LMFDB - Embedded newform 1859.4.a.q.1.1

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			1.1
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.57916 q^{2} +9.06032 q^{3} +23.1271 q^{4} -7.74998 q^{5} -50.5490 q^{6} +23.9301 q^{7} -84.3964 q^{8} +55.0894 q^{9} +O(q^{10})$	\(q-5.57916 q^{2} +9.06032 q^{3} +23.1271 q^{4} -7.74998 q^{5} -50.5490 q^{6} +23.9301 q^{7} -84.3964 q^{8} +55.0894 q^{9} +43.2384 q^{10} +11.0000 q^{11} +209.539 q^{12} -133.510 q^{14} -70.2173 q^{15} +285.845 q^{16} -76.7116 q^{17} -307.353 q^{18} -125.412 q^{19} -179.234 q^{20} +216.814 q^{21} -61.3708 q^{22} +31.3620 q^{23} -764.659 q^{24} -64.9379 q^{25} +254.499 q^{27} +553.433 q^{28} -81.5166 q^{29} +391.754 q^{30} -42.4475 q^{31} -919.605 q^{32} +99.6635 q^{33} +427.987 q^{34} -185.458 q^{35} +1274.06 q^{36} +300.951 q^{37} +699.694 q^{38} +654.071 q^{40} +67.1413 q^{41} -1209.64 q^{42} +302.197 q^{43} +254.398 q^{44} -426.942 q^{45} -174.974 q^{46} +93.6609 q^{47} +2589.85 q^{48} +229.650 q^{49} +362.299 q^{50} -695.032 q^{51} -326.224 q^{53} -1419.89 q^{54} -85.2498 q^{55} -2019.62 q^{56} -1136.27 q^{57} +454.795 q^{58} +253.817 q^{59} -1623.92 q^{60} +203.061 q^{61} +236.821 q^{62} +1318.30 q^{63} +2843.87 q^{64} -556.039 q^{66} +766.077 q^{67} -1774.12 q^{68} +284.150 q^{69} +1034.70 q^{70} +28.0671 q^{71} -4649.35 q^{72} -5.12982 q^{73} -1679.06 q^{74} -588.358 q^{75} -2900.41 q^{76} +263.231 q^{77} +895.725 q^{79} -2215.29 q^{80} +818.431 q^{81} -374.592 q^{82} +837.320 q^{83} +5014.28 q^{84} +594.513 q^{85} -1686.00 q^{86} -738.567 q^{87} -928.361 q^{88} +436.575 q^{89} +2381.98 q^{90} +725.311 q^{92} -384.588 q^{93} -522.550 q^{94} +971.940 q^{95} -8331.92 q^{96} +1336.58 q^{97} -1281.26 q^{98} +605.984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.57916	−1.97253	−0.986266	−	0.165163i	$-0.947185\pi$
$2$	−5.57916	−1.97253	−0.986266	+	0.165163i	$0.947185\pi$
$3$	9.06032	1.74366	0.871830	−	0.489809i	$-0.162933\pi$
$3$	9.06032	1.74366	0.871830	+	0.489809i	$0.162933\pi$
$4$	23.1271	2.89088
$5$	−7.74998	−0.693179	−0.346590	−	0.938017i	$-0.612660\pi$
$5$	−7.74998	−0.693179	−0.346590	+	0.938017i	$0.612660\pi$
$6$	−50.5490	−3.43943
$7$	23.9301	1.29210	0.646052	−	0.763293i	$-0.276419\pi$
$7$	23.9301	1.29210	0.646052	+	0.763293i	$0.276419\pi$
$8$	−84.3964	−3.72983
$9$	55.0894	2.04035
$10$	43.2384	1.36732
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	209.539	5.04072
$13$	0	0
$13$	0	0
$14$	−133.510	−2.54872
$15$	−70.2173	−1.20867
$16$	285.845	4.46633
$17$	−76.7116	−1.09443	−0.547215	−	0.836992i	$-0.684312\pi$
$17$	−76.7116	−1.09443	−0.547215	+	0.836992i	$0.684312\pi$
$18$	−307.353	−4.02466
$19$	−125.412	−1.51429	−0.757144	−	0.653248i	$-0.773406\pi$
$19$	−125.412	−1.51429	−0.757144	+	0.653248i	$0.773406\pi$
$20$	−179.234	−2.00390
$21$	216.814	2.25299
$22$	−61.3708	−0.594741
$23$	31.3620	0.284323	0.142161	−	0.989843i	$-0.454595\pi$
$23$	31.3620	0.284323	0.142161	+	0.989843i	$0.454595\pi$
$24$	−764.659	−6.50356
$25$	−64.9379	−0.519503
$26$	0	0
$27$	254.499	1.81402
$28$	553.433	3.73532
$29$	−81.5166	−0.521974	−0.260987	−	0.965342i	$-0.584048\pi$
$29$	−81.5166	−0.521974	−0.260987	+	0.965342i	$0.584048\pi$
$30$	391.754	2.38414
$31$	−42.4475	−0.245929	−0.122964	−	0.992411i	$-0.539240\pi$
$31$	−42.4475	−0.245929	−0.122964	+	0.992411i	$0.539240\pi$
$32$	−919.605	−5.08015
$33$	99.6635	0.525733
$34$	427.987	2.15880
$35$	−185.458	−0.895660
$36$	1274.06	5.89841
$37$	300.951	1.33719	0.668595	−	0.743626i	$-0.266896\pi$
$37$	300.951	1.33719	0.668595	+	0.743626i	$0.266896\pi$
$38$	699.694	2.98698
$39$	0	0
$40$	654.071	2.58544
$41$	67.1413	0.255749	0.127874	−	0.991790i	$-0.459185\pi$
$41$	67.1413	0.255749	0.127874	+	0.991790i	$0.459185\pi$
$42$	−1209.64	−4.44410
$43$	302.197	1.07173	0.535867	−	0.844303i	$-0.319985\pi$
$43$	302.197	1.07173	0.535867	+	0.844303i	$0.319985\pi$
$44$	254.398	0.871634
$45$	−426.942	−1.41433
$46$	−174.974	−0.560836
$47$	93.6609	0.290678	0.145339	−	0.989382i	$-0.453573\pi$
$47$	93.6609	0.290678	0.145339	+	0.989382i	$0.453573\pi$
$48$	2589.85	7.78776
$49$	229.650	0.669534
$50$	362.299	1.02474
$51$	−695.032	−1.90831
$52$	0	0
$53$	−326.224	−0.845478	−0.422739	−	0.906252i	$-0.638931\pi$
$53$	−326.224	−0.845478	−0.422739	+	0.906252i	$0.638931\pi$
$54$	−1419.89	−3.57820
$55$	−85.2498	−0.209001
$56$	−2019.62	−4.81933
$57$	−1136.27	−2.64040
$58$	454.795	1.02961
$59$	253.817	0.560071	0.280035	−	0.959990i	$-0.409654\pi$
$59$	253.817	0.560071	0.280035	+	0.959990i	$0.409654\pi$
$60$	−1623.92	−3.49412
$61$	203.061	0.426217	0.213109	−	0.977029i	$-0.431641\pi$
$61$	203.061	0.426217	0.213109	+	0.977029i	$0.431641\pi$
$62$	236.821	0.485102
$63$	1318.30	2.63634
$64$	2843.87	5.55443
$65$	0	0
$66$	−556.039	−1.03703
$67$	766.077	1.39688	0.698442	−	0.715667i	$-0.253877\pi$
$67$	766.077	1.39688	0.698442	+	0.715667i	$0.253877\pi$
$68$	−1774.12	−3.16387
$69$	284.150	0.495762
$70$	1034.70	1.76672
$71$	28.0671	0.0469148	0.0234574	−	0.999725i	$-0.492533\pi$
$71$	28.0671	0.0469148	0.0234574	+	0.999725i	$0.492533\pi$
$72$	−4649.35	−7.61016
$73$	−5.12982	−0.00822465	−0.00411233	−	0.999992i	$-0.501309\pi$
$73$	−5.12982	−0.00822465	−0.00411233	+	0.999992i	$0.501309\pi$
$74$	−1679.06	−2.63765
$75$	−588.358	−0.905836
$76$	−2900.41	−4.37763
$77$	263.231	0.389584
$78$	0	0
$79$	895.725	1.27566	0.637829	−	0.770178i	$-0.279833\pi$
$79$	895.725	1.27566	0.637829	+	0.770178i	$0.279833\pi$
$80$	−2215.29	−3.09597
$81$	818.431	1.12268
$82$	−374.592	−0.504473
$83$	837.320	1.10732	0.553662	−	0.832742i	$-0.313230\pi$
$83$	837.320	1.10732	0.553662	+	0.832742i	$0.313230\pi$
$84$	5014.28	6.51314
$85$	594.513	0.758636
$86$	−1686.00	−2.11403
$87$	−738.567	−0.910146
$88$	−928.361	−1.12459
$89$	436.575	0.519965	0.259982	−	0.965613i	$-0.416283\pi$
$89$	436.575	0.519965	0.259982	+	0.965613i	$0.416283\pi$
$90$	2381.98	2.78981
$91$	0	0
$92$	725.311	0.821944
$93$	−384.588	−0.428816
$94$	−522.550	−0.573371
$95$	971.940	1.04967
$96$	−8331.92	−8.85805
$97$	1336.58	1.39906	0.699531	−	0.714602i	$-0.253392\pi$
$97$	1336.58	1.39906	0.699531	+	0.714602i	$0.253392\pi$
$98$	−1281.26	−1.32068
$99$	605.984	0.615188
$100$	−1501.82	−1.50182
$101$	1217.54	1.19950	0.599750	−	0.800188i	$-0.295267\pi$
$101$	1217.54	1.19950	0.599750	+	0.800188i	$0.295267\pi$
$102$	3877.70	3.76421
$103$	1203.38	1.15119	0.575593	−	0.817736i	$-0.304771\pi$
$103$	1203.38	1.15119	0.575593	+	0.817736i	$0.304771\pi$
$104$	0	0
$105$	−1680.31	−1.56173
$106$	1820.06	1.66773
$107$	1229.26	1.11063	0.555313	−	0.831642i	$-0.312599\pi$
$107$	1229.26	1.11063	0.555313	+	0.831642i	$0.312599\pi$
$108$	5885.82	5.24411
$109$	46.8157	0.0411388	0.0205694	−	0.999788i	$-0.493452\pi$
$109$	46.8157	0.0411388	0.0205694	+	0.999788i	$0.493452\pi$
$110$	475.622	0.412262
$111$	2726.71	2.33161
$112$	6840.30	5.77096
$113$	1113.94	0.927354	0.463677	−	0.886004i	$-0.346530\pi$
$113$	1113.94	0.927354	0.463677	+	0.886004i	$0.346530\pi$
$114$	6339.45	5.20828
$115$	−243.055	−0.197087
$116$	−1885.24	−1.50897
$117$	0	0
$118$	−1416.09	−1.10476
$119$	−1835.72	−1.41412
$120$	5926.09	4.50813
$121$	121.000	0.0909091
$122$	−1132.91	−0.840728
$123$	608.322	0.445939
$124$	−981.686	−0.710951
$125$	1472.01	1.05329
$126$	−7354.99	−5.20027
$127$	−857.635	−0.599235	−0.299617	−	0.954059i	$-0.596859\pi$
$127$	−857.635	−0.599235	−0.299617	+	0.954059i	$0.596859\pi$
$128$	−8509.56	−5.87614
$129$	2738.00	1.86874
$130$	0	0
$131$	−818.889	−0.546158	−0.273079	−	0.961992i	$-0.588042\pi$
$131$	−818.889	−0.546158	−0.273079	+	0.961992i	$0.588042\pi$
$132$	2304.93	1.51983
$133$	−3001.12	−1.95662
$134$	−4274.07	−2.75540
$135$	−1972.36	−1.25744
$136$	6474.19	4.08204
$137$	2293.58	1.43032	0.715159	−	0.698962i	$-0.246354\pi$
$137$	2293.58	1.43032	0.715159	+	0.698962i	$0.246354\pi$
$138$	−1585.32	−0.977907
$139$	2516.25	1.53544	0.767719	−	0.640786i	$-0.221392\pi$
$139$	2516.25	1.53544	0.767719	+	0.640786i	$0.221392\pi$
$140$	−4289.10	−2.58925
$141$	848.598	0.506843
$142$	−156.591	−0.0925411
$143$	0	0
$144$	15747.0	9.11287
$145$	631.752	0.361822
$146$	28.6201	0.0162234
$147$	2080.70	1.16744
$148$	6960.12	3.86566
$149$	2345.24	1.28946	0.644730	−	0.764410i	$-0.276970\pi$
$149$	2345.24	1.28946	0.644730	+	0.764410i	$0.276970\pi$
$150$	3282.55	1.78679
$151$	−2053.62	−1.10676	−0.553382	−	0.832928i	$-0.686663\pi$
$151$	−2053.62	−1.10676	−0.553382	+	0.832928i	$0.686663\pi$
$152$	10584.3	5.64804
$153$	−4226.00	−2.23302
$154$	−1468.61	−0.768467
$155$	328.967	0.170473
$156$	0	0
$157$	588.540	0.299176	0.149588	−	0.988748i	$-0.452205\pi$
$157$	588.540	0.299176	0.149588	+	0.988748i	$0.452205\pi$
$158$	−4997.40	−2.51628
$159$	−2955.69	−1.47423
$160$	7126.92	3.52145
$161$	750.495	0.367375
$162$	−4566.16	−2.21451
$163$	−1041.12	−0.500288	−0.250144	−	0.968209i	$-0.580478\pi$
$163$	−1041.12	−0.500288	−0.250144	+	0.968209i	$0.580478\pi$
$164$	1552.78	0.739341
$165$	−772.390	−0.364427
$166$	−4671.55	−2.18423
$167$	671.486	0.311144	0.155572	−	0.987825i	$-0.450278\pi$
$167$	671.486	0.311144	0.155572	+	0.987825i	$0.450278\pi$
$168$	−18298.4	−8.40327
$169$	0	0
$170$	−3316.89	−1.49643
$171$	−6908.87	−3.08968
$172$	6988.92	3.09826
$173$	−3658.93	−1.60800	−0.803998	−	0.594632i	$-0.797298\pi$
$173$	−3658.93	−1.60800	−0.803998	+	0.594632i	$0.797298\pi$
$174$	4120.59	1.79529
$175$	−1553.97	−0.671252
$176$	3144.30	1.34665
$177$	2299.66	0.976572
$178$	−2435.73	−1.02565
$179$	−737.969	−0.308147	−0.154074	−	0.988059i	$-0.549239\pi$
$179$	−737.969	−0.308147	−0.154074	+	0.988059i	$0.549239\pi$
$180$	−9873.92	−4.08866
$181$	3004.00	1.23362	0.616812	−	0.787111i	$-0.288424\pi$
$181$	3004.00	1.23362	0.616812	+	0.787111i	$0.288424\pi$
$182$	0	0
$183$	1839.80	0.743178
$184$	−2646.84	−1.06048
$185$	−2332.36	−0.926912
$186$	2145.68	0.845853
$187$	−843.828	−0.329983
$188$	2166.10	0.840316
$189$	6090.20	2.34390
$190$	−5422.61	−2.07051
$191$	−2817.59	−1.06740	−0.533701	−	0.845673i	$-0.679199\pi$
$191$	−2817.59	−1.06740	−0.533701	+	0.845673i	$0.679199\pi$
$192$	25766.3	9.68503
$193$	−530.045	−0.197686	−0.0988432	−	0.995103i	$-0.531514\pi$
$193$	−530.045	−0.197686	−0.0988432	+	0.995103i	$0.531514\pi$
$194$	−7456.99	−2.75970
$195$	0	0
$196$	5311.14	1.93555
$197$	−1737.16	−0.628262	−0.314131	−	0.949380i	$-0.601713\pi$
$197$	−1737.16	−0.628262	−0.314131	+	0.949380i	$0.601713\pi$
$198$	−3380.88	−1.21348
$199$	4171.35	1.48593	0.742963	−	0.669332i	$-0.233420\pi$
$199$	4171.35	1.48593	0.742963	+	0.669332i	$0.233420\pi$
$200$	5480.52	1.93766
$201$	6940.91	2.43569
$202$	−6792.84	−2.36605
$203$	−1950.70	−0.674445
$204$	−16074.1	−5.51671
$205$	−520.343	−0.177280
$206$	−6713.84	−2.27075
$207$	1727.71	0.580118
$208$	0	0
$209$	−1379.53	−0.456575
$210$	9374.71	3.08055
$211$	2675.06	0.872789	0.436395	−	0.899755i	$-0.356255\pi$
$211$	2675.06	0.872789	0.436395	+	0.899755i	$0.356255\pi$
$212$	−7544.61	−2.44418
$213$	254.297	0.0818035
$214$	−6858.24	−2.19075
$215$	−2342.02	−0.742903
$216$	−21478.8	−6.76597
$217$	−1015.77	−0.317765
$218$	−261.193	−0.0811477
$219$	−46.4778	−0.0143410
$220$	−1971.58	−0.604199
$221$	0	0
$222$	−15212.8	−4.59917
$223$	2880.80	0.865079	0.432539	−	0.901615i	$-0.357618\pi$
$223$	2880.80	0.865079	0.432539	+	0.901615i	$0.357618\pi$
$224$	−22006.2	−6.56408
$225$	−3577.39	−1.05997
$226$	−6214.88	−1.82924
$227$	1350.34	0.394823	0.197412	−	0.980321i	$-0.436746\pi$
$227$	1350.34	0.394823	0.197412	+	0.980321i	$0.436746\pi$
$228$	−26278.7	−7.63310
$229$	−2050.18	−0.591613	−0.295807	−	0.955248i	$-0.595588\pi$
$229$	−2050.18	−0.591613	−0.295807	+	0.955248i	$0.595588\pi$
$230$	1356.04	0.388760
$231$	2384.96	0.679302
$232$	6879.71	1.94688
$233$	4660.49	1.31038	0.655191	−	0.755463i	$-0.272588\pi$
$233$	4660.49	1.31038	0.655191	+	0.755463i	$0.272588\pi$
$234$	0	0
$235$	−725.870	−0.201492
$236$	5870.05	1.61910
$237$	8115.56	2.22431
$238$	10241.8	2.78939
$239$	−5180.41	−1.40206	−0.701031	−	0.713131i	$-0.747277\pi$
$239$	−5180.41	−1.40206	−0.701031	+	0.713131i	$0.747277\pi$
$240$	−20071.3	−5.39831
$241$	5092.66	1.36119	0.680596	−	0.732659i	$-0.261721\pi$
$241$	5092.66	1.36119	0.680596	+	0.732659i	$0.261721\pi$
$242$	−675.079	−0.179321
$243$	543.764	0.143549
$244$	4696.20	1.23215
$245$	−1779.78	−0.464107
$246$	−3393.93	−0.879630
$247$	0	0
$248$	3582.41	0.917272
$249$	7586.39	1.93080
$250$	−8212.61	−2.07764
$251$	−4090.95	−1.02876	−0.514380	−	0.857563i	$-0.671978\pi$
$251$	−4090.95	−1.02876	−0.514380	+	0.857563i	$0.671978\pi$
$252$	30488.3	7.62137
$253$	344.982	0.0857265
$254$	4784.89	1.18201
$255$	5386.48	1.32280
$256$	24725.3	6.03645
$257$	−7467.72	−1.81254	−0.906271	−	0.422696i	$-0.861084\pi$
$257$	−7467.72	−1.81254	−0.906271	+	0.422696i	$0.861084\pi$
$258$	−15275.7	−3.68615
$259$	7201.79	1.72779
$260$	0	0
$261$	−4490.70	−1.06501
$262$	4568.72	1.07731
$263$	−7114.95	−1.66816	−0.834082	−	0.551641i	$-0.814002\pi$
$263$	−7114.95	−1.66816	−0.834082	+	0.551641i	$0.814002\pi$
$264$	−8411.25	−1.96090
$265$	2528.23	0.586067
$266$	16743.8	3.85949
$267$	3955.51	0.906642
$268$	17717.1	4.03823
$269$	−1250.30	−0.283390	−0.141695	−	0.989910i	$-0.545255\pi$
$269$	−1250.30	−0.283390	−0.141695	+	0.989910i	$0.545255\pi$
$270$	11004.1	2.48034
$271$	−794.940	−0.178189	−0.0890945	−	0.996023i	$-0.528397\pi$
$271$	−794.940	−0.178189	−0.0890945	+	0.996023i	$0.528397\pi$
$272$	−21927.6	−4.88808
$273$	0	0
$274$	−12796.2	−2.82135
$275$	−714.316	−0.156636
$276$	6571.55	1.43319
$277$	−8941.93	−1.93960	−0.969798	−	0.243908i	$-0.921571\pi$
$277$	−8941.93	−1.93960	−0.969798	+	0.243908i	$0.921571\pi$
$278$	−14038.6	−3.02870
$279$	−2338.41	−0.501780
$280$	15652.0	3.34066
$281$	−6726.74	−1.42806	−0.714028	−	0.700117i	$-0.753131\pi$
$281$	−6726.74	−1.42806	−0.714028	+	0.700117i	$0.753131\pi$
$282$	−4734.47	−0.999764
$283$	−1062.56	−0.223189	−0.111595	−	0.993754i	$-0.535596\pi$
$283$	−1062.56	−0.223189	−0.111595	+	0.993754i	$0.535596\pi$
$284$	649.110	0.135625
$285$	8806.09	1.83027
$286$	0	0
$287$	1606.70	0.330454
$288$	−50660.5	−10.3653
$289$	971.673	0.197776
$290$	−3524.65	−0.713705
$291$	12109.8	2.43949
$292$	−118.638	−0.0237765
$293$	−2685.37	−0.535430	−0.267715	−	0.963498i	$-0.586269\pi$
$293$	−2685.37	−0.535430	−0.267715	+	0.963498i	$0.586269\pi$
$294$	−11608.6	−2.30281
$295$	−1967.08	−0.388229
$296$	−25399.2	−4.98749
$297$	2799.49	0.546946
$298$	−13084.5	−2.54350
$299$	0	0
$300$	−13607.0	−2.61867
$301$	7231.60	1.38479
$302$	11457.5	2.18313
$303$	11031.3	2.09152
$304$	−35848.4	−6.76331
$305$	−1573.72	−0.295445
$306$	23577.5	4.40470
$307$	−4409.58	−0.819765	−0.409883	−	0.912138i	$-0.634430\pi$
$307$	−4409.58	−0.819765	−0.409883	+	0.912138i	$0.634430\pi$
$308$	6087.77	1.12624
$309$	10903.0	2.00728
$310$	−1835.36	−0.336263
$311$	3272.23	0.596628	0.298314	−	0.954468i	$-0.403576\pi$
$311$	3272.23	0.596628	0.298314	+	0.954468i	$0.403576\pi$
$312$	0	0
$313$	−2623.32	−0.473734	−0.236867	−	0.971542i	$-0.576121\pi$
$313$	−2623.32	−0.473734	−0.236867	+	0.971542i	$0.576121\pi$
$314$	−3283.56	−0.590134
$315$	−10216.8	−1.82746
$316$	20715.5	3.68778
$317$	7097.19	1.25747	0.628735	−	0.777620i	$-0.283573\pi$
$317$	7097.19	1.25747	0.628735	+	0.777620i	$0.283573\pi$
$318$	16490.3	2.90796
$319$	−896.683	−0.157381
$320$	−22039.9	−3.85021
$321$	11137.5	1.93655
$322$	−4187.14	−0.724658
$323$	9620.56	1.65728
$324$	18927.9	3.24553
$325$	0	0
$326$	5808.59	0.986834
$327$	424.165	0.0717321
$328$	−5666.49	−0.953900
$329$	2241.32	0.375586
$330$	4309.29	0.718845
$331$	−3402.35	−0.564984	−0.282492	−	0.959270i	$-0.591161\pi$
$331$	−3402.35	−0.564984	−0.282492	+	0.959270i	$0.591161\pi$
$332$	19364.8	3.20114
$333$	16579.2	2.72834
$334$	−3746.33	−0.613742
$335$	−5937.08	−0.968291
$336$	61975.3	10.0626
$337$	944.468	0.152666	0.0763330	−	0.997082i	$-0.475679\pi$
$337$	944.468	0.152666	0.0763330	+	0.997082i	$0.475679\pi$
$338$	0	0
$339$	10092.7	1.61699
$340$	13749.4	2.19313
$341$	−466.922	−0.0741503
$342$	38545.7	6.09449
$343$	−2712.47	−0.426997
$344$	−25504.3	−3.99738
$345$	−2202.15	−0.343652
$346$	20413.8	3.17183
$347$	6781.02	1.04906	0.524531	−	0.851391i	$-0.324241\pi$
$347$	6781.02	1.04906	0.524531	+	0.851391i	$0.324241\pi$
$348$	−17080.9	−2.63113
$349$	−2543.97	−0.390188	−0.195094	−	0.980785i	$-0.562501\pi$
$349$	−2543.97	−0.390188	−0.195094	+	0.980785i	$0.562501\pi$
$350$	8669.85	1.32407
$351$	0	0
$352$	−10115.7	−1.53172
$353$	6512.50	0.981942	0.490971	−	0.871176i	$-0.336642\pi$
$353$	6512.50	0.981942	0.490971	+	0.871176i	$0.336642\pi$
$354$	−12830.2	−1.92632
$355$	−217.520	−0.0325204
$356$	10096.7	1.50316
$357$	−16632.2	−2.46574
$358$	4117.25	0.607831
$359$	12320.7	1.81132	0.905660	−	0.424005i	$-0.139376\pi$
$359$	12320.7	1.81132	0.905660	+	0.424005i	$0.139376\pi$
$360$	36032.4	5.27520
$361$	8869.17	1.29307
$362$	−16759.8	−2.43336
$363$	1096.30	0.158515
$364$	0	0
$365$	39.7560	0.00570116
$366$	−10264.5	−1.46594
$367$	4306.89	0.612583	0.306292	−	0.951938i	$-0.400912\pi$
$367$	4306.89	0.612583	0.306292	+	0.951938i	$0.400912\pi$
$368$	8964.66	1.26988
$369$	3698.78	0.521817
$370$	13012.6	1.82836
$371$	−7806.58	−1.09245
$372$	−8894.39	−1.23966
$373$	5693.70	0.790372	0.395186	−	0.918601i	$-0.370680\pi$
$373$	5693.70	0.790372	0.395186	+	0.918601i	$0.370680\pi$
$374$	4707.85	0.650902
$375$	13336.9	1.83658
$376$	−7904.65	−1.08418
$377$	0	0
$378$	−33978.2	−4.62341
$379$	−3634.98	−0.492655	−0.246328	−	0.969187i	$-0.579224\pi$
$379$	−3634.98	−0.492655	−0.246328	+	0.969187i	$0.579224\pi$
$380$	22478.1	3.03448
$381$	−7770.45	−1.04486
$382$	15719.8	2.10549
$383$	5356.77	0.714669	0.357335	−	0.933976i	$-0.383686\pi$
$383$	5356.77	0.714669	0.357335	+	0.933976i	$0.383686\pi$
$384$	−77099.3	−10.2460
$385$	−2040.04	−0.270052
$386$	2957.21	0.389943
$387$	16647.8	2.18671
$388$	30911.2	4.04453
$389$	7895.99	1.02916	0.514579	−	0.857443i	$-0.327948\pi$
$389$	7895.99	1.02916	0.514579	+	0.857443i	$0.327948\pi$
$390$	0	0
$391$	−2405.83	−0.311171
$392$	−19381.7	−2.49725
$393$	−7419.40	−0.952314
$394$	9691.90	1.23927
$395$	−6941.85	−0.884259
$396$	14014.6	1.77844
$397$	−10684.6	−1.35074	−0.675369	−	0.737480i	$-0.736015\pi$
$397$	−10684.6	−1.35074	−0.675369	+	0.737480i	$0.736015\pi$
$398$	−23272.7	−2.93104
$399$	−27191.1	−3.41168
$400$	−18562.2	−2.32027
$401$	12212.0	1.52079	0.760397	−	0.649458i	$-0.225004\pi$
$401$	12212.0	1.52079	0.760397	+	0.649458i	$0.225004\pi$
$402$	−38724.5	−4.80448
$403$	0	0
$404$	28158.1	3.46761
$405$	−6342.82	−0.778215
$406$	10883.3	1.33037
$407$	3310.46	0.403178
$408$	58658.2	7.11768
$409$	−533.325	−0.0644773	−0.0322387	−	0.999480i	$-0.510264\pi$
$409$	−533.325	−0.0644773	−0.0322387	+	0.999480i	$0.510264\pi$
$410$	2903.08	0.349690
$411$	20780.5	2.49399
$412$	27830.6	3.32795
$413$	6073.87	0.723670
$414$	−9639.19	−1.14430
$415$	−6489.21	−0.767573
$416$	0	0
$417$	22798.1	2.67728
$418$	7696.63	0.900609
$419$	−5788.25	−0.674879	−0.337440	−	0.941347i	$-0.609561\pi$
$419$	−5788.25	−0.674879	−0.337440	+	0.941347i	$0.609561\pi$
$420$	−38860.6	−4.51477
$421$	−14097.9	−1.63205	−0.816024	−	0.578018i	$-0.803826\pi$
$421$	−14097.9	−1.63205	−0.816024	+	0.578018i	$0.803826\pi$
$422$	−14924.6	−1.72161
$423$	5159.73	0.593084
$424$	27532.1	3.15349
$425$	4981.49	0.568559
$426$	−1418.77	−0.161360
$427$	4859.26	0.550717
$428$	28429.2	3.21069
$429$	0	0
$430$	13066.5	1.46540
$431$	−12222.6	−1.36600	−0.682998	−	0.730420i	$-0.739324\pi$
$431$	−12222.6	−1.36600	−0.682998	+	0.730420i	$0.739324\pi$
$432$	72747.3	8.10199
$433$	−13261.9	−1.47188	−0.735940	−	0.677047i	$-0.763260\pi$
$433$	−13261.9	−1.47188	−0.735940	+	0.677047i	$0.763260\pi$
$434$	5667.16	0.626803
$435$	5723.88	0.630894
$436$	1082.71	0.118928
$437$	−3933.17	−0.430547
$438$	259.307	0.0282881
$439$	7.52329	0.000817921 0	0.000408960	−	1.00000i	$-0.499870\pi$
$439$	7.52329	0.000817921 0	0.000408960		1.00000i	$0.499870\pi$
$440$	7194.78	0.779540
$441$	12651.3	1.36608
$442$	0	0
$443$	−4348.42	−0.466365	−0.233182	−	0.972433i	$-0.574914\pi$
$443$	−4348.42	−0.466365	−0.233182	+	0.972433i	$0.574914\pi$
$444$	63060.9	6.74040
$445$	−3383.45	−0.360429
$446$	−16072.4	−1.70640
$447$	21248.6	2.24838
$448$	68054.0	7.17690
$449$	−9925.61	−1.04325	−0.521624	−	0.853175i	$-0.674674\pi$
$449$	−9925.61	−1.04325	−0.521624	+	0.853175i	$0.674674\pi$
$450$	19958.8	2.09082
$451$	738.554	0.0771112
$452$	25762.3	2.68087
$453$	−18606.5	−1.92982
$454$	−7533.74	−0.778802
$455$	0	0
$456$	95897.4	9.84826
$457$	−7695.44	−0.787697	−0.393849	−	0.919175i	$-0.628857\pi$
$457$	−7695.44	−0.787697	−0.393849	+	0.919175i	$0.628857\pi$
$458$	11438.3	1.16698
$459$	−19523.1	−1.98531
$460$	−5621.14	−0.569754
$461$	−4747.89	−0.479678	−0.239839	−	0.970813i	$-0.577095\pi$
$461$	−4747.89	−0.479678	−0.239839	+	0.970813i	$0.577095\pi$
$462$	−13306.1	−1.33995
$463$	−2253.75	−0.226222	−0.113111	−	0.993582i	$-0.536082\pi$
$463$	−2253.75	−0.226222	−0.113111	+	0.993582i	$0.536082\pi$
$464$	−23301.1	−2.33131
$465$	2980.55	0.297246
$466$	−26001.6	−2.58477
$467$	8134.54	0.806042	0.403021	−	0.915191i	$-0.367960\pi$
$467$	8134.54	0.806042	0.403021	+	0.915191i	$0.367960\pi$
$468$	0	0
$469$	18332.3	1.80492
$470$	4049.75	0.397449
$471$	5332.36	0.521661
$472$	−21421.3	−2.08897
$473$	3324.16	0.323140
$474$	−45278.0	−4.38753
$475$	8143.98	0.786677
$476$	−42454.8	−4.08805
$477$	−17971.5	−1.72507
$478$	28902.4	2.76561
$479$	−8774.16	−0.836955	−0.418478	−	0.908227i	$-0.637436\pi$
$479$	−8774.16	−0.836955	−0.418478	+	0.908227i	$0.637436\pi$
$480$	64572.2	6.14021
$481$	0	0
$482$	−28412.8	−2.68499
$483$	6799.73	0.640576
$484$	2798.38	0.262808
$485$	−10358.5	−0.969801
$486$	−3033.75	−0.283156
$487$	−16029.8	−1.49154	−0.745768	−	0.666205i	$-0.767917\pi$
$487$	−16029.8	−1.49154	−0.745768	+	0.666205i	$0.767917\pi$
$488$	−17137.6	−1.58972
$489$	−9432.89	−0.872331
$490$	9929.70	0.915466
$491$	7943.44	0.730107	0.365053	−	0.930987i	$-0.381051\pi$
$491$	7943.44	0.730107	0.365053	+	0.930987i	$0.381051\pi$
$492$	14068.7	1.28916
$493$	6253.27	0.571264
$494$	0	0
$495$	−4696.36	−0.426436
$496$	−12133.4	−1.09840
$497$	671.649	0.0606189
$498$	−42325.7	−3.80856
$499$	9304.54	0.834726	0.417363	−	0.908740i	$-0.362954\pi$
$499$	9304.54	0.834726	0.417363	+	0.908740i	$0.362954\pi$
$500$	34043.4	3.04493
$501$	6083.88	0.542530
$502$	22824.1	2.02926
$503$	7196.72	0.637944	0.318972	−	0.947764i	$-0.396662\pi$
$503$	7196.72	0.637944	0.318972	+	0.947764i	$0.396662\pi$
$504$	−111259.	−9.83312
$505$	−9435.88	−0.831468
$506$	−1924.71	−0.169098
$507$	0	0
$508$	−19834.6	−1.73232
$509$	−8150.74	−0.709774	−0.354887	−	0.934909i	$-0.615481\pi$
$509$	−8150.74	−0.709774	−0.354887	+	0.934909i	$0.615481\pi$
$510$	−30052.1	−2.60927
$511$	−122.757	−0.0106271
$512$	−69870.0	−6.03095
$513$	−31917.3	−2.74694
$514$	41663.6	3.57530
$515$	−9326.14	−0.797978
$516$	63321.9	5.40231
$517$	1030.27	0.0876426
$518$	−40180.0	−3.40812
$519$	−33151.1	−2.80380
$520$	0	0
$521$	11445.8	0.962474	0.481237	−	0.876591i	$-0.340188\pi$
$521$	11445.8	0.962474	0.481237	+	0.876591i	$0.340188\pi$
$522$	25054.4	2.10077
$523$	−12610.4	−1.05433	−0.527163	−	0.849764i	$-0.676744\pi$
$523$	−12610.4	−1.05433	−0.527163	+	0.849764i	$0.676744\pi$
$524$	−18938.5	−1.57888
$525$	−14079.5	−1.17043
$526$	39695.5	3.29051
$527$	3256.21	0.269152
$528$	28488.3	2.34810
$529$	−11183.4	−0.919161
$530$	−14105.4	−1.15604
$531$	13982.6	1.14274
$532$	−69407.2	−5.65636
$533$	0	0
$534$	−22068.5	−1.78838
$535$	−9526.73	−0.769862
$536$	−64654.2	−5.21014
$537$	−6686.24	−0.537304
$538$	6975.61	0.558996
$539$	2526.15	0.201872
$540$	−45615.0	−3.63511
$541$	13960.6	1.10945	0.554727	−	0.832032i	$-0.312823\pi$
$541$	13960.6	1.10945	0.554727	+	0.832032i	$0.312823\pi$
$542$	4435.10	0.351483
$543$	27217.2	2.15102
$544$	70544.4	5.55986
$545$	−362.821	−0.0285166
$546$	0	0
$547$	−10411.6	−0.813839	−0.406919	−	0.913464i	$-0.633397\pi$
$547$	−10411.6	−0.813839	−0.406919	+	0.913464i	$0.633397\pi$
$548$	53043.7	4.13488
$549$	11186.5	0.869632
$550$	3985.29	0.308970
$551$	10223.2	0.790420
$552$	−23981.2	−1.84911
$553$	21434.8	1.64828
$554$	49888.5	3.82592
$555$	−21132.0	−1.61622
$556$	58193.6	4.43877
$557$	−9860.39	−0.750086	−0.375043	−	0.927007i	$-0.622372\pi$
$557$	−9860.39	−0.750086	−0.375043	+	0.927007i	$0.622372\pi$
$558$	13046.4	0.989778
$559$	0	0
$560$	−53012.2	−4.00031
$561$	−7645.35	−0.575378
$562$	37529.6	2.81689
$563$	1707.96	0.127854	0.0639270	−	0.997955i	$-0.479638\pi$
$563$	1707.96	0.127854	0.0639270	+	0.997955i	$0.479638\pi$
$564$	19625.6	1.46522
$565$	−8633.04	−0.642822
$566$	5928.19	0.440248
$567$	19585.1	1.45061
$568$	−2368.76	−0.174984
$569$	−2774.94	−0.204449	−0.102225	−	0.994761i	$-0.532596\pi$
$569$	−2774.94	−0.204449	−0.102225	+	0.994761i	$0.532596\pi$
$570$	−49130.6	−3.61027
$571$	−13310.9	−0.975555	−0.487777	−	0.872968i	$-0.662192\pi$
$571$	−13310.9	−0.975555	−0.487777	+	0.872968i	$0.662192\pi$
$572$	0	0
$573$	−25528.3	−1.86119
$574$	−8964.03	−0.651832
$575$	−2036.58	−0.147706
$576$	156667.	11.3330
$577$	−17457.0	−1.25952	−0.629760	−	0.776789i	$-0.716847\pi$
$577$	−17457.0	−1.25952	−0.629760	+	0.776789i	$0.716847\pi$
$578$	−5421.12	−0.390119
$579$	−4802.38	−0.344698
$580$	14610.6	1.04598
$581$	20037.2	1.43078
$582$	−67562.8	−4.81197
$583$	−3588.46	−0.254921
$584$	432.938	0.0306766
$585$	0	0
$586$	14982.1	1.05615
$587$	−22436.1	−1.57758	−0.788788	−	0.614665i	$-0.789291\pi$
$587$	−22436.1	−1.57758	−0.788788	+	0.614665i	$0.789291\pi$
$588$	48120.6	3.37493
$589$	5323.42	0.372407
$590$	10974.6	0.765795
$591$	−15739.2	−1.09547
$592$	86025.4	5.97233
$593$	−9060.21	−0.627417	−0.313709	−	0.949519i	$-0.601572\pi$
$593$	−9060.21	−0.627417	−0.313709	+	0.949519i	$0.601572\pi$
$594$	−15618.8	−1.07887
$595$	14226.8	0.980236
$596$	54238.6	3.72768
$597$	37793.8	2.59095
$598$	0	0
$599$	26376.3	1.79918	0.899588	−	0.436740i	$-0.143867\pi$
$599$	26376.3	1.79918	0.899588	+	0.436740i	$0.143867\pi$
$600$	49655.3	3.37862
$601$	22290.6	1.51290	0.756448	−	0.654054i	$-0.226933\pi$
$601$	22290.6	1.51290	0.756448	+	0.654054i	$0.226933\pi$
$602$	−40346.3	−2.73155
$603$	42202.8	2.85013
$604$	−47494.3	−3.19953
$605$	−937.747	−0.0630163
$606$	−61545.3	−4.12559
$607$	22602.5	1.51138	0.755691	−	0.654929i	$-0.227301\pi$
$607$	22602.5	1.51138	0.755691	+	0.654929i	$0.227301\pi$
$608$	115329.	7.69281
$609$	−17674.0	−1.17600
$610$	8780.02	0.582775
$611$	0	0
$612$	−97735.0	−6.45540
$613$	3312.75	0.218272	0.109136	−	0.994027i	$-0.465192\pi$
$613$	3312.75	0.218272	0.109136	+	0.994027i	$0.465192\pi$
$614$	24601.8	1.61701
$615$	−4714.48	−0.309116
$616$	−22215.8	−1.45308
$617$	7262.98	0.473900	0.236950	−	0.971522i	$-0.423852\pi$
$617$	7262.98	0.473900	0.236950	+	0.971522i	$0.423852\pi$
$618$	−60829.5	−3.95942
$619$	12292.1	0.798161	0.399081	−	0.916916i	$-0.369329\pi$
$619$	12292.1	0.798161	0.399081	+	0.916916i	$0.369329\pi$
$620$	7608.04	0.492817
$621$	7981.60	0.515766
$622$	−18256.3	−1.17687
$623$	10447.3	0.671849
$624$	0	0
$625$	−3290.84	−0.210614
$626$	14635.9	0.934455
$627$	−12499.0	−0.796112
$628$	13611.2	0.864882
$629$	−23086.4	−1.46346
$630$	57001.0	3.60472
$631$	21638.7	1.36517	0.682585	−	0.730806i	$-0.260856\pi$
$631$	21638.7	1.36517	0.682585	+	0.730806i	$0.260856\pi$
$632$	−75596.0	−4.75799
$633$	24236.9	1.52185
$634$	−39596.4	−2.48040
$635$	6646.65	0.415377
$636$	−68356.6	−4.26181
$637$	0	0
$638$	5002.74	0.310440
$639$	1546.20	0.0957227
$640$	65948.9	4.07322
$641$	4161.84	0.256447	0.128224	−	0.991745i	$-0.459072\pi$
$641$	4161.84	0.256447	0.128224	+	0.991745i	$0.459072\pi$
$642$	−62137.8	−3.81991
$643$	−23299.4	−1.42898	−0.714492	−	0.699644i	$-0.753342\pi$
$643$	−23299.4	−1.42898	−0.714492	+	0.699644i	$0.753342\pi$
$644$	17356.8	1.06204
$645$	−21219.4	−1.29537
$646$	−53674.7	−3.26904
$647$	12703.6	0.771919	0.385960	−	0.922516i	$-0.373870\pi$
$647$	12703.6	0.771919	0.385960	+	0.922516i	$0.373870\pi$
$648$	−69072.6	−4.18739
$649$	2791.99	0.168868
$650$	0	0
$651$	−9203.22	−0.554075
$652$	−24078.1	−1.44627
$653$	5577.15	0.334228	0.167114	−	0.985938i	$-0.446555\pi$
$653$	5577.15	0.334228	0.167114	+	0.985938i	$0.446555\pi$
$654$	−2366.49	−0.141494
$655$	6346.37	0.378585
$656$	19192.0	1.14226
$657$	−282.599	−0.0167812
$658$	−12504.7	−0.740855
$659$	9952.02	0.588279	0.294139	−	0.955763i	$-0.404967\pi$
$659$	9952.02	0.588279	0.294139	+	0.955763i	$0.404967\pi$
$660$	−17863.1	−1.05352
$661$	5049.26	0.297115	0.148558	−	0.988904i	$-0.452537\pi$
$661$	5049.26	0.297115	0.148558	+	0.988904i	$0.452537\pi$
$662$	18982.2	1.11445
$663$	0	0
$664$	−70666.8	−4.13013
$665$	23258.6	1.35629
$666$	−92498.2	−5.38173
$667$	−2556.52	−0.148409
$668$	15529.5	0.899483
$669$	26101.0	1.50840
$670$	33124.0	1.90999
$671$	2233.67	0.128509
$672$	−199384.	−11.4455
$673$	−18851.9	−1.07978	−0.539888	−	0.841737i	$-0.681533\pi$
$673$	−18851.9	−1.07978	−0.539888	+	0.841737i	$0.681533\pi$
$674$	−5269.34	−0.301139
$675$	−16526.6	−0.942386
$676$	0	0
$677$	20369.0	1.15634	0.578171	−	0.815916i	$-0.303767\pi$
$677$	20369.0	1.15634	0.578171	+	0.815916i	$0.303767\pi$
$678$	−56308.8	−3.18957
$679$	31984.5	1.80773
$680$	−50174.8	−2.82958
$681$	12234.5	0.688437
$682$	2605.03	0.146264
$683$	17693.9	0.991272	0.495636	−	0.868530i	$-0.334935\pi$
$683$	17693.9	0.991272	0.495636	+	0.868530i	$0.334935\pi$
$684$	−159782.	−8.93190
$685$	−17775.2	−0.991466
$686$	15133.3	0.842265
$687$	−18575.3	−1.03157
$688$	86381.4	4.78671
$689$	0	0
$690$	12286.2	0.677864
$691$	−33738.3	−1.85740	−0.928701	−	0.370829i	$-0.879074\pi$
$691$	−33738.3	−1.85740	−0.928701	+	0.370829i	$0.879074\pi$
$692$	−84620.4	−4.64853
$693$	14501.3	0.794888
$694$	−37832.4	−2.06931
$695$	−19500.9	−1.06433
$696$	62332.4	3.39469
$697$	−5150.52	−0.279899
$698$	14193.2	0.769659
$699$	42225.5	2.28486
$700$	−35938.8	−1.94051
$701$	622.973	0.0335654	0.0167827	−	0.999859i	$-0.494658\pi$
$701$	622.973	0.0335654	0.0167827	+	0.999859i	$0.494658\pi$
$702$	0	0
$703$	−37742.9	−2.02489
$704$	31282.5	1.67472
$705$	−6576.62	−0.351333
$706$	−36334.3	−1.93691
$707$	29135.8	1.54988
$708$	53184.5	2.82316
$709$	−6403.42	−0.339190	−0.169595	−	0.985514i	$-0.554246\pi$
$709$	−6403.42	−0.339190	−0.169595	+	0.985514i	$0.554246\pi$
$710$	1213.58	0.0641475
$711$	49345.0	2.60279
$712$	−36845.4	−1.93938
$713$	−1331.24	−0.0699231
$714$	92793.7	4.86375
$715$	0	0
$716$	−17067.1	−0.890819
$717$	−46936.2	−2.44472
$718$	−68739.4	−3.57289
$719$	15923.7	0.825945	0.412972	−	0.910744i	$-0.364491\pi$
$719$	15923.7	0.825945	0.412972	+	0.910744i	$0.364491\pi$
$720$	−122039.	−6.31685
$721$	28796.9	1.48745
$722$	−49482.5	−2.55062
$723$	46141.1	2.37345
$724$	69473.8	3.56626
$725$	5293.51	0.271167
$726$	−6116.43	−0.312675
$727$	20766.3	1.05939	0.529696	−	0.848188i	$-0.322306\pi$
$727$	20766.3	1.05939	0.529696	+	0.848188i	$0.322306\pi$
$728$	0	0
$729$	−17170.9	−0.872374
$730$	−221.805	−0.0112457
$731$	−23182.0	−1.17294
$732$	42549.1	2.14844
$733$	30664.9	1.54520	0.772601	−	0.634892i	$-0.218955\pi$
$733$	30664.9	1.54520	0.772601	+	0.634892i	$0.218955\pi$
$734$	−24028.9	−1.20834
$735$	−16125.4	−0.809244
$736$	−28840.6	−1.44440
$737$	8426.85	0.421176
$738$	−20636.1	−1.02930
$739$	−8950.86	−0.445552	−0.222776	−	0.974870i	$-0.571512\pi$
$739$	−8950.86	−0.445552	−0.222776	+	0.974870i	$0.571512\pi$
$740$	−53940.8	−2.67960
$741$	0	0
$742$	43554.2	2.15488
$743$	35815.8	1.76844	0.884222	−	0.467067i	$-0.154689\pi$
$743$	35815.8	1.76844	0.884222	+	0.467067i	$0.154689\pi$
$744$	32457.8	1.59941
$745$	−18175.6	−0.893827
$746$	−31766.1	−1.55903
$747$	46127.5	2.25933
$748$	−19515.3	−0.953942
$749$	29416.3	1.43504
$750$	−74408.9	−3.62270
$751$	−23658.3	−1.14954	−0.574769	−	0.818316i	$-0.694908\pi$
$751$	−23658.3	−1.14954	−0.574769	+	0.818316i	$0.694908\pi$
$752$	26772.5	1.29826
$753$	−37065.3	−1.79381
$754$	0	0
$755$	15915.5	0.767186
$756$	140848.	6.77593
$757$	12463.9	0.598423	0.299212	−	0.954187i	$-0.403276\pi$
$757$	12463.9	0.598423	0.299212	+	0.954187i	$0.403276\pi$
$758$	20280.1	0.971778
$759$	3125.64	0.149478
$760$	−82028.3	−3.91510
$761$	25031.6	1.19237	0.596185	−	0.802847i	$-0.296682\pi$
$761$	25031.6	1.19237	0.596185	+	0.802847i	$0.296682\pi$
$762$	43352.6	2.06102
$763$	1120.30	0.0531557
$764$	−65162.7	−3.08574
$765$	32751.4	1.54788
$766$	−29886.3	−1.40971
$767$	0	0
$768$	224019.	10.5255
$769$	42061.4	1.97240	0.986198	−	0.165569i	$-0.0529460\pi$
$769$	42061.4	1.97240	0.986198	+	0.165569i	$0.0529460\pi$
$770$	11381.7	0.532685
$771$	−67659.9	−3.16046
$772$	−12258.4	−0.571489
$773$	−19186.5	−0.892743	−0.446372	−	0.894848i	$-0.647284\pi$
$773$	−19186.5	−0.892743	−0.446372	+	0.894848i	$0.647284\pi$
$774$	−92881.0	−4.31336
$775$	2756.45	0.127761
$776$	−112803.	−5.21827
$777$	65250.6	3.01268
$778$	−44053.0	−2.03005
$779$	−8420.32	−0.387278
$780$	0	0
$781$	308.738	0.0141454
$782$	13422.5	0.613795
$783$	−20745.9	−0.946869
$784$	65644.3	2.99036
$785$	−4561.17	−0.207382
$786$	41394.1	1.87847
$787$	3443.37	0.155963	0.0779814	−	0.996955i	$-0.475153\pi$
$787$	3443.37	0.155963	0.0779814	+	0.996955i	$0.475153\pi$
$788$	−40175.4	−1.81623
$789$	−64463.8	−2.90871
$790$	38729.7	1.74423
$791$	26656.8	1.19824
$792$	−51142.9	−2.29455
$793$	0	0
$794$	59610.9	2.66437
$795$	22906.6	1.02190
$796$	96471.2	4.29564
$797$	5678.07	0.252356	0.126178	−	0.992008i	$-0.459729\pi$
$797$	5678.07	0.252356	0.126178	+	0.992008i	$0.459729\pi$
$798$	151704.	6.72964
$799$	−7184.88	−0.318126
$800$	59717.2	2.63915
$801$	24050.7	1.06091
$802$	−68132.8	−2.99982
$803$	−56.4280	−0.00247983
$804$	160523.	7.04130
$805$	−5816.32	−0.254656
$806$	0	0
$807$	−11328.1	−0.494136
$808$	−102756.	−4.47393
$809$	−13983.4	−0.607702	−0.303851	−	0.952720i	$-0.598272\pi$
$809$	−13983.4	−0.607702	−0.303851	+	0.952720i	$0.598272\pi$
$810$	35387.6	1.53505
$811$	−2113.79	−0.0915230	−0.0457615	−	0.998952i	$-0.514571\pi$
$811$	−2113.79	−0.0915230	−0.0457615	+	0.998952i	$0.514571\pi$
$812$	−45114.0	−1.94974
$813$	−7202.42	−0.310701
$814$	−18469.6	−0.795282
$815$	8068.66	0.346789
$816$	−198671.	−8.52315
$817$	−37899.1	−1.62291
$818$	2975.51	0.127184
$819$	0	0
$820$	−12034.0	−0.512496
$821$	−17498.2	−0.743839	−0.371920	−	0.928265i	$-0.621300\pi$
$821$	−17498.2	−0.743839	−0.371920	+	0.928265i	$0.621300\pi$
$822$	−115938.	−4.91947
$823$	23091.0	0.978010	0.489005	−	0.872281i	$-0.337360\pi$
$823$	23091.0	0.978010	0.489005	+	0.872281i	$0.337360\pi$
$824$	−101561.	−4.29373
$825$	−6471.94	−0.273120
$826$	−33887.1	−1.42746
$827$	9821.25	0.412961	0.206480	−	0.978451i	$-0.433799\pi$
$827$	9821.25	0.412961	0.206480	+	0.978451i	$0.433799\pi$
$828$	39956.9	1.67705
$829$	−16049.6	−0.672407	−0.336204	−	0.941789i	$-0.609143\pi$
$829$	−16049.6	−0.672407	−0.336204	+	0.941789i	$0.609143\pi$
$830$	36204.4	1.51406
$831$	−81016.7	−3.38200
$832$	0	0
$833$	−17616.8	−0.732758
$834$	−127194.	−5.28103
$835$	−5204.00	−0.215679
$836$	−31904.5	−1.31991
$837$	−10802.8	−0.446118
$838$	32293.6	1.33122
$839$	31634.5	1.30172	0.650860	−	0.759198i	$-0.274409\pi$
$839$	31634.5	1.30172	0.650860	+	0.759198i	$0.274409\pi$
$840$	141812.	5.82497
$841$	−17744.0	−0.727543
$842$	78654.8	3.21927
$843$	−60946.5	−2.49005
$844$	61866.2	2.52313
$845$	0	0
$846$	−28787.0	−1.16988
$847$	2895.54	0.117464
$848$	−93249.5	−3.77618
$849$	−9627.12	−0.389166
$850$	−27792.5	−1.12150
$851$	9438.42	0.380194
$852$	5881.15	0.236485
$853$	−11173.0	−0.448485	−0.224242	−	0.974533i	$-0.571991\pi$
$853$	−11173.0	−0.448485	−0.224242	+	0.974533i	$0.571991\pi$
$854$	−27110.6	−1.08631
$855$	53543.6	2.14170
$856$	−103745.	−4.14245
$857$	31902.7	1.27162	0.635809	−	0.771846i	$-0.280667\pi$
$857$	31902.7	1.27162	0.635809	+	0.771846i	$0.280667\pi$
$858$	0	0
$859$	11265.7	0.447475	0.223738	−	0.974649i	$-0.428174\pi$
$859$	11265.7	0.447475	0.223738	+	0.974649i	$0.428174\pi$
$860$	−54164.0	−2.14765
$861$	14557.2	0.576200
$862$	68192.2	2.69447
$863$	8458.55	0.333641	0.166821	−	0.985987i	$-0.446650\pi$
$863$	8458.55	0.333641	0.166821	+	0.985987i	$0.446650\pi$
$864$	−234039.	−9.21546
$865$	28356.6	1.11463
$866$	73990.1	2.90333
$867$	8803.67	0.344854
$868$	−23491.8	−0.918623
$869$	9852.97	0.384625
$870$	−31934.4	−1.24446
$871$	0	0
$872$	−3951.08	−0.153441
$873$	73631.4	2.85458
$874$	21943.8	0.849267
$875$	35225.5	1.36096
$876$	−1074.90	−0.0414582
$877$	−23190.0	−0.892896	−0.446448	−	0.894810i	$-0.647311\pi$
$877$	−23190.0	−0.892896	−0.446448	+	0.894810i	$0.647311\pi$
$878$	−41.9737	−0.00161338
$879$	−24330.3	−0.933608
$880$	−24368.2	−0.933469
$881$	−22837.1	−0.873329	−0.436664	−	0.899625i	$-0.643840\pi$
$881$	−22837.1	−0.873329	−0.436664	+	0.899625i	$0.643840\pi$
$882$	−70583.6	−2.69464
$883$	18444.5	0.702951	0.351475	−	0.936197i	$-0.385680\pi$
$883$	18444.5	0.702951	0.351475	+	0.936197i	$0.385680\pi$
$884$	0	0
$885$	−17822.3	−0.676940
$886$	24260.5	0.919920
$887$	−304.853	−0.0115400	−0.00576998	−	0.999983i	$-0.501837\pi$
$887$	−304.853	−0.0115400	−0.00576998	+	0.999983i	$0.501837\pi$
$888$	−230125.	−8.69649
$889$	−20523.3	−0.774274
$890$	18876.8	0.710958
$891$	9002.74	0.338499
$892$	66624.4	2.50084
$893$	−11746.2	−0.440170
$894$	−118550.	−4.43500
$895$	5719.24	0.213601
$896$	−203635.	−7.59259
$897$	0	0
$898$	55376.6	2.05784
$899$	3460.17	0.128368
$900$	−82734.5	−3.06424
$901$	25025.2	0.925316
$902$	−4120.52	−0.152104
$903$	65520.6	2.41461
$904$	−94012.9	−3.45887
$905$	−23281.0	−0.855122
$906$	103809.	3.80663
$907$	−42544.0	−1.55750	−0.778749	−	0.627336i	$-0.784145\pi$
$907$	−42544.0	−1.55750	−0.778749	+	0.627336i	$0.784145\pi$
$908$	31229.3	1.14139
$909$	67073.4	2.44740
$910$	0	0
$911$	−29065.5	−1.05706	−0.528530	−	0.848915i	$-0.677257\pi$
$911$	−29065.5	−1.05706	−0.528530	+	0.848915i	$0.677257\pi$
$912$	−324798.	−11.7929
$913$	9210.52	0.333871
$914$	42934.1	1.55376
$915$	−14258.4	−0.515155
$916$	−47414.6	−1.71029
$917$	−19596.1	−0.705693
$918$	108922.	3.91609
$919$	28790.8	1.03343	0.516715	−	0.856158i	$-0.327155\pi$
$919$	28790.8	1.03343	0.516715	+	0.856158i	$0.327155\pi$
$920$	20512.9	0.735100
$921$	−39952.2	−1.42939
$922$	26489.3	0.946180
$923$	0	0
$924$	55157.1	1.96378
$925$	−19543.1	−0.694674
$926$	12574.1	0.446230
$927$	66293.3	2.34882
$928$	74963.1	2.65171
$929$	−51295.8	−1.81158	−0.905792	−	0.423722i	$-0.860723\pi$
$929$	−51295.8	−1.81158	−0.905792	+	0.423722i	$0.860723\pi$
$930$	−16629.0	−0.586328
$931$	−28800.9	−1.01387
$932$	107784.	3.78816
$933$	29647.5	1.04032
$934$	−45383.9	−1.58994
$935$	6539.65	0.228737
$936$	0	0
$937$	11292.9	0.393726	0.196863	−	0.980431i	$-0.436925\pi$
$937$	11292.9	0.393726	0.196863	+	0.980431i	$0.436925\pi$
$938$	−102279.	−3.56026
$939$	−23768.1	−0.826030
$940$	−16787.3	−0.582489
$941$	−41825.4	−1.44896	−0.724479	−	0.689297i	$-0.757919\pi$
$941$	−41825.4	−1.44896	−0.724479	+	0.689297i	$0.757919\pi$
$942$	−29750.1	−1.02899
$943$	2105.68	0.0727152
$944$	72552.3	2.50146
$945$	−47198.9	−1.62474
$946$	−18546.0	−0.637404
$947$	−9153.57	−0.314098	−0.157049	−	0.987591i	$-0.550198\pi$
$947$	−9153.57	−0.314098	−0.157049	+	0.987591i	$0.550198\pi$
$948$	187689.	6.43023
$949$	0	0
$950$	−45436.6	−1.55175
$951$	64302.8	2.19260
$952$	154928.	5.27442
$953$	−7688.60	−0.261341	−0.130671	−	0.991426i	$-0.541713\pi$
$953$	−7688.60	−0.261341	−0.130671	+	0.991426i	$0.541713\pi$
$954$	100266.	3.40276
$955$	21836.3	0.739901
$956$	−119808.	−4.05320
$957$	−8124.23	−0.274419
$958$	48952.5	1.65092
$959$	54885.6	1.84812
$960$	−199689.	−6.71346
$961$	−27989.2	−0.939519
$962$	0	0
$963$	67719.2	2.26606
$964$	117778.	3.93505
$965$	4107.84	0.137032
$966$	−37936.8	−1.26356
$967$	32976.1	1.09663	0.548314	−	0.836273i	$-0.315270\pi$
$967$	32976.1	1.09663	0.548314	+	0.836273i	$0.315270\pi$
$968$	−10212.0	−0.339076
$969$	87165.3	2.88974
$970$	57791.5	1.91296
$971$	−31050.0	−1.02620	−0.513101	−	0.858328i	$-0.671503\pi$
$971$	−31050.0	−1.02620	−0.513101	+	0.858328i	$0.671503\pi$
$972$	12575.7	0.414985
$973$	60214.2	1.98395
$974$	89432.7	2.94210
$975$	0	0
$976$	58043.9	1.90363
$977$	−4359.20	−0.142746	−0.0713731	−	0.997450i	$-0.522738\pi$
$977$	−4359.20	−0.142746	−0.0713731	+	0.997450i	$0.522738\pi$
$978$	52627.7	1.72070
$979$	4802.33	0.156775
$980$	−41161.2	−1.34168
$981$	2579.05	0.0839376
$982$	−44317.8	−1.44016
$983$	3892.72	0.126306	0.0631529	−	0.998004i	$-0.479884\pi$
$983$	3892.72	0.126306	0.0631529	+	0.998004i	$0.479884\pi$
$984$	−51340.2	−1.66328
$985$	13463.0	0.435498
$986$	−34888.0	−1.12684
$987$	20307.0	0.654894
$988$	0	0
$989$	9477.48	0.304718
$990$	26201.8	0.841158
$991$	20978.9	0.672470	0.336235	−	0.941778i	$-0.390846\pi$
$991$	20978.9	0.672470	0.336235	+	0.941778i	$0.390846\pi$
$992$	39034.9	1.24935
$993$	−30826.4	−0.985141
$994$	−3747.24	−0.119573
$995$	−32327.9	−1.03001
$996$	175451.	5.58171
$997$	−28328.2	−0.899861	−0.449931	−	0.893063i	$-0.648551\pi$
$997$	−28328.2	−0.899861	−0.449931	+	0.893063i	$0.648551\pi$
$998$	−51911.5	−1.64652
$999$	76591.8	2.42568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.1	yes	51
13.12	even	2		1859.4.a.p.1.51	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.51	✓	51	13.12	even	2
1859.4.a.q.1.1	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)

\(f(q)\)	\(=\)	\(q-5.57916 q^{2} +9.06032 q^{3} +23.1271 q^{4} -7.74998 q^{5} -50.5490 q^{6} +23.9301 q^{7} -84.3964 q^{8} +55.0894 q^{9} +O(q^{10})\)	\(q-5.57916 q^{2} +9.06032 q^{3} +23.1271 q^{4} -7.74998 q^{5} -50.5490 q^{6} +23.9301 q^{7} -84.3964 q^{8} +55.0894 q^{9} +43.2384 q^{10} +11.0000 q^{11} +209.539 q^{12} -133.510 q^{14} -70.2173 q^{15} +285.845 q^{16} -76.7116 q^{17} -307.353 q^{18} -125.412 q^{19} -179.234 q^{20} +216.814 q^{21} -61.3708 q^{22} +31.3620 q^{23} -764.659 q^{24} -64.9379 q^{25} +254.499 q^{27} +553.433 q^{28} -81.5166 q^{29} +391.754 q^{30} -42.4475 q^{31} -919.605 q^{32} +99.6635 q^{33} +427.987 q^{34} -185.458 q^{35} +1274.06 q^{36} +300.951 q^{37} +699.694 q^{38} +654.071 q^{40} +67.1413 q^{41} -1209.64 q^{42} +302.197 q^{43} +254.398 q^{44} -426.942 q^{45} -174.974 q^{46} +93.6609 q^{47} +2589.85 q^{48} +229.650 q^{49} +362.299 q^{50} -695.032 q^{51} -326.224 q^{53} -1419.89 q^{54} -85.2498 q^{55} -2019.62 q^{56} -1136.27 q^{57} +454.795 q^{58} +253.817 q^{59} -1623.92 q^{60} +203.061 q^{61} +236.821 q^{62} +1318.30 q^{63} +2843.87 q^{64} -556.039 q^{66} +766.077 q^{67} -1774.12 q^{68} +284.150 q^{69} +1034.70 q^{70} +28.0671 q^{71} -4649.35 q^{72} -5.12982 q^{73} -1679.06 q^{74} -588.358 q^{75} -2900.41 q^{76} +263.231 q^{77} +895.725 q^{79} -2215.29 q^{80} +818.431 q^{81} -374.592 q^{82} +837.320 q^{83} +5014.28 q^{84} +594.513 q^{85} -1686.00 q^{86} -738.567 q^{87} -928.361 q^{88} +436.575 q^{89} +2381.98 q^{90} +725.311 q^{92} -384.588 q^{93} -522.550 q^{94} +971.940 q^{95} -8331.92 q^{96} +1336.58 q^{97} -1281.26 q^{98} +605.984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 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

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Representations

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Database

Properties

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