	0.430092
$56$	−746.639	−1.78168
$57$	109.011	0.253314
$58$	489.275	1.10767
$59$	702.529	1.55020	0.775098	−	0.631842i	$-0.217701\pi$
$59$	702.529	1.55020	0.775098	+	0.631842i	$0.217701\pi$
$60$	−53.1174	−0.114290
$61$	810.313	1.70082	0.850410	−	0.526121i	$-0.176354\pi$
$61$	810.313	1.70082	0.850410	+	0.526121i	$0.176354\pi$
$62$	−294.138	−0.602509
$63$	749.202	1.49826
$64$	565.362	1.10422
$65$	0	0
$66$	−40.8144	−0.0761199
$67$	−735.538	−1.34120	−0.670599	−	0.741820i	$-0.733963\pi$
$67$	−735.538	−1.34120	−0.670599	+	0.741820i	$0.733963\pi$
$68$	196.791	0.350947
$69$	321.870	0.561573
$70$	1171.11	1.99963
$71$	85.4865	0.142893	0.0714463	−	0.997444i	$-0.477239\pi$
$71$	85.4865	0.142893	0.0714463	+	0.997444i	$0.477239\pi$
$72$	−605.027	−0.990321
$73$	−466.340	−0.747684	−0.373842	−	0.927492i	$-0.621960\pi$
$73$	−466.340	−0.747684	−0.373842	+	0.927492i	$0.621960\pi$
$74$	1043.27	1.63889
$75$	198.727	0.305961
$76$	−153.811	−0.232149
$77$	−334.472	−0.495022
$78$	0	0
$79$	−145.923	−0.207817	−0.103909	−	0.994587i	$-0.533135\pi$
$79$	−145.923	−0.207817	−0.103909	+	0.994587i	$0.533135\pi$
$80$	−669.159	−0.935178
$81$	543.369	0.745362
$82$	413.287	0.556585
$83$	−321.823	−0.425598	−0.212799	−	0.977096i	$-0.568258\pi$
$83$	−321.823	−0.425598	−0.212799	+	0.977096i	$0.568258\pi$
$84$	101.273	0.131545
$85$	−1447.76	−1.84744
$86$	668.687	0.838446
$87$	−311.273	−0.383586
$88$	270.107	0.327199
$89$	−175.825	−0.209409	−0.104704	−	0.994503i	$-0.533390\pi$
$89$	−175.825	−0.209409	−0.104704	+	0.994503i	$0.533390\pi$
$90$	948.986	1.11147
$91$	0	0
$92$	−454.145	−0.514651
$93$	187.128	0.208649
$94$	−853.941	−0.936992
$95$	1131.56	1.22206
$96$	−146.131	−0.155359
$97$	62.7289	0.0656614	0.0328307	−	0.999461i	$-0.489548\pi$
$97$	62.7289	0.0656614	0.0328307	+	0.999461i	$0.489548\pi$
$98$	−1404.47	−1.44768
$99$	−271.034	−0.275151
$100$	−280.396	−0.280396
$101$	1642.56	1.61822	0.809111	−	0.587656i	$-0.199949\pi$
$101$	1642.56	1.61822	0.809111	+	0.587656i	$0.199949\pi$
$102$	336.827	0.326969
$103$	704.626	0.674067	0.337033	−	0.941493i	$-0.390576\pi$
$103$	704.626	0.674067	0.337033	+	0.941493i	$0.390576\pi$
$104$	0	0
$105$	−745.049	−0.692470
$106$	841.626	0.771188
$107$	−358.791	−0.324165	−0.162083	−	0.986777i	$-0.551821\pi$
$107$	−358.791	−0.324165	−0.162083	+	0.986777i	$0.551821\pi$
$108$	171.991	0.153239
$109$	−1205.25	−1.05910	−0.529551	−	0.848278i	$-0.677640\pi$
$109$	−1205.25	−1.05910	−0.529551	+	0.848278i	$0.677640\pi$
$110$	−423.664	−0.367225
$111$	−663.722	−0.567547
$112$	1275.81	1.07636
$113$	842.447	0.701334	0.350667	−	0.936500i	$-0.385955\pi$
$113$	842.447	0.701334	0.350667	+	0.936500i	$0.385955\pi$
$114$	−263.262	−0.216287
$115$	3341.09	2.70920
$116$	439.194	0.351536
$117$	0	0
$118$	−1696.60	−1.32360
$119$	2760.28	2.12634
$120$	601.673	0.457708
$121$	121.000	0.0909091
$122$	−1956.90	−1.45221
$123$	−262.931	−0.192745
$124$	−264.031	−0.191215
$125$	69.3090	0.0495935
$126$	−1809.32	−1.27926
$127$	−1470.87	−1.02771	−0.513853	−	0.857878i	$-0.671782\pi$
$127$	−1470.87	−1.02771	−0.513853	+	0.857878i	$0.671782\pi$
$128$	−604.446	−0.417390
$129$	−425.414	−0.290353
$130$	0	0
$131$	758.344	0.505778	0.252889	−	0.967495i	$-0.418619\pi$
$131$	758.344	0.505778	0.252889	+	0.967495i	$0.418619\pi$
$132$	−36.6368	−0.0241577
$133$	−2157.42	−1.40656
$134$	1776.32	1.14515
$135$	−1265.32	−0.806675
$136$	−2229.09	−1.40547
$137$	2708.95	1.68935	0.844677	−	0.535277i	$-0.179793\pi$
$137$	2708.95	1.68935	0.844677	+	0.535277i	$0.179793\pi$
$138$	−777.314	−0.479488
$139$	137.570	0.0839462	0.0419731	−	0.999119i	$-0.486636\pi$
$139$	137.570	0.0839462	0.0419731	+	0.999119i	$0.486636\pi$
$140$	1051.23	0.634611
$141$	543.271	0.324480
$142$	−206.449	−0.122006
$143$	0	0
$144$	1033.83	0.598280
$145$	−3231.09	−1.85053
$146$	1126.21	0.638395
$147$	893.511	0.501330
$148$	936.485	0.520126
$149$	1118.11	0.614760	0.307380	−	0.951587i	$-0.400548\pi$
$149$	1118.11	0.614760	0.307380	+	0.951587i	$0.400548\pi$
$150$	−479.925	−0.261238
$151$	3.61844	0.00195009	0.000975047	−	1.00000i	$-0.499690\pi$
$151$	3.61844	0.00195009	0.000975047		1.00000i	$0.499690\pi$
$152$	1742.25	0.929704
$153$	2236.75	1.18190
$154$	807.749	0.422664
$155$	1942.44	1.00658
$156$	0	0
$157$	507.399	0.257929	0.128964	−	0.991649i	$-0.458835\pi$
$157$	507.399	0.257929	0.128964	+	0.991649i	$0.458835\pi$
$158$	352.402	0.177441
$159$	−535.436	−0.267062
$160$	−1516.88	−0.749498
$161$	−6370.05	−3.11820
$162$	−1312.23	−0.636412
$163$	−2611.19	−1.25475	−0.627375	−	0.778717i	$-0.715871\pi$
$163$	−2611.19	−1.25475	−0.627375	+	0.778717i	$0.715871\pi$
$164$	370.984	0.176640
$165$	269.532	0.127170
$166$	777.201	0.363388
$167$	−638.069	−0.295660	−0.147830	−	0.989013i	$-0.547229\pi$
$167$	−638.069	−0.295660	−0.147830	+	0.989013i	$0.547229\pi$
$168$	−1147.14	−0.526808
$169$	0	0
$170$	3496.34	1.57739
$171$	−1748.23	−0.781815
$172$	600.242	0.266093
$173$	3462.70	1.52176	0.760880	−	0.648892i	$-0.224767\pi$
$173$	3462.70	1.52176	0.760880	+	0.648892i	$0.224767\pi$
$174$	751.723	0.327517
$175$	−3932.97	−1.69888
$176$	−461.540	−0.197670
$177$	1079.37	0.458363
$178$	424.616	0.178799
$179$	2835.85	1.18414	0.592072	−	0.805885i	$-0.298310\pi$
$179$	2835.85	1.18414	0.592072	+	0.805885i	$0.298310\pi$
$180$	851.850	0.352740
$181$	−1804.72	−0.741125	−0.370563	−	0.928808i	$-0.620835\pi$
$181$	−1804.72	−0.741125	−0.370563	+	0.928808i	$0.620835\pi$
$182$	0	0
$183$	1244.97	0.502900
$184$	5144.21	2.06106
$185$	−6889.60	−2.73802
$186$	−451.914	−0.178150
$187$	−998.569	−0.390495
$188$	−766.534	−0.297368
$189$	2412.43	0.928457
$190$	−2732.72	−1.04343
$191$	−2548.20	−0.965348	−0.482674	−	0.875800i	$-0.660334\pi$
$191$	−2548.20	−0.965348	−0.482674	+	0.875800i	$0.660334\pi$
$192$	868.624	0.326498
$193$	1450.37	0.540933	0.270466	−	0.962729i	$-0.412822\pi$
$193$	1450.37	0.540933	0.270466	+	0.962729i	$0.412822\pi$
$194$	−151.490	−0.0560637
$195$	0	0
$196$	−1260.71	−0.459442
$197$	−2597.20	−0.939305	−0.469653	−	0.882851i	$-0.655621\pi$
$197$	−2597.20	−0.939305	−0.469653	+	0.882851i	$0.655621\pi$
$198$	654.546	0.234932
$199$	2771.66	0.987325	0.493663	−	0.869653i	$-0.335658\pi$
$199$	2771.66	0.987325	0.493663	+	0.869653i	$0.335658\pi$
$200$	3176.11	1.12293
$201$	−1130.08	−0.396566
$202$	−3966.76	−1.38169
$203$	6160.34	2.12991
$204$	302.350	0.103768
$205$	−2729.28	−0.929860
$206$	−1701.67	−0.575538
$207$	−5161.86	−1.73321
$208$	0	0
$209$	780.476	0.258309
$210$	1799.29	0.591251
$211$	602.214	0.196484	0.0982419	−	0.995163i	$-0.468678\pi$
$211$	602.214	0.196484	0.0982419	+	0.995163i	$0.468678\pi$
$212$	755.479	0.244748
$213$	131.342	0.0422506
$214$	866.479	0.276782
$215$	−4415.90	−1.40075
$216$	−1948.18	−0.613690
$217$	−3703.42	−1.15854
$218$	2910.68	0.904293
$219$	−716.485	−0.221076
$220$	−380.298	−0.116544
$221$	0	0
$222$	1602.89	0.484588
$223$	−3095.89	−0.929668	−0.464834	−	0.885398i	$-0.653886\pi$
$223$	−3095.89	−0.929668	−0.464834	+	0.885398i	$0.653886\pi$
$224$	2892.05	0.862648
$225$	−3187.01	−0.944300
$226$	−2034.50	−0.598819
$227$	3161.85	0.924492	0.462246	−	0.886752i	$-0.347044\pi$
$227$	3161.85	0.924492	0.462246	+	0.886752i	$0.347044\pi$
$228$	−236.315	−0.0686419
$229$	−796.620	−0.229878	−0.114939	−	0.993373i	$-0.536667\pi$
$229$	−796.620	−0.229878	−0.114939	+	0.993373i	$0.536667\pi$
$230$	−8068.70	−2.31319
$231$	−513.884	−0.146368
$232$	−4974.85	−1.40782
$233$	3721.55	1.04638	0.523190	−	0.852216i	$-0.324742\pi$
$233$	3721.55	1.04638	0.523190	+	0.852216i	$0.324742\pi$
$234$	0	0
$235$	5639.29	1.56539
$236$	−1522.94	−0.420064
$237$	−224.196	−0.0614476
$238$	−6666.06	−1.81553
$239$	6868.62	1.85897	0.929485	−	0.368859i	$-0.120251\pi$
$239$	6868.62	1.85897	0.929485	+	0.368859i	$0.120251\pi$
$240$	−1028.10	−0.276514
$241$	−4985.46	−1.33254	−0.666269	−	0.745712i	$-0.732110\pi$
$241$	−4985.46	−1.33254	−0.666269	+	0.745712i	$0.732110\pi$
$242$	−292.214	−0.0776209
$243$	2976.99	0.785900
$244$	−1756.60	−0.460880
$245$	9274.86	2.41857
$246$	634.976	0.164571
$247$	0	0
$248$	2990.74	0.765774
$249$	−494.450	−0.125841
$250$	−167.381	−0.0423444
$251$	2986.69	0.751070	0.375535	−	0.926808i	$-0.377459\pi$
$251$	2986.69	0.751070	0.375535	+	0.926808i	$0.377459\pi$
$252$	−1624.12	−0.405992
$253$	2304.45	0.572647
$254$	3552.14	0.877485
$255$	−2224.35	−0.546251
$256$	−3063.16	−0.747843
$257$	6830.25	1.65782	0.828909	−	0.559383i	$-0.188962\pi$
$257$	6830.25	1.65782	0.828909	+	0.559383i	$0.188962\pi$
$258$	1027.37	0.247912
$259$	13135.6	3.15137
$260$	0	0
$261$	4991.93	1.18388
$262$	−1831.40	−0.431848
$263$	1801.74	0.422434	0.211217	−	0.977439i	$-0.432257\pi$
$263$	1801.74	0.422434	0.211217	+	0.977439i	$0.432257\pi$
$264$	414.993	0.0967464
$265$	−5557.96	−1.28839
$266$	5210.16	1.20096
$267$	−270.137	−0.0619181
$268$	1594.50	0.363431
$269$	−3959.13	−0.897370	−0.448685	−	0.893690i	$-0.648107\pi$
$269$	−3959.13	−0.897370	−0.448685	+	0.893690i	$0.648107\pi$
$270$	3055.73	0.688763
$271$	3489.22	0.782121	0.391061	−	0.920365i	$-0.372108\pi$
$271$	3489.22	0.782121	0.391061	+	0.920365i	$0.372108\pi$
$272$	3808.92	0.849081
$273$	0	0
$274$	−6542.10	−1.44242
$275$	1422.80	0.311994
$276$	−697.750	−0.152172
$277$	6394.82	1.38710	0.693551	−	0.720408i	$-0.256045\pi$
$277$	6394.82	1.38710	0.693551	+	0.720408i	$0.256045\pi$
$278$	−332.231	−0.0716758
$279$	−3001.00	−0.643961
$280$	−11907.6	−2.54148
$281$	−1313.70	−0.278893	−0.139446	−	0.990230i	$-0.544532\pi$
$281$	−1313.70	−0.278893	−0.139446	+	0.990230i	$0.544532\pi$
$282$	−1312.00	−0.277051
$283$	−1083.46	−0.227580	−0.113790	−	0.993505i	$-0.536299\pi$
$283$	−1083.46	−0.227580	−0.113790	+	0.993505i	$0.536299\pi$
$284$	−185.318	−0.0387204
$285$	1738.54	0.361341
$286$	0	0
$287$	5203.60	1.07024
$288$	2343.52	0.479491
$289$	3327.82	0.677350
$290$	7803.07	1.58004
$291$	96.3769	0.0194148
$292$	1010.93	0.202604
$293$	−1458.12	−0.290731	−0.145366	−	0.989378i	$-0.546436\pi$
$293$	−1458.12	−0.290731	−0.145366	+	0.989378i	$0.546436\pi$
$294$	−2157.82	−0.428051
$295$	11204.1	2.21128
$296$	−10607.8	−2.08299
$297$	−872.729	−0.170508
$298$	−2700.23	−0.524900
$299$	0	0
$300$	−430.801	−0.0829078
$301$	8419.27	1.61222
$302$	−8.73850	−0.00166505
$303$	2523.63	0.478477
$304$	−2977.04	−0.561660
$305$	12923.1	2.42614
$306$	−5401.73	−1.00914
$307$	4498.80	0.836353	0.418176	−	0.908366i	$-0.362669\pi$
$307$	4498.80	0.836353	0.418176	+	0.908366i	$0.362669\pi$
$308$	725.070	0.134139
$309$	1082.59	0.199309
$310$	−4690.98	−0.859450
$311$	5700.59	1.03939	0.519696	−	0.854352i	$-0.326045\pi$
$311$	5700.59	1.03939	0.519696	+	0.854352i	$0.326045\pi$
$312$	0	0
$313$	−367.845	−0.0664276	−0.0332138	−	0.999448i	$-0.510574\pi$
$313$	−367.845	−0.0664276	−0.0332138	+	0.999448i	$0.510574\pi$
$314$	−1225.36	−0.220227
$315$	11948.4	2.13720
$316$	316.331	0.0563133
$317$	4209.84	0.745894	0.372947	−	0.927853i	$-0.378347\pi$
$317$	4209.84	0.745894	0.372947	+	0.927853i	$0.378347\pi$
$318$	1293.08	0.228025
$319$	−2228.59	−0.391150
$320$	9016.52	1.57512
$321$	−551.248	−0.0958494
$322$	15383.6	2.66241
$323$	−6440.98	−1.10955
$324$	−1177.92	−0.201975
$325$	0	0
$326$	6306.01	1.07134
$327$	−1851.75	−0.313156
$328$	−4202.23	−0.707406
$329$	−10751.8	−1.80171
$330$	−650.918	−0.108581
$331$	−684.069	−0.113595	−0.0567973	−	0.998386i	$-0.518089\pi$
$331$	−684.069	−0.113595	−0.0567973	+	0.998386i	$0.518089\pi$
$332$	697.648	0.115327
$333$	10644.2	1.75165
$334$	1540.93	0.252443
$335$	−11730.5	−1.91315
$336$	1960.15	0.318259
$337$	−3192.44	−0.516034	−0.258017	−	0.966140i	$-0.583069\pi$
$337$	−3192.44	−0.516034	−0.258017	+	0.966140i	$0.583069\pi$
$338$	0	0
$339$	1294.34	0.207371
$340$	3138.46	0.500609
$341$	1339.76	0.212763
$342$	4221.96	0.667537
$343$	−7253.81	−1.14189
$344$	−6799.07	−1.06564
$345$	5133.25	0.801058
$346$	−8362.41	−1.29932
$347$	3620.71	0.560144	0.280072	−	0.959979i	$-0.409642\pi$
$347$	3620.71	0.560144	0.280072	+	0.959979i	$0.409642\pi$
$348$	674.779	0.103942
$349$	4186.05	0.642047	0.321023	−	0.947071i	$-0.395973\pi$
$349$	4186.05	0.642047	0.321023	+	0.947071i	$0.395973\pi$
$350$	9498.09	1.45056
$351$	0	0
$352$	−1046.24	−0.158422
$353$	7946.90	1.19822	0.599109	−	0.800668i	$-0.295522\pi$
$353$	7946.90	1.19822	0.599109	+	0.800668i	$0.295522\pi$
$354$	−2606.67	−0.391364
$355$	1363.36	0.203830
$356$	381.153	0.0567446
$357$	4240.90	0.628718
$358$	−6848.57	−1.01106
$359$	2332.19	0.342864	0.171432	−	0.985196i	$-0.445161\pi$
$359$	2332.19	0.342864	0.171432	+	0.985196i	$0.445161\pi$
$360$	−9649.10	−1.41265
$361$	−1824.76	−0.266039
$362$	4358.38	0.632794
$363$	185.905	0.0268801
$364$	0	0
$365$	−7437.29	−1.06654
$366$	−3006.59	−0.429391
$367$	−8719.15	−1.24015	−0.620076	−	0.784542i	$-0.712898\pi$
$367$	−8719.15	−1.24015	−0.620076	+	0.784542i	$0.712898\pi$
$368$	−8790.07	−1.24515
$369$	4216.65	0.594878
$370$	16638.3	2.33780
$371$	10596.7	1.48289
$372$	−405.657	−0.0565386
$373$	2517.00	0.349398	0.174699	−	0.984622i	$-0.444105\pi$
$373$	2517.00	0.349398	0.174699	+	0.984622i	$0.444105\pi$
$374$	2411.54	0.333416
$375$	106.487	0.0146638
$376$	8682.70	1.19089
$377$	0	0
$378$	−5826.00	−0.792744
$379$	10238.9	1.38769	0.693846	−	0.720123i	$-0.255915\pi$
$379$	10238.9	1.38769	0.693846	+	0.720123i	$0.255915\pi$
$380$	−2453.01	−0.331149
$381$	−2259.85	−0.303873
$382$	6153.90	0.824243
$383$	−2484.23	−0.331431	−0.165716	−	0.986174i	$-0.552993\pi$
$383$	−2484.23	−0.331431	−0.165716	+	0.986174i	$0.552993\pi$
$384$	−928.672	−0.123414
$385$	−5334.24	−0.706125
$386$	−3502.64	−0.461864
$387$	6822.41	0.896131
$388$	−135.984	−0.0177926
$389$	6229.86	0.811996	0.405998	−	0.913874i	$-0.366924\pi$
$389$	6229.86	0.811996	0.405998	+	0.913874i	$0.366924\pi$
$390$	0	0
$391$	−19017.8	−2.45977
$392$	14280.3	1.83996
$393$	1165.12	0.149549
$394$	6272.23	0.802007
$395$	−2327.21	−0.296442
$396$	587.548	0.0745591
$397$	−2292.10	−0.289767	−0.144883	−	0.989449i	$-0.546281\pi$
$397$	−2292.10	−0.289767	−0.144883	+	0.989449i	$0.546281\pi$
$398$	−6693.54	−0.843008
$399$	−3314.67	−0.415892
$400$	−5427.12	−0.678390
$401$	11517.7	1.43433	0.717167	−	0.696902i	$-0.245439\pi$
$401$	11517.7	1.43433	0.717167	+	0.696902i	$0.245439\pi$
$402$	2729.14	0.338600
$403$	0	0
$404$	−3560.74	−0.438498
$405$	8665.77	1.06322
$406$	−14877.2	−1.81858
$407$	−4751.97	−0.578739
$408$	−3424.79	−0.415569
$409$	2539.94	0.307071	0.153535	−	0.988143i	$-0.450934\pi$
$409$	2539.94	0.307071	0.153535	+	0.988143i	$0.450934\pi$
$410$	6591.20	0.793942
$411$	4162.04	0.499509
$412$	−1527.49	−0.182655
$413$	−21361.5	−2.54511
$414$	12465.9	1.47987
$415$	−5132.51	−0.607096
$416$	0	0
$417$	211.363	0.0248213
$418$	−1884.85	−0.220552
$419$	11909.5	1.38859	0.694295	−	0.719691i	$-0.255717\pi$
$419$	11909.5	1.38859	0.694295	+	0.719691i	$0.255717\pi$
$420$	1615.12	0.187642
$421$	4808.58	0.556664	0.278332	−	0.960485i	$-0.410218\pi$
$421$	4808.58	0.556664	0.278332	+	0.960485i	$0.410218\pi$
$422$	−1454.34	−0.167764
$423$	−8712.50	−1.00146
$424$	−8557.48	−0.980160
$425$	−11741.9	−1.34015
$426$	−317.189	−0.0360748
$427$	−24638.9	−2.79241
$428$	777.788	0.0878407
$429$	0	0
$430$	10664.4	1.19600
$431$	11024.3	1.23207	0.616036	−	0.787718i	$-0.288738\pi$
$431$	11024.3	1.23207	0.616036	+	0.787718i	$0.288738\pi$
$432$	3328.92	0.370748
$433$	948.626	0.105284	0.0526421	−	0.998613i	$-0.483236\pi$
$433$	948.626	0.105284	0.0526421	+	0.998613i	$0.483236\pi$
$434$	8943.73	0.989200
$435$	−4964.26	−0.547168
$436$	2612.75	0.286991
$437$	14864.2	1.62712
$438$	1730.31	0.188761
$439$	2119.52	0.230431	0.115215	−	0.993341i	$-0.463244\pi$
$439$	2119.52	0.230431	0.115215	+	0.993341i	$0.463244\pi$
$440$	4307.73	0.466734
$441$	−14329.3	−1.54728
$442$	0	0
$443$	9103.07	0.976298	0.488149	−	0.872760i	$-0.337672\pi$
$443$	9103.07	0.976298	0.488149	+	0.872760i	$0.337672\pi$
$444$	1438.82	0.153791
$445$	−2804.09	−0.298712
$446$	7476.55	0.793778
$447$	1717.87	0.181773
$448$	−17190.7	−1.81291
$449$	−1573.43	−0.165378	−0.0826892	−	0.996575i	$-0.526351\pi$
$449$	−1573.43	−0.165378	−0.0826892	+	0.996575i	$0.526351\pi$
$450$	7696.62	0.806271
$451$	−1882.47	−0.196546
$452$	−1826.26	−0.190044
$453$	5.55937	0.000576605 0
$454$	−7635.86	−0.789358
$455$	0	0
$456$	2676.80	0.274896
$457$	−3407.94	−0.348833	−0.174417	−	0.984672i	$-0.555804\pi$
$457$	−3407.94	−0.348833	−0.174417	+	0.984672i	$0.555804\pi$
$458$	1923.83	0.196277
$459$	7202.31	0.732408
$460$	−7242.81	−0.734125
$461$	−5972.78	−0.603427	−0.301714	−	0.953399i	$-0.597559\pi$
$461$	−5972.78	−0.603427	−0.301714	+	0.953399i	$0.597559\pi$
$462$	1241.03	0.124974
$463$	12969.0	1.30177	0.650886	−	0.759176i	$-0.274398\pi$
$463$	12969.0	1.30177	0.650886	+	0.759176i	$0.274398\pi$
$464$	8500.68	0.850505
$465$	2984.37	0.297627
$466$	−8987.52	−0.893431
$467$	6536.18	0.647662	0.323831	−	0.946115i	$-0.395029\pi$
$467$	6536.18	0.647662	0.323831	+	0.946115i	$0.395029\pi$
$468$	0	0
$469$	22365.2	2.20198
$470$	−13618.8	−1.33658
$471$	779.569	0.0762646
$472$	17250.7	1.68227
$473$	−3045.79	−0.296079
$474$	541.431	0.0524658
$475$	9177.40	0.886501
$476$	−5983.74	−0.576185
$477$	8586.85	0.824245
$478$	−16587.7	−1.58724
$479$	5480.68	0.522795	0.261397	−	0.965231i	$-0.415817\pi$
$479$	5480.68	0.522795	0.261397	+	0.965231i	$0.415817\pi$
$480$	−2330.53	−0.221612
$481$	0	0
$482$	12039.8	1.13776
$483$	−9786.96	−0.921992
$484$	−262.304	−0.0246341
$485$	1000.42	0.0936629
$486$	−7189.41	−0.671025
$487$	12822.7	1.19312	0.596560	−	0.802568i	$-0.296534\pi$
$487$	12822.7	1.19312	0.596560	+	0.802568i	$0.296534\pi$
$488$	19897.4	1.84572
$489$	−4011.84	−0.371006
$490$	−22398.7	−2.06504
$491$	−16816.5	−1.54566	−0.772829	−	0.634615i	$-0.781159\pi$
$491$	−16816.5	−1.54566	−0.772829	+	0.634615i	$0.781159\pi$
$492$	569.981	0.0522292
$493$	18391.7	1.68016
$494$	0	0
$495$	−4322.51	−0.392490
$496$	−5110.36	−0.462625
$497$	−2599.35	−0.234601
$498$	1194.09	0.107447
$499$	6051.70	0.542908	0.271454	−	0.962451i	$-0.412496\pi$
$499$	6051.70	0.542908	0.271454	+	0.962451i	$0.412496\pi$
$500$	−150.248	−0.0134386
$501$	−980.330	−0.0874210
$502$	−7212.85	−0.641285
$503$	−17698.7	−1.56887	−0.784437	−	0.620208i	$-0.787048\pi$
$503$	−17698.7	−1.56887	−0.784437	+	0.620208i	$0.787048\pi$
$504$	18396.8	1.62591
$505$	26195.9	2.30832
$506$	−5565.24	−0.488943
$507$	0	0
$508$	3188.55	0.278483
$509$	9414.42	0.819817	0.409908	−	0.912127i	$-0.365561\pi$
$509$	9414.42	0.819817	0.409908	+	0.912127i	$0.365561\pi$
$510$	5371.79	0.466405
$511$	14179.8	1.22755
$512$	12233.1	1.05592
$513$	−5629.29	−0.484482
$514$	−16495.0	−1.41549
$515$	11237.5	0.961525
$516$	922.213	0.0786786
$517$	3889.60	0.330879
$518$	−31722.3	−2.69073
$519$	5320.11	0.449955
$520$	0	0
$521$	19436.9	1.63445	0.817225	−	0.576319i	$-0.195511\pi$
$521$	19436.9	1.63445	0.817225	+	0.576319i	$0.195511\pi$
$522$	−12055.5	−1.01083
$523$	7506.41	0.627596	0.313798	−	0.949490i	$-0.398399\pi$
$523$	7506.41	0.627596	0.313798	+	0.949490i	$0.398399\pi$
$524$	−1643.94	−0.137053
$525$	−6042.62	−0.502327
$526$	−4351.20	−0.360687
$527$	−11056.6	−0.913911
$528$	−709.112	−0.0584472
$529$	31721.5	2.60717
$530$	13422.4	1.10006
$531$	−17309.9	−1.41467
$532$	4676.86	0.381142
$533$	0	0
$534$	652.381	0.0528675
$535$	−5722.08	−0.462406
$536$	−18061.3	−1.45546
$537$	4357.01	0.350129
$538$	9561.28	0.766201
$539$	6397.16	0.511216
$540$	2742.95	0.218589
$541$	−12312.4	−0.978472	−0.489236	−	0.872151i	$-0.662724\pi$
$541$	−12312.4	−0.978472	−0.489236	+	0.872151i	$0.662724\pi$
$542$	−8426.44	−0.667798
$543$	−2772.77	−0.219136
$544$	8634.22	0.680495
$545$	−19221.6	−1.51076
$546$	0	0
$547$	−14662.7	−1.14613	−0.573065	−	0.819510i	$-0.694246\pi$
$547$	−14662.7	−1.14613	−0.573065	+	0.819510i	$0.694246\pi$
$548$	−5872.47	−0.457773
$549$	−19965.7	−1.55212
$550$	−3436.07	−0.266390
$551$	−14374.9	−1.11142
$552$	7903.57	0.609417
$553$	4437.01	0.341195
$554$	−15443.4	−1.18435
$555$	−10585.2	−0.809579
$556$	−298.224	−0.0227473
$557$	−3081.36	−0.234401	−0.117200	−	0.993108i	$-0.537392\pi$
$557$	−3081.36	−0.234401	−0.117200	+	0.993108i	$0.537392\pi$
$558$	7247.40	0.549833
$559$	0	0
$560$	20346.8	1.53538
$561$	−1534.20	−0.115462
$562$	3172.58	0.238127
$563$	23657.1	1.77092	0.885461	−	0.464715i	$-0.153843\pi$
$563$	23657.1	1.77092	0.885461	+	0.464715i	$0.153843\pi$
$564$	−1177.70	−0.0879261
$565$	13435.5	1.00042
$566$	2616.55	0.194314
$567$	−16522.0	−1.22374
$568$	2099.14	0.155067
$569$	−4296.93	−0.316585	−0.158292	−	0.987392i	$-0.550599\pi$
$569$	−4296.93	−0.316585	−0.158292	+	0.987392i	$0.550599\pi$
$570$	−4198.56	−0.308523
$571$	−7065.70	−0.517847	−0.258923	−	0.965898i	$-0.583368\pi$
$571$	−7065.70	−0.517847	−0.258923	+	0.965898i	$0.583368\pi$
$572$	0	0
$573$	−3915.07	−0.285435
$574$	−12566.7	−0.913802
$575$	27097.4	1.96529
$576$	−13930.2	−1.00768
$577$	441.510	0.0318550	0.0159275	−	0.999873i	$-0.494930\pi$
$577$	441.510	0.0318550	0.0159275	+	0.999873i	$0.494930\pi$
$578$	−8036.67	−0.578342
$579$	2228.35	0.159943
$580$	7004.36	0.501449
$581$	9785.54	0.698748
$582$	−232.750	−0.0165770
$583$	−3833.50	−0.272328
$584$	−11451.1	−0.811384
$585$	0	0
$586$	3521.35	0.248235
$587$	2673.79	0.188005	0.0940027	−	0.995572i	$-0.470034\pi$
$587$	2673.79	0.188005	0.0940027	+	0.995572i	$0.470034\pi$
$588$	−1936.95	−0.135848
$589$	8641.75	0.604545
$590$	−27057.8	−1.88806
$591$	−3990.35	−0.277735
$592$	18125.9	1.25839
$593$	−20921.2	−1.44879	−0.724393	−	0.689388i	$-0.757880\pi$
$593$	−20921.2	−1.44879	−0.724393	+	0.689388i	$0.757880\pi$
$594$	2107.64	0.145585
$595$	44021.5	3.03312
$596$	−2423.84	−0.166585
$597$	4258.39	0.291933
$598$	0	0
$599$	−12968.6	−0.884610	−0.442305	−	0.896865i	$-0.645839\pi$
$599$	−12968.6	−0.884610	−0.442305	+	0.896865i	$0.645839\pi$
$600$	4879.79	0.332027
$601$	11309.1	0.767565	0.383782	−	0.923424i	$-0.374621\pi$
$601$	11309.1	0.767565	0.383782	+	0.923424i	$0.374621\pi$
$602$	−20332.5	−1.37656
$603$	18123.3	1.22394
$604$	−7.84405	−0.000528427 0
$605$	1929.74	0.129678
$606$	−6094.55	−0.408538
$607$	−380.075	−0.0254148	−0.0127074	−	0.999919i	$-0.504045\pi$
$607$	−380.075	−0.0254148	−0.0127074	+	0.999919i	$0.504045\pi$
$608$	−6748.47	−0.450142
$609$	9464.76	0.629772
$610$	−31209.1	−2.07151
$611$	0	0
$612$	−4848.82	−0.320265
$613$	−3658.88	−0.241078	−0.120539	−	0.992709i	$-0.538462\pi$
$613$	−3658.88	−0.241078	−0.120539	+	0.992709i	$0.538462\pi$
$614$	−10864.6	−0.714103
$615$	−4193.28	−0.274942
$616$	−8213.03	−0.537196
$617$	15361.9	1.00235	0.501173	−	0.865347i	$-0.332902\pi$
$617$	15361.9	1.00235	0.501173	+	0.865347i	$0.332902\pi$
$618$	−2614.45	−0.170176
$619$	−11374.5	−0.738576	−0.369288	−	0.929315i	$-0.620398\pi$
$619$	−11374.5	−0.738576	−0.369288	+	0.929315i	$0.620398\pi$
$620$	−4210.82	−0.272759
$621$	−16621.2	−1.07405
$622$	−13766.9	−0.887463
$623$	5346.23	0.343808
$624$	0	0
$625$	−15062.9	−0.964024
$626$	888.344	0.0567178
$627$	1199.13	0.0763771
$628$	−1099.94	−0.0698923
$629$	39216.3	2.48594
$630$	−28855.4	−1.82481
$631$	−4493.96	−0.283521	−0.141760	−	0.989901i	$-0.545276\pi$
$631$	−4493.96	−0.283521	−0.141760	+	0.989901i	$0.545276\pi$
$632$	−3583.15	−0.225523
$633$	925.242	0.0580965
$634$	−10166.7	−0.636866
$635$	−23457.8	−1.46597
$636$	1160.72	0.0723672
$637$	0	0
$638$	5382.02	0.333976
$639$	−2106.34	−0.130400
$640$	−9639.84	−0.595388
$641$	−9958.90	−0.613655	−0.306827	−	0.951765i	$-0.599267\pi$
$641$	−9958.90	−0.613655	−0.306827	+	0.951765i	$0.599267\pi$
$642$	1331.26	0.0818390
$643$	−16305.3	−1.00003	−0.500014	−	0.866017i	$-0.666672\pi$
$643$	−16305.3	−1.00003	−0.500014	+	0.866017i	$0.666672\pi$
$644$	13809.0	0.844955
$645$	−6784.60	−0.414175
$646$	15554.9	0.947370
$647$	−21900.2	−1.33073	−0.665367	−	0.746517i	$-0.731725\pi$
$647$	−21900.2	−1.33073	−0.665367	+	0.746517i	$0.731725\pi$
$648$	13342.5	0.808864
$649$	7727.82	0.467401
$650$	0	0
$651$	−5689.94	−0.342559
$652$	5660.55	0.340006
$653$	9862.53	0.591042	0.295521	−	0.955336i	$-0.404507\pi$
$653$	9862.53	0.591042	0.295521	+	0.955336i	$0.404507\pi$
$654$	4471.97	0.267382
$655$	12094.2	0.721468
$656$	7180.48	0.427364
$657$	11490.4	0.682316
$658$	25965.4	1.53836
$659$	1644.06	0.0971829	0.0485915	−	0.998819i	$-0.484527\pi$
$659$	1644.06	0.0971829	0.0485915	+	0.998819i	$0.484527\pi$
$660$	−584.292	−0.0344599
$661$	−12848.5	−0.756047	−0.378024	−	0.925796i	$-0.623396\pi$
$661$	−12848.5	−0.756047	−0.378024	+	0.925796i	$0.623396\pi$
$662$	1652.02	0.0969904
$663$	0	0
$664$	−7902.42	−0.461858
$665$	−34407.0	−2.00639
$666$	−25705.7	−1.49561
$667$	−42443.6	−2.46390
$668$	1383.21	0.0801165
$669$	−4756.53	−0.274885
$670$	28329.1	1.63351
$671$	8913.45	0.512816
$672$	4443.35	0.255068
$673$	16676.1	0.955151	0.477576	−	0.878591i	$-0.341516\pi$
$673$	16676.1	0.955151	0.477576	+	0.878591i	$0.341516\pi$
$674$	7709.73	0.440605
$675$	−10262.2	−0.585172
$676$	0	0
$677$	−12210.1	−0.693165	−0.346583	−	0.938019i	$-0.612658\pi$
$677$	−12210.1	−0.693165	−0.346583	+	0.938019i	$0.612658\pi$
$678$	−3125.82	−0.177059
$679$	−1907.37	−0.107803
$680$	−35550.1	−2.00483
$681$	4857.88	0.273354
$682$	−3235.52	−0.181663
$683$	−10114.0	−0.566621	−0.283310	−	0.959028i	$-0.591433\pi$
$683$	−10114.0	−0.566621	−0.283310	+	0.959028i	$0.591433\pi$
$684$	3789.81	0.211853
$685$	43203.0	2.40978
$686$	17517.9	0.974981
$687$	−1223.93	−0.0679706
$688$	11617.8	0.643785
$689$	0	0
$690$	−12396.8	−0.683967
$691$	−1802.70	−0.0992445	−0.0496223	−	0.998768i	$-0.515802\pi$
$691$	−1802.70	−0.0992445	−0.0496223	+	0.998768i	$0.515802\pi$
$692$	−7506.46	−0.412359
$693$	8241.22	0.451743
$694$	−8744.00	−0.478268
$695$	2194.00	0.119745
$696$	−7643.37	−0.416266
$697$	15535.4	0.844252
$698$	−10109.3	−0.548198
$699$	5717.79	0.309395
$700$	8525.89	0.460355
$701$	30538.0	1.64537	0.822686	−	0.568496i	$-0.192474\pi$
$701$	30538.0	1.64537	0.822686	+	0.568496i	$0.192474\pi$
$702$	0	0
$703$	−30651.3	−1.64443
$704$	6218.98	0.332936
$705$	8664.21	0.462855
$706$	−19191.7	−1.02307
$707$	−49944.5	−2.65680
$708$	−2339.85	−0.124205
$709$	−16654.8	−0.882208	−0.441104	−	0.897456i	$-0.645413\pi$
$709$	−16654.8	−0.882208	−0.441104	+	0.897456i	$0.645413\pi$
$710$	−3292.50	−0.174036
$711$	3595.45	0.189648
$712$	−4317.41	−0.227250
$713$	25515.8	1.34022
$714$	−10241.7	−0.536818
$715$	0	0
$716$	−6147.57	−0.320874
$717$	10553.0	0.549662
$718$	−5632.23	−0.292748
$719$	19302.3	1.00119	0.500595	−	0.865682i	$-0.333115\pi$
$719$	19302.3	1.00119	0.500595	+	0.865682i	$0.333115\pi$
$720$	16487.7	0.853418
$721$	−21425.3	−1.10668
$722$	4406.78	0.227152
$723$	−7659.67	−0.394006
$724$	3912.27	0.200827
$725$	−26205.3	−1.34240
$726$	−448.959	−0.0229510
$727$	−31545.7	−1.60931	−0.804653	−	0.593745i	$-0.797649\pi$
$727$	−31545.7	−1.60931	−0.804653	+	0.593745i	$0.797649\pi$
$728$	0	0
$729$	−10097.1	−0.512986
$730$	17961.0	0.910640
$731$	25135.8	1.27179
$732$	−2698.84	−0.136273
$733$	−20643.2	−1.04021	−0.520105	−	0.854102i	$-0.674107\pi$
$733$	−20643.2	−1.04021	−0.520105	+	0.854102i	$0.674107\pi$
$734$	21056.7	1.05888
$735$	14249.9	0.715124
$736$	−19925.7	−0.997922
$737$	−8090.92	−0.404386
$738$	−10183.2	−0.507924
$739$	6172.94	0.307274	0.153637	−	0.988127i	$-0.450901\pi$
$739$	6172.94	0.307274	0.153637	+	0.988127i	$0.450901\pi$
$740$	14935.3	0.741935
$741$	0	0
$742$	−25591.0	−1.26614
$743$	−21152.8	−1.04444	−0.522220	−	0.852811i	$-0.674896\pi$
$743$	−21152.8	−1.04444	−0.522220	+	0.852811i	$0.674896\pi$
$744$	4594.97	0.226425
$745$	17831.9	0.876926
$746$	−6078.54	−0.298326
$747$	7929.55	0.388390
$748$	2164.70	0.105814
$749$	10909.6	0.532215
$750$	−257.164	−0.0125204
$751$	−5685.07	−0.276233	−0.138117	−	0.990416i	$-0.544105\pi$
$751$	−5685.07	−0.276233	−0.138117	+	0.990416i	$0.544105\pi$
$752$	−14836.4	−0.719452
$753$	4588.76	0.222077
$754$	0	0
$755$	57.7076	0.00278172
$756$	−5229.67	−0.251589
$757$	34474.5	1.65521	0.827606	−	0.561309i	$-0.189702\pi$
$757$	34474.5	1.65521	0.827606	+	0.561309i	$0.189702\pi$
$758$	−24726.8	−1.18485
$759$	3540.57	0.169321
$760$	27785.8	1.32618
$761$	9322.39	0.444069	0.222034	−	0.975039i	$-0.428730\pi$
$761$	9322.39	0.444069	0.222034	+	0.975039i	$0.428730\pi$
$762$	5457.52	0.259455
$763$	36647.6	1.73884
$764$	5524.00	0.261585
$765$	35672.1	1.68592
$766$	5999.40	0.282986
$767$	0	0
$768$	−4706.25	−0.221123
$769$	−2946.38	−0.138165	−0.0690827	−	0.997611i	$-0.522007\pi$
$769$	−2946.38	−0.138165	−0.0690827	+	0.997611i	$0.522007\pi$
$770$	12882.2	0.602910
$771$	10494.0	0.490185
$772$	−3144.12	−0.146579
$773$	25314.4	1.17787	0.588937	−	0.808179i	$-0.299547\pi$
$773$	25314.4	1.17787	0.588937	+	0.808179i	$0.299547\pi$
$774$	−16476.1	−0.765143
$775$	15753.9	0.730188
$776$	1540.32	0.0712555
$777$	20181.5	0.931800
$778$	−15045.1	−0.693306
$779$	−12142.4	−0.558466
$780$	0	0
$781$	940.351	0.0430838
$782$	45927.9	2.10023
$783$	16074.0	0.733637
$784$	−24401.2	−1.11157
$785$	8092.11	0.367923
$786$	−2813.76	−0.127689
$787$	−42757.8	−1.93666	−0.968330	−	0.249672i	$-0.919677\pi$
$787$	−42757.8	−1.93666	−0.968330	+	0.249672i	$0.919677\pi$
$788$	5630.22	0.254528
$789$	2768.20	0.124906
$790$	5620.19	0.253111
$791$	−25615.9	−1.15145
$792$	−6655.29	−0.298593
$793$	0	0
$794$	5535.42	0.247411
$795$	−8539.26	−0.380951
$796$	−6008.41	−0.267541
$797$	−15208.9	−0.675945	−0.337972	−	0.941156i	$-0.609741\pi$
$797$	−15208.9	−0.675945	−0.337972	+	0.941156i	$0.609741\pi$
$798$	8004.90	0.355101
$799$	−32099.4	−1.42127
$800$	−12302.4	−0.543695
$801$	4332.23	0.191101
$802$	−27815.2	−1.22468
$803$	−5129.74	−0.225435
$804$	2449.79	0.107460
$805$	−101591.	−4.44796
$806$	0	0
$807$	−6082.82	−0.265335
$808$	40333.3	1.75609
$809$	−30474.8	−1.32440	−0.662199	−	0.749328i	$-0.730377\pi$
$809$	−30474.8	−1.32440	−0.662199	+	0.749328i	$0.730377\pi$
$810$	−20927.8	−0.907812
$811$	−16231.2	−0.702778	−0.351389	−	0.936230i	$-0.614291\pi$
$811$	−16231.2	−0.702778	−0.351389	+	0.936230i	$0.614291\pi$
$812$	−13354.4	−0.577152
$813$	5360.84	0.231258
$814$	11476.0	0.494144
$815$	−41643.9	−1.78984
$816$	5852.04	0.251057
$817$	−19646.0	−0.841280
$818$	−6133.94	−0.262186
$819$	0	0
$820$	5916.54	0.251969
$821$	−26920.4	−1.14437	−0.572186	−	0.820124i	$-0.693905\pi$
$821$	−26920.4	−1.14437	−0.572186	+	0.820124i	$0.693905\pi$
$822$	−10051.3	−0.426496
$823$	−11791.6	−0.499428	−0.249714	−	0.968320i	$-0.580337\pi$
$823$	−11791.6	−0.499428	−0.249714	+	0.968320i	$0.580337\pi$
$824$	17302.2	0.731495
$825$	2186.00	0.0922506
$826$	51587.9	2.17309
$827$	32014.5	1.34613	0.673067	−	0.739581i	$-0.264976\pi$
$827$	32014.5	1.34613	0.673067	+	0.739581i	$0.264976\pi$
$828$	11189.9	0.469657
$829$	22573.8	0.945744	0.472872	−	0.881131i	$-0.343217\pi$
$829$	22573.8	0.945744	0.472872	+	0.881131i	$0.343217\pi$
$830$	12395.0	0.518356
$831$	9825.01	0.410139
$832$	0	0
$833$	−52793.5	−2.19590
$834$	−510.440	−0.0211932
$835$	−10176.1	−0.421745
$836$	−1691.92	−0.0699954
$837$	−9663.21	−0.399056
$838$	−28761.5	−1.18562
$839$	−6618.11	−0.272327	−0.136164	−	0.990686i	$-0.543477\pi$
$839$	−6618.11	−0.272327	−0.136164	+	0.990686i	$0.543477\pi$
$840$	−18294.8	−0.751466
$841$	16657.3	0.682983
$842$	−11612.7	−0.475296
$843$	−2018.37	−0.0824632
$844$	−1305.48	−0.0532422
$845$	0	0
$846$	21040.7	0.855074
$847$	−3679.20	−0.149255
$848$	14622.4	0.592142
$849$	−1664.63	−0.0672910
$850$	28356.6	1.14426
$851$	−90501.7	−3.64554
$852$	−284.723	−0.0114489
$853$	29314.3	1.17667	0.588336	−	0.808617i	$-0.299783\pi$
$853$	29314.3	1.17667	0.588336	+	0.808617i	$0.299783\pi$
$854$	59502.7	2.38424
$855$	−27881.1	−1.11522
$856$	−8810.19	−0.351783
$857$	−4185.62	−0.166835	−0.0834177	−	0.996515i	$-0.526584\pi$
$857$	−4185.62	−0.166835	−0.0834177	+	0.996515i	$0.526584\pi$
$858$	0	0
$859$	5803.56	0.230518	0.115259	−	0.993335i	$-0.463230\pi$
$859$	5803.56	0.230518	0.115259	+	0.993335i	$0.463230\pi$
$860$	9572.79	0.379569
$861$	7994.82	0.316449
$862$	−26623.7	−1.05198
$863$	977.621	0.0385615	0.0192808	−	0.999814i	$-0.493862\pi$
$863$	977.621	0.0385615	0.0192808	+	0.999814i	$0.493862\pi$
$864$	7546.14	0.297135
$865$	55224.0	2.17072
$866$	−2290.93	−0.0898948
$867$	5112.88	0.200280
$868$	8028.27	0.313937
$869$	−1605.15	−0.0626593
$870$	11988.7	0.467188
$871$	0	0
$872$	−29595.2	−1.14933
$873$	−1545.61	−0.0599208
$874$	−35897.0	−1.38928
$875$	−2107.45	−0.0814227
$876$	1553.20	0.0599061
$877$	47760.2	1.83894	0.919468	−	0.393164i	$-0.128620\pi$
$877$	47760.2	1.83894	0.919468	+	0.393164i	$0.128620\pi$
$878$	−5118.62	−0.196748
$879$	−2240.26	−0.0859637
$880$	−7360.75	−0.281967
$881$	−1857.80	−0.0710454	−0.0355227	−	0.999369i	$-0.511310\pi$
$881$	−1857.80	−0.0710454	−0.0355227	+	0.999369i	$0.511310\pi$
$882$	34605.3	1.32111
$883$	6489.60	0.247330	0.123665	−	0.992324i	$-0.460535\pi$
$883$	6489.60	0.247330	0.123665	+	0.992324i	$0.460535\pi$
$884$	0	0
$885$	17214.0	0.653833
$886$	−21983.9	−0.833592
$887$	51445.9	1.94745	0.973723	−	0.227737i	$-0.0731328\pi$
$887$	51445.9	1.94745	0.973723	+	0.227737i	$0.0731328\pi$
$888$	−16297.8	−0.615900
$889$	44724.1	1.68729
$890$	6771.87	0.255049
$891$	5977.06	0.224735
$892$	6711.27	0.251917
$893$	25088.7	0.940159
$894$	−4148.65	−0.155203
$895$	45226.8	1.68912
$896$	18379.1	0.685272
$897$	0	0
$898$	3799.83	0.141205
$899$	−24675.8	−0.915445
$900$	6908.81	0.255882
$901$	31636.5	1.16977
$902$	4546.16	0.167817
$903$	12935.4	0.476703
$904$	20686.4	0.761085
$905$	−28782.1	−1.05718
$906$	−13.4259	−0.000492323 0
$907$	35522.2	1.30044	0.650218	−	0.759747i	$-0.274677\pi$
$907$	35522.2	1.30044	0.650218	+	0.759747i	$0.274677\pi$
$908$	−6854.27	−0.250514
$909$	−40471.7	−1.47675
$910$	0	0
$911$	−17559.4	−0.638605	−0.319303	−	0.947653i	$-0.603449\pi$
$911$	−17559.4	−0.638605	−0.319303	+	0.947653i	$0.603449\pi$
$912$	−4573.93	−0.166072
$913$	−3540.05	−0.128323
$914$	8230.16	0.297844
$915$	19855.0	0.717363
$916$	1726.91	0.0622913
$917$	−23058.7	−0.830386
$918$	−17393.5	−0.625351
$919$	−26065.7	−0.935612	−0.467806	−	0.883831i	$-0.654955\pi$
$919$	−26065.7	−0.935612	−0.467806	+	0.883831i	$0.654955\pi$
$920$	82041.0	2.94001
$921$	6911.97	0.247293
$922$	14424.2	0.515224
$923$	0	0
$924$	1114.00	0.0396622
$925$	−55877.1	−1.98619
$926$	−31320.0	−1.11149
$927$	−17361.6	−0.615135
$928$	19269.7	0.681637
$929$	18847.3	0.665619	0.332809	−	0.942994i	$-0.392003\pi$
$929$	18847.3	0.665619	0.332809	+	0.942994i	$0.392003\pi$
$930$	−7207.23	−0.254123
$931$	41263.1	1.45257
$932$	−8067.58	−0.283543
$933$	8758.40	0.307328
$934$	−15784.8	−0.552993
$935$	−15925.4	−0.557023
$936$	0	0
$937$	24109.6	0.840582	0.420291	−	0.907389i	$-0.361928\pi$
$937$	24109.6	0.840582	0.420291	+	0.907389i	$0.361928\pi$
$938$	−54011.8	−1.88012
$939$	−565.158	−0.0196414
$940$	−12224.9	−0.424182
$941$	28485.2	0.986814	0.493407	−	0.869799i	$-0.335751\pi$
$941$	28485.2	0.986814	0.493407	+	0.869799i	$0.335751\pi$
$942$	−1882.65	−0.0651170
$943$	−35851.8	−1.23807
$944$	−29476.9	−1.01630
$945$	38474.0	1.32440
$946$	7355.55	0.252801
$947$	8243.78	0.282880	0.141440	−	0.989947i	$-0.454827\pi$
$947$	8243.78	0.282880	0.141440	+	0.989947i	$0.454827\pi$
$948$	486.012	0.0166508
$949$	0	0
$950$	−22163.4	−0.756921
$951$	6468.01	0.220546
$952$	67779.2	2.30749
$953$	18634.1	0.633388	0.316694	−	0.948528i	$-0.397427\pi$
$953$	18634.1	0.633388	0.316694	+	0.948528i	$0.397427\pi$
$954$	−20737.2	−0.703765
$955$	−40639.3	−1.37702
$956$	−14889.8	−0.503735
$957$	−3424.01	−0.115656
$958$	−13235.8	−0.446378
$959$	−82370.0	−2.77358
$960$	13853.0	0.465733
$961$	−14956.6	−0.502051
$962$	0	0
$963$	8840.43	0.295824
$964$	10807.5	0.361085
$965$	23130.8	0.771615
$966$	23635.5	0.787224
$967$	−97.2454	−0.00323392	−0.00161696	−	0.999999i	$-0.500515\pi$
$967$	−97.2454	−0.00323392	−0.00161696	+	0.999999i	$0.500515\pi$
$968$	2971.18	0.0986542
$969$	−9895.95	−0.328074
$970$	−2416.00	−0.0799722
$971$	15600.0	0.515579	0.257790	−	0.966201i	$-0.417006\pi$
$971$	15600.0	0.515579	0.257790	+	0.966201i	$0.417006\pi$
$972$	−6453.52	−0.212960
$973$	−4183.03	−0.137823
$974$	−30966.6	−1.01872
$975$	0	0
$976$	−33999.3	−1.11505
$977$	−29788.9	−0.975469	−0.487734	−	0.872992i	$-0.662177\pi$
$977$	−29788.9	−0.975469	−0.487734	+	0.872992i	$0.662177\pi$
$978$	9688.58	0.316776
$979$	−1934.07	−0.0631391
$980$	−20106.0	−0.655372
$981$	29696.8	0.966508
$982$	40611.7	1.31973
$983$	−29732.8	−0.964730	−0.482365	−	0.875970i	$-0.660222\pi$
$983$	−29732.8	−0.964730	−0.482365	+	0.875970i	$0.660222\pi$
$984$	−6456.31	−0.209166
$985$	−41420.8	−1.33987
$986$	−44415.9	−1.43457
$987$	−16519.0	−0.532732
$988$	0	0
$989$	−58007.2	−1.86504
$990$	10438.8	0.335120
$991$	−29315.6	−0.939699	−0.469850	−	0.882746i	$-0.655692\pi$
$991$	−29315.6	−0.939699	−0.469850	+	0.882746i	$0.655692\pi$
$992$	−11584.4	−0.370771
$993$	−1051.00	−0.0335877
$994$	6277.42	0.200310
$995$	44203.1	1.40837
$996$	1071.87	0.0340999
$997$	1897.50	0.0602753	0.0301376	−	0.999546i	$-0.490405\pi$
$997$	1897.50	0.0602753	0.0301376	+	0.999546i	$0.490405\pi$
$998$	−14614.8	−0.463551
$999$	34274.3	1.08548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.17	yes	51
13.12	even	2		1859.4.a.p.1.35	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.35	✓	51	13.12	even	2
1859.4.a.q.1.17	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)

\(f(q)\)	\(=\)	\(q-2.41499 q^{2} +1.53640 q^{3} -2.16780 q^{4} +15.9482 q^{5} -3.71040 q^{6} -30.4066 q^{7} +24.5552 q^{8} -24.6395 q^{9} +O(q^{10})\)	\(q-2.41499 q^{2} +1.53640 q^{3} -2.16780 q^{4} +15.9482 q^{5} -3.71040 q^{6} -30.4066 q^{7} +24.5552 q^{8} -24.6395 q^{9} -38.5149 q^{10} +11.0000 q^{11} -3.33062 q^{12} +73.4317 q^{14} +24.5029 q^{15} -41.9582 q^{16} -90.7790 q^{17} +59.5042 q^{18} +70.9524 q^{19} -34.5726 q^{20} -46.7168 q^{21} -26.5649 q^{22} +209.496 q^{23} +37.7266 q^{24} +129.346 q^{25} -79.3390 q^{27} +65.9154 q^{28} -202.599 q^{29} -59.1744 q^{30} +121.796 q^{31} -95.1126 q^{32} +16.9004 q^{33} +219.231 q^{34} -484.931 q^{35} +53.4135 q^{36} -431.998 q^{37} -171.350 q^{38} +391.612 q^{40} -171.134 q^{41} +112.821 q^{42} -276.890 q^{43} -23.8458 q^{44} -392.956 q^{45} -505.931 q^{46} +353.600 q^{47} -64.4647 q^{48} +581.560 q^{49} -312.370 q^{50} -139.473 q^{51} -348.500 q^{53} +191.603 q^{54} +175.430 q^{55} -746.639 q^{56} +109.011 q^{57} +489.275 q^{58} +702.529 q^{59} -53.1174 q^{60} +810.313 q^{61} -294.138 q^{62} +749.202 q^{63} +565.362 q^{64} -40.8144 q^{66} -735.538 q^{67} +196.791 q^{68} +321.870 q^{69} +1171.11 q^{70} +85.4865 q^{71} -605.027 q^{72} -466.340 q^{73} +1043.27 q^{74} +198.727 q^{75} -153.811 q^{76} -334.472 q^{77} -145.923 q^{79} -669.159 q^{80} +543.369 q^{81} +413.287 q^{82} -321.823 q^{83} +101.273 q^{84} -1447.76 q^{85} +668.687 q^{86} -311.273 q^{87} +270.107 q^{88} -175.825 q^{89} +948.986 q^{90} -454.145 q^{92} +187.128 q^{93} -853.941 q^{94} +1131.56 q^{95} -146.131 q^{96} +62.7289 q^{97} -1404.47 q^{98} -271.034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 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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