LMFDB - Embedded newform 1014.2.g.e.437.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.20
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.e.239.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.739750 - 1.56613i) q^{3} -1.00000i q^{4} +(2.01447 - 2.01447i) q^{5} +(-1.63050 - 0.584341i) q^{6} +(2.99993 - 2.99993i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.90554 + 2.31709i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.739750 - 1.56613i) q^{3} -1.00000i q^{4} +(2.01447 - 2.01447i) q^{5} +(-1.63050 - 0.584341i) q^{6} +(2.99993 - 2.99993i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.90554 + 2.31709i) q^{9} -2.84889i q^{10} +(-2.96449 - 2.96449i) q^{11} +(-1.56613 + 0.739750i) q^{12} -4.24255i q^{14} +(-4.64513 - 1.66472i) q^{15} -1.00000 q^{16} +0.381828 q^{17} +(0.291010 + 2.98585i) q^{18} +(5.03636 + 5.03636i) q^{19} +(-2.01447 - 2.01447i) q^{20} +(-6.91749 - 2.47909i) q^{21} -4.19242 q^{22} +1.83457 q^{23} +(-0.584341 + 1.63050i) q^{24} -3.11617i q^{25} +(5.03850 + 1.27026i) q^{27} +(-2.99993 - 2.99993i) q^{28} -0.246349i q^{29} +(-4.46174 + 2.10746i) q^{30} +(4.34970 + 4.34970i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.44980 + 6.83575i) q^{33} +(0.269993 - 0.269993i) q^{34} -12.0865i q^{35} +(2.31709 + 1.90554i) q^{36} +(-1.78595 + 1.78595i) q^{37} +7.12249 q^{38} -2.84889 q^{40} +(0.0932693 - 0.0932693i) q^{41} +(-6.64439 + 3.13842i) q^{42} +3.51595i q^{43} +(-2.96449 + 2.96449i) q^{44} +(0.829056 + 8.50636i) q^{45} +(1.29723 - 1.29723i) q^{46} +(-0.565492 - 0.565492i) q^{47} +(0.739750 + 1.56613i) q^{48} -10.9992i q^{49} +(-2.20346 - 2.20346i) q^{50} +(-0.282457 - 0.597994i) q^{51} +2.00124i q^{53} +(4.46096 - 2.66454i) q^{54} -11.9437 q^{55} -4.24255 q^{56} +(4.16196 - 11.6133i) q^{57} +(-0.174195 - 0.174195i) q^{58} +(5.80554 + 5.80554i) q^{59} +(-1.66472 + 4.64513i) q^{60} -9.90474 q^{61} +6.15141 q^{62} +(1.23462 + 12.6676i) q^{63} +1.00000i q^{64} +(3.10134 + 6.56588i) q^{66} +(3.97434 + 3.97434i) q^{67} -0.381828i q^{68} +(-1.35712 - 2.87317i) q^{69} +(-8.54648 - 8.54648i) q^{70} +(7.74822 - 7.74822i) q^{71} +(2.98585 - 0.291010i) q^{72} +(-8.12266 + 8.12266i) q^{73} +2.52572i q^{74} +(-4.88033 + 2.30518i) q^{75} +(5.03636 - 5.03636i) q^{76} -17.7865 q^{77} -5.47484 q^{79} +(-2.01447 + 2.01447i) q^{80} +(-1.73783 - 8.83063i) q^{81} -0.131903i q^{82} +(-12.8212 + 12.8212i) q^{83} +(-2.47909 + 6.91749i) q^{84} +(0.769181 - 0.769181i) q^{85} +(2.48615 + 2.48615i) q^{86} +(-0.385816 + 0.182237i) q^{87} +4.19242i q^{88} +(-6.79265 - 6.79265i) q^{89} +(6.60114 + 5.42867i) q^{90} -1.83457i q^{92} +(3.59452 - 10.0299i) q^{93} -0.799727 q^{94} +20.2912 q^{95} +(1.63050 + 0.584341i) q^{96} +(-2.90459 - 2.90459i) q^{97} +(-7.77762 - 7.77762i) q^{98} +(12.5179 - 1.22004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} + 20 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 + 20 * q^9	$ 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) $ 48 * q - 4 * q^3 + 20 * q^9 - 48 * q^16 - 32 * q^22 + 116 * q^27 + 8 * q^40 - 40 * q^42 + 4 * q^48 - 144 * q^55 - 80 * q^61 + 96 * q^66 - 56 * q^79 + 84 * q^81 + 224 * q^87 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.739750	−	1.56613i	−0.427095	−	0.904207i
$3$	−0.739750	−	1.56613i	−0.427095	−	0.904207i
$4$		−	1.00000i		−	0.500000i
$5$	2.01447	−	2.01447i	0.900898	−	0.900898i	−0.0946161	−	0.995514i	$-0.530162\pi$
$5$	2.01447	−	2.01447i	0.900898	−	0.900898i	0.995514	+	0.0946161i	$0.0301623\pi$
$6$	−1.63050	−	0.584341i	−0.665651	−	0.238556i
$7$	2.99993	−	2.99993i	1.13387	−	1.13387i	0.144341	−	0.989528i	$-0.453894\pi$
$7$	2.99993	−	2.99993i	1.13387	−	1.13387i	0.989528	−	0.144341i	$-0.0461061\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.90554	+	2.31709i	−0.635180	+	0.772364i
$10$		−	2.84889i		−	0.900898i
$11$	−2.96449	−	2.96449i	−0.893826	−	0.893826i	0.101055	−	0.994881i	$-0.467778\pi$
$11$	−2.96449	−	2.96449i	−0.893826	−	0.893826i	−0.994881	+	0.101055i	$0.967778\pi$
$12$	−1.56613	+	0.739750i	−0.452103	+	0.213547i
$13$		0			0
$13$		0			0
$14$		−	4.24255i		−	1.13387i
$15$	−4.64513	−	1.66472i	−1.19937	−	0.429829i
$16$	−1.00000			−0.250000
$17$	0.381828			0.0926070			0.0463035	−	0.998927i	$-0.485256\pi$
$17$	0.381828			0.0926070			0.0463035	+	0.998927i	$0.485256\pi$
$18$	0.291010	+	2.98585i	0.0685918	+	0.703772i
$19$	5.03636	+	5.03636i	1.15542	+	1.15542i	0.985449	+	0.169971i	$0.0543675\pi$
$19$	5.03636	+	5.03636i	1.15542	+	1.15542i	0.169971	+	0.985449i	$0.445632\pi$
$20$	−2.01447	−	2.01447i	−0.450449	−	0.450449i
$21$	−6.91749	−	2.47909i	−1.50952	−	0.540983i
$22$	−4.19242			−0.893826
$23$	1.83457			0.382533			0.191267	−	0.981538i	$-0.438740\pi$
$23$	1.83457			0.382533			0.191267	+	0.981538i	$0.438740\pi$
$24$	−0.584341	+	1.63050i	−0.119278	+	0.332825i
$25$		−	3.11617i		−	0.623234i
$26$		0			0
$27$	5.03850	+	1.27026i	0.969659	+	0.244462i
$28$	−2.99993	−	2.99993i	−0.566934	−	0.566934i
$29$		−	0.246349i		−	0.0457459i	−0.999738	−	0.0228730i	$-0.992719\pi$
$29$		−	0.246349i		−	0.0457459i	0.999738	−	0.0228730i	$-0.00728133\pi$
$30$	−4.46174	+	2.10746i	−0.814598	+	0.384769i
$31$	4.34970	+	4.34970i	0.781229	+	0.781229i	0.980038	−	0.198809i	$-0.0637073\pi$
$31$	4.34970	+	4.34970i	0.781229	+	0.781229i	−0.198809	+	0.980038i	$0.563707\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.44980	+	6.83575i	−0.426455	+	1.18995i
$34$	0.269993	−	0.269993i	0.0463035	−	0.0463035i
$35$		−	12.0865i		−	2.04300i
$36$	2.31709	+	1.90554i	0.386182	+	0.317590i
$37$	−1.78595	+	1.78595i	−0.293609	+	0.293609i	−0.838504	−	0.544895i	$-0.816569\pi$
$37$	−1.78595	+	1.78595i	−0.293609	+	0.293609i	0.544895	+	0.838504i	$0.316569\pi$
$38$	7.12249			1.15542
$39$		0			0
$40$	−2.84889			−0.450449
$41$	0.0932693	−	0.0932693i	0.0145662	−	0.0145662i	−0.699786	−	0.714352i	$-0.746721\pi$
$41$	0.0932693	−	0.0932693i	0.0145662	−	0.0145662i	0.714352	+	0.699786i	$0.246721\pi$
$42$	−6.64439	+	3.13842i	−1.02525	+	0.484269i
$43$			3.51595i			0.536177i	0.963394	+	0.268088i	$0.0863919\pi$
$43$			3.51595i			0.536177i	−0.963394	+	0.268088i	$0.913608\pi$
$44$	−2.96449	+	2.96449i	−0.446913	+	0.446913i
$45$	0.829056	+	8.50636i	0.123588	+	1.26805i
$46$	1.29723	−	1.29723i	0.191267	−	0.191267i
$47$	−0.565492	−	0.565492i	−0.0824855	−	0.0824855i	0.664660	−	0.747146i	$-0.268576\pi$
$47$	−0.565492	−	0.565492i	−0.0824855	−	0.0824855i	−0.747146	+	0.664660i	$0.768576\pi$
$48$	0.739750	+	1.56613i	0.106774	+	0.226052i
$49$		−	10.9992i		−	1.57132i
$50$	−2.20346	−	2.20346i	−0.311617	−	0.311617i
$51$	−0.282457	−	0.597994i	−0.0395519	−	0.0837359i
$52$		0			0
$53$			2.00124i			0.274891i	0.990509	+	0.137445i	$0.0438892\pi$
$53$			2.00124i			0.274891i	−0.990509	+	0.137445i	$0.956111\pi$
$54$	4.46096	−	2.66454i	0.607060	−	0.362598i
$55$	−11.9437			−1.61049
$56$	−4.24255			−0.566934
$57$	4.16196	−	11.6133i	0.551265	−	1.53821i
$58$	−0.174195	−	0.174195i	−0.0228730	−	0.0228730i
$59$	5.80554	+	5.80554i	0.755816	+	0.755816i	0.975558	−	0.219742i	$-0.0705215\pi$
$59$	5.80554	+	5.80554i	0.755816	+	0.755816i	−0.219742	+	0.975558i	$0.570521\pi$
$60$	−1.66472	+	4.64513i	−0.214915	+	0.599683i
$61$	−9.90474			−1.26817			−0.634086	−	0.773263i	$-0.718623\pi$
$61$	−9.90474			−1.26817			−0.634086	+	0.773263i	$0.718623\pi$
$62$	6.15141			0.781229
$63$	1.23462	+	12.6676i	0.155548	+	1.59597i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	3.10134	+	6.56588i	0.381748	+	0.808204i
$67$	3.97434	+	3.97434i	0.485543	+	0.485543i	0.906897	−	0.421353i	$-0.138445\pi$
$67$	3.97434	+	3.97434i	0.485543	+	0.485543i	−0.421353	+	0.906897i	$0.638445\pi$
$68$		−	0.381828i		−	0.0463035i
$69$	−1.35712	−	2.87317i	−0.163378	−	0.345889i
$70$	−8.54648	−	8.54648i	−1.02150	−	1.02150i
$71$	7.74822	−	7.74822i	0.919545	−	0.919545i	−0.0774514	−	0.996996i	$-0.524678\pi$
$71$	7.74822	−	7.74822i	0.919545	−	0.919545i	0.996996	+	0.0774514i	$0.0246782\pi$
$72$	2.98585	−	0.291010i	0.351886	−	0.0342959i
$73$	−8.12266	+	8.12266i	−0.950686	+	0.950686i	−0.998840	−	0.0481540i	$-0.984666\pi$
$73$	−8.12266	+	8.12266i	−0.950686	+	0.950686i	0.0481540	+	0.998840i	$0.484666\pi$
$74$			2.52572i			0.293609i
$75$	−4.88033	+	2.30518i	−0.563532	+	0.266180i
$76$	5.03636	−	5.03636i	0.577710	−	0.577710i
$77$	−17.7865			−2.02696
$78$		0			0
$79$	−5.47484			−0.615967			−0.307984	−	0.951392i	$-0.599654\pi$
$79$	−5.47484			−0.615967			−0.307984	+	0.951392i	$0.599654\pi$
$80$	−2.01447	+	2.01447i	−0.225224	+	0.225224i
$81$	−1.73783	−	8.83063i	−0.193092	−	0.981181i
$82$		−	0.131903i		−	0.0145662i
$83$	−12.8212	+	12.8212i	−1.40731	+	1.40731i	−0.633845	+	0.773460i	$0.718524\pi$
$83$	−12.8212	+	12.8212i	−1.40731	+	1.40731i	−0.773460	+	0.633845i	$0.781476\pi$
$84$	−2.47909	+	6.91749i	−0.270491	+	0.754761i
$85$	0.769181	−	0.769181i	0.0834294	−	0.0834294i
$86$	2.48615	+	2.48615i	0.268088	+	0.268088i
$87$	−0.385816	+	0.182237i	−0.0413638	+	0.0195378i
$88$			4.19242i			0.446913i
$89$	−6.79265	−	6.79265i	−0.720019	−	0.720019i	0.248590	−	0.968609i	$-0.420033\pi$
$89$	−6.79265	−	6.79265i	−0.720019	−	0.720019i	−0.968609	+	0.248590i	$0.920033\pi$
$90$	6.60114	+	5.42867i	0.695821	+	0.572233i
$91$		0			0
$92$		−	1.83457i		−	0.191267i
$93$	3.59452	−	10.0299i	0.372734	−	1.04005i
$94$	−0.799727			−0.0824855
$95$	20.2912			2.08183
$96$	1.63050	+	0.584341i	0.166413	+	0.0596390i
$97$	−2.90459	−	2.90459i	−0.294917	−	0.294917i	0.544102	−	0.839019i	$-0.316870\pi$
$97$	−2.90459	−	2.90459i	−0.294917	−	0.294917i	−0.839019	+	0.544102i	$0.816870\pi$
$98$	−7.77762	−	7.77762i	−0.785658	−	0.785658i
$99$	12.5179	−	1.22004i	1.25810	−	0.122618i
$100$	−3.11617			−0.311617
$101$	3.43482			0.341777			0.170889	−	0.985290i	$-0.445336\pi$
$101$	3.43482			0.341777			0.170889	+	0.985290i	$0.445336\pi$
$102$	−0.622573	−	0.223118i	−0.0616439	−	0.0220920i
$103$		−	6.79187i		−	0.669223i	−0.942356	−	0.334612i	$-0.891395\pi$
$103$		−	6.79187i		−	0.669223i	0.942356	−	0.334612i	$-0.108605\pi$
$104$		0			0
$105$	−18.9291	+	8.94102i	−1.84729	+	0.872554i
$106$	1.41509	+	1.41509i	0.137445	+	0.137445i
$107$		−	10.9914i		−	1.06257i	−0.847192	−	0.531287i	$-0.821709\pi$
$107$		−	10.9914i		−	1.06257i	0.847192	−	0.531287i	$-0.178291\pi$
$108$	1.27026	−	5.03850i	0.122231	−	0.484829i
$109$	5.58541	+	5.58541i	0.534985	+	0.534985i	0.922052	−	0.387066i	$-0.126512\pi$
$109$	5.58541	+	5.58541i	0.534985	+	0.534985i	−0.387066	+	0.922052i	$0.626512\pi$
$110$	−8.44549	+	8.44549i	−0.805246	+	0.805246i
$111$	4.11820	+	1.47588i	0.390882	+	0.140084i
$112$	−2.99993	+	2.99993i	−0.283467	+	0.283467i
$113$		−	3.17634i		−	0.298805i	−0.988776	−	0.149402i	$-0.952265\pi$
$113$		−	3.17634i		−	0.298805i	0.988776	−	0.149402i	$-0.0477350\pi$
$114$	−5.26886	−	11.1548i	−0.493474	−	1.04474i
$115$	3.69567	−	3.69567i	0.344623	−	0.344623i
$116$	−0.246349			−0.0228730
$117$		0			0
$118$	8.21027			0.755816
$119$	1.14546	−	1.14546i	0.105004	−	0.105004i
$120$	2.10746	+	4.46174i	0.192384	+	0.407299i
$121$			6.57635i			0.597850i
$122$	−7.00371	+	7.00371i	−0.634086	+	0.634086i
$123$	−0.215068	−	0.0770761i	−0.0193920	−	0.00694972i
$124$	4.34970	−	4.34970i	0.390615	−	0.390615i
$125$	3.79492	+	3.79492i	0.339428	+	0.339428i
$126$	9.83037	+	8.08435i	0.875759	+	0.720211i
$127$			4.32111i			0.383436i	0.981450	+	0.191718i	$0.0614059\pi$
$127$			4.32111i			0.383436i	−0.981450	+	0.191718i	$0.938594\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	5.50644	−	2.60092i	0.484815	−	0.228998i
$130$		0			0
$131$		−	9.52469i		−	0.832176i	−0.909324	−	0.416088i	$-0.863401\pi$
$131$		−	9.52469i		−	0.832176i	0.909324	−	0.416088i	$-0.136599\pi$
$132$	6.83575	+	2.44980i	0.594976	+	0.213228i
$133$	30.2175			2.62019
$134$	5.62057			0.485543
$135$	12.7088	−	7.59099i	1.09380	−	0.653328i
$136$	−0.269993	−	0.269993i	−0.0231517	−	0.0231517i
$137$	−11.9127	−	11.9127i	−1.01777	−	1.01777i	−0.999839	−	0.0179333i	$-0.994291\pi$
$137$	−11.9127	−	11.9127i	−1.01777	−	1.01777i	−0.0179333	−	0.999839i	$-0.505709\pi$
$138$	−2.99127	−	1.07201i	−0.254634	−	0.0912557i
$139$	13.5966			1.15325			0.576625	−	0.817009i	$-0.304369\pi$
$139$	13.5966			1.15325			0.576625	+	0.817009i	$0.304369\pi$
$140$	−12.0865			−1.02150
$141$	−0.467313	+	1.30396i	−0.0393549	+	0.109813i
$142$		−	10.9576i		−	0.919545i
$143$		0			0
$144$	1.90554	−	2.31709i	0.158795	−	0.193091i
$145$	−0.496263	−	0.496263i	−0.0412124	−	0.0412124i
$146$			11.4872i			0.950686i
$147$	−17.2262	+	8.13666i	−1.42079	+	0.671101i
$148$	1.78595	+	1.78595i	0.146804	+	0.146804i
$149$	13.1861	−	13.1861i	1.08025	−	1.08025i	0.0837654	−	0.996486i	$-0.473305\pi$
$149$	13.1861	−	13.1861i	1.08025	−	1.08025i	0.996486	−	0.0837654i	$-0.0266946\pi$
$150$	−1.82090	+	5.08093i	−0.148676	+	0.414856i
$151$	−1.11223	+	1.11223i	−0.0905122	+	0.0905122i	−0.750913	−	0.660401i	$-0.770386\pi$
$151$	−1.11223	+	1.11223i	−0.0905122	+	0.0905122i	0.660401	+	0.750913i	$0.270386\pi$
$152$		−	7.12249i		−	0.577710i
$153$	−0.727589	+	0.884731i	−0.0588221	+	0.0715263i
$154$	−12.5770	+	12.5770i	−1.01348	+	1.01348i
$155$	17.5247			1.40762
$156$		0			0
$157$	16.5615			1.32175			0.660876	−	0.750495i	$-0.270185\pi$
$157$	16.5615			1.32175			0.660876	+	0.750495i	$0.270185\pi$
$158$	−3.87129	+	3.87129i	−0.307984	+	0.307984i
$159$	3.13420	−	1.48041i	0.248558	−	0.117404i
$160$			2.84889i			0.225224i
$161$	5.50358	−	5.50358i	0.433743	−	0.433743i
$162$	−7.47302	−	5.01537i	−0.587136	−	0.394044i
$163$	−16.1810	+	16.1810i	−1.26739	+	1.26739i	−0.319964	+	0.947430i	$0.603671\pi$
$163$	−16.1810	+	16.1810i	−1.26739	+	1.26739i	−0.947430	+	0.319964i	$0.896329\pi$
$164$	−0.0932693	−	0.0932693i	−0.00728310	−	0.00728310i
$165$	8.83537	+	18.7055i	0.687832	+	1.45622i
$166$			18.1319i			1.40731i
$167$	15.8603	+	15.8603i	1.22731	+	1.22731i	0.964979	+	0.262329i	$0.0844904\pi$
$167$	15.8603	+	15.8603i	1.22731	+	1.22731i	0.262329	+	0.964979i	$0.415510\pi$
$168$	3.13842	+	6.64439i	0.242135	+	0.512626i
$169$		0			0
$170$		−	1.08779i		−	0.0834294i
$171$	−21.2667	+	2.07272i	−1.62631	+	0.158505i
$172$	3.51595			0.268088
$173$	3.49472			0.265699			0.132849	−	0.991136i	$-0.457587\pi$
$173$	3.49472			0.265699			0.132849	+	0.991136i	$0.457587\pi$
$174$	−0.143952	+	0.401674i	−0.0109130	+	0.0304508i
$175$	−9.34830	−	9.34830i	−0.706665	−	0.706665i
$176$	2.96449	+	2.96449i	0.223457	+	0.223457i
$177$	4.79759	−	13.3869i	0.360609	−	1.00622i
$178$	−9.60625			−0.720019
$179$	−0.620773			−0.0463988			−0.0231994	−	0.999731i	$-0.507385\pi$
$179$	−0.620773			−0.0463988			−0.0231994	+	0.999731i	$0.507385\pi$
$180$	8.50636	−	0.829056i	0.634027	−	0.0617942i
$181$			20.9189i			1.55489i	0.628951	+	0.777445i	$0.283485\pi$
$181$			20.9189i			1.55489i	−0.628951	+	0.777445i	$0.716515\pi$
$182$		0			0
$183$	7.32703	+	15.5121i	0.541629	+	1.14669i
$184$	−1.29723	−	1.29723i	−0.0956333	−	0.0956333i
$185$			7.19549i			0.529023i
$186$	−4.55050	−	9.63391i	−0.333659	−	0.706393i
$187$	−1.13192	−	1.13192i	−0.0827745	−	0.0827745i
$188$	−0.565492	+	0.565492i	−0.0412428	+	0.0412428i
$189$	18.9259	−	11.3045i	1.37665	−	0.822278i
$190$	14.3480	−	14.3480i	1.04092	−	1.04092i
$191$		−	9.97107i		−	0.721481i	−0.932666	−	0.360741i	$-0.882524\pi$
$191$		−	9.97107i		−	0.721481i	0.932666	−	0.360741i	$-0.117476\pi$
$192$	1.56613	−	0.739750i	0.113026	−	0.0533868i
$193$	12.9396	−	12.9396i	0.931410	−	0.931410i	−0.0663846	−	0.997794i	$-0.521146\pi$
$193$	12.9396	−	12.9396i	0.931410	−	0.931410i	0.997794	+	0.0663846i	$0.0211464\pi$
$194$	−4.10771			−0.294917
$195$		0			0
$196$	−10.9992			−0.785658
$197$	−4.88904	+	4.88904i	−0.348330	+	0.348330i	−0.859487	−	0.511157i	$-0.829217\pi$
$197$	−4.88904	+	4.88904i	−0.348330	+	0.348330i	0.511157	+	0.859487i	$0.329217\pi$
$198$	7.98882	−	9.71421i	0.567741	−	0.690359i
$199$		−	19.9097i		−	1.41136i	−0.708531	−	0.705680i	$-0.750642\pi$
$199$		−	19.9097i		−	1.41136i	0.708531	−	0.705680i	$-0.249358\pi$
$200$	−2.20346	+	2.20346i	−0.155808	+	0.155808i
$201$	3.28433	−	9.16437i	0.231659	−	0.646405i
$202$	2.42878	−	2.42878i	0.170889	−	0.170889i
$203$	−0.739032	−	0.739032i	−0.0518699	−	0.0518699i
$204$	−0.597994	+	0.282457i	−0.0418679	+	0.0197760i
$205$		−	0.375776i		−	0.0262453i
$206$	−4.80258	−	4.80258i	−0.334612	−	0.334612i
$207$	−3.49584	+	4.25086i	−0.242978	+	0.295455i
$208$		0			0
$209$		−	29.8604i		−	2.06549i
$210$	−7.06266	+	19.7072i	−0.487370	+	1.35992i
$211$	−1.55481			−0.107037			−0.0535187	−	0.998567i	$-0.517044\pi$
$211$	−1.55481			−0.107037			−0.0535187	+	0.998567i	$0.517044\pi$
$212$	2.00124			0.137445
$213$	−17.8665	−	6.40300i	−1.22419	−	0.438726i
$214$	−7.77206	−	7.77206i	−0.531287	−	0.531287i
$215$	7.08276	+	7.08276i	0.483040	+	0.483040i
$216$	−2.66454	−	4.46096i	−0.181299	−	0.303530i
$217$	26.0976			1.77162
$218$	7.89896			0.534985
$219$	18.7299	+	6.71243i	1.26565	+	0.453584i
$220$			11.9437i			0.805246i
$221$		0			0
$222$	3.95561	−	1.86840i	0.265483	−	0.125399i
$223$	7.97380	+	7.97380i	0.533965	+	0.533965i	0.921750	−	0.387785i	$-0.126760\pi$
$223$	7.97380	+	7.97380i	0.533965	+	0.533965i	−0.387785	+	0.921750i	$0.626760\pi$
$224$			4.24255i			0.283467i
$225$	7.22045	+	5.93799i	0.481363	+	0.395866i
$226$	−2.24601	−	2.24601i	−0.149402	−	0.149402i
$227$	−1.59491	+	1.59491i	−0.105858	+	0.105858i	−0.758052	−	0.652194i	$-0.773849\pi$
$227$	−1.59491	+	1.59491i	−0.105858	+	0.105858i	0.652194	+	0.758052i	$0.273849\pi$
$228$	−11.6133	−	4.16196i	−0.769107	−	0.275633i
$229$	12.3128	−	12.3128i	0.813654	−	0.813654i	−0.171525	−	0.985180i	$-0.554870\pi$
$229$	12.3128	−	12.3128i	0.813654	−	0.813654i	0.985180	+	0.171525i	$0.0548695\pi$
$230$		−	5.22647i		−	0.344623i
$231$	13.1576	+	27.8561i	0.865705	+	1.83279i
$232$	−0.174195	+	0.174195i	−0.0114365	+	0.0114365i
$233$	−20.4054			−1.33680			−0.668401	−	0.743801i	$-0.733021\pi$
$233$	−20.4054			−1.33680			−0.668401	+	0.743801i	$0.733021\pi$
$234$		0			0
$235$	−2.27833			−0.148622
$236$	5.80554	−	5.80554i	0.377908	−	0.377908i
$237$	4.05001	+	8.57432i	0.263076	+	0.556962i
$238$		−	1.61992i		−	0.105004i
$239$	12.5579	−	12.5579i	0.812306	−	0.812306i	−0.172674	−	0.984979i	$-0.555241\pi$
$239$	12.5579	−	12.5579i	0.812306	−	0.812306i	0.984979	+	0.172674i	$0.0552406\pi$
$240$	4.64513	+	1.66472i	0.299842	+	0.107457i
$241$	3.21797	−	3.21797i	0.207288	−	0.207288i	−0.595826	−	0.803114i	$-0.703175\pi$
$241$	3.21797	−	3.21797i	0.207288	−	0.207288i	0.803114	+	0.595826i	$0.203175\pi$
$242$	4.65018	+	4.65018i	0.298925	+	0.298925i
$243$	−12.5444	+	9.25412i	−0.804722	+	0.593652i
$244$			9.90474i			0.634086i
$245$	−22.1576	−	22.1576i	−1.41560	−	1.41560i
$246$	−0.206577	+	0.0975749i	−0.0131709	+	0.00622115i
$247$		0			0
$248$		−	6.15141i		−	0.390615i
$249$	29.5641	+	10.5952i	1.87355	+	0.671443i
$250$	5.36683			0.339428
$251$	−15.6207			−0.985972			−0.492986	−	0.870037i	$-0.664095\pi$
$251$	−15.6207			−0.985972			−0.492986	+	0.870037i	$0.664095\pi$
$252$	12.6676	−	1.23462i	0.797985	−	0.0777741i
$253$	−5.43854	−	5.43854i	−0.341918	−	0.341918i
$254$	3.05548	+	3.05548i	0.191718	+	0.191718i
$255$	−1.77364	−	0.635638i	−0.111070	−	0.0398052i
$256$	1.00000			0.0625000
$257$	−29.5534			−1.84349			−0.921745	−	0.387797i	$-0.873236\pi$
$257$	−29.5534			−1.84349			−0.921745	+	0.387797i	$0.873236\pi$
$258$	2.05451	−	5.73277i	0.127908	−	0.356906i
$259$			10.7155i			0.665828i
$260$		0			0
$261$	0.570814	+	0.469429i	0.0353325	+	0.0290569i
$262$	−6.73497	−	6.73497i	−0.416088	−	0.416088i
$263$			25.9835i			1.60221i	0.598525	+	0.801104i	$0.295754\pi$
$263$			25.9835i			1.60221i	−0.598525	+	0.801104i	$0.704246\pi$
$264$	6.56588	−	3.10134i	0.404102	−	0.190874i
$265$	4.03143	+	4.03143i	0.247649	+	0.247649i
$266$	21.3670	−	21.3670i	1.31009	−	1.31009i
$267$	−5.61333	+	15.6630i	−0.343530	+	0.958563i
$268$	3.97434	−	3.97434i	0.242772	−	0.242772i
$269$			2.65332i			0.161776i	0.996723	+	0.0808878i	$0.0257755\pi$
$269$			2.65332i			0.161776i	−0.996723	+	0.0808878i	$0.974224\pi$
$270$	3.61883	−	14.3541i	0.220235	−	0.873564i
$271$	−2.87419	+	2.87419i	−0.174595	+	0.174595i	−0.788995	−	0.614400i	$-0.789398\pi$
$271$	−2.87419	+	2.87419i	−0.174595	+	0.174595i	0.614400	+	0.788995i	$0.289398\pi$
$272$	−0.381828			−0.0231517
$273$		0			0
$274$	−16.8471			−1.01777
$275$	−9.23784	+	9.23784i	−0.557062	+	0.557062i
$276$	−2.87317	+	1.35712i	−0.172945	+	0.0816890i
$277$			9.93344i			0.596843i	0.954434	+	0.298421i	$0.0964601\pi$
$277$			9.93344i			0.596843i	−0.954434	+	0.298421i	$0.903540\pi$
$278$	9.61427	−	9.61427i	0.576625	−	0.576625i
$279$	−18.3672	+	1.79012i	−1.09961	+	0.107172i
$280$	−8.54648	+	8.54648i	−0.510750	+	0.510750i
$281$	7.34283	+	7.34283i	0.438037	+	0.438037i	0.891351	−	0.453314i	$-0.149758\pi$
$281$	7.34283	+	7.34283i	0.438037	+	0.438037i	−0.453314	+	0.891351i	$0.649758\pi$
$282$	0.591598	+	1.25248i	0.0352291	+	0.0745840i
$283$		−	16.9971i		−	1.01037i	−0.863010	−	0.505187i	$-0.831423\pi$
$283$		−	16.9971i		−	1.01037i	0.863010	−	0.505187i	$-0.168577\pi$
$284$	−7.74822	−	7.74822i	−0.459772	−	0.459772i
$285$	−15.0104	−	31.7787i	−0.889139	−	1.88241i
$286$		0			0
$287$		−	0.559603i		−	0.0330323i
$288$	−0.291010	−	2.98585i	−0.0171479	−	0.175943i
$289$	−16.8542			−0.991424
$290$	−0.701822			−0.0412124
$291$	−2.40030	+	6.69765i	−0.140708	+	0.392623i
$292$	8.12266	+	8.12266i	0.475343	+	0.475343i
$293$	−18.7020	−	18.7020i	−1.09258	−	1.09258i	−0.995252	−	0.0973321i	$-0.968969\pi$
$293$	−18.7020	−	18.7020i	−1.09258	−	1.09258i	−0.0973321	−	0.995252i	$-0.531031\pi$
$294$	−6.42729	+	17.9343i	−0.374847	+	1.04595i
$295$	23.3901			1.36183
$296$	2.52572			0.146804
$297$	−11.1709	−	18.7022i	−0.648200	−	1.08521i
$298$		−	18.6480i		−	1.08025i
$299$		0			0
$300$	2.30518	+	4.88033i	0.133090	+	0.281766i
$301$	10.5476	+	10.5476i	0.607954	+	0.607954i
$302$			1.57293i			0.0905122i
$303$	−2.54091	−	5.37938i	−0.145971	−	0.309037i
$304$	−5.03636	−	5.03636i	−0.288855	−	0.288855i
$305$	−19.9528	+	19.9528i	−1.14249	+	1.14249i
$306$	0.111116	+	1.14008i	0.00635208	+	0.0651742i
$307$	12.2506	−	12.2506i	0.699179	−	0.699179i	−0.265054	−	0.964234i	$-0.585390\pi$
$307$	12.2506	−	12.2506i	0.699179	−	0.699179i	0.964234	+	0.265054i	$0.0853898\pi$
$308$			17.7865i			1.01348i
$309$	−10.6370	+	5.02429i	−0.605116	+	0.285822i
$310$	12.3918	−	12.3918i	0.703808	−	0.703808i
$311$	13.1245			0.744223			0.372112	−	0.928188i	$-0.378634\pi$
$311$	13.1245			0.744223			0.372112	+	0.928188i	$0.378634\pi$
$312$		0			0
$313$	−8.98350			−0.507778			−0.253889	−	0.967233i	$-0.581710\pi$
$313$	−8.98350			−0.507778			−0.253889	+	0.967233i	$0.581710\pi$
$314$	11.7108	−	11.7108i	0.660876	−	0.660876i
$315$	28.0056	+	23.0314i	1.57794	+	1.29767i
$316$			5.47484i			0.307984i
$317$	−17.9291	+	17.9291i	−1.00700	+	1.00700i	−0.00702082	+	0.999975i	$0.502235\pi$
$317$	−17.9291	+	17.9291i	−1.00700	+	1.00700i	−0.999975	+	0.00702082i	$0.997765\pi$
$318$	1.16940	−	3.26302i	0.0655769	−	0.182981i
$319$	−0.730299	+	0.730299i	−0.0408889	+	0.0408889i
$320$	2.01447	+	2.01447i	0.112612	+	0.112612i
$321$	−17.2139	+	8.13085i	−0.960787	+	0.453820i
$322$		−	7.78323i		−	0.433743i
$323$	1.92303	+	1.92303i	0.107000	+	0.107000i
$324$	−8.83063	+	1.73783i	−0.490590	+	0.0965460i
$325$		0			0
$326$			22.8834i			1.26739i
$327$	4.61569	−	12.8793i	0.255248	−	0.712227i
$328$	−0.131903			−0.00728310
$329$	−3.39288			−0.187056
$330$	19.4743	+	6.97921i	1.07203	+	0.384193i
$331$	15.0659	+	15.0659i	0.828099	+	0.828099i	0.987254	−	0.159154i	$-0.0508768\pi$
$331$	15.0659	+	15.0659i	0.828099	+	0.828099i	−0.159154	+	0.987254i	$0.550877\pi$
$332$	12.8212	+	12.8212i	0.703653	+	0.703653i
$333$	−0.735010	−	7.54142i	−0.0402783	−	0.413268i
$334$	22.4299			1.22731
$335$	16.0124			0.874850
$336$	6.91749	+	2.47909i	0.377380	+	0.135246i
$337$		−	19.9965i		−	1.08928i	−0.838670	−	0.544640i	$-0.816666\pi$
$337$		−	19.9965i		−	1.08928i	0.838670	−	0.544640i	$-0.183334\pi$
$338$		0			0
$339$	−4.97456	+	2.34969i	−0.270181	+	0.127618i
$340$	−0.769181	−	0.769181i	−0.0417147	−	0.0417147i
$341$		−	25.7893i		−	1.39657i
$342$	−13.5722	+	16.5035i	−0.733900	+	0.892405i
$343$	−11.9974	−	11.9974i	−0.647797	−	0.647797i
$344$	2.48615	−	2.48615i	0.134044	−	0.134044i
$345$	−8.52179	−	3.05404i	−0.458798	−	0.164424i
$346$	2.47114	−	2.47114i	0.132849	−	0.132849i
$347$			23.5381i			1.26359i	0.775136	+	0.631795i	$0.217681\pi$
$347$			23.5381i			1.26359i	−0.775136	+	0.631795i	$0.782319\pi$
$348$	0.182237	+	0.385816i	0.00976892	+	0.0206819i
$349$	−9.20500	+	9.20500i	−0.492732	+	0.492732i	−0.909166	−	0.416434i	$-0.863280\pi$
$349$	−9.20500	+	9.20500i	−0.492732	+	0.492732i	0.416434	+	0.909166i	$0.363280\pi$
$350$	−13.2205			−0.706665
$351$		0			0
$352$	4.19242			0.223457
$353$	4.83197	−	4.83197i	0.257180	−	0.257180i	−0.566726	−	0.823906i	$-0.691790\pi$
$353$	4.83197	−	4.83197i	0.257180	−	0.257180i	0.823906	+	0.566726i	$0.191790\pi$
$354$	−6.07354	−	12.8584i	−0.322805	−	0.683414i
$355$		−	31.2171i		−	1.65683i
$356$	−6.79265	+	6.79265i	−0.360010	+	0.360010i
$357$	−2.64130	−	0.946588i	−0.139792	−	0.0500988i
$358$	−0.438953	+	0.438953i	−0.0231994	+	0.0231994i
$359$	−10.6230	−	10.6230i	−0.560662	−	0.560662i	0.368834	−	0.929495i	$-0.379757\pi$
$359$	−10.6230	−	10.6230i	−0.560662	−	0.560662i	−0.929495	+	0.368834i	$0.879757\pi$
$360$	5.42867	−	6.60114i	0.286116	−	0.347910i
$361$			31.7299i			1.66999i
$362$	14.7919	+	14.7919i	0.777445	+	0.777445i
$363$	10.2994	−	4.86485i	0.540580	−	0.255339i
$364$		0			0
$365$			32.7257i			1.71294i
$366$	16.1497	+	5.78774i	0.844160	+	0.302530i
$367$	−9.33416			−0.487239			−0.243620	−	0.969871i	$-0.578335\pi$
$367$	−9.33416			−0.487239			−0.243620	+	0.969871i	$0.578335\pi$
$368$	−1.83457			−0.0956333
$369$	0.0383850	+	0.393842i	0.00199824	+	0.0205026i
$370$	5.08798	+	5.08798i	0.264512	+	0.264512i
$371$	6.00357	+	6.00357i	0.311690	+	0.311690i
$372$	−10.0299	−	3.59452i	−0.520026	−	0.186367i
$373$	−26.7007			−1.38251			−0.691254	−	0.722612i	$-0.742941\pi$
$373$	−26.7007			−1.38251			−0.691254	+	0.722612i	$0.742941\pi$
$374$	−1.60078			−0.0827745
$375$	3.13606	−	8.75064i	0.161945	−	0.451881i
$376$			0.799727i			0.0412428i
$377$		0			0
$378$	5.38915	−	21.3761i	0.277188	−	1.09947i
$379$	−4.36387	−	4.36387i	−0.224157	−	0.224157i	0.586089	−	0.810246i	$-0.300667\pi$
$379$	−4.36387	−	4.36387i	−0.224157	−	0.224157i	−0.810246	+	0.586089i	$0.800667\pi$
$380$		−	20.2912i		−	1.04092i
$381$	6.76742	−	3.19654i	0.346706	−	0.163764i
$382$	−7.05061	−	7.05061i	−0.360741	−	0.360741i
$383$	11.1679	−	11.1679i	0.570655	−	0.570655i	−0.361656	−	0.932312i	$-0.617789\pi$
$383$	11.1679	−	11.1679i	0.570655	−	0.570655i	0.932312	+	0.361656i	$0.117789\pi$
$384$	0.584341	−	1.63050i	0.0298195	−	0.0832063i
$385$	−35.8304	+	35.8304i	−1.82609	+	1.82609i
$386$		−	18.2993i		−	0.931410i
$387$	−8.14677	−	6.69978i	−0.414123	−	0.340569i
$388$	−2.90459	+	2.90459i	−0.147458	+	0.147458i
$389$	12.2230			0.619729			0.309864	−	0.950781i	$-0.399716\pi$
$389$	12.2230			0.619729			0.309864	+	0.950781i	$0.399716\pi$
$390$		0			0
$391$	0.700489			0.0354252
$392$	−7.77762	+	7.77762i	−0.392829	+	0.392829i
$393$	−14.9169	+	7.04589i	−0.752459	+	0.355418i
$394$			6.91415i			0.348330i
$395$	−11.0289	+	11.0289i	−0.554924	+	0.554924i
$396$	−1.22004	−	12.5179i	−0.0613091	−	0.629050i
$397$	4.90733	−	4.90733i	0.246292	−	0.246292i	−0.573155	−	0.819447i	$-0.694281\pi$
$397$	4.90733	−	4.90733i	0.246292	−	0.246292i	0.819447	+	0.573155i	$0.194281\pi$
$398$	−14.0783	−	14.0783i	−0.705680	−	0.705680i
$399$	−22.3534	−	47.3246i	−1.11907	−	2.36919i
$400$			3.11617i			0.155808i
$401$	2.39655	+	2.39655i	0.119678	+	0.119678i	0.764409	−	0.644731i	$-0.223031\pi$
$401$	2.39655	+	2.39655i	0.119678	+	0.119678i	−0.644731	+	0.764409i	$0.723031\pi$
$402$	−4.15782	−	8.80256i	−0.207373	−	0.439032i
$403$		0			0
$404$		−	3.43482i		−	0.170889i
$405$	−21.2898	−	14.2882i	−1.05790	−	0.709987i
$406$	−1.04515			−0.0518699
$407$	10.5889			0.524871
$408$	−0.223118	+	0.622573i	−0.0110460	+	0.0308219i
$409$	−7.80855	−	7.80855i	−0.386108	−	0.386108i	0.487189	−	0.873297i	$-0.338022\pi$
$409$	−7.80855	−	7.80855i	−0.386108	−	0.386108i	−0.873297	+	0.487189i	$0.838022\pi$
$410$	−0.265714	−	0.265714i	−0.0131227	−	0.0131227i
$411$	−9.84447	+	27.4693i	−0.485592	+	1.35496i
$412$	−6.79187			−0.334612
$413$	34.8324			1.71399
$414$	0.533877	+	5.47774i	0.0262386	+	0.269216i
$415$			51.6556i			2.53568i
$416$		0			0
$417$	−10.0581	−	21.2941i	−0.492547	−	1.04278i
$418$	−21.1145	−	21.1145i	−1.03274	−	1.03274i
$419$			35.4666i			1.73266i	0.499475	+	0.866328i	$0.333526\pi$
$419$			35.4666i			1.73266i	−0.499475	+	0.866328i	$0.666474\pi$
$420$	8.94102	+	18.9291i	0.436277	+	0.923647i
$421$	15.7485	+	15.7485i	0.767535	+	0.767535i	0.977672	−	0.210137i	$-0.0673910\pi$
$421$	15.7485	+	15.7485i	0.767535	+	0.767535i	−0.210137	+	0.977672i	$0.567391\pi$
$422$	−1.09942	+	1.09942i	−0.0535187	+	0.0535187i
$423$	2.38787	−	0.232729i	0.116102	−	0.0113157i
$424$	1.41509	−	1.41509i	0.0687227	−	0.0687227i
$425$		−	1.18984i		−	0.0577158i
$426$	−17.1611	+	8.10591i	−0.831459	+	0.392733i
$427$	−29.7136	+	29.7136i	−1.43794	+	1.43794i
$428$	−10.9914			−0.531287
$429$		0			0
$430$	10.0165			0.483040
$431$	−10.6239	+	10.6239i	−0.511736	+	0.511736i	−0.915058	−	0.403322i	$-0.867856\pi$
$431$	−10.6239	+	10.6239i	−0.511736	+	0.511736i	0.403322	+	0.915058i	$0.367856\pi$
$432$	−5.03850	−	1.27026i	−0.242415	−	0.0611155i
$433$		−	14.7479i		−	0.708741i	−0.935105	−	0.354370i	$-0.884695\pi$
$433$		−	14.7479i		−	0.708741i	0.935105	−	0.354370i	$-0.115305\pi$
$434$	18.4538	−	18.4538i	0.885811	−	0.885811i
$435$	−0.410103	+	1.14432i	−0.0196629	+	0.0548662i
$436$	5.58541	−	5.58541i	0.267493	−	0.267493i
$437$	9.23953	+	9.23953i	0.441987	+	0.441987i
$438$	17.9904	−	8.49764i	0.859617	−	0.406033i
$439$		−	29.2651i		−	1.39674i	−0.715735	−	0.698372i	$-0.753908\pi$
$439$		−	29.2651i		−	1.39674i	0.715735	−	0.698372i	$-0.246092\pi$
$440$	8.44549	+	8.44549i	0.402623	+	0.402623i
$441$	25.4862	+	20.9594i	1.21363	+	0.998069i
$442$		0			0
$443$			2.98487i			0.141815i	0.997483	+	0.0709077i	$0.0225896\pi$
$443$			2.98487i			0.141815i	−0.997483	+	0.0709077i	$0.977410\pi$
$444$	1.47588	−	4.11820i	0.0700422	−	0.195441i
$445$	−27.3672			−1.29733
$446$	11.2767			0.533965
$447$	−30.4057	−	10.8968i	−1.43814	−	0.515401i
$448$	2.99993	+	2.99993i	0.141734	+	0.141734i
$449$	−3.17467	−	3.17467i	−0.149822	−	0.149822i	0.628216	−	0.778039i	$-0.283785\pi$
$449$	−3.17467	−	3.17467i	−0.149822	−	0.149822i	−0.778039	+	0.628216i	$0.783785\pi$
$450$	9.30442	−	0.906837i	0.438614	−	0.0427487i
$451$	−0.552991			−0.0260393
$452$	−3.17634			−0.149402
$453$	2.56468	+	0.919130i	0.120499	+	0.0431845i
$454$			2.25554i			0.105858i
$455$		0			0
$456$	−11.1548	+	5.26886i	−0.522370	+	0.246737i
$457$	10.8508	+	10.8508i	0.507578	+	0.507578i	0.913782	−	0.406204i	$-0.133148\pi$
$457$	10.8508	+	10.8508i	0.507578	+	0.507578i	−0.406204	+	0.913782i	$0.633148\pi$
$458$		−	17.4130i		−	0.813654i
$459$	1.92384	+	0.485022i	0.0897972	+	0.0226389i
$460$	−3.69567	−	3.69567i	−0.172312	−	0.172312i
$461$	−18.8326	+	18.8326i	−0.877120	+	0.877120i	−0.993236	−	0.116116i	$-0.962956\pi$
$461$	−18.8326	+	18.8326i	−0.877120	+	0.877120i	0.116116	+	0.993236i	$0.462956\pi$
$462$	29.0010	+	10.3934i	1.34925	+	0.483544i
$463$	3.47253	−	3.47253i	0.161382	−	0.161382i	−0.621796	−	0.783179i	$-0.713597\pi$
$463$	3.47253	−	3.47253i	0.161382	−	0.161382i	0.783179	+	0.621796i	$0.213597\pi$
$464$			0.246349i			0.0114365i
$465$	−12.9639	−	27.4460i	−0.601185	−	1.27278i
$466$	−14.4288	+	14.4288i	−0.668401	+	0.668401i
$467$	33.7531			1.56191			0.780954	−	0.624588i	$-0.214733\pi$
$467$	33.7531			1.56191			0.780954	+	0.624588i	$0.214733\pi$
$468$		0			0
$469$	23.8455			1.10108
$470$	−1.61103	+	1.61103i	−0.0743110	+	0.0743110i
$471$	−12.2514	−	25.9375i	−0.564514	−	1.19514i
$472$		−	8.21027i		−	0.377908i
$473$	10.4230	−	10.4230i	0.479249	−	0.479249i
$474$	8.92675	+	3.19917i	0.410019	+	0.146943i
$475$	15.6941	−	15.6941i	0.720097	−	0.720097i
$476$	−1.14546	−	1.14546i	−0.0525021	−	0.0525021i
$477$	−4.63705	−	3.81344i	−0.212316	−	0.174605i
$478$		−	17.7596i		−	0.812306i
$479$	8.39220	+	8.39220i	0.383450	+	0.383450i	0.872343	−	0.488894i	$-0.162599\pi$
$479$	8.39220	+	8.39220i	0.383450	+	0.383450i	−0.488894	+	0.872343i	$0.662599\pi$
$480$	4.46174	−	2.10746i	0.203650	−	0.0961922i
$481$		0			0
$482$		−	4.55090i		−	0.207288i
$483$	−12.6906	−	4.54806i	−0.577442	−	0.206944i
$484$	6.57635			0.298925
$485$	−11.7024			−0.531380
$486$	−2.32656	+	15.4139i	−0.105535	+	0.699187i
$487$	3.54101	+	3.54101i	0.160459	+	0.160459i	0.782770	−	0.622311i	$-0.213806\pi$
$487$	3.54101	+	3.54101i	0.160459	+	0.160459i	−0.622311	+	0.782770i	$0.713806\pi$
$488$	7.00371	+	7.00371i	0.317043	+	0.317043i
$489$	37.3115	+	13.3717i	1.68728	+	0.604689i
$490$	−31.3355			−1.41560
$491$	10.8960			0.491731			0.245866	−	0.969304i	$-0.420928\pi$
$491$	10.8960			0.491731			0.245866	+	0.969304i	$0.420928\pi$
$492$	−0.0770761	+	0.215068i	−0.00347486	+	0.00969601i
$493$		−	0.0940632i		−	0.00423639i
$494$		0			0
$495$	22.7593	−	27.6747i	1.02295	−	1.24389i
$496$	−4.34970	−	4.34970i	−0.195307	−	0.195307i
$497$		−	46.4883i		−	2.08529i
$498$	28.3969	−	13.4130i	1.27250	−	0.601052i
$499$	11.5496	+	11.5496i	0.517032	+	0.517032i	0.916672	−	0.399640i	$-0.130865\pi$
$499$	11.5496	+	11.5496i	0.517032	+	0.517032i	−0.399640	+	0.916672i	$0.630865\pi$
$500$	3.79492	−	3.79492i	0.169714	−	0.169714i
$501$	13.1067	−	36.5720i	0.585563	−	1.63392i
$502$	−11.0455	+	11.0455i	−0.492986	+	0.492986i
$503$		−	10.3237i		−	0.460310i	−0.973154	−	0.230155i	$-0.926077\pi$
$503$		−	10.3237i		−	0.460310i	0.973154	−	0.230155i	$-0.0739233\pi$
$504$	8.08435	−	9.83037i	0.360106	−	0.437880i
$505$	6.91933	−	6.91933i	0.307906	−	0.307906i
$506$	−7.69126			−0.341918
$507$		0			0
$508$	4.32111			0.191718
$509$	11.2367	−	11.2367i	0.498058	−	0.498058i	−0.412775	−	0.910833i	$-0.635440\pi$
$509$	11.2367	−	11.2367i	0.498058	−	0.498058i	0.910833	+	0.412775i	$0.135440\pi$
$510$	−1.70362	+	0.804690i	−0.0754374	+	0.0356323i
$511$			48.7349i			2.15591i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	18.9782	+	31.7732i	0.837907	+	1.40282i
$514$	−20.8974	+	20.8974i	−0.921745	+	0.921745i
$515$	−13.6820	−	13.6820i	−0.602902	−	0.602902i
$516$	−2.60092	−	5.50644i	−0.114499	−	0.242407i
$517$			3.35279i			0.147455i
$518$	7.57699	+	7.57699i	0.332914	+	0.332914i
$519$	−2.58522	−	5.47320i	−0.113479	−	0.240247i
$520$		0			0
$521$			22.4396i			0.983096i	0.870850	+	0.491548i	$0.163569\pi$
$521$			22.4396i			0.983096i	−0.870850	+	0.491548i	$0.836431\pi$
$522$	0.735563	−	0.0716902i	0.0321947	−	0.00313779i
$523$	1.45825			0.0637647			0.0318823	−	0.999492i	$-0.489850\pi$
$523$	1.45825			0.0637647			0.0318823	+	0.999492i	$0.489850\pi$
$524$	−9.52469			−0.416088
$525$	−7.72527	+	21.5561i	−0.337159	+	0.940784i
$526$	18.3731	+	18.3731i	0.801104	+	0.801104i
$527$	1.66084	+	1.66084i	0.0723473	+	0.0723473i
$528$	2.44980	−	6.83575i	0.106614	−	0.297488i
$529$	−19.6344			−0.853668
$530$	5.70130			0.247649
$531$	−24.5146	+	2.38927i	−1.06384	+	0.103686i
$532$		−	30.2175i		−	1.31009i
$533$		0			0
$534$	7.10622	+	15.0447i	0.307516	+	0.651046i
$535$	−22.1417	−	22.1417i	−0.957271	−	0.957271i
$536$		−	5.62057i		−	0.242772i
$537$	0.459217	+	0.972213i	0.0198167	+	0.0419541i
$538$	1.87618	+	1.87618i	0.0808878	+	0.0808878i
$539$	−32.6070	+	32.6070i	−1.40448	+	1.40448i
$540$	−7.59099	−	12.7088i	−0.326664	−	0.546899i
$541$	−4.70978	+	4.70978i	−0.202489	+	0.202489i	−0.801066	−	0.598576i	$-0.795733\pi$
$541$	−4.70978	+	4.70978i	−0.202489	+	0.202489i	0.598576	+	0.801066i	$0.295733\pi$
$542$			4.06472i			0.174595i
$543$	32.7618	−	15.4748i	1.40594	−	0.664085i
$544$	−0.269993	+	0.269993i	−0.0115759	+	0.0115759i
$545$	22.5033			0.963934
$546$		0			0
$547$	−0.346873			−0.0148312			−0.00741561	−	0.999973i	$-0.502360\pi$
$547$	−0.346873			−0.0148312			−0.00741561	+	0.999973i	$0.502360\pi$
$548$	−11.9127	+	11.9127i	−0.508886	+	0.508886i
$549$	18.8739	−	22.9502i	0.805518	−	0.979490i
$550$			13.0643i			0.557062i
$551$	1.24070	−	1.24070i	0.0528558	−	0.0528558i
$552$	−1.07201	+	2.99127i	−0.0456278	+	0.127317i
$553$	−16.4242	+	16.4242i	−0.698426	+	0.698426i
$554$	7.02400	+	7.02400i	0.298421	+	0.298421i
$555$	11.2691	−	5.32286i	0.478346	−	0.225943i
$556$		−	13.5966i		−	0.576625i
$557$	9.92282	+	9.92282i	0.420443	+	0.420443i	0.885356	−	0.464913i	$-0.153914\pi$
$557$	9.92282	+	9.92282i	0.420443	+	0.420443i	−0.464913	+	0.885356i	$0.653914\pi$
$558$	−11.7218	+	14.2534i	−0.496221	+	0.603393i
$559$		0			0
$560$			12.0865i			0.510750i
$561$	−0.935403	+	2.61008i	−0.0394927	+	0.110198i
$562$	10.3843			0.438037
$563$	−29.8606			−1.25848			−0.629238	−	0.777213i	$-0.716633\pi$
$563$	−29.8606			−1.25848			−0.629238	+	0.777213i	$0.716633\pi$
$564$	1.30396	+	0.467313i	0.0549066	+	0.0196774i
$565$	−6.39863	−	6.39863i	−0.269192	−	0.269192i
$566$	−12.0188	−	12.0188i	−0.505187	−	0.505187i
$567$	−31.7047	−	21.2779i	−1.33147	−	0.893589i
$568$	−10.9576			−0.459772
$569$	−32.1823			−1.34915			−0.674575	−	0.738206i	$-0.735673\pi$
$569$	−32.1823			−1.34915			−0.674575	+	0.738206i	$0.735673\pi$
$570$	−33.0849	−	11.8570i	−1.38577	−	0.496634i
$571$		−	24.7973i		−	1.03773i	−0.854855	−	0.518866i	$-0.826354\pi$
$571$		−	24.7973i		−	1.03773i	0.854855	−	0.518866i	$-0.173646\pi$
$572$		0			0
$573$	−15.6160	+	7.37610i	−0.652369	+	0.308141i
$574$	−0.395699	−	0.395699i	−0.0165162	−	0.0165162i
$575$		−	5.71681i		−	0.238408i
$576$	−2.31709	−	1.90554i	−0.0965455	−	0.0793975i
$577$	7.66470	+	7.66470i	0.319086	+	0.319086i	0.848416	−	0.529330i	$-0.177557\pi$
$577$	7.66470	+	7.66470i	0.319086	+	0.319086i	−0.529330	+	0.848416i	$0.677557\pi$
$578$	−11.9177	+	11.9177i	−0.495712	+	0.495712i
$579$	−29.8371	−	10.6930i	−1.23999	−	0.444387i
$580$	−0.496263	+	0.496263i	−0.0206062	+	0.0206062i
$581$			76.9253i			3.19140i
$582$	3.03868	+	6.43322i	0.125957	+	0.266666i
$583$	5.93263	−	5.93263i	0.245705	−	0.245705i
$584$	11.4872			0.475343
$585$		0			0
$586$	−26.4487			−1.09258
$587$	23.9071	−	23.9071i	0.986754	−	0.986754i	−0.0131598	−	0.999913i	$-0.504189\pi$
$587$	23.9071	−	23.9071i	0.986754	−	0.986754i	0.999913	+	0.0131598i	$0.00418902\pi$
$588$	8.13666	+	17.2262i	0.335550	+	0.710397i
$589$			43.8133i			1.80530i
$590$	16.5393	−	16.5393i	0.680913	−	0.680913i
$591$	11.2735	+	4.04022i	0.463732	+	0.166192i
$592$	1.78595	−	1.78595i	0.0734022	−	0.0734022i
$593$	−7.52375	−	7.52375i	−0.308964	−	0.308964i	0.535544	−	0.844507i	$-0.320107\pi$
$593$	−7.52375	−	7.52375i	−0.308964	−	0.308964i	−0.844507	+	0.535544i	$0.820107\pi$
$594$	−21.1235	−	5.32547i	−0.866706	−	0.218506i
$595$		−	4.61499i		−	0.189196i
$596$	−13.1861	−	13.1861i	−0.540125	−	0.540125i
$597$	−31.1812	+	14.7282i	−1.27616	+	0.602784i
$598$		0			0
$599$		−	10.2818i		−	0.420104i	−0.977690	−	0.210052i	$-0.932637\pi$
$599$		−	10.2818i		−	0.420104i	0.977690	−	0.210052i	$-0.0673633\pi$
$600$	5.08093	+	1.82090i	0.207428	+	0.0743381i
$601$	−7.48909			−0.305486			−0.152743	−	0.988266i	$-0.548811\pi$
$601$	−7.48909			−0.305486			−0.152743	+	0.988266i	$0.548811\pi$
$602$	14.9166			0.607954
$603$	−16.7822	+	1.63564i	−0.683424	+	0.0666086i
$604$	1.11223	+	1.11223i	0.0452561	+	0.0452561i
$605$	13.2479	+	13.2479i	0.538602	+	0.538602i
$606$	−5.60049	−	2.00710i	−0.227504	−	0.0815331i
$607$	−2.49156			−0.101129			−0.0505646	−	0.998721i	$-0.516102\pi$
$607$	−2.49156			−0.101129			−0.0505646	+	0.998721i	$0.516102\pi$
$608$	−7.12249			−0.288855
$609$	−0.610723	+	1.70412i	−0.0247478	+	0.0690545i
$610$			28.2175i			1.14249i
$611$		0			0
$612$	0.884731	+	0.727589i	0.0357631	+	0.0294111i
$613$	−19.0053	−	19.0053i	−0.767617	−	0.767617i	0.210070	−	0.977686i	$-0.432631\pi$
$613$	−19.0053	−	19.0053i	−0.767617	−	0.767617i	−0.977686	+	0.210070i	$0.932631\pi$
$614$		−	17.3250i		−	0.699179i
$615$	−0.588515	+	0.277980i	−0.0237312	+	0.0112092i
$616$	12.5770	+	12.5770i	0.506741	+	0.506741i
$617$	−7.84347	+	7.84347i	−0.315766	+	0.315766i	−0.847138	−	0.531372i	$-0.821677\pi$
$617$	−7.84347	+	7.84347i	−0.315766	+	0.315766i	0.531372	+	0.847138i	$0.321677\pi$
$618$	−3.96877	+	11.0742i	−0.159647	+	0.445469i
$619$	−26.2834	+	26.2834i	−1.05642	+	1.05642i	−0.0581088	+	0.998310i	$0.518507\pi$
$619$	−26.2834	+	26.2834i	−1.05642	+	1.05642i	−0.998310	+	0.0581088i	$0.981493\pi$
$620$		−	17.5247i		−	0.703808i
$621$	9.24345	+	2.33038i	0.370927	+	0.0935148i
$622$	9.28043	−	9.28043i	0.372112	−	0.372112i
$623$	−40.7550			−1.63281
$624$		0			0
$625$	30.8703			1.23481
$626$	−6.35230	+	6.35230i	−0.253889	+	0.253889i
$627$	−46.7654	+	22.0892i	−1.86763	+	0.882160i
$628$		−	16.5615i		−	0.660876i
$629$	−0.681927	+	0.681927i	−0.0271902	+	0.0271902i
$630$	36.0886	−	3.51731i	1.43781	−	0.140133i
$631$	28.1566	−	28.1566i	1.12090	−	1.12090i	0.129288	−	0.991607i	$-0.458731\pi$
$631$	28.1566	−	28.1566i	1.12090	−	1.12090i	0.991607	−	0.129288i	$-0.0412692\pi$
$632$	3.87129	+	3.87129i	0.153992	+	0.153992i
$633$	1.15017	+	2.43504i	0.0457151	+	0.0967840i
$634$			25.3555i			1.00700i
$635$	8.70473	+	8.70473i	0.345437	+	0.345437i
$636$	−1.48041	−	3.13420i	−0.0587022	−	0.124279i
$637$		0			0
$638$			1.03280i			0.0408889i
$639$	3.18879	+	32.7179i	0.126146	+	1.29430i
$640$	2.84889			0.112612
$641$	−12.0964			−0.477778			−0.238889	−	0.971047i	$-0.576783\pi$
$641$	−12.0964			−0.477778			−0.238889	+	0.971047i	$0.576783\pi$
$642$	−6.42270	+	17.9215i	−0.253484	+	0.707303i
$643$	17.2568	+	17.2568i	0.680540	+	0.680540i	0.960122	−	0.279582i	$-0.0901958\pi$
$643$	17.2568	+	17.2568i	0.680540	+	0.680540i	−0.279582	+	0.960122i	$0.590196\pi$
$644$	−5.50358	−	5.50358i	−0.216871	−	0.216871i
$645$	5.85307	−	16.3320i	0.230464	−	0.643072i
$646$	2.71957			0.107000
$647$	−29.0101			−1.14050			−0.570252	−	0.821470i	$-0.693154\pi$
$647$	−29.0101			−1.14050			−0.570252	+	0.821470i	$0.693154\pi$
$648$	−5.01537	+	7.47302i	−0.197022	+	0.293568i
$649$		−	34.4209i		−	1.35114i
$650$		0			0
$651$	−19.3057	−	40.8723i	−0.756651	−	1.60191i
$652$	16.1810	+	16.1810i	0.633697	+	0.633697i
$653$			31.6490i			1.23852i	0.785186	+	0.619260i	$0.212567\pi$
$653$			31.6490i			1.23852i	−0.785186	+	0.619260i	$0.787433\pi$
$654$	−5.84326	−	12.3708i	−0.228489	−	0.483737i
$655$	−19.1872	−	19.1872i	−0.749706	−	0.749706i
$656$	−0.0932693	+	0.0932693i	−0.00364155	+	0.00364155i
$657$	−3.34289	−	34.2990i	−0.130418	−	1.33813i
$658$	−2.39913	+	2.39913i	−0.0935278	+	0.0935278i
$659$		−	41.7745i		−	1.62730i	−0.581352	−	0.813652i	$-0.697476\pi$
$659$		−	41.7745i		−	1.62730i	0.581352	−	0.813652i	$-0.302524\pi$
$660$	18.7055	−	8.83537i	0.728109	−	0.343916i
$661$	28.9576	−	28.9576i	1.12632	−	1.12632i	0.135547	−	0.990771i	$-0.456721\pi$
$661$	28.9576	−	28.9576i	1.12632	−	1.12632i	0.990771	−	0.135547i	$-0.0432793\pi$
$662$	21.3065			0.828099
$663$		0			0
$664$	18.1319			0.703653
$665$	60.8722	−	60.8722i	2.36052	−	2.36052i
$666$	−5.85232	−	4.81286i	−0.226773	−	0.186495i
$667$		−	0.451944i		−	0.0174993i
$668$	15.8603	−	15.8603i	0.613654	−	0.613654i
$669$	6.58941	−	18.3867i	0.254761	−	0.710869i
$670$	11.3225	−	11.3225i	0.437425	−	0.437425i
$671$	29.3625	+	29.3625i	1.13353	+	1.13353i
$672$	6.64439	−	3.13842i	0.256313	−	0.121067i
$673$		−	31.2644i		−	1.20515i	−0.798061	−	0.602576i	$-0.794141\pi$
$673$		−	31.2644i		−	1.20515i	0.798061	−	0.602576i	$-0.205859\pi$
$674$	−14.1397	−	14.1397i	−0.544640	−	0.544640i
$675$	3.95835	−	15.7008i	0.152357	−	0.604324i
$676$		0			0
$677$			23.5943i			0.906803i	0.891306	+	0.453401i	$0.149790\pi$
$677$			23.5943i			0.906803i	−0.891306	+	0.453401i	$0.850210\pi$
$678$	−1.85606	+	5.17903i	−0.0712817	+	0.198900i
$679$	−17.4272			−0.668793
$680$	−1.08779			−0.0417147
$681$	3.67767	+	1.31800i	0.140929	+	0.0505061i
$682$	−18.2358	−	18.2358i	−0.698283	−	0.698283i
$683$	11.6086	+	11.6086i	0.444191	+	0.444191i	0.893418	−	0.449227i	$-0.148300\pi$
$683$	11.6086	+	11.6086i	0.444191	+	0.444191i	−0.449227	+	0.893418i	$0.648300\pi$
$684$	2.07272	+	21.2667i	0.0792523	+	0.813153i
$685$	−47.9956			−1.83382
$686$	−16.9668			−0.647797
$687$	−28.3919	−	10.1751i	−1.08322	−	0.388205i
$688$		−	3.51595i		−	0.134044i
$689$		0			0
$690$	−8.18535	+	3.86628i	−0.311611	+	0.147187i
$691$	5.69437	+	5.69437i	0.216624	+	0.216624i	0.807074	−	0.590450i	$-0.201050\pi$
$691$	5.69437	+	5.69437i	0.216624	+	0.216624i	−0.590450	+	0.807074i	$0.701050\pi$
$692$		−	3.49472i		−	0.132849i
$693$	33.8930	−	41.2130i	1.28749	−	1.56555i
$694$	16.6439	+	16.6439i	0.631795	+	0.631795i
$695$	27.3900	−	27.3900i	1.03896	−	1.03896i
$696$	0.401674	+	0.143952i	0.0152254	+	0.00545649i
$697$	0.0356128	−	0.0356128i	0.00134893	−	0.00134893i
$698$			13.0178i			0.492732i
$699$	15.0949	+	31.9576i	0.570941	+	1.20875i
$700$	−9.34830	+	9.34830i	−0.353333	+	0.353333i
$701$	−21.4294			−0.809379			−0.404689	−	0.914454i	$-0.632620\pi$
$701$	−21.4294			−0.809379			−0.404689	+	0.914454i	$0.632620\pi$
$702$		0			0
$703$	−17.9894			−0.678483
$704$	2.96449	−	2.96449i	0.111728	−	0.111728i
$705$	1.68540	+	3.56817i	0.0634757	+	0.134385i
$706$		−	6.83344i		−	0.257180i
$707$	10.3042	−	10.3042i	0.387530	−	0.387530i
$708$	−13.3869	−	4.79759i	−0.503110	−	0.180305i
$709$	−35.8873	+	35.8873i	−1.34778	+	1.34778i	−0.459704	+	0.888072i	$0.652045\pi$
$709$	−35.8873	+	35.8873i	−1.34778	+	1.34778i	−0.888072	+	0.459704i	$0.847955\pi$
$710$	−22.0738	−	22.0738i	−0.828416	−	0.828416i
$711$	10.4325	−	12.6857i	0.391250	−	0.475751i
$712$			9.60625i			0.360010i
$713$	7.97981	+	7.97981i	0.298846	+	0.298846i
$714$	−2.53702	+	1.19834i	−0.0949455	+	0.0448467i
$715$		0			0
$716$			0.620773i			0.0231994i
$717$	−28.9571	−	10.3777i	−1.08142	−	0.387561i
$718$	−15.0232			−0.560662
$719$	−47.3633			−1.76635			−0.883176	−	0.469042i	$-0.844599\pi$
$719$	−47.3633			−1.76635			−0.883176	+	0.469042i	$0.844599\pi$
$720$	−0.829056	−	8.50636i	−0.0308971	−	0.317013i
$721$	−20.3752	−	20.3752i	−0.758811	−	0.758811i
$722$	22.4364	+	22.4364i	0.834996	+	0.834996i
$723$	−7.42027	−	2.65928i	−0.275963	−	0.0988996i
$724$	20.9189			0.777445
$725$	−0.767666			−0.0285104
$726$	3.84283	−	10.7228i	0.142621	−	0.397959i
$727$			13.9420i			0.517079i	0.966001	+	0.258540i	$0.0832412\pi$
$727$			13.9420i			0.517079i	−0.966001	+	0.258540i	$0.916759\pi$
$728$		0			0
$729$	23.7729	+	12.8004i	0.880477	+	0.474089i
$730$	23.1406	+	23.1406i	0.856471	+	0.856471i
$731$			1.34249i			0.0496537i
$732$	15.5121	−	7.32703i	0.573345	−	0.270815i
$733$	−31.6486	−	31.6486i	−1.16897	−	1.16897i	−0.982452	−	0.186518i	$-0.940280\pi$
$733$	−31.6486	−	31.6486i	−1.16897	−	1.16897i	−0.186518	−	0.982452i	$-0.559720\pi$
$734$	−6.60025	+	6.60025i	−0.243620	+	0.243620i
$735$	−18.3106	+	51.0927i	−0.675398	+	1.88458i
$736$	−1.29723	+	1.29723i	−0.0478167	+	0.0478167i
$737$		−	23.5638i		−	0.867983i
$738$	0.305631	+	0.251346i	0.0112504	+	0.00925217i
$739$	13.6788	−	13.6788i	0.503184	−	0.503184i	−0.409242	−	0.912426i	$-0.634207\pi$
$739$	13.6788	−	13.6788i	0.503184	−	0.503184i	0.912426	+	0.409242i	$0.134207\pi$
$740$	7.19549			0.264512
$741$		0			0
$742$	8.49034			0.311690
$743$	−37.7501	+	37.7501i	−1.38492	+	1.38492i	−0.549271	+	0.835644i	$0.685095\pi$
$743$	−37.7501	+	37.7501i	−1.38492	+	1.38492i	−0.835644	+	0.549271i	$0.814905\pi$
$744$	−9.63391	+	4.55050i	−0.353196	+	0.166829i
$745$		−	53.1261i		−	1.94639i
$746$	−18.8802	+	18.8802i	−0.691254	+	0.691254i
$747$	−5.27656	−	54.1390i	−0.193059	−	1.98084i
$748$	−1.13192	+	1.13192i	−0.0413873	+	0.0413873i
$749$	−32.9733	−	32.9733i	−1.20482	−	1.20482i
$750$	−3.97011	−	8.40516i	−0.144968	−	0.306913i
$751$			17.8312i			0.650670i	0.945599	+	0.325335i	$0.105477\pi$
$751$			17.8312i			0.650670i	−0.945599	+	0.325335i	$0.894523\pi$
$752$	0.565492	+	0.565492i	0.0206214	+	0.0206214i
$753$	11.5554	+	24.4641i	0.421103	+	0.891522i
$754$		0			0
$755$			4.48112i			0.163085i
$756$	−11.3045	−	18.9259i	−0.411139	−	0.688327i
$757$	−6.51681			−0.236857			−0.118429	−	0.992963i	$-0.537786\pi$
$757$	−6.51681			−0.236857			−0.118429	+	0.992963i	$0.537786\pi$
$758$	−6.17145			−0.224157
$759$	−4.49432	+	12.5406i	−0.163133	+	0.455196i
$760$	−14.3480	−	14.3480i	−0.520458	−	0.520458i
$761$	24.5010	+	24.5010i	0.888159	+	0.888159i	0.994346	−	0.106187i	$-0.0338643\pi$
$761$	24.5010	+	24.5010i	0.888159	+	0.888159i	−0.106187	+	0.994346i	$0.533864\pi$
$762$	2.52500	−	7.04558i	0.0914711	−	0.255235i
$763$	33.5117			1.21321
$764$	−9.97107			−0.360741
$765$	0.316557	+	3.24797i	0.0114451	+	0.117431i
$766$		−	15.7939i		−	0.570655i
$767$		0			0
$768$	−0.739750	−	1.56613i	−0.0266934	−	0.0565129i
$769$	15.7626	+	15.7626i	0.568413	+	0.568413i	0.931684	−	0.363271i	$-0.118340\pi$
$769$	15.7626	+	15.7626i	0.568413	+	0.568413i	−0.363271	+	0.931684i	$0.618340\pi$
$770$			50.6718i			1.82609i
$771$	21.8621	+	46.2845i	0.787345	+	1.66690i
$772$	−12.9396	−	12.9396i	−0.465705	−	0.465705i
$773$	−11.4009	+	11.4009i	−0.410064	+	0.410064i	−0.881761	−	0.471697i	$-0.843642\pi$
$773$	−11.4009	+	11.4009i	−0.410064	+	0.410064i	0.471697	+	0.881761i	$0.343642\pi$
$774$	−10.4981	+	1.02318i	−0.377346	+	0.0367773i
$775$	13.5544	−	13.5544i	0.486888	−	0.486888i
$776$			4.10771i			0.147458i
$777$	16.7819	−	7.92678i	0.602046	−	0.284372i
$778$	8.64294	−	8.64294i	0.309864	−	0.309864i
$779$	0.939475			0.0336602
$780$		0			0
$781$	−45.9390			−1.64383
$782$	0.495320	−	0.495320i	0.0177126	−	0.0177126i
$783$	0.312928	−	1.24123i	0.0111831	−	0.0443580i
$784$			10.9992i			0.392829i
$785$	33.3627	−	33.3627i	1.19076	−	1.19076i
$786$	−5.56567	+	15.5301i	−0.198521	+	0.553939i
$787$	13.9004	−	13.9004i	0.495495	−	0.495495i	−0.414537	−	0.910032i	$-0.636057\pi$
$787$	13.9004	−	13.9004i	0.495495	−	0.495495i	0.910032	+	0.414537i	$0.136057\pi$
$788$	4.88904	+	4.88904i	0.174165	+	0.174165i
$789$	40.6935	−	19.2213i	1.44873	−	0.684295i
$790$			15.5972i			0.554924i
$791$	−9.52880	−	9.52880i	−0.338805	−	0.338805i
$792$	−9.71421	−	7.98882i	−0.345179	−	0.283870i
$793$		0			0
$794$		−	6.94001i		−	0.246292i
$795$	3.33150	−	9.29599i	0.118156	−	0.329695i
$796$	−19.9097			−0.705680
$797$	1.63938			0.0580697			0.0290349	−	0.999578i	$-0.490757\pi$
$797$	1.63938			0.0580697			0.0290349	+	0.999578i	$0.490757\pi$
$798$	−49.2698	−	17.6573i	−1.74413	−	0.625062i
$799$	−0.215921	−	0.215921i	−0.00763874	−	0.00763874i
$800$	2.20346	+	2.20346i	0.0779042	+	0.0779042i
$801$	28.6829	−	2.79552i	1.01346	−	0.0987748i
$802$	3.38923			0.119678
$803$	48.1590			1.69950
$804$	−9.16437	−	3.28433i	−0.323202	−	0.115829i
$805$		−	22.1736i		−	0.781515i
$806$		0			0
$807$	4.15545	−	1.96279i	0.146279	−	0.0690935i
$808$	−2.42878	−	2.42878i	−0.0854443	−	0.0854443i
$809$			26.0061i			0.914324i	0.889383	+	0.457162i	$0.151134\pi$
$809$			26.0061i			0.914324i	−0.889383	+	0.457162i	$0.848866\pi$
$810$	−25.1575	+	4.95088i	−0.883943	+	0.173956i
$811$	20.0016	+	20.0016i	0.702353	+	0.702353i	0.964915	−	0.262562i	$-0.0845675\pi$
$811$	20.0016	+	20.0016i	0.702353	+	0.702353i	−0.262562	+	0.964915i	$0.584567\pi$
$812$	−0.739032	+	0.739032i	−0.0259349	+	0.0259349i
$813$	6.62755	+	2.37518i	0.232438	+	0.0833013i
$814$	7.48746	−	7.48746i	0.262435	−	0.262435i
$815$			65.1922i			2.28358i
$816$	0.282457	+	0.597994i	0.00988798	+	0.0209340i
$817$	−17.7076	+	17.7076i	−0.619509	+	0.619509i
$818$	−11.0430			−0.386108
$819$		0			0
$820$	−0.375776			−0.0131227
$821$	−37.1913	+	37.1913i	−1.29798	+	1.29798i	−0.368262	+	0.929722i	$0.620047\pi$
$821$	−37.1913	+	37.1913i	−1.29798	+	1.29798i	−0.929722	+	0.368262i	$0.879953\pi$
$822$	12.4627	+	26.3848i	0.434685	+	0.920277i
$823$		−	47.5489i		−	1.65745i	−0.559657	−	0.828724i	$-0.689067\pi$
$823$		−	47.5489i		−	1.65745i	0.559657	−	0.828724i	$-0.310933\pi$
$824$	−4.80258	+	4.80258i	−0.167306	+	0.167306i
$825$	21.3014	+	7.63399i	0.741618	+	0.265781i
$826$	24.6303	−	24.6303i	0.856996	−	0.856996i
$827$	−20.0862	−	20.0862i	−0.698465	−	0.698465i	0.265615	−	0.964079i	$-0.414425\pi$
$827$	−20.0862	−	20.0862i	−0.698465	−	0.698465i	−0.964079	+	0.265615i	$0.914425\pi$
$828$	4.25086	+	3.49584i	0.147727	+	0.121489i
$829$		−	6.07832i		−	0.211109i	−0.994414	−	0.105554i	$-0.966338\pi$
$829$		−	6.07832i		−	0.211109i	0.994414	−	0.105554i	$-0.0336617\pi$
$830$	36.5261	+	36.5261i	1.26784	+	1.26784i
$831$	15.5571	−	7.34826i	0.539669	−	0.254908i
$832$		0			0
$833$		−	4.19981i		−	0.145515i
$834$	−22.1694	−	7.94506i	−0.767662	−	0.275115i
$835$	63.9002			2.21136
$836$	−29.8604			−1.03274
$837$	16.3907	+	27.4412i	0.566545	+	0.948507i
$838$	25.0787	+	25.0787i	0.866328	+	0.866328i
$839$	15.2708	+	15.2708i	0.527205	+	0.527205i	0.919738	−	0.392533i	$-0.128401\pi$
$839$	15.2708	+	15.2708i	0.527205	+	0.527205i	−0.392533	+	0.919738i	$0.628401\pi$
$840$	19.7072	+	7.06266i	0.679962	+	0.243685i
$841$	28.9393			0.997907
$842$	22.2717			0.767535
$843$	6.06799	−	16.9317i	0.208993	−	0.583159i
$844$			1.55481i			0.0535187i
$845$		0			0
$846$	1.52391	−	1.85304i	0.0523932	−	0.0637089i
$847$	19.7286	+	19.7286i	0.677884	+	0.677884i
$848$		−	2.00124i		−	0.0687227i
$849$	−26.6197	+	12.5736i	−0.913587	+	0.431525i
$850$	−0.841345	−	0.841345i	−0.0288579	−	0.0288579i
$851$	−3.27645	+	3.27645i	−0.112315	+	0.112315i
$852$	−6.40300	+	17.8665i	−0.219363	+	0.612096i
$853$	25.7979	−	25.7979i	0.883305	−	0.883305i	−0.110564	−	0.993869i	$-0.535266\pi$
$853$	25.7979	−	25.7979i	0.883305	−	0.883305i	0.993869	+	0.110564i	$0.0352657\pi$
$854$			42.0213i			1.43794i
$855$	−38.6657	+	47.0165i	−1.32234	+	1.60793i
$856$	−7.77206	+	7.77206i	−0.265644	+	0.265644i
$857$	−5.79839			−0.198069			−0.0990347	−	0.995084i	$-0.531575\pi$
$857$	−5.79839			−0.198069			−0.0990347	+	0.995084i	$0.531575\pi$
$858$		0			0
$859$	−20.5485			−0.701106			−0.350553	−	0.936543i	$-0.614006\pi$
$859$	−20.5485			−0.701106			−0.350553	+	0.936543i	$0.614006\pi$
$860$	7.08276	−	7.08276i	0.241520	−	0.241520i
$861$	−0.876413	+	0.413966i	−0.0298681	+	0.0141079i
$862$			15.0245i			0.511736i
$863$	14.7430	−	14.7430i	0.501857	−	0.501857i	−0.410158	−	0.912015i	$-0.634526\pi$
$863$	14.7430	−	14.7430i	0.501857	−	0.501857i	0.912015	+	0.410158i	$0.134526\pi$
$864$	−4.46096	+	2.66454i	−0.151765	+	0.0906496i
$865$	7.04001	−	7.04001i	0.239368	−	0.239368i
$866$	−10.4284	−	10.4284i	−0.354370	−	0.354370i
$867$	12.4679	+	26.3959i	0.423432	+	0.896452i
$868$		−	26.0976i		−	0.885811i
$869$	16.2301	+	16.2301i	0.550568	+	0.550568i
$870$	0.519173	+	1.09915i	0.0176016	+	0.0372645i
$871$		0			0
$872$		−	7.89896i		−	0.267493i
$873$	12.2650	−	1.19539i	0.415108	−	0.0404577i
$874$	13.0667			0.441987
$875$	22.7690			0.769733
$876$	6.71243	−	18.7299i	0.226792	−	0.632825i
$877$	24.7477	+	24.7477i	0.835671	+	0.835671i	0.988286	−	0.152615i	$-0.0487694\pi$
$877$	24.7477	+	24.7477i	0.835671	+	0.835671i	−0.152615	+	0.988286i	$0.548769\pi$
$878$	−20.6935	−	20.6935i	−0.698372	−	0.698372i
$879$	−15.4550	+	43.1247i	−0.521285	+	1.45456i
$880$	11.9437			0.402623
$881$	13.3252			0.448937			0.224468	−	0.974481i	$-0.427935\pi$
$881$	13.3252			0.448937			0.224468	+	0.974481i	$0.427935\pi$
$882$	32.8420	−	3.20088i	1.10585	−	0.107779i
$883$			10.0679i			0.338813i	0.985546	+	0.169406i	$0.0541851\pi$
$883$			10.0679i			0.338813i	−0.985546	+	0.169406i	$0.945815\pi$
$884$		0			0
$885$	−17.3028	−	36.6321i	−0.581629	−	1.23137i
$886$	2.11062	+	2.11062i	0.0709077	+	0.0709077i
$887$			10.2480i			0.344093i	0.985089	+	0.172046i	$0.0550379\pi$
$887$			10.2480i			0.344093i	−0.985089	+	0.172046i	$0.944962\pi$
$888$	−1.86840	−	3.95561i	−0.0626994	−	0.132742i
$889$	12.9630	+	12.9630i	0.434766	+	0.434766i
$890$	−19.3515	+	19.3515i	−0.648664	+	0.648664i
$891$	−21.0265	+	31.3300i	−0.704414	+	1.04960i
$892$	7.97380	−	7.97380i	0.266983	−	0.266983i
$893$		−	5.69605i		−	0.190611i
$894$	−29.2053	+	13.7949i	−0.976770	+	0.461369i
$895$	−1.25053	+	1.25053i	−0.0418006	+	0.0418006i
$896$	4.24255			0.141734
$897$		0			0
$898$	−4.48967			−0.149822
$899$	1.07155	−	1.07155i	0.0357381	−	0.0357381i
$900$	5.93799	−	7.22045i	0.197933	−	0.240682i
$901$			0.764128i			0.0254568i
$902$	−0.391023	+	0.391023i	−0.0130197	+	0.0130197i
$903$	8.71636	−	24.3215i	0.290062	−	0.809370i
$904$	−2.24601	+	2.24601i	−0.0747012	+	0.0747012i
$905$	42.1405	+	42.1405i	1.40080	+	1.40080i
$906$	2.46342	−	1.16358i	0.0818418	−	0.0386573i
$907$			34.0137i			1.12941i	0.825294	+	0.564703i	$0.191009\pi$
$907$			34.0137i			1.12941i	−0.825294	+	0.564703i	$0.808991\pi$
$908$	1.59491	+	1.59491i	0.0529289	+	0.0529289i
$909$	−6.54519	+	7.95879i	−0.217090	+	0.263976i
$910$		0			0
$911$			25.8368i			0.856011i	0.903776	+	0.428006i	$0.140784\pi$
$911$			25.8368i			0.856011i	−0.903776	+	0.428006i	$0.859216\pi$
$912$	−4.16196	+	11.6133i	−0.137816	+	0.384553i
$913$	76.0163			2.51577
$914$	15.3453			0.507578
$915$	46.0088	+	16.4886i	1.52100	+	0.545098i
$916$	−12.3128	−	12.3128i	−0.406827	−	0.406827i
$917$	−28.5734	−	28.5734i	−0.943578	−	0.943578i
$918$	1.70332	−	1.01740i	0.0562180	−	0.0335791i
$919$	−30.6194			−1.01004			−0.505020	−	0.863107i	$-0.668515\pi$
$919$	−30.6194			−1.01004			−0.505020	+	0.863107i	$0.668515\pi$
$920$	−5.22647			−0.172312
$921$	−28.2485	−	10.1237i	−0.930819	−	0.333587i
$922$			26.6333i			0.877120i
$923$		0			0
$924$	27.8561	−	13.1576i	0.916397	−	0.432852i
$925$	5.56533	+	5.56533i	0.182987	+	0.182987i
$926$		−	4.91091i		−	0.161382i
$927$	15.7374	+	12.9422i	0.516884	+	0.425077i
$928$	0.174195	+	0.174195i	0.00571824	+	0.00571824i
$929$	33.4306	−	33.4306i	1.09682	−	1.09682i	0.102042	−	0.994780i	$-0.467463\pi$
$929$	33.4306	−	33.4306i	1.09682	−	1.09682i	0.994780	−	0.102042i	$-0.0325375\pi$
$930$	−28.5741	−	10.2404i	−0.936980	−	0.335795i
$931$	55.3960	−	55.3960i	1.81553	−	1.81553i
$932$			20.4054i			0.668401i
$933$	−9.70886	−	20.5547i	−0.317854	−	0.672932i
$934$	23.8671	−	23.8671i	0.780954	−	0.780954i
$935$	−4.56045			−0.149143
$936$		0			0
$937$	9.11543			0.297788			0.148894	−	0.988853i	$-0.452429\pi$
$937$	9.11543			0.297788			0.148894	+	0.988853i	$0.452429\pi$
$938$	16.8613	−	16.8613i	0.550542	−	0.550542i
$939$	6.64554	+	14.0694i	0.216869	+	0.459136i
$940$			2.27833i			0.0743110i
$941$	−28.1431	+	28.1431i	−0.917439	+	0.917439i	−0.996843	−	0.0794035i	$-0.974698\pi$
$941$	−28.1431	+	28.1431i	−0.917439	+	0.917439i	0.0794035	+	0.996843i	$0.474698\pi$
$942$	−27.0036	−	9.67757i	−0.879826	−	0.315312i
$943$	0.171109	−	0.171109i	0.00557206	−	0.00557206i
$944$	−5.80554	−	5.80554i	−0.188954	−	0.188954i
$945$	15.3531	−	60.8980i	0.499436	−	1.98101i
$946$		−	14.7403i		−	0.479249i
$947$	−3.46350	−	3.46350i	−0.112549	−	0.112549i	0.648590	−	0.761138i	$-0.275359\pi$
$947$	−3.46350	−	3.46350i	−0.112549	−	0.112549i	−0.761138	+	0.648590i	$0.775359\pi$
$948$	8.57432	−	4.05001i	0.278481	−	0.131538i
$949$		0			0
$950$		−	22.1949i		−	0.720097i
$951$	41.3423	+	14.8163i	1.34062	+	0.480450i
$952$	−1.61992			−0.0525021
$953$	57.0639			1.84848			0.924240	−	0.381812i	$-0.124700\pi$
$953$	57.0639			1.84848			0.924240	+	0.381812i	$0.124700\pi$
$954$	−5.97539	+	0.582380i	−0.193460	+	0.0188552i
$955$	−20.0864	−	20.0864i	−0.649981	−	0.649981i
$956$	−12.5579	−	12.5579i	−0.406153	−	0.406153i
$957$	1.68398	+	0.603507i	0.0544355	+	0.0195086i
$958$	11.8684			0.383450
$959$	−71.4748			−2.30804
$960$	1.66472	−	4.64513i	0.0537287	−	0.149921i
$961$			6.83979i			0.220638i
$962$		0			0
$963$	25.4680	+	20.9445i	0.820694	+	0.674926i
$964$	−3.21797	−	3.21797i	−0.103644	−	0.103644i
$965$		−	52.1327i		−	1.67821i
$966$	−12.1896	+	5.75764i	−0.392193	+	0.185249i
$967$	21.8881	+	21.8881i	0.703873	+	0.703873i	0.965240	−	0.261367i	$-0.0841732\pi$
$967$	21.8881	+	21.8881i	0.703873	+	0.703873i	−0.261367	+	0.965240i	$0.584173\pi$
$968$	4.65018	−	4.65018i	0.149463	−	0.149463i
$969$	1.58915	−	4.43427i	0.0510510	−	0.142449i
$970$	−8.27486	+	8.27486i	−0.265690	+	0.265690i
$971$		−	2.20312i		−	0.0707016i	−0.999375	−	0.0353508i	$-0.988745\pi$
$971$		−	2.20312i		−	0.0707016i	0.999375	−	0.0353508i	$-0.0112548\pi$
$972$	9.25412	+	12.5444i	0.296826	+	0.402361i
$973$	40.7890	−	40.7890i	1.30763	−	1.30763i
$974$	5.00775			0.160459
$975$		0			0
$976$	9.90474			0.317043
$977$	−28.3964	+	28.3964i	−0.908481	+	0.908481i	−0.996150	−	0.0876691i	$-0.972058\pi$
$977$	−28.3964	+	28.3964i	−0.908481	+	0.908481i	0.0876691	+	0.996150i	$0.472058\pi$
$978$	35.8384	−	16.9280i	1.14599	−	0.541297i
$979$			40.2734i			1.28714i
$980$	−22.1576	+	22.1576i	−0.707798	+	0.707798i
$981$	−23.5851	+	2.29868i	−0.753016	+	0.0733912i
$982$	7.70466	−	7.70466i	0.245866	−	0.245866i
$983$	6.98688	+	6.98688i	0.222847	+	0.222847i	0.809696	−	0.586849i	$-0.199632\pi$
$983$	6.98688	+	6.98688i	0.222847	+	0.222847i	−0.586849	+	0.809696i	$0.699632\pi$
$984$	0.0975749	+	0.206577i	0.00311058	+	0.00658543i
$985$			19.6976i			0.627619i
$986$	−0.0665127	−	0.0665127i	−0.00211820	−	0.00211820i
$987$	2.50988	+	5.31370i	0.0798904	+	0.169137i
$988$		0			0
$989$			6.45023i			0.205105i
$990$	−3.47575	−	35.6622i	−0.110466	−	1.13342i
$991$	16.4450			0.522394			0.261197	−	0.965285i	$-0.415883\pi$
$991$	16.4450			0.522394			0.261197	+	0.965285i	$0.415883\pi$
$992$	−6.15141			−0.195307
$993$	12.4502	−	34.7403i	0.395096	−	1.10245i
$994$	−32.8722	−	32.8722i	−1.04264	−	1.04264i
$995$	−40.1074	−	40.1074i	−1.27149	−	1.27149i
$996$	10.5952	−	29.5641i	0.335721	−	0.936774i
$997$	23.8288			0.754667			0.377333	−	0.926077i	$-0.376841\pi$
$997$	23.8288			0.754667			0.377333	+	0.926077i	$0.376841\pi$
$998$	16.3336			0.517032
$999$	−11.2671	+	6.72989i	−0.356477	+	0.212924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.e.437.20	yes	48
3.2	odd	2	inner	1014.2.g.e.437.12	yes	48
13.5	odd	4	inner	1014.2.g.e.239.12	yes	48
13.8	odd	4	inner	1014.2.g.e.239.13	yes	48
13.12	even	2	inner	1014.2.g.e.437.5	yes	48
39.5	even	4	inner	1014.2.g.e.239.20	yes	48
39.8	even	4	inner	1014.2.g.e.239.5	✓	48
39.38	odd	2	inner	1014.2.g.e.437.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.g.e.239.5	✓	48	39.8	even	4	inner
1014.2.g.e.239.12	yes	48	13.5	odd	4	inner
1014.2.g.e.239.13	yes	48	13.8	odd	4	inner
1014.2.g.e.239.20	yes	48	39.5	even	4	inner
1014.2.g.e.437.5	yes	48	13.12	even	2	inner
1014.2.g.e.437.12	yes	48	3.2	odd	2	inner
1014.2.g.e.437.13	yes	48	39.38	odd	2	inner
1014.2.g.e.437.20	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.739750 - 1.56613i) q^{3} -1.00000i q^{4} +(2.01447 - 2.01447i) q^{5} +(-1.63050 - 0.584341i) q^{6} +(2.99993 - 2.99993i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.90554 + 2.31709i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.739750 - 1.56613i) q^{3} -1.00000i q^{4} +(2.01447 - 2.01447i) q^{5} +(-1.63050 - 0.584341i) q^{6} +(2.99993 - 2.99993i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.90554 + 2.31709i) q^{9} -2.84889i q^{10} +(-2.96449 - 2.96449i) q^{11} +(-1.56613 + 0.739750i) q^{12} -4.24255i q^{14} +(-4.64513 - 1.66472i) q^{15} -1.00000 q^{16} +0.381828 q^{17} +(0.291010 + 2.98585i) q^{18} +(5.03636 + 5.03636i) q^{19} +(-2.01447 - 2.01447i) q^{20} +(-6.91749 - 2.47909i) q^{21} -4.19242 q^{22} +1.83457 q^{23} +(-0.584341 + 1.63050i) q^{24} -3.11617i q^{25} +(5.03850 + 1.27026i) q^{27} +(-2.99993 - 2.99993i) q^{28} -0.246349i q^{29} +(-4.46174 + 2.10746i) q^{30} +(4.34970 + 4.34970i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.44980 + 6.83575i) q^{33} +(0.269993 - 0.269993i) q^{34} -12.0865i q^{35} +(2.31709 + 1.90554i) q^{36} +(-1.78595 + 1.78595i) q^{37} +7.12249 q^{38} -2.84889 q^{40} +(0.0932693 - 0.0932693i) q^{41} +(-6.64439 + 3.13842i) q^{42} +3.51595i q^{43} +(-2.96449 + 2.96449i) q^{44} +(0.829056 + 8.50636i) q^{45} +(1.29723 - 1.29723i) q^{46} +(-0.565492 - 0.565492i) q^{47} +(0.739750 + 1.56613i) q^{48} -10.9992i q^{49} +(-2.20346 - 2.20346i) q^{50} +(-0.282457 - 0.597994i) q^{51} +2.00124i q^{53} +(4.46096 - 2.66454i) q^{54} -11.9437 q^{55} -4.24255 q^{56} +(4.16196 - 11.6133i) q^{57} +(-0.174195 - 0.174195i) q^{58} +(5.80554 + 5.80554i) q^{59} +(-1.66472 + 4.64513i) q^{60} -9.90474 q^{61} +6.15141 q^{62} +(1.23462 + 12.6676i) q^{63} +1.00000i q^{64} +(3.10134 + 6.56588i) q^{66} +(3.97434 + 3.97434i) q^{67} -0.381828i q^{68} +(-1.35712 - 2.87317i) q^{69} +(-8.54648 - 8.54648i) q^{70} +(7.74822 - 7.74822i) q^{71} +(2.98585 - 0.291010i) q^{72} +(-8.12266 + 8.12266i) q^{73} +2.52572i q^{74} +(-4.88033 + 2.30518i) q^{75} +(5.03636 - 5.03636i) q^{76} -17.7865 q^{77} -5.47484 q^{79} +(-2.01447 + 2.01447i) q^{80} +(-1.73783 - 8.83063i) q^{81} -0.131903i q^{82} +(-12.8212 + 12.8212i) q^{83} +(-2.47909 + 6.91749i) q^{84} +(0.769181 - 0.769181i) q^{85} +(2.48615 + 2.48615i) q^{86} +(-0.385816 + 0.182237i) q^{87} +4.19242i q^{88} +(-6.79265 - 6.79265i) q^{89} +(6.60114 + 5.42867i) q^{90} -1.83457i q^{92} +(3.59452 - 10.0299i) q^{93} -0.799727 q^{94} +20.2912 q^{95} +(1.63050 + 0.584341i) q^{96} +(-2.90459 - 2.90459i) q^{97} +(-7.77762 - 7.77762i) q^{98} +(12.5179 - 1.22004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} + 20 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 + 20 * q^9	\( 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) \) 48 * q - 4 * q^3 + 20 * q^9 - 48 * q^16 - 32 * q^22 + 116 * q^27 + 8 * q^40 - 40 * q^42 + 4 * q^48 - 144 * q^55 - 80 * q^61 + 96 * q^66 - 56 * q^79 + 84 * q^81 + 224 * q^87 - 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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