LMFDB - Embedded newform 1573.4.a.o.1.21

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			1.21
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)

$f(q)$	$=$	$q+1.14032 q^{2} -1.98038 q^{3} -6.69966 q^{4} +4.19108 q^{5} -2.25828 q^{6} -2.88584 q^{7} -16.7624 q^{8} -23.0781 q^{9} +O(q^{10})$	\(q+1.14032 q^{2} -1.98038 q^{3} -6.69966 q^{4} +4.19108 q^{5} -2.25828 q^{6} -2.88584 q^{7} -16.7624 q^{8} -23.0781 q^{9} +4.77919 q^{10} +13.2679 q^{12} +13.0000 q^{13} -3.29080 q^{14} -8.29995 q^{15} +34.4828 q^{16} -32.5112 q^{17} -26.3165 q^{18} +69.3957 q^{19} -28.0788 q^{20} +5.71508 q^{21} +146.641 q^{23} +33.1959 q^{24} -107.435 q^{25} +14.8242 q^{26} +99.1738 q^{27} +19.3342 q^{28} +187.014 q^{29} -9.46463 q^{30} +271.488 q^{31} +173.420 q^{32} -37.0733 q^{34} -12.0948 q^{35} +154.615 q^{36} -225.767 q^{37} +79.1335 q^{38} -25.7450 q^{39} -70.2525 q^{40} -51.7009 q^{41} +6.51704 q^{42} -415.315 q^{43} -96.7221 q^{45} +167.218 q^{46} +237.033 q^{47} -68.2891 q^{48} -334.672 q^{49} -122.510 q^{50} +64.3847 q^{51} -87.0956 q^{52} -442.102 q^{53} +113.090 q^{54} +48.3736 q^{56} -137.430 q^{57} +213.256 q^{58} +661.958 q^{59} +55.6069 q^{60} -581.802 q^{61} +309.585 q^{62} +66.5997 q^{63} -78.1066 q^{64} +54.4841 q^{65} -683.486 q^{67} +217.814 q^{68} -290.406 q^{69} -13.7920 q^{70} +1138.75 q^{71} +386.843 q^{72} -267.821 q^{73} -257.447 q^{74} +212.762 q^{75} -464.928 q^{76} -29.3576 q^{78} +1109.33 q^{79} +144.520 q^{80} +426.706 q^{81} -58.9557 q^{82} -331.679 q^{83} -38.2891 q^{84} -136.257 q^{85} -473.593 q^{86} -370.359 q^{87} -1017.62 q^{89} -110.295 q^{90} -37.5160 q^{91} -982.447 q^{92} -537.651 q^{93} +270.294 q^{94} +290.843 q^{95} -343.439 q^{96} +181.771 q^{97} -381.634 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.14032	0.403165	0.201583	−	0.979472i	$-0.435392\pi$
$2$	1.14032	0.403165	0.201583	+	0.979472i	$0.435392\pi$
$3$	−1.98038	−0.381125	−0.190563	−	0.981675i	$-0.561031\pi$
$3$	−1.98038	−0.381125	−0.190563	+	0.981675i	$0.561031\pi$
$4$	−6.69966	−0.837458
$5$	4.19108	0.374862	0.187431	−	0.982278i	$-0.439984\pi$
$5$	4.19108	0.374862	0.187431	+	0.982278i	$0.439984\pi$
$6$	−2.25828	−0.153656
$7$	−2.88584	−0.155821	−0.0779105	−	0.996960i	$-0.524825\pi$
$7$	−2.88584	−0.155821	−0.0779105	+	0.996960i	$0.524825\pi$
$8$	−16.7624	−0.740799
$9$	−23.0781	−0.854744
$10$	4.77919	0.151131
$11$	0	0
$11$	0	0
$12$	13.2679	0.319176
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−3.29080	−0.0628216
$15$	−8.29995	−0.142869
$16$	34.4828	0.538793
$17$	−32.5112	−0.463831	−0.231916	−	0.972736i	$-0.574499\pi$
$17$	−32.5112	−0.463831	−0.231916	+	0.972736i	$0.574499\pi$
$18$	−26.3165	−0.344603
$19$	69.3957	0.837919	0.418959	−	0.908005i	$-0.362395\pi$
$19$	69.3957	0.837919	0.418959	+	0.908005i	$0.362395\pi$
$20$	−28.0788	−0.313931
$21$	5.71508	0.0593873
$22$	0	0
$23$	146.641	1.32943	0.664713	−	0.747099i	$-0.268554\pi$
$23$	146.641	1.32943	0.664713	+	0.747099i	$0.268554\pi$
$24$	33.1959	0.282337
$25$	−107.435	−0.859479
$26$	14.8242	0.111818
$27$	99.1738	0.706889
$28$	19.3342	0.130493
$29$	187.014	1.19750	0.598752	−	0.800935i	$-0.295664\pi$
$29$	187.014	1.19750	0.598752	+	0.800935i	$0.295664\pi$
$30$	−9.46463	−0.0575999
$31$	271.488	1.57293	0.786464	−	0.617637i	$-0.211910\pi$
$31$	271.488	1.57293	0.786464	+	0.617637i	$0.211910\pi$
$32$	173.420	0.958022
$33$	0	0
$34$	−37.0733	−0.187001
$35$	−12.0948	−0.0584113
$36$	154.615	0.715812
$37$	−225.767	−1.00313	−0.501566	−	0.865119i	$-0.667242\pi$
$37$	−225.767	−1.00313	−0.501566	+	0.865119i	$0.667242\pi$
$38$	79.1335	0.337820
$39$	−25.7450	−0.105705
$40$	−70.2525	−0.277697
$41$	−51.7009	−0.196935	−0.0984673	−	0.995140i	$-0.531394\pi$
$41$	−51.7009	−0.196935	−0.0984673	+	0.995140i	$0.531394\pi$
$42$	6.51704	0.0239429
$43$	−415.315	−1.47291	−0.736453	−	0.676489i	$-0.763501\pi$
$43$	−415.315	−1.47291	−0.736453	+	0.676489i	$0.763501\pi$
$44$	0	0
$45$	−96.7221	−0.320411
$46$	167.218	0.535979
$47$	237.033	0.735635	0.367817	−	0.929898i	$-0.380105\pi$
$47$	237.033	0.735635	0.367817	+	0.929898i	$0.380105\pi$
$48$	−68.2891	−0.205348
$49$	−334.672	−0.975720
$50$	−122.510	−0.346512
$51$	64.3847	0.176778
$52$	−87.0956	−0.232269
$53$	−442.102	−1.14580	−0.572900	−	0.819625i	$-0.694182\pi$
$53$	−442.102	−1.14580	−0.572900	+	0.819625i	$0.694182\pi$
$54$	113.090	0.284993
$55$	0	0
$56$	48.3736	0.115432
$57$	−137.430	−0.319352
$58$	213.256	0.482792
$59$	661.958	1.46067	0.730336	−	0.683088i	$-0.239364\pi$
$59$	661.958	1.46067	0.730336	+	0.683088i	$0.239364\pi$
$60$	55.6069	0.119647
$61$	−581.802	−1.22118	−0.610591	−	0.791946i	$-0.709068\pi$
$61$	−581.802	−1.22118	−0.610591	+	0.791946i	$0.709068\pi$
$62$	309.585	0.634150
$63$	66.5997	0.133187
$64$	−78.1066	−0.152552
$65$	54.4841	0.103968
$66$	0	0
$67$	−683.486	−1.24628	−0.623142	−	0.782108i	$-0.714144\pi$
$67$	−683.486	−1.24628	−0.623142	+	0.782108i	$0.714144\pi$
$68$	217.814	0.388439
$69$	−290.406	−0.506678
$70$	−13.7920	−0.0235494
$71$	1138.75	1.90344	0.951720	−	0.306967i	$-0.0993141\pi$
$71$	1138.75	1.90344	0.951720	+	0.306967i	$0.0993141\pi$
$72$	386.843	0.633193
$73$	−267.821	−0.429399	−0.214699	−	0.976680i	$-0.568877\pi$
$73$	−267.821	−0.429399	−0.214699	+	0.976680i	$0.568877\pi$
$74$	−257.447	−0.404428
$75$	212.762	0.327569
$76$	−464.928	−0.701722
$77$	0	0
$78$	−29.3576	−0.0426166
$79$	1109.33	1.57987	0.789934	−	0.613192i	$-0.210115\pi$
$79$	1109.33	1.57987	0.789934	+	0.613192i	$0.210115\pi$
$80$	144.520	0.201973
$81$	426.706	0.585331
$82$	−58.9557	−0.0793972
$83$	−331.679	−0.438632	−0.219316	−	0.975654i	$-0.570383\pi$
$83$	−331.679	−0.438632	−0.219316	+	0.975654i	$0.570383\pi$
$84$	−38.2891	−0.0497343
$85$	−136.257	−0.173873
$86$	−473.593	−0.593824
$87$	−370.359	−0.456398
$88$	0	0
$89$	−1017.62	−1.21200	−0.605998	−	0.795466i	$-0.707226\pi$
$89$	−1017.62	−1.21200	−0.605998	+	0.795466i	$0.707226\pi$
$90$	−110.295	−0.129178
$91$	−37.5160	−0.0432170
$92$	−982.447	−1.11334
$93$	−537.651	−0.599482
$94$	270.294	0.296582
$95$	290.843	0.314104
$96$	−343.439	−0.365126
$97$	181.771	0.190269	0.0951345	−	0.995464i	$-0.469672\pi$
$97$	181.771	0.190269	0.0951345	+	0.995464i	$0.469672\pi$
$98$	−381.634	−0.393376
$99$	0	0
$100$	719.777	0.719777
$101$	−865.620	−0.852796	−0.426398	−	0.904536i	$-0.640218\pi$
$101$	−865.620	−0.852796	−0.426398	+	0.904536i	$0.640218\pi$
$102$	73.4194	0.0712706
$103$	569.518	0.544818	0.272409	−	0.962182i	$-0.412180\pi$
$103$	569.518	0.544818	0.272409	+	0.962182i	$0.412180\pi$
$104$	−217.911	−0.205461
$105$	23.9524	0.0222620
$106$	−504.140	−0.461947
$107$	−1968.00	−1.77807	−0.889036	−	0.457837i	$-0.848624\pi$
$107$	−1968.00	−1.77807	−0.889036	+	0.457837i	$0.848624\pi$
$108$	−664.431	−0.591990
$109$	1268.71	1.11486	0.557431	−	0.830223i	$-0.311787\pi$
$109$	1268.71	1.11486	0.557431	+	0.830223i	$0.311787\pi$
$110$	0	0
$111$	447.105	0.382319
$112$	−99.5119	−0.0839553
$113$	−494.486	−0.411658	−0.205829	−	0.978588i	$-0.565989\pi$
$113$	−494.486	−0.411658	−0.205829	+	0.978588i	$0.565989\pi$
$114$	−156.715	−0.128752
$115$	614.585	0.498351
$116$	−1252.93	−1.00286
$117$	−300.015	−0.237063
$118$	754.847	0.588892
$119$	93.8223	0.0722746
$120$	139.127	0.105837
$121$	0	0
$122$	−663.443	−0.492338
$123$	102.388	0.0750567
$124$	−1818.88	−1.31726
$125$	−974.153	−0.697047
$126$	75.9453	0.0536964
$127$	−2347.91	−1.64050	−0.820251	−	0.572004i	$-0.806166\pi$
$127$	−2347.91	−1.64050	−0.820251	+	0.572004i	$0.806166\pi$
$128$	−1476.43	−1.01953
$129$	822.483	0.561361
$130$	62.1295	0.0419163
$131$	2049.09	1.36664	0.683320	−	0.730119i	$-0.260536\pi$
$131$	2049.09	1.36664	0.683320	+	0.730119i	$0.260536\pi$
$132$	0	0
$133$	−200.265	−0.130565
$134$	−779.395	−0.502459
$135$	415.646	0.264986
$136$	544.965	0.343606
$137$	234.319	0.146125	0.0730627	−	0.997327i	$-0.476723\pi$
$137$	234.319	0.146125	0.0730627	+	0.997327i	$0.476723\pi$
$138$	−331.157	−0.204275
$139$	619.204	0.377843	0.188922	−	0.981992i	$-0.439501\pi$
$139$	619.204	0.377843	0.188922	+	0.981992i	$0.439501\pi$
$140$	81.0311	0.0489170
$141$	−469.416	−0.280369
$142$	1298.54	0.767401
$143$	0	0
$144$	−795.796	−0.460530
$145$	783.790	0.448898
$146$	−305.403	−0.173119
$147$	662.779	0.371871
$148$	1512.56	0.840080
$149$	−588.968	−0.323826	−0.161913	−	0.986805i	$-0.551766\pi$
$149$	−588.968	−0.323826	−0.161913	+	0.986805i	$0.551766\pi$
$150$	242.618	0.132064
$151$	453.242	0.244267	0.122133	−	0.992514i	$-0.461026\pi$
$151$	453.242	0.244267	0.122133	+	0.992514i	$0.461026\pi$
$152$	−1163.24	−0.620730
$153$	750.297	0.396457
$154$	0	0
$155$	1137.83	0.589630
$156$	172.483	0.0885235
$157$	−2967.24	−1.50836	−0.754178	−	0.656670i	$-0.771964\pi$
$157$	−2967.24	−1.50836	−0.754178	+	0.656670i	$0.771964\pi$
$158$	1265.00	0.636948
$159$	875.532	0.436693
$160$	726.819	0.359126
$161$	−423.184	−0.207152
$162$	486.583	0.235985
$163$	−1848.80	−0.888401	−0.444200	−	0.895927i	$-0.646512\pi$
$163$	−1848.80	−0.888401	−0.444200	+	0.895927i	$0.646512\pi$
$164$	346.378	0.164924
$165$	0	0
$166$	−378.221	−0.176841
$167$	−3381.44	−1.56685	−0.783425	−	0.621487i	$-0.786529\pi$
$167$	−3381.44	−1.56685	−0.783425	+	0.621487i	$0.786529\pi$
$168$	−95.7983	−0.0439940
$169$	169.000	0.0769231
$170$	−155.377	−0.0700994
$171$	−1601.52	−0.716206
$172$	2782.47	1.23350
$173$	2961.98	1.30171	0.650853	−	0.759204i	$-0.274411\pi$
$173$	2961.98	1.30171	0.650853	+	0.759204i	$0.274411\pi$
$174$	−422.329	−0.184004
$175$	310.040	0.133925
$176$	0	0
$177$	−1310.93	−0.556699
$178$	−1160.42	−0.488635
$179$	−3123.86	−1.30440	−0.652201	−	0.758046i	$-0.726154\pi$
$179$	−3123.86	−1.30440	−0.652201	+	0.758046i	$0.726154\pi$
$180$	648.006	0.268330
$181$	−3691.76	−1.51606	−0.758030	−	0.652220i	$-0.773838\pi$
$181$	−3691.76	−1.51606	−0.758030	+	0.652220i	$0.773838\pi$
$182$	−42.7804	−0.0174236
$183$	1152.19	0.465423
$184$	−2458.06	−0.984838
$185$	−946.208	−0.376036
$186$	−613.096	−0.241690
$187$	0	0
$188$	−1588.04	−0.616063
$189$	−286.200	−0.110148
$190$	331.655	0.126636
$191$	594.237	0.225118	0.112559	−	0.993645i	$-0.464095\pi$
$191$	594.237	0.225118	0.112559	+	0.993645i	$0.464095\pi$
$192$	154.681	0.0581414
$193$	462.836	0.172620	0.0863101	−	0.996268i	$-0.472492\pi$
$193$	462.836	0.172620	0.0863101	+	0.996268i	$0.472492\pi$
$194$	207.278	0.0767099
$195$	−107.899	−0.0396248
$196$	2242.19	0.817124
$197$	−1314.81	−0.475516	−0.237758	−	0.971324i	$-0.576413\pi$
$197$	−1314.81	−0.475516	−0.237758	+	0.971324i	$0.576413\pi$
$198$	0	0
$199$	−1649.37	−0.587541	−0.293770	−	0.955876i	$-0.594910\pi$
$199$	−1649.37	−0.587541	−0.293770	+	0.955876i	$0.594910\pi$
$200$	1800.86	0.636701
$201$	1353.56	0.474990
$202$	−987.087	−0.343818
$203$	−539.693	−0.186596
$204$	−431.356	−0.148044
$205$	−216.683	−0.0738233
$206$	649.435	0.219652
$207$	−3384.20	−1.13632
$208$	448.276	0.149434
$209$	0	0
$210$	27.3134	0.00897527
$211$	1867.51	0.609310	0.304655	−	0.952463i	$-0.401459\pi$
$211$	1867.51	0.609310	0.304655	+	0.952463i	$0.401459\pi$
$212$	2961.94	0.959559
$213$	−2255.15	−0.725449
$214$	−2244.16	−0.716857
$215$	−1740.62	−0.552136
$216$	−1662.39	−0.523663
$217$	−783.473	−0.245095
$218$	1446.73	0.449474
$219$	530.389	0.163655
$220$	0	0
$221$	−422.646	−0.128644
$222$	509.845	0.154138
$223$	−5835.83	−1.75245	−0.876224	−	0.481904i	$-0.839945\pi$
$223$	−5835.83	−1.75245	−0.876224	+	0.481904i	$0.839945\pi$
$224$	−500.465	−0.149280
$225$	2479.39	0.734634
$226$	−563.874	−0.165966
$227$	4250.64	1.24284	0.621420	−	0.783477i	$-0.286556\pi$
$227$	4250.64	1.24284	0.621420	+	0.783477i	$0.286556\pi$
$228$	920.735	0.267444
$229$	−6034.87	−1.74146	−0.870732	−	0.491757i	$-0.836355\pi$
$229$	−6034.87	−1.74146	−0.870732	+	0.491757i	$0.836355\pi$
$230$	700.826	0.200918
$231$	0	0
$232$	−3134.80	−0.887109
$233$	−1671.95	−0.470098	−0.235049	−	0.971984i	$-0.575525\pi$
$233$	−1671.95	−0.470098	−0.235049	+	0.971984i	$0.575525\pi$
$234$	−342.114	−0.0955757
$235$	993.425	0.275761
$236$	−4434.90	−1.22325
$237$	−2196.90	−0.602127
$238$	106.988	0.0291386
$239$	2643.07	0.715340	0.357670	−	0.933848i	$-0.383571\pi$
$239$	2643.07	0.715340	0.357670	+	0.933848i	$0.383571\pi$
$240$	−286.205	−0.0769770
$241$	5418.20	1.44820	0.724102	−	0.689693i	$-0.242255\pi$
$241$	5418.20	1.44820	0.724102	+	0.689693i	$0.242255\pi$
$242$	0	0
$243$	−3522.73	−0.929973
$244$	3897.88	1.02269
$245$	−1402.64	−0.365760
$246$	116.755	0.0302603
$247$	902.144	0.232397
$248$	−4550.79	−1.16522
$249$	656.851	0.167174
$250$	−1110.85	−0.281025
$251$	−4742.68	−1.19265	−0.596325	−	0.802743i	$-0.703373\pi$
$251$	−4742.68	−1.19265	−0.596325	+	0.802743i	$0.703373\pi$
$252$	−446.196	−0.111538
$253$	0	0
$254$	−2677.38	−0.661393
$255$	269.842	0.0662672
$256$	−1058.76	−0.258485
$257$	−569.767	−0.138292	−0.0691461	−	0.997607i	$-0.522027\pi$
$257$	−569.767	−0.138292	−0.0691461	+	0.997607i	$0.522027\pi$
$258$	937.897	0.226321
$259$	651.528	0.156309
$260$	−365.025	−0.0870688
$261$	−4315.92	−1.02356
$262$	2336.62	0.550981
$263$	−109.246	−0.0256137	−0.0128069	−	0.999918i	$-0.504077\pi$
$263$	−109.246	−0.0256137	−0.0128069	+	0.999918i	$0.504077\pi$
$264$	0	0
$265$	−1852.89	−0.429517
$266$	−228.367	−0.0526394
$267$	2015.28	0.461922
$268$	4579.12	1.04371
$269$	6047.98	1.37082	0.685412	−	0.728156i	$-0.259622\pi$
$269$	6047.98	1.37082	0.685412	+	0.728156i	$0.259622\pi$
$270$	473.971	0.106833
$271$	2561.84	0.574247	0.287123	−	0.957894i	$-0.407301\pi$
$271$	2561.84	0.574247	0.287123	+	0.957894i	$0.407301\pi$
$272$	−1121.08	−0.249909
$273$	74.2960	0.0164711
$274$	267.199	0.0589127
$275$	0	0
$276$	1945.62	0.424321
$277$	−7388.69	−1.60268	−0.801342	−	0.598206i	$-0.795880\pi$
$277$	−7388.69	−1.60268	−0.801342	+	0.598206i	$0.795880\pi$
$278$	706.093	0.152333
$279$	−6265.43	−1.34445
$280$	202.738	0.0432711
$281$	3773.24	0.801041	0.400520	−	0.916288i	$-0.368829\pi$
$281$	3773.24	0.801041	0.400520	+	0.916288i	$0.368829\pi$
$282$	−535.287	−0.113035
$283$	−6792.65	−1.42679	−0.713394	−	0.700763i	$-0.752843\pi$
$283$	−6792.65	−1.42679	−0.713394	+	0.700763i	$0.752843\pi$
$284$	−7629.21	−1.59405
$285$	−575.981	−0.119713
$286$	0	0
$287$	149.201	0.0306865
$288$	−4002.21	−0.818863
$289$	−3856.02	−0.784861
$290$	893.775	0.180980
$291$	−359.977	−0.0725163
$292$	1794.31	0.359604
$293$	−3688.66	−0.735473	−0.367736	−	0.929930i	$-0.619867\pi$
$293$	−3688.66	−0.735473	−0.367736	+	0.929930i	$0.619867\pi$
$294$	755.782	0.149926
$295$	2774.32	0.547550
$296$	3784.39	0.743119
$297$	0	0
$298$	−671.614	−0.130555
$299$	1906.34	0.368717
$300$	−1425.43	−0.274325
$301$	1198.53	0.229510
$302$	516.842	0.0984799
$303$	1714.26	0.325022
$304$	2392.95	0.451465
$305$	−2438.38	−0.457774
$306$	855.581	0.159838
$307$	4881.88	0.907569	0.453784	−	0.891111i	$-0.350074\pi$
$307$	4881.88	0.907569	0.453784	+	0.891111i	$0.350074\pi$
$308$	0	0
$309$	−1127.86	−0.207644
$310$	1297.49	0.237718
$311$	−4862.34	−0.886553	−0.443277	−	0.896385i	$-0.646184\pi$
$311$	−4862.34	−0.886553	−0.443277	+	0.896385i	$0.646184\pi$
$312$	431.547	0.0783062
$313$	1598.46	0.288659	0.144330	−	0.989530i	$-0.453897\pi$
$313$	1598.46	0.288659	0.144330	+	0.989530i	$0.453897\pi$
$314$	−3383.62	−0.608117
$315$	279.125	0.0499267
$316$	−7432.15	−1.32307
$317$	−6636.65	−1.17587	−0.587936	−	0.808908i	$-0.700059\pi$
$317$	−6636.65	−1.17587	−0.587936	+	0.808908i	$0.700059\pi$
$318$	998.390	0.176060
$319$	0	0
$320$	−327.351	−0.0571859
$321$	3897.39	0.677668
$322$	−482.566	−0.0835167
$323$	−2256.14	−0.388653
$324$	−2858.79	−0.490190
$325$	−1396.65	−0.238376
$326$	−2108.23	−0.358172
$327$	−2512.52	−0.424902
$328$	866.629	0.145889
$329$	−684.040	−0.114627
$330$	0	0
$331$	−1547.63	−0.256995	−0.128498	−	0.991710i	$-0.541016\pi$
$331$	−1547.63	−0.256995	−0.128498	+	0.991710i	$0.541016\pi$
$332$	2222.13	0.367336
$333$	5210.27	0.857420
$334$	−3855.94	−0.631699
$335$	−2864.54	−0.467184
$336$	197.072	0.0319975
$337$	−77.6390	−0.0125498	−0.00627488	−	0.999980i	$-0.501997\pi$
$337$	−77.6390	−0.0125498	−0.00627488	+	0.999980i	$0.501997\pi$
$338$	192.715	0.0310127
$339$	979.272	0.156893
$340$	912.877	0.145611
$341$	0	0
$342$	−1826.25	−0.288749
$343$	1955.66	0.307859
$344$	6961.66	1.09113
$345$	−1217.12	−0.189934
$346$	3377.62	0.524803
$347$	−1017.48	−0.157410	−0.0787049	−	0.996898i	$-0.525078\pi$
$347$	−1017.48	−0.157410	−0.0787049	+	0.996898i	$0.525078\pi$
$348$	2481.28	0.382214
$349$	10902.4	1.67218	0.836091	−	0.548591i	$-0.184836\pi$
$349$	10902.4	1.67218	0.836091	+	0.548591i	$0.184836\pi$
$350$	353.546	0.0539938
$351$	1289.26	0.196056
$352$	0	0
$353$	10021.0	1.51094	0.755471	−	0.655182i	$-0.227408\pi$
$353$	10021.0	1.51094	0.755471	+	0.655182i	$0.227408\pi$
$354$	−1494.89	−0.224442
$355$	4772.58	0.713527
$356$	6817.72	1.01500
$357$	−185.804	−0.0275457
$358$	−3562.21	−0.525890
$359$	10980.3	1.61425	0.807127	−	0.590378i	$-0.201021\pi$
$359$	10980.3	1.61425	0.807127	+	0.590378i	$0.201021\pi$
$360$	1621.29	0.237360
$361$	−2043.24	−0.297892
$362$	−4209.81	−0.611222
$363$	0	0
$364$	251.344	0.0361924
$365$	−1122.46	−0.160965
$366$	1313.87	0.187642
$367$	5701.42	0.810931	0.405466	−	0.914110i	$-0.367109\pi$
$367$	5701.42	0.810931	0.405466	+	0.914110i	$0.367109\pi$
$368$	5056.60	0.716286
$369$	1193.16	0.168329
$370$	−1078.98	−0.151605
$371$	1275.84	0.178540
$372$	3602.08	0.502041
$373$	−4345.86	−0.603271	−0.301635	−	0.953423i	$-0.597533\pi$
$373$	−4345.86	−0.603271	−0.301635	+	0.953423i	$0.597533\pi$
$374$	0	0
$375$	1929.20	0.265662
$376$	−3973.24	−0.544958
$377$	2431.18	0.332128
$378$	−326.361	−0.0444079
$379$	−617.378	−0.0836743	−0.0418372	−	0.999124i	$-0.513321\pi$
$379$	−617.378	−0.0836743	−0.0418372	+	0.999124i	$0.513321\pi$
$380$	−1948.55	−0.263049
$381$	4649.77	0.625236
$382$	677.623	0.0907597
$383$	−489.713	−0.0653346	−0.0326673	−	0.999466i	$-0.510400\pi$
$383$	−489.713	−0.0653346	−0.0326673	+	0.999466i	$0.510400\pi$
$384$	2923.90	0.388567
$385$	0	0
$386$	527.783	0.0695944
$387$	9584.67	1.25896
$388$	−1217.81	−0.159342
$389$	5324.05	0.693933	0.346967	−	0.937877i	$-0.387212\pi$
$389$	5324.05	0.693933	0.346967	+	0.937877i	$0.387212\pi$
$390$	−123.040	−0.0159753
$391$	−4767.49	−0.616629
$392$	5609.90	0.722812
$393$	−4057.98	−0.520860
$394$	−1499.31	−0.191712
$395$	4649.30	0.592232
$396$	0	0
$397$	−7839.47	−0.991062	−0.495531	−	0.868590i	$-0.665027\pi$
$397$	−7839.47	−0.991062	−0.495531	+	0.868590i	$0.665027\pi$
$398$	−1880.81	−0.236876
$399$	396.602	0.0497617
$400$	−3704.65	−0.463081
$401$	4746.98	0.591154	0.295577	−	0.955319i	$-0.404488\pi$
$401$	4746.98	0.591154	0.295577	+	0.955319i	$0.404488\pi$
$402$	1543.50	0.191500
$403$	3529.35	0.436252
$404$	5799.36	0.714181
$405$	1788.36	0.219418
$406$	−615.424	−0.0752291
$407$	0	0
$408$	−1079.24	−0.130957
$409$	−10597.6	−1.28122	−0.640611	−	0.767866i	$-0.721319\pi$
$409$	−10597.6	−1.28122	−0.640611	+	0.767866i	$0.721319\pi$
$410$	−247.088	−0.0297630
$411$	−464.041	−0.0556921
$412$	−3815.58	−0.456262
$413$	−1910.31	−0.227603
$414$	−3859.08	−0.458124
$415$	−1390.09	−0.164426
$416$	2254.47	0.265707
$417$	−1226.26	−0.144006
$418$	0	0
$419$	−7085.07	−0.826082	−0.413041	−	0.910712i	$-0.635533\pi$
$419$	−7085.07	−0.826082	−0.413041	+	0.910712i	$0.635533\pi$
$420$	−160.473	−0.0186435
$421$	−4199.01	−0.486098	−0.243049	−	0.970014i	$-0.578148\pi$
$421$	−4199.01	−0.486098	−0.243049	+	0.970014i	$0.578148\pi$
$422$	2129.56	0.245653
$423$	−5470.27	−0.628779
$424$	7410.68	0.848808
$425$	3492.84	0.398653
$426$	−2571.61	−0.292476
$427$	1678.99	0.190286
$428$	13184.9	1.48906
$429$	0	0
$430$	−1984.87	−0.222602
$431$	4417.29	0.493674	0.246837	−	0.969057i	$-0.420609\pi$
$431$	4417.29	0.493674	0.246837	+	0.969057i	$0.420609\pi$
$432$	3419.79	0.380867
$433$	56.7394	0.00629728	0.00314864	−	0.999995i	$-0.498998\pi$
$433$	56.7394	0.00629728	0.00314864	+	0.999995i	$0.498998\pi$
$434$	−893.413	−0.0988138
$435$	−1552.21	−0.171086
$436$	−8499.90	−0.933650
$437$	10176.3	1.11395
$438$	604.815	0.0659799
$439$	−7912.14	−0.860195	−0.430098	−	0.902782i	$-0.641521\pi$
$439$	−7912.14	−0.860195	−0.430098	+	0.902782i	$0.641521\pi$
$440$	0	0
$441$	7723.58	0.833990
$442$	−481.953	−0.0518646
$443$	6655.49	0.713796	0.356898	−	0.934143i	$-0.383834\pi$
$443$	6655.49	0.713796	0.356898	+	0.934143i	$0.383834\pi$
$444$	−2995.45	−0.320176
$445$	−4264.93	−0.454331
$446$	−6654.73	−0.706526
$447$	1166.38	0.123418
$448$	225.404	0.0237708
$449$	3739.14	0.393008	0.196504	−	0.980503i	$-0.437041\pi$
$449$	3739.14	0.393008	0.196504	+	0.980503i	$0.437041\pi$
$450$	2827.31	0.296179
$451$	0	0
$452$	3312.89	0.344746
$453$	−897.592	−0.0930962
$454$	4847.11	0.501070
$455$	−157.233	−0.0162004
$456$	2303.65	0.236576
$457$	11679.3	1.19548	0.597741	−	0.801690i	$-0.296065\pi$
$457$	11679.3	1.19548	0.597741	+	0.801690i	$0.296065\pi$
$458$	−6881.71	−0.702098
$459$	−3224.26	−0.327877
$460$	−4117.51	−0.417348
$461$	8061.60	0.814460	0.407230	−	0.913326i	$-0.366495\pi$
$461$	8061.60	0.814460	0.407230	+	0.913326i	$0.366495\pi$
$462$	0	0
$463$	−6770.54	−0.679597	−0.339799	−	0.940498i	$-0.610359\pi$
$463$	−6770.54	−0.679597	−0.339799	+	0.940498i	$0.610359\pi$
$464$	6448.75	0.645207
$465$	−2253.34	−0.224723
$466$	−1906.56	−0.189527
$467$	−10073.9	−0.998207	−0.499104	−	0.866542i	$-0.666337\pi$
$467$	−10073.9	−0.998207	−0.499104	+	0.866542i	$0.666337\pi$
$468$	2010.00	0.198530
$469$	1972.43	0.194197
$470$	1132.83	0.111177
$471$	5876.28	0.574872
$472$	−11096.0	−1.08206
$473$	0	0
$474$	−2505.18	−0.242757
$475$	−7455.51	−0.720173
$476$	−628.578	−0.0605269
$477$	10202.9	0.979365
$478$	3013.96	0.288400
$479$	−12360.2	−1.17902	−0.589512	−	0.807760i	$-0.700680\pi$
$479$	−12360.2	−1.17902	−0.589512	+	0.807760i	$0.700680\pi$
$480$	−1439.38	−0.136872
$481$	−2934.97	−0.278219
$482$	6178.50	0.583865
$483$	838.066	0.0789510
$484$	0	0
$485$	761.819	0.0713246
$486$	−4017.06	−0.374933
$487$	2683.79	0.249721	0.124860	−	0.992174i	$-0.460152\pi$
$487$	2683.79	0.249721	0.124860	+	0.992174i	$0.460152\pi$
$488$	9752.38	0.904651
$489$	3661.34	0.338592
$490$	−1599.46	−0.147462
$491$	−990.037	−0.0909975	−0.0454987	−	0.998964i	$-0.514488\pi$
$491$	−990.037	−0.0909975	−0.0454987	+	0.998964i	$0.514488\pi$
$492$	−685.962	−0.0628568
$493$	−6080.05	−0.555439
$494$	1028.74	0.0936944
$495$	0	0
$496$	9361.67	0.847482
$497$	−3286.24	−0.296596
$498$	749.022	0.0673986
$499$	−7193.38	−0.645330	−0.322665	−	0.946513i	$-0.604579\pi$
$499$	−7193.38	−0.645330	−0.322665	+	0.946513i	$0.604579\pi$
$500$	6526.50	0.583748
$501$	6696.55	0.597166
$502$	−5408.19	−0.480835
$503$	−10002.6	−0.886664	−0.443332	−	0.896357i	$-0.646204\pi$
$503$	−10002.6	−0.886664	−0.443332	+	0.896357i	$0.646204\pi$
$504$	−1116.37	−0.0986648
$505$	−3627.89	−0.319681
$506$	0	0
$507$	−334.685	−0.0293173
$508$	15730.2	1.37385
$509$	−1731.94	−0.150819	−0.0754096	−	0.997153i	$-0.524026\pi$
$509$	−1731.94	−0.150819	−0.0754096	+	0.997153i	$0.524026\pi$
$510$	307.707	0.0267166
$511$	772.891	0.0669094
$512$	10604.1	0.915313
$513$	6882.23	0.592316
$514$	−649.719	−0.0557546
$515$	2386.90	0.204232
$516$	−5510.36	−0.470116
$517$	0	0
$518$	742.953	0.0630183
$519$	−5865.86	−0.496113
$520$	−913.282	−0.0770194
$521$	−9894.43	−0.832021	−0.416011	−	0.909360i	$-0.636572\pi$
$521$	−9894.43	−0.832021	−0.416011	+	0.909360i	$0.636572\pi$
$522$	−4921.55	−0.412663
$523$	11746.9	0.982138	0.491069	−	0.871121i	$-0.336606\pi$
$523$	11746.9	0.982138	0.491069	+	0.871121i	$0.336606\pi$
$524$	−13728.2	−1.14450
$525$	−613.999	−0.0510421
$526$	−124.576	−0.0103266
$527$	−8826.42	−0.729573
$528$	0	0
$529$	9336.65	0.767375
$530$	−2112.89	−0.173166
$531$	−15276.7	−1.24850
$532$	1341.71	0.109343
$533$	−672.111	−0.0546198
$534$	2298.07	0.186231
$535$	−8248.05	−0.666531
$536$	11456.8	0.923247
$537$	6186.43	0.497140
$538$	6896.65	0.552669
$539$	0	0
$540$	−2784.68	−0.221914
$541$	8867.36	0.704691	0.352345	−	0.935870i	$-0.385384\pi$
$541$	8867.36	0.704691	0.352345	+	0.935870i	$0.385384\pi$
$542$	2921.33	0.231516
$543$	7311.11	0.577808
$544$	−5638.11	−0.444360
$545$	5317.25	0.417919
$546$	84.7215	0.00664056
$547$	12669.1	0.990295	0.495148	−	0.868809i	$-0.335114\pi$
$547$	12669.1	0.990295	0.495148	+	0.868809i	$0.335114\pi$
$548$	−1569.86	−0.122374
$549$	13426.9	1.04380
$550$	0	0
$551$	12978.0	1.00341
$552$	4867.89	0.375346
$553$	−3201.36	−0.246177
$554$	−8425.50	−0.646147
$555$	1873.86	0.143317
$556$	−4148.46	−0.316428
$557$	−17304.2	−1.31634	−0.658172	−	0.752868i	$-0.728670\pi$
$557$	−17304.2	−1.31634	−0.658172	+	0.752868i	$0.728670\pi$
$558$	−7144.62	−0.542035
$559$	−5399.09	−0.408510
$560$	−417.062	−0.0314716
$561$	0	0
$562$	4302.71	0.322952
$563$	13923.5	1.04228	0.521142	−	0.853470i	$-0.325506\pi$
$563$	13923.5	1.04228	0.521142	+	0.853470i	$0.325506\pi$
$564$	3144.93	0.234797
$565$	−2072.43	−0.154315
$566$	−7745.81	−0.575231
$567$	−1231.41	−0.0912067
$568$	−19088.1	−1.41007
$569$	−7528.48	−0.554675	−0.277338	−	0.960773i	$-0.589452\pi$
$569$	−7528.48	−0.554675	−0.277338	+	0.960773i	$0.589452\pi$
$570$	−656.804	−0.0482640
$571$	−11039.1	−0.809057	−0.404528	−	0.914525i	$-0.632564\pi$
$571$	−11039.1	−0.809057	−0.404528	+	0.914525i	$0.632564\pi$
$572$	0	0
$573$	−1176.82	−0.0857980
$574$	170.137	0.0123717
$575$	−15754.4	−1.14261
$576$	1802.55	0.130393
$577$	−8304.65	−0.599181	−0.299590	−	0.954068i	$-0.596850\pi$
$577$	−8304.65	−0.599181	−0.299590	+	0.954068i	$0.596850\pi$
$578$	−4397.11	−0.316429
$579$	−916.593	−0.0657899
$580$	−5251.13	−0.375933
$581$	957.172	0.0683480
$582$	−410.491	−0.0292360
$583$	0	0
$584$	4489.32	0.318098
$585$	−1257.39	−0.0888659
$586$	−4206.26	−0.296517
$587$	−882.533	−0.0620546	−0.0310273	−	0.999519i	$-0.509878\pi$
$587$	−882.533	−0.0620546	−0.0310273	+	0.999519i	$0.509878\pi$
$588$	−4440.39	−0.311426
$589$	18840.1	1.31799
$590$	3163.62	0.220753
$591$	2603.84	0.181231
$592$	−7785.07	−0.540481
$593$	−7950.91	−0.550599	−0.275299	−	0.961359i	$-0.588777\pi$
$593$	−7950.91	−0.550599	−0.275299	+	0.961359i	$0.588777\pi$
$594$	0	0
$595$	393.217	0.0270930
$596$	3945.88	0.271191
$597$	3266.38	0.223927
$598$	2173.84	0.148654
$599$	18824.4	1.28405	0.642024	−	0.766685i	$-0.278095\pi$
$599$	18824.4	1.28405	0.642024	+	0.766685i	$0.278095\pi$
$600$	−3566.40	−0.242663
$601$	11277.7	0.765436	0.382718	−	0.923865i	$-0.374988\pi$
$601$	11277.7	0.765436	0.382718	+	0.923865i	$0.374988\pi$
$602$	1366.72	0.0925303
$603$	15773.5	1.06525
$604$	−3036.57	−0.204563
$605$	0	0
$606$	1954.81	0.131038
$607$	−25339.0	−1.69436	−0.847181	−	0.531304i	$-0.821702\pi$
$607$	−25339.0	−1.69436	−0.847181	+	0.531304i	$0.821702\pi$
$608$	12034.6	0.802745
$609$	1068.80	0.0711164
$610$	−2780.54	−0.184559
$611$	3081.43	0.204028
$612$	−5026.73	−0.332016
$613$	19403.5	1.27846	0.639232	−	0.769014i	$-0.279252\pi$
$613$	19403.5	1.27846	0.639232	+	0.769014i	$0.279252\pi$
$614$	5566.92	0.365900
$615$	429.115	0.0281359
$616$	0	0
$617$	14191.4	0.925969	0.462985	−	0.886366i	$-0.346779\pi$
$617$	14191.4	0.925969	0.462985	+	0.886366i	$0.346779\pi$
$618$	−1286.13	−0.0837148
$619$	14206.9	0.922493	0.461247	−	0.887272i	$-0.347402\pi$
$619$	14206.9	0.922493	0.461247	+	0.887272i	$0.347402\pi$
$620$	−7623.08	−0.493790
$621$	14543.0	0.939757
$622$	−5544.64	−0.357428
$623$	2936.70	0.188854
$624$	−887.758	−0.0569532
$625$	9346.60	0.598182
$626$	1822.76	0.116377
$627$	0	0
$628$	19879.5	1.26318
$629$	7339.96	0.465284
$630$	318.293	0.0201287
$631$	−11180.3	−0.705360	−0.352680	−	0.935744i	$-0.614730\pi$
$631$	−11180.3	−0.705360	−0.352680	+	0.935744i	$0.614730\pi$
$632$	−18595.0	−1.17037
$633$	−3698.38	−0.232223
$634$	−7567.93	−0.474071
$635$	−9840.30	−0.614961
$636$	−5865.77	−0.365712
$637$	−4350.73	−0.270616
$638$	0	0
$639$	−26280.1	−1.62695
$640$	−6187.84	−0.382181
$641$	−11621.4	−0.716099	−0.358049	−	0.933703i	$-0.616558\pi$
$641$	−11621.4	−0.716099	−0.358049	+	0.933703i	$0.616558\pi$
$642$	4444.29	0.273212
$643$	−6790.48	−0.416470	−0.208235	−	0.978079i	$-0.566772\pi$
$643$	−6790.48	−0.416470	−0.208235	+	0.978079i	$0.566772\pi$
$644$	2835.19	0.173481
$645$	3447.09	0.210433
$646$	−2572.73	−0.156691
$647$	−16870.8	−1.02513	−0.512565	−	0.858648i	$-0.671305\pi$
$647$	−16870.8	−1.02513	−0.512565	+	0.858648i	$0.671305\pi$
$648$	−7152.60	−0.433612
$649$	0	0
$650$	−1592.64	−0.0961051
$651$	1551.58	0.0934118
$652$	12386.3	0.743998
$653$	−12900.4	−0.773097	−0.386548	−	0.922269i	$-0.626333\pi$
$653$	−12900.4	−0.773097	−0.386548	+	0.922269i	$0.626333\pi$
$654$	−2865.09	−0.171306
$655$	8587.90	0.512301
$656$	−1782.79	−0.106107
$657$	6180.80	0.367026
$658$	−780.028	−0.0462137
$659$	−29635.8	−1.75181	−0.875907	−	0.482480i	$-0.839736\pi$
$659$	−29635.8	−1.75181	−0.875907	+	0.482480i	$0.839736\pi$
$660$	0	0
$661$	−4204.93	−0.247433	−0.123716	−	0.992318i	$-0.539481\pi$
$661$	−4204.93	−0.247433	−0.123716	+	0.992318i	$0.539481\pi$
$662$	−1764.80	−0.103612
$663$	837.001	0.0490293
$664$	5559.72	0.324938
$665$	−839.327	−0.0489439
$666$	5941.39	0.345682
$667$	27423.9	1.59199
$668$	22654.5	1.31217
$669$	11557.2	0.667902
$670$	−3266.51	−0.188353
$671$	0	0
$672$	991.112	0.0568943
$673$	−25375.9	−1.45344	−0.726722	−	0.686932i	$-0.758957\pi$
$673$	−25375.9	−1.45344	−0.726722	+	0.686932i	$0.758957\pi$
$674$	−88.5336	−0.00505963
$675$	−10654.7	−0.607556
$676$	−1132.24	−0.0644198
$677$	−18855.3	−1.07041	−0.535205	−	0.844722i	$-0.679766\pi$
$677$	−18855.3	−1.07041	−0.535205	+	0.844722i	$0.679766\pi$
$678$	1116.69	0.0632538
$679$	−524.564	−0.0296479
$680$	2283.99	0.128805
$681$	−8417.90	−0.473678
$682$	0	0
$683$	24983.4	1.39966	0.699828	−	0.714312i	$-0.253260\pi$
$683$	24983.4	1.39966	0.699828	+	0.714312i	$0.253260\pi$
$684$	10729.6	0.599792
$685$	982.048	0.0547768
$686$	2230.08	0.124118
$687$	11951.4	0.663716
$688$	−14321.2	−0.793591
$689$	−5747.33	−0.317788
$690$	−1387.91	−0.0765748
$691$	24619.1	1.35536	0.677682	−	0.735355i	$-0.262985\pi$
$691$	24619.1	1.35536	0.677682	+	0.735355i	$0.262985\pi$
$692$	−19844.3	−1.09012
$693$	0	0
$694$	−1160.26	−0.0634622
$695$	2595.14	0.141639
$696$	6208.10	0.338100
$697$	1680.86	0.0913444
$698$	12432.2	0.674166
$699$	3311.09	0.179166
$700$	−2077.16	−0.112156
$701$	14804.2	0.797644	0.398822	−	0.917028i	$-0.369419\pi$
$701$	14804.2	0.797644	0.398822	+	0.917028i	$0.369419\pi$
$702$	1470.17	0.0790429
$703$	−15667.3	−0.840543
$704$	0	0
$705$	−1967.36	−0.105100
$706$	11427.2	0.609160
$707$	2498.04	0.132884
$708$	8782.80	0.466212
$709$	7090.07	0.375562	0.187781	−	0.982211i	$-0.439871\pi$
$709$	7090.07	0.375562	0.187781	+	0.982211i	$0.439871\pi$
$710$	5442.28	0.287669
$711$	−25601.3	−1.35038
$712$	17057.7	0.897846
$713$	39811.4	2.09109
$714$	−211.877	−0.0111055
$715$	0	0
$716$	20928.8	1.09238
$717$	−5234.30	−0.272634
$718$	12521.1	0.650811
$719$	1222.15	0.0633914	0.0316957	−	0.999498i	$-0.489909\pi$
$719$	1222.15	0.0633914	0.0316957	+	0.999498i	$0.489909\pi$
$720$	−3335.25	−0.172635
$721$	−1643.54	−0.0848941
$722$	−2329.96	−0.120100
$723$	−10730.1	−0.551947
$724$	24733.6	1.26964
$725$	−20091.8	−1.02923
$726$	0	0
$727$	−4549.62	−0.232099	−0.116049	−	0.993243i	$-0.537023\pi$
$727$	−4549.62	−0.232099	−0.116049	+	0.993243i	$0.537023\pi$
$728$	628.857	0.0320151
$729$	−4544.69	−0.230894
$730$	−1279.97	−0.0648956
$731$	13502.4	0.683179
$732$	−7719.29	−0.389772
$733$	5745.88	0.289535	0.144767	−	0.989466i	$-0.453757\pi$
$733$	5745.88	0.289535	0.144767	+	0.989466i	$0.453757\pi$
$734$	6501.47	0.326939
$735$	2777.76	0.139400
$736$	25430.6	1.27362
$737$	0	0
$738$	1360.59	0.0678643
$739$	3680.07	0.183185	0.0915923	−	0.995797i	$-0.470804\pi$
$739$	3680.07	0.183185	0.0915923	+	0.995797i	$0.470804\pi$
$740$	6339.27	0.314914
$741$	−1786.59	−0.0885723
$742$	1454.87	0.0719810
$743$	28097.0	1.38732	0.693660	−	0.720303i	$-0.255997\pi$
$743$	28097.0	1.38732	0.693660	+	0.720303i	$0.255997\pi$
$744$	9012.31	0.444096
$745$	−2468.41	−0.121390
$746$	−4955.69	−0.243218
$747$	7654.50	0.374918
$748$	0	0
$749$	5679.34	0.277061
$750$	2199.91	0.107106
$751$	−7684.48	−0.373383	−0.186692	−	0.982419i	$-0.559777\pi$
$751$	−7684.48	−0.373383	−0.186692	+	0.982419i	$0.559777\pi$
$752$	8173.56	0.396355
$753$	9392.33	0.454549
$754$	2772.33	0.133902
$755$	1899.57	0.0915663
$756$	1917.44	0.0922444
$757$	−23395.5	−1.12328	−0.561641	−	0.827381i	$-0.689830\pi$
$757$	−23395.5	−1.12328	−0.561641	+	0.827381i	$0.689830\pi$
$758$	−704.010	−0.0337346
$759$	0	0
$760$	−4875.22	−0.232688
$761$	11901.9	0.566942	0.283471	−	0.958981i	$-0.408514\pi$
$761$	11901.9	0.566942	0.283471	+	0.958981i	$0.408514\pi$
$762$	5302.24	0.252074
$763$	−3661.29	−0.173719
$764$	−3981.19	−0.188527
$765$	3144.55	0.148616
$766$	−558.431	−0.0263407
$767$	8605.46	0.405118
$768$	2096.74	0.0985152
$769$	−24029.2	−1.12681	−0.563404	−	0.826181i	$-0.690509\pi$
$769$	−24029.2	−1.12681	−0.563404	+	0.826181i	$0.690509\pi$
$770$	0	0
$771$	1128.36	0.0527066
$772$	−3100.85	−0.144562
$773$	3698.28	0.172080	0.0860400	−	0.996292i	$-0.472579\pi$
$773$	3698.28	0.172080	0.0860400	+	0.996292i	$0.472579\pi$
$774$	10929.6	0.507568
$775$	−29167.3	−1.35190
$776$	−3046.92	−0.140951
$777$	−1290.28	−0.0595732
$778$	6071.14	0.279770
$779$	−3587.82	−0.165015
$780$	722.889	0.0331841
$781$	0	0
$782$	−5436.48	−0.248604
$783$	18546.9	0.846502
$784$	−11540.4	−0.525711
$785$	−12436.0	−0.565425
$786$	−4627.41	−0.209993
$787$	28098.1	1.27267	0.636333	−	0.771414i	$-0.280450\pi$
$787$	28098.1	1.27267	0.636333	+	0.771414i	$0.280450\pi$
$788$	8808.81	0.398225
$789$	216.349	0.00976203
$790$	5301.71	0.238767
$791$	1427.01	0.0641449
$792$	0	0
$793$	−7563.43	−0.338695
$794$	−8939.53	−0.399562
$795$	3669.43	0.163700
$796$	11050.2	0.492041
$797$	−5505.68	−0.244694	−0.122347	−	0.992487i	$-0.539042\pi$
$797$	−5505.68	−0.244694	−0.122347	+	0.992487i	$0.539042\pi$
$798$	452.254	0.0200622
$799$	−7706.23	−0.341210
$800$	−18631.4	−0.823399
$801$	23484.7	1.03595
$802$	5413.10	0.238333
$803$	0	0
$804$	−9068.42	−0.397784
$805$	−1773.60	−0.0776535
$806$	4024.60	0.175881
$807$	−11977.3	−0.522455
$808$	14509.8	0.631751
$809$	−5362.43	−0.233044	−0.116522	−	0.993188i	$-0.537175\pi$
$809$	−5362.43	−0.233044	−0.116522	+	0.993188i	$0.537175\pi$
$810$	2039.31	0.0884617
$811$	−38472.0	−1.66576	−0.832882	−	0.553450i	$-0.813311\pi$
$811$	−38472.0	−1.66576	−0.832882	+	0.553450i	$0.813311\pi$
$812$	3615.76	0.156266
$813$	−5073.43	−0.218860
$814$	0	0
$815$	−7748.48	−0.333027
$816$	2220.16	0.0952466
$817$	−28821.1	−1.23418
$818$	−12084.7	−0.516544
$819$	865.797	0.0369394
$820$	1451.70	0.0618239
$821$	14034.3	0.596590	0.298295	−	0.954474i	$-0.403582\pi$
$821$	14034.3	0.596590	0.298295	+	0.954474i	$0.403582\pi$
$822$	−529.157	−0.0224531
$823$	13194.2	0.558835	0.279417	−	0.960170i	$-0.409859\pi$
$823$	13194.2	0.558835	0.279417	+	0.960170i	$0.409859\pi$
$824$	−9546.47	−0.403601
$825$	0	0
$826$	−2178.37	−0.0917617
$827$	−28997.5	−1.21928	−0.609639	−	0.792679i	$-0.708685\pi$
$827$	−28997.5	−1.21928	−0.609639	+	0.792679i	$0.708685\pi$
$828$	22673.0	0.951619
$829$	−31169.7	−1.30587	−0.652937	−	0.757412i	$-0.726463\pi$
$829$	−31169.7	−1.30587	−0.652937	+	0.757412i	$0.726463\pi$
$830$	−1585.15	−0.0662910
$831$	14632.4	0.610823
$832$	−1015.39	−0.0423103
$833$	10880.6	0.452569
$834$	−1398.34	−0.0580581
$835$	−14171.9	−0.587352
$836$	0	0
$837$	26924.5	1.11189
$838$	−8079.27	−0.333048
$839$	2684.90	0.110480	0.0552402	−	0.998473i	$-0.482408\pi$
$839$	2684.90	0.110480	0.0552402	+	0.998473i	$0.482408\pi$
$840$	−401.498	−0.0164917
$841$	10585.2	0.434014
$842$	−4788.23	−0.195978
$843$	−7472.46	−0.305297
$844$	−12511.7	−0.510271
$845$	708.293	0.0288355
$846$	−6237.88	−0.253502
$847$	0	0
$848$	−15244.9	−0.617349
$849$	13452.0	0.543784
$850$	3982.97	0.160723
$851$	−33106.8	−1.33359
$852$	15108.8	0.607533
$853$	14670.3	0.588864	0.294432	−	0.955672i	$-0.404870\pi$
$853$	14670.3	0.588864	0.294432	+	0.955672i	$0.404870\pi$
$854$	1914.59	0.0767166
$855$	−6712.10	−0.268478
$856$	32988.3	1.31719
$857$	26463.5	1.05481	0.527406	−	0.849613i	$-0.323165\pi$
$857$	26463.5	1.05481	0.527406	+	0.849613i	$0.323165\pi$
$858$	0	0
$859$	4695.94	0.186523	0.0932616	−	0.995642i	$-0.470271\pi$
$859$	4695.94	0.186523	0.0932616	+	0.995642i	$0.470271\pi$
$860$	11661.6	0.462390
$861$	−295.475	−0.0116954
$862$	5037.14	0.199032
$863$	12262.1	0.483668	0.241834	−	0.970318i	$-0.422251\pi$
$863$	12262.1	0.483668	0.241834	+	0.970318i	$0.422251\pi$
$864$	17198.8	0.677215
$865$	12413.9	0.487960
$866$	64.7013	0.00253884
$867$	7636.40	0.299130
$868$	5249.00	0.205257
$869$	0	0
$870$	−1770.02	−0.0689761
$871$	−8885.31	−0.345657
$872$	−21266.5	−0.825889
$873$	−4194.94	−0.162631
$874$	11604.2	0.449107
$875$	2811.25	0.108615
$876$	−3553.43	−0.137054
$877$	−39674.1	−1.52759	−0.763796	−	0.645458i	$-0.776666\pi$
$877$	−39674.1	−1.52759	−0.763796	+	0.645458i	$0.776666\pi$
$878$	−9022.40	−0.346801
$879$	7304.95	0.280307
$880$	0	0
$881$	−10160.2	−0.388543	−0.194272	−	0.980948i	$-0.562234\pi$
$881$	−10160.2	−0.388543	−0.194272	+	0.980948i	$0.562234\pi$
$882$	8807.39	0.336236
$883$	42462.2	1.61831	0.809155	−	0.587595i	$-0.199925\pi$
$883$	42462.2	1.61831	0.809155	+	0.587595i	$0.199925\pi$
$884$	2831.58	0.107734
$885$	−5494.22	−0.208685
$886$	7589.41	0.287778
$887$	−15795.0	−0.597907	−0.298954	−	0.954268i	$-0.596638\pi$
$887$	−15795.0	−0.597907	−0.298954	+	0.954268i	$0.596638\pi$
$888$	−7494.55	−0.283221
$889$	6775.71	0.255624
$890$	−4863.41	−0.183170
$891$	0	0
$892$	39098.1	1.46760
$893$	16449.1	0.616402
$894$	1330.05	0.0497580
$895$	−13092.3	−0.488970
$896$	4260.75	0.158863
$897$	−3775.28	−0.140527
$898$	4263.82	0.158447
$899$	50772.1	1.88359
$900$	−16611.1	−0.615225
$901$	14373.3	0.531458
$902$	0	0
$903$	−2373.56	−0.0874718
$904$	8288.76	0.304956
$905$	−15472.5	−0.568313
$906$	−1023.55	−0.0375332
$907$	25503.7	0.933669	0.466835	−	0.884345i	$-0.345394\pi$
$907$	25503.7	0.933669	0.466835	+	0.884345i	$0.345394\pi$
$908$	−28477.9	−1.04083
$909$	19976.9	0.728922
$910$	−179.296	−0.00653143
$911$	−31901.8	−1.16021	−0.580107	−	0.814540i	$-0.696989\pi$
$911$	−31901.8	−1.16021	−0.580107	+	0.814540i	$0.696989\pi$
$912$	−4738.97	−0.172065
$913$	0	0
$914$	13318.2	0.481977
$915$	4828.93	0.174469
$916$	40431.6	1.45840
$917$	−5913.35	−0.212951
$918$	−3676.70	−0.132189
$919$	−12783.6	−0.458861	−0.229431	−	0.973325i	$-0.573686\pi$
$919$	−12783.6	−0.458861	−0.229431	+	0.973325i	$0.573686\pi$
$920$	−10301.9	−0.369178
$921$	−9668.00	−0.345897
$922$	9192.83	0.328362
$923$	14803.7	0.527919
$924$	0	0
$925$	24255.2	0.862170
$926$	−7720.60	−0.273990
$927$	−13143.4	−0.465680
$928$	32432.0	1.14723
$929$	−43787.3	−1.54641	−0.773204	−	0.634157i	$-0.781347\pi$
$929$	−43787.3	−1.54641	−0.773204	+	0.634157i	$0.781347\pi$
$930$	−2569.54	−0.0906005
$931$	−23224.8	−0.817574
$932$	11201.5	0.393687
$933$	9629.30	0.337888
$934$	−11487.5	−0.402443
$935$	0	0
$936$	5028.96	0.175616
$937$	−35373.1	−1.23329	−0.616643	−	0.787243i	$-0.711508\pi$
$937$	−35373.1	−1.23329	−0.616643	+	0.787243i	$0.711508\pi$
$938$	2249.21	0.0782936
$939$	−3165.57	−0.110015
$940$	−6655.61	−0.230938
$941$	52982.5	1.83547	0.917736	−	0.397190i	$-0.130015\pi$
$941$	52982.5	1.83547	0.917736	+	0.397190i	$0.130015\pi$
$942$	6700.86	0.231768
$943$	−7581.48	−0.261810
$944$	22826.2	0.787000
$945$	−1199.49	−0.0412903
$946$	0	0
$947$	−12609.4	−0.432683	−0.216341	−	0.976318i	$-0.569412\pi$
$947$	−12609.4	−0.432683	−0.216341	+	0.976318i	$0.569412\pi$
$948$	14718.5	0.504256
$949$	−3481.68	−0.119094
$950$	−8501.70	−0.290349
$951$	13143.1	0.448154
$952$	−1572.68	−0.0535410
$953$	−12354.5	−0.419937	−0.209969	−	0.977708i	$-0.567336\pi$
$953$	−12354.5	−0.419937	−0.209969	+	0.977708i	$0.567336\pi$
$954$	11634.6	0.394846
$955$	2490.50	0.0843881
$956$	−17707.7	−0.599067
$957$	0	0
$958$	−14094.6	−0.475341
$959$	−676.207	−0.0227694
$960$	648.281	0.0217950
$961$	43914.9	1.47410
$962$	−3346.82	−0.112168
$963$	45417.7	1.51980
$964$	−36300.1	−1.21281
$965$	1939.78	0.0647087
$966$	955.667	0.0318303
$967$	−6059.26	−0.201502	−0.100751	−	0.994912i	$-0.532125\pi$
$967$	−6059.26	−0.201502	−0.100751	+	0.994912i	$0.532125\pi$
$968$	0	0
$969$	4468.02	0.148125
$970$	868.720	0.0287556
$971$	−16270.3	−0.537734	−0.268867	−	0.963177i	$-0.586649\pi$
$971$	−16270.3	−0.537734	−0.268867	+	0.963177i	$0.586649\pi$
$972$	23601.1	0.778813
$973$	−1786.93	−0.0588759
$974$	3060.38	0.100679
$975$	2765.91	0.0908513
$976$	−20062.1	−0.657965
$977$	−7760.62	−0.254129	−0.127065	−	0.991894i	$-0.540556\pi$
$977$	−7760.62	−0.254129	−0.127065	+	0.991894i	$0.540556\pi$
$978$	4175.11	0.136508
$979$	0	0
$980$	9397.20	0.306309
$981$	−29279.3	−0.952921
$982$	−1128.96	−0.0366870
$983$	44101.1	1.43093	0.715467	−	0.698647i	$-0.246214\pi$
$983$	44101.1	1.43093	0.715467	+	0.698647i	$0.246214\pi$
$984$	−1716.26	−0.0556020
$985$	−5510.49	−0.178253
$986$	−6933.22	−0.223934
$987$	1354.66	0.0436873
$988$	−6044.06	−0.194623
$989$	−60902.3	−1.95812
$990$	0	0
$991$	−1242.45	−0.0398263	−0.0199132	−	0.999802i	$-0.506339\pi$
$991$	−1242.45	−0.0398263	−0.0199132	+	0.999802i	$0.506339\pi$
$992$	47081.6	1.50690
$993$	3064.90	0.0979474
$994$	−3747.38	−0.119577
$995$	−6912.64	−0.220247
$996$	−4400.68	−0.140001
$997$	−21545.9	−0.684419	−0.342210	−	0.939624i	$-0.611175\pi$
$997$	−21545.9	−0.684419	−0.342210	+	0.939624i	$0.611175\pi$
$998$	−8202.78	−0.260175
$999$	−22390.2	−0.709103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.o.1.21		34
11.3	even	5		143.4.h.a.53.11	yes	68
11.4	even	5		143.4.h.a.27.11	✓	68
11.10	odd	2		1573.4.a.p.1.14		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.11	✓	68	11.4	even	5
143.4.h.a.53.11	yes	68	11.3	even	5
1573.4.a.o.1.21		34	1.1	even	1	trivial
1573.4.a.p.1.14		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)

\(f(q)\)	\(=\)	\(q+1.14032 q^{2} -1.98038 q^{3} -6.69966 q^{4} +4.19108 q^{5} -2.25828 q^{6} -2.88584 q^{7} -16.7624 q^{8} -23.0781 q^{9} +O(q^{10})\)	\(q+1.14032 q^{2} -1.98038 q^{3} -6.69966 q^{4} +4.19108 q^{5} -2.25828 q^{6} -2.88584 q^{7} -16.7624 q^{8} -23.0781 q^{9} +4.77919 q^{10} +13.2679 q^{12} +13.0000 q^{13} -3.29080 q^{14} -8.29995 q^{15} +34.4828 q^{16} -32.5112 q^{17} -26.3165 q^{18} +69.3957 q^{19} -28.0788 q^{20} +5.71508 q^{21} +146.641 q^{23} +33.1959 q^{24} -107.435 q^{25} +14.8242 q^{26} +99.1738 q^{27} +19.3342 q^{28} +187.014 q^{29} -9.46463 q^{30} +271.488 q^{31} +173.420 q^{32} -37.0733 q^{34} -12.0948 q^{35} +154.615 q^{36} -225.767 q^{37} +79.1335 q^{38} -25.7450 q^{39} -70.2525 q^{40} -51.7009 q^{41} +6.51704 q^{42} -415.315 q^{43} -96.7221 q^{45} +167.218 q^{46} +237.033 q^{47} -68.2891 q^{48} -334.672 q^{49} -122.510 q^{50} +64.3847 q^{51} -87.0956 q^{52} -442.102 q^{53} +113.090 q^{54} +48.3736 q^{56} -137.430 q^{57} +213.256 q^{58} +661.958 q^{59} +55.6069 q^{60} -581.802 q^{61} +309.585 q^{62} +66.5997 q^{63} -78.1066 q^{64} +54.4841 q^{65} -683.486 q^{67} +217.814 q^{68} -290.406 q^{69} -13.7920 q^{70} +1138.75 q^{71} +386.843 q^{72} -267.821 q^{73} -257.447 q^{74} +212.762 q^{75} -464.928 q^{76} -29.3576 q^{78} +1109.33 q^{79} +144.520 q^{80} +426.706 q^{81} -58.9557 q^{82} -331.679 q^{83} -38.2891 q^{84} -136.257 q^{85} -473.593 q^{86} -370.359 q^{87} -1017.62 q^{89} -110.295 q^{90} -37.5160 q^{91} -982.447 q^{92} -537.651 q^{93} +270.294 q^{94} +290.843 q^{95} -343.439 q^{96} +181.771 q^{97} -381.634 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) \) 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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