LMFDB - Embedded newform 1573.4.a.p.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, 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("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.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:	$92.8100044390$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41223 q^{2} +3.79234 q^{3} -2.18115 q^{4} +17.1876 q^{5} -9.14801 q^{6} +7.32188 q^{7} +24.5593 q^{8} -12.6181 q^{9} +O(q^{10})$	\(q-2.41223 q^{2} +3.79234 q^{3} -2.18115 q^{4} +17.1876 q^{5} -9.14801 q^{6} +7.32188 q^{7} +24.5593 q^{8} -12.6181 q^{9} -41.4606 q^{10} -8.27166 q^{12} -13.0000 q^{13} -17.6621 q^{14} +65.1815 q^{15} -41.7934 q^{16} +67.3865 q^{17} +30.4378 q^{18} -3.50770 q^{19} -37.4888 q^{20} +27.7671 q^{21} -159.787 q^{23} +93.1372 q^{24} +170.415 q^{25} +31.3590 q^{26} -150.246 q^{27} -15.9701 q^{28} -288.532 q^{29} -157.233 q^{30} -232.343 q^{31} -95.6588 q^{32} -162.552 q^{34} +125.846 q^{35} +27.5220 q^{36} +268.166 q^{37} +8.46138 q^{38} -49.3005 q^{39} +422.116 q^{40} +197.904 q^{41} -66.9806 q^{42} +275.508 q^{43} -216.876 q^{45} +385.443 q^{46} -348.775 q^{47} -158.495 q^{48} -289.390 q^{49} -411.081 q^{50} +255.553 q^{51} +28.3549 q^{52} -424.783 q^{53} +362.427 q^{54} +179.820 q^{56} -13.3024 q^{57} +696.005 q^{58} -413.736 q^{59} -142.170 q^{60} -635.705 q^{61} +560.464 q^{62} -92.3884 q^{63} +565.098 q^{64} -223.439 q^{65} -800.615 q^{67} -146.980 q^{68} -605.967 q^{69} -303.569 q^{70} +64.3922 q^{71} -309.892 q^{72} -1112.91 q^{73} -646.879 q^{74} +646.273 q^{75} +7.65081 q^{76} +118.924 q^{78} +212.281 q^{79} -718.330 q^{80} -229.094 q^{81} -477.389 q^{82} +754.333 q^{83} -60.5641 q^{84} +1158.22 q^{85} -664.587 q^{86} -1094.21 q^{87} -413.348 q^{89} +523.154 q^{90} -95.1845 q^{91} +348.519 q^{92} -881.123 q^{93} +841.325 q^{94} -60.2891 q^{95} -362.771 q^{96} +1021.46 q^{97} +698.075 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) $ 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9 + 18 * q^10 - 262 * q^12 - 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 + 209 * q^17 + 190 * q^18 + 107 * q^19 - 211 * q^20 + 68 * q^21 - 632 * q^23 - 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 + 931 * q^28 + 32 * q^29 + 300 * q^30 - 290 * q^31 - 876 * q^32 - 602 * q^34 - 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 + 377 * q^39 - 1159 * q^40 + 1121 * q^41 + 79 * q^42 - 349 * q^43 - 1024 * q^45 - 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 + 1322 * q^50 - 1414 * q^51 - 1261 * q^52 - 2608 * q^53 - 3131 * q^54 - 1675 * q^56 + 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 + 236 * q^61 - 1396 * q^62 - 1206 * q^63 + 1331 * q^64 + 364 * q^65 - 3213 * q^67 + 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 + 5074 * q^72 - 823 * q^73 - 2550 * q^74 - 3063 * q^75 - 2004 * q^76 + 468 * q^78 + 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 + 3843 * q^83 - 7191 * q^84 - 1582 * q^85 - 3542 * q^86 - 962 * q^87 - 3633 * q^89 + 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 + 6309 * q^94 - 1916 * q^95 + 2150 * q^96 + 1195 * q^97 + 1487 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.41223	−0.852852	−0.426426	−	0.904522i	$-0.640228\pi$
$2$	−2.41223	−0.852852	−0.426426	+	0.904522i	$0.640228\pi$
$3$	3.79234	0.729837	0.364919	−	0.931039i	$-0.381097\pi$
$3$	3.79234	0.729837	0.364919	+	0.931039i	$0.381097\pi$
$4$	−2.18115	−0.272643
$5$	17.1876	1.53731	0.768655	−	0.639664i	$-0.220926\pi$
$5$	17.1876	1.53731	0.768655	+	0.639664i	$0.220926\pi$
$6$	−9.14801	−0.622443
$7$	7.32188	0.395344	0.197672	−	0.980268i	$-0.436662\pi$
$7$	7.32188	0.395344	0.197672	+	0.980268i	$0.436662\pi$
$8$	24.5593	1.08538
$9$	−12.6181	−0.467338
$10$	−41.4606	−1.31110
$11$	0	0
$11$	0	0
$12$	−8.27166	−0.198985
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−17.6621	−0.337170
$15$	65.1815	1.12199
$16$	−41.7934	−0.653022
$17$	67.3865	0.961390	0.480695	−	0.876888i	$-0.340384\pi$
$17$	67.3865	0.961390	0.480695	+	0.876888i	$0.340384\pi$
$18$	30.4378	0.398570
$19$	−3.50770	−0.0423538	−0.0211769	−	0.999776i	$-0.506741\pi$
$19$	−3.50770	−0.0423538	−0.0211769	+	0.999776i	$0.506741\pi$
$20$	−37.4888	−0.419137
$21$	27.7671	0.288537
$22$	0	0
$23$	−159.787	−1.44860	−0.724302	−	0.689483i	$-0.757838\pi$
$23$	−159.787	−1.44860	−0.724302	+	0.689483i	$0.757838\pi$
$24$	93.1372	0.792148
$25$	170.415	1.36332
$26$	31.3590	0.236539
$27$	−150.246	−1.07092
$28$	−15.9701	−0.107788
$29$	−288.532	−1.84755	−0.923776	−	0.382934i	$-0.874914\pi$
$29$	−288.532	−1.84755	−0.923776	+	0.382934i	$0.874914\pi$
$30$	−157.233	−0.956888
$31$	−232.343	−1.34613	−0.673064	−	0.739584i	$-0.735022\pi$
$31$	−232.343	−1.34613	−0.673064	+	0.739584i	$0.735022\pi$
$32$	−95.6588	−0.528445
$33$	0	0
$34$	−162.552	−0.819924
$35$	125.846	0.607767
$36$	27.5220	0.127417
$37$	268.166	1.19152	0.595761	−	0.803162i	$-0.296851\pi$
$37$	268.166	1.19152	0.595761	+	0.803162i	$0.296851\pi$
$38$	8.46138	0.0361215
$39$	−49.3005	−0.202420
$40$	422.116	1.66856
$41$	197.904	0.753838	0.376919	−	0.926246i	$-0.376983\pi$
$41$	197.904	0.753838	0.376919	+	0.926246i	$0.376983\pi$
$42$	−66.9806	−0.246079
$43$	275.508	0.977081	0.488541	−	0.872541i	$-0.337529\pi$
$43$	275.508	0.977081	0.488541	+	0.872541i	$0.337529\pi$
$44$	0	0
$45$	−216.876	−0.718443
$46$	385.443	1.23544
$47$	−348.775	−1.08243	−0.541213	−	0.840886i	$-0.682035\pi$
$47$	−348.775	−1.08243	−0.541213	+	0.840886i	$0.682035\pi$
$48$	−158.495	−0.476600
$49$	−289.390	−0.843703
$50$	−411.081	−1.16271
$51$	255.553	0.701658
$52$	28.3549	0.0756177
$53$	−424.783	−1.10091	−0.550457	−	0.834864i	$-0.685546\pi$
$53$	−424.783	−1.10091	−0.550457	+	0.834864i	$0.685546\pi$
$54$	362.427	0.913334
$55$	0	0
$56$	179.820	0.429098
$57$	−13.3024	−0.0309114
$58$	696.005	1.57569
$59$	−413.736	−0.912947	−0.456474	−	0.889737i	$-0.650888\pi$
$59$	−413.736	−0.912947	−0.456474	+	0.889737i	$0.650888\pi$
$60$	−142.170	−0.305902
$61$	−635.705	−1.33432	−0.667161	−	0.744914i	$-0.732491\pi$
$61$	−635.705	−1.33432	−0.667161	+	0.744914i	$0.732491\pi$
$62$	560.464	1.14805
$63$	−92.3884	−0.184759
$64$	565.098	1.10371
$65$	−223.439	−0.426373
$66$	0	0
$67$	−800.615	−1.45986	−0.729930	−	0.683522i	$-0.760447\pi$
$67$	−800.615	−1.45986	−0.729930	+	0.683522i	$0.760447\pi$
$68$	−146.980	−0.262117
$69$	−605.967	−1.05724
$70$	−303.569	−0.518335
$71$	64.3922	0.107633	0.0538166	−	0.998551i	$-0.482861\pi$
$71$	64.3922	0.107633	0.0538166	+	0.998551i	$0.482861\pi$
$72$	−309.892	−0.507237
$73$	−1112.91	−1.78434	−0.892170	−	0.451699i	$-0.850818\pi$
$73$	−1112.91	−1.78434	−0.892170	+	0.451699i	$0.850818\pi$
$74$	−646.879	−1.01619
$75$	646.273	0.995003
$76$	7.65081	0.0115475
$77$	0	0
$78$	118.924	0.172635
$79$	212.281	0.302322	0.151161	−	0.988509i	$-0.451699\pi$
$79$	212.281	0.302322	0.151161	+	0.988509i	$0.451699\pi$
$80$	−718.330	−1.00390
$81$	−229.094	−0.314258
$82$	−477.389	−0.642912
$83$	754.333	0.997576	0.498788	−	0.866724i	$-0.333779\pi$
$83$	754.333	0.997576	0.498788	+	0.866724i	$0.333779\pi$
$84$	−60.5641	−0.0786677
$85$	1158.22	1.47795
$86$	−664.587	−0.833306
$87$	−1094.21	−1.34841
$88$	0	0
$89$	−413.348	−0.492301	−0.246150	−	0.969232i	$-0.579166\pi$
$89$	−413.348	−0.492301	−0.246150	+	0.969232i	$0.579166\pi$
$90$	523.154	0.612726
$91$	−95.1845	−0.109649
$92$	348.519	0.394952
$93$	−881.123	−0.982454
$94$	841.325	0.923149
$95$	−60.2891	−0.0651109
$96$	−362.771	−0.385679
$97$	1021.46	1.06921	0.534607	−	0.845101i	$-0.320460\pi$
$97$	1021.46	1.06921	0.534607	+	0.845101i	$0.320460\pi$
$98$	698.075	0.719554
$99$	0	0
$100$	−371.701	−0.371701
$101$	1268.59	1.24979	0.624896	−	0.780708i	$-0.285141\pi$
$101$	1268.59	1.24979	0.624896	+	0.780708i	$0.285141\pi$
$102$	−616.453	−0.598411
$103$	−1326.63	−1.26909	−0.634547	−	0.772885i	$-0.718813\pi$
$103$	−1326.63	−1.26909	−0.634547	+	0.772885i	$0.718813\pi$
$104$	−319.270	−0.301029
$105$	477.251	0.443571
$106$	1024.67	0.938917
$107$	1361.08	1.22973	0.614863	−	0.788634i	$-0.289211\pi$
$107$	1361.08	1.22973	0.614863	+	0.788634i	$0.289211\pi$
$108$	327.708	0.291979
$109$	−789.635	−0.693884	−0.346942	−	0.937887i	$-0.612780\pi$
$109$	−789.635	−0.693884	−0.346942	+	0.937887i	$0.612780\pi$
$110$	0	0
$111$	1016.98	0.869616
$112$	−306.006	−0.258169
$113$	1791.64	1.49153	0.745767	−	0.666207i	$-0.232083\pi$
$113$	1791.64	1.49153	0.745767	+	0.666207i	$0.232083\pi$
$114$	32.0885	0.0263628
$115$	−2746.36	−2.22695
$116$	629.330	0.503723
$117$	164.036	0.129616
$118$	998.027	0.778609
$119$	493.396	0.380080
$120$	1600.81	1.21778
$121$	0	0
$122$	1533.47	1.13798
$123$	750.519	0.550179
$124$	506.774	0.367013
$125$	780.581	0.558538
$126$	222.862	0.157572
$127$	−476.833	−0.333166	−0.166583	−	0.986027i	$-0.553273\pi$
$127$	−476.833	−0.333166	−0.166583	+	0.986027i	$0.553273\pi$
$128$	−597.876	−0.412854
$129$	1044.82	0.713110
$130$	538.987	0.363633
$131$	419.974	0.280102	0.140051	−	0.990144i	$-0.455273\pi$
$131$	419.974	0.280102	0.140051	+	0.990144i	$0.455273\pi$
$132$	0	0
$133$	−25.6830	−0.0167443
$134$	1931.27	1.24504
$135$	−2582.37	−1.64633
$136$	1654.96	1.04347
$137$	150.961	0.0941419	0.0470709	−	0.998892i	$-0.485011\pi$
$137$	150.961	0.0941419	0.0470709	+	0.998892i	$0.485011\pi$
$138$	1461.73	0.901673
$139$	−932.707	−0.569145	−0.284573	−	0.958654i	$-0.591852\pi$
$139$	−932.707	−0.569145	−0.284573	+	0.958654i	$0.591852\pi$
$140$	−274.489	−0.165704
$141$	−1322.67	−0.789995
$142$	−155.329	−0.0917951
$143$	0	0
$144$	527.354	0.305182
$145$	−4959.18	−2.84026
$146$	2684.61	1.52178
$147$	−1097.47	−0.615766
$148$	−584.911	−0.324861
$149$	−51.9626	−0.0285701	−0.0142850	−	0.999898i	$-0.504547\pi$
$149$	−51.9626	−0.0285701	−0.0142850	+	0.999898i	$0.504547\pi$
$150$	−1558.96	−0.848590
$151$	−500.078	−0.269508	−0.134754	−	0.990879i	$-0.543024\pi$
$151$	−500.078	−0.269508	−0.134754	+	0.990879i	$0.543024\pi$
$152$	−86.1465	−0.0459698
$153$	−850.291	−0.449294
$154$	0	0
$155$	−3993.42	−2.06942
$156$	107.532	0.0551886
$157$	3151.79	1.60217	0.801084	−	0.598552i	$-0.204257\pi$
$157$	3151.79	1.60217	0.801084	+	0.598552i	$0.204257\pi$
$158$	−512.070	−0.257836
$159$	−1610.92	−0.803488
$160$	−1644.15	−0.812384
$161$	−1169.94	−0.572697
$162$	552.627	0.268015
$163$	264.277	0.126993	0.0634963	−	0.997982i	$-0.479775\pi$
$163$	264.277	0.126993	0.0634963	+	0.997982i	$0.479775\pi$
$164$	−431.657	−0.205529
$165$	0	0
$166$	−1819.62	−0.850785
$167$	1518.04	0.703410	0.351705	−	0.936111i	$-0.385602\pi$
$167$	1518.04	0.703410	0.351705	+	0.936111i	$0.385602\pi$
$168$	681.940	0.313171
$169$	169.000	0.0769231
$170$	−2793.88	−1.26048
$171$	44.2606	0.0197935
$172$	−600.923	−0.266395
$173$	2405.63	1.05721	0.528604	−	0.848868i	$-0.322716\pi$
$173$	2405.63	1.05721	0.528604	+	0.848868i	$0.322716\pi$
$174$	2639.49	1.15000
$175$	1247.76	0.538982
$176$	0	0
$177$	−1569.03	−0.666303
$178$	997.089	0.419860
$179$	−1964.79	−0.820421	−0.410211	−	0.911991i	$-0.634545\pi$
$179$	−1964.79	−0.820421	−0.410211	+	0.911991i	$0.634545\pi$
$180$	473.038	0.195879
$181$	930.401	0.382078	0.191039	−	0.981582i	$-0.438814\pi$
$181$	930.401	0.382078	0.191039	+	0.981582i	$0.438814\pi$
$182$	229.607	0.0935142
$183$	−2410.81	−0.973838
$184$	−3924.25	−1.57228
$185$	4609.15	1.83174
$186$	2125.47	0.837888
$187$	0	0
$188$	760.729	0.295116
$189$	−1100.08	−0.423381
$190$	145.431	0.0555299
$191$	−1619.05	−0.613353	−0.306676	−	0.951814i	$-0.599217\pi$
$191$	−1619.05	−0.613353	−0.306676	+	0.951814i	$0.599217\pi$
$192$	2143.05	0.805527
$193$	899.080	0.335322	0.167661	−	0.985845i	$-0.446379\pi$
$193$	899.080	0.335322	0.167661	+	0.985845i	$0.446379\pi$
$194$	−2464.00	−0.911882
$195$	−847.359	−0.311183
$196$	631.202	0.230030
$197$	3168.65	1.14597	0.572986	−	0.819565i	$-0.305785\pi$
$197$	3168.65	1.14597	0.572986	+	0.819565i	$0.305785\pi$
$198$	0	0
$199$	2859.26	1.01853	0.509265	−	0.860610i	$-0.329917\pi$
$199$	2859.26	1.01853	0.509265	+	0.860610i	$0.329917\pi$
$200$	4185.27	1.47972
$201$	−3036.21	−1.06546
$202$	−3060.12	−1.06589
$203$	−2112.59	−0.730419
$204$	−557.399	−0.191303
$205$	3401.50	1.15888
$206$	3200.13	1.08235
$207$	2016.21	0.676987
$208$	543.314	0.181116
$209$	0	0
$210$	−1151.24	−0.378300
$211$	−1558.77	−0.508579	−0.254290	−	0.967128i	$-0.581842\pi$
$211$	−1558.77	−0.508579	−0.254290	+	0.967128i	$0.581842\pi$
$212$	926.514	0.300157
$213$	244.198	0.0785547
$214$	−3283.24	−1.04877
$215$	4735.33	1.50208
$216$	−3689.92	−1.16235
$217$	−1701.19	−0.532184
$218$	1904.78	0.591780
$219$	−4220.56	−1.30228
$220$	0	0
$221$	−876.025	−0.266642
$222$	−2453.19	−0.741654
$223$	1459.53	0.438284	0.219142	−	0.975693i	$-0.429674\pi$
$223$	1459.53	0.438284	0.219142	+	0.975693i	$0.429674\pi$
$224$	−700.403	−0.208918
$225$	−2150.32	−0.637132
$226$	−4321.85	−1.27206
$227$	−5993.79	−1.75252	−0.876259	−	0.481840i	$-0.839968\pi$
$227$	−5993.79	−1.75252	−0.876259	+	0.481840i	$0.839968\pi$
$228$	29.0145	0.00842778
$229$	−2411.87	−0.695987	−0.347994	−	0.937497i	$-0.613137\pi$
$229$	−2411.87	−0.695987	−0.347994	+	0.937497i	$0.613137\pi$
$230$	6624.86	1.89926
$231$	0	0
$232$	−7086.13	−2.00529
$233$	952.481	0.267807	0.133904	−	0.990994i	$-0.457249\pi$
$233$	952.481	0.267807	0.133904	+	0.990994i	$0.457249\pi$
$234$	−395.691	−0.110543
$235$	−5994.62	−1.66402
$236$	902.420	0.248909
$237$	805.043	0.220646
$238$	−1190.19	−0.324152
$239$	−5704.62	−1.54394	−0.771969	−	0.635661i	$-0.780728\pi$
$239$	−5704.62	−1.54394	−0.771969	+	0.635661i	$0.780728\pi$
$240$	−2724.16	−0.732681
$241$	−1297.21	−0.346726	−0.173363	−	0.984858i	$-0.555463\pi$
$241$	−1297.21	−0.346726	−0.173363	+	0.984858i	$0.555463\pi$
$242$	0	0
$243$	3187.83	0.841561
$244$	1386.57	0.363794
$245$	−4973.93	−1.29703
$246$	−1810.42	−0.469221
$247$	45.6001	0.0117468
$248$	−5706.16	−1.46106
$249$	2860.69	0.728068
$250$	−1882.94	−0.476350
$251$	−1191.05	−0.299515	−0.149757	−	0.988723i	$-0.547849\pi$
$251$	−1191.05	−0.299515	−0.149757	+	0.988723i	$0.547849\pi$
$252$	201.513	0.0503734
$253$	0	0
$254$	1150.23	0.284141
$255$	4392.35	1.07867
$256$	−3078.57	−0.751604
$257$	−5263.44	−1.27753	−0.638763	−	0.769403i	$-0.720554\pi$
$257$	−5263.44	−1.27753	−0.638763	+	0.769403i	$0.720554\pi$
$258$	−2520.34	−0.608178
$259$	1963.48	0.471061
$260$	487.354	0.116248
$261$	3640.73	0.863430
$262$	−1013.07	−0.238885
$263$	4140.66	0.970814	0.485407	−	0.874288i	$-0.338672\pi$
$263$	4140.66	0.970814	0.485407	+	0.874288i	$0.338672\pi$
$264$	0	0
$265$	−7301.02	−1.69245
$266$	61.9532	0.0142804
$267$	−1567.56	−0.359299
$268$	1746.26	0.398021
$269$	4658.74	1.05594	0.527971	−	0.849263i	$-0.322953\pi$
$269$	4658.74	1.05594	0.527971	+	0.849263i	$0.322953\pi$
$270$	6229.26	1.40408
$271$	−2395.17	−0.536887	−0.268443	−	0.963295i	$-0.586509\pi$
$271$	−2395.17	−0.536887	−0.268443	+	0.963295i	$0.586509\pi$
$272$	−2816.31	−0.627809
$273$	−360.972	−0.0800258
$274$	−364.152	−0.0802891
$275$	0	0
$276$	1321.70	0.288251
$277$	5109.89	1.10839	0.554194	−	0.832388i	$-0.313027\pi$
$277$	5109.89	1.10839	0.554194	+	0.832388i	$0.313027\pi$
$278$	2249.90	0.485397
$279$	2931.73	0.629097
$280$	3090.68	0.659656
$281$	−5909.01	−1.25446	−0.627228	−	0.778836i	$-0.715811\pi$
$281$	−5909.01	−1.25446	−0.627228	+	0.778836i	$0.715811\pi$
$282$	3190.59	0.673748
$283$	−9392.52	−1.97289	−0.986444	−	0.164101i	$-0.947528\pi$
$283$	−9392.52	−1.97289	−0.986444	+	0.164101i	$0.947528\pi$
$284$	−140.449	−0.0293455
$285$	−228.637	−0.0475203
$286$	0	0
$287$	1449.03	0.298026
$288$	1207.03	0.246962
$289$	−372.054	−0.0757286
$290$	11962.7	2.42232
$291$	3873.74	0.780352
$292$	2427.43	0.486489
$293$	−847.820	−0.169045	−0.0845225	−	0.996422i	$-0.526936\pi$
$293$	−847.820	−0.169045	−0.0845225	+	0.996422i	$0.526936\pi$
$294$	2647.34	0.525157
$295$	−7111.15	−1.40348
$296$	6585.97	1.29325
$297$	0	0
$298$	125.346	0.0243661
$299$	2077.23	0.401770
$300$	−1409.62	−0.271281
$301$	2017.23	0.386284
$302$	1206.30	0.229851
$303$	4810.91	0.912145
$304$	146.599	0.0276579
$305$	−10926.3	−2.05127
$306$	2051.10	0.383181
$307$	2493.93	0.463635	0.231817	−	0.972759i	$-0.425533\pi$
$307$	2493.93	0.463635	0.231817	+	0.972759i	$0.425533\pi$
$308$	0	0
$309$	−5031.03	−0.926231
$310$	9633.05	1.76491
$311$	−7011.78	−1.27846	−0.639231	−	0.769015i	$-0.720747\pi$
$311$	−7011.78	−1.27846	−0.639231	+	0.769015i	$0.720747\pi$
$312$	−1210.78	−0.219702
$313$	−7860.53	−1.41950	−0.709750	−	0.704454i	$-0.751192\pi$
$313$	−7860.53	−1.41950	−0.709750	+	0.704454i	$0.751192\pi$
$314$	−7602.84	−1.36641
$315$	−1587.94	−0.284032
$316$	−463.016	−0.0824262
$317$	−3652.42	−0.647130	−0.323565	−	0.946206i	$-0.604882\pi$
$317$	−3652.42	−0.647130	−0.323565	+	0.946206i	$0.604882\pi$
$318$	3885.92	0.685256
$319$	0	0
$320$	9712.71	1.69674
$321$	5161.69	0.897500
$322$	2822.17	0.488426
$323$	−236.372	−0.0407185
$324$	499.687	0.0856803
$325$	−2215.40	−0.378117
$326$	−637.497	−0.108306
$327$	−2994.57	−0.506422
$328$	4860.37	0.818198
$329$	−2553.69	−0.427931
$330$	0	0
$331$	−213.852	−0.0355117	−0.0177559	−	0.999842i	$-0.505652\pi$
$331$	−213.852	−0.0355117	−0.0177559	+	0.999842i	$0.505652\pi$
$332$	−1645.31	−0.271983
$333$	−3383.76	−0.556843
$334$	−3661.86	−0.599905
$335$	−13760.7	−2.24426
$336$	−1160.48	−0.188421
$337$	4652.23	0.751997	0.375998	−	0.926620i	$-0.377300\pi$
$337$	4652.23	0.751997	0.375998	+	0.926620i	$0.377300\pi$
$338$	−407.667	−0.0656040
$339$	6794.51	1.08858
$340$	−2526.24	−0.402955
$341$	0	0
$342$	−106.767	−0.0168809
$343$	−4630.29	−0.728898
$344$	6766.26	1.06050
$345$	−10415.2	−1.62531
$346$	−5802.94	−0.901642
$347$	3363.27	0.520317	0.260159	−	0.965566i	$-0.416225\pi$
$347$	3363.27	0.520317	0.260159	+	0.965566i	$0.416225\pi$
$348$	2386.64	0.367636
$349$	2254.23	0.345749	0.172875	−	0.984944i	$-0.444694\pi$
$349$	2254.23	0.345749	0.172875	+	0.984944i	$0.444694\pi$
$350$	−3009.88	−0.459672
$351$	1953.19	0.297019
$352$	0	0
$353$	−8865.61	−1.33674	−0.668370	−	0.743829i	$-0.733008\pi$
$353$	−8865.61	−1.33674	−0.668370	+	0.743829i	$0.733008\pi$
$354$	3784.86	0.568258
$355$	1106.75	0.165465
$356$	901.572	0.134223
$357$	1871.13	0.277397
$358$	4739.53	0.699698
$359$	4790.73	0.704304	0.352152	−	0.935943i	$-0.385450\pi$
$359$	4790.73	0.704304	0.352152	+	0.935943i	$0.385450\pi$
$360$	−5326.31	−0.779781
$361$	−6846.70	−0.998206
$362$	−2244.34	−0.325856
$363$	0	0
$364$	207.611	0.0298950
$365$	−19128.4	−2.74308
$366$	5815.43	0.830539
$367$	5769.57	0.820624	0.410312	−	0.911945i	$-0.365420\pi$
$367$	5769.57	0.820624	0.410312	+	0.911945i	$0.365420\pi$
$368$	6678.04	0.945970
$369$	−2497.17	−0.352297
$370$	−11118.3	−1.56220
$371$	−3110.21	−0.435240
$372$	1921.86	0.267860
$373$	−4383.86	−0.608546	−0.304273	−	0.952585i	$-0.598413\pi$
$373$	−4383.86	−0.608546	−0.304273	+	0.952585i	$0.598413\pi$
$374$	0	0
$375$	2960.23	0.407642
$376$	−8565.65	−1.17484
$377$	3750.91	0.512418
$378$	2653.65	0.361082
$379$	−6589.59	−0.893099	−0.446550	−	0.894759i	$-0.647347\pi$
$379$	−6589.59	−0.893099	−0.446550	+	0.894759i	$0.647347\pi$
$380$	131.499	0.0177521
$381$	−1808.32	−0.243157
$382$	3905.52	0.523099
$383$	1626.04	0.216937	0.108468	−	0.994100i	$-0.465405\pi$
$383$	1626.04	0.216937	0.108468	+	0.994100i	$0.465405\pi$
$384$	−2267.35	−0.301316
$385$	0	0
$386$	−2168.79	−0.285980
$387$	−3476.39	−0.456627
$388$	−2227.96	−0.291514
$389$	−7659.06	−0.998277	−0.499138	−	0.866522i	$-0.666350\pi$
$389$	−7659.06	−0.998277	−0.499138	+	0.866522i	$0.666350\pi$
$390$	2044.03	0.265393
$391$	−10767.5	−1.39267
$392$	−7107.21	−0.915735
$393$	1592.69	0.204428
$394$	−7643.50	−0.977345
$395$	3648.61	0.464763
$396$	0	0
$397$	5168.89	0.653448	0.326724	−	0.945120i	$-0.394055\pi$
$397$	5168.89	0.653448	0.326724	+	0.945120i	$0.394055\pi$
$398$	−6897.19	−0.868655
$399$	−97.3987	−0.0122206
$400$	−7122.23	−0.890279
$401$	11185.7	1.39298	0.696492	−	0.717564i	$-0.254743\pi$
$401$	11185.7	1.39298	0.696492	+	0.717564i	$0.254743\pi$
$402$	7324.03	0.908680
$403$	3020.45	0.373349
$404$	−2766.97	−0.340748
$405$	−3937.58	−0.483111
$406$	5096.06	0.622939
$407$	0	0
$408$	6276.19	0.761564
$409$	−6520.38	−0.788293	−0.394147	−	0.919048i	$-0.628960\pi$
$409$	−6520.38	−0.788293	−0.394147	+	0.919048i	$0.628960\pi$
$410$	−8205.20	−0.988355
$411$	572.495	0.0687082
$412$	2893.57	0.346010
$413$	−3029.33	−0.360929
$414$	−4863.56	−0.577370
$415$	12965.2	1.53358
$416$	1243.56	0.146564
$417$	−3537.15	−0.415383
$418$	0	0
$419$	9241.58	1.07752	0.538760	−	0.842459i	$-0.318893\pi$
$419$	9241.58	1.07752	0.538760	+	0.842459i	$0.318893\pi$
$420$	−1040.96	−0.120937
$421$	−8616.46	−0.997483	−0.498742	−	0.866751i	$-0.666204\pi$
$421$	−8616.46	−0.997483	−0.498742	+	0.866751i	$0.666204\pi$
$422$	3760.12	0.433743
$423$	4400.88	0.505859
$424$	−10432.4	−1.19491
$425$	11483.7	1.31068
$426$	−589.061	−0.0669955
$427$	−4654.55	−0.527517
$428$	−2968.72	−0.335277
$429$	0	0
$430$	−11422.7	−1.28105
$431$	−5021.88	−0.561242	−0.280621	−	0.959819i	$-0.590540\pi$
$431$	−5021.88	−0.561242	−0.280621	+	0.959819i	$0.590540\pi$
$432$	6279.28	0.699333
$433$	−1472.99	−0.163481	−0.0817406	−	0.996654i	$-0.526048\pi$
$433$	−1472.99	−0.163481	−0.0817406	+	0.996654i	$0.526048\pi$
$434$	4103.65	0.453874
$435$	−18806.9	−2.07293
$436$	1722.31	0.189183
$437$	560.485	0.0613538
$438$	10181.0	1.11065
$439$	6468.42	0.703237	0.351618	−	0.936143i	$-0.385631\pi$
$439$	6468.42	0.703237	0.351618	+	0.936143i	$0.385631\pi$
$440$	0	0
$441$	3651.56	0.394294
$442$	2113.17	0.227406
$443$	16487.6	1.76828	0.884140	−	0.467221i	$-0.154745\pi$
$443$	16487.6	1.76828	0.884140	+	0.467221i	$0.154745\pi$
$444$	−2218.18	−0.237095
$445$	−7104.47	−0.756819
$446$	−3520.72	−0.373791
$447$	−197.060	−0.0208515
$448$	4137.58	0.436345
$449$	10308.6	1.08350	0.541752	−	0.840538i	$-0.317761\pi$
$449$	10308.6	1.08350	0.541752	+	0.840538i	$0.317761\pi$
$450$	5187.06	0.543379
$451$	0	0
$452$	−3907.83	−0.406657
$453$	−1896.47	−0.196697
$454$	14458.4	1.49464
$455$	−1636.00	−0.168564
$456$	−326.697	−0.0335505
$457$	3391.30	0.347130	0.173565	−	0.984822i	$-0.444471\pi$
$457$	3391.30	0.347130	0.173565	+	0.984822i	$0.444471\pi$
$458$	5817.99	0.593574
$459$	−10124.5	−1.02957
$460$	5990.22	0.607164
$461$	−5298.64	−0.535320	−0.267660	−	0.963513i	$-0.586250\pi$
$461$	−5298.64	−0.535320	−0.267660	+	0.963513i	$0.586250\pi$
$462$	0	0
$463$	−1103.69	−0.110783	−0.0553917	−	0.998465i	$-0.517641\pi$
$463$	−1103.69	−0.110783	−0.0553917	+	0.998465i	$0.517641\pi$
$464$	12058.7	1.20649
$465$	−15144.4	−1.51034
$466$	−2297.60	−0.228400
$467$	−11490.2	−1.13855	−0.569275	−	0.822147i	$-0.692776\pi$
$467$	−11490.2	−1.13855	−0.569275	+	0.822147i	$0.692776\pi$
$468$	−357.786	−0.0353390
$469$	−5862.01	−0.577148
$470$	14460.4	1.41917
$471$	11952.7	1.16932
$472$	−10161.1	−0.990891
$473$	0	0
$474$	−1941.95	−0.188178
$475$	−597.765	−0.0577418
$476$	−1076.17	−0.103626
$477$	5359.96	0.514499
$478$	13760.8	1.31675
$479$	526.960	0.0502661	0.0251330	−	0.999684i	$-0.491999\pi$
$479$	526.960	0.0502661	0.0251330	+	0.999684i	$0.491999\pi$
$480$	−6235.18	−0.592908
$481$	−3486.16	−0.330469
$482$	3129.18	0.295706
$483$	−4436.82	−0.417976
$484$	0	0
$485$	17556.5	1.64371
$486$	−7689.77	−0.717727
$487$	18624.5	1.73297	0.866485	−	0.499204i	$-0.166374\pi$
$487$	18624.5	1.73297	0.866485	+	0.499204i	$0.166374\pi$
$488$	−15612.4	−1.44824
$489$	1002.23	0.0926839
$490$	11998.3	1.10618
$491$	−20552.5	−1.88904	−0.944522	−	0.328447i	$-0.893475\pi$
$491$	−20552.5	−1.88904	−0.944522	+	0.328447i	$0.893475\pi$
$492$	−1636.99	−0.150003
$493$	−19443.1	−1.77622
$494$	−109.998	−0.0100183
$495$	0	0
$496$	9710.39	0.879051
$497$	471.472	0.0425522
$498$	−6900.64	−0.620934
$499$	−1527.85	−0.137066	−0.0685330	−	0.997649i	$-0.521832\pi$
$499$	−1527.85	−0.137066	−0.0685330	+	0.997649i	$0.521832\pi$
$500$	−1702.56	−0.152282
$501$	5756.93	0.513375
$502$	2873.08	0.255442
$503$	11618.0	1.02986	0.514932	−	0.857231i	$-0.327817\pi$
$503$	11618.0	1.02986	0.514932	+	0.857231i	$0.327817\pi$
$504$	−2268.99	−0.200534
$505$	21804.0	1.92132
$506$	0	0
$507$	640.906	0.0561413
$508$	1040.04	0.0908356
$509$	−4020.69	−0.350126	−0.175063	−	0.984557i	$-0.556013\pi$
$509$	−4020.69	−0.350126	−0.175063	+	0.984557i	$0.556013\pi$
$510$	−10595.4	−0.919943
$511$	−8148.63	−0.705429
$512$	12209.2	1.05386
$513$	527.016	0.0453574
$514$	12696.6	1.08954
$515$	−22801.6	−1.95099
$516$	−2278.91	−0.194425
$517$	0	0
$518$	−4736.37	−0.401746
$519$	9123.00	0.771590
$520$	−5487.51	−0.462775
$521$	19146.4	1.61002	0.805010	−	0.593261i	$-0.202160\pi$
$521$	19146.4	1.61002	0.805010	+	0.593261i	$0.202160\pi$
$522$	−8782.27	−0.736378
$523$	4957.97	0.414526	0.207263	−	0.978285i	$-0.433544\pi$
$523$	4957.97	0.414526	0.207263	+	0.978285i	$0.433544\pi$
$524$	−916.025	−0.0763678
$525$	4731.94	0.393369
$526$	−9988.22	−0.827960
$527$	−15656.8	−1.29415
$528$	0	0
$529$	13364.9	1.09845
$530$	17611.7	1.44341
$531$	5220.57	0.426655
$532$	56.0183	0.00456523
$533$	−2572.75	−0.209077
$534$	3781.31	0.306429
$535$	23393.8	1.89047
$536$	−19662.5	−1.58450
$537$	−7451.17	−0.598774
$538$	−11237.9	−0.900562
$539$	0	0
$540$	5632.53	0.448862
$541$	−15356.9	−1.22041	−0.610207	−	0.792242i	$-0.708914\pi$
$541$	−15356.9	−1.22041	−0.610207	+	0.792242i	$0.708914\pi$
$542$	5777.70	0.457885
$543$	3528.40	0.278855
$544$	−6446.12	−0.508042
$545$	−13572.0	−1.06671
$546$	870.748	0.0682501
$547$	4707.47	0.367965	0.183983	−	0.982929i	$-0.441101\pi$
$547$	4707.47	0.367965	0.183983	+	0.982929i	$0.441101\pi$
$548$	−329.267	−0.0256672
$549$	8021.40	0.623579
$550$	0	0
$551$	1012.08	0.0782508
$552$	−14882.1	−1.14751
$553$	1554.30	0.119521
$554$	−12326.2	−0.945291
$555$	17479.5	1.33687
$556$	2034.37	0.155174
$557$	9516.46	0.723924	0.361962	−	0.932193i	$-0.382107\pi$
$557$	9516.46	0.723924	0.361962	+	0.932193i	$0.382107\pi$
$558$	−7072.00	−0.536526
$559$	−3581.60	−0.270994
$560$	−5259.53	−0.396885
$561$	0	0
$562$	14253.9	1.06987
$563$	5369.31	0.401935	0.200967	−	0.979598i	$-0.435591\pi$
$563$	5369.31	0.401935	0.200967	+	0.979598i	$0.435591\pi$
$564$	2884.95	0.215387
$565$	30794.1	2.29295
$566$	22656.9	1.68258
$567$	−1677.40	−0.124240
$568$	1581.43	0.116822
$569$	−3349.04	−0.246747	−0.123373	−	0.992360i	$-0.539371\pi$
$569$	−3349.04	−0.246747	−0.123373	+	0.992360i	$0.539371\pi$
$570$	551.525	0.0405278
$571$	−17355.1	−1.27196	−0.635980	−	0.771705i	$-0.719404\pi$
$571$	−17355.1	−1.27196	−0.635980	+	0.771705i	$0.719404\pi$
$572$	0	0
$573$	−6140.00	−0.447648
$574$	−3495.39	−0.254172
$575$	−27230.1	−1.97491
$576$	−7130.48	−0.515804
$577$	4814.32	0.347353	0.173676	−	0.984803i	$-0.444435\pi$
$577$	4814.32	0.347353	0.173676	+	0.984803i	$0.444435\pi$
$578$	897.481	0.0645853
$579$	3409.62	0.244731
$580$	10816.7	0.774378
$581$	5523.14	0.394386
$582$	−9344.35	−0.665525
$583$	0	0
$584$	−27332.4	−1.93668
$585$	2819.39	0.199260
$586$	2045.14	0.144170
$587$	20307.1	1.42788	0.713939	−	0.700208i	$-0.246909\pi$
$587$	20307.1	1.42788	0.713939	+	0.700208i	$0.246909\pi$
$588$	2393.74	0.167884
$589$	814.988	0.0570136
$590$	17153.7	1.19696
$591$	12016.6	0.836374
$592$	−11207.6	−0.778090
$593$	−19625.9	−1.35909	−0.679544	−	0.733634i	$-0.737822\pi$
$593$	−19625.9	−1.35909	−0.679544	+	0.733634i	$0.737822\pi$
$594$	0	0
$595$	8480.32	0.584301
$596$	113.338	0.00778945
$597$	10843.3	0.743361
$598$	−5010.76	−0.342651
$599$	−21257.2	−1.44999	−0.724997	−	0.688752i	$-0.758159\pi$
$599$	−21257.2	−1.44999	−0.724997	+	0.688752i	$0.758159\pi$
$600$	15872.0	1.07995
$601$	462.647	0.0314006	0.0157003	−	0.999877i	$-0.495002\pi$
$601$	462.647	0.0314006	0.0157003	+	0.999877i	$0.495002\pi$
$602$	−4866.03	−0.329443
$603$	10102.3	0.682248
$604$	1090.74	0.0734797
$605$	0	0
$606$	−11605.0	−0.777924
$607$	16117.3	1.07773	0.538865	−	0.842392i	$-0.318853\pi$
$607$	16117.3	1.07773	0.538865	+	0.842392i	$0.318853\pi$
$608$	335.542	0.0223817
$609$	−8011.69	−0.533087
$610$	26356.7	1.74943
$611$	4534.07	0.300211
$612$	1854.61	0.122497
$613$	18882.4	1.24413	0.622065	−	0.782965i	$-0.286294\pi$
$613$	18882.4	1.24413	0.622065	+	0.782965i	$0.286294\pi$
$614$	−6015.92	−0.395412
$615$	12899.7	0.845796
$616$	0	0
$617$	−23670.8	−1.54449	−0.772244	−	0.635326i	$-0.780866\pi$
$617$	−23670.8	−1.54449	−0.772244	+	0.635326i	$0.780866\pi$
$618$	12136.0	0.789938
$619$	−2119.32	−0.137613	−0.0688066	−	0.997630i	$-0.521919\pi$
$619$	−2119.32	−0.137613	−0.0688066	+	0.997630i	$0.521919\pi$
$620$	8710.25	0.564213
$621$	24007.3	1.55134
$622$	16914.0	1.09034
$623$	−3026.48	−0.194628
$624$	2060.44	0.132185
$625$	−7885.56	−0.504676
$626$	18961.4	1.21062
$627$	0	0
$628$	−6874.52	−0.436820
$629$	18070.8	1.14552
$630$	3830.47	0.242238
$631$	8297.58	0.523489	0.261745	−	0.965137i	$-0.415702\pi$
$631$	8297.58	0.523489	0.261745	+	0.965137i	$0.415702\pi$
$632$	5213.46	0.328134
$633$	−5911.40	−0.371180
$634$	8810.48	0.551906
$635$	−8195.64	−0.512180
$636$	3513.66	0.219066
$637$	3762.07	0.234001
$638$	0	0
$639$	−812.509	−0.0503010
$640$	−10276.1	−0.634685
$641$	−9899.19	−0.609976	−0.304988	−	0.952356i	$-0.598652\pi$
$641$	−9899.19	−0.609976	−0.304988	+	0.952356i	$0.598652\pi$
$642$	−12451.2	−0.765435
$643$	−9767.83	−0.599076	−0.299538	−	0.954084i	$-0.596833\pi$
$643$	−9767.83	−0.599076	−0.299538	+	0.954084i	$0.596833\pi$
$644$	2551.81	0.156142
$645$	17958.0	1.09627
$646$	570.183	0.0347269
$647$	20185.3	1.22653	0.613266	−	0.789877i	$-0.289855\pi$
$647$	20185.3	1.22653	0.613266	+	0.789877i	$0.289855\pi$
$648$	−5626.38	−0.341088
$649$	0	0
$650$	5344.05	0.322478
$651$	−6451.48	−0.388408
$652$	−576.427	−0.0346237
$653$	15946.2	0.955623	0.477811	−	0.878462i	$-0.341430\pi$
$653$	15946.2	0.955623	0.477811	+	0.878462i	$0.341430\pi$
$654$	7223.59	0.431903
$655$	7218.36	0.430603
$656$	−8271.07	−0.492273
$657$	14042.9	0.833890
$658$	6160.08	0.364962
$659$	−690.376	−0.0408092	−0.0204046	−	0.999792i	$-0.506495\pi$
$659$	−690.376	−0.0408092	−0.0204046	+	0.999792i	$0.506495\pi$
$660$	0	0
$661$	11684.5	0.687557	0.343779	−	0.939051i	$-0.388293\pi$
$661$	11684.5	0.687557	0.343779	+	0.939051i	$0.388293\pi$
$662$	515.861	0.0302862
$663$	−3322.19	−0.194605
$664$	18525.9	1.08275
$665$	−441.430	−0.0257412
$666$	8162.40	0.474905
$667$	46103.6	2.67637
$668$	−3311.07	−0.191780
$669$	5535.04	0.319876
$670$	33193.9	1.91402
$671$	0	0
$672$	−2656.17	−0.152476
$673$	3996.15	0.228886	0.114443	−	0.993430i	$-0.463492\pi$
$673$	3996.15	0.228886	0.114443	+	0.993430i	$0.463492\pi$
$674$	−11222.2	−0.641342
$675$	−25604.1	−1.46001
$676$	−368.614	−0.0209726
$677$	−12432.8	−0.705810	−0.352905	−	0.935659i	$-0.614806\pi$
$677$	−12432.8	−0.705810	−0.352905	+	0.935659i	$0.614806\pi$
$678$	−16389.9	−0.928394
$679$	7479.03	0.422708
$680$	28444.9	1.60414
$681$	−22730.5	−1.27905
$682$	0	0
$683$	−833.000	−0.0466674	−0.0233337	−	0.999728i	$-0.507428\pi$
$683$	−833.000	−0.0466674	−0.0233337	+	0.999728i	$0.507428\pi$
$684$	−96.5389	−0.00539657
$685$	2594.66	0.144725
$686$	11169.3	0.621642
$687$	−9146.65	−0.507957
$688$	−11514.4	−0.638056
$689$	5522.18	0.305339
$690$	25123.7	1.38615
$691$	33.4649	0.00184235	0.000921176	−	1.00000i	$-0.499707\pi$
$691$	33.4649	0.00184235	0.000921176		1.00000i	$0.499707\pi$
$692$	−5247.04	−0.288241
$693$	0	0
$694$	−8112.99	−0.443754
$695$	−16031.0	−0.874953
$696$	−26873.0	−1.46353
$697$	13336.0	0.724733
$698$	−5437.73	−0.294873
$699$	3612.14	0.195456
$700$	−2721.55	−0.146950
$701$	−20217.9	−1.08933	−0.544664	−	0.838655i	$-0.683343\pi$
$701$	−20217.9	−1.08933	−0.544664	+	0.838655i	$0.683343\pi$
$702$	−4711.55	−0.253313
$703$	−940.647	−0.0504654
$704$	0	0
$705$	−22733.7	−1.21447
$706$	21385.9	1.14004
$707$	9288.44	0.494098
$708$	3422.29	0.181663
$709$	−5869.94	−0.310931	−0.155466	−	0.987841i	$-0.549688\pi$
$709$	−5869.94	−0.310931	−0.155466	+	0.987841i	$0.549688\pi$
$710$	−2669.74	−0.141118
$711$	−2678.59	−0.141287
$712$	−10151.5	−0.534331
$713$	37125.3	1.95001
$714$	−4513.59	−0.236578
$715$	0	0
$716$	4285.50	0.223683
$717$	−21633.9	−1.12682
$718$	−11556.3	−0.600667
$719$	−25778.8	−1.33712	−0.668558	−	0.743660i	$-0.733088\pi$
$719$	−25778.8	−1.33712	−0.668558	+	0.743660i	$0.733088\pi$
$720$	9063.98	0.469159
$721$	−9713.42	−0.501729
$722$	16515.8	0.851322
$723$	−4919.48	−0.253053
$724$	−2029.34	−0.104171
$725$	−49170.2	−2.51881
$726$	0	0
$727$	−9347.82	−0.476879	−0.238440	−	0.971157i	$-0.576636\pi$
$727$	−9347.82	−0.476879	−0.238440	+	0.971157i	$0.576636\pi$
$728$	−2337.66	−0.119010
$729$	18274.9	0.928460
$730$	46142.1	2.33944
$731$	18565.5	0.939357
$732$	5258.34	0.265510
$733$	−6190.76	−0.311952	−0.155976	−	0.987761i	$-0.549852\pi$
$733$	−6190.76	−0.311952	−0.155976	+	0.987761i	$0.549852\pi$
$734$	−13917.5	−0.699871
$735$	−18862.9	−0.946623
$736$	15285.0	0.765508
$737$	0	0
$738$	6023.75	0.300457
$739$	−23547.8	−1.17215	−0.586075	−	0.810257i	$-0.699328\pi$
$739$	−23547.8	−1.17215	−0.586075	+	0.810257i	$0.699328\pi$
$740$	−10053.2	−0.499411
$741$	172.931	0.00857327
$742$	7502.54	0.371195
$743$	−18481.6	−0.912550	−0.456275	−	0.889839i	$-0.650817\pi$
$743$	−18481.6	−0.912550	−0.456275	+	0.889839i	$0.650817\pi$
$744$	−21639.7	−1.06633
$745$	−893.115	−0.0439211
$746$	10574.9	0.519000
$747$	−9518.27	−0.466205
$748$	0	0
$749$	9965.68	0.486166
$750$	−7140.76	−0.347658
$751$	20978.6	1.01933	0.509666	−	0.860372i	$-0.329769\pi$
$751$	20978.6	1.01933	0.509666	+	0.860372i	$0.329769\pi$
$752$	14576.5	0.706848
$753$	−4516.86	−0.218597
$754$	−9048.06	−0.437017
$755$	−8595.16	−0.414318
$756$	2399.44	0.115432
$757$	−17940.0	−0.861349	−0.430675	−	0.902507i	$-0.641724\pi$
$757$	−17940.0	−0.861349	−0.430675	+	0.902507i	$0.641724\pi$
$758$	15895.6	0.761681
$759$	0	0
$760$	−1480.66	−0.0706698
$761$	26239.9	1.24993	0.624965	−	0.780653i	$-0.285113\pi$
$761$	26239.9	1.24993	0.624965	+	0.780653i	$0.285113\pi$
$762$	4362.07	0.207377
$763$	−5781.61	−0.274323
$764$	3531.39	0.167227
$765$	−14614.5	−0.690704
$766$	−3922.38	−0.185015
$767$	5378.57	0.253206
$768$	−11675.0	−0.548549
$769$	−36438.0	−1.70870	−0.854348	−	0.519702i	$-0.826043\pi$
$769$	−36438.0	−1.70870	−0.854348	+	0.519702i	$0.826043\pi$
$770$	0	0
$771$	−19960.8	−0.932386
$772$	−1961.03	−0.0914235
$773$	38075.8	1.77166	0.885829	−	0.464012i	$-0.153590\pi$
$773$	38075.8	1.77166	0.885829	+	0.464012i	$0.153590\pi$
$774$	8385.84	0.389435
$775$	−39594.7	−1.83521
$776$	25086.4	1.16050
$777$	7446.20	0.343798
$778$	18475.4	0.851382
$779$	−694.187	−0.0319279
$780$	1848.22	0.0848420
$781$	0	0
$782$	25973.7	1.18774
$783$	43350.6	1.97857
$784$	12094.6	0.550957
$785$	54171.9	2.46303
$786$	−3841.93	−0.174347
$787$	9247.26	0.418843	0.209421	−	0.977825i	$-0.432842\pi$
$787$	9247.26	0.418843	0.209421	+	0.977825i	$0.432842\pi$
$788$	−6911.28	−0.312442
$789$	15702.8	0.708536
$790$	−8801.29	−0.396374
$791$	13118.2	0.589669
$792$	0	0
$793$	8264.16	0.370074
$794$	−12468.5	−0.557295
$795$	−27688.0	−1.23521
$796$	−6236.47	−0.277696
$797$	13848.5	0.615483	0.307741	−	0.951470i	$-0.400427\pi$
$797$	13848.5	0.615483	0.307741	+	0.951470i	$0.400427\pi$
$798$	234.948	0.0104224
$799$	−23502.7	−1.04063
$800$	−16301.7	−0.720441
$801$	5215.67	0.230071
$802$	−26982.5	−1.18801
$803$	0	0
$804$	6622.42	0.290491
$805$	−20108.5	−0.880413
$806$	−7286.03	−0.318411
$807$	17667.5	0.770665
$808$	31155.5	1.35650
$809$	−16782.1	−0.729329	−0.364664	−	0.931139i	$-0.618816\pi$
$809$	−16782.1	−0.729329	−0.364664	+	0.931139i	$0.618816\pi$
$810$	9498.35	0.412022
$811$	−8878.44	−0.384419	−0.192210	−	0.981354i	$-0.561565\pi$
$811$	−8878.44	−0.384419	−0.192210	+	0.981354i	$0.561565\pi$
$812$	4607.88	0.199144
$813$	−9083.32	−0.391840
$814$	0	0
$815$	4542.30	0.195227
$816$	−10680.4	−0.458198
$817$	−966.398	−0.0413831
$818$	15728.7	0.672298
$819$	1201.05	0.0512430
$820$	−7419.17	−0.315962
$821$	34533.0	1.46798	0.733989	−	0.679161i	$-0.237656\pi$
$821$	34533.0	1.46798	0.733989	+	0.679161i	$0.237656\pi$
$822$	−1380.99	−0.0585979
$823$	29893.0	1.26611	0.633054	−	0.774108i	$-0.281801\pi$
$823$	29893.0	1.26611	0.633054	+	0.774108i	$0.281801\pi$
$824$	−32581.0	−1.37744
$825$	0	0
$826$	7307.44	0.307819
$827$	−2966.67	−0.124741	−0.0623707	−	0.998053i	$-0.519866\pi$
$827$	−2966.67	−0.124741	−0.0623707	+	0.998053i	$0.519866\pi$
$828$	−4397.65	−0.184576
$829$	−10997.5	−0.460747	−0.230374	−	0.973102i	$-0.573995\pi$
$829$	−10997.5	−0.460747	−0.230374	+	0.973102i	$0.573995\pi$
$830$	−31275.1	−1.30792
$831$	19378.5	0.808943
$832$	−7346.28	−0.306113
$833$	−19501.0	−0.811128
$834$	8532.41	0.354261
$835$	26091.5	1.08136
$836$	0	0
$837$	34908.5	1.44159
$838$	−22292.8	−0.918965
$839$	1378.37	0.0567182	0.0283591	−	0.999598i	$-0.490972\pi$
$839$	1378.37	0.0567182	0.0283591	+	0.999598i	$0.490972\pi$
$840$	11720.9	0.481441
$841$	58861.5	2.41345
$842$	20784.9	0.850706
$843$	−22409.0	−0.915549
$844$	3399.91	0.138661
$845$	2904.71	0.118255
$846$	−10615.9	−0.431422
$847$	0	0
$848$	17753.1	0.718921
$849$	−35619.7	−1.43989
$850$	−27701.3	−1.11782
$851$	−42849.5	−1.72604
$852$	−532.631	−0.0214174
$853$	23744.4	0.953098	0.476549	−	0.879148i	$-0.341888\pi$
$853$	23744.4	0.953098	0.476549	+	0.879148i	$0.341888\pi$
$854$	11227.9	0.449894
$855$	760.735	0.0304288
$856$	33427.2	1.33472
$857$	24816.0	0.989148	0.494574	−	0.869136i	$-0.335324\pi$
$857$	24816.0	0.989148	0.494574	+	0.869136i	$0.335324\pi$
$858$	0	0
$859$	−6772.20	−0.268992	−0.134496	−	0.990914i	$-0.542942\pi$
$859$	−6772.20	−0.268992	−0.134496	+	0.990914i	$0.542942\pi$
$860$	−10328.4	−0.409531
$861$	5495.21	0.217510
$862$	12113.9	0.478656
$863$	27671.8	1.09149	0.545747	−	0.837950i	$-0.316246\pi$
$863$	27671.8	1.09149	0.545747	+	0.837950i	$0.316246\pi$
$864$	14372.3	0.565921
$865$	41347.2	1.62526
$866$	3553.19	0.139425
$867$	−1410.96	−0.0552695
$868$	3710.54	0.145097
$869$	0	0
$870$	45366.6	1.76790
$871$	10408.0	0.404892
$872$	−19392.9	−0.753125
$873$	−12888.9	−0.499684
$874$	−1352.02	−0.0523257
$875$	5715.32	0.220815
$876$	9205.66	0.355058
$877$	7529.58	0.289915	0.144958	−	0.989438i	$-0.453695\pi$
$877$	7529.58	0.289915	0.144958	+	0.989438i	$0.453695\pi$
$878$	−15603.3	−0.599757
$879$	−3215.23	−0.123375
$880$	0	0
$881$	−1114.92	−0.0426363	−0.0213181	−	0.999773i	$-0.506786\pi$
$881$	−1114.92	−0.0426363	−0.0213181	+	0.999773i	$0.506786\pi$
$882$	−8808.40	−0.336275
$883$	−1062.97	−0.0405116	−0.0202558	−	0.999795i	$-0.506448\pi$
$883$	−1062.97	−0.0405116	−0.0202558	+	0.999795i	$0.506448\pi$
$884$	1910.74	0.0726981
$885$	−26967.9	−1.02431
$886$	−39771.8	−1.50808
$887$	11875.4	0.449533	0.224767	−	0.974413i	$-0.427838\pi$
$887$	11875.4	0.449533	0.224767	+	0.974413i	$0.427838\pi$
$888$	24976.3	0.943861
$889$	−3491.32	−0.131715
$890$	17137.6	0.645454
$891$	0	0
$892$	−3183.45	−0.119495
$893$	1223.40	0.0458448
$894$	475.354	0.0177832
$895$	−33770.1	−1.26124
$896$	−4377.58	−0.163220
$897$	7877.58	0.293227
$898$	−24866.7	−0.924068
$899$	67038.2	2.48704
$900$	4690.16	0.173710
$901$	−28624.7	−1.05841
$902$	0	0
$903$	7650.04	0.281924
$904$	44001.3	1.61888
$905$	15991.4	0.587373
$906$	4574.71	0.167754
$907$	−21831.9	−0.799247	−0.399623	−	0.916679i	$-0.630859\pi$
$907$	−21831.9	−0.799247	−0.399623	+	0.916679i	$0.630859\pi$
$908$	13073.3	0.477813
$909$	−16007.2	−0.584075
$910$	3946.40	0.143760
$911$	−52045.3	−1.89280	−0.946398	−	0.323003i	$-0.895307\pi$
$911$	−52045.3	−1.89280	−0.946398	+	0.323003i	$0.895307\pi$
$912$	555.953	0.0201858
$913$	0	0
$914$	−8180.59	−0.296050
$915$	−41436.2	−1.49709
$916$	5260.65	0.189756
$917$	3075.00	0.110737
$918$	24422.7	0.878071
$919$	25539.6	0.916730	0.458365	−	0.888764i	$-0.348435\pi$
$919$	25539.6	0.916730	0.458365	+	0.888764i	$0.348435\pi$
$920$	−67448.6	−2.41708
$921$	9457.83	0.338378
$922$	12781.5	0.456549
$923$	−837.099	−0.0298521
$924$	0	0
$925$	45699.6	1.62443
$926$	2662.35	0.0944818
$927$	16739.6	0.593095
$928$	27600.6	0.976330
$929$	14609.0	0.515937	0.257968	−	0.966153i	$-0.416947\pi$
$929$	14609.0	0.515937	0.257968	+	0.966153i	$0.416947\pi$
$930$	36531.9	1.28809
$931$	1015.09	0.0357340
$932$	−2077.50	−0.0730159
$933$	−26591.1	−0.933069
$934$	27717.0	0.971015
$935$	0	0
$936$	4028.59	0.140682
$937$	43047.3	1.50085	0.750425	−	0.660956i	$-0.229849\pi$
$937$	43047.3	1.50085	0.750425	+	0.660956i	$0.229849\pi$
$938$	14140.5	0.492222
$939$	−29809.9	−1.03600
$940$	13075.1	0.453685
$941$	−4555.54	−0.157818	−0.0789089	−	0.996882i	$-0.525144\pi$
$941$	−4555.54	−0.157818	−0.0789089	+	0.996882i	$0.525144\pi$
$942$	−28832.6	−0.997258
$943$	−31622.4	−1.09201
$944$	17291.5	0.596175
$945$	−18907.8	−0.650868
$946$	0	0
$947$	−27967.0	−0.959669	−0.479835	−	0.877359i	$-0.659303\pi$
$947$	−27967.0	−0.959669	−0.479835	+	0.877359i	$0.659303\pi$
$948$	−1755.92	−0.0601577
$949$	14467.9	0.494887
$950$	1441.95	0.0492452
$951$	−13851.2	−0.472300
$952$	12117.5	0.412530
$953$	−9826.71	−0.334017	−0.167009	−	0.985955i	$-0.553411\pi$
$953$	−9826.71	−0.334017	−0.167009	+	0.985955i	$0.553411\pi$
$954$	−12929.5	−0.438791
$955$	−27827.7	−0.942913
$956$	12442.6	0.420944
$957$	0	0
$958$	−1271.15	−0.0428695
$959$	1105.32	0.0372185
$960$	36834.0	1.23834
$961$	24192.1	0.812061
$962$	8409.43	0.281841
$963$	−17174.3	−0.574698
$964$	2829.41	0.0945325
$965$	15453.1	0.515494
$966$	10702.6	0.356472
$967$	50921.8	1.69342	0.846708	−	0.532057i	$-0.178581\pi$
$967$	50921.8	1.69342	0.846708	+	0.532057i	$0.178581\pi$
$968$	0	0
$969$	−896.403	−0.0297179
$970$	−42350.4	−1.40184
$971$	14834.5	0.490279	0.245139	−	0.969488i	$-0.421166\pi$
$971$	14834.5	0.490279	0.245139	+	0.969488i	$0.421166\pi$
$972$	−6953.12	−0.229446
$973$	−6829.17	−0.225008
$974$	−44926.5	−1.47797
$975$	−8401.55	−0.275964
$976$	26568.3	0.871342
$977$	1308.29	0.0428412	0.0214206	−	0.999771i	$-0.493181\pi$
$977$	1308.29	0.0428412	0.0214206	+	0.999771i	$0.493181\pi$
$978$	−2417.61	−0.0790456
$979$	0	0
$980$	10848.9	0.353627
$981$	9963.71	0.324278
$982$	49577.3	1.61108
$983$	−16458.0	−0.534007	−0.267004	−	0.963696i	$-0.586034\pi$
$983$	−16458.0	−0.534007	−0.267004	+	0.963696i	$0.586034\pi$
$984$	18432.2	0.597151
$985$	54461.6	1.76172
$986$	46901.3	1.51485
$987$	−9684.46	−0.312320
$988$	−99.4606	−0.00320269
$989$	−44022.5	−1.41540
$990$	0	0
$991$	−41552.6	−1.33195	−0.665975	−	0.745974i	$-0.731984\pi$
$991$	−41552.6	−1.33195	−0.665975	+	0.745974i	$0.731984\pi$
$992$	22225.6	0.711355
$993$	−811.001	−0.0259178
$994$	−1137.30	−0.0362907
$995$	49143.9	1.56580
$996$	−6239.59	−0.198503
$997$	41010.1	1.30271	0.651355	−	0.758773i	$-0.274201\pi$
$997$	41010.1	1.30271	0.651355	+	0.758773i	$0.274201\pi$
$998$	3685.52	0.116897
$999$	−40290.8	−1.27602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.p.1.10		34
11.2	odd	10		143.4.h.a.92.6	yes	68
11.6	odd	10		143.4.h.a.14.6	✓	68
11.10	odd	2		1573.4.a.o.1.25		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.6	✓	68	11.6	odd	10
143.4.h.a.92.6	yes	68	11.2	odd	10
1573.4.a.o.1.25		34	11.10	odd	2
1573.4.a.p.1.10		34	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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41223 q^{2} +3.79234 q^{3} -2.18115 q^{4} +17.1876 q^{5} -9.14801 q^{6} +7.32188 q^{7} +24.5593 q^{8} -12.6181 q^{9} +O(q^{10})\)	\(q-2.41223 q^{2} +3.79234 q^{3} -2.18115 q^{4} +17.1876 q^{5} -9.14801 q^{6} +7.32188 q^{7} +24.5593 q^{8} -12.6181 q^{9} -41.4606 q^{10} -8.27166 q^{12} -13.0000 q^{13} -17.6621 q^{14} +65.1815 q^{15} -41.7934 q^{16} +67.3865 q^{17} +30.4378 q^{18} -3.50770 q^{19} -37.4888 q^{20} +27.7671 q^{21} -159.787 q^{23} +93.1372 q^{24} +170.415 q^{25} +31.3590 q^{26} -150.246 q^{27} -15.9701 q^{28} -288.532 q^{29} -157.233 q^{30} -232.343 q^{31} -95.6588 q^{32} -162.552 q^{34} +125.846 q^{35} +27.5220 q^{36} +268.166 q^{37} +8.46138 q^{38} -49.3005 q^{39} +422.116 q^{40} +197.904 q^{41} -66.9806 q^{42} +275.508 q^{43} -216.876 q^{45} +385.443 q^{46} -348.775 q^{47} -158.495 q^{48} -289.390 q^{49} -411.081 q^{50} +255.553 q^{51} +28.3549 q^{52} -424.783 q^{53} +362.427 q^{54} +179.820 q^{56} -13.3024 q^{57} +696.005 q^{58} -413.736 q^{59} -142.170 q^{60} -635.705 q^{61} +560.464 q^{62} -92.3884 q^{63} +565.098 q^{64} -223.439 q^{65} -800.615 q^{67} -146.980 q^{68} -605.967 q^{69} -303.569 q^{70} +64.3922 q^{71} -309.892 q^{72} -1112.91 q^{73} -646.879 q^{74} +646.273 q^{75} +7.65081 q^{76} +118.924 q^{78} +212.281 q^{79} -718.330 q^{80} -229.094 q^{81} -477.389 q^{82} +754.333 q^{83} -60.5641 q^{84} +1158.22 q^{85} -664.587 q^{86} -1094.21 q^{87} -413.348 q^{89} +523.154 q^{90} -95.1845 q^{91} +348.519 q^{92} -881.123 q^{93} +841.325 q^{94} -60.2891 q^{95} -362.771 q^{96} +1021.46 q^{97} +698.075 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9 + 18 * q^10 - 262 * q^12 - 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 + 209 * q^17 + 190 * q^18 + 107 * q^19 - 211 * q^20 + 68 * q^21 - 632 * q^23 - 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 + 931 * q^28 + 32 * q^29 + 300 * q^30 - 290 * q^31 - 876 * q^32 - 602 * q^34 - 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 + 377 * q^39 - 1159 * q^40 + 1121 * q^41 + 79 * q^42 - 349 * q^43 - 1024 * q^45 - 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 + 1322 * q^50 - 1414 * q^51 - 1261 * q^52 - 2608 * q^53 - 3131 * q^54 - 1675 * q^56 + 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 + 236 * q^61 - 1396 * q^62 - 1206 * q^63 + 1331 * q^64 + 364 * q^65 - 3213 * q^67 + 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 + 5074 * q^72 - 823 * q^73 - 2550 * q^74 - 3063 * q^75 - 2004 * q^76 + 468 * q^78 + 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 + 3843 * q^83 - 7191 * q^84 - 1582 * q^85 - 3542 * q^86 - 962 * q^87 - 3633 * q^89 + 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 + 6309 * q^94 - 1916 * q^95 + 2150 * q^96 + 1195 * q^97 + 1487 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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