LMFDB - Embedded newform 1872.2.by.h.1297.1

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			1297.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1872.1297
Dual form			1872.2.by.h.433.2

$q$-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 $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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	$-0.980917\pi$
$5$		−	0.267949i		−	0.119831i	0.998203	−	0.0599153i	$-0.0190830\pi$
$6$		0			0
$7$	−0.633975	−	0.366025i	−0.239620	−	0.138345i	0.375382	−	0.926870i	$-0.377511\pi$
$7$	−0.633975	−	0.366025i	−0.239620	−	0.138345i	−0.615002	+	0.788526i	$0.710845\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.09808	+	2.36603i	−1.23562	+	0.713384i	−0.968195	−	0.250196i	$-0.919505\pi$
$11$	−4.09808	+	2.36603i	−1.23562	+	0.713384i	−0.267421	+	0.963580i	$0.586172\pi$
$12$		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	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	1.13397	−	1.96410i	0.275029	−	0.476365i	0.970143	+	0.242536i	$0.0779791\pi$
$18$		0			0
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	0.620641	−	0.784095i	$-0.286872\pi$
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	−0.368725	+	0.929538i	$0.620206\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.09808	−	5.36603i	−0.645994	−	1.11889i	−0.984071	−	0.177775i	$-0.943110\pi$
$23$	−3.09808	−	5.36603i	−0.645994	−	1.11889i	0.338078	−	0.941118i	$-0.390223\pi$
$24$		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	0.957449	−	0.288604i	$-0.0931910\pi$
$29$	1.23205	+	2.13397i	0.228786	+	0.396269i	−0.728663	+	0.684873i	$0.759858\pi$
$30$		0			0
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$		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	−0.999932	−	0.0116456i	$-0.996293\pi$
$37$	−9.06218	+	5.23205i	−1.48981	+	0.860144i	−0.489881	+	0.871789i	$0.662960\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.86603	+	5.69615i	−1.54081	+	0.889590i	−0.542027	+	0.840361i	$0.682343\pi$
$41$	−9.86603	+	5.69615i	−1.54081	+	0.889590i	−0.998788	+	0.0492283i	$0.984324\pi$
$42$		0			0
$43$	−3.83013	+	6.63397i	−0.584089	+	1.01167i	0.410899	+	0.911681i	$0.365215\pi$
$43$	−3.83013	+	6.63397i	−0.584089	+	1.01167i	−0.994988	+	0.0999910i	$0.968119\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			8.19615i			1.19553i	0.801671	+	0.597766i	$0.203945\pi$
$47$			8.19615i			1.19553i	−0.801671	+	0.597766i	$0.796055\pi$
$48$		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	0.877841	−	0.478953i	$-0.158984\pi$
$59$	6.92820	+	4.00000i	0.901975	+	0.520756i	0.0241347	+	0.999709i	$0.492317\pi$
$60$		0			0
$61$	−0.598076	+	1.03590i	−0.0765758	+	0.132633i	−0.901770	−	0.432215i	$-0.857732\pi$
$61$	−0.598076	+	1.03590i	−0.0765758	+	0.132633i	0.825195	+	0.564848i	$0.191065\pi$
$62$		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	0.221664	−	0.975123i	$-0.428851\pi$
$67$	9.63397	−	5.56218i	1.17698	−	0.679528i	0.955313	+	0.295595i	$0.0955179\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.09808	−	0.633975i	−0.130318	−	0.0752389i	0.433424	−	0.901190i	$-0.357305\pi$
$71$	−1.09808	−	0.633975i	−0.130318	−	0.0752389i	−0.563742	+	0.825951i	$0.690639\pi$
$72$		0			0
$73$			9.73205i			1.13905i	0.821974	+	0.569525i	$0.192873\pi$
$73$			9.73205i			1.13905i	−0.821974	+	0.569525i	$0.807127\pi$
$74$		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	$0.189040\pi$
$83$			10.1962i			1.11917i	−0.828772	+	0.559587i	$0.810960\pi$
$84$		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	−0.611859	−	0.790967i	$-0.709578\pi$
$89$	−2.19615	+	1.26795i	−0.232792	+	0.134402i	0.379068	+	0.925369i	$0.376245\pi$
$90$		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	0.740034	−	0.672569i	$-0.234809\pi$
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	−0.212445	+	0.977173i	$0.568143\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.96410	+	10.3301i	0.593450	+	1.02789i	0.993764	+	0.111508i	$0.0355680\pi$
$101$	5.96410	+	10.3301i	0.593450	+	1.02789i	−0.400313	+	0.916378i	$0.631099\pi$
$102$		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	0.870727	−	0.491766i	$-0.163649\pi$
$107$	0.0980762	+	0.169873i	0.00948139	+	0.0164222i	−0.861246	+	0.508189i	$0.830315\pi$
$108$		0			0
$109$		−	5.46410i		−	0.523366i	−0.965154	−	0.261683i	$-0.915723\pi$
$109$		−	5.46410i		−	0.523366i	0.965154	−	0.261683i	$-0.0842775\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.33013	+	16.1603i	−0.877705	+	1.52023i	−0.0238510	+	0.999716i	$0.507593\pi$
$113$	−9.33013	+	16.1603i	−0.877705	+	1.52023i	−0.853854	+	0.520513i	$0.825741\pi$
$114$		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	−0.924571	−	0.381010i	$-0.875576\pi$
$127$	−8.92820	−	15.4641i	−0.792250	−	1.37222i	0.132321	−	0.991207i	$-0.457757\pi$
$128$		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	0.569634	−	0.821898i	$-0.307085\pi$
$137$	1.66987	+	0.964102i	0.142667	+	0.0823688i	−0.426968	+	0.904267i	$0.640418\pi$
$138$		0			0
$139$	−4.92820	+	8.53590i	−0.418005	+	0.724005i	−0.995739	−	0.0922197i	$-0.970604\pi$
$139$	−4.92820	+	8.53590i	−0.418005	+	0.724005i	0.577734	+	0.816225i	$0.303937\pi$
$140$		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	0.596154	−	0.802870i	$-0.296695\pi$
$149$	2.42820	+	1.40192i	0.198926	+	0.114850i	−0.397228	+	0.917720i	$0.630028\pi$
$150$		0			0
$151$			3.26795i			0.265942i	0.991120	+	0.132971i	$0.0424517\pi$
$151$			3.26795i			0.265942i	−0.991120	+	0.132971i	$0.957548\pi$
$152$		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	0.705016	−	0.709192i	$-0.250940\pi$
$163$	5.66025	+	3.26795i	0.443345	+	0.255966i	−0.261670	+	0.965157i	$0.584273\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.19615	−	1.26795i	0.169943	−	0.0981169i	−0.412616	−	0.910905i	$-0.635385\pi$
$167$	2.19615	−	1.26795i	0.169943	−	0.0981169i	0.582559	+	0.812788i	$0.302051\pi$
$168$		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	−0.365755	−	0.930711i	$-0.619189\pi$
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	0.988897	−	0.148602i	$-0.0474774\pi$
$174$		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	0.902573	+	0.430538i	$0.141676\pi$
$179$	11.0263	+	19.0981i	0.824143	+	1.42746i	−0.0784298	+	0.996920i	$0.524991\pi$
$180$		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	−0.963706	−	0.266966i	$-0.913979\pi$
$191$	−3.46410	+	6.00000i	−0.250654	+	0.434145i	0.713052	+	0.701111i	$0.247312\pi$
$192$		0			0
$193$	7.16025	−	4.13397i	0.515406	−	0.297570i	−0.219647	−	0.975579i	$-0.570490\pi$
$193$	7.16025	−	4.13397i	0.515406	−	0.297570i	0.735053	+	0.678009i	$0.237157\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.53590	+	4.92820i	−0.608158	+	0.351120i	−0.772244	−	0.635326i	$-0.780866\pi$
$197$	−8.53590	+	4.92820i	−0.608158	+	0.351120i	0.164086	+	0.986446i	$0.447532\pi$
$198$		0			0
$199$	1.90192	−	3.29423i	0.134824	−	0.233522i	−0.790706	−	0.612196i	$-0.790286\pi$
$199$	1.90192	−	3.29423i	0.134824	−	0.233522i	0.925530	+	0.378674i	$0.123620\pi$
$200$		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	0.780476	−	0.625186i	$-0.214977\pi$
$211$	−2.19615	−	3.80385i	−0.151189	−	0.261868i	−0.931665	+	0.363319i	$0.881644\pi$
$212$		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	−0.0705277	−	0.997510i	$-0.522468\pi$
$223$	11.3205	−	6.53590i	0.758077	−	0.437676i	0.828605	+	0.559834i	$0.189135\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.56218	+	0.901924i	0.103685	+	0.0598628i	0.550946	−	0.834541i	$-0.314267\pi$
$227$	1.56218	+	0.901924i	0.103685	+	0.0598628i	−0.447261	+	0.894404i	$0.647600\pi$
$228$		0			0
$229$		−	15.8564i		−	1.04782i	−0.851773	−	0.523910i	$-0.824473\pi$
$229$		−	15.8564i		−	1.04782i	0.851773	−	0.523910i	$-0.175527\pi$
$230$		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	$-0.898855\pi$
$239$		−	9.66025i		−	0.624870i	0.949939	−	0.312435i	$-0.101145\pi$
$240$		0			0
$241$	−15.2321	−	8.79423i	−0.981183	−	0.566486i	−0.0785557	−	0.996910i	$-0.525031\pi$
$241$	−15.2321	−	8.79423i	−0.981183	−	0.566486i	−0.902627	+	0.430424i	$0.858364\pi$
$242$		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	−0.744266	−	0.667883i	$-0.767200\pi$
$251$	3.26795	−	5.66025i	0.206271	−	0.357272i	0.950537	+	0.310611i	$0.100534\pi$
$252$		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	−0.896840	−	0.442355i	$-0.854143\pi$
$257$	−13.3301	−	23.0885i	−0.831510	−	1.44022i	0.0653297	−	0.997864i	$-0.479190\pi$
$258$		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	−0.867149	−	0.498049i	$-0.834050\pi$
$263$	−14.0263	−	24.2942i	−0.864897	−	1.49805i	0.00225153	−	0.999997i	$-0.499283\pi$
$264$		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	−0.887479	−	0.460848i	$-0.847545\pi$
$269$	−0.732051	+	1.26795i	−0.0446339	+	0.0773082i	0.842845	+	0.538156i	$0.180879\pi$
$270$		0			0
$271$	5.07180	−	2.92820i	0.308090	−	0.177876i	−0.337982	−	0.941153i	$-0.609744\pi$
$271$	5.07180	−	2.92820i	0.308090	−	0.177876i	0.646071	+	0.763277i	$0.276411\pi$
$272$		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	−0.898080	−	0.439832i	$-0.855038\pi$
$277$	−1.13397	+	1.96410i	−0.0681339	+	0.118011i	0.829946	+	0.557844i	$0.188371\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	22.3205i		−	1.33153i	−0.746162	−	0.665765i	$-0.768105\pi$
$281$		−	22.3205i		−	1.33153i	0.746162	−	0.665765i	$-0.231895\pi$
$282$		0			0
$283$	−4.16987	−	7.22243i	−0.247873	−	0.429329i	0.715062	−	0.699061i	$-0.246398\pi$
$283$	−4.16987	−	7.22243i	−0.247873	−	0.429329i	−0.962936	+	0.269732i	$0.913065\pi$
$284$		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	0.820049	−	0.572294i	$-0.193946\pi$
$293$	12.5718	+	7.25833i	0.734452	+	0.424036i	−0.0855965	+	0.996330i	$0.527280\pi$
$294$		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	$0.0788157\pi$
$307$			8.58846i			0.490169i	−0.969502	+	0.245085i	$0.921184\pi$
$308$		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	$-0.970102\pi$
$317$		−	3.33975i		−	0.187579i	0.995592	−	0.0937894i	$-0.0298980\pi$
$318$		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	0.893708	−	0.448649i	$-0.148095\pi$
$331$	17.3205	+	10.0000i	0.952021	+	0.549650i	0.0583130	+	0.998298i	$0.481428\pi$
$332$		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	−0.960208	−	0.279286i	$-0.909902\pi$
$347$	−4.43782	+	7.68653i	−0.238235	+	0.412635i	0.721973	+	0.691921i	$0.243235\pi$
$348$		0			0
$349$	16.7321	−	9.66025i	0.895646	−	0.517102i	0.0198610	−	0.999803i	$-0.493678\pi$
$349$	16.7321	−	9.66025i	0.895646	−	0.517102i	0.875785	+	0.482701i	$0.160344\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.1340	+	9.89230i	−0.911949	+	0.526514i	−0.881058	−	0.473008i	$-0.843168\pi$
$353$	−17.1340	+	9.89230i	−0.911949	+	0.526514i	−0.0308916	+	0.999523i	$0.509835\pi$
$354$		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	$-0.791078\pi$
$359$		−	23.1244i		−	1.22046i	0.792226	−	0.610228i	$-0.208922\pi$
$360$		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	0.607197	−	0.794551i	$-0.292294\pi$
$367$	−7.36603	−	12.7583i	−0.384503	−	0.665979i	−0.991700	+	0.128572i	$0.958961\pi$
$368$		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	−0.701953	−	0.712223i	$-0.747688\pi$
$373$	5.13397	−	8.89230i	0.265827	−	0.460426i	0.967780	+	0.251797i	$0.0810216\pi$
$374$		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	−0.532211	−	0.846611i	$-0.678639\pi$
$379$	−1.26795	+	0.732051i	−0.0651302	+	0.0376029i	0.467081	+	0.884214i	$0.345306\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.73205	−	2.73205i	−0.241797	−	0.139601i	0.374206	−	0.927346i	$-0.377915\pi$
$383$	−4.73205	−	2.73205i	−0.241797	−	0.139601i	−0.616002	+	0.787744i	$0.711249\pi$
$384$		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	0.491450	−	0.870906i	$-0.336467\pi$
$397$	−0.339746	−	0.196152i	−0.0170514	−	0.00984461i	−0.508501	+	0.861061i	$0.669800\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.9904	−	10.9641i	0.948334	−	0.547521i	0.0557713	−	0.998444i	$-0.482238\pi$
$401$	18.9904	−	10.9641i	0.948334	−	0.547521i	0.892563	+	0.450922i	$0.148905\pi$
$402$		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	0.162366	−	0.986731i	$-0.448088\pi$
$409$	−12.3564	−	7.13397i	−0.610985	−	0.352752i	−0.773351	+	0.633978i	$0.781421\pi$
$410$		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	0.965533	−	0.260281i	$-0.0838153\pi$
$419$	5.26795	+	9.12436i	0.257356	+	0.445754i	−0.708177	+	0.706035i	$0.750482\pi$
$420$		0			0
$421$			32.7128i			1.59432i	0.603765	+	0.797162i	$0.293667\pi$
$421$			32.7128i			1.59432i	−0.603765	+	0.797162i	$0.706333\pi$
$422$		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	−0.713747	−	0.700404i	$-0.753003\pi$
$431$	−9.63397	+	5.56218i	−0.464052	+	0.267921i	0.249694	+	0.968325i	$0.419670\pi$
$432$		0			0
$433$	−7.42820	+	12.8660i	−0.356977	+	0.618302i	−0.987454	−	0.157906i	$-0.949526\pi$
$433$	−7.42820	+	12.8660i	−0.356977	+	0.618302i	0.630478	+	0.776208i	$0.282859\pi$
$434$		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	0.996080	−	0.0884515i	$-0.0281918\pi$
$439$	8.83013	+	15.2942i	0.421439	+	0.729954i	−0.574642	+	0.818405i	$0.694859\pi$
$440$		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	0.894047	−	0.447973i	$-0.147854\pi$
$449$	20.1962	+	11.6603i	0.953115	+	0.550281i	0.0590680	+	0.998254i	$0.481187\pi$
$450$		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	−0.0718931	−	0.997412i	$-0.522904\pi$
$457$	16.1603	−	9.33013i	0.755945	−	0.436445i	0.827838	+	0.560967i	$0.189571\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	22.2846	+	12.8660i	1.03790	+	0.599231i	0.919237	−	0.393704i	$-0.128807\pi$
$461$	22.2846	+	12.8660i	1.03790	+	0.599231i	0.118661	+	0.992935i	$0.462140\pi$
$462$		0			0
$463$		−	28.0526i		−	1.30371i	−0.758342	−	0.651856i	$-0.773990\pi$
$463$		−	28.0526i		−	1.30371i	0.758342	−	0.651856i	$-0.226010\pi$
$464$		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	−0.922654	−	0.385628i	$-0.873985\pi$
$479$	−22.9808	+	13.2679i	−1.05002	+	0.606228i	−0.127363	+	0.991856i	$0.540651\pi$
$480$		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	0.853507	−	0.521081i	$-0.174471\pi$
$487$	18.2942	+	10.5622i	0.828991	+	0.478618i	−0.0245163	+	0.999699i	$0.507805\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.63397	+	4.56218i	0.118870	+	0.205888i	0.919320	−	0.393511i	$-0.128740\pi$
$491$	2.63397	+	4.56218i	0.118870	+	0.205888i	−0.800450	+	0.599399i	$0.795406\pi$
$492$		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	$-0.745853\pi$
$499$		−	32.0000i		−	1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	5.49038	−	9.50962i	0.244804	−	0.424013i	−0.717272	−	0.696793i	$-0.754610\pi$
$503$	5.49038	−	9.50962i	0.244804	−	0.424013i	0.962076	+	0.272780i	$0.0879431\pi$
$504$		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	−0.683954	−	0.729525i	$-0.739741\pi$
$509$	−8.89230	+	5.13397i	−0.394144	+	0.227559i	0.289810	+	0.957084i	$0.406408\pi$
$510$		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	0.921683	+	0.387945i	$0.126815\pi$
$523$	18.2224	+	31.5622i	0.796811	+	1.38012i	−0.124871	+	0.992173i	$0.539852\pi$
$524$		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	$-0.666200\pi$
$541$		−	40.3205i		−	1.73351i	0.498731	−	0.866757i	$-0.333800\pi$
$542$		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	−0.939999	−	0.341178i	$-0.889174\pi$
$557$	−26.3038	+	15.1865i	−1.11453	+	0.643474i	−0.174531	+	0.984652i	$0.555841\pi$
$558$		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	−0.553949	−	0.832550i	$-0.686880\pi$
$563$	10.5359	−	18.2487i	0.444035	−	0.769091i	0.997984	+	0.0634589i	$0.0202132\pi$
$564$		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	0.912893	+	0.408200i	$0.133843\pi$
$569$	19.3205	+	33.4641i	0.809958	+	1.40289i	−0.102935	+	0.994688i	$0.532823\pi$
$570$		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	$0.00177536\pi$
$577$			0.267949i			0.0111549i	−0.999984	+	0.00557744i	$0.998225\pi$
$578$		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	−0.185999	−	0.982550i	$-0.559552\pi$
$587$	13.8564	−	8.00000i	0.571915	−	0.330195i	0.757914	+	0.652355i	$0.226219\pi$
$588$		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	$-0.726783\pi$
$593$		−	36.8564i		−	1.51351i	0.653698	−	0.756756i	$-0.273217\pi$
$594$		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	0.920126	−	0.391622i	$-0.128086\pi$
$601$	2.96410	+	5.13397i	0.120908	+	0.209419i	−0.799218	+	0.601041i	$0.794753\pi$
$602$		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	−0.857954	−	0.513726i	$-0.828265\pi$
$607$	0.392305	−	0.679492i	0.0159232	−	0.0275797i	0.873877	+	0.486147i	$0.161598\pi$
$608$		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	−0.287345	−	0.957827i	$-0.592773\pi$
$613$	9.86603	−	5.69615i	0.398485	−	0.230065i	0.685830	+	0.727762i	$0.259439\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	30.5263	+	17.6244i	1.22894	+	0.709530i	0.966809	−	0.255502i	$-0.0822407\pi$
$617$	30.5263	+	17.6244i	1.22894	+	0.709530i	0.262133	+	0.965032i	$0.415574\pi$
$618$		0			0
$619$			10.5359i			0.423474i	0.977327	+	0.211737i	$0.0679119\pi$
$619$			10.5359i			0.423474i	−0.977327	+	0.211737i	$0.932088\pi$
$620$		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	−0.979039	−	0.203671i	$-0.934713\pi$
$631$	−41.3205	−	23.8564i	−1.64494	−	0.949709i	−0.665904	−	0.746037i	$-0.731954\pi$
$632$		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	0.486796	+	0.873516i	$0.338166\pi$
$641$	−12.9904	+	22.5000i	−0.513089	+	0.888697i	−0.999885	+	0.0151806i	$0.995168\pi$
$642$		0			0
$643$	12.0000	+	6.92820i	0.473234	+	0.273222i	0.717592	−	0.696463i	$-0.245244\pi$
$643$	12.0000	+	6.92820i	0.473234	+	0.273222i	−0.244359	+	0.969685i	$0.578577\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.1244	+	22.7321i	0.515972	+	0.893689i	0.999828	+	0.0185417i	$0.00590236\pi$
$647$	13.1244	+	22.7321i	0.515972	+	0.893689i	−0.483856	+	0.875147i	$0.660764\pi$
$648$		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	0.744348	−	0.667792i	$-0.232760\pi$
$653$	−5.26795	−	9.12436i	−0.206151	−	0.357064i	−0.950499	+	0.310728i	$0.899427\pi$
$654$		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	0.205225	+	0.978715i	$0.434207\pi$
$659$	−19.1244	+	33.1244i	−0.744979	+	1.29034i	−0.950205	+	0.311627i	$0.899126\pi$
$660$		0			0
$661$	8.13397	−	4.69615i	0.316375	−	0.182659i	−0.333401	−	0.942785i	$-0.608196\pi$
$661$	8.13397	−	4.69615i	0.316375	−	0.182659i	0.649776	+	0.760126i	$0.274863\pi$
$662$		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	0.969173	−	0.246381i	$-0.0792416\pi$
$673$	7.03590	+	12.1865i	0.271214	+	0.469756i	−0.697959	+	0.716138i	$0.745908\pi$
$674$		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	−0.282475	−	0.959275i	$-0.591155\pi$
$683$	−32.7846	−	18.9282i	−1.25447	−	0.724268i	−0.971994	+	0.235007i	$0.924489\pi$
$684$		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	−0.866606	−	0.498994i	$-0.833703\pi$
$691$	−22.8109	+	13.1699i	−0.867767	+	0.501006i	−0.00116153	+	0.999999i	$0.500370\pi$
$692$		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	0.985118	−	0.171880i	$-0.0549841\pi$
$709$	35.3827	+	20.4282i	1.32882	+	0.767197i	0.343707	+	0.939077i	$0.388317\pi$
$710$		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	−0.995961	−	0.0897860i	$-0.971382\pi$
$719$	−11.2679	+	19.5167i	−0.420224	+	0.727849i	0.575737	+	0.817635i	$0.304715\pi$
$720$		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	$0.114121\pi$
$733$			19.0000i			0.701781i	−0.936416	+	0.350891i	$0.885879\pi$
$734$		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	−0.663867	−	0.747851i	$-0.731086\pi$
$739$	−9.46410	+	5.46410i	−0.348143	+	0.201000i	0.315724	+	0.948851i	$0.397753\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.9090	+	13.8038i	−0.877135	+	0.506414i	−0.869713	−	0.493558i	$-0.835696\pi$
$743$	−23.9090	+	13.8038i	−0.877135	+	0.506414i	−0.00742221	+	0.999972i	$0.502363\pi$
$744$		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	0.683609	−	0.729849i	$-0.260410\pi$
$751$	−7.95448	−	13.7776i	−0.290263	−	0.502751i	−0.973872	+	0.227098i	$0.927076\pi$
$752$		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	0.794587	−	0.607151i	$-0.207688\pi$
$757$	−3.53590	−	6.12436i	−0.128514	−	0.222593i	−0.923101	+	0.384557i	$0.874354\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	20.1962	+	11.6603i	0.732110	+	0.422684i	0.819194	−	0.573517i	$-0.194421\pi$
$761$	20.1962	+	11.6603i	0.732110	+	0.422684i	−0.0870836	+	0.996201i	$0.527755\pi$
$762$		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	−0.730429	−	0.682988i	$-0.760680\pi$
$769$	−13.9808	+	8.07180i	−0.504159	+	0.291076i	0.226270	+	0.974065i	$0.427347\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−30.3731	−	17.5359i	−1.09244	−	0.630722i	−0.158217	−	0.987404i	$-0.550575\pi$
$773$	−30.3731	−	17.5359i	−1.09244	−	0.630722i	−0.934226	+	0.356682i	$0.883908\pi$
$774$		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	−0.250248	−	0.968182i	$-0.580512\pi$
$787$	−34.0526	−	19.6603i	−1.21384	−	0.700812i	−0.963594	+	0.267369i	$0.913846\pi$
$788$		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	−0.390321	−	0.920679i	$-0.627636\pi$
$797$	17.0000	−	29.4449i	0.602171	−	1.04299i	0.992492	−	0.122312i	$-0.0390308\pi$
$798$		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	0.598996	−	0.800752i	$-0.295567\pi$
$809$	−11.2058	−	19.4090i	−0.393974	−	0.682383i	−0.992970	+	0.118369i	$0.962233\pi$
$810$		0			0
$811$			45.1769i			1.58638i	0.608977	+	0.793188i	$0.291580\pi$
$811$			45.1769i			1.58638i	−0.608977	+	0.793188i	$0.708420\pi$
$812$		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	−0.682484	−	0.730900i	$-0.739100\pi$
$821$	−11.1962	+	6.46410i	−0.390748	+	0.225599i	0.291736	+	0.956499i	$0.405767\pi$
$822$		0			0
$823$	20.7846	−	36.0000i	0.724506	−	1.25488i	−0.234671	−	0.972075i	$-0.575401\pi$
$823$	20.7846	−	36.0000i	0.724506	−	1.25488i	0.959177	−	0.282806i	$-0.0912654\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	33.4641i		−	1.16366i	−0.813310	−	0.581830i	$-0.802337\pi$
$827$		−	33.4641i		−	1.16366i	0.813310	−	0.581830i	$-0.197663\pi$
$828$		0			0
$829$	6.06218	+	10.5000i	0.210548	+	0.364680i	0.951886	−	0.306452i	$-0.0991418\pi$
$829$	6.06218	+	10.5000i	0.210548	+	0.364680i	−0.741338	+	0.671132i	$0.765808\pi$
$830$		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	0.696306	−	0.717745i	$-0.254826\pi$
$839$	12.2487	+	7.07180i	0.422872	+	0.244146i	−0.273433	+	0.961891i	$0.588159\pi$
$840$		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	$-0.955294\pi$
$853$		−	8.17691i		−	0.279972i	0.990153	−	0.139986i	$-0.0447058\pi$
$854$		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	$0.0386928\pi$
$863$			7.12436i			0.242516i	−0.992621	+	0.121258i	$0.961307\pi$
$864$		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	0.345450	−	0.938437i	$-0.387726\pi$
$877$	−8.72243	−	5.03590i	−0.294536	−	0.170050i	−0.639985	+	0.768387i	$0.721060\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−25.9186	−	44.8923i	−0.873219	−	1.51246i	−0.858648	−	0.512566i	$-0.828695\pi$
$881$	−25.9186	−	44.8923i	−0.873219	−	1.51246i	−0.0145717	−	0.999894i	$-0.504638\pi$
$882$		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	0.768228	−	0.640176i	$-0.221138\pi$
$887$	−5.07180	−	8.78461i	−0.170294	−	0.294958i	−0.938523	+	0.345217i	$0.887805\pi$
$888$		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	0.706885	−	0.707329i	$-0.250100\pi$
$907$	−7.80385	−	13.5167i	−0.259123	−	0.448813i	−0.966007	+	0.258516i	$0.916767\pi$
$908$		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	−0.223894	+	0.974613i	$0.571877\pi$
$919$	−28.9808	+	50.1962i	−0.955987	+	1.65582i	−0.732093	+	0.681205i	$0.761456\pi$
$920$		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	0.625605	−	0.780140i	$-0.284852\pi$
$929$	8.00962	+	4.62436i	0.262787	+	0.151720i	−0.362818	+	0.931860i	$0.618185\pi$
$930$		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	$0.374454\pi$
$941$			56.6410i			1.84644i	−0.384267	+	0.923222i	$0.625546\pi$
$942$		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	−0.903160	−	0.429305i	$-0.858759\pi$
$947$	−30.2487	+	17.4641i	−0.982951	+	0.567507i	−0.0797913	+	0.996812i	$0.525425\pi$
$948$		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	−0.303689	−	0.952771i	$-0.598218\pi$
$953$	20.7846	−	36.0000i	0.673280	−	1.16615i	0.976969	−	0.213383i	$-0.0684483\pi$
$954$		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	$0.0981552\pi$
$967$			18.8756i			0.607000i	−0.952831	+	0.303500i	$0.901845\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.12436	−	15.8038i	0.292815	−	0.507170i	−0.681660	−	0.731669i	$-0.738741\pi$
$971$	9.12436	−	15.8038i	0.292815	−	0.507170i	0.974474	+	0.224500i	$0.0720748\pi$
$972$		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	−0.873485	−	0.486852i	$-0.838145\pi$
$977$	−27.7750	+	16.0359i	−0.888601	+	0.513034i	−0.0151161	+	0.999886i	$0.504812\pi$
$978$		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	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$		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	0.789725	−	0.613461i	$-0.210223\pi$
$991$	−4.29423	−	7.43782i	−0.136411	−	0.236270i	−0.926135	+	0.377191i	$0.876890\pi$
$992$		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	0.378679	+	0.925528i	$0.376378\pi$
$997$	−19.3301	+	33.4808i	−0.612191	+	1.06035i	−0.990870	+	0.134818i	$0.956955\pi$
$998$		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.1297.1		4
3.2	odd	2		624.2.bv.e.49.2		4
4.3	odd	2		234.2.l.c.127.1		4
12.11	even	2		78.2.i.a.49.2	yes	4
13.4	even	6	inner	1872.2.by.h.433.2		4
39.2	even	12		8112.2.a.bp.1.1		2
39.11	even	12		8112.2.a.bj.1.2		2
39.17	odd	6		624.2.bv.e.433.1		4
52.3	odd	6		3042.2.b.i.1351.2		4
52.11	even	12		3042.2.a.y.1.1		2
52.15	even	12		3042.2.a.p.1.2		2
52.23	odd	6		3042.2.b.i.1351.3		4
52.43	odd	6		234.2.l.c.199.1		4
60.23	odd	4		1950.2.y.b.49.2		4
60.47	odd	4		1950.2.y.g.49.1		4
60.59	even	2		1950.2.bc.d.751.1		4
156.11	odd	12		1014.2.a.i.1.2		2
156.23	even	6		1014.2.b.e.337.2		4
156.35	even	6		1014.2.i.a.823.1		4
156.47	odd	4		1014.2.e.i.991.2		4
156.59	odd	12		1014.2.e.i.529.2		4
156.71	odd	12		1014.2.e.g.529.1		4
156.83	odd	4		1014.2.e.g.991.1		4
156.95	even	6		78.2.i.a.43.2	✓	4
156.107	even	6		1014.2.b.e.337.3		4
156.119	odd	12		1014.2.a.k.1.1		2
156.155	even	2		1014.2.i.a.361.1		4
780.407	odd	12		1950.2.y.b.199.2		4
780.563	odd	12		1950.2.y.g.199.1		4
780.719	even	6		1950.2.bc.d.901.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.2	✓	4	156.95	even	6
78.2.i.a.49.2	yes	4	12.11	even	2
234.2.l.c.127.1		4	4.3	odd	2
234.2.l.c.199.1		4	52.43	odd	6
624.2.bv.e.49.2		4	3.2	odd	2
624.2.bv.e.433.1		4	39.17	odd	6
1014.2.a.i.1.2		2	156.11	odd	12
1014.2.a.k.1.1		2	156.119	odd	12
1014.2.b.e.337.2		4	156.23	even	6
1014.2.b.e.337.3		4	156.107	even	6
1014.2.e.g.529.1		4	156.71	odd	12
1014.2.e.g.991.1		4	156.83	odd	4
1014.2.e.i.529.2		4	156.59	odd	12
1014.2.e.i.991.2		4	156.47	odd	4
1014.2.i.a.361.1		4	156.155	even	2
1014.2.i.a.823.1		4	156.35	even	6
1872.2.by.h.433.2		4	13.4	even	6	inner
1872.2.by.h.1297.1		4	1.1	even	1	trivial
1950.2.y.b.49.2		4	60.23	odd	4
1950.2.y.b.199.2		4	780.407	odd	12
1950.2.y.g.49.1		4	60.47	odd	4
1950.2.y.g.199.1		4	780.563	odd	12
1950.2.bc.d.751.1		4	60.59	even	2
1950.2.bc.d.901.1		4	780.719	even	6
3042.2.a.p.1.2		2	52.15	even	12
3042.2.a.y.1.1		2	52.11	even	12
3042.2.b.i.1351.2		4	52.3	odd	6
3042.2.b.i.1351.3		4	52.23	odd	6
8112.2.a.bj.1.2		2	39.11	even	12
8112.2.a.bp.1.1		2	39.2	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

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