LMFDB - Embedded newform 1859.4.a.q.1.13

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			1.13
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.39599 q^{2} +6.27073 q^{3} +3.53273 q^{4} -11.8750 q^{5} -21.2953 q^{6} -17.2790 q^{7} +15.1708 q^{8} +12.3221 q^{9} +O(q^{10})$	\(q-3.39599 q^{2} +6.27073 q^{3} +3.53273 q^{4} -11.8750 q^{5} -21.2953 q^{6} -17.2790 q^{7} +15.1708 q^{8} +12.3221 q^{9} +40.3274 q^{10} +11.0000 q^{11} +22.1528 q^{12} +58.6792 q^{14} -74.4650 q^{15} -79.7817 q^{16} +111.221 q^{17} -41.8456 q^{18} -54.9030 q^{19} -41.9512 q^{20} -108.352 q^{21} -37.3559 q^{22} +84.1209 q^{23} +95.1320 q^{24} +16.0158 q^{25} -92.0413 q^{27} -61.0419 q^{28} +50.2658 q^{29} +252.882 q^{30} -205.229 q^{31} +149.571 q^{32} +68.9780 q^{33} -377.706 q^{34} +205.188 q^{35} +43.5305 q^{36} -102.895 q^{37} +186.450 q^{38} -180.153 q^{40} +239.288 q^{41} +367.962 q^{42} -50.4632 q^{43} +38.8600 q^{44} -146.325 q^{45} -285.674 q^{46} +72.8888 q^{47} -500.289 q^{48} -44.4367 q^{49} -54.3893 q^{50} +697.440 q^{51} +191.741 q^{53} +312.571 q^{54} -130.625 q^{55} -262.136 q^{56} -344.282 q^{57} -170.702 q^{58} -883.017 q^{59} -263.064 q^{60} -128.928 q^{61} +696.957 q^{62} -212.913 q^{63} +130.312 q^{64} -234.249 q^{66} -835.862 q^{67} +392.915 q^{68} +527.500 q^{69} -696.816 q^{70} +739.396 q^{71} +186.936 q^{72} -93.7544 q^{73} +349.429 q^{74} +100.431 q^{75} -193.957 q^{76} -190.069 q^{77} -963.372 q^{79} +947.408 q^{80} -909.862 q^{81} -812.620 q^{82} -885.285 q^{83} -382.778 q^{84} -1320.75 q^{85} +171.373 q^{86} +315.203 q^{87} +166.879 q^{88} -386.022 q^{89} +496.917 q^{90} +297.176 q^{92} -1286.94 q^{93} -247.529 q^{94} +651.974 q^{95} +937.920 q^{96} +1713.35 q^{97} +150.907 q^{98} +135.543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.39599	−1.20066	−0.600331	−	0.799751i	$-0.704965\pi$
$2$	−3.39599	−1.20066	−0.600331	+	0.799751i	$0.704965\pi$
$3$	6.27073	1.20680	0.603401	−	0.797438i	$-0.293812\pi$
$3$	6.27073	1.20680	0.603401	+	0.797438i	$0.293812\pi$
$4$	3.53273	0.441591
$5$	−11.8750	−1.06213	−0.531066	−	0.847330i	$-0.678209\pi$
$5$	−11.8750	−1.06213	−0.531066	+	0.847330i	$0.678209\pi$
$6$	−21.2953	−1.44896
$7$	−17.2790	−0.932977	−0.466489	−	0.884527i	$-0.654481\pi$
$7$	−17.2790	−0.932977	−0.466489	+	0.884527i	$0.654481\pi$
$8$	15.1708	0.670461
$9$	12.3221	0.456373
$10$	40.3274	1.27526
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	22.1528	0.532913
$13$	0	0
$13$	0	0
$14$	58.6792	1.12019
$15$	−74.4650	−1.28178
$16$	−79.7817	−1.24659
$17$	111.221	1.58677	0.793387	−	0.608718i	$-0.208316\pi$
$17$	111.221	1.58677	0.793387	+	0.608718i	$0.208316\pi$
$18$	−41.8456	−0.547950
$19$	−54.9030	−0.662927	−0.331464	−	0.943468i	$-0.607542\pi$
$19$	−54.9030	−0.662927	−0.331464	+	0.943468i	$0.607542\pi$
$20$	−41.9512	−0.469028
$21$	−108.352	−1.12592
$22$	−37.3559	−0.362013
$23$	84.1209	0.762627	0.381314	−	0.924446i	$-0.375472\pi$
$23$	84.1209	0.762627	0.381314	+	0.924446i	$0.375472\pi$
$24$	95.1320	0.809114
$25$	16.0158	0.128126
$26$	0	0
$27$	−92.0413	−0.656050
$28$	−61.0419	−0.411994
$29$	50.2658	0.321866	0.160933	−	0.986965i	$-0.448550\pi$
$29$	50.2658	0.321866	0.160933	+	0.986965i	$0.448550\pi$
$30$	252.882	1.53899
$31$	−205.229	−1.18904	−0.594521	−	0.804080i	$-0.702658\pi$
$31$	−205.229	−1.18904	−0.594521	+	0.804080i	$0.702658\pi$
$32$	149.571	0.826271
$33$	68.9780	0.363865
$34$	−377.706	−1.90518
$35$	205.188	0.990946
$36$	43.5305	0.201530
$37$	−102.895	−0.457183	−0.228591	−	0.973522i	$-0.573412\pi$
$37$	−102.895	−0.457183	−0.228591	+	0.973522i	$0.573412\pi$
$38$	186.450	0.795952
$39$	0	0
$40$	−180.153	−0.712119
$41$	239.288	0.911477	0.455738	−	0.890114i	$-0.349375\pi$
$41$	239.288	0.911477	0.455738	+	0.890114i	$0.349375\pi$
$42$	367.962	1.35185
$43$	−50.4632	−0.178967	−0.0894834	−	0.995988i	$-0.528522\pi$
$43$	−50.4632	−0.178967	−0.0894834	+	0.995988i	$0.528522\pi$
$44$	38.8600	0.133145
$45$	−146.325	−0.484729
$46$	−285.674	−0.915658
$47$	72.8888	0.226211	0.113106	−	0.993583i	$-0.463920\pi$
$47$	72.8888	0.226211	0.113106	+	0.993583i	$0.463920\pi$
$48$	−500.289	−1.50439
$49$	−44.4367	−0.129553
$50$	−54.3893	−0.153836
$51$	697.440	1.91492
$52$	0	0
$53$	191.741	0.496938	0.248469	−	0.968640i	$-0.420073\pi$
$53$	191.741	0.496938	0.248469	+	0.968640i	$0.420073\pi$
$54$	312.571	0.787695
$55$	−130.625	−0.320245
$56$	−262.136	−0.625525
$57$	−344.282	−0.800023
$58$	−170.702	−0.386453
$59$	−883.017	−1.94846	−0.974229	−	0.225560i	$-0.927579\pi$
$59$	−883.017	−1.94846	−0.974229	+	0.225560i	$0.927579\pi$
$60$	−263.064	−0.566025
$61$	−128.928	−0.270615	−0.135308	−	0.990804i	$-0.543202\pi$
$61$	−128.928	−0.270615	−0.135308	+	0.990804i	$0.543202\pi$
$62$	696.957	1.42764
$63$	−212.913	−0.425786
$64$	130.312	0.254515
$65$	0	0
$66$	−234.249	−0.436879
$67$	−835.862	−1.52413	−0.762066	−	0.647500i	$-0.775815\pi$
$67$	−835.862	−1.52413	−0.762066	+	0.647500i	$0.775815\pi$
$68$	392.915	0.700705
$69$	527.500	0.920341
$70$	−696.816	−1.18979
$71$	739.396	1.23592	0.617959	−	0.786211i	$-0.287960\pi$
$71$	739.396	1.23592	0.617959	+	0.786211i	$0.287960\pi$
$72$	186.936	0.305980
$73$	−93.7544	−0.150317	−0.0751584	−	0.997172i	$-0.523946\pi$
$73$	−93.7544	−0.150317	−0.0751584	+	0.997172i	$0.523946\pi$
$74$	349.429	0.548922
$75$	100.431	0.154623
$76$	−193.957	−0.292743
$77$	−190.069	−0.281303
$78$	0	0
$79$	−963.372	−1.37200	−0.685999	−	0.727603i	$-0.740634\pi$
$79$	−963.372	−1.37200	−0.685999	+	0.727603i	$0.740634\pi$
$80$	947.408	1.32404
$81$	−909.862	−1.24810
$82$	−812.620	−1.09438
$83$	−885.285	−1.17076	−0.585378	−	0.810761i	$-0.699054\pi$
$83$	−885.285	−1.17076	−0.585378	+	0.810761i	$0.699054\pi$
$84$	−382.778	−0.497196
$85$	−1320.75	−1.68536
$86$	171.373	0.214879
$87$	315.203	0.388429
$88$	166.879	0.202152
$89$	−386.022	−0.459755	−0.229878	−	0.973220i	$-0.573833\pi$
$89$	−386.022	−0.459755	−0.229878	+	0.973220i	$0.573833\pi$
$90$	496.917	0.581996
$91$	0	0
$92$	297.176	0.336769
$93$	−1286.94	−1.43494
$94$	−247.529	−0.271603
$95$	651.974	0.704117
$96$	937.920	0.997146
$97$	1713.35	1.79345	0.896726	−	0.442586i	$-0.145939\pi$
$97$	1713.35	1.79345	0.896726	+	0.442586i	$0.145939\pi$
$98$	150.907	0.155550
$99$	135.543	0.137602
$100$	56.5793	0.0565793
$101$	1157.56	1.14041	0.570203	−	0.821504i	$-0.306864\pi$
$101$	1157.56	1.14041	0.570203	+	0.821504i	$0.306864\pi$
$102$	−2368.50	−2.29918
$103$	1152.26	1.10229	0.551146	−	0.834409i	$-0.314191\pi$
$103$	1152.26	1.10229	0.551146	+	0.834409i	$0.314191\pi$
$104$	0	0
$105$	1286.68	1.19588
$106$	−651.151	−0.596655
$107$	122.201	0.110408	0.0552040	−	0.998475i	$-0.482419\pi$
$107$	122.201	0.110408	0.0552040	+	0.998475i	$0.482419\pi$
$108$	−325.157	−0.289706
$109$	−266.553	−0.234231	−0.117115	−	0.993118i	$-0.537365\pi$
$109$	−266.553	−0.234231	−0.117115	+	0.993118i	$0.537365\pi$
$110$	443.601	0.384506
$111$	−645.224	−0.551730
$112$	1378.55	1.16304
$113$	−253.153	−0.210749	−0.105374	−	0.994433i	$-0.533604\pi$
$113$	−253.153	−0.210749	−0.105374	+	0.994433i	$0.533604\pi$
$114$	1169.18	0.960557
$115$	−998.937	−0.810011
$116$	177.575	0.142133
$117$	0	0
$118$	2998.72	2.33944
$119$	−1921.79	−1.48042
$120$	−1129.69	−0.859387
$121$	121.000	0.0909091
$122$	437.838	0.324918
$123$	1500.51	1.09997
$124$	−725.020	−0.525070
$125$	1294.19	0.926046
$126$	723.050	0.511225
$127$	699.162	0.488509	0.244254	−	0.969711i	$-0.421457\pi$
$127$	699.162	0.488509	0.244254	+	0.969711i	$0.421457\pi$
$128$	−1639.11	−1.13186
$129$	−316.441	−0.215978
$130$	0	0
$131$	−483.590	−0.322530	−0.161265	−	0.986911i	$-0.551557\pi$
$131$	−483.590	−0.322530	−0.161265	+	0.986911i	$0.551557\pi$
$132$	243.681	0.160679
$133$	948.669	0.618496
$134$	2838.58	1.82997
$135$	1092.99	0.696813
$136$	1687.32	1.06387
$137$	2729.68	1.70228	0.851139	−	0.524940i	$-0.175912\pi$
$137$	2729.68	1.70228	0.851139	+	0.524940i	$0.175912\pi$
$138$	−1791.38	−1.10502
$139$	−1161.95	−0.709030	−0.354515	−	0.935050i	$-0.615354\pi$
$139$	−1161.95	−0.709030	−0.354515	+	0.935050i	$0.615354\pi$
$140$	724.873	0.437593
$141$	457.066	0.272992
$142$	−2510.98	−1.48392
$143$	0	0
$144$	−983.076	−0.568909
$145$	−596.906	−0.341865
$146$	318.389	0.180480
$147$	−278.651	−0.156345
$148$	−363.499	−0.201888
$149$	3225.89	1.77366	0.886829	−	0.462097i	$-0.152903\pi$
$149$	3225.89	1.77366	0.886829	+	0.462097i	$0.152903\pi$
$150$	−341.061	−0.185650
$151$	1816.15	0.978782	0.489391	−	0.872064i	$-0.337219\pi$
$151$	1816.15	0.978782	0.489391	+	0.872064i	$0.337219\pi$
$152$	−832.923	−0.444467
$153$	1370.48	0.724161
$154$	645.471	0.337750
$155$	2437.10	1.26292
$156$	0	0
$157$	1753.98	0.891609	0.445805	−	0.895130i	$-0.352918\pi$
$157$	1753.98	0.891609	0.445805	+	0.895130i	$0.352918\pi$
$158$	3271.60	1.64731
$159$	1202.36	0.599706
$160$	−1776.16	−0.877610
$161$	−1453.52	−0.711514
$162$	3089.88	1.49854
$163$	3982.86	1.91387	0.956937	−	0.290296i	$-0.0937536\pi$
$163$	3982.86	1.91387	0.956937	+	0.290296i	$0.0937536\pi$
$164$	845.340	0.402500
$165$	−819.115	−0.386473
$166$	3006.42	1.40568
$167$	−2316.90	−1.07357	−0.536787	−	0.843718i	$-0.680362\pi$
$167$	−2316.90	−1.07357	−0.536787	+	0.843718i	$0.680362\pi$
$168$	−1643.78	−0.754885
$169$	0	0
$170$	4485.27	2.02355
$171$	−676.519	−0.302542
$172$	−178.273	−0.0790301
$173$	−119.282	−0.0524209	−0.0262104	−	0.999656i	$-0.508344\pi$
$173$	−119.282	−0.0524209	−0.0262104	+	0.999656i	$0.508344\pi$
$174$	−1070.43	−0.466372
$175$	−276.736	−0.119539
$176$	−877.598	−0.375861
$177$	−5537.16	−2.35141
$178$	1310.92	0.552011
$179$	−975.367	−0.407276	−0.203638	−	0.979046i	$-0.565277\pi$
$179$	−975.367	−0.407276	−0.203638	+	0.979046i	$0.565277\pi$
$180$	−516.925	−0.214052
$181$	−1425.45	−0.585377	−0.292688	−	0.956208i	$-0.594550\pi$
$181$	−1425.45	−0.585377	−0.292688	+	0.956208i	$0.594550\pi$
$182$	0	0
$183$	−808.473	−0.326579
$184$	1276.18	0.511312
$185$	1221.87	0.485589
$186$	4370.43	1.72288
$187$	1223.44	0.478430
$188$	257.496	0.0998928
$189$	1590.38	0.612080
$190$	−2214.09	−0.845407
$191$	−866.079	−0.328101	−0.164050	−	0.986452i	$-0.552456\pi$
$191$	−866.079	−0.328101	−0.164050	+	0.986452i	$0.552456\pi$
$192$	817.151	0.307150
$193$	3672.80	1.36981	0.684907	−	0.728631i	$-0.259843\pi$
$193$	3672.80	1.36981	0.684907	+	0.728631i	$0.259843\pi$
$194$	−5818.53	−2.15333
$195$	0	0
$196$	−156.983	−0.0572095
$197$	1225.63	0.443261	0.221631	−	0.975131i	$-0.428862\pi$
$197$	1225.63	0.443261	0.221631	+	0.975131i	$0.428862\pi$
$198$	−460.302	−0.165213
$199$	−382.479	−0.136247	−0.0681236	−	0.997677i	$-0.521701\pi$
$199$	−382.479	−0.136247	−0.0681236	+	0.997677i	$0.521701\pi$
$200$	242.972	0.0859035
$201$	−5241.47	−1.83933
$202$	−3931.04	−1.36924
$203$	−868.541	−0.300294
$204$	2463.86	0.845613
$205$	−2841.55	−0.968109
$206$	−3913.08	−1.32348
$207$	1036.54	0.348043
$208$	0	0
$209$	−603.933	−0.199880
$210$	−4369.55	−1.43584
$211$	−3770.33	−1.23014	−0.615072	−	0.788471i	$-0.710873\pi$
$211$	−3770.33	−1.23014	−0.615072	+	0.788471i	$0.710873\pi$
$212$	677.370	0.219443
$213$	4636.55	1.49151
$214$	−414.994	−0.132563
$215$	599.251	0.190087
$216$	−1396.34	−0.439856
$217$	3546.16	1.10935
$218$	905.211	0.281232
$219$	−587.909	−0.181403
$220$	−461.463	−0.141417
$221$	0	0
$222$	2191.17	0.662441
$223$	−5799.98	−1.74168	−0.870842	−	0.491563i	$-0.836426\pi$
$223$	−5799.98	−1.74168	−0.870842	+	0.491563i	$0.836426\pi$
$224$	−2584.44	−0.770892
$225$	197.347	0.0584733
$226$	859.703	0.253038
$227$	2854.97	0.834762	0.417381	−	0.908732i	$-0.362948\pi$
$227$	2854.97	0.834762	0.417381	+	0.908732i	$0.362948\pi$
$228$	−1216.26	−0.353283
$229$	5162.20	1.48964	0.744820	−	0.667265i	$-0.232535\pi$
$229$	5162.20	1.48964	0.744820	+	0.667265i	$0.232535\pi$
$230$	3392.38	0.972551
$231$	−1191.87	−0.339478
$232$	762.572	0.215799
$233$	6157.33	1.73125	0.865623	−	0.500697i	$-0.166923\pi$
$233$	6157.33	1.73125	0.865623	+	0.500697i	$0.166923\pi$
$234$	0	0
$235$	−865.555	−0.240266
$236$	−3119.46	−0.860422
$237$	−6041.05	−1.65573
$238$	6526.38	1.77749
$239$	−3833.06	−1.03741	−0.518703	−	0.854954i	$-0.673585\pi$
$239$	−3833.06	−1.03741	−0.518703	+	0.854954i	$0.673585\pi$
$240$	5940.94	1.59786
$241$	−3299.34	−0.881863	−0.440931	−	0.897541i	$-0.645352\pi$
$241$	−3299.34	−0.881863	−0.440931	+	0.897541i	$0.645352\pi$
$242$	−410.914	−0.109151
$243$	−3220.39	−0.850156
$244$	−455.467	−0.119501
$245$	527.686	0.137603
$246$	−5095.72	−1.32070
$247$	0	0
$248$	−3113.50	−0.797206
$249$	−5551.39	−1.41287
$250$	−4395.05	−1.11187
$251$	4359.64	1.09633	0.548164	−	0.836371i	$-0.315327\pi$
$251$	4359.64	1.09633	0.548164	+	0.836371i	$0.315327\pi$
$252$	−752.163	−0.188023
$253$	925.330	0.229941
$254$	−2374.35	−0.586534
$255$	−8282.10	−2.03390
$256$	4523.89	1.10446
$257$	2568.94	0.623526	0.311763	−	0.950160i	$-0.399081\pi$
$257$	2568.94	0.623526	0.311763	+	0.950160i	$0.399081\pi$
$258$	1074.63	0.259316
$259$	1777.91	0.426541
$260$	0	0
$261$	619.379	0.146891
$262$	1642.26	0.387250
$263$	−6393.40	−1.49899	−0.749495	−	0.662011i	$-0.769703\pi$
$263$	−6393.40	−1.49899	−0.749495	+	0.662011i	$0.769703\pi$
$264$	1046.45	0.243957
$265$	−2276.93	−0.527814
$266$	−3221.67	−0.742605
$267$	−2420.64	−0.554834
$268$	−2952.87	−0.673042
$269$	1120.49	0.253969	0.126985	−	0.991905i	$-0.459470\pi$
$269$	1120.49	0.253969	0.126985	+	0.991905i	$0.459470\pi$
$270$	−3711.78	−0.836637
$271$	421.418	0.0944624	0.0472312	−	0.998884i	$-0.484960\pi$
$271$	421.418	0.0944624	0.0472312	+	0.998884i	$0.484960\pi$
$272$	−8873.43	−1.97805
$273$	0	0
$274$	−9269.95	−2.04386
$275$	176.173	0.0386315
$276$	1863.51	0.406414
$277$	−1153.33	−0.250170	−0.125085	−	0.992146i	$-0.539920\pi$
$277$	−1153.33	−0.250170	−0.125085	+	0.992146i	$0.539920\pi$
$278$	3945.96	0.851306
$279$	−2528.85	−0.542647
$280$	3112.87	0.664391
$281$	−6451.10	−1.36954	−0.684769	−	0.728760i	$-0.740097\pi$
$281$	−6451.10	−1.36954	−0.684769	+	0.728760i	$0.740097\pi$
$282$	−1552.19	−0.327772
$283$	2268.44	0.476484	0.238242	−	0.971206i	$-0.423429\pi$
$283$	2268.44	0.476484	0.238242	+	0.971206i	$0.423429\pi$
$284$	2612.08	0.545770
$285$	4088.35	0.849730
$286$	0	0
$287$	−4134.66	−0.850387
$288$	1843.03	0.377088
$289$	7457.20	1.51785
$290$	2027.09	0.410464
$291$	10744.0	2.16434
$292$	−331.209	−0.0663785
$293$	6746.38	1.34515	0.672573	−	0.740030i	$-0.265189\pi$
$293$	6746.38	1.34515	0.672573	+	0.740030i	$0.265189\pi$
$294$	946.294	0.187718
$295$	10485.8	2.06952
$296$	−1560.99	−0.306523
$297$	−1012.45	−0.197807
$298$	−10955.1	−2.12957
$299$	0	0
$300$	354.794	0.0682801
$301$	871.954	0.166972
$302$	−6167.62	−1.17519
$303$	7258.72	1.37625
$304$	4380.26	0.826398
$305$	1531.02	0.287430
$306$	−4654.13	−0.869473
$307$	8170.24	1.51889	0.759446	−	0.650570i	$-0.225470\pi$
$307$	8170.24	1.51889	0.759446	+	0.650570i	$0.225470\pi$
$308$	−671.461	−0.124221
$309$	7225.54	1.33025
$310$	−8276.36	−1.51634
$311$	−1965.10	−0.358298	−0.179149	−	0.983822i	$-0.557334\pi$
$311$	−1965.10	−0.358298	−0.179149	+	0.983822i	$0.557334\pi$
$312$	0	0
$313$	8154.74	1.47263	0.736315	−	0.676639i	$-0.236564\pi$
$313$	8154.74	1.47263	0.736315	+	0.676639i	$0.236564\pi$
$314$	−5956.49	−1.07052
$315$	2528.34	0.452241
$316$	−3403.33	−0.605862
$317$	1645.52	0.291552	0.145776	−	0.989318i	$-0.453432\pi$
$317$	1645.52	0.291552	0.145776	+	0.989318i	$0.453432\pi$
$318$	−4083.19	−0.720045
$319$	552.924	0.0970463
$320$	−1547.45	−0.270329
$321$	766.292	0.133241
$322$	4936.15	0.854288
$323$	−6106.39	−1.05192
$324$	−3214.30	−0.551148
$325$	0	0
$326$	−13525.7	−2.29792
$327$	−1671.48	−0.282670
$328$	3630.19	0.611110
$329$	−1259.44	−0.211050
$330$	2781.70	0.464023
$331$	−1961.28	−0.325685	−0.162842	−	0.986652i	$-0.552066\pi$
$331$	−1961.28	−0.325685	−0.162842	+	0.986652i	$0.552066\pi$
$332$	−3127.47	−0.516995
$333$	−1267.87	−0.208646
$334$	7868.15	1.28900
$335$	9925.87	1.61883
$336$	8644.49	1.40356
$337$	−659.009	−0.106524	−0.0532619	−	0.998581i	$-0.516962\pi$
$337$	−659.009	−0.106524	−0.0532619	+	0.998581i	$0.516962\pi$
$338$	0	0
$339$	−1587.45	−0.254332
$340$	−4665.87	−0.744242
$341$	−2257.52	−0.358510
$342$	2297.45	0.363251
$343$	6694.51	1.05385
$344$	−765.568	−0.119990
$345$	−6264.06	−0.977524
$346$	405.079	0.0629398
$347$	740.844	0.114613	0.0573063	−	0.998357i	$-0.481749\pi$
$347$	740.844	0.114613	0.0573063	+	0.998357i	$0.481749\pi$
$348$	1113.53	0.171527
$349$	4734.37	0.726146	0.363073	−	0.931761i	$-0.381728\pi$
$349$	4734.37	0.726146	0.363073	+	0.931761i	$0.381728\pi$
$350$	939.792	0.143526
$351$	0	0
$352$	1645.28	0.249130
$353$	3598.61	0.542592	0.271296	−	0.962496i	$-0.412548\pi$
$353$	3598.61	0.542592	0.271296	+	0.962496i	$0.412548\pi$
$354$	18804.1	2.82324
$355$	−8780.33	−1.31271
$356$	−1363.71	−0.203024
$357$	−12051.0	−1.78658
$358$	3312.33	0.489001
$359$	−61.1213	−0.00898568	−0.00449284	−	0.999990i	$-0.501430\pi$
$359$	−61.1213	−0.00898568	−0.00449284	+	0.999990i	$0.501430\pi$
$360$	−2219.86	−0.324992
$361$	−3844.66	−0.560527
$362$	4840.82	0.702840
$363$	758.759	0.109709
$364$	0	0
$365$	1113.33	0.159656
$366$	2745.56	0.392112
$367$	−1446.95	−0.205804	−0.102902	−	0.994692i	$-0.532813\pi$
$367$	−1446.95	−0.205804	−0.102902	+	0.994692i	$0.532813\pi$
$368$	−6711.31	−0.950682
$369$	2948.53	0.415973
$370$	−4149.47	−0.583029
$371$	−3313.10	−0.463632
$372$	−4546.40	−0.633656
$373$	12808.9	1.77807	0.889036	−	0.457837i	$-0.151376\pi$
$373$	12808.9	1.77807	0.889036	+	0.457837i	$0.151376\pi$
$374$	−4154.77	−0.574433
$375$	8115.51	1.11755
$376$	1105.78	0.151666
$377$	0	0
$378$	−5400.91	−0.734902
$379$	−6800.85	−0.921731	−0.460866	−	0.887470i	$-0.652461\pi$
$379$	−6800.85	−0.921731	−0.460866	+	0.887470i	$0.652461\pi$
$380$	2303.25	0.310932
$381$	4384.26	0.589534
$382$	2941.19	0.393939
$383$	9049.19	1.20729	0.603645	−	0.797253i	$-0.293714\pi$
$383$	9049.19	1.20729	0.603645	+	0.797253i	$0.293714\pi$
$384$	−10278.4	−1.36593
$385$	2257.07	0.298781
$386$	−12472.8	−1.64468
$387$	−621.812	−0.0816756
$388$	6052.82	0.791972
$389$	708.472	0.0923417	0.0461709	−	0.998934i	$-0.485298\pi$
$389$	708.472	0.0923417	0.0461709	+	0.998934i	$0.485298\pi$
$390$	0	0
$391$	9356.05	1.21012
$392$	−674.141	−0.0868603
$393$	−3032.46	−0.389230
$394$	−4162.22	−0.532207
$395$	11440.0	1.45724
$396$	478.836	0.0607636
$397$	1678.10	0.212145	0.106073	−	0.994358i	$-0.466172\pi$
$397$	1678.10	0.212145	0.106073	+	0.994358i	$0.466172\pi$
$398$	1298.89	0.163587
$399$	5948.85	0.746403
$400$	−1277.76	−0.159720
$401$	13357.2	1.66340	0.831702	−	0.555223i	$-0.187367\pi$
$401$	13357.2	1.66340	0.831702	+	0.555223i	$0.187367\pi$
$402$	17799.9	2.20841
$403$	0	0
$404$	4089.33	0.503593
$405$	10804.6	1.32564
$406$	2949.56	0.360552
$407$	−1131.84	−0.137846
$408$	10580.7	1.28388
$409$	−1978.99	−0.239254	−0.119627	−	0.992819i	$-0.538170\pi$
$409$	−1978.99	−0.239254	−0.119627	+	0.992819i	$0.538170\pi$
$410$	9649.86	1.16237
$411$	17117.1	2.05431
$412$	4070.64	0.486762
$413$	15257.6	1.81787
$414$	−3520.09	−0.417882
$415$	10512.8	1.24350
$416$	0	0
$417$	−7286.27	−0.855660
$418$	2050.95	0.239989
$419$	3468.21	0.404375	0.202188	−	0.979347i	$-0.435195\pi$
$419$	3468.21	0.404375	0.202188	+	0.979347i	$0.435195\pi$
$420$	4545.49	0.528088
$421$	−1540.19	−0.178300	−0.0891500	−	0.996018i	$-0.528415\pi$
$421$	−1540.19	−0.178300	−0.0891500	+	0.996018i	$0.528415\pi$
$422$	12804.0	1.47699
$423$	898.141	0.103237
$424$	2908.87	0.333177
$425$	1781.30	0.203307
$426$	−15745.7	−1.79080
$427$	2227.74	0.252478
$428$	431.704	0.0487552
$429$	0	0
$430$	−2035.05	−0.228230
$431$	−9734.39	−1.08791	−0.543955	−	0.839115i	$-0.683074\pi$
$431$	−9734.39	−1.08791	−0.543955	+	0.839115i	$0.683074\pi$
$432$	7343.21	0.817825
$433$	589.612	0.0654386	0.0327193	−	0.999465i	$-0.489583\pi$
$433$	589.612	0.0654386	0.0327193	+	0.999465i	$0.489583\pi$
$434$	−12042.7	−1.33195
$435$	−3743.04	−0.412563
$436$	−941.659	−0.103434
$437$	−4618.49	−0.505567
$438$	1996.53	0.217803
$439$	−13771.6	−1.49723	−0.748615	−	0.663004i	$-0.769281\pi$
$439$	−13771.6	−1.49723	−0.748615	+	0.663004i	$0.769281\pi$
$440$	−1981.69	−0.214712
$441$	−547.553	−0.0591246
$442$	0	0
$443$	14442.0	1.54889	0.774446	−	0.632641i	$-0.218029\pi$
$443$	14442.0	1.54889	0.774446	+	0.632641i	$0.218029\pi$
$444$	−2279.40	−0.243639
$445$	4584.01	0.488321
$446$	19696.7	2.09118
$447$	20228.7	2.14046
$448$	−2251.66	−0.237457
$449$	15580.9	1.63766	0.818830	−	0.574036i	$-0.194623\pi$
$449$	15580.9	1.63766	0.818830	+	0.574036i	$0.194623\pi$
$450$	−670.189	−0.0702067
$451$	2632.17	0.274821
$452$	−894.319	−0.0930647
$453$	11388.6	1.18120
$454$	−9695.44	−1.00227
$455$	0	0
$456$	−5223.04	−0.536384
$457$	5049.69	0.516881	0.258441	−	0.966027i	$-0.416791\pi$
$457$	5049.69	0.516881	0.258441	+	0.966027i	$0.416791\pi$
$458$	−17530.8	−1.78856
$459$	−10237.0	−1.04100
$460$	−3528.97	−0.357694
$461$	6093.73	0.615647	0.307823	−	0.951444i	$-0.400399\pi$
$461$	6093.73	0.615647	0.307823	+	0.951444i	$0.400399\pi$
$462$	4047.58	0.407598
$463$	−1667.52	−0.167379	−0.0836893	−	0.996492i	$-0.526670\pi$
$463$	−1667.52	−0.167379	−0.0836893	+	0.996492i	$0.526670\pi$
$464$	−4010.29	−0.401235
$465$	15282.4	1.52410
$466$	−20910.2	−2.07864
$467$	−10968.5	−1.08685	−0.543426	−	0.839457i	$-0.682873\pi$
$467$	−10968.5	−1.08685	−0.543426	+	0.839457i	$0.682873\pi$
$468$	0	0
$469$	14442.8	1.42198
$470$	2939.41	0.288479
$471$	10998.7	1.07600
$472$	−13396.1	−1.30637
$473$	−555.096	−0.0539605
$474$	20515.3	1.98797
$475$	−879.314	−0.0849383
$476$	−6789.17	−0.653742
$477$	2362.65	0.226789
$478$	13017.0	1.24558
$479$	18716.7	1.78536	0.892679	−	0.450692i	$-0.148823\pi$
$479$	18716.7	1.78536	0.892679	+	0.450692i	$0.148823\pi$
$480$	−11137.8	−1.05910
$481$	0	0
$482$	11204.5	1.05882
$483$	−9114.66	−0.858657
$484$	427.460	0.0401446
$485$	−20346.1	−1.90488
$486$	10936.4	1.02075
$487$	212.131	0.0197383	0.00986916	−	0.999951i	$-0.496858\pi$
$487$	212.131	0.0197383	0.00986916	+	0.999951i	$0.496858\pi$
$488$	−1955.94	−0.181437
$489$	24975.4	2.30967
$490$	−1792.02	−0.165214
$491$	−15515.8	−1.42610	−0.713051	−	0.701112i	$-0.752687\pi$
$491$	−15515.8	−1.42610	−0.713051	+	0.701112i	$0.752687\pi$
$492$	5300.90	0.485738
$493$	5590.63	0.510729
$494$	0	0
$495$	−1609.57	−0.146151
$496$	16373.5	1.48225
$497$	−12776.0	−1.15308
$498$	18852.4	1.69638
$499$	−7740.24	−0.694390	−0.347195	−	0.937793i	$-0.612866\pi$
$499$	−7740.24	−0.694390	−0.347195	+	0.937793i	$0.612866\pi$
$500$	4572.01	0.408933
$501$	−14528.6	−1.29559
$502$	−14805.3	−1.31632
$503$	19198.9	1.70186	0.850932	−	0.525276i	$-0.176038\pi$
$503$	19198.9	1.70186	0.850932	+	0.525276i	$0.176038\pi$
$504$	−3230.06	−0.285473
$505$	−13746.0	−1.21126
$506$	−3142.41	−0.276081
$507$	0	0
$508$	2469.95	0.215721
$509$	19777.4	1.72224	0.861118	−	0.508406i	$-0.169765\pi$
$509$	19777.4	1.72224	0.861118	+	0.508406i	$0.169765\pi$
$510$	28125.9	2.44203
$511$	1619.98	0.140242
$512$	−2250.21	−0.194231
$513$	5053.35	0.434914
$514$	−8724.09	−0.748644
$515$	−13683.1	−1.17078
$516$	−1117.90	−0.0953738
$517$	801.777	0.0682052
$518$	−6037.77	−0.512132
$519$	−747.983	−0.0632617
$520$	0	0
$521$	−19127.9	−1.60846	−0.804230	−	0.594318i	$-0.797422\pi$
$521$	−19127.9	−1.60846	−0.804230	+	0.594318i	$0.797422\pi$
$522$	−2103.40	−0.176367
$523$	21247.7	1.77648	0.888238	−	0.459383i	$-0.151930\pi$
$523$	21247.7	1.77648	0.888238	+	0.459383i	$0.151930\pi$
$524$	−1708.39	−0.142426
$525$	−1735.34	−0.144260
$526$	21711.9	1.79978
$527$	−22825.9	−1.88674
$528$	−5503.18	−0.453590
$529$	−5090.67	−0.418400
$530$	7732.42	0.633726
$531$	−10880.6	−0.889224
$532$	3351.39	0.273122
$533$	0	0
$534$	8220.46	0.666168
$535$	−1451.14	−0.117268
$536$	−12680.7	−1.02187
$537$	−6116.27	−0.491502
$538$	−3805.18	−0.304931
$539$	−488.804	−0.0390617
$540$	3861.24	0.307706
$541$	−2978.09	−0.236669	−0.118335	−	0.992974i	$-0.537756\pi$
$541$	−2978.09	−0.236669	−0.118335	+	0.992974i	$0.537756\pi$
$542$	−1431.13	−0.113417
$543$	−8938.64	−0.706434
$544$	16635.5	1.31111
$545$	3165.32	0.248784
$546$	0	0
$547$	−6709.32	−0.524442	−0.262221	−	0.965008i	$-0.584455\pi$
$547$	−6709.32	−0.524442	−0.262221	+	0.965008i	$0.584455\pi$
$548$	9643.21	0.751711
$549$	−1588.66	−0.123502
$550$	−598.282	−0.0463834
$551$	−2759.74	−0.213374
$552$	8002.59	0.617053
$553$	16646.1	1.28004
$554$	3916.70	0.300369
$555$	7662.04	0.586010
$556$	−4104.85	−0.313101
$557$	−8545.16	−0.650036	−0.325018	−	0.945708i	$-0.605370\pi$
$557$	−8545.16	−0.650036	−0.325018	+	0.945708i	$0.605370\pi$
$558$	8587.95	0.651536
$559$	0	0
$560$	−16370.2	−1.23530
$561$	7671.84	0.577371
$562$	21907.8	1.64435
$563$	−19579.5	−1.46568	−0.732840	−	0.680402i	$-0.761805\pi$
$563$	−19579.5	−1.46568	−0.732840	+	0.680402i	$0.761805\pi$
$564$	1614.69	0.120551
$565$	3006.19	0.223843
$566$	−7703.60	−0.572097
$567$	15721.5	1.16445
$568$	11217.2	0.828634
$569$	9584.63	0.706166	0.353083	−	0.935592i	$-0.385133\pi$
$569$	9584.63	0.706166	0.353083	+	0.935592i	$0.385133\pi$
$570$	−13884.0	−1.02024
$571$	12017.9	0.880797	0.440398	−	0.897802i	$-0.354837\pi$
$571$	12017.9	0.880797	0.440398	+	0.897802i	$0.354837\pi$
$572$	0	0
$573$	−5430.95	−0.395953
$574$	14041.2	1.02103
$575$	1347.26	0.0977124
$576$	1605.71	0.116154
$577$	−21981.7	−1.58598	−0.792991	−	0.609234i	$-0.791477\pi$
$577$	−21981.7	−1.58598	−0.792991	+	0.609234i	$0.791477\pi$
$578$	−25324.6	−1.82243
$579$	23031.1	1.65309
$580$	−2108.71	−0.150964
$581$	15296.8	1.09229
$582$	−36486.4	−2.59865
$583$	2109.16	0.149832
$584$	−1422.33	−0.100781
$585$	0	0
$586$	−22910.6	−1.61507
$587$	11022.4	0.775034	0.387517	−	0.921863i	$-0.373333\pi$
$587$	11022.4	0.775034	0.387517	+	0.921863i	$0.373333\pi$
$588$	−984.397	−0.0690406
$589$	11267.7	0.788248
$590$	−35609.8	−2.48480
$591$	7685.59	0.534929
$592$	8209.10	0.569919
$593$	−4273.65	−0.295949	−0.147975	−	0.988991i	$-0.547275\pi$
$593$	−4273.65	−0.295949	−0.147975	+	0.988991i	$0.547275\pi$
$594$	3438.28	0.237499
$595$	22821.3	1.57241
$596$	11396.2	0.783231
$597$	−2398.42	−0.164423
$598$	0	0
$599$	18898.6	1.28911	0.644555	−	0.764558i	$-0.277042\pi$
$599$	18898.6	1.28911	0.644555	+	0.764558i	$0.277042\pi$
$600$	1523.61	0.103669
$601$	6356.75	0.431443	0.215721	−	0.976455i	$-0.430790\pi$
$601$	6356.75	0.431443	0.215721	+	0.976455i	$0.430790\pi$
$602$	−2961.14	−0.200477
$603$	−10299.6	−0.695573
$604$	6415.96	0.432221
$605$	−1436.88	−0.0965575
$606$	−24650.5	−1.65241
$607$	−27639.5	−1.84819	−0.924095	−	0.382162i	$-0.875180\pi$
$607$	−27639.5	−1.84819	−0.924095	+	0.382162i	$0.875180\pi$
$608$	−8211.91	−0.547758
$609$	−5446.39	−0.362396
$610$	−5199.33	−0.345106
$611$	0	0
$612$	4841.53	0.319783
$613$	27760.4	1.82909	0.914544	−	0.404487i	$-0.132550\pi$
$613$	27760.4	1.82909	0.914544	+	0.404487i	$0.132550\pi$
$614$	−27746.0	−1.82368
$615$	−17818.6	−1.16832
$616$	−2883.50	−0.188603
$617$	−22387.3	−1.46075	−0.730373	−	0.683049i	$-0.760654\pi$
$617$	−22387.3	−1.46075	−0.730373	+	0.683049i	$0.760654\pi$
$618$	−24537.8	−1.59718
$619$	4181.64	0.271526	0.135763	−	0.990741i	$-0.456651\pi$
$619$	4181.64	0.271526	0.135763	+	0.990741i	$0.456651\pi$
$620$	8609.61	0.557694
$621$	−7742.60	−0.500322
$622$	6673.47	0.430196
$623$	6670.06	0.428941
$624$	0	0
$625$	−17370.5	−1.11171
$626$	−27693.4	−1.76813
$627$	−3787.10	−0.241216
$628$	6196.33	0.393727
$629$	−11444.1	−0.725446
$630$	−8586.22	−0.542989
$631$	17331.6	1.09344	0.546720	−	0.837316i	$-0.315876\pi$
$631$	17331.6	1.09344	0.546720	+	0.837316i	$0.315876\pi$
$632$	−14615.1	−0.919871
$633$	−23642.7	−1.48454
$634$	−5588.18	−0.350055
$635$	−8302.56	−0.518861
$636$	4247.60	0.264825
$637$	0	0
$638$	−1877.72	−0.116520
$639$	9110.89	0.564039
$640$	19464.4	1.20218
$641$	3548.47	0.218652	0.109326	−	0.994006i	$-0.465131\pi$
$641$	3548.47	0.218652	0.109326	+	0.994006i	$0.465131\pi$
$642$	−2602.32	−0.159977
$643$	−3188.37	−0.195548	−0.0977738	−	0.995209i	$-0.531172\pi$
$643$	−3188.37	−0.195548	−0.0977738	+	0.995209i	$0.531172\pi$
$644$	−5134.90	−0.314198
$645$	3757.74	0.229397
$646$	20737.2	1.26300
$647$	26196.9	1.59182	0.795908	−	0.605417i	$-0.206994\pi$
$647$	26196.9	1.59182	0.795908	+	0.605417i	$0.206994\pi$
$648$	−13803.3	−0.836800
$649$	−9713.19	−0.587482
$650$	0	0
$651$	22237.0	1.33877
$652$	14070.3	0.845149
$653$	−10519.2	−0.630396	−0.315198	−	0.949026i	$-0.602071\pi$
$653$	−10519.2	−0.630396	−0.315198	+	0.949026i	$0.602071\pi$
$654$	5676.33	0.339392
$655$	5742.63	0.342570
$656$	−19090.8	−1.13624
$657$	−1155.25	−0.0686005
$658$	4277.06	0.253400
$659$	−13639.3	−0.806240	−0.403120	−	0.915147i	$-0.632074\pi$
$659$	−13639.3	−0.806240	−0.403120	+	0.915147i	$0.632074\pi$
$660$	−2893.71	−0.170663
$661$	−1068.19	−0.0628558	−0.0314279	−	0.999506i	$-0.510005\pi$
$661$	−1068.19	−0.0628558	−0.0314279	+	0.999506i	$0.510005\pi$
$662$	6660.48	0.391037
$663$	0	0
$664$	−13430.5	−0.784946
$665$	−11265.4	−0.656925
$666$	4305.69	0.250513
$667$	4228.40	0.245464
$668$	−8184.96	−0.474080
$669$	−36370.1	−2.10187
$670$	−33708.1	−1.94367
$671$	−1418.21	−0.0815936
$672$	−16206.3	−0.930315
$673$	15503.2	0.887972	0.443986	−	0.896034i	$-0.353564\pi$
$673$	15503.2	0.887972	0.443986	+	0.896034i	$0.353564\pi$
$674$	2237.98	0.127899
$675$	−1474.11	−0.0840572
$676$	0	0
$677$	−9837.18	−0.558455	−0.279227	−	0.960225i	$-0.590078\pi$
$677$	−9837.18	−0.558455	−0.279227	+	0.960225i	$0.590078\pi$
$678$	5390.97	0.305367
$679$	−29605.0	−1.67325
$680$	−20036.9	−1.12997
$681$	17902.7	1.00739
$682$	7666.52	0.430449
$683$	21940.0	1.22915	0.614575	−	0.788859i	$-0.289328\pi$
$683$	21940.0	1.22915	0.614575	+	0.788859i	$0.289328\pi$
$684$	−2389.96	−0.133600
$685$	−32414.9	−1.80805
$686$	−22734.5	−1.26532
$687$	32370.8	1.79770
$688$	4026.04	0.223098
$689$	0	0
$690$	21272.7	1.17368
$691$	811.252	0.0446621	0.0223310	−	0.999751i	$-0.492891\pi$
$691$	811.252	0.0446621	0.0223310	+	0.999751i	$0.492891\pi$
$692$	−421.389	−0.0231486
$693$	−2342.04	−0.128379
$694$	−2515.90	−0.137611
$695$	13798.1	0.753084
$696$	4781.88	0.260427
$697$	26614.0	1.44631
$698$	−16077.9	−0.871856
$699$	38611.0	2.08927
$700$	−977.633	−0.0527872
$701$	16482.1	0.888047	0.444024	−	0.896015i	$-0.353551\pi$
$701$	16482.1	0.888047	0.444024	+	0.896015i	$0.353551\pi$
$702$	0	0
$703$	5649.23	0.303079
$704$	1433.43	0.0767393
$705$	−5427.66	−0.289954
$706$	−12220.8	−0.651469
$707$	−20001.4	−1.06397
$708$	−19561.3	−1.03836
$709$	35300.0	1.86984	0.934922	−	0.354853i	$-0.115469\pi$
$709$	35300.0	1.86984	0.934922	+	0.354853i	$0.115469\pi$
$710$	29817.9	1.57612
$711$	−11870.7	−0.626143
$712$	−5856.26	−0.308248
$713$	−17264.1	−0.906796
$714$	40925.2	2.14508
$715$	0	0
$716$	−3445.71	−0.179849
$717$	−24036.1	−1.25195
$718$	207.567	0.0107888
$719$	34014.3	1.76429	0.882143	−	0.470982i	$-0.156100\pi$
$719$	34014.3	1.76429	0.882143	+	0.470982i	$0.156100\pi$
$720$	11674.0	0.604257
$721$	−19910.0	−1.02841
$722$	13056.4	0.673004
$723$	−20689.3	−1.06423
$724$	−5035.74	−0.258497
$725$	805.045	0.0412395
$726$	−2576.73	−0.131724
$727$	−36958.6	−1.88545	−0.942723	−	0.333575i	$-0.891745\pi$
$727$	−36958.6	−1.88545	−0.942723	+	0.333575i	$0.891745\pi$
$728$	0	0
$729$	4372.10	0.222126
$730$	−3780.87	−0.191693
$731$	−5612.59	−0.283980
$732$	−2856.11	−0.144215
$733$	6748.59	0.340061	0.170030	−	0.985439i	$-0.445613\pi$
$733$	6748.59	0.340061	0.170030	+	0.985439i	$0.445613\pi$
$734$	4913.81	0.247101
$735$	3308.98	0.166059
$736$	12582.1	0.630137
$737$	−9194.48	−0.459543
$738$	−10013.2	−0.499444
$739$	−12556.7	−0.625042	−0.312521	−	0.949911i	$-0.601173\pi$
$739$	−12556.7	−0.625042	−0.312521	+	0.949911i	$0.601173\pi$
$740$	4316.55	0.214432
$741$	0	0
$742$	11251.2	0.556665
$743$	−28585.9	−1.41146	−0.705730	−	0.708481i	$-0.749381\pi$
$743$	−28585.9	−1.41146	−0.705730	+	0.708481i	$0.749381\pi$
$744$	−19523.9	−0.962071
$745$	−38307.5	−1.88386
$746$	−43498.9	−2.13486
$747$	−10908.6	−0.534301
$748$	4322.06	0.211270
$749$	−2111.52	−0.103008
$750$	−27560.2	−1.34181
$751$	28874.1	1.40297	0.701486	−	0.712684i	$-0.252520\pi$
$751$	28874.1	1.40297	0.701486	+	0.712684i	$0.252520\pi$
$752$	−5815.19	−0.281992
$753$	27338.1	1.32305
$754$	0	0
$755$	−21566.8	−1.03960
$756$	5618.38	0.270289
$757$	9405.42	0.451580	0.225790	−	0.974176i	$-0.427504\pi$
$757$	9405.42	0.451580	0.225790	+	0.974176i	$0.427504\pi$
$758$	23095.6	1.10669
$759$	5802.50	0.277493
$760$	9890.97	0.472083
$761$	−23153.0	−1.10289	−0.551443	−	0.834213i	$-0.685923\pi$
$761$	−23153.0	−1.10289	−0.551443	+	0.834213i	$0.685923\pi$
$762$	−14888.9	−0.707831
$763$	4605.77	0.218532
$764$	−3059.62	−0.144886
$765$	−16274.4	−0.769155
$766$	−30730.9	−1.44955
$767$	0	0
$768$	28368.1	1.33287
$769$	−38625.0	−1.81125	−0.905627	−	0.424076i	$-0.860599\pi$
$769$	−38625.0	−1.81125	−0.905627	+	0.424076i	$0.860599\pi$
$770$	−7664.97	−0.358736
$771$	16109.1	0.752473
$772$	12975.0	0.604897
$773$	−20388.5	−0.948673	−0.474337	−	0.880344i	$-0.657312\pi$
$773$	−20388.5	−0.948673	−0.474337	+	0.880344i	$0.657312\pi$
$774$	2111.66	0.0980649
$775$	−3286.91	−0.152347
$776$	25993.0	1.20244
$777$	11148.8	0.514751
$778$	−2405.96	−0.110871
$779$	−13137.6	−0.604243
$780$	0	0
$781$	8133.35	0.372643
$782$	−31773.0	−1.45294
$783$	−4626.53	−0.211160
$784$	3545.24	0.161499
$785$	−20828.5	−0.947008
$786$	10298.2	0.467334
$787$	10004.5	0.453142	0.226571	−	0.973995i	$-0.427249\pi$
$787$	10004.5	0.453142	0.226571	+	0.973995i	$0.427249\pi$
$788$	4329.81	0.195740
$789$	−40091.3	−1.80898
$790$	−38850.2	−1.74966
$791$	4374.22	0.196624
$792$	2056.29	0.0922566
$793$	0	0
$794$	−5698.82	−0.254715
$795$	−14278.0	−0.636967
$796$	−1351.19	−0.0601655
$797$	26764.7	1.18953	0.594764	−	0.803901i	$-0.297246\pi$
$797$	26764.7	1.18953	0.594764	+	0.803901i	$0.297246\pi$
$798$	−20202.2	−0.896178
$799$	8106.79	0.358946
$800$	2395.49	0.105867
$801$	−4756.59	−0.209820
$802$	−45360.7	−1.99719
$803$	−1031.30	−0.0453222
$804$	−18516.7	−0.812230
$805$	17260.6	0.755722
$806$	0	0
$807$	7026.32	0.306491
$808$	17561.0	0.764598
$809$	−9269.88	−0.402857	−0.201429	−	0.979503i	$-0.564558\pi$
$809$	−9269.88	−0.402857	−0.201429	+	0.979503i	$0.564558\pi$
$810$	−36692.4	−1.59165
$811$	1569.95	0.0679759	0.0339879	−	0.999422i	$-0.489179\pi$
$811$	1569.95	0.0679759	0.0339879	+	0.999422i	$0.489179\pi$
$812$	−3068.32	−0.132607
$813$	2642.60	0.113997
$814$	3843.72	0.165506
$815$	−47296.5	−2.03279
$816$	−55642.9	−2.38712
$817$	2770.59	0.118642
$818$	6720.64	0.287264
$819$	0	0
$820$	−10038.4	−0.427508
$821$	23944.6	1.01787	0.508935	−	0.860805i	$-0.330039\pi$
$821$	23944.6	1.01787	0.508935	+	0.860805i	$0.330039\pi$
$822$	−58129.4	−2.46654
$823$	−13009.2	−0.550998	−0.275499	−	0.961301i	$-0.588843\pi$
$823$	−13009.2	−0.550998	−0.275499	+	0.961301i	$0.588843\pi$
$824$	17480.8	0.739043
$825$	1104.74	0.0466206
$826$	−51814.7	−2.18265
$827$	−42070.4	−1.76896	−0.884481	−	0.466576i	$-0.845487\pi$
$827$	−42070.4	−1.76896	−0.884481	+	0.466576i	$0.845487\pi$
$828$	3661.83	0.153692
$829$	−7854.42	−0.329066	−0.164533	−	0.986372i	$-0.552612\pi$
$829$	−7854.42	−0.329066	−0.164533	+	0.986372i	$0.552612\pi$
$830$	−35701.2	−1.49302
$831$	−7232.23	−0.301905
$832$	0	0
$833$	−4942.32	−0.205572
$834$	24744.1	1.02736
$835$	27513.2	1.14028
$836$	−2133.53	−0.0882652
$837$	18889.6	0.780072
$838$	−11778.0	−0.485518
$839$	21765.2	0.895611	0.447805	−	0.894131i	$-0.352206\pi$
$839$	21765.2	0.895611	0.447805	+	0.894131i	$0.352206\pi$
$840$	19520.0	0.801788
$841$	−21862.4	−0.896402
$842$	5230.47	0.214078
$843$	−40453.1	−1.65276
$844$	−13319.6	−0.543220
$845$	0	0
$846$	−3050.08	−0.123952
$847$	−2090.76	−0.0848161
$848$	−15297.4	−0.619477
$849$	14224.8	0.575022
$850$	−6049.26	−0.244103
$851$	−8655.59	−0.348660
$852$	16379.7	0.658637
$853$	40432.6	1.62296	0.811480	−	0.584380i	$-0.198662\pi$
$853$	40432.6	1.62296	0.811480	+	0.584380i	$0.198662\pi$
$854$	−7565.39	−0.303141
$855$	8033.67	0.321340
$856$	1853.89	0.0740243
$857$	−21757.7	−0.867246	−0.433623	−	0.901094i	$-0.642765\pi$
$857$	−21757.7	−0.867246	−0.433623	+	0.901094i	$0.642765\pi$
$858$	0	0
$859$	−860.116	−0.0341639	−0.0170819	−	0.999854i	$-0.505438\pi$
$859$	−860.116	−0.0341639	−0.0170819	+	0.999854i	$0.505438\pi$
$860$	2116.99	0.0839405
$861$	−25927.3	−1.02625
$862$	33057.9	1.30621
$863$	29843.7	1.17716	0.588582	−	0.808438i	$-0.299687\pi$
$863$	29843.7	1.17716	0.588582	+	0.808438i	$0.299687\pi$
$864$	−13766.7	−0.542076
$865$	1416.47	0.0556779
$866$	−2002.31	−0.0785697
$867$	46762.1	1.83175
$868$	12527.6	0.489879
$869$	−10597.1	−0.413673
$870$	12711.3	0.495349
$871$	0	0
$872$	−4043.82	−0.157043
$873$	21112.1	0.818483
$874$	15684.3	0.607015
$875$	−22362.3	−0.863980
$876$	−2076.92	−0.0801058
$877$	30296.3	1.16651	0.583257	−	0.812287i	$-0.301778\pi$
$877$	30296.3	1.16651	0.583257	+	0.812287i	$0.301778\pi$
$878$	46768.3	1.79767
$879$	42304.8	1.62333
$880$	10421.5	0.399214
$881$	18236.1	0.697378	0.348689	−	0.937238i	$-0.386627\pi$
$881$	18236.1	0.697378	0.348689	+	0.937238i	$0.386627\pi$
$882$	1859.48	0.0709887
$883$	36182.7	1.37899	0.689494	−	0.724292i	$-0.257833\pi$
$883$	36182.7	1.37899	0.689494	+	0.724292i	$0.257833\pi$
$884$	0	0
$885$	65753.9	2.49750
$886$	−49044.7	−1.85970
$887$	49217.1	1.86308	0.931538	−	0.363645i	$-0.118468\pi$
$887$	49217.1	1.86308	0.931538	+	0.363645i	$0.118468\pi$
$888$	−9788.57	−0.369913
$889$	−12080.8	−0.455768
$890$	−15567.2	−0.586309
$891$	−10008.5	−0.376315
$892$	−20489.8	−0.769112
$893$	−4001.82	−0.149962
$894$	−68696.3	−2.56997
$895$	11582.5	0.432581
$896$	28322.1	1.05600
$897$	0	0
$898$	−52912.6	−1.96628
$899$	−10316.0	−0.382712
$900$	697.175	0.0258213
$901$	21325.7	0.788528
$902$	−8938.82	−0.329967
$903$	5467.79	0.201502
$904$	−3840.53	−0.141299
$905$	16927.3	0.621748
$906$	−38675.5	−1.41822
$907$	−40841.7	−1.49518	−0.747589	−	0.664162i	$-0.768789\pi$
$907$	−40841.7	−1.49518	−0.747589	+	0.664162i	$0.768789\pi$
$908$	10085.8	0.368623
$909$	14263.5	0.520451
$910$	0	0
$911$	14440.5	0.525178	0.262589	−	0.964908i	$-0.415424\pi$
$911$	14440.5	0.525178	0.262589	+	0.964908i	$0.415424\pi$
$912$	27467.4	0.997299
$913$	−9738.14	−0.352996
$914$	−17148.7	−0.620600
$915$	9600.62	0.346871
$916$	18236.6	0.657812
$917$	8355.94	0.300913
$918$	34764.6	1.24989
$919$	−29649.2	−1.06424	−0.532119	−	0.846669i	$-0.678604\pi$
$919$	−29649.2	−1.06424	−0.532119	+	0.846669i	$0.678604\pi$
$920$	−15154.7	−0.543081
$921$	51233.4	1.83300
$922$	−20694.2	−0.739184
$923$	0	0
$924$	−4210.55	−0.149910
$925$	−1647.94	−0.0585771
$926$	5662.88	0.200965
$927$	14198.3	0.503056
$928$	7518.30	0.265949
$929$	−1787.94	−0.0631438	−0.0315719	−	0.999501i	$-0.510051\pi$
$929$	−1787.94	−0.0631438	−0.0315719	+	0.999501i	$0.510051\pi$
$930$	−51898.9	−1.82993
$931$	2439.71	0.0858843
$932$	21752.2	0.764502
$933$	−12322.6	−0.432396
$934$	37248.7	1.30494
$935$	−14528.3	−0.508156
$936$	0	0
$937$	−27934.6	−0.973941	−0.486970	−	0.873418i	$-0.661898\pi$
$937$	−27934.6	−0.973941	−0.486970	+	0.873418i	$0.661898\pi$
$938$	−49047.7	−1.70732
$939$	51136.2	1.77717
$940$	−3057.77	−0.106099
$941$	−38291.7	−1.32654	−0.663269	−	0.748381i	$-0.730831\pi$
$941$	−38291.7	−1.32654	−0.663269	+	0.748381i	$0.730831\pi$
$942$	−37351.5	−1.29191
$943$	20129.1	0.695117
$944$	70448.6	2.42893
$945$	−18885.8	−0.650111
$946$	1885.10	0.0647884
$947$	51840.1	1.77886	0.889428	−	0.457075i	$-0.151103\pi$
$947$	51840.1	1.77886	0.889428	+	0.457075i	$0.151103\pi$
$948$	−21341.4	−0.731155
$949$	0	0
$950$	2986.14	0.101982
$951$	10318.6	0.351845
$952$	−29155.1	−0.992567
$953$	3554.38	0.120816	0.0604081	−	0.998174i	$-0.480760\pi$
$953$	3554.38	0.120816	0.0604081	+	0.998174i	$0.480760\pi$
$954$	−8023.53	−0.272297
$955$	10284.7	0.348487
$956$	−13541.2	−0.458109
$957$	3467.23	0.117116
$958$	−63561.6	−2.14361
$959$	−47166.1	−1.58819
$960$	−9703.67	−0.326234
$961$	12328.1	0.413821
$962$	0	0
$963$	1505.78	0.0503873
$964$	−11655.7	−0.389423
$965$	−43614.5	−1.45492
$966$	30953.3	1.03096
$967$	−33048.9	−1.09905	−0.549524	−	0.835478i	$-0.685191\pi$
$967$	−33048.9	−1.09905	−0.549524	+	0.835478i	$0.685191\pi$
$968$	1835.67	0.0609510
$969$	−38291.5	−1.26945
$970$	69095.1	2.28712
$971$	30139.3	0.996102	0.498051	−	0.867148i	$-0.334049\pi$
$971$	30139.3	0.996102	0.498051	+	0.867148i	$0.334049\pi$
$972$	−11376.8	−0.375421
$973$	20077.3	0.661509
$974$	−720.393	−0.0236991
$975$	0	0
$976$	10286.1	0.337346
$977$	−10717.1	−0.350942	−0.175471	−	0.984485i	$-0.556145\pi$
$977$	−10717.1	−0.350942	−0.175471	+	0.984485i	$0.556145\pi$
$978$	−84816.2	−2.77313
$979$	−4246.24	−0.138621
$980$	1864.17	0.0607641
$981$	−3284.49	−0.106897
$982$	52691.3	1.71227
$983$	8269.67	0.268323	0.134161	−	0.990959i	$-0.457166\pi$
$983$	8269.67	0.268323	0.134161	+	0.990959i	$0.457166\pi$
$984$	22764.0	0.737489
$985$	−14554.3	−0.470802
$986$	−18985.7	−0.613213
$987$	−7897.64	−0.254696
$988$	0	0
$989$	−4245.02	−0.136485
$990$	5466.08	0.175478
$991$	−18259.7	−0.585305	−0.292652	−	0.956219i	$-0.594538\pi$
$991$	−18259.7	−0.585305	−0.292652	+	0.956219i	$0.594538\pi$
$992$	−30696.4	−0.982471
$993$	−12298.7	−0.393037
$994$	43387.1	1.38446
$995$	4541.94	0.144713
$996$	−19611.5	−0.623911
$997$	−6820.44	−0.216655	−0.108328	−	0.994115i	$-0.534550\pi$
$997$	−6820.44	−0.216655	−0.108328	+	0.994115i	$0.534550\pi$
$998$	26285.7	0.833728
$999$	9470.56	0.299935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.13	yes	51
13.12	even	2		1859.4.a.p.1.39	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.39	✓	51	13.12	even	2
1859.4.a.q.1.13	yes	51	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.39599 q^{2} +6.27073 q^{3} +3.53273 q^{4} -11.8750 q^{5} -21.2953 q^{6} -17.2790 q^{7} +15.1708 q^{8} +12.3221 q^{9} +O(q^{10})\)	\(q-3.39599 q^{2} +6.27073 q^{3} +3.53273 q^{4} -11.8750 q^{5} -21.2953 q^{6} -17.2790 q^{7} +15.1708 q^{8} +12.3221 q^{9} +40.3274 q^{10} +11.0000 q^{11} +22.1528 q^{12} +58.6792 q^{14} -74.4650 q^{15} -79.7817 q^{16} +111.221 q^{17} -41.8456 q^{18} -54.9030 q^{19} -41.9512 q^{20} -108.352 q^{21} -37.3559 q^{22} +84.1209 q^{23} +95.1320 q^{24} +16.0158 q^{25} -92.0413 q^{27} -61.0419 q^{28} +50.2658 q^{29} +252.882 q^{30} -205.229 q^{31} +149.571 q^{32} +68.9780 q^{33} -377.706 q^{34} +205.188 q^{35} +43.5305 q^{36} -102.895 q^{37} +186.450 q^{38} -180.153 q^{40} +239.288 q^{41} +367.962 q^{42} -50.4632 q^{43} +38.8600 q^{44} -146.325 q^{45} -285.674 q^{46} +72.8888 q^{47} -500.289 q^{48} -44.4367 q^{49} -54.3893 q^{50} +697.440 q^{51} +191.741 q^{53} +312.571 q^{54} -130.625 q^{55} -262.136 q^{56} -344.282 q^{57} -170.702 q^{58} -883.017 q^{59} -263.064 q^{60} -128.928 q^{61} +696.957 q^{62} -212.913 q^{63} +130.312 q^{64} -234.249 q^{66} -835.862 q^{67} +392.915 q^{68} +527.500 q^{69} -696.816 q^{70} +739.396 q^{71} +186.936 q^{72} -93.7544 q^{73} +349.429 q^{74} +100.431 q^{75} -193.957 q^{76} -190.069 q^{77} -963.372 q^{79} +947.408 q^{80} -909.862 q^{81} -812.620 q^{82} -885.285 q^{83} -382.778 q^{84} -1320.75 q^{85} +171.373 q^{86} +315.203 q^{87} +166.879 q^{88} -386.022 q^{89} +496.917 q^{90} +297.176 q^{92} -1286.94 q^{93} -247.529 q^{94} +651.974 q^{95} +937.920 q^{96} +1713.35 q^{97} +150.907 q^{98} +135.543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 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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Groups

Database

Properties

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