LMFDB - Embedded newform 1573.4.a.o.1.3

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			1.3
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)

$f(q)$	$=$	$q-4.49806 q^{2} -9.16217 q^{3} +12.2325 q^{4} +14.5583 q^{5} +41.2120 q^{6} -13.8178 q^{7} -19.0381 q^{8} +56.9454 q^{9} +O(q^{10})$	\(q-4.49806 q^{2} -9.16217 q^{3} +12.2325 q^{4} +14.5583 q^{5} +41.2120 q^{6} -13.8178 q^{7} -19.0381 q^{8} +56.9454 q^{9} -65.4843 q^{10} -112.076 q^{12} +13.0000 q^{13} +62.1532 q^{14} -133.386 q^{15} -12.2256 q^{16} +131.580 q^{17} -256.144 q^{18} +73.2249 q^{19} +178.085 q^{20} +126.601 q^{21} -15.4086 q^{23} +174.431 q^{24} +86.9455 q^{25} -58.4747 q^{26} -274.365 q^{27} -169.026 q^{28} +71.0891 q^{29} +599.978 q^{30} -100.932 q^{31} +207.296 q^{32} -591.856 q^{34} -201.164 q^{35} +696.586 q^{36} -84.6526 q^{37} -329.370 q^{38} -119.108 q^{39} -277.164 q^{40} -152.777 q^{41} -569.459 q^{42} -267.027 q^{43} +829.031 q^{45} +69.3089 q^{46} -402.318 q^{47} +112.013 q^{48} -152.069 q^{49} -391.086 q^{50} -1205.56 q^{51} +159.023 q^{52} -1.78587 q^{53} +1234.11 q^{54} +263.065 q^{56} -670.899 q^{57} -319.763 q^{58} +872.703 q^{59} -1631.65 q^{60} -352.533 q^{61} +453.999 q^{62} -786.860 q^{63} -834.626 q^{64} +189.259 q^{65} -753.649 q^{67} +1609.56 q^{68} +141.177 q^{69} +904.849 q^{70} -1126.55 q^{71} -1084.13 q^{72} -1053.18 q^{73} +380.772 q^{74} -796.610 q^{75} +895.725 q^{76} +535.756 q^{78} +1253.01 q^{79} -177.984 q^{80} +976.254 q^{81} +687.200 q^{82} +145.857 q^{83} +1548.65 q^{84} +1915.59 q^{85} +1201.10 q^{86} -651.330 q^{87} +911.594 q^{89} -3729.03 q^{90} -179.631 q^{91} -188.486 q^{92} +924.759 q^{93} +1809.65 q^{94} +1066.03 q^{95} -1899.29 q^{96} -723.825 q^{97} +684.013 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.49806	−1.59030	−0.795152	−	0.606411i	$-0.792609\pi$
$2$	−4.49806	−1.59030	−0.795152	+	0.606411i	$0.792609\pi$
$3$	−9.16217	−1.76326	−0.881631	−	0.471940i	$-0.843554\pi$
$3$	−9.16217	−1.76326	−0.881631	+	0.471940i	$0.843554\pi$
$4$	12.2325	1.52907
$5$	14.5583	1.30214	0.651069	−	0.759018i	$-0.274321\pi$
$5$	14.5583	1.30214	0.651069	+	0.759018i	$0.274321\pi$
$6$	41.2120	2.80412
$7$	−13.8178	−0.746091	−0.373045	−	0.927813i	$-0.621686\pi$
$7$	−13.8178	−0.746091	−0.373045	+	0.927813i	$0.621686\pi$
$8$	−19.0381	−0.841374
$9$	56.9454	2.10909
$10$	−65.4843	−2.07080
$11$	0	0
$11$	0	0
$12$	−112.076	−2.69614
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	62.1532	1.18651
$15$	−133.386	−2.29601
$16$	−12.2256	−0.191025
$17$	131.580	1.87723	0.938615	−	0.344967i	$-0.112110\pi$
$17$	131.580	1.87723	0.938615	+	0.344967i	$0.112110\pi$
$18$	−256.144	−3.35409
$19$	73.2249	0.884155	0.442077	−	0.896977i	$-0.354242\pi$
$19$	73.2249	0.884155	0.442077	+	0.896977i	$0.354242\pi$
$20$	178.085	1.99105
$21$	126.601	1.31555
$22$	0	0
$23$	−15.4086	−0.139692	−0.0698461	−	0.997558i	$-0.522251\pi$
$23$	−15.4086	−0.139692	−0.0698461	+	0.997558i	$0.522251\pi$
$24$	174.431	1.48356
$25$	86.9455	0.695564
$26$	−58.4747	−0.441071
$27$	−274.365	−1.95561
$28$	−169.026	−1.14082
$29$	71.0891	0.455204	0.227602	−	0.973754i	$-0.426912\pi$
$29$	71.0891	0.455204	0.227602	+	0.973754i	$0.426912\pi$
$30$	599.978	3.65135
$31$	−100.932	−0.584773	−0.292387	−	0.956300i	$-0.594449\pi$
$31$	−100.932	−0.584773	−0.292387	+	0.956300i	$0.594449\pi$
$32$	207.296	1.14516
$33$	0	0
$34$	−591.856	−2.98536
$35$	−201.164	−0.971513
$36$	696.586	3.22494
$37$	−84.6526	−0.376130	−0.188065	−	0.982157i	$-0.560222\pi$
$37$	−84.6526	−0.376130	−0.188065	+	0.982157i	$0.560222\pi$
$38$	−329.370	−1.40607
$39$	−119.108	−0.489041
$40$	−277.164	−1.09559
$41$	−152.777	−0.581946	−0.290973	−	0.956731i	$-0.593979\pi$
$41$	−152.777	−0.581946	−0.290973	+	0.956731i	$0.593979\pi$
$42$	−569.459	−2.09213
$43$	−267.027	−0.947005	−0.473503	−	0.880792i	$-0.657011\pi$
$43$	−267.027	−0.947005	−0.473503	+	0.880792i	$0.657011\pi$
$44$	0	0
$45$	829.031	2.74633
$46$	69.3089	0.222153
$47$	−402.318	−1.24860	−0.624299	−	0.781185i	$-0.714615\pi$
$47$	−402.318	−1.24860	−0.624299	+	0.781185i	$0.714615\pi$
$48$	112.013	0.336827
$49$	−152.069	−0.443348
$50$	−391.086	−1.10616
$51$	−1205.56	−3.31005
$52$	159.023	0.424086
$53$	−1.78587	−0.00462845	−0.00231423	−	0.999997i	$-0.500737\pi$
$53$	−1.78587	−0.00462845	−0.00231423	+	0.999997i	$0.500737\pi$
$54$	1234.11	3.11002
$55$	0	0
$56$	263.065	0.627742
$57$	−670.899	−1.55900
$58$	−319.763	−0.723912
$59$	872.703	1.92570	0.962849	−	0.270039i	$-0.0870367\pi$
$59$	872.703	1.92570	0.962849	+	0.270039i	$0.0870367\pi$
$60$	−1631.65	−3.51075
$61$	−352.533	−0.739955	−0.369978	−	0.929041i	$-0.620635\pi$
$61$	−352.533	−0.739955	−0.369978	+	0.929041i	$0.620635\pi$
$62$	453.999	0.929967
$63$	−786.860	−1.57357
$64$	−834.626	−1.63013
$65$	189.259	0.361148
$66$	0	0
$67$	−753.649	−1.37422	−0.687111	−	0.726552i	$-0.741122\pi$
$67$	−753.649	−1.37422	−0.687111	+	0.726552i	$0.741122\pi$
$68$	1609.56	2.87041
$69$	141.177	0.246314
$70$	904.849	1.54500
$71$	−1126.55	−1.88305	−0.941525	−	0.336943i	$-0.890607\pi$
$71$	−1126.55	−1.88305	−0.941525	+	0.336943i	$0.890607\pi$
$72$	−1084.13	−1.77453
$73$	−1053.18	−1.68857	−0.844284	−	0.535897i	$-0.819974\pi$
$73$	−1053.18	−1.68857	−0.844284	+	0.535897i	$0.819974\pi$
$74$	380.772	0.598161
$75$	−796.610	−1.22646
$76$	895.725	1.35193
$77$	0	0
$78$	535.756	0.777723
$79$	1253.01	1.78449	0.892244	−	0.451554i	$-0.149130\pi$
$79$	1253.01	1.78449	0.892244	+	0.451554i	$0.149130\pi$
$80$	−177.984	−0.248741
$81$	976.254	1.33917
$82$	687.200	0.925470
$83$	145.857	0.192890	0.0964450	−	0.995338i	$-0.469253\pi$
$83$	145.857	0.192890	0.0964450	+	0.995338i	$0.469253\pi$
$84$	1548.65	2.01157
$85$	1915.59	2.44441
$86$	1201.10	1.50603
$87$	−651.330	−0.802643
$88$	0	0
$89$	911.594	1.08572	0.542858	−	0.839824i	$-0.317342\pi$
$89$	911.594	1.08572	0.542858	+	0.839824i	$0.317342\pi$
$90$	−3729.03	−4.36749
$91$	−179.631	−0.206928
$92$	−188.486	−0.213599
$93$	924.759	1.03111
$94$	1809.65	1.98565
$95$	1066.03	1.15129
$96$	−1899.29	−2.01922
$97$	−723.825	−0.757662	−0.378831	−	0.925466i	$-0.623674\pi$
$97$	−723.825	−0.757662	−0.378831	+	0.925466i	$0.623674\pi$
$98$	684.013	0.705059
$99$	0	0
$100$	1063.56	1.06356
$101$	1173.07	1.15570	0.577848	−	0.816145i	$-0.303893\pi$
$101$	1173.07	1.15570	0.577848	+	0.816145i	$0.303893\pi$
$102$	5422.68	5.26398
$103$	−92.1367	−0.0881407	−0.0440704	−	0.999028i	$-0.514033\pi$
$103$	−92.1367	−0.0881407	−0.0440704	+	0.999028i	$0.514033\pi$
$104$	−247.496	−0.233355
$105$	1843.10	1.71303
$106$	8.03294	0.00736064
$107$	780.573	0.705241	0.352621	−	0.935766i	$-0.385291\pi$
$107$	780.573	0.705241	0.352621	+	0.935766i	$0.385291\pi$
$108$	−3356.18	−2.99026
$109$	−261.244	−0.229566	−0.114783	−	0.993391i	$-0.536617\pi$
$109$	−261.244	−0.229566	−0.114783	+	0.993391i	$0.536617\pi$
$110$	0	0
$111$	775.602	0.663215
$112$	168.931	0.142522
$113$	1061.74	0.883895	0.441947	−	0.897041i	$-0.354288\pi$
$113$	1061.74	0.883895	0.441947	+	0.897041i	$0.354288\pi$
$114$	3017.74	2.47928
$115$	−224.324	−0.181899
$116$	869.599	0.696036
$117$	740.290	0.584956
$118$	−3925.47	−3.06245
$119$	−1818.15	−1.40058
$120$	2539.42	1.93180
$121$	0	0
$122$	1585.72	1.17675
$123$	1399.77	1.02612
$124$	−1234.66	−0.894156
$125$	−554.010	−0.396418
$126$	3539.34	2.50246
$127$	−2207.47	−1.54237	−0.771185	−	0.636611i	$-0.780336\pi$
$127$	−2207.47	−1.54237	−0.771185	+	0.636611i	$0.780336\pi$
$128$	2095.83	1.44724
$129$	2446.55	1.66982
$130$	−851.296	−0.574335
$131$	−663.621	−0.442602	−0.221301	−	0.975206i	$-0.571030\pi$
$131$	−663.621	−0.442602	−0.221301	+	0.975206i	$0.571030\pi$
$132$	0	0
$133$	−1011.81	−0.659660
$134$	3389.96	2.18543
$135$	−3994.30	−2.54648
$136$	−2505.04	−1.57945
$137$	−295.180	−0.184080	−0.0920400	−	0.995755i	$-0.529339\pi$
$137$	−295.180	−0.184080	−0.0920400	+	0.995755i	$0.529339\pi$
$138$	−635.020	−0.391714
$139$	273.306	0.166773	0.0833866	−	0.996517i	$-0.473426\pi$
$139$	273.306	0.166773	0.0833866	+	0.996517i	$0.473426\pi$
$140$	−2460.75	−1.48551
$141$	3686.11	2.20161
$142$	5067.27	2.99462
$143$	0	0
$144$	−696.191	−0.402889
$145$	1034.94	0.592738
$146$	4737.26	2.68533
$147$	1393.28	0.781739
$148$	−1035.52	−0.575127
$149$	1276.52	0.701856	0.350928	−	0.936403i	$-0.385866\pi$
$149$	1276.52	0.701856	0.350928	+	0.936403i	$0.385866\pi$
$150$	3583.20	1.95045
$151$	2009.06	1.08275	0.541375	−	0.840781i	$-0.317904\pi$
$151$	2009.06	1.08275	0.541375	+	0.840781i	$0.317904\pi$
$152$	−1394.06	−0.743905
$153$	7492.89	3.95925
$154$	0	0
$155$	−1469.41	−0.761455
$156$	−1456.99	−0.747775
$157$	−264.421	−0.134415	−0.0672074	−	0.997739i	$-0.521409\pi$
$157$	−264.421	−0.134415	−0.0672074	+	0.997739i	$0.521409\pi$
$158$	−5636.11	−2.83788
$159$	16.3624	0.00816117
$160$	3017.89	1.49116
$161$	212.913	0.104223
$162$	−4391.25	−2.12969
$163$	−1905.41	−0.915605	−0.457802	−	0.889054i	$-0.651363\pi$
$163$	−1905.41	−0.915605	−0.457802	+	0.889054i	$0.651363\pi$
$164$	−1868.85	−0.889833
$165$	0	0
$166$	−656.073	−0.306754
$167$	−1630.44	−0.755494	−0.377747	−	0.925909i	$-0.623301\pi$
$167$	−1630.44	−0.755494	−0.377747	+	0.925909i	$0.623301\pi$
$168$	−2410.25	−1.10687
$169$	169.000	0.0769231
$170$	−8616.44	−3.88736
$171$	4169.82	1.86476
$172$	−3266.41	−1.44803
$173$	24.8931	0.0109398	0.00546990	−	0.999985i	$-0.498259\pi$
$173$	24.8931	0.0109398	0.00546990	+	0.999985i	$0.498259\pi$
$174$	2929.72	1.27645
$175$	−1201.40	−0.518954
$176$	0	0
$177$	−7995.85	−3.39551
$178$	−4100.40	−1.72662
$179$	−971.043	−0.405470	−0.202735	−	0.979234i	$-0.564983\pi$
$179$	−971.043	−0.405470	−0.202735	+	0.979234i	$0.564983\pi$
$180$	10141.1	4.19931
$181$	783.032	0.321560	0.160780	−	0.986990i	$-0.448599\pi$
$181$	783.032	0.321560	0.160780	+	0.986990i	$0.448599\pi$
$182$	807.992	0.329079
$183$	3229.97	1.30473
$184$	293.351	0.117533
$185$	−1232.40	−0.489773
$186$	−4159.62	−1.63977
$187$	0	0
$188$	−4921.36	−1.90919
$189$	3791.12	1.45907
$190$	−4795.08	−1.83090
$191$	−448.091	−0.169753	−0.0848763	−	0.996391i	$-0.527050\pi$
$191$	−448.091	−0.169753	−0.0848763	+	0.996391i	$0.527050\pi$
$192$	7646.99	2.87434
$193$	4855.91	1.81107	0.905533	−	0.424276i	$-0.139471\pi$
$193$	4855.91	1.81107	0.905533	+	0.424276i	$0.139471\pi$
$194$	3255.80	1.20491
$195$	−1734.02	−0.636799
$196$	−1860.18	−0.677909
$197$	−520.230	−0.188146	−0.0940731	−	0.995565i	$-0.529989\pi$
$197$	−520.230	−0.188146	−0.0940731	+	0.995565i	$0.529989\pi$
$198$	0	0
$199$	893.152	0.318160	0.159080	−	0.987266i	$-0.449147\pi$
$199$	893.152	0.318160	0.159080	+	0.987266i	$0.449147\pi$
$200$	−1655.28	−0.585230
$201$	6905.07	2.42311
$202$	−5276.56	−1.83791
$203$	−982.294	−0.339623
$204$	−14747.1	−5.06128
$205$	−2224.18	−0.757774
$206$	414.436	0.140171
$207$	−877.451	−0.294623
$208$	−158.933	−0.0529808
$209$	0	0
$210$	−8290.38	−2.72424
$211$	−4389.48	−1.43215	−0.716076	−	0.698022i	$-0.754064\pi$
$211$	−4389.48	−1.43215	−0.716076	+	0.698022i	$0.754064\pi$
$212$	−21.8457	−0.00707721
$213$	10321.6	3.32031
$214$	−3511.06	−1.12155
$215$	−3887.47	−1.23313
$216$	5223.40	1.64540
$217$	1394.66	0.436294
$218$	1175.09	0.365079
$219$	9649.42	2.97738
$220$	0	0
$221$	1710.54	0.520650
$222$	−3488.70	−1.05471
$223$	−5234.14	−1.57177	−0.785883	−	0.618375i	$-0.787791\pi$
$223$	−5234.14	−1.57177	−0.785883	+	0.618375i	$0.787791\pi$
$224$	−2864.38	−0.854395
$225$	4951.15	1.46701
$226$	−4775.77	−1.40566
$227$	450.347	0.131677	0.0658383	−	0.997830i	$-0.479028\pi$
$227$	450.347	0.131677	0.0658383	+	0.997830i	$0.479028\pi$
$228$	−8206.79	−2.38381
$229$	5847.12	1.68729	0.843644	−	0.536903i	$-0.180406\pi$
$229$	5847.12	1.68729	0.843644	+	0.536903i	$0.180406\pi$
$230$	1009.02	0.289274
$231$	0	0
$232$	−1353.40	−0.382997
$233$	434.954	0.122295	0.0611477	−	0.998129i	$-0.480524\pi$
$233$	434.954	0.122295	0.0611477	+	0.998129i	$0.480524\pi$
$234$	−3329.87	−0.930258
$235$	−5857.09	−1.62585
$236$	10675.4	2.94452
$237$	−11480.3	−3.14652
$238$	8178.14	2.22735
$239$	2660.37	0.720022	0.360011	−	0.932948i	$-0.382773\pi$
$239$	2660.37	0.720022	0.360011	+	0.932948i	$0.382773\pi$
$240$	1630.72	0.438595
$241$	−6180.22	−1.65188	−0.825939	−	0.563759i	$-0.809355\pi$
$241$	−6180.22	−1.65188	−0.825939	+	0.563759i	$0.809355\pi$
$242$	0	0
$243$	−1536.75	−0.405690
$244$	−4312.37	−1.13144
$245$	−2213.87	−0.577301
$246$	−6296.25	−1.63185
$247$	951.924	0.245220
$248$	1921.56	0.492013
$249$	−1336.37	−0.340115
$250$	2491.97	0.630424
$251$	−2130.69	−0.535809	−0.267904	−	0.963446i	$-0.586331\pi$
$251$	−2130.69	−0.535809	−0.267904	+	0.963446i	$0.586331\pi$
$252$	−9625.28	−2.40609
$253$	0	0
$254$	9929.31	2.45284
$255$	−17551.0	−4.31014
$256$	−2750.14	−0.671420
$257$	−2743.69	−0.665940	−0.332970	−	0.942938i	$-0.608051\pi$
$257$	−2743.69	−0.665940	−0.332970	+	0.942938i	$0.608051\pi$
$258$	−11004.7	−2.65552
$259$	1169.71	0.280627
$260$	2315.11	0.552219
$261$	4048.20	0.960065
$262$	2985.00	0.703871
$263$	−2373.29	−0.556438	−0.278219	−	0.960518i	$-0.589744\pi$
$263$	−2373.29	−0.556438	−0.278219	+	0.960518i	$0.589744\pi$
$264$	0	0
$265$	−25.9993	−0.00602689
$266$	4551.17	1.04906
$267$	−8352.18	−1.91440
$268$	−9219.03	−2.10128
$269$	−2062.97	−0.467590	−0.233795	−	0.972286i	$-0.575114\pi$
$269$	−2062.97	−0.467590	−0.233795	+	0.972286i	$0.575114\pi$
$270$	17966.6	4.04968
$271$	−2069.86	−0.463967	−0.231983	−	0.972720i	$-0.574522\pi$
$271$	−2069.86	−0.463967	−0.231983	+	0.972720i	$0.574522\pi$
$272$	−1608.65	−0.358598
$273$	1645.81	0.364869
$274$	1327.74	0.292743
$275$	0	0
$276$	1726.94	0.376630
$277$	−1391.80	−0.301897	−0.150948	−	0.988542i	$-0.548233\pi$
$277$	−1391.80	−0.301897	−0.150948	+	0.988542i	$0.548233\pi$
$278$	−1229.34	−0.265220
$279$	−5747.63	−1.23334
$280$	3829.79	0.817406
$281$	−324.660	−0.0689238	−0.0344619	−	0.999406i	$-0.510972\pi$
$281$	−324.660	−0.0689238	−0.0344619	+	0.999406i	$0.510972\pi$
$282$	−16580.3	−3.50122
$283$	7040.50	1.47885	0.739424	−	0.673240i	$-0.235098\pi$
$283$	7040.50	1.47885	0.739424	+	0.673240i	$0.235098\pi$
$284$	−13780.5	−2.87931
$285$	−9767.19	−2.03003
$286$	0	0
$287$	2111.04	0.434184
$288$	11804.6	2.41525
$289$	12400.4	2.52399
$290$	−4655.22	−0.942634
$291$	6631.81	1.33596
$292$	−12883.0	−2.58193
$293$	−6285.70	−1.25329	−0.626646	−	0.779304i	$-0.715573\pi$
$293$	−6285.70	−1.25329	−0.626646	+	0.779304i	$0.715573\pi$
$294$	−6267.04	−1.24320
$295$	12705.1	2.50753
$296$	1611.63	0.316466
$297$	0	0
$298$	−5741.85	−1.11616
$299$	−200.312	−0.0387436
$300$	−9744.55	−1.87534
$301$	3689.72	0.706552
$302$	−9036.88	−1.72190
$303$	−10747.9	−2.03779
$304$	−895.218	−0.168896
$305$	−5132.30	−0.963524
$306$	−33703.5	−6.29640
$307$	−4437.26	−0.824912	−0.412456	−	0.910977i	$-0.635329\pi$
$307$	−4437.26	−0.824912	−0.412456	+	0.910977i	$0.635329\pi$
$308$	0	0
$309$	844.172	0.155415
$310$	6609.48	1.21095
$311$	−4416.63	−0.805286	−0.402643	−	0.915357i	$-0.631908\pi$
$311$	−4416.63	−0.805286	−0.402643	+	0.915357i	$0.631908\pi$
$312$	2267.60	0.411466
$313$	−5382.29	−0.971965	−0.485983	−	0.873969i	$-0.661538\pi$
$313$	−5382.29	−0.971965	−0.485983	+	0.873969i	$0.661538\pi$
$314$	1189.38	0.213760
$315$	−11455.4	−2.04901
$316$	15327.5	2.72860
$317$	−3079.64	−0.545646	−0.272823	−	0.962064i	$-0.587957\pi$
$317$	−3079.64	−0.545646	−0.272823	+	0.962064i	$0.587957\pi$
$318$	−73.5992	−0.0129787
$319$	0	0
$320$	−12150.8	−2.12265
$321$	−7151.74	−1.24352
$322$	−957.696	−0.165746
$323$	9634.95	1.65976
$324$	11942.1	2.04768
$325$	1130.29	0.192915
$326$	8570.66	1.45609
$327$	2393.57	0.404784
$328$	2908.59	0.489634
$329$	5559.15	0.931568
$330$	0	0
$331$	4107.94	0.682154	0.341077	−	0.940035i	$-0.389208\pi$
$331$	4107.94	0.682154	0.341077	+	0.940035i	$0.389208\pi$
$332$	1784.20	0.294941
$333$	−4820.58	−0.793292
$334$	7333.83	1.20146
$335$	−10971.9	−1.78943
$336$	−1547.77	−0.251303
$337$	4337.06	0.701053	0.350526	−	0.936553i	$-0.386003\pi$
$337$	4337.06	0.701053	0.350526	+	0.936553i	$0.386003\pi$
$338$	−760.172	−0.122331
$339$	−9727.85	−1.55854
$340$	23432.5	3.73767
$341$	0	0
$342$	−18756.1	−2.96554
$343$	6840.76	1.07687
$344$	5083.69	0.796786
$345$	2055.30	0.320735
$346$	−111.970	−0.0173976
$347$	3322.80	0.514055	0.257028	−	0.966404i	$-0.417257\pi$
$347$	3322.80	0.514055	0.257028	+	0.966404i	$0.417257\pi$
$348$	−7967.41	−1.22729
$349$	6091.21	0.934255	0.467127	−	0.884190i	$-0.345289\pi$
$349$	6091.21	0.934255	0.467127	+	0.884190i	$0.345289\pi$
$350$	5403.95	0.825294
$351$	−3566.75	−0.542390
$352$	0	0
$353$	9535.99	1.43782	0.718909	−	0.695104i	$-0.244642\pi$
$353$	9535.99	1.43782	0.718909	+	0.695104i	$0.244642\pi$
$354$	35965.8	5.39989
$355$	−16400.7	−2.45199
$356$	11151.1	1.66013
$357$	16658.2	2.46959
$358$	4367.81	0.644821
$359$	−6180.09	−0.908559	−0.454280	−	0.890859i	$-0.650103\pi$
$359$	−6180.09	−0.908559	−0.454280	+	0.890859i	$0.650103\pi$
$360$	−15783.2	−2.31069
$361$	−1497.11	−0.218270
$362$	−3522.12	−0.511378
$363$	0	0
$364$	−2197.34	−0.316407
$365$	−15332.6	−2.19875
$366$	−14528.6	−2.07492
$367$	−9399.08	−1.33686	−0.668431	−	0.743774i	$-0.733034\pi$
$367$	−9399.08	−1.33686	−0.668431	+	0.743774i	$0.733034\pi$
$368$	188.380	0.0266847
$369$	−8699.95	−1.22738
$370$	5543.42	0.778888
$371$	24.6768	0.00345325
$372$	11312.1	1.57663
$373$	−390.145	−0.0541580	−0.0270790	−	0.999633i	$-0.508621\pi$
$373$	−390.145	−0.0541580	−0.0270790	+	0.999633i	$0.508621\pi$
$374$	0	0
$375$	5075.94	0.698988
$376$	7659.38	1.05054
$377$	924.158	0.126251
$378$	−17052.7	−2.32036
$379$	8249.28	1.11804	0.559020	−	0.829154i	$-0.311178\pi$
$379$	8249.28	1.11804	0.559020	+	0.829154i	$0.311178\pi$
$380$	13040.3	1.76040
$381$	20225.2	2.71960
$382$	2015.54	0.269958
$383$	−4330.05	−0.577690	−0.288845	−	0.957376i	$-0.593271\pi$
$383$	−4330.05	−0.577690	−0.288845	+	0.957376i	$0.593271\pi$
$384$	−19202.3	−2.55186
$385$	0	0
$386$	−21842.1	−2.88014
$387$	−15206.0	−1.99732
$388$	−8854.20	−1.15852
$389$	−14803.8	−1.92952	−0.964759	−	0.263136i	$-0.915243\pi$
$389$	−14803.8	−1.92952	−0.964759	+	0.263136i	$0.915243\pi$
$390$	7799.72	1.01270
$391$	−2027.47	−0.262234
$392$	2895.10	0.373022
$393$	6080.21	0.780422
$394$	2340.02	0.299210
$395$	18241.7	2.32365
$396$	0	0
$397$	3744.70	0.473403	0.236701	−	0.971582i	$-0.423934\pi$
$397$	3744.70	0.473403	0.236701	+	0.971582i	$0.423934\pi$
$398$	−4017.45	−0.505971
$399$	9270.35	1.16315
$400$	−1062.96	−0.132870
$401$	−6037.85	−0.751910	−0.375955	−	0.926638i	$-0.622685\pi$
$401$	−6037.85	−0.751910	−0.375955	+	0.926638i	$0.622685\pi$
$402$	−31059.4	−3.85349
$403$	−1312.12	−0.162187
$404$	14349.7	1.76713
$405$	14212.7	1.74378
$406$	4418.42	0.540104
$407$	0	0
$408$	22951.6	2.78499
$409$	−2120.04	−0.256307	−0.128153	−	0.991754i	$-0.540905\pi$
$409$	−2120.04	−0.256307	−0.128153	+	0.991754i	$0.540905\pi$
$410$	10004.5	1.20509
$411$	2704.49	0.324581
$412$	−1127.06	−0.134773
$413$	−12058.8	−1.43675
$414$	3946.82	0.468541
$415$	2123.44	0.251170
$416$	2694.85	0.317611
$417$	−2504.07	−0.294065
$418$	0	0
$419$	8401.52	0.979573	0.489787	−	0.871842i	$-0.337075\pi$
$419$	8401.52	0.979573	0.489787	+	0.871842i	$0.337075\pi$
$420$	22545.8	2.61934
$421$	5201.37	0.602136	0.301068	−	0.953603i	$-0.402657\pi$
$421$	5201.37	0.602136	0.301068	+	0.953603i	$0.402657\pi$
$422$	19744.1	2.27756
$423$	−22910.2	−2.63341
$424$	33.9996	0.00389426
$425$	11440.3	1.30573
$426$	−46427.2	−5.28030
$427$	4871.23	0.552074
$428$	9548.37	1.07836
$429$	0	0
$430$	17486.1	1.96105
$431$	10694.4	1.19520	0.597601	−	0.801794i	$-0.296121\pi$
$431$	10694.4	1.19520	0.597601	+	0.801794i	$0.296121\pi$
$432$	3354.28	0.373571
$433$	12076.2	1.34029	0.670147	−	0.742229i	$-0.266231\pi$
$433$	12076.2	1.34029	0.670147	+	0.742229i	$0.266231\pi$
$434$	−6273.27	−0.693840
$435$	−9482.29	−1.04515
$436$	−3195.68	−0.351021
$437$	−1128.30	−0.123510
$438$	−43403.6	−4.73495
$439$	−5279.06	−0.573931	−0.286966	−	0.957941i	$-0.592647\pi$
$439$	−5279.06	−0.573931	−0.286966	+	0.957941i	$0.592647\pi$
$440$	0	0
$441$	−8659.61	−0.935062
$442$	−7694.12	−0.827991
$443$	−11684.6	−1.25316	−0.626582	−	0.779355i	$-0.715547\pi$
$443$	−11684.6	−1.25316	−0.626582	+	0.779355i	$0.715547\pi$
$444$	9487.57	1.01410
$445$	13271.3	1.41375
$446$	23543.5	2.49959
$447$	−11695.7	−1.23755
$448$	11532.7	1.21622
$449$	17121.9	1.79963	0.899815	−	0.436271i	$-0.143701\pi$
$449$	17121.9	1.79963	0.899815	+	0.436271i	$0.143701\pi$
$450$	−22270.6	−2.33299
$451$	0	0
$452$	12987.8	1.35153
$453$	−18407.4	−1.90917
$454$	−2025.69	−0.209406
$455$	−2615.14	−0.269449
$456$	12772.7	1.31170
$457$	−14017.4	−1.43481	−0.717405	−	0.696657i	$-0.754670\pi$
$457$	−14017.4	−1.43481	−0.717405	+	0.696657i	$0.754670\pi$
$458$	−26300.7	−2.68330
$459$	−36101.0	−3.67114
$460$	−2744.05	−0.278135
$461$	−623.689	−0.0630110	−0.0315055	−	0.999504i	$-0.510030\pi$
$461$	−623.689	−0.0630110	−0.0315055	+	0.999504i	$0.510030\pi$
$462$	0	0
$463$	−9086.34	−0.912047	−0.456024	−	0.889968i	$-0.650727\pi$
$463$	−9086.34	−0.912047	−0.456024	+	0.889968i	$0.650727\pi$
$464$	−869.106	−0.0869552
$465$	13463.0	1.34264
$466$	−1956.45	−0.194487
$467$	−4283.52	−0.424449	−0.212225	−	0.977221i	$-0.568071\pi$
$467$	−4283.52	−0.424449	−0.212225	+	0.977221i	$0.568071\pi$
$468$	9055.62	0.894436
$469$	10413.8	1.02530
$470$	26345.5	2.58559
$471$	2422.68	0.237008
$472$	−16614.6	−1.62023
$473$	0	0
$474$	51639.0	5.00392
$475$	6366.58	0.614987
$476$	−22240.6	−2.14158
$477$	−101.697	−0.00976182
$478$	−11966.5	−1.14505
$479$	4528.98	0.432013	0.216006	−	0.976392i	$-0.430697\pi$
$479$	4528.98	0.432013	0.216006	+	0.976392i	$0.430697\pi$
$480$	−27650.5	−2.62930
$481$	−1100.48	−0.104320
$482$	27799.0	2.62699
$483$	−1950.75	−0.183773
$484$	0	0
$485$	−10537.7	−0.986581
$486$	6912.40	0.645171
$487$	7062.73	0.657172	0.328586	−	0.944474i	$-0.393428\pi$
$487$	7062.73	0.657172	0.328586	+	0.944474i	$0.393428\pi$
$488$	6711.57	0.622579
$489$	17457.7	1.61445
$490$	9958.10	0.918084
$491$	6762.50	0.621563	0.310781	−	0.950481i	$-0.399409\pi$
$491$	6762.50	0.621563	0.310781	+	0.950481i	$0.399409\pi$
$492$	17122.7	1.56901
$493$	9353.92	0.854522
$494$	−4281.81	−0.389975
$495$	0	0
$496$	1233.96	0.111706
$497$	15566.4	1.40493
$498$	6011.05	0.540887
$499$	1986.48	0.178211	0.0891054	−	0.996022i	$-0.471599\pi$
$499$	1986.48	0.178211	0.0891054	+	0.996022i	$0.471599\pi$
$500$	−6776.94	−0.606148
$501$	14938.4	1.33213
$502$	9583.97	0.852098
$503$	−8385.21	−0.743296	−0.371648	−	0.928374i	$-0.621207\pi$
$503$	−8385.21	−0.743296	−0.371648	+	0.928374i	$0.621207\pi$
$504$	14980.3	1.32396
$505$	17078.0	1.50488
$506$	0	0
$507$	−1548.41	−0.135635
$508$	−27002.9	−2.35838
$509$	16583.4	1.44410	0.722049	−	0.691842i	$-0.243201\pi$
$509$	16583.4	1.44410	0.722049	+	0.691842i	$0.243201\pi$
$510$	78945.3	6.85443
$511$	14552.6	1.25982
$512$	−4396.34	−0.379478
$513$	−20090.4	−1.72907
$514$	12341.3	1.05905
$515$	−1341.36	−0.114771
$516$	29927.4	2.55326
$517$	0	0
$518$	−5261.44	−0.446282
$519$	−228.075	−0.0192897
$520$	−3603.13	−0.303861
$521$	−18946.1	−1.59317	−0.796587	−	0.604524i	$-0.793363\pi$
$521$	−18946.1	−1.59317	−0.796587	+	0.604524i	$0.793363\pi$
$522$	−18209.0	−1.52680
$523$	−4168.16	−0.348491	−0.174246	−	0.984702i	$-0.555749\pi$
$523$	−4168.16	−0.348491	−0.174246	+	0.984702i	$0.555749\pi$
$524$	−8117.75	−0.676767
$525$	11007.4	0.915051
$526$	10675.2	0.884905
$527$	−13280.7	−1.09775
$528$	0	0
$529$	−11929.6	−0.980486
$530$	116.946	0.00958458
$531$	49696.4	4.06147
$532$	−12376.9	−1.00866
$533$	−1986.10	−0.161403
$534$	37568.6	3.04448
$535$	11363.9	0.918322
$536$	14348.1	1.15624
$537$	8896.87	0.714950
$538$	9279.38	0.743610
$539$	0	0
$540$	−48860.4	−3.89373
$541$	−15924.2	−1.26550	−0.632748	−	0.774358i	$-0.718073\pi$
$541$	−15924.2	−1.26550	−0.632748	+	0.774358i	$0.718073\pi$
$542$	9310.35	0.737848
$543$	−7174.27	−0.566994
$544$	27276.1	2.14973
$545$	−3803.29	−0.298926
$546$	−7402.96	−0.580252
$547$	16614.5	1.29869	0.649345	−	0.760494i	$-0.275043\pi$
$547$	16614.5	1.29869	0.649345	+	0.760494i	$0.275043\pi$
$548$	−3610.80	−0.281470
$549$	−20075.2	−1.56063
$550$	0	0
$551$	5205.49	0.402471
$552$	−2687.74	−0.207242
$553$	−17313.8	−1.33139
$554$	6260.42	0.480108
$555$	11291.5	0.863598
$556$	3343.22	0.255007
$557$	−8405.43	−0.639407	−0.319703	−	0.947518i	$-0.603583\pi$
$557$	−8405.43	−0.639407	−0.319703	+	0.947518i	$0.603583\pi$
$558$	25853.2	1.96138
$559$	−3471.35	−0.262652
$560$	2459.35	0.185583
$561$	0	0
$562$	1460.34	0.109610
$563$	−8988.90	−0.672890	−0.336445	−	0.941703i	$-0.609225\pi$
$563$	−8988.90	−0.672890	−0.336445	+	0.941703i	$0.609225\pi$
$564$	45090.4	3.36640
$565$	15457.2	1.15095
$566$	−31668.6	−2.35182
$567$	−13489.7	−0.999142
$568$	21447.3	1.58435
$569$	−19943.8	−1.46939	−0.734697	−	0.678395i	$-0.762676\pi$
$569$	−19943.8	−1.46939	−0.734697	+	0.678395i	$0.762676\pi$
$570$	43933.4	3.22836
$571$	−712.604	−0.0522269	−0.0261134	−	0.999659i	$-0.508313\pi$
$571$	−712.604	−0.0522269	−0.0261134	+	0.999659i	$0.508313\pi$
$572$	0	0
$573$	4105.49	0.299318
$574$	−9495.59	−0.690485
$575$	−1339.71	−0.0971649
$576$	−47528.2	−3.43809
$577$	1047.10	0.0755486	0.0377743	−	0.999286i	$-0.487973\pi$
$577$	1047.10	0.0755486	0.0377743	+	0.999286i	$0.487973\pi$
$578$	−55777.6	−4.01391
$579$	−44490.6	−3.19338
$580$	12659.9	0.906335
$581$	−2015.42	−0.143913
$582$	−29830.2	−2.12458
$583$	0	0
$584$	20050.6	1.42072
$585$	10777.4	0.761694
$586$	28273.4	1.99311
$587$	−20735.3	−1.45798	−0.728992	−	0.684522i	$-0.760011\pi$
$587$	−20735.3	−1.45798	−0.728992	+	0.684522i	$0.760011\pi$
$588$	17043.3	1.19533
$589$	−7390.75	−0.517030
$590$	−57148.3	−3.98773
$591$	4766.43	0.331751
$592$	1034.93	0.0718502
$593$	−17891.4	−1.23898	−0.619488	−	0.785006i	$-0.712660\pi$
$593$	−17891.4	−1.23898	−0.619488	+	0.785006i	$0.712660\pi$
$594$	0	0
$595$	−26469.3	−1.82375
$596$	15615.0	1.07318
$597$	−8183.21	−0.560999
$598$	901.016	0.0616142
$599$	8982.45	0.612710	0.306355	−	0.951917i	$-0.400891\pi$
$599$	8982.45	0.612710	0.306355	+	0.951917i	$0.400891\pi$
$600$	15166.0	1.03191
$601$	−9876.50	−0.670334	−0.335167	−	0.942159i	$-0.608793\pi$
$601$	−9876.50	−0.670334	−0.335167	+	0.942159i	$0.608793\pi$
$602$	−16596.6	−1.12363
$603$	−42916.9	−2.89836
$604$	24575.9	1.65559
$605$	0	0
$606$	48344.7	3.24071
$607$	16886.7	1.12918	0.564589	−	0.825372i	$-0.309035\pi$
$607$	16886.7	1.12918	0.564589	+	0.825372i	$0.309035\pi$
$608$	15179.3	1.01250
$609$	8999.95	0.598845
$610$	23085.4	1.53230
$611$	−5230.14	−0.346299
$612$	91657.0	6.05394
$613$	−6823.41	−0.449584	−0.224792	−	0.974407i	$-0.572170\pi$
$613$	−6823.41	−0.449584	−0.224792	+	0.974407i	$0.572170\pi$
$614$	19959.1	1.31186
$615$	20378.3	1.33615
$616$	0	0
$617$	4171.51	0.272186	0.136093	−	0.990696i	$-0.456545\pi$
$617$	4171.51	0.272186	0.136093	+	0.990696i	$0.456545\pi$
$618$	−3797.14	−0.247157
$619$	−17284.7	−1.12234	−0.561171	−	0.827700i	$-0.689649\pi$
$619$	−17284.7	−1.12234	−0.561171	+	0.827700i	$0.689649\pi$
$620$	−17974.5	−1.16431
$621$	4227.59	0.273184
$622$	19866.2	1.28065
$623$	−12596.2	−0.810043
$624$	1456.17	0.0934189
$625$	−18933.7	−1.21175
$626$	24209.9	1.54572
$627$	0	0
$628$	−3234.54	−0.205529
$629$	−11138.6	−0.706082
$630$	51527.0	3.25855
$631$	−14779.5	−0.932429	−0.466214	−	0.884672i	$-0.654382\pi$
$631$	−14779.5	−0.932429	−0.466214	+	0.884672i	$0.654382\pi$
$632$	−23854.9	−1.50142
$633$	40217.2	2.52526
$634$	13852.4	0.867743
$635$	−32137.1	−2.00838
$636$	200.154	0.0124790
$637$	−1976.89	−0.122963
$638$	0	0
$639$	−64151.7	−3.97152
$640$	30511.8	1.88451
$641$	4350.69	0.268084	0.134042	−	0.990976i	$-0.457204\pi$
$641$	4350.69	0.268084	0.134042	+	0.990976i	$0.457204\pi$
$642$	32169.0	1.97758
$643$	−7403.01	−0.454038	−0.227019	−	0.973890i	$-0.572898\pi$
$643$	−7403.01	−0.454038	−0.227019	+	0.973890i	$0.572898\pi$
$644$	2604.47	0.159364
$645$	35617.7	2.17433
$646$	−43338.6	−2.63953
$647$	−9768.39	−0.593563	−0.296781	−	0.954945i	$-0.595913\pi$
$647$	−9768.39	−0.593563	−0.296781	+	0.954945i	$0.595913\pi$
$648$	−18586.1	−1.12674
$649$	0	0
$650$	−5084.12	−0.306793
$651$	−12778.1	−0.769300
$652$	−23308.0	−1.40002
$653$	−14831.5	−0.888824	−0.444412	−	0.895822i	$-0.646587\pi$
$653$	−14831.5	−0.888824	−0.444412	+	0.895822i	$0.646587\pi$
$654$	−10766.4	−0.643730
$655$	−9661.22	−0.576328
$656$	1867.79	0.111166
$657$	−59973.8	−3.56134
$658$	−25005.4	−1.48148
$659$	9266.90	0.547780	0.273890	−	0.961761i	$-0.411690\pi$
$659$	9266.90	0.547780	0.273890	+	0.961761i	$0.411690\pi$
$660$	0	0
$661$	−3136.96	−0.184590	−0.0922948	−	0.995732i	$-0.529420\pi$
$661$	−3136.96	−0.184590	−0.0922948	+	0.995732i	$0.529420\pi$
$662$	−18477.8	−1.08483
$663$	−15672.3	−0.918042
$664$	−2776.84	−0.162293
$665$	−14730.2	−0.858968
$666$	21683.2	1.26157
$667$	−1095.38	−0.0635884
$668$	−19944.4	−1.15520
$669$	47956.1	2.77143
$670$	49352.2	2.84573
$671$	0	0
$672$	26243.9	1.50652
$673$	12072.6	0.691475	0.345737	−	0.938331i	$-0.387629\pi$
$673$	12072.6	0.691475	0.345737	+	0.938331i	$0.387629\pi$
$674$	−19508.4	−1.11489
$675$	−23854.8	−1.36026
$676$	2067.30	0.117620
$677$	−12251.5	−0.695517	−0.347759	−	0.937584i	$-0.613057\pi$
$677$	−12251.5	−0.695517	−0.347759	+	0.937584i	$0.613057\pi$
$678$	43756.4	2.47855
$679$	10001.7	0.565285
$680$	−36469.3	−2.05667
$681$	−4126.16	−0.232180
$682$	0	0
$683$	−20045.6	−1.12302	−0.561510	−	0.827470i	$-0.689779\pi$
$683$	−20045.6	−1.12302	−0.561510	+	0.827470i	$0.689779\pi$
$684$	51007.4	2.85134
$685$	−4297.34	−0.239698
$686$	−30770.1	−1.71255
$687$	−53572.4	−2.97513
$688$	3264.56	0.180902
$689$	−23.2163	−0.00128370
$690$	−9244.84	−0.510065
$691$	−25393.6	−1.39800	−0.699000	−	0.715121i	$-0.746371\pi$
$691$	−25393.6	−1.39800	−0.699000	+	0.715121i	$0.746371\pi$
$692$	304.505	0.0167277
$693$	0	0
$694$	−14946.1	−0.817504
$695$	3978.88	0.217162
$696$	12400.1	0.675323
$697$	−20102.4	−1.09245
$698$	−27398.6	−1.48575
$699$	−3985.13	−0.215639
$700$	−14696.1	−0.793515
$701$	−8000.44	−0.431059	−0.215530	−	0.976497i	$-0.569148\pi$
$701$	−8000.44	−0.431059	−0.215530	+	0.976497i	$0.569148\pi$
$702$	16043.4	0.862564
$703$	−6198.68	−0.332557
$704$	0	0
$705$	53663.6	2.86679
$706$	−42893.4	−2.28657
$707$	−16209.3	−0.862254
$708$	−97809.4	−5.19195
$709$	1254.61	0.0664569	0.0332285	−	0.999448i	$-0.489421\pi$
$709$	1254.61	0.0664569	0.0332285	+	0.999448i	$0.489421\pi$
$710$	73771.1	3.89941
$711$	71353.1	3.76364
$712$	−17355.0	−0.913493
$713$	1555.23	0.0816882
$714$	−74929.5	−3.92741
$715$	0	0
$716$	−11878.3	−0.619991
$717$	−24374.8	−1.26959
$718$	27798.4	1.44488
$719$	24378.1	1.26447	0.632233	−	0.774778i	$-0.282138\pi$
$719$	24378.1	1.26447	0.632233	+	0.774778i	$0.282138\pi$
$720$	−10135.4	−0.524617
$721$	1273.13	0.0657610
$722$	6734.10	0.347115
$723$	56624.2	2.91269
$724$	9578.46	0.491686
$725$	6180.88	0.316623
$726$	0	0
$727$	28582.1	1.45812	0.729058	−	0.684452i	$-0.239959\pi$
$727$	28582.1	1.45812	0.729058	+	0.684452i	$0.239959\pi$
$728$	3419.84	0.174104
$729$	−12278.9	−0.623831
$730$	68966.8	3.49668
$731$	−35135.5	−1.77775
$732$	39510.7	1.99502
$733$	16544.9	0.833696	0.416848	−	0.908976i	$-0.363135\pi$
$733$	16544.9	0.833696	0.416848	+	0.908976i	$0.363135\pi$
$734$	42277.6	2.12602
$735$	20283.8	1.01793
$736$	−3194.15	−0.159970
$737$	0	0
$738$	39132.9	1.95190
$739$	17935.5	0.892785	0.446392	−	0.894837i	$-0.352709\pi$
$739$	17935.5	0.892785	0.446392	+	0.894837i	$0.352709\pi$
$740$	−15075.4	−0.748895
$741$	−8721.69	−0.432388
$742$	−110.998	−0.00549171
$743$	12184.7	0.601633	0.300817	−	0.953682i	$-0.402741\pi$
$743$	12184.7	0.601633	0.300817	+	0.953682i	$0.402741\pi$
$744$	−17605.7	−0.867547
$745$	18584.0	0.913913
$746$	1754.89	0.0861276
$747$	8305.88	0.406822
$748$	0	0
$749$	−10785.8	−0.526174
$750$	−22831.9	−1.11160
$751$	30391.5	1.47670	0.738350	−	0.674418i	$-0.235605\pi$
$751$	30391.5	1.47670	0.738350	+	0.674418i	$0.235605\pi$
$752$	4918.58	0.238513
$753$	19521.7	0.944770
$754$	−4156.92	−0.200777
$755$	29248.6	1.40989
$756$	46375.0	2.23101
$757$	−4531.98	−0.217592	−0.108796	−	0.994064i	$-0.534700\pi$
$757$	−4531.98	−0.217592	−0.108796	+	0.994064i	$0.534700\pi$
$758$	−37105.7	−1.77802
$759$	0	0
$760$	−20295.3	−0.968667
$761$	−29029.1	−1.38279	−0.691397	−	0.722475i	$-0.743004\pi$
$761$	−29029.1	−1.38279	−0.691397	+	0.722475i	$0.743004\pi$
$762$	−90974.1	−4.32499
$763$	3609.82	0.171277
$764$	−5481.29	−0.259563
$765$	109084.	5.15549
$766$	19476.8	0.918702
$767$	11345.1	0.534093
$768$	25197.2	1.18389
$769$	−20609.2	−0.966433	−0.483216	−	0.875501i	$-0.660532\pi$
$769$	−20609.2	−0.966433	−0.483216	+	0.875501i	$0.660532\pi$
$770$	0	0
$771$	25138.1	1.17423
$772$	59400.0	2.76924
$773$	−2717.83	−0.126460	−0.0632300	−	0.997999i	$-0.520140\pi$
$773$	−2717.83	−0.126460	−0.0632300	+	0.997999i	$0.520140\pi$
$774$	68397.3	3.17634
$775$	−8775.61	−0.406747
$776$	13780.3	0.637478
$777$	−10717.1	−0.494819
$778$	66588.3	3.06852
$779$	−11187.1	−0.514530
$780$	−21211.4	−0.973706
$781$	0	0
$782$	9119.68	0.417032
$783$	−19504.4	−0.890203
$784$	1859.13	0.0846906
$785$	−3849.54	−0.175027
$786$	−27349.1	−1.24111
$787$	−21073.9	−0.954516	−0.477258	−	0.878763i	$-0.658369\pi$
$787$	−21073.9	−0.954516	−0.477258	+	0.878763i	$0.658369\pi$
$788$	−6363.72	−0.287688
$789$	21744.5	0.981145
$790$	−82052.4	−3.69531
$791$	−14670.9	−0.659466
$792$	0	0
$793$	−4582.93	−0.205227
$794$	−16843.9	−0.752854
$795$	238.210	0.0106270
$796$	10925.5	0.486488
$797$	37171.7	1.65206	0.826028	−	0.563629i	$-0.190595\pi$
$797$	37171.7	1.65206	0.826028	+	0.563629i	$0.190595\pi$
$798$	−41698.6	−1.84977
$799$	−52937.1	−2.34391
$800$	18023.5	0.796533
$801$	51911.1	2.28987
$802$	27158.6	1.19577
$803$	0	0
$804$	84466.4	3.70510
$805$	3099.67	0.135713
$806$	5901.99	0.257926
$807$	18901.3	0.824484
$808$	−22333.1	−0.972372
$809$	25691.5	1.11652	0.558260	−	0.829666i	$-0.311469\pi$
$809$	25691.5	1.11652	0.558260	+	0.829666i	$0.311469\pi$
$810$	−63929.3	−2.77314
$811$	−12815.5	−0.554887	−0.277443	−	0.960742i	$-0.589487\pi$
$811$	−12815.5	−0.554887	−0.277443	+	0.960742i	$0.589487\pi$
$812$	−12015.9	−0.519306
$813$	18964.4	0.818095
$814$	0	0
$815$	−27739.7	−1.19224
$816$	14738.7	0.632301
$817$	−19553.0	−0.837299
$818$	9536.08	0.407605
$819$	−10229.2	−0.436430
$820$	−27207.4	−1.15869
$821$	−17356.1	−0.737798	−0.368899	−	0.929470i	$-0.620265\pi$
$821$	−17356.1	−0.737798	−0.368899	+	0.929470i	$0.620265\pi$
$822$	−12165.0	−0.516182
$823$	44306.2	1.87657	0.938285	−	0.345862i	$-0.112414\pi$
$823$	44306.2	1.87657	0.938285	+	0.345862i	$0.112414\pi$
$824$	1754.11	0.0741593
$825$	0	0
$826$	54241.3	2.28486
$827$	28124.9	1.18259	0.591294	−	0.806456i	$-0.298617\pi$
$827$	28124.9	1.18259	0.591294	+	0.806456i	$0.298617\pi$
$828$	−10733.4	−0.450498
$829$	3461.97	0.145041	0.0725207	−	0.997367i	$-0.476896\pi$
$829$	3461.97	0.145041	0.0725207	+	0.997367i	$0.476896\pi$
$830$	−9551.33	−0.399436
$831$	12752.0	0.532323
$832$	−10850.1	−0.452117
$833$	−20009.2	−0.832267
$834$	11263.5	0.467652
$835$	−23736.6	−0.983757
$836$	0	0
$837$	27692.3	1.14359
$838$	−37790.5	−1.55782
$839$	35400.4	1.45668	0.728341	−	0.685215i	$-0.240292\pi$
$839$	35400.4	1.45668	0.728341	+	0.685215i	$0.240292\pi$
$840$	−35089.2	−1.44130
$841$	−19335.3	−0.792790
$842$	−23396.1	−0.957579
$843$	2974.59	0.121531
$844$	−53694.4	−2.18985
$845$	2460.36	0.100164
$846$	103051.	4.18791
$847$	0	0
$848$	21.8333	0.000884150 0
$849$	−64506.3	−2.60760
$850$	−51459.2	−2.07651
$851$	1304.38	0.0525424
$852$	126259.	5.07697
$853$	31096.6	1.24822	0.624108	−	0.781338i	$-0.285462\pi$
$853$	31096.6	1.24822	0.624108	+	0.781338i	$0.285462\pi$
$854$	−21911.1	−0.877965
$855$	60705.7	2.42818
$856$	−14860.6	−0.593372
$857$	−33754.0	−1.34541	−0.672704	−	0.739911i	$-0.734867\pi$
$857$	−33754.0	−1.34541	−0.672704	+	0.739911i	$0.734867\pi$
$858$	0	0
$859$	−20294.9	−0.806115	−0.403058	−	0.915175i	$-0.632053\pi$
$859$	−20294.9	−0.806115	−0.403058	+	0.915175i	$0.632053\pi$
$860$	−47553.6	−1.88554
$861$	−19341.7	−0.765580
$862$	−48104.1	−1.90073
$863$	18702.5	0.737707	0.368853	−	0.929488i	$-0.379750\pi$
$863$	18702.5	0.737707	0.368853	+	0.929488i	$0.379750\pi$
$864$	−56874.9	−2.23949
$865$	362.402	0.0142451
$866$	−54319.6	−2.13147
$867$	−113614.	−4.45046
$868$	17060.2	0.667122
$869$	0	0
$870$	42651.9	1.66211
$871$	−9797.44	−0.381141
$872$	4973.60	0.193151
$873$	−41218.5	−1.59798
$874$	5075.14	0.196418
$875$	7655.20	0.295764
$876$	118037.	4.55262
$877$	−10186.5	−0.392215	−0.196107	−	0.980582i	$-0.562830\pi$
$877$	−10186.5	−0.392215	−0.196107	+	0.980582i	$0.562830\pi$
$878$	23745.5	0.912724
$879$	57590.7	2.20988
$880$	0	0
$881$	1038.26	0.0397046	0.0198523	−	0.999803i	$-0.493680\pi$
$881$	1038.26	0.0397046	0.0198523	+	0.999803i	$0.493680\pi$
$882$	38951.4	1.48703
$883$	−7020.33	−0.267557	−0.133779	−	0.991011i	$-0.542711\pi$
$883$	−7020.33	−0.267557	−0.133779	+	0.991011i	$0.542711\pi$
$884$	20924.3	0.796108
$885$	−116406.	−4.42142
$886$	52558.0	1.99291
$887$	32677.0	1.23696	0.618481	−	0.785800i	$-0.287749\pi$
$887$	32677.0	1.23696	0.618481	+	0.785800i	$0.287749\pi$
$888$	−14766.0	−0.558012
$889$	30502.3	1.15075
$890$	−59695.1	−2.24830
$891$	0	0
$892$	−64026.7	−2.40333
$893$	−29459.7	−1.10395
$894$	52607.9	1.96809
$895$	−14136.8	−0.527978
$896$	−28959.7	−1.07977
$897$	1835.29	0.0683152
$898$	−77015.5	−2.86196
$899$	−7175.18	−0.266191
$900$	60565.0	2.24315
$901$	−234.985	−0.00868867
$902$	0	0
$903$	−33805.9	−1.24584
$904$	−20213.5	−0.743686
$905$	11399.7	0.418715
$906$	82797.4	3.03616
$907$	17910.7	0.655693	0.327847	−	0.944731i	$-0.393677\pi$
$907$	17910.7	0.655693	0.327847	+	0.944731i	$0.393677\pi$
$908$	5508.88	0.201342
$909$	66801.2	2.43747
$910$	11763.0	0.428506
$911$	24889.9	0.905202	0.452601	−	0.891713i	$-0.350496\pi$
$911$	24889.9	0.905202	0.452601	+	0.891713i	$0.350496\pi$
$912$	8202.14	0.297807
$913$	0	0
$914$	63051.2	2.28178
$915$	47023.0	1.69894
$916$	71525.1	2.57997
$917$	9169.78	0.330221
$918$	162385.	5.83822
$919$	−33938.8	−1.21821	−0.609107	−	0.793088i	$-0.708472\pi$
$919$	−33938.8	−1.21821	−0.609107	+	0.793088i	$0.708472\pi$
$920$	4270.71	0.153045
$921$	40655.0	1.45454
$922$	2805.39	0.100207
$923$	−14645.1	−0.522264
$924$	0	0
$925$	−7360.17	−0.261622
$926$	40870.9	1.45043
$927$	−5246.76	−0.185897
$928$	14736.5	0.521282
$929$	20247.8	0.715080	0.357540	−	0.933898i	$-0.383616\pi$
$929$	20247.8	0.715080	0.357540	+	0.933898i	$0.383616\pi$
$930$	−60557.2	−2.13521
$931$	−11135.2	−0.391989
$932$	5320.59	0.186998
$933$	40465.9	1.41993
$934$	19267.5	0.675003
$935$	0	0
$936$	−14093.7	−0.492167
$937$	35599.3	1.24117	0.620586	−	0.784138i	$-0.286895\pi$
$937$	35599.3	1.24117	0.620586	+	0.784138i	$0.286895\pi$
$938$	−46841.8	−1.63053
$939$	49313.5	1.71383
$940$	−71646.9	−2.48603
$941$	3327.43	0.115272	0.0576361	−	0.998338i	$-0.481644\pi$
$941$	3327.43	0.115272	0.0576361	+	0.998338i	$0.481644\pi$
$942$	−10897.3	−0.376915
$943$	2354.08	0.0812933
$944$	−10669.3	−0.367856
$945$	55192.5	1.89991
$946$	0	0
$947$	−27339.6	−0.938139	−0.469069	−	0.883161i	$-0.655411\pi$
$947$	−27339.6	−0.938139	−0.469069	+	0.883161i	$0.655411\pi$
$948$	−140433.	−4.81123
$949$	−13691.3	−0.468324
$950$	−28637.2	−0.978015
$951$	28216.2	0.962116
$952$	34614.2	1.17842
$953$	−17025.4	−0.578707	−0.289353	−	0.957222i	$-0.593440\pi$
$953$	−17025.4	−0.578707	−0.289353	+	0.957222i	$0.593440\pi$
$954$	457.439	0.0155243
$955$	−6523.47	−0.221041
$956$	32543.1	1.10096
$957$	0	0
$958$	−20371.6	−0.687032
$959$	4078.74	0.137340
$960$	111328.	3.74279
$961$	−19603.7	−0.658040
$962$	4950.04	0.165900
$963$	44450.0	1.48742
$964$	−75599.6	−2.52583
$965$	70694.0	2.35826
$966$	8774.58	0.292254
$967$	−2390.22	−0.0794875	−0.0397438	−	0.999210i	$-0.512654\pi$
$967$	−2390.22	−0.0794875	−0.0397438	+	0.999210i	$0.512654\pi$
$968$	0	0
$969$	−88277.1	−2.92659
$970$	47399.1	1.56896
$971$	−5143.97	−0.170008	−0.0850040	−	0.996381i	$-0.527090\pi$
$971$	−5143.97	−0.170008	−0.0850040	+	0.996381i	$0.527090\pi$
$972$	−18798.4	−0.620327
$973$	−3776.48	−0.124428
$974$	−31768.6	−1.04510
$975$	−10355.9	−0.340159
$976$	4309.93	0.141350
$977$	−787.351	−0.0257826	−0.0128913	−	0.999917i	$-0.504104\pi$
$977$	−787.351	−0.0257826	−0.0128913	+	0.999917i	$0.504104\pi$
$978$	−78525.9	−2.56747
$979$	0	0
$980$	−27081.2	−0.882731
$981$	−14876.7	−0.484175
$982$	−30418.1	−0.988474
$983$	−37452.1	−1.21520	−0.607598	−	0.794245i	$-0.707867\pi$
$983$	−37452.1	−1.21520	−0.607598	+	0.794245i	$0.707867\pi$
$984$	−26649.0	−0.863353
$985$	−7573.68	−0.244992
$986$	−42074.5	−1.35895
$987$	−50933.9	−1.64260
$988$	11644.4	0.374958
$989$	4114.52	0.132289
$990$	0	0
$991$	−30406.8	−0.974677	−0.487338	−	0.873213i	$-0.662032\pi$
$991$	−30406.8	−0.974677	−0.487338	+	0.873213i	$0.662032\pi$
$992$	−20922.9	−0.669660
$993$	−37637.7	−1.20282
$994$	−70018.6	−2.23426
$995$	13002.8	0.414289
$996$	−16347.1	−0.520059
$997$	−31247.5	−0.992596	−0.496298	−	0.868152i	$-0.665308\pi$
$997$	−31247.5	−0.992596	−0.496298	+	0.868152i	$0.665308\pi$
$998$	−8935.32	−0.283409
$999$	23225.7	0.735565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.o.1.3		34
11.3	even	5		143.4.h.a.53.2	yes	68
11.4	even	5		143.4.h.a.27.2	✓	68
11.10	odd	2		1573.4.a.p.1.32		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.2	✓	68	11.4	even	5
143.4.h.a.53.2	yes	68	11.3	even	5
1573.4.a.o.1.3		34	1.1	even	1	trivial
1573.4.a.p.1.32		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)

\(f(q)\)	\(=\)	\(q-4.49806 q^{2} -9.16217 q^{3} +12.2325 q^{4} +14.5583 q^{5} +41.2120 q^{6} -13.8178 q^{7} -19.0381 q^{8} +56.9454 q^{9} +O(q^{10})\)	\(q-4.49806 q^{2} -9.16217 q^{3} +12.2325 q^{4} +14.5583 q^{5} +41.2120 q^{6} -13.8178 q^{7} -19.0381 q^{8} +56.9454 q^{9} -65.4843 q^{10} -112.076 q^{12} +13.0000 q^{13} +62.1532 q^{14} -133.386 q^{15} -12.2256 q^{16} +131.580 q^{17} -256.144 q^{18} +73.2249 q^{19} +178.085 q^{20} +126.601 q^{21} -15.4086 q^{23} +174.431 q^{24} +86.9455 q^{25} -58.4747 q^{26} -274.365 q^{27} -169.026 q^{28} +71.0891 q^{29} +599.978 q^{30} -100.932 q^{31} +207.296 q^{32} -591.856 q^{34} -201.164 q^{35} +696.586 q^{36} -84.6526 q^{37} -329.370 q^{38} -119.108 q^{39} -277.164 q^{40} -152.777 q^{41} -569.459 q^{42} -267.027 q^{43} +829.031 q^{45} +69.3089 q^{46} -402.318 q^{47} +112.013 q^{48} -152.069 q^{49} -391.086 q^{50} -1205.56 q^{51} +159.023 q^{52} -1.78587 q^{53} +1234.11 q^{54} +263.065 q^{56} -670.899 q^{57} -319.763 q^{58} +872.703 q^{59} -1631.65 q^{60} -352.533 q^{61} +453.999 q^{62} -786.860 q^{63} -834.626 q^{64} +189.259 q^{65} -753.649 q^{67} +1609.56 q^{68} +141.177 q^{69} +904.849 q^{70} -1126.55 q^{71} -1084.13 q^{72} -1053.18 q^{73} +380.772 q^{74} -796.610 q^{75} +895.725 q^{76} +535.756 q^{78} +1253.01 q^{79} -177.984 q^{80} +976.254 q^{81} +687.200 q^{82} +145.857 q^{83} +1548.65 q^{84} +1915.59 q^{85} +1201.10 q^{86} -651.330 q^{87} +911.594 q^{89} -3729.03 q^{90} -179.631 q^{91} -188.486 q^{92} +924.759 q^{93} +1809.65 q^{94} +1066.03 q^{95} -1899.29 q^{96} -723.825 q^{97} +684.013 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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