LMFDB - Embedded newform 453.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [453,2,Mod(1,453)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(453, 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("453.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 453 = 3 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	453.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:	$3.61722321156$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	453.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.73205 q^{6} +1.00000 q^{7} -1.73205 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.73205 q^{6} +1.00000 q^{7} -1.73205 q^{8} +1.00000 q^{9} +3.46410 q^{10} +3.73205 q^{11} -1.00000 q^{12} +3.46410 q^{13} +1.73205 q^{14} -2.00000 q^{15} -5.00000 q^{16} +1.73205 q^{18} +2.00000 q^{20} -1.00000 q^{21} +6.46410 q^{22} +2.53590 q^{23} +1.73205 q^{24} -1.00000 q^{25} +6.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -3.46410 q^{29} -3.46410 q^{30} +9.46410 q^{31} -5.19615 q^{32} -3.73205 q^{33} +2.00000 q^{35} +1.00000 q^{36} -5.92820 q^{37} -3.46410 q^{39} -3.46410 q^{40} -11.1962 q^{41} -1.73205 q^{42} -3.46410 q^{43} +3.73205 q^{44} +2.00000 q^{45} +4.39230 q^{46} +0.267949 q^{47} +5.00000 q^{48} -6.00000 q^{49} -1.73205 q^{50} +3.46410 q^{52} +4.26795 q^{53} -1.73205 q^{54} +7.46410 q^{55} -1.73205 q^{56} -6.00000 q^{58} -6.66025 q^{59} -2.00000 q^{60} -7.46410 q^{61} +16.3923 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.92820 q^{65} -6.46410 q^{66} +5.00000 q^{67} -2.53590 q^{69} +3.46410 q^{70} +12.9282 q^{71} -1.73205 q^{72} -14.9282 q^{73} -10.2679 q^{74} +1.00000 q^{75} +3.73205 q^{77} -6.00000 q^{78} -11.9282 q^{79} -10.0000 q^{80} +1.00000 q^{81} -19.3923 q^{82} -5.46410 q^{83} -1.00000 q^{84} -6.00000 q^{86} +3.46410 q^{87} -6.46410 q^{88} +6.92820 q^{89} +3.46410 q^{90} +3.46410 q^{91} +2.53590 q^{92} -9.46410 q^{93} +0.464102 q^{94} +5.19615 q^{96} +5.92820 q^{97} -10.3923 q^{98} +3.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 4 q^{15} - 10 q^{16} + 4 q^{20} - 2 q^{21} + 6 q^{22} + 12 q^{23} - 2 q^{25} + 12 q^{26} - 2 q^{27} + 2 q^{28} + 12 q^{31} - 4 q^{33} + 4 q^{35} + 2 q^{36} + 2 q^{37} - 12 q^{41} + 4 q^{44} + 4 q^{45} - 12 q^{46} + 4 q^{47} + 10 q^{48} - 12 q^{49} + 12 q^{53} + 8 q^{55} - 12 q^{58} + 4 q^{59} - 4 q^{60} - 8 q^{61} + 12 q^{62} + 2 q^{63} + 2 q^{64} - 6 q^{66} + 10 q^{67} - 12 q^{69} + 12 q^{71} - 16 q^{73} - 24 q^{74} + 2 q^{75} + 4 q^{77} - 12 q^{78} - 10 q^{79} - 20 q^{80} + 2 q^{81} - 18 q^{82} - 4 q^{83} - 2 q^{84} - 12 q^{86} - 6 q^{88} + 12 q^{92} - 12 q^{93} - 6 q^{94} - 2 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^7 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 4 * q^15 - 10 * q^16 + 4 * q^20 - 2 * q^21 + 6 * q^22 + 12 * q^23 - 2 * q^25 + 12 * q^26 - 2 * q^27 + 2 * q^28 + 12 * q^31 - 4 * q^33 + 4 * q^35 + 2 * q^36 + 2 * q^37 - 12 * q^41 + 4 * q^44 + 4 * q^45 - 12 * q^46 + 4 * q^47 + 10 * q^48 - 12 * q^49 + 12 * q^53 + 8 * q^55 - 12 * q^58 + 4 * q^59 - 4 * q^60 - 8 * q^61 + 12 * q^62 + 2 * q^63 + 2 * q^64 - 6 * q^66 + 10 * q^67 - 12 * q^69 + 12 * q^71 - 16 * q^73 - 24 * q^74 + 2 * q^75 + 4 * q^77 - 12 * q^78 - 10 * q^79 - 20 * q^80 + 2 * q^81 - 18 * q^82 - 4 * q^83 - 2 * q^84 - 12 * q^86 - 6 * q^88 + 12 * q^92 - 12 * q^93 - 6 * q^94 - 2 * q^97 + 4 * 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 $

$2$	1.73205	1.22474	0.612372	−	0.790569i	$-0.290215\pi$
$2$	1.73205	1.22474	0.612372	+	0.790569i	$0.290215\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−1.73205	−0.707107
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−1.73205	−0.612372
$9$	1.00000	0.333333
$10$	3.46410	1.09545
$11$	3.73205	1.12526	0.562628	−	0.826710i	$-0.309790\pi$
$11$	3.73205	1.12526	0.562628	+	0.826710i	$0.309790\pi$
$12$	−1.00000	−0.288675
$13$	3.46410	0.960769	0.480384	−	0.877058i	$-0.340497\pi$
$13$	3.46410	0.960769	0.480384	+	0.877058i	$0.340497\pi$
$14$	1.73205	0.462910
$15$	−2.00000	−0.516398
$16$	−5.00000	−1.25000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	1.73205	0.408248
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	2.00000	0.447214
$21$	−1.00000	−0.218218
$22$	6.46410	1.37815
$23$	2.53590	0.528771	0.264386	−	0.964417i	$-0.414831\pi$
$23$	2.53590	0.528771	0.264386	+	0.964417i	$0.414831\pi$
$24$	1.73205	0.353553
$25$	−1.00000	−0.200000
$26$	6.00000	1.17670
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−3.46410	−0.643268	−0.321634	−	0.946864i	$-0.604232\pi$
$29$	−3.46410	−0.643268	−0.321634	+	0.946864i	$0.604232\pi$
$30$	−3.46410	−0.632456
$31$	9.46410	1.69980	0.849901	−	0.526942i	$-0.176661\pi$
$31$	9.46410	1.69980	0.849901	+	0.526942i	$0.176661\pi$
$32$	−5.19615	−0.918559
$33$	−3.73205	−0.649667
$34$	0	0
$35$	2.00000	0.338062
$36$	1.00000	0.166667
$37$	−5.92820	−0.974591	−0.487295	−	0.873237i	$-0.662016\pi$
$37$	−5.92820	−0.974591	−0.487295	+	0.873237i	$0.662016\pi$
$38$	0	0
$39$	−3.46410	−0.554700
$40$	−3.46410	−0.547723
$41$	−11.1962	−1.74855	−0.874273	−	0.485435i	$-0.838661\pi$
$41$	−11.1962	−1.74855	−0.874273	+	0.485435i	$0.838661\pi$
$42$	−1.73205	−0.267261
$43$	−3.46410	−0.528271	−0.264135	−	0.964486i	$-0.585087\pi$
$43$	−3.46410	−0.528271	−0.264135	+	0.964486i	$0.585087\pi$
$44$	3.73205	0.562628
$45$	2.00000	0.298142
$46$	4.39230	0.647610
$47$	0.267949	0.0390844	0.0195422	−	0.999809i	$-0.493779\pi$
$47$	0.267949	0.0390844	0.0195422	+	0.999809i	$0.493779\pi$
$48$	5.00000	0.721688
$49$	−6.00000	−0.857143
$50$	−1.73205	−0.244949
$51$	0	0
$52$	3.46410	0.480384
$53$	4.26795	0.586248	0.293124	−	0.956074i	$-0.405305\pi$
$53$	4.26795	0.586248	0.293124	+	0.956074i	$0.405305\pi$
$54$	−1.73205	−0.235702
$55$	7.46410	1.00646
$56$	−1.73205	−0.231455
$57$	0	0
$58$	−6.00000	−0.787839
$59$	−6.66025	−0.867091	−0.433546	−	0.901132i	$-0.642738\pi$
$59$	−6.66025	−0.867091	−0.433546	+	0.901132i	$0.642738\pi$
$60$	−2.00000	−0.258199
$61$	−7.46410	−0.955680	−0.477840	−	0.878447i	$-0.658580\pi$
$61$	−7.46410	−0.955680	−0.477840	+	0.878447i	$0.658580\pi$
$62$	16.3923	2.08182
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	6.92820	0.859338
$66$	−6.46410	−0.795676
$67$	5.00000	0.610847	0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000	0.610847	0.305424	+	0.952217i	$0.401202\pi$
$68$	0	0
$69$	−2.53590	−0.305286
$70$	3.46410	0.414039
$71$	12.9282	1.53430	0.767148	−	0.641470i	$-0.221675\pi$
$71$	12.9282	1.53430	0.767148	+	0.641470i	$0.221675\pi$
$72$	−1.73205	−0.204124
$73$	−14.9282	−1.74721	−0.873607	−	0.486632i	$-0.838225\pi$
$73$	−14.9282	−1.74721	−0.873607	+	0.486632i	$0.838225\pi$
$74$	−10.2679	−1.19362
$75$	1.00000	0.115470
$76$	0	0
$77$	3.73205	0.425307
$78$	−6.00000	−0.679366
$79$	−11.9282	−1.34203	−0.671014	−	0.741445i	$-0.734141\pi$
$79$	−11.9282	−1.34203	−0.671014	+	0.741445i	$0.734141\pi$
$80$	−10.0000	−1.11803
$81$	1.00000	0.111111
$82$	−19.3923	−2.14152
$83$	−5.46410	−0.599763	−0.299882	−	0.953976i	$-0.596947\pi$
$83$	−5.46410	−0.599763	−0.299882	+	0.953976i	$0.596947\pi$
$84$	−1.00000	−0.109109
$85$	0	0
$86$	−6.00000	−0.646997
$87$	3.46410	0.371391
$88$	−6.46410	−0.689076
$89$	6.92820	0.734388	0.367194	−	0.930144i	$-0.380318\pi$
$89$	6.92820	0.734388	0.367194	+	0.930144i	$0.380318\pi$
$90$	3.46410	0.365148
$91$	3.46410	0.363137
$92$	2.53590	0.264386
$93$	−9.46410	−0.981382
$94$	0.464102	0.0478684
$95$	0	0
$96$	5.19615	0.530330
$97$	5.92820	0.601918	0.300959	−	0.953637i	$-0.402693\pi$
$97$	5.92820	0.601918	0.300959	+	0.953637i	$0.402693\pi$
$98$	−10.3923	−1.04978
$99$	3.73205	0.375085
$100$	−1.00000	−0.100000
$101$	2.66025	0.264705	0.132353	−	0.991203i	$-0.457747\pi$
$101$	2.66025	0.264705	0.132353	+	0.991203i	$0.457747\pi$
$102$	0	0
$103$	−5.46410	−0.538394	−0.269197	−	0.963085i	$-0.586758\pi$
$103$	−5.46410	−0.538394	−0.269197	+	0.963085i	$0.586758\pi$
$104$	−6.00000	−0.588348
$105$	−2.00000	−0.195180
$106$	7.39230	0.718004
$107$	2.00000	0.193347	0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000	0.193347	0.0966736	+	0.995316i	$0.469180\pi$
$108$	−1.00000	−0.0962250
$109$	−8.39230	−0.803837	−0.401919	−	0.915675i	$-0.631656\pi$
$109$	−8.39230	−0.803837	−0.401919	+	0.915675i	$0.631656\pi$
$110$	12.9282	1.23266
$111$	5.92820	0.562680
$112$	−5.00000	−0.472456
$113$	12.0000	1.12887	0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000	1.12887	0.564433	+	0.825479i	$0.309095\pi$
$114$	0	0
$115$	5.07180	0.472947
$116$	−3.46410	−0.321634
$117$	3.46410	0.320256
$118$	−11.5359	−1.06197
$119$	0	0
$120$	3.46410	0.316228
$121$	2.92820	0.266200
$122$	−12.9282	−1.17046
$123$	11.1962	1.00952
$124$	9.46410	0.849901
$125$	−12.0000	−1.07331
$126$	1.73205	0.154303
$127$	−8.39230	−0.744697	−0.372348	−	0.928093i	$-0.621447\pi$
$127$	−8.39230	−0.744697	−0.372348	+	0.928093i	$0.621447\pi$
$128$	12.1244	1.07165
$129$	3.46410	0.304997
$130$	12.0000	1.05247
$131$	4.53590	0.396303	0.198152	−	0.980171i	$-0.436506\pi$
$131$	4.53590	0.396303	0.198152	+	0.980171i	$0.436506\pi$
$132$	−3.73205	−0.324833
$133$	0	0
$134$	8.66025	0.748132
$135$	−2.00000	−0.172133
$136$	0	0
$137$	15.3205	1.30892	0.654460	−	0.756097i	$-0.272896\pi$
$137$	15.3205	1.30892	0.654460	+	0.756097i	$0.272896\pi$
$138$	−4.39230	−0.373898
$139$	−10.5359	−0.893643	−0.446822	−	0.894623i	$-0.647444\pi$
$139$	−10.5359	−0.893643	−0.446822	+	0.894623i	$0.647444\pi$
$140$	2.00000	0.169031
$141$	−0.267949	−0.0225654
$142$	22.3923	1.87912
$143$	12.9282	1.08111
$144$	−5.00000	−0.416667
$145$	−6.92820	−0.575356
$146$	−25.8564	−2.13989
$147$	6.00000	0.494872
$148$	−5.92820	−0.487295
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	1.73205	0.141421
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	0	0
$153$	0	0
$154$	6.46410	0.520892
$155$	18.9282	1.52035
$156$	−3.46410	−0.277350
$157$	16.5359	1.31971	0.659854	−	0.751394i	$-0.270618\pi$
$157$	16.5359	1.31971	0.659854	+	0.751394i	$0.270618\pi$
$158$	−20.6603	−1.64364
$159$	−4.26795	−0.338470
$160$	−10.3923	−0.821584
$161$	2.53590	0.199857
$162$	1.73205	0.136083
$163$	14.9282	1.16927	0.584634	−	0.811297i	$-0.301238\pi$
$163$	14.9282	1.16927	0.584634	+	0.811297i	$0.301238\pi$
$164$	−11.1962	−0.874273
$165$	−7.46410	−0.581080
$166$	−9.46410	−0.734557
$167$	14.1244	1.09298	0.546488	−	0.837467i	$-0.315965\pi$
$167$	14.1244	1.09298	0.546488	+	0.837467i	$0.315965\pi$
$168$	1.73205	0.133631
$169$	−1.00000	−0.0769231
$170$	0	0
$171$	0	0
$172$	−3.46410	−0.264135
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	6.00000	0.454859
$175$	−1.00000	−0.0755929
$176$	−18.6603	−1.40657
$177$	6.66025	0.500615
$178$	12.0000	0.899438
$179$	0.535898	0.0400549	0.0200275	−	0.999799i	$-0.493625\pi$
$179$	0.535898	0.0400549	0.0200275	+	0.999799i	$0.493625\pi$
$180$	2.00000	0.149071
$181$	8.39230	0.623795	0.311898	−	0.950116i	$-0.399035\pi$
$181$	8.39230	0.623795	0.311898	+	0.950116i	$0.399035\pi$
$182$	6.00000	0.444750
$183$	7.46410	0.551762
$184$	−4.39230	−0.323805
$185$	−11.8564	−0.871700
$186$	−16.3923	−1.20194
$187$	0	0
$188$	0.267949	0.0195422
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	17.0526	1.23388	0.616940	−	0.787010i	$-0.288372\pi$
$191$	17.0526	1.23388	0.616940	+	0.787010i	$0.288372\pi$
$192$	−1.00000	−0.0721688
$193$	−16.8564	−1.21335	−0.606675	−	0.794950i	$-0.707497\pi$
$193$	−16.8564	−1.21335	−0.606675	+	0.794950i	$0.707497\pi$
$194$	10.2679	0.737196
$195$	−6.92820	−0.496139
$196$	−6.00000	−0.428571
$197$	5.85641	0.417252	0.208626	−	0.977996i	$-0.433101\pi$
$197$	5.85641	0.417252	0.208626	+	0.977996i	$0.433101\pi$
$198$	6.46410	0.459384
$199$	−10.9282	−0.774680	−0.387340	−	0.921937i	$-0.626606\pi$
$199$	−10.9282	−0.774680	−0.387340	+	0.921937i	$0.626606\pi$
$200$	1.73205	0.122474
$201$	−5.00000	−0.352673
$202$	4.60770	0.324196
$203$	−3.46410	−0.243132
$204$	0	0
$205$	−22.3923	−1.56395
$206$	−9.46410	−0.659395
$207$	2.53590	0.176257
$208$	−17.3205	−1.20096
$209$	0	0
$210$	−3.46410	−0.239046
$211$	9.92820	0.683486	0.341743	−	0.939794i	$-0.388983\pi$
$211$	9.92820	0.683486	0.341743	+	0.939794i	$0.388983\pi$
$212$	4.26795	0.293124
$213$	−12.9282	−0.885826
$214$	3.46410	0.236801
$215$	−6.92820	−0.472500
$216$	1.73205	0.117851
$217$	9.46410	0.642465
$218$	−14.5359	−0.984495
$219$	14.9282	1.00875
$220$	7.46410	0.503230
$221$	0	0
$222$	10.2679	0.689140
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	−5.19615	−0.347183
$225$	−1.00000	−0.0666667
$226$	20.7846	1.38257
$227$	−6.39230	−0.424272	−0.212136	−	0.977240i	$-0.568042\pi$
$227$	−6.39230	−0.424272	−0.212136	+	0.977240i	$0.568042\pi$
$228$	0	0
$229$	−13.9282	−0.920402	−0.460201	−	0.887815i	$-0.652223\pi$
$229$	−13.9282	−0.920402	−0.460201	+	0.887815i	$0.652223\pi$
$230$	8.78461	0.579240
$231$	−3.73205	−0.245551
$232$	6.00000	0.393919
$233$	−10.6603	−0.698376	−0.349188	−	0.937053i	$-0.613543\pi$
$233$	−10.6603	−0.698376	−0.349188	+	0.937053i	$0.613543\pi$
$234$	6.00000	0.392232
$235$	0.535898	0.0349582
$236$	−6.66025	−0.433546
$237$	11.9282	0.774820
$238$	0	0
$239$	27.4641	1.77651	0.888253	−	0.459355i	$-0.151920\pi$
$239$	27.4641	1.77651	0.888253	+	0.459355i	$0.151920\pi$
$240$	10.0000	0.645497
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	5.07180	0.326027
$243$	−1.00000	−0.0641500
$244$	−7.46410	−0.477840
$245$	−12.0000	−0.766652
$246$	19.3923	1.23641
$247$	0	0
$248$	−16.3923	−1.04091
$249$	5.46410	0.346273
$250$	−20.7846	−1.31453
$251$	−12.5359	−0.791259	−0.395629	−	0.918410i	$-0.629474\pi$
$251$	−12.5359	−0.791259	−0.395629	+	0.918410i	$0.629474\pi$
$252$	1.00000	0.0629941
$253$	9.46410	0.595003
$254$	−14.5359	−0.912063
$255$	0	0
$256$	19.0000	1.18750
$257$	−9.85641	−0.614826	−0.307413	−	0.951576i	$-0.599463\pi$
$257$	−9.85641	−0.614826	−0.307413	+	0.951576i	$0.599463\pi$
$258$	6.00000	0.373544
$259$	−5.92820	−0.368361
$260$	6.92820	0.429669
$261$	−3.46410	−0.214423
$262$	7.85641	0.485370
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	6.46410	0.397838
$265$	8.53590	0.524356
$266$	0	0
$267$	−6.92820	−0.423999
$268$	5.00000	0.305424
$269$	1.07180	0.0653486	0.0326743	−	0.999466i	$-0.489598\pi$
$269$	1.07180	0.0653486	0.0326743	+	0.999466i	$0.489598\pi$
$270$	−3.46410	−0.210819
$271$	28.7128	1.74418	0.872090	−	0.489346i	$-0.162765\pi$
$271$	28.7128	1.74418	0.872090	+	0.489346i	$0.162765\pi$
$272$	0	0
$273$	−3.46410	−0.209657
$274$	26.5359	1.60309
$275$	−3.73205	−0.225051
$276$	−2.53590	−0.152643
$277$	18.7846	1.12866	0.564329	−	0.825550i	$-0.309135\pi$
$277$	18.7846	1.12866	0.564329	+	0.825550i	$0.309135\pi$
$278$	−18.2487	−1.09448
$279$	9.46410	0.566601
$280$	−3.46410	−0.207020
$281$	9.58846	0.571999	0.286000	−	0.958230i	$-0.407674\pi$
$281$	9.58846	0.571999	0.286000	+	0.958230i	$0.407674\pi$
$282$	−0.464102	−0.0276368
$283$	−5.00000	−0.297219	−0.148610	−	0.988896i	$-0.547480\pi$
$283$	−5.00000	−0.297219	−0.148610	+	0.988896i	$0.547480\pi$
$284$	12.9282	0.767148
$285$	0	0
$286$	22.3923	1.32408
$287$	−11.1962	−0.660888
$288$	−5.19615	−0.306186
$289$	−17.0000	−1.00000
$290$	−12.0000	−0.704664
$291$	−5.92820	−0.347517
$292$	−14.9282	−0.873607
$293$	−6.66025	−0.389096	−0.194548	−	0.980893i	$-0.562324\pi$
$293$	−6.66025	−0.389096	−0.194548	+	0.980893i	$0.562324\pi$
$294$	10.3923	0.606092
$295$	−13.3205	−0.775550
$296$	10.2679	0.596812
$297$	−3.73205	−0.216556
$298$	6.92820	0.401340
$299$	8.78461	0.508027
$300$	1.00000	0.0577350
$301$	−3.46410	−0.199667
$302$	1.73205	0.0996683
$303$	−2.66025	−0.152828
$304$	0	0
$305$	−14.9282	−0.854786
$306$	0	0
$307$	−1.07180	−0.0611707	−0.0305853	−	0.999532i	$-0.509737\pi$
$307$	−1.07180	−0.0611707	−0.0305853	+	0.999532i	$0.509737\pi$
$308$	3.73205	0.212653
$309$	5.46410	0.310842
$310$	32.7846	1.86204
$311$	−21.3205	−1.20898	−0.604488	−	0.796615i	$-0.706622\pi$
$311$	−21.3205	−1.20898	−0.604488	+	0.796615i	$0.706622\pi$
$312$	6.00000	0.339683
$313$	28.8564	1.63106	0.815530	−	0.578714i	$-0.196445\pi$
$313$	28.8564	1.63106	0.815530	+	0.578714i	$0.196445\pi$
$314$	28.6410	1.61631
$315$	2.00000	0.112687
$316$	−11.9282	−0.671014
$317$	9.58846	0.538541	0.269271	−	0.963065i	$-0.413217\pi$
$317$	9.58846	0.538541	0.269271	+	0.963065i	$0.413217\pi$
$318$	−7.39230	−0.414540
$319$	−12.9282	−0.723840
$320$	2.00000	0.111803
$321$	−2.00000	−0.111629
$322$	4.39230	0.244774
$323$	0	0
$324$	1.00000	0.0555556
$325$	−3.46410	−0.192154
$326$	25.8564	1.43205
$327$	8.39230	0.464096
$328$	19.3923	1.07076
$329$	0.267949	0.0147725
$330$	−12.9282	−0.711674
$331$	12.9282	0.710598	0.355299	−	0.934753i	$-0.384379\pi$
$331$	12.9282	0.710598	0.355299	+	0.934753i	$0.384379\pi$
$332$	−5.46410	−0.299882
$333$	−5.92820	−0.324864
$334$	24.4641	1.33862
$335$	10.0000	0.546358
$336$	5.00000	0.272772
$337$	19.3205	1.05246	0.526228	−	0.850344i	$-0.323606\pi$
$337$	19.3205	1.05246	0.526228	+	0.850344i	$0.323606\pi$
$338$	−1.73205	−0.0942111
$339$	−12.0000	−0.651751
$340$	0	0
$341$	35.3205	1.91271
$342$	0	0
$343$	−13.0000	−0.701934
$344$	6.00000	0.323498
$345$	−5.07180	−0.273056
$346$	6.92820	0.372463
$347$	−23.7321	−1.27400	−0.637002	−	0.770862i	$-0.719826\pi$
$347$	−23.7321	−1.27400	−0.637002	+	0.770862i	$0.719826\pi$
$348$	3.46410	0.185695
$349$	6.85641	0.367015	0.183508	−	0.983018i	$-0.441255\pi$
$349$	6.85641	0.367015	0.183508	+	0.983018i	$0.441255\pi$
$350$	−1.73205	−0.0925820
$351$	−3.46410	−0.184900
$352$	−19.3923	−1.03361
$353$	−21.0526	−1.12051	−0.560257	−	0.828319i	$-0.689298\pi$
$353$	−21.0526	−1.12051	−0.560257	+	0.828319i	$0.689298\pi$
$354$	11.5359	0.613126
$355$	25.8564	1.37232
$356$	6.92820	0.367194
$357$	0	0
$358$	0.928203	0.0490571
$359$	−27.3205	−1.44192	−0.720961	−	0.692976i	$-0.756299\pi$
$359$	−27.3205	−1.44192	−0.720961	+	0.692976i	$0.756299\pi$
$360$	−3.46410	−0.182574
$361$	−19.0000	−1.00000
$362$	14.5359	0.763990
$363$	−2.92820	−0.153691
$364$	3.46410	0.181568
$365$	−29.8564	−1.56276
$366$	12.9282	0.675768
$367$	3.92820	0.205051	0.102525	−	0.994730i	$-0.467308\pi$
$367$	3.92820	0.205051	0.102525	+	0.994730i	$0.467308\pi$
$368$	−12.6795	−0.660964
$369$	−11.1962	−0.582848
$370$	−20.5359	−1.06761
$371$	4.26795	0.221581
$372$	−9.46410	−0.490691
$373$	33.8564	1.75302	0.876509	−	0.481385i	$-0.159866\pi$
$373$	33.8564	1.75302	0.876509	+	0.481385i	$0.159866\pi$
$374$	0	0
$375$	12.0000	0.619677
$376$	−0.464102	−0.0239342
$377$	−12.0000	−0.618031
$378$	−1.73205	−0.0890871
$379$	1.92820	0.0990451	0.0495226	−	0.998773i	$-0.484230\pi$
$379$	1.92820	0.0990451	0.0495226	+	0.998773i	$0.484230\pi$
$380$	0	0
$381$	8.39230	0.429951
$382$	29.5359	1.51119
$383$	−28.2679	−1.44442	−0.722212	−	0.691671i	$-0.756875\pi$
$383$	−28.2679	−1.44442	−0.722212	+	0.691671i	$0.756875\pi$
$384$	−12.1244	−0.618718
$385$	7.46410	0.380406
$386$	−29.1962	−1.48605
$387$	−3.46410	−0.176090
$388$	5.92820	0.300959
$389$	−25.0526	−1.27022	−0.635108	−	0.772424i	$-0.719044\pi$
$389$	−25.0526	−1.27022	−0.635108	+	0.772424i	$0.719044\pi$
$390$	−12.0000	−0.607644
$391$	0	0
$392$	10.3923	0.524891
$393$	−4.53590	−0.228806
$394$	10.1436	0.511027
$395$	−23.8564	−1.20035
$396$	3.73205	0.187543
$397$	−15.0000	−0.752828	−0.376414	−	0.926451i	$-0.622843\pi$
$397$	−15.0000	−0.752828	−0.376414	+	0.926451i	$0.622843\pi$
$398$	−18.9282	−0.948785
$399$	0	0
$400$	5.00000	0.250000
$401$	−8.39230	−0.419092	−0.209546	−	0.977799i	$-0.567199\pi$
$401$	−8.39230	−0.419092	−0.209546	+	0.977799i	$0.567199\pi$
$402$	−8.66025	−0.431934
$403$	32.7846	1.63312
$404$	2.66025	0.132353
$405$	2.00000	0.0993808
$406$	−6.00000	−0.297775
$407$	−22.1244	−1.09666
$408$	0	0
$409$	−18.9282	−0.935939	−0.467970	−	0.883745i	$-0.655014\pi$
$409$	−18.9282	−0.935939	−0.467970	+	0.883745i	$0.655014\pi$
$410$	−38.7846	−1.91544
$411$	−15.3205	−0.755705
$412$	−5.46410	−0.269197
$413$	−6.66025	−0.327730
$414$	4.39230	0.215870
$415$	−10.9282	−0.536444
$416$	−18.0000	−0.882523
$417$	10.5359	0.515945
$418$	0	0
$419$	−1.60770	−0.0785410	−0.0392705	−	0.999229i	$-0.512503\pi$
$419$	−1.60770	−0.0785410	−0.0392705	+	0.999229i	$0.512503\pi$
$420$	−2.00000	−0.0975900
$421$	−37.1769	−1.81189	−0.905946	−	0.423393i	$-0.860839\pi$
$421$	−37.1769	−1.81189	−0.905946	+	0.423393i	$0.860839\pi$
$422$	17.1962	0.837096
$423$	0.267949	0.0130281
$424$	−7.39230	−0.359002
$425$	0	0
$426$	−22.3923	−1.08491
$427$	−7.46410	−0.361213
$428$	2.00000	0.0966736
$429$	−12.9282	−0.624180
$430$	−12.0000	−0.578691
$431$	21.7128	1.04587	0.522935	−	0.852373i	$-0.324837\pi$
$431$	21.7128	1.04587	0.522935	+	0.852373i	$0.324837\pi$
$432$	5.00000	0.240563
$433$	25.8564	1.24258	0.621290	−	0.783581i	$-0.286609\pi$
$433$	25.8564	1.24258	0.621290	+	0.783581i	$0.286609\pi$
$434$	16.3923	0.786856
$435$	6.92820	0.332182
$436$	−8.39230	−0.401919
$437$	0	0
$438$	25.8564	1.23547
$439$	2.53590	0.121032	0.0605159	−	0.998167i	$-0.480725\pi$
$439$	2.53590	0.121032	0.0605159	+	0.998167i	$0.480725\pi$
$440$	−12.9282	−0.616328
$441$	−6.00000	−0.285714
$442$	0	0
$443$	29.3205	1.39306	0.696530	−	0.717528i	$-0.254726\pi$
$443$	29.3205	1.39306	0.696530	+	0.717528i	$0.254726\pi$
$444$	5.92820	0.281340
$445$	13.8564	0.656857
$446$	−6.92820	−0.328060
$447$	−4.00000	−0.189194
$448$	1.00000	0.0472456
$449$	26.6603	1.25818	0.629088	−	0.777334i	$-0.283429\pi$
$449$	26.6603	1.25818	0.629088	+	0.777334i	$0.283429\pi$
$450$	−1.73205	−0.0816497
$451$	−41.7846	−1.96756
$452$	12.0000	0.564433
$453$	−1.00000	−0.0469841
$454$	−11.0718	−0.519625
$455$	6.92820	0.324799
$456$	0	0
$457$	−19.0718	−0.892141	−0.446071	−	0.894998i	$-0.647177\pi$
$457$	−19.0718	−0.892141	−0.446071	+	0.894998i	$0.647177\pi$
$458$	−24.1244	−1.12726
$459$	0	0
$460$	5.07180	0.236474
$461$	29.4641	1.37228	0.686140	−	0.727470i	$-0.259304\pi$
$461$	29.4641	1.37228	0.686140	+	0.727470i	$0.259304\pi$
$462$	−6.46410	−0.300737
$463$	−14.2487	−0.662194	−0.331097	−	0.943597i	$-0.607419\pi$
$463$	−14.2487	−0.662194	−0.331097	+	0.943597i	$0.607419\pi$
$464$	17.3205	0.804084
$465$	−18.9282	−0.877774
$466$	−18.4641	−0.855333
$467$	19.0718	0.882538	0.441269	−	0.897375i	$-0.354529\pi$
$467$	19.0718	0.882538	0.441269	+	0.897375i	$0.354529\pi$
$468$	3.46410	0.160128
$469$	5.00000	0.230879
$470$	0.928203	0.0428148
$471$	−16.5359	−0.761934
$472$	11.5359	0.530983
$473$	−12.9282	−0.594439
$474$	20.6603	0.948957
$475$	0	0
$476$	0	0
$477$	4.26795	0.195416
$478$	47.5692	2.17577
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	10.3923	0.474342
$481$	−20.5359	−0.936356
$482$	−43.3013	−1.97232
$483$	−2.53590	−0.115387
$484$	2.92820	0.133100
$485$	11.8564	0.538372
$486$	−1.73205	−0.0785674
$487$	2.00000	0.0906287	0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000	0.0906287	0.0453143	+	0.998973i	$0.485571\pi$
$488$	12.9282	0.585232
$489$	−14.9282	−0.675077
$490$	−20.7846	−0.938953
$491$	10.3923	0.468998	0.234499	−	0.972116i	$-0.424655\pi$
$491$	10.3923	0.468998	0.234499	+	0.972116i	$0.424655\pi$
$492$	11.1962	0.504762
$493$	0	0
$494$	0	0
$495$	7.46410	0.335486
$496$	−47.3205	−2.12475
$497$	12.9282	0.579909
$498$	9.46410	0.424097
$499$	14.8564	0.665064	0.332532	−	0.943092i	$-0.392097\pi$
$499$	14.8564	0.665064	0.332532	+	0.943092i	$0.392097\pi$
$500$	−12.0000	−0.536656
$501$	−14.1244	−0.631030
$502$	−21.7128	−0.969090
$503$	−35.4449	−1.58041	−0.790204	−	0.612844i	$-0.790026\pi$
$503$	−35.4449	−1.58041	−0.790204	+	0.612844i	$0.790026\pi$
$504$	−1.73205	−0.0771517
$505$	5.32051	0.236760
$506$	16.3923	0.728727
$507$	1.00000	0.0444116
$508$	−8.39230	−0.372348
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	0	0
$511$	−14.9282	−0.660385
$512$	8.66025	0.382733
$513$	0	0
$514$	−17.0718	−0.753005
$515$	−10.9282	−0.481554
$516$	3.46410	0.152499
$517$	1.00000	0.0439799
$518$	−10.2679	−0.451148
$519$	−4.00000	−0.175581
$520$	−12.0000	−0.526235
$521$	−41.1769	−1.80399	−0.901997	−	0.431743i	$-0.857899\pi$
$521$	−41.1769	−1.80399	−0.901997	+	0.431743i	$0.857899\pi$
$522$	−6.00000	−0.262613
$523$	−41.6410	−1.82083	−0.910417	−	0.413691i	$-0.864239\pi$
$523$	−41.6410	−1.82083	−0.910417	+	0.413691i	$0.864239\pi$
$524$	4.53590	0.198152
$525$	1.00000	0.0436436
$526$	13.8564	0.604168
$527$	0	0
$528$	18.6603	0.812083
$529$	−16.5692	−0.720401
$530$	14.7846	0.642202
$531$	−6.66025	−0.289030
$532$	0	0
$533$	−38.7846	−1.67995
$534$	−12.0000	−0.519291
$535$	4.00000	0.172935
$536$	−8.66025	−0.374066
$537$	−0.535898	−0.0231257
$538$	1.85641	0.0800354
$539$	−22.3923	−0.964505
$540$	−2.00000	−0.0860663
$541$	17.0000	0.730887	0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000	0.730887	0.365444	+	0.930834i	$0.380917\pi$
$542$	49.7321	2.13617
$543$	−8.39230	−0.360148
$544$	0	0
$545$	−16.7846	−0.718974
$546$	−6.00000	−0.256776
$547$	26.5359	1.13459	0.567297	−	0.823514i	$-0.307989\pi$
$547$	26.5359	1.13459	0.567297	+	0.823514i	$0.307989\pi$
$548$	15.3205	0.654460
$549$	−7.46410	−0.318560
$550$	−6.46410	−0.275630
$551$	0	0
$552$	4.39230	0.186949
$553$	−11.9282	−0.507239
$554$	32.5359	1.38232
$555$	11.8564	0.503276
$556$	−10.5359	−0.446822
$557$	38.1244	1.61538	0.807690	−	0.589607i	$-0.200717\pi$
$557$	38.1244	1.61538	0.807690	+	0.589607i	$0.200717\pi$
$558$	16.3923	0.693942
$559$	−12.0000	−0.507546
$560$	−10.0000	−0.422577
$561$	0	0
$562$	16.6077	0.700553
$563$	27.7321	1.16877	0.584383	−	0.811478i	$-0.301336\pi$
$563$	27.7321	1.16877	0.584383	+	0.811478i	$0.301336\pi$
$564$	−0.267949	−0.0112827
$565$	24.0000	1.00969
$566$	−8.66025	−0.364018
$567$	1.00000	0.0419961
$568$	−22.3923	−0.939560
$569$	44.3923	1.86102	0.930511	−	0.366264i	$-0.119363\pi$
$569$	44.3923	1.86102	0.930511	+	0.366264i	$0.119363\pi$
$570$	0	0
$571$	−16.9282	−0.708423	−0.354212	−	0.935165i	$-0.615251\pi$
$571$	−16.9282	−0.708423	−0.354212	+	0.935165i	$0.615251\pi$
$572$	12.9282	0.540555
$573$	−17.0526	−0.712381
$574$	−19.3923	−0.809419
$575$	−2.53590	−0.105754
$576$	1.00000	0.0416667
$577$	−19.9282	−0.829622	−0.414811	−	0.909908i	$-0.636152\pi$
$577$	−19.9282	−0.829622	−0.414811	+	0.909908i	$0.636152\pi$
$578$	−29.4449	−1.22474
$579$	16.8564	0.700528
$580$	−6.92820	−0.287678
$581$	−5.46410	−0.226689
$582$	−10.2679	−0.425620
$583$	15.9282	0.659679
$584$	25.8564	1.06995
$585$	6.92820	0.286446
$586$	−11.5359	−0.476544
$587$	38.7846	1.60081	0.800406	−	0.599458i	$-0.204617\pi$
$587$	38.7846	1.60081	0.800406	+	0.599458i	$0.204617\pi$
$588$	6.00000	0.247436
$589$	0	0
$590$	−23.0718	−0.949851
$591$	−5.85641	−0.240900
$592$	29.6410	1.21824
$593$	6.12436	0.251497	0.125749	−	0.992062i	$-0.459867\pi$
$593$	6.12436	0.251497	0.125749	+	0.992062i	$0.459867\pi$
$594$	−6.46410	−0.265225
$595$	0	0
$596$	4.00000	0.163846
$597$	10.9282	0.447262
$598$	15.2154	0.622204
$599$	15.0718	0.615817	0.307908	−	0.951416i	$-0.400371\pi$
$599$	15.0718	0.615817	0.307908	+	0.951416i	$0.400371\pi$
$600$	−1.73205	−0.0707107
$601$	3.78461	0.154377	0.0771887	−	0.997016i	$-0.475406\pi$
$601$	3.78461	0.154377	0.0771887	+	0.997016i	$0.475406\pi$
$602$	−6.00000	−0.244542
$603$	5.00000	0.203616
$604$	1.00000	0.0406894
$605$	5.85641	0.238097
$606$	−4.60770	−0.187175
$607$	27.7128	1.12483	0.562414	−	0.826856i	$-0.309873\pi$
$607$	27.7128	1.12483	0.562414	+	0.826856i	$0.309873\pi$
$608$	0	0
$609$	3.46410	0.140372
$610$	−25.8564	−1.04690
$611$	0.928203	0.0375511
$612$	0	0
$613$	13.0000	0.525065	0.262533	−	0.964923i	$-0.415442\pi$
$613$	13.0000	0.525065	0.262533	+	0.964923i	$0.415442\pi$
$614$	−1.85641	−0.0749185
$615$	22.3923	0.902945
$616$	−6.46410	−0.260446
$617$	6.92820	0.278919	0.139459	−	0.990228i	$-0.455464\pi$
$617$	6.92820	0.278919	0.139459	+	0.990228i	$0.455464\pi$
$618$	9.46410	0.380702
$619$	−0.856406	−0.0344219	−0.0172109	−	0.999852i	$-0.505479\pi$
$619$	−0.856406	−0.0344219	−0.0172109	+	0.999852i	$0.505479\pi$
$620$	18.9282	0.760175
$621$	−2.53590	−0.101762
$622$	−36.9282	−1.48069
$623$	6.92820	0.277573
$624$	17.3205	0.693375
$625$	−19.0000	−0.760000
$626$	49.9808	1.99763
$627$	0	0
$628$	16.5359	0.659854
$629$	0	0
$630$	3.46410	0.138013
$631$	−29.8564	−1.18856	−0.594282	−	0.804256i	$-0.702564\pi$
$631$	−29.8564	−1.18856	−0.594282	+	0.804256i	$0.702564\pi$
$632$	20.6603	0.821821
$633$	−9.92820	−0.394611
$634$	16.6077	0.659576
$635$	−16.7846	−0.666077
$636$	−4.26795	−0.169235
$637$	−20.7846	−0.823516
$638$	−22.3923	−0.886520
$639$	12.9282	0.511432
$640$	24.2487	0.958514
$641$	21.8564	0.863276	0.431638	−	0.902047i	$-0.357936\pi$
$641$	21.8564	0.863276	0.431638	+	0.902047i	$0.357936\pi$
$642$	−3.46410	−0.136717
$643$	39.8564	1.57178	0.785892	−	0.618364i	$-0.212204\pi$
$643$	39.8564	1.57178	0.785892	+	0.618364i	$0.212204\pi$
$644$	2.53590	0.0999284
$645$	6.92820	0.272798
$646$	0	0
$647$	−40.2487	−1.58234	−0.791170	−	0.611596i	$-0.790528\pi$
$647$	−40.2487	−1.58234	−0.791170	+	0.611596i	$0.790528\pi$
$648$	−1.73205	−0.0680414
$649$	−24.8564	−0.975699
$650$	−6.00000	−0.235339
$651$	−9.46410	−0.370927
$652$	14.9282	0.584634
$653$	38.1051	1.49117	0.745584	−	0.666411i	$-0.232171\pi$
$653$	38.1051	1.49117	0.745584	+	0.666411i	$0.232171\pi$
$654$	14.5359	0.568399
$655$	9.07180	0.354464
$656$	55.9808	2.18568
$657$	−14.9282	−0.582405
$658$	0.464102	0.0180926
$659$	41.8372	1.62974	0.814872	−	0.579640i	$-0.196807\pi$
$659$	41.8372	1.62974	0.814872	+	0.579640i	$0.196807\pi$
$660$	−7.46410	−0.290540
$661$	−17.4641	−0.679275	−0.339637	−	0.940556i	$-0.610304\pi$
$661$	−17.4641	−0.679275	−0.339637	+	0.940556i	$0.610304\pi$
$662$	22.3923	0.870302
$663$	0	0
$664$	9.46410	0.367278
$665$	0	0
$666$	−10.2679	−0.397875
$667$	−8.78461	−0.340141
$668$	14.1244	0.546488
$669$	4.00000	0.154649
$670$	17.3205	0.669150
$671$	−27.8564	−1.07538
$672$	5.19615	0.200446
$673$	8.71281	0.335854	0.167927	−	0.985799i	$-0.446293\pi$
$673$	8.71281	0.335854	0.167927	+	0.985799i	$0.446293\pi$
$674$	33.4641	1.28899
$675$	1.00000	0.0384900
$676$	−1.00000	−0.0384615
$677$	19.1962	0.737768	0.368884	−	0.929475i	$-0.379740\pi$
$677$	19.1962	0.737768	0.368884	+	0.929475i	$0.379740\pi$
$678$	−20.7846	−0.798228
$679$	5.92820	0.227504
$680$	0	0
$681$	6.39230	0.244954
$682$	61.1769	2.34259
$683$	21.4641	0.821301	0.410651	−	0.911793i	$-0.365302\pi$
$683$	21.4641	0.821301	0.410651	+	0.911793i	$0.365302\pi$
$684$	0	0
$685$	30.6410	1.17073
$686$	−22.5167	−0.859690
$687$	13.9282	0.531394
$688$	17.3205	0.660338
$689$	14.7846	0.563249
$690$	−8.78461	−0.334424
$691$	39.9282	1.51894	0.759470	−	0.650542i	$-0.225458\pi$
$691$	39.9282	1.51894	0.759470	+	0.650542i	$0.225458\pi$
$692$	4.00000	0.152057
$693$	3.73205	0.141769
$694$	−41.1051	−1.56033
$695$	−21.0718	−0.799299
$696$	−6.00000	−0.227429
$697$	0	0
$698$	11.8756	0.449500
$699$	10.6603	0.403208
$700$	−1.00000	−0.0377964
$701$	−40.7846	−1.54041	−0.770207	−	0.637794i	$-0.779847\pi$
$701$	−40.7846	−1.54041	−0.770207	+	0.637794i	$0.779847\pi$
$702$	−6.00000	−0.226455
$703$	0	0
$704$	3.73205	0.140657
$705$	−0.535898	−0.0201831
$706$	−36.4641	−1.37234
$707$	2.66025	0.100049
$708$	6.66025	0.250308
$709$	5.21539	0.195868	0.0979340	−	0.995193i	$-0.468777\pi$
$709$	5.21539	0.195868	0.0979340	+	0.995193i	$0.468777\pi$
$710$	44.7846	1.68074
$711$	−11.9282	−0.447343
$712$	−12.0000	−0.449719
$713$	24.0000	0.898807
$714$	0	0
$715$	25.8564	0.966975
$716$	0.535898	0.0200275
$717$	−27.4641	−1.02567
$718$	−47.3205	−1.76599
$719$	−46.2487	−1.72479	−0.862393	−	0.506239i	$-0.831035\pi$
$719$	−46.2487	−1.72479	−0.862393	+	0.506239i	$0.831035\pi$
$720$	−10.0000	−0.372678
$721$	−5.46410	−0.203494
$722$	−32.9090	−1.22474
$723$	25.0000	0.929760
$724$	8.39230	0.311898
$725$	3.46410	0.128654
$726$	−5.07180	−0.188232
$727$	33.7128	1.25034	0.625170	−	0.780489i	$-0.285030\pi$
$727$	33.7128	1.25034	0.625170	+	0.780489i	$0.285030\pi$
$728$	−6.00000	−0.222375
$729$	1.00000	0.0370370
$730$	−51.7128	−1.91398
$731$	0	0
$732$	7.46410	0.275881
$733$	−18.9282	−0.699129	−0.349565	−	0.936912i	$-0.613670\pi$
$733$	−18.9282	−0.699129	−0.349565	+	0.936912i	$0.613670\pi$
$734$	6.80385	0.251135
$735$	12.0000	0.442627
$736$	−13.1769	−0.485708
$737$	18.6603	0.687359
$738$	−19.3923	−0.713841
$739$	40.0000	1.47142	0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000	1.47142	0.735712	+	0.677295i	$0.236848\pi$
$740$	−11.8564	−0.435850
$741$	0	0
$742$	7.39230	0.271380
$743$	−10.4115	−0.381962	−0.190981	−	0.981594i	$-0.561167\pi$
$743$	−10.4115	−0.381962	−0.190981	+	0.981594i	$0.561167\pi$
$744$	16.3923	0.600971
$745$	8.00000	0.293097
$746$	58.6410	2.14700
$747$	−5.46410	−0.199921
$748$	0	0
$749$	2.00000	0.0730784
$750$	20.7846	0.758947
$751$	24.7846	0.904403	0.452202	−	0.891916i	$-0.350639\pi$
$751$	24.7846	0.904403	0.452202	+	0.891916i	$0.350639\pi$
$752$	−1.33975	−0.0488555
$753$	12.5359	0.456834
$754$	−20.7846	−0.756931
$755$	2.00000	0.0727875
$756$	−1.00000	−0.0363696
$757$	25.6410	0.931939	0.465969	−	0.884801i	$-0.345706\pi$
$757$	25.6410	0.931939	0.465969	+	0.884801i	$0.345706\pi$
$758$	3.33975	0.121305
$759$	−9.46410	−0.343525
$760$	0	0
$761$	−47.4449	−1.71987	−0.859937	−	0.510399i	$-0.829498\pi$
$761$	−47.4449	−1.71987	−0.859937	+	0.510399i	$0.829498\pi$
$762$	14.5359	0.526580
$763$	−8.39230	−0.303822
$764$	17.0526	0.616940
$765$	0	0
$766$	−48.9615	−1.76905
$767$	−23.0718	−0.833074
$768$	−19.0000	−0.685603
$769$	−26.9282	−0.971056	−0.485528	−	0.874221i	$-0.661373\pi$
$769$	−26.9282	−0.971056	−0.485528	+	0.874221i	$0.661373\pi$
$770$	12.9282	0.465900
$771$	9.85641	0.354970
$772$	−16.8564	−0.606675
$773$	22.6410	0.814341	0.407170	−	0.913352i	$-0.366516\pi$
$773$	22.6410	0.814341	0.407170	+	0.913352i	$0.366516\pi$
$774$	−6.00000	−0.215666
$775$	−9.46410	−0.339961
$776$	−10.2679	−0.368598
$777$	5.92820	0.212673
$778$	−43.3923	−1.55569
$779$	0	0
$780$	−6.92820	−0.248069
$781$	48.2487	1.72647
$782$	0	0
$783$	3.46410	0.123797
$784$	30.0000	1.07143
$785$	33.0718	1.18038
$786$	−7.85641	−0.280229
$787$	2.14359	0.0764109	0.0382054	−	0.999270i	$-0.487836\pi$
$787$	2.14359	0.0764109	0.0382054	+	0.999270i	$0.487836\pi$
$788$	5.85641	0.208626
$789$	−8.00000	−0.284808
$790$	−41.3205	−1.47012
$791$	12.0000	0.426671
$792$	−6.46410	−0.229692
$793$	−25.8564	−0.918188
$794$	−25.9808	−0.922023
$795$	−8.53590	−0.302737
$796$	−10.9282	−0.387340
$797$	−3.32051	−0.117618	−0.0588092	−	0.998269i	$-0.518730\pi$
$797$	−3.32051	−0.117618	−0.0588092	+	0.998269i	$0.518730\pi$
$798$	0	0
$799$	0	0
$800$	5.19615	0.183712
$801$	6.92820	0.244796
$802$	−14.5359	−0.513280
$803$	−55.7128	−1.96606
$804$	−5.00000	−0.176336
$805$	5.07180	0.178757
$806$	56.7846	2.00015
$807$	−1.07180	−0.0377290
$808$	−4.60770	−0.162098
$809$	−26.3731	−0.927228	−0.463614	−	0.886037i	$-0.653447\pi$
$809$	−26.3731	−0.927228	−0.463614	+	0.886037i	$0.653447\pi$
$810$	3.46410	0.121716
$811$	16.7128	0.586866	0.293433	−	0.955980i	$-0.405202\pi$
$811$	16.7128	0.586866	0.293433	+	0.955980i	$0.405202\pi$
$812$	−3.46410	−0.121566
$813$	−28.7128	−1.00700
$814$	−38.3205	−1.34313
$815$	29.8564	1.04582
$816$	0	0
$817$	0	0
$818$	−32.7846	−1.14629
$819$	3.46410	0.121046
$820$	−22.3923	−0.781973
$821$	25.0526	0.874340	0.437170	−	0.899379i	$-0.355981\pi$
$821$	25.0526	0.874340	0.437170	+	0.899379i	$0.355981\pi$
$822$	−26.5359	−0.925546
$823$	41.1769	1.43534	0.717669	−	0.696385i	$-0.245209\pi$
$823$	41.1769	1.43534	0.717669	+	0.696385i	$0.245209\pi$
$824$	9.46410	0.329698
$825$	3.73205	0.129933
$826$	−11.5359	−0.401385
$827$	−40.8038	−1.41889	−0.709444	−	0.704761i	$-0.751054\pi$
$827$	−40.8038	−1.41889	−0.709444	+	0.704761i	$0.751054\pi$
$828$	2.53590	0.0881286
$829$	−14.7128	−0.510997	−0.255499	−	0.966809i	$-0.582240\pi$
$829$	−14.7128	−0.510997	−0.255499	+	0.966809i	$0.582240\pi$
$830$	−18.9282	−0.657008
$831$	−18.7846	−0.651631
$832$	3.46410	0.120096
$833$	0	0
$834$	18.2487	0.631901
$835$	28.2487	0.977587
$836$	0	0
$837$	−9.46410	−0.327127
$838$	−2.78461	−0.0961927
$839$	−12.5359	−0.432787	−0.216394	−	0.976306i	$-0.569429\pi$
$839$	−12.5359	−0.432787	−0.216394	+	0.976306i	$0.569429\pi$
$840$	3.46410	0.119523
$841$	−17.0000	−0.586207
$842$	−64.3923	−2.21911
$843$	−9.58846	−0.330244
$844$	9.92820	0.341743
$845$	−2.00000	−0.0688021
$846$	0.464102	0.0159561
$847$	2.92820	0.100614
$848$	−21.3397	−0.732810
$849$	5.00000	0.171600
$850$	0	0
$851$	−15.0333	−0.515336
$852$	−12.9282	−0.442913
$853$	3.85641	0.132041	0.0660204	−	0.997818i	$-0.478970\pi$
$853$	3.85641	0.132041	0.0660204	+	0.997818i	$0.478970\pi$
$854$	−12.9282	−0.442394
$855$	0	0
$856$	−3.46410	−0.118401
$857$	11.1962	0.382453	0.191227	−	0.981546i	$-0.438753\pi$
$857$	11.1962	0.382453	0.191227	+	0.981546i	$0.438753\pi$
$858$	−22.3923	−0.764461
$859$	−4.71281	−0.160799	−0.0803996	−	0.996763i	$-0.525620\pi$
$859$	−4.71281	−0.160799	−0.0803996	+	0.996763i	$0.525620\pi$
$860$	−6.92820	−0.236250
$861$	11.1962	0.381564
$862$	37.6077	1.28092
$863$	−20.1051	−0.684386	−0.342193	−	0.939630i	$-0.611170\pi$
$863$	−20.1051	−0.684386	−0.342193	+	0.939630i	$0.611170\pi$
$864$	5.19615	0.176777
$865$	8.00000	0.272008
$866$	44.7846	1.52184
$867$	17.0000	0.577350
$868$	9.46410	0.321233
$869$	−44.5167	−1.51012
$870$	12.0000	0.406838
$871$	17.3205	0.586883
$872$	14.5359	0.492248
$873$	5.92820	0.200639
$874$	0	0
$875$	−12.0000	−0.405674
$876$	14.9282	0.504377
$877$	−37.1769	−1.25538	−0.627688	−	0.778465i	$-0.715998\pi$
$877$	−37.1769	−1.25538	−0.627688	+	0.778465i	$0.715998\pi$
$878$	4.39230	0.148233
$879$	6.66025	0.224645
$880$	−37.3205	−1.25807
$881$	25.8756	0.871773	0.435886	−	0.900002i	$-0.356435\pi$
$881$	25.8756	0.871773	0.435886	+	0.900002i	$0.356435\pi$
$882$	−10.3923	−0.349927
$883$	50.1051	1.68617	0.843086	−	0.537779i	$-0.180737\pi$
$883$	50.1051	1.68617	0.843086	+	0.537779i	$0.180737\pi$
$884$	0	0
$885$	13.3205	0.447764
$886$	50.7846	1.70614
$887$	51.7128	1.73635	0.868173	−	0.496261i	$-0.165294\pi$
$887$	51.7128	1.73635	0.868173	+	0.496261i	$0.165294\pi$
$888$	−10.2679	−0.344570
$889$	−8.39230	−0.281469
$890$	24.0000	0.804482
$891$	3.73205	0.125028
$892$	−4.00000	−0.133930
$893$	0	0
$894$	−6.92820	−0.231714
$895$	1.07180	0.0358262
$896$	12.1244	0.405046
$897$	−8.78461	−0.293310
$898$	46.1769	1.54094
$899$	−32.7846	−1.09343
$900$	−1.00000	−0.0333333
$901$	0	0
$902$	−72.3731	−2.40976
$903$	3.46410	0.115278
$904$	−20.7846	−0.691286
$905$	16.7846	0.557939
$906$	−1.73205	−0.0575435
$907$	9.07180	0.301224	0.150612	−	0.988593i	$-0.451876\pi$
$907$	9.07180	0.301224	0.150612	+	0.988593i	$0.451876\pi$
$908$	−6.39230	−0.212136
$909$	2.66025	0.0882351
$910$	12.0000	0.397796
$911$	−23.1769	−0.767885	−0.383943	−	0.923357i	$-0.625434\pi$
$911$	−23.1769	−0.767885	−0.383943	+	0.923357i	$0.625434\pi$
$912$	0	0
$913$	−20.3923	−0.674887
$914$	−33.0333	−1.09265
$915$	14.9282	0.493511
$916$	−13.9282	−0.460201
$917$	4.53590	0.149789
$918$	0	0
$919$	−22.1436	−0.730450	−0.365225	−	0.930919i	$-0.619008\pi$
$919$	−22.1436	−0.730450	−0.365225	+	0.930919i	$0.619008\pi$
$920$	−8.78461	−0.289620
$921$	1.07180	0.0353169
$922$	51.0333	1.68069
$923$	44.7846	1.47410
$924$	−3.73205	−0.122775
$925$	5.92820	0.194918
$926$	−24.6795	−0.811018
$927$	−5.46410	−0.179465
$928$	18.0000	0.590879
$929$	41.8372	1.37263	0.686316	−	0.727303i	$-0.259227\pi$
$929$	41.8372	1.37263	0.686316	+	0.727303i	$0.259227\pi$
$930$	−32.7846	−1.07505
$931$	0	0
$932$	−10.6603	−0.349188
$933$	21.3205	0.698002
$934$	33.0333	1.08088
$935$	0	0
$936$	−6.00000	−0.196116
$937$	−51.8564	−1.69407	−0.847037	−	0.531533i	$-0.821616\pi$
$937$	−51.8564	−1.69407	−0.847037	+	0.531533i	$0.821616\pi$
$938$	8.66025	0.282767
$939$	−28.8564	−0.941693
$940$	0.535898	0.0174791
$941$	−43.9808	−1.43373	−0.716866	−	0.697211i	$-0.754424\pi$
$941$	−43.9808	−1.43373	−0.716866	+	0.697211i	$0.754424\pi$
$942$	−28.6410	−0.933175
$943$	−28.3923	−0.924581
$944$	33.3013	1.08386
$945$	−2.00000	−0.0650600
$946$	−22.3923	−0.728037
$947$	13.4641	0.437525	0.218762	−	0.975778i	$-0.429798\pi$
$947$	13.4641	0.437525	0.218762	+	0.975778i	$0.429798\pi$
$948$	11.9282	0.387410
$949$	−51.7128	−1.67867
$950$	0	0
$951$	−9.58846	−0.310927
$952$	0	0
$953$	−12.9282	−0.418786	−0.209393	−	0.977832i	$-0.567149\pi$
$953$	−12.9282	−0.418786	−0.209393	+	0.977832i	$0.567149\pi$
$954$	7.39230	0.239335
$955$	34.1051	1.10362
$956$	27.4641	0.888253
$957$	12.9282	0.417909
$958$	0	0
$959$	15.3205	0.494725
$960$	−2.00000	−0.0645497
$961$	58.5692	1.88933
$962$	−35.5692	−1.14680
$963$	2.00000	0.0644491
$964$	−25.0000	−0.805196
$965$	−33.7128	−1.08525
$966$	−4.39230	−0.141320
$967$	−35.7128	−1.14845	−0.574223	−	0.818699i	$-0.694696\pi$
$967$	−35.7128	−1.14845	−0.574223	+	0.818699i	$0.694696\pi$
$968$	−5.07180	−0.163014
$969$	0	0
$970$	20.5359	0.659368
$971$	−22.6795	−0.727820	−0.363910	−	0.931434i	$-0.618558\pi$
$971$	−22.6795	−0.727820	−0.363910	+	0.931434i	$0.618558\pi$
$972$	−1.00000	−0.0320750
$973$	−10.5359	−0.337765
$974$	3.46410	0.110997
$975$	3.46410	0.110940
$976$	37.3205	1.19460
$977$	37.5885	1.20256	0.601281	−	0.799038i	$-0.294657\pi$
$977$	37.5885	1.20256	0.601281	+	0.799038i	$0.294657\pi$
$978$	−25.8564	−0.826797
$979$	25.8564	0.826374
$980$	−12.0000	−0.383326
$981$	−8.39230	−0.267946
$982$	18.0000	0.574403
$983$	7.17691	0.228908	0.114454	−	0.993429i	$-0.463488\pi$
$983$	7.17691	0.228908	0.114454	+	0.993429i	$0.463488\pi$
$984$	−19.3923	−0.618204
$985$	11.7128	0.373201
$986$	0	0
$987$	−0.267949	−0.00852892
$988$	0	0
$989$	−8.78461	−0.279334
$990$	12.9282	0.410885
$991$	−16.1436	−0.512818	−0.256409	−	0.966568i	$-0.582539\pi$
$991$	−16.1436	−0.512818	−0.256409	+	0.966568i	$0.582539\pi$
$992$	−49.1769	−1.56137
$993$	−12.9282	−0.410264
$994$	22.3923	0.710241
$995$	−21.8564	−0.692895
$996$	5.46410	0.173137
$997$	−31.7846	−1.00663	−0.503314	−	0.864103i	$-0.667886\pi$
$997$	−31.7846	−1.00663	−0.503314	+	0.864103i	$0.667886\pi$
$998$	25.7321	0.814534
$999$	5.92820	0.187560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	453.2.a.c.1.2	✓	2
3.2	odd	2		1359.2.a.b.1.1		2
4.3	odd	2		7248.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
453.2.a.c.1.2	✓	2	1.1	even	1	trivial
1359.2.a.b.1.1		2	3.2	odd	2
7248.2.a.t.1.1		2	4.3	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:	\( N \)	\(=\)	\( 453 = 3 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	453.a (trivial)

\(f(q)\)	\(=\)	\(q+1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.73205 q^{6} +1.00000 q^{7} -1.73205 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.73205 q^{6} +1.00000 q^{7} -1.73205 q^{8} +1.00000 q^{9} +3.46410 q^{10} +3.73205 q^{11} -1.00000 q^{12} +3.46410 q^{13} +1.73205 q^{14} -2.00000 q^{15} -5.00000 q^{16} +1.73205 q^{18} +2.00000 q^{20} -1.00000 q^{21} +6.46410 q^{22} +2.53590 q^{23} +1.73205 q^{24} -1.00000 q^{25} +6.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -3.46410 q^{29} -3.46410 q^{30} +9.46410 q^{31} -5.19615 q^{32} -3.73205 q^{33} +2.00000 q^{35} +1.00000 q^{36} -5.92820 q^{37} -3.46410 q^{39} -3.46410 q^{40} -11.1962 q^{41} -1.73205 q^{42} -3.46410 q^{43} +3.73205 q^{44} +2.00000 q^{45} +4.39230 q^{46} +0.267949 q^{47} +5.00000 q^{48} -6.00000 q^{49} -1.73205 q^{50} +3.46410 q^{52} +4.26795 q^{53} -1.73205 q^{54} +7.46410 q^{55} -1.73205 q^{56} -6.00000 q^{58} -6.66025 q^{59} -2.00000 q^{60} -7.46410 q^{61} +16.3923 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.92820 q^{65} -6.46410 q^{66} +5.00000 q^{67} -2.53590 q^{69} +3.46410 q^{70} +12.9282 q^{71} -1.73205 q^{72} -14.9282 q^{73} -10.2679 q^{74} +1.00000 q^{75} +3.73205 q^{77} -6.00000 q^{78} -11.9282 q^{79} -10.0000 q^{80} +1.00000 q^{81} -19.3923 q^{82} -5.46410 q^{83} -1.00000 q^{84} -6.00000 q^{86} +3.46410 q^{87} -6.46410 q^{88} +6.92820 q^{89} +3.46410 q^{90} +3.46410 q^{91} +2.53590 q^{92} -9.46410 q^{93} +0.464102 q^{94} +5.19615 q^{96} +5.92820 q^{97} -10.3923 q^{98} +3.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 4 q^{15} - 10 q^{16} + 4 q^{20} - 2 q^{21} + 6 q^{22} + 12 q^{23} - 2 q^{25} + 12 q^{26} - 2 q^{27} + 2 q^{28} + 12 q^{31} - 4 q^{33} + 4 q^{35} + 2 q^{36} + 2 q^{37} - 12 q^{41} + 4 q^{44} + 4 q^{45} - 12 q^{46} + 4 q^{47} + 10 q^{48} - 12 q^{49} + 12 q^{53} + 8 q^{55} - 12 q^{58} + 4 q^{59} - 4 q^{60} - 8 q^{61} + 12 q^{62} + 2 q^{63} + 2 q^{64} - 6 q^{66} + 10 q^{67} - 12 q^{69} + 12 q^{71} - 16 q^{73} - 24 q^{74} + 2 q^{75} + 4 q^{77} - 12 q^{78} - 10 q^{79} - 20 q^{80} + 2 q^{81} - 18 q^{82} - 4 q^{83} - 2 q^{84} - 12 q^{86} - 6 q^{88} + 12 q^{92} - 12 q^{93} - 6 q^{94} - 2 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^7 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 4 * q^15 - 10 * q^16 + 4 * q^20 - 2 * q^21 + 6 * q^22 + 12 * q^23 - 2 * q^25 + 12 * q^26 - 2 * q^27 + 2 * q^28 + 12 * q^31 - 4 * q^33 + 4 * q^35 + 2 * q^36 + 2 * q^37 - 12 * q^41 + 4 * q^44 + 4 * q^45 - 12 * q^46 + 4 * q^47 + 10 * q^48 - 12 * q^49 + 12 * q^53 + 8 * q^55 - 12 * q^58 + 4 * q^59 - 4 * q^60 - 8 * q^61 + 12 * q^62 + 2 * q^63 + 2 * q^64 - 6 * q^66 + 10 * q^67 - 12 * q^69 + 12 * q^71 - 16 * q^73 - 24 * q^74 + 2 * q^75 + 4 * q^77 - 12 * q^78 - 10 * q^79 - 20 * q^80 + 2 * q^81 - 18 * q^82 - 4 * q^83 - 2 * q^84 - 12 * q^86 - 6 * q^88 + 12 * q^92 - 12 * q^93 - 6 * q^94 - 2 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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