LMFDB - Embedded newform 1274.2.v.h.361.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(361,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.v (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,4,10,0,0,0,0,32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 895 x^{16} + 9634 x^{14} + 62977 x^{12} + 257850 x^{10} + 656102 x^{8} + \cdots + 32041 $ x^20 + 46x^18 + 895x^16 + 9634x^14 + 62977x^12 + 257850x^10 + 656102x^8 + 989866x^6 + 795896x^4 + 273668*x^2 + 32041
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$2.35757i$ of defining polynomial
Character	$\chi$	$=$	1274.361
Dual form			1274.2.v.h.667.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +2.35757 q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.89612 + 1.67208i) q^{5} +(-2.04172 - 1.17879i) q^{6} -1.00000i q^{8} +2.55814 q^{9} +3.34415 q^{10} -5.03653i q^{11} +(1.17879 + 2.04172i) q^{12} +(1.92804 + 3.04674i) q^{13} +(-6.82781 + 3.94204i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.86635 + 3.23261i) q^{17} +(-2.21541 - 1.27907i) q^{18} +5.87400i q^{19} +(-2.89612 - 1.67208i) q^{20} +(-2.51826 + 4.36176i) q^{22} +(-1.89185 + 3.27678i) q^{23} -2.35757i q^{24} +(3.09168 - 5.35494i) q^{25} +(-0.146362 - 3.60258i) q^{26} -1.04172 q^{27} +(3.36143 + 5.82216i) q^{29} +7.88408 q^{30} +(0.884906 + 0.510901i) q^{31} +(0.866025 - 0.500000i) q^{32} -11.8740i q^{33} -3.73270i q^{34} +(1.27907 + 2.21541i) q^{36} +(-0.370851 - 0.214111i) q^{37} +(2.93700 - 5.08703i) q^{38} +(4.54550 + 7.18292i) q^{39} +(1.67208 + 2.89612i) q^{40} +(-0.917963 + 0.529986i) q^{41} +(1.65120 - 2.85996i) q^{43} +(4.36176 - 2.51826i) q^{44} +(-7.40868 + 4.27741i) q^{45} +(3.27678 - 1.89185i) q^{46} +(-4.60157 + 2.65672i) q^{47} +(-1.17879 + 2.04172i) q^{48} +(-5.35494 + 3.09168i) q^{50} +(4.40005 + 7.62112i) q^{51} +(-1.67454 + 3.19311i) q^{52} +(-1.15836 + 2.00634i) q^{53} +(0.902152 + 0.520858i) q^{54} +(8.42146 + 14.5864i) q^{55} +13.8484i q^{57} -6.72285i q^{58} +(-7.00324 + 4.04332i) q^{59} +(-6.82781 - 3.94204i) q^{60} +10.1010 q^{61} +(-0.510901 - 0.884906i) q^{62} -1.00000 q^{64} +(-10.6782 - 5.59991i) q^{65} +(-5.93699 + 10.2832i) q^{66} +13.2982i q^{67} +(-1.86635 + 3.23261i) q^{68} +(-4.46017 + 7.72525i) q^{69} +(2.35754 + 1.36113i) q^{71} -2.55814i q^{72} +(6.88886 + 3.97728i) q^{73} +(0.214111 + 0.370851i) q^{74} +(7.28885 - 12.6247i) q^{75} +(-5.08703 + 2.93700i) q^{76} +(-0.345059 - 8.49334i) q^{78} +(7.07112 + 12.2475i) q^{79} -3.34415i q^{80} -10.1303 q^{81} +1.05997 q^{82} -9.17859i q^{83} +(-10.8104 - 6.24136i) q^{85} +(-2.85996 + 1.65120i) q^{86} +(7.92480 + 13.7262i) q^{87} -5.03653 q^{88} +(-4.68772 - 2.70646i) q^{89} +8.55481 q^{90} -3.78370 q^{92} +(2.08623 + 1.20449i) q^{93} +5.31343 q^{94} +(-9.82177 - 17.0118i) q^{95} +(2.04172 - 1.17879i) q^{96} +(-14.8742 - 8.58763i) q^{97} -12.8842i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} + 10 q^{4} + 32 q^{9} - 8 q^{10} + 2 q^{12} - 6 q^{13} - 12 q^{15} - 10 q^{16} + 10 q^{17} - 24 q^{18} + 2 q^{22} + 18 q^{25} + 6 q^{26} + 28 q^{27} + 2 q^{29} + 4 q^{30} - 6 q^{31} + 16 q^{36}+ \cdots - 78 q^{97}+O(q^{100}) $ 20 * q + 4 * q^3 + 10 * q^4 + 32 * q^9 - 8 * q^10 + 2 * q^12 - 6 * q^13 - 12 * q^15 - 10 * q^16 + 10 * q^17 - 24 * q^18 + 2 * q^22 + 18 * q^25 + 6 * q^26 + 28 * q^27 + 2 * q^29 + 4 * q^30 - 6 * q^31 + 16 * q^36 - 36 * q^37 + 14 * q^38 - 26 * q^39 - 4 * q^40 - 18 * q^41 + 8 * q^43 - 6 * q^44 + 60 * q^45 + 12 * q^46 + 18 * q^47 - 2 * q^48 - 12 * q^50 - 22 * q^51 - 4 * q^53 + 18 * q^54 - 2 * q^55 - 12 * q^60 - 8 * q^61 + 24 * q^62 - 20 * q^64 - 18 * q^65 - 32 * q^66 - 10 * q^68 + 34 * q^69 - 18 * q^71 - 72 * q^73 + 12 * q^74 + 18 * q^75 - 24 * q^76 + 20 * q^78 + 42 * q^79 + 4 * q^81 - 32 * q^82 - 12 * q^85 - 42 * q^86 + 64 * q^87 + 4 * q^88 + 18 * q^89 - 52 * q^90 + 60 * q^93 + 32 * q^94 - 12 * q^95 - 78 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	2.35757			1.36114			0.680572	−	0.732681i	$-0.261731\pi$
$3$	2.35757			1.36114			0.680572	+	0.732681i	$0.261731\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.89612	+	1.67208i	−1.29518	+	0.747775i	−0.979568	−	0.201112i	$-0.935545\pi$
$5$	−2.89612	+	1.67208i	−1.29518	+	0.747775i	−0.315616	+	0.948887i	$0.602211\pi$
$6$	−2.04172	−	1.17879i	−0.833527	−	0.481237i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	2.55814			0.852713
$10$	3.34415			1.05751
$11$		−	5.03653i		−	1.51857i	−0.650758	−	0.759285i	$-0.725549\pi$
$11$		−	5.03653i		−	1.51857i	0.650758	−	0.759285i	$-0.274451\pi$
$12$	1.17879	+	2.04172i	0.340286	+	0.589393i
$13$	1.92804	+	3.04674i	0.534743	+	0.845015i
$13$	1.92804	+	3.04674i	0.534743	+	0.845015i
$14$		0			0
$15$	−6.82781	+	3.94204i	−1.76293	+	1.01783i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.86635	+	3.23261i	0.452657	+	0.784024i	0.998550	−	0.0538304i	$-0.0171430\pi$
$17$	1.86635	+	3.23261i	0.452657	+	0.784024i	−0.545894	+	0.837855i	$0.683810\pi$
$18$	−2.21541	−	1.27907i	−0.522178	−	0.301480i
$19$			5.87400i			1.34759i	0.738919	+	0.673794i	$0.235336\pi$
$19$			5.87400i			1.34759i	−0.738919	+	0.673794i	$0.764664\pi$
$20$	−2.89612	−	1.67208i	−0.647592	−	0.373888i
$21$		0			0
$22$	−2.51826	+	4.36176i	−0.536896	+	0.929931i
$23$	−1.89185	+	3.27678i	−0.394478	+	0.683257i	−0.993034	−	0.117824i	$-0.962408\pi$
$23$	−1.89185	+	3.27678i	−0.394478	+	0.683257i	0.598556	+	0.801081i	$0.295741\pi$
$24$		−	2.35757i		−	0.481237i
$25$	3.09168	−	5.35494i	0.618336	−	1.07099i
$26$	−0.146362	−	3.60258i	−0.0287039	−	0.706524i
$27$	−1.04172			−0.200478
$28$		0			0
$29$	3.36143	+	5.82216i	0.624201	+	1.08115i	0.988695	+	0.149942i	$0.0479088\pi$
$29$	3.36143	+	5.82216i	0.624201	+	1.08115i	−0.364494	+	0.931206i	$0.618758\pi$
$30$	7.88408			1.43943
$31$	0.884906	+	0.510901i	0.158934	+	0.0917605i	0.577357	−	0.816491i	$-0.304084\pi$
$31$	0.884906	+	0.510901i	0.158934	+	0.0917605i	−0.418424	+	0.908252i	$0.637417\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		−	11.8740i		−	2.06699i
$34$		−	3.73270i		−	0.640153i
$35$		0			0
$36$	1.27907	+	2.21541i	0.213178	+	0.369236i
$37$	−0.370851	−	0.214111i	−0.0609676	−	0.0351997i	0.469206	−	0.883089i	$-0.344540\pi$
$37$	−0.370851	−	0.214111i	−0.0609676	−	0.0351997i	−0.530174	+	0.847889i	$0.677873\pi$
$38$	2.93700	−	5.08703i	0.476444	−	0.825226i
$39$	4.54550	+	7.18292i	0.727862	+	1.15019i
$40$	1.67208	+	2.89612i	0.264378	+	0.457917i
$41$	−0.917963	+	0.529986i	−0.143362	+	0.0827699i	−0.569965	−	0.821669i	$-0.693043\pi$
$41$	−0.917963	+	0.529986i	−0.143362	+	0.0827699i	0.426603	+	0.904439i	$0.359710\pi$
$42$		0			0
$43$	1.65120	−	2.85996i	0.251805	−	0.436140i	−0.712217	−	0.701959i	$-0.752309\pi$
$43$	1.65120	−	2.85996i	0.251805	−	0.436140i	0.964023	+	0.265819i	$0.0856423\pi$
$44$	4.36176	−	2.51826i	0.657560	−	0.379643i
$45$	−7.40868	+	4.27741i	−1.10442	+	0.637638i
$46$	3.27678	−	1.89185i	0.483135	−	0.278938i
$47$	−4.60157	+	2.65672i	−0.671207	+	0.387522i	−0.796534	−	0.604594i	$-0.793335\pi$
$47$	−4.60157	+	2.65672i	−0.671207	+	0.387522i	0.125327	+	0.992116i	$0.460002\pi$
$48$	−1.17879	+	2.04172i	−0.170143	+	0.294696i
$49$		0			0
$50$	−5.35494	+	3.09168i	−0.757303	+	0.437229i
$51$	4.40005	+	7.62112i	0.616131	+	1.06717i
$52$	−1.67454	+	3.19311i	−0.232216	+	0.442804i
$53$	−1.15836	+	2.00634i	−0.159113	+	0.275592i	−0.934549	−	0.355834i	$-0.884197\pi$
$53$	−1.15836	+	2.00634i	−0.159113	+	0.275592i	0.775436	+	0.631426i	$0.217530\pi$
$54$	0.902152	+	0.520858i	0.122767	+	0.0708798i
$55$	8.42146	+	14.5864i	1.13555	+	1.96683i
$56$		0			0
$57$			13.8484i			1.83426i
$58$		−	6.72285i		−	0.882754i
$59$	−7.00324	+	4.04332i	−0.911745	+	0.526396i	−0.880992	−	0.473131i	$-0.843124\pi$
$59$	−7.00324	+	4.04332i	−0.911745	+	0.526396i	−0.0307526	+	0.999527i	$0.509790\pi$
$60$	−6.82781	−	3.94204i	−0.881467	−	0.508915i
$61$	10.1010			1.29330			0.646651	−	0.762786i	$-0.276169\pi$
$61$	10.1010			1.29330			0.646651	+	0.762786i	$0.276169\pi$
$62$	−0.510901	−	0.884906i	−0.0648845	−	0.112383i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−10.6782	−	5.59991i	−1.32447	−	0.694583i
$66$	−5.93699	+	10.2832i	−0.730793	+	1.26577i
$67$			13.2982i			1.62463i	0.583216	+	0.812317i	$0.301794\pi$
$67$			13.2982i			1.62463i	−0.583216	+	0.812317i	$0.698206\pi$
$68$	−1.86635	+	3.23261i	−0.226328	+	0.392012i
$69$	−4.46017	+	7.72525i	−0.536942	+	0.930011i
$70$		0			0
$71$	2.35754	+	1.36113i	0.279788	+	0.161536i	0.633328	−	0.773884i	$-0.281689\pi$
$71$	2.35754	+	1.36113i	0.279788	+	0.161536i	−0.353539	+	0.935420i	$0.615022\pi$
$72$		−	2.55814i		−	0.301480i
$73$	6.88886	+	3.97728i	0.806280	+	0.465506i	0.845662	−	0.533718i	$-0.179206\pi$
$73$	6.88886	+	3.97728i	0.806280	+	0.465506i	−0.0393824	+	0.999224i	$0.512539\pi$
$74$	0.214111	+	0.370851i	0.0248899	+	0.0431106i
$75$	7.28885	−	12.6247i	0.841644	−	1.45777i
$76$	−5.08703	+	2.93700i	−0.583523	+	0.336897i
$77$		0			0
$78$	−0.345059	−	8.49334i	−0.0390702	−	0.961681i
$79$	7.07112	+	12.2475i	0.795563	+	1.37796i	0.922481	+	0.386043i	$0.126158\pi$
$79$	7.07112	+	12.2475i	0.795563	+	1.37796i	−0.126918	+	0.991913i	$0.540508\pi$
$80$		−	3.34415i		−	0.373888i
$81$	−10.1303			−1.12559
$82$	1.05997			0.117054
$83$		−	9.17859i		−	1.00748i	−0.863855	−	0.503741i	$-0.831957\pi$
$83$		−	9.17859i		−	1.00748i	0.863855	−	0.503741i	$-0.168043\pi$
$84$		0			0
$85$	−10.8104	−	6.24136i	−1.17255	−	0.676971i
$86$	−2.85996	+	1.65120i	−0.308397	+	0.178053i
$87$	7.92480	+	13.7262i	0.849628	+	1.47160i
$88$	−5.03653			−0.536896
$89$	−4.68772	−	2.70646i	−0.496897	−	0.286884i	0.230534	−	0.973064i	$-0.425953\pi$
$89$	−4.68772	−	2.70646i	−0.496897	−	0.286884i	−0.727431	+	0.686181i	$0.759286\pi$
$90$	8.55481			0.901756
$91$		0			0
$92$	−3.78370			−0.394478
$93$	2.08623	+	1.20449i	0.216332	+	0.124899i
$94$	5.31343			0.548039
$95$	−9.82177	−	17.0118i	−1.00769	−	1.74537i
$96$	2.04172	−	1.17879i	0.208382	−	0.120309i
$97$	−14.8742	−	8.58763i	−1.51025	−	0.871941i	−0.999929	−	0.0119557i	$-0.996194\pi$
$97$	−14.8742	−	8.58763i	−1.51025	−	0.871941i	−0.510318	−	0.859986i	$-0.670472\pi$
$98$		0			0
$99$		−	12.8842i		−	1.29491i
$100$	6.18336			0.618336
$101$	−2.44826			−0.243611			−0.121806	−	0.992554i	$-0.538868\pi$
$101$	−2.44826			−0.243611			−0.121806	+	0.992554i	$0.538868\pi$
$102$		−	8.80011i		−	0.871341i
$103$	8.96428	+	15.5266i	0.883277	+	1.52988i	0.847676	+	0.530514i	$0.178001\pi$
$103$	8.96428	+	15.5266i	0.883277	+	1.52988i	0.0356010	+	0.999366i	$0.488665\pi$
$104$	3.04674	−	1.92804i	0.298758	−	0.189060i
$105$		0			0
$106$	2.00634	−	1.15836i	0.194873	−	0.112510i
$107$	4.95119	−	8.57572i	0.478650	−	0.829046i	−0.521050	−	0.853526i	$-0.674460\pi$
$107$	4.95119	−	8.57572i	0.478650	−	0.829046i	0.999700	+	0.0244799i	$0.00779297\pi$
$108$	−0.520858	−	0.902152i	−0.0501196	−	0.0868096i
$109$	3.08121	+	1.77894i	0.295127	+	0.170391i	0.640252	−	0.768165i	$-0.278830\pi$
$109$	3.08121	+	1.77894i	0.295127	+	0.170391i	−0.345125	+	0.938557i	$0.612163\pi$
$110$		−	16.8429i		−	1.60591i
$111$	−0.874309	−	0.504782i	−0.0829857	−	0.0479118i
$112$		0			0
$113$	2.44458	−	4.23414i	0.229967	−	0.398314i	−0.727831	−	0.685756i	$-0.759472\pi$
$113$	2.44458	−	4.23414i	0.229967	−	0.398314i	0.957798	+	0.287442i	$0.0928049\pi$
$114$	6.92418	−	11.9930i	0.648509	−	1.12325i
$115$		−	12.6533i		−	1.17992i
$116$	−3.36143	+	5.82216i	−0.312101	+	0.540574i
$117$	4.93220	+	7.79400i	0.455982	+	0.720556i
$118$	8.08665			0.744436
$119$		0			0
$120$	3.94204	+	6.82781i	0.359857	+	0.623291i
$121$	−14.3666			−1.30606
$122$	−8.74773	−	5.05050i	−0.791982	−	0.457251i
$123$	−2.16416	+	1.24948i	−0.195136	+	0.112662i
$124$			1.02180i			0.0917605i
$125$			3.95733i			0.353954i
$126$		0			0
$127$	−4.14641	−	7.18180i	−0.367935	−	0.637281i	0.621308	−	0.783567i	$-0.286602\pi$
$127$	−4.14641	−	7.18180i	−0.367935	−	0.637281i	−0.989242	+	0.146285i	$0.953268\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	3.89282	−	6.74256i	0.342744	−	0.593649i
$130$	6.44767	+	10.1888i	0.565498	+	0.893615i
$131$	3.08084	+	5.33618i	0.269174	+	0.466224i	0.968649	−	0.248434i	$-0.0799158\pi$
$131$	3.08084	+	5.33618i	0.269174	+	0.466224i	−0.699474	+	0.714658i	$0.746583\pi$
$132$	10.2832	−	5.93699i	0.895035	−	0.516748i
$133$		0			0
$134$	6.64910	−	11.5166i	0.574395	−	0.994881i
$135$	3.01693	−	1.74183i	0.259656	−	0.149913i
$136$	3.23261	−	1.86635i	0.277194	−	0.160038i
$137$	6.44163	−	3.71908i	0.550346	−	0.317742i	−0.198916	−	0.980017i	$-0.563742\pi$
$137$	6.44163	−	3.71908i	0.550346	−	0.317742i	0.749261	+	0.662274i	$0.230409\pi$
$138$	7.72525	−	4.46017i	0.657617	−	0.379675i
$139$	−2.44199	+	4.22965i	−0.207127	+	0.358754i	−0.950808	−	0.309780i	$-0.899745\pi$
$139$	−2.44199	+	4.22965i	−0.207127	+	0.358754i	0.743682	+	0.668534i	$0.233078\pi$
$140$		0			0
$141$	−10.8485	+	6.26339i	−0.913610	+	0.527473i
$142$	−1.36113	−	2.35754i	−0.114223	−	0.197840i
$143$	15.3450	−	9.71065i	1.28321	−	0.812045i
$144$	−1.27907	+	2.21541i	−0.106589	+	0.184618i
$145$	−19.4702	−	11.2411i	−1.61691	−	0.933524i
$146$	−3.97728	−	6.88886i	−0.329162	−	0.570126i
$147$		0			0
$148$		−	0.428222i		−	0.0351997i
$149$		−	5.61868i		−	0.460301i	−0.973155	−	0.230150i	$-0.926078\pi$
$149$		−	5.61868i		−	0.460301i	0.973155	−	0.230150i	$-0.0739218\pi$
$150$	−12.6247	+	7.28885i	−1.03080	+	0.595132i
$151$	7.19648	+	4.15489i	0.585641	+	0.338120i	0.763372	−	0.645959i	$-0.223542\pi$
$151$	7.19648	+	4.15489i	0.585641	+	0.338120i	−0.177731	+	0.984079i	$0.556876\pi$
$152$	5.87400			0.476444
$153$	4.77439	+	8.26948i	0.385986	+	0.668548i
$154$		0			0
$155$	−3.41706			−0.274465
$156$	−3.94784	+	7.52797i	−0.316080	+	0.602720i
$157$	2.60751	−	4.51635i	0.208102	−	0.360444i	−0.743014	−	0.669275i	$-0.766605\pi$
$157$	2.60751	−	4.51635i	0.208102	−	0.360444i	0.951117	+	0.308832i	$0.0999380\pi$
$158$		−	14.1422i		−	1.12510i
$159$	−2.73092	+	4.73009i	−0.216576	+	0.375121i
$160$	−1.67208	+	2.89612i	−0.132189	+	0.228958i
$161$		0			0
$162$	8.77313	+	5.06517i	0.689282	+	0.397957i
$163$		−	12.4796i		−	0.977481i	−0.872429	−	0.488741i	$-0.837456\pi$
$163$		−	12.4796i		−	0.977481i	0.872429	−	0.488741i	$-0.162544\pi$
$164$	−0.917963	−	0.529986i	−0.0716809	−	0.0413850i
$165$	19.8542	+	34.3885i	1.54565	+	2.67714i
$166$	−4.58930	+	7.94889i	−0.356198	+	0.616954i
$167$	0.409946	−	0.236682i	0.0317226	−	0.0183150i	−0.484055	−	0.875038i	$-0.660836\pi$
$167$	0.409946	−	0.236682i	0.0317226	−	0.0183150i	0.515777	+	0.856723i	$0.327503\pi$
$168$		0			0
$169$	−5.56530	+	11.7485i	−0.428100	+	0.903731i
$170$	6.24136	+	10.8104i	0.478691	+	0.829116i
$171$			15.0265i			1.14911i
$172$	3.30240			0.251805
$173$	−10.1320			−0.770323			−0.385162	−	0.922849i	$-0.625854\pi$
$173$	−10.1320			−0.770323			−0.385162	+	0.922849i	$0.625854\pi$
$174$		−	15.8496i		−	1.20156i
$175$		0			0
$176$	4.36176	+	2.51826i	0.328780	+	0.189821i
$177$	−16.5106	+	9.53242i	−1.24102	+	0.716501i
$178$	2.70646	+	4.68772i	0.202857	+	0.351359i
$179$	10.7142			0.800816			0.400408	−	0.916337i	$-0.368868\pi$
$179$	10.7142			0.800816			0.400408	+	0.916337i	$0.368868\pi$
$180$	−7.40868	−	4.27741i	−0.552211	−	0.318819i
$181$	−1.56347			−0.116212			−0.0581058	−	0.998310i	$-0.518506\pi$
$181$	−1.56347			−0.116212			−0.0581058	+	0.998310i	$0.518506\pi$
$182$		0			0
$183$	23.8138			1.76037
$184$	3.27678	+	1.89185i	0.241568	+	0.139469i
$185$	1.43204			0.105286
$186$	−1.20449	−	2.08623i	−0.0883171	−	0.152970i
$187$	16.2812	−	9.39993i	1.19060	−	0.687391i
$188$	−4.60157	−	2.65672i	−0.335604	−	0.193761i
$189$		0			0
$190$			19.6435i			1.42509i
$191$	−9.39317			−0.679666			−0.339833	−	0.940486i	$-0.610371\pi$
$191$	−9.39317			−0.679666			−0.339833	+	0.940486i	$0.610371\pi$
$192$	−2.35757			−0.170143
$193$		−	9.15989i		−	0.659343i	−0.944096	−	0.329672i	$-0.893062\pi$
$193$		−	9.15989i		−	0.659343i	0.944096	−	0.329672i	$-0.106938\pi$
$194$	8.58763	+	14.8742i	0.616556	+	1.06791i
$195$	−25.1747	−	13.2022i	−1.80280	−	0.945427i
$196$		0			0
$197$	13.4152	−	7.74526i	0.955793	−	0.551827i	0.0609170	−	0.998143i	$-0.480598\pi$
$197$	13.4152	−	7.74526i	0.955793	−	0.551827i	0.894876	+	0.446316i	$0.147264\pi$
$198$	−6.44208	+	11.1580i	−0.457818	+	0.792965i
$199$	−2.74194	−	4.74917i	−0.194371	−	0.336660i	0.752323	−	0.658794i	$-0.228933\pi$
$199$	−2.74194	−	4.74917i	−0.194371	−	0.336660i	−0.946694	+	0.322134i	$0.895600\pi$
$200$	−5.35494	−	3.09168i	−0.378652	−	0.218615i
$201$			31.3515i			2.21136i
$202$	2.12026	+	1.22413i	0.149181	+	0.0861295i
$203$		0			0
$204$	−4.40005	+	7.62112i	−0.308065	+	0.533585i
$205$	1.77235	−	3.06981i	0.123787	−	0.214405i
$206$		−	17.9286i		−	1.24914i
$207$	−4.83962	+	8.38247i	−0.336377	+	0.582622i
$208$	−3.60258	+	0.146362i	−0.249794	+	0.0101484i
$209$	29.5846			2.04641
$210$		0			0
$211$	−2.54733	−	4.41210i	−0.175365	−	0.303741i	0.764922	−	0.644122i	$-0.222777\pi$
$211$	−2.54733	−	4.41210i	−0.175365	−	0.303741i	−0.940288	+	0.340381i	$0.889444\pi$
$212$	−2.31672			−0.159113
$213$	5.55806	+	3.20895i	0.380832	+	0.219874i
$214$	−8.57572	+	4.95119i	−0.586224	+	0.338457i
$215$			11.0437i			0.753176i
$216$			1.04172i			0.0708798i
$217$		0			0
$218$	−1.77894	−	3.08121i	−0.120485	−	0.208686i
$219$	16.2410	+	9.37673i	1.09746	+	0.633621i
$220$	−8.42146	+	14.5864i	−0.567775	+	0.983415i
$221$	−6.25054	+	11.9189i	−0.420457	+	0.801753i
$222$	0.504782	+	0.874309i	0.0338788	+	0.0586798i
$223$	8.65366	−	4.99619i	0.579492	−	0.334570i	−0.181440	−	0.983402i	$-0.558076\pi$
$223$	8.65366	−	4.99619i	0.579492	−	0.334570i	0.760931	+	0.648832i	$0.224742\pi$
$224$		0			0
$225$	7.90895	−	13.6987i	0.527263	−	0.913247i
$226$	−4.23414	+	2.44458i	−0.281651	+	0.162611i
$227$	−11.4442	+	6.60729i	−0.759575	+	0.438541i	−0.829143	−	0.559036i	$-0.811171\pi$
$227$	−11.4442	+	6.60729i	−0.759575	+	0.438541i	0.0695679	+	0.997577i	$0.477838\pi$
$228$	−11.9930	+	6.92418i	−0.794258	+	0.458565i
$229$	−8.62549	+	4.97993i	−0.569989	+	0.329083i	−0.757145	−	0.653247i	$-0.773406\pi$
$229$	−8.62549	+	4.97993i	−0.569989	+	0.329083i	0.187156	+	0.982330i	$0.440073\pi$
$230$	−6.32664	+	10.9581i	−0.417166	+	0.722553i
$231$		0			0
$232$	5.82216	−	3.36143i	0.382244	−	0.220688i
$233$	−4.29233	−	7.43454i	−0.281200	−	0.487053i	0.690480	−	0.723351i	$-0.257399\pi$
$233$	−4.29233	−	7.43454i	−0.281200	−	0.487053i	−0.971681	+	0.236298i	$0.924066\pi$
$234$	−0.374414	−	9.21590i	−0.0244762	−	0.602462i
$235$	8.88446	−	15.3883i	0.579558	−	1.00382i
$236$	−7.00324	−	4.04332i	−0.455872	−	0.263198i
$237$	16.6707	+	28.8744i	1.08288	+	1.87560i
$238$		0			0
$239$		−	1.17300i		−	0.0758748i	−0.999280	−	0.0379374i	$-0.987921\pi$
$239$		−	1.17300i		−	0.0758748i	0.999280	−	0.0379374i	$-0.0120787\pi$
$240$		−	7.88408i		−	0.508915i
$241$	21.1208	−	12.1941i	1.36051	−	0.785490i	0.370817	−	0.928706i	$-0.379078\pi$
$241$	21.1208	−	12.1941i	1.36051	−	0.785490i	0.989691	+	0.143216i	$0.0457443\pi$
$242$	12.4419	+	7.18332i	0.799794	+	0.461761i
$243$	−20.7578			−1.33162
$244$	5.05050	+	8.74773i	0.323325	+	0.560016i
$245$		0			0
$246$	2.49896			0.159328
$247$	−17.8966	+	11.3253i	−1.13873	+	0.720613i
$248$	0.510901	−	0.884906i	0.0324422	−	0.0561916i
$249$		−	21.6392i		−	1.37133i
$250$	1.97866	−	3.42714i	0.125142	−	0.216752i
$251$	10.6649	−	18.4721i	0.673162	−	1.16595i	−0.303840	−	0.952723i	$-0.598269\pi$
$251$	10.6649	−	18.4721i	0.673162	−	1.16595i	0.977002	−	0.213228i	$-0.0683978\pi$
$252$		0			0
$253$	16.5036	+	9.52837i	1.03757	+	0.599043i
$254$			8.29282i			0.520338i
$255$	−25.4862	−	14.7145i	−1.59601	−	0.921455i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.42956	−	11.1363i	0.401065	−	0.694664i	−0.592790	−	0.805357i	$-0.701974\pi$
$257$	6.42956	−	11.1363i	0.401065	−	0.694664i	0.993855	+	0.110693i	$0.0353069\pi$
$258$	−6.74256	+	3.89282i	−0.419773	+	0.242356i
$259$		0			0
$260$	−0.489457	−	12.0476i	−0.0303548	−	0.747159i
$261$	8.59900	+	14.8939i	0.532265	+	0.921910i
$262$		−	6.16169i		−	0.380670i
$263$	24.8601			1.53294			0.766470	−	0.642281i	$-0.222012\pi$
$263$	24.8601			1.53294			0.766470	+	0.642281i	$0.222012\pi$
$264$	−11.8740			−0.730793
$265$		−	7.74748i		−	0.475924i
$266$		0			0
$267$	−11.0516	−	6.38066i	−0.676349	−	0.390490i
$268$	−11.5166	+	6.64910i	−0.703487	+	0.406158i
$269$	−10.3012	−	17.8422i	−0.628074	−	1.08786i	−0.987938	−	0.154851i	$-0.950510\pi$
$269$	−10.3012	−	17.8422i	−0.628074	−	1.08786i	0.359864	−	0.933005i	$-0.382823\pi$
$270$	−3.48366			−0.212009
$271$	4.57387	+	2.64072i	0.277843	+	0.160413i	0.632446	−	0.774604i	$-0.282051\pi$
$271$	4.57387	+	2.64072i	0.277843	+	0.160413i	−0.354604	+	0.935017i	$0.615384\pi$
$272$	−3.73270			−0.226328
$273$		0			0
$274$	−7.43816			−0.449355
$275$	−26.9703	−	15.5713i	−1.62637	−	0.938987i
$276$	−8.92035			−0.536942
$277$	−2.62506	−	4.54674i	−0.157725	−	0.273187i	0.776323	−	0.630335i	$-0.217083\pi$
$277$	−2.62506	−	4.54674i	−0.157725	−	0.273187i	−0.934048	+	0.357148i	$0.883749\pi$
$278$	4.22965	−	2.44199i	0.253677	−	0.146461i
$279$	2.26371	+	1.30696i	0.135525	+	0.0782454i
$280$		0			0
$281$		−	31.3151i		−	1.86810i	−0.357141	−	0.934051i	$-0.616248\pi$
$281$		−	31.3151i		−	1.86810i	0.357141	−	0.934051i	$-0.383752\pi$
$282$	12.5268			0.745959
$283$	−7.72040			−0.458930			−0.229465	−	0.973317i	$-0.573698\pi$
$283$	−7.72040			−0.458930			−0.229465	+	0.973317i	$0.573698\pi$
$284$			2.72225i			0.161536i
$285$	−23.1555	−	40.1065i	−1.37162	−	2.37571i
$286$	−18.1445	+	0.737156i	−1.07291	+	0.0435890i
$287$		0			0
$288$	2.21541	−	1.27907i	0.130545	−	0.0753699i
$289$	1.53347	−	2.65605i	0.0902041	−	0.156238i
$290$	11.2411	+	19.4702i	0.660101	+	1.14333i
$291$	−35.0670	−	20.2459i	−2.05566	−	1.18684i
$292$			7.95457i			0.465506i
$293$	−18.3856	−	10.6150i	−1.07410	−	0.620133i	−0.144802	−	0.989461i	$-0.546255\pi$
$293$	−18.3856	−	10.6150i	−1.07410	−	0.620133i	−0.929299	+	0.369328i	$0.879588\pi$
$294$		0			0
$295$	13.5215	−	23.4199i	0.787252	−	1.36356i
$296$	−0.214111	+	0.370851i	−0.0124450	+	0.0215553i
$297$			5.24663i			0.304440i
$298$	−2.80934	+	4.86592i	−0.162741	+	0.281875i
$299$	−13.6311	+	0.553790i	−0.788306	+	0.0320265i
$300$	14.5777			0.841644
$301$		0			0
$302$	−4.15489	−	7.19648i	−0.239087	−	0.414111i
$303$	−5.77195			−0.331590
$304$	−5.08703	−	2.93700i	−0.291761	−	0.168448i
$305$	−29.2537	+	16.8897i	−1.67506	+	0.967099i
$306$		−	9.54877i		−	0.545867i
$307$			33.9938i			1.94013i	0.242850	+	0.970064i	$0.421918\pi$
$307$			33.9938i			1.94013i	−0.242850	+	0.970064i	$0.578082\pi$
$308$		0			0
$309$	21.1339	+	36.6050i	1.20227	+	2.08239i
$310$	2.95926	+	1.70853i	0.168075	+	0.0970380i
$311$	0.365883	−	0.633728i	0.0207473	−	0.0359354i	−0.855465	−	0.517860i	$-0.826729\pi$
$311$	0.365883	−	0.633728i	0.0207473	−	0.0359354i	0.876213	+	0.481925i	$0.160062\pi$
$312$	7.18292	−	4.54550i	0.406653	−	0.257338i
$313$	−3.68359	−	6.38016i	−0.208209	−	0.360628i	0.742942	−	0.669356i	$-0.233430\pi$
$313$	−3.68359	−	6.38016i	−0.208209	−	0.360628i	−0.951150	+	0.308728i	$0.900097\pi$
$314$	−4.51635	+	2.60751i	−0.254872	+	0.147150i
$315$		0			0
$316$	−7.07112	+	12.2475i	−0.397782	+	0.688978i
$317$	24.6012	−	14.2035i	1.38174	−	0.797748i	0.389375	−	0.921079i	$-0.372691\pi$
$317$	24.6012	−	14.2035i	1.38174	−	0.797748i	0.992366	+	0.123331i	$0.0393577\pi$
$318$	4.73009	−	2.73092i	0.265251	−	0.153142i
$319$	29.3235	−	16.9299i	1.64180	−	0.947894i
$320$	2.89612	−	1.67208i	0.161898	−	0.0934719i
$321$	11.6728	−	20.2179i	0.651512	−	1.12845i
$322$		0			0
$323$	−18.9884	+	10.9629i	−1.05654	+	0.609994i
$324$	−5.06517	−	8.77313i	−0.281398	−	0.487396i
$325$	22.2760	−	0.905008i	1.23565	−	0.0502008i
$326$	−6.23982	+	10.8077i	−0.345592	+	0.598583i
$327$	7.26418	+	4.19398i	0.401710	+	0.231927i
$328$	0.529986	+	0.917963i	0.0292636	+	0.0506860i
$329$		0			0
$330$		−	39.7084i		−	2.18587i
$331$			20.2977i			1.11566i	0.829954	+	0.557832i	$0.188366\pi$
$331$			20.2977i			1.11566i	−0.829954	+	0.557832i	$0.811634\pi$
$332$	7.94889	−	4.58930i	0.436252	−	0.251870i
$333$	−0.948690	−	0.547726i	−0.0519879	−	0.0300152i
$334$	−0.473365			−0.0259014
$335$	−22.2356	−	38.5132i	−1.21486	−	2.10420i
$336$		0			0
$337$	−8.85616			−0.482426			−0.241213	−	0.970472i	$-0.577545\pi$
$337$	−8.85616			−0.482426			−0.241213	+	0.970472i	$0.577545\pi$
$338$	10.6939	−	7.39185i	0.581674	−	0.402064i
$339$	5.76327	−	9.98228i	0.313018	−	0.542163i
$340$		−	12.4827i		−	0.676971i
$341$	2.57317	−	4.45686i	0.139345	−	0.241352i
$342$	7.51326	−	13.0133i	0.406270	−	0.703681i
$343$		0			0
$344$	−2.85996	−	1.65120i	−0.154199	−	0.0890267i
$345$		−	29.8310i		−	1.60605i
$346$	8.77459	+	5.06601i	0.471725	+	0.272350i
$347$	−3.44861	−	5.97316i	−0.185131	−	0.320656i	0.758490	−	0.651685i	$-0.225938\pi$
$347$	−3.44861	−	5.97316i	−0.185131	−	0.320656i	−0.943621	+	0.331029i	$0.892604\pi$
$348$	−7.92480	+	13.7262i	−0.424814	+	0.735799i
$349$	3.63303	−	2.09753i	0.194472	−	0.112278i	−0.399602	−	0.916689i	$-0.630852\pi$
$349$	3.63303	−	2.09753i	0.194472	−	0.112278i	0.594074	+	0.804410i	$0.297518\pi$
$350$		0			0
$351$	−2.00847	−	3.17384i	−0.107204	−	0.169407i
$352$	−2.51826	−	4.36176i	−0.134224	−	0.232483i
$353$			25.0686i			1.33426i	0.744939	+	0.667132i	$0.232478\pi$
$353$			25.0686i			1.33426i	−0.744939	+	0.667132i	$0.767522\pi$
$354$	19.0648			1.01329
$355$	−9.10362			−0.483170
$356$		−	5.41291i		−	0.286884i
$357$		0			0
$358$	−9.27876	−	5.35710i	−0.490398	−	0.283131i
$359$	−17.2117	+	9.93716i	−0.908397	+	0.524463i	−0.879915	−	0.475131i	$-0.842401\pi$
$359$	−17.2117	+	9.93716i	−0.908397	+	0.524463i	−0.0284821	+	0.999594i	$0.509067\pi$
$360$	4.27741	+	7.40868i	0.225439	+	0.390472i
$361$	−15.5039			−0.815992
$362$	1.35400	+	0.781733i	0.0711648	+	0.0410870i
$363$	−33.8704			−1.77773
$364$		0			0
$365$	−26.6013			−1.39238
$366$	−20.6234	−	11.9069i	−1.07800	−	0.622385i
$367$	−14.2126			−0.741892			−0.370946	−	0.928654i	$-0.620967\pi$
$367$	−14.2126			−0.741892			−0.370946	+	0.928654i	$0.620967\pi$
$368$	−1.89185	−	3.27678i	−0.0986196	−	0.170814i
$369$	−2.34828	+	1.35578i	−0.122246	+	0.0705790i
$370$	−1.24018	−	0.716021i	−0.0644741	−	0.0372241i
$371$		0			0
$372$			2.40897i			0.124899i
$373$	−31.2599			−1.61858			−0.809288	−	0.587413i	$-0.800147\pi$
$373$	−31.2599			−1.61858			−0.809288	+	0.587413i	$0.800147\pi$
$374$	−18.7999			−0.972118
$375$			9.32968i			0.481782i
$376$	2.65672	+	4.60157i	0.137010	+	0.237308i
$377$	−11.2577	+	21.4668i	−0.579799	+	1.10560i
$378$		0			0
$379$	19.0369	−	10.9909i	0.977858	−	0.564567i	0.0762355	−	0.997090i	$-0.475710\pi$
$379$	19.0369	−	10.9909i	0.977858	−	0.564567i	0.901623	+	0.432523i	$0.142377\pi$
$380$	9.82177	−	17.0118i	0.503846	−	0.872687i
$381$	−9.77546	−	16.9316i	−0.500812	−	0.867432i
$382$	8.13473	+	4.69659i	0.416209	+	0.240298i
$383$			4.86532i			0.248606i	0.992244	+	0.124303i	$0.0396695\pi$
$383$			4.86532i			0.248606i	−0.992244	+	0.124303i	$0.960330\pi$
$384$	2.04172	+	1.17879i	0.104191	+	0.0601546i
$385$		0			0
$386$	−4.57994	+	7.93269i	−0.233113	+	0.403764i
$387$	4.22400	−	7.31618i	0.214718	−	0.371902i
$388$		−	17.1753i		−	0.871941i
$389$	6.43897	−	11.1526i	0.326469	−	0.565460i	−0.655340	−	0.755334i	$-0.727475\pi$
$389$	6.43897	−	11.1526i	0.326469	−	0.565460i	0.981809	+	0.189874i	$0.0608079\pi$
$390$	15.2008	+	24.0208i	0.769724	+	1.21634i
$391$	−14.1234			−0.714253
$392$		0			0
$393$	7.26330	+	12.5804i	0.366385	+	0.634598i
$394$	−15.4905			−0.780401
$395$	−40.9576	−	23.6469i	−2.06080	−	1.18980i
$396$	11.1580	−	6.44208i	0.560711	−	0.323726i
$397$		−	29.8018i		−	1.49571i	−0.663862	−	0.747855i	$-0.731084\pi$
$397$		−	29.8018i		−	1.49571i	0.663862	−	0.747855i	$-0.268916\pi$
$398$			5.48387i			0.274882i
$399$		0			0
$400$	3.09168	+	5.35494i	0.154584	+	0.267747i
$401$	−8.53523	−	4.92782i	−0.426229	−	0.246084i	0.271510	−	0.962436i	$-0.412477\pi$
$401$	−8.53523	−	4.92782i	−0.426229	−	0.246084i	−0.697739	+	0.716352i	$0.745810\pi$
$402$	15.6757	−	27.1512i	0.781834	−	1.35418i
$403$	0.149553	+	3.68112i	0.00744976	+	0.183370i
$404$	−1.22413	−	2.12026i	−0.0609028	−	0.105487i
$405$	29.3387	−	16.9387i	1.45785	−	0.841691i
$406$		0			0
$407$	−1.07838	+	1.86780i	−0.0534532	+	0.0925836i
$408$	7.62112	−	4.40005i	0.377302	−	0.217835i
$409$	22.0121	−	12.7087i	1.08843	−	0.628403i	0.155269	−	0.987872i	$-0.450376\pi$
$409$	22.0121	−	12.7087i	1.08843	−	0.628403i	0.933157	+	0.359469i	$0.117042\pi$
$410$	−3.06981	+	1.77235i	−0.151607	+	0.0875304i
$411$	15.1866	−	8.76799i	0.749100	−	0.432493i
$412$	−8.96428	+	15.5266i	−0.441638	+	0.764940i
$413$		0			0
$414$	8.38247	−	4.83962i	0.411976	−	0.237854i
$415$	15.3473	+	26.5823i	0.753370	+	1.30487i
$416$	3.19311	+	1.67454i	0.156555	+	0.0821009i
$417$	−5.75716	+	9.97169i	−0.281929	+	0.488316i
$418$	−25.6210	−	14.7923i	−1.25316	−	0.723514i
$419$	15.5587	+	26.9484i	0.760091	+	1.31652i	0.942803	+	0.333350i	$0.108179\pi$
$419$	15.5587	+	26.9484i	0.760091	+	1.31652i	−0.182712	+	0.983167i	$0.558488\pi$
$420$		0			0
$421$		−	13.8090i		−	0.673009i	−0.941682	−	0.336505i	$-0.890755\pi$
$421$		−	13.8090i		−	0.673009i	0.941682	−	0.336505i	$-0.109245\pi$
$422$			5.09465i			0.248004i
$423$	−11.7715	+	6.79625i	−0.572348	+	0.330445i
$424$	2.00634	+	1.15836i	0.0974366	+	0.0562551i
$425$	23.0806			1.11957
$426$	−3.20895	−	5.55806i	−0.155474	−	0.269289i
$427$		0			0
$428$	9.90239			0.478650
$429$	36.1770	−	22.8935i	1.74664	−	1.10531i
$430$	5.52186	−	9.56414i	0.266288	−	0.461224i
$431$			31.6788i			1.52592i	0.646449	+	0.762958i	$0.276253\pi$
$431$			31.6788i			1.52592i	−0.646449	+	0.762958i	$0.723747\pi$
$432$	0.520858	−	0.902152i	0.0250598	−	0.0434048i
$433$	13.7233	−	23.7695i	0.659500	−	1.14229i	−0.321245	−	0.946996i	$-0.604101\pi$
$433$	13.7233	−	23.7695i	0.659500	−	1.14229i	0.980745	−	0.195292i	$-0.0625655\pi$
$434$		0			0
$435$	−45.9024	−	26.5017i	−2.20085	−	1.27066i
$436$			3.55788i			0.170391i
$437$	−19.2478	−	11.1127i	−0.920748	−	0.531594i
$438$	−9.37673	−	16.2410i	−0.448037	−	0.776024i
$439$	6.09116	−	10.5502i	0.290715	−	0.503534i	−0.683264	−	0.730172i	$-0.739440\pi$
$439$	6.09116	−	10.5502i	0.290715	−	0.503534i	0.973979	+	0.226638i	$0.0727734\pi$
$440$	14.5864	−	8.42146i	0.695379	−	0.401477i
$441$		0			0
$442$	11.3726	−	7.19681i	0.540939	−	0.342317i
$443$	14.9531	+	25.8996i	0.710445	+	1.23053i	0.964690	+	0.263387i	$0.0848396\pi$
$443$	14.9531	+	25.8996i	0.710445	+	1.23053i	−0.254245	+	0.967140i	$0.581827\pi$
$444$		−	1.00956i		−	0.0479118i
$445$	18.1016			0.858098
$446$	−9.99239			−0.473153
$447$		−	13.2464i		−	0.626535i
$448$		0			0
$449$	30.6709	+	17.7079i	1.44745	+	0.835685i	0.998329	−	0.0577858i	$-0.0184040\pi$
$449$	30.6709	+	17.7079i	1.44745	+	0.835685i	0.449121	+	0.893471i	$0.351737\pi$
$450$	−13.6987	+	7.90895i	−0.645763	+	0.372831i
$451$	2.66929	+	4.62335i	0.125692	+	0.217705i
$452$	4.88916			0.229967
$453$	16.9662	+	9.79545i	0.797142	+	0.460230i
$454$	13.2146			0.620191
$455$		0			0
$456$	13.8484			0.648509
$457$	17.7635	+	10.2558i	0.830943	+	0.479745i	0.854175	−	0.519985i	$-0.174062\pi$
$457$	17.7635	+	10.2558i	0.830943	+	0.479745i	−0.0232325	+	0.999730i	$0.507396\pi$
$458$	9.95986			0.465394
$459$	−1.94421	−	3.36746i	−0.0907478	−	0.157180i
$460$	10.9581	−	6.32664i	0.510922	−	0.294981i
$461$	2.94204	+	1.69858i	0.137024	+	0.0791110i	0.566945	−	0.823756i	$-0.308125\pi$
$461$	2.94204	+	1.69858i	0.137024	+	0.0791110i	−0.429921	+	0.902867i	$0.641459\pi$
$462$		0			0
$463$			39.3586i			1.82915i	0.404417	+	0.914575i	$0.367474\pi$
$463$			39.3586i			1.82915i	−0.404417	+	0.914575i	$0.632526\pi$
$464$	−6.72285			−0.312101
$465$	−8.05596			−0.373586
$466$			8.58467i			0.397677i
$467$	−2.99442	−	5.18650i	−0.138565	−	0.240002i	0.788388	−	0.615178i	$-0.210916\pi$
$467$	−2.99442	−	5.18650i	−0.138565	−	0.240002i	−0.926954	+	0.375175i	$0.877582\pi$
$468$	−4.28370	+	8.16841i	−0.198014	+	0.377585i
$469$		0			0
$470$	−15.3883	+	8.88446i	−0.709811	+	0.409810i
$471$	6.14740	−	10.6476i	0.283257	−	0.490616i
$472$	4.04332	+	7.00324i	0.186109	+	0.322350i
$473$	−14.4043	−	8.31631i	−0.662309	−	0.382384i
$474$		−	33.3413i		−	1.53142i
$475$	31.4549	+	18.1605i	1.44325	+	0.833262i
$476$		0			0
$477$	−2.96325	+	5.13251i	−0.135678	+	0.235001i
$478$	−0.586498	+	1.01584i	−0.0268258	+	0.0464636i
$479$			13.6804i			0.625074i	0.949906	+	0.312537i	$0.101179\pi$
$479$			13.6804i			0.625074i	−0.949906	+	0.312537i	$0.898821\pi$
$480$	−3.94204	+	6.82781i	−0.179929	+	0.311645i
$481$	−0.0626755	−	1.54271i	−0.00285776	−	0.0703413i
$482$	−24.3882			−1.11085
$483$		0			0
$484$	−7.18332	−	12.4419i	−0.326514	−	0.565539i
$485$	57.4367			2.60806
$486$	17.9768	+	10.3789i	0.815445	+	0.470798i
$487$	0.910007	−	0.525393i	0.0412364	−	0.0238078i	−0.479240	−	0.877684i	$-0.659088\pi$
$487$	0.910007	−	0.525393i	0.0412364	−	0.0238078i	0.520476	+	0.853876i	$0.325754\pi$
$488$		−	10.1010i		−	0.457251i
$489$		−	29.4216i		−	1.33049i
$490$		0			0
$491$	−13.7757	−	23.8602i	−0.621688	−	1.07679i	−0.989171	−	0.146765i	$-0.953114\pi$
$491$	−13.7757	−	23.8602i	−0.621688	−	1.07679i	0.367484	−	0.930030i	$-0.380219\pi$
$492$	−2.16416	−	1.24948i	−0.0975680	−	0.0563309i
$493$	−12.5472	+	21.7324i	−0.565097	+	0.978778i
$494$	21.1615	−	0.859730i	0.952103	−	0.0386811i
$495$	21.5433	+	37.3141i	0.968299	+	1.67714i
$496$	−0.884906	+	0.510901i	−0.0397335	+	0.0229401i
$497$		0			0
$498$	−10.8196	+	18.7401i	−0.484837	+	0.839763i
$499$	1.82233	−	1.05212i	0.0815788	−	0.0470995i	−0.458656	−	0.888614i	$-0.651669\pi$
$499$	1.82233	−	1.05212i	0.0815788	−	0.0470995i	0.540235	+	0.841515i	$0.318336\pi$
$500$	−3.42714	+	1.97866i	−0.153267	+	0.0884885i
$501$	0.966477	−	0.557996i	0.0431790	−	0.0249294i
$502$	−18.4721	+	10.6649i	−0.824452	+	0.475998i
$503$	−19.3301	+	33.4807i	−0.861886	+	1.49283i	0.00822020	+	0.999966i	$0.497383\pi$
$503$	−19.3301	+	33.4807i	−0.861886	+	1.49283i	−0.870106	+	0.492864i	$0.835950\pi$
$504$		0			0
$505$	7.09046	−	4.09368i	0.315521	−	0.182166i
$506$	−9.52837	−	16.5036i	−0.423588	−	0.733675i
$507$	−13.1206	+	27.6979i	−0.582706	+	1.23011i
$508$	4.14641	−	7.18180i	0.183967	−	0.318641i
$509$	22.0326	+	12.7205i	0.976578	+	0.563828i	0.901235	−	0.433330i	$-0.142662\pi$
$509$	22.0326	+	12.7205i	0.976578	+	0.563828i	0.0753428	+	0.997158i	$0.475995\pi$
$510$	14.7145	+	25.4862i	0.651567	+	1.12855i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		−	6.11903i		−	0.270162i
$514$	−11.1363	+	6.42956i	−0.491202	+	0.283596i
$515$	−51.9233	−	29.9779i	−2.28801	−	1.32099i
$516$	7.78564			0.342744
$517$	13.3806	+	23.1759i	0.588479	+	1.01928i
$518$		0			0
$519$	−23.8870			−1.04852
$520$	−5.59991	+	10.6782i	−0.245572	+	0.468272i
$521$	−7.99393	+	13.8459i	−0.350221	+	0.606600i	−0.986288	−	0.165034i	$-0.947227\pi$
$521$	−7.99393	+	13.8459i	−0.350221	+	0.606600i	0.636067	+	0.771634i	$0.280560\pi$
$522$		−	17.1980i		−	0.752736i
$523$	9.11459	−	15.7869i	0.398553	−	0.690315i	−0.594994	−	0.803730i	$-0.702846\pi$
$523$	9.11459	−	15.7869i	0.398553	−	0.690315i	0.993548	+	0.113415i	$0.0361790\pi$
$524$	−3.08084	+	5.33618i	−0.134587	+	0.233112i
$525$		0			0
$526$	−21.5295	−	12.4300i	−0.938730	−	0.541976i
$527$			3.81408i			0.166144i
$528$	10.2832	+	5.93699i	0.447517	+	0.258374i
$529$	4.34179	+	7.52021i	0.188774	+	0.326966i
$530$	−3.87374	+	6.70952i	−0.168265	+	0.291443i
$531$	−17.9153	+	10.3434i	−0.777457	+	0.448865i
$532$		0			0
$533$	−3.38460	−	1.77496i	−0.146603	−	0.0768822i
$534$	6.38066	+	11.0516i	0.276118	+	0.478251i
$535$			33.1151i			1.43169i
$536$	13.2982			0.574395
$537$	25.2595			1.09003
$538$			20.6024i			0.888231i
$539$		0			0
$540$	3.01693	+	1.74183i	0.129828	+	0.0749563i
$541$	−16.6334	+	9.60332i	−0.715128	+	0.412879i	−0.812957	−	0.582324i	$-0.802143\pi$
$541$	−16.6334	+	9.60332i	−0.715128	+	0.412879i	0.0978290	+	0.995203i	$0.468810\pi$
$542$	−2.64072	−	4.57387i	−0.113429	−	0.196464i
$543$	−3.68598			−0.158181
$544$	3.23261	+	1.86635i	0.138597	+	0.0800191i
$545$	−11.8981			−0.509658
$546$		0			0
$547$	−12.3643			−0.528659			−0.264329	−	0.964432i	$-0.585151\pi$
$547$	−12.3643			−0.528659			−0.264329	+	0.964432i	$0.585151\pi$
$548$	6.44163	+	3.71908i	0.275173	+	0.158871i
$549$	25.8398			1.10282
$550$	15.5713	+	26.9703i	0.663964	+	1.15002i
$551$	−34.1994	+	19.7450i	−1.45694	+	0.841166i
$552$	7.72525	+	4.46017i	0.328808	+	0.189838i
$553$		0			0
$554$			5.25013i			0.223057i
$555$	3.37614			0.143309
$556$	−4.88398			−0.207127
$557$			29.5462i			1.25191i	0.779858	+	0.625956i	$0.215291\pi$
$557$			29.5462i			1.25191i	−0.779858	+	0.625956i	$0.784709\pi$
$558$	−1.30696	−	2.26371i	−0.0553279	−	0.0958307i
$559$	11.8972	−	0.483345i	0.503196	−	0.0204433i
$560$		0			0
$561$	38.3840	−	22.1610i	1.62057	−	0.935638i
$562$	−15.6575	+	27.1197i	−0.660474	+	1.14397i
$563$	−1.26155	−	2.18506i	−0.0531678	−	0.0920894i	0.838217	−	0.545337i	$-0.183598\pi$
$563$	−1.26155	−	2.18506i	−0.0531678	−	0.0920894i	−0.891384	+	0.453248i	$0.850265\pi$
$564$	−10.8485	−	6.26339i	−0.456805	−	0.263736i
$565$			16.3501i			0.687854i
$566$	6.68606	+	3.86020i	0.281036	+	0.162256i
$567$		0			0
$568$	1.36113	−	2.35754i	0.0571115	−	0.0989201i
$569$	−5.21623	+	9.03478i	−0.218676	+	0.378758i	−0.954403	−	0.298520i	$-0.903507\pi$
$569$	−5.21623	+	9.03478i	−0.218676	+	0.378758i	0.735728	+	0.677278i	$0.236840\pi$
$570$			46.3111i			1.93976i
$571$	0.0728934	−	0.126255i	0.00305049	−	0.00528361i	−0.864496	−	0.502639i	$-0.832362\pi$
$571$	0.0728934	−	0.126255i	0.00305049	−	0.00528361i	0.867547	+	0.497356i	$0.165696\pi$
$572$	16.0822	+	8.43385i	0.672429	+	0.352637i
$573$	−22.1451			−0.925124
$574$		0			0
$575$	11.6980	+	20.2615i	0.487840	+	0.844964i
$576$	−2.55814			−0.106589
$577$	19.4377	+	11.2223i	0.809201	+	0.467192i	0.846678	−	0.532105i	$-0.178599\pi$
$577$	19.4377	+	11.2223i	0.809201	+	0.467192i	−0.0374775	+	0.999297i	$0.511932\pi$
$578$	−2.65605	+	1.53347i	−0.110477	+	0.0637840i
$579$		−	21.5951i		−	0.897461i
$580$		−	22.4822i		−	0.933524i
$581$		0			0
$582$	20.2459	+	35.0670i	0.839221	+	1.45357i
$583$	10.1050	+	5.83413i	0.418507	+	0.241625i
$584$	3.97728	−	6.88886i	0.164581	−	0.285063i
$585$	−27.3164	−	14.3253i	−1.12940	−	0.592280i
$586$	10.6150	+	18.3856i	0.438500	+	0.759504i
$587$	18.2824	−	10.5554i	0.754596	−	0.435666i	−0.0727563	−	0.997350i	$-0.523180\pi$
$587$	18.2824	−	10.5554i	0.754596	−	0.435666i	0.827352	+	0.561684i	$0.189846\pi$
$588$		0			0
$589$	−3.00103	+	5.19794i	−0.123655	+	0.214177i
$590$	−23.4199	+	13.5215i	−0.964183	+	0.556671i
$591$	31.6273	−	18.2600i	1.30097	−	0.751116i
$592$	0.370851	−	0.214111i	0.0152419	−	0.00879992i
$593$	−25.8339	+	14.9152i	−1.06087	+	0.612494i	−0.925673	−	0.378324i	$-0.876500\pi$
$593$	−25.8339	+	14.9152i	−1.06087	+	0.612494i	−0.135198	+	0.990819i	$0.543167\pi$
$594$	2.62332	−	4.54372i	0.107636	−	0.186431i
$595$		0			0
$596$	4.86592	−	2.80934i	0.199316	−	0.115075i
$597$	−6.46431	−	11.1965i	−0.264566	−	0.458243i
$598$	12.0818	+	6.33595i	0.494060	+	0.259096i
$599$	−16.7520	+	29.0153i	−0.684469	+	1.18553i	0.289135	+	0.957288i	$0.406632\pi$
$599$	−16.7520	+	29.0153i	−0.684469	+	1.18553i	−0.973603	+	0.228246i	$0.926701\pi$
$600$	−12.6247	−	7.28885i	−0.515400	−	0.297566i
$601$	−18.9681	−	32.8537i	−0.773724	−	1.34013i	−0.935509	−	0.353303i	$-0.885058\pi$
$601$	−18.9681	−	32.8537i	−0.773724	−	1.34013i	0.161785	−	0.986826i	$-0.448275\pi$
$602$		0			0
$603$			34.0187i			1.38535i
$604$			8.30978i			0.338120i
$605$	41.6075	−	24.0221i	1.69159	−	0.976637i
$606$	4.99865	+	2.88597i	0.203056	+	0.117235i
$607$	−35.8671			−1.45580			−0.727900	−	0.685684i	$-0.759503\pi$
$607$	−35.8671			−1.45580			−0.727900	+	0.685684i	$0.759503\pi$
$608$	2.93700	+	5.08703i	0.119111	+	0.206306i
$609$		0			0
$610$	33.7793			1.36768
$611$	−16.9663	−	8.89753i	−0.686385	−	0.359956i
$612$	−4.77439	+	8.26948i	−0.192993	+	0.334274i
$613$		−	12.6512i		−	0.510979i	−0.966812	−	0.255489i	$-0.917763\pi$
$613$		−	12.6512i		−	0.510979i	0.966812	−	0.255489i	$-0.0822366\pi$
$614$	16.9969	−	29.4395i	0.685939	−	1.18808i
$615$	4.17845	−	7.23729i	0.168491	−	0.291836i
$616$		0			0
$617$	34.6231	+	19.9896i	1.39387	+	0.804753i	0.993741	−	0.111705i	$-0.0356312\pi$
$617$	34.6231	+	19.9896i	1.39387	+	0.804753i	0.400131	+	0.916458i	$0.368965\pi$
$618$		−	42.2679i		−	1.70026i
$619$	−8.58564	−	4.95692i	−0.345086	−	0.199235i	0.317433	−	0.948281i	$-0.397179\pi$
$619$	−8.58564	−	4.95692i	−0.345086	−	0.199235i	−0.662519	+	0.749045i	$0.730513\pi$
$620$	−1.70853	−	2.95926i	−0.0686162	−	0.118847i
$621$	1.97077	−	3.41348i	0.0790843	−	0.136978i
$622$	−0.633728	+	0.365883i	−0.0254102	+	0.0146706i
$623$		0			0
$624$	−8.49334	+	0.345059i	−0.340006	+	0.0138134i
$625$	8.84144	+	15.3138i	0.353658	+	0.612553i
$626$			7.36717i			0.294451i
$627$	69.7477			2.78546
$628$	5.21503			0.208102
$629$		−	1.59843i		−	0.0637334i
$630$		0			0
$631$	21.7056	+	12.5318i	0.864088	+	0.498881i	0.865379	−	0.501118i	$-0.167078\pi$
$631$	21.7056	+	12.5318i	0.864088	+	0.498881i	−0.00129129	+	0.999999i	$0.500411\pi$
$632$	12.2475	−	7.07112i	0.487181	−	0.281274i
$633$	−6.00550	−	10.4018i	−0.238697	−	0.413436i
$634$	−28.4070			−1.12819
$635$	24.0170	+	13.8662i	0.953087	+	0.550265i
$636$	−5.46184			−0.216576
$637$		0			0
$638$	−33.8598			−1.34052
$639$	6.03091	+	3.48195i	0.238579	+	0.137744i
$640$	−3.34415			−0.132189
$641$	4.01506	+	6.95429i	0.158585	+	0.274678i	0.934359	−	0.356334i	$-0.115973\pi$
$641$	4.01506	+	6.95429i	0.158585	+	0.274678i	−0.775773	+	0.631012i	$0.782640\pi$
$642$	−20.2179	+	11.6728i	−0.797935	+	0.460688i
$643$	13.3951	+	7.73367i	0.528251	+	0.304986i	0.740304	−	0.672272i	$-0.234682\pi$
$643$	13.3951	+	7.73367i	0.528251	+	0.304986i	−0.212053	+	0.977258i	$0.568015\pi$
$644$		0			0
$645$			26.0364i			1.02518i
$646$	21.9259			0.862662
$647$	−6.69236			−0.263104			−0.131552	−	0.991309i	$-0.541996\pi$
$647$	−6.69236			−0.263104			−0.131552	+	0.991309i	$0.541996\pi$
$648$			10.1303i			0.397957i
$649$	20.3643	+	35.2720i	0.799370	+	1.38455i
$650$	−19.7441	−	10.3543i	−0.774428	−	0.406127i
$651$		0			0
$652$	10.8077	−	6.23982i	0.423262	−	0.244370i
$653$	12.0804	−	20.9238i	0.472741	−	0.818811i	−0.526772	−	0.850006i	$-0.676598\pi$
$653$	12.0804	−	20.9238i	0.472741	−	0.818811i	0.999513	+	0.0311950i	$0.00993128\pi$
$654$	−4.19398	−	7.26418i	−0.163997	−	0.284052i
$655$	−17.8450	−	10.3028i	−0.697261	−	0.402564i
$656$		−	1.05997i		−	0.0413850i
$657$	17.6227	+	10.1745i	0.687526	+	0.396943i
$658$		0			0
$659$	−6.47769	+	11.2197i	−0.252335	+	0.437057i	−0.964168	−	0.265291i	$-0.914532\pi$
$659$	−6.47769	+	11.2197i	−0.252335	+	0.437057i	0.711833	+	0.702349i	$0.247865\pi$
$660$	−19.8542	+	34.3885i	−0.772823	+	1.33857i
$661$			19.2892i			0.750263i	0.926972	+	0.375132i	$0.122402\pi$
$661$			19.2892i			0.750263i	−0.926972	+	0.375132i	$0.877598\pi$
$662$	10.1489	−	17.5783i	0.394446	−	0.683201i
$663$	−14.7361	+	28.0997i	−0.572303	+	1.09130i
$664$	−9.17859			−0.356198
$665$		0			0
$666$	0.547726	+	0.948690i	0.0212240	+	0.0367610i
$667$	−25.4373			−0.984935
$668$	0.409946	+	0.236682i	0.0158613	+	0.00915752i
$669$	20.4016	−	11.7789i	0.788772	−	0.455398i
$670$			44.4712i			1.71807i
$671$		−	50.8740i		−	1.96397i
$672$		0			0
$673$	−14.7943	−	25.6245i	−0.570279	−	0.987752i	−0.996537	−	0.0831505i	$-0.973502\pi$
$673$	−14.7943	−	25.6245i	−0.570279	−	0.987752i	0.426258	−	0.904602i	$-0.359832\pi$
$674$	7.66966	+	4.42808i	0.295424	+	0.170563i
$675$	−3.22065	+	5.57833i	−0.123963	+	0.214710i
$676$	−12.9572	+	1.05456i	−0.498352	+	0.0405600i
$677$	−6.92108	−	11.9877i	−0.265999	−	0.460723i	0.701826	−	0.712348i	$-0.252368\pi$
$677$	−6.92108	−	11.9877i	−0.265999	−	0.460723i	−0.967825	+	0.251625i	$0.919035\pi$
$678$	−9.98228	+	5.76327i	−0.383367	+	0.221337i
$679$		0			0
$680$	−6.24136	+	10.8104i	−0.239345	+	0.414558i
$681$	−26.9804	+	15.5771i	−1.03389	+	0.596918i
$682$	−4.45686	+	2.57317i	−0.170662	+	0.0985317i
$683$	−30.9323	+	17.8588i	−1.18359	+	0.683347i	−0.956843	−	0.290607i	$-0.906143\pi$
$683$	−30.9323	+	17.8588i	−1.18359	+	0.683347i	−0.226749	+	0.973953i	$0.572810\pi$
$684$	−13.0133	+	7.51326i	−0.497578	+	0.287277i
$685$	−12.4372	+	21.5418i	−0.475200	+	0.823070i
$686$		0			0
$687$	−20.3352	+	11.7405i	−0.775837	+	0.447929i
$688$	1.65120	+	2.85996i	0.0629514	+	0.109035i
$689$	−8.34619	+	0.339080i	−0.317964	+	0.0129179i
$690$	−14.9155	+	25.8344i	−0.567824	+	0.983499i
$691$	−22.5221	−	13.0031i	−0.856782	−	0.494663i	0.00615160	−	0.999981i	$-0.498042\pi$
$691$	−22.5221	−	13.0031i	−0.856782	−	0.494663i	−0.862933	+	0.505318i	$0.831375\pi$
$692$	−5.06601	−	8.77459i	−0.192581	−	0.333560i
$693$		0			0
$694$			6.89722i			0.261815i
$695$		−	16.3328i		−	0.619537i
$696$	13.7262	−	7.92480i	0.520289	−	0.300389i
$697$	−3.42648	−	1.97828i	−0.129787	−	0.0749327i
$698$	−4.19507			−0.158786
$699$	−10.1195	−	17.5275i	−0.382754	−	0.662949i
$700$		0			0
$701$	24.7068			0.933164			0.466582	−	0.884478i	$-0.345485\pi$
$701$	24.7068			0.933164			0.466582	+	0.884478i	$0.345485\pi$
$702$	0.152467	+	3.75286i	0.00575451	+	0.141643i
$703$	1.25769	−	2.17838i	0.0474346	−	0.0821592i
$704$			5.03653i			0.189821i
$705$	20.9457	−	36.2791i	0.788863	−	1.36635i
$706$	12.5343	−	21.7100i	0.471734	−	0.817067i
$707$		0			0
$708$	−16.5106	−	9.53242i	−0.620508	−	0.358250i
$709$		−	22.3951i		−	0.841064i	−0.907278	−	0.420532i	$-0.861843\pi$
$709$		−	22.3951i		−	0.841064i	0.907278	−	0.420532i	$-0.138157\pi$
$710$	7.88397	+	4.55181i	0.295880	+	0.170826i
$711$	18.0889	+	31.3309i	0.678387	+	1.17500i
$712$	−2.70646	+	4.68772i	−0.101429	+	0.175680i
$713$	−3.34822	+	1.93310i	−0.125392	+	0.0723951i
$714$		0			0
$715$	−28.2041	+	53.7812i	−1.05477	+	2.01130i
$716$	5.35710	+	9.27876i	0.200204	+	0.346764i
$717$		−	2.76542i		−	0.103277i
$718$	19.8743			0.741703
$719$	25.2842			0.942943			0.471472	−	0.881881i	$-0.343723\pi$
$719$	25.2842			0.942943			0.471472	+	0.881881i	$0.343723\pi$
$720$		−	8.55481i		−	0.318819i
$721$		0			0
$722$	13.4267	+	7.75193i	0.499691	+	0.288497i
$723$	49.7937	−	28.7484i	1.85185	−	1.06917i
$724$	−0.781733	−	1.35400i	−0.0290529	−	0.0503211i
$725$	41.5698			1.54386
$726$	29.3326	+	16.9352i	1.08863	+	0.628523i
$727$	39.9649			1.48221			0.741107	−	0.671386i	$-0.234301\pi$
$727$	39.9649			1.48221			0.741107	+	0.671386i	$0.234301\pi$
$728$		0			0
$729$	−18.5471			−0.686929
$730$	23.0374	+	13.3006i	0.852652	+	0.492279i
$731$	12.3269			0.455926
$732$	11.9069	+	20.6234i	0.440093	+	0.762263i
$733$	−20.8858	+	12.0584i	−0.771433	+	0.445387i	−0.833386	−	0.552692i	$-0.813601\pi$
$733$	−20.8858	+	12.0584i	−0.771433	+	0.445387i	0.0619525	+	0.998079i	$0.480267\pi$
$734$	12.3085	+	7.10630i	0.454314	+	0.262298i
$735$		0			0
$736$			3.78370i			0.139469i
$737$	66.9768			2.46712
$738$	2.71156			0.0998138
$739$		−	28.5427i		−	1.04996i	−0.851114	−	0.524980i	$-0.824073\pi$
$739$		−	28.5427i		−	1.04996i	0.851114	−	0.524980i	$-0.175927\pi$
$740$	0.716021	+	1.24018i	0.0263214	+	0.0455901i
$741$	−42.1924	+	26.7002i	−1.54998	+	0.980858i
$742$		0			0
$743$	−37.9322	+	21.9001i	−1.39160	+	0.803438i	−0.993492	−	0.113902i	$-0.963665\pi$
$743$	−37.9322	+	21.9001i	−1.39160	+	0.803438i	−0.398104	+	0.917340i	$0.630332\pi$
$744$	1.20449	−	2.08623i	0.0441586	−	0.0764849i
$745$	9.39487	+	16.2724i	0.344201	+	0.596174i
$746$	27.0718	+	15.6299i	0.991171	+	0.572253i
$747$		−	23.4801i		−	0.859093i
$748$	16.2812	+	9.39993i	0.595298	+	0.343696i
$749$		0			0
$750$	4.66484	−	8.07974i	0.170336	−	0.295030i
$751$	20.2337	−	35.0458i	0.738338	−	1.27884i	−0.214906	−	0.976635i	$-0.568944\pi$
$751$	20.2337	−	35.0458i	0.738338	−	1.27884i	0.953243	−	0.302204i	$-0.0977223\pi$
$752$		−	5.31343i		−	0.193761i
$753$	25.1433	−	43.5494i	0.916271	−	1.58703i
$754$	20.4828	−	12.9619i	0.745940	−	0.472046i
$755$	−27.7892			−1.01135
$756$		0			0
$757$	−6.36103	−	11.0176i	−0.231196	−	0.400442i	0.726965	−	0.686675i	$-0.240930\pi$
$757$	−6.36103	−	11.0176i	−0.231196	−	0.400442i	−0.958160	+	0.286232i	$0.907597\pi$
$758$	−21.9819			−0.798418
$759$	38.9084	+	22.4638i	1.41229	+	0.815384i
$760$	−17.0118	+	9.82177i	−0.617083	+	0.356273i
$761$			30.7371i			1.11422i	0.830439	+	0.557110i	$0.188090\pi$
$761$			30.7371i			1.11422i	−0.830439	+	0.557110i	$0.811910\pi$
$762$			19.5509i			0.708255i
$763$		0			0
$764$	−4.69659	−	8.13473i	−0.169917	−	0.294304i
$765$	−27.6544	−	15.9663i	−0.999847	−	0.577262i
$766$	2.43266	−	4.21349i	0.0878956	−	0.152240i
$767$	−25.8215	−	13.5414i	−0.932361	−	0.488951i
$768$	−1.17879	−	2.04172i	−0.0425358	−	0.0736741i
$769$	10.0887	−	5.82469i	0.363806	−	0.210044i	−0.306943	−	0.951728i	$-0.599306\pi$
$769$	10.0887	−	5.82469i	0.363806	−	0.210044i	0.670749	+	0.741684i	$0.265973\pi$
$770$		0			0
$771$	15.1581	−	26.2547i	0.545907	−	0.945538i
$772$	7.93269	−	4.57994i	0.285504	−	0.164836i
$773$	−24.5544	+	14.1765i	−0.883159	+	0.509892i	−0.871699	−	0.490042i	$-0.836981\pi$
$773$	−24.5544	+	14.1765i	−0.883159	+	0.509892i	−0.0114603	+	0.999934i	$0.503648\pi$
$774$	−7.31618	+	4.22400i	−0.262975	+	0.151829i
$775$	5.47169	−	3.15908i	0.196549	−	0.113478i
$776$	−8.58763	+	14.8742i	−0.308278	+	0.533953i
$777$		0			0
$778$	−11.1526	+	6.43897i	−0.399841	+	0.230848i
$779$	−3.11314	−	5.39211i	−0.111540	−	0.193193i
$780$	−1.15393	−	28.4030i	−0.0413173	−	1.01699i
$781$	6.85535	−	11.8738i	0.245304	−	0.424878i
$782$	12.2313	+	7.06172i	0.437389	+	0.252527i
$783$	−3.50165	−	6.06503i	−0.125139	−	0.216747i
$784$		0			0
$785$			17.4398i			0.622455i
$786$		−	14.5266i		−	0.518147i
$787$	1.85099	−	1.06867i	0.0659808	−	0.0380940i	−0.466647	−	0.884444i	$-0.654538\pi$
$787$	1.85099	−	1.06867i	0.0659808	−	0.0380940i	0.532627	+	0.846350i	$0.321205\pi$
$788$	13.4152	+	7.74526i	0.477896	+	0.275914i
$789$	58.6094			2.08655
$790$	23.6469	+	40.9576i	0.841319	+	1.45721i
$791$		0			0
$792$	−12.8842			−0.457818
$793$	19.4752	+	30.7752i	0.691584	+	1.09286i
$794$	−14.9009	+	25.8091i	−0.528814	+	0.915932i
$795$		−	18.2652i		−	0.647801i
$796$	2.74194	−	4.74917i	0.0971853	−	0.168330i
$797$	13.9817	−	24.2170i	0.495257	−	0.857810i	−0.504728	−	0.863278i	$-0.668407\pi$
$797$	13.9817	−	24.2170i	0.495257	−	0.857810i	0.999985	+	0.00546806i	$0.00174055\pi$
$798$		0			0
$799$	−17.1763	−	9.91672i	−0.607653	−	0.350829i
$800$		−	6.18336i		−	0.218615i
$801$	−11.9918	−	6.92349i	−0.423711	−	0.244630i
$802$	4.92782	+	8.53523i	0.174007	+	0.301390i
$803$	20.0317	−	34.6959i	0.706904	−	1.22439i
$804$	−27.1512	+	15.6757i	−0.957547	+	0.552840i
$805$		0			0
$806$	1.71104	−	3.26272i	0.0602690	−	0.114924i
$807$	−24.2858	−	42.0642i	−0.854899	−	1.48073i
$808$			2.44826i			0.0861295i
$809$	−48.7243			−1.71305			−0.856527	−	0.516102i	$-0.827383\pi$
$809$	−48.7243			−1.71305			−0.856527	+	0.516102i	$0.827383\pi$
$810$	−33.8774			−1.19033
$811$		−	31.9965i		−	1.12355i	−0.827290	−	0.561774i	$-0.810119\pi$
$811$		−	31.9965i		−	1.12355i	0.827290	−	0.561774i	$-0.189881\pi$
$812$		0			0
$813$	10.7832	+	6.22569i	0.378184	+	0.218345i
$814$	1.86780	−	1.07838i	0.0654665	−	0.0377971i
$815$	20.8669	+	36.1426i	0.730936	+	1.26602i
$816$	−8.80011			−0.308065
$817$	16.7994	+	9.69914i	0.587737	+	0.339330i
$818$	−25.4173			−0.888696
$819$		0			0
$820$	3.54471			0.123787
$821$	10.8028	+	6.23701i	0.377021	+	0.217673i	0.676521	−	0.736423i	$-0.263487\pi$
$821$	10.8028	+	6.23701i	0.377021	+	0.217673i	−0.299500	+	0.954096i	$0.596820\pi$
$822$	−17.5360			−0.611638
$823$	8.01300	+	13.8789i	0.279316	+	0.483789i	0.971215	−	0.238205i	$-0.0765591\pi$
$823$	8.01300	+	13.8789i	0.279316	+	0.483789i	−0.691899	+	0.721994i	$0.743226\pi$
$824$	15.5266	−	8.96428i	0.540894	−	0.312286i
$825$	−63.5845	−	36.7105i	−2.21373	−	1.27810i
$826$		0			0
$827$		−	6.94225i		−	0.241406i	−0.992689	−	0.120703i	$-0.961485\pi$
$827$		−	6.94225i		−	0.241406i	0.992689	−	0.120703i	$-0.0385148\pi$
$828$	−9.67924			−0.336377
$829$	9.08891			0.315671			0.157835	−	0.987465i	$-0.449548\pi$
$829$	9.08891			0.315671			0.157835	+	0.987465i	$0.449548\pi$
$830$		−	30.6946i		−	1.06543i
$831$	−6.18877	−	10.7193i	−0.214686	−	0.371847i
$832$	−1.92804	−	3.04674i	−0.0668429	−	0.105627i
$833$		0			0
$834$	9.97169	−	5.75716i	0.345291	−	0.199354i
$835$	−0.791502	+	1.37092i	−0.0273911	+	0.0474427i
$836$	14.7923	+	25.6210i	0.511602	+	0.886120i
$837$	−0.921821	−	0.532213i	−0.0318628	−	0.0183960i
$838$		−	31.1174i		−	1.07493i
$839$	15.8840	+	9.17062i	0.548376	+	0.316605i	0.748467	−	0.663173i	$-0.230790\pi$
$839$	15.8840	+	9.17062i	0.548376	+	0.316605i	−0.200091	+	0.979777i	$0.564124\pi$
$840$		0			0
$841$	−8.09837	+	14.0268i	−0.279254	+	0.483683i
$842$	−6.90450	+	11.9589i	−0.237945	+	0.412132i
$843$		−	73.8275i		−	2.54276i
$844$	2.54733	−	4.41210i	0.0876826	−	0.151871i
$845$	−3.52661	−	43.3307i	−0.121319	−	1.49062i
$846$	13.5925			0.467320
$847$		0			0
$848$	−1.15836	−	2.00634i	−0.0397783	−	0.0688981i
$849$	−18.2014			−0.624670
$850$	−19.9884	−	11.5403i	−0.685597	−	0.395829i
$851$	1.40319	−	0.810133i	0.0481008	−	0.0277710i
$852$			6.41790i			0.219874i
$853$			53.7617i			1.84077i	0.391018	+	0.920383i	$0.372123\pi$
$853$			53.7617i			1.84077i	−0.391018	+	0.920383i	$0.627877\pi$
$854$		0			0
$855$	−25.1255	−	43.5186i	−0.859273	−	1.48830i
$856$	−8.57572	−	4.95119i	−0.293112	−	0.169228i
$857$	19.1290	−	33.1324i	0.653434	−	1.13178i	−0.328850	−	0.944382i	$-0.606661\pi$
$857$	19.1290	−	33.1324i	0.653434	−	1.13178i	0.982284	−	0.187399i	$-0.0600056\pi$
$858$	−42.7769	+	1.73790i	−1.46038	+	0.0593309i
$859$	−7.89494	−	13.6744i	−0.269372	−	0.466566i	0.699328	−	0.714801i	$-0.253483\pi$
$859$	−7.89494	−	13.6744i	−0.269372	−	0.466566i	−0.968700	+	0.248235i	$0.920149\pi$
$860$	−9.56414	+	5.52186i	−0.326135	+	0.188294i
$861$		0			0
$862$	15.8394	−	27.4347i	0.539492	−	0.934428i
$863$	−38.6063	+	22.2894i	−1.31417	+	0.758739i	−0.982785	−	0.184755i	$-0.940851\pi$
$863$	−38.6063	+	22.2894i	−1.31417	+	0.758739i	−0.331390	+	0.943494i	$0.607518\pi$
$864$	−0.902152	+	0.520858i	−0.0306918	+	0.0177199i
$865$	29.3436	−	16.9415i	0.997711	−	0.576029i
$866$	−23.7695	+	13.7233i	−0.807720	+	0.466337i
$867$	3.61527	−	6.26182i	0.122781	−	0.212663i
$868$		0			0
$869$	61.6851	−	35.6139i	2.09252	−	1.20812i
$870$	26.5017	+	45.9024i	0.898493	+	1.55624i
$871$	−40.5162	+	25.6395i	−1.37284	+	0.868761i
$872$	1.77894	−	3.08121i	0.0602425	−	0.104343i
$873$	−38.0503	−	21.9684i	−1.28781	−	0.743516i
$874$	11.1127	+	19.2478i	0.375894	+	0.651067i
$875$		0			0
$876$			18.7535i			0.633621i
$877$			0.139993i			0.00472721i	0.999997	+	0.00236361i	$0.000752360\pi$
$877$			0.139993i			0.00472721i	−0.999997	+	0.00236361i	$0.999248\pi$
$878$	−10.5502	+	6.09116i	−0.356052	+	0.205567i
$879$	−43.3455	−	25.0255i	−1.46201	−	0.844090i
$880$	−16.8429			−0.567775
$881$	22.6522	+	39.2347i	0.763172	+	1.32185i	0.941208	+	0.337828i	$0.109692\pi$
$881$	22.6522	+	39.2347i	0.763172	+	1.32185i	−0.178036	+	0.984024i	$0.556974\pi$
$882$		0			0
$883$	−46.5419			−1.56626			−0.783130	−	0.621858i	$-0.786378\pi$
$883$	−46.5419			−1.56626			−0.783130	+	0.621858i	$0.786378\pi$
$884$	−13.4474	+	0.546325i	−0.452283	+	0.0183749i
$885$	31.8779	−	55.2141i	1.07156	−	1.85600i
$886$		−	29.9063i		−	1.00472i
$887$	24.4650	−	42.3746i	0.821453	−	1.42280i	−0.0831471	−	0.996537i	$-0.526497\pi$
$887$	24.4650	−	42.3746i	0.821453	−	1.42280i	0.904600	−	0.426261i	$-0.140170\pi$
$888$	−0.504782	+	0.874309i	−0.0169394	+	0.0293399i
$889$		0			0
$890$	−15.6764	−	9.05080i	−0.525476	−	0.303383i
$891$			51.0218i			1.70929i
$892$	8.65366	+	4.99619i	0.289746	+	0.167285i
$893$	−15.6055	−	27.0296i	−0.522220	−	0.904511i
$894$	−6.62322	+	11.4718i	−0.221514	+	0.383673i
$895$	−31.0296	+	17.9149i	−1.03721	+	0.598831i
$896$		0			0
$897$	−32.1363	+	1.30560i	−1.07300	+	0.0435927i
$898$	−17.7079	−	30.6709i	−0.590919	−	1.02350i
$899$			6.86942i			0.229108i
$900$	15.8179			0.527263
$901$	−8.64764			−0.288095
$902$		−	5.33858i		−	0.177755i
$903$		0			0
$904$	−4.23414	−	2.44458i	−0.140825	−	0.0813056i
$905$	4.52799	−	2.61424i	0.150515	−	0.0869001i
$906$	−9.79545	−	16.9662i	−0.325432	−	0.563665i
$907$	49.9846			1.65971			0.829856	−	0.557978i	$-0.188423\pi$
$907$	49.9846			1.65971			0.829856	+	0.557978i	$0.188423\pi$
$908$	−11.4442	−	6.60729i	−0.379788	−	0.219271i
$909$	−6.26299			−0.207730
$910$		0			0
$911$	17.2655			0.572033			0.286016	−	0.958225i	$-0.407669\pi$
$911$	17.2655			0.572033			0.286016	+	0.958225i	$0.407669\pi$
$912$	−11.9930	−	6.92418i	−0.397129	−	0.229283i
$913$	−46.2282			−1.52993
$914$	−10.2558	−	17.7635i	−0.339231	−	0.587565i
$915$	−68.9678	+	39.8186i	−2.28000	+	1.31636i
$916$	−8.62549	−	4.97993i	−0.284994	−	0.164542i
$917$		0			0
$918$			3.88841i			0.128337i
$919$	15.9097			0.524813			0.262407	−	0.964957i	$-0.415484\pi$
$919$	15.9097			0.524813			0.262407	+	0.964957i	$0.415484\pi$
$920$	−12.6533			−0.417166
$921$			80.1427i			2.64079i
$922$	−1.69858	−	2.94204i	−0.0559399	−	0.0968908i
$923$	0.398434	+	9.80712i	0.0131146	+	0.322805i
$924$		0			0
$925$	−2.29311	+	1.32393i	−0.0753969	+	0.0435304i
$926$	19.6793	−	34.0856i	0.646702	−	1.12012i
$927$	22.9319	+	39.7192i	0.753182	+	1.30455i
$928$	5.82216	+	3.36143i	0.191122	+	0.110344i
$929$			22.6619i			0.743511i	0.928331	+	0.371756i	$0.121244\pi$
$929$			22.6619i			0.743511i	−0.928331	+	0.371756i	$0.878756\pi$
$930$	6.97667	+	4.02798i	0.228774	+	0.132083i
$931$		0			0
$932$	4.29233	−	7.43454i	0.140600	−	0.243527i
$933$	0.862595	−	1.49406i	0.0282401	−	0.0489133i
$934$			5.98885i			0.195961i
$935$	−31.4348	+	54.4467i	−1.02803	+	1.78060i
$936$	7.79400	−	4.93220i	0.254755	−	0.161214i
$937$	22.3601			0.730473			0.365237	−	0.930915i	$-0.380988\pi$
$937$	22.3601			0.730473			0.365237	+	0.930915i	$0.380988\pi$
$938$		0			0
$939$	−8.68432	−	15.0417i	−0.283402	−	0.490867i
$940$	17.7689			0.579558
$941$	24.4378	+	14.1092i	0.796650	+	0.459946i	0.842298	−	0.539012i	$-0.181202\pi$
$941$	24.4378	+	14.1092i	0.796650	+	0.459946i	−0.0456486	+	0.998958i	$0.514535\pi$
$942$	−10.6476	+	6.14740i	−0.346918	+	0.200293i
$943$		−	4.01062i		−	0.130604i
$944$		−	8.08665i		−	0.263198i
$945$		0			0
$946$	8.31631	+	14.4043i	0.270387	+	0.468323i
$947$	5.51380	+	3.18339i	0.179174	+	0.103446i	0.586905	−	0.809656i	$-0.300346\pi$
$947$	5.51380	+	3.18339i	0.179174	+	0.103446i	−0.407730	+	0.913102i	$0.633680\pi$
$948$	−16.6707	+	28.8744i	−0.541438	+	0.937798i
$949$	1.16425	+	28.6570i	0.0377930	+	0.930244i
$950$	−18.1605	−	31.4549i	−0.589205	−	1.02053i
$951$	57.9990	−	33.4858i	1.88075	−	1.08585i
$952$		0			0
$953$	1.16258	−	2.01365i	0.0376597	−	0.0652285i	−0.846581	−	0.532260i	$-0.821343\pi$
$953$	1.16258	−	2.01365i	0.0376597	−	0.0652285i	0.884241	+	0.467031i	$0.154676\pi$
$954$	5.13251	−	2.96325i	0.166171	−	0.0959389i
$955$	27.2038	−	15.7061i	0.880293	−	0.508238i
$956$	1.01584	−	0.586498i	0.0328547	−	0.0189687i
$957$	69.1322	−	39.9135i	2.23473	−	1.29022i
$958$	6.84021	−	11.8476i	0.220997	−	0.382778i
$959$		0			0
$960$	6.82781	−	3.94204i	0.220367	−	0.127229i
$961$	−14.9780	−	25.9426i	−0.483160	−	0.836858i
$962$	−0.717074	+	1.36736i	−0.0231194	+	0.0440854i
$963$	12.6658	−	21.9379i	0.408151	−	0.706939i
$964$	21.1208	+	12.1941i	0.680254	+	0.392745i
$965$	15.3160	+	26.5281i	0.493040	+	0.853971i
$966$		0			0
$967$		−	58.7262i		−	1.88851i	−0.329219	−	0.944254i	$-0.606785\pi$
$967$		−	58.7262i		−	1.88851i	0.329219	−	0.944254i	$-0.393215\pi$
$968$			14.3666i			0.461761i
$969$	−44.7664	+	25.8459i	−1.43810	+	0.830290i
$970$	−49.7416	−	28.7183i	−1.59711	−	0.922090i
$971$	10.0699			0.323160			0.161580	−	0.986860i	$-0.448341\pi$
$971$	10.0699			0.323160			0.161580	+	0.986860i	$0.448341\pi$
$972$	−10.3789	−	17.9768i	−0.332904	−	0.576607i
$973$		0			0
$974$	−1.05079			−0.0336693
$975$	52.5173	−	2.13362i	1.68190	−	0.0683306i
$976$	−5.05050	+	8.74773i	−0.161663	+	0.280008i
$977$		−	48.8242i		−	1.56202i	−0.624517	−	0.781012i	$-0.714704\pi$
$977$		−	48.8242i		−	1.56202i	0.624517	−	0.781012i	$-0.285296\pi$
$978$	−14.7108	+	25.4799i	−0.470400	+	0.814757i
$979$	−13.6311	+	23.6098i	−0.435653	+	0.754573i
$980$		0			0
$981$	7.88218	+	4.55078i	0.251658	+	0.145295i
$982$			27.5514i			0.879199i
$983$	−5.74087	−	3.31449i	−0.183105	−	0.105716i	0.405646	−	0.914030i	$-0.367047\pi$
$983$	−5.74087	−	3.31449i	−0.183105	−	0.105716i	−0.588751	+	0.808315i	$0.700380\pi$
$984$	1.24948	+	2.16416i	0.0398320	+	0.0689910i
$985$	−25.9013	+	44.8624i	−0.825285	+	1.42944i
$986$	21.7324	−	12.5472i	0.692100	−	0.399584i
$987$		0			0
$988$	−18.7563	−	9.83622i	−0.596717	−	0.312932i
$989$	6.24765	+	10.8212i	0.198664	+	0.344096i
$990$		−	43.0866i		−	1.36938i
$991$	24.9693			0.793177			0.396589	−	0.917996i	$-0.370194\pi$
$991$	24.9693			0.793177			0.396589	+	0.917996i	$0.370194\pi$
$992$	1.02180			0.0324422
$993$			47.8533i			1.51858i
$994$		0			0
$995$	15.8820	+	9.16945i	0.503492	+	0.290691i
$996$	18.7401	−	10.8196i	0.593802	−	0.342832i
$997$	−19.7584	−	34.2225i	−0.625754	−	1.08384i	−0.988394	−	0.151909i	$-0.951458\pi$
$997$	−19.7584	−	34.2225i	−0.625754	−	1.08384i	0.362640	−	0.931929i	$-0.381875\pi$
$998$	−2.10425			−0.0666088
$999$	0.386322	+	0.223043i	0.0122227	+	0.00705677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.v.h.361.4		20
7.2	even	3		1274.2.o.h.569.7		20
7.3	odd	6		1274.2.m.g.491.9		20
7.4	even	3		1274.2.m.f.491.7		20
7.5	odd	6		182.2.o.a.23.9	✓	20
7.6	odd	2		182.2.v.a.179.2	yes	20
13.4	even	6		1274.2.o.h.459.2		20
21.5	even	6		1638.2.dt.c.1297.5		20
21.20	even	2		1638.2.cr.c.361.6		20
91.4	even	6		1274.2.m.f.589.7		20
91.17	odd	6		1274.2.m.g.589.9		20
91.30	even	6	inner	1274.2.v.h.667.4		20
91.69	odd	6		182.2.o.a.95.4	yes	20
91.82	odd	6		182.2.v.a.121.2	yes	20
273.173	even	6		1638.2.cr.c.667.6		20
273.251	even	6		1638.2.dt.c.1369.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.9	✓	20	7.5	odd	6
182.2.o.a.95.4	yes	20	91.69	odd	6
182.2.v.a.121.2	yes	20	91.82	odd	6
182.2.v.a.179.2	yes	20	7.6	odd	2
1274.2.m.f.491.7		20	7.4	even	3
1274.2.m.f.589.7		20	91.4	even	6
1274.2.m.g.491.9		20	7.3	odd	6
1274.2.m.g.589.9		20	91.17	odd	6
1274.2.o.h.459.2		20	13.4	even	6
1274.2.o.h.569.7		20	7.2	even	3
1274.2.v.h.361.4		20	1.1	even	1	trivial
1274.2.v.h.667.4		20	91.30	even	6	inner
1638.2.cr.c.361.6		20	21.20	even	2
1638.2.cr.c.667.6		20	273.173	even	6
1638.2.dt.c.1297.5		20	21.5	even	6
1638.2.dt.c.1369.10		20	273.251	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.v (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +2.35757 q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.89612 + 1.67208i) q^{5} +(-2.04172 - 1.17879i) q^{6} -1.00000i q^{8} +2.55814 q^{9} +3.34415 q^{10} -5.03653i q^{11} +(1.17879 + 2.04172i) q^{12} +(1.92804 + 3.04674i) q^{13} +(-6.82781 + 3.94204i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.86635 + 3.23261i) q^{17} +(-2.21541 - 1.27907i) q^{18} +5.87400i q^{19} +(-2.89612 - 1.67208i) q^{20} +(-2.51826 + 4.36176i) q^{22} +(-1.89185 + 3.27678i) q^{23} -2.35757i q^{24} +(3.09168 - 5.35494i) q^{25} +(-0.146362 - 3.60258i) q^{26} -1.04172 q^{27} +(3.36143 + 5.82216i) q^{29} +7.88408 q^{30} +(0.884906 + 0.510901i) q^{31} +(0.866025 - 0.500000i) q^{32} -11.8740i q^{33} -3.73270i q^{34} +(1.27907 + 2.21541i) q^{36} +(-0.370851 - 0.214111i) q^{37} +(2.93700 - 5.08703i) q^{38} +(4.54550 + 7.18292i) q^{39} +(1.67208 + 2.89612i) q^{40} +(-0.917963 + 0.529986i) q^{41} +(1.65120 - 2.85996i) q^{43} +(4.36176 - 2.51826i) q^{44} +(-7.40868 + 4.27741i) q^{45} +(3.27678 - 1.89185i) q^{46} +(-4.60157 + 2.65672i) q^{47} +(-1.17879 + 2.04172i) q^{48} +(-5.35494 + 3.09168i) q^{50} +(4.40005 + 7.62112i) q^{51} +(-1.67454 + 3.19311i) q^{52} +(-1.15836 + 2.00634i) q^{53} +(0.902152 + 0.520858i) q^{54} +(8.42146 + 14.5864i) q^{55} +13.8484i q^{57} -6.72285i q^{58} +(-7.00324 + 4.04332i) q^{59} +(-6.82781 - 3.94204i) q^{60} +10.1010 q^{61} +(-0.510901 - 0.884906i) q^{62} -1.00000 q^{64} +(-10.6782 - 5.59991i) q^{65} +(-5.93699 + 10.2832i) q^{66} +13.2982i q^{67} +(-1.86635 + 3.23261i) q^{68} +(-4.46017 + 7.72525i) q^{69} +(2.35754 + 1.36113i) q^{71} -2.55814i q^{72} +(6.88886 + 3.97728i) q^{73} +(0.214111 + 0.370851i) q^{74} +(7.28885 - 12.6247i) q^{75} +(-5.08703 + 2.93700i) q^{76} +(-0.345059 - 8.49334i) q^{78} +(7.07112 + 12.2475i) q^{79} -3.34415i q^{80} -10.1303 q^{81} +1.05997 q^{82} -9.17859i q^{83} +(-10.8104 - 6.24136i) q^{85} +(-2.85996 + 1.65120i) q^{86} +(7.92480 + 13.7262i) q^{87} -5.03653 q^{88} +(-4.68772 - 2.70646i) q^{89} +8.55481 q^{90} -3.78370 q^{92} +(2.08623 + 1.20449i) q^{93} +5.31343 q^{94} +(-9.82177 - 17.0118i) q^{95} +(2.04172 - 1.17879i) q^{96} +(-14.8742 - 8.58763i) q^{97} -12.8842i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} + 10 q^{4} + 32 q^{9} - 8 q^{10} + 2 q^{12} - 6 q^{13} - 12 q^{15} - 10 q^{16} + 10 q^{17} - 24 q^{18} + 2 q^{22} + 18 q^{25} + 6 q^{26} + 28 q^{27} + 2 q^{29} + 4 q^{30} - 6 q^{31} + 16 q^{36}+ \cdots - 78 q^{97}+O(q^{100}) \) 20 * q + 4 * q^3 + 10 * q^4 + 32 * q^9 - 8 * q^10 + 2 * q^12 - 6 * q^13 - 12 * q^15 - 10 * q^16 + 10 * q^17 - 24 * q^18 + 2 * q^22 + 18 * q^25 + 6 * q^26 + 28 * q^27 + 2 * q^29 + 4 * q^30 - 6 * q^31 + 16 * q^36 - 36 * q^37 + 14 * q^38 - 26 * q^39 - 4 * q^40 - 18 * q^41 + 8 * q^43 - 6 * q^44 + 60 * q^45 + 12 * q^46 + 18 * q^47 - 2 * q^48 - 12 * q^50 - 22 * q^51 - 4 * q^53 + 18 * q^54 - 2 * q^55 - 12 * q^60 - 8 * q^61 + 24 * q^62 - 20 * q^64 - 18 * q^65 - 32 * q^66 - 10 * q^68 + 34 * q^69 - 18 * q^71 - 72 * q^73 + 12 * q^74 + 18 * q^75 - 24 * q^76 + 20 * q^78 + 42 * q^79 + 4 * q^81 - 32 * q^82 - 12 * q^85 - 42 * q^86 + 64 * q^87 + 4 * q^88 + 18 * q^89 - 52 * q^90 + 60 * q^93 + 32 * q^94 - 12 * q^95 - 78 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more