LMFDB - Embedded newform 1872.2.by.h.433.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1872,2,Mod(433,1872)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1872, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("1872.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1872 = 2^{4} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1872.by (of order $6$, degree $2$, not minimal)

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:	no
Analytic conductor:	$14.9479952584$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1872.433
Dual form			1872.2.by.h.1297.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.267949i q^{5} +(-0.633975 + 0.366025i) q^{7} +O(q^{10})$	$q+0.267949i q^{5} +(-0.633975 + 0.366025i) q^{7} +(-4.09808 - 2.36603i) q^{11} +(2.59808 - 2.50000i) q^{13} +(1.13397 + 1.96410i) q^{17} +(1.09808 - 0.633975i) q^{19} +(-3.09808 + 5.36603i) q^{23} +4.92820 q^{25} +(1.23205 - 2.13397i) q^{29} -5.46410i q^{31} +(-0.0980762 - 0.169873i) q^{35} +(-9.06218 - 5.23205i) q^{37} +(-9.86603 - 5.69615i) q^{41} +(-3.83013 - 6.63397i) q^{43} -8.19615i q^{47} +(-3.23205 + 5.59808i) q^{49} -0.464102 q^{53} +(0.633975 - 1.09808i) q^{55} +(6.92820 - 4.00000i) q^{59} +(-0.598076 - 1.03590i) q^{61} +(0.669873 + 0.696152i) q^{65} +(9.63397 + 5.56218i) q^{67} +(-1.09808 + 0.633975i) q^{71} -9.73205i q^{73} +3.46410 q^{77} +9.46410 q^{79} -10.1962i q^{83} +(-0.526279 + 0.303848i) q^{85} +(-2.19615 - 1.26795i) q^{89} +(-0.732051 + 2.53590i) q^{91} +(0.169873 + 0.294229i) q^{95} +(5.19615 - 3.00000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{7}+O(q^{10}) $ 4 * q - 6 * q^7	$ 4 q - 6 q^{7} - 6 q^{11} + 8 q^{17} - 6 q^{19} - 2 q^{23} - 8 q^{25} - 2 q^{29} + 10 q^{35} - 12 q^{37} - 36 q^{41} + 2 q^{43} - 6 q^{49} + 12 q^{53} + 6 q^{55} + 8 q^{61} + 20 q^{65} + 42 q^{67} + 6 q^{71} + 24 q^{79} + 36 q^{85} + 12 q^{89} + 4 q^{91} + 18 q^{95}+O(q^{100}) $ 4 * q - 6 * q^7 - 6 * q^11 + 8 * q^17 - 6 * q^19 - 2 * q^23 - 8 * q^25 - 2 * q^29 + 10 * q^35 - 12 * q^37 - 36 * q^41 + 2 * q^43 - 6 * q^49 + 12 * q^53 + 6 * q^55 + 8 * q^61 + 20 * q^65 + 42 * q^67 + 6 * q^71 + 24 * q^79 + 36 * q^85 + 12 * q^89 + 4 * q^91 + 18 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$			0.267949i			0.119831i	0.998203	+	0.0599153i	$0.0190830\pi$
$5$			0.267949i			0.119831i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$	−0.633975	+	0.366025i	−0.239620	+	0.138345i	−0.615002	−	0.788526i	$-0.710845\pi$
$7$	−0.633975	+	0.366025i	−0.239620	+	0.138345i	0.375382	+	0.926870i	$0.377511\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.09808	−	2.36603i	−1.23562	−	0.713384i	−0.267421	−	0.963580i	$-0.586172\pi$
$11$	−4.09808	−	2.36603i	−1.23562	−	0.713384i	−0.968195	+	0.250196i	$0.919505\pi$
$12$		0			0
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$13$	2.59808	−	2.50000i	0.720577	−	0.693375i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.13397	+	1.96410i	0.275029	+	0.476365i	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	1.13397	+	1.96410i	0.275029	+	0.476365i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		0			0
$19$	1.09808	−	0.633975i	0.251916	−	0.145444i	−0.368725	−	0.929538i	$-0.620206\pi$
$19$	1.09808	−	0.633975i	0.251916	−	0.145444i	0.620641	+	0.784095i	$0.286872\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.09808	+	5.36603i	−0.645994	+	1.11889i	0.338078	+	0.941118i	$0.390223\pi$
$23$	−3.09808	+	5.36603i	−0.645994	+	1.11889i	−0.984071	+	0.177775i	$0.943110\pi$
$24$		0			0
$25$	4.92820			0.985641
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.23205	−	2.13397i	0.228786	−	0.396269i	−0.728663	−	0.684873i	$-0.759858\pi$
$29$	1.23205	−	2.13397i	0.228786	−	0.396269i	0.957449	+	0.288604i	$0.0931910\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0980762	−	0.169873i	−0.0165779	−	0.0287138i
$36$		0			0
$37$	−9.06218	−	5.23205i	−1.48981	−	0.860144i	−0.489881	−	0.871789i	$-0.662960\pi$
$37$	−9.06218	−	5.23205i	−1.48981	−	0.860144i	−0.999932	+	0.0116456i	$0.996293\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.86603	−	5.69615i	−1.54081	−	0.889590i	−0.998788	−	0.0492283i	$-0.984324\pi$
$41$	−9.86603	−	5.69615i	−1.54081	−	0.889590i	−0.542027	−	0.840361i	$-0.682343\pi$
$42$		0			0
$43$	−3.83013	−	6.63397i	−0.584089	−	1.01167i	−0.994988	−	0.0999910i	$-0.968119\pi$
$43$	−3.83013	−	6.63397i	−0.584089	−	1.01167i	0.410899	−	0.911681i	$-0.365215\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	8.19615i		−	1.19553i	−0.801671	−	0.597766i	$-0.796055\pi$
$47$		−	8.19615i		−	1.19553i	0.801671	−	0.597766i	$-0.203945\pi$
$48$		0			0
$49$	−3.23205	+	5.59808i	−0.461722	+	0.799725i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.464102			−0.0637493			−0.0318746	−	0.999492i	$-0.510148\pi$
$53$	−0.464102			−0.0637493			−0.0318746	+	0.999492i	$0.510148\pi$
$54$		0			0
$55$	0.633975	−	1.09808i	0.0854851	−	0.148065i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.0241347	−	0.999709i	$-0.492317\pi$
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.877841	+	0.478953i	$0.158984\pi$
$60$		0			0
$61$	−0.598076	−	1.03590i	−0.0765758	−	0.132633i	0.825195	−	0.564848i	$-0.191065\pi$
$61$	−0.598076	−	1.03590i	−0.0765758	−	0.132633i	−0.901770	+	0.432215i	$0.857732\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.669873	+	0.696152i	0.0830875	+	0.0863471i
$66$		0			0
$67$	9.63397	+	5.56218i	1.17698	+	0.679528i	0.955313	−	0.295595i	$-0.0955179\pi$
$67$	9.63397	+	5.56218i	1.17698	+	0.679528i	0.221664	+	0.975123i	$0.428851\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.09808	+	0.633975i	−0.130318	+	0.0752389i	−0.563742	−	0.825951i	$-0.690639\pi$
$71$	−1.09808	+	0.633975i	−0.130318	+	0.0752389i	0.433424	+	0.901190i	$0.357305\pi$
$72$		0			0
$73$		−	9.73205i		−	1.13905i	−0.821974	−	0.569525i	$-0.807127\pi$
$73$		−	9.73205i		−	1.13905i	0.821974	−	0.569525i	$-0.192873\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.46410			0.394771
$78$		0			0
$79$	9.46410			1.06479			0.532397	−	0.846495i	$-0.321291\pi$
$79$	9.46410			1.06479			0.532397	+	0.846495i	$0.321291\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	10.1962i		−	1.11917i	−0.828772	−	0.559587i	$-0.810960\pi$
$83$		−	10.1962i		−	1.11917i	0.828772	−	0.559587i	$-0.189040\pi$
$84$		0			0
$85$	−0.526279	+	0.303848i	−0.0570830	+	0.0329569i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.19615	−	1.26795i	−0.232792	−	0.134402i	0.379068	−	0.925369i	$-0.376245\pi$
$89$	−2.19615	−	1.26795i	−0.232792	−	0.134402i	−0.611859	+	0.790967i	$0.709578\pi$
$90$		0			0
$91$	−0.732051	+	2.53590i	−0.0767398	+	0.265834i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.169873	+	0.294229i	0.0174286	+	0.0301872i
$96$		0			0
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	−0.212445	−	0.977173i	$-0.568143\pi$
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	0.740034	+	0.672569i	$0.234809\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.96410	−	10.3301i	0.593450	−	1.02789i	−0.400313	−	0.916378i	$-0.631099\pi$
$101$	5.96410	−	10.3301i	0.593450	−	1.02789i	0.993764	−	0.111508i	$-0.0355680\pi$
$102$		0			0
$103$	−18.7321			−1.84572			−0.922862	−	0.385131i	$-0.874156\pi$
$103$	−18.7321			−1.84572			−0.922862	+	0.385131i	$0.874156\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.0980762	−	0.169873i	0.00948139	−	0.0164222i	−0.861246	−	0.508189i	$-0.830315\pi$
$107$	0.0980762	−	0.169873i	0.00948139	−	0.0164222i	0.870727	+	0.491766i	$0.163649\pi$
$108$		0			0
$109$			5.46410i			0.523366i	0.965154	+	0.261683i	$0.0842775\pi$
$109$			5.46410i			0.523366i	−0.965154	+	0.261683i	$0.915723\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.33013	−	16.1603i	−0.877705	−	1.52023i	−0.853854	−	0.520513i	$-0.825741\pi$
$113$	−9.33013	−	16.1603i	−0.877705	−	1.52023i	−0.0238510	−	0.999716i	$-0.507593\pi$
$114$		0			0
$115$	−1.43782	−	0.830127i	−0.134078	−	0.0774097i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.43782	−	0.830127i	−0.131805	−	0.0760976i
$120$		0			0
$121$	5.69615	+	9.86603i	0.517832	+	0.896911i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			2.66025i			0.237940i
$126$		0			0
$127$	−8.92820	+	15.4641i	−0.792250	+	1.37222i	0.132321	+	0.991207i	$0.457757\pi$
$127$	−8.92820	+	15.4641i	−0.792250	+	1.37222i	−0.924571	+	0.381010i	$0.875576\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	13.4641			1.17636			0.588182	−	0.808729i	$-0.299844\pi$
$131$	13.4641			1.17636			0.588182	+	0.808729i	$0.299844\pi$
$132$		0			0
$133$	−0.464102	+	0.803848i	−0.0402427	+	0.0697024i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.66987	−	0.964102i	0.142667	−	0.0823688i	−0.426968	−	0.904267i	$-0.640418\pi$
$137$	1.66987	−	0.964102i	0.142667	−	0.0823688i	0.569634	+	0.821898i	$0.307085\pi$
$138$		0			0
$139$	−4.92820	−	8.53590i	−0.418005	−	0.724005i	0.577734	−	0.816225i	$-0.303937\pi$
$139$	−4.92820	−	8.53590i	−0.418005	−	0.724005i	−0.995739	+	0.0922197i	$0.970604\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−16.5622	+	4.09808i	−1.38500	+	0.342698i
$144$		0			0
$145$	0.571797	+	0.330127i	0.0474851	+	0.0274156i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.42820	−	1.40192i	0.198926	−	0.114850i	−0.397228	−	0.917720i	$-0.630028\pi$
$149$	2.42820	−	1.40192i	0.198926	−	0.114850i	0.596154	+	0.802870i	$0.296695\pi$
$150$		0			0
$151$		−	3.26795i		−	0.265942i	−0.991120	−	0.132971i	$-0.957548\pi$
$151$		−	3.26795i		−	0.265942i	0.991120	−	0.132971i	$-0.0424517\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.46410			0.117599
$156$		0			0
$157$	−23.5885			−1.88256			−0.941282	−	0.337622i	$-0.890378\pi$
$157$	−23.5885			−1.88256			−0.941282	+	0.337622i	$0.890378\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	4.53590i		−	0.357479i
$162$		0			0
$163$	5.66025	−	3.26795i	0.443345	−	0.255966i	−0.261670	−	0.965157i	$-0.584273\pi$
$163$	5.66025	−	3.26795i	0.443345	−	0.255966i	0.705016	+	0.709192i	$0.250940\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.19615	+	1.26795i	0.169943	+	0.0981169i	0.582559	−	0.812788i	$-0.302051\pi$
$167$	2.19615	+	1.26795i	0.169943	+	0.0981169i	−0.412616	+	0.910905i	$0.635385\pi$
$168$		0			0
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.19615	+	14.1962i	0.623142	+	1.07931i	0.988897	+	0.148602i	$0.0474774\pi$
$173$	8.19615	+	14.1962i	0.623142	+	1.07931i	−0.365755	+	0.930711i	$0.619189\pi$
$174$		0			0
$175$	−3.12436	+	1.80385i	−0.236179	+	0.136358i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.0263	−	19.0981i	0.824143	−	1.42746i	−0.0784298	−	0.996920i	$-0.524991\pi$
$179$	11.0263	−	19.0981i	0.824143	−	1.42746i	0.902573	−	0.430538i	$-0.141676\pi$
$180$		0			0
$181$	−8.80385			−0.654385			−0.327192	−	0.944958i	$-0.606103\pi$
$181$	−8.80385			−0.654385			−0.327192	+	0.944958i	$0.606103\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.40192	−	2.42820i	0.103071	−	0.178525i
$186$		0			0
$187$		−	10.7321i		−	0.784805i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	0.713052	−	0.701111i	$-0.247312\pi$
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	−0.963706	+	0.266966i	$0.913979\pi$
$192$		0			0
$193$	7.16025	+	4.13397i	0.515406	+	0.297570i	0.735053	−	0.678009i	$-0.237157\pi$
$193$	7.16025	+	4.13397i	0.515406	+	0.297570i	−0.219647	+	0.975579i	$0.570490\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.53590	−	4.92820i	−0.608158	−	0.351120i	0.164086	−	0.986446i	$-0.447532\pi$
$197$	−8.53590	−	4.92820i	−0.608158	−	0.351120i	−0.772244	+	0.635326i	$0.780866\pi$
$198$		0			0
$199$	1.90192	+	3.29423i	0.134824	+	0.233522i	0.925530	−	0.378674i	$-0.123620\pi$
$199$	1.90192	+	3.29423i	0.134824	+	0.233522i	−0.790706	+	0.612196i	$0.790286\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$			1.80385i			0.126605i
$204$		0			0
$205$	1.52628	−	2.64359i	0.106600	−	0.184637i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−2.19615	+	3.80385i	−0.151189	+	0.261868i	−0.931665	−	0.363319i	$-0.881644\pi$
$211$	−2.19615	+	3.80385i	−0.151189	+	0.261868i	0.780476	+	0.625186i	$0.214977\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.77757	−	1.02628i	0.121229	−	0.0699917i
$216$		0			0
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.85641	+	2.26795i	0.528479	+	0.152559i
$222$		0			0
$223$	11.3205	+	6.53590i	0.758077	+	0.437676i	0.828605	−	0.559834i	$-0.189135\pi$
$223$	11.3205	+	6.53590i	0.758077	+	0.437676i	−0.0705277	+	0.997510i	$0.522468\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.56218	−	0.901924i	0.103685	−	0.0598628i	−0.447261	−	0.894404i	$-0.647600\pi$
$227$	1.56218	−	0.901924i	0.103685	−	0.0598628i	0.550946	+	0.834541i	$0.314267\pi$
$228$		0			0
$229$			15.8564i			1.04782i	0.851773	+	0.523910i	$0.175527\pi$
$229$			15.8564i			1.04782i	−0.851773	+	0.523910i	$0.824473\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	19.8564			1.30084			0.650418	−	0.759576i	$-0.274594\pi$
$233$	19.8564			1.30084			0.650418	+	0.759576i	$0.274594\pi$
$234$		0			0
$235$	2.19615			0.143261
$236$		0			0
$237$		0			0
$238$		0			0
$239$			9.66025i			0.624870i	0.949939	+	0.312435i	$0.101145\pi$
$239$			9.66025i			0.624870i	−0.949939	+	0.312435i	$0.898855\pi$
$240$		0			0
$241$	−15.2321	+	8.79423i	−0.981183	+	0.566486i	−0.902627	−	0.430424i	$-0.858364\pi$
$241$	−15.2321	+	8.79423i	−0.981183	+	0.566486i	−0.0785557	+	0.996910i	$0.525031\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.50000	−	0.866025i	−0.0958315	−	0.0553283i
$246$		0			0
$247$	1.26795	−	4.39230i	0.0806777	−	0.279476i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	3.26795	+	5.66025i	0.206271	+	0.357272i	0.950537	−	0.310611i	$-0.100534\pi$
$251$	3.26795	+	5.66025i	0.206271	+	0.357272i	−0.744266	+	0.667883i	$0.767200\pi$
$252$		0			0
$253$	25.3923	−	14.6603i	1.59640	−	0.921682i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.3301	+	23.0885i	−0.831510	+	1.44022i	0.0653297	+	0.997864i	$0.479190\pi$
$257$	−13.3301	+	23.0885i	−0.831510	+	1.44022i	−0.896840	+	0.442355i	$0.854143\pi$
$258$		0			0
$259$	7.66025			0.475985
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−14.0263	+	24.2942i	−0.864897	+	1.49805i	0.00225153	+	0.999997i	$0.499283\pi$
$263$	−14.0263	+	24.2942i	−0.864897	+	1.49805i	−0.867149	+	0.498049i	$0.834050\pi$
$264$		0			0
$265$		−	0.124356i		−	0.00763911i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.732051	−	1.26795i	−0.0446339	−	0.0773082i	0.842845	−	0.538156i	$-0.180879\pi$
$269$	−0.732051	−	1.26795i	−0.0446339	−	0.0773082i	−0.887479	+	0.460848i	$0.847545\pi$
$270$		0			0
$271$	5.07180	+	2.92820i	0.308090	+	0.177876i	0.646071	−	0.763277i	$-0.276411\pi$
$271$	5.07180	+	2.92820i	0.308090	+	0.177876i	−0.337982	+	0.941153i	$0.609744\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−20.1962	−	11.6603i	−1.21787	−	0.703140i
$276$		0			0
$277$	−1.13397	−	1.96410i	−0.0681339	−	0.118011i	0.829946	−	0.557844i	$-0.188371\pi$
$277$	−1.13397	−	1.96410i	−0.0681339	−	0.118011i	−0.898080	+	0.439832i	$0.855038\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			22.3205i			1.33153i	0.746162	+	0.665765i	$0.231895\pi$
$281$			22.3205i			1.33153i	−0.746162	+	0.665765i	$0.768105\pi$
$282$		0			0
$283$	−4.16987	+	7.22243i	−0.247873	+	0.429329i	−0.962936	−	0.269732i	$-0.913065\pi$
$283$	−4.16987	+	7.22243i	−0.247873	+	0.429329i	0.715062	+	0.699061i	$0.246398\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.33975			0.492280
$288$		0			0
$289$	5.92820	−	10.2679i	0.348718	−	0.603997i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.5718	−	7.25833i	0.734452	−	0.424036i	−0.0855965	−	0.996330i	$-0.527280\pi$
$293$	12.5718	−	7.25833i	0.734452	−	0.424036i	0.820049	+	0.572294i	$0.193946\pi$
$294$		0			0
$295$	1.07180	+	1.85641i	0.0624024	+	0.108084i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.36603	+	21.6865i	0.310325	+	1.25416i
$300$		0			0
$301$	4.85641	+	2.80385i	0.279919	+	0.161611i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.277568	−	0.160254i	0.0158935	−	0.00917612i
$306$		0			0
$307$		−	8.58846i		−	0.490169i	−0.969502	−	0.245085i	$-0.921184\pi$
$307$		−	8.58846i		−	0.490169i	0.969502	−	0.245085i	$-0.0788157\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15.6603			−0.888012			−0.444006	−	0.896024i	$-0.646443\pi$
$311$	−15.6603			−0.888012			−0.444006	+	0.896024i	$0.646443\pi$
$312$		0			0
$313$	13.4641			0.761036			0.380518	−	0.924774i	$-0.375746\pi$
$313$	13.4641			0.761036			0.380518	+	0.924774i	$0.375746\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			3.33975i			0.187579i	0.995592	+	0.0937894i	$0.0298980\pi$
$317$			3.33975i			0.187579i	−0.995592	+	0.0937894i	$0.970102\pi$
$318$		0			0
$319$	−10.0981	+	5.83013i	−0.565384	+	0.326424i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.49038	+	1.43782i	0.138569	+	0.0800026i
$324$		0			0
$325$	12.8038	−	12.3205i	0.710230	−	0.683419i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.00000	+	5.19615i	0.165395	+	0.286473i
$330$		0			0
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.0583130	−	0.998298i	$-0.481428\pi$
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.893708	+	0.448649i	$0.148095\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.49038	+	2.58142i	−0.0814282	+	0.141038i
$336$		0			0
$337$	−6.85641			−0.373492			−0.186746	−	0.982408i	$-0.559794\pi$
$337$	−6.85641			−0.373492			−0.186746	+	0.982408i	$0.559794\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−12.9282	+	22.3923i	−0.700101	+	1.21261i
$342$		0			0
$343$		−	9.85641i		−	0.532196i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.43782	−	7.68653i	−0.238235	−	0.412635i	0.721973	−	0.691921i	$-0.243235\pi$
$347$	−4.43782	−	7.68653i	−0.238235	−	0.412635i	−0.960208	+	0.279286i	$0.909902\pi$
$348$		0			0
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.875785	−	0.482701i	$-0.160344\pi$
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.0198610	+	0.999803i	$0.493678\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.1340	−	9.89230i	−0.911949	−	0.526514i	−0.0308916	−	0.999523i	$-0.509835\pi$
$353$	−17.1340	−	9.89230i	−0.911949	−	0.526514i	−0.881058	+	0.473008i	$0.843168\pi$
$354$		0			0
$355$	−0.169873	−	0.294229i	−0.00901592	−	0.0156160i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			23.1244i			1.22046i	0.792226	+	0.610228i	$0.208922\pi$
$359$			23.1244i			1.22046i	−0.792226	+	0.610228i	$0.791078\pi$
$360$		0			0
$361$	−8.69615	+	15.0622i	−0.457692	+	0.792746i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.60770			0.136493
$366$		0			0
$367$	−7.36603	+	12.7583i	−0.384503	+	0.665979i	−0.991700	−	0.128572i	$-0.958961\pi$
$367$	−7.36603	+	12.7583i	−0.384503	+	0.665979i	0.607197	+	0.794551i	$0.292294\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.294229	−	0.169873i	0.0152756	−	0.00881937i
$372$		0			0
$373$	5.13397	+	8.89230i	0.265827	+	0.460426i	0.967780	−	0.251797i	$-0.0810216\pi$
$373$	5.13397	+	8.89230i	0.265827	+	0.460426i	−0.701953	+	0.712223i	$0.747688\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.13397	−	8.62436i	−0.109905	−	0.444177i
$378$		0			0
$379$	−1.26795	−	0.732051i	−0.0651302	−	0.0376029i	0.467081	−	0.884214i	$-0.345306\pi$
$379$	−1.26795	−	0.732051i	−0.0651302	−	0.0376029i	−0.532211	+	0.846611i	$0.678639\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.73205	+	2.73205i	−0.241797	+	0.139601i	−0.616002	−	0.787744i	$-0.711249\pi$
$383$	−4.73205	+	2.73205i	−0.241797	+	0.139601i	0.374206	+	0.927346i	$0.377915\pi$
$384$		0			0
$385$			0.928203i			0.0473056i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−29.7846			−1.51014			−0.755070	−	0.655644i	$-0.772397\pi$
$389$	−29.7846			−1.51014			−0.755070	+	0.655644i	$0.772397\pi$
$390$		0			0
$391$	−14.0526			−0.710668
$392$		0			0
$393$		0			0
$394$		0			0
$395$			2.53590i			0.127595i
$396$		0			0
$397$	−0.339746	+	0.196152i	−0.0170514	+	0.00984461i	−0.508501	−	0.861061i	$-0.669800\pi$
$397$	−0.339746	+	0.196152i	−0.0170514	+	0.00984461i	0.491450	+	0.870906i	$0.336467\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.9904	+	10.9641i	0.948334	+	0.547521i	0.892563	−	0.450922i	$-0.148905\pi$
$401$	18.9904	+	10.9641i	0.948334	+	0.547521i	0.0557713	+	0.998444i	$0.482238\pi$
$402$		0			0
$403$	−13.6603	−	14.1962i	−0.680466	−	0.707161i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	24.7583	+	42.8827i	1.22722	+	2.12562i
$408$		0			0
$409$	−12.3564	+	7.13397i	−0.610985	+	0.352752i	−0.773351	−	0.633978i	$-0.781421\pi$
$409$	−12.3564	+	7.13397i	−0.610985	+	0.352752i	0.162366	+	0.986731i	$0.448088\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.92820	+	5.07180i	−0.144087	+	0.249567i
$414$		0			0
$415$	2.73205			0.134111
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.26795	−	9.12436i	0.257356	−	0.445754i	−0.708177	−	0.706035i	$-0.750482\pi$
$419$	5.26795	−	9.12436i	0.257356	−	0.445754i	0.965533	+	0.260281i	$0.0838153\pi$
$420$		0			0
$421$		−	32.7128i		−	1.59432i	−0.603765	−	0.797162i	$-0.706333\pi$
$421$		−	32.7128i		−	1.59432i	0.603765	−	0.797162i	$-0.293667\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.58846	+	9.67949i	0.271080	+	0.469524i
$426$		0			0
$427$	0.758330	+	0.437822i	0.0366982	+	0.0211877i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.63397	−	5.56218i	−0.464052	−	0.267921i	0.249694	−	0.968325i	$-0.419670\pi$
$431$	−9.63397	−	5.56218i	−0.464052	−	0.267921i	−0.713747	+	0.700404i	$0.753003\pi$
$432$		0			0
$433$	−7.42820	−	12.8660i	−0.356977	−	0.618302i	0.630478	−	0.776208i	$-0.282859\pi$
$433$	−7.42820	−	12.8660i	−0.356977	−	0.618302i	−0.987454	+	0.157906i	$0.949526\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			7.85641i			0.375823i
$438$		0			0
$439$	8.83013	−	15.2942i	0.421439	−	0.729954i	−0.574642	−	0.818405i	$-0.694859\pi$
$439$	8.83013	−	15.2942i	0.421439	−	0.729954i	0.996080	+	0.0884515i	$0.0281918\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	36.3923			1.72905			0.864525	−	0.502589i	$-0.167619\pi$
$443$	36.3923			1.72905			0.864525	+	0.502589i	$0.167619\pi$
$444$		0			0
$445$	0.339746	−	0.588457i	0.0161055	−	0.0278955i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.1962	−	11.6603i	0.953115	−	0.550281i	0.0590680	−	0.998254i	$-0.481187\pi$
$449$	20.1962	−	11.6603i	0.953115	−	0.550281i	0.894047	+	0.447973i	$0.147854\pi$
$450$		0			0
$451$	26.9545	+	46.6865i	1.26924	+	2.19838i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.679492	−	0.196152i	−0.0318551	−	0.00919577i
$456$		0			0
$457$	16.1603	+	9.33013i	0.755945	+	0.436445i	0.827838	−	0.560967i	$-0.189571\pi$
$457$	16.1603	+	9.33013i	0.755945	+	0.436445i	−0.0718931	+	0.997412i	$0.522904\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	22.2846	−	12.8660i	1.03790	−	0.599231i	0.118661	−	0.992935i	$-0.462140\pi$
$461$	22.2846	−	12.8660i	1.03790	−	0.599231i	0.919237	+	0.393704i	$0.128807\pi$
$462$		0			0
$463$			28.0526i			1.30371i	0.758342	+	0.651856i	$0.226010\pi$
$463$			28.0526i			1.30371i	−0.758342	+	0.651856i	$0.773990\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.5885			0.582524			0.291262	−	0.956643i	$-0.405925\pi$
$467$	12.5885			0.582524			0.291262	+	0.956643i	$0.405925\pi$
$468$		0			0
$469$	−8.14359			−0.376036
$470$		0			0
$471$		0			0
$472$		0			0
$473$			36.2487i			1.66672i
$474$		0			0
$475$	5.41154	−	3.12436i	0.248299	−	0.143355i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−22.9808	−	13.2679i	−1.05002	−	0.606228i	−0.127363	−	0.991856i	$-0.540651\pi$
$479$	−22.9808	−	13.2679i	−1.05002	−	0.606228i	−0.922654	+	0.385628i	$0.873985\pi$
$480$		0			0
$481$	−36.6244	+	9.06218i	−1.66993	+	0.413200i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.803848	+	1.39230i	0.0365008	+	0.0632213i
$486$		0			0
$487$	18.2942	−	10.5622i	0.828991	−	0.478618i	−0.0245163	−	0.999699i	$-0.507805\pi$
$487$	18.2942	−	10.5622i	0.828991	−	0.478618i	0.853507	+	0.521081i	$0.174471\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.63397	−	4.56218i	0.118870	−	0.205888i	−0.800450	−	0.599399i	$-0.795406\pi$
$491$	2.63397	−	4.56218i	0.118870	−	0.205888i	0.919320	+	0.393511i	$0.128740\pi$
$492$		0			0
$493$	5.58846			0.251691
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.464102	−	0.803848i	0.0208178	−	0.0360575i
$498$		0			0
$499$			32.0000i			1.43252i	0.697835	+	0.716258i	$0.254147\pi$
$499$			32.0000i			1.43252i	−0.697835	+	0.716258i	$0.745853\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	5.49038	+	9.50962i	0.244804	+	0.424013i	0.962076	−	0.272780i	$-0.0879431\pi$
$503$	5.49038	+	9.50962i	0.244804	+	0.424013i	−0.717272	+	0.696793i	$0.754610\pi$
$504$		0			0
$505$	2.76795	+	1.59808i	0.123172	+	0.0711135i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.89230	−	5.13397i	−0.394144	−	0.227559i	0.289810	−	0.957084i	$-0.406408\pi$
$509$	−8.89230	−	5.13397i	−0.394144	−	0.227559i	−0.683954	+	0.729525i	$0.739741\pi$
$510$		0			0
$511$	3.56218	+	6.16987i	0.157581	+	0.272939i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	5.01924i		−	0.221174i
$516$		0			0
$517$	−19.3923	+	33.5885i	−0.852873	+	1.47722i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17.4449			0.764273			0.382137	−	0.924106i	$-0.375188\pi$
$521$	17.4449			0.764273			0.382137	+	0.924106i	$0.375188\pi$
$522$		0			0
$523$	18.2224	−	31.5622i	0.796811	−	1.38012i	−0.124871	−	0.992173i	$-0.539852\pi$
$523$	18.2224	−	31.5622i	0.796811	−	1.38012i	0.921683	−	0.387945i	$-0.126815\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.7321	−	6.19615i	0.467495	−	0.269909i
$528$		0			0
$529$	−7.69615	−	13.3301i	−0.334615	−	0.579571i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−39.8731	+	9.86603i	−1.72709	+	0.427345i
$534$		0			0
$535$	0.0455173	+	0.0262794i	0.00196789	+	0.00113616i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	26.4904	−	15.2942i	1.14102	−	0.658769i
$540$		0			0
$541$			40.3205i			1.73351i	0.498731	+	0.866757i	$0.333800\pi$
$541$			40.3205i			1.73351i	−0.498731	+	0.866757i	$0.666200\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.46410			−0.0627152
$546$		0			0
$547$	−6.19615			−0.264928			−0.132464	−	0.991188i	$-0.542289\pi$
$547$	−6.19615			−0.264928			−0.132464	+	0.991188i	$0.542289\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	3.12436i		−	0.133102i
$552$		0			0
$553$	−6.00000	+	3.46410i	−0.255146	+	0.147309i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−26.3038	−	15.1865i	−1.11453	−	0.643474i	−0.174531	−	0.984652i	$-0.555841\pi$
$557$	−26.3038	−	15.1865i	−1.11453	−	0.643474i	−0.939999	+	0.341178i	$0.889174\pi$
$558$		0			0
$559$	−26.5359	−	7.66025i	−1.12235	−	0.323994i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.5359	+	18.2487i	0.444035	+	0.769091i	0.997984	−	0.0634589i	$-0.0202132\pi$
$563$	10.5359	+	18.2487i	0.444035	+	0.769091i	−0.553949	+	0.832550i	$0.686880\pi$
$564$		0			0
$565$	4.33013	−	2.50000i	0.182170	−	0.105176i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	19.3205	−	33.4641i	0.809958	−	1.40289i	−0.102935	−	0.994688i	$-0.532823\pi$
$569$	19.3205	−	33.4641i	0.809958	−	1.40289i	0.912893	−	0.408200i	$-0.133843\pi$
$570$		0			0
$571$	−24.0526			−1.00657			−0.503284	−	0.864121i	$-0.667875\pi$
$571$	−24.0526			−1.00657			−0.503284	+	0.864121i	$0.667875\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−15.2679	+	26.4449i	−0.636717	+	1.10283i
$576$		0			0
$577$		−	0.267949i		−	0.0111549i	−0.999984	−	0.00557744i	$-0.998225\pi$
$577$		−	0.267949i		−	0.0111549i	0.999984	−	0.00557744i	$-0.00177536\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.73205	+	6.46410i	0.154832	+	0.268176i
$582$		0			0
$583$	1.90192	+	1.09808i	0.0787696	+	0.0454777i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	0.757914	−	0.652355i	$-0.226219\pi$
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	−0.185999	+	0.982550i	$0.559552\pi$
$588$		0			0
$589$	−3.46410	−	6.00000i	−0.142736	−	0.247226i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			36.8564i			1.51351i	0.653698	+	0.756756i	$0.273217\pi$
$593$			36.8564i			1.51351i	−0.653698	+	0.756756i	$0.726783\pi$
$594$		0			0
$595$	0.222432	−	0.385263i	0.00911882	−	0.0157943i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−9.46410			−0.386693			−0.193346	−	0.981131i	$-0.561934\pi$
$599$	−9.46410			−0.386693			−0.193346	+	0.981131i	$0.561934\pi$
$600$		0			0
$601$	2.96410	−	5.13397i	0.120908	−	0.209419i	−0.799218	−	0.601041i	$-0.794753\pi$
$601$	2.96410	−	5.13397i	0.120908	−	0.209419i	0.920126	+	0.391622i	$0.128086\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.64359	+	1.52628i	−0.107477	+	0.0620521i
$606$		0			0
$607$	0.392305	+	0.679492i	0.0159232	+	0.0275797i	0.873877	−	0.486147i	$-0.161598\pi$
$607$	0.392305	+	0.679492i	0.0159232	+	0.0275797i	−0.857954	+	0.513726i	$0.828265\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−20.4904	−	21.2942i	−0.828952	−	0.861472i
$612$		0			0
$613$	9.86603	+	5.69615i	0.398485	+	0.230065i	0.685830	−	0.727762i	$-0.259439\pi$
$613$	9.86603	+	5.69615i	0.398485	+	0.230065i	−0.287345	+	0.957827i	$0.592773\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	30.5263	−	17.6244i	1.22894	−	0.709530i	0.262133	−	0.965032i	$-0.415574\pi$
$617$	30.5263	−	17.6244i	1.22894	−	0.709530i	0.966809	+	0.255502i	$0.0822407\pi$
$618$		0			0
$619$		−	10.5359i		−	0.423474i	−0.977327	−	0.211737i	$-0.932088\pi$
$619$		−	10.5359i		−	0.423474i	0.977327	−	0.211737i	$-0.0679119\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.85641			0.0743754
$624$		0			0
$625$	23.9282			0.957128
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	23.7321i		−	0.946259i
$630$		0			0
$631$	−41.3205	+	23.8564i	−1.64494	+	0.949709i	−0.665904	+	0.746037i	$0.731954\pi$
$631$	−41.3205	+	23.8564i	−1.64494	+	0.949709i	−0.979039	+	0.203671i	$0.934713\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.14359	−	2.39230i	−0.164433	−	0.0949357i
$636$		0			0
$637$	5.59808	+	22.6244i	0.221804	+	0.896410i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.9904	−	22.5000i	−0.513089	−	0.888697i	−0.999885	−	0.0151806i	$-0.995168\pi$
$641$	−12.9904	−	22.5000i	−0.513089	−	0.888697i	0.486796	−	0.873516i	$-0.338166\pi$
$642$		0			0
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	−0.244359	−	0.969685i	$-0.578577\pi$
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	0.717592	+	0.696463i	$0.245244\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.1244	−	22.7321i	0.515972	−	0.893689i	−0.483856	−	0.875147i	$-0.660764\pi$
$647$	13.1244	−	22.7321i	0.515972	−	0.893689i	0.999828	−	0.0185417i	$-0.00590236\pi$
$648$		0			0
$649$	−37.8564			−1.48599
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.26795	+	9.12436i	−0.206151	+	0.357064i	−0.950499	−	0.310728i	$-0.899427\pi$
$653$	−5.26795	+	9.12436i	−0.206151	+	0.357064i	0.744348	+	0.667792i	$0.232760\pi$
$654$		0			0
$655$			3.60770i			0.140964i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.1244	−	33.1244i	−0.744979	−	1.29034i	−0.950205	−	0.311627i	$-0.899126\pi$
$659$	−19.1244	−	33.1244i	−0.744979	−	1.29034i	0.205225	−	0.978715i	$-0.434207\pi$
$660$		0			0
$661$	8.13397	+	4.69615i	0.316375	+	0.182659i	0.649776	−	0.760126i	$-0.274863\pi$
$661$	8.13397	+	4.69615i	0.316375	+	0.182659i	−0.333401	+	0.942785i	$0.608196\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.215390	−	0.124356i	−0.00835248	−	0.00482231i
$666$		0			0
$667$	7.63397	+	13.2224i	0.295589	+	0.511975i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			5.66025i			0.218512i
$672$		0			0
$673$	7.03590	−	12.1865i	0.271214	−	0.469756i	−0.697959	−	0.716138i	$-0.745908\pi$
$673$	7.03590	−	12.1865i	0.271214	−	0.469756i	0.969173	+	0.246381i	$0.0792416\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	38.5359			1.48105			0.740527	−	0.672026i	$-0.234576\pi$
$677$	38.5359			1.48105			0.740527	+	0.672026i	$0.234576\pi$
$678$		0			0
$679$	−2.19615	+	3.80385i	−0.0842806	+	0.145978i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−32.7846	+	18.9282i	−1.25447	+	0.724268i	−0.971994	−	0.235007i	$-0.924489\pi$
$683$	−32.7846	+	18.9282i	−1.25447	+	0.724268i	−0.282475	+	0.959275i	$0.591155\pi$
$684$		0			0
$685$	0.258330	+	0.447441i	0.00987029	+	0.0170958i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.20577	+	1.16025i	−0.0459362	+	0.0442022i
$690$		0			0
$691$	−22.8109	−	13.1699i	−0.867767	−	0.501006i	−0.00116153	−	0.999999i	$-0.500370\pi$
$691$	−22.8109	−	13.1699i	−0.867767	−	0.501006i	−0.866606	+	0.498994i	$0.833703\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.28719	−	1.32051i	0.0867580	−	0.0500897i
$696$		0			0
$697$		−	25.8372i		−	0.978653i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	31.3205			1.18296			0.591480	−	0.806320i	$-0.298544\pi$
$701$	31.3205			1.18296			0.591480	+	0.806320i	$0.298544\pi$
$702$		0			0
$703$	−13.2679			−0.500410
$704$		0			0
$705$		0			0
$706$		0			0
$707$			8.73205i			0.328403i
$708$		0			0
$709$	35.3827	−	20.4282i	1.32882	−	0.767197i	0.343707	−	0.939077i	$-0.388317\pi$
$709$	35.3827	−	20.4282i	1.32882	−	0.767197i	0.985118	+	0.171880i	$0.0549841\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	29.3205	+	16.9282i	1.09806	+	0.633966i
$714$		0			0
$715$	−1.09808	−	4.43782i	−0.0410657	−	0.165965i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.2679	−	19.5167i	−0.420224	−	0.727849i	0.575737	−	0.817635i	$-0.304715\pi$
$719$	−11.2679	−	19.5167i	−0.420224	−	0.727849i	−0.995961	+	0.0897860i	$0.971382\pi$
$720$		0			0
$721$	11.8756	−	6.85641i	0.442272	−	0.255346i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	6.07180	−	10.5167i	0.225501	−	0.390579i
$726$		0			0
$727$	20.9808			0.778133			0.389067	−	0.921210i	$-0.372798\pi$
$727$	20.9808			0.778133			0.389067	+	0.921210i	$0.372798\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.68653	−	15.0455i	0.321283	−	0.556479i
$732$		0			0
$733$		−	19.0000i		−	0.701781i	−0.936416	−	0.350891i	$-0.885879\pi$
$733$		−	19.0000i		−	0.701781i	0.936416	−	0.350891i	$-0.114121\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−26.3205	−	45.5885i	−0.969528	−	1.67927i
$738$		0			0
$739$	−9.46410	−	5.46410i	−0.348143	−	0.201000i	0.315724	−	0.948851i	$-0.397753\pi$
$739$	−9.46410	−	5.46410i	−0.348143	−	0.201000i	−0.663867	+	0.747851i	$0.731086\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.9090	−	13.8038i	−0.877135	−	0.506414i	−0.00742221	−	0.999972i	$-0.502363\pi$
$743$	−23.9090	−	13.8038i	−0.877135	−	0.506414i	−0.869713	+	0.493558i	$0.835696\pi$
$744$		0			0
$745$	0.375644	+	0.650635i	0.0137625	+	0.0238374i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			0.143594i			0.00524679i
$750$		0			0
$751$	−7.95448	+	13.7776i	−0.290263	+	0.502751i	−0.973872	−	0.227098i	$-0.927076\pi$
$751$	−7.95448	+	13.7776i	−0.290263	+	0.502751i	0.683609	+	0.729849i	$0.260410\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.875644			0.0318680
$756$		0			0
$757$	−3.53590	+	6.12436i	−0.128514	+	0.222593i	−0.923101	−	0.384557i	$-0.874354\pi$
$757$	−3.53590	+	6.12436i	−0.128514	+	0.222593i	0.794587	+	0.607151i	$0.207688\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	20.1962	−	11.6603i	0.732110	−	0.422684i	−0.0870836	−	0.996201i	$-0.527755\pi$
$761$	20.1962	−	11.6603i	0.732110	−	0.422684i	0.819194	+	0.573517i	$0.194421\pi$
$762$		0			0
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.00000	−	27.7128i	0.288863	−	1.00065i
$768$		0			0
$769$	−13.9808	−	8.07180i	−0.504159	−	0.291076i	0.226270	−	0.974065i	$-0.427347\pi$
$769$	−13.9808	−	8.07180i	−0.504159	−	0.291076i	−0.730429	+	0.682988i	$0.760680\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−30.3731	+	17.5359i	−1.09244	+	0.630722i	−0.934226	−	0.356682i	$-0.883908\pi$
$773$	−30.3731	+	17.5359i	−1.09244	+	0.630722i	−0.158217	+	0.987404i	$0.550575\pi$
$774$		0			0
$775$		−	26.9282i		−	0.967290i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−14.4449			−0.517541
$780$		0			0
$781$	6.00000			0.214697
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	6.32051i		−	0.225589i
$786$		0			0
$787$	−34.0526	+	19.6603i	−1.21384	+	0.700812i	−0.963594	−	0.267369i	$-0.913846\pi$
$787$	−34.0526	+	19.6603i	−1.21384	+	0.700812i	−0.250248	+	0.968182i	$0.580512\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	11.8301	+	6.83013i	0.420631	+	0.242851i
$792$		0			0
$793$	−4.14359	−	1.19615i	−0.147143	−	0.0424766i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$		0			0
$799$	16.0981	−	9.29423i	0.569509	−	0.328806i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−23.0263	+	39.8827i	−0.812580	+	1.40743i
$804$		0			0
$805$	1.21539			0.0428369
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.2058	+	19.4090i	−0.393974	+	0.682383i	−0.992970	−	0.118369i	$-0.962233\pi$
$809$	−11.2058	+	19.4090i	−0.393974	+	0.682383i	0.598996	+	0.800752i	$0.295567\pi$
$810$		0			0
$811$		−	45.1769i		−	1.58638i	−0.608977	−	0.793188i	$-0.708420\pi$
$811$		−	45.1769i		−	1.58638i	0.608977	−	0.793188i	$-0.291580\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.875644	+	1.51666i	0.0306725	+	0.0531263i
$816$		0			0
$817$	−8.41154	−	4.85641i	−0.294283	−	0.169904i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.1962	−	6.46410i	−0.390748	−	0.225599i	0.291736	−	0.956499i	$-0.405767\pi$
$821$	−11.1962	−	6.46410i	−0.390748	−	0.225599i	−0.682484	+	0.730900i	$0.739100\pi$
$822$		0			0
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	0.959177	+	0.282806i	$0.0912654\pi$
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	−0.234671	+	0.972075i	$0.575401\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			33.4641i			1.16366i	0.813310	+	0.581830i	$0.197663\pi$
$827$			33.4641i			1.16366i	−0.813310	+	0.581830i	$0.802337\pi$
$828$		0			0
$829$	6.06218	−	10.5000i	0.210548	−	0.364680i	−0.741338	−	0.671132i	$-0.765808\pi$
$829$	6.06218	−	10.5000i	0.210548	−	0.364680i	0.951886	+	0.306452i	$0.0991418\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−14.6603			−0.507948
$834$		0			0
$835$	−0.339746	+	0.588457i	−0.0117574	+	0.0203644i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.2487	−	7.07180i	0.422872	−	0.244146i	−0.273433	−	0.961891i	$-0.588159\pi$
$839$	12.2487	−	7.07180i	0.422872	−	0.244146i	0.696306	+	0.717745i	$0.254826\pi$
$840$		0			0
$841$	11.4641	+	19.8564i	0.395314	+	0.684704i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.48076	+	0.133975i	0.119742	+	0.00460887i
$846$		0			0
$847$	−7.22243	−	4.16987i	−0.248166	−	0.143279i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	56.1506	−	32.4186i	1.92482	−	1.11129i
$852$		0			0
$853$			8.17691i			0.279972i	0.990153	+	0.139986i	$0.0447058\pi$
$853$			8.17691i			0.279972i	−0.990153	+	0.139986i	$0.955294\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.4449			−0.664224			−0.332112	−	0.943240i	$-0.607761\pi$
$857$	−19.4449			−0.664224			−0.332112	+	0.943240i	$0.607761\pi$
$858$		0			0
$859$	22.8756			0.780507			0.390253	−	0.920707i	$-0.372387\pi$
$859$	22.8756			0.780507			0.390253	+	0.920707i	$0.372387\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	7.12436i		−	0.242516i	−0.992621	−	0.121258i	$-0.961307\pi$
$863$		−	7.12436i		−	0.242516i	0.992621	−	0.121258i	$-0.0386928\pi$
$864$		0			0
$865$	−3.80385	+	2.19615i	−0.129335	+	0.0746714i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−38.7846	−	22.3923i	−1.31568	−	0.759607i
$870$		0			0
$871$	38.9352	−	9.63397i	1.31927	−	0.326435i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.973721	−	1.68653i	−0.0329178	−	0.0570152i
$876$		0			0
$877$	−8.72243	+	5.03590i	−0.294536	+	0.170050i	−0.639985	−	0.768387i	$-0.721060\pi$
$877$	−8.72243	+	5.03590i	−0.294536	+	0.170050i	0.345450	+	0.938437i	$0.387726\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−25.9186	+	44.8923i	−0.873219	+	1.51246i	−0.0145717	+	0.999894i	$0.504638\pi$
$881$	−25.9186	+	44.8923i	−0.873219	+	1.51246i	−0.858648	+	0.512566i	$0.828695\pi$
$882$		0			0
$883$	29.0718			0.978344			0.489172	−	0.872187i	$-0.337299\pi$
$883$	29.0718			0.978344			0.489172	+	0.872187i	$0.337299\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.07180	+	8.78461i	−0.170294	+	0.294958i	−0.938523	−	0.345217i	$-0.887805\pi$
$887$	−5.07180	+	8.78461i	−0.170294	+	0.294958i	0.768228	+	0.640176i	$0.221138\pi$
$888$		0			0
$889$		−	13.0718i		−	0.438414i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.19615	−	9.00000i	−0.173883	−	0.301174i
$894$		0			0
$895$	5.11731	+	2.95448i	0.171053	+	0.0987575i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−11.6603	−	6.73205i	−0.388891	−	0.224526i
$900$		0			0
$901$	−0.526279	−	0.911543i	−0.0175329	−	0.0303679i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	2.35898i		−	0.0784153i
$906$		0			0
$907$	−7.80385	+	13.5167i	−0.259123	+	0.448813i	−0.966007	−	0.258516i	$-0.916767\pi$
$907$	−7.80385	+	13.5167i	−0.259123	+	0.448813i	0.706885	+	0.707329i	$0.250100\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.46410			−0.313560			−0.156780	−	0.987634i	$-0.550111\pi$
$911$	−9.46410			−0.313560			−0.156780	+	0.987634i	$0.550111\pi$
$912$		0			0
$913$	−24.1244	+	41.7846i	−0.798400	+	1.38287i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.53590	+	4.92820i	−0.281880	+	0.162744i
$918$		0			0
$919$	−28.9808	−	50.1962i	−0.955987	−	1.65582i	−0.732093	−	0.681205i	$-0.761456\pi$
$919$	−28.9808	−	50.1962i	−0.955987	−	1.65582i	−0.223894	−	0.974613i	$-0.571877\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.26795	+	4.39230i	−0.0417351	+	0.144574i
$924$		0			0
$925$	−44.6603	−	25.7846i	−1.46842	−	0.847793i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.00962	−	4.62436i	0.262787	−	0.151720i	−0.362818	−	0.931860i	$-0.618185\pi$
$929$	8.00962	−	4.62436i	0.262787	−	0.151720i	0.625605	+	0.780140i	$0.284852\pi$
$930$		0			0
$931$			8.19615i			0.268618i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.87564			0.0940436
$936$		0			0
$937$	43.2487			1.41287			0.706437	−	0.707776i	$-0.250301\pi$
$937$	43.2487			1.41287			0.706437	+	0.707776i	$0.250301\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	56.6410i		−	1.84644i	−0.384267	−	0.923222i	$-0.625546\pi$
$941$		−	56.6410i		−	1.84644i	0.384267	−	0.923222i	$-0.374454\pi$
$942$		0			0
$943$	61.1314	−	35.2942i	1.99071	−	1.14934i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.2487	−	17.4641i	−0.982951	−	0.567507i	−0.0797913	−	0.996812i	$-0.525425\pi$
$947$	−30.2487	−	17.4641i	−0.982951	−	0.567507i	−0.903160	+	0.429305i	$0.858759\pi$
$948$		0			0
$949$	−24.3301	−	25.2846i	−0.789789	−	0.820773i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	20.7846	+	36.0000i	0.673280	+	1.16615i	0.976969	+	0.213383i	$0.0684483\pi$
$953$	20.7846	+	36.0000i	0.673280	+	1.16615i	−0.303689	+	0.952771i	$0.598218\pi$
$954$		0			0
$955$	1.60770	−	0.928203i	0.0520238	−	0.0300360i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.705771	+	1.22243i	−0.0227905	+	0.0394744i
$960$		0			0
$961$	1.14359			0.0368901
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.10770	+	1.91858i	−0.0356580	+	0.0617614i
$966$		0			0
$967$		−	18.8756i		−	0.607000i	−0.952831	−	0.303500i	$-0.901845\pi$
$967$		−	18.8756i		−	0.607000i	0.952831	−	0.303500i	$-0.0981552\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.12436	+	15.8038i	0.292815	+	0.507170i	0.974474	−	0.224500i	$-0.0720748\pi$
$971$	9.12436	+	15.8038i	0.292815	+	0.507170i	−0.681660	+	0.731669i	$0.738741\pi$
$972$		0			0
$973$	6.24871	+	3.60770i	0.200324	+	0.115657i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27.7750	−	16.0359i	−0.888601	−	0.513034i	−0.0151161	−	0.999886i	$-0.504812\pi$
$977$	−27.7750	−	16.0359i	−0.888601	−	0.513034i	−0.873485	+	0.486852i	$0.838145\pi$
$978$		0			0
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		−	20.7846i		−	0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$983$		−	20.7846i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$984$		0			0
$985$	1.32051	−	2.28719i	0.0420749	−	0.0728758i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	47.4641			1.50927
$990$		0			0
$991$	−4.29423	+	7.43782i	−0.136411	+	0.236270i	−0.926135	−	0.377191i	$-0.876890\pi$
$991$	−4.29423	+	7.43782i	−0.136411	+	0.236270i	0.789725	+	0.613461i	$0.210223\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.882686	+	0.509619i	−0.0279830	+	0.0161560i
$996$		0			0
$997$	−19.3301	−	33.4808i	−0.612191	−	1.06035i	−0.990870	−	0.134818i	$-0.956955\pi$
$997$	−19.3301	−	33.4808i	−0.612191	−	1.06035i	0.378679	−	0.925528i	$-0.376378\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1872.2.by.h.433.2		4
3.2	odd	2		624.2.bv.e.433.1		4
4.3	odd	2		234.2.l.c.199.1		4
12.11	even	2		78.2.i.a.43.2	✓	4
13.10	even	6	inner	1872.2.by.h.1297.1		4
39.20	even	12		8112.2.a.bp.1.1		2
39.23	odd	6		624.2.bv.e.49.2		4
39.32	even	12		8112.2.a.bj.1.2		2
52.7	even	12		3042.2.a.p.1.2		2
52.19	even	12		3042.2.a.y.1.1		2
52.23	odd	6		234.2.l.c.127.1		4
52.35	odd	6		3042.2.b.i.1351.3		4
52.43	odd	6		3042.2.b.i.1351.2		4
60.23	odd	4		1950.2.y.g.199.1		4
60.47	odd	4		1950.2.y.b.199.2		4
60.59	even	2		1950.2.bc.d.901.1		4
156.11	odd	12		1014.2.e.g.991.1		4
156.23	even	6		78.2.i.a.49.2	yes	4
156.35	even	6		1014.2.b.e.337.2		4
156.47	odd	4		1014.2.e.g.529.1		4
156.59	odd	12		1014.2.a.k.1.1		2
156.71	odd	12		1014.2.a.i.1.2		2
156.83	odd	4		1014.2.e.i.529.2		4
156.95	even	6		1014.2.b.e.337.3		4
156.107	even	6		1014.2.i.a.361.1		4
156.119	odd	12		1014.2.e.i.991.2		4
156.155	even	2		1014.2.i.a.823.1		4
780.23	odd	12		1950.2.y.b.49.2		4
780.179	even	6		1950.2.bc.d.751.1		4
780.647	odd	12		1950.2.y.g.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.2	✓	4	12.11	even	2
78.2.i.a.49.2	yes	4	156.23	even	6
234.2.l.c.127.1		4	52.23	odd	6
234.2.l.c.199.1		4	4.3	odd	2
624.2.bv.e.49.2		4	39.23	odd	6
624.2.bv.e.433.1		4	3.2	odd	2
1014.2.a.i.1.2		2	156.71	odd	12
1014.2.a.k.1.1		2	156.59	odd	12
1014.2.b.e.337.2		4	156.35	even	6
1014.2.b.e.337.3		4	156.95	even	6
1014.2.e.g.529.1		4	156.47	odd	4
1014.2.e.g.991.1		4	156.11	odd	12
1014.2.e.i.529.2		4	156.83	odd	4
1014.2.e.i.991.2		4	156.119	odd	12
1014.2.i.a.361.1		4	156.107	even	6
1014.2.i.a.823.1		4	156.155	even	2
1872.2.by.h.433.2		4	1.1	even	1	trivial
1872.2.by.h.1297.1		4	13.10	even	6	inner
1950.2.y.b.49.2		4	780.23	odd	12
1950.2.y.b.199.2		4	60.47	odd	4
1950.2.y.g.49.1		4	780.647	odd	12
1950.2.y.g.199.1		4	60.23	odd	4
1950.2.bc.d.751.1		4	780.179	even	6
1950.2.bc.d.901.1		4	60.59	even	2
3042.2.a.p.1.2		2	52.7	even	12
3042.2.a.y.1.1		2	52.19	even	12
3042.2.b.i.1351.2		4	52.43	odd	6
3042.2.b.i.1351.3		4	52.35	odd	6
8112.2.a.bj.1.2		2	39.32	even	12
8112.2.a.bp.1.1		2	39.20	even	12

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:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.267949i q^{5} +(-0.633975 + 0.366025i) q^{7} +O(q^{10})\)	\(q+0.267949i q^{5} +(-0.633975 + 0.366025i) q^{7} +(-4.09808 - 2.36603i) q^{11} +(2.59808 - 2.50000i) q^{13} +(1.13397 + 1.96410i) q^{17} +(1.09808 - 0.633975i) q^{19} +(-3.09808 + 5.36603i) q^{23} +4.92820 q^{25} +(1.23205 - 2.13397i) q^{29} -5.46410i q^{31} +(-0.0980762 - 0.169873i) q^{35} +(-9.06218 - 5.23205i) q^{37} +(-9.86603 - 5.69615i) q^{41} +(-3.83013 - 6.63397i) q^{43} -8.19615i q^{47} +(-3.23205 + 5.59808i) q^{49} -0.464102 q^{53} +(0.633975 - 1.09808i) q^{55} +(6.92820 - 4.00000i) q^{59} +(-0.598076 - 1.03590i) q^{61} +(0.669873 + 0.696152i) q^{65} +(9.63397 + 5.56218i) q^{67} +(-1.09808 + 0.633975i) q^{71} -9.73205i q^{73} +3.46410 q^{77} +9.46410 q^{79} -10.1962i q^{83} +(-0.526279 + 0.303848i) q^{85} +(-2.19615 - 1.26795i) q^{89} +(-0.732051 + 2.53590i) q^{91} +(0.169873 + 0.294229i) q^{95} +(5.19615 - 3.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{7}+O(q^{10}) \) 4 * q - 6 * q^7	\( 4 q - 6 q^{7} - 6 q^{11} + 8 q^{17} - 6 q^{19} - 2 q^{23} - 8 q^{25} - 2 q^{29} + 10 q^{35} - 12 q^{37} - 36 q^{41} + 2 q^{43} - 6 q^{49} + 12 q^{53} + 6 q^{55} + 8 q^{61} + 20 q^{65} + 42 q^{67} + 6 q^{71} + 24 q^{79} + 36 q^{85} + 12 q^{89} + 4 q^{91} + 18 q^{95}+O(q^{100}) \) 4 * q - 6 * q^7 - 6 * q^11 + 8 * q^17 - 6 * q^19 - 2 * q^23 - 8 * q^25 - 2 * q^29 + 10 * q^35 - 12 * q^37 - 36 * q^41 + 2 * q^43 - 6 * q^49 + 12 * q^53 + 6 * q^55 + 8 * q^61 + 20 * q^65 + 42 * q^67 + 6 * q^71 + 24 * q^79 + 36 * q^85 + 12 * q^89 + 4 * q^91 + 18 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more