LMFDB - Embedded newform 1573.4.a.o.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.77160 q^{2} +7.63306 q^{3} -0.318244 q^{4} -4.52057 q^{5} -21.1558 q^{6} +2.79283 q^{7} +23.0548 q^{8} +31.2637 q^{9} +O(q^{10})$	\(q-2.77160 q^{2} +7.63306 q^{3} -0.318244 q^{4} -4.52057 q^{5} -21.1558 q^{6} +2.79283 q^{7} +23.0548 q^{8} +31.2637 q^{9} +12.5292 q^{10} -2.42917 q^{12} +13.0000 q^{13} -7.74059 q^{14} -34.5058 q^{15} -61.3528 q^{16} -56.1814 q^{17} -86.6503 q^{18} +40.8187 q^{19} +1.43864 q^{20} +21.3178 q^{21} +83.8545 q^{23} +175.979 q^{24} -104.564 q^{25} -36.0308 q^{26} +32.5448 q^{27} -0.888799 q^{28} -22.9531 q^{29} +95.6363 q^{30} -199.738 q^{31} -14.3934 q^{32} +155.712 q^{34} -12.6252 q^{35} -9.94946 q^{36} +47.5176 q^{37} -113.133 q^{38} +99.2298 q^{39} -104.221 q^{40} -50.5932 q^{41} -59.0845 q^{42} +330.544 q^{43} -141.330 q^{45} -232.411 q^{46} -387.177 q^{47} -468.310 q^{48} -335.200 q^{49} +289.811 q^{50} -428.836 q^{51} -4.13717 q^{52} -307.343 q^{53} -90.2011 q^{54} +64.3882 q^{56} +311.572 q^{57} +63.6167 q^{58} +78.1208 q^{59} +10.9813 q^{60} +430.061 q^{61} +553.594 q^{62} +87.3140 q^{63} +530.715 q^{64} -58.7675 q^{65} -393.806 q^{67} +17.8794 q^{68} +640.066 q^{69} +34.9919 q^{70} +379.023 q^{71} +720.778 q^{72} +87.7778 q^{73} -131.700 q^{74} -798.147 q^{75} -12.9903 q^{76} -275.025 q^{78} +787.707 q^{79} +277.350 q^{80} -595.702 q^{81} +140.224 q^{82} +597.501 q^{83} -6.78426 q^{84} +253.972 q^{85} -916.136 q^{86} -175.202 q^{87} +998.511 q^{89} +391.709 q^{90} +36.3068 q^{91} -26.6861 q^{92} -1524.62 q^{93} +1073.10 q^{94} -184.524 q^{95} -109.866 q^{96} -1594.44 q^{97} +929.040 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.77160	−0.979908	−0.489954	−	0.871748i	$-0.662986\pi$
$2$	−2.77160	−0.979908	−0.489954	+	0.871748i	$0.662986\pi$
$3$	7.63306	1.46898	0.734492	−	0.678617i	$-0.237421\pi$
$3$	7.63306	1.46898	0.734492	+	0.678617i	$0.237421\pi$
$4$	−0.318244	−0.0397804
$5$	−4.52057	−0.404332	−0.202166	−	0.979351i	$-0.564798\pi$
$5$	−4.52057	−0.404332	−0.202166	+	0.979351i	$0.564798\pi$
$6$	−21.1558	−1.43947
$7$	2.79283	0.150798	0.0753992	−	0.997153i	$-0.475977\pi$
$7$	2.79283	0.150798	0.0753992	+	0.997153i	$0.475977\pi$
$8$	23.0548	1.01889
$9$	31.2637	1.15791
$10$	12.5292	0.396209
$11$	0	0
$11$	0	0
$12$	−2.42917	−0.0584368
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−7.74059	−0.147769
$15$	−34.5058	−0.593958
$16$	−61.3528	−0.958637
$17$	−56.1814	−0.801529	−0.400765	−	0.916181i	$-0.631256\pi$
$17$	−56.1814	−0.801529	−0.400765	+	0.916181i	$0.631256\pi$
$18$	−86.6503	−1.13465
$19$	40.8187	0.492866	0.246433	−	0.969160i	$-0.420741\pi$
$19$	40.8187	0.492866	0.246433	+	0.969160i	$0.420741\pi$
$20$	1.43864	0.0160845
$21$	21.3178	0.221521
$22$	0	0
$23$	83.8545	0.760211	0.380106	−	0.924943i	$-0.375888\pi$
$23$	83.8545	0.760211	0.380106	+	0.924943i	$0.375888\pi$
$24$	175.979	1.49673
$25$	−104.564	−0.836515
$26$	−36.0308	−0.271778
$27$	32.5448	0.231972
$28$	−0.888799	−0.00599883
$29$	−22.9531	−0.146975	−0.0734875	−	0.997296i	$-0.523413\pi$
$29$	−22.9531	−0.146975	−0.0734875	+	0.997296i	$0.523413\pi$
$30$	95.6363	0.582024
$31$	−199.738	−1.15723	−0.578614	−	0.815602i	$-0.696406\pi$
$31$	−199.738	−1.15723	−0.578614	+	0.815602i	$0.696406\pi$
$32$	−14.3934	−0.0795130
$33$	0	0
$34$	155.712	0.785425
$35$	−12.6252	−0.0609727
$36$	−9.94946	−0.0460623
$37$	47.5176	0.211131	0.105566	−	0.994412i	$-0.466335\pi$
$37$	47.5176	0.211131	0.105566	+	0.994412i	$0.466335\pi$
$38$	−113.133	−0.482963
$39$	99.2298	0.407423
$40$	−104.221	−0.411970
$41$	−50.5932	−0.192715	−0.0963577	−	0.995347i	$-0.530719\pi$
$41$	−50.5932	−0.192715	−0.0963577	+	0.995347i	$0.530719\pi$
$42$	−59.0845	−0.217070
$43$	330.544	1.17227	0.586134	−	0.810214i	$-0.300649\pi$
$43$	330.544	1.17227	0.586134	+	0.810214i	$0.300649\pi$
$44$	0	0
$45$	−141.330	−0.468182
$46$	−232.411	−0.744937
$47$	−387.177	−1.20161	−0.600804	−	0.799396i	$-0.705153\pi$
$47$	−387.177	−1.20161	−0.600804	+	0.799396i	$0.705153\pi$
$48$	−468.310	−1.40822
$49$	−335.200	−0.977260
$50$	289.811	0.819708
$51$	−428.836	−1.17743
$52$	−4.13717	−0.0110331
$53$	−307.343	−0.796542	−0.398271	−	0.917268i	$-0.630390\pi$
$53$	−307.343	−0.796542	−0.398271	+	0.917268i	$0.630390\pi$
$54$	−90.2011	−0.227312
$55$	0	0
$56$	64.3882	0.153647
$57$	311.572	0.724012
$58$	63.6167	0.144022
$59$	78.1208	0.172381	0.0861904	−	0.996279i	$-0.472531\pi$
$59$	78.1208	0.172381	0.0861904	+	0.996279i	$0.472531\pi$
$60$	10.9813	0.0236279
$61$	430.061	0.902683	0.451342	−	0.892351i	$-0.350946\pi$
$61$	430.061	0.902683	0.451342	+	0.892351i	$0.350946\pi$
$62$	553.594	1.13398
$63$	87.3140	0.174612
$64$	530.715	1.03655
$65$	−58.7675	−0.112142
$66$	0	0
$67$	−393.806	−0.718076	−0.359038	−	0.933323i	$-0.616895\pi$
$67$	−393.806	−0.718076	−0.359038	+	0.933323i	$0.616895\pi$
$68$	17.8794	0.0318852
$69$	640.066	1.11674
$70$	34.9919	0.0597477
$71$	379.023	0.633546	0.316773	−	0.948501i	$-0.397401\pi$
$71$	379.023	0.633546	0.316773	+	0.948501i	$0.397401\pi$
$72$	720.778	1.17979
$73$	87.7778	0.140735	0.0703673	−	0.997521i	$-0.477583\pi$
$73$	87.7778	0.140735	0.0703673	+	0.997521i	$0.477583\pi$
$74$	−131.700	−0.206889
$75$	−798.147	−1.22883
$76$	−12.9903	−0.0196064
$77$	0	0
$78$	−275.025	−0.399237
$79$	787.707	1.12182	0.560911	−	0.827876i	$-0.310451\pi$
$79$	787.707	1.12182	0.560911	+	0.827876i	$0.310451\pi$
$80$	277.350	0.387608
$81$	−595.702	−0.817150
$82$	140.224	0.188843
$83$	597.501	0.790172	0.395086	−	0.918644i	$-0.370715\pi$
$83$	597.501	0.790172	0.395086	+	0.918644i	$0.370715\pi$
$84$	−6.78426	−0.00881219
$85$	253.972	0.324084
$86$	−916.136	−1.14872
$87$	−175.202	−0.215904
$88$	0	0
$89$	998.511	1.18924	0.594618	−	0.804009i	$-0.297303\pi$
$89$	998.511	1.18924	0.594618	+	0.804009i	$0.297303\pi$
$90$	391.709	0.458775
$91$	36.3068	0.0418240
$92$	−26.6861	−0.0302416
$93$	−1524.62	−1.69995
$94$	1073.10	1.17747
$95$	−184.524	−0.199282
$96$	−109.866	−0.116803
$97$	−1594.44	−1.66897	−0.834487	−	0.551028i	$-0.814236\pi$
$97$	−1594.44	−1.66897	−0.834487	+	0.551028i	$0.814236\pi$
$98$	929.040	0.957625
$99$	0	0
$100$	33.2770	0.0332770
$101$	−1417.86	−1.39685	−0.698427	−	0.715681i	$-0.746116\pi$
$101$	−1417.86	−1.39685	−0.698427	+	0.715681i	$0.746116\pi$
$102$	1188.56	1.15378
$103$	−1305.21	−1.24861	−0.624303	−	0.781183i	$-0.714617\pi$
$103$	−1305.21	−1.24861	−0.624303	+	0.781183i	$0.714617\pi$
$104$	299.713	0.282589
$105$	−96.3688	−0.0895679
$106$	851.830	0.780538
$107$	326.828	0.295286	0.147643	−	0.989041i	$-0.452831\pi$
$107$	326.828	0.295286	0.147643	+	0.989041i	$0.452831\pi$
$108$	−10.3572	−0.00922796
$109$	−1338.50	−1.17619	−0.588097	−	0.808791i	$-0.700123\pi$
$109$	−1338.50	−1.17619	−0.588097	+	0.808791i	$0.700123\pi$
$110$	0	0
$111$	362.705	0.310148
$112$	−171.348	−0.144561
$113$	480.550	0.400056	0.200028	−	0.979790i	$-0.435897\pi$
$113$	480.550	0.400056	0.200028	+	0.979790i	$0.435897\pi$
$114$	−863.552	−0.709465
$115$	−379.070	−0.307378
$116$	7.30467	0.00584673
$117$	406.428	0.321147
$118$	−216.520	−0.168917
$119$	−156.905	−0.120869
$120$	−795.526	−0.605177
$121$	0	0
$122$	−1191.96	−0.884547
$123$	−386.181	−0.283096
$124$	63.5655	0.0460351
$125$	1037.76	0.742563
$126$	−241.999	−0.171103
$127$	1605.91	1.12206	0.561028	−	0.827797i	$-0.310406\pi$
$127$	1605.91	1.12206	0.561028	+	0.827797i	$0.310406\pi$
$128$	−1355.78	−0.936213
$129$	2523.07	1.72204
$130$	162.880	0.109888
$131$	−2701.69	−1.80189	−0.900947	−	0.433930i	$-0.857127\pi$
$131$	−2701.69	−1.80189	−0.900947	+	0.433930i	$0.857127\pi$
$132$	0	0
$133$	114.000	0.0743234
$134$	1091.47	0.703648
$135$	−147.121	−0.0937939
$136$	−1295.25	−0.816670
$137$	−300.763	−0.187562	−0.0937808	−	0.995593i	$-0.529895\pi$
$137$	−300.763	−0.187562	−0.0937808	+	0.995593i	$0.529895\pi$
$138$	−1774.01	−1.09430
$139$	−1066.31	−0.650670	−0.325335	−	0.945599i	$-0.605477\pi$
$139$	−1066.31	−0.650670	−0.325335	+	0.945599i	$0.605477\pi$
$140$	4.01788	0.00242552
$141$	−2955.35	−1.76514
$142$	−1050.50	−0.620817
$143$	0	0
$144$	−1918.11	−1.11002
$145$	103.761	0.0594268
$146$	−243.285	−0.137907
$147$	−2558.60	−1.43558
$148$	−15.1222	−0.00839889
$149$	−2822.06	−1.55162	−0.775812	−	0.630964i	$-0.782659\pi$
$149$	−2822.06	−1.55162	−0.775812	+	0.630964i	$0.782659\pi$
$150$	2212.14	1.20414
$151$	−571.901	−0.308216	−0.154108	−	0.988054i	$-0.549250\pi$
$151$	−571.901	−0.308216	−0.154108	+	0.988054i	$0.549250\pi$
$152$	941.068	0.502176
$153$	−1756.44	−0.928102
$154$	0	0
$155$	902.932	0.467905
$156$	−31.5793	−0.0162075
$157$	−3468.67	−1.76325	−0.881623	−	0.471954i	$-0.843549\pi$
$157$	−3468.67	−1.76325	−0.881623	+	0.471954i	$0.843549\pi$
$158$	−2183.21	−1.09928
$159$	−2345.97	−1.17011
$160$	65.0664	0.0321497
$161$	234.191	0.114639
$162$	1651.05	0.800732
$163$	613.233	0.294676	0.147338	−	0.989086i	$-0.452930\pi$
$163$	613.233	0.294676	0.147338	+	0.989086i	$0.452930\pi$
$164$	16.1010	0.00766630
$165$	0	0
$166$	−1656.03	−0.774296
$167$	−318.770	−0.147708	−0.0738538	−	0.997269i	$-0.523530\pi$
$167$	−318.770	−0.147708	−0.0738538	+	0.997269i	$0.523530\pi$
$168$	491.479	0.225705
$169$	169.000	0.0769231
$170$	−703.909	−0.317573
$171$	1276.14	0.570696
$172$	−105.194	−0.0466334
$173$	2437.28	1.07111	0.535557	−	0.844499i	$-0.320102\pi$
$173$	2437.28	1.07111	0.535557	+	0.844499i	$0.320102\pi$
$174$	485.590	0.211566
$175$	−292.030	−0.126145
$176$	0	0
$177$	596.301	0.253225
$178$	−2767.47	−1.16534
$179$	−945.654	−0.394869	−0.197434	−	0.980316i	$-0.563261\pi$
$179$	−945.654	−0.394869	−0.197434	+	0.980316i	$0.563261\pi$
$180$	44.9773	0.0186245
$181$	1469.49	0.603461	0.301730	−	0.953393i	$-0.402436\pi$
$181$	1469.49	0.603461	0.301730	+	0.953393i	$0.402436\pi$
$182$	−100.628	−0.0409836
$183$	3282.68	1.32603
$184$	1933.25	0.774571
$185$	−214.807	−0.0853671
$186$	4225.62	1.66579
$187$	0	0
$188$	123.217	0.0478005
$189$	90.8920	0.0349811
$190$	511.426	0.195278
$191$	−1402.21	−0.531206	−0.265603	−	0.964082i	$-0.585571\pi$
$191$	−1402.21	−0.531206	−0.265603	+	0.964082i	$0.585571\pi$
$192$	4050.98	1.52268
$193$	655.467	0.244464	0.122232	−	0.992502i	$-0.460995\pi$
$193$	655.467	0.244464	0.122232	+	0.992502i	$0.460995\pi$
$194$	4419.14	1.63544
$195$	−448.576	−0.164734
$196$	106.675	0.0388758
$197$	−3298.27	−1.19285	−0.596426	−	0.802668i	$-0.703413\pi$
$197$	−3298.27	−1.19285	−0.596426	+	0.802668i	$0.703413\pi$
$198$	0	0
$199$	2887.63	1.02864	0.514319	−	0.857599i	$-0.328045\pi$
$199$	2887.63	1.02864	0.514319	+	0.857599i	$0.328045\pi$
$200$	−2410.71	−0.852316
$201$	−3005.95	−1.05484
$202$	3929.74	1.36879
$203$	−64.1039	−0.0221636
$204$	136.474	0.0468388
$205$	228.710	0.0779211
$206$	3617.52	1.22352
$207$	2621.60	0.880259
$208$	−797.586	−0.265878
$209$	0	0
$210$	267.096	0.0877683
$211$	3718.99	1.21339	0.606696	−	0.794934i	$-0.292494\pi$
$211$	3718.99	1.21339	0.606696	+	0.794934i	$0.292494\pi$
$212$	97.8098	0.0316868
$213$	2893.11	0.930669
$214$	−905.835	−0.289353
$215$	−1494.25	−0.473986
$216$	750.315	0.236354
$217$	−557.835	−0.174508
$218$	3709.78	1.15256
$219$	670.014	0.206737
$220$	0	0
$221$	−730.359	−0.222304
$222$	−1005.27	−0.303917
$223$	−4353.13	−1.30721	−0.653603	−	0.756838i	$-0.726743\pi$
$223$	−4353.13	−1.30721	−0.653603	+	0.756838i	$0.726743\pi$
$224$	−40.1983	−0.0119904
$225$	−3269.07	−0.968612
$226$	−1331.89	−0.392018
$227$	1211.93	0.354354	0.177177	−	0.984179i	$-0.443303\pi$
$227$	1211.93	0.354354	0.177177	+	0.984179i	$0.443303\pi$
$228$	−99.1557	−0.0288015
$229$	6626.75	1.91226	0.956131	−	0.292940i	$-0.0946337\pi$
$229$	6626.75	1.91226	0.956131	+	0.292940i	$0.0946337\pi$
$230$	1050.63	0.301202
$231$	0	0
$232$	−529.179	−0.149751
$233$	−3156.99	−0.887644	−0.443822	−	0.896115i	$-0.646378\pi$
$233$	−3156.99	−0.887644	−0.443822	+	0.896115i	$0.646378\pi$
$234$	−1126.45	−0.314695
$235$	1750.26	0.485849
$236$	−24.8615	−0.00685739
$237$	6012.62	1.64794
$238$	434.878	0.118441
$239$	−1350.47	−0.365501	−0.182751	−	0.983159i	$-0.558500\pi$
$239$	−1350.47	−0.365501	−0.182751	+	0.983159i	$0.558500\pi$
$240$	2117.03	0.569390
$241$	−6072.91	−1.62320	−0.811599	−	0.584215i	$-0.801402\pi$
$241$	−6072.91	−1.62320	−0.811599	+	0.584215i	$0.801402\pi$
$242$	0	0
$243$	−5425.74	−1.43235
$244$	−136.864	−0.0359091
$245$	1515.30	0.395138
$246$	1070.34	0.277408
$247$	530.643	0.136696
$248$	−4604.93	−1.17909
$249$	4560.76	1.16075
$250$	−2876.26	−0.727643
$251$	3983.62	1.00177	0.500884	−	0.865514i	$-0.333008\pi$
$251$	3983.62	1.00177	0.500884	+	0.865514i	$0.333008\pi$
$252$	−27.7871	−0.00694613
$253$	0	0
$254$	−4450.93	−1.09951
$255$	1938.59	0.476075
$256$	−488.038	−0.119150
$257$	−813.374	−0.197420	−0.0987099	−	0.995116i	$-0.531472\pi$
$257$	−813.374	−0.197420	−0.0987099	+	0.995116i	$0.531472\pi$
$258$	−6992.93	−1.68744
$259$	132.708	0.0318382
$260$	18.7024	0.00446104
$261$	−717.597	−0.170184
$262$	7488.01	1.76569
$263$	2046.13	0.479733	0.239867	−	0.970806i	$-0.422896\pi$
$263$	2046.13	0.479733	0.239867	+	0.970806i	$0.422896\pi$
$264$	0	0
$265$	1389.36	0.322068
$266$	−315.961	−0.0728301
$267$	7621.70	1.74697
$268$	125.326	0.0285654
$269$	−3390.09	−0.768391	−0.384196	−	0.923252i	$-0.625521\pi$
$269$	−3390.09	−0.768391	−0.384196	+	0.923252i	$0.625521\pi$
$270$	407.761	0.0919094
$271$	−357.445	−0.0801227	−0.0400613	−	0.999197i	$-0.512755\pi$
$271$	−357.445	−0.0801227	−0.0400613	+	0.999197i	$0.512755\pi$
$272$	3446.89	0.768376
$273$	277.132	0.0614387
$274$	833.595	0.183793
$275$	0	0
$276$	−203.697	−0.0444243
$277$	−4768.87	−1.03442	−0.517209	−	0.855859i	$-0.673029\pi$
$277$	−4768.87	−1.03442	−0.517209	+	0.855859i	$0.673029\pi$
$278$	2955.38	0.637596
$279$	−6244.55	−1.33997
$280$	−291.071	−0.0621244
$281$	−5353.58	−1.13654	−0.568270	−	0.822842i	$-0.692387\pi$
$281$	−5353.58	−1.13654	−0.568270	+	0.822842i	$0.692387\pi$
$282$	8191.04	1.72968
$283$	2101.64	0.441447	0.220724	−	0.975336i	$-0.429158\pi$
$283$	2101.64	0.441447	0.220724	+	0.975336i	$0.429158\pi$
$284$	−120.622	−0.0252027
$285$	−1408.48	−0.292742
$286$	0	0
$287$	−141.298	−0.0290612
$288$	−449.990	−0.0920692
$289$	−1756.65	−0.357551
$290$	−287.584	−0.0582328
$291$	−12170.4	−2.45170
$292$	−27.9347	−0.00559848
$293$	−5531.00	−1.10281	−0.551407	−	0.834236i	$-0.685909\pi$
$293$	−5531.00	−1.10281	−0.551407	+	0.834236i	$0.685909\pi$
$294$	7091.42	1.40674
$295$	−353.151	−0.0696991
$296$	1095.51	0.215119
$297$	0	0
$298$	7821.61	1.52045
$299$	1090.11	0.210845
$300$	254.005	0.0488833
$301$	923.153	0.176776
$302$	1585.08	0.302024
$303$	−10822.6	−2.05196
$304$	−2504.34	−0.472480
$305$	−1944.12	−0.364984
$306$	4868.14	0.909454
$307$	−8605.69	−1.59985	−0.799923	−	0.600103i	$-0.795126\pi$
$307$	−8605.69	−1.59985	−0.799923	+	0.600103i	$0.795126\pi$
$308$	0	0
$309$	−9962.76	−1.83418
$310$	−2502.56	−0.458504
$311$	78.1069	0.0142413	0.00712063	−	0.999975i	$-0.497733\pi$
$311$	78.1069	0.0142413	0.00712063	+	0.999975i	$0.497733\pi$
$312$	2287.73	0.415119
$313$	7364.46	1.32992	0.664958	−	0.746881i	$-0.268449\pi$
$313$	7364.46	1.32992	0.664958	+	0.746881i	$0.268449\pi$
$314$	9613.75	1.72782
$315$	−394.709	−0.0706011
$316$	−250.683	−0.0446266
$317$	−9915.01	−1.75673	−0.878364	−	0.477993i	$-0.841365\pi$
$317$	−9915.01	−1.75673	−0.878364	+	0.477993i	$0.841365\pi$
$318$	6502.07	1.14660
$319$	0	0
$320$	−2399.14	−0.419112
$321$	2494.70	0.433770
$322$	−649.083	−0.112335
$323$	−2293.25	−0.395047
$324$	189.578	0.0325066
$325$	−1359.34	−0.232008
$326$	−1699.64	−0.288755
$327$	−10216.9	−1.72781
$328$	−1166.42	−0.196356
$329$	−1081.32	−0.181201
$330$	0	0
$331$	−3797.60	−0.630619	−0.315310	−	0.948989i	$-0.602108\pi$
$331$	−3797.60	−0.630619	−0.315310	+	0.948989i	$0.602108\pi$
$332$	−190.151	−0.0314334
$333$	1485.57	0.244471
$334$	883.503	0.144740
$335$	1780.23	0.290341
$336$	−1307.91	−0.212358
$337$	8812.42	1.42446	0.712230	−	0.701946i	$-0.247685\pi$
$337$	8812.42	1.42446	0.712230	+	0.701946i	$0.247685\pi$
$338$	−468.400	−0.0753775
$339$	3668.07	0.587676
$340$	−80.8251	−0.0128922
$341$	0	0
$342$	−3536.95	−0.559230
$343$	−1894.10	−0.298168
$344$	7620.64	1.19441
$345$	−2893.47	−0.451533
$346$	−6755.15	−1.04959
$347$	−5765.02	−0.891880	−0.445940	−	0.895063i	$-0.647131\pi$
$347$	−5765.02	−0.891880	−0.445940	+	0.895063i	$0.647131\pi$
$348$	55.7570	0.00858876
$349$	−1603.62	−0.245960	−0.122980	−	0.992409i	$-0.539245\pi$
$349$	−1603.62	−0.245960	−0.122980	+	0.992409i	$0.539245\pi$
$350$	809.391	0.123611
$351$	423.083	0.0643375
$352$	0	0
$353$	186.282	0.0280873	0.0140436	−	0.999901i	$-0.495530\pi$
$353$	186.282	0.0280873	0.0140436	+	0.999901i	$0.495530\pi$
$354$	−1652.71	−0.248137
$355$	−1713.40	−0.256163
$356$	−317.770	−0.0473083
$357$	−1197.67	−0.177555
$358$	2620.97	0.386935
$359$	2372.08	0.348729	0.174364	−	0.984681i	$-0.444213\pi$
$359$	2372.08	0.348729	0.174364	+	0.984681i	$0.444213\pi$
$360$	−3258.33	−0.477025
$361$	−5192.83	−0.757083
$362$	−4072.84	−0.591336
$363$	0	0
$364$	−11.5544	−0.00166378
$365$	−396.806	−0.0569035
$366$	−9098.28	−1.29938
$367$	−10517.5	−1.49594	−0.747969	−	0.663734i	$-0.768971\pi$
$367$	−10517.5	−1.49594	−0.747969	+	0.663734i	$0.768971\pi$
$368$	−5144.70	−0.728767
$369$	−1581.73	−0.223148
$370$	595.358	0.0836519
$371$	−858.355	−0.120117
$372$	485.199	0.0676247
$373$	834.390	0.115826	0.0579130	−	0.998322i	$-0.481555\pi$
$373$	834.390	0.115826	0.0579130	+	0.998322i	$0.481555\pi$
$374$	0	0
$375$	7921.31	1.09081
$376$	−8926.30	−1.22431
$377$	−298.390	−0.0407636
$378$	−251.916	−0.0342782
$379$	−92.8785	−0.0125880	−0.00629399	−	0.999980i	$-0.502003\pi$
$379$	−92.8785	−0.0125880	−0.00629399	+	0.999980i	$0.502003\pi$
$380$	58.7236	0.00792751
$381$	12258.0	1.64828
$382$	3886.36	0.520533
$383$	−13562.9	−1.80948	−0.904740	−	0.425964i	$-0.859935\pi$
$383$	−13562.9	−1.80948	−0.904740	+	0.425964i	$0.859935\pi$
$384$	−10348.8	−1.37528
$385$	0	0
$386$	−1816.69	−0.239552
$387$	10334.0	1.35739
$388$	507.419	0.0663925
$389$	13319.2	1.73602	0.868011	−	0.496546i	$-0.165398\pi$
$389$	13319.2	1.73602	0.868011	+	0.496546i	$0.165398\pi$
$390$	1243.27	0.161424
$391$	−4711.06	−0.609332
$392$	−7727.98	−0.995719
$393$	−20622.2	−2.64695
$394$	9141.47	1.16888
$395$	−3560.89	−0.453589
$396$	0	0
$397$	9211.02	1.16445	0.582227	−	0.813027i	$-0.302182\pi$
$397$	9211.02	1.16445	0.582227	+	0.813027i	$0.302182\pi$
$398$	−8003.36	−1.00797
$399$	870.166	0.109180
$400$	6415.32	0.801915
$401$	−7180.64	−0.894224	−0.447112	−	0.894478i	$-0.647547\pi$
$401$	−7180.64	−0.894224	−0.447112	+	0.894478i	$0.647547\pi$
$402$	8331.28	1.03365
$403$	−2596.60	−0.320957
$404$	451.225	0.0555675
$405$	2692.92	0.330400
$406$	177.670	0.0217183
$407$	0	0
$408$	−9886.75	−1.19967
$409$	−7276.16	−0.879665	−0.439832	−	0.898080i	$-0.644962\pi$
$409$	−7276.16	−0.879665	−0.439832	+	0.898080i	$0.644962\pi$
$410$	−633.893	−0.0763555
$411$	−2295.74	−0.275525
$412$	415.375	0.0496701
$413$	218.178	0.0259948
$414$	−7266.01	−0.862573
$415$	−2701.05	−0.319492
$416$	−187.114	−0.0220530
$417$	−8139.20	−0.955823
$418$	0	0
$419$	1082.69	0.126236	0.0631179	−	0.998006i	$-0.479896\pi$
$419$	1082.69	0.126236	0.0631179	+	0.998006i	$0.479896\pi$
$420$	30.6688	0.00356305
$421$	−813.701	−0.0941980	−0.0470990	−	0.998890i	$-0.514998\pi$
$421$	−813.701	−0.0941980	−0.0470990	+	0.998890i	$0.514998\pi$
$422$	−10307.5	−1.18901
$423$	−12104.6	−1.39136
$424$	−7085.73	−0.811588
$425$	5874.58	0.670492
$426$	−8018.53	−0.911970
$427$	1201.09	0.136123
$428$	−104.011	−0.0117466
$429$	0	0
$430$	4141.46	0.464463
$431$	−15836.1	−1.76983	−0.884917	−	0.465748i	$-0.845785\pi$
$431$	−15836.1	−1.76983	−0.884917	+	0.465748i	$0.845785\pi$
$432$	−1996.71	−0.222377
$433$	−11570.8	−1.28420	−0.642099	−	0.766622i	$-0.721936\pi$
$433$	−11570.8	−1.28420	−0.642099	+	0.766622i	$0.721936\pi$
$434$	1546.09	0.171002
$435$	792.014	0.0872970
$436$	425.969	0.0467895
$437$	3422.83	0.374682
$438$	−1857.01	−0.202583
$439$	5263.59	0.572249	0.286125	−	0.958192i	$-0.407633\pi$
$439$	5263.59	0.572249	0.286125	+	0.958192i	$0.407633\pi$
$440$	0	0
$441$	−10479.6	−1.13158
$442$	2024.26	0.217838
$443$	3086.01	0.330972	0.165486	−	0.986212i	$-0.447081\pi$
$443$	3086.01	0.330972	0.165486	+	0.986212i	$0.447081\pi$
$444$	−115.429	−0.0123378
$445$	−4513.84	−0.480846
$446$	12065.1	1.28094
$447$	−21540.9	−2.27931
$448$	1482.20	0.156311
$449$	−14991.8	−1.57574	−0.787870	−	0.615842i	$-0.788816\pi$
$449$	−14991.8	−1.57574	−0.787870	+	0.615842i	$0.788816\pi$
$450$	9060.54	0.949151
$451$	0	0
$452$	−152.932	−0.0159144
$453$	−4365.36	−0.452765
$454$	−3358.98	−0.347235
$455$	−164.127	−0.0169108
$456$	7183.23	0.737688
$457$	14633.4	1.49786	0.748930	−	0.662649i	$-0.230568\pi$
$457$	14633.4	1.49786	0.748930	+	0.662649i	$0.230568\pi$
$458$	−18366.7	−1.87384
$459$	−1828.41	−0.185933
$460$	120.637	0.0122276
$461$	13992.5	1.41366	0.706831	−	0.707383i	$-0.250124\pi$
$461$	13992.5	1.41366	0.706831	+	0.707383i	$0.250124\pi$
$462$	0	0
$463$	−1490.58	−0.149618	−0.0748091	−	0.997198i	$-0.523835\pi$
$463$	−1490.58	−0.149618	−0.0748091	+	0.997198i	$0.523835\pi$
$464$	1408.23	0.140896
$465$	6892.14	0.687345
$466$	8749.90	0.869810
$467$	7056.20	0.699191	0.349595	−	0.936901i	$-0.386319\pi$
$467$	7056.20	0.699191	0.349595	+	0.936901i	$0.386319\pi$
$468$	−129.343	−0.0127754
$469$	−1099.83	−0.108285
$470$	−4851.03	−0.476087
$471$	−26476.6	−2.59018
$472$	1801.06	0.175637
$473$	0	0
$474$	−16664.6	−1.61483
$475$	−4268.18	−0.412290
$476$	49.9340	0.00480824
$477$	−9608.65	−0.922327
$478$	3742.97	0.358158
$479$	5036.37	0.480412	0.240206	−	0.970722i	$-0.422785\pi$
$479$	5036.37	0.480412	0.240206	+	0.970722i	$0.422785\pi$
$480$	496.656	0.0472274
$481$	617.729	0.0585572
$482$	16831.7	1.59058
$483$	1787.59	0.168402
$484$	0	0
$485$	7207.77	0.674820
$486$	15038.0	1.40357
$487$	16149.2	1.50265	0.751326	−	0.659931i	$-0.229415\pi$
$487$	16149.2	1.50265	0.751326	+	0.659931i	$0.229415\pi$
$488$	9914.99	0.919734
$489$	4680.85	0.432874
$490$	−4199.79	−0.387199
$491$	9611.24	0.883399	0.441700	−	0.897163i	$-0.354376\pi$
$491$	9611.24	0.883399	0.441700	+	0.897163i	$0.354376\pi$
$492$	122.900	0.0112617
$493$	1289.54	0.117805
$494$	−1470.73	−0.133950
$495$	0	0
$496$	12254.5	1.10936
$497$	1058.55	0.0955378
$498$	−12640.6	−1.13743
$499$	−13659.0	−1.22537	−0.612686	−	0.790327i	$-0.709911\pi$
$499$	−13659.0	−1.22537	−0.612686	+	0.790327i	$0.709911\pi$
$500$	−330.261	−0.0295395
$501$	−2433.19	−0.216980
$502$	−11041.0	−0.981641
$503$	7003.19	0.620789	0.310394	−	0.950608i	$-0.399539\pi$
$503$	7003.19	0.620789	0.310394	+	0.950608i	$0.399539\pi$
$504$	2013.01	0.177910
$505$	6409.54	0.564793
$506$	0	0
$507$	1289.99	0.112999
$508$	−511.069	−0.0446359
$509$	−6808.91	−0.592927	−0.296463	−	0.955044i	$-0.595807\pi$
$509$	−6808.91	−0.592927	−0.296463	+	0.955044i	$0.595807\pi$
$510$	−5372.98	−0.466509
$511$	245.148	0.0212226
$512$	12198.9	1.05297
$513$	1328.44	0.114331
$514$	2254.35	0.193453
$515$	5900.31	0.504851
$516$	−802.950	−0.0685037
$517$	0	0
$518$	−367.815	−0.0311985
$519$	18603.9	1.57345
$520$	−1354.87	−0.114260
$521$	13843.4	1.16409	0.582044	−	0.813157i	$-0.302253\pi$
$521$	13843.4	1.16409	0.582044	+	0.813157i	$0.302253\pi$
$522$	1988.89	0.166765
$523$	15870.3	1.32688	0.663440	−	0.748230i	$-0.269096\pi$
$523$	15870.3	1.32688	0.663440	+	0.748230i	$0.269096\pi$
$524$	859.796	0.0716801
$525$	−2229.09	−0.185305
$526$	−5671.05	−0.470094
$527$	11221.6	0.927552
$528$	0	0
$529$	−5135.43	−0.422079
$530$	−3850.76	−0.315597
$531$	2442.34	0.199602
$532$	−36.2796	−0.00295662
$533$	−657.712	−0.0534496
$534$	−21124.3	−1.71187
$535$	−1477.45	−0.119394
$536$	−9079.13	−0.731640
$537$	−7218.24	−0.580056
$538$	9395.96	0.752953
$539$	0	0
$540$	46.8204	0.00373116
$541$	−9664.93	−0.768074	−0.384037	−	0.923318i	$-0.625466\pi$
$541$	−9664.93	−0.768074	−0.384037	+	0.923318i	$0.625466\pi$
$542$	990.694	0.0785128
$543$	11216.7	0.886474
$544$	808.642	0.0637320
$545$	6050.79	0.475573
$546$	−768.098	−0.0602043
$547$	13683.4	1.06958	0.534790	−	0.844985i	$-0.320391\pi$
$547$	13683.4	1.06958	0.534790	+	0.844985i	$0.320391\pi$
$548$	95.7159	0.00746128
$549$	13445.3	1.04523
$550$	0	0
$551$	−936.914	−0.0724390
$552$	14756.6	1.13783
$553$	2199.93	0.169169
$554$	13217.4	1.01363
$555$	−1639.63	−0.125403
$556$	339.346	0.0258839
$557$	−20731.5	−1.57706	−0.788528	−	0.614999i	$-0.789156\pi$
$557$	−20731.5	−1.57706	−0.788528	+	0.614999i	$0.789156\pi$
$558$	17307.4	1.31305
$559$	4297.08	0.325129
$560$	774.590	0.0584507
$561$	0	0
$562$	14838.0	1.11371
$563$	19335.4	1.44741	0.723703	−	0.690111i	$-0.242438\pi$
$563$	19335.4	1.44741	0.723703	+	0.690111i	$0.242438\pi$
$564$	940.521	0.0702182
$565$	−2172.36	−0.161756
$566$	−5824.90	−0.432578
$567$	−1663.69	−0.123225
$568$	8738.31	0.645513
$569$	11715.7	0.863177	0.431588	−	0.902071i	$-0.357953\pi$
$569$	11715.7	0.863177	0.431588	+	0.902071i	$0.357953\pi$
$570$	3903.75	0.286860
$571$	10524.5	0.771343	0.385672	−	0.922636i	$-0.373970\pi$
$571$	10524.5	0.771343	0.385672	+	0.922636i	$0.373970\pi$
$572$	0	0
$573$	−10703.2	−0.780334
$574$	391.621	0.0284773
$575$	−8768.19	−0.635928
$576$	16592.1	1.20024
$577$	−22968.0	−1.65714	−0.828571	−	0.559884i	$-0.810846\pi$
$577$	−22968.0	−1.65714	−0.828571	+	0.559884i	$0.810846\pi$
$578$	4868.72	0.350367
$579$	5003.22	0.359114
$580$	−33.0213	−0.00236402
$581$	1668.72	0.119157
$582$	33731.6	2.40244
$583$	0	0
$584$	2023.70	0.143393
$585$	−1837.29	−0.129850
$586$	15329.7	1.08066
$587$	−12402.2	−0.872050	−0.436025	−	0.899935i	$-0.643614\pi$
$587$	−12402.2	−0.872050	−0.436025	+	0.899935i	$0.643614\pi$
$588$	814.259	0.0571080
$589$	−8153.06	−0.570358
$590$	978.793	0.0682987
$591$	−25175.9	−1.75228
$592$	−2915.34	−0.202398
$593$	−14697.7	−1.01781	−0.508907	−	0.860821i	$-0.669950\pi$
$593$	−14697.7	−1.01781	−0.508907	+	0.860821i	$0.669950\pi$
$594$	0	0
$595$	709.301	0.0488714
$596$	898.102	0.0617243
$597$	22041.5	1.51105
$598$	−3021.34	−0.206608
$599$	14830.6	1.01162	0.505811	−	0.862644i	$-0.331193\pi$
$599$	14830.6	1.01162	0.505811	+	0.862644i	$0.331193\pi$
$600$	−18401.1	−1.25204
$601$	−25135.8	−1.70601	−0.853004	−	0.521904i	$-0.825222\pi$
$601$	−25135.8	−1.70601	−0.853004	+	0.521904i	$0.825222\pi$
$602$	−2558.61	−0.173225
$603$	−12311.8	−0.831470
$604$	182.004	0.0122610
$605$	0	0
$606$	29995.9	2.01073
$607$	19114.2	1.27813	0.639063	−	0.769155i	$-0.279322\pi$
$607$	19114.2	1.27813	0.639063	+	0.769155i	$0.279322\pi$
$608$	−587.520	−0.0391893
$609$	−489.310	−0.0325580
$610$	5388.33	0.357651
$611$	−5033.30	−0.333266
$612$	558.975	0.0369203
$613$	24161.6	1.59197	0.795984	−	0.605318i	$-0.206954\pi$
$613$	24161.6	1.59197	0.795984	+	0.605318i	$0.206954\pi$
$614$	23851.5	1.56770
$615$	1745.76	0.114465
$616$	0	0
$617$	−8503.95	−0.554872	−0.277436	−	0.960744i	$-0.589485\pi$
$617$	−8503.95	−0.554872	−0.277436	+	0.960744i	$0.589485\pi$
$618$	27612.8	1.79733
$619$	−9897.30	−0.642659	−0.321330	−	0.946967i	$-0.604130\pi$
$619$	−9897.30	−0.642659	−0.321330	+	0.946967i	$0.604130\pi$
$620$	−287.352	−0.0186135
$621$	2729.03	0.176348
$622$	−216.481	−0.0139551
$623$	2788.67	0.179335
$624$	−6088.03	−0.390571
$625$	8379.27	0.536273
$626$	−20411.3	−1.30320
$627$	0	0
$628$	1103.88	0.0701428
$629$	−2669.61	−0.169228
$630$	1093.98	0.0691826
$631$	9964.67	0.628665	0.314332	−	0.949313i	$-0.398219\pi$
$631$	9964.67	0.628665	0.314332	+	0.949313i	$0.398219\pi$
$632$	18160.5	1.14301
$633$	28387.3	1.78245
$634$	27480.4	1.72143
$635$	−7259.62	−0.453684
$636$	746.588	0.0465474
$637$	−4357.60	−0.271043
$638$	0	0
$639$	11849.6	0.733591
$640$	6128.91	0.378541
$641$	−7808.50	−0.481150	−0.240575	−	0.970631i	$-0.577336\pi$
$641$	−7808.50	−0.481150	−0.240575	+	0.970631i	$0.577336\pi$
$642$	−6914.29	−0.425055
$643$	14727.0	0.903229	0.451614	−	0.892213i	$-0.350848\pi$
$643$	14727.0	0.903229	0.451614	+	0.892213i	$0.350848\pi$
$644$	−74.5298	−0.00456038
$645$	−11405.7	−0.696278
$646$	6355.98	0.387109
$647$	−19068.3	−1.15866	−0.579329	−	0.815094i	$-0.696685\pi$
$647$	−19068.3	−1.15866	−0.579329	+	0.815094i	$0.696685\pi$
$648$	−13733.8	−0.832585
$649$	0	0
$650$	3767.54	0.227346
$651$	−4257.99	−0.256350
$652$	−195.158	−0.0117223
$653$	5218.07	0.312709	0.156354	−	0.987701i	$-0.450026\pi$
$653$	5218.07	0.312709	0.156354	+	0.987701i	$0.450026\pi$
$654$	28317.0	1.69309
$655$	12213.2	0.728564
$656$	3104.03	0.184744
$657$	2744.26	0.162958
$658$	2996.98	0.177560
$659$	−33242.5	−1.96502	−0.982508	−	0.186219i	$-0.940377\pi$
$659$	−33242.5	−1.96502	−0.982508	+	0.186219i	$0.940377\pi$
$660$	0	0
$661$	17680.3	1.04037	0.520185	−	0.854053i	$-0.325863\pi$
$661$	17680.3	1.04037	0.520185	+	0.854053i	$0.325863\pi$
$662$	10525.4	0.617949
$663$	−5574.87	−0.326561
$664$	13775.3	0.805098
$665$	−515.343	−0.0300514
$666$	−4117.42	−0.239560
$667$	−1924.72	−0.111732
$668$	101.447	0.00587588
$669$	−33227.7	−1.92026
$670$	−4934.08	−0.284508
$671$	0	0
$672$	−306.836	−0.0176138
$673$	8624.89	0.494005	0.247002	−	0.969015i	$-0.420554\pi$
$673$	8624.89	0.494005	0.247002	+	0.969015i	$0.420554\pi$
$674$	−24424.5	−1.39584
$675$	−3403.03	−0.194048
$676$	−53.7832	−0.00306003
$677$	3089.38	0.175383	0.0876916	−	0.996148i	$-0.472051\pi$
$677$	3089.38	0.175383	0.0876916	+	0.996148i	$0.472051\pi$
$678$	−10166.4	−0.575869
$679$	−4452.99	−0.251679
$680$	5855.29	0.330206
$681$	9250.72	0.520541
$682$	0	0
$683$	−3329.00	−0.186502	−0.0932509	−	0.995643i	$-0.529726\pi$
$683$	−3329.00	−0.186502	−0.0932509	+	0.995643i	$0.529726\pi$
$684$	−406.124	−0.0227025
$685$	1359.62	0.0758372
$686$	5249.67	0.292177
$687$	50582.4	2.80908
$688$	−20279.8	−1.12378
$689$	−3995.45	−0.220921
$690$	8019.53	0.442461
$691$	−2993.75	−0.164816	−0.0824079	−	0.996599i	$-0.526261\pi$
$691$	−2993.75	−0.164816	−0.0824079	+	0.996599i	$0.526261\pi$
$692$	−775.648	−0.0426094
$693$	0	0
$694$	15978.3	0.873960
$695$	4820.32	0.263087
$696$	−4039.26	−0.219982
$697$	2842.40	0.154467
$698$	4444.60	0.241018
$699$	−24097.5	−1.30394
$700$	92.9368	0.00501811
$701$	2649.74	0.142766	0.0713832	−	0.997449i	$-0.477259\pi$
$701$	2649.74	0.142766	0.0713832	+	0.997449i	$0.477259\pi$
$702$	−1172.61	−0.0630449
$703$	1939.61	0.104059
$704$	0	0
$705$	13359.9	0.713705
$706$	−516.300	−0.0275230
$707$	−3959.84	−0.210643
$708$	−189.769	−0.0100734
$709$	23249.1	1.23151	0.615755	−	0.787938i	$-0.288851\pi$
$709$	23249.1	1.23151	0.615755	+	0.787938i	$0.288851\pi$
$710$	4748.86	0.251016
$711$	24626.6	1.29897
$712$	23020.5	1.21170
$713$	−16749.0	−0.879738
$714$	3319.45	0.173988
$715$	0	0
$716$	300.948	0.0157081
$717$	−10308.2	−0.536915
$718$	−6574.45	−0.341722
$719$	10009.1	0.519160	0.259580	−	0.965722i	$-0.416416\pi$
$719$	10009.1	0.519160	0.259580	+	0.965722i	$0.416416\pi$
$720$	8670.97	0.448817
$721$	−3645.23	−0.188288
$722$	14392.4	0.741872
$723$	−46354.9	−2.38445
$724$	−467.656	−0.0240059
$725$	2400.07	0.122947
$726$	0	0
$727$	2141.57	0.109252	0.0546262	−	0.998507i	$-0.482603\pi$
$727$	2141.57	0.109252	0.0546262	+	0.998507i	$0.482603\pi$
$728$	837.046	0.0426140
$729$	−25331.1	−1.28695
$730$	1099.79	0.0557602
$731$	−18570.5	−0.939608
$732$	−1044.69	−0.0527500
$733$	13877.0	0.699263	0.349632	−	0.936887i	$-0.386307\pi$
$733$	13877.0	0.699263	0.349632	+	0.936887i	$0.386307\pi$
$734$	29150.3	1.46588
$735$	11566.4	0.580451
$736$	−1206.95	−0.0604467
$737$	0	0
$738$	4383.92	0.218664
$739$	2634.77	0.131152	0.0655762	−	0.997848i	$-0.479111\pi$
$739$	2634.77	0.131152	0.0655762	+	0.997848i	$0.479111\pi$
$740$	68.3609	0.00339594
$741$	4050.43	0.200805
$742$	2379.01	0.117704
$743$	−17893.2	−0.883498	−0.441749	−	0.897139i	$-0.645642\pi$
$743$	−17893.2	−0.883498	−0.441749	+	0.897139i	$0.645642\pi$
$744$	−35149.8	−1.73206
$745$	12757.3	0.627372
$746$	−2312.59	−0.113499
$747$	18680.1	0.914951
$748$	0	0
$749$	912.773	0.0445287
$750$	−21954.7	−1.06890
$751$	27073.3	1.31547	0.657736	−	0.753248i	$-0.271514\pi$
$751$	27073.3	1.31547	0.657736	+	0.753248i	$0.271514\pi$
$752$	23754.4	1.15191
$753$	30407.2	1.47158
$754$	827.017	0.0399445
$755$	2585.32	0.124622
$756$	−28.9258	−0.00139156
$757$	−18847.4	−0.904914	−0.452457	−	0.891786i	$-0.649452\pi$
$757$	−18847.4	−0.904914	−0.452457	+	0.891786i	$0.649452\pi$
$758$	257.422	0.0123351
$759$	0	0
$760$	−4254.17	−0.203046
$761$	−35933.6	−1.71168	−0.855842	−	0.517237i	$-0.826961\pi$
$761$	−35933.6	−1.71168	−0.855842	+	0.517237i	$0.826961\pi$
$762$	−33974.2	−1.61517
$763$	−3738.20	−0.177368
$764$	446.245	0.0211316
$765$	7940.10	0.375262
$766$	37590.9	1.77312
$767$	1015.57	0.0478098
$768$	−3725.23	−0.175029
$769$	−21651.5	−1.01531	−0.507656	−	0.861560i	$-0.669488\pi$
$769$	−21651.5	−1.01531	−0.507656	+	0.861560i	$0.669488\pi$
$770$	0	0
$771$	−6208.54	−0.290007
$772$	−208.598	−0.00972489
$773$	31871.9	1.48299	0.741496	−	0.670958i	$-0.234117\pi$
$773$	31871.9	1.48299	0.741496	+	0.670958i	$0.234117\pi$
$774$	−28641.8	−1.33011
$775$	20885.5	0.968039
$776$	−36759.5	−1.70050
$777$	1012.97	0.0467699
$778$	−36915.6	−1.70114
$779$	−2065.15	−0.0949828
$780$	142.756	0.00655320
$781$	0	0
$782$	13057.2	0.597089
$783$	−747.003	−0.0340941
$784$	20565.5	0.936837
$785$	15680.4	0.712938
$786$	57156.4	2.59377
$787$	34045.6	1.54205	0.771027	−	0.636803i	$-0.219744\pi$
$787$	34045.6	1.54205	0.771027	+	0.636803i	$0.219744\pi$
$788$	1049.65	0.0474522
$789$	15618.2	0.704720
$790$	9869.35	0.444476
$791$	1342.09	0.0603279
$792$	0	0
$793$	5590.79	0.250359
$794$	−25529.3	−1.14106
$795$	10605.1	0.473113
$796$	−918.971	−0.0409197
$797$	23610.9	1.04936	0.524681	−	0.851299i	$-0.324184\pi$
$797$	23610.9	1.04936	0.524681	+	0.851299i	$0.324184\pi$
$798$	−2411.75	−0.106986
$799$	21752.2	0.963124
$800$	1505.04	0.0665139
$801$	31217.1	1.37703
$802$	19901.8	0.876257
$803$	0	0
$804$	956.624	0.0419621
$805$	−1058.68	−0.0463522
$806$	7196.73	0.314509
$807$	−25876.8	−1.12875
$808$	−32688.5	−1.42324
$809$	2353.50	0.102280	0.0511401	−	0.998691i	$-0.483714\pi$
$809$	2353.50	0.102280	0.0511401	+	0.998691i	$0.483714\pi$
$810$	−7463.68	−0.323762
$811$	−14156.7	−0.612960	−0.306480	−	0.951877i	$-0.599151\pi$
$811$	−14156.7	−0.612960	−0.306480	+	0.951877i	$0.599151\pi$
$812$	20.4007	0.000881679 0
$813$	−2728.40	−0.117699
$814$	0	0
$815$	−2772.17	−0.119147
$816$	26310.3	1.12873
$817$	13492.4	0.577771
$818$	20166.6	0.861991
$819$	1135.08	0.0484285
$820$	−72.7856	−0.00309973
$821$	−42888.4	−1.82316	−0.911581	−	0.411120i	$-0.865138\pi$
$821$	−42888.4	−1.82316	−0.911581	+	0.411120i	$0.865138\pi$
$822$	6362.88	0.269989
$823$	33290.8	1.41002	0.705009	−	0.709199i	$-0.250943\pi$
$823$	33290.8	1.41002	0.705009	+	0.709199i	$0.250943\pi$
$824$	−30091.4	−1.27219
$825$	0	0
$826$	−604.702	−0.0254725
$827$	41789.7	1.75716	0.878579	−	0.477597i	$-0.158492\pi$
$827$	41789.7	1.75716	0.878579	+	0.477597i	$0.158492\pi$
$828$	−834.307	−0.0350171
$829$	−18543.9	−0.776907	−0.388453	−	0.921468i	$-0.626991\pi$
$829$	−18543.9	−0.776907	−0.388453	+	0.921468i	$0.626991\pi$
$830$	7486.22	0.313073
$831$	−36401.1	−1.51954
$832$	6899.29	0.287488
$833$	18832.0	0.783302
$834$	22558.6	0.936619
$835$	1441.02	0.0597230
$836$	0	0
$837$	−6500.45	−0.268445
$838$	−3000.78	−0.123699
$839$	8085.53	0.332710	0.166355	−	0.986066i	$-0.446800\pi$
$839$	8085.53	0.332710	0.166355	+	0.986066i	$0.446800\pi$
$840$	−2221.77	−0.0912598
$841$	−23862.2	−0.978398
$842$	2255.25	0.0923054
$843$	−40864.2	−1.66956
$844$	−1183.54	−0.0482693
$845$	−763.977	−0.0311025
$846$	33549.0	1.36340
$847$	0	0
$848$	18856.3	0.763595
$849$	16042.0	0.648479
$850$	−16282.0	−0.657020
$851$	3984.56	0.160504
$852$	−920.713	−0.0370224
$853$	32344.6	1.29831	0.649154	−	0.760657i	$-0.275123\pi$
$853$	32344.6	1.29831	0.649154	+	0.760657i	$0.275123\pi$
$854$	−3328.93	−0.133388
$855$	−5768.89	−0.230751
$856$	7534.95	0.300864
$857$	26998.6	1.07614	0.538072	−	0.842899i	$-0.319153\pi$
$857$	26998.6	1.07614	0.538072	+	0.842899i	$0.319153\pi$
$858$	0	0
$859$	42220.3	1.67699	0.838497	−	0.544907i	$-0.183435\pi$
$859$	42220.3	1.67699	0.838497	+	0.544907i	$0.183435\pi$
$860$	475.535	0.0188554
$861$	−1078.54	−0.0426904
$862$	43891.3	1.73428
$863$	11324.1	0.446672	0.223336	−	0.974741i	$-0.428305\pi$
$863$	11324.1	0.446672	0.223336	+	0.974741i	$0.428305\pi$
$864$	−468.430	−0.0184448
$865$	−11017.9	−0.433086
$866$	32069.6	1.25840
$867$	−13408.6	−0.525236
$868$	177.527	0.00694202
$869$	0	0
$870$	−2195.15	−0.0855430
$871$	−5119.48	−0.199158
$872$	−30858.9	−1.19841
$873$	−49847.9	−1.93253
$874$	−9486.71	−0.367154
$875$	2898.29	0.111977
$876$	−213.228	−0.00822408
$877$	21748.6	0.837396	0.418698	−	0.908125i	$-0.362487\pi$
$877$	21748.6	0.837396	0.418698	+	0.908125i	$0.362487\pi$
$878$	−14588.6	−0.560752
$879$	−42218.5	−1.62002
$880$	0	0
$881$	−38151.8	−1.45899	−0.729493	−	0.683988i	$-0.760244\pi$
$881$	−38151.8	−1.45899	−0.729493	+	0.683988i	$0.760244\pi$
$882$	29045.2	1.10885
$883$	34211.2	1.30385	0.651924	−	0.758284i	$-0.273962\pi$
$883$	34211.2	1.30385	0.651924	+	0.758284i	$0.273962\pi$
$884$	232.432	0.00884336
$885$	−2695.62	−0.102387
$886$	−8553.18	−0.324322
$887$	−41729.1	−1.57962	−0.789811	−	0.613350i	$-0.789821\pi$
$887$	−41729.1	−1.57962	−0.789811	+	0.613350i	$0.789821\pi$
$888$	8362.10	0.316006
$889$	4485.02	0.169204
$890$	12510.6	0.471185
$891$	0	0
$892$	1385.35	0.0520012
$893$	−15804.1	−0.592232
$894$	59702.8	2.23351
$895$	4274.90	0.159658
$896$	−3786.46	−0.141180
$897$	8320.86	0.309727
$898$	41551.3	1.54408
$899$	4584.61	0.170084
$900$	1040.36	0.0385318
$901$	17266.9	0.638452
$902$	0	0
$903$	7046.49	0.259682
$904$	11079.0	0.407613
$905$	−6642.94	−0.243999
$906$	12099.0	0.443668
$907$	24010.7	0.879009	0.439505	−	0.898240i	$-0.355154\pi$
$907$	24010.7	0.879009	0.439505	+	0.898240i	$0.355154\pi$
$908$	−385.688	−0.0140964
$909$	−44327.5	−1.61744
$910$	454.895	0.0165710
$911$	−3626.76	−0.131899	−0.0659495	−	0.997823i	$-0.521008\pi$
$911$	−3626.76	−0.131899	−0.0659495	+	0.997823i	$0.521008\pi$
$912$	−19115.8	−0.694065
$913$	0	0
$914$	−40557.9	−1.46776
$915$	−14839.6	−0.536156
$916$	−2108.92	−0.0760706
$917$	−7545.36	−0.271723
$918$	5067.63	0.182197
$919$	14870.4	0.533763	0.266881	−	0.963729i	$-0.414007\pi$
$919$	14870.4	0.533763	0.266881	+	0.963729i	$0.414007\pi$
$920$	−8739.40	−0.313184
$921$	−65687.8	−2.35015
$922$	−38781.7	−1.38526
$923$	4927.30	0.175714
$924$	0	0
$925$	−4968.65	−0.176614
$926$	4131.30	0.146612
$927$	−40805.7	−1.44578
$928$	330.373	0.0116864
$929$	−21517.1	−0.759908	−0.379954	−	0.925005i	$-0.624060\pi$
$929$	−21517.1	−0.759908	−0.379954	+	0.925005i	$0.624060\pi$
$930$	−19102.2	−0.673534
$931$	−13682.4	−0.481658
$932$	1004.69	0.0353109
$933$	596.195	0.0209202
$934$	−19557.0	−0.685143
$935$	0	0
$936$	9370.12	0.327214
$937$	35005.1	1.22045	0.610227	−	0.792226i	$-0.291078\pi$
$937$	35005.1	1.22045	0.610227	+	0.792226i	$0.291078\pi$
$938$	3048.29	0.106109
$939$	56213.4	1.95363
$940$	−557.010	−0.0193273
$941$	41196.6	1.42718	0.713588	−	0.700566i	$-0.247069\pi$
$941$	41196.6	1.42718	0.713588	+	0.700566i	$0.247069\pi$
$942$	73382.4	2.53814
$943$	−4242.46	−0.146504
$944$	−4792.93	−0.165251
$945$	−410.884	−0.0141440
$946$	0	0
$947$	43619.3	1.49676	0.748382	−	0.663268i	$-0.230831\pi$
$947$	43619.3	1.49676	0.748382	+	0.663268i	$0.230831\pi$
$948$	−1913.48	−0.0655558
$949$	1141.11	0.0390327
$950$	11829.7	0.404006
$951$	−75681.9	−2.58060
$952$	−3617.42	−0.123153
$953$	−33874.3	−1.15141	−0.575706	−	0.817657i	$-0.695273\pi$
$953$	−33874.3	−1.15141	−0.575706	+	0.817657i	$0.695273\pi$
$954$	26631.3	0.903796
$955$	6338.80	0.214784
$956$	429.779	0.0145398
$957$	0	0
$958$	−13958.8	−0.470760
$959$	−839.980	−0.0282840
$960$	−18312.8	−0.615668
$961$	10104.4	0.339177
$962$	−1712.10	−0.0573807
$963$	10217.8	0.341916
$964$	1932.67	0.0645715
$965$	−2963.09	−0.0988447
$966$	−4954.49	−0.165019
$967$	44199.5	1.46987	0.734933	−	0.678140i	$-0.237214\pi$
$967$	44199.5	1.46987	0.734933	+	0.678140i	$0.237214\pi$
$968$	0	0
$969$	−17504.5	−0.580317
$970$	−19977.0	−0.661262
$971$	49668.1	1.64153	0.820765	−	0.571266i	$-0.193548\pi$
$971$	49668.1	1.64153	0.820765	+	0.571266i	$0.193548\pi$
$972$	1726.71	0.0569796
$973$	−2978.01	−0.0981200
$974$	−44759.2	−1.47246
$975$	−10375.9	−0.340815
$976$	−26385.4	−0.865346
$977$	−2389.08	−0.0782327	−0.0391164	−	0.999235i	$-0.512454\pi$
$977$	−2389.08	−0.0782327	−0.0391164	+	0.999235i	$0.512454\pi$
$978$	−12973.4	−0.424177
$979$	0	0
$980$	−482.233	−0.0157188
$981$	−41846.4	−1.36193
$982$	−26638.5	−0.865650
$983$	19399.5	0.629448	0.314724	−	0.949183i	$-0.398088\pi$
$983$	19399.5	0.629448	0.314724	+	0.949183i	$0.398088\pi$
$984$	−8903.34	−0.288443
$985$	14910.1	0.482309
$986$	−3574.08	−0.115438
$987$	−8253.78	−0.266181
$988$	−168.874	−0.00543784
$989$	27717.6	0.891172
$990$	0	0
$991$	34014.9	1.09033	0.545165	−	0.838328i	$-0.316467\pi$
$991$	34014.9	1.09033	0.545165	+	0.838328i	$0.316467\pi$
$992$	2874.91	0.0920147
$993$	−28987.3	−0.926370
$994$	−2933.86	−0.0936182
$995$	−13053.8	−0.415911
$996$	−1451.43	−0.0461752
$997$	40001.0	1.27066	0.635329	−	0.772242i	$-0.280865\pi$
$997$	40001.0	1.27066	0.635329	+	0.772242i	$0.280865\pi$
$998$	37857.2	1.20075
$999$	1546.45	0.0489765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.o.1.9		34
11.5	even	5		143.4.h.a.14.13	✓	68
11.9	even	5		143.4.h.a.92.13	yes	68
11.10	odd	2		1573.4.a.p.1.26		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.13	✓	68	11.5	even	5
143.4.h.a.92.13	yes	68	11.9	even	5
1573.4.a.o.1.9		34	1.1	even	1	trivial
1573.4.a.p.1.26		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)

\(f(q)\)	\(=\)	\(q-2.77160 q^{2} +7.63306 q^{3} -0.318244 q^{4} -4.52057 q^{5} -21.1558 q^{6} +2.79283 q^{7} +23.0548 q^{8} +31.2637 q^{9} +O(q^{10})\)	\(q-2.77160 q^{2} +7.63306 q^{3} -0.318244 q^{4} -4.52057 q^{5} -21.1558 q^{6} +2.79283 q^{7} +23.0548 q^{8} +31.2637 q^{9} +12.5292 q^{10} -2.42917 q^{12} +13.0000 q^{13} -7.74059 q^{14} -34.5058 q^{15} -61.3528 q^{16} -56.1814 q^{17} -86.6503 q^{18} +40.8187 q^{19} +1.43864 q^{20} +21.3178 q^{21} +83.8545 q^{23} +175.979 q^{24} -104.564 q^{25} -36.0308 q^{26} +32.5448 q^{27} -0.888799 q^{28} -22.9531 q^{29} +95.6363 q^{30} -199.738 q^{31} -14.3934 q^{32} +155.712 q^{34} -12.6252 q^{35} -9.94946 q^{36} +47.5176 q^{37} -113.133 q^{38} +99.2298 q^{39} -104.221 q^{40} -50.5932 q^{41} -59.0845 q^{42} +330.544 q^{43} -141.330 q^{45} -232.411 q^{46} -387.177 q^{47} -468.310 q^{48} -335.200 q^{49} +289.811 q^{50} -428.836 q^{51} -4.13717 q^{52} -307.343 q^{53} -90.2011 q^{54} +64.3882 q^{56} +311.572 q^{57} +63.6167 q^{58} +78.1208 q^{59} +10.9813 q^{60} +430.061 q^{61} +553.594 q^{62} +87.3140 q^{63} +530.715 q^{64} -58.7675 q^{65} -393.806 q^{67} +17.8794 q^{68} +640.066 q^{69} +34.9919 q^{70} +379.023 q^{71} +720.778 q^{72} +87.7778 q^{73} -131.700 q^{74} -798.147 q^{75} -12.9903 q^{76} -275.025 q^{78} +787.707 q^{79} +277.350 q^{80} -595.702 q^{81} +140.224 q^{82} +597.501 q^{83} -6.78426 q^{84} +253.972 q^{85} -916.136 q^{86} -175.202 q^{87} +998.511 q^{89} +391.709 q^{90} +36.3068 q^{91} -26.6861 q^{92} -1524.62 q^{93} +1073.10 q^{94} -184.524 q^{95} -109.866 q^{96} -1594.44 q^{97} +929.040 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) \) 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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