LMFDB - Embedded newform 1573.4.a.o.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$92.8100044390$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74116 q^{2} +6.45484 q^{3} -0.486036 q^{4} +6.42298 q^{5} -17.6937 q^{6} +11.8479 q^{7} +23.2616 q^{8} +14.6649 q^{9} +O(q^{10})$	\(q-2.74116 q^{2} +6.45484 q^{3} -0.486036 q^{4} +6.42298 q^{5} -17.6937 q^{6} +11.8479 q^{7} +23.2616 q^{8} +14.6649 q^{9} -17.6064 q^{10} -3.13728 q^{12} +13.0000 q^{13} -32.4769 q^{14} +41.4593 q^{15} -59.8755 q^{16} +28.8944 q^{17} -40.1989 q^{18} -126.470 q^{19} -3.12180 q^{20} +76.4760 q^{21} -8.23121 q^{23} +150.150 q^{24} -83.7453 q^{25} -35.6351 q^{26} -79.6209 q^{27} -5.75849 q^{28} +174.077 q^{29} -113.647 q^{30} -247.562 q^{31} -21.9644 q^{32} -79.2042 q^{34} +76.0986 q^{35} -7.12768 q^{36} -238.942 q^{37} +346.676 q^{38} +83.9129 q^{39} +149.409 q^{40} -178.576 q^{41} -209.633 q^{42} -336.857 q^{43} +94.1925 q^{45} +22.5631 q^{46} +257.326 q^{47} -386.487 q^{48} -202.628 q^{49} +229.559 q^{50} +186.509 q^{51} -6.31846 q^{52} -688.666 q^{53} +218.254 q^{54} +275.600 q^{56} -816.346 q^{57} -477.172 q^{58} +399.431 q^{59} -20.1507 q^{60} +26.9793 q^{61} +678.607 q^{62} +173.748 q^{63} +539.212 q^{64} +83.4987 q^{65} -767.765 q^{67} -14.0437 q^{68} -53.1311 q^{69} -208.599 q^{70} -335.419 q^{71} +341.129 q^{72} +791.129 q^{73} +654.978 q^{74} -540.563 q^{75} +61.4691 q^{76} -230.019 q^{78} -708.443 q^{79} -384.579 q^{80} -909.893 q^{81} +489.506 q^{82} +821.370 q^{83} -37.1701 q^{84} +185.588 q^{85} +923.379 q^{86} +1123.64 q^{87} +44.1841 q^{89} -258.197 q^{90} +154.022 q^{91} +4.00066 q^{92} -1597.97 q^{93} -705.373 q^{94} -812.317 q^{95} -141.777 q^{96} -886.256 q^{97} +555.436 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.74116	−0.969147	−0.484573	−	0.874751i	$-0.661025\pi$
$2$	−2.74116	−0.969147	−0.484573	+	0.874751i	$0.661025\pi$
$3$	6.45484	1.24223	0.621117	−	0.783718i	$-0.286679\pi$
$3$	6.45484	1.24223	0.621117	+	0.783718i	$0.286679\pi$
$4$	−0.486036	−0.0607545
$5$	6.42298	0.574489	0.287244	−	0.957857i	$-0.407261\pi$
$5$	6.42298	0.574489	0.287244	+	0.957857i	$0.407261\pi$
$6$	−17.6937	−1.20391
$7$	11.8479	0.639725	0.319862	−	0.947464i	$-0.396363\pi$
$7$	11.8479	0.639725	0.319862	+	0.947464i	$0.396363\pi$
$8$	23.2616	1.02803
$9$	14.6649	0.543145
$10$	−17.6064	−0.556764
$11$	0	0
$11$	0	0
$12$	−3.13728	−0.0754713
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−32.4769	−0.619987
$15$	41.4593	0.713649
$16$	−59.8755	−0.935554
$17$	28.8944	0.412231	0.206115	−	0.978528i	$-0.433918\pi$
$17$	28.8944	0.412231	0.206115	+	0.978528i	$0.433918\pi$
$18$	−40.1989	−0.526388
$19$	−126.470	−1.52707	−0.763534	−	0.645767i	$-0.776538\pi$
$19$	−126.470	−1.52707	−0.763534	+	0.645767i	$0.776538\pi$
$20$	−3.12180	−0.0349028
$21$	76.4760	0.794688
$22$	0	0
$23$	−8.23121	−0.0746228	−0.0373114	−	0.999304i	$-0.511879\pi$
$23$	−8.23121	−0.0746228	−0.0373114	+	0.999304i	$0.511879\pi$
$24$	150.150	1.27705
$25$	−83.7453	−0.669963
$26$	−35.6351	−0.268793
$27$	−79.6209	−0.567520
$28$	−5.75849	−0.0388661
$29$	174.077	1.11466	0.557331	−	0.830290i	$-0.311825\pi$
$29$	174.077	1.11466	0.557331	+	0.830290i	$0.311825\pi$
$30$	−113.647	−0.691631
$31$	−247.562	−1.43430	−0.717152	−	0.696916i	$-0.754555\pi$
$31$	−247.562	−1.43430	−0.717152	+	0.696916i	$0.754555\pi$
$32$	−21.9644	−0.121337
$33$	0	0
$34$	−79.2042	−0.399512
$35$	76.0986	0.367515
$36$	−7.12768	−0.0329985
$37$	−238.942	−1.06167	−0.530835	−	0.847475i	$-0.678122\pi$
$37$	−238.942	−1.06167	−0.530835	+	0.847475i	$0.678122\pi$
$38$	346.676	1.47995
$39$	83.9129	0.344534
$40$	149.409	0.590590
$41$	−178.576	−0.680217	−0.340109	−	0.940386i	$-0.610464\pi$
$41$	−178.576	−0.680217	−0.340109	+	0.940386i	$0.610464\pi$
$42$	−209.633	−0.770169
$43$	−336.857	−1.19466	−0.597328	−	0.801997i	$-0.703771\pi$
$43$	−336.857	−1.19466	−0.597328	+	0.801997i	$0.703771\pi$
$44$	0	0
$45$	94.1925	0.312031
$46$	22.5631	0.0723205
$47$	257.326	0.798615	0.399307	−	0.916817i	$-0.369251\pi$
$47$	257.326	0.798615	0.399307	+	0.916817i	$0.369251\pi$
$48$	−386.487	−1.16218
$49$	−202.628	−0.590752
$50$	229.559	0.649292
$51$	186.509	0.512087
$52$	−6.31846	−0.0168503
$53$	−688.666	−1.78482	−0.892411	−	0.451224i	$-0.850988\pi$
$53$	−688.666	−1.78482	−0.892411	+	0.451224i	$0.850988\pi$
$54$	218.254	0.550011
$55$	0	0
$56$	275.600	0.657654
$57$	−816.346	−1.89698
$58$	−477.172	−1.08027
$59$	399.431	0.881382	0.440691	−	0.897659i	$-0.354733\pi$
$59$	399.431	0.881382	0.440691	+	0.897659i	$0.354733\pi$
$60$	−20.1507	−0.0433574
$61$	26.9793	0.0566286	0.0283143	−	0.999599i	$-0.490986\pi$
$61$	26.9793	0.0566286	0.0283143	+	0.999599i	$0.490986\pi$
$62$	678.607	1.39005
$63$	173.748	0.347463
$64$	539.212	1.05315
$65$	83.4987	0.159334
$66$	0	0
$67$	−767.765	−1.39996	−0.699981	−	0.714161i	$-0.746808\pi$
$67$	−767.765	−1.39996	−0.699981	+	0.714161i	$0.746808\pi$
$68$	−14.0437	−0.0250449
$69$	−53.1311	−0.0926990
$70$	−208.599	−0.356176
$71$	−335.419	−0.560661	−0.280330	−	0.959904i	$-0.590444\pi$
$71$	−335.419	−0.560661	−0.280330	+	0.959904i	$0.590444\pi$
$72$	341.129	0.558368
$73$	791.129	1.26842	0.634210	−	0.773161i	$-0.281326\pi$
$73$	791.129	1.26842	0.634210	+	0.773161i	$0.281326\pi$
$74$	654.978	1.02891
$75$	−540.563	−0.832251
$76$	61.4691	0.0927762
$77$	0	0
$78$	−230.019	−0.333904
$79$	−708.443	−1.00894	−0.504469	−	0.863430i	$-0.668312\pi$
$79$	−708.443	−1.00894	−0.504469	+	0.863430i	$0.668312\pi$
$80$	−384.579	−0.537465
$81$	−909.893	−1.24814
$82$	489.506	0.659230
$83$	821.370	1.08623	0.543115	−	0.839658i	$-0.317245\pi$
$83$	821.370	1.08623	0.543115	+	0.839658i	$0.317245\pi$
$84$	−37.1701	−0.0482808
$85$	185.588	0.236822
$86$	923.379	1.15780
$87$	1123.64	1.38467
$88$	0	0
$89$	44.1841	0.0526237	0.0263118	−	0.999654i	$-0.491624\pi$
$89$	44.1841	0.0526237	0.0263118	+	0.999654i	$0.491624\pi$
$90$	−258.197	−0.302404
$91$	154.022	0.177428
$92$	4.00066	0.00453367
$93$	−1597.97	−1.78174
$94$	−705.373	−0.773975
$95$	−812.317	−0.877284
$96$	−141.777	−0.150729
$97$	−886.256	−0.927687	−0.463844	−	0.885917i	$-0.653530\pi$
$97$	−886.256	−0.927687	−0.463844	+	0.885917i	$0.653530\pi$
$98$	555.436	0.572526
$99$	0	0
$100$	40.7032	0.0407032
$101$	−153.088	−0.150820	−0.0754099	−	0.997153i	$-0.524027\pi$
$101$	−153.088	−0.150820	−0.0754099	+	0.997153i	$0.524027\pi$
$102$	−511.250	−0.496288
$103$	477.777	0.457056	0.228528	−	0.973537i	$-0.426609\pi$
$103$	477.777	0.457056	0.228528	+	0.973537i	$0.426609\pi$
$104$	302.401	0.285123
$105$	491.204	0.456539
$106$	1887.74	1.72975
$107$	779.559	0.704326	0.352163	−	0.935939i	$-0.385446\pi$
$107$	779.559	0.704326	0.352163	+	0.935939i	$0.385446\pi$
$108$	38.6986	0.0344794
$109$	1344.92	1.18184	0.590918	−	0.806731i	$-0.298766\pi$
$109$	1344.92	1.18184	0.590918	+	0.806731i	$0.298766\pi$
$110$	0	0
$111$	−1542.33	−1.31884
$112$	−709.397	−0.598497
$113$	265.242	0.220813	0.110406	−	0.993887i	$-0.464785\pi$
$113$	265.242	0.220813	0.110406	+	0.993887i	$0.464785\pi$
$114$	2237.74	1.83845
$115$	−52.8689	−0.0428700
$116$	−84.6074	−0.0677207
$117$	190.644	0.150641
$118$	−1094.91	−0.854189
$119$	342.337	0.263714
$120$	964.409	0.733651
$121$	0	0
$122$	−73.9546	−0.0548814
$123$	−1152.68	−0.844989
$124$	120.324	0.0871404
$125$	−1340.77	−0.959375
$126$	−476.271	−0.336743
$127$	−2710.62	−1.89392	−0.946962	−	0.321344i	$-0.895865\pi$
$127$	−2710.62	−1.89392	−0.946962	+	0.321344i	$0.895865\pi$
$128$	−1302.35	−0.899318
$129$	−2174.36	−1.48404
$130$	−228.883	−0.154419
$131$	−146.682	−0.0978293	−0.0489147	−	0.998803i	$-0.515576\pi$
$131$	−146.682	−0.0978293	−0.0489147	+	0.998803i	$0.515576\pi$
$132$	0	0
$133$	−1498.40	−0.976903
$134$	2104.57	1.35677
$135$	−511.403	−0.326034
$136$	672.130	0.423784
$137$	1020.60	0.636462	0.318231	−	0.948013i	$-0.396911\pi$
$137$	1020.60	0.636462	0.318231	+	0.948013i	$0.396911\pi$
$138$	145.641	0.0898390
$139$	402.255	0.245459	0.122730	−	0.992440i	$-0.460835\pi$
$139$	402.255	0.245459	0.122730	+	0.992440i	$0.460835\pi$
$140$	−36.9866	−0.0223282
$141$	1661.00	0.992066
$142$	919.437	0.543363
$143$	0	0
$144$	−878.069	−0.508142
$145$	1118.09	0.640361
$146$	−2168.61	−1.22928
$147$	−1307.93	−0.733853
$148$	116.134	0.0645012
$149$	2209.84	1.21501	0.607507	−	0.794315i	$-0.292170\pi$
$149$	2209.84	1.21501	0.607507	+	0.794315i	$0.292170\pi$
$150$	1481.77	0.806573
$151$	−1940.88	−1.04600	−0.523001	−	0.852332i	$-0.675188\pi$
$151$	−1940.88	−1.04600	−0.523001	+	0.852332i	$0.675188\pi$
$152$	−2941.90	−1.56987
$153$	423.734	0.223901
$154$	0	0
$155$	−1590.09	−0.823992
$156$	−40.7847	−0.0209320
$157$	3068.67	1.55991	0.779957	−	0.625833i	$-0.215241\pi$
$157$	3068.67	1.55991	0.779957	+	0.625833i	$0.215241\pi$
$158$	1941.96	0.977809
$159$	−4445.23	−2.21717
$160$	−141.077	−0.0697069
$161$	−97.5222	−0.0477381
$162$	2494.16	1.20963
$163$	−1440.08	−0.691998	−0.345999	−	0.938235i	$-0.612460\pi$
$163$	−1440.08	−0.691998	−0.345999	+	0.938235i	$0.612460\pi$
$164$	86.7944	0.0413262
$165$	0	0
$166$	−2251.51	−1.05272
$167$	−2279.71	−1.05634	−0.528172	−	0.849137i	$-0.677123\pi$
$167$	−2279.71	−1.05634	−0.528172	+	0.849137i	$0.677123\pi$
$168$	1778.95	0.816960
$169$	169.000	0.0769231
$170$	−508.727	−0.229515
$171$	−1854.68	−0.829420
$172$	163.724	0.0725807
$173$	−1028.14	−0.451840	−0.225920	−	0.974146i	$-0.572539\pi$
$173$	−1028.14	−0.451840	−0.225920	+	0.974146i	$0.572539\pi$
$174$	−3080.07	−1.34195
$175$	−992.204	−0.428592
$176$	0	0
$177$	2578.27	1.09488
$178$	−121.116	−0.0510001
$179$	−560.960	−0.234235	−0.117118	−	0.993118i	$-0.537365\pi$
$179$	−560.960	−0.234235	−0.117118	+	0.993118i	$0.537365\pi$
$180$	−45.7809	−0.0189573
$181$	2102.75	0.863516	0.431758	−	0.901990i	$-0.357894\pi$
$181$	2102.75	0.863516	0.431758	+	0.901990i	$0.357894\pi$
$182$	−422.200	−0.171953
$183$	174.147	0.0703460
$184$	−191.471	−0.0767143
$185$	−1534.72	−0.609917
$186$	4380.30	1.72677
$187$	0	0
$188$	−125.070	−0.0485194
$189$	−943.338	−0.363057
$190$	2226.69	0.850217
$191$	3786.37	1.43441	0.717204	−	0.696863i	$-0.245421\pi$
$191$	3786.37	1.43441	0.717204	+	0.696863i	$0.245421\pi$
$192$	3480.52	1.30826
$193$	1599.14	0.596417	0.298209	−	0.954501i	$-0.403611\pi$
$193$	1599.14	0.596417	0.298209	+	0.954501i	$0.403611\pi$
$194$	2429.37	0.899065
$195$	538.971	0.197931
$196$	98.4845	0.0358908
$197$	3796.39	1.37300	0.686502	−	0.727128i	$-0.259145\pi$
$197$	3796.39	1.37300	0.686502	+	0.727128i	$0.259145\pi$
$198$	0	0
$199$	1968.49	0.701220	0.350610	−	0.936522i	$-0.385974\pi$
$199$	1968.49	0.701220	0.350610	+	0.936522i	$0.385974\pi$
$200$	−1948.05	−0.688740
$201$	−4955.80	−1.73908
$202$	419.638	0.146166
$203$	2062.44	0.713077
$204$	−90.6499	−0.0311116
$205$	−1146.99	−0.390777
$206$	−1309.66	−0.442954
$207$	−120.710	−0.0405310
$208$	−778.381	−0.259476
$209$	0	0
$210$	−1346.47	−0.442453
$211$	−935.411	−0.305196	−0.152598	−	0.988288i	$-0.548764\pi$
$211$	−935.411	−0.305196	−0.152598	+	0.988288i	$0.548764\pi$
$212$	334.716	0.108436
$213$	−2165.07	−0.696472
$214$	−2136.90	−0.682595
$215$	−2163.62	−0.686316
$216$	−1852.11	−0.583426
$217$	−2933.08	−0.917560
$218$	−3686.65	−1.14537
$219$	5106.61	1.57567
$220$	0	0
$221$	375.627	0.114332
$222$	4227.77	1.27815
$223$	3825.18	1.14867	0.574333	−	0.818622i	$-0.305261\pi$
$223$	3825.18	1.14867	0.574333	+	0.818622i	$0.305261\pi$
$224$	−260.231	−0.0776224
$225$	−1228.12	−0.363887
$226$	−727.070	−0.214000
$227$	−4391.43	−1.28401	−0.642004	−	0.766702i	$-0.721897\pi$
$227$	−4391.43	−1.28401	−0.642004	+	0.766702i	$0.721897\pi$
$228$	396.773	0.115250
$229$	−4398.63	−1.26930	−0.634650	−	0.772800i	$-0.718856\pi$
$229$	−4398.63	−1.26930	−0.634650	+	0.772800i	$0.718856\pi$
$230$	144.922	0.0415473
$231$	0	0
$232$	4049.30	1.14590
$233$	6718.90	1.88914	0.944570	−	0.328310i	$-0.106479\pi$
$233$	6718.90	1.88914	0.944570	+	0.328310i	$0.106479\pi$
$234$	−522.586	−0.145994
$235$	1652.80	0.458795
$236$	−194.138	−0.0535479
$237$	−4572.89	−1.25334
$238$	−938.401	−0.255578
$239$	−2793.52	−0.756057	−0.378029	−	0.925794i	$-0.623398\pi$
$239$	−2793.52	−0.756057	−0.378029	+	0.925794i	$0.623398\pi$
$240$	−2482.39	−0.667658
$241$	−1560.19	−0.417014	−0.208507	−	0.978021i	$-0.566860\pi$
$241$	−1560.19	−0.417014	−0.208507	+	0.978021i	$0.566860\pi$
$242$	0	0
$243$	−3723.45	−0.982960
$244$	−13.1129	−0.00344044
$245$	−1301.48	−0.339381
$246$	3159.68	0.818918
$247$	−1644.12	−0.423533
$248$	−5758.69	−1.47450
$249$	5301.81	1.34935
$250$	3675.26	0.929775
$251$	−3479.53	−0.875005	−0.437502	−	0.899217i	$-0.644137\pi$
$251$	−3479.53	−0.875005	−0.437502	+	0.899217i	$0.644137\pi$
$252$	−84.4478	−0.0211100
$253$	0	0
$254$	7430.24	1.83549
$255$	1197.94	0.294188
$256$	−743.739	−0.181577
$257$	3947.32	0.958083	0.479041	−	0.877792i	$-0.340984\pi$
$257$	3947.32	0.958083	0.479041	+	0.877792i	$0.340984\pi$
$258$	5960.26	1.43825
$259$	−2830.95	−0.679176
$260$	−40.5834	−0.00968028
$261$	2552.82	0.605424
$262$	402.078	0.0948110
$263$	−4529.13	−1.06189	−0.530947	−	0.847405i	$-0.678164\pi$
$263$	−4529.13	−1.06189	−0.530947	+	0.847405i	$0.678164\pi$
$264$	0	0
$265$	−4423.29	−1.02536
$266$	4107.37	0.946763
$267$	285.201	0.0653709
$268$	373.161	0.0850540
$269$	−1892.61	−0.428975	−0.214488	−	0.976727i	$-0.568808\pi$
$269$	−1892.61	−0.428975	−0.214488	+	0.976727i	$0.568808\pi$
$270$	1401.84	0.315975
$271$	2314.70	0.518848	0.259424	−	0.965763i	$-0.416467\pi$
$271$	2314.70	0.518848	0.259424	+	0.965763i	$0.416467\pi$
$272$	−1730.07	−0.385664
$273$	994.189	0.220407
$274$	−2797.62	−0.616825
$275$	0	0
$276$	25.8236	0.00563188
$277$	−1677.72	−0.363915	−0.181958	−	0.983306i	$-0.558243\pi$
$277$	−1677.72	−0.363915	−0.181958	+	0.983306i	$0.558243\pi$
$278$	−1102.65	−0.237886
$279$	−3630.48	−0.779036
$280$	1770.17	0.377815
$281$	−1018.89	−0.216306	−0.108153	−	0.994134i	$-0.534494\pi$
$281$	−1018.89	−0.216306	−0.108153	+	0.994134i	$0.534494\pi$
$282$	−4553.07	−0.961458
$283$	729.505	0.153232	0.0766159	−	0.997061i	$-0.475588\pi$
$283$	729.505	0.153232	0.0766159	+	0.997061i	$0.475588\pi$
$284$	163.026	0.0340626
$285$	−5243.37	−1.08979
$286$	0	0
$287$	−2115.75	−0.435152
$288$	−322.106	−0.0659037
$289$	−4078.11	−0.830066
$290$	−3064.86	−0.620604
$291$	−5720.64	−1.15240
$292$	−384.517	−0.0770622
$293$	1800.83	0.359064	0.179532	−	0.983752i	$-0.442542\pi$
$293$	1800.83	0.359064	0.179532	+	0.983752i	$0.442542\pi$
$294$	3585.25	0.711211
$295$	2565.54	0.506344
$296$	−5558.16	−1.09142
$297$	0	0
$298$	−6057.52	−1.17753
$299$	−107.006	−0.0206967
$300$	262.733	0.0505629
$301$	−3991.03	−0.764251
$302$	5320.25	1.01373
$303$	−988.156	−0.187353
$304$	7572.48	1.42866
$305$	173.287	0.0325325
$306$	−1161.52	−0.216993
$307$	9880.21	1.83679	0.918393	−	0.395669i	$-0.129487\pi$
$307$	9880.21	1.83679	0.918393	+	0.395669i	$0.129487\pi$
$308$	0	0
$309$	3083.97	0.567770
$310$	4358.68	0.798569
$311$	−1135.46	−0.207029	−0.103515	−	0.994628i	$-0.533009\pi$
$311$	−1135.46	−0.207029	−0.103515	+	0.994628i	$0.533009\pi$
$312$	1951.95	0.354190
$313$	−2421.26	−0.437246	−0.218623	−	0.975809i	$-0.570156\pi$
$313$	−2421.26	−0.437246	−0.218623	+	0.975809i	$0.570156\pi$
$314$	−8411.72	−1.51179
$315$	1115.98	0.199614
$316$	344.329	0.0612975
$317$	5840.36	1.03479	0.517393	−	0.855748i	$-0.326902\pi$
$317$	5840.36	1.03479	0.517393	+	0.855748i	$0.326902\pi$
$318$	12185.1	2.14876
$319$	0	0
$320$	3463.35	0.605022
$321$	5031.93	0.874937
$322$	267.324	0.0462652
$323$	−3654.29	−0.629505
$324$	442.240	0.0758300
$325$	−1088.69	−0.185814
$326$	3947.49	0.670648
$327$	8681.26	1.46812
$328$	−4153.96	−0.699281
$329$	3048.77	0.510893
$330$	0	0
$331$	−11721.9	−1.94651	−0.973255	−	0.229727i	$-0.926217\pi$
$331$	−11721.9	−1.94651	−0.973255	+	0.229727i	$0.926217\pi$
$332$	−399.215	−0.0659933
$333$	−3504.06	−0.576641
$334$	6249.06	1.02375
$335$	−4931.34	−0.804263
$336$	−4579.04	−0.743474
$337$	−5816.16	−0.940138	−0.470069	−	0.882630i	$-0.655771\pi$
$337$	−5816.16	−0.940138	−0.470069	+	0.882630i	$0.655771\pi$
$338$	−463.256	−0.0745498
$339$	1712.09	0.274301
$340$	−90.2025	−0.0143880
$341$	0	0
$342$	5083.97	0.803830
$343$	−6464.53	−1.01764
$344$	−7835.83	−1.22814
$345$	−341.260	−0.0532545
$346$	2818.31	0.437900
$347$	318.503	0.0492742	0.0246371	−	0.999696i	$-0.492157\pi$
$347$	318.503	0.0492742	0.0246371	+	0.999696i	$0.492157\pi$
$348$	−546.127	−0.0841250
$349$	−8472.72	−1.29952	−0.649762	−	0.760137i	$-0.725132\pi$
$349$	−8472.72	−1.29952	−0.649762	+	0.760137i	$0.725132\pi$
$350$	2719.79	0.415368
$351$	−1035.07	−0.157402
$352$	0	0
$353$	−6551.05	−0.987754	−0.493877	−	0.869532i	$-0.664421\pi$
$353$	−6551.05	−0.987754	−0.493877	+	0.869532i	$0.664421\pi$
$354$	−7067.44	−1.06110
$355$	−2154.39	−0.322093
$356$	−21.4751	−0.00319712
$357$	2209.73	0.327595
$358$	1537.68	0.227009
$359$	−8284.19	−1.21789	−0.608945	−	0.793212i	$-0.708407\pi$
$359$	−8284.19	−1.21789	−0.608945	+	0.793212i	$0.708407\pi$
$360$	2191.07	0.320776
$361$	9135.77	1.33194
$362$	−5763.98	−0.836873
$363$	0	0
$364$	−74.8603	−0.0107795
$365$	5081.40	0.728693
$366$	−477.365	−0.0681756
$367$	−10965.3	−1.55963	−0.779814	−	0.626011i	$-0.784686\pi$
$367$	−10965.3	−1.55963	−0.779814	+	0.626011i	$0.784686\pi$
$368$	492.847	0.0698137
$369$	−2618.81	−0.369457
$370$	4206.91	0.591099
$371$	−8159.22	−1.14179
$372$	776.672	0.108249
$373$	−149.528	−0.0207567	−0.0103784	−	0.999946i	$-0.503304\pi$
$373$	−149.528	−0.0207567	−0.0103784	+	0.999946i	$0.503304\pi$
$374$	0	0
$375$	−8654.43	−1.19177
$376$	5985.82	0.820997
$377$	2262.99	0.309152
$378$	2585.84	0.351855
$379$	12796.0	1.73426	0.867129	−	0.498083i	$-0.165963\pi$
$379$	12796.0	1.73426	0.867129	+	0.498083i	$0.165963\pi$
$380$	394.815	0.0532989
$381$	−17496.6	−2.35270
$382$	−10379.0	−1.39015
$383$	5275.81	0.703868	0.351934	−	0.936025i	$-0.385524\pi$
$383$	5275.81	0.703868	0.351934	+	0.936025i	$0.385524\pi$
$384$	−8406.47	−1.11716
$385$	0	0
$386$	−4383.50	−0.578016
$387$	−4939.98	−0.648872
$388$	430.752	0.0563611
$389$	−3870.70	−0.504505	−0.252252	−	0.967661i	$-0.581171\pi$
$389$	−3870.70	−0.504505	−0.252252	+	0.967661i	$0.581171\pi$
$390$	−1477.41	−0.191824
$391$	−237.836	−0.0307618
$392$	−4713.45	−0.607309
$393$	−946.807	−0.121527
$394$	−10406.5	−1.33064
$395$	−4550.32	−0.579624
$396$	0	0
$397$	−13053.5	−1.65021	−0.825107	−	0.564977i	$-0.808885\pi$
$397$	−13053.5	−1.65021	−0.825107	+	0.564977i	$0.808885\pi$
$398$	−5395.96	−0.679585
$399$	−9671.96	−1.21354
$400$	5014.29	0.626787
$401$	7487.14	0.932394	0.466197	−	0.884681i	$-0.345624\pi$
$401$	7487.14	0.932394	0.466197	+	0.884681i	$0.345624\pi$
$402$	13584.6	1.68542
$403$	−3218.31	−0.397805
$404$	74.4061	0.00916297
$405$	−5844.22	−0.717041
$406$	−5653.47	−0.691076
$407$	0	0
$408$	4338.49	0.526439
$409$	−12866.2	−1.55548	−0.777741	−	0.628585i	$-0.783635\pi$
$409$	−12866.2	−1.55548	−0.777741	+	0.628585i	$0.783635\pi$
$410$	3144.09	0.378720
$411$	6587.78	0.790635
$412$	−232.217	−0.0277682
$413$	4732.41	0.563842
$414$	330.886	0.0392805
$415$	5275.64	0.624027
$416$	−285.537	−0.0336529
$417$	2596.49	0.304918
$418$	0	0
$419$	−5102.25	−0.594896	−0.297448	−	0.954738i	$-0.596135\pi$
$419$	−5102.25	−0.594896	−0.297448	+	0.954738i	$0.596135\pi$
$420$	−238.743	−0.0277368
$421$	−11685.5	−1.35277	−0.676385	−	0.736549i	$-0.736454\pi$
$421$	−11685.5	−1.35277	−0.676385	+	0.736549i	$0.736454\pi$
$422$	2564.11	0.295780
$423$	3773.67	0.433764
$424$	−16019.5	−1.83484
$425$	−2419.77	−0.276179
$426$	5934.82	0.674983
$427$	319.647	0.0362267
$428$	−378.894	−0.0427909
$429$	0	0
$430$	5930.84	0.665141
$431$	−9740.02	−1.08854	−0.544269	−	0.838911i	$-0.683193\pi$
$431$	−9740.02	−1.08854	−0.544269	+	0.838911i	$0.683193\pi$
$432$	4767.34	0.530946
$433$	2235.01	0.248054	0.124027	−	0.992279i	$-0.460419\pi$
$433$	2235.01	0.248054	0.124027	+	0.992279i	$0.460419\pi$
$434$	8040.05	0.889251
$435$	7217.09	0.795478
$436$	−653.680	−0.0718019
$437$	1041.00	0.113954
$438$	−13998.0	−1.52706
$439$	−5942.10	−0.646016	−0.323008	−	0.946396i	$-0.604694\pi$
$439$	−5942.10	−0.646016	−0.323008	+	0.946396i	$0.604694\pi$
$440$	0	0
$441$	−2971.53	−0.320864
$442$	−1029.66	−0.110805
$443$	3674.40	0.394077	0.197039	−	0.980396i	$-0.436868\pi$
$443$	3674.40	0.394077	0.197039	+	0.980396i	$0.436868\pi$
$444$	749.627	0.0801255
$445$	283.794	0.0302317
$446$	−10485.4	−1.11323
$447$	14264.1	1.50933
$448$	6388.51	0.673725
$449$	−7109.28	−0.747233	−0.373616	−	0.927583i	$-0.621882\pi$
$449$	−7109.28	−0.747233	−0.373616	+	0.927583i	$0.621882\pi$
$450$	3366.47	0.352660
$451$	0	0
$452$	−128.917	−0.0134154
$453$	−12528.0	−1.29938
$454$	12037.6	1.24439
$455$	989.282	0.101930
$456$	−18989.5	−1.95014
$457$	1236.47	0.126564	0.0632818	−	0.997996i	$-0.479843\pi$
$457$	1236.47	0.126564	0.0632818	+	0.997996i	$0.479843\pi$
$458$	12057.4	1.23014
$459$	−2300.60	−0.233949
$460$	25.6962	0.00260454
$461$	−16234.6	−1.64018	−0.820090	−	0.572235i	$-0.806077\pi$
$461$	−16234.6	−1.64018	−0.820090	+	0.572235i	$0.806077\pi$
$462$	0	0
$463$	12760.1	1.28080	0.640400	−	0.768041i	$-0.278768\pi$
$463$	12760.1	1.28080	0.640400	+	0.768041i	$0.278768\pi$
$464$	−10422.9	−1.04283
$465$	−10263.7	−1.02359
$466$	−18417.6	−1.83085
$467$	4165.54	0.412758	0.206379	−	0.978472i	$-0.433832\pi$
$467$	4165.54	0.412758	0.206379	+	0.978472i	$0.433832\pi$
$468$	−92.6598	−0.00915214
$469$	−9096.38	−0.895590
$470$	−4530.59	−0.444640
$471$	19807.8	1.93778
$472$	9291.41	0.906085
$473$	0	0
$474$	12535.0	1.21467
$475$	10591.3	1.02308
$476$	−166.388	−0.0160218
$477$	−10099.2	−0.969418
$478$	7657.48	0.732730
$479$	4314.66	0.411570	0.205785	−	0.978597i	$-0.434025\pi$
$479$	4314.66	0.411570	0.205785	+	0.978597i	$0.434025\pi$
$480$	−910.628	−0.0865922
$481$	−3106.24	−0.294454
$482$	4276.72	0.404148
$483$	−629.490	−0.0593018
$484$	0	0
$485$	−5692.40	−0.532946
$486$	10206.6	0.952632
$487$	−10237.5	−0.952575	−0.476287	−	0.879290i	$-0.658018\pi$
$487$	−10237.5	−0.952575	−0.476287	+	0.879290i	$0.658018\pi$
$488$	627.581	0.0582157
$489$	−9295.48	−0.859624
$490$	3567.55	0.328910
$491$	14700.6	1.35118	0.675590	−	0.737278i	$-0.263889\pi$
$491$	14700.6	1.35118	0.675590	+	0.737278i	$0.263889\pi$
$492$	560.243	0.0513368
$493$	5029.84	0.459498
$494$	4506.79	0.410465
$495$	0	0
$496$	14822.9	1.34187
$497$	−3974.00	−0.358668
$498$	−14533.1	−1.30772
$499$	−9368.46	−0.840461	−0.420231	−	0.907417i	$-0.638051\pi$
$499$	−9368.46	−0.840461	−0.420231	+	0.907417i	$0.638051\pi$
$500$	651.661	0.0582863
$501$	−14715.2	−1.31223
$502$	9537.96	0.848008
$503$	−2328.19	−0.206379	−0.103190	−	0.994662i	$-0.532905\pi$
$503$	−2328.19	−0.206379	−0.103190	+	0.994662i	$0.532905\pi$
$504$	4041.66	0.357202
$505$	−983.279	−0.0866443
$506$	0	0
$507$	1090.87	0.0955565
$508$	1317.46	0.115064
$509$	12803.9	1.11498	0.557490	−	0.830184i	$-0.311764\pi$
$509$	12803.9	1.11498	0.557490	+	0.830184i	$0.311764\pi$
$510$	−3283.75	−0.285112
$511$	9373.19	0.811439
$512$	12457.5	1.07529
$513$	10069.7	0.866643
$514$	−10820.2	−0.928523
$515$	3068.75	0.262573
$516$	1056.81	0.0901622
$517$	0	0
$518$	7760.09	0.658221
$519$	−6636.51	−0.561292
$520$	1942.31	0.163800
$521$	−6553.55	−0.551087	−0.275544	−	0.961289i	$-0.588858\pi$
$521$	−6553.55	−0.551087	−0.275544	+	0.961289i	$0.588858\pi$
$522$	−6997.69	−0.586744
$523$	17975.9	1.50293	0.751465	−	0.659772i	$-0.229347\pi$
$523$	17975.9	1.50293	0.751465	+	0.659772i	$0.229347\pi$
$524$	71.2926	0.00594357
$525$	−6404.51	−0.532411
$526$	12415.1	1.02913
$527$	−7153.16	−0.591265
$528$	0	0
$529$	−12099.2	−0.994431
$530$	12124.9	0.993724
$531$	5857.63	0.478719
$532$	728.278	0.0593512
$533$	−2321.49	−0.188658
$534$	−781.783	−0.0633540
$535$	5007.09	0.404627
$536$	−17859.4	−1.43920
$537$	−3620.91	−0.290975
$538$	5187.95	0.415740
$539$	0	0
$540$	248.560	0.0198080
$541$	10913.5	0.867294	0.433647	−	0.901083i	$-0.357227\pi$
$541$	10913.5	0.867294	0.433647	+	0.901083i	$0.357227\pi$
$542$	−6344.96	−0.502840
$543$	13572.9	1.07269
$544$	−634.648	−0.0500189
$545$	8638.41	0.678952
$546$	−2725.23	−0.213606
$547$	17756.0	1.38792	0.693960	−	0.720013i	$-0.255864\pi$
$547$	17756.0	1.38792	0.693960	+	0.720013i	$0.255864\pi$
$548$	−496.046	−0.0386679
$549$	395.649	0.0307576
$550$	0	0
$551$	−22015.5	−1.70217
$552$	−1235.91	−0.0952971
$553$	−8393.54	−0.645443
$554$	4598.90	0.352687
$555$	−9906.35	−0.757660
$556$	−195.510	−0.0149127
$557$	5104.86	0.388330	0.194165	−	0.980969i	$-0.437800\pi$
$557$	5104.86	0.388330	0.194165	+	0.980969i	$0.437800\pi$
$558$	9951.73	0.755000
$559$	−4379.14	−0.331338
$560$	−4556.44	−0.343830
$561$	0	0
$562$	2792.95	0.209633
$563$	10312.2	0.771951	0.385976	−	0.922509i	$-0.373865\pi$
$563$	10312.2	0.771951	0.385976	+	0.922509i	$0.373865\pi$
$564$	−807.305	−0.0602725
$565$	1703.64	0.126854
$566$	−1999.69	−0.148504
$567$	−10780.3	−0.798465
$568$	−7802.38	−0.576374
$569$	25108.1	1.84989	0.924944	−	0.380103i	$-0.124111\pi$
$569$	25108.1	1.84989	0.924944	+	0.380103i	$0.124111\pi$
$570$	14372.9	1.05617
$571$	6657.00	0.487893	0.243947	−	0.969789i	$-0.421558\pi$
$571$	6657.00	0.487893	0.243947	+	0.969789i	$0.421558\pi$
$572$	0	0
$573$	24440.4	1.78187
$574$	5799.60	0.421726
$575$	689.325	0.0499945
$576$	7907.50	0.572012
$577$	16007.7	1.15495	0.577477	−	0.816407i	$-0.304037\pi$
$577$	16007.7	1.15495	0.577477	+	0.816407i	$0.304037\pi$
$578$	11178.8	0.804456
$579$	10322.2	0.740890
$580$	−543.432	−0.0389048
$581$	9731.48	0.694888
$582$	15681.2	1.11685
$583$	0	0
$584$	18402.9	1.30397
$585$	1224.50	0.0865418
$586$	−4936.38	−0.347986
$587$	−8868.71	−0.623596	−0.311798	−	0.950148i	$-0.600931\pi$
$587$	−8868.71	−0.623596	−0.311798	+	0.950148i	$0.600931\pi$
$588$	635.701	0.0445848
$589$	31309.3	2.19028
$590$	−7032.56	−0.490722
$591$	24505.1	1.70559
$592$	14306.7	0.993250
$593$	−14032.9	−0.971776	−0.485888	−	0.874021i	$-0.661504\pi$
$593$	−14032.9	−0.971776	−0.485888	+	0.874021i	$0.661504\pi$
$594$	0	0
$595$	2198.82	0.151501
$596$	−1074.06	−0.0738175
$597$	12706.3	0.871080
$598$	293.320	0.0200581
$599$	−700.332	−0.0477710	−0.0238855	−	0.999715i	$-0.507604\pi$
$599$	−700.332	−0.0477710	−0.0238855	+	0.999715i	$0.507604\pi$
$600$	−12574.3	−0.855576
$601$	7170.01	0.486641	0.243320	−	0.969946i	$-0.421763\pi$
$601$	7170.01	0.486641	0.243320	+	0.969946i	$0.421763\pi$
$602$	10940.1	0.740671
$603$	−11259.2	−0.760383
$604$	943.335	0.0635493
$605$	0	0
$606$	2708.70	0.181573
$607$	3601.91	0.240852	0.120426	−	0.992722i	$-0.461574\pi$
$607$	3601.91	0.240852	0.120426	+	0.992722i	$0.461574\pi$
$608$	2777.84	0.185290
$609$	13312.7	0.885808
$610$	−475.009	−0.0315288
$611$	3345.24	0.221496
$612$	−205.950	−0.0136030
$613$	−22733.0	−1.49784	−0.748920	−	0.662660i	$-0.769427\pi$
$613$	−22733.0	−1.49784	−0.748920	+	0.662660i	$0.769427\pi$
$614$	−27083.2	−1.78012
$615$	−7403.64	−0.485437
$616$	0	0
$617$	3377.01	0.220346	0.110173	−	0.993912i	$-0.464860\pi$
$617$	3377.01	0.220346	0.110173	+	0.993912i	$0.464860\pi$
$618$	−8453.67	−0.550253
$619$	21458.3	1.39335	0.696675	−	0.717387i	$-0.254662\pi$
$619$	21458.3	1.39335	0.696675	+	0.717387i	$0.254662\pi$
$620$	772.838	0.0500612
$621$	655.376	0.0423500
$622$	3112.48	0.200642
$623$	523.487	0.0336647
$624$	−5024.32	−0.322330
$625$	1856.45	0.118813
$626$	6637.08	0.423755
$627$	0	0
$628$	−1491.48	−0.0947718
$629$	−6904.08	−0.437653
$630$	−3059.08	−0.193455
$631$	−522.005	−0.0329330	−0.0164665	−	0.999864i	$-0.505242\pi$
$631$	−522.005	−0.0329330	−0.0164665	+	0.999864i	$0.505242\pi$
$632$	−16479.5	−1.03722
$633$	−6037.93	−0.379125
$634$	−16009.4	−1.00286
$635$	−17410.2	−1.08804
$636$	2160.54	0.134703
$637$	−2634.16	−0.163845
$638$	0	0
$639$	−4918.89	−0.304520
$640$	−8364.97	−0.516648
$641$	29005.3	1.78727	0.893637	−	0.448791i	$-0.148145\pi$
$641$	29005.3	1.78727	0.893637	+	0.448791i	$0.148145\pi$
$642$	−13793.3	−0.847943
$643$	−12739.8	−0.781351	−0.390675	−	0.920529i	$-0.627759\pi$
$643$	−12739.8	−0.781351	−0.390675	+	0.920529i	$0.627759\pi$
$644$	47.3993	0.00290030
$645$	−13965.8	−0.852565
$646$	10017.0	0.610083
$647$	−7919.69	−0.481229	−0.240614	−	0.970621i	$-0.577349\pi$
$647$	−7919.69	−0.481229	−0.240614	+	0.970621i	$0.577349\pi$
$648$	−21165.6	−1.28312
$649$	0	0
$650$	2984.27	0.180081
$651$	−18932.6	−1.13982
$652$	699.930	0.0420420
$653$	−24265.4	−1.45418	−0.727090	−	0.686542i	$-0.759128\pi$
$653$	−24265.4	−1.45418	−0.727090	+	0.686542i	$0.759128\pi$
$654$	−23796.7	−1.42282
$655$	−942.134	−0.0562018
$656$	10692.3	0.636380
$657$	11601.8	0.688936
$658$	−8357.16	−0.495131
$659$	18366.0	1.08564	0.542820	−	0.839849i	$-0.317356\pi$
$659$	18366.0	1.08564	0.542820	+	0.839849i	$0.317356\pi$
$660$	0	0
$661$	5671.15	0.333710	0.166855	−	0.985981i	$-0.446639\pi$
$661$	5671.15	0.333710	0.166855	+	0.985981i	$0.446639\pi$
$662$	32131.7	1.88645
$663$	2424.61	0.142027
$664$	19106.4	1.11667
$665$	−9624.22	−0.561220
$666$	9605.20	0.558850
$667$	−1432.86	−0.0831792
$668$	1108.02	0.0641777
$669$	24690.9	1.42691
$670$	13517.6	0.779448
$671$	0	0
$672$	−1679.75	−0.0964252
$673$	25014.1	1.43272	0.716361	−	0.697729i	$-0.245806\pi$
$673$	25014.1	1.43272	0.716361	+	0.697729i	$0.245806\pi$
$674$	15943.0	0.911132
$675$	6667.88	0.380218
$676$	−82.1400	−0.00467342
$677$	19365.2	1.09936	0.549678	−	0.835376i	$-0.314750\pi$
$677$	19365.2	1.09936	0.549678	+	0.835376i	$0.314750\pi$
$678$	−4693.12	−0.265838
$679$	−10500.2	−0.593464
$680$	4317.08	0.243459
$681$	−28346.0	−1.59504
$682$	0	0
$683$	12269.1	0.687357	0.343679	−	0.939087i	$-0.388327\pi$
$683$	12269.1	0.687357	0.343679	+	0.939087i	$0.388327\pi$
$684$	901.440	0.0503910
$685$	6555.26	0.365640
$686$	17720.3	0.986246
$687$	−28392.4	−1.57677
$688$	20169.5	1.11767
$689$	−8952.66	−0.495021
$690$	935.448	0.0516115
$691$	−7851.67	−0.432260	−0.216130	−	0.976365i	$-0.569344\pi$
$691$	−7851.67	−0.432260	−0.216130	+	0.976365i	$0.569344\pi$
$692$	499.715	0.0274513
$693$	0	0
$694$	−873.069	−0.0477540
$695$	2583.67	0.141013
$696$	26137.6	1.42348
$697$	−5159.85	−0.280406
$698$	23225.1	1.25943
$699$	43369.4	2.34675
$700$	482.246	0.0260389
$701$	2411.31	0.129920	0.0649600	−	0.997888i	$-0.479308\pi$
$701$	2411.31	0.129920	0.0649600	+	0.997888i	$0.479308\pi$
$702$	2837.30	0.152545
$703$	30219.1	1.62124
$704$	0	0
$705$	10668.6	0.569931
$706$	17957.5	0.957279
$707$	−1813.76	−0.0964831
$708$	−1253.13	−0.0665190
$709$	14927.1	0.790688	0.395344	−	0.918533i	$-0.370625\pi$
$709$	14927.1	0.790688	0.395344	+	0.918533i	$0.370625\pi$
$710$	5905.53	0.312156
$711$	−10389.3	−0.548000
$712$	1027.79	0.0540985
$713$	2037.73	0.107032
$714$	−6057.23	−0.317487
$715$	0	0
$716$	272.647	0.0142309
$717$	−18031.7	−0.939200
$718$	22708.3	1.18031
$719$	26655.2	1.38257	0.691287	−	0.722581i	$-0.257044\pi$
$719$	26655.2	1.38257	0.691287	+	0.722581i	$0.257044\pi$
$720$	−5639.82	−0.291922
$721$	5660.64	0.292390
$722$	−25042.6	−1.29084
$723$	−10070.7	−0.518029
$724$	−1022.01	−0.0524624
$725$	−14578.1	−0.746782
$726$	0	0
$727$	7253.73	0.370049	0.185025	−	0.982734i	$-0.440764\pi$
$727$	7253.73	0.370049	0.185025	+	0.982734i	$0.440764\pi$
$728$	3582.80	0.182400
$729$	532.868	0.0270725
$730$	−13928.9	−0.706210
$731$	−9733.28	−0.492474
$732$	−84.6416	−0.00427383
$733$	11539.7	0.581485	0.290742	−	0.956801i	$-0.406098\pi$
$733$	11539.7	0.581485	0.290742	+	0.956801i	$0.406098\pi$
$734$	30057.6	1.51151
$735$	−8400.81	−0.421590
$736$	180.793	0.00905453
$737$	0	0
$738$	7178.57	0.358058
$739$	−18477.5	−0.919765	−0.459882	−	0.887980i	$-0.652108\pi$
$739$	−18477.5	−0.919765	−0.459882	+	0.887980i	$0.652108\pi$
$740$	745.927	0.0370552
$741$	−10612.5	−0.526127
$742$	22365.7	1.10657
$743$	−35737.3	−1.76457	−0.882284	−	0.470718i	$-0.843995\pi$
$743$	−35737.3	−1.76457	−0.882284	+	0.470718i	$0.843995\pi$
$744$	−37171.4	−1.83168
$745$	14193.7	0.698011
$746$	409.879	0.0201163
$747$	12045.3	0.589981
$748$	0	0
$749$	9236.11	0.450574
$750$	23723.2	1.15500
$751$	−10462.9	−0.508386	−0.254193	−	0.967153i	$-0.581810\pi$
$751$	−10462.9	−0.508386	−0.254193	+	0.967153i	$0.581810\pi$
$752$	−15407.5	−0.747148
$753$	−22459.8	−1.08696
$754$	−6203.23	−0.299613
$755$	−12466.2	−0.600916
$756$	458.496	0.0220573
$757$	22149.3	1.06345	0.531723	−	0.846918i	$-0.321545\pi$
$757$	22149.3	1.06345	0.531723	+	0.846918i	$0.321545\pi$
$758$	−35075.8	−1.68075
$759$	0	0
$760$	−18895.8	−0.901871
$761$	−20621.6	−0.982301	−0.491151	−	0.871075i	$-0.663423\pi$
$761$	−20621.6	−0.982301	−0.491151	+	0.871075i	$0.663423\pi$
$762$	47961.0	2.28011
$763$	15934.5	0.756050
$764$	−1840.31	−0.0871467
$765$	2721.64	0.128629
$766$	−14461.8	−0.682151
$767$	5192.61	0.244451
$768$	−4800.72	−0.225561
$769$	11029.1	0.517191	0.258595	−	0.965986i	$-0.416740\pi$
$769$	11029.1	0.517191	0.258595	+	0.965986i	$0.416740\pi$
$770$	0	0
$771$	25479.3	1.19016
$772$	−777.239	−0.0362350
$773$	4034.81	0.187739	0.0938693	−	0.995585i	$-0.470076\pi$
$773$	4034.81	0.187739	0.0938693	+	0.995585i	$0.470076\pi$
$774$	13541.3	0.628852
$775$	20732.2	0.960931
$776$	−20615.7	−0.953687
$777$	−18273.3	−0.843696
$778$	10610.2	0.488939
$779$	22584.6	1.03874
$780$	−261.959	−0.0120252
$781$	0	0
$782$	651.946	0.0298127
$783$	−13860.1	−0.632593
$784$	12132.5	0.552681
$785$	19710.0	0.896153
$786$	2595.35	0.117777
$787$	14830.3	0.671719	0.335859	−	0.941912i	$-0.390973\pi$
$787$	14830.3	0.671719	0.335859	+	0.941912i	$0.390973\pi$
$788$	−1845.18	−0.0834162
$789$	−29234.8	−1.31912
$790$	12473.2	0.561740
$791$	3142.55	0.141259
$792$	0	0
$793$	350.731	0.0157059
$794$	35781.7	1.59930
$795$	−28551.6	−1.27374
$796$	−956.758	−0.0426023
$797$	−14863.5	−0.660594	−0.330297	−	0.943877i	$-0.607149\pi$
$797$	−14863.5	−0.660594	−0.330297	+	0.943877i	$0.607149\pi$
$798$	26512.4	1.17610
$799$	7435.29	0.329214
$800$	1839.41	0.0812914
$801$	647.957	0.0285823
$802$	−20523.5	−0.903627
$803$	0	0
$804$	2408.70	0.105657
$805$	−626.383	−0.0274250
$806$	8821.90	0.385531
$807$	−12216.5	−0.532888
$808$	−3561.06	−0.155047
$809$	−38102.8	−1.65590	−0.827951	−	0.560801i	$-0.810493\pi$
$809$	−38102.8	−1.65590	−0.827951	+	0.560801i	$0.810493\pi$
$810$	16020.0	0.694918
$811$	−5682.59	−0.246045	−0.123023	−	0.992404i	$-0.539259\pi$
$811$	−5682.59	−0.246045	−0.123023	+	0.992404i	$0.539259\pi$
$812$	−1002.42	−0.0433226
$813$	14941.0	0.644531
$814$	0	0
$815$	−9249.60	−0.397545
$816$	−11167.3	−0.479085
$817$	42602.4	1.82432
$818$	35268.3	1.50749
$819$	2258.72	0.0963690
$820$	557.478	0.0237414
$821$	8095.12	0.344119	0.172059	−	0.985087i	$-0.444958\pi$
$821$	8095.12	0.344119	0.172059	+	0.985087i	$0.444958\pi$
$822$	−18058.2	−0.766242
$823$	31491.5	1.33381	0.666904	−	0.745144i	$-0.267619\pi$
$823$	31491.5	1.33381	0.666904	+	0.745144i	$0.267619\pi$
$824$	11113.9	0.469866
$825$	0	0
$826$	−12972.3	−0.546446
$827$	−19957.4	−0.839162	−0.419581	−	0.907718i	$-0.637823\pi$
$827$	−19957.4	−0.839162	−0.419581	+	0.907718i	$0.637823\pi$
$828$	58.6694	0.00246244
$829$	−30724.7	−1.28723	−0.643614	−	0.765350i	$-0.722566\pi$
$829$	−30724.7	−1.28723	−0.643614	+	0.765350i	$0.722566\pi$
$830$	−14461.4	−0.604773
$831$	−10829.4	−0.452068
$832$	7009.75	0.292091
$833$	−5854.82	−0.243526
$834$	−7117.39	−0.295510
$835$	−14642.6	−0.606858
$836$	0	0
$837$	19711.1	0.813997
$838$	13986.1	0.576541
$839$	−5845.86	−0.240550	−0.120275	−	0.992741i	$-0.538378\pi$
$839$	−5845.86	−0.240550	−0.120275	+	0.992741i	$0.538378\pi$
$840$	11426.2	0.469334
$841$	5913.64	0.242472
$842$	32031.8	1.31103
$843$	−6576.79	−0.268703
$844$	454.643	0.0185420
$845$	1085.48	0.0441914
$846$	−10344.2	−0.420381
$847$	0	0
$848$	41234.2	1.66980
$849$	4708.84	0.190350
$850$	6632.99	0.267658
$851$	1966.78	0.0792248
$852$	1052.30	0.0423138
$853$	−7389.71	−0.296622	−0.148311	−	0.988941i	$-0.547384\pi$
$853$	−7389.71	−0.296622	−0.148311	+	0.988941i	$0.547384\pi$
$854$	−876.204	−0.0351090
$855$	−11912.6	−0.476493
$856$	18133.8	0.724066
$857$	−1153.62	−0.0459824	−0.0229912	−	0.999736i	$-0.507319\pi$
$857$	−1153.62	−0.0459824	−0.0229912	+	0.999736i	$0.507319\pi$
$858$	0	0
$859$	−27141.2	−1.07805	−0.539025	−	0.842290i	$-0.681207\pi$
$859$	−27141.2	−1.07805	−0.539025	+	0.842290i	$0.681207\pi$
$860$	1051.60	0.0416968
$861$	−13656.8	−0.540560
$862$	26699.0	1.05495
$863$	−27066.2	−1.06761	−0.533803	−	0.845609i	$-0.679238\pi$
$863$	−27066.2	−1.06761	−0.533803	+	0.845609i	$0.679238\pi$
$864$	1748.82	0.0688613
$865$	−6603.75	−0.259577
$866$	−6126.51	−0.240401
$867$	−26323.6	−1.03114
$868$	1425.58	0.0557459
$869$	0	0
$870$	−19783.2	−0.770935
$871$	−9980.95	−0.388280
$872$	31285.0	1.21496
$873$	−12996.9	−0.503869
$874$	−2853.56	−0.110438
$875$	−15885.2	−0.613736
$876$	−2481.99	−0.0957292
$877$	28364.5	1.09213	0.546066	−	0.837742i	$-0.316125\pi$
$877$	28364.5	1.09213	0.546066	+	0.837742i	$0.316125\pi$
$878$	16288.2	0.626084
$879$	11624.1	0.446042
$880$	0	0
$881$	47799.4	1.82792	0.913962	−	0.405799i	$-0.133007\pi$
$881$	47799.4	1.82792	0.913962	+	0.405799i	$0.133007\pi$
$882$	8145.43	0.310965
$883$	−43112.7	−1.64310	−0.821551	−	0.570135i	$-0.806891\pi$
$883$	−43112.7	−1.64310	−0.821551	+	0.570135i	$0.806891\pi$
$884$	−182.568	−0.00694620
$885$	16560.1	0.628998
$886$	−10072.1	−0.381919
$887$	16423.9	0.621713	0.310856	−	0.950457i	$-0.399384\pi$
$887$	16423.9	0.621713	0.310856	+	0.950457i	$0.399384\pi$
$888$	−35877.0	−1.35580
$889$	−32115.0	−1.21159
$890$	−777.924	−0.0292990
$891$	0	0
$892$	−1859.17	−0.0697866
$893$	−32544.2	−1.21954
$894$	−39100.3	−1.46276
$895$	−3603.04	−0.134566
$896$	−15430.1	−0.575316
$897$	−690.704	−0.0257101
$898$	19487.7	0.724178
$899$	−43094.7	−1.59877
$900$	596.910	0.0221078
$901$	−19898.6	−0.735759
$902$	0	0
$903$	−25761.5	−0.949378
$904$	6169.94	0.227001
$905$	13505.9	0.496080
$906$	34341.4	1.25929
$907$	27518.0	1.00741	0.503705	−	0.863876i	$-0.331970\pi$
$907$	27518.0	1.00741	0.503705	+	0.863876i	$0.331970\pi$
$908$	2134.39	0.0780092
$909$	−2245.02	−0.0819171
$910$	−2711.78	−0.0987853
$911$	30022.2	1.09186	0.545928	−	0.837832i	$-0.316177\pi$
$911$	30022.2	1.09186	0.545928	+	0.837832i	$0.316177\pi$
$912$	48879.1	1.77472
$913$	0	0
$914$	−3389.36	−0.122659
$915$	1118.54	0.0404130
$916$	2137.89	0.0771157
$917$	−1737.87	−0.0625838
$918$	6306.31	0.226731
$919$	−5023.55	−0.180317	−0.0901587	−	0.995927i	$-0.528737\pi$
$919$	−5023.55	−0.180317	−0.0901587	+	0.995927i	$0.528737\pi$
$920$	−1229.81	−0.0440715
$921$	63775.1	2.28172
$922$	44501.8	1.58957
$923$	−4360.45	−0.155499
$924$	0	0
$925$	20010.3	0.711279
$926$	−34977.4	−1.24128
$927$	7006.56	0.248248
$928$	−3823.48	−0.135250
$929$	−27305.8	−0.964344	−0.482172	−	0.876077i	$-0.660152\pi$
$929$	−27305.8	−0.964344	−0.482172	+	0.876077i	$0.660152\pi$
$930$	28134.6	0.992010
$931$	25626.5	0.902119
$932$	−3265.62	−0.114774
$933$	−7329.22	−0.257179
$934$	−11418.4	−0.400023
$935$	0	0
$936$	4434.68	0.154863
$937$	21720.8	0.757296	0.378648	−	0.925541i	$-0.376389\pi$
$937$	21720.8	0.757296	0.378648	+	0.925541i	$0.376389\pi$
$938$	24934.6	0.867959
$939$	−15628.9	−0.543162
$940$	−803.320	−0.0278739
$941$	−43011.0	−1.49003	−0.745015	−	0.667048i	$-0.767558\pi$
$941$	−43011.0	−1.49003	−0.745015	+	0.667048i	$0.767558\pi$
$942$	−54296.3	−1.87799
$943$	1469.90	0.0507597
$944$	−23916.2	−0.824581
$945$	−6059.04	−0.208572
$946$	0	0
$947$	27400.4	0.940226	0.470113	−	0.882606i	$-0.344213\pi$
$947$	27400.4	0.940226	0.470113	+	0.882606i	$0.344213\pi$
$948$	2222.59	0.0761458
$949$	10284.7	0.351796
$950$	−29032.5	−0.991514
$951$	37698.6	1.28545
$952$	7963.31	0.271105
$953$	56931.4	1.93514	0.967570	−	0.252603i	$-0.0812867\pi$
$953$	56931.4	1.93514	0.967570	+	0.252603i	$0.0812867\pi$
$954$	27683.6	0.939508
$955$	24319.8	0.824052
$956$	1357.75	0.0459338
$957$	0	0
$958$	−11827.2	−0.398871
$959$	12091.9	0.407161
$960$	22355.3	0.751578
$961$	31496.0	1.05723
$962$	8514.71	0.285369
$963$	11432.2	0.382551
$964$	758.306	0.0253355
$965$	10271.2	0.342635
$966$	1725.53	0.0574722
$967$	56583.6	1.88170	0.940852	−	0.338818i	$-0.110027\pi$
$967$	56583.6	1.88170	0.940852	+	0.338818i	$0.110027\pi$
$968$	0	0
$969$	−23587.8	−0.781992
$970$	15603.8	0.516503
$971$	−17988.7	−0.594526	−0.297263	−	0.954796i	$-0.596074\pi$
$971$	−17988.7	−0.594526	−0.297263	+	0.954796i	$0.596074\pi$
$972$	1809.73	0.0597192
$973$	4765.86	0.157026
$974$	28062.5	0.923185
$975$	−7027.31	−0.230825
$976$	−1615.40	−0.0529791
$977$	−15197.5	−0.497658	−0.248829	−	0.968547i	$-0.580046\pi$
$977$	−15197.5	−0.497658	−0.248829	+	0.968547i	$0.580046\pi$
$978$	25480.4	0.833102
$979$	0	0
$980$	632.564	0.0206189
$981$	19723.2	0.641909
$982$	−40296.7	−1.30949
$983$	−51622.4	−1.67497	−0.837487	−	0.546457i	$-0.815976\pi$
$983$	−51622.4	−1.67497	−0.837487	+	0.546457i	$0.815976\pi$
$984$	−26813.2	−0.868671
$985$	24384.2	0.788776
$986$	−13787.6	−0.445321
$987$	19679.3	0.634649
$988$	799.099	0.0257315
$989$	2772.74	0.0891486
$990$	0	0
$991$	12481.7	0.400095	0.200048	−	0.979786i	$-0.435890\pi$
$991$	12481.7	0.400095	0.200048	+	0.979786i	$0.435890\pi$
$992$	5437.55	0.174035
$993$	−75663.1	−2.41802
$994$	10893.4	0.347602
$995$	12643.6	0.402843
$996$	−2576.87	−0.0819791
$997$	32585.6	1.03510	0.517551	−	0.855652i	$-0.326844\pi$
$997$	32585.6	1.03510	0.517551	+	0.855652i	$0.326844\pi$
$998$	25680.5	0.814530
$999$	19024.8	0.602519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.o.1.10		34
11.3	even	5		143.4.h.a.53.5	yes	68
11.4	even	5		143.4.h.a.27.5	✓	68
11.10	odd	2		1573.4.a.p.1.25		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.5	✓	68	11.4	even	5
143.4.h.a.53.5	yes	68	11.3	even	5
1573.4.a.o.1.10		34	1.1	even	1	trivial
1573.4.a.p.1.25		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)

\(f(q)\)	\(=\)	\(q-2.74116 q^{2} +6.45484 q^{3} -0.486036 q^{4} +6.42298 q^{5} -17.6937 q^{6} +11.8479 q^{7} +23.2616 q^{8} +14.6649 q^{9} +O(q^{10})\)	\(q-2.74116 q^{2} +6.45484 q^{3} -0.486036 q^{4} +6.42298 q^{5} -17.6937 q^{6} +11.8479 q^{7} +23.2616 q^{8} +14.6649 q^{9} -17.6064 q^{10} -3.13728 q^{12} +13.0000 q^{13} -32.4769 q^{14} +41.4593 q^{15} -59.8755 q^{16} +28.8944 q^{17} -40.1989 q^{18} -126.470 q^{19} -3.12180 q^{20} +76.4760 q^{21} -8.23121 q^{23} +150.150 q^{24} -83.7453 q^{25} -35.6351 q^{26} -79.6209 q^{27} -5.75849 q^{28} +174.077 q^{29} -113.647 q^{30} -247.562 q^{31} -21.9644 q^{32} -79.2042 q^{34} +76.0986 q^{35} -7.12768 q^{36} -238.942 q^{37} +346.676 q^{38} +83.9129 q^{39} +149.409 q^{40} -178.576 q^{41} -209.633 q^{42} -336.857 q^{43} +94.1925 q^{45} +22.5631 q^{46} +257.326 q^{47} -386.487 q^{48} -202.628 q^{49} +229.559 q^{50} +186.509 q^{51} -6.31846 q^{52} -688.666 q^{53} +218.254 q^{54} +275.600 q^{56} -816.346 q^{57} -477.172 q^{58} +399.431 q^{59} -20.1507 q^{60} +26.9793 q^{61} +678.607 q^{62} +173.748 q^{63} +539.212 q^{64} +83.4987 q^{65} -767.765 q^{67} -14.0437 q^{68} -53.1311 q^{69} -208.599 q^{70} -335.419 q^{71} +341.129 q^{72} +791.129 q^{73} +654.978 q^{74} -540.563 q^{75} +61.4691 q^{76} -230.019 q^{78} -708.443 q^{79} -384.579 q^{80} -909.893 q^{81} +489.506 q^{82} +821.370 q^{83} -37.1701 q^{84} +185.588 q^{85} +923.379 q^{86} +1123.64 q^{87} +44.1841 q^{89} -258.197 q^{90} +154.022 q^{91} +4.00066 q^{92} -1597.97 q^{93} -705.373 q^{94} -812.317 q^{95} -141.777 q^{96} -886.256 q^{97} +555.436 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) \) 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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