LMFDB - Embedded newform 1573.4.a.o.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.02870 q^{2} -4.53812 q^{3} -3.88438 q^{4} -12.2012 q^{5} +9.20648 q^{6} +12.3738 q^{7} +24.1098 q^{8} -6.40548 q^{9} +O(q^{10})$	\(q-2.02870 q^{2} -4.53812 q^{3} -3.88438 q^{4} -12.2012 q^{5} +9.20648 q^{6} +12.3738 q^{7} +24.1098 q^{8} -6.40548 q^{9} +24.7525 q^{10} +17.6278 q^{12} +13.0000 q^{13} -25.1027 q^{14} +55.3703 q^{15} -17.8366 q^{16} -109.152 q^{17} +12.9948 q^{18} -118.154 q^{19} +47.3939 q^{20} -56.1537 q^{21} +70.2429 q^{23} -109.413 q^{24} +23.8682 q^{25} -26.3731 q^{26} +151.598 q^{27} -48.0645 q^{28} +66.1107 q^{29} -112.330 q^{30} -24.4805 q^{31} -156.694 q^{32} +221.436 q^{34} -150.974 q^{35} +24.8813 q^{36} -165.150 q^{37} +239.699 q^{38} -58.9955 q^{39} -294.168 q^{40} +453.175 q^{41} +113.919 q^{42} -409.892 q^{43} +78.1543 q^{45} -142.502 q^{46} +462.592 q^{47} +80.9445 q^{48} -189.889 q^{49} -48.4215 q^{50} +495.343 q^{51} -50.4969 q^{52} -22.1093 q^{53} -307.547 q^{54} +298.330 q^{56} +536.197 q^{57} -134.119 q^{58} -89.2440 q^{59} -215.079 q^{60} +602.575 q^{61} +49.6636 q^{62} -79.2600 q^{63} +460.577 q^{64} -158.615 q^{65} +419.882 q^{67} +423.986 q^{68} -318.771 q^{69} +306.282 q^{70} +805.330 q^{71} -154.435 q^{72} +655.582 q^{73} +335.040 q^{74} -108.317 q^{75} +458.955 q^{76} +119.684 q^{78} +771.961 q^{79} +217.627 q^{80} -515.022 q^{81} -919.356 q^{82} +215.244 q^{83} +218.122 q^{84} +1331.78 q^{85} +831.548 q^{86} -300.018 q^{87} -1549.25 q^{89} -158.552 q^{90} +160.859 q^{91} -272.850 q^{92} +111.095 q^{93} -938.460 q^{94} +1441.62 q^{95} +711.094 q^{96} +812.695 q^{97} +385.229 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.02870	−0.717254	−0.358627	−	0.933481i	$-0.616755\pi$
$2$	−2.02870	−0.717254	−0.358627	+	0.933481i	$0.616755\pi$
$3$	−4.53812	−0.873361	−0.436681	−	0.899617i	$-0.643846\pi$
$3$	−4.53812	−0.873361	−0.436681	+	0.899617i	$0.643846\pi$
$4$	−3.88438	−0.485547
$5$	−12.2012	−1.09130	−0.545652	−	0.838012i	$-0.683718\pi$
$5$	−12.2012	−1.09130	−0.545652	+	0.838012i	$0.683718\pi$
$6$	9.20648	0.626421
$7$	12.3738	0.668122	0.334061	−	0.942552i	$-0.391581\pi$
$7$	12.3738	0.668122	0.334061	+	0.942552i	$0.391581\pi$
$8$	24.1098	1.06551
$9$	−6.40548	−0.237240
$10$	24.7525	0.782742
$11$	0	0
$11$	0	0
$12$	17.6278	0.424058
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−25.1027	−0.479213
$15$	55.3703	0.953103
$16$	−17.8366	−0.278696
$17$	−109.152	−1.55724	−0.778622	−	0.627493i	$-0.784081\pi$
$17$	−109.152	−1.55724	−0.778622	+	0.627493i	$0.784081\pi$
$18$	12.9948	0.170161
$19$	−118.154	−1.42665	−0.713326	−	0.700832i	$-0.752812\pi$
$19$	−118.154	−1.42665	−0.713326	+	0.700832i	$0.752812\pi$
$20$	47.3939	0.529880
$21$	−56.1537	−0.583511
$22$	0	0
$23$	70.2429	0.636811	0.318405	−	0.947955i	$-0.396853\pi$
$23$	70.2429	0.636811	0.318405	+	0.947955i	$0.396853\pi$
$24$	−109.413	−0.930579
$25$	23.8682	0.190946
$26$	−26.3731	−0.198930
$27$	151.598	1.08056
$28$	−48.0645	−0.324405
$29$	66.1107	0.423326	0.211663	−	0.977343i	$-0.432112\pi$
$29$	66.1107	0.423326	0.211663	+	0.977343i	$0.432112\pi$
$30$	−112.330	−0.683617
$31$	−24.4805	−0.141833	−0.0709166	−	0.997482i	$-0.522592\pi$
$31$	−24.4805	−0.141833	−0.0709166	+	0.997482i	$0.522592\pi$
$32$	−156.694	−0.865618
$33$	0	0
$34$	221.436	1.11694
$35$	−150.974	−0.729124
$36$	24.8813	0.115191
$37$	−165.150	−0.733798	−0.366899	−	0.930261i	$-0.619581\pi$
$37$	−165.150	−0.733798	−0.366899	+	0.930261i	$0.619581\pi$
$38$	239.699	1.02327
$39$	−58.9955	−0.242227
$40$	−294.168	−1.16280
$41$	453.175	1.72620	0.863098	−	0.505037i	$-0.168521\pi$
$41$	453.175	1.72620	0.863098	+	0.505037i	$0.168521\pi$
$42$	113.919	0.418526
$43$	−409.892	−1.45367	−0.726837	−	0.686810i	$-0.759010\pi$
$43$	−409.892	−1.45367	−0.726837	+	0.686810i	$0.759010\pi$
$44$	0	0
$45$	78.1543	0.258901
$46$	−142.502	−0.456755
$47$	462.592	1.43566	0.717830	−	0.696219i	$-0.245136\pi$
$47$	462.592	1.43566	0.717830	+	0.696219i	$0.245136\pi$
$48$	80.9445	0.243403
$49$	−189.889	−0.553614
$50$	−48.4215	−0.136957
$51$	495.343	1.36004
$52$	−50.4969	−0.134667
$53$	−22.1093	−0.0573008	−0.0286504	−	0.999589i	$-0.509121\pi$
$53$	−22.1093	−0.0573008	−0.0286504	+	0.999589i	$0.509121\pi$
$54$	−307.547	−0.775034
$55$	0	0
$56$	298.330	0.711893
$57$	536.197	1.24598
$58$	−134.119	−0.303632
$59$	−89.2440	−0.196925	−0.0984625	−	0.995141i	$-0.531392\pi$
$59$	−89.2440	−0.196925	−0.0984625	+	0.995141i	$0.531392\pi$
$60$	−215.079	−0.462777
$61$	602.575	1.26478	0.632392	−	0.774649i	$-0.282073\pi$
$61$	602.575	1.26478	0.632392	+	0.774649i	$0.282073\pi$
$62$	49.6636	0.101730
$63$	−79.2600	−0.158505
$64$	460.577	0.899564
$65$	−158.615	−0.302673
$66$	0	0
$67$	419.882	0.765623	0.382811	−	0.923827i	$-0.374956\pi$
$67$	419.882	0.765623	0.382811	+	0.923827i	$0.374956\pi$
$68$	423.986	0.756116
$69$	−318.771	−0.556166
$70$	306.282	0.522967
$71$	805.330	1.34613	0.673064	−	0.739585i	$-0.264978\pi$
$71$	805.330	1.34613	0.673064	+	0.739585i	$0.264978\pi$
$72$	−154.435	−0.252783
$73$	655.582	1.05110	0.525548	−	0.850764i	$-0.323860\pi$
$73$	655.582	1.05110	0.525548	+	0.850764i	$0.323860\pi$
$74$	335.040	0.526319
$75$	−108.317	−0.166765
$76$	458.955	0.692707
$77$	0	0
$78$	119.684	0.173738
$79$	771.961	1.09940	0.549699	−	0.835363i	$-0.314743\pi$
$79$	771.961	1.09940	0.549699	+	0.835363i	$0.314743\pi$
$80$	217.627	0.304143
$81$	−515.022	−0.706477
$82$	−919.356	−1.23812
$83$	215.244	0.284652	0.142326	−	0.989820i	$-0.454542\pi$
$83$	215.244	0.284652	0.142326	+	0.989820i	$0.454542\pi$
$84$	218.122	0.283322
$85$	1331.78	1.69943
$86$	831.548	1.04265
$87$	−300.018	−0.369717
$88$	0	0
$89$	−1549.25	−1.84517	−0.922583	−	0.385798i	$-0.873926\pi$
$89$	−1549.25	−1.84517	−0.922583	+	0.385798i	$0.873926\pi$
$90$	−158.552	−0.185698
$91$	160.859	0.185304
$92$	−272.850	−0.309202
$93$	111.095	0.123872
$94$	−938.460	−1.02973
$95$	1441.62	1.55691
$96$	711.094	0.755997
$97$	812.695	0.850687	0.425344	−	0.905032i	$-0.360153\pi$
$97$	812.695	0.850687	0.425344	+	0.905032i	$0.360153\pi$
$98$	385.229	0.397081
$99$	0	0
$100$	−92.7133	−0.0927133
$101$	218.450	0.215214	0.107607	−	0.994194i	$-0.465681\pi$
$101$	218.450	0.215214	0.107607	+	0.994194i	$0.465681\pi$
$102$	−1004.90	−0.975491
$103$	1568.86	1.50082	0.750408	−	0.660975i	$-0.229857\pi$
$103$	1568.86	1.50082	0.750408	+	0.660975i	$0.229857\pi$
$104$	313.428	0.295520
$105$	685.140	0.636789
$106$	44.8531	0.0410992
$107$	−454.112	−0.410286	−0.205143	−	0.978732i	$-0.565766\pi$
$107$	−454.112	−0.410286	−0.205143	+	0.978732i	$0.565766\pi$
$108$	−588.864	−0.524662
$109$	−1451.20	−1.27522	−0.637612	−	0.770358i	$-0.720078\pi$
$109$	−1451.20	−1.27522	−0.637612	+	0.770358i	$0.720078\pi$
$110$	0	0
$111$	749.471	0.640871
$112$	−220.706	−0.186203
$113$	473.904	0.394524	0.197262	−	0.980351i	$-0.436795\pi$
$113$	473.904	0.394524	0.197262	+	0.980351i	$0.436795\pi$
$114$	−1087.78	−0.893686
$115$	−857.044	−0.694955
$116$	−256.799	−0.205545
$117$	−83.2712	−0.0657985
$118$	181.049	0.141245
$119$	−1350.62	−1.04043
$120$	1334.97	1.01554
$121$	0	0
$122$	−1222.44	−0.907171
$123$	−2056.56	−1.50759
$124$	95.0916	0.0688668
$125$	1233.92	0.882925
$126$	160.795	0.113688
$127$	528.078	0.368972	0.184486	−	0.982835i	$-0.440938\pi$
$127$	528.078	0.368972	0.184486	+	0.982835i	$0.440938\pi$
$128$	319.177	0.220403
$129$	1860.14	1.26958
$130$	321.782	0.217094
$131$	−817.964	−0.545541	−0.272770	−	0.962079i	$-0.587940\pi$
$131$	−817.964	−0.545541	−0.272770	+	0.962079i	$0.587940\pi$
$132$	0	0
$133$	−1462.01	−0.953177
$134$	−851.814	−0.549146
$135$	−1849.67	−1.17922
$136$	−2631.63	−1.65927
$137$	26.6528	0.0166212	0.00831058	−	0.999965i	$-0.497355\pi$
$137$	26.6528	0.0166212	0.00831058	+	0.999965i	$0.497355\pi$
$138$	646.690	0.398912
$139$	8.83152	0.00538906	0.00269453	−	0.999996i	$-0.499142\pi$
$139$	8.83152	0.00538906	0.00269453	+	0.999996i	$0.499142\pi$
$140$	586.442	0.354024
$141$	−2099.30	−1.25385
$142$	−1633.77	−0.965515
$143$	0	0
$144$	114.252	0.0661179
$145$	−806.627	−0.461978
$146$	−1329.98	−0.753903
$147$	861.741	0.483505
$148$	641.506	0.356294
$149$	−2202.50	−1.21098	−0.605490	−	0.795853i	$-0.707023\pi$
$149$	−2202.50	−1.21098	−0.605490	+	0.795853i	$0.707023\pi$
$150$	219.742	0.119613
$151$	2594.44	1.39823	0.699115	−	0.715009i	$-0.253577\pi$
$151$	2594.44	1.39823	0.699115	+	0.715009i	$0.253577\pi$
$152$	−2848.67	−1.52012
$153$	699.169	0.369441
$154$	0	0
$155$	298.691	0.154783
$156$	229.161	0.117613
$157$	1883.46	0.957427	0.478714	−	0.877971i	$-0.341103\pi$
$157$	1883.46	0.957427	0.478714	+	0.877971i	$0.341103\pi$
$158$	−1566.08	−0.788547
$159$	100.335	0.0500443
$160$	1911.84	0.944653
$161$	869.170	0.425467
$162$	1044.82	0.506723
$163$	1579.24	0.758871	0.379436	−	0.925218i	$-0.376118\pi$
$163$	1579.24	0.758871	0.379436	+	0.925218i	$0.376118\pi$
$164$	−1760.30	−0.838150
$165$	0	0
$166$	−436.666	−0.204168
$167$	−3857.14	−1.78727	−0.893636	−	0.448793i	$-0.851854\pi$
$167$	−3857.14	−1.78727	−0.893636	+	0.448793i	$0.851854\pi$
$168$	−1353.86	−0.621740
$169$	169.000	0.0769231
$170$	−2701.77	−1.21892
$171$	756.833	0.338459
$172$	1592.18	0.705827
$173$	−3095.99	−1.36060	−0.680299	−	0.732935i	$-0.738150\pi$
$173$	−3095.99	−1.36060	−0.680299	+	0.732935i	$0.738150\pi$
$174$	608.647	0.265181
$175$	295.340	0.127575
$176$	0	0
$177$	405.000	0.171987
$178$	3142.96	1.32345
$179$	2297.31	0.959267	0.479633	−	0.877469i	$-0.340770\pi$
$179$	2297.31	0.959267	0.479633	+	0.877469i	$0.340770\pi$
$180$	−303.581	−0.125709
$181$	−3283.60	−1.34844	−0.674221	−	0.738529i	$-0.735521\pi$
$181$	−3283.60	−1.34844	−0.674221	+	0.738529i	$0.735521\pi$
$182$	−326.335	−0.132910
$183$	−2734.56	−1.10461
$184$	1693.54	0.678531
$185$	2015.02	0.800797
$186$	−225.379	−0.0888474
$187$	0	0
$188$	−1796.88	−0.697081
$189$	1875.84	0.721944
$190$	−2924.61	−1.11670
$191$	−5000.32	−1.89430	−0.947149	−	0.320795i	$-0.896050\pi$
$191$	−5000.32	−1.89430	−0.947149	+	0.320795i	$0.896050\pi$
$192$	−2090.15	−0.785644
$193$	2689.80	1.00319	0.501596	−	0.865102i	$-0.332746\pi$
$193$	2689.80	1.00319	0.501596	+	0.865102i	$0.332746\pi$
$194$	−1648.71	−0.610158
$195$	719.814	0.264343
$196$	737.603	0.268806
$197$	389.063	0.140709	0.0703543	−	0.997522i	$-0.477587\pi$
$197$	389.063	0.140709	0.0703543	+	0.997522i	$0.477587\pi$
$198$	0	0
$199$	−264.770	−0.0943169	−0.0471585	−	0.998887i	$-0.515017\pi$
$199$	−264.770	−0.0943169	−0.0471585	+	0.998887i	$0.515017\pi$
$200$	575.459	0.203456
$201$	−1905.47	−0.668665
$202$	−443.169	−0.154363
$203$	818.040	0.282833
$204$	−1924.10	−0.660362
$205$	−5529.26	−1.88381
$206$	−3182.74	−1.07647
$207$	−449.939	−0.151077
$208$	−231.875	−0.0772965
$209$	0	0
$210$	−1389.94	−0.456739
$211$	3025.73	0.987201	0.493601	−	0.869689i	$-0.335680\pi$
$211$	3025.73	0.987201	0.493601	+	0.869689i	$0.335680\pi$
$212$	85.8808	0.0278223
$213$	−3654.68	−1.17566
$214$	921.256	0.294279
$215$	5001.16	1.58640
$216$	3655.00	1.15135
$217$	−302.917	−0.0947618
$218$	2944.04	0.914659
$219$	−2975.11	−0.917987
$220$	0	0
$221$	−1418.97	−0.431902
$222$	−1520.45	−0.459667
$223$	1673.47	0.502528	0.251264	−	0.967919i	$-0.419154\pi$
$223$	1673.47	0.502528	0.251264	+	0.967919i	$0.419154\pi$
$224$	−1938.89	−0.578338
$225$	−152.888	−0.0453000
$226$	−961.409	−0.282973
$227$	4180.49	1.22233	0.611164	−	0.791504i	$-0.290701\pi$
$227$	4180.49	1.22233	0.611164	+	0.791504i	$0.290701\pi$
$228$	−2082.79	−0.604984
$229$	−741.587	−0.213998	−0.106999	−	0.994259i	$-0.534124\pi$
$229$	−741.587	−0.213998	−0.106999	+	0.994259i	$0.534124\pi$
$230$	1738.69	0.498459
$231$	0	0
$232$	1593.92	0.451060
$233$	−4483.96	−1.26075	−0.630373	−	0.776292i	$-0.717098\pi$
$233$	−4483.96	−1.26075	−0.630373	+	0.776292i	$0.717098\pi$
$234$	168.932	0.0471942
$235$	−5644.16	−1.56674
$236$	346.657	0.0956164
$237$	−3503.25	−0.960171
$238$	2740.00	0.746251
$239$	1779.55	0.481631	0.240815	−	0.970571i	$-0.422585\pi$
$239$	1779.55	0.481631	0.240815	+	0.970571i	$0.422585\pi$
$240$	−987.616	−0.265626
$241$	−6135.62	−1.63996	−0.819979	−	0.572393i	$-0.806015\pi$
$241$	−6135.62	−1.63996	−0.819979	+	0.572393i	$0.806015\pi$
$242$	0	0
$243$	−1755.92	−0.463548
$244$	−2340.63	−0.614112
$245$	2316.87	0.604161
$246$	4172.15	1.08133
$247$	−1536.00	−0.395682
$248$	−590.221	−0.151125
$249$	−976.805	−0.248604
$250$	−2503.26	−0.633281
$251$	−3446.00	−0.866572	−0.433286	−	0.901256i	$-0.642646\pi$
$251$	−3446.00	−0.866572	−0.433286	+	0.901256i	$0.642646\pi$
$252$	307.876	0.0769618
$253$	0	0
$254$	−1071.31	−0.264646
$255$	−6043.76	−1.48421
$256$	−4332.13	−1.05765
$257$	−697.637	−0.169328	−0.0846642	−	0.996410i	$-0.526982\pi$
$257$	−697.637	−0.169328	−0.0846642	+	0.996410i	$0.526982\pi$
$258$	−3773.66	−0.910612
$259$	−2043.53	−0.490266
$260$	616.121	0.146962
$261$	−423.471	−0.100430
$262$	1659.40	0.391291
$263$	1244.02	0.291672	0.145836	−	0.989309i	$-0.453413\pi$
$263$	1244.02	0.291672	0.145836	+	0.989309i	$0.453413\pi$
$264$	0	0
$265$	269.759	0.0625327
$266$	2965.98	0.683670
$267$	7030.66	1.61150
$268$	−1630.98	−0.371746
$269$	−7237.63	−1.64047	−0.820234	−	0.572028i	$-0.806157\pi$
$269$	−7237.63	−1.64047	−0.820234	+	0.572028i	$0.806157\pi$
$270$	3752.43	0.845798
$271$	3712.06	0.832073	0.416036	−	0.909348i	$-0.363419\pi$
$271$	3712.06	0.832073	0.416036	+	0.909348i	$0.363419\pi$
$272$	1946.89	0.433998
$273$	−729.998	−0.161837
$274$	−54.0704	−0.0119216
$275$	0	0
$276$	1238.23	0.270045
$277$	1790.14	0.388299	0.194149	−	0.980972i	$-0.437805\pi$
$277$	1790.14	0.388299	0.194149	+	0.980972i	$0.437805\pi$
$278$	−17.9165	−0.00386532
$279$	156.809	0.0336485
$280$	−3639.97	−0.776892
$281$	5357.45	1.13736	0.568681	−	0.822558i	$-0.307454\pi$
$281$	5357.45	1.13736	0.568681	+	0.822558i	$0.307454\pi$
$282$	4258.84	0.899328
$283$	−2536.11	−0.532708	−0.266354	−	0.963875i	$-0.585819\pi$
$283$	−2536.11	−0.532708	−0.266354	+	0.963875i	$0.585819\pi$
$284$	−3128.21	−0.653609
$285$	−6542.22	−1.35975
$286$	0	0
$287$	5607.49	1.15331
$288$	1003.70	0.205359
$289$	7001.07	1.42501
$290$	1636.40	0.331355
$291$	−3688.10	−0.742957
$292$	−2546.53	−0.510357
$293$	7609.61	1.51726	0.758632	−	0.651520i	$-0.225868\pi$
$293$	7609.61	1.51726	0.758632	+	0.651520i	$0.225868\pi$
$294$	−1748.21	−0.346795
$295$	1088.88	0.214905
$296$	−3981.74	−0.781872
$297$	0	0
$298$	4468.22	0.868580
$299$	913.157	0.176620
$300$	420.744	0.0809722
$301$	−5071.92	−0.971231
$302$	−5263.35	−1.00289
$303$	−991.352	−0.187959
$304$	2107.46	0.397603
$305$	−7352.11	−1.38026
$306$	−1418.40	−0.264983
$307$	8064.37	1.49921	0.749606	−	0.661884i	$-0.230243\pi$
$307$	8064.37	1.49921	0.749606	+	0.661884i	$0.230243\pi$
$308$	0	0
$309$	−7119.66	−1.31075
$310$	−605.953	−0.111019
$311$	5558.49	1.01348	0.506741	−	0.862098i	$-0.330850\pi$
$311$	5558.49	1.01348	0.506741	+	0.862098i	$0.330850\pi$
$312$	−1422.37	−0.258096
$313$	−5651.75	−1.02063	−0.510313	−	0.859989i	$-0.670470\pi$
$313$	−5651.75	−1.02063	−0.510313	+	0.859989i	$0.670470\pi$
$314$	−3820.96	−0.686718
$315$	967.064	0.172977
$316$	−2998.59	−0.533809
$317$	93.3972	0.0165480	0.00827399	−	0.999966i	$-0.497366\pi$
$317$	93.3972	0.0165480	0.00827399	+	0.999966i	$0.497366\pi$
$318$	−203.549	−0.0358945
$319$	0	0
$320$	−5619.57	−0.981698
$321$	2060.81	0.358328
$322$	−1763.28	−0.305168
$323$	12896.7	2.22165
$324$	2000.54	0.343028
$325$	310.287	0.0529589
$326$	−3203.81	−0.544303
$327$	6585.70	1.11373
$328$	10926.0	1.83929
$329$	5724.02	0.959195
$330$	0	0
$331$	2863.00	0.475423	0.237711	−	0.971336i	$-0.423603\pi$
$331$	2863.00	0.475423	0.237711	+	0.971336i	$0.423603\pi$
$332$	−836.091	−0.138212
$333$	1057.87	0.174086
$334$	7824.97	1.28193
$335$	−5123.04	−0.835528
$336$	1001.59	0.162623
$337$	1169.21	0.188994	0.0944971	−	0.995525i	$-0.469876\pi$
$337$	1169.21	0.188994	0.0944971	+	0.995525i	$0.469876\pi$
$338$	−342.850	−0.0551733
$339$	−2150.63	−0.344562
$340$	−5173.12	−0.825153
$341$	0	0
$342$	−1535.39	−0.242761
$343$	−6593.86	−1.03800
$344$	−9882.43	−1.54891
$345$	3889.37	0.606947
$346$	6280.83	0.975894
$347$	7011.96	1.08479	0.542394	−	0.840124i	$-0.317518\pi$
$347$	7011.96	1.08479	0.542394	+	0.840124i	$0.317518\pi$
$348$	1165.38	0.179515
$349$	1965.26	0.301426	0.150713	−	0.988578i	$-0.451843\pi$
$349$	1965.26	0.301426	0.150713	+	0.988578i	$0.451843\pi$
$350$	−599.157	−0.0915037
$351$	1970.77	0.299693
$352$	0	0
$353$	−9022.46	−1.36039	−0.680194	−	0.733032i	$-0.738105\pi$
$353$	−9022.46	−1.36039	−0.680194	+	0.733032i	$0.738105\pi$
$354$	−821.623	−0.123358
$355$	−9825.95	−1.46903
$356$	6017.86	0.895916
$357$	6129.27	0.908670
$358$	−4660.54	−0.688037
$359$	−6663.48	−0.979624	−0.489812	−	0.871828i	$-0.662935\pi$
$359$	−6663.48	−0.979624	−0.489812	+	0.871828i	$0.662935\pi$
$360$	1884.29	0.275863
$361$	7101.38	1.03534
$362$	6661.44	0.967175
$363$	0	0
$364$	−624.838	−0.0899737
$365$	−7998.86	−1.14707
$366$	5547.59	0.792288
$367$	−4597.61	−0.653933	−0.326966	−	0.945036i	$-0.606026\pi$
$367$	−4597.61	−0.653933	−0.326966	+	0.945036i	$0.606026\pi$
$368$	−1252.89	−0.177477
$369$	−2902.80	−0.409523
$370$	−4087.88	−0.574375
$371$	−273.575	−0.0382839
$372$	−431.537	−0.0601456
$373$	−2001.74	−0.277872	−0.138936	−	0.990301i	$-0.544368\pi$
$373$	−2001.74	−0.277872	−0.138936	+	0.990301i	$0.544368\pi$
$374$	0	0
$375$	−5599.70	−0.771112
$376$	11153.0	1.52972
$377$	859.440	0.117410
$378$	−3805.52	−0.517817
$379$	−781.588	−0.105930	−0.0529650	−	0.998596i	$-0.516867\pi$
$379$	−781.588	−0.105930	−0.0529650	+	0.998596i	$0.516867\pi$
$380$	−5599.78	−0.755955
$381$	−2396.48	−0.322245
$382$	10144.2	1.35869
$383$	4199.51	0.560274	0.280137	−	0.959960i	$-0.409620\pi$
$383$	4199.51	0.560274	0.280137	+	0.959960i	$0.409620\pi$
$384$	−1448.46	−0.192491
$385$	0	0
$386$	−5456.80	−0.719544
$387$	2625.56	0.344870
$388$	−3156.81	−0.413049
$389$	−8729.15	−1.13775	−0.568876	−	0.822423i	$-0.692622\pi$
$389$	−8729.15	−1.13775	−0.568876	+	0.822423i	$0.692622\pi$
$390$	−1460.29	−0.189601
$391$	−7667.12	−0.991670
$392$	−4578.20	−0.589883
$393$	3712.02	0.476454
$394$	−789.292	−0.100924
$395$	−9418.82	−1.19978
$396$	0	0
$397$	7196.25	0.909747	0.454873	−	0.890556i	$-0.349685\pi$
$397$	7196.25	0.909747	0.454873	+	0.890556i	$0.349685\pi$
$398$	537.139	0.0676491
$399$	6634.79	0.832468
$400$	−425.727	−0.0532159
$401$	6445.55	0.802682	0.401341	−	0.915929i	$-0.368544\pi$
$401$	6445.55	0.802682	0.401341	+	0.915929i	$0.368544\pi$
$402$	3865.63	0.479603
$403$	−318.247	−0.0393375
$404$	−848.543	−0.104496
$405$	6283.86	0.770982
$406$	−1659.56	−0.202863
$407$	0	0
$408$	11942.6	1.44914
$409$	−12932.3	−1.56348	−0.781740	−	0.623605i	$-0.785667\pi$
$409$	−12932.3	−1.56348	−0.781740	+	0.623605i	$0.785667\pi$
$410$	11217.2	1.35117
$411$	−120.953	−0.0145163
$412$	−6094.03	−0.728717
$413$	−1104.29	−0.131570
$414$	912.792	0.108361
$415$	−2626.23	−0.310643
$416$	−2037.02	−0.240079
$417$	−40.0785	−0.00470660
$418$	0	0
$419$	−1715.51	−0.200019	−0.100010	−	0.994986i	$-0.531887\pi$
$419$	−1715.51	−0.200019	−0.100010	+	0.994986i	$0.531887\pi$
$420$	−2661.34	−0.309191
$421$	−12589.1	−1.45738	−0.728688	−	0.684845i	$-0.759870\pi$
$421$	−12589.1	−1.45738	−0.728688	+	0.684845i	$0.759870\pi$
$422$	−6138.29	−0.708074
$423$	−2963.13	−0.340596
$424$	−533.051	−0.0610548
$425$	−2605.26	−0.297349
$426$	7414.25	0.843243
$427$	7456.13	0.845029
$428$	1763.94	0.199213
$429$	0	0
$430$	−10145.8	−1.13785
$431$	−8863.64	−0.990595	−0.495298	−	0.868723i	$-0.664941\pi$
$431$	−8863.64	−0.990595	−0.495298	+	0.868723i	$0.664941\pi$
$432$	−2703.99	−0.301148
$433$	−6733.12	−0.747282	−0.373641	−	0.927573i	$-0.621891\pi$
$433$	−6733.12	−0.747282	−0.373641	+	0.927573i	$0.621891\pi$
$434$	614.527	0.0679683
$435$	3660.57	0.403473
$436$	5637.00	0.619182
$437$	−8299.48	−0.908508
$438$	6035.60	0.658430
$439$	7643.95	0.831038	0.415519	−	0.909584i	$-0.363600\pi$
$439$	7643.95	0.831038	0.415519	+	0.909584i	$0.363600\pi$
$440$	0	0
$441$	1216.33	0.131339
$442$	2878.67	0.309783
$443$	−13323.3	−1.42891	−0.714455	−	0.699682i	$-0.753325\pi$
$443$	−13323.3	−1.42891	−0.714455	+	0.699682i	$0.753325\pi$
$444$	−2911.23	−0.311173
$445$	18902.6	2.01364
$446$	−3394.96	−0.360440
$447$	9995.22	1.05762
$448$	5699.08	0.601018
$449$	5359.97	0.563369	0.281684	−	0.959507i	$-0.409107\pi$
$449$	5359.97	0.563369	0.281684	+	0.959507i	$0.409107\pi$
$450$	310.163	0.0324916
$451$	0	0
$452$	−1840.82	−0.191560
$453$	−11773.9	−1.22116
$454$	−8480.95	−0.876720
$455$	−1962.67	−0.202223
$456$	12927.6	1.32761
$457$	−2909.18	−0.297780	−0.148890	−	0.988854i	$-0.547570\pi$
$457$	−2909.18	−0.297780	−0.148890	+	0.988854i	$0.547570\pi$
$458$	1504.46	0.153490
$459$	−16547.2	−1.68269
$460$	3329.09	0.337433
$461$	−6043.36	−0.610558	−0.305279	−	0.952263i	$-0.598750\pi$
$461$	−6043.36	−0.610558	−0.305279	+	0.952263i	$0.598750\pi$
$462$	0	0
$463$	3643.02	0.365671	0.182835	−	0.983144i	$-0.441472\pi$
$463$	3643.02	0.365671	0.182835	+	0.983144i	$0.441472\pi$
$464$	−1179.19	−0.117979
$465$	−1355.49	−0.135182
$466$	9096.61	0.904275
$467$	−15767.1	−1.56234	−0.781170	−	0.624319i	$-0.785377\pi$
$467$	−15767.1	−1.56234	−0.781170	+	0.624319i	$0.785377\pi$
$468$	323.457	0.0319483
$469$	5195.53	0.511529
$470$	11450.3	1.12375
$471$	−8547.34	−0.836180
$472$	−2151.66	−0.209826
$473$	0	0
$474$	7107.04	0.688686
$475$	−2820.13	−0.272413
$476$	5246.31	0.505177
$477$	141.621	0.0135940
$478$	−3610.18	−0.345451
$479$	−8898.50	−0.848816	−0.424408	−	0.905471i	$-0.639518\pi$
$479$	−8898.50	−0.848816	−0.424408	+	0.905471i	$0.639518\pi$
$480$	−8676.17	−0.825023
$481$	−2146.95	−0.203519
$482$	12447.3	1.17627
$483$	−3944.40	−0.371587
$484$	0	0
$485$	−9915.82	−0.928359
$486$	3562.23	0.332481
$487$	2422.22	0.225383	0.112691	−	0.993630i	$-0.464053\pi$
$487$	2422.22	0.225383	0.112691	+	0.993630i	$0.464053\pi$
$488$	14528.0	1.34764
$489$	−7166.80	−0.662769
$490$	−4700.24	−0.433337
$491$	−12874.9	−1.18337	−0.591685	−	0.806169i	$-0.701537\pi$
$491$	−12874.9	−1.18337	−0.591685	+	0.806169i	$0.701537\pi$
$492$	7988.46	0.732008
$493$	−7216.09	−0.659222
$494$	3116.09	0.283804
$495$	0	0
$496$	436.648	0.0395284
$497$	9964.97	0.899377
$498$	1981.64	0.178312
$499$	16734.0	1.50123	0.750617	−	0.660737i	$-0.229756\pi$
$499$	16734.0	1.50123	0.750617	+	0.660737i	$0.229756\pi$
$500$	−4793.03	−0.428702
$501$	17504.2	1.56093
$502$	6990.90	0.621552
$503$	−14351.1	−1.27214	−0.636068	−	0.771633i	$-0.719440\pi$
$503$	−14351.1	−1.27214	−0.636068	+	0.771633i	$0.719440\pi$
$504$	−1910.95	−0.168889
$505$	−2665.34	−0.234864
$506$	0	0
$507$	−766.942	−0.0671816
$508$	−2051.26	−0.179153
$509$	−1054.22	−0.0918025	−0.0459012	−	0.998946i	$-0.514616\pi$
$509$	−1054.22	−0.0918025	−0.0459012	+	0.998946i	$0.514616\pi$
$510$	12261.0	1.06456
$511$	8112.03	0.702260
$512$	6235.17	0.538200
$513$	−17911.9	−1.54158
$514$	1415.30	0.121451
$515$	−19141.9	−1.63785
$516$	−7225.48	−0.616442
$517$	0	0
$518$	4145.71	0.351645
$519$	14050.0	1.18829
$520$	−3824.18	−0.322503
$521$	−14135.2	−1.18862	−0.594312	−	0.804234i	$-0.702576\pi$
$521$	−14135.2	−1.18862	−0.594312	+	0.804234i	$0.702576\pi$
$522$	859.095	0.0720337
$523$	4179.09	0.349405	0.174702	−	0.984621i	$-0.444104\pi$
$523$	4179.09	0.349405	0.174702	+	0.984621i	$0.444104\pi$
$524$	3177.28	0.264886
$525$	−1340.29	−0.111419
$526$	−2523.75	−0.209203
$527$	2672.09	0.220869
$528$	0	0
$529$	−7232.94	−0.594472
$530$	−547.260	−0.0448518
$531$	571.651	0.0467185
$532$	5679.01	0.462813
$533$	5891.27	0.478761
$534$	−14263.1	−1.15585
$535$	5540.69	0.447747
$536$	10123.3	0.815782
$537$	−10425.4	−0.837786
$538$	14683.0	1.17663
$539$	0	0
$540$	7184.82	0.572566
$541$	3047.56	0.242190	0.121095	−	0.992641i	$-0.461359\pi$
$541$	3047.56	0.242190	0.121095	+	0.992641i	$0.461359\pi$
$542$	−7530.66	−0.596807
$543$	14901.4	1.17768
$544$	17103.4	1.34798
$545$	17706.3	1.39166
$546$	1480.95	0.116078
$547$	−8448.68	−0.660401	−0.330201	−	0.943911i	$-0.607116\pi$
$547$	−8448.68	−0.660401	−0.330201	+	0.943911i	$0.607116\pi$
$548$	−103.529	−0.00807036
$549$	−3859.78	−0.300057
$550$	0	0
$551$	−7811.25	−0.603939
$552$	−7685.50	−0.592603
$553$	9552.08	0.734531
$554$	−3631.65	−0.278509
$555$	−9144.42	−0.699385
$556$	−34.3050	−0.00261664
$557$	2637.59	0.200643	0.100322	−	0.994955i	$-0.468013\pi$
$557$	2637.59	0.200643	0.100322	+	0.994955i	$0.468013\pi$
$558$	−318.119	−0.0241345
$559$	−5328.60	−0.403177
$560$	2692.87	0.203204
$561$	0	0
$562$	−10868.7	−0.815777
$563$	22300.3	1.66935	0.834676	−	0.550741i	$-0.185655\pi$
$563$	22300.3	1.66935	0.834676	+	0.550741i	$0.185655\pi$
$564$	8154.47	0.608803
$565$	−5782.18	−0.430545
$566$	5145.01	0.382086
$567$	−6372.77	−0.472013
$568$	19416.4	1.43432
$569$	−2691.72	−0.198318	−0.0991588	−	0.995072i	$-0.531615\pi$
$569$	−2691.72	−0.198318	−0.0991588	+	0.995072i	$0.531615\pi$
$570$	13272.2	0.975284
$571$	−3927.91	−0.287877	−0.143939	−	0.989587i	$-0.545977\pi$
$571$	−3927.91	−0.287877	−0.143939	+	0.989587i	$0.545977\pi$
$572$	0	0
$573$	22692.1	1.65441
$574$	−11375.9	−0.827215
$575$	1676.57	0.121596
$576$	−2950.22	−0.213413
$577$	−5559.88	−0.401145	−0.200573	−	0.979679i	$-0.564280\pi$
$577$	−5559.88	−0.401145	−0.200573	+	0.979679i	$0.564280\pi$
$578$	−14203.1	−1.02209
$579$	−12206.6	−0.876150
$580$	3133.25	0.224312
$581$	2663.39	0.190182
$582$	7482.06	0.532889
$583$	0	0
$584$	15806.0	1.11996
$585$	1016.01	0.0718063
$586$	−15437.6	−1.08826
$587$	−11911.4	−0.837542	−0.418771	−	0.908092i	$-0.637539\pi$
$587$	−11911.4	−0.837542	−0.418771	+	0.908092i	$0.637539\pi$
$588$	−3347.33	−0.234764
$589$	2892.47	0.202347
$590$	−2209.01	−0.154142
$591$	−1765.61	−0.122889
$592$	2945.71	0.204507
$593$	20149.1	1.39532	0.697659	−	0.716430i	$-0.254225\pi$
$593$	20149.1	1.39532	0.697659	+	0.716430i	$0.254225\pi$
$594$	0	0
$595$	16479.1	1.13542
$596$	8555.36	0.587988
$597$	1201.56	0.0823728
$598$	−1852.52	−0.126681
$599$	13383.7	0.912924	0.456462	−	0.889743i	$-0.349116\pi$
$599$	13383.7	0.912924	0.456462	+	0.889743i	$0.349116\pi$
$600$	−2611.50	−0.177690
$601$	19126.1	1.29812	0.649060	−	0.760737i	$-0.275163\pi$
$601$	19126.1	1.29812	0.649060	+	0.760737i	$0.275163\pi$
$602$	10289.4	0.696619
$603$	−2689.54	−0.181636
$604$	−10077.8	−0.678907
$605$	0	0
$606$	2011.16	0.134815
$607$	5680.25	0.379826	0.189913	−	0.981801i	$-0.439179\pi$
$607$	5680.25	0.379826	0.189913	+	0.981801i	$0.439179\pi$
$608$	18514.0	1.23494
$609$	−3712.36	−0.247016
$610$	14915.2	0.990000
$611$	6013.70	0.398180
$612$	−2715.84	−0.179381
$613$	−16912.6	−1.11434	−0.557172	−	0.830397i	$-0.688114\pi$
$613$	−16912.6	−1.11434	−0.557172	+	0.830397i	$0.688114\pi$
$614$	−16360.2	−1.07532
$615$	25092.4	1.64524
$616$	0	0
$617$	5711.30	0.372655	0.186328	−	0.982488i	$-0.440341\pi$
$617$	5711.30	0.372655	0.186328	+	0.982488i	$0.440341\pi$
$618$	14443.6	0.940143
$619$	9116.37	0.591951	0.295976	−	0.955196i	$-0.404355\pi$
$619$	9116.37	0.591951	0.295976	+	0.955196i	$0.404355\pi$
$620$	−1160.23	−0.0751546
$621$	10648.7	0.688111
$622$	−11276.5	−0.726923
$623$	−19170.0	−1.23280
$624$	1052.28	0.0675078
$625$	−18038.8	−1.15449
$626$	11465.7	0.732047
$627$	0	0
$628$	−7316.05	−0.464876
$629$	18026.4	1.14270
$630$	−1961.88	−0.124069
$631$	4093.54	0.258259	0.129129	−	0.991628i	$-0.458782\pi$
$631$	4093.54	0.258259	0.129129	+	0.991628i	$0.458782\pi$
$632$	18611.8	1.17142
$633$	−13731.1	−0.862184
$634$	−189.475	−0.0118691
$635$	−6443.17	−0.402660
$636$	−389.737	−0.0242989
$637$	−2468.56	−0.153545
$638$	0	0
$639$	−5158.52	−0.319355
$640$	−3894.33	−0.240526
$641$	20030.2	1.23424	0.617119	−	0.786870i	$-0.288300\pi$
$641$	20030.2	1.23424	0.617119	+	0.786870i	$0.288300\pi$
$642$	−4180.77	−0.257012
$643$	27742.3	1.70147	0.850737	−	0.525591i	$-0.176156\pi$
$643$	27742.3	1.70147	0.850737	+	0.525591i	$0.176156\pi$
$644$	−3376.19	−0.206584
$645$	−22695.8	−1.38550
$646$	−26163.5	−1.59348
$647$	−2495.88	−0.151659	−0.0758293	−	0.997121i	$-0.524160\pi$
$647$	−2495.88	−0.151659	−0.0758293	+	0.997121i	$0.524160\pi$
$648$	−12417.1	−0.752761
$649$	0	0
$650$	−629.479	−0.0379849
$651$	1374.67	0.0827613
$652$	−6134.39	−0.368468
$653$	13353.0	0.800217	0.400108	−	0.916468i	$-0.368972\pi$
$653$	13353.0	0.800217	0.400108	+	0.916468i	$0.368972\pi$
$654$	−13360.4	−0.798828
$655$	9980.11	0.595351
$656$	−8083.09	−0.481085
$657$	−4199.32	−0.249362
$658$	−11612.3	−0.687986
$659$	−2132.14	−0.126034	−0.0630171	−	0.998012i	$-0.520072\pi$
$659$	−2132.14	−0.126034	−0.0630171	+	0.998012i	$0.520072\pi$
$660$	0	0
$661$	16411.5	0.965708	0.482854	−	0.875701i	$-0.339600\pi$
$661$	16411.5	0.965708	0.482854	+	0.875701i	$0.339600\pi$
$662$	−5808.18	−0.340999
$663$	6439.46	0.377206
$664$	5189.51	0.303301
$665$	17838.2	1.04021
$666$	−2146.09	−0.124864
$667$	4643.81	0.269579
$668$	14982.6	0.867805
$669$	−7594.40	−0.438888
$670$	10393.1	0.599285
$671$	0	0
$672$	8798.93	0.505098
$673$	27980.4	1.60262	0.801312	−	0.598247i	$-0.204136\pi$
$673$	27980.4	1.60262	0.801312	+	0.598247i	$0.204136\pi$
$674$	−2371.98	−0.135557
$675$	3618.38	0.206328
$676$	−656.460	−0.0373498
$677$	−7760.09	−0.440538	−0.220269	−	0.975439i	$-0.570694\pi$
$677$	−7760.09	−0.440538	−0.220269	+	0.975439i	$0.570694\pi$
$678$	4362.99	0.247138
$679$	10056.1	0.568362
$680$	32108.9	1.81076
$681$	−18971.5	−1.06753
$682$	0	0
$683$	−23905.0	−1.33924	−0.669618	−	0.742706i	$-0.733542\pi$
$683$	−23905.0	−1.33924	−0.669618	+	0.742706i	$0.733542\pi$
$684$	−2939.83	−0.164338
$685$	−325.194	−0.0181387
$686$	13377.0	0.744511
$687$	3365.41	0.186897
$688$	7311.07	0.405134
$689$	−287.421	−0.0158924
$690$	−7890.36	−0.435335
$691$	−18565.9	−1.02211	−0.511057	−	0.859547i	$-0.670746\pi$
$691$	−18565.9	−1.02211	−0.511057	+	0.859547i	$0.670746\pi$
$692$	12026.0	0.660635
$693$	0	0
$694$	−14225.2	−0.778068
$695$	−107.755	−0.00588111
$696$	−7233.39	−0.393938
$697$	−49464.8	−2.68811
$698$	−3986.91	−0.216199
$699$	20348.7	1.10109
$700$	−1147.21	−0.0619437
$701$	7350.04	0.396016	0.198008	−	0.980200i	$-0.436553\pi$
$701$	7350.04	0.396016	0.198008	+	0.980200i	$0.436553\pi$
$702$	−3998.11	−0.214956
$703$	19513.2	1.04687
$704$	0	0
$705$	25613.9	1.36833
$706$	18303.9	0.975743
$707$	2703.05	0.143789
$708$	−1573.17	−0.0835077
$709$	−26875.2	−1.42358	−0.711792	−	0.702390i	$-0.752116\pi$
$709$	−26875.2	−1.42358	−0.711792	+	0.702390i	$0.752116\pi$
$710$	19933.9	1.05367
$711$	−4944.78	−0.260821
$712$	−37352.1	−1.96605
$713$	−1719.58	−0.0903210
$714$	−12434.4	−0.651747
$715$	0	0
$716$	−8923.61	−0.465769
$717$	−8075.83	−0.420638
$718$	13518.2	0.702639
$719$	7971.74	0.413485	0.206743	−	0.978395i	$-0.433714\pi$
$719$	7971.74	0.413485	0.206743	+	0.978395i	$0.433714\pi$
$720$	−1394.00	−0.0721548
$721$	19412.7	1.00273
$722$	−14406.6	−0.742599
$723$	27844.2	1.43228
$724$	12754.7	0.654733
$725$	1577.95	0.0808324
$726$	0	0
$727$	22663.3	1.15617	0.578084	−	0.815977i	$-0.303801\pi$
$727$	22663.3	1.15617	0.578084	+	0.815977i	$0.303801\pi$
$728$	3878.29	0.197444
$729$	21874.1	1.11132
$730$	16227.3	0.822738
$731$	44740.4	2.26373
$732$	10622.1	0.536342
$733$	−483.636	−0.0243704	−0.0121852	−	0.999926i	$-0.503879\pi$
$733$	−483.636	−0.0243704	−0.0121852	+	0.999926i	$0.503879\pi$
$734$	9327.17	0.469036
$735$	−10514.2	−0.527651
$736$	−11006.6	−0.551235
$737$	0	0
$738$	5888.92	0.293732
$739$	17715.0	0.881807	0.440904	−	0.897554i	$-0.354658\pi$
$739$	17715.0	0.881807	0.440904	+	0.897554i	$0.354658\pi$
$740$	−7827.12	−0.388825
$741$	6970.56	0.345574
$742$	555.002	0.0274593
$743$	−28219.3	−1.39336	−0.696681	−	0.717382i	$-0.745340\pi$
$743$	−28219.3	−1.39336	−0.696681	+	0.717382i	$0.745340\pi$
$744$	2678.49	0.131987
$745$	26873.1	1.32155
$746$	4060.93	0.199304
$747$	−1378.74	−0.0675309
$748$	0	0
$749$	−5619.08	−0.274121
$750$	11360.1	0.553083
$751$	−14617.1	−0.710233	−0.355117	−	0.934822i	$-0.615559\pi$
$751$	−14617.1	−0.710233	−0.355117	+	0.934822i	$0.615559\pi$
$752$	−8251.06	−0.400113
$753$	15638.4	0.756831
$754$	−1743.54	−0.0842124
$755$	−31655.2	−1.52590
$756$	−7286.48	−0.350538
$757$	2116.36	0.101612	0.0508061	−	0.998709i	$-0.483821\pi$
$757$	2116.36	0.101612	0.0508061	+	0.998709i	$0.483821\pi$
$758$	1585.61	0.0759786
$759$	0	0
$760$	34757.1	1.65891
$761$	272.064	0.0129597	0.00647985	−	0.999979i	$-0.497937\pi$
$761$	272.064	0.0129597	0.00647985	+	0.999979i	$0.497937\pi$
$762$	4861.74	0.231132
$763$	−17956.8	−0.852005
$764$	19423.2	0.919771
$765$	−8530.67	−0.403172
$766$	−8519.54	−0.401858
$767$	−1160.17	−0.0546172
$768$	19659.7	0.923709
$769$	32768.9	1.53664	0.768320	−	0.640066i	$-0.221093\pi$
$769$	32768.9	1.53664	0.768320	+	0.640066i	$0.221093\pi$
$770$	0	0
$771$	3165.96	0.147885
$772$	−10448.2	−0.487098
$773$	−37429.6	−1.74159	−0.870794	−	0.491647i	$-0.836395\pi$
$773$	−37429.6	−1.74159	−0.870794	+	0.491647i	$0.836395\pi$
$774$	−5326.46	−0.247359
$775$	−584.307	−0.0270825
$776$	19593.9	0.906419
$777$	9273.79	0.428180
$778$	17708.8	0.816057
$779$	−53544.5	−2.46268
$780$	−2796.03	−0.128351
$781$	0	0
$782$	15554.3	0.711279
$783$	10022.3	0.457428
$784$	3386.98	0.154290
$785$	−22980.3	−1.04484
$786$	−7530.57	−0.341738
$787$	16274.3	0.737123	0.368561	−	0.929603i	$-0.379850\pi$
$787$	16274.3	0.737123	0.368561	+	0.929603i	$0.379850\pi$
$788$	−1511.27	−0.0683207
$789$	−5645.53	−0.254735
$790$	19107.9	0.860545
$791$	5863.99	0.263590
$792$	0	0
$793$	7833.47	0.350788
$794$	−14599.0	−0.652519
$795$	−1224.20	−0.0546136
$796$	1028.47	0.0457953
$797$	−36996.3	−1.64426	−0.822132	−	0.569297i	$-0.807215\pi$
$797$	−36996.3	−1.64426	−0.822132	+	0.569297i	$0.807215\pi$
$798$	−13460.0	−0.597091
$799$	−50492.7	−2.23567
$800$	−3740.00	−0.165286
$801$	9923.67	0.437747
$802$	−13076.1	−0.575727
$803$	0	0
$804$	7401.58	0.324669
$805$	−10604.9	−0.464314
$806$	645.627	0.0282149
$807$	32845.2	1.43272
$808$	5266.79	0.229313
$809$	5270.62	0.229054	0.114527	−	0.993420i	$-0.463465\pi$
$809$	5270.62	0.229054	0.114527	+	0.993420i	$0.463465\pi$
$810$	−12748.1	−0.552989
$811$	−3809.16	−0.164929	−0.0824646	−	0.996594i	$-0.526279\pi$
$811$	−3809.16	−0.164929	−0.0824646	+	0.996594i	$0.526279\pi$
$812$	−3177.58	−0.137329
$813$	−16845.8	−0.726700
$814$	0	0
$815$	−19268.6	−0.828160
$816$	−8835.22	−0.379037
$817$	48430.4	2.07389
$818$	26235.8	1.12141
$819$	−1030.38	−0.0439614
$820$	21477.7	0.914677
$821$	31936.9	1.35762	0.678809	−	0.734315i	$-0.262496\pi$
$821$	31936.9	1.35762	0.678809	+	0.734315i	$0.262496\pi$
$822$	245.378	0.0104119
$823$	−21080.4	−0.892853	−0.446427	−	0.894820i	$-0.647304\pi$
$823$	−21080.4	−0.892853	−0.446427	+	0.894820i	$0.647304\pi$
$824$	37824.9	1.59914
$825$	0	0
$826$	2240.26	0.0943689
$827$	−3297.45	−0.138650	−0.0693250	−	0.997594i	$-0.522085\pi$
$827$	−3297.45	−0.138650	−0.0693250	+	0.997594i	$0.522085\pi$
$828$	1747.74	0.0733551
$829$	34618.3	1.45036	0.725178	−	0.688562i	$-0.241758\pi$
$829$	34618.3	1.45036	0.725178	+	0.688562i	$0.241758\pi$
$830$	5327.83	0.222809
$831$	−8123.84	−0.339125
$832$	5987.50	0.249494
$833$	20726.7	0.862112
$834$	81.3072	0.00337582
$835$	47061.6	1.95046
$836$	0	0
$837$	−3711.20	−0.153259
$838$	3480.25	0.143465
$839$	−34955.4	−1.43837	−0.719187	−	0.694816i	$-0.755486\pi$
$839$	−34955.4	−1.43837	−0.719187	+	0.694816i	$0.755486\pi$
$840$	16518.6	0.678507
$841$	−20018.4	−0.820795
$842$	25539.5	1.04531
$843$	−24312.8	−0.993328
$844$	−11753.1	−0.479333
$845$	−2062.00	−0.0839465
$846$	6011.29	0.244294
$847$	0	0
$848$	394.354	0.0159695
$849$	11509.2	0.465246
$850$	5285.28	0.213275
$851$	−11600.6	−0.467291
$852$	14196.2	0.570836
$853$	−10949.4	−0.439507	−0.219753	−	0.975555i	$-0.570525\pi$
$853$	−10949.4	−0.439507	−0.219753	+	0.975555i	$0.570525\pi$
$854$	−15126.2	−0.606100
$855$	−9234.24	−0.369362
$856$	−10948.6	−0.437166
$857$	14839.6	0.591496	0.295748	−	0.955266i	$-0.404431\pi$
$857$	14839.6	0.591496	0.295748	+	0.955266i	$0.404431\pi$
$858$	0	0
$859$	4944.62	0.196401	0.0982003	−	0.995167i	$-0.468691\pi$
$859$	4944.62	0.196401	0.0982003	+	0.995167i	$0.468691\pi$
$860$	−19426.4	−0.770273
$861$	−25447.4	−1.00726
$862$	17981.7	0.710508
$863$	−5385.81	−0.212439	−0.106220	−	0.994343i	$-0.533875\pi$
$863$	−5385.81	−0.212439	−0.106220	+	0.994343i	$0.533875\pi$
$864$	−23754.4	−0.935350
$865$	37774.6	1.48483
$866$	13659.5	0.535991
$867$	−31771.7	−1.24455
$868$	1176.64	0.0460114
$869$	0	0
$870$	−7426.20	−0.289393
$871$	5458.46	0.212346
$872$	−34988.1	−1.35877
$873$	−5205.70	−0.201817
$874$	16837.2	0.651631
$875$	15268.3	0.589901
$876$	11556.4	0.445726
$877$	−35455.7	−1.36517	−0.682585	−	0.730806i	$-0.739144\pi$
$877$	−35455.7	−1.36517	−0.682585	+	0.730806i	$0.739144\pi$
$878$	−15507.3	−0.596065
$879$	−34533.3	−1.32512
$880$	0	0
$881$	20178.1	0.771644	0.385822	−	0.922573i	$-0.373918\pi$
$881$	20178.1	0.771644	0.385822	+	0.922573i	$0.373918\pi$
$882$	−2467.57	−0.0942036
$883$	−23854.2	−0.909127	−0.454564	−	0.890714i	$-0.650205\pi$
$883$	−23854.2	−0.909127	−0.454564	+	0.890714i	$0.650205\pi$
$884$	5511.82	0.209709
$885$	−4941.47	−0.187690
$886$	27028.9	1.02489
$887$	−29965.8	−1.13433	−0.567166	−	0.823604i	$-0.691960\pi$
$887$	−29965.8	−1.13433	−0.567166	+	0.823604i	$0.691960\pi$
$888$	18069.6	0.682857
$889$	6534.33	0.246518
$890$	−38347.7	−1.44429
$891$	0	0
$892$	−6500.39	−0.244001
$893$	−54657.1	−2.04819
$894$	−20277.3	−0.758584
$895$	−28029.8	−1.04685
$896$	3949.43	0.147256
$897$	−4144.02	−0.154253
$898$	−10873.8	−0.404078
$899$	−1618.42	−0.0600417
$900$	593.873	0.0219953
$901$	2413.26	0.0892314
$902$	0	0
$903$	23017.0	0.848235
$904$	11425.8	0.420370
$905$	40063.7	1.47156
$906$	23885.7	0.875882
$907$	−37026.9	−1.35552	−0.677760	−	0.735283i	$-0.737049\pi$
$907$	−37026.9	−1.35552	−0.677760	+	0.735283i	$0.737049\pi$
$908$	−16238.6	−0.593499
$909$	−1399.28	−0.0510573
$910$	3981.66	0.145045
$911$	−18655.1	−0.678453	−0.339226	−	0.940705i	$-0.610165\pi$
$911$	−18655.1	−0.678453	−0.339226	+	0.940705i	$0.610165\pi$
$912$	−9563.92	−0.347251
$913$	0	0
$914$	5901.84	0.213584
$915$	33364.8	1.20547
$916$	2880.60	0.103906
$917$	−10121.3	−0.364488
$918$	33569.2	1.20692
$919$	5193.15	0.186405	0.0932024	−	0.995647i	$-0.470290\pi$
$919$	5193.15	0.186405	0.0932024	+	0.995647i	$0.470290\pi$
$920$	−20663.2	−0.740484
$921$	−36597.1	−1.30935
$922$	12260.2	0.437925
$923$	10469.3	0.373349
$924$	0	0
$925$	−3941.84	−0.140116
$926$	−7390.59	−0.262279
$927$	−10049.3	−0.356054
$928$	−10359.1	−0.366439
$929$	−2986.98	−0.105490	−0.0527448	−	0.998608i	$-0.516797\pi$
$929$	−2986.98	−0.105490	−0.0527448	+	0.998608i	$0.516797\pi$
$930$	2749.89	0.0969596
$931$	22436.2	0.789814
$932$	17417.4	0.612152
$933$	−25225.1	−0.885136
$934$	31986.6	1.12059
$935$	0	0
$936$	−2007.66	−0.0701093
$937$	−33341.9	−1.16247	−0.581233	−	0.813737i	$-0.697430\pi$
$937$	−33341.9	−1.16247	−0.581233	+	0.813737i	$0.697430\pi$
$938$	−10540.2	−0.366896
$939$	25648.3	0.891375
$940$	21924.1	0.760727
$941$	−40081.2	−1.38853	−0.694267	−	0.719717i	$-0.744271\pi$
$941$	−40081.2	−1.38853	−0.694267	+	0.719717i	$0.744271\pi$
$942$	17340.0	0.599753
$943$	31832.3	1.09926
$944$	1591.81	0.0548823
$945$	−22887.4	−0.787861
$946$	0	0
$947$	−43601.9	−1.49617	−0.748084	−	0.663604i	$-0.769026\pi$
$947$	−43601.9	−1.49617	−0.748084	+	0.663604i	$0.769026\pi$
$948$	13608.0	0.466209
$949$	8522.57	0.291522
$950$	5721.19	0.195389
$951$	−423.848	−0.0144524
$952$	−32563.2	−1.10859
$953$	−41139.9	−1.39837	−0.699187	−	0.714939i	$-0.746455\pi$
$953$	−41139.9	−1.39837	−0.699187	+	0.714939i	$0.746455\pi$
$954$	−287.306	−0.00975038
$955$	61009.7	2.06726
$956$	−6912.46	−0.233855
$957$	0	0
$958$	18052.4	0.608816
$959$	329.795	0.0111050
$960$	25502.3	0.857377
$961$	−29191.7	−0.979883
$962$	4355.52	0.145975
$963$	2908.80	0.0973363
$964$	23833.1	0.796277
$965$	−32818.7	−1.09479
$966$	8002.00	0.266522
$967$	−13610.9	−0.452633	−0.226316	−	0.974054i	$-0.572668\pi$
$967$	−13610.9	−0.452633	−0.226316	+	0.974054i	$0.572668\pi$
$968$	0	0
$969$	−58526.8	−1.94030
$970$	20116.2	0.665869
$971$	56287.0	1.86028	0.930141	−	0.367201i	$-0.119684\pi$
$971$	56287.0	1.86028	0.930141	+	0.367201i	$0.119684\pi$
$972$	6820.65	0.225074
$973$	109.279	0.00360055
$974$	−4913.96	−0.161657
$975$	−1408.12	−0.0462522
$976$	−10747.9	−0.352491
$977$	−25067.6	−0.820864	−0.410432	−	0.911891i	$-0.634622\pi$
$977$	−25067.6	−0.820864	−0.410432	+	0.911891i	$0.634622\pi$
$978$	14539.3	0.475373
$979$	0	0
$980$	−8999.61	−0.293349
$981$	9295.61	0.302534
$982$	26119.2	0.848776
$983$	32764.6	1.06310	0.531550	−	0.847027i	$-0.321610\pi$
$983$	32764.6	1.06310	0.531550	+	0.847027i	$0.321610\pi$
$984$	−49583.4	−1.60636
$985$	−4747.02	−0.153556
$986$	14639.3	0.472829
$987$	−25976.3	−0.837724
$988$	5966.42	0.192122
$989$	−28792.0	−0.925715
$990$	0	0
$991$	−55825.8	−1.78947	−0.894735	−	0.446597i	$-0.852636\pi$
$991$	−55825.8	−1.78947	−0.894735	+	0.446597i	$0.852636\pi$
$992$	3835.94	0.122773
$993$	−12992.7	−0.415216
$994$	−20215.9	−0.645081
$995$	3230.50	0.102928
$996$	3794.28	0.120709
$997$	9812.64	0.311705	0.155852	−	0.987780i	$-0.450188\pi$
$997$	9812.64	0.311705	0.155852	+	0.987780i	$0.450188\pi$
$998$	−33948.2	−1.07677
$999$	−25036.4	−0.792911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.o.1.12		34
11.5	even	5		143.4.h.a.14.11	✓	68
11.9	even	5		143.4.h.a.92.11	yes	68
11.10	odd	2		1573.4.a.p.1.23		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.14.11	✓	68	11.5	even	5
143.4.h.a.92.11	yes	68	11.9	even	5
1573.4.a.o.1.12		34	1.1	even	1	trivial
1573.4.a.p.1.23		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)

\(f(q)\)	\(=\)	\(q-2.02870 q^{2} -4.53812 q^{3} -3.88438 q^{4} -12.2012 q^{5} +9.20648 q^{6} +12.3738 q^{7} +24.1098 q^{8} -6.40548 q^{9} +O(q^{10})\)	\(q-2.02870 q^{2} -4.53812 q^{3} -3.88438 q^{4} -12.2012 q^{5} +9.20648 q^{6} +12.3738 q^{7} +24.1098 q^{8} -6.40548 q^{9} +24.7525 q^{10} +17.6278 q^{12} +13.0000 q^{13} -25.1027 q^{14} +55.3703 q^{15} -17.8366 q^{16} -109.152 q^{17} +12.9948 q^{18} -118.154 q^{19} +47.3939 q^{20} -56.1537 q^{21} +70.2429 q^{23} -109.413 q^{24} +23.8682 q^{25} -26.3731 q^{26} +151.598 q^{27} -48.0645 q^{28} +66.1107 q^{29} -112.330 q^{30} -24.4805 q^{31} -156.694 q^{32} +221.436 q^{34} -150.974 q^{35} +24.8813 q^{36} -165.150 q^{37} +239.699 q^{38} -58.9955 q^{39} -294.168 q^{40} +453.175 q^{41} +113.919 q^{42} -409.892 q^{43} +78.1543 q^{45} -142.502 q^{46} +462.592 q^{47} +80.9445 q^{48} -189.889 q^{49} -48.4215 q^{50} +495.343 q^{51} -50.4969 q^{52} -22.1093 q^{53} -307.547 q^{54} +298.330 q^{56} +536.197 q^{57} -134.119 q^{58} -89.2440 q^{59} -215.079 q^{60} +602.575 q^{61} +49.6636 q^{62} -79.2600 q^{63} +460.577 q^{64} -158.615 q^{65} +419.882 q^{67} +423.986 q^{68} -318.771 q^{69} +306.282 q^{70} +805.330 q^{71} -154.435 q^{72} +655.582 q^{73} +335.040 q^{74} -108.317 q^{75} +458.955 q^{76} +119.684 q^{78} +771.961 q^{79} +217.627 q^{80} -515.022 q^{81} -919.356 q^{82} +215.244 q^{83} +218.122 q^{84} +1331.78 q^{85} +831.548 q^{86} -300.018 q^{87} -1549.25 q^{89} -158.552 q^{90} +160.859 q^{91} -272.850 q^{92} +111.095 q^{93} -938.460 q^{94} +1441.62 q^{95} +711.094 q^{96} +812.695 q^{97} +385.229 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} + 36 q^{6} - 36 q^{7} - 57 q^{8} + 265 q^{9}+O(q^{10}) \) 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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