LMFDB - Embedded newform 1805.2.a.w.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 29x^{14} + 339x^{12} - 2038x^{10} + 6639x^{8} - 11261x^{6} + 8701x^{4} - 2592x^{2} + 256 $ x^16 - 29x^14 + 339x^12 - 2038x^10 + 6639x^8 - 11261x^6 + 8701x^4 - 2592*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.01007$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.01007 q^{2} +2.79667 q^{3} -0.979758 q^{4} +1.00000 q^{5} -2.82483 q^{6} -1.25546 q^{7} +3.00976 q^{8} +4.82135 q^{9} +O(q^{10})$	\(q-1.01007 q^{2} +2.79667 q^{3} -0.979758 q^{4} +1.00000 q^{5} -2.82483 q^{6} -1.25546 q^{7} +3.00976 q^{8} +4.82135 q^{9} -1.01007 q^{10} -3.20895 q^{11} -2.74006 q^{12} +2.07323 q^{13} +1.26810 q^{14} +2.79667 q^{15} -1.08056 q^{16} -5.18871 q^{17} -4.86990 q^{18} -0.979758 q^{20} -3.51109 q^{21} +3.24126 q^{22} +9.33549 q^{23} +8.41731 q^{24} +1.00000 q^{25} -2.09411 q^{26} +5.09371 q^{27} +1.23004 q^{28} +8.56068 q^{29} -2.82483 q^{30} +3.10614 q^{31} -4.92809 q^{32} -8.97436 q^{33} +5.24096 q^{34} -1.25546 q^{35} -4.72376 q^{36} +7.83291 q^{37} +5.79815 q^{39} +3.00976 q^{40} +4.42119 q^{41} +3.54645 q^{42} +7.55632 q^{43} +3.14399 q^{44} +4.82135 q^{45} -9.42950 q^{46} +5.90103 q^{47} -3.02196 q^{48} -5.42383 q^{49} -1.01007 q^{50} -14.5111 q^{51} -2.03127 q^{52} -12.2935 q^{53} -5.14501 q^{54} -3.20895 q^{55} -3.77863 q^{56} -8.64689 q^{58} +2.01396 q^{59} -2.74006 q^{60} +12.4426 q^{61} -3.13742 q^{62} -6.05299 q^{63} +7.13883 q^{64} +2.07323 q^{65} +9.06473 q^{66} -11.5533 q^{67} +5.08368 q^{68} +26.1083 q^{69} +1.26810 q^{70} -0.135122 q^{71} +14.5111 q^{72} +6.62195 q^{73} -7.91178 q^{74} +2.79667 q^{75} +4.02869 q^{77} -5.85654 q^{78} -5.30166 q^{79} -1.08056 q^{80} -0.218633 q^{81} -4.46571 q^{82} +1.79512 q^{83} +3.44002 q^{84} -5.18871 q^{85} -7.63241 q^{86} +23.9414 q^{87} -9.65818 q^{88} +15.7945 q^{89} -4.86990 q^{90} -2.60285 q^{91} -9.14652 q^{92} +8.68684 q^{93} -5.96045 q^{94} -13.7822 q^{96} -4.67613 q^{97} +5.47845 q^{98} -15.4715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.01007	−0.714227	−0.357114	−	0.934061i	$-0.616239\pi$
$2$	−1.01007	−0.714227	−0.357114	+	0.934061i	$0.616239\pi$
$3$	2.79667	1.61466	0.807328	−	0.590102i	$-0.200913\pi$
$3$	2.79667	1.61466	0.807328	+	0.590102i	$0.200913\pi$
$4$	−0.979758	−0.489879
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.82483	−1.15323
$7$	−1.25546	−0.474518	−0.237259	−	0.971446i	$-0.576249\pi$
$7$	−1.25546	−0.474518	−0.237259	+	0.971446i	$0.576249\pi$
$8$	3.00976	1.06411
$9$	4.82135	1.60712
$10$	−1.01007	−0.319412
$11$	−3.20895	−0.967534	−0.483767	−	0.875197i	$-0.660732\pi$
$11$	−3.20895	−0.967534	−0.483767	+	0.875197i	$0.660732\pi$
$12$	−2.74006	−0.790987
$13$	2.07323	0.575012	0.287506	−	0.957779i	$-0.407174\pi$
$13$	2.07323	0.575012	0.287506	+	0.957779i	$0.407174\pi$
$14$	1.26810	0.338914
$15$	2.79667	0.722096
$16$	−1.08056	−0.270139
$17$	−5.18871	−1.25845	−0.629223	−	0.777225i	$-0.716627\pi$
$17$	−5.18871	−1.25845	−0.629223	+	0.777225i	$0.716627\pi$
$18$	−4.86990	−1.14785
$19$	0	0
$19$	0	0
$20$	−0.979758	−0.219081
$21$	−3.51109	−0.766183
$22$	3.24126	0.691039
$23$	9.33549	1.94658	0.973292	−	0.229572i	$-0.0737327\pi$
$23$	9.33549	1.94658	0.973292	+	0.229572i	$0.0737327\pi$
$24$	8.41731	1.71818
$25$	1.00000	0.200000
$26$	−2.09411	−0.410689
$27$	5.09371	0.980285
$28$	1.23004	0.232456
$29$	8.56068	1.58968	0.794839	−	0.606820i	$-0.207555\pi$
$29$	8.56068	1.58968	0.794839	+	0.606820i	$0.207555\pi$
$30$	−2.82483	−0.515741
$31$	3.10614	0.557879	0.278940	−	0.960309i	$-0.410017\pi$
$31$	3.10614	0.557879	0.278940	+	0.960309i	$0.410017\pi$
$32$	−4.92809	−0.871172
$33$	−8.97436	−1.56224
$34$	5.24096	0.898817
$35$	−1.25546	−0.212211
$36$	−4.72376	−0.787293
$37$	7.83291	1.28772	0.643861	−	0.765143i	$-0.277332\pi$
$37$	7.83291	1.28772	0.643861	+	0.765143i	$0.277332\pi$
$38$	0	0
$39$	5.79815	0.928447
$40$	3.00976	0.475886
$41$	4.42119	0.690474	0.345237	−	0.938516i	$-0.387799\pi$
$41$	4.42119	0.690474	0.345237	+	0.938516i	$0.387799\pi$
$42$	3.54645	0.547229
$43$	7.55632	1.15233	0.576164	−	0.817334i	$-0.304549\pi$
$43$	7.55632	1.15233	0.576164	+	0.817334i	$0.304549\pi$
$44$	3.14399	0.473975
$45$	4.82135	0.718724
$46$	−9.42950	−1.39030
$47$	5.90103	0.860753	0.430377	−	0.902649i	$-0.358381\pi$
$47$	5.90103	0.860753	0.430377	+	0.902649i	$0.358381\pi$
$48$	−3.02196	−0.436182
$49$	−5.42383	−0.774833
$50$	−1.01007	−0.142845
$51$	−14.5111	−2.03196
$52$	−2.03127	−0.281686
$53$	−12.2935	−1.68864	−0.844319	−	0.535841i	$-0.819995\pi$
$53$	−12.2935	−1.68864	−0.844319	+	0.535841i	$0.819995\pi$
$54$	−5.14501	−0.700147
$55$	−3.20895	−0.432694
$56$	−3.77863	−0.504940
$57$	0	0
$58$	−8.64689	−1.13539
$59$	2.01396	0.262195	0.131098	−	0.991369i	$-0.458150\pi$
$59$	2.01396	0.262195	0.131098	+	0.991369i	$0.458150\pi$
$60$	−2.74006	−0.353740
$61$	12.4426	1.59311	0.796556	−	0.604564i	$-0.206653\pi$
$61$	12.4426	1.59311	0.796556	+	0.604564i	$0.206653\pi$
$62$	−3.13742	−0.398453
$63$	−6.05299	−0.762605
$64$	7.13883	0.892354
$65$	2.07323	0.257153
$66$	9.06473	1.11579
$67$	−11.5533	−1.41146	−0.705730	−	0.708481i	$-0.749381\pi$
$67$	−11.5533	−1.41146	−0.705730	+	0.708481i	$0.749381\pi$
$68$	5.08368	0.616486
$69$	26.1083	3.14306
$70$	1.26810	0.151567
$71$	−0.135122	−0.0160360	−0.00801800	−	0.999968i	$-0.502552\pi$
$71$	−0.135122	−0.0160360	−0.00801800	+	0.999968i	$0.502552\pi$
$72$	14.5111	1.71015
$73$	6.62195	0.775041	0.387520	−	0.921861i	$-0.373332\pi$
$73$	6.62195	0.775041	0.387520	+	0.921861i	$0.373332\pi$
$74$	−7.91178	−0.919726
$75$	2.79667	0.322931
$76$	0	0
$77$	4.02869	0.459112
$78$	−5.85654	−0.663122
$79$	−5.30166	−0.596483	−0.298242	−	0.954490i	$-0.596400\pi$
$79$	−5.30166	−0.596483	−0.298242	+	0.954490i	$0.596400\pi$
$80$	−1.08056	−0.120810
$81$	−0.218633	−0.0242926
$82$	−4.46571	−0.493155
$83$	1.79512	0.197040	0.0985201	−	0.995135i	$-0.468589\pi$
$83$	1.79512	0.197040	0.0985201	+	0.995135i	$0.468589\pi$
$84$	3.44002	0.375337
$85$	−5.18871	−0.562794
$86$	−7.63241	−0.823024
$87$	23.9414	2.56679
$88$	−9.65818	−1.02957
$89$	15.7945	1.67421	0.837106	−	0.547041i	$-0.184246\pi$
$89$	15.7945	1.67421	0.837106	+	0.547041i	$0.184246\pi$
$90$	−4.86990	−0.513333
$91$	−2.60285	−0.272853
$92$	−9.14652	−0.953591
$93$	8.68684	0.900784
$94$	−5.96045	−0.614774
$95$	0	0
$96$	−13.7822	−1.40664
$97$	−4.67613	−0.474789	−0.237394	−	0.971413i	$-0.576293\pi$
$97$	−4.67613	−0.474789	−0.237394	+	0.971413i	$0.576293\pi$
$98$	5.47845	0.553407
$99$	−15.4715	−1.55494
$100$	−0.979758	−0.0979758
$101$	8.04679	0.800686	0.400343	−	0.916365i	$-0.368891\pi$
$101$	8.04679	0.800686	0.400343	+	0.916365i	$0.368891\pi$
$102$	14.6572	1.45128
$103$	0.157475	0.0155164	0.00775822	−	0.999970i	$-0.497530\pi$
$103$	0.157475	0.0155164	0.00775822	+	0.999970i	$0.497530\pi$
$104$	6.23995	0.611877
$105$	−3.51109	−0.342648
$106$	12.4173	1.20607
$107$	−3.70918	−0.358580	−0.179290	−	0.983796i	$-0.557380\pi$
$107$	−3.70918	−0.358580	−0.179290	+	0.983796i	$0.557380\pi$
$108$	−4.99061	−0.480221
$109$	−13.4746	−1.29063	−0.645315	−	0.763916i	$-0.723274\pi$
$109$	−13.4746	−1.29063	−0.645315	+	0.763916i	$0.723274\pi$
$110$	3.24126	0.309042
$111$	21.9060	2.07923
$112$	1.35659	0.128186
$113$	−10.7524	−1.01150	−0.505752	−	0.862679i	$-0.668785\pi$
$113$	−10.7524	−1.01150	−0.505752	+	0.862679i	$0.668785\pi$
$114$	0	0
$115$	9.33549	0.870539
$116$	−8.38740	−0.778750
$117$	9.99579	0.924111
$118$	−2.03424	−0.187267
$119$	6.51419	0.597155
$120$	8.41731	0.768392
$121$	−0.702655	−0.0638777
$122$	−12.5679	−1.13784
$123$	12.3646	1.11488
$124$	−3.04327	−0.273293
$125$	1.00000	0.0894427
$126$	6.11395	0.544674
$127$	8.45812	0.750537	0.375268	−	0.926916i	$-0.377551\pi$
$127$	8.45812	0.750537	0.375268	+	0.926916i	$0.377551\pi$
$128$	2.64546	0.233828
$129$	21.1325	1.86061
$130$	−2.09411	−0.183666
$131$	3.43098	0.299766	0.149883	−	0.988704i	$-0.452110\pi$
$131$	3.43098	0.299766	0.149883	+	0.988704i	$0.452110\pi$
$132$	8.79270	0.765307
$133$	0	0
$134$	11.6696	1.00810
$135$	5.09371	0.438397
$136$	−15.6168	−1.33913
$137$	−8.07266	−0.689694	−0.344847	−	0.938659i	$-0.612069\pi$
$137$	−8.07266	−0.689694	−0.344847	+	0.938659i	$0.612069\pi$
$138$	−26.3712	−2.24486
$139$	15.2253	1.29139	0.645695	−	0.763595i	$-0.276568\pi$
$139$	15.2253	1.29139	0.645695	+	0.763595i	$0.276568\pi$
$140$	1.23004	0.103958
$141$	16.5032	1.38982
$142$	0.136482	0.0114533
$143$	−6.65290	−0.556343
$144$	−5.20974	−0.434145
$145$	8.56068	0.710926
$146$	−6.68864	−0.553555
$147$	−15.1687	−1.25109
$148$	−7.67435	−0.630828
$149$	0.0275183	0.00225439	0.00112719	−	0.999999i	$-0.499641\pi$
$149$	0.0275183	0.00225439	0.00112719	+	0.999999i	$0.499641\pi$
$150$	−2.82483	−0.230646
$151$	−1.29200	−0.105141	−0.0525707	−	0.998617i	$-0.516741\pi$
$151$	−1.29200	−0.105141	−0.0525707	+	0.998617i	$0.516741\pi$
$152$	0	0
$153$	−25.0166	−2.02247
$154$	−4.06926	−0.327910
$155$	3.10614	0.249491
$156$	−5.68078	−0.454827
$157$	−11.8697	−0.947303	−0.473652	−	0.880712i	$-0.657064\pi$
$157$	−11.8697	−0.947303	−0.473652	+	0.880712i	$0.657064\pi$
$158$	5.35505	0.426025
$159$	−34.3808	−2.72657
$160$	−4.92809	−0.389600
$161$	−11.7203	−0.923688
$162$	0.220835	0.0173504
$163$	5.82502	0.456251	0.228125	−	0.973632i	$-0.426740\pi$
$163$	5.82502	0.456251	0.228125	+	0.973632i	$0.426740\pi$
$164$	−4.33170	−0.338249
$165$	−8.97436	−0.698653
$166$	−1.81320	−0.140732
$167$	2.89002	0.223637	0.111818	−	0.993729i	$-0.464333\pi$
$167$	2.89002	0.223637	0.111818	+	0.993729i	$0.464333\pi$
$168$	−10.5676	−0.815305
$169$	−8.70170	−0.669362
$170$	5.24096	0.401963
$171$	0	0
$172$	−7.40337	−0.564501
$173$	−13.3903	−1.01804	−0.509022	−	0.860754i	$-0.669993\pi$
$173$	−13.3903	−1.01804	−0.509022	+	0.860754i	$0.669993\pi$
$174$	−24.1825	−1.83327
$175$	−1.25546	−0.0949035
$176$	3.46745	0.261369
$177$	5.63237	0.423355
$178$	−15.9535	−1.19577
$179$	−16.1184	−1.20474	−0.602372	−	0.798215i	$-0.705778\pi$
$179$	−16.1184	−1.20474	−0.602372	+	0.798215i	$0.705778\pi$
$180$	−4.72376	−0.352088
$181$	−2.97210	−0.220914	−0.110457	−	0.993881i	$-0.535231\pi$
$181$	−2.97210	−0.220914	−0.110457	+	0.993881i	$0.535231\pi$
$182$	2.62907	0.194879
$183$	34.7978	2.57233
$184$	28.0976	2.07138
$185$	7.83291	0.575887
$186$	−8.77432	−0.643364
$187$	16.6503	1.21759
$188$	−5.78158	−0.421665
$189$	−6.39493	−0.465163
$190$	0	0
$191$	−12.3135	−0.890977	−0.445488	−	0.895288i	$-0.646970\pi$
$191$	−12.3135	−0.890977	−0.445488	+	0.895288i	$0.646970\pi$
$192$	19.9649	1.44085
$193$	14.4322	1.03886	0.519428	−	0.854514i	$-0.326145\pi$
$193$	14.4322	1.03886	0.519428	+	0.854514i	$0.326145\pi$
$194$	4.72321	0.339107
$195$	5.79815	0.415214
$196$	5.31404	0.379574
$197$	13.1174	0.934574	0.467287	−	0.884106i	$-0.345232\pi$
$197$	13.1174	0.934574	0.467287	+	0.884106i	$0.345232\pi$
$198$	15.6273	1.11058
$199$	−7.60558	−0.539145	−0.269573	−	0.962980i	$-0.586882\pi$
$199$	−7.60558	−0.539145	−0.269573	+	0.962980i	$0.586882\pi$
$200$	3.00976	0.212823
$201$	−32.3107	−2.27902
$202$	−8.12783	−0.571872
$203$	−10.7476	−0.754331
$204$	14.2174	0.995414
$205$	4.42119	0.308789
$206$	−0.159060	−0.0110823
$207$	45.0096	3.12839
$208$	−2.24025	−0.155333
$209$	0	0
$210$	3.54645	0.244728
$211$	10.8141	0.744475	0.372237	−	0.928138i	$-0.378591\pi$
$211$	10.8141	0.744475	0.372237	+	0.928138i	$0.378591\pi$
$212$	12.0446	0.827229
$213$	−0.377891	−0.0258926
$214$	3.74653	0.256108
$215$	7.55632	0.515337
$216$	15.3309	1.04313
$217$	−3.89962	−0.264724
$218$	13.6103	0.921804
$219$	18.5194	1.25142
$220$	3.14399	0.211968
$221$	−10.7574	−0.723621
$222$	−22.1266	−1.48504
$223$	7.04338	0.471660	0.235830	−	0.971794i	$-0.424219\pi$
$223$	7.04338	0.471660	0.235830	+	0.971794i	$0.424219\pi$
$224$	6.18700	0.413386
$225$	4.82135	0.321423
$226$	10.8607	0.722444
$227$	−0.574181	−0.0381097	−0.0190549	−	0.999818i	$-0.506066\pi$
$227$	−0.574181	−0.0381097	−0.0190549	+	0.999818i	$0.506066\pi$
$228$	0	0
$229$	−17.9431	−1.18571	−0.592856	−	0.805309i	$-0.702000\pi$
$229$	−17.9431	−1.18571	−0.592856	+	0.805309i	$0.702000\pi$
$230$	−9.42950	−0.621763
$231$	11.2669	0.741308
$232$	25.7656	1.69160
$233$	−9.38900	−0.615094	−0.307547	−	0.951533i	$-0.599508\pi$
$233$	−9.38900	−0.615094	−0.307547	+	0.951533i	$0.599508\pi$
$234$	−10.0964	−0.660025
$235$	5.90103	0.384940
$236$	−1.97319	−0.128444
$237$	−14.8270	−0.963116
$238$	−6.57979	−0.426504
$239$	5.58369	0.361179	0.180590	−	0.983559i	$-0.442199\pi$
$239$	5.58369	0.361179	0.180590	+	0.983559i	$0.442199\pi$
$240$	−3.02196	−0.195067
$241$	12.0202	0.774289	0.387144	−	0.922019i	$-0.373461\pi$
$241$	12.0202	0.774289	0.387144	+	0.922019i	$0.373461\pi$
$242$	0.709731	0.0456232
$243$	−15.8926	−1.01951
$244$	−12.1907	−0.780433
$245$	−5.42383	−0.346516
$246$	−12.4891	−0.796277
$247$	0	0
$248$	9.34875	0.593646
$249$	5.02036	0.318152
$250$	−1.01007	−0.0638824
$251$	4.94854	0.312349	0.156175	−	0.987729i	$-0.450084\pi$
$251$	4.94854	0.312349	0.156175	+	0.987729i	$0.450084\pi$
$252$	5.93047	0.373584
$253$	−29.9571	−1.88339
$254$	−8.54330	−0.536054
$255$	−14.5111	−0.908719
$256$	−16.9498	−1.05936
$257$	18.5425	1.15665	0.578326	−	0.815806i	$-0.303706\pi$
$257$	18.5425	1.15665	0.578326	+	0.815806i	$0.303706\pi$
$258$	−21.3453	−1.32890
$259$	−9.83387	−0.611047
$260$	−2.03127	−0.125974
$261$	41.2740	2.55480
$262$	−3.46553	−0.214101
$263$	−13.8308	−0.852843	−0.426422	−	0.904525i	$-0.640226\pi$
$263$	−13.8308	−0.852843	−0.426422	+	0.904525i	$0.640226\pi$
$264$	−27.0107	−1.66239
$265$	−12.2935	−0.755182
$266$	0	0
$267$	44.1719	2.70328
$268$	11.3194	0.691445
$269$	−11.9348	−0.727679	−0.363840	−	0.931462i	$-0.618534\pi$
$269$	−11.9348	−0.727679	−0.363840	+	0.931462i	$0.618534\pi$
$270$	−5.14501	−0.313115
$271$	32.7768	1.99105	0.995525	−	0.0944957i	$-0.0301239\pi$
$271$	32.7768	1.99105	0.995525	+	0.0944957i	$0.0301239\pi$
$272$	5.60669	0.339956
$273$	−7.27932	−0.440564
$274$	8.15396	0.492598
$275$	−3.20895	−0.193507
$276$	−25.5798	−1.53972
$277$	3.59699	0.216122	0.108061	−	0.994144i	$-0.465536\pi$
$277$	3.59699	0.216122	0.108061	+	0.994144i	$0.465536\pi$
$278$	−15.3786	−0.922346
$279$	14.9758	0.896577
$280$	−3.77863	−0.225816
$281$	−12.9755	−0.774056	−0.387028	−	0.922068i	$-0.626498\pi$
$281$	−12.9755	−0.774056	−0.387028	+	0.922068i	$0.626498\pi$
$282$	−16.6694	−0.992648
$283$	3.88716	0.231067	0.115534	−	0.993304i	$-0.463142\pi$
$283$	3.88716	0.231067	0.115534	+	0.993304i	$0.463142\pi$
$284$	0.132387	0.00785570
$285$	0	0
$286$	6.71990	0.397356
$287$	−5.55061	−0.327642
$288$	−23.7601	−1.40007
$289$	9.92267	0.583686
$290$	−8.64689	−0.507763
$291$	−13.0776	−0.766621
$292$	−6.48791	−0.379676
$293$	0.0658502	0.00384701	0.00192350	−	0.999998i	$-0.499388\pi$
$293$	0.0658502	0.00384701	0.00192350	+	0.999998i	$0.499388\pi$
$294$	15.3214	0.893562
$295$	2.01396	0.117257
$296$	23.5752	1.37028
$297$	−16.3455	−0.948459
$298$	−0.0277954	−0.00161014
$299$	19.3546	1.11931
$300$	−2.74006	−0.158197
$301$	−9.48663	−0.546800
$302$	1.30501	0.0750949
$303$	22.5042	1.29283
$304$	0	0
$305$	12.4426	0.712462
$306$	25.2685	1.44450
$307$	30.3647	1.73300	0.866502	−	0.499173i	$-0.166363\pi$
$307$	30.3647	1.73300	0.866502	+	0.499173i	$0.166363\pi$
$308$	−3.94714	−0.224909
$309$	0.440404	0.0250537
$310$	−3.13742	−0.178193
$311$	−19.9542	−1.13150	−0.565750	−	0.824577i	$-0.691413\pi$
$311$	−19.9542	−1.13150	−0.565750	+	0.824577i	$0.691413\pi$
$312$	17.4511	0.987972
$313$	−6.12969	−0.346471	−0.173235	−	0.984880i	$-0.555422\pi$
$313$	−6.12969	−0.346471	−0.173235	+	0.984880i	$0.555422\pi$
$314$	11.9892	0.676590
$315$	−6.05299	−0.341047
$316$	5.19434	0.292205
$317$	5.12277	0.287723	0.143862	−	0.989598i	$-0.454048\pi$
$317$	5.12277	0.287723	0.143862	+	0.989598i	$0.454048\pi$
$318$	34.7270	1.94739
$319$	−27.4708	−1.53807
$320$	7.13883	0.399073
$321$	−10.3734	−0.578984
$322$	11.8383	0.659724
$323$	0	0
$324$	0.214208	0.0119004
$325$	2.07323	0.115002
$326$	−5.88368	−0.325867
$327$	−37.6839	−2.08393
$328$	13.3067	0.734742
$329$	−7.40848	−0.408443
$330$	9.06473	0.498997
$331$	1.80926	0.0994457	0.0497228	−	0.998763i	$-0.484166\pi$
$331$	1.80926	0.0994457	0.0497228	+	0.998763i	$0.484166\pi$
$332$	−1.75879	−0.0965259
$333$	37.7652	2.06952
$334$	−2.91912	−0.159727
$335$	−11.5533	−0.631224
$336$	3.79394	0.206976
$337$	−11.9648	−0.651764	−0.325882	−	0.945410i	$-0.605661\pi$
$337$	−11.9648	−0.651764	−0.325882	+	0.945410i	$0.605661\pi$
$338$	8.78933	0.478076
$339$	−30.0710	−1.63323
$340$	5.08368	0.275701
$341$	−9.96744	−0.539767
$342$	0	0
$343$	15.5976	0.842190
$344$	22.7427	1.22621
$345$	26.1083	1.40562
$346$	13.5251	0.727115
$347$	−10.6377	−0.571061	−0.285530	−	0.958370i	$-0.592170\pi$
$347$	−10.6377	−0.571061	−0.285530	+	0.958370i	$0.592170\pi$
$348$	−23.4568	−1.25741
$349$	−8.44790	−0.452206	−0.226103	−	0.974103i	$-0.572599\pi$
$349$	−8.44790	−0.452206	−0.226103	+	0.974103i	$0.572599\pi$
$350$	1.26810	0.0677827
$351$	10.5605	0.563675
$352$	15.8140	0.842888
$353$	9.51550	0.506459	0.253229	−	0.967406i	$-0.418507\pi$
$353$	9.51550	0.506459	0.253229	+	0.967406i	$0.418507\pi$
$354$	−5.68909	−0.302372
$355$	−0.135122	−0.00717152
$356$	−15.4748	−0.820161
$357$	18.2180	0.964200
$358$	16.2807	0.860462
$359$	−6.59901	−0.348282	−0.174141	−	0.984721i	$-0.555715\pi$
$359$	−6.59901	−0.348282	−0.174141	+	0.984721i	$0.555715\pi$
$360$	14.5111	0.764804
$361$	0	0
$362$	3.00203	0.157783
$363$	−1.96509	−0.103141
$364$	2.55017	0.133665
$365$	6.62195	0.346609
$366$	−35.1483	−1.83723
$367$	19.5088	1.01835	0.509174	−	0.860663i	$-0.329951\pi$
$367$	19.5088	1.01835	0.509174	+	0.860663i	$0.329951\pi$
$368$	−10.0875	−0.525849
$369$	21.3161	1.10967
$370$	−7.91178	−0.411314
$371$	15.4339	0.801289
$372$	−8.51101	−0.441275
$373$	−25.5363	−1.32222	−0.661110	−	0.750289i	$-0.729914\pi$
$373$	−25.5363	−1.32222	−0.661110	+	0.750289i	$0.729914\pi$
$374$	−16.8180	−0.869636
$375$	2.79667	0.144419
$376$	17.7607	0.915938
$377$	17.7483	0.914084
$378$	6.45933	0.332232
$379$	−5.71477	−0.293548	−0.146774	−	0.989170i	$-0.546889\pi$
$379$	−5.71477	−0.293548	−0.146774	+	0.989170i	$0.546889\pi$
$380$	0	0
$381$	23.6546	1.21186
$382$	12.4375	0.636360
$383$	−33.5520	−1.71443	−0.857213	−	0.514962i	$-0.827806\pi$
$383$	−33.5520	−1.71443	−0.857213	+	0.514962i	$0.827806\pi$
$384$	7.39847	0.377552
$385$	4.02869	0.205321
$386$	−14.5776	−0.741979
$387$	36.4317	1.85193
$388$	4.58147	0.232589
$389$	−14.2558	−0.722799	−0.361400	−	0.932411i	$-0.617701\pi$
$389$	−14.2558	−0.722799	−0.361400	+	0.932411i	$0.617701\pi$
$390$	−5.85654	−0.296557
$391$	−48.4391	−2.44967
$392$	−16.3245	−0.824509
$393$	9.59531	0.484019
$394$	−13.2495	−0.667498
$395$	−5.30166	−0.266755
$396$	15.1583	0.761733
$397$	24.0565	1.20736	0.603681	−	0.797226i	$-0.293700\pi$
$397$	24.0565	1.20736	0.603681	+	0.797226i	$0.293700\pi$
$398$	7.68217	0.385072
$399$	0	0
$400$	−1.08056	−0.0540279
$401$	−36.4798	−1.82172	−0.910858	−	0.412721i	$-0.864579\pi$
$401$	−36.4798	−1.82172	−0.910858	+	0.412721i	$0.864579\pi$
$402$	32.6361	1.62774
$403$	6.43976	0.320787
$404$	−7.88391	−0.392239
$405$	−0.218633	−0.0108640
$406$	10.8558	0.538764
$407$	−25.1354	−1.24591
$408$	−43.6750	−2.16223
$409$	−11.2232	−0.554951	−0.277475	−	0.960733i	$-0.589498\pi$
$409$	−11.2232	−0.554951	−0.277475	+	0.960733i	$0.589498\pi$
$410$	−4.46571	−0.220546
$411$	−22.5766	−1.11362
$412$	−0.154287	−0.00760118
$413$	−2.52844	−0.124416
$414$	−45.4629	−2.23438
$415$	1.79512	0.0881191
$416$	−10.2171	−0.500934
$417$	42.5800	2.08515
$418$	0	0
$419$	−26.6376	−1.30133	−0.650666	−	0.759364i	$-0.725510\pi$
$419$	−26.6376	−1.30133	−0.650666	+	0.759364i	$0.725510\pi$
$420$	3.44002	0.167856
$421$	−16.1430	−0.786763	−0.393382	−	0.919375i	$-0.628695\pi$
$421$	−16.1430	−0.786763	−0.393382	+	0.919375i	$0.628695\pi$
$422$	−10.9230	−0.531724
$423$	28.4509	1.38333
$424$	−37.0005	−1.79690
$425$	−5.18871	−0.251689
$426$	0.381696	0.0184932
$427$	−15.6211	−0.755960
$428$	3.63410	0.175661
$429$	−18.6060	−0.898304
$430$	−7.63241	−0.368068
$431$	−35.6479	−1.71710	−0.858549	−	0.512731i	$-0.828634\pi$
$431$	−35.6479	−1.71710	−0.858549	+	0.512731i	$0.828634\pi$
$432$	−5.50405	−0.264814
$433$	22.6358	1.08781	0.543904	−	0.839147i	$-0.316945\pi$
$433$	22.6358	1.08781	0.543904	+	0.839147i	$0.316945\pi$
$434$	3.93889	0.189073
$435$	23.9414	1.14790
$436$	13.2018	0.632253
$437$	0	0
$438$	−18.7059	−0.893802
$439$	6.59479	0.314752	0.157376	−	0.987539i	$-0.449697\pi$
$439$	6.59479	0.314752	0.157376	+	0.987539i	$0.449697\pi$
$440$	−9.65818	−0.460436
$441$	−26.1502	−1.24525
$442$	10.8657	0.516830
$443$	34.4053	1.63464	0.817322	−	0.576182i	$-0.195458\pi$
$443$	34.4053	1.63464	0.817322	+	0.576182i	$0.195458\pi$
$444$	−21.4626	−1.01857
$445$	15.7945	0.748730
$446$	−7.11431	−0.336872
$447$	0.0769595	0.00364006
$448$	−8.96249	−0.423438
$449$	3.07741	0.145232	0.0726159	−	0.997360i	$-0.476865\pi$
$449$	3.07741	0.145232	0.0726159	+	0.997360i	$0.476865\pi$
$450$	−4.86990	−0.229569
$451$	−14.1874	−0.668057
$452$	10.5348	0.495514
$453$	−3.61329	−0.169767
$454$	0.579963	0.0272190
$455$	−2.60285	−0.122024
$456$	0	0
$457$	−17.2797	−0.808309	−0.404154	−	0.914691i	$-0.632434\pi$
$457$	−17.2797	−0.808309	−0.404154	+	0.914691i	$0.632434\pi$
$458$	18.1238	0.846868
$459$	−26.4298	−1.23364
$460$	−9.14652	−0.426459
$461$	−11.0269	−0.513572	−0.256786	−	0.966468i	$-0.582664\pi$
$461$	−11.0269	−0.513572	−0.256786	+	0.966468i	$0.582664\pi$
$462$	−11.3804	−0.529463
$463$	12.2637	0.569941	0.284970	−	0.958536i	$-0.408016\pi$
$463$	12.2637	0.569941	0.284970	+	0.958536i	$0.408016\pi$
$464$	−9.25031	−0.429435
$465$	8.68684	0.402843
$466$	9.48355	0.439317
$467$	−14.0261	−0.649050	−0.324525	−	0.945877i	$-0.605204\pi$
$467$	−14.0261	−0.649050	−0.324525	+	0.945877i	$0.605204\pi$
$468$	−9.79346	−0.452703
$469$	14.5047	0.669763
$470$	−5.96045	−0.274935
$471$	−33.1955	−1.52957
$472$	6.06154	0.279005
$473$	−24.2478	−1.11492
$474$	14.9763	0.687884
$475$	0	0
$476$	−6.38233	−0.292534
$477$	−59.2711	−2.71384
$478$	−5.63992	−0.257964
$479$	−20.4644	−0.935043	−0.467522	−	0.883982i	$-0.654853\pi$
$479$	−20.4644	−0.935043	−0.467522	+	0.883982i	$0.654853\pi$
$480$	−13.7822	−0.629070
$481$	16.2394	0.740455
$482$	−12.1412	−0.553018
$483$	−32.7778	−1.49144
$484$	0.688432	0.0312924
$485$	−4.67613	−0.212332
$486$	16.0526	0.728162
$487$	−19.3780	−0.878103	−0.439051	−	0.898462i	$-0.644685\pi$
$487$	−19.3780	−0.878103	−0.439051	+	0.898462i	$0.644685\pi$
$488$	37.4493	1.69525
$489$	16.2906	0.736688
$490$	5.47845	0.247491
$491$	−35.0468	−1.58164	−0.790820	−	0.612049i	$-0.790346\pi$
$491$	−35.0468	−1.58164	−0.790820	+	0.612049i	$0.790346\pi$
$492$	−12.1143	−0.546156
$493$	−44.4189	−2.00052
$494$	0	0
$495$	−15.4715	−0.695390
$496$	−3.35636	−0.150705
$497$	0.169639	0.00760936
$498$	−5.07092	−0.227233
$499$	−16.6218	−0.744092	−0.372046	−	0.928214i	$-0.621344\pi$
$499$	−16.6218	−0.744092	−0.372046	+	0.928214i	$0.621344\pi$
$500$	−0.979758	−0.0438161
$501$	8.08243	0.361096
$502$	−4.99838	−0.223088
$503$	33.7542	1.50503	0.752513	−	0.658577i	$-0.228841\pi$
$503$	33.7542	1.50503	0.752513	+	0.658577i	$0.228841\pi$
$504$	−18.2181	−0.811498
$505$	8.04679	0.358078
$506$	30.2588	1.34517
$507$	−24.3358	−1.08079
$508$	−8.28691	−0.367672
$509$	−21.8305	−0.967620	−0.483810	−	0.875173i	$-0.660747\pi$
$509$	−21.8305	−0.967620	−0.483810	+	0.875173i	$0.660747\pi$
$510$	14.6572	0.649032
$511$	−8.31357	−0.367771
$512$	11.8295	0.522796
$513$	0	0
$514$	−18.7293	−0.826113
$515$	0.157475	0.00693916
$516$	−20.7048	−0.911476
$517$	−18.9361	−0.832808
$518$	9.93290	0.436426
$519$	−37.4481	−1.64379
$520$	6.23995	0.273640
$521$	−21.3065	−0.933455	−0.466727	−	0.884401i	$-0.654567\pi$
$521$	−21.3065	−0.933455	−0.466727	+	0.884401i	$0.654567\pi$
$522$	−41.6897	−1.82471
$523$	−18.5998	−0.813311	−0.406655	−	0.913582i	$-0.633305\pi$
$523$	−18.5998	−0.813311	−0.406655	+	0.913582i	$0.633305\pi$
$524$	−3.36153	−0.146849
$525$	−3.51109	−0.153237
$526$	13.9701	0.609124
$527$	−16.1169	−0.702061
$528$	9.69731	0.422021
$529$	64.1513	2.78919
$530$	12.4173	0.539372
$531$	9.71000	0.421378
$532$	0	0
$533$	9.16616	0.397031
$534$	−44.6167	−1.93075
$535$	−3.70918	−0.160362
$536$	−34.7727	−1.50195
$537$	−45.0778	−1.94525
$538$	12.0550	0.519729
$539$	17.4048	0.749677
$540$	−4.99061	−0.214761
$541$	−17.0257	−0.731993	−0.365996	−	0.930616i	$-0.619272\pi$
$541$	−17.0257	−0.731993	−0.365996	+	0.930616i	$0.619272\pi$
$542$	−33.1069	−1.42206
$543$	−8.31197	−0.356701
$544$	25.5704	1.09632
$545$	−13.4746	−0.577188
$546$	7.35262	0.314663
$547$	−34.7441	−1.48555	−0.742775	−	0.669541i	$-0.766491\pi$
$547$	−34.7441	−1.48555	−0.742775	+	0.669541i	$0.766491\pi$
$548$	7.90926	0.337867
$549$	59.9902	2.56032
$550$	3.24126	0.138208
$551$	0	0
$552$	78.5797	3.34457
$553$	6.65600	0.283042
$554$	−3.63322	−0.154361
$555$	21.9060	0.929859
$556$	−14.9171	−0.632625
$557$	18.0200	0.763531	0.381766	−	0.924259i	$-0.375316\pi$
$557$	18.0200	0.763531	0.381766	+	0.924259i	$0.375316\pi$
$558$	−15.1266	−0.640360
$559$	15.6660	0.662602
$560$	1.35659	0.0573265
$561$	46.5653	1.96599
$562$	13.1062	0.552852
$563$	29.4618	1.24167	0.620833	−	0.783943i	$-0.286794\pi$
$563$	29.4618	1.24167	0.620833	+	0.783943i	$0.286794\pi$
$564$	−16.1692	−0.680844
$565$	−10.7524	−0.452358
$566$	−3.92630	−0.165035
$567$	0.274485	0.0115273
$568$	−0.406685	−0.0170641
$569$	−36.0323	−1.51055	−0.755277	−	0.655406i	$-0.772498\pi$
$569$	−36.0323	−1.51055	−0.755277	+	0.655406i	$0.772498\pi$
$570$	0	0
$571$	44.2424	1.85149	0.925744	−	0.378151i	$-0.123440\pi$
$571$	44.2424	1.85149	0.925744	+	0.378151i	$0.123440\pi$
$572$	6.51823	0.272541
$573$	−34.4369	−1.43862
$574$	5.60650	0.234011
$575$	9.33549	0.389317
$576$	34.4188	1.43412
$577$	42.1289	1.75385	0.876924	−	0.480629i	$-0.159592\pi$
$577$	42.1289	1.75385	0.876924	+	0.480629i	$0.159592\pi$
$578$	−10.0226	−0.416885
$579$	40.3622	1.67740
$580$	−8.38740	−0.348268
$581$	−2.25370	−0.0934991
$582$	13.2093	0.547542
$583$	39.4491	1.63381
$584$	19.9305	0.824731
$585$	9.99579	0.413275
$586$	−0.0665133	−0.00274764
$587$	−19.3645	−0.799260	−0.399630	−	0.916676i	$-0.630861\pi$
$587$	−19.3645	−0.799260	−0.399630	+	0.916676i	$0.630861\pi$
$588$	14.8616	0.612883
$589$	0	0
$590$	−2.03424	−0.0837483
$591$	36.6849	1.50902
$592$	−8.46390	−0.347864
$593$	−34.8028	−1.42918	−0.714589	−	0.699545i	$-0.753386\pi$
$593$	−34.8028	−1.42918	−0.714589	+	0.699545i	$0.753386\pi$
$594$	16.5101	0.677416
$595$	6.51419	0.267056
$596$	−0.0269613	−0.00110438
$597$	−21.2703	−0.870534
$598$	−19.5496	−0.799441
$599$	14.3868	0.587827	0.293914	−	0.955832i	$-0.405042\pi$
$599$	14.3868	0.587827	0.293914	+	0.955832i	$0.405042\pi$
$600$	8.41731	0.343635
$601$	−29.0097	−1.18333	−0.591664	−	0.806185i	$-0.701529\pi$
$601$	−29.0097	−1.18333	−0.591664	+	0.806185i	$0.701529\pi$
$602$	9.58216	0.390540
$603$	−55.7025	−2.26838
$604$	1.26585	0.0515066
$605$	−0.702655	−0.0285670
$606$	−22.7308	−0.923377
$607$	−21.9571	−0.891212	−0.445606	−	0.895229i	$-0.647012\pi$
$607$	−21.9571	−0.891212	−0.445606	+	0.895229i	$0.647012\pi$
$608$	0	0
$609$	−30.0573	−1.21799
$610$	−12.5679	−0.508860
$611$	12.2342	0.494943
$612$	24.5102	0.990766
$613$	39.2480	1.58521	0.792606	−	0.609734i	$-0.208724\pi$
$613$	39.2480	1.58521	0.792606	+	0.609734i	$0.208724\pi$
$614$	−30.6705	−1.23776
$615$	12.3646	0.498589
$616$	12.1254	0.488547
$617$	−5.81759	−0.234207	−0.117104	−	0.993120i	$-0.537361\pi$
$617$	−5.81759	−0.234207	−0.117104	+	0.993120i	$0.537361\pi$
$618$	−0.444839	−0.0178941
$619$	44.4614	1.78706	0.893528	−	0.449008i	$-0.148222\pi$
$619$	44.4614	1.78706	0.893528	+	0.449008i	$0.148222\pi$
$620$	−3.04327	−0.122221
$621$	47.5523	1.90821
$622$	20.1552	0.808148
$623$	−19.8293	−0.794443
$624$	−6.26523	−0.250810
$625$	1.00000	0.0400000
$626$	6.19142	0.247459
$627$	0	0
$628$	11.6294	0.464064
$629$	−40.6426	−1.62053
$630$	6.11395	0.243585
$631$	0.433910	0.0172737	0.00863684	−	0.999963i	$-0.497251\pi$
$631$	0.433910	0.0172737	0.00863684	+	0.999963i	$0.497251\pi$
$632$	−15.9567	−0.634725
$633$	30.2435	1.20207
$634$	−5.17435	−0.205500
$635$	8.45812	0.335650
$636$	33.6848	1.33569
$637$	−11.2449	−0.445538
$638$	27.7474	1.09853
$639$	−0.651469	−0.0257717
$640$	2.64546	0.104571
$641$	1.01215	0.0399775	0.0199888	−	0.999800i	$-0.493637\pi$
$641$	1.01215	0.0399775	0.0199888	+	0.999800i	$0.493637\pi$
$642$	10.4778	0.413526
$643$	15.2759	0.602424	0.301212	−	0.953557i	$-0.402609\pi$
$643$	15.2759	0.602424	0.301212	+	0.953557i	$0.402609\pi$
$644$	11.4831	0.452496
$645$	21.1325	0.832092
$646$	0	0
$647$	−35.7223	−1.40439	−0.702194	−	0.711986i	$-0.747796\pi$
$647$	−35.7223	−1.40439	−0.702194	+	0.711986i	$0.747796\pi$
$648$	−0.658035	−0.0258501
$649$	−6.46269	−0.253683
$650$	−2.09411	−0.0821378
$651$	−10.9059	−0.427438
$652$	−5.70711	−0.223508
$653$	17.8345	0.697918	0.348959	−	0.937138i	$-0.386535\pi$
$653$	17.8345	0.697918	0.348959	+	0.937138i	$0.386535\pi$
$654$	38.0634	1.48840
$655$	3.43098	0.134059
$656$	−4.77735	−0.186524
$657$	31.9267	1.24558
$658$	7.48308	0.291721
$659$	−31.4420	−1.22481	−0.612403	−	0.790546i	$-0.709797\pi$
$659$	−31.4420	−1.22481	−0.612403	+	0.790546i	$0.709797\pi$
$660$	8.79270	0.342256
$661$	28.0124	1.08956	0.544778	−	0.838581i	$-0.316614\pi$
$661$	28.0124	1.08956	0.544778	+	0.838581i	$0.316614\pi$
$662$	−1.82748	−0.0710268
$663$	−30.0849	−1.16840
$664$	5.40290	0.209673
$665$	0	0
$666$	−38.1455	−1.47811
$667$	79.9181	3.09444
$668$	−2.83152	−0.109555
$669$	19.6980	0.761569
$670$	11.6696	0.450838
$671$	−39.9277	−1.54139
$672$	17.3030	0.667477
$673$	18.2319	0.702789	0.351394	−	0.936228i	$-0.385708\pi$
$673$	18.2319	0.702789	0.351394	+	0.936228i	$0.385708\pi$
$674$	12.0853	0.465508
$675$	5.09371	0.196057
$676$	8.52556	0.327906
$677$	8.52508	0.327646	0.163823	−	0.986490i	$-0.447617\pi$
$677$	8.52508	0.327646	0.163823	+	0.986490i	$0.447617\pi$
$678$	30.3738	1.16650
$679$	5.87067	0.225296
$680$	−15.6168	−0.598876
$681$	−1.60579	−0.0615342
$682$	10.0678	0.385517
$683$	1.72716	0.0660879	0.0330439	−	0.999454i	$-0.489480\pi$
$683$	1.72716	0.0660879	0.0330439	+	0.999454i	$0.489480\pi$
$684$	0	0
$685$	−8.07266	−0.308441
$686$	−15.7546	−0.601515
$687$	−50.1808	−1.91452
$688$	−8.16504	−0.311289
$689$	−25.4872	−0.970987
$690$	−26.3712	−1.00393
$691$	−46.8789	−1.78336	−0.891678	−	0.452670i	$-0.850472\pi$
$691$	−46.8789	−1.78336	−0.891678	+	0.452670i	$0.850472\pi$
$692$	13.1192	0.498718
$693$	19.4237	0.737847
$694$	10.7448	0.407867
$695$	15.2253	0.577527
$696$	72.0579	2.73135
$697$	−22.9403	−0.868924
$698$	8.53297	0.322978
$699$	−26.2579	−0.993165
$700$	1.23004	0.0464913
$701$	5.28063	0.199447	0.0997233	−	0.995015i	$-0.468204\pi$
$701$	5.28063	0.199447	0.0997233	+	0.995015i	$0.468204\pi$
$702$	−10.6668	−0.402592
$703$	0	0
$704$	−22.9081	−0.863383
$705$	16.5032	0.621547
$706$	−9.61132	−0.361727
$707$	−10.1024	−0.379940
$708$	−5.51837	−0.207393
$709$	24.6647	0.926302	0.463151	−	0.886280i	$-0.346719\pi$
$709$	24.6647	0.926302	0.463151	+	0.886280i	$0.346719\pi$
$710$	0.136482	0.00512209
$711$	−25.5611	−0.958618
$712$	47.5377	1.78155
$713$	28.9973	1.08596
$714$	−18.4015	−0.688658
$715$	−6.65290	−0.248804
$716$	15.7921	0.590179
$717$	15.6157	0.583180
$718$	6.66546	0.248753
$719$	−45.9415	−1.71333	−0.856664	−	0.515874i	$-0.827467\pi$
$719$	−45.9415	−1.71333	−0.856664	+	0.515874i	$0.827467\pi$
$720$	−5.20974	−0.194156
$721$	−0.197702	−0.00736282
$722$	0	0
$723$	33.6165	1.25021
$724$	2.91194	0.108221
$725$	8.56068	0.317936
$726$	1.98488	0.0736658
$727$	26.2219	0.972516	0.486258	−	0.873815i	$-0.338361\pi$
$727$	26.2219	0.972516	0.486258	+	0.873815i	$0.338361\pi$
$728$	−7.83398	−0.290347
$729$	−43.7904	−1.62187
$730$	−6.68864	−0.247558
$731$	−39.2075	−1.45014
$732$	−34.0935	−1.26013
$733$	−28.0359	−1.03553	−0.517765	−	0.855523i	$-0.673236\pi$
$733$	−28.0359	−1.03553	−0.517765	+	0.855523i	$0.673236\pi$
$734$	−19.7052	−0.727332
$735$	−15.1687	−0.559504
$736$	−46.0061	−1.69581
$737$	37.0739	1.36564
$738$	−21.5308	−0.792558
$739$	44.7366	1.64566	0.822831	−	0.568286i	$-0.192393\pi$
$739$	44.7366	1.64566	0.822831	+	0.568286i	$0.192393\pi$
$740$	−7.67435	−0.282115
$741$	0	0
$742$	−15.5893	−0.572302
$743$	3.49164	0.128096	0.0640479	−	0.997947i	$-0.479599\pi$
$743$	3.49164	0.128096	0.0640479	+	0.997947i	$0.479599\pi$
$744$	26.1454	0.958535
$745$	0.0275183	0.00100819
$746$	25.7935	0.944366
$747$	8.65491	0.316667
$748$	−16.3133	−0.596472
$749$	4.65671	0.170153
$750$	−2.82483	−0.103148
$751$	4.98458	0.181890	0.0909449	−	0.995856i	$-0.471011\pi$
$751$	4.98458	0.181890	0.0909449	+	0.995856i	$0.471011\pi$
$752$	−6.37640	−0.232523
$753$	13.8394	0.504337
$754$	−17.9270	−0.652864
$755$	−1.29200	−0.0470207
$756$	6.26548	0.227873
$757$	−11.2592	−0.409223	−0.204612	−	0.978843i	$-0.565593\pi$
$757$	−11.2592	−0.409223	−0.204612	+	0.978843i	$0.565593\pi$
$758$	5.77232	0.209660
$759$	−83.7800	−3.04102
$760$	0	0
$761$	−11.1898	−0.405630	−0.202815	−	0.979217i	$-0.565009\pi$
$761$	−11.1898	−0.405630	−0.202815	+	0.979217i	$0.565009\pi$
$762$	−23.8928	−0.865543
$763$	16.9167	0.612427
$764$	12.0643	0.436471
$765$	−25.0166	−0.904476
$766$	33.8899	1.22449
$767$	4.17541	0.150765
$768$	−47.4029	−1.71050
$769$	31.9842	1.15338	0.576690	−	0.816963i	$-0.304344\pi$
$769$	31.9842	1.15338	0.576690	+	0.816963i	$0.304344\pi$
$770$	−4.06926	−0.146646
$771$	51.8573	1.86760
$772$	−14.1401	−0.508914
$773$	−46.0341	−1.65573	−0.827865	−	0.560928i	$-0.810445\pi$
$773$	−46.0341	−1.65573	−0.827865	+	0.560928i	$0.810445\pi$
$774$	−36.7985	−1.32270
$775$	3.10614	0.111576
$776$	−14.0740	−0.505229
$777$	−27.5021	−0.986631
$778$	14.3994	0.516243
$779$	0	0
$780$	−5.68078	−0.203405
$781$	0.433598	0.0155154
$782$	48.9269	1.74962
$783$	43.6056	1.55834
$784$	5.86076	0.209313
$785$	−11.8697	−0.423647
$786$	−9.69193	−0.345700
$787$	9.33505	0.332759	0.166379	−	0.986062i	$-0.446792\pi$
$787$	9.33505	0.332759	0.166379	+	0.986062i	$0.446792\pi$
$788$	−12.8519	−0.457828
$789$	−38.6801	−1.37705
$790$	5.35505	0.190524
$791$	13.4992	0.479976
$792$	−46.5655	−1.65463
$793$	25.7964	0.916058
$794$	−24.2988	−0.862330
$795$	−34.3808	−1.21936
$796$	7.45163	0.264116
$797$	17.7062	0.627184	0.313592	−	0.949558i	$-0.398467\pi$
$797$	17.7062	0.627184	0.313592	+	0.949558i	$0.398467\pi$
$798$	0	0
$799$	−30.6187	−1.08321
$800$	−4.92809	−0.174234
$801$	76.1507	2.69065
$802$	36.8472	1.30112
$803$	−21.2495	−0.749878
$804$	31.6567	1.11645
$805$	−11.7203	−0.413086
$806$	−6.50461	−0.229115
$807$	−33.3777	−1.17495
$808$	24.2190	0.852020
$809$	−41.1692	−1.44743	−0.723717	−	0.690097i	$-0.757568\pi$
$809$	−41.1692	−1.44743	−0.723717	+	0.690097i	$0.757568\pi$
$810$	0.220835	0.00775935
$811$	11.7160	0.411405	0.205703	−	0.978615i	$-0.434052\pi$
$811$	11.7160	0.411405	0.205703	+	0.978615i	$0.434052\pi$
$812$	10.5300	0.369531
$813$	91.6659	3.21486
$814$	25.3885	0.889866
$815$	5.82502	0.204041
$816$	15.6801	0.548912
$817$	0	0
$818$	11.3362	0.396361
$819$	−12.5493	−0.438507
$820$	−4.33170	−0.151269
$821$	47.3142	1.65128	0.825639	−	0.564199i	$-0.190815\pi$
$821$	47.3142	1.65128	0.825639	+	0.564199i	$0.190815\pi$
$822$	22.8039	0.795377
$823$	−6.94608	−0.242125	−0.121063	−	0.992645i	$-0.538630\pi$
$823$	−6.94608	−0.242125	−0.121063	+	0.992645i	$0.538630\pi$
$824$	0.473962	0.0165112
$825$	−8.97436	−0.312447
$826$	2.55390	0.0888615
$827$	−13.1897	−0.458652	−0.229326	−	0.973350i	$-0.573652\pi$
$827$	−13.1897	−0.458652	−0.229326	+	0.973350i	$0.573652\pi$
$828$	−44.0986	−1.53253
$829$	5.57119	0.193495	0.0967477	−	0.995309i	$-0.469156\pi$
$829$	5.57119	0.193495	0.0967477	+	0.995309i	$0.469156\pi$
$830$	−1.81320	−0.0629371
$831$	10.0596	0.348964
$832$	14.8005	0.513114
$833$	28.1427	0.975085
$834$	−43.0088	−1.48927
$835$	2.89002	0.100013
$836$	0	0
$837$	15.8218	0.546881
$838$	26.9058	0.929446
$839$	44.4242	1.53369	0.766847	−	0.641830i	$-0.221825\pi$
$839$	44.4242	1.53369	0.766847	+	0.641830i	$0.221825\pi$
$840$	−10.5676	−0.364616
$841$	44.2853	1.52708
$842$	16.3056	0.561928
$843$	−36.2883	−1.24984
$844$	−10.5952	−0.364703
$845$	−8.70170	−0.299348
$846$	−28.7374	−0.988013
$847$	0.882152	0.0303111
$848$	13.2838	0.456168
$849$	10.8711	0.373095
$850$	5.24096	0.179763
$851$	73.1240	2.50666
$852$	0.370241	0.0126843
$853$	−39.3519	−1.34738	−0.673692	−	0.739012i	$-0.735293\pi$
$853$	−39.3519	−1.34738	−0.673692	+	0.739012i	$0.735293\pi$
$854$	15.7785	0.539927
$855$	0	0
$856$	−11.1638	−0.381570
$857$	32.8848	1.12332	0.561662	−	0.827367i	$-0.310162\pi$
$857$	32.8848	1.12332	0.561662	+	0.827367i	$0.310162\pi$
$858$	18.7933	0.641593
$859$	−11.4370	−0.390227	−0.195114	−	0.980781i	$-0.562508\pi$
$859$	−11.4370	−0.390227	−0.195114	+	0.980781i	$0.562508\pi$
$860$	−7.40337	−0.252453
$861$	−15.5232	−0.529029
$862$	36.0069	1.22640
$863$	26.5278	0.903017	0.451508	−	0.892267i	$-0.350886\pi$
$863$	26.5278	0.903017	0.451508	+	0.892267i	$0.350886\pi$
$864$	−25.1023	−0.853997
$865$	−13.3903	−0.455283
$866$	−22.8638	−0.776943
$867$	27.7504	0.942453
$868$	3.82069	0.129683
$869$	17.0127	0.577118
$870$	−24.1825	−0.819863
$871$	−23.9527	−0.811606
$872$	−40.5553	−1.37338
$873$	−22.5452	−0.763041
$874$	0	0
$875$	−1.25546	−0.0424422
$876$	−18.1445	−0.613047
$877$	−32.3178	−1.09129	−0.545647	−	0.838015i	$-0.683716\pi$
$877$	−32.3178	−1.09129	−0.545647	+	0.838015i	$0.683716\pi$
$878$	−6.66120	−0.224805
$879$	0.184161	0.00621160
$880$	3.46745	0.116888
$881$	43.3258	1.45968	0.729841	−	0.683617i	$-0.239594\pi$
$881$	43.3258	1.45968	0.729841	+	0.683617i	$0.239594\pi$
$882$	26.4135	0.889390
$883$	19.5774	0.658833	0.329417	−	0.944185i	$-0.393148\pi$
$883$	19.5774	0.658833	0.329417	+	0.944185i	$0.393148\pi$
$884$	10.5397	0.354487
$885$	5.63237	0.189330
$886$	−34.7517	−1.16751
$887$	−4.28937	−0.144023	−0.0720115	−	0.997404i	$-0.522942\pi$
$887$	−4.28937	−0.144023	−0.0720115	+	0.997404i	$0.522942\pi$
$888$	65.9320	2.21253
$889$	−10.6188	−0.356143
$890$	−15.9535	−0.534764
$891$	0.701583	0.0235039
$892$	−6.90081	−0.231056
$893$	0	0
$894$	−0.0777345	−0.00259983
$895$	−16.1184	−0.538778
$896$	−3.32126	−0.110955
$897$	54.1285	1.80730
$898$	−3.10840	−0.103729
$899$	26.5907	0.886849
$900$	−4.72376	−0.157459
$901$	63.7872	2.12506
$902$	14.3302	0.477145
$903$	−26.5309	−0.882894
$904$	−32.3623	−1.07635
$905$	−2.97210	−0.0987959
$906$	3.64968	0.121252
$907$	−18.6499	−0.619259	−0.309629	−	0.950857i	$-0.600205\pi$
$907$	−18.6499	−0.619259	−0.309629	+	0.950857i	$0.600205\pi$
$908$	0.562559	0.0186692
$909$	38.7964	1.28680
$910$	2.62907	0.0871527
$911$	−13.8965	−0.460410	−0.230205	−	0.973142i	$-0.573940\pi$
$911$	−13.8965	−0.460410	−0.230205	+	0.973142i	$0.573940\pi$
$912$	0	0
$913$	−5.76045	−0.190643
$914$	17.4537	0.577316
$915$	34.7978	1.15038
$916$	17.5799	0.580855
$917$	−4.30744	−0.142244
$918$	26.6959	0.881097
$919$	22.1126	0.729429	0.364714	−	0.931119i	$-0.381167\pi$
$919$	22.1126	0.729429	0.364714	+	0.931119i	$0.381167\pi$
$920$	28.0976	0.926351
$921$	84.9200	2.79821
$922$	11.1379	0.366807
$923$	−0.280139	−0.00922089
$924$	−11.0389	−0.363152
$925$	7.83291	0.257544
$926$	−12.3872	−0.407067
$927$	0.759240	0.0249367
$928$	−42.1878	−1.38488
$929$	−21.7242	−0.712746	−0.356373	−	0.934344i	$-0.615987\pi$
$929$	−21.7242	−0.712746	−0.356373	+	0.934344i	$0.615987\pi$
$930$	−8.77432	−0.287721
$931$	0	0
$932$	9.19895	0.301322
$933$	−55.8053	−1.82698
$934$	14.1673	0.463569
$935$	16.6503	0.544523
$936$	30.0850	0.983358
$937$	−12.9077	−0.421676	−0.210838	−	0.977521i	$-0.567619\pi$
$937$	−12.9077	−0.421676	−0.210838	+	0.977521i	$0.567619\pi$
$938$	−14.6507	−0.478363
$939$	−17.1427	−0.559431
$940$	−5.78158	−0.188574
$941$	−6.80952	−0.221984	−0.110992	−	0.993821i	$-0.535403\pi$
$941$	−6.80952	−0.221984	−0.110992	+	0.993821i	$0.535403\pi$
$942$	33.5298	1.09246
$943$	41.2740	1.34406
$944$	−2.17620	−0.0708292
$945$	−6.39493	−0.208027
$946$	24.4920	0.796304
$947$	6.48072	0.210595	0.105298	−	0.994441i	$-0.466421\pi$
$947$	6.48072	0.210595	0.105298	+	0.994441i	$0.466421\pi$
$948$	14.5269	0.471810
$949$	13.7289	0.445658
$950$	0	0
$951$	14.3267	0.464574
$952$	19.6062	0.635440
$953$	15.6100	0.505658	0.252829	−	0.967511i	$-0.418639\pi$
$953$	15.6100	0.505658	0.252829	+	0.967511i	$0.418639\pi$
$954$	59.8680	1.93830
$955$	−12.3135	−0.398457
$956$	−5.47067	−0.176934
$957$	−76.8266	−2.48345
$958$	20.6705	0.667834
$959$	10.1349	0.327272
$960$	19.9649	0.644366
$961$	−21.3519	−0.688771
$962$	−16.4030	−0.528853
$963$	−17.8833	−0.576280
$964$	−11.7769	−0.379308
$965$	14.4322	0.464590
$966$	33.1078	1.06523
$967$	6.77672	0.217925	0.108962	−	0.994046i	$-0.465247\pi$
$967$	6.77672	0.217925	0.108962	+	0.994046i	$0.465247\pi$
$968$	−2.11483	−0.0679731
$969$	0	0
$970$	4.72321	0.151653
$971$	35.7484	1.14722	0.573611	−	0.819128i	$-0.305542\pi$
$971$	35.7484	1.14722	0.573611	+	0.819128i	$0.305542\pi$
$972$	15.5709	0.499436
$973$	−19.1146	−0.612787
$974$	19.5732	0.627165
$975$	5.79815	0.185689
$976$	−13.4449	−0.430362
$977$	−15.7243	−0.503066	−0.251533	−	0.967849i	$-0.580935\pi$
$977$	−15.7243	−0.503066	−0.251533	+	0.967849i	$0.580935\pi$
$978$	−16.4547	−0.526163
$979$	−50.6836	−1.61986
$980$	5.31404	0.169751
$981$	−64.9657	−2.07419
$982$	35.3997	1.12965
$983$	5.11102	0.163016	0.0815081	−	0.996673i	$-0.474026\pi$
$983$	5.11102	0.163016	0.0815081	+	0.996673i	$0.474026\pi$
$984$	37.2145	1.18636
$985$	13.1174	0.417954
$986$	44.8662	1.42883
$987$	−20.7191	−0.659495
$988$	0	0
$989$	70.5419	2.24310
$990$	15.6273	0.496667
$991$	−22.5697	−0.716949	−0.358475	−	0.933539i	$-0.616703\pi$
$991$	−22.5697	−0.716949	−0.358475	+	0.933539i	$0.616703\pi$
$992$	−15.3073	−0.486009
$993$	5.05989	0.160571
$994$	−0.171348	−0.00543482
$995$	−7.60558	−0.241113
$996$	−4.91874	−0.155856
$997$	−7.69445	−0.243686	−0.121843	−	0.992549i	$-0.538880\pi$
$997$	−7.69445	−0.243686	−0.121843	+	0.992549i	$0.538880\pi$
$998$	16.7891	0.531451
$999$	39.8986	1.26233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.w.1.6	✓	16
5.4	even	2		9025.2.a.cm.1.11		16
19.18	odd	2	inner	1805.2.a.w.1.11	yes	16
95.94	odd	2		9025.2.a.cm.1.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.w.1.6	✓	16	1.1	even	1	trivial
1805.2.a.w.1.11	yes	16	19.18	odd	2	inner
9025.2.a.cm.1.6		16	95.94	odd	2
9025.2.a.cm.1.11		16	5.4	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.01007 q^{2} +2.79667 q^{3} -0.979758 q^{4} +1.00000 q^{5} -2.82483 q^{6} -1.25546 q^{7} +3.00976 q^{8} +4.82135 q^{9} +O(q^{10})\)	\(q-1.01007 q^{2} +2.79667 q^{3} -0.979758 q^{4} +1.00000 q^{5} -2.82483 q^{6} -1.25546 q^{7} +3.00976 q^{8} +4.82135 q^{9} -1.01007 q^{10} -3.20895 q^{11} -2.74006 q^{12} +2.07323 q^{13} +1.26810 q^{14} +2.79667 q^{15} -1.08056 q^{16} -5.18871 q^{17} -4.86990 q^{18} -0.979758 q^{20} -3.51109 q^{21} +3.24126 q^{22} +9.33549 q^{23} +8.41731 q^{24} +1.00000 q^{25} -2.09411 q^{26} +5.09371 q^{27} +1.23004 q^{28} +8.56068 q^{29} -2.82483 q^{30} +3.10614 q^{31} -4.92809 q^{32} -8.97436 q^{33} +5.24096 q^{34} -1.25546 q^{35} -4.72376 q^{36} +7.83291 q^{37} +5.79815 q^{39} +3.00976 q^{40} +4.42119 q^{41} +3.54645 q^{42} +7.55632 q^{43} +3.14399 q^{44} +4.82135 q^{45} -9.42950 q^{46} +5.90103 q^{47} -3.02196 q^{48} -5.42383 q^{49} -1.01007 q^{50} -14.5111 q^{51} -2.03127 q^{52} -12.2935 q^{53} -5.14501 q^{54} -3.20895 q^{55} -3.77863 q^{56} -8.64689 q^{58} +2.01396 q^{59} -2.74006 q^{60} +12.4426 q^{61} -3.13742 q^{62} -6.05299 q^{63} +7.13883 q^{64} +2.07323 q^{65} +9.06473 q^{66} -11.5533 q^{67} +5.08368 q^{68} +26.1083 q^{69} +1.26810 q^{70} -0.135122 q^{71} +14.5111 q^{72} +6.62195 q^{73} -7.91178 q^{74} +2.79667 q^{75} +4.02869 q^{77} -5.85654 q^{78} -5.30166 q^{79} -1.08056 q^{80} -0.218633 q^{81} -4.46571 q^{82} +1.79512 q^{83} +3.44002 q^{84} -5.18871 q^{85} -7.63241 q^{86} +23.9414 q^{87} -9.65818 q^{88} +15.7945 q^{89} -4.86990 q^{90} -2.60285 q^{91} -9.14652 q^{92} +8.68684 q^{93} -5.96045 q^{94} -13.7822 q^{96} -4.67613 q^{97} +5.47845 q^{98} -15.4715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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