LMFDB - Embedded newform 1573.4.a.o.1.25

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			1.25
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	$-0.359772\pi$
$2$	2.41223	0.852852	0.426426	+	0.904522i	$0.359772\pi$
$3$	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	$-0.563338\pi$
$7$	−7.32188	−0.395344	−0.197672	+	0.980268i	$0.563338\pi$
$8$	−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	$-0.659616\pi$
$17$	−67.3865	−0.961390	−0.480695	+	0.876888i	$0.659616\pi$
$18$	−30.4378	−0.398570
$19$	3.50770	0.0423538	0.0211769	−	0.999776i	$-0.493259\pi$
$19$	3.50770	0.0423538	0.0211769	+	0.999776i	$0.493259\pi$
$20$	−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	$-0.125086\pi$
$29$	288.532	1.84755	0.923776	+	0.382934i	$0.125086\pi$
$30$	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	$-0.623017\pi$
$41$	−197.904	−0.753838	−0.376919	+	0.926246i	$0.623017\pi$
$42$	−66.9806	−0.246079
$43$	−275.508	−0.977081	−0.488541	−	0.872541i	$-0.662471\pi$
$43$	−275.508	−0.977081	−0.488541	+	0.872541i	$0.662471\pi$
$44$	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	$-0.267509\pi$
$61$	635.705	1.33432	0.667161	+	0.744914i	$0.267509\pi$
$62$	−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	$-0.149182\pi$
$73$	1112.91	1.78434	0.892170	+	0.451699i	$0.149182\pi$
$74$	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	$-0.548301\pi$
$79$	−212.281	−0.302322	−0.151161	+	0.988509i	$0.548301\pi$
$80$	−718.330	−1.00390
$81$	−229.094	−0.314258
$82$	−477.389	−0.642912
$83$	−754.333	−0.997576	−0.498788	−	0.866724i	$-0.666221\pi$
$83$	−754.333	−0.997576	−0.498788	+	0.866724i	$0.666221\pi$
$84$	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	$-0.714859\pi$
$101$	−1268.59	−1.24979	−0.624896	+	0.780708i	$0.714859\pi$
$102$	−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	$-0.710789\pi$
$107$	−1361.08	−1.22973	−0.614863	+	0.788634i	$0.710789\pi$
$108$	327.708	0.291979
$109$	789.635	0.693884	0.346942	−	0.937887i	$-0.387220\pi$
$109$	789.635	0.693884	0.346942	+	0.937887i	$0.387220\pi$
$110$	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	$-0.446727\pi$
$127$	476.833	0.333166	0.166583	+	0.986027i	$0.446727\pi$
$128$	597.876	0.412854
$129$	−1044.82	−0.713110
$130$	538.987	0.363633
$131$	−419.974	−0.280102	−0.140051	−	0.990144i	$-0.544727\pi$
$131$	−419.974	−0.280102	−0.140051	+	0.990144i	$0.544727\pi$
$132$	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	$-0.408148\pi$
$139$	932.707	0.569145	0.284573	+	0.958654i	$0.408148\pi$
$140$	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	$-0.495453\pi$
$149$	51.9626	0.0285701	0.0142850	+	0.999898i	$0.495453\pi$
$150$	1558.96	0.848590
$151$	500.078	0.269508	0.134754	−	0.990879i	$-0.456976\pi$
$151$	500.078	0.269508	0.134754	+	0.990879i	$0.456976\pi$
$152$	−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	$-0.614398\pi$
$167$	−1518.04	−0.703410	−0.351705	+	0.936111i	$0.614398\pi$
$168$	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	$-0.677284\pi$
$173$	−2405.63	−1.05721	−0.528604	+	0.848868i	$0.677284\pi$
$174$	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	$-0.553621\pi$
$193$	−899.080	−0.335322	−0.167661	+	0.985845i	$0.553621\pi$
$194$	2464.00	0.911882
$195$	847.359	0.311183
$196$	631.202	0.230030
$197$	−3168.65	−1.14597	−0.572986	−	0.819565i	$-0.694215\pi$
$197$	−3168.65	−1.14597	−0.572986	+	0.819565i	$0.694215\pi$
$198$	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	$-0.418158\pi$
$211$	1558.77	0.508579	0.254290	+	0.967128i	$0.418158\pi$
$212$	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	$-0.160032\pi$
$227$	5993.79	1.75252	0.876259	+	0.481840i	$0.160032\pi$
$228$	−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	$-0.542751\pi$
$233$	−952.481	−0.267807	−0.133904	+	0.990994i	$0.542751\pi$
$234$	−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	$-0.219272\pi$
$239$	5704.62	1.54394	0.771969	+	0.635661i	$0.219272\pi$
$240$	−2724.16	−0.732681
$241$	1297.21	0.346726	0.173363	−	0.984858i	$-0.444537\pi$
$241$	1297.21	0.346726	0.173363	+	0.984858i	$0.444537\pi$
$242$	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	$-0.661328\pi$
$263$	−4140.66	−0.970814	−0.485407	+	0.874288i	$0.661328\pi$
$264$	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	$-0.413491\pi$
$271$	2395.17	0.536887	0.268443	+	0.963295i	$0.413491\pi$
$272$	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	$-0.686973\pi$
$277$	−5109.89	−1.10839	−0.554194	+	0.832388i	$0.686973\pi$
$278$	2249.90	0.485397
$279$	2931.73	0.629097
$280$	3090.68	0.659656
$281$	5909.01	1.25446	0.627228	−	0.778836i	$-0.284189\pi$
$281$	5909.01	1.25446	0.627228	+	0.778836i	$0.284189\pi$
$282$	−3190.59	−0.673748
$283$	9392.52	1.97289	0.986444	−	0.164101i	$-0.0524722\pi$
$283$	9392.52	1.97289	0.986444	+	0.164101i	$0.0524722\pi$
$284$	−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	$-0.473064\pi$
$293$	847.820	0.169045	0.0845225	+	0.996422i	$0.473064\pi$
$294$	−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	$-0.574467\pi$
$307$	−2493.93	−0.463635	−0.231817	+	0.972759i	$0.574467\pi$
$308$	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	$-0.622700\pi$
$337$	−4652.23	−0.751997	−0.375998	+	0.926620i	$0.622700\pi$
$338$	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	$-0.583775\pi$
$347$	−3363.27	−0.520317	−0.260159	+	0.965566i	$0.583775\pi$
$348$	−2386.64	−0.367636
$349$	−2254.23	−0.345749	−0.172875	−	0.984944i	$-0.555306\pi$
$349$	−2254.23	−0.345749	−0.172875	+	0.984944i	$0.555306\pi$
$350$	−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	$-0.614550\pi$
$359$	−4790.73	−0.704304	−0.352152	+	0.935943i	$0.614550\pi$
$360$	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	$-0.401587\pi$
$373$	4383.86	0.608546	0.304273	+	0.952585i	$0.401587\pi$
$374$	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	$-0.371040\pi$
$409$	6520.38	0.788293	0.394147	+	0.919048i	$0.371040\pi$
$410$	−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	$-0.409460\pi$
$431$	5021.88	0.561242	0.280621	+	0.959819i	$0.409460\pi$
$432$	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	$-0.614369\pi$
$439$	−6468.42	−0.703237	−0.351618	+	0.936143i	$0.614369\pi$
$440$	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	$-0.555529\pi$
$457$	−3391.30	−0.347130	−0.173565	+	0.984822i	$0.555529\pi$
$458$	−5817.99	−0.593574
$459$	10124.5	1.02957
$460$	5990.22	0.607164
$461$	5298.64	0.535320	0.267660	−	0.963513i	$-0.413750\pi$
$461$	5298.64	0.535320	0.267660	+	0.963513i	$0.413750\pi$
$462$	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	$-0.508001\pi$
$479$	−526.960	−0.0502661	−0.0251330	+	0.999684i	$0.508001\pi$
$480$	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	$-0.106525\pi$
$491$	20552.5	1.88904	0.944522	+	0.328447i	$0.106525\pi$
$492$	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	$-0.672183\pi$
$503$	−11618.0	−1.02986	−0.514932	+	0.857231i	$0.672183\pi$
$504$	−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	$-0.566456\pi$
$523$	−4957.97	−0.414526	−0.207263	+	0.978285i	$0.566456\pi$
$524$	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	$-0.291086\pi$
$541$	15356.9	1.22041	0.610207	+	0.792242i	$0.291086\pi$
$542$	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	$-0.558899\pi$
$547$	−4707.47	−0.367965	−0.183983	+	0.982929i	$0.558899\pi$
$548$	−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	$-0.617893\pi$
$557$	−9516.46	−0.723924	−0.361962	+	0.932193i	$0.617893\pi$
$558$	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	$-0.564409\pi$
$563$	−5369.31	−0.401935	−0.200967	+	0.979598i	$0.564409\pi$
$564$	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	$-0.460629\pi$
$569$	3349.04	0.246747	0.123373	+	0.992360i	$0.460629\pi$
$570$	551.525	0.0405278
$571$	17355.1	1.27196	0.635980	−	0.771705i	$-0.280596\pi$
$571$	17355.1	1.27196	0.635980	+	0.771705i	$0.280596\pi$
$572$	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	$-0.262178\pi$
$593$	19625.9	1.35909	0.679544	+	0.733634i	$0.262178\pi$
$594$	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	$-0.504998\pi$
$601$	−462.647	−0.0314006	−0.0157003	+	0.999877i	$0.504998\pi$
$602$	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	$-0.681147\pi$
$607$	−16117.3	−1.07773	−0.538865	+	0.842392i	$0.681147\pi$
$608$	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	$-0.713706\pi$
$613$	−18882.4	−1.24413	−0.622065	+	0.782965i	$0.713706\pi$
$614$	−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	$-0.493505\pi$
$659$	690.376	0.0408092	0.0204046	+	0.999792i	$0.493505\pi$
$660$	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	$-0.536508\pi$
$673$	−3996.15	−0.228886	−0.114443	+	0.993430i	$0.536508\pi$
$674$	−11222.2	−0.641342
$675$	−25604.1	−1.46001
$676$	−368.614	−0.0209726
$677$	12432.8	0.705810	0.352905	−	0.935659i	$-0.385194\pi$
$677$	12432.8	0.705810	0.352905	+	0.935659i	$0.385194\pi$
$678$	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	$-0.316657\pi$
$701$	20217.9	1.08933	0.544664	+	0.838655i	$0.316657\pi$
$702$	−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	$-0.450148\pi$
$733$	6190.76	0.311952	0.155976	+	0.987761i	$0.450148\pi$
$734$	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	$-0.300672\pi$
$739$	23547.8	1.17215	0.586075	+	0.810257i	$0.300672\pi$
$740$	−10053.2	−0.499411
$741$	172.931	0.00857327
$742$	7502.54	0.371195
$743$	18481.6	0.912550	0.456275	−	0.889839i	$-0.349183\pi$
$743$	18481.6	0.912550	0.456275	+	0.889839i	$0.349183\pi$
$744$	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	$-0.714887\pi$
$761$	−26239.9	−1.24993	−0.624965	+	0.780653i	$0.714887\pi$
$762$	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	$-0.173957\pi$
$769$	36438.0	1.70870	0.854348	+	0.519702i	$0.173957\pi$
$770$	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	$-0.567158\pi$
$787$	−9247.26	−0.418843	−0.209421	+	0.977825i	$0.567158\pi$
$788$	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	$-0.381184\pi$
$809$	16782.1	0.729329	0.364664	+	0.931139i	$0.381184\pi$
$810$	−9498.35	−0.412022
$811$	8878.44	0.384419	0.192210	−	0.981354i	$-0.438435\pi$
$811$	8878.44	0.384419	0.192210	+	0.981354i	$0.438435\pi$
$812$	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	$-0.762344\pi$
$821$	−34533.0	−1.46798	−0.733989	+	0.679161i	$0.762344\pi$
$822$	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	$-0.480134\pi$
$827$	2966.67	0.124741	0.0623707	+	0.998053i	$0.480134\pi$
$828$	−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	$-0.658112\pi$
$853$	−23744.4	−0.953098	−0.476549	+	0.879148i	$0.658112\pi$
$854$	−11227.9	−0.449894
$855$	−760.735	−0.0304288
$856$	33427.2	1.33472
$857$	−24816.0	−0.989148	−0.494574	−	0.869136i	$-0.664676\pi$
$857$	−24816.0	−0.989148	−0.494574	+	0.869136i	$0.664676\pi$
$858$	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	$-0.546305\pi$
$877$	−7529.58	−0.289915	−0.144958	+	0.989438i	$0.546305\pi$
$878$	−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	$-0.572162\pi$
$887$	−11875.4	−0.449533	−0.224767	+	0.974413i	$0.572162\pi$
$888$	−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	$-0.651565\pi$
$919$	−25539.6	−0.916730	−0.458365	+	0.888764i	$0.651565\pi$
$920$	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	$-0.770151\pi$
$937$	−43047.3	−1.50085	−0.750425	+	0.660956i	$0.770151\pi$
$938$	14140.5	0.492222
$939$	−29809.9	−1.03600
$940$	13075.1	0.453685
$941$	4555.54	0.157818	0.0789089	−	0.996882i	$-0.474856\pi$
$941$	4555.54	0.157818	0.0789089	+	0.996882i	$0.474856\pi$
$942$	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	$-0.446589\pi$
$953$	9826.71	0.334017	0.167009	+	0.985955i	$0.446589\pi$
$954$	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	$-0.821419\pi$
$967$	−50921.8	−1.69342	−0.846708	+	0.532057i	$0.821419\pi$
$968$	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	$-0.725799\pi$
$997$	−41010.1	−1.30271	−0.651355	+	0.758773i	$0.725799\pi$
$998$	−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.o.1.25		34
11.5	even	5		143.4.h.a.14.6	✓	68
11.9	even	5		143.4.h.a.92.6	yes	68
11.10	odd	2		1573.4.a.p.1.10		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.6	✓	68	11.5	even	5
143.4.h.a.92.6	yes	68	11.9	even	5
1573.4.a.o.1.25		34	1.1	even	1	trivial
1573.4.a.p.1.10		34	11.10	odd	2

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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